LMFDB - Embedded newform 735.2.d.e.589.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(589,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("735.589");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.d (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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.2058981376.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 18x^{4} - 34x^{3} + 32x^{2} - 8x + 1 $ x^8 - 2x^7 + 2x^6 + 18x^4 - 34x^3 + 32x^2 - 8x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			589.7
Root			$0.148421 - 0.148421i$ of defining polynomial
Character	$\chi$	$=$	735.589
Dual form			735.2.d.e.589.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.78165i q^{2} +1.00000i q^{3} -1.17429 q^{4} +(-2.22038 + 0.264435i) q^{5} -1.78165 q^{6} +1.47113i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.78165i q^{2} +1.00000i q^{3} -1.17429 q^{4} +(-2.22038 + 0.264435i) q^{5} -1.78165 q^{6} +1.47113i q^{8} -1.00000 q^{9} +(-0.471131 - 3.95594i) q^{10} -2.07850 q^{11} -1.17429i q^{12} -3.13023i q^{13} +(-0.264435 - 2.22038i) q^{15} -4.96962 q^{16} -2.13023i q^{17} -1.78165i q^{18} -7.73760 q^{19} +(2.60736 - 0.310523i) q^{20} -3.70316i q^{22} +5.53655i q^{23} -1.47113 q^{24} +(4.86015 - 1.17429i) q^{25} +5.57699 q^{26} -1.00000i q^{27} +4.01368 q^{29} +(3.95594 - 0.471131i) q^{30} -2.91188 q^{31} -5.91188i q^{32} -2.07850i q^{33} +3.79533 q^{34} +1.17429 q^{36} -3.51519i q^{37} -13.7857i q^{38} +3.13023 q^{39} +(-0.389018 - 3.26647i) q^{40} -7.99038 q^{41} -4.99038i q^{43} +2.44075 q^{44} +(2.22038 - 0.264435i) q^{45} -9.86421 q^{46} +2.44075i q^{47} -4.96962i q^{48} +(2.09218 + 8.65910i) q^{50} +2.13023 q^{51} +3.67580i q^{52} +9.91188i q^{53} +1.78165 q^{54} +(4.61504 - 0.549626i) q^{55} -7.73760i q^{57} +7.15099i q^{58} +2.95594 q^{59} +(0.310523 + 2.60736i) q^{60} +10.8946 q^{61} -5.18797i q^{62} +0.593684 q^{64} +(0.827742 + 6.95029i) q^{65} +3.70316 q^{66} -3.83939i q^{67} +2.50151i q^{68} -5.53655 q^{69} -15.0248 q^{71} -1.47113i q^{72} +8.55369i q^{73} +6.26285 q^{74} +(1.17429 + 4.86015i) q^{75} +9.08617 q^{76} +5.57699i q^{78} -8.11354 q^{79} +(11.0344 - 1.31414i) q^{80} +1.00000 q^{81} -14.2361i q^{82} +8.75128i q^{83} +(0.563307 + 4.72992i) q^{85} +8.89113 q^{86} +4.01368i q^{87} -3.05774i q^{88} +0.618661 q^{89} +(0.471131 + 3.95594i) q^{90} -6.50151i q^{92} -2.91188i q^{93} -4.34858 q^{94} +(17.1804 - 2.04609i) q^{95} +5.91188 q^{96} -0.296842i q^{97} +2.07850 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 2 q^{5} + 4 q^{6} - 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 + 2 * q^5 + 4 * q^6 - 8 * q^9	$ 8 q - 8 q^{4} + 2 q^{5} + 4 q^{6} - 8 q^{9} - 4 q^{10} - 2 q^{15} - 24 q^{19} + 4 q^{20} - 12 q^{24} + 4 q^{25} - 12 q^{26} + 12 q^{29} + 12 q^{30} + 16 q^{31} - 8 q^{34} + 8 q^{36} + 4 q^{39} + 32 q^{40} - 8 q^{41} - 20 q^{44} - 2 q^{45} + 32 q^{46} - 20 q^{50} - 4 q^{51} - 4 q^{54} - 4 q^{55} + 4 q^{59} - 16 q^{60} + 16 q^{61} + 8 q^{64} - 30 q^{65} + 28 q^{66} - 20 q^{69} - 28 q^{71} - 40 q^{74} + 8 q^{75} + 32 q^{76} + 16 q^{79} + 52 q^{80} + 8 q^{81} - 32 q^{85} + 48 q^{86} + 16 q^{89} + 4 q^{90} - 32 q^{94} + 22 q^{95} + 8 q^{96}+O(q^{100}) $ 8 * q - 8 * q^4 + 2 * q^5 + 4 * q^6 - 8 * q^9 - 4 * q^10 - 2 * q^15 - 24 * q^19 + 4 * q^20 - 12 * q^24 + 4 * q^25 - 12 * q^26 + 12 * q^29 + 12 * q^30 + 16 * q^31 - 8 * q^34 + 8 * q^36 + 4 * q^39 + 32 * q^40 - 8 * q^41 - 20 * q^44 - 2 * q^45 + 32 * q^46 - 20 * q^50 - 4 * q^51 - 4 * q^54 - 4 * q^55 + 4 * q^59 - 16 * q^60 + 16 * q^61 + 8 * q^64 - 30 * q^65 + 28 * q^66 - 20 * q^69 - 28 * q^71 - 40 * q^74 + 8 * q^75 + 32 * q^76 + 16 * q^79 + 52 * q^80 + 8 * q^81 - 32 * q^85 + 48 * q^86 + 16 * q^89 + 4 * q^90 - 32 * q^94 + 22 * q^95 + 8 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$			1.78165i			1.25982i	0.776668	+	0.629910i	$0.216908\pi$
$2$			1.78165i			1.25982i	−0.776668	+	0.629910i	$0.783092\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.17429			−0.587145
$5$	−2.22038	+	0.264435i	−0.992983	+	0.118259i
$5$	−2.22038	+	0.264435i	−0.992983	+	0.118259i
$6$	−1.78165			−0.727357
$7$		0			0
$7$		0			0
$8$			1.47113i			0.520123i
$9$	−1.00000			−0.333333
$10$	−0.471131	−	3.95594i	−0.148985	−	1.25098i
$11$	−2.07850			−0.626690			−0.313345	−	0.949639i	$-0.601450\pi$
$11$	−2.07850			−0.626690			−0.313345	+	0.949639i	$0.601450\pi$
$12$		−	1.17429i		−	0.338988i
$13$		−	3.13023i		−	0.868170i	−0.900872	−	0.434085i	$-0.857072\pi$
$13$		−	3.13023i		−	0.868170i	0.900872	−	0.434085i	$-0.142928\pi$
$14$		0			0
$15$	−0.264435	−	2.22038i	−0.0682767	−	0.573299i
$16$	−4.96962			−1.24241
$17$		−	2.13023i		−	0.516657i	−0.966057	−	0.258329i	$-0.916828\pi$
$17$		−	2.13023i		−	0.516657i	0.966057	−	0.258329i	$-0.0831717\pi$
$18$		−	1.78165i		−	0.419940i
$19$	−7.73760			−1.77513			−0.887563	−	0.460686i	$-0.847603\pi$
$19$	−7.73760			−1.77513			−0.887563	+	0.460686i	$0.847603\pi$
$20$	2.60736	−	0.310523i	0.583024	−	0.0694350i
$21$		0			0
$22$		−	3.70316i		−	0.789516i
$23$			5.53655i			1.15445i	0.816585	+	0.577225i	$0.195864\pi$
$23$			5.53655i			1.15445i	−0.816585	+	0.577225i	$0.804136\pi$
$24$	−1.47113			−0.300293
$25$	4.86015	−	1.17429i	0.972030	−	0.234858i
$26$	5.57699			1.09374
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	4.01368			0.745322			0.372661	−	0.927968i	$-0.378445\pi$
$29$	4.01368			0.745322			0.372661	+	0.927968i	$0.378445\pi$
$30$	3.95594	−	0.471131i	0.722253	−	0.0860163i
$31$	−2.91188			−0.522990			−0.261495	−	0.965205i	$-0.584215\pi$
$31$	−2.91188			−0.522990			−0.261495	+	0.965205i	$0.584215\pi$
$32$		−	5.91188i		−	1.04508i
$33$		−	2.07850i		−	0.361820i
$34$	3.79533			0.650894
$35$		0			0
$36$	1.17429			0.195715
$37$		−	3.51519i		−	0.577893i	−0.957345	−	0.288947i	$-0.906695\pi$
$37$		−	3.51519i		−	0.577893i	0.957345	−	0.288947i	$-0.0933050\pi$
$38$		−	13.7857i		−	2.23634i
$39$	3.13023			0.501238
$40$	−0.389018	−	3.26647i	−0.0615091	−	0.516473i
$41$	−7.99038			−1.24789			−0.623944	−	0.781469i	$-0.714471\pi$
$41$	−7.99038			−1.24789			−0.623944	+	0.781469i	$0.714471\pi$
$42$		0			0
$43$		−	4.99038i		−	0.761026i	−0.924776	−	0.380513i	$-0.875747\pi$
$43$		−	4.99038i		−	0.761026i	0.924776	−	0.380513i	$-0.124253\pi$
$44$	2.44075			0.367958
$45$	2.22038	−	0.264435i	0.330994	−	0.0394196i
$46$	−9.86421			−1.45440
$47$			2.44075i			0.356021i	0.984029	+	0.178010i	$0.0569660\pi$
$47$			2.44075i			0.356021i	−0.984029	+	0.178010i	$0.943034\pi$
$48$		−	4.96962i		−	0.717303i
$49$		0			0
$50$	2.09218	+	8.65910i	0.295878	+	1.22458i
$51$	2.13023			0.298292
$52$			3.67580i			0.509741i
$53$			9.91188i			1.36150i	0.732515	+	0.680751i	$0.238346\pi$
$53$			9.91188i			1.36150i	−0.732515	+	0.680751i	$0.761654\pi$
$54$	1.78165			0.242452
$55$	4.61504	−	0.549626i	0.622292	−	0.0741116i
$56$		0			0
$57$		−	7.73760i		−	1.02487i
$58$			7.15099i			0.938971i
$59$	2.95594			0.384831			0.192415	−	0.981314i	$-0.438368\pi$
$59$	2.95594			0.384831			0.192415	+	0.981314i	$0.438368\pi$
