LMFDB - Embedded newform 430.2.b.b.259.9

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			259.9
Root			$-2.26167i$ of defining polynomial
Character	$\chi$	$=$	430.259
Dual form			430.2.b.b.259.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -3.26167i q^{3} -1.00000 q^{4} +(0.904683 - 2.04488i) q^{5} +3.26167 q^{6} -1.22270i q^{7} -1.00000i q^{8} -7.63849 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -3.26167i q^{3} -1.00000 q^{4} +(0.904683 - 2.04488i) q^{5} +3.26167 q^{6} -1.22270i q^{7} -1.00000i q^{8} -7.63849 q^{9} +(2.04488 + 0.904683i) q^{10} +4.91802 q^{11} +3.26167i q^{12} +3.77142i q^{13} +1.22270 q^{14} +(-6.66973 - 2.95078i) q^{15} +1.00000 q^{16} -6.24639i q^{17} -7.63849i q^{18} -5.03206 q^{19} +(-0.904683 + 2.04488i) q^{20} -3.98803 q^{21} +4.91802i q^{22} +4.72739i q^{23} -3.26167 q^{24} +(-3.36310 - 3.69994i) q^{25} -3.77142 q^{26} +15.1292i q^{27} +1.22270i q^{28} -4.33418 q^{29} +(2.95078 - 6.66973i) q^{30} +1.96103 q^{31} +1.00000i q^{32} -16.0410i q^{33} +6.24639 q^{34} +(-2.50027 - 1.10615i) q^{35} +7.63849 q^{36} -4.33168i q^{37} -5.03206i q^{38} +12.3011 q^{39} +(-2.04488 - 0.904683i) q^{40} +6.72628 q^{41} -3.98803i q^{42} -1.00000i q^{43} -4.91802 q^{44} +(-6.91041 + 15.6198i) q^{45} -4.72739 q^{46} +4.48186i q^{47} -3.26167i q^{48} +5.50501 q^{49} +(3.69994 - 3.36310i) q^{50} -20.3737 q^{51} -3.77142i q^{52} -1.85921i q^{53} -15.1292 q^{54} +(4.44925 - 10.0568i) q^{55} -1.22270 q^{56} +16.4129i q^{57} -4.33418i q^{58} +10.1421 q^{59} +(6.66973 + 2.95078i) q^{60} +9.35152 q^{61} +1.96103i q^{62} +9.33955i q^{63} -1.00000 q^{64} +(7.71211 + 3.41194i) q^{65} +16.0410 q^{66} -11.0005i q^{67} +6.24639i q^{68} +15.4192 q^{69} +(1.10615 - 2.50027i) q^{70} -10.0275 q^{71} +7.63849i q^{72} +1.14660i q^{73} +4.33168 q^{74} +(-12.0680 + 10.9693i) q^{75} +5.03206 q^{76} -6.01325i q^{77} +12.3011i q^{78} +15.7544 q^{79} +(0.904683 - 2.04488i) q^{80} +26.4310 q^{81} +6.72628i q^{82} +9.21208i q^{83} +3.98803 q^{84} +(-12.7731 - 5.65100i) q^{85} +1.00000 q^{86} +14.1367i q^{87} -4.91802i q^{88} +3.91635 q^{89} +(-15.6198 - 6.91041i) q^{90} +4.61130 q^{91} -4.72739i q^{92} -6.39622i q^{93} -4.48186 q^{94} +(-4.55242 + 10.2900i) q^{95} +3.26167 q^{96} -5.00032i q^{97} +5.50501i q^{98} -37.5662 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$		−	3.26167i		−	1.88313i	−0.336837	−	0.941563i	$-0.609357\pi$
$3$		−	3.26167i		−	1.88313i	0.336837	−	0.941563i	$-0.390643\pi$
$4$	−1.00000			−0.500000
$5$	0.904683	−	2.04488i	0.404586	−	0.914500i
$5$	0.904683	−	2.04488i	0.404586	−	0.914500i
$6$	3.26167			1.33157
$7$		−	1.22270i		−	0.462136i	−0.972938	−	0.231068i	$-0.925778\pi$
$7$		−	1.22270i		−	0.462136i	0.972938	−	0.231068i	$-0.0742220\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−7.63849			−2.54616
$10$	2.04488	+	0.904683i	0.646649	+	0.286086i
$11$	4.91802			1.48284			0.741419	−	0.671042i	$-0.234153\pi$
$11$	4.91802			1.48284			0.741419	+	0.671042i	$0.234153\pi$
$12$			3.26167i			0.941563i
$13$			3.77142i			1.04600i	0.852332	+	0.523001i	$0.175188\pi$
$13$			3.77142i			1.04600i	−0.852332	+	0.523001i	$0.824812\pi$
$14$	1.22270			0.326779
$15$	−6.66973	−	2.95078i	−1.72212	−	0.761887i
$16$	1.00000			0.250000
$17$		−	6.24639i		−	1.51497i	−0.652851	−	0.757486i	$-0.726427\pi$
$17$		−	6.24639i		−	1.51497i	0.652851	−	0.757486i	$-0.273573\pi$
$18$		−	7.63849i		−	1.80041i
$19$	−5.03206			−1.15443			−0.577217	−	0.816591i	$-0.695861\pi$
$19$	−5.03206			−1.15443			−0.577217	+	0.816591i	$0.695861\pi$
$20$	−0.904683	+	2.04488i	−0.202293	+	0.457250i
$21$	−3.98803			−0.870260
$22$			4.91802i			1.04853i
$23$			4.72739i			0.985728i	0.870106	+	0.492864i	$0.164050\pi$
$23$			4.72739i			0.985728i	−0.870106	+	0.492864i	$0.835950\pi$
$24$	−3.26167			−0.665785
$25$	−3.36310	−	3.69994i	−0.672620	−	0.739988i
$26$	−3.77142			−0.739636
$27$			15.1292i			2.91162i
$28$			1.22270i			0.231068i
$29$	−4.33418			−0.804838			−0.402419	−	0.915456i	$-0.631830\pi$
$29$	−4.33418			−0.804838			−0.402419	+	0.915456i	$0.631830\pi$
$30$	2.95078	−	6.66973i	0.538736	−	1.21772i
$31$	1.96103			0.352211			0.176105	−	0.984371i	$-0.443650\pi$
$31$	1.96103			0.352211			0.176105	+	0.984371i	$0.443650\pi$
$32$			1.00000i			0.176777i
$33$		−	16.0410i		−	2.79237i
$34$	6.24639			1.07125
$35$	−2.50027	−	1.10615i	−0.422623	−	0.186974i
$36$	7.63849			1.27308
$37$		−	4.33168i		−	0.712124i	−0.934462	−	0.356062i	$-0.884119\pi$
$37$		−	4.33168i		−	0.712124i	0.934462	−	0.356062i	$-0.115881\pi$
$38$		−	5.03206i		−	0.816308i
$39$	12.3011			1.96975
$40$	−2.04488	−	0.904683i	−0.323324	−	0.143043i
$41$	6.72628			1.05047			0.525234	−	0.850958i	$-0.323978\pi$
$41$	6.72628			1.05047			0.525234	+	0.850958i	$0.323978\pi$
$42$		−	3.98803i		−	0.615367i
$43$		−	1.00000i		−	0.152499i
$43$		−	1.00000i		−	0.152499i
$44$	−4.91802			−0.741419
$45$	−6.91041	+	15.6198i	−1.03014	+	2.32846i
$46$	−4.72739			−0.697015
$47$			4.48186i			0.653747i	0.945068	+	0.326873i	$0.105995\pi$
$47$			4.48186i			0.653747i	−0.945068	+	0.326873i	$0.894005\pi$
$48$		−	3.26167i		−	0.470781i
$49$	5.50501			0.786430
$50$	3.69994	−	3.36310i	0.523251	−	0.475614i
$51$	−20.3737			−2.85288
$52$		−	3.77142i		−	0.523001i
$53$		−	1.85921i		−	0.255382i	−0.991814	−	0.127691i	$-0.959243\pi$
$53$		−	1.85921i		−	0.255382i	0.991814	−	0.127691i	$-0.0407566\pi$
$54$	−15.1292			−2.05882
$55$	4.44925	−	10.0568i	0.599937	−	1.35606i
$56$	−1.22270			−0.163390
$57$			16.4129i			2.17394i
$58$		−	4.33418i		−	0.569106i
$59$	10.1421			1.32039			0.660193	−	0.751096i	$-0.270475\pi$
$59$	10.1421			1.32039			0.660193	+	0.751096i	$0.270475\pi$
$60$	6.66973	+	2.95078i	0.861059	+	0.380944i
$61$	9.35152			1.19734			0.598670	−	0.800996i	$-0.295696\pi$
$61$	9.35152			1.19734			0.598670	+	0.800996i	$0.295696\pi$
$62$			1.96103i			0.249051i
$63$			9.33955i			1.17667i
$64$	−1.00000			−0.125000
$65$	7.71211	+	3.41194i	0.956569	+	0.423198i
$66$	16.0410			1.97451
$67$		−	11.0005i		−	1.34392i	−0.740587	−	0.671961i	$-0.765452\pi$
$67$		−	11.0005i		−	1.34392i	0.740587	−	0.671961i	$-0.234548\pi$
$68$			6.24639i			0.757486i
$69$	15.4192			1.85625
$70$	1.10615	−	2.50027i	0.132211	−	0.298840i
$71$	−10.0275			−1.19005			−0.595025	−	0.803707i	$-0.702858\pi$
$71$	−10.0275			−1.19005			−0.595025	+	0.803707i	$0.702858\pi$
$72$			7.63849i			0.900204i
$73$			1.14660i			0.134200i	0.997746	+	0.0670999i	$0.0213746\pi$
$73$			1.14660i			0.134200i	−0.997746	+	0.0670999i	$0.978625\pi$
$74$	4.33168			0.503548
$75$	−12.0680	+	10.9693i	−1.39349	+	1.26663i
$76$	5.03206			0.577217
$77$		−	6.01325i		−	0.685273i
$78$			12.3011i			1.39283i
$79$	15.7544			1.77250			0.886252	−	0.463203i	$-0.153300\pi$
$79$	15.7544			1.77250			0.886252	+	0.463203i	$0.153300\pi$
