LMFDB - Embedded newform 40.4.f.a.29.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,4,Mod(29,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("40.29");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	40.f (of order $2$, degree $1$, 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:	$2.36007640023$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} + 44x^{12} + 400x^{10} - 3200x^{8} + 25600x^{6} + 180224x^{4} - 524288x^{2} + 16777216 $ x^16 - 2x^14 + 44x^12 + 400x^10 - 3200x^8 + 25600x^6 + 180224x^4 - 524288*x^2 + 16777216
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{21}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.3
Root			$-2.15123 - 1.83636i$ of defining polynomial
Character	$\chi$	$=$	40.29
Dual form			40.4.f.a.29.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.15123 - 1.83636i) q^{2} +8.63004 q^{3} +(1.25556 + 7.90086i) q^{4} +(2.63740 + 10.8648i) q^{5} +(-18.5652 - 15.8479i) q^{6} -4.74133i q^{7} +(11.8078 - 19.3022i) q^{8} +47.4777 q^{9} +O(q^{10})$	\(q+(-2.15123 - 1.83636i) q^{2} +8.63004 q^{3} +(1.25556 + 7.90086i) q^{4} +(2.63740 + 10.8648i) q^{5} +(-18.5652 - 15.8479i) q^{6} -4.74133i q^{7} +(11.8078 - 19.3022i) q^{8} +47.4777 q^{9} +(14.2781 - 28.2159i) q^{10} -31.8831i q^{11} +(10.8355 + 68.1848i) q^{12} -59.2167 q^{13} +(-8.70679 + 10.1997i) q^{14} +(22.7609 + 93.7638i) q^{15} +(-60.8472 + 19.8399i) q^{16} -80.9370i q^{17} +(-102.135 - 87.1861i) q^{18} +114.647i q^{19} +(-82.5299 + 34.4791i) q^{20} -40.9179i q^{21} +(-58.5490 + 68.5879i) q^{22} +28.3687i q^{23} +(101.902 - 166.579i) q^{24} +(-111.088 + 57.3097i) q^{25} +(127.389 + 108.743i) q^{26} +176.723 q^{27} +(37.4606 - 5.95300i) q^{28} -146.340i q^{29} +(123.220 - 243.504i) q^{30} +77.6995 q^{31} +(167.329 + 69.0571i) q^{32} -275.153i q^{33} +(-148.630 + 174.114i) q^{34} +(51.5136 - 12.5048i) q^{35} +(59.6108 + 375.114i) q^{36} -201.444 q^{37} +(210.534 - 246.633i) q^{38} -511.042 q^{39} +(240.857 + 77.3824i) q^{40} -99.3433 q^{41} +(-75.1400 + 88.0236i) q^{42} -210.291 q^{43} +(251.904 - 40.0311i) q^{44} +(125.217 + 515.836i) q^{45} +(52.0952 - 61.0275i) q^{46} -33.3026i q^{47} +(-525.114 + 171.220i) q^{48} +320.520 q^{49} +(344.217 + 80.7121i) q^{50} -698.490i q^{51} +(-74.3498 - 467.863i) q^{52} +255.386 q^{53} +(-380.171 - 324.527i) q^{54} +(346.404 - 84.0885i) q^{55} +(-91.5180 - 55.9848i) q^{56} +989.413i q^{57} +(-268.734 + 314.812i) q^{58} +589.854i q^{59} +(-712.237 + 297.556i) q^{60} -573.462i q^{61} +(-167.149 - 142.684i) q^{62} -225.107i q^{63} +(-233.150 - 455.835i) q^{64} +(-156.178 - 643.378i) q^{65} +(-505.280 + 591.916i) q^{66} -23.9755 q^{67} +(639.472 - 101.621i) q^{68} +244.823i q^{69} +(-133.781 - 67.6970i) q^{70} +470.655 q^{71} +(560.609 - 916.423i) q^{72} +676.417i q^{73} +(433.352 + 369.924i) q^{74} +(-958.697 + 494.585i) q^{75} +(-905.814 + 143.946i) q^{76} -151.168 q^{77} +(1099.37 + 938.458i) q^{78} +1085.76 q^{79} +(-376.035 - 608.767i) q^{80} +243.231 q^{81} +(213.710 + 182.430i) q^{82} +78.2562 q^{83} +(323.286 - 51.3747i) q^{84} +(879.366 - 213.463i) q^{85} +(452.384 + 386.171i) q^{86} -1262.92i q^{87} +(-615.415 - 376.471i) q^{88} -606.174 q^{89} +(677.889 - 1339.62i) q^{90} +280.766i q^{91} +(-224.137 + 35.6185i) q^{92} +670.550 q^{93} +(-61.1557 + 71.6416i) q^{94} +(-1245.62 + 302.371i) q^{95} +(1444.06 + 595.966i) q^{96} -151.583i q^{97} +(-689.511 - 588.590i) q^{98} -1513.74i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 12 q^{6} + 104 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 - 12 * q^6 + 104 * q^9	$ 16 q + 4 q^{4} - 12 q^{6} + 104 q^{9} - 48 q^{10} + 28 q^{14} - 56 q^{15} - 168 q^{16} - 196 q^{20} - 112 q^{24} - 24 q^{25} + 200 q^{26} + 492 q^{30} - 112 q^{31} + 408 q^{34} - 84 q^{36} - 736 q^{39} + 672 q^{40} + 232 q^{41} + 920 q^{44} + 212 q^{46} - 200 q^{49} - 648 q^{50} - 2320 q^{54} + 392 q^{55} + 1120 q^{56} - 1208 q^{60} - 2912 q^{64} - 600 q^{65} - 2488 q^{66} + 1532 q^{70} + 2096 q^{71} + 4224 q^{74} - 3000 q^{76} + 2992 q^{79} + 2280 q^{80} - 728 q^{81} + 7304 q^{84} + 3076 q^{86} - 208 q^{89} - 4280 q^{90} - 7036 q^{94} - 1064 q^{95} + 3632 q^{96}+O(q^{100}) $ 16 * q + 4 * q^4 - 12 * q^6 + 104 * q^9 - 48 * q^10 + 28 * q^14 - 56 * q^15 - 168 * q^16 - 196 * q^20 - 112 * q^24 - 24 * q^25 + 200 * q^26 + 492 * q^30 - 112 * q^31 + 408 * q^34 - 84 * q^36 - 736 * q^39 + 672 * q^40 + 232 * q^41 + 920 * q^44 + 212 * q^46 - 200 * q^49 - 648 * q^50 - 2320 * q^54 + 392 * q^55 + 1120 * q^56 - 1208 * q^60 - 2912 * q^64 - 600 * q^65 - 2488 * q^66 + 1532 * q^70 + 2096 * q^71 + 4224 * q^74 - 3000 * q^76 + 2992 * q^79 + 2280 * q^80 - 728 * q^81 + 7304 * q^84 + 3076 * q^86 - 208 * q^89 - 4280 * q^90 - 7036 * q^94 - 1064 * q^95 + 3632 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.15123	−	1.83636i	−0.760574	−	0.649252i
$2$	−2.15123	−	1.83636i	−0.760574	−	0.649252i
$3$	8.63004			1.66085			0.830426	−	0.557128i	$-0.188097\pi$
$3$	8.63004			1.66085			0.830426	+	0.557128i	$0.188097\pi$
$4$	1.25556	+	7.90086i	0.156945	+	0.987607i
$5$	2.63740	+	10.8648i	0.235896	+	0.971778i
$5$	2.63740	+	10.8648i	0.235896	+	0.971778i
$6$	−18.5652	−	15.8479i	−1.26320	−	1.07831i
$7$		−	4.74133i		−	0.256008i	−0.991774	−	0.128004i	$-0.959143\pi$
$7$		−	4.74133i		−	0.256008i	0.991774	−	0.128004i	$-0.0408570\pi$
$8$	11.8078	−	19.3022i	0.521838	−	0.853045i
$9$	47.4777			1.75843
$10$	14.2781	−	28.2159i	0.451512	−	0.892265i
$11$		−	31.8831i		−	0.873921i	−0.899481	−	0.436960i	$-0.856055\pi$
$11$		−	31.8831i		−	0.873921i	0.899481	−	0.436960i	$-0.143945\pi$
$12$	10.8355	+	68.1848i	0.260662	+	1.64027i
$13$	−59.2167			−1.26337			−0.631683	−	0.775227i	$-0.717635\pi$
$13$	−59.2167			−1.26337			−0.631683	+	0.775227i	$0.717635\pi$
$14$	−8.70679	+	10.1997i	−0.166213	+	0.194713i
$15$	22.7609	+	93.7638i	0.391789	+	1.61398i
$16$	−60.8472	+	19.8399i	−0.950737	+	0.309999i
$17$		−	80.9370i		−	1.15471i	−0.816492	−	0.577356i	$-0.804084\pi$
$17$		−	80.9370i		−	1.15471i	0.816492	−	0.577356i	$-0.195916\pi$
$18$	−102.135	−	87.1861i	−1.33742	−	1.14166i
$19$			114.647i			1.38431i	0.721748	+	0.692156i	$0.243339\pi$
$19$			114.647i			1.38431i	−0.721748	+	0.692156i	$0.756661\pi$
$20$	−82.5299	+	34.4791i	−0.922713	+	0.385488i
$21$		−	40.9179i		−	0.425191i
$22$	−58.5490	+	68.5879i	−0.567394	+	0.664681i
$23$			28.3687i			0.257186i	0.991697	+	0.128593i	$0.0410461\pi$
$23$			28.3687i			0.257186i	−0.991697	+	0.128593i	$0.958954\pi$
$24$	101.902	−	166.579i	0.866696	−	1.41678i
$25$	−111.088	+	57.3097i	−0.888706	+	0.458477i
$26$	127.389	+	108.743i	0.960882	+	0.820242i
$27$	176.723			1.25964
$28$	37.4606	−	5.95300i	0.252835	−	0.0401790i
$29$		−	146.340i		−	0.937060i	−0.883448	−	0.468530i	$-0.844784\pi$
$29$		−	146.340i		−	0.937060i	0.883448	−	0.468530i	$-0.155216\pi$
$30$	123.220	−	243.504i	0.749896	−	1.48192i
$31$	77.6995			0.450169			0.225085	−	0.974339i	$-0.427734\pi$
$31$	77.6995			0.450169			0.225085	+	0.974339i	$0.427734\pi$
$32$	167.329	+	69.0571i	0.924373	+	0.381490i
$33$		−	275.153i		−	1.45145i
$34$	−148.630	+	174.114i	−0.749699	+	0.878244i
$35$	51.5136	−	12.5048i	0.248783	−	0.0603912i
$36$	59.6108	+	375.114i	0.275976	+	1.73664i
$37$	−201.444			−0.895060			−0.447530	−	0.894269i	$-0.647696\pi$
$37$	−201.444			−0.895060			−0.447530	+	0.894269i	$0.647696\pi$
$38$	210.534	−	246.633i	0.898767	−	1.05287i
$39$	−511.042			−2.09826
$40$	240.857	+	77.3824i	0.952070	+	0.305881i
$41$	−99.3433			−0.378410			−0.189205	−	0.981938i	$-0.560591\pi$
$41$	−99.3433			−0.378410			−0.189205	+	0.981938i	$0.560591\pi$
$42$	−75.1400	+	88.0236i	−0.276056	+	0.323389i
$43$	−210.291			−0.745794			−0.372897	−	0.927873i	$-0.621635\pi$
$43$	−210.291			−0.745794			−0.372897	+	0.927873i	$0.621635\pi$
$44$	251.904	−	40.0311i	0.863091	−	0.137157i
$45$	125.217	+	515.836i	0.414807	+	1.70881i
$46$	52.0952	−	61.0275i	0.166979	−	0.195609i
$47$		−	33.3026i		−	0.103355i	−0.998664	−	0.0516776i	$-0.983543\pi$
$47$		−	33.3026i		−	0.103355i	0.998664	−	0.0516776i	$-0.0164568\pi$
$48$	−525.114	+	171.220i	−1.57903	+	0.514863i
$49$	320.520			0.934460
$50$	344.217	+	80.7121i	0.973594	+	0.228288i
$51$		−	698.490i		−	1.91781i
$52$	−74.3498	−	467.863i	−0.198278	−	1.24771i
$53$	255.386			0.661886			0.330943	−	0.943651i	$-0.392633\pi$
$53$	255.386			0.661886			0.330943	+	0.943651i	$0.392633\pi$
$54$	−380.171	−	324.527i	−0.958051	−	0.817825i
$55$	346.404	−	84.0885i	0.849257	−	0.206154i