$60$	0.310523	+	2.60736i	0.0400883	+	0.336609i
$61$	10.8946			1.39491			0.697454	−	0.716629i	$-0.254316\pi$
$61$	10.8946			1.39491			0.697454	+	0.716629i	$0.254316\pi$
$62$		−	5.18797i		−	0.658873i
$63$		0			0
$64$	0.593684			0.0742104
$65$	0.827742	+	6.95029i	0.102669	+	0.862078i
$66$	3.70316			0.455827
$67$		−	3.83939i		−	0.469056i	−0.972109	−	0.234528i	$-0.924645\pi$
$67$		−	3.83939i		−	0.469056i	0.972109	−	0.234528i	$-0.0753545\pi$
$68$			2.50151i			0.303352i
$69$	−5.53655			−0.666522
$70$		0			0
$71$	−15.0248			−1.78312			−0.891559	−	0.452905i	$-0.850388\pi$
$71$	−15.0248			−1.78312			−0.891559	+	0.452905i	$0.850388\pi$
$72$		−	1.47113i		−	0.173374i
$73$			8.55369i			1.00113i	0.865698	+	0.500567i	$0.166875\pi$
$73$			8.55369i			1.00113i	−0.865698	+	0.500567i	$0.833125\pi$
$74$	6.26285			0.728041
$75$	1.17429	+	4.86015i	0.135595	+	0.561202i
$76$	9.08617			1.04226
$77$		0			0
$78$			5.57699i			0.631470i
$79$	−8.11354			−0.912844			−0.456422	−	0.889763i	$-0.650869\pi$
$79$	−8.11354			−0.912844			−0.456422	+	0.889763i	$0.650869\pi$
$80$	11.0344	−	1.31414i	1.23369	−	0.146925i
$81$	1.00000			0.111111
$82$		−	14.2361i		−	1.57211i
$83$			8.75128i			0.960577i	0.877110	+	0.480289i	$0.159468\pi$
$83$			8.75128i			0.960577i	−0.877110	+	0.480289i	$0.840532\pi$
$84$		0			0
$85$	0.563307	+	4.72992i	0.0610992	+	0.513032i
$86$	8.89113			0.958755
$87$			4.01368i			0.430312i
$88$		−	3.05774i		−	0.325956i
$89$	0.618661			0.0655779			0.0327890	−	0.999462i	$-0.489561\pi$
$89$	0.618661			0.0655779			0.0327890	+	0.999462i	$0.489561\pi$
$90$	0.471131	+	3.95594i	0.0496615	+	0.416993i
$91$		0			0
$92$		−	6.50151i		−	0.677829i
$93$		−	2.91188i		−	0.301948i
$94$	−4.34858			−0.448522
$95$	17.1804	−	2.04609i	1.76267	−	0.209924i
$96$	5.91188			0.603379
$97$		−	0.296842i		−	0.0301397i	−0.999886	−	0.0150699i	$-0.995203\pi$
$97$		−	0.296842i		−	0.0301397i	0.999886	−	0.0150699i	$-0.00479707\pi$
$98$		0			0
$99$	2.07850			0.208897
$100$	−5.70722	+	1.37895i	−0.570722	+	0.137895i
$101$	−8.25879			−0.821780			−0.410890	−	0.911685i	$-0.634782\pi$
$101$	−8.25879			−0.821780			−0.410890	+	0.911685i	$0.634782\pi$
$102$			3.79533i			0.375794i
$103$			17.0866i			1.68359i	0.539794	+	0.841797i	$0.318502\pi$
$103$			17.0866i			1.68359i	−0.539794	+	0.841797i	$0.681498\pi$
$104$	4.60498			0.451555
$105$		0			0
$106$	−17.6595			−1.71525
$107$		−	6.31052i		−	0.610061i	−0.952343	−	0.305031i	$-0.901333\pi$
$107$		−	6.31052i		−	0.610061i	0.952343	−	0.305031i	$-0.0986667\pi$
$108$			1.17429i			0.112996i
$109$	−2.44676			−0.234357			−0.117178	−	0.993111i	$-0.537385\pi$
$109$	−2.44676			−0.234357			−0.117178	+	0.993111i	$0.537385\pi$
$110$	0.979243	+	8.22241i	0.0933672	+	0.783976i
$111$	3.51519			0.333647
$112$		0			0
$113$			10.1570i			0.955489i	0.878499	+	0.477745i	$0.158546\pi$
$113$			10.1570i			0.955489i	−0.878499	+	0.477745i	$0.841454\pi$
$114$	13.7857			1.29115
$115$	−1.46405	−	12.2932i	−0.136524	−	1.14635i
$116$	−4.71322			−0.437612
$117$			3.13023i			0.289390i
$118$			5.26647i			0.484817i
$119$		0			0
$120$	3.26647	−	0.389018i	0.298186	−	0.0355123i
$121$	−6.67986			−0.607260
$122$			19.4104i			1.75733i
$123$		−	7.99038i		−	0.720468i
$124$	3.41939			0.307071
$125$	−10.4808	+	3.89256i	−0.937435	+	0.348161i
$126$		0			0
$127$		−	8.86977i		−	0.787065i	−0.919311	−	0.393532i	$-0.871253\pi$
$127$		−	8.86977i		−	0.787065i	0.919311	−	0.393532i	$-0.128747\pi$
$128$		−	10.7660i		−	0.951592i
$129$	4.99038			0.439378
$130$	−12.3830	+	1.47475i	−1.08606	+	0.129344i
$131$	−5.34150			−0.466689			−0.233345	−	0.972394i	$-0.574967\pi$
$131$	−5.34150			−0.466689			−0.233345	+	0.972394i	$0.574967\pi$
$132$			2.44075i			0.212440i
$133$		0			0
$134$	6.84047			0.590926
$135$	0.264435	+	2.22038i	0.0227589	+	0.191100i
$136$	3.13385			0.268725
$137$			13.1039i			1.11954i	0.828647	+	0.559772i	$0.189111\pi$
$137$			13.1039i			1.11954i	−0.828647	+	0.559772i	$0.810889\pi$
$138$		−	9.86421i		−	0.839697i
$139$	0.243164			0.0206249			0.0103125	−	0.999947i	$-0.496717\pi$
$139$	0.243164			0.0206249			0.0103125	+	0.999947i	$0.496717\pi$
$140$		0			0
$141$	−2.44075			−0.205549
$142$		−	26.7690i		−	2.24641i
$143$			6.50617i			0.544073i
$144$	4.96962			0.414135
$145$	−8.91188	+	1.06136i	−0.740092	+	0.0881408i
$146$	−15.2397			−1.26125
$147$		0			0
$148$			4.12785i			0.339307i
$149$	−2.33728			−0.191478			−0.0957388	−	0.995406i	$-0.530521\pi$
$149$	−2.33728			−0.191478			−0.0957388	+	0.995406i	$0.530521\pi$
$150$	−8.65910	+	2.09218i	−0.707013	+	0.170825i
$151$	−11.1135			−0.904407			−0.452203	−	0.891915i	$-0.649362\pi$
$151$	−11.1135			−0.904407			−0.452203	+	0.891915i	$0.649362\pi$
$152$		−	11.3830i		−	0.923284i
$153$			2.13023i			0.172219i
$154$		0			0
$155$	6.46548	−	0.770003i	0.519320	−	0.0618481i
$156$	−3.67580			−0.294299
$157$			11.3182i			0.903291i	0.892198	+	0.451645i	$0.149163\pi$
$157$			11.3182i			0.903291i	−0.892198	+	0.451645i	$0.850837\pi$
$158$		−	14.4555i		−	1.15002i
$159$	−9.91188			−0.786064
$160$	1.56331	+	13.1266i	0.123590	+	1.03775i
$161$		0			0
$162$			1.78165i			0.139980i
$163$		−	2.10347i		−	0.164757i	−0.996601	−	0.0823783i	$-0.973748\pi$
$163$		−	2.10347i		−	0.164757i	0.996601	−	0.0823783i	$-0.0262516\pi$
$164$	9.38302			0.732690
$165$	0.549626	+	4.61504i	0.0427883	+	0.359281i
$166$	−15.5917			−1.21015
$167$		−	3.58600i		−	0.277493i	−0.990328	−	0.138747i	$-0.955693\pi$
$167$		−	3.58600i		−	0.277493i	0.990328	−	0.138747i	$-0.0443074\pi$
$168$		0			0
$169$	3.20165			0.246281
$170$	−8.42707	+	1.00362i	−0.646327	+	0.0769740i
$171$	7.73760			0.591709
$172$			5.86015i			0.446832i
$173$		−	15.5400i		−	1.18148i	−0.806860	−	0.590742i	$-0.798835\pi$
$173$		−	15.5400i		−	1.18148i	0.806860	−	0.590742i	$-0.201165\pi$
$174$	−7.15099			−0.542115
$175$		0			0
$176$	10.3293			0.778603
$177$			2.95594i			0.222182i
$178$			1.10224i			0.0826163i
$179$	−15.7357			−1.17614			−0.588069	−	0.808811i	$-0.700112\pi$
$179$	−15.7357			−1.17614			−0.588069	+	0.808811i	$0.700112\pi$
$180$	−2.60736	+	0.310523i	−0.194341	+	0.0231450i
$181$	4.98692			0.370675			0.185337	−	0.982675i	$-0.440662\pi$
$181$	4.98692			0.370675			0.185337	+	0.982675i	$0.440662\pi$
$182$		0			0
$183$			10.8946i			0.805351i
$184$	−8.14499			−0.600456
$185$	0.929537	+	7.80504i	0.0683409	+	0.573838i
$186$	5.18797			0.380400
$187$			4.42768i			0.323784i
$188$		−	2.86615i		−	0.209036i
$189$		0			0
$190$	3.64542	+	30.6095i	0.264467	+	2.22065i
$191$	11.8084			0.854427			0.427213	−	0.904151i	$-0.359495\pi$
$191$	11.8084			0.854427			0.427213	+	0.904151i	$0.359495\pi$
$192$			0.593684i			0.0428454i
$193$			24.7380i			1.78068i	0.455293	+	0.890342i	$0.349534\pi$
$193$			24.7380i			1.78068i	−0.455293	+	0.890342i	$0.650466\pi$
$194$	0.528869			0.0379706
$195$	−6.95029	+	0.827742i	−0.497721	+	0.0592758i
$196$		0			0
$197$		−	19.5526i		−	1.39307i	−0.717525	−	0.696533i	$-0.754725\pi$
$197$		−	19.5526i		−	1.39307i	0.717525	−	0.696533i	$-0.245275\pi$
$198$			3.70316i			0.263172i
