LMFDB - Embedded newform 1716.2.z.f.1093.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1716,2,Mod(157,1716)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1716, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8, 0]))

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

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

chi := DirichletCharacter("1716.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1716 = 2^{2} \cdot 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1716.z (of order $5$, degree $4$, 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:	$13.7023289869$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{19} + 41 x^{18} - 146 x^{17} + 650 x^{16} - 1400 x^{15} + 5756 x^{14} - 2122 x^{13} + \cdots + 4096 $ x^20 - 6x^19 + 41x^18 - 146x^17 + 650x^16 - 1400x^15 + 5756x^14 - 2122x^13 + 27469x^12 + 11286x^11 + 72308x^10 + 48512x^9 + 142448x^8 - 37952x^7 + 295552x^6 + 300160x^5 + 272128x^4 + 194048x^3 + 236544x^2 + 49152*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			1093.4
Root			$-1.06605 + 3.28095i$ of defining polynomial
Character	$\chi$	$=$	1716.1093
Dual form			1716.2.z.f.157.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{3} +(2.84595 - 2.06771i) q^{5} +(0.644587 + 1.98383i) q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{3} +(2.84595 - 2.06771i) q^{5} +(0.644587 + 1.98383i) q^{7} +(-0.809017 - 0.587785i) q^{9} +(3.15787 + 1.01385i) q^{11} +(-0.809017 - 0.587785i) q^{13} +(1.08706 + 3.34562i) q^{15} +(-5.50267 + 3.99792i) q^{17} +(-1.95519 + 6.01744i) q^{19} -2.08593 q^{21} +6.52330 q^{23} +(2.27896 - 7.01390i) q^{25} +(0.809017 - 0.587785i) q^{27} +(2.26803 + 6.98027i) q^{29} +(2.68502 + 1.95078i) q^{31} +(-1.94006 + 2.69001i) q^{33} +(5.93645 + 4.31308i) q^{35} +(-1.96669 - 6.05285i) q^{37} +(0.809017 - 0.587785i) q^{39} +(-1.14543 + 3.52527i) q^{41} -4.14536 q^{43} -3.51779 q^{45} +(-0.514594 + 1.58376i) q^{47} +(2.14301 - 1.55699i) q^{49} +(-2.10183 - 6.46878i) q^{51} +(4.08875 + 2.97065i) q^{53} +(11.0835 - 3.64418i) q^{55} +(-5.11874 - 3.71899i) q^{57} +(-3.92076 - 12.0669i) q^{59} +(3.18995 - 2.31763i) q^{61} +(0.644587 - 1.98383i) q^{63} -3.51779 q^{65} +7.45708 q^{67} +(-2.01581 + 6.20403i) q^{69} +(3.31083 - 2.40546i) q^{71} +(1.63348 + 5.02734i) q^{73} +(5.96638 + 4.33483i) q^{75} +(0.0242166 + 6.91819i) q^{77} +(-2.14095 - 1.55549i) q^{79} +(0.309017 + 0.951057i) q^{81} +(13.2283 - 9.61089i) q^{83} +(-7.39381 + 22.7558i) q^{85} -7.33949 q^{87} +4.92182 q^{89} +(0.644587 - 1.98383i) q^{91} +(-2.68502 + 1.95078i) q^{93} +(6.87794 + 21.1681i) q^{95} +(-14.1548 - 10.2841i) q^{97} +(-1.95884 - 2.67637i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 5 q^{3} + 4 q^{5} - q^{7} - 5 q^{9}+O(q^{10}) $ 20 * q + 5 * q^3 + 4 * q^5 - q^7 - 5 * q^9	$ 20 q + 5 q^{3} + 4 q^{5} - q^{7} - 5 q^{9} - 24 q^{11} - 5 q^{13} - 4 q^{15} - 6 q^{17} - 16 q^{19} + 6 q^{21} - 34 q^{23} + 13 q^{25} + 5 q^{27} + 4 q^{29} - 12 q^{31} - 11 q^{33} - 20 q^{37} + 5 q^{39} + 24 q^{41} - 32 q^{43} - 16 q^{45} - 6 q^{47} + 6 q^{49} - 9 q^{51} + 3 q^{53} - 20 q^{55} - 14 q^{57} - 61 q^{59} + 18 q^{61} - q^{63} - 16 q^{65} - 32 q^{67} - 6 q^{69} + 16 q^{71} + 17 q^{73} + 37 q^{75} + 22 q^{77} - 41 q^{79} - 5 q^{81} + 58 q^{83} + 42 q^{85} - 4 q^{87} - 6 q^{89} - q^{91} + 12 q^{93} + 55 q^{95} - 62 q^{97} + 6 q^{99}+O(q^{100}) $ 20 * q + 5 * q^3 + 4 * q^5 - q^7 - 5 * q^9 - 24 * q^11 - 5 * q^13 - 4 * q^15 - 6 * q^17 - 16 * q^19 + 6 * q^21 - 34 * q^23 + 13 * q^25 + 5 * q^27 + 4 * q^29 - 12 * q^31 - 11 * q^33 - 20 * q^37 + 5 * q^39 + 24 * q^41 - 32 * q^43 - 16 * q^45 - 6 * q^47 + 6 * q^49 - 9 * q^51 + 3 * q^53 - 20 * q^55 - 14 * q^57 - 61 * q^59 + 18 * q^61 - q^63 - 16 * q^65 - 32 * q^67 - 6 * q^69 + 16 * q^71 + 17 * q^73 + 37 * q^75 + 22 * q^77 - 41 * q^79 - 5 * q^81 + 58 * q^83 + 42 * q^85 - 4 * q^87 - 6 * q^89 - q^91 + 12 * q^93 + 55 * q^95 - 62 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1716\mathbb{Z}\right)^\times$.

$n$	$859$	$925$	$937$	$1145$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$	$1$

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
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$		0			0
$5$	2.84595	−	2.06771i	1.27275	−	0.924706i	0.273440	−	0.961889i	$-0.411838\pi$
$5$	2.84595	−	2.06771i	1.27275	−	0.924706i	0.999308	+	0.0371828i	$0.0118384\pi$
$6$		0			0
$7$	0.644587	+	1.98383i	0.243631	+	0.749819i	0.995859	+	0.0909156i	$0.0289793\pi$
$7$	0.644587	+	1.98383i	0.243631	+	0.749819i	−0.752228	+	0.658903i	$0.771021\pi$
$8$		0			0
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$		0			0
$11$	3.15787	+	1.01385i	0.952132	+	0.305686i
$11$	3.15787	+	1.01385i	0.952132	+	0.305686i
$12$		0			0
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$14$		0			0
$15$	1.08706	+	3.34562i	0.280677	+	0.863835i
$16$		0			0
$17$	−5.50267	+	3.99792i	−1.33459	+	0.969639i	−0.334969	+	0.942229i	$0.608726\pi$
$17$	−5.50267	+	3.99792i	−1.33459	+	0.969639i	−0.999624	+	0.0274101i	$0.991274\pi$
$18$		0			0
$19$	−1.95519	+	6.01744i	−0.448550	+	1.38050i	0.429992	+	0.902833i	$0.358516\pi$
$19$	−1.95519	+	6.01744i	−0.448550	+	1.38050i	−0.878543	+	0.477664i	$0.841484\pi$
$20$		0			0
$21$	−2.08593			−0.455186
$22$		0			0
$23$	6.52330			1.36020			0.680101	−	0.733118i	$-0.261936\pi$
$23$	6.52330			1.36020			0.680101	+	0.733118i	$0.261936\pi$
$24$		0			0
$25$	2.27896	−	7.01390i	0.455791	−	1.40278i
$26$		0			0
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$		0			0
$29$	2.26803	+	6.98027i	0.421162	+	1.29620i	0.906622	+	0.421945i	$0.138652\pi$
$29$	2.26803	+	6.98027i	0.421162	+	1.29620i	−0.485459	+	0.874259i	$0.661348\pi$
$30$		0			0
$31$	2.68502	+	1.95078i	0.482243	+	0.350370i	0.802193	−	0.597064i	$-0.203666\pi$
$31$	2.68502	+	1.95078i	0.482243	+	0.350370i	−0.319950	+	0.947434i	$0.603666\pi$
$32$		0			0
$33$	−1.94006	+	2.69001i	−0.337721	+	0.468271i
$34$		0			0
$35$	5.93645	+	4.31308i	1.00344	+	0.729044i
$36$		0			0
$37$	−1.96669	−	6.05285i	−0.323322	−	0.995082i	−0.972192	−	0.234183i	$-0.924758\pi$
$37$	−1.96669	−	6.05285i	−0.323322	−	0.995082i	0.648871	−	0.760899i	$-0.275242\pi$
$38$		0			0
$39$	0.809017	−	0.587785i	0.129546	−	0.0941210i
$40$		0			0
$41$	−1.14543	+	3.52527i	−0.178886	+	0.550555i	−0.999790	−	0.0205118i	$-0.993470\pi$
$41$	−1.14543	+	3.52527i	−0.178886	+	0.550555i	0.820903	+	0.571067i	$0.193470\pi$
$42$		0			0
$43$	−4.14536			−0.632161			−0.316081	−	0.948732i	$-0.602367\pi$
$43$	−4.14536			−0.632161			−0.316081	+	0.948732i	$0.602367\pi$
$44$		0			0
$45$	−3.51779			−0.524401
$46$		0			0
$47$	−0.514594	+	1.58376i	−0.0750613	+	0.231015i	−0.981547	−	0.191222i	$-0.938755\pi$
$47$	−0.514594	+	1.58376i	−0.0750613	+	0.231015i	0.906486	+	0.422237i	$0.138755\pi$
$48$		0			0
$49$	2.14301	−	1.55699i	0.306145	−	0.222427i
$50$		0			0
$51$	−2.10183	−	6.46878i	−0.294316	−	0.905810i
$52$		0			0
