LMFDB - Embedded newform 1530.2.n.q.1279.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1530,2,Mod(829,1530)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1530, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("1530.829");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1530.n (of order $4$, degree $2$, 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:	$12.2171115093$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.110166016.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 10x^{6} + 19x^{4} + 10x^{2} + 1 $ x^8 + 10x^6 + 19x^4 + 10*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 510)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1279.1
Root			$-2.77462i$ of defining polynomial
Character	$\chi$	$=$	1530.1279
Dual form			1530.2.n.q.829.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(-2.21680 - 0.292893i) q^{5} +(2.56350 - 2.56350i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(-2.21680 - 0.292893i) q^{5} +(2.56350 - 2.56350i) q^{7} -1.00000 q^{8} +(2.21680 + 0.292893i) q^{10} +(3.41421 + 3.41421i) q^{11} +4.05894i q^{13} +(-2.56350 + 2.56350i) q^{14} +1.00000 q^{16} +(1.65898 - 3.77462i) q^{17} -2.82843i q^{19} +(-2.21680 - 0.292893i) q^{20} +(-3.41421 - 3.41421i) q^{22} +(-2.33812 + 2.33812i) q^{23} +(4.82843 + 1.29857i) q^{25} -4.05894i q^{26} +(2.56350 - 2.56350i) q^{28} +(-4.13503 + 4.13503i) q^{29} +(-3.75234 + 3.75234i) q^{31} -1.00000 q^{32} +(-1.65898 + 3.77462i) q^{34} +(-6.43361 + 4.93194i) q^{35} +(0.422246 + 0.422246i) q^{37} +2.82843i q^{38} +(2.21680 + 0.292893i) q^{40} +(4.18884 + 4.18884i) q^{41} +4.93194 q^{43} +(3.41421 + 3.41421i) q^{44} +(2.33812 - 2.33812i) q^{46} -11.8193i q^{47} -6.14306i q^{49} +(-4.82843 - 1.29857i) q^{50} +4.05894i q^{52} +11.2895 q^{53} +(-6.56864 - 8.56864i) q^{55} +(-2.56350 + 2.56350i) q^{56} +(4.13503 - 4.13503i) q^{58} +1.65276i q^{59} +(3.62534 + 3.62534i) q^{61} +(3.75234 - 3.75234i) q^{62} +1.00000 q^{64} +(1.18884 - 8.99787i) q^{65} +6.58880i q^{67} +(1.65898 - 3.77462i) q^{68} +(6.43361 - 4.93194i) q^{70} +(10.9097 - 10.9097i) q^{71} +(-5.17671 - 5.17671i) q^{73} +(-0.422246 - 0.422246i) q^{74} -2.82843i q^{76} +17.5047 q^{77} +(1.90452 + 1.90452i) q^{79} +(-2.21680 - 0.292893i) q^{80} +(-4.18884 - 4.18884i) q^{82} -7.42557 q^{83} +(-4.78320 + 7.88169i) q^{85} -4.93194 q^{86} +(-3.41421 - 3.41421i) q^{88} +10.1179 q^{89} +(10.4051 + 10.4051i) q^{91} +(-2.33812 + 2.33812i) q^{92} +11.8193i q^{94} +(-0.828427 + 6.27006i) q^{95} +(7.36342 + 7.36342i) q^{97} +6.14306i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} + 4 q^{7} - 8 q^{8}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^4 + 4 * q^7 - 8 * q^8	$ 8 q - 8 q^{2} + 8 q^{4} + 4 q^{7} - 8 q^{8} + 16 q^{11} - 4 q^{14} + 8 q^{16} - 4 q^{17} - 16 q^{22} + 16 q^{23} + 16 q^{25} + 4 q^{28} - 8 q^{29} + 16 q^{31} - 8 q^{32} + 4 q^{34} - 16 q^{35} + 4 q^{41} + 24 q^{43} + 16 q^{44} - 16 q^{46} - 16 q^{50} + 16 q^{53} + 8 q^{55} - 4 q^{56} + 8 q^{58} + 16 q^{61} - 16 q^{62} + 8 q^{64} - 20 q^{65} - 4 q^{68} + 16 q^{70} + 44 q^{71} - 20 q^{73} + 48 q^{77} + 16 q^{79} - 4 q^{82} - 16 q^{83} - 56 q^{85} - 24 q^{86} - 16 q^{88} - 16 q^{89} + 8 q^{91} + 16 q^{92} + 16 q^{95} - 20 q^{97}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 + 4 * q^7 - 8 * q^8 + 16 * q^11 - 4 * q^14 + 8 * q^16 - 4 * q^17 - 16 * q^22 + 16 * q^23 + 16 * q^25 + 4 * q^28 - 8 * q^29 + 16 * q^31 - 8 * q^32 + 4 * q^34 - 16 * q^35 + 4 * q^41 + 24 * q^43 + 16 * q^44 - 16 * q^46 - 16 * q^50 + 16 * q^53 + 8 * q^55 - 4 * q^56 + 8 * q^58 + 16 * q^61 - 16 * q^62 + 8 * q^64 - 20 * q^65 - 4 * q^68 + 16 * q^70 + 44 * q^71 - 20 * q^73 + 48 * q^77 + 16 * q^79 - 4 * q^82 - 16 * q^83 - 56 * q^85 - 24 * q^86 - 16 * q^88 - 16 * q^89 + 8 * q^91 + 16 * q^92 + 16 * q^95 - 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1530\mathbb{Z}\right)^\times$.

$n$	$307$	$1261$	$1361$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−2.21680	−	0.292893i	−0.991384	−	0.130986i
$5$	−2.21680	−	0.292893i	−0.991384	−	0.130986i
$6$		0			0
$7$	2.56350	−	2.56350i	0.968912	−	0.968912i	−0.0306192	−	0.999531i	$-0.509748\pi$
$7$	2.56350	−	2.56350i	0.968912	−	0.968912i	0.999531	+	0.0306192i	$0.00974792\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	2.21680	+	0.292893i	0.701015	+	0.0926210i
$11$	3.41421	+	3.41421i	1.02942	+	1.02942i	0.999554	+	0.0298703i	$0.00950944\pi$
$11$	3.41421	+	3.41421i	1.02942	+	1.02942i	0.0298703	+	0.999554i	$0.490491\pi$
$12$		0			0
$13$			4.05894i			1.12575i	0.826543	+	0.562874i	$0.190304\pi$
$13$			4.05894i			1.12575i	−0.826543	+	0.562874i	$0.809696\pi$
$14$	−2.56350	+	2.56350i	−0.685124	+	0.685124i
$15$		0			0
$16$	1.00000			0.250000
$17$	1.65898	−	3.77462i	0.402362	−	0.915481i
$17$	1.65898	−	3.77462i	0.402362	−	0.915481i
$18$		0			0
$19$		−	2.82843i		−	0.648886i	−0.945905	−	0.324443i	$-0.894823\pi$
$19$		−	2.82843i		−	0.648886i	0.945905	−	0.324443i	$-0.105177\pi$
$20$	−2.21680	−	0.292893i	−0.495692	−	0.0654929i
$21$		0			0
$22$	−3.41421	−	3.41421i	−0.727913	−	0.727913i
$23$	−2.33812	+	2.33812i	−0.487532	+	0.487532i	−0.907527	−	0.419994i	$-0.862032\pi$
$23$	−2.33812	+	2.33812i	−0.487532	+	0.487532i	0.419994	+	0.907527i	$0.362032\pi$
$24$		0			0
$25$	4.82843	+	1.29857i	0.965685	+	0.259715i
$26$		−	4.05894i		−	0.796024i
$27$		0			0
$28$	2.56350	−	2.56350i	0.484456	−	0.484456i
$29$	−4.13503	+	4.13503i	−0.767856	+	0.767856i	−0.977729	−	0.209873i	$-0.932695\pi$
$29$	−4.13503	+	4.13503i	−0.767856	+	0.767856i	0.209873	+	0.977729i	$0.432695\pi$
$30$		0			0
$31$	−3.75234	+	3.75234i	−0.673940	+	0.673940i	−0.958622	−	0.284682i	$-0.908112\pi$
$31$	−3.75234	+	3.75234i	−0.673940	+	0.673940i	0.284682	+	0.958622i	$0.408112\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−1.65898	+	3.77462i	−0.284513	+	0.647342i
$35$	−6.43361	+	4.93194i	−1.08748	+	0.833650i
$36$		0			0
$37$	0.422246	+	0.422246i	0.0694168	+	0.0694168i	0.740963	−	0.671546i	$-0.234369\pi$
$37$	0.422246	+	0.422246i	0.0694168	+	0.0694168i	−0.671546	+	0.740963i	$0.734369\pi$
$38$			2.82843i			0.458831i
$39$		0			0
$40$	2.21680	+	0.292893i	0.350507	+	0.0463105i
$41$	4.18884	+	4.18884i	0.654186	+	0.654186i	0.953998	−	0.299812i	$-0.0969239\pi$
$41$	4.18884	+	4.18884i	0.654186	+	0.654186i	−0.299812	+	0.953998i	$0.596924\pi$
$42$		0			0
$43$	4.93194			0.752114			0.376057	−	0.926597i	$-0.377280\pi$
$43$	4.93194			0.752114			0.376057	+	0.926597i	$0.377280\pi$
$44$	3.41421	+	3.41421i	0.514712	+	0.514712i
$45$		0			0
$46$	2.33812	−	2.33812i	0.344737	−	0.344737i
$47$		−	11.8193i		−	1.72402i	−0.506888	−	0.862012i	$-0.669204\pi$
$47$		−	11.8193i		−	1.72402i	0.506888	−	0.862012i	$-0.330796\pi$
$48$		0			0
$49$		−	6.14306i		−	0.877581i
$50$	−4.82843	−	1.29857i	−0.682843	−	0.183646i
$51$		0			0
$52$			4.05894i			0.562874i
$53$	11.2895			1.55073			0.775363	−	0.631516i	$-0.217567\pi$
$53$	11.2895			1.55073			0.775363	+	0.631516i	$0.217567\pi$
$54$		0			0
$55$	−6.56864	−	8.56864i	−0.885715	−	1.15539i
$56$	−2.56350	+	2.56350i	−0.342562	+	0.342562i
$57$		0			0
$58$	4.13503	−	4.13503i	0.542956	−	0.542956i
$59$			1.65276i			0.215171i	0.994196	+	0.107586i	$0.0343119\pi$
