LMFDB - Embedded newform 400.2.y.b.289.1

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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 100)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			289.1
Root			$1.66637 - 0.917186i$ of defining polynomial
Character	$\chi$	$=$	400.289
Dual form			400.2.y.b.209.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07822 - 0.350334i) q^{3} +(0.279141 + 2.21858i) q^{5} +0.768409i q^{7} +(-1.38723 - 1.00788i) q^{9} +O(q^{10})$	\(q+(-1.07822 - 0.350334i) q^{3} +(0.279141 + 2.21858i) q^{5} +0.768409i q^{7} +(-1.38723 - 1.00788i) q^{9} +(-2.47539 + 1.79848i) q^{11} +(0.132701 - 0.182648i) q^{13} +(0.476268 - 2.48990i) q^{15} +(-5.57734 + 1.81219i) q^{17} +(1.90570 + 5.86514i) q^{19} +(0.269200 - 0.828511i) q^{21} +(-3.05035 - 4.19845i) q^{23} +(-4.84416 + 1.23859i) q^{25} +(3.14177 + 4.32427i) q^{27} +(-0.0146672 + 0.0451411i) q^{29} +(1.80522 + 5.55590i) q^{31} +(3.29908 - 1.07193i) q^{33} +(-1.70477 + 0.214494i) q^{35} +(-4.99060 + 6.86897i) q^{37} +(-0.207068 + 0.150444i) q^{39} +(5.71146 + 4.14962i) q^{41} -3.14793i q^{43} +(1.84883 - 3.35903i) q^{45} +(-10.8295 - 3.51872i) q^{47} +6.40955 q^{49} +6.64845 q^{51} +(3.01846 + 0.980759i) q^{53} +(-4.68104 - 4.98982i) q^{55} -6.99152i q^{57} +(2.36263 + 1.71655i) q^{59} +(6.43232 - 4.67335i) q^{61} +(0.774467 - 1.06596i) q^{63} +(0.442260 + 0.243423i) q^{65} +(-0.281520 + 0.0914714i) q^{67} +(1.81808 + 5.59548i) q^{69} +(4.13182 - 12.7164i) q^{71} +(-8.49858 - 11.6973i) q^{73} +(5.65697 + 0.361604i) q^{75} +(-1.38197 - 1.90211i) q^{77} +(1.40423 - 4.32177i) q^{79} +(-0.282938 - 0.870794i) q^{81} +(6.45367 - 2.09692i) q^{83} +(-5.57734 - 11.8679i) q^{85} +(0.0316289 - 0.0435334i) q^{87} +(-6.90006 + 5.01319i) q^{89} +(0.140348 + 0.101969i) q^{91} -6.62289i q^{93} +(-12.4803 + 5.86514i) q^{95} +(18.2325 + 5.92411i) q^{97} +5.24660 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{5} + 2 q^{9}+O(q^{10}) $ 8 * q + 5 * q^5 + 2 * q^9	$ 8 q + 5 q^{5} + 2 q^{9} - 5 q^{11} + 20 q^{15} - 5 q^{17} + 8 q^{19} - 2 q^{21} + 20 q^{23} - 5 q^{25} - 8 q^{29} + 12 q^{31} + 15 q^{33} + 5 q^{35} - 10 q^{37} - 22 q^{39} + 13 q^{41} + 10 q^{45} - 45 q^{47} + 14 q^{49} + 14 q^{51} + 30 q^{53} - 35 q^{55} - 9 q^{59} + 16 q^{61} - 20 q^{63} - 25 q^{65} + 5 q^{67} - 14 q^{69} + q^{71} - 60 q^{73} + 5 q^{75} - 20 q^{77} + 24 q^{79} - 3 q^{81} + 10 q^{83} - 5 q^{85} + 55 q^{87} - 37 q^{89} - 32 q^{91} - 30 q^{95} + 25 q^{97} - 20 q^{99}+O(q^{100}) $ 8 * q + 5 * q^5 + 2 * q^9 - 5 * q^11 + 20 * q^15 - 5 * q^17 + 8 * q^19 - 2 * q^21 + 20 * q^23 - 5 * q^25 - 8 * q^29 + 12 * q^31 + 15 * q^33 + 5 * q^35 - 10 * q^37 - 22 * q^39 + 13 * q^41 + 10 * q^45 - 45 * q^47 + 14 * q^49 + 14 * q^51 + 30 * q^53 - 35 * q^55 - 9 * q^59 + 16 * q^61 - 20 * q^63 - 25 * q^65 + 5 * q^67 - 14 * q^69 + q^71 - 60 * q^73 + 5 * q^75 - 20 * q^77 + 24 * q^79 - 3 * q^81 + 10 * q^83 - 5 * q^85 + 55 * q^87 - 37 * q^89 - 32 * q^91 - 30 * q^95 + 25 * q^97 - 20 * 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
$3$	−1.07822	−	0.350334i	−0.622509	−	0.202265i	−0.0192549	−	0.999815i	$-0.506129\pi$
$3$	−1.07822	−	0.350334i	−0.622509	−	0.202265i	−0.603254	+	0.797549i	$0.706129\pi$
$4$		0			0
$5$	0.279141	+	2.21858i	0.124836	+	0.992177i
$5$	0.279141	+	2.21858i	0.124836	+	0.992177i
$6$		0			0
$7$			0.768409i			0.290431i	0.989400	+	0.145216i	$0.0463876\pi$
$7$			0.768409i			0.290431i	−0.989400	+	0.145216i	$0.953612\pi$
$8$		0			0
$9$	−1.38723	−	1.00788i	−0.462411	−	0.335961i
$10$		0			0
$11$	−2.47539	+	1.79848i	−0.746359	+	0.542261i	−0.894696	−	0.446676i	$-0.852608\pi$
$11$	−2.47539	+	1.79848i	−0.746359	+	0.542261i	0.148337	+	0.988937i	$0.452608\pi$
$12$		0			0
$13$	0.132701	−	0.182648i	0.0368047	−	0.0506573i	−0.790218	−	0.612826i	$-0.790033\pi$
$13$	0.132701	−	0.182648i	0.0368047	−	0.0506573i	0.827023	+	0.562168i	$0.190033\pi$
$14$		0			0
$15$	0.476268	−	2.48990i	0.122972	−	0.642889i
$16$		0			0
$17$	−5.57734	+	1.81219i	−1.35270	+	0.439520i	−0.893601	−	0.448863i	$-0.851829\pi$
$17$	−5.57734	+	1.81219i	−1.35270	+	0.439520i	−0.459103	+	0.888383i	$0.651829\pi$
$18$		0			0
$19$	1.90570	+	5.86514i	0.437197	+	1.34555i	0.890818	+	0.454360i	$0.150132\pi$
$19$	1.90570	+	5.86514i	0.437197	+	1.34555i	−0.453621	+	0.891195i	$0.649868\pi$
$20$		0			0
$21$	0.269200	−	0.828511i	0.0587442	−	0.180796i
$22$		0			0
$23$	−3.05035	−	4.19845i	−0.636042	−	0.875437i	0.362354	−	0.932040i	$-0.381973\pi$
$23$	−3.05035	−	4.19845i	−0.636042	−	0.875437i	−0.998397	+	0.0566031i	$0.981973\pi$
$24$		0			0
$25$	−4.84416	+	1.23859i	−0.968832	+	0.247718i
$26$		0			0
$27$	3.14177	+	4.32427i	0.604633	+	0.832206i
$28$		0			0
$29$	−0.0146672	+	0.0451411i	−0.00272364	+	0.00838249i	−0.952409	−	0.304823i	$-0.901403\pi$
$29$	−0.0146672	+	0.0451411i	−0.00272364	+	0.00838249i	0.949685	+	0.313205i	$0.101403\pi$
$30$		0			0
$31$	1.80522	+	5.55590i	0.324227	+	0.997868i	0.971788	+	0.235855i	$0.0757890\pi$
$31$	1.80522	+	5.55590i	0.324227	+	0.997868i	−0.647561	+	0.762013i	$0.724211\pi$
$32$		0			0
$33$	3.29908	−	1.07193i	0.574295	−	0.186600i
$34$		0			0
$35$	−1.70477	+	0.214494i	−0.288159	+	0.0362562i
$36$		0			0
$37$	−4.99060	+	6.86897i	−0.820450	+	1.12925i	0.169177	+	0.985586i	$0.445889\pi$
$37$	−4.99060	+	6.86897i	−0.820450	+	1.12925i	−0.989626	+	0.143666i	$0.954111\pi$
$38$		0			0
$39$	−0.207068	+	0.150444i	−0.0331575	+	0.0240903i
$40$		0			0
$41$	5.71146	+	4.14962i	0.891980	+	0.648061i	0.936394	−	0.350952i	$-0.114142\pi$
$41$	5.71146	+	4.14962i	0.891980	+	0.648061i	−0.0444134	+	0.999013i	$0.514142\pi$
$42$		0			0
$43$		−	3.14793i		−	0.480054i	−0.970766	−	0.240027i	$-0.922844\pi$
$43$		−	3.14793i		−	0.480054i	0.970766	−	0.240027i	$-0.0771563\pi$
$44$		0			0
$45$	1.84883	−	3.35903i	0.275608	−	0.500734i
$46$		0			0
$47$	−10.8295	−	3.51872i	−1.57964	−	0.513257i	−0.617679	−	0.786430i	$-0.711927\pi$
$47$	−10.8295	−	3.51872i	−1.57964	−	0.513257i	−0.961965	+	0.273173i	$0.911927\pi$
$48$		0			0
$49$	6.40955			0.915650
$50$		0			0
$51$	6.64845			0.930969
$52$		0			0
$53$	3.01846	+	0.980759i	0.414618	+	0.134718i	0.508895	−	0.860828i	$-0.330054\pi$
$53$	3.01846	+	0.980759i	0.414618	+	0.134718i	−0.0942773	+	0.995546i	$0.530054\pi$
$54$		0			0
$55$	−4.68104	−	4.98982i	−0.631192	−	0.672827i
$56$		0			0
$57$		−	6.99152i		−	0.926049i
$58$		0			0
$59$	2.36263	+	1.71655i	0.307588	+	0.223475i	0.730861	−	0.682527i	$-0.239119\pi$
$59$	2.36263	+	1.71655i	0.307588	+	0.223475i	−0.423273	+	0.906002i	$0.639119\pi$
$60$		0			0
$61$	6.43232	−	4.67335i	0.823574	−	0.598362i	−0.0941600	−	0.995557i	$-0.530017\pi$
$61$	6.43232	−	4.67335i	0.823574	−	0.598362i	0.917734	+	0.397196i	$0.130017\pi$
$62$		0			0
$63$	0.774467	−	1.06596i	0.0975737	−	0.134299i
$64$		0			0
$65$	0.442260	+	0.243423i	0.0548556	+	0.0301930i
$66$		0			0
$67$	−0.281520	+	0.0914714i	−0.0343932	+	0.0111750i	−0.326163	−	0.945314i	$-0.605756\pi$
$67$	−0.281520	+	0.0914714i	−0.0343932	+	0.0111750i	0.291770	+	0.956489i	$0.405756\pi$
