LMFDB - Embedded newform 400.2.y.d.289.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(129,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("400.129");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.y (of order $10$, 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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			289.2
Character	$\chi$	$=$	400.289
Dual form			400.2.y.d.209.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.92858 - 0.626633i) q^{3} +(1.20432 - 1.88404i) q^{5} +0.498275i q^{7} +(0.899692 + 0.653665i) q^{9} +O(q^{10})$	\(q+(-1.92858 - 0.626633i) q^{3} +(1.20432 - 1.88404i) q^{5} +0.498275i q^{7} +(0.899692 + 0.653665i) q^{9} +(1.49086 - 1.08317i) q^{11} +(0.541607 - 0.745458i) q^{13} +(-3.50322 + 2.87886i) q^{15} +(-6.51739 + 2.11763i) q^{17} +(-1.86127 - 5.72840i) q^{19} +(0.312235 - 0.960962i) q^{21} +(-4.56304 - 6.28049i) q^{23} +(-2.09925 - 4.53797i) q^{25} +(2.25026 + 3.09722i) q^{27} +(1.30891 - 4.02840i) q^{29} +(0.963592 + 2.96563i) q^{31} +(-3.55399 + 1.15476i) q^{33} +(0.938772 + 0.600080i) q^{35} +(-1.83171 + 2.52113i) q^{37} +(-1.51166 + 1.09828i) q^{39} +(-3.94180 - 2.86388i) q^{41} -5.22863i q^{43} +(2.31505 - 0.907842i) q^{45} +(2.19204 + 0.712238i) q^{47} +6.75172 q^{49} +13.8963 q^{51} +(-10.8522 - 3.52610i) q^{53} +(-0.245280 - 4.11333i) q^{55} +12.2140i q^{57} +(5.58897 + 4.06063i) q^{59} +(4.42709 - 3.21647i) q^{61} +(-0.325705 + 0.448294i) q^{63} +(-0.752210 - 1.91818i) q^{65} +(0.761157 - 0.247315i) q^{67} +(4.86462 + 14.9718i) q^{69} +(-1.83274 + 5.64060i) q^{71} +(8.49411 + 11.6911i) q^{73} +(1.20492 + 10.0673i) q^{75} +(0.539717 + 0.742857i) q^{77} +(-3.60137 + 11.0839i) q^{79} +(-3.42994 - 10.5563i) q^{81} +(13.3287 - 4.33075i) q^{83} +(-3.85929 + 14.8293i) q^{85} +(-5.04866 + 6.94889i) q^{87} +(14.2425 - 10.3478i) q^{89} +(0.371443 + 0.269869i) q^{91} -6.32327i q^{93} +(-13.0341 - 3.39209i) q^{95} +(6.40268 + 2.08036i) q^{97} +2.04935 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{5} + 10 q^{9}+O(q^{10}) $ 32 * q + 2 * q^5 + 10 * q^9	$ 32 q + 2 q^{5} + 10 q^{9} - 6 q^{11} - 12 q^{15} + 6 q^{19} - 4 q^{21} + 30 q^{23} + 6 q^{25} - 2 q^{29} - 6 q^{31} - 8 q^{35} - 40 q^{37} + 12 q^{39} - 12 q^{45} + 20 q^{47} - 60 q^{49} + 60 q^{51} - 30 q^{53} + 28 q^{55} + 30 q^{59} + 14 q^{61} + 20 q^{63} - 26 q^{65} - 4 q^{69} - 12 q^{71} + 40 q^{73} - 16 q^{75} - 16 q^{79} - 52 q^{81} - 30 q^{83} + 60 q^{85} - 110 q^{87} + 24 q^{89} + 4 q^{91} - 68 q^{95} + 30 q^{97} - 92 q^{99}+O(q^{100}) $ 32 * q + 2 * q^5 + 10 * q^9 - 6 * q^11 - 12 * q^15 + 6 * q^19 - 4 * q^21 + 30 * q^23 + 6 * q^25 - 2 * q^29 - 6 * q^31 - 8 * q^35 - 40 * q^37 + 12 * q^39 - 12 * q^45 + 20 * q^47 - 60 * q^49 + 60 * q^51 - 30 * q^53 + 28 * q^55 + 30 * q^59 + 14 * q^61 + 20 * q^63 - 26 * q^65 - 4 * q^69 - 12 * q^71 + 40 * q^73 - 16 * q^75 - 16 * q^79 - 52 * q^81 - 30 * q^83 + 60 * q^85 - 110 * q^87 + 24 * q^89 + 4 * q^91 - 68 * q^95 + 30 * q^97 - 92 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$	$1$

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
$3$	−1.92858	−	0.626633i	−1.11346	−	0.361787i	−0.306195	−	0.951969i	$-0.599056\pi$
$3$	−1.92858	−	0.626633i	−1.11346	−	0.361787i	−0.807270	+	0.590182i	$0.799056\pi$
$4$		0			0
$5$	1.20432	−	1.88404i	0.538586	−	0.842570i
$5$	1.20432	−	1.88404i	0.538586	−	0.842570i
$6$		0			0
$7$			0.498275i			0.188330i	0.995557	+	0.0941651i	$0.0300181\pi$
$7$			0.498275i			0.188330i	−0.995557	+	0.0941651i	$0.969982\pi$
$8$		0			0
$9$	0.899692	+	0.653665i	0.299897	+	0.217888i
$10$		0			0
$11$	1.49086	−	1.08317i	0.449511	−	0.326589i	−0.339892	−	0.940465i	$-0.610390\pi$
$11$	1.49086	−	1.08317i	0.449511	−	0.326589i	0.789403	+	0.613876i	$0.210390\pi$
$12$		0			0
$13$	0.541607	−	0.745458i	0.150215	−	0.206753i	−0.727278	−	0.686343i	$-0.759215\pi$
$13$	0.541607	−	0.745458i	0.150215	−	0.206753i	0.877492	+	0.479590i	$0.159215\pi$
$14$		0			0
$15$	−3.50322	+	2.87886i	−0.904528	+	0.743319i
$16$		0			0
$17$	−6.51739	+	2.11763i	−1.58070	+	0.513600i	−0.962237	−	0.272214i	$-0.912244\pi$
$17$	−6.51739	+	2.11763i	−1.58070	+	0.513600i	−0.618463	+	0.785814i	$0.712244\pi$
$18$		0			0
$19$	−1.86127	−	5.72840i	−0.427004	−	1.31418i	−0.901062	−	0.433691i	$-0.857211\pi$
$19$	−1.86127	−	5.72840i	−0.427004	−	1.31418i	0.474057	−	0.880494i	$-0.342789\pi$
$20$		0			0
$21$	0.312235	−	0.960962i	0.0681353	−	0.209699i
$22$		0			0
$23$	−4.56304	−	6.28049i	−0.951460	−	1.30957i	−0.950876	−	0.309572i	$-0.899814\pi$
$23$	−4.56304	−	6.28049i	−0.951460	−	1.30957i	−0.000583617	−	1.00000i	$-0.500186\pi$
$24$		0			0
$25$	−2.09925	−	4.53797i	−0.419849	−	0.907594i
$26$		0			0
$27$	2.25026	+	3.09722i	0.433063	+	0.596060i
$28$		0			0
$29$	1.30891	−	4.02840i	0.243058	−	0.748056i	−0.752892	−	0.658144i	$-0.771342\pi$
$29$	1.30891	−	4.02840i	0.243058	−	0.748056i	0.995950	−	0.0899115i	$-0.0286584\pi$
$30$		0			0
$31$	0.963592	+	2.96563i	0.173066	+	0.532643i	0.999540	−	0.0303324i	$-0.00965658\pi$
$31$	0.963592	+	2.96563i	0.173066	+	0.532643i	−0.826474	+	0.562975i	$0.809657\pi$
$32$		0			0
$33$	−3.55399	+	1.15476i	−0.618670	+	0.201018i
$34$		0			0
$35$	0.938772	+	0.600080i	0.158681	+	0.101432i
$36$		0			0
$37$	−1.83171	+	2.52113i	−0.301131	+	0.414471i	−0.932590	−	0.360938i	$-0.882456\pi$
$37$	−1.83171	+	2.52113i	−0.301131	+	0.414471i	0.631459	+	0.775409i	$0.282456\pi$
$38$		0			0
$39$	−1.51166	+	1.09828i	−0.242059	+	0.175866i
$40$		0			0
$41$	−3.94180	−	2.86388i	−0.615606	−	0.447264i	0.235778	−	0.971807i	$-0.424236\pi$
$41$	−3.94180	−	2.86388i	−0.615606	−	0.447264i	−0.851384	+	0.524543i	$0.824236\pi$
$42$		0			0
$43$		−	5.22863i		−	0.797358i	−0.917091	−	0.398679i	$-0.869469\pi$
$43$		−	5.22863i		−	0.797358i	0.917091	−	0.398679i	$-0.130531\pi$
$44$		0			0
$45$	2.31505	−	0.907842i	0.345107	−	0.135333i
$46$		0			0
$47$	2.19204	+	0.712238i	0.319742	+	0.103891i	0.464491	−	0.885578i	$-0.346237\pi$
$47$	2.19204	+	0.712238i	0.319742	+	0.103891i	−0.144749	+	0.989468i	$0.546237\pi$
$48$		0			0
$49$	6.75172			0.964532
$50$		0			0
$51$	13.8963			1.94587
$52$		0			0
$53$	−10.8522	−	3.52610i	−1.49067	−	0.484348i	−0.553388	−	0.832923i	$-0.686665\pi$
$53$	−10.8522	−	3.52610i	−1.49067	−	0.484348i	−0.937281	+	0.348576i	$0.886665\pi$
$54$		0			0
$55$	−0.245280	−	4.11333i	−0.0330736	−	0.554641i
$56$		0			0
$57$			12.2140i			1.61778i
$58$		0			0
$59$	5.58897	+	4.06063i	0.727622	+	0.528649i	0.888810	−	0.458275i	$-0.151533\pi$
$59$	5.58897	+	4.06063i	0.727622	+	0.528649i	−0.161188	+	0.986924i	$0.551533\pi$
$60$		0			0
$61$	4.42709	−	3.21647i	0.566831	−	0.411827i	−0.267122	−	0.963663i	$-0.586073\pi$
$61$	4.42709	−	3.21647i	0.566831	−	0.411827i	0.833953	+	0.551836i	$0.186073\pi$
$62$		0			0
$63$	−0.325705	+	0.448294i	−0.0410349	+	0.0564797i
$64$		0			0
$65$	−0.752210	−	1.91818i	−0.0933002	−	0.237921i
$66$		0			0
$67$	0.761157	−	0.247315i	0.0929901	−	0.0302143i	−0.262152	−	0.965026i	$-0.584432\pi$
