LMFDB - Embedded newform 400.2.u.d.321.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(81,400)]

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, 4]))

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

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

chi := DirichletCharacter("400.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.u (of order $5$, 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 $\Q(\zeta_{5})$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			321.2
Root			$1.17421 - 0.0566033i$ of defining polynomial
Character	$\chi$	$=$	400.321
Dual form			400.2.u.d.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.39991 + 1.74363i) q^{3} +(2.15743 + 0.587785i) q^{5} -1.83337 q^{7} +(1.79224 + 5.51595i) q^{9} +O(q^{10})$	\(q+(2.39991 + 1.74363i) q^{3} +(2.15743 + 0.587785i) q^{5} -1.83337 q^{7} +(1.79224 + 5.51595i) q^{9} +(0.566541 - 1.74363i) q^{11} +(-0.747156 - 2.29951i) q^{13} +(4.15275 + 5.17240i) q^{15} +(-2.25284 + 1.63679i) q^{17} +(-1.35294 + 0.982966i) q^{19} +(-4.39991 - 3.19672i) q^{21} +(2.39991 - 7.38615i) q^{23} +(4.30902 + 2.53621i) q^{25} +(-2.56654 + 7.89900i) q^{27} +(-6.13597 - 4.45805i) q^{29} +(-4.28304 + 3.11181i) q^{31} +(4.39991 - 3.19672i) q^{33} +(-3.95536 - 1.07763i) q^{35} +(-0.406315 - 1.25051i) q^{37} +(2.21640 - 6.82138i) q^{39} +(1.08621 + 3.34301i) q^{41} +4.30550 q^{43} +(0.624442 + 12.9537i) q^{45} +(1.48322 + 1.07763i) q^{47} -3.63877 q^{49} -8.26057 q^{51} +(5.27267 + 3.83082i) q^{53} +(2.24716 - 3.42877i) q^{55} -4.96086 q^{57} +(2.79981 + 8.61694i) q^{59} +(0.799717 - 2.46127i) q^{61} +(-3.28583 - 10.1128i) q^{63} +(-0.260320 - 5.40020i) q^{65} +(7.68574 - 5.58402i) q^{67} +(18.6383 - 13.5415i) q^{69} +(0.247156 + 0.179569i) q^{71} +(4.61920 - 14.2164i) q^{73} +(5.91901 + 13.6000i) q^{75} +(-1.03868 + 3.19672i) q^{77} +(-2.79981 - 2.03418i) q^{79} +(-5.85599 + 4.25462i) q^{81} +(-5.15555 + 3.74572i) q^{83} +(-5.82243 + 2.20707i) q^{85} +(-6.95256 - 21.3978i) q^{87} +(-1.02608 + 3.15794i) q^{89} +(1.36981 + 4.21584i) q^{91} -15.7047 q^{93} +(-3.49664 + 1.32545i) q^{95} +(-8.97214 - 6.51864i) q^{97} +10.6332 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{3} - 4 q^{7} - q^{9}+O(q^{10}) $ 8 * q + 3 * q^3 - 4 * q^7 - q^9	$ 8 q + 3 q^{3} - 4 q^{7} - q^{9} - q^{11} - 13 q^{13} + 10 q^{15} - 11 q^{17} - 20 q^{19} - 19 q^{21} + 3 q^{23} + 30 q^{25} - 15 q^{27} - 15 q^{29} + 9 q^{31} + 19 q^{33} + 15 q^{35} - 6 q^{37} + 12 q^{39} - 9 q^{41} - 12 q^{43} + 15 q^{45} + q^{47} - 4 q^{49} - 26 q^{51} + 7 q^{53} + 25 q^{55} - 10 q^{59} + 6 q^{61} + 8 q^{63} - 10 q^{65} + 11 q^{67} + 43 q^{69} + 9 q^{71} - 8 q^{73} - 30 q^{75} + 33 q^{77} + 10 q^{79} - 17 q^{81} - 27 q^{83} + 5 q^{85} - 15 q^{89} - q^{91} - 46 q^{93} + 30 q^{95} - 36 q^{97} + 42 q^{99}+O(q^{100}) $ 8 * q + 3 * q^3 - 4 * q^7 - q^9 - q^11 - 13 * q^13 + 10 * q^15 - 11 * q^17 - 20 * q^19 - 19 * q^21 + 3 * q^23 + 30 * q^25 - 15 * q^27 - 15 * q^29 + 9 * q^31 + 19 * q^33 + 15 * q^35 - 6 * q^37 + 12 * q^39 - 9 * q^41 - 12 * q^43 + 15 * q^45 + q^47 - 4 * q^49 - 26 * q^51 + 7 * q^53 + 25 * q^55 - 10 * q^59 + 6 * q^61 + 8 * q^63 - 10 * q^65 + 11 * q^67 + 43 * q^69 + 9 * q^71 - 8 * q^73 - 30 * q^75 + 33 * q^77 + 10 * q^79 - 17 * q^81 - 27 * q^83 + 5 * q^85 - 15 * q^89 - q^91 - 46 * q^93 + 30 * q^95 - 36 * q^97 + 42 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

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
$3$	2.39991	+	1.74363i	1.38559	+	1.00669i	0.996333	+	0.0855571i	$0.0272670\pi$
$3$	2.39991	+	1.74363i	1.38559	+	1.00669i	0.389254	+	0.921131i	$0.372733\pi$
$4$		0			0
$5$	2.15743	+	0.587785i	0.964832	+	0.262866i
$5$	2.15743	+	0.587785i	0.964832	+	0.262866i
$6$		0			0
$7$	−1.83337			−0.692947			−0.346474	−	0.938060i	$-0.612621\pi$
$7$	−1.83337			−0.692947			−0.346474	+	0.938060i	$0.612621\pi$
$8$		0			0
$9$	1.79224	+	5.51595i	0.597414	+	1.83865i
$10$		0			0
$11$	0.566541	−	1.74363i	0.170819	−	0.525726i	−0.828599	−	0.559842i	$-0.810862\pi$
$11$	0.566541	−	1.74363i	0.170819	−	0.525726i	0.999418	+	0.0341166i	$0.0108618\pi$
$12$		0			0
$13$	−0.747156	−	2.29951i	−0.207224	−	0.637769i	−0.999615	−	0.0277557i	$-0.991164\pi$
$13$	−0.747156	−	2.29951i	−0.207224	−	0.637769i	0.792391	−	0.610014i	$-0.208836\pi$
$14$		0			0
$15$	4.15275	+	5.17240i	1.07224	+	1.33551i
$16$		0			0
$17$	−2.25284	+	1.63679i	−0.546395	+	0.396979i	−0.826455	−	0.563003i	$-0.809646\pi$
$17$	−2.25284	+	1.63679i	−0.546395	+	0.396979i	0.280060	+	0.959983i	$0.409646\pi$
$18$		0			0
$19$	−1.35294	+	0.982966i	−0.310385	+	0.225508i	−0.732062	−	0.681238i	$-0.761442\pi$
$19$	−1.35294	+	0.982966i	−0.310385	+	0.225508i	0.421677	+	0.906746i	$0.361442\pi$
$20$		0			0
$21$	−4.39991	−	3.19672i	−0.960138	−	0.697581i
$22$		0			0
$23$	2.39991	−	7.38615i	0.500415	−	1.54012i	−0.307929	−	0.951409i	$-0.599636\pi$
$23$	2.39991	−	7.38615i	0.500415	−	1.54012i	0.808344	−	0.588710i	$-0.200364\pi$
$24$		0			0
$25$	4.30902	+	2.53621i	0.861803	+	0.507242i
$26$		0			0
$27$	−2.56654	+	7.89900i	−0.493931	+	1.52016i
$28$		0			0
$29$	−6.13597	−	4.45805i	−1.13942	−	0.827838i	−0.152383	−	0.988321i	$-0.548695\pi$
$29$	−6.13597	−	4.45805i	−1.13942	−	0.827838i	−0.987039	+	0.160483i	$0.948695\pi$
$30$		0			0
$31$	−4.28304	+	3.11181i	−0.769256	+	0.558897i	−0.901735	−	0.432288i	$-0.857706\pi$
$31$	−4.28304	+	3.11181i	−0.769256	+	0.558897i	0.132479	+	0.991186i	$0.457706\pi$
$32$		0			0
$33$	4.39991	−	3.19672i	0.765925	−	0.556477i
$34$		0			0
$35$	−3.95536	−	1.07763i	−0.668578	−	0.182152i
$36$		0			0
$37$	−0.406315	−	1.25051i	−0.0667977	−	0.205582i	0.912086	−	0.409998i	$-0.134471\pi$
$37$	−0.406315	−	1.25051i	−0.0667977	−	0.205582i	−0.978884	+	0.204416i	$0.934471\pi$
$38$		0			0
$39$	2.21640	−	6.82138i	0.354908	−	1.09229i
$40$		0			0
$41$	1.08621	+	3.34301i	0.169637	+	0.522090i	0.999348	−	0.0361034i	$-0.0114946\pi$
$41$	1.08621	+	3.34301i	0.169637	+	0.522090i	−0.829711	+	0.558194i	$0.811495\pi$
$42$		0			0
$43$	4.30550			0.656583			0.328291	−	0.944576i	$-0.393527\pi$
$43$	4.30550			0.656583			0.328291	+	0.944576i	$0.393527\pi$
$44$		0			0
$45$	0.624442	+	12.9537i	0.0930863	+	1.93103i
$46$		0			0
$47$	1.48322	+	1.07763i	0.216350	+	0.157188i	0.690682	−	0.723158i	$-0.257310\pi$
$47$	1.48322	+	1.07763i	0.216350	+	0.157188i	−0.474332	+	0.880346i	$0.657310\pi$
$48$		0			0
$49$	−3.63877			−0.519824
$50$		0			0
$51$	−8.26057			−1.15671
$52$		0			0
$53$	5.27267	+	3.83082i	0.724257	+	0.526203i	0.887741	−	0.460342i	$-0.152273\pi$
$53$	5.27267	+	3.83082i	0.724257	+	0.526203i	−0.163485	+	0.986546i	$0.552273\pi$
$54$		0			0
$55$	2.24716	−	3.42877i	0.303006	−	0.462335i
$56$		0			0
$57$	−4.96086			−0.657082
$58$		0			0
$59$	2.79981	+	8.61694i	0.364505	+	1.12183i	0.950291	+	0.311364i	$0.100786\pi$
$59$	2.79981	+	8.61694i	0.364505	+	1.12183i	−0.585786	+	0.810466i	$0.699214\pi$
$60$		0			0
$61$	0.799717	−	2.46127i	0.102393	−	0.315134i	−0.886717	−	0.462313i	$-0.847019\pi$
