LMFDB - Embedded newform 570.2.q.a.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(49,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("570.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.q (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.4
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	570.49
Dual form			570.2.q.a.349.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.81431 + 1.30701i) q^{5} +(0.500000 + 0.866025i) q^{6} -3.00000i q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.81431 + 1.30701i) q^{5} +(0.500000 + 0.866025i) q^{6} -3.00000i q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.917738 + 2.03906i) q^{10} +2.00000 q^{11} +1.00000i q^{12} +(-2.98735 + 1.72474i) q^{13} +(1.50000 - 2.59808i) q^{14} +(0.917738 + 2.03906i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(4.24264 + 2.44949i) q^{17} +1.00000i q^{18} +(1.00000 - 4.24264i) q^{19} +(-0.224745 + 2.22474i) q^{20} +(1.50000 - 2.59808i) q^{21} +(1.73205 + 1.00000i) q^{22} +(-2.12132 + 1.22474i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(1.58346 + 4.74264i) q^{25} -3.44949 q^{26} +1.00000i q^{27} +(2.59808 - 1.50000i) q^{28} +(-4.67423 - 8.09601i) q^{29} +(-0.224745 + 2.22474i) q^{30} -7.89898 q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.73205 + 1.00000i) q^{33} +(2.44949 + 4.24264i) q^{34} +(3.92102 - 5.44294i) q^{35} +(-0.500000 + 0.866025i) q^{36} +4.55051i q^{37} +(2.98735 - 3.17423i) q^{38} -3.44949 q^{39} +(-1.30701 + 1.81431i) q^{40} +(-1.22474 + 2.12132i) q^{41} +(2.59808 - 1.50000i) q^{42} +(-0.476756 - 0.275255i) q^{43} +(1.00000 + 1.73205i) q^{44} +(-0.224745 + 2.22474i) q^{45} -2.44949 q^{46} +(-3.07483 + 1.77526i) q^{47} +(-0.866025 + 0.500000i) q^{48} -2.00000 q^{49} +(-1.00000 + 4.89898i) q^{50} +(2.44949 + 4.24264i) q^{51} +(-2.98735 - 1.72474i) q^{52} +(-2.68556 + 1.55051i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(3.62863 + 2.61401i) q^{55} +3.00000 q^{56} +(2.98735 - 3.17423i) q^{57} -9.34847i q^{58} +(5.89898 - 10.2173i) q^{59} +(-1.30701 + 1.81431i) q^{60} +(-2.17423 - 3.76588i) q^{61} +(-6.84072 - 3.94949i) q^{62} +(2.59808 - 1.50000i) q^{63} -1.00000 q^{64} +(-7.67423 - 0.775255i) q^{65} +(1.00000 + 1.73205i) q^{66} +(-1.25529 + 0.724745i) q^{67} +4.89898i q^{68} -2.44949 q^{69} +(6.11717 - 2.75321i) q^{70} +(1.77526 - 3.07483i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(10.3048 + 5.94949i) q^{73} +(-2.27526 + 3.94086i) q^{74} +(-1.00000 + 4.89898i) q^{75} +(4.17423 - 1.25529i) q^{76} -6.00000i q^{77} +(-2.98735 - 1.72474i) q^{78} +(8.39898 - 14.5475i) q^{79} +(-2.03906 + 0.917738i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.12132 + 1.22474i) q^{82} +1.34847i q^{83} +3.00000 q^{84} +(4.49598 + 9.98930i) q^{85} +(-0.275255 - 0.476756i) q^{86} -9.34847i q^{87} +2.00000i q^{88} +(-5.77526 - 10.0030i) q^{89} +(-1.30701 + 1.81431i) q^{90} +(5.17423 + 8.96204i) q^{91} +(-2.12132 - 1.22474i) q^{92} +(-6.84072 - 3.94949i) q^{93} -3.55051 q^{94} +(7.35948 - 6.39047i) q^{95} -1.00000 q^{96} +(-16.1920 - 9.34847i) q^{97} +(-1.73205 - 1.00000i) q^{98} +(1.00000 + 1.73205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^4 + 4 * q^5 + 4 * q^6 + 4 * q^9	$ 8 q + 4 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{9} + 4 q^{10} + 16 q^{11} + 12 q^{14} + 4 q^{15} - 4 q^{16} + 8 q^{19} + 8 q^{20} + 12 q^{21} - 4 q^{24} - 8 q^{26} - 8 q^{29} + 8 q^{30} - 24 q^{31} + 12 q^{35} - 4 q^{36} - 8 q^{39} - 4 q^{40} + 8 q^{44} + 8 q^{45} - 16 q^{49} - 8 q^{50} - 4 q^{54} + 8 q^{55} + 24 q^{56} + 8 q^{59} - 4 q^{60} + 12 q^{61} - 8 q^{64} - 32 q^{65} + 8 q^{66} - 12 q^{70} + 24 q^{71} - 28 q^{74} - 8 q^{75} + 4 q^{76} + 28 q^{79} + 4 q^{80} - 4 q^{81} + 24 q^{84} + 24 q^{85} - 12 q^{86} - 56 q^{89} - 4 q^{90} + 12 q^{91} - 48 q^{94} + 40 q^{95} - 8 q^{96} + 8 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 + 4 * q^5 + 4 * q^6 + 4 * q^9 + 4 * q^10 + 16 * q^11 + 12 * q^14 + 4 * q^15 - 4 * q^16 + 8 * q^19 + 8 * q^20 + 12 * q^21 - 4 * q^24 - 8 * q^26 - 8 * q^29 + 8 * q^30 - 24 * q^31 + 12 * q^35 - 4 * q^36 - 8 * q^39 - 4 * q^40 + 8 * q^44 + 8 * q^45 - 16 * q^49 - 8 * q^50 - 4 * q^54 + 8 * q^55 + 24 * q^56 + 8 * q^59 - 4 * q^60 + 12 * q^61 - 8 * q^64 - 32 * q^65 + 8 * q^66 - 12 * q^70 + 24 * q^71 - 28 * q^74 - 8 * q^75 + 4 * q^76 + 28 * q^79 + 4 * q^80 - 4 * q^81 + 24 * q^84 + 24 * q^85 - 12 * q^86 - 56 * q^89 - 4 * q^90 + 12 * q^91 - 48 * q^94 + 40 * q^95 - 8 * q^96 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.81431	+	1.30701i	0.811386	+	0.584511i
$5$	1.81431	+	1.30701i	0.811386	+	0.584511i
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$		−	3.00000i		−	1.13389i	−0.823754	−	0.566947i	$-0.808125\pi$
$7$		−	3.00000i		−	1.13389i	0.823754	−	0.566947i	$-0.191875\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.917738	+	2.03906i	0.290214	+	0.644807i
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$			1.00000i			0.288675i
$13$	−2.98735	+	1.72474i	−0.828541	+	0.478358i	−0.853353	−	0.521334i	$-0.825435\pi$
$13$	−2.98735	+	1.72474i	−0.828541	+	0.478358i	0.0248121	+	0.999692i	$0.492101\pi$
$14$	1.50000	−	2.59808i	0.400892	−	0.694365i
$15$	0.917738	+	2.03906i	0.236959	+	0.526483i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	4.24264	+	2.44949i	1.02899	+	0.594089i	0.916696	−	0.399586i	$-0.130846\pi$
$17$	4.24264	+	2.44949i	1.02899	+	0.594089i	0.112296	+	0.993675i	$0.464180\pi$
$18$			1.00000i			0.235702i
$19$	1.00000	−	4.24264i	0.229416	−	0.973329i
$19$	1.00000	−	4.24264i	0.229416	−	0.973329i
$20$	−0.224745	+	2.22474i	−0.0502545	+	0.497468i
$21$	1.50000	−	2.59808i	0.327327	−	0.566947i
$22$	1.73205	+	1.00000i	0.369274	+	0.213201i
$23$	−2.12132	+	1.22474i	−0.442326	+	0.255377i	−0.704584	−	0.709621i	$-0.748866\pi$
$23$	−2.12132	+	1.22474i	−0.442326	+	0.255377i	0.262258	+	0.964998i	$0.415533\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	1.58346	+	4.74264i	0.316693	+	0.948528i
$26$	−3.44949			−0.676501
$27$			1.00000i			0.192450i
$28$	2.59808	−	1.50000i	0.490990	−	0.283473i
$29$	−4.67423	−	8.09601i	−0.867984	−	1.50339i	−0.864054	−	0.503399i	$-0.832082\pi$
$29$	−4.67423	−	8.09601i	−0.867984	−	1.50339i	−0.00392972	−	0.999992i	$-0.501251\pi$
$30$	−0.224745	+	2.22474i	−0.0410326	+	0.406181i
$31$	−7.89898			−1.41870			−0.709349	−	0.704857i	$-0.751011\pi$
$31$	−7.89898			−1.41870			−0.709349	+	0.704857i	$0.751011\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	1.73205	+	1.00000i	0.301511	+	0.174078i
$34$	2.44949	+	4.24264i	0.420084	+	0.727607i
$35$	3.92102	−	5.44294i	0.662774	−	0.920025i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$			4.55051i			0.748099i	0.927409	+	0.374050i	$0.122031\pi$
$37$			4.55051i			0.748099i	−0.927409	+	0.374050i	$0.877969\pi$
$38$	2.98735	−	3.17423i	0.484611	−	0.514929i
$39$	−3.44949			−0.552360
$40$	−1.30701	+	1.81431i	−0.206656	+	0.286868i
$41$	−1.22474	+	2.12132i	−0.191273	+	0.331295i	−0.945672	−	0.325121i	$-0.894595\pi$
$41$	−1.22474	+	2.12132i	−0.191273	+	0.331295i	0.754399	+	0.656416i	$0.227928\pi$
$42$	2.59808	−	1.50000i	0.400892	−	0.231455i
$43$	−0.476756	−	0.275255i	−0.0727046	−	0.0419760i	0.463207	−	0.886250i	$-0.346699\pi$
$43$	−0.476756	−	0.275255i	−0.0727046	−	0.0419760i	−0.535912	+	0.844274i	$0.680032\pi$
$44$	1.00000	+	1.73205i	0.150756	+	0.261116i
$45$	−0.224745	+	2.22474i	−0.0335030	+	0.331645i
$46$	−2.44949			−0.361158
$47$	−3.07483	+	1.77526i	−0.448510	+	0.258948i	−0.707201	−	0.707013i	$-0.750042\pi$
$47$	−3.07483	+	1.77526i	−0.448510	+	0.258948i	0.258691	+	0.965960i	$0.416709\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	−2.00000			−0.285714
$50$	−1.00000	+	4.89898i	−0.141421	+	0.692820i
$51$	2.44949	+	4.24264i	0.342997	+	0.594089i
$52$	−2.98735	−	1.72474i	−0.414270	−	0.239179i
$53$	−2.68556	+	1.55051i	−0.368890	+	0.212979i	−0.672974	−	0.739667i	$-0.734983\pi$
$53$	−2.68556	+	1.55051i	−0.368890	+	0.212979i	0.304083	+	0.952645i	$0.401650\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	3.62863	+	2.61401i	0.489284	+	0.352474i
$56$	3.00000			0.400892
$57$	2.98735	−	3.17423i	0.395684	−	0.420438i
$58$		−	9.34847i		−	1.22751i
$59$	5.89898	−	10.2173i	0.767982	−	1.33018i	−0.170674	−	0.985328i	$-0.554594\pi$
$59$	5.89898	−	10.2173i	0.767982	−	1.33018i	0.938656	−	0.344856i	$-0.112072\pi$
$60$	−1.30701	+	1.81431i	−0.168734	+	0.234227i
$61$	−2.17423	−	3.76588i	−0.278382	−	0.482172i	0.692601	−	0.721321i	$-0.256465\pi$
$61$	−2.17423	−	3.76588i	−0.278382	−	0.482172i	−0.970983	+	0.239149i	$0.923132\pi$
$62$	−6.84072	−	3.94949i	−0.868772	−	0.501586i
$63$	2.59808	−	1.50000i	0.327327	−	0.188982i
$64$	−1.00000			−0.125000
$65$	−7.67423	−	0.775255i	−0.951872	−	0.0961586i
$66$	1.00000	+	1.73205i	0.123091	+	0.213201i
$67$	−1.25529	+	0.724745i	−0.153359	+	0.0885417i	−0.574716	−	0.818353i	$-0.694887\pi$
$67$	−1.25529	+	0.724745i	−0.153359	+	0.0885417i	0.421357	+	0.906895i	$0.361554\pi$