$67$	0.761157	−	0.247315i	0.0929901	−	0.0302143i	0.355143	+	0.934812i	$0.384432\pi$
$68$		0			0
$69$	4.86462	+	14.9718i	0.585631	+	1.80239i
$70$		0			0
$71$	−1.83274	+	5.64060i	−0.217507	+	0.669416i	0.781460	+	0.623956i	$0.214476\pi$
$71$	−1.83274	+	5.64060i	−0.217507	+	0.669416i	−0.998966	+	0.0454605i	$0.985524\pi$
$72$		0			0
$73$	8.49411	+	11.6911i	0.994161	+	1.36834i	0.928840	+	0.370480i	$0.120807\pi$
$73$	8.49411	+	11.6911i	0.994161	+	1.36834i	0.0653205	+	0.997864i	$0.479193\pi$
$74$		0			0
$75$	1.20492	+	10.0673i	0.139132	+	1.16247i
$76$		0			0
$77$	0.539717	+	0.742857i	0.0615065	+	0.0846564i
$78$		0			0
$79$	−3.60137	+	11.0839i	−0.405186	+	1.24703i	0.515555	+	0.856857i	$0.327586\pi$
$79$	−3.60137	+	11.0839i	−0.405186	+	1.24703i	−0.920740	+	0.390176i	$0.872414\pi$
$80$		0			0
$81$	−3.42994	−	10.5563i	−0.381104	−	1.17292i
$82$		0			0
$83$	13.3287	−	4.33075i	1.46301	−	0.475362i	0.534024	−	0.845469i	$-0.320679\pi$
$83$	13.3287	−	4.33075i	1.46301	−	0.475362i	0.928989	+	0.370107i	$0.120679\pi$
$84$		0			0
$85$	−3.85929	+	14.8293i	−0.418599	+	1.60847i
$86$		0			0
$87$	−5.04866	+	6.94889i	−0.541273	+	0.744999i
$88$		0			0
$89$	14.2425	−	10.3478i	1.50970	−	1.09686i	0.543395	−	0.839477i	$-0.317139\pi$
$89$	14.2425	−	10.3478i	1.50970	−	1.09686i	0.966308	−	0.257387i	$-0.0828615\pi$
$90$		0			0
$91$	0.371443	+	0.269869i	0.0389378	+	0.0282900i
$92$		0			0
$93$		−	6.32327i		−	0.655692i
$94$		0			0
$95$	−13.0341	−	3.39209i	−1.33727	−	0.348021i
$96$		0			0
$97$	6.40268	+	2.08036i	0.650094	+	0.211228i	0.615456	−	0.788172i	$-0.288972\pi$
$97$	6.40268	+	2.08036i	0.650094	+	0.211228i	0.0346385	+	0.999400i	$0.488972\pi$
$98$		0			0
$99$	2.04935			0.205967
$100$		0			0
$101$	13.6456			1.35779			0.678893	−	0.734238i	$-0.262460\pi$
$101$	13.6456			1.35779			0.678893	+	0.734238i	$0.262460\pi$
$102$		0			0
$103$	−12.9590	−	4.21062i	−1.27688	−	0.414885i	−0.409402	−	0.912354i	$-0.634263\pi$
$103$	−12.9590	−	4.21062i	−1.27688	−	0.414885i	−0.867482	+	0.497469i	$0.834263\pi$
$104$		0			0
$105$	−1.43446	−	1.74557i	−0.139989	−	0.170350i
$106$		0			0
$107$		−	1.69243i		−	0.163613i	−0.996648	−	0.0818067i	$-0.973931\pi$
$107$		−	1.69243i		−	0.163613i	0.996648	−	0.0818067i	$-0.0260690\pi$
$108$		0			0
$109$	1.33202	+	0.967767i	0.127584	+	0.0926953i	0.649747	−	0.760150i	$-0.274875\pi$
$109$	1.33202	+	0.967767i	0.127584	+	0.0926953i	−0.522163	+	0.852846i	$0.674875\pi$
$110$		0			0
$111$	5.11241	−	3.71438i	0.485249	−	0.352554i
$112$		0			0
$113$	7.67640	−	10.5657i	0.722135	−	0.993933i	−0.277315	−	0.960779i	$-0.589445\pi$
$113$	7.67640	−	10.5657i	0.722135	−	0.993933i	0.999450	−	0.0331545i	$-0.0105553\pi$
$114$		0			0
$115$	−17.3281	+	1.03328i	−1.61585	+	0.0963541i
$116$		0			0
$117$	0.974559	−	0.316653i	0.0900980	−	0.0292746i
$118$		0			0
$119$	−1.05516	−	3.24745i	−0.0967264	−	0.297693i
$120$		0			0
$121$	−2.34979	+	7.23191i	−0.213617	+	0.657446i
$122$		0			0
$123$	5.80746	+	7.99329i	0.523641	+	0.720730i
$124$		0			0
$125$	−11.0779	−	1.51007i	−0.990837	−	0.135065i
$126$		0			0
$127$	4.24647	+	5.84476i	0.376813	+	0.518639i	0.954737	−	0.297452i	$-0.0961369\pi$
$127$	4.24647	+	5.84476i	0.376813	+	0.518639i	−0.577924	+	0.816091i	$0.696137\pi$
$128$		0			0
$129$	−3.27643	+	10.0838i	−0.288473	+	0.887830i
$130$		0			0
$131$	−5.80640	−	17.8703i	−0.507307	−	1.56133i	−0.796857	−	0.604168i	$-0.793506\pi$
$131$	−5.80640	−	17.8703i	−0.507307	−	1.56133i	0.289550	−	0.957163i	$-0.406494\pi$
$132$		0			0
$133$	2.85432	−	0.927423i	0.247501	−	0.0804178i
$134$		0			0
$135$	8.54532	−	0.509563i	0.735464	−	0.0438562i
$136$		0			0
$137$	1.20520	−	1.65881i	0.102967	−	0.141722i	−0.754424	−	0.656387i	$-0.772084\pi$
$137$	1.20520	−	1.65881i	0.102967	−	0.141722i	0.857391	+	0.514665i	$0.172084\pi$
$138$		0			0
$139$	5.62722	−	4.08841i	0.477294	−	0.346775i	−0.322983	−	0.946405i	$-0.604686\pi$
$139$	5.62722	−	4.08841i	0.477294	−	0.346775i	0.800277	+	0.599630i	$0.204686\pi$
$140$		0			0
$141$	−3.78121	−	2.74721i	−0.318436	−	0.231357i
$142$		0			0
$143$		−	1.69803i		−	0.141996i
$144$		0			0
$145$	−6.01335	−	7.31751i	−0.499382	−	0.607686i
$146$		0			0
$147$	−13.0212	−	4.23085i	−1.07397	−	0.348955i
$148$		0			0
$149$	−21.7422			−1.78119			−0.890595	−	0.454798i	$-0.849711\pi$
$149$	−21.7422			−1.78119			−0.890595	+	0.454798i	$0.849711\pi$
$150$		0			0
$151$	−10.2705			−0.835802			−0.417901	−	0.908492i	$-0.637234\pi$
$151$	−10.2705			−0.835802			−0.417901	+	0.908492i	$0.637234\pi$
$152$		0			0
$153$	−7.24787	−	2.35497i	−0.585955	−	0.190388i
$154$		0			0
$155$	6.74785	+	1.75611i	0.542000	+	0.141054i
$156$		0			0
$157$		−	10.1496i		−	0.810026i	−0.914311	−	0.405013i	$-0.867267\pi$
$157$		−	10.1496i		−	0.810026i	0.914311	−	0.405013i	$-0.132733\pi$
$158$		0			0
$159$	18.7198	+	13.6007i	1.48458	+	1.07861i
$160$		0			0
$161$	3.12941	−	2.27365i	0.246632	−	0.179189i
$162$		0			0
$163$	−0.345868	+	0.476046i	−0.0270904	+	0.0372868i	−0.822347	−	0.568986i	$-0.807336\pi$
$163$	−0.345868	+	0.476046i	−0.0270904	+	0.0372868i	0.795257	+	0.606273i	$0.207336\pi$
$164$		0			0
$165$	−2.10450	+	8.08657i	−0.163835	+	0.629538i
$166$		0			0
$167$	18.3377	−	5.95827i	1.41901	−	0.461064i	0.503723	−	0.863865i	$-0.331963\pi$
$167$	18.3377	−	5.95827i	1.41901	−	0.461064i	0.915288	+	0.402801i	$0.131963\pi$
$168$		0			0
$169$	3.75485	+	11.5562i	0.288835	+	0.888942i
$170$		0			0
$171$	2.06988	−	6.37044i	0.158288	−	0.487160i
$172$		0			0
$173$	0.449853	+	0.619169i	0.0342017	+	0.0470746i	0.825775	−	0.563999i	$-0.190738\pi$
$173$	0.449853	+	0.619169i	0.0342017	+	0.0470746i	−0.791574	+	0.611074i	$0.790738\pi$
$174$		0			0
$175$	2.26116	−	1.04600i	0.170927	−	0.0790703i
$176$		0			0
$177$	−8.23425	−	11.3335i	−0.618924	−	0.851876i
$178$		0			0
$179$	−2.42579	+	7.46581i	−0.181312	+	0.558021i	−0.999865	−	0.0164098i	$-0.994776\pi$
$179$	−2.42579	+	7.46581i	−0.181312	+	0.558021i	0.818553	+	0.574430i	$0.194776\pi$
$180$		0			0
$181$	2.18999	+	6.74010i	0.162781	+	0.500987i	0.998866	−	0.0476121i	$-0.0151611\pi$
$181$	2.18999	+	6.74010i	0.162781	+	0.500987i	−0.836085	+	0.548600i	$0.815161\pi$
$182$		0			0
$183$	−10.5535	+	3.42905i	−0.780140	+	0.253483i
$184$		0			0
$185$	2.54396	+	6.48725i	0.187036	+	0.476952i
$186$		0			0
$187$	−7.42275	+	10.2165i	−0.542805	+	0.747107i
$188$		0			0
$189$	−1.54327	+	1.12125i	−0.112256	+	0.0815588i
$190$		0			0
$191$	−17.2833	−	12.5571i	−1.25058	−	0.908598i	−0.252323	−	0.967643i	$-0.581194\pi$
$191$	−17.2833	−	12.5571i	−1.25058	−	0.908598i	−0.998255	+	0.0590449i	$0.981194\pi$
$192$		0			0
$193$		−	9.15396i		−	0.658916i	−0.944170	−	0.329458i	$-0.893134\pi$
$193$		−	9.15396i		−	0.658916i	0.944170	−	0.329458i	$-0.106866\pi$
$194$		0			0
$195$	0.248702	+	4.17072i	0.0178099	+	0.298671i
$196$		0			0
$197$	6.15330	+	1.99933i	0.438404	+	0.142446i	0.519899	−	0.854228i	$-0.325969\pi$
$197$	6.15330	+	1.99933i	0.438404	+	0.142446i	−0.0814950	+	0.996674i	$0.525969\pi$
$198$		0			0
