LMFDB - Embedded newform 1000.2.q.a.649.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1000,2,Mod(49,1000)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1000, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

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

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

chi := DirichletCharacter("1000.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.q (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			649.2
Root			$-0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	1000.649
Dual form			1000.2.q.a.849.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.31433 - 1.80902i) q^{3} +2.61803i q^{7} +(-0.618034 - 1.90211i) q^{9} +O(q^{10})$	\(q+(1.31433 - 1.80902i) q^{3} +2.61803i q^{7} +(-0.618034 - 1.90211i) q^{9} +(0.381966 - 1.17557i) q^{11} +(3.21644 - 1.04508i) q^{13} +(-3.07768 - 4.23607i) q^{17} +(6.16312 - 4.47777i) q^{19} +(4.73607 + 3.44095i) q^{21} +(-5.20431 - 1.69098i) q^{23} +(2.12663 + 0.690983i) q^{27} +(3.54508 + 2.57565i) q^{29} +(3.80902 - 2.76741i) q^{31} +(-1.62460 - 2.23607i) q^{33} +(7.83297 - 2.54508i) q^{37} +(2.33688 - 7.19218i) q^{39} +(1.76393 + 5.42882i) q^{41} -4.38197i q^{43} +(0.0857567 - 0.118034i) q^{47} +0.145898 q^{49} -11.7082 q^{51} +(-4.66953 + 6.42705i) q^{53} -17.0344i q^{57} +(-0.736068 - 2.26538i) q^{59} +(-4.07295 + 12.5352i) q^{61} +(4.97980 - 1.61803i) q^{63} +(-8.05748 - 11.0902i) q^{67} +(-9.89919 + 7.19218i) q^{69} +(6.97214 + 5.06555i) q^{71} +(-10.4616 - 3.39919i) q^{73} +(3.07768 + 1.00000i) q^{77} +(-4.30902 - 3.13068i) q^{79} +(8.89919 - 6.46564i) q^{81} +(-2.66141 - 3.66312i) q^{83} +(9.31881 - 3.02786i) q^{87} +(-1.23607 + 3.80423i) q^{89} +(2.73607 + 8.42075i) q^{91} -10.5279i q^{93} +(-8.97578 + 12.3541i) q^{97} -2.47214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^9	$ 8 q + 4 q^{9} + 12 q^{11} + 18 q^{19} + 20 q^{21} + 6 q^{29} + 26 q^{31} + 50 q^{39} + 32 q^{41} + 28 q^{49} - 40 q^{51} + 12 q^{59} - 46 q^{61} - 30 q^{69} + 20 q^{71} - 30 q^{79} + 22 q^{81} + 8 q^{89} + 4 q^{91} + 16 q^{99}+O(q^{100}) $ 8 * q + 4 * q^9 + 12 * q^11 + 18 * q^19 + 20 * q^21 + 6 * q^29 + 26 * q^31 + 50 * q^39 + 32 * q^41 + 28 * q^49 - 40 * q^51 + 12 * q^59 - 46 * q^61 - 30 * q^69 + 20 * q^71 - 30 * q^79 + 22 * q^81 + 8 * q^89 + 4 * q^91 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	1.31433	−	1.80902i	0.758827	−	1.04444i	−0.238483	−	0.971147i	$-0.576650\pi$
$3$	1.31433	−	1.80902i	0.758827	−	1.04444i	0.997311	−	0.0732898i	$-0.0233498\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$			2.61803i			0.989524i	0.869029	+	0.494762i	$0.164745\pi$
$7$			2.61803i			0.989524i	−0.869029	+	0.494762i	$0.835255\pi$
$8$		0			0
$9$	−0.618034	−	1.90211i	−0.206011	−	0.634038i
$10$		0			0
$11$	0.381966	−	1.17557i	0.115167	−	0.354448i	−0.876815	−	0.480828i	$-0.840336\pi$
$11$	0.381966	−	1.17557i	0.115167	−	0.354448i	0.991982	+	0.126380i	$0.0403360\pi$
$12$		0			0
$13$	3.21644	−	1.04508i	0.892080	−	0.289854i	0.173116	−	0.984901i	$-0.444616\pi$
$13$	3.21644	−	1.04508i	0.892080	−	0.289854i	0.718964	+	0.695047i	$0.244616\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.07768	−	4.23607i	−0.746448	−	1.02740i	−0.998222	−	0.0596113i	$-0.981014\pi$
$17$	−3.07768	−	4.23607i	−0.746448	−	1.02740i	0.251774	−	0.967786i	$-0.418986\pi$
$18$		0			0
$19$	6.16312	−	4.47777i	1.41392	−	1.02727i	0.421178	−	0.906978i	$-0.361617\pi$
$19$	6.16312	−	4.47777i	1.41392	−	1.02727i	0.992739	−	0.120292i	$-0.0383832\pi$
$20$		0			0
$21$	4.73607	+	3.44095i	1.03349	+	0.750878i
$22$		0			0
$23$	−5.20431	−	1.69098i	−1.08517	−	0.352594i	−0.288794	−	0.957391i	$-0.593254\pi$
$23$	−5.20431	−	1.69098i	−1.08517	−	0.352594i	−0.796380	+	0.604797i	$0.793254\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	2.12663	+	0.690983i	0.409270	+	0.132980i
$28$		0			0
$29$	3.54508	+	2.57565i	0.658306	+	0.478287i	0.866090	−	0.499887i	$-0.166625\pi$
$29$	3.54508	+	2.57565i	0.658306	+	0.478287i	−0.207785	+	0.978175i	$0.566625\pi$
$30$		0			0
$31$	3.80902	−	2.76741i	0.684120	−	0.497042i	−0.190602	−	0.981667i	$-0.561044\pi$
$31$	3.80902	−	2.76741i	0.684120	−	0.497042i	0.874722	+	0.484625i	$0.161044\pi$
$32$		0			0
$33$	−1.62460	−	2.23607i	−0.282806	−	0.389249i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	7.83297	−	2.54508i	1.28773	−	0.418409i	0.416435	−	0.909166i	$-0.363279\pi$
$37$	7.83297	−	2.54508i	1.28773	−	0.418409i	0.871297	+	0.490756i	$0.163279\pi$
$38$		0			0
$39$	2.33688	−	7.19218i	0.374200	−	1.15167i
$40$		0			0
$41$	1.76393	+	5.42882i	0.275480	+	0.847840i	0.989092	+	0.147299i	$0.0470579\pi$
$41$	1.76393	+	5.42882i	0.275480	+	0.847840i	−0.713612	+	0.700541i	$0.752942\pi$
$42$		0			0
$43$		−	4.38197i		−	0.668244i	−0.942530	−	0.334122i	$-0.891560\pi$
$43$		−	4.38197i		−	0.668244i	0.942530	−	0.334122i	$-0.108440\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.0857567	−	0.118034i	0.0125089	−	0.0172170i	−0.802717	−	0.596360i	$-0.796613\pi$
$47$	0.0857567	−	0.118034i	0.0125089	−	0.0172170i	0.815226	+	0.579143i	$0.196613\pi$
$48$		0			0
$49$	0.145898			0.0208426
$50$		0			0
$51$	−11.7082			−1.63948
$52$		0			0
$53$	−4.66953	+	6.42705i	−0.641409	+	0.882823i	−0.998690	−	0.0511736i	$-0.983704\pi$
$53$	−4.66953	+	6.42705i	−0.641409	+	0.882823i	0.357281	+	0.933997i	$0.383704\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	17.0344i		−	2.25627i
$58$		0			0
$59$	−0.736068	−	2.26538i	−0.0958279	−	0.294928i	0.891641	−	0.452744i	$-0.149555\pi$
$59$	−0.736068	−	2.26538i	−0.0958279	−	0.294928i	−0.987469	+	0.157816i	$0.949555\pi$
$60$		0			0
$61$	−4.07295	+	12.5352i	−0.521488	+	1.60497i	0.249671	+	0.968331i	$0.419678\pi$
$61$	−4.07295	+	12.5352i	−0.521488	+	1.60497i	−0.771158	+	0.636643i	$0.780322\pi$
$62$		0			0
$63$	4.97980	−	1.61803i	0.627395	−	0.203853i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−8.05748	−	11.0902i	−0.984378	−	1.35488i	−0.934437	−	0.356128i	$-0.884097\pi$
$67$	−8.05748	−	11.0902i	−0.984378	−	1.35488i	−0.0499406	−	0.998752i	$-0.515903\pi$
$68$		0			0
$69$	−9.89919	+	7.19218i	−1.19172	+	0.865837i
$70$		0			0
$71$	6.97214	+	5.06555i	0.827440	+	0.601171i	0.918834	−	0.394644i	$-0.129132\pi$
$71$	6.97214	+	5.06555i	0.827440	+	0.601171i	−0.0913937	+	0.995815i	$0.529132\pi$
$72$		0			0
$73$	−10.4616	−	3.39919i	−1.22444	−	0.397845i	−0.375743	−	0.926724i	$-0.622612\pi$
