LMFDB - Embedded newform 820.2.u.b.201.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(141,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.141"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.u (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			201.7
Character	$\chi$	$=$	820.201
Dual form			820.2.u.b.461.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.19153 q^{3} +(-0.309017 + 0.951057i) q^{5} +(1.32809 + 0.964915i) q^{7} +1.80282 q^{9} +(0.350697 + 1.07933i) q^{11} +(-4.20663 + 3.05630i) q^{13} +(-0.677221 + 2.08427i) q^{15} +(1.10772 + 3.40923i) q^{17} +(6.46733 + 4.69879i) q^{19} +(2.91056 + 2.11464i) q^{21} +(5.76416 - 4.18791i) q^{23} +(-0.809017 - 0.587785i) q^{25} -2.62367 q^{27} +(0.846567 - 2.60546i) q^{29} +(-1.42070 - 4.37246i) q^{31} +(0.768563 + 2.36539i) q^{33} +(-1.32809 + 0.964915i) q^{35} +(2.46732 - 7.59364i) q^{37} +(-9.21898 + 6.69798i) q^{39} +(-0.540510 + 6.38027i) q^{41} +(-5.00327 + 3.63509i) q^{43} +(-0.557101 + 1.71458i) q^{45} +(9.80804 - 7.12596i) q^{47} +(-1.33035 - 4.09440i) q^{49} +(2.42762 + 7.47143i) q^{51} +(-1.74877 + 5.38217i) q^{53} -1.13488 q^{55} +(14.1734 + 10.2976i) q^{57} +(-2.98906 + 2.17168i) q^{59} +(-6.23688 - 4.53136i) q^{61} +(2.39431 + 1.73957i) q^{63} +(-1.60679 - 4.94519i) q^{65} +(1.71907 - 5.29074i) q^{67} +(12.6323 - 9.17793i) q^{69} +(-0.714113 - 2.19781i) q^{71} -5.12044 q^{73} +(-1.77299 - 1.28815i) q^{75} +(-0.575708 + 1.77185i) q^{77} +15.1613 q^{79} -11.1583 q^{81} -8.41696 q^{83} -3.58467 q^{85} +(1.85528 - 5.70996i) q^{87} +(-7.06638 - 5.13403i) q^{89} -8.53586 q^{91} +(-3.11351 - 9.58239i) q^{93} +(-6.46733 + 4.69879i) q^{95} +(2.81546 - 8.66510i) q^{97} +(0.632242 + 1.94584i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{3} + 8 q^{5} - 5 q^{7} + 46 q^{9} + q^{11} + q^{13} - 2 q^{15} + 7 q^{17} - 13 q^{19} - 6 q^{21} + 4 q^{23} - 8 q^{25} - 28 q^{27} + 3 q^{29} - q^{31} + 14 q^{33} + 5 q^{35} - 25 q^{37} + 26 q^{41}+ \cdots + 30 q^{99}+O(q^{100}) $ 32 * q + 2 * q^3 + 8 * q^5 - 5 * q^7 + 46 * q^9 + q^11 + q^13 - 2 * q^15 + 7 * q^17 - 13 * q^19 - 6 * q^21 + 4 * q^23 - 8 * q^25 - 28 * q^27 + 3 * q^29 - q^31 + 14 * q^33 + 5 * q^35 - 25 * q^37 + 26 * q^41 + 8 * q^43 + 19 * q^45 + q^47 - 15 * q^49 + 29 * q^51 - 33 * q^53 + 4 * q^55 - 29 * q^57 + 20 * q^59 - 24 * q^61 - 66 * q^63 - q^65 - 48 * q^67 - 16 * q^69 + 5 * q^71 + 4 * q^73 - 3 * q^75 - 16 * q^77 - 102 * q^79 + 200 * q^81 - 110 * q^83 + 8 * q^85 + 25 * q^87 - 34 * q^89 - 10 * q^91 - 18 * q^93 + 13 * q^95 - 36 * q^97 + 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

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
$3$	2.19153			1.26528			0.632641	−	0.774445i	$-0.281971\pi$
$3$	2.19153			1.26528			0.632641	+	0.774445i	$0.281971\pi$
$4$		0			0
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$6$		0			0
$7$	1.32809	+	0.964915i	0.501971	+	0.364704i	0.809770	−	0.586748i	$-0.199592\pi$
$7$	1.32809	+	0.964915i	0.501971	+	0.364704i	−0.307798	+	0.951452i	$0.599592\pi$
$8$		0			0
$9$	1.80282			0.600939
$10$		0			0
$11$	0.350697	+	1.07933i	0.105739	+	0.325431i	0.989903	−	0.141745i	$-0.0452713\pi$
$11$	0.350697	+	1.07933i	0.105739	+	0.325431i	−0.884164	+	0.467176i	$0.845271\pi$
$12$		0			0
$13$	−4.20663	+	3.05630i	−1.16671	+	0.847665i	−0.990611	−	0.136708i	$-0.956348\pi$
$13$	−4.20663	+	3.05630i	−1.16671	+	0.847665i	−0.176099	+	0.984372i	$0.556348\pi$
$14$		0			0
$15$	−0.677221	+	2.08427i	−0.174858	+	0.538157i
$16$		0			0
$17$	1.10772	+	3.40923i	0.268663	+	0.826859i	0.990827	+	0.135137i	$0.0431475\pi$
$17$	1.10772	+	3.40923i	0.268663	+	0.826859i	−0.722164	+	0.691722i	$0.756852\pi$
$18$		0			0
$19$	6.46733	+	4.69879i	1.48371	+	1.07798i	0.976339	+	0.216247i	$0.0693815\pi$
$19$	6.46733	+	4.69879i	1.48371	+	1.07798i	0.507368	+	0.861730i	$0.330618\pi$
$20$		0			0
$21$	2.91056	+	2.11464i	0.635136	+	0.461453i
$22$		0			0
$23$	5.76416	−	4.18791i	1.20191	−	0.873239i	0.207439	−	0.978248i	$-0.433487\pi$
$23$	5.76416	−	4.18791i	1.20191	−	0.873239i	0.994471	+	0.105009i	$0.0334873\pi$
$24$		0			0
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$		0			0
$27$	−2.62367			−0.504925
$28$		0			0
$29$	0.846567	−	2.60546i	0.157204	−	0.483823i	−0.841174	−	0.540765i	$-0.818135\pi$
$29$	0.846567	−	2.60546i	0.157204	−	0.483823i	0.998377	+	0.0569419i	$0.0181350\pi$
$30$		0			0
$31$	−1.42070	−	4.37246i	−0.255165	−	0.785317i	−0.993797	−	0.111208i	$-0.964528\pi$
$31$	−1.42070	−	4.37246i	−0.255165	−	0.785317i	0.738632	−	0.674109i	$-0.235472\pi$
$32$		0			0
$33$	0.768563	+	2.36539i	0.133790	+	0.411762i
$34$		0			0
$35$	−1.32809	+	0.964915i	−0.224488	+	0.163100i
$36$		0			0
$37$	2.46732	−	7.59364i	0.405626	−	1.24839i	−0.514746	−	0.857343i	$-0.672114\pi$
$37$	2.46732	−	7.59364i	0.405626	−	1.24839i	0.920372	−	0.391045i	$-0.127886\pi$
$38$		0			0
$39$	−9.21898	+	6.69798i	−1.47622	+	1.07254i
$40$		0			0
$41$	−0.540510	+	6.38027i	−0.0844134	+	0.996431i
$41$	−0.540510	+	6.38027i	−0.0844134	+	0.996431i
$42$		0			0
$43$	−5.00327	+	3.63509i	−0.762992	+	0.554346i	−0.899826	−	0.436248i	$-0.856307\pi$
$43$	−5.00327	+	3.63509i	−0.762992	+	0.554346i	0.136835	+	0.990594i	$0.456307\pi$
$44$		0			0
$45$	−0.557101	+	1.71458i	−0.0830477	+	0.255595i
$46$		0			0
$47$	9.80804	−	7.12596i	1.43065	−	1.03943i	0.440754	−	0.897628i	$-0.354711\pi$
$47$	9.80804	−	7.12596i	1.43065	−	1.03943i	0.989895	−	0.141800i	$-0.0452889\pi$
$48$		0			0
$49$	−1.33035	−	4.09440i	−0.190050	−	0.584915i
$50$		0			0
$51$	2.42762	+	7.47143i	0.339934	+	1.04621i
$52$		0			0
$53$	−1.74877	+	5.38217i	−0.240213	+	0.739298i	0.756175	+	0.654370i	$0.227066\pi$
$53$	−1.74877	+	5.38217i	−0.240213	+	0.739298i	−0.996387	+	0.0849282i	$0.972934\pi$
$54$		0			0
$55$	−1.13488			−0.153027
$56$		0			0
$57$	14.1734	+	10.2976i	1.87731	+	1.36394i
$58$		0			0
$59$	−2.98906	+	2.17168i	−0.389143	+	0.282729i	−0.765104	−	0.643906i	$-0.777313\pi$
$59$	−2.98906	+	2.17168i	−0.389143	+	0.282729i	0.375961	+	0.926635i	$0.377313\pi$
$60$		0			0
$61$	−6.23688	−	4.53136i	−0.798551	−	0.580181i	0.111938	−	0.993715i	$-0.464294\pi$
$61$	−6.23688	−	4.53136i	−0.798551	−	0.580181i	−0.910489	+	0.413534i	$0.864294\pi$
$62$		0			0
$63$	2.39431	+	1.73957i	0.301654	+	0.219165i
$64$		0			0
$65$	−1.60679	−	4.94519i	−0.199298	−	0.613376i
$66$		0			0
$67$	1.71907	−	5.29074i	0.210017	−	0.646367i	−0.789453	−	0.613811i	$-0.789636\pi$
$67$	1.71907	−	5.29074i	0.210017	−	0.646367i	0.999470	−	0.0325552i	$-0.0103645\pi$
$68$		0			0
$69$	12.6323	−	9.17793i	1.52076	−	1.10489i
$70$		0			0
$71$	−0.714113	−	2.19781i	−0.0847496	−	0.260832i	0.899697	−	0.436514i	$-0.143787\pi$