$199$	21.6502			1.53474			0.767369	−	0.641205i	$-0.221565\pi$
$199$	21.6502			1.53474			0.767369	+	0.641205i	$0.221565\pi$
$200$		0			0
$201$	−1.62293			−0.114472
$202$		0			0
$203$	2.00725	+	0.652196i	0.140881	+	0.0457752i
$204$		0			0
$205$	−10.1429	+	3.97750i	−0.708408	+	0.277801i
$206$		0			0
$207$		−	8.63320i		−	0.600049i
$208$		0			0
$209$	−8.97973	−	6.52416i	−0.621141	−	0.451285i
$210$		0			0
$211$	5.39542	−	3.92000i	0.371436	−	0.269864i	−0.386370	−	0.922344i	$-0.626271\pi$
$211$	5.39542	−	3.92000i	0.371436	−	0.269864i	0.757806	+	0.652480i	$0.226271\pi$
$212$		0			0
$213$	7.06917	−	9.72988i	0.484372	−	0.666681i
$214$		0			0
$215$	−9.85096	−	6.29692i	−0.671830	−	0.429446i
$216$		0			0
$217$	−1.47770	+	0.480133i	−0.100313	+	0.0325936i
$218$		0			0
$219$	−9.05550	−	27.8700i	−0.611914	−	1.88328i
$220$		0			0
$221$	−1.95126	+	6.00536i	−0.131256	+	0.403964i
$222$		0			0
$223$	10.6966	+	14.7226i	0.716297	+	0.985898i	0.999639	+	0.0268789i	$0.00855685\pi$
$223$	10.6966	+	14.7226i	0.716297	+	0.985898i	−0.283342	+	0.959019i	$0.591443\pi$
$224$		0			0
$225$	1.07763	−	5.45498i	0.0718423	−	0.363665i
$226$		0			0
$227$	3.38442	+	4.65826i	0.224632	+	0.309180i	0.906426	−	0.422365i	$-0.138800\pi$
$227$	3.38442	+	4.65826i	0.224632	+	0.309180i	−0.681794	+	0.731544i	$0.738800\pi$
$228$		0			0
$229$	0.762431	−	2.34652i	0.0503829	−	0.155063i	−0.922700	−	0.385520i	$-0.874022\pi$
$229$	0.762431	−	2.34652i	0.0503829	−	0.155063i	0.973082	+	0.230457i	$0.0740222\pi$
$230$		0			0
$231$	−0.575388	−	1.77086i	−0.0378578	−	0.116514i
$232$		0			0
$233$	3.70287	−	1.20314i	0.242583	−	0.0788201i	−0.185202	−	0.982700i	$-0.559294\pi$
$233$	3.70287	−	1.20314i	0.242583	−	0.0788201i	0.427785	+	0.903880i	$0.359294\pi$
$234$		0			0
$235$	3.98180	−	3.27215i	0.259744	−	0.213451i
$236$		0			0
$237$	13.8910	−	19.1194i	0.902320	−	1.24194i
$238$		0			0
$239$	−8.87004	+	6.44446i	−0.573755	+	0.416858i	−0.836467	−	0.548017i	$-0.815383\pi$
$239$	−8.87004	+	6.44446i	−0.573755	+	0.416858i	0.262712	+	0.964874i	$0.415383\pi$
$240$		0			0
$241$	1.45519	+	1.05726i	0.0937373	+	0.0681041i	0.633667	−	0.773606i	$-0.281549\pi$
$241$	1.45519	+	1.05726i	0.0937373	+	0.0681041i	−0.539929	+	0.841710i	$0.681549\pi$
$242$		0			0
$243$			11.0228i			0.707112i
$244$		0			0
$245$	8.13121	−	12.7205i	0.519484	−	0.812686i
$246$		0			0
$247$	−5.27836	−	1.71504i	−0.335854	−	0.109125i
$248$		0			0
$249$	−28.4192			−1.80099
$250$		0			0
$251$	8.33867			0.526332			0.263166	−	0.964751i	$-0.415233\pi$
$251$	8.33867			0.526332			0.263166	+	0.964751i	$0.415233\pi$
$252$		0			0
$253$	−13.6057	−	4.42076i	−0.855383	−	0.277931i
$254$		0			0
$255$	16.7355	−	26.1812i	1.04802	−	1.63953i
$256$		0			0
$257$			21.5633i			1.34508i	0.740059	+	0.672542i	$0.234797\pi$
$257$			21.5633i			1.34508i	−0.740059	+	0.672542i	$0.765203\pi$
$258$		0			0
$259$	−1.25621	−	0.912693i	−0.0780574	−	0.0567120i
$260$		0			0
$261$	3.81084	−	2.76874i	0.235885	−	0.171381i
$262$		0			0
$263$	13.9820	−	19.2446i	0.862168	−	1.18667i	−0.118881	−	0.992909i	$-0.537931\pi$
$263$	13.9820	−	19.2446i	0.862168	−	1.18667i	0.981048	−	0.193764i	$-0.0620694\pi$
$264$		0			0
$265$	−19.7129	+	16.1995i	−1.21095	+	0.995130i
$266$		0			0
$267$	−33.9521	+	11.0317i	−2.07783	+	0.675129i
$268$		0			0
$269$	−8.61497	−	26.5141i	−0.525264	−	1.61660i	−0.763794	−	0.645460i	$-0.776666\pi$
$269$	−8.61497	−	26.5141i	−0.525264	−	1.61660i	0.238530	−	0.971135i	$-0.423334\pi$
$270$		0			0
$271$	−6.37885	+	19.6321i	−0.387488	+	1.19256i	0.547172	+	0.837020i	$0.315704\pi$
$271$	−6.37885	+	19.6321i	−0.387488	+	1.19256i	−0.934660	+	0.355544i	$0.884296\pi$
$272$		0			0
$273$	−0.547248	−	0.753222i	−0.0331209	−	0.0455870i
$274$		0			0
$275$	−8.04508	−	4.49162i	−0.485137	−	0.270855i
$276$		0			0
$277$	1.66549	+	2.29235i	0.100070	+	0.137734i	0.856115	−	0.516785i	$-0.172871\pi$
$277$	1.66549	+	2.29235i	0.100070	+	0.137734i	−0.756046	+	0.654519i	$0.772871\pi$
$278$		0			0
$279$	−1.07159	+	3.29802i	−0.0641545	+	0.197447i
$280$		0			0
$281$	3.93432	+	12.1086i	0.234702	+	0.722339i	0.997161	+	0.0753019i	$0.0239920\pi$
$281$	3.93432	+	12.1086i	0.234702	+	0.722339i	−0.762459	+	0.647037i	$0.776008\pi$
$282$		0			0
$283$	−15.6377	+	5.08101i	−0.929567	+	0.302035i	−0.734385	−	0.678733i	$-0.762530\pi$
$283$	−15.6377	+	5.08101i	−0.929567	+	0.302035i	−0.195181	+	0.980767i	$0.562530\pi$
$284$		0			0
$285$	23.0117	+	14.7095i	1.36310	+	0.871316i
$286$		0			0
$287$	1.42700	−	1.96410i	0.0842332	−	0.115937i
$288$		0			0
$289$	24.2387	−	17.6105i	1.42581	−	1.03591i
$290$		0			0
$291$	−11.0445	−	8.02427i	−0.647437	−	0.470391i
$292$		0			0
$293$			4.37642i			0.255673i	0.991795	+	0.127836i	$0.0408033\pi$
$293$			4.37642i			0.255673i	−0.991795	+	0.127836i	$0.959197\pi$
$294$		0			0
$295$	14.3813	−	5.63960i	0.837311	−	0.328350i
$296$		0			0
$297$	6.70964	+	2.18009i	0.389333	+	0.126502i
$298$		0			0
$299$	−7.15321			−0.413681
$300$		0			0
$301$	2.60529			0.150167
$302$		0			0
$303$	−26.3166	−	8.55077i	−1.51185	−	0.491229i
$304$		0			0
$305$	−0.728357	−	12.2145i	−0.0417056	−	0.699400i
$306$		0			0
$307$		−	3.37417i		−	0.192574i	−0.995354	−	0.0962870i	$-0.969303\pi$
$307$		−	3.37417i		−	0.192574i	0.995354	−	0.0962870i	$-0.0306967\pi$
$308$		0			0
$309$	22.3538	+	16.2410i	1.27167	+	0.923919i
$310$		0			0
$311$	−15.1154	+	10.9819i	−0.857113	+	0.622729i	−0.927098	−	0.374819i	$-0.877705\pi$
$311$	−15.1154	+	10.9819i	−0.857113	+	0.622729i	0.0699849	+	0.997548i	$0.477705\pi$
$312$		0			0
$313$	−8.37289	+	11.5243i	−0.473264	+	0.651392i	−0.977193	−	0.212353i	$-0.931887\pi$
$313$	−8.37289	+	11.5243i	−0.473264	+	0.651392i	0.503929	+	0.863745i	$0.331887\pi$
$314$		0			0
$315$	0.452355	+	1.15353i	0.0254873	+	0.0649940i
$316$		0			0
$317$	−3.03035	+	0.984621i	−0.170202	+	0.0553018i	−0.392878	−	0.919591i	$-0.628521\pi$
$317$	−3.03035	+	0.984621i	−0.170202	+	0.0553018i	0.222677	+	0.974892i	$0.428521\pi$
$318$		0			0
$319$	−2.41206	−	7.42355i	−0.135049	−	0.415639i
$320$		0			0
$321$	−1.06053	+	3.26398i	−0.0591932	+	0.182178i
$322$		0			0
$323$	24.2612	+	33.3927i	1.34993	+	1.85802i
$324$		0			0
$325$	−4.51983	−	0.892895i	−0.250715	−	0.0495289i
$326$		0			0
$327$	−1.96246	−	2.70110i	−0.108525	−	0.149371i
$328$		0			0
$329$	−0.354890	+	1.09224i	−0.0195657	+	0.0602171i
$330$		0			0
$331$	9.20914	+	28.3428i	0.506180	+	1.55786i	0.798778	+	0.601626i	$0.205480\pi$
$331$	9.20914	+	28.3428i	0.506180	+	1.55786i	−0.292598	+	0.956236i	$0.594520\pi$
$332$		0			0
$333$	−3.29595	+	1.07092i	−0.180617	+	0.0586859i
$334$		0			0
$335$	0.450721	−	1.73190i	0.0246255	−	0.0946238i
$336$		0			0
$337$	12.6278	−	17.3806i	0.687879	−	0.946784i	−0.312116	−	0.950044i	$-0.601038\pi$
$337$	12.6278	−	17.3806i	0.687879	−	0.946784i	0.999995	+	0.00326034i	$0.00103780\pi$
$338$		0			0
$339$	−21.4253	+	15.5664i	−1.16366	+	0.845451i
$340$		0			0
$341$	4.64887	+	3.37760i	0.251750	+	0.182907i
$342$		0			0
$343$			6.85214i			0.369981i
$344$		0			0