$73$	−10.4616	−	3.39919i	−1.22444	−	0.397845i	−0.848697	+	0.528879i	$0.822612\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.07768	+	1.00000i	0.350735	+	0.113961i
$78$		0			0
$79$	−4.30902	−	3.13068i	−0.484802	−	0.352229i	0.318380	−	0.947963i	$-0.396861\pi$
$79$	−4.30902	−	3.13068i	−0.484802	−	0.352229i	−0.803182	+	0.595734i	$0.796861\pi$
$80$		0			0
$81$	8.89919	−	6.46564i	0.988799	−	0.718404i
$82$		0			0
$83$	−2.66141	−	3.66312i	−0.292128	−	0.402080i	0.637576	−	0.770387i	$-0.279937\pi$
$83$	−2.66141	−	3.66312i	−0.292128	−	0.402080i	−0.929704	+	0.368308i	$0.879937\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	9.31881	−	3.02786i	0.999081	−	0.324621i
$88$		0			0
$89$	−1.23607	+	3.80423i	−0.131023	+	0.403247i	−0.994950	−	0.100369i	$-0.967998\pi$
$89$	−1.23607	+	3.80423i	−0.131023	+	0.403247i	0.863927	+	0.503617i	$0.167998\pi$
$90$		0			0
$91$	2.73607	+	8.42075i	0.286818	+	0.882735i
$92$		0			0
$93$		−	10.5279i		−	1.09169i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−8.97578	+	12.3541i	−0.911352	+	1.25437i	0.0553503	+	0.998467i	$0.482372\pi$
$97$	−8.97578	+	12.3541i	−0.911352	+	1.25437i	−0.966703	+	0.255902i	$0.917628\pi$
$98$		0			0
$99$	−2.47214			−0.248459
$100$		0			0
$101$	−17.9443			−1.78552			−0.892761	−	0.450531i	$-0.851235\pi$
$101$	−17.9443			−1.78552			−0.892761	+	0.450531i	$0.851235\pi$
$102$		0			0
$103$	1.84911	−	2.54508i	0.182198	−	0.250775i	−0.708142	−	0.706070i	$-0.750466\pi$
$103$	1.84911	−	2.54508i	0.182198	−	0.250775i	0.890340	+	0.455295i	$0.150466\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			16.7082i			1.61524i	0.589701	+	0.807622i	$0.299246\pi$
$107$			16.7082i			1.61524i	−0.589701	+	0.807622i	$0.700754\pi$
$108$		0			0
$109$	−0.909830	−	2.80017i	−0.0871459	−	0.268208i	0.897981	−	0.440033i	$-0.145033\pi$
$109$	−0.909830	−	2.80017i	−0.0871459	−	0.268208i	−0.985127	+	0.171826i	$0.945033\pi$
$110$		0			0
$111$	5.69098	−	17.5150i	0.540164	−	1.66245i
$112$		0			0
$113$	−10.0453	+	3.26393i	−0.944987	+	0.307045i	−0.740677	−	0.671861i	$-0.765495\pi$
$113$	−10.0453	+	3.26393i	−0.944987	+	0.307045i	−0.204310	+	0.978906i	$0.565495\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−3.97574	−	5.47214i	−0.367557	−	0.505899i
$118$		0			0
$119$	11.0902	−	8.05748i	1.01663	−	0.738628i
$120$		0			0
$121$	7.66312	+	5.56758i	0.696647	+	0.506144i
$122$		0			0
$123$	12.1392	+	3.94427i	1.09456	+	0.355643i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	7.15942	+	2.32624i	0.635296	+	0.206420i	0.608920	−	0.793232i	$-0.291603\pi$
$127$	7.15942	+	2.32624i	0.635296	+	0.206420i	0.0263764	+	0.999652i	$0.491603\pi$
$128$		0			0
$129$	−7.92705	−	5.75934i	−0.697938	−	0.507082i
$130$		0			0
$131$	0.881966	−	0.640786i	0.0770577	−	0.0559857i	−0.548589	−	0.836092i	$-0.684835\pi$
$131$	0.881966	−	0.640786i	0.0770577	−	0.0559857i	0.625647	+	0.780106i	$0.284835\pi$
$132$		0			0
$133$	11.7229	+	16.1353i	1.01651	+	1.39910i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.75528	+	1.54508i	−0.406271	+	0.132006i	−0.505022	−	0.863107i	$-0.668515\pi$
$137$	−4.75528	+	1.54508i	−0.406271	+	0.132006i	0.0987504	+	0.995112i	$0.468515\pi$
$138$		0			0
$139$	−3.01722	+	9.28605i	−0.255917	+	0.787633i	0.737730	+	0.675096i	$0.235898\pi$
$139$	−3.01722	+	9.28605i	−0.255917	+	0.787633i	−0.993648	+	0.112537i	$0.964102\pi$
$140$		0			0
$141$	−0.100813	−	0.310271i	−0.00848999	−	0.0261295i
$142$		0			0
$143$		−	4.18034i		−	0.349578i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	0.191758	−	0.263932i	0.0158159	−	0.0217687i
$148$		0			0
$149$	18.4164			1.50873			0.754365	−	0.656455i	$-0.227945\pi$
$149$	18.4164			1.50873			0.754365	+	0.656455i	$0.227945\pi$
$150$		0			0
$151$	0.381966			0.0310840			0.0155420	−	0.999879i	$-0.495053\pi$
$151$	0.381966			0.0310840			0.0155420	+	0.999879i	$0.495053\pi$
$152$		0			0
$153$	−6.15537	+	8.47214i	−0.497632	+	0.684932i
$154$		0			0
$155$		0			0
$156$		0			0
$157$			4.23607i			0.338075i	0.985610	+	0.169038i	$0.0540659\pi$
$157$			4.23607i			0.338075i	−0.985610	+	0.169038i	$0.945934\pi$
$158$		0			0
$159$	5.48936	+	16.8945i	0.435334	+	1.33982i
$160$		0			0
$161$	4.42705	−	13.6251i	0.348900	−	1.07381i
$162$		0			0
$163$	14.4374	−	4.69098i	1.13082	−	0.367426i	0.316933	−	0.948448i	$-0.397347\pi$
$163$	14.4374	−	4.69098i	1.13082	−	0.367426i	0.813888	+	0.581022i	$0.197347\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	11.1882	+	15.3992i	0.865766	+	1.19162i	0.980164	+	0.198190i	$0.0635062\pi$
$167$	11.1882	+	15.3992i	0.865766	+	1.19162i	−0.114398	+	0.993435i	$0.536494\pi$
$168$		0			0
$169$	−1.26393	+	0.918300i	−0.0972255	+	0.0706385i
$170$		0			0
$171$	−12.3262	−	8.95554i	−0.942611	−	0.684847i
$172$		0			0
$173$	−6.20837	−	2.01722i	−0.472013	−	0.153366i	0.0633445	−	0.997992i	$-0.479823\pi$
$173$	−6.20837	−	2.01722i	−0.472013	−	0.153366i	−0.535358	+	0.844625i	$0.679823\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−5.06555	−	1.64590i	−0.380750	−	0.123713i
$178$		0			0
$179$	2.66312	+	1.93487i	0.199051	+	0.144619i	0.682846	−	0.730562i	$-0.260742\pi$
$179$	2.66312	+	1.93487i	0.199051	+	0.144619i	−0.483795	+	0.875181i	$0.660742\pi$
$180$		0			0
$181$	6.70820	−	4.87380i	0.498617	−	0.362266i	−0.309872	−	0.950778i	$-0.600286\pi$
$181$	6.70820	−	4.87380i	0.498617	−	0.362266i	0.808488	+	0.588512i	$0.200286\pi$
$182$		0			0
$183$	17.3233	+	23.8435i	1.28057	+	1.76256i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−6.15537	+	2.00000i	−0.450125	+	0.146254i
$188$		0			0
$189$	−1.80902	+	5.56758i	−0.131587	+	0.404982i
$190$		0			0
$191$	−0.0901699	−	0.277515i	−0.00652447	−	0.0200802i	0.947741	−	0.319040i	$-0.103360\pi$
$191$	−0.0901699	−	0.277515i	−0.00652447	−	0.0200802i	−0.954266	+	0.298960i	$0.903360\pi$
$192$		0			0
$193$			7.70820i			0.554849i	0.960747	+	0.277424i	$0.0894808\pi$
$193$			7.70820i			0.554849i	−0.960747	+	0.277424i	$0.910519\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−8.67802	+	11.9443i	−0.618283	+	0.850994i	−0.997227	−	0.0744258i	$-0.976288\pi$
$197$	−8.67802	+	11.9443i	−0.618283	+	0.850994i	0.378943	+	0.925420i	$0.376288\pi$
$198$		0			0
$199$	−9.38197			−0.665070			−0.332535	−	0.943091i	$-0.607904\pi$
$199$	−9.38197			−0.665070			−0.332535	+	0.943091i	$0.607904\pi$
$200$		0			0
$201$	−30.6525			−2.16206
$202$		0			0
$203$	−6.74315	+	9.28115i	−0.473277	+	0.651409i
