LMFDB - Embedded newform 624.4.bv.h.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,4,Mod(49,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("624.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	624.bv (of order $6$, degree $2$, 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:	$36.8171918436$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 70x^{8} + 1645x^{6} + 14700x^{4} + 44100x^{2} + 27648 $ x^10 + 70x^8 + 1645x^6 + 14700x^4 + 44100x^2 + 27648
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.3
Root			$-5.36472i$ of defining polynomial
Character	$\chi$	$=$	624.49
Dual form			624.4.bv.h.433.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 2.59808i) q^{3} +2.69631i q^{5} +(-13.1657 - 7.60123i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(1.50000 + 2.59808i) q^{3} +2.69631i q^{5} +(-13.1657 - 7.60123i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-57.9240 + 33.4424i) q^{11} +(46.8650 + 0.818689i) q^{13} +(-7.00522 + 4.04447i) q^{15} +(2.08177 - 3.60573i) q^{17} +(22.5903 + 13.0425i) q^{19} -45.6074i q^{21} +(-23.6621 - 40.9839i) q^{23} +117.730 q^{25} -27.0000 q^{27} +(-128.503 - 222.575i) q^{29} -206.242i q^{31} +(-173.772 - 100.327i) q^{33} +(20.4953 - 35.4989i) q^{35} +(-152.149 + 87.8430i) q^{37} +(68.1705 + 122.987i) q^{39} +(135.501 - 78.2313i) q^{41} +(-25.9922 + 45.0199i) q^{43} +(-21.0157 - 12.1334i) q^{45} -354.222i q^{47} +(-55.9425 - 96.8953i) q^{49} +12.4906 q^{51} -10.4723 q^{53} +(-90.1712 - 156.181i) q^{55} +78.2550i q^{57} +(-385.480 - 222.557i) q^{59} +(-59.8481 + 103.660i) q^{61} +(118.491 - 68.4111i) q^{63} +(-2.20744 + 126.363i) q^{65} +(19.4057 - 11.2039i) q^{67} +(70.9863 - 122.952i) q^{69} +(246.997 + 142.604i) q^{71} -740.989i q^{73} +(176.595 + 305.871i) q^{75} +1016.81 q^{77} +547.679 q^{79} +(-40.5000 - 70.1481i) q^{81} -603.056i q^{83} +(9.72218 + 5.61310i) q^{85} +(385.510 - 667.724i) q^{87} +(-186.774 + 107.834i) q^{89} +(-610.789 - 367.011i) q^{91} +(535.833 - 309.363i) q^{93} +(-35.1666 + 60.9104i) q^{95} +(-1253.58 - 723.752i) q^{97} -601.964i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 15 q^{3} - 30 q^{7} - 45 q^{9}+O(q^{10}) $ 10 * q + 15 * q^3 - 30 * q^7 - 45 * q^9	$ 10 q + 15 q^{3} - 30 q^{7} - 45 q^{9} - 60 q^{11} + 25 q^{13} - 45 q^{15} + 105 q^{17} - 180 q^{19} + 60 q^{23} - 960 q^{25} - 270 q^{27} - 495 q^{29} - 180 q^{33} - 60 q^{35} - 405 q^{37} - 345 q^{39} + 1065 q^{41} + 370 q^{43} - 135 q^{45} + 775 q^{49} + 630 q^{51} + 330 q^{53} + 260 q^{55} - 780 q^{59} - 1375 q^{61} + 270 q^{63} + 1605 q^{65} - 1590 q^{67} - 180 q^{69} - 1620 q^{71} - 1440 q^{75} - 4320 q^{77} - 1100 q^{79} - 405 q^{81} + 525 q^{85} + 1485 q^{87} + 2040 q^{89} - 4770 q^{91} - 990 q^{93} + 1380 q^{95} - 3750 q^{97}+O(q^{100}) $ 10 * q + 15 * q^3 - 30 * q^7 - 45 * q^9 - 60 * q^11 + 25 * q^13 - 45 * q^15 + 105 * q^17 - 180 * q^19 + 60 * q^23 - 960 * q^25 - 270 * q^27 - 495 * q^29 - 180 * q^33 - 60 * q^35 - 405 * q^37 - 345 * q^39 + 1065 * q^41 + 370 * q^43 - 135 * q^45 + 775 * q^49 + 630 * q^51 + 330 * q^53 + 260 * q^55 - 780 * q^59 - 1375 * q^61 + 270 * q^63 + 1605 * q^65 - 1590 * q^67 - 180 * q^69 - 1620 * q^71 - 1440 * q^75 - 4320 * q^77 - 1100 * q^79 - 405 * q^81 + 525 * q^85 + 1485 * q^87 + 2040 * q^89 - 4770 * q^91 - 990 * q^93 + 1380 * q^95 - 3750 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$		0			0
$5$			2.69631i			0.241165i	0.992703	+	0.120583i	$0.0384763\pi$
$5$			2.69631i			0.241165i	−0.992703	+	0.120583i	$0.961524\pi$
$6$		0			0
$7$	−13.1657	−	7.60123i	−0.710882	−	0.410428i	0.100505	−	0.994937i	$-0.467954\pi$
$7$	−13.1657	−	7.60123i	−0.710882	−	0.410428i	−0.811388	+	0.584509i	$0.801287\pi$
$8$		0			0
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$		0			0
$11$	−57.9240	+	33.4424i	−1.58770	+	0.916661i	−0.594018	+	0.804451i	$0.702459\pi$
$11$	−57.9240	+	33.4424i	−1.58770	+	0.916661i	−0.993685	+	0.112209i	$0.964207\pi$
$12$		0			0
$13$	46.8650	+	0.818689i	0.999847	+	0.0174664i
$13$	46.8650	+	0.818689i	0.999847	+	0.0174664i
$14$		0			0
$15$	−7.00522	+	4.04447i	−0.120583	+	0.0696185i
$16$		0			0
$17$	2.08177	−	3.60573i	0.0297002	−	0.0514422i	−0.850793	−	0.525501i	$-0.823878\pi$
$17$	2.08177	−	3.60573i	0.0297002	−	0.0514422i	0.880493	+	0.474058i	$0.157211\pi$
$18$		0			0
$19$	22.5903	+	13.0425i	0.272766	+	0.157482i	0.630144	−	0.776478i	$-0.282996\pi$
$19$	22.5903	+	13.0425i	0.272766	+	0.157482i	−0.357378	+	0.933960i	$0.616329\pi$
$20$		0			0
$21$		−	45.6074i		−	0.473921i
$22$		0			0
$23$	−23.6621	−	40.9839i	−0.214517	−	0.371554i	0.738606	−	0.674137i	$-0.235484\pi$
$23$	−23.6621	−	40.9839i	−0.214517	−	0.371554i	−0.953123	+	0.302583i	$0.902151\pi$
$24$		0			0
$25$	117.730			0.941839
$26$		0			0
$27$	−27.0000			−0.192450
$28$		0			0
$29$	−128.503	−	222.575i	−0.822845	−	1.42521i	−0.903555	−	0.428471i	$-0.859052\pi$
$29$	−128.503	−	222.575i	−0.822845	−	1.42521i	0.0807106	−	0.996738i	$-0.474281\pi$
$30$		0			0
$31$		−	206.242i		−	1.19491i	−0.801903	−	0.597455i	$-0.796179\pi$
$31$		−	206.242i		−	1.19491i	0.801903	−	0.597455i	$-0.203821\pi$
$32$		0			0
$33$	−173.772	−	100.327i	−0.916661	−	0.529234i
$34$		0			0
$35$	20.4953	−	35.4989i	0.0989811	−	0.171440i
$36$		0			0
$37$	−152.149	+	87.8430i	−0.676029	+	0.390305i	−0.798357	−	0.602184i	$-0.794297\pi$
$37$	−152.149	+	87.8430i	−0.676029	+	0.390305i	0.122328	+	0.992490i	$0.460964\pi$
$38$		0			0
$39$	68.1705	+	122.987i	0.279898	+	0.504966i
$40$		0			0
$41$	135.501	−	78.2313i	0.516137	−	0.297992i	−0.219216	−	0.975676i	$-0.570350\pi$
$41$	135.501	−	78.2313i	0.516137	−	0.297992i	0.735353	+	0.677684i	$0.237016\pi$
$42$		0			0
$43$	−25.9922	+	45.0199i	−0.0921809	+	0.159662i	−0.908429	−	0.418040i	$-0.862717\pi$
$43$	−25.9922	+	45.0199i	−0.0921809	+	0.159662i	0.816248	+	0.577702i	$0.196050\pi$
$44$		0			0
$45$	−21.0157	−	12.1334i	−0.0696185	−	0.0401942i
$46$		0			0
$47$		−	354.222i		−	1.09933i	−0.835384	−	0.549666i	$-0.814755\pi$
$47$		−	354.222i		−	1.09933i	0.835384	−	0.549666i	$-0.185245\pi$
$48$		0			0
$49$	−55.9425	−	96.8953i	−0.163098	−	0.282494i
$50$		0			0
$51$	12.4906			0.0342948
$52$		0			0
$53$	−10.4723			−0.0271412			−0.0135706	−	0.999908i	$-0.504320\pi$
$53$	−10.4723			−0.0271412			−0.0135706	+	0.999908i	$0.504320\pi$
$54$		0			0
$55$	−90.1712	−	156.181i	−0.221067	−	0.382899i
$56$		0			0
$57$			78.2550i			0.181844i
$58$		0			0
$59$	−385.480	−	222.557i	−0.850597	−	0.491092i	0.0102552	−	0.999947i	$-0.496736\pi$
$59$	−385.480	−	222.557i	−0.850597	−	0.491092i	−0.860852	+	0.508855i	$0.830069\pi$
$60$		0			0
$61$	−59.8481	+	103.660i	−0.125619	+	0.217579i	−0.921975	−	0.387250i	$-0.873425\pi$
$61$	−59.8481	+	103.660i	−0.125619	+	0.217579i	0.796356	+	0.604829i	$0.206758\pi$
