LMFDB - Embedded newform 1110.2.ba.a.619.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(529,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("1110.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.ba (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			619.5
Character	$\chi$	$=$	1110.619
Dual form			1110.2.ba.a.529.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.51023 + 1.64901i) q^{5} -1.00000i q^{6} +(0.0701099 - 0.0404780i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.51023 + 1.64901i) q^{5} -1.00000i q^{6} +(0.0701099 - 0.0404780i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.18319 + 0.483391i) q^{10} -3.93468 q^{11} +(0.866025 + 0.500000i) q^{12} +(1.78579 + 3.09309i) q^{13} +0.0809559i q^{14} +(-2.13240 - 0.672968i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.563300 - 0.975664i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-1.70412 + 0.983874i) q^{19} +(0.672968 - 2.13240i) q^{20} +(-0.0404780 + 0.0701099i) q^{21} +(1.96734 - 3.40754i) q^{22} -2.93551 q^{23} +(-0.866025 + 0.500000i) q^{24} +(-0.438440 + 4.98074i) q^{25} -3.57159 q^{26} +1.00000i q^{27} +(-0.0701099 - 0.0404780i) q^{28} -2.65993i q^{29} +(1.64901 - 1.51023i) q^{30} +6.08031i q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.40754 - 1.96734i) q^{33} +(0.563300 + 0.975664i) q^{34} +(0.172630 + 0.0544808i) q^{35} -1.00000 q^{36} +(1.49939 + 5.89507i) q^{37} -1.96775i q^{38} +(-3.09309 - 1.78579i) q^{39} +(1.51023 + 1.64901i) q^{40} +(-3.72081 - 6.44463i) q^{41} +(-0.0404780 - 0.0701099i) q^{42} -5.69104 q^{43} +(1.96734 + 3.40754i) q^{44} +(2.18319 - 0.483391i) q^{45} +(1.46775 - 2.54222i) q^{46} +10.7878i q^{47} -1.00000i q^{48} +(-3.49672 + 6.05650i) q^{49} +(-4.09423 - 2.87007i) q^{50} +1.12660i q^{51} +(1.78579 - 3.09309i) q^{52} +(-0.118647 - 0.0685008i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-5.94226 - 6.48832i) q^{55} +(0.0701099 - 0.0404780i) q^{56} +(0.983874 - 1.70412i) q^{57} +(2.30357 + 1.32997i) q^{58} +(-2.46559 - 1.42351i) q^{59} +(0.483391 + 2.18319i) q^{60} +(8.34607 - 4.81861i) q^{61} +(-5.26570 - 3.04016i) q^{62} -0.0809559i q^{63} +1.00000 q^{64} +(-2.40357 + 7.61604i) q^{65} +3.93468i q^{66} +(-3.06184 + 1.76776i) q^{67} -1.12660 q^{68} +(2.54222 - 1.46775i) q^{69} +(-0.133497 + 0.122262i) q^{70} +(-3.49001 - 6.04487i) q^{71} +(0.500000 - 0.866025i) q^{72} -5.98563i q^{73} +(-5.85497 - 1.64903i) q^{74} +(-2.11067 - 4.53267i) q^{75} +(1.70412 + 0.983874i) q^{76} +(-0.275860 + 0.159268i) q^{77} +(3.09309 - 1.78579i) q^{78} +(-3.95064 + 2.28090i) q^{79} +(-2.18319 + 0.483391i) q^{80} +(-0.500000 - 0.866025i) q^{81} +7.44162 q^{82} +(-10.6365 - 6.14100i) q^{83} +0.0809559 q^{84} +(2.45959 - 0.544588i) q^{85} +(2.84552 - 4.92859i) q^{86} +(1.32997 + 2.30357i) q^{87} -3.93468 q^{88} +(-11.3025 - 6.52551i) q^{89} +(-0.672968 + 2.13240i) q^{90} +(0.250404 + 0.144571i) q^{91} +(1.46775 + 2.54222i) q^{92} +(-3.04016 - 5.26570i) q^{93} +(-9.34248 - 5.39388i) q^{94} +(-4.19602 - 1.32423i) q^{95} +(0.866025 + 0.500000i) q^{96} +0.882847 q^{97} +(-3.49672 - 6.05650i) q^{98} +(-1.96734 + 3.40754i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9}+O(q^{10}) $ 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9	$ 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} - 14 q^{13} - 2 q^{15} - 18 q^{16} + 18 q^{18} + 6 q^{19} - 4 q^{20} - 2 q^{22} - 20 q^{23} + 4 q^{25} + 28 q^{26} - 2 q^{30} - 18 q^{32} - 6 q^{33} - 40 q^{35} - 36 q^{36} + 20 q^{37} + 6 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} - 2 q^{45} + 10 q^{46} + 10 q^{49} - 2 q^{50} - 14 q^{52} - 12 q^{53} + 56 q^{55} + 8 q^{57} + 30 q^{58} + 18 q^{59} + 4 q^{60} - 6 q^{61} - 12 q^{62} + 36 q^{64} + 40 q^{65} + 36 q^{67} + 12 q^{69} + 20 q^{70} - 24 q^{71} + 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} - 24 q^{77} - 6 q^{78} + 2 q^{80} - 18 q^{81} - 20 q^{82} + 36 q^{83} + 26 q^{85} - 10 q^{87} + 4 q^{88} + 4 q^{90} - 36 q^{91} + 10 q^{92} + 12 q^{93} + 12 q^{94} - 30 q^{95} + 52 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) $ 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9 + 2 * q^10 + 4 * q^11 - 14 * q^13 - 2 * q^15 - 18 * q^16 + 18 * q^18 + 6 * q^19 - 4 * q^20 - 2 * q^22 - 20 * q^23 + 4 * q^25 + 28 * q^26 - 2 * q^30 - 18 * q^32 - 6 * q^33 - 40 * q^35 - 36 * q^36 + 20 * q^37 + 6 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 - 2 * q^45 + 10 * q^46 + 10 * q^49 - 2 * q^50 - 14 * q^52 - 12 * q^53 + 56 * q^55 + 8 * q^57 + 30 * q^58 + 18 * q^59 + 4 * q^60 - 6 * q^61 - 12 * q^62 + 36 * q^64 + 40 * q^65 + 36 * q^67 + 12 * q^69 + 20 * q^70 - 24 * q^71 + 18 * q^72 - 34 * q^74 + 8 * q^75 - 6 * q^76 - 24 * q^77 - 6 * q^78 + 2 * q^80 - 18 * q^81 - 20 * q^82 + 36 * q^83 + 26 * q^85 - 10 * q^87 + 4 * q^88 + 4 * q^90 - 36 * q^91 + 10 * q^92 + 12 * q^93 + 12 * q^94 - 30 * q^95 + 52 * q^97 + 10 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.51023	+	1.64901i	0.675393	+	0.737458i
$5$	1.51023	+	1.64901i	0.675393	+	0.737458i
$6$		−	1.00000i		−	0.408248i
$7$	0.0701099	−	0.0404780i	0.0264990	−	0.0152992i	−0.486692	−	0.873574i	$-0.661797\pi$
$7$	0.0701099	−	0.0404780i	0.0264990	−	0.0152992i	0.513191	+	0.858274i	$0.328463\pi$
$8$	1.00000			0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−2.18319	+	0.483391i	−0.690386	+	0.152862i
$11$	−3.93468			−1.18635			−0.593176	−	0.805073i	$-0.702126\pi$
$11$	−3.93468			−1.18635			−0.593176	+	0.805073i	$0.702126\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	1.78579	+	3.09309i	0.495290	+	0.857868i	0.999985	−	0.00542977i	$-0.00172836\pi$
$13$	1.78579	+	3.09309i	0.495290	+	0.857868i	−0.504695	+	0.863298i	$0.668395\pi$
$14$			0.0809559i			0.0216364i
$15$	−2.13240	−	0.672968i	−0.550582	−	0.173760i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.563300	−	0.975664i	0.136620	−	0.236633i	−0.789595	−	0.613628i	$-0.789709\pi$
$17$	0.563300	−	0.975664i	0.136620	−	0.236633i	0.926215	+	0.376995i	$0.123043\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−1.70412	+	0.983874i	−0.390952	+	0.225716i	−0.682572	−	0.730818i	$-0.739139\pi$
$19$	−1.70412	+	0.983874i	−0.390952	+	0.225716i	0.291621	+	0.956534i	$0.405805\pi$
$20$	0.672968	−	2.13240i	0.150480	−	0.476818i
$21$	−0.0404780	+	0.0701099i	−0.00883302	+	0.0152992i
$22$	1.96734	−	3.40754i	0.419439	−	0.726489i
$23$	−2.93551			−0.612096			−0.306048	−	0.952016i	$-0.599007\pi$
$23$	−2.93551			−0.612096			−0.306048	+	0.952016i	$0.599007\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	−0.438440	+	4.98074i	−0.0876879	+	0.996148i
$26$	−3.57159			−0.700446
$27$			1.00000i			0.192450i
$28$	−0.0701099	−	0.0404780i	−0.0132495	−	0.00764962i
$29$		−	2.65993i		−	0.493937i	−0.969023	−	0.246969i	$-0.920566\pi$
$29$		−	2.65993i		−	0.493937i	0.969023	−	0.246969i	$-0.0794345\pi$
$30$	1.64901	−	1.51023i	0.301066	−	0.275728i
$31$			6.08031i			1.09206i	0.837767	+	0.546028i	$0.183861\pi$
$31$			6.08031i			1.09206i	−0.837767	+	0.546028i	$0.816139\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	3.40754	−	1.96734i	0.593176	−	0.342470i
$34$	0.563300	+	0.975664i	0.0966051	+	0.167325i
$35$	0.172630	+	0.0544808i	0.0291798	+	0.00920893i
$36$	−1.00000			−0.166667
$37$	1.49939	+	5.89507i	0.246498	+	0.969143i
$37$	1.49939	+	5.89507i	0.246498	+	0.969143i
$38$		−	1.96775i		−	0.319211i
$39$	−3.09309	−	1.78579i	−0.495290	−	0.285956i
$40$	1.51023	+	1.64901i	0.238788	+	0.260731i
$41$	−3.72081	−	6.44463i	−0.581093	−	1.00648i	−0.995350	−	0.0963225i	$-0.969292\pi$
$41$	−3.72081	−	6.44463i	−0.581093	−	1.00648i	0.414257	−	0.910160i	$-0.364041\pi$
$42$	−0.0404780	−	0.0701099i	−0.00624589	−	0.0108182i
$43$	−5.69104			−0.867876			−0.433938	−	0.900943i	$-0.642876\pi$
$43$	−5.69104			−0.867876			−0.433938	+	0.900943i	$0.642876\pi$
$44$	1.96734	+	3.40754i	0.296588	+	0.513705i
$45$	2.18319	−	0.483391i	0.325451	−	0.0720596i
$46$	1.46775	−	2.54222i	0.216409	−	0.374831i
$47$			10.7878i			1.57356i	0.617235	+	0.786779i	$0.288253\pi$
$47$			10.7878i			1.57356i	−0.617235	+	0.786779i	$0.711747\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−3.49672	+	6.05650i	−0.499532	+	0.865215i
$50$	−4.09423	−	2.87007i	−0.579011	−	0.405889i
$51$			1.12660i			0.157756i
$52$	1.78579	−	3.09309i	0.247645	−	0.428934i
$53$	−0.118647	−	0.0685008i	−0.0162974	−	0.00940931i	0.491829	−	0.870692i	$-0.336328\pi$
$53$	−0.118647	−	0.0685008i	−0.0162974	−	0.00940931i	−0.508127	+	0.861282i	$0.669662\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	−5.94226	−	6.48832i	−0.801254	−	0.874885i
$56$	0.0701099	−	0.0404780i	0.00936883	−	0.00540910i
$57$	0.983874	−	1.70412i	0.130317	−	0.225716i
$58$	2.30357	+	1.32997i	0.302474	+	0.174633i
$59$	−2.46559	−	1.42351i	−0.320992	−	0.185325i	0.330842	−	0.943686i	$-0.392667\pi$
$59$	−2.46559	−	1.42351i	−0.320992	−	0.185325i	−0.651835	+	0.758361i	$0.726000\pi$
$60$	0.483391	+	2.18319i	0.0624054	+	0.281849i
$61$	8.34607	−	4.81861i	1.06861	−	0.616960i	0.140805	−	0.990037i	$-0.455031\pi$
$61$	8.34607	−	4.81861i	1.06861	−	0.616960i	0.927800	+	0.373078i	$0.121698\pi$