$56$	−91.5180	−	55.9848i	−0.218386	−	0.133594i
$57$			989.413i			2.29914i
$58$	−268.734	+	314.812i	−0.608388	+	0.712703i
$59$			589.854i			1.30157i	0.759263	+	0.650783i	$0.225559\pi$
$59$			589.854i			1.30157i	−0.759263	+	0.650783i	$0.774441\pi$
$60$	−712.237	+	297.556i	−1.53249	+	0.640239i
$61$		−	573.462i		−	1.20368i	−0.798618	−	0.601838i	$-0.794435\pi$
$61$		−	573.462i		−	1.20368i	0.798618	−	0.601838i	$-0.205565\pi$
$62$	−167.149	−	142.684i	−0.342387	−	0.292273i
$63$		−	225.107i		−	0.450172i
$64$	−233.150	−	455.835i	−0.455370	−	0.890302i
$65$	−156.178	−	643.378i	−0.298023	−	1.22771i
$66$	−505.280	+	591.916i	−0.942359	+	1.10394i
$67$	−23.9755			−0.0437176			−0.0218588	−	0.999761i	$-0.506958\pi$
$67$	−23.9755			−0.0437176			−0.0218588	+	0.999761i	$0.506958\pi$
$68$	639.472	−	101.621i	1.14040	−	0.181226i
$69$			244.823i			0.427148i
$70$	−133.781	−	67.6970i	−0.228427	−	0.115591i
$71$	470.655			0.786711			0.393355	−	0.919386i	$-0.371314\pi$
$71$	470.655			0.786711			0.393355	+	0.919386i	$0.371314\pi$
$72$	560.609	−	916.423i	0.917616	−	1.50002i
$73$			676.417i			1.08450i	0.840217	+	0.542251i	$0.182428\pi$
$73$			676.417i			1.08450i	−0.840217	+	0.542251i	$0.817572\pi$
$74$	433.352	+	369.924i	0.680759	+	0.581119i
$75$	−958.697	+	494.585i	−1.47601	+	0.761463i
$76$	−905.814	+	143.946i	−1.36716	+	0.217260i
$77$	−151.168			−0.223730
$78$	1099.37	+	938.458i	1.59588	+	1.36230i
$79$	1085.76			1.54630			0.773152	−	0.634221i	$-0.218679\pi$
$79$	1085.76			1.54630			0.773152	+	0.634221i	$0.218679\pi$
$80$	−376.035	−	608.767i	−0.525525	−	0.850778i
$81$	243.231			0.333650
$82$	213.710	+	182.430i	0.287809	+	0.245683i
$83$	78.2562			0.103491			0.0517454	−	0.998660i	$-0.483522\pi$
$83$	78.2562			0.103491			0.0517454	+	0.998660i	$0.483522\pi$
$84$	323.286	−	51.3747i	0.419922	−	0.0667314i
$85$	879.366	−	213.463i	1.12212	−	0.272392i
$86$	452.384	+	386.171i	0.567231	+	0.484208i
$87$		−	1262.92i		−	1.55632i
$88$	−615.415	−	376.471i	−0.745493	−	0.456045i
$89$	−606.174			−0.721959			−0.360979	−	0.932574i	$-0.617558\pi$
$89$	−606.174			−0.721959			−0.360979	+	0.932574i	$0.617558\pi$
$90$	677.889	−	1339.62i	0.793954	−	1.56899i
$91$			280.766i			0.323431i
$92$	−224.137	+	35.6185i	−0.253999	+	0.0403639i
$93$	670.550			0.747665
$94$	−61.1557	+	71.6416i	−0.0671035	+	0.0786092i
$95$	−1245.62	+	302.371i	−1.34524	+	0.326554i
$96$	1444.06	+	595.966i	1.53525	+	0.633599i
$97$		−	151.583i		−	0.158670i	−0.996848	−	0.0793349i	$-0.974720\pi$
$97$		−	151.583i		−	0.158670i	0.996848	−	0.0793349i	$-0.0252796\pi$
$98$	−689.511	−	588.590i	−0.710726	−	0.606700i
$99$		−	1513.74i		−	1.53673i
$100$	−592.273	−	805.737i	−0.592273	−	0.805737i
$101$			64.6577i			0.0636999i	0.999493	+	0.0318499i	$0.0101399\pi$
$101$			64.6577i			0.0636999i	−0.999493	+	0.0318499i	$0.989860\pi$
$102$	−1282.68	+	1502.61i	−1.24514	+	1.45863i
$103$			1294.08i			1.23796i	0.785409	+	0.618978i	$0.212453\pi$
$103$			1294.08i			1.23796i	−0.785409	+	0.618978i	$0.787547\pi$
$104$	−699.221	+	1143.01i	−0.659272	+	1.07771i
$105$	444.565	−	107.917i	0.413191	−	0.100301i
$106$	−549.393	−	468.981i	−0.503413	−	0.429731i
$107$	1624.59			1.46780			0.733902	−	0.679256i	$-0.237697\pi$
$107$	1624.59			1.46780			0.733902	+	0.679256i	$0.237697\pi$
$108$	221.886	+	1396.26i	0.197694	+	1.24403i
$109$			1247.60i			1.09632i	0.836375	+	0.548158i	$0.184671\pi$
$109$			1247.60i			1.09632i	−0.836375	+	0.548158i	$0.815329\pi$
$110$	−899.611	−	455.230i	−0.779769	−	0.394586i
$111$	−1738.47			−1.48656
$112$	94.0676	+	288.496i	0.0793621	+	0.243396i
$113$		−	261.173i		−	0.217426i	−0.994073	−	0.108713i	$-0.965327\pi$
$113$		−	261.173i		−	0.217426i	0.994073	−	0.108713i	$-0.0346729\pi$
$114$	1816.92	−	2128.45i	1.49272	−	1.74866i
$115$	−308.220	+	74.8195i	−0.249928	+	0.0606692i
$116$	1156.22	−	183.739i	0.925448	−	0.147066i
$117$	−2811.47			−2.22154
$118$	1083.18	−	1268.91i	0.845045	−	0.989938i
$119$	−383.749			−0.295615
$120$	2078.60	+	667.814i	1.58125	+	0.508023i
$121$	314.466			0.236263
$122$	−1053.08	+	1233.65i	−0.781489	+	0.915484i
$123$	−857.337			−0.628483
$124$	97.5561	+	613.893i	0.0706516	+	0.444590i
$125$	−915.643	−	1055.80i	−0.655181	−	0.755472i
$126$	−413.378	+	484.256i	−0.292275	+	0.342389i
$127$		−	1916.02i		−	1.33874i	−0.742931	−	0.669368i	$-0.766565\pi$
$127$		−	1916.02i		−	1.33874i	0.742931	−	0.669368i	$-0.233435\pi$
$128$	−335.519	+	1408.75i	−0.231687	+	0.972790i
$129$	−1814.82			−1.23865
$130$	−845.500	+	1670.85i	−0.570425	+	1.12726i
$131$			126.455i			0.0843394i	0.999110	+	0.0421697i	$0.0134270\pi$
$131$			126.455i			0.0843394i	−0.999110	+	0.0421697i	$0.986573\pi$
$132$	2173.94	−	345.470i	1.43347	−	0.227798i
$133$	543.581			0.354395
$134$	51.5768	+	44.0278i	0.0332504	+	0.0283837i
$135$	466.089	+	1920.06i	0.297145	+	1.22409i
$136$	−1562.26	−	955.692i	−0.985021	−	0.602573i
$137$		−	491.778i		−	0.306682i	−0.988173	−	0.153341i	$-0.950997\pi$
$137$		−	491.778i		−	0.306682i	0.988173	−	0.153341i	$-0.0490033\pi$
$138$	449.584	−	526.670i	0.277327	−	0.324878i
$139$			393.926i			0.240377i	0.992751	+	0.120188i	$0.0383498\pi$
$139$			393.926i			0.240377i	−0.992751	+	0.120188i	$0.961650\pi$
$140$	163.477	+	391.301i	0.0986878	+	0.236221i
$141$		−	287.403i		−	0.171658i
$142$	−1012.49	−	864.293i	−0.598352	−	0.510773i
$143$			1888.01i			1.10408i
$144$	−2888.88	+	941.954i	−1.67181	+	0.545112i
$145$	1589.96	−	385.958i	0.910615	−	0.221049i
$146$	1242.15	−	1455.13i	0.704115	−	0.824844i
$147$	2766.10			1.55200
$148$	−252.924	−	1591.58i	−0.140475	−	0.883967i
$149$		−	1074.70i		−	0.590893i	−0.955359	−	0.295446i	$-0.904532\pi$
$149$		−	1074.70i		−	0.590893i	0.955359	−	0.295446i	$-0.0954684\pi$
$150$	2970.61	+	696.549i	1.61700	+	0.379153i
$151$	1130.15			0.609075			0.304537	−	0.952500i	$-0.401498\pi$
$151$	1130.15			0.609075			0.304537	+	0.952500i	$0.401498\pi$
$152$	2212.95	+	1353.74i	1.18088	+	0.722387i
$153$		−	3842.70i		−	2.03048i
$154$	325.197	+	277.600i	0.170163	+	0.145257i
$155$	204.925	+	844.191i	0.106193	+	0.437465i
$156$	−641.642	−	4037.67i	−0.329311	−	2.07226i
$157$	1126.04			0.572407			0.286204	−	0.958169i	$-0.407607\pi$
$157$	1126.04			0.572407			0.286204	+	0.958169i	$0.407607\pi$
$158$	−2335.73	−	1993.85i	−1.17608	−	1.00394i
$159$	2203.99			1.09930
$160$	−308.979	+	2000.13i	−0.152668	+	0.988278i
$161$	134.505			0.0658416
$162$	−523.245	−	446.659i	−0.253765	−	0.216623i
$163$	309.194			0.148576			0.0742882	−	0.997237i	$-0.476332\pi$
$163$	309.194			0.148576			0.0742882	+	0.997237i	$0.476332\pi$
$164$	−124.731	−	784.897i	−0.0593894	−	0.373721i
$165$	2989.48	−	725.688i	1.41049	−	0.342392i
$166$	−168.347	−	143.707i	−0.0787123	−	0.0671915i
$167$			2556.08i			1.18440i	0.805790	+	0.592201i	$0.201741\pi$
$167$			2556.08i			1.18440i	−0.805790	+	0.592201i	$0.798259\pi$
$168$	−789.804	−	483.152i	−0.362707	−	0.221881i
$169$	1309.61			0.596092
$170$	−2283.71	−	1155.62i	−1.03031	−	0.521367i
$171$			5443.19i			2.43422i
$172$	−264.033	−	1661.48i	−0.117048	−	0.736551i
$173$	−3229.54			−1.41929			−0.709645	−	0.704559i	$-0.751145\pi$
$173$	−3229.54			−1.41929			−0.709645	+	0.704559i	$0.751145\pi$
$174$	−2319.19	+	2716.84i	−1.01044	+	1.18370i
$175$	271.724	+	526.706i	0.117374	+	0.227515i
$176$	632.560	+	1940.00i	0.270915	+	0.830869i
$177$			5090.47i			2.16171i
$178$	1304.02	+	1113.15i	0.549103	+	0.468733i
$179$		−	3074.45i		−	1.28377i	−0.766799	−	0.641887i	$-0.778152\pi$
$179$		−	3074.45i		−	1.28377i	0.766799	−	0.641887i	$-0.221848\pi$
$180$	−3918.33	+	1636.99i	−1.62253	+	0.677854i
$181$			3277.05i			1.34575i	0.739755	+	0.672876i	$0.234941\pi$
$181$			3277.05i			1.34575i	−0.739755	+	0.672876i	$0.765059\pi$
$182$	515.587	−	603.990i	0.209988	−	0.245993i
$183$		−	4949.00i		−	1.99913i
$184$	547.578	+	334.973i	0.219391	+	0.134209i
$185$	−531.288	−	2188.65i	−0.211141	−	0.869799i
$186$	−1442.51	−	1231.37i	−0.568654	−	0.485423i
$187$	−2580.53			−1.00913
$188$	263.120	−	41.8133i	0.102074	−	0.0162210i
$189$		−	837.902i		−	0.322478i
$190$	3234.88	+	1636.95i	1.23517	+	0.625034i
$191$	195.880			0.0742061			0.0371030	−	0.999311i	$-0.488187\pi$
$191$	195.880			0.0742061			0.0371030	+	0.999311i	$0.488187\pi$
$192$	−2012.09	−	3933.87i	−0.756303	−	1.47866i
$193$			2873.89i			1.07185i	0.844265	+	0.535926i	$0.180037\pi$
$193$			2873.89i			1.07185i	−0.844265	+	0.535926i	$0.819963\pi$
$194$	−278.362	+	326.090i	−0.103017	+	0.120680i
$195$	−1347.82	−	5552.38i	−0.494972	−	2.03905i
$196$	402.431	+	2532.38i	0.146658	+	0.922880i
