LMFDB - Embedded newform 1110.2.ba.a.529.12

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			529.12
Character	$\chi$	$=$	1110.529
Dual form			1110.2.ba.a.619.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.12688 + 0.690199i) q^{5} -1.00000i q^{6} +(3.89483 + 2.24868i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.12688 + 0.690199i) q^{5} -1.00000i q^{6} +(3.89483 + 2.24868i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(1.66117 + 1.49683i) q^{10} +0.412574 q^{11} +(-0.866025 + 0.500000i) q^{12} +(1.10249 - 1.90957i) q^{13} -4.49736i q^{14} +(-2.18703 - 0.465711i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.63267 - 2.82787i) q^{17} +(0.500000 - 0.866025i) q^{18} +(2.06416 + 1.19174i) q^{19} +(0.465711 - 2.18703i) q^{20} +(2.24868 + 3.89483i) q^{21} +(-0.206287 - 0.357299i) q^{22} -1.63566 q^{23} +(0.866025 + 0.500000i) q^{24} +(4.04725 - 2.93594i) q^{25} -2.20498 q^{26} +1.00000i q^{27} +(-3.89483 + 2.24868i) q^{28} +9.16257i q^{29} +(0.690199 + 2.12688i) q^{30} +6.51360i q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.357299 + 0.206287i) q^{33} +(-1.63267 + 2.82787i) q^{34} +(-9.83588 - 2.09447i) q^{35} -1.00000 q^{36} +(5.42955 + 2.74226i) q^{37} -2.38348i q^{38} +(1.90957 - 1.10249i) q^{39} +(-2.12688 + 0.690199i) q^{40} +(-1.68174 + 2.91286i) q^{41} +(2.24868 - 3.89483i) q^{42} -9.32116 q^{43} +(-0.206287 + 0.357299i) q^{44} +(-1.66117 - 1.49683i) q^{45} +(0.817829 + 1.41652i) q^{46} +6.71516i q^{47} -1.00000i q^{48} +(6.61313 + 11.4543i) q^{49} +(-4.56623 - 2.03705i) q^{50} -3.26535i q^{51} +(1.10249 + 1.90957i) q^{52} +(10.0924 - 5.82686i) q^{53} +(0.866025 - 0.500000i) q^{54} +(-0.877496 + 0.284758i) q^{55} +(3.89483 + 2.24868i) q^{56} +(1.19174 + 2.06416i) q^{57} +(7.93502 - 4.58129i) q^{58} +(4.76276 - 2.74978i) q^{59} +(1.49683 - 1.66117i) q^{60} +(6.46982 + 3.73535i) q^{61} +(5.64095 - 3.25680i) q^{62} +4.49736i q^{63} +1.00000 q^{64} +(-1.02688 + 4.82237i) q^{65} -0.412574i q^{66} +(2.71578 + 1.56796i) q^{67} +3.26535 q^{68} +(-1.41652 - 0.817829i) q^{69} +(3.10407 + 9.56535i) q^{70} +(-1.01489 + 1.75784i) q^{71} +(0.500000 + 0.866025i) q^{72} -6.57476i q^{73} +(-0.339909 - 6.07326i) q^{74} +(4.97299 - 0.518977i) q^{75} +(-2.06416 + 1.19174i) q^{76} +(1.60690 + 0.927747i) q^{77} +(-1.90957 - 1.10249i) q^{78} +(-7.72926 - 4.46249i) q^{79} +(1.66117 + 1.49683i) q^{80} +(-0.500000 + 0.866025i) q^{81} +3.36348 q^{82} +(3.38588 - 1.95484i) q^{83} -4.49736 q^{84} +(5.42430 + 4.88768i) q^{85} +(4.66058 + 8.07236i) q^{86} +(-4.58129 + 7.93502i) q^{87} +0.412574 q^{88} +(-2.49674 + 1.44149i) q^{89} +(-0.465711 + 2.18703i) q^{90} +(8.58804 - 4.95830i) q^{91} +(0.817829 - 1.41652i) q^{92} +(-3.25680 + 5.64095i) q^{93} +(5.81550 - 3.35758i) q^{94} +(-5.21275 - 1.11001i) q^{95} +(-0.866025 + 0.500000i) q^{96} +10.9274 q^{97} +(6.61313 - 11.4543i) q^{98} +(0.206287 + 0.357299i) 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 $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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
