LMFDB - Embedded newform 145.2.b.b.59.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [145,2,Mod(59,145)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(145, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("145.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 145 = 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	145.b (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:	$1.15783082931$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 4x^{2} + 1 $ x^4 + 4*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			59.1
Root			$-1.93185i$ of defining polynomial
Character	$\chi$	$=$	145.59
Dual form			145.2.b.b.59.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.93185i q^{2} -1.41421i q^{3} -1.73205 q^{4} +(1.73205 - 1.41421i) q^{5} -2.73205 q^{6} +2.44949i q^{7} -0.517638i q^{8} +1.00000 q^{9} +(-2.73205 - 3.34607i) q^{10} -4.73205 q^{11} +2.44949i q^{12} +6.69213i q^{13} +4.73205 q^{14} +(-2.00000 - 2.44949i) q^{15} -4.46410 q^{16} +1.41421i q^{17} -1.93185i q^{18} +6.73205 q^{19} +(-3.00000 + 2.44949i) q^{20} +3.46410 q^{21} +9.14162i q^{22} -3.48477i q^{23} -0.732051 q^{24} +(1.00000 - 4.89898i) q^{25} +12.9282 q^{26} -5.65685i q^{27} -4.24264i q^{28} -1.00000 q^{29} +(-4.73205 + 3.86370i) q^{30} -5.26795 q^{31} +7.58871i q^{32} +6.69213i q^{33} +2.73205 q^{34} +(3.46410 + 4.24264i) q^{35} -1.73205 q^{36} -0.656339i q^{37} -13.0053i q^{38} +9.46410 q^{39} +(-0.732051 - 0.896575i) q^{40} +6.92820 q^{41} -6.69213i q^{42} +0.656339i q^{43} +8.19615 q^{44} +(1.73205 - 1.41421i) q^{45} -6.73205 q^{46} +1.41421i q^{47} +6.31319i q^{48} +1.00000 q^{49} +(-9.46410 - 1.93185i) q^{50} +2.00000 q^{51} -11.5911i q^{52} +8.76268i q^{53} -10.9282 q^{54} +(-8.19615 + 6.69213i) q^{55} +1.26795 q^{56} -9.52056i q^{57} +1.93185i q^{58} -10.3923 q^{59} +(3.46410 + 4.24264i) q^{60} -10.9282 q^{61} +10.1769i q^{62} +2.44949i q^{63} +5.73205 q^{64} +(9.46410 + 11.5911i) q^{65} +12.9282 q^{66} +4.24264i q^{67} -2.44949i q^{68} -4.92820 q^{69} +(8.19615 - 6.69213i) q^{70} -3.46410 q^{71} -0.517638i q^{72} -7.34847i q^{73} -1.26795 q^{74} +(-6.92820 - 1.41421i) q^{75} -11.6603 q^{76} -11.5911i q^{77} -18.2832i q^{78} -6.19615 q^{79} +(-7.73205 + 6.31319i) q^{80} -5.00000 q^{81} -13.3843i q^{82} +4.52004i q^{83} -6.00000 q^{84} +(2.00000 + 2.44949i) q^{85} +1.26795 q^{86} +1.41421i q^{87} +2.44949i q^{88} +10.3923 q^{89} +(-2.73205 - 3.34607i) q^{90} -16.3923 q^{91} +6.03579i q^{92} +7.45001i q^{93} +2.73205 q^{94} +(11.6603 - 9.52056i) q^{95} +10.7321 q^{96} -6.03579i q^{97} -1.93185i q^{98} -4.73205 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{6} + 4 q^{9} - 4 q^{10} - 12 q^{11} + 12 q^{14} - 8 q^{15} - 4 q^{16} + 20 q^{19} - 12 q^{20} + 4 q^{24} + 4 q^{25} + 24 q^{26} - 4 q^{29} - 12 q^{30} - 28 q^{31} + 4 q^{34} + 24 q^{39} + 4 q^{40}+ \cdots - 12 q^{99}+O(q^{100}) $ 4 * q - 4 * q^6 + 4 * q^9 - 4 * q^10 - 12 * q^11 + 12 * q^14 - 8 * q^15 - 4 * q^16 + 20 * q^19 - 12 * q^20 + 4 * q^24 + 4 * q^25 + 24 * q^26 - 4 * q^29 - 12 * q^30 - 28 * q^31 + 4 * q^34 + 24 * q^39 + 4 * q^40 + 12 * q^44 - 20 * q^46 + 4 * q^49 - 24 * q^50 + 8 * q^51 - 16 * q^54 - 12 * q^55 + 12 * q^56 - 16 * q^61 + 16 * q^64 + 24 * q^65 + 24 * q^66 + 8 * q^69 + 12 * q^70 - 12 * q^74 - 12 * q^76 - 4 * q^79 - 24 * q^80 - 20 * q^81 - 24 * q^84 + 8 * q^85 + 12 * q^86 - 4 * q^90 - 24 * q^91 + 4 * q^94 + 12 * q^95 + 36 * q^96 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/145\mathbb{Z}\right)^\times$.

$n$	$31$	$117$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	1.93185i		−	1.36603i	−0.730406	−	0.683013i	$-0.760669\pi$
$2$		−	1.93185i		−	1.36603i	0.730406	−	0.683013i	$-0.239331\pi$
$3$		−	1.41421i		−	0.816497i	−0.912871	−	0.408248i	$-0.866140\pi$
$3$		−	1.41421i		−	0.816497i	0.912871	−	0.408248i	$-0.133860\pi$
$4$	−1.73205			−0.866025
$5$	1.73205	−	1.41421i	0.774597	−	0.632456i
$5$	1.73205	−	1.41421i	0.774597	−	0.632456i
$6$	−2.73205			−1.11536
$7$			2.44949i			0.925820i	0.886405	+	0.462910i	$0.153195\pi$
$7$			2.44949i			0.925820i	−0.886405	+	0.462910i	$0.846805\pi$
$8$		−	0.517638i		−	0.183013i
$9$	1.00000			0.333333
$10$	−2.73205	−	3.34607i	−0.863950	−	1.05812i
$11$	−4.73205			−1.42677			−0.713384	−	0.700774i	$-0.752838\pi$
$11$	−4.73205			−1.42677			−0.713384	+	0.700774i	$0.752838\pi$
$12$			2.44949i			0.707107i
$13$			6.69213i			1.85606i	0.372502	+	0.928032i	$0.378500\pi$
$13$			6.69213i			1.85606i	−0.372502	+	0.928032i	$0.621500\pi$
$14$	4.73205			1.26469
$15$	−2.00000	−	2.44949i	−0.516398	−	0.632456i
$16$	−4.46410			−1.11603
$17$			1.41421i			0.342997i	0.985184	+	0.171499i	$0.0548609\pi$
$17$			1.41421i			0.342997i	−0.985184	+	0.171499i	$0.945139\pi$
$18$		−	1.93185i		−	0.455342i
$19$	6.73205			1.54444			0.772219	−	0.635356i	$-0.219147\pi$
$19$	6.73205			1.54444			0.772219	+	0.635356i	$0.219147\pi$
$20$	−3.00000	+	2.44949i	−0.670820	+	0.547723i
$21$	3.46410			0.755929
$22$			9.14162i			1.94900i
$23$		−	3.48477i		−	0.726624i	−0.931668	−	0.363312i	$-0.881646\pi$
$23$		−	3.48477i		−	0.726624i	0.931668	−	0.363312i	$-0.118354\pi$
$24$	−0.732051			−0.149429
$25$	1.00000	−	4.89898i	0.200000	−	0.979796i
$26$	12.9282			2.53543
$27$		−	5.65685i		−	1.08866i
$28$		−	4.24264i		−	0.801784i
$29$	−1.00000			−0.185695
$29$	−1.00000			−0.185695
$30$	−4.73205	+	3.86370i	−0.863950	+	0.705412i
$31$	−5.26795			−0.946152			−0.473076	−	0.881022i	$-0.656856\pi$
$31$	−5.26795			−0.946152			−0.473076	+	0.881022i	$0.656856\pi$
$32$			7.58871i			1.34151i
$33$			6.69213i			1.16495i
$34$	2.73205			0.468543
$35$	3.46410	+	4.24264i	0.585540	+	0.717137i
$36$	−1.73205			−0.288675
$37$		−	0.656339i		−	0.107901i	−0.998544	−	0.0539507i	$-0.982819\pi$
$37$		−	0.656339i		−	0.107901i	0.998544	−	0.0539507i	$-0.0171814\pi$
$38$		−	13.0053i		−	2.10974i
$39$	9.46410			1.51547
$40$	−0.732051	−	0.896575i	−0.115747	−	0.141761i
$41$	6.92820			1.08200			0.541002	−	0.841021i	$-0.318045\pi$
$41$	6.92820			1.08200			0.541002	+	0.841021i	$0.318045\pi$
$42$		−	6.69213i		−	1.03262i
$43$			0.656339i			0.100091i	0.998747	+	0.0500454i	$0.0159366\pi$
$43$			0.656339i			0.100091i	−0.998747	+	0.0500454i	$0.984063\pi$
$44$	8.19615			1.23562
$45$	1.73205	−	1.41421i	0.258199	−	0.210819i
$46$	−6.73205			−0.992587
$47$			1.41421i			0.206284i	0.994667	+	0.103142i	$0.0328896\pi$
$47$			1.41421i			0.206284i	−0.994667	+	0.103142i	$0.967110\pi$
$48$			6.31319i			0.911231i
$49$	1.00000			0.142857
$50$	−9.46410	−	1.93185i	−1.33843	−	0.273205i
$51$	2.00000			0.280056
$52$		−	11.5911i		−	1.60740i
$53$			8.76268i			1.20365i	0.798629	+	0.601824i	$0.205559\pi$
$53$			8.76268i			1.20365i	−0.798629	+	0.601824i	$0.794441\pi$
$54$	−10.9282			−1.48714
$55$	−8.19615	+	6.69213i	−1.10517	+	0.902367i
$56$	1.26795			0.169437
$57$		−	9.52056i		−	1.26103i
$58$			1.93185i			0.253665i
$59$	−10.3923			−1.35296			−0.676481	−	0.736460i	$-0.736496\pi$
$59$	−10.3923			−1.35296			−0.676481	+	0.736460i	$0.736496\pi$
$60$	3.46410	+	4.24264i	0.447214	+	0.547723i
$61$	−10.9282			−1.39921			−0.699607	−	0.714528i	$-0.746641\pi$