$197$	−4109.31			−1.48617			−0.743087	−	0.669195i	$-0.766639\pi$
$197$	−4109.31			−1.48617			−0.743087	+	0.669195i	$0.766639\pi$
$198$	−2779.77	+	3256.39i	−0.997724	+	1.16880i
$199$	−2649.19			−0.943700			−0.471850	−	0.881679i	$-0.656414\pi$
$199$	−2649.19			−0.943700			−0.471850	+	0.881679i	$0.656414\pi$
$200$	−205.511	+	2820.95i	−0.0726589	+	0.997357i
$201$	−206.910			−0.0726085
$202$	118.735	−	139.093i	0.0413572	−	0.0484484i
$203$	−693.848			−0.239895
$204$	5518.67	−	876.993i	1.89404	−	0.300989i
$205$	−262.008	−	1079.35i	−0.0892655	−	0.367731i
$206$	2376.40	−	2783.86i	0.803745	−	0.941556i
$207$			1346.88i			0.452244i
$208$	3603.17	−	1174.86i	1.20113	−	0.391642i
$209$	3655.32			1.20978
$210$	−1154.53	−	584.228i	−0.379383	−	0.191979i
$211$		−	4482.21i		−	1.46241i	−0.682160	−	0.731203i	$-0.738959\pi$
$211$		−	4482.21i		−	1.46241i	0.682160	−	0.731203i	$-0.261041\pi$
$212$	320.651	+	2017.77i	0.103879	+	0.653684i
$213$	4061.77			1.30661
$214$	−3494.86	−	2983.33i	−1.11637	−	0.952974i
$215$	−554.622	−	2284.78i	−0.175930	−	0.724746i
$216$	2086.72	−	3411.14i	0.657329	−	1.07453i
$217$		−	368.399i		−	0.115247i
$218$	2291.04	−	2683.87i	0.711785	−	0.833828i
$219$			5837.51i			1.80120i
$220$	1099.30	+	2631.31i	0.336886	+	0.806378i
$221$			4792.82i			1.45882i
$222$	3739.85	+	3192.46i	1.13064	+	0.965153i
$223$		−	1605.92i		−	0.482244i	−0.970495	−	0.241122i	$-0.922485\pi$
$223$		−	1605.92i		−	0.482244i	0.970495	−	0.241122i	$-0.0775153\pi$
$224$	327.422	−	793.363i	0.0976644	−	0.236646i
$225$	−5274.21	+	2720.93i	−1.56273	+	0.806201i
$226$	−479.608	+	561.842i	−0.141164	+	0.165368i
$227$	1611.34			0.471139			0.235570	−	0.971857i	$-0.424304\pi$
$227$	1611.34			0.471139			0.235570	+	0.971857i	$0.424304\pi$
$228$	−7817.21	+	1242.26i	−2.27065	+	0.360837i
$229$		−	2221.77i		−	0.641129i	−0.947227	−	0.320565i	$-0.896127\pi$
$229$		−	2221.77i		−	0.641129i	0.947227	−	0.320565i	$-0.103873\pi$
$230$	800.448	+	405.050i	0.229478	+	0.116123i
$231$	−1304.59			−0.371583
$232$	−2824.69	−	1727.97i	−0.799354	−	0.488994i
$233$		−	424.194i		−	0.119270i	−0.998220	−	0.0596350i	$-0.981006\pi$
$233$		−	424.194i		−	0.119270i	0.998220	−	0.0596350i	$-0.0189937\pi$
$234$	6048.11	+	5162.87i	1.68965	+	1.44234i
$235$	361.827	−	87.8323i	0.100438	−	0.0243811i
$236$	−4660.35	+	740.595i	−1.28544	+	0.204274i
$237$	9370.19			2.56818
$238$	825.531	+	704.702i	0.224837	+	0.191929i
$239$	−4772.32			−1.29161			−0.645807	−	0.763501i	$-0.723479\pi$
$239$	−4772.32			−1.29161			−0.645807	+	0.763501i	$0.723479\pi$
$240$	−3245.20	−	5253.69i	−0.872820	−	1.41302i
$241$	−5675.88			−1.51708			−0.758539	−	0.651628i	$-0.774086\pi$
$241$	−5675.88			−1.51708			−0.758539	+	0.651628i	$0.774086\pi$
$242$	−676.487	−	577.472i	−0.179695	−	0.153394i
$243$	−2672.43			−0.705500
$244$	4530.84	−	720.013i	1.18876	−	0.188910i
$245$	845.338	+	3482.39i	0.220435	+	0.908088i
$246$	1844.33	+	1574.38i	0.478008	+	0.408044i
$247$		−	6789.04i		−	1.74889i
$248$	917.464	−	1499.77i	0.234915	−	0.384014i
$249$	675.354			0.171883
$250$	30.9167	+	3952.73i	0.00782137	+	0.999969i
$251$			334.026i			0.0839982i	0.999118	+	0.0419991i	$0.0133727\pi$
$251$			334.026i			0.0839982i	−0.999118	+	0.0419991i	$0.986627\pi$
$252$	1778.54	−	282.635i	0.444593	−	0.0706520i
$253$	904.483			0.224760
$254$	−3518.51	+	4121.80i	−0.869177	+	1.01821i
$255$	7588.96	−	1842.20i	1.86368	−	0.452403i
$256$	3308.75	−	2414.41i	0.807801	−	0.589455i
$257$		−	3516.77i		−	0.853580i	−0.904351	−	0.426790i	$-0.859644\pi$
$257$		−	3516.77i		−	0.853580i	0.904351	−	0.426790i	$-0.140356\pi$
$258$	3904.10	+	3332.67i	0.942087	+	0.804198i
$259$			955.112i			0.229142i
$260$	4887.15	−	2041.74i	1.16572	−	0.487012i
$261$		−	6947.90i		−	1.64776i
$262$	232.218	−	272.034i	0.0547575	−	0.0641463i
$263$			7550.95i			1.77039i	0.465224	+	0.885193i	$0.345974\pi$
$263$			7550.95i			1.77039i	−0.465224	+	0.885193i	$0.654026\pi$
$264$	−5311.05	−	3248.96i	−1.23815	−	0.757423i
$265$	673.554	+	2774.72i	0.156136	+	0.643206i
$266$	−1169.37	−	998.211i	−0.269543	−	0.230091i
$267$	−5231.31			−1.19907
$268$	−30.1026	−	189.427i	−0.00686124	−	0.0431758i
$269$		−	5979.76i		−	1.35536i	−0.735356	−	0.677681i	$-0.762985\pi$
$269$		−	5979.76i		−	1.35536i	0.735356	−	0.677681i	$-0.237015\pi$
$270$	2523.26	−	4986.40i	0.568744	−	1.12394i
$271$	2543.95			0.570237			0.285118	−	0.958492i	$-0.407967\pi$
$271$	2543.95			0.570237			0.285118	+	0.958492i	$0.407967\pi$
$272$	1605.79	+	4924.79i	0.357960	+	1.09783i
$273$			2423.02i			0.537171i
$274$	−903.083	+	1057.93i	−0.199114	+	0.233254i
$275$	1827.21	+	3541.84i	0.400673	+	0.776659i
$276$	−1934.31	+	307.389i	−0.421855	+	0.0670386i
$277$	−5858.01			−1.27066			−0.635332	−	0.772239i	$-0.719137\pi$
$277$	−5858.01			−1.27066			−0.635332	+	0.772239i	$0.719137\pi$
$278$	723.390	−	847.424i	0.156065	−	0.182824i
$279$	3688.99			0.791592
$280$	366.895	−	1141.98i	0.0783078	−	0.243737i
$281$	998.531			0.211983			0.105992	−	0.994367i	$-0.466198\pi$
$281$	998.531			0.211983			0.105992	+	0.994367i	$0.466198\pi$
$282$	−527.776	+	618.270i	−0.111449	+	0.130558i
$283$	2850.81			0.598809			0.299404	−	0.954126i	$-0.403212\pi$
$283$	2850.81			0.598809			0.299404	+	0.954126i	$0.403212\pi$
$284$	590.934	+	3718.58i	0.123470	+	0.776962i
$285$	−10749.8	+	2609.48i	−2.23425	+	0.542358i
$286$	3467.07	−	4061.55i	0.716826	−	0.839735i
$287$			471.019i			0.0968759i
$288$	7944.40	+	3278.67i	1.62545	+	0.670825i
$289$	−1637.80			−0.333361
$290$	−4129.13	−	2089.46i	−0.836106	−	0.423094i
$291$		−	1308.17i		−	0.263527i
$292$	−5344.28	+	849.280i	−1.07106	+	0.170207i
$293$	75.5914			0.0150720			0.00753601	−	0.999972i	$-0.497601\pi$
$293$	75.5914			0.0150720			0.00753601	+	0.999972i	$0.497601\pi$
$294$	−5950.51	−	5079.56i	−1.18041	−	1.00764i
$295$	−6408.65	+	1555.68i	−1.26483	+	0.307035i
$296$	−2378.62	+	3888.31i	−0.467076	+	0.763526i
$297$		−	5634.48i		−	1.10083i
$298$	−1973.54	+	2311.93i	−0.383638	+	0.449418i
$299$		−	1679.90i		−	0.324920i
$300$	−5111.34	−	6953.55i	−0.983678	−	1.33821i
$301$			997.060i			0.190929i
$302$	−2431.21	−	2075.36i	−0.463246	−	0.395443i
$303$			557.999i			0.105796i
$304$	−2274.60	−	6975.97i	−0.429136	−	1.31612i
$305$	6230.55	−	1512.45i	1.16971	−	0.283942i
$306$	−7056.58	+	8266.52i	−1.31829	+	1.54433i
$307$	−3156.88			−0.586881			−0.293441	−	0.955977i	$-0.594800\pi$
$307$	−3156.88			−0.586881			−0.293441	+	0.955977i	$0.594800\pi$
$308$	−189.800	−	1194.36i	−0.0351132	−	0.220958i
$309$			11168.0i			2.05606i
$310$	1109.40	−	2192.36i	0.203257	−	0.401670i
$311$	5028.64			0.916874			0.458437	−	0.888727i	$-0.348409\pi$
$311$	5028.64			0.916874			0.458437	+	0.888727i	$0.348409\pi$
$312$	−6034.31	+	9864.24i	−1.09495	+	1.78991i
$313$			8961.07i			1.61824i	0.587642	+	0.809121i	$0.300056\pi$
$313$			8961.07i			1.61824i	−0.587642	+	0.809121i	$0.699944\pi$
$314$	−2422.37	−	2067.82i	−0.435358	−	0.371636i
$315$	2445.75	−	593.697i	0.437467	−	0.106194i
$316$	1363.24	+	8578.47i	0.242684	+	1.52714i
$317$	8441.61			1.49567			0.747836	−	0.663884i	$-0.231093\pi$
$317$	8441.61			1.49567			0.747836	+	0.663884i	$0.231093\pi$
$318$	−4741.29	−	4047.32i	−0.836095	−	0.713719i
$319$	−4665.79			−0.818916
$320$	4337.65	−	3735.34i	0.757756	−	0.652538i
$321$	14020.3			2.43780
$322$	−289.351	−	247.000i	−0.0500774	−	0.0427478i
$323$	9279.23			1.59848
$324$	305.390	+	1921.73i	0.0523645	+	0.329515i
$325$	6578.28	−	3393.69i	1.12276	−	0.579224i
$326$	−665.147	−	567.792i	−0.113003	−	0.0964635i
$327$			10766.8i			1.82082i
$328$	−1173.03	+	1917.54i	−0.197469	+	0.322801i
$329$	−157.899			−0.0264597
$330$	−7763.68	−	3928.65i	−1.29508	−	0.655349i
$331$		−	3295.83i		−	0.547297i	−0.961830	−	0.273649i	$-0.911769\pi$
$331$		−	3295.83i		−	0.547297i	0.961830	−	0.273649i	$-0.0882305\pi$
$332$	98.2550	+	618.291i	0.0162423	+	0.102208i
$333$	−9564.09			−1.57390
$334$	4693.88	−	5498.70i	0.768975	−	0.900825i
$335$	−63.2330	−	260.490i	−0.0103128	−	0.0424838i
$336$	811.808	+	2489.74i	0.131809	+	0.404245i
$337$		−	12162.4i		−	1.96596i	−0.183709	−	0.982981i	$-0.558811\pi$
$337$		−	12162.4i		−	1.96596i	0.183709	−	0.982981i	$-0.441189\pi$
$338$	−2817.28	−	2404.92i	−0.453372	−	0.387014i
$339$		−	2253.93i		−	0.361112i
$340$	2790.64	+	6679.73i	0.445128	+	1.06547i
$341$		−	2477.30i		−	0.393412i
$342$	9995.67	−	11709.5i	1.58042	−	1.85140i
$343$		−	3145.96i		−	0.495236i
$344$	−2483.09	+	4059.08i	−0.389183	+	0.636195i
$345$	−2659.96	+	645.696i	−0.415093	+	0.100763i
$346$	6947.47	+	5930.60i	1.07947	+	0.921477i