$68$			4.89898i			0.594089i
$69$	−2.44949			−0.294884
$70$	6.11717	−	2.75321i	0.731142	−	0.329072i
$71$	1.77526	−	3.07483i	0.210684	−	0.364915i	−0.741245	−	0.671235i	$-0.765764\pi$
$71$	1.77526	−	3.07483i	0.210684	−	0.364915i	0.951929	+	0.306319i	$0.0990976\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	10.3048	+	5.94949i	1.20609	+	0.696335i	0.961902	−	0.273393i	$-0.0881461\pi$
$73$	10.3048	+	5.94949i	1.20609	+	0.696335i	0.244185	+	0.969729i	$0.421479\pi$
$74$	−2.27526	+	3.94086i	−0.264493	+	0.458115i
$75$	−1.00000	+	4.89898i	−0.115470	+	0.565685i
$76$	4.17423	−	1.25529i	0.478818	−	0.143992i
$77$		−	6.00000i		−	0.683763i
$78$	−2.98735	−	1.72474i	−0.338250	−	0.195289i
$79$	8.39898	−	14.5475i	0.944959	−	1.63672i	0.189126	−	0.981953i	$-0.439435\pi$
$79$	8.39898	−	14.5475i	0.944959	−	1.63672i	0.755833	−	0.654764i	$-0.227232\pi$
$80$	−2.03906	+	0.917738i	−0.227974	+	0.102606i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.12132	+	1.22474i	−0.234261	+	0.135250i
$83$			1.34847i			0.148014i	0.997258	+	0.0740069i	$0.0235787\pi$
$83$			1.34847i			0.148014i	−0.997258	+	0.0740069i	$0.976421\pi$
$84$	3.00000			0.327327
$85$	4.49598	+	9.98930i	0.487657	+	1.08349i
$86$	−0.275255	−	0.476756i	−0.0296815	−	0.0514099i
$87$		−	9.34847i		−	1.00226i
$88$			2.00000i			0.213201i
$89$	−5.77526	−	10.0030i	−0.612176	−	1.06032i	−0.990873	−	0.134799i	$-0.956961\pi$
$89$	−5.77526	−	10.0030i	−0.612176	−	1.06032i	0.378697	−	0.925521i	$-0.376372\pi$
$90$	−1.30701	+	1.81431i	−0.137771	+	0.191245i
$91$	5.17423	+	8.96204i	0.542407	+	0.939477i
$92$	−2.12132	−	1.22474i	−0.221163	−	0.127688i
$93$	−6.84072	−	3.94949i	−0.709349	−	0.409543i
$94$	−3.55051			−0.366207
$95$	7.35948	−	6.39047i	0.755066	−	0.655649i
$96$	−1.00000			−0.102062
$97$	−16.1920	−	9.34847i	−1.64405	−	0.949193i	−0.979372	−	0.202064i	$-0.935235\pi$
$97$	−16.1920	−	9.34847i	−1.64405	−	0.949193i	−0.664679	−	0.747129i	$-0.731431\pi$
$98$	−1.73205	−	1.00000i	−0.174964	−	0.101015i
$99$	1.00000	+	1.73205i	0.100504	+	0.174078i
$100$	−3.31552	+	3.74264i	−0.331552	+	0.374264i
$101$	1.89898	+	3.28913i	0.188956	+	0.327281i	0.944902	−	0.327353i	$-0.106156\pi$
$101$	1.89898	+	3.28913i	0.188956	+	0.327281i	−0.755947	+	0.654633i	$0.772823\pi$
$102$			4.89898i			0.485071i
$103$			9.89898i			0.975375i	0.873018	+	0.487688i	$0.162160\pi$
$103$			9.89898i			0.975375i	−0.873018	+	0.487688i	$0.837840\pi$
$104$	−1.72474	−	2.98735i	−0.169125	−	0.292933i
$105$	6.11717	−	2.75321i	0.596975	−	0.268686i
$106$	−3.10102			−0.301198
$107$		−	10.4495i		−	1.01019i	−0.863064	−	0.505095i	$-0.831457\pi$
$107$		−	10.4495i		−	1.01019i	0.863064	−	0.505095i	$-0.168543\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	0.307290	+	0.951616i	$0.400578\pi$
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	−0.977769	+	0.209687i	$0.932756\pi$
$110$	1.83548	+	4.07812i	0.175006	+	0.388833i
$111$	−2.27526	+	3.94086i	−0.215958	+	0.374050i
$112$	2.59808	+	1.50000i	0.245495	+	0.141737i
$113$		−	14.8990i		−	1.40158i	−0.713369	−	0.700789i	$-0.752831\pi$
$113$		−	14.8990i		−	1.40158i	0.713369	−	0.700789i	$-0.247169\pi$
$114$	4.17423	−	1.25529i	0.390953	−	0.117569i
$115$	−5.44949	−	0.550510i	−0.508168	−	0.0513353i
$116$	4.67423	−	8.09601i	0.433992	−	0.751696i
$117$	−2.98735	−	1.72474i	−0.276180	−	0.159453i
$118$	10.2173	−	5.89898i	0.940582	−	0.543045i
$119$	7.34847	−	12.7279i	0.673633	−	1.16677i
$120$	−2.03906	+	0.917738i	−0.186140	+	0.0837776i
$121$	−7.00000			−0.636364
$122$		−	4.34847i		−	0.393692i
$123$	−2.12132	+	1.22474i	−0.191273	+	0.110432i
$124$	−3.94949	−	6.84072i	−0.354675	−	0.614315i
$125$	−3.32577	+	10.6742i	−0.297465	+	0.954733i
$126$	3.00000			0.267261
$127$	−14.4600	+	8.34847i	−1.28312	+	0.740807i	−0.977417	−	0.211322i	$-0.932223\pi$
$127$	−14.4600	+	8.34847i	−1.28312	+	0.740807i	−0.305699	+	0.952128i	$0.598890\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−0.275255	−	0.476756i	−0.0242349	−	0.0419760i
$130$	−6.25845	−	4.50851i	−0.548903	−	0.395422i
$131$	−3.89898	+	6.75323i	−0.340655	+	0.590032i	−0.984555	−	0.175078i	$-0.943982\pi$
$131$	−3.89898	+	6.75323i	−0.340655	+	0.590032i	0.643899	+	0.765110i	$0.277316\pi$
$132$			2.00000i			0.174078i
$133$	−12.7279	−	3.00000i	−1.10365	−	0.260133i
$134$	−1.44949			−0.125217
$135$	−1.30701	+	1.81431i	−0.112489	+	0.156151i
$136$	−2.44949	+	4.24264i	−0.210042	+	0.363803i
$137$	−0.953512	+	0.550510i	−0.0814640	+	0.0470333i	−0.540179	−	0.841550i	$-0.681643\pi$
$137$	−0.953512	+	0.550510i	−0.0814640	+	0.0470333i	0.458715	+	0.888584i	$0.348310\pi$
$138$	−2.12132	−	1.22474i	−0.180579	−	0.104257i
$139$	3.27526	+	5.67291i	0.277804	+	0.481170i	0.970839	−	0.239734i	$-0.0770602\pi$
$139$	3.27526	+	5.67291i	0.277804	+	0.481170i	−0.693035	+	0.720904i	$0.743727\pi$
$140$	6.67423	+	0.674235i	0.564076	+	0.0569832i
$141$	−3.55051			−0.299007
$142$	3.07483	−	1.77526i	0.258034	−	0.148976i
$143$	−5.97469	+	3.44949i	−0.499629	+	0.288461i
$144$	−1.00000			−0.0833333
$145$	2.10102	−	20.7980i	0.174480	−	1.72718i
$146$	5.94949	+	10.3048i	0.492383	+	0.852833i
$147$	−1.73205	−	1.00000i	−0.142857	−	0.0824786i
$148$	−3.94086	+	2.27526i	−0.323936	+	0.187025i
$149$	1.89898	−	3.28913i	0.155570	−	0.269456i	−0.777696	−	0.628640i	$-0.783612\pi$
$149$	1.89898	−	3.28913i	0.155570	−	0.269456i	0.933267	+	0.359184i	$0.116945\pi$
$150$	−3.31552	+	3.74264i	−0.270711	+	0.305585i
$151$	19.7980			1.61114			0.805568	−	0.592504i	$-0.201861\pi$
$151$	19.7980			1.61114			0.805568	+	0.592504i	$0.201861\pi$
$152$	4.24264	+	1.00000i	0.344124	+	0.0811107i
$153$			4.89898i			0.396059i
$154$	3.00000	−	5.19615i	0.241747	−	0.418718i
$155$	−14.3312	−	10.3240i	−1.15111	−	0.829245i
$156$	−1.72474	−	2.98735i	−0.138090	−	0.239179i
$157$	4.71940	+	2.72474i	0.376649	+	0.217458i	0.676359	−	0.736572i	$-0.263557\pi$
$157$	4.71940	+	2.72474i	0.376649	+	0.217458i	−0.299710	+	0.954030i	$0.596890\pi$
$158$	14.5475	−	8.39898i	1.15733	−	0.668187i
$159$	−3.10102			−0.245927
$160$	−2.22474	−	0.224745i	−0.175882	−	0.0177676i
$161$	3.67423	+	6.36396i	0.289570	+	0.501550i
$162$	−0.866025	+	0.500000i	−0.0680414	+	0.0392837i
$163$			6.34847i			0.497250i	0.968600	+	0.248625i	$0.0799788\pi$
$163$			6.34847i			0.497250i	−0.968600	+	0.248625i	$0.920021\pi$
$164$	−2.44949			−0.191273
$165$	1.83548	+	4.07812i	0.142892	+	0.317481i
$166$	−0.674235	+	1.16781i	−0.0523308	+	0.0906395i
$167$	13.6814	−	7.89898i	1.05870	−	0.611241i	0.133628	−	0.991032i	$-0.457337\pi$
$167$	13.6814	−	7.89898i	1.05870	−	0.611241i	0.925073	+	0.379790i	$0.124004\pi$
$168$	2.59808	+	1.50000i	0.200446	+	0.115728i
$169$	−0.550510	+	0.953512i	−0.0423469	+	0.0733471i
$170$	−1.10102	+	10.8990i	−0.0844444	+	0.835914i
$171$	4.17423	−	1.25529i	0.319212	−	0.0959948i
$172$		−	0.550510i		−	0.0419760i
$173$	3.85337	+	2.22474i	0.292966	+	0.169144i	0.639279	−	0.768975i	$-0.279233\pi$
$173$	3.85337	+	2.22474i	0.292966	+	0.169144i	−0.346312	+	0.938119i	$0.612566\pi$
$174$	4.67423	−	8.09601i	0.354353	−	0.613757i
$175$	14.2279	−	4.75039i	1.07553	−	0.359096i
$176$	−1.00000	+	1.73205i	−0.0753778	+	0.130558i
$177$	10.2173	−	5.89898i	0.767982	−	0.443394i
$178$		−	11.5505i		−	0.865747i
$179$	18.2474			1.36388			0.681939	−	0.731409i	$-0.261137\pi$
$179$	18.2474			1.36388			0.681939	+	0.731409i	$0.261137\pi$
$180$	−2.03906	+	0.917738i	−0.151982	+	0.0684041i
$181$	5.55051	+	9.61377i	0.412566	+	0.714586i	0.995170	−	0.0981710i	$-0.0312992\pi$
$181$	5.55051	+	9.61377i	0.412566	+	0.714586i	−0.582603	+	0.812757i	$0.697966\pi$
$182$			10.3485i			0.767080i
$183$		−	4.34847i		−	0.321448i
$184$	−1.22474	−	2.12132i	−0.0902894	−	0.156386i
$185$	−5.94755	+	8.25605i	−0.437273	+	0.606997i
$186$	−3.94949	−	6.84072i	−0.289591	−	0.501586i
$187$	8.48528	+	4.89898i	0.620505	+	0.358249i
$188$	−3.07483	−	1.77526i	−0.224255	−	0.129474i
$189$	3.00000			0.218218
$190$	9.56873	−	1.85457i	0.694189	−	0.134545i
$191$	−14.6969			−1.06343			−0.531717	−	0.846922i	$-0.678453\pi$
$191$	−14.6969			−1.06343			−0.531717	+	0.846922i	$0.678453\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	1.81954	+	1.05051i	0.130973	+	0.0756174i	0.564055	−	0.825737i	$-0.309241\pi$
$193$	1.81954	+	1.05051i	0.130973	+	0.0756174i	−0.433082	+	0.901355i	$0.642574\pi$
$194$	−9.34847	−	16.1920i	−0.671181	−	1.16252i
$195$	−6.25845	−	4.50851i	−0.448177	−	0.322861i
$196$	−1.00000	−	1.73205i	−0.0714286	−	0.123718i
$197$		−	16.6969i		−	1.18961i	−0.803871	−	0.594804i	$-0.797230\pi$
$197$		−	16.6969i		−	1.18961i	0.803871	−	0.594804i	$-0.202770\pi$
$198$			2.00000i			0.142134i
$199$	−4.05051	−	7.01569i	−0.287133	−	0.497329i	0.685991	−	0.727610i	$-0.259369\pi$
$199$	−4.05051	−	7.01569i	−0.287133	−	0.497329i	−0.973124	+	0.230281i	$0.926036\pi$
$200$	−4.74264	+	1.58346i	−0.335355	+	0.111968i
$201$	−1.44949			−0.102239
$202$			3.79796i			0.267223i
$203$	−24.2880	+	14.0227i	−1.70469	+	0.984201i
