LMFDB - Embedded newform 400.2.y.d.369.7

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			369.7
Character	$\chi$	$=$	400.369
Dual form			400.2.y.d.129.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.31712 + 1.81286i) q^{3} +(2.19384 + 0.432536i) q^{5} +1.85909i q^{7} +(-0.624612 + 1.92236i) q^{9} +(0.681343 + 2.09696i) q^{11} +(-4.55205 - 1.47905i) q^{13} +(2.10542 + 4.54683i) q^{15} +(3.76158 - 5.17737i) q^{17} +(-3.01005 - 2.18693i) q^{19} +(-3.37028 + 2.44865i) q^{21} +(0.905170 - 0.294107i) q^{23} +(4.62582 + 1.89783i) q^{25} +(2.08578 - 0.677713i) q^{27} +(-4.71315 + 3.42430i) q^{29} +(-5.42789 - 3.94359i) q^{31} +(-2.90409 + 3.99713i) q^{33} +(-0.804125 + 4.07854i) q^{35} +(9.69306 + 3.14947i) q^{37} +(-3.31429 - 10.2003i) q^{39} +(-1.82997 + 5.63206i) q^{41} +3.96247i q^{43} +(-2.20178 + 3.94717i) q^{45} +(-5.93038 - 8.16246i) q^{47} +3.54377 q^{49} +14.3403 q^{51} +(-2.46759 - 3.39634i) q^{53} +(0.587744 + 4.89509i) q^{55} -8.33725i q^{57} +(-1.86474 + 5.73908i) q^{59} +(-1.13650 - 3.49779i) q^{61} +(-3.57384 - 1.16121i) q^{63} +(-9.34670 - 5.21372i) q^{65} +(8.45537 - 11.6378i) q^{67} +(1.72540 + 1.25357i) q^{69} +(7.82527 - 5.68539i) q^{71} +(3.43698 - 1.11674i) q^{73} +(2.65228 + 10.8857i) q^{75} +(-3.89844 + 1.26668i) q^{77} +(-9.13049 + 6.63369i) q^{79} +(8.88160 + 6.45286i) q^{81} +(4.08493 - 5.62242i) q^{83} +(10.4917 - 9.73128i) q^{85} +(-12.4156 - 4.03407i) q^{87} +(-3.23757 - 9.96423i) q^{89} +(2.74969 - 8.46268i) q^{91} -15.0342i q^{93} +(-5.65762 - 6.09971i) q^{95} +(0.275879 + 0.379715i) q^{97} -4.45668 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

Character values

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

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$	$1$

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
$3$	1.31712	+	1.81286i	0.760441	+	1.04666i	0.997177	+	0.0750833i	$0.0239223\pi$
$3$	1.31712	+	1.81286i	0.760441	+	1.04666i	−0.236736	+	0.971574i	$0.576078\pi$
$4$		0			0
$5$	2.19384	+	0.432536i	0.981113	+	0.193436i
$5$	2.19384	+	0.432536i	0.981113	+	0.193436i
$6$		0			0
$7$			1.85909i			0.702671i	0.936250	+	0.351336i	$0.114272\pi$
$7$			1.85909i			0.702671i	−0.936250	+	0.351336i	$0.885728\pi$
$8$		0			0
$9$	−0.624612	+	1.92236i	−0.208204	+	0.640786i
$10$		0			0
$11$	0.681343	+	2.09696i	0.205433	+	0.632257i	0.999695	+	0.0246823i	$0.00785741\pi$
$11$	0.681343	+	2.09696i	0.205433	+	0.632257i	−0.794263	+	0.607575i	$0.792143\pi$
$12$		0			0
$13$	−4.55205	−	1.47905i	−1.26251	−	0.410215i	−0.400122	−	0.916462i	$-0.631032\pi$
$13$	−4.55205	−	1.47905i	−1.26251	−	0.410215i	−0.862388	+	0.506247i	$0.831032\pi$
$14$		0			0
$15$	2.10542	+	4.54683i	0.543617	+	1.17399i
$16$		0			0
$17$	3.76158	−	5.17737i	0.912317	−	1.25570i	−0.0540522	−	0.998538i	$-0.517214\pi$
$17$	3.76158	−	5.17737i	0.912317	−	1.25570i	0.966369	−	0.257159i	$-0.0827863\pi$
$18$		0			0
$19$	−3.01005	−	2.18693i	−0.690552	−	0.501715i	0.186289	−	0.982495i	$-0.440354\pi$
$19$	−3.01005	−	2.18693i	−0.690552	−	0.501715i	−0.876842	+	0.480779i	$0.840354\pi$
$20$		0			0
$21$	−3.37028	+	2.44865i	−0.735456	+	0.534340i
$22$		0			0
$23$	0.905170	−	0.294107i	0.188741	−	0.0613256i	−0.213121	−	0.977026i	$-0.568363\pi$
$23$	0.905170	−	0.294107i	0.188741	−	0.0613256i	0.401862	+	0.915700i	$0.368363\pi$
$24$		0			0
$25$	4.62582	+	1.89783i	0.925165	+	0.379565i
$26$		0			0
$27$	2.08578	−	0.677713i	0.401409	−	0.130426i
$28$		0			0
$29$	−4.71315	+	3.42430i	−0.875210	+	0.635877i	−0.931980	−	0.362510i	$-0.881920\pi$
$29$	−4.71315	+	3.42430i	−0.875210	+	0.635877i	0.0567701	+	0.998387i	$0.481920\pi$
$30$		0			0
$31$	−5.42789	−	3.94359i	−0.974878	−	0.708290i	−0.0183199	−	0.999832i	$-0.505832\pi$
$31$	−5.42789	−	3.94359i	−0.974878	−	0.708290i	−0.956558	+	0.291542i	$0.905832\pi$
$32$		0			0
$33$	−2.90409	+	3.99713i	−0.505537	+	0.695812i
$34$		0			0
$35$	−0.804125	+	4.07854i	−0.135922	+	0.689400i
$36$		0			0
$37$	9.69306	+	3.14947i	1.59353	+	0.517769i	0.965496	−	0.260418i	$-0.0838602\pi$
$37$	9.69306	+	3.14947i	1.59353	+	0.517769i	0.628033	+	0.778187i	$0.283860\pi$
$38$		0			0
$39$	−3.31429	−	10.2003i	−0.530711	−	1.63336i
$40$		0			0
$41$	−1.82997	+	5.63206i	−0.285793	+	0.879580i	0.700367	+	0.713783i	$0.253020\pi$
$41$	−1.82997	+	5.63206i	−0.285793	+	0.879580i	−0.986160	+	0.165797i	$0.946980\pi$
$42$		0			0
$43$			3.96247i			0.604272i	0.953265	+	0.302136i	$0.0976996\pi$
$43$			3.96247i			0.604272i	−0.953265	+	0.302136i	$0.902300\pi$
$44$		0			0
$45$	−2.20178	+	3.94717i	−0.328223	+	0.588409i
$46$		0			0
$47$	−5.93038	−	8.16246i	−0.865034	−	1.19062i	−0.980345	−	0.197288i	$-0.936786\pi$
$47$	−5.93038	−	8.16246i	−0.865034	−	1.19062i	0.115311	−	0.993329i	$-0.463214\pi$
$48$		0			0
$49$	3.54377			0.506253
$50$		0			0
$51$	14.3403			2.00805
$52$		0			0
$53$	−2.46759	−	3.39634i	−0.338949	−	0.466523i	0.605185	−	0.796085i	$-0.293099\pi$
$53$	−2.46759	−	3.39634i	−0.338949	−	0.466523i	−0.944134	+	0.329562i	$0.893099\pi$
$54$		0			0
$55$	0.587744	+	4.89509i	0.0792513	+	0.660053i
$56$		0			0
$57$		−	8.33725i		−	1.10430i
$58$		0			0
$59$	−1.86474	+	5.73908i	−0.242769	+	0.747165i	0.753227	+	0.657761i	$0.228496\pi$
$59$	−1.86474	+	5.73908i	−0.242769	+	0.747165i	−0.995995	+	0.0894039i	$0.971504\pi$
$60$		0			0
$61$	−1.13650	−	3.49779i	−0.145514	−	0.447847i	0.851563	−	0.524253i	$-0.175655\pi$
$61$	−1.13650	−	3.49779i	−0.145514	−	0.447847i	−0.997077	+	0.0764064i	$0.975655\pi$
$62$		0			0
$63$	−3.57384	−	1.16121i	−0.450262	−	0.146299i
$64$		0			0
$65$	−9.34670	−	5.21372i	−1.15931	−	0.646682i
$66$		0			0
$67$	8.45537	−	11.6378i	1.03299	−	1.42179i	0.130307	−	0.991474i	$-0.458404\pi$
$67$	8.45537	−	11.6378i	1.03299	−	1.42179i	0.902680	−	0.430312i	$-0.141596\pi$
$68$		0			0
$69$	1.72540	+	1.25357i	0.207713	+	0.150913i
$70$		0			0
$71$	7.82527	−	5.68539i	0.928688	−	0.674732i	−0.0169829	−	0.999856i	$-0.505406\pi$
$71$	7.82527	−	5.68539i	0.928688	−	0.674732i	0.945671	+	0.325124i	$0.105406\pi$
$72$		0			0
$73$	3.43698	−	1.11674i	0.402268	−	0.130705i	−0.100894	−	0.994897i	$-0.532170\pi$
$73$	3.43698	−	1.11674i	0.402268	−	0.130705i	0.503161	+	0.864193i	$0.332170\pi$
$74$		0			0
$75$	2.65228	+	10.8857i	0.306258	+	1.25697i
$76$		0			0
$77$	−3.89844	+	1.26668i	−0.444269	+	0.144352i
$78$		0			0
$79$	−9.13049	+	6.63369i	−1.02726	+	0.746348i	−0.967759	−	0.251880i	$-0.918951\pi$
$79$	−9.13049	+	6.63369i	−1.02726	+	0.746348i	−0.0595020	+	0.998228i	$0.518951\pi$
$80$		0			0
$81$	8.88160	+	6.45286i	0.986844	+	0.716984i
$82$		0			0
$83$	4.08493	−	5.62242i	0.448379	−	0.617141i	−0.523669	−	0.851922i	$-0.675437\pi$
$83$	4.08493	−	5.62242i	0.448379	−	0.617141i	0.972048	+	0.234781i	$0.0754371\pi$