$68$		0			0
$69$	1.81808	+	5.59548i	0.218871	+	0.673617i
$70$		0			0
$71$	4.13182	−	12.7164i	0.490357	−	1.50916i	−0.333711	−	0.942675i	$-0.608301\pi$
$71$	4.13182	−	12.7164i	0.490357	−	1.50916i	0.824069	−	0.566490i	$-0.191699\pi$
$72$		0			0
$73$	−8.49858	−	11.6973i	−0.994684	−	1.36906i	−0.928531	−	0.371255i	$-0.878927\pi$
$73$	−8.49858	−	11.6973i	−0.994684	−	1.36906i	−0.0661529	−	0.997809i	$-0.521073\pi$
$74$		0			0
$75$	5.65697	+	0.361604i	0.653211	+	0.0417545i
$76$		0			0
$77$	−1.38197	−	1.90211i	−0.157490	−	0.216766i
$78$		0			0
$79$	1.40423	−	4.32177i	0.157988	−	0.486237i	−0.840463	−	0.541868i	$-0.817717\pi$
$79$	1.40423	−	4.32177i	0.157988	−	0.486237i	0.998451	+	0.0556314i	$0.0177172\pi$
$80$		0			0
$81$	−0.282938	−	0.870794i	−0.0314376	−	0.0967549i
$82$		0			0
$83$	6.45367	−	2.09692i	0.708382	−	0.230167i	0.0674034	−	0.997726i	$-0.478529\pi$
$83$	6.45367	−	2.09692i	0.708382	−	0.230167i	0.640979	+	0.767558i	$0.278529\pi$
$84$		0			0
$85$	−5.57734	−	11.8679i	−0.604947	−	1.28725i
$86$		0			0
$87$	0.0316289	−	0.0435334i	0.00339097	−	0.00466728i
$88$		0			0
$89$	−6.90006	+	5.01319i	−0.731405	+	0.531397i	−0.890008	−	0.455946i	$-0.849301\pi$
$89$	−6.90006	+	5.01319i	−0.731405	+	0.531397i	0.158602	+	0.987343i	$0.449301\pi$
$90$		0			0
$91$	0.140348	+	0.101969i	0.0147125	+	0.0106892i
$92$		0			0
$93$		−	6.62289i		−	0.686762i
$94$		0			0
$95$	−12.4803	+	5.86514i	−1.28045	+	0.601750i
$96$		0			0
$97$	18.2325	+	5.92411i	1.85123	+	0.601502i	0.996612	+	0.0822501i	$0.0262106\pi$
$97$	18.2325	+	5.92411i	1.85123	+	0.601502i	0.854621	+	0.519252i	$0.173789\pi$
$98$		0			0
$99$	5.24660			0.527303
$100$		0			0
$101$	−10.8910			−1.08370			−0.541849	−	0.840476i	$-0.682276\pi$
$101$	−10.8910			−1.08370			−0.541849	+	0.840476i	$0.682276\pi$
$102$		0			0
$103$	15.4956	+	5.03482i	1.52683	+	0.496096i	0.947705	−	0.319147i	$-0.103396\pi$
$103$	15.4956	+	5.03482i	1.52683	+	0.496096i	0.579120	+	0.815242i	$0.303396\pi$
$104$		0			0
$105$	1.91326	+	0.365969i	0.186715	+	0.0357149i
$106$		0			0
$107$			17.1850i			1.66133i	0.556770	+	0.830667i	$0.312041\pi$
$107$			17.1850i			1.66133i	−0.556770	+	0.830667i	$0.687959\pi$
$108$		0			0
$109$	10.5627	+	7.67427i	1.01173	+	0.735062i	0.964570	−	0.263826i	$-0.0849844\pi$
$109$	10.5627	+	7.67427i	1.01173	+	0.735062i	0.0471553	+	0.998888i	$0.484984\pi$
$110$		0			0
$111$	7.78738	−	5.65786i	0.739146	−	0.537021i
$112$		0			0
$113$	1.95784	−	2.69473i	0.184178	−	0.253499i	−0.706937	−	0.707276i	$-0.749924\pi$
$113$	1.95784	−	2.69473i	0.184178	−	0.253499i	0.891115	+	0.453777i	$0.149924\pi$
$114$		0			0
$115$	8.46310	−	7.93940i	0.789188	−	0.740353i
$116$		0			0
$117$	−0.368175	+	0.119627i	−0.0340378	+	0.0110596i
$118$		0			0
$119$	−1.39250	−	4.28568i	−0.127650	−	0.392867i
$120$		0			0
$121$	−0.506144	+	1.55775i	−0.0460131	+	0.141614i
$122$		0			0
$123$	−4.70444	−	6.47510i	−0.424185	−	0.583841i
$124$		0			0
$125$	−4.10011	−	10.4014i	−0.366725	−	0.930329i
$126$		0			0
$127$	−6.73610	−	9.27145i	−0.597732	−	0.822708i	0.397766	−	0.917487i	$-0.369786\pi$
$127$	−6.73610	−	9.27145i	−0.597732	−	0.822708i	−0.995498	+	0.0947790i	$0.969786\pi$
$128$		0			0
$129$	−1.10283	+	3.39415i	−0.0970983	+	0.298838i
$130$		0			0
$131$	1.09196	+	3.36069i	0.0954046	+	0.293625i	0.987359	−	0.158500i	$-0.0506659\pi$
$131$	1.09196	+	3.36069i	0.0954046	+	0.293625i	−0.891954	+	0.452125i	$0.850666\pi$
$132$		0			0
$133$	−4.50682	+	1.46436i	−0.390791	+	0.126976i
$134$		0			0
$135$	−8.71673	+	8.17733i	−0.750216	+	0.703792i
$136$		0			0
$137$	−5.79549	+	7.97680i	−0.495142	+	0.681504i	−0.981326	−	0.192352i	$-0.938388\pi$
$137$	−5.79549	+	7.97680i	−0.495142	+	0.681504i	0.486184	+	0.873856i	$0.338388\pi$
$138$		0			0
$139$	−13.3035	+	9.66553i	−1.12839	+	0.819820i	−0.985459	−	0.169913i	$-0.945651\pi$
$139$	−13.3035	+	9.66553i	−1.12839	+	0.819820i	−0.142926	+	0.989733i	$0.545651\pi$
$140$		0			0
$141$	10.4438	+	7.58788i	0.879528	+	0.639014i
$142$		0			0
$143$			0.690784i			0.0577663i
$144$		0			0
$145$	−0.104243	−	0.0199396i	−0.00865692	−	0.00165590i
$146$		0			0
$147$	−6.91088	−	2.24548i	−0.570000	−	0.185204i
$148$		0			0
$149$	−1.32340			−0.108417			−0.0542087	−	0.998530i	$-0.517264\pi$
$149$	−1.32340			−0.108417			−0.0542087	+	0.998530i	$0.517264\pi$
$150$		0			0
$151$	5.90626			0.480645			0.240322	−	0.970693i	$-0.422747\pi$
$151$	5.90626			0.480645			0.240322	+	0.970693i	$0.422747\pi$
$152$		0			0
$153$	9.56355	+	3.10739i	0.773167	+	0.251217i
$154$		0			0
$155$	−11.8223	+	5.55590i	−0.949587	+	0.446260i
$156$		0			0
$157$		−	3.69212i		−	0.294663i	−0.989087	−	0.147331i	$-0.952932\pi$
$157$		−	3.69212i		−	0.294663i	0.989087	−	0.147331i	$-0.0470684\pi$
$158$		0			0
$159$	−2.91097	−	2.11494i	−0.230855	−	0.167726i
$160$		0			0
$161$	3.22613	−	2.34392i	0.254254	−	0.184727i
$162$		0			0
$163$	0.438830	−	0.603997i	0.0343718	−	0.0473087i	−0.791485	−	0.611188i	$-0.790692\pi$
$163$	0.438830	−	0.603997i	0.0343718	−	0.0473087i	0.825857	+	0.563880i	$0.190692\pi$
$164$		0			0
$165$	3.29908	+	7.02003i	0.256833	+	0.546509i
$166$		0			0
$167$	−2.42421	+	0.787675i	−0.187591	+	0.0609521i	−0.401306	−	0.915944i	$-0.631444\pi$
$167$	−2.42421	+	0.787675i	−0.187591	+	0.0609521i	0.213715	+	0.976896i	$0.431444\pi$
$168$		0			0
$169$	4.00147	+	12.3153i	0.307805	+	0.947328i
$170$		0			0
$171$	3.26773	−	10.0570i	0.249890	−	0.769081i
$172$		0			0
$173$	1.28817	+	1.77302i	0.0979380	+	0.134800i	0.855174	−	0.518342i	$-0.173450\pi$
$173$	1.28817	+	1.77302i	0.0979380	+	0.134800i	−0.757236	+	0.653142i	$0.773450\pi$
$174$		0			0
$175$	−0.951744	−	3.72230i	−0.0719451	−	0.281379i
$176$		0			0
$177$	−1.94606	−	2.67852i	−0.146275	−	0.201330i
$178$		0			0
$179$	−3.58728	+	11.0405i	−0.268126	+	0.825207i	0.722831	+	0.691025i	$0.242841\pi$
$179$	−3.58728	+	11.0405i	−0.268126	+	0.825207i	−0.990957	+	0.134182i	$0.957159\pi$
$180$		0			0
$181$	−3.20766	−	9.87217i	−0.238424	−	0.733793i	−0.996649	−	0.0817997i	$-0.973933\pi$
$181$	−3.20766	−	9.87217i	−0.238424	−	0.733793i	0.758225	−	0.651993i	$-0.226067\pi$
$182$		0			0
$183$	−8.57267	+	2.78543i	−0.633710	+	0.205905i
$184$		0			0
$185$	−16.6324	−	9.15462i	−1.22284	−	0.673061i
$186$		0			0
$187$	10.5469	−	14.5166i	0.771267	−	1.06156i
$188$		0			0
$189$	−3.32281	+	2.41416i	−0.241699	+	0.175604i
$190$		0			0
$191$	6.58261	+	4.78254i	0.476301	+	0.346053i	0.799892	−	0.600144i	$-0.204890\pi$
$191$	6.58261	+	4.78254i	0.476301	+	0.346053i	−0.323591	+	0.946197i	$0.604890\pi$
$192$		0			0
$193$		−	2.84942i		−	0.205106i	−0.994728	−	0.102553i	$-0.967299\pi$
$193$		−	2.84942i		−	0.205106i	0.994728	−	0.102553i	$-0.0327011\pi$
$194$		0			0
$195$	−0.391573	−	0.417402i	−0.0280411	−	0.0298908i
$196$		0			0
$197$	−7.87032	−	2.55722i	−0.560737	−	0.182195i	0.0149155	−	0.999889i	$-0.495252\pi$
$197$	−7.87032	−	2.55722i	−0.560737	−	0.182195i	−0.575653	+	0.817694i	$0.695252\pi$
$198$		0			0
$199$	9.41714			0.667564			0.333782	−	0.942650i	$-0.391675\pi$
$199$	9.41714			0.667564			0.333782	+	0.942650i	$0.391675\pi$
