LMFDB - Embedded newform 1014.2.i.g.361.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(361,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("1014.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.i (of order $6$, degree $2$, not 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:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.17213603549184.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 $ x^12 - 5x^10 + 19x^8 - 28x^6 + 31x^4 - 6*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.4
Root			$-1.56052 - 0.900969i$ of defining polynomial
Character	$\chi$	$=$	1014.361
Dual form			1014.2.i.g.823.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -4.04892i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-0.599308 - 0.346011i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -4.04892i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-0.599308 - 0.346011i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.02446 - 3.50647i) q^{10} +(-4.20096 + 2.42543i) q^{11} -1.00000 q^{12} -0.692021 q^{14} +(-3.50647 + 2.02446i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.69202 - 6.39477i) q^{17} +1.00000i q^{18} +(-1.54167 - 0.890084i) q^{19} +(-3.50647 - 2.02446i) q^{20} +0.692021i q^{21} +(-2.42543 + 4.20096i) q^{22} +(2.55496 + 4.42532i) q^{23} +(-0.866025 + 0.500000i) q^{24} -11.3937 q^{25} +1.00000 q^{27} +(-0.599308 + 0.346011i) q^{28} +(1.67241 + 2.89669i) q^{29} +(-2.02446 + 3.50647i) q^{30} -0.972853i q^{31} +(-0.866025 - 0.500000i) q^{32} +(4.20096 + 2.42543i) q^{33} -7.38404i q^{34} +(-1.40097 + 2.42655i) q^{35} +(0.500000 + 0.866025i) q^{36} +(1.11389 - 0.643104i) q^{37} -1.78017 q^{38} -4.04892 q^{40} +(-1.30427 + 0.753020i) q^{41} +(0.346011 + 0.599308i) q^{42} +(-4.15883 + 7.20331i) q^{43} +4.85086i q^{44} +(3.50647 + 2.02446i) q^{45} +(4.42532 + 2.55496i) q^{46} -7.20775i q^{47} +(-0.500000 + 0.866025i) q^{48} +(-3.26055 - 5.64744i) q^{49} +(-9.86726 + 5.69687i) q^{50} -7.38404 q^{51} +13.4765 q^{53} +(0.866025 - 0.500000i) q^{54} +(9.82036 + 17.0094i) q^{55} +(-0.346011 + 0.599308i) q^{56} +1.78017i q^{57} +(2.89669 + 1.67241i) q^{58} +(-1.13274 - 0.653989i) q^{59} +4.04892i q^{60} +(0.198062 - 0.343054i) q^{61} +(-0.486426 - 0.842515i) q^{62} +(0.599308 - 0.346011i) q^{63} -1.00000 q^{64} +4.85086 q^{66} +(-5.24317 + 3.02715i) q^{67} +(-3.69202 - 6.39477i) q^{68} +(2.55496 - 4.42532i) q^{69} +2.80194i q^{70} +(-1.15160 - 0.664874i) q^{71} +(0.866025 + 0.500000i) q^{72} -7.65279i q^{73} +(0.643104 - 1.11389i) q^{74} +(5.69687 + 9.86726i) q^{75} +(-1.54167 + 0.890084i) q^{76} +3.35690 q^{77} -8.33944 q^{79} +(-3.50647 + 2.02446i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.753020 + 1.30427i) q^{82} -15.3274i q^{83} +(0.599308 + 0.346011i) q^{84} +(-25.8919 - 14.9487i) q^{85} +8.31767i q^{86} +(1.67241 - 2.89669i) q^{87} +(2.42543 + 4.20096i) q^{88} +(2.69327 - 1.55496i) q^{89} +4.04892 q^{90} +5.10992 q^{92} +(-0.842515 + 0.486426i) q^{93} +(-3.60388 - 6.24210i) q^{94} +(-3.60388 + 6.24210i) q^{95} +1.00000i q^{96} +(-7.39835 - 4.27144i) q^{97} +(-5.64744 - 3.26055i) q^{98} -4.85086i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} + 6 q^{4} - 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 + 6 * q^4 - 6 * q^9	$ 12 q - 6 q^{3} + 6 q^{4} - 6 q^{9} - 6 q^{10} - 12 q^{12} + 12 q^{14} - 6 q^{16} + 24 q^{17} - 2 q^{22} + 32 q^{23} - 8 q^{25} + 12 q^{27} - 26 q^{29} - 6 q^{30} - 8 q^{35} + 6 q^{36} - 16 q^{38} - 12 q^{40} - 6 q^{42} - 16 q^{43} - 6 q^{48} - 8 q^{49} - 48 q^{51} + 60 q^{53} + 44 q^{55} + 6 q^{56} + 20 q^{61} - 18 q^{62} - 12 q^{64} + 4 q^{66} - 24 q^{68} + 32 q^{69} + 24 q^{74} + 4 q^{75} + 24 q^{77} - 20 q^{79} - 6 q^{81} - 28 q^{82} - 26 q^{87} + 2 q^{88} + 12 q^{90} + 64 q^{92} - 8 q^{94} - 8 q^{95}+O(q^{100}) $ 12 * q - 6 * q^3 + 6 * q^4 - 6 * q^9 - 6 * q^10 - 12 * q^12 + 12 * q^14 - 6 * q^16 + 24 * q^17 - 2 * q^22 + 32 * q^23 - 8 * q^25 + 12 * q^27 - 26 * q^29 - 6 * q^30 - 8 * q^35 + 6 * q^36 - 16 * q^38 - 12 * q^40 - 6 * q^42 - 16 * q^43 - 6 * q^48 - 8 * q^49 - 48 * q^51 + 60 * q^53 + 44 * q^55 + 6 * q^56 + 20 * q^61 - 18 * q^62 - 12 * q^64 + 4 * q^66 - 24 * q^68 + 32 * q^69 + 24 * q^74 + 4 * q^75 + 24 * q^77 - 20 * q^79 - 6 * q^81 - 28 * q^82 - 26 * q^87 + 2 * q^88 + 12 * q^90 + 64 * q^92 - 8 * q^94 - 8 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		−	4.04892i		−	1.81073i	−0.424633	−	0.905365i	$-0.639597\pi$
$5$		−	4.04892i		−	1.81073i	0.424633	−	0.905365i	$-0.360403\pi$
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	−0.599308	−	0.346011i	−0.226517	−	0.130780i	0.382447	−	0.923977i	$-0.375081\pi$
$7$	−0.599308	−	0.346011i	−0.226517	−	0.130780i	−0.608964	+	0.793198i	$0.708415\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−2.02446	−	3.50647i	−0.640190	−	1.10884i
$11$	−4.20096	+	2.42543i	−1.26664	+	0.731294i	−0.974350	−	0.225036i	$-0.927750\pi$
$11$	−4.20096	+	2.42543i	−1.26664	+	0.731294i	−0.292288	+	0.956330i	$0.594417\pi$
$12$	−1.00000			−0.288675
$13$		0			0
$13$		0			0
$14$	−0.692021			−0.184951
$15$	−3.50647	+	2.02446i	−0.905365	+	0.522713i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.69202	−	6.39477i	0.895447	−	1.55096i	0.0621960	−	0.998064i	$-0.480190\pi$
$17$	3.69202	−	6.39477i	0.895447	−	1.55096i	0.833251	−	0.552895i	$-0.186477\pi$
$18$			1.00000i			0.235702i
$19$	−1.54167	−	0.890084i	−0.353683	−	0.204199i	0.312623	−	0.949877i	$-0.398792\pi$
$19$	−1.54167	−	0.890084i	−0.353683	−	0.204199i	−0.666306	+	0.745678i	$0.732126\pi$
$20$	−3.50647	−	2.02446i	−0.784069	−	0.452683i
$21$			0.692021i			0.151011i
$22$	−2.42543	+	4.20096i	−0.517103	+	0.895648i
$23$	2.55496	+	4.42532i	0.532746	+	0.922742i	0.999269	+	0.0382335i	$0.0121731\pi$
$23$	2.55496	+	4.42532i	0.532746	+	0.922742i	−0.466523	+	0.884509i	$0.654494\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	−11.3937			−2.27875
$26$		0			0
$27$	1.00000			0.192450
$28$	−0.599308	+	0.346011i	−0.113259	+	0.0653899i
$29$	1.67241	+	2.89669i	0.310558	+	0.537903i	0.978483	−	0.206326i	$-0.0661507\pi$
$29$	1.67241	+	2.89669i	0.310558	+	0.537903i	−0.667925	+	0.744228i	$0.732817\pi$
$30$	−2.02446	+	3.50647i	−0.369614	+	0.640190i
$31$		−	0.972853i		−	0.174730i	−0.996176	−	0.0873648i	$-0.972155\pi$
$31$		−	0.972853i		−	0.174730i	0.996176	−	0.0873648i	$-0.0278446\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	4.20096	+	2.42543i	0.731294	+	0.422213i
$34$		−	7.38404i		−	1.26635i
$35$	−1.40097	+	2.42655i	−0.236807	+	0.410162i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	1.11389	−	0.643104i	0.183122	−	0.105726i	−0.405637	−	0.914034i	$-0.632950\pi$
$37$	1.11389	−	0.643104i	0.183122	−	0.105726i	0.588759	+	0.808309i	$0.299617\pi$
$38$	−1.78017			−0.288781
$39$		0			0
$40$	−4.04892			−0.640190
$41$	−1.30427	+	0.753020i	−0.203693	+	0.117602i	−0.598377	−	0.801215i	$-0.704187\pi$
$41$	−1.30427	+	0.753020i	−0.203693	+	0.117602i	0.394684	+	0.918817i	$0.370854\pi$
$42$	0.346011	+	0.599308i	0.0533906	+	0.0924753i
$43$	−4.15883	+	7.20331i	−0.634216	+	1.09849i	0.352464	+	0.935825i	$0.385344\pi$
$43$	−4.15883	+	7.20331i	−0.634216	+	1.09849i	−0.986681	+	0.162669i	$0.947990\pi$
$44$			4.85086i			0.731294i
$45$	3.50647	+	2.02446i	0.522713	+	0.301788i
$46$	4.42532	+	2.55496i	0.652477	+	0.376708i
$47$		−	7.20775i		−	1.05136i	−0.850683	−	0.525679i	$-0.823811\pi$
$47$		−	7.20775i		−	1.05136i	0.850683	−	0.525679i	$-0.176189\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−3.26055	−	5.64744i	−0.465793	−	0.806778i
$50$	−9.86726	+	5.69687i	−1.39544	+	0.805658i
$51$	−7.38404			−1.03397
$52$		0			0
$53$	13.4765			1.85114			0.925570	−	0.378577i	$-0.123586\pi$
$53$	13.4765			1.85114			0.925570	+	0.378577i	$0.123586\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	9.82036	+	17.0094i	1.32418	+	2.29354i
$56$	−0.346011	+	0.599308i	−0.0462376	+	0.0800859i
$57$			1.78017i			0.235789i
$58$	2.89669	+	1.67241i	0.380355	+	0.219598i
$59$	−1.13274	−	0.653989i	−0.147471	−	0.0851422i	0.424449	−	0.905452i	$-0.360468\pi$
$59$	−1.13274	−	0.653989i	−0.147471	−	0.0851422i	−0.571920	+	0.820310i	$0.693801\pi$
$60$			4.04892i			0.522713i
$61$	0.198062	−	0.343054i	0.0253593	−	0.0439236i	−0.853067	−	0.521801i	$-0.825260\pi$
$61$	0.198062	−	0.343054i	0.0253593	−	0.0439236i	0.878427	+	0.477877i	$0.158594\pi$
$62$	−0.486426	−	0.842515i	−0.0617762	−	0.107000i
$63$	0.599308	−	0.346011i	0.0755057	−	0.0435933i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	4.85086			0.597099