$62$	−5.26570	−	3.04016i	−0.668745	−	0.386100i
$63$		−	0.0809559i		−	0.0101995i
$64$	1.00000			0.125000
$65$	−2.40357	+	7.61604i	−0.298126	+	0.944654i
$66$			3.93468i			0.484326i
$67$	−3.06184	+	1.76776i	−0.374064	+	0.215966i	−0.675232	−	0.737605i	$-0.735957\pi$
$67$	−3.06184	+	1.76776i	−0.374064	+	0.215966i	0.301169	+	0.953571i	$0.402623\pi$
$68$	−1.12660			−0.136620
$69$	2.54222	−	1.46775i	0.306048	−	0.176697i
$70$	−0.133497	+	0.122262i	−0.0159559	+	0.0146131i
$71$	−3.49001	−	6.04487i	−0.414188	−	0.717394i	0.581155	−	0.813793i	$-0.302601\pi$
$71$	−3.49001	−	6.04487i	−0.414188	−	0.717394i	−0.995343	+	0.0963986i	$0.969268\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$		−	5.98563i		−	0.700565i	−0.936644	−	0.350282i	$-0.886086\pi$
$73$		−	5.98563i		−	0.700565i	0.936644	−	0.350282i	$-0.113914\pi$
$74$	−5.85497	−	1.64903i	−0.680627	−	0.191696i
$75$	−2.11067	−	4.53267i	−0.243719	−	0.523387i
$76$	1.70412	+	0.983874i	0.195476	+	0.112858i
$77$	−0.275860	+	0.159268i	−0.0314372	+	0.0181503i
$78$	3.09309	−	1.78579i	0.350223	−	0.202201i
$79$	−3.95064	+	2.28090i	−0.444481	+	0.256621i	−0.705497	−	0.708713i	$-0.749276\pi$
$79$	−3.95064	+	2.28090i	−0.444481	+	0.256621i	0.261015	+	0.965335i	$0.415943\pi$
$80$	−2.18319	+	0.483391i	−0.244088	+	0.0540447i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	7.44162			0.821789
$83$	−10.6365	−	6.14100i	−1.16751	−	0.674062i	−0.214418	−	0.976742i	$-0.568785\pi$
$83$	−10.6365	−	6.14100i	−1.16751	−	0.674062i	−0.953092	+	0.302680i	$0.902119\pi$
$84$	0.0809559			0.00883302
$85$	2.45959	−	0.544588i	0.266779	−	0.0590688i
$86$	2.84552	−	4.92859i	0.306840	−	0.531463i
$87$	1.32997	+	2.30357i	0.142587	+	0.246969i
$88$	−3.93468			−0.419439
$89$	−11.3025	−	6.52551i	−1.19806	−	0.691703i	−0.237941	−	0.971280i	$-0.576473\pi$
$89$	−11.3025	−	6.52551i	−1.19806	−	0.691703i	−0.960123	+	0.279577i	$0.909806\pi$
$90$	−0.672968	+	2.13240i	−0.0709371	+	0.224774i
$91$	0.250404	+	0.144571i	0.0262494	+	0.0151551i
$92$	1.46775	+	2.54222i	0.153024	+	0.265045i
$93$	−3.04016	−	5.26570i	−0.315249	−	0.546028i
$94$	−9.34248	−	5.39388i	−0.963603	−	0.556337i
$95$	−4.19602	−	1.32423i	−0.430502	−	0.135863i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	0.882847			0.0896396			0.0448198	−	0.998995i	$-0.485729\pi$
$97$	0.882847			0.0896396			0.0448198	+	0.998995i	$0.485729\pi$
$98$	−3.49672	−	6.05650i	−0.353222	−	0.611799i
$99$	−1.96734	+	3.40754i	−0.197725	+	0.342470i
$100$	4.53267	−	2.11067i	0.453267	−	0.211067i
$101$	−5.69660			−0.566833			−0.283417	−	0.958997i	$-0.591468\pi$
$101$	−5.69660			−0.566833			−0.283417	+	0.958997i	$0.591468\pi$
$102$	−0.975664	−	0.563300i	−0.0966051	−	0.0557750i
$103$	−6.74171			−0.664280			−0.332140	−	0.943230i	$-0.607771\pi$
$103$	−6.74171			−0.664280			−0.332140	+	0.943230i	$0.607771\pi$
$104$	1.78579	+	3.09309i	0.175112	+	0.303302i
$105$	−0.176742	+	0.0391333i	−0.0172483	+	0.00381902i
$106$	0.118647	−	0.0685008i	0.0115240	−	0.00665339i
$107$	−0.309869	+	0.178903i	−0.0299562	+	0.0172952i	−0.514903	−	0.857248i	$-0.672172\pi$
$107$	−0.309869	+	0.178903i	−0.0299562	+	0.0172952i	0.484947	+	0.874543i	$0.338839\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	−1.10002	−	0.635097i	−0.105363	−	0.0608312i	0.446393	−	0.894837i	$-0.352708\pi$
$109$	−1.10002	−	0.635097i	−0.105363	−	0.0608312i	−0.551755	+	0.834006i	$0.686042\pi$
$110$	8.59018	−	1.90199i	0.819041	−	0.181348i
$111$	−4.24604	−	4.35559i	−0.403016	−	0.413414i
$112$			0.0809559i			0.00764962i
$113$	−7.99299	+	13.8443i	−0.751917	+	1.30236i	0.194975	+	0.980808i	$0.437537\pi$
$113$	−7.99299	+	13.8443i	−0.751917	+	1.30236i	−0.946892	+	0.321551i	$0.895796\pi$
$114$	0.983874	+	1.70412i	0.0921482	+	0.159605i
$115$	−4.43328	−	4.84067i	−0.413405	−	0.451395i
$116$	−2.30357	+	1.32997i	−0.213881	+	0.123484i
$117$	3.57159			0.330194
$118$	2.46559	−	1.42351i	0.226976	−	0.131045i
$119$		−	0.0912049i		−	0.00836074i
$120$	−2.13240	−	0.672968i	−0.194660	−	0.0614333i
$121$	4.48174			0.407431
$122$			9.63722i			0.872513i
$123$	6.44463	+	3.72081i	0.581093	+	0.335494i
$124$	5.26570	−	3.04016i	0.472874	−	0.273014i
$125$	−8.87541	+	6.79905i	−0.793841	+	0.608125i
$126$	0.0701099	+	0.0404780i	0.00624589	+	0.00360606i
$127$	14.2361	+	8.21923i	1.26325	+	0.729339i	0.973702	−	0.227824i	$-0.0731611\pi$
$127$	14.2361	+	8.21923i	1.26325	+	0.729339i	0.289550	+	0.957163i	$0.406494\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	4.92859	−	2.84552i	0.433938	−	0.250534i
$130$	−5.39390	−	5.88957i	−0.473077	−	0.516550i
$131$	1.69785	+	0.980254i	0.148342	+	0.0856452i	0.572334	−	0.820021i	$-0.306038\pi$
$131$	1.69785	+	0.980254i	0.148342	+	0.0856452i	−0.423992	+	0.905666i	$0.639372\pi$
$132$	−3.40754	−	1.96734i	−0.296588	−	0.171235i
$133$	−0.0796504	+	0.137959i	−0.00690657	+	0.0119625i
$134$		−	3.53551i		−	0.305422i
$135$	−1.64901	+	1.51023i	−0.141924	+	0.129979i
$136$	0.563300	−	0.975664i	0.0483026	−	0.0836625i
$137$			20.5579i			1.75638i	0.478314	+	0.878189i	$0.341248\pi$
$137$			20.5579i			1.75638i	−0.478314	+	0.878189i	$0.658752\pi$
$138$			2.93551i			0.249887i
$139$	6.49951	−	11.2575i	0.551281	−	0.954848i	−0.446901	−	0.894583i	$-0.647472\pi$
$139$	6.49951	−	11.2575i	0.551281	−	0.954848i	0.998182	−	0.0602641i	$-0.0191943\pi$
$140$	−0.0391333	−	0.176742i	−0.00330737	−	0.0149375i
$141$	−5.39388	−	9.34248i	−0.454247	−	0.786779i
$142$	6.98002			0.585750
$143$	−7.02654	−	12.1703i	−0.587589	−	1.01773i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	4.38625	−	4.01710i	0.364258	−	0.333602i
$146$	5.18371	+	2.99281i	0.429007	+	0.247687i
$147$		−	6.99345i		−	0.576810i
$148$	4.35559	−	4.24604i	0.358027	−	0.349022i
$149$	22.5829			1.85006			0.925031	−	0.379891i	$-0.124039\pi$
$149$	22.5829			1.85006			0.925031	+	0.379891i	$0.124039\pi$
$150$	4.98074	+	0.438440i	0.406676	+	0.0357985i
$151$	3.99191	+	6.91418i	0.324857	+	0.562668i	0.981483	−	0.191547i	$-0.0613506\pi$
$151$	3.99191	+	6.91418i	0.324857	+	0.562668i	−0.656627	+	0.754216i	$0.728017\pi$
$152$	−1.70412	+	0.983874i	−0.138222	+	0.0798027i
$153$	−0.563300	−	0.975664i	−0.0455401	−	0.0788778i
$154$		−	0.318536i		−	0.0256684i
$155$	−10.0265	+	9.18264i	−0.805345	+	0.737567i
$156$			3.57159i			0.285956i
$157$	−4.93908	−	2.85158i	−0.394182	−	0.227581i	0.289789	−	0.957091i	$-0.406415\pi$
$157$	−4.93908	−	2.85158i	−0.394182	−	0.227581i	−0.683970	+	0.729510i	$0.739748\pi$
$158$		−	4.56180i		−	0.362917i
$159$	0.137002			0.0108649
$160$	0.672968	−	2.13240i	0.0532028	−	0.168581i
$161$	−0.205808	+	0.118823i	−0.0162200	+	0.00936460i
$162$	1.00000			0.0785674
$163$	5.46907	−	9.47271i	0.428371	−	0.741960i	−0.568358	−	0.822781i	$-0.692421\pi$
$163$	5.46907	−	9.47271i	0.428371	−	0.741960i	0.996729	+	0.0808216i	$0.0257544\pi$
$164$	−3.72081	+	6.44463i	−0.290546	+	0.503241i
$165$	8.39031	+	2.64792i	0.653184	+	0.206140i
$166$	10.6365	−	6.14100i	0.825554	−	0.476634i
$167$	4.59649	+	7.96135i	0.355687	+	0.616068i	0.987235	−	0.159268i	$-0.0509135\pi$
$167$	4.59649	+	7.96135i	0.355687	+	0.616068i	−0.631548	+	0.775337i	$0.717580\pi$
$168$	−0.0404780	+	0.0701099i	−0.00312294	+	0.00540910i
$169$	0.121875	−	0.211094i	0.00937502	−	0.0162380i
$170$	−0.758166	+	2.40236i	−0.0581487	+	0.184252i
$171$			1.96775i			0.150477i
$172$	2.84552	+	4.92859i	0.216969	+	0.375801i
$173$	−4.32016	−	2.49425i	−0.328456	−	0.189634i	0.326700	−	0.945128i	$-0.394063\pi$
$173$	−4.32016	−	2.49425i	−0.328456	−	0.189634i	−0.655155	+	0.755494i	$0.727397\pi$
$174$	−2.65993			−0.201649
$175$	0.170871	+	0.366946i	0.0129167	+	0.0277385i
$176$	1.96734	−	3.40754i	0.148294	−	0.256853i
$177$	2.84702			0.213995
$178$	11.3025	−	6.52551i	0.847160	−	0.489108i
$179$		−	9.29758i		−	0.694934i	−0.937692	−	0.347467i	$-0.887042\pi$
$179$		−	9.29758i		−	0.694934i	0.937692	−	0.347467i	$-0.112958\pi$
$180$	−1.51023	−	1.64901i	−0.112566	−	0.122910i
$181$	3.79019	+	6.56480i	0.281722	+	0.487958i	0.971809	−	0.235769i	$-0.0757609\pi$
$181$	3.79019	+	6.56480i	0.281722	+	0.487958i	−0.690087	+	0.723727i	$0.742428\pi$
$182$	−0.250404	+	0.144571i	−0.0185612	+	0.0107163i
$183$	−4.81861	+	8.34607i	−0.356202	+	0.616960i
$184$	−2.93551			−0.216409
$185$	−7.45659	+	11.3754i	−0.548219	+	0.836335i
$186$	6.08031			0.445830
$187$	−2.21641	+	3.83893i	−0.162080	+	0.280730i
$188$	9.34248	−	5.39388i	0.681370	−	0.393389i
$189$	0.0404780	+	0.0701099i	0.00294434	+	0.00509974i
$190$	3.24483	−	2.97174i	0.235404	−	0.215593i
$191$		−	0.0853502i		−	0.00617573i	−0.999995	−	0.00308786i	$-0.999017\pi$
$191$		−	0.0853502i		−	0.00617573i	0.999995	−	0.00308786i	$-0.000982899\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	5.16516			0.371796			0.185898	−	0.982569i	$-0.440481\pi$
$193$	5.16516			0.371796			0.185898	+	0.982569i	$0.440481\pi$
$194$	−0.441424	+	0.764568i	−0.0316924	+	0.0548928i
$195$	−1.72647	−	7.79747i	−0.123635	−	0.558388i
$196$	6.99345			0.499532
$197$	9.34387	+	5.39468i	0.665723	+	0.384355i	0.794454	−	0.607324i	$-0.207757\pi$
$197$	9.34387	+	5.39468i	0.665723	+	0.384355i	−0.128731	+	0.991680i	$0.541090\pi$
$198$	−1.96734	−	3.40754i	−0.139813	−	0.242163i