$59$			1.65276i			0.215171i	−0.994196	+	0.107586i	$0.965688\pi$
$60$		0			0
$61$	3.62534	+	3.62534i	0.464177	+	0.464177i	0.900022	−	0.435845i	$-0.143550\pi$
$61$	3.62534	+	3.62534i	0.464177	+	0.464177i	−0.435845	+	0.900022i	$0.643550\pi$
$62$	3.75234	−	3.75234i	0.476547	−	0.476547i
$63$		0			0
$64$	1.00000			0.125000
$65$	1.18884	−	8.99787i	0.147457	−	1.11605i
$66$		0			0
$67$			6.58880i			0.804950i	0.915431	+	0.402475i	$0.131850\pi$
$67$			6.58880i			0.804950i	−0.915431	+	0.402475i	$0.868150\pi$
$68$	1.65898	−	3.77462i	0.201181	−	0.457740i
$69$		0			0
$70$	6.43361	−	4.93194i	0.768963	−	0.589480i
$71$	10.9097	−	10.9097i	1.29474	−	1.29474i	0.362916	−	0.931822i	$-0.381781\pi$
$71$	10.9097	−	10.9097i	1.29474	−	1.29474i	0.931822	−	0.362916i	$-0.118219\pi$
$72$		0			0
$73$	−5.17671	−	5.17671i	−0.605888	−	0.605888i	0.335981	−	0.941869i	$-0.390932\pi$
$73$	−5.17671	−	5.17671i	−0.605888	−	0.605888i	−0.941869	+	0.335981i	$0.890932\pi$
$74$	−0.422246	−	0.422246i	−0.0490851	−	0.0490851i
$75$		0			0
$76$		−	2.82843i		−	0.324443i
$77$	17.5047			1.99484
$78$		0			0
$79$	1.90452	+	1.90452i	0.214275	+	0.214275i	0.806081	−	0.591806i	$-0.201585\pi$
$79$	1.90452	+	1.90452i	0.214275	+	0.214275i	−0.591806	+	0.806081i	$0.701585\pi$
$80$	−2.21680	−	0.292893i	−0.247846	−	0.0327465i
$81$		0			0
$82$	−4.18884	−	4.18884i	−0.462580	−	0.462580i
$83$	−7.42557			−0.815063			−0.407531	−	0.913191i	$-0.633610\pi$
$83$	−7.42557			−0.815063			−0.407531	+	0.913191i	$0.633610\pi$
$84$		0			0
$85$	−4.78320	+	7.88169i	−0.518811	+	0.854889i
$86$	−4.93194			−0.531825
$87$		0			0
$88$	−3.41421	−	3.41421i	−0.363956	−	0.363956i
$89$	10.1179			1.07249			0.536247	−	0.844061i	$-0.319842\pi$
$89$	10.1179			1.07249			0.536247	+	0.844061i	$0.319842\pi$
$90$		0			0
$91$	10.4051	+	10.4051i	1.09075	+	1.09075i
$92$	−2.33812	+	2.33812i	−0.243766	+	0.243766i
$93$		0			0
$94$			11.8193i			1.21907i
$95$	−0.828427	+	6.27006i	−0.0849948	+	0.643295i
$96$		0			0
$97$	7.36342	+	7.36342i	0.747642	+	0.747642i	0.974036	−	0.226394i	$-0.0726937\pi$
$97$	7.36342	+	7.36342i	0.747642	+	0.747642i	−0.226394	+	0.974036i	$0.572694\pi$
$98$			6.14306i			0.620543i
$99$		0			0
$100$	4.82843	+	1.29857i	0.482843	+	0.129857i
$101$	5.10684			0.508150			0.254075	−	0.967185i	$-0.418229\pi$
$101$	5.10684			0.508150			0.254075	+	0.967185i	$0.418229\pi$
$102$		0			0
$103$			4.78811i			0.471787i	0.971779	+	0.235893i	$0.0758016\pi$
$103$			4.78811i			0.471787i	−0.971779	+	0.235893i	$0.924198\pi$
$104$		−	4.05894i		−	0.398012i
$105$		0			0
$106$	−11.2895			−1.09653
$107$	8.77249	+	8.77249i	0.848069	+	0.848069i	0.989892	−	0.141823i	$-0.0452964\pi$
$107$	8.77249	+	8.77249i	0.848069	+	0.848069i	−0.141823	+	0.989892i	$0.545296\pi$
$108$		0			0
$109$	12.1666	+	12.1666i	1.16534	+	1.16534i	0.983288	+	0.182056i	$0.0582752\pi$
$109$	12.1666	+	12.1666i	1.16534	+	1.16534i	0.182056	+	0.983288i	$0.441725\pi$
$110$	6.56864	+	8.56864i	0.626295	+	0.816988i
$111$		0			0
$112$	2.56350	−	2.56350i	0.242228	−	0.242228i
$113$	4.52182	−	4.52182i	0.425377	−	0.425377i	−0.461673	−	0.887050i	$-0.652751\pi$
$113$	4.52182	−	4.52182i	0.425377	−	0.425377i	0.887050	+	0.461673i	$0.152751\pi$
$114$		0			0
$115$	5.86798	−	4.49834i	0.547192	−	0.419472i
$116$	−4.13503	+	4.13503i	−0.383928	+	0.383928i
$117$		0			0
$118$		−	1.65276i		−	0.152149i
$119$	−5.42344	−	13.9290i	−0.497166	−	1.27687i
$120$		0			0
$121$			12.3137i			1.11943i
$122$	−3.62534	−	3.62534i	−0.328223	−	0.328223i
$123$		0			0
$124$	−3.75234	+	3.75234i	−0.336970	+	0.336970i
$125$	−10.3233	−	4.29289i	−0.923346	−	0.383968i
$126$		0			0
$127$	−20.1524			−1.78824			−0.894119	−	0.447830i	$-0.852197\pi$
$127$	−20.1524			−1.78824			−0.894119	+	0.447830i	$0.852197\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	−1.18884	+	8.99787i	−0.104268	+	0.789166i
$131$	6.83569	−	6.83569i	0.597237	−	0.597237i	−0.342339	−	0.939576i	$-0.611219\pi$
$131$	6.83569	−	6.83569i	0.597237	−	0.597237i	0.939576	+	0.342339i	$0.111219\pi$
$132$		0			0
$133$	−7.25067	−	7.25067i	−0.628713	−	0.628713i
$134$		−	6.58880i		−	0.569185i
$135$		0			0
$136$	−1.65898	+	3.77462i	−0.142257	+	0.323671i
$137$			12.1464i			1.03774i	0.854854	+	0.518868i	$0.173646\pi$
$137$			12.1464i			1.03774i	−0.854854	+	0.518868i	$0.826354\pi$
$138$		0			0
$139$	15.7919	−	15.7919i	1.33945	−	1.33945i	0.442859	−	0.896591i	$-0.353964\pi$
$139$	15.7919	−	15.7919i	1.33945	−	1.33945i	0.896591	−	0.442859i	$-0.146036\pi$
$140$	−6.43361	+	4.93194i	−0.543739	+	0.416825i
$141$		0			0
$142$	−10.9097	+	10.9097i	−0.915518	+	0.915518i
$143$	−13.8581	+	13.8581i	−1.15887	+	1.15887i
$144$		0			0
$145$	10.3777	−	7.95543i	0.861819	−	0.660662i
$146$	5.17671	+	5.17671i	0.428428	+	0.428428i
$147$		0			0
$148$	0.422246	+	0.422246i	0.0347084	+	0.0347084i
$149$	2.89316			0.237017			0.118508	−	0.992953i	$-0.462189\pi$
$149$	2.89316			0.237017			0.118508	+	0.992953i	$0.462189\pi$
$150$		0			0
$151$		−	7.26312i		−	0.591064i	−0.955333	−	0.295532i	$-0.904503\pi$
$151$		−	7.26312i		−	0.591064i	0.955333	−	0.295532i	$-0.0954969\pi$
$152$			2.82843i			0.229416i
$153$		0			0
$154$	−17.5047			−1.41057
$155$	9.41722	−	7.21916i	0.756410	−	0.579856i
$156$		0			0
$157$		−	4.17081i		−	0.332867i	−0.986053	−	0.166433i	$-0.946775\pi$
$157$		−	4.17081i		−	0.332867i	0.986053	−	0.166433i	$-0.0532250\pi$
$158$	−1.90452	−	1.90452i	−0.151515	−	0.151515i
$159$		0			0
$160$	2.21680	+	0.292893i	0.175254	+	0.0231552i
$161$			11.9876i			0.944752i
$162$		0			0
$163$	10.5888	−	10.5888i	0.829378	−	0.829378i	−0.158052	−	0.987431i	$-0.550521\pi$
$163$	10.5888	−	10.5888i	0.829378	−	0.829378i	0.987431	+	0.158052i	$0.0505214\pi$
$164$	4.18884	+	4.18884i	0.327093	+	0.327093i
$165$		0			0
$166$	7.42557			0.576336
$167$	12.0396	+	12.0396i	0.931648	+	0.931648i	0.997809	−	0.0661606i	$-0.0210750\pi$
$167$	12.0396	+	12.0396i	0.931648	+	0.931648i	−0.0661606	+	0.997809i	$0.521075\pi$
$168$		0			0
$169$	−3.47501			−0.267308
$170$	4.78320	−	7.88169i	0.366854	−	0.604498i
$171$		0			0
$172$	4.93194			0.376057
$173$	−16.0703	−	16.0703i	−1.22180	−	1.22180i	−0.966991	−	0.254812i	$-0.917987\pi$
$173$	−16.0703	−	16.0703i	−1.22180	−	1.22180i	−0.254812	−	0.966991i	$-0.582013\pi$
$174$		0			0
$175$	15.7066	−	9.04878i	1.18730	−	0.684024i
$176$	3.41421	+	3.41421i	0.257356	+	0.257356i
$177$		0			0
$178$	−10.1179			−0.758367
$179$			14.2559i			1.06554i	0.846261	+	0.532769i	$0.178849\pi$
$179$			14.2559i			1.06554i	−0.846261	+	0.532769i	$0.821151\pi$
$180$		0			0
$181$	−5.20201	−	5.20201i	−0.386662	−	0.386662i	0.486833	−	0.873495i	$-0.338152\pi$
$181$	−5.20201	−	5.20201i	−0.386662	−	0.386662i	−0.873495	+	0.486833i	$0.838152\pi$
$182$	−10.4051	−	10.4051i	−0.771277	−	0.771277i
$183$		0			0
$184$	2.33812	−	2.33812i	0.172369	−	0.172369i
$185$	−0.812363	−	1.05971i	−0.0597261	−	0.0779113i
$186$		0			0
$187$	18.5515	−	7.22325i	1.35662	−	0.528216i
$188$		−	11.8193i		−	0.862012i
$189$		0			0
$190$	0.828427	−	6.27006i	0.0601004	−	0.454878i
$191$	4.37767			0.316757			0.158379	−	0.987378i	$-0.449373\pi$
$191$	4.37767			0.316757			0.158379	+	0.987378i	$0.449373\pi$
$192$		0			0
$193$	4.49621	−	4.49621i	0.323644	−	0.323644i	−0.526519	−	0.850163i	$-0.676503\pi$