$84$		0			0
$85$	10.4917	−	9.73128i	1.13798	−	1.05551i
$86$		0			0
$87$	−12.4156	−	4.03407i	−1.33109	−	0.432498i
$88$		0			0
$89$	−3.23757	−	9.96423i	−0.343182	−	1.05621i	−0.962550	−	0.271105i	$-0.912611\pi$
$89$	−3.23757	−	9.96423i	−0.343182	−	1.05621i	0.619368	−	0.785101i	$-0.287389\pi$
$90$		0			0
$91$	2.74969	−	8.46268i	0.288246	−	0.887130i
$92$		0			0
$93$		−	15.0342i		−	1.55898i
$94$		0			0
$95$	−5.65762	−	6.09971i	−0.580460	−	0.625817i
$96$		0			0
$97$	0.275879	+	0.379715i	0.0280113	+	0.0385542i	0.822793	−	0.568341i	$-0.192415\pi$
$97$	0.275879	+	0.379715i	0.0280113	+	0.0385542i	−0.794782	+	0.606895i	$0.792415\pi$
$98$		0			0
$99$	−4.45668			−0.447913
$100$		0			0
$101$	−1.01547			−0.101043			−0.0505214	−	0.998723i	$-0.516088\pi$
$101$	−1.01547			−0.101043			−0.0505214	+	0.998723i	$0.516088\pi$
$102$		0			0
$103$	−9.68658	−	13.3324i	−0.954447	−	1.31368i	−0.949524	−	0.313696i	$-0.898433\pi$
$103$	−9.68658	−	13.3324i	−0.954447	−	1.31368i	−0.00492362	−	0.999988i	$-0.501567\pi$
$104$		0			0
$105$	−8.45298	+	3.91417i	−0.824926	+	0.381984i
$106$		0			0
$107$			14.9910i			1.44923i	0.689153	+	0.724616i	$0.257983\pi$
$107$			14.9910i			1.44923i	−0.689153	+	0.724616i	$0.742017\pi$
$108$		0			0
$109$	−3.03784	+	9.34952i	−0.290972	+	0.895521i	0.693572	+	0.720387i	$0.256036\pi$
$109$	−3.03784	+	9.34952i	−0.290972	+	0.895521i	−0.984545	+	0.175134i	$0.943964\pi$
$110$		0			0
$111$	7.05739	+	21.7204i	0.669858	+	2.06161i
$112$		0			0
$113$	−15.9570	−	5.18475i	−1.50111	−	0.487740i	−0.560769	−	0.827973i	$-0.689494\pi$
$113$	−15.9570	−	5.18475i	−1.50111	−	0.487740i	−0.940341	+	0.340232i	$0.889494\pi$
$114$		0			0
$115$	2.11301	−	0.253704i	0.197039	−	0.0236581i
$116$		0			0
$117$	5.68652	−	7.82683i	0.525719	−	0.723591i
$118$		0			0
$119$	9.62521	+	6.99313i	0.882342	+	0.641059i
$120$		0			0
$121$	4.96618	−	3.60814i	0.451471	−	0.328013i
$122$		0			0
$123$	−12.6204	+	4.10063i	−1.13795	+	0.369741i
$124$		0			0
$125$	9.32742	+	6.16436i	0.834270	+	0.551357i
$126$		0			0
$127$	3.78159	−	1.22871i	0.335562	−	0.109031i	−0.136389	−	0.990655i	$-0.543550\pi$
$127$	3.78159	−	1.22871i	0.335562	−	0.109031i	0.471951	+	0.881625i	$0.343550\pi$
$128$		0			0
$129$	−7.18342	+	5.21906i	−0.632465	+	0.459513i
$130$		0			0
$131$	−8.60768	−	6.25385i	−0.752057	−	0.546401i	0.144407	−	0.989518i	$-0.453873\pi$
$131$	−8.60768	−	6.25385i	−0.752057	−	0.546401i	−0.896464	+	0.443117i	$0.853873\pi$
$132$		0			0
$133$	4.06570	−	5.59596i	0.352541	−	0.485231i
$134$		0			0
$135$	4.86900	−	0.584612i	0.419057	−	0.0503154i
$136$		0			0
$137$	−10.7203	−	3.48323i	−0.915896	−	0.297593i	−0.187114	−	0.982338i	$-0.559913\pi$
$137$	−10.7203	−	3.48323i	−0.915896	−	0.297593i	−0.728782	+	0.684745i	$0.759913\pi$
$138$		0			0
$139$	1.12959	+	3.47652i	0.0958105	+	0.294874i	0.987464	−	0.157844i	$-0.0504543\pi$
$139$	1.12959	+	3.47652i	0.0958105	+	0.294874i	−0.891654	+	0.452718i	$0.850454\pi$
$140$		0			0
$141$	6.98640	−	21.5019i	0.588361	−	1.81079i
$142$		0			0
$143$		−	10.5532i		−	0.882502i
$144$		0			0
$145$	−11.8210	+	5.47375i	−0.981681	+	0.454570i
$146$		0			0
$147$	4.66758	+	6.42438i	0.384976	+	0.529874i
$148$		0			0
$149$	−8.64836			−0.708501			−0.354250	−	0.935151i	$-0.615264\pi$
$149$	−8.64836			−0.708501			−0.354250	+	0.935151i	$0.615264\pi$
$150$		0			0
$151$	−6.30755			−0.513301			−0.256650	−	0.966504i	$-0.582619\pi$
$151$	−6.30755			−0.513301			−0.256650	+	0.966504i	$0.582619\pi$
$152$		0			0
$153$	7.60323	+	10.4649i	0.614685	+	0.846041i
$154$		0			0
$155$	−10.2021	−	10.9994i	−0.819456	−	0.883489i
$156$		0			0
$157$			11.9460i			0.953395i	0.879067	+	0.476698i	$0.158166\pi$
$157$			11.9460i			0.953395i	−0.879067	+	0.476698i	$0.841834\pi$
$158$		0			0
$159$	2.90699	−	8.94679i	0.230539	−	0.709527i
$160$		0			0
$161$	0.546773	+	1.68279i	0.0430918	+	0.132623i
$162$		0			0
$163$	16.4856	+	5.35650i	1.29125	+	0.419553i	0.872530	−	0.488561i	$-0.162478\pi$
$163$	16.4856	+	5.35650i	1.29125	+	0.419553i	0.418723	+	0.908114i	$0.362478\pi$
$164$		0			0
$165$	−8.10000	+	7.51293i	−0.630584	+	0.584881i
$166$		0			0
$167$	4.09258	−	5.63295i	0.316693	−	0.435891i	−0.620761	−	0.784000i	$-0.713176\pi$
$167$	4.09258	−	5.63295i	0.316693	−	0.435891i	0.937454	+	0.348109i	$0.113176\pi$
$168$		0			0
$169$	8.01632	+	5.82419i	0.616640	+	0.448015i
$170$		0			0
$171$	6.08417	−	4.42041i	0.465268	−	0.338037i
$172$		0			0
$173$	−1.36718	+	0.444224i	−0.103945	+	0.0337737i	−0.360528	−	0.932749i	$-0.617403\pi$
$173$	−1.36718	+	0.444224i	−0.103945	+	0.0337737i	0.256583	+	0.966522i	$0.417403\pi$
$174$		0			0
$175$	−3.52824	+	8.59984i	−0.266710	+	0.650087i
$176$		0			0
$177$	−12.8603	+	4.17855i	−0.966636	+	0.314079i
$178$		0			0
$179$	−14.6030	+	10.6097i	−1.09148	+	0.793006i	−0.979648	−	0.200722i	$-0.935671\pi$
$179$	−14.6030	+	10.6097i	−1.09148	+	0.793006i	−0.111830	+	0.993727i	$0.535671\pi$
$180$		0			0
$181$	16.1239	+	11.7147i	1.19848	+	0.870745i	0.994134	−	0.108154i	$-0.0344941\pi$
$181$	16.1239	+	11.7147i	1.19848	+	0.870745i	0.204343	+	0.978899i	$0.434494\pi$
$182$		0			0
$183$	4.84411	−	6.66735i	0.358087	−	0.492864i
$184$		0			0
$185$	19.9027	+	11.1020i	1.46328	+	0.816236i
$186$		0			0
$187$	13.4197	+	4.36031i	0.981343	+	0.318858i
$188$		0			0
$189$	1.25993	+	3.87767i	0.0916465	+	0.282059i
$190$		0			0
$191$	−5.97693	+	18.3951i	−0.432476	+	1.33102i	0.463176	+	0.886266i	$0.346710\pi$
$191$	−5.97693	+	18.3951i	−0.432476	+	1.33102i	−0.895652	+	0.444756i	$0.853290\pi$
$192$		0			0
$193$		−	1.51392i		−	0.108974i	−0.998514	−	0.0544872i	$-0.982648\pi$
$193$		−	1.51392i		−	0.108974i	0.998514	−	0.0544872i	$-0.0173524\pi$
$194$		0			0
$195$	−2.85899	−	23.8114i	−0.204736	−	1.70517i
$196$		0			0
$197$	4.41595	+	6.07803i	0.314623	+	0.433042i	0.936816	−	0.349822i	$-0.113758\pi$
$197$	4.41595	+	6.07803i	0.314623	+	0.433042i	−0.622193	+	0.782864i	$0.713758\pi$
$198$		0			0
$199$	21.1916			1.50223			0.751117	−	0.660169i	$-0.229515\pi$
$199$	21.1916			1.50223			0.751117	+	0.660169i	$0.229515\pi$
$200$		0			0
$201$	32.2345			2.27365
$202$		0			0
$203$	−6.36610	−	8.76218i	−0.446812	−	0.614985i
$204$		0			0
$205$	−6.45072	+	11.5643i	−0.450538	+	0.807684i
$206$		0			0
$207$			1.92376i			0.133711i
$208$		0			0
$209$	2.53502	−	7.80199i	0.175351	−	0.539675i
$210$		0			0
$211$	1.83425	+	5.64523i	0.126275	+	0.388634i	0.994131	−	0.108181i	$-0.0345027\pi$
$211$	1.83425	+	5.64523i	0.126275	+	0.388634i	−0.867856	+	0.496815i	$0.834503\pi$
$212$		0			0
$213$	20.6137	+	6.69779i	1.41243	+	0.458925i
$214$		0			0
$215$	−1.71391	+	8.69301i	−0.116888	+	0.592859i
$216$		0			0
$217$	7.33151	−	10.0910i	0.497695	−	0.685019i
$218$		0			0