$71$	−0.714113	−	2.19781i	−0.0847496	−	0.260832i	−0.984447	+	0.175682i	$0.943787\pi$
$72$		0			0
$73$	−5.12044			−0.599302			−0.299651	−	0.954049i	$-0.596870\pi$
$73$	−5.12044			−0.599302			−0.299651	+	0.954049i	$0.596870\pi$
$74$		0			0
$75$	−1.77299	−	1.28815i	−0.204727	−	0.148743i
$76$		0			0
$77$	−0.575708	+	1.77185i	−0.0656080	+	0.201921i
$78$		0			0
$79$	15.1613			1.70578			0.852888	−	0.522093i	$-0.174849\pi$
$79$	15.1613			1.70578			0.852888	+	0.522093i	$0.174849\pi$
$80$		0			0
$81$	−11.1583			−1.23981
$82$		0			0
$83$	−8.41696			−0.923882			−0.461941	−	0.886911i	$-0.652847\pi$
$83$	−8.41696			−0.923882			−0.461941	+	0.886911i	$0.652847\pi$
$84$		0			0
$85$	−3.58467			−0.388812
$86$		0			0
$87$	1.85528	−	5.70996i	0.198907	−	0.612172i
$88$		0			0
$89$	−7.06638	−	5.13403i	−0.749035	−	0.544206i	0.146492	−	0.989212i	$-0.453202\pi$
$89$	−7.06638	−	5.13403i	−0.749035	−	0.544206i	−0.895528	+	0.445006i	$0.853202\pi$
$90$		0			0
$91$	−8.53586			−0.894802
$92$		0			0
$93$	−3.11351	−	9.58239i	−0.322856	−	0.993647i
$94$		0			0
$95$	−6.46733	+	4.69879i	−0.663534	+	0.482086i
$96$		0			0
$97$	2.81546	−	8.66510i	0.285867	−	0.879808i	−0.700271	−	0.713877i	$-0.746937\pi$
$97$	2.81546	−	8.66510i	0.285867	−	0.879808i	0.986137	−	0.165930i	$-0.0530627\pi$
$98$		0			0
$99$	0.632242	+	1.94584i	0.0635427	+	0.195564i
$100$		0			0
$101$	5.45136	+	3.96065i	0.542431	+	0.394099i	0.824987	−	0.565152i	$-0.191182\pi$
$101$	5.45136	+	3.96065i	0.542431	+	0.394099i	−0.282556	+	0.959251i	$0.591182\pi$
$102$		0			0
$103$	−15.5758	−	11.3164i	−1.53472	−	1.11504i	−0.953538	−	0.301272i	$-0.902589\pi$
$103$	−15.5758	−	11.3164i	−1.53472	−	1.11504i	−0.581186	−	0.813770i	$-0.697411\pi$
$104$		0			0
$105$	−2.91056	+	2.11464i	−0.284041	+	0.206368i
$106$		0			0
$107$	9.83902	+	7.14847i	0.951174	+	0.691068i	0.951084	−	0.308932i	$-0.0999714\pi$
$107$	9.83902	+	7.14847i	0.951174	+	0.691068i	8.96990e−5		1.00000i	$0.499971\pi$
$108$		0			0
$109$	13.0994			1.25470			0.627350	−	0.778738i	$-0.284140\pi$
$109$	13.0994			1.25470			0.627350	+	0.778738i	$0.284140\pi$
$110$		0			0
$111$	5.40722	−	16.6417i	0.513231	−	1.57956i
$112$		0			0
$113$	3.63195	+	11.1780i	0.341665	+	1.05154i	0.963345	+	0.268265i	$0.0864504\pi$
$113$	3.63195	+	11.1780i	0.341665	+	1.05154i	−0.621680	+	0.783271i	$0.713550\pi$
$114$		0			0
$115$	2.20171	+	6.77617i	0.205311	+	0.631881i
$116$		0			0
$117$	−7.58379	+	5.50995i	−0.701122	+	0.509395i
$118$		0			0
$119$	−1.81845	+	5.59663i	−0.166697	+	0.513042i
$120$		0			0
$121$	7.85721	−	5.70860i	0.714292	−	0.518964i
$122$		0			0
$123$	−1.18454	+	13.9826i	−0.106807	+	1.26077i
$124$		0			0
$125$	0.809017	−	0.587785i	0.0723607	−	0.0525731i
$126$		0			0
$127$	−1.32333	+	4.07280i	−0.117427	+	0.361402i	−0.992445	−	0.122687i	$-0.960849\pi$
$127$	−1.32333	+	4.07280i	−0.117427	+	0.361402i	0.875019	+	0.484089i	$0.160849\pi$
$128$		0			0
$129$	−10.9648	+	7.96642i	−0.965400	+	0.701404i
$130$		0			0
$131$	4.31892	+	13.2923i	0.377345	+	1.16135i	0.941883	+	0.335942i	$0.109055\pi$
$131$	4.31892	+	13.2923i	0.377345	+	1.16135i	−0.564537	+	0.825408i	$0.690945\pi$
$132$		0			0
$133$	4.05527	+	12.4808i	0.351637	+	1.08223i
$134$		0			0
$135$	0.810757	−	2.49525i	0.0697789	−	0.214757i
$136$		0			0
$137$	9.83411			0.840185			0.420093	−	0.907481i	$-0.361998\pi$
$137$	9.83411			0.840185			0.420093	+	0.907481i	$0.361998\pi$
$138$		0			0
$139$	−17.1316	−	12.4468i	−1.45308	−	1.05573i	−0.985099	−	0.171988i	$-0.944981\pi$
$139$	−17.1316	−	12.4468i	−1.45308	−	1.05573i	−0.467982	−	0.883738i	$-0.655019\pi$
$140$		0			0
$141$	21.4946	−	15.6168i	1.81018	−	1.31517i
$142$		0			0
$143$	−4.77402	−	3.46853i	−0.399223	−	0.290053i
$144$		0			0
$145$	2.21634	+	1.61027i	0.184057	+	0.133725i
$146$		0			0
$147$	−2.91551	−	8.97302i	−0.240467	−	0.740082i
$148$		0			0
$149$	5.17634	−	15.9312i	0.424063	−	1.30513i	−0.479826	−	0.877364i	$-0.659300\pi$
$149$	5.17634	−	15.9312i	0.424063	−	1.30513i	0.903889	−	0.427767i	$-0.140700\pi$
$150$		0			0
$151$	−8.45975	+	6.14637i	−0.688445	+	0.500184i	−0.876148	−	0.482041i	$-0.839896\pi$
$151$	−8.45975	+	6.14637i	−0.688445	+	0.500184i	0.187704	+	0.982226i	$0.439896\pi$
$152$		0			0
$153$	1.99703	+	6.14621i	0.161450	+	0.496892i
$154$		0			0
$155$	4.59748			0.369278
$156$		0			0
$157$	−6.85297	−	4.97897i	−0.546927	−	0.397365i	0.279724	−	0.960080i	$-0.409757\pi$
$157$	−6.85297	−	4.97897i	−0.546927	−	0.397365i	−0.826651	+	0.562715i	$0.809757\pi$
$158$		0			0
$159$	−3.83250	+	11.7952i	−0.303937	+	0.935421i
$160$		0			0
$161$	11.6963			0.921798
$162$		0			0
$163$	−21.5103			−1.68481			−0.842407	−	0.538841i	$-0.818862\pi$
$163$	−21.5103			−1.68481			−0.842407	+	0.538841i	$0.818862\pi$
$164$		0			0
$165$	−2.48712			−0.193622
$166$		0			0
$167$	−15.3123			−1.18490			−0.592451	−	0.805606i	$-0.701840\pi$
$167$	−15.3123			−1.18490			−0.592451	+	0.805606i	$0.701840\pi$
$168$		0			0
$169$	4.33759	−	13.3497i	0.333661	−	1.02690i
$170$		0			0
$171$	11.6594	+	8.47106i	0.891617	+	0.647798i
$172$		0			0
$173$	−6.18476			−0.470218			−0.235109	−	0.971969i	$-0.575545\pi$
$173$	−6.18476			−0.470218			−0.235109	+	0.971969i	$0.575545\pi$
$174$		0			0
$175$	−0.507286	−	1.56127i	−0.0383472	−	0.118021i
$176$		0			0
$177$	−6.55063	+	4.75931i	−0.492376	+	0.357732i
$178$		0			0
$179$	−1.67116	+	5.14330i	−0.124908	+	0.384428i	−0.993884	−	0.110426i	$-0.964779\pi$
$179$	−1.67116	+	5.14330i	−0.124908	+	0.384428i	0.868976	+	0.494854i	$0.164779\pi$
$180$		0			0
$181$	0.362043	+	1.11425i	0.0269104	+	0.0828218i	0.963610	−	0.267313i	$-0.0861358\pi$
$181$	0.362043	+	1.11425i	0.0269104	+	0.0828218i	−0.936699	+	0.350135i	$0.886136\pi$
$182$		0			0
$183$	−13.6683	−	9.93063i	−1.01039	−	0.734093i
$184$		0			0
$185$	6.45954	+	4.69313i	0.474915	+	0.345046i
$186$		0			0
$187$	−3.29122	+	2.39121i	−0.240678	+	0.174863i
$188$		0			0
$189$	−3.48447	−	2.53161i	−0.253458	−	0.184148i
$190$		0			0
$191$	8.40810			0.608389			0.304195	−	0.952610i	$-0.401613\pi$
$191$	8.40810			0.608389			0.304195	+	0.952610i	$0.401613\pi$
$192$		0			0
$193$	0.897313	−	2.76165i	0.0645900	−	0.198788i	−0.913553	−	0.406719i	$-0.866673\pi$
$193$	0.897313	−	2.76165i	0.0645900	−	0.198788i	0.978143	+	0.207931i	$0.0666730\pi$
$194$		0			0
$195$	−3.52134	−	10.8376i	−0.252168	−	0.776094i
$196$		0			0
$197$	−3.83527	−	11.8037i	−0.273251	−	0.840981i	−0.989677	−	0.143318i	$-0.954223\pi$
$197$	−3.83527	−	11.8037i	−0.273251	−	0.840981i	0.716425	−	0.697664i	$-0.245777\pi$
$198$		0			0
$199$	2.65384	−	1.92812i	0.188125	−	0.136681i	−0.489736	−	0.871871i	$-0.662907\pi$
$199$	2.65384	−	1.92812i	0.188125	−	0.136681i	0.677862	+	0.735190i	$0.262907\pi$
