LMFDB - Embedded newform 70.2.c.a.29.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [70,2,Mod(29,70)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(70, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("70.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	70.c (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:	$0.558952814149$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.4
Root			$1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	70.29
Dual form			70.2.c.a.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +2.44949i q^{3} -1.00000 q^{4} +(-0.224745 - 2.22474i) q^{5} -2.44949 q^{6} +1.00000i q^{7} -1.00000i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +2.44949i q^{3} -1.00000 q^{4} +(-0.224745 - 2.22474i) q^{5} -2.44949 q^{6} +1.00000i q^{7} -1.00000i q^{8} -3.00000 q^{9} +(2.22474 - 0.224745i) q^{10} +4.89898 q^{11} -2.44949i q^{12} -0.449490i q^{13} -1.00000 q^{14} +(5.44949 - 0.550510i) q^{15} +1.00000 q^{16} -2.00000i q^{17} -3.00000i q^{18} -6.44949 q^{19} +(0.224745 + 2.22474i) q^{20} -2.44949 q^{21} +4.89898i q^{22} -6.89898i q^{23} +2.44949 q^{24} +(-4.89898 + 1.00000i) q^{25} +0.449490 q^{26} -1.00000i q^{28} +2.89898 q^{29} +(0.550510 + 5.44949i) q^{30} -0.898979 q^{31} +1.00000i q^{32} +12.0000i q^{33} +2.00000 q^{34} +(2.22474 - 0.224745i) q^{35} +3.00000 q^{36} -2.00000i q^{37} -6.44949i q^{38} +1.10102 q^{39} +(-2.22474 + 0.224745i) q^{40} -10.8990 q^{41} -2.44949i q^{42} +8.89898i q^{43} -4.89898 q^{44} +(0.674235 + 6.67423i) q^{45} +6.89898 q^{46} +0.898979i q^{47} +2.44949i q^{48} -1.00000 q^{49} +(-1.00000 - 4.89898i) q^{50} +4.89898 q^{51} +0.449490i q^{52} -1.10102i q^{53} +(-1.10102 - 10.8990i) q^{55} +1.00000 q^{56} -15.7980i q^{57} +2.89898i q^{58} +6.44949 q^{59} +(-5.44949 + 0.550510i) q^{60} +8.44949 q^{61} -0.898979i q^{62} -3.00000i q^{63} -1.00000 q^{64} +(-1.00000 + 0.101021i) q^{65} -12.0000 q^{66} +8.00000i q^{67} +2.00000i q^{68} +16.8990 q^{69} +(0.224745 + 2.22474i) q^{70} -10.8990 q^{71} +3.00000i q^{72} -6.89898i q^{73} +2.00000 q^{74} +(-2.44949 - 12.0000i) q^{75} +6.44949 q^{76} +4.89898i q^{77} +1.10102i q^{78} +2.89898 q^{79} +(-0.224745 - 2.22474i) q^{80} -9.00000 q^{81} -10.8990i q^{82} +2.44949i q^{83} +2.44949 q^{84} +(-4.44949 + 0.449490i) q^{85} -8.89898 q^{86} +7.10102i q^{87} -4.89898i q^{88} +10.0000 q^{89} +(-6.67423 + 0.674235i) q^{90} +0.449490 q^{91} +6.89898i q^{92} -2.20204i q^{93} -0.898979 q^{94} +(1.44949 + 14.3485i) q^{95} -2.44949 q^{96} +3.79796i q^{97} -1.00000i q^{98} -14.6969 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 4 q^{5} - 12 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 + 4 * q^5 - 12 * q^9	$ 4 q - 4 q^{4} + 4 q^{5} - 12 q^{9} + 4 q^{10} - 4 q^{14} + 12 q^{15} + 4 q^{16} - 16 q^{19} - 4 q^{20} - 8 q^{26} - 8 q^{29} + 12 q^{30} + 16 q^{31} + 8 q^{34} + 4 q^{35} + 12 q^{36} + 24 q^{39} - 4 q^{40} - 24 q^{41} - 12 q^{45} + 8 q^{46} - 4 q^{49} - 4 q^{50} - 24 q^{55} + 4 q^{56} + 16 q^{59} - 12 q^{60} + 24 q^{61} - 4 q^{64} - 4 q^{65} - 48 q^{66} + 48 q^{69} - 4 q^{70} - 24 q^{71} + 8 q^{74} + 16 q^{76} - 8 q^{79} + 4 q^{80} - 36 q^{81} - 8 q^{85} - 16 q^{86} + 40 q^{89} - 12 q^{90} - 8 q^{91} + 16 q^{94} - 4 q^{95}+O(q^{100}) $ 4 * q - 4 * q^4 + 4 * q^5 - 12 * q^9 + 4 * q^10 - 4 * q^14 + 12 * q^15 + 4 * q^16 - 16 * q^19 - 4 * q^20 - 8 * q^26 - 8 * q^29 + 12 * q^30 + 16 * q^31 + 8 * q^34 + 4 * q^35 + 12 * q^36 + 24 * q^39 - 4 * q^40 - 24 * q^41 - 12 * q^45 + 8 * q^46 - 4 * q^49 - 4 * q^50 - 24 * q^55 + 4 * q^56 + 16 * q^59 - 12 * q^60 + 24 * q^61 - 4 * q^64 - 4 * q^65 - 48 * q^66 + 48 * q^69 - 4 * q^70 - 24 * q^71 + 8 * q^74 + 16 * q^76 - 8 * q^79 + 4 * q^80 - 36 * q^81 - 8 * q^85 - 16 * q^86 + 40 * q^89 - 12 * q^90 - 8 * q^91 + 16 * q^94 - 4 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$.

$n$	$31$	$57$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$			2.44949i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$3$			2.44949i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$4$	−1.00000			−0.500000
$5$	−0.224745	−	2.22474i	−0.100509	−	0.994936i
$5$	−0.224745	−	2.22474i	−0.100509	−	0.994936i
$6$	−2.44949			−1.00000
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$		−	1.00000i		−	0.353553i
$9$	−3.00000			−1.00000
$10$	2.22474	−	0.224745i	0.703526	−	0.0710706i
$11$	4.89898			1.47710			0.738549	−	0.674200i	$-0.235511\pi$
$11$	4.89898			1.47710			0.738549	+	0.674200i	$0.235511\pi$
$12$		−	2.44949i		−	0.707107i
$13$		−	0.449490i		−	0.124666i	−0.998055	−	0.0623330i	$-0.980146\pi$
$13$		−	0.449490i		−	0.124666i	0.998055	−	0.0623330i	$-0.0198541\pi$
$14$	−1.00000			−0.267261
$15$	5.44949	−	0.550510i	1.40705	−	0.142141i
$16$	1.00000			0.250000
$17$		−	2.00000i		−	0.485071i	−0.970143	−	0.242536i	$-0.922021\pi$
$17$		−	2.00000i		−	0.485071i	0.970143	−	0.242536i	$-0.0779791\pi$
$18$		−	3.00000i		−	0.707107i
$19$	−6.44949			−1.47961			−0.739807	−	0.672819i	$-0.765083\pi$
$19$	−6.44949			−1.47961			−0.739807	+	0.672819i	$0.765083\pi$
$20$	0.224745	+	2.22474i	0.0502545	+	0.497468i
$21$	−2.44949			−0.534522
$22$			4.89898i			1.04447i
$23$		−	6.89898i		−	1.43854i	−0.694732	−	0.719268i	$-0.744477\pi$
$23$		−	6.89898i		−	1.43854i	0.694732	−	0.719268i	$-0.255523\pi$
$24$	2.44949			0.500000
$25$	−4.89898	+	1.00000i	−0.979796	+	0.200000i
$26$	0.449490			0.0881522
$27$		0			0
$28$		−	1.00000i		−	0.188982i
$29$	2.89898			0.538327			0.269163	−	0.963095i	$-0.413253\pi$
$29$	2.89898			0.538327			0.269163	+	0.963095i	$0.413253\pi$
$30$	0.550510	+	5.44949i	0.100509	+	0.994936i
$31$	−0.898979			−0.161461			−0.0807307	−	0.996736i	$-0.525725\pi$
$31$	−0.898979			−0.161461			−0.0807307	+	0.996736i	$0.525725\pi$
$32$			1.00000i			0.176777i
$33$			12.0000i			2.08893i
$34$	2.00000			0.342997
$35$	2.22474	−	0.224745i	0.376051	−	0.0379888i
$36$	3.00000			0.500000
$37$		−	2.00000i		−	0.328798i	−0.986394	−	0.164399i	$-0.947432\pi$
$37$		−	2.00000i		−	0.328798i	0.986394	−	0.164399i	$-0.0525685\pi$
$38$		−	6.44949i		−	1.04625i
$39$	1.10102			0.176304
$40$	−2.22474	+	0.224745i	−0.351763	+	0.0355353i
$41$	−10.8990			−1.70213			−0.851067	−	0.525057i	$-0.824044\pi$
$41$	−10.8990			−1.70213			−0.851067	+	0.525057i	$0.824044\pi$
$42$		−	2.44949i		−	0.377964i
$43$			8.89898i			1.35708i	0.734563	+	0.678541i	$0.237387\pi$
$43$			8.89898i			1.35708i	−0.734563	+	0.678541i	$0.762613\pi$
$44$	−4.89898			−0.738549
$45$	0.674235	+	6.67423i	0.100509	+	0.994936i
$46$	6.89898			1.01720
$47$			0.898979i			0.131130i	0.997848	+	0.0655648i	$0.0208849\pi$
$47$			0.898979i			0.131130i	−0.997848	+	0.0655648i	$0.979115\pi$
$48$			2.44949i			0.353553i
$49$	−1.00000			−0.142857
$50$	−1.00000	−	4.89898i	−0.141421	−	0.692820i
$51$	4.89898			0.685994
$52$			0.449490i			0.0623330i
$53$		−	1.10102i		−	0.151237i	−0.997137	−	0.0756184i	$-0.975907\pi$
$53$		−	1.10102i		−	0.151237i	0.997137	−	0.0756184i	$-0.0240931\pi$
$54$		0			0
$55$	−1.10102	−	10.8990i	−0.148462	−	1.46962i
$56$	1.00000			0.133631
$57$		−	15.7980i		−	2.09249i
$58$			2.89898i			0.380655i
$59$	6.44949			0.839652			0.419826	−	0.907605i	$-0.362091\pi$
$59$	6.44949			0.839652			0.419826	+	0.907605i	$0.362091\pi$
$60$	−5.44949	+	0.550510i	−0.703526	+	0.0710706i
$61$	8.44949			1.08185			0.540923	−	0.841072i	$-0.318075\pi$