$204$		0			0
$205$		0			0
$206$		0			0
$207$			10.9443i			0.760679i
$208$		0			0
$209$	−2.90983	−	8.95554i	−0.201277	−	0.619467i
$210$		0			0
$211$	6.16312	−	18.9681i	0.424287	−	1.30582i	−0.479389	−	0.877602i	$-0.659142\pi$
$211$	6.16312	−	18.9681i	0.424287	−	1.30582i	0.903676	−	0.428217i	$-0.140858\pi$
$212$		0			0
$213$	18.3273	−	5.95492i	1.25577	−	0.408024i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	7.24518	+	9.97214i	0.491835	+	0.676953i
$218$		0			0
$219$	−19.8992	+	14.4576i	−1.34466	+	0.976954i
$220$		0			0
$221$	−14.3262	−	10.4086i	−0.963687	−	0.700160i
$222$		0			0
$223$	−5.42882	−	1.76393i	−0.363541	−	0.118122i	0.121550	−	0.992585i	$-0.461214\pi$
$223$	−5.42882	−	1.76393i	−0.363541	−	0.118122i	−0.485091	+	0.874464i	$0.661214\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−24.3440	−	7.90983i	−1.61576	−	0.524994i	−0.644828	−	0.764328i	$-0.723071\pi$
$227$	−24.3440	−	7.90983i	−1.61576	−	0.524994i	−0.970937	+	0.239334i	$0.923071\pi$
$228$		0			0
$229$	16.3262	+	11.8617i	1.07887	+	0.783844i	0.977485	−	0.211004i	$-0.0676733\pi$
$229$	16.3262	+	11.8617i	1.07887	+	0.783844i	0.101383	+	0.994847i	$0.467673\pi$
$230$		0			0
$231$	5.85410	−	4.25325i	0.385172	−	0.279844i
$232$		0			0
$233$	3.52671	+	4.85410i	0.231043	+	0.318003i	0.908760	−	0.417320i	$-0.137031\pi$
$233$	3.52671	+	4.85410i	0.231043	+	0.318003i	−0.677717	+	0.735323i	$0.737031\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−11.3269	+	3.68034i	−0.735763	+	0.239064i
$238$		0			0
$239$	6.87132	−	21.1478i	0.444469	−	1.36793i	−0.438596	−	0.898684i	$-0.644524\pi$
$239$	6.87132	−	21.1478i	0.444469	−	1.36793i	0.883065	−	0.469250i	$-0.155476\pi$
$240$		0			0
$241$	3.54508	+	10.9106i	0.228359	+	0.702817i	0.997933	+	0.0642594i	$0.0204685\pi$
$241$	3.54508	+	10.9106i	0.228359	+	0.702817i	−0.769574	+	0.638557i	$0.779532\pi$
$242$		0			0
$243$		−	17.8885i		−	1.14755i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	15.1437	−	20.8435i	0.963568	−	1.32624i
$248$		0			0
$249$	−10.1246			−0.641621
$250$		0			0
$251$	−8.05573			−0.508473			−0.254237	−	0.967142i	$-0.581824\pi$
$251$	−8.05573			−0.508473			−0.254237	+	0.967142i	$0.581824\pi$
$252$		0			0
$253$	−3.97574	+	5.47214i	−0.249953	+	0.344030i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	3.61803i		−	0.225687i	−0.993613	−	0.112843i	$-0.964004\pi$
$257$		−	3.61803i		−	0.225687i	0.993613	−	0.112843i	$-0.0359958\pi$
$258$		0			0
$259$	6.66312	+	20.5070i	0.414026	+	1.27424i
$260$		0			0
$261$	2.70820	−	8.33499i	0.167634	−	0.515923i
$262$		0			0
$263$	−13.1760	+	4.28115i	−0.812469	+	0.263987i	−0.685643	−	0.727938i	$-0.740479\pi$
$263$	−13.1760	+	4.28115i	−0.812469	+	0.263987i	−0.126826	+	0.991925i	$0.540479\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	5.25731	+	7.23607i	0.321742	+	0.442840i
$268$		0			0
$269$	−11.5623	+	8.40051i	−0.704966	+	0.512188i	−0.881546	−	0.472098i	$-0.843497\pi$
$269$	−11.5623	+	8.40051i	−0.704966	+	0.512188i	0.176580	+	0.984286i	$0.443497\pi$
$270$		0			0
$271$	−10.4721	−	7.60845i	−0.636137	−	0.462181i	0.222384	−	0.974959i	$-0.428616\pi$
$271$	−10.4721	−	7.60845i	−0.636137	−	0.462181i	−0.858521	+	0.512779i	$0.828616\pi$
$272$		0			0
$273$	18.8294	+	6.11803i	1.13961	+	0.370280i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	20.1437	+	6.54508i	1.21032	+	0.393256i	0.843547	−	0.537055i	$-0.180463\pi$
$277$	20.1437	+	6.54508i	1.21032	+	0.393256i	0.366771	+	0.930311i	$0.380463\pi$
$278$		0			0
$279$	−7.61803	−	5.53483i	−0.456080	−	0.331361i
$280$		0			0
$281$	−7.39919	+	5.37582i	−0.441398	+	0.320695i	−0.786190	−	0.617984i	$-0.787949\pi$
$281$	−7.39919	+	5.37582i	−0.441398	+	0.320695i	0.344792	+	0.938679i	$0.387949\pi$
$282$		0			0
$283$	−4.27350	−	5.88197i	−0.254033	−	0.349647i	0.662886	−	0.748721i	$-0.269332\pi$
$283$	−4.27350	−	5.88197i	−0.254033	−	0.349647i	−0.916919	+	0.399074i	$0.869332\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−14.2128	+	4.61803i	−0.838958	+	0.272594i
$288$		0			0
$289$	−3.21885	+	9.90659i	−0.189344	+	0.582741i
$290$		0			0
$291$	10.5517	+	32.4747i	0.618549	+	1.90370i
$292$		0			0
$293$		−	0.472136i		−	0.0275825i	−0.999905	−	0.0137912i	$-0.995610\pi$
$293$		−	0.472136i		−	0.0275825i	0.999905	−	0.0137912i	$-0.00439003\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	1.62460	−	2.23607i	0.0942688	−	0.129750i
$298$		0			0
$299$	−18.5066			−1.07026
$300$		0			0
$301$	11.4721			0.661243
$302$		0			0
$303$	−23.5847	+	32.4615i	−1.35490	+	1.86486i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			10.7639i			0.614330i	0.951656	+	0.307165i	$0.0993804\pi$
$307$			10.7639i			0.614330i	−0.951656	+	0.307165i	$0.900620\pi$
$308$		0			0
$309$	−2.17376	−	6.69015i	−0.123661	−	0.380589i
$310$		0			0
$311$	−1.51722	+	4.66953i	−0.0860337	+	0.264785i	−0.984813	−	0.173616i	$-0.944455\pi$
$311$	−1.51722	+	4.66953i	−0.0860337	+	0.264785i	0.898780	+	0.438401i	$0.144455\pi$
$312$		0			0
$313$	5.42882	−	1.76393i	0.306855	−	0.0997033i	−0.151542	−	0.988451i	$-0.548424\pi$
$313$	5.42882	−	1.76393i	0.306855	−	0.0997033i	0.458397	+	0.888748i	$0.348424\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	8.36775	+	11.5172i	0.469980	+	0.646872i	0.976541	−	0.215333i	$-0.0690835\pi$
$317$	8.36775	+	11.5172i	0.469980	+	0.646872i	−0.506561	+	0.862204i	$0.669084\pi$
$318$		0			0
$319$	4.38197	−	3.18368i	0.245343	−	0.178252i
$320$		0			0
$321$	30.2254	+	21.9601i	1.68702	+	1.22569i
$322$		0			0
$323$	−37.9363	−	12.3262i	−2.11083	−	0.685850i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−6.26137	−	2.03444i	−0.346254	−	0.112505i
$328$		0			0
$329$	0.309017	+	0.224514i	0.0170367	+	0.0123779i
$330$		0			0
$331$	−25.9443	+	18.8496i	−1.42603	+	1.03607i	−0.435287	+	0.900292i	$0.643353\pi$
$331$	−25.9443	+	18.8496i	−1.42603	+	1.03607i	−0.990739	+	0.135777i	$0.956647\pi$
$332$		0			0
$333$	−9.68208	−	13.3262i	−0.530575	−	0.730273i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	8.64527	−	2.80902i	0.470938	−	0.153017i	−0.0639272	−	0.997955i	$-0.520363\pi$
$337$	8.64527	−	2.80902i	0.470938	−	0.153017i	0.534865	+	0.844938i	$0.320363\pi$
$338$		0			0
$339$	−7.29837	+	22.4621i	−0.396393	+	1.21997i
$340$		0			0
$341$	−1.79837	−	5.53483i	−0.0973874	−	0.299728i
$342$		0			0
$343$			18.7082i			1.01015i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.02874	−	5.54508i	0.216274	−	0.297676i	−0.687071	−	0.726590i	$-0.741104\pi$
