LMFDB - Embedded newform 430.2.b.b.259.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(259,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, 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("430.259");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 38x^{14} + 525x^{12} + 3518x^{10} + 12216x^{8} + 20990x^{6} + 15229x^{4} + 4754x^{2} + 529 $ x^16 + 38x^14 + 525x^12 + 3518x^10 + 12216x^8 + 20990x^6 + 15229x^4 + 4754*x^2 + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			259.7
Root			$1.99373i$ of defining polynomial
Character	$\chi$	$=$	430.259
Dual form			430.2.b.b.259.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +2.99373i q^{3} -1.00000 q^{4} +(0.260869 - 2.22080i) q^{5} +2.99373 q^{6} -4.62603i q^{7} +1.00000i q^{8} -5.96240 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +2.99373i q^{3} -1.00000 q^{4} +(0.260869 - 2.22080i) q^{5} +2.99373 q^{6} -4.62603i q^{7} +1.00000i q^{8} -5.96240 q^{9} +(-2.22080 - 0.260869i) q^{10} -3.48854 q^{11} -2.99373i q^{12} -4.77797i q^{13} -4.62603 q^{14} +(6.64846 + 0.780970i) q^{15} +1.00000 q^{16} -2.65039i q^{17} +5.96240i q^{18} +2.10429 q^{19} +(-0.260869 + 2.22080i) q^{20} +13.8491 q^{21} +3.48854i q^{22} +4.96680i q^{23} -2.99373 q^{24} +(-4.86390 - 1.15867i) q^{25} -4.77797 q^{26} -8.86861i q^{27} +4.62603i q^{28} +10.1703 q^{29} +(0.780970 - 6.64846i) q^{30} -3.61975 q^{31} -1.00000i q^{32} -10.4437i q^{33} -2.65039 q^{34} +(-10.2735 - 1.20679i) q^{35} +5.96240 q^{36} -5.36680i q^{37} -2.10429i q^{38} +14.3039 q^{39} +(2.22080 + 0.260869i) q^{40} -0.557498 q^{41} -13.8491i q^{42} +1.00000i q^{43} +3.48854 q^{44} +(-1.55540 + 13.2413i) q^{45} +4.96680 q^{46} -3.17119i q^{47} +2.99373i q^{48} -14.4001 q^{49} +(-1.15867 + 4.86390i) q^{50} +7.93453 q^{51} +4.77797i q^{52} -2.74193i q^{53} -8.86861 q^{54} +(-0.910050 + 7.74734i) q^{55} +4.62603 q^{56} +6.29967i q^{57} -10.1703i q^{58} +7.03093 q^{59} +(-6.64846 - 0.780970i) q^{60} -9.73316 q^{61} +3.61975i q^{62} +27.5822i q^{63} -1.00000 q^{64} +(-10.6109 - 1.24642i) q^{65} -10.4437 q^{66} +7.69046i q^{67} +2.65039i q^{68} -14.8692 q^{69} +(-1.20679 + 10.2735i) q^{70} +6.01121 q^{71} -5.96240i q^{72} +8.26651i q^{73} -5.36680 q^{74} +(3.46875 - 14.5612i) q^{75} -2.10429 q^{76} +16.1381i q^{77} -14.3039i q^{78} +7.97824 q^{79} +(0.260869 - 2.22080i) q^{80} +8.66301 q^{81} +0.557498i q^{82} +3.32959i q^{83} -13.8491 q^{84} +(-5.88598 - 0.691403i) q^{85} +1.00000 q^{86} +30.4470i q^{87} -3.48854i q^{88} +15.8770 q^{89} +(13.2413 + 1.55540i) q^{90} -22.1030 q^{91} -4.96680i q^{92} -10.8366i q^{93} -3.17119 q^{94} +(0.548943 - 4.67320i) q^{95} +2.99373 q^{96} -11.0593i q^{97} +14.4001i q^{98} +20.8000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} + 2 q^{5} + 8 q^{6} - 28 q^{9}+O(q^{10}) $ 16 * q - 16 * q^4 + 2 * q^5 + 8 * q^6 - 28 * q^9	$ 16 q - 16 q^{4} + 2 q^{5} + 8 q^{6} - 28 q^{9} + 4 q^{11} - 6 q^{14} - 4 q^{15} + 16 q^{16} - 30 q^{19} - 2 q^{20} + 32 q^{21} - 8 q^{24} - 10 q^{25} - 6 q^{26} + 6 q^{29} - 12 q^{30} + 50 q^{31} - 36 q^{35} + 28 q^{36} - 4 q^{39} + 38 q^{41} - 4 q^{44} - 50 q^{45} + 24 q^{46} - 38 q^{49} - 8 q^{50} + 8 q^{51} - 20 q^{54} - 28 q^{55} + 6 q^{56} + 24 q^{59} + 4 q^{60} + 58 q^{61} - 16 q^{64} - 32 q^{65} + 36 q^{66} - 4 q^{69} - 22 q^{70} + 24 q^{71} + 4 q^{74} - 36 q^{75} + 30 q^{76} - 10 q^{79} + 2 q^{80} + 80 q^{81} - 32 q^{84} - 56 q^{85} + 16 q^{86} + 40 q^{89} - 22 q^{90} + 46 q^{91} - 12 q^{94} - 52 q^{95} + 8 q^{96} + 32 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 + 2 * q^5 + 8 * q^6 - 28 * q^9 + 4 * q^11 - 6 * q^14 - 4 * q^15 + 16 * q^16 - 30 * q^19 - 2 * q^20 + 32 * q^21 - 8 * q^24 - 10 * q^25 - 6 * q^26 + 6 * q^29 - 12 * q^30 + 50 * q^31 - 36 * q^35 + 28 * q^36 - 4 * q^39 + 38 * q^41 - 4 * q^44 - 50 * q^45 + 24 * q^46 - 38 * q^49 - 8 * q^50 + 8 * q^51 - 20 * q^54 - 28 * q^55 + 6 * q^56 + 24 * q^59 + 4 * q^60 + 58 * q^61 - 16 * q^64 - 32 * q^65 + 36 * q^66 - 4 * q^69 - 22 * q^70 + 24 * q^71 + 4 * q^74 - 36 * q^75 + 30 * q^76 - 10 * q^79 + 2 * q^80 + 80 * q^81 - 32 * q^84 - 56 * q^85 + 16 * q^86 + 40 * q^89 - 22 * q^90 + 46 * q^91 - 12 * q^94 - 52 * q^95 + 8 * q^96 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$			2.99373i			1.72843i	0.503124	+	0.864214i	$0.332184\pi$
$3$			2.99373i			1.72843i	−0.503124	+	0.864214i	$0.667816\pi$
$4$	−1.00000			−0.500000
$5$	0.260869	−	2.22080i	0.116664	−	0.993171i
$5$	0.260869	−	2.22080i	0.116664	−	0.993171i
$6$	2.99373			1.22218
$7$		−	4.62603i		−	1.74847i	−0.485500	−	0.874237i	$-0.661362\pi$
$7$		−	4.62603i		−	1.74847i	0.485500	−	0.874237i	$-0.338638\pi$
$8$			1.00000i			0.353553i
$9$	−5.96240			−1.98747
$10$	−2.22080	−	0.260869i	−0.702278	−	0.0824939i
$11$	−3.48854			−1.05183			−0.525917	−	0.850536i	$-0.676278\pi$
$11$	−3.48854			−1.05183			−0.525917	+	0.850536i	$0.676278\pi$
$12$		−	2.99373i		−	0.864214i
$13$		−	4.77797i		−	1.32517i	−0.748986	−	0.662585i	$-0.769459\pi$
$13$		−	4.77797i		−	1.32517i	0.748986	−	0.662585i	$-0.230541\pi$
$14$	−4.62603			−1.23636
$15$	6.64846	+	0.780970i	1.71663	+	0.201645i
$16$	1.00000			0.250000
$17$		−	2.65039i		−	0.642813i	−0.946941	−	0.321407i	$-0.895844\pi$
$17$		−	2.65039i		−	0.642813i	0.946941	−	0.321407i	$-0.104156\pi$
$18$			5.96240i			1.40535i
$19$	2.10429			0.482757			0.241378	−	0.970431i	$-0.422400\pi$
$19$	2.10429			0.482757			0.241378	+	0.970431i	$0.422400\pi$
$20$	−0.260869	+	2.22080i	−0.0583320	+	0.496586i
$21$	13.8491			3.02211
$22$			3.48854i			0.743758i
$23$			4.96680i			1.03565i	0.855487	+	0.517825i	$0.173258\pi$
$23$			4.96680i			1.03565i	−0.855487	+	0.517825i	$0.826742\pi$
$24$	−2.99373			−0.611092
$25$	−4.86390	−	1.15867i	−0.972779	−	0.231735i
$26$	−4.77797			−0.937037
$27$		−	8.86861i		−	1.70677i
$28$			4.62603i			0.874237i
$29$	10.1703			1.88857			0.944287	−	0.329123i	$-0.106753\pi$
$29$	10.1703			1.88857			0.944287	+	0.329123i	$0.106753\pi$
$30$	0.780970	−	6.64846i	0.142585	−	1.21384i
$31$	−3.61975			−0.650127			−0.325063	−	0.945692i	$-0.605386\pi$
$31$	−3.61975			−0.650127			−0.325063	+	0.945692i	$0.605386\pi$
$32$		−	1.00000i		−	0.176777i
$33$		−	10.4437i		−	1.81802i
$34$	−2.65039			−0.454538
$35$	−10.2735	−	1.20679i	−1.73653	−	0.203984i
$36$	5.96240			0.993733
$37$		−	5.36680i		−	0.882296i	−0.897434	−	0.441148i	$-0.854571\pi$
$37$		−	5.36680i		−	0.882296i	0.897434	−	0.441148i	$-0.145429\pi$
$38$		−	2.10429i		−	0.341361i
$39$	14.3039			2.29046
$40$	2.22080	+	0.260869i	0.351139	+	0.0412470i
$41$	−0.557498			−0.0870665			−0.0435332	−	0.999052i	$-0.513861\pi$
$41$	−0.557498			−0.0870665			−0.0435332	+	0.999052i	$0.513861\pi$
$42$		−	13.8491i		−	2.13696i
$43$			1.00000i			0.152499i
$43$			1.00000i			0.152499i
$44$	3.48854			0.525917
$45$	−1.55540	+	13.2413i	−0.231866	+	1.97389i
$46$	4.96680			0.732315
$47$		−	3.17119i		−	0.462565i	−0.972887	−	0.231283i	$-0.925708\pi$
$47$		−	3.17119i		−	0.462565i	0.972887	−	0.231283i	$-0.0742922\pi$
$48$			2.99373i			0.432107i
$49$	−14.4001			−2.05716
$50$	−1.15867	+	4.86390i	−0.163861	+	0.687859i
$51$	7.93453			1.11106
$52$			4.77797i			0.662585i
$53$		−	2.74193i		−	0.376633i	−0.982108	−	0.188316i	$-0.939697\pi$