$199$			7.93361i			0.562399i	0.959649	+	0.281200i	$0.0907323\pi$
$199$			7.93361i			0.562399i	−0.959649	+	0.281200i	$0.909268\pi$
$200$	−0.438440	+	4.98074i	−0.0310024	+	0.352192i
$201$	1.76776	−	3.06184i	0.124688	−	0.215966i
$202$	2.84830	−	4.93340i	0.200406	−	0.347113i
$203$	−0.107669	−	0.186488i	−0.00755686	−	0.0130889i
$204$	0.975664	−	0.563300i	0.0683101	−	0.0394389i
$205$	5.00797	−	15.8685i	0.349772	−	1.10830i
$206$	3.37085	−	5.83849i	0.234858	−	0.406787i
$207$	−1.46775	+	2.54222i	−0.102016	+	0.176697i
$208$	−3.57159			−0.247645
$209$	6.70517	−	3.87123i	0.463806	−	0.267779i
$210$	0.0544808	−	0.172630i	0.00375953	−	0.0119126i
$211$	24.3190			1.67419			0.837093	−	0.547060i	$-0.184253\pi$
$211$	24.3190			1.67419			0.837093	+	0.547060i	$0.184253\pi$
$212$			0.137002i			0.00940931i
$213$	6.04487	+	3.49001i	0.414188	+	0.239131i
$214$		−	0.357806i		−	0.0244591i
$215$	−8.59476	−	9.38456i	−0.586158	−	0.640022i
$216$			1.00000i			0.0680414i
$217$	0.246119	+	0.426290i	0.0167076	+	0.0289384i
$218$	1.10002	−	0.635097i	0.0745027	−	0.0430142i
$219$	2.99281	+	5.18371i	0.202236	+	0.350282i
$220$	−2.64792	+	8.39031i	−0.178523	+	0.565674i
$221$	4.02375			0.270667
$222$	5.89507	−	1.49939i	0.395651	−	0.100632i
$223$			18.2474i			1.22193i	0.791656	+	0.610967i	$0.209219\pi$
$223$			18.2474i			1.22193i	−0.791656	+	0.610967i	$0.790781\pi$
$224$	−0.0701099	−	0.0404780i	−0.00468441	−	0.00270455i
$225$	4.09423	+	2.87007i	0.272948	+	0.191338i
$226$	−7.99299	−	13.8443i	−0.531686	−	0.920907i
$227$	4.95426	+	8.58102i	0.328826	+	0.569543i	0.982279	−	0.187424i	$-0.0600138\pi$
$227$	4.95426	+	8.58102i	0.328826	+	0.569543i	−0.653454	+	0.756967i	$0.726681\pi$
$228$	−1.96775			−0.130317
$229$	12.8080	+	22.1841i	0.846376	+	1.46597i	0.884421	+	0.466690i	$0.154554\pi$
$229$	12.8080	+	22.1841i	0.846376	+	1.46597i	−0.0380447	+	0.999276i	$0.512113\pi$
$230$	6.40878	−	1.41900i	0.422583	−	0.0935659i
$231$	0.159268	−	0.275860i	0.0104791	−	0.0181503i
$232$		−	2.65993i		−	0.174633i
$233$		−	3.44779i		−	0.225872i	−0.993602	−	0.112936i	$-0.963974\pi$
$233$		−	3.44779i		−	0.225872i	0.993602	−	0.112936i	$-0.0360256\pi$
$234$	−1.78579	+	3.09309i	−0.116741	+	0.202201i
$235$	−17.7891	+	16.2920i	−1.16043	+	1.06277i
$236$			2.84702i			0.185325i
$237$	2.28090	−	3.95064i	0.148160	−	0.256621i
$238$	0.0789858	+	0.0456025i	0.00511989	+	0.00295597i
$239$	12.3341	+	7.12108i	0.797824	+	0.460624i	0.842710	−	0.538368i	$-0.180959\pi$
$239$	12.3341	+	7.12108i	0.797824	+	0.460624i	−0.0448854	+	0.998992i	$0.514292\pi$
$240$	1.64901	−	1.51023i	0.106443	−	0.0974846i
$241$	−17.9025	+	10.3360i	−1.15320	+	0.665801i	−0.949665	−	0.313266i	$-0.898577\pi$
$241$	−17.9025	+	10.3360i	−1.15320	+	0.665801i	−0.203536	+	0.979067i	$0.565244\pi$
$242$	−2.24087	+	3.88130i	−0.144049	+	0.249500i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−8.34607	−	4.81861i	−0.534303	−	0.308480i
$245$	−15.2680	+	3.38057i	−0.975440	+	0.215976i
$246$	−6.44463	+	3.72081i	−0.410895	+	0.237230i
$247$	−6.08641	−	3.51399i	−0.387269	−	0.223590i
$248$			6.08031i			0.386100i
$249$	12.2820			0.778340
$250$	−1.45044	−	11.0859i	−0.0917341	−	0.701131i
$251$		−	8.24545i		−	0.520448i	−0.965548	−	0.260224i	$-0.916204\pi$
$251$		−	8.24545i		−	0.520448i	0.965548	−	0.260224i	$-0.0837965\pi$
$252$	−0.0701099	+	0.0404780i	−0.00441651	+	0.00254987i
$253$	11.5503			0.726161
$254$	−14.2361	+	8.21923i	−0.893254	+	0.515721i
$255$	−1.85777	+	1.70142i	−0.116338	+	0.106547i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.41974	−	5.92316i	0.213317	−	0.369476i	−0.739433	−	0.673230i	$-0.764907\pi$
$257$	3.41974	−	5.92316i	0.213317	−	0.369476i	0.952751	+	0.303753i	$0.0982399\pi$
$258$			5.69104i			0.354309i
$259$	0.343742	+	0.352611i	0.0213591	+	0.0219102i
$260$	7.79747	−	1.72647i	0.483579	−	0.107071i
$261$	−2.30357	−	1.32997i	−0.142587	−	0.0823229i
$262$	−1.69785	+	0.980254i	−0.104894	+	0.0605603i
$263$	−12.7454	+	7.35858i	−0.785917	+	0.453750i	−0.838523	−	0.544866i	$-0.816581\pi$
$263$	−12.7454	+	7.35858i	−0.785917	+	0.453750i	0.0526059	+	0.998615i	$0.483247\pi$
$264$	3.40754	−	1.96734i	0.209719	−	0.121082i
$265$	−0.0662253	−	0.299101i	−0.00406819	−	0.0183736i
$266$	−0.0796504	−	0.137959i	−0.00488368	−	0.00845878i
$267$	13.0510			0.798710
$268$	3.06184	+	1.76776i	0.187032	+	0.107983i
$269$	26.5270			1.61738			0.808691	−	0.588234i	$-0.200177\pi$
$269$	26.5270			1.61738			0.808691	+	0.588234i	$0.200177\pi$
$270$	−0.483391	−	2.18319i	−0.0294182	−	0.132865i
$271$	6.61234	−	11.4529i	0.401671	−	0.695715i	−0.592257	−	0.805749i	$-0.701763\pi$
$271$	6.61234	−	11.4529i	0.401671	−	0.695715i	0.993928	+	0.110035i	$0.0350962\pi$
$272$	0.563300	+	0.975664i	0.0341551	+	0.0591583i
$273$	−0.289141			−0.0174996
$274$	−17.8036	−	10.2789i	−1.07556	−	0.620973i
$275$	1.72512	−	19.5976i	0.104029	−	1.18178i
$276$	−2.54222	−	1.46775i	−0.153024	−	0.0883484i
$277$	6.30776	+	10.9254i	0.378997	+	0.656442i	0.990917	−	0.134478i	$-0.0429358\pi$
$277$	6.30776	+	10.9254i	0.378997	+	0.656442i	−0.611920	+	0.790920i	$0.709602\pi$
$278$	6.49951	+	11.2575i	0.389815	+	0.675179i
$279$	5.26570	+	3.04016i	0.315249	+	0.182009i
$280$	0.172630	+	0.0544808i	0.0103166	+	0.00325585i
$281$	−10.1405	−	5.85462i	−0.604931	−	0.349257i	0.166048	−	0.986118i	$-0.446899\pi$
$281$	−10.1405	−	5.85462i	−0.604931	−	0.349257i	−0.770979	+	0.636860i	$0.780233\pi$
$282$	10.7878			0.642402
$283$	−8.13334	−	14.0874i	−0.483477	−	0.837406i	0.516343	−	0.856382i	$-0.327293\pi$
$283$	−8.13334	−	14.0874i	−0.483477	−	0.837406i	−0.999820	+	0.0189756i	$0.993960\pi$
$284$	−3.49001	+	6.04487i	−0.207094	+	0.358697i
$285$	4.29597	−	0.951190i	0.254471	−	0.0563437i
$286$	14.0531			0.830976
$287$	−0.521731	−	0.301222i	−0.0307968	−	0.0177805i
$288$	−1.00000			−0.0589256
$289$	7.86539	+	13.6232i	0.462670	+	0.801368i
$290$	1.28579	+	5.80715i	0.0755040	+	0.341008i
$291$	−0.764568	+	0.441424i	−0.0448198	+	0.0258767i
$292$	−5.18371	+	2.99281i	−0.303354	+	0.175141i
$293$	−4.62415	+	2.66975i	−0.270146	+	0.155969i	−0.628954	−	0.777443i	$-0.716517\pi$
$293$	−4.62415	+	2.66975i	−0.270146	+	0.155969i	0.358808	+	0.933411i	$0.383183\pi$
$294$	6.05650	+	3.49672i	0.353222	+	0.203933i
$295$	−1.37622	−	6.21559i	−0.0801267	−	0.361886i
$296$	1.49939	+	5.89507i	0.0871501	+	0.342644i
$297$		−	3.93468i		−	0.228314i
$298$	−11.2914	+	19.5574i	−0.654096	+	1.13293i
$299$	−5.24221	−	9.07978i	−0.303165	−	0.525097i
$300$	−2.87007	+	4.09423i	−0.165704	+	0.236380i
$301$	−0.398998	+	0.230362i	−0.0229979	+	0.0132778i
$302$	−7.98381			−0.459417
$303$	4.93340	−	2.84830i	0.283417	−	0.163631i
$304$		−	1.96775i		−	0.112858i
$305$	20.5504	+	6.48554i	1.17671	+	0.371361i
$306$	1.12660			0.0644034
$307$			23.4241i			1.33689i	0.743763	+	0.668443i	$0.233039\pi$
$307$			23.4241i			1.33689i	−0.743763	+	0.668443i	$0.766961\pi$
$308$	0.275860	+	0.159268i	0.0157186	+	0.00907514i
$309$	5.83849	−	3.37085i	0.332140	−	0.191761i
$310$	−2.93916	−	13.2745i	−0.166933	−	0.753941i
$311$	19.5018	+	11.2594i	1.10584	+	0.638460i	0.937750	−	0.347311i	$-0.112905\pi$
$311$	19.5018	+	11.2594i	1.10584	+	0.638460i	0.168095	+	0.985771i	$0.446239\pi$
$312$	−3.09309	−	1.78579i	−0.175112	−	0.101101i
$313$	−4.65775	+	8.06746i	−0.263272	+	0.456000i	−0.967109	−	0.254361i	$-0.918135\pi$
$313$	−4.65775	+	8.06746i	−0.263272	+	0.456000i	0.703838	+	0.710361i	$0.251468\pi$
$314$	4.93908	−	2.85158i	0.278729	−	0.160924i
$315$	0.133497	−	0.122262i	0.00752169	−	0.00688867i
$316$	3.95064	+	2.28090i	0.222241	+	0.128311i
$317$	18.6912	+	10.7914i	1.04980	+	0.606104i	0.922594	−	0.385772i	$-0.126065\pi$
$317$	18.6912	+	10.7914i	1.04980	+	0.606104i	0.127209	+	0.991876i	$0.459398\pi$
$318$	−0.0685008	+	0.118647i	−0.00384133	+	0.00665339i
$319$			10.4660i			0.585984i
$320$	1.51023	+	1.64901i	0.0844242	+	0.0921822i
$321$	0.178903	−	0.309869i	0.00998540	−	0.0172952i
$322$		−	0.237647i		−	0.0132435i
$323$			2.21686i			0.123350i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−16.1888	+	7.53845i	−0.897994	+	0.418158i
$326$	5.46907	+	9.47271i	0.302904	+	0.524645i
$327$	1.27019			0.0702419
$328$	−3.72081	−	6.44463i	−0.205447	−	0.355845i
$329$	0.436667	+	0.756329i	0.0240742	+	0.0416978i
$330$	−6.48832	+	5.94226i	−0.357170	+	0.327111i
$331$	3.45970	+	1.99746i	0.190162	+	0.109790i	0.592059	−	0.805895i	$-0.298315\pi$
$331$	3.45970	+	1.99746i	0.190162	+	0.109790i	−0.401896	+	0.915685i	$0.631649\pi$
$332$			12.2820i			0.674062i
$333$	5.85497	+	1.64903i	0.320851	+	0.0903661i
$334$	−9.19298			−0.503018
$335$	−7.53911	−	2.37929i	−0.411906	−	0.129994i
$336$	−0.0404780	−	0.0701099i	−0.00220825	−	0.00382481i
$337$	4.81065	−	2.77743i	0.262053	−	0.151296i	−0.363218	−	0.931704i	$-0.618322\pi$
$337$	4.81065	−	2.77743i	0.262053	−	0.151296i	0.625271	+	0.780408i	$0.284989\pi$
$338$	0.121875	+	0.211094i	0.00662914	+	0.0114820i
$339$		−	15.9860i		−	0.868239i
$340$	−1.70142	−	1.85777i	−0.0922724	−	0.100752i
$341$		−	23.9241i		−	1.29556i
$342$	−1.70412	−	0.983874i	−0.0921482	−	0.0532018i
$343$			1.13285i			0.0611683i
$344$	−5.69104			−0.306840
