LMFDB - Embedded newform 570.2.d.d.229.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(229,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("570.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			229.4
Root			$0.403032 - 0.403032i$ of defining polynomial
Character	$\chi$	$=$	570.229
Dual form			570.2.d.d.229.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-1.48119 - 1.67513i) q^{5} +1.00000 q^{6} +3.35026i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-1.48119 - 1.67513i) q^{5} +1.00000 q^{6} +3.35026i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(1.67513 - 1.48119i) q^{10} -1.61213 q^{11} +1.00000i q^{12} +1.35026i q^{13} -3.35026 q^{14} +(-1.67513 + 1.48119i) q^{15} +1.00000 q^{16} +6.96239i q^{17} -1.00000i q^{18} +1.00000 q^{19} +(1.48119 + 1.67513i) q^{20} +3.35026 q^{21} -1.61213i q^{22} +1.35026i q^{23} -1.00000 q^{24} +(-0.612127 + 4.96239i) q^{25} -1.35026 q^{26} +1.00000i q^{27} -3.35026i q^{28} -3.61213 q^{29} +(-1.48119 - 1.67513i) q^{30} -2.31265 q^{31} +1.00000i q^{32} +1.61213i q^{33} -6.96239 q^{34} +(5.61213 - 4.96239i) q^{35} +1.00000 q^{36} +11.2750i q^{37} +1.00000i q^{38} +1.35026 q^{39} +(-1.67513 + 1.48119i) q^{40} -3.35026 q^{41} +3.35026i q^{42} +10.3127i q^{43} +1.61213 q^{44} +(1.48119 + 1.67513i) q^{45} -1.35026 q^{46} -4.57452i q^{47} -1.00000i q^{48} -4.22425 q^{49} +(-4.96239 - 0.612127i) q^{50} +6.96239 q^{51} -1.35026i q^{52} -11.9248i q^{53} -1.00000 q^{54} +(2.38787 + 2.70052i) q^{55} +3.35026 q^{56} -1.00000i q^{57} -3.61213i q^{58} -1.03761 q^{59} +(1.67513 - 1.48119i) q^{60} +2.00000 q^{61} -2.31265i q^{62} -3.35026i q^{63} -1.00000 q^{64} +(2.26187 - 2.00000i) q^{65} -1.61213 q^{66} -9.92478i q^{67} -6.96239i q^{68} +1.35026 q^{69} +(4.96239 + 5.61213i) q^{70} -0.775746 q^{71} +1.00000i q^{72} +3.22425i q^{73} -11.2750 q^{74} +(4.96239 + 0.612127i) q^{75} -1.00000 q^{76} -5.40105i q^{77} +1.35026i q^{78} -14.3127 q^{79} +(-1.48119 - 1.67513i) q^{80} +1.00000 q^{81} -3.35026i q^{82} -10.8872i q^{83} -3.35026 q^{84} +(11.6629 - 10.3127i) q^{85} -10.3127 q^{86} +3.61213i q^{87} +1.61213i q^{88} +2.57452 q^{89} +(-1.67513 + 1.48119i) q^{90} -4.52373 q^{91} -1.35026i q^{92} +2.31265i q^{93} +4.57452 q^{94} +(-1.48119 - 1.67513i) q^{95} +1.00000 q^{96} -1.16362i q^{97} -4.22425i q^{98} +1.61213 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} + 2 q^{5} + 6 q^{6} - 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 + 2 * q^5 + 6 * q^6 - 6 * q^9	$ 6 q - 6 q^{4} + 2 q^{5} + 6 q^{6} - 6 q^{9} - 8 q^{11} + 6 q^{16} + 6 q^{19} - 2 q^{20} - 6 q^{24} - 2 q^{25} + 12 q^{26} - 20 q^{29} + 2 q^{30} + 28 q^{31} - 20 q^{34} + 32 q^{35} + 6 q^{36} - 12 q^{39} + 8 q^{44} - 2 q^{45} + 12 q^{46} - 22 q^{49} - 8 q^{50} + 20 q^{51} - 6 q^{54} + 16 q^{55} - 28 q^{59} + 12 q^{61} - 6 q^{64} + 32 q^{65} - 8 q^{66} - 12 q^{69} + 8 q^{70} - 8 q^{71} - 4 q^{74} + 8 q^{75} - 6 q^{76} - 44 q^{79} + 2 q^{80} + 6 q^{81} + 8 q^{85} - 20 q^{86} - 8 q^{89} - 64 q^{91} + 4 q^{94} + 2 q^{95} + 6 q^{96} + 8 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 + 2 * q^5 + 6 * q^6 - 6 * q^9 - 8 * q^11 + 6 * q^16 + 6 * q^19 - 2 * q^20 - 6 * q^24 - 2 * q^25 + 12 * q^26 - 20 * q^29 + 2 * q^30 + 28 * q^31 - 20 * q^34 + 32 * q^35 + 6 * q^36 - 12 * q^39 + 8 * q^44 - 2 * q^45 + 12 * q^46 - 22 * q^49 - 8 * q^50 + 20 * q^51 - 6 * q^54 + 16 * q^55 - 28 * q^59 + 12 * q^61 - 6 * q^64 + 32 * q^65 - 8 * q^66 - 12 * q^69 + 8 * q^70 - 8 * q^71 - 4 * q^74 + 8 * q^75 - 6 * q^76 - 44 * q^79 + 2 * q^80 + 6 * q^81 + 8 * q^85 - 20 * q^86 - 8 * q^89 - 64 * q^91 + 4 * q^94 + 2 * q^95 + 6 * q^96 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.00000			−0.500000
$5$	−1.48119	−	1.67513i	−0.662410	−	0.749141i
$5$	−1.48119	−	1.67513i	−0.662410	−	0.749141i
$6$	1.00000			0.408248
$7$			3.35026i			1.26628i	0.774037	+	0.633140i	$0.218234\pi$
$7$			3.35026i			1.26628i	−0.774037	+	0.633140i	$0.781766\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.00000			−0.333333
$10$	1.67513	−	1.48119i	0.529723	−	0.468395i
$11$	−1.61213			−0.486075			−0.243037	−	0.970017i	$-0.578144\pi$
$11$	−1.61213			−0.486075			−0.243037	+	0.970017i	$0.578144\pi$
$12$			1.00000i			0.288675i
$13$			1.35026i			0.374495i	0.982313	+	0.187248i	$0.0599567\pi$
$13$			1.35026i			0.374495i	−0.982313	+	0.187248i	$0.940043\pi$
$14$	−3.35026			−0.895395
$15$	−1.67513	+	1.48119i	−0.432517	+	0.382443i
$16$	1.00000			0.250000
$17$			6.96239i			1.68863i	0.535849	+	0.844314i	$0.319992\pi$
$17$			6.96239i			1.68863i	−0.535849	+	0.844314i	$0.680008\pi$
$18$		−	1.00000i		−	0.235702i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	1.48119	+	1.67513i	0.331205	+	0.374571i
$21$	3.35026			0.731087
$22$		−	1.61213i		−	0.343707i
$23$			1.35026i			0.281549i	0.990042	+	0.140775i	$0.0449593\pi$
$23$			1.35026i			0.281549i	−0.990042	+	0.140775i	$0.955041\pi$
$24$	−1.00000			−0.204124
$25$	−0.612127	+	4.96239i	−0.122425	+	0.992478i
$26$	−1.35026			−0.264808
$27$			1.00000i			0.192450i
$28$		−	3.35026i		−	0.633140i
$29$	−3.61213			−0.670755			−0.335378	−	0.942084i	$-0.608864\pi$
$29$	−3.61213			−0.670755			−0.335378	+	0.942084i	$0.608864\pi$
$30$	−1.48119	−	1.67513i	−0.270428	−	0.305836i
$31$	−2.31265			−0.415364			−0.207682	−	0.978196i	$-0.566592\pi$
$31$	−2.31265			−0.415364			−0.207682	+	0.978196i	$0.566592\pi$
$32$			1.00000i			0.176777i
$33$			1.61213i			0.280635i
$34$	−6.96239			−1.19404
$35$	5.61213	−	4.96239i	0.948623	−	0.838797i
$36$	1.00000			0.166667
$37$			11.2750i			1.85360i	0.375549	+	0.926802i	$0.377454\pi$
$37$			11.2750i			1.85360i	−0.375549	+	0.926802i	$0.622546\pi$
$38$			1.00000i			0.162221i
$39$	1.35026			0.216215
$40$	−1.67513	+	1.48119i	−0.264861	+	0.234197i
$41$	−3.35026			−0.523223			−0.261611	−	0.965173i	$-0.584254\pi$
$41$	−3.35026			−0.523223			−0.261611	+	0.965173i	$0.584254\pi$
$42$			3.35026i			0.516957i
$43$			10.3127i			1.57266i	0.617804	+	0.786332i	$0.288023\pi$
$43$			10.3127i			1.57266i	−0.617804	+	0.786332i	$0.711977\pi$
$44$	1.61213			0.243037
$45$	1.48119	+	1.67513i	0.220803	+	0.249714i
$46$	−1.35026			−0.199085
$47$		−	4.57452i		−	0.667262i	−0.942704	−	0.333631i	$-0.891726\pi$
$47$		−	4.57452i		−	0.667262i	0.942704	−	0.333631i	$-0.108274\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−4.22425			−0.603465
$50$	−4.96239	−	0.612127i	−0.701788	−	0.0865678i
$51$	6.96239			0.974929
$52$		−	1.35026i		−	0.187248i
$53$		−	11.9248i		−	1.63799i	−0.573798	−	0.818997i	$-0.694530\pi$
$53$		−	11.9248i		−	1.63799i	0.573798	−	0.818997i	$-0.305470\pi$
$54$	−1.00000			−0.136083
$55$	2.38787	+	2.70052i	0.321981	+	0.364139i
$56$	3.35026			0.447698
$57$		−	1.00000i		−	0.132453i
$58$		−	3.61213i		−	0.474295i
$59$	−1.03761			−0.135085			−0.0675427	−	0.997716i	$-0.521516\pi$
$59$	−1.03761			−0.135085			−0.0675427	+	0.997716i	$0.521516\pi$
$60$	1.67513	−	1.48119i	0.216258	−	0.191221i
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$		−	2.31265i		−	0.293707i
$63$		−	3.35026i		−	0.422093i
$64$	−1.00000			−0.125000
$65$	2.26187	−	2.00000i	0.280550	−	0.248069i
$66$	−1.61213			−0.198439