$199$	−22.2401			−1.57656			−0.788281	−	0.615315i	$-0.789029\pi$
$199$	−22.2401			−1.57656			−0.788281	+	0.615315i	$0.789029\pi$
$200$	1.72753	+	7.14991i	0.122155	+	0.505575i
$201$	3.83939			0.270810
$202$		−	14.7143i		−	1.03529i
$203$		0			0
$204$	−2.50151			−0.175141
$205$	17.7417	−	2.11293i	1.23913	−	0.147574i
$206$	−30.4424			−2.12102
$207$		−	5.53655i		−	0.384817i
$208$			15.5561i			1.07862i
$209$	16.0826			1.11245
$210$		0			0
$211$	23.6191			1.62601			0.813003	−	0.582259i	$-0.197831\pi$
$211$	23.6191			1.62601			0.813003	+	0.582259i	$0.197831\pi$
$212$		−	11.6394i		−	0.799398i
$213$		−	15.0248i		−	1.02948i
$214$	11.2432			0.768567
$215$	1.31963	+	11.0805i	0.0899980	+	0.755686i
$216$	1.47113			0.100098
$217$		0			0
$218$		−	4.35927i		−	0.295247i
$219$	−8.55369			−0.578005
$220$	−5.41939	+	0.645420i	−0.365376	+	0.0435142i
$221$	−6.66812			−0.448546
$222$			6.26285i			0.420335i
$223$			25.1420i			1.68363i	0.539765	+	0.841815i	$0.318513\pi$
$223$			25.1420i			1.68363i	−0.539765	+	0.841815i	$0.681487\pi$
$224$		0			0
$225$	−4.86015	+	1.17429i	−0.324010	+	0.0782859i
$226$	−18.0962			−1.20374
$227$			23.6702i			1.57105i	0.618831	+	0.785524i	$0.287607\pi$
$227$			23.6702i			1.57105i	−0.618831	+	0.785524i	$0.712393\pi$
$228$			9.08617i			0.601747i
$229$	0.406316			0.0268501			0.0134251	−	0.999910i	$-0.495727\pi$
$229$	0.406316			0.0268501			0.0134251	+	0.999910i	$0.495727\pi$
$230$	21.9023	−	2.60844i	1.44419	−	0.171995i
$231$		0			0
$232$			5.90465i			0.387659i
$233$		−	7.16527i		−	0.469413i	−0.972066	−	0.234706i	$-0.924587\pi$
$233$		−	7.16527i		−	0.469413i	0.972066	−	0.234706i	$-0.0754128\pi$
$234$	−5.57699			−0.364579
$235$	−0.645420	−	5.41939i	−0.0421025	−	0.353522i
$236$	−3.47113			−0.225951
$237$		−	8.11354i		−	0.527031i
$238$		0			0
$239$	−10.0922			−0.652809			−0.326404	−	0.945230i	$-0.605837\pi$
$239$	−10.0922			−0.652809			−0.326404	+	0.945230i	$0.605837\pi$
$240$	1.31414	+	11.0344i	0.0848274	+	0.712270i
$241$	4.60676			0.296748			0.148374	−	0.988931i	$-0.452596\pi$
$241$	4.60676			0.296748			0.148374	+	0.988931i	$0.452596\pi$
$242$		−	11.9012i		−	0.765038i
$243$			1.00000i			0.0641500i
$244$	−12.7934			−0.819013
$245$		0			0
$246$	14.2361			0.907660
$247$			24.2205i			1.54111i
$248$		−	4.28376i		−	0.272019i
$249$	−8.75128			−0.554590
$250$	−6.93519	−	18.6732i	−0.438620	−	1.18100i
$251$	0.311597			0.0196678			0.00983390	−	0.999952i	$-0.496870\pi$
$251$	0.311597			0.0196678			0.00983390	+	0.999952i	$0.496870\pi$
$252$		0			0
$253$		−	11.5077i		−	0.723482i
$254$	15.8029			0.991559
$255$	−4.72992	+	0.563307i	−0.296199	+	0.0352756i
$256$	20.3687			1.27304
$257$		−	2.50211i		−	0.156077i	−0.996950	−	0.0780387i	$-0.975134\pi$
$257$		−	2.50211i		−	0.156077i	0.996950	−	0.0780387i	$-0.0248658\pi$
$258$			8.89113i			0.553537i
$259$		0			0
$260$	−0.972008	−	8.16165i	−0.0602814	−	0.506164i
$261$	−4.01368			−0.248441
$262$		−	9.51671i		−	0.587944i
$263$		−	4.62511i		−	0.285196i	−0.989781	−	0.142598i	$-0.954454\pi$
$263$		−	4.62511i		−	0.285196i	0.989781	−	0.142598i	$-0.0455457\pi$
$264$	3.05774			0.188191
$265$	−2.62105	−	22.0081i	−0.161010	−	1.35195i
$266$		0			0
$267$			0.618661i			0.0378614i
$268$			4.50856i			0.275404i
$269$	12.0233			0.733074			0.366537	−	0.930404i	$-0.380543\pi$
$269$	12.0233			0.733074			0.366537	+	0.930404i	$0.380543\pi$
$270$	−3.95594	+	0.471131i	−0.240751	+	0.0286721i
$271$	5.46935			0.332239			0.166120	−	0.986106i	$-0.446876\pi$
$271$	5.46935			0.332239			0.166120	+	0.986106i	$0.446876\pi$
$272$			10.5864i			0.641898i
$273$		0			0
$274$	−23.3466			−1.41042
$275$	−10.1018	+	2.44075i	−0.609161	+	0.147183i
$276$	6.50151			0.391345
$277$		−	29.8099i		−	1.79111i	−0.444956	−	0.895553i	$-0.646781\pi$
$277$		−	29.8099i		−	1.79111i	0.444956	−	0.895553i	$-0.353219\pi$
$278$			0.433235i			0.0259837i
$279$	2.91188			0.174330
$280$		0			0
$281$	7.78511			0.464421			0.232210	−	0.972666i	$-0.425404\pi$
$281$	7.78511			0.464421			0.232210	+	0.972666i	$0.425404\pi$
$282$		−	4.34858i		−	0.258954i
$283$			2.61444i			0.155412i	0.996976	+	0.0777062i	$0.0247596\pi$
$283$			2.61444i			0.155412i	−0.996976	+	0.0777062i	$0.975240\pi$
$284$	17.6435			1.04695
$285$	2.04609	+	17.1804i	0.121200	+	1.01768i
$286$	−11.5917			−0.685434
$287$		0			0
$288$			5.91188i			0.348361i
$289$	12.4621			0.733066
$290$	−1.89097	−	15.8779i	−0.111042	−	0.932382i
$291$	0.296842			0.0174012
$292$		−	10.0445i		−	0.587810i
$293$		−	12.7559i		−	0.745210i	−0.927990	−	0.372605i	$-0.878465\pi$
$293$		−	12.7559i		−	0.745210i	0.927990	−	0.372605i	$-0.121535\pi$
$294$		0			0
$295$	−6.56331	+	0.781653i	−0.382131	+	0.0455096i
$296$	5.17130			0.300576
$297$			2.07850i			0.120607i
$298$		−	4.16423i		−	0.241227i
$299$	17.3307			1.00226
$300$	−1.37895	−	5.70722i	−0.0796140	−	0.329506i
$301$		0			0
$302$		−	19.8005i		−	1.13939i
$303$		−	8.25879i		−	0.474455i
$304$	38.4529			2.20543
$305$	−24.1901	+	2.88091i	−1.38512	+	0.164960i
$306$	−3.79533			−0.216965
$307$			13.1919i			0.752900i	0.926437	+	0.376450i	$0.122855\pi$
$307$			13.1919i			0.752900i	−0.926437	+	0.376450i	$0.877145\pi$
$308$		0			0
$309$	−17.0866			−0.972024
$310$	1.37188	+	11.5192i	0.0779175	+	0.654249i
$311$	14.2823			0.809873			0.404937	−	0.914345i	$-0.367294\pi$
$311$	14.2823			0.809873			0.404937	+	0.914345i	$0.367294\pi$
$312$			4.60498i			0.260706i
$313$			4.77143i			0.269697i	0.990866	+	0.134849i	$0.0430548\pi$
$313$			4.77143i			0.269697i	−0.990866	+	0.134849i	$0.956945\pi$
$314$	−20.1651			−1.13798
$315$		0			0
$316$	9.52764			0.535971
$317$		−	18.8048i		−	1.05618i	−0.849188	−	0.528091i	$-0.822908\pi$
$317$		−	18.8048i		−	1.05618i	0.849188	−	0.528091i	$-0.177092\pi$
$318$		−	17.6595i		−	0.990298i
$319$	−8.34242			−0.467086
$320$	−1.31820	+	0.156990i	−0.0736897	+	0.00877603i
$321$	6.31052			0.352219
$322$		0			0
$323$			16.4829i			0.917131i
$324$	−1.17429			−0.0652383
$325$	−3.67580	−	15.2134i	−0.203897	−	0.843887i
$326$	3.74766			0.207564
$327$		−	2.44676i		−	0.135306i
$328$		−	11.7549i		−	0.649055i
$329$		0			0
$330$	−8.22241	+	0.979243i	−0.452629	+	0.0539056i
$331$	17.7742			0.976956			0.488478	−	0.872576i	$-0.337552\pi$
$331$	17.7742			0.976956			0.488478	+	0.872576i	$0.337552\pi$
$332$		−	10.2765i		−	0.563998i
$333$			3.51519i			0.192631i
$334$	6.38902			0.349592
$335$	1.01527	+	8.52490i	0.0554700	+	0.465765i
$336$		0			0
$337$			3.86675i			0.210635i	0.994439	+	0.105318i	$0.0335860\pi$
$337$			3.86675i			0.210635i	−0.994439	+	0.105318i	$0.966414\pi$
$338$			5.70423i			0.310269i
$339$	−10.1570			−0.551652
$340$	−0.661485	−	5.55429i	−0.0358741	−	0.301224i
$341$	6.05234			0.327753
$342$			13.7857i			0.745446i
$343$		0			0
$344$	7.34150			0.395827
$345$	12.2932	−	1.46405i	0.661845	−	0.0788221i
$346$	27.6869			1.48846
$347$			10.2725i			0.551455i	0.961236	+	0.275727i	$0.0889187\pi$
$347$			10.2725i			0.551455i	−0.961236	+	0.275727i	$0.911081\pi$
$348$		−	4.71322i		−	0.252655i
$349$	23.6180			1.26424			0.632122	−	0.774869i	$-0.282184\pi$