$345$	34.0660	+	8.86556i	1.83405	+	0.477306i
$346$		0			0
$347$	−22.8207	−	7.41490i	−1.22508	−	0.398053i	−0.376150	−	0.926559i	$-0.622752\pi$
$347$	−22.8207	−	7.41490i	−1.22508	−	0.398053i	−0.848930	+	0.528506i	$0.822752\pi$
$348$		0			0
$349$	−16.8260			−0.900674			−0.450337	−	0.892859i	$-0.648696\pi$
$349$	−16.8260			−0.900674			−0.450337	+	0.892859i	$0.648696\pi$
$350$		0			0
$351$	3.52760			0.188290
$352$		0			0
$353$	−8.44056	−	2.74251i	−0.449246	−	0.145969i	0.0756516	−	0.997134i	$-0.475896\pi$
$353$	−8.44056	−	2.74251i	−0.449246	−	0.145969i	−0.524897	+	0.851165i	$0.675896\pi$
$354$		0			0
$355$	8.41994	+	10.2460i	0.446884	+	0.543803i
$356$		0			0
$357$			6.92416i			0.366465i
$358$		0			0
$359$	2.84343	+	2.06587i	0.150071	+	0.109033i	0.660287	−	0.751013i	$-0.270435\pi$
$359$	2.84343	+	2.06587i	0.150071	+	0.109033i	−0.510216	+	0.860046i	$0.670435\pi$
$360$		0			0
$361$	−13.9789	+	10.1563i	−0.735731	+	0.534540i
$362$		0			0
$363$	9.06350	−	12.4748i	0.475711	−	0.654759i
$364$		0			0
$365$	32.2562	−	1.92346i	1.68837	−	0.100678i
$366$		0			0
$367$	33.9894	−	11.0438i	1.77423	−	0.576482i	0.775722	−	0.631075i	$-0.217386\pi$
$367$	33.9894	−	11.0438i	1.77423	−	0.576482i	0.998509	+	0.0545928i	$0.0173861\pi$
$368$		0			0
$369$	−1.67439	−	5.15323i	−0.0871651	−	0.268266i
$370$		0			0
$371$	1.75697	−	5.40739i	0.0912173	−	0.280738i
$372$		0			0
$373$	9.42902	+	12.9779i	0.488216	+	0.671972i	0.980058	−	0.198713i	$-0.0636761\pi$
$373$	9.42902	+	12.9779i	0.488216	+	0.671972i	−0.491842	+	0.870685i	$0.663676\pi$
$374$		0			0
$375$	20.4183	+	9.85406i	1.05440	+	0.508862i
$376$		0			0
$377$	−2.29409	−	3.15755i	−0.118152	−	0.162622i
$378$		0			0
$379$	7.46298	−	22.9687i	0.383348	−	1.17982i	−0.554324	−	0.832301i	$-0.687023\pi$
$379$	7.46298	−	22.9687i	0.383348	−	1.17982i	0.937672	−	0.347522i	$-0.112977\pi$
$380$		0			0
$381$	−4.52712	−	13.9330i	−0.231931	−	0.713812i
$382$		0			0
$383$	2.10126	−	0.682742i	0.107370	−	0.0348865i	−0.254840	−	0.966983i	$-0.582023\pi$
$383$	2.10126	−	0.682742i	0.107370	−	0.0348865i	0.362209	+	0.932097i	$0.382023\pi$
$384$		0			0
$385$	2.04957	−	0.122217i	0.104456	−	0.00622875i
$386$		0			0
$387$	3.41777	−	4.70415i	0.173735	−	0.239126i
$388$		0			0
$389$	6.89059	−	5.00630i	0.349367	−	0.253830i	−0.399237	−	0.916848i	$-0.630725\pi$
$389$	6.89059	−	5.00630i	0.349367	−	0.253830i	0.748603	+	0.663018i	$0.230725\pi$
$390$		0			0
$391$	43.0388	+	31.2696i	2.17657	+	1.58137i
$392$		0			0
$393$			38.1026i			1.92202i
$394$		0			0
$395$	16.5453	+	20.1336i	0.832485	+	1.01303i
$396$		0			0
$397$	1.12415	+	0.365258i	0.0564193	+	0.0183318i	0.337091	−	0.941472i	$-0.390557\pi$
$397$	1.12415	+	0.365258i	0.0564193	+	0.0183318i	−0.280671	+	0.959804i	$0.590557\pi$
$398$		0			0
$399$	−6.08592			−0.304677
$400$		0			0
$401$	6.65832			0.332501			0.166250	−	0.986084i	$-0.446834\pi$
$401$	6.65832			0.332501			0.166250	+	0.986084i	$0.446834\pi$
$402$		0			0
$403$	2.73264	+	0.887889i	0.136123	+	0.0442289i
$404$		0			0
$405$	−24.0192	−	6.25092i	−1.19352	−	0.310611i
$406$		0			0
$407$			5.74270i			0.284655i
$408$		0			0
$409$	−15.5680	−	11.3108i	−0.769789	−	0.559284i	0.132108	−	0.991235i	$-0.457825\pi$
$409$	−15.5680	−	11.3108i	−0.769789	−	0.559284i	−0.901897	+	0.431951i	$0.857825\pi$
$410$		0			0
$411$	−3.36378	+	2.44393i	−0.165923	+	0.120550i
$412$		0			0
$413$	−2.02331	+	2.78484i	−0.0995605	+	0.137033i
$414$		0			0
$415$	7.89262	−	30.3274i	0.387433	−	1.48872i
$416$		0			0
$417$	−13.4145	+	4.35862i	−0.656909	+	0.213443i
$418$		0			0
$419$	−4.83681	−	14.8862i	−0.236294	−	0.727237i	−0.996947	−	0.0780789i	$-0.975121\pi$
$419$	−4.83681	−	14.8862i	−0.236294	−	0.727237i	0.760654	−	0.649158i	$-0.224879\pi$
$420$		0			0
$421$	−5.21282	+	16.0434i	−0.254057	+	0.781909i	0.739956	+	0.672655i	$0.234846\pi$
$421$	−5.21282	+	16.0434i	−0.254057	+	0.781909i	−0.994014	+	0.109254i	$0.965154\pi$
$422$		0			0
$423$	1.50660	+	2.07366i	0.0732534	+	0.100825i
$424$		0			0
$425$	23.2913	+	25.1303i	1.12980	+	1.21900i
$426$		0			0
$427$	1.60269	+	2.20591i	0.0775594	+	0.106751i
$428$		0			0
$429$	−1.06404	+	3.27477i	−0.0513723	+	0.158108i
$430$		0			0
$431$	−4.89820	−	15.0751i	−0.235938	−	0.726142i	−0.996996	−	0.0774578i	$-0.975320\pi$
$431$	−4.89820	−	15.0751i	−0.235938	−	0.726142i	0.761058	−	0.648684i	$-0.224680\pi$
$432$		0			0
$433$	12.5981	−	4.09336i	0.605425	−	0.196714i	0.00976628	−	0.999952i	$-0.496891\pi$
$433$	12.5981	−	4.09336i	0.605425	−	0.196714i	0.595658	+	0.803238i	$0.296891\pi$
$434$		0			0
$435$	7.01183	+	17.8806i	0.336191	+	0.857307i
$436$		0			0
$437$	−27.4841	+	37.8286i	−1.31474	+	1.80959i
$438$		0			0
$439$	7.43337	−	5.40066i	0.354775	−	0.257759i	−0.396094	−	0.918210i	$-0.629635\pi$
$439$	7.43337	−	5.40066i	0.354775	−	0.257759i	0.750870	+	0.660450i	$0.229635\pi$
$440$		0			0
$441$	6.07447	+	4.41336i	0.289261	+	0.210160i
$442$		0			0
$443$			10.8958i			0.517677i	0.965921	+	0.258838i	$0.0833397\pi$
$443$			10.8958i			0.517677i	−0.965921	+	0.258838i	$0.916660\pi$
$444$		0			0
$445$	−2.34322	−	39.2955i	−0.111079	−	1.86279i
$446$		0			0
$447$	41.9315	+	13.6244i	1.98329	+	0.644411i
$448$		0			0
$449$	−8.90687			−0.420341			−0.210171	−	0.977665i	$-0.567402\pi$
$449$	−8.90687			−0.420341			−0.210171	+	0.977665i	$0.567402\pi$
$450$		0			0
$451$	−8.97875			−0.422793
$452$		0			0
$453$	19.8075	+	6.43584i	0.930637	+	0.302382i
$454$		0			0
$455$	0.955780	−	0.374807i	0.0448076	−	0.0175712i
$456$		0			0
$457$		−	38.2615i		−	1.78980i	−0.446268	−	0.894899i	$-0.647247\pi$
$457$		−	38.2615i		−	1.78980i	0.446268	−	0.894899i	$-0.352753\pi$
$458$		0			0
$459$	−21.2246	−	15.4206i	−0.990679	−	0.719770i
$460$		0			0
$461$	−23.2835	+	16.9164i	−1.08442	+	0.787878i	−0.978448	−	0.206492i	$-0.933795\pi$
$461$	−23.2835	+	16.9164i	−1.08442	+	0.787878i	−0.105972	+	0.994369i	$0.533795\pi$
$462$		0			0
$463$	2.90864	−	4.00340i	0.135176	−	0.186054i	−0.736063	−	0.676913i	$-0.763317\pi$
$463$	2.90864	−	4.00340i	0.135176	−	0.186054i	0.871239	+	0.490860i	$0.163317\pi$
$464$		0			0
$465$	−11.9133	−	7.61521i	−0.552467	−	0.353147i
$466$		0			0
$467$	21.7463	−	7.06581i	1.00630	−	0.326967i	0.240919	−	0.970545i	$-0.422551\pi$
$467$	21.7463	−	7.06581i	1.00630	−	0.326967i	0.765380	+	0.643579i	$0.222551\pi$
$468$		0			0
$469$	0.123231	+	0.379265i	0.00569027	+	0.0175128i
$470$		0			0
$471$	−6.36007	+	19.5743i	−0.293056	+	0.901935i
$472$		0			0
$473$	−5.66350	−	7.79514i	−0.260408	−	0.358421i
$474$		0			0
$475$	−22.0880	+	20.4717i	−1.01347	+	0.939306i
$476$		0			0
$477$	−7.45878	−	10.2661i	−0.341514	−	0.470054i
$478$		0			0
$479$	−5.71266	+	17.5818i	−0.261018	+	0.803332i	0.731566	+	0.681771i	$0.238790\pi$
$479$	−5.71266	+	17.5818i	−0.261018	+	0.803332i	−0.992584	+	0.121561i	$0.961210\pi$
$480$		0			0
$481$	0.887330	+	2.73092i	0.0404588	+	0.124519i
$482$		0			0
$483$	−7.46005	+	2.42392i	−0.339444	+	0.110292i
$484$		0			0
$485$	11.6303	−	9.55753i	0.528107	−	0.433985i
$486$		0			0