$53$		−	2.74193i		−	0.376633i	0.982108	−	0.188316i	$-0.0603030\pi$
$54$	−8.86861			−1.20687
$55$	−0.910050	+	7.74734i	−0.122711	+	1.04465i
$56$	4.62603			0.618179
$57$			6.29967i			0.834411i
$58$		−	10.1703i		−	1.33542i
$59$	7.03093			0.915349			0.457674	−	0.889120i	$-0.348683\pi$
$59$	7.03093			0.915349			0.457674	+	0.889120i	$0.348683\pi$
$60$	−6.64846	−	0.780970i	−0.858313	−	0.100823i
$61$	−9.73316			−1.24620			−0.623102	−	0.782141i	$-0.714128\pi$
$61$	−9.73316			−1.24620			−0.623102	+	0.782141i	$0.714128\pi$
$62$			3.61975i			0.459709i
$63$			27.5822i			3.47503i
$64$	−1.00000			−0.125000
$65$	−10.6109	−	1.24642i	−1.31612	−	0.154600i
$66$	−10.4437			−1.28553
$67$			7.69046i			0.939539i	0.882789	+	0.469770i	$0.155663\pi$
$67$			7.69046i			0.939539i	−0.882789	+	0.469770i	$0.844337\pi$
$68$			2.65039i			0.321407i
$69$	−14.8692			−1.79005
$70$	−1.20679	+	10.2735i	−0.144238	+	1.22792i
$71$	6.01121			0.713399			0.356700	−	0.934219i	$-0.383902\pi$
$71$	6.01121			0.713399			0.356700	+	0.934219i	$0.383902\pi$
$72$		−	5.96240i		−	0.702676i
$73$			8.26651i			0.967521i	0.875200	+	0.483761i	$0.160730\pi$
$73$			8.26651i			0.967521i	−0.875200	+	0.483761i	$0.839270\pi$
$74$	−5.36680			−0.623877
$75$	3.46875	−	14.5612i	0.400537	−	1.68138i
$76$	−2.10429			−0.241378
$77$			16.1381i			1.83910i
$78$		−	14.3039i		−	1.61960i
$79$	7.97824			0.897622			0.448811	−	0.893627i	$-0.351848\pi$
$79$	7.97824			0.897622			0.448811	+	0.893627i	$0.351848\pi$
$80$	0.260869	−	2.22080i	0.0291660	−	0.248293i
$81$	8.66301			0.962557
$82$			0.557498i			0.0615653i
$83$			3.32959i			0.365470i	0.983162	+	0.182735i	$0.0584951\pi$
$83$			3.32959i			0.365470i	−0.983162	+	0.182735i	$0.941505\pi$
$84$	−13.8491			−1.51106
$85$	−5.88598	−	0.691403i	−0.638424	−	0.0749932i
$86$	1.00000			0.107833
$87$			30.4470i			3.26427i
$88$		−	3.48854i		−	0.371879i
$89$	15.8770			1.68296			0.841480	−	0.540288i	$-0.181685\pi$
$89$	15.8770			1.68296			0.841480	+	0.540288i	$0.181685\pi$
$90$	13.2413	+	1.55540i	1.39575	+	0.163954i
$91$	−22.1030			−2.31703
$92$		−	4.96680i		−	0.517825i
$93$		−	10.8366i		−	1.12370i
$94$	−3.17119			−0.327083
$95$	0.548943	−	4.67320i	0.0563204	−	0.479460i
$96$	2.99373			0.305546
$97$		−	11.0593i		−	1.12291i	−0.827508	−	0.561453i	$-0.810242\pi$
$97$		−	11.0593i		−	1.12291i	0.827508	−	0.561453i	$-0.189758\pi$
$98$			14.4001i			1.45463i
$99$	20.8000			2.09048
$100$	4.86390	+	1.15867i	0.486390	+	0.115867i
$101$	0.530536			0.0527903			0.0263952	−	0.999652i	$-0.491597\pi$
$101$	0.530536			0.0527903			0.0263952	+	0.999652i	$0.491597\pi$
$102$		−	7.93453i		−	0.785636i
$103$		−	9.08431i		−	0.895104i	−0.894258	−	0.447552i	$-0.852296\pi$
$103$		−	9.08431i		−	0.895104i	0.894258	−	0.447552i	$-0.147704\pi$
$104$	4.77797			0.468519
$105$	3.61279	−	30.7560i	0.352572	−	3.00148i
$106$	−2.74193			−0.266319
$107$		−	9.47586i		−	0.916066i	−0.888935	−	0.458033i	$-0.848554\pi$
$107$		−	9.47586i		−	0.916066i	0.888935	−	0.458033i	$-0.151446\pi$
$108$			8.86861i			0.853383i
$109$	−5.58242			−0.534699			−0.267350	−	0.963600i	$-0.586148\pi$
$109$	−5.58242			−0.534699			−0.267350	+	0.963600i	$0.586148\pi$
$110$	7.74734	+	0.910050i	0.738680	+	0.0867699i
$111$	16.0667			1.52499
$112$		−	4.62603i		−	0.437118i
$113$		−	6.79611i		−	0.639324i	−0.947532	−	0.319662i	$-0.896431\pi$
$113$		−	6.79611i		−	0.639324i	0.947532	−	0.319662i	$-0.103569\pi$
$114$	6.29967			0.590018
$115$	11.0303	+	1.29568i	1.02858	+	0.120823i
$116$	−10.1703			−0.944287
$117$			28.4882i			2.63373i
$118$		−	7.03093i		−	0.647249i
$119$	−12.2608			−1.12394
$120$	−0.780970	+	6.64846i	−0.0712924	+	0.606919i
$121$	1.16989			0.106353
$122$			9.73316i			0.881199i
$123$		−	1.66900i		−	0.150488i
$124$	3.61975			0.325063
$125$	−3.84202	+	10.4995i	−0.343641	+	0.939101i
$126$	27.5822			2.45722
$127$			7.52237i			0.667503i	0.942661	+	0.333751i	$0.108315\pi$
$127$			7.52237i			0.667503i	−0.942661	+	0.333751i	$0.891685\pi$
$128$			1.00000i			0.0883883i
$129$	−2.99373			−0.263583
$130$	−1.24642	+	10.6109i	−0.109319	+	0.930639i
$131$	12.0252			1.05065			0.525325	−	0.850902i	$-0.323944\pi$
$131$	12.0252			1.05065			0.525325	+	0.850902i	$0.323944\pi$
$132$			10.4437i			0.909010i
$133$		−	9.73450i		−	0.844088i
$134$	7.69046			0.664354
$135$	−19.6954	−	2.31354i	−1.69511	−	0.199118i
$136$	2.65039			0.227269
$137$			14.3770i			1.22831i	0.789186	+	0.614155i	$0.210503\pi$
$137$			14.3770i			1.22831i	−0.789186	+	0.614155i	$0.789497\pi$
$138$			14.8692i			1.26575i
$139$	−18.1019			−1.53538			−0.767691	−	0.640820i	$-0.778594\pi$
$139$	−18.1019			−1.53538			−0.767691	+	0.640820i	$0.778594\pi$
$140$	10.2735	+	1.20679i	0.868267	+	0.101992i
$141$	9.49367			0.799511
$142$		−	6.01121i		−	0.504449i
$143$			16.6681i			1.39386i
$144$	−5.96240			−0.496867
$145$	2.65311	−	22.5862i	0.220329	−	1.87568i
$146$	8.26651			0.684141
$147$		−	43.1100i		−	3.55565i
$148$			5.36680i			0.441148i
$149$	−14.8545			−1.21693			−0.608464	−	0.793581i	$-0.708214\pi$
$149$	−14.8545			−1.21693			−0.608464	+	0.793581i	$0.708214\pi$
$150$	−14.5612	−	3.46875i	−1.18891	−	0.283222i
$151$	14.7035			1.19655			0.598276	−	0.801290i	$-0.295853\pi$
$151$	14.7035			1.19655			0.598276	+	0.801290i	$0.295853\pi$
$152$			2.10429i			0.170680i
$153$			15.8027i			1.27757i
$154$	16.1381			1.30044
$155$	−0.944280	+	8.03874i	−0.0758464	+	0.645687i
$156$	−14.3039			−1.14523
$157$		−	17.9265i		−	1.43069i	−0.698773	−	0.715343i	$-0.746270\pi$
$157$		−	17.9265i		−	1.43069i	0.698773	−	0.715343i	$-0.253730\pi$
$158$		−	7.97824i		−	0.634715i
$159$	8.20858			0.650983
$160$	−2.22080	−	0.260869i	−0.175570	−	0.0206235i
$161$	22.9765			1.81081
$162$		−	8.66301i		−	0.680630i
$163$		−	12.5006i		−	0.979120i	−0.871970	−	0.489560i	$-0.837157\pi$
$163$		−	12.5006i		−	0.979120i	0.871970	−	0.489560i	$-0.162843\pi$
$164$	0.557498			0.0435332
$165$	−23.1934	−	2.72444i	−1.80560	−	0.212097i
$166$	3.32959			0.258427
$167$			22.1166i			1.71144i	0.517442	+	0.855718i	$0.326884\pi$
$167$			22.1166i			1.71144i	−0.517442	+	0.855718i	$0.673116\pi$
$168$			13.8491i			1.06848i
$169$	−9.82901			−0.756077
$170$	−0.691403	+	5.88598i	−0.0530282	+	0.451434i
$171$	−12.5466			−0.959463
$172$		−	1.00000i		−	0.0762493i
$173$		−	4.53486i		−	0.344779i	−0.985029	−	0.172390i	$-0.944851\pi$
$173$		−	4.53486i		−	0.344779i	0.985029	−	0.172390i	$-0.0551488\pi$
$174$	30.4470			2.30818
$175$	−5.36006	+	22.5005i	−0.405182	+	1.70088i
$176$	−3.48854			−0.262958
$177$			21.0487i			1.58212i
$178$		−	15.8770i		−	1.19003i
$179$	15.9501			1.19216			0.596082	−	0.802923i	$-0.296723\pi$
$179$	15.9501			1.19216			0.596082	+	0.802923i	$0.296723\pi$
$180$	1.55540	−	13.2413i	0.115933	−	0.986947i
$181$	26.2357			1.95008			0.975041	−	0.222026i	$-0.0712669\pi$
$181$	26.2357			1.95008			0.975041	+	0.222026i	$0.0712669\pi$
$182$			22.1030i			1.63838i
$183$		−	29.1384i		−	2.15397i
$184$	−4.96680			−0.366157
$185$	−11.9186	−	1.40003i	−0.876271	−	0.102932i
$186$	−10.8366			−0.794574
$187$			9.24597i			0.676132i
$188$			3.17119i			0.231283i
$189$	−41.0264			−2.98423
$190$	−4.67320	−	0.548943i	−0.339030	−	0.0398245i
$191$	−8.68534			−0.628449			−0.314225	−	0.949349i	$-0.601745\pi$