$80$	0.904683	−	2.04488i	0.101147	−	0.228625i
$81$	26.4310			2.93678
$82$			6.72628i			0.742793i
$83$			9.21208i			1.01116i	0.862781	+	0.505579i	$0.168721\pi$
$83$			9.21208i			1.01116i	−0.862781	+	0.505579i	$0.831279\pi$
$84$	3.98803			0.435130
$85$	−12.7731	−	5.65100i	−1.38544	−	0.612937i
$86$	1.00000			0.107833
$87$			14.1367i			1.51561i
$88$		−	4.91802i		−	0.524263i
$89$	3.91635			0.415132			0.207566	−	0.978221i	$-0.433446\pi$
$89$	3.91635			0.415132			0.207566	+	0.978221i	$0.433446\pi$
$90$	−15.6198	−	6.91041i	−1.64647	−	0.728421i
$91$	4.61130			0.483395
$92$		−	4.72739i		−	0.492864i
$93$		−	6.39622i		−	0.663257i
$94$	−4.48186			−0.462269
$95$	−4.55242	+	10.2900i	−0.467068	+	1.05573i
$96$	3.26167			0.332893
$97$		−	5.00032i		−	0.507706i	−0.967243	−	0.253853i	$-0.918302\pi$
$97$		−	5.00032i		−	0.507706i	0.967243	−	0.253853i	$-0.0816979\pi$
$98$			5.50501i			0.556090i
$99$	−37.5662			−3.77555
$100$	3.36310	+	3.69994i	0.336310	+	0.369994i
$101$	−8.43326			−0.839141			−0.419570	−	0.907723i	$-0.637819\pi$
$101$	−8.43326			−0.839141			−0.419570	+	0.907723i	$0.637819\pi$
$102$		−	20.3737i		−	2.01729i
$103$			3.50317i			0.345178i	0.984994	+	0.172589i	$0.0552132\pi$
$103$			3.50317i			0.345178i	−0.984994	+	0.172589i	$0.944787\pi$
$104$	3.77142			0.369818
$105$	−3.60790	+	8.15506i	−0.352095	+	0.795852i
$106$	1.85921			0.180582
$107$			10.7600i			1.04021i	0.854103	+	0.520104i	$0.174107\pi$
$107$			10.7600i			1.04021i	−0.854103	+	0.520104i	$0.825893\pi$
$108$		−	15.1292i		−	1.45581i
$109$	−6.31325			−0.604699			−0.302350	−	0.953197i	$-0.597771\pi$
$109$	−6.31325			−0.604699			−0.302350	+	0.953197i	$0.597771\pi$
$110$	10.0568	+	4.44925i	0.958876	+	0.424219i
$111$	−14.1285			−1.34102
$112$		−	1.22270i		−	0.115534i
$113$		−	15.1501i		−	1.42520i	−0.701570	−	0.712601i	$-0.747517\pi$
$113$		−	15.1501i		−	1.42520i	0.701570	−	0.712601i	$-0.252483\pi$
$114$	−16.4129			−1.53721
$115$	9.66695	+	4.27678i	0.901448	+	0.398812i
$116$	4.33418			0.402419
$117$		−	28.8079i		−	2.66329i
$118$			10.1421i			0.933653i
$119$	−7.63744			−0.700123
$120$	−2.95078	+	6.66973i	−0.269368	+	0.608861i
$121$	13.1869			1.19881
$122$			9.35152i			0.846647i
$123$		−	21.9389i		−	1.97816i
$124$	−1.96103			−0.176105
$125$	−10.6085	+	3.52987i	−0.948852	+	0.315721i
$126$	−9.33955			−0.832033
$127$			2.39838i			0.212822i	0.994322	+	0.106411i	$0.0339359\pi$
$127$			2.39838i			0.212822i	−0.994322	+	0.106411i	$0.966064\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−3.26167			−0.287174
$130$	−3.41194	+	7.71211i	−0.299247	+	0.676397i
$131$	5.13706			0.448827			0.224414	−	0.974494i	$-0.427953\pi$
$131$	5.13706			0.448827			0.224414	+	0.974494i	$0.427953\pi$
$132$			16.0410i			1.39619i
$133$			6.15269i			0.533505i
$134$	11.0005			0.950296
$135$	30.9375	+	13.6871i	2.66267	+	1.17800i
$136$	−6.24639			−0.535624
$137$		−	5.77327i		−	0.493244i	−0.969112	−	0.246622i	$-0.920679\pi$
$137$		−	5.77327i		−	0.493244i	0.969112	−	0.246622i	$-0.0793206\pi$
$138$			15.4192i			1.31257i
$139$	−13.5373			−1.14822			−0.574109	−	0.818779i	$-0.694652\pi$
$139$	−13.5373			−1.14822			−0.574109	+	0.818779i	$0.694652\pi$
$140$	2.50027	+	1.10615i	0.211312	+	0.0934869i
$141$	14.6184			1.23109
$142$		−	10.0275i		−	0.841493i
$143$			18.5479i			1.55105i
$144$	−7.63849			−0.636541
$145$	−3.92106	+	8.86290i	−0.325626	+	0.736024i
$146$	−1.14660			−0.0948936
$147$		−	17.9555i		−	1.48095i
$148$			4.33168i			0.356062i
$149$	10.0609			0.824224			0.412112	−	0.911133i	$-0.364791\pi$
$149$	10.0609			0.824224			0.412112	+	0.911133i	$0.364791\pi$
$150$	−10.9693	−	12.0680i	−0.895641	−	0.985347i
$151$	−3.40960			−0.277469			−0.138735	−	0.990330i	$-0.544303\pi$
$151$	−3.40960			−0.277469			−0.138735	+	0.990330i	$0.544303\pi$
$152$			5.03206i			0.408154i
$153$			47.7130i			3.85737i
$154$	6.01325			0.484561
$155$	1.77411	−	4.01007i	0.142500	−	0.322097i
$156$	−12.3011			−0.984877
$157$		−	12.8021i		−	1.02172i	−0.859664	−	0.510860i	$-0.829327\pi$
$157$		−	12.8021i		−	1.02172i	0.859664	−	0.510860i	$-0.170673\pi$
$158$			15.7544i			1.25335i
$159$	−6.06412			−0.480916
$160$	2.04488	+	0.904683i	0.161662	+	0.0715215i
$161$	5.78016			0.455540
$162$			26.4310i			2.07662i
$163$		−	12.6377i		−	0.989863i	−0.868932	−	0.494931i	$-0.835193\pi$
$163$		−	12.6377i		−	0.989863i	0.868932	−	0.494931i	$-0.164807\pi$
$164$	−6.72628			−0.525234
$165$	−32.8019	−	14.5120i	−2.55362	−	1.12976i
$166$	−9.21208			−0.714996
$167$			10.7191i			0.829467i	0.909943	+	0.414734i	$0.136125\pi$
$167$			10.7191i			0.829467i	−0.909943	+	0.414734i	$0.863875\pi$
$168$			3.98803i			0.307683i
$169$	−1.22358			−0.0941215
$170$	5.65100	−	12.7731i	0.433412	−	0.979655i
$171$	38.4373			2.93938
$172$			1.00000i			0.0762493i
$173$			8.86733i			0.674171i	0.941474	+	0.337085i	$0.109441\pi$
$173$			8.86733i			0.674171i	−0.941474	+	0.337085i	$0.890559\pi$
$174$	−14.1367			−1.07170
$175$	−4.52391	+	4.11205i	−0.341975	+	0.310842i
$176$	4.91802			0.370710
$177$		−	33.0801i		−	2.48645i
$178$			3.91635i			0.293543i
$179$	9.87763			0.738289			0.369144	−	0.929372i	$-0.379651\pi$
$179$	9.87763			0.738289			0.369144	+	0.929372i	$0.379651\pi$
$180$	6.91041	−	15.6198i	0.515071	−	1.16423i
$181$	22.6841			1.68610			0.843049	−	0.537837i	$-0.180759\pi$
$181$	22.6841			1.68610			0.843049	+	0.537837i	$0.180759\pi$
$182$			4.61130i			0.341812i
$183$		−	30.5016i		−	2.25474i
$184$	4.72739			0.348508
$185$	−8.85778	−	3.91880i	−0.651237	−	0.288116i
$186$	6.39622			0.468994
$187$		−	30.7199i		−	2.24646i
$188$		−	4.48186i		−	0.326873i
$189$	18.4984			1.34556
$190$	−10.2900	−	4.55242i	−0.746514	−	0.330267i
$191$	−11.5119			−0.832973			−0.416486	−	0.909142i	$-0.636739\pi$
$191$	−11.5119			−0.832973			−0.416486	+	0.909142i	$0.636739\pi$
$192$			3.26167i			0.235391i
$193$		−	0.154906i		−	0.0111504i	−0.999984	−	0.00557519i	$-0.998225\pi$
$193$		−	0.154906i		−	0.0111504i	0.999984	−	0.00557519i	$-0.00177465\pi$
$194$	5.00032			0.359002
$195$	11.1286	−	25.1543i	0.796936	−	1.80134i
$196$	−5.50501			−0.393215
$197$			15.6346i			1.11392i	0.830540	+	0.556959i	$0.188032\pi$
$197$			15.6346i			1.11392i	−0.830540	+	0.556959i	$0.811968\pi$
$198$		−	37.5662i		−	2.66972i
$199$	16.3977			1.16240			0.581201	−	0.813760i	$-0.302583\pi$
$199$	16.3977			1.16240			0.581201	+	0.813760i	$0.302583\pi$
$200$	−3.69994	+	3.36310i	−0.261625	+	0.237807i
$201$	−35.8799			−2.53077
$202$		−	8.43326i		−	0.593362i
$203$			5.29939i			0.371944i
$204$	20.3737			1.42644
$205$	6.08515	−	13.7545i	0.425005	−	0.960653i
$206$	−3.50317			−0.244077
$207$		−	36.1101i		−	2.50982i
$208$			3.77142i			0.261501i
$209$	−24.7478			−1.71184
$210$	−8.15506	−	3.60790i	−0.562753	−	0.248969i
$211$	−11.7456			−0.808600			−0.404300	−	0.914626i	$-0.632485\pi$