$349$	23.6180			1.26424			0.632122	+	0.774869i	$0.282184\pi$
$350$		0			0
$351$	−3.13023			−0.167079
$352$			12.2878i			0.654943i
$353$			5.77759i			0.307510i	0.988109	+	0.153755i	$0.0491367\pi$
$353$			5.77759i			0.307510i	−0.988109	+	0.153755i	$0.950863\pi$
$354$	−5.26647			−0.279909
$355$	33.3608	−	3.97308i	1.77061	−	0.210869i
$356$	−0.726487			−0.0385037
$357$		0			0
$358$		−	28.0355i		−	1.48172i
$359$	−31.3054			−1.65224			−0.826118	−	0.563497i	$-0.809456\pi$
$359$	−31.3054			−1.65224			−0.826118	+	0.563497i	$0.809456\pi$
$360$	0.389018	+	3.26647i	0.0205030	+	0.172158i
$361$	40.8704			2.15107
$362$			8.88497i			0.466983i
$363$		−	6.67986i		−	0.350602i
$364$		0			0
$365$	−2.26189	−	18.9924i	−0.118393	−	0.994108i
$366$	−19.4104			−1.01460
$367$		−	16.5519i		−	0.864002i	−0.901873	−	0.432001i	$-0.857808\pi$
$367$		−	16.5519i		−	0.864002i	0.901873	−	0.432001i	$-0.142192\pi$
$368$		−	27.5146i		−	1.43430i
$369$	7.99038			0.415963
$370$	−13.9059	+	1.65611i	−0.722932	+	0.0860972i
$371$		0			0
$372$			3.41939i			0.177287i
$373$			32.1426i			1.66428i	0.554566	+	0.832140i	$0.312884\pi$
$373$			32.1426i			1.66428i	−0.554566	+	0.832140i	$0.687116\pi$
$374$	−7.88858			−0.407909
$375$	−3.89256	−	10.4808i	−0.201011	−	0.541228i
$376$	−3.59067			−0.185175
$377$		−	12.5638i		−	0.647066i
$378$		0			0
$379$	4.98800			0.256216			0.128108	−	0.991760i	$-0.459110\pi$
$379$	4.98800			0.256216			0.128108	+	0.991760i	$0.459110\pi$
$380$	−20.1747	+	2.40270i	−1.03494	+	0.123256i
$381$	8.86977			0.454412
$382$			21.0385i			1.07642i
$383$		−	26.4568i		−	1.35188i	−0.736957	−	0.675940i	$-0.763738\pi$
$383$		−	26.4568i		−	1.35188i	0.736957	−	0.675940i	$-0.236262\pi$
$384$	10.7660			0.549402
$385$		0			0
$386$	−44.0746			−2.24334
$387$			4.99038i			0.253675i
$388$			0.348578i			0.0176964i
$389$	12.7716			0.647545			0.323773	−	0.946135i	$-0.395049\pi$
$389$	12.7716			0.647545			0.323773	+	0.946135i	$0.395049\pi$
$390$	−1.47475	−	12.3830i	−0.0746768	−	0.627038i
$391$	11.7941			0.596455
$392$		0			0
$393$		−	5.34150i		−	0.269443i
$394$	34.8360			1.75501
$395$	18.0151	−	2.14550i	0.906438	−	0.107952i
$396$	−2.44075			−0.122653
$397$		−	15.1212i		−	0.758912i	−0.925210	−	0.379456i	$-0.876111\pi$
$397$		−	15.1212i		−	0.758912i	0.925210	−	0.379456i	$-0.123889\pi$
$398$		−	39.6242i		−	1.98618i
$399$		0			0
$400$	−24.1531	+	5.83577i	−1.20766	+	0.291789i
$401$	12.3606			0.617258			0.308629	−	0.951182i	$-0.400130\pi$
$401$	12.3606			0.617258			0.308629	+	0.951182i	$0.400130\pi$
$402$			6.84047i			0.341171i
$403$			9.11487i			0.454044i
$404$	9.69820			0.482504
$405$	−2.22038	+	0.264435i	−0.110331	+	0.0131399i
$406$		0			0
$407$			7.30630i			0.362160i
$408$			3.13385i			0.155149i
$409$	−10.5287			−0.520611			−0.260306	−	0.965526i	$-0.583823\pi$
$409$	−10.5287			−0.520611			−0.260306	+	0.965526i	$0.583823\pi$
$410$	3.76451	+	31.6095i	0.185916	+	1.56108i
$411$	−13.1039			−0.646369
$412$		−	20.0646i		−	0.988513i
$413$		0			0
$414$	9.86421			0.484799
$415$	−2.31414	−	19.4311i	−0.113597	−	0.953837i
$416$	−18.5056			−0.907310
$417$			0.243164i			0.0119078i
$418$			28.6535i			1.40149i
$419$	13.3110			0.650283			0.325142	−	0.945665i	$-0.394588\pi$
$419$	13.3110			0.650283			0.325142	+	0.945665i	$0.394588\pi$
$420$		0			0
$421$	19.1520			0.933413			0.466707	−	0.884412i	$-0.345440\pi$
$421$	19.1520			0.933413			0.466707	+	0.884412i	$0.345440\pi$
$422$			42.0811i			2.04847i
$423$		−	2.44075i		−	0.118674i
$424$	−14.5817			−0.708149
$425$	−2.50151	−	10.3532i	−0.121341	−	0.502206i
$426$	26.7690			1.29696
$427$		0			0
$428$			7.41038i			0.358194i
$429$	−6.50617			−0.314121
$430$	−19.7417	+	2.35112i	−0.952027	+	0.113381i
$431$	10.8964			0.524860			0.262430	−	0.964951i	$-0.415476\pi$
$431$	10.8964			0.524860			0.262430	+	0.964951i	$0.415476\pi$
$432$			4.96962i			0.239101i
$433$		−	19.4869i		−	0.936482i	−0.883601	−	0.468241i	$-0.844888\pi$
$433$		−	19.4869i		−	0.936482i	0.883601	−	0.468241i	$-0.155112\pi$
$434$		0			0
$435$	−1.06136	−	8.91188i	−0.0508881	−	0.427292i
$436$	2.87320			0.137601
$437$		−	42.8396i		−	2.04929i
$438$		−	15.2397i		−	0.728181i
$439$	13.5310			0.645799			0.322899	−	0.946433i	$-0.395342\pi$
$439$	13.5310			0.645799			0.322899	+	0.946433i	$0.395342\pi$
$440$	0.808572	+	6.78933i	0.0385471	+	0.323669i
$441$		0			0
$442$		−	11.8803i		−	0.565087i
$443$			28.8663i			1.37148i	0.727846	+	0.685740i	$0.240521\pi$
$443$			28.8663i			1.37148i	−0.727846	+	0.685740i	$0.759479\pi$
$444$	−4.12785			−0.195899
$445$	−1.37366	+	0.163595i	−0.0651177	+	0.00775516i
$446$	−44.7943			−2.12107
$447$		−	2.33728i		−	0.110550i
$448$		0			0
$449$	−23.4298			−1.10572			−0.552860	−	0.833274i	$-0.686464\pi$
$449$	−23.4298			−1.10572			−0.552860	+	0.833274i	$0.686464\pi$
$450$	−2.09218	−	8.65910i	−0.0986261	−	0.408194i
$451$	16.6080			0.782039
$452$		−	11.9272i		−	0.561010i
$453$		−	11.1135i		−	0.522159i
$454$	−42.1722			−1.97924
$455$		0			0
$456$	11.3830			0.533059
$457$		−	30.2876i		−	1.41679i	−0.705815	−	0.708396i	$-0.749419\pi$
$457$		−	30.2876i		−	1.41679i	0.705815	−	0.708396i	$-0.250581\pi$
$458$			0.723915i			0.0338263i
$459$	−2.13023			−0.0994307
$460$	1.71922	+	14.4358i	0.0801592	+	0.673073i
$461$	7.02196			0.327045			0.163523	−	0.986540i	$-0.447714\pi$
$461$	7.02196			0.327045			0.163523	+	0.986540i	$0.447714\pi$
$462$		0			0
$463$			2.97324i			0.138178i	0.997610	+	0.0690891i	$0.0220093\pi$
$463$			2.97324i			0.138178i	−0.997610	+	0.0690891i	$0.977991\pi$
$464$	−19.9465			−0.925992
$465$	0.770003	+	6.46548i	0.0357080	+	0.299830i
$466$	12.7660			0.591375
$467$			23.7549i			1.09925i	0.835413	+	0.549623i	$0.185229\pi$
$467$			23.7549i			1.09925i	−0.835413	+	0.549623i	$0.814771\pi$
$468$		−	3.67580i		−	0.169914i
$469$		0			0
$470$	9.65548	−	1.14991i	0.445374	−	0.0530416i
$471$	−11.3182			−0.521515
$472$			4.34858i			0.200160i
$473$			10.3725i			0.476927i
$474$	14.4555			0.663964
$475$	−37.6059	+	9.08617i	−1.72548	+	0.416902i
$476$		0			0
$477$		−	9.91188i		−	0.453834i
$478$		−	17.9808i		−	0.822421i
$479$	−6.54423			−0.299013			−0.149507	−	0.988761i	$-0.547769\pi$
$479$	−6.54423			−0.299013			−0.149507	+	0.988761i	$0.547769\pi$
$480$	−13.1266	+	1.56331i	−0.599145	+	0.0713549i
$481$	−11.0034			−0.501710
$482$			8.20765i			0.373848i
$483$		0			0
$484$	7.84408			0.356549
$485$	0.0784952	+	0.659101i	0.00356429	+	0.0299282i
$486$	−1.78165			−0.0808174
$487$		−	16.3269i		−	0.739844i	−0.929063	−	0.369922i	$-0.879384\pi$
$487$		−	16.3269i		−	0.739844i	0.929063	−	0.369922i	$-0.120616\pi$
$488$			16.0274i			0.725525i
$489$	2.10347			0.0951223
$490$		0			0
$491$	24.9009			1.12376			0.561882	−	0.827218i	$-0.310078\pi$
$491$	24.9009			1.12376			0.561882	+	0.827218i	$0.310078\pi$
$492$			9.38302i			0.423019i
$493$		−	8.55007i		−	0.385076i
$494$	−43.1525			−1.94152
$495$	−4.61504	+	0.549626i	−0.207431	+	0.0247039i
$496$	14.4710			0.649766
$497$		0			0
$498$		−	15.5917i		−	0.698683i
$499$	12.2039			0.546323			0.273161	−	0.961968i	$-0.411931\pi$
