LMFDB - Embedded newform 1000.2.f.e.749.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1000,2,Mod(749,1000)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1000, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("1000.749");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.f (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			749.14
Character	$\chi$	$=$	1000.749
Dual form			1000.2.f.e.749.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.865034 + 1.11880i) q^{2} -0.323264 q^{3} +(-0.503434 - 1.93560i) q^{4} +(0.279634 - 0.361668i) q^{6} -4.71845i q^{7} +(2.60104 + 1.11112i) q^{8} -2.89550 q^{9} +O(q^{10})$	\(q+(-0.865034 + 1.11880i) q^{2} -0.323264 q^{3} +(-0.503434 - 1.93560i) q^{4} +(0.279634 - 0.361668i) q^{6} -4.71845i q^{7} +(2.60104 + 1.11112i) q^{8} -2.89550 q^{9} +2.86225i q^{11} +(0.162742 + 0.625711i) q^{12} +3.62139 q^{13} +(5.27901 + 4.08162i) q^{14} +(-3.49311 + 1.94889i) q^{16} -3.76612i q^{17} +(2.50471 - 3.23949i) q^{18} +4.25662i q^{19} +1.52531i q^{21} +(-3.20229 - 2.47594i) q^{22} -0.157690i q^{23} +(-0.840823 - 0.359185i) q^{24} +(-3.13263 + 4.05162i) q^{26} +1.90580 q^{27} +(-9.13304 + 2.37543i) q^{28} -8.42137i q^{29} -6.04113 q^{31} +(0.841231 - 5.59395i) q^{32} -0.925263i q^{33} +(4.21354 + 3.25782i) q^{34} +(1.45769 + 5.60454i) q^{36} -8.66483 q^{37} +(-4.76231 - 3.68212i) q^{38} -1.17067 q^{39} -5.07418 q^{41} +(-1.70651 - 1.31944i) q^{42} -5.63606 q^{43} +(5.54018 - 1.44095i) q^{44} +(0.176424 + 0.136407i) q^{46} +0.287245i q^{47} +(1.12920 - 0.630008i) q^{48} -15.2638 q^{49} +1.21745i q^{51} +(-1.82313 - 7.00958i) q^{52} +3.84392 q^{53} +(-1.64858 + 2.13222i) q^{54} +(5.24275 - 12.2729i) q^{56} -1.37601i q^{57} +(9.42184 + 7.28476i) q^{58} -4.25007i q^{59} +0.316291i q^{61} +(5.22578 - 6.75883i) q^{62} +13.6623i q^{63} +(5.53083 + 5.78013i) q^{64} +(1.03519 + 0.800384i) q^{66} -10.7686 q^{67} +(-7.28970 + 1.89599i) q^{68} +0.0509756i q^{69} +10.2316 q^{71} +(-7.53132 - 3.21724i) q^{72} -11.6170i q^{73} +(7.49537 - 9.69422i) q^{74} +(8.23912 - 2.14293i) q^{76} +13.5054 q^{77} +(1.01267 - 1.30974i) q^{78} -15.9022 q^{79} +8.07042 q^{81} +(4.38934 - 5.67701i) q^{82} -11.7661 q^{83} +(2.95238 - 0.767890i) q^{84} +(4.87538 - 6.30563i) q^{86} +2.72233i q^{87} +(-3.18030 + 7.44483i) q^{88} +4.33875 q^{89} -17.0874i q^{91} +(-0.305225 + 0.0793865i) q^{92} +1.95288 q^{93} +(-0.321370 - 0.248477i) q^{94} +(-0.271940 + 1.80833i) q^{96} +1.48092i q^{97} +(13.2037 - 17.0771i) q^{98} -8.28765i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{4} - 4 q^{6} + 48 q^{9}+O(q^{10}) $ 48 * q + 4 * q^4 - 4 * q^6 + 48 * q^9	$ 48 q + 4 q^{4} - 4 q^{6} + 48 q^{9} + 12 q^{14} + 16 q^{16} + 20 q^{24} - 12 q^{26} - 16 q^{31} + 40 q^{36} + 12 q^{44} - 12 q^{46} - 48 q^{49} - 68 q^{54} + 8 q^{56} + 28 q^{64} - 88 q^{66} - 48 q^{71} - 20 q^{74} + 24 q^{76} - 16 q^{79} + 72 q^{81} - 28 q^{84} - 96 q^{86} + 24 q^{89} - 32 q^{94} - 40 q^{96}+O(q^{100}) $ 48 * q + 4 * q^4 - 4 * q^6 + 48 * q^9 + 12 * q^14 + 16 * q^16 + 20 * q^24 - 12 * q^26 - 16 * q^31 + 40 * q^36 + 12 * q^44 - 12 * q^46 - 48 * q^49 - 68 * q^54 + 8 * q^56 + 28 * q^64 - 88 * q^66 - 48 * q^71 - 20 * q^74 + 24 * q^76 - 16 * q^79 + 72 * q^81 - 28 * q^84 - 96 * q^86 + 24 * q^89 - 32 * q^94 - 40 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−0.865034	+	1.11880i	−0.611671	+	0.791112i
$2$	−0.865034	+	1.11880i	−0.611671	+	0.791112i
$3$	−0.323264			−0.186637			−0.0933183	−	0.995636i	$-0.529747\pi$
$3$	−0.323264			−0.186637			−0.0933183	+	0.995636i	$0.529747\pi$
$4$	−0.503434	−	1.93560i	−0.251717	−	0.967801i
$5$		0			0
$5$		0			0
$6$	0.279634	−	0.361668i	0.114160	−	0.147651i
$7$		−	4.71845i		−	1.78341i	−0.452621	−	0.891703i	$-0.649511\pi$
$7$		−	4.71845i		−	1.78341i	0.452621	−	0.891703i	$-0.350489\pi$
$8$	2.60104	+	1.11112i	0.919607	+	0.392840i
$9$	−2.89550			−0.965167
$10$		0			0
$11$			2.86225i			0.863001i	0.902113	+	0.431501i	$0.142016\pi$
$11$			2.86225i			0.863001i	−0.902113	+	0.431501i	$0.857984\pi$
$12$	0.162742	+	0.625711i	0.0469796	+	0.180627i
$13$	3.62139			1.00439			0.502197	−	0.864753i	$-0.332525\pi$
$13$	3.62139			1.00439			0.502197	+	0.864753i	$0.332525\pi$
$14$	5.27901	+	4.08162i	1.41087	+	1.09086i
$15$		0			0
$16$	−3.49311	+	1.94889i	−0.873277	+	0.487224i
$17$		−	3.76612i		−	0.913417i	−0.889616	−	0.456709i	$-0.849028\pi$
$17$		−	3.76612i		−	0.913417i	0.889616	−	0.456709i	$-0.150972\pi$
$18$	2.50471	−	3.23949i	0.590365	−	0.763555i
$19$			4.25662i			0.976536i	0.872694	+	0.488268i	$0.162371\pi$
$19$			4.25662i			0.976536i	−0.872694	+	0.488268i	$0.837629\pi$
$20$		0			0
$21$			1.52531i			0.332849i
$22$	−3.20229	−	2.47594i	−0.682731	−	0.527873i
$23$		−	0.157690i		−	0.0328807i	−0.999865	−	0.0164403i	$-0.994767\pi$
$23$		−	0.157690i		−	0.0328807i	0.999865	−	0.0164403i	$-0.00523336\pi$
$24$	−0.840823	−	0.359185i	−0.171632	−	0.0733183i
$25$		0			0
$26$	−3.13263	+	4.05162i	−0.614359	+	0.794588i
$27$	1.90580			0.366772
$28$	−9.13304	+	2.37543i	−1.72598	+	0.448913i
$29$		−	8.42137i		−	1.56381i	−0.623399	−	0.781904i	$-0.714249\pi$
$29$		−	8.42137i		−	1.56381i	0.623399	−	0.781904i	$-0.285751\pi$
$30$		0			0
$31$	−6.04113			−1.08502			−0.542510	−	0.840049i	$-0.682526\pi$
$31$	−6.04113			−1.08502			−0.542510	+	0.840049i	$0.682526\pi$
$32$	0.841231	−	5.59395i	0.148710	−	0.988881i
$33$		−	0.925263i		−	0.161068i
$34$	4.21354	+	3.25782i	0.722616	+	0.558711i
$35$		0			0
$36$	1.45769	+	5.60454i	0.242949	+	0.934089i
$37$	−8.66483			−1.42449			−0.712244	−	0.701932i	$-0.752321\pi$
$37$	−8.66483			−1.42449			−0.712244	+	0.701932i	$0.752321\pi$
$38$	−4.76231	−	3.68212i	−0.772549	−	0.597319i
$39$	−1.17067			−0.187457
$40$		0			0
$41$	−5.07418			−0.792455			−0.396227	−	0.918152i	$-0.629681\pi$
$41$	−5.07418			−0.792455			−0.396227	+	0.918152i	$0.629681\pi$
$42$	−1.70651	−	1.31944i	−0.263321	−	0.203594i
$43$	−5.63606			−0.859491			−0.429746	−	0.902950i	$-0.641397\pi$
$43$	−5.63606			−0.859491			−0.429746	+	0.902950i	$0.641397\pi$
$44$	5.54018	−	1.44095i	0.835214	−	0.217232i
$45$		0			0
$46$	0.176424	+	0.136407i	0.0260123	+	0.0201122i
$47$			0.287245i			0.0418990i	0.999781	+	0.0209495i	$0.00666892\pi$
$47$			0.287245i			0.0418990i	−0.999781	+	0.0209495i	$0.993331\pi$
$48$	1.12920	−	0.630008i	0.162986	−	0.0909338i
$49$	−15.2638			−2.18054
$50$		0			0
$51$			1.21745i			0.170477i
$52$	−1.82313	−	7.00958i	−0.252823	−	0.972054i
$53$	3.84392			0.528003			0.264002	−	0.964522i	$-0.414958\pi$
$53$	3.84392			0.528003			0.264002	+	0.964522i	$0.414958\pi$
$54$	−1.64858	+	2.13222i	−0.224344	+	0.290158i
$55$		0			0
$56$	5.24275	−	12.2729i	0.700593	−	1.64003i
$57$		−	1.37601i		−	0.182257i
$58$	9.42184	+	7.28476i	1.23715	+	0.956536i
$59$		−	4.25007i		−	0.553312i	−0.960969	−	0.276656i	$-0.910774\pi$
$59$		−	4.25007i		−	0.553312i	0.960969	−	0.276656i	$-0.0892262\pi$
$60$		0			0
$61$			0.316291i			0.0404970i	0.999795	+	0.0202485i	$0.00644573\pi$
$61$			0.316291i			0.0404970i	−0.999795	+	0.0202485i	$0.993554\pi$
$62$	5.22578	−	6.75883i	0.663675	−	0.858372i
$63$			13.6623i			1.72128i
$64$	5.53083	+	5.78013i	0.691354	+	0.722516i
$65$		0			0
$66$	1.03519	+	0.800384i	0.127423	+	0.0985205i
$67$	−10.7686			−1.31560			−0.657799	−	0.753193i	$-0.728513\pi$
