LMFDB - Embedded newform 574.2.c.c.491.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [574,2,Mod(491,574)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(574, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("574.491");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 574 = 2 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	574.c (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:	$4.58341307602$
Analytic rank:	$0$
Dimension:	$10$
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} + 22x^{8} + 153x^{6} + 340x^{4} + 144x^{2} + 16 $ x^10 + 22x^8 + 153x^6 + 340x^4 + 144x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			491.1
Root			$-3.06582i$ of defining polynomial
Character	$\chi$	$=$	574.491
Dual form			574.2.c.c.491.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.06582i q^{3} +1.00000 q^{4} -2.41347 q^{5} +3.06582i q^{6} +1.00000i q^{7} -1.00000 q^{8} -6.39928 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.06582i q^{3} +1.00000 q^{4} -2.41347 q^{5} +3.06582i q^{6} +1.00000i q^{7} -1.00000 q^{8} -6.39928 q^{9} +2.41347 q^{10} +0.652353i q^{11} -3.06582i q^{12} +4.52883i q^{13} -1.00000i q^{14} +7.39928i q^{15} +1.00000 q^{16} -1.06582i q^{17} +6.39928 q^{18} +5.22413i q^{19} -2.41347 q^{20} +3.06582 q^{21} -0.652353i q^{22} -4.52883 q^{23} +3.06582i q^{24} +0.824846 q^{25} -4.52883i q^{26} +10.4216i q^{27} +1.00000i q^{28} -6.05163i q^{29} -7.39928i q^{30} +0.158303 q^{31} -1.00000 q^{32} +2.00000 q^{33} +1.06582i q^{34} -2.41347i q^{35} -6.39928 q^{36} +4.13165 q^{37} -5.22413i q^{38} +13.8846 q^{39} +2.41347 q^{40} +(5.87648 + 2.54302i) q^{41} -3.06582 q^{42} -7.53093 q^{43} +0.652353i q^{44} +15.4445 q^{45} +4.52883 q^{46} +8.26973i q^{47} -3.06582i q^{48} -1.00000 q^{49} -0.824846 q^{50} -3.26763 q^{51} +4.52883i q^{52} +0.0516348i q^{53} -10.4216i q^{54} -1.57444i q^{55} -1.00000i q^{56} +16.0163 q^{57} +6.05163i q^{58} +2.12352 q^{59} +7.39928i q^{60} -1.32742 q^{61} -0.158303 q^{62} -6.39928i q^{63} +1.00000 q^{64} -10.9302i q^{65} -2.00000 q^{66} +14.2779i q^{67} -1.06582i q^{68} +13.8846i q^{69} +2.41347i q^{70} -9.39928i q^{71} +6.39928 q^{72} -14.9302 q^{73} -4.13165 q^{74} -2.52883i q^{75} +5.22413i q^{76} -0.652353 q^{77} -13.8846 q^{78} +2.35368i q^{79} -2.41347 q^{80} +12.7530 q^{81} +(-5.87648 - 2.54302i) q^{82} -15.0942 q^{83} +3.06582 q^{84} +2.57234i q^{85} +7.53093 q^{86} -18.5533 q^{87} -0.652353i q^{88} +4.42160i q^{89} -15.4445 q^{90} -4.52883 q^{91} -4.52883 q^{92} -0.485330i q^{93} -8.26973i q^{94} -12.6083i q^{95} +3.06582i q^{96} +11.5947i q^{97} +1.00000 q^{98} -4.17459i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 10 q^{4} - 4 q^{5} - 10 q^{8} - 14 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 10 * q^4 - 4 * q^5 - 10 * q^8 - 14 * q^9	$ 10 q - 10 q^{2} + 10 q^{4} - 4 q^{5} - 10 q^{8} - 14 q^{9} + 4 q^{10} + 10 q^{16} + 14 q^{18} - 4 q^{20} + 4 q^{21} + 26 q^{25} - 4 q^{31} - 10 q^{32} + 20 q^{33} - 14 q^{36} - 12 q^{37} + 8 q^{39} + 4 q^{40} + 20 q^{41} - 4 q^{42} + 28 q^{43} - 4 q^{45} - 10 q^{49} - 26 q^{50} - 36 q^{51} - 24 q^{57} + 60 q^{59} - 24 q^{61} + 4 q^{62} + 10 q^{64} - 20 q^{66} + 14 q^{72} + 4 q^{73} + 12 q^{74} - 8 q^{78} - 4 q^{80} + 50 q^{81} - 20 q^{82} - 28 q^{83} + 4 q^{84} - 28 q^{86} - 20 q^{87} + 4 q^{90} + 10 q^{98}+O(q^{100}) $ 10 * q - 10 * q^2 + 10 * q^4 - 4 * q^5 - 10 * q^8 - 14 * q^9 + 4 * q^10 + 10 * q^16 + 14 * q^18 - 4 * q^20 + 4 * q^21 + 26 * q^25 - 4 * q^31 - 10 * q^32 + 20 * q^33 - 14 * q^36 - 12 * q^37 + 8 * q^39 + 4 * q^40 + 20 * q^41 - 4 * q^42 + 28 * q^43 - 4 * q^45 - 10 * q^49 - 26 * q^50 - 36 * q^51 - 24 * q^57 + 60 * q^59 - 24 * q^61 + 4 * q^62 + 10 * q^64 - 20 * q^66 + 14 * q^72 + 4 * q^73 + 12 * q^74 - 8 * q^78 - 4 * q^80 + 50 * q^81 - 20 * q^82 - 28 * q^83 + 4 * q^84 - 28 * q^86 - 20 * q^87 + 4 * q^90 + 10 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/574\mathbb{Z}\right)^\times$.

$n$	$211$	$493$
$\chi(n)$	$-1$	$1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		−	3.06582i		−	1.77005i	−0.465539	−	0.885027i	$-0.654139\pi$
$3$		−	3.06582i		−	1.77005i	0.465539	−	0.885027i	$-0.345861\pi$
$4$	1.00000			0.500000
$5$	−2.41347			−1.07934			−0.539669	−	0.841877i	$-0.681450\pi$
$5$	−2.41347			−1.07934			−0.539669	+	0.841877i	$0.681450\pi$
$6$			3.06582i			1.25162i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−1.00000			−0.353553
$9$	−6.39928			−2.13309
$10$	2.41347			0.763207
$11$			0.652353i			0.196692i	0.995152	+	0.0983459i	$0.0313552\pi$
$11$			0.652353i			0.196692i	−0.995152	+	0.0983459i	$0.968645\pi$
$12$		−	3.06582i		−	0.885027i
$13$			4.52883i			1.25607i	0.778184	+	0.628036i	$0.216141\pi$
$13$			4.52883i			1.25607i	−0.778184	+	0.628036i	$0.783859\pi$
$14$		−	1.00000i		−	0.267261i
$15$			7.39928i			1.91049i
$16$	1.00000			0.250000
$17$		−	1.06582i		−	0.258500i	−0.991612	−	0.129250i	$-0.958743\pi$
$17$		−	1.06582i		−	0.258500i	0.991612	−	0.129250i	$-0.0412570\pi$
$18$	6.39928			1.50833
$19$			5.22413i			1.19850i	0.800563	+	0.599249i	$0.204534\pi$
$19$			5.22413i			1.19850i	−0.800563	+	0.599249i	$0.795466\pi$
$20$	−2.41347			−0.539669
$21$	3.06582			0.669018
$22$		−	0.652353i		−	0.139082i
$23$	−4.52883			−0.944327			−0.472164	−	0.881511i	$-0.656527\pi$
$23$	−4.52883			−0.944327			−0.472164	+	0.881511i	$0.656527\pi$
$24$			3.06582i			0.625809i
$25$	0.824846			0.164969
$26$		−	4.52883i		−	0.888177i
$27$			10.4216i			2.00564i
$28$			1.00000i			0.188982i
$29$		−	6.05163i		−	1.12376i	−0.827219	−	0.561880i	$-0.810078\pi$
$29$		−	6.05163i		−	1.12376i	0.827219	−	0.561880i	$-0.189922\pi$
$30$		−	7.39928i		−	1.35092i
$31$	0.158303			0.0284321			0.0142160	−	0.999899i	$-0.495475\pi$
$31$	0.158303			0.0284321			0.0142160	+	0.999899i	$0.495475\pi$
$32$	−1.00000			−0.176777
$33$	2.00000			0.348155
$34$			1.06582i			0.182787i
$35$		−	2.41347i		−	0.407951i
$36$	−6.39928			−1.06655
$37$	4.13165			0.679239			0.339620	−	0.940563i	$-0.389702\pi$
$37$	4.13165			0.679239			0.339620	+	0.940563i	$0.389702\pi$
$38$		−	5.22413i		−	0.847465i
$39$	13.8846			2.22332
$40$	2.41347			0.381603
$41$	5.87648	+	2.54302i	0.917752	+	0.397154i
$41$	5.87648	+	2.54302i	0.917752	+	0.397154i
$42$	−3.06582			−0.473067
$43$	−7.53093			−1.14846			−0.574228	−	0.818695i	$-0.694698\pi$
$43$	−7.53093			−1.14846			−0.574228	+	0.818695i	$0.694698\pi$
$44$			0.652353i			0.0983459i
$45$	15.4445			2.30233
$46$	4.52883			0.667740
$47$			8.26973i			1.20626i	0.797641	+	0.603132i	$0.206081\pi$
$47$			8.26973i			1.20626i	−0.797641	+	0.603132i	$0.793919\pi$
$48$		−	3.06582i		−	0.442514i
$49$	−1.00000			−0.142857
$50$	−0.824846			−0.116651
$51$	−3.26763			−0.457560