$219$	6.55142	+	4.75988i	0.442704	+	0.321643i
$220$		0			0
$221$	−24.7805	+	18.0041i	−1.66691	+	1.21108i
$222$		0			0
$223$	1.31652	−	0.427764i	0.0881609	−	0.0286452i	−0.264604	−	0.964357i	$-0.585241\pi$
$223$	1.31652	−	0.427764i	0.0881609	−	0.0286452i	0.352765	+	0.935712i	$0.385241\pi$
$224$		0			0
$225$	−6.53765	+	7.70708i	−0.435843	+	0.513806i
$226$		0			0
$227$	−9.45162	+	3.07102i	−0.627326	+	0.203831i	−0.605390	−	0.795929i	$-0.706983\pi$
$227$	−9.45162	+	3.07102i	−0.627326	+	0.203831i	−0.0219357	+	0.999759i	$0.506983\pi$
$228$		0			0
$229$	−11.6668	+	8.47640i	−0.770962	+	0.560136i	−0.902253	−	0.431207i	$-0.858088\pi$
$229$	−11.6668	+	8.47640i	−0.770962	+	0.560136i	0.131291	+	0.991344i	$0.458088\pi$
$230$		0			0
$231$	−7.43104	−	5.39897i	−0.488927	−	0.355226i
$232$		0			0
$233$	−7.85246	+	10.8080i	−0.514431	+	0.708054i	−0.984659	−	0.174491i	$-0.944172\pi$
$233$	−7.85246	+	10.8080i	−0.514431	+	0.708054i	0.470227	+	0.882545i	$0.344172\pi$
$234$		0			0
$235$	−9.47971	−	20.4722i	−0.618388	−	1.33546i
$236$		0			0
$237$	−24.0520	−	7.81495i	−1.56234	−	0.507636i
$238$		0			0
$239$	4.26572	+	13.1285i	0.275926	+	0.849213i	0.988973	+	0.148097i	$0.0473148\pi$
$239$	4.26572	+	13.1285i	0.275926	+	0.849213i	−0.713047	+	0.701117i	$0.752685\pi$
$240$		0			0
$241$	4.40966	−	13.5715i	0.284051	−	0.874219i	−0.702631	−	0.711555i	$-0.747991\pi$
$241$	4.40966	−	13.5715i	0.284051	−	0.874219i	0.986682	−	0.162664i	$-0.0520087\pi$
$242$		0			0
$243$			18.0210i			1.15605i
$244$		0			0
$245$	7.77445	+	1.53281i	0.496692	+	0.0979277i
$246$		0			0
$247$	10.4673	+	14.4070i	0.666018	+	0.916695i
$248$		0			0
$249$	15.5730			0.986902
$250$		0			0
$251$	−0.758323			−0.0478649			−0.0239325	−	0.999714i	$-0.507619\pi$
$251$	−0.758323			−0.0478649			−0.0239325	+	0.999714i	$0.507619\pi$
$252$		0			0
$253$	1.23346	+	1.69772i	0.0775471	+	0.106734i
$254$		0			0
$255$	31.4603	+	6.20271i	1.97012	+	0.388429i
$256$		0			0
$257$			15.3091i			0.954957i	0.878643	+	0.477478i	$0.158449\pi$
$257$			15.3091i			0.954957i	−0.878643	+	0.477478i	$0.841551\pi$
$258$		0			0
$259$	−5.85515	+	18.0203i	−0.363821	+	1.11973i
$260$		0			0
$261$	−3.63885	−	11.1992i	−0.225239	−	0.693214i
$262$		0			0
$263$	−12.8524	−	4.17599i	−0.792511	−	0.257502i	−0.115338	−	0.993326i	$-0.536795\pi$
$263$	−12.8524	−	4.17599i	−0.792511	−	0.257502i	−0.677173	+	0.735824i	$0.736795\pi$
$264$		0			0
$265$	−3.94443	−	8.51833i	−0.242305	−	0.523277i
$266$		0			0
$267$	13.7995	−	18.9934i	0.844516	−	1.16238i
$268$		0			0
$269$	−10.2780	−	7.46742i	−0.626662	−	0.455296i	0.228580	−	0.973525i	$-0.426592\pi$
$269$	−10.2780	−	7.46742i	−0.626662	−	0.455296i	−0.855242	+	0.518229i	$0.826592\pi$
$270$		0			0
$271$	−7.85337	+	5.70581i	−0.477058	+	0.346603i	−0.800186	−	0.599752i	$-0.795266\pi$
$271$	−7.85337	+	5.70581i	−0.477058	+	0.346603i	0.323127	+	0.946356i	$0.395266\pi$
$272$		0			0
$273$	18.9634	−	6.16157i	1.14771	−	0.372915i
$274$		0			0
$275$	−0.827891	+	10.9932i	−0.0499237	+	0.662917i
$276$		0			0
$277$	−4.87910	+	1.58532i	−0.293157	+	0.0952524i	−0.451903	−	0.892067i	$-0.649255\pi$
$277$	−4.87910	+	1.58532i	−0.293157	+	0.0952524i	0.158746	+	0.987319i	$0.449255\pi$
$278$		0			0
$279$	10.9713	−	7.97113i	0.656836	−	0.477219i
$280$		0			0
$281$	−20.1560	−	14.6442i	−1.20241	−	0.873599i	−0.207887	−	0.978153i	$-0.566659\pi$
$281$	−20.1560	−	14.6442i	−1.20241	−	0.873599i	−0.994519	+	0.104554i	$0.966659\pi$
$282$		0			0
$283$	−8.99734	+	12.3838i	−0.534836	+	0.736139i	−0.987858	−	0.155361i	$-0.950346\pi$
$283$	−8.99734	+	12.3838i	−0.534836	+	0.736139i	0.453021	+	0.891500i	$0.350346\pi$
$284$		0			0
$285$	3.60617	−	18.2906i	0.213611	−	1.08344i
$286$		0			0
$287$	−10.4705	−	3.40208i	−0.618055	−	0.200818i
$288$		0			0
$289$	−7.40239	−	22.7822i	−0.435435	−	1.34013i
$290$		0			0
$291$	−0.325005	+	1.00026i	−0.0190521	+	0.0586365i
$292$		0			0
$293$			14.5144i			0.847941i	0.905676	+	0.423971i	$0.139364\pi$
$293$			14.5144i			0.847941i	−0.905676	+	0.423971i	$0.860636\pi$
$294$		0			0
$295$	−6.57329	+	11.7840i	−0.382712	+	0.686093i
$296$		0			0
$297$	2.84227	+	3.91205i	0.164925	+	0.227000i
$298$		0			0
$299$	−4.55537			−0.263444
$300$		0			0
$301$	−7.36661			−0.424604
$302$		0			0
$303$	−1.33750	−	1.84091i	−0.0768371	−	0.105757i
$304$		0			0
$305$	−0.980375	−	8.16516i	−0.0561361	−	0.467536i
$306$		0			0
$307$		−	24.0722i		−	1.37387i	−0.726717	−	0.686937i	$-0.758955\pi$
$307$		−	24.0722i		−	1.37387i	0.726717	−	0.686937i	$-0.241045\pi$
$308$		0			0
$309$	11.4115	−	35.1209i	0.649176	−	1.99796i
$310$		0			0
$311$	2.30411	+	7.09133i	0.130654	+	0.402113i	0.994889	−	0.100977i	$-0.0321967\pi$
$311$	2.30411	+	7.09133i	0.130654	+	0.402113i	−0.864235	+	0.503089i	$0.832197\pi$
$312$		0			0
$313$	−1.21839	−	0.395878i	−0.0688672	−	0.0223763i	0.274381	−	0.961621i	$-0.411527\pi$
$313$	−1.21839	−	0.395878i	−0.0688672	−	0.0223763i	−0.343248	+	0.939245i	$0.611527\pi$
$314$		0			0
$315$	−7.33815	−	4.09332i	−0.413458	−	0.230633i
$316$		0			0
$317$	9.21939	−	12.6894i	0.517813	−	0.712708i	−0.467400	−	0.884046i	$-0.654809\pi$
$317$	9.21939	−	12.6894i	0.517813	−	0.712708i	0.985212	+	0.171338i	$0.0548091\pi$
$318$		0			0
$319$	−10.3919	−	7.55015i	−0.581834	−	0.422727i
$320$		0			0
$321$	−27.1766	+	19.7449i	−1.51685	+	1.10206i
$322$		0			0
$323$	−22.6451	+	7.35783i	−1.26000	+	0.409400i
$324$		0			0
$325$	−18.2500	−	15.4808i	−1.01233	−	0.858721i
$326$		0			0
$327$	−20.9506	+	6.80726i	−1.15857	+	0.376443i
$328$		0			0
$329$	15.1748	−	11.0251i	0.836613	−	0.607835i
$330$		0			0
$331$	−17.9852	−	13.0670i	−0.988557	−	0.718228i	−0.0289521	−	0.999581i	$-0.509217\pi$
$331$	−17.9852	−	13.0670i	−0.988557	−	0.718228i	−0.959605	+	0.281352i	$0.909217\pi$
$332$		0			0
$333$	−12.1088	+	16.6663i	−0.663558	+	0.913309i
$334$		0			0
$335$	23.5835	−	21.8742i	1.28850	−	1.19511i
$336$		0			0
$337$	−1.72123	−	0.559261i	−0.0937613	−	0.0304649i	0.261761	−	0.965133i	$-0.415697\pi$
$337$	−1.72123	−	0.559261i	−0.0937613	−	0.0304649i	−0.355522	+	0.934668i	$0.615697\pi$
$338$		0			0
$339$	−11.6181	−	35.7568i	−0.631009	−	1.94205i
$340$		0			0
$341$	4.57130	−	14.0690i	0.247550	−	0.761879i
$342$		0			0
$343$			19.6019i			1.05840i
$344$		0			0
$345$	3.24302	+	3.49643i	0.174598	+	0.188241i
$346$		0			0
$347$	12.8352	+	17.6661i	0.689030	+	0.948368i	0.999998	−	0.00205222i	$-0.000653241\pi$
$347$	12.8352	+	17.6661i	0.689030	+	0.948368i	−0.310968	+	0.950420i	$0.600653\pi$
$348$		0			0
$349$	10.7589			0.575909			0.287955	−	0.957644i	$-0.407025\pi$
$349$	10.7589			0.575909			0.287955	+	0.957644i	$0.407025\pi$
$350$		0			0
$351$	−10.4970			−0.560286
$352$		0			0
$353$	15.1356	+	20.8324i	0.805586	+	1.10879i	0.991989	+	0.126321i	$0.0403170\pi$