$204$	−2.44949	+	4.24264i	−0.171499	+	0.297044i
$205$	−4.99465	+	2.24799i	−0.348842	+	0.157006i
$206$	−4.94949	+	8.57277i	−0.344847	+	0.597293i
$207$	−2.12132	−	1.22474i	−0.147442	−	0.0851257i
$208$		−	3.44949i		−	0.239179i
$209$	2.00000	−	8.48528i	0.138343	−	0.586939i
$210$	6.67423	+	0.674235i	0.460566	+	0.0465266i
$211$	−1.17423	+	2.03383i	−0.0808376	+	0.140015i	−0.903610	−	0.428356i	$-0.859093\pi$
$211$	−1.17423	+	2.03383i	−0.0808376	+	0.140015i	0.822772	+	0.568371i	$0.192426\pi$
$212$	−2.68556	−	1.55051i	−0.184445	−	0.106489i
$213$	3.07483	−	1.77526i	0.210684	−	0.121638i
$214$	5.22474	−	9.04952i	0.357156	−	0.618613i
$215$	−0.505224	−	1.12252i	−0.0344560	−	0.0765554i
$216$	−1.00000			−0.0680414
$217$			23.6969i			1.60865i
$218$	−12.1244	+	7.00000i	−0.821165	+	0.474100i
$219$	5.94949	+	10.3048i	0.402029	+	0.696335i
$220$	−0.449490	+	4.44949i	−0.0303046	+	0.299985i
$221$	−16.8990			−1.13675
$222$	−3.94086	+	2.27526i	−0.264493	+	0.152705i
$223$	11.8619	+	6.84847i	0.794331	+	0.458607i	0.841485	−	0.540280i	$-0.181682\pi$
$223$	11.8619	+	6.84847i	0.794331	+	0.458607i	−0.0471538	+	0.998888i	$0.515015\pi$
$224$	1.50000	+	2.59808i	0.100223	+	0.173591i
$225$	−3.31552	+	3.74264i	−0.221034	+	0.249509i
$226$	7.44949	−	12.9029i	0.495533	−	0.858288i
$227$			13.3485i			0.885969i	0.896529	+	0.442985i	$0.146080\pi$
$227$			13.3485i			0.885969i	−0.896529	+	0.442985i	$0.853920\pi$
$228$	4.24264	+	1.00000i	0.280976	+	0.0662266i
$229$	−27.0454			−1.78721			−0.893605	−	0.448853i	$-0.851833\pi$
$229$	−27.0454			−1.78721			−0.893605	+	0.448853i	$0.851833\pi$
$230$	−4.44414	−	3.20150i	−0.293038	−	0.211101i
$231$	3.00000	−	5.19615i	0.197386	−	0.341882i
$232$	8.09601	−	4.67423i	0.531529	−	0.306879i
$233$	12.6886	+	7.32577i	0.831258	+	0.479927i	0.854283	−	0.519808i	$-0.173997\pi$
$233$	12.6886	+	7.32577i	0.831258	+	0.479927i	−0.0230254	+	0.999735i	$0.507330\pi$
$234$	−1.72474	−	2.98735i	−0.112750	−	0.195289i
$235$	−7.89898	−	0.797959i	−0.515273	−	0.0520531i
$236$	11.7980			0.767982
$237$	14.5475	−	8.39898i	0.944959	−	0.545572i
$238$	12.7279	−	7.34847i	0.825029	−	0.476331i
$239$	−8.65153			−0.559621			−0.279811	−	0.960055i	$-0.590272\pi$
$239$	−8.65153			−0.559621			−0.279811	+	0.960055i	$0.590272\pi$
$240$	−2.22474	−	0.224745i	−0.143607	−	0.0145072i
$241$	−5.50000	−	9.52628i	−0.354286	−	0.613642i	0.632709	−	0.774389i	$-0.281943\pi$
$241$	−5.50000	−	9.52628i	−0.354286	−	0.613642i	−0.986996	+	0.160748i	$0.948609\pi$
$242$	−6.06218	−	3.50000i	−0.389692	−	0.224989i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	2.17423	−	3.76588i	0.139191	−	0.241086i
$245$	−3.62863	−	2.61401i	−0.231824	−	0.167003i
$246$	−2.44949			−0.156174
$247$	4.33013	+	14.3990i	0.275519	+	0.916185i
$248$		−	7.89898i		−	0.501586i
$249$	−0.674235	+	1.16781i	−0.0427279	+	0.0740069i
$250$	−8.21731	+	7.58128i	−0.519709	+	0.479482i
$251$	10.3485	+	17.9241i	0.653190	+	1.13136i	0.982344	+	0.187082i	$0.0599029\pi$
$251$	10.3485	+	17.9241i	0.653190	+	1.13136i	−0.329155	+	0.944276i	$0.606764\pi$
$252$	2.59808	+	1.50000i	0.163663	+	0.0944911i
$253$	−4.24264	+	2.44949i	−0.266733	+	0.153998i
$254$	−16.6969			−1.04766
$255$	−1.10102	+	10.8990i	−0.0689486	+	0.682521i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	21.7774	−	12.5732i	1.35844	−	0.784296i	0.369026	−	0.929419i	$-0.379691\pi$
$257$	21.7774	−	12.5732i	1.35844	−	0.784296i	0.989414	+	0.145123i	$0.0463579\pi$
$258$		−	0.550510i		−	0.0342733i
$259$	13.6515			0.848265
$260$	−3.16573	−	7.03371i	−0.196330	−	0.436212i
$261$	4.67423	−	8.09601i	0.289328	−	0.501131i
$262$	−6.75323	+	3.89898i	−0.417216	+	0.240880i
$263$	12.1244	+	7.00000i	0.747620	+	0.431638i	0.824833	−	0.565376i	$-0.191269\pi$
$263$	12.1244	+	7.00000i	0.747620	+	0.431638i	−0.0772134	+	0.997015i	$0.524602\pi$
$264$	−1.00000	+	1.73205i	−0.0615457	+	0.106600i
$265$	−6.89898	−	0.696938i	−0.423801	−	0.0428126i
$266$	−9.52270	−	8.96204i	−0.583874	−	0.549498i
$267$		−	11.5505i		−	0.706880i
$268$	−1.25529	−	0.724745i	−0.0766793	−	0.0442708i
$269$	−13.2474	+	22.9453i	−0.807711	+	1.39900i	0.106734	+	0.994288i	$0.465961\pi$
$269$	−13.2474	+	22.9453i	−0.807711	+	1.39900i	−0.914445	+	0.404709i	$0.867373\pi$
$270$	−2.03906	+	0.917738i	−0.124093	+	0.0558517i
$271$	2.55051	−	4.41761i	0.154932	−	0.268351i	−0.778102	−	0.628138i	$-0.783817\pi$
$271$	2.55051	−	4.41761i	0.154932	−	0.268351i	0.933034	+	0.359787i	$0.117151\pi$
$272$	−4.24264	+	2.44949i	−0.257248	+	0.148522i
$273$			10.3485i			0.626318i
$274$	−1.10102			−0.0665151
$275$	3.16693	+	9.48528i	0.190973	+	0.571984i
$276$	−1.22474	−	2.12132i	−0.0737210	−	0.127688i
$277$			32.4949i			1.95243i	0.216807	+	0.976215i	$0.430436\pi$
$277$			32.4949i			1.95243i	−0.216807	+	0.976215i	$0.569564\pi$
$278$			6.55051i			0.392873i
$279$	−3.94949	−	6.84072i	−0.236450	−	0.409543i
$280$	5.44294	+	3.92102i	0.325278	+	0.234326i
$281$	13.2247	+	22.9059i	0.788922	+	1.36645i	0.926628	+	0.375980i	$0.122694\pi$
$281$	13.2247	+	22.9059i	0.788922	+	1.36645i	−0.137706	+	0.990473i	$0.543973\pi$
$282$	−3.07483	−	1.77526i	−0.183104	−	0.105715i
$283$	−7.70674	−	4.44949i	−0.458118	−	0.264495i	0.253134	−	0.967431i	$-0.418539\pi$
$283$	−7.70674	−	4.44949i	−0.458118	−	0.264495i	−0.711253	+	0.702936i	$0.751872\pi$
$284$	3.55051			0.210684
$285$	9.56873	−	1.85457i	0.566803	−	0.109855i
$286$	−6.89898			−0.407945
$287$	6.36396	+	3.67423i	0.375653	+	0.216883i
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	3.50000	+	6.06218i	0.205882	+	0.356599i
$290$	12.2185	−	16.9611i	0.717496	−	0.995987i
$291$	−9.34847	−	16.1920i	−0.548017	−	0.949193i
$292$			11.8990i			0.696335i
$293$			18.8990i			1.10409i	0.833814	+	0.552045i	$0.186152\pi$
$293$			18.8990i			1.10409i	−0.833814	+	0.552045i	$0.813848\pi$
$294$	−1.00000	−	1.73205i	−0.0583212	−	0.101015i
$295$	24.0567	−	10.8274i	1.40064	−	0.630397i
$296$	−4.55051			−0.264493
$297$			2.00000i			0.116052i
$298$	3.28913	−	1.89898i	0.190534	−	0.110005i
$299$	4.22474	−	7.31747i	0.244323	−	0.423180i
$300$	−4.74264	+	1.58346i	−0.273816	+	0.0914214i
$301$	−0.825765	+	1.43027i	−0.0475963	+	0.0824393i
$302$	17.1455	+	9.89898i	0.986615	+	0.569622i
$303$			3.79796i			0.218187i
$304$	3.17423	+	2.98735i	0.182055	+	0.171336i
$305$	0.977296	−	9.67423i	0.0559598	−	0.553945i
$306$	−2.44949	+	4.24264i	−0.140028	+	0.242536i
$307$	1.90702	+	1.10102i	0.108840	+	0.0628386i	0.553432	−	0.832895i	$-0.313318\pi$
$307$	1.90702	+	1.10102i	0.108840	+	0.0628386i	−0.444592	+	0.895733i	$0.646651\pi$
$308$	5.19615	−	3.00000i	0.296078	−	0.170941i
$309$	−4.94949	+	8.57277i	−0.281567	+	0.487688i
$310$	−7.24919	−	16.1065i	−0.411726	−	0.914786i
$311$	10.8990			0.618024			0.309012	−	0.951058i	$-0.400002\pi$
$311$	10.8990			0.618024			0.309012	+	0.951058i	$0.400002\pi$
$312$		−	3.44949i		−	0.195289i
$313$	−13.0779	+	7.55051i	−0.739205	+	0.426780i	−0.821780	−	0.569805i	$-0.807019\pi$
$313$	−13.0779	+	7.55051i	−0.739205	+	0.426780i	0.0825753	+	0.996585i	$0.473685\pi$
$314$	2.72474	+	4.71940i	0.153766	+	0.266331i
$315$	6.67423	+	0.674235i	0.376051	+	0.0379888i
$316$	16.7980			0.944959
$317$	−5.41045	+	3.12372i	−0.303881	+	0.175446i	−0.644185	−	0.764870i	$-0.722803\pi$
$317$	−5.41045	+	3.12372i	−0.303881	+	0.175446i	0.340304	+	0.940315i	$0.389470\pi$
$318$	−2.68556	−	1.55051i	−0.150599	−	0.0869483i
$319$	−9.34847	−	16.1920i	−0.523414	−	0.906579i
$320$	−1.81431	−	1.30701i	−0.101423	−	0.0730639i
$321$	5.22474	−	9.04952i	0.291617	−	0.505095i
$322$			7.34847i			0.409514i
$323$	14.6349	−	15.5505i	0.814310	−	0.865254i
$324$	−1.00000			−0.0555556
$325$	−12.9102	−	11.4368i	−0.716129	−	0.634401i
$326$	−3.17423	+	5.49794i	−0.175805	+	0.304502i
$327$	−12.1244	+	7.00000i	−0.670478	+	0.387101i
$328$	−2.12132	−	1.22474i	−0.117130	−	0.0676252i
$329$	5.32577	+	9.22450i	0.293619	+	0.508563i
$330$	−0.449490	+	4.44949i	−0.0247436	+	0.244936i
$331$	23.2474			1.27780			0.638898	−	0.769292i	$-0.279391\pi$
$331$	23.2474			1.27780			0.638898	+	0.769292i	$0.279391\pi$
$332$	−1.16781	+	0.674235i	−0.0640918	+	0.0370034i
$333$	−3.94086	+	2.27526i	−0.215958	+	0.124683i
$334$	15.7980			0.864426
$335$	−3.22474	−	0.325765i	−0.176187	−	0.0177985i
$336$	1.50000	+	2.59808i	0.0818317	+	0.141737i
$337$	−3.55159	−	2.05051i	−0.193467	−	0.111698i	0.400137	−	0.916455i	$-0.368962\pi$
$337$	−3.55159	−	2.05051i	−0.193467	−	0.111698i	−0.593605	+	0.804757i	$0.702296\pi$
$338$	−0.953512	+	0.550510i	−0.0518642	+	0.0299438i
$339$	7.44949	−	12.9029i	0.404601	−	0.700789i
$340$	−6.40300	+	8.88828i	−0.347252	+	0.482035i
$341$	−15.7980			−0.855507
$342$	4.24264	+	1.00000i	0.229416	+	0.0540738i
$343$		−	15.0000i		−	0.809924i
$344$	0.275255	−	0.476756i	0.0148408	−	0.0257050i
$345$	−4.44414	−	3.20150i	−0.239265	−	0.172363i
$346$	2.22474	+	3.85337i	0.119603	+	0.207159i
$347$	−24.6773	−	14.2474i	−1.32475	−	0.764843i	−0.340265	−	0.940329i	$-0.610517\pi$
$347$	−24.6773	−	14.2474i	−1.32475	−	0.764843i	−0.984482	+	0.175486i	$0.943850\pi$