$61$	0.799717	−	2.46127i	0.102393	−	0.315134i	0.989110	+	0.147180i	$0.0470195\pi$
$62$		0			0
$63$	−3.28583	−	10.1128i	−0.413976	−	1.27409i
$64$		0			0
$65$	−0.260320	−	5.40020i	−0.0322887	−	0.669812i
$66$		0			0
$67$	7.68574	−	5.58402i	0.938963	−	0.682196i	−0.00920814	−	0.999958i	$-0.502931\pi$
$67$	7.68574	−	5.58402i	0.938963	−	0.682196i	0.948171	+	0.317761i	$0.102931\pi$
$68$		0			0
$69$	18.6383	−	13.5415i	2.24379	−	1.63021i
$70$		0			0
$71$	0.247156	+	0.179569i	0.0293320	+	0.0213110i	0.602355	−	0.798229i	$-0.294229\pi$
$71$	0.247156	+	0.179569i	0.0293320	+	0.0213110i	−0.573023	+	0.819540i	$0.694229\pi$
$72$		0			0
$73$	4.61920	−	14.2164i	0.540636	−	1.66391i	−0.190509	−	0.981685i	$-0.561014\pi$
$73$	4.61920	−	14.2164i	0.540636	−	1.66391i	0.731145	−	0.682222i	$-0.238986\pi$
$74$		0			0
$75$	5.91901	+	13.6000i	0.683469	+	1.57040i
$76$		0			0
$77$	−1.03868	+	3.19672i	−0.118368	+	0.364300i
$78$		0			0
$79$	−2.79981	−	2.03418i	−0.315004	−	0.228864i	0.419037	−	0.907969i	$-0.362368\pi$
$79$	−2.79981	−	2.03418i	−0.315004	−	0.228864i	−0.734041	+	0.679106i	$0.762368\pi$
$80$		0			0
$81$	−5.85599	+	4.25462i	−0.650665	+	0.472736i
$82$		0			0
$83$	−5.15555	+	3.74572i	−0.565895	+	0.411147i	−0.833612	−	0.552351i	$-0.813731\pi$
$83$	−5.15555	+	3.74572i	−0.565895	+	0.411147i	0.267717	+	0.963498i	$0.413731\pi$
$84$		0			0
$85$	−5.82243	+	2.20707i	−0.631532	+	0.239390i
$86$		0			0
$87$	−6.95256	−	21.3978i	−0.745393	−	2.29408i
$88$		0			0
$89$	−1.02608	+	3.15794i	−0.108764	+	0.334741i	−0.990595	−	0.136824i	$-0.956311\pi$
$89$	−1.02608	+	3.15794i	−0.108764	+	0.334741i	0.881832	+	0.471565i	$0.156311\pi$
$90$		0			0
$91$	1.36981	+	4.21584i	0.143595	+	0.441940i
$92$		0			0
$93$	−15.7047			−1.62851
$94$		0			0
$95$	−3.49664	+	1.32545i	−0.358748	+	0.135988i
$96$		0			0
$97$	−8.97214	−	6.51864i	−0.910982	−	0.661867i	0.0302807	−	0.999541i	$-0.490360\pi$
$97$	−8.97214	−	6.51864i	−0.910982	−	0.661867i	−0.941263	+	0.337674i	$0.890360\pi$
$98$		0			0
$99$	10.6332			1.06867
$100$		0			0
$101$	−13.1807			−1.31152			−0.655762	−	0.754968i	$-0.727653\pi$
$101$	−13.1807			−1.31152			−0.655762	+	0.754968i	$0.727653\pi$
$102$		0			0
$103$	−2.13029	−	1.54774i	−0.209903	−	0.152504i	0.477867	−	0.878432i	$-0.341410\pi$
$103$	−2.13029	−	1.54774i	−0.209903	−	0.152504i	−0.687770	+	0.725929i	$0.741410\pi$
$104$		0			0
$105$	−7.61351	−	9.48290i	−0.743003	−	0.925436i
$106$		0			0
$107$	−18.8045			−1.81790			−0.908949	−	0.416908i	$-0.863114\pi$
$107$	−18.8045			−1.81790			−0.908949	+	0.416908i	$0.863114\pi$
$108$		0			0
$109$	3.18574	+	9.80470i	0.305139	+	0.939120i	0.979625	+	0.200833i	$0.0643649\pi$
$109$	3.18574	+	9.80470i	0.305139	+	0.939120i	−0.674487	+	0.738287i	$0.735635\pi$
$110$		0			0
$111$	1.20531	−	3.70957i	0.114403	−	0.352097i
$112$		0			0
$113$	1.87160	+	5.76019i	0.176065	+	0.541873i	0.999681	−	0.0252760i	$-0.00804646\pi$
$113$	1.87160	+	5.76019i	0.176065	+	0.541873i	−0.823615	+	0.567149i	$0.808046\pi$
$114$		0			0
$115$	9.51911	−	14.5245i	0.887661	−	1.35442i
$116$		0			0
$117$	11.3449	−	8.24255i	1.04884	−	0.762024i
$118$		0			0
$119$	4.13029	−	3.00083i	0.378623	−	0.275086i
$120$		0			0
$121$	6.17989	+	4.48996i	0.561809	+	0.408178i
$122$		0			0
$123$	−3.22218	+	9.91686i	−0.290535	+	0.894174i
$124$		0			0
$125$	7.80566	+	8.00448i	0.698159	+	0.715942i
$126$		0			0
$127$	−0.102986	+	0.316957i	−0.00913850	+	0.0281254i	−0.955522	−	0.294921i	$-0.904707\pi$
$127$	−0.102986	+	0.316957i	−0.00913850	+	0.0281254i	0.946383	+	0.323046i	$0.104707\pi$
$128$		0			0
$129$	10.3328	+	7.50722i	0.909753	+	0.660974i
$130$		0			0
$131$	−4.18910	+	3.04356i	−0.366003	+	0.265917i	−0.755552	−	0.655089i	$-0.772631\pi$
$131$	−4.18910	+	3.04356i	−0.366003	+	0.265917i	0.389548	+	0.921006i	$0.372631\pi$
$132$		0			0
$133$	2.48043	−	1.80214i	0.215080	−	0.156265i
$134$		0			0
$135$	−10.1801	+	15.5330i	−0.876159	+	1.33687i
$136$		0			0
$137$	−6.03299	−	18.5676i	−0.515433	−	1.58634i	−0.782493	−	0.622660i	$-0.786052\pi$
$137$	−6.03299	−	18.5676i	−0.515433	−	1.58634i	0.267060	−	0.963680i	$-0.413948\pi$
$138$		0			0
$139$	2.45825	−	7.56572i	0.208506	−	0.641716i	−0.791045	−	0.611758i	$-0.790463\pi$
$139$	2.45825	−	7.56572i	0.208506	−	0.641716i	0.999551	−	0.0299582i	$-0.00953741\pi$
$140$		0			0
$141$	1.68061	+	5.17240i	0.141533	+	0.435595i
$142$		0			0
$143$	−4.43280			−0.370689
$144$		0			0
$145$	−10.6176	−	13.2246i	−0.881741	−	1.09824i
$146$		0			0
$147$	−8.73271	−	6.34468i	−0.720262	−	0.523301i
$148$		0			0
$149$	−1.67955			−0.137594			−0.0687969	−	0.997631i	$-0.521916\pi$
$149$	−1.67955			−0.137594			−0.0687969	+	0.997631i	$0.521916\pi$
$150$		0			0
$151$	21.2664			1.73063			0.865316	−	0.501227i	$-0.167118\pi$
$151$	21.2664			1.73063			0.865316	+	0.501227i	$0.167118\pi$
$152$		0			0
$153$	−13.0661	−	9.49306i	−1.05633	−	0.767468i
$154$		0			0
$155$	−11.0694	+	4.19601i	−0.889118	+	0.337031i
$156$		0			0
$157$	10.4514			0.834113			0.417056	−	0.908881i	$-0.363062\pi$
$157$	10.4514			0.834113			0.417056	+	0.908881i	$0.363062\pi$
$158$		0			0
$159$	5.97437	+	18.3872i	0.473798	+	1.45820i
$160$		0			0
$161$	−4.39991	+	13.5415i	−0.346761	+	1.06722i
$162$		0			0
$163$	−3.21706	−	9.90109i	−0.251980	−	0.775513i	−0.994410	−	0.105590i	$-0.966327\pi$
$163$	−3.21706	−	9.90109i	−0.251980	−	0.775513i	0.742430	−	0.669923i	$-0.233673\pi$
$164$		0			0
$165$	11.3715	−	4.31050i	0.885269	−	0.335572i
$166$		0			0
$167$	1.71650	−	1.24711i	0.132826	−	0.0965041i	−0.519388	−	0.854538i	$-0.673840\pi$
$167$	1.71650	−	1.24711i	0.132826	−	0.0965041i	0.652215	+	0.758034i	$0.273840\pi$
$168$		0			0
$169$	5.78772	−	4.20502i	0.445209	−	0.323463i
$170$		0			0
$171$	−7.84678	−	5.70102i	−0.600059	−	0.435968i
$172$		0			0
$173$	−5.59774	+	17.2281i	−0.425588	+	1.30983i	0.476841	+	0.878989i	$0.341782\pi$
$173$	−5.59774	+	17.2281i	−0.425588	+	1.30983i	−0.902430	+	0.430837i	$0.858218\pi$
$174$		0			0
$175$	−7.90000	−	4.64980i	−0.597184	−	0.351492i
$176$		0			0
$177$	−8.30550	+	25.5617i	−0.624280	+	1.92134i
$178$		0			0
$179$	8.54361	+	6.20730i	0.638579	+	0.463955i	0.859362	−	0.511368i	$-0.170861\pi$
$179$	8.54361	+	6.20730i	0.638579	+	0.463955i	−0.220782	+	0.975323i	$0.570861\pi$
$180$		0			0
$181$	−14.6886	+	10.6719i	−1.09180	+	0.793237i	−0.979702	−	0.200460i	$-0.935756\pi$
$181$	−14.6886	+	10.6719i	−1.09180	+	0.793237i	−0.112096	+	0.993697i	$0.535756\pi$
$182$		0			0
$183$	6.21081	−	4.51242i	0.459116	−	0.333567i
$184$		0			0
$185$	−0.141566	−	2.93671i	−0.0104081	−	0.215911i
$186$		0			0
$187$	1.57763	+	4.85544i	0.115368	+	0.355065i
$188$		0			0
$189$	4.70541	−	14.4818i	0.342268	−	1.05339i
$190$		0			0
$191$	6.76906	+	20.8330i	0.489792	+	1.50742i	0.824919	+	0.565251i	$0.191221\pi$
$191$	6.76906	+	20.8330i	0.489792	+	1.50742i	−0.335127	+	0.942173i	$0.608779\pi$
$192$		0			0
$193$	27.4248			1.97408			0.987041	−	0.160465i	$-0.0512995\pi$
$193$	27.4248			1.97408			0.987041	+	0.160465i	$0.0512995\pi$
$194$		0			0
$195$	8.79123	−	13.4139i	0.629553	−	0.960588i
$196$		0			0