$200$		0			0
$201$	0.335585			0.0236704
$202$		0			0
$203$	−0.0346868	−	0.0112704i	−0.00243454	−	0.000791029i
$204$		0			0
$205$	−7.61194	+	13.8296i	−0.531641	+	0.965904i
$206$		0			0
$207$			8.89863i			0.618498i
$208$		0			0
$209$	−15.2657	−	11.0912i	−1.05595	−	0.767191i
$210$		0			0
$211$	−21.7434	+	15.7975i	−1.49688	+	1.08755i	−0.525276	+	0.850932i	$0.676038\pi$
$211$	−21.7434	+	15.7975i	−1.49688	+	1.08755i	−0.971604	+	0.236615i	$0.923962\pi$
$212$		0			0
$213$	−8.91000	+	12.2636i	−0.610503	+	0.840286i
$214$		0			0
$215$	6.98391	−	0.878715i	0.476299	−	0.0599279i
$216$		0			0
$217$	−4.26920	+	1.38715i	−0.289812	+	0.0941657i
$218$		0			0
$219$	5.06535	+	15.5896i	0.342285	+	1.05344i
$220$		0			0
$221$	−0.409128	+	1.25917i	−0.0275209	+	0.0847007i
$222$		0			0
$223$	1.44028	+	1.98238i	0.0964483	+	0.132750i	0.854514	−	0.519429i	$-0.173855\pi$
$223$	1.44028	+	1.98238i	0.0964483	+	0.132750i	−0.758065	+	0.652179i	$0.773855\pi$
$224$		0			0
$225$	7.96834	+	3.16414i	0.531223	+	0.210943i
$226$		0			0
$227$	11.7853	+	16.2211i	0.782219	+	1.07663i	0.995034	+	0.0995395i	$0.0317370\pi$
$227$	11.7853	+	16.2211i	0.782219	+	1.07663i	−0.212815	+	0.977093i	$0.568263\pi$
$228$		0			0
$229$	5.14616	−	15.8382i	0.340068	−	1.04662i	−0.624104	−	0.781341i	$-0.714536\pi$
$229$	5.14616	−	15.8382i	0.340068	−	1.04662i	0.964172	−	0.265279i	$-0.0854642\pi$
$230$		0			0
$231$	0.823684	+	2.53504i	0.0541944	+	0.166793i
$232$		0			0
$233$	−0.0605762	+	0.0196824i	−0.00396848	+	0.00128944i	−0.311001	−	0.950410i	$-0.600664\pi$
$233$	−0.0605762	+	0.0196824i	−0.00396848	+	0.00128944i	0.307032	+	0.951699i	$0.400664\pi$
$234$		0			0
$235$	4.78358	−	25.0083i	0.312047	−	1.63136i
$236$		0			0
$237$	−3.02812	+	4.16785i	−0.196698	+	0.270731i
$238$		0			0
$239$	8.70532	−	6.32478i	0.563100	−	0.409116i	−0.269492	−	0.963003i	$-0.586856\pi$
$239$	8.70532	−	6.32478i	0.563100	−	0.409116i	0.832592	+	0.553886i	$0.186856\pi$
$240$		0			0
$241$	0.895672	+	0.650744i	0.0576953	+	0.0419181i	0.616259	−	0.787543i	$-0.288647\pi$
$241$	0.895672	+	0.650744i	0.0576953	+	0.0419181i	−0.558564	+	0.829462i	$0.688647\pi$
$242$		0			0
$243$		−	14.9972i		−	0.962074i
$244$		0			0
$245$	1.78917	+	14.2201i	0.114306	+	0.908487i
$246$		0			0
$247$	1.32414	+	0.430240i	0.0842531	+	0.0273755i
$248$		0			0
$249$	−7.69308			−0.487529
$250$		0			0
$251$	−18.8723			−1.19121			−0.595606	−	0.803277i	$-0.703088\pi$
$251$	−18.8723			−1.19121			−0.595606	+	0.803277i	$0.703088\pi$
$252$		0			0
$253$	15.1016	+	4.90682i	0.949432	+	0.308489i
$254$		0			0
$255$	1.85585	+	14.7501i	0.116218	+	0.923687i
$256$		0			0
$257$		−	0.325489i		−	0.0203035i	−0.999948	−	0.0101517i	$-0.996769\pi$
$257$		−	0.325489i		−	0.0203035i	0.999948	−	0.0101517i	$-0.00323145\pi$
$258$		0			0
$259$	−5.27818	−	3.83482i	−0.327970	−	0.238284i
$260$		0			0
$261$	0.0658439	−	0.0478384i	0.00407563	−	0.00296112i
$262$		0			0
$263$	−18.4391	+	25.3792i	−1.13700	+	1.56495i	−0.362969	+	0.931801i	$0.618237\pi$
$263$	−18.4391	+	25.3792i	−1.13700	+	1.56495i	−0.774032	+	0.633146i	$0.781763\pi$
$264$		0			0
$265$	−1.33331	+	6.97046i	−0.0819046	+	0.428192i
$266$		0			0
$267$	9.19605	−	2.98798i	0.562789	−	0.182861i
$268$		0			0
$269$	−1.07587	−	3.31119i	−0.0655969	−	0.201887i	0.912886	−	0.408215i	$-0.133849\pi$
$269$	−1.07587	−	3.31119i	−0.0655969	−	0.201887i	−0.978483	+	0.206328i	$0.933849\pi$
$270$		0			0
$271$	−5.87022	+	18.0667i	−0.356590	+	1.09747i	0.598491	+	0.801129i	$0.295767\pi$
$271$	−5.87022	+	18.0667i	−0.356590	+	1.09747i	−0.955082	+	0.296343i	$0.904233\pi$
$272$		0			0
$273$	−0.115602	−	0.159113i	−0.00699658	−	0.00962996i
$274$		0			0
$275$	9.76362	−	11.7781i	0.588768	−	0.710247i
$276$		0			0
$277$	4.00765	+	5.51605i	0.240796	+	0.331427i	0.912261	−	0.409609i	$-0.134335\pi$
$277$	4.00765	+	5.51605i	0.240796	+	0.331427i	−0.671465	+	0.741036i	$0.734335\pi$
$278$		0			0
$279$	3.09544	−	9.52678i	0.185319	−	0.570353i
$280$		0			0
$281$	2.13774	+	6.57929i	0.127527	+	0.392488i	0.994353	−	0.106123i	$-0.0338437\pi$
$281$	2.13774	+	6.57929i	0.127527	+	0.392488i	−0.866826	+	0.498611i	$0.833844\pi$
$282$		0			0
$283$	−8.41536	+	2.73432i	−0.500241	+	0.162538i	−0.548259	−	0.836308i	$-0.684709\pi$
$283$	−8.41536	+	2.73432i	−0.500241	+	0.162538i	0.0480184	+	0.998846i	$0.484709\pi$
$284$		0			0
$285$	15.5112	−	1.95162i	0.918805	−	0.115604i
$286$		0			0
$287$	−3.18860	+	4.38874i	−0.188217	+	0.259059i
$288$		0			0
$289$	14.0694	−	10.2220i	0.827612	−	0.601296i
$290$		0			0
$291$	−17.5832	−	12.7749i	−1.03075	−	0.748880i
$292$		0			0
$293$			6.75047i			0.394367i	0.980367	+	0.197183i	$0.0631795\pi$
$293$			6.75047i			0.394367i	−0.980367	+	0.197183i	$0.936821\pi$
$294$		0			0
$295$	−3.14879	+	5.72082i	−0.183329	+	0.333079i
$296$		0			0
$297$	−15.5542	−	5.05387i	−0.902546	−	0.293255i
$298$		0			0
$299$	−1.17162			−0.0677567
$300$		0			0
$301$	2.41889			0.139423
$302$		0			0
$303$	11.7429	+	3.81550i	0.674611	+	0.219195i
$304$		0			0
$305$	12.1637	+	12.9661i	0.696492	+	0.742435i
$306$		0			0
$307$		−	18.5112i		−	1.05649i	−0.849092	−	0.528245i	$-0.822850\pi$
$307$		−	18.5112i		−	1.05649i	0.849092	−	0.528245i	$-0.177150\pi$
$308$		0			0
$309$	−14.9437	−	10.8573i	−0.850119	−	0.617648i
$310$		0			0
$311$	8.29197	−	6.02447i	0.470195	−	0.341616i	−0.327323	−	0.944913i	$-0.606146\pi$
$311$	8.29197	−	6.02447i	0.470195	−	0.341616i	0.797517	+	0.603296i	$0.206146\pi$
$312$		0			0
$313$	−12.5902	+	17.3289i	−0.711640	+	0.979489i	0.288120	+	0.957594i	$0.406970\pi$
$313$	−12.5902	+	17.3289i	−0.711640	+	0.979489i	−0.999760	+	0.0218945i	$0.993030\pi$
$314$		0			0
$315$	2.58111	+	1.42066i	0.145429	+	0.0800452i
$316$		0			0
$317$	2.70679	−	0.879488i	0.152028	−	0.0493970i	−0.232014	−	0.972712i	$-0.574532\pi$
$317$	2.70679	−	0.879488i	0.152028	−	0.0493970i	0.384043	+	0.923315i	$0.374532\pi$
$318$		0			0
$319$	−0.0448781	−	0.138121i	−0.00251269	−	0.00773327i
$320$		0			0
$321$	6.02048	−	18.5291i	0.336030	−	1.03419i
$322$		0			0
$323$	−21.2575	−	29.2584i	−1.18280	−	1.62798i
$324$		0			0
$325$	−0.416600	+	1.04914i	−0.0231088	+	0.0581956i
$326$		0			0
$327$	−8.70035	−	11.9750i	−0.481130	−	0.662219i
$328$		0			0
$329$	2.70381	−	8.32148i	0.149066	−	0.458778i
$330$		0			0
$331$	0.0150343	+	0.0462710i	0.000826362	+	0.00254328i	0.951469	−	0.307745i	$-0.0995744\pi$
$331$	0.0150343	+	0.0462710i	0.000826362	+	0.00254328i	−0.950642	+	0.310288i	$0.899574\pi$
$332$		0			0
$333$	13.8463	−	4.49892i	0.758770	−	0.246539i
$334$		0			0
$335$	−0.281520	−	0.599040i	−0.0153811	−	0.0327291i
$336$		0			0
$337$	13.6571	−	18.7973i	0.743947	−	1.02396i	−0.254434	−	0.967090i	$-0.581889\pi$
$337$	13.6571	−	18.7973i	0.743947	−	1.02396i	0.998382	−	0.0568658i	$-0.0181107\pi$
$338$		0			0
$339$	−3.05503	+	2.21961i	−0.165926	+	0.120552i
$340$		0			0
$341$	−14.4608	−	10.5064i	−0.783095	−	0.568952i
$342$		0			0
$343$			10.3040i			0.556365i
$344$		0			0
$345$	−11.9065	+	5.59548i	−0.641024	+	0.301251i
$346$		0			0
$347$	16.2131	+	5.26797i	0.870367	+	0.282799i	0.709952	−	0.704250i	$-0.248717\pi$