$61$	−10.9282			−1.39921			−0.699607	+	0.714528i	$0.746641\pi$
$62$			10.1769i			1.29247i
$63$			2.44949i			0.308607i
$64$	5.73205			0.716506
$65$	9.46410	+	11.5911i	1.17388	+	1.43770i
$66$	12.9282			1.59135
$67$			4.24264i			0.518321i	0.965834	+	0.259161i	$0.0834459\pi$
$67$			4.24264i			0.518321i	−0.965834	+	0.259161i	$0.916554\pi$
$68$		−	2.44949i		−	0.297044i
$69$	−4.92820			−0.593286
$70$	8.19615	−	6.69213i	0.979628	−	0.799863i
$71$	−3.46410			−0.411113			−0.205557	−	0.978645i	$-0.565900\pi$
$71$	−3.46410			−0.411113			−0.205557	+	0.978645i	$0.565900\pi$
$72$		−	0.517638i		−	0.0610042i
$73$		−	7.34847i		−	0.860073i	−0.902811	−	0.430037i	$-0.858501\pi$
$73$		−	7.34847i		−	0.860073i	0.902811	−	0.430037i	$-0.141499\pi$
$74$	−1.26795			−0.147396
$75$	−6.92820	−	1.41421i	−0.800000	−	0.163299i
$76$	−11.6603			−1.33752
$77$		−	11.5911i		−	1.32093i
$78$		−	18.2832i		−	2.07017i
$79$	−6.19615			−0.697122			−0.348561	−	0.937286i	$-0.613330\pi$
$79$	−6.19615			−0.697122			−0.348561	+	0.937286i	$0.613330\pi$
$80$	−7.73205	+	6.31319i	−0.864470	+	0.705836i
$81$	−5.00000			−0.555556
$82$		−	13.3843i		−	1.47804i
$83$			4.52004i			0.496139i	0.968742	+	0.248070i	$0.0797961\pi$
$83$			4.52004i			0.496139i	−0.968742	+	0.248070i	$0.920204\pi$
$84$	−6.00000			−0.654654
$85$	2.00000	+	2.44949i	0.216930	+	0.265684i
$86$	1.26795			0.136726
$87$			1.41421i			0.151620i
$88$			2.44949i			0.261116i
$89$	10.3923			1.10158			0.550791	−	0.834643i	$-0.314326\pi$
$89$	10.3923			1.10158			0.550791	+	0.834643i	$0.314326\pi$
$90$	−2.73205	−	3.34607i	−0.287983	−	0.352706i
$91$	−16.3923			−1.71838
$92$			6.03579i			0.629275i
$93$			7.45001i			0.772530i
$94$	2.73205			0.281790
$95$	11.6603	−	9.52056i	1.19632	−	0.976789i
$96$	10.7321			1.09534
$97$		−	6.03579i		−	0.612842i	−0.951896	−	0.306421i	$-0.900869\pi$
$97$		−	6.03579i		−	0.612842i	0.951896	−	0.306421i	$-0.0991315\pi$
$98$		−	1.93185i		−	0.195146i
$99$	−4.73205			−0.475589
$100$	−1.73205	+	8.48528i	−0.173205	+	0.848528i
$101$	−6.00000			−0.597022			−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000			−0.597022			−0.298511	+	0.954406i	$0.596490\pi$
$102$		−	3.86370i		−	0.382564i
$103$			0.656339i			0.0646710i	0.999477	+	0.0323355i	$0.0102945\pi$
$103$			0.656339i			0.0646710i	−0.999477	+	0.0323355i	$0.989705\pi$
$104$	3.46410			0.339683
$105$	6.00000	−	4.89898i	0.585540	−	0.478091i
$106$	16.9282			1.64421
$107$		−	3.96524i		−	0.383334i	−0.981460	−	0.191667i	$-0.938611\pi$
$107$		−	3.96524i		−	0.383334i	0.981460	−	0.191667i	$-0.0613894\pi$
$108$			9.79796i			0.942809i
$109$	9.85641			0.944073			0.472036	−	0.881579i	$-0.343519\pi$
$109$	9.85641			0.944073			0.472036	+	0.881579i	$0.343519\pi$
$110$	12.9282	+	15.8338i	1.23266	+	1.50969i
$111$	−0.928203			−0.0881012
$112$		−	10.9348i		−	1.03324i
$113$		−	1.69161i		−	0.159134i	−0.996830	−	0.0795669i	$-0.974646\pi$
$113$		−	1.69161i		−	0.159134i	0.996830	−	0.0795669i	$-0.0253537\pi$
$114$	−18.3923			−1.72260
$115$	−4.92820	−	6.03579i	−0.459557	−	0.562840i
$116$	1.73205			0.160817
$117$			6.69213i			0.618688i
$118$			20.0764i			1.84818i
$119$	−3.46410			−0.317554
$120$	−1.26795	+	1.03528i	−0.115747	+	0.0945074i
$121$	11.3923			1.03566
$122$			21.1117i			1.91136i
$123$		−	9.79796i		−	0.883452i
$124$	9.12436			0.819391
$125$	−5.19615	−	9.89949i	−0.464758	−	0.885438i
$126$	4.73205			0.421565
$127$			4.24264i			0.376473i	0.982124	+	0.188237i	$0.0602772\pi$
$127$			4.24264i			0.376473i	−0.982124	+	0.188237i	$0.939723\pi$
$128$			4.10394i			0.362740i
$129$	0.928203			0.0817237
$130$	22.3923	−	18.2832i	1.96394	−	1.60355i
$131$	−1.26795			−0.110781			−0.0553906	−	0.998465i	$-0.517640\pi$
$131$	−1.26795			−0.110781			−0.0553906	+	0.998465i	$0.517640\pi$
$132$		−	11.5911i		−	1.00888i
$133$			16.4901i			1.42987i
$134$	8.19615			0.708040
$135$	−8.00000	−	9.79796i	−0.688530	−	0.843274i
$136$	0.732051			0.0627728
$137$			5.00052i			0.427223i	0.976919	+	0.213611i	$0.0685226\pi$
$137$			5.00052i			0.427223i	−0.976919	+	0.213611i	$0.931477\pi$
$138$			9.52056i			0.810444i
$139$	8.00000			0.678551			0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000			0.678551			0.339276	+	0.940687i	$0.389818\pi$
$140$	−6.00000	−	7.34847i	−0.507093	−	0.621059i
$141$	2.00000			0.168430
$142$			6.69213i			0.561591i
$143$		−	31.6675i		−	2.64817i
$144$	−4.46410			−0.372008
$145$	−1.73205	+	1.41421i	−0.143839	+	0.117444i
$146$	−14.1962			−1.17488
$147$		−	1.41421i		−	0.116642i
$148$			1.13681i			0.0934454i
$149$	−12.9282			−1.05912			−0.529560	−	0.848273i	$-0.677643\pi$
$149$	−12.9282			−1.05912			−0.529560	+	0.848273i	$0.677643\pi$
$150$	−2.73205	+	13.3843i	−0.223071	+	1.09282i
$151$	22.7846			1.85419			0.927093	−	0.374832i	$-0.122300\pi$
$151$	22.7846			1.85419			0.927093	+	0.374832i	$0.122300\pi$
$152$		−	3.48477i		−	0.282652i
$153$			1.41421i			0.114332i
$154$	−22.3923			−1.80442
$155$	−9.12436	+	7.45001i	−0.732886	+	0.598399i
$156$	−16.3923			−1.31243
$157$			6.03579i			0.481709i	0.970561	+	0.240854i	$0.0774276\pi$
$157$			6.03579i			0.481709i	−0.970561	+	0.240854i	$0.922572\pi$
$158$			11.9700i			0.952286i
$159$	12.3923			0.982774
$160$	10.7321	+	13.1440i	0.848443	+	1.03913i
$161$	8.53590			0.672723
$162$			9.65926i			0.758903i
$163$			5.55532i			0.435126i	0.976046	+	0.217563i	$0.0698108\pi$
$163$			5.55532i			0.435126i	−0.976046	+	0.217563i	$0.930189\pi$
$164$	−12.0000			−0.937043
$165$	9.46410	+	11.5911i	0.736779	+	0.902367i
$166$	8.73205			0.677739
$167$		−	8.38375i		−	0.648754i	−0.945928	−	0.324377i	$-0.894845\pi$
$167$		−	8.38375i		−	0.648754i	0.945928	−	0.324377i	$-0.105155\pi$
$168$		−	1.79315i		−	0.138345i
$169$	−31.7846			−2.44497
$170$	4.73205	−	3.86370i	0.362932	−	0.296333i
$171$	6.73205			0.514813
$172$		−	1.13681i		−	0.0866811i
$173$		−	9.52056i		−	0.723835i	−0.932210	−	0.361917i	$-0.882122\pi$
$173$		−	9.52056i		−	0.723835i	0.932210	−	0.361917i	$-0.117878\pi$
$174$	2.73205			0.207116
$175$	12.0000	+	2.44949i	0.907115	+	0.185164i
$176$	21.1244			1.59231
$177$			14.6969i			1.10469i
$178$		−	20.0764i		−	1.50479i
$179$	−9.46410			−0.707380			−0.353690	−	0.935363i	$-0.615073\pi$
$179$	−9.46410			−0.707380			−0.353690	+	0.935363i	$0.615073\pi$
$180$	−3.00000	+	2.44949i	−0.223607	+	0.182574i
$181$	−16.0000			−1.18927			−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000			−1.18927			−0.594635	+	0.803996i	$0.702704\pi$
$182$			31.6675i			2.34735i
$183$			15.4548i			1.14245i
$184$	−1.80385			−0.132981
$185$	−0.928203	−	1.13681i	−0.0682429	−	0.0835801i
$186$	14.3923			1.05529
$187$		−	6.69213i		−	0.489377i
$188$		−	2.44949i		−	0.178647i
$189$	13.8564			1.00791
$190$	−18.3923	−	22.5259i	−1.33432	−	1.63420i
$191$	−9.12436			−0.660215			−0.330108	−	0.943943i	$-0.607085\pi$
$191$	−9.12436			−0.660215			−0.330108	+	0.943943i	$0.607085\pi$
$192$		−	8.10634i		−	0.585025i
$193$		−	9.14162i		−	0.658028i	−0.944325	−	0.329014i	$-0.893284\pi$
$193$		−	9.14162i		−	0.658028i	0.944325	−	0.329014i	$-0.106716\pi$
$194$	−11.6603			−0.837157
$195$	16.3923	−	13.3843i	1.17388	−	0.958467i