$345$	6.25967	+	1.97550i	0.337009	+	0.106358i
$346$	4.32016	−	2.49425i	0.232253	−	0.134092i
$347$	−25.2200			−1.35388			−0.676940	−	0.736038i	$-0.736694\pi$
$347$	−25.2200			−1.35388			−0.676940	+	0.736038i	$0.736694\pi$
$348$	1.32997	−	2.30357i	0.0712937	−	0.123484i
$349$	−4.14403	+	7.17766i	−0.221825	+	0.384211i	−0.955362	−	0.295438i	$-0.904535\pi$
$349$	−4.14403	+	7.17766i	−0.221825	+	0.384211i	0.733537	+	0.679649i	$0.237868\pi$
$350$	−0.403220	−	0.0354943i	−0.0215530	−	0.00189725i
$351$	−3.09309	+	1.78579i	−0.165097	+	0.0953187i
$352$	1.96734	+	3.40754i	0.104860	+	0.181622i
$353$	14.1316	−	24.4767i	0.752150	−	1.30276i	−0.194628	−	0.980877i	$-0.562350\pi$
$353$	14.1316	−	24.4767i	0.752150	−	1.30276i	0.946779	−	0.321886i	$-0.104317\pi$
$354$	−1.42351	+	2.46559i	−0.0756586	+	0.131045i
$355$	4.69733	−	14.8842i	0.249308	−	0.789969i
$356$			13.0510i			0.691703i
$357$	0.0456025	+	0.0789858i	0.00241354	+	0.00418037i
$358$	8.05194	+	4.64879i	0.425558	+	0.245696i
$359$	4.51937			0.238523			0.119262	−	0.992863i	$-0.461947\pi$
$359$	4.51937			0.238523			0.119262	+	0.992863i	$0.461947\pi$
$360$	2.18319	−	0.483391i	0.115064	−	0.0254769i
$361$	−7.56399	+	13.1012i	−0.398105	+	0.689537i
$362$	−7.58038			−0.398416
$363$	−3.88130	+	2.24087i	−0.203716	+	0.117615i
$364$		−	0.289141i		−	0.0151551i
$365$	9.87034	−	9.03965i	0.516637	−	0.473157i
$366$	−4.81861	−	8.34607i	−0.251873	−	0.436256i
$367$	−13.0478	+	7.53314i	−0.681089	+	0.393227i	−0.800265	−	0.599646i	$-0.795308\pi$
$367$	−13.0478	+	7.53314i	−0.681089	+	0.393227i	0.119176	+	0.992873i	$0.461975\pi$
$368$	1.46775	−	2.54222i	0.0765120	−	0.132523i
$369$	−7.44162			−0.387395
$370$	−6.12307	−	12.1453i	−0.318323	−	0.631403i
$371$	−0.0110911			−0.000575821
$372$	−3.04016	+	5.26570i	−0.157625	+	0.273014i
$373$	25.0921	−	14.4869i	1.29922	−	0.750105i	0.318950	−	0.947772i	$-0.396670\pi$
$373$	25.0921	−	14.4869i	1.29922	−	0.750105i	0.980269	+	0.197667i	$0.0633364\pi$
$374$	−2.21641	−	3.83893i	−0.114608	−	0.198506i
$375$	4.28681	−	10.3259i	0.221370	−	0.533225i
$376$			10.7878i			0.556337i
$377$	8.22741	−	4.75010i	0.423733	−	0.244642i
$378$	−0.0809559			−0.00416392
$379$	13.4494	−	23.2950i	0.690848	−	1.19658i	−0.280713	−	0.959792i	$-0.590571\pi$
$379$	13.4494	−	23.2950i	0.690848	−	1.19658i	0.971560	−	0.236792i	$-0.0760959\pi$
$380$	0.951190	+	4.29597i	0.0487950	+	0.220379i
$381$	−16.4385			−0.842168
$382$	0.0739155	+	0.0426751i	0.00378184	+	0.00218345i
$383$	−4.83015	−	8.36606i	−0.246809	−	0.427486i	0.715830	−	0.698275i	$-0.246049\pi$
$383$	−4.83015	−	8.36606i	−0.246809	−	0.427486i	−0.962639	+	0.270789i	$0.912715\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−0.679245	−	0.214365i	−0.0346175	−	0.0109250i
$386$	−2.58258	+	4.47316i	−0.131450	+	0.227678i
$387$	−2.84552	+	4.92859i	−0.144646	+	0.250534i
$388$	−0.441424	−	0.764568i	−0.0224099	−	0.0388151i
$389$	−21.6494	+	12.4993i	−1.09767	+	0.633739i	−0.935607	−	0.353042i	$-0.885147\pi$
$389$	−21.6494	+	12.4993i	−1.09767	+	0.633739i	−0.162060	+	0.986781i	$0.551814\pi$
$390$	7.61604	+	2.40357i	0.385653	+	0.121709i
$391$	−1.65357	+	2.86407i	−0.0836247	+	0.144842i
$392$	−3.49672	+	6.05650i	−0.176611	+	0.305900i
$393$	−1.96051			−0.0988945
$394$	−9.34387	+	5.39468i	−0.470737	+	0.271780i
$395$	−9.72757	−	3.06995i	−0.489447	−	0.154466i
$396$	3.93468			0.197725
$397$		−	8.82419i		−	0.442873i	−0.975175	−	0.221437i	$-0.928925\pi$
$397$		−	8.82419i		−	0.442873i	0.975175	−	0.221437i	$-0.0710746\pi$
$398$	−6.87071	−	3.96681i	−0.344398	−	0.198838i
$399$		−	0.159301i		−	0.00797501i
$400$	−4.09423	−	2.87007i	−0.204711	−	0.143503i
$401$		−	21.1757i		−	1.05746i	−0.848789	−	0.528732i	$-0.822668\pi$
$401$		−	21.1757i		−	1.05746i	0.848789	−	0.528732i	$-0.177332\pi$
$402$	1.76776	+	3.06184i	0.0881676	+	0.152711i
$403$	−18.8069	+	10.8582i	−0.936840	+	0.540885i
$404$	2.84830	+	4.93340i	0.141708	+	0.245446i
$405$	0.672968	−	2.13240i	0.0334401	−	0.105960i
$406$	0.215337			0.0106870
$407$	−5.89961	−	23.1952i	−0.292433	−	1.14975i
$408$			1.12660i			0.0557750i
$409$	−19.6743	−	11.3590i	−0.972831	−	0.561664i	−0.0727331	−	0.997351i	$-0.523172\pi$
$409$	−19.6743	−	11.3590i	−0.972831	−	0.561664i	−0.900098	+	0.435687i	$0.856505\pi$
$410$	11.2385	+	12.2713i	0.555031	+	0.606035i
$411$	−10.2789	−	17.8036i	−0.507023	−	0.878189i
$412$	3.37085	+	5.83849i	0.166070	+	0.287642i
$413$	−0.230483			−0.0113413
$414$	−1.46775	−	2.54222i	−0.0721362	−	0.124944i
$415$	−5.93700	−	26.8140i	−0.291436	−	1.31625i
$416$	1.78579	−	3.09309i	0.0875558	−	0.151651i
$417$			12.9990i			0.636565i
$418$			7.74246i			0.378696i
$419$	−3.92133	+	6.79195i	−0.191570	+	0.331808i	−0.945771	−	0.324835i	$-0.894691\pi$
$419$	−3.92133	+	6.79195i	−0.191570	+	0.331808i	0.754201	+	0.656644i	$0.228024\pi$
$420$	0.122262	+	0.133497i	0.00596576	+	0.00651398i
$421$		−	10.2402i		−	0.499077i	−0.968365	−	0.249539i	$-0.919721\pi$
$421$		−	10.2402i		−	0.499077i	0.968365	−	0.249539i	$-0.0802789\pi$
$422$	−12.1595	+	21.0608i	−0.591914	+	1.02523i
$423$	9.34248	+	5.39388i	0.454247	+	0.262260i
$424$	−0.118647	−	0.0685008i	−0.00576200	−	0.00332669i
$425$	4.61256	+	3.23342i	0.223742	+	0.156844i
$426$	−6.04487	+	3.49001i	−0.292875	+	0.169091i
$427$	0.390095	−	0.675664i	0.0188780	−	0.0326977i
$428$	0.309869	+	0.178903i	0.0149781	+	0.00864761i
$429$	12.1703	+	7.02654i	0.587589	+	0.339244i
$430$	12.4246	−	2.75100i	0.599170	−	0.132665i
$431$	−25.4351	+	14.6850i	−1.22517	+	0.707349i	−0.966015	−	0.258488i	$-0.916776\pi$
$431$	−25.4351	+	14.6850i	−1.22517	+	0.707349i	−0.259150	+	0.965837i	$0.583443\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$			0.284291i			0.0136621i	0.999977	+	0.00683107i	$0.00217441\pi$
$433$			0.284291i			0.0136621i	−0.999977	+	0.00683107i	$0.997826\pi$
$434$	−0.492237			−0.0236281
$435$	−1.79005	+	5.67203i	−0.0858264	+	0.271953i
$436$			1.27019i			0.0608312i
$437$	5.00246	−	2.88817i	0.239300	−	0.138160i
$438$	−5.98563			−0.286004
$439$	−0.313552	+	0.181029i	−0.0149650	+	0.00864004i	−0.507464	−	0.861673i	$-0.669417\pi$
$439$	−0.313552	+	0.181029i	−0.0149650	+	0.00864004i	0.492499	+	0.870313i	$0.336084\pi$
$440$	−5.94226	−	6.48832i	−0.283286	−	0.309318i
$441$	3.49672	+	6.05650i	0.166511	+	0.288405i
$442$	−2.01188	+	3.48467i	−0.0956952	+	0.165749i
$443$		−	31.7244i		−	1.50727i	−0.657292	−	0.753636i	$-0.728298\pi$
$443$		−	31.7244i		−	1.50727i	0.657292	−	0.753636i	$-0.271702\pi$
$444$	−1.64903	+	5.85497i	−0.0782594	+	0.277865i
$445$	−6.30874	−	28.4929i	−0.299063	−	1.35069i
$446$	−15.8027	−	9.12368i	−0.748279	−	0.432019i
$447$	−19.5574	+	11.2914i	−0.925031	+	0.534067i
$448$	0.0701099	−	0.0404780i	0.00331238	−	0.00191240i
$449$	−4.41326	+	2.54800i	−0.208275	+	0.120248i	−0.600509	−	0.799618i	$-0.705035\pi$
$449$	−4.41326	+	2.54800i	−0.208275	+	0.120248i	0.392235	+	0.919865i	$0.371702\pi$
$450$	−4.53267	+	2.11067i	−0.213672	+	0.0994979i
$451$	14.6402	+	25.3576i	0.689381	+	1.19404i
$452$	15.9860			0.751917
$453$	−6.91418	−	3.99191i	−0.324857	−	0.187556i
$454$	−9.90851			−0.465030
$455$	0.139768	+	0.631251i	0.00655243	+	0.0295935i
$456$	0.983874	−	1.70412i	0.0460741	−	0.0798027i
$457$	15.4321	+	26.7292i	0.721885	+	1.25034i	0.960244	+	0.279164i	$0.0900572\pi$
$457$	15.4321	+	26.7292i	0.721885	+	1.25034i	−0.238359	+	0.971177i	$0.576610\pi$
$458$	−25.6160			−1.19696
$459$	0.975664	+	0.563300i	0.0455401	+	0.0262926i
$460$	−1.97550	+	6.25967i	−0.0921083	+	0.291858i
$461$	19.0806	+	11.0162i	0.888670	+	0.513074i	0.873507	−	0.486811i	$-0.161840\pi$
$461$	19.0806	+	11.0162i	0.888670	+	0.513074i	0.0151628	+	0.999885i	$0.495173\pi$
$462$	0.159268	+	0.275860i	0.00740982	+	0.0128342i
$463$	−17.1390	−	29.6855i	−0.796515	−	1.37960i	−0.921873	−	0.387492i	$-0.873341\pi$
$463$	−17.1390	−	29.6855i	−0.796515	−	1.37960i	0.125358	−	0.992112i	$-0.459992\pi$
$464$	2.30357	+	1.32997i	0.106941	+	0.0617422i
$465$	4.09186	−	12.9656i	0.189755	−	0.601267i
$466$	2.98587	+	1.72390i	0.138318	+	0.0798579i
$467$	25.6755			1.18812			0.594060	−	0.804421i	$-0.297524\pi$
$467$	25.6755			1.18812			0.594060	+	0.804421i	$0.297524\pi$
$468$	−1.78579	−	3.09309i	−0.0825484	−	0.142978i
$469$	−0.143110	+	0.247874i	−0.00660822	+	0.0114458i
$470$	−5.21470	−	23.5518i	−0.240536	−	1.08636i
$471$	5.70316			0.262788
$472$	−2.46559	−	1.42351i	−0.113488	−	0.0655223i
$473$	22.3925			1.02961
$474$	2.28090	+	3.95064i	0.104765	+	0.181459i
$475$	−4.15326	−	8.91914i	−0.190565	−	0.409238i
$476$	−0.0789858	+	0.0456025i	−0.00362031	+	0.00209019i
$477$	−0.118647	+	0.0685008i	−0.00543247	+	0.00313644i
$478$	−12.3341	+	7.12108i	−0.564147	+	0.325710i
$479$	30.5619	+	17.6449i	1.39641	+	0.806217i	0.994014	−	0.109249i	$-0.0348446\pi$
$479$	30.5619	+	17.6449i	1.39641	+	0.806217i	0.402395	+	0.915466i	$0.368178\pi$
$480$	0.483391	+	2.18319i	0.0220637	+	0.0996487i
$481$	−15.5564	+	15.1651i	−0.709309	+	0.691470i
$482$		−	20.6720i		−	0.941585i
$483$	0.118823	−	0.205808i	0.00540665	−	0.00936460i
$484$	−2.24087	−	3.88130i	−0.101858	−	0.176423i
$485$	1.33330	+	1.45582i	0.0605420	+	0.0661054i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	24.8974			1.12821			0.564105	−	0.825703i	$-0.309221\pi$