$347$	2870.18			0.444032			0.222016	−	0.975043i	$-0.428736\pi$
$347$	2870.18			0.444032			0.222016	+	0.975043i	$0.428736\pi$
$348$	9978.19	−	1585.67i	1.53703	−	0.244256i
$349$			4290.16i			0.658015i	0.944327	+	0.329007i	$0.106714\pi$
$349$			4290.16i			0.658015i	−0.944327	+	0.329007i	$0.893286\pi$
$350$	382.682	−	1632.05i	0.0584435	−	0.249247i
$351$	−10464.9			−1.59139
$352$	2201.76	−	5334.98i	0.333392	−	0.807829i
$353$		−	11246.6i		−	1.69574i	−0.530201	−	0.847872i	$-0.677883\pi$
$353$		−	11246.6i		−	1.69574i	0.530201	−	0.847872i	$-0.322117\pi$
$354$	9347.93	−	10950.7i	1.40349	−	1.64414i
$355$	1241.30	+	5113.58i	0.185582	+	0.764509i
$356$	−761.085	−	4789.30i	−0.113307	−	0.713012i
$357$	−3311.77			−0.490973
$358$	−5645.81	+	6613.85i	−0.833492	+	0.976405i
$359$	10864.7			1.59726			0.798632	−	0.601820i	$-0.205558\pi$
$359$	10864.7			1.59726			0.798632	+	0.601820i	$0.205558\pi$
$360$	11435.3	+	3673.94i	1.67415	+	0.537871i
$361$	−6285.05			−0.916322
$362$	6017.84	−	7049.68i	0.873732	−	1.02354i
$363$	2713.85			0.392397
$364$	−2218.29	+	352.517i	−0.319423	+	0.0507607i
$365$	−7349.15	+	1783.98i	−1.05390	+	0.255830i
$366$	−9088.15	+	10646.4i	−1.29794	+	1.52048i
$367$			11131.3i			1.58323i	0.611018	+	0.791617i	$0.290760\pi$
$367$			11131.3i			1.58323i	−0.611018	+	0.791617i	$0.709240\pi$
$368$	−562.833	−	1726.15i	−0.0797275	−	0.244516i
$369$	−4716.59			−0.665408
$370$	−2876.23	+	5683.92i	−0.404130	+	0.798630i
$371$		−	1210.87i		−	0.169448i
$372$	841.913	+	5297.92i	0.117342	+	0.738399i
$373$	−3357.27			−0.466040			−0.233020	−	0.972472i	$-0.574861\pi$
$373$	−3357.27			−0.466040			−0.233020	+	0.972472i	$0.574861\pi$
$374$	5551.30	+	4738.78i	0.767515	+	0.655177i
$375$	−7902.04	−	9111.64i	−1.08816	−	1.25473i
$376$	−642.814	−	393.232i	−0.0881665	−	0.0539346i
$377$			8665.80i			1.18385i
$378$	−1538.69	+	1802.52i	−0.209369	+	0.245268i
$379$			2203.08i			0.298587i	0.988793	+	0.149293i	$0.0476999\pi$
$379$			2203.08i			0.298587i	−0.988793	+	0.149293i	$0.952300\pi$
$380$	−3952.94	−	9461.85i	−0.533636	−	1.27732i
$381$		−	16535.4i		−	2.22344i
$382$	−421.382	−	359.706i	−0.0564392	−	0.0481784i
$383$		−	8022.25i		−	1.07028i	−0.844763	−	0.535141i	$-0.820259\pi$
$383$		−	8022.25i		−	1.07028i	0.844763	−	0.535141i	$-0.179741\pi$
$384$	−2895.55	+	12157.6i	−0.384799	+	1.61566i
$385$	−398.691	−	1642.42i	−0.0527771	−	0.217416i
$386$	5277.51	−	6182.40i	0.695902	−	0.815222i
$387$	−9984.14			−1.31143
$388$	1197.64	−	190.322i	0.156703	−	0.0249023i
$389$		−	5583.44i		−	0.727741i	−0.931449	−	0.363871i	$-0.881455\pi$
$389$		−	5583.44i		−	0.727741i	0.931449	−	0.363871i	$-0.118545\pi$
$390$	−7296.70	+	14419.5i	−0.947392	+	1.87221i
$391$	2296.08			0.296976
$392$	3784.65	−	6186.74i	0.487637	−	0.797136i
$393$			1091.32i			0.140075i
$394$	8840.06	+	7546.18i	1.13034	+	0.964901i
$395$	2863.59	+	11796.6i	0.364767	+	1.50266i
$396$	11959.8	−	1900.58i	1.51769	−	0.241181i
$397$	12509.3			1.58142			0.790708	−	0.612194i	$-0.209713\pi$
$397$	12509.3			1.58142			0.790708	+	0.612194i	$0.209713\pi$
$398$	5699.01	+	4864.87i	0.717753	+	0.612699i
$399$	4691.13			0.588597
$400$	5622.38	−	5691.11i	0.702798	−	0.711389i
$401$	−12573.4			−1.56579			−0.782897	−	0.622151i	$-0.786259\pi$
$401$	−12573.4			−1.56579			−0.782897	+	0.622151i	$0.786259\pi$
$402$	445.110	+	379.961i	0.0552241	+	0.0471412i
$403$	−4601.11			−0.568728
$404$	−510.852	+	81.1814i	−0.0629105	+	0.00999734i
$405$	641.496	+	2642.66i	0.0787067	+	0.324234i
$406$	1492.62	+	1274.16i	0.182457	+	0.155752i
$407$			6422.67i			0.782211i
$408$	−13482.4	−	8247.66i	−1.63598	−	1.00078i
$409$	−9675.87			−1.16978			−0.584891	−	0.811112i	$-0.698863\pi$
$409$	−9675.87			−1.16978			−0.584891	+	0.811112i	$0.698863\pi$
$410$	−1418.43	+	2803.06i	−0.170857	+	0.337642i
$411$		−	4244.07i		−	0.509354i
$412$	−10224.3	+	1624.79i	−1.22261	+	0.194290i
$413$	2796.69			0.333211
$414$	2473.36	−	2897.44i	0.293620	−	0.343965i
$415$	206.393	+	850.239i	0.0244131	+	0.100570i
$416$	−9908.69	−	4089.33i	−1.16782	−	0.481962i
$417$			3399.60i			0.399230i
$418$	−7863.43	−	6712.49i	−0.920126	−	0.785451i
$419$		−	1832.65i		−	0.213677i	−0.994276	−	0.106839i	$-0.965927\pi$
$419$		−	1832.65i		−	0.213677i	0.994276	−	0.106839i	$-0.0340728\pi$
$420$	1410.81	+	3376.95i	0.163906	+	0.392329i
$421$		−	1917.39i		−	0.221967i	−0.993822	−	0.110983i	$-0.964600\pi$
$421$		−	1917.39i		−	0.221967i	0.993822	−	0.110983i	$-0.0354000\pi$
$422$	−8230.95	+	9642.24i	−0.949470	+	1.11227i
$423$		−	1581.13i		−	0.181743i
$424$	3015.56	−	4929.51i	0.345397	−	0.564618i
$425$	4638.47	+	8991.15i	0.529409	+	1.02620i
$426$	−8737.80	−	7458.88i	−0.993774	−	0.848319i
$427$	−2718.97			−0.308150
$428$	2039.76	+	12835.6i	0.230364	+	1.44961i
$429$			16293.6i			1.83372i
$430$	−3002.56	+	5933.56i	−0.336735	+	0.665445i
$431$	−6563.74			−0.733559			−0.366780	−	0.930308i	$-0.619540\pi$
$431$	−6563.74			−0.733559			−0.366780	+	0.930308i	$0.619540\pi$
$432$	−10753.1	+	3506.17i	−1.19759	+	0.390488i
$433$		−	6985.19i		−	0.775258i	−0.921816	−	0.387629i	$-0.873294\pi$
$433$		−	6985.19i		−	0.775258i	0.921816	−	0.387629i	$-0.126706\pi$
$434$	−676.513	+	792.509i	−0.0748241	+	0.0876536i
$435$	13721.4	−	3330.84i	1.51240	−	0.367129i
$436$	−9857.11	+	1566.43i	−1.08273	+	0.172061i
$437$	−3252.40			−0.356026
$438$	10719.8	−	12557.8i	1.16943	−	1.36994i
$439$	−1340.81			−0.145771			−0.0728855	−	0.997340i	$-0.523221\pi$
$439$	−1340.81			−0.145771			−0.0728855	+	0.997340i	$0.523221\pi$
$440$	2467.19	−	7679.27i	0.267316	−	0.832033i
$441$	15217.5			1.64318
$442$	8801.35	−	10310.4i	0.947144	−	1.10954i
$443$	−14680.3			−1.57445			−0.787225	−	0.616666i	$-0.788483\pi$
$443$	−14680.3			−1.57445			−0.787225	+	0.616666i	$0.788483\pi$
$444$	−2182.75	−	13735.4i	−0.233308	−	1.46814i
$445$	−1598.72	−	6585.97i	−0.170307	−	0.701584i
$446$	−2949.05	+	3454.70i	−0.313098	+	0.366782i
$447$		−	9274.73i		−	0.981386i
$448$	−2161.26	+	1105.44i	−0.227924	+	0.116578i
$449$	2927.44			0.307694			0.153847	−	0.988095i	$-0.450834\pi$
$449$	2927.44			0.307694			0.153847	+	0.988095i	$0.450834\pi$
$450$	16342.6	+	3832.02i	1.71200	+	0.401429i
$451$			3167.38i			0.330700i
$452$	2063.49	−	327.917i	0.214731	−	0.0341237i
$453$	9753.24			1.01158
$454$	−3466.37	−	2959.01i	−0.358336	−	0.305888i
$455$	−3050.47	+	740.491i	−0.314303	+	0.0762961i
$456$	19097.8	+	11682.8i	1.96127	+	1.19978i
$457$			2998.66i			0.306940i	0.988153	+	0.153470i	$0.0490448\pi$
$457$			2998.66i			0.306940i	−0.988153	+	0.153470i	$0.950955\pi$
$458$	−4079.97	+	4779.53i	−0.416254	+	0.487626i
$459$		−	14303.4i		−	1.45453i
$460$	−978.127	−	2341.27i	−0.0991422	−	0.237309i
$461$			13198.4i			1.33343i	0.745314	+	0.666714i	$0.232300\pi$
$461$			13198.4i			1.33343i	−0.745314	+	0.666714i	$0.767700\pi$
$462$	2806.47	+	2395.70i	0.282616	+	0.241251i
$463$		−	4324.69i		−	0.434094i	−0.976161	−	0.217047i	$-0.930358\pi$
$463$		−	4324.69i		−	0.434094i	0.976161	−	0.217047i	$-0.0696425\pi$
$464$	2903.39	+	8904.40i	0.290488	+	0.890898i
$465$	1768.51	+	7285.40i	0.176371	+	0.726564i
$466$	−778.974	+	912.538i	−0.0774362	+	0.0907135i
$467$	−7778.87			−0.770799			−0.385400	−	0.922750i	$-0.625936\pi$
$467$	−7778.87			−0.770799			−0.385400	+	0.922750i	$0.625936\pi$
$468$	−3529.96	−	22213.0i	−0.348659	−	2.19401i
$469$			113.676i			0.0111920i
$470$	−939.664	−	475.498i	−0.0922201	−	0.0466661i
$471$	9717.79			0.950684
$472$	11385.5	+	6964.90i	1.11029	+	0.679207i
$473$			6704.75i			0.651765i
$474$	−20157.4	−	17207.1i	−1.95329	−	1.66740i
$475$	−6570.41	−	12736.0i	−0.634676	−	1.23025i
$476$	−481.818	−	3031.95i	−0.0463952	−	0.291952i
$477$	12125.1			1.16388
$478$	10266.3	+	8763.70i	0.982368	+	0.838583i
$479$	5114.22			0.487838			0.243919	−	0.969796i	$-0.421567\pi$
$479$	5114.22			0.487838			0.243919	+	0.969796i	$0.421567\pi$
$480$	−2666.50	+	17261.2i	−0.253559	+	1.64138i
$481$	11928.8			1.13079
$482$	12210.1	+	10423.0i	1.15385	+	0.984965i
$483$	1160.79			0.109353
$484$	394.829	+	2484.55i	0.0370801	+	0.233335i
$485$	1646.93	−	399.786i	0.154192	−	0.0374296i
$486$	5749.00	+	4907.55i	0.536585	+	0.458047i
$487$		−	10457.3i		−	0.973030i	−0.873672	−	0.486515i	$-0.838268\pi$
$487$		−	10457.3i		−	0.973030i	0.873672	−	0.486515i	$-0.161732\pi$
$488$	−11069.1	−	6771.35i	−1.02679	−	0.628124i
$489$	2668.36			0.246764
$490$	4576.41	−	9043.75i	0.421920	−	0.833786i
$491$		−	3777.66i		−	0.347217i	−0.984815	−	0.173608i	$-0.944457\pi$
$491$		−	3777.66i		−	0.347217i	0.984815	−	0.173608i	$-0.0555427\pi$