$487$	3.12372	−	4.29944i	0.141549	−	0.194826i	−0.732356	−	0.680922i	$-0.761579\pi$
$487$	3.12372	−	4.29944i	0.141549	−	0.194826i	0.873906	+	0.486096i	$0.161579\pi$
$488$		0			0
$489$	0.965339	−	0.701360i	0.0436541	−	0.0317166i
$490$		0			0
$491$	−8.53199	−	6.19885i	−0.385043	−	0.279750i	0.378378	−	0.925651i	$-0.376482\pi$
$491$	−8.53199	−	6.19885i	−0.385043	−	0.279750i	−0.763421	+	0.645901i	$0.776482\pi$
$492$		0			0
$493$			29.0265i			1.30729i
$494$		0			0
$495$	2.46806	−	3.86106i	0.110931	−	0.173542i
$496$		0			0
$497$	−2.81057	−	0.913209i	−0.126071	−	0.0409630i
$498$		0			0
$499$	−19.3342			−0.865516			−0.432758	−	0.901510i	$-0.642459\pi$
$499$	−19.3342			−0.865516			−0.432758	+	0.901510i	$0.642459\pi$
$500$		0			0
$501$	−39.0992			−1.74683
$502$		0			0
$503$	−15.8702	−	5.15653i	−0.707616	−	0.229918i	−0.0669703	−	0.997755i	$-0.521333\pi$
$503$	−15.8702	−	5.15653i	−0.707616	−	0.229918i	−0.640646	+	0.767837i	$0.721333\pi$
$504$		0			0
$505$	16.4336	−	25.7089i	0.731285	−	1.14403i
$506$		0			0
$507$		−	24.6400i		−	1.09430i
$508$		0			0
$509$	8.90706	+	6.47136i	0.394798	+	0.286838i	0.767419	−	0.641146i	$-0.221541\pi$
$509$	8.90706	+	6.47136i	0.394798	+	0.286838i	−0.372621	+	0.927984i	$0.621541\pi$
$510$		0			0
$511$	−5.82540	+	4.23240i	−0.257701	+	0.187230i
$512$		0			0
$513$	13.5538	−	18.6551i	0.598413	−	0.823645i
$514$		0			0
$515$	−23.5397	+	19.3443i	−1.03728	+	0.852413i
$516$		0			0
$517$	4.03950	−	1.31251i	0.177657	−	0.0577243i
$518$		0			0
$519$	−0.479584	−	1.47601i	−0.0210514	−	0.0647896i
$520$		0			0
$521$	5.96500	−	18.3584i	0.261331	−	0.804295i	−0.731185	−	0.682180i	$-0.761032\pi$
$521$	5.96500	−	18.3584i	0.261331	−	0.804295i	0.992516	−	0.122115i	$-0.0389678\pi$
$522$		0			0
$523$	−7.26069	−	9.99348i	−0.317488	−	0.436985i	0.620210	−	0.784436i	$-0.287047\pi$
$523$	−7.26069	−	9.99348i	−0.317488	−	0.436985i	−0.937698	+	0.347451i	$0.887047\pi$
$524$		0			0
$525$	−5.01627	+	0.600381i	−0.218928	+	0.0262028i
$526$		0			0
$527$	−12.5602	−	17.2876i	−0.547131	−	0.753062i
$528$		0			0
$529$	−11.5158	+	35.4419i	−0.500686	+	1.54095i
$530$		0			0
$531$	2.37407	+	7.30663i	0.103026	+	0.317081i
$532$		0			0
$533$	−4.26981	+	1.38735i	−0.184946	+	0.0600926i
$534$		0			0
$535$	−3.18861	−	2.03822i	−0.137856	−	0.0881200i
$536$		0			0
$537$	9.35664	−	12.8783i	0.403769	−	0.555740i
$538$		0			0
$539$	10.0659	−	7.31328i	0.433567	−	0.315005i
$540$		0			0
$541$	−19.9058	−	14.4624i	−0.855819	−	0.621789i	0.0709252	−	0.997482i	$-0.477405\pi$
$541$	−19.9058	−	14.4624i	−0.855819	−	0.621789i	−0.926744	+	0.375693i	$0.877405\pi$
$542$		0			0
$543$		−	14.3711i		−	0.616724i
$544$		0			0
$545$	3.42749	−	1.34408i	0.146817	−	0.0575742i
$546$		0			0
$547$	−10.4890	−	3.40807i	−0.448476	−	0.145719i	0.0760670	−	0.997103i	$-0.475764\pi$
$547$	−10.4890	−	3.40807i	−0.448476	−	0.145719i	−0.524543	+	0.851384i	$0.675764\pi$
$548$		0			0
$549$	6.08552			0.259724
$550$		0			0
$551$	−25.5125			−1.08687
$552$		0			0
$553$	−5.52281	−	1.79447i	−0.234854	−	0.0763086i
$554$		0			0
$555$	−0.841108	−	14.1053i	−0.0357030	−	0.598737i
$556$		0			0
$557$		−	3.20178i		−	0.135664i	−0.997697	−	0.0678319i	$-0.978392\pi$
$557$		−	3.20178i		−	0.135664i	0.997697	−	0.0678319i	$-0.0216081\pi$
$558$		0			0
$559$	−3.89772	−	2.83186i	−0.164856	−	0.119775i
$560$		0			0
$561$	20.7174	−	15.0521i	0.874688	−	0.635498i
$562$		0			0
$563$	24.6896	−	33.9823i	1.04054	−	1.43218i	0.143811	−	0.989605i	$-0.454064\pi$
$563$	24.6896	−	33.9823i	1.04054	−	1.43218i	0.896731	−	0.442577i	$-0.145936\pi$
$564$		0			0
$565$	−10.6614	−	27.1871i	−0.448527	−	1.14377i
$566$		0			0
$567$	5.25992	−	1.70905i	0.220896	−	0.0717735i
$568$		0			0
$569$	4.25532	+	13.0965i	0.178392	+	0.549034i	0.999772	−	0.0213469i	$-0.00679544\pi$
$569$	4.25532	+	13.0965i	0.178392	+	0.549034i	−0.821380	+	0.570381i	$0.806795\pi$
$570$		0			0
$571$	9.02167	−	27.7659i	0.377545	−	1.16196i	−0.564200	−	0.825638i	$-0.690815\pi$
$571$	9.02167	−	27.7659i	0.377545	−	1.16196i	0.941745	−	0.336327i	$-0.109185\pi$
$572$		0			0
$573$	25.4636	+	35.0476i	1.06376	+	1.46413i
$574$		0			0
$575$	−18.9217	+	33.8912i	−0.789089	+	1.41336i
$576$		0			0
$577$	−12.5692	−	17.3001i	−0.523264	−	0.720211i	0.462821	−	0.886452i	$-0.346837\pi$
$577$	−12.5692	−	17.3001i	−0.523264	−	0.720211i	−0.986085	+	0.166241i	$0.946837\pi$
$578$		0			0
$579$	−5.73617	+	17.6541i	−0.238387	+	0.733680i
$580$		0			0
$581$	2.15790	+	6.64135i	0.0895250	+	0.275530i
$582$		0			0
$583$	−19.9985	+	6.49791i	−0.828254	+	0.269116i
$584$		0			0
$585$	0.577088	−	2.21746i	0.0238596	−	0.0916808i
$586$		0			0
$587$	9.38775	−	12.9211i	0.387474	−	0.533312i	−0.570071	−	0.821595i	$-0.693084\pi$
$587$	9.38775	−	12.9211i	0.387474	−	0.533312i	0.957545	+	0.288283i	$0.0930844\pi$
$588$		0			0
$589$	15.1948	−	11.0397i	0.626091	−	0.454882i
$590$		0			0
$591$	−10.6143	−	7.71172i	−0.436613	−	0.317218i
$592$		0			0
$593$			1.35121i			0.0554874i	0.999615	+	0.0277437i	$0.00883223\pi$
$593$			1.35121i			0.0554874i	−0.999615	+	0.0277437i	$0.991168\pi$
$594$		0			0
$595$	−7.38909	−	1.92299i	−0.302923	−	0.0788348i
$596$		0			0
$597$	−41.7540	−	13.5667i	−1.70888	−	0.555248i
$598$		0			0
$599$	−25.6391			−1.04759			−0.523793	−	0.851846i	$-0.675483\pi$
$599$	−25.6391			−1.04759			−0.523793	+	0.851846i	$0.675483\pi$
$600$		0			0
$601$	−18.6688			−0.761518			−0.380759	−	0.924674i	$-0.624337\pi$
$601$	−18.6688			−0.761518			−0.380759	+	0.924674i	$0.624337\pi$
$602$		0			0
$603$	0.846468	+	0.275034i	0.0344709	+	0.0112003i
$604$		0			0
$605$	10.7953	+	13.1366i	0.438893	+	0.534079i
$606$		0			0
$607$		−	32.1342i		−	1.30429i	−0.758095	−	0.652144i	$-0.773870\pi$
$607$		−	32.1342i		−	1.30429i	0.758095	−	0.652144i	$-0.226130\pi$
$608$		0			0
$609$	−3.46245	−	2.51562i	−0.140306	−	0.101938i
$610$		0			0
$611$	1.71817	−	1.24832i	0.0695097	−	0.0505017i
$612$		0			0
$613$	7.09225	−	9.76164i	0.286453	−	0.394269i	−0.641405	−	0.767203i	$-0.721648\pi$
$613$	7.09225	−	9.76164i	0.286453	−	0.394269i	0.927858	+	0.372934i	$0.121648\pi$
$614$		0			0
$615$	22.0537	−	1.31508i	0.889292	−	0.0530290i
$616$		0			0
$617$	13.1415	−	4.26994i	0.529058	−	0.171901i	−0.0322941	−	0.999478i	$-0.510281\pi$
$617$	13.1415	−	4.26994i	0.529058	−	0.171901i	0.561352	+	0.827577i	$0.310281\pi$
$618$		0			0
$619$	−2.20378	−	6.78254i	−0.0885774	−	0.272613i	0.896949	−	0.442133i	$-0.145778\pi$
$619$	−2.20378	−	6.78254i	−0.0885774	−	0.272613i	−0.985527	+	0.169520i	$0.945778\pi$
$620$		0			0
$621$	9.18401	−	28.2655i	0.368541	−	1.13425i
$622$		0			0
$623$	5.15604	+	7.09669i	0.206573	+	0.284323i
$624$		0			0
$625$	−16.1863	+	19.0526i	−0.647453	+	0.762105i
$626$		0			0
$627$	13.2299	+	18.2093i	0.528350	+	0.727211i
$628$		0			0
$629$	6.59914	−	20.3101i	0.263125	−	0.809815i
$630$		0			0
$631$	1.77445	+	5.46120i	0.0706398	+	0.217407i	0.980144	−	0.198288i	$-0.0635382\pi$
$631$	1.77445	+	5.46120i	0.0706398	+	0.217407i	−0.909504	+	0.415695i	$0.863538\pi$
$632$		0			0