$193$	4.49621	−	4.49621i	0.323644	−	0.323644i	0.850163	+	0.526519i	$0.176503\pi$
$194$	−7.36342	−	7.36342i	−0.528663	−	0.528663i
$195$		0			0
$196$		−	6.14306i		−	0.438790i
$197$	10.6447	−	10.6447i	0.758405	−	0.758405i	−0.217627	−	0.976032i	$-0.569832\pi$
$197$	10.6447	−	10.6447i	0.758405	−	0.758405i	0.976032	+	0.217627i	$0.0698315\pi$
$198$		0			0
$199$	−3.53712	+	3.53712i	−0.250740	+	0.250740i	−0.821274	−	0.570534i	$-0.806736\pi$
$199$	−3.53712	+	3.53712i	−0.250740	+	0.250740i	0.570534	+	0.821274i	$0.306736\pi$
$200$	−4.82843	−	1.29857i	−0.341421	−	0.0918230i
$201$		0			0
$202$	−5.10684			−0.359316
$203$			21.2003i			1.48797i
$204$		0			0
$205$	−8.05894	−	10.5127i	−0.562861	−	0.734239i
$206$		−	4.78811i		−	0.333603i
$207$		0			0
$208$			4.05894i			0.281437i
$209$	9.65685	−	9.65685i	0.667979	−	0.667979i
$210$		0			0
$211$	−2.21522	−	2.21522i	−0.152502	−	0.152502i	0.626733	−	0.779234i	$-0.284392\pi$
$211$	−2.21522	−	2.21522i	−0.152502	−	0.152502i	−0.779234	+	0.626733i	$0.784392\pi$
$212$	11.2895			0.775363
$213$		0			0
$214$	−8.77249	−	8.77249i	−0.599675	−	0.599675i
$215$	−10.9331	−	1.44453i	−0.745634	−	0.0985163i
$216$		0			0
$217$			19.2382i			1.30598i
$218$	−12.1666	−	12.1666i	−0.824023	−	0.824023i
$219$		0			0
$220$	−6.56864	−	8.56864i	−0.442857	−	0.577697i
$221$	15.3210	+	6.73371i	1.03060	+	0.452958i
$222$		0			0
$223$	−14.6923			−0.983870			−0.491935	−	0.870632i	$-0.663710\pi$
$223$	−14.6923			−0.983870			−0.491935	+	0.870632i	$0.663710\pi$
$224$	−2.56350	+	2.56350i	−0.171281	+	0.171281i
$225$		0			0
$226$	−4.52182	+	4.52182i	−0.300787	+	0.300787i
$227$	6.55728	−	6.55728i	0.435222	−	0.435222i	−0.455178	−	0.890400i	$-0.650425\pi$
$227$	6.55728	−	6.55728i	0.435222	−	0.435222i	0.890400	+	0.455178i	$0.150425\pi$
$228$		0			0
$229$			11.2346i			0.742404i	0.928552	+	0.371202i	$0.121054\pi$
$229$			11.2346i			0.742404i	−0.928552	+	0.371202i	$0.878946\pi$
$230$	−5.86798	+	4.49834i	−0.386923	+	0.296612i
$231$		0			0
$232$	4.13503	−	4.13503i	0.271478	−	0.271478i
$233$	−7.10652	−	7.10652i	−0.465564	−	0.465564i	0.434910	−	0.900474i	$-0.356780\pi$
$233$	−7.10652	−	7.10652i	−0.465564	−	0.465564i	−0.900474	+	0.434910i	$0.856780\pi$
$234$		0			0
$235$	−3.46180	+	26.2011i	−0.225823	+	1.70917i
$236$			1.65276i			0.107586i
$237$		0			0
$238$	5.42344	+	13.9290i	0.351550	+	0.902886i
$239$	−21.5638			−1.39484			−0.697422	−	0.716660i	$-0.745670\pi$
$239$	−21.5638			−1.39484			−0.697422	+	0.716660i	$0.745670\pi$
$240$		0			0
$241$	8.71170	−	8.71170i	0.561170	−	0.561170i	−0.368470	−	0.929640i	$-0.620118\pi$
$241$	8.71170	−	8.71170i	0.561170	−	0.561170i	0.929640	+	0.368470i	$0.120118\pi$
$242$		−	12.3137i		−	0.791555i
$243$		0			0
$244$	3.62534	+	3.62534i	0.232088	+	0.232088i
$245$	−1.79926	+	13.6180i	−0.114951	+	0.870020i
$246$		0			0
$247$	11.4804			0.730482
$248$	3.75234	−	3.75234i	0.238274	−	0.238274i
$249$		0			0
$250$	10.3233	+	4.29289i	0.652904	+	0.271506i
$251$	16.1768			1.02107			0.510536	−	0.859856i	$-0.329447\pi$
$251$	16.1768			1.02107			0.510536	+	0.859856i	$0.329447\pi$
$252$		0			0
$253$	−15.9657			−1.00376
$254$	20.1524			1.26447
$255$		0			0
$256$	1.00000			0.0625000
$257$	−30.3895			−1.89564			−0.947822	−	0.318800i	$-0.896720\pi$
$257$	−30.3895			−1.89564			−0.947822	+	0.318800i	$0.896720\pi$
$258$		0			0
$259$	2.16485			0.134517
$260$	1.18884	−	8.99787i	0.0737285	−	0.558024i
$261$		0			0
$262$	−6.83569	+	6.83569i	−0.422310	+	0.422310i
$263$	16.8344			1.03806			0.519028	−	0.854757i	$-0.326294\pi$
$263$	16.8344			1.03806			0.519028	+	0.854757i	$0.326294\pi$
$264$		0			0
$265$	−25.0265	−	3.30661i	−1.53737	−	0.203123i
$266$	7.25067	+	7.25067i	0.444567	+	0.444567i
$267$		0			0
$268$			6.58880i			0.402475i
$269$	−22.4092	+	22.4092i	−1.36631	+	1.36631i	−0.500680	+	0.865632i	$0.666917\pi$
$269$	−22.4092	+	22.4092i	−1.36631	+	1.36631i	−0.865632	+	0.500680i	$0.833083\pi$
$270$		0			0
$271$	22.4392			1.36308			0.681541	−	0.731780i	$-0.261310\pi$
$271$	22.4392			1.36308			0.681541	+	0.731780i	$0.261310\pi$
$272$	1.65898	−	3.77462i	0.100591	−	0.228870i
$273$		0			0
$274$		−	12.1464i		−	0.733790i
$275$	12.0517	+	20.9189i	0.726743	+	1.26146i
$276$		0			0
$277$	0.538204	+	0.538204i	0.0323376	+	0.0323376i	0.723091	−	0.690753i	$-0.242721\pi$
$277$	0.538204	+	0.538204i	0.0323376	+	0.0323376i	−0.690753	+	0.723091i	$0.742721\pi$
$278$	−15.7919	+	15.7919i	−0.947134	+	0.947134i
$279$		0			0
$280$	6.43361	−	4.93194i	0.384481	−	0.294740i
$281$			5.52074i			0.329340i	0.986349	+	0.164670i	$0.0526558\pi$
$281$			5.52074i			0.329340i	−0.986349	+	0.164670i	$0.947344\pi$
$282$		0			0
$283$	−10.3290	+	10.3290i	−0.613996	+	0.613996i	−0.943985	−	0.329989i	$-0.892955\pi$
$283$	−10.3290	+	10.3290i	−0.613996	+	0.613996i	0.329989	+	0.943985i	$0.392955\pi$
$284$	10.9097	−	10.9097i	0.647369	−	0.647369i
$285$		0			0
$286$	13.8581	−	13.8581i	0.819446	−	0.819446i
$287$	21.4762			1.26770
$288$		0			0
$289$	−11.4956	−	12.5241i	−0.676209	−	0.736710i
$290$	−10.3777	+	7.95543i	−0.609398	+	0.467159i
$291$		0			0
$292$	−5.17671	−	5.17671i	−0.302944	−	0.302944i
$293$			1.88212i			0.109954i	0.998488	+	0.0549772i	$0.0175086\pi$
$293$			1.88212i			0.109954i	−0.998488	+	0.0549772i	$0.982491\pi$
$294$		0			0
$295$	0.484082	−	3.66384i	0.0281844	−	0.213317i
$296$	−0.422246	−	0.422246i	−0.0245425	−	0.0245425i
$297$		0			0
$298$	−2.89316			−0.167596
$299$	−9.49030	−	9.49030i	−0.548838	−	0.548838i
$300$		0			0
$301$	12.6430	−	12.6430i	0.728732	−	0.728732i
$302$			7.26312i			0.417945i
$303$		0			0
$304$		−	2.82843i		−	0.162221i
$305$	−6.97482	−	9.09849i	−0.399377	−	0.520978i
$306$		0			0
$307$			20.2396i			1.15514i	0.816342	+	0.577568i	$0.195998\pi$
$307$			20.2396i			1.15514i	−0.816342	+	0.577568i	$0.804002\pi$
$308$	17.5047			0.997421
$309$		0			0
$310$	−9.41722	+	7.21916i	−0.534862	+	0.410020i
$311$	−5.93058	+	5.93058i	−0.336292	+	0.336292i	−0.854970	−	0.518678i	$-0.826425\pi$
$311$	−5.93058	+	5.93058i	−0.336292	+	0.336292i	0.518678	+	0.854970i	$0.326425\pi$
$312$		0			0
$313$	−5.12186	+	5.12186i	−0.289505	+	0.289505i	−0.836884	−	0.547380i	$-0.815625\pi$
$313$	−5.12186	+	5.12186i	−0.289505	+	0.289505i	0.547380	+	0.836884i	$0.315625\pi$
$314$			4.17081i			0.235372i
$315$		0			0
$316$	1.90452	+	1.90452i	0.107137	+	0.107137i
$317$	−23.2822	+	23.2822i	−1.30766	+	1.30766i	−0.384557	+	0.923101i	$0.625646\pi$
$317$	−23.2822	+	23.2822i	−1.30766	+	1.30766i	−0.923101	+	0.384557i	$0.874354\pi$
$318$		0			0
$319$	−28.2358			−1.58090
$320$	−2.21680	−	0.292893i	−0.123923	−	0.0163732i
$321$		0			0
$322$		−	11.9876i		−	0.668040i
$323$	−10.6762	−	4.69231i	−0.594042	−	0.261087i
$324$		0			0
$325$	−5.27083	+	19.5983i	−0.292373	+	1.08712i
$326$	−10.5888	+	10.5888i	−0.586459	+	0.586459i
$327$		0			0
$328$	−4.18884	−	4.18884i	−0.231290	−	0.231290i
$329$	−30.2988	−	30.2988i	−1.67043	−	1.67043i
$330$		0			0
$331$		−	33.2779i		−	1.82912i	−0.404453	−	0.914559i	$-0.632538\pi$
$331$		−	33.2779i		−	1.82912i	0.404453	−	0.914559i	$-0.367462\pi$
$332$	−7.42557			−0.407531
$333$		0			0
$334$	−12.0396	−	12.0396i	−0.658775	−	0.658775i
$335$	1.92981	−	14.6061i	0.105437	−	0.798014i
$336$		0			0
$337$	−4.55106	−	4.55106i	−0.247912	−	0.247912i	0.572201	−	0.820113i	$-0.306090\pi$