$67$		−	9.92478i		−	1.21250i	−0.795272	−	0.606252i	$-0.792672\pi$
$67$		−	9.92478i		−	1.21250i	0.795272	−	0.606252i	$-0.207328\pi$
$68$		−	6.96239i		−	0.844314i
$69$	1.35026			0.162552
$70$	4.96239	+	5.61213i	0.593119	+	0.670777i
$71$	−0.775746			−0.0920641			−0.0460321	−	0.998940i	$-0.514658\pi$
$71$	−0.775746			−0.0920641			−0.0460321	+	0.998940i	$0.514658\pi$
$72$			1.00000i			0.117851i
$73$			3.22425i			0.377370i	0.982038	+	0.188685i	$0.0604226\pi$
$73$			3.22425i			0.377370i	−0.982038	+	0.188685i	$0.939577\pi$
$74$	−11.2750			−1.31070
$75$	4.96239	+	0.612127i	0.573007	+	0.0706823i
$76$	−1.00000			−0.114708
$77$		−	5.40105i		−	0.615506i
$78$			1.35026i			0.152887i
$79$	−14.3127			−1.61030			−0.805149	−	0.593072i	$-0.797915\pi$
$79$	−14.3127			−1.61030			−0.805149	+	0.593072i	$0.797915\pi$
$80$	−1.48119	−	1.67513i	−0.165603	−	0.187285i
$81$	1.00000			0.111111
$82$		−	3.35026i		−	0.369975i
$83$		−	10.8872i		−	1.19502i	−0.801861	−	0.597511i	$-0.796156\pi$
$83$		−	10.8872i		−	1.19502i	0.801861	−	0.597511i	$-0.203844\pi$
$84$	−3.35026			−0.365544
$85$	11.6629	−	10.3127i	1.26502	−	1.11856i
$86$	−10.3127			−1.11204
$87$			3.61213i			0.387261i
$88$			1.61213i			0.171853i
$89$	2.57452			0.272898			0.136449	−	0.990647i	$-0.456431\pi$
$89$	2.57452			0.272898			0.136449	+	0.990647i	$0.456431\pi$
$90$	−1.67513	+	1.48119i	−0.176574	+	0.156132i
$91$	−4.52373			−0.474216
$92$		−	1.35026i		−	0.140775i
$93$			2.31265i			0.239811i
$94$	4.57452			0.471825
$95$	−1.48119	−	1.67513i	−0.151967	−	0.171865i
$96$	1.00000			0.102062
$97$		−	1.16362i		−	0.118148i	−0.998254	−	0.0590738i	$-0.981185\pi$
$97$		−	1.16362i		−	0.118148i	0.998254	−	0.0590738i	$-0.0188147\pi$
$98$		−	4.22425i		−	0.426714i
$99$	1.61213			0.162025
$100$	0.612127	−	4.96239i	0.0612127	−	0.496239i
$101$	8.88717			0.884306			0.442153	−	0.896940i	$-0.354215\pi$
$101$	8.88717			0.884306			0.442153	+	0.896940i	$0.354215\pi$
$102$			6.96239i			0.689379i
$103$			7.03761i			0.693436i	0.937969	+	0.346718i	$0.112704\pi$
$103$			7.03761i			0.693436i	−0.937969	+	0.346718i	$0.887296\pi$
$104$	1.35026			0.132404
$105$	−4.96239	−	5.61213i	−0.484280	−	0.547688i
$106$	11.9248			1.15824
$107$			0.775746i			0.0749942i	0.999297	+	0.0374971i	$0.0119385\pi$
$107$			0.775746i			0.0749942i	−0.999297	+	0.0374971i	$0.988062\pi$
$108$		−	1.00000i		−	0.0962250i
$109$	20.1622			1.93119			0.965594	−	0.260052i	$-0.0837399\pi$
$109$	20.1622			1.93119			0.965594	+	0.260052i	$0.0837399\pi$
$110$	−2.70052	+	2.38787i	−0.257485	+	0.227675i
$111$	11.2750			1.07018
$112$			3.35026i			0.316570i
$113$			11.1490i			1.04881i	0.851468	+	0.524406i	$0.175713\pi$
$113$			11.1490i			1.04881i	−0.851468	+	0.524406i	$0.824287\pi$
$114$	1.00000			0.0936586
$115$	2.26187	−	2.00000i	0.210920	−	0.186501i
$116$	3.61213			0.335378
$117$		−	1.35026i		−	0.124832i
$118$		−	1.03761i		−	0.0955199i
$119$	−23.3258			−2.13827
$120$	1.48119	+	1.67513i	0.135214	+	0.152918i
$121$	−8.40105			−0.763732
$122$			2.00000i			0.181071i
$123$			3.35026i			0.302083i
$124$	2.31265			0.207682
$125$	9.21933	−	6.32487i	0.824602	−	0.565713i
$126$	3.35026			0.298465
$127$		−	13.7381i		−	1.21906i	−0.792762	−	0.609531i	$-0.791358\pi$
$127$		−	13.7381i		−	1.21906i	0.792762	−	0.609531i	$-0.208642\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	10.3127			0.907978
$130$	2.00000	+	2.26187i	0.175412	+	0.198379i
$131$	5.61213			0.490334			0.245167	−	0.969481i	$-0.421157\pi$
$131$	5.61213			0.490334			0.245167	+	0.969481i	$0.421157\pi$
$132$		−	1.61213i		−	0.140318i
$133$			3.35026i			0.290505i
$134$	9.92478			0.857370
$135$	1.67513	−	1.48119i	0.144172	−	0.127481i
$136$	6.96239			0.597020
$137$			17.6629i			1.50904i	0.656275	+	0.754522i	$0.272131\pi$
$137$			17.6629i			1.50904i	−0.656275	+	0.754522i	$0.727869\pi$
$138$			1.35026i			0.114942i
$139$	−10.7005			−0.907607			−0.453803	−	0.891102i	$-0.649933\pi$
$139$	−10.7005			−0.907607			−0.453803	+	0.891102i	$0.649933\pi$
$140$	−5.61213	+	4.96239i	−0.474311	+	0.419398i
$141$	−4.57452			−0.385244
$142$		−	0.775746i		−	0.0650992i
$143$		−	2.17679i		−	0.182033i
$144$	−1.00000			−0.0833333
$145$	5.35026	+	6.05079i	0.444315	+	0.502490i
$146$	−3.22425			−0.266841
$147$			4.22425i			0.348411i
$148$		−	11.2750i		−	0.926802i
$149$	−1.03761			−0.0850044			−0.0425022	−	0.999096i	$-0.513533\pi$
$149$	−1.03761			−0.0850044			−0.0425022	+	0.999096i	$0.513533\pi$
$150$	−0.612127	+	4.96239i	−0.0499799	+	0.405177i
$151$	1.16362			0.0946940			0.0473470	−	0.998879i	$-0.484923\pi$
$151$	1.16362			0.0946940			0.0473470	+	0.998879i	$0.484923\pi$
$152$		−	1.00000i		−	0.0811107i
$153$		−	6.96239i		−	0.562876i
$154$	5.40105			0.435229
$155$	3.42548	+	3.87399i	0.275142	+	0.311167i
$156$	−1.35026			−0.108107
$157$		−	10.9624i		−	0.874894i	−0.899244	−	0.437447i	$-0.855883\pi$
$157$		−	10.9624i		−	0.874894i	0.899244	−	0.437447i	$-0.144117\pi$
$158$		−	14.3127i		−	1.13865i
$159$	−11.9248			−0.945696
$160$	1.67513	−	1.48119i	0.132431	−	0.117099i
$161$	−4.52373			−0.356520
$162$			1.00000i			0.0785674i
$163$			21.0132i			1.64588i	0.568129	+	0.822939i	$0.307667\pi$
$163$			21.0132i			1.64588i	−0.568129	+	0.822939i	$0.692333\pi$
$164$	3.35026			0.261611
$165$	2.70052	−	2.38787i	0.210235	−	0.185896i
$166$	10.8872			0.845008
$167$		−	9.92478i		−	0.768002i	−0.923333	−	0.384001i	$-0.874546\pi$
$167$		−	9.92478i		−	0.768002i	0.923333	−	0.384001i	$-0.125454\pi$
$168$		−	3.35026i		−	0.258478i
$169$	11.1768			0.859753
$170$	10.3127	+	11.6629i	0.790944	+	0.894505i
$171$	−1.00000			−0.0764719
$172$		−	10.3127i		−	0.786332i
$173$			14.6253i			1.11194i	0.831202	+	0.555971i	$0.187653\pi$
$173$			14.6253i			1.11194i	−0.831202	+	0.555971i	$0.812347\pi$
$174$	−3.61213			−0.273835
$175$	−16.6253	−	2.05079i	−1.25675	−	0.155025i
$176$	−1.61213			−0.121519
$177$			1.03761i			0.0779916i
$178$			2.57452i			0.192968i
$179$	−11.7381			−0.877349			−0.438675	−	0.898646i	$-0.644552\pi$
$179$	−11.7381			−0.877349			−0.438675	+	0.898646i	$0.644552\pi$
$180$	−1.48119	−	1.67513i	−0.110402	−	0.124857i
$181$	21.4617			1.59523			0.797617	−	0.603164i	$-0.206094\pi$
$181$	21.4617			1.59523			0.797617	+	0.603164i	$0.206094\pi$
$182$		−	4.52373i		−	0.335321i
$183$		−	2.00000i		−	0.147844i
$184$	1.35026			0.0995426
$185$	18.8872	−	16.7005i	1.38861	−	1.22785i
$186$	−2.31265			−0.169572
$187$		−	11.2243i		−	0.820799i
$188$			4.57452i			0.333631i
$189$	−3.35026			−0.243696
$190$	1.67513	−	1.48119i	0.121527	−	0.107457i
$191$	−21.2750			−1.53941			−0.769704	−	0.638401i	$-0.779596\pi$
$191$	−21.2750			−1.53941			−0.769704	+	0.638401i	$0.779596\pi$
$192$			1.00000i			0.0721688i
$193$		−	14.1622i		−	1.01942i	−0.860347	−	0.509709i	$-0.829753\pi$
$193$		−	14.1622i		−	1.01942i	0.860347	−	0.509709i	$-0.170247\pi$
$194$	1.16362			0.0835430
$195$	−2.00000	−	2.26187i	−0.143223	−	0.161976i
$196$	4.22425			0.301732
$197$		−	3.87399i		−	0.276011i	−0.990431	−	0.138005i	$-0.955931\pi$
$197$		−	3.87399i		−	0.276011i	0.990431	−	0.138005i	$-0.0440691\pi$
$198$			1.61213i			0.114569i
$199$	−3.47627			−0.246426			−0.123213	−	0.992380i	$-0.539320\pi$