$67$	−5.24317	+	3.02715i	−0.640555	+	0.369825i	−0.784828	−	0.619713i	$-0.787249\pi$
$67$	−5.24317	+	3.02715i	−0.640555	+	0.369825i	0.144273	+	0.989538i	$0.453916\pi$
$68$	−3.69202	−	6.39477i	−0.447723	−	0.775480i
$69$	2.55496	−	4.42532i	0.307581	−	0.532746i
$70$			2.80194i			0.334896i
$71$	−1.15160	−	0.664874i	−0.136669	−	0.0789061i	0.430106	−	0.902778i	$-0.358476\pi$
$71$	−1.15160	−	0.664874i	−0.136669	−	0.0789061i	−0.566776	+	0.823872i	$0.691809\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$		−	7.65279i		−	0.895692i	−0.894111	−	0.447846i	$-0.852191\pi$
$73$		−	7.65279i		−	0.895692i	0.894111	−	0.447846i	$-0.147809\pi$
$74$	0.643104	−	1.11389i	0.0747593	−	0.129487i
$75$	5.69687	+	9.86726i	0.657817	+	1.13937i
$76$	−1.54167	+	0.890084i	−0.176842	+	0.102100i
$77$	3.35690			0.382554
$78$		0			0
$79$	−8.33944			−0.938260			−0.469130	−	0.883129i	$-0.655432\pi$
$79$	−8.33944			−0.938260			−0.469130	+	0.883129i	$0.655432\pi$
$80$	−3.50647	+	2.02446i	−0.392035	+	0.226341i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.753020	+	1.30427i	−0.0831572	+	0.144032i
$83$		−	15.3274i		−	1.68240i	−0.540727	−	0.841198i	$-0.681851\pi$
$83$		−	15.3274i		−	1.68240i	0.540727	−	0.841198i	$-0.318149\pi$
$84$	0.599308	+	0.346011i	0.0653899	+	0.0377529i
$85$	−25.8919	−	14.9487i	−2.80837	−	1.62141i
$86$			8.31767i			0.896917i
$87$	1.67241	−	2.89669i	0.179301	−	0.310558i
$88$	2.42543	+	4.20096i	0.258551	+	0.447824i
$89$	2.69327	−	1.55496i	0.285486	−	0.164825i	−0.350419	−	0.936593i	$-0.613961\pi$
$89$	2.69327	−	1.55496i	0.285486	−	0.164825i	0.635904	+	0.771768i	$0.280627\pi$
$90$	4.04892			0.426793
$91$		0			0
$92$	5.10992			0.532746
$93$	−0.842515	+	0.486426i	−0.0873648	+	0.0504401i
$94$	−3.60388	−	6.24210i	−0.371711	−	0.643823i
$95$	−3.60388	+	6.24210i	−0.369750	+	0.640425i
$96$			1.00000i			0.102062i
$97$	−7.39835	−	4.27144i	−0.751188	−	0.433699i	0.0749347	−	0.997188i	$-0.476125\pi$
$97$	−7.39835	−	4.27144i	−0.751188	−	0.433699i	−0.826123	+	0.563490i	$0.809458\pi$
$98$	−5.64744	−	3.26055i	−0.570478	−	0.329366i
$99$		−	4.85086i		−	0.487529i
$100$	−5.69687	+	9.86726i	−0.569687	+	0.986726i
$101$	−5.99880	−	10.3902i	−0.596903	−	1.03387i	−0.993275	−	0.115777i	$-0.963064\pi$
$101$	−5.99880	−	10.3902i	−0.596903	−	1.03387i	0.396372	−	0.918090i	$-0.370269\pi$
$102$	−6.39477	+	3.69202i	−0.633176	+	0.365565i
$103$	12.3230			1.21423			0.607113	−	0.794616i	$-0.292328\pi$
$103$	12.3230			1.21423			0.607113	+	0.794616i	$0.292328\pi$
$104$		0			0
$105$	2.80194			0.273441
$106$	11.6710	−	6.73825i	1.13359	−	0.654477i
$107$	−2.94989	−	5.10935i	−0.285176	−	0.493940i	0.687476	−	0.726207i	$-0.258719\pi$
$107$	−2.94989	−	5.10935i	−0.285176	−	0.493940i	−0.972652	+	0.232268i	$0.925385\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$		−	0.792249i		−	0.0758837i	−0.999280	−	0.0379418i	$-0.987920\pi$
$109$		−	0.792249i		−	0.0758837i	0.999280	−	0.0379418i	$-0.0120802\pi$
$110$	17.0094	+	9.82036i	1.62178	+	0.936334i
$111$	−1.11389	−	0.643104i	−0.105726	−	0.0610407i
$112$			0.692021i			0.0653899i
$113$	−3.10992	+	5.38653i	−0.292556	+	0.506722i	−0.974413	−	0.224763i	$-0.927839\pi$
$113$	−3.10992	+	5.38653i	−0.292556	+	0.506722i	0.681857	+	0.731485i	$0.261173\pi$
$114$	0.890084	+	1.54167i	0.0833640	+	0.144391i
$115$	17.9177	−	10.3448i	1.67084	−	0.964659i
$116$	3.34481			0.310558
$117$		0			0
$118$	−1.30798			−0.120409
$119$	−4.42532	+	2.55496i	−0.405668	+	0.234213i
$120$	2.02446	+	3.50647i	0.184807	+	0.320095i
$121$	6.26540	−	10.8520i	0.569582	−	0.986544i
$122$		−	0.396125i		−	0.0358634i
$123$	1.30427	+	0.753020i	0.117602	+	0.0678976i
$124$	−0.842515	−	0.486426i	−0.0756601	−	0.0436824i
$125$			25.8877i			2.31547i
$126$	0.346011	−	0.599308i	0.0308251	−	0.0533906i
$127$	−3.00269	−	5.20081i	−0.266446	−	0.461497i	0.701496	−	0.712674i	$-0.252516\pi$
$127$	−3.00269	−	5.20081i	−0.266446	−	0.461497i	−0.967941	+	0.251176i	$0.919183\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	8.31767			0.732330
$130$		0			0
$131$	8.81700			0.770345			0.385173	−	0.922845i	$-0.374142\pi$
$131$	8.81700			0.770345			0.385173	+	0.922845i	$0.374142\pi$
$132$	4.20096	−	2.42543i	0.365647	−	0.211106i
$133$	0.615957	+	1.06687i	0.0534103	+	0.0925093i
$134$	−3.02715	+	5.24317i	−0.261506	+	0.452941i
$135$		−	4.04892i		−	0.348475i
$136$	−6.39477	−	3.69202i	−0.548347	−	0.316588i
$137$	13.6451	+	7.87800i	1.16578	+	0.673063i	0.952682	−	0.303968i	$-0.0983115\pi$
$137$	13.6451	+	7.87800i	1.16578	+	0.673063i	0.213097	+	0.977031i	$0.431645\pi$
$138$		−	5.10992i		−	0.434985i
$139$	3.04892	−	5.28088i	0.258606	−	0.447918i	−0.707263	−	0.706951i	$-0.750070\pi$
$139$	3.04892	−	5.28088i	0.258606	−	0.447918i	0.965869	+	0.259032i	$0.0834036\pi$
$140$	1.40097	+	2.42655i	0.118403	+	0.205081i
$141$	−6.24210	+	3.60388i	−0.525679	+	0.303501i
$142$	−1.32975			−0.111590
$143$		0			0
$144$	1.00000			0.0833333
$145$	11.7285	−	6.77144i	0.973997	−	0.562337i
$146$	−3.82640	−	6.62751i	−0.316675	−	0.548497i
$147$	−3.26055	+	5.64744i	−0.268926	+	0.465793i
$148$		−	1.28621i		−	0.105726i
$149$	−2.21059	−	1.27628i	−0.181098	−	0.104557i	0.406710	−	0.913557i	$-0.366676\pi$
$149$	−2.21059	−	1.27628i	−0.181098	−	0.104557i	−0.587809	+	0.809000i	$0.700009\pi$
$150$	9.86726	+	5.69687i	0.805658	+	0.465147i
$151$		−	17.7168i		−	1.44177i	−0.693054	−	0.720885i	$-0.743735\pi$
$151$		−	17.7168i		−	1.44177i	0.693054	−	0.720885i	$-0.256265\pi$
$152$	−0.890084	+	1.54167i	−0.0721953	+	0.125046i
$153$	3.69202	+	6.39477i	0.298482	+	0.516986i
$154$	2.90716	−	1.67845i	0.234265	−	0.135253i
$155$	−3.93900			−0.316388
$156$		0			0
$157$	−6.31767			−0.504205			−0.252102	−	0.967701i	$-0.581122\pi$
$157$	−6.31767			−0.504205			−0.252102	+	0.967701i	$0.581122\pi$
$158$	−7.22216	+	4.16972i	−0.574565	+	0.331725i
$159$	−6.73825	−	11.6710i	−0.534378	−	0.925570i
$160$	−2.02446	+	3.50647i	−0.160048	+	0.277210i
$161$		−	3.53617i		−	0.278689i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	12.6369	+	7.29590i	0.989796	+	0.571459i	0.905213	−	0.424958i	$-0.139711\pi$
$163$	12.6369	+	7.29590i	0.989796	+	0.571459i	0.0845824	+	0.996416i	$0.473044\pi$
$164$			1.50604i			0.117602i
$165$	9.82036	−	17.0094i	0.764514	−	1.32418i
$166$	−7.66368	−	13.2739i	−0.594817	−	1.03025i
$167$	16.8886	−	9.75063i	1.30688	−	0.754526i	0.325304	−	0.945610i	$-0.394533\pi$
$167$	16.8886	−	9.75063i	1.30688	−	0.754526i	0.981574	+	0.191083i	$0.0612001\pi$
$168$	0.692021			0.0533906
$169$		0			0
$170$	−29.8974			−2.29302
$171$	1.54167	−	0.890084i	0.117894	−	0.0680664i
$172$	4.15883	+	7.20331i	0.317108	+	0.549247i
$173$	−4.64526	+	8.04583i	−0.353173	+	0.611713i	−0.986803	−	0.161923i	$-0.948230\pi$
$173$	−4.64526	+	8.04583i	−0.353173	+	0.611713i	0.633631	+	0.773636i	$0.281564\pi$
$174$		−	3.34481i		−	0.253570i
$175$	6.82836	+	3.94235i	0.516175	+	0.298014i
$176$	4.20096	+	2.42543i	0.316660	+	0.182823i
$177$			1.30798i			0.0983137i
$178$	1.55496	−	2.69327i	0.116549	−	0.201869i
$179$	11.3964	+	19.7392i	0.851808	+	1.47538i	0.879575	+	0.475761i	$0.157827\pi$
$179$	11.3964	+	19.7392i	0.851808	+	1.47538i	−0.0277662	+	0.999614i	$0.508839\pi$
$180$	3.50647	−	2.02446i	0.261356	−	0.150894i
$181$	−0.537500			−0.0399520			−0.0199760	−	0.999800i	$-0.506359\pi$
$181$	−0.537500			−0.0399520			−0.0199760	+	0.999800i	$0.506359\pi$
$182$		0			0
$183$	−0.396125			−0.0292824
$184$	4.42532	−	2.55496i	0.326239	−	0.188354i
$185$	−2.60388	−	4.51004i	−0.191441	−	0.331585i
$186$	−0.486426	+	0.842515i	−0.0356665	+	0.0617762i
$187$			35.8189i			2.61934i
$188$	−6.24210	−	3.60388i	−0.455252	−	0.262840i
$189$	−0.599308	−	0.346011i	−0.0435933	−	0.0251686i
$190$			7.20775i			0.522905i
$191$	4.89977	−	8.48665i	0.354535	−	0.614073i	−0.632503	−	0.774558i	$-0.717972\pi$
$191$	4.89977	−	8.48665i	0.354535	−	0.614073i	0.987038	+	0.160485i	$0.0513058\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	12.2938	−	7.09783i	0.884928	−	0.510913i	0.0126478	−	0.999920i	$-0.495974\pi$
$193$	12.2938	−	7.09783i	0.884928	−	0.510913i	0.872280	+	0.489007i	$0.162641\pi$
$194$	−8.54288			−0.613343
$195$		0			0
$196$	−6.52111			−0.465793
$197$	−2.60647	+	1.50484i	−0.185703	+	0.107216i	−0.589969	−	0.807426i	$-0.700860\pi$
$197$	−2.60647	+	1.50484i	−0.185703	+	0.107216i	0.404266	+	0.914641i	$0.367527\pi$
$198$	−2.42543	−	4.20096i	−0.172368	−	0.298549i
$199$	6.44720	−	11.1669i	0.457030	−	0.791599i	−0.541773	−	0.840525i	$-0.682247\pi$
$199$	6.44720	−	11.1669i	0.457030	−	0.791599i	0.998802	+	0.0489263i	$0.0155800\pi$
$200$			11.3937i			0.805658i