$61$	8.44949			1.08185			0.540923	+	0.841072i	$0.318075\pi$
$62$		−	0.898979i		−	0.114171i
$63$		−	3.00000i		−	0.377964i
$64$	−1.00000			−0.125000
$65$	−1.00000	+	0.101021i	−0.124035	+	0.0125301i
$66$	−12.0000			−1.47710
$67$			8.00000i			0.977356i	0.872464	+	0.488678i	$0.162521\pi$
$67$			8.00000i			0.977356i	−0.872464	+	0.488678i	$0.837479\pi$
$68$			2.00000i			0.242536i
$69$	16.8990			2.03440
$70$	0.224745	+	2.22474i	0.0268622	+	0.265908i
$71$	−10.8990			−1.29347			−0.646735	−	0.762714i	$-0.723866\pi$
$71$	−10.8990			−1.29347			−0.646735	+	0.762714i	$0.723866\pi$
$72$			3.00000i			0.353553i
$73$		−	6.89898i		−	0.807464i	−0.914877	−	0.403732i	$-0.867713\pi$
$73$		−	6.89898i		−	0.807464i	0.914877	−	0.403732i	$-0.132287\pi$
$74$	2.00000			0.232495
$75$	−2.44949	−	12.0000i	−0.282843	−	1.38564i
$76$	6.44949			0.739807
$77$			4.89898i			0.558291i
$78$			1.10102i			0.124666i
$79$	2.89898			0.326161			0.163080	−	0.986613i	$-0.447857\pi$
$79$	2.89898			0.326161			0.163080	+	0.986613i	$0.447857\pi$
$80$	−0.224745	−	2.22474i	−0.0251272	−	0.248734i
$81$	−9.00000			−1.00000
$82$		−	10.8990i		−	1.20359i
$83$			2.44949i			0.268866i	0.990923	+	0.134433i	$0.0429214\pi$
$83$			2.44949i			0.268866i	−0.990923	+	0.134433i	$0.957079\pi$
$84$	2.44949			0.267261
$85$	−4.44949	+	0.449490i	−0.482615	+	0.0487540i
$86$	−8.89898			−0.959602
$87$			7.10102i			0.761309i
$88$		−	4.89898i		−	0.522233i
$89$	10.0000			1.06000			0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000			1.06000			0.529999	+	0.847998i	$0.322192\pi$
$90$	−6.67423	+	0.674235i	−0.703526	+	0.0710706i
$91$	0.449490			0.0471193
$92$			6.89898i			0.719268i
$93$		−	2.20204i		−	0.228341i
$94$	−0.898979			−0.0927227
$95$	1.44949	+	14.3485i	0.148715	+	1.47212i
$96$	−2.44949			−0.250000
$97$			3.79796i			0.385624i	0.981236	+	0.192812i	$0.0617608\pi$
$97$			3.79796i			0.385624i	−0.981236	+	0.192812i	$0.938239\pi$
$98$		−	1.00000i		−	0.101015i
$99$	−14.6969			−1.47710
$100$	4.89898	−	1.00000i	0.489898	−	0.100000i
$101$	8.44949			0.840756			0.420378	−	0.907349i	$-0.361898\pi$
$101$	8.44949			0.840756			0.420378	+	0.907349i	$0.361898\pi$
$102$			4.89898i			0.485071i
$103$			3.10102i			0.305553i	0.988261	+	0.152776i	$0.0488214\pi$
$103$			3.10102i			0.305553i	−0.988261	+	0.152776i	$0.951179\pi$
$104$	−0.449490			−0.0440761
$105$	0.550510	+	5.44949i	0.0537243	+	0.531816i
$106$	1.10102			0.106941
$107$			8.00000i			0.773389i	0.922208	+	0.386695i	$0.126383\pi$
$107$			8.00000i			0.773389i	−0.922208	+	0.386695i	$0.873617\pi$
$108$		0			0
$109$	2.89898			0.277672			0.138836	−	0.990315i	$-0.455664\pi$
$109$	2.89898			0.277672			0.138836	+	0.990315i	$0.455664\pi$
$110$	10.8990	−	1.10102i	1.03918	−	0.104978i
$111$	4.89898			0.464991
$112$			1.00000i			0.0944911i
$113$			0.202041i			0.0190064i	0.999955	+	0.00950321i	$0.00302501\pi$
$113$			0.202041i			0.0190064i	−0.999955	+	0.00950321i	$0.996975\pi$
$114$	15.7980			1.47961
$115$	−15.3485	+	1.55051i	−1.43125	+	0.144586i
$116$	−2.89898			−0.269163
$117$			1.34847i			0.124666i
$118$			6.44949i			0.593724i
$119$	2.00000			0.183340
$120$	−0.550510	−	5.44949i	−0.0502545	−	0.497468i
$121$	13.0000			1.18182
$122$			8.44949i			0.764981i
$123$		−	26.6969i		−	2.40718i
$124$	0.898979			0.0807307
$125$	3.32577	+	10.6742i	0.297465	+	0.954733i
$126$	3.00000			0.267261
$127$			5.10102i			0.452642i	0.974053	+	0.226321i	$0.0726699\pi$
$127$			5.10102i			0.452642i	−0.974053	+	0.226321i	$0.927330\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−21.7980			−1.91920
$130$	−0.101021	−	1.00000i	−0.00886009	−	0.0877058i
$131$	−1.55051			−0.135469			−0.0677344	−	0.997703i	$-0.521577\pi$
$131$	−1.55051			−0.135469			−0.0677344	+	0.997703i	$0.521577\pi$
$132$		−	12.0000i		−	1.04447i
$133$		−	6.44949i		−	0.559242i
$134$	−8.00000			−0.691095
$135$		0			0
$136$	−2.00000			−0.171499
$137$		−	17.7980i		−	1.52058i	−0.649582	−	0.760291i	$-0.725056\pi$
$137$		−	17.7980i		−	1.52058i	0.649582	−	0.760291i	$-0.274944\pi$
$138$			16.8990i			1.43854i
$139$	−6.44949			−0.547039			−0.273519	−	0.961867i	$-0.588188\pi$
$139$	−6.44949			−0.547039			−0.273519	+	0.961867i	$0.588188\pi$
$140$	−2.22474	+	0.224745i	−0.188025	+	0.0189944i
$141$	−2.20204			−0.185445
$142$		−	10.8990i		−	0.914622i
$143$		−	2.20204i		−	0.184144i
$144$	−3.00000			−0.250000
$145$	−0.651531	−	6.44949i	−0.0541067	−	0.535601i
$146$	6.89898			0.570964
$147$		−	2.44949i		−	0.202031i
$148$			2.00000i			0.164399i
$149$	−15.7980			−1.29422			−0.647110	−	0.762397i	$-0.724022\pi$
$149$	−15.7980			−1.29422			−0.647110	+	0.762397i	$0.724022\pi$
$150$	12.0000	−	2.44949i	0.979796	−	0.200000i
$151$	−19.5959			−1.59469			−0.797347	−	0.603522i	$-0.793764\pi$
$151$	−19.5959			−1.59469			−0.797347	+	0.603522i	$0.793764\pi$
$152$			6.44949i			0.523123i
$153$			6.00000i			0.485071i
$154$	−4.89898			−0.394771
$155$	0.202041	+	2.00000i	0.0162283	+	0.160644i
$156$	−1.10102			−0.0881522
$157$		−	8.44949i		−	0.674343i	−0.941443	−	0.337171i	$-0.890530\pi$
$157$		−	8.44949i		−	0.674343i	0.941443	−	0.337171i	$-0.109470\pi$
$158$			2.89898i			0.230630i
$159$	2.69694			0.213881
$160$	2.22474	−	0.224745i	0.175882	−	0.0177676i
$161$	6.89898			0.543716
$162$		−	9.00000i		−	0.707107i
$163$		−	16.8990i		−	1.32363i	−0.749667	−	0.661815i	$-0.769786\pi$
$163$		−	16.8990i		−	1.32363i	0.749667	−	0.661815i	$-0.230214\pi$
$164$	10.8990			0.851067
$165$	26.6969	−	2.69694i	2.07835	−	0.209956i
$166$	−2.44949			−0.190117
$167$		−	4.89898i		−	0.379094i	−0.981872	−	0.189547i	$-0.939298\pi$
$167$		−	4.89898i		−	0.379094i	0.981872	−	0.189547i	$-0.0607020\pi$
$168$			2.44949i			0.188982i
$169$	12.7980			0.984458
$170$	−0.449490	−	4.44949i	−0.0344743	−	0.341260i
$171$	19.3485			1.47961
$172$		−	8.89898i		−	0.678541i
$173$			18.2474i			1.38733i	0.720299	+	0.693664i	$0.244005\pi$
$173$			18.2474i			1.38733i	−0.720299	+	0.693664i	$0.755995\pi$
$174$	−7.10102			−0.538327
$175$	−1.00000	−	4.89898i	−0.0755929	−	0.370328i
$176$	4.89898			0.369274
$177$			15.7980i			1.18745i
$178$			10.0000i			0.749532i
$179$	5.79796			0.433360			0.216680	−	0.976243i	$-0.430477\pi$
$179$	5.79796			0.433360			0.216680	+	0.976243i	$0.430477\pi$
$180$	−0.674235	−	6.67423i	−0.0502545	−	0.497468i
$181$	14.2474			1.05900			0.529502	−	0.848309i	$-0.322379\pi$
$181$	14.2474			1.05900			0.529502	+	0.848309i	$0.322379\pi$
$182$			0.449490i			0.0333184i
$183$			20.6969i			1.52996i
$184$	−6.89898			−0.508600
$185$	−4.44949	+	0.449490i	−0.327133	+	0.0330471i
$186$	2.20204			0.161461
$187$		−	9.79796i		−	0.716498i
$188$		−	0.898979i		−	0.0655648i
$189$		0			0
$190$	−14.3485	+	1.44949i	−1.04095	+	0.105157i
$191$	−16.6969			−1.20815			−0.604074	−	0.796928i	$-0.706457\pi$
$191$	−16.6969			−1.20815			−0.604074	+	0.796928i	$0.706457\pi$
$192$		−	2.44949i		−	0.176777i
$193$			17.5959i			1.26658i	0.773914	+	0.633291i	$0.218296\pi$
$193$			17.5959i			1.26658i	−0.773914	+	0.633291i	$0.781704\pi$
$194$	−3.79796			−0.272678
$195$	−0.247449	−	2.44949i	−0.0177202	−	0.175412i
$196$	1.00000			0.0714286
$197$		−	9.10102i		−	0.648421i	−0.945985	−	0.324210i	$-0.894901\pi$
$197$		−	9.10102i		−	0.648421i	0.945985	−	0.324210i	$-0.105099\pi$
$198$		−	14.6969i		−	1.04447i
$199$	−7.10102			−0.503378			−0.251689	−	0.967808i	$-0.580986\pi$