$211$	−11.7456			−0.808600			−0.404300	+	0.914626i	$0.632485\pi$
$212$			1.85921i			0.127691i
$213$			32.7065i			2.24101i
$214$	−10.7600			−0.735538
$215$	−2.04488	−	0.904683i	−0.139460	−	0.0616989i
$216$	15.1292			1.02941
$217$		−	2.39774i		−	0.162769i
$218$		−	6.31325i		−	0.427587i
$219$	3.73984			0.252715
$220$	−4.44925	+	10.0568i	−0.299968	+	0.678028i
$221$	23.5577			1.58466
$222$		−	14.1285i		−	0.948244i
$223$			17.7754i			1.19033i	0.803604	+	0.595165i	$0.202913\pi$
$223$			17.7754i			1.19033i	−0.803604	+	0.595165i	$0.797087\pi$
$224$	1.22270			0.0816949
$225$	25.6890	+	28.2620i	1.71260	+	1.88413i
$226$	15.1501			1.00777
$227$			23.8528i			1.58316i	0.611063	+	0.791582i	$0.290742\pi$
$227$			23.8528i			1.58316i	−0.611063	+	0.791582i	$0.709258\pi$
$228$		−	16.4129i		−	1.08697i
$229$	1.37004			0.0905347			0.0452674	−	0.998975i	$-0.485586\pi$
$229$	1.37004			0.0905347			0.0452674	+	0.998975i	$0.485586\pi$
$230$	−4.27678	+	9.66695i	−0.282003	+	0.637420i
$231$	−19.6132			−1.29046
$232$			4.33418i			0.284553i
$233$		−	0.102850i		−	0.00673793i	−0.999994	−	0.00336896i	$-0.998928\pi$
$233$		−	0.102850i		−	0.00673793i	0.999994	−	0.00336896i	$-0.00107238\pi$
$234$	28.8079			1.88323
$235$	9.16489	+	4.05466i	0.597851	+	0.264497i
$236$	−10.1421			−0.660193
$237$		−	51.3855i		−	3.33785i
$238$		−	7.63744i		−	0.495062i
$239$	15.9437			1.03131			0.515657	−	0.856795i	$-0.327548\pi$
$239$	15.9437			1.03131			0.515657	+	0.856795i	$0.327548\pi$
$240$	−6.66973	−	2.95078i	−0.430529	−	0.190472i
$241$	−21.0937			−1.35876			−0.679381	−	0.733786i	$-0.737752\pi$
$241$	−21.0937			−1.35876			−0.679381	+	0.733786i	$0.737752\pi$
$242$			13.1869i			0.847688i
$243$		−	40.8216i		−	2.61871i
$244$	−9.35152			−0.598670
$245$	4.98029	−	11.2571i	0.318179	−	0.719190i
$246$	21.9389			1.39877
$247$		−	18.9780i		−	1.20754i
$248$		−	1.96103i		−	0.124525i
$249$	30.0468			1.90414
$250$	−3.52987	−	10.6085i	−0.223249	−	0.670940i
$251$	5.44690			0.343805			0.171902	−	0.985114i	$-0.445009\pi$
$251$	5.44690			0.343805			0.171902	+	0.985114i	$0.445009\pi$
$252$		−	9.33955i		−	0.588336i
$253$			23.2494i			1.46168i
$254$	−2.39838			−0.150488
$255$	−18.4317	+	41.6618i	−1.15424	+	2.60896i
$256$	1.00000			0.0625000
$257$			19.9144i			1.24222i	0.783722	+	0.621112i	$0.213319\pi$
$257$			19.9144i			1.24222i	−0.783722	+	0.621112i	$0.786681\pi$
$258$		−	3.26167i		−	0.203063i
$259$	−5.29633			−0.329098
$260$	−7.71211	−	3.41194i	−0.478285	−	0.211599i
$261$	33.1066			2.04925
$262$			5.13706i			0.317369i
$263$			14.3351i			0.883940i	0.897030	+	0.441970i	$0.145720\pi$
$263$			14.3351i			0.883940i	−0.897030	+	0.441970i	$0.854280\pi$
$264$	−16.0410			−0.987253
$265$	−3.80187	−	1.68199i	−0.233547	−	0.103324i
$266$	−6.15269			−0.377245
$267$		−	12.7738i		−	0.781747i
$268$			11.0005i			0.671961i
$269$	−21.7497			−1.32610			−0.663052	−	0.748574i	$-0.730739\pi$
$269$	−21.7497			−1.32610			−0.663052	+	0.748574i	$0.730739\pi$
$270$	−13.6871	+	30.9375i	−0.832973	+	1.88279i
$271$	3.63298			0.220688			0.110344	−	0.993893i	$-0.464805\pi$
$271$	3.63298			0.220688			0.110344	+	0.993893i	$0.464805\pi$
$272$		−	6.24639i		−	0.378743i
$273$		−	15.0405i		−	0.910294i
$274$	5.77327			0.348776
$275$	−16.5398	−	18.1964i	−0.997387	−	1.09728i
$276$	−15.4192			−0.928125
$277$		−	19.8902i		−	1.19509i	−0.801836	−	0.597545i	$-0.796143\pi$
$277$		−	19.8902i		−	1.19509i	0.801836	−	0.597545i	$-0.203857\pi$
$278$		−	13.5373i		−	0.811913i
$279$	−14.9793			−0.896786
$280$	−1.10615	+	2.50027i	−0.0661053	+	0.149420i
$281$	−9.28266			−0.553757			−0.276879	−	0.960905i	$-0.589300\pi$
$281$	−9.28266			−0.553757			−0.276879	+	0.960905i	$0.589300\pi$
$282$			14.6184i			0.870510i
$283$		−	20.0343i		−	1.19091i	−0.803387	−	0.595457i	$-0.796971\pi$
$283$		−	20.0343i		−	1.19091i	0.803387	−	0.595457i	$-0.203029\pi$
$284$	10.0275			0.595025
$285$	33.5625	+	14.8485i	1.98807	+	0.879549i
$286$	−18.5479			−1.09676
$287$		−	8.22420i		−	0.485459i
$288$		−	7.63849i		−	0.450102i
$289$	−22.0174			−1.29514
$290$	−8.86290	−	3.92106i	−0.520447	−	0.230253i
$291$	−16.3094			−0.956074
$292$		−	1.14660i		−	0.0670999i
$293$		−	15.3892i		−	0.899048i	−0.893268	−	0.449524i	$-0.851594\pi$
$293$		−	15.3892i		−	0.899048i	0.893268	−	0.449524i	$-0.148406\pi$
$294$	17.9555			1.04719
$295$	9.17536	−	20.7394i	0.534210	−	1.20749i
$296$	−4.33168			−0.251774
$297$			74.4058i			4.31746i
$298$			10.0609i			0.582814i
$299$	−17.8289			−1.03107
$300$	12.0680	−	10.9693i	0.696746	−	0.633314i
$301$	−1.22270			−0.0704751
$302$		−	3.40960i		−	0.196200i
$303$			27.5065i			1.58021i
$304$	−5.03206			−0.288609
$305$	8.46016	−	19.1228i	0.484427	−	1.09497i
$306$	−47.7130			−2.72757
$307$			27.3859i			1.56299i	0.623909	+	0.781497i	$0.285544\pi$
$307$			27.3859i			1.56299i	−0.623909	+	0.781497i	$0.714456\pi$
$308$			6.01325i			0.342637i
$309$	11.4262			0.650013
$310$	4.01007	+	1.77411i	0.227757	+	0.100763i
$311$	−5.23705			−0.296966			−0.148483	−	0.988915i	$-0.547439\pi$
$311$	−5.23705			−0.296966			−0.148483	+	0.988915i	$0.547439\pi$
$312$		−	12.3011i		−	0.696413i
$313$		−	2.85664i		−	0.161467i	−0.996736	−	0.0807334i	$-0.974274\pi$
$313$		−	2.85664i		−	0.161467i	0.996736	−	0.0807334i	$-0.0257263\pi$
$314$	12.8021			0.722465
$315$	19.0983	+	8.44933i	1.07607	+	0.476066i
$316$	−15.7544			−0.886252
$317$			10.1054i			0.567577i	0.958887	+	0.283788i	$0.0915913\pi$
$317$			10.1054i			0.567577i	−0.958887	+	0.283788i	$0.908409\pi$
$318$		−	6.06412i		−	0.340059i
$319$	−21.3156			−1.19344
$320$	−0.904683	+	2.04488i	−0.0505733	+	0.114312i
$321$	35.0955			1.95884
$322$			5.78016i			0.322116i
$323$			31.4322i			1.74894i
$324$	−26.4310			−1.46839
$325$	13.9540	−	12.6836i	0.774030	−	0.703562i
$326$	12.6377			0.699938
$327$			20.5917i			1.13872i
$328$		−	6.72628i		−	0.371397i
$329$	5.47996			0.302120
$330$	14.5120	−	32.8019i	0.798858	−	1.80568i
$331$	−21.9153			−1.20457			−0.602286	−	0.798280i	$-0.705743\pi$
$331$	−21.9153			−1.20457			−0.602286	+	0.798280i	$0.705743\pi$
$332$		−	9.21208i		−	0.505579i
$333$			33.0875i			1.81318i
$334$	−10.7191			−0.586522
$335$	−22.4947	−	9.95194i	−1.22902	−	0.543732i
$336$	−3.98803			−0.217565
$337$			16.7325i			0.911475i	0.890114	+	0.455738i	$0.150624\pi$
$337$			16.7325i			0.911475i	−0.890114	+	0.455738i	$0.849376\pi$
$338$		−	1.22358i		−	0.0665539i
$339$	−49.4146			−2.68383
$340$	12.7731	+	5.65100i	0.692721	+	0.306469i
$341$	9.64437			0.522272
$342$			38.4373i			2.07845i
$343$		−	15.2898i		−	0.825574i
$344$	−1.00000			−0.0539164
$345$	13.9495	−	31.5304i	0.751014	−	1.69754i
$346$	−8.86733			−0.476711
$347$			16.4411i			0.882603i	0.897359	+	0.441302i	$0.145483\pi$
$347$			16.4411i			0.882603i	−0.897359	+	0.441302i	$0.854517\pi$
$348$		−	14.1367i		−	0.757805i
$349$	−22.8270			−1.22190			−0.610952	−	0.791668i	$-0.709213\pi$