$492$	−1076.43	−	6773.70i	−0.0986370	−	0.620695i
$493$	−11844.4			−1.08204
$494$	−12467.1	+	14604.8i	−1.13547	+	1.33016i
$495$	16446.5	−	3992.33i	1.49336	−	0.362508i
$496$	−4727.79	+	1541.55i	−0.427992	+	0.139552i
$497$		−	2231.53i		−	0.201404i
$498$	−1452.84	−	1240.19i	−0.130730	−	0.111595i
$499$			18387.4i			1.64957i	0.565447	+	0.824785i	$0.308704\pi$
$499$			18387.4i			1.64957i	−0.565447	+	0.824785i	$0.691296\pi$
$500$	7192.12	−	8559.99i	0.643283	−	0.765628i
$501$			22059.1i			1.96712i
$502$	613.393	−	718.566i	0.0545360	−	0.0638868i
$503$		−	6909.13i		−	0.612451i	−0.951959	−	0.306226i	$-0.900934\pi$
$503$		−	6909.13i		−	0.612451i	0.951959	−	0.306226i	$-0.0990662\pi$
$504$	−4345.06	−	2658.03i	−0.384017	−	0.234917i
$505$	−702.494	+	170.528i	−0.0619021	+	0.0150265i
$506$	−1945.75	−	1660.96i	−0.170947	−	0.145926i
$507$	11302.0			0.990021
$508$	15138.2	−	2405.67i	1.32215	−	0.210107i
$509$		−	19760.1i		−	1.72073i	−0.509680	−	0.860364i	$-0.670236\pi$
$509$		−	19760.1i		−	1.72073i	0.509680	−	0.860364i	$-0.329764\pi$
$510$	−19708.5	−	9973.09i	−1.71119	−	0.865914i
$511$	3207.11			0.277641
$512$	−11551.6	−	882.125i	−0.997097	−	0.0761422i
$513$			20260.9i			1.74374i
$514$	−6458.06	+	7565.37i	−0.554188	+	0.649210i
$515$	−14059.9	+	3413.00i	−1.20302	+	0.292029i
$516$	−2278.61	−	14338.7i	−0.194400	−	1.22330i
$517$	−1061.79			−0.0903242
$518$	1753.93	−	2054.66i	0.148771	−	0.174279i
$519$	−27871.1			−2.35723
$520$	−14262.7	−	4582.33i	−1.20281	−	0.386439i
$521$	−16342.3			−1.37422			−0.687109	−	0.726554i	$-0.741120\pi$
$521$	−16342.3			−1.37422			−0.687109	+	0.726554i	$0.741120\pi$
$522$	−12758.9	+	14946.5i	−1.06981	+	1.25324i
$523$	22862.3			1.91147			0.955735	−	0.294230i	$-0.0950632\pi$
$523$	22862.3			1.91147			0.955735	+	0.294230i	$0.0950632\pi$
$524$	−999.107	+	158.772i	−0.0832942	+	0.0132366i
$525$	2344.99	+	4545.49i	0.194940	+	0.377870i
$526$	13866.3	−	16243.8i	1.14943	−	1.34651i
$527$		−	6288.77i		−	0.519816i
$528$	5459.02	+	16742.3i	0.449949	+	1.37995i
$529$	11362.2			0.933855
$530$	3646.42	−	7205.94i	0.298850	−	0.590578i
$531$			28004.9i			2.28872i
$532$	682.497	+	4294.76i	0.0556203	+	0.350003i
$533$	5882.78			0.478070
$534$	11253.7	+	9606.57i	0.911979	+	0.778496i
$535$	4284.69	+	17650.9i	0.346249	+	1.42638i
$536$	−283.099	+	462.781i	−0.0228135	+	0.0372931i
$537$		−	26532.7i		−	2.13216i
$538$	−10981.0	+	12863.8i	−0.879972	+	1.03085i
$539$		−	10219.2i		−	0.816644i
$540$	−14584.9	+	6093.25i	−1.16229	+	0.485577i
$541$		−	6981.75i		−	0.554841i	−0.960749	−	0.277421i	$-0.910520\pi$
$541$		−	6981.75i		−	0.554841i	0.960749	−	0.277421i	$-0.0894795\pi$
$542$	−5472.62	−	4671.62i	−0.433707	−	0.370227i
$543$			28281.1i			2.23510i
$544$	5589.28	−	13543.1i	0.440512	−	1.06738i
$545$	−13554.9	+	3290.42i	−1.06538	+	0.258616i
$546$	4449.54	−	5212.46i	0.348759	−	0.408558i
$547$	−1515.34			−0.118449			−0.0592243	−	0.998245i	$-0.518863\pi$
$547$	−1515.34			−0.118449			−0.0592243	+	0.998245i	$0.518863\pi$
$548$	3885.47	−	617.455i	0.302882	−	0.0481321i
$549$		−	27226.6i		−	2.11658i
$550$	2573.35	−	10974.7i	0.199506	−	0.850844i
$551$	16777.6			1.29718
$552$	4725.62	+	2890.83i	0.364377	+	0.222902i
$553$		−	5147.96i		−	0.395865i
$554$	12601.9	+	10757.4i	0.966433	+	0.824980i
$555$	−4585.04	−	18888.2i	−0.350674	−	1.44461i
$556$	−3112.35	+	494.596i	−0.237398	+	0.0377258i
$557$	−9210.22			−0.700628			−0.350314	−	0.936632i	$-0.613925\pi$
$557$	−9210.22			−0.700628			−0.350314	+	0.936632i	$0.613925\pi$
$558$	−7935.86	−	6774.32i	−0.602064	−	0.513942i
$559$	12452.8			0.942210
$560$	−2886.36	+	1782.91i	−0.217806	+	0.134538i
$561$	−22270.1			−1.67601
$562$	−2148.07	−	1833.66i	−0.161229	−	0.137631i
$563$	−13512.5			−1.01152			−0.505758	−	0.862675i	$-0.668787\pi$
$563$	−13512.5			−1.01152			−0.505758	+	0.862675i	$0.668787\pi$
$564$	2270.73	−	360.851i	0.169530	−	0.0269407i
$565$	2837.60	−	688.817i	0.211289	−	0.0512898i
$566$	−6132.73	−	5235.11i	−0.455438	−	0.388778i
$567$		−	1153.24i		−	0.0854169i
$568$	5557.42	−	9084.68i	0.410536	−	0.671100i
$569$	14779.9			1.08893			0.544467	−	0.838782i	$-0.316732\pi$
$569$	14779.9			1.08893			0.544467	+	0.838782i	$0.316732\pi$
$570$	27917.2	+	14126.9i	2.05144	+	1.03809i
$571$		−	10948.6i		−	0.802423i	−0.915985	−	0.401211i	$-0.868589\pi$
$571$		−	10948.6i		−	0.802423i	0.915985	−	0.401211i	$-0.131411\pi$
$572$	−14916.9	+	2370.51i	−1.09040	+	0.173279i
$573$	1690.45			0.123245
$574$	864.961	−	1013.27i	0.0628968	−	0.0736812i
$575$	−1625.80	−	3151.43i	−0.117914	−	0.228563i
$576$	−11069.4	−	21642.0i	−0.800738	−	1.56554i
$577$			9935.61i			0.716854i	0.933558	+	0.358427i	$0.116687\pi$
$577$			9935.61i			0.716854i	−0.933558	+	0.358427i	$0.883313\pi$
$578$	3523.29	+	3007.60i	0.253546	+	0.216435i
$579$			24801.8i			1.78019i
$580$	5045.69	+	12077.5i	0.361225	+	0.864638i
$581$		−	371.038i		−	0.0264944i
$582$	−2402.28	+	2814.17i	−0.171095	+	0.200432i
$583$		−	8142.51i		−	0.578436i
$584$	13056.3	+	7987.03i	0.925129	+	0.565934i
$585$	−7414.96	−	30546.1i	−0.524053	−	2.15885i
$586$	−162.614	−	138.813i	−0.0114634	−	0.00978553i
$587$	802.589			0.0564334			0.0282167	−	0.999602i	$-0.491017\pi$
$587$	802.589			0.0564334			0.0282167	+	0.999602i	$0.491017\pi$
$588$	3472.99	+	21854.6i	0.243578	+	1.53277i
$589$			8908.05i			0.623175i
$590$	16643.3	+	8421.98i	1.16134	+	0.587674i
$591$	−35463.5			−2.46831
$592$	12257.3	−	3996.64i	0.850966	−	0.277468i
$593$			3331.26i			0.230689i	0.993326	+	0.115344i	$0.0367972\pi$
$593$			3331.26i			0.230689i	−0.993326	+	0.115344i	$0.963203\pi$
$594$	−10346.9	+	12121.1i	−0.714714	+	0.837261i
$595$	−1012.10	−	4169.36i	−0.0697344	−	0.287272i
$596$	8491.07	−	1349.35i	0.583570	−	0.0927374i
$597$	−22862.6			−1.56735
$598$	−3084.90	+	3613.85i	−0.210955	+	0.247126i
$599$	−28945.9			−1.97445			−0.987225	−	0.159330i	$-0.949067\pi$
$599$	−28945.9			−1.97445			−0.987225	+	0.159330i	$0.949067\pi$
$600$	−1773.56	+	24344.9i	−0.120676	+	1.65646i
$601$	−1611.28			−0.109360			−0.0546801	−	0.998504i	$-0.517414\pi$
$601$	−1611.28			−0.109360			−0.0546801	+	0.998504i	$0.517414\pi$
$602$	1830.96	−	2144.90i	0.123961	−	0.145215i
$603$	−1138.30			−0.0768744
$604$	1418.97	+	8929.15i	0.0955909	+	0.601527i
$605$	829.371	+	3416.61i	0.0557334	+	0.229595i
$606$	1024.69	−	1200.38i	0.0686883	−	0.0804657i
$607$			18635.9i			1.24614i	0.782165	+	0.623072i	$0.214115\pi$
$607$			18635.9i			1.24614i	−0.782165	+	0.623072i	$0.785885\pi$
$608$	−7917.23	+	19183.9i	−0.528102	+	1.27962i
$609$	−5987.94			−0.398429
$610$	−16180.7	−	8187.93i	−1.07400	−	0.543475i
$611$			1972.07i			0.130575i
$612$	30360.6	−	4824.72i	2.00532	−	0.318673i
$613$	−8792.08			−0.579296			−0.289648	−	0.957133i	$-0.593538\pi$
$613$	−8792.08			−0.579296			−0.289648	+	0.957133i	$0.593538\pi$
$614$	6791.16	+	5797.17i	0.446367	+	0.381034i
$615$	−2261.14	−	9314.80i	−0.148257	−	0.610747i
$616$	−1784.97	+	2917.88i	−0.116751	+	0.190852i
$617$			13584.0i			0.886340i	0.896438	+	0.443170i	$0.146146\pi$
$617$			13584.0i			0.886340i	−0.896438	+	0.443170i	$0.853854\pi$
$618$	20508.4	−	24024.8i	1.33490	−	1.56379i
$619$			1425.16i			0.0925394i	0.998929	+	0.0462697i	$0.0147334\pi$
$619$			1425.16i			0.0925394i	−0.998929	+	0.0462697i	$0.985267\pi$
$620$	−6412.54	+	2679.01i	−0.415377	+	0.173535i
$621$			5013.40i			0.323963i
$622$	−10817.7	−	9234.40i	−0.697351	−	0.595282i
$623$			2874.07i			0.184827i
$624$	31095.5	−	10139.1i	1.99490	−	0.650460i
$625$	9056.20	−	12732.9i	0.579597	−	0.814903i
$626$	16455.8	−	19277.3i	1.05065	−	1.23079i
$627$	31545.6			2.00927
$628$	1413.81	+	8896.70i	0.0898361	+	0.565313i
$629$			16304.3i			1.03354i
$630$	−6351.60	−	3214.10i	−0.401672	−	0.203258i
$631$	9225.47			0.582029			0.291014	−	0.956719i	$-0.406007\pi$
$631$	9225.47			0.582029			0.291014	+	0.956719i	$0.406007\pi$
$632$	12820.5	−	20957.6i	0.806920	−	1.31907i
$633$		−	38681.6i		−	2.42884i
$634$	−18159.8	−	15501.8i	−1.13757	−	0.971067i
$635$	20817.2	−	5053.32i	1.30096	−	0.315803i
$636$	2767.24	+	17413.4i	0.172528	+	1.08567i
$637$	−18980.1			−1.18056
$638$	10037.2	+	8568.08i	0.622846	+	0.531683i
$639$	22345.6			1.38338
$640$	−16190.7	+	70.0824i	−0.999991	+	0.00432852i
$641$	14596.9			0.899445			0.449723	−	0.893168i	$-0.351523\pi$
$641$	14596.9			0.899445			0.449723	+	0.893168i	$0.351523\pi$
$642$	−30160.8	−	25746.3i	−1.85413	−	1.58275i
$643$	23710.2			1.45418			0.727092	−	0.686540i	$-0.240871\pi$
$643$	23710.2			1.45418			0.727092	+	0.686540i	$0.240871\pi$