$487$	24.8974			1.12821			0.564105	+	0.825703i	$0.309221\pi$
$488$	8.34607	−	4.81861i	0.377809	−	0.218128i
$489$			10.9381i			0.494640i
$490$	4.70637	−	14.9128i	0.212612	−	0.673692i
$491$	−11.8114			−0.533040			−0.266520	−	0.963829i	$-0.585874\pi$
$491$	−11.8114			−0.533040			−0.266520	+	0.963829i	$0.585874\pi$
$492$		−	7.44162i		−	0.335494i
$493$	−2.59520	−	1.49834i	−0.116882	−	0.0674819i
$494$	6.08641	−	3.51399i	0.273841	−	0.158102i
$495$	−8.59018	+	1.90199i	−0.386100	+	0.0854881i
$496$	−5.26570	−	3.04016i	−0.236437	−	0.136507i
$497$	−0.489368	−	0.282537i	−0.0219512	−	0.0126735i
$498$	−6.14100	+	10.6365i	−0.275185	+	0.476634i
$499$	3.41972	−	1.97438i	0.153088	−	0.0883852i	−0.421499	−	0.906829i	$-0.638496\pi$
$499$	3.41972	−	1.97438i	0.153088	−	0.0883852i	0.574587	+	0.818444i	$0.305163\pi$
$500$	10.3259	+	4.28681i	0.461786	+	0.191712i
$501$	−7.96135	−	4.59649i	−0.355687	−	0.205356i
$502$	7.14077	+	4.12273i	0.318708	+	0.184006i
$503$	18.5458	−	32.1223i	0.826916	−	1.43226i	−0.0735293	−	0.997293i	$-0.523426\pi$
$503$	18.5458	−	32.1223i	0.826916	−	1.43226i	0.900446	−	0.434968i	$-0.143240\pi$
$504$		−	0.0809559i		−	0.00360606i
$505$	−8.60315	−	9.39373i	−0.382835	−	0.418016i
$506$	−5.77515	+	10.0029i	−0.256737	+	0.444681i
$507$			0.243751i			0.0108253i
$508$		−	16.4385i		−	0.729339i
$509$	−0.0856429	+	0.148338i	−0.00379605	+	0.00657496i	−0.867917	−	0.496709i	$-0.834542\pi$
$509$	−0.0856429	+	0.148338i	−0.00379605	+	0.00657496i	0.864121	+	0.503284i	$0.167875\pi$
$510$	−0.544588	−	2.45959i	−0.0241147	−	0.108912i
$511$	−0.242286	−	0.419652i	−0.0107181	−	0.0185643i
$512$	1.00000			0.0441942
$513$	−0.983874	−	1.70412i	−0.0434391	−	0.0752387i
$514$	3.41974	+	5.92316i	0.150838	+	0.261259i
$515$	−10.1815	−	11.1171i	−0.448650	−	0.489878i
$516$	−4.92859	−	2.84552i	−0.216969	−	0.125267i
$517$		−	42.4465i		−	1.86679i
$518$	−0.477241	+	0.121384i	−0.0209688	+	0.00533332i
$519$	4.98849			0.218971
$520$	−2.40357	+	7.61604i	−0.105403	+	0.333986i
$521$	−6.76509	−	11.7175i	−0.296384	−	0.513352i	0.678922	−	0.734210i	$-0.262447\pi$
$521$	−6.76509	−	11.7175i	−0.296384	−	0.513352i	−0.975306	+	0.220859i	$0.929114\pi$
$522$	2.30357	−	1.32997i	0.100825	−	0.0582111i
$523$	16.3542	+	28.3263i	0.715118	+	1.23862i	0.962914	+	0.269809i	$0.0869605\pi$
$523$	16.3542	+	28.3263i	0.715118	+	1.23862i	−0.247796	+	0.968812i	$0.579706\pi$
$524$		−	1.96051i		−	0.0856452i
$525$	−0.331452	−	0.232349i	−0.0144658	−	0.0101405i
$526$		−	14.7172i		−	0.641699i
$527$	5.93234	+	3.42504i	0.258417	+	0.149197i
$528$			3.93468i			0.171235i
$529$	−14.3828			−0.625339
$530$	0.292142	+	0.0921977i	0.0126898	+	0.00400481i
$531$	−2.46559	+	1.42351i	−0.106997	+	0.0617750i
$532$	0.159301			0.00690657
$533$	13.2892	−	23.0176i	0.575619	−	0.997002i
$534$	−6.52551	+	11.3025i	−0.282387	+	0.489108i
$535$	−0.762985	−	0.240792i	−0.0329867	−	0.0104104i
$536$	−3.06184	+	1.76776i	−0.132251	+	0.0763554i
$537$	4.64879	+	8.05194i	0.200610	+	0.347467i
$538$	−13.2635	+	22.9731i	−0.571831	+	0.990440i
$539$	13.7585	−	23.8304i	0.592621	−	1.02645i
$540$	2.13240	+	0.672968i	0.0917637	+	0.0289599i
$541$			29.1310i			1.25244i	0.779647	+	0.626220i	$0.215399\pi$
$541$			29.1310i			1.25244i	−0.779647	+	0.626220i	$0.784601\pi$
$542$	6.61234	+	11.4529i	0.284024	+	0.491945i
$543$	−6.56480	−	3.79019i	−0.281722	−	0.162653i
$544$	−1.12660			−0.0483026
$545$	−0.613999	−	2.77308i	−0.0263008	−	0.118786i
$546$	0.144571	−	0.250404i	0.00618705	−	0.0107163i
$547$	−25.3366			−1.08332			−0.541658	−	0.840599i	$-0.682203\pi$
$547$	−25.3366			−1.08332			−0.541658	+	0.840599i	$0.682203\pi$
$548$	17.8036	−	10.2789i	0.760534	−	0.439094i
$549$		−	9.63722i		−	0.411306i
$550$	16.1095	+	11.2928i	0.686911	+	0.481527i
$551$	2.61704	+	4.53284i	0.111490	+	0.193106i
$552$	2.54222	−	1.46775i	0.108204	−	0.0624718i
$553$	−0.184652	+	0.319827i	−0.00785222	+	0.0136004i
$554$	−12.6155			−0.535982
$555$	0.769907	−	13.5797i	0.0326807	−	0.576425i
$556$	−12.9990			−0.551281
$557$	2.18960	−	3.79250i	0.0927765	−	0.160694i	−0.815902	−	0.578190i	$-0.803759\pi$
$557$	2.18960	−	3.79250i	0.0927765	−	0.160694i	0.908678	+	0.417497i	$0.137092\pi$
$558$	−5.26570	+	3.04016i	−0.222915	+	0.128700i
$559$	−10.1630	−	17.6029i	−0.429851	−	0.744523i
$560$	−0.133497	+	0.122262i	−0.00564127	+	0.00516650i
$561$		−	4.43281i		−	0.187154i
$562$	10.1405	−	5.85462i	0.427751	−	0.246962i
$563$	12.3285			0.519586			0.259793	−	0.965664i	$-0.416346\pi$
$563$	12.3285			0.519586			0.259793	+	0.965664i	$0.416346\pi$
$564$	−5.39388	+	9.34248i	−0.227123	+	0.393389i
$565$	−34.9005	+	7.72747i	−1.46827	+	0.325097i
$566$	16.2667			0.683739
$567$	−0.0701099	−	0.0404780i	−0.00294434	−	0.00169991i
$568$	−3.49001	−	6.04487i	−0.146437	−	0.253637i
$569$			33.7423i			1.41455i	0.706939	+	0.707274i	$0.250075\pi$
$569$			33.7423i			1.41455i	−0.706939	+	0.707274i	$0.749925\pi$
$570$	−1.32423	+	4.19602i	−0.0554659	+	0.175752i
$571$	1.27841	−	2.21428i	0.0535000	−	0.0926647i	−0.838035	−	0.545616i	$-0.816296\pi$
$571$	1.27841	−	2.21428i	0.0535000	−	0.0926647i	0.891535	+	0.452952i	$0.149629\pi$
$572$	−7.02654	+	12.1703i	−0.293794	+	0.508867i
$573$	0.0426751	+	0.0739155i	0.00178278	+	0.00308786i
$574$	0.521731	−	0.301222i	0.0217766	−	0.0125727i
$575$	1.28704	−	14.6210i	0.0536734	−	0.609738i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	20.7924	−	36.0134i	0.865598	−	1.49926i	−0.000854926	−	1.00000i	$-0.500272\pi$
$577$	20.7924	−	36.0134i	0.865598	−	1.49926i	0.866453	−	0.499259i	$-0.166395\pi$
$578$	−15.7308			−0.654314
$579$	−4.47316	+	2.58258i	−0.185898	+	0.107328i
$580$	−5.67203	−	1.79005i	−0.235518	−	0.0743278i
$581$	−0.994300			−0.0412505
$582$		−	0.882847i		−	0.0365952i
$583$	0.466838	+	0.269529i	0.0193345	+	0.0111628i
$584$		−	5.98563i		−	0.247687i
$585$	5.39390	+	5.88957i	0.223010	+	0.243504i
$586$		−	5.33950i		−	0.220573i
$587$	−5.77378	−	10.0005i	−0.238310	−	0.412764i	0.721920	−	0.691977i	$-0.243260\pi$
$587$	−5.77378	−	10.0005i	−0.238310	−	0.412764i	−0.960229	+	0.279213i	$0.909927\pi$
$588$	−6.05650	+	3.49672i	−0.249766	+	0.144202i
$589$	−5.98226	−	10.3616i	−0.246495	−	0.426941i
$590$	6.07097	+	1.91595i	0.249938	+	0.0788785i
$591$	−10.7894			−0.443815
$592$	−5.85497	−	1.64903i	−0.240638	−	0.0677746i
$593$			2.72675i			0.111974i	0.998431	+	0.0559872i	$0.0178306\pi$
$593$			2.72675i			0.111974i	−0.998431	+	0.0559872i	$0.982169\pi$
$594$	3.40754	+	1.96734i	0.139813	+	0.0807210i
$595$	0.150397	−	0.137740i	0.00616569	−	0.00564679i
$596$	−11.2914	−	19.5574i	−0.462516	−	0.801101i
$597$	−3.96681	−	6.87071i	−0.162351	−	0.281200i
$598$	10.4844			0.428740
$599$	2.29323	+	3.97199i	0.0936988	+	0.162291i	0.909065	−	0.416655i	$-0.136798\pi$
$599$	2.29323	+	3.97199i	0.0936988	+	0.162291i	−0.815366	+	0.578946i	$0.803464\pi$
$600$	−2.11067	−	4.53267i	−0.0861677	−	0.185045i
$601$	4.07826	−	7.06376i	0.166356	−	0.288137i	−0.770780	−	0.637101i	$-0.780133\pi$
$601$	4.07826	−	7.06376i	0.166356	−	0.288137i	0.937136	+	0.348965i	$0.113467\pi$
$602$		−	0.460724i		−	0.0187777i
$603$			3.53551i			0.143977i
$604$	3.99191	−	6.91418i	0.162428	−	0.281334i
$605$	6.76844	+	7.39042i	0.275176	+	0.300463i
$606$			5.69660i			0.231409i
$607$	−10.9036	+	18.8855i	−0.442562	+	0.766540i	−0.997879	−	0.0650990i	$-0.979264\pi$
$607$	−10.9036	+	18.8855i	−0.442562	+	0.766540i	0.555317	+	0.831639i	$0.312597\pi$
$608$	1.70412	+	0.983874i	0.0691112	+	0.0399013i
$609$	0.186488	+	0.107669i	0.00755686	+	0.00436296i
$610$	−15.8918	+	14.5544i	−0.643441	+	0.589289i
$611$	−33.3675	+	19.2647i	−1.34990	+	0.779368i
$612$	−0.563300	+	0.975664i	−0.0227700	+	0.0394389i
$613$	−11.2580	−	6.49980i	−0.454706	−	0.262525i	0.255110	−	0.966912i	$-0.417888\pi$
$613$	−11.2580	−	6.49980i	−0.454706	−	0.262525i	−0.709816	+	0.704387i	$0.751222\pi$
$614$	−20.2859	−	11.7121i	−0.818672	−	0.472661i
$615$	3.59721	+	16.2465i	0.145053	+	0.655122i
$616$	−0.275860	+	0.159268i	−0.0111147	+	0.00641709i
$617$	18.7829	+	10.8443i	0.756170	+	0.436575i	0.827919	−	0.560848i	$-0.189525\pi$
$617$	18.7829	+	10.8443i	0.756170	+	0.436575i	−0.0717491	+	0.997423i	$0.522858\pi$
$618$			6.74171i			0.271191i
$619$	−16.7055			−0.671450			−0.335725	−	0.941960i	$-0.608981\pi$
$619$	−16.7055			−0.671450			−0.335725	+	0.941960i	$0.608981\pi$
$620$	12.9656	+	4.09186i	0.520712	+	0.164333i
$621$		−	2.93551i		−	0.117798i
$622$	−19.5018	+	11.2594i	−0.781950	+	0.451459i
$623$	−1.05656			−0.0423301
$624$	3.09309	−	1.78579i	0.123823	−	0.0714890i
$625$	−24.6155	−	4.36751i	−0.984622	−	0.174700i
$626$	−4.65775	−	8.06746i	−0.186161	−	0.322441i
$627$	−3.87123	+	6.70517i	−0.154602	+	0.267779i
$628$			5.70316i			0.227581i
$629$	6.59621	+	1.85779i	0.263008	+	0.0740751i
$630$	0.0391333	+	0.176742i	0.00155911	+	0.00704159i
$631$	12.8764	+	7.43418i	0.512600	+	0.295950i	0.733902	−	0.679255i	$-0.237697\pi$
$631$	12.8764	+	7.43418i	0.512600	+	0.295950i	−0.221301	+	0.975205i	$0.571030\pi$
$632$	−3.95064	+	2.28090i	−0.157148	+	0.0907294i
$633$	−21.0608	+	12.1595i	−0.837093	+	0.483296i