$347$	16.2131	+	5.26797i	0.870367	+	0.282799i	0.160415	+	0.987050i	$0.448717\pi$
$348$		0			0
$349$	22.0421			1.17989			0.589944	−	0.807444i	$-0.299150\pi$
$349$	22.0421			1.17989			0.589944	+	0.807444i	$0.299150\pi$
$350$		0			0
$351$	1.20673			0.0644107
$352$		0			0
$353$	10.2524	+	3.33121i	0.545681	+	0.177302i	0.568868	−	0.822429i	$-0.307381\pi$
$353$	10.2524	+	3.33121i	0.545681	+	0.177302i	−0.0231874	+	0.999731i	$0.507381\pi$
$354$		0			0
$355$	29.3658	+	5.61709i	1.55857	+	0.298124i
$356$		0			0
$357$			5.10873i			0.270383i
$358$		0			0
$359$	−12.7121	−	9.23585i	−0.670917	−	0.487449i	0.199415	−	0.979915i	$-0.436096\pi$
$359$	−12.7121	−	9.23585i	−0.670917	−	0.487449i	−0.870332	+	0.492466i	$0.836096\pi$
$360$		0			0
$361$	−15.3968	+	11.1864i	−0.810358	+	0.588760i
$362$		0			0
$363$	1.09147	−	1.50227i	0.0572871	−	0.0788489i
$364$		0			0
$365$	23.5790	−	22.1199i	1.23418	−	1.15781i
$366$		0			0
$367$	11.0761	−	3.59884i	0.578168	−	0.187858i	−0.00531195	−	0.999986i	$-0.501691\pi$
$367$	11.0761	−	3.59884i	0.578168	−	0.187858i	0.583479	+	0.812128i	$0.301691\pi$
$368$		0			0
$369$	−3.74079	−	11.5130i	−0.194738	−	0.599342i
$370$		0			0
$371$	−0.753624	+	2.31942i	−0.0391262	+	0.120418i
$372$		0			0
$373$	−19.4387	−	26.7551i	−1.00650	−	1.38532i	−0.921253	−	0.388964i	$-0.872833\pi$
$373$	−19.4387	−	26.7551i	−1.00650	−	1.38532i	−0.0852444	−	0.996360i	$-0.527167\pi$
$374$		0			0
$375$	0.776846	+	12.6514i	0.0401162	+	0.653314i
$376$		0			0
$377$	0.00629855	+	0.00866921i	0.000324392	+	0.000446487i
$378$		0			0
$379$	6.64703	−	20.4575i	0.341435	−	1.05083i	−0.622029	−	0.782994i	$-0.713692\pi$
$379$	6.64703	−	20.4575i	0.341435	−	1.05083i	0.963465	−	0.267836i	$-0.0863084\pi$
$380$		0			0
$381$	4.01487	+	12.3565i	0.205688	+	0.633043i
$382$		0			0
$383$	26.0531	−	8.46516i	1.33125	−	0.432549i	0.444906	−	0.895577i	$-0.353237\pi$
$383$	26.0531	−	8.46516i	1.33125	−	0.432549i	0.886344	+	0.463028i	$0.153237\pi$
$384$		0			0
$385$	3.83422	−	3.59695i	0.195410	−	0.183318i
$386$		0			0
$387$	−3.17275	+	4.36691i	−0.161280	+	0.221982i
$388$		0			0
$389$	−18.8999	+	13.7316i	−0.958261	+	0.696218i	−0.952746	−	0.303767i	$-0.901755\pi$
$389$	−18.8999	+	13.7316i	−0.958261	+	0.696218i	−0.00551496	+	0.999985i	$0.501755\pi$
$390$		0			0
$391$	24.6212	+	17.8884i	1.24515	+	0.904654i
$392$		0			0
$393$		−	4.00610i		−	0.202081i
$394$		0			0
$395$	9.98015	+	1.90900i	0.502156	+	0.0960524i
$396$		0			0
$397$	3.60455	+	1.17119i	0.180907	+	0.0587804i	0.398070	−	0.917355i	$-0.369680\pi$
$397$	3.60455	+	1.17119i	0.180907	+	0.0587804i	−0.217162	+	0.976135i	$0.569680\pi$
$398$		0			0
$399$	5.37234			0.268954
$400$		0			0
$401$	−9.49569			−0.474192			−0.237096	−	0.971486i	$-0.576196\pi$
$401$	−9.49569			−0.474192			−0.237096	+	0.971486i	$0.576196\pi$
$402$		0			0
$403$	1.25433	+	0.407555i	0.0624824	+	0.0203018i
$404$		0			0
$405$	1.85294	−	0.870794i	0.0920735	−	0.0432701i
$406$		0			0
$407$		−	25.9789i		−	1.28773i
$408$		0			0
$409$	−5.13650	−	3.73188i	−0.253984	−	0.184530i	0.453507	−	0.891253i	$-0.350173\pi$
$409$	−5.13650	−	3.73188i	−0.253984	−	0.184530i	−0.707490	+	0.706723i	$0.750173\pi$
$410$		0			0
$411$	9.04333	−	6.57037i	0.446075	−	0.324092i
$412$		0			0
$413$	−1.31901	+	1.81546i	−0.0649043	+	0.0893331i
$414$		0			0
$415$	6.45367	+	13.7326i	0.316798	+	0.674108i
$416$		0			0
$417$	17.7302	−	5.76089i	0.868251	−	0.282112i
$418$		0			0
$419$	−2.49417	−	7.67627i	−0.121848	−	0.375010i	0.871465	−	0.490457i	$-0.163170\pi$
$419$	−2.49417	−	7.67627i	−0.121848	−	0.375010i	−0.993314	+	0.115447i	$0.963170\pi$
$420$		0			0
$421$	−6.07412	+	18.6942i	−0.296034	+	0.911100i	0.686838	+	0.726811i	$0.258998\pi$
$421$	−6.07412	+	18.6942i	−0.296034	+	0.911100i	−0.982872	+	0.184289i	$0.941002\pi$
$422$		0			0
$423$	11.4766	+	15.7962i	0.558010	+	0.768035i
$424$		0			0
$425$	24.7730	−	15.6866i	1.20167	−	0.760910i
$426$		0			0
$427$	3.59105	+	4.94265i	0.173783	+	0.239192i
$428$		0			0
$429$	0.242005	−	0.744815i	0.0116841	−	0.0359600i
$430$		0			0
$431$	−6.76654	−	20.8253i	−0.325933	−	1.00312i	−0.971018	−	0.239007i	$-0.923178\pi$
$431$	−6.76654	−	20.8253i	−0.325933	−	1.00312i	0.645085	−	0.764111i	$-0.276822\pi$
$432$		0			0
$433$	−17.3639	+	5.64187i	−0.834456	+	0.271131i	−0.694921	−	0.719086i	$-0.744561\pi$
$433$	−17.3639	+	5.64187i	−0.834456	+	0.271131i	−0.139535	+	0.990217i	$0.544561\pi$
$434$		0			0
$435$	0.105411	+	0.0580192i	0.00505408	+	0.00278181i
$436$		0			0
$437$	18.8114	−	25.8917i	0.899873	−	1.23857i
$438$		0			0
$439$	1.79995	−	1.30774i	0.0859070	−	0.0624151i	−0.544003	−	0.839083i	$-0.683092\pi$
$439$	1.79995	−	1.30774i	0.0859070	−	0.0624151i	0.629910	+	0.776668i	$0.283092\pi$
$440$		0			0
$441$	−8.89154	−	6.46008i	−0.423407	−	0.307623i
$442$		0			0
$443$			7.37253i			0.350280i	0.984544	+	0.175140i	$0.0560377\pi$
$443$			7.37253i			0.350280i	−0.984544	+	0.175140i	$0.943962\pi$
$444$		0			0
$445$	−13.0482	−	13.9089i	−0.618546	−	0.659347i
$446$		0			0
$447$	1.42691	+	0.463632i	0.0674907	+	0.0219291i
$448$		0			0
$449$	27.5371			1.29956			0.649778	−	0.760124i	$-0.274862\pi$
$449$	27.5371			1.29956			0.649778	+	0.760124i	$0.274862\pi$
$450$		0			0
$451$	−21.6011			−1.01716
$452$		0			0
$453$	−6.36823	−	2.06916i	−0.299205	−	0.0972177i
$454$		0			0
$455$	−0.187049	+	0.339836i	−0.00876898	+	0.0159318i
$456$		0			0
$457$			19.3611i			0.905672i	0.891594	+	0.452836i	$0.149588\pi$
$457$			19.3611i			0.905672i	−0.891594	+	0.452836i	$0.850412\pi$
$458$		0			0
$459$	−25.3591	−	18.4245i	−1.18366	−	0.859980i
$460$		0			0
$461$	−8.32051	+	6.04521i	−0.387525	+	0.281553i	−0.764441	−	0.644694i	$-0.776985\pi$
$461$	−8.32051	+	6.04521i	−0.387525	+	0.281553i	0.376916	+	0.926248i	$0.376985\pi$
$462$		0			0
$463$	−17.8958	+	24.6315i	−0.831690	+	1.14472i	0.155916	+	0.987770i	$0.450167\pi$
$463$	−17.8958	+	24.6315i	−0.831690	+	1.14472i	−0.987606	+	0.156953i	$0.949833\pi$
$464$		0			0
$465$	14.6934	−	1.84872i	0.681389	−	0.0857323i
$466$		0			0
$467$	−22.4011	+	7.27857i	−1.03660	+	0.336812i	−0.777397	−	0.629010i	$-0.783460\pi$
$467$	−22.4011	+	7.27857i	−1.03660	+	0.336812i	−0.259204	+	0.965822i	$0.583460\pi$
$468$		0			0
$469$	−0.0702875	−	0.216323i	−0.00324557	−	0.00998885i
$470$		0			0
$471$	−1.29347	+	3.98090i	−0.0596001	+	0.183430i
$472$		0			0
$473$	5.66147	+	7.79235i	0.260315	+	0.358293i
$474$		0			0
$475$	−16.4960	−	26.0513i	−0.756889	−	1.19531i
$476$		0			0
$477$	−3.19882	−	4.40280i	−0.146464	−	0.201591i
$478$		0			0
$479$	11.8898	−	36.5932i	0.543261	−	1.67198i	−0.181829	−	0.983330i	$-0.558202\pi$
$479$	11.8898	−	36.5932i	0.543261	−	1.67198i	0.725090	−	0.688654i	$-0.241798\pi$
$480$		0			0
$481$	0.592342	+	1.82304i	0.0270085	+	0.0831236i
$482$		0			0
$483$	−4.29962	+	1.39703i	−0.195639	+	0.0635671i
$484$		0			0
$485$	−8.05364	+	42.1039i	−0.365697	+	1.91184i
$486$		0			0
$487$	−16.6004	+	22.8484i	−0.752235	+	1.03536i	0.245586	+	0.969375i	$0.421020\pi$
$487$	−16.6004	+	22.8484i	−0.752235	+	1.03536i	−0.997820	+	0.0659872i	$0.978980\pi$