$644$	168.879	+	1062.71i	0.0103335	+	0.0650257i
$645$	−4786.41	−	19717.7i	−0.292193	−	1.20370i
$646$	−19961.7	−	17040.0i	−1.21576	−	1.03782i
$647$		−	15897.0i		−	0.965962i	−0.875631	−	0.482981i	$-0.839554\pi$
$647$		−	15897.0i		−	0.965962i	0.875631	−	0.482981i	$-0.160446\pi$
$648$	2872.03	−	4694.89i	0.174111	−	0.284618i
$649$	18806.4			1.13747
$650$	−20383.4	−	4779.50i	−1.23000	−	0.288411i
$651$		−	3179.30i		−	0.191408i
$652$	388.211	+	2442.90i	0.0233183	+	0.146735i
$653$	31188.2			1.86905			0.934524	−	0.355900i	$-0.115826\pi$
$653$	31188.2			1.86905			0.934524	+	0.355900i	$0.115826\pi$
$654$	19771.8	−	23161.9i	1.18217	−	1.38487i
$655$	−1373.91	+	333.513i	−0.0819592	+	0.0198953i
$656$	6044.76	−	1970.97i	0.359768	−	0.117307i
$657$			32114.7i			1.90702i
$658$	339.676	+	289.959i	0.0201245	+	0.0171790i
$659$		−	26334.9i		−	1.55670i	−0.627832	−	0.778349i	$-0.716058\pi$
$659$		−	26334.9i		−	1.55670i	0.627832	−	0.778349i	$-0.283942\pi$
$660$	9487.02	+	22708.4i	0.559518	+	1.33927i
$661$			20361.4i			1.19813i	0.800700	+	0.599066i	$0.204461\pi$
$661$			20361.4i			1.19813i	−0.800700	+	0.599066i	$0.795539\pi$
$662$	−6052.34	+	7090.08i	−0.355334	+	0.416260i
$663$			41362.3i			2.42289i
$664$	924.037	−	1510.52i	0.0540054	−	0.0882822i
$665$	1433.64	+	5905.91i	0.0836003	+	0.344393i
$666$	20574.5	+	17563.1i	1.19707	+	1.02186i
$667$	4151.49			0.240999
$668$	−20195.2	+	3209.30i	−1.16972	+	0.185885i
$669$		−	13859.2i		−	0.800936i
$670$	−342.325	+	676.491i	−0.0197390	+	0.0390077i
$671$	−18283.8			−1.05192
$672$	2825.67	−	6846.76i	0.162206	−	0.393035i
$673$		−	1622.72i		−	0.0929438i	−0.998920	−	0.0464719i	$-0.985202\pi$
$673$		−	1622.72i		−	0.0929438i	0.998920	−	0.0464719i	$-0.0147978\pi$
$674$	−22334.6	+	26164.1i	−1.27640	+	1.49526i
$675$	−19631.9	+	10127.9i	−1.11945	+	0.577518i
$676$	1644.29	+	10347.1i	0.0935533	+	0.588705i
$677$	15796.0			0.896733			0.448367	−	0.893850i	$-0.352006\pi$
$677$	15796.0			0.896733			0.448367	+	0.893850i	$0.352006\pi$
$678$	−4139.04	+	4848.72i	−0.234452	+	0.274652i
$679$	−718.707			−0.0406207
$680$	6263.10	−	19494.2i	0.353205	−	1.09937i
$681$	13906.0			0.782493
$682$	−4549.22	+	5329.24i	−0.255423	+	0.299219i
$683$	−15901.0			−0.890828			−0.445414	−	0.895325i	$-0.646943\pi$
$683$	−15901.0			−0.890828			−0.445414	+	0.895325i	$0.646943\pi$
$684$	−43005.9	+	6834.23i	−2.40405	+	0.382037i
$685$	5343.08	−	1297.02i	0.298027	−	0.0723451i
$686$	−5777.13	+	6767.68i	−0.321533	+	0.376664i
$687$		−	19174.0i		−	1.06482i
$688$	12795.6	−	4172.17i	0.709054	−	0.231195i
$689$	−15123.1			−0.836204
$690$	6907.90	+	3495.60i	0.381129	+	0.192863i
$691$			14869.9i			0.818638i	0.912391	+	0.409319i	$0.134234\pi$
$691$			14869.9i			0.818638i	−0.912391	+	0.409319i	$0.865766\pi$
$692$	−4054.87	−	25516.1i	−0.222750	−	1.40170i
$693$	−7177.12			−0.393414
$694$	−6174.40	−	5270.68i	−0.337719	−	0.288289i
$695$	−4279.93	+	1038.94i	−0.233593	+	0.0567039i
$696$	−24377.2	−	14912.4i	−1.32761	−	0.812146i
$697$			8040.55i			0.436955i
$698$	7878.29	−	9229.11i	0.427217	−	0.500469i
$699$		−	3660.81i		−	0.198090i
$700$	−3820.26	+	2808.16i	−0.206275	+	0.151626i
$701$			15260.7i			0.822237i	0.911582	+	0.411118i	$0.134862\pi$
$701$			15260.7i			0.822237i	−0.911582	+	0.411118i	$0.865138\pi$
$702$	22512.5	+	19217.4i	1.21037	+	1.03321i
$703$		−	23095.1i		−	1.23904i
$704$	−14533.4	+	7433.54i	−0.778053	+	0.397958i
$705$	3122.58	−	757.997i	0.166813	−	0.0404933i
$706$	−20652.9	+	24194.1i	−1.10096	+	1.28974i
$707$	306.563			0.0163076
$708$	−40219.1	+	6391.36i	−2.13492	+	0.339269i
$709$			1280.70i			0.0678387i	0.999425	+	0.0339194i	$0.0107989\pi$
$709$			1280.70i			0.0678387i	−0.999425	+	0.0339194i	$0.989201\pi$
$710$	6720.05	−	13280.0i	0.355210	−	0.701955i
$711$	51549.5			2.71907
$712$	−7157.61	+	11700.5i	−0.376745	+	0.615863i
$713$			2204.23i			0.115777i
$714$	7124.37	+	6081.60i	0.373421	+	0.318765i
$715$	−20512.9	+	4979.44i	−1.07292	+	0.260448i
$716$	24290.8	−	3860.15i	1.26786	−	0.201481i
$717$	−41185.3			−2.14518
$718$	−23372.5	−	19951.5i	−1.21484	−	1.03703i
$719$	17279.4			0.896264			0.448132	−	0.893967i	$-0.352089\pi$
$719$	17279.4			0.896264			0.448132	+	0.893967i	$0.352089\pi$
$720$	−17853.3	−	28902.8i	−0.924101	−	1.49603i
$721$	6135.65			0.316926
$722$	13520.6	+	11541.6i	0.696930	+	0.594923i
$723$	−48983.1			−2.51964
$724$	−25891.5	+	4114.52i	−1.32907	+	0.211208i
$725$	8386.72	+	16256.7i	0.429621	+	0.832771i
$726$	−5838.11	−	4983.61i	−0.298447	−	0.254765i
$727$			34013.1i			1.73518i	0.497280	+	0.867590i	$0.334332\pi$
$727$			34013.1i			1.73518i	−0.497280	+	0.867590i	$0.665668\pi$
$728$	5419.39	+	3315.24i	0.275901	+	0.168779i
$729$	−29630.4			−1.50538
$730$	19085.7	+	9657.94i	0.967663	+	0.489666i
$731$			17020.4i			0.861177i
$732$	39101.4	−	6213.75i	1.97435	−	0.313752i
$733$	−12918.8			−0.650976			−0.325488	−	0.945546i	$-0.605529\pi$
$733$	−12918.8			−0.650976			−0.325488	+	0.945546i	$0.605529\pi$
$734$	20441.0	−	23945.9i	1.02792	−	1.20417i
$735$	7295.31	+	30053.2i	0.366111	+	1.50820i
$736$	−1959.06	+	4746.91i	−0.0981140	+	0.237736i
$737$			764.415i			0.0382057i
$738$	10146.4	+	8661.36i	0.506092	+	0.432017i
$739$			6230.77i			0.310152i	0.987903	+	0.155076i	$0.0495623\pi$
$739$			6230.77i			0.310152i	−0.987903	+	0.155076i	$0.950438\pi$
$740$	16625.2	−	6945.61i	0.825883	−	0.345035i
$741$		−	58589.7i		−	2.90465i
$742$	−2223.59	+	2604.85i	−0.110014	+	0.128878i
$743$		−	27113.4i		−	1.33875i	−0.742924	−	0.669376i	$-0.766561\pi$
$743$		−	27113.4i		−	1.33875i	0.742924	−	0.669376i	$-0.233439\pi$
$744$	7917.75	−	12943.1i	0.390160	−	0.637791i
$745$	11676.4	−	2834.42i	0.574217	−	0.139389i
$746$	7222.25	+	6165.16i	0.354457	+	0.302577i
$747$	3715.42			0.181981
$748$	−3240.00	−	20388.4i	−0.158377	−	0.996621i
$749$		−	7702.71i		−	0.375769i
$750$	266.812	+	34112.2i	0.0129901	+	1.66080i
$751$	−17626.9			−0.856479			−0.428239	−	0.903665i	$-0.640866\pi$
$751$	−17626.9			−0.856479			−0.428239	+	0.903665i	$0.640866\pi$
$752$	660.723	+	2026.37i	0.0320400	+	0.0982635i
$753$			2882.66i			0.139509i
$754$	15913.5	−	18642.1i	0.768616	−	0.900405i
$755$	2980.65	+	12278.9i	0.143678	+	0.591885i
$756$	6620.14	−	1052.03i	0.318482	−	0.0506112i
$757$	33113.0			1.58984			0.794921	−	0.606712i	$-0.207512\pi$
$757$	33113.0			1.58984			0.794921	+	0.606712i	$0.207512\pi$
$758$	4045.64	−	4739.32i	0.193858	−	0.227097i
$759$	7805.73			0.373294
$760$	−8871.70	+	27613.6i	−0.423435	+	1.31796i
$761$	3327.92			0.158524			0.0792622	−	0.996854i	$-0.474744\pi$
$761$	3327.92			0.158524			0.0792622	+	0.996854i	$0.474744\pi$
$762$	−30364.9	+	35571.3i	−1.44358	+	1.69109i
$763$	5915.28			0.280665
$764$	245.938	+	1547.62i	0.0116462	+	0.0732865i
$765$	41750.2	−	10134.7i	1.97318	−	0.478983i
$766$	−14731.7	+	17257.7i	−0.694882	+	0.814028i
$767$		−	34929.2i		−	1.64435i
$768$	28554.7	−	20836.4i	1.34164	−	0.978998i
$769$	−7278.36			−0.341306			−0.170653	−	0.985331i	$-0.554588\pi$
$769$	−7278.36			−0.341306			−0.170653	+	0.985331i	$0.554588\pi$
$770$	−2158.39	+	4265.35i	−0.101017	+	0.199627i
$771$		−	30349.9i		−	1.41767i
$772$	−22706.2	+	3608.34i	−1.05857	+	0.168221i
$773$	8158.35			0.379606			0.189803	−	0.981822i	$-0.439215\pi$
$773$	8158.35			0.379606			0.189803	+	0.981822i	$0.439215\pi$
$774$	21478.1	+	18334.5i	0.997437	+	0.851446i
$775$	−8631.50	+	4452.93i	−0.400068	+	0.206392i
$776$	−2925.89	−	1789.87i	−0.135352	−	0.0827999i
$777$			8242.66i			0.380571i
$778$	−10253.2	+	12011.2i	−0.472487	+	0.553501i
$779$		−	11389.5i		−	0.523838i
$780$	42176.3	−	17620.3i	1.93609	−	0.808855i
$781$		−	15006.0i		−	0.687523i
$782$	−4939.38	−	4216.43i	−0.225872	−	0.192812i
$783$		−	25861.7i		−	1.18036i
$784$	−19502.7	+	6359.09i	−0.888426	+	0.289682i
$785$	2969.82	+	12234.2i	0.135029	+	0.556253i
$786$	2004.05	−	2347.67i	0.0909442	−	0.106538i
$787$	19256.9			0.872217			0.436109	−	0.899894i	$-0.356356\pi$
$787$	19256.9			0.872217			0.436109	+	0.899894i	$0.356356\pi$
$788$	−5159.47	−	32467.1i	−0.233247	−	1.46776i
$789$			65165.0i			2.94035i
$790$	15502.6	−	30635.8i	0.698175	−	1.37971i
$791$	−1238.31			−0.0556626
$792$	−29218.4	−	17874.0i	−1.31090	−	0.801924i
$793$			33958.5i			1.52068i
$794$	−26910.3	−	22971.5i	−1.20278	−	1.02674i
$795$	5812.80	+	23946.0i	0.259319	+	1.06827i
$796$	−3326.21	−	20930.9i	−0.148108	−	0.932005i
$797$	−9099.25			−0.404407			−0.202203	−	0.979344i	$-0.564810\pi$
$797$	−9099.25			−0.404407			−0.202203	+	0.979344i	$0.564810\pi$