$62$		0			0
$63$	118.491	−	68.4111i	0.236961	−	0.136809i
$64$		0			0
$65$	−2.20744	+	126.363i	−0.00421230	+	0.241129i
$66$		0			0
$67$	19.4057	−	11.2039i	0.0353848	−	0.0204294i	−0.482203	−	0.876059i	$-0.660163\pi$
$67$	19.4057	−	11.2039i	0.0353848	−	0.0204294i	0.517588	+	0.855630i	$0.326830\pi$
$68$		0			0
$69$	70.9863	−	122.952i	0.123851	−	0.214517i
$70$		0			0
$71$	246.997	+	142.604i	0.412861	+	0.238365i	0.692018	−	0.721880i	$-0.256722\pi$
$71$	246.997	+	142.604i	0.412861	+	0.238365i	−0.279157	+	0.960245i	$0.590055\pi$
$72$		0			0
$73$		−	740.989i		−	1.18803i	−0.804454	−	0.594015i	$-0.797542\pi$
$73$		−	740.989i		−	1.18803i	0.804454	−	0.594015i	$-0.202458\pi$
$74$		0			0
$75$	176.595	+	305.871i	0.271886	+	0.470920i
$76$		0			0
$77$	1016.81			1.50489
$78$		0			0
$79$	547.679			0.779983			0.389992	−	0.920818i	$-0.372478\pi$
$79$	547.679			0.779983			0.389992	+	0.920818i	$0.372478\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	603.056i		−	0.797518i	−0.917056	−	0.398759i	$-0.869441\pi$
$83$		−	603.056i		−	0.797518i	0.917056	−	0.398759i	$-0.130559\pi$
$84$		0			0
$85$	9.72218	+	5.61310i	0.0124061	+	0.00716266i
$86$		0			0
$87$	385.510	−	667.724i	0.475070	−	0.822845i
$88$		0			0
$89$	−186.774	+	107.834i	−0.222450	+	0.128431i	−0.607084	−	0.794638i	$-0.707661\pi$
$89$	−186.774	+	107.834i	−0.222450	+	0.128431i	0.384634	+	0.923069i	$0.374328\pi$
$90$		0			0
$91$	−610.789	−	367.011i	−0.703605	−	0.422782i
$92$		0			0
$93$	535.833	−	309.363i	0.597455	−	0.344941i
$94$		0			0
$95$	−35.1666	+	60.9104i	−0.0379792	+	0.0657818i
$96$		0			0
$97$	−1253.58	−	723.752i	−1.31218	−	0.757586i	−0.329722	−	0.944078i	$-0.606955\pi$
$97$	−1253.58	−	723.752i	−1.31218	−	0.757586i	−0.982457	+	0.186492i	$0.940288\pi$
$98$		0			0
$99$		−	601.964i		−	0.611107i
$100$		0			0
$101$	−441.725	−	765.090i	−0.435181	−	0.753756i	0.562129	−	0.827049i	$-0.309982\pi$
$101$	−441.725	−	765.090i	−0.435181	−	0.753756i	−0.997310	+	0.0732935i	$0.976649\pi$
$102$		0			0
$103$	1251.74			1.19745			0.598726	−	0.800954i	$-0.295674\pi$
$103$	1251.74			1.19745			0.598726	+	0.800954i	$0.295674\pi$
$104$		0			0
$105$	122.972			0.114293
$106$		0			0
$107$	−170.807	−	295.846i	−0.154323	−	0.267294i	0.778490	−	0.627658i	$-0.215986\pi$
$107$	−170.807	−	295.846i	−0.154323	−	0.267294i	−0.932812	+	0.360363i	$0.882653\pi$
$108$		0			0
$109$			775.177i			0.681179i	0.940212	+	0.340589i	$0.110627\pi$
$109$			775.177i			0.681179i	−0.940212	+	0.340589i	$0.889373\pi$
$110$		0			0
$111$	−456.446	−	263.529i	−0.390305	−	0.225343i
$112$		0			0
$113$	−639.524	+	1107.69i	−0.532402	+	0.922147i	0.466883	+	0.884319i	$0.345377\pi$
$113$	−639.524	+	1107.69i	−0.532402	+	0.922147i	−0.999284	+	0.0378273i	$0.987956\pi$
$114$		0			0
$115$	110.505	−	63.8004i	0.0896060	−	0.0517340i
$116$		0			0
$117$	−217.274	+	361.593i	−0.171683	+	0.285720i
$118$		0			0
$119$	−54.8160	+	31.6480i	−0.0422267	+	0.0243796i
$120$		0			0
$121$	1571.29	−	2721.55i	1.18053	−	2.04474i
$122$		0			0
$123$	406.502	+	234.694i	0.297992	+	0.172046i
$124$		0			0
$125$			654.476i			0.468305i
$126$		0			0
$127$	556.910	+	964.597i	0.389117	+	0.673970i	0.992331	−	0.123609i	$-0.0394470\pi$
$127$	556.910	+	964.597i	0.389117	+	0.673970i	−0.603214	+	0.797579i	$0.706114\pi$
$128$		0			0
$129$	−155.953			−0.106441
$130$		0			0
$131$	−2100.12			−1.40068			−0.700339	−	0.713811i	$-0.746968\pi$
$131$	−2100.12			−1.40068			−0.700339	+	0.713811i	$0.746968\pi$
$132$		0			0
$133$	−198.278	−	343.428i	−0.129270	−	0.223902i
$134$		0			0
$135$		−	72.8004i		−	0.0464123i
$136$		0			0
$137$	−1043.58	−	602.509i	−0.650793	−	0.375736i	0.137967	−	0.990437i	$-0.455943\pi$
$137$	−1043.58	−	602.509i	−0.650793	−	0.375736i	−0.788760	+	0.614701i	$0.789277\pi$
$138$		0			0
$139$	161.445	−	279.631i	0.0985149	−	0.170633i	−0.812555	−	0.582884i	$-0.801924\pi$
$139$	161.445	−	279.631i	0.0985149	−	0.170633i	0.911070	+	0.412251i	$0.135257\pi$
$140$		0			0
$141$	920.297	−	531.334i	0.549666	−	0.317350i
$142$		0			0
$143$	−2741.99	+	1519.86i	−1.60347	+	0.888789i
$144$		0			0
$145$	600.131	−	346.486i	0.343711	−	0.198442i
$146$		0			0
$147$	167.828	−	290.686i	0.0941645	−	0.163098i
$148$		0			0
$149$	−977.620	−	564.429i	−0.537515	−	0.310335i	0.206556	−	0.978435i	$-0.433774\pi$
$149$	−977.620	−	564.429i	−0.537515	−	0.310335i	−0.744071	+	0.668100i	$0.767108\pi$
$150$		0			0
$151$		−	2940.44i		−	1.58470i	−0.610066	−	0.792350i	$-0.708857\pi$
$151$		−	2940.44i		−	1.58470i	0.610066	−	0.792350i	$-0.291143\pi$
$152$		0			0
$153$	18.7359	+	32.4516i	0.00990006	+	0.0171474i
$154$		0			0
$155$	556.093			0.288171
$156$		0			0
$157$	629.388			0.319940			0.159970	−	0.987122i	$-0.448860\pi$
$157$	629.388			0.319940			0.159970	+	0.987122i	$0.448860\pi$
$158$		0			0
$159$	−15.7085	−	27.2079i	−0.00783500	−	0.0135706i
$160$		0			0
$161$			719.444i			0.352175i
$162$		0			0
$163$	342.004	+	197.456i	0.164343	+	0.0948832i	0.579915	−	0.814677i	$-0.303086\pi$
$163$	342.004	+	197.456i	0.164343	+	0.0948832i	−0.415573	+	0.909560i	$0.636419\pi$
$164$		0			0
$165$	270.514	−	468.543i	0.127633	−	0.221067i
$166$		0			0
$167$	−131.515	+	75.9299i	−0.0609395	+	0.0351834i	−0.530160	−	0.847898i	$-0.677868\pi$
$167$	−131.515	+	75.9299i	−0.0609395	+	0.0351834i	0.469221	+	0.883081i	$0.344535\pi$
$168$		0			0
$169$	2195.66	+	76.7357i	0.999390	+	0.0349275i
$170$		0			0
$171$	−203.312	+	117.382i	−0.0909221	+	0.0524939i
$172$		0			0
$173$	269.407	−	466.626i	0.118397	−	0.205069i	−0.800736	−	0.599018i	$-0.795558\pi$
$173$	269.407	−	466.626i	0.118397	−	0.205069i	0.919132	+	0.393949i	$0.128891\pi$
$174$		0			0
$175$	−1550.00	−	894.892i	−0.669537	−	0.386557i
$176$		0			0
$177$		−	1335.34i		−	0.567065i
$178$		0			0
$179$	1110.40	+	1923.27i	0.463659	+	0.803081i	0.999140	−	0.0414660i	$-0.0132028\pi$
$179$	1110.40	+	1923.27i	0.463659	+	0.803081i	−0.535481	+	0.844548i	$0.679870\pi$
$180$		0			0
$181$	3822.78			1.56986			0.784932	−	0.619582i	$-0.212698\pi$
$181$	3822.78			1.56986			0.784932	+	0.619582i	$0.212698\pi$
$182$		0			0
$183$	−359.089			−0.145052
$184$		0			0
$185$	−236.852	−	410.240i	−0.0941282	−	0.163035i
$186$		0			0
$187$			278.478i			0.108900i
$188$		0			0
$189$	355.474	+	205.233i	0.136809	+	0.0789869i
$190$		0			0
$191$	1732.09	−	3000.08i	0.656178	−	1.13653i	−0.325419	−	0.945570i	$-0.605505\pi$
$191$	1732.09	−	3000.08i	0.656178	−	1.13653i	0.981597	−	0.190964i	$-0.0611612\pi$
$192$		0			0
$193$	−4068.07	+	2348.70i	−1.51723	+	0.875975i	−0.517438	+	0.855721i	$0.673114\pi$
$193$	−4068.07	+	2348.70i	−1.51723	+	0.875975i	−0.999795	+	0.0202541i	$0.993552\pi$
$194$		0			0
$195$	−331.611	+	183.809i	−0.121780	+	0.0675017i
$196$		0			0
$197$	−2500.98	+	1443.94i	−0.904506	+	0.522217i	−0.878660	−	0.477449i	$-0.841562\pi$