$349$	−22.8270			−1.22190			−0.610952	+	0.791668i	$0.709213\pi$
$350$	−4.11205	−	4.52391i	−0.219798	−	0.241813i
$351$	−57.0585			−3.04556
$352$			4.91802i			0.262131i
$353$			23.2472i			1.23732i	0.785658	+	0.618661i	$0.212325\pi$
$353$			23.2472i			1.23732i	−0.785658	+	0.618661i	$0.787675\pi$
$354$	33.0801			1.75819
$355$	−9.07175	+	20.5052i	−0.481478	+	1.08830i
$356$	−3.91635			−0.207566
$357$			24.9108i			1.31842i
$358$			9.87763i			0.522049i
$359$	20.9495			1.10567			0.552836	−	0.833290i	$-0.313546\pi$
$359$	20.9495			1.10567			0.552836	+	0.833290i	$0.313546\pi$
$360$	15.6198	+	6.91041i	0.823237	+	0.364210i
$361$	6.32165			0.332718
$362$			22.6841i			1.19225i
$363$		−	43.0114i		−	2.25751i
$364$	−4.61130			−0.241698
$365$	2.34467	+	1.03731i	0.122726	+	0.0542954i
$366$	30.5016			1.59434
$367$			24.6439i			1.28640i	0.765697	+	0.643201i	$0.222394\pi$
$367$			24.6439i			1.28640i	−0.765697	+	0.643201i	$0.777606\pi$
$368$			4.72739i			0.246432i
$369$	−51.3786			−2.67466
$370$	3.91880	−	8.85778i	0.203729	−	0.460494i
$371$	−2.27325			−0.118021
$372$			6.39622i			0.331629i
$373$		−	6.54983i		−	0.339137i	−0.985518	−	0.169569i	$-0.945763\pi$
$373$		−	6.54983i		−	0.339137i	0.985518	−	0.169569i	$-0.0542374\pi$
$374$	30.7199			1.58849
$375$	11.5133	+	34.6014i	0.594543	+	1.78681i
$376$	4.48186			0.231134
$377$		−	16.3460i		−	0.841862i
$378$			18.4984i			0.951457i
$379$	−12.3493			−0.634340			−0.317170	−	0.948369i	$-0.602733\pi$
$379$	−12.3493			−0.634340			−0.317170	+	0.948369i	$0.602733\pi$
$380$	4.55242	−	10.2900i	0.233534	−	0.527865i
$381$	7.82273			0.400770
$382$		−	11.5119i		−	0.589001i
$383$			11.7119i			0.598451i	0.954182	+	0.299226i	$0.0967283\pi$
$383$			11.7119i			0.598451i	−0.954182	+	0.299226i	$0.903272\pi$
$384$	−3.26167			−0.166446
$385$	−12.2964	−	5.44008i	−0.626682	−	0.277252i
$386$	0.154906			0.00788451
$387$			7.63849i			0.388286i
$388$			5.00032i			0.253853i
$389$	36.4134			1.84623			0.923116	−	0.384521i	$-0.125634\pi$
$389$	36.4134			1.84623			0.923116	+	0.384521i	$0.125634\pi$
$390$	25.1543	+	11.1286i	1.27374	+	0.563519i
$391$	29.5291			1.49335
$392$		−	5.50501i		−	0.278045i
$393$		−	16.7554i		−	0.845198i
$394$	−15.6346			−0.787658
$395$	14.2527	−	32.2158i	0.717131	−	1.62096i
$396$	37.5662			1.88777
$397$			15.9505i			0.800533i	0.916399	+	0.400267i	$0.131083\pi$
$397$			15.9505i			0.800533i	−0.916399	+	0.400267i	$0.868917\pi$
$398$			16.3977i			0.821942i
$399$	20.0680			1.00466
$400$	−3.36310	−	3.69994i	−0.168155	−	0.184997i
$401$	−37.3371			−1.86452			−0.932262	−	0.361784i	$-0.882168\pi$
$401$	−37.3371			−1.86452			−0.932262	+	0.361784i	$0.882168\pi$
$402$		−	35.8799i		−	1.78953i
$403$			7.39585i			0.368414i
$404$	8.43326			0.419570
$405$	23.9117	−	54.0484i	1.18818	−	2.68568i
$406$	−5.29939			−0.263004
$407$		−	21.3033i		−	1.05597i
$408$			20.3737i			1.00865i
$409$	−0.372941			−0.0184407			−0.00922037	−	0.999957i	$-0.502935\pi$
$409$	−0.372941			−0.0184407			−0.00922037	+	0.999957i	$0.502935\pi$
$410$	13.7545	+	6.08515i	0.679284	+	0.300524i
$411$	−18.8305			−0.928840
$412$		−	3.50317i		−	0.172589i
$413$		−	12.4007i		−	0.610197i
$414$	36.1101			1.77471
$415$	18.8376	+	8.33401i	0.924703	+	0.409101i
$416$	−3.77142			−0.184909
$417$			44.1542i			2.16224i
$418$		−	24.7478i		−	1.21045i
$419$	−2.83899			−0.138694			−0.0693470	−	0.997593i	$-0.522092\pi$
$419$	−2.83899			−0.138694			−0.0693470	+	0.997593i	$0.522092\pi$
$420$	3.60790	−	8.15506i	0.176048	−	0.397926i
$421$	−11.4590			−0.558478			−0.279239	−	0.960222i	$-0.590082\pi$
$421$	−11.4590			−0.558478			−0.279239	+	0.960222i	$0.590082\pi$
$422$		−	11.7456i		−	0.571766i
$423$		−	34.2347i		−	1.66455i
$424$	−1.85921			−0.0902912
$425$	−23.1113	+	21.0072i	−1.12106	+	1.01900i
$426$	−32.7065			−1.58464
$427$		−	11.4341i		−	0.553333i
$428$		−	10.7600i		−	0.520104i
$429$	60.4971			2.92083
$430$	0.904683	−	2.04488i	0.0436277	−	0.0986130i
$431$	24.8735			1.19811			0.599057	−	0.800706i	$-0.295542\pi$
$431$	24.8735			1.19811			0.599057	+	0.800706i	$0.295542\pi$
$432$			15.1292i			0.727904i
$433$		−	17.4420i		−	0.838208i	−0.907938	−	0.419104i	$-0.862344\pi$
$433$		−	17.4420i		−	0.838208i	0.907938	−	0.419104i	$-0.137656\pi$
$434$	2.39774			0.115095
$435$	28.9078	+	12.7892i	1.38603	+	0.613195i
$436$	6.31325			0.302350
$437$		−	23.7885i		−	1.13796i
$438$			3.73984i			0.178697i
$439$	20.9147			0.998203			0.499102	−	0.866543i	$-0.333663\pi$
$439$	20.9147			0.998203			0.499102	+	0.866543i	$0.333663\pi$
$440$	−10.0568	−	4.44925i	−0.479438	−	0.212110i
$441$	−42.0500			−2.00238
$442$			23.5577i			1.12053i
$443$		−	24.4329i		−	1.16084i	−0.814317	−	0.580420i	$-0.802888\pi$
$443$		−	24.4329i		−	1.16084i	0.814317	−	0.580420i	$-0.197112\pi$
$444$	14.1285			0.670509
$445$	3.54306	−	8.00848i	0.167957	−	0.379639i
$446$	−17.7754			−0.841690
$447$		−	32.8154i		−	1.55212i
$448$			1.22270i			0.0577670i
$449$	1.89679			0.0895151			0.0447575	−	0.998998i	$-0.485748\pi$
$449$	1.89679			0.0895151			0.0447575	+	0.998998i	$0.485748\pi$
$450$	−28.2620	+	25.6890i	−1.33228	+	1.21099i
$451$	33.0800			1.55768
$452$			15.1501i			0.712601i
$453$			11.1210i			0.522509i
$454$	−23.8528			−1.11947
$455$	4.17176	−	9.42957i	0.195575	−	0.442065i
$456$	16.4129			0.768606
$457$			3.61887i			0.169284i	0.996411	+	0.0846418i	$0.0269746\pi$
$457$			3.61887i			0.169284i	−0.996411	+	0.0846418i	$0.973025\pi$
$458$			1.37004i			0.0640177i
$459$	94.5030			4.41102
$460$	−9.66695	−	4.27678i	−0.450724	−	0.199406i
$461$	−5.91589			−0.275531			−0.137765	−	0.990465i	$-0.543992\pi$
$461$	−5.91589			−0.275531			−0.137765	+	0.990465i	$0.543992\pi$
$462$		−	19.6132i		−	0.912490i
$463$			30.8874i			1.43546i	0.696321	+	0.717731i	$0.254819\pi$
$463$			30.8874i			1.43546i	−0.696321	+	0.717731i	$0.745181\pi$
$464$	−4.33418			−0.201209
$465$	−13.0795	−	5.78655i	−0.606549	−	0.268345i
$466$	0.102850			0.00476443
$467$		−	12.9717i		−	0.600259i	−0.953898	−	0.300130i	$-0.902970\pi$
$467$		−	12.9717i		−	0.600259i	0.953898	−	0.300130i	$-0.0970299\pi$
$468$			28.8079i			1.33165i
$469$	−13.4502			−0.621074
$470$	−4.05466	+	9.16489i	−0.187028	+	0.422745i
$471$	−41.7562			−1.92403
$472$		−	10.1421i		−	0.466827i
$473$		−	4.91802i		−	0.226131i
$474$	51.3855			2.36022
$475$	16.9233	+	18.6183i	0.776495	+	0.854268i
$476$	7.63744			0.350061
$477$			14.2015i			0.650244i
$478$			15.9437i			0.729249i
$479$	8.82445			0.403200			0.201600	−	0.979468i	$-0.435386\pi$
$479$	8.82445			0.403200			0.201600	+	0.979468i	$0.435386\pi$
$480$	2.95078	−	6.66973i	0.134684	−	0.304430i
$481$	16.3366			0.744884
$482$		−	21.0937i		−	0.960790i
$483$		−	18.8530i		−	0.857840i
$484$	−13.1869			−0.599406
$485$	−10.2251	−	4.52371i	−0.464297	−	0.205411i
$486$	40.8216			1.85171