$499$	12.2039			0.546323			0.273161	+	0.961968i	$0.411931\pi$
$500$	12.3075	−	4.57099i	0.550410	−	0.204421i
$501$	3.58600			0.160211
$502$			0.555157i			0.0247779i
$503$			27.8165i			1.24028i	0.784492	+	0.620139i	$0.212924\pi$
$503$			27.8165i			1.24028i	−0.784492	+	0.620139i	$0.787076\pi$
$504$		0			0
$505$	18.3376	−	2.18391i	0.816013	−	0.0971827i
$506$	20.5027			0.911457
$507$			3.20165i			0.142190i
$508$			10.4157i			0.462121i
$509$	−27.8199			−1.23309			−0.616547	−	0.787318i	$-0.711469\pi$
$509$	−27.8199			−1.23309			−0.616547	+	0.787318i	$0.711469\pi$
$510$	−1.00362	−	8.42707i	−0.0444409	−	0.373157i
$511$		0			0
$512$			14.7579i			0.652214i
$513$			7.73760i			0.341623i
$514$	4.45789			0.196629
$515$	−4.51829	−	37.9387i	−0.199100	−	1.67178i
$516$	−5.86015			−0.257979
$517$		−	5.07310i		−	0.223115i
$518$		0			0
$519$	15.5400			0.682131
$520$	−10.2248	+	1.21772i	−0.448387	+	0.0534004i
$521$	−33.5026			−1.46777			−0.733887	−	0.679272i	$-0.762296\pi$
$521$	−33.5026			−1.46777			−0.733887	+	0.679272i	$0.762296\pi$
$522$		−	7.15099i		−	0.312990i
$523$		−	12.7958i		−	0.559522i	−0.960070	−	0.279761i	$-0.909745\pi$
$523$		−	12.7958i		−	0.559522i	0.960070	−	0.279761i	$-0.0902551\pi$
$524$	6.27247			0.274014
$525$		0			0
$526$	8.24034			0.359296
$527$			6.20299i			0.270206i
$528$			10.3293i			0.449527i
$529$	−7.65336			−0.332755
$530$	39.2108	−	4.66979i	1.70321	−	0.202843i
$531$	−2.95594			−0.128277
$532$		0			0
$533$			25.0117i			1.08338i
$534$	−1.10224			−0.0476986
$535$	1.66872	+	14.0117i	0.0721451	+	0.605780i
$536$	5.64825			0.243967
$537$		−	15.7357i		−	0.679044i
$538$			21.4214i			0.923540i
$539$		0			0
$540$	−0.310523	−	2.60736i	−0.0133628	−	0.112203i
$541$	25.2566			1.08587			0.542933	−	0.839776i	$-0.317314\pi$
$541$	25.2566			1.08587			0.542933	+	0.839776i	$0.317314\pi$
$542$			9.74448i			0.418561i
$543$			4.98692i			0.214009i
$544$	−12.5937			−0.539950
$545$	5.43272	−	0.647007i	0.232712	−	0.0277147i
$546$		0			0
$547$			38.8743i			1.66214i	0.556165	+	0.831072i	$0.312272\pi$
$547$			38.8743i			1.66214i	−0.556165	+	0.831072i	$0.687728\pi$
$548$		−	15.3878i		−	0.657334i
$549$	−10.8946			−0.464970
$550$	−4.34858	−	17.9979i	−0.185424	−	0.767433i
$551$	−31.0562			−1.32304
$552$		−	8.14499i		−	0.346674i
$553$		0			0
$554$	53.1110			2.25647
$555$	−7.80504	+	0.929537i	−0.331306	+	0.0394567i
$556$	−0.285545			−0.0121098
$557$			1.36378i			0.0577850i	0.999583	+	0.0288925i	$0.00919806\pi$
$557$			1.36378i			0.0577850i	−0.999583	+	0.0288925i	$0.990802\pi$
$558$			5.18797i			0.219624i
$559$	−15.6210			−0.660700
$560$		0			0
$561$	−4.42768			−0.186937
$562$			13.8704i			0.585086i
$563$		−	10.5744i		−	0.445660i	−0.974857	−	0.222830i	$-0.928471\pi$
$563$		−	10.5744i		−	0.445660i	0.974857	−	0.222830i	$-0.0715294\pi$
$564$	2.86615			0.120687
$565$	−2.68586	−	22.5523i	−0.112995	−	0.948784i
$566$	−4.65803			−0.195791
$567$		0			0
$568$		−	22.1035i		−	0.927441i
$569$	−37.9865			−1.59248			−0.796238	−	0.604983i	$-0.793180\pi$
$569$	−37.9865			−1.59248			−0.796238	+	0.604983i	$0.793180\pi$
$570$	−30.6095	+	3.64542i	−1.28209	+	0.152690i
$571$	−15.6910			−0.656648			−0.328324	−	0.944565i	$-0.606484\pi$
$571$	−15.6910			−0.656648			−0.328324	+	0.944565i	$0.606484\pi$
$572$		−	7.64013i		−	0.319450i
$573$			11.8084i			0.493304i
$574$		0			0
$575$	6.50151	+	26.9084i	0.271132	+	1.12216i
$576$	−0.593684			−0.0247368
$577$		−	3.44809i		−	0.143546i	−0.997421	−	0.0717730i	$-0.977134\pi$
$577$		−	3.44809i		−	0.143546i	0.997421	−	0.0717730i	$-0.0228657\pi$
$578$			22.2032i			0.923530i
$579$	−24.7380			−1.02808
$580$	10.4651	−	1.24634i	0.434541	−	0.0517514i
$581$		0			0
$582$			0.528869i			0.0219223i
$583$		−	20.6018i		−	0.853240i
$584$	−12.5836			−0.520713
$585$	−0.827742	−	6.95029i	−0.0342229	−	0.287359i
$586$	22.7267			0.938830
$587$			10.5983i			0.437441i	0.975788	+	0.218720i	$0.0701882\pi$
$587$			10.5983i			0.437441i	−0.975788	+	0.218720i	$0.929812\pi$
$588$		0			0
$589$	22.5310			0.928373
$590$	−1.39264	−	11.6935i	−0.0573339	−	0.481415i
$591$	19.5526			0.804287
$592$			17.4692i			0.717978i
$593$			0.234412i			0.00962614i	0.999988	+	0.00481307i	$0.00153205\pi$
$593$			0.234412i			0.00962614i	−0.999988	+	0.00481307i	$0.998468\pi$
$594$	−3.70316			−0.151942
$595$		0			0
$596$	2.74464			0.112425
$597$		−	22.2401i		−	0.910229i
$598$			30.8773i			1.26267i
$599$	25.8290			1.05535			0.527673	−	0.849448i	$-0.323065\pi$
$599$	25.8290			1.05535			0.527673	+	0.849448i	$0.323065\pi$
$600$	−7.14991	+	1.72753i	−0.291894	+	0.0705262i
$601$	1.15592			0.0471508			0.0235754	−	0.999722i	$-0.492495\pi$
$601$	1.15592			0.0471508			0.0235754	+	0.999722i	$0.492495\pi$
$602$		0			0
$603$			3.83939i			0.156352i
$604$	13.0505			0.531017
$605$	14.8318	−	1.76639i	0.602999	−	0.0718138i
$606$	14.7143			0.597727
$607$			23.2111i			0.942110i	0.882104	+	0.471055i	$0.156127\pi$
$607$			23.2111i			0.942110i	−0.882104	+	0.471055i	$0.843873\pi$
$608$			45.7438i			1.85516i
$609$		0			0
$610$	−5.13278	−	43.0984i	−0.207820	−	1.74500i
$611$	7.64013			0.309086
$612$		−	2.50151i		−	0.101117i
$613$			6.33144i			0.255724i	0.991792	+	0.127862i	$0.0408115\pi$
$613$			6.33144i			0.255724i	−0.991792	+	0.127862i	$0.959188\pi$
$614$	−23.5033			−0.948518
$615$	2.11293	+	17.7417i	0.0852017	+	0.715413i
$616$		0			0
$617$			25.9546i			1.04489i	0.852672	+	0.522447i	$0.174981\pi$
$617$			25.9546i			1.04489i	−0.852672	+	0.522447i	$0.825019\pi$
$618$		−	30.4424i		−	1.22457i
$619$	−29.0962			−1.16948			−0.584738	−	0.811222i	$-0.698803\pi$
$619$	−29.0962			−1.16948			−0.584738	+	0.811222i	$0.698803\pi$
$620$	−7.59235	+	0.904206i	−0.304916	+	0.0363138i
$621$	5.53655			0.222174
$622$			25.4460i			1.02029i
$623$		0			0
$624$	−15.5561			−0.622741
$625$	22.2421	−	11.4144i	0.889684	−	0.456578i
$626$	−8.50104			−0.339770
$627$			16.0826i			0.642275i
$628$		−	13.2908i		−	0.530362i
$629$	−7.48816			−0.298573
$630$		0			0
$631$	−37.3609			−1.48731			−0.743657	−	0.668561i	$-0.766911\pi$
$631$	−37.3609			−1.48731			−0.743657	+	0.668561i	$0.766911\pi$
$632$		−	11.9361i		−	0.474791i
$633$			23.6191i			0.938775i
$634$	33.5036			1.33060
$635$	2.34547	+	19.6942i	0.0930773	+	0.781542i
$636$	11.6394			0.461533
$637$		0			0
$638$		−	14.8633i		−	0.588443i
$639$	15.0248			0.594373
$640$	2.84691	+	23.9046i	0.112534	+	0.944914i
$641$	−27.8535			−1.10015			−0.550074	−	0.835116i	$-0.685400\pi$
$641$	−27.8535			−1.10015			−0.550074	+	0.835116i	$0.685400\pi$
$642$			11.2432i			0.443732i
$643$		−	20.3104i		−	0.800963i	−0.916305	−	0.400481i	$-0.868843\pi$
$643$		−	20.3104i		−	0.800963i	0.916305	−	0.400481i	$-0.131157\pi$
$644$		0			0
$645$	−11.0805	+	1.31963i	−0.436295	+	0.0519603i
$646$	−29.3668			−1.15542
$647$		−	22.4329i		−	0.881929i	−0.897525	−	0.440964i	$-0.854636\pi$
$647$		−	22.4329i		−	0.881929i	0.897525	−	0.440964i	$-0.145364\pi$
$648$			1.47113i			0.0577915i
$649$	−6.14391			−0.241170
$650$	27.1050	−	6.54900i	1.06315	−	0.256873i
$651$		0			0