$201$	5.24317	+	3.02715i	0.369825	+	0.213518i
$202$	−10.3902	−	5.99880i	−0.731054	−	0.422074i
$203$		−	2.31468i		−	0.162459i
$204$	−3.69202	+	6.39477i	−0.258493	+	0.447723i
$205$	3.04892	+	5.28088i	0.212946	+	0.368833i
$206$	10.6721	−	6.16152i	0.743558	−	0.429294i
$207$	−5.10992			−0.355164
$208$		0			0
$209$	8.63533			0.597319
$210$	2.42655	−	1.40097i	0.167448	−	0.0966760i
$211$	−3.89977	−	6.75460i	−0.268471	−	0.465006i	0.699996	−	0.714147i	$-0.253185\pi$
$211$	−3.89977	−	6.75460i	−0.268471	−	0.465006i	−0.968467	+	0.249141i	$0.919852\pi$
$212$	6.73825	−	11.6710i	0.462785	−	0.801567i
$213$			1.32975i			0.0911129i
$214$	−5.10935	−	2.94989i	−0.349268	−	0.201650i
$215$	29.1656	+	16.8388i	1.98908	+	1.14839i
$216$		−	1.00000i		−	0.0680414i
$217$	−0.336618	+	0.583039i	−0.0228511	+	0.0395792i
$218$	−0.396125	−	0.686108i	−0.0268289	−	0.0464691i
$219$	−6.62751	+	3.82640i	−0.447846	+	0.258564i
$220$	19.6407			1.32418
$221$		0			0
$222$	−1.28621			−0.0863246
$223$	−10.5618	+	6.09783i	−0.707268	+	0.408341i	−0.810049	−	0.586363i	$-0.800559\pi$
$223$	−10.5618	+	6.09783i	−0.707268	+	0.408341i	0.102781	+	0.994704i	$0.467226\pi$
$224$	0.346011	+	0.599308i	0.0231188	+	0.0400430i
$225$	5.69687	−	9.86726i	0.379791	−	0.657817i
$226$			6.21983i			0.413737i
$227$	−5.83990	−	3.37167i	−0.387608	−	0.223785i	0.293515	−	0.955954i	$-0.405175\pi$
$227$	−5.83990	−	3.37167i	−0.387608	−	0.223785i	−0.681123	+	0.732169i	$0.738508\pi$
$228$	1.54167	+	0.890084i	0.102100	+	0.0589472i
$229$			19.8237i			1.30999i	0.755634	+	0.654994i	$0.227329\pi$
$229$			19.8237i			1.30999i	−0.755634	+	0.654994i	$0.772671\pi$
$230$	10.3448	−	17.9177i	0.682117	−	1.18146i
$231$	−1.67845	−	2.90716i	−0.110434	−	0.191277i
$232$	2.89669	−	1.67241i	0.190177	−	0.109799i
$233$	30.0301			1.96734			0.983670	−	0.179983i	$-0.0576044\pi$
$233$	30.0301			1.96734			0.983670	+	0.179983i	$0.0576044\pi$
$234$		0			0
$235$	−29.1836			−1.90373
$236$	−1.13274	+	0.653989i	−0.0737353	+	0.0425711i
$237$	4.16972	+	7.22216i	0.270852	+	0.469130i
$238$	−2.55496	+	4.42532i	−0.165613	+	0.286851i
$239$			22.0978i			1.42939i	0.699436	+	0.714695i	$0.253435\pi$
$239$			22.0978i			1.42939i	−0.699436	+	0.714695i	$0.746565\pi$
$240$	3.50647	+	2.02446i	0.226341	+	0.130678i
$241$	8.77056	+	5.06369i	0.564962	+	0.326181i	0.755135	−	0.655570i	$-0.227572\pi$
$241$	8.77056	+	5.06369i	0.564962	+	0.326181i	−0.190173	+	0.981751i	$0.560905\pi$
$242$		−	12.5308i		−	0.805510i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−0.198062	−	0.343054i	−0.0126796	−	0.0219618i
$245$	−22.8660	+	13.2017i	−1.46086	+	0.843426i
$246$	1.50604			0.0960217
$247$		0			0
$248$	−0.972853			−0.0617762
$249$	−13.2739	+	7.66368i	−0.841198	+	0.485666i
$250$	12.9438	+	22.4194i	0.818641	+	1.41793i
$251$	2.77359	−	4.80401i	0.175068	−	0.303226i	−0.765117	−	0.643891i	$-0.777319\pi$
$251$	2.77359	−	4.80401i	0.175068	−	0.303226i	0.940185	+	0.340665i	$0.110652\pi$
$252$		−	0.692021i		−	0.0435933i
$253$	−21.4666	−	12.3937i	−1.34959	−	0.779187i
$254$	−5.20081	−	3.00269i	−0.326328	−	0.188405i
$255$			29.8974i			1.87225i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.89977	−	11.9508i	−0.430396	−	0.745468i	0.566511	−	0.824054i	$-0.308293\pi$
$257$	−6.89977	−	11.9508i	−0.430396	−	0.745468i	−0.996907	+	0.0785862i	$0.974959\pi$
$258$	7.20331	−	4.15883i	0.448459	−	0.258918i
$259$	−0.890084			−0.0553071
$260$		0			0
$261$	−3.34481			−0.207039
$262$	7.63575	−	4.40850i	0.471738	−	0.272358i
$263$	11.2349	+	19.4594i	0.692773	+	1.19992i	0.970926	+	0.239382i	$0.0769448\pi$
$263$	11.2349	+	19.4594i	0.692773	+	1.19992i	−0.278152	+	0.960537i	$0.589722\pi$
$264$	2.42543	−	4.20096i	0.149275	−	0.258551i
$265$		−	54.5652i		−	3.35192i
$266$	1.06687	+	0.615957i	0.0654139	+	0.0377668i
$267$	−2.69327	−	1.55496i	−0.164825	−	0.0951619i
$268$			6.05429i			0.369825i
$269$	13.0070	−	22.5288i	0.793051	−	1.37360i	−0.131019	−	0.991380i	$-0.541825\pi$
$269$	13.0070	−	22.5288i	0.793051	−	1.37360i	0.924070	−	0.382224i	$-0.124842\pi$
$270$	−2.02446	−	3.50647i	−0.123205	−	0.213397i
$271$	−2.49823	+	1.44235i	−0.151757	+	0.0876167i	−0.573955	−	0.818887i	$-0.694592\pi$
$271$	−2.49823	+	1.44235i	−0.151757	+	0.0876167i	0.422199	+	0.906503i	$0.361258\pi$
$272$	−7.38404			−0.447723
$273$		0			0
$274$	15.7560			0.951855
$275$	47.8647	−	27.6347i	2.88635	−	1.66643i
$276$	−2.55496	−	4.42532i	−0.153790	−	0.266373i
$277$	−0.731250	+	1.26656i	−0.0439366	+	0.0761004i	−0.887157	−	0.461467i	$-0.847323\pi$
$277$	−0.731250	+	1.26656i	−0.0439366	+	0.0761004i	0.843221	+	0.537567i	$0.180657\pi$
$278$		−	6.09783i		−	0.365724i
$279$	0.842515	+	0.486426i	0.0504401	+	0.0291216i
$280$	2.42655	+	1.40097i	0.145014	+	0.0837239i
$281$		−	5.68233i		−	0.338980i	−0.985532	−	0.169490i	$-0.945788\pi$
$281$		−	5.68233i		−	0.338980i	0.985532	−	0.169490i	$-0.0542120\pi$
$282$	−3.60388	+	6.24210i	−0.214608	+	0.371711i
$283$	−12.6039	−	21.8306i	−0.749223	−	1.29769i	−0.948196	−	0.317687i	$-0.897094\pi$
$283$	−12.6039	−	21.8306i	−0.749223	−	1.29769i	0.198973	−	0.980005i	$-0.436239\pi$
$284$	−1.15160	+	0.664874i	−0.0683347	+	0.0394530i
$285$	7.20775			0.426950
$286$		0			0
$287$	1.04221			0.0615199
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	−18.7620	−	32.4968i	−1.10365	−	1.91158i
$290$	6.77144	−	11.7285i	0.397633	−	0.688720i
$291$			8.54288i			0.500792i
$292$	−6.62751	−	3.82640i	−0.387846	−	0.223923i
$293$	−6.19134	−	3.57457i	−0.361702	−	0.208829i	0.308125	−	0.951346i	$-0.400298\pi$
$293$	−6.19134	−	3.57457i	−0.361702	−	0.208829i	−0.669827	+	0.742517i	$0.733632\pi$
$294$			6.52111i			0.380319i
$295$	−2.64795	+	4.58638i	−0.154170	+	0.267029i
$296$	−0.643104	−	1.11389i	−0.0373797	−	0.0647435i
$297$	−4.20096	+	2.42543i	−0.243765	+	0.140738i
$298$	−2.55257			−0.147866
$299$		0			0
$300$	11.3937			0.657817
$301$	4.98485	−	2.87800i	0.287322	−	0.165885i
$302$	−8.85839	−	15.3432i	−0.509743	−	0.882901i
$303$	−5.99880	+	10.3902i	−0.344622	+	0.596903i
$304$			1.78017i			0.102100i
$305$	−1.38900	−	0.801938i	−0.0795337	−	0.0459188i
$306$	6.39477	+	3.69202i	0.365565	+	0.211059i
$307$			17.9952i			1.02704i	0.858077	+	0.513521i	$0.171659\pi$
$307$			17.9952i			1.02704i	−0.858077	+	0.513521i	$0.828341\pi$
$308$	1.67845	−	2.90716i	0.0956384	−	0.165651i
$309$	−6.16152	−	10.6721i	−0.350517	−	0.607113i
$310$	−3.41127	+	1.96950i	−0.193747	+	0.111860i
$311$	−3.32975			−0.188813			−0.0944064	−	0.995534i	$-0.530095\pi$
$311$	−3.32975			−0.188813			−0.0944064	+	0.995534i	$0.530095\pi$
$312$		0			0
$313$	−17.8834			−1.01083			−0.505414	−	0.862877i	$-0.668660\pi$
$313$	−17.8834			−1.01083			−0.505414	+	0.862877i	$0.668660\pi$
$314$	−5.47126	+	3.15883i	−0.308761	+	0.178263i
$315$	−1.40097	−	2.42655i	−0.0789357	−	0.136721i
$316$	−4.16972	+	7.22216i	−0.234565	+	0.406279i
$317$			4.39373i			0.246777i	0.992358	+	0.123388i	$0.0393761\pi$
$317$			4.39373i			0.246777i	−0.992358	+	0.123388i	$0.960624\pi$
$318$	−11.6710	−	6.73825i	−0.654477	−	0.377862i
$319$	−14.0514	−	8.11260i	−0.786730	−	0.454219i
$320$			4.04892i			0.226341i
$321$	−2.94989	+	5.10935i	−0.164647	+	0.285176i
$322$	−1.76809	−	3.06241i	−0.0985316	−	0.170662i
$323$	−11.3838	+	6.57242i	−0.633409	+	0.365699i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	14.5918			0.808165
$327$	−0.686108	+	0.396125i	−0.0379418	+	0.0219057i
$328$	0.753020	+	1.30427i	0.0415786	+	0.0720162i
$329$	−2.49396	+	4.31966i	−0.137496	+	0.238151i
$330$		−	19.6407i		−	1.08119i
$331$	22.2374	+	12.8388i	1.22228	+	0.705683i	0.965403	−	0.260762i	$-0.0839737\pi$
$331$	22.2374	+	12.8388i	1.22228	+	0.705683i	0.256875	+	0.966445i	$0.417307\pi$
$332$	−13.2739	−	7.66368i	−0.728499	−	0.420599i
$333$			1.28621i			0.0704838i
$334$	9.75063	−	16.8886i	0.533531	−	0.924102i
$335$	12.2567	+	21.2292i	0.669653	+	1.15987i
$336$	0.599308	−	0.346011i	0.0326949	−	0.0188764i
$337$	24.6504			1.34279			0.671396	−	0.741098i	$-0.265695\pi$
$337$	24.6504			1.34279			0.671396	+	0.741098i	$0.265695\pi$
$338$		0			0
$339$	6.21983			0.337815
$340$	−25.8919	+	14.9487i	−1.40418	+	0.810707i
$341$	2.35958	+	4.08692i	0.127779	+	0.221319i
$342$	0.890084	−	1.54167i	0.0481302	−	0.0833640i
$343$			9.35690i			0.505225i
$344$	7.20331	+	4.15883i	0.388377	+	0.224229i
$345$	−17.9177	−	10.3448i	−0.964659	−	0.556946i
$346$			9.29052i			0.499461i
$347$	−7.14795	+	12.3806i	−0.383722	+	0.664626i	−0.991591	−	0.129411i	$-0.958691\pi$
$347$	−7.14795	+	12.3806i	−0.383722	+	0.664626i	0.607869	+	0.794037i	$0.292025\pi$