$67$	−10.7686			−1.31560			−0.657799	+	0.753193i	$0.728513\pi$
$68$	−7.28970	+	1.89599i	−0.884006	+	0.229923i
$69$			0.0509756i			0.00613674i
$70$		0			0
$71$	10.2316			1.21427			0.607134	−	0.794599i	$-0.292319\pi$
$71$	10.2316			1.21427			0.607134	+	0.794599i	$0.292319\pi$
$72$	−7.53132	−	3.21724i	−0.887574	−	0.379156i
$73$		−	11.6170i		−	1.35967i	−0.733364	−	0.679836i	$-0.762051\pi$
$73$		−	11.6170i		−	1.35967i	0.733364	−	0.679836i	$-0.237949\pi$
$74$	7.49537	−	9.69422i	0.871318	−	1.12693i
$75$		0			0
$76$	8.23912	−	2.14293i	0.945092	−	0.245810i
$77$	13.5054			1.53908
$78$	1.01267	−	1.30974i	0.114662	−	0.148299i
$79$	−15.9022			−1.78914			−0.894568	−	0.446931i	$-0.852517\pi$
$79$	−15.9022			−1.78914			−0.894568	+	0.446931i	$0.852517\pi$
$80$		0			0
$81$	8.07042			0.896714
$82$	4.38934	−	5.67701i	0.484722	−	0.626920i
$83$	−11.7661			−1.29150			−0.645748	−	0.763550i	$-0.723454\pi$
$83$	−11.7661			−1.29150			−0.645748	+	0.763550i	$0.723454\pi$
$84$	2.95238	−	0.767890i	0.322131	−	0.0837837i
$85$		0			0
$86$	4.87538	−	6.30563i	0.525726	−	0.679954i
$87$			2.72233i			0.291864i
$88$	−3.18030	+	7.44483i	−0.339021	+	0.793622i
$89$	4.33875			0.459907			0.229953	−	0.973202i	$-0.426143\pi$
$89$	4.33875			0.459907			0.229953	+	0.973202i	$0.426143\pi$
$90$		0			0
$91$		−	17.0874i		−	1.79124i
$92$	−0.305225	+	0.0793865i	−0.0318219	+	0.00827662i
$93$	1.95288			0.202504
$94$	−0.321370	−	0.248477i	−0.0331468	−	0.0256284i
$95$		0			0
$96$	−0.271940	+	1.80833i	−0.0277548	+	0.184561i
$97$			1.48092i			0.150364i	0.997170	+	0.0751821i	$0.0239538\pi$
$97$			1.48092i			0.150364i	−0.997170	+	0.0751821i	$0.976046\pi$
$98$	13.2037	−	17.0771i	1.33377	−	1.72505i
$99$		−	8.28765i		−	0.832940i
$100$		0			0
$101$		−	9.78361i		−	0.973505i	−0.873540	−	0.486753i	$-0.838181\pi$
$101$		−	9.78361i		−	0.973505i	0.873540	−	0.486753i	$-0.161819\pi$
$102$	−1.36209	−	1.05314i	−0.134867	−	0.104276i
$103$			0.417967i			0.0411835i	0.999788	+	0.0205917i	$0.00655502\pi$
$103$			0.417967i			0.0411835i	−0.999788	+	0.0205917i	$0.993445\pi$
$104$	9.41940	+	4.02380i	0.923648	+	0.394566i
$105$		0			0
$106$	−3.32512	+	4.30058i	−0.322964	+	0.417710i
$107$	1.14284			0.110483			0.0552413	−	0.998473i	$-0.482407\pi$
$107$	1.14284			0.110483			0.0552413	+	0.998473i	$0.482407\pi$
$108$	−0.959446	−	3.68888i	−0.0923227	−	0.354962i
$109$			16.1100i			1.54306i	0.636191	+	0.771531i	$0.280509\pi$
$109$			16.1100i			1.54306i	−0.636191	+	0.771531i	$0.719491\pi$
$110$		0			0
$111$	2.80103			0.265862
$112$	9.19576	+	16.4821i	0.868917	+	1.55741i
$113$		−	12.7367i		−	1.19817i	−0.800687	−	0.599083i	$-0.795532\pi$
$113$		−	12.7367i		−	1.19817i	0.800687	−	0.599083i	$-0.204468\pi$
$114$	1.53949	+	1.19030i	0.144186	+	0.111482i
$115$		0			0
$116$	−16.3004	+	4.23960i	−1.51346	+	0.393637i
$117$	−10.4857			−0.969408
$118$	4.75498	+	3.67645i	0.437732	+	0.338445i
$119$	−17.7702			−1.62899
$120$		0			0
$121$	2.80752			0.255229
$122$	−0.353867	−	0.273603i	−0.0320376	−	0.0247708i
$123$	1.64030			0.147901
$124$	3.04131	+	11.6932i	0.273118	+	1.05008i
$125$		0			0
$126$	−15.2854	−	11.8183i	−1.36173	−	1.05286i
$127$		−	4.67321i		−	0.414680i	−0.978269	−	0.207340i	$-0.933519\pi$
$127$		−	4.67321i		−	0.414680i	0.978269	−	0.207340i	$-0.0664807\pi$
$128$	−11.2512	+	1.18790i	−0.994473	+	0.104996i
$129$	1.82194			0.160413
$130$		0			0
$131$			21.4337i			1.87267i	0.351103	+	0.936337i	$0.385807\pi$
$131$			21.4337i			1.87267i	−0.351103	+	0.936337i	$0.614193\pi$
$132$	−1.79094	+	0.465809i	−0.155881	+	0.0405434i
$133$	20.0846			1.74156
$134$	9.31523	−	12.0480i	0.804714	−	1.04079i
$135$		0			0
$136$	4.18460	−	9.79582i	0.358827	−	0.839985i
$137$		−	9.11855i		−	0.779050i	−0.921016	−	0.389525i	$-0.872639\pi$
$137$		−	9.11855i		−	0.779050i	0.921016	−	0.389525i	$-0.127361\pi$
$138$	−0.0570316	−	0.0440956i	−0.00485485	−	0.00375367i
$139$		−	15.5393i		−	1.31802i	−0.752133	−	0.659011i	$-0.770975\pi$
$139$		−	15.5393i		−	1.31802i	0.752133	−	0.659011i	$-0.229025\pi$
$140$		0			0
$141$		−	0.0928560i		−	0.00781989i
$142$	−8.85069	+	11.4471i	−0.742733	+	0.960623i
$143$			10.3653i			0.866794i
$144$	10.1143	−	5.64302i	0.842858	−	0.470252i
$145$		0			0
$146$	12.9972	+	10.0491i	1.07565	+	0.831672i
$147$	4.93422			0.406968
$148$	4.36216	+	16.7717i	0.358568	+	1.37862i
$149$			3.29517i			0.269951i	0.990849	+	0.134975i	$0.0430956\pi$
$149$			3.29517i			0.269951i	−0.990849	+	0.134975i	$0.956904\pi$
$150$		0			0
$151$	−17.3828			−1.41459			−0.707296	−	0.706918i	$-0.750085\pi$
$151$	−17.3828			−1.41459			−0.707296	+	0.706918i	$0.750085\pi$
$152$	−4.72961	+	11.0716i	−0.383622	+	0.898029i
$153$			10.9048i			0.881600i
$154$	−11.6826	+	15.1098i	−0.941412	+	1.21759i
$155$		0			0
$156$	0.589353	+	2.26595i	0.0471860	+	0.181421i
$157$	21.2590			1.69665			0.848327	−	0.529472i	$-0.177610\pi$
$157$	21.2590			1.69665			0.848327	+	0.529472i	$0.177610\pi$
$158$	13.7559	−	17.7914i	1.09436	−	1.41541i
$159$	−1.24260			−0.0985447
$160$		0			0
$161$	−0.744053			−0.0586396
$162$	−6.98119	+	9.02920i	−0.548494	+	0.709401i
$163$	−7.71716			−0.604455			−0.302227	−	0.953236i	$-0.597730\pi$
$163$	−7.71716			−0.604455			−0.302227	+	0.953236i	$0.597730\pi$
$164$	2.55452	+	9.82160i	0.199474	+	0.766938i
$165$		0			0
$166$	10.1781	−	13.1639i	0.789971	−	1.02172i
$167$			6.34283i			0.490823i	0.969419	+	0.245411i	$0.0789230\pi$
$167$			6.34283i			0.490823i	−0.969419	+	0.245411i	$0.921077\pi$
$168$	−1.69479	+	3.96738i	−0.130756	+	0.306090i
$169$	0.114500			0.00880766
$170$		0			0
$171$		−	12.3250i		−	0.942520i
$172$	2.83738	+	10.9092i	0.216348	+	0.831817i
$173$	17.3353			1.31798			0.658990	−	0.752151i	$-0.270984\pi$
$173$	17.3353			1.31798			0.658990	+	0.752151i	$0.270984\pi$
$174$	−3.04574	−	2.35490i	−0.230897	−	0.178525i
$175$		0			0
$176$	−5.57823	−	9.99816i	−0.420475	−	0.753639i
$177$			1.37389i			0.103268i
$178$	−3.75317	+	4.85420i	−0.281312	+	0.363838i
$179$			2.31057i			0.172700i	0.996265	+	0.0863502i	$0.0275204\pi$
$179$			2.31057i			0.172700i	−0.996265	+	0.0863502i	$0.972480\pi$
$180$		0			0
$181$			7.14757i			0.531275i	0.964073	+	0.265638i	$0.0855824\pi$
$181$			7.14757i			0.531275i	−0.964073	+	0.265638i	$0.914418\pi$
$182$	19.1174	+	14.7811i	1.41707	+	1.09565i
$183$		−	0.102246i		−	0.00755822i
$184$	0.175212	−	0.410159i	0.0129168	−	0.0302373i
$185$		0			0
$186$	−1.68931	+	2.18489i	−0.123866	+	0.160204i
$187$	10.7796			0.788281
$188$	0.555992	−	0.144609i	0.0405499	−	0.0105467i
$189$		−	8.99244i		−	0.654104i
$190$		0			0
$191$	11.5287			0.834185			0.417092	−	0.908864i	$-0.363049\pi$
$191$	11.5287			0.834185			0.417092	+	0.908864i	$0.363049\pi$
$192$	−1.78792	−	1.86851i	−0.129032	−	0.134848i
$193$		−	15.3998i		−	1.10850i	−0.832350	−	0.554250i	$-0.813005\pi$
$193$		−	15.3998i		−	1.10850i	0.832350	−	0.554250i	$-0.186995\pi$
$194$	−1.65685	−	1.28104i	−0.118955	−	0.0919735i
$195$		0			0
$196$	7.68429	+	29.5445i	0.548878	+	2.11032i
$197$	−17.4236			−1.24138			−0.620692	−	0.784055i	$-0.713148\pi$
$197$	−17.4236			−1.24138			−0.620692	+	0.784055i	$0.713148\pi$
$198$	9.27224	+	7.16910i	0.658949	+	0.509486i
$199$	6.89181			0.488547			0.244274	−	0.969706i	$-0.421450\pi$
$199$	6.89181			0.488547			0.244274	+	0.969706i	$0.421450\pi$
$200$		0			0
$201$	3.48112			0.245539
$202$	10.9459	+	8.46315i	0.770152	+	0.595465i
