LMFDB - Embedded newform 570.2.d.c.229.3

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			229.3
Root			$1.45161 + 1.45161i$ of defining polynomial
Character	$\chi$	$=$	570.229
Dual form			570.2.d.c.229.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(2.21432 + 0.311108i) q^{5} -1.00000 q^{6} +4.42864i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(2.21432 + 0.311108i) q^{5} -1.00000 q^{6} +4.42864i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(0.311108 - 2.21432i) q^{10} +2.62222 q^{11} +1.00000i q^{12} +5.80642i q^{13} +4.42864 q^{14} +(0.311108 - 2.21432i) q^{15} +1.00000 q^{16} +3.80642i q^{17} +1.00000i q^{18} -1.00000 q^{19} +(-2.21432 - 0.311108i) q^{20} +4.42864 q^{21} -2.62222i q^{22} -2.62222i q^{23} +1.00000 q^{24} +(4.80642 + 1.37778i) q^{25} +5.80642 q^{26} +1.00000i q^{27} -4.42864i q^{28} -3.37778 q^{29} +(-2.21432 - 0.311108i) q^{30} -4.42864 q^{31} -1.00000i q^{32} -2.62222i q^{33} +3.80642 q^{34} +(-1.37778 + 9.80642i) q^{35} +1.00000 q^{36} -5.80642i q^{37} +1.00000i q^{38} +5.80642 q^{39} +(-0.311108 + 2.21432i) q^{40} +5.67307 q^{41} -4.42864i q^{42} -10.9906i q^{43} -2.62222 q^{44} +(-2.21432 - 0.311108i) q^{45} -2.62222 q^{46} -2.62222i q^{47} -1.00000i q^{48} -12.6128 q^{49} +(1.37778 - 4.80642i) q^{50} +3.80642 q^{51} -5.80642i q^{52} -6.00000i q^{53} +1.00000 q^{54} +(5.80642 + 0.815792i) q^{55} -4.42864 q^{56} +1.00000i q^{57} +3.37778i q^{58} +1.05086 q^{59} +(-0.311108 + 2.21432i) q^{60} +4.75557 q^{61} +4.42864i q^{62} -4.42864i q^{63} -1.00000 q^{64} +(-1.80642 + 12.8573i) q^{65} -2.62222 q^{66} -15.6128i q^{67} -3.80642i q^{68} -2.62222 q^{69} +(9.80642 + 1.37778i) q^{70} +15.6128 q^{71} -1.00000i q^{72} +11.6128i q^{73} -5.80642 q^{74} +(1.37778 - 4.80642i) q^{75} +1.00000 q^{76} +11.6128i q^{77} -5.80642i q^{78} -4.42864 q^{79} +(2.21432 + 0.311108i) q^{80} +1.00000 q^{81} -5.67307i q^{82} +11.9081i q^{83} -4.42864 q^{84} +(-1.18421 + 8.42864i) q^{85} -10.9906 q^{86} +3.37778i q^{87} +2.62222i q^{88} -12.4286 q^{89} +(-0.311108 + 2.21432i) q^{90} -25.7146 q^{91} +2.62222i q^{92} +4.42864i q^{93} -2.62222 q^{94} +(-2.21432 - 0.311108i) q^{95} -1.00000 q^{96} -7.37778i q^{97} +12.6128i q^{98} -2.62222 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9	$ 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9} + 2 q^{10} + 16 q^{11} + 2 q^{15} + 6 q^{16} - 6 q^{19} + 6 q^{24} + 2 q^{25} + 8 q^{26} - 20 q^{29} - 4 q^{34} - 8 q^{35} + 6 q^{36} + 8 q^{39} - 2 q^{40} + 8 q^{41} - 16 q^{44} - 16 q^{46} - 22 q^{49} + 8 q^{50} - 4 q^{51} + 6 q^{54} + 8 q^{55} - 20 q^{59} - 2 q^{60} + 28 q^{61} - 6 q^{64} + 16 q^{65} - 16 q^{66} - 16 q^{69} + 32 q^{70} + 40 q^{71} - 8 q^{74} + 8 q^{75} + 6 q^{76} + 6 q^{81} + 20 q^{85} - 12 q^{86} - 48 q^{89} - 2 q^{90} - 48 q^{91} - 16 q^{94} - 6 q^{96} - 16 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9 + 2 * q^10 + 16 * q^11 + 2 * q^15 + 6 * q^16 - 6 * q^19 + 6 * q^24 + 2 * q^25 + 8 * q^26 - 20 * q^29 - 4 * q^34 - 8 * q^35 + 6 * q^36 + 8 * q^39 - 2 * q^40 + 8 * q^41 - 16 * q^44 - 16 * q^46 - 22 * q^49 + 8 * q^50 - 4 * q^51 + 6 * q^54 + 8 * q^55 - 20 * q^59 - 2 * q^60 + 28 * q^61 - 6 * q^64 + 16 * q^65 - 16 * q^66 - 16 * q^69 + 32 * q^70 + 40 * q^71 - 8 * q^74 + 8 * q^75 + 6 * q^76 + 6 * q^81 + 20 * q^85 - 12 * q^86 - 48 * q^89 - 2 * q^90 - 48 * q^91 - 16 * q^94 - 6 * q^96 - 16 * 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
$5$	2.21432	+	0.311108i	0.990274	+	0.139132i
$5$	2.21432	+	0.311108i	0.990274	+	0.139132i
$6$	−1.00000			−0.408248
$7$			4.42864i			1.67387i	0.547304	+	0.836934i	$0.315654\pi$
$7$			4.42864i			1.67387i	−0.547304	+	0.836934i	$0.684346\pi$
$8$			1.00000i			0.353553i
$9$	−1.00000			−0.333333
$10$	0.311108	−	2.21432i	0.0983809	−	0.700229i
$11$	2.62222			0.790628			0.395314	−	0.918546i	$-0.370636\pi$
$11$	2.62222			0.790628			0.395314	+	0.918546i	$0.370636\pi$
$12$			1.00000i			0.288675i
$13$			5.80642i			1.61041i	0.592995	+	0.805206i	$0.297945\pi$
$13$			5.80642i			1.61041i	−0.592995	+	0.805206i	$0.702055\pi$
$14$	4.42864			1.18360
$15$	0.311108	−	2.21432i	0.0803277	−	0.571735i
$16$	1.00000			0.250000
$17$			3.80642i			0.923193i	0.887090	+	0.461597i	$0.152723\pi$
$17$			3.80642i			0.923193i	−0.887090	+	0.461597i	$0.847277\pi$
$18$			1.00000i			0.235702i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	−2.21432	−	0.311108i	−0.495137	−	0.0695658i
$21$	4.42864			0.966408
$22$		−	2.62222i		−	0.559058i
$23$		−	2.62222i		−	0.546770i	−0.961905	−	0.273385i	$-0.911857\pi$
$23$		−	2.62222i		−	0.546770i	0.961905	−	0.273385i	$-0.0881433\pi$
$24$	1.00000			0.204124
$25$	4.80642	+	1.37778i	0.961285	+	0.275557i
$26$	5.80642			1.13873
$27$			1.00000i			0.192450i
$28$		−	4.42864i		−	0.836934i
$29$	−3.37778			−0.627239			−0.313619	−	0.949549i	$-0.601542\pi$
$29$	−3.37778			−0.627239			−0.313619	+	0.949549i	$0.601542\pi$
$30$	−2.21432	−	0.311108i	−0.404278	−	0.0568003i
$31$	−4.42864			−0.795407			−0.397704	−	0.917514i	$-0.630193\pi$
$31$	−4.42864			−0.795407			−0.397704	+	0.917514i	$0.630193\pi$
$32$		−	1.00000i		−	0.176777i
$33$		−	2.62222i		−	0.456469i
$34$	3.80642			0.652796
$35$	−1.37778	+	9.80642i	−0.232888	+	1.65759i
$36$	1.00000			0.166667
$37$		−	5.80642i		−	0.954570i	−0.878749	−	0.477285i	$-0.841621\pi$
$37$		−	5.80642i		−	0.954570i	0.878749	−	0.477285i	$-0.158379\pi$
$38$			1.00000i			0.162221i
$39$	5.80642			0.929772
$40$	−0.311108	+	2.21432i	−0.0491905	+	0.350115i
$41$	5.67307			0.885985			0.442992	−	0.896525i	$-0.353917\pi$
$41$	5.67307			0.885985			0.442992	+	0.896525i	$0.353917\pi$
$42$		−	4.42864i		−	0.683354i
$43$		−	10.9906i		−	1.67606i	−0.545627	−	0.838028i	$-0.683709\pi$
$43$		−	10.9906i		−	1.67606i	0.545627	−	0.838028i	$-0.316291\pi$
$44$	−2.62222			−0.395314
$45$	−2.21432	−	0.311108i	−0.330091	−	0.0463772i
$46$	−2.62222			−0.386625
$47$		−	2.62222i		−	0.382489i	−0.981542	−	0.191245i	$-0.938748\pi$
$47$		−	2.62222i		−	0.382489i	0.981542	−	0.191245i	$-0.0612524\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−12.6128			−1.80184
$50$	1.37778	−	4.80642i	0.194848	−	0.679731i
$51$	3.80642			0.533006
$52$		−	5.80642i		−	0.805206i
$53$		−	6.00000i		−	0.824163i	−0.911147	−	0.412082i	$-0.864802\pi$
$53$		−	6.00000i		−	0.824163i	0.911147	−	0.412082i	$-0.135198\pi$
$54$	1.00000			0.136083
$55$	5.80642	+	0.815792i	0.782938	+	0.110001i
$56$	−4.42864			−0.591802
$57$			1.00000i			0.132453i
$58$			3.37778i			0.443525i
$59$	1.05086			0.136810			0.0684048	−	0.997658i	$-0.478209\pi$
$59$	1.05086			0.136810			0.0684048	+	0.997658i	$0.478209\pi$
$60$	−0.311108	+	2.21432i	−0.0401638	+	0.285867i
$61$	4.75557			0.608888			0.304444	−	0.952530i	$-0.401529\pi$
$61$	4.75557			0.608888			0.304444	+	0.952530i	$0.401529\pi$
$62$			4.42864i			0.562438i
$63$		−	4.42864i		−	0.557956i
$64$	−1.00000			−0.125000
$65$	−1.80642	+	12.8573i	−0.224059	+	1.59475i
$66$	−2.62222			−0.322772
$67$		−	15.6128i		−	1.90741i	−0.300739	−	0.953706i	$-0.597233\pi$
$67$		−	15.6128i		−	1.90741i	0.300739	−	0.953706i	$-0.402767\pi$
$68$		−	3.80642i		−	0.461597i