$52$			4.52883i			0.628036i
$53$			0.0516348i			0.00709258i	0.999994	+	0.00354629i	$0.00112882\pi$
$53$			0.0516348i			0.00709258i	−0.999994	+	0.00354629i	$0.998871\pi$
$54$		−	10.4216i		−	1.41820i
$55$		−	1.57444i		−	0.212297i
$56$		−	1.00000i		−	0.133631i
$57$	16.0163			2.12141
$58$			6.05163i			0.794619i
$59$	2.12352			0.276459			0.138229	−	0.990400i	$-0.455859\pi$
$59$	2.12352			0.276459			0.138229	+	0.990400i	$0.455859\pi$
$60$			7.39928i			0.955243i
$61$	−1.32742			−0.169959			−0.0849796	−	0.996383i	$-0.527083\pi$
$61$	−1.32742			−0.169959			−0.0849796	+	0.996383i	$0.527083\pi$
$62$	−0.158303			−0.0201045
$63$		−	6.39928i		−	0.806234i
$64$	1.00000			0.125000
$65$		−	10.9302i		−	1.35573i
$66$	−2.00000			−0.246183
$67$			14.2779i			1.74432i	0.489222	+	0.872159i	$0.337281\pi$
$67$			14.2779i			1.74432i	−0.489222	+	0.872159i	$0.662719\pi$
$68$		−	1.06582i		−	0.129250i
$69$			13.8846i			1.67151i
$70$			2.41347i			0.288465i
$71$		−	9.39928i		−	1.11549i	−0.830013	−	0.557745i	$-0.811667\pi$
$71$		−	9.39928i		−	1.11549i	0.830013	−	0.557745i	$-0.188333\pi$
$72$	6.39928			0.754163
$73$	−14.9302			−1.74745			−0.873725	−	0.486421i	$-0.838302\pi$
$73$	−14.9302			−1.74745			−0.873725	+	0.486421i	$0.838302\pi$
$74$	−4.13165			−0.480295
$75$		−	2.52883i		−	0.292005i
$76$			5.22413i			0.599249i
$77$	−0.652353			−0.0743425
$78$	−13.8846			−1.57212
$79$			2.35368i			0.264810i	0.991196	+	0.132405i	$0.0422699\pi$
$79$			2.35368i			0.264810i	−0.991196	+	0.132405i	$0.957730\pi$
$80$	−2.41347			−0.269834
$81$	12.7530			1.41700
$82$	−5.87648	−	2.54302i	−0.648949	−	0.280830i
$83$	−15.0942			−1.65680			−0.828401	−	0.560136i	$-0.810749\pi$
$83$	−15.0942			−1.65680			−0.828401	+	0.560136i	$0.810749\pi$
$84$	3.06582			0.334509
$85$			2.57234i			0.279009i
$86$	7.53093			0.812081
$87$	−18.5533			−1.98912
$88$		−	0.652353i		−	0.0695411i
$89$			4.42160i			0.468689i	0.972154	+	0.234344i	$0.0752944\pi$
$89$			4.42160i			0.468689i	−0.972154	+	0.234344i	$0.924706\pi$
$90$	−15.4445			−1.62799
$91$	−4.52883			−0.474751
$92$	−4.52883			−0.472164
$93$		−	0.485330i		−	0.0503264i
$94$		−	8.26973i		−	0.852957i
$95$		−	12.6083i		−	1.29358i
$96$			3.06582i			0.312904i
$97$			11.5947i			1.17726i	0.808403	+	0.588630i	$0.200332\pi$
$97$			11.5947i			1.17726i	−0.808403	+	0.588630i	$0.799668\pi$
$98$	1.00000			0.101015
$99$		−	4.17459i		−	0.419562i
$100$	0.824846			0.0824846
$101$			17.2283i			1.71428i	0.515082	+	0.857141i	$0.327762\pi$
$101$			17.2283i			1.71428i	−0.515082	+	0.857141i	$0.672238\pi$
$102$	3.26763			0.323544
$103$	15.3356			1.51106			0.755529	−	0.655116i	$-0.227380\pi$
$103$	15.3356			1.51106			0.755529	+	0.655116i	$0.227380\pi$
$104$		−	4.52883i		−	0.444089i
$105$	−7.39928			−0.722096
$106$		−	0.0516348i		−	0.00501521i
$107$	−9.79004			−0.946438			−0.473219	−	0.880945i	$-0.656908\pi$
$107$	−9.79004			−0.946438			−0.473219	+	0.880945i	$0.656908\pi$
$108$			10.4216i			1.00282i
$109$		−	9.84167i		−	0.942661i	−0.881957	−	0.471331i	$-0.843774\pi$
$109$		−	9.84167i		−	0.942661i	0.881957	−	0.471331i	$-0.156226\pi$
$110$			1.57444i			0.150117i
$111$		−	12.6669i		−	1.20229i
$112$			1.00000i			0.0944911i
$113$	−14.6976			−1.38263			−0.691315	−	0.722554i	$-0.742968\pi$
$113$	−14.6976			−1.38263			−0.691315	+	0.722554i	$0.742968\pi$
$114$	−16.0163			−1.50006
$115$	10.9302			1.01925
$116$		−	6.05163i		−	0.561880i
$117$		−	28.9813i		−	2.67932i
$118$	−2.12352			−0.195486
$119$	1.06582			0.0977040
$120$		−	7.39928i		−	0.675459i
$121$	10.5744			0.961312
$122$	1.32742			0.120179
$123$	7.79647	−	18.0163i	0.702984	−	1.62447i
$124$	0.158303			0.0142160
$125$	10.0766			0.901280
$126$			6.39928i			0.570093i
$127$	4.21223			0.373775			0.186887	−	0.982381i	$-0.440160\pi$
$127$	4.21223			0.373775			0.186887	+	0.982381i	$0.440160\pi$
$128$	−1.00000			−0.0883883
$129$			23.0885i			2.03283i
$130$			10.9302i			0.958643i
$131$	−14.5185			−1.26848			−0.634242	−	0.773134i	$-0.718688\pi$
$131$	−14.5185			−1.26848			−0.634242	+	0.773134i	$0.718688\pi$
$132$	2.00000			0.174078
$133$	−5.22413			−0.452989
$134$		−	14.2779i		−	1.23342i
$135$		−	25.1522i		−	2.16476i
$136$			1.06582i			0.0913937i
$137$		−	2.09907i		−	0.179336i	−0.995972	−	0.0896680i	$-0.971419\pi$
$137$		−	2.09907i		−	0.179336i	0.995972	−	0.0896680i	$-0.0285806\pi$
$138$		−	13.8846i		−	1.18194i
$139$	−22.4280			−1.90232			−0.951159	−	0.308700i	$-0.900106\pi$
$139$	−22.4280			−1.90232			−0.951159	+	0.308700i	$0.900106\pi$
$140$		−	2.41347i		−	0.203976i
$141$	25.3535			2.13515
$142$			9.39928i			0.788770i
$143$	−2.95440			−0.247059
$144$	−6.39928			−0.533273
$145$			14.6054i			1.21292i
$146$	14.9302			1.23563
$147$			3.06582i			0.252865i
$148$	4.13165			0.339620
$149$			3.44222i			0.281998i	0.990010	+	0.140999i	$0.0450314\pi$
$149$			3.44222i			0.281998i	−0.990010	+	0.140999i	$0.954969\pi$
$150$			2.52883i			0.206478i
$151$		−	13.5714i		−	1.10442i	−0.833704	−	0.552212i	$-0.813784\pi$
$151$		−	13.5714i		−	1.10442i	0.833704	−	0.552212i	$-0.186216\pi$
$152$		−	5.22413i		−	0.423733i
$153$			6.82051i			0.551406i
$154$	0.652353			0.0525681
$155$	−0.382060			−0.0306878
$156$	13.8846			1.11166
$157$		−	5.44279i		−	0.434382i	−0.976129	−	0.217191i	$-0.930311\pi$
$157$		−	5.44279i		−	0.434382i	0.976129	−	0.217191i	$-0.0696894\pi$
$158$		−	2.35368i		−	0.187249i
$159$	0.158303			0.0125543
$160$	2.41347			0.190802
$161$		−	4.52883i		−	0.356922i
$162$	−12.7530			−1.00197
$163$	−13.6539			−1.06945			−0.534727	−	0.845025i	$-0.679586\pi$
$163$	−13.6539			−1.06945			−0.534727	+	0.845025i	$0.679586\pi$
$164$	5.87648	+	2.54302i	0.458876	+	0.198577i
$165$	−4.82694			−0.375777
$166$	15.0942			1.17154
$167$		−	3.27520i		−	0.253443i	−0.991938	−	0.126721i	$-0.959555\pi$
$167$		−	3.27520i		−	0.253443i	0.991938	−	0.126721i	$-0.0404454\pi$
$168$	−3.06582			−0.236534
$169$	−7.51034			−0.577718
$170$		−	2.57234i		−	0.197289i
$171$		−	33.4307i		−	2.55651i
$172$	−7.53093			−0.574228
$173$	11.7757			0.895288			0.447644	−	0.894212i	$-0.352263\pi$
$173$	11.7757			0.895288			0.447644	+	0.894212i	$0.352263\pi$
$174$	18.5533			1.40652
$175$			0.824846i			0.0623525i
$176$			0.652353i			0.0491730i
$177$		−	6.51034i		−	0.489347i
$178$		−	4.42160i		−	0.331413i
$179$		−	4.05920i		−	0.303399i	−0.988427	−	0.151700i	$-0.951525\pi$
$179$		−	4.05920i		−	0.303399i	0.988427	−	0.151700i	$-0.0484746\pi$
$180$	15.4445			1.15116
$181$		−	10.4298i		−	0.775238i	−0.921820	−	0.387619i	$-0.873298\pi$
$181$		−	10.4298i		−	0.775238i	0.921820	−	0.387619i	$-0.126702\pi$
$182$	4.52883			0.335700
$183$			4.06965i			0.300837i
$184$	4.52883			0.333870
$185$	−9.97162			−0.733128
$186$			0.485330i			0.0355861i
$187$	0.695294			0.0508449