$353$	15.1356	+	20.8324i	0.805586	+	1.10879i	−0.186403	+	0.982473i	$0.559683\pi$
$354$		0			0
$355$	19.6265	−	9.08809i	1.04167	−	0.482346i
$356$		0			0
$357$			26.6600i			1.41100i
$358$		0			0
$359$	3.91090	−	12.0365i	0.206409	−	0.635263i	−0.793243	−	0.608905i	$-0.791609\pi$
$359$	3.91090	−	12.0365i	0.206409	−	0.635263i	0.999653	−	0.0263579i	$-0.00839095\pi$
$360$		0			0
$361$	−1.59359	−	4.90457i	−0.0838732	−	0.258135i
$362$		0			0
$363$	13.0821	+	4.25064i	0.686634	+	0.223101i
$364$		0			0
$365$	8.02319	−	0.963329i	0.419953	−	0.0504229i
$366$		0			0
$367$	6.61059	−	9.09869i	0.345070	−	0.474948i	−0.600844	−	0.799366i	$-0.705169\pi$
$367$	6.61059	−	9.09869i	0.345070	−	0.474948i	0.945914	+	0.324419i	$0.105169\pi$
$368$		0			0
$369$	−9.68381	−	7.03570i	−0.504119	−	0.366264i
$370$		0			0
$371$	6.31411	−	4.58747i	0.327812	−	0.238170i
$372$		0			0
$373$	7.66947	−	2.49196i	0.397110	−	0.129029i	−0.103652	−	0.994614i	$-0.533053\pi$
$373$	7.66947	−	2.49196i	0.397110	−	0.129029i	0.500763	+	0.865585i	$0.333053\pi$
$374$		0			0
$375$	1.11021	+	25.0285i	0.0573311	+	1.29247i
$376$		0			0
$377$	26.5192	−	8.61660i	1.36581	−	0.443778i
$378$		0			0
$379$	6.51391	−	4.73263i	0.334597	−	0.243099i	−0.407782	−	0.913079i	$-0.633698\pi$
$379$	6.51391	−	4.73263i	0.334597	−	0.243099i	0.742379	+	0.669980i	$0.233698\pi$
$380$		0			0
$381$	7.20831	+	5.23714i	0.369293	+	0.268307i
$382$		0			0
$383$	14.4091	−	19.8324i	0.736270	−	1.01339i	−0.262555	−	0.964917i	$-0.584565\pi$
$383$	14.4091	−	19.8324i	0.736270	−	1.01339i	0.998825	−	0.0484712i	$-0.0154349\pi$
$384$		0			0
$385$	−9.10042	+	1.09267i	−0.463801	+	0.0556876i
$386$		0			0
$387$	−7.61729	−	2.47501i	−0.387209	−	0.125812i
$388$		0			0
$389$	−0.720320	−	2.21692i	−0.0365217	−	0.112402i	0.931134	−	0.364678i	$-0.118821\pi$
$389$	−0.720320	−	2.21692i	−0.0365217	−	0.112402i	−0.967655	+	0.252276i	$0.918821\pi$
$390$		0			0
$391$	1.88216	−	5.79271i	0.0951852	−	0.292950i
$392$		0			0
$393$		−	23.8416i		−	1.20265i
$394$		0			0
$395$	−22.9001	+	10.6040i	−1.15223	+	0.533543i
$396$		0			0
$397$	−9.42301	−	12.9697i	−0.472927	−	0.650929i	0.504199	−	0.863587i	$-0.331788\pi$
$397$	−9.42301	−	12.9697i	−0.472927	−	0.650929i	−0.977127	+	0.212659i	$0.931788\pi$
$398$		0			0
$399$	15.4997			0.775957
$400$		0			0
$401$	−19.3238			−0.964984			−0.482492	−	0.875900i	$-0.660268\pi$
$401$	−19.3238			−0.964984			−0.482492	+	0.875900i	$0.660268\pi$
$402$		0			0
$403$	18.8752	+	25.9795i	0.940243	+	1.29413i
$404$		0			0
$405$	16.6937	+	17.9981i	0.829515	+	0.894334i
$406$		0			0
$407$			22.4718i			1.11389i
$408$		0			0
$409$	−11.9419	+	36.7534i	−0.590490	+	1.81734i	−0.0144830	+	0.999895i	$0.504610\pi$
$409$	−11.9419	+	36.7534i	−0.590490	+	1.81734i	−0.576007	+	0.817445i	$0.695390\pi$
$410$		0			0
$411$	−7.80531	−	24.0223i	−0.385008	−	1.18493i
$412$		0			0
$413$	−10.6695	−	3.46673i	−0.525011	−	0.170586i
$414$		0			0
$415$	11.3936	−	10.5678i	0.559288	−	0.518752i
$416$		0			0
$417$	−4.81465	+	6.62679i	−0.235774	+	0.324515i
$418$		0			0
$419$	−3.88236	−	2.82070i	−0.189666	−	0.137800i	0.488900	−	0.872340i	$-0.337398\pi$
$419$	−3.88236	−	2.82070i	−0.189666	−	0.137800i	−0.678566	+	0.734540i	$0.737398\pi$
$420$		0			0
$421$	−26.0151	+	18.9011i	−1.26790	+	0.921182i	−0.999117	−	0.0420195i	$-0.986621\pi$
$421$	−26.0151	+	18.9011i	−1.26790	+	0.921182i	−0.268781	+	0.963201i	$0.586621\pi$
$422$		0			0
$423$	19.3954	−	6.30193i	0.943035	−	0.306411i
$424$		0			0
$425$	27.2262	−	16.8108i	1.32066	−	0.815443i
$426$		0			0
$427$	6.50272	−	2.11286i	0.314689	−	0.102249i
$428$		0			0
$429$	19.1315	−	13.8998i	0.923678	−	0.671091i
$430$		0			0
$431$	−1.16017	−	0.842909i	−0.0558832	−	0.0406015i	0.559493	−	0.828835i	$-0.310996\pi$
$431$	−1.16017	−	0.842909i	−0.0558832	−	0.0406015i	−0.615376	+	0.788234i	$0.710996\pi$
$432$		0			0
$433$	0.854327	−	1.17588i	0.0410563	−	0.0565092i	−0.787995	−	0.615681i	$-0.788881\pi$
$433$	0.854327	−	1.17588i	0.0410563	−	0.0565092i	0.829052	+	0.559172i	$0.188881\pi$
$434$		0			0
$435$	−25.4929	−	14.2203i	−1.22229	−	0.681810i
$436$		0			0
$437$	−3.36779	−	1.09426i	−0.161103	−	0.0523457i
$438$		0			0
$439$	2.54098	+	7.82032i	0.121274	+	0.373244i	0.993204	−	0.116387i	$-0.0371314\pi$
$439$	2.54098	+	7.82032i	0.121274	+	0.373244i	−0.871930	+	0.489631i	$0.837131\pi$
$440$		0			0
$441$	−2.21348	+	6.81240i	−0.105404	+	0.324400i
$442$		0			0
$443$		−	22.7301i		−	1.07994i	−0.841684	−	0.539971i	$-0.818435\pi$
$443$		−	22.7301i		−	1.07994i	0.841684	−	0.539971i	$-0.181565\pi$
$444$		0			0
$445$	−2.79281	−	23.2602i	−0.132392	−	1.10264i
$446$		0			0
$447$	−11.3909	−	15.6783i	−0.538773	−	0.741558i
$448$		0			0
$449$	−5.30862			−0.250529			−0.125265	−	0.992123i	$-0.539978\pi$
$449$	−5.30862			−0.250529			−0.125265	+	0.992123i	$0.539978\pi$
$450$		0			0
$451$	−13.0570			−0.614832
$452$		0			0
$453$	−8.30781	−	11.4347i	−0.390335	−	0.537250i
$454$		0			0
$455$	9.69278	−	17.3764i	0.454405	−	0.814617i
$456$		0			0
$457$			25.3646i			1.18651i	0.805016	+	0.593253i	$0.202156\pi$
$457$			25.3646i			1.18651i	−0.805016	+	0.593253i	$0.797844\pi$
$458$		0			0
$459$	4.33708	−	13.3481i	0.202437	−	0.623038i
$460$		0			0
$461$	7.82214	+	24.0741i	0.364314	+	1.12124i	0.950410	+	0.311000i	$0.100664\pi$
$461$	7.82214	+	24.0741i	0.364314	+	1.12124i	−0.586096	+	0.810241i	$0.699336\pi$
$462$		0			0
$463$	30.8240	+	10.0153i	1.43251	+	0.465452i	0.919555	−	0.392962i	$-0.128550\pi$
$463$	30.8240	+	10.0153i	1.43251	+	0.465452i	0.512958	+	0.858414i	$0.328550\pi$
$464$		0			0
$465$	6.50285	−	32.9826i	0.301562	−	1.52953i
$466$		0			0
$467$	−13.9120	+	19.1483i	−0.643773	+	0.886077i	−0.998810	−	0.0487749i	$-0.984468\pi$
$467$	−13.9120	+	19.1483i	−0.643773	+	0.886077i	0.355037	+	0.934852i	$0.384468\pi$
$468$		0			0
$469$	21.6358	+	15.7193i	0.999048	+	0.725851i
$470$		0			0
$471$	−21.6565	+	15.7344i	−0.997878	+	0.725001i
$472$		0			0
$473$	−8.30914	+	2.69980i	−0.382055	+	0.124137i
$474$		0			0
$475$	−9.77354	−	15.8289i	−0.448441	−	0.726279i
$476$		0			0
$477$	8.07026	−	2.62219i	0.369512	−	0.120062i
$478$		0			0
$479$	25.7721	−	18.7245i	1.17756	−	0.855546i	0.185664	−	0.982613i	$-0.440556\pi$
$479$	25.7721	−	18.7245i	1.17756	−	0.855546i	0.991894	+	0.127067i	$0.0405565\pi$
$480$		0			0
$481$	−39.4650	−	28.6730i	−1.79945	−	1.30738i
$482$		0			0
$483$	−2.33051	+	3.20767i	−0.106042	+	0.145954i
$484$		0			0
$485$	0.440993	+	0.952360i	0.0200245	+	0.0432445i
$486$		0			0
$487$	−10.7893	−	3.50567i	−0.488912	−	0.158857i	0.0541786	−	0.998531i	$-0.482746\pi$
$487$	−10.7893	−	3.50567i	−0.488912	−	0.158857i	−0.543091	+	0.839674i	$0.682746\pi$
$488$		0			0