$196$	−1.73205			−0.123718
$197$			16.7675i			1.19463i	0.802005	+	0.597317i	$0.203767\pi$
$197$			16.7675i			1.19463i	−0.802005	+	0.597317i	$0.796233\pi$
$198$			9.14162i			0.649667i
$199$	14.0000			0.992434			0.496217	−	0.868199i	$-0.334722\pi$
$199$	14.0000			0.992434			0.496217	+	0.868199i	$0.334722\pi$
$200$	−2.53590	−	0.517638i	−0.179315	−	0.0366025i
$201$	6.00000			0.423207
$202$			11.5911i			0.815548i
$203$		−	2.44949i		−	0.171920i
$204$	−3.46410			−0.242536
$205$	12.0000	−	9.79796i	0.838116	−	0.684319i
$206$	1.26795			0.0883422
$207$		−	3.48477i		−	0.242208i
$208$		−	29.8744i		−	2.07141i
$209$	−31.8564			−2.20355
$210$	−9.46410	−	11.5911i	−0.653085	−	0.799863i
$211$	−11.2679			−0.775718			−0.387859	−	0.921719i	$-0.626785\pi$
$211$	−11.2679			−0.775718			−0.387859	+	0.921719i	$0.626785\pi$
$212$		−	15.1774i		−	1.04239i
$213$			4.89898i			0.335673i
$214$	−7.66025			−0.523644
$215$	0.928203	+	1.13681i	0.0633029	+	0.0775299i
$216$	−2.92820			−0.199239
$217$		−	12.9038i		−	0.875966i
$218$		−	19.0411i		−	1.28963i
$219$	−10.3923			−0.702247
$220$	14.1962	−	11.5911i	0.957104	−	0.781472i
$221$	−9.46410			−0.636624
$222$			1.79315i			0.120348i
$223$		−	23.8386i		−	1.59635i	−0.602427	−	0.798174i	$-0.705800\pi$
$223$		−	23.8386i		−	1.59635i	0.602427	−	0.798174i	$-0.294200\pi$
$224$	−18.5885			−1.24199
$225$	1.00000	−	4.89898i	0.0666667	−	0.326599i
$226$	−3.26795			−0.217381
$227$		−	10.6574i		−	0.707354i	−0.935368	−	0.353677i	$-0.884931\pi$
$227$		−	10.6574i		−	0.707354i	0.935368	−	0.353677i	$-0.115069\pi$
$228$			16.4901i			1.09208i
$229$	22.7846			1.50565			0.752825	−	0.658221i	$-0.228691\pi$
$229$	22.7846			1.50565			0.752825	+	0.658221i	$0.228691\pi$
$230$	−11.6603	+	9.52056i	−0.768854	+	0.627767i
$231$	−16.3923			−1.07853
$232$			0.517638i			0.0339846i
$233$		−	26.0106i		−	1.70401i	−0.523530	−	0.852007i	$-0.675385\pi$
$233$		−	26.0106i		−	1.70401i	0.523530	−	0.852007i	$-0.324615\pi$
$234$	12.9282			0.845143
$235$	2.00000	+	2.44949i	0.130466	+	0.159787i
$236$	18.0000			1.17170
$237$			8.76268i			0.569197i
$238$			6.69213i			0.433786i
$239$	10.3923			0.672222			0.336111	−	0.941822i	$-0.390888\pi$
$239$	10.3923			0.672222			0.336111	+	0.941822i	$0.390888\pi$
$240$	8.92820	+	10.9348i	0.576313	+	0.705836i
$241$	4.53590			0.292183			0.146091	−	0.989271i	$-0.453331\pi$
$241$	4.53590			0.292183			0.146091	+	0.989271i	$0.453331\pi$
$242$		−	22.0082i		−	1.41474i
$243$		−	9.89949i		−	0.635053i
$244$	18.9282			1.21175
$245$	1.73205	−	1.41421i	0.110657	−	0.0903508i
$246$	−18.9282			−1.20682
$247$			45.0518i			2.86657i
$248$			2.72689i			0.173158i
$249$	6.39230			0.405096
$250$	−19.1244	+	10.0382i	−1.20953	+	0.634871i
$251$	−9.12436			−0.575924			−0.287962	−	0.957642i	$-0.592978\pi$
$251$	−9.12436			−0.575924			−0.287962	+	0.957642i	$0.592978\pi$
$252$		−	4.24264i		−	0.267261i
$253$			16.4901i			1.03672i
$254$	8.19615			0.514272
$255$	3.46410	−	2.82843i	0.216930	−	0.177123i
$256$	19.3923			1.21202
$257$		−	4.62158i		−	0.288286i	−0.989557	−	0.144143i	$-0.953957\pi$
$257$		−	4.62158i		−	0.288286i	0.989557	−	0.144143i	$-0.0460425\pi$
$258$		−	1.79315i		−	0.111637i
$259$	1.60770			0.0998973
$260$	−16.3923	−	20.0764i	−1.01661	−	1.24508i
$261$	−1.00000			−0.0618984
$262$			2.44949i			0.151330i
$263$			24.5964i			1.51668i	0.651859	+	0.758341i	$0.273990\pi$
$263$			24.5964i			1.51668i	−0.651859	+	0.758341i	$0.726010\pi$
$264$	3.46410			0.213201
$265$	12.3923	+	15.1774i	0.761253	+	0.932341i
$266$	31.8564			1.95324
$267$		−	14.6969i		−	0.899438i
$268$		−	7.34847i		−	0.448879i
$269$	12.0000			0.731653			0.365826	−	0.930683i	$-0.380786\pi$
$269$	12.0000			0.731653			0.365826	+	0.930683i	$0.380786\pi$
$270$	−18.9282	+	15.4548i	−1.15193	+	0.940550i
$271$	−23.2679			−1.41343			−0.706714	−	0.707500i	$-0.749823\pi$
$271$	−23.2679			−1.41343			−0.706714	+	0.707500i	$0.749823\pi$
$272$		−	6.31319i		−	0.382794i
$273$			23.1822i			1.40305i
$274$	9.66025			0.583597
$275$	−4.73205	+	23.1822i	−0.285353	+	1.39794i
$276$	8.53590			0.513801
$277$			23.6627i			1.42175i	0.703317	+	0.710877i	$0.251702\pi$
$277$			23.6627i			1.42175i	−0.703317	+	0.710877i	$0.748298\pi$
$278$		−	15.4548i		−	0.926918i
$279$	−5.26795			−0.315384
$280$	2.19615	−	1.79315i	0.131245	−	0.107161i
$281$	−8.78461			−0.524046			−0.262023	−	0.965062i	$-0.584390\pi$
$281$	−8.78461			−0.524046			−0.262023	+	0.965062i	$0.584390\pi$
$282$		−	3.86370i		−	0.230080i
$283$		−	1.96902i		−	0.117046i	−0.998286	−	0.0585229i	$-0.981361\pi$
$283$		−	1.96902i		−	0.117046i	0.998286	−	0.0585229i	$-0.0186391\pi$
$284$	6.00000			0.356034
$285$	−13.4641	−	16.4901i	−0.797545	−	0.976789i
$286$	−61.1769			−3.61747
$287$			16.9706i			1.00174i
$288$			7.58871i			0.447169i
$289$	15.0000			0.882353
$290$	2.73205	+	3.34607i	0.160432	+	0.196488i
$291$	−8.53590			−0.500383
$292$			12.7279i			0.744845i
$293$		−	25.8348i		−	1.50928i	−0.656137	−	0.754642i	$-0.727811\pi$
$293$		−	25.8348i		−	1.50928i	0.656137	−	0.754642i	$-0.272189\pi$
$294$	−2.73205			−0.159336
$295$	−18.0000	+	14.6969i	−1.04800	+	0.855689i
$296$	−0.339746			−0.0197473
$297$			26.7685i			1.55327i
$298$			24.9754i			1.44678i
$299$	23.3205			1.34866
$300$	12.0000	+	2.44949i	0.692820	+	0.141421i
$301$	−1.60770			−0.0926660
$302$		−	44.0165i		−	2.53286i
$303$			8.48528i			0.487467i
$304$	−30.0526			−1.72363
$305$	−18.9282	+	15.4548i	−1.08383	+	0.884940i
$306$	2.73205			0.156181
$307$		−	18.9396i		−	1.08094i	−0.841364	−	0.540469i	$-0.818247\pi$
$307$		−	18.9396i		−	1.08094i	0.841364	−	0.540469i	$-0.181753\pi$
$308$			20.0764i			1.14396i
$309$	0.928203			0.0528036
$310$	14.3923	+	17.6269i	0.817428	+	1.00114i
$311$	24.5885			1.39428			0.697142	−	0.716933i	$-0.254455\pi$
$311$	24.5885			1.39428			0.697142	+	0.716933i	$0.254455\pi$
$312$		−	4.89898i		−	0.277350i
$313$			18.7637i			1.06059i	0.847814	+	0.530294i	$0.177918\pi$
$313$			18.7637i			1.06059i	−0.847814	+	0.530294i	$0.822082\pi$
$314$	11.6603			0.658026
$315$	3.46410	+	4.24264i	0.195180	+	0.239046i
$316$	10.7321			0.603725
$317$		−	25.3543i		−	1.42404i	−0.702159	−	0.712020i	$-0.747781\pi$
$317$		−	25.3543i		−	1.42404i	0.702159	−	0.712020i	$-0.252219\pi$
$318$		−	23.9401i		−	1.34249i
$319$	4.73205			0.264944
$320$	9.92820	−	8.10634i	0.555003	−	0.453158i
$321$	−5.60770			−0.312991
$322$		−	16.4901i		−	0.918957i
$323$			9.52056i			0.529738i
$324$	8.66025			0.481125
$325$	32.7846	+	6.69213i	1.81856	+	0.371213i
$326$	10.7321			0.594393
$327$		−	13.9391i		−	0.770832i
$328$		−	3.58630i		−	0.198020i
$329$	−3.46410			−0.190982
$330$	22.3923	−	18.2832i	1.23266	−	1.00646i
$331$	−7.80385			−0.428938			−0.214469	−	0.976731i	$-0.568802\pi$
$331$	−7.80385			−0.428938			−0.214469	+	0.976731i	$0.568802\pi$
$332$		−	7.82894i		−	0.429669i
$333$		−	0.656339i		−	0.0359671i
$334$	−16.1962			−0.886214
$335$	6.00000	+	7.34847i	0.327815	+	0.401490i
$336$	−15.4641			−0.843636
$337$		−	23.0064i		−	1.25324i	−0.779327	−	0.626618i	$-0.784439\pi$
$337$		−	23.0064i		−	1.25324i	0.779327	−	0.626618i	$-0.215561\pi$
$338$			61.4032i			3.33989i