$188$			8.26973i			0.603132i
$189$	−10.4216			−0.758060
$190$			12.6083i			0.914701i
$191$			4.60491i			0.333200i	0.986025	+	0.166600i	$0.0532788\pi$
$191$			4.60491i			0.333200i	−0.986025	+	0.166600i	$0.946721\pi$
$192$		−	3.06582i		−	0.221257i
$193$		−	20.3949i		−	1.46806i	−0.679117	−	0.734030i	$-0.737637\pi$
$193$		−	20.3949i		−	1.46806i	0.679117	−	0.734030i	$-0.262363\pi$
$194$		−	11.5947i		−	0.832448i
$195$	−33.5101			−2.39971
$196$	−1.00000			−0.0714286
$197$	−22.1195			−1.57595			−0.787976	−	0.615706i	$-0.788871\pi$
$197$	−22.1195			−1.57595			−0.787976	+	0.615706i	$0.788871\pi$
$198$			4.17459i			0.296675i
$199$		−	0.993404i		−	0.0704205i	−0.999380	−	0.0352103i	$-0.988790\pi$
$199$		−	0.993404i		−	0.0704205i	0.999380	−	0.0352103i	$-0.0112101\pi$
$200$	−0.824846			−0.0583254
$201$	43.7734			3.08754
$202$		−	17.2283i		−	1.21218i
$203$	6.05163			0.424741
$204$	−3.26763			−0.228780
$205$	−14.1827	−	6.13752i	−0.990564	−	0.428663i
$206$	−15.3356			−1.06848
$207$	28.9813			2.01434
$208$			4.52883i			0.314018i
$209$	−3.40798			−0.235735
$210$	7.39928			0.510599
$211$			17.2323i			1.18632i	0.805085	+	0.593159i	$0.202119\pi$
$211$			17.2323i			1.18632i	−0.805085	+	0.593159i	$0.797881\pi$
$212$			0.0516348i			0.00354629i
$213$	−28.8166			−1.97448
$214$	9.79004			0.669233
$215$	18.1757			1.23957
$216$		−	10.4216i		−	0.709100i
$217$			0.158303i			0.0107463i
$218$			9.84167i			0.666562i
$219$			45.7734i			3.09308i
$220$		−	1.57444i		−	0.106148i
$221$	4.82694			0.324695
$222$			12.6669i			0.850148i
$223$	9.97754			0.668146			0.334073	−	0.942547i	$-0.391577\pi$
$223$	9.97754			0.668146			0.334073	+	0.942547i	$0.391577\pi$
$224$		−	1.00000i		−	0.0668153i
$225$	−5.27842			−0.351895
$226$	14.6976			0.977667
$227$		−	20.1561i		−	1.33781i	−0.743350	−	0.668903i	$-0.766764\pi$
$227$		−	20.1561i		−	1.33781i	0.743350	−	0.668903i	$-0.233236\pi$
$228$	16.0163			1.06070
$229$			23.9652i			1.58366i	0.610739	+	0.791832i	$0.290873\pi$
$229$			23.9652i			1.58366i	−0.610739	+	0.791832i	$0.709127\pi$
$230$	−10.9302			−0.720717
$231$			2.00000i			0.131590i
$232$			6.05163i			0.397309i
$233$		−	10.4820i		−	0.686696i	−0.939208	−	0.343348i	$-0.888439\pi$
$233$		−	10.4820i		−	0.686696i	0.939208	−	0.343348i	$-0.111561\pi$
$234$			28.9813i			1.89457i
$235$		−	19.9588i		−	1.30197i
$236$	2.12352			0.138229
$237$	7.21597			0.468728
$238$	−1.06582			−0.0690872
$239$			26.2054i			1.69509i	0.530726	+	0.847544i	$0.321919\pi$
$239$			26.2054i			1.69509i	−0.530726	+	0.847544i	$0.678081\pi$
$240$			7.39928i			0.477622i
$241$	20.6995			1.33337			0.666686	−	0.745339i	$-0.267712\pi$
$241$	20.6995			1.33337			0.666686	+	0.745339i	$0.267712\pi$
$242$	−10.5744			−0.679750
$243$		−	7.83354i		−	0.502522i
$244$	−1.32742			−0.0849796
$245$	2.41347			0.154191
$246$	−7.79647	+	18.0163i	−0.497085	+	1.14867i
$247$	−23.6592			−1.50540
$248$	−0.158303			−0.0100523
$249$			46.2761i			2.93263i
$250$	−10.0766			−0.637301
$251$	−21.1528			−1.33515			−0.667577	−	0.744541i	$-0.732668\pi$
$251$	−21.1528			−1.33515			−0.667577	+	0.744541i	$0.732668\pi$
$252$		−	6.39928i		−	0.403117i
$253$		−	2.95440i		−	0.185741i
$254$	−4.21223			−0.264299
$255$	7.88634			0.493862
$256$	1.00000			0.0625000
$257$			31.3476i			1.95541i	0.209981	+	0.977705i	$0.432660\pi$
$257$			31.3476i			1.95541i	−0.209981	+	0.977705i	$0.567340\pi$
$258$		−	23.0885i		−	1.43743i
$259$			4.13165i			0.256728i
$260$		−	10.9302i		−	0.677863i
$261$			38.7261i			2.39709i
$262$	14.5185			0.896954
$263$		−	4.79437i		−	0.295633i	−0.989015	−	0.147817i	$-0.952775\pi$
$263$		−	4.79437i		−	0.295633i	0.989015	−	0.147817i	$-0.0472246\pi$
$264$	−2.00000			−0.123091
$265$		−	0.124619i		−	0.00765529i
$266$	5.22413			0.320312
$267$	13.5559			0.829605
$268$			14.2779i			0.872159i
$269$	9.02116			0.550030			0.275015	−	0.961440i	$-0.411317\pi$
$269$	9.02116			0.550030			0.275015	+	0.961440i	$0.411317\pi$
$270$			25.1522i			1.53072i
$271$	23.1609			1.40693			0.703463	−	0.710732i	$-0.251636\pi$
$271$	23.1609			1.40693			0.703463	+	0.710732i	$0.251636\pi$
$272$		−	1.06582i		−	0.0646251i
$273$			13.8846i			0.840335i
$274$			2.09907i			0.126810i
$275$			0.538091i			0.0324481i
$276$			13.8846i			0.835755i
$277$	−18.6136			−1.11838			−0.559192	−	0.829038i	$-0.688888\pi$
$277$	−18.6136			−1.11838			−0.559192	+	0.829038i	$0.688888\pi$
$278$	22.4280			1.34514
$279$	−1.01303			−0.0606483
$280$			2.41347i			0.144233i
$281$			6.52240i			0.389094i	0.980893	+	0.194547i	$0.0623237\pi$
$281$			6.52240i			0.389094i	−0.980893	+	0.194547i	$0.937676\pi$
$282$	−25.3535			−1.50978
$283$	−8.54339			−0.507852			−0.253926	−	0.967224i	$-0.581722\pi$
$283$	−8.54339			−0.507852			−0.253926	+	0.967224i	$0.581722\pi$
$284$		−	9.39928i		−	0.557745i
$285$	−38.6548			−2.28971
$286$	2.95440			0.174697
$287$	−2.54302	+	5.87648i	−0.150110	+	0.346878i
$288$	6.39928			0.377081
$289$	15.8640			0.933177
$290$		−	14.6054i		−	0.857662i
$291$	35.5472			2.08381
$292$	−14.9302			−0.873725
$293$		−	21.5449i		−	1.25867i	−0.777135	−	0.629334i	$-0.783328\pi$
$293$		−	21.5449i		−	1.25867i	0.777135	−	0.629334i	$-0.216672\pi$
$294$		−	3.06582i		−	0.178803i
$295$	−5.12505			−0.298392
$296$	−4.13165			−0.240147
$297$	−6.79856			−0.394493
$298$		−	3.44222i		−	0.199403i
$299$		−	20.5103i		−	1.18614i
$300$		−	2.52883i		−	0.146002i
$301$		−	7.53093i		−	0.434076i
$302$			13.5714i			0.780945i
$303$	52.8190			3.03437
$304$			5.22413i			0.299624i
$305$	3.20370			0.183443
$306$		−	6.82051i		−	0.389903i
$307$	−20.6164			−1.17664			−0.588321	−	0.808628i	$-0.700211\pi$
$307$	−20.6164			−1.17664			−0.588321	+	0.808628i	$0.700211\pi$
$308$	−0.652353			−0.0371713
$309$		−	47.0161i		−	2.67465i
$310$	0.382060			0.0216996
$311$		−	9.99431i		−	0.566725i	−0.959013	−	0.283363i	$-0.908550\pi$
$311$		−	9.99431i		−	0.566725i	0.959013	−	0.283363i	$-0.0914500\pi$
$312$	−13.8846			−0.786061
$313$		−	5.44279i		−	0.307644i	−0.988099	−	0.153822i	$-0.950842\pi$
$313$		−	5.44279i		−	0.307644i	0.988099	−	0.153822i	$-0.0491583\pi$
$314$			5.44279i			0.307154i
$315$			15.4445i			0.870198i
$316$			2.35368i			0.132405i
$317$			18.1788i			1.02102i	0.859871	+	0.510511i	$0.170544\pi$
$317$			18.1788i			1.02102i	−0.859871	+	0.510511i	$0.829456\pi$
$318$	−0.158303			−0.00887720
$319$	3.94780			0.221034
$320$	−2.41347			−0.134917
$321$			30.0145i			1.67525i
$322$			4.52883i			0.252382i
$323$	5.56801			0.309812
$324$	12.7530			0.708498
$325$			3.73559i			0.207213i
$326$	13.6539			0.756219
$327$	−30.1728			−1.66856
$328$	−5.87648	−	2.54302i	−0.324474	−	0.140415i
$329$	−8.26973			−0.455925
$330$	4.82694			0.265715
$331$		−	14.5945i		−	0.802184i	−0.916038	−	0.401092i	$-0.868631\pi$