$337$	−4.55106	−	4.55106i	−0.247912	−	0.247912i	−0.820113	+	0.572201i	$0.806090\pi$
$338$	3.47501			0.189015
$339$		0			0
$340$	−4.78320	+	7.88169i	−0.259405	+	0.427445i
$341$	−25.6226			−1.38754
$342$		0			0
$343$	2.19675	+	2.19675i	0.118614	+	0.118614i
$344$	−4.93194			−0.265912
$345$		0			0
$346$	16.0703	+	16.0703i	0.863945	+	0.863945i
$347$	−16.1798	+	16.1798i	−0.868579	+	0.868579i	−0.992315	−	0.123736i	$-0.960512\pi$
$347$	−16.1798	+	16.1798i	−0.868579	+	0.868579i	0.123736	+	0.992315i	$0.460512\pi$
$348$		0			0
$349$		−	17.7763i		−	0.951542i	−0.879569	−	0.475771i	$-0.842169\pi$
$349$		−	17.7763i		−	0.951542i	0.879569	−	0.475771i	$-0.157831\pi$
$350$	−15.7066	+	9.04878i	−0.839551	+	0.483678i
$351$		0			0
$352$	−3.41421	−	3.41421i	−0.181978	−	0.181978i
$353$		−	30.9911i		−	1.64949i	−0.565504	−	0.824745i	$-0.691318\pi$
$353$		−	30.9911i		−	1.64949i	0.565504	−	0.824745i	$-0.308682\pi$
$354$		0			0
$355$	−27.3799	+	20.9892i	−1.45318	+	1.11399i
$356$	10.1179			0.536247
$357$		0			0
$358$		−	14.2559i		−	0.753449i
$359$		−	8.11788i		−	0.428445i	−0.976785	−	0.214223i	$-0.931278\pi$
$359$		−	8.11788i		−	0.428445i	0.976785	−	0.214223i	$-0.0687218\pi$
$360$		0			0
$361$	11.0000			0.578947
$362$	5.20201	+	5.20201i	0.273411	+	0.273411i
$363$		0			0
$364$	10.4051	+	10.4051i	0.545375	+	0.545375i
$365$	9.95952	+	12.9920i	0.521305	+	0.680031i
$366$		0			0
$367$	15.8530	−	15.8530i	0.827518	−	0.827518i	−0.159655	−	0.987173i	$-0.551038\pi$
$367$	15.8530	−	15.8530i	0.827518	−	0.827518i	0.987173	+	0.159655i	$0.0510383\pi$
$368$	−2.33812	+	2.33812i	−0.121883	+	0.121883i
$369$		0			0
$370$	0.812363	+	1.05971i	0.0422327	+	0.0550916i
$371$	28.9405	−	28.9405i	1.50252	−	1.50252i
$372$		0			0
$373$		−	7.14290i		−	0.369845i	−0.982753	−	0.184923i	$-0.940797\pi$
$373$		−	7.14290i		−	0.369845i	0.982753	−	0.184923i	$-0.0592035\pi$
$374$	−18.5515	+	7.22325i	−0.959275	+	0.373505i
$375$		0			0
$376$			11.8193i			0.609534i
$377$	−16.7839	−	16.7839i	−0.864412	−	0.864412i
$378$		0			0
$379$	19.6155	−	19.6155i	1.00758	−	1.00758i	0.00760706	−	0.999971i	$-0.497579\pi$
$379$	19.6155	−	19.6155i	1.00758	−	1.00758i	0.999971	−	0.00760706i	$-0.00242143\pi$
$380$	−0.828427	+	6.27006i	−0.0424974	+	0.321648i
$381$		0			0
$382$	−4.37767			−0.223981
$383$	−16.2373			−0.829687			−0.414844	−	0.909893i	$-0.636164\pi$
$383$	−16.2373			−0.829687			−0.414844	+	0.909893i	$0.636164\pi$
$384$		0			0
$385$	−38.8044	−	5.12700i	−1.97766	−	0.261296i
$386$	−4.49621	+	4.49621i	−0.228851	+	0.228851i
$387$		0			0
$388$	7.36342	+	7.36342i	0.373821	+	0.373821i
$389$			12.7622i			0.647067i	0.946217	+	0.323534i	$0.104871\pi$
$389$			12.7622i			0.647067i	−0.946217	+	0.323534i	$0.895129\pi$
$390$		0			0
$391$	4.94663	+	12.7044i	0.250162	+	0.642491i
$392$			6.14306i			0.310272i
$393$		0			0
$394$	−10.6447	+	10.6447i	−0.536274	+	0.536274i
$395$	−3.66412	−	4.77976i	−0.184362	−	0.240496i
$396$		0			0
$397$	−1.22024	+	1.22024i	−0.0612421	+	0.0612421i	−0.737064	−	0.675822i	$-0.763789\pi$
$397$	−1.22024	+	1.22024i	−0.0612421	+	0.0612421i	0.675822	+	0.737064i	$0.263789\pi$
$398$	3.53712	−	3.53712i	0.177300	−	0.177300i
$399$		0			0
$400$	4.82843	+	1.29857i	0.241421	+	0.0649286i
$401$	−5.35462	−	5.35462i	−0.267397	−	0.267397i	0.560654	−	0.828050i	$-0.310550\pi$
$401$	−5.35462	−	5.35462i	−0.267397	−	0.267397i	−0.828050	+	0.560654i	$0.810550\pi$
$402$		0			0
$403$	−15.2305	−	15.2305i	−0.758686	−	0.758686i
$404$	5.10684			0.254075
$405$		0			0
$406$		−	21.2003i		−	1.05215i
$407$			2.88327i			0.142919i
$408$		0			0
$409$	−27.8663			−1.37790			−0.688949	−	0.724809i	$-0.741928\pi$
$409$	−27.8663			−1.37790			−0.688949	+	0.724809i	$0.741928\pi$
$410$	8.05894	+	10.5127i	0.398003	+	0.519186i
$411$		0			0
$412$			4.78811i			0.235893i
$413$	4.23685	+	4.23685i	0.208482	+	0.208482i
$414$		0			0
$415$	16.4610	+	2.17490i	0.808040	+	0.106762i
$416$		−	4.05894i		−	0.199006i
$417$		0			0
$418$	−9.65685	+	9.65685i	−0.472332	+	0.472332i
$419$	12.1738	+	12.1738i	0.594730	+	0.594730i	0.938905	−	0.344176i	$-0.111842\pi$
$419$	12.1738	+	12.1738i	0.594730	+	0.594730i	−0.344176	+	0.938905i	$0.611842\pi$
$420$		0			0
$421$	−22.6520			−1.10399			−0.551995	−	0.833847i	$-0.686133\pi$
$421$	−22.6520			−1.10399			−0.551995	+	0.833847i	$0.686133\pi$
$422$	2.21522	+	2.21522i	0.107835	+	0.107835i
$423$		0			0
$424$	−11.2895			−0.548264
$425$	12.9119	−	16.0712i	0.626319	−	0.779567i
$426$		0			0
$427$	18.5871			0.899493
$428$	8.77249	+	8.77249i	0.424035	+	0.424035i
$429$		0			0
$430$	10.9331	+	1.44453i	0.527243	+	0.0696615i
$431$	13.7220	+	13.7220i	0.660966	+	0.660966i	0.955608	−	0.294642i	$-0.0952002\pi$
$431$	13.7220	+	13.7220i	0.660966	+	0.660966i	−0.294642	+	0.955608i	$0.595200\pi$
$432$		0			0
$433$	−32.8226			−1.57736			−0.788678	−	0.614807i	$-0.789234\pi$
$433$	−32.8226			−1.57736			−0.788678	+	0.614807i	$0.789234\pi$
$434$		−	19.2382i		−	0.923465i
$435$		0			0
$436$	12.1666	+	12.1666i	0.582672	+	0.582672i
$437$	6.61321	+	6.61321i	0.316353	+	0.316353i
$438$		0			0
$439$	5.00301	−	5.00301i	0.238781	−	0.238781i	−0.577564	−	0.816345i	$-0.695997\pi$
$439$	5.00301	−	5.00301i	0.238781	−	0.238781i	0.816345	+	0.577564i	$0.195997\pi$
$440$	6.56864	+	8.56864i	0.313147	+	0.408494i
$441$		0			0
$442$	−15.3210	−	6.73371i	−0.728744	−	0.320290i
$443$			9.49648i			0.451192i	0.974221	+	0.225596i	$0.0724329\pi$
$443$			9.49648i			0.451192i	−0.974221	+	0.225596i	$0.927567\pi$
$444$		0			0
$445$	−22.4293	−	2.96346i	−1.06325	−	0.140481i
$446$	14.6923			0.695701
$447$		0			0
$448$	2.56350	−	2.56350i	0.121114	−	0.121114i
$449$	13.9963	+	13.9963i	0.660528	+	0.660528i	0.955505	−	0.294976i	$-0.0953118\pi$
$449$	13.9963	+	13.9963i	0.660528	+	0.660528i	−0.294976	+	0.955505i	$0.595312\pi$
$450$		0			0
$451$			28.6032i			1.34687i
$452$	4.52182	−	4.52182i	0.212689	−	0.212689i
$453$		0			0
$454$	−6.55728	+	6.55728i	−0.307748	+	0.307748i
$455$	−20.0185	−	26.1136i	−0.938480	−	1.22423i
$456$		0			0
$457$	−13.8823			−0.649389			−0.324694	−	0.945819i	$-0.605261\pi$
$457$	−13.8823			−0.649389			−0.324694	+	0.945819i	$0.605261\pi$
$458$		−	11.2346i		−	0.524959i
$459$		0			0
$460$	5.86798	−	4.49834i	0.273596	−	0.209736i
$461$		−	15.6082i		−	0.726946i	−0.931605	−	0.363473i	$-0.881591\pi$
$461$		−	15.6082i		−	0.726946i	0.931605	−	0.363473i	$-0.118409\pi$
$462$		0			0
$463$			5.08396i			0.236272i	0.992997	+	0.118136i	$0.0376918\pi$
$463$			5.08396i			0.236272i	−0.992997	+	0.118136i	$0.962308\pi$
$464$	−4.13503	+	4.13503i	−0.191964	+	0.191964i
$465$		0			0
$466$	7.10652	+	7.10652i	0.329203	+	0.329203i
$467$	−22.0615			−1.02088			−0.510442	−	0.859912i	$-0.670518\pi$
$467$	−22.0615			−1.02088			−0.510442	+	0.859912i	$0.670518\pi$
$468$		0			0
$469$	16.8904	+	16.8904i	0.779925	+	0.779925i
$470$	3.46180	−	26.2011i	0.159681	−	1.20857i
$471$		0			0
$472$		−	1.65276i		−	0.0760745i
$473$	16.8387	+	16.8387i	0.774244	+	0.774244i
$474$		0			0
$475$	3.67292	−	13.6569i	0.168525	−	0.626619i
$476$	−5.42344	−	13.9290i	−0.248583	−	0.638437i
$477$		0			0
$478$	21.5638			0.986304
$479$	−15.0721	+	15.0721i	−0.688662	+	0.688662i	−0.961936	−	0.273274i	$-0.911893\pi$
$479$	−15.0721	+	15.0721i	−0.688662	+	0.688662i	0.273274	+	0.961936i	$0.411893\pi$