$191$	−8.68534			−0.628449			−0.314225	+	0.949349i	$0.601745\pi$
$192$		−	2.99373i		−	0.216054i
$193$			14.3676i			1.03420i	0.855925	+	0.517101i	$0.172989\pi$
$193$			14.3676i			1.03420i	−0.855925	+	0.517101i	$0.827011\pi$
$194$	−11.0593			−0.794015
$195$	3.73145	−	31.7662i	0.267215	−	2.27482i
$196$	14.4001			1.02858
$197$		−	6.19264i		−	0.441208i	−0.975364	−	0.220604i	$-0.929197\pi$
$197$		−	6.19264i		−	0.441208i	0.975364	−	0.220604i	$-0.0708028\pi$
$198$		−	20.8000i		−	1.47819i
$199$	−0.211786			−0.0150131			−0.00750657	−	0.999972i	$-0.502389\pi$
$199$	−0.211786			−0.0150131			−0.00750657	+	0.999972i	$0.502389\pi$
$200$	1.15867	−	4.86390i	0.0819306	−	0.343929i
$201$	−23.0231			−1.62393
$202$		−	0.530536i		−	0.0373284i
$203$		−	47.0480i		−	3.30212i
$204$	−7.93453			−0.555528
$205$	−0.145434	+	1.23809i	−0.0101575	+	0.0864720i
$206$	−9.08431			−0.632934
$207$		−	29.6140i		−	2.05832i
$208$		−	4.77797i		−	0.331293i
$209$	−7.34089			−0.507780
$210$	−30.7560	−	3.61279i	−2.12236	−	0.249306i
$211$	3.04207			0.209425			0.104712	−	0.994503i	$-0.466608\pi$
$211$	3.04207			0.209425			0.104712	+	0.994503i	$0.466608\pi$
$212$			2.74193i			0.188316i
$213$			17.9959i			1.23306i
$214$	−9.47586			−0.647756
$215$	2.22080	+	0.260869i	0.151457	+	0.0177911i
$216$	8.86861			0.603433
$217$			16.7451i			1.13673i
$218$			5.58242i			0.378089i
$219$	−24.7477			−1.67229
$220$	0.910050	−	7.74734i	0.0613556	−	0.522325i
$221$	−12.6635			−0.851837
$222$		−	16.0667i		−	1.07833i
$223$		−	2.70190i		−	0.180933i	−0.995900	−	0.0904665i	$-0.971164\pi$
$223$		−	2.70190i		−	0.180933i	0.995900	−	0.0904665i	$-0.0288358\pi$
$224$	−4.62603			−0.309089
$225$	29.0005	+	6.90848i	1.93337	+	0.460565i
$226$	−6.79611			−0.452070
$227$		−	4.81420i		−	0.319530i	−0.987155	−	0.159765i	$-0.948926\pi$
$227$		−	4.81420i		−	0.319530i	0.987155	−	0.159765i	$-0.0510736\pi$
$228$		−	6.29967i		−	0.417206i
$229$	9.80736			0.648089			0.324044	−	0.946042i	$-0.394957\pi$
$229$	9.80736			0.648089			0.324044	+	0.946042i	$0.394957\pi$
$230$	1.29568	−	11.0303i	0.0854348	−	0.727314i
$231$	−48.3129			−3.17876
$232$			10.1703i			0.667712i
$233$			22.4499i			1.47074i	0.677666	+	0.735369i	$0.262991\pi$
$233$			22.4499i			1.47074i	−0.677666	+	0.735369i	$0.737009\pi$
$234$	28.4882			1.86233
$235$	−7.04257	−	0.827264i	−0.459407	−	0.0539647i
$236$	−7.03093			−0.457674
$237$			23.8847i			1.55148i
$238$			12.2608i			0.794747i
$239$	14.1375			0.914481			0.457241	−	0.889343i	$-0.348838\pi$
$239$	14.1375			0.914481			0.457241	+	0.889343i	$0.348838\pi$
$240$	6.64846	+	0.780970i	0.429157	+	0.0504114i
$241$	21.9544			1.41421			0.707104	−	0.707110i	$-0.250001\pi$
$241$	21.9544			1.41421			0.707104	+	0.707110i	$0.250001\pi$
$242$		−	1.16989i		−	0.0752031i
$243$		−	0.671161i		−	0.0430550i
$244$	9.73316			0.623102
$245$	−3.75654	+	31.9798i	−0.239997	+	2.04311i
$246$	−1.66900			−0.106411
$247$		−	10.0542i		−	0.639735i
$248$		−	3.61975i		−	0.229855i
$249$	−9.96789			−0.631690
$250$	10.4995	+	3.84202i	0.664045	+	0.242991i
$251$	−6.04703			−0.381685			−0.190843	−	0.981621i	$-0.561122\pi$
$251$	−6.04703			−0.381685			−0.190843	+	0.981621i	$0.561122\pi$
$252$		−	27.5822i		−	1.73752i
$253$		−	17.3269i		−	1.08933i
$254$	7.52237			0.471996
$255$	2.06987	−	17.6210i	0.129620	−	1.10347i
$256$	1.00000			0.0625000
$257$		−	2.09214i		−	0.130504i	−0.997869	−	0.0652522i	$-0.979215\pi$
$257$		−	2.09214i		−	0.130504i	0.997869	−	0.0652522i	$-0.0207852\pi$
$258$			2.99373i			0.186381i
$259$	−24.8269			−1.54267
$260$	10.6109	+	1.24642i	0.658061	+	0.0772999i
$261$	−60.6393			−3.75348
$262$		−	12.0252i		−	0.742921i
$263$		−	2.57171i		−	0.158578i	−0.996852	−	0.0792891i	$-0.974735\pi$
$263$		−	2.57171i		−	0.158578i	0.996852	−	0.0792891i	$-0.0252650\pi$
$264$	10.4437			0.642767
$265$	−6.08927	−	0.715283i	−0.374061	−	0.0439395i
$266$	−9.73450			−0.596860
$267$			47.5314i			2.90888i
$268$		−	7.69046i		−	0.469770i
$269$	17.4914			1.06647			0.533235	−	0.845967i	$-0.320976\pi$
$269$	17.4914			1.06647			0.533235	+	0.845967i	$0.320976\pi$
$270$	−2.31354	+	19.6954i	−0.140798	+	1.19862i
$271$	32.7476			1.98928			0.994638	−	0.103421i	$-0.0329790\pi$
$271$	32.7476			1.98928			0.994638	+	0.103421i	$0.0329790\pi$
$272$		−	2.65039i		−	0.160703i
$273$		−	66.1704i		−	4.00481i
$274$	14.3770			0.868546
$275$	16.9679	+	4.04208i	1.02320	+	0.243746i
$276$	14.8692			0.895023
$277$		−	13.0999i		−	0.787098i	−0.919304	−	0.393549i	$-0.871247\pi$
$277$		−	13.0999i		−	0.787098i	0.919304	−	0.393549i	$-0.128753\pi$
$278$			18.1019i			1.08568i
$279$	21.5824			1.29211
$280$	1.20679	−	10.2735i	0.0721192	−	0.613958i
$281$	16.7089			0.996772			0.498386	−	0.866955i	$-0.333926\pi$
$281$	16.7089			0.996772			0.498386	+	0.866955i	$0.333926\pi$
$282$		−	9.49367i		−	0.565340i
$283$		−	6.89032i		−	0.409587i	−0.978805	−	0.204794i	$-0.934348\pi$
$283$		−	6.89032i		−	0.409587i	0.978805	−	0.204794i	$-0.0656523\pi$
$284$	−6.01121			−0.356700
$285$	13.9903	+	1.64339i	0.828713	+	0.0973458i
$286$	16.6681			0.985607
$287$			2.57900i			0.152233i
$288$			5.96240i			0.351338i
$289$	9.97545			0.586791
$290$	−22.5862	−	2.65311i	−1.32630	−	0.155796i
$291$	33.1087			1.94086
$292$		−	8.26651i		−	0.483761i
$293$		−	28.8728i		−	1.68677i	−0.537310	−	0.843385i	$-0.680559\pi$
$293$		−	28.8728i		−	1.68677i	0.537310	−	0.843385i	$-0.319441\pi$
$294$	−43.1100			−2.51423
$295$	1.83415	−	15.6143i	0.106788	−	0.909098i
$296$	5.36680			0.311939
$297$			30.9385i			1.79523i
$298$			14.8545i			0.860498i
$299$	23.7312			1.37241
$300$	−3.46875	+	14.5612i	−0.200269	+	0.840690i
$301$	4.62603			0.266640
$302$		−	14.7035i		−	0.846090i
$303$			1.58828i			0.0912443i
$304$	2.10429			0.120689
$305$	−2.53908	+	21.6154i	−0.145387	+	1.23769i
$306$	15.8027			0.903378
$307$			18.0013i			1.02739i	0.857973	+	0.513695i	$0.171724\pi$
$307$			18.0013i			1.02739i	−0.857973	+	0.513695i	$0.828276\pi$
$308$		−	16.1381i		−	0.919551i
$309$	27.1959			1.54712
$310$	8.03874	+	0.944280i	0.456570	+	0.0536315i
$311$	−31.8831			−1.80792			−0.903962	−	0.427613i	$-0.859355\pi$
$311$	−31.8831			−1.80792			−0.903962	+	0.427613i	$0.859355\pi$
$312$			14.3039i			0.809801i
$313$			10.9625i			0.619635i	0.950796	+	0.309818i	$0.100268\pi$
$313$			10.9625i			0.619635i	−0.950796	+	0.309818i	$0.899732\pi$
$314$	−17.9265			−1.01165
$315$	61.2546	+	7.19534i	3.45130	+	0.405411i
$316$	−7.97824			−0.448811
$317$			13.6282i			0.765436i	0.923865	+	0.382718i	$0.125012\pi$
$317$			13.6282i			0.765436i	−0.923865	+	0.382718i	$0.874988\pi$
$318$		−	8.20858i		−	0.460314i
$319$	−35.4794			−1.98647
$320$	−0.260869	+	2.22080i	−0.0145830	+	0.124146i
$321$	28.3681			1.58335
$322$		−	22.9765i		−	1.28043i
$323$		−	5.57718i		−	0.310323i
$324$	−8.66301			−0.481278
$325$	−5.53611	+	23.2395i	−0.307088	+	1.28910i
$326$	−12.5006			−0.692343
$327$		−	16.7122i		−	0.924189i
$328$		−	0.557498i		−	0.0307827i
$329$	−14.6700			−0.808783
$330$	−2.72444	+	23.1934i	−0.149976	+	1.27676i
$331$	−8.55144			−0.470029			−0.235015	−	0.971992i	$-0.575514\pi$
$331$	−8.55144			−0.470029			−0.235015	+	0.971992i	$0.575514\pi$
$332$		−	3.32959i		−	0.182735i
$333$			31.9990i			1.75353i
$334$	22.1166			1.21017
$335$	17.0790	+	2.00620i	0.933123	+	0.109610i