$348$	−1.67241	−	2.89669i	−0.0896504	−	0.155279i
$349$	−9.57962	+	5.53079i	−0.512785	+	0.296057i	−0.733978	−	0.679173i	$-0.762338\pi$
$349$	−9.57962	+	5.53079i	−0.512785	+	0.296057i	0.221193	+	0.975230i	$0.429005\pi$
$350$	7.88471			0.421455
$351$		0			0
$352$	4.85086			0.258551
$353$	−9.09735	+	5.25236i	−0.484203	+	0.279555i	−0.722166	−	0.691719i	$-0.756854\pi$
$353$	−9.09735	+	5.25236i	−0.484203	+	0.279555i	0.237963	+	0.971274i	$0.423520\pi$
$354$	0.653989	+	1.13274i	0.0347591	+	0.0602046i
$355$	−2.69202	+	4.66272i	−0.142878	+	0.247471i
$356$		−	3.10992i		−	0.164825i
$357$	4.42532	+	2.55496i	0.234213	+	0.135223i
$358$	19.7392	+	11.3964i	1.04325	+	0.602320i
$359$		−	5.10992i		−	0.269691i	−0.990867	−	0.134846i	$-0.956946\pi$
$359$		−	5.10992i		−	0.269691i	0.990867	−	0.134846i	$-0.0430538\pi$
$360$	2.02446	−	3.50647i	0.106698	−	0.184807i
$361$	−7.91550	−	13.7101i	−0.416605	−	0.721582i
$362$	−0.465488	+	0.268750i	−0.0244655	+	0.0141252i
$363$	−12.5308			−0.657696
$364$		0			0
$365$	−30.9855			−1.62186
$366$	−0.343054	+	0.198062i	−0.0179317	+	0.0103529i
$367$	4.22401	+	7.31620i	0.220492	+	0.381903i	0.954957	−	0.296743i	$-0.0959005\pi$
$367$	4.22401	+	7.31620i	0.220492	+	0.381903i	−0.734466	+	0.678646i	$0.762567\pi$
$368$	2.55496	−	4.42532i	0.133186	−	0.230686i
$369$		−	1.50604i		−	0.0784014i
$370$	−4.51004	−	2.60388i	−0.234466	−	0.135369i
$371$	−8.07658	−	4.66301i	−0.419315	−	0.242092i
$372$			0.972853i			0.0504401i
$373$	−3.84548	+	6.66056i	−0.199111	+	0.344871i	−0.948241	−	0.317553i	$-0.897139\pi$
$373$	−3.84548	+	6.66056i	−0.199111	+	0.344871i	0.749129	+	0.662424i	$0.230472\pi$
$374$	17.9095	+	31.0201i	0.926076	+	1.60401i
$375$	22.4194	−	12.9438i	1.15773	−	0.668417i
$376$	−7.20775			−0.371711
$377$		0			0
$378$	−0.692021			−0.0355937
$379$	−9.87565	+	5.70171i	−0.507278	+	0.292877i	−0.731714	−	0.681612i	$-0.761279\pi$
$379$	−9.87565	+	5.70171i	−0.507278	+	0.292877i	0.224436	+	0.974489i	$0.427946\pi$
$380$	3.60388	+	6.24210i	0.184875	+	0.320213i
$381$	−3.00269	+	5.20081i	−0.153832	+	0.266446i
$382$		−	9.79954i		−	0.501388i
$383$	−17.9010	−	10.3351i	−0.914696	−	0.528100i	−0.0327572	−	0.999463i	$-0.510429\pi$
$383$	−17.9010	−	10.3351i	−0.914696	−	0.528100i	−0.881939	+	0.471363i	$0.843762\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$		−	13.5918i		−	0.692702i
$386$	7.09783	−	12.2938i	0.361270	−	0.625738i
$387$	−4.15883	−	7.20331i	−0.211405	−	0.366165i
$388$	−7.39835	+	4.27144i	−0.375594	+	0.216849i
$389$	−17.4776			−0.886148			−0.443074	−	0.896485i	$-0.646112\pi$
$389$	−17.4776			−0.886148			−0.443074	+	0.896485i	$0.646112\pi$
$390$		0			0
$391$	37.7318			1.90818
$392$	−5.64744	+	3.26055i	−0.285239	+	0.164683i
$393$	−4.40850	−	7.63575i	−0.222379	−	0.385173i
$394$	−1.50484	+	2.60647i	−0.0758130	+	0.131312i
$395$			33.7657i			1.69894i
$396$	−4.20096	−	2.42543i	−0.211106	−	0.121882i
$397$	−16.7661	−	9.67994i	−0.841469	−	0.485822i	0.0162944	−	0.999867i	$-0.494813\pi$
$397$	−16.7661	−	9.67994i	−0.841469	−	0.485822i	−0.857763	+	0.514045i	$0.828146\pi$
$398$		−	12.8944i		−	0.646338i
$399$	0.615957	−	1.06687i	0.0308364	−	0.0534103i
$400$	5.69687	+	9.86726i	0.284843	+	0.493363i
$401$	12.5428	−	7.24160i	0.626359	−	0.361628i	−0.152982	−	0.988229i	$-0.548888\pi$
$401$	12.5428	−	7.24160i	0.626359	−	0.361628i	0.779341	+	0.626601i	$0.215554\pi$
$402$	6.05429			0.301961
$403$		0			0
$404$	−11.9976			−0.596903
$405$	−3.50647	+	2.02446i	−0.174238	+	0.100596i
$406$	−1.15734	−	2.00457i	−0.0574379	−	0.0994854i
$407$	−3.11960	+	5.40331i	−0.154633	+	0.267832i
$408$			7.38404i			0.365565i
$409$	16.3665	+	9.44922i	0.809273	+	0.467234i	0.846703	−	0.532065i	$-0.178584\pi$
$409$	16.3665	+	9.44922i	0.809273	+	0.467234i	−0.0374304	+	0.999299i	$0.511917\pi$
$410$	5.28088	+	3.04892i	0.260804	+	0.150575i
$411$		−	15.7560i		−	0.777186i
$412$	6.16152	−	10.6721i	0.303556	−	0.525775i
$413$	0.452575	+	0.783882i	0.0222697	+	0.0385723i
$414$	−4.42532	+	2.55496i	−0.217492	+	0.125569i
$415$	−62.0592			−3.04637
$416$		0			0
$417$	−6.09783			−0.298612
$418$	7.47842	−	4.31767i	0.365781	−	0.211184i
$419$	10.8802	+	18.8450i	0.531531	+	0.920638i	0.999323	+	0.0367993i	$0.0117162\pi$
$419$	10.8802	+	18.8450i	0.531531	+	0.920638i	−0.467792	+	0.883838i	$0.654950\pi$
$420$	1.40097	−	2.42655i	0.0683603	−	0.118403i
$421$			20.5918i			1.00358i	0.864989	+	0.501791i	$0.167325\pi$
$421$			20.5918i			1.00358i	−0.864989	+	0.501791i	$0.832675\pi$
$422$	−6.75460	−	3.89977i	−0.328809	−	0.189838i
$423$	6.24210	+	3.60388i	0.303501	+	0.175226i
$424$		−	13.4765i		−	0.654477i
$425$	−42.0659	+	72.8603i	−2.04050	+	3.53424i
$426$	0.664874	+	1.15160i	0.0322133	+	0.0557950i
$427$	−0.237401	+	0.137063i	−0.0114886	+	0.00663296i
$428$	−5.89977			−0.285176
$429$		0			0
$430$	33.6775			1.62408
$431$	29.8894	−	17.2567i	1.43972	−	0.831224i	0.441893	−	0.897068i	$-0.354307\pi$
$431$	29.8894	−	17.2567i	1.43972	−	0.831224i	0.997830	+	0.0658433i	$0.0209737\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−1.06315	+	1.84144i	−0.0510920	+	0.0884939i	−0.890440	−	0.455100i	$-0.849603\pi$
$433$	−1.06315	+	1.84144i	−0.0510920	+	0.0884939i	0.839348	+	0.543594i	$0.182937\pi$
$434$			0.673235i			0.0323163i
$435$	−11.7285	−	6.77144i	−0.562337	−	0.324666i
$436$	−0.686108	−	0.396125i	−0.0328586	−	0.0189709i
$437$		−	9.09651i		−	0.435145i
$438$	−3.82640	+	6.62751i	−0.182832	+	0.316675i
$439$	10.9160	+	18.9071i	0.520994	+	0.902388i	0.999702	+	0.0244137i	$0.00777191\pi$
$439$	10.9160	+	18.9071i	0.520994	+	0.902388i	−0.478708	+	0.877974i	$0.658895\pi$
$440$	17.0094	−	9.82036i	0.810889	−	0.468167i
$441$	6.52111			0.310529
$442$		0			0
$443$	−7.54048			−0.358259			−0.179130	−	0.983825i	$-0.557328\pi$
$443$	−7.54048			−0.358259			−0.179130	+	0.983825i	$0.557328\pi$
$444$	−1.11389	+	0.643104i	−0.0528628	+	0.0305204i
$445$	−6.29590	−	10.9048i	−0.298454	−	0.516938i
$446$	−6.09783	+	10.5618i	−0.288741	+	0.500114i
$447$			2.55257i			0.120732i
$448$	0.599308	+	0.346011i	0.0283146	+	0.0163475i
$449$	17.1092	+	9.87800i	0.807433	+	0.466172i	0.846064	−	0.533082i	$-0.178966\pi$
$449$	17.1092	+	9.87800i	0.807433	+	0.466172i	−0.0386305	+	0.999254i	$0.512300\pi$
$450$		−	11.3937i		−	0.537106i
$451$	3.65279	−	6.32682i	0.172003	−	0.297918i
$452$	3.10992	+	5.38653i	0.146278	+	0.253361i
$453$	−15.3432	+	8.85839i	−0.720885	+	0.416203i
$454$	−6.74333			−0.316480
$455$		0			0
$456$	1.78017			0.0833640
$457$	20.6618	−	11.9291i	0.966517	−	0.558019i	0.0683441	−	0.997662i	$-0.478228\pi$
$457$	20.6618	−	11.9291i	0.966517	−	0.558019i	0.898173	+	0.439643i	$0.144895\pi$
$458$	9.91185	+	17.1678i	0.463151	+	0.802200i
$459$	3.69202	−	6.39477i	0.172329	−	0.298482i
$460$		−	20.6896i		−	0.964659i
$461$	15.2224	+	8.78866i	0.708978	+	0.409329i	0.810683	−	0.585486i	$-0.199096\pi$
$461$	15.2224	+	8.78866i	0.708978	+	0.409329i	−0.101704	+	0.994815i	$0.532430\pi$
$462$	−2.90716	−	1.67845i	−0.135253	−	0.0780885i
$463$		−	23.8431i		−	1.10808i	−0.832489	−	0.554041i	$-0.813085\pi$
$463$		−	23.8431i		−	1.10808i	0.832489	−	0.554041i	$-0.186915\pi$
$464$	1.67241	−	2.89669i	0.0776396	−	0.134476i
$465$	1.96950	+	3.41127i	0.0913334	+	0.158194i
$466$	26.0069	−	15.0151i	1.20474	−	0.695559i
$467$	−8.61058			−0.398450			−0.199225	−	0.979954i	$-0.563842\pi$
$467$	−8.61058			−0.398450			−0.199225	+	0.979954i	$0.563842\pi$
$468$		0			0
$469$	4.18970			0.193462
$470$	−25.2737	+	14.5918i	−1.16579	+	0.673069i
$471$	3.15883	+	5.47126i	0.145551	+	0.252102i
$472$	−0.653989	+	1.13274i	−0.0301023	+	0.0521387i
$473$		−	40.3478i		−	1.85519i
$474$	7.22216	+	4.16972i	0.331725	+	0.191522i
$475$	17.5654	+	10.1414i	0.805955	+	0.465318i
$476$			5.10992i			0.234213i
$477$	−6.73825	+	11.6710i	−0.308523	+	0.534378i
$478$	11.0489	+	19.1373i	0.505366	+	0.875319i
$479$	−5.69935	+	3.29052i	−0.260410	+	0.150348i	−0.624522	−	0.781008i	$-0.714706\pi$
$479$	−5.69935	+	3.29052i	−0.260410	+	0.150348i	0.364112	+	0.931355i	$0.381373\pi$
$480$	4.04892			0.184807
$481$		0			0
$482$	10.1274			0.461289
$483$	−3.06241	+	1.76809i	−0.139345	+	0.0804507i
$484$	−6.26540	−	10.8520i	−0.284791	−	0.493272i
$485$	−17.2947	+	29.9553i	−0.785312	+	1.36020i
$486$			1.00000i			0.0453609i
$487$	20.1576	+	11.6380i	0.913430	+	0.527369i	0.881533	−	0.472122i	$-0.156512\pi$
$487$	20.1576	+	11.6380i	0.913430	+	0.527369i	0.0318970	+	0.999491i	$0.489845\pi$
$488$	−0.343054	−	0.198062i	−0.0155293	−	0.00896586i
$489$		−	14.5918i		−	0.659864i
$490$	−13.2017	+	22.8660i	−0.596392	+	1.03298i
$491$	−7.77024	−	13.4585i	−0.350666	−	0.607372i	0.635700	−	0.771936i	$-0.280711\pi$