$199$	−7.10102			−0.503378			−0.251689	+	0.967808i	$0.580986\pi$
$200$	1.00000	+	4.89898i	0.0707107	+	0.346410i
$201$	−19.5959			−1.38219
$202$			8.44949i			0.594504i
$203$			2.89898i			0.203468i
$204$	−4.89898			−0.342997
$205$	2.44949	+	24.2474i	0.171080	+	1.69352i
$206$	−3.10102			−0.216058
$207$			20.6969i			1.43854i
$208$		−	0.449490i		−	0.0311665i
$209$	−31.5959			−2.18554
$210$	−5.44949	+	0.550510i	−0.376051	+	0.0379888i
$211$	12.0000			0.826114			0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000			0.826114			0.413057	+	0.910705i	$0.364461\pi$
$212$			1.10102i			0.0756184i
$213$		−	26.6969i		−	1.82924i
$214$	−8.00000			−0.546869
$215$	19.7980	−	2.00000i	1.35021	−	0.136399i
$216$		0			0
$217$		−	0.898979i		−	0.0610267i
$218$			2.89898i			0.196344i
$219$	16.8990			1.14193
$220$	1.10102	+	10.8990i	0.0742308	+	0.734809i
$221$	−0.898979			−0.0604719
$222$			4.89898i			0.328798i
$223$		−	4.00000i		−	0.267860i	−0.990991	−	0.133930i	$-0.957240\pi$
$223$		−	4.00000i		−	0.267860i	0.990991	−	0.133930i	$-0.0427597\pi$
$224$	−1.00000			−0.0668153
$225$	14.6969	−	3.00000i	0.979796	−	0.200000i
$226$	−0.202041			−0.0134396
$227$			7.34847i			0.487735i	0.969809	+	0.243868i	$0.0784162\pi$
$227$			7.34847i			0.487735i	−0.969809	+	0.243868i	$0.921584\pi$
$228$			15.7980i			1.04625i
$229$	−15.1464			−1.00090			−0.500452	−	0.865764i	$-0.666833\pi$
$229$	−15.1464			−1.00090			−0.500452	+	0.865764i	$0.666833\pi$
$230$	−1.55051	−	15.3485i	−0.102238	−	1.01205i
$231$	−12.0000			−0.789542
$232$		−	2.89898i		−	0.190327i
$233$			10.2020i			0.668358i	0.942510	+	0.334179i	$0.108459\pi$
$233$			10.2020i			0.668358i	−0.942510	+	0.334179i	$0.891541\pi$
$234$	−1.34847			−0.0881522
$235$	2.00000	−	0.202041i	0.130466	−	0.0131797i
$236$	−6.44949			−0.419826
$237$			7.10102i			0.461261i
$238$			2.00000i			0.129641i
$239$	25.7980			1.66873			0.834366	−	0.551211i	$-0.185834\pi$
$239$	25.7980			1.66873			0.834366	+	0.551211i	$0.185834\pi$
$240$	5.44949	−	0.550510i	0.351763	−	0.0355353i
$241$	20.6969			1.33321			0.666604	−	0.745412i	$-0.267747\pi$
$241$	20.6969			1.33321			0.666604	+	0.745412i	$0.267747\pi$
$242$			13.0000i			0.835672i
$243$		−	22.0454i		−	1.41421i
$244$	−8.44949			−0.540923
$245$	0.224745	+	2.22474i	0.0143584	+	0.142134i
$246$	26.6969			1.70213
$247$			2.89898i			0.184458i
$248$			0.898979i			0.0570853i
$249$	−6.00000			−0.380235
$250$	−10.6742	+	3.32577i	−0.675098	+	0.210340i
$251$	−1.55051			−0.0978673			−0.0489337	−	0.998802i	$-0.515582\pi$
$251$	−1.55051			−0.0978673			−0.0489337	+	0.998802i	$0.515582\pi$
$252$			3.00000i			0.188982i
$253$		−	33.7980i		−	2.12486i
$254$	−5.10102			−0.320066
$255$	−1.10102	−	10.8990i	−0.0689486	−	0.682521i
$256$	1.00000			0.0625000
$257$		−	20.6969i		−	1.29104i	−0.763744	−	0.645520i	$-0.776641\pi$
$257$		−	20.6969i		−	1.29104i	0.763744	−	0.645520i	$-0.223359\pi$
$258$		−	21.7980i		−	1.35708i
$259$	2.00000			0.124274
$260$	1.00000	−	0.101021i	0.0620174	−	0.00626503i
$261$	−8.69694			−0.538327
$262$		−	1.55051i		−	0.0957908i
$263$		−	9.79796i		−	0.604168i	−0.953281	−	0.302084i	$-0.902318\pi$
$263$		−	9.79796i		−	0.604168i	0.953281	−	0.302084i	$-0.0976823\pi$
$264$	12.0000			0.738549
$265$	−2.44949	+	0.247449i	−0.150471	+	0.0152007i
$266$	6.44949			0.395444
$267$			24.4949i			1.49906i
$268$		−	8.00000i		−	0.488678i
$269$	15.1464			0.923494			0.461747	−	0.887012i	$-0.347223\pi$
$269$	15.1464			0.923494			0.461747	+	0.887012i	$0.347223\pi$
$270$		0			0
$271$	12.0000			0.728948			0.364474	−	0.931214i	$-0.381249\pi$
$271$	12.0000			0.728948			0.364474	+	0.931214i	$0.381249\pi$
$272$		−	2.00000i		−	0.121268i
$273$			1.10102i			0.0666368i
$274$	17.7980			1.07521
$275$	−24.0000	+	4.89898i	−1.44725	+	0.295420i
$276$	−16.8990			−1.01720
$277$			5.10102i			0.306491i	0.988188	+	0.153245i	$0.0489725\pi$
$277$			5.10102i			0.306491i	−0.988188	+	0.153245i	$0.951028\pi$
$278$		−	6.44949i		−	0.386815i
$279$	2.69694			0.161461
$280$	−0.224745	−	2.22474i	−0.0134311	−	0.132954i
$281$	−18.0000			−1.07379			−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000			−1.07379			−0.536895	+	0.843649i	$0.680403\pi$
$282$		−	2.20204i		−	0.131130i
$283$			28.2474i			1.67914i	0.543254	+	0.839568i	$0.317192\pi$
$283$			28.2474i			1.67914i	−0.543254	+	0.839568i	$0.682808\pi$
$284$	10.8990			0.646735
$285$	−35.1464	+	3.55051i	−2.08189	+	0.210314i
$286$	2.20204			0.130209
$287$		−	10.8990i		−	0.643346i
$288$		−	3.00000i		−	0.176777i
$289$	13.0000			0.764706
$290$	6.44949	−	0.651531i	0.378727	−	0.0382592i
$291$	−9.30306			−0.545355
$292$			6.89898i			0.403732i
$293$		−	6.24745i		−	0.364980i	−0.983208	−	0.182490i	$-0.941584\pi$
$293$		−	6.24745i		−	0.364980i	0.983208	−	0.182490i	$-0.0584157\pi$
$294$	2.44949			0.142857
$295$	−1.44949	−	14.3485i	−0.0843926	−	0.835400i
$296$	−2.00000			−0.116248
$297$		0			0
$298$		−	15.7980i		−	0.915151i
$299$	−3.10102			−0.179337
$300$	2.44949	+	12.0000i	0.141421	+	0.692820i
$301$	−8.89898			−0.512929
$302$		−	19.5959i		−	1.12762i
$303$			20.6969i			1.18901i
$304$	−6.44949			−0.369904
$305$	−1.89898	−	18.7980i	−0.108735	−	1.07637i
$306$	−6.00000			−0.342997
$307$		−	4.24745i		−	0.242415i	−0.992627	−	0.121207i	$-0.961323\pi$
$307$		−	4.24745i		−	0.242415i	0.992627	−	0.121207i	$-0.0386766\pi$
$308$		−	4.89898i		−	0.279145i
$309$	−7.59592			−0.432117
$310$	−2.00000	+	0.202041i	−0.113592	+	0.0114752i
$311$	12.0000			0.680458			0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000			0.680458			0.340229	+	0.940343i	$0.389495\pi$
$312$		−	1.10102i		−	0.0623330i
$313$			17.5959i			0.994580i	0.867584	+	0.497290i	$0.165672\pi$
$313$			17.5959i			0.994580i	−0.867584	+	0.497290i	$0.834328\pi$
$314$	8.44949			0.476832
$315$	−6.67423	+	0.674235i	−0.376051	+	0.0379888i
$316$	−2.89898			−0.163080
$317$		−	26.4949i		−	1.48810i	−0.668123	−	0.744051i	$-0.732902\pi$
$317$		−	26.4949i		−	1.48810i	0.668123	−	0.744051i	$-0.267098\pi$
$318$			2.69694i			0.151237i
$319$	14.2020			0.795162
$320$	0.224745	+	2.22474i	0.0125636	+	0.124367i
$321$	−19.5959			−1.09374
$322$			6.89898i			0.384465i
$323$			12.8990i			0.717718i
$324$	9.00000			0.500000
$325$	0.449490	+	2.20204i	0.0249332	+	0.122147i
$326$	16.8990			0.935948
$327$			7.10102i			0.392687i
$328$			10.8990i			0.601795i
$329$	−0.898979			−0.0495623
$330$	2.69694	+	26.6969i	0.148462	+	1.46962i
$331$	10.6969			0.587957			0.293978	−	0.955812i	$-0.405021\pi$
$331$	10.6969			0.587957			0.293978	+	0.955812i	$0.405021\pi$
$332$		−	2.44949i		−	0.134433i
$333$			6.00000i			0.328798i
$334$	4.89898			0.268060
$335$	17.7980	−	1.79796i	0.972406	−	0.0982330i
$336$	−2.44949			−0.133631
$337$			29.5959i			1.61219i	0.591785	+	0.806096i	$0.298424\pi$
$337$			29.5959i			1.61219i	−0.591785	+	0.806096i	$0.701576\pi$
$338$			12.7980i			0.696117i
$339$	−0.494897			−0.0268791
$340$	4.44949	−	0.449490i	0.241307	−	0.0243770i
$341$	−4.40408			−0.238494
$342$			19.3485i			1.04625i
$343$		−	1.00000i		−	0.0539949i
$344$	8.89898			0.479801
$345$	−3.79796	−	37.5959i	−0.204475	−	2.02410i
$346$	−18.2474			−0.980989
$347$		−	19.1010i		−	1.02540i	−0.858569	−	0.512698i	$-0.828646\pi$
$347$		−	19.1010i		−	1.02540i	0.858569	−	0.512698i	$-0.171354\pi$
$348$		−	7.10102i		−	0.380655i
$349$	3.55051			0.190054			0.0950272	−	0.995475i	$-0.469706\pi$