$347$	4.02874	−	5.54508i	0.216274	−	0.297676i	0.903345	+	0.428915i	$0.141104\pi$
$348$		0			0
$349$	−25.1246			−1.34489			−0.672445	−	0.740147i	$-0.734756\pi$
$349$	−25.1246			−1.34489			−0.672445	+	0.740147i	$0.734756\pi$
$350$		0			0
$351$	7.56231			0.403646
$352$		0			0
$353$	17.3763	−	23.9164i	0.924846	−	1.27294i	−0.0369896	−	0.999316i	$-0.511777\pi$
$353$	17.3763	−	23.9164i	0.924846	−	1.27294i	0.961836	−	0.273626i	$-0.0882232\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		−	30.6525i		−	1.62230i
$358$		0			0
$359$	−7.80902	−	24.0337i	−0.412144	−	1.26845i	−0.914780	−	0.403951i	$-0.867637\pi$
$359$	−7.80902	−	24.0337i	−0.412144	−	1.26845i	0.502636	−	0.864498i	$-0.332363\pi$
$360$		0			0
$361$	12.0623	−	37.1240i	0.634858	−	1.95389i
$362$		0			0
$363$	20.1437	−	6.54508i	1.05727	−	0.343528i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−11.3269	−	15.5902i	−0.591260	−	0.813800i	0.403613	−	0.914930i	$-0.367754\pi$
$367$	−11.3269	−	15.5902i	−0.591260	−	0.813800i	−0.994873	+	0.101130i	$0.967754\pi$
$368$		0			0
$369$	9.23607	−	6.71040i	0.480810	−	0.349329i
$370$		0			0
$371$	−16.8262	−	12.2250i	−0.873575	−	0.634689i
$372$		0			0
$373$	−15.3027	−	4.97214i	−0.792342	−	0.257447i	−0.115241	−	0.993338i	$-0.536764\pi$
$373$	−15.3027	−	4.97214i	−0.792342	−	0.257447i	−0.677101	+	0.735890i	$0.736764\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	14.0943	+	4.57953i	0.725895	+	0.235858i
$378$		0			0
$379$	−4.04508	−	2.93893i	−0.207782	−	0.150963i	0.479028	−	0.877800i	$-0.340989\pi$
$379$	−4.04508	−	2.93893i	−0.207782	−	0.150963i	−0.686810	+	0.726837i	$0.740989\pi$
$380$		0			0
$381$	13.6180	−	9.89408i	0.697673	−	0.506889i
$382$		0			0
$383$	8.09024	+	11.1353i	0.413392	+	0.568985i	0.964042	−	0.265751i	$-0.0856200\pi$
$383$	8.09024	+	11.1353i	0.413392	+	0.568985i	−0.550650	+	0.834736i	$0.685620\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−8.33499	+	2.70820i	−0.423692	+	0.137666i
$388$		0			0
$389$	3.83688	−	11.8087i	0.194538	−	0.598725i	−0.805444	−	0.592672i	$-0.798073\pi$
$389$	3.83688	−	11.8087i	0.194538	−	0.598725i	0.999982	−	0.00605338i	$-0.00192686\pi$
$390$		0			0
$391$	8.85410	+	27.2501i	0.447771	+	1.37810i
$392$		0			0
$393$		−	2.43769i		−	0.122965i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	11.8087	−	16.2533i	0.592662	−	0.815729i	−0.402350	−	0.915486i	$-0.631806\pi$
$397$	11.8087	−	16.2533i	0.592662	−	0.815729i	0.995012	+	0.0997568i	$0.0318065\pi$
$398$		0			0
$399$	44.5967			2.23263
$400$		0			0
$401$	−36.5967			−1.82755			−0.913777	−	0.406216i	$-0.866848\pi$
$401$	−36.5967			−1.82755			−0.913777	+	0.406216i	$0.866848\pi$
$402$		0			0
$403$	9.35930	−	12.8820i	0.466220	−	0.641696i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	10.1803i		−	0.504621i
$408$		0			0
$409$	6.34346	+	19.5232i	0.313664	+	0.965358i	0.976301	+	0.216417i	$0.0694372\pi$
$409$	6.34346	+	19.5232i	0.313664	+	0.965358i	−0.662637	+	0.748941i	$0.730563\pi$
$410$		0			0
$411$	−3.45492	+	10.6331i	−0.170418	+	0.524494i
$412$		0			0
$413$	5.93085	−	1.92705i	0.291838	−	0.0948240i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	12.8330	+	17.6631i	0.628435	+	0.864967i
$418$		0			0
$419$	21.1353	−	15.3557i	1.03252	−	0.750173i	0.0637123	−	0.997968i	$-0.479706\pi$
$419$	21.1353	−	15.3557i	1.03252	−	0.750173i	0.968812	+	0.247795i	$0.0797060\pi$
$420$		0			0
$421$	−4.00000	−	2.90617i	−0.194948	−	0.141638i	0.486029	−	0.873943i	$-0.338445\pi$
$421$	−4.00000	−	2.90617i	−0.194948	−	0.141638i	−0.680977	+	0.732304i	$0.738445\pi$
$422$		0			0
$423$	−0.277515	−	0.0901699i	−0.0134932	−	0.00438421i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−32.8177	−	10.6631i	−1.58816	−	0.516024i
$428$		0			0
$429$	−7.56231	−	5.49434i	−0.365112	−	0.265269i
$430$		0			0
$431$	−2.66312	+	1.93487i	−0.128278	+	0.0931994i	−0.650074	−	0.759871i	$-0.725262\pi$
$431$	−2.66312	+	1.93487i	−0.128278	+	0.0931994i	0.521796	+	0.853070i	$0.325262\pi$
$432$		0			0
$433$	1.33457	+	1.83688i	0.0641354	+	0.0882749i	0.839880	−	0.542772i	$-0.182625\pi$
$433$	1.33457	+	1.83688i	0.0641354	+	0.0882749i	−0.775744	+	0.631047i	$0.782625\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−39.6466	+	12.8820i	−1.89655	+	0.616228i
$438$		0			0
$439$	−5.19098	+	15.9762i	−0.247752	+	0.762503i	0.747420	+	0.664352i	$0.231293\pi$
$439$	−5.19098	+	15.9762i	−0.247752	+	0.762503i	−0.995172	+	0.0981502i	$0.968707\pi$
$440$		0			0
$441$	−0.0901699	−	0.277515i	−0.00429381	−	0.0132150i
$442$		0			0
$443$			8.34752i			0.396603i	0.980141	+	0.198301i	$0.0635425\pi$
$443$			8.34752i			0.396603i	−0.980141	+	0.198301i	$0.936458\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	24.2052	−	33.3156i	1.14487	−	1.57577i
$448$		0			0
$449$	23.9098			1.12837			0.564187	−	0.825647i	$-0.309190\pi$
$449$	23.9098			1.12837			0.564187	+	0.825647i	$0.309190\pi$
$450$		0			0
$451$	7.05573			0.332241
$452$		0			0
$453$	0.502029	−	0.690983i	0.0235874	−	0.0324652i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	4.47214i		−	0.209198i	−0.994514	−	0.104599i	$-0.966644\pi$
$457$		−	4.47214i		−	0.209198i	0.994514	−	0.104599i	$-0.0333559\pi$
$458$		0			0
$459$	−3.61803	−	11.1352i	−0.168875	−	0.519745i
$460$		0			0
$461$	−6.57953	+	20.2497i	−0.306439	+	0.943123i	0.672697	+	0.739918i	$0.265136\pi$
$461$	−6.57953	+	20.2497i	−0.306439	+	0.943123i	−0.979136	+	0.203205i	$0.934864\pi$
$462$		0			0
$463$	−15.1639	+	4.92705i	−0.704726	+	0.228979i	−0.639389	−	0.768884i	$-0.720812\pi$
$463$	−15.1639	+	4.92705i	−0.704726	+	0.228979i	−0.0653377	+	0.997863i	$0.520812\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	4.27350	+	5.88197i	0.197754	+	0.272185i	0.896365	−	0.443317i	$-0.146198\pi$
$467$	4.27350	+	5.88197i	0.197754	+	0.272185i	−0.698611	+	0.715502i	$0.746198\pi$
$468$		0			0
$469$	29.0344	−	21.0948i	1.34069	−	0.974065i
$470$		0			0
$471$	7.66312	+	5.56758i	0.353098	+	0.256541i
$472$		0			0
$473$	−5.15131	−	1.67376i	−0.236857	−	0.0769597i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	15.1109	+	4.90983i	0.691881	+	0.224806i
$478$		0			0
$479$	18.1074	+	13.1558i	0.827348	+	0.601103i	0.918808	−	0.394705i	$-0.129153\pi$
$479$	18.1074	+	13.1558i	0.827348	+	0.601103i	−0.0914599	+	0.995809i	$0.529153\pi$
$480$		0			0
$481$	22.5344	−	16.3722i	1.02748	−	0.746509i
$482$		0			0