$331$		−	14.5945i		−	0.802184i	0.916038	−	0.401092i	$-0.131369\pi$
$332$	−15.0942			−0.828401
$333$	−26.4396			−1.44888
$334$			3.27520i			0.179211i
$335$		−	34.4592i		−	1.88271i
$336$	3.06582			0.167254
$337$	25.7617			1.40333			0.701663	−	0.712509i	$-0.252441\pi$
$337$	25.7617			1.40333			0.701663	+	0.712509i	$0.252441\pi$
$338$	7.51034			0.408508
$339$			45.0601i			2.44733i
$340$			2.57234i			0.139505i
$341$			0.103270i			0.00559236i
$342$			33.4307i			1.80772i
$343$		−	1.00000i		−	0.0539949i
$344$	7.53093			0.406041
$345$		−	33.5101i		−	1.80412i
$346$	−11.7757			−0.633064
$347$		−	23.3235i		−	1.25207i	−0.779795	−	0.626035i	$-0.784677\pi$
$347$		−	23.3235i		−	1.25207i	0.779795	−	0.626035i	$-0.215323\pi$
$348$	−18.5533			−0.994559
$349$	−30.9383			−1.65609			−0.828046	−	0.560660i	$-0.810547\pi$
$349$	−30.9383			−1.65609			−0.828046	+	0.560660i	$0.810547\pi$
$350$		−	0.824846i		−	0.0440899i
$351$	−47.1977			−2.51923
$352$		−	0.652353i		−	0.0347705i
$353$	−12.0000			−0.638696			−0.319348	−	0.947638i	$-0.603464\pi$
$353$	−12.0000			−0.638696			−0.319348	+	0.947638i	$0.603464\pi$
$354$			6.51034i			0.346021i
$355$			22.6849i			1.20399i
$356$			4.42160i			0.234344i
$357$		−	3.26763i		−	0.172941i
$358$			4.05920i			0.214536i
$359$	−5.42316			−0.286224			−0.143112	−	0.989707i	$-0.545711\pi$
$359$	−5.42316			−0.286224			−0.143112	+	0.989707i	$0.545711\pi$
$360$	−15.4445			−0.813996
$361$	−8.29151			−0.436395
$362$			10.4298i			0.548176i
$363$		−	32.4194i		−	1.70158i
$364$	−4.52883			−0.237375
$365$	36.0336			1.88609
$366$		−	4.06965i		−	0.212724i
$367$	12.9319			0.675042			0.337521	−	0.941318i	$-0.390412\pi$
$367$	12.9319			0.675042			0.337521	+	0.941318i	$0.390412\pi$
$368$	−4.52883			−0.236082
$369$	−37.6053	−	16.2735i	−1.95765	−	0.847166i
$370$	9.97162			0.518400
$371$	−0.0516348			−0.00268074
$372$		−	0.485330i		−	0.0251632i
$373$	19.2794			0.998249			0.499125	−	0.866530i	$-0.333655\pi$
$373$	19.2794			0.998249			0.499125	+	0.866530i	$0.333655\pi$
$374$	−0.695294			−0.0359528
$375$		−	30.8931i		−	1.59531i
$376$		−	8.26973i		−	0.426479i
$377$	27.4068			1.41152
$378$	10.4216			0.536029
$379$	27.4730			1.41120			0.705598	−	0.708613i	$-0.250679\pi$
$379$	27.4730			1.41120			0.705598	+	0.708613i	$0.250679\pi$
$380$		−	12.6083i		−	0.646791i
$381$		−	12.9140i		−	0.661602i
$382$		−	4.60491i		−	0.235608i
$383$			11.6418i			0.594869i	0.954742	+	0.297435i	$0.0961310\pi$
$383$			11.6418i			0.594869i	−0.954742	+	0.297435i	$0.903869\pi$
$384$			3.06582i			0.156452i
$385$	1.57444			0.0802407
$386$			20.3949i			1.03808i
$387$	48.1926			2.44977
$388$			11.5947i			0.588630i
$389$	9.74509			0.494096			0.247048	−	0.969003i	$-0.420540\pi$
$389$	9.74509			0.494096			0.247048	+	0.969003i	$0.420540\pi$
$390$	33.5101			1.69685
$391$			4.82694i			0.244109i
$392$	1.00000			0.0505076
$393$			44.5111i			2.24529i
$394$	22.1195			1.11437
$395$		−	5.68054i		−	0.285819i
$396$		−	4.17459i		−	0.209781i
$397$		−	23.7473i		−	1.19184i	−0.803043	−	0.595921i	$-0.796787\pi$
$397$		−	23.7473i		−	1.19184i	0.803043	−	0.595921i	$-0.203213\pi$
$398$			0.993404i			0.0497948i
$399$			16.0163i			0.801816i
$400$	0.824846			0.0412423
$401$	−9.91605			−0.495184			−0.247592	−	0.968864i	$-0.579639\pi$
$401$	−9.91605			−0.495184			−0.247592	+	0.968864i	$0.579639\pi$
$402$	−43.7734			−2.18322
$403$			0.716929i			0.0357128i
$404$			17.2283i			0.857141i
$405$	−30.7789			−1.52942
$406$	−6.05163			−0.300338
$407$			2.69529i			0.133601i
$408$	3.26763			0.161772
$409$	32.5092			1.60747			0.803737	−	0.594984i	$-0.202842\pi$
$409$	32.5092			1.60747			0.803737	+	0.594984i	$0.202842\pi$
$410$	14.1827	+	6.13752i	0.700435	+	0.303110i
$411$	−6.43540			−0.317435
$412$	15.3356			0.755529
$413$			2.12352i			0.104492i
$414$	−28.9813			−1.42435
$415$	36.4294			1.78825
$416$		−	4.52883i		−	0.222044i
$417$			68.7603i			3.36721i
$418$	3.40798			0.166690
$419$	28.4031			1.38758			0.693791	−	0.720177i	$-0.255939\pi$
$419$	28.4031			1.38758			0.693791	+	0.720177i	$0.255939\pi$
$420$	−7.39928			−0.361048
$421$		−	20.0637i		−	0.977845i	−0.872327	−	0.488922i	$-0.837390\pi$
$421$		−	20.0637i		−	0.977845i	0.872327	−	0.488922i	$-0.162610\pi$
$422$		−	17.2323i		−	0.838853i
$423$		−	52.9203i		−	2.57307i
$424$		−	0.0516348i		−	0.00250761i
$425$		−	0.879142i		−	0.0426446i
$426$	28.8166			1.39617
$427$		−	1.32742i		−	0.0642385i
$428$	−9.79004			−0.473219
$429$			9.05767i			0.437308i
$430$	−18.1757			−0.876510
$431$	−16.0106			−0.771205			−0.385602	−	0.922665i	$-0.626006\pi$
$431$	−16.0106			−0.771205			−0.385602	+	0.922665i	$0.626006\pi$
$432$			10.4216i			0.501410i
$433$	−4.86739			−0.233912			−0.116956	−	0.993137i	$-0.537314\pi$
$433$	−4.86739			−0.233912			−0.116956	+	0.993137i	$0.537314\pi$
$434$		−	0.158303i		−	0.00759880i
$435$	44.7778			2.14693
$436$		−	9.84167i		−	0.471331i
$437$		−	23.6592i		−	1.13177i
$438$		−	45.7734i		−	2.18714i
$439$		−	6.54515i		−	0.312383i	−0.987727	−	0.156191i	$-0.950078\pi$
$439$		−	6.54515i		−	0.312383i	0.987727	−	0.156191i	$-0.0499217\pi$
$440$			1.57444i			0.0750583i
$441$	6.39928			0.304728
$442$	−4.82694			−0.229594
$443$	14.6624			0.696632			0.348316	−	0.937377i	$-0.386754\pi$
$443$	14.6624			0.696632			0.348316	+	0.937377i	$0.386754\pi$
$444$		−	12.6669i		−	0.601145i
$445$		−	10.6714i		−	0.505873i
$446$	−9.97754			−0.472450
$447$	10.5533			0.499152
$448$			1.00000i			0.0472456i
$449$	22.5179			1.06269			0.531343	−	0.847157i	$-0.321688\pi$
$449$	22.5179			1.06269			0.531343	+	0.847157i	$0.321688\pi$
$450$	5.27842			0.248827
$451$	−1.65895	+	3.83354i	−0.0781169	+	0.180514i
$452$	−14.6976			−0.691315
$453$	−41.6075			−1.95489
$454$			20.1561i			0.945971i
$455$	10.9302			0.512416
$456$	−16.0163			−0.750030
$457$		−	22.3037i		−	1.04333i	−0.853152	−	0.521663i	$-0.825312\pi$
$457$		−	22.3037i		−	1.04333i	0.853152	−	0.521663i	$-0.174688\pi$
$458$		−	23.9652i		−	1.11982i
$459$	11.1076			0.518458
$460$	10.9302			0.509624
$461$	34.4589			1.60491			0.802454	−	0.596713i	$-0.203527\pi$
$461$	34.4589			1.60491			0.802454	+	0.596713i	$0.203527\pi$
$462$		−	2.00000i		−	0.0930484i
$463$			34.7199i			1.61357i	0.590843	+	0.806786i	$0.298795\pi$
$463$			34.7199i			1.61357i	−0.590843	+	0.806786i	$0.701205\pi$
$464$		−	6.05163i		−	0.280940i
$465$			1.17133i			0.0543191i
$466$			10.4820i			0.485567i
$467$	−18.4159			−0.852188			−0.426094	−	0.904679i	$-0.640111\pi$
$467$	−18.4159			−0.852188			−0.426094	+	0.904679i	$0.640111\pi$
$468$		−	28.9813i		−	1.33966i
$469$	−14.2779			−0.659290
$470$			19.9588i			0.920629i
$471$	−16.6866			−0.768879
$472$	−2.12352			−0.0977429
$473$		−	4.91283i		−	0.225892i
$474$	−7.21597			−0.331441