$199$	−3.47627			−0.246426			−0.123213	+	0.992380i	$0.539320\pi$
$200$	4.96239	+	0.612127i	0.350894	+	0.0432839i
$201$	−9.92478			−0.700040
$202$			8.88717i			0.625299i
$203$		−	12.1016i		−	0.849364i
$204$	−6.96239			−0.487465
$205$	4.96239	+	5.61213i	0.346588	+	0.391968i
$206$	−7.03761			−0.490334
$207$		−	1.35026i		−	0.0938497i
$208$			1.35026i			0.0936238i
$209$	−1.61213			−0.111513
$210$	5.61213	−	4.96239i	0.387274	−	0.342437i
$211$	9.92478			0.683250			0.341625	−	0.939836i	$-0.389023\pi$
$211$	9.92478			0.683250			0.341625	+	0.939836i	$0.389023\pi$
$212$			11.9248i			0.818997i
$213$			0.775746i			0.0531533i
$214$	−0.775746			−0.0530289
$215$	17.2750	−	15.2750i	1.17815	−	1.04175i
$216$	1.00000			0.0680414
$217$		−	7.74798i		−	0.525967i
$218$			20.1622i			1.36556i
$219$	3.22425			0.217875
$220$	−2.38787	−	2.70052i	−0.160990	−	0.182069i
$221$	−9.40105			−0.632383
$222$			11.2750i			0.756731i
$223$			7.03761i			0.471273i	0.971841	+	0.235637i	$0.0757175\pi$
$223$			7.03761i			0.471273i	−0.971841	+	0.235637i	$0.924282\pi$
$224$	−3.35026			−0.223849
$225$	0.612127	−	4.96239i	0.0408085	−	0.330826i
$226$	−11.1490			−0.741623
$227$			14.5501i			0.965723i	0.875697	+	0.482861i	$0.160402\pi$
$227$			14.5501i			0.965723i	−0.875697	+	0.482861i	$0.839598\pi$
$228$			1.00000i			0.0662266i
$229$	−11.4010			−0.753402			−0.376701	−	0.926335i	$-0.622942\pi$
$229$	−11.4010			−0.753402			−0.376701	+	0.926335i	$0.622942\pi$
$230$	2.00000	+	2.26187i	0.131876	+	0.149143i
$231$	−5.40105			−0.355363
$232$			3.61213i			0.237148i
$233$			21.9149i			1.43569i	0.696201	+	0.717847i	$0.254872\pi$
$233$			21.9149i			1.43569i	−0.696201	+	0.717847i	$0.745128\pi$
$234$	1.35026			0.0882694
$235$	−7.66291	+	6.77575i	−0.499873	+	0.442001i
$236$	1.03761			0.0675427
$237$			14.3127i			0.929707i
$238$		−	23.3258i		−	1.51199i
$239$	13.2750			0.858691			0.429345	−	0.903140i	$-0.358744\pi$
$239$	13.2750			0.858691			0.429345	+	0.903140i	$0.358744\pi$
$240$	−1.67513	+	1.48119i	−0.108129	+	0.0956107i
$241$	21.3258			1.37372			0.686859	−	0.726791i	$-0.258989\pi$
$241$	21.3258			1.37372			0.686859	+	0.726791i	$0.258989\pi$
$242$		−	8.40105i		−	0.540040i
$243$		−	1.00000i		−	0.0641500i
$244$	−2.00000			−0.128037
$245$	6.25694	+	7.07618i	0.399741	+	0.452080i
$246$	−3.35026			−0.213605
$247$			1.35026i			0.0859151i
$248$			2.31265i			0.146853i
$249$	−10.8872			−0.689946
$250$	6.32487	+	9.21933i	0.400020	+	0.583082i
$251$	16.3127			1.02965			0.514823	−	0.857297i	$-0.327858\pi$
$251$	16.3127			1.02965			0.514823	+	0.857297i	$0.327858\pi$
$252$			3.35026i			0.211047i
$253$		−	2.17679i		−	0.136854i
$254$	13.7381			0.862007
$255$	−10.3127	−	11.6629i	−0.645803	−	0.730360i
$256$	1.00000			0.0625000
$257$			24.5501i			1.53139i	0.643203	+	0.765696i	$0.277605\pi$
$257$			24.5501i			1.53139i	−0.643203	+	0.765696i	$0.722395\pi$
$258$			10.3127i			0.642038i
$259$	−37.7743			−2.34718
$260$	−2.26187	+	2.00000i	−0.140275	+	0.124035i
$261$	3.61213			0.223585
$262$			5.61213i			0.346718i
$263$		−	30.3488i		−	1.87139i	−0.352810	−	0.935695i	$-0.614774\pi$
$263$		−	30.3488i		−	1.87139i	0.352810	−	0.935695i	$-0.385226\pi$
$264$	1.61213			0.0992195
$265$	−19.9756	+	17.6629i	−1.22709	+	1.08502i
$266$	−3.35026			−0.205418
$267$		−	2.57452i		−	0.157558i
$268$			9.92478i			0.606252i
$269$	−14.3127			−0.872658			−0.436329	−	0.899787i	$-0.643722\pi$
$269$	−14.3127			−0.872658			−0.436329	+	0.899787i	$0.643722\pi$
$270$	1.48119	+	1.67513i	0.0901426	+	0.101945i
$271$	−7.32582			−0.445012			−0.222506	−	0.974931i	$-0.571424\pi$
$271$	−7.32582			−0.445012			−0.222506	+	0.974931i	$0.571424\pi$
$272$			6.96239i			0.422157i
$273$			4.52373i			0.273789i
$274$	−17.6629			−1.06706
$275$	0.986826	−	8.00000i	0.0595079	−	0.482418i
$276$	−1.35026			−0.0812762
$277$		−	14.4387i		−	0.867535i	−0.901025	−	0.433767i	$-0.857184\pi$
$277$		−	14.4387i		−	0.867535i	0.901025	−	0.433767i	$-0.142816\pi$
$278$		−	10.7005i		−	0.641775i
$279$	2.31265			0.138455
$280$	−4.96239	−	5.61213i	−0.296559	−	0.335389i
$281$	−11.9756			−0.714402			−0.357201	−	0.934028i	$-0.616269\pi$
$281$	−11.9756			−0.714402			−0.357201	+	0.934028i	$0.616269\pi$
$282$		−	4.57452i		−	0.272408i
$283$			24.4894i			1.45575i	0.685712	+	0.727873i	$0.259491\pi$
$283$			24.4894i			1.45575i	−0.685712	+	0.727873i	$0.740509\pi$
$284$	0.775746			0.0460321
$285$	−1.67513	+	1.48119i	−0.0992262	+	0.0877384i
$286$	2.17679			0.128716
$287$		−	11.2243i		−	0.662547i
$288$		−	1.00000i		−	0.0589256i
$289$	−31.4749			−1.85146
$290$	−6.05079	+	5.35026i	−0.355314	+	0.314178i
$291$	−1.16362			−0.0682126
$292$		−	3.22425i		−	0.188685i
$293$			18.1016i			1.05751i	0.848776	+	0.528753i	$0.177340\pi$
$293$			18.1016i			1.05751i	−0.848776	+	0.528753i	$0.822660\pi$
$294$	−4.22425			−0.246363
$295$	1.53690	+	1.73813i	0.0894820	+	0.101198i
$296$	11.2750			0.655348
$297$		−	1.61213i		−	0.0935451i
$298$		−	1.03761i		−	0.0601072i
$299$	−1.82321			−0.105439
$300$	−4.96239	−	0.612127i	−0.286504	−	0.0353412i
$301$	−34.5501			−1.99143
$302$			1.16362i			0.0669588i
$303$		−	8.88717i		−	0.510554i
$304$	1.00000			0.0573539
$305$	−2.96239	−	3.35026i	−0.169626	−	0.191835i
$306$	6.96239			0.398013
$307$		−	29.9248i		−	1.70790i	−0.520357	−	0.853949i	$-0.674201\pi$
$307$		−	29.9248i		−	1.70790i	0.520357	−	0.853949i	$-0.325799\pi$
$308$			5.40105i			0.307753i
$309$	7.03761			0.400356
$310$	−3.87399	+	3.42548i	−0.220028	+	0.194554i
$311$	−21.2750			−1.20640			−0.603198	−	0.797591i	$-0.706107\pi$
$311$	−21.2750			−1.20640			−0.603198	+	0.797591i	$0.706107\pi$
$312$		−	1.35026i		−	0.0764435i
$313$			17.4010i			0.983565i	0.870718	+	0.491783i	$0.163655\pi$
$313$			17.4010i			0.983565i	−0.870718	+	0.491783i	$0.836345\pi$
$314$	10.9624			0.618643
$315$	−5.61213	+	4.96239i	−0.316208	+	0.279599i
$316$	14.3127			0.805149
$317$		−	14.1016i		−	0.792023i	−0.918246	−	0.396012i	$-0.870394\pi$
$317$		−	14.1016i		−	0.792023i	0.918246	−	0.396012i	$-0.129606\pi$
$318$		−	11.9248i		−	0.668708i
$319$	5.82321			0.326037
$320$	1.48119	+	1.67513i	0.0828013	+	0.0936427i
$321$	0.775746			0.0432979
$322$		−	4.52373i		−	0.252098i
$323$			6.96239i			0.387398i
$324$	−1.00000			−0.0555556
$325$	−6.70052	−	0.826531i	−0.371678	−	0.0458477i
$326$	−21.0132			−1.16381
$327$		−	20.1622i		−	1.11497i
$328$			3.35026i			0.184987i
$329$	15.3258			0.844940
$330$	2.38787	+	2.70052i	0.131448	+	0.148659i
$331$	6.85097			0.376563			0.188282	−	0.982115i	$-0.439708\pi$
$331$	6.85097			0.376563			0.188282	+	0.982115i	$0.439708\pi$
$332$			10.8872i			0.597511i
$333$		−	11.2750i		−	0.617868i
$334$	9.92478			0.543060
$335$	−16.6253	+	14.7005i	−0.908337	+	0.803175i
$336$	3.35026			0.182772
$337$		−	24.2374i		−	1.32030i	−0.751135	−	0.660148i	$-0.770493\pi$
$337$		−	24.2374i		−	1.32030i	0.751135	−	0.660148i	$-0.229507\pi$
$338$			11.1768i			0.607937i
$339$	11.1490			0.605532
$340$	−11.6629	+	10.3127i	−0.632510	+	0.559282i
$341$	3.72829			0.201898
$342$		−	1.00000i		−	0.0540738i
$343$			9.29948i			0.502125i
$344$	10.3127			0.556021
$345$	−2.00000	−	2.26187i	−0.107676	−	0.121775i