$69$	−2.62222			−0.315678
$70$	9.80642	+	1.37778i	1.17209	+	0.164677i
$71$	15.6128			1.85290			0.926452	−	0.376413i	$-0.122843\pi$
$71$	15.6128			1.85290			0.926452	+	0.376413i	$0.122843\pi$
$72$		−	1.00000i		−	0.117851i
$73$			11.6128i			1.35918i	0.733592	+	0.679591i	$0.237843\pi$
$73$			11.6128i			1.35918i	−0.733592	+	0.679591i	$0.762157\pi$
$74$	−5.80642			−0.674983
$75$	1.37778	−	4.80642i	0.159093	−	0.554998i
$76$	1.00000			0.114708
$77$			11.6128i			1.32341i
$78$		−	5.80642i		−	0.657448i
$79$	−4.42864			−0.498261			−0.249130	−	0.968470i	$-0.580145\pi$
$79$	−4.42864			−0.498261			−0.249130	+	0.968470i	$0.580145\pi$
$80$	2.21432	+	0.311108i	0.247568	+	0.0347829i
$81$	1.00000			0.111111
$82$		−	5.67307i		−	0.626486i
$83$			11.9081i			1.30709i	0.756889	+	0.653544i	$0.226718\pi$
$83$			11.9081i			1.30709i	−0.756889	+	0.653544i	$0.773282\pi$
$84$	−4.42864			−0.483204
$85$	−1.18421	+	8.42864i	−0.128445	+	0.914214i
$86$	−10.9906			−1.18515
$87$			3.37778i			0.362136i
$88$			2.62222i			0.279529i
$89$	−12.4286			−1.31743			−0.658717	−	0.752391i	$-0.728900\pi$
$89$	−12.4286			−1.31743			−0.658717	+	0.752391i	$0.728900\pi$
$90$	−0.311108	+	2.21432i	−0.0327936	+	0.233410i
$91$	−25.7146			−2.69562
$92$			2.62222i			0.273385i
$93$			4.42864i			0.459229i
$94$	−2.62222			−0.270461
$95$	−2.21432	−	0.311108i	−0.227184	−	0.0319190i
$96$	−1.00000			−0.102062
$97$		−	7.37778i		−	0.749101i	−0.927207	−	0.374550i	$-0.877797\pi$
$97$		−	7.37778i		−	0.749101i	0.927207	−	0.374550i	$-0.122203\pi$
$98$			12.6128i			1.27409i
$99$	−2.62222			−0.263543
$100$	−4.80642	−	1.37778i	−0.480642	−	0.137778i
$101$	17.6731			1.75854			0.879268	−	0.476327i	$-0.158032\pi$
$101$	17.6731			1.75854			0.879268	+	0.476327i	$0.158032\pi$
$102$		−	3.80642i		−	0.376892i
$103$		−	1.18421i		−	0.116684i	−0.998297	−	0.0583418i	$-0.981419\pi$
$103$		−	1.18421i		−	0.116684i	0.998297	−	0.0583418i	$-0.0185813\pi$
$104$	−5.80642			−0.569367
$105$	9.80642	+	1.37778i	0.957009	+	0.134458i
$106$	−6.00000			−0.582772
$107$		−	4.85728i		−	0.469571i	−0.972047	−	0.234785i	$-0.924561\pi$
$107$		−	4.85728i		−	0.469571i	0.972047	−	0.234785i	$-0.0754388\pi$
$108$		−	1.00000i		−	0.0962250i
$109$	6.04149			0.578670			0.289335	−	0.957228i	$-0.406566\pi$
$109$	6.04149			0.578670			0.289335	+	0.957228i	$0.406566\pi$
$110$	0.815792	−	5.80642i	0.0777827	−	0.553621i
$111$	−5.80642			−0.551121
$112$			4.42864i			0.418467i
$113$			9.34614i			0.879211i	0.898191	+	0.439606i	$0.144882\pi$
$113$			9.34614i			0.879211i	−0.898191	+	0.439606i	$0.855118\pi$
$114$	1.00000			0.0936586
$115$	0.815792	−	5.80642i	0.0760730	−	0.541452i
$116$	3.37778			0.313619
$117$		−	5.80642i		−	0.536804i
$118$		−	1.05086i		−	0.0967391i
$119$	−16.8573			−1.54530
$120$	2.21432	+	0.311108i	0.202139	+	0.0284001i
$121$	−4.12399			−0.374908
$122$		−	4.75557i		−	0.430549i
$123$		−	5.67307i		−	0.511524i
$124$	4.42864			0.397704
$125$	10.2143	+	4.54617i	0.913597	+	0.406622i
$126$	−4.42864			−0.394535
$127$		−	6.42864i		−	0.570450i	−0.958461	−	0.285225i	$-0.907932\pi$
$127$		−	6.42864i		−	0.570450i	0.958461	−	0.285225i	$-0.0920682\pi$
$128$			1.00000i			0.0883883i
$129$	−10.9906			−0.967671
$130$	12.8573	+	1.80642i	1.12766	+	0.158434i
$131$	−15.0923			−1.31862			−0.659312	−	0.751869i	$-0.729152\pi$
$131$	−15.0923			−1.31862			−0.659312	+	0.751869i	$0.729152\pi$
$132$			2.62222i			0.228235i
$133$		−	4.42864i		−	0.384012i
$134$	−15.6128			−1.34874
$135$	−0.311108	+	2.21432i	−0.0267759	+	0.190578i
$136$	−3.80642			−0.326398
$137$			7.53972i			0.644162i	0.946712	+	0.322081i	$0.104382\pi$
$137$			7.53972i			0.644162i	−0.946712	+	0.322081i	$0.895618\pi$
$138$			2.62222i			0.223218i
$139$	−0.387152			−0.0328378			−0.0164189	−	0.999865i	$-0.505227\pi$
$139$	−0.387152			−0.0328378			−0.0164189	+	0.999865i	$0.505227\pi$
$140$	1.37778	−	9.80642i	0.116444	−	0.828794i
$141$	−2.62222			−0.220830
$142$		−	15.6128i		−	1.31020i
$143$			15.2257i			1.27324i
$144$	−1.00000			−0.0833333
$145$	−7.47949	−	1.05086i	−0.621138	−	0.0872688i
$146$	11.6128			0.961086
$147$			12.6128i			1.04029i
$148$			5.80642i			0.477285i
$149$	14.5303			1.19037			0.595186	−	0.803588i	$-0.297078\pi$
$149$	14.5303			1.19037			0.595186	+	0.803588i	$0.297078\pi$
$150$	−4.80642	−	1.37778i	−0.392443	−	0.112496i
$151$	4.69535			0.382102			0.191051	−	0.981580i	$-0.438810\pi$
$151$	4.69535			0.382102			0.191051	+	0.981580i	$0.438810\pi$
$152$		−	1.00000i		−	0.0811107i
$153$		−	3.80642i		−	0.307731i
$154$	11.6128			0.935790
$155$	−9.80642	−	1.37778i	−0.787671	−	0.110666i
$156$	−5.80642			−0.464886
$157$			21.5210i			1.71756i	0.512343	+	0.858781i	$0.328778\pi$
$157$			21.5210i			1.71756i	−0.512343	+	0.858781i	$0.671222\pi$
$158$			4.42864i			0.352324i
$159$	−6.00000			−0.475831
$160$	0.311108	−	2.21432i	0.0245952	−	0.175057i
$161$	11.6128			0.915221
$162$		−	1.00000i		−	0.0785674i
$163$		−	8.23506i		−	0.645020i	−0.946566	−	0.322510i	$-0.895473\pi$
$163$		−	8.23506i		−	0.645020i	0.946566	−	0.322510i	$-0.104527\pi$
$164$	−5.67307			−0.442992
$165$	0.815792	−	5.80642i	0.0635093	−	0.452029i
$166$	11.9081			0.924250
$167$		−	8.47013i		−	0.655438i	−0.944775	−	0.327719i	$-0.893720\pi$
$167$		−	8.47013i		−	0.655438i	0.944775	−	0.327719i	$-0.106280\pi$
$168$			4.42864i			0.341677i
$169$	−20.7146			−1.59343
$170$	8.42864	+	1.18421i	0.646447	+	0.0908246i
$171$	1.00000			0.0764719
$172$			10.9906i			0.838028i
$173$		−	22.4701i		−	1.70837i	−0.519967	−	0.854186i	$-0.674056\pi$
$173$		−	22.4701i		−	1.70837i	0.519967	−	0.854186i	$-0.325944\pi$
$174$	3.37778			0.256069
$175$	−6.10171	+	21.2859i	−0.461246	+	1.60906i
$176$	2.62222			0.197657
$177$		−	1.05086i		−	0.0789871i
$178$			12.4286i			0.931566i
$179$	2.94914			0.220429			0.110215	−	0.993908i	$-0.464846\pi$
$179$	2.94914			0.220429			0.110215	+	0.993908i	$0.464846\pi$
$180$	2.21432	+	0.311108i	0.165046	+	0.0231886i
$181$	22.8988			1.70205			0.851026	−	0.525124i	$-0.175981\pi$
$181$	22.8988			1.70205			0.851026	+	0.525124i	$0.175981\pi$
$182$			25.7146i			1.90609i
$183$		−	4.75557i		−	0.351542i
$184$	2.62222			0.193312
$185$	1.80642	−	12.8573i	0.132811	−	0.945286i
$186$	4.42864			0.324724
$187$			9.98126i			0.729902i
$188$			2.62222i			0.191245i
$189$	−4.42864			−0.322136
$190$	−0.311108	+	2.21432i	−0.0225701	+	0.160644i
$191$	−9.05086			−0.654897			−0.327448	−	0.944869i	$-0.606189\pi$
$191$	−9.05086			−0.654897			−0.327448	+	0.944869i	$0.606189\pi$
$192$			1.00000i			0.0721688i
$193$			18.7239i			1.34778i	0.738833	+	0.673889i	$0.235377\pi$
$193$			18.7239i			1.34778i	−0.738833	+	0.673889i	$0.764623\pi$
$194$	−7.37778			−0.529694
$195$	12.8573	+	1.80642i	0.920729	+	0.129361i
$196$	12.6128			0.900918
$197$		−	0.888922i		−	0.0633331i	−0.999498	−	0.0316665i	$-0.989919\pi$
$197$		−	0.888922i		−	0.0633331i	0.999498	−	0.0316665i	$-0.0100815\pi$
$198$			2.62222i			0.186353i
$199$	−21.7146			−1.53930			−0.769652	−	0.638464i	$-0.779570\pi$
$199$	−21.7146			−1.53930			−0.769652	+	0.638464i	$0.779570\pi$
$200$	−1.37778	+	4.80642i	−0.0974241	+	0.339865i
$201$	−15.6128			−1.10125