$339$	−2.39230			−0.129932
$340$	−3.46410	−	4.24264i	−0.187867	−	0.230089i
$341$	24.9282			1.34994
$342$		−	13.0053i		−	0.703247i
$343$			19.5959i			1.05808i
$344$	0.339746			0.0183179
$345$	−8.53590	+	6.96953i	−0.459557	+	0.375227i
$346$	−18.3923			−0.988776
$347$			6.79367i			0.364703i	0.983233	+	0.182352i	$0.0583709\pi$
$347$			6.79367i			0.364703i	−0.983233	+	0.182352i	$0.941629\pi$
$348$		−	2.44949i		−	0.131306i
$349$	−18.7846			−1.00552			−0.502759	−	0.864427i	$-0.667682\pi$
$349$	−18.7846			−1.00552			−0.502759	+	0.864427i	$0.667682\pi$
$350$	4.73205	−	23.1822i	0.252939	−	1.23914i
$351$	37.8564			2.02063
$352$		−	35.9101i		−	1.91402i
$353$		−	12.1459i		−	0.646462i	−0.946320	−	0.323231i	$-0.895231\pi$
$353$		−	12.1459i		−	0.646462i	0.946320	−	0.323231i	$-0.104769\pi$
$354$	28.3923			1.50903
$355$	−6.00000	+	4.89898i	−0.318447	+	0.260011i
$356$	−18.0000			−0.953998
$357$			4.89898i			0.259281i
$358$			18.2832i			0.966299i
$359$	10.7321			0.566416			0.283208	−	0.959059i	$-0.408601\pi$
$359$	10.7321			0.566416			0.283208	+	0.959059i	$0.408601\pi$
$360$	−0.732051	−	0.896575i	−0.0385825	−	0.0472537i
$361$	26.3205			1.38529
$362$			30.9096i			1.62457i
$363$		−	16.1112i		−	0.845616i
$364$	28.3923			1.48816
$365$	−10.3923	−	12.7279i	−0.543958	−	0.666210i
$366$	29.8564			1.56062
$367$			25.1512i			1.31288i	0.754377	+	0.656442i	$0.227939\pi$
$367$			25.1512i			1.31288i	−0.754377	+	0.656442i	$0.772061\pi$
$368$			15.5563i			0.810931i
$369$	6.92820			0.360668
$370$	−2.19615	+	1.79315i	−0.114173	+	0.0932215i
$371$	−21.4641			−1.11436
$372$		−	12.9038i		−	0.669030i
$373$		−	19.5959i		−	1.01464i	−0.861758	−	0.507319i	$-0.830637\pi$
$373$		−	19.5959i		−	1.01464i	0.861758	−	0.507319i	$-0.169363\pi$
$374$	−12.9282			−0.668501
$375$	−14.0000	+	7.34847i	−0.722957	+	0.379473i
$376$	0.732051			0.0377526
$377$		−	6.69213i		−	0.344662i
$378$		−	26.7685i		−	1.37682i
$379$	5.80385			0.298124			0.149062	−	0.988828i	$-0.452375\pi$
$379$	5.80385			0.298124			0.149062	+	0.988828i	$0.452375\pi$
$380$	−20.1962	+	16.4901i	−1.03604	+	0.845924i
$381$	6.00000			0.307389
$382$			17.6269i			0.901871i
$383$		−	23.5612i		−	1.20392i	−0.798527	−	0.601959i	$-0.794387\pi$
$383$		−	23.5612i		−	1.20392i	0.798527	−	0.601959i	$-0.205613\pi$
$384$	5.80385			0.296176
$385$	−16.3923	−	20.0764i	−0.835429	−	1.02319i
$386$	−17.6603			−0.898883
$387$			0.656339i			0.0333636i
$388$			10.4543i			0.530737i
$389$	−20.7846			−1.05382			−0.526911	−	0.849921i	$-0.676650\pi$
$389$	−20.7846			−1.05382			−0.526911	+	0.849921i	$0.676650\pi$
$390$	−25.8564	−	31.6675i	−1.30929	−	1.60355i
$391$	4.92820			0.249230
$392$		−	0.517638i		−	0.0261447i
$393$			1.79315i			0.0904525i
$394$	32.3923			1.63190
$395$	−10.7321	+	8.76268i	−0.539988	+	0.440898i
$396$	8.19615			0.411872
$397$		−	4.89898i		−	0.245873i	−0.992415	−	0.122936i	$-0.960769\pi$
$397$		−	4.89898i		−	0.245873i	0.992415	−	0.122936i	$-0.0392311\pi$
$398$		−	27.0459i		−	1.35569i
$399$	23.3205			1.16749
$400$	−4.46410	+	21.8695i	−0.223205	+	1.09348i
$401$	10.1436			0.506547			0.253273	−	0.967395i	$-0.418493\pi$
$401$	10.1436			0.506547			0.253273	+	0.967395i	$0.418493\pi$
$402$		−	11.5911i		−	0.578112i
$403$		−	35.2538i		−	1.75612i
$404$	10.3923			0.517036
$405$	−8.66025	+	7.07107i	−0.430331	+	0.351364i
$406$	−4.73205			−0.234848
$407$			3.10583i			0.153950i
$408$		−	1.03528i		−	0.0512538i
$409$	−22.9282			−1.13373			−0.566863	−	0.823812i	$-0.691843\pi$
$409$	−22.9282			−1.13373			−0.566863	+	0.823812i	$0.691843\pi$
$410$	−18.9282	−	23.1822i	−0.934797	−	1.14489i
$411$	7.07180			0.348826
$412$		−	1.13681i		−	0.0560067i
$413$		−	25.4558i		−	1.25260i
$414$	−6.73205			−0.330862
$415$	6.39230	+	7.82894i	0.313786	+	0.384308i
$416$	−50.7846			−2.48992
$417$		−	11.3137i		−	0.554035i
$418$			61.5419i			3.01011i
$419$	6.00000			0.293119			0.146560	−	0.989202i	$-0.453180\pi$
$419$	6.00000			0.293119			0.146560	+	0.989202i	$0.453180\pi$
$420$	−10.3923	+	8.48528i	−0.507093	+	0.414039i
$421$	−1.46410			−0.0713559			−0.0356780	−	0.999363i	$-0.511359\pi$
$421$	−1.46410			−0.0713559			−0.0356780	+	0.999363i	$0.511359\pi$
$422$			21.7680i			1.05965i
$423$			1.41421i			0.0687614i
$424$	4.53590			0.220283
$425$	6.92820	+	1.41421i	0.336067	+	0.0685994i
$426$	9.46410			0.458537
$427$		−	26.7685i		−	1.29542i
$428$			6.86800i			0.331977i
$429$	−44.7846			−2.16222
$430$	2.19615	−	1.79315i	0.105908	−	0.0864734i
$431$	25.1769			1.21273			0.606365	−	0.795187i	$-0.292627\pi$
$431$	25.1769			1.21273			0.606365	+	0.795187i	$0.292627\pi$
$432$			25.2528i			1.21497i
$433$			22.5259i			1.08252i	0.840854	+	0.541262i	$0.182053\pi$
$433$			22.5259i			1.08252i	−0.840854	+	0.541262i	$0.817947\pi$
$434$	−24.9282			−1.19659
$435$	2.00000	+	2.44949i	0.0958927	+	0.117444i
$436$	−17.0718			−0.817591
$437$		−	23.4596i		−	1.12223i
$438$			20.0764i			0.959287i
$439$	20.9282			0.998849			0.499424	−	0.866358i	$-0.333545\pi$
$439$	20.9282			0.998849			0.499424	+	0.866358i	$0.333545\pi$
$440$	3.46410	+	4.24264i	0.165145	+	0.202260i
$441$	1.00000			0.0476190
$442$			18.2832i			0.869645i
$443$			21.0101i			0.998221i	0.866538	+	0.499111i	$0.166340\pi$
$443$			21.0101i			0.998221i	−0.866538	+	0.499111i	$0.833660\pi$
$444$	1.60770			0.0762978
$445$	18.0000	−	14.6969i	0.853282	−	0.696702i
$446$	−46.0526			−2.18065
$447$			18.2832i			0.864768i
$448$			14.0406i			0.663356i
$449$	−1.85641			−0.0876092			−0.0438046	−	0.999040i	$-0.513948\pi$
$449$	−1.85641			−0.0876092			−0.0438046	+	0.999040i	$0.513948\pi$
$450$	−9.46410	−	1.93185i	−0.446142	−	0.0910684i
$451$	−32.7846			−1.54377
$452$			2.92996i			0.137814i
$453$		−	32.2223i		−	1.51394i
$454$	−20.5885			−0.966264
$455$	−28.3923	+	23.1822i	−1.33105	+	1.08680i
$456$	−4.92820			−0.230784
$457$		−	18.7637i		−	0.877730i	−0.898553	−	0.438865i	$-0.855381\pi$
$457$		−	18.7637i		−	0.877730i	0.898553	−	0.438865i	$-0.144619\pi$
$458$		−	44.0165i		−	2.05676i
$459$	8.00000			0.373408
$460$	8.53590	+	10.4543i	0.397988	+	0.487434i
$461$	11.0718			0.515665			0.257832	−	0.966190i	$-0.416992\pi$
$461$	11.0718			0.515665			0.257832	+	0.966190i	$0.416992\pi$
$462$			31.6675i			1.47331i
$463$			32.3238i			1.50222i	0.660179	+	0.751108i	$0.270480\pi$
$463$			32.3238i			1.50222i	−0.660179	+	0.751108i	$0.729520\pi$
$464$	4.46410			0.207241
$465$	10.5359	+	12.9038i	0.488591	+	0.598399i
$466$	−50.2487			−2.32773
$467$		−	18.1817i		−	0.841349i	−0.907212	−	0.420674i	$-0.861793\pi$
$467$		−	18.1817i		−	0.841349i	0.907212	−	0.420674i	$-0.138207\pi$
$468$		−	11.5911i		−	0.535799i
$469$	−10.3923			−0.479872
$470$	4.73205	−	3.86370i	0.218273	−	0.178219i
$471$	8.53590			0.393313
$472$			5.37945i			0.247609i
$473$		−	3.10583i		−	0.142806i
$474$	16.9282			0.777538
$475$	6.73205	−	32.9802i	0.308888	−	1.51323i
$476$	6.00000			0.275010
$477$			8.76268i			0.401216i
$478$		−	20.0764i		−	0.918273i
$479$	11.6603			0.532771			0.266385	−	0.963867i	$-0.414171\pi$
$479$	11.6603			0.532771			0.266385	+	0.963867i	$0.414171\pi$
$480$	18.5885	−	15.1774i	0.848443	−	0.692751i
$481$	4.39230			0.200272