$200$		0			0
$201$	3.76739	−	11.5948i	0.265731	−	0.817836i
$202$		0			0
$203$	3.63837	−	2.64343i	0.255364	−	0.185532i
$204$		0			0
$205$	−5.90097	−	2.48567i	−0.412142	−	0.173607i
$206$		0			0
$207$	10.3917	−	7.55003i	0.722275	−	0.524763i
$208$		0			0
$209$	−2.80349	+	8.62825i	−0.193921	+	0.596829i
$210$		0			0
$211$	12.8019	−	9.30114i	0.881321	−	0.640317i	−0.0522798	−	0.998632i	$-0.516649\pi$
$211$	12.8019	−	9.30114i	0.881321	−	0.640317i	0.933601	+	0.358315i	$0.116649\pi$
$212$		0			0
$213$	−1.56500	−	4.81658i	−0.107232	−	0.330027i
$214$		0			0
$215$	−1.91108	−	5.88170i	−0.130335	−	0.401128i
$216$		0			0
$217$	2.33223	−	7.17788i	0.158322	−	0.487266i
$218$		0			0
$219$	−11.2216			−0.758286
$220$		0			0
$221$	−15.0794	−	10.9558i	−1.01435	−	0.736969i
$222$		0			0
$223$	−13.0330	+	9.46904i	−0.872755	+	0.634094i	−0.931325	−	0.364190i	$-0.881346\pi$
$223$	−13.0330	+	9.46904i	−0.872755	+	0.634094i	0.0585697	+	0.998283i	$0.481346\pi$
$224$		0			0
$225$	−1.45851	−	1.05967i	−0.0972340	−	0.0706446i
$226$		0			0
$227$	−19.8584	−	14.4280i	−1.31805	−	0.957618i	−0.999954	−	0.00955858i	$-0.996957\pi$
$227$	−19.8584	−	14.4280i	−1.31805	−	0.957618i	−0.318094	−	0.948059i	$-0.603043\pi$
$228$		0			0
$229$	0.984738	+	3.03071i	0.0650733	+	0.200275i	0.978307	−	0.207162i	$-0.0664227\pi$
$229$	0.984738	+	3.03071i	0.0650733	+	0.200275i	−0.913233	+	0.407437i	$0.866423\pi$
$230$		0			0
$231$	−1.26168	+	3.88306i	−0.0830126	+	0.255487i
$232$		0			0
$233$	1.94807	−	1.41535i	0.127622	−	0.0927229i	−0.522143	−	0.852858i	$-0.674867\pi$
$233$	1.94807	−	1.41535i	0.127622	−	0.0927229i	0.649765	+	0.760135i	$0.274867\pi$
$234$		0			0
$235$	3.74634	+	11.5300i	0.244384	+	0.752137i
$236$		0			0
$237$	33.2264			2.15829
$238$		0			0
$239$	7.50888	+	5.45552i	0.485709	+	0.352888i	0.803532	−	0.595262i	$-0.202952\pi$
$239$	7.50888	+	5.45552i	0.485709	+	0.352888i	−0.317823	+	0.948150i	$0.602952\pi$
$240$		0			0
$241$	4.07626	−	12.5454i	0.262575	−	0.808123i	−0.729667	−	0.683803i	$-0.760325\pi$
$241$	4.07626	−	12.5454i	0.262575	−	0.808123i	0.992242	−	0.124320i	$-0.0396751\pi$
$242$		0			0
$243$	−16.5828			−1.06379
$244$		0			0
$245$	4.30511			0.275043
$246$		0			0
$247$	−41.5666			−2.64482
$248$		0			0
$249$	−18.4461			−1.16897
$250$		0			0
$251$	2.76296	−	8.50353i	0.174397	−	0.536738i	−0.825209	−	0.564828i	$-0.808942\pi$
$251$	2.76296	−	8.50353i	0.174397	−	0.536738i	0.999605	+	0.0280900i	$0.00894250\pi$
$252$		0			0
$253$	6.54162	+	4.75276i	0.411268	+	0.298804i
$254$		0			0
$255$	−7.85593			−0.491957
$256$		0			0
$257$	7.70264	+	23.7063i	0.480478	+	1.47876i	0.838425	+	0.545017i	$0.183477\pi$
$257$	7.70264	+	23.7063i	0.480478	+	1.47876i	−0.357947	+	0.933742i	$0.616523\pi$
$258$		0			0
$259$	10.6041	−	7.70430i	0.658904	−	0.478722i
$260$		0			0
$261$	1.52621	−	4.69718i	0.0944697	−	0.290748i
$262$		0			0
$263$	3.90645	+	12.0228i	0.240882	+	0.741358i	0.996287	+	0.0860994i	$0.0274403\pi$
$263$	3.90645	+	12.0228i	0.240882	+	0.741358i	−0.755405	+	0.655258i	$0.772560\pi$
$264$		0			0
$265$	−4.57835	−	3.32637i	−0.281246	−	0.204337i
$266$		0			0
$267$	−15.4862	−	11.2514i	−0.947741	−	0.688574i
$268$		0			0
$269$	22.3692	−	16.2522i	1.36387	−	0.990912i	0.365685	−	0.930739i	$-0.380835\pi$
$269$	22.3692	−	16.2522i	1.36387	−	0.990912i	0.998188	−	0.0601731i	$-0.0191653\pi$
$270$		0			0
$271$	−0.454560	−	0.330257i	−0.0276126	−	0.0200617i	0.573893	−	0.818930i	$-0.305432\pi$
$271$	−0.454560	−	0.330257i	−0.0276126	−	0.0200617i	−0.601506	+	0.798868i	$0.705432\pi$
$272$		0			0
$273$	−18.7066			−1.13218
$274$		0			0
$275$	0.350697	−	1.07933i	0.0211478	−	0.0650863i
$276$		0			0
$277$	2.58859	+	7.96688i	0.155534	+	0.478683i	0.998215	−	0.0597300i	$-0.0190240\pi$
$277$	2.58859	+	7.96688i	0.155534	+	0.478683i	−0.842681	+	0.538413i	$0.819024\pi$
$278$		0			0
$279$	−2.56126	−	7.88274i	−0.153339	−	0.471927i
$280$		0			0
$281$	12.9039	−	9.37521i	0.769780	−	0.559278i	−0.132114	−	0.991235i	$-0.542177\pi$
$281$	12.9039	−	9.37521i	0.769780	−	0.559278i	0.901895	+	0.431956i	$0.142177\pi$
$282$		0			0
$283$	4.02623	−	12.3915i	0.239335	−	0.736596i	−0.757182	−	0.653204i	$-0.773424\pi$
$283$	4.02623	−	12.3915i	0.239335	−	0.736596i	0.996517	−	0.0833925i	$-0.0265755\pi$
$284$		0			0
$285$	−14.1734	+	10.2976i	−0.839558	+	0.609974i
$286$		0			0
$287$	−6.87427	+	7.95204i	−0.405775	+	0.469394i
$288$		0			0
$289$	3.35752	−	2.43938i	0.197501	−	0.143493i
$290$		0			0
$291$	6.17018	−	18.9899i	0.361702	−	1.11321i
$292$		0			0
$293$	−7.24313	+	5.26244i	−0.423148	+	0.307435i	−0.778903	−	0.627144i	$-0.784224\pi$
$293$	−7.24313	+	5.26244i	−0.423148	+	0.307435i	0.355755	+	0.934579i	$0.384224\pi$
$294$		0			0
$295$	−1.14172	−	3.51386i	−0.0664736	−	0.204585i
$296$		0			0
$297$	−0.920111	−	2.83181i	−0.0533903	−	0.164318i
$298$		0			0
$299$	−11.4482	+	35.2340i	−0.662067	+	2.03763i
$300$		0			0
$301$	−10.1524			−0.585172
$302$		0			0
$303$	11.9468	+	8.67989i	0.686328	+	0.498647i
$304$		0			0
$305$	6.23688	−	4.53136i	0.357123	−	0.259465i
$306$		0			0
$307$	24.2745	+	17.6364i	1.38542	+	1.00656i	0.996351	+	0.0853537i	$0.0272020\pi$
$307$	24.2745	+	17.6364i	1.38542	+	1.00656i	0.389065	+	0.921210i	$0.372798\pi$
$308$		0			0
$309$	−34.1348	−	24.8004i	−1.94186	−	1.41084i
$310$		0			0
$311$	−7.10279	−	21.8601i	−0.402762	−	1.23957i	−0.922750	−	0.385400i	$-0.874063\pi$
$311$	−7.10279	−	21.8601i	−0.402762	−	1.23957i	0.519988	−	0.854174i	$-0.325937\pi$
$312$		0			0
$313$	3.99612	−	12.2988i	0.225874	−	0.695169i	−0.772328	−	0.635224i	$-0.780908\pi$
$313$	3.99612	−	12.2988i	0.225874	−	0.695169i	0.998202	−	0.0599444i	$-0.0190923\pi$
$314$		0			0
$315$	−2.39431	+	1.73957i	−0.134904	+	0.0980134i
$316$		0			0
$317$	4.34412	+	13.3698i	0.243990	+	0.750924i	0.995801	+	0.0915450i	$0.0291805\pi$
$317$	4.34412	+	13.3698i	0.243990	+	0.750924i	−0.751811	+	0.659379i	$0.770819\pi$
$318$		0			0
$319$	3.10905			0.174074
$320$		0			0
$321$	21.5625	+	15.6661i	1.20350	+	0.874396i
$322$		0			0
$323$	−8.85522	+	27.2536i	−0.492717	+	1.51643i
$324$		0			0
$325$	5.19969			0.288427
$326$		0			0
$327$	28.7079			1.58755
$328$		0			0
$329$	19.9019			1.09723
$330$		0			0
$331$	1.82608			0.100371			0.0501853	−	0.998740i	$-0.484019\pi$
$331$	1.82608			0.100371			0.0501853	+	0.998740i	$0.484019\pi$
$332$		0			0
$333$	4.44813	−	13.6900i	0.243756	−	0.750205i
$334$		0			0
$335$	4.50057	+	3.26986i	0.245892	+	0.178651i
$336$		0			0
$337$	−11.5965			−0.631703			−0.315852	−	0.948809i	$-0.602290\pi$
$337$	−11.5965			−0.631703			−0.315852	+	0.948809i	$0.602290\pi$
$338$		0			0
$339$	7.95953	+	24.4969i	0.432303	+	1.33049i
$340$		0			0
$341$	4.22111	−	3.06681i	0.228586	−	0.166077i