$348$	8.09601	−	4.67423i	0.433992	−	0.250565i
$349$	26.5505			1.42122			0.710608	−	0.703588i	$-0.248420\pi$
$349$	26.5505			1.42122			0.710608	+	0.703588i	$0.248420\pi$
$350$	14.6969	+	3.00000i	0.785584	+	0.160357i
$351$	−1.72474	−	2.98735i	−0.0920601	−	0.159453i
$352$	−1.73205	+	1.00000i	−0.0923186	+	0.0533002i
$353$			21.1464i			1.12551i	0.826623	+	0.562755i	$0.190259\pi$
$353$			21.1464i			1.12551i	−0.826623	+	0.562755i	$0.809741\pi$
$354$	11.7980			0.627054
$355$	7.23970	−	3.25844i	0.384243	−	0.172940i
$356$	5.77526	−	10.0030i	0.306088	−	0.530160i
$357$	12.7279	−	7.34847i	0.673633	−	0.388922i
$358$	15.8028	+	9.12372i	0.835202	+	0.482204i
$359$	−10.1237	+	17.5348i	−0.534310	+	0.925452i	0.464887	+	0.885370i	$0.346095\pi$
$359$	−10.1237	+	17.5348i	−0.534310	+	0.925452i	−0.999196	+	0.0400814i	$0.987238\pi$
$360$	−2.22474	−	0.224745i	−0.117254	−	0.0118451i
$361$	−17.0000	−	8.48528i	−0.894737	−	0.446594i
$362$			11.1010i			0.583457i
$363$	−6.06218	−	3.50000i	−0.318182	−	0.183702i
$364$	−5.17423	+	8.96204i	−0.271204	+	0.469738i
$365$	10.9201	+	24.2627i	0.571586	+	1.26997i
$366$	2.17423	−	3.76588i	0.113649	−	0.196846i
$367$	−14.3725	+	8.29796i	−0.750238	+	0.433150i	−0.825780	−	0.563993i	$-0.809265\pi$
$367$	−14.3725	+	8.29796i	−0.750238	+	0.433150i	0.0755421	+	0.997143i	$0.475931\pi$
$368$		−	2.44949i		−	0.127688i
$369$	−2.44949			−0.127515
$370$	−9.27875	+	4.17617i	−0.482379	+	0.217109i
$371$	4.65153	+	8.05669i	0.241495	+	0.418282i
$372$		−	7.89898i		−	0.409543i
$373$			25.1010i			1.29968i	0.760070	+	0.649841i	$0.225164\pi$
$373$			25.1010i			1.29968i	−0.760070	+	0.649841i	$0.774836\pi$
$374$	4.89898	+	8.48528i	0.253320	+	0.438763i
$375$	−8.21731	+	7.58128i	−0.424340	+	0.391495i
$376$	−1.77526	−	3.07483i	−0.0915518	−	0.158572i
$377$	27.9271	+	16.1237i	1.43832	+	0.830414i
$378$	2.59808	+	1.50000i	0.133631	+	0.0771517i
$379$	−8.75255			−0.449588			−0.224794	−	0.974406i	$-0.572171\pi$
$379$	−8.75255			−0.449588			−0.224794	+	0.974406i	$0.572171\pi$
$380$	9.21405	+	3.17826i	0.472671	+	0.163041i
$381$	−16.6969			−0.855410
$382$	−12.7279	−	7.34847i	−0.651217	−	0.375980i
$383$	−1.16781	−	0.674235i	−0.0596722	−	0.0344518i	0.469867	−	0.882737i	$-0.344302\pi$
$383$	−1.16781	−	0.674235i	−0.0596722	−	0.0344518i	−0.529539	+	0.848285i	$0.677635\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	7.84204	−	10.8859i	0.399668	−	0.554796i
$386$	1.05051	+	1.81954i	0.0534696	+	0.0926120i
$387$		−	0.550510i		−	0.0279840i
$388$		−	18.6969i		−	0.949193i
$389$	7.12372	+	12.3387i	0.361187	+	0.625595i	0.988157	−	0.153449i	$-0.0490382\pi$
$389$	7.12372	+	12.3387i	0.361187	+	0.625595i	−0.626969	+	0.779044i	$0.715705\pi$
$390$	−3.16573	−	7.03371i	−0.160303	−	0.356166i
$391$	−12.0000			−0.606866
$392$		−	2.00000i		−	0.101015i
$393$	−6.75323	+	3.89898i	−0.340655	+	0.196677i
$394$	8.34847	−	14.4600i	0.420590	−	0.728483i
$395$	34.2520	−	15.4161i	1.72341	−	0.775669i
$396$	−1.00000	+	1.73205i	−0.0502519	+	0.0870388i
$397$	8.00853	+	4.62372i	0.401936	+	0.232058i	0.687319	−	0.726356i	$-0.258787\pi$
$397$	8.00853	+	4.62372i	0.401936	+	0.232058i	−0.285383	+	0.958414i	$0.592121\pi$
$398$		−	8.10102i		−	0.406067i
$399$	−9.52270	−	8.96204i	−0.476731	−	0.448663i
$400$	−4.89898	−	1.00000i	−0.244949	−	0.0500000i
$401$	−16.1464	+	27.9664i	−0.806314	+	1.39658i	0.109086	+	0.994032i	$0.465208\pi$
$401$	−16.1464	+	27.9664i	−0.806314	+	1.39658i	−0.915400	+	0.402545i	$0.868126\pi$
$402$	−1.25529	−	0.724745i	−0.0626084	−	0.0361470i
$403$	23.5970	−	13.6237i	1.17545	−	0.678646i
$404$	−1.89898	+	3.28913i	−0.0944778	+	0.163640i
$405$	−2.03906	+	0.917738i	−0.101322	+	0.0456028i
$406$	−28.0454			−1.39187
$407$			9.10102i			0.451121i
$408$	−4.24264	+	2.44949i	−0.210042	+	0.121268i
$409$	−5.55051	−	9.61377i	−0.274455	−	0.475370i	0.695542	−	0.718485i	$-0.255164\pi$
$409$	−5.55051	−	9.61377i	−0.274455	−	0.475370i	−0.969997	+	0.243115i	$0.921831\pi$
$410$	−5.44949	−	0.550510i	−0.269131	−	0.0271878i
$411$	−1.10102			−0.0543093
$412$	−8.57277	+	4.94949i	−0.422350	+	0.243844i
$413$	−30.6520	−	17.6969i	−1.50829	−	0.870809i
$414$	−1.22474	−	2.12132i	−0.0601929	−	0.104257i
$415$	−1.76246	+	2.44655i	−0.0865157	+	0.120096i
$416$	1.72474	−	2.98735i	0.0845626	−	0.146467i
$417$			6.55051i			0.320780i
$418$	5.97469	−	6.34847i	0.292232	−	0.310514i
$419$	26.0454			1.27240			0.636201	−	0.771524i	$-0.280505\pi$
$419$	26.0454			1.27240			0.636201	+	0.771524i	$0.280505\pi$
$420$	5.44294	+	3.92102i	0.265588	+	0.191326i
$421$	10.7980	−	18.7026i	0.526260	−	0.911510i	−0.473272	−	0.880917i	$-0.656927\pi$
$421$	10.7980	−	18.7026i	0.526260	−	0.911510i	0.999532	−	0.0305930i	$-0.00973959\pi$
$422$	−2.03383	+	1.17423i	−0.0990055	+	0.0571608i
$423$	−3.07483	−	1.77526i	−0.149503	−	0.0863159i
$424$	−1.55051	−	2.68556i	−0.0752994	−	0.130422i
$425$	−4.89898	+	24.0000i	−0.237635	+	1.16417i
$426$	3.55051			0.172023
$427$	−11.2977	+	6.52270i	−0.546732	+	0.315656i
$428$	9.04952	−	5.22474i	0.437425	−	0.252548i
$429$	−6.89898			−0.333086
$430$	0.123724	−	1.22474i	0.00596652	−	0.0590624i
$431$	−15.1237	−	26.1951i	−0.728484	−	1.26177i	−0.957524	−	0.288354i	$-0.906892\pi$
$431$	−15.1237	−	26.1951i	−0.728484	−	1.26177i	0.229040	−	0.973417i	$-0.426441\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$	−16.2795	+	9.39898i	−0.782343	+	0.451686i	−0.837260	−	0.546805i	$-0.815844\pi$
$433$	−16.2795	+	9.39898i	−0.782343	+	0.451686i	0.0549168	+	0.998491i	$0.482511\pi$
$434$	−11.8485	+	20.5222i	−0.568745	+	0.985095i
$435$	12.2185	−	16.9611i	0.585833	−	0.813220i
$436$	−14.0000			−0.670478
$437$	3.07483	+	10.2247i	0.147089	+	0.489116i
$438$			11.8990i			0.568555i
$439$	−8.74745	+	15.1510i	−0.417493	+	0.723119i	−0.995687	−	0.0927806i	$-0.970424\pi$
$439$	−8.74745	+	15.1510i	−0.417493	+	0.723119i	0.578194	+	0.815900i	$0.303758\pi$
$440$	−2.61401	+	3.62863i	−0.124618	+	0.172988i
$441$	−1.00000	−	1.73205i	−0.0476190	−	0.0824786i
$442$	−14.6349	−	8.44949i	−0.696113	−	0.401901i
$443$	8.48528	−	4.89898i	0.403148	−	0.232758i	−0.284693	−	0.958619i	$-0.591892\pi$
$443$	8.48528	−	4.89898i	0.403148	−	0.232758i	0.687841	+	0.725861i	$0.258558\pi$
$444$	−4.55051			−0.215958
$445$	2.59592	−	25.6969i	0.123058	−	1.21815i
$446$	6.84847	+	11.8619i	0.324284	+	0.561677i
$447$	3.28913	−	1.89898i	0.155570	−	0.0898186i
$448$			3.00000i			0.141737i
$449$	10.6969			0.504820			0.252410	−	0.967620i	$-0.418777\pi$
$449$	10.6969			0.504820			0.252410	+	0.967620i	$0.418777\pi$
$450$	−4.74264	+	1.58346i	−0.223570	+	0.0746452i
$451$	−2.44949	+	4.24264i	−0.115342	+	0.199778i
$452$	12.9029	−	7.44949i	0.606901	−	0.350395i
$453$	17.1455	+	9.89898i	0.805568	+	0.465095i
$454$	−6.67423	+	11.5601i	−0.313237	+	0.542543i
$455$	−2.32577	+	23.0227i	−0.109034	+	1.07932i
$456$	3.17423	+	2.98735i	0.148647	+	0.139895i
$457$		−	14.1010i		−	0.659618i	−0.944048	−	0.329809i	$-0.893016\pi$
$457$		−	14.1010i		−	0.659618i	0.944048	−	0.329809i	$-0.106984\pi$
$458$	−23.4220	−	13.5227i	−1.09444	−	0.631874i
$459$	−2.44949	+	4.24264i	−0.114332	+	0.198030i
$460$	−2.24799	−	4.99465i	−0.104813	−	0.232877i
$461$	12.1237	−	20.9989i	0.564658	−	0.978017i	−0.432423	−	0.901671i	$-0.642341\pi$
$461$	12.1237	−	20.9989i	0.564658	−	0.978017i	0.997081	−	0.0763458i	$-0.0243253\pi$
$462$	5.19615	−	3.00000i	0.241747	−	0.139573i
$463$		−	39.2929i		−	1.82609i	−0.407854	−	0.913047i	$-0.633723\pi$
$463$		−	39.2929i		−	1.82609i	0.407854	−	0.913047i	$-0.366277\pi$
$464$	9.34847			0.433992
$465$	−7.24919	−	16.1065i	−0.336173	−	0.746920i
$466$	7.32577	+	12.6886i	0.339360	+	0.587788i
$467$		−	3.55051i		−	0.164298i	−0.996620	−	0.0821490i	$-0.973822\pi$
$467$		−	3.55051i		−	0.164298i	0.996620	−	0.0821490i	$-0.0261783\pi$
$468$		−	3.44949i		−	0.159453i
$469$	2.17423	+	3.76588i	0.100397	+	0.173892i
$470$	−6.44174	−	4.64054i	−0.297135	−	0.214052i
$471$	2.72474	+	4.71940i	0.125550	+	0.217458i
$472$	10.2173	+	5.89898i	0.470291	+	0.271523i
$473$	−0.953512	−	0.550510i	−0.0438425	−	0.0253125i
$474$	16.7980			0.771556
$475$	21.7048	−	1.97543i	0.995884	−	0.0906389i
$476$	14.6969			0.673633
$477$	−2.68556	−	1.55051i	−0.122963	−	0.0709930i
$478$	−7.49245	−	4.32577i	−0.342696	−	0.197856i
$479$	14.3485	+	24.8523i	0.655598	+	1.13553i	0.981743	+	0.190210i	$0.0609168\pi$
$479$	14.3485	+	24.8523i	0.655598	+	1.13553i	−0.326145	+	0.945320i	$0.605750\pi$
$480$	−1.81431	−	1.30701i	−0.0828117	−	0.0596564i
$481$	−7.84847	−	13.5939i	−0.357859	−	0.619831i
$482$		−	11.0000i		−	0.501036i
$483$			7.34847i			0.334367i
$484$	−3.50000	−	6.06218i	−0.159091	−	0.275554i
$485$	−17.1589	−	38.1241i	−0.779145	−	1.73113i
$486$	−1.00000			−0.0453609
$487$		−	34.8990i		−	1.58142i	−0.612188	−	0.790712i	$-0.709711\pi$
$487$		−	34.8990i		−	1.58142i	0.612188	−	0.790712i	$-0.290289\pi$
$488$	3.76588	−	2.17423i	0.170474	−	0.0984230i
$489$	−3.17423	+	5.49794i	−0.143544	+	0.248625i