$480$		0			0
$481$	−1.71387	+	1.71387i	−0.0781458	+	0.0781458i
$482$	−8.71170	+	8.71170i	−0.396807	+	0.396807i
$483$		0			0
$484$			12.3137i			0.559714i
$485$	−14.1666	−	18.4799i	−0.643270	−	0.839131i
$486$		0			0
$487$	−26.6368	+	26.6368i	−1.20703	+	1.20703i	−0.235044	+	0.971985i	$0.575524\pi$
$487$	−26.6368	+	26.6368i	−1.20703	+	1.20703i	−0.971985	+	0.235044i	$0.924476\pi$
$488$	−3.62534	−	3.62534i	−0.164111	−	0.164111i
$489$		0			0
$490$	1.79926	−	13.6180i	0.0812824	−	0.615197i
$491$			2.10930i			0.0951916i	0.998867	+	0.0475958i	$0.0151559\pi$
$491$			2.10930i			0.0951916i	−0.998867	+	0.0475958i	$0.984844\pi$
$492$		0			0
$493$	8.74824	+	22.4681i	0.394001	+	1.01191i
$494$	−11.4804			−0.516529
$495$		0			0
$496$	−3.75234	+	3.75234i	−0.168485	+	0.168485i
$497$		−	55.9338i		−	2.50897i
$498$		0			0
$499$	−20.0045	−	20.0045i	−0.895524	−	0.895524i	0.0995126	−	0.995036i	$-0.468272\pi$
$499$	−20.0045	−	20.0045i	−0.895524	−	0.895524i	−0.995036	+	0.0995126i	$0.968272\pi$
$500$	−10.3233	−	4.29289i	−0.461673	−	0.191984i
$501$		0			0
$502$	−16.1768			−0.722007
$503$	5.09772	−	5.09772i	0.227296	−	0.227296i	−0.584266	−	0.811562i	$-0.698617\pi$
$503$	5.09772	−	5.09772i	0.227296	−	0.227296i	0.811562	+	0.584266i	$0.198617\pi$
$504$		0			0
$505$	−11.3209	−	1.49576i	−0.503772	−	0.0665604i
$506$	15.9657			0.709762
$507$		0			0
$508$	−20.1524			−0.894119
$509$	−36.8488			−1.63329			−0.816647	−	0.577137i	$-0.804170\pi$
$509$	−36.8488			−1.63329			−0.816647	+	0.577137i	$0.804170\pi$
$510$		0			0
$511$	−26.5410			−1.17410
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	30.3895			1.34042
$515$	1.40240	−	10.6143i	0.0617973	−	0.467722i
$516$		0			0
$517$	40.3536	−	40.3536i	1.77475	−	1.77475i
$518$	−2.16485			−0.0951182
$519$		0			0
$520$	−1.18884	+	8.99787i	−0.0521339	+	0.394583i
$521$	21.9678	+	21.9678i	0.962428	+	0.962428i	0.999319	−	0.0368912i	$-0.0117455\pi$
$521$	21.9678	+	21.9678i	0.962428	+	0.962428i	−0.0368912	+	0.999319i	$0.511745\pi$
$522$		0			0
$523$		−	5.46605i		−	0.239014i	−0.992833	−	0.119507i	$-0.961869\pi$
$523$		−	5.46605i		−	0.239014i	0.992833	−	0.119507i	$-0.0381314\pi$
$524$	6.83569	−	6.83569i	0.298619	−	0.298619i
$525$		0			0
$526$	−16.8344			−0.734017
$527$	7.93860	+	20.3887i	0.345811	+	0.888146i
$528$		0			0
$529$			12.0664i			0.524624i
$530$	25.0265	+	3.30661i	1.08708	+	0.143630i
$531$		0			0
$532$	−7.25067	−	7.25067i	−0.314357	−	0.314357i
$533$	−17.0022	+	17.0022i	−0.736449	+	0.736449i
$534$		0			0
$535$	−16.8775	−	22.0163i	−0.729677	−	0.951847i
$536$		−	6.58880i		−	0.284593i
$537$		0			0
$538$	22.4092	−	22.4092i	0.966129	−	0.966129i
$539$	20.9737	−	20.9737i	0.903403	−	0.903403i
$540$		0			0
$541$	−25.0730	+	25.0730i	−1.07797	+	1.07797i	−0.0812809	+	0.996691i	$0.525901\pi$
$541$	−25.0730	+	25.0730i	−1.07797	+	1.07797i	−0.996691	+	0.0812809i	$0.974099\pi$
$542$	−22.4392			−0.963845
$543$		0			0
$544$	−1.65898	+	3.77462i	−0.0711283	+	0.161836i
$545$	−23.4073	−	30.5343i	−1.00266	−	1.30795i
$546$		0			0
$547$	4.08319	+	4.08319i	0.174585	+	0.174585i	0.788990	−	0.614406i	$-0.210604\pi$
$547$	4.08319	+	4.08319i	0.174585	+	0.174585i	−0.614406	+	0.788990i	$0.710604\pi$
$548$			12.1464i			0.518868i
$549$		0			0
$550$	−12.0517	−	20.9189i	−0.513885	−	0.891984i
$551$	11.6956	+	11.6956i	0.498251	+	0.498251i
$552$		0			0
$553$	9.76446			0.415227
$554$	−0.538204	−	0.538204i	−0.0228661	−	0.0228661i
$555$		0			0
$556$	15.7919	−	15.7919i	0.669725	−	0.669725i
$557$		−	7.99847i		−	0.338906i	−0.985538	−	0.169453i	$-0.945800\pi$
$557$		−	7.99847i		−	0.338906i	0.985538	−	0.169453i	$-0.0542001\pi$
$558$		0			0
$559$			20.0185i			0.846691i
$560$	−6.43361	+	4.93194i	−0.271869	+	0.208413i
$561$		0			0
$562$		−	5.52074i		−	0.232878i
$563$	35.2734			1.48660			0.743298	−	0.668960i	$-0.233260\pi$
$563$	35.2734			1.48660			0.743298	+	0.668960i	$0.233260\pi$
$564$		0			0
$565$	−11.3484	+	8.69958i	−0.477431	+	0.365994i
$566$	10.3290	−	10.3290i	0.434161	−	0.434161i
$567$		0			0
$568$	−10.9097	+	10.9097i	−0.457759	+	0.457759i
$569$			0.465285i			0.0195058i	0.999952	+	0.00975288i	$0.00310449\pi$
$569$			0.465285i			0.0195058i	−0.999952	+	0.00975288i	$0.996896\pi$
$570$		0			0
$571$	−1.18872	−	1.18872i	−0.0497465	−	0.0497465i	0.681796	−	0.731542i	$-0.261199\pi$
$571$	−1.18872	−	1.18872i	−0.0497465	−	0.0497465i	−0.731542	+	0.681796i	$0.761199\pi$
$572$	−13.8581	+	13.8581i	−0.579436	+	0.579436i
$573$		0			0
$574$	−21.4762			−0.896398
$575$	−14.3257	+	8.25323i	−0.597422	+	0.344184i
$576$		0			0
$577$		−	7.16578i		−	0.298315i	−0.988813	−	0.149158i	$-0.952344\pi$
$577$		−	7.16578i		−	0.298315i	0.988813	−	0.149158i	$-0.0476562\pi$
$578$	11.4956	+	12.5241i	0.478152	+	0.520932i
$579$		0			0
$580$	10.3777	−	7.95543i	0.430909	−	0.330331i
$581$	−19.0355	+	19.0355i	−0.789724	+	0.789724i
$582$		0			0
$583$	38.5446	+	38.5446i	1.59635	+	1.59635i
$584$	5.17671	+	5.17671i	0.214214	+	0.214214i
$585$		0			0
$586$		−	1.88212i		−	0.0777495i
$587$	−17.0742			−0.704729			−0.352365	−	0.935863i	$-0.614622\pi$
$587$	−17.0742			−0.704729			−0.352365	+	0.935863i	$0.614622\pi$
$588$		0			0
$589$	10.6132	+	10.6132i	0.437310	+	0.437310i
$590$	−0.484082	+	3.66384i	−0.0199294	+	0.150838i
$591$		0			0
$592$	0.422246	+	0.422246i	0.0173542	+	0.0173542i
$593$	−1.83329			−0.0752841			−0.0376421	−	0.999291i	$-0.511985\pi$
$593$	−1.83329			−0.0752841			−0.0376421	+	0.999291i	$0.511985\pi$
$594$		0			0
$595$	7.94298	+	32.4664i	0.325631	+	1.33099i
$596$	2.89316			0.118508
$597$		0			0
$598$	9.49030	+	9.49030i	0.388087	+	0.388087i
$599$	−12.4677			−0.509416			−0.254708	−	0.967018i	$-0.581979\pi$
$599$	−12.4677			−0.509416			−0.254708	+	0.967018i	$0.581979\pi$
$600$		0			0
$601$	−8.30552	−	8.30552i	−0.338789	−	0.338789i	0.517122	−	0.855912i	$-0.327003\pi$
$601$	−8.30552	−	8.30552i	−0.338789	−	0.338789i	−0.855912	+	0.517122i	$0.827003\pi$
$602$	−12.6430	+	12.6430i	−0.515292	+	0.515292i
$603$		0			0
$604$		−	7.26312i		−	0.295532i
$605$	3.60660	−	27.2971i	0.146629	−	1.10978i
$606$		0			0
$607$	17.7939	+	17.7939i	0.722230	+	0.722230i	0.969059	−	0.246829i	$-0.0793886\pi$
$607$	17.7939	+	17.7939i	0.722230	+	0.722230i	−0.246829	+	0.969059i	$0.579389\pi$
$608$			2.82843i			0.114708i
$609$		0			0
$610$	6.97482	+	9.09849i	0.282402	+	0.368387i
$611$	47.9739			1.94082
$612$		0			0
$613$			3.46180i			0.139821i	0.997553	+	0.0699103i	$0.0222713\pi$
$613$			3.46180i			0.139821i	−0.997553	+	0.0699103i	$0.977729\pi$
$614$		−	20.2396i		−	0.816805i
$615$		0			0
$616$	−17.5047			−0.705283
$617$	25.8888	+	25.8888i	1.04225	+	1.04225i	0.999067	+	0.0431782i	$0.0137483\pi$
$617$	25.8888	+	25.8888i	1.04225	+	1.04225i	0.0431782	+	0.999067i	$0.486252\pi$
$618$		0			0
$619$	24.9448	+	24.9448i	1.00262	+	1.00262i	0.999997	+	0.00261864i	$0.000833541\pi$
$619$	24.9448	+	24.9448i	1.00262	+	1.00262i	0.00261864	+	0.999997i	$0.499166\pi$
$620$	9.41722	−	7.21916i	0.378205	−	0.289928i
$621$		0			0
$622$	5.93058	−	5.93058i	0.237795	−	0.237795i
$623$	25.9372	−	25.9372i	1.03915	−	1.03915i
$624$		0			0
$625$	21.6274	+	12.5401i	0.865097	+	0.501605i
$626$	5.12186	−	5.12186i	0.204711	−	0.204711i
$627$		0			0
$628$		−	4.17081i		−	0.166433i
$629$	2.29432	−	0.893320i	0.0914804	−	0.0356190i