$487$			25.7761i			1.16803i	0.811744	+	0.584014i	$0.198519\pi$
$487$			25.7761i			1.16803i	−0.811744	+	0.584014i	$0.801481\pi$
$488$		−	9.35152i		−	0.423323i
$489$	−41.2201			−1.86404
$490$	11.2571	+	4.98029i	0.508544	+	0.224987i
$491$	−14.9616			−0.675209			−0.337605	−	0.941288i	$-0.609617\pi$
$491$	−14.9616			−0.675209			−0.337605	+	0.941288i	$0.609617\pi$
$492$			21.9389i			0.989082i
$493$			27.0730i			1.21931i
$494$	18.9780			0.853861
$495$	−33.9855	+	76.8186i	−1.52754	+	3.45274i
$496$	1.96103			0.0880527
$497$			12.2606i			0.549965i
$498$			30.0468i			1.34643i
$499$	−34.9662			−1.56530			−0.782651	−	0.622461i	$-0.786133\pi$
$499$	−34.9662			−1.56530			−0.782651	+	0.622461i	$0.786133\pi$
$500$	10.6085	−	3.52987i	0.474426	−	0.157861i
$501$	34.9621			1.56199
$502$			5.44690i			0.243107i
$503$			6.04969i			0.269742i	0.990863	+	0.134871i	$0.0430621\pi$
$503$			6.04969i			0.269742i	−0.990863	+	0.134871i	$0.956938\pi$
$504$	9.33955			0.416017
$505$	−7.62942	+	17.2450i	−0.339505	+	0.767394i
$506$	−23.2494			−1.03356
$507$			3.99091i			0.177243i
$508$		−	2.39838i		−	0.106411i
$509$	−11.9703			−0.530573			−0.265286	−	0.964170i	$-0.585466\pi$
$509$	−11.9703			−0.530573			−0.265286	+	0.964170i	$0.585466\pi$
$510$	−41.6618	−	18.4317i	−1.84481	−	0.816169i
$511$	1.40195			0.0620186
$512$			1.00000i			0.0441942i
$513$		−	76.1311i		−	3.36127i
$514$	−19.9144			−0.878385
$515$	7.16358	+	3.16926i	0.315665	+	0.139654i
$516$	3.26167			0.143587
$517$			22.0419i			0.969401i
$518$		−	5.29633i		−	0.232707i
$519$	28.9223			1.26955
$520$	3.41194	−	7.71211i	0.149623	−	0.338198i
$521$	−28.0682			−1.22969			−0.614845	−	0.788648i	$-0.710781\pi$
$521$	−28.0682			−1.22969			−0.614845	+	0.788648i	$0.710781\pi$
$522$			33.1066i			1.44904i
$523$			35.4749i			1.55121i	0.631219	+	0.775604i	$0.282555\pi$
$523$			35.4749i			1.55121i	−0.631219	+	0.775604i	$0.717445\pi$
$524$	−5.13706			−0.224414
$525$	13.4121	+	14.7555i	0.585354	+	0.643982i
$526$	−14.3351			−0.625040
$527$		−	12.2493i		−	0.533590i
$528$		−	16.0410i		−	0.698093i
$529$	0.651823			0.0283401
$530$	1.68199	−	3.80187i	0.0730612	−	0.165142i
$531$	−77.4701			−3.36191
$532$		−	6.15269i		−	0.266753i
$533$			25.3676i			1.09879i
$534$	12.7738			0.552778
$535$	22.0029	+	9.73438i	0.951270	+	0.420854i
$536$	−11.0005			−0.475148
$537$		−	32.2176i		−	1.39029i
$538$		−	21.7497i		−	0.937697i
$539$	27.0738			1.16615
$540$	−30.9375	−	13.6871i	−1.33134	−	0.589001i
$541$	26.5967			1.14348			0.571741	−	0.820434i	$-0.306268\pi$
$541$	26.5967			1.14348			0.571741	+	0.820434i	$0.306268\pi$
$542$			3.63298i			0.156050i
$543$		−	73.9881i		−	3.17513i
$544$	6.24639			0.267812
$545$	−5.71149	+	12.9099i	−0.244653	+	0.552997i
$546$	15.0405			0.643675
$547$		−	38.1446i		−	1.63095i	−0.578795	−	0.815473i	$-0.696477\pi$
$547$		−	38.1446i		−	1.63095i	0.578795	−	0.815473i	$-0.303523\pi$
$548$			5.77327i			0.246622i
$549$	−71.4315			−3.04862
$550$	18.1964	−	16.5398i	0.775897	−	0.705259i
$551$	21.8099			0.929132
$552$		−	15.4192i		−	0.656283i
$553$		−	19.2628i		−	0.819138i
$554$	19.8902			0.845056
$555$	−12.7818	+	28.8912i	−0.542558	+	1.22636i
$556$	13.5373			0.574109
$557$			27.2829i			1.15601i	0.816032	+	0.578007i	$0.196170\pi$
$557$			27.2829i			1.15601i	−0.816032	+	0.578007i	$0.803830\pi$
$558$		−	14.9793i		−	0.634124i
$559$	3.77142			0.159514
$560$	−2.50027	−	1.10615i	−0.105656	−	0.0467435i
$561$	−100.198			−4.23037
$562$		−	9.28266i		−	0.391565i
$563$		−	26.0672i		−	1.09860i	−0.835625	−	0.549300i	$-0.814894\pi$
$563$		−	26.0672i		−	1.09860i	0.835625	−	0.549300i	$-0.185106\pi$
$564$	−14.6184			−0.615544
$565$	−30.9802	−	13.7060i	−1.30335	−	0.576617i
$566$	20.0343			0.842103
$567$		−	32.3171i		−	1.35719i
$568$			10.0275i			0.420746i
$569$	−9.00035			−0.377314			−0.188657	−	0.982043i	$-0.560413\pi$
$569$	−9.00035			−0.377314			−0.188657	+	0.982043i	$0.560413\pi$
$570$	−14.8485	+	33.5625i	−0.621935	+	1.40578i
$571$	−5.35035			−0.223905			−0.111953	−	0.993714i	$-0.535710\pi$
$571$	−5.35035			−0.223905			−0.111953	+	0.993714i	$0.535710\pi$
$572$		−	18.5479i		−	0.775527i
$573$			37.5481i			1.56859i
$574$	8.22420			0.343271
$575$	17.4911	−	15.8987i	0.729427	−	0.663020i
$576$	7.63849			0.318270
$577$			25.4884i			1.06110i	0.847655	+	0.530548i	$0.178014\pi$
$577$			25.4884i			1.06110i	−0.847655	+	0.530548i	$0.821986\pi$
$578$		−	22.0174i		−	0.915803i
$579$	−0.505252			−0.0209976
$580$	3.92106	−	8.86290i	0.162813	−	0.368012i
$581$	11.2636			0.467292
$582$		−	16.3094i		−	0.676046i
$583$		−	9.14363i		−	0.378690i
$584$	1.14660			0.0474468
$585$	−58.9088	−	26.0620i	−2.43558	−	1.07753i
$586$	15.3892			0.635723
$587$			3.03587i			0.125304i	0.998035	+	0.0626519i	$0.0199558\pi$
$587$			3.03587i			0.125304i	−0.998035	+	0.0626519i	$0.980044\pi$
$588$			17.9555i			0.740474i
$589$	−9.86801			−0.406604
$590$	20.7394	+	9.17536i	0.853826	+	0.377743i
$591$	50.9948			2.09765
$592$		−	4.33168i		−	0.178031i
$593$			9.58136i			0.393459i	0.980458	+	0.196730i	$0.0630321\pi$
$593$			9.58136i			0.393459i	−0.980458	+	0.196730i	$0.936968\pi$
$594$	−74.4058			−3.05291
$595$	−6.90946	+	15.6177i	−0.283260	+	0.640262i
$596$	−10.0609			−0.412112
$597$		−	53.4839i		−	2.18895i
$598$		−	17.8289i		−	0.729080i
$599$	−24.9960			−1.02131			−0.510654	−	0.859786i	$-0.670597\pi$
$599$	−24.9960			−1.02131			−0.510654	+	0.859786i	$0.670597\pi$
$600$	10.9693	+	12.0680i	0.447820	+	0.492674i
$601$	11.7446			0.479074			0.239537	−	0.970887i	$-0.423004\pi$
$601$	11.7446			0.479074			0.239537	+	0.970887i	$0.423004\pi$
$602$		−	1.22270i		−	0.0498334i
$603$			84.0269i			3.42184i
$604$	3.40960			0.138735
$605$	11.9300	−	26.9657i	0.485023	−	1.09631i
$606$	−27.5065			−1.11738
$607$			26.2153i			1.06404i	0.846730	+	0.532022i	$0.178568\pi$
$607$			26.2153i			1.06404i	−0.846730	+	0.532022i	$0.821432\pi$
$608$		−	5.03206i		−	0.204077i
$609$	17.2849			0.700418
$610$	19.1228	+	8.46016i	0.774258	+	0.342542i
$611$	−16.9030			−0.683821
$612$		−	47.7130i		−	1.92868i
$613$		−	32.0799i		−	1.29569i	−0.761771	−	0.647847i	$-0.775670\pi$
$613$		−	32.0799i		−	1.29569i	0.761771	−	0.647847i	$-0.224330\pi$
$614$	−27.3859			−1.10520
$615$	−44.8625	−	19.8477i	−1.80903	−	0.800338i
$616$	−6.01325			−0.242281
$617$		−	38.3500i		−	1.54391i	−0.635675	−	0.771957i	$-0.719278\pi$
$617$		−	38.3500i		−	1.54391i	0.635675	−	0.771957i	$-0.280722\pi$
$618$			11.4262i			0.459628i
$619$	−2.70119			−0.108570			−0.0542849	−	0.998525i	$-0.517288\pi$
$619$	−2.70119			−0.108570			−0.0542849	+	0.998525i	$0.517288\pi$
$620$	−1.77411	+	4.01007i	−0.0712499	+	0.161048i
$621$	−71.5216			−2.87006
$622$		−	5.23705i		−	0.209987i
$623$		−	4.78851i		−	0.191848i
$624$	12.3011			0.492439
$625$	−2.37914	+	24.8865i	−0.0951656	+	0.995461i
$626$	2.85664			0.114174