$197$	0.909110	+	0.660507i	0.0647714	+	0.0470592i	0.619700	−	0.784839i	$-0.287254\pi$
$197$	0.909110	+	0.660507i	0.0647714	+	0.0470592i	−0.554928	+	0.831898i	$0.687254\pi$
$198$		0			0
$199$	−25.4992			−1.80759			−0.903794	−	0.427968i	$-0.859230\pi$
$199$	−25.4992			−1.80759			−0.903794	+	0.427968i	$0.859230\pi$
$200$		0			0
$201$	28.1815			1.98777
$202$		0			0
$203$	11.2495	+	8.17323i	0.789559	+	0.573648i
$204$		0			0
$205$	0.378451	+	7.85077i	0.0264321	+	0.548322i
$206$		0			0
$207$	45.0429			3.13070
$208$		0			0
$209$	0.947439	+	2.91592i	0.0655358	+	0.201698i
$210$		0			0
$211$	−6.58341	+	20.2617i	−0.453221	+	1.39487i	0.419990	+	0.907529i	$0.362033\pi$
$211$	−6.58341	+	20.2617i	−0.453221	+	1.39487i	−0.873211	+	0.487342i	$0.837967\pi$
$212$		0			0
$213$	0.280048	+	0.861899i	0.0191886	+	0.0590564i
$214$		0			0
$215$	9.28882	+	2.53071i	0.633492	+	0.172593i
$216$		0			0
$217$	7.85237	−	5.70508i	0.533054	−	0.387286i
$218$		0			0
$219$	35.8739	−	26.0639i	2.42413	−	1.76124i
$220$		0			0
$221$	5.44703	+	3.95750i	0.366407	+	0.266210i
$222$		0			0
$223$	−1.00280	+	3.08629i	−0.0671522	+	0.206673i	−0.979002	−	0.203851i	$-0.934654\pi$
$223$	−1.00280	+	3.08629i	−0.0671522	+	0.206673i	0.911850	+	0.410524i	$0.134654\pi$
$224$		0			0
$225$	−6.26682	+	28.3138i	−0.417788	+	1.88759i
$226$		0			0
$227$	−5.06085	+	15.5757i	−0.335901	+	1.03380i	0.630376	+	0.776290i	$0.282901\pi$
$227$	−5.06085	+	15.5757i	−0.335901	+	1.03380i	−0.966277	+	0.257506i	$0.917099\pi$
$228$		0			0
$229$	4.11788	+	2.99181i	0.272117	+	0.197705i	0.715472	−	0.698642i	$-0.246212\pi$
$229$	4.11788	+	2.99181i	0.272117	+	0.197705i	−0.443355	+	0.896346i	$0.646212\pi$
$230$		0			0
$231$	−8.06664	+	5.86076i	−0.530746	+	0.385609i
$232$		0			0
$233$	1.34536	−	0.977464i	0.0881378	−	0.0640358i	−0.542844	−	0.839834i	$-0.682652\pi$
$233$	1.34536	−	0.977464i	0.0881378	−	0.0640358i	0.630981	+	0.775798i	$0.282652\pi$
$234$		0			0
$235$	2.56654	+	3.19672i	0.167423	+	0.208531i
$236$		0			0
$237$	−3.17242	−	9.76370i	−0.206071	−	0.634221i
$238$		0			0
$239$	−3.95536	+	12.1733i	−0.255851	+	0.787428i	0.737810	+	0.675009i	$0.235860\pi$
$239$	−3.95536	+	12.1733i	−0.255851	+	0.787428i	−0.993661	+	0.112420i	$0.964140\pi$
$240$		0			0
$241$	0.122209	+	0.376121i	0.00787219	+	0.0242281i	0.954915	−	0.296878i	$-0.0959454\pi$
$241$	0.122209	+	0.376121i	0.00787219	+	0.0242281i	−0.947043	+	0.321106i	$0.895945\pi$
$242$		0			0
$243$	3.44417			0.220944
$244$		0			0
$245$	−7.85040	−	2.13882i	−0.501543	−	0.136644i
$246$		0			0
$247$	3.27120	+	2.37666i	0.208141	+	0.151223i
$248$		0			0
$249$	−18.9040			−1.19799
$250$		0			0
$251$	−9.36589			−0.591170			−0.295585	−	0.955316i	$-0.595515\pi$
$251$	−9.36589			−0.591170			−0.295585	+	0.955316i	$0.595515\pi$
$252$		0			0
$253$	−11.5191	−	8.36912i	−0.724200	−	0.526162i
$254$		0			0
$255$	−17.8216	−	4.85544i	−1.11603	−	0.304060i
$256$		0			0
$257$	−4.97926			−0.310598			−0.155299	−	0.987868i	$-0.549634\pi$
$257$	−4.97926			−0.310598			−0.155299	+	0.987868i	$0.549634\pi$
$258$		0			0
$259$	0.744923	+	2.29264i	0.0462873	+	0.142458i
$260$		0			0
$261$	13.5932	−	41.8356i	0.841399	−	2.58956i
$262$		0			0
$263$	6.12199	+	18.8416i	0.377498	+	1.16182i	0.941778	+	0.336236i	$0.109154\pi$
$263$	6.12199	+	18.8416i	0.377498	+	1.16182i	−0.564279	+	0.825584i	$0.690846\pi$
$264$		0			0
$265$	9.12372	+	11.3639i	0.560466	+	0.698080i
$266$		0			0
$267$	−7.96878	+	5.78966i	−0.487681	+	0.354321i
$268$		0			0
$269$	−11.9685	+	8.69564i	−0.729734	+	0.530183i	−0.889479	−	0.456976i	$-0.848933\pi$
$269$	−11.9685	+	8.69564i	−0.729734	+	0.530183i	0.159745	+	0.987158i	$0.448933\pi$
$270$		0			0
$271$	−10.1583	−	7.38047i	−0.617075	−	0.448331i	0.234823	−	0.972038i	$-0.424549\pi$
$271$	−10.1583	−	7.38047i	−0.617075	−	0.448331i	−0.851899	+	0.523707i	$0.824549\pi$
$272$		0			0
$273$	−4.06347	+	12.5061i	−0.245932	+	0.756902i
$274$		0			0
$275$	6.86346	−	6.07648i	0.413882	−	0.366426i
$276$		0			0
$277$	−1.95664	+	6.02193i	−0.117563	+	0.361823i	−0.992473	−	0.122463i	$-0.960921\pi$
$277$	−1.95664	+	6.02193i	−0.117563	+	0.361823i	0.874910	+	0.484286i	$0.160921\pi$
$278$		0			0
$279$	−24.8408	−	18.0479i	−1.48718	−	1.08050i
$280$		0			0
$281$	16.2525	−	11.8082i	0.969545	−	0.704416i	0.0141971	−	0.999899i	$-0.495481\pi$
$281$	16.2525	−	11.8082i	0.969545	−	0.704416i	0.955348	+	0.295484i	$0.0954808\pi$
$282$		0			0
$283$	1.46981	−	1.06788i	0.0873709	−	0.0634787i	−0.543242	−	0.839576i	$-0.682803\pi$
$283$	1.46981	−	1.06788i	0.0873709	−	0.0634787i	0.630613	+	0.776097i	$0.282803\pi$
$284$		0			0
$285$	−10.7027	−	2.91592i	−0.633974	−	0.172724i
$286$		0			0
$287$	−1.99142	−	6.12896i	−0.117550	−	0.361781i
$288$		0			0
$289$	−2.85705	+	8.79311i	−0.168062	+	0.517242i
$290$		0			0
$291$	−10.1662	−	31.2882i	−0.595951	−	1.83415i
$292$		0			0
$293$	−6.85931			−0.400725			−0.200363	−	0.979722i	$-0.564212\pi$
$293$	−6.85931			−0.400725			−0.200363	+	0.979722i	$0.564212\pi$
$294$		0			0
$295$	0.975494	+	20.2361i	0.0567955	+	1.17819i
$296$		0			0
$297$	12.3189	+	8.95022i	0.714816	+	0.519344i
$298$		0			0
$299$	−18.7776			−1.08594
$300$		0			0
$301$	−7.89356			−0.454977
$302$		0			0
$303$	−31.6323	−	22.9822i	−1.81723	−	1.32030i
$304$		0			0
$305$	3.17203	−	4.83997i	0.181630	−	0.277136i
$306$		0			0
$307$	2.89526			0.165241			0.0826206	−	0.996581i	$-0.473671\pi$
$307$	2.89526			0.165241			0.0826206	+	0.996581i	$0.473671\pi$
$308$		0			0
$309$	−2.41379	−	7.42888i	−0.137316	−	0.422614i
$310$		0			0
$311$	6.38090	−	19.6384i	0.361828	−	1.11359i	−0.590116	−	0.807318i	$-0.700918\pi$
$311$	6.38090	−	19.6384i	0.361828	−	1.11359i	0.951944	−	0.306272i	$-0.0990819\pi$
$312$		0			0
$313$	5.07629	+	15.6232i	0.286929	+	0.883076i	0.985814	+	0.167842i	$0.0536798\pi$
$313$	5.07629	+	15.6232i	0.286929	+	0.883076i	−0.698885	+	0.715234i	$0.746320\pi$
$314$		0			0
$315$	−1.14483	−	23.7489i	−0.0645039	−	1.33810i
$316$		0			0
$317$	−13.3535	+	9.70191i	−0.750009	+	0.544914i	−0.895830	−	0.444397i	$-0.853418\pi$
$317$	−13.3535	+	9.70191i	−0.750009	+	0.544914i	0.145820	+	0.989311i	$0.453418\pi$
$318$		0			0
$319$	−11.2495	+	8.17323i	−0.629850	+	0.457613i
$320$		0			0
$321$	−45.1290	−	32.7881i	−2.51885	−	1.83005i
$322$		0			0
$323$	1.43905	−	4.42894i	0.0800709	−	0.246433i
$324$		0			0
$325$	2.61254	−	11.8036i	0.144917	−	0.654744i
$326$		0			0
$327$	−9.45033	+	29.0851i	−0.522605	+	1.60841i
$328$		0			0
$329$	−2.71929	−	1.97568i	−0.149919	−	0.108923i
$330$		0			0
$331$	22.2245	−	16.1471i	1.22157	−	0.887522i	0.225340	−	0.974280i	$-0.427651\pi$
$331$	22.2245	−	16.1471i	1.22157	−	0.887522i	0.996229	+	0.0867577i	$0.0276506\pi$
$332$		0			0
$333$	6.16953	−	4.48242i	0.338088	−	0.245635i
$334$		0			0
$335$	19.8637	−	7.52957i	1.08527	−	0.411384i
$336$		0			0
$337$	−0.848317	−	2.61085i	−0.0462108	−	0.142222i	0.925289	−	0.379263i	$-0.123822\pi$
$337$	−0.848317	−	2.61085i	−0.0462108	−	0.142222i	−0.971500	+	0.237041i	$0.923822\pi$
$338$		0			0
$339$	−5.55200	+	17.0873i	−0.301543	+	0.928054i
$340$		0			0