$798$	−10091.7	−	8614.61i	−0.447671	−	0.382148i
$799$	−2695.42			−0.119345
$800$	−22546.0	+	1918.15i	−0.996400	+	0.0847712i
$801$	−28779.7			−1.26951
$802$	27048.1	+	23089.2i	1.19090	+	1.01659i
$803$	21566.3			0.947769
$804$	−259.787	−	1634.77i	−0.0113955	−	0.0717087i
$805$	354.744	+	1461.37i	0.0155318	+	0.0639834i
$806$	9898.02	+	8449.29i	0.432560	+	0.369248i
$807$		−	51605.6i		−	2.25106i
$808$	1248.04	+	763.469i	0.0543388	+	0.0332410i
$809$	−32295.7			−1.40353			−0.701766	−	0.712408i	$-0.747605\pi$
$809$	−32295.7			−1.40353			−0.701766	+	0.712408i	$0.747605\pi$
$810$	3472.87	−	6862.97i	0.150647	−	0.297704i
$811$		−	38607.7i		−	1.67164i	−0.549005	−	0.835819i	$-0.684993\pi$
$811$		−	38607.7i		−	1.67164i	0.549005	−	0.835819i	$-0.315007\pi$
$812$	−871.165	−	5482.00i	−0.0376501	−	0.236922i
$813$	21954.4			0.947079
$814$	11794.3	−	13816.6i	0.507852	−	0.594929i
$815$	815.468	+	3359.34i	0.0350486	+	0.144383i
$816$	13858.0	+	42501.1i	0.594519	+	1.82333i
$817$		−	24109.4i		−	1.03241i
$818$	20815.0	+	17768.4i	0.889706	+	0.759484i
$819$			13330.1i			0.568731i
$820$	8198.80	−	3425.27i	0.349164	−	0.145873i
$821$		−	5586.10i		−	0.237462i	−0.992926	−	0.118731i	$-0.962117\pi$
$821$		−	5586.10i		−	0.237462i	0.992926	−	0.118731i	$-0.0378826\pi$
$822$	−7793.64	+	9129.96i	−0.330699	+	0.387401i
$823$			3121.31i			0.132202i	0.997813	+	0.0661008i	$0.0210559\pi$
$823$			3121.31i			0.132202i	−0.997813	+	0.0661008i	$0.978944\pi$
$824$	24978.6	+	15280.3i	1.05603	+	0.646012i
$825$	15768.9	+	30566.3i	0.665458	+	1.28992i
$826$	−6016.32	−	5135.73i	−0.253432	−	0.216338i
$827$	−10702.5			−0.450017			−0.225008	−	0.974357i	$-0.572241\pi$
$827$	−10702.5			−0.450017			−0.225008	+	0.974357i	$0.572241\pi$
$828$	−10641.5	+	1691.08i	−0.446640	+	0.0709772i
$829$			28818.9i			1.20739i	0.797217	+	0.603693i	$0.206305\pi$
$829$			28818.9i			1.20739i	−0.797217	+	0.603693i	$0.793695\pi$
$830$	1117.35	−	2208.07i	0.0467273	−	0.0923411i
$831$	−50554.9			−2.11038
$832$	13806.3	+	26993.0i	0.575299	+	1.12478i
$833$		−	25941.9i		−	1.07903i
$834$	6242.88	−	7313.30i	0.259201	−	0.303644i
$835$	−27771.3	+	6741.39i	−1.15098	+	0.279396i
$836$	4589.46	+	28880.2i	0.189868	+	1.19479i
$837$	13731.3			0.567052
$838$	−3365.40	+	3942.44i	−0.138730	+	0.162517i
$839$	19119.3			0.786736			0.393368	−	0.919381i	$-0.371310\pi$
$839$	19119.3			0.786736			0.393368	+	0.919381i	$0.371310\pi$
$840$	3166.32	−	9855.34i	0.130058	−	0.404811i
$841$	2973.46			0.121918
$842$	−3521.02	+	4124.74i	−0.144112	+	0.168822i
$843$	8617.36			0.352073
$844$	35413.3	−	5627.66i	1.44428	−	0.229517i
$845$	3453.97	+	14228.7i	0.140616	+	0.579269i
$846$	−2903.53	+	3401.37i	−0.117997	+	0.138229i
$847$		−	1490.98i		−	0.0604850i
$848$	−15539.5	+	5066.84i	−0.629279	+	0.205184i
$849$	24602.6			0.994533
$850$	6532.59	−	27859.9i	0.263607	−	1.12422i
$851$		−	5714.71i		−	0.230197i
$852$	5099.78	+	32091.5i	0.205065	+	1.29042i
$853$	−38038.6			−1.52686			−0.763432	−	0.645888i	$-0.776487\pi$
$853$	−38038.6			−1.52686			−0.763432	+	0.645888i	$0.776487\pi$
$854$	5849.12	+	4993.01i	0.234371	+	0.200067i
$855$	−59139.3	+	14355.9i	−2.36552	+	0.574223i
$856$	19182.9	−	31358.1i	0.765955	−	1.25210i
$857$			22594.3i			0.900589i	0.892880	+	0.450295i	$0.148681\pi$
$857$			22594.3i			0.900589i	−0.892880	+	0.450295i	$0.851319\pi$
$858$	29921.0	−	35051.3i	1.19054	−	1.39468i
$859$		−	34869.4i		−	1.38502i	−0.721410	−	0.692508i	$-0.756506\pi$
$859$		−	34869.4i		−	1.38502i	0.721410	−	0.692508i	$-0.243494\pi$
$860$	17355.3	−	7250.65i	0.688153	−	0.287494i
$861$			4064.91i			0.160897i
$862$	14120.1	+	12053.4i	0.557926	+	0.476265i
$863$			40314.4i			1.59017i	0.606496	+	0.795087i	$0.292575\pi$
$863$			40314.4i			1.59017i	−0.606496	+	0.795087i	$0.707425\pi$
$864$	29570.9	+	12204.0i	1.16438	+	0.480542i
$865$	−8517.58	−	35088.3i	−0.334805	−	1.37924i
$866$	−12827.3	+	15026.7i	−0.503337	+	0.589641i
$867$	−14134.3			−0.553664
$868$	2910.67	−	462.545i	0.113819	−	0.0180873i
$869$		−	34617.6i		−	1.35135i
$870$	−35634.6	−	18032.1i	−1.38865	−	0.702697i
$871$	1419.75			0.0552313
$872$	24081.4	+	14731.5i	0.935206	+	0.572099i
$873$		−	7196.83i		−	0.279010i
$874$	6996.65	+	5972.58i	0.270784	+	0.231150i
$875$	−5005.91	+	4341.36i	−0.193407	+	0.167731i
$876$	−46121.3	+	7329.32i	−1.77888	+	0.282688i
$877$	−9266.02			−0.356775			−0.178387	−	0.983960i	$-0.557088\pi$
$877$	−9266.02			−0.356775			−0.178387	+	0.983960i	$0.557088\pi$
$878$	2884.39	+	2462.22i	0.110870	+	0.0946421i
$879$	652.357			0.0250324
$880$	−19409.4	+	11989.2i	−0.743512	+	0.459268i
$881$	50175.7			1.91880			0.959400	−	0.282048i	$-0.0910138\pi$
$881$	50175.7			1.91880			0.959400	+	0.282048i	$0.0910138\pi$
$882$	−32736.4	−	27944.9i	−1.24976	−	1.06684i
$883$	−36118.4			−1.37653			−0.688267	−	0.725457i	$-0.741628\pi$
$883$	−36118.4			−1.37653			−0.688267	+	0.725457i	$0.741628\pi$
$884$	−37867.4	+	6017.66i	−1.44075	+	0.228954i
$885$	−55307.0	+	13425.6i	−2.10070	+	0.509939i
$886$	31580.6	+	26958.3i	1.19748	+	1.02221i
$887$		−	5070.40i		−	0.191936i	−0.995384	−	0.0959680i	$-0.969405\pi$
$887$		−	5070.40i		−	0.191936i	0.995384	−	0.0959680i	$-0.0305946\pi$
$888$	−20527.6	+	33556.3i	−0.775744	+	1.26810i
$889$	−9084.49			−0.342727
$890$	−8655.00	+	17103.7i	−0.325973	+	0.644178i
$891$		−	7754.96i		−	0.291583i
$892$	12688.1	−	2016.32i	0.476267	−	0.0756855i
$893$	3818.06			0.143076
$894$	−17031.7	+	19952.0i	−0.637166	+	0.746416i
$895$	33403.4	−	8108.56i	1.24754	−	0.302837i
$896$	6679.35	+	1590.81i	0.249042	+	0.0593137i
$897$		−	14497.6i		−	0.539644i
$898$	−6297.60	−	5375.84i	−0.234024	−	0.199771i
$899$		−	11370.6i		−	0.421836i
$900$	−28119.7	−	38254.5i	−1.04147	−	1.41683i
$901$		−	20670.2i		−	0.764288i
$902$	5816.45	−	6813.74i	0.214708	−	0.251522i
$903$			8604.67i			0.317105i
$904$	−5041.21	−	3083.89i	−0.185474	−	0.113461i
$905$	−35604.5	+	8642.88i	−1.30777	+	0.317458i
$906$	−20981.4	−	17910.5i	−0.769383	−	0.656772i
$907$	14784.3			0.541241			0.270620	−	0.962686i	$-0.412771\pi$
$907$	14784.3			0.541241			0.270620	+	0.962686i	$0.412771\pi$
$908$	2023.13	+	12731.0i	0.0739428	+	0.465301i
$909$			3069.80i			0.112012i
$910$	7922.05	+	4008.79i	0.288586	+	0.146033i
$911$	30678.1			1.11571			0.557854	−	0.829939i	$-0.311625\pi$
$911$	30678.1			1.11571			0.557854	+	0.829939i	$0.311625\pi$
$912$	−19629.9	−	60203.0i	−0.712731	−	2.18588i
$913$		−	2495.05i		−	0.0904427i
$914$	5506.63	−	6450.81i	0.199281	−	0.233450i
$915$	53770.0	−	13052.5i	1.94271	−	0.471587i
$916$	17553.9	−	2789.55i	0.633184	−	0.100622i
$917$	599.567			0.0215915
$918$	−26266.3	+	30769.9i	−0.944353	+	1.10627i
$919$	−13617.4			−0.488790			−0.244395	−	0.969676i	$-0.578589\pi$
$919$	−13617.4			−0.488790			−0.244395	+	0.969676i	$0.578589\pi$
$920$	−2195.24	+	6832.79i	−0.0786683	+	0.244859i
$921$	−27244.0			−0.974724
$922$	24237.0	−	28392.7i	0.865730	−	1.01417i
$923$	−27870.6			−0.993903
$924$	−1637.99	−	10307.4i	−0.0583179	−	0.366978i
$925$	22378.1	−	11544.7i	0.795445	−	0.410364i
$926$	−7941.69	+	9303.39i	−0.281836	+	0.330160i
$927$			61439.8i			2.17686i
$928$	10105.9	−	24487.1i	0.357479	−	0.866193i
$929$	15277.5			0.539548			0.269774	−	0.962924i	$-0.413051\pi$
$929$	15277.5			0.539548			0.269774	+	0.962924i	$0.413051\pi$
$930$	9574.17	−	18920.2i	0.337580	−	0.667115i
$931$			36746.8i			1.29358i
$932$	3351.50	−	532.600i	0.117792	−	0.0187188i
$933$	43397.4			1.52279
$934$	16734.1	+	14284.8i	0.586250	+	0.500443i
$935$	−6805.87	−	28036.9i	−0.238049	−	0.980648i
$936$	−33197.4	+	54267.5i	−1.15928	+	1.89507i
$937$			16196.6i			0.564697i	0.959312	+	0.282348i	$0.0911134\pi$
$937$			16196.6i			0.564697i	−0.959312	+	0.282348i	$0.908887\pi$
$938$	208.750	−	244.543i	0.00726645	−	0.00851237i
$939$			77334.4i			2.68766i
$940$	1148.24	+	2748.47i	0.0398421	+	0.0953671i
$941$		−	17503.4i		−	0.606371i	−0.952932	−	0.303186i	$-0.901950\pi$
$941$		−	17503.4i		−	0.606371i	0.952932	−	0.303186i	$-0.0980502\pi$
$942$	−20905.2	−	17845.4i	−0.723065	−	0.617233i
$943$		−	2818.24i		−	0.0973218i
$944$	−11702.7	−	35890.9i	−0.403485	−	1.23745i
$945$	9103.64	−	2209.88i	0.313377	−	0.0760713i
$946$	12312.3	−	14423.4i	0.423159	−	0.495715i
$947$	12098.6			0.415154			0.207577	−	0.978219i	$-0.433442\pi$
$947$	12098.6			0.415154			0.207577	+	0.978219i	$0.433442\pi$
$948$	11764.8	+	74032.6i	0.403062	+	2.53636i
$949$		−	40055.2i		−	1.37012i
$950$	−9253.44	+	39463.7i	−0.316022	+	1.34776i
$951$	72851.4			2.48409
$952$	−4531.25	+	7407.20i	−0.154263	+	0.252173i