$349$	3.55051			0.190054			0.0950272	+	0.995475i	$0.469706\pi$
$350$	4.89898	−	1.00000i	0.261861	−	0.0534522i
$351$		0			0
$352$			4.89898i			0.261116i
$353$			13.1010i			0.697297i	0.937254	+	0.348648i	$0.113359\pi$
$353$			13.1010i			0.697297i	−0.937254	+	0.348648i	$0.886641\pi$
$354$	−15.7980			−0.839652
$355$	2.44949	+	24.2474i	0.130005	+	1.28692i
$356$	−10.0000			−0.529999
$357$			4.89898i			0.259281i
$358$			5.79796i			0.306432i
$359$	−11.5959			−0.612009			−0.306005	−	0.952030i	$-0.598992\pi$
$359$	−11.5959			−0.612009			−0.306005	+	0.952030i	$0.598992\pi$
$360$	6.67423	−	0.674235i	0.351763	−	0.0355353i
$361$	22.5959			1.18926
$362$			14.2474i			0.748829i
$363$			31.8434i			1.67134i
$364$	−0.449490			−0.0235597
$365$	−15.3485	+	1.55051i	−0.803376	+	0.0811574i
$366$	−20.6969			−1.08185
$367$		−	32.0000i		−	1.67039i	−0.549957	−	0.835193i	$-0.685356\pi$
$367$		−	32.0000i		−	1.67039i	0.549957	−	0.835193i	$-0.314644\pi$
$368$		−	6.89898i		−	0.359634i
$369$	32.6969			1.70213
$370$	−0.449490	−	4.44949i	−0.0233679	−	0.231318i
$371$	1.10102			0.0571621
$372$			2.20204i			0.114171i
$373$			24.6969i			1.27876i	0.768891	+	0.639380i	$0.220809\pi$
$373$			24.6969i			1.27876i	−0.768891	+	0.639380i	$0.779191\pi$
$374$	9.79796			0.506640
$375$	−26.1464	+	8.14643i	−1.35020	+	0.420680i
$376$	0.898979			0.0463613
$377$		−	1.30306i		−	0.0671111i
$378$		0			0
$379$	−1.30306			−0.0669338			−0.0334669	−	0.999440i	$-0.510655\pi$
$379$	−1.30306			−0.0669338			−0.0334669	+	0.999440i	$0.510655\pi$
$380$	−1.44949	−	14.3485i	−0.0743573	−	0.736061i
$381$	−12.4949			−0.640133
$382$		−	16.6969i		−	0.854290i
$383$		−	16.8990i		−	0.863498i	−0.901994	−	0.431749i	$-0.857897\pi$
$383$		−	16.8990i		−	0.863498i	0.901994	−	0.431749i	$-0.142103\pi$
$384$	2.44949			0.125000
$385$	10.8990	−	1.10102i	0.555463	−	0.0561132i
$386$	−17.5959			−0.895609
$387$		−	26.6969i		−	1.35708i
$388$		−	3.79796i		−	0.192812i
$389$	−22.8990			−1.16102			−0.580512	−	0.814252i	$-0.697148\pi$
$389$	−22.8990			−1.16102			−0.580512	+	0.814252i	$0.697148\pi$
$390$	2.44949	−	0.247449i	0.124035	−	0.0125301i
$391$	−13.7980			−0.697793
$392$			1.00000i			0.0505076i
$393$		−	3.79796i		−	0.191582i
$394$	9.10102			0.458503
$395$	−0.651531	−	6.44949i	−0.0327821	−	0.324509i
$396$	14.6969			0.738549
$397$			17.3485i			0.870695i	0.900263	+	0.435347i	$0.143374\pi$
$397$			17.3485i			0.870695i	−0.900263	+	0.435347i	$0.856626\pi$
$398$		−	7.10102i		−	0.355942i
$399$	15.7980			0.790887
$400$	−4.89898	+	1.00000i	−0.244949	+	0.0500000i
$401$	29.3939			1.46786			0.733930	−	0.679225i	$-0.237684\pi$
$401$	29.3939			1.46786			0.733930	+	0.679225i	$0.237684\pi$
$402$		−	19.5959i		−	0.977356i
$403$			0.404082i			0.0201288i
$404$	−8.44949			−0.420378
$405$	2.02270	+	20.0227i	0.100509	+	0.994936i
$406$	−2.89898			−0.143874
$407$		−	9.79796i		−	0.485667i
$408$		−	4.89898i		−	0.242536i
$409$	14.4949			0.716727			0.358363	−	0.933582i	$-0.383335\pi$
$409$	14.4949			0.716727			0.358363	+	0.933582i	$0.383335\pi$
$410$	−24.2474	+	2.44949i	−1.19750	+	0.120972i
$411$	43.5959			2.15043
$412$		−	3.10102i		−	0.152776i
$413$			6.44949i			0.317359i
$414$	−20.6969			−1.01720
$415$	5.44949	−	0.550510i	0.267505	−	0.0270235i
$416$	0.449490			0.0220380
$417$		−	15.7980i		−	0.773629i
$418$		−	31.5959i		−	1.54541i
$419$	6.44949			0.315078			0.157539	−	0.987513i	$-0.449644\pi$
$419$	6.44949			0.315078			0.157539	+	0.987513i	$0.449644\pi$
$420$	−0.550510	−	5.44949i	−0.0268622	−	0.265908i
$421$	−23.7980			−1.15984			−0.579921	−	0.814673i	$-0.696917\pi$
$421$	−23.7980			−1.15984			−0.579921	+	0.814673i	$0.696917\pi$
$422$			12.0000i			0.584151i
$423$		−	2.69694i		−	0.131130i
$424$	−1.10102			−0.0534703
$425$	2.00000	+	9.79796i	0.0970143	+	0.475271i
$426$	26.6969			1.29347
$427$			8.44949i			0.408899i
$428$		−	8.00000i		−	0.386695i
$429$	5.39388			0.260419
$430$	2.00000	+	19.7980i	0.0964486	+	0.954742i
$431$	17.7980			0.857298			0.428649	−	0.903471i	$-0.358990\pi$
$431$	17.7980			0.857298			0.428649	+	0.903471i	$0.358990\pi$
$432$		0			0
$433$		−	19.7980i		−	0.951429i	−0.879600	−	0.475715i	$-0.842190\pi$
$433$		−	19.7980i		−	0.951429i	0.879600	−	0.475715i	$-0.157810\pi$
$434$	0.898979			0.0431524
$435$	15.7980	−	1.59592i	0.757454	−	0.0765184i
$436$	−2.89898			−0.138836
$437$			44.4949i			2.12848i
$438$			16.8990i			0.807464i
$439$	−37.3939			−1.78471			−0.892356	−	0.451332i	$-0.850949\pi$
$439$	−37.3939			−1.78471			−0.892356	+	0.451332i	$0.850949\pi$
$440$	−10.8990	+	1.10102i	−0.519588	+	0.0524891i
$441$	3.00000			0.142857
$442$		−	0.898979i		−	0.0427601i
$443$		−	9.79796i		−	0.465515i	−0.972535	−	0.232758i	$-0.925225\pi$
$443$		−	9.79796i		−	0.465515i	0.972535	−	0.232758i	$-0.0747749\pi$
$444$	−4.89898			−0.232495
$445$	−2.24745	−	22.2474i	−0.106539	−	1.05463i
$446$	4.00000			0.189405
$447$		−	38.6969i		−	1.83030i
$448$		−	1.00000i		−	0.0472456i
$449$	10.0000			0.471929			0.235965	−	0.971762i	$-0.424175\pi$
$449$	10.0000			0.471929			0.235965	+	0.971762i	$0.424175\pi$
$450$	3.00000	+	14.6969i	0.141421	+	0.692820i
$451$	−53.3939			−2.51422
$452$		−	0.202041i		−	0.00950321i
$453$		−	48.0000i		−	2.25524i
$454$	−7.34847			−0.344881
$455$	−0.101021	−	1.00000i	−0.00473591	−	0.0468807i
$456$	−15.7980			−0.739807
$457$			9.59592i			0.448878i	0.974488	+	0.224439i	$0.0720550\pi$
$457$			9.59592i			0.448878i	−0.974488	+	0.224439i	$0.927945\pi$
$458$		−	15.1464i		−	0.707746i
$459$		0			0
$460$	15.3485	−	1.55051i	0.715626	−	0.0722929i
$461$	2.65153			0.123494			0.0617470	−	0.998092i	$-0.480333\pi$
$461$	2.65153			0.123494			0.0617470	+	0.998092i	$0.480333\pi$
$462$		−	12.0000i		−	0.558291i
$463$		−	35.5959i		−	1.65428i	−0.561994	−	0.827141i	$-0.689966\pi$
$463$		−	35.5959i		−	1.65428i	0.561994	−	0.827141i	$-0.310034\pi$
$464$	2.89898			0.134582
$465$	−4.89898	+	0.494897i	−0.227185	+	0.0229503i
$466$	−10.2020			−0.472600
$467$		−	5.55051i		−	0.256847i	−0.991719	−	0.128423i	$-0.959008\pi$
$467$		−	5.55051i		−	0.256847i	0.991719	−	0.128423i	$-0.0409917\pi$
$468$		−	1.34847i		−	0.0623330i
$469$	−8.00000			−0.369406
$470$	0.202041	+	2.00000i	0.00931946	+	0.0922531i
$471$	20.6969			0.953665
$472$		−	6.44949i		−	0.296862i
$473$			43.5959i			2.00454i
$474$	−7.10102			−0.326161
$475$	31.5959	−	6.44949i	1.44972	−	0.295923i
$476$	−2.00000			−0.0916698
$477$			3.30306i			0.151237i
$478$			25.7980i			1.17997i
$479$	−38.6969			−1.76811			−0.884054	−	0.467385i	$-0.845196\pi$
$479$	−38.6969			−1.76811			−0.884054	+	0.467385i	$0.845196\pi$
$480$	0.550510	+	5.44949i	0.0251272	+	0.248734i
$481$	−0.898979			−0.0409899
$482$			20.6969i			0.942720i
$483$			16.8990i			0.768930i
$484$	−13.0000			−0.590909
$485$	8.44949	−	0.853572i	0.383672	−	0.0387587i
$486$	22.0454			1.00000
$487$			36.6969i			1.66290i	0.555602	+	0.831449i	$0.312488\pi$
$487$			36.6969i			1.66290i	−0.555602	+	0.831449i	$0.687512\pi$
$488$		−	8.44949i		−	0.382490i
$489$	41.3939			1.87190
$490$	−2.22474	+	0.224745i	−0.100504	+	0.0101529i
$491$	−19.5959			−0.884351			−0.442176	−	0.896928i	$-0.645793\pi$
$491$	−19.5959			−0.884351			−0.442176	+	0.896928i	$0.645793\pi$
$492$			26.6969i			1.20359i
$493$		−	5.79796i		−	0.261127i
$494$	−2.89898			−0.130431
$495$	3.30306	+	32.6969i	0.148462	+	1.46962i
$496$	−0.898979			−0.0403654