$202$		−	17.6731i		−	1.24347i
$203$		−	14.9590i		−	1.04992i
$204$	−3.80642			−0.266503
$205$	12.5620	+	1.76494i	0.877368	+	0.123269i
$206$	−1.18421			−0.0825077
$207$			2.62222i			0.182257i
$208$			5.80642i			0.402603i
$209$	−2.62222			−0.181382
$210$	1.37778	−	9.80642i	0.0950762	−	0.676708i
$211$	−3.61285			−0.248719			−0.124359	−	0.992237i	$-0.539688\pi$
$211$	−3.61285			−0.248719			−0.124359	+	0.992237i	$0.539688\pi$
$212$			6.00000i			0.412082i
$213$		−	15.6128i		−	1.06977i
$214$	−4.85728			−0.332037
$215$	3.41927	−	24.3368i	0.233192	−	1.65975i
$216$	−1.00000			−0.0680414
$217$		−	19.6128i		−	1.33141i
$218$		−	6.04149i		−	0.409181i
$219$	11.6128			0.784724
$220$	−5.80642	−	0.815792i	−0.391469	−	0.0550007i
$221$	−22.1017			−1.48672
$222$			5.80642i			0.389702i
$223$		−	21.3876i		−	1.43222i	−0.697987	−	0.716111i	$-0.745921\pi$
$223$		−	21.3876i		−	1.43222i	0.697987	−	0.716111i	$-0.254079\pi$
$224$	4.42864			0.295901
$225$	−4.80642	−	1.37778i	−0.320428	−	0.0918523i
$226$	9.34614			0.621696
$227$		−	8.47013i		−	0.562182i	−0.959681	−	0.281091i	$-0.909304\pi$
$227$		−	8.47013i		−	0.562182i	0.959681	−	0.281091i	$-0.0906963\pi$
$228$		−	1.00000i		−	0.0662266i
$229$	16.9590			1.12068			0.560341	−	0.828262i	$-0.310670\pi$
$229$	16.9590			1.12068			0.560341	+	0.828262i	$0.310670\pi$
$230$	−5.80642	−	0.815792i	−0.382864	−	0.0537917i
$231$	11.6128			0.764069
$232$		−	3.37778i		−	0.221762i
$233$		−	17.9081i		−	1.17320i	−0.809876	−	0.586600i	$-0.800466\pi$
$233$		−	17.9081i		−	1.17320i	0.809876	−	0.586600i	$-0.199534\pi$
$234$	−5.80642			−0.379578
$235$	0.815792	−	5.80642i	0.0532164	−	0.378769i
$236$	−1.05086			−0.0684048
$237$			4.42864i			0.287671i
$238$			16.8573i			1.09270i
$239$	28.2766			1.82906			0.914529	−	0.404520i	$-0.132562\pi$
$239$	28.2766			1.82906			0.914529	+	0.404520i	$0.132562\pi$
$240$	0.311108	−	2.21432i	0.0200819	−	0.142934i
$241$	−11.5111			−0.741498			−0.370749	−	0.928733i	$-0.620899\pi$
$241$	−11.5111			−0.741498			−0.370749	+	0.928733i	$0.620899\pi$
$242$			4.12399i			0.265100i
$243$		−	1.00000i		−	0.0641500i
$244$	−4.75557			−0.304444
$245$	−27.9289	−	3.92396i	−1.78431	−	0.250692i
$246$	−5.67307			−0.361702
$247$		−	5.80642i		−	0.369454i
$248$		−	4.42864i		−	0.281219i
$249$	11.9081			0.754647
$250$	4.54617	−	10.2143i	0.287525	−	0.646010i
$251$	−7.74620			−0.488936			−0.244468	−	0.969657i	$-0.578613\pi$
$251$	−7.74620			−0.488936			−0.244468	+	0.969657i	$0.578613\pi$
$252$			4.42864i			0.278978i
$253$		−	6.87601i		−	0.432291i
$254$	−6.42864			−0.403369
$255$	8.42864	+	1.18421i	0.527822	+	0.0741580i
$256$	1.00000			0.0625000
$257$			13.8796i			0.865783i	0.901446	+	0.432891i	$0.142507\pi$
$257$			13.8796i			0.865783i	−0.901446	+	0.432891i	$0.857493\pi$
$258$			10.9906i			0.684247i
$259$	25.7146			1.59782
$260$	1.80642	−	12.8573i	0.112030	−	0.797375i
$261$	3.37778			0.209080
$262$			15.0923i			0.932408i
$263$		−	18.6222i		−	1.14830i	−0.818752	−	0.574148i	$-0.805334\pi$
$263$		−	18.6222i		−	1.14830i	0.818752	−	0.574148i	$-0.194666\pi$
$264$	2.62222			0.161386
$265$	1.86665	−	13.2859i	0.114667	−	0.816147i
$266$	−4.42864			−0.271537
$267$			12.4286i			0.760620i
$268$			15.6128i			0.953706i
$269$	−15.8479			−0.966264			−0.483132	−	0.875547i	$-0.660501\pi$
$269$	−15.8479			−0.966264			−0.483132	+	0.875547i	$0.660501\pi$
$270$	2.21432	+	0.311108i	0.134759	+	0.0189334i
$271$	1.51114			0.0917951			0.0458975	−	0.998946i	$-0.485385\pi$
$271$	1.51114			0.0917951			0.0458975	+	0.998946i	$0.485385\pi$
$272$			3.80642i			0.230798i
$273$			25.7146i			1.55632i
$274$	7.53972			0.455491
$275$	12.6035	+	3.61285i	0.760018	+	0.217863i
$276$	2.62222			0.157839
$277$		−	1.05086i		−	0.0631398i	−0.999502	−	0.0315699i	$-0.989949\pi$
$277$		−	1.05086i		−	0.0631398i	0.999502	−	0.0315699i	$-0.0100507\pi$
$278$			0.387152i			0.0232199i
$279$	4.42864			0.265136
$280$	−9.80642	−	1.37778i	−0.586046	−	0.0823384i
$281$	3.45091			0.205864			0.102932	−	0.994688i	$-0.467178\pi$
$281$	3.45091			0.205864			0.102932	+	0.994688i	$0.467178\pi$
$282$			2.62222i			0.156151i
$283$			15.5812i			0.926206i	0.886304	+	0.463103i	$0.153264\pi$
$283$			15.5812i			0.926206i	−0.886304	+	0.463103i	$0.846736\pi$
$284$	−15.6128			−0.926452
$285$	−0.311108	+	2.21432i	−0.0184284	+	0.131165i
$286$	15.2257			0.900314
$287$			25.1240i			1.48302i
$288$			1.00000i			0.0589256i
$289$	2.51114			0.147714
$290$	−1.05086	+	7.47949i	−0.0617083	+	0.439211i
$291$	−7.37778			−0.432493
$292$		−	11.6128i		−	0.679591i
$293$			7.12399i			0.416188i	0.978109	+	0.208094i	$0.0667259\pi$
$293$			7.12399i			0.416188i	−0.978109	+	0.208094i	$0.933274\pi$
$294$	12.6128			0.735596
$295$	2.32693	+	0.326929i	0.135479	+	0.0190346i
$296$	5.80642			0.337492
$297$			2.62222i			0.152156i
$298$		−	14.5303i		−	0.841721i
$299$	15.2257			0.880525
$300$	−1.37778	+	4.80642i	−0.0795464	+	0.277499i
$301$	48.6735			2.80550
$302$		−	4.69535i		−	0.270187i
$303$		−	17.6731i		−	1.01529i
$304$	−1.00000			−0.0573539
$305$	10.5303	+	1.47949i	0.602966	+	0.0847156i
$306$	−3.80642			−0.217599
$307$		−	1.12399i		−	0.0641492i	−0.999485	−	0.0320746i	$-0.989789\pi$
$307$		−	1.12399i		−	0.0641492i	0.999485	−	0.0320746i	$-0.0102114\pi$
$308$		−	11.6128i		−	0.661703i
$309$	−1.18421			−0.0673673
$310$	−1.37778	+	9.80642i	−0.0782529	+	0.556967i
$311$	14.9491			0.847688			0.423844	−	0.905735i	$-0.360680\pi$
$311$	14.9491			0.847688			0.423844	+	0.905735i	$0.360680\pi$
$312$			5.80642i			0.328724i
$313$			3.14272i			0.177637i	0.996048	+	0.0888185i	$0.0283091\pi$
$313$			3.14272i			0.177637i	−0.996048	+	0.0888185i	$0.971691\pi$
$314$	21.5210			1.21450
$315$	1.37778	−	9.80642i	0.0776294	−	0.552529i
$316$	4.42864			0.249130
$317$		−	10.5906i		−	0.594826i	−0.954749	−	0.297413i	$-0.903876\pi$
$317$		−	10.5906i		−	0.594826i	0.954749	−	0.297413i	$-0.0961238\pi$
$318$			6.00000i			0.336463i
$319$	−8.85728			−0.495912
$320$	−2.21432	−	0.311108i	−0.123784	−	0.0173915i
$321$	−4.85728			−0.271107
$322$		−	11.6128i		−	0.647159i
$323$		−	3.80642i		−	0.211795i
$324$	−1.00000			−0.0555556
$325$	−8.00000	+	27.9081i	−0.443760	+	1.54806i
$326$	−8.23506			−0.456098
$327$		−	6.04149i		−	0.334095i
$328$			5.67307i			0.313243i
$329$	11.6128			0.640237
$330$	−5.80642	−	0.815792i	−0.319633	−	0.0449079i
$331$	−15.1427			−0.832319			−0.416160	−	0.909292i	$-0.636624\pi$
$331$	−15.1427			−0.832319			−0.416160	+	0.909292i	$0.636624\pi$
$332$		−	11.9081i		−	0.653544i
$333$			5.80642i			0.318190i
$334$	−8.47013			−0.463465
$335$	4.85728	−	34.5718i	0.265381	−	1.88886i
$336$	4.42864			0.241602
$337$		−	11.1111i		−	0.605259i	−0.953108	−	0.302629i	$-0.902136\pi$
$337$		−	11.1111i		−	0.605259i	0.953108	−	0.302629i	$-0.0978645\pi$
$338$			20.7146i			1.12672i
$339$	9.34614			0.507613
$340$	1.18421	−	8.42864i	0.0642227	−	0.457107i
$341$	−11.6128			−0.628871
$342$		−	1.00000i		−	0.0540738i
$343$		−	24.8573i		−	1.34217i
$344$	10.9906			0.592575
$345$	−5.80642	−	0.815792i	−0.312607	−	0.0439208i
$346$	−22.4701			−1.20800
$347$			14.1936i			0.761951i	0.924585	+	0.380976i	$0.124412\pi$