$342$		0			0
$343$	5.73492	−	17.6503i	0.309657	−	0.953025i
$344$		0			0
$345$	4.82512	+	14.8502i	0.259776	+	0.799508i
$346$		0			0
$347$	−3.89268	−	2.82820i	−0.208970	−	0.151826i	0.478378	−	0.878154i	$-0.341225\pi$
$347$	−3.89268	−	2.82820i	−0.208970	−	0.151826i	−0.687348	+	0.726329i	$0.741225\pi$
$348$		0			0
$349$	−19.7054	−	14.3168i	−1.05481	−	0.766361i	−0.0816855	−	0.996658i	$-0.526030\pi$
$349$	−19.7054	−	14.3168i	−1.05481	−	0.766361i	−0.973120	+	0.230297i	$0.926030\pi$
$350$		0			0
$351$	11.0368	−	8.01871i	0.589101	−	0.428007i
$352$		0			0
$353$	−6.43617	−	4.67615i	−0.342563	−	0.248886i	0.403180	−	0.915121i	$-0.367905\pi$
$353$	−6.43617	−	4.67615i	−0.342563	−	0.248886i	−0.745742	+	0.666235i	$0.767905\pi$
$354$		0			0
$355$	2.31092			0.122651
$356$		0			0
$357$	−3.98520	+	12.2652i	−0.210919	+	0.649143i
$358$		0			0
$359$	0.181527	+	0.558683i	0.00958064	+	0.0294862i	0.955733	−	0.294237i	$-0.0950654\pi$
$359$	0.181527	+	0.558683i	0.00958064	+	0.0294862i	−0.946152	+	0.323723i	$0.895065\pi$
$360$		0			0
$361$	13.8764	+	42.7071i	0.730336	+	2.24774i
$362$		0			0
$363$	17.2193	−	12.5106i	0.903781	−	0.656636i
$364$		0			0
$365$	1.58230	−	4.86982i	0.0828215	−	0.254898i
$366$		0			0
$367$	4.97233	−	3.61261i	0.259554	−	0.188577i	−0.450397	−	0.892829i	$-0.648717\pi$
$367$	4.97233	−	3.61261i	0.259554	−	0.188577i	0.709950	+	0.704252i	$0.248717\pi$
$368$		0			0
$369$	−0.974440	+	11.5025i	−0.0507273	+	0.598794i
$370$		0			0
$371$	−7.51587	+	5.46060i	−0.390205	+	0.283500i
$372$		0			0
$373$	3.92559	−	12.0817i	0.203259	−	0.625568i	−0.796521	−	0.604611i	$-0.793329\pi$
$373$	3.92559	−	12.0817i	0.203259	−	0.625568i	0.999780	−	0.0209573i	$-0.00667140\pi$
$374$		0			0
$375$	1.77299	−	1.28815i	0.0915567	−	0.0665198i
$376$		0			0
$377$	4.40188	+	13.5476i	0.226708	+	0.697737i
$378$		0			0
$379$	10.4802	+	32.2548i	0.538333	+	1.65682i	0.736336	+	0.676616i	$0.236554\pi$
$379$	10.4802	+	32.2548i	0.538333	+	1.65682i	−0.198003	+	0.980201i	$0.563446\pi$
$380$		0			0
$381$	−2.90013	+	8.92567i	−0.148578	+	0.457276i
$382$		0			0
$383$	−25.7310			−1.31479			−0.657396	−	0.753545i	$-0.728342\pi$
$383$	−25.7310			−1.31479			−0.657396	+	0.753545i	$0.728342\pi$
$384$		0			0
$385$	−1.50722	−	1.09506i	−0.0768152	−	0.0558095i
$386$		0			0
$387$	−9.01998	+	6.55340i	−0.458511	+	0.333128i
$388$		0			0
$389$	14.5168	+	10.5471i	0.736033	+	0.534759i	0.891466	−	0.453087i	$-0.149677\pi$
$389$	14.5168	+	10.5471i	0.736033	+	0.534759i	−0.155433	+	0.987846i	$0.549677\pi$
$390$		0			0
$391$	20.6626	+	15.0123i	1.04495	+	0.759203i
$392$		0			0
$393$	9.46505	+	29.1304i	0.477448	+	1.46944i
$394$		0			0
$395$	−4.68509	+	14.4192i	−0.235733	+	0.725510i
$396$		0			0
$397$	−31.7114	+	23.0396i	−1.59155	+	1.15633i	−0.689856	+	0.723947i	$0.742326\pi$
$397$	−31.7114	+	23.0396i	−1.59155	+	1.15633i	−0.901692	+	0.432380i	$0.857674\pi$
$398$		0			0
$399$	8.88726	+	27.3522i	0.444920	+	1.36932i
$400$		0			0
$401$	35.9619			1.79585			0.897925	−	0.440149i	$-0.145074\pi$
$401$	35.9619			1.79585			0.897925	+	0.440149i	$0.145074\pi$
$402$		0			0
$403$	19.3399	+	14.0513i	0.963389	+	0.699943i
$404$		0			0
$405$	3.44810	−	10.6122i	0.171338	−	0.527323i
$406$		0			0
$407$	9.06136			0.449155
$408$		0			0
$409$	3.80637			0.188213			0.0941066	−	0.995562i	$-0.470001\pi$
$409$	3.80637			0.188213			0.0941066	+	0.995562i	$0.470001\pi$
$410$		0			0
$411$	21.5518			1.06307
$412$		0			0
$413$	−6.06524			−0.298451
$414$		0			0
$415$	2.60098	−	8.00501i	0.127677	−	0.392950i
$416$		0			0
$417$	−37.5444	−	27.2776i	−1.83856	−	1.33579i
$418$		0			0
$419$	−0.243846			−0.0119126			−0.00595632	−	0.999982i	$-0.501896\pi$
$419$	−0.243846			−0.0119126			−0.00595632	+	0.999982i	$0.501896\pi$
$420$		0			0
$421$	−2.36161	−	7.26829i	−0.115098	−	0.354235i	0.876870	−	0.480728i	$-0.159628\pi$
$421$	−2.36161	−	7.26829i	−0.115098	−	0.354235i	−0.991967	+	0.126493i	$0.959628\pi$
$422$		0			0
$423$	17.6821	−	12.8468i	0.859733	−	0.624633i
$424$		0			0
$425$	1.10772	−	3.40923i	0.0537326	−	0.165372i
$426$		0			0
$427$	−3.91077	−	12.0361i	−0.189256	−	0.582469i
$428$		0			0
$429$	−10.4624	−	7.60139i	−0.505130	−	0.366999i
$430$		0			0
$431$	0.221876	+	0.161202i	0.0106874	+	0.00776485i	0.593116	−	0.805117i	$-0.297897\pi$
$431$	0.221876	+	0.161202i	0.0106874	+	0.00776485i	−0.582429	+	0.812882i	$0.697897\pi$
$432$		0			0
$433$	−5.13666	+	3.73200i	−0.246852	+	0.179349i	−0.704331	−	0.709872i	$-0.748753\pi$
$433$	−5.13666	+	3.73200i	−0.246852	+	0.179349i	0.457478	+	0.889221i	$0.348753\pi$
$434$		0			0
$435$	4.85718	+	3.52895i	0.232884	+	0.169200i
$436$		0			0
$437$	56.9568			2.72461
$438$		0			0
$439$	−2.59846	+	7.99722i	−0.124017	+	0.381687i	−0.993721	−	0.111888i	$-0.964310\pi$
$439$	−2.59846	+	7.99722i	−0.124017	+	0.381687i	0.869703	+	0.493575i	$0.164310\pi$
$440$		0			0
$441$	−2.39838	−	7.38146i	−0.114209	−	0.351498i
$442$		0			0
$443$	9.52638	+	29.3192i	0.452612	+	1.39300i	0.873916	+	0.486077i	$0.161573\pi$
$443$	9.52638	+	29.3192i	0.452612	+	1.39300i	−0.421304	+	0.906919i	$0.638427\pi$
$444$		0			0
$445$	7.06638	−	5.13403i	0.334979	−	0.243376i
$446$		0			0
$447$	11.3441	−	34.9136i	0.536559	−	1.65136i
$448$		0			0
$449$	9.82818	−	7.14059i	0.463820	−	0.336985i	−0.331208	−	0.943558i	$-0.607456\pi$
$449$	9.82818	−	7.14059i	0.463820	−	0.336985i	0.795028	+	0.606573i	$0.207456\pi$
$450$		0			0
$451$	−7.07599	+	1.65415i	−0.333196	+	0.0778909i
$452$		0			0
$453$	−18.5398	+	13.4700i	−0.871077	+	0.632874i
$454$		0			0
$455$	2.63773	−	8.11809i	0.123659	−	0.380582i
$456$		0			0
$457$	−23.4185	+	17.0145i	−1.09547	+	0.795906i	−0.980315	−	0.197441i	$-0.936737\pi$
$457$	−23.4185	+	17.0145i	−1.09547	+	0.795906i	−0.115156	+	0.993347i	$0.536737\pi$
$458$		0			0
$459$	−2.90630	−	8.94467i	−0.135654	−	0.417502i
$460$		0			0
$461$	9.19319	+	28.2937i	0.428170	+	1.31777i	0.899926	+	0.436042i	$0.143620\pi$
$461$	9.19319	+	28.2937i	0.428170	+	1.31777i	−0.471756	+	0.881729i	$0.656380\pi$
$462$		0			0
$463$	−3.01803	+	9.28856i	−0.140260	+	0.431676i	−0.996371	−	0.0851161i	$-0.972874\pi$
$463$	−3.01803	+	9.28856i	−0.140260	+	0.431676i	0.856111	+	0.516792i	$0.172874\pi$
$464$		0			0
$465$	10.0755			0.467241
$466$		0			0
$467$	19.2051	+	13.9533i	0.888704	+	0.645682i	0.935540	−	0.353221i	$-0.114914\pi$
$467$	19.2051	+	13.9533i	0.888704	+	0.645682i	−0.0468354	+	0.998903i	$0.514914\pi$
$468$		0			0
$469$	7.38819	−	5.36783i	0.341155	−	0.247864i
$470$		0			0
$471$	−15.0185	−	10.9116i	−0.692016	−	0.502779i
$472$		0			0
$473$	−5.67810	−	4.12538i	−0.261079	−	0.189685i
$474$		0			0
$475$	−2.47030	−	7.60280i	−0.113345	−	0.348840i
$476$		0			0