$5$	−2.12688	+	0.690199i	−0.951170	+	0.308666i
$5$	−2.12688	+	0.690199i	−0.951170	+	0.308666i
$6$		−	1.00000i		−	0.408248i
$7$	3.89483	+	2.24868i	1.47211	+	0.849921i	0.999508	−	0.0313565i	$-0.00998272\pi$
$7$	3.89483	+	2.24868i	1.47211	+	0.849921i	0.472599	+	0.881278i	$0.343316\pi$
$8$	1.00000			0.353553
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	1.66117	+	1.49683i	0.525308	+	0.473340i
$11$	0.412574			0.124396			0.0621979	−	0.998064i	$-0.480189\pi$
$11$	0.412574			0.124396			0.0621979	+	0.998064i	$0.480189\pi$
$12$	−0.866025	+	0.500000i	−0.250000	+	0.144338i
$13$	1.10249	−	1.90957i	0.305776	−	0.529620i	−0.671658	−	0.740862i	$-0.734417\pi$
$13$	1.10249	−	1.90957i	0.305776	−	0.529620i	0.977434	+	0.211242i	$0.0677507\pi$
$14$		−	4.49736i		−	1.20197i
$15$	−2.18703	−	0.465711i	−0.564690	−	0.120246i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.63267	−	2.82787i	−0.395981	−	0.685860i	0.597245	−	0.802059i	$-0.296262\pi$
$17$	−1.63267	−	2.82787i	−0.395981	−	0.685860i	−0.993226	+	0.116199i	$0.962929\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	2.06416	+	1.19174i	0.473550	+	0.273404i	0.717725	−	0.696327i	$-0.245184\pi$
$19$	2.06416	+	1.19174i	0.473550	+	0.273404i	−0.244175	+	0.969731i	$0.578517\pi$
$20$	0.465711	−	2.18703i	0.104136	−	0.489035i
$21$	2.24868	+	3.89483i	0.490702	+	0.849921i
$22$	−0.206287	−	0.357299i	−0.0439805	−	0.0761765i
$23$	−1.63566			−0.341058			−0.170529	−	0.985353i	$-0.554548\pi$
$23$	−1.63566			−0.341058			−0.170529	+	0.985353i	$0.554548\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	4.04725	−	2.93594i	0.809450	−	0.587189i
$26$	−2.20498			−0.432433
$27$			1.00000i			0.192450i
$28$	−3.89483	+	2.24868i	−0.736053	+	0.424961i
$29$			9.16257i			1.70145i	0.525614	+	0.850723i	$0.323836\pi$
$29$			9.16257i			1.70145i	−0.525614	+	0.850723i	$0.676164\pi$
$30$	0.690199	+	2.12688i	0.126013	+	0.388314i
$31$			6.51360i			1.16988i	0.811077	+	0.584939i	$0.198882\pi$
$31$			6.51360i			1.16988i	−0.811077	+	0.584939i	$0.801118\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	0.357299	+	0.206287i	0.0621979	+	0.0359099i
$34$	−1.63267	+	2.82787i	−0.280001	+	0.484976i
$35$	−9.83588	−	2.09447i	−1.66257	−	0.354030i
$36$	−1.00000			−0.166667
$37$	5.42955	+	2.74226i	0.892613	+	0.450825i
$37$	5.42955	+	2.74226i	0.892613	+	0.450825i
$38$		−	2.38348i		−	0.386652i