$482$		−	8.76268i		−	0.399129i
$483$		−	12.0716i		−	0.549276i
$484$	−19.7321			−0.896911
$485$	−8.53590	−	10.4543i	−0.387595	−	0.474705i
$486$	−19.1244			−0.867498
$487$		−	6.03579i		−	0.273508i	−0.990605	−	0.136754i	$-0.956333\pi$
$487$		−	6.03579i		−	0.273508i	0.990605	−	0.136754i	$-0.0436670\pi$
$488$			5.65685i			0.256074i
$489$	7.85641			0.355279
$490$	−2.73205	−	3.34607i	−0.123421	−	0.151160i
$491$	10.7321			0.484331			0.242165	−	0.970235i	$-0.422142\pi$
$491$	10.7321			0.484331			0.242165	+	0.970235i	$0.422142\pi$
$492$			16.9706i			0.765092i
$493$		−	1.41421i		−	0.0636930i
$494$	87.0333			3.91581
$495$	−8.19615	+	6.69213i	−0.368390	+	0.300789i
$496$	23.5167			1.05593
$497$		−	8.48528i		−	0.380617i
$498$		−	12.3490i		−	0.553371i
$499$	14.9282			0.668278			0.334139	−	0.942524i	$-0.391554\pi$
$499$	14.9282			0.668278			0.334139	+	0.942524i	$0.391554\pi$
$500$	9.00000	+	17.1464i	0.402492	+	0.766812i
$501$	−11.8564			−0.529705
$502$			17.6269i			0.786727i
$503$			41.5670i			1.85338i	0.375826	+	0.926690i	$0.377359\pi$
$503$			41.5670i			1.85338i	−0.375826	+	0.926690i	$0.622641\pi$
$504$	1.26795			0.0564789
$505$	−10.3923	+	8.48528i	−0.462451	+	0.377590i
$506$	31.8564			1.41619
$507$			44.9502i			1.99631i
$508$		−	7.34847i		−	0.326036i
$509$	−26.5359			−1.17618			−0.588092	−	0.808794i	$-0.700121\pi$
$509$	−26.5359			−1.17618			−0.588092	+	0.808794i	$0.700121\pi$
$510$	−5.46410	−	6.69213i	−0.241954	−	0.296333i
$511$	18.0000			0.796273
$512$		−	29.2552i		−	1.29291i
$513$		−	38.0822i		−	1.68137i
$514$	−8.92820			−0.393806
$515$	0.928203	+	1.13681i	0.0409015	+	0.0500939i
$516$	−1.60770			−0.0707748
$517$		−	6.69213i		−	0.294320i
$518$		−	3.10583i		−	0.136462i
$519$	−13.4641			−0.591008
$520$	6.00000	−	4.89898i	0.263117	−	0.214834i
$521$	−16.3923			−0.718160			−0.359080	−	0.933307i	$-0.616909\pi$
$521$	−16.3923			−0.718160			−0.359080	+	0.933307i	$0.616909\pi$
$522$			1.93185i			0.0845548i
$523$		−	40.8091i		−	1.78446i	−0.451583	−	0.892229i	$-0.649140\pi$
$523$		−	40.8091i		−	1.78446i	0.451583	−	0.892229i	$-0.350860\pi$
$524$	2.19615			0.0959394
$525$	3.46410	−	16.9706i	0.151186	−	0.740656i
$526$	47.5167			2.07182
$527$		−	7.45001i		−	0.324527i
$528$		−	29.8744i		−	1.30011i
$529$	10.8564			0.472018
$530$	29.3205	−	23.9401i	1.27360	−	1.03989i
$531$	−10.3923			−0.450988
$532$		−	28.5617i		−	1.23831i
$533$			46.3644i			2.00827i
$534$	−28.3923			−1.22866
$535$	−5.60770	−	6.86800i	−0.242442	−	0.296929i
$536$	2.19615			0.0948593
$537$			13.3843i			0.577573i
$538$		−	23.1822i		−	0.999456i
$539$	−4.73205			−0.203824
$540$	13.8564	+	16.9706i	0.596285	+	0.730297i
$541$	21.6077			0.928987			0.464494	−	0.885576i	$-0.346236\pi$
$541$	21.6077			0.928987			0.464494	+	0.885576i	$0.346236\pi$
$542$			44.9502i			1.93078i
$543$			22.6274i			0.971035i
$544$	−10.7321			−0.460133
$545$	17.0718	−	13.9391i	0.731275	−	0.597084i
$546$	44.7846			1.91660
$547$			2.44949i			0.104733i	0.998628	+	0.0523663i	$0.0166763\pi$
$547$			2.44949i			0.104733i	−0.998628	+	0.0523663i	$0.983324\pi$
$548$		−	8.66115i		−	0.369986i
$549$	−10.9282			−0.466404
$550$	44.7846	+	9.14162i	1.90962	+	0.389800i
$551$	−6.73205			−0.286795
$552$			2.55103i			0.108579i
$553$		−	15.1774i		−	0.645409i
$554$	45.7128			1.94215
$555$	−1.60770	+	1.31268i	−0.0682429	+	0.0557201i
$556$	−13.8564			−0.587643
$557$			28.8391i			1.22195i	0.791650	+	0.610975i	$0.209223\pi$
$557$			28.8391i			1.22195i	−0.791650	+	0.610975i	$0.790777\pi$
$558$			10.1769i			0.430822i
$559$	−4.39230			−0.185775
$560$	−15.4641	−	18.9396i	−0.653478	−	0.800343i
$561$	−9.46410			−0.399575
$562$			16.9706i			0.715860i
$563$			16.1112i			0.679004i	0.940605	+	0.339502i	$0.110259\pi$
$563$			16.1112i			0.679004i	−0.940605	+	0.339502i	$0.889741\pi$
$564$	−3.46410			−0.145865
$565$	−2.39230	−	2.92996i	−0.100645	−	0.123264i
$566$	−3.80385			−0.159888
$567$		−	12.2474i		−	0.514344i
$568$			1.79315i			0.0752389i
$569$	−14.5359			−0.609377			−0.304688	−	0.952452i	$-0.598552\pi$
$569$	−14.5359			−0.609377			−0.304688	+	0.952452i	$0.598552\pi$
$570$	−31.8564	+	26.0106i	−1.33432	+	1.08947i
$571$	−4.67949			−0.195831			−0.0979153	−	0.995195i	$-0.531217\pi$
$571$	−4.67949			−0.195831			−0.0979153	+	0.995195i	$0.531217\pi$
$572$			54.8497i			2.29338i
$573$			12.9038i			0.539063i
$574$	32.7846			1.36840
$575$	−17.0718	−	3.48477i	−0.711943	−	0.145325i
$576$	5.73205			0.238835
$577$		−	0.656339i		−	0.0273237i	−0.999907	−	0.0136619i	$-0.995651\pi$
$577$		−	0.656339i		−	0.0273237i	0.999907	−	0.0136619i	$-0.00434884\pi$
$578$		−	28.9778i		−	1.20532i
$579$	−12.9282			−0.537278
$580$	3.00000	−	2.44949i	0.124568	−	0.101710i
$581$	−11.0718			−0.459336
$582$			16.4901i			0.683536i
$583$		−	41.4655i		−	1.71732i
$584$	−3.80385			−0.157404
$585$	9.46410	+	11.5911i	0.391292	+	0.479233i
$586$	−49.9090			−2.06172
$587$		−	15.5563i		−	0.642079i	−0.947066	−	0.321040i	$-0.895968\pi$
$587$		−	15.5563i		−	0.642079i	0.947066	−	0.321040i	$-0.104032\pi$
$588$			2.44949i			0.101015i
$589$	−35.4641			−1.46127
$590$	28.3923	+	34.7733i	1.16889	+	1.43160i
$591$	23.7128			0.975415
$592$			2.92996i			0.120421i
$593$			28.3586i			1.16455i	0.812993	+	0.582274i	$0.197837\pi$
$593$			28.3586i			1.16455i	−0.812993	+	0.582274i	$0.802163\pi$
$594$	51.7128			2.12180
$595$	−6.00000	+	4.89898i	−0.245976	+	0.200839i
$596$	22.3923			0.917225
$597$		−	19.7990i		−	0.810319i
$598$		−	45.0518i		−	1.84230i
$599$	−4.73205			−0.193346			−0.0966732	−	0.995316i	$-0.530820\pi$
$599$	−4.73205			−0.193346			−0.0966732	+	0.995316i	$0.530820\pi$
$600$	−0.732051	+	3.58630i	−0.0298858	+	0.146410i
$601$	−24.7846			−1.01099			−0.505493	−	0.862831i	$-0.668689\pi$
$601$	−24.7846			−1.01099			−0.505493	+	0.862831i	$0.668689\pi$
$602$			3.10583i			0.126584i
$603$			4.24264i			0.172774i
$604$	−39.4641			−1.60577
$605$	19.7321	−	16.1112i	0.802222	−	0.655011i
$606$	16.3923			0.665892
$607$			26.1122i			1.05986i	0.848041	+	0.529930i	$0.177782\pi$
$607$			26.1122i			1.05986i	−0.848041	+	0.529930i	$0.822218\pi$
$608$			51.0876i			2.07187i
$609$	−3.46410			−0.140372
$610$	29.8564	+	36.5665i	1.20885	+	1.48053i
$611$	−9.46410			−0.382877
$612$		−	2.44949i		−	0.0990148i
$613$			1.31268i			0.0530185i	0.999649	+	0.0265093i	$0.00843915\pi$
$613$			1.31268i			0.0530185i	−0.999649	+	0.0265093i	$0.991561\pi$
$614$	−36.5885			−1.47659
$615$	−13.8564	−	16.9706i	−0.558744	−	0.684319i
$616$	−6.00000			−0.241747
$617$		−	7.55154i		−	0.304014i	−0.988379	−	0.152007i	$-0.951426\pi$
$617$		−	7.55154i		−	0.304014i	0.988379	−	0.152007i	$-0.0485736\pi$
$618$		−	1.79315i		−	0.0721311i
$619$	34.1962			1.37446			0.687230	−	0.726440i	$-0.258827\pi$
$619$	34.1962			1.37446			0.687230	+	0.726440i	$0.258827\pi$
$620$	15.8038	−	12.9038i	0.634698	−	0.518229i
$621$	−19.7128			−0.791048
$622$		−	47.5013i		−	1.90463i
$623$			25.4558i			1.01987i
$624$	−42.2487			−1.69130
$625$	−23.0000	−	9.79796i	−0.920000	−	0.391918i
$626$	36.2487			1.44879
$627$			45.0518i			1.79919i
$628$		−	10.4543i		−	0.417172i
$629$	0.928203			0.0370099