$197$	−2500.98	+	1443.94i	−0.904506	+	0.522217i	−0.0258469	+	0.999666i	$0.508228\pi$
$198$		0			0
$199$	−31.5046	+	54.5676i	−0.0112226	+	0.0194382i	−0.871582	−	0.490249i	$-0.836906\pi$
$199$	−31.5046	+	54.5676i	−0.0112226	+	0.0194382i	0.860360	+	0.509688i	$0.170239\pi$
$200$		0			0
$201$	58.2171	+	33.6117i	0.0204294	+	0.0117949i
$202$		0			0
$203$			3907.14i			1.35087i
$204$		0			0
$205$	210.936	+	365.352i	0.0718654	+	0.124474i
$206$		0			0
$207$	425.918			0.143011
$208$		0			0
$209$	−1744.69			−0.577429
$210$		0			0
$211$	−524.848	−	909.064i	−0.171242	−	0.296600i	0.767612	−	0.640914i	$-0.221445\pi$
$211$	−524.848	−	909.064i	−0.171242	−	0.296600i	−0.938854	+	0.344315i	$0.888111\pi$
$212$		0			0
$213$			855.622i			0.275241i
$214$		0			0
$215$	−121.388	−	70.0832i	−0.0385050	−	0.0222309i
$216$		0			0
$217$	−1567.69	+	2715.33i	−0.490424	+	0.849440i
$218$		0			0
$219$	1925.15	−	1111.48i	0.594015	−	0.342955i
$220$		0			0
$221$	100.514	−	167.278i	0.0305942	−	0.0509156i
$222$		0			0
$223$	−2003.54	+	1156.75i	−0.601647	+	0.347361i	−0.769689	−	0.638419i	$-0.779589\pi$
$223$	−2003.54	+	1156.75i	−0.601647	+	0.347361i	0.168042	+	0.985780i	$0.446255\pi$
$224$		0			0
$225$	−529.785	+	917.614i	−0.156973	+	0.271886i
$226$		0			0
$227$	3290.43	+	1899.73i	0.962085	+	0.555460i	0.896814	−	0.442407i	$-0.145875\pi$
$227$	3290.43	+	1899.73i	0.962085	+	0.555460i	0.0652711	+	0.997868i	$0.479209\pi$
$228$		0			0
$229$			4321.07i			1.24692i	0.781856	+	0.623459i	$0.214273\pi$
$229$			4321.07i			1.24692i	−0.781856	+	0.623459i	$0.785727\pi$
$230$		0			0
$231$	1525.22	+	2641.76i	0.434425	+	0.752446i
$232$		0			0
$233$	−5279.77			−1.48450			−0.742251	−	0.670122i	$-0.766242\pi$
$233$	−5279.77			−1.48450			−0.742251	+	0.670122i	$0.766242\pi$
$234$		0			0
$235$	955.094			0.265121
$236$		0			0
$237$	821.518	+	1422.91i	0.225162	+	0.389992i
$238$		0			0
$239$		−	1547.92i		−	0.418939i	−0.977815	−	0.209469i	$-0.932826\pi$
$239$		−	1547.92i		−	0.418939i	0.977815	−	0.209469i	$-0.0671737\pi$
$240$		0			0
$241$	−4259.12	−	2459.00i	−1.13840	−	0.657255i	−0.192365	−	0.981323i	$-0.561616\pi$
$241$	−4259.12	−	2459.00i	−1.13840	−	0.657255i	−0.946033	+	0.324069i	$0.894949\pi$
$242$		0			0
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$		0			0
$245$	261.260	−	150.839i	0.0681277	−	0.0393336i
$246$		0			0
$247$	1048.02	+	629.731i	0.269974	+	0.162222i
$248$		0			0
$249$	1566.78	−	904.584i	0.398759	−	0.230224i
$250$		0			0
$251$	−577.890	+	1000.94i	−0.145323	+	0.251707i	−0.929493	−	0.368839i	$-0.879756\pi$
$251$	−577.890	+	1000.94i	−0.145323	+	0.251707i	0.784170	+	0.620546i	$0.213089\pi$
$252$		0			0
$253$	2741.20	+	1582.63i	0.681178	+	0.393278i
$254$		0			0
$255$			33.6786i			0.00827073i
$256$		0			0
$257$	1175.98	+	2036.85i	0.285429	+	0.494378i	0.972713	−	0.232011i	$-0.0745304\pi$
$257$	1175.98	+	2036.85i	0.285429	+	0.494378i	−0.687284	+	0.726389i	$0.741197\pi$
$258$		0			0
$259$	2670.86			0.640769
$260$		0			0
$261$	2313.06			0.548563
$262$		0			0
$263$	2760.94	+	4782.09i	0.647326	+	1.12120i	0.983759	+	0.179494i	$0.0574461\pi$
$263$	2760.94	+	4782.09i	0.647326	+	1.12120i	−0.336433	+	0.941707i	$0.609221\pi$
$264$		0			0
$265$		−	28.2367i		−	0.00654553i
$266$		0			0
$267$	−560.322	−	323.502i	−0.128431	−	0.0741499i
$268$		0			0
$269$	−1958.48	+	3392.18i	−0.443905	+	0.768866i	−0.997975	−	0.0636038i	$-0.979741\pi$
$269$	−1958.48	+	3392.18i	−0.443905	+	0.768866i	0.554070	+	0.832470i	$0.313074\pi$
$270$		0			0
$271$	−2405.41	+	1388.76i	−0.539182	+	0.311297i	−0.744747	−	0.667347i	$-0.767430\pi$
$271$	−2405.41	+	1388.76i	−0.539182	+	0.311297i	0.205566	+	0.978643i	$0.434097\pi$
$272$		0			0
$273$	37.3383	−	2137.39i	0.00827771	−	0.473849i
$274$		0			0
$275$	−6819.38	+	3937.17i	−1.49536	+	0.863347i
$276$		0			0
$277$	3291.54	−	5701.12i	0.713969	−	1.23663i	−0.249386	−	0.968404i	$-0.580229\pi$
$277$	3291.54	−	5701.12i	0.713969	−	1.23663i	0.963356	−	0.268227i	$-0.0864378\pi$
$278$		0			0
$279$	1607.50	+	928.090i	0.344941	+	0.199152i
$280$		0			0
$281$		−	2871.66i		−	0.609640i	−0.952410	−	0.304820i	$-0.901404\pi$
$281$		−	2871.66i		−	0.609640i	0.952410	−	0.304820i	$-0.0985963\pi$
$282$		0			0
$283$	−3759.02	−	6510.81i	−0.789578	−	1.36759i	−0.926226	−	0.376969i	$-0.876966\pi$
$283$	−3759.02	−	6510.81i	−0.789578	−	1.36759i	0.136648	−	0.990620i	$-0.456367\pi$
$284$		0			0
$285$	−211.000			−0.0438546
$286$		0			0
$287$	−2378.62			−0.489217
$288$		0			0
$289$	2447.83	+	4239.77i	0.498236	+	0.862970i
$290$		0			0
$291$		−	4342.51i		−	0.874785i
$292$		0			0
$293$	3902.80	+	2253.28i	0.778171	+	0.449278i	0.835782	−	0.549062i	$-0.185015\pi$
$293$	3902.80	+	2253.28i	0.778171	+	0.449278i	−0.0576104	+	0.998339i	$0.518348\pi$
$294$		0			0
$295$	600.083	−	1039.37i	0.118435	−	0.205135i
$296$		0			0
$297$	1563.95	−	902.945i	0.305554	−	0.176411i
$298$		0			0
$299$	−1075.37	−	1940.08i	−0.207994	−	0.375244i
$300$		0			0
$301$	684.413	−	395.146i	0.131060	−	0.0756673i
$302$		0			0
$303$	1325.18	−	2295.27i	0.251252	−	0.435181i
$304$		0			0
$305$	−279.500	−	161.369i	−0.0524725	−	0.0302950i
$306$		0			0
$307$			9538.89i			1.77333i	0.462409	+	0.886667i	$0.346985\pi$
$307$			9538.89i			1.77333i	−0.462409	+	0.886667i	$0.653015\pi$
$308$		0			0
$309$	1877.61	+	3252.12i	0.345675	+	0.598726i
$310$		0			0
$311$	−7466.28			−1.36133			−0.680666	−	0.732594i	$-0.738309\pi$
$311$	−7466.28			−1.36133			−0.680666	+	0.732594i	$0.738309\pi$
$312$		0			0
$313$	−1821.65			−0.328964			−0.164482	−	0.986380i	$-0.552595\pi$
$313$	−1821.65			−0.328964			−0.164482	+	0.986380i	$0.552595\pi$
$314$		0			0
$315$	184.458	+	319.490i	0.0329937	+	0.0571467i
$316$		0			0
$317$			3125.14i			0.553708i	0.960912	+	0.276854i	$0.0892918\pi$
$317$			3125.14i			0.553708i	−0.960912	+	0.276854i	$0.910708\pi$
$318$		0			0
$319$	14886.9	+	8594.93i	2.61287	+	1.50854i
$320$		0			0
$321$	512.420	−	887.538i	0.0890982	−	0.154323i
$322$		0			0
$323$	94.0554	−	54.3029i	0.0162024	−	0.00935448i
$324$		0			0
$325$	5517.41	+	96.3842i	0.941696	+	0.0164506i
$326$		0			0
$327$	−2013.97	+	1162.77i	−0.340589	+	0.196639i
$328$		0			0
$329$	−2692.53	+	4663.59i	−0.451197	+	0.781496i
$330$		0			0
$331$	−1345.52	−	776.836i	−0.223433	−	0.128999i	0.384106	−	0.923289i	$-0.374510\pi$
$331$	−1345.52	−	776.836i	−0.223433	−	0.128999i	−0.607539	+	0.794290i	$0.707843\pi$
$332$		0			0
$333$		−	1581.17i		−	0.260204i
$334$		0			0
$335$	30.2092	+	52.3238i	0.00492688	+	0.00853360i
$336$		0			0
$337$	3190.43			0.515709			0.257855	−	0.966184i	$-0.416984\pi$
$337$	3190.43			0.515709			0.257855	+	0.966184i	$0.416984\pi$
$338$		0			0
$339$	−3837.15			−0.614764
$340$		0			0
$341$	6897.24	+	11946.4i	1.09533	+	1.89716i
$342$		0			0
$343$			6915.37i			1.08862i
$344$		0			0