$53$	4.08875	+	2.97065i	0.561633	+	0.408050i	0.832056	−	0.554691i	$-0.187164\pi$
$53$	4.08875	+	2.97065i	0.561633	+	0.408050i	−0.270423	+	0.962741i	$0.587164\pi$
$54$		0			0
$55$	11.0835	−	3.64418i	1.49450	−	0.491381i
$56$		0			0
$57$	−5.11874	−	3.71899i	−0.677994	−	0.492592i
$58$		0			0
$59$	−3.92076	−	12.0669i	−0.510439	−	1.57097i	−0.791430	−	0.611260i	$-0.790663\pi$
$59$	−3.92076	−	12.0669i	−0.510439	−	1.57097i	0.280990	−	0.959711i	$-0.409337\pi$
$60$		0			0
$61$	3.18995	−	2.31763i	0.408431	−	0.296743i	−0.364535	−	0.931190i	$-0.618772\pi$
$61$	3.18995	−	2.31763i	0.408431	−	0.296743i	0.772966	+	0.634447i	$0.218772\pi$
$62$		0			0
$63$	0.644587	−	1.98383i	0.0812103	−	0.249940i
$64$		0			0
$65$	−3.51779			−0.436328
$66$		0			0
$67$	7.45708			0.911027			0.455513	−	0.890229i	$-0.349456\pi$
$67$	7.45708			0.911027			0.455513	+	0.890229i	$0.349456\pi$
$68$		0			0
$69$	−2.01581	+	6.20403i	−0.242675	+	0.746877i
$70$		0			0
$71$	3.31083	−	2.40546i	0.392924	−	0.285476i	−0.373729	−	0.927538i	$-0.621921\pi$
$71$	3.31083	−	2.40546i	0.392924	−	0.285476i	0.766653	+	0.642062i	$0.221921\pi$
$72$		0			0
$73$	1.63348	+	5.02734i	0.191185	+	0.588406i	1.00000		0.000343273i	$0.000109267\pi$
$73$	1.63348	+	5.02734i	0.191185	+	0.588406i	−0.808815	+	0.588063i	$0.799891\pi$
$74$		0			0
$75$	5.96638	+	4.33483i	0.688939	+	0.500543i
$76$		0			0
$77$	0.0242166	+	6.91819i	0.00275974	+	0.788401i
$78$		0			0
$79$	−2.14095	−	1.55549i	−0.240876	−	0.175007i	0.460797	−	0.887505i	$-0.347564\pi$
$79$	−2.14095	−	1.55549i	−0.240876	−	0.175007i	−0.701674	+	0.712499i	$0.747564\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		0			0
$83$	13.2283	−	9.61089i	1.45199	−	1.05493i	0.466628	−	0.884454i	$-0.345469\pi$
$83$	13.2283	−	9.61089i	1.45199	−	1.05493i	0.985361	−	0.170479i	$-0.0545313\pi$
$84$		0			0
$85$	−7.39381	+	22.7558i	−0.801971	+	2.46821i
$86$		0			0
$87$	−7.33949			−0.786876
$88$		0			0
$89$	4.92182			0.521712			0.260856	−	0.965378i	$-0.415995\pi$
$89$	4.92182			0.521712			0.260856	+	0.965378i	$0.415995\pi$
$90$		0			0
$91$	0.644587	−	1.98383i	0.0675711	−	0.207962i
$92$		0			0
$93$	−2.68502	+	1.95078i	−0.278423	+	0.202286i
$94$		0			0
$95$	6.87794	+	21.1681i	0.705661	+	2.17180i
$96$		0			0
$97$	−14.1548	−	10.2841i	−1.43721	−	1.04419i	−0.988617	−	0.150452i	$-0.951927\pi$
$97$	−14.1548	−	10.2841i	−1.43721	−	1.04419i	−0.448588	−	0.893739i	$-0.648073\pi$
$98$		0			0
$99$	−1.95884	−	2.67637i	−0.196871	−	0.268985i
$100$		0			0
$101$	−7.13433	−	5.18340i	−0.709893	−	0.515767i	0.173246	−	0.984878i	$-0.444574\pi$
$101$	−7.13433	−	5.18340i	−0.709893	−	0.515767i	−0.883139	+	0.469111i	$0.844574\pi$
$102$		0			0
$103$	5.11739	+	15.7497i	0.504232	+	1.55187i	0.802058	+	0.597246i	$0.203738\pi$
$103$	5.11739	+	15.7497i	0.504232	+	1.55187i	−0.297826	+	0.954620i	$0.596262\pi$
$104$		0			0
$105$	−5.93645	+	4.31308i	−0.579338	+	0.420914i
$106$		0			0
$107$	−4.26705	+	13.1326i	−0.412511	+	1.26958i	0.501947	+	0.864898i	$0.332617\pi$
$107$	−4.26705	+	13.1326i	−0.412511	+	1.26958i	−0.914458	+	0.404680i	$0.867383\pi$
$108$		0			0
$109$	13.3153			1.27538			0.637689	−	0.770294i	$-0.279890\pi$
$109$	13.3153			1.27538			0.637689	+	0.770294i	$0.279890\pi$
$110$		0			0
$111$	6.36434			0.604076
$112$		0			0
$113$	−3.84834	+	11.8440i	−0.362022	+	1.11419i	0.589804	+	0.807547i	$0.299205\pi$
$113$	−3.84834	+	11.8440i	−0.362022	+	1.11419i	−0.951825	+	0.306641i	$0.900795\pi$
$114$		0			0
$115$	18.5650	−	13.4883i	1.73120	−	1.25779i
$116$		0			0
$117$	0.309017	+	0.951057i	0.0285686	+	0.0879252i
$118$		0			0
$119$	−11.4782	−	8.33938i	−1.05220	−	0.764469i
$120$		0			0
$121$	8.94423	+	6.40318i	0.813112	+	0.582107i
$122$		0			0
$123$	−2.99878	−	2.17874i	−0.270391	−	0.196450i
$124$		0			0
$125$	−2.58160	−	7.94536i	−0.230906	−	0.710655i
$126$		0			0
$127$	13.0229	−	9.46170i	1.15560	−	0.839590i	0.166381	−	0.986061i	$-0.446792\pi$
$127$	13.0229	−	9.46170i	1.15560	−	0.839590i	0.989215	+	0.146472i	$0.0467917\pi$
$128$		0			0
$129$	1.28099	−	3.94247i	0.112785	−	0.347115i
$130$		0			0
$131$	−19.7029			−1.72145			−0.860725	−	0.509070i	$-0.829989\pi$
$131$	−19.7029			−1.72145			−0.860725	+	0.509070i	$0.829989\pi$
$132$		0			0
$133$	−13.1979			−1.14440
$134$		0			0
$135$	1.08706	−	3.34562i	0.0935590	−	0.287945i
$136$		0			0
$137$	−10.3956	+	7.55283i	−0.888154	+	0.645282i	−0.935396	−	0.353602i	$-0.884957\pi$
$137$	−10.3956	+	7.55283i	−0.888154	+	0.645282i	0.0472418	+	0.998883i	$0.484957\pi$
$138$		0			0
$139$	−1.36567	−	4.20309i	−0.115834	−	0.356502i	0.876286	−	0.481792i	$-0.160014\pi$
$139$	−1.36567	−	4.20309i	−0.115834	−	0.356502i	−0.992120	+	0.125290i	$0.960014\pi$
$140$		0			0
$141$	−1.34723	−	0.978816i	−0.113457	−	0.0824312i
$142$		0			0
$143$	−1.95884	−	2.67637i	−0.163807	−	0.223809i
$144$		0			0
$145$	20.8878	+	15.1759i	1.73464	+	1.26029i
$146$		0			0
$147$	0.818558	+	2.51926i	0.0675136	+	0.207785i
$148$		0			0
$149$	2.74491	−	1.99429i	0.224872	−	0.163379i	−0.469645	−	0.882855i	$-0.655618\pi$
$149$	2.74491	−	1.99429i	0.224872	−	0.163379i	0.694517	+	0.719476i	$0.255618\pi$
$150$		0			0
$151$	2.00118	−	6.15901i	0.162854	−	0.501213i	−0.836018	−	0.548702i	$-0.815122\pi$
$151$	2.00118	−	6.15901i	0.162854	−	0.501213i	0.998872	+	0.0474895i	$0.0151221\pi$
$152$		0			0
$153$	6.80168			0.549883
$154$		0			0
$155$	11.6751			0.937764
$156$		0			0
$157$	0.478962	−	1.47409i	0.0382253	−	0.117645i	−0.930123	−	0.367248i	$-0.880300\pi$
$157$	0.478962	−	1.47409i	0.0382253	−	0.117645i	0.968348	+	0.249603i	$0.0803000\pi$
$158$		0			0
$159$	−4.08875	+	2.97065i	−0.324259	+	0.235588i
$160$		0			0
$161$	4.20483	+	12.9411i	0.331387	+	1.01991i
$162$		0			0
$163$	−2.19401	−	1.59404i	−0.171848	−	0.124855i	0.498537	−	0.866869i	$-0.333871\pi$
$163$	−2.19401	−	1.59404i	−0.171848	−	0.124855i	−0.670385	+	0.742014i	$0.733871\pi$
$164$		0			0
$165$	0.0408399	+	11.6671i	0.00317938	+	0.908284i
$166$		0			0
$167$	−4.70407	−	3.41771i	−0.364012	−	0.264470i	0.390711	−	0.920513i	$-0.372229\pi$
$167$	−4.70407	−	3.41771i	−0.364012	−	0.264470i	−0.754724	+	0.656043i	$0.772229\pi$
$168$		0			0
$169$	0.309017	+	0.951057i	0.0237705	+	0.0731582i
$170$		0			0
$171$	5.11874	−	3.71899i	0.391440	−	0.284398i
$172$		0			0
$173$	6.62975	−	20.4043i	0.504051	−	1.55131i	−0.298310	−	0.954469i	$-0.596423\pi$
$173$	6.62975	−	20.4043i	0.504051	−	1.55131i	0.802361	−	0.596839i	$-0.203577\pi$
$174$		0			0
$175$	15.3834			1.16288
$176$		0			0
$177$	12.6878			0.953677
$178$		0			0
$179$	0.0797572	−	0.245467i	0.00596133	−	0.0183471i	−0.948032	−	0.318176i	$-0.896930\pi$
$179$	0.0797572	−	0.245467i	0.00596133	−	0.0183471i	0.953993	+	0.299829i	$0.0969296\pi$
$180$		0			0
$181$	−18.0581	+	13.1200i	−1.34225	+	0.975203i	−0.342894	+	0.939374i	$0.611407\pi$
$181$	−18.0581	+	13.1200i	−1.34225	+	0.975203i	−0.999358	+	0.0358285i	$0.988593\pi$
$182$		0			0
$183$	1.21845	+	3.75001i	0.0900706	+	0.277209i
$184$		0			0