$346$	−14.6253			−0.786261
$347$		−	0.962389i		−	0.0516637i	−0.999666	−	0.0258319i	$-0.991777\pi$
$347$		−	0.962389i		−	0.0516637i	0.999666	−	0.0258319i	$-0.00822345\pi$
$348$		−	3.61213i		−	0.193630i
$349$	1.37470			0.0735860			0.0367930	−	0.999323i	$-0.488286\pi$
$349$	1.37470			0.0735860			0.0367930	+	0.999323i	$0.488286\pi$
$350$	2.05079	−	16.6253i	0.109619	−	0.888660i
$351$	−1.35026			−0.0720716
$352$		−	1.61213i		−	0.0859267i
$353$			28.7367i			1.52950i	0.644326	+	0.764751i	$0.277138\pi$
$353$			28.7367i			1.52950i	−0.644326	+	0.764751i	$0.722862\pi$
$354$	−1.03761			−0.0551484
$355$	1.14903	+	1.29948i	0.0609842	+	0.0689691i
$356$	−2.57452			−0.136449
$357$			23.3258i			1.23453i
$358$		−	11.7381i		−	0.620380i
$359$	−31.1998			−1.64666			−0.823332	−	0.567561i	$-0.807887\pi$
$359$	−31.1998			−1.64666			−0.823332	+	0.567561i	$0.807887\pi$
$360$	1.67513	−	1.48119i	0.0882871	−	0.0780658i
$361$	1.00000			0.0526316
$362$			21.4617i			1.12800i
$363$			8.40105i			0.440941i
$364$	4.52373			0.237108
$365$	5.40105	−	4.77575i	0.282704	−	0.249974i
$366$	2.00000			0.104542
$367$		−	20.1260i		−	1.05057i	−0.850927	−	0.525285i	$-0.823959\pi$
$367$		−	20.1260i		−	1.05057i	0.850927	−	0.525285i	$-0.176041\pi$
$368$			1.35026i			0.0703873i
$369$	3.35026			0.174408
$370$	16.7005	+	18.8872i	0.868219	+	0.981897i
$371$	39.9511			2.07416
$372$		−	2.31265i		−	0.119905i
$373$		−	17.9756i		−	0.930739i	−0.885116	−	0.465370i	$-0.845921\pi$
$373$		−	17.9756i		−	0.930739i	0.885116	−	0.465370i	$-0.154079\pi$
$374$	11.2243			0.580392
$375$	−6.32487	−	9.21933i	−0.326615	−	0.476084i
$376$	−4.57452			−0.235913
$377$		−	4.87732i		−	0.251195i
$378$		−	3.35026i		−	0.172319i
$379$	−1.67276			−0.0859240			−0.0429620	−	0.999077i	$-0.513679\pi$
$379$	−1.67276			−0.0859240			−0.0429620	+	0.999077i	$0.513679\pi$
$380$	1.48119	+	1.67513i	0.0759837	+	0.0859324i
$381$	−13.7381			−0.703826
$382$		−	21.2750i		−	1.08853i
$383$			31.8496i			1.62744i	0.581260	+	0.813718i	$0.302560\pi$
$383$			31.8496i			1.62744i	−0.581260	+	0.813718i	$0.697440\pi$
$384$	−1.00000			−0.0510310
$385$	−9.04746	+	8.00000i	−0.461101	+	0.407718i
$386$	14.1622			0.720837
$387$		−	10.3127i		−	0.524221i
$388$			1.16362i			0.0590738i
$389$	10.3371			0.524111			0.262056	−	0.965053i	$-0.415600\pi$
$389$	10.3371			0.524111			0.262056	+	0.965053i	$0.415600\pi$
$390$	2.26187	−	2.00000i	0.114534	−	0.101274i
$391$	−9.40105			−0.475431
$392$			4.22425i			0.213357i
$393$		−	5.61213i		−	0.283094i
$394$	3.87399			0.195169
$395$	21.1998	+	23.9756i	1.06668	+	1.20634i
$396$	−1.61213			−0.0810124
$397$			31.4372i			1.57779i	0.614528	+	0.788895i	$0.289346\pi$
$397$			31.4372i			1.57779i	−0.614528	+	0.788895i	$0.710654\pi$
$398$		−	3.47627i		−	0.174250i
$399$	3.35026			0.167723
$400$	−0.612127	+	4.96239i	−0.0306063	+	0.248119i
$401$	5.94921			0.297090			0.148545	−	0.988906i	$-0.452541\pi$
$401$	5.94921			0.297090			0.148545	+	0.988906i	$0.452541\pi$
$402$		−	9.92478i		−	0.495003i
$403$		−	3.12268i		−	0.155552i
$404$	−8.88717			−0.442153
$405$	−1.48119	−	1.67513i	−0.0736011	−	0.0832379i
$406$	12.1016			0.600591
$407$		−	18.1768i		−	0.900990i
$408$		−	6.96239i		−	0.344690i
$409$	30.9986			1.53278			0.766391	−	0.642375i	$-0.222051\pi$
$409$	30.9986			1.53278			0.766391	+	0.642375i	$0.222051\pi$
$410$	−5.61213	+	4.96239i	−0.277163	+	0.245075i
$411$	17.6629			0.871247
$412$		−	7.03761i		−	0.346718i
$413$		−	3.47627i		−	0.171056i
$414$	1.35026			0.0663617
$415$	−18.2374	+	16.1260i	−0.895240	+	0.791595i
$416$	−1.35026			−0.0662020
$417$			10.7005i			0.524007i
$418$		−	1.61213i		−	0.0788517i
$419$	34.3390			1.67757			0.838785	−	0.544463i	$-0.183266\pi$
$419$	34.3390			1.67757			0.838785	+	0.544463i	$0.183266\pi$
$420$	4.96239	+	5.61213i	0.242140	+	0.273844i
$421$	22.8627			1.11426			0.557131	−	0.830425i	$-0.311902\pi$
$421$	22.8627			1.11426			0.557131	+	0.830425i	$0.311902\pi$
$422$			9.92478i			0.483131i
$423$			4.57452i			0.222421i
$424$	−11.9248			−0.579118
$425$	−34.5501	−	4.26187i	−1.67592	−	0.206731i
$426$	−0.775746			−0.0375850
$427$			6.70052i			0.324261i
$428$		−	0.775746i		−	0.0374971i
$429$	−2.17679			−0.105097
$430$	15.2750	+	17.2750i	0.736628	+	0.833076i
$431$	11.5975			0.558634			0.279317	−	0.960199i	$-0.409892\pi$
$431$	11.5975			0.558634			0.279317	+	0.960199i	$0.409892\pi$
$432$			1.00000i			0.0481125i
$433$			27.8350i			1.33766i	0.743414	+	0.668832i	$0.233205\pi$
$433$			27.8350i			1.33766i	−0.743414	+	0.668832i	$0.766795\pi$
$434$	7.74798			0.371915
$435$	6.05079	−	5.35026i	0.290113	−	0.256525i
$436$	−20.1622			−0.965594
$437$			1.35026i			0.0645918i
$438$			3.22425i			0.154061i
$439$	38.7875			1.85123			0.925613	−	0.378471i	$-0.123550\pi$
$439$	38.7875			1.85123			0.925613	+	0.378471i	$0.123550\pi$
$440$	2.70052	−	2.38787i	0.128742	−	0.113837i
$441$	4.22425			0.201155
$442$		−	9.40105i		−	0.447162i
$443$		−	29.2144i		−	1.38802i	−0.719966	−	0.694009i	$-0.755843\pi$
$443$		−	29.2144i		−	1.38802i	0.719966	−	0.694009i	$-0.244157\pi$
$444$	−11.2750			−0.535090
$445$	−3.81336	−	4.31265i	−0.180770	−	0.204439i
$446$	−7.03761			−0.333241
$447$			1.03761i			0.0490773i
$448$		−	3.35026i		−	0.158285i
$449$	20.4993			0.967421			0.483711	−	0.875228i	$-0.339289\pi$
$449$	20.4993			0.967421			0.483711	+	0.875228i	$0.339289\pi$
$450$	4.96239	+	0.612127i	0.233929	+	0.0288559i
$451$	5.40105			0.254325
$452$		−	11.1490i		−	0.524406i
$453$		−	1.16362i		−	0.0546716i
$454$	−14.5501			−0.682869
$455$	6.70052	+	7.57784i	0.314125	+	0.355255i
$456$	−1.00000			−0.0468293
$457$		−	6.44851i		−	0.301648i	−0.988561	−	0.150824i	$-0.951807\pi$
$457$		−	6.44851i		−	0.301648i	0.988561	−	0.150824i	$-0.0481927\pi$
$458$		−	11.4010i		−	0.532736i
$459$	−6.96239			−0.324976
$460$	−2.26187	+	2.00000i	−0.105460	+	0.0932505i
$461$	−13.5125			−0.629338			−0.314669	−	0.949201i	$-0.601894\pi$
$461$	−13.5125			−0.629338			−0.314669	+	0.949201i	$0.601894\pi$
$462$		−	5.40105i		−	0.251279i
$463$			6.20123i			0.288196i	0.989563	+	0.144098i	$0.0460280\pi$
$463$			6.20123i			0.288196i	−0.989563	+	0.144098i	$0.953972\pi$
$464$	−3.61213			−0.167689
$465$	3.87399	−	3.42548i	0.179652	−	0.158853i
$466$	−21.9149			−1.01519
$467$			16.5599i			0.766302i	0.923686	+	0.383151i	$0.125161\pi$
$467$			16.5599i			0.766302i	−0.923686	+	0.383151i	$0.874839\pi$
$468$			1.35026i			0.0624159i
$469$	33.2506			1.53537
$470$	−6.77575	−	7.66291i	−0.312542	−	0.353464i
$471$	−10.9624			−0.505120
$472$			1.03761i			0.0477599i
$473$		−	16.6253i		−	0.764432i
$474$	−14.3127			−0.657402
$475$	−0.612127	+	4.96239i	−0.0280863	+	0.227690i
$476$	23.3258			1.06914
$477$			11.9248i			0.545998i
$478$			13.2750i			0.607186i
$479$	30.5256			1.39475			0.697376	−	0.716705i	$-0.254351\pi$
$479$	30.5256			1.39475			0.697376	+	0.716705i	$0.254351\pi$
$480$	−1.48119	−	1.67513i	−0.0676070	−	0.0764589i
$481$	−15.2243			−0.694166
$482$			21.3258i			0.971365i
$483$			4.52373i			0.205837i
$484$	8.40105			0.381866
$485$	−1.94921	+	1.72355i	−0.0885093	+	0.0782622i
$486$	1.00000			0.0453609
$487$			2.51388i			0.113915i	0.998377	+	0.0569574i	$0.0181399\pi$