$345$	331.516	+	191.401i	0.0517340	+	0.0298687i
$346$		0			0
$347$	−2859.34	+	4952.53i	−0.442356	+	0.766183i	−0.997864	−	0.0653283i	$-0.979191\pi$
$347$	−2859.34	+	4952.53i	−0.442356	+	0.766183i	0.555508	+	0.831511i	$0.312524\pi$
$348$		0			0
$349$	2882.53	−	1664.23i	0.442116	−	0.255256i	−0.262379	−	0.964965i	$-0.584507\pi$
$349$	2882.53	−	1664.23i	0.442116	−	0.255256i	0.704495	+	0.709709i	$0.251174\pi$
$350$		0			0
$351$	−1265.36	−	22.1046i	−0.192421	−	0.00336141i
$352$		0			0
$353$	−10657.7	+	6153.25i	−1.60695	+	0.927774i	−0.616905	+	0.787037i	$0.711614\pi$
$353$	−10657.7	+	6153.25i	−1.60695	+	0.927774i	−0.990047	+	0.140737i	$0.955053\pi$
$354$		0			0
$355$	−384.504	+	665.981i	−0.0574855	+	0.0995679i
$356$		0			0
$357$	−164.448	−	94.9441i	−0.0243796	−	0.0140756i
$358$		0			0
$359$			8539.97i			1.25549i	0.778418	+	0.627747i	$0.216023\pi$
$359$			8539.97i			1.25549i	−0.778418	+	0.627747i	$0.783977\pi$
$360$		0			0
$361$	−3089.29	−	5350.80i	−0.450399	−	0.780114i
$362$		0			0
$363$	9427.74			1.36316
$364$		0			0
$365$	1997.94			0.286512
$366$		0			0
$367$	1248.33	+	2162.17i	0.177553	+	0.307532i	0.941042	−	0.338290i	$-0.109848\pi$
$367$	1248.33	+	2162.17i	0.177553	+	0.307532i	−0.763489	+	0.645821i	$0.776515\pi$
$368$		0			0
$369$			1408.16i			0.198661i
$370$		0			0
$371$	137.876	+	79.6026i	0.0192942	+	0.0111395i
$372$		0			0
$373$	571.454	−	989.787i	0.0793264	−	0.137397i	−0.823633	−	0.567123i	$-0.808056\pi$
$373$	571.454	−	989.787i	0.0793264	−	0.137397i	0.902960	+	0.429726i	$0.141390\pi$
$374$		0			0
$375$	−1700.38	+	981.713i	−0.234152	+	0.135188i
$376$		0			0
$377$	−5840.10	−	10536.2i	−0.797826	−	1.43936i
$378$		0			0
$379$	10549.8	−	6090.91i	1.42983	−	0.825512i	0.432723	−	0.901527i	$-0.357553\pi$
$379$	10549.8	−	6090.91i	1.42983	−	0.825512i	0.997107	+	0.0760146i	$0.0242196\pi$
$380$		0			0
$381$	−1670.73	+	2893.79i	−0.224657	+	0.389117i
$382$		0			0
$383$	−8816.66	−	5090.30i	−1.17627	−	0.679118i	−0.221119	−	0.975247i	$-0.570971\pi$
$383$	−8816.66	−	5090.30i	−1.17627	−	0.679118i	−0.955148	+	0.296129i	$0.904304\pi$
$384$		0			0
$385$			2741.65i			0.362928i
$386$		0			0
$387$	−233.930	−	405.179i	−0.0307270	−	0.0532207i
$388$		0			0
$389$	−5845.83			−0.761941			−0.380971	−	0.924587i	$-0.624410\pi$
$389$	−5845.83			−0.761941			−0.380971	+	0.924587i	$0.624410\pi$
$390$		0			0
$391$	−197.036			−0.0254848
$392$		0			0
$393$	−3150.19	−	5456.28i	−0.404341	−	0.700339i
$394$		0			0
$395$			1476.71i			0.188105i
$396$		0			0
$397$	−2165.86	−	1250.46i	−0.273807	−	0.158083i	0.356809	−	0.934177i	$-0.383865\pi$
$397$	−2165.86	−	1250.46i	−0.273807	−	0.158083i	−0.630617	+	0.776094i	$0.717198\pi$
$398$		0			0
$399$	594.834	−	1030.28i	0.0746340	−	0.129270i
$400$		0			0
$401$	7958.12	−	4594.62i	0.991046	−	0.572181i	0.0854594	−	0.996342i	$-0.472764\pi$
$401$	7958.12	−	4594.62i	0.991046	−	0.572181i	0.905587	+	0.424161i	$0.139431\pi$
$402$		0			0
$403$	168.848	−	9665.54i	0.0208708	−	1.19473i
$404$		0			0
$405$	189.141	−	109.201i	0.0232062	−	0.0133981i
$406$		0			0
$407$	5875.36	−	10176.4i	0.715555	−	1.23938i
$408$		0			0
$409$	−7979.89	−	4607.19i	−0.964744	−	0.556995i	−0.0671140	−	0.997745i	$-0.521379\pi$
$409$	−7979.89	−	4607.19i	−0.964744	−	0.556995i	−0.897630	+	0.440750i	$0.854712\pi$
$410$		0			0
$411$		−	3615.05i		−	0.433862i
$412$		0			0
$413$	3383.42	+	5860.25i	0.403116	+	0.698218i
$414$		0			0
$415$	1626.03			0.192334
$416$		0			0
$417$	968.669			0.113755
$418$		0			0
$419$	−3247.20	−	5624.32i	−0.378607	−	0.655767i	0.612253	−	0.790662i	$-0.290263\pi$
$419$	−3247.20	−	5624.32i	−0.378607	−	0.655767i	−0.990860	+	0.134895i	$0.956930\pi$
$420$		0			0
$421$			3059.56i			0.354190i	0.984194	+	0.177095i	$0.0566699\pi$
$421$			3059.56i			0.354190i	−0.984194	+	0.177095i	$0.943330\pi$
$422$		0			0
$423$	2760.89	+	1594.00i	0.317350	+	0.183222i
$424$		0			0
$425$	245.087	−	424.502i	0.0279728	−	0.0484503i
$426$		0			0
$427$	1575.89	−	909.839i	0.178601	−	0.103115i
$428$		0			0
$429$	−8061.69	−	4844.10i	−0.907277	−	0.545164i
$430$		0			0
$431$	−6873.69	+	3968.53i	−0.768199	+	0.443520i	−0.832232	−	0.554428i	$-0.812937\pi$
$431$	−6873.69	+	3968.53i	−0.768199	+	0.443520i	0.0640325	+	0.997948i	$0.479604\pi$
$432$		0			0
$433$	3647.19	−	6317.11i	0.404786	−	0.701111i	−0.589510	−	0.807761i	$-0.700679\pi$
$433$	3647.19	−	6317.11i	0.404786	−	0.701111i	0.994297	+	0.106650i	$0.0340125\pi$
$434$		0			0
$435$	1800.39	+	1039.46i	0.198442	+	0.114570i
$436$		0			0
$437$		−	1234.45i		−	0.135130i
$438$		0			0
$439$	−7607.35	−	13176.3i	−0.827059	−	1.43251i	−0.900335	−	0.435197i	$-0.856679\pi$
$439$	−7607.35	−	13176.3i	−0.827059	−	1.43251i	0.0732765	−	0.997312i	$-0.476654\pi$
$440$		0			0
$441$	1006.97			0.108732
$442$		0			0
$443$	−1517.05			−0.162703			−0.0813515	−	0.996685i	$-0.525924\pi$
$443$	−1517.05			−0.162703			−0.0813515	+	0.996685i	$0.525924\pi$
$444$		0			0
$445$	−290.754	−	503.601i	−0.0309732	−	0.0536472i
$446$		0			0
$447$		−	3386.58i		−	0.358343i
$448$		0			0
$449$	−610.761	−	352.623i	−0.0641951	−	0.0370631i	0.467559	−	0.883962i	$-0.345134\pi$
$449$	−610.761	−	352.623i	−0.0641951	−	0.0370631i	−0.531754	+	0.846899i	$0.678467\pi$
$450$		0			0
$451$	−5232.48	+	9062.93i	−0.546315	+	0.946245i
$452$		0			0
$453$	7639.49	−	4410.66i	0.792350	−	0.457464i
$454$		0			0
$455$	989.575	−	1646.88i	0.101960	−	0.169685i
$456$		0			0
$457$	−6302.69	+	3638.86i	−0.645137	+	0.372470i	−0.786591	−	0.617475i	$-0.788156\pi$
$457$	−6302.69	+	3638.86i	−0.645137	+	0.372470i	0.141454	+	0.989945i	$0.454822\pi$
$458$		0			0
$459$	−56.2078	+	97.3547i	−0.00571580	+	0.00990006i
$460$		0			0
$461$	−1699.04	−	980.941i	−0.171653	−	0.0991041i	0.411712	−	0.911314i	$-0.364931\pi$
$461$	−1699.04	−	980.941i	−0.171653	−	0.0991041i	−0.583365	+	0.812210i	$0.698264\pi$
$462$		0			0
$463$		−	10374.1i		−	1.04131i	−0.853768	−	0.520653i	$-0.825689\pi$
$463$		−	10374.1i		−	1.04131i	0.853768	−	0.520653i	$-0.174311\pi$
$464$		0			0
$465$	834.140	+	1444.77i	0.0831878	+	0.144085i
$466$		0			0
$467$	8788.92			0.870883			0.435442	−	0.900217i	$-0.356592\pi$
$467$	8788.92			0.870883			0.435442	+	0.900217i	$0.356592\pi$
$468$		0			0
$469$	−340.653			−0.0335392
$470$		0			0
$471$	944.082	+	1635.20i	0.0923588	+	0.159970i
$472$		0			0
$473$		−	3476.97i		−	0.337995i
$474$		0			0
$475$	2659.55	+	1535.49i	0.256902	+	0.148322i
$476$		0			0
$477$	47.1255	−	81.6237i	0.00452354	−	0.00783500i
$478$		0			0
$479$	−9648.96	+	5570.83i	−0.920401	+	0.531394i	−0.883763	−	0.467935i	$-0.844998\pi$
$479$	−9648.96	+	5570.83i	−0.920401	+	0.531394i	−0.0366382	+	0.999329i	$0.511665\pi$
$480$		0			0
$481$	−7202.36	+	3992.20i	−0.682743	+	0.378438i
$482$		0			0
$483$	−1869.17	+	1079.17i	−0.176087	+	0.101664i
$484$		0			0