$203$	−39.7358			−2.78890
$204$	2.35650	−	0.612906i	0.164988	−	0.0429120i
$205$		0			0
$206$	−0.467622	−	0.361555i	−0.0325807	−	0.0251907i
$207$			0.456592i			0.0317353i
$208$	−12.6499	+	7.05771i	−0.877115	+	0.489364i
$209$	−12.1835			−0.842752
$210$		0			0
$211$		−	0.0316505i		−	0.00217891i	−0.999999	−	0.00108946i	$-0.999653\pi$
$211$		−	0.0316505i		−	0.00217891i	0.999999	−	0.00108946i	$-0.000346785\pi$
$212$	−1.93516	−	7.44030i	−0.132907	−	0.511002i
$213$	−3.30751			−0.226627
$214$	−0.988596	+	1.27861i	−0.0675790	+	0.0874041i
$215$		0			0
$216$	4.95708	+	2.11757i	0.337286	+	0.144083i
$217$			28.5048i			1.93503i
$218$	−18.0239	−	13.9357i	−1.22074	−	0.943847i
$219$			3.75537i			0.253765i
$220$		0			0
$221$		−	13.6386i		−	0.917431i
$222$	−2.42298	+	3.13379i	−0.162620	+	0.210326i
$223$			8.27491i			0.554129i	0.960851	+	0.277065i	$0.0893616\pi$
$223$			8.27491i			0.554129i	−0.960851	+	0.277065i	$0.910638\pi$
$224$	−26.3948	−	3.96931i	−1.76358	−	0.265210i
$225$		0			0
$226$	14.2498	+	11.0176i	0.947883	+	0.732883i
$227$	7.68711			0.510211			0.255106	−	0.966913i	$-0.417890\pi$
$227$	7.68711			0.510211			0.255106	+	0.966913i	$0.417890\pi$
$228$	−2.66341	+	0.692731i	−0.176389	+	0.0458772i
$229$		−	13.8586i		−	0.915803i	−0.889003	−	0.457901i	$-0.848601\pi$
$229$		−	13.8586i		−	0.915803i	0.889003	−	0.457901i	$-0.151399\pi$
$230$		0			0
$231$	−4.36581			−0.287249
$232$	9.35713	−	21.9043i	0.614326	−	1.43809i
$233$		−	10.2971i		−	0.674586i	−0.941400	−	0.337293i	$-0.890489\pi$
$233$		−	10.2971i		−	0.674586i	0.941400	−	0.337293i	$-0.109511\pi$
$234$	9.07053	−	11.7315i	0.592959	−	0.766910i
$235$		0			0
$236$	−8.22644	+	2.13963i	−0.535496	+	0.139278i
$237$	5.14061			0.333918
$238$	15.3718	−	19.8814i	0.996409	−	1.28872i
$239$	11.9208			0.771092			0.385546	−	0.922689i	$-0.374013\pi$
$239$	11.9208			0.771092			0.385546	+	0.922689i	$0.374013\pi$
$240$		0			0
$241$	−17.2915			−1.11385			−0.556923	−	0.830564i	$-0.688018\pi$
$241$	−17.2915			−1.11385			−0.556923	+	0.830564i	$0.688018\pi$
$242$	−2.42859	+	3.14105i	−0.156116	+	0.201914i
$243$	−8.32629			−0.534132
$244$	0.612214	−	0.159232i	0.0391930	−	0.0101938i
$245$		0			0
$246$	−1.41892	+	1.83517i	−0.0904668	+	0.117006i
$247$			15.4149i			0.980827i
$248$	−15.7132	−	6.71241i	−0.997792	−	0.426239i
$249$	3.80356			0.241041
$250$		0			0
$251$			10.4897i			0.662107i	0.943612	+	0.331053i	$0.107404\pi$
$251$			10.4897i			0.662107i	−0.943612	+	0.331053i	$0.892596\pi$
$252$	26.4447	−	6.87804i	1.66586	−	0.433276i
$253$	0.451349			0.0283761
$254$	5.22839	+	4.04248i	0.328059	+	0.253648i
$255$		0			0
$256$	8.40362	−	13.6154i	0.525226	−	0.850963i
$257$			23.9098i			1.49145i	0.666254	+	0.745725i	$0.267897\pi$
$257$			23.9098i			1.49145i	−0.666254	+	0.745725i	$0.732103\pi$
$258$	−1.57604	+	2.03839i	−0.0981198	+	0.126904i
$259$			40.8845i			2.54044i
$260$		0			0
$261$			24.3841i			1.50934i
$262$	−23.9801	−	18.5409i	−1.48149	−	1.14546i
$263$			1.18356i			0.0729817i	0.999334	+	0.0364909i	$0.0116180\pi$
$263$			1.18356i			0.0729817i	−0.999334	+	0.0364909i	$0.988382\pi$
$264$	1.02808	−	2.40665i	0.0632738	−	0.148119i
$265$		0			0
$266$	−17.3739	+	22.4707i	−1.06526	+	1.37777i
$267$	−1.40256			−0.0858355
$268$	5.42129	+	20.8438i	0.331158	+	1.27324i
$269$		−	0.499118i		−	0.0304318i	−0.999884	−	0.0152159i	$-0.995156\pi$
$269$		−	0.499118i		−	0.0304318i	0.999884	−	0.0152159i	$-0.00484355\pi$
$270$		0			0
$271$	−1.15624			−0.0702367			−0.0351184	−	0.999383i	$-0.511181\pi$
$271$	−1.15624			−0.0702367			−0.0351184	+	0.999383i	$0.511181\pi$
$272$	7.33976	+	13.1555i	0.445038	+	0.797667i
$273$			5.52373i			0.334311i
$274$	10.2018	+	7.88785i	0.616316	+	0.476523i
$275$		0			0
$276$	0.0986684	−	0.0256628i	0.00593914	−	0.00154472i
$277$	−19.3757			−1.16417			−0.582086	−	0.813127i	$-0.697763\pi$
$277$	−19.3757			−1.16417			−0.582086	+	0.813127i	$0.697763\pi$
$278$	17.3853	+	13.4420i	1.04270	+	0.806196i
$279$	17.4921			1.04722
$280$		0			0
$281$	−10.6439			−0.634963			−0.317481	−	0.948265i	$-0.602837\pi$
$281$	−10.6439			−0.634963			−0.317481	+	0.948265i	$0.602837\pi$
$282$	0.103887	+	0.0803236i	0.00618641	+	0.00478320i
$283$	16.9135			1.00541			0.502703	−	0.864459i	$-0.332339\pi$
$283$	16.9135			1.00541			0.502703	+	0.864459i	$0.332339\pi$
$284$	−5.15094	−	19.8043i	−0.305652	−	1.17517i
$285$		0			0
$286$	−11.5968	−	8.96637i	−0.685731	−	0.530193i
$287$			23.9423i			1.41327i
$288$	−2.43579	+	16.1973i	−0.143530	+	0.954435i
$289$	2.81637			0.165669
$290$		0			0
$291$		−	0.478727i		−	0.0280635i
$292$	−22.4860	+	5.84841i	−1.31589	+	0.342252i
$293$	−5.43507			−0.317520			−0.158760	−	0.987317i	$-0.550750\pi$
$293$	−5.43507			−0.317520			−0.158760	+	0.987317i	$0.550750\pi$
$294$	−4.26827	+	5.52042i	−0.248931	+	0.321957i
$295$		0			0
$296$	−22.5376	−	9.62765i	−1.30997	−	0.559596i
$297$			5.45489i			0.316525i
$298$	−3.68664	−	2.85043i	−0.213561	−	0.165121i
$299$		−	0.571058i		−	0.0330252i
$300$		0			0
$301$			26.5935i			1.53282i
$302$	15.0367	−	19.4479i	0.865265	−	1.11910i
$303$			3.16269i			0.181692i
$304$	−8.29570	−	14.8688i	−0.475791	−	0.852786i
$305$		0			0
$306$	−12.2003	−	9.43301i	−0.697445	−	0.539249i
$307$	5.14312			0.293533			0.146767	−	0.989171i	$-0.453113\pi$
$307$	5.14312			0.293533			0.146767	+	0.989171i	$0.453113\pi$
$308$	−6.79907	−	26.1410i	−0.387413	−	1.48952i
$309$		−	0.135114i		−	0.00768634i
$310$		0			0
$311$	6.31496			0.358088			0.179044	−	0.983841i	$-0.442700\pi$
$311$	6.31496			0.358088			0.179044	+	0.983841i	$0.442700\pi$
$312$	−3.04495	−	1.30075i	−0.172387	−	0.0736405i
$313$		−	4.41203i		−	0.249383i	−0.992196	−	0.124691i	$-0.960206\pi$
$313$		−	4.41203i		−	0.249383i	0.992196	−	0.124691i	$-0.0397941\pi$
$314$	−18.3898	+	23.7846i	−1.03779	+	1.34224i
$315$		0			0
$316$	8.00570	+	30.7803i	0.450356	+	1.73153i
$317$	21.6943			1.21847			0.609236	−	0.792989i	$-0.291476\pi$
$317$	21.6943			1.21847			0.609236	+	0.792989i	$0.291476\pi$
$318$	1.07489	−	1.39022i	0.0602770	−	0.0779599i
$319$	24.1041			1.34957
$320$		0			0
$321$	−0.369440			−0.0206201
$322$	0.643631	−	0.832447i	0.0358681	−	0.0463905i
$323$	16.0309			0.891985
$324$	−4.06292	−	15.6211i	−0.225718	−	0.867840i
$325$		0			0
$326$	6.67560	−	8.63397i	0.369728	−	0.478192i
$327$		−	5.20780i		−	0.287992i
$328$	−13.1982	−	5.63802i	−0.728747	−	0.311308i
$329$	1.35535			0.0747229
$330$		0			0
$331$			6.76824i			0.372016i	0.982548	+	0.186008i	$0.0595550\pi$
$331$			6.76824i			0.372016i	−0.982548	+	0.186008i	$0.940445\pi$
$332$	5.92345	+	22.7745i	0.325091	+	1.24991i
$333$	25.0890			1.37487
$334$	−7.09637	−	5.48676i	−0.388296	−	0.300222i
$335$		0			0
$336$	−2.97266	−	5.32806i	−0.162172	−	0.290669i
$337$		−	17.1785i		−	0.935775i	−0.883788	−	0.467887i	$-0.845015\pi$
$337$		−	17.1785i		−	0.935775i	0.883788	−	0.467887i	$-0.154985\pi$
$338$	−0.0990459	+	0.128102i	−0.00538739	+	0.00696784i
$339$			4.11731i			0.223622i
$340$		0			0
$341$		−	17.2912i		−	0.936373i
$342$	13.7893	+	10.6616i	0.745639	+	0.576512i
$343$			38.9921i			2.10537i
$344$	−14.6596	−	6.26233i	−0.790394	−	0.337642i
$345$		0			0
$346$	−14.9956	+	19.3948i	−0.806171	+	1.04267i
$347$	−29.9680			−1.60877			−0.804383	−	0.594112i	$-0.797504\pi$
$347$	−29.9680			−1.60877			−0.804383	+	0.594112i	$0.797504\pi$