$475$			4.30910i			0.197715i
$476$	1.06582			0.0488520
$477$		−	0.330425i		−	0.0151291i
$478$		−	26.2054i		−	1.19861i
$479$			15.7791i			0.720966i	0.932766	+	0.360483i	$0.117388\pi$
$479$			15.7791i			0.720966i	−0.932766	+	0.360483i	$0.882612\pi$
$480$		−	7.39928i		−	0.337729i
$481$			18.7116i			0.853173i
$482$	−20.6995			−0.942836
$483$	−13.8846			−0.631772
$484$	10.5744			0.480656
$485$		−	27.9834i		−	1.27066i
$486$			7.83354i			0.355337i
$487$	0.476636			0.0215984			0.0107992	−	0.999942i	$-0.496562\pi$
$487$	0.476636			0.0215984			0.0107992	+	0.999942i	$0.496562\pi$
$488$	1.32742			0.0600897
$489$			41.8604i			1.89299i
$490$	−2.41347			−0.109030
$491$	−27.0369			−1.22016			−0.610078	−	0.792341i	$-0.708862\pi$
$491$	−27.0369			−1.22016			−0.610078	+	0.792341i	$0.708862\pi$
$492$	7.79647	−	18.0163i	0.351492	−	0.812236i
$493$	−6.44998			−0.290493
$494$	23.6592			1.06448
$495$			10.0753i			0.452849i
$496$	0.158303			0.00710802
$497$	9.39928			0.421615
$498$		−	46.2761i		−	2.07368i
$499$		−	7.65219i		−	0.342559i	−0.985222	−	0.171279i	$-0.945210\pi$
$499$		−	7.65219i		−	0.342559i	0.985222	−	0.171279i	$-0.0547901\pi$
$500$	10.0766			0.450640
$501$	−10.0412			−0.448607
$502$	21.1528			0.944096
$503$		−	31.8309i		−	1.41927i	−0.704569	−	0.709635i	$-0.748860\pi$
$503$		−	31.8309i		−	1.41927i	0.704569	−	0.709635i	$-0.251140\pi$
$504$			6.39928i			0.285047i
$505$		−	41.5801i		−	1.85029i
$506$			2.95440i			0.131339i
$507$			23.0254i			1.02259i
$508$	4.21223			0.186887
$509$		−	2.71492i		−	0.120337i	−0.998188	−	0.0601683i	$-0.980836\pi$
$509$		−	2.71492i		−	0.120337i	0.998188	−	0.0601683i	$-0.0191637\pi$
$510$	−7.88634			−0.349213
$511$		−	14.9302i		−	0.660474i
$512$	−1.00000			−0.0441942
$513$	−54.4438			−2.40375
$514$		−	31.3476i		−	1.38268i
$515$	−37.0119			−1.63094
$516$			23.0885i			1.01642i
$517$	−5.39478			−0.237262
$518$		−	4.13165i		−	0.181534i
$519$		−	36.1022i		−	1.58471i
$520$			10.9302i			0.479322i
$521$			13.9822i			0.612573i	0.951939	+	0.306287i	$0.0990866\pi$
$521$			13.9822i			0.612573i	−0.951939	+	0.306287i	$0.900913\pi$
$522$		−	38.7261i		−	1.69500i
$523$	−26.6906			−1.16710			−0.583548	−	0.812078i	$-0.698336\pi$
$523$	−26.6906			−1.16710			−0.583548	+	0.812078i	$0.698336\pi$
$524$	−14.5185			−0.634242
$525$	2.52883			0.110367
$526$			4.79437i			0.209044i
$527$		−	0.168723i		−	0.00734971i
$528$	2.00000			0.0870388
$529$	−2.48966			−0.108246
$530$			0.124619i			0.00541311i
$531$	−13.5890			−0.589712
$532$	−5.22413			−0.226495
$533$	−11.5169	+	26.6136i	−0.498854	+	1.15276i
$534$	−13.5559			−0.586619
$535$	23.6280			1.02153
$536$		−	14.2779i		−	0.616710i
$537$	−12.4448			−0.537033
$538$	−9.02116			−0.388930
$539$		−	0.652353i		−	0.0280988i
$540$		−	25.1522i		−	1.08238i
$541$	−3.58874			−0.154292			−0.0771459	−	0.997020i	$-0.524581\pi$
$541$	−3.58874			−0.154292			−0.0771459	+	0.997020i	$0.524581\pi$
$542$	−23.1609			−0.994847
$543$	−31.9758			−1.37221
$544$			1.06582i			0.0456969i
$545$			23.7526i			1.01745i
$546$		−	13.8846i		−	0.594207i
$547$			12.5619i			0.537108i	0.963265	+	0.268554i	$0.0865457\pi$
$547$			12.5619i			0.537108i	−0.963265	+	0.268554i	$0.913454\pi$
$548$		−	2.09907i		−	0.0896680i
$549$	8.49456			0.362539
$550$		−	0.538091i		−	0.0229443i
$551$	31.6145			1.34682
$552$		−	13.8846i		−	0.590968i
$553$	−2.35368			−0.100089
$554$	18.6136			0.790816
$555$			30.5712i			1.29768i
$556$	−22.4280			−0.951159
$557$			29.9037i			1.26706i	0.773718	+	0.633530i	$0.218395\pi$
$557$			29.9037i			1.26706i	−0.773718	+	0.633530i	$0.781605\pi$
$558$	1.01303			0.0428848
$559$		−	34.1063i		−	1.44254i
$560$		−	2.41347i		−	0.101988i
$561$		−	2.13165i		−	0.0899983i
$562$		−	6.52240i		−	0.275131i
$563$			25.1836i			1.06136i	0.847571	+	0.530682i	$0.178064\pi$
$563$			25.1836i			1.06136i	−0.847571	+	0.530682i	$0.821936\pi$
$564$	25.3535			1.06758
$565$	35.4721			1.49232
$566$	8.54339			0.359106
$567$			12.7530i			0.535574i
$568$			9.39928i			0.394385i
$569$	1.13068			0.0474005			0.0237003	−	0.999719i	$-0.492455\pi$
$569$	1.13068			0.0474005			0.0237003	+	0.999719i	$0.492455\pi$
$570$	38.6548			1.61907
$571$			23.1755i			0.969864i	0.874552	+	0.484932i	$0.161156\pi$
$571$			23.1755i			0.969864i	−0.874552	+	0.484932i	$0.838844\pi$
$572$	−2.95440			−0.123530
$573$	14.1179			0.589782
$574$	2.54302	−	5.87648i	0.106144	−	0.245280i
$575$	−3.73559			−0.155785
$576$	−6.39928			−0.266637
$577$		−	36.3609i		−	1.51372i	−0.653575	−	0.756862i	$-0.726732\pi$
$577$		−	36.3609i		−	1.51372i	0.653575	−	0.756862i	$-0.273268\pi$
$578$	−15.8640			−0.659856
$579$	−62.5273			−2.59855
$580$			14.6054i			0.606458i
$581$		−	15.0942i		−	0.626212i
$582$	−35.5472			−1.47348
$583$	−0.0336841			−0.00139505
$584$	14.9302			0.617817
$585$			69.9455i			2.89189i
$586$			21.5449i			0.890013i
$587$		−	4.91791i		−	0.202984i	−0.994836	−	0.101492i	$-0.967638\pi$
$587$		−	4.91791i		−	0.202984i	0.994836	−	0.101492i	$-0.0323616\pi$
$588$			3.06582i			0.126432i
$589$			0.826996i			0.0340758i
$590$	5.12505			0.210995
$591$			67.8146i			2.78952i
$592$	4.13165			0.169810
$593$		−	22.1081i		−	0.907869i	−0.891035	−	0.453935i	$-0.850020\pi$
$593$		−	22.1081i		−	0.907869i	0.891035	−	0.453935i	$-0.149980\pi$
$594$	6.79856			0.278948
$595$	−2.57234			−0.105456
$596$			3.44222i			0.140999i
$597$	−3.04560			−0.124648
$598$			20.5103i			0.838730i
$599$	6.88790			0.281432			0.140716	−	0.990050i	$-0.455060\pi$
$599$	6.88790			0.281432			0.140716	+	0.990050i	$0.455060\pi$
$600$			2.52883i			0.103239i
$601$		−	17.3420i		−	0.707394i	−0.935360	−	0.353697i	$-0.884924\pi$
$601$		−	17.3420i		−	0.707394i	0.935360	−	0.353697i	$-0.115076\pi$
$602$			7.53093i			0.306938i
$603$		−	91.3681i		−	3.72079i
$604$		−	13.5714i		−	0.552212i
$605$	−25.5211			−1.03758
$606$	−52.8190			−2.14563
$607$	−28.9773			−1.17615			−0.588077	−	0.808805i	$-0.700115\pi$
$607$	−28.9773			−1.17615			−0.588077	+	0.808805i	$0.700115\pi$
$608$		−	5.22413i		−	0.211866i
$609$		−	18.5533i		−	0.751816i
$610$	−3.20370			−0.129714
$611$	−37.4522			−1.51516
$612$			6.82051i			0.275703i
$613$	26.3261			1.06330			0.531651	−	0.846964i	$-0.321572\pi$
$613$	26.3261			1.06330			0.531651	+	0.846964i	$0.321572\pi$
$614$	20.6164			0.832011
$615$	−18.8166	+	43.4817i	−0.758757	+	1.75335i
$616$	0.652353			0.0262841
$617$	−4.87881			−0.196413			−0.0982067	−	0.995166i	$-0.531311\pi$
$617$	−4.87881			−0.196413			−0.0982067	+	0.995166i	$0.531311\pi$
$618$			47.0161i			1.89127i
$619$	−22.8555			−0.918641			−0.459321	−	0.888271i	$-0.651907\pi$
$619$	−22.8555			−0.918641			−0.459321	+	0.888271i	$0.651907\pi$
$620$	−0.382060			−0.0153439
$621$		−	47.1977i		−	1.89398i
$622$			9.99431i			0.400735i