$483$	−18.8294	−	25.9164i	−0.856766	−	1.17924i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	25.4010	−	8.25329i	1.15103	−	0.373992i	0.329499	−	0.944156i	$-0.393120\pi$
$487$	25.4010	−	8.25329i	1.15103	−	0.373992i	0.821531	+	0.570164i	$0.193120\pi$
$488$		0			0
$489$	10.4894	−	32.2829i	0.474345	−	1.45988i
$490$		0			0
$491$	1.16312	+	3.57971i	0.0524908	+	0.161550i	0.973866	−	0.227125i	$-0.0729327\pi$
$491$	1.16312	+	3.57971i	0.0524908	+	0.161550i	−0.921375	+	0.388676i	$0.872933\pi$
$492$		0			0
$493$		−	22.9443i		−	1.03336i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−13.2618	+	18.2533i	−0.594873	+	0.818772i
$498$		0			0
$499$	−29.5623			−1.32339			−0.661695	−	0.749773i	$-0.730163\pi$
$499$	−29.5623			−1.32339			−0.661695	+	0.749773i	$0.730163\pi$
$500$		0			0
$501$	42.5623			1.90154
$502$		0			0
$503$	9.33905	−	12.8541i	0.416408	−	0.573136i	−0.548359	−	0.836243i	$-0.684747\pi$
$503$	9.33905	−	12.8541i	0.416408	−	0.573136i	0.964767	+	0.263107i	$0.0847472\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$			3.49342i			0.155148i
$508$		0			0
$509$	−9.60739	−	29.5685i	−0.425840	−	1.31060i	−0.902188	−	0.431344i	$-0.858040\pi$
$509$	−9.60739	−	29.5685i	−0.425840	−	1.31060i	0.476347	−	0.879257i	$-0.341960\pi$
$510$		0			0
$511$	8.89919	−	27.3889i	0.393677	−	1.21161i
$512$		0			0
$513$	16.2007	−	5.26393i	0.715279	−	0.232408i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−0.106001	−	0.145898i	−0.00466192	−	0.00641659i
$518$		0			0
$519$	−11.8090	+	8.57975i	−0.518358	+	0.376609i
$520$		0			0
$521$	−6.80902	−	4.94704i	−0.298308	−	0.216734i	0.428555	−	0.903516i	$-0.359023\pi$
$521$	−6.80902	−	4.94704i	−0.298308	−	0.216734i	−0.726864	+	0.686782i	$0.759023\pi$
$522$		0			0
$523$	17.4823	+	5.68034i	0.764447	+	0.248384i	0.665186	−	0.746678i	$-0.268352\pi$
$523$	17.4823	+	5.68034i	0.764447	+	0.248384i	0.0992609	+	0.995061i	$0.468352\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−23.4459	−	7.61803i	−1.02132	−	0.331847i
$528$		0			0
$529$	5.61803	+	4.08174i	0.244262	+	0.177467i
$530$		0			0
$531$	−3.85410	+	2.80017i	−0.167254	+	0.121517i
$532$		0			0
$533$	11.3472	+	15.6180i	0.491500	+	0.676492i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	7.00042	−	2.27458i	0.302091	−	0.0981552i
$538$		0			0
$539$	0.0557281	−	0.171513i	0.00240038	−	0.00738761i
$540$		0			0
$541$	2.67376	+	8.22899i	0.114954	+	0.353792i	0.991937	−	0.126729i	$-0.0404477\pi$
$541$	2.67376	+	8.22899i	0.114954	+	0.353792i	−0.876983	+	0.480521i	$0.840448\pi$
$542$		0			0
$543$		−	18.5410i		−	0.795671i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	5.50207	−	7.57295i	0.235252	−	0.323796i	−0.675026	−	0.737794i	$-0.735868\pi$
$547$	5.50207	−	7.57295i	0.235252	−	0.323796i	0.910278	+	0.413998i	$0.135868\pi$
$548$		0			0
$549$	26.3607			1.12505
$550$		0			0
$551$	33.3820			1.42212
$552$		0			0
$553$	8.19624	−	11.2812i	0.348539	−	0.479723i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	7.81966i		−	0.331330i	−0.986182	−	0.165665i	$-0.947023\pi$
$557$		−	7.81966i		−	0.331330i	0.986182	−	0.165665i	$-0.0529770\pi$
$558$		0			0
$559$	−4.57953	−	14.0943i	−0.193693	−	0.596127i
$560$		0			0
$561$	−4.47214	+	13.7638i	−0.188814	+	0.581109i
$562$		0			0
$563$	1.86936	−	0.607391i	0.0787840	−	0.0255985i	−0.269360	−	0.963040i	$-0.586812\pi$
$563$	1.86936	−	0.607391i	0.0787840	−	0.0255985i	0.348144	+	0.937441i	$0.386812\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	16.9273	+	23.2984i	0.710878	+	0.978440i
$568$		0			0
$569$	14.1353	−	10.2699i	0.592581	−	0.430535i	−0.250657	−	0.968076i	$-0.580647\pi$
$569$	14.1353	−	10.2699i	0.592581	−	0.430535i	0.843238	+	0.537541i	$0.180647\pi$
$570$		0			0
$571$	26.1353	+	18.9884i	1.09373	+	0.794639i	0.980025	−	0.198876i	$-0.0637292\pi$
$571$	26.1353	+	18.9884i	1.09373	+	0.794639i	0.113702	+	0.993515i	$0.463729\pi$
$572$		0			0
$573$	−0.620541	−	0.201626i	−0.0259235	−	0.00842305i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	15.1109	+	4.90983i	0.629075	+	0.204399i	0.606165	−	0.795339i	$-0.292707\pi$
$577$	15.1109	+	4.90983i	0.629075	+	0.204399i	0.0229098	+	0.999738i	$0.492707\pi$
$578$		0			0
$579$	13.9443	+	10.1311i	0.579504	+	0.421034i
$580$		0			0
$581$	9.59017	−	6.96767i	0.397867	−	0.289068i
$582$		0			0
$583$	5.77185	+	7.94427i	0.239046	+	0.329018i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	29.9318	−	9.72542i	1.23542	−	0.401411i	0.382743	−	0.923855i	$-0.374979\pi$
$587$	29.9318	−	9.72542i	1.23542	−	0.401411i	0.852674	+	0.522444i	$0.174979\pi$
$588$		0			0
$589$	11.0836	−	34.1118i	0.456691	−	1.40555i
$590$		0			0
$591$	10.2016	+	31.3974i	0.419639	+	1.29152i
$592$		0			0
$593$		−	19.5623i		−	0.803328i	−0.915787	−	0.401664i	$-0.868432\pi$
$593$		−	19.5623i		−	0.803328i	0.915787	−	0.401664i	$-0.131568\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−12.3310	+	16.9721i	−0.504673	+	0.694623i
$598$		0			0
$599$	15.1803			0.620252			0.310126	−	0.950695i	$-0.399629\pi$
$599$	15.1803			0.620252			0.310126	+	0.950695i	$0.399629\pi$
$600$		0			0
$601$	−22.4377			−0.915253			−0.457626	−	0.889145i	$-0.651300\pi$
$601$	−22.4377			−0.915253			−0.457626	+	0.889145i	$0.651300\pi$
$602$		0			0
$603$	−16.1150	+	22.1803i	−0.656252	+	0.903253i
$604$		0			0
$605$		0			0
$606$		0			0
$607$			1.27051i			0.0515684i	0.999668	+	0.0257842i	$0.00820828\pi$
$607$			1.27051i			0.0515684i	−0.999668	+	0.0257842i	$0.991792\pi$
$608$		0			0
$609$	7.92705	+	24.3970i	0.321220	+	0.988614i
$610$		0			0
$611$	0.152476	−	0.469272i	0.00616851	−	0.0189847i
$612$		0			0
$613$	−9.54332	+	3.10081i	−0.385451	+	0.125241i	−0.495331	−	0.868704i	$-0.664953\pi$
$613$	−9.54332	+	3.10081i	−0.385451	+	0.125241i	0.109880	+	0.993945i	$0.464953\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−17.9843	−	24.7533i	−0.724021	−	0.996530i	−0.999381	−	0.0351885i	$-0.988797\pi$
$617$	−17.9843	−	24.7533i	−0.724021	−	0.996530i	0.275359	−	0.961341i	$-0.411203\pi$
$618$		0			0
$619$	−32.9336	+	23.9277i	−1.32371	+	0.961735i	−0.323836	+	0.946113i	$0.604973\pi$
$619$	−32.9336	+	23.9277i	−1.32371	+	0.961735i	−0.999878	+	0.0156216i	$0.995027\pi$
$620$		0			0
$621$	−9.89919	−	7.19218i	−0.397241	−	0.288612i
$622$		0			0
$623$	−9.95959	−	3.23607i	−0.399023	−	0.129650i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−20.0252	−	6.50658i	−0.799729	−	0.259848i
$628$		0			0