$348$	5.26934	−	1.37051i	0.282466	−	0.0734671i
$349$			2.64481i			0.141573i	0.997491	+	0.0707867i	$0.0225510\pi$
$349$			2.64481i			0.141573i	−0.997491	+	0.0707867i	$0.977449\pi$
$350$		0			0
$351$	6.90167			0.368384
$352$	16.0113	+	2.40782i	0.853406	+	0.128337i
$353$		−	18.3223i		−	0.975200i	−0.873067	−	0.487600i	$-0.837872\pi$
$353$		−	18.3223i		−	0.975200i	0.873067	−	0.487600i	$-0.162128\pi$
$354$	−1.53712	−	1.18846i	−0.0816968	−	0.0631662i
$355$		0			0
$356$	−2.18427	−	8.39810i	−0.115766	−	0.445098i
$357$	5.74448			0.304030
$358$	−2.58507	−	1.99872i	−0.136625	−	0.105636i
$359$	7.70888			0.406859			0.203430	−	0.979090i	$-0.434791\pi$
$359$	7.70888			0.406859			0.203430	+	0.979090i	$0.434791\pi$
$360$		0			0
$361$	0.881182			0.0463780
$362$	−7.99672	−	6.18289i	−0.420298	−	0.324966i
$363$	−0.907569			−0.0476350
$364$	−33.0743	+	8.60235i	−1.73357	+	0.450886i
$365$		0			0
$366$	0.114393	+	0.0884460i	0.00597940	+	0.00462314i
$367$		−	25.7332i		−	1.34326i	−0.740887	−	0.671630i	$-0.765595\pi$
$367$		−	25.7332i		−	1.34326i	0.740887	−	0.671630i	$-0.234405\pi$
$368$	0.307321	+	0.550829i	0.0160202	+	0.0287139i
$369$	14.6923			0.764851
$370$		0			0
$371$		−	18.1373i		−	0.941644i
$372$	−0.983146	−	3.78000i	−0.0509738	−	0.195984i
$373$	16.7096			0.865192			0.432596	−	0.901588i	$-0.357598\pi$
$373$	16.7096			0.865192			0.432596	+	0.901588i	$0.357598\pi$
$374$	−9.32469	+	12.0602i	−0.482168	+	0.623618i
$375$		0			0
$376$	−0.319163	+	0.747136i	−0.0164596	+	0.0385306i
$377$		−	30.4971i		−	1.57068i
$378$	10.0608	+	7.77876i	0.517469	+	0.400096i
$379$		−	26.8739i		−	1.38042i	−0.723610	−	0.690209i	$-0.757519\pi$
$379$		−	26.8739i		−	1.38042i	0.723610	−	0.690209i	$-0.242481\pi$
$380$		0			0
$381$			1.51068i			0.0773945i
$382$	−9.97268	+	12.8983i	−0.510247	+	0.659934i
$383$		−	27.1824i		−	1.38896i	−0.719513	−	0.694479i	$-0.755635\pi$
$383$		−	27.1824i		−	1.38896i	0.719513	−	0.694479i	$-0.244365\pi$
$384$	3.63710	−	0.384004i	0.185605	−	0.0195961i
$385$		0			0
$386$	17.2293	+	13.3213i	0.876948	+	0.678037i
$387$	16.3192			0.829552
$388$	2.86646	−	0.745543i	0.145523	−	0.0378492i
$389$		−	16.4273i		−	0.832896i	−0.909160	−	0.416448i	$-0.863275\pi$
$389$		−	16.4273i		−	0.832896i	0.909160	−	0.416448i	$-0.136725\pi$
$390$		0			0
$391$	−0.593880			−0.0300338
$392$	−39.7016	−	16.9598i	−2.00524	−	0.856601i
$393$		−	6.92876i		−	0.349509i
$394$	15.0720	−	19.4936i	0.759318	−	0.982074i
$395$		0			0
$396$	−16.0416	+	4.17228i	−0.806120	+	0.209665i
$397$	2.76108			0.138575			0.0692874	−	0.997597i	$-0.477927\pi$
$397$	2.76108			0.138575			0.0692874	+	0.997597i	$0.477927\pi$
$398$	−5.96165	+	7.71057i	−0.298830	+	0.386496i
$399$	−6.49265			−0.325039
$400$		0			0
$401$	9.94183			0.496471			0.248236	−	0.968700i	$-0.420149\pi$
$401$	9.94183			0.496471			0.248236	+	0.968700i	$0.420149\pi$
$402$	−3.01128	+	3.89468i	−0.150189	+	0.194249i
$403$	−21.8773			−1.08979
$404$	−18.9372	+	4.92540i	−0.942159	+	0.245048i
$405$		0			0
$406$	34.3728	−	44.4564i	1.70589	−	2.20634i
$407$		−	24.8009i		−	1.22934i
$408$	−1.35273	+	3.16664i	−0.0669702	+	0.156772i
$409$	16.4835			0.815057			0.407528	−	0.913192i	$-0.366391\pi$
$409$	16.4835			0.815057			0.407528	+	0.913192i	$0.366391\pi$
$410$		0			0
$411$			2.94770i			0.145399i
$412$	0.809017	−	0.210418i	0.0398574	−	0.0103666i
$413$	−20.0537			−0.986779
$414$	−0.510836	−	0.394967i	−0.0251062	−	0.0194116i
$415$		0			0
$416$	3.04643	−	20.2579i	0.149364	−	0.993226i
$417$			5.02328i			0.245991i
$418$	10.5392	−	13.6309i	0.515487	−	0.666711i
$419$			15.2916i			0.747046i	0.927621	+	0.373523i	$0.121850\pi$
$419$			15.2916i			0.747046i	−0.927621	+	0.373523i	$0.878150\pi$
$420$		0			0
$421$		−	31.9774i		−	1.55848i	−0.626725	−	0.779240i	$-0.715605\pi$
$421$		−	31.9774i		−	1.55848i	0.626725	−	0.779240i	$-0.284395\pi$
$422$	0.0354106	+	0.0273788i	0.00172376	+	0.00133278i
$423$		−	0.831718i		−	0.0404395i
$424$	9.99819	+	4.27105i	0.485555	+	0.207421i
$425$		0			0
$426$	2.86111	−	3.70045i	0.138621	−	0.179287i
$427$	1.49240			0.0722225
$428$	−0.575345	−	2.21209i	−0.0278103	−	0.106925i
$429$		−	3.35074i		−	0.161775i
$430$		0			0
$431$	14.5832			0.702446			0.351223	−	0.936292i	$-0.385766\pi$
$431$	14.5832			0.702446			0.351223	+	0.936292i	$0.385766\pi$
$432$	−6.65718	+	3.71421i	−0.320294	+	0.178700i
$433$			29.9399i			1.43882i	0.694585	+	0.719411i	$0.255588\pi$
$433$			29.9399i			1.43882i	−0.694585	+	0.719411i	$0.744412\pi$
$434$	−31.8912	−	24.6576i	−1.53083	−	1.18360i
$435$		0			0
$436$	31.1826	−	8.11034i	1.49338	−	0.388415i
$437$	0.671227			0.0321092
$438$	−4.20152	−	3.24852i	−0.200756	−	0.155221i
$439$	5.88876			0.281055			0.140528	−	0.990077i	$-0.455120\pi$
$439$	5.88876			0.281055			0.140528	+	0.990077i	$0.455120\pi$
$440$		0			0
$441$	44.1962			2.10458
$442$	15.2589	+	11.7978i	0.725791	+	0.561166i
$443$	31.5216			1.49764			0.748818	−	0.662775i	$-0.230622\pi$
$443$	31.5216			1.49764			0.748818	+	0.662775i	$0.230622\pi$
$444$	−1.41013	−	5.42167i	−0.0669219	−	0.257301i
$445$		0			0
$446$	−9.25798	−	7.15808i	−0.438378	−	0.338945i
$447$		−	1.06521i		−	0.0503827i
$448$	27.2732	−	26.0969i	1.28854	−	1.23296i
$449$	36.4487			1.72012			0.860061	−	0.510192i	$-0.170426\pi$
$449$	36.4487			1.72012			0.860061	+	0.510192i	$0.170426\pi$
$450$		0			0
$451$		−	14.5236i		−	0.683889i
$452$	−24.6531	+	6.41207i	−1.15959	+	0.301598i
$453$	5.61923			0.264015
$454$	−6.64960	+	8.60035i	−0.312081	+	0.403634i
$455$		0			0
$456$	1.52891	−	3.57907i	0.0715979	−	0.167605i
$457$		−	24.6472i		−	1.15295i	−0.817116	−	0.576473i	$-0.804428\pi$
$457$		−	24.6472i		−	1.15295i	0.817116	−	0.576473i	$-0.195572\pi$
$458$	15.5050	+	11.9882i	0.724503	+	0.560170i
$459$		−	7.17748i		−	0.335016i
$460$		0			0
$461$		−	6.58567i		−	0.306725i	−0.988170	−	0.153363i	$-0.950990\pi$
$461$		−	6.58567i		−	0.306725i	0.988170	−	0.153363i	$-0.0490103\pi$
$462$	3.77657	−	4.88447i	0.175702	−	0.227246i
$463$		−	3.47363i		−	0.161433i	−0.996737	−	0.0807166i	$-0.974279\pi$
$463$		−	3.47363i		−	0.161433i	0.996737	−	0.0807166i	$-0.0257209\pi$
$464$	16.4124	+	29.4168i	0.761924	+	1.36564i
$465$		0			0
$466$	11.5204	+	8.90735i	0.533673	+	0.412625i
$467$	−34.5272			−1.59773			−0.798863	−	0.601513i	$-0.794565\pi$
$467$	−34.5272			−1.59773			−0.798863	+	0.601513i	$0.794565\pi$
$468$	5.27888	+	20.2962i	0.244016	+	0.938194i
$469$			50.8113i			2.34625i
$470$		0			0
$471$	−6.87228			−0.316658
$472$	4.72233	−	11.0546i	0.217363	−	0.508829i
$473$		−	16.1318i		−	0.741742i
$474$	−4.44680	+	5.75132i	−0.204248	+	0.264167i
$475$		0			0
$476$	8.94613	+	34.3961i	0.410045	+	1.57654i
$477$	−11.1301			−0.509611
$478$	−10.3119	+	13.3370i	−0.471655	+	0.610020i
$479$	36.0433			1.64686			0.823430	−	0.567418i	$-0.192058\pi$
$479$	36.0433			1.64686			0.823430	+	0.567418i	$0.192058\pi$
$480$		0			0
$481$	−31.3788			−1.43075
$482$	14.9578	−	19.3458i	0.681307	−	0.881177i
$483$	0.240526			0.0109443
$484$	−1.41340	−	5.43423i	−0.0642453	−	0.247011i
$485$		0			0
$486$	7.20252	−	9.31547i	0.326713	−	0.422558i
$487$			2.90750i			0.131752i	0.997828	+	0.0658758i	$0.0209841\pi$
$487$			2.90750i			0.131752i	−0.997828	+	0.0658758i	$0.979016\pi$
$488$	−0.351437	+	0.822687i	−0.0159088	+	0.0372413i
$489$	2.49468			0.112813
$490$		0			0
$491$		−	0.899573i		−	0.0405972i	−0.999794	−	0.0202986i	$-0.993538\pi$