$623$	−4.42160			−0.177148
$624$	13.8846			0.555829
$625$	−28.4439			−1.13775
$626$			5.44279i			0.217537i
$627$			10.4483i			0.417263i
$628$		−	5.44279i		−	0.217191i
$629$		−	4.40361i		−	0.175584i
$630$		−	15.4445i		−	0.615323i
$631$	−48.0847			−1.91422			−0.957111	−	0.289721i	$-0.906438\pi$
$631$	−48.0847			−1.91422			−0.957111	+	0.289721i	$0.906438\pi$
$632$		−	2.35368i		−	0.0936244i
$633$	52.8311			2.09985
$634$		−	18.1788i		−	0.721972i
$635$	−10.1661			−0.403429
$636$	0.158303			0.00627713
$637$		−	4.52883i		−	0.179439i
$638$	−3.94780			−0.156295
$639$			60.1487i			2.37944i
$640$	2.41347			0.0954009
$641$		−	11.4697i		−	0.453025i	−0.974008	−	0.226512i	$-0.927268\pi$
$641$		−	11.4697i		−	0.453025i	0.974008	−	0.226512i	$-0.0727324\pi$
$642$		−	30.0145i		−	1.18458i
$643$			28.9504i			1.14169i	0.821057	+	0.570847i	$0.193385\pi$
$643$			28.9504i			1.14169i	−0.821057	+	0.570847i	$0.806615\pi$
$644$		−	4.52883i		−	0.178461i
$645$		−	55.7235i		−	2.19411i
$646$	−5.56801			−0.219070
$647$	9.66881			0.380120			0.190060	−	0.981772i	$-0.439132\pi$
$647$	9.66881			0.380120			0.190060	+	0.981772i	$0.439132\pi$
$648$	−12.7530			−0.500984
$649$			1.38528i			0.0543772i
$650$		−	3.73559i		−	0.146522i
$651$	0.485330			0.0190216
$652$	−13.6539			−0.534727
$653$			31.6476i			1.23847i	0.785207	+	0.619234i	$0.212557\pi$
$653$			31.6476i			1.23847i	−0.785207	+	0.619234i	$0.787443\pi$
$654$	30.1728			1.17985
$655$	35.0399			1.36912
$656$	5.87648	+	2.54302i	0.229438	+	0.0992884i
$657$	95.5426			3.72747
$658$	8.26973			0.322388
$659$		−	14.5412i		−	0.566443i	−0.959055	−	0.283222i	$-0.908597\pi$
$659$		−	14.5412i		−	0.566443i	0.959055	−	0.283222i	$-0.0914032\pi$
$660$	−4.82694			−0.187889
$661$	13.8155			0.537362			0.268681	−	0.963229i	$-0.413412\pi$
$661$	13.8155			0.537362			0.268681	+	0.963229i	$0.413412\pi$
$662$			14.5945i			0.567230i
$663$		−	14.7986i		−	0.574729i
$664$	15.0942			0.585768
$665$	12.6083			0.488928
$666$	26.4396			1.02451
$667$			27.4068i			1.06120i
$668$		−	3.27520i		−	0.126721i
$669$		−	30.5894i		−	1.18265i
$670$			34.4592i			1.33128i
$671$		−	0.865949i		−	0.0334296i
$672$	−3.06582			−0.118267
$673$		−	39.0203i		−	1.50412i	−0.659094	−	0.752061i	$-0.729060\pi$
$673$		−	39.0203i		−	1.50412i	0.659094	−	0.752061i	$-0.270940\pi$
$674$	−25.7617			−0.992302
$675$			8.59622i			0.330869i
$676$	−7.51034			−0.288859
$677$	8.05357			0.309524			0.154762	−	0.987952i	$-0.450539\pi$
$677$	8.05357			0.309524			0.154762	+	0.987952i	$0.450539\pi$
$678$		−	45.0601i		−	1.73052i
$679$	−11.5947			−0.444962
$680$		−	2.57234i		−	0.0986447i
$681$	−61.7950			−2.36799
$682$		−	0.103270i		−	0.00395440i
$683$			35.2406i			1.34845i	0.738528	+	0.674223i	$0.235521\pi$
$683$			35.2406i			1.34845i	−0.738528	+	0.674223i	$0.764479\pi$
$684$		−	33.4307i		−	1.27825i
$685$			5.06606i			0.193564i
$686$			1.00000i			0.0381802i
$687$	73.4731			2.80317
$688$	−7.53093			−0.287114
$689$	−0.233845			−0.00890880
$690$			33.5101i			1.27571i
$691$		−	9.00720i		−	0.342650i	−0.985215	−	0.171325i	$-0.945195\pi$
$691$		−	9.00720i		−	0.342650i	0.985215	−	0.171325i	$-0.0548048\pi$
$692$	11.7757			0.447644
$693$	4.17459			0.158580
$694$			23.3235i			0.885347i
$695$	54.1294			2.05324
$696$	18.5533			0.703259
$697$	2.71042	−	6.26330i	0.102664	−	0.237239i
$698$	30.9383			1.17103
$699$	−32.1358			−1.21549
$700$			0.824846i			0.0311763i
$701$	−27.5680			−1.04123			−0.520615	−	0.853792i	$-0.674297\pi$
$701$	−27.5680			−1.04123			−0.520615	+	0.853792i	$0.674297\pi$
$702$	47.1977			1.78136
$703$			21.5843i			0.814066i
$704$			0.652353i			0.0245865i
$705$	−61.1901			−2.30455
$706$	12.0000			0.451626
$707$	−17.2283			−0.647938
$708$		−	6.51034i		−	0.244673i
$709$		−	22.5010i		−	0.845043i	−0.906353	−	0.422522i	$-0.861145\pi$
$709$		−	22.5010i		−	0.845043i	0.906353	−	0.422522i	$-0.138855\pi$
$710$		−	22.6849i		−	0.851349i
$711$		−	15.0619i		−	0.564864i
$712$		−	4.42160i		−	0.165707i
$713$	−0.716929			−0.0268492
$714$			3.26763i			0.122288i
$715$	7.13036			0.266660
$716$		−	4.05920i		−	0.151700i
$717$	80.3412			3.00040
$718$	5.42316			0.202391
$719$		−	2.82769i		−	0.105455i	−0.998609	−	0.0527274i	$-0.983209\pi$
$719$		−	2.82769i		−	0.105455i	0.998609	−	0.0527274i	$-0.0167915\pi$
$720$	15.4445			0.575582
$721$			15.3356i			0.571126i
$722$	8.29151			0.308578
$723$		−	63.4610i		−	2.36014i
$724$		−	10.4298i		−	0.387619i
$725$		−	4.99167i		−	0.185386i
$726$			32.4194i			1.20320i
$727$			39.2393i			1.45530i	0.685946	+	0.727652i	$0.259388\pi$
$727$			39.2393i			1.45530i	−0.685946	+	0.727652i	$0.740612\pi$
$728$	4.52883			0.167850
$729$	14.2426			0.527505
$730$	−36.0336			−1.33367
$731$			8.02665i			0.296877i
$732$			4.06965i			0.150419i
$733$	8.49181			0.313652			0.156826	−	0.987626i	$-0.449874\pi$
$733$	8.49181			0.313652			0.156826	+	0.987626i	$0.449874\pi$
$734$	−12.9319			−0.477327
$735$		−	7.39928i		−	0.272927i
$736$	4.52883			0.166935
$737$	−9.31420			−0.343093
$738$	37.6053	+	16.2735i	1.38427	+	0.599037i
$739$	−17.5480			−0.645513			−0.322757	−	0.946482i	$-0.604610\pi$
$739$	−17.5480			−0.645513			−0.322757	+	0.946482i	$0.604610\pi$
$740$	−9.97162			−0.366564
$741$			72.5350i			2.66464i
$742$	0.0516348			0.00189557
$743$	−31.8842			−1.16972			−0.584859	−	0.811135i	$-0.698850\pi$
$743$	−31.8842			−1.16972			−0.584859	+	0.811135i	$0.698850\pi$
$744$			0.485330i			0.0177931i
$745$		−	8.30771i		−	0.304371i
$746$	−19.2794			−0.705869
$747$	96.5919			3.53411
$748$	0.695294			0.0254225
$749$		−	9.79004i		−	0.357720i
$750$			30.8931i			1.12806i
$751$			0.447130i			0.0163160i	0.999967	+	0.00815800i	$0.00259680\pi$
$751$			0.447130i			0.0163160i	−0.999967	+	0.00815800i	$0.997403\pi$
$752$			8.26973i			0.301566i
$753$			64.8508i			2.36329i
$754$	−27.4068			−0.998099
$755$			32.7541i			1.19205i
$756$	−10.4216			−0.379030
$757$			36.3933i			1.32274i	0.750062	+	0.661368i	$0.230024\pi$
$757$			36.3933i			1.32274i	−0.750062	+	0.661368i	$0.769976\pi$
$758$	−27.4730			−0.997866
$759$	−9.05767			−0.328773
$760$			12.6083i			0.457351i
$761$	49.0444			1.77786			0.888929	−	0.458044i	$-0.151450\pi$
$761$	49.0444			1.77786			0.888929	+	0.458044i	$0.151450\pi$
$762$			12.9140i			0.467823i
$763$	9.84167			0.356292
$764$			4.60491i			0.166600i
$765$		−	16.4611i		−	0.595153i
$766$		−	11.6418i		−	0.420636i
$767$			9.61707i			0.347252i
$768$		−	3.06582i		−	0.110628i
$769$	−3.71177			−0.133850			−0.0669250	−	0.997758i	$-0.521319\pi$
$769$	−3.71177			−0.133850			−0.0669250	+	0.997758i	$0.521319\pi$
$770$	−1.57444			−0.0567387
$771$	96.1063			3.46118
$772$		−	20.3949i		−	0.734030i
$773$			18.9855i			0.682860i	0.939907	+	0.341430i	$0.110911\pi$