$497$		−	10.8990i		−	0.488886i
$498$		−	6.00000i		−	0.268866i
$499$	−25.7980			−1.15488			−0.577438	−	0.816435i	$-0.695947\pi$
$499$	−25.7980			−1.15488			−0.577438	+	0.816435i	$0.695947\pi$
$500$	−3.32577	−	10.6742i	−0.148733	−	0.477366i
$501$	12.0000			0.536120
$502$		−	1.55051i		−	0.0692027i
$503$		−	4.00000i		−	0.178351i	−0.996016	−	0.0891756i	$-0.971577\pi$
$503$		−	4.00000i		−	0.178351i	0.996016	−	0.0891756i	$-0.0284232\pi$
$504$	−3.00000			−0.133631
$505$	−1.89898	−	18.7980i	−0.0845035	−	0.836498i
$506$	33.7980			1.50250
$507$			31.3485i			1.39223i
$508$		−	5.10102i		−	0.226321i
$509$	36.4495			1.61560			0.807798	−	0.589460i	$-0.200659\pi$
$509$	36.4495			1.61560			0.807798	+	0.589460i	$0.200659\pi$
$510$	10.8990	−	1.10102i	0.482615	−	0.0487540i
$511$	6.89898			0.305193
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	20.6969			0.912903
$515$	6.89898	−	0.696938i	0.304005	−	0.0307108i
$516$	21.7980			0.959602
$517$			4.40408i			0.193691i
$518$			2.00000i			0.0878750i
$519$	−44.6969			−1.96198
$520$	0.101021	+	1.00000i	0.00443004	+	0.0438529i
$521$	3.30306			0.144710			0.0723549	−	0.997379i	$-0.476949\pi$
$521$	3.30306			0.144710			0.0723549	+	0.997379i	$0.476949\pi$
$522$		−	8.69694i		−	0.380655i
$523$			1.14643i			0.0501298i	0.999686	+	0.0250649i	$0.00797924\pi$
$523$			1.14643i			0.0501298i	−0.999686	+	0.0250649i	$0.992021\pi$
$524$	1.55051			0.0677344
$525$	12.0000	−	2.44949i	0.523723	−	0.106904i
$526$	9.79796			0.427211
$527$			1.79796i			0.0783203i
$528$			12.0000i			0.522233i
$529$	−24.5959			−1.06939
$530$	−0.247449	−	2.44949i	−0.0107485	−	0.106399i
$531$	−19.3485			−0.839652
$532$			6.44949i			0.279621i
$533$			4.89898i			0.212198i
$534$	−24.4949			−1.06000
$535$	17.7980	−	1.79796i	0.769473	−	0.0777325i
$536$	8.00000			0.345547
$537$			14.2020i			0.612863i
$538$			15.1464i			0.653009i
$539$	−4.89898			−0.211014
$540$		0			0
$541$	−29.5959			−1.27243			−0.636214	−	0.771513i	$-0.719500\pi$
$541$	−29.5959			−1.27243			−0.636214	+	0.771513i	$0.719500\pi$
$542$			12.0000i			0.515444i
$543$			34.8990i			1.49766i
$544$	2.00000			0.0857493
$545$	−0.651531	−	6.44949i	−0.0279085	−	0.276266i
$546$	−1.10102			−0.0471193
$547$		−	10.6969i		−	0.457368i	−0.973501	−	0.228684i	$-0.926558\pi$
$547$		−	10.6969i		−	0.457368i	0.973501	−	0.228684i	$-0.0734423\pi$
$548$			17.7980i			0.760291i
$549$	−25.3485			−1.08185
$550$	−4.89898	−	24.0000i	−0.208893	−	1.02336i
$551$	−18.6969			−0.796516
$552$		−	16.8990i		−	0.719268i
$553$			2.89898i			0.123277i
$554$	−5.10102			−0.216722
$555$	−1.10102	−	10.8990i	−0.0467357	−	0.462636i
$556$	6.44949			0.273519
$557$			16.6969i			0.707472i	0.935345	+	0.353736i	$0.115089\pi$
$557$			16.6969i			0.707472i	−0.935345	+	0.353736i	$0.884911\pi$
$558$			2.69694i			0.114171i
$559$	4.00000			0.169182
$560$	2.22474	−	0.224745i	0.0940126	−	0.00949720i
$561$	24.0000			1.01328
$562$		−	18.0000i		−	0.759284i
$563$			14.0454i			0.591943i	0.955197	+	0.295972i	$0.0956434\pi$
$563$			14.0454i			0.591943i	−0.955197	+	0.295972i	$0.904357\pi$
$564$	2.20204			0.0927227
$565$	0.449490	−	0.0454077i	0.0189102	−	0.00191032i
$566$	−28.2474			−1.18733
$567$		−	9.00000i		−	0.377964i
$568$			10.8990i			0.457311i
$569$	−14.2020			−0.595381			−0.297690	−	0.954663i	$-0.596216\pi$
$569$	−14.2020			−0.595381			−0.297690	+	0.954663i	$0.596216\pi$
$570$	−3.55051	−	35.1464i	−0.148715	−	1.47212i
$571$	−20.8990			−0.874595			−0.437298	−	0.899317i	$-0.644064\pi$
$571$	−20.8990			−0.874595			−0.437298	+	0.899317i	$0.644064\pi$
$572$			2.20204i			0.0920720i
$573$		−	40.8990i		−	1.70858i
$574$	10.8990			0.454915
$575$	6.89898	+	33.7980i	0.287707	+	1.40947i
$576$	3.00000			0.125000
$577$		−	46.4949i		−	1.93561i	−0.251705	−	0.967804i	$-0.580991\pi$
$577$		−	46.4949i		−	1.93561i	0.251705	−	0.967804i	$-0.419009\pi$
$578$			13.0000i			0.540729i
$579$	−43.1010			−1.79122
$580$	0.651531	+	6.44949i	0.0270533	+	0.267800i
$581$	−2.44949			−0.101622
$582$		−	9.30306i		−	0.385624i
$583$		−	5.39388i		−	0.223392i
$584$	−6.89898			−0.285482
$585$	3.00000	−	0.303062i	0.124035	−	0.0125301i
$586$	6.24745			0.258080
$587$			33.1464i			1.36810i	0.729435	+	0.684050i	$0.239783\pi$
$587$			33.1464i			1.36810i	−0.729435	+	0.684050i	$0.760217\pi$
$588$			2.44949i			0.101015i
$589$	5.79796			0.238901
$590$	14.3485	−	1.44949i	0.590717	−	0.0596745i
$591$	22.2929			0.917006
$592$		−	2.00000i		−	0.0821995i
$593$		−	1.10102i		−	0.0452135i	−0.999744	−	0.0226067i	$-0.992803\pi$
$593$		−	1.10102i		−	0.0452135i	0.999744	−	0.0226067i	$-0.00719656\pi$
$594$		0			0
$595$	−0.449490	−	4.44949i	−0.0184273	−	0.182411i
$596$	15.7980			0.647110
$597$		−	17.3939i		−	0.711884i
$598$		−	3.10102i		−	0.126810i
$599$	22.8990			0.935627			0.467813	−	0.883827i	$-0.345042\pi$
$599$	22.8990			0.935627			0.467813	+	0.883827i	$0.345042\pi$
$600$	−12.0000	+	2.44949i	−0.489898	+	0.100000i
$601$	19.3939			0.791093			0.395546	−	0.918446i	$-0.370555\pi$
$601$	19.3939			0.791093			0.395546	+	0.918446i	$0.370555\pi$
$602$		−	8.89898i		−	0.362695i
$603$		−	24.0000i		−	0.977356i
$604$	19.5959			0.797347
$605$	−2.92168	−	28.9217i	−0.118783	−	1.17583i
$606$	−20.6969			−0.840756
$607$			25.3939i			1.03071i	0.856978	+	0.515353i	$0.172339\pi$
$607$			25.3939i			1.03071i	−0.856978	+	0.515353i	$0.827661\pi$
$608$		−	6.44949i		−	0.261561i
$609$	−7.10102			−0.287748
$610$	18.7980	−	1.89898i	0.761107	−	0.0768874i
$611$	0.404082			0.0163474
$612$		−	6.00000i		−	0.242536i
$613$		−	8.20204i		−	0.331277i	−0.986187	−	0.165639i	$-0.947031\pi$
$613$		−	8.20204i		−	0.331277i	0.986187	−	0.165639i	$-0.0529685\pi$
$614$	4.24745			0.171413
$615$	−59.3939	+	6.00000i	−2.39499	+	0.241943i
$616$	4.89898			0.197386
$617$			9.59592i			0.386317i	0.981168	+	0.193159i	$0.0618732\pi$
$617$			9.59592i			0.386317i	−0.981168	+	0.193159i	$0.938127\pi$
$618$		−	7.59592i		−	0.305553i
$619$	46.4495			1.86696			0.933481	−	0.358626i	$-0.116755\pi$
$619$	46.4495			1.86696			0.933481	+	0.358626i	$0.116755\pi$
$620$	−0.202041	−	2.00000i	−0.00811416	−	0.0803219i
$621$		0			0
$622$			12.0000i			0.481156i
$623$			10.0000i			0.400642i
$624$	1.10102			0.0440761
$625$	23.0000	−	9.79796i	0.920000	−	0.391918i
$626$	−17.5959			−0.703274
$627$		−	77.3939i		−	3.09081i
$628$			8.44949i			0.337171i
$629$	−4.00000			−0.159490
$630$	−0.674235	−	6.67423i	−0.0268622	−	0.265908i
$631$	6.49490			0.258558			0.129279	−	0.991608i	$-0.458734\pi$
$631$	6.49490			0.258558			0.129279	+	0.991608i	$0.458734\pi$
$632$		−	2.89898i		−	0.115315i
$633$			29.3939i			1.16830i
$634$	26.4949			1.05225
$635$	11.3485	−	1.14643i	0.450350	−	0.0454946i
$636$	−2.69694			−0.106941
$637$			0.449490i			0.0178094i
$638$			14.2020i			0.562264i
$639$	32.6969			1.29347
$640$	−2.22474	+	0.224745i	−0.0879408	+	0.00888382i
$641$	6.20204			0.244966			0.122483	−	0.992471i	$-0.460914\pi$
$641$	6.20204			0.244966			0.122483	+	0.992471i	$0.460914\pi$
$642$		−	19.5959i		−	0.773389i
$643$		−	9.14643i		−	0.360700i	−0.983603	−	0.180350i	$-0.942277\pi$
$643$		−	9.14643i		−	0.360700i	0.983603	−	0.180350i	$-0.0577230\pi$
$644$	−6.89898			−0.271858
$645$	4.89898	+	48.4949i	0.192897	+	1.90948i
$646$	−12.8990			−0.507504
$647$		−	22.2929i		−	0.876423i	−0.898872	−	0.438211i	$-0.855612\pi$
$647$		−	22.2929i		−	0.876423i	0.898872	−	0.438211i	$-0.144388\pi$