$634$	−18.6912	+	10.7914i	−0.742323	+	0.428580i
$635$	7.94620	+	35.8884i	0.315335	+	1.42419i
$636$	−0.0685008	−	0.118647i	−0.00271623	−	0.00470465i
$637$	−24.9777			−0.989653
$638$	−9.06382	−	5.23300i	−0.358840	−	0.207176i
$639$	−6.98002			−0.276125
$640$	−2.18319	+	0.483391i	−0.0862983	+	0.0191077i
$641$	−22.7322	+	39.3734i	−0.897869	+	1.55516i	−0.0676565	+	0.997709i	$0.521552\pi$
$641$	−22.7322	+	39.3734i	−0.897869	+	1.55516i	−0.830213	+	0.557447i	$0.811781\pi$
$642$	0.178903	+	0.309869i	0.00706075	+	0.0122296i
$643$	−1.49694			−0.0590335			−0.0295167	−	0.999564i	$-0.509397\pi$
$643$	−1.49694			−0.0590335			−0.0295167	+	0.999564i	$0.509397\pi$
$644$	0.205808	+	0.118823i	0.00810998	+	0.00468230i
$645$	12.1356	+	3.82989i	0.477837	+	0.150802i
$646$	−1.91986	−	1.10843i	−0.0755359	−	0.0436107i
$647$	−8.29567	−	14.3685i	−0.326136	−	0.564885i	0.655605	−	0.755104i	$-0.272413\pi$
$647$	−8.29567	−	14.3685i	−0.326136	−	0.564885i	−0.981742	+	0.190219i	$0.939080\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	9.70131	+	5.60106i	0.380810	+	0.219861i
$650$	1.56593	−	17.7892i	0.0614207	−	0.697748i
$651$	−0.426290	−	0.246119i	−0.0167076	−	0.00964615i
$652$	−10.9381			−0.428371
$653$	15.6069	+	27.0320i	0.610747	+	1.05784i	0.991115	+	0.133009i	$0.0424640\pi$
$653$	15.6069	+	27.0320i	0.610747	+	1.05784i	−0.380368	+	0.924835i	$0.624203\pi$
$654$	−0.635097	+	1.10002i	−0.0248342	+	0.0430142i
$655$	0.947691	+	4.28017i	0.0370294	+	0.167240i
$656$	7.44162			0.290546
$657$	−5.18371	−	2.99281i	−0.202236	−	0.116761i
$658$	−0.873334			−0.0340461
$659$	−17.9421	−	31.0766i	−0.698925	−	1.21057i	−0.968840	−	0.247689i	$-0.920329\pi$
$659$	−17.9421	−	31.0766i	−0.698925	−	1.21057i	0.269914	−	0.962884i	$-0.413005\pi$
$660$	−1.90199	−	8.59018i	−0.0740348	−	0.334372i
$661$	−10.6343	+	6.13969i	−0.413624	+	0.238806i	−0.692346	−	0.721566i	$-0.743423\pi$
$661$	−10.6343	+	6.13969i	−0.413624	+	0.238806i	0.278721	+	0.960372i	$0.410089\pi$
$662$	−3.45970	+	1.99746i	−0.134465	+	0.0776334i
$663$	−3.48467	+	2.01188i	−0.135333	+	0.0781348i
$664$	−10.6365	−	6.14100i	−0.412777	−	0.238317i
$665$	−0.347784	+	0.0770045i	−0.0134865	+	0.00298611i
$666$	−4.35559	+	4.24604i	−0.168776	+	0.164531i
$667$			7.80826i			0.302337i
$668$	4.59649	−	7.96135i	0.177844	−	0.308034i
$669$	−9.12368	−	15.8027i	−0.352742	−	0.610967i
$670$	5.83008	−	5.33942i	0.225236	−	0.206280i
$671$	−32.8392	+	18.9597i	−1.26774	+	0.731931i
$672$	0.0809559			0.00312294
$673$	1.05405	−	0.608554i	0.0406305	−	0.0234580i	−0.479547	−	0.877516i	$-0.659199\pi$
$673$	1.05405	−	0.608554i	0.0406305	−	0.0234580i	0.520178	+	0.854058i	$0.325866\pi$
$674$			5.55486i			0.213965i
$675$	−4.98074	−	0.438440i	−0.191709	−	0.0168756i
$676$	−0.243751			−0.00937502
$677$		−	28.6640i		−	1.10165i	−0.834622	−	0.550823i	$-0.814314\pi$
$677$		−	28.6640i		−	1.10165i	0.834622	−	0.550823i	$-0.185686\pi$
$678$	13.8443	+	7.99299i	0.531686	+	0.306969i
$679$	0.0618963	−	0.0357359i	0.00237536	−	0.00137142i
$680$	2.45959	−	0.544588i	0.0943208	−	0.0208840i
$681$	−8.58102	−	4.95426i	−0.328826	−	0.189848i
$682$	20.7189	+	11.9621i	0.793367	+	0.458051i
$683$	−18.2271	+	31.5702i	−0.697439	+	1.20800i	0.271913	+	0.962322i	$0.412344\pi$
$683$	−18.2271	+	31.5702i	−0.697439	+	1.20800i	−0.969352	+	0.245677i	$0.920990\pi$
$684$	1.70412	−	0.983874i	0.0651586	−	0.0376193i
$685$	−33.9001	+	31.0470i	−1.29525	+	1.18625i
$686$	−0.981079	−	0.566426i	−0.0374578	−	0.0216263i
$687$	−22.1841	−	12.8080i	−0.846376	−	0.488655i
$688$	2.84552	−	4.92859i	0.108484	−	0.187901i
$689$		−	0.489313i		−	0.0186414i
$690$	−4.84067	+	4.43328i	−0.184281	+	0.168772i
$691$	4.52772	−	7.84224i	0.172243	−	0.298333i	−0.766961	−	0.641694i	$-0.778232\pi$
$691$	4.52772	−	7.84224i	0.172243	−	0.298333i	0.939204	+	0.343361i	$0.111565\pi$
$692$			4.98849i			0.189634i
$693$			0.318536i			0.0121002i
$694$	12.6100	−	21.8412i	0.478669	−	0.829079i
$695$	28.3794	−	6.28361i	1.07649	−	0.238351i
$696$	1.32997	+	2.30357i	0.0504123	+	0.0873166i
$697$	−8.38373			−0.317556
$698$	−4.14403	−	7.17766i	−0.156854	−	0.271679i
$699$	1.72390	+	2.98587i	0.0652037	+	0.112936i
$700$	0.232349	−	0.331452i	0.00878197	−	0.0125277i
$701$	−16.7531	−	9.67242i	−0.632757	−	0.365322i	0.149062	−	0.988828i	$-0.452375\pi$
$701$	−16.7531	−	9.67242i	−0.632757	−	0.365322i	−0.781819	+	0.623505i	$0.785708\pi$
$702$		−	3.57159i		−	0.134801i
$703$	−8.35514	−	8.57069i	−0.315120	−	0.323250i
$704$	−3.93468			−0.148294
$705$	7.25983	−	23.0038i	0.273421	−	0.866373i
$706$	14.1316	+	24.4767i	0.531851	+	0.921192i
$707$	−0.399388	+	0.230587i	−0.0150205	+	0.00867211i
$708$	−1.42351	−	2.46559i	−0.0534987	−	0.0926625i
$709$		−	46.2387i		−	1.73653i	−0.496100	−	0.868265i	$-0.665235\pi$
$709$		−	46.2387i		−	1.73653i	0.496100	−	0.868265i	$-0.334765\pi$
$710$	10.5414	+	11.5101i	0.395612	+	0.431966i
$711$			4.56180i			0.171081i
$712$	−11.3025	−	6.52551i	−0.423580	−	0.244554i
$713$		−	17.8488i		−	0.668443i
$714$	−0.0912049			−0.00341326
$715$	9.45727	−	29.9667i	0.353682	−	1.12069i
$716$	−8.05194	+	4.64879i	−0.300915	+	0.173734i
$717$	−14.2422			−0.531883
$718$	−2.25969	+	3.91389i	−0.0843307	+	0.146065i
$719$	−12.4040	+	21.4844i	−0.462592	+	0.801233i	−0.999089	−	0.0426691i	$-0.986414\pi$
$719$	−12.4040	+	21.4844i	−0.462592	+	0.801233i	0.536497	+	0.843902i	$0.319747\pi$
$720$	−0.672968	+	2.13240i	−0.0250800	+	0.0794697i
$721$	−0.472660	+	0.272891i	−0.0176028	+	0.0101630i
$722$	−7.56399	−	13.1012i	−0.281502	−	0.487576i
$723$	10.3360	−	17.9025i	0.384401	−	0.665801i
$724$	3.79019	−	6.56480i	0.140861	−	0.243979i
$725$	13.2484	+	1.16622i	0.492035	+	0.0433123i
$726$		−	4.48174i		−	0.166333i
$727$	3.14633	+	5.44961i	0.116691	+	0.202115i	0.918454	−	0.395527i	$-0.129438\pi$
$727$	3.14633	+	5.44961i	0.116691	+	0.202115i	−0.801763	+	0.597641i	$0.796105\pi$
$728$	0.250404	+	0.144571i	0.00928058	+	0.00535815i
$729$	−1.00000			−0.0370370
$730$	2.89340	+	13.0678i	0.107089	+	0.483661i
$731$	−3.20576	+	5.55255i	−0.118569	+	0.205368i
$732$	9.63722			0.356202
$733$	−19.0928	+	11.0232i	−0.705210	+	0.407153i	−0.809285	−	0.587416i	$-0.800145\pi$
$733$	−19.0928	+	11.0232i	−0.705210	+	0.407153i	0.104075	+	0.994569i	$0.466812\pi$
$734$		−	15.0663i		−	0.556107i
$735$	11.5322	−	10.5617i	0.425373	−	0.389573i
$736$	1.46775	+	2.54222i	0.0541021	+	0.0937077i
$737$	12.0474	−	6.95556i	0.443771	−	0.256211i
$738$	3.72081	−	6.44463i	0.136965	−	0.237230i
$739$	43.2559			1.59120			0.795598	−	0.605825i	$-0.207157\pi$
$739$	43.2559			1.59120			0.795598	+	0.605825i	$0.207157\pi$
$740$	13.5797	+	0.769907i	0.499198	+	0.0283024i
$741$	7.02798			0.258179
$742$	0.00554555	−	0.00960517i	0.000203583	−	0.000352617i
$743$	0.357720	−	0.206529i	0.0131235	−	0.00757683i	−0.493424	−	0.869789i	$-0.664255\pi$
$743$	0.357720	−	0.206529i	0.0131235	−	0.00757683i	0.506547	+	0.862212i	$0.330922\pi$
$744$	−3.04016	−	5.26570i	−0.111458	−	0.193050i
$745$	34.1053	+	37.2393i	1.24952	+	1.36434i
$746$			28.9739i			1.06081i
$747$	−10.6365	+	6.14100i	−0.389170	+	0.224687i
$748$	4.43281			0.162080
$749$	−0.0144833	+	0.0250858i	−0.000529207	+	0.000916614i
$750$	6.79905	+	8.87541i	0.248266	+	0.324084i
$751$	43.8781			1.60114			0.800568	−	0.599243i	$-0.204531\pi$
$751$	43.8781			1.60114			0.800568	+	0.599243i	$0.204531\pi$
$752$	−9.34248	−	5.39388i	−0.340685	−	0.196695i
$753$	4.12273	+	7.14077i	0.150241	+	0.260224i
$754$			9.50019i			0.345977i
$755$	−5.37285	+	17.0247i	−0.195538	+	0.619591i
$756$	0.0404780	−	0.0701099i	0.00147217	−	0.00254987i
$757$	−12.6101	+	21.8413i	−0.458321	+	0.793835i	−0.998872	−	0.0474758i	$-0.984882\pi$
$757$	−12.6101	+	21.8413i	−0.458321	+	0.793835i	0.540551	+	0.841311i	$0.318216\pi$
$758$	13.4494	+	23.2950i	0.488503	+	0.846112i
$759$	−10.0029	+	5.77515i	−0.363081	+	0.209625i
$760$	−4.19602	−	1.32423i	−0.152206	−	0.0480349i
$761$	13.9826	−	24.2185i	0.506868	−	0.877921i	−0.493101	−	0.869972i	$-0.664137\pi$
$761$	13.9826	−	24.2185i	0.506868	−	0.877921i	0.999968	−	0.00794833i	$-0.00253006\pi$
$762$	8.21923	−	14.2361i	0.297751	−	0.515721i
$763$	−0.102830			−0.00372268
$764$	−0.0739155	+	0.0426751i	−0.00267417	+	0.00154393i
$765$	0.758166	−	2.40236i	0.0274115	−	0.0868574i
$766$	9.66029			0.349041
$767$		−	10.1684i		−	0.367159i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$			51.0104i			1.83948i	0.392527	+	0.919740i	$0.371601\pi$
$769$			51.0104i			1.83948i	−0.392527	+	0.919740i	$0.628399\pi$
$770$	0.525268	−	0.481061i	0.0189293	−	0.0173362i
$771$			6.83947i			0.246318i
$772$	−2.58258	−	4.47316i	−0.0929490	−	0.160992i
$773$	−31.2064	+	18.0170i	−1.12242	+	0.648028i	−0.942017	−	0.335565i	$-0.891073\pi$
$773$	−31.2064	+	18.0170i	−1.12242	+	0.648028i	−0.180400	+	0.983593i	$0.557739\pi$
$774$	−2.84552	−	4.92859i	−0.102280	−	0.177154i
$775$	−30.2845	−	2.66585i	−1.08785	−	0.0957602i
$776$	0.882847			0.0316924
$777$	−0.473995	−	0.133499i	−0.0170045	−	0.00478923i
$778$		−	24.9986i		−	0.896242i
$779$	12.6814	+	7.32161i	0.454358	+	0.262324i
$780$	−5.88957	+	5.39390i	−0.210880	+	0.193133i
$781$	13.7321	+	23.7847i	0.491373	+	0.851082i