$485$	1951.46	−	3380.03i	0.182704	−	0.316452i
$486$		0			0
$487$	−17009.1	−	9820.23i	−1.58266	−	0.913752i	−0.994469	−	0.105033i	$-0.966505\pi$
$487$	−17009.1	−	9820.23i	−1.58266	−	0.913752i	−0.588195	−	0.808719i	$-0.700161\pi$
$488$		0			0
$489$			1184.74i			0.109562i
$490$		0			0
$491$	1705.16	+	2953.42i	0.156726	+	0.271458i	0.933686	−	0.358092i	$-0.116573\pi$
$491$	1705.16	+	2953.42i	0.156726	+	0.271458i	−0.776960	+	0.629550i	$0.783239\pi$
$492$		0			0
$493$	−1070.06			−0.0977546
$494$		0			0
$495$	1623.08			0.147378
$496$		0			0
$497$	−2167.93	−	3754.96i	−0.195664	−	0.338899i
$498$		0			0
$499$			5032.44i			0.451469i	0.974189	+	0.225735i	$0.0724782\pi$
$499$			5032.44i			0.451469i	−0.974189	+	0.225735i	$0.927522\pi$
$500$		0			0
$501$	−394.544	−	227.790i	−0.0351834	−	0.0203132i
$502$		0			0
$503$	8594.69	−	14886.4i	0.761866	−	1.31959i	−0.180022	−	0.983663i	$-0.557617\pi$
$503$	8594.69	−	14886.4i	0.761866	−	1.31959i	0.941888	−	0.335927i	$-0.109050\pi$
$504$		0			0
$505$	2062.92	−	1191.03i	0.181780	−	0.104951i
$506$		0			0
$507$	3094.12	+	5819.59i	0.271035	+	0.509778i
$508$		0			0
$509$	−805.889	+	465.280i	−0.0701776	+	0.0405170i	−0.534678	−	0.845056i	$-0.679567\pi$
$509$	−805.889	+	465.280i	−0.0701776	+	0.0405170i	0.464501	+	0.885573i	$0.346234\pi$
$510$		0			0
$511$	−5632.43	+	9755.65i	−0.487601	+	0.844549i
$512$		0			0
$513$	−609.937	−	352.147i	−0.0524939	−	0.0303074i
$514$		0			0
$515$			3375.08i			0.288784i
$516$		0			0
$517$	11846.1	+	20518.0i	1.00772	+	1.74541i
$518$		0			0
$519$	1616.44			0.136713
$520$		0			0
$521$	−9869.60			−0.829933			−0.414966	−	0.909837i	$-0.636207\pi$
$521$	−9869.60			−0.829933			−0.414966	+	0.909837i	$0.636207\pi$
$522$		0			0
$523$	−10710.3	−	18550.8i	−0.895466	−	1.55099i	−0.833226	−	0.552932i	$-0.813509\pi$
$523$	−10710.3	−	18550.8i	−0.895466	−	1.55099i	−0.0622398	−	0.998061i	$-0.519824\pi$
$524$		0			0
$525$		−	5369.35i		−	0.446358i
$526$		0			0
$527$	−743.654	−	429.349i	−0.0614688	−	0.0354890i
$528$		0			0
$529$	4963.71	−	8597.40i	0.407965	−	0.706616i
$530$		0			0
$531$	3469.32	−	2003.01i	0.283532	−	0.163697i
$532$		0			0
$533$	6414.28	−	3555.38i	0.521263	−	0.288931i
$534$		0			0
$535$	797.693	−	460.548i	0.0644622	−	0.0372173i
$536$		0			0
$537$	−3331.19	+	5769.80i	−0.267694	+	0.463659i
$538$		0			0
$539$	6480.83	+	3741.71i	0.517902	+	0.299011i
$540$		0			0
$541$		−	7771.50i		−	0.617602i	−0.951127	−	0.308801i	$-0.900072\pi$
$541$		−	7771.50i		−	0.617602i	0.951127	−	0.308801i	$-0.0999277\pi$
$542$		0			0
$543$	5734.17	+	9931.88i	0.453180	+	0.784932i
$544$		0			0
$545$	−2090.12			−0.164277
$546$		0			0
$547$	15577.5			1.21763			0.608817	−	0.793310i	$-0.291644\pi$
$547$	15577.5			1.21763			0.608817	+	0.793310i	$0.291644\pi$
$548$		0			0
$549$	−538.633	−	932.940i	−0.0418730	−	0.0725262i
$550$		0			0
$551$		−	6704.02i		−	0.518332i
$552$		0			0
$553$	−7210.58	−	4163.03i	−0.554476	−	0.320127i
$554$		0			0
$555$	710.556	−	1230.72i	0.0543449	−	0.0941282i
$556$		0			0
$557$	19749.3	−	11402.3i	1.50234	−	0.867377i	0.502345	−	0.864667i	$-0.332471\pi$
$557$	19749.3	−	11402.3i	1.50234	−	0.867377i	0.999996	−	0.00270962i	$-0.000862500\pi$
$558$		0			0
$559$	−1254.98	+	2088.58i	−0.0949556	+	0.158028i
$560$		0			0
$561$	−723.506	+	417.716i	−0.0544500	+	0.0314367i
$562$		0			0
$563$	1758.71	−	3046.17i	0.131653	−	0.228030i	−0.792661	−	0.609663i	$-0.791305\pi$
$563$	1758.71	−	3046.17i	0.131653	−	0.228030i	0.924314	+	0.381633i	$0.124638\pi$
$564$		0			0
$565$	−2986.67	−	1724.36i	−0.222390	−	0.128397i
$566$		0			0
$567$			1231.40i			0.0912062i
$568$		0			0
$569$	−3046.72	−	5277.08i	−0.224473	−	0.388799i	0.731688	−	0.681640i	$-0.238733\pi$
$569$	−3046.72	−	5277.08i	−0.224473	−	0.388799i	−0.956161	+	0.292841i	$0.905399\pi$
$570$		0			0
$571$	10460.2			0.766630			0.383315	−	0.923618i	$-0.374782\pi$
$571$	10460.2			0.766630			0.383315	+	0.923618i	$0.374782\pi$
$572$		0			0
$573$	10392.6			0.757689
$574$		0			0
$575$	−2785.74	−	4825.03i	−0.202040	−	0.349944i
$576$		0			0
$577$		−	9648.19i		−	0.696117i	−0.937473	−	0.348058i	$-0.886841\pi$
$577$		−	9648.19i		−	0.696117i	0.937473	−	0.348058i	$-0.113159\pi$
$578$		0			0
$579$	−12204.2	−	7046.10i	−0.875975	−	0.505744i
$580$		0			0
$581$	−4583.97	+	7939.66i	−0.327324	+	0.566941i
$582$		0			0
$583$	606.599	−	350.220i	0.0430922	−	0.0248793i
$584$		0			0
$585$	−974.966	−	585.838i	−0.0689058	−	0.0414041i
$586$		0			0
$587$	−1879.91	+	1085.37i	−0.132184	+	0.0763166i	−0.564634	−	0.825341i	$-0.690983\pi$
$587$	−1879.91	+	1085.37i	−0.132184	+	0.0763166i	0.432450	+	0.901658i	$0.357649\pi$
$588$		0			0
$589$	2689.91	−	4659.06i	0.188176	−	0.325931i
$590$		0			0
$591$	−7502.95	−	4331.83i	−0.522217	−	0.301502i
$592$		0			0
$593$		−	22885.9i		−	1.58484i	−0.609975	−	0.792421i	$-0.708820\pi$
$593$		−	22885.9i		−	1.58484i	0.609975	−	0.792421i	$-0.291180\pi$
$594$		0			0
$595$	−85.3330	−	147.801i	−0.00587951	−	0.0101836i
$596$		0			0
$597$	−189.028			−0.0129588
$598$		0			0
$599$	23978.7			1.63563			0.817815	−	0.575482i	$-0.195185\pi$
$599$	23978.7			1.63563			0.817815	+	0.575482i	$0.195185\pi$
$600$		0			0
$601$	−6436.62	−	11148.6i	−0.436864	−	0.756671i	0.560582	−	0.828099i	$-0.310578\pi$
$601$	−6436.62	−	11148.6i	−0.436864	−	0.756671i	−0.997446	+	0.0714284i	$0.977244\pi$
$602$		0			0
$603$			201.670i			0.0136196i
$604$		0			0
$605$	7338.16	+	4236.69i	0.493122	+	0.284704i
$606$		0			0
$607$	−3558.57	+	6163.63i	−0.237954	+	0.412148i	−0.960127	−	0.279564i	$-0.909810\pi$
$607$	−3558.57	+	6163.63i	−0.237954	+	0.412148i	0.722173	+	0.691712i	$0.243143\pi$
$608$		0			0
$609$	−10151.0	+	5860.71i	−0.675437	+	0.389964i
$610$		0			0
$611$	289.998	−	16600.6i	0.0192014	−	1.09917i
$612$		0			0
$613$	150.079	−	86.6484i	0.00988850	−	0.00570913i	−0.495048	−	0.868866i	$-0.664849\pi$
$613$	150.079	−	86.6484i	0.00988850	−	0.00570913i	0.504936	+	0.863157i	$0.331516\pi$
$614$		0			0
$615$	−632.808	+	1096.06i	−0.0414915	+	0.0718654i
$616$		0			0
$617$	5285.14	+	3051.38i	0.344849	+	0.199099i	0.662414	−	0.749138i	$-0.269532\pi$
$617$	5285.14	+	3051.38i	0.344849	+	0.199099i	−0.317565	+	0.948236i	$0.602865\pi$
$618$		0			0
$619$		−	14867.8i		−	0.965409i	−0.875783	−	0.482705i	$-0.839654\pi$
$619$		−	14867.8i		−	0.965409i	0.875783	−	0.482705i	$-0.160346\pi$
$620$		0			0
$621$	638.876	+	1106.57i	0.0412838	+	0.0715056i
$622$		0			0
$623$	3278.69			0.210847
$624$		0			0
$625$	12951.6			0.828900
$626$		0			0
$627$	−2617.03	−	4532.84i	−0.166689	−	0.288715i
$628$		0			0
$629$			731.475i			0.0463686i
$630$		0			0
$631$	14904.8	+	8605.29i	0.940334	+	0.542902i	0.890065	−	0.455834i	$-0.150659\pi$
$631$	14904.8	+	8605.29i	0.940334	+	0.542902i	0.0502690	+	0.998736i	$0.483992\pi$
$632$		0			0
$633$	1574.55	−	2727.19i	0.0988666	−	0.171242i