$185$	−18.1126	−	13.1596i	−1.33167	−	0.967512i
$186$		0			0
$187$	−21.4300	+	7.04605i	−1.56712	+	0.515258i
$188$		0			0
$189$	1.68755	+	1.22608i	0.122751	+	0.0891840i
$190$		0			0
$191$	7.22066	+	22.2229i	0.522468	+	1.60799i	0.769268	+	0.638926i	$0.220621\pi$
$191$	7.22066	+	22.2229i	0.522468	+	1.60799i	−0.246800	+	0.969066i	$0.579379\pi$
$192$		0			0
$193$	4.48455	−	3.25821i	0.322805	−	0.234531i	−0.414567	−	0.910019i	$-0.636067\pi$
$193$	4.48455	−	3.25821i	0.322805	−	0.234531i	0.737371	+	0.675488i	$0.236067\pi$
$194$		0			0
$195$	1.08706	−	3.34562i	0.0778458	−	0.239585i
$196$		0			0
$197$	−17.0335			−1.21359			−0.606794	−	0.794859i	$-0.707545\pi$
$197$	−17.0335			−1.21359			−0.606794	+	0.794859i	$0.707545\pi$
$198$		0			0
$199$	13.0479			0.924943			0.462471	−	0.886634i	$-0.346963\pi$
$199$	13.0479			0.924943			0.462471	+	0.886634i	$0.346963\pi$
$200$		0			0
$201$	−2.30436	+	7.09210i	−0.162537	+	0.500238i
$202$		0			0
$203$	−12.3858	+	8.99878i	−0.869310	+	0.631591i
$204$		0			0
$205$	4.02939	+	12.4012i	0.281425	+	0.866136i
$206$		0			0
$207$	−5.27746	−	3.83430i	−0.366809	−	0.266502i
$208$		0			0
$209$	−12.2750	+	17.0200i	−0.849078	+	1.17730i
$210$		0			0
$211$	10.2383	+	7.43853i	0.704830	+	0.512089i	0.881502	−	0.472181i	$-0.156533\pi$
$211$	10.2383	+	7.43853i	0.704830	+	0.512089i	−0.176671	+	0.984270i	$0.556533\pi$
$212$		0			0
$213$	1.26463	+	3.89212i	0.0866508	+	0.266684i
$214$		0			0
$215$	−11.7975	+	8.57138i	−0.804583	+	0.584563i
$216$		0			0
$217$	−2.13929	+	6.58407i	−0.145225	+	0.446956i
$218$		0			0
$219$	−5.28606			−0.357199
$220$		0			0
$221$	6.80168			0.457530
$222$		0			0
$223$	0.980761	−	3.01847i	0.0656766	−	0.202132i	−0.912833	−	0.408333i	$-0.866110\pi$
$223$	0.980761	−	3.01847i	0.0656766	−	0.202132i	0.978510	+	0.206201i	$0.0661102\pi$
$224$		0			0
$225$	−5.96638	+	4.33483i	−0.397759	+	0.288989i
$226$		0			0
$227$	−3.92372	−	12.0760i	−0.260426	−	0.801510i	−0.992712	−	0.120512i	$-0.961546\pi$
$227$	−3.92372	−	12.0760i	−0.260426	−	0.801510i	0.732285	−	0.680998i	$-0.238454\pi$
$228$		0			0
$229$	2.68013	+	1.94723i	0.177108	+	0.128676i	0.672807	−	0.739818i	$-0.265088\pi$
$229$	2.68013	+	1.94723i	0.177108	+	0.128676i	−0.495700	+	0.868494i	$0.665088\pi$
$230$		0			0
$231$	−6.58708	−	2.11481i	−0.433398	−	0.139144i
$232$		0			0
$233$	−9.53208	−	6.92546i	−0.624467	−	0.453702i	0.230012	−	0.973188i	$-0.426124\pi$
$233$	−9.53208	−	6.92546i	−0.624467	−	0.453702i	−0.854479	+	0.519486i	$0.826124\pi$
$234$		0			0
$235$	1.81023	+	5.57133i	0.118087	+	0.363434i
$236$		0			0
$237$	2.14095	−	1.55549i	0.139070	−	0.101040i
$238$		0			0
$239$	−0.755957	+	2.32660i	−0.0488988	+	0.150495i	−0.972524	−	0.232801i	$-0.925211\pi$
$239$	−0.755957	+	2.32660i	−0.0488988	+	0.150495i	0.923626	+	0.383296i	$0.125211\pi$
$240$		0			0
$241$	2.18341			0.140646			0.0703228	−	0.997524i	$-0.477597\pi$
$241$	2.18341			0.140646			0.0703228	+	0.997524i	$0.477597\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	2.87952	−	8.86224i	0.183966	−	0.566188i
$246$		0			0
$247$	5.11874	−	3.71899i	0.325698	−	0.236633i
$248$		0			0
$249$	5.05274	+	15.5507i	0.320205	+	0.985488i
$250$		0			0
$251$	−7.51733	−	5.46166i	−0.474489	−	0.344737i	0.324699	−	0.945817i	$-0.394737\pi$
$251$	−7.51733	−	5.46166i	−0.474489	−	0.344737i	−0.799188	+	0.601081i	$0.794737\pi$
$252$		0			0
$253$	20.5997	+	6.61362i	1.29509	+	0.415795i
$254$		0			0
$255$	−19.3572	−	14.0639i	−1.21220	−	0.880713i
$256$		0			0
$257$	−9.40808	−	28.9551i	−0.586860	−	1.80617i	−0.591669	−	0.806181i	$-0.701531\pi$
$257$	−9.40808	−	28.9551i	−0.586860	−	1.80617i	0.00480879	−	0.999988i	$-0.498469\pi$
$258$		0			0
$259$	10.7401	−	7.80317i	0.667360	−	0.484865i
$260$		0			0
$261$	2.26803	−	6.98027i	0.140387	−	0.432068i
$262$		0			0
$263$	−4.88349			−0.301129			−0.150565	−	0.988600i	$-0.548109\pi$
$263$	−4.88349			−0.301129			−0.150565	+	0.988600i	$0.548109\pi$
$264$		0			0
$265$	17.7788			1.09214
$266$		0			0
$267$	−1.52093	+	4.68093i	−0.0930792	+	0.286468i
$268$		0			0
$269$	20.3651	−	14.7961i	1.24168	−	0.902137i	0.243975	−	0.969781i	$-0.421548\pi$
$269$	20.3651	−	14.7961i	1.24168	−	0.902137i	0.997709	+	0.0676446i	$0.0215484\pi$
$270$		0			0
$271$	−3.36904	−	10.3689i	−0.204655	−	0.629863i	−0.999727	−	0.0233485i	$-0.992567\pi$
$271$	−3.36904	−	10.3689i	−0.204655	−	0.629863i	0.795073	−	0.606514i	$-0.207433\pi$
$272$		0			0
$273$	1.68755	+	1.22608i	0.102135	+	0.0742055i
$274$		0			0
$275$	14.3077	−	19.8385i	0.862784	−	1.19630i
$276$		0			0
$277$	−12.7939	−	9.29529i	−0.768709	−	0.558500i	0.132860	−	0.991135i	$-0.457584\pi$
$277$	−12.7939	−	9.29529i	−0.768709	−	0.558500i	−0.901569	+	0.432635i	$0.857584\pi$
$278$		0			0
$279$	−1.02558	−	3.15643i	−0.0614002	−	0.188970i
$280$		0			0
$281$	5.30362	−	3.85331i	0.316387	−	0.229869i	−0.418245	−	0.908334i	$-0.637355\pi$
$281$	5.30362	−	3.85331i	0.316387	−	0.229869i	0.734632	+	0.678465i	$0.237355\pi$
$282$		0			0
$283$	8.95235	−	27.5525i	0.532162	−	1.63783i	−0.217540	−	0.976051i	$-0.569803\pi$
$283$	8.95235	−	27.5525i	0.532162	−	1.63783i	0.749702	−	0.661775i	$-0.230197\pi$
$284$		0			0
$285$	−22.2575			−1.31842
$286$		0			0
$287$	−7.73189			−0.456399
$288$		0			0
$289$	9.04270	−	27.8306i	0.531923	−	1.63709i
$290$		0			0
$291$	14.1548	−	10.2841i	0.829771	−	0.602864i
$292$		0			0
$293$	−5.45395	−	16.7855i	−0.318623	−	0.980622i	−0.974237	−	0.225526i	$-0.927590\pi$
$293$	−5.45395	−	16.7855i	−0.318623	−	0.980622i	0.655614	−	0.755096i	$-0.272410\pi$
$294$		0			0
$295$	−36.1090	−	26.2347i	−2.10235	−	1.52745i
$296$		0			0
$297$	3.15069	−	1.03593i	0.182822	−	0.0601107i
$298$		0			0
$299$	−5.27746	−	3.83430i	−0.305204	−	0.221743i
$300$		0			0
$301$	−2.67204	−	8.22370i	−0.154014	−	0.474006i
$302$		0			0
$303$	7.13433	−	5.18340i	0.409857	−	0.297778i
$304$		0			0
$305$	4.28626	−	13.1918i	0.245431	−	0.755358i
$306$		0			0
$307$	−6.44669			−0.367932			−0.183966	−	0.982933i	$-0.558894\pi$
$307$	−6.44669			−0.367932			−0.183966	+	0.982933i	$0.558894\pi$
$308$		0			0
$309$	−16.5602			−0.942079
$310$		0			0
$311$	−8.88331	+	27.3400i	−0.503726	+	1.55031i	0.299176	+	0.954198i	$0.403288\pi$
$311$	−8.88331	+	27.3400i	−0.503726	+	1.55031i	−0.802902	+	0.596112i	$0.796712\pi$
$312$		0			0
$313$	11.2501	−	8.17370i	0.635895	−	0.462005i	−0.222542	−	0.974923i	$-0.571436\pi$
$313$	11.2501	−	8.17370i	0.635895	−	0.462005i	0.858437	+	0.512918i	$0.171436\pi$
$314$		0			0
$315$	−2.26752	−	6.97871i	−0.127760	−	0.393206i
$316$		0			0
$317$	19.5135	+	14.1774i	1.09599	+	0.796280i	0.980400	−	0.197017i	$-0.0631254\pi$
$317$	19.5135	+	14.1774i	1.09599	+	0.796280i	0.115586	+	0.993297i	$0.463125\pi$
$318$		0			0
$319$	0.0852081	+	24.3422i	0.00477074	+	1.36290i
$320$		0			0
$321$	−11.1713	−	8.11640i	−0.623520	−	0.453014i
$322$		0			0
$323$	−13.2985	−	40.9287i	−0.739951	−	2.27733i
$324$		0			0
$325$	−5.96638	+	4.33483i	−0.330955	+	0.240453i
$326$		0			0