$490$	−1.83548	−	4.07812i	−0.0829183	−	0.184231i
$491$	5.02270	−	8.69958i	0.226671	−	0.392606i	−0.730148	−	0.683289i	$-0.760549\pi$
$491$	5.02270	−	8.69958i	0.226671	−	0.392606i	0.956820	+	0.290682i	$0.0938823\pi$
$492$	−2.12132	−	1.22474i	−0.0956365	−	0.0552158i
$493$		−	45.7980i		−	2.06264i
$494$	−3.44949	+	14.6349i	−0.155200	+	0.658457i
$495$	−0.449490	+	4.44949i	−0.0202031	+	0.199990i
$496$	3.94949	−	6.84072i	0.177337	−	0.307157i
$497$	−9.22450	−	5.32577i	−0.413775	−	0.238893i
$498$	−1.16781	+	0.674235i	−0.0523308	+	0.0302132i
$499$	−16.4217	+	28.4432i	−0.735136	+	1.27329i	0.219528	+	0.975606i	$0.429548\pi$
$499$	−16.4217	+	28.4432i	−0.735136	+	1.27329i	−0.954664	+	0.297686i	$0.903785\pi$
$500$	−10.9070	+	2.45692i	−0.487778	+	0.109877i
$501$	15.7980			0.705801
$502$			20.6969i			0.923750i
$503$	−5.02118	+	2.89898i	−0.223883	+	0.129259i	−0.607747	−	0.794131i	$-0.707927\pi$
$503$	−5.02118	+	2.89898i	−0.223883	+	0.129259i	0.383864	+	0.923390i	$0.374593\pi$
$504$	1.50000	+	2.59808i	0.0668153	+	0.115728i
$505$	−0.853572	+	8.44949i	−0.0379834	+	0.375997i
$506$	−4.89898			−0.217786
$507$	−0.953512	+	0.550510i	−0.0423469	+	0.0244490i
$508$	−14.4600	−	8.34847i	−0.641558	−	0.370403i
$509$	−7.22474	−	12.5136i	−0.320231	−	0.554657i	0.660304	−	0.750998i	$-0.270427\pi$
$509$	−7.22474	−	12.5136i	−0.320231	−	0.554657i	−0.980536	+	0.196341i	$0.937094\pi$
$510$	−6.40300	+	8.88828i	−0.283530	+	0.393580i
$511$	17.8485	−	30.9145i	0.789570	−	1.36757i
$512$		−	1.00000i		−	0.0441942i
$513$	4.24264	+	1.00000i	0.187317	+	0.0441511i
$514$	25.1464			1.10916
$515$	−12.9380	+	17.9598i	−0.570118	+	0.791405i
$516$	0.275255	−	0.476756i	0.0121174	−	0.0209880i
$517$	−6.14966	+	3.55051i	−0.270462	+	0.156151i
$518$	11.8226	+	6.82577i	0.519454	+	0.299907i
$519$	2.22474	+	3.85337i	0.0976555	+	0.169144i
$520$	0.775255	−	7.67423i	0.0339972	−	0.336537i
$521$	18.2474			0.799435			0.399718	−	0.916638i	$-0.369108\pi$
$521$	18.2474			0.799435			0.399718	+	0.916638i	$0.369108\pi$
$522$	8.09601	−	4.67423i	0.354353	−	0.204586i
$523$	14.1582	−	8.17423i	0.619094	−	0.357434i	−0.157422	−	0.987531i	$-0.550318\pi$
$523$	14.1582	−	8.17423i	0.619094	−	0.357434i	0.776516	+	0.630097i	$0.216985\pi$
$524$	−7.79796			−0.340655
$525$	14.6969	+	3.00000i	0.641427	+	0.130931i
$526$	7.00000	+	12.1244i	0.305215	+	0.528647i
$527$	−33.5125	−	19.3485i	−1.45983	−	0.842833i
$528$	−1.73205	+	1.00000i	−0.0753778	+	0.0435194i
$529$	−8.50000	+	14.7224i	−0.369565	+	0.640106i
$530$	−5.62622	−	4.05306i	−0.244387	−	0.176054i
$531$	11.7980			0.511988
$532$	−3.76588	−	12.5227i	−0.163272	−	0.542928i
$533$		−	8.44949i		−	0.365988i
$534$	5.77526	−	10.0030i	0.249920	−	0.432874i
$535$	13.6576	−	18.9586i	0.590468	−	0.819654i
$536$	−0.724745	−	1.25529i	−0.0313042	−	0.0542205i
$537$	15.8028	+	9.12372i	0.681939	+	0.393718i
$538$	−22.9453	+	13.2474i	−0.989240	+	0.571138i
$539$	−4.00000			−0.172292
$540$	−2.22474	−	0.224745i	−0.0957378	−	0.00967148i
$541$	7.17423	+	12.4261i	0.308444	+	0.534241i	0.978022	−	0.208500i	$-0.0668583\pi$
$541$	7.17423	+	12.4261i	0.308444	+	0.534241i	−0.669578	+	0.742742i	$0.733525\pi$
$542$	4.41761	−	2.55051i	0.189753	−	0.109554i
$543$			11.1010i			0.476390i
$544$	−4.89898			−0.210042
$545$	−28.5468	+	12.8483i	−1.22281	+	0.550362i
$546$	−5.17423	+	8.96204i	−0.221437	+	0.383540i
$547$	−12.2512	+	7.07321i	−0.523822	+	0.302429i	−0.738497	−	0.674257i	$-0.764464\pi$
$547$	−12.2512	+	7.07321i	−0.523822	+	0.302429i	0.214675	+	0.976686i	$0.431131\pi$
$548$	−0.953512	−	0.550510i	−0.0407320	−	0.0235166i
$549$	2.17423	−	3.76588i	0.0927941	−	0.160724i
$550$	−2.00000	+	9.79796i	−0.0852803	+	0.417786i
$551$	−39.0227	+	11.7351i	−1.66242	+	0.499931i
$552$		−	2.44949i		−	0.104257i
$553$	−43.6424	−	25.1969i	−1.85586	−	1.07148i
$554$	−16.2474	+	28.1414i	−0.690288	+	1.19561i
$555$	−9.27875	+	4.17617i	−0.393861	+	0.177269i
$556$	−3.27526	+	5.67291i	−0.138902	+	0.240585i
$557$	31.8198	−	18.3712i	1.34825	−	0.778412i	0.360247	−	0.932857i	$-0.382692\pi$
$557$	31.8198	−	18.3712i	1.34825	−	0.778412i	0.988001	+	0.154445i	$0.0493591\pi$
$558$		−	7.89898i		−	0.334390i
$559$	1.89898			0.0803183
$560$	2.75321	+	6.11717i	0.116344	+	0.258498i
$561$	4.89898	+	8.48528i	0.206835	+	0.358249i
$562$			26.4495i			1.11570i
$563$			25.5959i			1.07874i	0.842069	+	0.539370i	$0.181337\pi$
$563$			25.5959i			1.07874i	−0.842069	+	0.539370i	$0.818663\pi$
$564$	−1.77526	−	3.07483i	−0.0747517	−	0.129474i
$565$	19.4731	−	27.0314i	0.819238	−	1.13722i
$566$	−4.44949	−	7.70674i	−0.187026	−	0.323939i
$567$	2.59808	+	1.50000i	0.109109	+	0.0629941i
$568$	3.07483	+	1.77526i	0.129017	+	0.0744881i
$569$	32.8990			1.37920			0.689598	−	0.724192i	$-0.257787\pi$
$569$	32.8990			1.37920			0.689598	+	0.724192i	$0.257787\pi$
$570$	9.21405	+	3.17826i	0.385934	+	0.133123i
$571$	−20.5505			−0.860012			−0.430006	−	0.902826i	$-0.641489\pi$
$571$	−20.5505			−0.860012			−0.430006	+	0.902826i	$0.641489\pi$
$572$	−5.97469	−	3.44949i	−0.249814	−	0.144230i
$573$	−12.7279	−	7.34847i	−0.531717	−	0.306987i
$574$	3.67423	+	6.36396i	0.153360	+	0.265627i
$575$	−9.16756	−	8.12132i	−0.382314	−	0.338682i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$		−	22.0000i		−	0.915872i	−0.888985	−	0.457936i	$-0.848589\pi$
$577$		−	22.0000i		−	0.915872i	0.888985	−	0.457936i	$-0.151411\pi$
$578$			7.00000i			0.291162i
$579$	1.05051	+	1.81954i	0.0436577	+	0.0756174i
$580$	19.0621	−	8.57944i	0.791509	−	0.356242i
$581$	4.04541			0.167832
$582$		−	18.6969i		−	0.775013i
$583$	−5.37113	+	3.10102i	−0.222449	+	0.128431i
$584$	−5.94949	+	10.3048i	−0.246192	+	0.426416i
$585$	−3.16573	−	7.03371i	−0.130887	−	0.290808i
$586$	−9.44949	+	16.3670i	−0.390355	+	0.676114i
$587$	−27.9664	−	16.1464i	−1.15430	−	0.666434i	−0.204367	−	0.978894i	$-0.565514\pi$
$587$	−27.9664	−	16.1464i	−1.15430	−	0.666434i	−0.949931	+	0.312460i	$0.898847\pi$
$588$		−	2.00000i		−	0.0824786i
$589$	−7.89898	+	33.5125i	−0.325472	+	1.38086i
$590$	26.2474	+	2.65153i	1.08059	+	0.109162i
$591$	8.34847	−	14.4600i	0.343410	−	0.594804i
$592$	−3.94086	−	2.27526i	−0.161968	−	0.0935124i
$593$	16.5813	−	9.57321i	0.680912	−	0.393125i	−0.119287	−	0.992860i	$-0.538061\pi$
$593$	16.5813	−	9.57321i	0.680912	−	0.393125i	0.800199	+	0.599735i	$0.204727\pi$
$594$	−1.00000	+	1.73205i	−0.0410305	+	0.0710669i
$595$	29.9679	−	13.4879i	1.22856	−	0.552951i
$596$	3.79796			0.155570
$597$		−	8.10102i		−	0.331553i
$598$	7.31747	−	4.22474i	0.299234	−	0.172763i
$599$	−15.1237	−	26.1951i	−0.617939	−	1.07030i	−0.989861	−	0.142037i	$-0.954635\pi$
$599$	−15.1237	−	26.1951i	−0.617939	−	1.07030i	0.371923	−	0.928264i	$-0.378699\pi$
$600$	−4.89898	−	1.00000i	−0.200000	−	0.0408248i
$601$	−15.0000			−0.611863			−0.305931	−	0.952054i	$-0.598968\pi$
$601$	−15.0000			−0.611863			−0.305931	+	0.952054i	$0.598968\pi$
$602$	−1.43027	+	0.825765i	−0.0582934	+	0.0336557i
$603$	−1.25529	−	0.724745i	−0.0511196	−	0.0295139i
$604$	9.89898	+	17.1455i	0.402784	+	0.697642i
$605$	−12.7002	−	9.14905i	−0.516336	−	0.371962i
$606$	−1.89898	+	3.28913i	−0.0771408	+	0.133612i
$607$			27.0000i			1.09590i	0.836512	+	0.547948i	$0.184591\pi$
$607$			27.0000i			1.09590i	−0.836512	+	0.547948i	$0.815409\pi$
$608$	1.25529	+	4.17423i	0.0509089	+	0.169288i
$609$	−28.0454			−1.13646
$610$	5.68348	−	7.88948i	0.230117	−	0.319436i
$611$	6.12372	−	10.6066i	0.247739	−	0.429097i
$612$	−4.24264	+	2.44949i	−0.171499	+	0.0990148i
$613$	−26.7593	−	15.4495i	−1.08080	−	0.623999i	−0.149686	−	0.988734i	$-0.547826\pi$
$613$	−26.7593	−	15.4495i	−1.08080	−	0.623999i	−0.931112	+	0.364735i	$0.881160\pi$
$614$	1.10102	+	1.90702i	0.0444336	+	0.0769612i
$615$	−5.44949	−	0.550510i	−0.219745	−	0.0221987i
$616$	6.00000			0.241747
$617$	7.74607	−	4.47219i	0.311845	−	0.180044i	−0.335907	−	0.941895i	$-0.609043\pi$
$617$	7.74607	−	4.47219i	0.311845	−	0.180044i	0.647752	+	0.761851i	$0.275709\pi$
$618$	−8.57277	+	4.94949i	−0.344847	+	0.199098i
$619$	11.0454			0.443952			0.221976	−	0.975052i	$-0.428749\pi$
$619$	11.0454			0.443952			0.221976	+	0.975052i	$0.428749\pi$
$620$	1.77526	−	17.5732i	0.0712960	−	0.705757i
$621$	−1.22474	−	2.12132i	−0.0491473	−	0.0851257i
$622$	9.43879	+	5.44949i	0.378461	+	0.218505i
$623$	−30.0091	+	17.3258i	−1.20229	+	0.694142i
$624$	1.72474	−	2.98735i	0.0690451	−	0.119590i
$625$	−19.9853	+	15.0196i	−0.799411	+	0.600784i
$626$	−15.1010			−0.603558
$627$	5.97469	−	6.34847i	0.238606	−	0.253533i
$628$			5.44949i			0.217458i
$629$	−11.1464	+	19.3062i	−0.444437	+	0.769788i
$630$	5.44294	+	3.92102i	0.216852	+	0.156217i
$631$	−20.9495	−	36.2856i	−0.833986	−	1.44451i	−0.894853	−	0.446360i	$-0.852720\pi$
$631$	−20.9495	−	36.2856i	−0.833986	−	1.44451i	0.0608673	−	0.998146i	$-0.480613\pi$
$632$	14.5475	+	8.39898i	0.578667	+	0.334093i
$633$	−2.03383	+	1.17423i	−0.0808376	+	0.0466716i
$634$	−6.24745			−0.248118
$635$	−37.1464	−	3.75255i	−1.47411	−	0.148915i
$636$	−1.55051	−	2.68556i	−0.0614817	−	0.106489i