$341$	2.99934	+	9.23102i	0.162423	+	0.499888i
$342$		0			0
$343$	19.5048			1.05316
$344$		0			0
$345$	48.1704	−	18.2596i	2.59341	−	0.983063i
$346$		0			0
$347$	−17.2637	−	12.5428i	−0.926762	−	0.673332i	0.0184361	−	0.999830i	$-0.494131\pi$
$347$	−17.2637	−	12.5428i	−0.926762	−	0.673332i	−0.945198	+	0.326498i	$0.894131\pi$
$348$		0			0
$349$	−16.7650			−0.897411			−0.448705	−	0.893680i	$-0.648115\pi$
$349$	−16.7650			−0.897411			−0.448705	+	0.893680i	$0.648115\pi$
$350$		0			0
$351$	20.0814			1.07187
$352$		0			0
$353$	−2.41785	−	1.75667i	−0.128689	−	0.0934981i	0.521579	−	0.853203i	$-0.325343\pi$
$353$	−2.41785	−	1.75667i	−0.128689	−	0.0934981i	−0.650268	+	0.759705i	$0.725343\pi$
$354$		0			0
$355$	0.427674	+	0.532683i	0.0226986	+	0.0282719i
$356$		0			0
$357$	15.1447			0.801540
$358$		0			0
$359$	−2.07194	−	6.37678i	−0.109353	−	0.336554i	0.881375	−	0.472418i	$-0.156619\pi$
$359$	−2.07194	−	6.37678i	−0.109353	−	0.336554i	−0.990727	+	0.135865i	$0.956619\pi$
$360$		0			0
$361$	−5.00711	+	15.4103i	−0.263532	+	0.811068i
$362$		0			0
$363$	7.00233	+	21.5510i	0.367527	+	1.13113i
$364$		0			0
$365$	18.3218	−	27.9559i	0.959007	−	1.46328i
$366$		0			0
$367$	3.24949	−	2.36089i	0.169622	−	0.123237i	−0.499736	−	0.866178i	$-0.666570\pi$
$367$	3.24949	−	2.36089i	0.169622	−	0.123237i	0.669357	+	0.742941i	$0.266570\pi$
$368$		0			0
$369$	−16.4931	+	11.9830i	−0.858598	+	0.623808i
$370$		0			0
$371$	−9.66673	−	7.02329i	−0.501872	−	0.364631i
$372$		0			0
$373$	8.21467	−	25.2822i	0.425340	−	1.30906i	−0.477329	−	0.878725i	$-0.658395\pi$
$373$	8.21467	−	25.2822i	0.425340	−	1.30906i	0.902669	−	0.430336i	$-0.141605\pi$
$374$		0			0
$375$	4.77597	+	32.8202i	0.246630	+	1.69483i
$376$		0			0
$377$	−5.66679	+	17.4406i	−0.291855	+	0.898236i
$378$		0			0
$379$	−12.6431	−	9.18578i	−0.649435	−	0.471842i	0.213644	−	0.976912i	$-0.431467\pi$
$379$	−12.6431	−	9.18578i	−0.649435	−	0.471842i	−0.863079	+	0.505070i	$0.831467\pi$
$380$		0			0
$381$	−0.799814	+	0.581099i	−0.0409757	+	0.0297706i
$382$		0			0
$383$	10.8776	−	7.90306i	0.555821	−	0.403828i	−0.274106	−	0.961699i	$-0.588382\pi$
$383$	10.8776	−	7.90306i	0.555821	−	0.403828i	0.829927	+	0.557872i	$0.188382\pi$
$384$		0			0
$385$	−4.11986	+	6.28618i	−0.209967	+	0.320374i
$386$		0			0
$387$	7.71650	+	23.7489i	0.392252	+	1.20723i
$388$		0			0
$389$	−7.75991	+	23.8826i	−0.393443	+	1.21089i	0.536724	+	0.843758i	$0.319662\pi$
$389$	−7.75991	+	23.8826i	−0.393443	+	1.21089i	−0.930167	+	0.367136i	$0.880338\pi$
$390$		0			0
$391$	6.68294	+	20.5680i	0.337971	+	1.04017i
$392$		0			0
$393$	−15.3603			−0.774825
$394$		0			0
$395$	−4.84474	−	6.03430i	−0.243765	−	0.303619i
$396$		0			0
$397$	−2.84628	−	2.06794i	−0.142850	−	0.103787i	0.514065	−	0.857751i	$-0.328139\pi$
$397$	−2.84628	−	2.06794i	−0.142850	−	0.103787i	−0.656915	+	0.753964i	$0.728139\pi$
$398$		0			0
$399$	9.09507			0.455323
$400$		0			0
$401$	29.8696			1.49161			0.745807	−	0.666162i	$-0.232064\pi$
$401$	29.8696			1.49161			0.745807	+	0.666162i	$0.232064\pi$
$402$		0			0
$403$	10.3557	+	7.52388i	0.515856	+	0.374791i
$404$		0			0
$405$	−15.1347	+	5.73699i	−0.752049	+	0.285074i
$406$		0			0
$407$	−2.41062			−0.119490
$408$		0			0
$409$	−11.9784	−	36.8656i	−0.592291	−	1.82289i	−0.567771	−	0.823186i	$-0.692194\pi$
$409$	−11.9784	−	36.8656i	−0.592291	−	1.82289i	−0.0245200	−	0.999699i	$-0.507806\pi$
$410$		0			0
$411$	17.8965	−	55.0799i	0.882772	−	2.71689i
$412$		0			0
$413$	−5.13308	−	15.7980i	−0.252582	−	0.777369i
$414$		0			0
$415$	−13.3244	+	5.05079i	−0.654070	+	0.247933i
$416$		0			0
$417$	19.0914	−	13.8707i	0.934911	−	0.679253i
$418$		0			0
$419$	−15.2988	+	11.1152i	−0.747395	+	0.543014i	−0.895018	−	0.446030i	$-0.852838\pi$
$419$	−15.2988	+	11.1152i	−0.747395	+	0.543014i	0.147624	+	0.989044i	$0.452838\pi$
$420$		0			0
$421$	17.8414	+	12.9625i	0.869536	+	0.631755i	0.930462	−	0.366388i	$-0.119406\pi$
$421$	17.8414	+	12.9625i	0.869536	+	0.631755i	−0.0609265	+	0.998142i	$0.519406\pi$
$422$		0			0
$423$	−3.28583	+	10.1128i	−0.159763	+	0.491699i
$424$		0			0
$425$	−13.8588	+	1.33925i	−0.672250	+	0.0649633i
$426$		0			0
$427$	−1.46617	+	4.51242i	−0.0709531	+	0.218371i
$428$		0			0
$429$	−10.6383	−	7.72918i	−0.513622	−	0.373168i
$430$		0			0
$431$	−7.44763	+	5.41102i	−0.358740	+	0.260640i	−0.752526	−	0.658562i	$-0.771165\pi$
$431$	−7.44763	+	5.41102i	−0.358740	+	0.260640i	0.393787	+	0.919202i	$0.371165\pi$
$432$		0			0
$433$	−28.1516	+	20.4533i	−1.35288	+	0.982923i	−0.354015	+	0.935240i	$0.615184\pi$
$433$	−28.1516	+	20.4533i	−1.35288	+	0.982923i	−0.998862	+	0.0476837i	$0.984816\pi$
$434$		0			0
$435$	−2.42237	−	50.2509i	−0.116144	−	2.40935i
$436$		0			0
$437$	4.01342	+	12.3520i	0.191988	+	0.590878i
$438$		0			0
$439$	2.58025	−	7.94118i	0.123148	−	0.379012i	−0.870411	−	0.492326i	$-0.836147\pi$
$439$	2.58025	−	7.94118i	0.123148	−	0.379012i	0.993559	+	0.113314i	$0.0361467\pi$
$440$		0			0
$441$	−6.52155	−	20.0713i	−0.310550	−	0.955775i
$442$		0			0
$443$	1.19887			0.0569599			0.0284799	−	0.999594i	$-0.490933\pi$
$443$	1.19887			0.0569599			0.0284799	+	0.999594i	$0.490933\pi$
$444$		0			0
$445$	−4.06988	+	6.20992i	−0.192931	+	0.294379i
$446$		0			0
$447$	−4.03076	−	2.92852i	−0.190648	−	0.138514i
$448$		0			0
$449$	32.7953			1.54771			0.773853	−	0.633365i	$-0.218327\pi$
$449$	32.7953			1.54771			0.773853	+	0.633365i	$0.218327\pi$
$450$		0			0
$451$	6.44437			0.303453
$452$		0			0
$453$	51.0373	+	37.0808i	2.39794	+	1.74221i
$454$		0			0
$455$	0.477261	+	9.90054i	0.0223743	+	0.464145i
$456$		0			0
$457$	19.7884			0.925664			0.462832	−	0.886446i	$-0.346833\pi$
$457$	19.7884			0.925664			0.462832	+	0.886446i	$0.346833\pi$
$458$		0			0
$459$	−7.14697	−	21.9961i	−0.333592	−	1.02669i
$460$		0			0
$461$	2.90468	−	8.93970i	0.135285	−	0.416363i	−0.860350	−	0.509704i	$-0.829755\pi$
$461$	2.90468	−	8.93970i	0.135285	−	0.416363i	0.995634	+	0.0933412i	$0.0297547\pi$
$462$		0			0
$463$	−5.47977	−	16.8650i	−0.254666	−	0.783783i	−0.993895	−	0.110328i	$-0.964810\pi$
$463$	−5.47977	−	16.8650i	−0.254666	−	0.783783i	0.739229	−	0.673454i	$-0.235190\pi$
$464$		0			0
$465$	−33.8819	−	9.23102i	−1.57124	−	0.428078i
$466$		0			0
$467$	17.6857	−	12.8494i	0.818398	−	0.594601i	−0.0978549	−	0.995201i	$-0.531198\pi$
$467$	17.6857	−	12.8494i	0.818398	−	0.594601i	0.916253	+	0.400599i	$0.131198\pi$
$468$		0			0
$469$	−14.0908	+	10.2375i	−0.650651	+	0.472726i
$470$		0			0
$471$	25.0824	+	18.2234i	1.15574	+	0.839691i
$472$		0			0
$473$	2.43924	−	7.50722i	0.112157	−	0.345182i
$474$		0			0
$475$	−8.32284	+	0.804283i	−0.381878	+	0.0369030i
$476$		0			0
$477$	−11.6807	+	35.9495i	−0.534823	+	1.64602i
$478$		0			0
$479$	−4.94352	−	3.59168i	−0.225875	−	0.164108i	0.469092	−	0.883149i	$-0.344581\pi$
$479$	−4.94352	−	3.59168i	−0.225875	−	0.164108i	−0.694967	+	0.719041i	$0.744581\pi$
$480$		0			0
$481$	−2.57198	+	1.86865i	−0.117272	+	0.0852031i
$482$		0			0
$483$	−34.1708	+	24.8266i	−1.55483	+	1.12965i
$484$		0			0
$485$	−15.5252	−	19.3372i	−0.704963	−	0.878057i