$953$			9549.00i			0.324578i	0.986743	+	0.162289i	$0.0518876\pi$
$953$			9549.00i			0.324578i	−0.986743	+	0.162289i	$0.948112\pi$
$954$	−26083.9	−	22266.1i	−0.885217	−	0.755652i
$955$	516.613	+	2128.20i	0.0175049	+	0.0721118i
$956$	−5991.92	−	37705.4i	−0.202712	−	1.27561i
$957$	−40266.0			−1.36010
$958$	−11001.8	−	9391.55i	−0.371037	−	0.316730i
$959$	−2331.68			−0.0785130
$960$	37434.1	−	32236.2i	1.25852	−	1.08377i
$961$	−23753.8			−0.797348
$962$	−25661.7	−	21905.7i	−0.860047	−	0.734165i
$963$	77131.7			2.58103
$964$	−7126.39	−	44844.3i	−0.238097	−	1.49828i
$965$	−31224.3	+	7579.60i	−1.04160	+	0.252846i
$966$	−2497.11	−	2131.62i	−0.0831712	−	0.0709977i
$967$			27009.8i			0.898216i	0.893477	+	0.449108i	$0.148258\pi$
$967$			27009.8i			0.898216i	−0.893477	+	0.449108i	$0.851742\pi$
$968$	3713.16	−	6069.88i	0.123291	−	0.201543i
$969$	80080.1			2.65484
$970$	−4277.06	−	2164.32i	−0.141575	−	0.0716414i
$971$			35347.4i			1.16823i	0.811671	+	0.584115i	$0.198558\pi$
$971$			35347.4i			1.16823i	−0.811671	+	0.584115i	$0.801442\pi$
$972$	−3355.39	−	21114.5i	−0.110724	−	0.696757i
$973$	1867.73			0.0615382
$974$	−19203.4	+	22496.0i	−0.631741	+	0.740061i
$975$	56770.8	−	29287.7i	1.86474	−	0.962006i
$976$	11377.4	+	34893.5i	0.373139	+	1.14438i
$977$		−	32592.0i		−	1.06726i	−0.845719	−	0.533629i	$-0.820828\pi$
$977$		−	32592.0i		−	1.06726i	0.845719	−	0.533629i	$-0.179172\pi$
$978$	−5740.25	−	4900.07i	−0.187682	−	0.160212i
$979$			19326.7i			0.630935i
$980$	−26452.5	+	11051.2i	−0.862238	+	0.360223i
$981$			59233.1i			1.92780i
$982$	−6937.15	+	8126.60i	−0.225431	+	0.264084i
$983$			45120.5i			1.46401i	0.681300	+	0.732004i	$0.261415\pi$
$983$			45120.5i			1.46401i	−0.681300	+	0.732004i	$0.738585\pi$
$984$	−10123.3	+	16548.5i	−0.327967	+	0.536124i
$985$	−10837.9	−	44646.9i	−0.350582	−	1.44423i
$986$	25479.9	+	21750.5i	0.822967	+	0.702513i
$987$	−1362.67			−0.0439456
$988$	53639.3	−	8524.02i	1.72722	−	0.274479i
$989$		−	5965.69i		−	0.191808i
$990$	−42711.4	−	21613.2i	−1.37117	−	0.693852i
$991$	−24588.7			−0.788179			−0.394089	−	0.919072i	$-0.628940\pi$
$991$	−24588.7			−0.788179			−0.394089	+	0.919072i	$0.628940\pi$
$992$	13001.4	+	5365.71i	0.416124	+	0.171735i
$993$		−	28443.2i		−	0.908980i
$994$	−4097.89	+	4800.53i	−0.130762	+	0.153183i
$995$	−6986.97	−	28783.0i	−0.222615	−	0.917067i
$996$	847.945	+	5335.88i	0.0269761	+	0.169753i
$997$	42000.6			1.33418			0.667088	−	0.744979i	$-0.267541\pi$
$997$	42000.6			1.33418			0.667088	+	0.744979i	$0.267541\pi$
$998$	33766.0	−	39555.6i	1.07099	−	1.25462i
$999$	−35599.8			−1.12746

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.4.f.a.29.3	✓	16
3.2	odd	2		360.4.d.d.109.14		16
4.3	odd	2		160.4.f.a.49.2		16
5.2	odd	4		200.4.d.e.101.11		16
5.3	odd	4		200.4.d.e.101.6		16
5.4	even	2	inner	40.4.f.a.29.14	yes	16
8.3	odd	2		160.4.f.a.49.15		16
8.5	even	2	inner	40.4.f.a.29.13	yes	16
12.11	even	2		1440.4.d.d.1009.7		16
15.14	odd	2		360.4.d.d.109.3		16
20.3	even	4		800.4.d.e.401.2		16
20.7	even	4		800.4.d.e.401.15		16
20.19	odd	2		160.4.f.a.49.16		16
24.5	odd	2		360.4.d.d.109.4		16
24.11	even	2		1440.4.d.d.1009.10		16
40.3	even	4		800.4.d.e.401.16		16
40.13	odd	4		200.4.d.e.101.5		16
40.19	odd	2		160.4.f.a.49.1		16
40.27	even	4		800.4.d.e.401.1		16
40.29	even	2	inner	40.4.f.a.29.4	yes	16
40.37	odd	4		200.4.d.e.101.12		16
60.59	even	2		1440.4.d.d.1009.9		16
120.29	odd	2		360.4.d.d.109.13		16
120.59	even	2		1440.4.d.d.1009.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.4.f.a.29.3	✓	16	1.1	even	1	trivial
40.4.f.a.29.4	yes	16	40.29	even	2	inner
40.4.f.a.29.13	yes	16	8.5	even	2	inner
40.4.f.a.29.14	yes	16	5.4	even	2	inner
160.4.f.a.49.1		16	40.19	odd	2
160.4.f.a.49.2		16	4.3	odd	2
160.4.f.a.49.15		16	8.3	odd	2
160.4.f.a.49.16		16	20.19	odd	2
200.4.d.e.101.5		16	40.13	odd	4
200.4.d.e.101.6		16	5.3	odd	4
200.4.d.e.101.11		16	5.2	odd	4
200.4.d.e.101.12		16	40.37	odd	4
360.4.d.d.109.3		16	15.14	odd	2
360.4.d.d.109.4		16	24.5	odd	2
360.4.d.d.109.13		16	120.29	odd	2
360.4.d.d.109.14		16	3.2	odd	2
800.4.d.e.401.1		16	40.27	even	4
800.4.d.e.401.2		16	20.3	even	4
800.4.d.e.401.15		16	20.7	even	4
800.4.d.e.401.16		16	40.3	even	4
1440.4.d.d.1009.7		16	12.11	even	2
1440.4.d.d.1009.8		16	120.59	even	2
1440.4.d.d.1009.9		16	60.59	even	2
1440.4.d.d.1009.10		16	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	40.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.15123 - 1.83636i) q^{2} +8.63004 q^{3} +(1.25556 + 7.90086i) q^{4} +(2.63740 + 10.8648i) q^{5} +(-18.5652 - 15.8479i) q^{6} -4.74133i q^{7} +(11.8078 - 19.3022i) q^{8} +47.4777 q^{9} +O(q^{10})\)	\(q+(-2.15123 - 1.83636i) q^{2} +8.63004 q^{3} +(1.25556 + 7.90086i) q^{4} +(2.63740 + 10.8648i) q^{5} +(-18.5652 - 15.8479i) q^{6} -4.74133i q^{7} +(11.8078 - 19.3022i) q^{8} +47.4777 q^{9} +(14.2781 - 28.2159i) q^{10} -31.8831i q^{11} +(10.8355 + 68.1848i) q^{12} -59.2167 q^{13} +(-8.70679 + 10.1997i) q^{14} +(22.7609 + 93.7638i) q^{15} +(-60.8472 + 19.8399i) q^{16} -80.9370i q^{17} +(-102.135 - 87.1861i) q^{18} +114.647i q^{19} +(-82.5299 + 34.4791i) q^{20} -40.9179i q^{21} +(-58.5490 + 68.5879i) q^{22} +28.3687i q^{23} +(101.902 - 166.579i) q^{24} +(-111.088 + 57.3097i) q^{25} +(127.389 + 108.743i) q^{26} +176.723 q^{27} +(37.4606 - 5.95300i) q^{28} -146.340i q^{29} +(123.220 - 243.504i) q^{30} +77.6995 q^{31} +(167.329 + 69.0571i) q^{32} -275.153i q^{33} +(-148.630 + 174.114i) q^{34} +(51.5136 - 12.5048i) q^{35} +(59.6108 + 375.114i) q^{36} -201.444 q^{37} +(210.534 - 246.633i) q^{38} -511.042 q^{39} +(240.857 + 77.3824i) q^{40} -99.3433 q^{41} +(-75.1400 + 88.0236i) q^{42} -210.291 q^{43} +(251.904 - 40.0311i) q^{44} +(125.217 + 515.836i) q^{45} +(52.0952 - 61.0275i) q^{46} -33.3026i q^{47} +(-525.114 + 171.220i) q^{48} +320.520 q^{49} +(344.217 + 80.7121i) q^{50} -698.490i q^{51} +(-74.3498 - 467.863i) q^{52} +255.386 q^{53} +(-380.171 - 324.527i) q^{54} +(346.404 - 84.0885i) q^{55} +(-91.5180 - 55.9848i) q^{56} +989.413i q^{57} +(-268.734 + 314.812i) q^{58} +589.854i q^{59} +(-712.237 + 297.556i) q^{60} -573.462i q^{61} +(-167.149 - 142.684i) q^{62} -225.107i q^{63} +(-233.150 - 455.835i) q^{64} +(-156.178 - 643.378i) q^{65} +(-505.280 + 591.916i) q^{66} -23.9755 q^{67} +(639.472 - 101.621i) q^{68} +244.823i q^{69} +(-133.781 - 67.6970i) q^{70} +470.655 q^{71} +(560.609 - 916.423i) q^{72} +676.417i q^{73} +(433.352 + 369.924i) q^{74} +(-958.697 + 494.585i) q^{75} +(-905.814 + 143.946i) q^{76} -151.168 q^{77} +(1099.37 + 938.458i) q^{78} +1085.76 q^{79} +(-376.035 - 608.767i) q^{80} +243.231 q^{81} +(213.710 + 182.430i) q^{82} +78.2562 q^{83} +(323.286 - 51.3747i) q^{84} +(879.366 - 213.463i) q^{85} +(452.384 + 386.171i) q^{86} -1262.92i q^{87} +(-615.415 - 376.471i) q^{88} -606.174 q^{89} +(677.889 - 1339.62i) q^{90} +280.766i q^{91} +(-224.137 + 35.6185i) q^{92} +670.550 q^{93} +(-61.1557 + 71.6416i) q^{94} +(-1245.62 + 302.371i) q^{95} +(1444.06 + 595.966i) q^{96} -151.583i q^{97} +(-689.511 - 588.590i) q^{98} -1513.74i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 12 q^{6} + 104 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 - 12 * q^6 + 104 * q^9	\( 16 q + 4 q^{4} - 12 q^{6} + 104 q^{9} - 48 q^{10} + 28 q^{14} - 56 q^{15} - 168 q^{16} - 196 q^{20} - 112 q^{24} - 24 q^{25} + 200 q^{26} + 492 q^{30} - 112 q^{31} + 408 q^{34} - 84 q^{36} - 736 q^{39} + 672 q^{40} + 232 q^{41} + 920 q^{44} + 212 q^{46} - 200 q^{49} - 648 q^{50} - 2320 q^{54} + 392 q^{55} + 1120 q^{56} - 1208 q^{60} - 2912 q^{64} - 600 q^{65} - 2488 q^{66} + 1532 q^{70} + 2096 q^{71} + 4224 q^{74} - 3000 q^{76} + 2992 q^{79} + 2280 q^{80} - 728 q^{81} + 7304 q^{84} + 3076 q^{86} - 208 q^{89} - 4280 q^{90} - 7036 q^{94} - 1064 q^{95} + 3632 q^{96}+O(q^{100}) \) 16 * q + 4 * q^4 - 12 * q^6 + 104 * q^9 - 48 * q^10 + 28 * q^14 - 56 * q^15 - 168 * q^16 - 196 * q^20 - 112 * q^24 - 24 * q^25 + 200 * q^26 + 492 * q^30 - 112 * q^31 + 408 * q^34 - 84 * q^36 - 736 * q^39 + 672 * q^40 + 232 * q^41 + 920 * q^44 + 212 * q^46 - 200 * q^49 - 648 * q^50 - 2320 * q^54 + 392 * q^55 + 1120 * q^56 - 1208 * q^60 - 2912 * q^64 - 600 * q^65 - 2488 * q^66 + 1532 * q^70 + 2096 * q^71 + 4224 * q^74 - 3000 * q^76 + 2992 * q^79 + 2280 * q^80 - 728 * q^81 + 7304 * q^84 + 3076 * q^86 - 208 * q^89 - 4280 * q^90 - 7036 * q^94 - 1064 * q^95 + 3632 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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