$637$	5.97469	−	3.44949i	0.236726	−	0.136674i
$638$		−	18.6969i		−	0.740219i
$639$	3.55051			0.140456
$640$	−0.917738	−	2.03906i	−0.0362768	−	0.0806008i
$641$	21.1237	−	36.5874i	0.834337	−	1.44511i	−0.0602322	−	0.998184i	$-0.519184\pi$
$641$	21.1237	−	36.5874i	0.834337	−	1.44511i	0.894569	−	0.446930i	$-0.147483\pi$
$642$	9.04952	−	5.22474i	0.357156	−	0.206204i
$643$	31.4787	+	18.1742i	1.24140	+	0.716722i	0.969379	−	0.245570i	$-0.0789751\pi$
$643$	31.4787	+	18.1742i	1.24140	+	0.716722i	0.272020	+	0.962292i	$0.412308\pi$
$644$	−3.67423	+	6.36396i	−0.144785	+	0.250775i
$645$	0.123724	−	1.22474i	0.00487164	−	0.0482243i
$646$	20.4495	−	6.14966i	0.804574	−	0.241955i
$647$		−	31.8434i		−	1.25189i	−0.779866	−	0.625946i	$-0.784713\pi$
$647$		−	31.8434i		−	1.25189i	0.779866	−	0.625946i	$-0.215287\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	11.7980	−	20.4347i	0.463110	−	0.802131i
$650$	−5.46214	−	16.3597i	−0.214243	−	0.641680i
$651$	−11.8485	+	20.5222i	−0.464378	+	0.804327i
$652$	−5.49794	+	3.17423i	−0.215316	+	0.124313i
$653$			2.44949i			0.0958559i	0.998851	+	0.0479280i	$0.0152618\pi$
$653$			2.44949i			0.0958559i	−0.998851	+	0.0479280i	$0.984738\pi$
$654$	−14.0000			−0.547443
$655$	−15.9005	+	7.15648i	−0.621284	+	0.279627i
$656$	−1.22474	−	2.12132i	−0.0478183	−	0.0828236i
$657$			11.8990i			0.464223i
$658$			10.6515i			0.415240i
$659$	0.348469	+	0.603566i	0.0135744	+	0.0235116i	0.872733	−	0.488198i	$-0.162346\pi$
$659$	0.348469	+	0.603566i	0.0135744	+	0.0235116i	−0.859158	+	0.511710i	$0.829012\pi$
$660$	−2.61401	+	3.62863i	−0.101750	+	0.141244i
$661$	3.44949	+	5.97469i	0.134170	+	0.232389i	0.925280	−	0.379285i	$-0.123830\pi$
$661$	3.44949	+	5.97469i	0.134170	+	0.232389i	−0.791110	+	0.611673i	$0.790497\pi$
$662$	20.1329	+	11.6237i	0.782487	+	0.451769i
$663$	−14.6349	−	8.44949i	−0.568374	−	0.328151i
$664$	−1.34847			−0.0523308
$665$	−19.1714	−	22.0784i	−0.743436	−	0.856165i
$666$	−4.55051			−0.176329
$667$	19.8311	+	11.4495i	0.767863	+	0.443326i
$668$	13.6814	+	7.89898i	0.529351	+	0.305621i
$669$	6.84847	+	11.8619i	0.264777	+	0.458607i
$670$	−2.62983	−	1.89449i	−0.101599	−	0.0731907i
$671$	−4.34847	−	7.53177i	−0.167871	−	0.290761i
$672$			3.00000i			0.115728i
$673$		−	10.3031i		−	0.397154i	−0.980085	−	0.198577i	$-0.936368\pi$
$673$		−	10.3031i		−	0.397154i	0.980085	−	0.198577i	$-0.0636320\pi$
$674$	−2.05051	−	3.55159i	−0.0789827	−	0.136802i
$675$	−4.74264	+	1.58346i	−0.182544	+	0.0609476i
$676$	−1.10102			−0.0423469
$677$		−	6.85357i		−	0.263404i	−0.991289	−	0.131702i	$-0.957956\pi$
$677$		−	6.85357i		−	0.263404i	0.991289	−	0.131702i	$-0.0420442\pi$
$678$	12.9029	−	7.44949i	0.495533	−	0.286096i
$679$	−28.0454	+	48.5761i	−1.07628	+	1.86418i
$680$	−9.98930	+	4.49598i	−0.383072	+	0.172413i
$681$	−6.67423	+	11.5601i	−0.255757	+	0.442985i
$682$	−13.6814	−	7.89898i	−0.523889	−	0.302468i
$683$			39.1918i			1.49963i	0.661645	+	0.749817i	$0.269858\pi$
$683$			39.1918i			1.49963i	−0.661645	+	0.749817i	$0.730142\pi$
$684$	3.17423	+	2.98735i	0.121370	+	0.114224i
$685$	−2.44949	−	0.247449i	−0.0935902	−	0.00945453i
$686$	7.50000	−	12.9904i	0.286351	−	0.495975i
$687$	−23.4220	−	13.5227i	−0.893605	−	0.515923i
$688$	0.476756	−	0.275255i	0.0181761	−	0.0104940i
$689$	5.34847	−	9.26382i	0.203760	−	0.352923i
$690$	−2.24799	−	4.99465i	−0.0855795	−	0.190143i
$691$	0.404082			0.0153720			0.00768600	−	0.999970i	$-0.497553\pi$
$691$	0.404082			0.0153720			0.00768600	+	0.999970i	$0.497553\pi$
$692$			4.44949i			0.169144i
$693$	5.19615	−	3.00000i	0.197386	−	0.113961i
$694$	−14.2474	−	24.6773i	−0.540826	−	0.936738i
$695$	−1.47219	+	14.5732i	−0.0558435	+	0.552794i
$696$	9.34847			0.354353
$697$	−10.3923	+	6.00000i	−0.393637	+	0.227266i
$698$	22.9934	+	13.2753i	0.870314	+	0.502476i
$699$	7.32577	+	12.6886i	0.277086	+	0.479927i
$700$	11.2279	+	9.94655i	0.424376	+	0.375944i
$701$	9.10102	−	15.7634i	0.343741	−	0.595377i	−0.641383	−	0.767221i	$-0.721639\pi$
$701$	9.10102	−	15.7634i	0.343741	−	0.595377i	0.985124	+	0.171844i	$0.0549725\pi$
$702$		−	3.44949i		−	0.130193i
$703$	19.3062	+	4.55051i	0.728146	+	0.171626i
$704$	−2.00000			−0.0753778
$705$	−6.44174	−	4.64054i	−0.242610	−	0.174773i
$706$	−10.5732	+	18.3133i	−0.397928	+	0.689232i
$707$	9.86739	−	5.69694i	0.371101	−	0.214255i
$708$	10.2173	+	5.89898i	0.383991	+	0.221697i
$709$	−20.6237	−	35.7213i	−0.774540	−	1.34154i	−0.935053	−	0.354509i	$-0.884648\pi$
$709$	−20.6237	−	35.7213i	−0.774540	−	1.34154i	0.160512	−	0.987034i	$-0.448685\pi$
$710$	7.89898	+	0.797959i	0.296443	+	0.0299469i
$711$	16.7980			0.629973
$712$	10.0030	−	5.77526i	0.374880	−	0.216437i
$713$	16.7563	−	9.67423i	0.627527	−	0.362303i
$714$	14.6969			0.550019
$715$	−15.3485	−	1.55051i	−0.574000	−	0.0579858i
$716$	9.12372	+	15.8028i	0.340970	+	0.590577i
$717$	−7.49245	−	4.32577i	−0.279811	−	0.161549i
$718$	−17.5348	+	10.1237i	−0.654393	+	0.377814i
$719$	16.7753	−	29.0556i	0.625611	−	1.08359i	−0.362811	−	0.931863i	$-0.618183\pi$
$719$	16.7753	−	29.0556i	0.625611	−	1.08359i	0.988422	−	0.151728i	$-0.0484838\pi$
$720$	−1.81431	−	1.30701i	−0.0676155	−	0.0487093i
$721$	29.6969			1.10597
$722$	−10.4798	−	15.8485i	−0.390017	−	0.589819i
$723$		−	11.0000i		−	0.409094i
$724$	−5.55051	+	9.61377i	−0.206283	+	0.357293i
$725$	30.9950	−	34.9880i	1.15113	−	1.29942i
$726$	−3.50000	−	6.06218i	−0.129897	−	0.224989i
$727$	23.2077	+	13.3990i	0.860726	+	0.496941i	0.864255	−	0.503053i	$-0.167790\pi$
$727$	23.2077	+	13.3990i	0.860726	+	0.496941i	−0.00352905	+	0.999994i	$0.501123\pi$
$728$	−8.96204	+	5.17423i	−0.332155	+	0.191770i
$729$	−1.00000			−0.0370370
$730$	−2.67423	+	26.4722i	−0.0989779	+	0.979780i
$731$	−1.34847	−	2.33562i	−0.0498749	−	0.0863859i
$732$	3.76588	−	2.17423i	0.139191	−	0.0803620i
$733$			30.6969i			1.13382i	0.823781	+	0.566909i	$0.191861\pi$
$733$			30.6969i			1.13382i	−0.823781	+	0.566909i	$0.808139\pi$
$734$	−16.5959			−0.612567
$735$	−1.83548	−	4.07812i	−0.0677025	−	0.150424i
$736$	1.22474	−	2.12132i	0.0451447	−	0.0781929i
$737$	−2.51059	+	1.44949i	−0.0924788	+	0.0533926i
$738$	−2.12132	−	1.22474i	−0.0780869	−	0.0450835i
$739$	10.8258	−	18.7508i	0.398232	−	0.689758i	−0.595276	−	0.803522i	$-0.702957\pi$
$739$	10.8258	−	18.7508i	0.398232	−	0.689758i	0.993508	+	0.113763i	$0.0362905\pi$
$740$	−10.1237	−	1.02270i	−0.372156	−	0.0375953i
$741$	−3.44949	+	14.6349i	−0.126720	+	0.537628i
$742$			9.30306i			0.341526i
$743$	−39.8372	−	23.0000i	−1.46148	−	0.843788i	−0.462404	−	0.886669i	$-0.653013\pi$
$743$	−39.8372	−	23.0000i	−1.46148	−	0.843788i	−0.999080	+	0.0428813i	$0.986346\pi$
$744$	3.94949	−	6.84072i	0.144795	−	0.250793i
$745$	7.74426	−	3.48553i	0.283728	−	0.127700i
$746$	−12.5505	+	21.7381i	−0.459507	+	0.795889i
$747$	−1.16781	+	0.674235i	−0.0427279	+	0.0246690i
$748$			9.79796i			0.358249i
$749$	−31.3485			−1.14545
$750$	−10.9070	+	2.45692i	−0.398269	+	0.0897140i
$751$	10.1515	+	17.5830i	0.370435	+	0.641612i	0.989632	−	0.143623i	$-0.0458754\pi$
$751$	10.1515	+	17.5830i	0.370435	+	0.641612i	−0.619198	+	0.785235i	$0.712542\pi$
$752$		−	3.55051i		−	0.129474i
$753$			20.6969i			0.754238i
$754$	16.1237	+	27.9271i	0.587191	+	1.01705i
$755$	35.9197	+	25.8761i	1.30725	+	0.941727i
$756$	1.50000	+	2.59808i	0.0545545	+	0.0944911i
$757$	−10.6941	−	6.17423i	−0.388683	−	0.224406i	0.292906	−	0.956141i	$-0.405378\pi$
$757$	−10.6941	−	6.17423i	−0.388683	−	0.224406i	−0.681589	+	0.731735i	$0.738711\pi$
$758$	−7.57993	−	4.37628i	−0.275316	−	0.158953i
$759$	−4.89898			−0.177822
$760$	6.39047	+	7.35948i	0.231807	+	0.266956i
$761$	34.8990			1.26509			0.632544	−	0.774525i	$-0.282011\pi$
$761$	34.8990			1.26509			0.632544	+	0.774525i	$0.282011\pi$
$762$	−14.4600	−	8.34847i	−0.523830	−	0.302433i
$763$	36.3731	+	21.0000i	1.31679	+	0.760251i
$764$	−7.34847	−	12.7279i	−0.265858	−	0.460480i
$765$	−6.40300	+	8.88828i	−0.231501	+	0.321357i
$766$	−0.674235	−	1.16781i	−0.0243611	−	0.0421946i
$767$			40.6969i			1.46948i
$768$		−	1.00000i		−	0.0360844i
$769$	0.297959	+	0.516080i	0.0107447	+	0.0186103i	0.871348	−	0.490666i	$-0.163246\pi$
$769$	0.297959	+	0.516080i	0.0107447	+	0.0186103i	−0.860603	+	0.509276i	$0.829913\pi$
$770$	12.2343	−	5.50643i	0.440895	−	0.198438i
$771$	25.1464			0.905626
$772$			2.10102i			0.0756174i
$773$	33.6875	−	19.4495i	1.21166	−	0.699550i	0.248536	−	0.968623i	$-0.420051\pi$
$773$	33.6875	−	19.4495i	1.21166	−	0.699550i	0.963120	+	0.269073i	$0.0867174\pi$
$774$	0.275255	−	0.476756i	0.00989384	−	0.0171366i
$775$	−12.5078	−	37.4620i	−0.449292	−	1.34568i
$776$	9.34847	−	16.1920i	0.335590	−	0.581260i
$777$	11.8226	+	6.82577i	0.424132	+	0.244873i
$778$			14.2474i			0.510796i
$779$	7.77526	+	7.31747i	0.278577	+	0.262176i
$780$	0.775255	−	7.67423i	0.0277586	−	0.274782i
$781$	3.55051	−	6.14966i	0.127047	−	0.220052i
$782$	−10.3923	−	6.00000i	−0.371628	−	0.214560i
$783$	8.09601	−	4.67423i	0.289328	−	0.167044i