$327$	−4.11467	+	12.6636i	−0.227542	+	0.700301i
$328$		0			0
$329$	−3.47361			−0.191507
$330$		0			0
$331$	16.9396			0.931086			0.465543	−	0.885025i	$-0.345859\pi$
$331$	16.9396			0.931086			0.465543	+	0.885025i	$0.345859\pi$
$332$		0			0
$333$	−1.96669	+	6.05285i	−0.107774	+	0.331694i
$334$		0			0
$335$	21.2225	−	15.4190i	1.15951	−	0.842432i
$336$		0			0
$337$	−5.55470	−	17.0956i	−0.302584	−	0.931257i	−0.980568	−	0.196180i	$-0.937146\pi$
$337$	−5.55470	−	17.0956i	−0.302584	−	0.931257i	0.677984	−	0.735076i	$-0.262854\pi$
$338$		0			0
$339$	−10.0751	−	7.31998i	−0.547204	−	0.397567i
$340$		0			0
$341$	6.50113	+	8.88249i	0.352056	+	0.481014i
$342$		0			0
$343$	16.2830	+	11.8303i	0.879200	+	0.638776i
$344$		0			0
$345$	7.09120	+	21.8245i	0.381778	+	1.17499i
$346$		0			0
$347$	−23.4380	+	17.0287i	−1.25822	+	0.914150i	−0.998669	−	0.0515800i	$-0.983574\pi$
$347$	−23.4380	+	17.0287i	−1.25822	+	0.914150i	−0.259550	+	0.965730i	$0.583574\pi$
$348$		0			0
$349$	6.80973	−	20.9582i	0.364517	−	1.12187i	−0.585767	−	0.810480i	$-0.699207\pi$
$349$	6.80973	−	20.9582i	0.364517	−	1.12187i	0.950283	−	0.311387i	$-0.100793\pi$
$350$		0			0
$351$	−1.00000			−0.0533761
$352$		0			0
$353$	−27.9123			−1.48562			−0.742811	−	0.669502i	$-0.766508\pi$
$353$	−27.9123			−1.48562			−0.742811	+	0.669502i	$0.766508\pi$
$354$		0			0
$355$	4.44869	−	13.6917i	0.236112	−	0.726678i
$356$		0			0
$357$	11.4782	−	8.33938i	0.607489	−	0.441367i
$358$		0			0
$359$	−2.49319	−	7.67326i	−0.131586	−	0.404979i	0.863458	−	0.504421i	$-0.168294\pi$
$359$	−2.49319	−	7.67326i	−0.131586	−	0.404979i	−0.995043	+	0.0994423i	$0.968294\pi$
$360$		0			0
$361$	−17.0156	−	12.3625i	−0.895556	−	0.650659i
$362$		0			0
$363$	−8.85370	+	6.52778i	−0.464699	+	0.342620i
$364$		0			0
$365$	15.0439	+	10.9300i	0.787433	+	0.572104i
$366$		0			0
$367$	−4.99583	−	15.3756i	−0.260780	−	0.802599i	−0.992636	−	0.121139i	$-0.961345\pi$
$367$	−4.99583	−	15.3756i	−0.260780	−	0.802599i	0.731855	−	0.681460i	$-0.238655\pi$
$368$		0			0
$369$	2.99878	−	2.17874i	0.156110	−	0.113421i
$370$		0			0
$371$	−3.25772	+	10.0262i	−0.169133	+	0.520536i
$372$		0			0
$373$	−9.57630			−0.495842			−0.247921	−	0.968780i	$-0.579747\pi$
$373$	−9.57630			−0.495842			−0.247921	+	0.968780i	$0.579747\pi$
$374$		0			0
$375$	8.35425			0.431411
$376$		0			0
$377$	2.26803	−	6.98027i	0.116809	−	0.359502i
$378$		0			0
$379$	17.2991	−	12.5685i	0.888596	−	0.645603i	−0.0469154	−	0.998899i	$-0.514939\pi$
$379$	17.2991	−	12.5685i	0.888596	−	0.645603i	0.935512	+	0.353296i	$0.114939\pi$
$380$		0			0
$381$	4.97431	+	15.3093i	0.254842	+	0.784322i
$382$		0			0
$383$	−1.21003	−	0.879139i	−0.0618297	−	0.0449219i	0.556441	−	0.830887i	$-0.312166\pi$
$383$	−1.21003	−	0.879139i	−0.0618297	−	0.0449219i	−0.618271	+	0.785965i	$0.712166\pi$
$384$		0			0
$385$	14.3737	+	19.6388i	0.732552	+	1.00088i
$386$		0			0
$387$	3.35367	+	2.43658i	0.170476	+	0.123858i
$388$		0			0
$389$	−0.260598	−	0.802040i	−0.0132129	−	0.0406650i	0.944233	−	0.329279i	$-0.106806\pi$
$389$	−0.260598	−	0.802040i	−0.0132129	−	0.0406650i	−0.957446	+	0.288614i	$0.906806\pi$
$390$		0			0
$391$	−35.8956	+	26.0797i	−1.81532	+	1.31891i
$392$		0			0
$393$	6.08853	−	18.7386i	0.307126	−	0.945235i
$394$		0			0
$395$	−9.30936			−0.468405
$396$		0			0
$397$	−26.2039			−1.31513			−0.657567	−	0.753396i	$-0.728415\pi$
$397$	−26.2039			−1.31513			−0.657567	+	0.753396i	$0.728415\pi$
$398$		0			0
$399$	4.07837	−	12.5519i	0.204174	−	0.628383i
$400$		0			0
$401$	−22.7013	+	16.4935i	−1.13365	+	0.823645i	−0.986222	−	0.165427i	$-0.947100\pi$
$401$	−22.7013	+	16.4935i	−1.13365	+	0.823645i	−0.147429	+	0.989073i	$0.547100\pi$
$402$		0			0
$403$	−1.02558	−	3.15643i	−0.0510880	−	0.157233i
$404$		0			0
$405$	2.84595	+	2.06771i	0.141417	+	0.102745i
$406$		0			0
$407$	−0.0738871	−	21.1080i	−0.00366245	−	1.04628i
$408$		0			0
$409$	1.56223	+	1.13503i	0.0772475	+	0.0561236i	0.625739	−	0.780033i	$-0.284798\pi$
$409$	1.56223	+	1.13503i	0.0772475	+	0.0561236i	−0.548491	+	0.836156i	$0.684798\pi$
$410$		0			0
$411$	−3.97076	−	12.2207i	−0.195863	−	0.602805i
$412$		0			0
$413$	21.4114	−	15.5563i	1.05358	−	0.765474i
$414$		0			0
$415$	17.7745	−	54.7043i	0.872516	−	2.68533i
$416$		0			0
$417$	4.41939			0.216419
$418$		0			0
$419$	26.0766			1.27393			0.636964	−	0.770894i	$-0.280190\pi$
$419$	26.0766			1.27393			0.636964	+	0.770894i	$0.280190\pi$
$420$		0			0
$421$	8.19273	−	25.2146i	0.399289	−	1.22889i	−0.526281	−	0.850311i	$-0.676414\pi$
$421$	8.19273	−	25.2146i	0.399289	−	1.22889i	0.925570	−	0.378576i	$-0.123586\pi$
$422$		0			0
$423$	1.34723	−	0.978816i	0.0655043	−	0.0475917i
$424$		0			0
$425$	15.5007	+	47.7063i	0.751895	+	2.31410i
$426$		0			0
$427$	6.65400	+	4.83441i	0.322010	+	0.233954i
$428$		0			0
$429$	3.15069	−	1.03593i	0.152117	−	0.0500151i
$430$		0			0
$431$	−7.86363	−	5.71326i	−0.378778	−	0.275198i	0.382064	−	0.924136i	$-0.375214\pi$
$431$	−7.86363	−	5.71326i	−0.378778	−	0.275198i	−0.760841	+	0.648938i	$0.775214\pi$
$432$		0			0
$433$	−3.33216	−	10.2553i	−0.160133	−	0.492839i	0.838512	−	0.544884i	$-0.183426\pi$
$433$	−3.33216	−	10.2553i	−0.160133	−	0.492839i	−0.998645	+	0.0520445i	$0.983426\pi$
$434$		0			0
$435$	−20.8878	+	15.1759i	−1.00150	+	0.727629i
$436$		0			0
$437$	−12.7543	+	39.2536i	−0.610119	+	1.87775i
$438$		0			0
$439$	4.25507			0.203084			0.101542	−	0.994831i	$-0.467622\pi$
$439$	4.25507			0.203084			0.101542	+	0.994831i	$0.467622\pi$
$440$		0			0
$441$	−2.64891			−0.126139
$442$		0			0
$443$	2.04916	−	6.30668i	0.0973587	−	0.299639i	−0.890503	−	0.454978i	$-0.849647\pi$
$443$	2.04916	−	6.30668i	0.0973587	−	0.299639i	0.987861	+	0.155339i	$0.0496470\pi$
$444$		0			0
$445$	14.0073	−	10.1769i	0.664008	−	0.482430i
$446$		0			0
$447$	1.04846	+	3.22684i	0.0495906	+	0.152624i
$448$		0			0
$449$	−7.09835	−	5.15725i	−0.334992	−	0.243386i	0.407554	−	0.913181i	$-0.366382\pi$
$449$	−7.09835	−	5.15725i	−0.334992	−	0.243386i	−0.742546	+	0.669795i	$0.766382\pi$
$450$		0			0
$451$	−7.19120	+	9.97105i	−0.338621	+	0.469519i
$452$		0			0
$453$	5.23916	+	3.80647i	0.246157	+	0.178844i
$454$		0			0
$455$	−2.26752	−	6.97871i	−0.106303	−	0.327167i
$456$		0			0
$457$	14.1525	−	10.2824i	0.662028	−	0.480992i	−0.205319	−	0.978695i	$-0.565823\pi$
$457$	14.1525	−	10.2824i	0.662028	−	0.480992i	0.867347	+	0.497703i	$0.165823\pi$
$458$		0			0
$459$	−2.10183	+	6.46878i	−0.0981052	+	0.301937i
$460$		0			0
$461$	−4.75048			−0.221252			−0.110626	−	0.993862i	$-0.535286\pi$
$461$	−4.75048			−0.221252			−0.110626	+	0.993862i	$0.535286\pi$
$462$		0			0
$463$	−36.4543			−1.69418			−0.847088	−	0.531453i	$-0.821646\pi$
$463$	−36.4543			−1.69418			−0.847088	+	0.531453i	$0.821646\pi$
$464$		0			0
$465$	−3.60779	+	11.1036i	−0.167307	+	0.514919i
$466$		0			0
$467$	6.43538	−	4.67557i	0.297794	−	0.216360i	−0.428848	−	0.903377i	$-0.641080\pi$
$467$	6.43538	−	4.67557i	0.297794	−	0.216360i	0.726641	+	0.687017i	$0.241080\pi$