$634$		0			0
$635$	−2600.86	+	1501.60i	−0.162538	+	0.0938415i
$636$		0			0
$637$	−2542.42	−	4586.80i	−0.158139	−	0.285299i
$638$		0			0
$639$	−2222.97	+	1283.43i	−0.137620	+	0.0794552i
$640$		0			0
$641$	−6318.01	+	10943.1i	−0.389308	+	0.674301i	−0.992357	−	0.123403i	$-0.960619\pi$
$641$	−6318.01	+	10943.1i	−0.389308	+	0.674301i	0.603049	+	0.797704i	$0.293953\pi$
$642$		0			0
$643$	−8302.04	−	4793.19i	−0.509177	−	0.293973i	0.223318	−	0.974746i	$-0.428311\pi$
$643$	−8302.04	−	4793.19i	−0.509177	−	0.293973i	−0.732495	+	0.680772i	$0.761644\pi$
$644$		0			0
$645$		−	420.499i		−	0.0256700i
$646$		0			0
$647$	−2622.16	−	4541.72i	−0.159332	−	0.275971i	0.775296	−	0.631598i	$-0.217601\pi$
$647$	−2622.16	−	4541.72i	−0.159332	−	0.275971i	−0.934628	+	0.355627i	$0.884267\pi$
$648$		0			0
$649$	29771.4			1.80066
$650$		0			0
$651$	−9406.17			−0.566293
$652$		0			0
$653$	−9434.51	−	16341.1i	−0.565392	−	0.979288i	−0.997013	−	0.0772326i	$-0.975392\pi$
$653$	−9434.51	−	16341.1i	−0.565392	−	0.979288i	0.431621	−	0.902055i	$-0.357942\pi$
$654$		0			0
$655$		−	5662.59i		−	0.337795i
$656$		0			0
$657$	5775.44	+	3334.45i	0.342955	+	0.198005i
$658$		0			0
$659$	−12149.9	+	21044.2i	−0.718197	+	1.24395i	0.243516	+	0.969897i	$0.421699\pi$
$659$	−12149.9	+	21044.2i	−0.718197	+	1.24395i	−0.961713	+	0.274057i	$0.911634\pi$
$660$		0			0
$661$	−25907.2	+	14957.5i	−1.52447	+	0.880151i	−0.524886	+	0.851173i	$0.675892\pi$
$661$	−25907.2	+	14957.5i	−1.52447	+	0.880151i	−0.999580	+	0.0289779i	$0.990775\pi$
$662$		0			0
$663$	585.373	+	10.2259i	0.0342896	+	0.000599008i
$664$		0			0
$665$	925.988	−	534.620i	0.0539974	−	0.0311754i
$666$		0			0
$667$	−6081.32	+	10533.2i	−0.353028	+	0.611462i
$668$		0			0
$669$	−6010.63	−	3470.24i	−0.347361	−	0.200549i
$670$		0			0
$671$		−	8005.86i		−	0.460600i
$672$		0			0
$673$	7746.84	+	13417.9i	0.443713	+	0.768533i	0.997962	−	0.0638177i	$-0.0203276\pi$
$673$	7746.84	+	13417.9i	0.443713	+	0.768533i	−0.554249	+	0.832351i	$0.686994\pi$
$674$		0			0
$675$	−3178.71			−0.181257
$676$		0			0
$677$	11729.7			0.665891			0.332945	−	0.942946i	$-0.391958\pi$
$677$	11729.7			0.665891			0.332945	+	0.942946i	$0.391958\pi$
$678$		0			0
$679$	11002.8	+	19057.4i	0.621869	+	1.07711i
$680$		0			0
$681$			11398.4i			0.641390i
$682$		0			0
$683$	1011.88	+	584.210i	0.0566889	+	0.0327294i	0.528077	−	0.849197i	$-0.322913\pi$
$683$	1011.88	+	584.210i	0.0566889	+	0.0327294i	−0.471388	+	0.881926i	$0.656247\pi$
$684$		0			0
$685$	1624.55	−	2813.81i	0.0906145	−	0.156949i
$686$		0			0
$687$	−11226.5	+	6481.61i	−0.623459	+	0.359955i
$688$		0			0
$689$	−490.786	−	8.57358i	−0.0271371	−	0.000474060i
$690$		0			0
$691$	−28572.7	+	16496.4i	−1.57302	+	0.908183i	−0.577222	+	0.816587i	$0.695863\pi$
$691$	−28572.7	+	16496.4i	−1.57302	+	0.908183i	−0.995796	+	0.0915952i	$0.970803\pi$
$692$		0			0
$693$	−4575.66	+	7925.28i	−0.250815	+	0.434425i
$694$		0			0
$695$	753.972	+	435.306i	0.0411508	+	0.0237584i
$696$		0			0
$697$		−	651.438i		−	0.0354017i
$698$		0			0
$699$	−7919.65	−	13717.2i	−0.428539	−	0.742251i
$700$		0			0
$701$	14785.8			0.796651			0.398326	−	0.917244i	$-0.369591\pi$
$701$	14785.8			0.796651			0.398326	+	0.917244i	$0.369591\pi$
$702$		0			0
$703$	−4582.77			−0.245864
$704$		0			0
$705$	1432.64	+	2481.41i	0.0765339	+	0.132561i
$706$		0			0
$707$			13430.6i			0.714442i
$708$		0			0
$709$	10941.4	+	6317.00i	0.579565	+	0.334612i	0.760961	−	0.648798i	$-0.224728\pi$
$709$	10941.4	+	6317.00i	0.579565	+	0.334612i	−0.181395	+	0.983410i	$0.558061\pi$
$710$		0			0
$711$	−2464.55	+	4268.73i	−0.129997	+	0.225162i
$712$		0			0
$713$	−8452.62	+	4880.12i	−0.443973	+	0.256328i
$714$		0			0
$715$	−4098.01	−	7393.25i	−0.214345	−	0.386702i
$716$		0			0
$717$	4021.60	−	2321.87i	0.209469	−	0.120937i
$718$		0			0
$719$	13648.3	−	23639.5i	0.707920	−	1.22615i	−0.257707	−	0.966223i	$-0.582967\pi$
$719$	13648.3	−	23639.5i	0.707920	−	1.22615i	0.965627	−	0.259931i	$-0.0836998\pi$
$720$		0			0
$721$	−16480.1	−	9514.77i	−0.851248	−	0.491468i
$722$		0			0
$723$		−	14754.0i		−	0.758932i
$724$		0			0
$725$	−15128.7	−	26203.7i	−0.774987	−	1.34232i
$726$		0			0
$727$	4658.21			0.237639			0.118819	−	0.992916i	$-0.462089\pi$
$727$	4658.21			0.237639			0.118819	+	0.992916i	$0.462089\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	108.220	+	187.442i	0.00547558	+	0.00948399i
$732$		0			0
$733$		−	166.474i		−	0.00838864i	−0.999991	−	0.00419432i	$-0.998665\pi$
$733$		−	166.474i		−	0.00838864i	0.999991	−	0.00419432i	$-0.00133510\pi$
$734$		0			0
$735$	783.780	+	452.516i	0.0393336	+	0.0227092i
$736$		0			0
$737$	−749.370	+	1297.95i	−0.0374537	+	0.0648718i
$738$		0			0
$739$	11031.5	−	6369.03i	0.549120	−	0.317035i	−0.199647	−	0.979868i	$-0.563980\pi$
$739$	11031.5	−	6369.03i	0.549120	−	0.317035i	0.748767	+	0.662833i	$0.230646\pi$
$740$		0			0
$741$	−64.0665	+	3667.42i	−0.00317617	+	0.181817i
$742$		0			0
$743$	26608.2	−	15362.2i	1.31381	−	0.758527i	0.331083	−	0.943602i	$-0.392586\pi$
$743$	26608.2	−	15362.2i	1.31381	−	0.758527i	0.982725	+	0.185074i	$0.0592526\pi$
$744$		0			0
$745$	1521.88	−	2635.97i	0.0748420	−	0.129630i
$746$		0			0
$747$	4700.35	+	2713.75i	0.230224	+	0.132920i
$748$		0			0
$749$			5193.37i			0.253353i
$750$		0			0
$751$	19769.3	+	34241.4i	0.960575	+	1.66376i	0.721061	+	0.692872i	$0.243655\pi$
$751$	19769.3	+	34241.4i	0.960575	+	1.66376i	0.239514	+	0.970893i	$0.423012\pi$
$752$		0			0
$753$	−3467.34			−0.167805
$754$		0			0
$755$	7928.35			0.382175
$756$		0			0
$757$	−11517.6	−	19949.0i	−0.552990	−	0.957807i	−0.998057	−	0.0623093i	$-0.980153\pi$
$757$	−11517.6	−	19949.0i	−0.552990	−	0.957807i	0.445067	−	0.895497i	$-0.353180\pi$
$758$		0			0
$759$			9495.81i			0.454119i
$760$		0			0
$761$	28106.0	+	16227.0i	1.33882	+	0.772968i	0.986632	−	0.162962i	$-0.0521047\pi$
$761$	28106.0	+	16227.0i	1.33882	+	0.772968i	0.352187	+	0.935930i	$0.385438\pi$
$762$		0			0
$763$	5892.30	−	10205.8i	0.279575	−	0.484238i
$764$		0			0
$765$	−87.4996	+	50.5179i	−0.00413536	+	0.00238755i
$766$		0			0
$767$	−17883.3	−	10745.7i	−0.841890	−	0.505874i
$768$		0			0
$769$	−27900.1	+	16108.1i	−1.30833	+	0.755362i	−0.981817	−	0.189831i	$-0.939206\pi$
$769$	−27900.1	+	16108.1i	−1.30833	+	0.755362i	−0.326509	+	0.945194i	$0.605873\pi$
$770$		0			0
$771$	−3527.93	+	6110.55i	−0.164793	+	0.285429i
$772$		0			0
$773$	−2532.78	−	1462.30i	−0.117849	−	0.0680404i	0.439917	−	0.898039i	$-0.355008\pi$
$773$	−2532.78	−	1462.30i	−0.117849	−	0.0680404i	−0.557766	+	0.829998i	$0.688341\pi$
$774$		0			0
$775$		−	24280.9i		−	1.12541i
$776$		0			0
$777$	4006.29	+	6939.10i	0.184974	+	0.320384i
$778$		0			0
$779$	4081.32			0.187713
$780$		0			0
$781$	−19076.1			−0.874001
$782$		0			0