$491$	−7.77024	−	13.4585i	−0.350666	−	0.607372i	−0.986366	+	0.164565i	$0.947378\pi$
$492$	1.30427	−	0.753020i	0.0588010	−	0.0339488i
$493$	24.6983			1.11235
$494$		0			0
$495$	−19.6407			−0.882784
$496$	−0.842515	+	0.486426i	−0.0378301	+	0.0218412i
$497$	0.460107	+	0.796929i	0.0206386	+	0.0357472i
$498$	−7.66368	+	13.2739i	−0.343418	+	0.594817i
$499$			9.53617i			0.426898i	0.976954	+	0.213449i	$0.0684697\pi$
$499$			9.53617i			0.426898i	−0.976954	+	0.213449i	$0.931530\pi$
$500$	22.4194	+	12.9438i	1.00263	+	0.578866i
$501$	−16.8886	−	9.75063i	−0.754526	−	0.435626i
$502$		−	5.54719i		−	0.247583i
$503$	6.91723	−	11.9810i	0.308424	−	0.534206i	−0.669594	−	0.742728i	$-0.733532\pi$
$503$	6.91723	−	11.9810i	0.308424	−	0.534206i	0.978018	+	0.208521i	$0.0668651\pi$
$504$	−0.346011	−	0.599308i	−0.0154125	−	0.0266953i
$505$	−42.0692	+	24.2887i	−1.87205	+	1.08083i
$506$	−24.7875			−1.10194
$507$		0			0
$508$	−6.00538			−0.266446
$509$	−35.4757	+	20.4819i	−1.57243	+	0.907843i	−0.576560	+	0.817054i	$0.695605\pi$
$509$	−35.4757	+	20.4819i	−1.57243	+	0.907843i	−0.995870	+	0.0907888i	$0.971061\pi$
$510$	14.9487	+	25.8919i	0.661939	+	1.14651i
$511$	−2.64795	+	4.58638i	−0.117138	+	0.202890i
$512$			1.00000i			0.0441942i
$513$	−1.54167	−	0.890084i	−0.0680664	−	0.0392982i
$514$	−11.9508	−	6.89977i	−0.527125	−	0.304336i
$515$		−	49.8950i		−	2.19864i
$516$	4.15883	−	7.20331i	0.183082	−	0.317108i
$517$	17.4819	+	30.2795i	0.768852	+	1.33169i
$518$	−0.770835	+	0.445042i	−0.0338686	+	0.0195540i
$519$	9.29052			0.407809
$520$		0			0
$521$	36.3672			1.59327			0.796637	−	0.604457i	$-0.206610\pi$
$521$	36.3672			1.59327			0.796637	+	0.604457i	$0.206610\pi$
$522$	−2.89669	+	1.67241i	−0.126785	+	0.0731993i
$523$	3.01507	+	5.22225i	0.131840	+	0.228353i	0.924386	−	0.381459i	$-0.124578\pi$
$523$	3.01507	+	5.22225i	0.131840	+	0.228353i	−0.792546	+	0.609812i	$0.791245\pi$
$524$	4.40850	−	7.63575i	0.192586	−	0.333569i
$525$		−	7.88471i		−	0.344117i
$526$	19.4594	+	11.2349i	0.848471	+	0.489865i
$527$	−6.22117	−	3.59179i	−0.270998	−	0.156461i
$528$		−	4.85086i		−	0.211106i
$529$	−1.55562	+	2.69442i	−0.0676357	+	0.117149i
$530$	−27.2826	−	47.2549i	−1.18508	−	2.05262i
$531$	1.13274	−	0.653989i	0.0491568	−	0.0283807i
$532$	1.23191			0.0534103
$533$		0			0
$534$	−3.10992			−0.134579
$535$	−20.6873	+	11.9438i	−0.894392	+	0.516377i
$536$	3.02715	+	5.24317i	0.130753	+	0.226471i
$537$	11.3964	−	19.7392i	0.491792	−	0.851808i
$538$		−	26.0140i		−	1.12154i
$539$	27.3949	+	15.8165i	1.17998	+	0.681264i
$540$	−3.50647	−	2.02446i	−0.150894	−	0.0871188i
$541$			7.92154i			0.340574i	0.985395	+	0.170287i	$0.0544694\pi$
$541$			7.92154i			0.340574i	−0.985395	+	0.170287i	$0.945531\pi$
$542$	−1.44235	+	2.49823i	−0.0619544	+	0.107308i
$543$	0.268750	+	0.465488i	0.0115332	+	0.0199760i
$544$	−6.39477	+	3.69202i	−0.274173	+	0.158294i
$545$	−3.20775			−0.137405
$546$		0			0
$547$	18.4155			0.787390			0.393695	−	0.919241i	$-0.371197\pi$
$547$	18.4155			0.787390			0.393695	+	0.919241i	$0.371197\pi$
$548$	13.6451	−	7.87800i	0.582890	−	0.336532i
$549$	0.198062	+	0.343054i	0.00845309	+	0.0146412i
$550$	27.6347	−	47.8647i	1.17835	−	2.04096i
$551$		−	5.95433i		−	0.253663i
$552$	−4.42532	−	2.55496i	−0.188354	−	0.108746i
$553$	4.99789	+	2.88553i	0.212532	+	0.122705i
$554$			1.46250i			0.0621357i
$555$	−2.60388	+	4.51004i	−0.110528	+	0.191441i
$556$	−3.04892	−	5.28088i	−0.129303	−	0.223959i
$557$	20.7637	−	11.9879i	0.879786	−	0.507944i	0.00919783	−	0.999958i	$-0.497072\pi$
$557$	20.7637	−	11.9879i	0.879786	−	0.507944i	0.870588	+	0.492013i	$0.163739\pi$
$558$	0.972853			0.0411841
$559$		0			0
$560$	2.80194			0.118403
$561$	31.0201	−	17.9095i	1.30967	−	0.756138i
$562$	−2.84117	−	4.92104i	−0.119847	−	0.207582i
$563$	−1.14646	+	1.98572i	−0.0483174	+	0.0836882i	−0.889173	−	0.457572i	$-0.848719\pi$
$563$	−1.14646	+	1.98572i	−0.0483174	+	0.0836882i	0.840855	+	0.541260i	$0.182053\pi$
$564$			7.20775i			0.303501i
$565$	21.8096	+	12.5918i	0.917538	+	0.529741i
$566$	−21.8306	−	12.6039i	−0.917607	−	0.529780i
$567$			0.692021i			0.0290622i
$568$	−0.664874	+	1.15160i	−0.0278975	+	0.0483199i
$569$	−22.1715	−	38.4022i	−0.929478	−	1.60990i	−0.784197	−	0.620513i	$-0.786925\pi$
$569$	−22.1715	−	38.4022i	−0.929478	−	1.60990i	−0.145281	−	0.989390i	$-0.546409\pi$
$570$	6.24210	−	3.60388i	0.261453	−	0.150950i
$571$	15.2707			0.639058			0.319529	−	0.947577i	$-0.396475\pi$
$571$	15.2707			0.639058			0.319529	+	0.947577i	$0.396475\pi$
$572$		0			0
$573$	−9.79954			−0.409382
$574$	0.902583	−	0.521106i	0.0376731	−	0.0217506i
$575$	−29.1105	−	50.4209i	−1.21399	−	2.10270i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$			8.77048i			0.365120i	0.983195	+	0.182560i	$0.0584383\pi$
$577$			8.77048i			0.365120i	−0.983195	+	0.182560i	$0.941562\pi$
$578$	−32.4968	−	18.7620i	−1.35169	−	0.780398i
$579$	−12.2938	−	7.09783i	−0.510913	−	0.294976i
$580$		−	13.5429i		−	0.562337i
$581$	−5.30343	+	9.18581i	−0.220023	+	0.381092i
$582$	4.27144	+	7.39835i	0.177057	+	0.306671i
$583$	−56.6143	+	32.6863i	−2.34472	+	1.35373i
$584$	−7.65279			−0.316675
$585$		0			0
$586$	−7.14914			−0.295328
$587$	−33.0328	+	19.0715i	−1.36341	+	0.787166i	−0.990076	−	0.140531i	$-0.955119\pi$
$587$	−33.0328	+	19.0715i	−1.36341	+	0.787166i	−0.373335	+	0.927697i	$0.621786\pi$
$588$	3.26055	+	5.64744i	0.134463	+	0.232897i
$589$	−0.865921	+	1.49982i	−0.0356796	+	0.0617989i
$590$			5.29590i			0.218029i
$591$	2.60647	+	1.50484i	0.107216	+	0.0619010i
$592$	−1.11389	−	0.643104i	−0.0457806	−	0.0264314i
$593$			37.9517i			1.55849i	0.626720	+	0.779244i	$0.284397\pi$
$593$			37.9517i			1.55849i	−0.626720	+	0.779244i	$0.715603\pi$
$594$	−2.42543	+	4.20096i	−0.0995165	+	0.172368i
$595$	10.3448	+	17.9177i	0.424096	+	0.734556i
$596$	−2.21059	+	1.27628i	−0.0905491	+	0.0522786i
$597$	−12.8944			−0.527732
$598$		0			0
$599$	−3.57971			−0.146263			−0.0731315	−	0.997322i	$-0.523299\pi$
$599$	−3.57971			−0.146263			−0.0731315	+	0.997322i	$0.523299\pi$
$600$	9.86726	−	5.69687i	0.402829	−	0.232574i
$601$	2.85839	+	4.95087i	0.116596	+	0.201950i	0.918417	−	0.395615i	$-0.129468\pi$
$601$	2.85839	+	4.95087i	0.116596	+	0.201950i	−0.801821	+	0.597565i	$0.796135\pi$
$602$	2.87800	−	4.98485i	0.117299	−	0.203167i
$603$		−	6.05429i		−	0.246550i
$604$	−15.3432	−	8.85839i	−0.624305	−	0.360443i
$605$	−43.9388	−	25.3681i	−1.78637	−	1.03136i
$606$			11.9976i			0.487369i
$607$	−11.2143	+	19.4238i	−0.455175	+	0.788387i	−0.998698	−	0.0510075i	$-0.983757\pi$
$607$	−11.2143	+	19.4238i	−0.455175	+	0.788387i	0.543523	+	0.839394i	$0.317090\pi$
$608$	0.890084	+	1.54167i	0.0360977	+	0.0625230i
$609$	−2.00457	+	1.15734i	−0.0812295	+	0.0468979i
$610$	−1.60388			−0.0649390
$611$		0			0
$612$	7.38404			0.298482
$613$	−34.6066	+	19.9801i	−1.39775	+	0.806991i	−0.994157	−	0.107948i	$-0.965572\pi$
$613$	−34.6066	+	19.9801i	−1.39775	+	0.806991i	−0.403592	+	0.914939i	$0.632239\pi$
$614$	8.99761	+	15.5843i	0.363114	+	0.628932i
$615$	3.04892	−	5.28088i	0.122944	−	0.212946i
$616$		−	3.35690i		−	0.135253i
$617$	−27.2339	−	15.7235i	−1.09639	−	0.633003i	−0.161123	−	0.986934i	$-0.551511\pi$
$617$	−27.2339	−	15.7235i	−1.09639	−	0.633003i	−0.935272	+	0.353931i	$0.884845\pi$
$618$	−10.6721	−	6.16152i	−0.429294	−	0.247853i
$619$			29.3685i			1.18042i	0.807250	+	0.590210i	$0.200955\pi$
$619$			29.3685i			1.18042i	−0.807250	+	0.590210i	$0.799045\pi$
$620$	−1.96950	+	3.41127i	−0.0790970	+	0.137000i
$621$	2.55496	+	4.42532i	0.102527	+	0.177582i
$622$	−2.88365	+	1.66487i	−0.115624	+	0.0667554i
$623$	−2.15213			−0.0862232
$624$		0			0
$625$	47.8485			1.91394
$626$	−15.4875	+	8.94169i	−0.619003	+	0.357382i
$627$	−4.31767	−	7.47842i	−0.172431	−	0.298659i
$628$	−3.15883	+	5.47126i	−0.126051	+	0.218327i
$629$		−	9.49742i		−	0.378687i
$630$	−2.42655	−	1.40097i	−0.0966760	−	0.0558159i
$631$	18.7754	+	10.8400i	0.747436	+	0.431532i	0.824767	−	0.565473i	$-0.191306\pi$
$631$	18.7754	+	10.8400i	0.747436	+	0.431532i	−0.0773307	+	0.997005i	$0.524640\pi$
$632$			8.33944i			0.331725i
$633$	−3.89977	+	6.75460i	−0.155002	+	0.268471i
$634$	2.19687	+	3.80508i	0.0872487	+	0.151119i
$635$	−21.0576	+	12.1576i	−0.835647	+	0.482461i
$636$	−13.4765			−0.534378
$637$		0			0
$638$	−16.2252			−0.642362
$639$	1.15160	−	0.664874i	0.0455564	−	0.0263020i
$640$	2.02446	+	3.50647i	0.0800238	+	0.138605i
$641$	7.00538	−	12.1337i	0.276696	−	0.479251i	−0.693866	−	0.720104i	$-0.744094\pi$