$487$			2.51388i			0.113915i	−0.998377	+	0.0569574i	$0.981860\pi$
$488$		−	2.00000i		−	0.0905357i
$489$	21.0132			0.950249
$490$	−7.07618	+	6.25694i	−0.319669	+	0.282660i
$491$	1.46168			0.0659648			0.0329824	−	0.999456i	$-0.489499\pi$
$491$	1.46168			0.0659648			0.0329824	+	0.999456i	$0.489499\pi$
$492$		−	3.35026i		−	0.151041i
$493$		−	25.1490i		−	1.13266i
$494$	−1.35026			−0.0607511
$495$	−2.38787	−	2.70052i	−0.107327	−	0.121380i
$496$	−2.31265			−0.103841
$497$		−	2.59895i		−	0.116579i
$498$		−	10.8872i		−	0.487866i
$499$	5.55149			0.248519			0.124259	−	0.992250i	$-0.460344\pi$
$499$	5.55149			0.248519			0.124259	+	0.992250i	$0.460344\pi$
$500$	−9.21933	+	6.32487i	−0.412301	+	0.282857i
$501$	−9.92478			−0.443406
$502$			16.3127i			0.728069i
$503$			6.90175i			0.307734i	0.988092	+	0.153867i	$0.0491727\pi$
$503$			6.90175i			0.307734i	−0.988092	+	0.153867i	$0.950827\pi$
$504$	−3.35026			−0.149233
$505$	−13.1636	−	14.8872i	−0.585773	−	0.662470i
$506$	2.17679			0.0967703
$507$		−	11.1768i		−	0.496379i
$508$			13.7381i			0.609531i
$509$	−8.76116			−0.388331			−0.194166	−	0.980969i	$-0.562200\pi$
$509$	−8.76116			−0.388331			−0.194166	+	0.980969i	$0.562200\pi$
$510$	11.6629	−	10.3127i	0.516442	−	0.456652i
$511$	−10.8021			−0.477857
$512$			1.00000i			0.0441942i
$513$			1.00000i			0.0441511i
$514$	−24.5501			−1.08286
$515$	11.7889	−	10.4241i	0.519482	−	0.459339i
$516$	−10.3127			−0.453989
$517$			7.37470i			0.324339i
$518$		−	37.7743i		−	1.65971i
$519$	14.6253			0.641979
$520$	−2.00000	−	2.26187i	−0.0877058	−	0.0991893i
$521$	39.4518			1.72842			0.864208	−	0.503135i	$-0.167820\pi$
$521$	39.4518			1.72842			0.864208	+	0.503135i	$0.167820\pi$
$522$			3.61213i			0.158098i
$523$		−	37.5026i		−	1.63987i	−0.572453	−	0.819937i	$-0.694008\pi$
$523$		−	37.5026i		−	1.63987i	0.572453	−	0.819937i	$-0.305992\pi$
$524$	−5.61213			−0.245167
$525$	−2.05079	+	16.6253i	−0.0895036	+	0.725588i
$526$	30.3488			1.32327
$527$		−	16.1016i		−	0.701395i
$528$			1.61213i			0.0701588i
$529$	21.1768			0.920730
$530$	−17.6629	−	19.9756i	−0.767228	−	0.867683i
$531$	1.03761			0.0450285
$532$		−	3.35026i		−	0.145252i
$533$		−	4.52373i		−	0.195945i
$534$	2.57452			0.111410
$535$	1.29948	−	1.14903i	0.0561813	−	0.0496769i
$536$	−9.92478			−0.428685
$537$			11.7381i			0.506538i
$538$		−	14.3127i		−	0.617062i
$539$	6.81003			0.293329
$540$	−1.67513	+	1.48119i	−0.0720862	+	0.0637405i
$541$	−30.7757			−1.32315			−0.661576	−	0.749878i	$-0.730112\pi$
$541$	−30.7757			−1.32315			−0.661576	+	0.749878i	$0.730112\pi$
$542$		−	7.32582i		−	0.314671i
$543$		−	21.4617i		−	0.921009i
$544$	−6.96239			−0.298510
$545$	−29.8641	−	33.7743i	−1.27924	−	1.44673i
$546$	−4.52373			−0.193598
$547$			1.77433i			0.0758649i	0.999280	+	0.0379325i	$0.0120772\pi$
$547$			1.77433i			0.0758649i	−0.999280	+	0.0379325i	$0.987923\pi$
$548$		−	17.6629i		−	0.754522i
$549$	−2.00000			−0.0853579
$550$	8.00000	+	0.986826i	0.341121	+	0.0420784i
$551$	−3.61213			−0.153882
$552$		−	1.35026i		−	0.0574710i
$553$		−	47.9511i		−	2.03909i
$554$	14.4387			0.613440
$555$	−16.7005	−	18.8872i	−0.708898	−	0.801716i
$556$	10.7005			0.453803
$557$			8.90175i			0.377179i	0.982056	+	0.188590i	$0.0603916\pi$
$557$			8.90175i			0.377179i	−0.982056	+	0.188590i	$0.939608\pi$
$558$			2.31265i			0.0979023i
$559$	−13.9248			−0.588955
$560$	5.61213	−	4.96239i	0.237156	−	0.209699i
$561$	−11.2243			−0.473888
$562$		−	11.9756i		−	0.505159i
$563$		−	10.9525i		−	0.461595i	−0.973002	−	0.230797i	$-0.925867\pi$
$563$		−	10.9525i		−	0.461595i	0.973002	−	0.230797i	$-0.0741334\pi$
$564$	4.57452			0.192622
$565$	18.6761	−	16.5139i	0.785709	−	0.694744i
$566$	−24.4894			−1.02937
$567$			3.35026i			0.140698i
$568$			0.775746i			0.0325496i
$569$	10.2012			0.427658			0.213829	−	0.976871i	$-0.431406\pi$
$569$	10.2012			0.427658			0.213829	+	0.976871i	$0.431406\pi$
$570$	−1.48119	−	1.67513i	−0.0620404	−	0.0701635i
$571$	−25.6531			−1.07355			−0.536774	−	0.843726i	$-0.680357\pi$
$571$	−25.6531			−1.07355			−0.536774	+	0.843726i	$0.680357\pi$
$572$			2.17679i			0.0910163i
$573$			21.2750i			0.888778i
$574$	11.2243			0.468491
$575$	−6.70052	−	0.826531i	−0.279431	−	0.0344687i
$576$	1.00000			0.0416667
$577$		−	6.44851i		−	0.268455i	−0.990951	−	0.134227i	$-0.957145\pi$
$577$		−	6.44851i		−	0.268455i	0.990951	−	0.134227i	$-0.0428553\pi$
$578$		−	31.4749i		−	1.30918i
$579$	−14.1622			−0.588561
$580$	−5.35026	−	6.05079i	−0.222158	−	0.251245i
$581$	36.4749			1.51323
$582$		−	1.16362i		−	0.0482336i
$583$			19.2243i			0.796187i
$584$	3.22425			0.133421
$585$	−2.26187	+	2.00000i	−0.0935166	+	0.0826898i
$586$	−18.1016			−0.747769
$587$			41.8397i			1.72691i	0.504426	+	0.863455i	$0.331704\pi$
$587$			41.8397i			1.72691i	−0.504426	+	0.863455i	$0.668296\pi$
$588$		−	4.22425i		−	0.174205i
$589$	−2.31265			−0.0952911
$590$	−1.73813	+	1.53690i	−0.0715579	+	0.0632733i
$591$	−3.87399			−0.159355
$592$			11.2750i			0.463401i
$593$			8.73672i			0.358774i	0.983779	+	0.179387i	$0.0574114\pi$
$593$			8.73672i			0.358774i	−0.983779	+	0.179387i	$0.942589\pi$
$594$	1.61213			0.0661464
$595$	34.5501	+	39.0738i	1.41642	+	1.60187i
$596$	1.03761			0.0425022
$597$			3.47627i			0.142274i
$598$		−	1.82321i		−	0.0745565i
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$	0.612127	−	4.96239i	0.0249900	−	0.202589i
$601$	30.6253			1.24923			0.624616	−	0.780932i	$-0.285255\pi$
$601$	30.6253			1.24923			0.624616	+	0.780932i	$0.285255\pi$
$602$		−	34.5501i		−	1.40816i
$603$			9.92478i			0.404168i
$604$	−1.16362			−0.0473470
$605$	12.4436	+	14.0729i	0.505904	+	0.572143i
$606$	8.88717			0.361016
$607$			2.51388i			0.102035i	0.998698	+	0.0510176i	$0.0162465\pi$
$607$			2.51388i			0.102035i	−0.998698	+	0.0510176i	$0.983754\pi$
$608$			1.00000i			0.0405554i
$609$	−12.1016			−0.490380
$610$	3.35026	−	2.96239i	0.135648	−	0.119944i
$611$	6.17679			0.249886
$612$			6.96239i			0.281438i
$613$		−	2.96239i		−	0.119650i	−0.998209	−	0.0598249i	$-0.980946\pi$
$613$		−	2.96239i		−	0.119650i	0.998209	−	0.0598249i	$-0.0190542\pi$
$614$	29.9248			1.20767
$615$	5.61213	−	4.96239i	0.226303	−	0.200103i
$616$	−5.40105			−0.217614
$617$			18.3371i			0.738223i	0.929385	+	0.369112i	$0.120338\pi$
$617$			18.3371i			0.738223i	−0.929385	+	0.369112i	$0.879662\pi$
$618$			7.03761i			0.283094i
$619$	40.7269			1.63695			0.818476	−	0.574541i	$-0.194820\pi$
$619$	40.7269			1.63695			0.818476	+	0.574541i	$0.194820\pi$
$620$	−3.42548	−	3.87399i	−0.137571	−	0.155583i
$621$	−1.35026			−0.0541841
$622$		−	21.2750i		−	0.853051i
$623$			8.62530i			0.345565i
$624$	1.35026			0.0540537
$625$	−24.2506	−	6.07522i	−0.970024	−	0.243009i
$626$	−17.4010			−0.695486
$627$			1.61213i			0.0643821i
$628$			10.9624i			0.437447i
$629$	−78.5012			−3.13005
$630$	−4.96239	−	5.61213i	−0.197706	−	0.223592i
$631$	−5.92478			−0.235862			−0.117931	−	0.993022i	$-0.537626\pi$
$631$	−5.92478			−0.235862			−0.117931	+	0.993022i	$0.537626\pi$
$632$			14.3127i			0.569327i
$633$		−	9.92478i		−	0.394474i
$634$	14.1016			0.560045
$635$	−23.0132	+	20.3488i	−0.913250	+	0.807519i