$784$	1.00000	−	1.73205i	0.0357143	−	0.0618590i
$785$	5.00120	+	11.1118i	0.178501	+	0.396598i
$786$	−7.79796			−0.278144
$787$		−	17.9444i		−	0.639648i	−0.947477	−	0.319824i	$-0.896376\pi$
$787$		−	17.9444i		−	0.639648i	0.947477	−	0.319824i	$-0.103624\pi$
$788$	14.4600	−	8.34847i	0.515115	−	0.297402i
$789$	7.00000	+	12.1244i	0.249207	+	0.431638i
$790$	37.3712	+	3.77526i	1.32961	+	0.134318i
$791$	−44.6969			−1.58924
$792$	−1.73205	+	1.00000i	−0.0615457	+	0.0355335i
$793$	12.9904	+	7.50000i	0.461302	+	0.266333i
$794$	4.62372	+	8.00853i	0.164090	+	0.284212i
$795$	−5.62622	−	4.05306i	−0.199542	−	0.143747i
$796$	4.05051	−	7.01569i	0.143567	−	0.248665i
$797$		−	10.8990i		−	0.386062i	−0.981193	−	0.193031i	$-0.938168\pi$
$797$		−	10.8990i		−	0.386062i	0.981193	−	0.193031i	$-0.0618317\pi$
$798$	−3.76588	−	12.5227i	−0.133311	−	0.443299i
$799$	−17.3939			−0.615351
$800$	−3.74264	−	3.31552i	−0.132322	−	0.117221i
$801$	5.77526	−	10.0030i	0.204059	−	0.353440i
$802$	−27.9664	+	16.1464i	−0.987529	+	0.570150i
$803$	20.6096	+	11.8990i	0.727298	+	0.419906i
$804$	−0.724745	−	1.25529i	−0.0255598	−	0.0442708i
$805$	−1.65153	+	16.3485i	−0.0582088	+	0.576208i
$806$	27.2474			0.959750
$807$	−22.9453	+	13.2474i	−0.807711	+	0.466332i
$808$	−3.28913	+	1.89898i	−0.115711	+	0.0668059i
$809$	11.3485			0.398991			0.199495	−	0.979899i	$-0.436070\pi$
$809$	11.3485			0.398991			0.199495	+	0.979899i	$0.436070\pi$
$810$	−2.22474	−	0.224745i	−0.0781696	−	0.00789673i
$811$	5.79796	+	10.0424i	0.203594	+	0.352635i	0.949684	−	0.313210i	$-0.101404\pi$
$811$	5.79796	+	10.0424i	0.203594	+	0.352635i	−0.746090	+	0.665845i	$0.768071\pi$
$812$	−24.2880	−	14.0227i	−0.852343	−	0.492100i
$813$	4.41761	−	2.55051i	0.154932	−	0.0894503i
$814$	−4.55051	+	7.88171i	−0.159495	+	0.276254i
$815$	−8.29750	+	11.5181i	−0.290649	+	0.403462i
$816$	−4.89898			−0.171499
$817$	−1.64456	+	1.74745i	−0.0575360	+	0.0611355i
$818$		−	11.1010i		−	0.388138i
$819$	−5.17423	+	8.96204i	−0.180802	+	0.313159i
$820$	−4.44414	−	3.20150i	−0.155196	−	0.111801i
$821$	−10.6742	−	18.4883i	−0.372533	−	0.645247i	0.617421	−	0.786633i	$-0.288177\pi$
$821$	−10.6742	−	18.4883i	−0.372533	−	0.645247i	−0.989955	+	0.141386i	$0.954844\pi$
$822$	−0.953512	−	0.550510i	−0.0332575	−	0.0192013i
$823$	23.5488	−	13.5959i	0.820860	−	0.473924i	−0.0298528	−	0.999554i	$-0.509504\pi$
$823$	23.5488	−	13.5959i	0.820860	−	0.473924i	0.850713	+	0.525630i	$0.176171\pi$
$824$	−9.89898			−0.344847
$825$	−2.00000	+	9.79796i	−0.0696311	+	0.341121i
$826$	−17.6969	−	30.6520i	−0.615755	−	1.06652i
$827$	−16.2313	+	9.37117i	−0.564419	+	0.325868i	−0.754917	−	0.655820i	$-0.772323\pi$
$827$	−16.2313	+	9.37117i	−0.564419	+	0.325868i	0.190498	+	0.981688i	$0.438990\pi$
$828$		−	2.44949i		−	0.0851257i
$829$	46.5505			1.61677			0.808383	−	0.588657i	$-0.200343\pi$
$829$	46.5505			1.61677			0.808383	+	0.588657i	$0.200343\pi$
$830$	−2.74961	+	1.23754i	−0.0954403	+	0.0429557i
$831$	−16.2474	+	28.1414i	−0.563618	+	0.976215i
$832$	2.98735	−	1.72474i	0.103568	−	0.0597948i
$833$	−8.48528	−	4.89898i	−0.293998	−	0.169740i
$834$	−3.27526	+	5.67291i	−0.113413	+	0.196437i
$835$	35.1464	+	3.55051i	1.21629	+	0.122870i
$836$	8.34847	−	2.51059i	0.288738	−	0.0868306i
$837$		−	7.89898i		−	0.273029i
$838$	22.5560	+	13.0227i	0.779184	+	0.449862i
$839$	−0.651531	+	1.12848i	−0.0224933	+	0.0389596i	−0.877053	−	0.480394i	$-0.840494\pi$
$839$	−0.651531	+	1.12848i	−0.0224933	+	0.0389596i	0.854560	+	0.519353i	$0.173827\pi$
$840$	2.75321	+	6.11717i	0.0949949	+	0.211063i
$841$	−29.1969	+	50.5706i	−1.00679	+	1.74381i
$842$	18.7026	−	10.7980i	0.644535	−	0.372122i
$843$			26.4495i			0.910969i
$844$	−2.34847			−0.0808376
$845$	−2.24504	+	1.01045i	−0.0772319	+	0.0347605i
$846$	−1.77526	−	3.07483i	−0.0610345	−	0.105715i
$847$			21.0000i			0.721569i
$848$		−	3.10102i		−	0.106489i
$849$	−4.44949	−	7.70674i	−0.152706	−	0.264495i
$850$	−16.2426	+	18.3351i	−0.557118	+	0.628889i
$851$	−5.57321	−	9.65309i	−0.191047	−	0.330904i
$852$	3.07483	+	1.77526i	0.105342	+	0.0608192i
$853$	49.4028	+	28.5227i	1.69152	+	0.976599i	0.953294	+	0.302044i	$0.0976689\pi$
$853$	49.4028	+	28.5227i	1.69152	+	0.976599i	0.738225	+	0.674555i	$0.235664\pi$
$854$	−13.0454			−0.446405
$855$	9.21405	+	3.17826i	0.315114	+	0.108694i
$856$	10.4495			0.357156
$857$	−20.0454	−	11.5732i	−0.684738	−	0.395333i	0.116900	−	0.993144i	$-0.462704\pi$
$857$	−20.0454	−	11.5732i	−0.684738	−	0.395333i	−0.801638	+	0.597810i	$0.796038\pi$
$858$	−5.97469	−	3.44949i	−0.203973	−	0.117764i
$859$	19.8258	+	34.3392i	0.676446	+	1.17164i	0.976044	+	0.217574i	$0.0698143\pi$
$859$	19.8258	+	34.3392i	0.676446	+	1.17164i	−0.299597	+	0.954066i	$0.596852\pi$
$860$	0.719521	−	0.998798i	0.0245355	−	0.0340587i
$861$	3.67423	+	6.36396i	0.125218	+	0.216883i
$862$		−	30.2474i		−	1.03023i
$863$			8.20204i			0.279201i	0.990208	+	0.139600i	$0.0445818\pi$
$863$			8.20204i			0.279201i	−0.990208	+	0.139600i	$0.955418\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	4.08346	+	9.07277i	0.138842	+	0.308483i
$866$	−18.7980			−0.638781
$867$			7.00000i			0.237732i
$868$	−20.5222	+	11.8485i	−0.696567	+	0.402163i
$869$	16.7980	−	29.0949i	0.569832	−	0.986978i
$870$	19.0621	−	8.57944i	0.646265	−	0.290870i
$871$	2.50000	−	4.33013i	0.0847093	−	0.146721i
$872$	−12.1244	−	7.00000i	−0.410582	−	0.237050i
$873$		−	18.6969i		−	0.632795i
$874$	−2.44949	+	10.3923i	−0.0828552	+	0.351525i
$875$	32.0227	+	9.97730i	1.08256	+	0.337294i
$876$	−5.94949	+	10.3048i	−0.201015	+	0.348168i
$877$	29.1431	+	16.8258i	0.984092	+	0.568166i	0.903503	−	0.428582i	$-0.140987\pi$
$877$	29.1431	+	16.8258i	0.984092	+	0.568166i	0.0805889	+	0.996747i	$0.474320\pi$
$878$	−15.1510	+	8.74745i	−0.511322	+	0.295212i
$879$	−9.44949	+	16.3670i	−0.318723	+	0.552045i
$880$	−4.07812	+	1.83548i	−0.137473	+	0.0618739i
$881$	26.4495			0.891106			0.445553	−	0.895256i	$-0.353007\pi$
$881$	26.4495			0.891106			0.445553	+	0.895256i	$0.353007\pi$
$882$		−	2.00000i		−	0.0673435i
$883$	−22.4685	+	12.9722i	−0.756125	+	0.436549i	−0.827903	−	0.560872i	$-0.810466\pi$
$883$	−22.4685	+	12.9722i	−0.756125	+	0.436549i	0.0717776	+	0.997421i	$0.477133\pi$
$884$	−8.44949	−	14.6349i	−0.284187	−	0.492226i
$885$	26.2474	+	2.65153i	0.882298	+	0.0891302i
$886$	9.79796			0.329169
$887$	−13.4671	+	7.77526i	−0.452182	+	0.261068i	−0.708751	−	0.705458i	$-0.750741\pi$
$887$	−13.4671	+	7.77526i	−0.452182	+	0.261068i	0.256569	+	0.966526i	$0.417408\pi$
$888$	−3.94086	−	2.27526i	−0.132247	−	0.0763526i
$889$	25.0454	+	43.3799i	0.839996	+	1.45492i
$890$	15.0966	−	20.9562i	0.506039	−	0.702455i
$891$	−1.00000	+	1.73205i	−0.0335013	+	0.0580259i
$892$			13.6969i			0.458607i
$893$	4.45694	+	14.8207i	0.149146	+	0.495955i
$894$	3.79796			0.127023
$895$	33.1066	+	23.8495i	1.10663	+	0.797202i
$896$	−1.50000	+	2.59808i	−0.0501115	+	0.0867956i
$897$	7.31747	−	4.22474i	0.244323	−	0.141060i
$898$	9.26382	+	5.34847i	0.309138	+	0.178481i
$899$	36.9217	+	63.9502i	1.23141	+	2.13286i
$900$	−4.89898	−	1.00000i	−0.163299	−	0.0333333i
$901$	−15.1918			−0.506113
$902$	−4.24264	+	2.44949i	−0.141264	+	0.0815591i
$903$	−1.43027	+	0.825765i	−0.0475963	+	0.0274798i
$904$	14.8990			0.495533
$905$	−2.49490	+	24.6969i	−0.0829332	+	0.820954i
$906$	9.89898	+	17.1455i	0.328872	+	0.569622i
$907$	−35.4196	−	20.4495i	−1.17609	−	0.679014i	−0.220981	−	0.975278i	$-0.570926\pi$
$907$	−35.4196	−	20.4495i	−1.17609	−	0.679014i	−0.955106	+	0.296264i	$0.904259\pi$
$908$	−11.5601	+	6.67423i	−0.383636	+	0.221492i
$909$	−1.89898	+	3.28913i	−0.0629852	+	0.109094i
$910$	−13.5255	+	18.7754i	−0.448367	+	0.622397i
$911$	−45.5505			−1.50916			−0.754578	−	0.656211i	$-0.772158\pi$
$911$	−45.5505			−1.50916			−0.754578	+	0.656211i	$0.772158\pi$
$912$	1.25529	+	4.17423i	0.0415670	+	0.138223i
$913$			2.69694i			0.0892556i
$914$	7.05051	−	12.2118i	0.233210	−	0.403932i
$915$	5.68348	−	7.88948i	0.187890	−	0.260818i
$916$	−13.5227	−	23.4220i	−0.446803	−	0.773885i
$917$	20.2597	+	11.6969i	0.669034	+	0.386267i
$918$	−4.24264	+	2.44949i	−0.140028	+	0.0808452i
$919$	20.7980			0.686061			0.343031	−	0.939324i	$-0.388547\pi$
$919$	20.7980			0.686061			0.343031	+	0.939324i	$0.388547\pi$
$920$	0.550510	−	5.44949i	0.0181498	−	0.179664i
$921$	1.10102	+	1.90702i	0.0362799	+	0.0628386i
$922$	20.9989	−	12.1237i	0.691562	−	0.399274i
$923$			12.2474i			0.403130i
$924$	6.00000			0.197386
$925$	−21.5814	+	7.20557i	−0.709593	+	0.236918i
$926$	19.6464	−	34.0286i	0.645622	−	1.11825i
$927$	−8.57277	+	4.94949i	−0.281567	+	0.162563i
$928$	8.09601	+	4.67423i	0.265765	+	0.153439i
$929$	8.44949	−	14.6349i	0.277219	−	0.480157i	−0.693474	−	0.720482i	$-0.743921\pi$
$929$	8.44949	−	14.6349i	0.277219	−	0.480157i	0.970693	+	0.240325i	$0.0772540\pi$
$930$	1.77526	−	17.5732i	0.0582129	−	0.576248i
$931$	−2.00000	+	8.48528i	−0.0655474	+	0.278094i
$932$			14.6515i			0.479927i
$933$	9.43879	+	5.44949i	0.309012	+	0.178408i