$633$	−12.8619	+	4.17908i	−0.511214	+	0.166104i
$634$		0			0
$635$	16.1259	−	0.961595i	0.639936	−	0.0381597i
$636$		0			0
$637$	3.65678	−	5.03312i	0.144887	−	0.199420i
$638$		0			0
$639$	−5.33597	+	3.87681i	−0.211088	+	0.153364i
$640$		0			0
$641$	2.82998	+	2.05610i	0.111777	+	0.0812110i	0.642270	−	0.766479i	$-0.277993\pi$
$641$	2.82998	+	2.05610i	0.111777	+	0.0812110i	−0.530492	+	0.847690i	$0.677993\pi$
$642$		0			0
$643$			44.4192i			1.75172i	0.482564	+	0.875861i	$0.339705\pi$
$643$			44.4192i			1.75172i	−0.482564	+	0.875861i	$0.660295\pi$
$644$		0			0
$645$	15.0525	+	18.3170i	0.592691	+	0.721232i
$646$		0			0
$647$	−4.14140	−	1.34562i	−0.162815	−	0.0529019i	0.226475	−	0.974017i	$-0.427280\pi$
$647$	−4.14140	−	1.34562i	−0.162815	−	0.0529019i	−0.389290	+	0.921115i	$0.627280\pi$
$648$		0			0
$649$	12.7307			0.499725
$650$		0			0
$651$	3.15072			0.123487
$652$		0			0
$653$	14.2468	+	4.62907i	0.557521	+	0.181150i	0.574206	−	0.818711i	$-0.305311\pi$
$653$	14.2468	+	4.62907i	0.557521	+	0.181150i	−0.0166843	+	0.999861i	$0.505311\pi$
$654$		0			0
$655$	−40.6611	−	10.5819i	−1.58876	−	0.413470i
$656$		0			0
$657$			16.0707i			0.626979i
$658$		0			0
$659$	−6.34893	−	4.61277i	−0.247319	−	0.179688i	0.457219	−	0.889354i	$-0.348846\pi$
$659$	−6.34893	−	4.61277i	−0.247319	−	0.179688i	−0.704538	+	0.709666i	$0.748846\pi$
$660$		0			0
$661$	6.92047	−	5.02802i	0.269175	−	0.195567i	−0.445007	−	0.895527i	$-0.646799\pi$
$661$	6.92047	−	5.02802i	0.269175	−	0.195567i	0.714182	+	0.699960i	$0.246799\pi$
$662$		0			0
$663$	7.52632	−	10.3591i	0.292298	−	0.402313i
$664$		0			0
$665$	1.69019	−	6.49457i	0.0655428	−	0.251849i
$666$		0			0
$667$	−31.2729	+	10.1612i	−1.21089	+	0.393443i
$668$		0			0
$669$	−11.4035	−	35.0965i	−0.440887	−	1.35691i
$670$		0			0
$671$	3.11618	−	9.59061i	0.120299	−	0.370241i
$672$		0			0
$673$	1.82102	+	2.50641i	0.0701950	+	0.0966151i	0.842671	−	0.538429i	$-0.180982\pi$
$673$	1.82102	+	2.50641i	0.0701950	+	0.0966151i	−0.772476	+	0.635044i	$0.780982\pi$
$674$		0			0
$675$	9.33123	−	16.7134i	0.359159	−	0.643301i
$676$		0			0
$677$	19.8794	+	27.3616i	0.764026	+	1.05159i	0.996869	+	0.0790771i	$0.0251973\pi$
$677$	19.8794	+	27.3616i	0.764026	+	1.05159i	−0.232843	+	0.972514i	$0.574803\pi$
$678$		0			0
$679$	−1.03659	+	3.19030i	−0.0397807	+	0.122432i
$680$		0			0
$681$	−3.60811	−	11.1046i	−0.138263	−	0.425529i
$682$		0			0
$683$	27.3557	−	8.88840i	1.04674	−	0.340105i	0.265349	−	0.964152i	$-0.414513\pi$
$683$	27.3557	−	8.88840i	1.04674	−	0.340105i	0.781386	+	0.624047i	$0.214513\pi$
$684$		0			0
$685$	−1.67383	−	4.26837i	−0.0639539	−	0.163086i
$686$		0			0
$687$	−2.94082	+	4.04769i	−0.112199	+	0.154429i
$688$		0			0
$689$	−8.50621	+	6.18012i	−0.324061	+	0.235444i
$690$		0			0
$691$	20.8515	+	15.1495i	0.793227	+	0.576313i	0.908919	−	0.416972i	$-0.136909\pi$
$691$	20.8515	+	15.1495i	0.793227	+	0.576313i	−0.115692	+	0.993285i	$0.536909\pi$
$692$		0			0
$693$			1.02114i			0.0387898i
$694$		0			0
$695$	−0.925804	−	15.5257i	−0.0351178	−	0.588922i
$696$		0			0
$697$	31.7549	+	10.3178i	1.20280	+	0.390814i
$698$		0			0
$699$	−7.89520			−0.298624
$700$		0			0
$701$	−33.0074			−1.24667			−0.623336	−	0.781954i	$-0.714223\pi$
$701$	−33.0074			−1.24667			−0.623336	+	0.781954i	$0.714223\pi$
$702$		0			0
$703$	17.8513	+	5.80025i	0.673276	+	0.218761i
$704$		0			0
$705$	−9.72964	+	3.81546i	−0.366440	+	0.143699i
$706$		0			0
$707$			6.79924i			0.255712i
$708$		0			0
$709$	38.1833	+	27.7418i	1.43400	+	1.04186i	0.989254	+	0.146209i	$0.0467073\pi$
$709$	38.1833	+	27.7418i	1.43400	+	1.04186i	0.444749	+	0.895655i	$0.353293\pi$
$710$		0			0
$711$	−10.4853	+	7.61799i	−0.393228	+	0.285697i
$712$		0			0
$713$	14.2287	−	19.5841i	0.532869	−	0.733431i
$714$		0			0
$715$	−3.19916	−	2.04496i	−0.119642	−	0.0764771i
$716$		0			0
$717$	21.1449	−	6.87039i	0.789670	−	0.256579i
$718$		0			0
$719$	10.5182	+	32.3716i	0.392262	+	1.20726i	0.931074	+	0.364832i	$0.118873\pi$
$719$	10.5182	+	32.3716i	0.392262	+	1.20726i	−0.538812	+	0.842426i	$0.681127\pi$
$720$		0			0
$721$	2.09805	−	6.45712i	0.0781353	−	0.240476i
$722$		0			0
$723$	−2.14394	−	2.95088i	−0.0797340	−	0.109744i
$724$		0			0
$725$	−21.0285	+	2.51683i	−0.780979	+	0.0934728i
$726$		0			0
$727$	−16.9713	−	23.3589i	−0.629429	−	0.866335i	0.368567	−	0.929601i	$-0.379848\pi$
$727$	−16.9713	−	23.3589i	−0.629429	−	0.866335i	−0.997997	+	0.0632658i	$0.979848\pi$
$728$		0			0
$729$	−3.38258	+	10.4105i	−0.125281	+	0.385575i
$730$		0			0
$731$	11.0723	+	34.0770i	0.409523	+	1.26038i
$732$		0			0
$733$	−29.8238	+	9.69033i	−1.10157	+	0.357921i	−0.802705	−	0.596376i	$-0.796607\pi$
$733$	−29.8238	+	9.69033i	−1.10157	+	0.357921i	−0.298861	+	0.954297i	$0.596607\pi$
$734$		0			0
$735$	−23.6528	+	19.4373i	−0.872446	+	0.716955i
$736$		0			0
$737$	0.866893	−	1.19318i	0.0319324	−	0.0439512i
$738$		0			0
$739$	36.5989	−	26.5907i	1.34631	−	0.978154i	0.347127	−	0.937818i	$-0.387157\pi$
$739$	36.5989	−	26.5907i	1.34631	−	0.978154i	0.999186	−	0.0403362i	$-0.0128429\pi$
$740$		0			0
$741$	9.10502	+	6.61518i	0.334481	+	0.243015i
$742$		0			0
$743$			0.842287i			0.0309005i	0.999881	+	0.0154503i	$0.00491817\pi$
$743$			0.842287i			0.0309005i	−0.999881	+	0.0154503i	$0.995082\pi$
$744$		0			0
$745$	−26.1845	+	40.9632i	−0.959324	+	1.50078i
$746$		0			0
$747$	14.8226	+	4.81615i	0.542330	+	0.176214i
$748$		0			0
$749$	0.843296			0.0308133
$750$		0			0
$751$	−35.3880			−1.29132			−0.645662	−	0.763623i	$-0.723419\pi$
$751$	−35.3880			−1.29132			−0.645662	+	0.763623i	$0.723419\pi$
$752$		0			0
$753$	−16.0818	−	5.22528i	−0.586052	−	0.190420i
$754$		0			0
$755$	−12.3689	+	19.3501i	−0.450152	+	0.704222i
$756$		0			0
$757$		−	18.4440i		−	0.670360i	−0.942154	−	0.335180i	$-0.891203\pi$
$757$		−	18.4440i		−	0.670360i	0.942154	−	0.335180i	$-0.108797\pi$
$758$		0			0
$759$	23.4694	+	17.0516i	0.851887	+	0.618932i
$760$		0			0
$761$	−24.9055	+	18.0949i	−0.902823	+	0.655939i	−0.939190	−	0.343399i	$-0.888422\pi$
$761$	−24.9055	+	18.0949i	−0.902823	+	0.655939i	0.0363664	+	0.999339i	$0.488422\pi$
$762$		0			0
$763$	−0.482214	+	0.663711i	−0.0174573	+	0.0240279i
$764$		0			0
$765$	−13.1656	+	10.8192i	−0.476003	+	0.391168i
$766$		0			0
$767$	6.05405	−	1.96708i	0.218599	−	0.0710272i
$768$		0			0
$769$	−0.160573	−	0.494191i	−0.00579039	−	0.0178210i	0.948120	−	0.317914i	$-0.102982\pi$
$769$	−0.160573	−	0.494191i	−0.00579039	−	0.0178210i	−0.953910	+	0.300093i	$0.902982\pi$
$770$		0			0
$771$	13.5123	−	41.5866i	0.486633	−	1.49770i
$772$		0			0
$773$	−8.80690	−	12.1217i	−0.316762	−	0.435986i	0.620713	−	0.784038i	$-0.286843\pi$
$773$	−8.80690	−	12.1217i	−0.316762	−	0.435986i	−0.937475	+	0.348052i	$0.886843\pi$
$774$		0			0
$775$	11.4351	−	10.5983i	0.410762	−	0.380704i
$776$		0			0
$777$	1.85078	+	2.54739i	0.0663965	+	0.0913870i
$778$		0			0
$779$	−9.06872	+	27.9107i	−0.324921	+	1.00000i
$780$		0			0
$781$	3.37738	+	10.3945i	0.120852	+	0.371945i
$782$		0			0