$652$			2.47008i			0.0967360i
$653$		−	19.8051i		−	0.775035i	−0.921862	−	0.387517i	$-0.873333\pi$
$653$		−	19.8051i		−	0.775035i	0.921862	−	0.387517i	$-0.126667\pi$
$654$	4.35927			0.170461
$655$	11.8601	−	1.41248i	0.463414	−	0.0551901i
$656$	39.7092			1.55038
$657$		−	8.55369i		−	0.333711i
$658$		0			0
$659$	−38.3567			−1.49416			−0.747082	−	0.664731i	$-0.768546\pi$
$659$	−38.3567			−1.49416			−0.747082	+	0.664731i	$0.768546\pi$
$660$	−0.645420	−	5.41939i	−0.0251229	−	0.210950i
$661$	−2.97492			−0.115711			−0.0578554	−	0.998325i	$-0.518426\pi$
$661$	−2.97492			−0.115711			−0.0578554	+	0.998325i	$0.518426\pi$
$662$			31.6674i			1.23079i
$663$		−	6.66812i		−	0.258968i
$664$	−12.8743			−0.499619
$665$		0			0
$666$	−6.26285			−0.242680
$667$			22.2219i			0.860437i
$668$			4.21101i			0.162929i
$669$	−25.1420			−0.972045
$670$	−15.1884	+	1.80886i	−0.586780	+	0.0698822i
$671$	−22.6443			−0.874175
$672$		0			0
$673$			22.8397i			0.880407i	0.897898	+	0.440203i	$0.145094\pi$
$673$			22.8397i			0.880407i	−0.897898	+	0.440203i	$0.854906\pi$
$674$	−6.88921			−0.265363
$675$	−1.17429	−	4.86015i	−0.0451984	−	0.187067i
$676$	−3.75966			−0.144602
$677$		−	7.19609i		−	0.276568i	−0.990393	−	0.138284i	$-0.955841\pi$
$677$		−	7.19609i		−	0.276568i	0.990393	−	0.138284i	$-0.0441587\pi$
$678$		−	18.0962i		−	0.694982i
$679$		0			0
$680$	−6.95833	+	0.828698i	−0.266840	+	0.0317791i
$681$	−23.6702			−0.907045
$682$			10.7832i			0.412909i
$683$			4.55442i			0.174270i	0.996197	+	0.0871351i	$0.0277712\pi$
$683$			4.55442i			0.174270i	−0.996197	+	0.0871351i	$0.972229\pi$
$684$	−9.08617			−0.347419
$685$	−3.46513	−	29.0956i	−0.132396	−	1.11169i
$686$		0			0
$687$			0.406316i			0.0155019i
$688$			24.8003i			0.945503i
$689$	31.0265			1.18202
$690$	2.60844	+	21.9023i	0.0993015	+	0.833805i
$691$	−3.53896			−0.134628			−0.0673142	−	0.997732i	$-0.521443\pi$
$691$	−3.53896			−0.134628			−0.0673142	+	0.997732i	$0.521443\pi$
$692$			18.2485i			0.693702i
$693$		0			0
$694$	−18.3020			−0.694734
$695$	−0.539917	+	0.0643011i	−0.0204802	+	0.00243908i
$696$	−5.90465			−0.223815
$697$			17.0214i			0.644730i
$698$			42.0791i			1.59272i
$699$	7.16527			0.271015
$700$		0			0
$701$	−16.8111			−0.634948			−0.317474	−	0.948267i	$-0.602835\pi$
$701$	−16.8111			−0.634948			−0.317474	+	0.948267i	$0.602835\pi$
$702$		−	5.57699i		−	0.210490i
$703$			27.1991i			1.02583i
$704$	−1.23397			−0.0465069
$705$	5.41939	−	0.645420i	0.204106	−	0.0243079i
$706$	−10.2937			−0.387407
$707$		0			0
$708$		−	3.47113i		−	0.130453i
$709$	−31.8176			−1.19494			−0.597468	−	0.801893i	$-0.703826\pi$
$709$	−31.8176			−1.19494			−0.597468	+	0.801893i	$0.703826\pi$
$710$	7.07865	+	59.4373i	0.265657	+	2.23064i
$711$	8.11354			0.304281
$712$			0.910131i			0.0341086i
$713$		−	16.1218i		−	0.603766i
$714$		0			0
$715$	−1.72046	−	14.4462i	−0.0643414	−	0.540256i
$716$	18.4782			0.690563
$717$		−	10.0922i		−	0.376899i
$718$		−	55.7754i		−	2.08152i
$719$	15.2807			0.569876			0.284938	−	0.958546i	$-0.408027\pi$
$719$	15.2807			0.569876			0.284938	+	0.958546i	$0.408027\pi$
$720$	−11.0344	+	1.31414i	−0.411229	+	0.0489751i
$721$		0			0
$722$			72.8169i			2.70996i
$723$			4.60676i			0.171327i
$724$	−5.85609			−0.217640
$725$	19.5071	−	4.71322i	0.724475	−	0.175045i
$726$	11.9012			0.441695
$727$			19.1829i			0.711453i	0.934590	+	0.355726i	$0.115766\pi$
$727$			19.1829i			0.711453i	−0.934590	+	0.355726i	$0.884234\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	33.8379	−	4.02991i	1.25240	−	0.149153i
$731$	−10.6307			−0.393189
$732$		−	12.7934i		−	0.472857i
$733$		−	48.7218i		−	1.79958i	−0.436323	−	0.899790i	$-0.643719\pi$
$733$		−	48.7218i		−	1.79958i	0.436323	−	0.899790i	$-0.356281\pi$
$734$	29.4898			1.08849
$735$		0			0
$736$	32.7314			1.20650
$737$			7.98016i			0.293953i
$738$			14.2361i			0.524038i
$739$	9.48405			0.348876			0.174438	−	0.984668i	$-0.444189\pi$
$739$	9.48405			0.348876			0.174438	+	0.984668i	$0.444189\pi$
$740$	−1.09155	−	9.16538i	−0.0401260	−	0.336926i
$741$	−24.2205			−0.889761
$742$		0			0
$743$		−	30.2032i		−	1.10805i	−0.832501	−	0.554023i	$-0.813092\pi$
$743$		−	30.2032i		−	1.10805i	0.832501	−	0.554023i	$-0.186908\pi$
$744$	4.28376			0.157050
$745$	5.18965	−	0.618058i	0.190134	−	0.0226439i
$746$	−57.2669			−2.09669
$747$		−	8.75128i		−	0.320192i
$748$		−	5.19937i		−	0.190108i
$749$		0			0
$750$	18.6732	−	6.93519i	0.681850	−	0.253237i
$751$	−7.32934			−0.267451			−0.133726	−	0.991018i	$-0.542694\pi$
$751$	−7.32934			−0.267451			−0.133726	+	0.991018i	$0.542694\pi$
$752$		−	12.1296i		−	0.442322i
$753$			0.311597i			0.0113552i
$754$	22.3842			0.815186
$755$	24.6762	−	2.93880i	0.898060	−	0.106954i
$756$		0			0
$757$		−	14.1603i		−	0.514666i	−0.966323	−	0.257333i	$-0.917156\pi$
$757$		−	14.1603i		−	0.514666i	0.966323	−	0.257333i	$-0.0828438\pi$
$758$			8.88688i			0.322786i
$759$	11.5077			0.417703
$760$	3.01006	+	25.2746i	0.109186	+	0.916806i
$761$	23.9183			0.867039			0.433519	−	0.901144i	$-0.357272\pi$
$761$	23.9183			0.867039			0.433519	+	0.901144i	$0.357272\pi$
$762$			15.8029i			0.572477i
$763$		0			0
$764$	−13.8665			−0.501672
$765$	−0.563307	−	4.72992i	−0.0203664	−	0.171011i
$766$	47.1369			1.70312
$767$		−	9.25278i		−	0.334099i
$768$			20.3687i			0.734992i
$769$	14.1358			0.509750			0.254875	−	0.966974i	$-0.417966\pi$
$769$	14.1358			0.509750			0.254875	+	0.966974i	$0.417966\pi$
$770$		0			0
$771$	2.50211			0.0901113
$772$		−	29.0496i		−	1.04552i
$773$		−	6.75972i		−	0.243130i	−0.992583	−	0.121565i	$-0.961209\pi$
$773$		−	6.75972i		−	0.243130i	0.992583	−	0.121565i	$-0.0387913\pi$
$774$	−8.89113			−0.319585
$775$	−14.1522	+	3.41939i	−0.508362	+	0.122828i
$776$	0.436693			0.0156764
$777$		0			0
$778$			22.7545i			0.815790i
$779$	61.8263			2.21516
$780$	8.16165	−	0.972008i	0.292234	−	0.0348035i
$781$	31.2290			1.11746
$782$			21.0131i			0.751425i
$783$		−	4.01368i		−	0.143437i
$784$		0			0
$785$	−2.99292	−	25.1307i	−0.106822	−	0.896952i
$786$	9.51671			0.339450
$787$			15.3751i			0.548062i	0.961721	+	0.274031i	$0.0883571\pi$
$787$			15.3751i			0.548062i	−0.961721	+	0.274031i	$0.911643\pi$
$788$			22.9604i			0.817931i
$789$	4.62511			0.164658
$790$	3.82254	+	32.0967i	0.136000	+	1.14195i
$791$		0			0
$792$			3.05774i			0.108652i
$793$		−	34.1026i		−	1.21102i
$794$	26.9408			0.956092
$795$	22.0081	−	2.62105i	0.780548	−	0.0929589i
$796$	26.1164			0.925670
$797$		−	9.46785i		−	0.335369i	−0.985841	−	0.167684i	$-0.946371\pi$
$797$		−	9.46785i		−	0.335369i	0.985841	−	0.167684i	$-0.0536289\pi$
$798$		0			0
$799$	5.19937			0.183941
$800$	−6.94226	−	28.7326i	−0.245446	−	1.01585i
$801$	−0.618661			−0.0218593
$802$			22.0223i			0.777634i
$803$		−	17.7788i		−	0.627400i
$804$	−4.50856			−0.159004
$805$		0			0
$806$	−16.2395			−0.572014
$807$			12.0233i			0.423240i
$808$		−	12.1498i		−	0.427427i
$809$	−5.63745			−0.198202			−0.0991011	−	0.995077i	$-0.531597\pi$
$809$	−5.63745			−0.198202			−0.0991011	+	0.995077i	$0.531597\pi$