$641$	7.00538	−	12.1337i	0.276696	−	0.479251i	0.970562	+	0.240853i	$0.0774272\pi$
$642$			5.89977i			0.232845i
$643$	−26.6627	−	15.3937i	−1.05148	−	0.607070i	−0.128413	−	0.991721i	$-0.540988\pi$
$643$	−26.6627	−	15.3937i	−1.05148	−	0.607070i	−0.923062	+	0.384651i	$0.874322\pi$
$644$	−3.06241	−	1.76809i	−0.120676	−	0.0696723i
$645$		−	33.6775i		−	1.32605i
$646$	−6.57242	+	11.3838i	−0.258588	+	0.447888i
$647$	−8.30127	−	14.3782i	−0.326357	−	0.565266i	0.655429	−	0.755257i	$-0.272488\pi$
$647$	−8.30127	−	14.3782i	−0.326357	−	0.565266i	−0.981786	+	0.189990i	$0.939154\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	6.34481			0.249056
$650$		0			0
$651$	0.673235			0.0263862
$652$	12.6369	−	7.29590i	0.494898	−	0.285729i
$653$	−14.2729	−	24.7214i	−0.558543	−	0.967425i	−0.997618	−	0.0689745i	$-0.978027\pi$
$653$	−14.2729	−	24.7214i	−0.558543	−	0.967425i	0.439075	−	0.898450i	$-0.355306\pi$
$654$	−0.396125	+	0.686108i	−0.0154897	+	0.0268289i
$655$		−	35.6993i		−	1.39489i
$656$	1.30427	+	0.753020i	0.0509232	+	0.0294005i
$657$	6.62751	+	3.82640i	0.258564	+	0.149282i
$658$			4.98792i			0.194449i
$659$	−13.8593	+	24.0051i	−0.539884	+	0.935106i	0.459026	+	0.888423i	$0.348198\pi$
$659$	−13.8593	+	24.0051i	−0.539884	+	0.935106i	−0.998910	+	0.0466830i	$0.985135\pi$
$660$	−9.82036	−	17.0094i	−0.382257	−	0.662088i
$661$	−9.35383	+	5.40044i	−0.363822	+	0.210053i	−0.670756	−	0.741678i	$-0.734030\pi$
$661$	−9.35383	+	5.40044i	−0.363822	+	0.210053i	0.306934	+	0.951731i	$0.400697\pi$
$662$	25.6775			0.997986
$663$		0			0
$664$	−15.3274			−0.594817
$665$	4.31966	−	2.49396i	0.167509	−	0.0967116i
$666$	0.643104	+	1.11389i	0.0249198	+	0.0431623i
$667$	−8.54586	+	14.8019i	−0.330897	+	0.573130i
$668$		−	19.5013i		−	0.754526i
$669$	10.5618	+	6.09783i	0.408341	+	0.235756i
$670$	21.2292	+	12.2567i	0.820154	+	0.473516i
$671$			1.92154i			0.0741803i
$672$	0.346011	−	0.599308i	0.0133477	−	0.0231188i
$673$	8.16301	+	14.1388i	0.314661	+	0.545009i	0.979365	−	0.202098i	$-0.0647758\pi$
$673$	8.16301	+	14.1388i	0.314661	+	0.545009i	−0.664704	+	0.747107i	$0.731442\pi$
$674$	21.3479	−	12.3252i	0.822289	−	0.474749i
$675$	−11.3937			−0.438545
$676$		0			0
$677$	41.4252			1.59210			0.796050	−	0.605231i	$-0.206919\pi$
$677$	41.4252			1.59210			0.796050	+	0.605231i	$0.206919\pi$
$678$	5.38653	−	3.10992i	0.206869	−	0.119436i
$679$	2.95593	+	5.11982i	0.113438	+	0.196480i
$680$	−14.9487	+	25.8919i	−0.573256	+	0.992909i
$681$			6.74333i			0.258405i
$682$	4.08692	+	2.35958i	0.156496	+	0.0903532i
$683$	27.0481	+	15.6163i	1.03497	+	0.597539i	0.918404	−	0.395644i	$-0.129479\pi$
$683$	27.0481	+	15.6163i	1.03497	+	0.597539i	0.116564	+	0.993183i	$0.462812\pi$
$684$		−	1.78017i		−	0.0680664i
$685$	31.8974	−	55.2479i	1.21874	−	2.11091i
$686$	4.67845	+	8.10331i	0.178624	+	0.309386i
$687$	17.1678	−	9.91185i	0.654994	−	0.378161i
$688$	8.31767			0.317108
$689$		0			0
$690$	−20.6896			−0.787641
$691$	21.6192	−	12.4819i	0.822435	−	0.474833i	−0.0288205	−	0.999585i	$-0.509175\pi$
$691$	21.6192	−	12.4819i	0.822435	−	0.474833i	0.851255	+	0.524752i	$0.175842\pi$
$692$	4.64526	+	8.04583i	0.176586	+	0.305856i
$693$	−1.67845	+	2.90716i	−0.0637590	+	0.110434i
$694$			14.2959i			0.542665i
$695$	−21.3818	−	12.3448i	−0.811060	−	0.468265i
$696$	−2.89669	−	1.67241i	−0.109799	−	0.0633924i
$697$			11.1207i			0.421225i
$698$	−5.53079	+	9.57962i	−0.209344	+	0.362594i
$699$	−15.0151	−	26.0069i	−0.567922	−	0.983670i
$700$	6.82836	−	3.94235i	0.258088	−	0.149007i
$701$	−8.17151			−0.308634			−0.154317	−	0.988021i	$-0.549318\pi$
$701$	−8.17151			−0.308634			−0.154317	+	0.988021i	$0.549318\pi$
$702$		0			0
$703$	−2.28967			−0.0863564
$704$	4.20096	−	2.42543i	0.158330	−	0.0914117i
$705$	14.5918	+	25.2737i	0.549559	+	0.951864i
$706$	−5.25236	+	9.09735i	−0.197675	+	0.342383i
$707$			8.30260i			0.312251i
$708$	1.13274	+	0.653989i	0.0425711	+	0.0245784i
$709$	−31.8682	−	18.3991i	−1.19684	−	0.690993i	−0.236987	−	0.971513i	$-0.576160\pi$
$709$	−31.8682	−	18.3991i	−1.19684	−	0.690993i	−0.959848	+	0.280520i	$0.909493\pi$
$710$			5.38404i			0.202060i
$711$	4.16972	−	7.22216i	0.156377	−	0.270852i
$712$	−1.55496	−	2.69327i	−0.0582745	−	0.100934i
$713$	4.30518	−	2.48560i	0.161230	−	0.0930864i
$714$	5.10992			0.191234
$715$		0			0
$716$	22.7928			0.851808
$717$	19.1373	−	11.0489i	0.714695	−	0.412629i
$718$	−2.55496	−	4.42532i	−0.0953502	−	0.165151i
$719$	17.6112	−	30.5034i	0.656786	−	1.13759i	−0.324657	−	0.945832i	$-0.605249\pi$
$719$	17.6112	−	30.5034i	0.656786	−	1.13759i	0.981443	−	0.191755i	$-0.0614178\pi$
$720$		−	4.04892i		−	0.150894i
$721$	−7.38530	−	4.26391i	−0.275043	−	0.158796i
$722$	−13.7101	−	7.91550i	−0.510235	−	0.294584i
$723$		−	10.1274i		−	0.376641i
$724$	−0.268750	+	0.465488i	−0.00998801	+	0.0172997i
$725$	−19.0550	−	33.0042i	−0.707683	−	1.22574i
$726$	−10.8520	+	6.26540i	−0.402755	+	0.232531i
$727$	−40.6872			−1.50901			−0.754503	−	0.656297i	$-0.772122\pi$
$727$	−40.6872			−1.50901			−0.754503	+	0.656297i	$0.772122\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−26.8343	+	15.4928i	−0.993180	+	0.573413i
$731$	30.7090	+	53.1896i	1.13581	+	1.96729i
$732$	−0.198062	+	0.343054i	−0.00732059	+	0.0126796i
$733$			27.1400i			1.00244i	0.865320	+	0.501220i	$0.167115\pi$
$733$			27.1400i			1.00244i	−0.865320	+	0.501220i	$0.832885\pi$
$734$	7.31620	+	4.22401i	0.270046	+	0.155911i
$735$	22.8660	+	13.2017i	0.843426	+	0.486952i
$736$		−	5.10992i		−	0.188354i
$737$	14.6843	−	25.4339i	0.540901	−	0.936869i
$738$	−0.753020	−	1.30427i	−0.0277191	−	0.0480108i
$739$	−3.22670	+	1.86294i	−0.118696	+	0.0685292i	−0.558173	−	0.829725i	$-0.688497\pi$
$739$	−3.22670	+	1.86294i	−0.118696	+	0.0685292i	0.439476	+	0.898254i	$0.355164\pi$
$740$	−5.20775			−0.191441
$741$		0			0
$742$	−9.32603			−0.342369
$743$	18.9301	−	10.9293i	0.694479	−	0.400958i	−0.110809	−	0.993842i	$-0.535344\pi$
$743$	18.9301	−	10.9293i	0.694479	−	0.400958i	0.805288	+	0.592884i	$0.202011\pi$
$744$	0.486426	+	0.842515i	0.0178333	+	0.0308881i
$745$	−5.16756	+	8.95048i	−0.189325	+	0.327920i
$746$			7.69096i			0.281586i
$747$	13.2739	+	7.66368i	0.485666	+	0.280399i
$748$	31.0201	+	17.9095i	1.13421	+	0.654835i
$749$			4.08277i			0.149181i
$750$	12.9438	−	22.4194i	0.472642	−	0.818641i
$751$	26.6821	+	46.2147i	0.973644	+	1.68640i	0.684341	+	0.729162i	$0.260090\pi$
$751$	26.6821	+	46.2147i	0.973644	+	1.68640i	0.289303	+	0.957238i	$0.406577\pi$
$752$	−6.24210	+	3.60388i	−0.227626	+	0.131420i
$753$	−5.54719			−0.202151
$754$		0			0
$755$	−71.7338			−2.61066
$756$	−0.599308	+	0.346011i	−0.0217966	+	0.0125843i
$757$	2.31767	+	4.01432i	0.0842370	+	0.145903i	0.905066	−	0.425271i	$-0.139821\pi$
$757$	2.31767	+	4.01432i	0.0842370	+	0.145903i	−0.820829	+	0.571174i	$0.806488\pi$
$758$	−5.70171	+	9.87565i	−0.207095	+	0.358700i
$759$			24.7875i			0.899728i
$760$	6.24210	+	3.60388i	0.226425	+	0.130726i
$761$	10.0115	+	5.78017i	0.362918	+	0.209531i	0.670360	−	0.742036i	$-0.266140\pi$
$761$	10.0115	+	5.78017i	0.362918	+	0.209531i	−0.307442	+	0.951567i	$0.599473\pi$
$762$			6.00538i			0.217552i
$763$	−0.274127	+	0.474801i	−0.00992405	+	0.0171890i
$764$	−4.89977	−	8.48665i	−0.177268	−	0.307036i
$765$	25.8919	−	14.9487i	0.936123	−	0.540471i
$766$	−20.6703			−0.746847
$767$		0			0
$768$	1.00000			0.0360844
$769$	12.7686	−	7.37196i	0.460448	−	0.265840i	−0.251785	−	0.967783i	$-0.581017\pi$
$769$	12.7686	−	7.37196i	0.460448	−	0.265840i	0.712233	+	0.701944i	$0.247684\pi$
$770$	−6.79590	−	11.7708i	−0.244907	−	0.424192i
$771$	−6.89977	+	11.9508i	−0.248489	+	0.430396i
$772$		−	14.1957i		−	0.510913i
$773$	5.56220	+	3.21134i	0.200059	+	0.115504i	0.596683	−	0.802477i	$-0.296485\pi$
$773$	5.56220	+	3.21134i	0.200059	+	0.115504i	−0.396624	+	0.917981i	$0.629818\pi$
$774$	−7.20331	−	4.15883i	−0.258918	−	0.149486i
$775$			11.0844i			0.398164i
$776$	−4.27144	+	7.39835i	−0.153336	+	0.265585i
$777$	0.445042	+	0.770835i	0.0159658	+	0.0276536i
$778$	−15.1360	+	8.73878i	−0.542652	+	0.313301i
$779$	2.68100			0.0960570
$780$		0			0
$781$	6.45042			0.230814
$782$	32.6767	−	18.8659i	1.16852	−	0.674644i
$783$	1.67241	+	2.89669i	0.0597670	+	0.103519i
$784$	−3.26055	+	5.64744i	−0.116448	+	0.201694i
$785$			25.5797i			0.912979i
$786$	−7.63575	−	4.40850i	−0.272358	−	0.157246i
$787$	37.6146	+	21.7168i	1.34081	+	0.774119i	0.986927	−	0.161169i	$-0.0515263\pi$
$787$	37.6146	+	21.7168i	1.34081	+	0.774119i	0.353887	+	0.935288i	$0.384860\pi$
$788$			3.00969i			0.107216i
$789$	11.2349	−	19.4594i	0.399973	−	0.692773i