$630$	8.19615	−	6.69213i	0.326543	−	0.266621i
$631$	36.3923			1.44875			0.724377	−	0.689404i	$-0.242127\pi$
$631$	36.3923			1.44875			0.724377	+	0.689404i	$0.242127\pi$
$632$			3.20736i			0.127582i
$633$			15.9353i			0.633371i
$634$	−48.9808			−1.94527
$635$	6.00000	+	7.34847i	0.238103	+	0.291615i
$636$	−21.4641			−0.851107
$637$			6.69213i			0.265152i
$638$		−	9.14162i		−	0.361920i
$639$	−3.46410			−0.137038
$640$	5.80385	+	7.10823i	0.229417	+	0.280978i
$641$	−34.6410			−1.36824			−0.684119	−	0.729370i	$-0.739813\pi$
$641$	−34.6410			−1.36824			−0.684119	+	0.729370i	$0.739813\pi$
$642$			10.8332i			0.427554i
$643$		−	18.9396i		−	0.746904i	−0.927649	−	0.373452i	$-0.878174\pi$
$643$		−	18.9396i		−	0.746904i	0.927649	−	0.373452i	$-0.121826\pi$
$644$	−14.7846			−0.582595
$645$	1.60770	−	1.31268i	0.0633029	−	0.0516866i
$646$	18.3923			0.723636
$647$		−	19.9749i		−	0.785293i	−0.919690	−	0.392646i	$-0.871560\pi$
$647$		−	19.9749i		−	0.785293i	0.919690	−	0.392646i	$-0.128440\pi$
$648$			2.58819i			0.101674i
$649$	49.1769			1.93036
$650$	12.9282	−	63.3350i	0.507086	−	2.48420i
$651$	−18.2487			−0.715223
$652$		−	9.62209i		−	0.376830i
$653$		−	1.69161i		−	0.0661980i	−0.999452	−	0.0330990i	$-0.989462\pi$
$653$		−	1.69161i		−	0.0661980i	0.999452	−	0.0330990i	$-0.0105377\pi$
$654$	−26.9282			−1.05298
$655$	−2.19615	+	1.79315i	−0.0858108	+	0.0700642i
$656$	−30.9282			−1.20754
$657$		−	7.34847i		−	0.286691i
$658$			6.69213i			0.260886i
$659$	26.4449			1.03015			0.515073	−	0.857146i	$-0.327765\pi$
$659$	26.4449			1.03015			0.515073	+	0.857146i	$0.327765\pi$
$660$	−16.3923	−	20.0764i	−0.638070	−	0.781472i
$661$	40.7846			1.58634			0.793169	−	0.609002i	$-0.208430\pi$
$661$	40.7846			1.58634			0.793169	+	0.609002i	$0.208430\pi$
$662$			15.0759i			0.585941i
$663$			13.3843i			0.519802i
$664$	2.33975			0.0907998
$665$	23.3205	+	28.5617i	0.904331	+	1.10757i
$666$	−1.26795			−0.0491320
$667$			3.48477i			0.134931i
$668$			14.5211i			0.561837i
$669$	−33.7128			−1.30341
$670$	14.1962	−	11.5911i	0.548445	−	0.447804i
$671$	51.7128			1.99635
$672$			26.2880i			1.01408i
$673$			12.4233i			0.478884i	0.970911	+	0.239442i	$0.0769644\pi$
$673$			12.4233i			0.478884i	−0.970911	+	0.239442i	$0.923036\pi$
$674$	−44.4449			−1.71195
$675$	−27.7128	−	5.65685i	−1.06667	−	0.217732i
$676$	55.0526			2.11741
$677$			46.9464i			1.80430i	0.431424	+	0.902149i	$0.358011\pi$
$677$			46.9464i			1.80430i	−0.431424	+	0.902149i	$0.641989\pi$
$678$			4.62158i			0.177491i
$679$	14.7846			0.567381
$680$	1.26795	−	1.03528i	0.0486236	−	0.0397010i
$681$	−15.0718			−0.577553
$682$		−	48.1576i		−	1.84405i
$683$			31.7690i			1.21561i	0.794087	+	0.607804i	$0.207949\pi$
$683$			31.7690i			1.21561i	−0.794087	+	0.607804i	$0.792051\pi$
$684$	−11.6603			−0.445841
$685$	7.07180	+	8.66115i	0.270199	+	0.330925i
$686$	37.8564			1.44536
$687$		−	32.2223i		−	1.22936i
$688$		−	2.92996i		−	0.111704i
$689$	−58.6410			−2.23404
$690$	13.4641	+	16.4901i	0.512570	+	0.627767i
$691$	−13.7128			−0.521660			−0.260830	−	0.965385i	$-0.583996\pi$
$691$	−13.7128			−0.521660			−0.260830	+	0.965385i	$0.583996\pi$
$692$			16.4901i			0.626859i
$693$		−	11.5911i		−	0.440310i
$694$	13.1244			0.498194
$695$	13.8564	−	11.3137i	0.525603	−	0.429153i
$696$	0.732051			0.0277483
$697$			9.79796i			0.371124i
$698$			36.2891i			1.37356i
$699$	−36.7846			−1.39132
$700$	−20.7846	−	4.24264i	−0.785584	−	0.160357i
$701$	−27.7128			−1.04670			−0.523349	−	0.852118i	$-0.675318\pi$
$701$	−27.7128			−1.04670			−0.523349	+	0.852118i	$0.675318\pi$
$702$		−	73.1330i		−	2.76023i
$703$		−	4.41851i		−	0.166647i
$704$	−27.1244			−1.02229
$705$	3.46410	−	2.82843i	0.130466	−	0.106525i
$706$	−23.4641			−0.883083
$707$		−	14.6969i		−	0.552735i
$708$		−	25.4558i		−	0.956689i
$709$	0.392305			0.0147333			0.00736666	−	0.999973i	$-0.497655\pi$
$709$	0.392305			0.0147333			0.00736666	+	0.999973i	$0.497655\pi$
$710$	9.46410	+	11.5911i	0.355181	+	0.435007i
$711$	−6.19615			−0.232374
$712$		−	5.37945i		−	0.201604i
$713$			18.3576i			0.687496i
$714$	9.46410			0.354185
$715$	−44.7846	−	54.8497i	−1.67485	−	2.05126i
$716$	16.3923			0.612609
$717$		−	14.6969i		−	0.548867i
$718$		−	20.7327i		−	0.773739i
$719$	−7.85641			−0.292995			−0.146497	−	0.989211i	$-0.546800\pi$
$719$	−7.85641			−0.292995			−0.146497	+	0.989211i	$0.546800\pi$
$720$	−7.73205	+	6.31319i	−0.288157	+	0.235279i
$721$	−1.60770			−0.0598737
$722$		−	50.8473i		−	1.89234i
$723$		−	6.41473i		−	0.238566i
$724$	27.7128			1.02994
$725$	−1.00000	+	4.89898i	−0.0371391	+	0.181944i
$726$	−31.1244			−1.15513
$727$		−	46.6690i		−	1.73086i	−0.501031	−	0.865430i	$-0.667046\pi$
$727$		−	46.6690i		−	1.73086i	0.501031	−	0.865430i	$-0.332954\pi$
$728$			8.48528i			0.314485i
$729$	−29.0000			−1.07407
$730$	−24.5885	+	20.0764i	−0.910060	+	0.743061i
$731$	−0.928203			−0.0343308
$732$		−	26.7685i		−	0.989393i
$733$		−	12.7279i		−	0.470117i	−0.971981	−	0.235058i	$-0.924472\pi$
$733$		−	12.7279i		−	0.470117i	0.971981	−	0.235058i	$-0.0755281\pi$
$734$	48.5885			1.79343
$735$	−2.00000	−	2.44949i	−0.0737711	−	0.0903508i
$736$	26.4449			0.974771
$737$		−	20.0764i		−	0.739523i
$738$		−	13.3843i		−	0.492681i
$739$	−32.9808			−1.21322			−0.606608	−	0.795001i	$-0.707470\pi$
$739$	−32.9808			−1.21322			−0.606608	+	0.795001i	$0.707470\pi$
$740$	1.60770	+	1.96902i	0.0591000	+	0.0723825i
$741$	63.7128			2.34055
$742$			41.4655i			1.52224i
$743$			9.89949i			0.363177i	0.983375	+	0.181589i	$0.0581239\pi$
$743$			9.89949i			0.363177i	−0.983375	+	0.181589i	$0.941876\pi$
$744$	3.85641			0.141383
$745$	−22.3923	+	18.2832i	−0.820391	+	0.669846i
$746$	−37.8564			−1.38602
$747$			4.52004i			0.165380i
$748$			11.5911i			0.423813i
$749$	9.71281			0.354898
$750$	14.1962	+	27.0459i	0.518370	+	0.987577i
$751$	−15.9090			−0.580526			−0.290263	−	0.956947i	$-0.593743\pi$
$751$	−15.9090			−0.580526			−0.290263	+	0.956947i	$0.593743\pi$
$752$		−	6.31319i		−	0.230218i
$753$			12.9038i			0.470240i
$754$	−12.9282			−0.470817
$755$	39.4641	−	32.2223i	1.43625	−	1.17269i
$756$	−24.0000			−0.872872
$757$			6.03579i			0.219375i	0.993966	+	0.109687i	$0.0349849\pi$
$757$			6.03579i			0.219375i	−0.993966	+	0.109687i	$0.965015\pi$
$758$		−	11.2122i		−	0.407244i
$759$	23.3205			0.846481
$760$	−4.92820	−	6.03579i	−0.178765	−	0.218941i
$761$	47.5692			1.72438			0.862191	−	0.506583i	$-0.169091\pi$
$761$	47.5692			1.72438			0.862191	+	0.506583i	$0.169091\pi$
$762$		−	11.5911i		−	0.419902i
$763$			24.1432i			0.874041i
$764$	15.8038			0.571763
$765$	2.00000	+	2.44949i	0.0723102	+	0.0885615i
$766$	−45.5167			−1.64458
$767$		−	69.5467i		−	2.51118i
$768$		−	27.4249i		−	0.989609i
$769$	32.9282			1.18742			0.593711	−	0.804679i	$-0.297662\pi$
$769$	32.9282			1.18742			0.593711	+	0.804679i	$0.297662\pi$
$770$	−38.7846	+	31.6675i	−1.39770	+	1.14122i
$771$	−6.53590			−0.235385
$772$			15.8338i			0.569869i
$773$		−	8.38375i		−	0.301542i	−0.988569	−	0.150771i	$-0.951824\pi$
$773$		−	8.38375i		−	0.301542i	0.988569	−	0.150771i	$-0.0481757\pi$
$774$	1.26795			0.0455755
$775$	−5.26795	+	25.8076i	−0.189230	+	0.927035i