$468$		0			0
$469$	4.80673	+	14.7936i	0.221954	+	0.683105i
$470$		0			0
$471$	1.25394	+	0.911039i	0.0577784	+	0.0419785i
$472$		0			0
$473$	−13.0905	−	4.20275i	−0.601901	−	0.193243i
$474$		0			0
$475$	37.7500	+	27.4270i	1.73209	+	1.25844i
$476$		0			0
$477$	−1.56176	−	4.80661i	−0.0715082	−	0.220080i
$478$		0			0
$479$	13.8040	−	10.0292i	0.630721	−	0.458246i	−0.225929	−	0.974144i	$-0.572542\pi$
$479$	13.8040	−	10.0292i	0.630721	−	0.458246i	0.856650	+	0.515898i	$0.172542\pi$
$480$		0			0
$481$	−1.96669	+	6.05285i	−0.0896733	+	0.275986i
$482$		0			0
$483$	−13.6071			−0.619146
$484$		0			0
$485$	−61.5485			−2.79477
$486$		0			0
$487$	4.24454	−	13.0633i	0.192338	−	0.591956i	−0.807659	−	0.589650i	$-0.799266\pi$
$487$	4.24454	−	13.0633i	0.192338	−	0.591956i	0.999997	−	0.00230657i	$-0.000734203\pi$
$488$		0			0
$489$	2.19401	−	1.59404i	0.0992165	−	0.0720850i
$490$		0			0
$491$	6.93094	+	21.3312i	0.312789	+	0.962666i	0.976655	+	0.214814i	$0.0689146\pi$
$491$	6.93094	+	21.3312i	0.312789	+	0.962666i	−0.663866	+	0.747852i	$0.731085\pi$
$492$		0			0
$493$	−40.3868	−	29.3427i	−1.81893	−	1.32153i
$494$		0			0
$495$	−11.1087	−	3.56650i	−0.499300	−	0.160302i
$496$		0			0
$497$	6.90616	+	5.01762i	0.309784	+	0.225071i
$498$		0			0
$499$	5.90438	+	18.1718i	0.264316	+	0.813481i	0.991850	+	0.127410i	$0.0406664\pi$
$499$	5.90438	+	18.1718i	0.264316	+	0.813481i	−0.727534	+	0.686072i	$0.759334\pi$
$500$		0			0
$501$	4.70407	−	3.41771i	0.210162	−	0.152692i
$502$		0			0
$503$	−4.00857	+	12.3371i	−0.178733	+	0.550085i	−0.999784	−	0.0207701i	$-0.993388\pi$
$503$	−4.00857	+	12.3371i	−0.178733	+	0.550085i	0.821051	+	0.570855i	$0.193388\pi$
$504$		0			0
$505$	−31.0217			−1.38045
$506$		0			0
$507$	−1.00000			−0.0444116
$508$		0			0
$509$	−12.2634	+	37.7429i	−0.543566	+	1.67292i	0.180810	+	0.983518i	$0.442128\pi$
$509$	−12.2634	+	37.7429i	−0.543566	+	1.67292i	−0.724376	+	0.689406i	$0.757872\pi$
$510$		0			0
$511$	−8.92050	+	6.48112i	−0.394620	+	0.286708i
$512$		0			0
$513$	1.95519	+	6.01744i	0.0863236	+	0.265677i
$514$		0			0
$515$	47.1297	+	34.2417i	2.07678	+	1.50887i
$516$		0			0
$517$	−3.23071	+	4.47958i	−0.142086	+	0.197012i
$518$		0			0
$519$	17.3569	+	12.6105i	0.761884	+	0.553541i
$520$		0			0
$521$	−12.4097	−	38.1930i	−0.543677	−	1.67327i	−0.724114	−	0.689680i	$-0.757751\pi$
$521$	−12.4097	−	38.1930i	−0.543677	−	1.67327i	0.180437	−	0.983587i	$-0.442249\pi$
$522$		0			0
$523$	−15.4022	+	11.1903i	−0.673491	+	0.489320i	−0.871192	−	0.490943i	$-0.836652\pi$
$523$	−15.4022	+	11.1903i	−0.673491	+	0.489320i	0.197701	+	0.980262i	$0.436652\pi$
$524$		0			0
$525$	−4.75373	+	14.6305i	−0.207470	+	0.638527i
$526$		0			0
$527$	−22.5738			−0.983331
$528$		0			0
$529$	19.5535			0.850151
$530$		0			0
$531$	−3.92076	+	12.0669i	−0.170146	+	0.523657i
$532$		0			0
$533$	2.99878	−	2.17874i	0.129891	−	0.0943717i
$534$		0			0
$535$	15.0106	+	46.1978i	0.648964	+	1.99731i
$536$		0			0
$537$	0.208807	+	0.151707i	0.00901069	+	0.00654665i
$538$		0			0
$539$	8.34590	−	2.74408i	0.359483	−	0.118196i
$540$		0			0
$541$	−14.1557	−	10.2847i	−0.608601	−	0.442175i	0.240320	−	0.970694i	$-0.422748\pi$
$541$	−14.1557	−	10.2847i	−0.608601	−	0.442175i	−0.848921	+	0.528519i	$0.822748\pi$
$542$		0			0
$543$	−6.89760	−	21.2286i	−0.296004	−	0.911007i
$544$		0			0
$545$	37.8948	−	27.5322i	1.62324	−	1.17935i
$546$		0			0
$547$	−0.845760	+	2.60298i	−0.0361621	+	0.111295i	−0.967508	−	0.252840i	$-0.918635\pi$
$547$	−0.845760	+	2.60298i	−0.0361621	+	0.111295i	0.931346	+	0.364135i	$0.118635\pi$
$548$		0			0
$549$	−3.94299			−0.168283
$550$		0			0
$551$	−46.4378			−1.97832
$552$		0			0
$553$	1.70581	−	5.24995i	0.0725385	−	0.223251i
$554$		0			0
$555$	18.1126	−	13.1596i	0.768838	−	0.558593i
$556$		0			0
$557$	1.68955	+	5.19989i	0.0715884	+	0.220326i	0.980449	−	0.196774i	$-0.0630464\pi$
$557$	1.68955	+	5.19989i	0.0715884	+	0.220326i	−0.908861	+	0.417100i	$0.863046\pi$
$558$		0			0
$559$	3.35367	+	2.43658i	0.141845	+	0.103056i
$560$		0			0
$561$	−0.0789643	−	22.5585i	−0.00333388	−	0.952419i
$562$		0			0
$563$	−28.6992	−	20.8512i	−1.20953	−	0.878774i	−0.214340	−	0.976759i	$-0.568760\pi$
$563$	−28.6992	−	20.8512i	−1.20953	−	0.878774i	−0.995188	+	0.0979855i	$0.968760\pi$
$564$		0			0
$565$	13.5377	+	41.6646i	0.569534	+	1.75284i
$566$		0			0
$567$	−1.68755	+	1.22608i	−0.0708704	+	0.0514904i
$568$		0			0
$569$	−13.3104	+	40.9654i	−0.558003	+	1.71736i	0.129875	+	0.991530i	$0.458542\pi$
$569$	−13.3104	+	40.9654i	−0.558003	+	1.71736i	−0.687878	+	0.725826i	$0.741458\pi$
$570$		0			0
$571$	9.67681			0.404962			0.202481	−	0.979286i	$-0.435100\pi$
$571$	9.67681			0.404962			0.202481	+	0.979286i	$0.435100\pi$
$572$		0			0
$573$	−23.3665			−0.976151
$574$		0			0
$575$	14.8663	−	45.7538i	0.619968	−	1.90807i
$576$		0			0
$577$	−20.5998	+	14.9666i	−0.857579	+	0.623068i	−0.927225	−	0.374504i	$-0.877813\pi$
$577$	−20.5998	+	14.9666i	−0.857579	+	0.623068i	0.0696460	+	0.997572i	$0.477813\pi$
$578$		0			0
$579$	1.71294	+	5.27190i	0.0711875	+	0.219093i
$580$		0			0
$581$	27.5932	+	20.0476i	1.14476	+	0.831715i
$582$		0			0
$583$	9.89994	+	13.5263i	0.410013	+	0.560201i
$584$		0			0
$585$	2.84595	+	2.06771i	0.117666	+	0.0854891i
$586$		0			0
$587$	11.4610	+	35.2733i	0.473045	+	1.45588i	0.848576	+	0.529074i	$0.177461\pi$
$587$	11.4610	+	35.2733i	0.473045	+	1.45588i	−0.375530	+	0.926810i	$0.622539\pi$
$588$		0			0
$589$	−16.9884	+	12.3428i	−0.699995	+	0.508576i
$590$		0			0
$591$	5.26365	−	16.1998i	0.216518	−	0.666373i
$592$		0			0
$593$	15.5203			0.637342			0.318671	−	0.947865i	$-0.396763\pi$
$593$	15.5203			0.637342			0.318671	+	0.947865i	$0.396763\pi$
$594$		0			0
$595$	−49.9097			−2.04610
$596$		0			0
$597$	−4.03203	+	12.4093i	−0.165020	+	0.507879i
$598$		0			0
$599$	20.3498	−	14.7850i	0.831469	−	0.604097i	−0.0885057	−	0.996076i	$-0.528209\pi$
$599$	20.3498	−	14.7850i	0.831469	−	0.604097i	0.919974	+	0.391978i	$0.128209\pi$
$600$		0			0
$601$	−1.31867	−	4.05844i	−0.0537895	−	0.165547i	0.920553	−	0.390618i	$-0.127739\pi$
$601$	−1.31867	−	4.05844i	−0.0537895	−	0.165547i	−0.974342	+	0.225071i	$0.927739\pi$
$602$		0			0
$603$	−6.03290	−	4.38316i	−0.245679	−	0.178496i
$604$		0			0
$605$	38.6948	−	0.270900i	1.57317	−	0.0110136i
$606$		0			0
$607$	22.5892	+	16.4120i	0.916866	+	0.666142i	0.942742	−	0.333523i	$-0.108237\pi$
$607$	22.5892	+	16.4120i	0.916866	+	0.666142i	−0.0258759	+	0.999665i	$0.508237\pi$
$608$		0			0
$609$	−4.73094	−	14.5603i	−0.191707	−	0.590015i
$610$		0			0
$611$	1.34723	−	0.978816i	0.0545029	−	0.0395987i
$612$		0			0
$613$	−3.25450	+	10.0163i	−0.131448	+	0.404555i	−0.995021	−	0.0996692i	$-0.968222\pi$
$613$	−3.25450	+	10.0163i	−0.131448	+	0.404555i	0.863573	+	0.504224i	$0.168222\pi$
$614$		0			0
$615$	−13.0394			−0.525798
$616$		0			0
$617$	−23.1493			−0.931957			−0.465978	−	0.884796i	$-0.654298\pi$
$617$	−23.1493			−0.931957			−0.465978	+	0.884796i	$0.654298\pi$