$629$	−34.8885	−	25.3480i	−1.39110	−	1.01069i
$630$		0			0
$631$	−6.33688	+	4.60401i	−0.252267	+	0.183283i	−0.706731	−	0.707482i	$-0.749831\pi$
$631$	−6.33688	+	4.60401i	−0.252267	+	0.183283i	0.454464	+	0.890765i	$0.349831\pi$
$632$		0			0
$633$	−26.2133	−	36.0795i	−1.04189	−	1.43403i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	0.469272	−	0.152476i	0.0185932	−	0.00604131i
$638$		0			0
$639$	5.32624	−	16.3925i	0.210703	−	0.648476i
$640$		0			0
$641$	−5.39261	−	16.5967i	−0.212995	−	0.655532i	−0.999290	−	0.0376802i	$-0.988003\pi$
$641$	−5.39261	−	16.5967i	−0.212995	−	0.655532i	0.786295	−	0.617852i	$-0.211997\pi$
$642$		0			0
$643$		−	19.0557i		−	0.751485i	−0.926724	−	0.375742i	$-0.877388\pi$
$643$		−	19.0557i		−	0.751485i	0.926724	−	0.375742i	$-0.122612\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−13.3148	+	18.3262i	−0.523458	+	0.720479i	−0.986116	−	0.166058i	$-0.946896\pi$
$647$	−13.3148	+	18.3262i	−0.523458	+	0.720479i	0.462657	+	0.886537i	$0.346896\pi$
$648$		0			0
$649$	−2.94427			−0.115573
$650$		0			0
$651$	27.5623			1.08025
$652$		0			0
$653$	−17.9313	+	24.6803i	−0.701707	+	0.965816i	0.298229	+	0.954494i	$0.403604\pi$
$653$	−17.9313	+	24.6803i	−0.701707	+	0.965816i	−0.999936	+	0.0113221i	$0.996396\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			22.0000i			0.858302i
$658$		0			0
$659$	−0.0344419	−	0.106001i	−0.00134166	−	0.00412922i	0.950383	−	0.311081i	$-0.100691\pi$
$659$	−0.0344419	−	0.106001i	−0.00134166	−	0.00412922i	−0.951725	+	0.306952i	$0.900691\pi$
$660$		0			0
$661$	−10.6803	+	32.8707i	−0.415417	+	1.27852i	0.496460	+	0.868059i	$0.334633\pi$
$661$	−10.6803	+	32.8707i	−0.415417	+	1.27852i	−0.911877	+	0.410463i	$0.865367\pi$
$662$		0			0
$663$	−37.6587	+	12.2361i	−1.46254	+	0.475210i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−14.0943	−	19.3992i	−0.545735	−	0.751140i
$668$		0			0
$669$	−10.3262	+	7.50245i	−0.399235	+	0.290062i
$670$		0			0
$671$	13.1803	+	9.57608i	0.508821	+	0.369680i
$672$		0			0
$673$	31.5034	+	10.2361i	1.21437	+	0.394571i	0.845027	−	0.534723i	$-0.179584\pi$
$673$	31.5034	+	10.2361i	1.21437	+	0.394571i	0.369339	+	0.929295i	$0.379584\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−7.46969	−	2.42705i	−0.287084	−	0.0932791i	0.161935	−	0.986801i	$-0.448226\pi$
$677$	−7.46969	−	2.42705i	−0.287084	−	0.0932791i	−0.449019	+	0.893522i	$0.648226\pi$
$678$		0			0
$679$	−32.3435	−	23.4989i	−1.24123	−	0.901805i
$680$		0			0
$681$	−46.3050	+	33.6425i	−1.77441	+	1.28918i
$682$		0			0
$683$	−12.1720	−	16.7533i	−0.465748	−	0.641047i	0.509941	−	0.860210i	$-0.329667\pi$
$683$	−12.1720	−	16.7533i	−0.465748	−	0.641047i	−0.975688	+	0.219163i	$0.929667\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	42.9161	−	13.9443i	1.63735	−	0.532007i
$688$		0			0
$689$	−8.30244	+	25.5523i	−0.316298	+	0.973464i
$690$		0			0
$691$	−14.4787	−	44.5609i	−0.550796	−	1.69518i	−0.706794	−	0.707419i	$-0.749859\pi$
$691$	−14.4787	−	44.5609i	−0.550796	−	1.69518i	0.155998	−	0.987757i	$-0.450141\pi$
$692$		0			0
$693$		−	6.47214i		−	0.245856i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	17.5680	−	24.1803i	0.665437	−	0.915896i
$698$		0			0
$699$	13.4164			0.507455
$700$		0			0
$701$	2.18034			0.0823503			0.0411752	−	0.999152i	$-0.486890\pi$
$701$	2.18034			0.0823503			0.0411752	+	0.999152i	$0.486890\pi$
$702$		0			0
$703$	36.8792	−	50.7599i	1.39093	−	1.91444i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	46.9787i		−	1.76682i
$708$		0			0
$709$	11.3090	+	34.8056i	0.424719	+	1.30715i	0.903263	+	0.429087i	$0.141165\pi$
$709$	11.3090	+	34.8056i	0.424719	+	1.30715i	−0.478544	+	0.878064i	$0.658835\pi$
$710$		0			0
$711$	−3.29180	+	10.1311i	−0.123452	+	0.379946i
$712$		0			0
$713$	−24.5030	+	7.96149i	−0.917643	+	0.298160i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−29.2255	−	40.2254i	−1.09145	−	1.50225i
$718$		0			0
$719$	−30.9894	+	22.5151i	−1.15571	+	0.839671i	−0.989229	−	0.146374i	$-0.953240\pi$
$719$	−30.9894	+	22.5151i	−1.15571	+	0.839671i	−0.166479	+	0.986045i	$0.553240\pi$
$720$		0			0
$721$	6.66312	+	4.84104i	0.248148	+	0.180290i
$722$		0			0
$723$	24.3970	+	7.92705i	0.907332	+	0.294810i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	10.7719	+	3.50000i	0.399507	+	0.129808i	0.501878	−	0.864939i	$-0.332643\pi$
$727$	10.7719	+	3.50000i	0.399507	+	0.129808i	−0.102370	+	0.994746i	$0.532643\pi$
$728$		0			0
$729$	−5.66312	−	4.11450i	−0.209745	−	0.152389i
$730$		0			0
$731$	−18.5623	+	13.4863i	−0.686552	+	0.498809i
$732$		0			0
$733$	6.37988	+	8.78115i	0.235646	+	0.324339i	0.910420	−	0.413686i	$-0.135759\pi$
$733$	6.37988	+	8.78115i	0.235646	+	0.324339i	−0.674774	+	0.738025i	$0.735759\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−16.1150	+	5.23607i	−0.593602	+	0.192873i
$738$		0			0
$739$	−3.50000	+	10.7719i	−0.128750	+	0.396250i	−0.994566	−	0.104112i	$-0.966800\pi$
$739$	−3.50000	+	10.7719i	−0.128750	+	0.396250i	0.865816	+	0.500363i	$0.166800\pi$
$740$		0			0
$741$	−17.8024	−	54.7903i	−0.653989	−	2.01277i
$742$		0			0
$743$			46.2492i			1.69672i	0.529420	+	0.848360i	$0.322409\pi$
$743$			46.2492i			1.69672i	−0.529420	+	0.848360i	$0.677591\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−5.32282	+	7.32624i	−0.194752	+	0.268053i
$748$		0			0
$749$	−43.7426			−1.59832
$750$		0			0
$751$	−31.7639			−1.15908			−0.579541	−	0.814943i	$-0.696768\pi$
$751$	−31.7639			−1.15908			−0.579541	+	0.814943i	$0.696768\pi$
$752$		0			0
$753$	−10.5879	+	14.5729i	−0.385843	+	0.531068i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			15.0000i			0.545184i	0.962130	+	0.272592i	$0.0878810\pi$
$757$			15.0000i			0.545184i	−0.962130	+	0.272592i	$0.912119\pi$
$758$		0			0
$759$	4.67376	+	14.3844i	0.169647	+	0.522119i
$760$		0			0
$761$	−7.77051	+	23.9152i	−0.281681	+	0.866924i	0.705693	+	0.708518i	$0.250636\pi$
$761$	−7.77051	+	23.9152i	−0.281681	+	0.866924i	−0.987374	+	0.158407i	$0.949364\pi$
$762$		0			0
$763$	7.33094	−	2.38197i	0.265398	−	0.0862330i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.73504	−	6.51722i	−0.170972	−	0.235323i
$768$		0			0
$769$	31.9787	−	23.2339i	1.15318	−	0.837836i	0.164281	−	0.986414i	$-0.447470\pi$
$769$	31.9787	−	23.2339i	1.15318	−	0.837836i	0.988901	+	0.148578i	$0.0474696\pi$
$770$		0			0
$771$	−6.54508	−	4.75528i	−0.235715	−	0.171257i
$772$		0			0