$477$	−3.15272	+	9.70307i	−0.144353	+	0.444273i
$478$		0			0
$479$	7.95890	−	5.78248i	0.363651	−	0.264208i	−0.390922	−	0.920424i	$-0.627844\pi$
$479$	7.95890	−	5.78248i	0.363651	−	0.264208i	0.754573	+	0.656216i	$0.227844\pi$
$480$		0			0
$481$	12.8293	+	39.4846i	0.584966	+	1.80034i
$482$		0			0
$483$	25.6328			1.16633
$484$		0			0
$485$	7.37098	+	5.35533i	0.334699	+	0.243173i
$486$		0			0
$487$	−0.136199	+	0.419177i	−0.00617176	+	0.0189947i	−0.954095	−	0.299504i	$-0.903179\pi$
$487$	−0.136199	+	0.419177i	−0.00617176	+	0.0189947i	0.947923	+	0.318499i	$0.103179\pi$
$488$		0			0
$489$	−47.1405			−2.13177
$490$		0			0
$491$	−21.8149			−0.984493			−0.492247	−	0.870456i	$-0.663824\pi$
$491$	−21.8149			−0.984493			−0.492247	+	0.870456i	$0.663824\pi$
$492$		0			0
$493$	9.82038			0.442288
$494$		0			0
$495$	−2.04598			−0.0919599
$496$		0			0
$497$	1.17230	−	3.60796i	0.0525847	−	0.161839i
$498$		0			0
$499$	10.5828	+	7.68887i	0.473752	+	0.344201i	0.798902	−	0.601461i	$-0.205415\pi$
$499$	10.5828	+	7.68887i	0.473752	+	0.344201i	−0.325149	+	0.945663i	$0.605415\pi$
$500$		0			0
$501$	−33.5575			−1.49924
$502$		0			0
$503$	6.65513	+	20.4824i	0.296738	+	0.913265i	0.982632	+	0.185564i	$0.0594112\pi$
$503$	6.65513	+	20.4824i	0.296738	+	0.913265i	−0.685894	+	0.727701i	$0.740589\pi$
$504$		0			0
$505$	−5.45136	+	3.96065i	−0.242582	+	0.176246i
$506$		0			0
$507$	9.50597	−	29.2564i	0.422175	−	1.29932i
$508$		0			0
$509$	5.66350	+	17.4305i	0.251030	+	0.772591i	0.994586	+	0.103917i	$0.0331377\pi$
$509$	5.66350	+	17.4305i	0.251030	+	0.772591i	−0.743556	+	0.668674i	$0.766862\pi$
$510$		0			0
$511$	−6.80041	−	4.94079i	−0.300832	−	0.218568i
$512$		0			0
$513$	−16.9681	−	12.3281i	−0.749160	−	0.544297i
$514$		0			0
$515$	15.5758	−	11.3164i	0.686350	−	0.498662i
$516$		0			0
$517$	11.1309	+	8.08709i	0.489538	+	0.355670i
$518$		0			0
$519$	−13.5541			−0.594959
$520$		0			0
$521$	4.26460	−	13.1251i	0.186835	−	0.575020i	−0.813140	−	0.582068i	$-0.802244\pi$
$521$	4.26460	−	13.1251i	0.186835	−	0.575020i	0.999975	+	0.00704838i	$0.00224359\pi$
$522$		0			0
$523$	−4.59607	−	14.1452i	−0.200972	−	0.618528i	−0.999855	−	0.0170414i	$-0.994575\pi$
$523$	−4.59607	−	14.1452i	−0.200972	−	0.618528i	0.798883	−	0.601487i	$-0.205425\pi$
$524$		0			0
$525$	−1.11173	−	3.42156i	−0.0485200	−	0.149329i
$526$		0			0
$527$	13.3330	−	9.68696i	0.580793	−	0.421971i
$528$		0			0
$529$	8.57957	−	26.4052i	0.373025	−	1.14805i
$530$		0			0
$531$	−5.38874	+	3.91515i	−0.233851	+	0.169903i
$532$		0			0
$533$	−17.2263	−	28.4914i	−0.746153	−	1.23410i
$534$		0			0
$535$	−9.83902	+	7.14847i	−0.425378	+	0.309055i
$536$		0			0
$537$	−3.66240	+	11.2717i	−0.158044	+	0.486410i
$538$		0			0
$539$	3.95268	−	2.87179i	0.170254	−	0.123697i
$540$		0			0
$541$	−6.84596	−	21.0697i	−0.294331	−	0.905857i	−0.983445	−	0.181205i	$-0.942000\pi$
$541$	−6.84596	−	21.0697i	−0.294331	−	0.905857i	0.689115	−	0.724652i	$-0.258000\pi$
$542$		0			0
$543$	0.793429	+	2.44192i	0.0340493	+	0.104793i
$544$		0			0
$545$	−4.04795	+	12.4583i	−0.173395	+	0.533656i
$546$		0			0
$547$	25.7682			1.10177			0.550884	−	0.834582i	$-0.314291\pi$
$547$	25.7682			1.10177			0.550884	+	0.834582i	$0.314291\pi$
$548$		0			0
$549$	−11.2440	−	8.16921i	−0.479880	−	0.348654i
$550$		0			0
$551$	17.7176	−	12.8726i	0.754793	−	0.548389i
$552$		0			0
$553$	20.1356	+	14.6293i	0.856251	+	0.622103i
$554$		0			0
$555$	14.1563	+	10.2851i	0.600901	+	0.436580i
$556$		0			0
$557$	7.61218	+	23.4279i	0.322538	+	0.992671i	0.972540	+	0.232738i	$0.0747684\pi$
$557$	7.61218	+	23.4279i	0.322538	+	0.992671i	−0.650001	+	0.759933i	$0.725232\pi$
$558$		0			0
$559$	9.93701	−	30.5830i	0.420291	−	1.29352i
$560$		0			0
$561$	−7.21281	+	5.24041i	−0.304525	+	0.221250i
$562$		0			0
$563$	7.39362	+	22.7552i	0.311604	+	0.959018i	0.977130	+	0.212644i	$0.0682073\pi$
$563$	7.39362	+	22.7552i	0.311604	+	0.959018i	−0.665526	+	0.746375i	$0.731793\pi$
$564$		0			0
$565$	−11.7532			−0.494462
$566$		0			0
$567$	−14.8192	−	10.7668i	−0.622350	−	0.452164i
$568$		0			0
$569$	−3.59503	+	11.0644i	−0.150711	+	0.463842i	−0.997701	−	0.0677672i	$-0.978412\pi$
$569$	−3.59503	+	11.0644i	−0.150711	+	0.463842i	0.846990	+	0.531609i	$0.178412\pi$
$570$		0			0
$571$	−27.2402			−1.13997			−0.569983	−	0.821656i	$-0.693050\pi$
$571$	−27.2402			−1.13997			−0.569983	+	0.821656i	$0.693050\pi$
$572$		0			0
$573$	18.4266			0.769784
$574$		0			0
$575$	−7.12489			−0.297128
$576$		0			0
$577$	−19.6631			−0.818585			−0.409292	−	0.912403i	$-0.634224\pi$
$577$	−19.6631			−0.818585			−0.409292	+	0.912403i	$0.634224\pi$
$578$		0			0
$579$	1.96649	−	6.05224i	0.0817246	−	0.251522i
$580$		0			0
$581$	−11.1785	−	8.12165i	−0.463762	−	0.336943i
$582$		0			0
$583$	−6.42245			−0.265991
$584$		0			0
$585$	−2.89675	−	8.91528i	−0.119766	−	0.368602i
$586$		0			0
$587$	−3.41153	+	2.47862i	−0.140809	+	0.102304i	−0.655960	−	0.754796i	$-0.727736\pi$
$587$	−3.41153	+	2.47862i	−0.140809	+	0.102304i	0.515151	+	0.857100i	$0.327736\pi$
$588$		0			0
$589$	11.3571	−	34.9537i	0.467963	−	1.44024i
$590$		0			0
$591$	−8.40511	−	25.8683i	−0.345740	−	1.06408i
$592$		0			0
$593$	13.6980	+	9.95214i	0.562507	+	0.408686i	0.832376	−	0.554212i	$-0.186980\pi$
$593$	13.6980	+	9.95214i	0.562507	+	0.408686i	−0.269868	+	0.962897i	$0.586980\pi$
$594$		0			0
$595$	−4.76077	−	3.45891i	−0.195173	−	0.141801i
$596$		0			0
$597$	5.81597	−	4.22555i	0.238032	−	0.172940i
$598$		0			0
$599$	2.05515	+	1.49315i	0.0839711	+	0.0610086i	0.628979	−	0.777423i	$-0.283473\pi$
$599$	2.05515	+	1.49315i	0.0839711	+	0.0610086i	−0.545008	+	0.838431i	$0.683473\pi$
$600$		0			0
$601$	−30.3057			−1.23619			−0.618097	−	0.786102i	$-0.712096\pi$
$601$	−30.3057			−1.23619			−0.618097	+	0.786102i	$0.712096\pi$
$602$		0			0
$603$	3.09916	−	9.53823i	0.126208	−	0.388427i
$604$		0			0
$605$	3.00119	+	9.23671i	0.122016	+	0.375526i
$606$		0			0
$607$	−12.4187	−	38.2209i	−0.504060	−	1.55134i	−0.802345	−	0.596860i	$-0.796415\pi$
$607$	−12.4187	−	38.2209i	−0.504060	−	1.55134i	0.298285	−	0.954477i	$-0.403585\pi$
$608$		0			0
$609$	7.97361	−	5.79317i	0.323107	−	0.234751i
$610$		0			0
$611$	−19.4798	+	59.9526i	−0.788067	+	2.42542i
$612$		0			0
$613$	−26.4211	+	19.1961i	−1.06714	+	0.775322i	−0.975396	−	0.220461i	$-0.929244\pi$
$613$	−26.4211	+	19.1961i	−1.06714	+	0.775322i	−0.0917431	+	0.995783i	$0.529244\pi$
$614$		0			0
$615$	−12.9322	−	5.44742i	−0.521476	−	0.219661i
$616$		0			0
$617$	−8.54800	+	6.21048i	−0.344129	+	0.250025i	−0.746402	−	0.665495i	$-0.768220\pi$
$617$	−8.54800	+	6.21048i	−0.344129	+	0.250025i	0.402273	+	0.915520i	$0.368220\pi$
$618$		0			0