$773$			18.9855i			0.682860i	−0.939907	+	0.341430i	$0.889089\pi$
$774$	−48.1926			−1.73225
$775$	0.130576			0.00469042
$776$		−	11.5947i		−	0.416224i
$777$	12.6669			0.454423
$778$	−9.74509			−0.349378
$779$	−13.2851	+	30.6995i	−0.475987	+	1.09992i
$780$	−33.5101			−1.19985
$781$	6.13165			0.219408
$782$		−	4.82694i		−	0.172611i
$783$	63.0677			2.25386
$784$	−1.00000			−0.0357143
$785$			13.1360i			0.468844i
$786$		−	44.5111i		−	1.58766i
$787$	−22.9959			−0.819715			−0.409858	−	0.912150i	$-0.634422\pi$
$787$	−22.9959			−0.819715			−0.409858	+	0.912150i	$0.634422\pi$
$788$	−22.1195			−0.787976
$789$	−14.6987			−0.523287
$790$			5.68054i			0.202105i
$791$		−	14.6976i		−	0.522585i
$792$			4.17459i			0.148338i
$793$		−	6.01168i		−	0.213481i
$794$			23.7473i			0.842759i
$795$	−0.382060			−0.0135503
$796$		−	0.993404i		−	0.0352103i
$797$	33.4537			1.18499			0.592495	−	0.805574i	$-0.298143\pi$
$797$	33.4537			1.18499			0.592495	+	0.805574i	$0.298143\pi$
$798$		−	16.0163i		−	0.566970i
$799$	8.81408			0.311820
$800$	−0.824846			−0.0291627
$801$		−	28.2951i		−	0.999757i
$802$	9.91605			0.350148
$803$		−	9.73977i		−	0.343709i
$804$	43.7734			1.54377
$805$			10.9302i			0.385239i
$806$		−	0.716929i		−	0.0252527i
$807$		−	27.6573i		−	0.973583i
$808$		−	17.2283i		−	0.606090i
$809$		−	47.8941i		−	1.68387i	−0.539581	−	0.841934i	$-0.681417\pi$
$809$		−	47.8941i		−	1.68387i	0.539581	−	0.841934i	$-0.318583\pi$
$810$	30.7789			1.08146
$811$	−51.6620			−1.81410			−0.907048	−	0.421026i	$-0.861670\pi$
$811$	−51.6620			−1.81410			−0.907048	+	0.421026i	$0.861670\pi$
$812$	6.05163			0.212371
$813$		−	71.0074i		−	2.49034i
$814$		−	2.69529i		−	0.0944700i
$815$	32.9533			1.15430
$816$	−3.26763			−0.114390
$817$		−	39.3425i		−	1.37642i
$818$	−32.5092			−1.13666
$819$	28.9813			1.01269
$820$	−14.1827	−	6.13752i	−0.495282	−	0.214331i
$821$	−1.02090			−0.0356296			−0.0178148	−	0.999841i	$-0.505671\pi$
$821$	−1.02090			−0.0356296			−0.0178148	+	0.999841i	$0.505671\pi$
$822$	6.43540			0.224460
$823$		−	29.1315i		−	1.01546i	−0.861516	−	0.507730i	$-0.830485\pi$
$823$		−	29.1315i		−	1.01546i	0.861516	−	0.507730i	$-0.169515\pi$
$824$	−15.3356			−0.534239
$825$	1.64969			0.0574349
$826$		−	2.12352i		−	0.0738867i
$827$			44.0603i			1.53213i	0.642766	+	0.766063i	$0.277787\pi$
$827$			44.0603i			1.53213i	−0.642766	+	0.766063i	$0.722213\pi$
$828$	28.9813			1.00717
$829$	2.12599			0.0738386			0.0369193	−	0.999318i	$-0.488246\pi$
$829$	2.12599			0.0738386			0.0369193	+	0.999318i	$0.488246\pi$
$830$	−36.4294			−1.26448
$831$			57.0661i			1.97960i
$832$			4.52883i			0.157009i
$833$			1.06582i			0.0369286i
$834$		−	68.7603i		−	2.38098i
$835$			7.90460i			0.273550i
$836$	−3.40798			−0.117867
$837$			1.64977i			0.0570245i
$838$	−28.4031			−0.981168
$839$		−	31.4288i		−	1.08504i	−0.840042	−	0.542521i	$-0.817470\pi$
$839$		−	31.4288i		−	1.08504i	0.840042	−	0.542521i	$-0.182530\pi$
$840$	7.39928			0.255299
$841$	−7.62228			−0.262837
$842$			20.0637i			0.691441i
$843$	19.9965			0.688718
$844$			17.2323i			0.593159i
$845$	18.1260			0.623553
$846$			52.9203i			1.81944i
$847$			10.5744i			0.363342i
$848$			0.0516348i			0.00177315i
$849$			26.1926i			0.898926i
$850$			0.879142i			0.0301543i
$851$	−18.7116			−0.641424
$852$	−28.8166			−0.987239
$853$	−6.07636			−0.208050			−0.104025	−	0.994575i	$-0.533172\pi$
$853$	−6.07636			−0.208050			−0.104025	+	0.994575i	$0.533172\pi$
$854$			1.32742i			0.0454235i
$855$			80.6840i			2.75933i
$856$	9.79004			0.334617
$857$	−21.8279			−0.745625			−0.372813	−	0.927907i	$-0.621607\pi$
$857$	−21.8279			−0.745625			−0.372813	+	0.927907i	$0.621607\pi$
$858$		−	9.05767i		−	0.309224i
$859$	12.9050			0.440314			0.220157	−	0.975464i	$-0.429343\pi$
$859$	12.9050			0.440314			0.220157	+	0.975464i	$0.429343\pi$
$860$	18.1757			0.619786
$861$	18.0163	+	7.79647i	0.613993	+	0.265703i
$862$	16.0106			0.545324
$863$	14.9551			0.509079			0.254539	−	0.967062i	$-0.418076\pi$
$863$	14.9551			0.509079			0.254539	+	0.967062i	$0.418076\pi$
$864$		−	10.4216i		−	0.354550i
$865$	−28.4203			−0.966318
$866$	4.86739			0.165401
$867$		−	48.6363i		−	1.65178i
$868$			0.158303i			0.00537316i
$869$	−1.53543			−0.0520859
$870$	−44.7778			−1.51811
$871$	−64.6621			−2.19099
$872$			9.84167i			0.333281i
$873$		−	74.1975i		−	2.51120i
$874$			23.6592i			0.800285i
$875$			10.0766i			0.340652i
$876$			45.7734i			1.54654i
$877$	−25.9304			−0.875607			−0.437803	−	0.899071i	$-0.644243\pi$
$877$	−25.9304			−0.875607			−0.437803	+	0.899071i	$0.644243\pi$
$878$			6.54515i			0.220888i
$879$	−66.0530			−2.22791
$880$		−	1.57444i		−	0.0530742i
$881$	7.83498			0.263967			0.131984	−	0.991252i	$-0.457865\pi$
$881$	7.83498			0.263967			0.131984	+	0.991252i	$0.457865\pi$
$882$	−6.39928			−0.215475
$883$		−	34.9035i		−	1.17460i	−0.809370	−	0.587299i	$-0.800191\pi$
$883$		−	34.9035i		−	1.17460i	0.809370	−	0.587299i	$-0.199809\pi$
$884$	4.82694			0.162348
$885$			15.7125i			0.528170i
$886$	−14.6624			−0.492593
$887$			24.9366i			0.837291i	0.908150	+	0.418645i	$0.137495\pi$
$887$			24.9366i			0.837291i	−0.908150	+	0.418645i	$0.862505\pi$
$888$			12.6669i			0.425074i
$889$			4.21223i			0.141274i
$890$			10.6714i			0.357707i
$891$			8.31943i			0.278711i
$892$	9.97754			0.334073
$893$	−43.2021			−1.44570
$894$	−10.5533			−0.352954
$895$			9.79677i			0.327470i
$896$		−	1.00000i		−	0.0334077i
$897$	−62.8811			−2.09954
$898$	−22.5179			−0.751432
$899$		−	0.957993i		−	0.0319509i
$900$	−5.27842			−0.175947
$901$	0.0550336			0.00183344
$902$	1.65895	−	3.83354i	0.0552370	−	0.127643i
$903$	−23.0885			−0.768338
$904$	14.6976			0.488833
$905$			25.1719i			0.836743i
$906$	41.6075			1.38232
$907$	54.7781			1.81888			0.909438	−	0.415839i	$-0.136512\pi$
$907$	54.7781			1.81888			0.909438	+	0.415839i	$0.136512\pi$
$908$		−	20.1561i		−	0.668903i
$909$		−	110.249i		−	3.65672i
$910$	−10.9302			−0.362333
$911$	−55.6800			−1.84476			−0.922380	−	0.386284i	$-0.873759\pi$
$911$	−55.6800			−1.84476			−0.922380	+	0.386284i	$0.873759\pi$
$912$	16.0163			0.530351
$913$		−	9.84673i		−	0.325879i
$914$			22.3037i			0.737742i
$915$		−	9.82198i		−	0.324705i
$916$			23.9652i			0.791832i
$917$		−	14.5185i		−	0.479442i
$918$	−11.1076			−0.366606
$919$		−	21.2253i		−	0.700157i	−0.936720	−	0.350078i	$-0.886155\pi$
$919$		−	21.2253i		−	0.700157i	0.936720	−	0.350078i	$-0.113845\pi$
$920$	−10.9302			−0.360358
$921$			63.2063i			2.08272i
$922$	−34.4589			−1.13484
$923$	42.5678			1.40114
$924$			2.00000i			0.0657952i
$925$	3.40798			0.112054
$926$		−	34.7199i		−	1.14097i
$927$	−98.1365			−3.22323
$928$			6.05163i			0.198655i
$929$			26.6624i			0.874766i	0.899275	+	0.437383i	$0.144095\pi$