$648$			9.00000i			0.353553i
$649$	31.5959			1.24025
$650$	−2.20204	+	0.449490i	−0.0863712	+	0.0176304i
$651$	2.20204			0.0863048
$652$			16.8990i			0.661815i
$653$		−	39.7980i		−	1.55741i	−0.627387	−	0.778707i	$-0.715876\pi$
$653$		−	39.7980i		−	1.55741i	0.627387	−	0.778707i	$-0.284124\pi$
$654$	−7.10102			−0.277672
$655$	0.348469	+	3.44949i	0.0136158	+	0.134783i
$656$	−10.8990			−0.425534
$657$			20.6969i			0.807464i
$658$		−	0.898979i		−	0.0350459i
$659$	−7.10102			−0.276616			−0.138308	−	0.990389i	$-0.544166\pi$
$659$	−7.10102			−0.276616			−0.138308	+	0.990389i	$0.544166\pi$
$660$	−26.6969	+	2.69694i	−1.03918	+	0.104978i
$661$	12.9444			0.503478			0.251739	−	0.967795i	$-0.418997\pi$
$661$	12.9444			0.503478			0.251739	+	0.967795i	$0.418997\pi$
$662$			10.6969i			0.415748i
$663$		−	2.20204i		−	0.0855202i
$664$	2.44949			0.0950586
$665$	−14.3485	+	1.44949i	−0.556410	+	0.0562088i
$666$	−6.00000			−0.232495
$667$		−	20.0000i		−	0.774403i
$668$			4.89898i			0.189547i
$669$	9.79796			0.378811
$670$	1.79796	+	17.7980i	0.0694612	+	0.687595i
$671$	41.3939			1.59799
$672$		−	2.44949i		−	0.0944911i
$673$			1.79796i			0.0693062i	0.999399	+	0.0346531i	$0.0110326\pi$
$673$			1.79796i			0.0693062i	−0.999399	+	0.0346531i	$0.988967\pi$
$674$	−29.5959			−1.13999
$675$		0			0
$676$	−12.7980			−0.492229
$677$			31.5505i			1.21258i	0.795242	+	0.606292i	$0.207344\pi$
$677$			31.5505i			1.21258i	−0.795242	+	0.606292i	$0.792656\pi$
$678$		−	0.494897i		−	0.0190064i
$679$	−3.79796			−0.145752
$680$	0.449490	+	4.44949i	0.0172371	+	0.170630i
$681$	−18.0000			−0.689761
$682$		−	4.40408i		−	0.168641i
$683$		−	35.5959i		−	1.36204i	−0.732265	−	0.681020i	$-0.761537\pi$
$683$		−	35.5959i		−	1.36204i	0.732265	−	0.681020i	$-0.238463\pi$
$684$	−19.3485			−0.739807
$685$	−39.5959	+	4.00000i	−1.51288	+	0.152832i
$686$	1.00000			0.0381802
$687$		−	37.1010i		−	1.41549i
$688$			8.89898i			0.339270i
$689$	−0.494897			−0.0188541
$690$	37.5959	−	3.79796i	1.43125	−	0.144586i
$691$	−13.1464			−0.500114			−0.250057	−	0.968231i	$-0.580449\pi$
$691$	−13.1464			−0.500114			−0.250057	+	0.968231i	$0.580449\pi$
$692$		−	18.2474i		−	0.693664i
$693$		−	14.6969i		−	0.558291i
$694$	19.1010			0.725065
$695$	1.44949	+	14.3485i	0.0549823	+	0.544268i
$696$	7.10102			0.269163
$697$			21.7980i			0.825657i
$698$			3.55051i			0.134389i
$699$	−24.9898			−0.945201
$700$	1.00000	+	4.89898i	0.0377964	+	0.185164i
$701$	40.6969			1.53710			0.768551	−	0.639788i	$-0.220978\pi$
$701$	40.6969			1.53710			0.768551	+	0.639788i	$0.220978\pi$
$702$		0			0
$703$			12.8990i			0.486494i
$704$	−4.89898			−0.184637
$705$	0.494897	+	4.89898i	0.0186389	+	0.184506i
$706$	−13.1010			−0.493063
$707$			8.44949i			0.317776i
$708$		−	15.7980i		−	0.593724i
$709$	−40.2929			−1.51323			−0.756615	−	0.653861i	$-0.773148\pi$
$709$	−40.2929			−1.51323			−0.756615	+	0.653861i	$0.773148\pi$
$710$	−24.2474	+	2.44949i	−0.909991	+	0.0919277i
$711$	−8.69694			−0.326161
$712$		−	10.0000i		−	0.374766i
$713$			6.20204i			0.232268i
$714$	−4.89898			−0.183340
$715$	−4.89898	+	0.494897i	−0.183211	+	0.0185081i
$716$	−5.79796			−0.216680
$717$			63.1918i			2.35994i
$718$		−	11.5959i		−	0.432756i
$719$	−44.4949			−1.65938			−0.829690	−	0.558225i	$-0.811483\pi$
$719$	−44.4949			−1.65938			−0.829690	+	0.558225i	$0.811483\pi$
$720$	0.674235	+	6.67423i	0.0251272	+	0.248734i
$721$	−3.10102			−0.115488
$722$			22.5959i			0.840933i
$723$			50.6969i			1.88544i
$724$	−14.2474			−0.529502
$725$	−14.2020	+	2.89898i	−0.527451	+	0.107665i
$726$	−31.8434			−1.18182
$727$			6.69694i			0.248376i	0.992259	+	0.124188i	$0.0396325\pi$
$727$			6.69694i			0.248376i	−0.992259	+	0.124188i	$0.960367\pi$
$728$		−	0.449490i		−	0.0166592i
$729$	27.0000			1.00000
$730$	−1.55051	−	15.3485i	−0.0573870	−	0.568072i
$731$	17.7980			0.658281
$732$		−	20.6969i		−	0.764981i
$733$		−	43.6413i		−	1.61193i	−0.591964	−	0.805965i	$-0.701647\pi$
$733$		−	43.6413i		−	1.61193i	0.591964	−	0.805965i	$-0.298353\pi$
$734$	32.0000			1.18114
$735$	−5.44949	+	0.550510i	−0.201007	+	0.0203059i
$736$	6.89898			0.254300
$737$			39.1918i			1.44365i
$738$			32.6969i			1.20359i
$739$	44.4949			1.63677			0.818386	−	0.574669i	$-0.194869\pi$
$739$	44.4949			1.63677			0.818386	+	0.574669i	$0.194869\pi$
$740$	4.44949	−	0.449490i	0.163566	−	0.0165236i
$741$	−7.10102			−0.260863
$742$			1.10102i			0.0404197i
$743$		−	15.3031i		−	0.561415i	−0.959793	−	0.280707i	$-0.909431\pi$
$743$		−	15.3031i		−	0.561415i	0.959793	−	0.280707i	$-0.0905691\pi$
$744$	−2.20204			−0.0807307
$745$	3.55051	+	35.1464i	0.130081	+	1.28767i
$746$	−24.6969			−0.904219
$747$		−	7.34847i		−	0.268866i
$748$			9.79796i			0.358249i
$749$	−8.00000			−0.292314
$750$	−8.14643	−	26.1464i	−0.297465	−	0.954733i
$751$	−22.2020			−0.810164			−0.405082	−	0.914280i	$-0.632757\pi$
$751$	−22.2020			−0.810164			−0.405082	+	0.914280i	$0.632757\pi$
$752$			0.898979i			0.0327824i
$753$		−	3.79796i		−	0.138405i
$754$	1.30306			0.0474547
$755$	4.40408	+	43.5959i	0.160281	+	1.58662i
$756$		0			0
$757$			32.2020i			1.17040i	0.810888	+	0.585202i	$0.198985\pi$
$757$			32.2020i			1.17040i	−0.810888	+	0.585202i	$0.801015\pi$
$758$		−	1.30306i		−	0.0473293i
$759$	82.7878			3.00501
$760$	14.3485	−	1.44949i	0.520474	−	0.0525785i
$761$	−30.8990			−1.12009			−0.560044	−	0.828463i	$-0.689216\pi$
$761$	−30.8990			−1.12009			−0.560044	+	0.828463i	$0.689216\pi$
$762$		−	12.4949i		−	0.452642i
$763$			2.89898i			0.104950i
$764$	16.6969			0.604074
$765$	13.3485	−	1.34847i	0.482615	−	0.0487540i
$766$	16.8990			0.610585
$767$		−	2.89898i		−	0.104676i
$768$			2.44949i			0.0883883i
$769$	11.3031			0.407599			0.203799	−	0.979013i	$-0.434671\pi$
$769$	11.3031			0.407599			0.203799	+	0.979013i	$0.434671\pi$
$770$	1.10102	+	10.8990i	0.0396780	+	0.392772i
$771$	50.6969			1.82581
$772$		−	17.5959i		−	0.633291i
$773$		−	13.3485i		−	0.480111i	−0.970759	−	0.240056i	$-0.922834\pi$
$773$		−	13.3485i		−	0.480111i	0.970759	−	0.240056i	$-0.0771657\pi$
$774$	26.6969			0.959602
$775$	4.40408	−	0.898979i	0.158199	−	0.0322923i
$776$	3.79796			0.136339
$777$			4.89898i			0.175750i
$778$		−	22.8990i		−	0.820968i
$779$	70.2929			2.51850
$780$	0.247449	+	2.44949i	0.00886009	+	0.0877058i
$781$	−53.3939			−1.91058
$782$		−	13.7980i		−	0.493414i
$783$		0			0
$784$	−1.00000			−0.0357143
$785$	−18.7980	+	1.89898i	−0.670928	+	0.0677775i
$786$	3.79796			0.135469
$787$		−	45.5505i		−	1.62370i	−0.583866	−	0.811850i	$-0.698461\pi$
$787$		−	45.5505i		−	1.62370i	0.583866	−	0.811850i	$-0.301539\pi$
$788$			9.10102i			0.324210i
$789$	24.0000			0.854423
$790$	6.44949	−	0.651531i	0.229463	−	0.0231804i
$791$	−0.202041			−0.00718375
$792$			14.6969i			0.522233i
$793$		−	3.79796i		−	0.134869i
$794$	−17.3485			−0.615674
$795$	−0.606123	−	6.00000i	−0.0214970	−	0.212798i
$796$	7.10102			0.251689
$797$		−	52.9444i		−	1.87539i	−0.347464	−	0.937693i	$-0.612957\pi$
$797$		−	52.9444i		−	1.87539i	0.347464	−	0.937693i	$-0.387043\pi$
$798$			15.7980i			0.559242i
$799$	1.79796			0.0636072
$800$	−1.00000	−	4.89898i	−0.0353553	−	0.173205i
$801$	−30.0000			−1.06000
$802$			29.3939i			1.03793i
$803$		−	33.7980i		−	1.19270i
$804$	19.5959			0.691095
$805$	−1.55051	−	15.3485i	−0.0546483	−	0.540962i
$806$	−0.404082			−0.0142332