$619$	1.98160	−	6.09875i	0.0796473	−	0.245129i	−0.903302	−	0.429005i	$-0.858864\pi$
$619$	1.98160	−	6.09875i	0.0796473	−	0.245129i	0.982950	+	0.183876i	$0.0588643\pi$
$620$		0			0
$621$	−15.1232	+	10.9877i	−0.606874	+	0.440920i
$622$		0			0
$623$	−4.43090	−	13.6369i	−0.177520	−	0.546352i
$624$		0			0
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$		0			0
$627$	−6.14394	+	18.9091i	−0.245365	+	0.755157i
$628$		0			0
$629$	28.6216			1.14122
$630$		0			0
$631$	−1.11053	−	0.806849i	−0.0442096	−	0.0321201i	0.565461	−	0.824775i	$-0.308698\pi$
$631$	−1.11053	−	0.806849i	−0.0442096	−	0.0321201i	−0.609671	+	0.792655i	$0.708698\pi$
$632$		0			0
$633$	28.0558	−	20.3838i	1.11512	−	0.810182i
$634$		0			0
$635$	−3.46453	−	2.51713i	−0.137486	−	0.0998891i
$636$		0			0
$637$	18.1100	+	13.1577i	0.717545	+	0.521327i
$638$		0			0
$639$	−1.28741	−	3.96226i	−0.0509293	−	0.156744i
$640$		0			0
$641$	−13.8833	+	42.7284i	−0.548357	+	1.68767i	0.164515	+	0.986375i	$0.447394\pi$
$641$	−13.8833	+	42.7284i	−0.548357	+	1.68767i	−0.712872	+	0.701294i	$0.752606\pi$
$642$		0			0
$643$	18.7947	−	13.6552i	0.741193	−	0.538508i	−0.151892	−	0.988397i	$-0.548537\pi$
$643$	18.7947	−	13.6552i	0.741193	−	0.538508i	0.893084	+	0.449889i	$0.148537\pi$
$644$		0			0
$645$	−4.18819	−	12.8899i	−0.164910	−	0.507541i
$646$		0			0
$647$	−8.89098			−0.349541			−0.174770	−	0.984609i	$-0.555918\pi$
$647$	−8.89098			−0.349541			−0.174770	+	0.984609i	$0.555918\pi$
$648$		0			0
$649$	−3.39222	−	2.46460i	−0.133156	−	0.0967438i
$650$		0			0
$651$	5.11117	−	15.7306i	0.200322	−	0.616529i
$652$		0			0
$653$	16.4185			0.642506			0.321253	−	0.946993i	$-0.395896\pi$
$653$	16.4185			0.642506			0.321253	+	0.946993i	$0.395896\pi$
$654$		0			0
$655$	−13.9763			−0.546099
$656$		0			0
$657$	−9.23121			−0.360144
$658$		0			0
$659$	32.4165			1.26277			0.631384	−	0.775470i	$-0.282487\pi$
$659$	32.4165			1.26277			0.631384	+	0.775470i	$0.282487\pi$
$660$		0			0
$661$	6.03165	−	18.5635i	0.234604	−	0.722037i	−0.762569	−	0.646906i	$-0.776062\pi$
$661$	6.03165	−	18.5635i	0.234604	−	0.722037i	0.997174	−	0.0751311i	$-0.0239375\pi$
$662$		0			0
$663$	−33.0470	−	24.0101i	−1.28344	−	0.932474i
$664$		0			0
$665$	−13.1231			−0.508893
$666$		0			0
$667$	−6.03170	−	18.5637i	−0.233548	−	0.718787i
$668$		0			0
$669$	−28.5623	+	20.7517i	−1.10428	+	0.802307i
$670$		0			0
$671$	2.70359	−	8.32081i	0.104371	−	0.321221i
$672$		0			0
$673$	−10.2229	−	31.4630i	−0.394065	−	1.21281i	−0.929687	−	0.368350i	$-0.879923\pi$
$673$	−10.2229	−	31.4630i	−0.394065	−	1.21281i	0.535622	−	0.844458i	$-0.320077\pi$
$674$		0			0
$675$	2.12259	+	1.54215i	0.0816985	+	0.0593575i
$676$		0			0
$677$	−34.5829	−	25.1260i	−1.32913	−	0.965669i	−0.999770	−	0.0214641i	$-0.993167\pi$
$677$	−34.5829	−	25.1260i	−1.32913	−	0.965669i	−0.329359	−	0.944205i	$-0.606833\pi$
$678$		0			0
$679$	12.1003	−	8.79137i	0.464366	−	0.337382i
$680$		0			0
$681$	−43.5203	−	31.6194i	−1.66770	−	1.21166i
$682$		0			0
$683$	29.3904			1.12459			0.562296	−	0.826936i	$-0.309918\pi$
$683$	29.3904			1.12459			0.562296	+	0.826936i	$0.309918\pi$
$684$		0			0
$685$	−3.03891	+	9.35280i	−0.116111	+	0.357352i
$686$		0			0
$687$	2.15809	+	6.64190i	0.0823361	+	0.253404i
$688$		0			0
$689$	−9.09307	−	27.9856i	−0.346419	−	1.06617i
$690$		0			0
$691$	−37.7349	+	27.4160i	−1.43550	+	1.04295i	−0.446546	+	0.894761i	$0.647346\pi$
$691$	−37.7349	+	27.4160i	−1.43550	+	1.04295i	−0.988958	+	0.148194i	$0.952654\pi$
$692$		0			0
$693$	−1.03790	+	3.19431i	−0.0394264	+	0.121342i
$694$		0			0
$695$	17.1316	−	12.4468i	0.649838	−	0.472135i
$696$		0			0
$697$	−22.3505	+	5.22486i	−0.846586	+	0.197906i
$698$		0			0
$699$	4.26926	−	3.10180i	0.161478	−	0.117321i
$700$		0			0
$701$	−13.9859	+	43.0443i	−0.528242	+	1.62576i	0.229573	+	0.973291i	$0.426267\pi$
$701$	−13.9859	+	43.0443i	−0.528242	+	1.62576i	−0.757815	+	0.652470i	$0.773733\pi$
$702$		0			0
$703$	51.6379	−	37.5171i	1.94756	−	1.41499i
$704$		0			0
$705$	8.21022	+	25.2685i	0.309215	+	0.951665i
$706$		0			0
$707$	3.41822	+	10.5202i	0.128555	+	0.395653i
$708$		0			0
$709$	−11.3353	+	34.8864i	−0.425706	+	1.31019i	0.476611	+	0.879114i	$0.341865\pi$
$709$	−11.3353	+	34.8864i	−0.425706	+	1.31019i	−0.902317	+	0.431073i	$0.858135\pi$
$710$		0			0
$711$	27.3330			1.02507
$712$		0			0
$713$	−26.5006	−	19.2538i	−0.992454	−	0.721060i
$714$		0			0
$715$	4.77402	−	3.46853i	0.178538	−	0.129716i
$716$		0			0
$717$	16.4560	+	11.9560i	0.614559	+	0.446503i
$718$		0			0
$719$	−16.2078	−	11.7756i	−0.604448	−	0.439157i	0.243007	−	0.970025i	$-0.421866\pi$
$719$	−16.2078	−	11.7756i	−0.604448	−	0.439157i	−0.847455	+	0.530867i	$0.821866\pi$
$720$		0			0
$721$	−9.76662	−	30.0586i	−0.363728	−	1.11944i
$722$		0			0
$723$	8.93326	−	27.4938i	0.332232	−	1.02250i
$724$		0			0
$725$	−2.21634	+	1.61027i	−0.0823128	+	0.0598038i
$726$		0			0
$727$	8.89058	+	27.3624i	0.329733	+	1.01482i	0.969258	+	0.246045i	$0.0791311\pi$
$727$	8.89058	+	27.3624i	0.329733	+	1.01482i	−0.639525	+	0.768770i	$0.720869\pi$
$728$		0			0
$729$	−2.86682			−0.106179
$730$		0			0
$731$	−17.9351	−	13.0306i	−0.663353	−	0.481954i
$732$		0			0
$733$	−8.32468	+	25.6207i	−0.307479	+	0.946324i	0.671261	+	0.741221i	$0.265753\pi$
$733$	−8.32468	+	25.6207i	−0.307479	+	0.946324i	−0.978740	+	0.205103i	$0.934247\pi$
$734$		0			0
$735$	9.43479			0.348008
$736$		0			0
$737$	6.31334			0.232555
$738$		0			0
$739$	20.2645			0.745442			0.372721	−	0.927943i	$-0.378425\pi$
$739$	20.2645			0.745442			0.372721	+	0.927943i	$0.378425\pi$
$740$		0			0
$741$	−91.0945			−3.34644
$742$		0			0
$743$	7.68092	−	23.6394i	0.281786	−	0.867247i	−0.705558	−	0.708652i	$-0.749304\pi$
$743$	7.68092	−	23.6394i	0.281786	−	0.867247i	0.987344	−	0.158595i	$-0.0506963\pi$
$744$		0			0
$745$	13.5518	+	9.84599i	0.496501	+	0.360729i
$746$		0			0
$747$	−15.1742			−0.555197
$748$		0			0
$749$	6.16946	+	18.9876i	0.225427	+	0.693793i
$750$		0			0
$751$	9.08489	−	6.60056i	0.331512	−	0.240858i	−0.409560	−	0.912283i	$-0.634318\pi$
$751$	9.08489	−	6.60056i	0.331512	−	0.240858i	0.741072	+	0.671425i	$0.234318\pi$
$752$		0			0
$753$	6.05513	−	18.6358i	0.220661	−	0.679125i
$754$		0			0
$755$	−3.23134	−	9.94503i	−0.117600	−	0.361937i
$756$		0			0
$757$	5.92701	+	4.30622i	0.215421	+	0.156512i	0.690263	−	0.723559i	$-0.257495\pi$
$757$	5.92701	+	4.30622i	0.215421	+	0.156512i	−0.474842	+	0.880071i	$0.657495\pi$
$758$		0			0
$759$	14.3362	+	10.4158i	0.520370	+	0.378071i
$760$		0			0
$761$	20.2174	−	14.6888i	0.732880	−	0.532469i	−0.157593	−	0.987504i	$-0.550373\pi$
$761$	20.2174	−	14.6888i	0.732880	−	0.532469i	0.890473	+	0.455035i	$0.150373\pi$
$762$		0			0