$489$	12.0030	+	36.9413i	0.542793	+	1.67054i
$490$		0			0
$491$	8.29887	−	25.5413i	0.374523	−	1.15266i	−0.569277	−	0.822146i	$-0.692777\pi$
$491$	8.29887	−	25.5413i	0.374523	−	1.15266i	0.943800	−	0.330517i	$-0.107223\pi$
$492$		0			0
$493$			37.2825i			1.67912i
$494$		0			0
$495$	−9.77722	−	1.92768i	−0.439453	−	0.0866426i
$496$		0			0
$497$	10.5697	+	14.5479i	0.474114	+	0.652563i
$498$		0			0
$499$	−36.3336			−1.62651			−0.813257	−	0.581904i	$-0.802308\pi$
$499$	−36.3336			−1.62651			−0.813257	+	0.581904i	$0.802308\pi$
$500$		0			0
$501$	15.6022			0.697055
$502$		0			0
$503$	−2.99740	−	4.12557i	−0.133648	−	0.183950i	0.736948	−	0.675949i	$-0.236266\pi$
$503$	−2.99740	−	4.12557i	−0.133648	−	0.183950i	−0.870596	+	0.491999i	$0.836266\pi$
$504$		0			0
$505$	−2.22777	−	0.439227i	−0.0991344	−	0.0195453i
$506$		0			0
$507$			22.2037i			0.986099i
$508$		0			0
$509$	−4.80173	+	14.7782i	−0.212833	+	0.655032i	0.786468	+	0.617631i	$0.211908\pi$
$509$	−4.80173	+	14.7782i	−0.212833	+	0.655032i	−0.999300	+	0.0374003i	$0.988092\pi$
$510$		0			0
$511$	2.07613	+	6.38966i	0.0918424	+	0.282662i
$512$		0			0
$513$	−7.76042	−	2.52151i	−0.342631	−	0.111327i
$514$		0			0
$515$	−15.4840	−	33.4390i	−0.682306	−	1.47350i
$516$		0			0
$517$	13.0757	−	17.9972i	0.575070	−	0.791516i
$518$		0			0
$519$	−2.60606	−	1.89341i	−0.114393	−	0.0831116i
$520$		0			0
$521$	7.86009	−	5.71069i	0.344357	−	0.250190i	−0.402141	−	0.915578i	$-0.631734\pi$
$521$	7.86009	−	5.71069i	0.344357	−	0.250190i	0.746498	+	0.665388i	$0.231734\pi$
$522$		0			0
$523$	−2.08311	+	0.676843i	−0.0910880	+	0.0295963i	−0.354206	−	0.935167i	$-0.615249\pi$
$523$	−2.08311	+	0.676843i	−0.0910880	+	0.0295963i	0.263118	+	0.964764i	$0.415249\pi$
$524$		0			0
$525$	−20.2375	+	4.93083i	−0.883235	+	0.215199i
$526$		0			0
$527$	−40.8349	+	13.2681i	−1.77880	+	0.577966i
$528$		0			0
$529$	−17.8746	+	12.9866i	−0.777155	+	0.564636i
$530$		0			0
$531$	−9.86783	−	7.16940i	−0.428227	−	0.311125i
$532$		0			0
$533$	16.6602	−	22.9308i	0.721633	−	0.993242i
$534$		0			0
$535$	−6.48414	+	32.8877i	−0.280334	+	1.42186i
$536$		0			0
$537$	−38.4679	−	12.4990i	−1.66001	−	0.539370i
$538$		0			0
$539$	2.41453	+	7.43115i	0.104001	+	0.320082i
$540$		0			0
$541$	13.5299	−	41.6406i	0.581694	−	1.79027i	−0.0304661	−	0.999536i	$-0.509699\pi$
$541$	13.5299	−	41.6406i	0.581694	−	1.79027i	0.612160	−	0.790734i	$-0.290301\pi$
$542$		0			0
$543$			44.6600i			1.91655i
$544$		0			0
$545$	−10.7085	+	19.1973i	−0.458703	+	0.822323i
$546$		0			0
$547$	16.5184	+	22.7356i	0.706275	+	0.972104i	0.999869	+	0.0161740i	$0.00514857\pi$
$547$	16.5184	+	22.7356i	0.706275	+	0.972104i	−0.293594	+	0.955930i	$0.594851\pi$
$548$		0			0
$549$	7.43388			0.317270
$550$		0			0
$551$	21.6755			0.923407
$552$		0			0
$553$	−12.3326	−	16.9744i	−0.524438	−	0.721826i
$554$		0			0
$555$	6.08788	+	50.7036i	0.258416	+	2.15225i
$556$		0			0
$557$		−	24.1061i		−	1.02141i	−0.859757	−	0.510703i	$-0.829385\pi$
$557$		−	24.1061i		−	1.02141i	0.859757	−	0.510703i	$-0.170615\pi$
$558$		0			0
$559$	5.86069	−	18.0374i	0.247881	−	0.762899i
$560$		0			0
$561$	9.77068	+	30.0711i	0.412519	+	1.26960i
$562$		0			0
$563$	27.4814	+	8.92924i	1.15820	+	0.376323i	0.824227	−	0.566259i	$-0.191610\pi$
$563$	27.4814	+	8.92924i	1.15820	+	0.376323i	0.333975	+	0.942582i	$0.391610\pi$
$564$		0			0
$565$	−32.7645	−	18.2765i	−1.37841	−	0.768897i
$566$		0			0
$567$	−11.9965	+	16.5117i	−0.503804	+	0.693427i
$568$		0			0
$569$	0.0640223	+	0.0465149i	0.00268395	+	0.00195001i	0.589126	−	0.808041i	$-0.299472\pi$
$569$	0.0640223	+	0.0465149i	0.00268395	+	0.00195001i	−0.586442	+	0.809991i	$0.699472\pi$
$570$		0			0
$571$	22.3019	−	16.2033i	0.933307	−	0.678088i	−0.0134930	−	0.999909i	$-0.504295\pi$
$571$	22.3019	−	16.2033i	0.933307	−	0.678088i	0.946800	+	0.321821i	$0.104295\pi$
$572$		0			0
$573$	−41.2202	+	13.3932i	−1.72200	+	0.559511i
$574$		0			0
$575$	4.74532	+	0.357366i	0.197894	+	0.0149032i
$576$		0			0
$577$	13.8267	−	4.49258i	0.575615	−	0.187029i	−0.00672030	−	0.999977i	$-0.502139\pi$
$577$	13.8267	−	4.49258i	0.575615	−	0.187029i	0.582335	+	0.812949i	$0.302139\pi$
$578$		0			0
$579$	2.74453	−	1.99402i	0.114059	−	0.0828686i
$580$		0			0
$581$	10.4526	+	7.59427i	0.433647	+	0.315063i
$582$		0			0
$583$	5.44071	−	7.48850i	0.225331	−	0.310142i
$584$		0			0
$585$	15.8607	−	14.7111i	0.655759	−	0.608231i
$586$		0			0
$587$	−20.0294	−	6.50795i	−0.826702	−	0.268612i	−0.135046	−	0.990839i	$-0.543118\pi$
$587$	−20.0294	−	6.50795i	−0.826702	−	0.268612i	−0.691656	+	0.722227i	$0.743118\pi$
$588$		0			0
$589$	7.71385	+	23.7408i	0.317844	+	0.978223i
$590$		0			0
$591$	−5.20230	+	16.0110i	−0.213994	+	0.658605i
$592$		0			0
$593$		−	19.9763i		−	0.820328i	−0.912012	−	0.410164i	$-0.865471\pi$
$593$		−	19.9763i		−	0.820328i	0.912012	−	0.410164i	$-0.134529\pi$
$594$		0			0
$595$	18.0913	+	19.5050i	0.741673	+	0.799628i
$596$		0			0
$597$	27.9120	+	38.4175i	1.14236	+	1.57232i
$598$		0			0
$599$	33.0408			1.35001			0.675005	−	0.737813i	$-0.264141\pi$
$599$	33.0408			1.35001			0.675005	+	0.737813i	$0.264141\pi$
$600$		0			0
$601$	6.72970			0.274510			0.137255	−	0.990536i	$-0.456172\pi$
$601$	6.72970			0.274510			0.137255	+	0.990536i	$0.456172\pi$
$602$		0			0
$603$	17.0907	+	23.5234i	0.695988	+	0.957945i
$604$		0			0
$605$	12.4556	−	5.76761i	0.506393	−	0.234487i
$606$		0			0
$607$		−	4.56961i		−	0.185475i	−0.995691	−	0.0927374i	$-0.970438\pi$
$607$		−	4.56961i		−	0.185475i	0.995691	−	0.0927374i	$-0.0295617\pi$
$608$		0			0
$609$	7.49971	−	23.0817i	0.303904	−	0.935319i
$610$		0			0
$611$	14.9227	+	45.9272i	0.603706	+	1.85802i
$612$		0			0
$613$	21.3226	+	6.92814i	0.861213	+	0.279825i	0.706135	−	0.708077i	$-0.250437\pi$
$613$	21.3226	+	6.92814i	0.861213	+	0.279825i	0.155078	+	0.987902i	$0.450437\pi$
$614$		0			0
$615$	−29.4608	+	3.53731i	−1.18798	+	0.142638i
$616$		0			0
$617$	−5.49011	+	7.55649i	−0.221023	+	0.304213i	−0.905101	−	0.425197i	$-0.860205\pi$
$617$	−5.49011	+	7.55649i	−0.221023	+	0.304213i	0.684078	+	0.729409i	$0.260205\pi$
$618$		0			0
$619$	12.9673	+	9.42126i	0.521198	+	0.378673i	0.817055	−	0.576560i	$-0.195605\pi$
$619$	12.9673	+	9.42126i	0.521198	+	0.378673i	−0.295857	+	0.955232i	$0.595605\pi$
$620$		0			0
$621$	1.68867	−	1.22689i	0.0677639	−	0.0492334i
$622$		0			0
$623$	18.5244	−	6.01895i	0.742166	−	0.241144i
$624$		0			0
$625$	17.7965	+	17.5580i	0.711860	+	0.702321i
$626$		0			0
$627$	17.4829	−	5.68053i	0.698199	−	0.226859i
$628$		0			0
$629$	52.7672	−	38.3376i	2.10396	−	1.52862i
$630$		0			0
$631$	0.205708	+	0.149456i	0.00818912	+	0.00594975i	0.591872	−	0.806032i	$-0.298389\pi$