$636$	11.9248			0.472848
$637$		−	5.70385i		−	0.225995i
$638$			5.82321i			0.230543i
$639$	0.775746			0.0306880
$640$	−1.67513	+	1.48119i	−0.0662154	+	0.0585493i
$641$	19.0494			0.752405			0.376202	−	0.926537i	$-0.377230\pi$
$641$	19.0494			0.752405			0.376202	+	0.926537i	$0.377230\pi$
$642$			0.775746i			0.0306163i
$643$		−	1.06205i		−	0.0418831i	−0.999781	−	0.0209416i	$-0.993334\pi$
$643$		−	1.06205i		−	0.0418831i	0.999781	−	0.0209416i	$-0.00666639\pi$
$644$	4.52373			0.178260
$645$	−15.2750	−	17.2750i	−0.601454	−	0.680204i
$646$	−6.96239			−0.273932
$647$		−	26.6497i		−	1.04771i	−0.851808	−	0.523855i	$-0.824493\pi$
$647$		−	26.6497i		−	1.04771i	0.851808	−	0.523855i	$-0.175507\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	1.67276			0.0656616
$650$	0.826531	−	6.70052i	0.0324192	−	0.262816i
$651$	−7.74798			−0.303667
$652$		−	21.0132i		−	0.822939i
$653$		−	9.64832i		−	0.377568i	−0.982019	−	0.188784i	$-0.939545\pi$
$653$		−	9.64832i		−	0.377568i	0.982019	−	0.188784i	$-0.0604546\pi$
$654$	20.1622			0.788405
$655$	−8.31265	−	9.40105i	−0.324802	−	0.367329i
$656$	−3.35026			−0.130806
$657$		−	3.22425i		−	0.125790i
$658$			15.3258i			0.597463i
$659$	−10.0654			−0.392091			−0.196046	−	0.980595i	$-0.562810\pi$
$659$	−10.0654			−0.392091			−0.196046	+	0.980595i	$0.562810\pi$
$660$	−2.70052	+	2.38787i	−0.105118	+	0.0929478i
$661$	13.5633			0.527549			0.263775	−	0.964584i	$-0.415032\pi$
$661$	13.5633			0.527549			0.263775	+	0.964584i	$0.415032\pi$
$662$			6.85097i			0.266270i
$663$			9.40105i			0.365106i
$664$	−10.8872			−0.422504
$665$	5.61213	−	4.96239i	0.217629	−	0.192433i
$666$	11.2750			0.436899
$667$		−	4.87732i		−	0.188850i
$668$			9.92478i			0.384001i
$669$	7.03761			0.272090
$670$	−14.7005	−	16.6253i	−0.567931	−	0.642291i
$671$	−3.22425			−0.124471
$672$			3.35026i			0.129239i
$673$		−	5.93937i		−	0.228946i	−0.993426	−	0.114473i	$-0.963482\pi$
$673$		−	5.93937i		−	0.228946i	0.993426	−	0.114473i	$-0.0365179\pi$
$674$	24.2374			0.933591
$675$	−4.96239	−	0.612127i	−0.191002	−	0.0235608i
$676$	−11.1768			−0.429877
$677$			24.9525i			0.959004i	0.877541	+	0.479502i	$0.159183\pi$
$677$			24.9525i			0.959004i	−0.877541	+	0.479502i	$0.840817\pi$
$678$			11.1490i			0.428176i
$679$	3.89843			0.149608
$680$	−10.3127	−	11.6629i	−0.395472	−	0.447252i
$681$	14.5501			0.557560
$682$			3.72829i			0.142763i
$683$			45.6239i			1.74575i	0.487944	+	0.872875i	$0.337747\pi$
$683$			45.6239i			1.74575i	−0.487944	+	0.872875i	$0.662253\pi$
$684$	1.00000			0.0382360
$685$	29.5877	−	26.1622i	1.13049	−	0.999606i
$686$	−9.29948			−0.355056
$687$			11.4010i			0.434977i
$688$			10.3127i			0.393166i
$689$	16.1016			0.613421
$690$	2.26187	−	2.00000i	0.0861077	−	0.0761387i
$691$	−11.7480			−0.446914			−0.223457	−	0.974714i	$-0.571734\pi$
$691$	−11.7480			−0.446914			−0.223457	+	0.974714i	$0.571734\pi$
$692$		−	14.6253i		−	0.555971i
$693$			5.40105i			0.205169i
$694$	0.962389			0.0365318
$695$	15.8496	+	17.9248i	0.601208	+	0.679926i
$696$	3.61213			0.136917
$697$		−	23.3258i		−	0.883529i
$698$			1.37470i			0.0520331i
$699$	21.9149			0.828899
$700$	16.6253	+	2.05079i	0.628377	+	0.0775124i
$701$	−43.8105			−1.65470			−0.827350	−	0.561686i	$-0.810153\pi$
$701$	−43.8105			−1.65470			−0.827350	+	0.561686i	$0.810153\pi$
$702$		−	1.35026i		−	0.0509623i
$703$			11.2750i			0.425246i
$704$	1.61213			0.0607593
$705$	6.77575	+	7.66291i	0.255189	+	0.288602i
$706$	−28.7367			−1.08152
$707$			29.7743i			1.11978i
$708$		−	1.03761i		−	0.0389958i
$709$	29.5975			1.11156			0.555779	−	0.831330i	$-0.312420\pi$
$709$	29.5975			1.11156			0.555779	+	0.831330i	$0.312420\pi$
$710$	−1.29948	+	1.14903i	−0.0487685	+	0.0431224i
$711$	14.3127			0.536766
$712$		−	2.57452i		−	0.0964840i
$713$		−	3.12268i		−	0.116945i
$714$	−23.3258			−0.872947
$715$	−3.64641	+	3.22425i	−0.136368	+	0.120580i
$716$	11.7381			0.438675
$717$		−	13.2750i		−	0.495765i
$718$		−	31.1998i		−	1.16437i
$719$	−7.45183			−0.277906			−0.138953	−	0.990299i	$-0.544374\pi$
$719$	−7.45183			−0.277906			−0.138953	+	0.990299i	$0.544374\pi$
$720$	1.48119	+	1.67513i	0.0552009	+	0.0624284i
$721$	−23.5778			−0.878085
$722$			1.00000i			0.0372161i
$723$		−	21.3258i		−	0.793116i
$724$	−21.4617			−0.797617
$725$	2.21108	−	17.9248i	0.0821174	−	0.665710i
$726$	−8.40105			−0.311792
$727$			0.600863i			0.0222848i	0.999938	+	0.0111424i	$0.00354681\pi$
$727$			0.600863i			0.0222848i	−0.999938	+	0.0111424i	$0.996453\pi$
$728$			4.52373i			0.167661i
$729$	−1.00000			−0.0370370
$730$	4.77575	+	5.40105i	0.176758	+	0.199902i
$731$	−71.8007			−2.65564
$732$			2.00000i			0.0739221i
$733$		−	36.0625i		−	1.33200i	−0.745952	−	0.666000i	$-0.768005\pi$
$733$		−	36.0625i		−	1.33200i	0.745952	−	0.666000i	$-0.231995\pi$
$734$	20.1260			0.742865
$735$	7.07618	−	6.25694i	0.261009	−	0.230791i
$736$	−1.35026			−0.0497713
$737$			16.0000i			0.589368i
$738$			3.35026i			0.123325i
$739$	14.1768			0.521502			0.260751	−	0.965406i	$-0.416030\pi$
$739$	14.1768			0.521502			0.260751	+	0.965406i	$0.416030\pi$
$740$	−18.8872	+	16.7005i	−0.694306	+	0.613923i
$741$	1.35026			0.0496031
$742$			39.9511i			1.46665i
$743$		−	24.9986i		−	0.917109i	−0.888666	−	0.458555i	$-0.848367\pi$
$743$		−	24.9986i		−	0.917109i	0.888666	−	0.458555i	$-0.151633\pi$
$744$	2.31265			0.0847859
$745$	1.53690	+	1.73813i	0.0563078	+	0.0636803i
$746$	17.9756			0.658132
$747$			10.8872i			0.398341i
$748$			11.2243i			0.410399i
$749$	−2.59895			−0.0949637
$750$	9.21933	−	6.32487i	0.336642	−	0.230952i
$751$	−10.2111			−0.372608			−0.186304	−	0.982492i	$-0.559651\pi$
$751$	−10.2111			−0.372608			−0.186304	+	0.982492i	$0.559651\pi$
$752$		−	4.57452i		−	0.166815i
$753$		−	16.3127i		−	0.594466i
$754$	4.87732			0.177621
$755$	−1.72355	−	1.94921i	−0.0627263	−	0.0709392i
$756$	3.35026			0.121848
$757$			44.4847i			1.61682i	0.588617	+	0.808412i	$0.299673\pi$
$757$			44.4847i			1.61682i	−0.588617	+	0.808412i	$0.700327\pi$
$758$		−	1.67276i		−	0.0607574i
$759$	−2.17679			−0.0790126
$760$	−1.67513	+	1.48119i	−0.0607634	+	0.0537286i
$761$	27.1490			0.984152			0.492076	−	0.870552i	$-0.336238\pi$
$761$	27.1490			0.984152			0.492076	+	0.870552i	$0.336238\pi$
$762$		−	13.7381i		−	0.497680i
$763$			67.5487i			2.44543i
$764$	21.2750			0.769704
$765$	−11.6629	+	10.3127i	−0.421673	+	0.372855i
$766$	−31.8496			−1.15077
$767$		−	1.40105i		−	0.0505889i
$768$		−	1.00000i		−	0.0360844i
$769$	31.4010			1.13235			0.566175	−	0.824285i	$-0.308422\pi$
$769$	31.4010			1.13235			0.566175	+	0.824285i	$0.308422\pi$
$770$	−8.00000	−	9.04746i	−0.288300	−	0.326048i
$771$	24.5501			0.884149
$772$			14.1622i			0.509709i
$773$		−	4.02635i		−	0.144818i	−0.997375	−	0.0724088i	$-0.976931\pi$
$773$		−	4.02635i		−	0.144818i	0.997375	−	0.0724088i	$-0.0230686\pi$
$774$	10.3127			0.370681
$775$	1.41564	−	11.4763i	0.0508511	−	0.412240i
$776$	−1.16362			−0.0417715
$777$			37.7743i			1.35515i
$778$			10.3371i			0.370603i
$779$	−3.35026			−0.120036
$780$	2.00000	+	2.26187i	0.0716115	+	0.0809878i
$781$	1.25060			0.0447500
$782$		−	9.40105i		−	0.336181i
$783$		−	3.61213i		−	0.129087i