$488$		0			0
$489$	−0.684754	+	0.497503i	−0.0309657	+	0.0224979i
$490$		0			0
$491$	−15.8032	−	11.4817i	−0.713188	−	0.518161i	0.171013	−	0.985269i	$-0.445296\pi$
$491$	−15.8032	−	11.4817i	−0.713188	−	0.518161i	−0.884200	+	0.467108i	$0.845296\pi$
$492$		0			0
$493$		−	0.278347i		−	0.0125361i
$494$		0			0
$495$	1.46454	+	11.6400i	0.0658262	+	0.523179i
$496$		0			0
$497$	9.77143	+	3.17493i	0.438309	+	0.142415i
$498$		0			0
$499$	4.64369			0.207880			0.103940	−	0.994584i	$-0.466855\pi$
$499$	4.64369			0.207880			0.103940	+	0.994584i	$0.466855\pi$
$500$		0			0
$501$	2.88978			0.129106
$502$		0			0
$503$	35.9369	+	11.6766i	1.60235	+	0.520635i	0.967687	−	0.252155i	$-0.0811393\pi$
$503$	35.9369	+	11.6766i	1.60235	+	0.520635i	0.634662	+	0.772790i	$0.281139\pi$
$504$		0			0
$505$	−3.04013	−	24.1626i	−0.135284	−	1.07522i
$506$		0			0
$507$		−	14.6804i		−	0.651978i
$508$		0			0
$509$	−8.87013	−	6.44453i	−0.393162	−	0.285649i	0.373588	−	0.927595i	$-0.378127\pi$
$509$	−8.87013	−	6.44453i	−0.393162	−	0.285649i	−0.766750	+	0.641946i	$0.778127\pi$
$510$		0			0
$511$	8.98831	−	6.53039i	0.397619	−	0.288887i
$512$		0			0
$513$	−19.3752	+	26.6676i	−0.855435	+	1.17740i
$514$		0			0
$515$	−6.84468	+	35.7836i	−0.301613	+	1.57681i
$516$		0			0
$517$	33.1356	−	10.7664i	1.45730	−	0.473506i
$518$		0			0
$519$	−0.767782	−	2.36299i	−0.0337019	−	0.103724i
$520$		0			0
$521$	−2.96568	+	9.12742i	−0.129929	+	0.399879i	−0.994767	−	0.102171i	$-0.967421\pi$
$521$	−2.96568	+	9.12742i	−0.129929	+	0.399879i	0.864838	+	0.502051i	$0.167421\pi$
$522$		0			0
$523$	−0.287230	−	0.395339i	−0.0125597	−	0.0172870i	0.802691	−	0.596395i	$-0.203401\pi$
$523$	−0.287230	−	0.395339i	−0.0125597	−	0.0172870i	−0.815251	+	0.579108i	$0.803401\pi$
$524$		0			0
$525$	−0.277860	+	4.34687i	−0.0121268	+	0.189713i
$526$		0			0
$527$	−20.1366	−	27.7157i	−0.877166	−	1.20732i
$528$		0			0
$529$	−1.21494	+	3.73921i	−0.0528236	+	0.162574i
$530$		0			0
$531$	−1.54743	−	4.76251i	−0.0671528	−	0.206675i
$532$		0			0
$533$	1.51584	−	0.492525i	0.0656581	−	0.0213336i
$534$		0			0
$535$	−38.1262	+	4.79703i	−1.64834	+	0.207394i
$536$		0			0
$537$	7.73573	−	10.6473i	0.333822	−	0.459466i
$538$		0			0
$539$	−15.8661	+	11.5274i	−0.683403	+	0.496521i
$540$		0			0
$541$	−13.7712	−	10.0054i	−0.592071	−	0.430164i	0.250985	−	0.967991i	$-0.419246\pi$
$541$	−13.7712	−	10.0054i	−0.592071	−	0.430164i	−0.843056	+	0.537827i	$0.819246\pi$
$542$		0			0
$543$			11.7681i			0.505017i
$544$		0			0
$545$	−14.0775	+	25.5764i	−0.603012	+	1.09557i
$546$		0			0
$547$	38.1281	+	12.3886i	1.63024	+	0.529696i	0.974326	−	0.225141i	$-0.0722843\pi$
$547$	38.1281	+	12.3886i	1.63024	+	0.529696i	0.655912	+	0.754838i	$0.272284\pi$
$548$		0			0
$549$	−13.6333			−0.581856
$550$		0			0
$551$	−0.292710			−0.0124699
$552$		0			0
$553$	3.32089	+	1.07902i	0.141218	+	0.0458846i
$554$		0			0
$555$	14.7262	+	15.6976i	0.625091	+	0.666324i
$556$		0			0
$557$			5.28208i			0.223809i	0.993719	+	0.111904i	$0.0356951\pi$
$557$			5.28208i			0.223809i	−0.993719	+	0.111904i	$0.964305\pi$
$558$		0			0
$559$	−0.574961	−	0.417734i	−0.0243183	−	0.0176683i
$560$		0			0
$561$	−16.4575	+	11.9571i	−0.694837	+	0.504829i
$562$		0			0
$563$	−18.6147	+	25.6209i	−0.784516	+	1.07979i	0.210253	+	0.977647i	$0.432571\pi$
$563$	−18.6147	+	25.6209i	−0.784516	+	1.07979i	−0.994769	+	0.102147i	$0.967429\pi$
$564$		0			0
$565$	6.52498	+	3.59140i	0.274508	+	0.151091i
$566$		0			0
$567$	0.669126	−	0.217412i	0.0281006	−	0.00913045i
$568$		0			0
$569$	9.18719	+	28.2753i	0.385147	+	1.18536i	0.936374	+	0.351005i	$0.114160\pi$
$569$	9.18719	+	28.2753i	0.385147	+	1.18536i	−0.551227	+	0.834355i	$0.685840\pi$
$570$		0			0
$571$	−5.95339	+	18.3226i	−0.249142	+	0.766779i	0.745786	+	0.666186i	$0.232074\pi$
$571$	−5.95339	+	18.3226i	−0.249142	+	0.766779i	−0.994928	+	0.100593i	$0.967926\pi$
$572$		0			0
$573$	−5.42199	−	7.46273i	−0.226507	−	0.311760i
$574$		0			0
$575$	19.9766	+	16.5598i	0.833080	+	0.690593i
$576$		0			0
$577$	−6.24635	−	8.59737i	−0.260039	−	0.357913i	0.658956	−	0.752181i	$-0.270998\pi$
$577$	−6.24635	−	8.59737i	−0.260039	−	0.357913i	−0.918995	+	0.394268i	$0.870998\pi$
$578$		0			0
$579$	−0.998247	+	3.07229i	−0.0414857	+	0.127680i
$580$		0			0
$581$	1.61130	+	4.95906i	0.0668478	+	0.205736i
$582$		0			0
$583$	−9.23575	+	3.00088i	−0.382506	+	0.124284i
$584$		0			0
$585$	−0.368175	−	0.783432i	−0.0152222	−	0.0323909i
$586$		0			0
$587$	3.84936	−	5.29818i	0.158880	−	0.218679i	−0.722154	−	0.691732i	$-0.756848\pi$
$587$	3.84936	−	5.29818i	0.158880	−	0.218679i	0.881034	+	0.473053i	$0.156848\pi$
$588$		0			0
$589$	−29.1459	+	21.1757i	−1.20093	+	0.872530i
$590$		0			0
$591$	7.59003	+	5.51448i	0.312212	+	0.226835i
$592$		0			0
$593$		−	0.908895i		−	0.0373238i	−0.999826	−	0.0186619i	$-0.994059\pi$
$593$		−	0.908895i		−	0.0373238i	0.999826	−	0.0186619i	$-0.00594062\pi$
$594$		0			0
$595$	9.11940	−	4.28568i	0.373859	−	0.175696i
$596$		0			0
$597$	−10.1537	−	3.29914i	−0.415564	−	0.135025i
$598$		0			0
$599$	−15.4696			−0.632073			−0.316036	−	0.948747i	$-0.602352\pi$
$599$	−15.4696			−0.632073			−0.316036	+	0.948747i	$0.602352\pi$
$600$		0			0
$601$	8.98715			0.366593			0.183297	−	0.983058i	$-0.441323\pi$
$601$	8.98715			0.366593			0.183297	+	0.983058i	$0.441323\pi$
$602$		0			0
$603$	0.482727	+	0.156847i	0.0196582	+	0.00638732i
$604$		0			0
$605$	−3.59728	−	0.688087i	−0.146250	−	0.0279747i
$606$		0			0
$607$		−	10.7032i		−	0.434431i	−0.976124	−	0.217215i	$-0.930303\pi$
$607$		−	10.7032i		−	0.434431i	0.976124	−	0.217215i	$-0.0696974\pi$
$608$		0			0
$609$	0.0334515	+	0.0243039i	0.00135552	+	0.000984845i
$610$		0			0
$611$	−2.07977	+	1.51104i	−0.0841386	+	0.0611302i
$612$		0			0
$613$	−28.2798	+	38.9238i	−1.14221	+	1.57212i	−0.379740	+	0.925093i	$0.623987\pi$
$613$	−28.2798	+	38.9238i	−1.14221	+	1.57212i	−0.762470	+	0.647024i	$0.776013\pi$
$614$		0			0
$615$	13.0523	−	12.2446i	0.526320	−	0.493751i
$616$		0			0
$617$	−29.0057	+	9.42453i	−1.16773	+	0.379417i	−0.827794	−	0.561033i	$-0.810404\pi$
$617$	−29.0057	+	9.42453i	−1.16773	+	0.379417i	−0.339932	+	0.940450i	$0.610404\pi$
$618$		0			0
$619$	9.48007	+	29.1766i	0.381036	+	1.17271i	0.939315	+	0.343055i	$0.111462\pi$
$619$	9.48007	+	29.1766i	0.381036	+	1.17271i	−0.558279	+	0.829653i	$0.688538\pi$
$620$		0			0
$621$	8.57174	−	26.3811i	0.343972	−	1.05864i
$622$		0			0
$623$	−3.85218	−	5.30207i	−0.154334	−	0.212423i
$624$		0			0
$625$	21.9318	−	11.9999i	0.877271	−	0.479995i
$626$		0			0
$627$	12.5741	+	17.3067i	0.502161	+	0.691165i
$628$		0			0
$629$	15.3864	−	47.3545i	0.613496	−	1.88815i
$630$		0			0
$631$	−8.91352	−	27.4330i	−0.354842	−	1.09209i	−0.956101	−	0.293036i	$-0.905334\pi$
$631$	−8.91352	−	27.4330i	−0.354842	−	1.09209i	0.601260	−	0.799054i	$-0.294666\pi$
$632$		0			0
$633$	28.9785	−	9.41570i	1.15179	−	0.374240i
$634$		0			0
$635$	18.6891	−	17.5326i	0.741654	−	0.695760i
$636$		0			0
$637$	0.850555	−	1.17069i	0.0337002	−	0.0463844i
$638$		0			0