$630$		0			0
$631$		−	13.3077i		−	0.529771i	−0.964280	−	0.264885i	$-0.914666\pi$
$631$		−	13.3077i		−	0.529771i	0.964280	−	0.264885i	$-0.0853341\pi$
$632$	−1.90452	−	1.90452i	−0.0757577	−	0.0757577i
$633$		0			0
$634$	23.2822	−	23.2822i	0.924654	−	0.924654i
$635$	44.6739	+	5.90250i	1.77283	+	0.234234i
$636$		0			0
$637$	24.9343			0.987935
$638$	28.2358			1.11786
$639$		0			0
$640$	2.21680	+	0.292893i	0.0876268	+	0.0115776i
$641$	28.5810	−	28.5810i	1.12888	−	1.12888i	0.138524	−	0.990359i	$-0.455764\pi$
$641$	28.5810	−	28.5810i	1.12888	−	1.12888i	0.990359	−	0.138524i	$-0.0442359\pi$
$642$		0			0
$643$	−28.2684	−	28.2684i	−1.11480	−	1.11480i	−0.992493	−	0.122303i	$-0.960972\pi$
$643$	−28.2684	−	28.2684i	−1.11480	−	1.11480i	−0.122303	−	0.992493i	$-0.539028\pi$
$644$			11.9876i			0.472376i
$645$		0			0
$646$	10.6762	+	4.69231i	0.420051	+	0.184616i
$647$		−	20.6647i		−	0.812412i	−0.913782	−	0.406206i	$-0.866852\pi$
$647$		−	20.6647i		−	0.812412i	0.913782	−	0.406206i	$-0.133148\pi$
$648$		0			0
$649$	−5.64288	+	5.64288i	−0.221502	+	0.221502i
$650$	5.27083	−	19.5983i	0.206739	−	0.768709i
$651$		0			0
$652$	10.5888	−	10.5888i	0.414689	−	0.414689i
$653$	−6.51571	+	6.51571i	−0.254980	+	0.254980i	−0.823009	−	0.568029i	$-0.807706\pi$
$653$	−6.51571	+	6.51571i	−0.254980	+	0.254980i	0.568029	+	0.823009i	$0.307706\pi$
$654$		0			0
$655$	−17.1555	+	13.1513i	−0.670321	+	0.513862i
$656$	4.18884	+	4.18884i	0.163547	+	0.163547i
$657$		0			0
$658$	30.2988	+	30.2988i	1.18117	+	1.18117i
$659$	0.673686			0.0262431			0.0131215	−	0.999914i	$-0.495823\pi$
$659$	0.673686			0.0262431			0.0131215	+	0.999914i	$0.495823\pi$
$660$		0			0
$661$		−	32.5156i		−	1.26471i	−0.774679	−	0.632354i	$-0.782089\pi$
$661$		−	32.5156i		−	1.26471i	0.774679	−	0.632354i	$-0.217911\pi$
$662$			33.2779i			1.29338i
$663$		0			0
$664$	7.42557			0.288168
$665$	13.9496	+	18.1970i	0.540944	+	0.705649i
$666$		0			0
$667$		−	19.3364i		−	0.748709i
$668$	12.0396	+	12.0396i	0.465824	+	0.465824i
$669$		0			0
$670$	−1.92981	+	14.6061i	−0.0745552	+	0.564281i
$671$			24.7553i			0.955670i
$672$		0			0
$673$	7.18915	−	7.18915i	0.277122	−	0.277122i	−0.554837	−	0.831959i	$-0.687220\pi$
$673$	7.18915	−	7.18915i	0.277122	−	0.277122i	0.831959	+	0.554837i	$0.187220\pi$
$674$	4.55106	+	4.55106i	0.175300	+	0.175300i
$675$		0			0
$676$	−3.47501			−0.133654
$677$	28.7298	+	28.7298i	1.10418	+	1.10418i	0.993901	+	0.110277i	$0.0351737\pi$
$677$	28.7298	+	28.7298i	1.10418	+	1.10418i	0.110277	+	0.993901i	$0.464826\pi$
$678$		0			0
$679$	37.7522			1.44880
$680$	4.78320	−	7.88169i	0.183427	−	0.302249i
$681$		0			0
$682$	25.6226			0.981138
$683$	21.5595	+	21.5595i	0.824952	+	0.824952i	0.986814	−	0.161861i	$-0.0517497\pi$
$683$	21.5595	+	21.5595i	0.824952	+	0.824952i	−0.161861	+	0.986814i	$0.551750\pi$
$684$		0			0
$685$	3.55760	−	26.9262i	0.135929	−	1.02880i
$686$	−2.19675	−	2.19675i	−0.0838725	−	0.0838725i
$687$		0			0
$688$	4.93194			0.188029
$689$			45.8232i			1.74573i
$690$		0			0
$691$	24.7714	+	24.7714i	0.942349	+	0.942349i	0.998426	−	0.0560776i	$-0.0178594\pi$
$691$	24.7714	+	24.7714i	0.942349	+	0.942349i	−0.0560776	+	0.998426i	$0.517859\pi$
$692$	−16.0703	−	16.0703i	−0.610901	−	0.610901i
$693$		0			0
$694$	16.1798	−	16.1798i	0.614178	−	0.614178i
$695$	−39.6328	+	30.3822i	−1.50336	+	1.15246i
$696$		0			0
$697$	22.7605	−	8.86207i	0.862115	−	0.335675i
$698$			17.7763i			0.672842i
$699$		0			0
$700$	15.7066	−	9.04878i	0.593652	−	0.342012i
$701$	−42.3963			−1.60129			−0.800643	−	0.599142i	$-0.795509\pi$
$701$	−42.3963			−1.60129			−0.800643	+	0.599142i	$0.795509\pi$
$702$		0			0
$703$	1.19429	−	1.19429i	0.0450436	−	0.0450436i
$704$	3.41421	+	3.41421i	0.128678	+	0.128678i
$705$		0			0
$706$			30.9911i			1.16637i
$707$	13.0914	−	13.0914i	0.492352	−	0.492352i
$708$		0			0
$709$	−20.6750	+	20.6750i	−0.776466	+	0.776466i	−0.979228	−	0.202762i	$-0.935008\pi$
$709$	−20.6750	+	20.6750i	−0.776466	+	0.776466i	0.202762	+	0.979228i	$0.435008\pi$
$710$	27.3799	−	20.9892i	1.02755	−	0.787710i
$711$		0			0
$712$	−10.1179			−0.379184
$713$		−	17.5468i		−	0.657135i
$714$		0			0
$715$	34.7796	−	26.6617i	1.30068	−	0.997092i
$716$			14.2559i			0.532769i
$717$		0			0
$718$			8.11788i			0.302957i
$719$	17.2998	−	17.2998i	0.645173	−	0.645173i	−0.306650	−	0.951822i	$-0.599208\pi$
$719$	17.2998	−	17.2998i	0.645173	−	0.645173i	0.951822	+	0.306650i	$0.0992080\pi$
$720$		0			0
$721$	12.2743	+	12.2743i	0.457120	+	0.457120i
$722$	−11.0000			−0.409378
$723$		0			0
$724$	−5.20201	−	5.20201i	−0.193331	−	0.193331i
$725$	−25.3353	+	14.5961i	−0.940931	+	0.542084i
$726$		0			0
$727$		−	43.5553i		−	1.61538i	−0.589611	−	0.807688i	$-0.700719\pi$
$727$		−	43.5553i		−	1.61538i	0.589611	−	0.807688i	$-0.299281\pi$
$728$	−10.4051	−	10.4051i	−0.385639	−	0.385639i
$729$		0			0
$730$	−9.95952	−	12.9920i	−0.368618	−	0.480854i
$731$	8.18200	−	18.6162i	0.302622	−	0.688546i
$732$		0			0
$733$	40.5875			1.49913			0.749567	−	0.661929i	$-0.230262\pi$
$733$	40.5875			1.49913			0.749567	+	0.661929i	$0.230262\pi$
$734$	−15.8530	+	15.8530i	−0.585143	+	0.585143i
$735$		0			0
$736$	2.33812	−	2.33812i	0.0861844	−	0.0861844i
$737$	−22.4956	+	22.4956i	−0.828634	+	0.828634i
$738$		0			0
$739$		−	51.1190i		−	1.88044i	−0.340562	−	0.940222i	$-0.610617\pi$
$739$		−	51.1190i		−	1.88044i	0.340562	−	0.940222i	$-0.389383\pi$
$740$	−0.812363	−	1.05971i	−0.0298630	−	0.0389557i
$741$		0			0
$742$	−28.9405	+	28.9405i	−1.06244	+	1.06244i
$743$	1.23538	+	1.23538i	0.0453215	+	0.0453215i	0.729404	−	0.684083i	$-0.239797\pi$
$743$	1.23538	+	1.23538i	0.0453215	+	0.0453215i	−0.684083	+	0.729404i	$0.739797\pi$
$744$		0			0
$745$	−6.41356	−	0.847387i	−0.234975	−	0.0310458i
$746$			7.14290i			0.261520i
$747$		0			0
$748$	18.5515	−	7.22325i	0.678310	−	0.264108i
$749$	44.9766			1.64341
$750$		0			0
$751$	−32.7777	+	32.7777i	−1.19608	+	1.19608i	−0.220746	+	0.975331i	$0.570849\pi$
$751$	−32.7777	+	32.7777i	−1.19608	+	1.19608i	−0.975331	+	0.220746i	$0.929151\pi$
$752$		−	11.8193i		−	0.431006i
$753$		0			0
$754$	16.7839	+	16.7839i	0.611232	+	0.611232i
$755$	−2.12732	+	16.1009i	−0.0774210	+	0.585972i
$756$		0			0
$757$	10.0835			0.366492			0.183246	−	0.983067i	$-0.441340\pi$
$757$	10.0835			0.366492			0.183246	+	0.983067i	$0.441340\pi$
$758$	−19.6155	+	19.6155i	−0.712465	+	0.712465i
$759$		0			0
$760$	0.828427	−	6.27006i	0.0300502	−	0.227439i
$761$	−46.1020			−1.67120			−0.835599	−	0.549340i	$-0.814879\pi$
$761$	−46.1020			−1.67120			−0.835599	+	0.549340i	$0.814879\pi$
$762$		0			0
$763$	62.3779			2.25823
$764$	4.37767			0.158379
$765$		0			0
$766$	16.2373			0.586678
$767$	−6.70846			−0.242228
$768$		0			0
$769$	−5.16130			−0.186121			−0.0930606	−	0.995660i	$-0.529665\pi$
$769$	−5.16130			−0.186121			−0.0930606	+	0.995660i	$0.529665\pi$
$770$	38.8044	+	5.12700i	1.39841	+	0.184764i
$771$		0			0
$772$	4.49621	−	4.49621i	0.161822	−	0.161822i
$773$	−21.3853			−0.769174			−0.384587	−	0.923089i	$-0.625656\pi$
$773$	−21.3853			−0.769174			−0.384587	+	0.923089i	$0.625656\pi$
$774$		0			0
$775$	−22.9906	+	13.2452i	−0.825845	+	0.475782i
$776$	−7.36342	−	7.36342i	−0.264331	−	0.264331i
$777$		0			0
$778$		−	12.7622i		−	0.457546i