$347$			14.1936i			0.761951i	−0.924585	+	0.380976i	$0.875588\pi$
$348$		−	3.37778i		−	0.181068i
$349$	−32.3684			−1.73264			−0.866321	−	0.499488i	$-0.833521\pi$
$349$	−32.3684			−1.73264			−0.866321	+	0.499488i	$0.833521\pi$
$350$	21.2859	+	6.10171i	1.13778	+	0.326150i
$351$	−5.80642			−0.309924
$352$		−	2.62222i		−	0.139765i
$353$		−	11.8064i		−	0.628393i	−0.949358	−	0.314196i	$-0.898265\pi$
$353$		−	11.8064i		−	0.628393i	0.949358	−	0.314196i	$-0.101735\pi$
$354$	−1.05086			−0.0558523
$355$	34.5718	+	4.85728i	1.83488	+	0.257798i
$356$	12.4286			0.658717
$357$			16.8573i			0.892182i
$358$		−	2.94914i		−	0.155867i
$359$	10.8287			0.571517			0.285758	−	0.958302i	$-0.407755\pi$
$359$	10.8287			0.571517			0.285758	+	0.958302i	$0.407755\pi$
$360$	0.311108	−	2.21432i	0.0163968	−	0.116705i
$361$	1.00000			0.0526316
$362$		−	22.8988i		−	1.20353i
$363$			4.12399i			0.216453i
$364$	25.7146			1.34781
$365$	−3.61285	+	25.7146i	−0.189105	+	1.34596i
$366$	−4.75557			−0.248578
$367$			1.46965i			0.0767151i	0.999264	+	0.0383576i	$0.0122126\pi$
$367$			1.46965i			0.0767151i	−0.999264	+	0.0383576i	$0.987787\pi$
$368$		−	2.62222i		−	0.136692i
$369$	−5.67307			−0.295328
$370$	−12.8573	−	1.80642i	−0.668418	−	0.0939115i
$371$	26.5718			1.37954
$372$		−	4.42864i		−	0.229614i
$373$			24.3783i			1.26226i	0.775678	+	0.631129i	$0.217408\pi$
$373$			24.3783i			1.26226i	−0.775678	+	0.631129i	$0.782592\pi$
$374$	9.98126			0.516119
$375$	4.54617	−	10.2143i	0.234763	−	0.527465i
$376$	2.62222			0.135230
$377$		−	19.6128i		−	1.01011i
$378$			4.42864i			0.227785i
$379$	−18.9590			−0.973858			−0.486929	−	0.873442i	$-0.661883\pi$
$379$	−18.9590			−0.973858			−0.486929	+	0.873442i	$0.661883\pi$
$380$	2.21432	+	0.311108i	0.113592	+	0.0159595i
$381$	−6.42864			−0.329349
$382$			9.05086i			0.463082i
$383$		−	26.1017i		−	1.33374i	−0.745176	−	0.666868i	$-0.767635\pi$
$383$		−	26.1017i		−	1.33374i	0.745176	−	0.666868i	$-0.232365\pi$
$384$	1.00000			0.0510310
$385$	−3.61285	+	25.7146i	−0.184128	+	1.31054i
$386$	18.7239			0.953023
$387$			10.9906i			0.558685i
$388$			7.37778i			0.374550i
$389$	3.57136			0.181075			0.0905376	−	0.995893i	$-0.471141\pi$
$389$	3.57136			0.181075			0.0905376	+	0.995893i	$0.471141\pi$
$390$	1.80642	−	12.8573i	0.0914718	−	0.651054i
$391$	9.98126			0.504774
$392$		−	12.6128i		−	0.637045i
$393$			15.0923i			0.761308i
$394$	−0.888922			−0.0447832
$395$	−9.80642	−	1.37778i	−0.493415	−	0.0693239i
$396$	2.62222			0.131771
$397$		−	31.4193i		−	1.57689i	−0.615107	−	0.788444i	$-0.710887\pi$
$397$		−	31.4193i		−	1.57689i	0.615107	−	0.788444i	$-0.289113\pi$
$398$			21.7146i			1.08845i
$399$	−4.42864			−0.221709
$400$	4.80642	+	1.37778i	0.240321	+	0.0688892i
$401$	12.0415			0.601323			0.300662	−	0.953731i	$-0.402793\pi$
$401$	12.0415			0.601323			0.300662	+	0.953731i	$0.402793\pi$
$402$			15.6128i			0.778698i
$403$		−	25.7146i		−	1.28093i
$404$	−17.6731			−0.879268
$405$	2.21432	+	0.311108i	0.110030	+	0.0154591i
$406$	−14.9590			−0.742402
$407$		−	15.2257i		−	0.754710i
$408$			3.80642i			0.188446i
$409$	−26.4701			−1.30886			−0.654432	−	0.756121i	$-0.727092\pi$
$409$	−26.4701			−1.30886			−0.654432	+	0.756121i	$0.727092\pi$
$410$	1.76494	−	12.5620i	0.0871640	−	0.620393i
$411$	7.53972			0.371907
$412$			1.18421i			0.0583418i
$413$			4.65386i			0.229001i
$414$	2.62222			0.128875
$415$	−3.70471	+	26.3684i	−0.181857	+	1.29437i
$416$	5.80642			0.284683
$417$			0.387152i			0.0189589i
$418$			2.62222i			0.128257i
$419$	25.9684			1.26864			0.634319	−	0.773072i	$-0.281281\pi$
$419$	25.9684			1.26864			0.634319	+	0.773072i	$0.281281\pi$
$420$	−9.80642	−	1.37778i	−0.478504	−	0.0672290i
$421$	−29.2672			−1.42640			−0.713198	−	0.700963i	$-0.752754\pi$
$421$	−29.2672			−1.42640			−0.713198	+	0.700963i	$0.752754\pi$
$422$			3.61285i			0.175871i
$423$			2.62222i			0.127496i
$424$	6.00000			0.291386
$425$	−5.24443	+	18.2953i	−0.254392	+	0.887452i
$426$	−15.6128			−0.756445
$427$			21.0607i			1.01920i
$428$			4.85728i			0.234785i
$429$	15.2257			0.735104
$430$	−24.3368	−	3.41927i	−1.17362	−	0.164892i
$431$	14.8385			0.714747			0.357374	−	0.933961i	$-0.383672\pi$
$431$	14.8385			0.714747			0.357374	+	0.933961i	$0.383672\pi$
$432$			1.00000i			0.0481125i
$433$		−	5.27607i		−	0.253552i	−0.991931	−	0.126776i	$-0.959537\pi$
$433$		−	5.27607i		−	0.253552i	0.991931	−	0.126776i	$-0.0404629\pi$
$434$	−19.6128			−0.941447
$435$	−1.05086	+	7.47949i	−0.0503846	+	0.358614i
$436$	−6.04149			−0.289335
$437$			2.62222i			0.125438i
$438$		−	11.6128i		−	0.554883i
$439$	−31.8578			−1.52049			−0.760244	−	0.649638i	$-0.774921\pi$
$439$	−31.8578			−1.52049			−0.760244	+	0.649638i	$0.774921\pi$
$440$	−0.815792	+	5.80642i	−0.0388913	+	0.276810i
$441$	12.6128			0.600612
$442$			22.1017i			1.05127i
$443$		−	4.94914i		−	0.235141i	−0.993065	−	0.117570i	$-0.962489\pi$
$443$		−	4.94914i		−	0.235141i	0.993065	−	0.117570i	$-0.0375106\pi$
$444$	5.80642			0.275561
$445$	−27.5210	−	3.86665i	−1.30462	−	0.183297i
$446$	−21.3876			−1.01273
$447$		−	14.5303i		−	0.687262i
$448$		−	4.42864i		−	0.209234i
$449$	−9.75605			−0.460416			−0.230208	−	0.973141i	$-0.573941\pi$
$449$	−9.75605			−0.460416			−0.230208	+	0.973141i	$0.573941\pi$
$450$	−1.37778	+	4.80642i	−0.0649494	+	0.226577i
$451$	14.8760			0.700484
$452$		−	9.34614i		−	0.439606i
$453$		−	4.69535i		−	0.220607i
$454$	−8.47013			−0.397523
$455$	−56.9403	−	8.00000i	−2.66940	−	0.375046i
$456$	−1.00000			−0.0468293
$457$		−	8.00000i		−	0.374224i	−0.982339	−	0.187112i	$-0.940087\pi$
$457$		−	8.00000i		−	0.374224i	0.982339	−	0.187112i	$-0.0599128\pi$
$458$		−	16.9590i		−	0.792442i
$459$	−3.80642			−0.177669
$460$	−0.815792	+	5.80642i	−0.0380365	+	0.270726i
$461$	−36.1245			−1.68248			−0.841242	−	0.540659i	$-0.818175\pi$
$461$	−36.1245			−1.68248			−0.841242	+	0.540659i	$0.818175\pi$
$462$		−	11.6128i		−	0.540279i
$463$			35.1209i			1.63221i	0.577905	+	0.816104i	$0.303870\pi$
$463$			35.1209i			1.63221i	−0.577905	+	0.816104i	$0.696130\pi$
$464$	−3.37778			−0.156810
$465$	−1.37778	+	9.80642i	−0.0638932	+	0.454762i
$466$	−17.9081			−0.829578
$467$			4.56199i			0.211104i	0.994414	+	0.105552i	$0.0336609\pi$
$467$			4.56199i			0.211104i	−0.994414	+	0.105552i	$0.966339\pi$
$468$			5.80642i			0.268402i
$469$	69.1437			3.19276
$470$	−5.80642	−	0.815792i	−0.267830	−	0.0376297i
$471$	21.5210			0.991634
$472$			1.05086i			0.0483695i
$473$		−	28.8198i		−	1.32514i
$474$	4.42864			0.203414
$475$	−4.80642	−	1.37778i	−0.220534	−	0.0632171i
$476$	16.8573			0.772652
$477$			6.00000i			0.274721i
$478$		−	28.2766i		−	1.29334i
$479$	−37.4005			−1.70887			−0.854437	−	0.519555i	$-0.826098\pi$
$479$	−37.4005			−1.70887			−0.854437	+	0.519555i	$0.826098\pi$
$480$	−2.21432	−	0.311108i	−0.101069	−	0.0142001i
$481$	33.7146			1.53725
$482$			11.5111i			0.524318i
$483$		−	11.6128i		−	0.528403i
$484$	4.12399			0.187454
$485$	2.29529	−	16.3368i	0.104224	−	0.741815i
$486$	−1.00000			−0.0453609
$487$			20.9175i			0.947862i	0.880562	+	0.473931i	$0.157165\pi$
$487$			20.9175i			0.947862i	−0.880562	+	0.473931i	$0.842835\pi$