$631$	0.205708	+	0.149456i	0.00818912	+	0.00594975i	−0.583683	+	0.811982i	$0.698389\pi$
$632$		0			0
$633$	−7.81811	+	10.7607i	−0.310742	+	0.427699i
$634$		0			0
$635$	8.82765	−	1.05992i	0.350314	−	0.0420616i
$636$		0			0
$637$	−16.1314	−	5.24141i	−0.639150	−	0.207672i
$638$		0			0
$639$	6.04160	+	18.5941i	0.239002	+	0.735572i
$640$		0			0
$641$	−14.0339	+	43.1918i	−0.554305	+	1.70598i	0.143467	+	0.989655i	$0.454175\pi$
$641$	−14.0339	+	43.1918i	−0.554305	+	1.70598i	−0.697772	+	0.716320i	$0.745825\pi$
$642$		0			0
$643$		−	7.01215i		−	0.276532i	−0.990395	−	0.138266i	$-0.955847\pi$
$643$		−	7.01215i		−	0.276532i	0.990395	−	0.138266i	$-0.0441529\pi$
$644$		0			0
$645$	−18.0167	+	8.34267i	−0.709406	+	0.328492i
$646$		0			0
$647$	7.34966	+	10.1159i	0.288945	+	0.397698i	0.928671	−	0.370904i	$-0.120952\pi$
$647$	7.34966	+	10.1159i	0.288945	+	0.397698i	−0.639726	+	0.768603i	$0.720952\pi$
$648$		0			0
$649$	−13.3051			−0.522273
$650$		0			0
$651$	27.9500			1.09545
$652$		0			0
$653$	11.0961	+	15.2725i	0.434224	+	0.597658i	0.968916	−	0.247389i	$-0.0795725\pi$
$653$	11.0961	+	15.2725i	0.434224	+	0.597658i	−0.534692	+	0.845047i	$0.679572\pi$
$654$		0			0
$655$	−16.1788	−	17.4430i	−0.632159	−	0.681556i
$656$		0			0
$657$			7.30463i			0.284981i
$658$		0			0
$659$	−7.82961	+	24.0971i	−0.304998	+	0.938689i	0.674679	+	0.738111i	$0.264282\pi$
$659$	−7.82961	+	24.0971i	−0.304998	+	0.938689i	−0.979678	+	0.200578i	$0.935718\pi$
$660$		0			0
$661$	2.51468	+	7.73937i	0.0978095	+	0.301027i	0.987976	−	0.154609i	$-0.0494119\pi$
$661$	2.51468	+	7.73937i	0.0978095	+	0.301027i	−0.890166	+	0.455636i	$0.849412\pi$
$662$		0			0
$663$	−65.2778	−	21.2101i	−2.53518	−	0.823730i
$664$		0			0
$665$	11.3399	−	10.5180i	0.439744	−	0.407872i
$666$		0			0
$667$	−3.25909	+	4.48575i	−0.126192	+	0.173689i
$668$		0			0
$669$	2.50950	+	1.82326i	0.0970229	+	0.0704912i
$670$		0			0
$671$	6.56038	−	4.76640i	0.253261	−	0.184005i
$672$		0			0
$673$	41.5233	−	13.4917i	1.60061	−	0.520069i	0.633349	−	0.773866i	$-0.281680\pi$
$673$	41.5233	−	13.4917i	1.60061	−	0.520069i	0.967257	+	0.253798i	$0.0816797\pi$
$674$		0			0
$675$	10.9347	+	0.823479i	0.420875	+	0.0316957i
$676$		0			0
$677$	−23.5415	+	7.64908i	−0.904772	+	0.293978i	−0.724205	−	0.689585i	$-0.757793\pi$
$677$	−23.5415	+	7.64908i	−0.904772	+	0.293978i	−0.180567	+	0.983563i	$0.557793\pi$
$678$		0			0
$679$	−0.705926	+	0.512885i	−0.0270910	+	0.0196827i
$680$		0			0
$681$	−18.0163	−	13.0896i	−0.690385	−	0.501594i
$682$		0			0
$683$	−11.0504	+	15.2095i	−0.422830	+	0.581976i	−0.966289	−	0.257460i	$-0.917114\pi$
$683$	−11.0504	+	15.2095i	−0.422830	+	0.581976i	0.543459	+	0.839436i	$0.317114\pi$
$684$		0			0
$685$	−22.0119	−	12.2786i	−0.841032	−	0.469140i
$686$		0			0
$687$	−30.7331	−	9.98580i	−1.17254	−	0.380982i
$688$		0			0
$689$	6.20921	+	19.1100i	0.236552	+	0.728032i
$690$		0			0
$691$	9.31610	−	28.6720i	0.354401	−	1.09073i	−0.601955	−	0.798530i	$-0.705611\pi$
$691$	9.31610	−	28.6720i	0.354401	−	1.09073i	0.956356	−	0.292204i	$-0.0943887\pi$
$692$		0			0
$693$		−	8.28538i		−	0.314736i
$694$		0			0
$695$	0.974412	+	8.11549i	0.0369615	+	0.307838i
$696$		0			0
$697$	22.2757	+	30.6599i	0.843752	+	1.16132i
$698$		0			0
$699$	−29.9360			−1.13228
$700$		0			0
$701$	−5.93443			−0.224140			−0.112070	−	0.993700i	$-0.535748\pi$
$701$	−5.93443			−0.224140			−0.112070	+	0.993700i	$0.535748\pi$
$702$		0			0
$703$	−22.2889	−	30.6781i	−0.840642	−	1.15704i
$704$		0			0
$705$	24.6274	−	44.1498i	0.927521	−	1.66278i
$706$		0			0
$707$		−	1.88785i		−	0.0709999i
$708$		0			0
$709$	−2.05638	+	6.32887i	−0.0772288	+	0.237686i	−0.982216	−	0.187752i	$-0.939880\pi$
$709$	−2.05638	+	6.32887i	−0.0772288	+	0.237686i	0.904988	+	0.425438i	$0.139880\pi$
$710$		0			0
$711$	−7.04931	−	21.6956i	−0.264370	−	0.813647i
$712$		0			0
$713$	−6.07300	−	1.97324i	−0.227436	−	0.0738983i
$714$		0			0
$715$	4.56464	−	23.1520i	0.170708	−	0.865834i
$716$		0			0
$717$	−18.1818	+	25.0250i	−0.679010	+	0.934577i
$718$		0			0
$719$	−15.0272	−	10.9179i	−0.560420	−	0.407169i	0.271192	−	0.962525i	$-0.412582\pi$
$719$	−15.0272	−	10.9179i	−0.560420	−	0.407169i	−0.831613	+	0.555356i	$0.812582\pi$
$720$		0			0
$721$	24.7862	−	18.0083i	0.923088	−	0.670662i
$722$		0			0
$723$	30.4114	−	9.88126i	1.13101	−	0.367488i
$724$		0			0
$725$	−28.3009	+	6.89548i	−1.05107	+	0.256092i
$726$		0			0
$727$	35.3130	−	11.4739i	1.30969	−	0.425543i	0.430746	−	0.902473i	$-0.358250\pi$
$727$	35.3130	−	11.4739i	1.30969	−	0.425543i	0.878942	+	0.476930i	$0.158250\pi$
$728$		0			0
$729$	−6.02475	+	4.37724i	−0.223139	+	0.162120i
$730$		0			0
$731$	20.5152	+	14.9052i	0.758782	+	0.551287i
$732$		0			0
$733$	14.6472	−	20.1602i	0.541008	−	0.744634i	−0.447750	−	0.894159i	$-0.647774\pi$
$733$	14.6472	−	20.1602i	0.541008	−	0.744634i	0.988758	+	0.149525i	$0.0477744\pi$
$734$		0			0
$735$	7.46113	+	16.1129i	0.275208	+	0.594334i
$736$		0			0
$737$	30.1650	+	9.80121i	1.11114	+	0.361032i
$738$		0			0
$739$	12.3983	+	38.1581i	0.456080	+	1.40367i	0.869862	+	0.493294i	$0.164207\pi$
$739$	12.3983	+	38.1581i	0.456080	+	1.40367i	−0.413782	+	0.910376i	$0.635793\pi$
$740$		0			0
$741$	−12.3312	+	37.9516i	−0.452998	+	1.39419i
$742$		0			0
$743$		−	31.3057i		−	1.14850i	−0.818681	−	0.574248i	$-0.805295\pi$
$743$		−	31.3057i		−	1.14850i	0.818681	−	0.574248i	$-0.194705\pi$
$744$		0			0
$745$	−18.9731	−	3.74073i	−0.695119	−	0.137050i
$746$		0			0
$747$	8.25681	+	11.3645i	0.302101	+	0.415806i
$748$		0			0
$749$	−27.8696			−1.01833
$750$		0			0
$751$	8.67841			0.316680			0.158340	−	0.987385i	$-0.449386\pi$
$751$	8.67841			0.316680			0.158340	+	0.987385i	$0.449386\pi$
$752$		0			0
$753$	−0.998805	−	1.37474i	−0.0363985	−	0.0500982i
$754$		0			0
$755$	−13.8377	−	2.72824i	−0.503606	−	0.0992909i
$756$		0			0
$757$		−	27.9929i		−	1.01742i	−0.860938	−	0.508709i	$-0.830123\pi$
$757$		−	27.9929i		−	1.01742i	0.860938	−	0.508709i	$-0.169877\pi$
$758$		0			0
$759$	−1.45311	+	4.47220i	−0.0527444	+	0.162331i
$760$		0			0
$761$	−7.51220	−	23.1202i	−0.272317	−	0.838106i	−0.989917	−	0.141650i	$-0.954759\pi$
$761$	−7.51220	−	23.1202i	−0.272317	−	0.838106i	0.717600	−	0.696456i	$-0.245241\pi$
$762$		0			0
$763$	−17.3816	−	5.64763i	−0.629257	−	0.204458i
$764$		0			0
$765$	12.1538	+	26.2470i	0.439420	+	0.948964i
$766$		0			0
$767$	16.9768	−	23.3665i	0.612996	−	0.843716i
$768$		0			0
$769$	4.52205	+	3.28546i	0.163069	+	0.118477i	0.666327	−	0.745660i	$-0.267865\pi$
$769$	4.52205	+	3.28546i	0.163069	+	0.118477i	−0.503258	+	0.864136i	$0.667865\pi$
$770$		0			0
$771$	−27.7534	+	20.1640i	−0.999513	+	0.726188i
$772$		0			0
$773$	−3.24785	+	1.05529i	−0.116817	+	0.0379562i	−0.366842	−	0.930283i	$-0.619561\pi$