$486$		0			0
$487$	−1.56421	−	4.81415i	−0.0708812	−	0.218150i	0.909340	−	0.416053i	$-0.136587\pi$
$487$	−1.56421	−	4.81415i	−0.0708812	−	0.218150i	−0.980222	+	0.197903i	$0.936587\pi$
$488$		0			0
$489$	9.54324	−	29.3711i	0.431560	−	1.32821i
$490$		0			0
$491$	−0.736165	−	2.26568i	−0.0332227	−	0.102249i	0.933070	−	0.359695i	$-0.117119\pi$
$491$	−0.736165	−	2.26568i	−0.0332227	−	0.102249i	−0.966293	+	0.257446i	$0.917119\pi$
$492$		0			0
$493$	21.1203			0.951209
$494$		0			0
$495$	22.9404	+	6.25003i	1.03109	+	0.280918i
$496$		0			0
$497$	−0.453127	−	0.329216i	−0.0203255	−	0.0147674i
$498$		0			0
$499$	0.0503313			0.00225314			0.00112657	−	0.999999i	$-0.499641\pi$
$499$	0.0503313			0.00225314			0.00112657	+	0.999999i	$0.499641\pi$
$500$		0			0
$501$	6.29393			0.281192
$502$		0			0
$503$	−4.37744	−	3.18040i	−0.195181	−	0.141807i	0.485903	−	0.874013i	$-0.338491\pi$
$503$	−4.37744	−	3.18040i	−0.195181	−	0.141807i	−0.681083	+	0.732206i	$0.738491\pi$
$504$		0			0
$505$	−28.4364	−	7.74739i	−1.26540	−	0.344755i
$506$		0			0
$507$	21.2220			0.942502
$508$		0			0
$509$	5.85472	+	18.0190i	0.259506	+	0.798678i	0.992908	+	0.118883i	$0.0379312\pi$
$509$	5.85472	+	18.0190i	0.259506	+	0.798678i	−0.733402	+	0.679795i	$0.762069\pi$
$510$		0			0
$511$	−8.46868	+	26.0639i	−0.374632	+	1.15300i
$512$		0			0
$513$	−4.29208	−	13.2097i	−0.189500	−	0.583221i
$514$		0			0
$515$	−3.68621	−	4.59130i	−0.162434	−	0.202317i
$516$		0			0
$517$	2.71929	−	1.97568i	0.119594	−	0.0868904i
$518$		0			0
$519$	−43.4735	+	31.5854i	−1.90828	+	1.38644i
$520$		0			0
$521$	−31.0817	−	22.5822i	−1.36171	−	0.989342i	−0.998334	−	0.0577005i	$-0.981623\pi$
$521$	−31.0817	−	22.5822i	−1.36171	−	0.989342i	−0.363379	−	0.931642i	$-0.618377\pi$
$522$		0			0
$523$	3.79057	−	11.6662i	0.165750	−	0.510127i	−0.833341	−	0.552760i	$-0.813575\pi$
$523$	3.79057	−	11.6662i	0.165750	−	0.510127i	0.999091	+	0.0426332i	$0.0135747\pi$
$524$		0			0
$525$	−10.8517	−	24.9338i	−0.473608	−	1.08820i
$526$		0			0
$527$	4.55565	−	14.0208i	0.198447	−	0.610757i
$528$		0			0
$529$	−30.1883	−	21.9331i	−1.31254	−	0.953613i
$530$		0			0
$531$	−42.5127	+	30.8873i	−1.84489	+	1.34039i
$532$		0			0
$533$	6.87572	−	4.99550i	0.297820	−	0.216379i
$534$		0			0
$535$	−40.5694	−	11.0530i	−1.75397	−	0.477863i
$536$		0			0
$537$	9.68061	+	29.7939i	0.417749	+	1.28570i
$538$		0			0
$539$	−2.06151	+	6.34468i	−0.0887957	+	0.273285i
$540$		0			0
$541$	12.9872	+	39.9704i	0.558362	+	1.71846i	0.686896	+	0.726756i	$0.258973\pi$
$541$	12.9872	+	39.9704i	0.558362	+	1.71846i	−0.128534	+	0.991705i	$0.541027\pi$
$542$		0			0
$543$	−53.8593			−2.31132
$544$		0			0
$545$	1.10996	+	23.0255i	0.0475453	+	0.986304i
$546$		0			0
$547$	15.6719	+	11.3863i	0.670080	+	0.486842i	0.870052	−	0.492960i	$-0.164085\pi$
$547$	15.6719	+	11.3863i	0.670080	+	0.486842i	−0.199972	+	0.979802i	$0.564085\pi$
$548$		0			0
$549$	15.0096			0.640592
$550$		0			0
$551$	12.6837			0.540344
$552$		0			0
$553$	5.13308	+	3.72940i	0.218281	+	0.158590i
$554$		0			0
$555$	4.78081	−	7.29467i	0.202934	−	0.309642i
$556$		0			0
$557$	8.54685			0.362142			0.181071	−	0.983470i	$-0.442044\pi$
$557$	8.54685			0.362142			0.181071	+	0.983470i	$0.442044\pi$
$558$		0			0
$559$	−3.21688	−	9.90054i	−0.136060	−	0.418748i
$560$		0			0
$561$	−4.67995	+	14.4034i	−0.197588	+	0.608113i
$562$		0			0
$563$	7.24949	+	22.3116i	0.305529	+	0.940323i	0.979479	+	0.201546i	$0.0645964\pi$
$563$	7.24949	+	22.3116i	0.305529	+	0.940323i	−0.673950	+	0.738777i	$0.735404\pi$
$564$		0			0
$565$	0.652091	+	13.5273i	0.0274337	+	0.569098i
$566$		0			0
$567$	10.7362	−	7.80028i	0.450877	−	0.327581i
$568$		0			0
$569$	5.74445	−	4.17359i	0.240820	−	0.174966i	−0.460829	−	0.887489i	$-0.652448\pi$
$569$	5.74445	−	4.17359i	0.240820	−	0.174966i	0.701649	+	0.712523i	$0.252448\pi$
$570$		0			0
$571$	−9.67745	−	7.03108i	−0.404989	−	0.294241i	0.366581	−	0.930386i	$-0.380528\pi$
$571$	−9.67745	−	7.03108i	−0.404989	−	0.294241i	−0.771570	+	0.636145i	$0.780528\pi$
$572$		0			0
$573$	−20.0801	+	61.8001i	−0.838856	+	2.58173i
$574$		0			0
$575$	29.0741	−	25.7404i	1.21247	−	1.07345i
$576$		0			0
$577$	12.8457	−	39.5350i	0.534774	−	1.64587i	−0.209362	−	0.977838i	$-0.567139\pi$
$577$	12.8457	−	39.5350i	0.534774	−	1.64587i	0.744137	−	0.668027i	$-0.232861\pi$
$578$		0			0
$579$	65.8171	+	47.8189i	2.73526	+	1.98729i
$580$		0			0
$581$	9.45200	−	6.86728i	0.392135	−	0.284903i
$582$		0			0
$583$	9.66673	−	7.02329i	0.400355	−	0.290875i
$584$		0			0
$585$	29.3207	−	11.1144i	1.21226	−	0.459523i
$586$		0			0
$587$	−5.91072	−	18.1913i	−0.243962	−	0.750836i	−0.995806	−	0.0914953i	$-0.970835\pi$
$587$	−5.91072	−	18.1913i	−0.243962	−	0.750836i	0.751844	−	0.659341i	$-0.229165\pi$
$588$		0			0
$589$	2.73588	−	8.42016i	0.112730	−	0.346947i
$590$		0			0
$591$	1.03010	+	3.17031i	0.0423725	+	0.130409i
$592$		0			0
$593$	0.538428			0.0221106			0.0110553	−	0.999939i	$-0.496481\pi$
$593$	0.538428			0.0221106			0.0110553	+	0.999939i	$0.496481\pi$
$594$		0			0
$595$	10.6747	−	4.04636i	0.437618	−	0.165885i
$596$		0			0
$597$	−61.1956	−	44.4612i	−2.50457	−	1.81968i
$598$		0			0
$599$	38.4209			1.56983			0.784917	−	0.619601i	$-0.212705\pi$
$599$	38.4209			1.56983			0.784917	+	0.619601i	$0.212705\pi$
$600$		0			0
$601$	19.6034			0.799639			0.399820	−	0.916594i	$-0.369073\pi$
$601$	19.6034			0.799639			0.399820	+	0.916594i	$0.369073\pi$
$602$		0			0
$603$	44.5759	+	32.3863i	1.81527	+	1.31887i
$604$		0			0
$605$	10.6936	+	13.3192i	0.434755	+	0.541503i
$606$		0			0
$607$	32.4415			1.31676			0.658381	−	0.752685i	$-0.271242\pi$
$607$	32.4415			1.31676			0.658381	+	0.752685i	$0.271242\pi$
$608$		0			0
$609$	12.7466	+	39.2300i	0.516518	+	1.58968i
$610$		0			0
$611$	1.36981	−	4.21584i	0.0554166	−	0.170555i
$612$		0			0
$613$	−7.25273	−	22.3216i	−0.292935	−	0.901561i	−0.983907	−	0.178680i	$-0.942817\pi$
$613$	−7.25273	−	22.3216i	−0.292935	−	0.901561i	0.690972	−	0.722881i	$-0.257183\pi$
$614$		0			0
$615$	−12.7806	+	19.5010i	−0.515365	+	0.786356i
$616$		0			0
$617$	−14.0876	+	10.2353i	−0.567147	+	0.412056i	−0.834068	−	0.551662i	$-0.813994\pi$
$617$	−14.0876	+	10.2353i	−0.567147	+	0.412056i	0.266921	+	0.963718i	$0.413994\pi$
$618$		0			0
$619$	10.1801	−	7.39624i	0.409171	−	0.297280i	−0.364095	−	0.931362i	$-0.618622\pi$
$619$	10.1801	−	7.39624i	0.409171	−	0.297280i	0.773266	+	0.634082i	$0.218622\pi$
$620$		0			0
$621$	52.1838	+	37.9137i	2.09406	+	1.52143i
$622$		0			0
$623$	1.88117	−	5.78966i	0.0753676	−	0.231958i
$624$		0			0
$625$	12.1353	+	21.8572i	0.485410	+	0.874287i
$626$		0			0
$627$	−2.81053	+	8.64992i	−0.112242	+	0.345445i
$628$		0			0
$629$	2.96218	+	2.15215i	0.118110	+	0.0858118i
$630$		0			0
$631$	33.7653	−	24.5319i	1.34418	−	0.976601i	0.344897	−	0.938640i	$-0.387914\pi$
$631$	33.7653	−	24.5319i	1.34418	−	0.976601i	0.999279	−	0.0379610i	$-0.0120863\pi$
$632$		0			0
$633$	−51.1285	+	37.1470i	−2.03218	+	1.47646i
$634$		0			0
$635$	−0.408487	+	0.623280i	−0.0162103	+	0.0247341i
$636$		0			0