$488$			4.75557i			0.215274i
$489$	−8.23506			−0.372402
$490$	−3.92396	+	27.9289i	−0.177266	+	1.26170i
$491$	−15.8666			−0.716052			−0.358026	−	0.933712i	$-0.616550\pi$
$491$	−15.8666			−0.716052			−0.358026	+	0.933712i	$0.616550\pi$
$492$			5.67307i			0.255762i
$493$		−	12.8573i		−	0.579063i
$494$	−5.80642			−0.261243
$495$	−5.80642	−	0.815792i	−0.260979	−	0.0366671i
$496$	−4.42864			−0.198852
$497$			69.1437i			3.10152i
$498$		−	11.9081i		−	0.533616i
$499$	−16.7368			−0.749244			−0.374622	−	0.927178i	$-0.622227\pi$
$499$	−16.7368			−0.749244			−0.374622	+	0.927178i	$0.622227\pi$
$500$	−10.2143	−	4.54617i	−0.456798	−	0.203311i
$501$	−8.47013			−0.378417
$502$			7.74620i			0.345730i
$503$			21.9684i			0.979521i	0.871857	+	0.489760i	$0.162916\pi$
$503$			21.9684i			0.979521i	−0.871857	+	0.489760i	$0.837084\pi$
$504$	4.42864			0.197267
$505$	39.1338	+	5.49823i	1.74143	+	0.244668i
$506$	−6.87601			−0.305676
$507$			20.7146i			0.919966i
$508$			6.42864i			0.285225i
$509$	15.2573			0.676270			0.338135	−	0.941098i	$-0.390204\pi$
$509$	15.2573			0.676270			0.338135	+	0.941098i	$0.390204\pi$
$510$	1.18421	−	8.42864i	0.0524376	−	0.373226i
$511$	−51.4291			−2.27509
$512$		−	1.00000i		−	0.0441942i
$513$		−	1.00000i		−	0.0441511i
$514$	13.8796			0.612201
$515$	0.368416	−	2.62222i	0.0162344	−	0.115549i
$516$	10.9906			0.483836
$517$		−	6.87601i		−	0.302407i
$518$		−	25.7146i		−	1.12983i
$519$	−22.4701			−0.986329
$520$	−12.8573	−	1.80642i	−0.563829	−	0.0792169i
$521$	−18.3269			−0.802917			−0.401459	−	0.915877i	$-0.631497\pi$
$521$	−18.3269			−0.802917			−0.401459	+	0.915877i	$0.631497\pi$
$522$		−	3.37778i		−	0.147842i
$523$			24.8573i			1.08693i	0.839431	+	0.543466i	$0.182888\pi$
$523$			24.8573i			1.08693i	−0.839431	+	0.543466i	$0.817112\pi$
$524$	15.0923			0.659312
$525$	21.2859	+	6.10171i	0.928994	+	0.266300i
$526$	−18.6222			−0.811967
$527$		−	16.8573i		−	0.734315i
$528$		−	2.62222i		−	0.114117i
$529$	16.1240			0.701043
$530$	−13.2859	−	1.86665i	−0.577103	−	0.0810820i
$531$	−1.05086			−0.0456032
$532$			4.42864i			0.192006i
$533$			32.9403i			1.42680i
$534$	12.4286			0.537840
$535$	1.51114	−	10.7556i	0.0653322	−	0.465004i
$536$	15.6128			0.674372
$537$		−	2.94914i		−	0.127265i
$538$			15.8479i			0.683252i
$539$	−33.0736			−1.42458
$540$	0.311108	−	2.21432i	0.0133879	−	0.0952891i
$541$	−1.34614			−0.0578751			−0.0289376	−	0.999581i	$-0.509212\pi$
$541$	−1.34614			−0.0578751			−0.0289376	+	0.999581i	$0.509212\pi$
$542$		−	1.51114i		−	0.0649089i
$543$		−	22.8988i		−	0.982680i
$544$	3.80642			0.163199
$545$	13.3778	+	1.87955i	0.573041	+	0.0805112i
$546$	25.7146			1.10048
$547$			8.59057i			0.367306i	0.982991	+	0.183653i	$0.0587923\pi$
$547$			8.59057i			0.367306i	−0.982991	+	0.183653i	$0.941208\pi$
$548$		−	7.53972i		−	0.322081i
$549$	−4.75557			−0.202963
$550$	3.61285	−	12.6035i	0.154052	−	0.537414i
$551$	3.37778			0.143898
$552$		−	2.62222i		−	0.111609i
$553$		−	19.6128i		−	0.834023i
$554$	−1.05086			−0.0446466
$555$	−12.8573	−	1.80642i	−0.545761	−	0.0766784i
$556$	0.387152			0.0164189
$557$			5.86665i			0.248578i	0.992246	+	0.124289i	$0.0396650\pi$
$557$			5.86665i			0.248578i	−0.992246	+	0.124289i	$0.960335\pi$
$558$		−	4.42864i		−	0.187479i
$559$	63.8163			2.69914
$560$	−1.37778	+	9.80642i	−0.0582220	+	0.414397i
$561$	9.98126			0.421409
$562$		−	3.45091i		−	0.145568i
$563$			31.4291i			1.32458i	0.749248	+	0.662290i	$0.230415\pi$
$563$			31.4291i			1.32458i	−0.749248	+	0.662290i	$0.769585\pi$
$564$	2.62222			0.110415
$565$	−2.90766	+	20.6953i	−0.122326	+	0.870660i
$566$	15.5812			0.654927
$567$			4.42864i			0.185985i
$568$			15.6128i			0.655101i
$569$	7.95851			0.333638			0.166819	−	0.985988i	$-0.446650\pi$
$569$	7.95851			0.333638			0.166819	+	0.985988i	$0.446650\pi$
$570$	2.21432	+	0.311108i	0.0927476	+	0.0130309i
$571$	−30.8385			−1.29055			−0.645276	−	0.763949i	$-0.723258\pi$
$571$	−30.8385			−1.29055			−0.645276	+	0.763949i	$0.723258\pi$
$572$		−	15.2257i		−	0.636618i
$573$			9.05086i			0.378105i
$574$	25.1240			1.04865
$575$	3.61285	−	12.6035i	0.150666	−	0.525601i
$576$	1.00000			0.0416667
$577$		−	32.0000i		−	1.33218i	−0.745873	−	0.666089i	$-0.767967\pi$
$577$		−	32.0000i		−	1.33218i	0.745873	−	0.666089i	$-0.232033\pi$
$578$		−	2.51114i		−	0.104450i
$579$	18.7239			0.778140
$580$	7.47949	+	1.05086i	0.310569	+	0.0436344i
$581$	−52.7368			−2.18789
$582$			7.37778i			0.305819i
$583$		−	15.7333i		−	0.651606i
$584$	−11.6128			−0.480543
$585$	1.80642	−	12.8573i	0.0746864	−	0.531583i
$586$	7.12399			0.294289
$587$		−	17.8064i		−	0.734950i	−0.930033	−	0.367475i	$-0.880222\pi$
$587$		−	17.8064i		−	0.734950i	0.930033	−	0.367475i	$-0.119778\pi$
$588$		−	12.6128i		−	0.520145i
$589$	4.42864			0.182479
$590$	0.326929	−	2.32693i	0.0134595	−	0.0957982i
$591$	−0.888922			−0.0365654
$592$		−	5.80642i		−	0.238643i
$593$		−	13.3176i		−	0.546887i	−0.961888	−	0.273443i	$-0.911837\pi$
$593$		−	13.3176i		−	0.546887i	0.961888	−	0.273443i	$-0.0881626\pi$
$594$	2.62222			0.107591
$595$	−37.3274	−	5.24443i	−1.53027	−	0.215001i
$596$	−14.5303			−0.595186
$597$			21.7146i			0.888718i
$598$		−	15.2257i		−	0.622625i
$599$	43.8163			1.79028			0.895142	−	0.445781i	$-0.147074\pi$
$599$	43.8163			1.79028			0.895142	+	0.445781i	$0.147074\pi$
$600$	4.80642	+	1.37778i	0.196221	+	0.0562478i
$601$	−9.73329			−0.397029			−0.198515	−	0.980098i	$-0.563612\pi$
$601$	−9.73329			−0.397029			−0.198515	+	0.980098i	$0.563612\pi$
$602$		−	48.6735i		−	1.98379i
$603$			15.6128i			0.635804i
$604$	−4.69535			−0.191051
$605$	−9.13182	−	1.28300i	−0.371261	−	0.0521615i
$606$	−17.6731			−0.717919
$607$			31.9398i			1.29640i	0.761472	+	0.648198i	$0.224477\pi$
$607$			31.9398i			1.29640i	−0.761472	+	0.648198i	$0.775523\pi$
$608$			1.00000i			0.0405554i
$609$	−14.9590			−0.606169
$610$	1.47949	−	10.5303i	0.0599030	−	0.426361i
$611$	15.2257			0.615966
$612$			3.80642i			0.153866i
$613$			11.8064i			0.476857i	0.971160	+	0.238428i	$0.0766323\pi$
$613$			11.8064i			0.476857i	−0.971160	+	0.238428i	$0.923368\pi$
$614$	−1.12399			−0.0453603
$615$	1.76494	−	12.5620i	0.0711691	−	0.506548i
$616$	−11.6128			−0.467895
$617$		−	26.5620i		−	1.06935i	−0.845059	−	0.534673i	$-0.820435\pi$
$617$		−	26.5620i		−	1.06935i	0.845059	−	0.534673i	$-0.179565\pi$
$618$			1.18421i			0.0476358i
$619$	−7.34614			−0.295266			−0.147633	−	0.989042i	$-0.547166\pi$
$619$	−7.34614			−0.295266			−0.147633	+	0.989042i	$0.547166\pi$
$620$	9.80642	+	1.37778i	0.393835	+	0.0553332i
$621$	2.62222			0.105226
$622$		−	14.9491i		−	0.599406i
$623$		−	55.0420i		−	2.20521i
$624$	5.80642			0.232443
$625$	21.2034	+	13.2444i	0.848137	+	0.529777i
$626$	3.14272			0.125608
$627$			2.62222i			0.104721i
$628$		−	21.5210i		−	0.858781i
$629$	22.1017			0.881253
$630$	−9.80642	−	1.37778i	−0.390697	−	0.0548922i
$631$	−30.7556			−1.22436			−0.612180	−	0.790718i	$-0.709707\pi$
$631$	−30.7556			−1.22436			−0.612180	+	0.790718i	$0.709707\pi$
$632$		−	4.42864i		−	0.176162i
$633$			3.61285i			0.143598i
$634$	−10.5906			−0.420605