$773$	−25.3683	−	8.24265i	−0.912433	−	0.296467i	−0.185074	−	0.982725i	$-0.559252\pi$
$773$	−25.3683	−	8.24265i	−0.912433	−	0.296467i	−0.727359	+	0.686257i	$0.759252\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	45.8550	+	14.8992i	1.64504	+	0.534505i
$778$		0			0
$779$	35.1803	+	25.5600i	1.26047	+	0.915783i
$780$		0			0
$781$	8.61803	−	6.26137i	0.308378	−	0.224049i
$782$		0			0
$783$	5.75934	+	7.92705i	0.205822	+	0.283290i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−28.8092	+	9.36068i	−1.02694	+	0.333672i	−0.773579	−	0.633700i	$-0.781535\pi$
$787$	−28.8092	+	9.36068i	−1.02694	+	0.333672i	−0.253359	+	0.967372i	$0.581535\pi$
$788$		0			0
$789$	−9.57295	+	29.4625i	−0.340806	+	1.04889i
$790$		0			0
$791$	−8.54508	−	26.2991i	−0.303828	−	0.935087i
$792$		0			0
$793$			44.5755i			1.58292i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−3.11044	+	4.28115i	−0.110177	+	0.151646i	−0.860545	−	0.509375i	$-0.829877\pi$
$797$	−3.11044	+	4.28115i	−0.110177	+	0.151646i	0.750367	+	0.661021i	$0.229877\pi$
$798$		0			0
$799$	−0.763932			−0.0270260
$800$		0			0
$801$	8.00000			0.282666
$802$		0			0
$803$	−7.99197	+	11.0000i	−0.282030	+	0.388182i
$804$		0			0
$805$		0			0
$806$		0			0
$807$			31.9574i			1.12495i
$808$		0			0
$809$	−2.22542	−	6.84915i	−0.0782418	−	0.240803i	0.904284	−	0.426932i	$-0.140406\pi$
$809$	−2.22542	−	6.84915i	−0.0782418	−	0.240803i	−0.982525	+	0.186129i	$0.940406\pi$
$810$		0			0
$811$	−14.0172	+	43.1406i	−0.492211	+	1.51487i	0.329047	+	0.944314i	$0.393273\pi$
$811$	−14.0172	+	43.1406i	−0.492211	+	1.51487i	−0.821258	+	0.570557i	$0.806727\pi$
$812$		0			0
$813$	−27.5276	+	8.94427i	−0.965436	+	0.313689i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−19.6214	−	27.0066i	−0.686467	−	0.944841i
$818$		0			0
$819$	14.3262	−	10.4086i	0.500599	−	0.363707i
$820$		0			0
$821$	11.2082	+	8.14324i	0.391169	+	0.284201i	0.765934	−	0.642919i	$-0.222277\pi$
$821$	11.2082	+	8.14324i	0.391169	+	0.284201i	−0.374765	+	0.927120i	$0.622277\pi$
$822$		0			0
$823$	12.9313	+	4.20163i	0.450756	+	0.146459i	0.525593	−	0.850736i	$-0.323844\pi$
$823$	12.9313	+	4.20163i	0.450756	+	0.146459i	−0.0748368	+	0.997196i	$0.523844\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	31.2461	+	10.1525i	1.08653	+	0.353036i	0.796906	−	0.604103i	$-0.206469\pi$
$827$	31.2461	+	10.1525i	1.08653	+	0.353036i	0.289628	+	0.957139i	$0.406469\pi$
$828$		0			0
$829$	−3.59017	−	2.60841i	−0.124692	−	0.0905939i	0.523691	−	0.851908i	$-0.324554\pi$
$829$	−3.59017	−	2.60841i	−0.124692	−	0.0905939i	−0.648383	+	0.761314i	$0.724554\pi$
$830$		0			0
$831$	38.3156	−	27.8379i	1.32915	−	0.965686i
$832$		0			0
$833$	−0.449028	−	0.618034i	−0.0155579	−	0.0214136i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	10.0126	−	3.25329i	0.346086	−	0.112450i
$838$		0			0
$839$	3.02786	−	9.31881i	0.104533	−	0.321721i	−0.885087	−	0.465425i	$-0.845901\pi$
$839$	3.02786	−	9.31881i	0.104533	−	0.321721i	0.989621	+	0.143704i	$0.0459014\pi$
$840$		0			0
$841$	−3.02786	−	9.31881i	−0.104409	−	0.321338i
$842$		0			0
$843$			20.4508i			0.704365i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−14.5761	+	20.0623i	−0.500841	+	0.689349i
$848$		0			0
$849$	−16.2574			−0.557951
$850$		0			0
$851$	−45.0689			−1.54494
$852$		0			0
$853$	−3.18368	+	4.38197i	−0.109007	+	0.150036i	−0.860035	−	0.510235i	$-0.829558\pi$
$853$	−3.18368	+	4.38197i	−0.109007	+	0.150036i	0.751028	+	0.660271i	$0.229558\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	3.14590i		−	0.107462i	−0.998555	−	0.0537309i	$-0.982889\pi$
$857$		−	3.14590i		−	0.107462i	0.998555	−	0.0537309i	$-0.0171113\pi$
$858$		0			0
$859$	−9.45492	−	29.0992i	−0.322598	−	0.992853i	−0.972513	−	0.232847i	$-0.925196\pi$
$859$	−9.45492	−	29.0992i	−0.322598	−	0.992853i	0.649916	−	0.760006i	$-0.274804\pi$
$860$		0			0
$861$	−10.3262	+	31.7809i	−0.351917	+	1.08309i
$862$		0			0
$863$	−12.8455	+	4.17376i	−0.437267	+	0.142077i	−0.519374	−	0.854547i	$-0.673835\pi$
$863$	−12.8455	+	4.17376i	−0.437267	+	0.142077i	0.0821076	+	0.996623i	$0.473835\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	13.6906	+	18.8435i	0.464956	+	0.639957i
$868$		0			0
$869$	−5.32624	+	3.86974i	−0.180680	+	0.131272i
$870$		0			0
$871$	−37.5066	−	27.2501i	−1.27086	−	0.923335i
$872$		0			0
$873$	29.0462	+	9.43769i	0.983066	+	0.319418i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	32.9565	+	10.7082i	1.11286	+	0.361590i	0.807039	−	0.590498i	$-0.201069\pi$
$877$	32.9565	+	10.7082i	1.11286	+	0.361590i	0.305822	+	0.952089i	$0.401069\pi$
$878$		0			0
$879$	−0.854102	−	0.620541i	−0.0288081	−	0.0209303i
$880$		0			0
$881$	35.1246	−	25.5195i	1.18338	−	0.859775i	0.190830	−	0.981623i	$-0.438882\pi$
$881$	35.1246	−	25.5195i	1.18338	−	0.859775i	0.992549	+	0.121849i	$0.0388822\pi$
$882$		0			0
$883$	17.9111	+	24.6525i	0.602756	+	0.829622i	0.995957	−	0.0898305i	$-0.0286325\pi$
$883$	17.9111	+	24.6525i	0.602756	+	0.829622i	−0.393202	+	0.919452i	$0.628633\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	2.00811	−	0.652476i	0.0674259	−	0.0219080i	−0.275110	−	0.961413i	$-0.588714\pi$
$887$	2.00811	−	0.652476i	0.0674259	−	0.0219080i	0.342536	+	0.939505i	$0.388714\pi$
$888$		0			0
$889$	−6.09017	+	18.7436i	−0.204258	+	0.628641i
$890$		0			0
$891$	−4.20163	−	12.9313i	−0.140760	−	0.433214i
$892$		0			0
$893$		−	1.11146i		−	0.0371935i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−24.3237	+	33.4787i	−0.812145	+	1.11782i
$898$		0			0
$899$	20.6312			0.688089
$900$		0			0
$901$	41.5967			1.38579
$902$		0			0
$903$	15.0781	−	20.7533i	0.501769	−	0.690626i
$904$		0			0
$905$		0			0
$906$		0			0
$907$			33.1803i			1.10174i	0.834593	+	0.550868i	$0.185703\pi$
$907$			33.1803i			1.10174i	−0.834593	+	0.550868i	$0.814297\pi$
$908$		0			0
$909$	11.0902	+	34.1320i	0.367838	+	1.13209i
$910$		0			0
$911$	8.45492	−	26.0216i	0.280124	−	0.862133i	−0.707694	−	0.706519i	$-0.750265\pi$
$911$	8.45492	−	26.0216i	0.280124	−	0.862133i	0.987818	−	0.155614i	$-0.0497355\pi$
$912$		0			0
$913$	−5.32282	+	1.72949i	−0.176160	+	0.0572378i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.67760	+	2.30902i	0.0553992	+	0.0762505i
$918$		0			0
$919$	−3.69098	+	2.68166i	−0.121754	+	0.0884597i	−0.646996	−	0.762493i	$-0.723975\pi$
$919$	−3.69098	+	2.68166i	−0.121754	+	0.0884597i	0.525242	+	0.850953i	$0.323975\pi$
$920$		0			0