$810$	−0.471131	−	3.95594i	−0.0165538	−	0.138998i
$811$	−24.3625			−0.855485			−0.427742	−	0.903901i	$-0.640691\pi$
$811$	−24.3625			−0.855485			−0.427742	+	0.903901i	$0.640691\pi$
$812$		0			0
$813$			5.46935i			0.191818i
$814$	−13.0173			−0.456256
$815$	0.556231	+	4.67050i	0.0194839	+	0.163601i
$816$	−10.5864			−0.370600
$817$			38.6135i			1.35092i
$818$		−	18.7585i		−	0.655876i
$819$		0			0
$820$	−20.8338	+	2.48119i	−0.727549	+	0.0866471i
$821$	−31.7462			−1.10795			−0.553974	−	0.832534i	$-0.686889\pi$
$821$	−31.7462			−1.10795			−0.553974	+	0.832534i	$0.686889\pi$
$822$		−	23.3466i		−	0.814307i
$823$		−	3.97563i		−	0.138582i	−0.997597	−	0.0692908i	$-0.977926\pi$
$823$		−	3.97563i		−	0.138582i	0.997597	−	0.0692908i	$-0.0220736\pi$
$824$	−25.1366			−0.875677
$825$	−2.44075	−	10.1018i	−0.0849762	−	0.351699i
$826$		0			0
$827$		−	6.80348i		−	0.236580i	−0.992979	−	0.118290i	$-0.962259\pi$
$827$		−	6.80348i		−	0.236580i	0.992979	−	0.118290i	$-0.0377413\pi$
$828$			6.50151i			0.225943i
$829$	23.0606			0.800927			0.400463	−	0.916313i	$-0.368849\pi$
$829$	23.0606			0.800927			0.400463	+	0.916313i	$0.368849\pi$
$830$	34.6195	−	4.12300i	1.20166	−	0.143111i
$831$	29.8099			1.03410
$832$		−	1.85837i		−	0.0644273i
$833$		0			0
$834$	−0.433235			−0.0150017
$835$	0.948264	+	7.96228i	0.0328160	+	0.275546i
$836$	−18.8856			−0.653171
$837$			2.91188i			0.100649i
$838$			23.7155i			0.819239i
$839$	−35.0723			−1.21083			−0.605415	−	0.795910i	$-0.706993\pi$
$839$	−35.0723			−1.21083			−0.605415	+	0.795910i	$0.706993\pi$
$840$		0			0
$841$	−12.8904			−0.444495
$842$			34.1223i			1.17593i
$843$			7.78511i			0.268133i
$844$	−27.7357			−0.954701
$845$	−7.10887	+	0.846627i	−0.244553	+	0.0291249i
$846$	4.34858			0.149507
$847$		0			0
$848$		−	49.2583i		−	1.69154i
$849$	−2.61444			−0.0897274
$850$	18.4459	−	4.45682i	0.632689	−	0.152868i
$851$	19.4620			0.667149
$852$			17.6435i			0.604456i
$853$			12.3125i			0.421571i	0.977532	+	0.210785i	$0.0676021\pi$
$853$			12.3125i			0.421571i	−0.977532	+	0.210785i	$0.932398\pi$
$854$		0			0
$855$	−17.1804	+	2.04609i	−0.587557	+	0.0699747i
$856$	9.28360			0.317307
$857$			33.2498i			1.13579i	0.823101	+	0.567896i	$0.192242\pi$
$857$			33.2498i			1.13579i	−0.823101	+	0.567896i	$0.807758\pi$
$858$		−	11.5917i		−	0.395736i
$859$	−3.01395			−0.102834			−0.0514172	−	0.998677i	$-0.516374\pi$
$859$	−3.01395			−0.102834			−0.0514172	+	0.998677i	$0.516374\pi$
$860$	−1.54963	−	13.0117i	−0.0528418	−	0.443697i
$861$		0			0
$862$			19.4136i			0.661228i
$863$		−	22.2360i		−	0.756921i	−0.925617	−	0.378460i	$-0.876454\pi$
$863$		−	22.2360i		−	0.756921i	0.925617	−	0.378460i	$-0.123546\pi$
$864$	−5.91188			−0.201126
$865$	4.10932	+	34.5047i	0.139721	+	1.17319i
$866$	34.7190			1.17980
$867$			12.4621i			0.423236i
$868$		0			0
$869$	16.8639			0.572070
$870$	15.8779	−	1.89097i	0.538311	−	0.0641098i
$871$	−12.0182			−0.407221
$872$		−	3.59950i		−	0.121894i
$873$			0.296842i			0.0100466i
$874$	76.3253			2.58174
$875$		0			0
$876$	10.0445			0.339372
$877$			14.3221i			0.483623i	0.970323	+	0.241812i	$0.0777416\pi$
$877$			14.3221i			0.483623i	−0.970323	+	0.241812i	$0.922258\pi$
$878$			24.1075i			0.813590i
$879$	12.7559			0.430247
$880$	−22.9350	+	2.73143i	−0.773140	+	0.0920766i
$881$	−49.9929			−1.68431			−0.842153	−	0.539239i	$-0.818712\pi$
$881$	−49.9929			−1.68431			−0.842153	+	0.539239i	$0.818712\pi$
$882$		0			0
$883$			44.3095i			1.49113i	0.666432	+	0.745566i	$0.267821\pi$
$883$			44.3095i			1.49113i	−0.666432	+	0.745566i	$0.732179\pi$
$884$	7.83030			0.263361
$885$	−0.781653	−	6.56331i	−0.0262750	−	0.220623i
$886$	−51.4298			−1.72782
$887$		−	10.2985i		−	0.345790i	−0.984940	−	0.172895i	$-0.944688\pi$
$887$		−	10.2985i		−	0.345790i	0.984940	−	0.172895i	$-0.0553122\pi$
$888$			5.17130i			0.173538i
$889$		0			0
$890$	−0.291470	−	2.44739i	−0.00977010	−	0.0820366i
$891$	−2.07850			−0.0696322
$892$		−	29.5239i		−	0.988535i
$893$		−	18.8856i		−	0.631981i
$894$	4.16423			0.139273
$895$	34.9391	−	4.16105i	1.16788	−	0.139089i
$896$		0			0
$897$			17.3307i			0.578654i
$898$		−	41.7438i		−	1.39301i
$899$	−11.6874			−0.389796
$900$	5.70722	−	1.37895i	0.190241	−	0.0459652i
$901$	21.1146			0.703430
$902$			29.5896i			0.985227i
$903$		0			0
$904$	−14.9423			−0.496972
$905$	−11.0728	+	1.31871i	−0.368074	+	0.0438356i
$906$	19.8005			0.657827
$907$		−	29.4280i		−	0.977139i	−0.872525	−	0.488570i	$-0.837519\pi$
$907$		−	29.4280i		−	0.977139i	0.872525	−	0.488570i	$-0.162481\pi$
$908$		−	27.7957i		−	0.922433i
$909$	8.25879			0.273927
$910$		0			0
$911$	−24.8078			−0.821918			−0.410959	−	0.911654i	$-0.634806\pi$
$911$	−24.8078			−0.821918			−0.410959	+	0.911654i	$0.634806\pi$
$912$			38.4529i			1.27330i
$913$		−	18.1895i		−	0.601984i
$914$	53.9619			1.78490
$915$	−2.88091	−	24.1901i	−0.0952398	−	0.799700i
$916$	−0.477133			−0.0157649
$917$		0			0
$918$		−	3.79533i		−	0.125265i
$919$	−13.0093			−0.429138			−0.214569	−	0.976709i	$-0.568835\pi$
$919$	−13.0093			−0.429138			−0.214569	+	0.976709i	$0.568835\pi$
$920$	18.0849	−	2.15382i	0.596243	−	0.0710092i
$921$	−13.1919			−0.434687
$922$			12.5107i			0.412018i
$923$			47.0312i			1.54805i
$924$		0			0
$925$	−4.12785	−	17.0843i	−0.135723	−	0.561730i
$926$	−5.29729			−0.174080
$927$		−	17.0866i		−	0.561198i
$928$		−	23.7284i		−	0.778924i
$929$	24.9185			0.817549			0.408775	−	0.912635i	$-0.365956\pi$
$929$	24.9185			0.817549			0.408775	+	0.912635i	$0.365956\pi$
$930$	−11.5192	+	1.37188i	−0.377731	+	0.0449857i
$931$		0			0
$932$			8.41410i			0.275613i
$933$			14.2823i			0.467580i
$934$	−42.3230			−1.38485
$935$	−1.17083	−	9.83111i	−0.0382903	−	0.321512i
$936$	−4.60498			−0.150518
$937$			55.1260i			1.80089i	0.434973	+	0.900444i	$0.356758\pi$
$937$			55.1260i			1.80089i	−0.434973	+	0.900444i	$0.643242\pi$
$938$		0			0
$939$	−4.77143			−0.155710
$940$	0.757909	+	6.36394i	0.0247203	+	0.207569i
$941$	−13.6447			−0.444803			−0.222402	−	0.974955i	$-0.571390\pi$
$941$	−13.6447			−0.444803			−0.222402	+	0.974955i	$0.571390\pi$
$942$		−	20.1651i		−	0.657015i
$943$		−	44.2391i		−	1.44062i
$944$	−14.6899			−0.478116
$945$		0			0
$946$	−18.4802			−0.600842
$947$		−	0.893089i		−	0.0290215i	−0.999895	−	0.0145107i	$-0.995381\pi$
$947$		−	0.893089i		−	0.0290215i	0.999895	−	0.0145107i	$-0.00461907\pi$
$948$			9.52764i			0.309443i
$949$	26.7750			0.869154
$950$	−16.1884	−	67.0006i	−0.525221	−	2.17379i
$951$	18.8048			0.609787
$952$		0			0
$953$		−	34.5636i		−	1.11963i	−0.828619	−	0.559813i	$-0.810873\pi$
$953$		−	34.5636i		−	1.11963i	0.828619	−	0.559813i	$-0.189127\pi$
$954$	17.6595			0.571749
$955$	−26.2191	+	3.12255i	−0.848431	+	0.101043i
$956$	11.8511			0.383293
$957$		−	8.34242i		−	0.269672i
$958$		−	11.6595i		−	0.376703i
$959$		0			0
$960$	−0.156990	−	1.31820i	−0.00506685	−	0.0425448i
$961$	−22.5209			−0.726481
$962$		−	19.6042i		−	0.632064i
$963$			6.31052i			0.203354i
$964$	−5.40967			−0.174234
$965$	−6.54159	−	54.9278i	−0.210581	−	1.76819i
$966$		0			0