$773$	−3.24785	+	1.05529i	−0.116817	+	0.0379562i	0.250025	+	0.968239i	$0.419561\pi$
$774$		0			0
$775$	−17.6242	−	28.5436i	−0.633080	−	1.02532i
$776$		0			0
$777$	−40.3803	+	13.1204i	−1.44864	+	0.470690i
$778$		0			0
$779$	17.8252	−	12.9508i	0.638654	−	0.464009i
$780$		0			0
$781$	17.2537	+	12.5356i	0.617387	+	0.448558i
$782$		0			0
$783$	−7.50992	+	10.3365i	−0.268383	+	0.369397i
$784$		0			0
$785$	−5.16708	+	26.2076i	−0.184421	+	0.935388i
$786$		0			0
$787$	−45.8378	−	14.8936i	−1.63394	−	0.530899i	−0.658768	−	0.752346i	$-0.728922\pi$
$787$	−45.8378	−	14.8936i	−1.63394	−	0.530899i	−0.975172	+	0.221447i	$0.928922\pi$
$788$		0			0
$789$	−9.35764	−	28.7999i	−0.333141	−	1.02530i
$790$		0			0
$791$	9.63893	−	29.6656i	0.342721	−	1.05479i
$792$		0			0
$793$			17.6031i			0.625103i
$794$		0			0
$795$	10.2473	−	18.3704i	0.363433	−	0.651531i
$796$		0			0
$797$	−6.10087	−	8.39713i	−0.216104	−	0.297442i	0.687178	−	0.726489i	$-0.258849\pi$
$797$	−6.10087	−	8.39713i	−0.216104	−	0.297442i	−0.903282	+	0.429048i	$0.858849\pi$
$798$		0			0
$799$	−64.5677			−2.28424
$800$		0			0
$801$	21.1770			0.748254
$802$		0			0
$803$	4.68352	+	6.44631i	0.165278	+	0.227485i
$804$		0			0
$805$	0.471660	+	3.92827i	0.0166238	+	0.138453i
$806$		0			0
$807$		−	28.4681i		−	1.00213i
$808$		0			0
$809$	4.30668	−	13.2546i	0.151415	−	0.466007i	−0.846365	−	0.532603i	$-0.821214\pi$
$809$	4.30668	−	13.2546i	0.151415	−	0.466007i	0.997780	+	0.0665959i	$0.0212138\pi$
$810$		0			0
$811$	−3.49190	−	10.7470i	−0.122617	−	0.377377i	0.870842	−	0.491563i	$-0.163574\pi$
$811$	−3.49190	−	10.7470i	−0.122617	−	0.377377i	−0.993459	+	0.114186i	$0.963574\pi$
$812$		0			0
$813$	−20.6877	−	6.72184i	−0.725550	−	0.235745i
$814$		0			0
$815$	33.8498	+	18.8819i	1.18571	+	0.661404i
$816$		0			0
$817$	8.66564	−	11.9272i	0.303172	−	0.417281i
$818$		0			0
$819$	14.5508	+	10.5718i	0.508446	+	0.369408i
$820$		0			0
$821$	19.6322	−	14.2636i	0.685169	−	0.497805i	−0.189899	−	0.981804i	$-0.560816\pi$
$821$	19.6322	−	14.2636i	0.685169	−	0.497805i	0.875069	+	0.483999i	$0.160816\pi$
$822$		0			0
$823$	1.00113	−	0.325286i	0.0348971	−	0.0113387i	−0.291516	−	0.956566i	$-0.594160\pi$
$823$	1.00113	−	0.325286i	0.0348971	−	0.0113387i	0.326414	+	0.945227i	$0.394160\pi$
$824$		0			0
$825$	−21.0197	+	12.9786i	−0.731811	+	0.451856i
$826$		0			0
$827$	30.3729	−	9.86874i	1.05617	−	0.343170i	0.271082	−	0.962556i	$-0.412619\pi$
$827$	30.3729	−	9.86874i	1.05617	−	0.343170i	0.785086	+	0.619387i	$0.212619\pi$
$828$		0			0
$829$	−23.5676	+	17.1229i	−0.818536	+	0.594701i	−0.916293	−	0.400509i	$-0.868833\pi$
$829$	−23.5676	+	17.1229i	−0.818536	+	0.594701i	0.0977566	+	0.995210i	$0.468833\pi$
$830$		0			0
$831$	−9.30034	−	6.75709i	−0.322625	−	0.234401i
$832$		0			0
$833$	13.3302	−	18.3474i	0.461863	−	0.635700i
$834$		0			0
$835$	11.4149	−	10.5876i	0.395029	−	0.366398i
$836$		0			0
$837$	−13.9940	−	4.54694i	−0.483705	−	0.157165i
$838$		0			0
$839$	3.70912	+	11.4155i	0.128053	+	0.394107i	0.994445	−	0.105258i	$-0.0335667\pi$
$839$	3.70912	+	11.4155i	0.128053	+	0.394107i	−0.866392	+	0.499365i	$0.833567\pi$
$840$		0			0
$841$	1.52643	−	4.69786i	0.0526354	−	0.161995i
$842$		0			0
$843$		−	55.8283i		−	1.92283i
$844$		0			0
$845$	15.0673	+	16.2447i	0.518331	+	0.558834i
$846$		0			0
$847$	6.70787	+	9.23259i	0.230485	+	0.317236i
$848$		0			0
$849$	−34.3007			−1.17720
$850$		0			0
$851$	9.70015			0.332517
$852$		0			0
$853$	−4.02243	−	5.53640i	−0.137725	−	0.189563i	0.734583	−	0.678519i	$-0.237378\pi$
$853$	−4.02243	−	5.53640i	−0.137725	−	0.189563i	−0.872308	+	0.488956i	$0.837378\pi$
$854$		0			0
$855$	15.2596	−	7.06602i	0.521869	−	0.241653i
$856$		0			0
$857$		−	51.2474i		−	1.75058i	−0.483601	−	0.875289i	$-0.660671\pi$
$857$		−	51.2474i		−	1.75058i	0.483601	−	0.875289i	$-0.339329\pi$
$858$		0			0
$859$	4.14366	−	12.7529i	0.141380	−	0.435123i	−0.855148	−	0.518384i	$-0.826534\pi$
$859$	4.14366	−	12.7529i	0.141380	−	0.435123i	0.996528	+	0.0832616i	$0.0265337\pi$
$860$		0			0
$861$	−7.62346	−	23.4626i	−0.259807	−	0.799603i
$862$		0			0
$863$	−12.3753	−	4.02097i	−0.421260	−	0.136876i	0.0907135	−	0.995877i	$-0.471085\pi$
$863$	−12.3753	−	4.02097i	−0.421260	−	0.136876i	−0.511973	+	0.859001i	$0.671085\pi$
$864$		0			0
$865$	−3.19151	+	0.383198i	−0.108515	+	0.0130291i
$866$		0			0
$867$	31.5512	−	43.4265i	1.07153	−	1.47484i
$868$		0			0
$869$	−20.1316	−	14.6264i	−0.682917	−	0.496168i
$870$		0			0
$871$	−55.7021	+	40.4700i	−1.88739	+	1.37127i
$872$		0			0
$873$	−0.902266	+	0.293164i	−0.0305371	+	0.00992210i
$874$		0			0
$875$	−11.4601	+	17.3405i	−0.387423	+	0.586217i
$876$		0			0
$877$	19.0208	−	6.18024i	0.642288	−	0.208692i	0.0302772	−	0.999542i	$-0.490361\pi$
$877$	19.0208	−	6.18024i	0.642288	−	0.208692i	0.612011	+	0.790850i	$0.290361\pi$
$878$		0			0
$879$	−26.3127	+	19.1173i	−0.887504	+	0.644809i
$880$		0			0
$881$	−15.3624	−	11.1614i	−0.517572	−	0.376038i	0.298116	−	0.954530i	$-0.403642\pi$
$881$	−15.3624	−	11.1614i	−0.517572	−	0.376038i	−0.815689	+	0.578491i	$0.803642\pi$
$882$		0			0
$883$	−16.1290	+	22.1997i	−0.542784	+	0.747078i	−0.989011	−	0.147842i	$-0.952767\pi$
$883$	−16.1290	+	22.1997i	−0.542784	+	0.747078i	0.446227	+	0.894920i	$0.352767\pi$
$884$		0			0
$885$	−30.0207	+	3.60452i	−1.00913	+	0.121165i
$886$		0			0
$887$	0.524691	+	0.170483i	0.0176174	+	0.00572424i	0.317812	−	0.948154i	$-0.397052\pi$
$887$	0.524691	+	0.170483i	0.0176174	+	0.00572424i	−0.300195	+	0.953878i	$0.597052\pi$
$888$		0			0
$889$	2.28429	+	7.03033i	0.0766127	+	0.235790i
$890$		0			0
$891$	−7.47996	+	23.0210i	−0.250588	+	0.771231i
$892$		0			0
$893$			37.5387i			1.25618i
$894$		0			0
$895$	−36.6256	+	16.9596i	−1.22426	+	0.566897i
$896$		0			0
$897$	−5.99999	−	8.25827i	−0.200334	−	0.275736i
$898$		0			0
$899$	39.0865			1.30361
$900$		0			0
$901$	−26.8661			−0.895040
$902$		0			0
$903$	−9.70272	−	13.3547i	−0.322886	−	0.444415i
$904$		0			0
$905$	30.3061	+	32.6742i	1.00741	+	1.08613i
$906$		0			0
$907$			25.7362i			0.854556i	0.904120	+	0.427278i	$0.140527\pi$
$907$			25.7362i			0.854556i	−0.904120	+	0.427278i	$0.859473\pi$
$908$		0			0
$909$	0.634273	−	1.95209i	0.0210375	−	0.0647468i
$910$		0			0
$911$	−2.28613	−	7.03599i	−0.0757429	−	0.233113i	0.906016	−	0.423244i	$-0.139109\pi$
$911$	−2.28613	−	7.03599i	−0.0757429	−	0.233113i	−0.981759	+	0.190131i	$0.939109\pi$
$912$		0			0
$913$	14.5732	+	4.73513i	0.482304	+	0.156710i
$914$		0			0
$915$	13.5110	−	12.5318i	0.446661	−	0.414289i
$916$		0			0
$917$	11.6265	−	16.0025i	0.383940	−	0.528449i
$918$		0			0
$919$	−44.0259	−	31.9867i	−1.45228	−	1.05514i	−0.985292	−	0.170880i	$-0.945339\pi$