$637$	2.71873	+	8.36739i	0.107720	+	0.331528i
$638$		0			0
$639$	−0.547533	+	1.68513i	−0.0216601	+	0.0666628i
$640$		0			0
$641$	−4.44926	−	13.6934i	−0.175735	−	0.540858i	0.823931	−	0.566690i	$-0.191776\pi$
$641$	−4.44926	−	13.6934i	−0.175735	−	0.540858i	−0.999666	+	0.0258324i	$0.991776\pi$
$642$		0			0
$643$	−30.1666			−1.18966			−0.594828	−	0.803853i	$-0.702780\pi$
$643$	−30.1666			−1.18966			−0.594828	+	0.803853i	$0.702780\pi$
$644$		0			0
$645$	17.8797	+	22.2698i	0.704012	+	0.876872i
$646$		0			0
$647$	−8.64660	−	6.28212i	−0.339933	−	0.246976i	0.404701	−	0.914449i	$-0.367376\pi$
$647$	−8.64660	−	6.28212i	−0.339933	−	0.246976i	−0.744633	+	0.667474i	$0.767376\pi$
$648$		0			0
$649$	16.6110			0.652039
$650$		0			0
$651$	28.7925			1.12847
$652$		0			0
$653$	−8.22432	−	5.97532i	−0.321843	−	0.233832i	0.415119	−	0.909767i	$-0.363740\pi$
$653$	−8.22432	−	5.97532i	−0.321843	−	0.233832i	−0.736961	+	0.675935i	$0.763740\pi$
$654$		0			0
$655$	−10.8266	+	4.10398i	−0.423032	+	0.160356i
$656$		0			0
$657$	86.6959			3.38233
$658$		0			0
$659$	−9.61668	−	29.5971i	−0.374613	−	1.15294i	−0.943740	−	0.330689i	$-0.892719\pi$
$659$	−9.61668	−	29.5971i	−0.374613	−	1.15294i	0.569127	−	0.822250i	$-0.307281\pi$
$660$		0			0
$661$	12.8131	−	39.4347i	0.498372	−	1.53383i	−0.313262	−	0.949667i	$-0.601422\pi$
$661$	12.8131	−	39.4347i	0.498372	−	1.53383i	0.811635	−	0.584165i	$-0.198578\pi$
$662$		0			0
$663$	6.17194	+	18.9953i	0.239698	+	0.737715i
$664$		0			0
$665$	6.41062	−	2.43003i	0.248593	−	0.0942324i
$666$		0			0
$667$	−47.6536	+	34.6224i	−1.84515	+	1.34058i
$668$		0			0
$669$	−7.78797	+	5.65829i	−0.301100	+	0.218762i
$670$		0			0
$671$	−3.83849	−	2.78883i	−0.148183	−	0.107661i
$672$		0			0
$673$	0.662831	−	2.03998i	0.0255503	−	0.0786356i	−0.937468	−	0.348071i	$-0.886837\pi$
$673$	0.662831	−	2.03998i	0.0255503	−	0.0786356i	0.963019	+	0.269435i	$0.0868369\pi$
$674$		0			0
$675$	−31.0928	+	27.5276i	−1.19676	+	1.05954i
$676$		0			0
$677$	12.8391	−	39.5147i	0.493446	−	1.51867i	−0.325918	−	0.945398i	$-0.605673\pi$
$677$	12.8391	−	39.5147i	0.493446	−	1.51867i	0.819364	−	0.573274i	$-0.194327\pi$
$678$		0			0
$679$	16.4492	+	11.9510i	0.631263	+	0.458639i
$680$		0			0
$681$	−39.3039	+	28.5560i	−1.50613	+	1.09427i
$682$		0			0
$683$	−23.3247	+	16.9464i	−0.892495	+	0.648436i	−0.936527	−	0.350595i	$-0.885980\pi$
$683$	−23.3247	+	16.9464i	−0.892495	+	0.648436i	0.0440323	+	0.999030i	$0.485980\pi$
$684$		0			0
$685$	−2.10198	−	43.6045i	−0.0803124	−	1.66604i
$686$		0			0
$687$	4.66589	+	14.3601i	0.178015	+	0.547874i
$688$		0			0
$689$	4.86950	−	14.9868i	0.185513	−	0.570951i
$690$		0			0
$691$	15.2050	+	46.7963i	0.578426	+	1.78021i	0.624204	+	0.781262i	$0.285424\pi$
$691$	15.2050	+	46.7963i	0.578426	+	1.78021i	−0.0457774	+	0.998952i	$0.514576\pi$
$692$		0			0
$693$	−19.4945			−0.740535
$694$		0			0
$695$	9.75053	−	14.8776i	0.369859	−	0.564340i
$696$		0			0
$697$	−7.91886	−	5.75339i	−0.299948	−	0.217925i
$698$		0			0
$699$	4.93309			0.186587
$700$		0			0
$701$	−24.9783			−0.943419			−0.471709	−	0.881754i	$-0.656363\pi$
$701$	−24.9783			−0.943419			−0.471709	+	0.881754i	$0.656363\pi$
$702$		0			0
$703$	1.77893	+	1.29247i	0.0670935	+	0.0487462i
$704$		0			0
$705$	0.585550	+	12.1469i	0.0220531	+	0.457480i
$706$		0			0
$707$	24.1650			0.908817
$708$		0			0
$709$	3.02602	+	9.31312i	0.113644	+	0.349762i	0.991662	−	0.128867i	$-0.0411340\pi$
$709$	3.02602	+	9.31312i	0.113644	+	0.349762i	−0.878017	+	0.478629i	$0.841134\pi$
$710$		0			0
$711$	6.20252	−	19.0894i	0.232613	−	0.715908i
$712$		0			0
$713$	12.7054	+	39.1032i	0.475821	+	1.46443i
$714$		0			0
$715$	−9.56346	−	2.60553i	−0.357653	−	0.0974414i
$716$		0			0
$717$	−30.7184	+	22.3182i	−1.14720	+	0.833488i
$718$		0			0
$719$	−6.94474	+	5.04565i	−0.258995	+	0.188171i	−0.709704	−	0.704500i	$-0.751171\pi$
$719$	−6.94474	+	5.04565i	−0.258995	+	0.188171i	0.450709	+	0.892671i	$0.351171\pi$
$720$		0			0
$721$	3.90559	+	2.83758i	0.145452	+	0.105677i
$722$		0			0
$723$	−0.362527	+	1.11574i	−0.0134825	+	0.0414950i
$724$		0			0
$725$	−15.1335	−	34.7719i	−0.562043	−	1.29140i
$726$		0			0
$727$	7.42142	−	22.8408i	0.275245	−	0.847118i	−0.713909	−	0.700238i	$-0.753077\pi$
$727$	7.42142	−	22.8408i	0.275245	−	0.847118i	0.989154	−	0.146880i	$-0.0469230\pi$
$728$		0			0
$729$	25.8337	+	18.7693i	0.956802	+	0.695157i
$730$		0			0
$731$	−9.69962	+	7.04719i	−0.358754	+	0.260650i
$732$		0			0
$733$	15.3787	−	11.1733i	0.568025	−	0.412695i	−0.266362	−	0.963873i	$-0.585822\pi$
$733$	15.3787	−	11.1733i	0.568025	−	0.412695i	0.834387	+	0.551178i	$0.185822\pi$
$734$		0			0
$735$	−15.1109	−	18.8212i	−0.557374	−	0.694230i
$736$		0			0
$737$	−5.38220	−	16.5647i	−0.198256	−	0.610168i
$738$		0			0
$739$	6.42507	−	19.7743i	0.236350	−	0.727411i	−0.760589	−	0.649233i	$-0.775090\pi$
$739$	6.42507	−	19.7743i	0.236350	−	0.727411i	0.996939	−	0.0781776i	$-0.0249101\pi$
$740$		0			0
$741$	3.70653	+	11.4075i	0.136163	+	0.419066i
$742$		0			0
$743$	−6.53365			−0.239696			−0.119848	−	0.992792i	$-0.538241\pi$
$743$	−6.53365			−0.239696			−0.119848	+	0.992792i	$0.538241\pi$
$744$		0			0
$745$	−3.62351	−	0.987213i	−0.132755	−	0.0361687i
$746$		0			0
$747$	−29.9012	−	21.7245i	−1.09403	−	0.794858i
$748$		0			0
$749$	34.4755			1.25971
$750$		0			0
$751$	−27.9879			−1.02129			−0.510646	−	0.859791i	$-0.670594\pi$
$751$	−27.9879			−1.02129			−0.510646	+	0.859791i	$0.670594\pi$
$752$		0			0
$753$	−22.4773	−	16.3307i	−0.819117	−	0.595123i
$754$		0			0
$755$	45.8807	+	12.5001i	1.66977	+	0.454923i
$756$		0			0
$757$	4.48558			0.163031			0.0815156	−	0.996672i	$-0.474024\pi$
$757$	4.48558			0.163031			0.0815156	+	0.996672i	$0.474024\pi$
$758$		0			0
$759$	−13.0521	−	40.1702i	−0.473761	−	1.45809i
$760$		0			0
$761$	0.138770	−	0.427091i	0.00503042	−	0.0154820i	−0.948510	−	0.316748i	$-0.897409\pi$
$761$	0.138770	−	0.427091i	0.00503042	−	0.0154820i	0.953540	+	0.301266i	$0.0974091\pi$
$762$		0			0
$763$	−5.84063	−	17.9756i	−0.211445	−	0.650760i
$764$		0			0
$765$	−22.6093	−	28.1607i	−0.817440	−	1.01815i
$766$		0			0
$767$	17.7228	−	12.8764i	0.639935	−	0.464940i
$768$		0			0
$769$	−16.9783	+	12.3355i	−0.612254	+	0.444829i	−0.850207	−	0.526448i	$-0.823524\pi$
$769$	−16.9783	+	12.3355i	−0.612254	+	0.444829i	0.237953	+	0.971277i	$0.423524\pi$
$770$		0			0
$771$	−11.9498	−	8.68202i	−0.430360	−	0.312675i
$772$		0			0
$773$	10.8283	−	33.3262i	0.389468	−	1.19866i	−0.543718	−	0.839268i	$-0.682984\pi$
$773$	10.8283	−	33.3262i	0.389468	−	1.19866i	0.933187	−	0.359392i	$-0.117016\pi$
$774$		0			0
$775$	−26.3479	+	2.54615i	−0.946444	+	0.0914602i
$776$		0			0
$777$	−2.20978	+	6.80099i	−0.0792753	+	0.243984i
$778$		0			0
$779$	−4.75564	−	3.45517i	−0.170388	−	0.123794i
$780$		0			0
$781$	0.453127	−	0.329216i	0.0162142	−	0.0117803i
$782$		0			0
$783$	50.9623	−	37.0263i	1.82125	−	1.32321i
$784$		0			0
$785$	22.5482	+	6.14318i	0.804779	+	0.219259i
$786$		0			0
$787$	−12.1132	−	37.2807i	−0.431790	−	1.32891i	−0.896340	−	0.443367i	$-0.853784\pi$