$491$		−	0.899573i		−	0.0405972i	0.999794	−	0.0202986i	$-0.00646168\pi$
$492$	−0.825783	−	3.17497i	−0.0372292	−	0.143139i
$493$	−31.7158			−1.42841
$494$	−17.2462	−	13.3344i	−0.775944	−	0.599943i
$495$		0			0
$496$	21.1023	−	11.7735i	0.947523	−	0.528647i
$497$		−	48.2773i		−	2.16553i
$498$	−3.29020	+	4.25543i	−0.147438	+	0.190690i
$499$			30.0557i			1.34548i	0.739880	+	0.672739i	$0.234882\pi$
$499$			30.0557i			1.34548i	−0.739880	+	0.672739i	$0.765118\pi$
$500$		0			0
$501$		−	2.05041i		−	0.0916055i
$502$	−11.7359	−	9.07398i	−0.523801	−	0.404992i
$503$		−	30.6055i		−	1.36463i	−0.731057	−	0.682316i	$-0.760973\pi$
$503$		−	30.6055i		−	1.36463i	0.731057	−	0.682316i	$-0.239027\pi$
$504$	−15.1804	+	35.5361i	−0.676189	+	1.58290i
$505$		0			0
$506$	−0.390432	+	0.504970i	−0.0173568	+	0.0224486i
$507$	−0.0370136			−0.00164383
$508$	−9.04547	+	2.35265i	−0.401328	+	0.104382i
$509$			30.6454i			1.35833i	0.733984	+	0.679167i	$0.237659\pi$
$509$			30.6454i			1.35833i	−0.733984	+	0.679167i	$0.762341\pi$
$510$		0			0
$511$	−54.8144			−2.42485
$512$	7.96351	+	21.1798i	0.351941	+	0.936022i
$513$			8.11228i			0.358166i
$514$	−26.7503	−	20.6828i	−1.17990	−	0.912277i
$515$		0			0
$516$	−0.917224	−	3.52654i	−0.0403785	−	0.155247i
$517$	−0.822167			−0.0361589
$518$	−45.7417	−	35.3665i	−2.00977	−	1.55391i
$519$	−5.60389			−0.245984
$520$		0			0
$521$	2.26302			0.0991445			0.0495723	−	0.998771i	$-0.484214\pi$
$521$	2.26302			0.0991445			0.0495723	+	0.998771i	$0.484214\pi$
$522$	−27.2809	−	21.0930i	−1.19405	−	0.923217i
$523$	−32.9299			−1.43992			−0.719962	−	0.694014i	$-0.755841\pi$
$523$	−32.9299			−1.43992			−0.719962	+	0.694014i	$0.755841\pi$
$524$	41.4872	−	10.7905i	1.81238	−	0.471383i
$525$		0			0
$526$	−1.32417	−	1.02382i	−0.0577367	−	0.0446408i
$527$			22.7516i			0.991076i
$528$	1.80324	+	3.23205i	0.0784760	+	0.140657i
$529$	22.9751			0.998919
$530$		0			0
$531$			12.3061i			0.534038i
$532$	−10.1113	−	38.8759i	−0.438380	−	1.68548i
$533$	−18.3756			−0.795937
$534$	1.21326	−	1.56919i	0.0525031	−	0.0679055i
$535$		0			0
$536$	−28.0097	−	11.9652i	−1.20983	−	0.516819i
$537$		−	0.746926i		−	0.0322322i
$538$	0.558414	+	0.431754i	0.0240749	+	0.0186142i
$539$		−	43.6887i		−	1.88181i
$540$		0			0
$541$		−	29.3315i		−	1.26106i	−0.776164	−	0.630531i	$-0.782837\pi$
$541$		−	29.3315i		−	1.26106i	0.776164	−	0.630531i	$-0.217163\pi$
$542$	1.00019	−	1.29361i	0.0429618	−	0.0555651i
$543$		−	2.31055i		−	0.0991554i
$544$	−21.0675	−	3.16817i	−0.903261	−	0.135834i
$545$		0			0
$546$	−6.17996	−	4.77821i	−0.264478	−	0.204489i
$547$	32.0181			1.36899			0.684497	−	0.729016i	$-0.260022\pi$
$547$	32.0181			1.36899			0.684497	+	0.729016i	$0.260022\pi$
$548$	−17.6499	+	4.59059i	−0.753966	+	0.196100i
$549$		−	0.915822i		−	0.0390863i
$550$		0			0
$551$	35.8466			1.52711
$552$	−0.0566399	+	0.132590i	−0.00241075	+	0.00564339i
$553$			75.0337i			3.19076i
$554$	16.7606	−	21.6775i	0.712090	−	0.920991i
$555$		0			0
$556$	−30.0778	+	7.82298i	−1.27558	+	0.331768i
$557$	−6.50974			−0.275827			−0.137913	−	0.990444i	$-0.544040\pi$
$557$	−6.50974			−0.275827			−0.137913	+	0.990444i	$0.544040\pi$
$558$	−15.1313	+	19.5702i	−0.640557	+	0.828472i
$559$	−20.4104			−0.863268
$560$		0			0
$561$	−3.48465			−0.147122
$562$	9.20734	−	11.9084i	0.388388	−	0.502327i
$563$	6.08661			0.256520			0.128260	−	0.991741i	$-0.459061\pi$
$563$	6.08661			0.256520			0.128260	+	0.991741i	$0.459061\pi$
$564$	−0.179732	+	0.0467468i	−0.00756809	+	0.00196840i
$565$		0			0
$566$	−14.6308	+	18.9229i	−0.614978	+	0.795389i
$567$		−	38.0799i		−	1.59920i
$568$	26.6128	+	11.3685i	1.11665	+	0.477013i
$569$	−11.1778			−0.468598			−0.234299	−	0.972165i	$-0.575280\pi$
$569$	−11.1778			−0.468598			−0.234299	+	0.972165i	$0.575280\pi$
$570$		0			0
$571$			0.183735i			0.00768905i	0.999993	+	0.00384453i	$0.00122375\pi$
$571$			0.183735i			0.00768905i	−0.999993	+	0.00384453i	$0.998776\pi$
$572$	20.0632	−	5.21826i	0.838884	−	0.218187i
$573$	−3.72680			−0.155689
$574$	−26.7867	−	20.7109i	−1.11805	−	0.864455i
$575$		0			0
$576$	−16.0145	−	16.7364i	−0.667272	−	0.697349i
$577$			21.8571i			0.909923i	0.890511	+	0.454962i	$0.150347\pi$
$577$			21.8571i			0.909923i	−0.890511	+	0.454962i	$0.849653\pi$
$578$	−2.43625	+	3.15095i	−0.101335	+	0.131062i
$579$			4.97819i			0.206887i
$580$		0			0
$581$			55.5177i			2.30326i
$582$	0.535601	+	0.414115i	0.0222014	+	0.0171656i
$583$			11.0023i			0.455667i
$584$	12.9079	−	30.2164i	0.534133	−	1.25036i
$585$		0			0
$586$	4.70151	−	6.08076i	0.194218	−	0.251194i
$587$	−15.6117			−0.644363			−0.322182	−	0.946678i	$-0.604416\pi$
$587$	−15.6117			−0.644363			−0.322182	+	0.946678i	$0.604416\pi$
$588$	−2.48405	−	9.55069i	−0.102441	−	0.393864i
$589$		−	25.7148i		−	1.05956i
$590$		0			0
$591$	5.63244			0.231688
$592$	30.2672	−	16.8868i	1.24397	−	0.694044i
$593$		−	43.2945i		−	1.77789i	−0.458013	−	0.888946i	$-0.651439\pi$
$593$		−	43.2945i		−	1.77789i	0.458013	−	0.888946i	$-0.348561\pi$
$594$	−6.10294	−	4.71866i	−0.250407	−	0.193609i
$595$		0			0
$596$	6.37814	−	1.65890i	0.261259	−	0.0679512i
$597$	−2.22788			−0.0911809
$598$	0.638901	+	0.493985i	0.0261266	+	0.0202005i
$599$	2.30130			0.0940285			0.0470143	−	0.998894i	$-0.485029\pi$
$599$	2.30130			0.0940285			0.0470143	+	0.998894i	$0.485029\pi$
$600$		0			0
$601$	−32.2443			−1.31527			−0.657637	−	0.753335i	$-0.728444\pi$
$601$	−32.2443			−1.31527			−0.657637	+	0.753335i	$0.728444\pi$
$602$	−29.7528	−	23.0042i	−1.21263	−	0.937583i
$603$	31.1806			1.26977
$604$	8.75108	+	33.6462i	0.356076	+	1.36904i
$605$		0			0
$606$	−3.53842	−	2.73583i	−0.143739	−	0.111136i
$607$		−	20.2336i		−	0.821256i	−0.911803	−	0.410628i	$-0.865309\pi$
$607$		−	20.2336i		−	0.821256i	0.911803	−	0.410628i	$-0.134691\pi$
$608$	23.8113	+	3.58080i	0.965677	+	0.145221i
$609$	12.8452			0.520512
$610$		0			0
$611$			1.04023i			0.0420831i
$612$	21.1073	−	5.48984i	0.853213	−	0.221914i
$613$	3.20558			0.129472			0.0647360	−	0.997902i	$-0.479379\pi$
$613$	3.20558			0.129472			0.0647360	+	0.997902i	$0.479379\pi$
$614$	−4.44897	+	5.75413i	−0.179546	+	0.232218i
$615$		0			0
$616$	35.1281	+	15.0061i	1.41535	+	0.604612i
$617$			37.9199i			1.52660i	0.646046	+	0.763298i	$0.276421\pi$
$617$			37.9199i			1.52660i	−0.646046	+	0.763298i	$0.723579\pi$
$618$	0.151165	+	0.116878i	0.00608076	+	0.00470152i
$619$		−	28.9002i		−	1.16160i	−0.814047	−	0.580799i	$-0.802740\pi$
$619$		−	28.9002i		−	1.16160i	0.814047	−	0.580799i	$-0.197260\pi$
$620$		0			0
$621$		−	0.300527i		−	0.0120597i
$622$	−5.46265	+	7.06518i	−0.219032	+	0.283288i
$623$		−	20.4722i		−	0.820200i
$624$	4.08927	−	2.28151i	0.163702	−	0.0913334i
$625$		0			0
$626$	4.93619	+	3.81656i	0.197290	+	0.152540i
$627$	3.93850			0.157288
$628$	−10.7025	−	41.1490i	−0.427077	−	1.64202i
$629$			32.6327i			1.30115i
$630$		0			0
$631$	−4.07798			−0.162342			−0.0811708	−	0.996700i	$-0.525866\pi$
$631$	−4.07798			−0.162342			−0.0811708	+	0.996700i	$0.525866\pi$
$632$	−41.3623	−	17.6692i	−1.64530	−	0.702844i
$633$			0.0102315i			0.000406665i
$634$	−18.7663	+	24.2716i	−0.745305	+	0.963949i
$635$		0			0
$636$	0.625567	+	2.40518i	0.0248054	+	0.0953717i
$637$	−55.2761			−2.19012
$638$	−20.8508	+	26.9677i	−0.825492	+	1.06766i
$639$	−29.6256			−1.17197