$635$	2.00000	−	14.2351i	0.0793676	−	0.564901i
$636$	6.00000			0.237915
$637$		−	73.2355i		−	2.90170i
$638$			8.85728i			0.350663i
$639$	−15.6128			−0.617635
$640$	−0.311108	+	2.21432i	−0.0122976	+	0.0875287i
$641$	−39.3876			−1.55572			−0.777859	−	0.628439i	$-0.783694\pi$
$641$	−39.3876			−1.55572			−0.777859	+	0.628439i	$0.783694\pi$
$642$			4.85728i			0.191702i
$643$			24.1146i			0.950988i	0.879719	+	0.475494i	$0.157731\pi$
$643$			24.1146i			0.950988i	−0.879719	+	0.475494i	$0.842269\pi$
$644$	−11.6128			−0.457610
$645$	−24.3368	−	3.41927i	−0.958260	−	0.134634i
$646$	−3.80642			−0.149762
$647$			47.6829i			1.87461i	0.348512	+	0.937304i	$0.386687\pi$
$647$			47.6829i			1.87461i	−0.348512	+	0.937304i	$0.613313\pi$
$648$			1.00000i			0.0392837i
$649$	2.75557			0.108166
$650$	27.9081	+	8.00000i	1.09465	+	0.313786i
$651$	−19.6128			−0.768688
$652$			8.23506i			0.322510i
$653$			21.7462i			0.850995i	0.904960	+	0.425497i	$0.139901\pi$
$653$			21.7462i			0.850995i	−0.904960	+	0.425497i	$0.860099\pi$
$654$	−6.04149			−0.236241
$655$	−33.4193	−	4.69535i	−1.30580	−	0.183462i
$656$	5.67307			0.221496
$657$		−	11.6128i		−	0.453060i
$658$		−	11.6128i		−	0.452716i
$659$	16.1936			0.630812			0.315406	−	0.948957i	$-0.397859\pi$
$659$	16.1936			0.630812			0.315406	+	0.948957i	$0.397859\pi$
$660$	−0.815792	+	5.80642i	−0.0317547	+	0.226015i
$661$	−22.5116			−0.875600			−0.437800	−	0.899072i	$-0.644242\pi$
$661$	−22.5116			−0.875600			−0.437800	+	0.899072i	$0.644242\pi$
$662$			15.1427i			0.588539i
$663$			22.1017i			0.858359i
$664$	−11.9081			−0.462125
$665$	1.37778	−	9.80642i	0.0534282	−	0.380277i
$666$	5.80642			0.224994
$667$			8.85728i			0.342955i
$668$			8.47013i			0.327719i
$669$	−21.3876			−0.826893
$670$	−34.5718	−	4.85728i	−1.33563	−	0.187653i
$671$	12.4701			0.481404
$672$		−	4.42864i		−	0.170838i
$673$			9.66323i			0.372490i	0.982503	+	0.186245i	$0.0596318\pi$
$673$			9.66323i			0.372490i	−0.982503	+	0.186245i	$0.940368\pi$
$674$	−11.1111			−0.427983
$675$	−1.37778	+	4.80642i	−0.0530309	+	0.184999i
$676$	20.7146			0.796714
$677$			6.85728i			0.263547i	0.991280	+	0.131773i	$0.0420671\pi$
$677$			6.85728i			0.263547i	−0.991280	+	0.131773i	$0.957933\pi$
$678$		−	9.34614i		−	0.358936i
$679$	32.6735			1.25390
$680$	−8.42864	−	1.18421i	−0.323224	−	0.0454123i
$681$	−8.47013			−0.324576
$682$			11.6128i			0.444679i
$683$			30.3051i			1.15959i	0.814761	+	0.579797i	$0.196868\pi$
$683$			30.3051i			1.15959i	−0.814761	+	0.579797i	$0.803132\pi$
$684$	−1.00000			−0.0382360
$685$	−2.34567	+	16.6953i	−0.0896233	+	0.637896i
$686$	−24.8573			−0.949055
$687$		−	16.9590i		−	0.647026i
$688$		−	10.9906i		−	0.419014i
$689$	34.8385			1.32724
$690$	−0.815792	+	5.80642i	−0.0310567	+	0.221047i
$691$	7.61285			0.289606			0.144803	−	0.989460i	$-0.453745\pi$
$691$	7.61285			0.289606			0.144803	+	0.989460i	$0.453745\pi$
$692$			22.4701i			0.854186i
$693$		−	11.6128i		−	0.441136i
$694$	14.1936			0.538781
$695$	−0.857279	−	0.120446i	−0.0325184	−	0.00456878i
$696$	−3.37778			−0.128035
$697$			21.5941i			0.817935i
$698$			32.3684i			1.22516i
$699$	−17.9081			−0.677348
$700$	6.10171	−	21.2859i	0.230623	−	0.804532i
$701$	−32.3654			−1.22242			−0.611211	−	0.791467i	$-0.709317\pi$
$701$	−32.3654			−1.22242			−0.611211	+	0.791467i	$0.709317\pi$
$702$			5.80642i			0.219149i
$703$			5.80642i			0.218993i
$704$	−2.62222			−0.0988285
$705$	−5.80642	−	0.815792i	−0.218683	−	0.0307245i
$706$	−11.8064			−0.444341
$707$			78.2677i			2.94356i
$708$			1.05086i			0.0394936i
$709$	49.8992			1.87401			0.937003	−	0.349322i	$-0.113588\pi$
$709$	49.8992			1.87401			0.937003	+	0.349322i	$0.113588\pi$
$710$	4.85728	−	34.5718i	0.182290	−	1.29746i
$711$	4.42864			0.166087
$712$		−	12.4286i		−	0.465783i
$713$			11.6128i			0.434905i
$714$	16.8573			0.630868
$715$	−4.73683	+	33.7146i	−0.177148	+	1.26085i
$716$	−2.94914			−0.110215
$717$		−	28.2766i		−	1.05601i
$718$		−	10.8287i		−	0.404123i
$719$	26.4415			0.986103			0.493052	−	0.870000i	$-0.335881\pi$
$719$	26.4415			0.986103			0.493052	+	0.870000i	$0.335881\pi$
$720$	−2.21432	−	0.311108i	−0.0825228	−	0.0115943i
$721$	5.24443			0.195313
$722$		−	1.00000i		−	0.0372161i
$723$			11.5111i			0.428104i
$724$	−22.8988			−0.851026
$725$	−16.2351	−	4.65386i	−0.602955	−	0.172840i
$726$	4.12399			0.153055
$727$		−	48.1245i		−	1.78484i	−0.451208	−	0.892419i	$-0.649007\pi$
$727$		−	48.1245i		−	1.78484i	0.451208	−	0.892419i	$-0.350993\pi$
$728$		−	25.7146i		−	0.953045i
$729$	−1.00000			−0.0370370
$730$	25.7146	+	3.61285i	0.951738	+	0.133717i
$731$	41.8350			1.54732
$732$			4.75557i			0.175771i
$733$		−	14.0286i		−	0.518157i	−0.965856	−	0.259079i	$-0.916581\pi$
$733$		−	14.0286i		−	0.518157i	0.965856	−	0.259079i	$-0.0834189\pi$
$734$	1.46965			0.0542458
$735$	−3.92396	+	27.9289i	−0.144737	+	1.03017i
$736$	−2.62222			−0.0966562
$737$		−	40.9403i		−	1.50805i
$738$			5.67307i			0.208829i
$739$	−10.1847			−0.374650			−0.187325	−	0.982298i	$-0.559982\pi$
$739$	−10.1847			−0.374650			−0.187325	+	0.982298i	$0.559982\pi$
$740$	−1.80642	+	12.8573i	−0.0664055	+	0.472643i
$741$	−5.80642			−0.213304
$742$		−	26.5718i		−	0.975483i
$743$		−	42.9590i		−	1.57601i	−0.615667	−	0.788006i	$-0.711113\pi$
$743$		−	42.9590i		−	1.57601i	0.615667	−	0.788006i	$-0.288887\pi$
$744$	−4.42864			−0.162362
$745$	32.1748	+	4.52051i	1.17879	+	0.165619i
$746$	24.3783			0.892552
$747$		−	11.9081i		−	0.435696i
$748$		−	9.98126i		−	0.364951i
$749$	21.5111			0.786000
$750$	−10.2143	−	4.54617i	−0.372974	−	0.166003i
$751$	−7.18421			−0.262155			−0.131078	−	0.991372i	$-0.541844\pi$
$751$	−7.18421			−0.262155			−0.131078	+	0.991372i	$0.541844\pi$
$752$		−	2.62222i		−	0.0956224i
$753$			7.74620i			0.282287i
$754$	−19.6128			−0.714258
$755$	10.3970	+	1.46076i	0.378385	+	0.0531625i
$756$	4.42864			0.161068
$757$		−	41.2543i		−	1.49941i	−0.661771	−	0.749706i	$-0.730195\pi$
$757$		−	41.2543i		−	1.49941i	0.661771	−	0.749706i	$-0.269805\pi$
$758$			18.9590i			0.688621i
$759$	−6.87601			−0.249584
$760$	0.311108	−	2.21432i	0.0112851	−	0.0803218i
$761$	44.3051			1.60606			0.803030	−	0.595939i	$-0.203220\pi$
$761$	44.3051			1.60606			0.803030	+	0.595939i	$0.203220\pi$
$762$			6.42864i			0.232885i
$763$			26.7556i			0.968617i
$764$	9.05086			0.327448
$765$	1.18421	−	8.42864i	0.0428151	−	0.304738i
$766$	−26.1017			−0.943093
$767$			6.10171i			0.220320i
$768$		−	1.00000i		−	0.0360844i
$769$	6.59057			0.237662			0.118831	−	0.992914i	$-0.462085\pi$
$769$	6.59057			0.237662			0.118831	+	0.992914i	$0.462085\pi$
$770$	25.7146	+	3.61285i	0.926688	+	0.130198i
$771$	13.8796			0.499860
$772$		−	18.7239i		−	0.673889i
$773$		−	8.83854i		−	0.317900i	−0.987287	−	0.158950i	$-0.949189\pi$
$773$		−	8.83854i		−	0.317900i	0.987287	−	0.158950i	$-0.0508109\pi$
$774$	10.9906			0.395050
$775$	−21.2859	−	6.10171i	−0.764613	−	0.219180i
$776$	7.37778			0.264847
$777$		−	25.7146i		−	0.922505i
$778$		−	3.57136i		−	0.128039i
$779$	−5.67307			−0.203259
$780$	−12.8573	−	1.80642i	−0.460364	−	0.0646803i
$781$	40.9403			1.46496
$782$		−	9.98126i		−	0.356929i