$919$	−44.0259	−	31.9867i	−1.45228	−	1.05514i	−0.466989	−	0.884263i	$-0.654661\pi$
$920$		0			0
$921$	43.6397	−	31.7061i	1.43798	−	1.04475i
$922$		0			0
$923$	−44.0300	+	14.3062i	−1.44926	+	0.470894i
$924$		0			0
$925$	38.8613	+	32.9646i	1.27775	+	1.08387i
$926$		0			0
$927$	31.6801	−	10.2935i	1.04051	−	0.338082i
$928$		0			0
$929$	26.2460	−	19.0689i	0.861105	−	0.625629i	−0.0670805	−	0.997748i	$-0.521368\pi$
$929$	26.2460	−	19.0689i	0.861105	−	0.625629i	0.928185	+	0.372118i	$0.121368\pi$
$930$		0			0
$931$	−10.6669	−	7.74997i	−0.349594	−	0.253995i
$932$		0			0
$933$	−9.82082	+	13.5172i	−0.321519	+	0.442533i
$934$		0			0
$935$	27.5545	+	15.3703i	0.901129	+	0.502662i
$936$		0			0
$937$	0.0671382	+	0.0218145i	0.00219331	+	0.000712649i	0.310113	−	0.950700i	$-0.399633\pi$
$937$	0.0671382	+	0.0218145i	0.00219331	+	0.000712649i	−0.307920	+	0.951412i	$0.599633\pi$
$938$		0			0
$939$	−0.887091	−	2.73019i	−0.0289491	−	0.0890963i
$940$		0			0
$941$	12.1981	−	37.5418i	0.397646	−	1.22383i	−0.529235	−	0.848475i	$-0.677521\pi$
$941$	12.1981	−	37.5418i	0.397646	−	1.22383i	0.926881	−	0.375354i	$-0.122479\pi$
$942$		0			0
$943$			5.63618i			0.183539i
$944$		0			0
$945$	1.08685	+	9.05193i	0.0353552	+	0.294459i
$946$		0			0
$947$	−12.9232	−	17.7872i	−0.419946	−	0.578007i	0.545663	−	0.838005i	$-0.316278\pi$
$947$	−12.9232	−	17.7872i	−0.419946	−	0.578007i	−0.965609	+	0.259998i	$0.916278\pi$
$948$		0			0
$949$	−17.2970			−0.561484
$950$		0			0
$951$	35.1472			1.13973
$952$		0			0
$953$	−6.81994	−	9.38684i	−0.220920	−	0.304070i	0.684143	−	0.729348i	$-0.260176\pi$
$953$	−6.81994	−	9.38684i	−0.220920	−	0.304070i	−0.905063	+	0.425278i	$0.860176\pi$
$954$		0			0
$955$	−21.0690	+	37.7706i	−0.681775	+	1.22223i
$956$		0			0
$957$		−	28.7836i		−	0.930440i
$958$		0			0
$959$	6.47566	−	19.9300i	0.209110	−	0.643574i
$960$		0			0
$961$	4.33054	+	13.3280i	0.139695	+	0.429937i
$962$		0			0
$963$	−28.8180	−	9.36354i	−0.928647	−	0.301736i
$964$		0			0
$965$	0.654826	−	3.32129i	0.0210796	−	0.106916i
$966$		0			0
$967$	2.31918	−	3.19207i	0.0745797	−	0.102650i	−0.770097	−	0.637926i	$-0.779792\pi$
$967$	2.31918	−	3.19207i	0.0745797	−	0.102650i	0.844677	+	0.535276i	$0.179792\pi$
$968$		0			0
$969$	−43.1651	−	31.3612i	−1.38666	−	1.00747i
$970$		0			0
$971$	−38.8777	+	28.2463i	−1.24765	+	0.906467i	−0.998083	−	0.0618915i	$-0.980287\pi$
$971$	−38.8777	+	28.2463i	−1.24765	+	0.906467i	−0.249562	+	0.968359i	$0.580287\pi$
$972$		0			0
$973$	−6.46317	+	2.10001i	−0.207200	+	0.0673233i
$974$		0			0
$975$	4.02715	−	53.4749i	0.128972	−	1.71257i
$976$		0			0
$977$	0.652788	−	0.212104i	0.0208845	−	0.00678580i	−0.298556	−	0.954392i	$-0.596505\pi$
$977$	0.652788	−	0.212104i	0.0208845	−	0.00678580i	0.319441	+	0.947606i	$0.396505\pi$
$978$		0			0
$979$	18.6887	−	13.5781i	0.597293	−	0.433959i
$980$		0			0
$981$	−16.0756	−	11.6796i	−0.513256	−	0.372902i
$982$		0			0
$983$	−7.37476	+	10.1505i	−0.235218	+	0.323750i	−0.910266	−	0.414024i	$-0.864123\pi$
$983$	−7.37476	+	10.1505i	−0.235218	+	0.323750i	0.675048	+	0.737774i	$0.264123\pi$
$984$		0			0
$985$	7.05889	+	15.2443i	0.224915	+	0.485722i
$986$		0			0
$987$	39.9741	+	12.9884i	1.27239	+	0.413424i
$988$		0			0
$989$	1.16539	+	3.58671i	0.0370573	+	0.114051i
$990$		0			0
$991$	0.697131	−	2.14555i	0.0221451	−	0.0681556i	−0.939373	−	0.342896i	$-0.888592\pi$
$991$	0.697131	−	2.14555i	0.0221451	−	0.0681556i	0.961518	+	0.274741i	$0.0885920\pi$
$992$		0			0
$993$		−	49.8156i		−	1.58085i
$994$		0			0
$995$	46.4909	+	9.16615i	1.47386	+	0.290586i
$996$		0			0
$997$	−8.75386	−	12.0487i	−0.277238	−	0.381585i	0.647579	−	0.761998i	$-0.275782\pi$
$997$	−8.75386	−	12.0487i	−0.277238	−	0.381585i	−0.924816	+	0.380414i	$0.875782\pi$
$998$		0			0
$999$	22.3521			0.707188

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.y.d.369.7		32
4.3	odd	2		200.2.q.a.169.2	yes	32
20.3	even	4		1000.2.m.d.401.7		32
20.7	even	4		1000.2.m.e.401.2		32
20.19	odd	2		1000.2.q.c.849.7		32
25.2	odd	20		10000.2.a.br.1.3		16
25.4	even	10	inner	400.2.y.d.129.7		32
25.23	odd	20		10000.2.a.bq.1.14		16
100.3	even	20		1000.2.m.d.601.7		32
100.23	even	20		5000.2.a.r.1.3		16
100.27	even	20		5000.2.a.q.1.14		16
100.47	even	20		1000.2.m.e.601.2		32
100.71	odd	10		1000.2.q.c.649.7		32
100.79	odd	10		200.2.q.a.129.2	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.q.a.129.2	✓	32	100.79	odd	10
200.2.q.a.169.2	yes	32	4.3	odd	2
400.2.y.d.129.7		32	25.4	even	10	inner
400.2.y.d.369.7		32	1.1	even	1	trivial
1000.2.m.d.401.7		32	20.3	even	4
1000.2.m.d.601.7		32	100.3	even	20
1000.2.m.e.401.2		32	20.7	even	4
1000.2.m.e.601.2		32	100.47	even	20
1000.2.q.c.649.7		32	100.71	odd	10
1000.2.q.c.849.7		32	20.19	odd	2
5000.2.a.q.1.14		16	100.27	even	20
5000.2.a.r.1.3		16	100.23	even	20
10000.2.a.bq.1.14		16	25.23	odd	20
10000.2.a.br.1.3		16	25.2	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)

\(f(q)\)	\(=\)	\(q+(1.31712 + 1.81286i) q^{3} +(2.19384 + 0.432536i) q^{5} +1.85909i q^{7} +(-0.624612 + 1.92236i) q^{9} +(0.681343 + 2.09696i) q^{11} +(-4.55205 - 1.47905i) q^{13} +(2.10542 + 4.54683i) q^{15} +(3.76158 - 5.17737i) q^{17} +(-3.01005 - 2.18693i) q^{19} +(-3.37028 + 2.44865i) q^{21} +(0.905170 - 0.294107i) q^{23} +(4.62582 + 1.89783i) q^{25} +(2.08578 - 0.677713i) q^{27} +(-4.71315 + 3.42430i) q^{29} +(-5.42789 - 3.94359i) q^{31} +(-2.90409 + 3.99713i) q^{33} +(-0.804125 + 4.07854i) q^{35} +(9.69306 + 3.14947i) q^{37} +(-3.31429 - 10.2003i) q^{39} +(-1.82997 + 5.63206i) q^{41} +3.96247i q^{43} +(-2.20178 + 3.94717i) q^{45} +(-5.93038 - 8.16246i) q^{47} +3.54377 q^{49} +14.3403 q^{51} +(-2.46759 - 3.39634i) q^{53} +(0.587744 + 4.89509i) q^{55} -8.33725i q^{57} +(-1.86474 + 5.73908i) q^{59} +(-1.13650 - 3.49779i) q^{61} +(-3.57384 - 1.16121i) q^{63} +(-9.34670 - 5.21372i) q^{65} +(8.45537 - 11.6378i) q^{67} +(1.72540 + 1.25357i) q^{69} +(7.82527 - 5.68539i) q^{71} +(3.43698 - 1.11674i) q^{73} +(2.65228 + 10.8857i) q^{75} +(-3.89844 + 1.26668i) q^{77} +(-9.13049 + 6.63369i) q^{79} +(8.88160 + 6.45286i) q^{81} +(4.08493 - 5.62242i) q^{83} +(10.4917 - 9.73128i) q^{85} +(-12.4156 - 4.03407i) q^{87} +(-3.23757 - 9.96423i) q^{89} +(2.74969 - 8.46268i) q^{91} -15.0342i q^{93} +(-5.65762 - 6.09971i) q^{95} +(0.275879 + 0.379715i) q^{97} -4.45668 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{5} + 10 q^{9} - 6 q^{11} - 12 q^{15} + 6 q^{19} - 4 q^{21} + 30 q^{23} + 6 q^{25} - 2 q^{29} - 6 q^{31} - 8 q^{35} - 40 q^{37} + 12 q^{39} - 12 q^{45} + 20 q^{47} - 60 q^{49} + 60 q^{51} - 30 q^{53}+ \cdots - 92 q^{99}+O(q^{100}) \) 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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