$929$			26.6624i			0.874766i	−0.899275	+	0.437383i	$0.855905\pi$
$930$		−	1.17133i		−	0.0384094i
$931$		−	5.22413i		−	0.171214i
$932$		−	10.4820i		−	0.343348i
$933$	−30.6408			−1.00314
$934$	18.4159			0.602588
$935$	−1.67807			−0.0548788
$936$			28.9813i			0.947283i
$937$		−	8.56650i		−	0.279855i	−0.990162	−	0.139928i	$-0.955313\pi$
$937$		−	8.56650i		−	0.279855i	0.990162	−	0.139928i	$-0.0446870\pi$
$938$	14.2779			0.466189
$939$	−16.6866			−0.544548
$940$		−	19.9588i		−	0.650983i
$941$	39.2875			1.28074			0.640368	−	0.768068i	$-0.278782\pi$
$941$	39.2875			1.28074			0.640368	+	0.768068i	$0.278782\pi$
$942$	16.6866			0.543680
$943$	−26.6136	−	11.5169i	−0.866658	−	0.375043i
$944$	2.12352			0.0691147
$945$	25.1522			0.818203
$946$			4.91283i			0.159730i
$947$	14.4483			0.469505			0.234753	−	0.972055i	$-0.424572\pi$
$947$	14.4483			0.469505			0.234753	+	0.972055i	$0.424572\pi$
$948$	7.21597			0.234364
$949$		−	67.6165i		−	2.19492i
$950$		−	4.30910i		−	0.139806i
$951$	55.7330			1.80727
$952$	−1.06582			−0.0345436
$953$	42.6973			1.38310			0.691550	−	0.722329i	$-0.256928\pi$
$953$	42.6973			1.38310			0.691550	+	0.722329i	$0.256928\pi$
$954$			0.330425i			0.0106979i
$955$		−	11.1138i		−	0.359635i
$956$			26.2054i			0.847544i
$957$		−	12.1033i		−	0.391243i
$958$		−	15.7791i		−	0.509800i
$959$	2.09907			0.0677827
$960$			7.39928i			0.238811i
$961$	−30.9749			−0.999192
$962$		−	18.7116i		−	0.603285i
$963$	62.6492			2.01884
$964$	20.6995			0.666686
$965$			49.2226i			1.58453i
$966$	13.8846			0.446730
$967$			9.62926i			0.309656i	0.987941	+	0.154828i	$0.0494824\pi$
$967$			9.62926i			0.309656i	−0.987941	+	0.154828i	$0.950518\pi$
$968$	−10.5744			−0.339875
$969$		−	17.0705i		−	0.548384i
$970$			27.9834i			0.898492i
$971$			44.9099i			1.44123i	0.693336	+	0.720614i	$0.256140\pi$
$971$			44.9099i			1.44123i	−0.693336	+	0.720614i	$0.743860\pi$
$972$		−	7.83354i		−	0.251261i
$973$		−	22.4280i		−	0.719009i
$974$	−0.476636			−0.0152724
$975$	11.4527			0.366779
$976$	−1.32742			−0.0424898
$977$			43.3202i			1.38594i	0.720969	+	0.692968i	$0.243697\pi$
$977$			43.3202i			1.38594i	−0.720969	+	0.692968i	$0.756303\pi$
$978$		−	41.8604i		−	1.33855i
$979$	−2.88445			−0.0921873
$980$	2.41347			0.0770955
$981$			62.9796i			2.01078i
$982$	27.0369			0.862781
$983$	−51.2780			−1.63551			−0.817757	−	0.575563i	$-0.804783\pi$
$983$	−51.2780			−1.63551			−0.817757	+	0.575563i	$0.804783\pi$
$984$	−7.79647	+	18.0163i	−0.248542	+	0.574337i
$985$	53.3849			1.70098
$986$	6.44998			0.205409
$987$			25.3535i			0.807012i
$988$	−23.6592			−0.752700
$989$	34.1063			1.08452
$990$		−	10.0753i		−	0.320213i
$991$		−	10.7974i		−	0.342992i	−0.985185	−	0.171496i	$-0.945140\pi$
$991$		−	10.7974i		−	0.342992i	0.985185	−	0.171496i	$-0.0548600\pi$
$992$	−0.158303			−0.00502613
$993$	−44.7441			−1.41991
$994$	−9.39928			−0.298127
$995$			2.39755i			0.0760075i
$996$			46.2761i			1.46631i
$997$			18.7524i			0.593895i	0.954894	+	0.296948i	$0.0959687\pi$
$997$			18.7524i			0.593895i	−0.954894	+	0.296948i	$0.904031\pi$
$998$			7.65219i			0.242226i
$999$			43.0584i			1.36231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	574.2.c.c.491.1	✓	10
41.40	even	2	inner	574.2.c.c.491.10	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.c.c.491.1	✓	10	1.1	even	1	trivial
574.2.c.c.491.10	yes	10	41.40	even	2	inner

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:	\( N \)	\(=\)	\( 574 = 2 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	574.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.06582i q^{3} +1.00000 q^{4} -2.41347 q^{5} +3.06582i q^{6} +1.00000i q^{7} -1.00000 q^{8} -6.39928 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.06582i q^{3} +1.00000 q^{4} -2.41347 q^{5} +3.06582i q^{6} +1.00000i q^{7} -1.00000 q^{8} -6.39928 q^{9} +2.41347 q^{10} +0.652353i q^{11} -3.06582i q^{12} +4.52883i q^{13} -1.00000i q^{14} +7.39928i q^{15} +1.00000 q^{16} -1.06582i q^{17} +6.39928 q^{18} +5.22413i q^{19} -2.41347 q^{20} +3.06582 q^{21} -0.652353i q^{22} -4.52883 q^{23} +3.06582i q^{24} +0.824846 q^{25} -4.52883i q^{26} +10.4216i q^{27} +1.00000i q^{28} -6.05163i q^{29} -7.39928i q^{30} +0.158303 q^{31} -1.00000 q^{32} +2.00000 q^{33} +1.06582i q^{34} -2.41347i q^{35} -6.39928 q^{36} +4.13165 q^{37} -5.22413i q^{38} +13.8846 q^{39} +2.41347 q^{40} +(5.87648 + 2.54302i) q^{41} -3.06582 q^{42} -7.53093 q^{43} +0.652353i q^{44} +15.4445 q^{45} +4.52883 q^{46} +8.26973i q^{47} -3.06582i q^{48} -1.00000 q^{49} -0.824846 q^{50} -3.26763 q^{51} +4.52883i q^{52} +0.0516348i q^{53} -10.4216i q^{54} -1.57444i q^{55} -1.00000i q^{56} +16.0163 q^{57} +6.05163i q^{58} +2.12352 q^{59} +7.39928i q^{60} -1.32742 q^{61} -0.158303 q^{62} -6.39928i q^{63} +1.00000 q^{64} -10.9302i q^{65} -2.00000 q^{66} +14.2779i q^{67} -1.06582i q^{68} +13.8846i q^{69} +2.41347i q^{70} -9.39928i q^{71} +6.39928 q^{72} -14.9302 q^{73} -4.13165 q^{74} -2.52883i q^{75} +5.22413i q^{76} -0.652353 q^{77} -13.8846 q^{78} +2.35368i q^{79} -2.41347 q^{80} +12.7530 q^{81} +(-5.87648 - 2.54302i) q^{82} -15.0942 q^{83} +3.06582 q^{84} +2.57234i q^{85} +7.53093 q^{86} -18.5533 q^{87} -0.652353i q^{88} +4.42160i q^{89} -15.4445 q^{90} -4.52883 q^{91} -4.52883 q^{92} -0.485330i q^{93} -8.26973i q^{94} -12.6083i q^{95} +3.06582i q^{96} +11.5947i q^{97} +1.00000 q^{98} -4.17459i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 10 q^{4} - 4 q^{5} - 10 q^{8} - 14 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 10 * q^4 - 4 * q^5 - 10 * q^8 - 14 * q^9	\( 10 q - 10 q^{2} + 10 q^{4} - 4 q^{5} - 10 q^{8} - 14 q^{9} + 4 q^{10} + 10 q^{16} + 14 q^{18} - 4 q^{20} + 4 q^{21} + 26 q^{25} - 4 q^{31} - 10 q^{32} + 20 q^{33} - 14 q^{36} - 12 q^{37} + 8 q^{39} + 4 q^{40} + 20 q^{41} - 4 q^{42} + 28 q^{43} - 4 q^{45} - 10 q^{49} - 26 q^{50} - 36 q^{51} - 24 q^{57} + 60 q^{59} - 24 q^{61} + 4 q^{62} + 10 q^{64} - 20 q^{66} + 14 q^{72} + 4 q^{73} + 12 q^{74} - 8 q^{78} - 4 q^{80} + 50 q^{81} - 20 q^{82} - 28 q^{83} + 4 q^{84} - 28 q^{86} - 20 q^{87} + 4 q^{90} + 10 q^{98}+O(q^{100}) \) 10 * q - 10 * q^2 + 10 * q^4 - 4 * q^5 - 10 * q^8 - 14 * q^9 + 4 * q^10 + 10 * q^16 + 14 * q^18 - 4 * q^20 + 4 * q^21 + 26 * q^25 - 4 * q^31 - 10 * q^32 + 20 * q^33 - 14 * q^36 - 12 * q^37 + 8 * q^39 + 4 * q^40 + 20 * q^41 - 4 * q^42 + 28 * q^43 - 4 * q^45 - 10 * q^49 - 26 * q^50 - 36 * q^51 - 24 * q^57 + 60 * q^59 - 24 * q^61 + 4 * q^62 + 10 * q^64 - 20 * q^66 + 14 * q^72 + 4 * q^73 + 12 * q^74 - 8 * q^78 - 4 * q^80 + 50 * q^81 - 20 * q^82 - 28 * q^83 + 4 * q^84 - 28 * q^86 - 20 * q^87 + 4 * q^90 + 10 * q^98

Introduction

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