$776$	−3.12436			−0.112158
$777$		−	2.27362i		−	0.0815658i
$778$			40.1528i			1.43955i
$779$	46.6410			1.67109
$780$	−28.3923	+	23.1822i	−1.01661	+	0.830057i
$781$	16.3923			0.586563
$782$		−	9.52056i		−	0.340454i
$783$			5.65685i			0.202159i
$784$	−4.46410			−0.159432
$785$	8.53590	+	10.4543i	0.304659	+	0.373130i
$786$	3.46410			0.123560
$787$			49.7749i			1.77428i	0.461498	+	0.887141i	$0.347312\pi$
$787$			49.7749i			1.77428i	−0.461498	+	0.887141i	$0.652688\pi$
$788$		−	29.0421i		−	1.03458i
$789$	34.7846			1.23836
$790$	16.9282	+	20.7327i	0.602278	+	0.737637i
$791$	4.14359			0.147329
$792$			2.44949i			0.0870388i
$793$		−	73.1330i		−	2.59703i
$794$	−9.46410			−0.335868
$795$	21.4641	−	17.5254i	0.761253	−	0.621561i
$796$	−24.2487			−0.859473
$797$		−	34.6718i		−	1.22814i	−0.789252	−	0.614069i	$-0.789532\pi$
$797$		−	34.6718i		−	1.22814i	0.789252	−	0.614069i	$-0.210468\pi$
$798$		−	45.0518i		−	1.59482i
$799$	−2.00000			−0.0707549
$800$	37.1769	+	7.58871i	1.31440	+	0.268301i
$801$	10.3923			0.367194
$802$		−	19.5959i		−	0.691956i
$803$			34.7733i			1.22712i
$804$	−10.3923			−0.366508
$805$	14.7846	−	12.0716i	0.521089	−	0.425467i
$806$	−68.1051			−2.39890
$807$		−	16.9706i		−	0.597392i
$808$			3.10583i			0.109263i
$809$	−34.3923			−1.20917			−0.604585	−	0.796541i	$-0.706661\pi$
$809$	−34.3923			−1.20917			−0.604585	+	0.796541i	$0.706661\pi$
$810$	13.6603	+	16.7303i	0.479972	+	0.587844i
$811$	4.78461			0.168010			0.0840052	−	0.996465i	$-0.473229\pi$
$811$	4.78461			0.168010			0.0840052	+	0.996465i	$0.473229\pi$
$812$			4.24264i			0.148888i
$813$			32.9058i			1.15406i
$814$	6.00000			0.210300
$815$	7.85641	+	9.62209i	0.275198	+	0.337047i
$816$	−8.92820			−0.312550
$817$			4.41851i			0.154584i
$818$			44.2939i			1.54870i
$819$	−16.3923			−0.572793
$820$	−20.7846	+	16.9706i	−0.725830	+	0.592638i
$821$	50.7846			1.77240			0.886198	−	0.463308i	$-0.153337\pi$
$821$	50.7846			1.77240			0.886198	+	0.463308i	$0.153337\pi$
$822$		−	13.6617i		−	0.476505i
$823$			1.61729i			0.0563750i	0.999603	+	0.0281875i	$0.00897355\pi$
$823$			1.61729i			0.0563750i	−0.999603	+	0.0281875i	$0.991026\pi$
$824$	0.339746			0.0118356
$825$	32.7846	+	6.69213i	1.14141	+	0.232990i
$826$	−49.1769			−1.71108
$827$			33.0817i			1.15036i	0.818025	+	0.575182i	$0.195069\pi$
$827$			33.0817i			1.15036i	−0.818025	+	0.575182i	$0.804931\pi$
$828$			6.03579i			0.209758i
$829$	−24.7846			−0.860805			−0.430403	−	0.902637i	$-0.641628\pi$
$829$	−24.7846			−0.860805			−0.430403	+	0.902637i	$0.641628\pi$
$830$	15.1244	−	12.3490i	0.524974	−	0.428640i
$831$	33.4641			1.16086
$832$			38.3596i			1.32988i
$833$			1.41421i			0.0489996i
$834$	−21.8564			−0.756825
$835$	−11.8564	−	14.5211i	−0.410308	−	0.502522i
$836$	55.1769			1.90833
$837$			29.8000i			1.03004i
$838$		−	11.5911i		−	0.400408i
$839$	10.9808			0.379098			0.189549	−	0.981871i	$-0.439297\pi$
$839$	10.9808			0.379098			0.189549	+	0.981871i	$0.439297\pi$
$840$	−2.53590	−	3.10583i	−0.0874968	−	0.107161i
$841$	1.00000			0.0344828
$842$			2.82843i			0.0974740i
$843$			12.4233i			0.427882i
$844$	19.5167			0.671791
$845$	−55.0526	+	44.9502i	−1.89387	+	1.54633i
$846$	2.73205			0.0939298
$847$			27.9053i			0.958839i
$848$		−	39.1175i		−	1.34330i
$849$	−2.78461			−0.0955676
$850$	2.73205	−	13.3843i	0.0937086	−	0.459076i
$851$	−2.28719			−0.0784038
$852$		−	8.48528i		−	0.290701i
$853$			6.86800i			0.235156i	0.993064	+	0.117578i	$0.0375130\pi$
$853$			6.86800i			0.235156i	−0.993064	+	0.117578i	$0.962487\pi$
$854$	−51.7128			−1.76958
$855$	11.6603	−	9.52056i	0.398772	−	0.325596i
$856$	−2.05256			−0.0701550
$857$		−	30.4292i		−	1.03944i	−0.854337	−	0.519720i	$-0.826036\pi$
$857$		−	30.4292i		−	1.03944i	0.854337	−	0.519720i	$-0.173964\pi$
$858$			86.5172i			2.95365i
$859$	15.2679			0.520936			0.260468	−	0.965483i	$-0.416123\pi$
$859$	15.2679			0.520936			0.260468	+	0.965483i	$0.416123\pi$
$860$	−1.60770	−	1.96902i	−0.0548219	−	0.0671429i
$861$	24.0000			0.817918
$862$		−	48.6381i		−	1.65662i
$863$			13.0053i			0.442706i	0.975194	+	0.221353i	$0.0710474\pi$
$863$			13.0053i			0.442706i	−0.975194	+	0.221353i	$0.928953\pi$
$864$	42.9282			1.46045
$865$	−13.4641	−	16.4901i	−0.457793	−	0.560680i
$866$	43.5167			1.47876
$867$		−	21.2132i		−	0.720438i
$868$			22.3500i			0.758609i
$869$	29.3205			0.994630
$870$	4.73205	−	3.86370i	0.160432	−	0.130992i
$871$	−28.3923			−0.962037
$872$		−	5.10205i		−	0.172777i
$873$		−	6.03579i		−	0.204281i
$874$	−45.3205			−1.53299
$875$	24.2487	−	12.7279i	0.819756	−	0.430282i
$876$	18.0000			0.608164
$877$			0.480473i			0.0162244i	0.999967	+	0.00811222i	$0.00258223\pi$
$877$			0.480473i			0.0162244i	−0.999967	+	0.00811222i	$0.997418\pi$
$878$		−	40.4302i		−	1.36445i
$879$	−36.5359			−1.23233
$880$	36.5885	−	29.8744i	1.23340	−	1.00706i
$881$	−57.4641			−1.93601			−0.968007	−	0.250922i	$-0.919266\pi$
$881$	−57.4641			−1.93601			−0.968007	+	0.250922i	$0.919266\pi$
$882$		−	1.93185i		−	0.0650488i
$883$			52.4002i			1.76341i	0.471803	+	0.881704i	$0.343603\pi$
$883$			52.4002i			1.76341i	−0.471803	+	0.881704i	$0.656397\pi$
$884$	16.3923			0.551333
$885$	20.7846	+	25.4558i	0.698667	+	0.855689i
$886$	40.5885			1.36360
$887$		−	18.1817i		−	0.610482i	−0.952275	−	0.305241i	$-0.901263\pi$
$887$		−	18.1817i		−	0.610482i	0.952275	−	0.305241i	$-0.0987370\pi$
$888$			0.480473i			0.0161236i
$889$	−10.3923			−0.348547
$890$	−28.3923	−	34.7733i	−0.951712	−	1.16560i
$891$	23.6603			0.792648
$892$			41.2896i			1.38248i
$893$			9.52056i			0.318593i
$894$	35.3205			1.18129
$895$	−16.3923	+	13.3843i	−0.547934	+	0.447386i
$896$	−10.0526			−0.335832
$897$		−	32.9802i		−	1.10118i
$898$			3.58630i			0.119676i
$899$	5.26795			0.175696
$900$	−1.73205	+	8.48528i	−0.0577350	+	0.282843i
$901$	−12.3923			−0.412848
$902$			63.3350i			2.10882i
$903$			2.27362i			0.0756615i
$904$	−0.875644			−0.0291235
$905$	−27.7128	+	22.6274i	−0.921205	+	0.752161i
$906$	−62.2487			−2.06807
$907$			3.28169i			0.108967i	0.998515	+	0.0544834i	$0.0173512\pi$
$907$			3.28169i			0.108967i	−0.998515	+	0.0544834i	$0.982649\pi$
$908$			18.4591i			0.612587i
$909$	−6.00000			−0.199007
$910$	44.7846	+	54.8497i	1.48460	+	1.81825i
$911$	−20.1962			−0.669128			−0.334564	−	0.942373i	$-0.608589\pi$
$911$	−20.1962			−0.669128			−0.334564	+	0.942373i	$0.608589\pi$
$912$			42.5007i			1.40734i
$913$		−	21.3891i		−	0.707875i
$914$	−36.2487			−1.19900
$915$	21.8564	+	26.7685i	0.722551	+	0.884940i
$916$	−39.4641			−1.30393
$917$		−	3.10583i		−	0.102563i
$918$		−	15.4548i		−	0.510085i
$919$	59.9615			1.97795			0.988974	−	0.148089i	$-0.0473121\pi$
$919$	59.9615			1.97795			0.988974	+	0.148089i	$0.0473121\pi$
$920$	−3.12436	+	2.55103i	−0.103007	+	0.0841048i
$921$	−26.7846			−0.882583
$922$		−	21.3891i		−	0.704411i
$923$		−	23.1822i		−	0.763052i
$924$	28.3923			0.934038
$925$	−3.21539	−	0.656339i	−0.105721	−	0.0215803i
$926$	62.4449			2.05207
$927$			0.656339i			0.0215570i
$928$		−	7.58871i		−	0.249111i
$929$	−28.1436			−0.923361			−0.461681	−	0.887046i	$-0.652753\pi$