$779$	11.8478	−	11.8478i	0.424492	−	0.424492i
$780$		0			0
$781$	74.4958			2.66567
$782$	−4.94663	−	12.7044i	−0.176891	−	0.454310i
$783$		0			0
$784$		−	6.14306i		−	0.219395i
$785$	−1.22160	+	9.24585i	−0.0436008	+	0.329999i
$786$		0			0
$787$	11.4358	+	11.4358i	0.407644	+	0.407644i	0.880916	−	0.473272i	$-0.156927\pi$
$787$	11.4358	+	11.4358i	0.407644	+	0.407644i	−0.473272	+	0.880916i	$0.656927\pi$
$788$	10.6447	−	10.6447i	0.379203	−	0.379203i
$789$		0			0
$790$	3.66412	+	4.77976i	0.130364	+	0.170056i
$791$		−	23.1834i		−	0.824306i
$792$		0			0
$793$	−14.7150	+	14.7150i	−0.522546	+	0.522546i
$794$	1.22024	−	1.22024i	0.0433047	−	0.0433047i
$795$		0			0
$796$	−3.53712	+	3.53712i	−0.125370	+	0.125370i
$797$	6.55049			0.232030			0.116015	−	0.993247i	$-0.462988\pi$
$797$	6.55049			0.232030			0.116015	+	0.993247i	$0.462988\pi$
$798$		0			0
$799$	−44.6134	−	19.6080i	−1.57831	−	0.693682i
$800$	−4.82843	−	1.29857i	−0.170711	−	0.0459115i
$801$		0			0
$802$	5.35462	+	5.35462i	0.189078	+	0.189078i
$803$		−	35.3488i		−	1.24743i
$804$		0			0
$805$	3.51107	−	26.5740i	0.123749	−	0.936612i
$806$	15.2305	+	15.2305i	0.536472	+	0.536472i
$807$		0			0
$808$	−5.10684			−0.179658
$809$	−27.0436	−	27.0436i	−0.950802	−	0.950802i	0.0480428	−	0.998845i	$-0.484702\pi$
$809$	−27.0436	−	27.0436i	−0.950802	−	0.950802i	−0.998845	+	0.0480428i	$0.984702\pi$
$810$		0			0
$811$	−11.2335	+	11.2335i	−0.394462	+	0.394462i	−0.876275	−	0.481812i	$-0.839979\pi$
$811$	−11.2335	+	11.2335i	−0.394462	+	0.394462i	0.481812	+	0.876275i	$0.339979\pi$
$812$			21.2003i			0.743985i
$813$		0			0
$814$		−	2.88327i		−	0.101059i
$815$	−26.5747	+	20.3719i	−0.930870	+	0.713596i
$816$		0			0
$817$		−	13.9496i		−	0.488036i
$818$	27.8663			0.974322
$819$		0			0
$820$	−8.05894	−	10.5127i	−0.281430	−	0.367120i
$821$	−29.1729	+	29.1729i	−1.01814	+	1.01814i	−0.0183084	+	0.999832i	$0.505828\pi$
$821$	−29.1729	+	29.1729i	−1.01814	+	1.01814i	−0.999832	+	0.0183084i	$0.994172\pi$
$822$		0			0
$823$	9.12186	−	9.12186i	0.317968	−	0.317968i	−0.530018	−	0.847986i	$-0.677815\pi$
$823$	9.12186	−	9.12186i	0.317968	−	0.317968i	0.847986	+	0.530018i	$0.177815\pi$
$824$		−	4.78811i		−	0.166802i
$825$		0			0
$826$	−4.23685	−	4.23685i	−0.147419	−	0.147419i
$827$	10.6147	−	10.6147i	0.369111	−	0.369111i	−0.498042	−	0.867153i	$-0.665947\pi$
$827$	10.6147	−	10.6147i	0.369111	−	0.369111i	0.867153	+	0.498042i	$0.165947\pi$
$828$		0			0
$829$	27.7117			0.962467			0.481234	−	0.876592i	$-0.340189\pi$
$829$	27.7117			0.962467			0.481234	+	0.876592i	$0.340189\pi$
$830$	−16.4610	−	2.17490i	−0.571371	−	0.0754919i
$831$		0			0
$832$			4.05894i			0.140718i
$833$	−23.1878	−	10.1912i	−0.803408	−	0.353105i
$834$		0			0
$835$	−23.1630	−	30.2156i	−0.801589	−	1.04565i
$836$	9.65685	−	9.65685i	0.333989	−	0.333989i
$837$		0			0
$838$	−12.1738	−	12.1738i	−0.420537	−	0.420537i
$839$	−9.34009	−	9.34009i	−0.322456	−	0.322456i	0.527253	−	0.849708i	$-0.323222\pi$
$839$	−9.34009	−	9.34009i	−0.322456	−	0.322456i	−0.849708	+	0.527253i	$0.823222\pi$
$840$		0			0
$841$		−	5.19698i		−	0.179206i
$842$	22.6520			0.780639
$843$		0			0
$844$	−2.21522	−	2.21522i	−0.0762509	−	0.0762509i
$845$	7.70340	+	1.01781i	0.265005	+	0.0350136i
$846$		0			0
$847$	31.5662	+	31.5662i	1.08463	+	1.08463i
$848$	11.2895			0.387682
$849$		0			0
$850$	−12.9119	+	16.0712i	−0.442874	+	0.551237i
$851$	−1.97453			−0.0676859
$852$		0			0
$853$	−12.9665	−	12.9665i	−0.443963	−	0.443963i	0.449378	−	0.893342i	$-0.351646\pi$
$853$	−12.9665	−	12.9665i	−0.443963	−	0.443963i	−0.893342	+	0.449378i	$0.851646\pi$
$854$	−18.5871			−0.636037
$855$		0			0
$856$	−8.77249	−	8.77249i	−0.299838	−	0.299838i
$857$	0.345388	−	0.345388i	0.0117982	−	0.0117982i	−0.701183	−	0.712981i	$-0.747344\pi$
$857$	0.345388	−	0.345388i	0.0117982	−	0.0117982i	0.712981	+	0.701183i	$0.247344\pi$
$858$		0			0
$859$		−	22.6274i		−	0.772038i	−0.922491	−	0.386019i	$-0.873850\pi$
$859$		−	22.6274i		−	0.772038i	0.922491	−	0.386019i	$-0.126150\pi$
$860$	−10.9331	−	1.44453i	−0.372817	−	0.0492581i
$861$		0			0
$862$	−13.7220	−	13.7220i	−0.467374	−	0.467374i
$863$		−	5.61228i		−	0.191044i	−0.995427	−	0.0955221i	$-0.969548\pi$
$863$		−	5.61228i		−	0.191044i	0.995427	−	0.0955221i	$-0.0304521\pi$
$864$		0			0
$865$	30.9178	+	40.3316i	1.05124	+	1.37131i
$866$	32.8226			1.11536
$867$		0			0
$868$			19.2382i			0.652988i
$869$			13.0049i			0.441160i
$870$		0			0
$871$	−26.7435			−0.906170
$872$	−12.1666	−	12.1666i	−0.412011	−	0.412011i
$873$		0			0
$874$	−6.61321	−	6.61321i	−0.223695	−	0.223695i
$875$	−37.4687	+	15.4590i	−1.26667	+	0.522610i
$876$		0			0
$877$	31.9781	−	31.9781i	1.07983	−	1.07983i	0.0833008	−	0.996524i	$-0.473454\pi$
$877$	31.9781	−	31.9781i	1.07983	−	1.07983i	0.996524	−	0.0833008i	$-0.0265462\pi$
$878$	−5.00301	+	5.00301i	−0.168843	+	0.168843i
$879$		0			0
$880$	−6.56864	−	8.56864i	−0.221429	−	0.288849i
$881$	−20.5650	+	20.5650i	−0.692852	+	0.692852i	−0.962858	−	0.270007i	$-0.912974\pi$
$881$	−20.5650	+	20.5650i	−0.692852	+	0.692852i	0.270007	+	0.962858i	$0.412974\pi$
$882$		0			0
$883$			54.8649i			1.84635i	0.384380	+	0.923175i	$0.374415\pi$
$883$			54.8649i			1.84635i	−0.384380	+	0.923175i	$0.625585\pi$
$884$	15.3210	+	6.73371i	0.515300	+	0.226479i
$885$		0			0
$886$		−	9.49648i		−	0.319041i
$887$	0.510625	+	0.510625i	0.0171451	+	0.0171451i	0.715627	−	0.698482i	$-0.246141\pi$
$887$	0.510625	+	0.510625i	0.0171451	+	0.0171451i	−0.698482	+	0.715627i	$0.746141\pi$
$888$		0			0
$889$	−51.6607	+	51.6607i	−1.73264	+	1.73264i
$890$	22.4293	+	2.96346i	0.751833	+	0.0993354i
$891$		0			0
$892$	−14.6923			−0.491935
$893$	−33.4301			−1.11869
$894$		0			0
$895$	4.17546	−	31.6026i	0.139570	−	1.05636i
$896$	−2.56350	+	2.56350i	−0.0856405	+	0.0856405i
$897$		0			0
$898$	−13.9963	−	13.9963i	−0.467064	−	0.467064i
$899$		−	31.0321i		−	1.03498i
$900$		0			0
$901$	18.7290	−	42.6134i	0.623954	−	1.41966i
$902$		−	28.6032i		−	0.952381i
$903$		0			0
$904$	−4.52182	+	4.52182i	−0.150394	+	0.150394i
$905$	10.0082	+	13.0555i	0.332683	+	0.433978i
$906$		0			0
$907$	−15.9554	+	15.9554i	−0.529791	+	0.529791i	−0.920510	−	0.390719i	$-0.872226\pi$
$907$	−15.9554	+	15.9554i	−0.529791	+	0.529791i	0.390719	+	0.920510i	$0.372226\pi$
$908$	6.55728	−	6.55728i	0.217611	−	0.217611i
$909$		0			0
$910$	20.0185	+	26.1136i	0.663606	+	0.865658i
$911$	19.7608	+	19.7608i	0.654705	+	0.654705i	0.954122	−	0.299418i	$-0.0967924\pi$
$911$	19.7608	+	19.7608i	0.654705	+	0.654705i	−0.299418	+	0.954122i	$0.596792\pi$
$912$		0			0
$913$	−25.3525	−	25.3525i	−0.839045	−	0.839045i
$914$	13.8823			0.459187
$915$		0			0
$916$			11.2346i			0.371202i
$917$		−	35.0466i		−	1.15734i
$918$		0			0
$919$	−38.4512			−1.26839			−0.634194	−	0.773174i	$-0.718668\pi$
$919$	−38.4512			−1.26839			−0.634194	+	0.773174i	$0.718668\pi$
$920$	−5.86798	+	4.49834i	−0.193461	+	0.148306i
$921$		0			0
$922$			15.6082i			0.514028i
$923$	44.2817	+	44.2817i	1.45755	+	1.45755i
$924$		0			0
$925$	1.49047	+	2.58710i	0.0490062	+	0.0850633i
$926$		−	5.08396i		−	0.167069i
$927$		0			0
$928$	4.13503	−	4.13503i	0.135739	−	0.135739i
$929$	8.35346	+	8.35346i	0.274068	+	0.274068i	0.830736	−	0.556667i	$-0.187920\pi$