$790$	16.8828	+	29.2419i	0.600665	+	1.04038i
$791$	3.72760	−	2.15213i	0.132538	−	0.0765209i
$792$	−4.85086			−0.172368
$793$		0			0
$794$	−19.3599			−0.687056
$795$	−47.2549	+	27.2826i	−1.67596	+	0.967615i
$796$	−6.44720	−	11.1669i	−0.228515	−	0.395799i
$797$	10.5082	−	18.2007i	0.372219	−	0.644703i	−0.617687	−	0.786424i	$-0.711930\pi$
$797$	10.5082	−	18.2007i	0.372219	−	0.644703i	0.989907	+	0.141721i	$0.0452636\pi$
$798$		−	1.23191i		−	0.0436093i
$799$	−46.0919	−	26.6112i	−1.63061	−	0.941436i
$800$	9.86726	+	5.69687i	0.348860	+	0.201415i
$801$			3.10992i			0.109883i
$802$	7.24160	−	12.5428i	0.255710	−	0.442903i
$803$	18.5613	+	32.1491i	0.655014	+	1.13452i
$804$	5.24317	−	3.02715i	0.184912	−	0.106759i
$805$	−14.3177			−0.504631
$806$		0			0
$807$	−26.0140			−0.915736
$808$	−10.3902	+	5.99880i	−0.365527	+	0.211037i
$809$	4.16123	+	7.20746i	0.146301	+	0.253401i	0.929858	−	0.367920i	$-0.119930\pi$
$809$	4.16123	+	7.20746i	0.146301	+	0.253401i	−0.783557	+	0.621320i	$0.786597\pi$
$810$	−2.02446	+	3.50647i	−0.0711322	+	0.123205i
$811$			14.4638i			0.507894i	0.967218	+	0.253947i	$0.0817288\pi$
$811$			14.4638i			0.507894i	−0.967218	+	0.253947i	$0.918271\pi$
$812$	−2.00457	−	1.15734i	−0.0703468	−	0.0406147i
$813$	2.49823	+	1.44235i	0.0876167	+	0.0505855i
$814$			6.23921i			0.218684i
$815$	29.5405	−	51.1656i	1.03476	−	1.79225i
$816$	3.69202	+	6.39477i	0.129247	+	0.223862i
$817$	12.8231	−	7.40342i	0.448623	−	0.259013i
$818$	18.8984			0.660769
$819$		0			0
$820$	6.09783			0.212946
$821$	33.2693	−	19.2080i	1.16111	−	0.670365i	0.209538	−	0.977801i	$-0.432804\pi$
$821$	33.2693	−	19.2080i	1.16111	−	0.670365i	0.951569	+	0.307435i	$0.0994707\pi$
$822$	−7.87800	−	13.6451i	−0.274777	−	0.475928i
$823$	−20.4874	+	35.4852i	−0.714145	+	1.23694i	0.249143	+	0.968467i	$0.419851\pi$
$823$	−20.4874	+	35.4852i	−0.714145	+	1.23694i	−0.963288	+	0.268469i	$0.913482\pi$
$824$		−	12.3230i		−	0.429294i
$825$	−47.8647	−	27.6347i	−1.66643	−	0.962116i
$826$	0.783882	+	0.452575i	0.0272748	+	0.0157471i
$827$			3.51035i			0.122067i	0.998136	+	0.0610335i	$0.0194396\pi$
$827$			3.51035i			0.122067i	−0.998136	+	0.0610335i	$0.980560\pi$
$828$	−2.55496	+	4.42532i	−0.0887909	+	0.153790i
$829$	−6.60925	−	11.4476i	−0.229549	−	0.397590i	0.728126	−	0.685444i	$-0.240392\pi$
$829$	−6.60925	−	11.4476i	−0.229549	−	0.397590i	−0.957674	+	0.287853i	$0.907058\pi$
$830$	−53.7448	+	31.0296i	−1.86551	+	1.07705i
$831$	1.46250			0.0507336
$832$		0			0
$833$	−48.1521			−1.66837
$834$	−5.28088	+	3.04892i	−0.182862	+	0.105575i
$835$	−39.4795	−	68.3805i	−1.36624	−	2.36640i
$836$	4.31767	−	7.47842i	0.149330	−	0.258647i
$837$		−	0.972853i		−	0.0336267i
$838$	18.8450	+	10.8802i	0.650989	+	0.375849i
$839$	−48.3667	−	27.9245i	−1.66980	−	0.964062i	−0.967741	−	0.251947i	$-0.918929\pi$
$839$	−48.3667	−	27.9245i	−1.66980	−	0.964062i	−0.702063	−	0.712115i	$-0.747737\pi$
$840$		−	2.80194i		−	0.0966760i
$841$	8.90611	−	15.4258i	0.307107	−	0.531925i
$842$	10.2959	+	17.8330i	0.354820	+	0.614566i
$843$	−4.92104	+	2.84117i	−0.169490	+	0.0978550i
$844$	−7.79954			−0.268471
$845$		0			0
$846$	7.20775			0.247808
$847$	−7.50981	+	4.33579i	−0.258040	+	0.148979i
$848$	−6.73825	−	11.6710i	−0.231392	−	0.400784i
$849$	−12.6039	+	21.8306i	−0.432564	+	0.749223i
$850$			84.1318i			2.88570i
$851$	5.69188	+	3.28621i	0.195115	+	0.112650i
$852$	1.15160	+	0.664874i	0.0394530	+	0.0227782i
$853$			21.8103i			0.746770i	0.927676	+	0.373385i	$0.121803\pi$
$853$			21.8103i			0.746770i	−0.927676	+	0.373385i	$0.878197\pi$
$854$	−0.137063	+	0.237401i	−0.00469021	+	0.00812368i
$855$	−3.60388	−	6.24210i	−0.123250	−	0.213475i
$856$	−5.10935	+	2.94989i	−0.174634	+	0.100825i
$857$	−28.8961			−0.987070			−0.493535	−	0.869726i	$-0.664296\pi$
$857$	−28.8961			−0.987070			−0.493535	+	0.869726i	$0.664296\pi$
$858$		0			0
$859$	−17.2755			−0.589431			−0.294715	−	0.955585i	$-0.595225\pi$
$859$	−17.2755			−0.589431			−0.294715	+	0.955585i	$0.595225\pi$
$860$	29.1656	−	16.8388i	0.994539	−	0.574197i
$861$	−0.521106	−	0.902583i	−0.0177593	−	0.0307599i
$862$	17.2567	−	29.8894i	0.587764	−	1.01804i
$863$		−	44.7741i		−	1.52413i	−0.647503	−	0.762063i	$-0.724187\pi$
$863$		−	44.7741i		−	1.52413i	0.647503	−	0.762063i	$-0.275813\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	32.5769	+	18.8083i	1.10765	+	0.639501i
$866$			2.12631i			0.0722549i
$867$	−18.7620	+	32.4968i	−0.637192	+	1.10365i
$868$	0.336618	+	0.583039i	0.0114255	+	0.0197896i
$869$	35.0337	−	20.2267i	1.18844	−	0.686144i
$870$	−13.5429			−0.459147
$871$		0			0
$872$	−0.792249			−0.0268289
$873$	7.39835	−	4.27144i	0.250396	−	0.144566i
$874$	−4.54825	−	7.87781i	−0.153847	−	0.266471i
$875$	8.95742	−	15.5147i	0.302816	−	0.524493i
$876$			7.65279i			0.258564i
$877$	34.8784	+	20.1371i	1.17776	+	0.679980i	0.955495	−	0.295006i	$-0.0953216\pi$
$877$	34.8784	+	20.1371i	1.17776	+	0.679980i	0.222265	+	0.974986i	$0.428655\pi$
$878$	18.9071	+	10.9160i	0.638085	+	0.368398i
$879$			7.14914i			0.241135i
$880$	9.82036	−	17.0094i	0.331044	−	0.573385i
$881$	4.70410	+	8.14775i	0.158485	+	0.274505i	0.934323	−	0.356428i	$-0.116006\pi$
$881$	4.70410	+	8.14775i	0.158485	+	0.274505i	−0.775837	+	0.630933i	$0.782672\pi$
$882$	5.64744	−	3.26055i	0.190159	−	0.109789i
$883$	51.2271			1.72393			0.861965	−	0.506968i	$-0.169234\pi$
$883$	51.2271			1.72393			0.861965	+	0.506968i	$0.169234\pi$
$884$		0			0
$885$	5.29590			0.178020
$886$	−6.53025	+	3.77024i	−0.219388	+	0.126664i
$887$	19.9608	+	34.5731i	0.670217	+	1.16085i	0.977842	+	0.209342i	$0.0671324\pi$
$887$	19.9608	+	34.5731i	0.670217	+	1.16085i	−0.307625	+	0.951508i	$0.599534\pi$
$888$	−0.643104	+	1.11389i	−0.0215812	+	0.0373797i
$889$			4.15585i			0.139383i
$890$	−10.9048	−	6.29590i	−0.365530	−	0.211039i
$891$	4.20096	+	2.42543i	0.140738	+	0.0812549i
$892$			12.1957i			0.408341i
$893$	−6.41550	+	11.1120i	−0.214687	+	0.371848i
$894$	1.27628	+	2.21059i	0.0426853	+	0.0739331i
$895$	79.9223	−	46.1432i	2.67151	−	1.54240i
$896$	0.692021			0.0231188
$897$		0			0
$898$	19.7560			0.659266
$899$	2.81806	−	1.62701i	0.0939875	−	0.0542637i
$900$	−5.69687	−	9.86726i	−0.189896	−	0.328909i
$901$	49.7555	−	86.1791i	1.65760	−	2.87104i
$902$		−	7.30559i		−	0.243249i
$903$	−4.98485	−	2.87800i	−0.165885	−	0.0957739i
$904$	5.38653	+	3.10992i	0.179153	+	0.103434i
$905$			2.17629i			0.0723424i
$906$	−8.85839	+	15.3432i	−0.294300	+	0.509743i
$907$	−17.4155	−	30.1645i	−0.578272	−	1.00160i	−0.995678	−	0.0928765i	$-0.970394\pi$
$907$	−17.4155	−	30.1645i	−0.578272	−	1.00160i	0.417405	−	0.908720i	$-0.362940\pi$
$908$	−5.83990	+	3.37167i	−0.193804	+	0.111893i
$909$	11.9976			0.397936
$910$		0			0
$911$	13.2125			0.437751			0.218875	−	0.975753i	$-0.429761\pi$
$911$	13.2125			0.437751			0.218875	+	0.975753i	$0.429761\pi$
$912$	1.54167	−	0.890084i	0.0510498	−	0.0294736i
$913$	37.1754	+	64.3897i	1.23033	+	2.13099i
$914$	11.9291	−	20.6618i	0.394579	−	0.683430i
$915$			1.60388i			0.0530225i
$916$	17.1678	+	9.91185i	0.567241	+	0.327497i
$917$	−5.28410	−	3.05078i	−0.174496	−	0.100746i
$918$		−	7.38404i		−	0.243710i
$919$	−10.5087	+	18.2017i	−0.346651	+	0.600417i	−0.985652	−	0.168789i	$-0.946015\pi$
$919$	−10.5087	+	18.2017i	−0.346651	+	0.600417i	0.639001	+	0.769206i	$0.279348\pi$
$920$	−10.3448	−	17.9177i	−0.341058	−	0.590731i
$921$	15.5843	−	8.99761i	0.513521	−	0.296481i
$922$	17.5773			0.578878
$923$		0			0
$924$	−3.35690			−0.110434
$925$	−12.6914	+	7.32736i	−0.417289	+	0.240922i
$926$	−11.9215	−	20.6487i	−0.391766	−	0.678559i
$927$	−6.16152	+	10.6721i	−0.202371	+	0.350517i
$928$		−	3.34481i		−	0.109799i
$929$	23.3797	+	13.4983i	0.767063	+	0.442864i	0.831826	−	0.555037i	$-0.187296\pi$
$929$	23.3797	+	13.4983i	0.767063	+	0.442864i	−0.0647630	+	0.997901i	$0.520629\pi$
$930$	3.41127	+	1.96950i	0.111860	+	0.0645825i
$931$			11.6087i			0.380459i
$932$	15.0151	−	26.0069i	0.491835	−	0.851883i
$933$	1.66487	+	2.88365i	0.0545055	+	0.0944064i
$934$	−7.45698	+	4.30529i	−0.244000	+	0.140873i
$935$	145.028			4.74292
$936$		0			0
$937$	23.1745			0.757078			0.378539	−	0.925585i	$-0.376427\pi$
$937$	23.1745			0.757078			0.378539	+	0.925585i	$0.376427\pi$
$938$	3.62839	−	2.09485i	0.118471	−	0.0683993i
$939$	8.94169	+	15.4875i	0.291801	+	0.505414i
$940$	−14.5918	+	25.2737i	−0.475932	+	0.824338i
$941$			7.54048i			0.245813i	0.992418	+	0.122906i	$0.0392215\pi$
$941$			7.54048i			0.245813i	−0.992418	+	0.122906i	$0.960779\pi$
$942$	5.47126	+	3.15883i	0.178263	+	0.102920i
$943$	−6.66471	−	3.84787i	−0.217033	−	0.125304i