$783$	15.4222	−	5.01099i	0.551146	−	0.179078i
$784$		0			0
$785$	−19.1223	−	12.2233i	−0.682503	−	0.436269i
$786$		0			0
$787$	27.0360	−	37.2119i	0.963729	−	1.32646i	0.0185779	−	0.999827i	$-0.494086\pi$
$787$	27.0360	−	37.2119i	0.963729	−	1.32646i	0.945151	−	0.326632i	$-0.105914\pi$
$788$		0			0
$789$	−39.0247	+	28.3531i	−1.38932	+	1.00940i
$790$		0			0
$791$	5.26460	+	3.82496i	0.187188	+	0.136000i
$792$		0			0
$793$		−	5.04228i		−	0.179056i
$794$		0			0
$795$	48.1689	−	18.8894i	1.70838	−	0.669937i
$796$		0			0
$797$	−2.88712	−	0.938081i	−0.102267	−	0.0332285i	0.257437	−	0.966295i	$-0.417122\pi$
$797$	−2.88712	−	0.938081i	−0.102267	−	0.0332285i	−0.359704	+	0.933067i	$0.617122\pi$
$798$		0			0
$799$	−15.7947			−0.558775
$800$		0			0
$801$	19.5779			0.691750
$802$		0			0
$803$	25.3270	+	8.22926i	0.893772	+	0.290404i
$804$		0			0
$805$	−0.514858	−	8.63413i	−0.0181464	−	0.304313i
$806$		0			0
$807$			56.5330i			1.99006i
$808$		0			0
$809$	−32.7524	−	23.7960i	−1.15151	−	0.836623i	−0.162831	−	0.986654i	$-0.552063\pi$
$809$	−32.7524	−	23.7960i	−1.15151	−	0.836623i	−0.988681	+	0.150031i	$0.952063\pi$
$810$		0			0
$811$	8.48948	−	6.16797i	0.298106	−	0.216587i	−0.428670	−	0.903461i	$-0.641018\pi$
$811$	8.48948	−	6.16797i	0.298106	−	0.216587i	0.726776	+	0.686874i	$0.241018\pi$
$812$		0			0
$813$	24.6042	−	33.8648i	0.862907	−	1.18769i
$814$		0			0
$815$	0.480358	+	1.22494i	0.0168262	+	0.0429078i
$816$		0			0
$817$	−29.9516	+	9.73188i	−1.04788	+	0.340475i
$818$		0			0
$819$	0.157780	+	0.485598i	0.00551329	+	0.0169682i
$820$		0			0
$821$	13.0342	−	40.1153i	0.454898	−	1.40003i	−0.416357	−	0.909201i	$-0.636693\pi$
$821$	13.0342	−	40.1153i	0.454898	−	1.40003i	0.871255	−	0.490831i	$-0.163307\pi$
$822$		0			0
$823$	−23.2545	−	32.0070i	−0.810600	−	1.11569i	−0.991231	−	0.132144i	$-0.957814\pi$
$823$	−23.2545	−	32.0070i	−0.810600	−	1.11569i	0.180631	−	0.983551i	$-0.442186\pi$
$824$		0			0
$825$	12.7010	+	13.7038i	0.442191	+	0.477104i
$826$		0			0
$827$	9.87202	+	13.5877i	0.343284	+	0.472489i	0.945397	−	0.325921i	$-0.105674\pi$
$827$	9.87202	+	13.5877i	0.343284	+	0.472489i	−0.602113	+	0.798411i	$0.705674\pi$
$828$		0			0
$829$	9.37542	−	28.8546i	0.325622	−	1.00216i	−0.645538	−	0.763728i	$-0.723367\pi$
$829$	9.37542	−	28.8546i	0.325622	−	1.00216i	0.971159	−	0.238432i	$-0.0766334\pi$
$830$		0			0
$831$	−1.77557	−	5.46463i	−0.0615937	−	0.189566i
$832$		0			0
$833$	−44.0036	+	14.2976i	−1.52463	+	0.495384i
$834$		0			0
$835$	10.8587	−	41.7246i	0.375780	−	1.44394i
$836$		0			0
$837$	−7.01687	+	9.65790i	−0.242539	+	0.333826i
$838$		0			0
$839$	22.5154	−	16.3584i	0.777320	−	0.564756i	−0.126854	−	0.991921i	$-0.540488\pi$
$839$	22.5154	−	16.3584i	0.777320	−	0.564756i	0.904173	+	0.427166i	$0.140488\pi$
$840$		0			0
$841$	8.94669	+	6.50015i	0.308506	+	0.224143i
$842$		0			0
$843$		−	25.8178i		−	0.889211i
$844$		0			0
$845$	26.2945	+	6.84306i	0.904558	+	0.235408i
$846$		0			0
$847$	−3.60348	−	1.17084i	−0.123817	−	0.0402306i
$848$		0			0
$849$	33.3425			1.14431
$850$		0			0
$851$	24.1921			0.829293
$852$		0			0
$853$	−41.0752	−	13.3461i	−1.40639	−	0.456963i	−0.495136	−	0.868815i	$-0.664882\pi$
$853$	−41.0752	−	13.3461i	−1.40639	−	0.456963i	−0.911251	+	0.411852i	$0.864882\pi$
$854$		0			0
$855$	−9.50940	−	11.5718i	−0.325215	−	0.395746i
$856$		0			0
$857$			3.52734i			0.120492i	0.998184	+	0.0602458i	$0.0191885\pi$
$857$			3.52734i			0.120492i	−0.998184	+	0.0602458i	$0.980812\pi$
$858$		0			0
$859$	43.6675	+	31.7263i	1.48992	+	1.08249i	0.974189	+	0.225733i	$0.0724777\pi$
$859$	43.6675	+	31.7263i	1.48992	+	1.08249i	0.515726	+	0.856754i	$0.327522\pi$
$860$		0			0
$861$	−3.98285	+	2.89371i	−0.135735	+	0.0986174i
$862$		0			0
$863$	−29.9982	+	41.2890i	−1.02115	+	1.40549i	−0.109757	+	0.993958i	$0.535007\pi$
$863$	−29.9982	+	41.2890i	−1.02115	+	1.40549i	−0.911394	+	0.411535i	$0.864993\pi$
$864$		0			0
$865$	1.70831	−	0.101867i	0.0580842	−	0.00346359i
$866$		0			0
$867$	−57.7816	+	18.7744i	−1.96237	+	0.637611i
$868$		0			0
$869$	6.63661	+	20.4254i	0.225132	+	0.692884i
$870$		0			0
$871$	0.227885	−	0.701358i	0.00772159	−	0.0237646i
$872$		0			0
$873$	4.40059	+	6.05689i	0.148937	+	0.204995i
$874$		0			0
$875$	0.752431	−	5.51983i	0.0254368	−	0.186604i
$876$		0			0
$877$	21.6715	+	29.8283i	0.731795	+	1.00723i	0.999049	+	0.0436036i	$0.0138838\pi$
$877$	21.6715	+	29.8283i	0.731795	+	1.00723i	−0.267254	+	0.963626i	$0.586116\pi$
$878$		0			0
$879$	2.74241	−	8.44026i	0.0924991	−	0.284683i
$880$		0			0
$881$	11.6761	+	35.9354i	0.393379	+	1.21070i	0.930217	+	0.367010i	$0.119619\pi$
$881$	11.6761	+	35.9354i	0.393379	+	1.21070i	−0.536838	+	0.843685i	$0.680381\pi$
$882$		0			0
$883$	−30.7552	+	9.99297i	−1.03499	+	0.336290i	−0.776763	−	0.629793i	$-0.783140\pi$
$883$	−30.7552	+	9.99297i	−1.03499	+	0.336290i	−0.258232	+	0.966083i	$0.583140\pi$
$884$		0			0
$885$	−31.2694	+	1.86461i	−1.05111	+	0.0626783i
$886$		0			0
$887$	−28.9820	+	39.8903i	−0.973120	+	1.33939i	−0.0326656	+	0.999466i	$0.510400\pi$
$887$	−28.9820	+	39.8903i	−0.973120	+	1.33939i	−0.940455	+	0.339919i	$0.889600\pi$
$888$		0			0
$889$	−2.91230	+	2.11591i	−0.0976753	+	0.0709652i
$890$		0			0
$891$	−16.5478	−	12.0227i	−0.554373	−	0.402775i
$892$		0			0
$893$		−	13.8826i		−	0.464562i
$894$		0			0
$895$	11.1445	+	13.5615i	0.372519	+	0.453310i
$896$		0			0
$897$	13.7955	+	4.48244i	0.460619	+	0.149664i
$898$		0			0
$899$	13.2080			0.440512
$900$		0			0
$901$	78.1952			2.60506
$902$		0			0
$903$	−5.02451	−	1.63256i	−0.167205	−	0.0543283i
$904$		0			0
$905$	15.3361	+	3.99117i	0.509789	+	0.132671i
$906$		0			0
$907$			35.9031i			1.19214i	0.802932	+	0.596071i	$0.203272\pi$
$907$			35.9031i			1.19214i	−0.802932	+	0.596071i	$0.796728\pi$
$908$		0			0
$909$	12.2768	+	8.91963i	0.407196	+	0.295845i
$910$		0			0
$911$	30.3991	−	22.0862i	1.00717	−	0.731749i	0.0435536	−	0.999051i	$-0.486132\pi$
$911$	30.3991	−	22.0862i	1.00717	−	0.731749i	0.963613	+	0.267302i	$0.0861321\pi$
$912$		0			0
$913$	15.1802	−	20.8938i	0.502393	−	0.691484i
$914$		0			0
$915$	−6.24931	+	24.0130i	−0.206596	+	0.793845i
$916$		0			0
$917$	8.90429	−	2.89318i	0.294046	−	0.0955412i
$918$		0			0
$919$	0.907105	+	2.79178i	0.0299226	+	0.0920924i	0.964902	−	0.262608i	$-0.0845827\pi$
$919$	0.907105	+	2.79178i	0.0299226	+	0.0920924i	−0.934980	+	0.354701i	$0.884583\pi$
$920$		0			0
$921$	−2.11436	+	6.50735i	−0.0696707	+	0.214424i
$922$		0			0
$923$	3.21221	+	4.42122i	0.105731	+	0.145526i
$924$		0			0
$925$	15.2860	+	3.01976i	0.502601	+	0.0992891i
$926$		0			0
$927$	−8.90674	−	12.2591i	−0.292536	−	0.402641i
$928$		0			0
$929$	−17.4285	+	53.6393i	−0.571810	+	1.75985i	0.0749847	+	0.997185i	$0.476109\pi$
$929$	−17.4285	+	53.6393i	−0.571810	+	1.75985i	−0.646794	+	0.762664i	$0.723891\pi$
$930$		0			0
$931$	−12.5668	−	38.6766i	−0.411859	−	1.26757i
$932$		0			0
$933$	36.0328	−	11.7078i	1.17966	−	0.383295i
$934$		0			0
$935$	10.3091	+	26.2887i	0.337143	+	0.859734i