$807$			37.1010i			1.30602i
$808$		−	8.44949i		−	0.297252i
$809$	−8.40408			−0.295472			−0.147736	−	0.989027i	$-0.547199\pi$
$809$	−8.40408			−0.295472			−0.147736	+	0.989027i	$0.547199\pi$
$810$	−20.0227	+	2.02270i	−0.703526	+	0.0710706i
$811$	−38.9444			−1.36752			−0.683761	−	0.729706i	$-0.739657\pi$
$811$	−38.9444			−1.36752			−0.683761	+	0.729706i	$0.739657\pi$
$812$		−	2.89898i		−	0.101734i
$813$			29.3939i			1.03089i
$814$	9.79796			0.343418
$815$	−37.5959	+	3.79796i	−1.31693	+	0.133037i
$816$	4.89898			0.171499
$817$		−	57.3939i		−	2.00796i
$818$			14.4949i			0.506802i
$819$	−1.34847			−0.0471193
$820$	−2.44949	−	24.2474i	−0.0855399	−	0.846758i
$821$	27.7980			0.970155			0.485078	−	0.874471i	$-0.338791\pi$
$821$	27.7980			0.970155			0.485078	+	0.874471i	$0.338791\pi$
$822$			43.5959i			1.52058i
$823$			39.1918i			1.36614i	0.730352	+	0.683071i	$0.239356\pi$
$823$			39.1918i			1.36614i	−0.730352	+	0.683071i	$0.760644\pi$
$824$	3.10102			0.108029
$825$	−12.0000	−	58.7878i	−0.417786	−	2.04673i
$826$	−6.44949			−0.224406
$827$		−	23.5959i		−	0.820510i	−0.911971	−	0.410255i	$-0.865440\pi$
$827$		−	23.5959i		−	0.820510i	0.911971	−	0.410255i	$-0.134560\pi$
$828$		−	20.6969i		−	0.719268i
$829$	−39.6413			−1.37680			−0.688400	−	0.725331i	$-0.741687\pi$
$829$	−39.6413			−1.37680			−0.688400	+	0.725331i	$0.741687\pi$
$830$	0.550510	+	5.44949i	0.0191085	+	0.189155i
$831$	−12.4949			−0.433443
$832$			0.449490i			0.0155833i
$833$			2.00000i			0.0692959i
$834$	15.7980			0.547039
$835$	−10.8990	+	1.10102i	−0.377175	+	0.0381024i
$836$	31.5959			1.09277
$837$		0			0
$838$			6.44949i			0.222794i
$839$	−27.1010			−0.935631			−0.467816	−	0.883826i	$-0.654959\pi$
$839$	−27.1010			−0.935631			−0.467816	+	0.883826i	$0.654959\pi$
$840$	5.44949	−	0.550510i	0.188025	−	0.0189944i
$841$	−20.5959			−0.710204
$842$		−	23.7980i		−	0.820132i
$843$		−	44.0908i		−	1.51857i
$844$	−12.0000			−0.413057
$845$	−2.87628	−	28.4722i	−0.0989469	−	0.979473i
$846$	2.69694			0.0927227
$847$			13.0000i			0.446685i
$848$		−	1.10102i		−	0.0378092i
$849$	−69.1918			−2.37466
$850$	−9.79796	+	2.00000i	−0.336067	+	0.0685994i
$851$	−13.7980			−0.472988
$852$			26.6969i			0.914622i
$853$			29.8434i			1.02182i	0.859635	+	0.510909i	$0.170691\pi$
$853$			29.8434i			1.02182i	−0.859635	+	0.510909i	$0.829309\pi$
$854$	−8.44949			−0.289136
$855$	−4.34847	−	43.0454i	−0.148715	−	1.47212i
$856$	8.00000			0.273434
$857$		−	25.1918i		−	0.860537i	−0.902701	−	0.430268i	$-0.858419\pi$
$857$		−	25.1918i		−	0.860537i	0.902701	−	0.430268i	$-0.141581\pi$
$858$			5.39388i			0.184144i
$859$	29.6413			1.01135			0.505674	−	0.862724i	$-0.331244\pi$
$859$	29.6413			1.01135			0.505674	+	0.862724i	$0.331244\pi$
$860$	−19.7980	+	2.00000i	−0.675105	+	0.0681994i
$861$	26.6969			0.909829
$862$			17.7980i			0.606201i
$863$			13.3939i			0.455933i	0.973669	+	0.227966i	$0.0732076\pi$
$863$			13.3939i			0.455933i	−0.973669	+	0.227966i	$0.926792\pi$
$864$		0			0
$865$	40.5959	−	4.10102i	1.38030	−	0.139439i
$866$	19.7980			0.672762
$867$			31.8434i			1.08146i
$868$			0.898979i			0.0305134i
$869$	14.2020			0.481771
$870$	1.59592	+	15.7980i	0.0541067	+	0.535601i
$871$	3.59592			0.121843
$872$		−	2.89898i		−	0.0981718i
$873$		−	11.3939i		−	0.385624i
$874$	−44.4949			−1.50506
$875$	−10.6742	+	3.32577i	−0.360855	+	0.112431i
$876$	−16.8990			−0.570964
$877$		−	19.3939i		−	0.654885i	−0.944871	−	0.327442i	$-0.893813\pi$
$877$		−	19.3939i		−	0.654885i	0.944871	−	0.327442i	$-0.106187\pi$
$878$		−	37.3939i		−	1.26198i
$879$	15.3031			0.516159
$880$	−1.10102	−	10.8990i	−0.0371154	−	0.367405i
$881$	27.7980			0.936537			0.468269	−	0.883586i	$-0.344878\pi$
$881$	27.7980			0.936537			0.468269	+	0.883586i	$0.344878\pi$
$882$			3.00000i			0.101015i
$883$			41.7980i			1.40661i	0.710887	+	0.703307i	$0.248294\pi$
$883$			41.7980i			1.40661i	−0.710887	+	0.703307i	$0.751706\pi$
$884$	0.898979			0.0302360
$885$	35.1464	−	3.55051i	1.18143	−	0.119349i
$886$	9.79796			0.329169
$887$			26.6969i			0.896395i	0.893934	+	0.448198i	$0.147934\pi$
$887$			26.6969i			0.896395i	−0.893934	+	0.448198i	$0.852066\pi$
$888$		−	4.89898i		−	0.164399i
$889$	−5.10102			−0.171083
$890$	22.2474	−	2.24745i	0.745736	−	0.0753347i
$891$	−44.0908			−1.47710
$892$			4.00000i			0.133930i
$893$		−	5.79796i		−	0.194021i
$894$	38.6969			1.29422
$895$	−1.30306	−	12.8990i	−0.0435565	−	0.431165i
$896$	1.00000			0.0334077
$897$		−	7.59592i		−	0.253620i
$898$			10.0000i			0.333704i
$899$	−2.60612			−0.0869191
$900$	−14.6969	+	3.00000i	−0.489898	+	0.100000i
$901$	−2.20204			−0.0733606
$902$		−	53.3939i		−	1.77782i
$903$		−	21.7980i		−	0.725391i
$904$	0.202041			0.00671978
$905$	−3.20204	−	31.6969i	−0.106439	−	1.05364i
$906$	48.0000			1.59469
$907$			22.2020i			0.737207i	0.929587	+	0.368603i	$0.120164\pi$
$907$			22.2020i			0.737207i	−0.929587	+	0.368603i	$0.879836\pi$
$908$		−	7.34847i		−	0.243868i
$909$	−25.3485			−0.840756
$910$	1.00000	−	0.101021i	0.0331497	−	0.00334880i
$911$	3.59592			0.119138			0.0595690	−	0.998224i	$-0.481027\pi$
$911$	3.59592			0.119138			0.0595690	+	0.998224i	$0.481027\pi$
$912$		−	15.7980i		−	0.523123i
$913$			12.0000i			0.397142i
$914$	−9.59592			−0.317405
$915$	46.0454	−	4.65153i	1.52221	−	0.153775i
$916$	15.1464			0.500452
$917$		−	1.55051i		−	0.0512024i
$918$		0			0
$919$	17.1010			0.564111			0.282055	−	0.959398i	$-0.408984\pi$
$919$	17.1010			0.564111			0.282055	+	0.959398i	$0.408984\pi$
$920$	1.55051	+	15.3485i	0.0511188	+	0.506024i
$921$	10.4041			0.342826
$922$			2.65153i			0.0873235i
$923$			4.89898i			0.161252i
$924$	12.0000			0.394771
$925$	2.00000	+	9.79796i	0.0657596	+	0.322155i
$926$	35.5959			1.16975
$927$		−	9.30306i		−	0.305553i
$928$			2.89898i			0.0951637i
$929$	−40.2929			−1.32197			−0.660983	−	0.750401i	$-0.729860\pi$
$929$	−40.2929			−1.32197			−0.660983	+	0.750401i	$0.729860\pi$
$930$	−0.494897	−	4.89898i	−0.0162283	−	0.160644i
$931$	6.44949			0.211373
$932$		−	10.2020i		−	0.334179i
$933$			29.3939i			0.962312i
$934$	5.55051			0.181618
$935$	−21.7980	+	2.20204i	−0.712869	+	0.0720144i
$936$	1.34847			0.0440761
$937$			50.8990i			1.66280i	0.555677	+	0.831399i	$0.312459\pi$
$937$			50.8990i			1.66280i	−0.555677	+	0.831399i	$0.687541\pi$
$938$		−	8.00000i		−	0.261209i
$939$	−43.1010			−1.40655
$940$	−2.00000	+	0.202041i	−0.0652328	+	0.00658985i
$941$	−24.4495			−0.797031			−0.398515	−	0.917162i	$-0.630474\pi$
$941$	−24.4495			−0.797031			−0.398515	+	0.917162i	$0.630474\pi$
$942$			20.6969i			0.674343i
$943$			75.1918i			2.44858i
$944$	6.44949			0.209913
$945$		0			0
$946$	−43.5959			−1.41743
$947$			44.0908i			1.43276i	0.697711	+	0.716379i	$0.254202\pi$
$947$			44.0908i			1.43276i	−0.697711	+	0.716379i	$0.745798\pi$
$948$		−	7.10102i		−	0.230630i
$949$	−3.10102			−0.100663
$950$	6.44949	+	31.5959i	0.209249	+	1.02511i
$951$	64.8990			2.10449
$952$		−	2.00000i		−	0.0648204i
$953$			21.7980i			0.706105i	0.935603	+	0.353053i	$0.114856\pi$
$953$			21.7980i			0.706105i	−0.935603	+	0.353053i	$0.885144\pi$
$954$	−3.30306			−0.106941
$955$	3.75255	+	37.1464i	0.121430	+	1.20203i
$956$	−25.7980			−0.834366
$957$			34.7878i			1.12453i
$958$		−	38.6969i		−	1.25024i
$959$	17.7980			0.574726
$960$	−5.44949	+	0.550510i	−0.175882	+	0.0177676i