$934$	1.77526	−	3.07483i	0.0580881	−	0.100612i
$935$	8.99196	+	19.9786i	0.294068	+	0.653370i
$936$	1.72474	−	2.98735i	0.0563750	−	0.0976445i
$937$	13.7689	−	7.94949i	0.449811	−	0.259699i	−0.257939	−	0.966161i	$-0.583043\pi$
$937$	13.7689	−	7.94949i	0.449811	−	0.259699i	0.707750	+	0.706463i	$0.249710\pi$
$938$			4.34847i			0.141983i
$939$	−15.1010			−0.492803
$940$	−3.25844	−	7.23970i	−0.106278	−	0.236133i
$941$	−4.02270	−	6.96753i	−0.131136	−	0.227135i	0.792979	−	0.609250i	$-0.208529\pi$
$941$	−4.02270	−	6.96753i	−0.131136	−	0.227135i	−0.924115	+	0.382115i	$0.875196\pi$
$942$			5.44949i			0.177554i
$943$		−	6.00000i		−	0.195387i
$944$	5.89898	+	10.2173i	0.191995	+	0.332546i
$945$	5.44294	+	3.92102i	0.177059	+	0.127551i
$946$	−0.550510	−	0.953512i	−0.0178986	−	0.0310013i
$947$	−2.16064	−	1.24745i	−0.0702115	−	0.0405366i	0.464483	−	0.885582i	$-0.346240\pi$
$947$	−2.16064	−	1.24745i	−0.0702115	−	0.0405366i	−0.534695	+	0.845045i	$0.679573\pi$
$948$	14.5475	+	8.39898i	0.472480	+	0.272786i
$949$	−41.0454			−1.33239
$950$	19.7846	+	9.14162i	0.641898	+	0.296593i
$951$	−6.24745			−0.202587
$952$	12.7279	+	7.34847i	0.412514	+	0.238165i
$953$	−26.1951	−	15.1237i	−0.848541	−	0.489905i	0.0116172	−	0.999933i	$-0.496302\pi$
$953$	−26.1951	−	15.1237i	−0.848541	−	0.489905i	−0.860158	+	0.510027i	$0.829635\pi$
$954$	−1.55051	−	2.68556i	−0.0501996	−	0.0869483i
$955$	−26.6648	−	19.2090i	−0.862854	−	0.621589i
$956$	−4.32577	−	7.49245i	−0.139905	−	0.242323i
$957$		−	18.6969i		−	0.604386i
$958$			28.6969i			0.927156i
$959$	1.65153	+	2.86054i	0.0533307	+	0.0923715i
$960$	−0.917738	−	2.03906i	−0.0296199	−	0.0658103i
$961$	31.3939			1.01271
$962$		−	15.6969i		−	0.506090i
$963$	9.04952	−	5.22474i	0.291617	−	0.168365i
$964$	5.50000	−	9.52628i	0.177143	−	0.306821i
$965$	1.92819	+	4.28410i	0.0620705	+	0.137910i
$966$	−3.67423	+	6.36396i	−0.118217	+	0.204757i
$967$	−42.5139	−	24.5454i	−1.36715	−	0.789327i	−0.376591	−	0.926380i	$-0.622904\pi$
$967$	−42.5139	−	24.5454i	−1.36715	−	0.789327i	−0.990564	+	0.137053i	$0.956237\pi$
$968$		−	7.00000i		−	0.224989i
$969$	20.4495	−	6.14966i	0.656932	−	0.197556i
$970$	4.20204	−	41.5959i	0.134919	−	1.33556i
$971$	20.1237	−	34.8553i	0.645801	−	1.11856i	−0.338315	−	0.941033i	$-0.609857\pi$
$971$	20.1237	−	34.8553i	0.645801	−	1.11856i	0.984116	−	0.177527i	$-0.0568098\pi$
$972$	−0.866025	−	0.500000i	−0.0277778	−	0.0160375i
$973$	17.0187	−	9.82577i	0.545595	−	0.315000i
$974$	17.4495	−	30.2234i	0.559118	−	0.968420i
$975$	−5.46214	−	16.3597i	−0.174929	−	0.523929i
$976$	4.34847			0.139191
$977$			48.2929i			1.54503i	0.634999	+	0.772513i	$0.281000\pi$
$977$			48.2929i			1.54503i	−0.634999	+	0.772513i	$0.719000\pi$
$978$	−5.49794	+	3.17423i	−0.175805	+	0.101501i
$979$	−11.5505	−	20.0061i	−0.369156	−	0.639397i
$980$	0.449490	−	4.44949i	0.0143584	−	0.142134i
$981$	−14.0000			−0.446986
$982$	8.69958	−	5.02270i	0.277615	−	0.160281i
$983$	4.63191	+	2.67423i	0.147735	+	0.0852948i	0.572045	−	0.820222i	$-0.306150\pi$
$983$	4.63191	+	2.67423i	0.147735	+	0.0852948i	−0.424310	+	0.905517i	$0.639483\pi$
$984$	−1.22474	−	2.12132i	−0.0390434	−	0.0676252i
$985$	21.8230	−	30.2935i	0.695339	−	0.965230i
$986$	22.8990	−	39.6622i	0.729252	−	1.26310i
$987$			10.6515i			0.339042i
$988$	−10.3048	+	10.9495i	−0.327840	+	0.348350i
$989$	1.34847			0.0428788
$990$	−2.61401	+	3.62863i	−0.0830788	+	0.115325i
$991$	−17.8485	+	30.9145i	−0.566975	+	0.982030i	0.429888	+	0.902882i	$0.358553\pi$
$991$	−17.8485	+	30.9145i	−0.566975	+	0.982030i	−0.996863	+	0.0791476i	$0.974780\pi$
$992$	6.84072	−	3.94949i	0.217193	−	0.125396i
$993$	20.1329	+	11.6237i	0.638898	+	0.368868i
$994$	−5.32577	−	9.22450i	−0.168923	−	0.292583i
$995$	1.82066	−	18.0227i	0.0577189	−	0.571358i
$996$	−1.34847			−0.0427279
$997$	−2.03383	+	1.17423i	−0.0644122	+	0.0371884i	−0.531860	−	0.846832i	$-0.678507\pi$
$997$	−2.03383	+	1.17423i	−0.0644122	+	0.0371884i	0.467448	+	0.884021i	$0.345173\pi$
$998$	−28.4432	+	16.4217i	−0.900353	+	0.519819i
$999$	−4.55051			−0.143972

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.q.a.49.4	yes	8
3.2	odd	2		1710.2.t.a.1189.1		8
5.4	even	2	inner	570.2.q.a.49.1	✓	8
15.14	odd	2		1710.2.t.a.1189.4		8
19.7	even	3	inner	570.2.q.a.349.1	yes	8
57.26	odd	6		1710.2.t.a.919.4		8
95.64	even	6	inner	570.2.q.a.349.4	yes	8
285.254	odd	6		1710.2.t.a.919.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.q.a.49.1	✓	8	5.4	even	2	inner
570.2.q.a.49.4	yes	8	1.1	even	1	trivial
570.2.q.a.349.1	yes	8	19.7	even	3	inner
570.2.q.a.349.4	yes	8	95.64	even	6	inner
1710.2.t.a.919.1		8	285.254	odd	6
1710.2.t.a.919.4		8	57.26	odd	6
1710.2.t.a.1189.1		8	3.2	odd	2
1710.2.t.a.1189.4		8	15.14	odd	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.81431 + 1.30701i) q^{5} +(0.500000 + 0.866025i) q^{6} -3.00000i q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.81431 + 1.30701i) q^{5} +(0.500000 + 0.866025i) q^{6} -3.00000i q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.917738 + 2.03906i) q^{10} +2.00000 q^{11} +1.00000i q^{12} +(-2.98735 + 1.72474i) q^{13} +(1.50000 - 2.59808i) q^{14} +(0.917738 + 2.03906i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(4.24264 + 2.44949i) q^{17} +1.00000i q^{18} +(1.00000 - 4.24264i) q^{19} +(-0.224745 + 2.22474i) q^{20} +(1.50000 - 2.59808i) q^{21} +(1.73205 + 1.00000i) q^{22} +(-2.12132 + 1.22474i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(1.58346 + 4.74264i) q^{25} -3.44949 q^{26} +1.00000i q^{27} +(2.59808 - 1.50000i) q^{28} +(-4.67423 - 8.09601i) q^{29} +(-0.224745 + 2.22474i) q^{30} -7.89898 q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.73205 + 1.00000i) q^{33} +(2.44949 + 4.24264i) q^{34} +(3.92102 - 5.44294i) q^{35} +(-0.500000 + 0.866025i) q^{36} +4.55051i q^{37} +(2.98735 - 3.17423i) q^{38} -3.44949 q^{39} +(-1.30701 + 1.81431i) q^{40} +(-1.22474 + 2.12132i) q^{41} +(2.59808 - 1.50000i) q^{42} +(-0.476756 - 0.275255i) q^{43} +(1.00000 + 1.73205i) q^{44} +(-0.224745 + 2.22474i) q^{45} -2.44949 q^{46} +(-3.07483 + 1.77526i) q^{47} +(-0.866025 + 0.500000i) q^{48} -2.00000 q^{49} +(-1.00000 + 4.89898i) q^{50} +(2.44949 + 4.24264i) q^{51} +(-2.98735 - 1.72474i) q^{52} +(-2.68556 + 1.55051i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(3.62863 + 2.61401i) q^{55} +3.00000 q^{56} +(2.98735 - 3.17423i) q^{57} -9.34847i q^{58} +(5.89898 - 10.2173i) q^{59} +(-1.30701 + 1.81431i) q^{60} +(-2.17423 - 3.76588i) q^{61} +(-6.84072 - 3.94949i) q^{62} +(2.59808 - 1.50000i) q^{63} -1.00000 q^{64} +(-7.67423 - 0.775255i) q^{65} +(1.00000 + 1.73205i) q^{66} +(-1.25529 + 0.724745i) q^{67} +4.89898i q^{68} -2.44949 q^{69} +(6.11717 - 2.75321i) q^{70} +(1.77526 - 3.07483i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(10.3048 + 5.94949i) q^{73} +(-2.27526 + 3.94086i) q^{74} +(-1.00000 + 4.89898i) q^{75} +(4.17423 - 1.25529i) q^{76} -6.00000i q^{77} +(-2.98735 - 1.72474i) q^{78} +(8.39898 - 14.5475i) q^{79} +(-2.03906 + 0.917738i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.12132 + 1.22474i) q^{82} +1.34847i q^{83} +3.00000 q^{84} +(4.49598 + 9.98930i) q^{85} +(-0.275255 - 0.476756i) q^{86} -9.34847i q^{87} +2.00000i q^{88} +(-5.77526 - 10.0030i) q^{89} +(-1.30701 + 1.81431i) q^{90} +(5.17423 + 8.96204i) q^{91} +(-2.12132 - 1.22474i) q^{92} +(-6.84072 - 3.94949i) q^{93} -3.55051 q^{94} +(7.35948 - 6.39047i) q^{95} -1.00000 q^{96} +(-16.1920 - 9.34847i) q^{97} +(-1.73205 - 1.00000i) q^{98} +(1.00000 + 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^4 + 4 * q^5 + 4 * q^6 + 4 * q^9	\( 8 q + 4 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{9} + 4 q^{10} + 16 q^{11} + 12 q^{14} + 4 q^{15} - 4 q^{16} + 8 q^{19} + 8 q^{20} + 12 q^{21} - 4 q^{24} - 8 q^{26} - 8 q^{29} + 8 q^{30} - 24 q^{31} + 12 q^{35} - 4 q^{36} - 8 q^{39} - 4 q^{40} + 8 q^{44} + 8 q^{45} - 16 q^{49} - 8 q^{50} - 4 q^{54} + 8 q^{55} + 24 q^{56} + 8 q^{59} - 4 q^{60} + 12 q^{61} - 8 q^{64} - 32 q^{65} + 8 q^{66} - 12 q^{70} + 24 q^{71} - 28 q^{74} - 8 q^{75} + 4 q^{76} + 28 q^{79} + 4 q^{80} - 4 q^{81} + 24 q^{84} + 24 q^{85} - 12 q^{86} - 56 q^{89} - 4 q^{90} + 12 q^{91} - 48 q^{94} + 40 q^{95} - 8 q^{96} + 8 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 + 4 * q^5 + 4 * q^6 + 4 * q^9 + 4 * q^10 + 16 * q^11 + 12 * q^14 + 4 * q^15 - 4 * q^16 + 8 * q^19 + 8 * q^20 + 12 * q^21 - 4 * q^24 - 8 * q^26 - 8 * q^29 + 8 * q^30 - 24 * q^31 + 12 * q^35 - 4 * q^36 - 8 * q^39 - 4 * q^40 + 8 * q^44 + 8 * q^45 - 16 * q^49 - 8 * q^50 - 4 * q^54 + 8 * q^55 + 24 * q^56 + 8 * q^59 - 4 * q^60 + 12 * q^61 - 8 * q^64 - 32 * q^65 + 8 * q^66 - 12 * q^70 + 24 * q^71 - 28 * q^74 - 8 * q^75 + 4 * q^76 + 28 * q^79 + 4 * q^80 - 4 * q^81 + 24 * q^84 + 24 * q^85 - 12 * q^86 - 56 * q^89 - 4 * q^90 + 12 * q^91 - 48 * q^94 + 40 * q^95 - 8 * q^96 + 8 * q^99

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