$627$			80.7191i			3.22361i
$628$			12.8021i			0.510860i
$629$	−27.0574			−1.07885
$630$	−8.44933	+	19.0983i	−0.336629	+	0.760894i
$631$	47.2640			1.88155			0.940776	−	0.339029i	$-0.110098\pi$
$631$	47.2640			1.88155			0.940776	+	0.339029i	$0.110098\pi$
$632$		−	15.7544i		−	0.626675i
$633$			38.3102i			1.52270i
$634$	−10.1054			−0.401337
$635$	4.90441	+	2.16977i	0.194626	+	0.0861049i
$636$	6.06412			0.240458
$637$			20.7617i			0.822608i
$638$		−	21.3156i		−	0.843893i
$639$	76.5953			3.03006
$640$	−2.04488	−	0.904683i	−0.0808311	−	0.0357607i
$641$	38.5680			1.52334			0.761671	−	0.647964i	$-0.224379\pi$
$641$	38.5680			1.52334			0.761671	+	0.647964i	$0.224379\pi$
$642$			35.0955i			1.38511i
$643$		−	6.97039i		−	0.274885i	−0.990510	−	0.137443i	$-0.956112\pi$
$643$		−	6.97039i		−	0.274885i	0.990510	−	0.137443i	$-0.0438883\pi$
$644$	−5.78016			−0.227770
$645$	−2.95078	+	6.66973i	−0.116187	+	0.262621i
$646$	−31.4322			−1.23668
$647$			30.4764i			1.19815i	0.800693	+	0.599075i	$0.204465\pi$
$647$			30.4764i			1.19815i	−0.800693	+	0.599075i	$0.795535\pi$
$648$		−	26.4310i		−	1.03831i
$649$	49.8789			1.95792
$650$	12.6836	+	13.9540i	0.497493	+	0.547322i
$651$	−7.82064			−0.306515
$652$			12.6377i			0.494931i
$653$			22.9520i			0.898179i	0.893487	+	0.449090i	$0.148252\pi$
$653$			22.9520i			0.898179i	−0.893487	+	0.449090i	$0.851748\pi$
$654$	−20.5917			−0.805200
$655$	4.64741	−	10.5047i	0.181589	−	0.410452i
$656$	6.72628			0.262617
$657$		−	8.75832i		−	0.341695i
$658$			5.47996i			0.213631i
$659$	5.12527			0.199652			0.0998261	−	0.995005i	$-0.468171\pi$
$659$	5.12527			0.199652			0.0998261	+	0.995005i	$0.468171\pi$
$660$	32.8019	+	14.5120i	1.27681	+	0.564878i
$661$	15.0708			0.586188			0.293094	−	0.956084i	$-0.405315\pi$
$661$	15.0708			0.586188			0.293094	+	0.956084i	$0.405315\pi$
$662$		−	21.9153i		−	0.851761i
$663$		−	76.8376i		−	2.98412i
$664$	9.21208			0.357498
$665$	12.5815	+	5.56623i	0.487891	+	0.215849i
$666$	−33.0875			−1.28211
$667$		−	20.4894i		−	0.793351i
$668$		−	10.7191i		−	0.414734i
$669$	57.9775			2.24154
$670$	9.95194	−	22.4947i	0.384477	−	0.869045i
$671$	45.9910			1.77546
$672$		−	3.98803i		−	0.153842i
$673$		−	7.09132i		−	0.273350i	−0.990616	−	0.136675i	$-0.956358\pi$
$673$		−	7.09132i		−	0.273350i	0.990616	−	0.136675i	$-0.0436417\pi$
$674$	−16.7325			−0.644510
$675$	55.9772	−	50.8810i	2.15456	−	1.95841i
$676$	1.22358			0.0470607
$677$		−	39.9807i		−	1.53658i	−0.640099	−	0.768292i	$-0.721107\pi$
$677$		−	39.9807i		−	1.53658i	0.640099	−	0.768292i	$-0.278893\pi$
$678$		−	49.4146i		−	1.89776i
$679$	−6.11388			−0.234629
$680$	−5.65100	+	12.7731i	−0.216706	+	0.489828i
$681$	77.7999			2.98130
$682$			9.64437i			0.369302i
$683$			16.1038i			0.616195i	0.951355	+	0.308097i	$0.0996923\pi$
$683$			16.1038i			0.616195i	−0.951355	+	0.308097i	$0.900308\pi$
$684$	−38.4373			−1.46969
$685$	−11.8057	−	5.22298i	−0.451071	−	0.199560i
$686$	15.2898			0.583769
$687$		−	4.46861i		−	0.170488i
$688$		−	1.00000i		−	0.0381246i
$689$	7.01185			0.267130
$690$	31.5304	+	13.9495i	1.20034	+	0.531047i
$691$	12.6027			0.479429			0.239715	−	0.970843i	$-0.422946\pi$
$691$	12.6027			0.479429			0.239715	+	0.970843i	$0.422946\pi$
$692$		−	8.86733i		−	0.337085i
$693$			45.9321i			1.74482i
$694$	−16.4411			−0.624095
$695$	−12.2470	+	27.6822i	−0.464554	+	1.05005i
$696$	14.1367			0.535849
$697$		−	42.0150i		−	1.59143i
$698$		−	22.8270i		−	0.864016i
$699$	−0.335463			−0.0126884
$700$	4.52391	−	4.11205i	0.170988	−	0.155421i
$701$	−18.5314			−0.699922			−0.349961	−	0.936764i	$-0.613805\pi$
$701$	−18.5314			−0.699922			−0.349961	+	0.936764i	$0.613805\pi$
$702$		−	57.0585i		−	2.15354i
$703$			21.7973i			0.822100i
$704$	−4.91802			−0.185355
$705$	13.2250	−	29.8928i	0.498081	−	1.12583i
$706$	−23.2472			−0.874919
$707$			10.3113i			0.387797i
$708$			33.0801i			1.24323i
$709$	−45.3138			−1.70180			−0.850898	−	0.525331i	$-0.823942\pi$
$709$	−45.3138			−1.70180			−0.850898	+	0.525331i	$0.823942\pi$
$710$	−20.5052	−	9.07175i	−0.769545	−	0.340457i
$711$	−120.340			−4.51308
$712$		−	3.91635i		−	0.146771i
$713$			9.27053i			0.347184i
$714$	−24.9108			−0.932263
$715$	37.9283	+	16.7800i	1.41844	+	0.627535i
$716$	−9.87763			−0.369144
$717$		−	52.0032i		−	1.94209i
$718$			20.9495i			0.781828i
$719$	−9.74378			−0.363382			−0.181691	−	0.983356i	$-0.558157\pi$
$719$	−9.74378			−0.363382			−0.181691	+	0.983356i	$0.558157\pi$
$720$	−6.91041	+	15.6198i	−0.257536	+	0.582116i
$721$	4.28331			0.159519
$722$			6.32165i			0.235267i
$723$			68.8005i			2.55872i
$724$	−22.6841			−0.843049
$725$	14.5763	+	16.0362i	0.541350	+	0.595570i
$726$	43.0114			1.59630
$727$		−	46.9330i		−	1.74065i	−0.492480	−	0.870324i	$-0.663910\pi$
$727$		−	46.9330i		−	1.74065i	0.492480	−	0.870324i	$-0.336090\pi$
$728$		−	4.61130i		−	0.170906i
$729$	−53.8536			−1.99458
$730$	−1.03731	+	2.34467i	−0.0383927	+	0.0867802i
$731$	−6.24639			−0.231031
$732$			30.5016i			1.12737i
$733$		−	43.9195i		−	1.62220i	−0.584906	−	0.811101i	$-0.698869\pi$
$733$		−	43.9195i		−	1.62220i	0.584906	−	0.811101i	$-0.301131\pi$
$734$	−24.6439			−0.909624
$735$	−36.7170	−	16.2441i	−1.35433	−	0.599171i
$736$	−4.72739			−0.174254
$737$		−	54.1005i		−	1.99282i
$738$		−	51.3786i		−	1.89127i
$739$	−2.38607			−0.0877731			−0.0438866	−	0.999037i	$-0.513974\pi$
$739$	−2.38607			−0.0877731			−0.0438866	+	0.999037i	$0.513974\pi$
$740$	8.85778	+	3.91880i	0.325619	+	0.144058i
$741$	−61.9000			−2.27395
$742$		−	2.27325i		−	0.0834536i
$743$			12.6362i			0.463579i	0.972766	+	0.231789i	$0.0744580\pi$
$743$			12.6362i			0.463579i	−0.972766	+	0.231789i	$0.925542\pi$
$744$	−6.39622			−0.234497
$745$	9.10195	−	20.5734i	0.333470	−	0.753753i
$746$	6.54983			0.239806
$747$		−	70.3664i		−	2.57457i
$748$			30.7199i			1.12323i
$749$	13.1562			0.480717
$750$	−34.6014	+	11.5133i	−1.26346	+	0.420405i
$751$	34.8092			1.27020			0.635102	−	0.772428i	$-0.280958\pi$
$751$	34.8092			1.27020			0.635102	+	0.772428i	$0.280958\pi$
$752$			4.48186i			0.163437i
$753$		−	17.7660i		−	0.647428i
$754$	16.3460			0.595287
$755$	−3.08460	+	6.97223i	−0.112260	+	0.253745i
$756$	−18.4984			−0.672782
$757$		−	21.5099i		−	0.781790i	−0.920435	−	0.390895i	$-0.872166\pi$
$757$		−	21.5099i		−	0.781790i	0.920435	−	0.390895i	$-0.127834\pi$
$758$		−	12.3493i		−	0.448546i
$759$	75.8318			2.75252
$760$	10.2900	+	4.55242i	0.373257	+	0.165134i
$761$	10.7127			0.388334			0.194167	−	0.980968i	$-0.437800\pi$
$761$	10.7127			0.388334			0.194167	+	0.980968i	$0.437800\pi$
$762$			7.82273i			0.283388i
$763$			7.71918i			0.279453i
$764$	11.5119			0.416486
$765$	97.5675	+	43.1651i	3.52756	+	1.56064i
$766$	−11.7119			−0.423169
$767$			38.2500i			1.38113i
$768$		−	3.26167i		−	0.117695i