$961$	−30.1918			−0.973930
$962$		−	0.898979i		−	0.0289843i
$963$		−	24.0000i		−	0.773389i
$964$	−20.6969			−0.666604
$965$	39.1464	−	3.95459i	1.26017	−	0.127303i
$966$	−16.8990			−0.543716
$967$		−	32.2929i		−	1.03847i	−0.854632	−	0.519234i	$-0.826217\pi$
$967$		−	32.2929i		−	1.03847i	0.854632	−	0.519234i	$-0.173783\pi$
$968$		−	13.0000i		−	0.417836i
$969$	−31.5959			−1.01501
$970$	0.853572	+	8.44949i	0.0274065	+	0.271297i
$971$	−14.4495			−0.463706			−0.231853	−	0.972751i	$-0.574479\pi$
$971$	−14.4495			−0.463706			−0.231853	+	0.972751i	$0.574479\pi$
$972$			22.0454i			0.707107i
$973$		−	6.44949i		−	0.206761i
$974$	−36.6969			−1.17585
$975$	−5.39388	+	1.10102i	−0.172742	+	0.0352609i
$976$	8.44949			0.270462
$977$		−	29.3939i		−	0.940393i	−0.882562	−	0.470197i	$-0.844183\pi$
$977$		−	29.3939i		−	0.940393i	0.882562	−	0.470197i	$-0.155817\pi$
$978$			41.3939i			1.32363i
$979$	48.9898			1.56572
$980$	−0.224745	−	2.22474i	−0.00717921	−	0.0710669i
$981$	−8.69694			−0.277672
$982$		−	19.5959i		−	0.625331i
$983$		−	42.6969i		−	1.36182i	−0.732367	−	0.680910i	$-0.761584\pi$
$983$		−	42.6969i		−	1.36182i	0.732367	−	0.680910i	$-0.238416\pi$
$984$	−26.6969			−0.851067
$985$	−20.2474	+	2.04541i	−0.645137	+	0.0651721i
$986$	5.79796			0.184645
$987$		−	2.20204i		−	0.0700917i
$988$		−	2.89898i		−	0.0922288i
$989$	61.3939			1.95221
$990$	−32.6969	+	3.30306i	−1.03918	+	0.104978i
$991$	60.6969			1.92810			0.964051	−	0.265718i	$-0.0856089\pi$
$991$	60.6969			1.92810			0.964051	+	0.265718i	$0.0856089\pi$
$992$		−	0.898979i		−	0.0285426i
$993$			26.2020i			0.831497i
$994$	10.8990			0.345695
$995$	1.59592	+	15.7980i	0.0505940	+	0.500829i
$996$	6.00000			0.190117
$997$		−	42.6515i		−	1.35079i	−0.737457	−	0.675394i	$-0.763974\pi$
$997$		−	42.6515i		−	1.35079i	0.737457	−	0.675394i	$-0.236026\pi$
$998$		−	25.7980i		−	0.816620i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.2.c.a.29.4	yes	4
3.2	odd	2		630.2.g.g.379.2		4
4.3	odd	2		560.2.g.e.449.1		4
5.2	odd	4		350.2.a.g.1.2		2
5.3	odd	4		350.2.a.h.1.1		2
5.4	even	2	inner	70.2.c.a.29.1	✓	4
7.2	even	3		490.2.i.c.459.3		8
7.3	odd	6		490.2.i.f.79.1		8
7.4	even	3		490.2.i.c.79.2		8
7.5	odd	6		490.2.i.f.459.4		8
7.6	odd	2		490.2.c.e.99.3		4
8.3	odd	2		2240.2.g.i.449.4		4
8.5	even	2		2240.2.g.j.449.2		4
12.11	even	2		5040.2.t.t.1009.4		4
15.2	even	4		3150.2.a.bt.1.1		2
15.8	even	4		3150.2.a.bs.1.1		2
15.14	odd	2		630.2.g.g.379.4		4
20.3	even	4		2800.2.a.bl.1.2		2
20.7	even	4		2800.2.a.bm.1.1		2
20.19	odd	2		560.2.g.e.449.3		4
35.4	even	6		490.2.i.c.79.3		8
35.9	even	6		490.2.i.c.459.2		8
35.13	even	4		2450.2.a.bq.1.2		2
35.19	odd	6		490.2.i.f.459.1		8
35.24	odd	6		490.2.i.f.79.4		8
35.27	even	4		2450.2.a.bl.1.1		2
35.34	odd	2		490.2.c.e.99.2		4
40.19	odd	2		2240.2.g.i.449.2		4
40.29	even	2		2240.2.g.j.449.4		4
60.59	even	2		5040.2.t.t.1009.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.c.a.29.1	✓	4	5.4	even	2	inner
70.2.c.a.29.4	yes	4	1.1	even	1	trivial
350.2.a.g.1.2		2	5.2	odd	4
350.2.a.h.1.1		2	5.3	odd	4
490.2.c.e.99.2		4	35.34	odd	2
490.2.c.e.99.3		4	7.6	odd	2
490.2.i.c.79.2		8	7.4	even	3
490.2.i.c.79.3		8	35.4	even	6
490.2.i.c.459.2		8	35.9	even	6
490.2.i.c.459.3		8	7.2	even	3
490.2.i.f.79.1		8	7.3	odd	6
490.2.i.f.79.4		8	35.24	odd	6
490.2.i.f.459.1		8	35.19	odd	6
490.2.i.f.459.4		8	7.5	odd	6
560.2.g.e.449.1		4	4.3	odd	2
560.2.g.e.449.3		4	20.19	odd	2
630.2.g.g.379.2		4	3.2	odd	2
630.2.g.g.379.4		4	15.14	odd	2
2240.2.g.i.449.2		4	40.19	odd	2
2240.2.g.i.449.4		4	8.3	odd	2
2240.2.g.j.449.2		4	8.5	even	2
2240.2.g.j.449.4		4	40.29	even	2
2450.2.a.bl.1.1		2	35.27	even	4
2450.2.a.bq.1.2		2	35.13	even	4
2800.2.a.bl.1.2		2	20.3	even	4
2800.2.a.bm.1.1		2	20.7	even	4
3150.2.a.bs.1.1		2	15.8	even	4
3150.2.a.bt.1.1		2	15.2	even	4
5040.2.t.t.1009.3		4	60.59	even	2
5040.2.t.t.1009.4		4	12.11	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:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	70.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +2.44949i q^{3} -1.00000 q^{4} +(-0.224745 - 2.22474i) q^{5} -2.44949 q^{6} +1.00000i q^{7} -1.00000i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +2.44949i q^{3} -1.00000 q^{4} +(-0.224745 - 2.22474i) q^{5} -2.44949 q^{6} +1.00000i q^{7} -1.00000i q^{8} -3.00000 q^{9} +(2.22474 - 0.224745i) q^{10} +4.89898 q^{11} -2.44949i q^{12} -0.449490i q^{13} -1.00000 q^{14} +(5.44949 - 0.550510i) q^{15} +1.00000 q^{16} -2.00000i q^{17} -3.00000i q^{18} -6.44949 q^{19} +(0.224745 + 2.22474i) q^{20} -2.44949 q^{21} +4.89898i q^{22} -6.89898i q^{23} +2.44949 q^{24} +(-4.89898 + 1.00000i) q^{25} +0.449490 q^{26} -1.00000i q^{28} +2.89898 q^{29} +(0.550510 + 5.44949i) q^{30} -0.898979 q^{31} +1.00000i q^{32} +12.0000i q^{33} +2.00000 q^{34} +(2.22474 - 0.224745i) q^{35} +3.00000 q^{36} -2.00000i q^{37} -6.44949i q^{38} +1.10102 q^{39} +(-2.22474 + 0.224745i) q^{40} -10.8990 q^{41} -2.44949i q^{42} +8.89898i q^{43} -4.89898 q^{44} +(0.674235 + 6.67423i) q^{45} +6.89898 q^{46} +0.898979i q^{47} +2.44949i q^{48} -1.00000 q^{49} +(-1.00000 - 4.89898i) q^{50} +4.89898 q^{51} +0.449490i q^{52} -1.10102i q^{53} +(-1.10102 - 10.8990i) q^{55} +1.00000 q^{56} -15.7980i q^{57} +2.89898i q^{58} +6.44949 q^{59} +(-5.44949 + 0.550510i) q^{60} +8.44949 q^{61} -0.898979i q^{62} -3.00000i q^{63} -1.00000 q^{64} +(-1.00000 + 0.101021i) q^{65} -12.0000 q^{66} +8.00000i q^{67} +2.00000i q^{68} +16.8990 q^{69} +(0.224745 + 2.22474i) q^{70} -10.8990 q^{71} +3.00000i q^{72} -6.89898i q^{73} +2.00000 q^{74} +(-2.44949 - 12.0000i) q^{75} +6.44949 q^{76} +4.89898i q^{77} +1.10102i q^{78} +2.89898 q^{79} +(-0.224745 - 2.22474i) q^{80} -9.00000 q^{81} -10.8990i q^{82} +2.44949i q^{83} +2.44949 q^{84} +(-4.44949 + 0.449490i) q^{85} -8.89898 q^{86} +7.10102i q^{87} -4.89898i q^{88} +10.0000 q^{89} +(-6.67423 + 0.674235i) q^{90} +0.449490 q^{91} +6.89898i q^{92} -2.20204i q^{93} -0.898979 q^{94} +(1.44949 + 14.3485i) q^{95} -2.44949 q^{96} +3.79796i q^{97} -1.00000i q^{98} -14.6969 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 4 q^{5} - 12 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 4 * q^5 - 12 * q^9	\( 4 q - 4 q^{4} + 4 q^{5} - 12 q^{9} + 4 q^{10} - 4 q^{14} + 12 q^{15} + 4 q^{16} - 16 q^{19} - 4 q^{20} - 8 q^{26} - 8 q^{29} + 12 q^{30} + 16 q^{31} + 8 q^{34} + 4 q^{35} + 12 q^{36} + 24 q^{39} - 4 q^{40} - 24 q^{41} - 12 q^{45} + 8 q^{46} - 4 q^{49} - 4 q^{50} - 24 q^{55} + 4 q^{56} + 16 q^{59} - 12 q^{60} + 24 q^{61} - 4 q^{64} - 4 q^{65} - 48 q^{66} + 48 q^{69} - 4 q^{70} - 24 q^{71} + 8 q^{74} + 16 q^{76} - 8 q^{79} + 4 q^{80} - 36 q^{81} - 8 q^{85} - 16 q^{86} + 40 q^{89} - 12 q^{90} - 8 q^{91} + 16 q^{94} - 4 q^{95}+O(q^{100}) \) 4 * q - 4 * q^4 + 4 * q^5 - 12 * q^9 + 4 * q^10 - 4 * q^14 + 12 * q^15 + 4 * q^16 - 16 * q^19 - 4 * q^20 - 8 * q^26 - 8 * q^29 + 12 * q^30 + 16 * q^31 + 8 * q^34 + 4 * q^35 + 12 * q^36 + 24 * q^39 - 4 * q^40 - 24 * q^41 - 12 * q^45 + 8 * q^46 - 4 * q^49 - 4 * q^50 - 24 * q^55 + 4 * q^56 + 16 * q^59 - 12 * q^60 + 24 * q^61 - 4 * q^64 - 4 * q^65 - 48 * q^66 + 48 * q^69 - 4 * q^70 - 24 * q^71 + 8 * q^74 + 16 * q^76 - 8 * q^79 + 4 * q^80 - 36 * q^81 - 8 * q^85 - 16 * q^86 + 40 * q^89 - 12 * q^90 - 8 * q^91 + 16 * q^94 - 4 * q^95

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