$763$	17.3973	+	12.6399i	0.629823	+	0.457593i
$764$		0			0
$765$	−6.46251			−0.233653
$766$		0			0
$767$	5.93659	−	18.2709i	0.214358	−	0.659726i
$768$		0			0
$769$	−7.34500	−	22.6056i	−0.264868	−	0.815179i	−0.991724	−	0.128389i	$-0.959019\pi$
$769$	−7.34500	−	22.6056i	−0.264868	−	0.815179i	0.726856	−	0.686790i	$-0.240981\pi$
$770$		0			0
$771$	16.8806	+	51.9531i	0.607940	+	1.87105i
$772$		0			0
$773$	−27.1021	+	19.6908i	−0.974794	+	0.708230i	−0.956539	−	0.291604i	$-0.905811\pi$
$773$	−27.1021	+	19.6908i	−0.974794	+	0.708230i	−0.0182553	+	0.999833i	$0.505811\pi$
$774$		0			0
$775$	−1.42070	+	4.37246i	−0.0510330	+	0.157063i
$776$		0			0
$777$	23.2391	−	16.8842i	0.833699	−	0.605718i
$778$		0			0
$779$	−33.4752	+	38.7236i	−1.19937	+	1.38742i
$780$		0			0
$781$	2.12174	−	1.54153i	0.0759217	−	0.0551603i
$782$		0			0
$783$	−2.22111	+	6.83587i	−0.0793759	+	0.244294i
$784$		0			0
$785$	6.85297	−	4.97897i	0.244593	−	0.177707i
$786$		0			0
$787$	5.23116	+	16.0999i	0.186471	+	0.573898i	0.999971	−	0.00766710i	$-0.00244054\pi$
$787$	5.23116	+	16.0999i	0.186471	+	0.573898i	−0.813500	+	0.581565i	$0.802441\pi$
$788$		0			0
$789$	8.56110	+	26.3484i	0.304783	+	0.938027i
$790$		0			0
$791$	−5.96225	+	18.3499i	−0.211993	+	0.652448i
$792$		0			0
$793$	40.0855			1.42348
$794$		0			0
$795$	−10.0336	−	7.28984i	−0.355855	−	0.258544i
$796$		0			0
$797$	31.9564	−	23.2177i	1.13195	−	0.822412i	0.145975	−	0.989288i	$-0.453368\pi$
$797$	31.9564	−	23.2177i	1.13195	−	0.822412i	0.985978	+	0.166876i	$0.0533680\pi$
$798$		0			0
$799$	35.1586	+	25.5442i	1.24382	+	0.903690i
$800$		0			0
$801$	−12.7394	−	9.25571i	−0.450124	−	0.327035i
$802$		0			0
$803$	−1.79572	−	5.52666i	−0.0633696	−	0.195032i
$804$		0			0
$805$	−3.61436	+	11.1238i	−0.127389	+	0.392064i
$806$		0			0
$807$	49.0228	−	35.6171i	1.72568	−	1.25378i
$808$		0			0
$809$	−14.8231	−	45.6208i	−0.521152	−	1.60394i	−0.771801	−	0.635864i	$-0.780644\pi$
$809$	−14.8231	−	45.6208i	−0.521152	−	1.60394i	0.250649	−	0.968078i	$-0.419356\pi$
$810$		0			0
$811$	−15.0733			−0.529294			−0.264647	−	0.964345i	$-0.585255\pi$
$811$	−15.0733			−0.529294			−0.264647	+	0.964345i	$0.585255\pi$
$812$		0			0
$813$	−0.996184	−	0.723770i	−0.0349377	−	0.0253837i
$814$		0			0
$815$	6.64704	−	20.4575i	0.232836	−	0.716594i
$816$		0			0
$817$	−49.4383			−1.72963
$818$		0			0
$819$	−15.3886			−0.537721
$820$		0			0
$821$	−35.5310			−1.24004			−0.620020	−	0.784586i	$-0.712876\pi$
$821$	−35.5310			−1.24004			−0.620020	+	0.784586i	$0.712876\pi$
$822$		0			0
$823$	−4.83727			−0.168617			−0.0843083	−	0.996440i	$-0.526868\pi$
$823$	−4.83727			−0.168617			−0.0843083	+	0.996440i	$0.526868\pi$
$824$		0			0
$825$	0.768563	−	2.36539i	0.0267579	−	0.0823525i
$826$		0			0
$827$	−11.8350	−	8.59861i	−0.411542	−	0.299003i	0.362684	−	0.931912i	$-0.381861\pi$
$827$	−11.8350	−	8.59861i	−0.411542	−	0.299003i	−0.774226	+	0.632909i	$0.781861\pi$
$828$		0			0
$829$	12.3635			0.429401			0.214700	−	0.976680i	$-0.431123\pi$
$829$	12.3635			0.429401			0.214700	+	0.976680i	$0.431123\pi$
$830$		0			0
$831$	5.67299	+	17.4597i	0.196794	+	0.605669i
$832$		0			0
$833$	12.4851	−	9.07095i	0.432583	−	0.314290i
$834$		0			0
$835$	4.73177	−	14.5629i	0.163750	−	0.503969i
$836$		0			0
$837$	3.72744	+	11.4719i	0.128839	+	0.396526i
$838$		0			0
$839$	−38.9745	−	28.3166i	−1.34555	−	0.977597i	−0.999220	−	0.0394837i	$-0.987429\pi$
$839$	−38.9745	−	28.3166i	−1.34555	−	0.977597i	−0.346327	−	0.938114i	$-0.612571\pi$
$840$		0			0
$841$	17.3897	+	12.6344i	0.599646	+	0.435668i
$842$		0			0
$843$	28.2793	−	20.5461i	0.973989	−	0.707645i
$844$		0			0
$845$	11.3560	+	8.25058i	0.390657	+	0.283829i
$846$		0			0
$847$	15.9434			0.547822
$848$		0			0
$849$	8.82362	−	27.1563i	0.302826	−	0.932002i
$850$		0			0
$851$	−17.5794	−	54.1039i	−0.602615	−	1.85466i
$852$		0			0
$853$	9.22063	+	28.3782i	0.315708	+	0.971650i	0.975462	+	0.220168i	$0.0706606\pi$
$853$	9.22063	+	28.3782i	0.315708	+	0.971650i	−0.659754	+	0.751482i	$0.729339\pi$
$854$		0			0
$855$	−11.6594	+	8.47106i	−0.398743	+	0.289704i
$856$		0			0
$857$	11.8196	−	36.3770i	0.403749	−	1.24261i	−0.518186	−	0.855268i	$-0.673392\pi$
$857$	11.8196	−	36.3770i	0.403749	−	1.24261i	0.921935	−	0.387345i	$-0.126608\pi$
$858$		0			0
$859$	−17.8754	+	12.9872i	−0.609900	+	0.443118i	−0.849379	−	0.527783i	$-0.823023\pi$
$859$	−17.8754	+	12.9872i	−0.609900	+	0.443118i	0.239479	+	0.970902i	$0.423023\pi$
$860$		0			0
$861$	−15.0652	+	17.4272i	−0.513420	+	0.593916i
$862$		0			0
$863$	−27.9666	+	20.3190i	−0.951995	+	0.691665i	−0.951278	−	0.308335i	$-0.900228\pi$
$863$	−27.9666	+	20.3190i	−0.951995	+	0.691665i	−0.000717415		1.00000i	$0.500228\pi$
$864$		0			0
$865$	1.91119	−	5.88205i	0.0649826	−	0.199996i
$866$		0			0
$867$	7.35811	−	5.34598i	0.249894	−	0.181559i
$868$		0			0
$869$	5.31701	+	16.3641i	0.180367	+	0.555113i
$870$		0			0
$871$	8.93860	+	27.5102i	0.302873	+	0.932147i
$872$		0			0
$873$	5.07576	−	15.6216i	0.171789	−	0.528711i
$874$		0			0
$875$	1.64161			0.0554966
$876$		0			0
$877$	−18.0950	−	13.1468i	−0.611025	−	0.443936i	0.238750	−	0.971081i	$-0.423262\pi$
$877$	−18.0950	−	13.1468i	−0.611025	−	0.443936i	−0.849775	+	0.527145i	$0.823262\pi$
$878$		0			0
$879$	−15.8736	+	11.5328i	−0.535402	+	0.388992i
$880$		0			0
$881$	−1.09078	−	0.792500i	−0.0367494	−	0.0267000i	0.569259	−	0.822158i	$-0.307230\pi$
$881$	−1.09078	−	0.792500i	−0.0367494	−	0.0267000i	−0.606008	+	0.795458i	$0.707230\pi$
$882$		0			0
$883$	3.26024	+	2.36870i	0.109716	+	0.0797132i	0.641290	−	0.767298i	$-0.278399\pi$
$883$	3.26024	+	2.36870i	0.109716	+	0.0797132i	−0.531574	+	0.847012i	$0.678399\pi$
$884$		0			0
$885$	−2.50212	−	7.70073i	−0.0841078	−	0.258857i
$886$		0			0
$887$	7.75237	−	23.8593i	0.260299	−	0.801118i	−0.732440	−	0.680831i	$-0.761619\pi$
$887$	7.75237	−	23.8593i	0.260299	−	0.801118i	0.992739	−	0.120287i	$-0.0383814\pi$
$888$		0			0
$889$	−5.68741	+	4.13215i	−0.190750	+	0.138588i
$890$		0			0
$891$	−3.91318	−	12.0435i	−0.131096	−	0.403473i
$892$		0			0
$893$	96.9152			3.24314
$894$		0			0
$895$	−4.37515	−	3.17873i	−0.146245	−	0.106253i
$896$		0			0
$897$	−25.0891	+	77.2164i	−0.837702	+	2.57818i
$898$		0			0
$899$	−12.5950			−0.420067
$900$		0			0
$901$	−20.2862			−0.675831
$902$		0			0
$903$	−22.2492			−0.740408
$904$		0			0
$905$	−1.17160			−0.0389452
$906$		0			0
$907$	3.12845	−	9.62837i	0.103878	−	0.319705i	−0.885587	−	0.464473i	$-0.846244\pi$
$907$	3.12845	−	9.62837i	0.103878	−	0.319705i	0.989466	+	0.144768i	$0.0462437\pi$
$908$		0			0
$909$	9.82781	+	7.14032i	0.325968	+	0.236830i
$910$		0			0
$911$	−27.6630			−0.916517			−0.458258	−	0.888819i	$-0.651527\pi$