$782$	−1.65357	−	2.86407i	−0.0591316	−	0.102419i
$783$	2.65993			0.0950583
$784$	−3.49672	−	6.05650i	−0.124883	−	0.216304i
$785$	−2.75685	−	12.4511i	−0.0983964	−	0.444399i
$786$	0.980254	−	1.69785i	0.0349645	−	0.0605603i
$787$		−	49.6923i		−	1.77134i	−0.464317	−	0.885669i	$-0.653700\pi$
$787$		−	49.6923i		−	1.77134i	0.464317	−	0.885669i	$-0.346300\pi$
$788$		−	10.7894i		−	0.384355i
$789$	7.35858	−	12.7454i	0.261972	−	0.453750i
$790$	7.52244	−	6.88935i	0.267636	−	0.245112i
$791$			1.29416i			0.0460150i
$792$	−1.96734	+	3.40754i	−0.0699065	+	0.121082i
$793$	29.8087	+	17.2101i	1.05854	+	0.611148i
$794$	7.64197	+	4.41209i	0.271203	+	0.156579i
$795$	0.206903	+	0.225916i	0.00733810	+	0.00801243i
$796$	6.87071	−	3.96681i	0.243526	−	0.140600i
$797$	22.4128	−	38.8201i	0.793902	−	1.37508i	−0.129632	−	0.991562i	$-0.541380\pi$
$797$	22.4128	−	38.8201i	0.793902	−	1.37508i	0.923534	−	0.383516i	$-0.125287\pi$
$798$	0.137959	+	0.0796504i	0.00488368	+	0.00281959i
$799$	10.5252	+	6.07675i	0.372356	+	0.214980i
$800$	4.53267	−	2.11067i	0.160254	−	0.0746235i
$801$	−11.3025	+	6.52551i	−0.399355	+	0.230568i
$802$	18.3387	+	10.5878i	0.647561	+	0.373870i
$803$			23.5516i			0.831117i
$804$	−3.53551			−0.124688
$805$	−0.506757	−	0.159929i	−0.0178608	−	0.00563675i
$806$		−	21.7164i		−	0.764927i
$807$	−22.9731	+	13.2635i	−0.808691	+	0.466898i
$808$	−5.69660			−0.200406
$809$	36.6153	−	21.1399i	1.28733	−	0.743238i	0.309149	−	0.951014i	$-0.399956\pi$
$809$	36.6153	−	21.1399i	1.28733	−	0.743238i	0.978176	+	0.207776i	$0.0666225\pi$
$810$	1.51023	+	1.64901i	0.0530639	+	0.0579402i
$811$	20.1394	+	34.8824i	0.707189	+	1.22489i	0.965896	+	0.258931i	$0.0833702\pi$
$811$	20.1394	+	34.8824i	0.707189	+	1.22489i	−0.258707	+	0.965956i	$0.583296\pi$
$812$	−0.107669	+	0.186488i	−0.00377843	+	0.00654443i
$813$			13.2247i			0.463810i
$814$	23.0375	+	6.48840i	0.807463	+	0.227418i
$815$	23.8801	−	5.28739i	0.836483	−	0.185209i
$816$	−0.975664	−	0.563300i	−0.0341551	−	0.0197194i
$817$	9.69821	−	5.59927i	0.339298	−	0.195894i
$818$	19.6743	−	11.3590i	0.687896	−	0.397157i
$819$	0.250404	−	0.144571i	0.00874981	−	0.00505171i
$820$	−16.2465	+	3.59721i	−0.567352	+	0.125620i
$821$	−13.3498	−	23.1225i	−0.465910	−	0.806980i	0.533332	−	0.845906i	$-0.320940\pi$
$821$	−13.3498	−	23.1225i	−0.465910	−	0.806980i	−0.999242	+	0.0389258i	$0.987606\pi$
$822$	20.5579			0.717038
$823$	−29.7911	−	17.1999i	−1.03845	−	0.599551i	−0.119058	−	0.992887i	$-0.537988\pi$
$823$	−29.7911	−	17.1999i	−1.03845	−	0.599551i	−0.919395	+	0.393336i	$0.871321\pi$
$824$	−6.74171			−0.234858
$825$	8.30482	+	17.8346i	0.289137	+	0.620922i
$826$	0.115241	−	0.199604i	0.00400976	−	0.00694511i
$827$	20.7432	+	35.9282i	0.721310	+	1.24935i	0.960475	+	0.278367i	$0.0897931\pi$
$827$	20.7432	+	35.9282i	0.721310	+	1.24935i	−0.239165	+	0.970979i	$0.576874\pi$
$828$	2.93551			0.102016
$829$	−22.2080	−	12.8218i	−0.771316	−	0.445319i	0.0620281	−	0.998074i	$-0.480243\pi$
$829$	−22.2080	−	12.8218i	−0.771316	−	0.445319i	−0.833344	+	0.552755i	$0.813576\pi$
$830$	26.1901	+	8.26539i	0.909071	+	0.286896i
$831$	−10.9254	−	6.30776i	−0.378997	−	0.218814i
$832$	1.78579	+	3.09309i	0.0619113	+	0.107233i
$833$	3.93941	+	6.82325i	0.136492	+	0.236412i
$834$	−11.2575	−	6.49951i	−0.389815	−	0.225060i
$835$	−6.18658	+	19.6031i	−0.214096	+	0.678392i
$836$	−6.70517	−	3.87123i	−0.231903	−	0.133889i
$837$	−6.08031			−0.210166
$838$	−3.92133	−	6.79195i	−0.135460	−	0.234624i
$839$	−21.5082	+	37.2532i	−0.742544	+	1.28612i	0.208789	+	0.977961i	$0.433048\pi$
$839$	−21.5082	+	37.2532i	−0.742544	+	1.28612i	−0.951333	+	0.308163i	$0.900286\pi$
$840$	−0.176742	+	0.0391333i	−0.00609819	+	0.00135023i
$841$	21.9248			0.756026
$842$	8.86828	+	5.12010i	0.305621	+	0.176450i
$843$	11.7092			0.403287
$844$	−12.1595	−	21.0608i	−0.418547	−	0.724944i
$845$	0.532155	−	0.117827i	0.0183067	−	0.00405336i
$846$	−9.34248	+	5.39388i	−0.321201	+	0.185446i
$847$	0.314214	−	0.181412i	0.0107965	−	0.00623338i
$848$	0.118647	−	0.0685008i	0.00407435	−	0.00235233i
$849$	14.0874	+	8.13334i	0.483477	+	0.279135i
$850$	−5.10650	+	2.37788i	−0.175152	+	0.0815606i
$851$	−4.40146	−	17.3050i	−0.150880	−	0.593209i
$852$		−	6.98002i		−	0.239131i
$853$	−16.9920	+	29.4310i	−0.581794	+	1.00770i	0.413473	+	0.910517i	$0.364316\pi$
$853$	−16.9920	+	29.4310i	−0.581794	+	1.00770i	−0.995267	+	0.0971804i	$0.969018\pi$
$854$	0.390095	+	0.675664i	0.0133488	+	0.0231208i
$855$	−3.24483	+	2.97174i	−0.110971	+	0.101631i
$856$	−0.309869	+	0.178903i	−0.0105911	+	0.00611479i
$857$	21.8401			0.746044			0.373022	−	0.927822i	$-0.378322\pi$
$857$	21.8401			0.746044			0.373022	+	0.927822i	$0.378322\pi$
$858$	−12.1703	+	7.02654i	−0.415488	+	0.239882i
$859$		−	17.1572i		−	0.585398i	−0.956205	−	0.292699i	$-0.905447\pi$
$859$		−	17.1572i		−	0.585398i	0.956205	−	0.292699i	$-0.0945534\pi$
$860$	−3.82989	+	12.1356i	−0.130598	+	0.413819i
$861$	0.602443			0.0205312
$862$		−	29.3699i		−	1.00034i
$863$	22.0352	+	12.7221i	0.750089	+	0.433064i	0.825726	−	0.564072i	$-0.190766\pi$
$863$	22.0352	+	12.7221i	0.750089	+	0.433064i	−0.0756373	+	0.997135i	$0.524099\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	−2.41139	−	10.8908i	−0.0819897	−	0.370300i
$866$	−0.246203	−	0.142145i	−0.00836632	−	0.00483030i
$867$	−13.6232	−	7.86539i	−0.462670	−	0.267123i
$868$	0.246119	−	0.426290i	0.00835381	−	0.0144692i
$869$	15.5445	−	8.97462i	0.527311	−	0.304443i
$870$	−4.01710	−	4.38625i	−0.136192	−	0.148708i
$871$	−10.9356	−	6.31370i	−0.370540	−	0.213931i
$872$	−1.10002	−	0.635097i	−0.0372514	−	0.0215071i
$873$	0.441424	−	0.764568i	0.0149399	−	0.0258767i
$874$			5.77634i			0.195388i
$875$	−0.347042	+	0.835939i	−0.0117322	+	0.0282599i
$876$	2.99281	−	5.18371i	0.101118	−	0.175141i
$877$		−	47.4680i		−	1.60288i	−0.598074	−	0.801441i	$-0.704067\pi$
$877$		−	47.4680i		−	1.60288i	0.598074	−	0.801441i	$-0.295933\pi$
$878$		−	0.362058i		−	0.0122189i
$879$	2.66975	−	4.62415i	0.0900485	−	0.155969i
$880$	8.59018	−	1.90199i	0.289575	−	0.0641160i
$881$	−8.58706	−	14.8732i	−0.289305	−	0.501091i	0.684339	−	0.729164i	$-0.260091\pi$
$881$	−8.58706	−	14.8732i	−0.289305	−	0.501091i	−0.973644	+	0.228073i	$0.926758\pi$
$882$	−6.99345			−0.235482
$883$	6.83447	+	11.8376i	0.229998	+	0.398369i	0.957807	−	0.287411i	$-0.0927946\pi$
$883$	6.83447	+	11.8376i	0.229998	+	0.398369i	−0.727809	+	0.685780i	$0.759461\pi$
$884$	−2.01188	−	3.48467i	−0.0676667	−	0.117202i
$885$	4.29964	+	4.69475i	0.144531	+	0.157812i
$886$	27.4741	+	15.8622i	0.923011	+	0.532901i
$887$		−	2.71620i		−	0.0912011i	−0.998960	−	0.0456006i	$-0.985480\pi$
$887$		−	2.71620i		−	0.0912011i	0.998960	−	0.0456006i	$-0.0145201\pi$
$888$	−4.24604	−	4.35559i	−0.142488	−	0.146164i
$889$	1.33079			0.0446333
$890$	27.8300	+	8.78292i	0.932862	+	0.294404i
$891$	1.96734	+	3.40754i	0.0659084	+	0.114157i
$892$	15.8027	−	9.12368i	0.529113	−	0.305484i
$893$	−10.6138	−	18.3836i	−0.355177	−	0.615185i
$894$		−	22.5829i		−	0.755285i
$895$	15.3318	−	14.0414i	0.512485	−	0.469354i
$896$			0.0809559i			0.00270455i
$897$	9.07978	+	5.24221i	0.303165	+	0.175032i
$898$		−	5.09600i		−	0.170056i
$899$	16.1732			0.539407
$900$	0.438440	−	4.98074i	0.0146147	−	0.166025i
$901$	−0.133668	+	0.0771730i	−0.00445311	+	0.00257100i
$902$	−29.2804			−0.974931
$903$	0.230362	−	0.398998i	0.00766596	−	0.0132778i
$904$	−7.99299	+	13.8443i	−0.265843	+	0.460453i
$905$	−5.10135	+	16.1644i	−0.169575	+	0.537322i
$906$	6.91418	−	3.99191i	0.229708	−	0.132622i
$907$	20.3707	+	35.2832i	0.676399	+	1.17156i	0.976058	+	0.217512i	$0.0697940\pi$
$907$	20.3707	+	35.2832i	0.676399	+	1.17156i	−0.299658	+	0.954047i	$0.596873\pi$
$908$	4.95426	−	8.58102i	0.164413	−	0.284771i
$909$	−2.84830	+	4.93340i	−0.0944722	+	0.163631i
$910$	−0.616564	−	0.194583i	−0.0204389	−	0.00645036i
$911$			8.06856i			0.267323i	0.991027	+	0.133662i	$0.0426736\pi$
$911$			8.06856i			0.267323i	−0.991027	+	0.133662i	$0.957326\pi$
$912$	0.983874	+	1.70412i	0.0325793	+	0.0564290i
$913$	41.8514	+	24.1629i	1.38508	+	0.799675i
$914$	−30.8643			−1.02090
$915$	−21.0399	+	4.65854i	−0.695558	+	0.154007i
$916$	12.8080	−	22.1841i	0.423188	−	0.732983i
$917$	0.158715			0.00524122
$918$	−0.975664	+	0.563300i	−0.0322017	+	0.0185917i
$919$		−	43.7448i		−	1.44301i	−0.692411	−	0.721504i	$-0.743451\pi$
$919$		−	43.7448i		−	1.44301i	0.692411	−	0.721504i	$-0.256549\pi$
$920$	−4.43328	−	4.84067i	−0.146161	−	0.159592i
$921$	−11.7121	−	20.2859i	−0.385926	−	0.668443i
$922$	−19.0806	+	11.0162i	−0.628385	+	0.362798i
$923$	12.4649	−	21.5898i	0.410286	−	0.710637i
$924$	−0.318536			−0.0104791
$925$	−30.0192	+	4.88342i	−0.987025	+	0.160566i
$926$	34.2779			1.12644
$927$	−3.37085	+	5.83849i	−0.110713	+	0.191761i
$928$	−2.30357	+	1.32997i	−0.0756184	+	0.0436583i
$929$	−12.0745	−	20.9137i	−0.396152	−	0.686155i	0.597095	−	0.802170i	$-0.296321\pi$
$929$	−12.0745	−	20.9137i	−0.396152	−	0.686155i	−0.993247	+	0.116015i	$0.962988\pi$
$930$	9.18264	+	10.0265i	0.301111	+	0.328781i
$931$		−	13.7613i		−	0.451009i
$932$	−2.98587	+	1.72390i	−0.0978056	+	0.0564681i
$933$	−22.5187			−0.737230