$639$	−18.5485	+	13.4763i	−0.733768	+	0.533114i
$640$		0			0
$641$	−25.4725	−	18.5068i	−1.00610	−	0.730976i	−0.0427145	−	0.999087i	$-0.513601\pi$
$641$	−25.4725	−	18.5068i	−1.00610	−	0.730976i	−0.963388	+	0.268111i	$0.913601\pi$
$642$		0			0
$643$		−	23.8940i		−	0.942286i	−0.882057	−	0.471143i	$-0.843842\pi$
$643$		−	23.8940i		−	0.942286i	0.882057	−	0.471143i	$-0.156158\pi$
$644$		0			0
$645$	−7.83802	−	1.49926i	−0.308622	−	0.0590332i
$646$		0			0
$647$	30.5948	+	9.94087i	1.20281	+	0.390816i	0.840793	−	0.541357i	$-0.182089\pi$
$647$	30.5948	+	9.94087i	1.20281	+	0.390816i	0.362014	+	0.932173i	$0.382089\pi$
$648$		0			0
$649$	−8.93559			−0.350753
$650$		0			0
$651$	5.08909			0.199457
$652$		0			0
$653$	13.7064	+	4.45349i	0.536374	+	0.174278i	0.564663	−	0.825321i	$-0.309006\pi$
$653$	13.7064	+	4.45349i	0.536374	+	0.174278i	−0.0282896	+	0.999600i	$0.509006\pi$
$654$		0			0
$655$	−7.15114	+	3.36069i	−0.279418	+	0.131313i
$656$		0			0
$657$			24.7925i			0.967246i
$658$		0			0
$659$	29.5713	+	21.4848i	1.15194	+	0.836930i	0.988737	−	0.149663i	$-0.0478188\pi$
$659$	29.5713	+	21.4848i	1.15194	+	0.836930i	0.163199	+	0.986593i	$0.447819\pi$
$660$		0			0
$661$	−15.0538	+	10.9372i	−0.585524	+	0.425408i	−0.840711	−	0.541483i	$-0.817863\pi$
$661$	−15.0538	+	10.9372i	−0.585524	+	0.425408i	0.255187	+	0.966892i	$0.417863\pi$
$662$		0			0
$663$	0.882258	−	1.21432i	0.0342640	−	0.0471604i
$664$		0			0
$665$	−4.50682	−	9.58997i	−0.174767	−	0.371883i
$666$		0			0
$667$	0.234263	−	0.0761166i	0.00907069	−	0.00294725i
$668$		0			0
$669$	−0.858441	−	2.64201i	−0.0331892	−	0.102146i
$670$		0			0
$671$	−7.51759	+	23.1368i	−0.290213	+	0.893185i
$672$		0			0
$673$	1.17488	+	1.61708i	0.0452882	+	0.0623339i	0.831061	−	0.556182i	$-0.187734\pi$
$673$	1.17488	+	1.61708i	0.0452882	+	0.0623339i	−0.785772	+	0.618516i	$0.787734\pi$
$674$		0			0
$675$	−20.5752	−	17.0561i	−0.791941	−	0.656489i
$676$		0			0
$677$	23.0507	+	31.7265i	0.885910	+	1.21935i	0.974749	+	0.223304i	$0.0716843\pi$
$677$	23.0507	+	31.7265i	0.885910	+	1.21935i	−0.0888390	+	0.996046i	$0.528316\pi$
$678$		0			0
$679$	−4.55214	+	14.0100i	−0.174695	+	0.537656i
$680$		0			0
$681$	−7.02433	−	21.6187i	−0.269173	−	0.828429i
$682$		0			0
$683$	28.5069	−	9.26246i	1.09079	−	0.354418i	0.292236	−	0.956346i	$-0.405601\pi$
$683$	28.5069	−	9.26246i	1.09079	−	0.354418i	0.798550	+	0.601928i	$0.205601\pi$
$684$		0			0
$685$	−19.3149	−	10.6311i	−0.737984	−	0.406192i
$686$		0			0
$687$	−11.0973	+	15.2742i	−0.423390	+	0.582747i
$688$		0			0
$689$	0.579687	−	0.421167i	0.0220843	−	0.0160452i
$690$		0			0
$691$	−12.1095	−	8.79807i	−0.460668	−	0.334695i	0.333126	−	0.942882i	$-0.391897\pi$
$691$	−12.1095	−	8.79807i	−0.460668	−	0.334695i	−0.793793	+	0.608188i	$0.791897\pi$
$692$		0			0
$693$			4.03154i			0.153145i
$694$		0			0
$695$	−25.1573	−	26.8167i	−0.954270	−	1.01722i
$696$		0			0
$697$	−39.3746	−	12.7936i	−1.49142	−	0.484592i
$698$		0			0
$699$	0.0722097			0.00273122
$700$		0			0
$701$	48.8940			1.84670			0.923350	−	0.383959i	$-0.125440\pi$
$701$	48.8940			1.84670			0.923350	+	0.383959i	$0.125440\pi$
$702$		0			0
$703$	−49.7980	−	16.1804i	−1.87817	−	0.610254i
$704$		0			0
$705$	−13.9190	+	25.2885i	−0.524219	+	0.952419i
$706$		0			0
$707$		−	8.36877i		−	0.314740i
$708$		0			0
$709$	14.4200	+	10.4768i	0.541556	+	0.393463i	0.824662	−	0.565625i	$-0.191365\pi$
$709$	14.4200	+	10.4768i	0.541556	+	0.393463i	−0.283107	+	0.959088i	$0.591365\pi$
$710$		0			0
$711$	−6.30383	+	4.58000i	−0.236412	+	0.171764i
$712$		0			0
$713$	17.8196	−	24.5266i	0.667349	−	0.918527i
$714$		0			0
$715$	−1.53256	+	0.192826i	−0.0573144	+	0.00721129i
$716$		0			0
$717$	−11.6020	+	3.76972i	−0.433285	+	0.140783i
$718$		0			0
$719$	−5.52169	−	16.9940i	−0.205924	−	0.633770i	−0.999674	−	0.0255253i	$-0.991874\pi$
$719$	−5.52169	−	16.9940i	−0.205924	−	0.633770i	0.793750	−	0.608244i	$-0.208126\pi$
$720$		0			0
$721$	−3.86880	+	11.9069i	−0.144082	+	0.443438i
$722$		0			0
$723$	−0.737751	−	1.01543i	−0.0274373	−	0.0377641i
$724$		0			0
$725$	0.0151391	−	0.236837i	0.000562251	−	0.00879592i
$726$		0			0
$727$	−7.96253	−	10.9595i	−0.295314	−	0.406465i	0.635417	−	0.772169i	$-0.280828\pi$
$727$	−7.96253	−	10.9595i	−0.295314	−	0.406465i	−0.930731	+	0.365704i	$0.880828\pi$
$728$		0			0
$729$	−6.10286	+	18.7827i	−0.226032	+	0.695654i
$730$		0			0
$731$	5.70463	+	17.5571i	0.210993	+	0.649371i
$732$		0			0
$733$	22.6901	−	7.37247i	0.838079	−	0.272308i	0.141635	−	0.989919i	$-0.454764\pi$
$733$	22.6901	−	7.37247i	0.838079	−	0.272308i	0.696445	+	0.717611i	$0.254764\pi$
$734$		0			0
$735$	3.05266	−	15.9591i	0.112599	−	0.588661i
$736$		0			0
$737$	0.532363	−	0.732735i	0.0196098	−	0.0269906i
$738$		0			0
$739$	−1.52365	+	1.10699i	−0.0560483	+	0.0407215i	−0.615457	−	0.788171i	$-0.711028\pi$
$739$	−1.52365	+	1.10699i	−0.0560483	+	0.0407215i	0.559408	+	0.828892i	$0.311028\pi$
$740$		0			0
$741$	−1.27698	−	0.927783i	−0.0469112	−	0.0340830i
$742$		0			0
$743$		−	17.2103i		−	0.631383i	−0.948862	−	0.315692i	$-0.897764\pi$
$743$		−	17.2103i		−	0.631383i	0.948862	−	0.315692i	$-0.102236\pi$
$744$		0			0
$745$	−0.369416	−	2.93607i	−0.0135343	−	0.107569i
$746$		0			0
$747$	−11.0662	−	3.59563i	−0.404891	−	0.131557i
$748$		0			0
$749$	−13.2051			−0.482503
$750$		0			0
$751$	−9.79316			−0.357358			−0.178679	−	0.983907i	$-0.557182\pi$
$751$	−9.79316			−0.357358			−0.178679	+	0.983907i	$0.557182\pi$
$752$		0			0
$753$	20.3485	+	6.61162i	0.741539	+	0.240941i
$754$		0			0
$755$	1.64868	+	13.1035i	0.0600016	+	0.476885i
$756$		0			0
$757$		−	37.4221i		−	1.36013i	−0.733152	−	0.680065i	$-0.761952\pi$
$757$		−	37.4221i		−	1.36013i	0.733152	−	0.680065i	$-0.238048\pi$
$758$		0			0
$759$	−14.5638	−	10.5812i	−0.528633	−	0.384074i
$760$		0			0
$761$	42.4457	−	30.8386i	1.53866	−	1.11790i	0.587485	−	0.809235i	$-0.300118\pi$
$761$	42.4457	−	30.8386i	1.53866	−	1.11790i	0.951171	−	0.308664i	$-0.0998819\pi$
$762$		0			0
$763$	−5.89698	+	8.11649i	−0.213485	+	0.293837i
$764$		0			0
$765$	−4.22439	+	22.0849i	−0.152733	+	0.798480i
$766$		0			0
$767$	0.627046	−	0.203740i	0.0226413	−	0.00735662i
$768$		0			0
$769$	−7.64354	−	23.5244i	−0.275633	−	0.848311i	−0.989051	−	0.147573i	$-0.952854\pi$
$769$	−7.64354	−	23.5244i	−0.275633	−	0.848311i	0.713418	−	0.700739i	$-0.247146\pi$
$770$		0			0
$771$	−0.114030	+	0.350948i	−0.00410669	+	0.0126391i
$772$		0			0
$773$	21.4594	+	29.5363i	0.771841	+	1.06235i	0.996136	+	0.0878271i	$0.0279923\pi$
$773$	21.4594	+	29.5363i	0.771841	+	1.06235i	−0.224294	+	0.974521i	$0.572008\pi$
$774$		0			0
$775$	−15.6263	−	24.6777i	−0.561312	−	0.886450i
$776$		0			0
$777$	4.34755	+	5.98389i	0.155968	+	0.214671i
$778$		0			0
$779$	−13.4538	+	41.4064i	−0.482031	+	1.48354i
$780$		0			0
$781$	12.6424	+	38.9092i	0.452379	+	1.39228i
$782$		0			0
$783$	−0.241283	+	0.0783977i	−0.00862276	+	0.00280170i
$784$		0			0
$785$	8.19124	−	1.03062i	0.292358	−	0.0367844i
$786$		0			0
$787$	19.2482	−	26.4929i	0.686125	−	0.944370i	−0.313862	−	0.949468i	$-0.601623\pi$