$787$	−12.1132	−	37.2807i	−0.431790	−	1.32891i	0.464550	−	0.885547i	$-0.346216\pi$
$788$		0			0
$789$	−18.1606	+	55.8925i	−0.646534	+	1.98983i
$790$		0			0
$791$	−3.43132	−	10.5605i	−0.122004	−	0.375489i
$792$		0			0
$793$	−6.25724			−0.222201
$794$		0			0
$795$	2.08155	+	43.1808i	0.0738251	+	1.53146i
$796$		0			0
$797$	6.98479	+	5.07475i	0.247414	+	0.179757i	0.704580	−	0.709625i	$-0.251135\pi$
$797$	6.98479	+	5.07475i	0.247414	+	0.179757i	−0.457166	+	0.889381i	$0.651135\pi$
$798$		0			0
$799$	−5.10532			−0.180613
$800$		0			0
$801$	−19.2580			−0.680448
$802$		0			0
$803$	−22.1713	−	16.1084i	−0.782408	−	0.568453i
$804$		0			0
$805$	−17.4520	+	26.6287i	−0.615102	+	0.938538i
$806$		0			0
$807$	−43.8854			−1.54484
$808$		0			0
$809$	−14.1830	−	43.6508i	−0.498648	−	1.53468i	−0.811194	−	0.584778i	$-0.801182\pi$
$809$	−14.1830	−	43.6508i	−0.498648	−	1.53468i	0.312546	−	0.949903i	$-0.398818\pi$
$810$		0			0
$811$	−12.1734	+	37.4660i	−0.427467	+	1.31561i	0.473145	+	0.880984i	$0.343119\pi$
$811$	−12.1734	+	37.4660i	−0.427467	+	1.31561i	−0.900612	+	0.434623i	$0.856881\pi$
$812$		0			0
$813$	−11.5102	−	35.4249i	−0.403682	−	1.24240i
$814$		0			0
$815$	−1.12087	−	23.2519i	−0.0392623	−	0.814477i
$816$		0			0
$817$	−5.82507	+	4.23216i	−0.203794	+	0.148065i
$818$		0			0
$819$	−20.7993	+	15.1116i	−0.726788	+	0.528042i
$820$		0			0
$821$	−22.0672	−	16.0328i	−0.770152	−	0.559548i	0.131855	−	0.991269i	$-0.457907\pi$
$821$	−22.0672	−	16.0328i	−0.770152	−	0.559548i	−0.902007	+	0.431721i	$0.857907\pi$
$822$		0			0
$823$	−1.89701	+	5.83841i	−0.0661258	+	0.203514i	−0.978660	−	0.205486i	$-0.934122\pi$
$823$	−1.89701	+	5.83841i	−0.0661258	+	0.203514i	0.912534	+	0.409000i	$0.134122\pi$
$824$		0			0
$825$	27.0668	−	2.61562i	0.942346	−	0.0910642i
$826$		0			0
$827$	−13.6170	+	41.9087i	−0.473508	+	1.45731i	0.374451	+	0.927247i	$0.377831\pi$
$827$	−13.6170	+	41.9087i	−0.473508	+	1.45731i	−0.847959	+	0.530062i	$0.822169\pi$
$828$		0			0
$829$	−3.80236	−	2.76257i	−0.132061	−	0.0959481i	0.519794	−	0.854292i	$-0.326009\pi$
$829$	−3.80236	−	2.76257i	−0.132061	−	0.0959481i	−0.651855	+	0.758344i	$0.726009\pi$
$830$		0			0
$831$	−15.1958	+	11.0404i	−0.527136	+	0.382987i
$832$		0			0
$833$	8.19758	−	5.95589i	0.284029	−	0.206359i
$834$		0			0
$835$	4.43625	−	1.68162i	0.153523	−	0.0581948i
$836$		0			0
$837$	−13.5876	−	41.8183i	−0.469656	−	1.44545i
$838$		0			0
$839$	14.2747	−	43.9331i	0.492819	−	1.51674i	−0.327509	−	0.944848i	$-0.606209\pi$
$839$	14.2747	−	43.9331i	0.492819	−	1.51674i	0.820328	−	0.571893i	$-0.193791\pi$
$840$		0			0
$841$	8.81451	+	27.1283i	0.303949	+	0.935458i
$842$		0			0
$843$	59.5937			2.05252
$844$		0			0
$845$	14.9583	−	5.67011i	0.514580	−	0.195058i
$846$		0			0
$847$	−11.3300	−	8.23173i	−0.389304	−	0.282846i
$848$		0			0
$849$	5.38938			0.184963
$850$		0			0
$851$	−10.2116			−0.350048
$852$		0			0
$853$	−10.2282	−	7.43121i	−0.350206	−	0.254440i	0.398749	−	0.917060i	$-0.369444\pi$
$853$	−10.2282	−	7.43121i	−0.350206	−	0.254440i	−0.748956	+	0.662620i	$0.769444\pi$
$854$		0			0
$855$	−13.5779	−	16.9118i	−0.464355	−	0.578371i
$856$		0			0
$857$	−19.4162			−0.663245			−0.331623	−	0.943412i	$-0.607596\pi$
$857$	−19.4162			−0.663245			−0.331623	+	0.943412i	$0.607596\pi$
$858$		0			0
$859$	−2.88593	−	8.88197i	−0.0984665	−	0.303049i	0.889675	−	0.456594i	$-0.150931\pi$
$859$	−2.88593	−	8.88197i	−0.0984665	−	0.303049i	−0.988142	+	0.153545i	$0.950931\pi$
$860$		0			0
$861$	5.90744	−	18.1812i	0.201325	−	0.619615i
$862$		0			0
$863$	5.05071	+	15.5445i	0.171928	+	0.529141i	0.999480	−	0.0322489i	$-0.0102669\pi$
$863$	5.05071	+	15.5445i	0.171928	+	0.529141i	−0.827552	+	0.561390i	$0.810267\pi$
$864$		0			0
$865$	−22.2032	+	33.8781i	−0.754930	+	1.15189i
$866$		0			0
$867$	−22.1886	+	16.1210i	−0.753565	+	0.547497i
$868$		0			0
$869$	−5.13308	+	3.72940i	−0.174128	+	0.126511i
$870$		0			0
$871$	−18.5829	−	13.5013i	−0.629659	−	0.457474i
$872$		0			0
$873$	19.8763	−	61.1728i	0.672709	−	2.07039i
$874$		0			0
$875$	−14.3106	−	14.6751i	−0.483787	−	0.496110i
$876$		0			0
$877$	−10.9717	+	33.7673i	−0.370487	+	1.14024i	0.575986	+	0.817459i	$0.304618\pi$
$877$	−10.9717	+	33.7673i	−0.370487	+	1.14024i	−0.946473	+	0.322782i	$0.895382\pi$
$878$		0			0
$879$	−16.4617	−	11.9601i	−0.555240	−	0.403405i
$880$		0			0
$881$	25.5378	−	18.5543i	0.860390	−	0.625110i	−0.0676008	−	0.997712i	$-0.521534\pi$
$881$	25.5378	−	18.5543i	0.860390	−	0.625110i	0.927991	+	0.372602i	$0.121534\pi$
$882$		0			0
$883$	28.2592	−	20.5315i	0.950997	−	0.690940i	−4.54670e−5	−	1.00000i	$-0.500014\pi$
$883$	28.2592	−	20.5315i	0.950997	−	0.690940i	0.951042	+	0.309060i	$0.100014\pi$
$884$		0			0
$885$	−32.9433	+	50.2658i	−1.10738	+	1.68967i
$886$		0			0
$887$	13.2668	+	40.8311i	0.445456	+	1.37097i	0.881982	+	0.471282i	$0.156209\pi$
$887$	13.2668	+	40.8311i	0.445456	+	1.37097i	−0.436526	+	0.899692i	$0.643791\pi$
$888$		0			0
$889$	0.188810	−	0.581099i	0.00633250	−	0.0194894i
$890$		0			0
$891$	4.10085	+	12.6211i	0.137384	+	0.422823i
$892$		0			0
$893$	−3.06598			−0.102599
$894$		0			0
$895$	14.7837	+	18.4136i	0.494164	+	0.615500i
$896$		0			0
$897$	−45.0646	−	32.7413i	−1.50466	−	1.09320i
$898$		0			0
$899$	40.1532			1.33918
$900$		0			0
$901$	−18.1487			−0.604622
$902$		0			0
$903$	−18.9438	−	13.7635i	−0.630410	−	0.458020i
$904$		0			0
$905$	−37.9625	+	14.3902i	−1.26192	+	0.478345i
$906$		0			0
$907$	39.8259			1.32240			0.661199	−	0.750211i	$-0.270048\pi$
$907$	39.8259			1.32240			0.661199	+	0.750211i	$0.270048\pi$
$908$		0			0
$909$	−23.6229	−	72.7038i	−0.783522	−	2.41143i
$910$		0			0
$911$	0.522189	−	1.60713i	0.0173009	−	0.0532467i	−0.942033	−	0.335519i	$-0.891088\pi$
$911$	0.522189	−	1.60713i	0.0173009	−	0.0532467i	0.959334	+	0.282273i	$0.0910882\pi$
$912$		0			0
$913$	3.61034	+	11.1115i	0.119485	+	0.367737i
$914$		0			0
$915$	16.0517	−	6.08461i	0.530654	−	0.201151i
$916$		0			0
$917$	7.68015	−	5.57995i	0.253621	−	0.184266i
$918$		0			0
$919$	−24.2013	+	17.5833i	−0.798327	+	0.580019i	−0.910423	−	0.413679i	$-0.864244\pi$
$919$	−24.2013	+	17.5833i	−0.798327	+	0.580019i	0.112096	+	0.993697i	$0.464244\pi$
$920$		0			0
$921$	6.94836	+	5.04828i	0.228956	+	0.166346i
$922$		0			0
$923$	0.228257	−	0.702504i	0.00751318	−	0.0231232i
$924$		0			0
$925$	1.42074	−	6.41896i	0.0467135	−	0.211054i
$926$		0			0
$927$	4.71929	−	14.5245i	0.155002	−	0.477047i
$928$		0			0
$929$	12.8664	+	9.34795i	0.422131	+	0.306696i	0.778495	−	0.627651i	$-0.215983\pi$
$929$	12.8664	+	9.34795i	0.422131	+	0.306696i	−0.356363	+	0.934347i	$0.615983\pi$
$930$		0			0
$931$	4.92303	−	3.57679i	0.161346	−	0.117225i
$932$		0			0
$933$	49.5557	−	36.0043i	1.62238	−	1.17873i
$934$		0			0
$935$	0.549668	+	11.4026i	0.0179761	+	0.372905i
$936$		0			0
$937$	14.2973	+	44.0026i	0.467073	+	1.43750i	0.856357	+	0.516384i	$0.172722\pi$
$937$	14.2973	+	44.0026i	0.467073	+	1.43750i	−0.389284	+	0.921118i	$0.627278\pi$
$938$		0			0
$939$	−15.0585	+	46.3454i	−0.491417	+	1.51243i