$640$		0			0
$641$	45.3395			1.79080			0.895401	−	0.445261i	$-0.146889\pi$
$641$	45.3395			1.79080			0.895401	+	0.445261i	$0.146889\pi$
$642$	0.319578	−	0.413330i	0.0126127	−	0.0163128i
$643$	44.5316			1.75616			0.878078	−	0.478518i	$-0.158826\pi$
$643$	44.5316			1.75616			0.878078	+	0.478518i	$0.158826\pi$
$644$	0.374581	+	1.44019i	0.0147606	+	0.0567514i
$645$		0			0
$646$	−13.8673	+	17.9354i	−0.545601	+	0.705660i
$647$			16.0199i			0.629807i	0.949124	+	0.314904i	$0.101972\pi$
$647$			16.0199i			0.629807i	−0.949124	+	0.314904i	$0.898028\pi$
$648$	20.9915	+	8.96720i	0.824624	+	0.352265i
$649$	12.1648			0.477509
$650$		0			0
$651$		−	9.21457i		−	0.361148i
$652$	3.88508	+	14.9374i	0.152151	+	0.584992i
$653$	18.6061			0.728112			0.364056	−	0.931377i	$-0.381392\pi$
$653$	18.6061			0.728112			0.364056	+	0.931377i	$0.381392\pi$
$654$	5.82650	+	4.50492i	0.227834	+	0.176156i
$655$		0			0
$656$	17.7247	−	9.88905i	0.692033	−	0.386102i
$657$			33.6372i			1.31231i
$658$	−1.17242	+	1.51637i	−0.0457058	+	0.0591142i
$659$			18.2698i			0.711692i	0.934545	+	0.355846i	$0.115807\pi$
$659$			18.2698i			0.711692i	−0.934545	+	0.355846i	$0.884193\pi$
$660$		0			0
$661$		−	15.0955i		−	0.587147i	−0.955936	−	0.293574i	$-0.905155\pi$
$661$		−	15.0955i		−	0.587147i	0.955936	−	0.293574i	$-0.0948446\pi$
$662$	−7.57231	−	5.85475i	−0.294306	−	0.227551i
$663$			4.40887i			0.171226i
$664$	−30.6041	−	13.0735i	−1.18767	−	0.507351i
$665$		0			0
$666$	−21.7028	+	28.0696i	−0.840968	+	1.08768i
$667$	−1.32797			−0.0514191
$668$	12.2772	−	3.19319i	0.475019	−	0.123548i
$669$		−	2.67498i		−	0.103421i
$670$		0			0
$671$	−0.905306			−0.0349489
$672$	8.53249	+	1.28313i	0.329148	+	0.0494980i
$673$			26.0956i			1.00591i	0.864312	+	0.502956i	$0.167754\pi$
$673$			26.0956i			1.00591i	−0.864312	+	0.502956i	$0.832246\pi$
$674$	19.2194	+	14.8600i	0.740303	+	0.572386i
$675$		0			0
$676$	−0.0576429	−	0.221625i	−0.00221704	−	0.00852406i
$677$	40.6451			1.56212			0.781060	−	0.624456i	$-0.214679\pi$
$677$	40.6451			1.56212			0.781060	+	0.624456i	$0.214679\pi$
$678$	−4.60645	−	3.56161i	−0.176910	−	0.136783i
$679$	6.98763			0.268161
$680$		0			0
$681$	−2.48497			−0.0952241
$682$	19.3455	+	14.9575i	0.740776	+	0.572753i
$683$	−38.3590			−1.46777			−0.733883	−	0.679276i	$-0.762294\pi$
$683$	−38.3590			−1.46777			−0.733883	+	0.679276i	$0.762294\pi$
$684$	−23.8564	+	6.20484i	−0.912172	+	0.237248i
$685$		0			0
$686$	−43.6244	−	33.7295i	−1.66559	−	1.28780i
$687$			4.47999i			0.170922i
$688$	19.6874	−	10.9841i	0.750574	−	0.418764i
$689$	13.9204			0.530323
$690$		0			0
$691$			1.88222i			0.0716028i	0.999359	+	0.0358014i	$0.0113984\pi$
$691$			1.88222i			0.0716028i	−0.999359	+	0.0358014i	$0.988602\pi$
$692$	−8.72719	−	33.5543i	−0.331758	−	1.27554i
$693$	−39.1048			−1.48547
$694$	25.9233	−	33.5282i	0.984035	−	1.27271i
$695$		0			0
$696$	−3.02483	+	7.08088i	−0.114656	+	0.268400i
$697$			19.1100i			0.723842i
$698$	−2.95901	−	2.28785i	−0.112000	−	0.0865963i
$699$			3.32869i			0.125902i
$700$		0			0
$701$			14.9150i			0.563331i	0.959513	+	0.281665i	$0.0908868\pi$
$701$			14.9150i			0.563331i	−0.959513	+	0.281665i	$0.909113\pi$
$702$	−5.97018	+	7.72160i	−0.225330	+	0.291433i
$703$		−	36.8829i		−	1.39106i
$704$	−16.5442	+	15.8306i	−0.623532	+	0.596639i
$705$		0			0
$706$	20.4991	+	15.8494i	0.771493	+	0.596502i
$707$	−46.1634			−1.73615
$708$	2.65931	−	0.691665i	0.0999431	−	0.0259944i
$709$		−	29.0982i		−	1.09281i	−0.837522	−	0.546404i	$-0.815996\pi$
$709$		−	29.0982i		−	1.09281i	0.837522	−	0.546404i	$-0.184004\pi$
$710$		0			0
$711$	46.0448			1.72682
$712$	11.2853	+	4.82087i	0.422933	+	0.180670i
$713$			0.952627i			0.0356762i
$714$	−4.96917	+	6.42693i	−0.185966	+	0.240522i
$715$		0			0
$716$	4.47235	−	1.16322i	0.167140	−	0.0434716i
$717$	−3.85356			−0.143914
$718$	−6.66844	+	8.62471i	−0.248864	+	0.321871i
$719$	14.1860			0.529049			0.264525	−	0.964379i	$-0.414785\pi$
$719$	14.1860			0.529049			0.264525	+	0.964379i	$0.414785\pi$
$720$		0			0
$721$	1.97215			0.0734468
$722$	−0.762252	+	0.985868i	−0.0283681	+	0.0366902i
$723$	5.58973			0.207884
$724$	13.8349	−	3.59833i	0.514168	−	0.133731i
$725$		0			0
$726$	0.785078	−	1.01539i	0.0291370	−	0.0376846i
$727$			20.3389i			0.754328i	0.926146	+	0.377164i	$0.123101\pi$
$727$			20.3389i			0.754328i	−0.926146	+	0.377164i	$0.876899\pi$
$728$	18.9861	−	44.4449i	0.703671	−	1.64724i
$729$	−21.5197			−0.797025
$730$		0			0
$731$			21.2261i			0.785074i
$732$	−0.197907	+	0.0514739i	−0.00731485	+	0.00190253i
$733$	−29.7084			−1.09730			−0.548652	−	0.836051i	$-0.684859\pi$
$733$	−29.7084			−1.09730			−0.548652	+	0.836051i	$0.684859\pi$
$734$	28.7903	+	22.2600i	1.06267	+	0.821633i
$735$		0			0
$736$	−0.882112	−	0.132654i	−0.0325151	−	0.00488969i
$737$		−	30.8226i		−	1.13536i
$738$	−12.7093	+	16.4378i	−0.467837	+	0.605083i
$739$		−	7.11077i		−	0.261574i	−0.991410	−	0.130787i	$-0.958250\pi$
$739$		−	7.11077i		−	0.261574i	0.991410	−	0.130787i	$-0.0417504\pi$
$740$		0			0
$741$		−	4.98309i		−	0.183058i
$742$	20.2921	+	15.6894i	0.744946	+	0.575976i
$743$		−	5.09897i		−	0.187063i	−0.995616	−	0.0935316i	$-0.970184\pi$
$743$		−	5.09897i		−	0.187063i	0.995616	−	0.0935316i	$-0.0298156\pi$
$744$	5.07953	+	2.16988i	0.186224	+	0.0795518i
$745$		0			0
$746$	−14.4544	+	18.6948i	−0.529213	+	0.684464i
$747$	34.0687			1.24651
$748$	−5.42680	−	20.8650i	−0.198423	−	0.762899i
$749$		−	5.39244i		−	0.197035i
$750$		0			0
$751$	−3.29049			−0.120072			−0.0600358	−	0.998196i	$-0.519121\pi$
$751$	−3.29049			−0.120072			−0.0600358	+	0.998196i	$0.519121\pi$
$752$	−0.559810	−	1.00338i	−0.0204142	−	0.0365894i
$753$		−	3.39096i		−	0.123573i
$754$	34.1202	+	26.3810i	1.24258	+	0.960740i
$755$		0			0
$756$	−17.4058	+	4.52710i	−0.633042	+	0.164649i
$757$	16.5103			0.600077			0.300038	−	0.953927i	$-0.403001\pi$
$757$	16.5103			0.600077			0.300038	+	0.953927i	$0.403001\pi$
$758$	30.0665	+	23.2468i	1.09207	+	0.844362i
$759$	−0.145905			−0.00529601
$760$		0			0
$761$	−4.13320			−0.149828			−0.0749142	−	0.997190i	$-0.523868\pi$
$761$	−4.13320			−0.149828			−0.0749142	+	0.997190i	$0.523868\pi$
$762$	−1.69015	−	1.30679i	−0.0612277	−	0.0473400i
$763$	76.0144			2.75191
$764$	−5.80392	−	22.3149i	−0.209978	−	0.807325i
$765$		0			0
$766$	30.4117	+	23.5137i	1.09882	+	0.849585i
$767$		−	15.3912i		−	0.555743i
$768$	−2.71659	+	4.40137i	−0.0980265	+	0.158821i
$769$	−47.1093			−1.69880			−0.849402	−	0.527746i	$-0.823037\pi$
$769$	−47.1093			−1.69880			−0.849402	+	0.527746i	$0.823037\pi$
$770$		0			0
$771$		−	7.72917i		−	0.278359i
$772$	−29.8078	+	7.75276i	−1.07281	+	0.279028i
$773$	−51.4583			−1.85083			−0.925414	−	0.378959i	$-0.876282\pi$
$773$	−51.4583			−1.85083			−0.925414	+	0.378959i	$0.876282\pi$
$774$	−14.1167	+	18.2580i	−0.507413	+	0.656269i
$775$		0			0
$776$	−1.64547	+	3.85192i	−0.0590691	+	0.138276i
$777$		−	13.2165i		−	0.474139i
$778$	18.3789	+	14.2101i	0.658914	+	0.509458i
$779$		−	21.5989i		−	0.773860i
$780$		0			0
$781$			29.2854i			1.04792i
$782$	0.513726	−	0.664433i	0.0183708	−	0.0237601i
$783$		−	16.0495i		−	0.573561i
$784$	53.3179	−	29.7474i	1.90421	−	1.06241i
$785$		0			0
$786$	7.75190	+	5.99361i	0.276501	+	0.213785i
$787$	38.4432			1.37035			0.685177	−	0.728377i	$-0.259725\pi$