$921$	19.4721	+	14.1473i	0.641629	+	0.466171i
$922$		0			0
$923$	27.7194	+	9.00658i	0.912395	+	0.296455i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−5.98385	−	1.94427i	−0.196536	−	0.0638583i
$928$		0			0
$929$	31.0967	+	22.5931i	1.02025	+	0.741256i	0.966334	−	0.257290i	$-0.0828294\pi$
$929$	31.0967	+	22.5931i	1.02025	+	0.741256i	0.0539168	+	0.998545i	$0.482829\pi$
$930$		0			0
$931$	0.899187	−	0.653298i	0.0294697	−	0.0214110i
$932$		0			0
$933$	6.45313	+	8.88197i	0.211266	+	0.290783i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−19.5559	+	6.35410i	−0.638864	+	0.207579i	−0.610498	−	0.792018i	$-0.709030\pi$
$937$	−19.5559	+	6.35410i	−0.638864	+	0.207579i	−0.0283663	+	0.999598i	$0.509030\pi$
$938$		0			0
$939$	3.94427	−	12.1392i	0.128716	−	0.396148i
$940$		0			0
$941$	−14.8156	−	45.5977i	−0.482975	−	1.48644i	−0.834893	−	0.550412i	$-0.814471\pi$
$941$	−14.8156	−	45.5977i	−0.482975	−	1.48644i	0.351918	−	0.936031i	$-0.385529\pi$
$942$		0			0
$943$		−	31.2361i		−	1.01719i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−32.3359	+	44.5066i	−1.05078	+	1.44627i	−0.162642	+	0.986685i	$0.552002\pi$
$947$	−32.3359	+	44.5066i	−1.05078	+	1.44627i	−0.888134	+	0.459584i	$0.847998\pi$
$948$		0			0
$949$	−37.2016			−1.20762
$950$		0			0
$951$	31.8328			1.03225
$952$		0			0
$953$	24.8132	−	34.1525i	0.803779	−	1.10631i	−0.188474	−	0.982078i	$-0.560354\pi$
$953$	24.8132	−	34.1525i	0.803779	−	1.10631i	0.992254	−	0.124229i	$-0.0396458\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		−	12.1115i		−	0.391508i
$958$		0			0
$959$	−4.04508	−	12.4495i	−0.130623	−	0.402015i
$960$		0			0
$961$	−2.72949	+	8.40051i	−0.0880481	+	0.270984i
$962$		0			0
$963$	31.7809	−	10.3262i	1.02412	−	0.332758i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−0.277515	−	0.381966i	−0.00892427	−	0.0122832i	0.804532	−	0.593910i	$-0.202416\pi$
$967$	−0.277515	−	0.381966i	−0.00892427	−	0.0122832i	−0.813456	+	0.581627i	$0.802416\pi$
$968$		0			0
$969$	−72.1591	+	52.4266i	−2.31808	+	1.68419i
$970$		0			0
$971$	−22.1976	−	16.1275i	−0.712354	−	0.517555i	0.171578	−	0.985170i	$-0.445113\pi$
$971$	−22.1976	−	16.1275i	−0.712354	−	0.517555i	−0.883932	+	0.467615i	$0.845113\pi$
$972$		0			0
$973$	−24.3112	−	7.89919i	−0.779381	−	0.253236i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−17.7926	−	5.78115i	−0.569234	−	0.184955i	0.0102376	−	0.999948i	$-0.496741\pi$
$977$	−17.7926	−	5.78115i	−0.569234	−	0.184955i	−0.579472	+	0.814992i	$0.696741\pi$
$978$		0			0
$979$	4.00000	+	2.90617i	0.127841	+	0.0928816i
$980$		0			0
$981$	−4.76393	+	3.46120i	−0.152101	+	0.110508i
$982$		0			0
$983$	2.23263	+	3.07295i	0.0712098	+	0.0980119i	0.843136	−	0.537700i	$-0.180707\pi$
$983$	2.23263	+	3.07295i	0.0712098	+	0.0980119i	−0.771926	+	0.635712i	$0.780707\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	0.812299	−	0.263932i	0.0258558	−	0.00840105i
$988$		0			0
$989$	−7.40983	+	22.8051i	−0.235619	+	0.725160i
$990$		0			0
$991$	−15.8156	−	48.6754i	−0.502399	−	1.54622i	−0.805100	−	0.593139i	$-0.797888\pi$
$991$	−15.8156	−	48.6754i	−0.502399	−	1.54622i	0.302701	−	0.953086i	$-0.402112\pi$
$992$		0			0
$993$			71.7082i			2.27559i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−22.6461	+	31.1697i	−0.717210	+	0.987154i	0.282402	+	0.959296i	$0.408869\pi$
$997$	−22.6461	+	31.1697i	−0.717210	+	0.987154i	−0.999612	+	0.0278582i	$0.991131\pi$
$998$		0			0
$999$	18.4164			0.582669

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.q.a.649.2		8
5.2	odd	4		1000.2.m.a.601.1		4
5.3	odd	4		200.2.m.a.121.1	yes	4
5.4	even	2	inner	1000.2.q.a.649.1		8
20.3	even	4		400.2.u.a.321.1		4
25.6	even	5	inner	1000.2.q.a.849.1		8
25.8	odd	20		200.2.m.a.81.1	✓	4
25.12	odd	20		5000.2.a.a.1.2		2
25.13	odd	20		5000.2.a.c.1.1		2
25.17	odd	20		1000.2.m.a.401.1		4
25.19	even	10	inner	1000.2.q.a.849.2		8
100.63	even	20		10000.2.a.g.1.2		2
100.83	even	20		400.2.u.a.81.1		4
100.87	even	20		10000.2.a.i.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.m.a.81.1	✓	4	25.8	odd	20
200.2.m.a.121.1	yes	4	5.3	odd	4
400.2.u.a.81.1		4	100.83	even	20
400.2.u.a.321.1		4	20.3	even	4
1000.2.m.a.401.1		4	25.17	odd	20
1000.2.m.a.601.1		4	5.2	odd	4
1000.2.q.a.649.1		8	5.4	even	2	inner
1000.2.q.a.649.2		8	1.1	even	1	trivial
1000.2.q.a.849.1		8	25.6	even	5	inner
1000.2.q.a.849.2		8	25.19	even	10	inner
5000.2.a.a.1.2		2	25.12	odd	20
5000.2.a.c.1.1		2	25.13	odd	20
10000.2.a.g.1.2		2	100.63	even	20
10000.2.a.i.1.1		2	100.87	even	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.q (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.31433 - 1.80902i) q^{3} +2.61803i q^{7} +(-0.618034 - 1.90211i) q^{9} +O(q^{10})\)	\(q+(1.31433 - 1.80902i) q^{3} +2.61803i q^{7} +(-0.618034 - 1.90211i) q^{9} +(0.381966 - 1.17557i) q^{11} +(3.21644 - 1.04508i) q^{13} +(-3.07768 - 4.23607i) q^{17} +(6.16312 - 4.47777i) q^{19} +(4.73607 + 3.44095i) q^{21} +(-5.20431 - 1.69098i) q^{23} +(2.12663 + 0.690983i) q^{27} +(3.54508 + 2.57565i) q^{29} +(3.80902 - 2.76741i) q^{31} +(-1.62460 - 2.23607i) q^{33} +(7.83297 - 2.54508i) q^{37} +(2.33688 - 7.19218i) q^{39} +(1.76393 + 5.42882i) q^{41} -4.38197i q^{43} +(0.0857567 - 0.118034i) q^{47} +0.145898 q^{49} -11.7082 q^{51} +(-4.66953 + 6.42705i) q^{53} -17.0344i q^{57} +(-0.736068 - 2.26538i) q^{59} +(-4.07295 + 12.5352i) q^{61} +(4.97980 - 1.61803i) q^{63} +(-8.05748 - 11.0902i) q^{67} +(-9.89919 + 7.19218i) q^{69} +(6.97214 + 5.06555i) q^{71} +(-10.4616 - 3.39919i) q^{73} +(3.07768 + 1.00000i) q^{77} +(-4.30902 - 3.13068i) q^{79} +(8.89919 - 6.46564i) q^{81} +(-2.66141 - 3.66312i) q^{83} +(9.31881 - 3.02786i) q^{87} +(-1.23607 + 3.80423i) q^{89} +(2.73607 + 8.42075i) q^{91} -10.5279i q^{93} +(-8.97578 + 12.3541i) q^{97} -2.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^9	\( 8 q + 4 q^{9} + 12 q^{11} + 18 q^{19} + 20 q^{21} + 6 q^{29} + 26 q^{31} + 50 q^{39} + 32 q^{41} + 28 q^{49} - 40 q^{51} + 12 q^{59} - 46 q^{61} - 30 q^{69} + 20 q^{71} - 30 q^{79} + 22 q^{81} + 8 q^{89} + 4 q^{91} + 16 q^{99}+O(q^{100}) \) 8 * q + 4 * q^9 + 12 * q^11 + 18 * q^19 + 20 * q^21 + 6 * q^29 + 26 * q^31 + 50 * q^39 + 32 * q^41 + 28 * q^49 - 40 * q^51 + 12 * q^59 - 46 * q^61 - 30 * q^69 + 20 * q^71 - 30 * q^79 + 22 * q^81 + 8 * q^89 + 4 * q^91 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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