$618$		0			0
$619$	−1.01271	+	3.11679i	−0.0407042	+	0.125275i	−0.969344	−	0.245709i	$-0.920979\pi$
$619$	−1.01271	+	3.11679i	−0.0407042	+	0.125275i	0.928640	+	0.370983i	$0.120979\pi$
$620$		0			0
$621$	5.27746	−	3.83430i	0.211777	−	0.153865i
$622$		0			0
$623$	3.17254	+	9.76407i	0.127105	+	0.391189i
$624$		0			0
$625$	6.05613	+	4.40003i	0.242245	+	0.176001i
$626$		0			0
$627$	−12.3938	−	16.9337i	−0.494962	−	0.676266i
$628$		0			0
$629$	35.0209	+	25.4442i	1.39637	+	1.01452i
$630$		0			0
$631$	−15.2747	−	47.0106i	−0.608075	−	1.87146i	−0.474083	−	0.880480i	$-0.657220\pi$
$631$	−15.2747	−	47.0106i	−0.608075	−	1.87146i	−0.133992	−	0.990982i	$-0.542780\pi$
$632$		0			0
$633$	−10.2383	+	7.43853i	−0.406934	+	0.295655i
$634$		0			0
$635$	17.4986	−	53.8551i	0.694410	−	2.13717i
$636$		0			0
$637$	−2.64891			−0.104954
$638$		0			0
$639$	−4.09242			−0.161894
$640$		0			0
$641$	0.743297	−	2.28763i	0.0293585	−	0.0903561i	−0.935304	−	0.353846i	$-0.884874\pi$
$641$	0.743297	−	2.28763i	0.0293585	−	0.0903561i	0.964662	+	0.263490i	$0.0848736\pi$
$642$		0			0
$643$	11.3458	−	8.24318i	0.447433	−	0.325079i	−0.341148	−	0.940010i	$-0.610816\pi$
$643$	11.3458	−	8.24318i	0.447433	−	0.325079i	0.788582	+	0.614930i	$0.210816\pi$
$644$		0			0
$645$	−4.50624	−	13.8688i	−0.177433	−	0.546083i
$646$		0			0
$647$	−8.50867	−	6.18191i	−0.334510	−	0.243036i	0.407832	−	0.913057i	$-0.366285\pi$
$647$	−8.50867	−	6.18191i	−0.334510	−	0.243036i	−0.742342	+	0.670021i	$0.766285\pi$
$648$		0			0
$649$	−0.147300	−	42.0806i	−0.00578203	−	1.65181i
$650$		0			0
$651$	−5.60075	−	4.06918i	−0.219511	−	0.159484i
$652$		0			0
$653$	6.19805	+	19.0756i	0.242548	+	0.746487i	0.996030	+	0.0890179i	$0.0283728\pi$
$653$	6.19805	+	19.0756i	0.242548	+	0.746487i	−0.753482	+	0.657469i	$0.771627\pi$
$654$		0			0
$655$	−56.0735	+	40.7398i	−2.19097	+	1.59184i
$656$		0			0
$657$	1.63348	−	5.02734i	0.0637283	−	0.196135i
$658$		0			0
$659$	13.5068			0.526149			0.263074	−	0.964776i	$-0.415264\pi$
$659$	13.5068			0.526149			0.263074	+	0.964776i	$0.415264\pi$
$660$		0			0
$661$	5.28662			0.205626			0.102813	−	0.994701i	$-0.467216\pi$
$661$	5.28662			0.205626			0.102813	+	0.994701i	$0.467216\pi$
$662$		0			0
$663$	−2.10183	+	6.46878i	−0.0816284	+	0.251227i
$664$		0			0
$665$	−37.5606	+	27.2894i	−1.45654	+	1.05824i
$666$		0			0
$667$	14.7950	+	45.5344i	0.572866	+	1.76310i
$668$		0			0
$669$	2.56767	+	1.86552i	0.0992717	+	0.0721251i
$670$		0			0
$671$	12.4232	−	4.08466i	0.479591	−	0.157687i
$672$		0			0
$673$	−33.3837	−	24.2547i	−1.28685	−	0.934949i	−0.287111	−	0.957897i	$-0.592695\pi$
$673$	−33.3837	−	24.2547i	−1.28685	−	0.934949i	−0.999737	+	0.0229482i	$0.992695\pi$
$674$		0			0
$675$	−2.27896	−	7.01390i	−0.0877170	−	0.269965i
$676$		0			0
$677$	16.7510	−	12.1703i	0.643793	−	0.467743i	−0.217358	−	0.976092i	$-0.569744\pi$
$677$	16.7510	−	12.1703i	0.643793	−	0.467743i	0.861151	+	0.508349i	$0.169744\pi$
$678$		0			0
$679$	11.2779	−	34.7098i	0.432806	−	1.33204i
$680$		0			0
$681$	12.6974			0.486566
$682$		0			0
$683$	18.0953			0.692397			0.346199	−	0.938161i	$-0.387472\pi$
$683$	18.0953			0.692397			0.346199	+	0.938161i	$0.387472\pi$
$684$		0			0
$685$	−13.9683	+	42.9900i	−0.533701	+	1.64256i
$686$		0			0
$687$	−2.68013	+	1.94723i	−0.102253	+	0.0742913i
$688$		0			0
$689$	−1.56176	−	4.80661i	−0.0594984	−	0.183117i
$690$		0			0
$691$	26.3122	+	19.1169i	1.00096	+	0.727242i	0.962294	−	0.272010i	$-0.0876885\pi$
$691$	26.3122	+	19.1169i	1.00096	+	0.727242i	0.0386682	+	0.999252i	$0.487688\pi$
$692$		0			0
$693$	4.04682	−	5.61117i	0.153726	−	0.213151i
$694$		0			0
$695$	−12.5774	−	9.13801i	−0.477088	−	0.346624i
$696$		0			0
$697$	−7.79085	−	23.9778i	−0.295100	−	0.908223i
$698$		0			0
$699$	9.53208	−	6.92546i	0.360536	−	0.261945i
$700$		0			0
$701$	13.2865	−	40.8917i	0.501825	−	1.54446i	−0.304219	−	0.952602i	$-0.598395\pi$
$701$	13.2865	−	40.8917i	0.501825	−	1.54446i	0.806044	−	0.591856i	$-0.201605\pi$
$702$		0			0
$703$	40.2679			1.51873
$704$		0			0
$705$	−5.85804			−0.220627
$706$		0			0
$707$	5.68430	−	17.4945i	0.213780	−	0.657948i
$708$		0			0
$709$	−12.5908	+	9.14775i	−0.472857	+	0.343551i	−0.798554	−	0.601923i	$-0.794401\pi$
$709$	−12.5908	+	9.14775i	−0.472857	+	0.343551i	0.325696	+	0.945474i	$0.394401\pi$
$710$		0			0
$711$	0.817772	+	2.51684i	0.0306688	+	0.0943890i
$712$		0			0
$713$	17.5152	+	12.7255i	0.655948	+	0.476574i
$714$		0			0
$715$	−11.1087	−	3.56650i	−0.415442	−	0.133379i
$716$		0			0
$717$	−1.97912	−	1.43791i	−0.0739116	−	0.0536999i
$718$		0			0
$719$	0.739446	+	2.27578i	0.0275767	+	0.0848723i	0.963898	−	0.266273i	$-0.0857923\pi$
$719$	0.739446	+	2.27578i	0.0275767	+	0.0848723i	−0.936321	+	0.351145i	$0.885792\pi$
$720$		0			0
$721$	−27.9462	+	20.3041i	−1.04077	+	0.756165i
$722$		0			0
$723$	−0.674710	+	2.07654i	−0.0250927	+	0.0772275i
$724$		0			0
$725$	54.1277			2.01025
$726$		0			0
$727$	5.88291			0.218185			0.109092	−	0.994032i	$-0.465206\pi$
$727$	5.88291			0.218185			0.109092	+	0.994032i	$0.465206\pi$
$728$		0			0
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$		0			0
$731$	22.8105	−	16.5728i	0.843678	−	0.612968i
$732$		0			0
$733$	2.76643	+	8.51419i	0.102180	+	0.314479i	0.989058	−	0.147525i	$-0.0471307\pi$
$733$	2.76643	+	8.51419i	0.102180	+	0.314479i	−0.886878	+	0.462004i	$0.847131\pi$
$734$		0			0
$735$	7.53867	+	5.47717i	0.278068	+	0.202028i
$736$		0			0
$737$	23.5484	+	7.56033i	0.867418	+	0.278488i
$738$		0			0
$739$	29.5755	+	21.4878i	1.08795	+	0.790442i	0.979052	−	0.203610i	$-0.0652676\pi$
$739$	29.5755	+	21.4878i	1.08795	+	0.790442i	0.108899	+	0.994053i	$0.465268\pi$
$740$		0			0
$741$	1.95519	+	6.01744i	0.0718256	+	0.221056i
$742$		0			0
$743$	38.2744	−	27.8079i	1.40415	−	1.02017i	0.410009	−	0.912081i	$-0.365525\pi$
$743$	38.2744	−	27.8079i	1.40415	−	1.02017i	0.994141	−	0.108093i	$-0.0344745\pi$
$744$		0			0
$745$	3.68827	−	11.3513i	0.135128	−	0.415881i
$746$		0			0
$747$	−16.3510			−0.598253
$748$		0			0
$749$	−28.8034			−1.05245
$750$		0			0
$751$	3.87460	−	11.9248i	0.141386	−	0.435142i	−0.855142	−	0.518393i	$-0.826530\pi$
$751$	3.87460	−	11.9248i	0.141386	−	0.435142i	0.996529	+	0.0832512i	$0.0265304\pi$
$752$		0			0
$753$	7.51733	−	5.46166i	0.273947	−	0.199034i
$754$		0			0
$755$	−7.03974	−	21.6661i	−0.256202	−	0.788510i
$756$		0			0
$757$	−34.6252	−	25.1567i	−1.25848	−	0.914336i	−0.259794	−	0.965664i	$-0.583655\pi$
$757$	−34.6252	−	25.1567i	−1.25848	−	0.914336i	−0.998682	+	0.0513283i	$0.983655\pi$
$758$		0			0
$759$	−12.6556	+	17.5478i	−0.459369	+	0.636944i
$760$		0			0
$761$	20.5321	+	14.9174i	0.744286	+	0.540756i	0.894051	−	0.447966i	$-0.147851\pi$
$761$	20.5321	+	14.9174i	0.744286	+	0.540756i	−0.149764	+	0.988722i	$0.547851\pi$
$762$		0			0
$763$	8.58289	+	26.4154i	0.310722	+	0.956303i
$764$		0			0
$765$	19.3572	−	14.0639i	0.699863	−	0.508480i
$766$		0			0