$934$	−12.8377	+	22.2356i	−0.420064	+	0.727572i
$935$	−9.67769	+	2.14278i	−0.316494	+	0.0700764i
$936$	3.57159			0.116741
$937$	−18.5144	−	10.6893i	−0.604840	−	0.349204i	0.166103	−	0.986108i	$-0.446881\pi$
$937$	−18.5144	−	10.6893i	−0.604840	−	0.349204i	−0.770943	+	0.636904i	$0.780215\pi$
$938$	−0.143110	−	0.247874i	−0.00467272	−	0.00809338i
$939$		−	9.31550i		−	0.304000i
$940$	23.0038	+	7.25983i	0.750301	+	0.236789i
$941$	−10.2496	+	17.7528i	−0.334127	+	0.578725i	−0.983317	−	0.181902i	$-0.941775\pi$
$941$	−10.2496	+	17.7528i	−0.334127	+	0.578725i	0.649190	+	0.760627i	$0.275108\pi$
$942$	−2.85158	+	4.93908i	−0.0929095	+	0.160924i
$943$	10.9225	+	18.9183i	0.355684	+	0.616064i
$944$	2.46559	−	1.42351i	0.0802481	−	0.0463312i
$945$	−0.0544808	+	0.172630i	−0.00177226	+	0.00561566i
$946$	−11.1962	+	19.3924i	−0.364021	+	0.630503i
$947$	8.96917	−	15.5351i	0.291459	−	0.504822i	−0.682696	−	0.730703i	$-0.739193\pi$
$947$	8.96917	−	15.5351i	0.291459	−	0.504822i	0.974155	+	0.225881i	$0.0725260\pi$
$948$	−4.56180			−0.148160
$949$	18.5141	−	10.6891i	0.600992	−	0.346983i
$950$	9.80084	+	0.862739i	0.317981	+	0.0279909i
$951$	−21.5828			−0.699869
$952$		−	0.0912049i		−	0.00295597i
$953$	7.64774	+	4.41542i	0.247734	+	0.143030i	0.618726	−	0.785607i	$-0.287649\pi$
$953$	7.64774	+	4.41542i	0.247734	+	0.143030i	−0.370992	+	0.928636i	$0.620982\pi$
$954$		−	0.137002i		−	0.00443559i
$955$	0.140743	−	0.128898i	0.00455434	−	0.00417104i
$956$		−	14.2422i		−	0.460624i
$957$	−5.23300	−	9.06382i	−0.169159	−	0.292992i
$958$	−30.5619	+	17.6449i	−0.987410	+	0.570082i
$959$	0.832141	+	1.44131i	0.0268712	+	0.0465423i
$960$	−2.13240	−	0.672968i	−0.0688228	−	0.0217200i
$961$	−5.97019			−0.192587
$962$	−5.35519	−	21.0548i	−0.172658	−	0.678833i
$963$			0.357806i			0.0115302i
$964$	17.9025	+	10.3360i	0.576601	+	0.332901i
$965$	7.80055	+	8.51737i	0.251109	+	0.274184i
$966$	0.118823	+	0.205808i	0.00382308	+	0.00662177i
$967$	−2.30225	−	3.98762i	−0.0740354	−	0.128233i	0.826631	−	0.562744i	$-0.190254\pi$
$967$	−2.30225	−	3.98762i	−0.0740354	−	0.128233i	−0.900666	+	0.434511i	$0.856921\pi$
$968$	4.48174			0.144049
$969$	−1.10843	−	1.91986i	−0.0356080	−	0.0616748i
$970$	−1.92743	+	0.426760i	−0.0618859	+	0.0137024i
$971$	9.30668	−	16.1197i	0.298666	−	0.517304i	−0.677165	−	0.735831i	$-0.736792\pi$
$971$	9.30668	−	16.1197i	0.298666	−	0.517304i	0.975831	+	0.218527i	$0.0701251\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		−	1.05235i		−	0.0337367i
$974$	−12.4487	+	21.5618i	−0.398882	+	0.690884i
$975$	10.2507	−	14.6229i	0.328285	−	0.468308i
$976$			9.63722i			0.308480i
$977$	−0.151620	+	0.262614i	−0.00485076	+	0.00840176i	−0.868441	−	0.495793i	$-0.834877\pi$
$977$	−0.151620	+	0.262614i	−0.00485076	+	0.00840176i	0.863590	+	0.504195i	$0.168211\pi$
$978$	−9.47271	−	5.46907i	−0.302904	−	0.174882i
$979$	44.4718	+	25.6758i	1.42133	+	0.820603i
$980$	10.5617	+	11.5322i	0.337380	+	0.368384i
$981$	−1.10002	+	0.635097i	−0.0351209	+	0.0202771i
$982$	5.90569	−	10.2290i	0.188458	−	0.326419i
$983$	13.3666	+	7.71719i	0.426327	+	0.246140i	0.697781	−	0.716311i	$-0.254171\pi$
$983$	13.3666	+	7.71719i	0.426327	+	0.246140i	−0.271454	+	0.962452i	$0.587504\pi$
$984$	6.44463	+	3.72081i	0.205447	+	0.118615i
$985$	5.21548	+	23.5553i	0.166179	+	0.750534i
$986$	2.59520	−	1.49834i	0.0826481	−	0.0477169i
$987$	−0.756329	−	0.436667i	−0.0240742	−	0.0138993i
$988$			7.02798i			0.223590i
$989$	16.7061			0.531223
$990$	2.64792	−	8.39031i	0.0841563	−	0.266661i
$991$			14.1840i			0.450569i	0.974293	+	0.225284i	$0.0723311\pi$
$991$			14.1840i			0.450569i	−0.974293	+	0.225284i	$0.927669\pi$
$992$	5.26570	−	3.04016i	0.167186	−	0.0965250i
$993$	−3.99492			−0.126775
$994$	0.489368	−	0.282537i	0.0155218	−	0.00896153i
$995$	−13.0826	+	11.9815i	−0.414746	+	0.379841i
$996$	−6.14100	−	10.6365i	−0.194585	−	0.337031i
$997$	−19.4261	+	33.6469i	−0.615230	+	1.06561i	0.375114	+	0.926979i	$0.377603\pi$
$997$	−19.4261	+	33.6469i	−0.615230	+	1.06561i	−0.990344	+	0.138631i	$0.955730\pi$
$998$			3.94875i			0.124995i
$999$	−5.89507	+	1.49939i	−0.186512	+	0.0474385i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.ba.a.619.5	yes	36
5.4	even	2		1110.2.ba.b.619.14	yes	36
37.11	even	6		1110.2.ba.b.529.14	yes	36
185.159	even	6	inner	1110.2.ba.a.529.5	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.ba.a.529.5	✓	36	185.159	even	6	inner
1110.2.ba.a.619.5	yes	36	1.1	even	1	trivial
1110.2.ba.b.529.14	yes	36	37.11	even	6
1110.2.ba.b.619.14	yes	36	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.51023 + 1.64901i) q^{5} -1.00000i q^{6} +(0.0701099 - 0.0404780i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.51023 + 1.64901i) q^{5} -1.00000i q^{6} +(0.0701099 - 0.0404780i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.18319 + 0.483391i) q^{10} -3.93468 q^{11} +(0.866025 + 0.500000i) q^{12} +(1.78579 + 3.09309i) q^{13} +0.0809559i q^{14} +(-2.13240 - 0.672968i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.563300 - 0.975664i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-1.70412 + 0.983874i) q^{19} +(0.672968 - 2.13240i) q^{20} +(-0.0404780 + 0.0701099i) q^{21} +(1.96734 - 3.40754i) q^{22} -2.93551 q^{23} +(-0.866025 + 0.500000i) q^{24} +(-0.438440 + 4.98074i) q^{25} -3.57159 q^{26} +1.00000i q^{27} +(-0.0701099 - 0.0404780i) q^{28} -2.65993i q^{29} +(1.64901 - 1.51023i) q^{30} +6.08031i q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.40754 - 1.96734i) q^{33} +(0.563300 + 0.975664i) q^{34} +(0.172630 + 0.0544808i) q^{35} -1.00000 q^{36} +(1.49939 + 5.89507i) q^{37} -1.96775i q^{38} +(-3.09309 - 1.78579i) q^{39} +(1.51023 + 1.64901i) q^{40} +(-3.72081 - 6.44463i) q^{41} +(-0.0404780 - 0.0701099i) q^{42} -5.69104 q^{43} +(1.96734 + 3.40754i) q^{44} +(2.18319 - 0.483391i) q^{45} +(1.46775 - 2.54222i) q^{46} +10.7878i q^{47} -1.00000i q^{48} +(-3.49672 + 6.05650i) q^{49} +(-4.09423 - 2.87007i) q^{50} +1.12660i q^{51} +(1.78579 - 3.09309i) q^{52} +(-0.118647 - 0.0685008i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-5.94226 - 6.48832i) q^{55} +(0.0701099 - 0.0404780i) q^{56} +(0.983874 - 1.70412i) q^{57} +(2.30357 + 1.32997i) q^{58} +(-2.46559 - 1.42351i) q^{59} +(0.483391 + 2.18319i) q^{60} +(8.34607 - 4.81861i) q^{61} +(-5.26570 - 3.04016i) q^{62} -0.0809559i q^{63} +1.00000 q^{64} +(-2.40357 + 7.61604i) q^{65} +3.93468i q^{66} +(-3.06184 + 1.76776i) q^{67} -1.12660 q^{68} +(2.54222 - 1.46775i) q^{69} +(-0.133497 + 0.122262i) q^{70} +(-3.49001 - 6.04487i) q^{71} +(0.500000 - 0.866025i) q^{72} -5.98563i q^{73} +(-5.85497 - 1.64903i) q^{74} +(-2.11067 - 4.53267i) q^{75} +(1.70412 + 0.983874i) q^{76} +(-0.275860 + 0.159268i) q^{77} +(3.09309 - 1.78579i) q^{78} +(-3.95064 + 2.28090i) q^{79} +(-2.18319 + 0.483391i) q^{80} +(-0.500000 - 0.866025i) q^{81} +7.44162 q^{82} +(-10.6365 - 6.14100i) q^{83} +0.0809559 q^{84} +(2.45959 - 0.544588i) q^{85} +(2.84552 - 4.92859i) q^{86} +(1.32997 + 2.30357i) q^{87} -3.93468 q^{88} +(-11.3025 - 6.52551i) q^{89} +(-0.672968 + 2.13240i) q^{90} +(0.250404 + 0.144571i) q^{91} +(1.46775 + 2.54222i) q^{92} +(-3.04016 - 5.26570i) q^{93} +(-9.34248 - 5.39388i) q^{94} +(-4.19602 - 1.32423i) q^{95} +(0.866025 + 0.500000i) q^{96} +0.882847 q^{97} +(-3.49672 - 6.05650i) q^{98} +(-1.96734 + 3.40754i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9}+O(q^{10}) \) 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9	\( 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} - 14 q^{13} - 2 q^{15} - 18 q^{16} + 18 q^{18} + 6 q^{19} - 4 q^{20} - 2 q^{22} - 20 q^{23} + 4 q^{25} + 28 q^{26} - 2 q^{30} - 18 q^{32} - 6 q^{33} - 40 q^{35} - 36 q^{36} + 20 q^{37} + 6 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} - 2 q^{45} + 10 q^{46} + 10 q^{49} - 2 q^{50} - 14 q^{52} - 12 q^{53} + 56 q^{55} + 8 q^{57} + 30 q^{58} + 18 q^{59} + 4 q^{60} - 6 q^{61} - 12 q^{62} + 36 q^{64} + 40 q^{65} + 36 q^{67} + 12 q^{69} + 20 q^{70} - 24 q^{71} + 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} - 24 q^{77} - 6 q^{78} + 2 q^{80} - 18 q^{81} - 20 q^{82} + 36 q^{83} + 26 q^{85} - 10 q^{87} + 4 q^{88} + 4 q^{90} - 36 q^{91} + 10 q^{92} + 12 q^{93} + 12 q^{94} - 30 q^{95} + 52 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9 + 2 * q^10 + 4 * q^11 - 14 * q^13 - 2 * q^15 - 18 * q^16 + 18 * q^18 + 6 * q^19 - 4 * q^20 - 2 * q^22 - 20 * q^23 + 4 * q^25 + 28 * q^26 - 2 * q^30 - 18 * q^32 - 6 * q^33 - 40 * q^35 - 36 * q^36 + 20 * q^37 + 6 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 - 2 * q^45 + 10 * q^46 + 10 * q^49 - 2 * q^50 - 14 * q^52 - 12 * q^53 + 56 * q^55 + 8 * q^57 + 30 * q^58 + 18 * q^59 + 4 * q^60 - 6 * q^61 - 12 * q^62 + 36 * q^64 + 40 * q^65 + 36 * q^67 + 12 * q^69 + 20 * q^70 - 24 * q^71 + 18 * q^72 - 34 * q^74 + 8 * q^75 - 6 * q^76 - 24 * q^77 - 6 * q^78 + 2 * q^80 - 18 * q^81 - 20 * q^82 + 36 * q^83 + 26 * q^85 - 10 * q^87 + 4 * q^88 + 4 * q^90 - 36 * q^91 + 10 * q^92 + 12 * q^93 + 12 * q^94 - 30 * q^95 + 52 * q^97 + 10 * q^98 + 2 * q^99

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