$783$	3469.59	+	6009.51i	0.158357	+	0.274282i
$784$		0			0
$785$			1697.03i			0.0771586i
$786$		0			0
$787$	−22089.8	−	12753.6i	−1.00053	−	0.577656i	−0.0921250	−	0.995747i	$-0.529366\pi$
$787$	−22089.8	−	12753.6i	−1.00053	−	0.577656i	−0.908405	+	0.418091i	$0.862699\pi$
$788$		0			0
$789$	−8282.82	+	14346.3i	−0.373734	+	0.647326i
$790$		0			0
$791$	16839.6	−	9722.34i	0.756949	−	0.437025i
$792$		0			0
$793$	−2889.65	+	4809.03i	−0.129400	+	0.215351i
$794$		0			0
$795$	73.3610	−	42.3550i	0.00327276	−	0.00188953i
$796$		0			0
$797$	2724.49	−	4718.95i	0.121087	−	0.209729i	−0.799110	−	0.601185i	$-0.794695\pi$
$797$	2724.49	−	4718.95i	0.121087	−	0.209729i	0.920197	+	0.391457i	$0.128029\pi$
$798$		0			0
$799$	−1277.23	−	737.409i	−0.0565521	−	0.0326504i
$800$		0			0
$801$		−	1941.01i		−	0.0856209i
$802$		0			0
$803$	24780.5	+	42921.0i	1.08902	+	1.88624i
$804$		0			0
$805$	−1939.85			−0.0849324
$806$		0			0
$807$	−11750.9			−0.512577
$808$		0			0
$809$	1226.56	+	2124.46i	0.0533048	+	0.0923266i	0.891447	−	0.453126i	$-0.149691\pi$
$809$	1226.56	+	2124.46i	0.0533048	+	0.0923266i	−0.838142	+	0.545452i	$0.816358\pi$
$810$		0			0
$811$			5133.85i			0.222286i	0.993804	+	0.111143i	$0.0354512\pi$
$811$			5133.85i			0.222286i	−0.993804	+	0.111143i	$0.964549\pi$
$812$		0			0
$813$	−7216.23	−	4166.29i	−0.311297	−	0.179727i
$814$		0			0
$815$	−532.404	+	922.150i	−0.0228826	+	0.0396338i
$816$		0			0
$817$	−1174.34	+	678.007i	−0.0502877	+	0.0290336i
$818$		0			0
$819$	5609.11	−	3109.08i	0.239314	−	0.132650i
$820$		0			0
$821$	−20658.1	+	11927.0i	−0.878166	+	0.507009i	−0.870053	−	0.492958i	$-0.835916\pi$
$821$	−20658.1	+	11927.0i	−0.878166	+	0.507009i	−0.00811266	+	0.999967i	$0.502582\pi$
$822$		0			0
$823$	−378.578	+	655.716i	−0.0160345	+	0.0277726i	−0.873931	−	0.486049i	$-0.838437\pi$
$823$	−378.578	+	655.716i	−0.0160345	+	0.0277726i	0.857897	+	0.513822i	$0.171771\pi$
$824$		0			0
$825$	−20458.1	−	11811.5i	−0.863347	−	0.498454i
$826$		0			0
$827$			28621.2i			1.20345i	0.798702	+	0.601726i	$0.205520\pi$
$827$			28621.2i			1.20345i	−0.798702	+	0.601726i	$0.794480\pi$
$828$		0			0
$829$	13714.6	+	23754.4i	0.574582	+	0.995204i	0.996087	+	0.0883785i	$0.0281685\pi$
$829$	13714.6	+	23754.4i	0.574582	+	0.995204i	−0.421505	+	0.906826i	$0.638498\pi$
$830$		0			0
$831$	19749.2			0.824421
$832$		0			0
$833$	−465.838			−0.0193761
$834$		0			0
$835$	−204.731	−	354.604i	−0.00848503	−	0.0146965i
$836$		0			0
$837$			5568.54i			0.229960i
$838$		0			0
$839$	4012.83	+	2316.81i	0.165123	+	0.0953339i	0.580284	−	0.814414i	$-0.302941\pi$
$839$	4012.83	+	2316.81i	0.165123	+	0.0953339i	−0.415161	+	0.909748i	$0.636275\pi$
$840$		0			0
$841$	−20831.8	+	36081.7i	−0.854147	+	1.47943i
$842$		0			0
$843$	7460.79	−	4307.49i	0.304820	−	0.175988i
$844$		0			0
$845$	−206.904	+	5920.18i	−0.00842331	+	0.241018i
$846$		0			0
$847$	−41374.3	+	23887.5i	−1.67844	+	0.969048i
$848$		0			0
$849$	11277.1	−	19532.4i	0.455863	−	0.789578i
$850$		0			0
$851$	7200.30	+	4157.10i	0.290039	+	0.167454i
$852$		0			0
$853$			14854.6i			0.596261i	0.954525	+	0.298131i	$0.0963631\pi$
$853$			14854.6i			0.596261i	−0.954525	+	0.298131i	$0.903637\pi$
$854$		0			0
$855$	−316.500	−	548.194i	−0.0126597	−	0.0219273i
$856$		0			0
$857$	42799.5			1.70595			0.852977	−	0.521948i	$-0.174794\pi$
$857$	42799.5			1.70595			0.852977	+	0.521948i	$0.174794\pi$
$858$		0			0
$859$	8246.47			0.327551			0.163775	−	0.986498i	$-0.447633\pi$
$859$	8246.47			0.327551			0.163775	+	0.986498i	$0.447633\pi$
$860$		0			0
$861$	−3567.92	−	6179.83i	−0.141225	−	0.244608i
$862$		0			0
$863$		−	17695.4i		−	0.697983i	−0.937126	−	0.348991i	$-0.886524\pi$
$863$		−	17695.4i		−	0.697983i	0.937126	−	0.348991i	$-0.113476\pi$
$864$		0			0
$865$	1258.17	+	726.405i	0.0494556	+	0.0285532i
$866$		0			0
$867$	−7343.50	+	12719.3i	−0.287657	+	0.498236i
$868$		0			0
$869$	−31723.7	+	18315.7i	−1.23838	+	0.714980i
$870$		0			0
$871$	918.621	−	509.183i	0.0357363	−	0.0198083i
$872$		0			0
$873$	11282.2	−	6513.77i	0.437393	−	0.252529i
$874$		0			0
$875$	4974.82	−	8616.64i	0.192205	−	0.332909i
$876$		0			0
$877$	12424.7	+	7173.38i	0.478393	+	0.276200i	0.719747	−	0.694237i	$-0.244258\pi$
$877$	12424.7	+	7173.38i	0.478393	+	0.276200i	−0.241353	+	0.970437i	$0.577591\pi$
$878$		0			0
$879$			13519.7i			0.518781i
$880$		0			0
$881$	−1031.76	−	1787.06i	−0.0394560	−	0.0683399i	0.845623	−	0.533781i	$-0.179229\pi$
$881$	−1031.76	−	1787.06i	−0.0394560	−	0.0683399i	−0.885079	+	0.465441i	$0.845896\pi$
$882$		0			0
$883$	−34137.1			−1.30103			−0.650513	−	0.759495i	$-0.725446\pi$
$883$	−34137.1			−1.30103			−0.650513	+	0.759495i	$0.725446\pi$
$884$		0			0
$885$	3600.50			0.136756
$886$		0			0
$887$	−11119.2	−	19259.1i	−0.420910	−	0.729038i	0.575118	−	0.818070i	$-0.304956\pi$
$887$	−11119.2	−	19259.1i	−0.420910	−	0.729038i	−0.996029	+	0.0890320i	$0.971623\pi$
$888$		0			0
$889$		−	16932.8i		−	0.638817i
$890$		0			0
$891$	4691.84	+	2708.84i	0.176411	+	0.101851i
$892$		0			0
$893$	4619.94	−	8001.98i	0.173125	−	0.299861i
$894$		0			0
$895$	−5185.72	+	2993.98i	−0.193676	+	0.111819i
$896$		0			0
$897$	3427.43	−	5704.02i	0.127579	−	0.212321i
$898$		0			0
$899$	−45904.3	+	26502.8i	−1.70300	+	0.983225i
$900$		0			0
$901$	−21.8010	+	37.7604i	−0.000806100	+	0.00139621i
$902$		0			0
$903$	2053.24	+	1185.44i	0.0756673	+	0.0436865i
$904$		0			0
$905$			10307.4i			0.378597i
$906$		0			0
$907$	22080.2	+	38243.9i	0.808335	+	1.40008i	0.914017	+	0.405677i	$0.132964\pi$
$907$	22080.2	+	38243.9i	0.808335	+	1.40008i	−0.105682	+	0.994400i	$0.533703\pi$
$908$		0			0
$909$	7951.05			0.290121
$910$		0			0
$911$	−11916.3			−0.433376			−0.216688	−	0.976241i	$-0.569525\pi$
$911$	−11916.3			−0.433376			−0.216688	+	0.976241i	$0.569525\pi$
$912$		0			0
$913$	20167.6	+	34931.4i	0.731053	+	1.26622i
$914$		0			0
$915$		−	968.215i		−	0.0349816i
$916$		0			0
$917$	27649.6	+	15963.5i	0.995716	+	0.574877i
$918$		0			0
$919$	−10064.5	+	17432.2i	−0.361258	+	0.625717i	−0.988168	−	0.153375i	$-0.950986\pi$
$919$	−10064.5	+	17432.2i	−0.361258	+	0.625717i	0.626910	+	0.779091i	$0.284319\pi$
$920$		0			0
$921$	−24782.8	+	14308.3i	−0.886667	+	0.511917i
$922$		0			0
$923$	11458.8	+	6885.34i	0.408635	+	0.245540i
$924$		0			0
$925$	−17912.4	+	10341.7i	−0.636710	+	0.367605i
$926$		0			0
$927$	−5632.83	+	9756.35i	−0.199575	+	0.345675i
$928$		0			0
$929$	27217.8	+	15714.2i	0.961234	+	0.554969i	0.896553	−	0.442937i	$-0.146064\pi$
$929$	27217.8	+	15714.2i	0.961234	+	0.554969i	0.0646814	+	0.997906i	$0.479397\pi$
$930$		0			0
$931$		−	2918.52i		−	0.102740i
$932$		0			0
$933$	−11199.4	−	19398.0i	−0.392983	−	0.680666i
$934$		0			0
$935$	−750.863			−0.0262629
$936$		0			0
$937$	42473.2			1.48083			0.740416	−	0.672149i	$-0.234629\pi$