$784$	−4.22425			−0.150866
$785$	−18.3634	+	16.2374i	−0.655419	+	0.579539i
$786$	5.61213			0.200178
$787$			18.2981i			0.652255i	0.945326	+	0.326128i	$0.105744\pi$
$787$			18.2981i			0.652255i	−0.945326	+	0.326128i	$0.894256\pi$
$788$			3.87399i			0.138005i
$789$	−30.3488			−1.08045
$790$	−23.9756	+	21.1998i	−0.853012	+	0.754256i
$791$	−37.3522			−1.32809
$792$		−	1.61213i		−	0.0572844i
$793$			2.70052i			0.0958984i
$794$	−31.4372			−1.11567
$795$	17.6629	+	19.9756i	0.626439	+	0.708460i
$796$	3.47627			0.123213
$797$		−	8.55008i		−	0.302859i	−0.988468	−	0.151430i	$-0.951612\pi$
$797$		−	8.55008i		−	0.302859i	0.988468	−	0.151430i	$-0.0483877\pi$
$798$			3.35026i			0.118598i
$799$	31.8496			1.12676
$800$	−4.96239	−	0.612127i	−0.175447	−	0.0216420i
$801$	−2.57452			−0.0909660
$802$			5.94921i			0.210074i
$803$		−	5.19791i		−	0.183430i
$804$	9.92478			0.350020
$805$	6.70052	+	7.57784i	0.236162	+	0.267084i
$806$	3.12268			0.109992
$807$			14.3127i			0.503829i
$808$		−	8.88717i		−	0.312649i
$809$	−50.7269			−1.78346			−0.891731	−	0.452566i	$-0.850509\pi$
$809$	−50.7269			−1.78346			−0.891731	+	0.452566i	$0.850509\pi$
$810$	1.67513	−	1.48119i	0.0588581	−	0.0520439i
$811$	10.3272			0.362638			0.181319	−	0.983424i	$-0.441963\pi$
$811$	10.3272			0.362638			0.181319	+	0.983424i	$0.441963\pi$
$812$			12.1016i			0.424682i
$813$			7.32582i			0.256928i
$814$	18.1768			0.637096
$815$	35.1998	−	31.1246i	1.23300	−	1.09025i
$816$	6.96239			0.243732
$817$			10.3127i			0.360794i
$818$			30.9986i			1.08384i
$819$	4.52373			0.158072
$820$	−4.96239	−	5.61213i	−0.173294	−	0.195984i
$821$	36.5139			1.27434			0.637172	−	0.770722i	$-0.280104\pi$
$821$	36.5139			1.27434			0.637172	+	0.770722i	$0.280104\pi$
$822$			17.6629i			0.616065i
$823$		−	23.0982i		−	0.805154i	−0.915386	−	0.402577i	$-0.868115\pi$
$823$		−	23.0982i		−	0.805154i	0.915386	−	0.402577i	$-0.131885\pi$
$824$	7.03761			0.245167
$825$	−8.00000	−	0.986826i	−0.278524	−	0.0343569i
$826$	3.47627			0.120955
$827$		−	3.37470i		−	0.117350i	−0.998277	−	0.0586749i	$-0.981312\pi$
$827$		−	3.37470i		−	0.117350i	0.998277	−	0.0586749i	$-0.0186875\pi$
$828$			1.35026i			0.0469248i
$829$	−22.6399			−0.786316			−0.393158	−	0.919471i	$-0.628617\pi$
$829$	−22.6399			−0.786316			−0.393158	+	0.919471i	$0.628617\pi$
$830$	−16.1260	−	18.2374i	−0.559742	−	0.633030i
$831$	−14.4387			−0.500872
$832$		−	1.35026i		−	0.0468119i
$833$		−	29.4109i		−	1.01903i
$834$	−10.7005			−0.370529
$835$	−16.6253	+	14.7005i	−0.575342	+	0.508733i
$836$	1.61213			0.0557566
$837$		−	2.31265i		−	0.0799369i
$838$			34.3390i			1.18622i
$839$	9.02776			0.311673			0.155836	−	0.987783i	$-0.450193\pi$
$839$	9.02776			0.311673			0.155836	+	0.987783i	$0.450193\pi$
$840$	−5.61213	+	4.96239i	−0.193637	+	0.171219i
$841$	−15.9525			−0.550088
$842$			22.8627i			0.787902i
$843$			11.9756i			0.412460i
$844$	−9.92478			−0.341625
$845$	−16.5550	−	18.7226i	−0.569509	−	0.644077i
$846$	−4.57452			−0.157275
$847$		−	28.1457i		−	0.967098i
$848$		−	11.9248i		−	0.409499i
$849$	24.4894			0.840476
$850$	4.26187	−	34.5501i	0.146181	−	1.18506i
$851$	−15.2243			−0.521881
$852$		−	0.775746i		−	0.0265766i
$853$			43.1852i			1.47863i	0.673358	+	0.739317i	$0.264851\pi$
$853$			43.1852i			1.47863i	−0.673358	+	0.739317i	$0.735149\pi$
$854$	−6.70052			−0.229287
$855$	1.48119	+	1.67513i	0.0506558	+	0.0572883i
$856$	0.775746			0.0265145
$857$		−	33.0249i		−	1.12811i	−0.825737	−	0.564055i	$-0.809241\pi$
$857$		−	33.0249i		−	1.12811i	0.825737	−	0.564055i	$-0.190759\pi$
$858$		−	2.17679i		−	0.0743145i
$859$	−15.1754			−0.517777			−0.258889	−	0.965907i	$-0.583356\pi$
$859$	−15.1754			−0.517777			−0.258889	+	0.965907i	$0.583356\pi$
$860$	−17.2750	+	15.2750i	−0.589074	+	0.520875i
$861$	−11.2243			−0.382522
$862$			11.5975i			0.395014i
$863$			39.4763i			1.34379i	0.740647	+	0.671894i	$0.234519\pi$
$863$			39.4763i			1.34379i	−0.740647	+	0.671894i	$0.765481\pi$
$864$	−1.00000			−0.0340207
$865$	24.4993	−	21.6629i	0.833001	−	0.736561i
$866$	−27.8350			−0.945871
$867$			31.4749i			1.06894i
$868$			7.74798i			0.262984i
$869$	23.0738			0.782725
$870$	5.35026	+	6.05079i	0.181391	+	0.205141i
$871$	13.4010			0.454077
$872$		−	20.1622i		−	0.682778i
$873$			1.16362i			0.0393825i
$874$	−1.35026			−0.0456733
$875$	21.1900	+	30.8872i	0.716352	+	1.04418i
$876$	−3.22425			−0.108937
$877$		−	52.5256i		−	1.77366i	−0.462091	−	0.886832i	$-0.652901\pi$
$877$		−	52.5256i		−	1.77366i	0.462091	−	0.886832i	$-0.347099\pi$
$878$			38.7875i			1.30901i
$879$	18.1016			0.610551
$880$	2.38787	+	2.70052i	0.0804952	+	0.0910346i
$881$	−41.8007			−1.40830			−0.704150	−	0.710051i	$-0.748672\pi$
$881$	−41.8007			−1.40830			−0.704150	+	0.710051i	$0.748672\pi$
$882$			4.22425i			0.142238i
$883$		−	36.9643i		−	1.24395i	−0.783038	−	0.621974i	$-0.786331\pi$
$883$		−	36.9643i		−	1.24395i	0.783038	−	0.621974i	$-0.213669\pi$
$884$	9.40105			0.316191
$885$	1.73813	−	1.53690i	0.0584268	−	0.0516625i
$886$	29.2144			0.981477
$887$		−	36.0724i		−	1.21119i	−0.795772	−	0.605596i	$-0.792935\pi$
$887$		−	36.0724i		−	1.21119i	0.795772	−	0.605596i	$-0.207065\pi$
$888$		−	11.2750i		−	0.378366i
$889$	46.0263			1.54367
$890$	4.31265	−	3.81336i	0.144560	−	0.127824i
$891$	−1.61213			−0.0540083
$892$		−	7.03761i		−	0.235637i
$893$		−	4.57452i		−	0.153080i
$894$	−1.03761			−0.0347029
$895$	17.3865	+	19.6629i	0.581165	+	0.657259i
$896$	3.35026			0.111924
$897$			1.82321i			0.0608751i
$898$			20.4993i			0.684070i
$899$	8.35359			0.278608
$900$	−0.612127	+	4.96239i	−0.0204042	+	0.165413i
$901$	83.0249			2.76596
$902$			5.40105i			0.179835i
$903$			34.5501i			1.14975i
$904$	11.1490			0.370811
$905$	−31.7889	−	35.9511i	−1.05670	−	1.19506i
$906$	1.16362			0.0386587
$907$			57.6239i			1.91337i	0.291126	+	0.956685i	$0.405970\pi$
$907$			57.6239i			1.91337i	−0.291126	+	0.956685i	$0.594030\pi$
$908$		−	14.5501i		−	0.482861i
$909$	−8.88717			−0.294769
$910$	−7.57784	+	6.70052i	−0.251203	+	0.222120i
$911$	30.9234			1.02454			0.512268	−	0.858825i	$-0.328805\pi$
$911$	30.9234			1.02454			0.512268	+	0.858825i	$0.328805\pi$
$912$		−	1.00000i		−	0.0331133i
$913$			17.5515i			0.580870i
$914$	6.44851			0.213298
$915$	−3.35026	+	2.96239i	−0.110756	+	0.0979335i
$916$	11.4010			0.376701
$917$			18.8021i			0.620900i
$918$		−	6.96239i		−	0.229793i
$919$	−33.7743			−1.11411			−0.557056	−	0.830475i	$-0.688069\pi$
$919$	−33.7743			−1.11411			−0.557056	+	0.830475i	$0.688069\pi$
$920$	−2.00000	−	2.26187i	−0.0659380	−	0.0745715i
$921$	−29.9248			−0.986055
$922$		−	13.5125i		−	0.445009i
$923$		−	1.04746i		−	0.0344776i
$924$	5.40105			0.177681
$925$	−55.9511	−	6.90175i	−1.83966	−	0.226928i
$926$	−6.20123			−0.203785
$927$		−	7.03761i		−	0.231145i
$928$		−	3.61213i		−	0.118574i
$929$	−48.6516			−1.59621			−0.798104	−	0.602519i	$-0.794164\pi$
$929$	−48.6516			−1.59621			−0.798104	+	0.602519i	$0.794164\pi$
$930$	3.42548	+	3.87399i	0.112326	+	0.127033i
$931$	−4.22425			−0.138444
$932$		−	21.9149i		−	0.717847i
$933$			21.2750i			0.696514i
$934$	−16.5599			−0.541857
$935$	−18.8021	+	16.6253i	−0.614894	+	0.543705i