$336$	13.8491			0.755528
$337$		−	29.4041i		−	1.60175i	−0.598835	−	0.800873i	$-0.704369\pi$
$337$		−	29.4041i		−	1.60175i	0.598835	−	0.800873i	$-0.295631\pi$
$338$			9.82901i			0.534627i
$339$	20.3457			1.10503
$340$	5.88598	+	0.691403i	0.319212	+	0.0374966i
$341$	12.6276			0.683825
$342$			12.5466i			0.678443i
$343$			34.2331i			1.84842i
$344$	−1.00000			−0.0539164
$345$	−3.87892	+	33.0216i	−0.208834	+	1.77782i
$346$	−4.53486			−0.243796
$347$			9.69759i			0.520594i	0.965529	+	0.260297i	$0.0838205\pi$
$347$			9.69759i			0.520594i	−0.965529	+	0.260297i	$0.916179\pi$
$348$		−	30.4470i		−	1.63213i
$349$	−9.38543			−0.502391			−0.251195	−	0.967936i	$-0.580824\pi$
$349$	−9.38543			−0.502391			−0.251195	+	0.967936i	$0.580824\pi$
$350$	22.5005	+	5.36006i	1.20270	+	0.286507i
$351$	−42.3740			−2.26176
$352$			3.48854i			0.185940i
$353$			20.8583i			1.11018i	0.831792	+	0.555088i	$0.187315\pi$
$353$			20.8583i			1.11018i	−0.831792	+	0.555088i	$0.812685\pi$
$354$	21.0487			1.11872
$355$	1.56814	−	13.3497i	0.0832280	−	0.708528i
$356$	−15.8770			−0.841480
$357$		−	36.7054i		−	1.94265i
$358$		−	15.9501i		−	0.842987i
$359$	13.6002			0.717789			0.358894	−	0.933378i	$-0.383154\pi$
$359$	13.6002			0.717789			0.358894	+	0.933378i	$0.383154\pi$
$360$	−13.2413	−	1.55540i	−0.697877	−	0.0819770i
$361$	−14.5720			−0.766946
$362$		−	26.2357i		−	1.37892i
$363$			3.50232i			0.183824i
$364$	22.1030			1.15851
$365$	18.3582	+	2.15647i	0.960915	+	0.112875i
$366$	−29.1384			−1.52309
$367$		−	19.7084i		−	1.02877i	−0.857559	−	0.514385i	$-0.828020\pi$
$367$		−	19.7084i		−	1.02877i	0.857559	−	0.514385i	$-0.171980\pi$
$368$			4.96680i			0.258912i
$369$	3.32402			0.173042
$370$	−1.40003	+	11.9186i	−0.0727840	+	0.619617i
$371$	−12.6842			−0.658532
$372$			10.8366i			0.561849i
$373$		−	13.6028i		−	0.704329i	−0.935938	−	0.352164i	$-0.885446\pi$
$373$		−	13.6028i		−	0.704329i	0.935938	−	0.352164i	$-0.114554\pi$
$374$	9.24597			0.478098
$375$	−31.4325	−	11.5020i	−1.62317	−	0.593959i
$376$	3.17119			0.163542
$377$		−	48.5933i		−	2.50268i
$378$			41.0264i			2.11017i
$379$	−7.71555			−0.396321			−0.198161	−	0.980170i	$-0.563497\pi$
$379$	−7.71555			−0.396321			−0.198161	+	0.980170i	$0.563497\pi$
$380$	−0.548943	+	4.67320i	−0.0281602	+	0.239730i
$381$	−22.5199			−1.15373
$382$			8.68534i			0.444381i
$383$			30.6014i			1.56366i	0.623493	+	0.781829i	$0.285713\pi$
$383$			30.6014i			1.56366i	−0.623493	+	0.781829i	$0.714287\pi$
$384$	−2.99373			−0.152773
$385$	35.8394	+	4.20992i	1.82654	+	0.214557i
$386$	14.3676			0.731291
$387$		−	5.96240i		−	0.303086i
$388$			11.0593i			0.561453i
$389$	−5.44823			−0.276236			−0.138118	−	0.990416i	$-0.544105\pi$
$389$	−5.44823			−0.276236			−0.138118	+	0.990416i	$0.544105\pi$
$390$	−31.7662	−	3.73145i	−1.60854	−	0.188949i
$391$	13.1639			0.665729
$392$		−	14.4001i		−	0.727316i
$393$			36.0003i			1.81597i
$394$	−6.19264			−0.311981
$395$	2.08127	−	17.7181i	0.104720	−	0.891493i
$396$	−20.8000			−1.04524
$397$			6.54409i			0.328438i	0.986424	+	0.164219i	$0.0525104\pi$
$397$			6.54409i			0.328438i	−0.986424	+	0.164219i	$0.947490\pi$
$398$			0.211786i			0.0106159i
$399$	29.1424			1.45895
$400$	−4.86390	−	1.15867i	−0.243195	−	0.0579337i
$401$	−3.13834			−0.156721			−0.0783606	−	0.996925i	$-0.524969\pi$
$401$	−3.13834			−0.156721			−0.0783606	+	0.996925i	$0.524969\pi$
$402$			23.0231i			1.14829i
$403$			17.2951i			0.861529i
$404$	−0.530536			−0.0263952
$405$	2.25991	−	19.2388i	0.112296	−	0.955984i
$406$	−47.0480			−2.33495
$407$			18.7223i			0.928028i
$408$			7.93453i			0.392818i
$409$	−10.2908			−0.508849			−0.254425	−	0.967093i	$-0.581886\pi$
$409$	−10.2908			−0.508849			−0.254425	+	0.967093i	$0.581886\pi$
$410$	1.23809	+	0.145434i	0.0611449	+	0.00718246i
$411$	−43.0408			−2.12305
$412$			9.08431i			0.447552i
$413$		−	32.5253i		−	1.60046i
$414$	−29.6140			−1.45545
$415$	7.39436	+	0.868587i	0.362975	+	0.0426373i
$416$	−4.77797			−0.234259
$417$		−	54.1921i		−	2.65380i
$418$			7.34089i			0.359055i
$419$	−16.4773			−0.804967			−0.402484	−	0.915427i	$-0.631853\pi$
$419$	−16.4773			−0.804967			−0.402484	+	0.915427i	$0.631853\pi$
$420$	−3.61279	+	30.7560i	−0.176286	+	1.50074i
$421$	−30.5518			−1.48901			−0.744503	−	0.667619i	$-0.767313\pi$
$421$	−30.5518			−1.48901			−0.744503	+	0.667619i	$0.767313\pi$
$422$		−	3.04207i		−	0.148086i
$423$			18.9079i			0.919333i
$424$	2.74193			0.133160
$425$	−3.07093	+	12.8912i	−0.148962	+	0.625315i
$426$	17.9959			0.871905
$427$			45.0258i			2.17895i
$428$			9.47586i			0.458033i
$429$	−49.8998			−2.40919
$430$	0.260869	−	2.22080i	0.0125802	−	0.107096i
$431$	11.2043			0.539693			0.269847	−	0.962903i	$-0.413027\pi$
$431$	11.2043			0.539693			0.269847	+	0.962903i	$0.413027\pi$
$432$		−	8.86861i		−	0.426691i
$433$		−	23.8671i		−	1.14698i	−0.819212	−	0.573490i	$-0.805589\pi$
$433$		−	23.8671i		−	1.14698i	0.819212	−	0.573490i	$-0.194411\pi$
$434$	16.7451			0.803789
$435$	67.6168	+	7.94268i	3.24198	+	0.380822i
$436$	5.58242			0.267350
$437$			10.4516i			0.499967i
$438$			24.7477i			1.18249i
$439$	−8.60578			−0.410732			−0.205366	−	0.978685i	$-0.565838\pi$
$439$	−8.60578			−0.410732			−0.205366	+	0.978685i	$0.565838\pi$
$440$	−7.74734	−	0.910050i	−0.369340	−	0.0433849i
$441$	85.8593			4.08854
$442$			12.6635i			0.602340i
$443$		−	4.88400i		−	0.232046i	−0.993247	−	0.116023i	$-0.962985\pi$
$443$		−	4.88400i		−	0.232046i	0.993247	−	0.116023i	$-0.0370146\pi$
$444$	−16.0667			−0.762493
$445$	4.14182	−	35.2597i	0.196341	−	1.67147i
$446$	−2.70190			−0.127939
$447$		−	44.4703i		−	2.10337i
$448$			4.62603i			0.218559i
$449$	−8.03223			−0.379064			−0.189532	−	0.981875i	$-0.560697\pi$
$449$	−8.03223			−0.379064			−0.189532	+	0.981875i	$0.560697\pi$
$450$	6.90848	−	29.0005i	0.325669	−	1.36710i
$451$	1.94485			0.0915794
$452$			6.79611i			0.319662i
$453$			44.0182i			2.06816i
$454$	−4.81420			−0.225942
$455$	−5.76599	+	49.0864i	−0.270314	+	2.30120i
$456$	−6.29967			−0.295009
$457$		−	0.0987491i		−	0.00461929i	−0.999997	−	0.00230964i	$-0.999265\pi$
$457$		−	0.0987491i		−	0.00461929i	0.999997	−	0.00230964i	$-0.000735183\pi$
$458$		−	9.80736i		−	0.458268i
$459$	−23.5053			−1.09713
$460$	−11.0303	−	1.29568i	−0.514289	−	0.0604115i
$461$	−11.1908			−0.521208			−0.260604	−	0.965446i	$-0.583922\pi$
$461$	−11.1908			−0.521208			−0.260604	+	0.965446i	$0.583922\pi$
$462$			48.3129i			2.24772i
$463$		−	2.98990i		−	0.138952i	−0.997584	−	0.0694762i	$-0.977867\pi$
$463$		−	2.98990i		−	0.138952i	0.997584	−	0.0694762i	$-0.0221328\pi$
$464$	10.1703			0.472144
$465$	−24.0658	−	2.82692i	−1.11602	−	0.131095i
$466$	22.4499			1.03997
$467$		−	7.76496i		−	0.359319i	−0.983729	−	0.179660i	$-0.942500\pi$
$467$		−	7.76496i		−	0.359319i	0.983729	−	0.179660i	$-0.0574997\pi$
$468$		−	28.4882i		−	1.31687i
$469$	35.5763			1.64276
$470$	−0.827264	+	7.04257i	−0.0381588	+	0.324850i
$471$	53.6669			2.47284
$472$			7.03093i			0.323625i
$473$		−	3.48854i		−	0.160403i
$474$	23.8847			1.09706
$475$	−10.2350	−	2.43818i	−0.469616	−	0.111872i
$476$	12.2608			0.561971
$477$			16.3485i			0.748545i
$478$		−	14.1375i		−	0.646636i
$479$	10.4742			0.478579			0.239289	−	0.970948i	$-0.423086\pi$