$787$	38.4432			1.37035			0.685177	+	0.728377i	$0.259725\pi$
$788$	8.77165	+	33.7252i	0.312477	+	1.20141i
$789$		−	0.382604i		−	0.0136211i
$790$		0			0
$791$	−60.0973			−2.13681
$792$	9.20856	−	21.5565i	0.327212	−	0.765978i
$793$			1.14542i			0.0406749i
$794$	−2.38843	+	3.08910i	−0.0847622	+	0.109628i
$795$		0			0
$796$	−3.46957	−	13.3398i	−0.122976	−	0.472817i
$797$	−0.892951			−0.0316299			−0.0158150	−	0.999875i	$-0.505034\pi$
$797$	−0.892951			−0.0316299			−0.0158150	+	0.999875i	$0.505034\pi$
$798$	5.61636	−	7.26398i	0.198817	−	0.257142i
$799$	1.08180			0.0382713
$800$		0			0
$801$	−12.5629			−0.443887
$802$	−8.60001	+	11.1229i	−0.303677	+	0.392764i
$803$	33.2509			1.17340
$804$	−1.75251	−	6.73805i	−0.0618063	−	0.237633i
$805$		0			0
$806$	18.9246	−	24.4764i	0.666591	−	0.862144i
$807$			0.161347i			0.00567968i
$808$	10.8707	−	25.4476i	0.382431	−	0.895242i
$809$	−38.6943			−1.36042			−0.680210	−	0.733018i	$-0.738111\pi$
$809$	−38.6943			−1.36042			−0.680210	+	0.733018i	$0.738111\pi$
$810$		0			0
$811$			39.9633i			1.40330i	0.712521	+	0.701651i	$0.247553\pi$
$811$			39.9633i			1.40330i	−0.712521	+	0.701651i	$0.752447\pi$
$812$	20.0043	+	76.9126i	0.702014	+	2.69910i
$813$	0.373772			0.0131087
$814$	27.7473	+	21.4536i	0.972542	+	0.751949i
$815$		0			0
$816$	−2.37268	−	4.25269i	−0.0830605	−	0.148874i
$817$		−	23.9906i		−	0.839324i
$818$	−14.2588	+	18.4418i	−0.498547	+	0.644801i
$819$			49.4765i			1.72885i
$820$		0			0
$821$			3.13047i			0.109254i	0.998507	+	0.0546272i	$0.0173970\pi$
$821$			3.13047i			0.109254i	−0.998507	+	0.0546272i	$0.982603\pi$
$822$	−3.29789	−	2.54986i	−0.115027	−	0.0889366i
$823$		−	4.54244i		−	0.158339i	−0.996861	−	0.0791697i	$-0.974773\pi$
$823$		−	4.54244i		−	0.158339i	0.996861	−	0.0791697i	$-0.0252269\pi$
$824$	−0.464410	+	1.08715i	−0.0161785	+	0.0378726i
$825$		0			0
$826$	17.3471	−	22.4361i	0.603584	−	0.780653i
$827$	30.1264			1.04760			0.523799	−	0.851842i	$-0.324514\pi$
$827$	30.1264			1.04760			0.523799	+	0.851842i	$0.324514\pi$
$828$	0.883780	−	0.229864i	0.0307135	−	0.00798832i
$829$		−	31.9720i		−	1.11043i	−0.831705	−	0.555217i	$-0.812635\pi$
$829$		−	31.9720i		−	1.11043i	0.831705	−	0.555217i	$-0.187365\pi$
$830$		0			0
$831$	6.26346			0.217277
$832$	20.0293	+	20.9321i	0.694392	+	0.725691i
$833$			57.4851i			1.99174i
$834$	−5.62006	−	4.34531i	−0.194607	−	0.150466i
$835$		0			0
$836$	6.13359	+	23.5824i	0.212135	+	0.815616i
$837$	−11.5132			−0.397955
$838$	−17.1083	−	13.2278i	−0.590997	−	0.456946i
$839$	6.08976			0.210242			0.105121	−	0.994459i	$-0.466477\pi$
$839$	6.08976			0.210242			0.105121	+	0.994459i	$0.466477\pi$
$840$		0			0
$841$	−41.9194			−1.44550
$842$	35.7763	+	27.6615i	1.23293	+	0.953278i
$843$	3.44080			0.118507
$844$	−0.0612628	+	0.0159339i	−0.00210875	+	0.000548469i
$845$		0			0
$846$	0.930527	+	0.719464i	0.0319922	+	0.0247357i
$847$		−	13.2471i		−	0.455176i
$848$	−13.4272	+	7.49139i	−0.461093	+	0.257255i
$849$	−5.46754			−0.187646
$850$		0			0
$851$			1.36636i			0.0468381i
$852$	1.66511	+	6.40203i	0.0570458	+	0.219330i
$853$	18.7518			0.642048			0.321024	−	0.947071i	$-0.395973\pi$
$853$	18.7518			0.642048			0.321024	+	0.947071i	$0.395973\pi$
$854$	−1.29098	+	1.66970i	−0.0441764	+	0.0571361i
$855$		0			0
$856$	2.97258	+	1.26983i	0.101601	+	0.0434020i
$857$		−	3.22352i		−	0.110113i	−0.998483	−	0.0550567i	$-0.982466\pi$
$857$		−	3.22352i		−	0.110113i	0.998483	−	0.0550567i	$-0.0175340\pi$
$858$	3.74882	+	2.89851i	0.127983	+	0.0989534i
$859$			6.35330i			0.216772i	0.994109	+	0.108386i	$0.0345682\pi$
$859$			6.35330i			0.216772i	−0.994109	+	0.108386i	$0.965432\pi$
$860$		0			0
$861$		−	7.73968i		−	0.263768i
$862$	−12.6149	+	16.3157i	−0.429666	+	0.555714i
$863$			24.0344i			0.818139i	0.912503	+	0.409070i	$0.134147\pi$
$863$			24.0344i			0.818139i	−0.912503	+	0.409070i	$0.865853\pi$
$864$	1.60322	−	10.6610i	0.0545427	−	0.362694i
$865$		0			0
$866$	−33.4968	−	25.8990i	−1.13827	−	0.880085i
$867$	−0.910430			−0.0309198
$868$	55.1739	−	14.3503i	1.87272	−	0.487080i
$869$		−	45.5161i		−	1.54403i
$870$		0			0
$871$	−38.9975			−1.32138
$872$	−17.9002	+	41.9029i	−0.606176	+	1.41901i
$873$		−	4.28799i		−	0.145127i
$874$	−0.580634	+	0.750970i	−0.0196402	+	0.0254019i
$875$		0			0
$876$	7.26891	−	1.89058i	0.245594	−	0.0638768i
$877$	−39.9446			−1.34883			−0.674416	−	0.738351i	$-0.735605\pi$
$877$	−39.9446			−1.34883			−0.674416	+	0.738351i	$0.735605\pi$
$878$	−5.09398	+	6.58836i	−0.171913	+	0.222346i
$879$	1.75696			0.0592609
$880$		0			0
$881$	21.8685			0.736767			0.368384	−	0.929674i	$-0.379911\pi$
$881$	21.8685			0.736767			0.368384	+	0.929674i	$0.379911\pi$
$882$	−38.2312	+	49.4468i	−1.28731	+	1.66496i
$883$	−16.1822			−0.544573			−0.272286	−	0.962216i	$-0.587780\pi$
$883$	−16.1822			−0.544573			−0.272286	+	0.962216i	$0.587780\pi$
$884$	−26.3989	+	6.86613i	−0.887891	+	0.230933i
$885$		0			0
$886$	−27.2672	+	35.2664i	−0.916061	+	1.18480i
$887$			49.2517i			1.65371i	0.562416	+	0.826854i	$0.309872\pi$
$887$			49.2517i			1.65371i	−0.562416	+	0.826854i	$0.690128\pi$
$888$	7.28559	+	3.11227i	0.244488	+	0.104441i
$889$	−22.0503			−0.739543
$890$		0			0
$891$			23.0996i			0.773865i
$892$	16.0169	−	4.16587i	0.536287	−	0.139484i
$893$	−1.22269			−0.0409158
$894$	1.19176	+	0.921443i	0.0398584	+	0.0308177i
$895$		0			0
$896$	5.60503	+	53.0881i	0.187251	+	1.77355i
$897$			0.184603i			0.00616370i
$898$	−31.5294	+	40.7789i	−1.05215	+	1.36081i
$899$			50.8746i			1.69676i
$900$		0			0
$901$		−	14.4767i		−	0.482287i
$902$	16.2490	+	12.5634i	0.541033	+	0.418315i
$903$		−	8.59671i		−	0.286081i
$904$	14.1519	−	33.1286i	0.470687	−	1.10184i
$905$		0			0
$906$	−4.86083	+	6.28681i	−0.161490	+	0.208865i
$907$	−18.5720			−0.616674			−0.308337	−	0.951277i	$-0.599772\pi$
$907$	−18.5720			−0.616674			−0.308337	+	0.951277i	$0.599772\pi$
$908$	−3.86995	−	14.8792i	−0.128429	−	0.493783i
$909$			28.3284i			0.939595i
$910$		0			0
$911$	−16.3379			−0.541299			−0.270650	−	0.962678i	$-0.587239\pi$
$911$	−16.3379			−0.541299			−0.270650	+	0.962678i	$0.587239\pi$
$912$	2.68170	+	4.80656i	0.0888001	+	0.159161i
$913$		−	33.6775i		−	1.11456i
$914$	27.5753	+	21.3206i	0.912110	+	0.705224i
$915$		0			0
$916$	−26.8248	+	6.97689i	−0.886315	+	0.230523i
$917$	101.134			3.33974
$918$	8.03018	+	6.20876i	0.265035	+	0.204920i
$919$	−14.4754			−0.477500			−0.238750	−	0.971081i	$-0.576738\pi$
$919$	−14.4754			−0.477500			−0.238750	+	0.971081i	$0.576738\pi$
$920$		0			0
$921$	−1.66259			−0.0547841
$922$	7.36806	+	5.69683i	0.242654	+	0.187615i
$923$	37.0527			1.21960
$924$	2.19789	+	8.45046i	0.0723054	+	0.278000i
$925$		0			0
$926$	3.88630	+	3.00480i	0.127712	+	0.0987440i
$927$		−	1.21022i		−	0.0397489i
$928$	−47.1087	−	7.08432i	−1.54642	−	0.232554i
$929$	−51.1398			−1.67784			−0.838921	−	0.544254i	$-0.816813\pi$
$929$	−51.1398			−1.67784			−0.838921	+	0.544254i	$0.816813\pi$
$930$		0			0
$931$		−	64.9720i		−	2.12937i
$932$	−19.9311	+	5.18391i	−0.652865	+	0.169805i
$933$	−2.04140			−0.0668324
$934$	29.8671	−	38.6290i	0.977283	−	1.26398i
$935$		0			0
$936$	−27.2739	−	11.6509i	−0.891474	−	0.380822i
$937$		−	24.1089i		−	0.787603i	−0.919195	−	0.393802i	$-0.871160\pi$
$937$		−	24.1089i		−	0.787603i	0.919195	−	0.393802i	$-0.128840\pi$
$938$	−56.8477	−	43.9534i	−1.85614	−	1.43513i