$940$		0			0
$941$	−3.60650	−	11.0997i	−0.117569	−	0.361839i	0.874906	−	0.484294i	$-0.160923\pi$
$941$	−3.60650	−	11.0997i	−0.117569	−	0.361839i	−0.992474	+	0.122455i	$0.960923\pi$
$942$		0			0
$943$	27.2988			0.888971
$944$		0			0
$945$	18.6638	−	28.4776i	0.607132	−	0.926377i
$946$		0			0
$947$	−2.37336	−	1.72435i	−0.0771238	−	0.0560337i	0.548555	−	0.836114i	$-0.315178\pi$
$947$	−2.37336	−	1.72435i	−0.0771238	−	0.0560337i	−0.625679	+	0.780081i	$0.715178\pi$
$948$		0			0
$949$	−36.1421			−1.17322
$950$		0			0
$951$	−48.9638			−1.58776
$952$		0			0
$953$	8.03924	+	5.84085i	0.260417	+	0.189204i	0.710331	−	0.703868i	$-0.248545\pi$
$953$	8.03924	+	5.84085i	0.260417	+	0.189204i	−0.449914	+	0.893072i	$0.648545\pi$
$954$		0			0
$955$	2.35843	+	48.9245i	0.0763171	+	1.58316i
$956$		0			0
$957$	−41.2488			−1.33339
$958$		0			0
$959$	11.0607	+	34.0413i	0.357168	+	1.09925i
$960$		0			0
$961$	−0.918471	+	2.82676i	−0.0296281	+	0.0911859i
$962$		0			0
$963$	−33.7021	−	103.725i	−1.08604	−	3.34248i
$964$		0			0
$965$	59.1672	+	16.1199i	1.90466	+	0.518918i
$966$		0			0
$967$	36.7193	−	26.6781i	1.18081	−	0.857910i	0.188549	−	0.982064i	$-0.439621\pi$
$967$	36.7193	−	26.6781i	1.18081	−	0.857910i	0.992263	+	0.124153i	$0.0396215\pi$
$968$		0			0
$969$	11.1760	−	8.11987i	0.359026	−	0.260848i
$970$		0			0
$971$	−3.78844	−	2.75246i	−0.121577	−	0.0883307i	0.525335	−	0.850895i	$-0.323940\pi$
$971$	−3.78844	−	2.75246i	−0.121577	−	0.0883307i	−0.646912	+	0.762565i	$0.723940\pi$
$972$		0			0
$973$	−4.50688	+	13.8707i	−0.144484	+	0.444675i
$974$		0			0
$975$	26.8510	−	23.7722i	0.859919	−	0.761319i
$976$		0			0
$977$	0.991339	−	3.05103i	0.0317157	−	0.0976110i	−0.933946	−	0.357415i	$-0.883658\pi$
$977$	0.991339	−	3.05103i	0.0317157	−	0.0976110i	0.965661	+	0.259804i	$0.0836581\pi$
$978$		0			0
$979$	4.92498	+	3.57820i	0.157403	+	0.114360i
$980$		0			0
$981$	−48.3726	+	35.1448i	−1.54442	+	1.12209i
$982$		0			0
$983$	15.8337	−	11.5038i	0.505015	−	0.366915i	−0.305914	−	0.952059i	$-0.598962\pi$
$983$	15.8337	−	11.5038i	0.505015	−	0.366915i	0.810929	+	0.585144i	$0.198962\pi$
$984$		0			0
$985$	1.57311	+	1.95936i	0.0501233	+	0.0624304i
$986$		0			0
$987$	−3.08118	−	9.48290i	−0.0980751	−	0.301844i
$988$		0			0
$989$	10.3328	−	31.8011i	0.328564	−	1.01122i
$990$		0			0
$991$	−13.9762	−	43.0144i	−0.443969	−	1.36640i	−0.883610	−	0.468223i	$-0.844894\pi$
$991$	−13.9762	−	43.0144i	−0.443969	−	1.36640i	0.439641	−	0.898173i	$-0.355106\pi$
$992$		0			0
$993$	81.4913			2.58605
$994$		0			0
$995$	−55.0127	−	14.9880i	−1.74402	−	0.475153i
$996$		0			0
$997$	46.9808	+	34.1335i	1.48790	+	1.08102i	0.974904	+	0.222626i	$0.0714627\pi$
$997$	46.9808	+	34.1335i	1.48790	+	1.08102i	0.512991	+	0.858394i	$0.328537\pi$
$998$		0			0
$999$	10.9206			0.345512

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.u.d.321.2		8
4.3	odd	2		50.2.d.b.21.1	✓	8
12.11	even	2		450.2.h.e.271.1		8
20.3	even	4		250.2.e.c.149.2		16
20.7	even	4		250.2.e.c.149.3		16
20.19	odd	2		250.2.d.d.101.2		8
25.6	even	5	inner	400.2.u.d.81.2		8
25.9	even	10		10000.2.a.x.1.4		4
25.16	even	5		10000.2.a.t.1.1		4
100.19	odd	10		250.2.d.d.151.2		8
100.31	odd	10		50.2.d.b.31.1	yes	8
100.59	odd	10		1250.2.a.f.1.1		4
100.63	even	20		1250.2.b.e.1249.4		8
100.67	even	20		250.2.e.c.99.2		16
100.83	even	20		250.2.e.c.99.3		16
100.87	even	20		1250.2.b.e.1249.5		8
100.91	odd	10		1250.2.a.l.1.4		4
300.131	even	10		450.2.h.e.181.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.d.b.21.1	✓	8	4.3	odd	2
50.2.d.b.31.1	yes	8	100.31	odd	10
250.2.d.d.101.2		8	20.19	odd	2
250.2.d.d.151.2		8	100.19	odd	10
250.2.e.c.99.2		16	100.67	even	20
250.2.e.c.99.3		16	100.83	even	20
250.2.e.c.149.2		16	20.3	even	4
250.2.e.c.149.3		16	20.7	even	4
400.2.u.d.81.2		8	25.6	even	5	inner
400.2.u.d.321.2		8	1.1	even	1	trivial
450.2.h.e.181.1		8	300.131	even	10
450.2.h.e.271.1		8	12.11	even	2
1250.2.a.f.1.1		4	100.59	odd	10
1250.2.a.l.1.4		4	100.91	odd	10
1250.2.b.e.1249.4		8	100.63	even	20
1250.2.b.e.1249.5		8	100.87	even	20
10000.2.a.t.1.1		4	25.16	even	5
10000.2.a.x.1.4		4	25.9	even	10

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.u (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.39991 + 1.74363i) q^{3} +(2.15743 + 0.587785i) q^{5} -1.83337 q^{7} +(1.79224 + 5.51595i) q^{9} +O(q^{10})\)	\(q+(2.39991 + 1.74363i) q^{3} +(2.15743 + 0.587785i) q^{5} -1.83337 q^{7} +(1.79224 + 5.51595i) q^{9} +(0.566541 - 1.74363i) q^{11} +(-0.747156 - 2.29951i) q^{13} +(4.15275 + 5.17240i) q^{15} +(-2.25284 + 1.63679i) q^{17} +(-1.35294 + 0.982966i) q^{19} +(-4.39991 - 3.19672i) q^{21} +(2.39991 - 7.38615i) q^{23} +(4.30902 + 2.53621i) q^{25} +(-2.56654 + 7.89900i) q^{27} +(-6.13597 - 4.45805i) q^{29} +(-4.28304 + 3.11181i) q^{31} +(4.39991 - 3.19672i) q^{33} +(-3.95536 - 1.07763i) q^{35} +(-0.406315 - 1.25051i) q^{37} +(2.21640 - 6.82138i) q^{39} +(1.08621 + 3.34301i) q^{41} +4.30550 q^{43} +(0.624442 + 12.9537i) q^{45} +(1.48322 + 1.07763i) q^{47} -3.63877 q^{49} -8.26057 q^{51} +(5.27267 + 3.83082i) q^{53} +(2.24716 - 3.42877i) q^{55} -4.96086 q^{57} +(2.79981 + 8.61694i) q^{59} +(0.799717 - 2.46127i) q^{61} +(-3.28583 - 10.1128i) q^{63} +(-0.260320 - 5.40020i) q^{65} +(7.68574 - 5.58402i) q^{67} +(18.6383 - 13.5415i) q^{69} +(0.247156 + 0.179569i) q^{71} +(4.61920 - 14.2164i) q^{73} +(5.91901 + 13.6000i) q^{75} +(-1.03868 + 3.19672i) q^{77} +(-2.79981 - 2.03418i) q^{79} +(-5.85599 + 4.25462i) q^{81} +(-5.15555 + 3.74572i) q^{83} +(-5.82243 + 2.20707i) q^{85} +(-6.95256 - 21.3978i) q^{87} +(-1.02608 + 3.15794i) q^{89} +(1.36981 + 4.21584i) q^{91} -15.7047 q^{93} +(-3.49664 + 1.32545i) q^{95} +(-8.97214 - 6.51864i) q^{97} +10.6332 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{3} - 4 q^{7} - q^{9}+O(q^{10}) \) 8 * q + 3 * q^3 - 4 * q^7 - q^9	\( 8 q + 3 q^{3} - 4 q^{7} - q^{9} - q^{11} - 13 q^{13} + 10 q^{15} - 11 q^{17} - 20 q^{19} - 19 q^{21} + 3 q^{23} + 30 q^{25} - 15 q^{27} - 15 q^{29} + 9 q^{31} + 19 q^{33} + 15 q^{35} - 6 q^{37} + 12 q^{39} - 9 q^{41} - 12 q^{43} + 15 q^{45} + q^{47} - 4 q^{49} - 26 q^{51} + 7 q^{53} + 25 q^{55} - 10 q^{59} + 6 q^{61} + 8 q^{63} - 10 q^{65} + 11 q^{67} + 43 q^{69} + 9 q^{71} - 8 q^{73} - 30 q^{75} + 33 q^{77} + 10 q^{79} - 17 q^{81} - 27 q^{83} + 5 q^{85} - 15 q^{89} - q^{91} - 46 q^{93} + 30 q^{95} - 36 q^{97} + 42 q^{99}+O(q^{100}) \) 8 * q + 3 * q^3 - 4 * q^7 - q^9 - q^11 - 13 * q^13 + 10 * q^15 - 11 * q^17 - 20 * q^19 - 19 * q^21 + 3 * q^23 + 30 * q^25 - 15 * q^27 - 15 * q^29 + 9 * q^31 + 19 * q^33 + 15 * q^35 - 6 * q^37 + 12 * q^39 - 9 * q^41 - 12 * q^43 + 15 * q^45 + q^47 - 4 * q^49 - 26 * q^51 + 7 * q^53 + 25 * q^55 - 10 * q^59 + 6 * q^61 + 8 * q^63 - 10 * q^65 + 11 * q^67 + 43 * q^69 + 9 * q^71 - 8 * q^73 - 30 * q^75 + 33 * q^77 + 10 * q^79 - 17 * q^81 - 27 * q^83 + 5 * q^85 - 15 * q^89 - q^91 - 46 * q^93 + 30 * q^95 - 36 * q^97 + 42 * q^99

Introduction

L-functions

Modular forms

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