$936$	−1.35026			−0.0441347
$937$			18.7005i			0.610919i	0.952205	+	0.305460i	$0.0988101\pi$
$937$			18.7005i			0.610919i	−0.952205	+	0.305460i	$0.901190\pi$
$938$			33.2506i			1.08567i
$939$	17.4010			0.567862
$940$	7.66291	−	6.77575i	0.249937	−	0.221000i
$941$	38.4142			1.25227			0.626134	−	0.779716i	$-0.284636\pi$
$941$	38.4142			1.25227			0.626134	+	0.779716i	$0.284636\pi$
$942$		−	10.9624i		−	0.357174i
$943$		−	4.52373i		−	0.147313i
$944$	−1.03761			−0.0337714
$945$	4.96239	+	5.61213i	0.161427	+	0.182563i
$946$	16.6253			0.540535
$947$		−	44.0362i		−	1.43098i	−0.698621	−	0.715492i	$-0.746203\pi$
$947$		−	44.0362i		−	1.43098i	0.698621	−	0.715492i	$-0.253797\pi$
$948$		−	14.3127i		−	0.464853i
$949$	−4.35359			−0.141323
$950$	−4.96239	−	0.612127i	−0.161001	−	0.0198600i
$951$	−14.1016			−0.457275
$952$			23.3258i			0.755994i
$953$		−	38.0724i		−	1.23329i	−0.787243	−	0.616643i	$-0.788492\pi$
$953$		−	38.0724i		−	1.23329i	0.787243	−	0.616643i	$-0.211508\pi$
$954$	−11.9248			−0.386079
$955$	31.5125	+	35.6385i	1.01972	+	1.15323i
$956$	−13.2750			−0.429345
$957$		−	5.82321i		−	0.188238i
$958$			30.5256i			0.986239i
$959$	−59.1754			−1.91087
$960$	1.67513	−	1.48119i	0.0540646	−	0.0478053i
$961$	−25.6516			−0.827473
$962$		−	15.2243i		−	0.490850i
$963$		−	0.775746i		−	0.0249981i
$964$	−21.3258			−0.686859
$965$	−23.7235	+	20.9770i	−0.763688	+	0.675273i
$966$	−4.52373			−0.145549
$967$		−	42.5256i		−	1.36753i	−0.729701	−	0.683766i	$-0.760341\pi$
$967$		−	42.5256i		−	1.36753i	0.729701	−	0.683766i	$-0.239659\pi$
$968$			8.40105i			0.270020i
$969$	6.96239			0.223664
$970$	−1.72355	−	1.94921i	−0.0553397	−	0.0625855i
$971$	−22.1378			−0.710435			−0.355217	−	0.934784i	$-0.615593\pi$
$971$	−22.1378			−0.710435			−0.355217	+	0.934784i	$0.615593\pi$
$972$			1.00000i			0.0320750i
$973$		−	35.8496i		−	1.14928i
$974$	−2.51388			−0.0805499
$975$	−0.826531	+	6.70052i	−0.0264702	+	0.214588i
$976$	2.00000			0.0640184
$977$			21.7480i			0.695780i	0.937535	+	0.347890i	$0.113102\pi$
$977$			21.7480i			0.695780i	−0.937535	+	0.347890i	$0.886898\pi$
$978$			21.0132i			0.671927i
$979$	−4.15045			−0.132649
$980$	−6.25694	−	7.07618i	−0.199871	−	0.226040i
$981$	−20.1622			−0.643730
$982$			1.46168i			0.0466441i
$983$			9.04746i			0.288569i	0.989536	+	0.144285i	$0.0460881\pi$
$983$			9.04746i			0.288569i	−0.989536	+	0.144285i	$0.953912\pi$
$984$	3.35026			0.106802
$985$	−6.48944	+	5.73813i	−0.206771	+	0.182832i
$986$	25.1490			0.800908
$987$		−	15.3258i		−	0.487826i
$988$		−	1.35026i		−	0.0429575i
$989$	−13.9248			−0.442782
$990$	2.70052	−	2.38787i	0.0858283	−	0.0758916i
$991$	−26.0606			−0.827843			−0.413922	−	0.910313i	$-0.635841\pi$
$991$	−26.0606			−0.827843			−0.413922	+	0.910313i	$0.635841\pi$
$992$		−	2.31265i		−	0.0734267i
$993$		−	6.85097i		−	0.217409i
$994$	2.59895			0.0824338
$995$	5.14903	+	5.82321i	0.163235	+	0.184608i
$996$	10.8872			0.344973
$997$		−	28.2130i		−	0.893514i	−0.894655	−	0.446757i	$-0.852579\pi$
$997$		−	28.2130i		−	0.893514i	0.894655	−	0.446757i	$-0.147421\pi$
$998$			5.55149i			0.175729i
$999$	−11.2750			−0.356726

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.d.d.229.4	yes	6
3.2	odd	2		1710.2.d.e.1369.3		6
5.2	odd	4		2850.2.a.bk.1.1		3
5.3	odd	4		2850.2.a.bn.1.3		3
5.4	even	2	inner	570.2.d.d.229.1	✓	6
15.2	even	4		8550.2.a.cr.1.1		3
15.8	even	4		8550.2.a.cf.1.3		3
15.14	odd	2		1710.2.d.e.1369.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.d.d.229.1	✓	6	5.4	even	2	inner
570.2.d.d.229.4	yes	6	1.1	even	1	trivial
1710.2.d.e.1369.3		6	3.2	odd	2
1710.2.d.e.1369.6		6	15.14	odd	2
2850.2.a.bk.1.1		3	5.2	odd	4
2850.2.a.bn.1.3		3	5.3	odd	4
8550.2.a.cf.1.3		3	15.8	even	4
8550.2.a.cr.1.1		3	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-1.48119 - 1.67513i) q^{5} +1.00000 q^{6} +3.35026i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-1.48119 - 1.67513i) q^{5} +1.00000 q^{6} +3.35026i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(1.67513 - 1.48119i) q^{10} -1.61213 q^{11} +1.00000i q^{12} +1.35026i q^{13} -3.35026 q^{14} +(-1.67513 + 1.48119i) q^{15} +1.00000 q^{16} +6.96239i q^{17} -1.00000i q^{18} +1.00000 q^{19} +(1.48119 + 1.67513i) q^{20} +3.35026 q^{21} -1.61213i q^{22} +1.35026i q^{23} -1.00000 q^{24} +(-0.612127 + 4.96239i) q^{25} -1.35026 q^{26} +1.00000i q^{27} -3.35026i q^{28} -3.61213 q^{29} +(-1.48119 - 1.67513i) q^{30} -2.31265 q^{31} +1.00000i q^{32} +1.61213i q^{33} -6.96239 q^{34} +(5.61213 - 4.96239i) q^{35} +1.00000 q^{36} +11.2750i q^{37} +1.00000i q^{38} +1.35026 q^{39} +(-1.67513 + 1.48119i) q^{40} -3.35026 q^{41} +3.35026i q^{42} +10.3127i q^{43} +1.61213 q^{44} +(1.48119 + 1.67513i) q^{45} -1.35026 q^{46} -4.57452i q^{47} -1.00000i q^{48} -4.22425 q^{49} +(-4.96239 - 0.612127i) q^{50} +6.96239 q^{51} -1.35026i q^{52} -11.9248i q^{53} -1.00000 q^{54} +(2.38787 + 2.70052i) q^{55} +3.35026 q^{56} -1.00000i q^{57} -3.61213i q^{58} -1.03761 q^{59} +(1.67513 - 1.48119i) q^{60} +2.00000 q^{61} -2.31265i q^{62} -3.35026i q^{63} -1.00000 q^{64} +(2.26187 - 2.00000i) q^{65} -1.61213 q^{66} -9.92478i q^{67} -6.96239i q^{68} +1.35026 q^{69} +(4.96239 + 5.61213i) q^{70} -0.775746 q^{71} +1.00000i q^{72} +3.22425i q^{73} -11.2750 q^{74} +(4.96239 + 0.612127i) q^{75} -1.00000 q^{76} -5.40105i q^{77} +1.35026i q^{78} -14.3127 q^{79} +(-1.48119 - 1.67513i) q^{80} +1.00000 q^{81} -3.35026i q^{82} -10.8872i q^{83} -3.35026 q^{84} +(11.6629 - 10.3127i) q^{85} -10.3127 q^{86} +3.61213i q^{87} +1.61213i q^{88} +2.57452 q^{89} +(-1.67513 + 1.48119i) q^{90} -4.52373 q^{91} -1.35026i q^{92} +2.31265i q^{93} +4.57452 q^{94} +(-1.48119 - 1.67513i) q^{95} +1.00000 q^{96} -1.16362i q^{97} -4.22425i q^{98} +1.61213 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} + 2 q^{5} + 6 q^{6} - 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 + 2 * q^5 + 6 * q^6 - 6 * q^9	\( 6 q - 6 q^{4} + 2 q^{5} + 6 q^{6} - 6 q^{9} - 8 q^{11} + 6 q^{16} + 6 q^{19} - 2 q^{20} - 6 q^{24} - 2 q^{25} + 12 q^{26} - 20 q^{29} + 2 q^{30} + 28 q^{31} - 20 q^{34} + 32 q^{35} + 6 q^{36} - 12 q^{39} + 8 q^{44} - 2 q^{45} + 12 q^{46} - 22 q^{49} - 8 q^{50} + 20 q^{51} - 6 q^{54} + 16 q^{55} - 28 q^{59} + 12 q^{61} - 6 q^{64} + 32 q^{65} - 8 q^{66} - 12 q^{69} + 8 q^{70} - 8 q^{71} - 4 q^{74} + 8 q^{75} - 6 q^{76} - 44 q^{79} + 2 q^{80} + 6 q^{81} + 8 q^{85} - 20 q^{86} - 8 q^{89} - 64 q^{91} + 4 q^{94} + 2 q^{95} + 6 q^{96} + 8 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 + 2 * q^5 + 6 * q^6 - 6 * q^9 - 8 * q^11 + 6 * q^16 + 6 * q^19 - 2 * q^20 - 6 * q^24 - 2 * q^25 + 12 * q^26 - 20 * q^29 + 2 * q^30 + 28 * q^31 - 20 * q^34 + 32 * q^35 + 6 * q^36 - 12 * q^39 + 8 * q^44 - 2 * q^45 + 12 * q^46 - 22 * q^49 - 8 * q^50 + 20 * q^51 - 6 * q^54 + 16 * q^55 - 28 * q^59 + 12 * q^61 - 6 * q^64 + 32 * q^65 - 8 * q^66 - 12 * q^69 + 8 * q^70 - 8 * q^71 - 4 * q^74 + 8 * q^75 - 6 * q^76 - 44 * q^79 + 2 * q^80 + 6 * q^81 + 8 * q^85 - 20 * q^86 - 8 * q^89 - 64 * q^91 + 4 * q^94 + 2 * q^95 + 6 * q^96 + 8 * q^99

Introduction

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