$939$			1.42625i			0.0465440i
$940$		0			0
$941$			5.00952i			0.163306i	0.996661	+	0.0816528i	$0.0260199\pi$
$941$			5.00952i			0.163306i	−0.996661	+	0.0816528i	$0.973980\pi$
$942$	5.94475	−	7.68872i	0.193691	−	0.250512i
$943$			0.800149i			0.0260564i
$944$	8.28293	+	14.8459i	0.269586	+	0.483194i
$945$		0			0
$946$	18.0483	+	13.9546i	0.586801	+	0.453702i
$947$	−9.53019			−0.309690			−0.154845	−	0.987939i	$-0.549488\pi$
$947$	−9.53019			−0.309690			−0.154845	+	0.987939i	$0.549488\pi$
$948$	−2.58796	−	9.95017i	−0.0840529	−	0.323167i
$949$		−	42.0699i		−	1.36565i
$950$		0			0
$951$	−7.01299			−0.227412
$952$	−46.2211	−	19.7448i	−1.49803	−	0.639933i
$953$			43.1662i			1.39829i	0.714979	+	0.699146i	$0.246436\pi$
$953$			43.1662i			1.39829i	−0.714979	+	0.699146i	$0.753564\pi$
$954$	9.62789	−	12.4523i	0.311714	−	0.403159i
$955$		0			0
$956$	−6.00133	−	23.0739i	−0.194097	−	0.746263i
$957$	−7.79198			−0.251879
$958$	−31.1787	+	40.3253i	−1.00734	+	1.30285i
$959$	−43.0254			−1.38936
$960$		0			0
$961$	5.49529			0.177268
$962$	27.1437	−	35.1066i	0.875147	−	1.13188i
$963$	−3.30910			−0.106634
$964$	8.70514	+	33.4695i	0.280374	+	1.07798i
$965$		0			0
$966$	−0.208063	+	0.269100i	−0.00669431	+	0.00865816i
$967$			18.4254i			0.592522i	0.955107	+	0.296261i	$0.0957399\pi$
$967$			18.4254i			0.592522i	−0.955107	+	0.296261i	$0.904260\pi$
$968$	7.30246	+	3.11948i	0.234710	+	0.100264i
$969$	−5.18223			−0.166477
$970$		0			0
$971$		−	0.0806617i		−	0.00258856i	−0.999999	−	0.00129428i	$-0.999588\pi$
$971$		−	0.0806617i		−	0.00258856i	0.999999	−	0.00129428i	$-0.000411982\pi$
$972$	4.19173	+	16.1164i	0.134450	+	0.516933i
$973$	−73.3212			−2.35057
$974$	−3.25292	−	2.51509i	−0.104230	−	0.0805887i
$975$		0			0
$976$	−0.616419	−	1.10484i	−0.0197311	−	0.0353651i
$977$			37.0473i			1.18525i	0.805479	+	0.592624i	$0.201908\pi$
$977$			37.0473i			1.18525i	−0.805479	+	0.592624i	$0.798092\pi$
$978$	−2.15798	+	2.79105i	−0.0690047	+	0.0892481i
$979$			12.4186i			0.396900i
$980$		0			0
$981$		−	46.6467i		−	1.48931i
$982$	1.00644	+	0.778161i	0.0321169	+	0.0248321i
$983$		−	55.8530i		−	1.78143i	−0.454559	−	0.890717i	$-0.650203\pi$
$983$		−	55.8530i		−	1.78143i	0.454559	−	0.890717i	$-0.349797\pi$
$984$	4.26649	+	1.82257i	0.136011	+	0.0581014i
$985$		0			0
$986$	27.4353	−	35.4837i	0.873717	−	1.13003i
$987$	−0.438136			−0.0139460
$988$	29.8371	−	7.76038i	0.949245	−	0.246891i
$989$			0.888751i			0.0282607i
$990$		0			0
$991$	44.4145			1.41087			0.705436	−	0.708774i	$-0.250751\pi$
$991$	44.4145			1.41087			0.705436	+	0.708774i	$0.250751\pi$
$992$	−5.08199	+	33.7938i	−0.161353	+	1.07296i
$993$		−	2.18793i		−	0.0694318i
$994$	54.0127	+	41.7615i	1.71318	+	1.32459i
$995$		0			0
$996$	−1.91484	−	7.36217i	−0.0606740	−	0.233279i
$997$	28.6670			0.907895			0.453947	−	0.891029i	$-0.350015\pi$
$997$	28.6670			0.907895			0.453947	+	0.891029i	$0.350015\pi$
$998$	−33.6264	−	25.9992i	−1.06442	−	0.822990i
$999$	−16.5135			−0.522463

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.f.e.749.14		48
4.3	odd	2		4000.2.f.e.3249.27		48
5.2	odd	4		1000.2.d.d.501.11	✓	48
5.3	odd	4		1000.2.d.d.501.38	yes	48
5.4	even	2	inner	1000.2.f.e.749.35		48
8.3	odd	2		4000.2.f.e.3249.21		48
8.5	even	2	inner	1000.2.f.e.749.36		48
20.3	even	4		4000.2.d.d.2001.44		48
20.7	even	4		4000.2.d.d.2001.5		48
20.19	odd	2		4000.2.f.e.3249.22		48
40.3	even	4		4000.2.d.d.2001.43		48
40.13	odd	4		1000.2.d.d.501.37	yes	48
40.19	odd	2		4000.2.f.e.3249.28		48
40.27	even	4		4000.2.d.d.2001.6		48
40.29	even	2	inner	1000.2.f.e.749.13		48
40.37	odd	4		1000.2.d.d.501.12	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1000.2.d.d.501.11	✓	48	5.2	odd	4
1000.2.d.d.501.12	yes	48	40.37	odd	4
1000.2.d.d.501.37	yes	48	40.13	odd	4
1000.2.d.d.501.38	yes	48	5.3	odd	4
1000.2.f.e.749.13		48	40.29	even	2	inner
1000.2.f.e.749.14		48	1.1	even	1	trivial
1000.2.f.e.749.35		48	5.4	even	2	inner
1000.2.f.e.749.36		48	8.5	even	2	inner
4000.2.d.d.2001.5		48	20.7	even	4
4000.2.d.d.2001.6		48	40.27	even	4
4000.2.d.d.2001.43		48	40.3	even	4
4000.2.d.d.2001.44		48	20.3	even	4
4000.2.f.e.3249.21		48	8.3	odd	2
4000.2.f.e.3249.22		48	20.19	odd	2
4000.2.f.e.3249.27		48	4.3	odd	2
4000.2.f.e.3249.28		48	40.19	odd	2

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:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.865034 + 1.11880i) q^{2} -0.323264 q^{3} +(-0.503434 - 1.93560i) q^{4} +(0.279634 - 0.361668i) q^{6} -4.71845i q^{7} +(2.60104 + 1.11112i) q^{8} -2.89550 q^{9} +O(q^{10})\)	\(q+(-0.865034 + 1.11880i) q^{2} -0.323264 q^{3} +(-0.503434 - 1.93560i) q^{4} +(0.279634 - 0.361668i) q^{6} -4.71845i q^{7} +(2.60104 + 1.11112i) q^{8} -2.89550 q^{9} +2.86225i q^{11} +(0.162742 + 0.625711i) q^{12} +3.62139 q^{13} +(5.27901 + 4.08162i) q^{14} +(-3.49311 + 1.94889i) q^{16} -3.76612i q^{17} +(2.50471 - 3.23949i) q^{18} +4.25662i q^{19} +1.52531i q^{21} +(-3.20229 - 2.47594i) q^{22} -0.157690i q^{23} +(-0.840823 - 0.359185i) q^{24} +(-3.13263 + 4.05162i) q^{26} +1.90580 q^{27} +(-9.13304 + 2.37543i) q^{28} -8.42137i q^{29} -6.04113 q^{31} +(0.841231 - 5.59395i) q^{32} -0.925263i q^{33} +(4.21354 + 3.25782i) q^{34} +(1.45769 + 5.60454i) q^{36} -8.66483 q^{37} +(-4.76231 - 3.68212i) q^{38} -1.17067 q^{39} -5.07418 q^{41} +(-1.70651 - 1.31944i) q^{42} -5.63606 q^{43} +(5.54018 - 1.44095i) q^{44} +(0.176424 + 0.136407i) q^{46} +0.287245i q^{47} +(1.12920 - 0.630008i) q^{48} -15.2638 q^{49} +1.21745i q^{51} +(-1.82313 - 7.00958i) q^{52} +3.84392 q^{53} +(-1.64858 + 2.13222i) q^{54} +(5.24275 - 12.2729i) q^{56} -1.37601i q^{57} +(9.42184 + 7.28476i) q^{58} -4.25007i q^{59} +0.316291i q^{61} +(5.22578 - 6.75883i) q^{62} +13.6623i q^{63} +(5.53083 + 5.78013i) q^{64} +(1.03519 + 0.800384i) q^{66} -10.7686 q^{67} +(-7.28970 + 1.89599i) q^{68} +0.0509756i q^{69} +10.2316 q^{71} +(-7.53132 - 3.21724i) q^{72} -11.6170i q^{73} +(7.49537 - 9.69422i) q^{74} +(8.23912 - 2.14293i) q^{76} +13.5054 q^{77} +(1.01267 - 1.30974i) q^{78} -15.9022 q^{79} +8.07042 q^{81} +(4.38934 - 5.67701i) q^{82} -11.7661 q^{83} +(2.95238 - 0.767890i) q^{84} +(4.87538 - 6.30563i) q^{86} +2.72233i q^{87} +(-3.18030 + 7.44483i) q^{88} +4.33875 q^{89} -17.0874i q^{91} +(-0.305225 + 0.0793865i) q^{92} +1.95288 q^{93} +(-0.321370 - 0.248477i) q^{94} +(-0.271940 + 1.80833i) q^{96} +1.48092i q^{97} +(13.2037 - 17.0771i) q^{98} -8.28765i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{4} - 4 q^{6} + 48 q^{9}+O(q^{10}) \) 48 * q + 4 * q^4 - 4 * q^6 + 48 * q^9	\( 48 q + 4 q^{4} - 4 q^{6} + 48 q^{9} + 12 q^{14} + 16 q^{16} + 20 q^{24} - 12 q^{26} - 16 q^{31} + 40 q^{36} + 12 q^{44} - 12 q^{46} - 48 q^{49} - 68 q^{54} + 8 q^{56} + 28 q^{64} - 88 q^{66} - 48 q^{71} - 20 q^{74} + 24 q^{76} - 16 q^{79} + 72 q^{81} - 28 q^{84} - 96 q^{86} + 24 q^{89} - 32 q^{94} - 40 q^{96}+O(q^{100}) \) 48 * q + 4 * q^4 - 4 * q^6 + 48 * q^9 + 12 * q^14 + 16 * q^16 + 20 * q^24 - 12 * q^26 - 16 * q^31 + 40 * q^36 + 12 * q^44 - 12 * q^46 - 48 * q^49 - 68 * q^54 + 8 * q^56 + 28 * q^64 - 88 * q^66 - 48 * q^71 - 20 * q^74 + 24 * q^76 - 16 * q^79 + 72 * q^81 - 28 * q^84 - 96 * q^86 + 24 * q^89 - 32 * q^94 - 40 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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