$479$	10.4742			0.478579			0.239289	+	0.970948i	$0.423086\pi$
$480$	0.780970	−	6.64846i	0.0356462	−	0.303460i
$481$	−25.6424			−1.16919
$482$		−	21.9544i		−	0.999996i
$483$			68.7855i			3.12985i
$484$	−1.16989			−0.0531766
$485$	−24.5606	−	2.88504i	−1.11524	−	0.131003i
$486$	−0.671161			−0.0304445
$487$			27.1578i			1.23064i	0.788278	+	0.615320i	$0.210973\pi$
$487$			27.1578i			1.23064i	−0.788278	+	0.615320i	$0.789027\pi$
$488$		−	9.73316i		−	0.440599i
$489$	37.4233			1.69234
$490$	31.9798	+	3.75654i	1.44470	+	0.169703i
$491$	−29.6634			−1.33869			−0.669346	−	0.742951i	$-0.733426\pi$
$491$	−29.6634			−1.33869			−0.669346	+	0.742951i	$0.733426\pi$
$492$			1.66900i			0.0752441i
$493$		−	26.9552i		−	1.21400i
$494$	−10.0542			−0.452361
$495$	5.42608	−	46.1927i	0.243884	−	2.07621i
$496$	−3.61975			−0.162532
$497$		−	27.8080i		−	1.24736i
$498$			9.96789i			0.446672i
$499$	−33.5426			−1.50157			−0.750787	−	0.660544i	$-0.770326\pi$
$499$	−33.5426			−1.50157			−0.750787	+	0.660544i	$0.770326\pi$
$500$	3.84202	−	10.4995i	0.171820	−	0.469551i
$501$	−66.2111			−2.95810
$502$			6.04703i			0.269892i
$503$		−	8.10256i		−	0.361275i	−0.983550	−	0.180638i	$-0.942184\pi$
$503$		−	8.10256i		−	0.361275i	0.983550	−	0.180638i	$-0.0578161\pi$
$504$	−27.5822			−1.22861
$505$	0.138400	−	1.17821i	0.00615873	−	0.0524298i
$506$	−17.3269			−0.770273
$507$		−	29.4254i		−	1.30683i
$508$		−	7.52237i		−	0.333751i
$509$	19.6854			0.872541			0.436271	−	0.899816i	$-0.356299\pi$
$509$	19.6854			0.872541			0.436271	+	0.899816i	$0.356299\pi$
$510$	−17.6210	−	2.06987i	−0.780271	−	0.0916555i
$511$	38.2411			1.69169
$512$		−	1.00000i		−	0.0441942i
$513$		−	18.6621i		−	0.823953i
$514$	−2.09214			−0.0922805
$515$	−20.1744	−	2.36981i	−0.888992	−	0.104426i
$516$	2.99373			0.131791
$517$			11.0628i			0.486542i
$518$			24.8269i			1.09083i
$519$	13.5761			0.595927
$520$	1.24642	−	10.6109i	0.0546593	−	0.465319i
$521$	31.2317			1.36829			0.684143	−	0.729348i	$-0.260176\pi$
$521$	31.2317			1.36829			0.684143	+	0.729348i	$0.260176\pi$
$522$			60.6393i			2.65411i
$523$			6.74845i			0.295089i	0.989055	+	0.147545i	$0.0471370\pi$
$523$			6.74845i			0.295089i	−0.989055	+	0.147545i	$0.952863\pi$
$524$	−12.0252			−0.525325
$525$	−67.3604	−	16.0465i	−2.93985	−	0.700329i
$526$	−2.57171			−0.112132
$527$			9.59375i			0.417910i
$528$		−	10.4437i		−	0.454505i
$529$	−1.66909			−0.0725691
$530$	−0.715283	+	6.08927i	−0.0310699	+	0.264501i
$531$	−41.9212			−1.81923
$532$			9.73450i			0.422044i
$533$			2.66371i			0.115378i
$534$	47.5314			2.05689
$535$	−21.0440	−	2.47196i	−0.909811	−	0.106872i
$536$	−7.69046			−0.332177
$537$			47.7502i			2.06057i
$538$		−	17.4914i		−	0.754108i
$539$	50.2353			2.16379
$540$	19.6954	+	2.31354i	0.847555	+	0.0995591i
$541$	13.1053			0.563440			0.281720	−	0.959497i	$-0.409095\pi$
$541$	13.1053			0.563440			0.281720	+	0.959497i	$0.409095\pi$
$542$		−	32.7476i		−	1.40663i
$543$			78.5424i			3.37058i
$544$	−2.65039			−0.113634
$545$	−1.45628	+	12.3974i	−0.0623802	+	0.531048i
$546$	−66.1704			−2.83183
$547$			19.6089i			0.838417i	0.907890	+	0.419209i	$0.137692\pi$
$547$			19.6089i			0.838417i	−0.907890	+	0.419209i	$0.862308\pi$
$548$		−	14.3770i		−	0.614155i
$549$	58.0330			2.47679
$550$	4.04208	−	16.9679i	0.172355	−	0.723513i
$551$	21.4012			0.911722
$552$		−	14.8692i		−	0.632877i
$553$		−	36.9076i		−	1.56947i
$554$	−13.0999			−0.556562
$555$	4.19130	−	35.6810i	0.177911	−	1.51457i
$556$	18.1019			0.767691
$557$		−	29.6319i		−	1.25555i	−0.778396	−	0.627773i	$-0.783967\pi$
$557$		−	29.6319i		−	1.25555i	0.778396	−	0.627773i	$-0.216033\pi$
$558$		−	21.5824i		−	0.913656i
$559$	4.77797			0.202087
$560$	−10.2735	−	1.20679i	−0.434134	−	0.0509960i
$561$	−27.6799			−1.16865
$562$		−	16.7089i		−	0.704824i
$563$			39.7808i			1.67656i	0.545239	+	0.838280i	$0.316439\pi$
$563$			39.7808i			1.67656i	−0.545239	+	0.838280i	$0.683561\pi$
$564$	−9.49367			−0.399756
$565$	−15.0928	−	1.77289i	−0.634958	−	0.0745861i
$566$	−6.89032			−0.289622
$567$		−	40.0753i		−	1.68300i
$568$			6.01121i			0.252225i
$569$	34.6114			1.45099			0.725493	−	0.688230i	$-0.241612\pi$
$569$	34.6114			1.45099			0.725493	+	0.688230i	$0.241612\pi$
$570$	1.64339	−	13.9903i	0.0688339	−	0.585989i
$571$	8.87445			0.371384			0.185692	−	0.982608i	$-0.440547\pi$
$571$	8.87445			0.371384			0.185692	+	0.982608i	$0.440547\pi$
$572$		−	16.6681i		−	0.696929i
$573$		−	26.0015i		−	1.08623i
$574$	2.57900			0.107645
$575$	5.75490	−	24.1580i	0.239996	−	1.00746i
$576$	5.96240			0.248433
$577$			6.57391i			0.273676i	0.990593	+	0.136838i	$0.0436939\pi$
$577$			6.57391i			0.273676i	−0.990593	+	0.136838i	$0.956306\pi$
$578$		−	9.97545i		−	0.414924i
$579$	−43.0126			−1.78754
$580$	−2.65311	+	22.5862i	−0.110164	+	0.937839i
$581$	15.4028			0.639015
$582$		−	33.1087i		−	1.37240i
$583$			9.56531i			0.396155i
$584$	−8.26651			−0.342070
$585$	63.2665	+	7.43167i	2.61575	+	0.307262i
$586$	−28.8728			−1.19273
$587$		−	9.82626i		−	0.405573i	−0.979223	−	0.202787i	$-0.935000\pi$
$587$		−	9.82626i		−	0.405573i	0.979223	−	0.202787i	$-0.0649998\pi$
$588$			43.1100i			1.77783i
$589$	−7.61701			−0.313853
$590$	−15.6143	−	1.83415i	−0.642830	−	0.0755107i
$591$	18.5391			0.762596
$592$		−	5.36680i		−	0.220574i
$593$			18.4695i			0.758450i	0.925304	+	0.379225i	$0.123809\pi$
$593$			18.4695i			0.758450i	−0.925304	+	0.379225i	$0.876191\pi$
$594$	30.9385			1.26942
$595$	−3.19845	+	27.2287i	−0.131124	+	1.11627i
$596$	14.8545			0.608464
$597$		−	0.634031i		−	0.0259491i
$598$		−	23.7312i		−	0.970442i
$599$	−4.56033			−0.186330			−0.0931649	−	0.995651i	$-0.529698\pi$
$599$	−4.56033			−0.186330			−0.0931649	+	0.995651i	$0.529698\pi$
$600$	14.5612	+	3.46875i	0.594457	+	0.141611i
$601$	14.2645			0.581861			0.290930	−	0.956744i	$-0.406035\pi$
$601$	14.2645			0.581861			0.290930	+	0.956744i	$0.406035\pi$
$602$		−	4.62603i		−	0.188543i
$603$		−	45.8536i		−	1.86730i
$604$	−14.7035			−0.598276
$605$	0.305186	−	2.59808i	0.0124076	−	0.105627i
$606$	1.58828			0.0645195
$607$			13.2840i			0.539181i	0.962975	+	0.269590i	$0.0868883\pi$
$607$			13.2840i			0.539181i	−0.962975	+	0.269590i	$0.913112\pi$
$608$		−	2.10429i		−	0.0853402i
$609$	140.849			5.70748
$610$	21.6154	+	2.53908i	0.875181	+	0.102804i
$611$	−15.1518			−0.612978
$612$		−	15.8027i		−	0.638785i
$613$			21.5258i			0.869420i	0.900570	+	0.434710i	$0.143149\pi$
$613$			21.5258i			0.869420i	−0.900570	+	0.434710i	$0.856851\pi$
$614$	18.0013			0.726474
$615$	−3.70650	−	0.435389i	−0.149461	−	0.0175566i
$616$	−16.1381			−0.650221
$617$			1.62412i			0.0653848i	0.999465	+	0.0326924i	$0.0104082\pi$
$617$			1.62412i			0.0653848i	−0.999465	+	0.0326924i	$0.989592\pi$
$618$		−	27.1959i		−	1.09398i
$619$	−4.73821			−0.190445			−0.0952223	−	0.995456i	$-0.530356\pi$
$619$	−4.73821			−0.190445			−0.0952223	+	0.995456i	$0.530356\pi$
$620$	0.944280	−	8.03874i	0.0379232	−	0.322844i
$621$	44.0486			1.76761
$622$			31.8831i			1.27840i
$623$		−	73.4475i		−	2.94261i
$624$	14.3039			0.572616
$625$	22.3149	+	11.2713i	0.892598	+	0.450853i
$626$	10.9625			0.438148
$627$		−	21.9766i		−	0.877661i
$628$			17.9265i			0.715343i
$629$	−14.2241			−0.567151