$769$	45.8339			1.65281			0.826406	−	0.563075i	$-0.190382\pi$
$769$	45.8339			1.65281			0.826406	+	0.563075i	$0.190382\pi$
$770$	5.44008	−	12.2964i	0.196047	−	0.443131i
$771$	64.9541			2.33926
$772$			0.154906i			0.00557519i
$773$		−	16.7306i		−	0.601758i	−0.953662	−	0.300879i	$-0.902720\pi$
$773$		−	16.7306i		−	0.601758i	0.953662	−	0.300879i	$-0.0972800\pi$
$774$	−7.63849			−0.274560
$775$	−6.59513	−	7.25569i	−0.236904	−	0.260632i
$776$	−5.00032			−0.179501
$777$			17.2749i			0.619733i
$778$			36.4134i			1.30548i
$779$	−33.8471			−1.21270
$780$	−11.1286	+	25.1543i	−0.398468	+	0.900670i
$781$	−49.3157			−1.76465
$782$			29.5291i			1.05596i
$783$		−	65.5728i		−	2.34338i
$784$	5.50501			0.196608
$785$	−26.1788	−	11.5818i	−0.934362	−	0.413374i
$786$	16.7554			0.597645
$787$			8.81384i			0.314179i	0.987584	+	0.157090i	$0.0502112\pi$
$787$			8.81384i			0.314179i	−0.987584	+	0.157090i	$0.949789\pi$
$788$		−	15.6346i		−	0.556959i
$789$	46.7563			1.66457
$790$	32.2158	+	14.2527i	1.14619	+	0.507088i
$791$	−18.5240			−0.658637
$792$			37.5662i			1.33486i
$793$			35.2685i			1.25242i
$794$	−15.9505			−0.566063
$795$	−5.48611	+	12.4004i	−0.194572	+	0.439798i
$796$	−16.3977			−0.581201
$797$		−	13.1646i		−	0.466315i	−0.972439	−	0.233157i	$-0.925094\pi$
$797$		−	13.1646i		−	0.466315i	0.972439	−	0.233157i	$-0.0749057\pi$
$798$			20.0680i			0.710400i
$799$	27.9955			0.990409
$800$	3.69994	−	3.36310i	0.130813	−	0.118903i
$801$	−29.9150			−1.05699
$802$		−	37.3371i		−	1.31842i
$803$			5.63902i			0.198997i
$804$	35.8799			1.26539
$805$	5.22921	−	11.8198i	0.184305	−	0.416592i
$806$	−7.39585			−0.260508
$807$			70.9404i			2.49722i
$808$			8.43326i			0.296681i
$809$	3.52719			0.124009			0.0620047	−	0.998076i	$-0.480251\pi$
$809$	3.52719			0.124009			0.0620047	+	0.998076i	$0.480251\pi$
$810$	54.0484	+	23.9117i	1.89907	+	0.840171i
$811$	47.0612			1.65254			0.826271	−	0.563272i	$-0.190458\pi$
$811$	47.0612			1.65254			0.826271	+	0.563272i	$0.190458\pi$
$812$		−	5.29939i		−	0.185972i
$813$		−	11.8496i		−	0.415583i
$814$	21.3033			0.746680
$815$	−25.8427	−	11.4331i	−0.905229	−	0.400485i
$816$	−20.3737			−0.713221
$817$			5.03206i			0.176050i
$818$		−	0.372941i		−	0.0130396i
$819$	−35.2233			−1.23080
$820$	−6.08515	+	13.7545i	−0.212503	+	0.480327i
$821$	−0.641395			−0.0223848			−0.0111924	−	0.999937i	$-0.503563\pi$
$821$	−0.641395			−0.0223848			−0.0111924	+	0.999937i	$0.503563\pi$
$822$		−	18.8305i		−	0.656789i
$823$		−	24.3706i		−	0.849506i	−0.905309	−	0.424753i	$-0.860361\pi$
$823$		−	24.3706i		−	0.849506i	0.905309	−	0.424753i	$-0.139639\pi$
$824$	3.50317			0.122039
$825$	−59.3506	+	53.9473i	−2.06632	+	1.87820i
$826$	12.4007			0.431475
$827$			37.4161i			1.30109i	0.759470	+	0.650543i	$0.225458\pi$
$827$			37.4161i			1.30109i	−0.759470	+	0.650543i	$0.774542\pi$
$828$			36.1101i			1.25491i
$829$	−22.6235			−0.785745			−0.392873	−	0.919593i	$-0.628519\pi$
$829$	−22.6235			−0.785745			−0.392873	+	0.919593i	$0.628519\pi$
$830$	−8.33401	+	18.8376i	−0.289278	+	0.653864i
$831$	−64.8754			−2.25050
$832$		−	3.77142i		−	0.130750i
$833$		−	34.3865i		−	1.19142i
$834$	−44.1542			−1.52893
$835$	21.9193	+	9.69736i	0.758548	+	0.335591i
$836$	24.7478			0.855920
$837$			29.6688i			1.02550i
$838$		−	2.83899i		−	0.0980714i
$839$	15.9162			0.549490			0.274745	−	0.961517i	$-0.411407\pi$
$839$	15.9162			0.549490			0.274745	+	0.961517i	$0.411407\pi$
$840$	8.15506	+	3.60790i	0.281376	+	0.124485i
$841$	−10.2149			−0.352236
$842$		−	11.4590i		−	0.394904i
$843$			30.2770i			1.04279i
$844$	11.7456			0.404300
$845$	−1.10695	+	2.50208i	−0.0380803	+	0.0860741i
$846$	34.2347			1.17701
$847$		−	16.1236i		−	0.554014i
$848$		−	1.85921i		−	0.0638455i
$849$	−65.3451			−2.24264
$850$	−21.0072	−	23.1113i	−0.720542	−	0.792710i
$851$	20.4775			0.701961
$852$		−	32.7065i		−	1.12051i
$853$		−	35.3813i		−	1.21143i	−0.795681	−	0.605716i	$-0.792887\pi$
$853$		−	35.3813i		−	1.21143i	0.795681	−	0.605716i	$-0.207113\pi$
$854$	11.4341			0.391266
$855$	34.7736	−	78.5999i	1.18923	−	2.68806i
$856$	10.7600			0.367769
$857$			23.5470i			0.804352i	0.915562	+	0.402176i	$0.131746\pi$
$857$			23.5470i			0.804352i	−0.915562	+	0.402176i	$0.868254\pi$
$858$			60.4971i			2.06534i
$859$	−15.5370			−0.530114			−0.265057	−	0.964233i	$-0.585391\pi$
$859$	−15.5370			−0.530114			−0.265057	+	0.964233i	$0.585391\pi$
$860$	2.04488	+	0.904683i	0.0697300	+	0.0308494i
$861$	−26.8246			−0.914181
$862$			24.8735i			0.847195i
$863$		−	9.06488i		−	0.308572i	−0.988026	−	0.154286i	$-0.950692\pi$
$863$		−	9.06488i		−	0.308572i	0.988026	−	0.154286i	$-0.0493078\pi$
$864$	−15.1292			−0.514706
$865$	18.1327	+	8.02212i	0.616529	+	0.272760i
$866$	17.4420			0.592703
$867$			71.8135i			2.43891i
$868$			2.39774i			0.0813846i
$869$	77.4803			2.62834
$870$	−12.7892	+	28.9078i	−0.433595	+	0.980068i
$871$	41.4873			1.40575
$872$			6.31325i			0.213794i
$873$			38.1949i			1.29270i
$874$	23.7885			0.804658
$875$	4.31596	+	12.9710i	0.145906	+	0.438499i
$876$	−3.73984			−0.126358
$877$			25.1478i			0.849179i	0.905386	+	0.424590i	$0.139582\pi$
$877$			25.1478i			0.849179i	−0.905386	+	0.424590i	$0.860418\pi$
$878$			20.9147i			0.705836i
$879$	−50.1946			−1.69302
$880$	4.44925	−	10.0568i	0.149984	−	0.339014i
$881$	−36.2242			−1.22042			−0.610212	−	0.792238i	$-0.708916\pi$
$881$	−36.2242			−1.22042			−0.610212	+	0.792238i	$0.708916\pi$
$882$		−	42.0500i		−	1.41590i
$883$		−	21.4494i		−	0.721829i	−0.932599	−	0.360915i	$-0.882465\pi$
$883$		−	21.4494i		−	0.721829i	0.932599	−	0.360915i	$-0.117535\pi$
$884$	−23.5577			−0.792332
$885$	−67.6449	−	29.9270i	−2.27386	−	1.00598i
$886$	24.4329			0.820838
$887$			44.7948i			1.50406i	0.659129	+	0.752030i	$0.270925\pi$
$887$			44.7948i			1.50406i	−0.659129	+	0.752030i	$0.729075\pi$
$888$			14.1285i			0.474122i
$889$	2.93249			0.0983527
$890$	8.00848	+	3.54306i	0.268445	+	0.118764i
$891$	129.988			4.35477
$892$		−	17.7754i		−	0.595165i
$893$		−	22.5530i		−	0.754708i
$894$	32.8154			1.09751
$895$	8.93612	−	20.1986i	0.298702	−	0.675165i
$896$	−1.22270			−0.0408474
$897$			58.1521i			1.94164i
$898$			1.89679i			0.0632967i
$899$	−8.49945			−0.283473
$900$	−25.6890	−	28.2620i	−0.856299	−	0.942065i
$901$	−11.6133			−0.386897
$902$			33.0800i			1.10144i
$903$			3.98803i			0.132713i
$904$	−15.1501			−0.503885
$905$	20.5219	−	46.3864i	0.682172	−	1.54194i
$906$	−11.1210			−0.369470
$907$			11.8316i			0.392863i	0.980518	+	0.196431i	$0.0629353\pi$
$907$			11.8316i			0.392863i	−0.980518	+	0.196431i	$0.937065\pi$
$908$		−	23.8528i		−	0.791582i
$909$	64.4173			2.13659
$910$	9.42957	+	4.17176i	0.312587	+	0.138293i
$911$	−10.2650			−0.340096			−0.170048	−	0.985436i	$-0.554392\pi$
$911$	−10.2650			−0.340096			−0.170048	+	0.985436i	$0.554392\pi$
$912$			16.4129i			0.543486i