$967$			22.1811i			0.713296i	0.934239	+	0.356648i	$0.116080\pi$
$967$			22.1811i			0.713296i	−0.934239	+	0.356648i	$0.883920\pi$
$968$		−	9.82694i		−	0.315850i
$969$	−16.4829			−0.529506
$970$	−1.17429	+	0.139851i	−0.0377041	+	0.00449035i
$971$	−0.0759319			−0.00243677			−0.00121839	−	0.999999i	$-0.500388\pi$
$971$	−0.0759319			−0.00243677			−0.00121839	+	0.999999i	$0.500388\pi$
$972$		−	1.17429i		−	0.0376653i
$973$		0			0
$974$	29.0889			0.932069
$975$	15.2134	−	3.67580i	0.487218	−	0.117720i
$976$	−54.1420			−1.73304
$977$		−	43.2114i		−	1.38246i	−0.722636	−	0.691228i	$-0.757070\pi$
$977$		−	43.2114i		−	1.38246i	0.722636	−	0.691228i	$-0.242930\pi$
$978$			3.74766i			0.119837i
$979$	−1.28588			−0.0410970
$980$		0			0
$981$	2.44676			0.0781189
$982$			44.3648i			1.41574i
$983$		−	18.3208i		−	0.584343i	−0.956366	−	0.292171i	$-0.905622\pi$
$983$		−	18.3208i		−	0.584343i	0.956366	−	0.292171i	$-0.0943777\pi$
$984$	11.7549			0.374732
$985$	5.17039	+	43.4142i	0.164742	+	1.38329i
$986$	15.2333			0.485126
$987$		0			0
$988$		−	28.4418i		−	0.904855i
$989$	27.6295			0.878566
$990$	−0.979243	−	8.22241i	−0.0311224	−	0.261325i
$991$	−31.5776			−1.00310			−0.501548	−	0.865130i	$-0.667236\pi$
$991$	−31.5776			−1.00310			−0.501548	+	0.865130i	$0.667236\pi$
$992$			17.2147i			0.546568i
$993$			17.7742i			0.564046i
$994$		0			0
$995$	49.3815	−	5.88106i	1.56550	−	0.186442i
$996$	10.2765			0.325624
$997$		−	39.7315i		−	1.25831i	−0.777281	−	0.629154i	$-0.783401\pi$
$997$		−	39.7315i		−	1.25831i	0.777281	−	0.629154i	$-0.216599\pi$
$998$			21.7432i			0.688268i
$999$	−3.51519			−0.111216

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.d.e.589.7		8
3.2	odd	2		2205.2.d.o.1324.2		8
5.2	odd	4		3675.2.a.cb.1.1		4
5.3	odd	4		3675.2.a.bn.1.4		4
5.4	even	2	inner	735.2.d.e.589.2		8
7.2	even	3		735.2.q.g.214.7		16
7.3	odd	6		105.2.q.a.79.2	yes	16
7.4	even	3		735.2.q.g.79.2		16
7.5	odd	6		105.2.q.a.4.7	yes	16
7.6	odd	2		735.2.d.d.589.7		8
15.14	odd	2		2205.2.d.o.1324.7		8
21.5	even	6		315.2.bf.b.109.2		16
21.17	even	6		315.2.bf.b.289.7		16
21.20	even	2		2205.2.d.s.1324.2		8
28.3	even	6		1680.2.di.d.289.6		16
28.19	even	6		1680.2.di.d.529.2		16
35.3	even	12		525.2.i.k.226.1		8
35.4	even	6		735.2.q.g.79.7		16
35.9	even	6		735.2.q.g.214.2		16
35.12	even	12		525.2.i.h.151.4		8
35.13	even	4		3675.2.a.bp.1.4		4
35.17	even	12		525.2.i.h.226.4		8
35.19	odd	6		105.2.q.a.4.2	✓	16
35.24	odd	6		105.2.q.a.79.7	yes	16
35.27	even	4		3675.2.a.bz.1.1		4
35.33	even	12		525.2.i.k.151.1		8
35.34	odd	2		735.2.d.d.589.2		8
105.59	even	6		315.2.bf.b.289.2		16
105.89	even	6		315.2.bf.b.109.7		16
105.104	even	2		2205.2.d.s.1324.7		8
140.19	even	6		1680.2.di.d.529.6		16
140.59	even	6		1680.2.di.d.289.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.q.a.4.2	✓	16	35.19	odd	6
105.2.q.a.4.7	yes	16	7.5	odd	6
105.2.q.a.79.2	yes	16	7.3	odd	6
105.2.q.a.79.7	yes	16	35.24	odd	6
315.2.bf.b.109.2		16	21.5	even	6
315.2.bf.b.109.7		16	105.89	even	6
315.2.bf.b.289.2		16	105.59	even	6
315.2.bf.b.289.7		16	21.17	even	6
525.2.i.h.151.4		8	35.12	even	12
525.2.i.h.226.4		8	35.17	even	12
525.2.i.k.151.1		8	35.33	even	12
525.2.i.k.226.1		8	35.3	even	12
735.2.d.d.589.2		8	35.34	odd	2
735.2.d.d.589.7		8	7.6	odd	2
735.2.d.e.589.2		8	5.4	even	2	inner
735.2.d.e.589.7		8	1.1	even	1	trivial
735.2.q.g.79.2		16	7.4	even	3
735.2.q.g.79.7		16	35.4	even	6
735.2.q.g.214.2		16	35.9	even	6
735.2.q.g.214.7		16	7.2	even	3
1680.2.di.d.289.2		16	140.59	even	6
1680.2.di.d.289.6		16	28.3	even	6
1680.2.di.d.529.2		16	28.19	even	6
1680.2.di.d.529.6		16	140.19	even	6
2205.2.d.o.1324.2		8	3.2	odd	2
2205.2.d.o.1324.7		8	15.14	odd	2
2205.2.d.s.1324.2		8	21.20	even	2
2205.2.d.s.1324.7		8	105.104	even	2
3675.2.a.bn.1.4		4	5.3	odd	4
3675.2.a.bp.1.4		4	35.13	even	4
3675.2.a.bz.1.1		4	35.27	even	4
3675.2.a.cb.1.1		4	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.78165i q^{2} +1.00000i q^{3} -1.17429 q^{4} +(-2.22038 + 0.264435i) q^{5} -1.78165 q^{6} +1.47113i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.78165i q^{2} +1.00000i q^{3} -1.17429 q^{4} +(-2.22038 + 0.264435i) q^{5} -1.78165 q^{6} +1.47113i q^{8} -1.00000 q^{9} +(-0.471131 - 3.95594i) q^{10} -2.07850 q^{11} -1.17429i q^{12} -3.13023i q^{13} +(-0.264435 - 2.22038i) q^{15} -4.96962 q^{16} -2.13023i q^{17} -1.78165i q^{18} -7.73760 q^{19} +(2.60736 - 0.310523i) q^{20} -3.70316i q^{22} +5.53655i q^{23} -1.47113 q^{24} +(4.86015 - 1.17429i) q^{25} +5.57699 q^{26} -1.00000i q^{27} +4.01368 q^{29} +(3.95594 - 0.471131i) q^{30} -2.91188 q^{31} -5.91188i q^{32} -2.07850i q^{33} +3.79533 q^{34} +1.17429 q^{36} -3.51519i q^{37} -13.7857i q^{38} +3.13023 q^{39} +(-0.389018 - 3.26647i) q^{40} -7.99038 q^{41} -4.99038i q^{43} +2.44075 q^{44} +(2.22038 - 0.264435i) q^{45} -9.86421 q^{46} +2.44075i q^{47} -4.96962i q^{48} +(2.09218 + 8.65910i) q^{50} +2.13023 q^{51} +3.67580i q^{52} +9.91188i q^{53} +1.78165 q^{54} +(4.61504 - 0.549626i) q^{55} -7.73760i q^{57} +7.15099i q^{58} +2.95594 q^{59} +(0.310523 + 2.60736i) q^{60} +10.8946 q^{61} -5.18797i q^{62} +0.593684 q^{64} +(0.827742 + 6.95029i) q^{65} +3.70316 q^{66} -3.83939i q^{67} +2.50151i q^{68} -5.53655 q^{69} -15.0248 q^{71} -1.47113i q^{72} +8.55369i q^{73} +6.26285 q^{74} +(1.17429 + 4.86015i) q^{75} +9.08617 q^{76} +5.57699i q^{78} -8.11354 q^{79} +(11.0344 - 1.31414i) q^{80} +1.00000 q^{81} -14.2361i q^{82} +8.75128i q^{83} +(0.563307 + 4.72992i) q^{85} +8.89113 q^{86} +4.01368i q^{87} -3.05774i q^{88} +0.618661 q^{89} +(0.471131 + 3.95594i) q^{90} -6.50151i q^{92} -2.91188i q^{93} -4.34858 q^{94} +(17.1804 - 2.04609i) q^{95} +5.91188 q^{96} -0.296842i q^{97} +2.07850 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 2 q^{5} + 4 q^{6} - 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 + 2 * q^5 + 4 * q^6 - 8 * q^9	\( 8 q - 8 q^{4} + 2 q^{5} + 4 q^{6} - 8 q^{9} - 4 q^{10} - 2 q^{15} - 24 q^{19} + 4 q^{20} - 12 q^{24} + 4 q^{25} - 12 q^{26} + 12 q^{29} + 12 q^{30} + 16 q^{31} - 8 q^{34} + 8 q^{36} + 4 q^{39} + 32 q^{40} - 8 q^{41} - 20 q^{44} - 2 q^{45} + 32 q^{46} - 20 q^{50} - 4 q^{51} - 4 q^{54} - 4 q^{55} + 4 q^{59} - 16 q^{60} + 16 q^{61} + 8 q^{64} - 30 q^{65} + 28 q^{66} - 20 q^{69} - 28 q^{71} - 40 q^{74} + 8 q^{75} + 32 q^{76} + 16 q^{79} + 52 q^{80} + 8 q^{81} - 32 q^{85} + 48 q^{86} + 16 q^{89} + 4 q^{90} - 32 q^{94} + 22 q^{95} + 8 q^{96}+O(q^{100}) \) 8 * q - 8 * q^4 + 2 * q^5 + 4 * q^6 - 8 * q^9 - 4 * q^10 - 2 * q^15 - 24 * q^19 + 4 * q^20 - 12 * q^24 + 4 * q^25 - 12 * q^26 + 12 * q^29 + 12 * q^30 + 16 * q^31 - 8 * q^34 + 8 * q^36 + 4 * q^39 + 32 * q^40 - 8 * q^41 - 20 * q^44 - 2 * q^45 + 32 * q^46 - 20 * q^50 - 4 * q^51 - 4 * q^54 - 4 * q^55 + 4 * q^59 - 16 * q^60 + 16 * q^61 + 8 * q^64 - 30 * q^65 + 28 * q^66 - 20 * q^69 - 28 * q^71 - 40 * q^74 + 8 * q^75 + 32 * q^76 + 16 * q^79 + 52 * q^80 + 8 * q^81 - 32 * q^85 + 48 * q^86 + 16 * q^89 + 4 * q^90 - 32 * q^94 + 22 * q^95 + 8 * q^96

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