$630$	7.19534	−	61.2546i	0.286669	−	2.44044i
$631$	−47.5754			−1.89395			−0.946974	−	0.321311i	$-0.895876\pi$
$631$	−47.5754			−1.89395			−0.946974	+	0.321311i	$0.895876\pi$
$632$			7.97824i			0.317357i
$633$			9.10714i			0.361976i
$634$	13.6282			0.541245
$635$	16.7057	+	1.96235i	0.662945	+	0.0778736i
$636$	−8.20858			−0.325491
$637$			68.8034i			2.72609i
$638$			35.4794i			1.40464i
$639$	−35.8412			−1.41786
$640$	2.22080	+	0.260869i	0.0877848	+	0.0103117i
$641$	−21.5564			−0.851428			−0.425714	−	0.904858i	$-0.639977\pi$
$641$	−21.5564			−0.851428			−0.425714	+	0.904858i	$0.639977\pi$
$642$		−	28.3681i		−	1.11960i
$643$		−	15.6344i		−	0.616561i	−0.951296	−	0.308280i	$-0.900246\pi$
$643$		−	15.6344i		−	0.616561i	0.951296	−	0.308280i	$-0.0997535\pi$
$644$	−22.9765			−0.905403
$645$	−0.780970	+	6.64846i	−0.0307506	+	0.261783i
$646$	−5.57718			−0.219431
$647$		−	10.0084i		−	0.393469i	−0.980457	−	0.196734i	$-0.936966\pi$
$647$		−	10.0084i		−	0.393469i	0.980457	−	0.196734i	$-0.0630337\pi$
$648$			8.66301i			0.340315i
$649$	−24.5276			−0.962794
$650$	23.2395	+	5.53611i	0.911530	+	0.217144i
$651$	−50.1302			−1.96476
$652$			12.5006i			0.489560i
$653$		−	32.9927i		−	1.29110i	−0.763717	−	0.645552i	$-0.776628\pi$
$653$		−	32.9927i		−	1.29110i	0.763717	−	0.645552i	$-0.223372\pi$
$654$	−16.7122			−0.653501
$655$	3.13701	−	26.7056i	0.122573	−	1.04348i
$656$	−0.557498			−0.0217666
$657$		−	49.2882i		−	1.92292i
$658$			14.6700i			0.571896i
$659$	−24.4298			−0.951648			−0.475824	−	0.879540i	$-0.657850\pi$
$659$	−24.4298			−0.951648			−0.475824	+	0.879540i	$0.657850\pi$
$660$	23.1934	+	2.72444i	0.902802	+	0.106049i
$661$	38.2001			1.48581			0.742906	−	0.669395i	$-0.233447\pi$
$661$	38.2001			1.48581			0.742906	+	0.669395i	$0.233447\pi$
$662$			8.55144i			0.332361i
$663$		−	37.9110i		−	1.47234i
$664$	−3.32959			−0.129213
$665$	−21.6184	−	2.53943i	−0.838324	−	0.0984747i
$666$	31.9990			1.23994
$667$			50.5138i			1.95590i
$668$		−	22.1166i		−	0.855718i
$669$	8.08876			0.312730
$670$	2.00620	−	17.0790i	0.0775063	−	0.659818i
$671$	33.9545			1.31080
$672$		−	13.8491i		−	0.534239i
$673$			20.3916i			0.786039i	0.919530	+	0.393020i	$0.128570\pi$
$673$			20.3916i			0.786039i	−0.919530	+	0.393020i	$0.871430\pi$
$674$	−29.4041			−1.13261
$675$	−10.2758	+	43.1360i	−0.395517	+	1.66031i
$676$	9.82901			0.378039
$677$			41.7872i			1.60601i	0.595971	+	0.803006i	$0.296767\pi$
$677$			41.7872i			1.60601i	−0.595971	+	0.803006i	$0.703233\pi$
$678$		−	20.3457i		−	0.781371i
$679$	−51.1608			−1.96337
$680$	0.691403	−	5.88598i	0.0265141	−	0.225717i
$681$	14.4124			0.552285
$682$		−	12.6276i		−	0.483537i
$683$			16.9413i			0.648241i	0.946016	+	0.324120i	$0.105068\pi$
$683$			16.9413i			0.648241i	−0.946016	+	0.324120i	$0.894932\pi$
$684$	12.5466			0.479732
$685$	31.9284	+	3.75051i	1.21992	+	0.143300i
$686$	34.2331			1.30703
$687$			29.3606i			1.12018i
$688$			1.00000i			0.0381246i
$689$	−13.1008			−0.499102
$690$	33.0216	+	3.87892i	1.25711	+	0.147668i
$691$	14.5712			0.554316			0.277158	−	0.960824i	$-0.410607\pi$
$691$	14.5712			0.554316			0.277158	+	0.960824i	$0.410607\pi$
$692$			4.53486i			0.172390i
$693$		−	96.2216i		−	3.65515i
$694$	9.69759			0.368116
$695$	−4.72222	+	40.2006i	−0.179124	+	1.52490i
$696$	−30.4470			−1.15409
$697$			1.47758i			0.0559675i
$698$			9.38543i			0.355244i
$699$	−67.2087			−2.54207
$700$	5.36006	−	22.5005i	0.202591	−	0.850439i
$701$	−18.2538			−0.689438			−0.344719	−	0.938706i	$-0.612026\pi$
$701$	−18.2538			−0.689438			−0.344719	+	0.938706i	$0.612026\pi$
$702$			42.3740i			1.59930i
$703$		−	11.2933i		−	0.425934i
$704$	3.48854			0.131479
$705$	2.47660	−	21.0835i	0.0932742	−	0.794052i
$706$	20.8583			0.785012
$707$		−	2.45427i		−	0.0923024i
$708$		−	21.0487i		−	0.791058i
$709$	0.140181			0.00526462			0.00263231	−	0.999997i	$-0.499162\pi$
$709$	0.140181			0.00526462			0.00263231	+	0.999997i	$0.499162\pi$
$710$	−13.3497	−	1.56814i	−0.501005	−	0.0588511i
$711$	−47.5695			−1.78399
$712$			15.8770i			0.595016i
$713$		−	17.9786i		−	0.673303i
$714$	−36.7054			−1.37366
$715$	37.0166	+	4.34819i	1.38434	+	0.162613i
$716$	−15.9501			−0.596082
$717$			42.3239i			1.58062i
$718$		−	13.6002i		−	0.507553i
$719$	3.15758			0.117758			0.0588790	−	0.998265i	$-0.481247\pi$
$719$	3.15758			0.117758			0.0588790	+	0.998265i	$0.481247\pi$
$720$	−1.55540	+	13.2413i	−0.0579665	+	0.493474i
$721$	−42.0243			−1.56507
$722$			14.5720i			0.542313i
$723$			65.7255i			2.44436i
$724$	−26.2357			−0.975041
$725$	−49.4672	−	11.7840i	−1.83717	−	0.437648i
$726$	3.50232			0.129983
$727$		−	23.4997i		−	0.871554i	−0.900055	−	0.435777i	$-0.856474\pi$
$727$		−	23.4997i		−	0.871554i	0.900055	−	0.435777i	$-0.143526\pi$
$728$		−	22.1030i		−	0.819192i
$729$	27.9983			1.03697
$730$	2.15647	−	18.3582i	0.0798147	−	0.679469i
$731$	2.65039			0.0980281
$732$			29.1384i			1.07699i
$733$		−	36.0182i		−	1.33036i	−0.746682	−	0.665181i	$-0.768355\pi$
$733$		−	36.0182i		−	1.33036i	0.746682	−	0.665181i	$-0.231645\pi$
$734$	−19.7084			−0.727450
$735$	−95.7387	−	11.2461i	−3.53137	−	0.414817i
$736$	4.96680			0.183079
$737$		−	26.8284i		−	0.988238i
$738$		−	3.32402i		−	0.122359i
$739$	−13.7081			−0.504262			−0.252131	−	0.967693i	$-0.581131\pi$
$739$	−13.7081			−0.504262			−0.252131	+	0.967693i	$0.581131\pi$
$740$	11.9186	+	1.40003i	0.438135	+	0.0514661i
$741$	30.0996			1.10574
$742$			12.6842i			0.465652i
$743$			17.1729i			0.630013i	0.949090	+	0.315006i	$0.102007\pi$
$743$			17.1729i			0.630013i	−0.949090	+	0.315006i	$0.897993\pi$
$744$	10.8366			0.397287
$745$	−3.87508	+	32.9889i	−0.141972	+	1.20862i
$746$	−13.6028			−0.498036
$747$		−	19.8524i		−	0.726360i
$748$		−	9.24597i		−	0.338066i
$749$	−43.8356			−1.60172
$750$	−11.5020	+	31.4325i	−0.419992	+	1.14775i
$751$	−40.3567			−1.47264			−0.736319	−	0.676635i	$-0.763438\pi$
$751$	−40.3567			−1.47264			−0.736319	+	0.676635i	$0.763438\pi$
$752$		−	3.17119i		−	0.115641i
$753$		−	18.1031i		−	0.659715i
$754$	−48.5933			−1.76966
$755$	3.83568	−	32.6535i	0.139595	−	1.18838i
$756$	41.0264			1.49212
$757$		−	11.1114i		−	0.403852i	−0.979401	−	0.201926i	$-0.935280\pi$
$757$		−	11.1114i		−	0.403852i	0.979401	−	0.201926i	$-0.0647200\pi$
$758$			7.71555i			0.280242i
$759$	51.8719			1.88283
$760$	4.67320	+	0.548943i	0.169515	+	0.0199123i
$761$	−13.4225			−0.486565			−0.243282	−	0.969956i	$-0.578224\pi$
$761$	−13.4225			−0.486565			−0.243282	+	0.969956i	$0.578224\pi$
$762$			22.5199i			0.815811i
$763$			25.8244i			0.934907i
$764$	8.68534			0.314225
$765$	35.0945	+	4.12242i	1.26885	+	0.149046i
$766$	30.6014			1.10567
$767$		−	33.5936i		−	1.21299i
$768$			2.99373i			0.108027i
$769$	−41.6170			−1.50075			−0.750374	−	0.661014i	$-0.770127\pi$
$769$	−41.6170			−1.50075			−0.750374	+	0.661014i	$0.770127\pi$
$770$	4.20992	−	35.8394i	0.151715	−	1.29156i
$771$	6.26331			0.225568
$772$		−	14.3676i		−	0.517101i
$773$		−	28.1444i		−	1.01228i	−0.862450	−	0.506142i	$-0.831071\pi$
$773$		−	28.1444i		−	1.01228i	0.862450	−	0.506142i	$-0.168929\pi$
$774$	−5.96240			−0.214314
$775$	17.6061	+	4.19411i	0.632430	+	0.150657i
$776$	11.0593			0.397007
$777$		−	74.3251i		−	2.66640i
$778$			5.44823i			0.195329i
$779$	−1.17314			−0.0420320