$944$			1.30798i			0.0425711i
$945$	−1.40097	+	2.42655i	−0.0455735	+	0.0789357i
$946$	−20.1739	−	34.9422i	−0.655910	−	1.13607i
$947$	−17.8922	+	10.3300i	−0.581417	+	0.335681i	−0.761696	−	0.647934i	$-0.775633\pi$
$947$	−17.8922	+	10.3300i	−0.581417	+	0.335681i	0.180279	+	0.983615i	$0.442300\pi$
$948$	8.33944			0.270852
$949$		0			0
$950$	20.2828			0.658059
$951$	3.80508	−	2.19687i	0.123388	−	0.0712383i
$952$	2.55496	+	4.42532i	0.0828067	+	0.143425i
$953$	−15.1468	+	26.2349i	−0.490651	+	0.849833i	−0.999942	−	0.0107614i	$-0.996574\pi$
$953$	−15.1468	+	26.2349i	−0.490651	+	0.849833i	0.509291	+	0.860595i	$0.329908\pi$
$954$			13.4765i			0.436318i
$955$	−34.3618	−	19.8388i	−1.11192	−	0.641968i
$956$	19.1373	+	11.0489i	0.618944	+	0.357348i
$957$			16.2252i			0.524487i
$958$	−3.29052	+	5.69935i	−0.106312	+	0.184138i
$959$	−5.45175	−	9.44270i	−0.176046	−	0.304921i
$960$	3.50647	−	2.02446i	0.113171	−	0.0653391i
$961$	30.0536			0.969470
$962$		0			0
$963$	5.89977			0.190118
$964$	8.77056	−	5.06369i	0.282481	−	0.163090i
$965$	−28.7385	−	49.7766i	−0.925127	−	1.60237i
$966$	−1.76809	+	3.06241i	−0.0568872	+	0.0985316i
$967$		−	20.7289i		−	0.666595i	−0.942822	−	0.333298i	$-0.891839\pi$
$967$		−	20.7289i		−	0.666595i	0.942822	−	0.333298i	$-0.108161\pi$
$968$	−10.8520	−	6.26540i	−0.348796	−	0.201378i
$969$	11.3838	+	6.57242i	0.365699	+	0.211136i
$970$			34.5894i			1.11060i
$971$	19.5547	−	33.8698i	0.627541	−	1.08693i	−0.360503	−	0.932758i	$-0.617395\pi$
$971$	19.5547	−	33.8698i	0.627541	−	1.08693i	0.988044	−	0.154175i	$-0.0492718\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−3.65448	+	2.10992i	−0.117157	+	0.0676408i
$974$	23.2760			0.745813
$975$		0			0
$976$	−0.396125			−0.0126796
$977$	6.30073	−	3.63773i	0.201578	−	0.116381i	−0.395813	−	0.918331i	$-0.629537\pi$
$977$	6.30073	−	3.63773i	0.201578	−	0.116381i	0.597391	+	0.801950i	$0.296204\pi$
$978$	−7.29590	−	12.6369i	−0.233297	−	0.404082i
$979$	−7.54288	+	13.0646i	−0.241071	+	0.417548i
$980$			26.4034i			0.843426i
$981$	0.686108	+	0.396125i	0.0219057	+	0.0126473i
$982$	−13.4585	−	7.77024i	−0.429477	−	0.247958i
$983$		−	53.4857i		−	1.70593i	−0.521969	−	0.852965i	$-0.674802\pi$
$983$		−	53.4857i		−	1.70593i	0.521969	−	0.852965i	$-0.325198\pi$
$984$	0.753020	−	1.30427i	0.0240054	−	0.0415786i
$985$	6.09299	+	10.5534i	0.194139	+	0.336258i
$986$	21.3893	−	12.3491i	0.681175	−	0.393276i
$987$	4.98792			0.158767
$988$		0			0
$989$	−42.5026			−1.35150
$990$	−17.0094	+	9.82036i	−0.540593	+	0.312111i
$991$	−8.02877	−	13.9062i	−0.255042	−	0.441746i	0.709865	−	0.704338i	$-0.248756\pi$
$991$	−8.02877	−	13.9062i	−0.255042	−	0.441746i	−0.964907	+	0.262592i	$0.915423\pi$
$992$	−0.486426	+	0.842515i	−0.0154441	+	0.0267499i
$993$		−	25.6775i		−	0.814852i
$994$	0.796929	+	0.460107i	0.0252771	+	0.0145937i
$995$	−45.2138	−	26.1042i	−1.43337	−	0.827558i
$996$			15.3274i			0.485666i
$997$	−11.2131	+	19.4217i	−0.355123	+	0.615092i	−0.987139	−	0.159864i	$-0.948894\pi$
$997$	−11.2131	+	19.4217i	−0.355123	+	0.615092i	0.632016	+	0.774956i	$0.282228\pi$
$998$	4.76809	+	8.25857i	0.150931	+	0.261420i
$999$	1.11389	−	0.643104i	0.0352419	−	0.0203469i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.i.g.361.4		12
13.2	odd	12		1014.2.a.o.1.1	yes	3
13.3	even	3		1014.2.b.g.337.4		6
13.4	even	6	inner	1014.2.i.g.823.6		12
13.5	odd	4		1014.2.e.k.991.1		6
13.6	odd	12		1014.2.e.k.529.1		6
13.7	odd	12		1014.2.e.m.529.3		6
13.8	odd	4		1014.2.e.m.991.3		6
13.9	even	3	inner	1014.2.i.g.823.1		12
13.10	even	6		1014.2.b.g.337.3		6
13.11	odd	12		1014.2.a.m.1.3	✓	3
13.12	even	2	inner	1014.2.i.g.361.3		12
39.2	even	12		3042.2.a.bd.1.3		3
39.11	even	12		3042.2.a.be.1.1		3
39.23	odd	6		3042.2.b.r.1351.4		6
39.29	odd	6		3042.2.b.r.1351.3		6
52.11	even	12		8112.2.a.ce.1.3		3
52.15	even	12		8112.2.a.bz.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1014.2.a.m.1.3	✓	3	13.11	odd	12
1014.2.a.o.1.1	yes	3	13.2	odd	12
1014.2.b.g.337.3		6	13.10	even	6
1014.2.b.g.337.4		6	13.3	even	3
1014.2.e.k.529.1		6	13.6	odd	12
1014.2.e.k.991.1		6	13.5	odd	4
1014.2.e.m.529.3		6	13.7	odd	12
1014.2.e.m.991.3		6	13.8	odd	4
1014.2.i.g.361.3		12	13.12	even	2	inner
1014.2.i.g.361.4		12	1.1	even	1	trivial
1014.2.i.g.823.1		12	13.9	even	3	inner
1014.2.i.g.823.6		12	13.4	even	6	inner
3042.2.a.bd.1.3		3	39.2	even	12
3042.2.a.be.1.1		3	39.11	even	12
3042.2.b.r.1351.3		6	39.29	odd	6
3042.2.b.r.1351.4		6	39.23	odd	6
8112.2.a.bz.1.1		3	52.15	even	12
8112.2.a.ce.1.3		3	52.11	even	12

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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -4.04892i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-0.599308 - 0.346011i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -4.04892i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-0.599308 - 0.346011i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.02446 - 3.50647i) q^{10} +(-4.20096 + 2.42543i) q^{11} -1.00000 q^{12} -0.692021 q^{14} +(-3.50647 + 2.02446i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.69202 - 6.39477i) q^{17} +1.00000i q^{18} +(-1.54167 - 0.890084i) q^{19} +(-3.50647 - 2.02446i) q^{20} +0.692021i q^{21} +(-2.42543 + 4.20096i) q^{22} +(2.55496 + 4.42532i) q^{23} +(-0.866025 + 0.500000i) q^{24} -11.3937 q^{25} +1.00000 q^{27} +(-0.599308 + 0.346011i) q^{28} +(1.67241 + 2.89669i) q^{29} +(-2.02446 + 3.50647i) q^{30} -0.972853i q^{31} +(-0.866025 - 0.500000i) q^{32} +(4.20096 + 2.42543i) q^{33} -7.38404i q^{34} +(-1.40097 + 2.42655i) q^{35} +(0.500000 + 0.866025i) q^{36} +(1.11389 - 0.643104i) q^{37} -1.78017 q^{38} -4.04892 q^{40} +(-1.30427 + 0.753020i) q^{41} +(0.346011 + 0.599308i) q^{42} +(-4.15883 + 7.20331i) q^{43} +4.85086i q^{44} +(3.50647 + 2.02446i) q^{45} +(4.42532 + 2.55496i) q^{46} -7.20775i q^{47} +(-0.500000 + 0.866025i) q^{48} +(-3.26055 - 5.64744i) q^{49} +(-9.86726 + 5.69687i) q^{50} -7.38404 q^{51} +13.4765 q^{53} +(0.866025 - 0.500000i) q^{54} +(9.82036 + 17.0094i) q^{55} +(-0.346011 + 0.599308i) q^{56} +1.78017i q^{57} +(2.89669 + 1.67241i) q^{58} +(-1.13274 - 0.653989i) q^{59} +4.04892i q^{60} +(0.198062 - 0.343054i) q^{61} +(-0.486426 - 0.842515i) q^{62} +(0.599308 - 0.346011i) q^{63} -1.00000 q^{64} +4.85086 q^{66} +(-5.24317 + 3.02715i) q^{67} +(-3.69202 - 6.39477i) q^{68} +(2.55496 - 4.42532i) q^{69} +2.80194i q^{70} +(-1.15160 - 0.664874i) q^{71} +(0.866025 + 0.500000i) q^{72} -7.65279i q^{73} +(0.643104 - 1.11389i) q^{74} +(5.69687 + 9.86726i) q^{75} +(-1.54167 + 0.890084i) q^{76} +3.35690 q^{77} -8.33944 q^{79} +(-3.50647 + 2.02446i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.753020 + 1.30427i) q^{82} -15.3274i q^{83} +(0.599308 + 0.346011i) q^{84} +(-25.8919 - 14.9487i) q^{85} +8.31767i q^{86} +(1.67241 - 2.89669i) q^{87} +(2.42543 + 4.20096i) q^{88} +(2.69327 - 1.55496i) q^{89} +4.04892 q^{90} +5.10992 q^{92} +(-0.842515 + 0.486426i) q^{93} +(-3.60388 - 6.24210i) q^{94} +(-3.60388 + 6.24210i) q^{95} +1.00000i q^{96} +(-7.39835 - 4.27144i) q^{97} +(-5.64744 - 3.26055i) q^{98} -4.85086i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} + 6 q^{4} - 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 + 6 * q^4 - 6 * q^9	\( 12 q - 6 q^{3} + 6 q^{4} - 6 q^{9} - 6 q^{10} - 12 q^{12} + 12 q^{14} - 6 q^{16} + 24 q^{17} - 2 q^{22} + 32 q^{23} - 8 q^{25} + 12 q^{27} - 26 q^{29} - 6 q^{30} - 8 q^{35} + 6 q^{36} - 16 q^{38} - 12 q^{40} - 6 q^{42} - 16 q^{43} - 6 q^{48} - 8 q^{49} - 48 q^{51} + 60 q^{53} + 44 q^{55} + 6 q^{56} + 20 q^{61} - 18 q^{62} - 12 q^{64} + 4 q^{66} - 24 q^{68} + 32 q^{69} + 24 q^{74} + 4 q^{75} + 24 q^{77} - 20 q^{79} - 6 q^{81} - 28 q^{82} - 26 q^{87} + 2 q^{88} + 12 q^{90} + 64 q^{92} - 8 q^{94} - 8 q^{95}+O(q^{100}) \) 12 * q - 6 * q^3 + 6 * q^4 - 6 * q^9 - 6 * q^10 - 12 * q^12 + 12 * q^14 - 6 * q^16 + 24 * q^17 - 2 * q^22 + 32 * q^23 - 8 * q^25 + 12 * q^27 - 26 * q^29 - 6 * q^30 - 8 * q^35 + 6 * q^36 - 16 * q^38 - 12 * q^40 - 6 * q^42 - 16 * q^43 - 6 * q^48 - 8 * q^49 - 48 * q^51 + 60 * q^53 + 44 * q^55 + 6 * q^56 + 20 * q^61 - 18 * q^62 - 12 * q^64 + 4 * q^66 - 24 * q^68 + 32 * q^69 + 24 * q^74 + 4 * q^75 + 24 * q^77 - 20 * q^79 - 6 * q^81 - 28 * q^82 - 26 * q^87 + 2 * q^88 + 12 * q^90 + 64 * q^92 - 8 * q^94 - 8 * q^95

Introduction

L-functions

Modular forms

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Representations

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Database

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