$767$	−3.92076	+	12.0669i	−0.141570	+	0.435709i
$768$		0			0
$769$	−37.9148			−1.36724			−0.683620	−	0.729838i	$-0.739596\pi$
$769$	−37.9148			−1.36724			−0.683620	+	0.729838i	$0.739596\pi$
$770$		0			0
$771$	30.4452			1.09646
$772$		0			0
$773$	−8.48550	+	26.1157i	−0.305202	+	0.939316i	0.674399	+	0.738367i	$0.264403\pi$
$773$	−8.48550	+	26.1157i	−0.305202	+	0.939316i	−0.979602	+	0.200949i	$0.935597\pi$
$774$		0			0
$775$	19.8016	−	14.3867i	0.711295	−	0.516786i
$776$		0			0
$777$	4.10237	+	12.6258i	0.147172	+	0.452948i
$778$		0			0
$779$	−18.9736	−	13.7851i	−0.679800	−	0.493904i
$780$		0			0
$781$	12.8939	−	4.23945i	0.461381	−	0.151699i
$782$		0			0
$783$	5.93777	+	4.31405i	0.212199	+	0.154171i
$784$		0			0
$785$	−1.68489	−	5.18555i	−0.0601362	−	0.185080i
$786$		0			0
$787$	13.0936	−	9.51307i	0.466737	−	0.339104i	−0.329431	−	0.944180i	$-0.606857\pi$
$787$	13.0936	−	9.51307i	0.466737	−	0.339104i	0.796168	+	0.605075i	$0.206857\pi$
$788$		0			0
$789$	1.50908	−	4.64448i	0.0537248	−	0.165348i
$790$		0			0
$791$	−25.9771			−0.923639
$792$		0			0
$793$	−3.94299			−0.140020
$794$		0			0
$795$	−5.49396	+	16.9087i	−0.194851	+	0.599688i
$796$		0			0
$797$	23.1488	−	16.8186i	0.819974	−	0.595746i	−0.0967310	−	0.995311i	$-0.530839\pi$
$797$	23.1488	−	16.8186i	0.819974	−	0.595746i	0.916705	+	0.399564i	$0.130839\pi$
$798$		0			0
$799$	−3.50010	−	10.7722i	−0.123825	−	0.381093i
$800$		0			0
$801$	−3.98184	−	2.89297i	−0.140691	−	0.102218i
$802$		0			0
$803$	0.0613688	+	17.5318i	0.00216566	+	0.618683i
$804$		0			0
$805$	38.7252	+	28.1355i	1.36489	+	0.991647i
$806$		0			0
$807$	7.77879	+	23.9407i	0.273826	+	0.842751i
$808$		0			0
$809$	−0.156885	+	0.113984i	−0.00551579	+	0.00400745i	−0.590540	−	0.807009i	$-0.701085\pi$
$809$	−0.156885	+	0.113984i	−0.00551579	+	0.00400745i	0.585024	+	0.811016i	$0.301085\pi$
$810$		0			0
$811$	16.6992	−	51.3949i	0.586389	−	1.80472i	−0.00722970	−	0.999974i	$-0.502301\pi$
$811$	16.6992	−	51.3949i	0.586389	−	1.80472i	0.593619	−	0.804746i	$-0.297699\pi$
$812$		0			0
$813$	10.9025			0.382366
$814$		0			0
$815$	−9.54005			−0.334173
$816$		0			0
$817$	8.10495	−	24.9445i	0.283556	−	0.872696i
$818$		0			0
$819$	−1.68755	+	1.22608i	−0.0589678	+	0.0428426i
$820$		0			0
$821$	9.74297	+	29.9858i	0.340032	+	1.04651i	0.964190	+	0.265212i	$0.0854421\pi$
$821$	9.74297	+	29.9858i	0.340032	+	1.04651i	−0.624158	+	0.781298i	$0.714558\pi$
$822$		0			0
$823$	19.5667	+	14.2161i	0.682054	+	0.495541i	0.874038	−	0.485857i	$-0.161492\pi$
$823$	19.5667	+	14.2161i	0.682054	+	0.495541i	−0.191985	+	0.981398i	$0.561492\pi$
$824$		0			0
$825$	14.4462	+	19.7378i	0.502952	+	0.687182i
$826$		0			0
$827$	31.0542	+	22.5622i	1.07986	+	0.784564i	0.977659	−	0.210199i	$-0.0674113\pi$
$827$	31.0542	+	22.5622i	1.07986	+	0.784564i	0.102202	+	0.994764i	$0.467411\pi$
$828$		0			0
$829$	7.78773	+	23.9682i	0.270479	+	0.832449i	0.990380	+	0.138372i	$0.0441870\pi$
$829$	7.78773	+	23.9682i	0.270479	+	0.832449i	−0.719901	+	0.694076i	$0.755813\pi$
$830$		0			0
$831$	12.7939	−	9.29529i	0.443814	−	0.322450i
$832$		0			0
$833$	−5.56757	+	17.1352i	−0.192905	+	0.593700i
$834$		0			0
$835$	−20.4544			−0.707853
$836$		0			0
$837$	3.31886			0.114717
$838$		0			0
$839$	−0.291068	+	0.895816i	−0.0100488	+	0.0309270i	−0.955955	−	0.293513i	$-0.905176\pi$
$839$	−0.291068	+	0.895816i	−0.0100488	+	0.0309270i	0.945906	+	0.324440i	$0.105176\pi$
$840$		0			0
$841$	−20.1187	+	14.6171i	−0.693750	+	0.504039i
$842$		0			0
$843$	2.02580	+	6.23478i	0.0697723	+	0.214737i
$844$		0			0
$845$	2.84595	+	2.06771i	0.0979038	+	0.0711312i
$846$		0			0
$847$	−6.93751	+	21.8713i	−0.238376	+	0.751506i
$848$		0			0
$849$	23.4376	+	17.0284i	0.804375	+	0.584413i
$850$		0			0
$851$	−12.8293	−	39.4846i	−0.439783	−	1.35351i
$852$		0			0
$853$	25.1885	−	18.3005i	0.862437	−	0.626597i	−0.0661097	−	0.997812i	$-0.521059\pi$
$853$	25.1885	−	18.3005i	0.862437	−	0.626597i	0.928547	+	0.371215i	$0.121059\pi$
$854$		0			0
$855$	6.87794	−	21.1681i	0.235220	−	0.723934i
$856$		0			0
$857$	−22.1265			−0.755825			−0.377913	−	0.925841i	$-0.623358\pi$
$857$	−22.1265			−0.755825			−0.377913	+	0.925841i	$0.623358\pi$
$858$		0			0
$859$	11.2069			0.382373			0.191186	−	0.981554i	$-0.438767\pi$
$859$	11.2069			0.382373			0.191186	+	0.981554i	$0.438767\pi$
$860$		0			0
$861$	2.38929	−	7.35346i	0.0814266	−	0.250605i
$862$		0			0
$863$	−22.5630	+	16.3930i	−0.768055	+	0.558025i	−0.901370	−	0.433049i	$-0.857438\pi$
$863$	−22.5630	+	16.3930i	−0.768055	+	0.558025i	0.133315	+	0.991074i	$0.457438\pi$
$864$		0			0
$865$	−23.3221	−	71.7780i	−0.792974	−	2.44052i
$866$		0			0
$867$	23.6741	+	17.2002i	0.804014	+	0.584151i
$868$		0			0
$869$	−5.18382	−	7.08264i	−0.175849	−	0.240262i
$870$		0			0
$871$	−6.03290	−	4.38316i	−0.204417	−	0.148518i
$872$		0			0
$873$	5.40666	+	16.6400i	0.182988	+	0.563179i
$874$		0			0
$875$	14.0982	−	10.2429i	0.476606	−	0.346275i
$876$		0			0
$877$	−3.55931	+	10.9544i	−0.120189	+	0.369904i	−0.992994	−	0.118165i	$-0.962299\pi$
$877$	−3.55931	+	10.9544i	−0.120189	+	0.369904i	0.872805	+	0.488070i	$0.162299\pi$
$878$		0			0
$879$	17.6494			0.595298
$880$		0			0
$881$	−22.1357			−0.745771			−0.372886	−	0.927877i	$-0.621632\pi$
$881$	−22.1357			−0.745771			−0.372886	+	0.927877i	$0.621632\pi$
$882$		0			0
$883$	−6.98279	+	21.4908i	−0.234990	+	0.723224i	0.762133	+	0.647420i	$0.224152\pi$
$883$	−6.98279	+	21.4908i	−0.234990	+	0.723224i	−0.997123	+	0.0758035i	$0.975848\pi$
$884$		0			0
$885$	36.1090	−	26.2347i	1.21379	−	0.881871i
$886$		0			0
$887$	−6.15764	−	18.9513i	−0.206753	−	0.636321i	−0.999637	−	0.0269481i	$-0.991421\pi$
$887$	−6.15764	−	18.9513i	−0.206753	−	0.636321i	0.792884	−	0.609373i	$-0.208579\pi$
$888$		0			0
$889$	27.1648	+	19.7364i	0.911079	+	0.661938i
$890$		0			0
$891$	0.0116095	+	3.31660i	0.000388934	+	0.111110i
$892$		0			0
$893$	−8.52405	−	6.19308i	−0.285246	−	0.207244i
$894$		0			0
$895$	−0.280569	−	0.863503i	−0.00937839	−	0.0288637i
$896$		0			0
$897$	5.27746	−	3.83430i	0.176209	−	0.128024i
$898$		0			0
$899$	−7.52727	+	23.1666i	−0.251049	+	0.772648i
$900$		0			0
$901$	−34.3755			−1.14521
$902$		0			0
$903$	8.64691			0.287751
$904$		0			0
$905$	−24.2643	+	74.6779i	−0.806573	+	2.48238i
$906$		0			0
$907$	−11.4781	+	8.33930i	−0.381123	+	0.276902i	−0.761808	−	0.647803i	$-0.775688\pi$
$907$	−11.4781	+	8.33930i	−0.381123	+	0.276902i	0.380685	+	0.924705i	$0.375688\pi$
$908$		0			0
$909$	2.72507	+	8.38691i	0.0903849	+	0.278176i
$910$		0			0
$911$	0.632492	+	0.459532i	0.0209554	+	0.0152250i	0.598214	−	0.801337i	$-0.295877\pi$
$911$	0.632492	+	0.459532i	0.0209554	+	0.0152250i	−0.577258	+	0.816562i	$0.695877\pi$
$912$		0			0
$913$	51.5170	−	16.9385i	1.70496	−	0.560582i
$914$		0			0
$915$	11.2216	+	8.15295i	0.370974	+	0.269528i
$916$		0			0
$917$	−12.7002	−	39.0873i	−0.419398	−	1.29078i
$918$		0			0
$919$	−33.7173	+	24.4970i	−1.11223	+	0.808083i	−0.983013	−	0.183533i	$-0.941246\pi$