$929$	−28.1436			−0.923361			−0.461681	+	0.887046i	$0.652753\pi$
$930$	24.9282	−	20.3538i	0.817428	−	0.667427i
$931$	6.73205			0.220634
$932$			45.0518i			1.47572i
$933$		−	34.7733i		−	1.13843i
$934$	−35.1244			−1.14930
$935$	−9.46410	−	11.5911i	−0.309509	−	0.379070i
$936$	3.46410			0.113228
$937$			56.6429i			1.85044i	0.379429	+	0.925221i	$0.376121\pi$
$937$			56.6429i			1.85044i	−0.379429	+	0.925221i	$0.623879\pi$
$938$			20.0764i			0.655517i
$939$	26.5359			0.865966
$940$	−3.46410	−	4.24264i	−0.112987	−	0.138380i
$941$	19.8564			0.647300			0.323650	−	0.946177i	$-0.395090\pi$
$941$	19.8564			0.647300			0.323650	+	0.946177i	$0.395090\pi$
$942$		−	16.4901i		−	0.537276i
$943$		−	24.1432i		−	0.786210i
$944$	46.3923			1.50994
$945$	24.0000	−	19.5959i	0.780720	−	0.637455i
$946$	−6.00000			−0.195077
$947$			30.8081i			1.00113i	0.865699	+	0.500564i	$0.166874\pi$
$947$			30.8081i			1.00113i	−0.865699	+	0.500564i	$0.833126\pi$
$948$		−	15.1774i		−	0.492939i
$949$	49.1769			1.59635
$950$	−63.7128	−	13.0053i	−2.06712	−	0.421948i
$951$	−35.8564			−1.16272
$952$			1.79315i			0.0581164i
$953$			5.65685i			0.183243i	0.995794	+	0.0916217i	$0.0292051\pi$
$953$			5.65685i			0.183243i	−0.995794	+	0.0916217i	$0.970795\pi$
$954$	16.9282			0.548071
$955$	−15.8038	+	12.9038i	−0.511400	+	0.417557i
$956$	−18.0000			−0.582162
$957$		−	6.69213i		−	0.216326i
$958$		−	22.5259i		−	0.727778i
$959$	−12.2487			−0.395532
$960$	−11.4641	−	14.0406i	−0.370002	−	0.453158i
$961$	−3.24871			−0.104797
$962$		−	8.48528i		−	0.273576i
$963$		−	3.96524i		−	0.127778i
$964$	−7.85641			−0.253038
$965$	−12.9282	−	15.8338i	−0.416174	−	0.509706i
$966$	−23.3205			−0.750325
$967$			27.4249i			0.881924i	0.897526	+	0.440962i	$0.145363\pi$
$967$			27.4249i			0.881924i	−0.897526	+	0.440962i	$0.854637\pi$
$968$		−	5.89709i		−	0.189540i
$969$	13.4641			0.432529
$970$	−20.1962	+	16.4901i	−0.648459	+	0.529465i
$971$	−4.48334			−0.143877			−0.0719386	−	0.997409i	$-0.522919\pi$
$971$	−4.48334			−0.143877			−0.0719386	+	0.997409i	$0.522919\pi$
$972$			17.1464i			0.549972i
$973$			19.5959i			0.628216i
$974$	−11.6603			−0.373619
$975$	9.46410	−	46.3644i	0.303094	−	1.48485i
$976$	48.7846			1.56156
$977$		−	8.20788i		−	0.262593i	−0.991343	−	0.131297i	$-0.958086\pi$
$977$		−	8.20788i		−	0.262593i	0.991343	−	0.131297i	$-0.0419140\pi$
$978$		−	15.1774i		−	0.485320i
$979$	−49.1769			−1.57170
$980$	−3.00000	+	2.44949i	−0.0958315	+	0.0782461i
$981$	9.85641			0.314691
$982$		−	20.7327i		−	0.661608i
$983$		−	0.859411i		−	0.0274109i	−0.999906	−	0.0137055i	$-0.995637\pi$
$983$		−	0.859411i		−	0.0274109i	0.999906	−	0.0137055i	$-0.00436272\pi$
$984$	−5.07180			−0.161683
$985$	23.7128	+	29.0421i	0.755553	+	0.925360i
$986$	−2.73205			−0.0870062
$987$			4.89898i			0.155936i
$988$		−	78.0319i		−	2.48253i
$989$	2.28719			0.0727283
$990$	12.9282	+	15.8338i	0.410885	+	0.503230i
$991$	−6.78461			−0.215520			−0.107760	−	0.994177i	$-0.534368\pi$
$991$	−6.78461			−0.215520			−0.107760	+	0.994177i	$0.534368\pi$
$992$		−	39.9769i		−	1.26927i
$993$			11.0363i			0.350227i
$994$	−16.3923			−0.519932
$995$	24.2487	−	19.7990i	0.768736	−	0.627670i
$996$	−11.0718			−0.350823
$997$			41.2896i			1.30765i	0.756644	+	0.653827i	$0.226838\pi$
$997$			41.2896i			1.30765i	−0.756644	+	0.653827i	$0.773162\pi$
$998$		−	28.8391i		−	0.912885i
$999$	−3.71281			−0.117468

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	145.2.b.b.59.1	✓	4
3.2	odd	2		1305.2.c.f.784.4		4
4.3	odd	2		2320.2.d.f.929.4		4
5.2	odd	4		725.2.a.f.1.4		4
5.3	odd	4		725.2.a.f.1.1		4
5.4	even	2	inner	145.2.b.b.59.4	yes	4
15.2	even	4		6525.2.a.bj.1.1		4
15.8	even	4		6525.2.a.bj.1.4		4
15.14	odd	2		1305.2.c.f.784.1		4
20.19	odd	2		2320.2.d.f.929.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.b.b.59.1	✓	4	1.1	even	1	trivial
145.2.b.b.59.4	yes	4	5.4	even	2	inner
725.2.a.f.1.1		4	5.3	odd	4
725.2.a.f.1.4		4	5.2	odd	4
1305.2.c.f.784.1		4	15.14	odd	2
1305.2.c.f.784.4		4	3.2	odd	2
2320.2.d.f.929.2		4	20.19	odd	2
2320.2.d.f.929.4		4	4.3	odd	2
6525.2.a.bj.1.1		4	15.2	even	4
6525.2.a.bj.1.4		4	15.8	even	4

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:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	145.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.93185i q^{2} -1.41421i q^{3} -1.73205 q^{4} +(1.73205 - 1.41421i) q^{5} -2.73205 q^{6} +2.44949i q^{7} -0.517638i q^{8} +1.00000 q^{9} +(-2.73205 - 3.34607i) q^{10} -4.73205 q^{11} +2.44949i q^{12} +6.69213i q^{13} +4.73205 q^{14} +(-2.00000 - 2.44949i) q^{15} -4.46410 q^{16} +1.41421i q^{17} -1.93185i q^{18} +6.73205 q^{19} +(-3.00000 + 2.44949i) q^{20} +3.46410 q^{21} +9.14162i q^{22} -3.48477i q^{23} -0.732051 q^{24} +(1.00000 - 4.89898i) q^{25} +12.9282 q^{26} -5.65685i q^{27} -4.24264i q^{28} -1.00000 q^{29} +(-4.73205 + 3.86370i) q^{30} -5.26795 q^{31} +7.58871i q^{32} +6.69213i q^{33} +2.73205 q^{34} +(3.46410 + 4.24264i) q^{35} -1.73205 q^{36} -0.656339i q^{37} -13.0053i q^{38} +9.46410 q^{39} +(-0.732051 - 0.896575i) q^{40} +6.92820 q^{41} -6.69213i q^{42} +0.656339i q^{43} +8.19615 q^{44} +(1.73205 - 1.41421i) q^{45} -6.73205 q^{46} +1.41421i q^{47} +6.31319i q^{48} +1.00000 q^{49} +(-9.46410 - 1.93185i) q^{50} +2.00000 q^{51} -11.5911i q^{52} +8.76268i q^{53} -10.9282 q^{54} +(-8.19615 + 6.69213i) q^{55} +1.26795 q^{56} -9.52056i q^{57} +1.93185i q^{58} -10.3923 q^{59} +(3.46410 + 4.24264i) q^{60} -10.9282 q^{61} +10.1769i q^{62} +2.44949i q^{63} +5.73205 q^{64} +(9.46410 + 11.5911i) q^{65} +12.9282 q^{66} +4.24264i q^{67} -2.44949i q^{68} -4.92820 q^{69} +(8.19615 - 6.69213i) q^{70} -3.46410 q^{71} -0.517638i q^{72} -7.34847i q^{73} -1.26795 q^{74} +(-6.92820 - 1.41421i) q^{75} -11.6603 q^{76} -11.5911i q^{77} -18.2832i q^{78} -6.19615 q^{79} +(-7.73205 + 6.31319i) q^{80} -5.00000 q^{81} -13.3843i q^{82} +4.52004i q^{83} -6.00000 q^{84} +(2.00000 + 2.44949i) q^{85} +1.26795 q^{86} +1.41421i q^{87} +2.44949i q^{88} +10.3923 q^{89} +(-2.73205 - 3.34607i) q^{90} -16.3923 q^{91} +6.03579i q^{92} +7.45001i q^{93} +2.73205 q^{94} +(11.6603 - 9.52056i) q^{95} +10.7321 q^{96} -6.03579i q^{97} -1.93185i q^{98} -4.73205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{6} + 4 q^{9} - 4 q^{10} - 12 q^{11} + 12 q^{14} - 8 q^{15} - 4 q^{16} + 20 q^{19} - 12 q^{20} + 4 q^{24} + 4 q^{25} + 24 q^{26} - 4 q^{29} - 12 q^{30} - 28 q^{31} + 4 q^{34} + 24 q^{39} + 4 q^{40}+ \cdots - 12 q^{99}+O(q^{100}) \) 4 * q - 4 * q^6 + 4 * q^9 - 4 * q^10 - 12 * q^11 + 12 * q^14 - 8 * q^15 - 4 * q^16 + 20 * q^19 - 12 * q^20 + 4 * q^24 + 4 * q^25 + 24 * q^26 - 4 * q^29 - 12 * q^30 - 28 * q^31 + 4 * q^34 + 24 * q^39 + 4 * q^40 + 12 * q^44 - 20 * q^46 + 4 * q^49 - 24 * q^50 + 8 * q^51 - 16 * q^54 - 12 * q^55 + 12 * q^56 - 16 * q^61 + 16 * q^64 + 24 * q^65 + 24 * q^66 + 8 * q^69 + 12 * q^70 - 12 * q^74 - 12 * q^76 - 4 * q^79 - 24 * q^80 - 20 * q^81 - 24 * q^84 + 8 * q^85 + 12 * q^86 - 4 * q^90 - 24 * q^91 + 4 * q^94 + 12 * q^95 + 36 * q^96 - 12 * q^99

Introduction

L-functions

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