$787$	19.2482	−	26.4929i	0.686125	−	0.944370i	0.999987	+	0.00509897i	$0.00162306\pi$
$788$		0			0
$789$	28.7725	−	20.9044i	1.02433	−	0.744218i
$790$		0			0
$791$	2.07065	+	1.50442i	0.0736240	+	0.0534910i
$792$		0			0
$793$		−	1.79501i		−	0.0637426i
$794$		0			0
$795$	3.87959	−	7.04857i	0.137595	−	0.249987i
$796$		0			0
$797$	−22.3999	−	7.27816i	−0.793444	−	0.257806i	−0.115874	−	0.993264i	$-0.536967\pi$
$797$	−22.3999	−	7.27816i	−0.793444	−	0.257806i	−0.677570	+	0.735458i	$0.736967\pi$
$798$		0			0
$799$	66.7763			2.36238
$800$		0			0
$801$	14.6247			0.516739
$802$		0			0
$803$	42.0746	+	13.6709i	1.48478	+	0.482435i
$804$		0			0
$805$	6.10071	+	6.50312i	0.215022	+	0.229205i
$806$		0			0
$807$			3.94709i			0.138944i
$808$		0			0
$809$	−24.0951	−	17.5061i	−0.847139	−	0.615482i	0.0772169	−	0.997014i	$-0.475397\pi$
$809$	−24.0951	−	17.5061i	−0.847139	−	0.615482i	−0.924356	+	0.381532i	$0.875397\pi$
$810$		0			0
$811$	−7.38769	+	5.36747i	−0.259417	+	0.188477i	−0.709890	−	0.704313i	$-0.751255\pi$
$811$	−7.38769	+	5.36747i	−0.259417	+	0.188477i	0.450473	+	0.892790i	$0.351255\pi$
$812$		0			0
$813$	12.6587	−	17.4233i	0.443961	−	0.611060i
$814$		0			0
$815$	1.46251	+	0.804977i	0.0512295	+	0.0281971i
$816$		0			0
$817$	18.4630	−	5.99900i	0.645939	−	0.209878i
$818$		0			0
$819$	−0.0919227	−	0.282909i	−0.00321204	−	0.00988564i
$820$		0			0
$821$	10.4663	−	32.2120i	0.365277	−	1.12421i	−0.584530	−	0.811372i	$-0.698721\pi$
$821$	10.4663	−	32.2120i	0.365277	−	1.12421i	0.949807	−	0.312836i	$-0.101279\pi$
$822$		0			0
$823$	−13.3213	−	18.3352i	−0.464353	−	0.639126i	0.511052	−	0.859550i	$-0.329256\pi$
$823$	−13.3213	−	18.3352i	−0.464353	−	0.639126i	−0.975404	+	0.220424i	$0.929256\pi$
$824$		0			0
$825$	−14.6536	+	9.27883i	−0.510172	+	0.323047i
$826$		0			0
$827$	29.8102	+	41.0303i	1.03660	+	1.42676i	0.899872	+	0.436154i	$0.143660\pi$
$827$	29.8102	+	41.0303i	1.03660	+	1.42676i	0.136731	+	0.990608i	$0.456340\pi$
$828$		0			0
$829$	−7.10718	+	21.8737i	−0.246843	+	0.759704i	0.748485	+	0.663151i	$0.230781\pi$
$829$	−7.10718	+	21.8737i	−0.246843	+	0.759704i	−0.995328	+	0.0965522i	$0.969219\pi$
$830$		0			0
$831$	−2.38865	−	7.35151i	−0.0828614	−	0.255021i
$832$		0			0
$833$	−35.7482	+	11.6153i	−1.23860	+	0.402446i
$834$		0			0
$835$	−2.42421	−	5.15843i	−0.0838934	−	0.178515i
$836$		0			0
$837$	−18.3536	+	25.2616i	−0.634394	+	0.873168i
$838$		0			0
$839$	8.22783	−	5.97787i	0.284056	−	0.206379i	−0.436629	−	0.899642i	$-0.643828\pi$
$839$	8.22783	−	5.97787i	0.284056	−	0.206379i	0.720685	+	0.693263i	$0.243828\pi$
$840$		0			0
$841$	23.4597	+	17.0444i	0.808954	+	0.587740i
$842$		0			0
$843$		−	7.84283i		−	0.270121i
$844$		0			0
$845$	−26.2054	+	12.3153i	−0.901492	+	0.423658i
$846$		0			0
$847$	−1.19699	−	0.388926i	−0.0411291	−	0.0133636i
$848$		0			0
$849$	10.0315			0.344280
$850$		0			0
$851$	44.0621			1.51043
$852$		0			0
$853$	−7.97562	−	2.59144i	−0.273080	−	0.0887291i	0.169276	−	0.985569i	$-0.445857\pi$
$853$	−7.97562	−	2.59144i	−0.273080	−	0.0887291i	−0.442356	+	0.896840i	$0.645857\pi$
$854$		0			0
$855$	23.2245	+	4.44238i	0.794260	+	0.151926i
$856$		0			0
$857$			5.16914i			0.176574i	0.996095	+	0.0882872i	$0.0281393\pi$
$857$			5.16914i			0.176574i	−0.996095	+	0.0882872i	$0.971861\pi$
$858$		0			0
$859$	8.61458	+	6.25886i	0.293926	+	0.213550i	0.724969	−	0.688782i	$-0.241854\pi$
$859$	8.61458	+	6.25886i	0.293926	+	0.213550i	−0.431043	+	0.902331i	$0.641854\pi$
$860$		0			0
$861$	4.97553	−	3.61493i	0.169566	−	0.123197i
$862$		0			0
$863$	8.35044	−	11.4934i	0.284252	−	0.391240i	−0.642884	−	0.765963i	$-0.722262\pi$
$863$	8.35044	−	11.4934i	0.284252	−	0.391240i	0.927137	+	0.374724i	$0.122262\pi$
$864$		0			0
$865$	−3.57399	+	3.35283i	−0.121519	+	0.114000i
$866$		0			0
$867$	−18.7510	+	6.09257i	−0.636817	+	0.206914i
$868$		0			0
$869$	4.29659	+	13.2235i	0.145752	+	0.448578i
$870$		0			0
$871$	−0.0206510	+	0.0635573i	−0.000699733	+	0.00215356i
$872$		0			0
$873$	−19.3220	−	26.5944i	−0.653949	−	0.900084i
$874$		0			0
$875$	7.99253	−	3.15056i	0.270197	−	0.106508i
$876$		0			0
$877$	−10.0395	−	13.8182i	−0.339010	−	0.466608i	0.605142	−	0.796118i	$-0.293116\pi$
$877$	−10.0395	−	13.8182i	−0.339010	−	0.466608i	−0.944152	+	0.329510i	$0.893116\pi$
$878$		0			0
$879$	2.36492	−	7.27847i	0.0797668	−	0.245497i
$880$		0			0
$881$	−8.82576	−	27.1629i	−0.297347	−	0.915141i	−0.982423	−	0.186669i	$-0.940231\pi$
$881$	−8.82576	−	27.1629i	−0.297347	−	0.915141i	0.685075	−	0.728472i	$-0.259769\pi$
$882$		0			0
$883$	−29.8714	+	9.70581i	−1.00525	+	0.326626i	−0.764963	−	0.644075i	$-0.777243\pi$
$883$	−29.8714	+	9.70581i	−1.00525	+	0.326626i	−0.240290	+	0.970701i	$0.577243\pi$
$884$		0			0
$885$	5.39927	−	5.06516i	0.181495	−	0.170263i
$886$		0			0
$887$	−2.41456	+	3.32335i	−0.0810729	+	0.111587i	−0.847627	−	0.530592i	$-0.821970\pi$
$887$	−2.41456	+	3.32335i	−0.0810729	+	0.111587i	0.766554	+	0.642179i	$0.221970\pi$
$888$		0			0
$889$	7.12426	−	5.17608i	0.238940	−	0.173600i
$890$		0			0
$891$	2.26649	+	1.64670i	0.0759301	+	0.0551665i
$892$		0			0
$893$		−	70.2221i		−	2.34989i
$894$		0			0
$895$	−25.4956	−	4.87680i	−0.852223	−	0.163013i
$896$		0			0
$897$	1.26326	+	0.410459i	0.0421791	+	0.0137048i
$898$		0			0
$899$	−0.277277			−0.00924770
$900$		0			0
$901$	−18.6123			−0.620066
$902$		0			0
$903$	−2.60809	−	0.847421i	−0.0867919	−	0.0282004i
$904$		0			0
$905$	21.0068	−	9.87217i	0.698289	−	0.328162i
$906$		0			0
$907$			15.9013i			0.527993i	0.964524	+	0.263996i	$0.0850407\pi$
$907$			15.9013i			0.527993i	−0.964524	+	0.263996i	$0.914959\pi$
$908$		0			0
$909$	15.1084	+	10.9769i	0.501114	+	0.364081i
$910$		0			0
$911$	40.5143	−	29.4354i	1.34230	−	0.975238i	0.342944	−	0.939356i	$-0.388576\pi$
$911$	40.5143	−	29.4354i	1.34230	−	0.975238i	0.999356	−	0.0358817i	$-0.0114240\pi$
$912$		0			0
$913$	−12.2041	+	16.7975i	−0.403896	+	0.555916i
$914$		0			0
$915$	−8.57267	−	18.2416i	−0.283404	−	0.603048i
$916$		0			0
$917$	−2.58239	+	0.839068i	−0.0852779	+	0.0277085i
$918$		0			0
$919$	7.33439	+	22.5729i	0.241939	+	0.744613i	0.996125	+	0.0879512i	$0.0280320\pi$
$919$	7.33439	+	22.5729i	0.241939	+	0.744613i	−0.754185	+	0.656661i	$0.771968\pi$
$920$		0			0
$921$	−6.48509	+	19.9591i	−0.213691	+	0.657674i
$922$		0			0
$923$	−1.77433	−	2.44216i	−0.0584028	−	0.0803845i
$924$		0			0
$925$	15.6674	−	39.4557i	0.515142	−	1.29730i
$926$		0			0
$927$	−16.4215	−	22.6022i	−0.539352	−	0.742355i
$928$		0			0
$929$	8.38778	−	25.8149i	0.275194	−	0.846960i	−0.713974	−	0.700172i	$-0.753107\pi$
$929$	8.38778	−	25.8149i	0.275194	−	0.846960i	0.989168	−	0.146788i	$-0.0468934\pi$
$930$		0			0
$931$	12.2147	+	37.5929i	0.400319	+	1.23206i
$932$		0			0
$933$	−11.0511	+	3.59073i	−0.361797	+	0.117555i
$934$		0			0
$935$	35.1502	+	19.3470i	1.14954	+	0.632714i
$936$		0			0
$937$	−0.110140	+	0.151595i	−0.00359813	+	0.00495240i	−0.810812	−	0.585306i	$-0.800974\pi$
$937$	−0.110140	+	0.151595i	−0.00359813	+	0.00495240i	0.807214	+	0.590259i	$0.200974\pi$