$911$	−27.6630			−0.916517			−0.458258	+	0.888819i	$0.651527\pi$
$912$		0			0
$913$	−2.95180	−	9.08471i	−0.0976903	−	0.300660i
$914$		0			0
$915$	13.6683	−	9.93063i	0.451861	−	0.328296i
$916$		0			0
$917$	−7.08998	+	21.8207i	−0.234132	+	0.720584i
$918$		0			0
$919$	−5.66205	−	17.4260i	−0.186774	−	0.574830i	0.813201	−	0.581983i	$-0.197723\pi$
$919$	−5.66205	−	17.4260i	−0.186774	−	0.574830i	−0.999974	+	0.00715295i	$0.997723\pi$
$920$		0			0
$921$	53.1983	+	38.6508i	1.75294	+	1.27359i
$922$		0			0
$923$	9.72118	+	7.06285i	0.319977	+	0.232477i
$924$		0			0
$925$	−6.45954	+	4.69313i	−0.212388	+	0.154309i
$926$		0			0
$927$	−28.0802	−	20.4015i	−0.922276	−	0.670073i
$928$		0			0
$929$	−12.7993			−0.419932			−0.209966	−	0.977709i	$-0.567335\pi$
$929$	−12.7993			−0.419932			−0.209966	+	0.977709i	$0.567335\pi$
$930$		0			0
$931$	10.6349	−	32.7309i	0.348545	−	1.07271i
$932$		0			0
$933$	−15.5660	−	47.9072i	−0.509608	−	1.56841i
$934$		0			0
$935$	−1.25713	−	3.86906i	−0.0411126	−	0.126532i
$936$		0			0
$937$	5.82749	−	4.23392i	0.190376	−	0.138316i	−0.488515	−	0.872556i	$-0.662461\pi$
$937$	5.82749	−	4.23392i	0.190376	−	0.138316i	0.678890	+	0.734240i	$0.262461\pi$
$938$		0			0
$939$	8.75763	−	26.9532i	0.285794	−	0.879585i
$940$		0			0
$941$	−25.4844	+	18.5155i	−0.830769	+	0.603589i	−0.919777	−	0.392442i	$-0.871630\pi$
$941$	−25.4844	+	18.5155i	−0.830769	+	0.603589i	0.0890078	+	0.996031i	$0.471630\pi$
$942$		0			0
$943$	23.6044	+	39.0405i	0.768665	+	1.27133i
$944$		0			0
$945$	3.48447	−	2.53161i	0.113350	−	0.0823534i
$946$		0			0
$947$	−0.870580	+	2.67937i	−0.0282901	+	0.0870678i	−0.964205	−	0.265159i	$-0.914575\pi$
$947$	−0.870580	+	2.67937i	−0.0282901	+	0.0870678i	0.935915	+	0.352227i	$0.114575\pi$
$948$		0			0
$949$	21.5398	−	15.6496i	0.699212	−	0.508007i
$950$		0			0
$951$	9.52027	+	29.3004i	0.308716	+	0.950130i
$952$		0			0
$953$	−11.8667	−	36.5219i	−0.384399	−	1.18306i	−0.936915	−	0.349557i	$-0.886332\pi$
$953$	−11.8667	−	36.5219i	−0.384399	−	1.18306i	0.552516	−	0.833502i	$-0.313668\pi$
$954$		0			0
$955$	−2.59825	+	7.99658i	−0.0840773	+	0.258763i
$956$		0			0
$957$	6.81359			0.220252
$958$		0			0
$959$	13.0606	+	9.48909i	0.421749	+	0.306419i
$960$		0			0
$961$	7.97951	−	5.79746i	0.257404	−	0.187015i
$962$		0			0
$963$	17.7380	+	12.8874i	0.571598	+	0.415290i
$964$		0			0
$965$	2.34920	+	1.70679i	0.0756233	+	0.0549435i
$966$		0			0
$967$	4.26257	+	13.1189i	0.137075	+	0.421874i	0.995907	−	0.0903836i	$-0.0288093\pi$
$967$	4.26257	+	13.1189i	0.137075	+	0.421874i	−0.858832	+	0.512258i	$0.828809\pi$
$968$		0			0
$969$	−19.4065	+	59.7271i	−0.623427	+	1.91871i
$970$		0			0
$971$	−0.999494	+	0.726175i	−0.0320753	+	0.0233041i	−0.603707	−	0.797206i	$-0.706310\pi$
$971$	−0.999494	+	0.726175i	−0.0320753	+	0.0233041i	0.571632	+	0.820510i	$0.306310\pi$
$972$		0			0
$973$	−10.7422	−	33.0610i	−0.344379	−	1.05989i
$974$		0			0
$975$	11.3953			0.364941
$976$		0			0
$977$	−27.5516	−	20.0174i	−0.881455	−	0.640415i	0.0521808	−	0.998638i	$-0.483383\pi$
$977$	−27.5516	−	20.0174i	−0.881455	−	0.640415i	−0.933636	+	0.358223i	$0.883383\pi$
$978$		0			0
$979$	3.06317	−	9.42747i	0.0978994	−	0.301303i
$980$		0			0
$981$	23.6159			0.753998
$982$		0			0
$983$	−41.6280			−1.32773			−0.663863	−	0.747854i	$-0.731084\pi$
$983$	−41.6280			−1.32773			−0.663863	+	0.747854i	$0.731084\pi$
$984$		0			0
$985$	12.4112			0.395453
$986$		0			0
$987$	43.6157			1.38830
$988$		0			0
$989$	−13.6162	+	41.9064i	−0.432971	+	1.33255i
$990$		0			0
$991$	30.2656	+	21.9892i	0.961418	+	0.698511i	0.953480	−	0.301458i	$-0.0974732\pi$
$991$	30.2656	+	21.9892i	0.961418	+	0.698511i	0.00793821	+	0.999968i	$0.497473\pi$
$992$		0			0
$993$	4.00192			0.126997
$994$		0			0
$995$	1.01368	+	3.11977i	0.0321357	+	0.0989034i
$996$		0			0
$997$	−12.1126	+	8.80030i	−0.383609	+	0.278708i	−0.762832	−	0.646597i	$-0.776191\pi$
$997$	−12.1126	+	8.80030i	−0.383609	+	0.278708i	0.379223	+	0.925305i	$0.376191\pi$
$998$		0			0
$999$	−6.47344	+	19.9232i	−0.204810	+	0.630342i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.u.b.201.7	✓	32
41.10	even	5	inner	820.2.u.b.461.7	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.u.b.201.7	✓	32	1.1	even	1	trivial
820.2.u.b.461.7	yes	32	41.10	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.u (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+2.19153 q^{3} +(-0.309017 + 0.951057i) q^{5} +(1.32809 + 0.964915i) q^{7} +1.80282 q^{9} +(0.350697 + 1.07933i) q^{11} +(-4.20663 + 3.05630i) q^{13} +(-0.677221 + 2.08427i) q^{15} +(1.10772 + 3.40923i) q^{17} +(6.46733 + 4.69879i) q^{19} +(2.91056 + 2.11464i) q^{21} +(5.76416 - 4.18791i) q^{23} +(-0.809017 - 0.587785i) q^{25} -2.62367 q^{27} +(0.846567 - 2.60546i) q^{29} +(-1.42070 - 4.37246i) q^{31} +(0.768563 + 2.36539i) q^{33} +(-1.32809 + 0.964915i) q^{35} +(2.46732 - 7.59364i) q^{37} +(-9.21898 + 6.69798i) q^{39} +(-0.540510 + 6.38027i) q^{41} +(-5.00327 + 3.63509i) q^{43} +(-0.557101 + 1.71458i) q^{45} +(9.80804 - 7.12596i) q^{47} +(-1.33035 - 4.09440i) q^{49} +(2.42762 + 7.47143i) q^{51} +(-1.74877 + 5.38217i) q^{53} -1.13488 q^{55} +(14.1734 + 10.2976i) q^{57} +(-2.98906 + 2.17168i) q^{59} +(-6.23688 - 4.53136i) q^{61} +(2.39431 + 1.73957i) q^{63} +(-1.60679 - 4.94519i) q^{65} +(1.71907 - 5.29074i) q^{67} +(12.6323 - 9.17793i) q^{69} +(-0.714113 - 2.19781i) q^{71} -5.12044 q^{73} +(-1.77299 - 1.28815i) q^{75} +(-0.575708 + 1.77185i) q^{77} +15.1613 q^{79} -11.1583 q^{81} -8.41696 q^{83} -3.58467 q^{85} +(1.85528 - 5.70996i) q^{87} +(-7.06638 - 5.13403i) q^{89} -8.53586 q^{91} +(-3.11351 - 9.58239i) q^{93} +(-6.46733 + 4.69879i) q^{95} +(2.81546 - 8.66510i) q^{97} +(0.632242 + 1.94584i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{3} + 8 q^{5} - 5 q^{7} + 46 q^{9} + q^{11} + q^{13} - 2 q^{15} + 7 q^{17} - 13 q^{19} - 6 q^{21} + 4 q^{23} - 8 q^{25} - 28 q^{27} + 3 q^{29} - q^{31} + 14 q^{33} + 5 q^{35} - 25 q^{37} + 26 q^{41}+ \cdots + 30 q^{99}+O(q^{100}) \) 32 * q + 2 * q^3 + 8 * q^5 - 5 * q^7 + 46 * q^9 + q^11 + q^13 - 2 * q^15 + 7 * q^17 - 13 * q^19 - 6 * q^21 + 4 * q^23 - 8 * q^25 - 28 * q^27 + 3 * q^29 - q^31 + 14 * q^33 + 5 * q^35 - 25 * q^37 + 26 * q^41 + 8 * q^43 + 19 * q^45 + q^47 - 15 * q^49 + 29 * q^51 - 33 * q^53 + 4 * q^55 - 29 * q^57 + 20 * q^59 - 24 * q^61 - 66 * q^63 - q^65 - 48 * q^67 - 16 * q^69 + 5 * q^71 + 4 * q^73 - 3 * q^75 - 16 * q^77 - 102 * q^79 + 200 * q^81 - 110 * q^83 + 8 * q^85 + 25 * q^87 - 34 * q^89 - 10 * q^91 - 18 * q^93 + 13 * q^95 - 36 * q^97 + 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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