$783$		−	3.37778i		−	0.120712i
$784$	−12.6128			−0.450459
$785$	−6.69535	+	47.6543i	−0.238967	+	1.70086i
$786$	15.0923			0.538326
$787$			16.9403i			0.603855i	0.953331	+	0.301927i	$0.0976300\pi$
$787$			16.9403i			0.603855i	−0.953331	+	0.301927i	$0.902370\pi$
$788$			0.888922i			0.0316665i
$789$	−18.6222			−0.662968
$790$	−1.37778	+	9.80642i	−0.0490194	+	0.348897i
$791$	−41.3907			−1.47168
$792$		−	2.62222i		−	0.0931764i
$793$			27.6128i			0.980561i
$794$	−31.4193			−1.11503
$795$	−13.2859	−	1.86665i	−0.471203	−	0.0662031i
$796$	21.7146			0.769652
$797$			40.1847i			1.42341i	0.702476	+	0.711707i	$0.252078\pi$
$797$			40.1847i			1.42341i	−0.702476	+	0.711707i	$0.747922\pi$
$798$			4.42864i			0.156772i
$799$	9.98126			0.353112
$800$	1.37778	−	4.80642i	0.0487120	−	0.169933i
$801$	12.4286			0.439144
$802$		−	12.0415i		−	0.425200i
$803$			30.4514i			1.07461i
$804$	15.6128			0.550623
$805$	25.7146	+	3.61285i	0.906319	+	0.127336i
$806$	−25.7146			−0.905757
$807$			15.8479i			0.557873i
$808$			17.6731i			0.621736i
$809$	−29.1052			−1.02329			−0.511643	−	0.859198i	$-0.670963\pi$
$809$	−29.1052			−1.02329			−0.511643	+	0.859198i	$0.670963\pi$
$810$	0.311108	−	2.21432i	0.0109312	−	0.0778033i
$811$	38.7753			1.36158			0.680792	−	0.732477i	$-0.261636\pi$
$811$	38.7753			1.36158			0.680792	+	0.732477i	$0.261636\pi$
$812$			14.9590i			0.524958i
$813$		−	1.51114i		−	0.0529979i
$814$	−15.2257			−0.533660
$815$	2.56199	−	18.2351i	0.0897427	−	0.638746i
$816$	3.80642			0.133251
$817$			10.9906i			0.384514i
$818$			26.4701i			0.925506i
$819$	25.7146			0.898539
$820$	−12.5620	−	1.76494i	−0.438684	−	0.0616343i
$821$	2.53035			0.0883098			0.0441549	−	0.999025i	$-0.485940\pi$
$821$	2.53035			0.0883098			0.0441549	+	0.999025i	$0.485940\pi$
$822$		−	7.53972i		−	0.262978i
$823$		−	24.0415i		−	0.838034i	−0.907978	−	0.419017i	$-0.862375\pi$
$823$		−	24.0415i		−	0.838034i	0.907978	−	0.419017i	$-0.137625\pi$
$824$	1.18421			0.0412538
$825$	3.61285	−	12.6035i	0.125783	−	0.438797i
$826$	4.65386			0.161928
$827$			6.57184i			0.228525i	0.993451	+	0.114263i	$0.0364505\pi$
$827$			6.57184i			0.228525i	−0.993451	+	0.114263i	$0.963549\pi$
$828$		−	2.62222i		−	0.0911283i
$829$	28.7338			0.997965			0.498983	−	0.866612i	$-0.333707\pi$
$829$	28.7338			0.997965			0.498983	+	0.866612i	$0.333707\pi$
$830$	26.3684	+	3.70471i	0.915261	+	0.128592i
$831$	−1.05086			−0.0364538
$832$		−	5.80642i		−	0.201302i
$833$		−	48.0098i		−	1.66344i
$834$	0.387152			0.0134060
$835$	2.63512	−	18.7556i	0.0911922	−	0.649063i
$836$	2.62222			0.0906912
$837$		−	4.42864i		−	0.153076i
$838$		−	25.9684i		−	0.897062i
$839$	50.5718			1.74593			0.872967	−	0.487780i	$-0.162193\pi$
$839$	50.5718			1.74593			0.872967	+	0.487780i	$0.162193\pi$
$840$	−1.37778	+	9.80642i	−0.0475381	+	0.338354i
$841$	−17.5906			−0.606571
$842$			29.2672i			1.00861i
$843$		−	3.45091i		−	0.118856i
$844$	3.61285			0.124359
$845$	−45.8687	−	6.44446i	−1.57793	−	0.221696i
$846$	2.62222			0.0901536
$847$		−	18.2636i		−	0.627546i
$848$		−	6.00000i		−	0.206041i
$849$	15.5812			0.534746
$850$	18.2953	+	5.24443i	0.627523	+	0.179883i
$851$	−15.2257			−0.521930
$852$			15.6128i			0.534887i
$853$		−	31.2355i		−	1.06948i	−0.845015	−	0.534742i	$-0.820409\pi$
$853$		−	31.2355i		−	1.06948i	0.845015	−	0.534742i	$-0.179591\pi$
$854$	21.0607			0.720682
$855$	2.21432	+	0.311108i	0.0757281	+	0.0106397i
$856$	4.85728			0.166018
$857$		−	27.3274i		−	0.933486i	−0.884393	−	0.466743i	$-0.845427\pi$
$857$		−	27.3274i		−	0.933486i	0.884393	−	0.466743i	$-0.154573\pi$
$858$		−	15.2257i		−	0.519797i
$859$	34.7753			1.18652			0.593258	−	0.805012i	$-0.297841\pi$
$859$	34.7753			1.18652			0.593258	+	0.805012i	$0.297841\pi$
$860$	−3.41927	+	24.3368i	−0.116596	+	0.829877i
$861$	25.1240			0.856223
$862$		−	14.8385i		−	0.505403i
$863$			21.2444i			0.723169i	0.932339	+	0.361584i	$0.117764\pi$
$863$			21.2444i			0.723169i	−0.932339	+	0.361584i	$0.882236\pi$
$864$	1.00000			0.0340207
$865$	6.99063	−	49.7560i	0.237689	−	1.69176i
$866$	−5.27607			−0.179288
$867$		−	2.51114i		−	0.0852827i
$868$			19.6128i			0.665703i
$869$	−11.6128			−0.393939
$870$	7.47949	+	1.05086i	0.253579	+	0.0356273i
$871$	90.6548			3.07172
$872$			6.04149i			0.204591i
$873$			7.37778i			0.249700i
$874$	2.62222			0.0886978
$875$	−20.1334	+	45.2355i	−0.680632	+	1.52924i
$876$	−11.6128			−0.392362
$877$		−	22.3970i		−	0.756293i	−0.925746	−	0.378146i	$-0.876562\pi$
$877$		−	22.3970i		−	0.756293i	0.925746	−	0.378146i	$-0.123438\pi$
$878$			31.8578i			1.07515i
$879$	7.12399			0.240286
$880$	5.80642	+	0.815792i	0.195735	+	0.0275003i
$881$	−20.3684			−0.686229			−0.343115	−	0.939294i	$-0.611482\pi$
$881$	−20.3684			−0.686229			−0.343115	+	0.939294i	$0.611482\pi$
$882$		−	12.6128i		−	0.424697i
$883$			21.6829i			0.729688i	0.931069	+	0.364844i	$0.118878\pi$
$883$			21.6829i			0.729688i	−0.931069	+	0.364844i	$0.881122\pi$
$884$	22.1017			0.743361
$885$	0.326929	−	2.32693i	0.0109896	−	0.0782189i
$886$	−4.94914			−0.166270
$887$			7.14272i			0.239829i	0.992784	+	0.119915i	$0.0382621\pi$
$887$			7.14272i			0.239829i	−0.992784	+	0.119915i	$0.961738\pi$
$888$		−	5.80642i		−	0.194851i
$889$	28.4701			0.954857
$890$	−3.86665	+	27.5210i	−0.129610	+	0.922505i
$891$	2.62222			0.0878475
$892$			21.3876i			0.716111i
$893$			2.62222i			0.0877491i
$894$	−14.5303			−0.485968
$895$	6.53035	+	0.917502i	0.218286	+	0.0306687i
$896$	−4.42864			−0.147950
$897$		−	15.2257i		−	0.508371i
$898$			9.75605i			0.325563i
$899$	14.9590			0.498910
$900$	4.80642	+	1.37778i	0.160214	+	0.0459261i
$901$	22.8385			0.760862
$902$		−	14.8760i		−	0.495317i
$903$		−	48.6735i		−	1.61975i
$904$	−9.34614			−0.310848
$905$	50.7052	+	7.12399i	1.68550	+	0.236809i
$906$	−4.69535			−0.155992
$907$		−	15.3461i		−	0.509560i	−0.966999	−	0.254780i	$-0.917997\pi$
$907$		−	15.3461i		−	0.509560i	0.966999	−	0.254780i	$-0.0820031\pi$
$908$			8.47013i			0.281091i
$909$	−17.6731			−0.586179
$910$	−8.00000	+	56.9403i	−0.265197	+	1.88755i
$911$	12.1204			0.401568			0.200784	−	0.979636i	$-0.435651\pi$
$911$	12.1204			0.401568			0.200784	+	0.979636i	$0.435651\pi$
$912$			1.00000i			0.0331133i
$913$			31.2257i			1.03342i
$914$	−8.00000			−0.264616
$915$	1.47949	−	10.5303i	0.0489106	−	0.348123i
$916$	−16.9590			−0.560341
$917$		−	66.8385i		−	2.20720i
$918$			3.80642i			0.125631i
$919$	12.2667			0.404641			0.202321	−	0.979319i	$-0.435152\pi$
$919$	12.2667			0.404641			0.202321	+	0.979319i	$0.435152\pi$
$920$	5.80642	+	0.815792i	0.191432	+	0.0268959i
$921$	−1.12399			−0.0370366
$922$			36.1245i			1.18970i
$923$			90.6548i			2.98394i
$924$	−11.6128			−0.382035
$925$	8.00000	−	27.9081i	0.263038	−	0.917614i
$926$	35.1209			1.15415
$927$			1.18421i			0.0388945i
$928$			3.37778i			0.110881i
$929$	40.1847			1.31842			0.659208	−	0.751960i	$-0.270892\pi$
$929$	40.1847			1.31842			0.659208	+	0.751960i	$0.270892\pi$
$930$	9.80642	+	1.37778i	0.321565	+	0.0451793i
$931$	12.6128			0.413369
$932$			17.9081i			0.586600i
$933$		−	14.9491i		−	0.489413i
$934$	4.56199			0.149273