$938$		0			0
$939$	19.6459	−	14.2736i	0.641119	−	0.465800i
$940$		0			0
$941$	23.5700	+	17.1246i	0.768358	+	0.558245i	0.901463	−	0.432857i	$-0.142494\pi$
$941$	23.5700	+	17.1246i	0.768358	+	0.558245i	−0.133104	+	0.991102i	$0.542494\pi$
$942$		0			0
$943$		−	36.6371i		−	1.19307i
$944$		0			0
$945$	−6.28353	−	6.69801i	−0.204403	−	0.217886i
$946$		0			0
$947$	−50.9446	−	16.5529i	−1.65548	−	0.537897i	−0.675561	−	0.737304i	$-0.736099\pi$
$947$	−50.9446	−	16.5529i	−1.65548	−	0.537897i	−0.979917	+	0.199406i	$0.936099\pi$
$948$		0			0
$949$	−3.26425			−0.105962
$950$		0			0
$951$	−3.22662			−0.104630
$952$		0			0
$953$	−5.41410	−	1.75915i	−0.175380	−	0.0569844i	0.220011	−	0.975497i	$-0.429391\pi$
$953$	−5.41410	−	1.75915i	−0.175380	−	0.0569844i	−0.395391	+	0.918513i	$0.629391\pi$
$954$		0			0
$955$	−8.77296	+	15.9390i	−0.283886	+	0.515775i
$956$		0			0
$957$			0.164646i			0.00532225i
$958$		0			0
$959$	−6.12945	−	4.45330i	−0.197930	−	0.143805i
$960$		0			0
$961$	−2.52963	+	1.83788i	−0.0816008	+	0.0592865i
$962$		0			0
$963$	17.3205	−	23.8396i	0.558144	−	0.768219i
$964$		0			0
$965$	6.32165	−	0.795389i	0.203501	−	0.0256045i
$966$		0			0
$967$	31.6887	−	10.2963i	1.01904	−	0.331106i	0.248591	−	0.968609i	$-0.420032\pi$
$967$	31.6887	−	10.2963i	1.01904	−	0.331106i	0.770448	+	0.637503i	$0.220032\pi$
$968$		0			0
$969$	12.6699	+	38.9941i	0.407017	+	1.25267i
$970$		0			0
$971$	9.43685	−	29.0436i	0.302843	−	0.932055i	−0.677630	−	0.735403i	$-0.736993\pi$
$971$	9.43685	−	29.0436i	0.302843	−	0.932055i	0.980473	−	0.196652i	$-0.0630070\pi$
$972$		0			0
$973$	−7.42708	−	10.2225i	−0.238101	−	0.327718i
$974$		0			0
$975$	0.816734	−	0.985247i	0.0261564	−	0.0315532i
$976$		0			0
$977$	−1.50226	−	2.06768i	−0.0480615	−	0.0661509i	0.784310	−	0.620369i	$-0.213017\pi$
$977$	−1.50226	−	2.06768i	−0.0480615	−	0.0661509i	−0.832371	+	0.554218i	$0.813017\pi$
$978$		0			0
$979$	8.06425	−	24.8192i	0.257735	−	0.793226i
$980$		0			0
$981$	−6.91819	−	21.2920i	−0.220881	−	0.679802i
$982$		0			0
$983$	17.6690	−	5.74101i	0.563554	−	0.183110i	−0.0133659	−	0.999911i	$-0.504255\pi$
$983$	17.6690	−	5.74101i	0.563554	−	0.183110i	0.576920	+	0.816801i	$0.304255\pi$
$984$		0			0
$985$	3.47647	−	18.1747i	0.110769	−	0.579095i
$986$		0			0
$987$	−5.83059	+	8.02512i	−0.185590	+	0.255442i
$988$		0			0
$989$	−13.2164	+	9.60229i	−0.420257	+	0.305335i
$990$		0			0
$991$	−10.3956	−	7.55282i	−0.330226	−	0.239923i	0.410301	−	0.911950i	$-0.365424\pi$
$991$	−10.3956	−	7.55282i	−0.330226	−	0.239923i	−0.740526	+	0.672027i	$0.765424\pi$
$992$		0			0
$993$		−	0.0551572i		−	0.00175036i
$994$		0			0
$995$	2.62871	+	20.8926i	0.0833357	+	0.662341i
$996$		0			0
$997$	25.9306	+	8.42535i	0.821229	+	0.266834i	0.689347	−	0.724432i	$-0.257898\pi$
$997$	25.9306	+	8.42535i	0.821229	+	0.266834i	0.131883	+	0.991265i	$0.457898\pi$
$998$		0			0
$999$	−45.3826			−1.43584

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.y.b.289.1		8
4.3	odd	2		100.2.i.a.89.2	yes	8
12.11	even	2		900.2.w.a.289.2		8
20.3	even	4		500.2.g.b.301.2		16
20.7	even	4		500.2.g.b.301.3		16
20.19	odd	2		500.2.i.a.449.1		8
25.3	odd	20		10000.2.a.bi.1.6		8
25.9	even	10	inner	400.2.y.b.209.1		8
25.22	odd	20		10000.2.a.bi.1.3		8
100.3	even	20		2500.2.a.f.1.3		8
100.47	even	20		2500.2.a.f.1.6		8
100.59	odd	10		100.2.i.a.9.2	✓	8
100.63	even	20		500.2.g.b.201.2		16
100.71	odd	10		2500.2.c.b.1249.6		8
100.79	odd	10		2500.2.c.b.1249.3		8
100.87	even	20		500.2.g.b.201.3		16
100.91	odd	10		500.2.i.a.49.1		8
300.59	even	10		900.2.w.a.109.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.2.i.a.9.2	✓	8	100.59	odd	10
100.2.i.a.89.2	yes	8	4.3	odd	2
400.2.y.b.209.1		8	25.9	even	10	inner
400.2.y.b.289.1		8	1.1	even	1	trivial
500.2.g.b.201.2		16	100.63	even	20
500.2.g.b.201.3		16	100.87	even	20
500.2.g.b.301.2		16	20.3	even	4
500.2.g.b.301.3		16	20.7	even	4
500.2.i.a.49.1		8	100.91	odd	10
500.2.i.a.449.1		8	20.19	odd	2
900.2.w.a.109.2		8	300.59	even	10
900.2.w.a.289.2		8	12.11	even	2
2500.2.a.f.1.3		8	100.3	even	20
2500.2.a.f.1.6		8	100.47	even	20
2500.2.c.b.1249.3		8	100.79	odd	10
2500.2.c.b.1249.6		8	100.71	odd	10
10000.2.a.bi.1.3		8	25.22	odd	20
10000.2.a.bi.1.6		8	25.3	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)

\(f(q)\)	\(=\)	\(q+(-1.07822 - 0.350334i) q^{3} +(0.279141 + 2.21858i) q^{5} +0.768409i q^{7} +(-1.38723 - 1.00788i) q^{9} +O(q^{10})\)	\(q+(-1.07822 - 0.350334i) q^{3} +(0.279141 + 2.21858i) q^{5} +0.768409i q^{7} +(-1.38723 - 1.00788i) q^{9} +(-2.47539 + 1.79848i) q^{11} +(0.132701 - 0.182648i) q^{13} +(0.476268 - 2.48990i) q^{15} +(-5.57734 + 1.81219i) q^{17} +(1.90570 + 5.86514i) q^{19} +(0.269200 - 0.828511i) q^{21} +(-3.05035 - 4.19845i) q^{23} +(-4.84416 + 1.23859i) q^{25} +(3.14177 + 4.32427i) q^{27} +(-0.0146672 + 0.0451411i) q^{29} +(1.80522 + 5.55590i) q^{31} +(3.29908 - 1.07193i) q^{33} +(-1.70477 + 0.214494i) q^{35} +(-4.99060 + 6.86897i) q^{37} +(-0.207068 + 0.150444i) q^{39} +(5.71146 + 4.14962i) q^{41} -3.14793i q^{43} +(1.84883 - 3.35903i) q^{45} +(-10.8295 - 3.51872i) q^{47} +6.40955 q^{49} +6.64845 q^{51} +(3.01846 + 0.980759i) q^{53} +(-4.68104 - 4.98982i) q^{55} -6.99152i q^{57} +(2.36263 + 1.71655i) q^{59} +(6.43232 - 4.67335i) q^{61} +(0.774467 - 1.06596i) q^{63} +(0.442260 + 0.243423i) q^{65} +(-0.281520 + 0.0914714i) q^{67} +(1.81808 + 5.59548i) q^{69} +(4.13182 - 12.7164i) q^{71} +(-8.49858 - 11.6973i) q^{73} +(5.65697 + 0.361604i) q^{75} +(-1.38197 - 1.90211i) q^{77} +(1.40423 - 4.32177i) q^{79} +(-0.282938 - 0.870794i) q^{81} +(6.45367 - 2.09692i) q^{83} +(-5.57734 - 11.8679i) q^{85} +(0.0316289 - 0.0435334i) q^{87} +(-6.90006 + 5.01319i) q^{89} +(0.140348 + 0.101969i) q^{91} -6.62289i q^{93} +(-12.4803 + 5.86514i) q^{95} +(18.2325 + 5.92411i) q^{97} +5.24660 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{5} + 2 q^{9}+O(q^{10}) \) 8 * q + 5 * q^5 + 2 * q^9	\( 8 q + 5 q^{5} + 2 q^{9} - 5 q^{11} + 20 q^{15} - 5 q^{17} + 8 q^{19} - 2 q^{21} + 20 q^{23} - 5 q^{25} - 8 q^{29} + 12 q^{31} + 15 q^{33} + 5 q^{35} - 10 q^{37} - 22 q^{39} + 13 q^{41} + 10 q^{45} - 45 q^{47} + 14 q^{49} + 14 q^{51} + 30 q^{53} - 35 q^{55} - 9 q^{59} + 16 q^{61} - 20 q^{63} - 25 q^{65} + 5 q^{67} - 14 q^{69} + q^{71} - 60 q^{73} + 5 q^{75} - 20 q^{77} + 24 q^{79} - 3 q^{81} + 10 q^{83} - 5 q^{85} + 55 q^{87} - 37 q^{89} - 32 q^{91} - 30 q^{95} + 25 q^{97} - 20 q^{99}+O(q^{100}) \) 8 * q + 5 * q^5 + 2 * q^9 - 5 * q^11 + 20 * q^15 - 5 * q^17 + 8 * q^19 - 2 * q^21 + 20 * q^23 - 5 * q^25 - 8 * q^29 + 12 * q^31 + 15 * q^33 + 5 * q^35 - 10 * q^37 - 22 * q^39 + 13 * q^41 + 10 * q^45 - 45 * q^47 + 14 * q^49 + 14 * q^51 + 30 * q^53 - 35 * q^55 - 9 * q^59 + 16 * q^61 - 20 * q^63 - 25 * q^65 + 5 * q^67 - 14 * q^69 + q^71 - 60 * q^73 + 5 * q^75 - 20 * q^77 + 24 * q^79 - 3 * q^81 + 10 * q^83 - 5 * q^85 + 55 * q^87 - 37 * q^89 - 32 * q^91 - 30 * q^95 + 25 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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