$780$	−3.73145	+	31.7662i	−0.133607	+	1.13741i
$781$	−20.9703			−0.750377
$782$		−	13.1639i		−	0.470741i
$783$		−	90.1963i		−	3.22335i
$784$	−14.4001			−0.514290
$785$	−39.8110	−	4.67645i	−1.42092	−	0.166910i
$786$	36.0003			1.28409
$787$		−	44.7773i		−	1.59614i	−0.602565	−	0.798070i	$-0.705854\pi$
$787$		−	44.7773i		−	1.59614i	0.602565	−	0.798070i	$-0.294146\pi$
$788$			6.19264i			0.220604i
$789$	7.69899			0.274091
$790$	−17.7181	−	2.08127i	−0.630381	−	0.0740484i
$791$	−31.4390			−1.11784
$792$			20.8000i			0.739097i
$793$			46.5047i			1.65143i
$794$	6.54409			0.232241
$795$	2.14136	−	18.2296i	0.0759463	−	0.646537i
$796$	0.211786			0.00750657
$797$			34.8205i			1.23340i	0.787196	+	0.616702i	$0.211532\pi$
$797$			34.8205i			1.23340i	−0.787196	+	0.616702i	$0.788468\pi$
$798$		−	29.1424i		−	1.03163i
$799$	−8.40488			−0.297343
$800$	−1.15867	+	4.86390i	−0.0409653	+	0.171965i
$801$	−94.6651			−3.34483
$802$			3.13834i			0.110819i
$803$		−	28.8380i		−	1.01767i
$804$	23.0231			0.811963
$805$	5.99386	−	51.0263i	0.211256	−	1.79844i
$806$	17.2951			0.609193
$807$			52.3645i			1.84332i
$808$			0.530536i			0.0186642i
$809$	−55.3571			−1.94625			−0.973126	−	0.230275i	$-0.926038\pi$
$809$	−55.3571			−1.94625			−0.973126	+	0.230275i	$0.926038\pi$
$810$	−19.2388	−	2.25991i	−0.675983	−	0.0794051i
$811$	31.3299			1.10014			0.550071	−	0.835118i	$-0.314601\pi$
$811$	31.3299			1.10014			0.550071	+	0.835118i	$0.314601\pi$
$812$			47.0480i			1.65106i
$813$			98.0374i			3.43832i
$814$	18.7223			0.656215
$815$	−27.7613	−	3.26101i	−0.972434	−	0.114228i
$816$	7.93453			0.277764
$817$			2.10429i			0.0736198i
$818$			10.2908i			0.359811i
$819$	131.787			4.60501
$820$	0.145434	−	1.23809i	0.00507876	−	0.0432360i
$821$	19.5486			0.682250			0.341125	−	0.940018i	$-0.389192\pi$
$821$	19.5486			0.682250			0.341125	+	0.940018i	$0.389192\pi$
$822$			43.0408i			1.50122i
$823$		−	10.7039i		−	0.373115i	−0.982444	−	0.186557i	$-0.940267\pi$
$823$		−	10.7039i		−	0.373115i	0.982444	−	0.186557i	$-0.0597330\pi$
$824$	9.08431			0.316467
$825$	−12.1009	+	50.7972i	−0.421298	+	1.76853i
$826$	−32.5253			−1.13170
$827$		−	10.3788i		−	0.360907i	−0.983583	−	0.180454i	$-0.942243\pi$
$827$		−	10.3788i		−	0.360907i	0.983583	−	0.180454i	$-0.0577566\pi$
$828$			29.6140i			1.02916i
$829$	8.66013			0.300779			0.150389	−	0.988627i	$-0.451947\pi$
$829$	8.66013			0.300779			0.150389	+	0.988627i	$0.451947\pi$
$830$	0.868587	−	7.39436i	0.0301491	−	0.256662i
$831$	39.2176			1.36044
$832$			4.77797i			0.165646i
$833$			38.1659i			1.32237i
$834$	−54.1921			−1.87652
$835$	49.1166	+	5.76954i	1.69975	+	0.199663i
$836$	7.34089			0.253890
$837$			32.1022i			1.10961i
$838$			16.4773i			0.569198i
$839$	−23.7506			−0.819961			−0.409980	−	0.912094i	$-0.634464\pi$
$839$	−23.7506			−0.819961			−0.409980	+	0.912094i	$0.634464\pi$
$840$	30.7560	+	3.61279i	1.06118	+	0.124653i
$841$	74.4347			2.56671
$842$			30.5518i			1.05289i
$843$			50.0220i			1.72285i
$844$	−3.04207			−0.104712
$845$	−2.56408	+	21.8282i	−0.0882070	+	0.750914i
$846$	18.9079			0.650067
$847$		−	5.41192i		−	0.185956i
$848$		−	2.74193i		−	0.0941581i
$849$	20.6277			0.707942
$850$	12.8912	+	3.07093i	0.442165	+	0.105332i
$851$	26.6558			0.913749
$852$		−	17.9959i		−	0.616530i
$853$		−	32.1905i		−	1.10218i	−0.834446	−	0.551090i	$-0.814212\pi$
$853$		−	32.1905i		−	1.10218i	0.834446	−	0.551090i	$-0.185788\pi$
$854$	45.0258			1.54075
$855$	−3.27302	+	27.8635i	−0.111935	+	0.952912i
$856$	9.47586			0.323878
$857$			2.66981i			0.0911989i	0.998960	+	0.0455995i	$0.0145198\pi$
$857$			2.66981i			0.0911989i	−0.998960	+	0.0455995i	$0.985480\pi$
$858$			49.8998i			1.70355i
$859$	1.16650			0.0398004			0.0199002	−	0.999802i	$-0.493665\pi$
$859$	1.16650			0.0398004			0.0199002	+	0.999802i	$0.493665\pi$
$860$	−2.22080	−	0.260869i	−0.0757286	−	0.00889555i
$861$	−7.72082			−0.263125
$862$		−	11.2043i		−	0.381621i
$863$			38.0660i			1.29578i	0.761733	+	0.647891i	$0.224349\pi$
$863$			38.0660i			1.29578i	−0.761733	+	0.647891i	$0.775651\pi$
$864$	−8.86861			−0.301716
$865$	−10.0710	−	1.18300i	−0.342425	−	0.0402234i
$866$	−23.8671			−0.811038
$867$			29.8638i			1.01423i
$868$		−	16.7451i		−	0.568365i
$869$	−27.8324			−0.944149
$870$	7.94268	−	67.6168i	0.269282	−	2.29242i
$871$	36.7448			1.24505
$872$		−	5.58242i		−	0.189045i
$873$			65.9402i			2.23174i
$874$	10.4516			0.353530
$875$	48.5708	+	17.7733i	1.64199	+	0.600847i
$876$	24.7477			0.836146
$877$			14.1633i			0.478262i	0.970987	+	0.239131i	$0.0768626\pi$
$877$			14.1633i			0.478262i	−0.970987	+	0.239131i	$0.923137\pi$
$878$			8.60578i			0.290431i
$879$	86.4374			2.91546
$880$	−0.910050	+	7.74734i	−0.0306778	+	0.261163i
$881$	−2.58856			−0.0872109			−0.0436055	−	0.999049i	$-0.513884\pi$
$881$	−2.58856			−0.0872109			−0.0436055	+	0.999049i	$0.513884\pi$
$882$		−	85.8593i		−	2.89103i
$883$			23.8437i			0.802403i	0.915990	+	0.401202i	$0.131407\pi$
$883$			23.8437i			0.802403i	−0.915990	+	0.401202i	$0.868593\pi$
$884$	12.6635			0.425919
$885$	46.7449	+	5.49094i	1.57131	+	0.184576i
$886$	−4.88400			−0.164081
$887$		−	13.0391i		−	0.437809i	−0.975746	−	0.218905i	$-0.929752\pi$
$887$		−	13.0391i		−	0.437809i	0.975746	−	0.218905i	$-0.0702484\pi$
$888$			16.0667i			0.539164i
$889$	34.7987			1.16711
$890$	−35.2597	−	4.14182i	−1.18191	−	0.138834i
$891$	−30.2212			−1.01245
$892$			2.70190i			0.0904665i
$893$		−	6.67310i		−	0.223307i
$894$	−44.4703			−1.48731
$895$	4.16087	−	35.4219i	0.139083	−	1.18402i
$896$	4.62603			0.154545
$897$			71.0448i			2.37212i
$898$			8.03223i			0.268039i
$899$	−36.8139			−1.22781
$900$	−29.0005	−	6.90848i	−0.966683	−	0.230283i
$901$	−7.26716			−0.242104
$902$		−	1.94485i		−	0.0647564i
$903$			13.8491i			0.460868i
$904$	6.79611			0.226035
$905$	6.84406	−	58.2641i	0.227504	−	1.93677i
$906$	44.0182			1.46241
$907$		−	20.1873i		−	0.670307i	−0.942164	−	0.335154i	$-0.891212\pi$
$907$		−	20.1873i		−	0.670307i	0.942164	−	0.335154i	$-0.108788\pi$
$908$			4.81420i			0.159765i
$909$	−3.16327			−0.104919
$910$	49.0864	+	5.76599i	1.62720	+	0.191141i
$911$	−35.7967			−1.18600			−0.592998	−	0.805204i	$-0.702056\pi$
$911$	−35.7967			−1.18600			−0.592998	+	0.805204i	$0.702056\pi$
$912$			6.29967i			0.208603i
$913$		−	11.6154i		−	0.384414i
$914$	−0.0987491			−0.00326633
$915$	−64.7106	−	7.60130i	−2.13927	−	0.251291i
$916$	−9.80736			−0.324044
$917$		−	55.6290i		−	1.83703i
$918$			23.5053i			0.775789i
$919$	8.73432			0.288119			0.144059	−	0.989569i	$-0.453984\pi$
$919$	8.73432			0.288119			0.144059	+	0.989569i	$0.453984\pi$
$920$	−1.29568	+	11.0303i	−0.0427174	+	0.363657i
$921$	−53.8910			−1.77577
$922$			11.1908i			0.368550i
$923$		−	28.7214i		−	0.945376i
$924$	48.3129			1.58938
$925$	−6.21837	+	26.1035i	−0.204459	+	0.858279i
$926$	−2.98990			−0.0982542
$927$			54.1643i			1.77899i
$928$		−	10.1703i		−	0.333856i
$929$	21.4292			0.703068			0.351534	−	0.936175i	$-0.385660\pi$
$929$	21.4292			0.703068			0.351534	+	0.936175i	$0.385660\pi$
$930$	−2.82692	+	24.0658i	−0.0926983	+	0.789149i
$931$	−30.3020			−0.993108
$932$		−	22.4499i		−	0.735369i
$933$		−	95.4493i		−	3.12487i
$934$	−7.76496			−0.254077