$937$	42473.2			1.48083			0.740416	+	0.672149i	$0.234629\pi$
$938$		0			0
$939$	−2732.47	−	4732.78i	−0.0949636	−	0.164482i
$940$		0			0
$941$		−	42644.0i		−	1.47732i	−0.674079	−	0.738659i	$-0.735459\pi$
$941$		−	42644.0i		−	1.47732i	0.674079	−	0.738659i	$-0.264541\pi$
$942$		0			0
$943$	−6412.45	−	3702.23i	−0.221440	−	0.127849i
$944$		0			0
$945$	−553.373	+	958.470i	−0.0190489	+	0.0329937i
$946$		0			0
$947$	3709.14	−	2141.47i	0.127277	−	0.0734831i	−0.435010	−	0.900426i	$-0.643255\pi$
$947$	3709.14	−	2141.47i	0.127277	−	0.0734831i	0.562286	+	0.826943i	$0.309922\pi$
$948$		0			0
$949$	606.639	−	34726.5i	0.0207506	−	1.18785i
$950$		0			0
$951$	−8119.35	+	4687.71i	−0.276854	+	0.159842i
$952$		0			0
$953$	20297.0	−	35155.4i	0.689908	−	1.19496i	−0.281959	−	0.959427i	$-0.590984\pi$
$953$	20297.0	−	35155.4i	0.689908	−	1.19496i	0.971867	−	0.235530i	$-0.0756826\pi$
$954$		0			0
$955$	8089.14	+	4670.27i	0.274093	+	0.158247i
$956$		0			0
$957$			51569.6i			1.74191i
$958$		0			0
$959$	9159.61	+	15864.9i	0.308425	+	0.534207i
$960$		0			0
$961$	−12744.8			−0.427808
$962$		0			0
$963$	3074.52			0.102882
$964$		0			0
$965$	−6332.83	−	10968.8i	−0.211255	−	0.365904i
$966$		0			0
$967$		−	17709.4i		−	0.588931i	−0.955662	−	0.294466i	$-0.904858\pi$
$967$		−	17709.4i		−	0.588931i	0.955662	−	0.294466i	$-0.0951416\pi$
$968$		0			0
$969$	282.166	+	162.909i	0.00935448	+	0.00540081i
$970$		0			0
$971$	2019.49	−	3497.85i	0.0667440	−	0.115604i	−0.830722	−	0.556687i	$-0.812072\pi$
$971$	2019.49	−	3497.85i	0.0667440	−	0.115604i	0.897466	+	0.441083i	$0.145406\pi$
$972$		0			0
$973$	−4251.08	+	2454.36i	−0.140065	+	0.0808666i
$974$		0			0
$975$	8025.71	+	14479.2i	0.263619	+	0.475597i
$976$		0			0
$977$	−2393.95	+	1382.15i	−0.0783924	+	0.0452598i	−0.538684	−	0.842508i	$-0.681078\pi$
$977$	−2393.95	+	1382.15i	−0.0783924	+	0.0452598i	0.460291	+	0.887768i	$0.347745\pi$
$978$		0			0
$979$	7212.46	−	12492.4i	0.235456	−	0.407822i
$980$		0			0
$981$	−6041.91	−	3488.30i	−0.196639	−	0.113530i
$982$		0			0
$983$		−	17804.5i		−	0.577695i	−0.957375	−	0.288848i	$-0.906728\pi$
$983$		−	17804.5i		−	0.577695i	0.957375	−	0.288848i	$-0.0932721\pi$
$984$		0			0
$985$	−3893.32	−	6743.43i	−0.125941	−	0.218136i
$986$		0			0
$987$	−16155.2			−0.520997
$988$		0			0
$989$	2460.12			0.0790974
$990$		0			0
$991$	−4064.84	−	7040.52i	−0.130297	−	0.225680i	0.793494	−	0.608578i	$-0.208260\pi$
$991$	−4064.84	−	7040.52i	−0.130297	−	0.225680i	−0.923791	+	0.382897i	$0.874926\pi$
$992$		0			0
$993$		−	4661.02i		−	0.148956i
$994$		0			0
$995$	−147.131	−	84.9463i	−0.00468781	−	0.00270651i
$996$		0			0
$997$	14726.4	−	25507.0i	0.467795	−	0.810244i	−0.531528	−	0.847041i	$-0.678382\pi$
$997$	14726.4	−	25507.0i	0.467795	−	0.810244i	0.999323	+	0.0367966i	$0.0117154\pi$
$998$		0			0
$999$	4108.01	−	2371.76i	0.130102	−	0.0751143i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.4.bv.h.49.3		10
4.3	odd	2		39.4.j.c.10.1	yes	10
12.11	even	2		117.4.q.e.10.5		10
13.4	even	6	inner	624.4.bv.h.433.3		10
52.3	odd	6		507.4.b.i.337.1		10
52.11	even	12		507.4.a.r.1.10		10
52.15	even	12		507.4.a.r.1.1		10
52.23	odd	6		507.4.b.i.337.10		10
52.43	odd	6		39.4.j.c.4.1	✓	10
156.11	odd	12		1521.4.a.bk.1.1		10
156.95	even	6		117.4.q.e.82.5		10
156.119	odd	12		1521.4.a.bk.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.j.c.4.1	✓	10	52.43	odd	6
39.4.j.c.10.1	yes	10	4.3	odd	2
117.4.q.e.10.5		10	12.11	even	2
117.4.q.e.82.5		10	156.95	even	6
507.4.a.r.1.1		10	52.15	even	12
507.4.a.r.1.10		10	52.11	even	12
507.4.b.i.337.1		10	52.3	odd	6
507.4.b.i.337.10		10	52.23	odd	6
624.4.bv.h.49.3		10	1.1	even	1	trivial
624.4.bv.h.433.3		10	13.4	even	6	inner
1521.4.a.bk.1.1		10	156.11	odd	12
1521.4.a.bk.1.10		10	156.119	odd	12

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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	624.bv (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 2.59808i) q^{3} +2.69631i q^{5} +(-13.1657 - 7.60123i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 2.59808i) q^{3} +2.69631i q^{5} +(-13.1657 - 7.60123i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-57.9240 + 33.4424i) q^{11} +(46.8650 + 0.818689i) q^{13} +(-7.00522 + 4.04447i) q^{15} +(2.08177 - 3.60573i) q^{17} +(22.5903 + 13.0425i) q^{19} -45.6074i q^{21} +(-23.6621 - 40.9839i) q^{23} +117.730 q^{25} -27.0000 q^{27} +(-128.503 - 222.575i) q^{29} -206.242i q^{31} +(-173.772 - 100.327i) q^{33} +(20.4953 - 35.4989i) q^{35} +(-152.149 + 87.8430i) q^{37} +(68.1705 + 122.987i) q^{39} +(135.501 - 78.2313i) q^{41} +(-25.9922 + 45.0199i) q^{43} +(-21.0157 - 12.1334i) q^{45} -354.222i q^{47} +(-55.9425 - 96.8953i) q^{49} +12.4906 q^{51} -10.4723 q^{53} +(-90.1712 - 156.181i) q^{55} +78.2550i q^{57} +(-385.480 - 222.557i) q^{59} +(-59.8481 + 103.660i) q^{61} +(118.491 - 68.4111i) q^{63} +(-2.20744 + 126.363i) q^{65} +(19.4057 - 11.2039i) q^{67} +(70.9863 - 122.952i) q^{69} +(246.997 + 142.604i) q^{71} -740.989i q^{73} +(176.595 + 305.871i) q^{75} +1016.81 q^{77} +547.679 q^{79} +(-40.5000 - 70.1481i) q^{81} -603.056i q^{83} +(9.72218 + 5.61310i) q^{85} +(385.510 - 667.724i) q^{87} +(-186.774 + 107.834i) q^{89} +(-610.789 - 367.011i) q^{91} +(535.833 - 309.363i) q^{93} +(-35.1666 + 60.9104i) q^{95} +(-1253.58 - 723.752i) q^{97} -601.964i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 15 q^{3} - 30 q^{7} - 45 q^{9}+O(q^{10}) \) 10 * q + 15 * q^3 - 30 * q^7 - 45 * q^9	\( 10 q + 15 q^{3} - 30 q^{7} - 45 q^{9} - 60 q^{11} + 25 q^{13} - 45 q^{15} + 105 q^{17} - 180 q^{19} + 60 q^{23} - 960 q^{25} - 270 q^{27} - 495 q^{29} - 180 q^{33} - 60 q^{35} - 405 q^{37} - 345 q^{39} + 1065 q^{41} + 370 q^{43} - 135 q^{45} + 775 q^{49} + 630 q^{51} + 330 q^{53} + 260 q^{55} - 780 q^{59} - 1375 q^{61} + 270 q^{63} + 1605 q^{65} - 1590 q^{67} - 180 q^{69} - 1620 q^{71} - 1440 q^{75} - 4320 q^{77} - 1100 q^{79} - 405 q^{81} + 525 q^{85} + 1485 q^{87} + 2040 q^{89} - 4770 q^{91} - 990 q^{93} + 1380 q^{95} - 3750 q^{97}+O(q^{100}) \) 10 * q + 15 * q^3 - 30 * q^7 - 45 * q^9 - 60 * q^11 + 25 * q^13 - 45 * q^15 + 105 * q^17 - 180 * q^19 + 60 * q^23 - 960 * q^25 - 270 * q^27 - 495 * q^29 - 180 * q^33 - 60 * q^35 - 405 * q^37 - 345 * q^39 + 1065 * q^41 + 370 * q^43 - 135 * q^45 + 775 * q^49 + 630 * q^51 + 330 * q^53 + 260 * q^55 - 780 * q^59 - 1375 * q^61 + 270 * q^63 + 1605 * q^65 - 1590 * q^67 - 180 * q^69 - 1620 * q^71 - 1440 * q^75 - 4320 * q^77 - 1100 * q^79 - 405 * q^81 + 525 * q^85 + 1485 * q^87 + 2040 * q^89 - 4770 * q^91 - 990 * q^93 + 1380 * q^95 - 3750 * q^97

Introduction

L-functions

Modular forms

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Representations

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