$929$	8.35346	+	8.35346i	0.274068	+	0.274068i	−0.556667	+	0.830736i	$0.687920\pi$
$930$		0			0
$931$	−17.3752			−0.569450
$932$	−7.10652	−	7.10652i	−0.232782	−	0.232782i
$933$		0			0
$934$	22.0615			0.721874
$935$	−43.2406	+	10.5789i	−1.41412	+	0.345967i
$936$		0			0
$937$	−18.8139			−0.614623			−0.307312	−	0.951609i	$-0.599429\pi$
$937$	−18.8139			−0.614623			−0.307312	+	0.951609i	$0.599429\pi$
$938$	−16.8904	−	16.8904i	−0.551490	−	0.551490i
$939$		0			0
$940$	−3.46180	+	26.2011i	−0.112911	+	0.854585i
$941$	−8.74245	−	8.74245i	−0.284996	−	0.284996i	0.550102	−	0.835098i	$-0.314589\pi$
$941$	−8.74245	−	8.74245i	−0.284996	−	0.284996i	−0.835098	+	0.550102i	$0.814589\pi$
$942$		0			0
$943$	−19.5880			−0.637874
$944$			1.65276i			0.0537928i
$945$		0			0
$946$	−16.8387	−	16.8387i	−0.547473	−	0.547473i
$947$	−4.32753	−	4.32753i	−0.140626	−	0.140626i	0.633289	−	0.773915i	$-0.281704\pi$
$947$	−4.32753	−	4.32753i	−0.140626	−	0.140626i	−0.773915	+	0.633289i	$0.781704\pi$
$948$		0			0
$949$	21.0120	−	21.0120i	0.682077	−	0.682077i
$950$	−3.67292	+	13.6569i	−0.119165	+	0.443087i
$951$		0			0
$952$	5.42344	+	13.9290i	0.175775	+	0.451443i
$953$		−	39.7689i		−	1.28824i	−0.764923	−	0.644121i	$-0.777223\pi$
$953$		−	39.7689i		−	1.28824i	0.764923	−	0.644121i	$-0.222777\pi$
$954$		0			0
$955$	−9.70444	−	1.28219i	−0.314028	−	0.0414907i
$956$	−21.5638			−0.697422
$957$		0			0
$958$	15.0721	−	15.0721i	0.486958	−	0.486958i
$959$	31.1373	+	31.1373i	1.00548	+	1.00548i
$960$		0			0
$961$			2.83994i			0.0916110i
$962$	1.71387	−	1.71387i	0.0552574	−	0.0552574i
$963$		0			0
$964$	8.71170	−	8.71170i	0.280585	−	0.280585i
$965$	−11.2841	+	8.65030i	−0.363249	+	0.278463i
$966$		0			0
$967$	0.532576			0.0171265			0.00856325	−	0.999963i	$-0.497274\pi$
$967$	0.532576			0.0171265			0.00856325	+	0.999963i	$0.497274\pi$
$968$		−	12.3137i		−	0.395778i
$969$		0			0
$970$	14.1666	+	18.4799i	0.454861	+	0.593355i
$971$		−	39.1947i		−	1.25782i	−0.777479	−	0.628909i	$-0.783502\pi$
$971$		−	39.1947i		−	1.25782i	0.777479	−	0.628909i	$-0.216498\pi$
$972$		0			0
$973$		−	80.9650i		−	2.59562i
$974$	26.6368	−	26.6368i	0.853498	−	0.853498i
$975$		0			0
$976$	3.62534	+	3.62534i	0.116044	+	0.116044i
$977$	3.19429			0.102194			0.0510972	−	0.998694i	$-0.483728\pi$
$977$	3.19429			0.102194			0.0510972	+	0.998694i	$0.483728\pi$
$978$		0			0
$979$	34.5446	+	34.5446i	1.10405	+	1.10405i
$980$	−1.79926	+	13.6180i	−0.0574753	+	0.435010i
$981$		0			0
$982$		−	2.10930i		−	0.0673106i
$983$	−23.3072	−	23.3072i	−0.743383	−	0.743383i	0.229845	−	0.973227i	$-0.426178\pi$
$983$	−23.3072	−	23.3072i	−0.743383	−	0.743383i	−0.973227	+	0.229845i	$0.926178\pi$
$984$		0			0
$985$	−26.7150	+	20.4795i	−0.851212	+	0.652531i
$986$	−8.74824	−	22.4681i	−0.278601	−	0.715531i
$987$		0			0
$988$	11.4804			0.365241
$989$	−11.5315	+	11.5315i	−0.366680	+	0.366680i
$990$		0			0
$991$	−21.7305	+	21.7305i	−0.690292	+	0.690292i	−0.962296	−	0.272004i	$-0.912313\pi$
$991$	−21.7305	+	21.7305i	−0.690292	+	0.690292i	0.272004	+	0.962296i	$0.412313\pi$
$992$	3.75234	−	3.75234i	0.119137	−	0.119137i
$993$		0			0
$994$			55.9338i			1.77411i
$995$	8.87709	−	6.80510i	0.281423	−	0.215736i
$996$		0			0
$997$	−11.4029	+	11.4029i	−0.361132	+	0.361132i	−0.864230	−	0.503098i	$-0.832194\pi$
$997$	−11.4029	+	11.4029i	−0.361132	+	0.361132i	0.503098	+	0.864230i	$0.332194\pi$
$998$	20.0045	+	20.0045i	0.633231	+	0.633231i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1530.2.n.q.1279.1		8
3.2	odd	2		510.2.m.b.259.2	yes	8
5.4	even	2		1530.2.n.r.1279.2		8
15.14	odd	2		510.2.m.a.259.3	✓	8
17.13	even	4		1530.2.n.r.829.1		8
51.47	odd	4		510.2.m.a.319.4	yes	8
85.64	even	4	inner	1530.2.n.q.829.1		8
255.149	odd	4		510.2.m.b.319.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.m.a.259.3	✓	8	15.14	odd	2
510.2.m.a.319.4	yes	8	51.47	odd	4
510.2.m.b.259.2	yes	8	3.2	odd	2
510.2.m.b.319.2	yes	8	255.149	odd	4
1530.2.n.q.829.1		8	85.64	even	4	inner
1530.2.n.q.1279.1		8	1.1	even	1	trivial
1530.2.n.r.829.1		8	17.13	even	4
1530.2.n.r.1279.2		8	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1530.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-2.21680 - 0.292893i) q^{5} +(2.56350 - 2.56350i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-2.21680 - 0.292893i) q^{5} +(2.56350 - 2.56350i) q^{7} -1.00000 q^{8} +(2.21680 + 0.292893i) q^{10} +(3.41421 + 3.41421i) q^{11} +4.05894i q^{13} +(-2.56350 + 2.56350i) q^{14} +1.00000 q^{16} +(1.65898 - 3.77462i) q^{17} -2.82843i q^{19} +(-2.21680 - 0.292893i) q^{20} +(-3.41421 - 3.41421i) q^{22} +(-2.33812 + 2.33812i) q^{23} +(4.82843 + 1.29857i) q^{25} -4.05894i q^{26} +(2.56350 - 2.56350i) q^{28} +(-4.13503 + 4.13503i) q^{29} +(-3.75234 + 3.75234i) q^{31} -1.00000 q^{32} +(-1.65898 + 3.77462i) q^{34} +(-6.43361 + 4.93194i) q^{35} +(0.422246 + 0.422246i) q^{37} +2.82843i q^{38} +(2.21680 + 0.292893i) q^{40} +(4.18884 + 4.18884i) q^{41} +4.93194 q^{43} +(3.41421 + 3.41421i) q^{44} +(2.33812 - 2.33812i) q^{46} -11.8193i q^{47} -6.14306i q^{49} +(-4.82843 - 1.29857i) q^{50} +4.05894i q^{52} +11.2895 q^{53} +(-6.56864 - 8.56864i) q^{55} +(-2.56350 + 2.56350i) q^{56} +(4.13503 - 4.13503i) q^{58} +1.65276i q^{59} +(3.62534 + 3.62534i) q^{61} +(3.75234 - 3.75234i) q^{62} +1.00000 q^{64} +(1.18884 - 8.99787i) q^{65} +6.58880i q^{67} +(1.65898 - 3.77462i) q^{68} +(6.43361 - 4.93194i) q^{70} +(10.9097 - 10.9097i) q^{71} +(-5.17671 - 5.17671i) q^{73} +(-0.422246 - 0.422246i) q^{74} -2.82843i q^{76} +17.5047 q^{77} +(1.90452 + 1.90452i) q^{79} +(-2.21680 - 0.292893i) q^{80} +(-4.18884 - 4.18884i) q^{82} -7.42557 q^{83} +(-4.78320 + 7.88169i) q^{85} -4.93194 q^{86} +(-3.41421 - 3.41421i) q^{88} +10.1179 q^{89} +(10.4051 + 10.4051i) q^{91} +(-2.33812 + 2.33812i) q^{92} +11.8193i q^{94} +(-0.828427 + 6.27006i) q^{95} +(7.36342 + 7.36342i) q^{97} +6.14306i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} + 4 q^{7} - 8 q^{8}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^4 + 4 * q^7 - 8 * q^8	\( 8 q - 8 q^{2} + 8 q^{4} + 4 q^{7} - 8 q^{8} + 16 q^{11} - 4 q^{14} + 8 q^{16} - 4 q^{17} - 16 q^{22} + 16 q^{23} + 16 q^{25} + 4 q^{28} - 8 q^{29} + 16 q^{31} - 8 q^{32} + 4 q^{34} - 16 q^{35} + 4 q^{41} + 24 q^{43} + 16 q^{44} - 16 q^{46} - 16 q^{50} + 16 q^{53} + 8 q^{55} - 4 q^{56} + 8 q^{58} + 16 q^{61} - 16 q^{62} + 8 q^{64} - 20 q^{65} - 4 q^{68} + 16 q^{70} + 44 q^{71} - 20 q^{73} + 48 q^{77} + 16 q^{79} - 4 q^{82} - 16 q^{83} - 56 q^{85} - 24 q^{86} - 16 q^{88} - 16 q^{89} + 8 q^{91} + 16 q^{92} + 16 q^{95} - 20 q^{97}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 + 4 * q^7 - 8 * q^8 + 16 * q^11 - 4 * q^14 + 8 * q^16 - 4 * q^17 - 16 * q^22 + 16 * q^23 + 16 * q^25 + 4 * q^28 - 8 * q^29 + 16 * q^31 - 8 * q^32 + 4 * q^34 - 16 * q^35 + 4 * q^41 + 24 * q^43 + 16 * q^44 - 16 * q^46 - 16 * q^50 + 16 * q^53 + 8 * q^55 - 4 * q^56 + 8 * q^58 + 16 * q^61 - 16 * q^62 + 8 * q^64 - 20 * q^65 - 4 * q^68 + 16 * q^70 + 44 * q^71 - 20 * q^73 + 48 * q^77 + 16 * q^79 - 4 * q^82 - 16 * q^83 - 56 * q^85 - 24 * q^86 - 16 * q^88 - 16 * q^89 + 8 * q^91 + 16 * q^92 + 16 * q^95 - 20 * q^97

Introduction

L-functions

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