$913$			45.3052i			1.49938i
$914$	−3.61887			−0.119702
$915$	−62.3722	−	27.5942i	−2.06196	−	0.912237i
$916$	−1.37004			−0.0452674
$917$		−	6.28107i		−	0.207419i
$918$			94.5030i			3.11906i
$919$	−52.3365			−1.72642			−0.863211	−	0.504842i	$-0.831551\pi$
$919$	−52.3365			−1.72642			−0.863211	+	0.504842i	$0.831551\pi$
$920$	4.27678	−	9.66695i	0.141001	−	0.318710i
$921$	89.3237			2.94332
$922$		−	5.91589i		−	0.194830i
$923$		−	37.8180i		−	1.24480i
$924$	19.6132			0.645228
$925$	−16.0270	+	14.5679i	−0.526963	+	0.478989i
$926$	−30.8874			−1.01502
$927$		−	26.7589i		−	0.878878i
$928$		−	4.33418i		−	0.142277i
$929$	−36.7879			−1.20697			−0.603486	−	0.797374i	$-0.706222\pi$
$929$	−36.7879			−1.20697			−0.603486	+	0.797374i	$0.706222\pi$
$930$	5.78655	−	13.0795i	0.189749	−	0.428895i
$931$	−27.7016			−0.907882
$932$			0.102850i			0.00336896i
$933$			17.0815i			0.559224i
$934$	12.9717			0.424447
$935$	−62.8186	−	27.7917i	−2.05439	−	0.908887i
$936$	−28.8079			−0.941616
$937$		−	5.80080i		−	0.189504i	−0.995501	−	0.0947519i	$-0.969794\pi$
$937$		−	5.80080i		−	0.189504i	0.995501	−	0.0947519i	$-0.0302058\pi$
$938$		−	13.4502i		−	0.439166i
$939$	−9.31742			−0.304062
$940$	−9.16489	−	4.05466i	−0.298926	−	0.132249i
$941$	1.34759			0.0439303			0.0219652	−	0.999759i	$-0.493008\pi$
$941$	1.34759			0.0439303			0.0219652	+	0.999759i	$0.493008\pi$
$942$		−	41.7562i		−	1.36049i
$943$			31.7977i			1.03548i
$944$	10.1421			0.330096
$945$	16.7352	−	37.8271i	0.544397	−	1.23052i
$946$	4.91802			0.159899
$947$		−	58.3185i		−	1.89510i	−0.319613	−	0.947548i	$-0.603553\pi$
$947$		−	58.3185i		−	1.89510i	0.319613	−	0.947548i	$-0.396447\pi$
$948$			51.3855i			1.66892i
$949$	−4.32432			−0.140373
$950$	−18.6183	+	16.9233i	−0.604059	+	0.549065i
$951$	32.9605			1.06882
$952$			7.63744i			0.247531i
$953$			48.3124i			1.56499i	0.622655	+	0.782496i	$0.286054\pi$
$953$			48.3124i			1.56499i	−0.622655	+	0.782496i	$0.713946\pi$
$954$	−14.2015			−0.459792
$955$	−10.4146	+	23.5405i	−0.337010	+	0.761754i
$956$	−15.9437			−0.515657
$957$			69.5244i			2.24741i
$958$			8.82445i			0.285105i
$959$	−7.05896			−0.227946
$960$	6.66973	+	2.95078i	0.215265	+	0.0952359i
$961$	−27.1544			−0.875947
$962$			16.3366i			0.526712i
$963$		−	82.1901i		−	2.64854i
$964$	21.0937			0.679381
$965$	−0.316765	−	0.140141i	−0.0101970	−	0.00451129i
$966$	18.8530			0.606584
$967$		−	47.1740i		−	1.51701i	−0.651666	−	0.758506i	$-0.725929\pi$
$967$		−	47.1740i		−	1.51701i	0.651666	−	0.758506i	$-0.274071\pi$
$968$		−	13.1869i		−	0.423844i
$969$	102.522			3.29347
$970$	4.52371	−	10.2251i	0.145247	−	0.328308i
$971$	15.0433			0.482761			0.241381	−	0.970431i	$-0.422400\pi$
$971$	15.0433			0.482761			0.241381	+	0.970431i	$0.422400\pi$
$972$			40.8216i			1.30935i
$973$			16.5520i			0.530633i
$974$	−25.7761			−0.825921
$975$	−41.3698	−	45.5134i	−1.32490	−	1.45760i
$976$	9.35152			0.299335
$977$		−	47.8490i		−	1.53082i	−0.643541	−	0.765412i	$-0.722535\pi$
$977$		−	47.8490i		−	1.53082i	0.643541	−	0.765412i	$-0.277465\pi$
$978$		−	41.2201i		−	1.31807i
$979$	19.2607			0.615575
$980$	−4.98029	+	11.2571i	−0.159090	+	0.359595i
$981$	48.2236			1.53966
$982$		−	14.9616i		−	0.477445i
$983$		−	3.99338i		−	0.127369i	−0.997970	−	0.0636845i	$-0.979715\pi$
$983$		−	3.99338i		−	0.127369i	0.997970	−	0.0636845i	$-0.0202851\pi$
$984$	−21.9389			−0.699387
$985$	31.9709	+	14.1443i	1.01868	+	0.450676i
$986$	−27.0730			−0.862180
$987$		−	17.8738i		−	0.568930i
$988$			18.9780i			0.603771i
$989$	4.72739			0.150322
$990$	−76.8186	−	33.9855i	−2.44145	−	1.08013i
$991$	−41.5092			−1.31858			−0.659292	−	0.751887i	$-0.729144\pi$
$991$	−41.5092			−1.31858			−0.659292	+	0.751887i	$0.729144\pi$
$992$			1.96103i			0.0622627i
$993$			71.4803i			2.26836i
$994$	−12.2606			−0.388884
$995$	14.8347	−	33.5314i	0.470292	−	1.06302i
$996$	−30.0468			−0.952068
$997$			5.23797i			0.165888i	0.996554	+	0.0829441i	$0.0264323\pi$
$997$			5.23797i			0.165888i	−0.996554	+	0.0829441i	$0.973568\pi$
$998$		−	34.9662i		−	1.10684i
$999$	65.5349			2.07343

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.b.b.259.9	yes	16
5.2	odd	4		2150.2.a.bg.1.1		8
5.3	odd	4		2150.2.a.bh.1.8		8
5.4	even	2	inner	430.2.b.b.259.8	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.b.b.259.8	✓	16	5.4	even	2	inner
430.2.b.b.259.9	yes	16	1.1	even	1	trivial
2150.2.a.bg.1.1		8	5.2	odd	4
2150.2.a.bh.1.8		8	5.3	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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -3.26167i q^{3} -1.00000 q^{4} +(0.904683 - 2.04488i) q^{5} +3.26167 q^{6} -1.22270i q^{7} -1.00000i q^{8} -7.63849 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -3.26167i q^{3} -1.00000 q^{4} +(0.904683 - 2.04488i) q^{5} +3.26167 q^{6} -1.22270i q^{7} -1.00000i q^{8} -7.63849 q^{9} +(2.04488 + 0.904683i) q^{10} +4.91802 q^{11} +3.26167i q^{12} +3.77142i q^{13} +1.22270 q^{14} +(-6.66973 - 2.95078i) q^{15} +1.00000 q^{16} -6.24639i q^{17} -7.63849i q^{18} -5.03206 q^{19} +(-0.904683 + 2.04488i) q^{20} -3.98803 q^{21} +4.91802i q^{22} +4.72739i q^{23} -3.26167 q^{24} +(-3.36310 - 3.69994i) q^{25} -3.77142 q^{26} +15.1292i q^{27} +1.22270i q^{28} -4.33418 q^{29} +(2.95078 - 6.66973i) q^{30} +1.96103 q^{31} +1.00000i q^{32} -16.0410i q^{33} +6.24639 q^{34} +(-2.50027 - 1.10615i) q^{35} +7.63849 q^{36} -4.33168i q^{37} -5.03206i q^{38} +12.3011 q^{39} +(-2.04488 - 0.904683i) q^{40} +6.72628 q^{41} -3.98803i q^{42} -1.00000i q^{43} -4.91802 q^{44} +(-6.91041 + 15.6198i) q^{45} -4.72739 q^{46} +4.48186i q^{47} -3.26167i q^{48} +5.50501 q^{49} +(3.69994 - 3.36310i) q^{50} -20.3737 q^{51} -3.77142i q^{52} -1.85921i q^{53} -15.1292 q^{54} +(4.44925 - 10.0568i) q^{55} -1.22270 q^{56} +16.4129i q^{57} -4.33418i q^{58} +10.1421 q^{59} +(6.66973 + 2.95078i) q^{60} +9.35152 q^{61} +1.96103i q^{62} +9.33955i q^{63} -1.00000 q^{64} +(7.71211 + 3.41194i) q^{65} +16.0410 q^{66} -11.0005i q^{67} +6.24639i q^{68} +15.4192 q^{69} +(1.10615 - 2.50027i) q^{70} -10.0275 q^{71} +7.63849i q^{72} +1.14660i q^{73} +4.33168 q^{74} +(-12.0680 + 10.9693i) q^{75} +5.03206 q^{76} -6.01325i q^{77} +12.3011i q^{78} +15.7544 q^{79} +(0.904683 - 2.04488i) q^{80} +26.4310 q^{81} +6.72628i q^{82} +9.21208i q^{83} +3.98803 q^{84} +(-12.7731 - 5.65100i) q^{85} +1.00000 q^{86} +14.1367i q^{87} -4.91802i q^{88} +3.91635 q^{89} +(-15.6198 - 6.91041i) q^{90} +4.61130 q^{91} -4.72739i q^{92} -6.39622i q^{93} -4.48186 q^{94} +(-4.55242 + 10.2900i) q^{95} +3.26167 q^{96} -5.00032i q^{97} +5.50501i q^{98} -37.5662 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 2 q^{5} + 8 q^{6} - 28 q^{9}+O(q^{10}) \) 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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