$935$	20.5334	+	2.41198i	0.671515	+	0.0788803i
$936$	−28.4882			−0.931165
$937$		−	11.0274i		−	0.360249i	−0.983644	−	0.180125i	$-0.942350\pi$
$937$		−	11.0274i		−	0.360249i	0.983644	−	0.180125i	$-0.0576501\pi$
$938$		−	35.5763i		−	1.16161i
$939$	−32.8186			−1.07100
$940$	7.04257	+	0.827264i	0.229703	+	0.0269824i
$941$	−11.6424			−0.379532			−0.189766	−	0.981829i	$-0.560773\pi$
$941$	−11.6424			−0.379532			−0.189766	+	0.981829i	$0.560773\pi$
$942$		−	53.6669i		−	1.74856i
$943$		−	2.76898i		−	0.0901703i
$944$	7.03093			0.228837
$945$	−10.7025	+	91.1115i	−0.348153	+	2.96386i
$946$	−3.48854			−0.113422
$947$		−	43.0973i		−	1.40048i	−0.713910	−	0.700238i	$-0.753077\pi$
$947$		−	43.0973i		−	1.40048i	0.713910	−	0.700238i	$-0.246923\pi$
$948$		−	23.8847i		−	0.775738i
$949$	39.4971			1.28213
$950$	−2.43818	+	10.2350i	−0.0791052	+	0.332069i
$951$	−40.7991			−1.32300
$952$		−	12.2608i		−	0.397373i
$953$			17.1976i			0.557084i	0.960424	+	0.278542i	$0.0898511\pi$
$953$			17.1976i			0.557084i	−0.960424	+	0.278542i	$0.910149\pi$
$954$	16.3485			0.529301
$955$	−2.26573	+	19.2884i	−0.0733174	+	0.624158i
$956$	−14.1375			−0.457241
$957$		−	106.216i		−	3.43346i
$958$		−	10.4742i		−	0.338406i
$959$	66.5084			2.14767
$960$	−6.64846	−	0.780970i	−0.214578	−	0.0252057i
$961$	−17.8974			−0.577335
$962$			25.6424i			0.826744i
$963$			56.4989i			1.82065i
$964$	−21.9544			−0.707104
$965$	31.9075	+	3.74805i	1.02714	+	0.120654i
$966$	68.7855			2.21314
$967$		−	29.2625i		−	0.941019i	−0.882395	−	0.470510i	$-0.844070\pi$
$967$		−	29.2625i		−	0.941019i	0.882395	−	0.470510i	$-0.155930\pi$
$968$			1.16989i			0.0376015i
$969$	16.6966			0.536370
$970$	−2.88504	+	24.5606i	−0.0926330	+	0.788593i
$971$	26.8793			0.862599			0.431300	−	0.902209i	$-0.358055\pi$
$971$	26.8793			0.862599			0.431300	+	0.902209i	$0.358055\pi$
$972$			0.671161i			0.0215275i
$973$			83.7398i			2.68457i
$974$	27.1578			0.870193
$975$	−69.5729	−	16.5736i	−2.22811	−	0.530780i
$976$	−9.73316			−0.311551
$977$		−	18.7699i		−	0.600504i	−0.953860	−	0.300252i	$-0.902929\pi$
$977$		−	18.7699i		−	0.600504i	0.953860	−	0.300252i	$-0.0970707\pi$
$978$		−	37.4233i		−	1.19666i
$979$	−55.3875			−1.77019
$980$	3.75654	−	31.9798i	0.119998	−	1.02156i
$981$	33.2846			1.06270
$982$			29.6634i			0.946599i
$983$			3.92823i			0.125291i	0.998036	+	0.0626456i	$0.0199538\pi$
$983$			3.92823i			0.125291i	−0.998036	+	0.0626456i	$0.980046\pi$
$984$	1.66900			0.0532056
$985$	−13.7526	−	1.61547i	−0.438195	−	0.0514731i
$986$	−26.9552			−0.858428
$987$		−	43.9180i		−	1.39792i
$988$			10.0542i			0.319868i
$989$	−4.96680			−0.157935
$990$	−46.1927	−	5.42608i	−1.46810	−	0.172452i
$991$	−14.4084			−0.457697			−0.228848	−	0.973462i	$-0.573496\pi$
$991$	−14.4084			−0.457697			−0.228848	+	0.973462i	$0.573496\pi$
$992$			3.61975i			0.114927i
$993$		−	25.6007i		−	0.812412i
$994$	−27.8080			−0.882017
$995$	−0.0552484	+	0.470335i	−0.00175149	+	0.0149106i
$996$	9.96789			0.315845
$997$			50.9001i			1.61202i	0.591900	+	0.806012i	$0.298378\pi$
$997$			50.9001i			1.61202i	−0.591900	+	0.806012i	$0.701622\pi$
$998$			33.5426i			1.06177i
$999$	−47.5960			−1.50587

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.b.b.259.7	✓	16
5.2	odd	4		2150.2.a.bh.1.7		8
5.3	odd	4		2150.2.a.bg.1.2		8
5.4	even	2	inner	430.2.b.b.259.10	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.b.b.259.7	✓	16	1.1	even	1	trivial
430.2.b.b.259.10	yes	16	5.4	even	2	inner
2150.2.a.bg.1.2		8	5.3	odd	4
2150.2.a.bh.1.7		8	5.2	odd	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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +2.99373i q^{3} -1.00000 q^{4} +(0.260869 - 2.22080i) q^{5} +2.99373 q^{6} -4.62603i q^{7} +1.00000i q^{8} -5.96240 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +2.99373i q^{3} -1.00000 q^{4} +(0.260869 - 2.22080i) q^{5} +2.99373 q^{6} -4.62603i q^{7} +1.00000i q^{8} -5.96240 q^{9} +(-2.22080 - 0.260869i) q^{10} -3.48854 q^{11} -2.99373i q^{12} -4.77797i q^{13} -4.62603 q^{14} +(6.64846 + 0.780970i) q^{15} +1.00000 q^{16} -2.65039i q^{17} +5.96240i q^{18} +2.10429 q^{19} +(-0.260869 + 2.22080i) q^{20} +13.8491 q^{21} +3.48854i q^{22} +4.96680i q^{23} -2.99373 q^{24} +(-4.86390 - 1.15867i) q^{25} -4.77797 q^{26} -8.86861i q^{27} +4.62603i q^{28} +10.1703 q^{29} +(0.780970 - 6.64846i) q^{30} -3.61975 q^{31} -1.00000i q^{32} -10.4437i q^{33} -2.65039 q^{34} +(-10.2735 - 1.20679i) q^{35} +5.96240 q^{36} -5.36680i q^{37} -2.10429i q^{38} +14.3039 q^{39} +(2.22080 + 0.260869i) q^{40} -0.557498 q^{41} -13.8491i q^{42} +1.00000i q^{43} +3.48854 q^{44} +(-1.55540 + 13.2413i) q^{45} +4.96680 q^{46} -3.17119i q^{47} +2.99373i q^{48} -14.4001 q^{49} +(-1.15867 + 4.86390i) q^{50} +7.93453 q^{51} +4.77797i q^{52} -2.74193i q^{53} -8.86861 q^{54} +(-0.910050 + 7.74734i) q^{55} +4.62603 q^{56} +6.29967i q^{57} -10.1703i q^{58} +7.03093 q^{59} +(-6.64846 - 0.780970i) q^{60} -9.73316 q^{61} +3.61975i q^{62} +27.5822i q^{63} -1.00000 q^{64} +(-10.6109 - 1.24642i) q^{65} -10.4437 q^{66} +7.69046i q^{67} +2.65039i q^{68} -14.8692 q^{69} +(-1.20679 + 10.2735i) q^{70} +6.01121 q^{71} -5.96240i q^{72} +8.26651i q^{73} -5.36680 q^{74} +(3.46875 - 14.5612i) q^{75} -2.10429 q^{76} +16.1381i q^{77} -14.3039i q^{78} +7.97824 q^{79} +(0.260869 - 2.22080i) q^{80} +8.66301 q^{81} +0.557498i q^{82} +3.32959i q^{83} -13.8491 q^{84} +(-5.88598 - 0.691403i) q^{85} +1.00000 q^{86} +30.4470i q^{87} -3.48854i q^{88} +15.8770 q^{89} +(13.2413 + 1.55540i) q^{90} -22.1030 q^{91} -4.96680i q^{92} -10.8366i q^{93} -3.17119 q^{94} +(0.548943 - 4.67320i) q^{95} +2.99373 q^{96} -11.0593i q^{97} +14.4001i q^{98} +20.8000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 2 q^{5} + 8 q^{6} - 28 q^{9}+O(q^{10}) \) 16 * q - 16 * q^4 + 2 * q^5 + 8 * q^6 - 28 * q^9	\( 16 q - 16 q^{4} + 2 q^{5} + 8 q^{6} - 28 q^{9} + 4 q^{11} - 6 q^{14} - 4 q^{15} + 16 q^{16} - 30 q^{19} - 2 q^{20} + 32 q^{21} - 8 q^{24} - 10 q^{25} - 6 q^{26} + 6 q^{29} - 12 q^{30} + 50 q^{31} - 36 q^{35} + 28 q^{36} - 4 q^{39} + 38 q^{41} - 4 q^{44} - 50 q^{45} + 24 q^{46} - 38 q^{49} - 8 q^{50} + 8 q^{51} - 20 q^{54} - 28 q^{55} + 6 q^{56} + 24 q^{59} + 4 q^{60} + 58 q^{61} - 16 q^{64} - 32 q^{65} + 36 q^{66} - 4 q^{69} - 22 q^{70} + 24 q^{71} + 4 q^{74} - 36 q^{75} + 30 q^{76} - 10 q^{79} + 2 q^{80} + 80 q^{81} - 32 q^{84} - 56 q^{85} + 16 q^{86} + 40 q^{89} - 22 q^{90} + 46 q^{91} - 12 q^{94} - 52 q^{95} + 8 q^{96} + 32 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 + 2 * q^5 + 8 * q^6 - 28 * q^9 + 4 * q^11 - 6 * q^14 - 4 * q^15 + 16 * q^16 - 30 * q^19 - 2 * q^20 + 32 * q^21 - 8 * q^24 - 10 * q^25 - 6 * q^26 + 6 * q^29 - 12 * q^30 + 50 * q^31 - 36 * q^35 + 28 * q^36 - 4 * q^39 + 38 * q^41 - 4 * q^44 - 50 * q^45 + 24 * q^46 - 38 * q^49 - 8 * q^50 + 8 * q^51 - 20 * q^54 - 28 * q^55 + 6 * q^56 + 24 * q^59 + 4 * q^60 + 58 * q^61 - 16 * q^64 - 32 * q^65 + 36 * q^66 - 4 * q^69 - 22 * q^70 + 24 * q^71 + 4 * q^74 - 36 * q^75 + 30 * q^76 - 10 * q^79 + 2 * q^80 + 80 * q^81 - 32 * q^84 - 56 * q^85 + 16 * q^86 + 40 * q^89 - 22 * q^90 + 46 * q^91 - 12 * q^94 - 52 * q^95 + 8 * q^96 + 32 * q^99

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