$919$	−33.7173	+	24.4970i	−1.11223	+	0.808083i	−0.129217	+	0.991616i	$0.541246\pi$
$920$		0			0
$921$	1.99214	−	6.13117i	0.0656431	−	0.202029i
$922$		0			0
$923$	−4.09242			−0.134704
$924$		0			0
$925$	−46.9361			−1.54325
$926$		0			0
$927$	5.11739	−	15.7497i	0.168077	−	0.517289i
$928$		0			0
$929$	39.9912	−	29.0553i	1.31207	−	0.953273i	0.312073	−	0.950058i	$-0.398976\pi$
$929$	39.9912	−	29.0553i	1.31207	−	0.953273i	0.999995	−	0.00321542i	$-0.00102350\pi$
$930$		0			0
$931$	5.17911	+	15.9397i	0.169739	+	0.522402i
$932$		0			0
$933$	−23.2568	−	16.8971i	−0.761393	−	0.553185i
$934$		0			0
$935$	−46.4195	+	64.3636i	−1.51808	+	2.10492i
$936$		0			0
$937$	31.7963	+	23.1013i	1.03874	+	0.754688i	0.970039	−	0.242950i	$-0.0781149\pi$
$937$	31.7963	+	23.1013i	1.03874	+	0.754688i	0.0686998	+	0.997637i	$0.478115\pi$
$938$		0			0
$939$	4.29717	+	13.2253i	0.140233	+	0.431592i
$940$		0			0
$941$	−24.4869	+	17.7908i	−0.798251	+	0.579963i	−0.910400	−	0.413728i	$-0.864226\pi$
$941$	−24.4869	+	17.7908i	−0.798251	+	0.579963i	0.112150	+	0.993691i	$0.464226\pi$
$942$		0			0
$943$	−7.47199	+	22.9964i	−0.243322	+	0.748867i
$944$		0			0
$945$	7.33785			0.238700
$946$		0			0
$947$	−6.50003			−0.211222			−0.105611	−	0.994407i	$-0.533680\pi$
$947$	−6.50003			−0.211222			−0.105611	+	0.994407i	$0.533680\pi$
$948$		0			0
$949$	1.63348	−	5.02734i	0.0530251	−	0.163195i
$950$		0			0
$951$	−19.5135	+	14.1774i	−0.632768	+	0.459733i
$952$		0			0
$953$	−4.21135	−	12.9612i	−0.136419	−	0.419854i	0.859389	−	0.511322i	$-0.170844\pi$
$953$	−4.21135	−	12.9612i	−0.136419	−	0.419854i	−0.995808	+	0.0914680i	$0.970844\pi$
$954$		0			0
$955$	66.5001	+	48.3151i	2.15189	+	1.56344i
$956$		0			0
$957$	−23.1771	−	7.44111i	−0.749210	−	0.240537i
$958$		0			0
$959$	−21.6844	−	15.7547i	−0.700226	−	0.508744i
$960$		0			0
$961$	−6.17575	−	19.0070i	−0.199218	−	0.613129i
$962$		0			0
$963$	11.1713	−	8.11640i	0.359989	−	0.261547i
$964$		0			0
$965$	6.02578	−	18.5454i	0.193977	−	0.596999i
$966$		0			0
$967$	−48.4879			−1.55927			−0.779633	−	0.626237i	$-0.784594\pi$
$967$	−48.4879			−1.55927			−0.779633	+	0.626237i	$0.784594\pi$
$968$		0			0
$969$	43.0350			1.38248
$970$		0			0
$971$	−15.8048	+	48.6423i	−0.507202	+	1.56101i	0.289836	+	0.957076i	$0.406399\pi$
$971$	−15.8048	+	48.6423i	−0.507202	+	1.56101i	−0.797037	+	0.603930i	$0.793601\pi$
$972$		0			0
$973$	7.45795	−	5.41852i	0.239091	−	0.173710i
$974$		0			0
$975$	−2.27896	−	7.01390i	−0.0729850	−	0.224625i
$976$		0			0
$977$	−47.4798	−	34.4961i	−1.51901	−	1.10363i	−0.961973	−	0.273143i	$-0.911937\pi$
$977$	−47.4798	−	34.4961i	−1.51901	−	1.10363i	−0.557041	−	0.830485i	$-0.688063\pi$
$978$		0			0
$979$	15.5424	+	4.98997i	0.496739	+	0.159480i
$980$		0			0
$981$	−10.7723	−	7.82656i	−0.343934	−	0.249883i
$982$		0			0
$983$	−6.17819	−	19.0145i	−0.197054	−	0.606469i	−0.999946	−	0.0103454i	$-0.996707\pi$
$983$	−6.17819	−	19.0145i	−0.197054	−	0.606469i	0.802893	−	0.596123i	$-0.203293\pi$
$984$		0			0
$985$	−48.4766	+	35.2203i	−1.54459	+	1.12221i
$986$		0			0
$987$	1.07341	−	3.30360i	0.0341669	−	0.105155i
$988$		0			0
$989$	−27.0414			−0.859867
$990$		0			0
$991$	−23.2371			−0.738152			−0.369076	−	0.929399i	$-0.620326\pi$
$991$	−23.2371			−0.738152			−0.369076	+	0.929399i	$0.620326\pi$
$992$		0			0
$993$	−5.23463	+	16.1105i	−0.166116	+	0.511252i
$994$		0			0
$995$	37.1338	−	26.9793i	1.17722	−	0.855300i
$996$		0			0
$997$	2.75868	+	8.49035i	0.0873683	+	0.268892i	0.985190	−	0.171468i	$-0.0548509\pi$
$997$	2.75868	+	8.49035i	0.0873683	+	0.268892i	−0.897821	+	0.440360i	$0.854851\pi$
$998$		0			0
$999$	−5.14886	−	3.74087i	−0.162903	−	0.118356i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1716.2.z.f.1093.4	yes	20
11.3	even	5	inner	1716.2.z.f.157.4	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1716.2.z.f.157.4	✓	20	11.3	even	5	inner
1716.2.z.f.1093.4	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1716 = 2^{2} \cdot 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1716.z (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{3} +(2.84595 - 2.06771i) q^{5} +(0.644587 + 1.98383i) q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{3} +(2.84595 - 2.06771i) q^{5} +(0.644587 + 1.98383i) q^{7} +(-0.809017 - 0.587785i) q^{9} +(3.15787 + 1.01385i) q^{11} +(-0.809017 - 0.587785i) q^{13} +(1.08706 + 3.34562i) q^{15} +(-5.50267 + 3.99792i) q^{17} +(-1.95519 + 6.01744i) q^{19} -2.08593 q^{21} +6.52330 q^{23} +(2.27896 - 7.01390i) q^{25} +(0.809017 - 0.587785i) q^{27} +(2.26803 + 6.98027i) q^{29} +(2.68502 + 1.95078i) q^{31} +(-1.94006 + 2.69001i) q^{33} +(5.93645 + 4.31308i) q^{35} +(-1.96669 - 6.05285i) q^{37} +(0.809017 - 0.587785i) q^{39} +(-1.14543 + 3.52527i) q^{41} -4.14536 q^{43} -3.51779 q^{45} +(-0.514594 + 1.58376i) q^{47} +(2.14301 - 1.55699i) q^{49} +(-2.10183 - 6.46878i) q^{51} +(4.08875 + 2.97065i) q^{53} +(11.0835 - 3.64418i) q^{55} +(-5.11874 - 3.71899i) q^{57} +(-3.92076 - 12.0669i) q^{59} +(3.18995 - 2.31763i) q^{61} +(0.644587 - 1.98383i) q^{63} -3.51779 q^{65} +7.45708 q^{67} +(-2.01581 + 6.20403i) q^{69} +(3.31083 - 2.40546i) q^{71} +(1.63348 + 5.02734i) q^{73} +(5.96638 + 4.33483i) q^{75} +(0.0242166 + 6.91819i) q^{77} +(-2.14095 - 1.55549i) q^{79} +(0.309017 + 0.951057i) q^{81} +(13.2283 - 9.61089i) q^{83} +(-7.39381 + 22.7558i) q^{85} -7.33949 q^{87} +4.92182 q^{89} +(0.644587 - 1.98383i) q^{91} +(-2.68502 + 1.95078i) q^{93} +(6.87794 + 21.1681i) q^{95} +(-14.1548 - 10.2841i) q^{97} +(-1.95884 - 2.67637i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 5 q^{3} + 4 q^{5} - q^{7} - 5 q^{9}+O(q^{10}) \) 20 * q + 5 * q^3 + 4 * q^5 - q^7 - 5 * q^9	\( 20 q + 5 q^{3} + 4 q^{5} - q^{7} - 5 q^{9} - 24 q^{11} - 5 q^{13} - 4 q^{15} - 6 q^{17} - 16 q^{19} + 6 q^{21} - 34 q^{23} + 13 q^{25} + 5 q^{27} + 4 q^{29} - 12 q^{31} - 11 q^{33} - 20 q^{37} + 5 q^{39} + 24 q^{41} - 32 q^{43} - 16 q^{45} - 6 q^{47} + 6 q^{49} - 9 q^{51} + 3 q^{53} - 20 q^{55} - 14 q^{57} - 61 q^{59} + 18 q^{61} - q^{63} - 16 q^{65} - 32 q^{67} - 6 q^{69} + 16 q^{71} + 17 q^{73} + 37 q^{75} + 22 q^{77} - 41 q^{79} - 5 q^{81} + 58 q^{83} + 42 q^{85} - 4 q^{87} - 6 q^{89} - q^{91} + 12 q^{93} + 55 q^{95} - 62 q^{97} + 6 q^{99}+O(q^{100}) \) 20 * q + 5 * q^3 + 4 * q^5 - q^7 - 5 * q^9 - 24 * q^11 - 5 * q^13 - 4 * q^15 - 6 * q^17 - 16 * q^19 + 6 * q^21 - 34 * q^23 + 13 * q^25 + 5 * q^27 + 4 * q^29 - 12 * q^31 - 11 * q^33 - 20 * q^37 + 5 * q^39 + 24 * q^41 - 32 * q^43 - 16 * q^45 - 6 * q^47 + 6 * q^49 - 9 * q^51 + 3 * q^53 - 20 * q^55 - 14 * q^57 - 61 * q^59 + 18 * q^61 - q^63 - 16 * q^65 - 32 * q^67 - 6 * q^69 + 16 * q^71 + 17 * q^73 + 37 * q^75 + 22 * q^77 - 41 * q^79 - 5 * q^81 + 58 * q^83 + 42 * q^85 - 4 * q^87 - 6 * q^89 - q^91 + 12 * q^93 + 55 * q^95 - 62 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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