$935$	−3.10525	+	22.1017i	−0.101553	+	0.722803i
$936$	5.80642			0.189789
$937$			24.7368i			0.808117i	0.914733	+	0.404059i	$0.132401\pi$
$937$			24.7368i			0.808117i	−0.914733	+	0.404059i	$0.867599\pi$
$938$		−	69.1437i		−	2.25762i
$939$	3.14272			0.102559
$940$	−0.815792	+	5.80642i	−0.0266082	+	0.189385i
$941$	−1.66323			−0.0542196			−0.0271098	−	0.999632i	$-0.508630\pi$
$941$	−1.66323			−0.0542196			−0.0271098	+	0.999632i	$0.508630\pi$
$942$		−	21.5210i		−	0.701191i
$943$		−	14.8760i		−	0.484430i
$944$	1.05086			0.0342024
$945$	−9.80642	−	1.37778i	−0.319003	−	0.0448193i
$946$	−28.8198			−0.937013
$947$		−	14.8671i		−	0.483117i	−0.970386	−	0.241558i	$-0.922341\pi$
$947$		−	14.8671i		−	0.483117i	0.970386	−	0.241558i	$-0.0776585\pi$
$948$		−	4.42864i		−	0.143836i
$949$	−67.4291			−2.18884
$950$	−1.37778	+	4.80642i	−0.0447012	+	0.155941i
$951$	−10.5906			−0.343423
$952$		−	16.8573i		−	0.546348i
$953$		−	8.83854i		−	0.286308i	−0.989700	−	0.143154i	$-0.954275\pi$
$953$		−	8.83854i		−	0.286308i	0.989700	−	0.143154i	$-0.0457245\pi$
$954$	6.00000			0.194257
$955$	−20.0415	−	2.81579i	−0.648527	−	0.0911169i
$956$	−28.2766			−0.914529
$957$			8.85728i			0.286315i
$958$			37.4005i			1.20836i
$959$	−33.3907			−1.07824
$960$	−0.311108	+	2.21432i	−0.0100410	+	0.0714669i
$961$	−11.3872			−0.367327
$962$		−	33.7146i		−	1.08700i
$963$			4.85728i			0.156524i
$964$	11.5111			0.370749
$965$	−5.82516	+	41.4608i	−0.187519	+	1.33467i
$966$	−11.6128			−0.373637
$967$		−	1.55262i		−	0.0499290i	−0.999688	−	0.0249645i	$-0.992053\pi$
$967$		−	1.55262i		−	0.0499290i	0.999688	−	0.0249645i	$-0.00794728\pi$
$968$		−	4.12399i		−	0.132550i
$969$	−3.80642			−0.122280
$970$	−16.3368	−	2.29529i	−0.524542	−	0.0736972i
$971$	44.5433			1.42946			0.714731	−	0.699400i	$-0.246549\pi$
$971$	44.5433			1.42946			0.714731	+	0.699400i	$0.246549\pi$
$972$			1.00000i			0.0320750i
$973$		−	1.71456i		−	0.0549662i
$974$	20.9175			0.670240
$975$	27.9081	+	8.00000i	0.893776	+	0.256205i
$976$	4.75557			0.152222
$977$		−	15.8350i		−	0.506607i	−0.967387	−	0.253303i	$-0.918483\pi$
$977$		−	15.8350i		−	0.506607i	0.967387	−	0.253303i	$-0.0815171\pi$
$978$			8.23506i			0.263328i
$979$	−32.5906			−1.04160
$980$	27.9289	+	3.92396i	0.892155	+	0.125346i
$981$	−6.04149			−0.192890
$982$			15.8666i			0.506325i
$983$			6.87601i			0.219311i	0.993970	+	0.109655i	$0.0349747\pi$
$983$			6.87601i			0.219311i	−0.993970	+	0.109655i	$0.965025\pi$
$984$	5.67307			0.180851
$985$	0.276551	−	1.96836i	0.00881163	−	0.0627171i
$986$	−12.8573			−0.409459
$987$		−	11.6128i		−	0.369641i
$988$			5.80642i			0.184727i
$989$	−28.8198			−0.916417
$990$	−0.815792	+	5.80642i	−0.0259276	+	0.184540i
$991$	−29.8765			−0.949058			−0.474529	−	0.880240i	$-0.657382\pi$
$991$	−29.8765			−0.949058			−0.474529	+	0.880240i	$0.657382\pi$
$992$			4.42864i			0.140609i
$993$			15.1427i			0.480540i
$994$	69.1437			2.19310
$995$	−48.0830	−	6.75557i	−1.52433	−	0.214166i
$996$	−11.9081			−0.377324
$997$		−	5.90813i		−	0.187112i	−0.995614	−	0.0935562i	$-0.970177\pi$
$997$		−	5.90813i		−	0.187112i	0.995614	−	0.0935562i	$-0.0298235\pi$
$998$			16.7368i			0.529795i
$999$	5.80642			0.183707

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.d.c.229.3	✓	6
3.2	odd	2		1710.2.d.f.1369.4		6
5.2	odd	4		2850.2.a.bm.1.1		3
5.3	odd	4		2850.2.a.bl.1.3		3
5.4	even	2	inner	570.2.d.c.229.6	yes	6
15.2	even	4		8550.2.a.ce.1.1		3
15.8	even	4		8550.2.a.cq.1.3		3
15.14	odd	2		1710.2.d.f.1369.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.d.c.229.3	✓	6	1.1	even	1	trivial
570.2.d.c.229.6	yes	6	5.4	even	2	inner
1710.2.d.f.1369.1		6	15.14	odd	2
1710.2.d.f.1369.4		6	3.2	odd	2
2850.2.a.bl.1.3		3	5.3	odd	4
2850.2.a.bm.1.1		3	5.2	odd	4
8550.2.a.ce.1.1		3	15.2	even	4
8550.2.a.cq.1.3		3	15.8	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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(2.21432 + 0.311108i) q^{5} -1.00000 q^{6} +4.42864i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(2.21432 + 0.311108i) q^{5} -1.00000 q^{6} +4.42864i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(0.311108 - 2.21432i) q^{10} +2.62222 q^{11} +1.00000i q^{12} +5.80642i q^{13} +4.42864 q^{14} +(0.311108 - 2.21432i) q^{15} +1.00000 q^{16} +3.80642i q^{17} +1.00000i q^{18} -1.00000 q^{19} +(-2.21432 - 0.311108i) q^{20} +4.42864 q^{21} -2.62222i q^{22} -2.62222i q^{23} +1.00000 q^{24} +(4.80642 + 1.37778i) q^{25} +5.80642 q^{26} +1.00000i q^{27} -4.42864i q^{28} -3.37778 q^{29} +(-2.21432 - 0.311108i) q^{30} -4.42864 q^{31} -1.00000i q^{32} -2.62222i q^{33} +3.80642 q^{34} +(-1.37778 + 9.80642i) q^{35} +1.00000 q^{36} -5.80642i q^{37} +1.00000i q^{38} +5.80642 q^{39} +(-0.311108 + 2.21432i) q^{40} +5.67307 q^{41} -4.42864i q^{42} -10.9906i q^{43} -2.62222 q^{44} +(-2.21432 - 0.311108i) q^{45} -2.62222 q^{46} -2.62222i q^{47} -1.00000i q^{48} -12.6128 q^{49} +(1.37778 - 4.80642i) q^{50} +3.80642 q^{51} -5.80642i q^{52} -6.00000i q^{53} +1.00000 q^{54} +(5.80642 + 0.815792i) q^{55} -4.42864 q^{56} +1.00000i q^{57} +3.37778i q^{58} +1.05086 q^{59} +(-0.311108 + 2.21432i) q^{60} +4.75557 q^{61} +4.42864i q^{62} -4.42864i q^{63} -1.00000 q^{64} +(-1.80642 + 12.8573i) q^{65} -2.62222 q^{66} -15.6128i q^{67} -3.80642i q^{68} -2.62222 q^{69} +(9.80642 + 1.37778i) q^{70} +15.6128 q^{71} -1.00000i q^{72} +11.6128i q^{73} -5.80642 q^{74} +(1.37778 - 4.80642i) q^{75} +1.00000 q^{76} +11.6128i q^{77} -5.80642i q^{78} -4.42864 q^{79} +(2.21432 + 0.311108i) q^{80} +1.00000 q^{81} -5.67307i q^{82} +11.9081i q^{83} -4.42864 q^{84} +(-1.18421 + 8.42864i) q^{85} -10.9906 q^{86} +3.37778i q^{87} +2.62222i q^{88} -12.4286 q^{89} +(-0.311108 + 2.21432i) q^{90} -25.7146 q^{91} +2.62222i q^{92} +4.42864i q^{93} -2.62222 q^{94} +(-2.21432 - 0.311108i) q^{95} -1.00000 q^{96} -7.37778i q^{97} +12.6128i q^{98} -2.62222 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9	\( 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9} + 2 q^{10} + 16 q^{11} + 2 q^{15} + 6 q^{16} - 6 q^{19} + 6 q^{24} + 2 q^{25} + 8 q^{26} - 20 q^{29} - 4 q^{34} - 8 q^{35} + 6 q^{36} + 8 q^{39} - 2 q^{40} + 8 q^{41} - 16 q^{44} - 16 q^{46} - 22 q^{49} + 8 q^{50} - 4 q^{51} + 6 q^{54} + 8 q^{55} - 20 q^{59} - 2 q^{60} + 28 q^{61} - 6 q^{64} + 16 q^{65} - 16 q^{66} - 16 q^{69} + 32 q^{70} + 40 q^{71} - 8 q^{74} + 8 q^{75} + 6 q^{76} + 6 q^{81} + 20 q^{85} - 12 q^{86} - 48 q^{89} - 2 q^{90} - 48 q^{91} - 16 q^{94} - 6 q^{96} - 16 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9 + 2 * q^10 + 16 * q^11 + 2 * q^15 + 6 * q^16 - 6 * q^19 + 6 * q^24 + 2 * q^25 + 8 * q^26 - 20 * q^29 - 4 * q^34 - 8 * q^35 + 6 * q^36 + 8 * q^39 - 2 * q^40 + 8 * q^41 - 16 * q^44 - 16 * q^46 - 22 * q^49 + 8 * q^50 - 4 * q^51 + 6 * q^54 + 8 * q^55 - 20 * q^59 - 2 * q^60 + 28 * q^61 - 6 * q^64 + 16 * q^65 - 16 * q^66 - 16 * q^69 + 32 * q^70 + 40 * q^71 - 8 * q^74 + 8 * q^75 + 6 * q^76 + 6 * q^81 + 20 * q^85 - 12 * q^86 - 48 * q^89 - 2 * q^90 - 48 * q^91 - 16 * q^94 - 6 * q^96 - 16 * q^99

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