$936$		0			0
$937$	1.65512	−	2.27808i	0.0540704	−	0.0744215i	−0.781126	−	0.624374i	$-0.785354\pi$
$937$	1.65512	−	2.27808i	0.0540704	−	0.0744215i	0.835196	+	0.549952i	$0.185354\pi$
$938$		0			0
$939$	23.3693	−	16.9788i	0.762628	−	0.554081i
$940$		0			0
$941$	43.3104	+	31.4668i	1.41188	+	1.02579i	0.993046	+	0.117725i	$0.0375601\pi$
$941$	43.3104	+	31.4668i	1.41188	+	1.02579i	0.418831	+	0.908064i	$0.362440\pi$
$942$		0			0
$943$			37.8244i			1.23173i
$944$		0			0
$945$	0.253902	+	4.25792i	0.00825944	+	0.138510i
$946$		0			0
$947$	5.78394	+	1.87931i	0.187953	+	0.0610695i	0.401481	−	0.915867i	$-0.368496\pi$
$947$	5.78394	+	1.87931i	0.187953	+	0.0610695i	−0.213528	+	0.976937i	$0.568496\pi$
$948$		0			0
$949$	13.3157			0.432247
$950$		0			0
$951$	6.46127			0.209521
$952$		0			0
$953$	2.16886	+	0.704707i	0.0702564	+	0.0228277i	0.343934	−	0.938994i	$-0.388240\pi$
$953$	2.16886	+	0.704707i	0.0702564	+	0.0228277i	−0.273678	+	0.961821i	$0.588240\pi$
$954$		0			0
$955$	−44.4727	+	17.4399i	−1.43910	+	0.564341i
$956$		0			0
$957$			15.8284i			0.511659i
$958$		0			0
$959$	0.826543	+	0.600518i	0.0266905	+	0.0193918i
$960$		0			0
$961$	17.2131	−	12.5060i	0.555260	−	0.403420i
$962$		0			0
$963$	1.10628	−	1.52267i	0.0356495	−	0.0490673i
$964$		0			0
$965$	−17.2465	−	11.0243i	−0.555183	−	0.354883i
$966$		0			0
$967$	−18.7949	+	6.10684i	−0.604404	+	0.196383i	−0.595204	−	0.803575i	$-0.702929\pi$
$967$	−18.7949	+	6.10684i	−0.604404	+	0.196383i	−0.00920044	+	0.999958i	$0.502929\pi$
$968$		0			0
$969$	−25.8647	−	79.6034i	−0.830894	−	2.55723i
$970$		0			0
$971$	−4.44752	+	13.6881i	−0.142728	+	0.439271i	−0.996712	−	0.0810284i	$-0.974180\pi$
$971$	−4.44752	+	13.6881i	−0.142728	+	0.439271i	0.853984	+	0.520299i	$0.174180\pi$
$972$		0			0
$973$	2.03715	+	2.80390i	0.0653081	+	0.0898889i
$974$		0			0
$975$	8.15733	+	4.55429i	0.261244	+	0.145854i
$976$		0			0
$977$	10.5895	+	14.5752i	0.338788	+	0.466302i	0.944087	−	0.329696i	$-0.106946\pi$
$977$	10.5895	+	14.5752i	0.338788	+	0.466302i	−0.605299	+	0.795998i	$0.706946\pi$
$978$		0			0
$979$	10.0251	−	30.8542i	0.320405	−	0.986104i
$980$		0			0
$981$	0.565810	+	1.74139i	0.0180649	+	0.0555982i
$982$		0			0
$983$	−28.8047	+	9.35921i	−0.918726	+	0.298512i	−0.729944	−	0.683507i	$-0.760454\pi$
$983$	−28.8047	+	9.35921i	−0.918726	+	0.298512i	−0.188782	+	0.982019i	$0.560454\pi$
$984$		0			0
$985$	11.1773	−	9.18527i	0.356140	−	0.292667i
$986$		0			0
$987$	1.36887	−	1.88408i	0.0435715	−	0.0599710i
$988$		0			0
$989$	−32.8383	+	23.8584i	−1.04420	+	0.758654i
$990$		0			0
$991$	25.7497	+	18.7083i	0.817967	+	0.594288i	0.916130	−	0.400882i	$-0.131296\pi$
$991$	25.7497	+	18.7083i	0.817967	+	0.594288i	−0.0981622	+	0.995170i	$0.531296\pi$
$992$		0			0
$993$		−	60.4321i		−	1.91775i
$994$		0			0
$995$	26.0736	−	40.7899i	0.826589	−	1.29313i
$996$		0			0
$997$	−17.7820	−	5.77774i	−0.563163	−	0.182983i	0.0135809	−	0.999908i	$-0.495677\pi$
$997$	−17.7820	−	5.77774i	−0.563163	−	0.182983i	−0.576744	+	0.816925i	$0.695677\pi$
$998$		0			0
$999$	−11.9303			−0.377458

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.y.d.289.2		32
4.3	odd	2		200.2.q.a.89.7	yes	32
20.3	even	4		1000.2.m.d.801.2		32
20.7	even	4		1000.2.m.e.801.7		32
20.19	odd	2		1000.2.q.c.449.2		32
25.3	odd	20		10000.2.a.bq.1.13		16
25.9	even	10	inner	400.2.y.d.209.2		32
25.22	odd	20		10000.2.a.br.1.4		16
100.3	even	20		5000.2.a.r.1.4		16
100.47	even	20		5000.2.a.q.1.13		16
100.59	odd	10		200.2.q.a.9.7	✓	32
100.63	even	20		1000.2.m.d.201.2		32
100.87	even	20		1000.2.m.e.201.7		32
100.91	odd	10		1000.2.q.c.49.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.q.a.9.7	✓	32	100.59	odd	10
200.2.q.a.89.7	yes	32	4.3	odd	2
400.2.y.d.209.2		32	25.9	even	10	inner
400.2.y.d.289.2		32	1.1	even	1	trivial
1000.2.m.d.201.2		32	100.63	even	20
1000.2.m.d.801.2		32	20.3	even	4
1000.2.m.e.201.7		32	100.87	even	20
1000.2.m.e.801.7		32	20.7	even	4
1000.2.q.c.49.2		32	100.91	odd	10
1000.2.q.c.449.2		32	20.19	odd	2
5000.2.a.q.1.13		16	100.47	even	20
5000.2.a.r.1.4		16	100.3	even	20
10000.2.a.bq.1.13		16	25.3	odd	20
10000.2.a.br.1.4		16	25.22	odd	20

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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.y (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.92858 - 0.626633i) q^{3} +(1.20432 - 1.88404i) q^{5} +0.498275i q^{7} +(0.899692 + 0.653665i) q^{9} +O(q^{10})\)	\(q+(-1.92858 - 0.626633i) q^{3} +(1.20432 - 1.88404i) q^{5} +0.498275i q^{7} +(0.899692 + 0.653665i) q^{9} +(1.49086 - 1.08317i) q^{11} +(0.541607 - 0.745458i) q^{13} +(-3.50322 + 2.87886i) q^{15} +(-6.51739 + 2.11763i) q^{17} +(-1.86127 - 5.72840i) q^{19} +(0.312235 - 0.960962i) q^{21} +(-4.56304 - 6.28049i) q^{23} +(-2.09925 - 4.53797i) q^{25} +(2.25026 + 3.09722i) q^{27} +(1.30891 - 4.02840i) q^{29} +(0.963592 + 2.96563i) q^{31} +(-3.55399 + 1.15476i) q^{33} +(0.938772 + 0.600080i) q^{35} +(-1.83171 + 2.52113i) q^{37} +(-1.51166 + 1.09828i) q^{39} +(-3.94180 - 2.86388i) q^{41} -5.22863i q^{43} +(2.31505 - 0.907842i) q^{45} +(2.19204 + 0.712238i) q^{47} +6.75172 q^{49} +13.8963 q^{51} +(-10.8522 - 3.52610i) q^{53} +(-0.245280 - 4.11333i) q^{55} +12.2140i q^{57} +(5.58897 + 4.06063i) q^{59} +(4.42709 - 3.21647i) q^{61} +(-0.325705 + 0.448294i) q^{63} +(-0.752210 - 1.91818i) q^{65} +(0.761157 - 0.247315i) q^{67} +(4.86462 + 14.9718i) q^{69} +(-1.83274 + 5.64060i) q^{71} +(8.49411 + 11.6911i) q^{73} +(1.20492 + 10.0673i) q^{75} +(0.539717 + 0.742857i) q^{77} +(-3.60137 + 11.0839i) q^{79} +(-3.42994 - 10.5563i) q^{81} +(13.3287 - 4.33075i) q^{83} +(-3.85929 + 14.8293i) q^{85} +(-5.04866 + 6.94889i) q^{87} +(14.2425 - 10.3478i) q^{89} +(0.371443 + 0.269869i) q^{91} -6.32327i q^{93} +(-13.0341 - 3.39209i) q^{95} +(6.40268 + 2.08036i) q^{97} +2.04935 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{5} + 10 q^{9}+O(q^{10}) \) 32 * q + 2 * q^5 + 10 * q^9	\( 32 q + 2 q^{5} + 10 q^{9} - 6 q^{11} - 12 q^{15} + 6 q^{19} - 4 q^{21} + 30 q^{23} + 6 q^{25} - 2 q^{29} - 6 q^{31} - 8 q^{35} - 40 q^{37} + 12 q^{39} - 12 q^{45} + 20 q^{47} - 60 q^{49} + 60 q^{51} - 30 q^{53} + 28 q^{55} + 30 q^{59} + 14 q^{61} + 20 q^{63} - 26 q^{65} - 4 q^{69} - 12 q^{71} + 40 q^{73} - 16 q^{75} - 16 q^{79} - 52 q^{81} - 30 q^{83} + 60 q^{85} - 110 q^{87} + 24 q^{89} + 4 q^{91} - 68 q^{95} + 30 q^{97} - 92 q^{99}+O(q^{100}) \) 32 * q + 2 * q^5 + 10 * q^9 - 6 * q^11 - 12 * q^15 + 6 * q^19 - 4 * q^21 + 30 * q^23 + 6 * q^25 - 2 * q^29 - 6 * q^31 - 8 * q^35 - 40 * q^37 + 12 * q^39 - 12 * q^45 + 20 * q^47 - 60 * q^49 + 60 * q^51 - 30 * q^53 + 28 * q^55 + 30 * q^59 + 14 * q^61 + 20 * q^63 - 26 * q^65 - 4 * q^69 - 12 * q^71 + 40 * q^73 - 16 * q^75 - 16 * q^79 - 52 * q^81 - 30 * q^83 + 60 * q^85 - 110 * q^87 + 24 * q^89 + 4 * q^91 - 68 * q^95 + 30 * q^97 - 92 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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