$39$	1.90957	−	1.10249i	0.305776	−	0.176540i
$40$	−2.12688	+	0.690199i	−0.336289	+	0.109130i
$41$	−1.68174	+	2.91286i	−0.262644	+	0.454913i	−0.966944	−	0.254990i	$-0.917928\pi$
$41$	−1.68174	+	2.91286i	−0.262644	+	0.454913i	0.704300	+	0.709903i	$0.251261\pi$
$42$	2.24868	−	3.89483i	0.346979	−	0.600985i
$43$	−9.32116			−1.42146			−0.710732	−	0.703463i	$-0.751636\pi$
$43$	−9.32116			−1.42146			−0.710732	+	0.703463i	$0.751636\pi$
$44$	−0.206287	+	0.357299i	−0.0310989	+	0.0538649i
$45$	−1.66117	−	1.49683i	−0.247633	−	0.223135i
$46$	0.817829	+	1.41652i	0.120582	+	0.208855i
$47$			6.71516i			0.979507i	0.871861	+	0.489753i	$0.162913\pi$
$47$			6.71516i			0.979507i	−0.871861	+	0.489753i	$0.837087\pi$
$48$		−	1.00000i		−	0.144338i
$49$	6.61313	+	11.4543i	0.944732	+	1.63632i
$50$	−4.56623	−	2.03705i	−0.645762	−	0.288082i
$51$		−	3.26535i		−	0.457240i
$52$	1.10249	+	1.90957i	0.152888	+	0.264810i
$53$	10.0924	−	5.82686i	1.38630	−	0.800380i	0.393403	−	0.919366i	$-0.371298\pi$
$53$	10.0924	−	5.82686i	1.38630	−	0.800380i	0.992896	+	0.118986i	$0.0379643\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	−0.877496	+	0.284758i	−0.118322	+	0.0383968i
$56$	3.89483	+	2.24868i	0.520468	+	0.300493i
$57$	1.19174	+	2.06416i	0.157850	+	0.273404i
$58$	7.93502	−	4.58129i	1.04192	−	0.601552i
$59$	4.76276	−	2.74978i	0.620058	−	0.357991i	−0.156834	−	0.987625i	$-0.550129\pi$
$59$	4.76276	−	2.74978i	0.620058	−	0.357991i	0.776892	+	0.629634i	$0.216795\pi$
$60$	1.49683	−	1.66117i	0.193240	−	0.214456i
$61$	6.46982	+	3.73535i	0.828376	+	0.478263i	0.853296	−	0.521426i	$-0.174600\pi$
$61$	6.46982	+	3.73535i	0.828376	+	0.478263i	−0.0249202	+	0.999689i	$0.507933\pi$
$62$	5.64095	−	3.25680i	0.716401	−	0.413614i
$63$			4.49736i			0.566614i
$64$	1.00000			0.125000
$65$	−1.02688	+	4.82237i	−0.127369	+	0.598142i
$66$		−	0.412574i		−	0.0507843i
$67$	2.71578	+	1.56796i	0.331785	+	0.191556i	0.656633	−	0.754210i	$-0.271980\pi$
$67$	2.71578	+	1.56796i	0.331785	+	0.191556i	−0.324848	+	0.945766i	$0.605313\pi$
$68$	3.26535			0.395981
$69$	−1.41652	−	0.817829i	−0.170529	−	0.0984550i
$70$	3.10407	+	9.56535i	0.371008	+	1.14328i
$71$	−1.01489	+	1.75784i	−0.120445	+	0.208617i	−0.919943	−	0.392051i	$-0.871766\pi$
$71$	−1.01489	+	1.75784i	−0.120445	+	0.208617i	0.799498	+	0.600669i	$0.205099\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$		−	6.57476i		−	0.769517i	−0.923017	−	0.384759i	$-0.874285\pi$
$73$		−	6.57476i		−	0.769517i	0.923017	−	0.384759i	$-0.125715\pi$
$74$	−0.339909	−	6.07326i	−0.0395136	−	0.706002i
$75$	4.97299	−	0.518977i	0.574232	−	0.0599263i
$76$	−2.06416	+	1.19174i	−0.236775	+	0.136702i
$77$	1.60690	+	0.927747i	0.183124	+	0.105727i
$78$	−1.90957	−	1.10249i	−0.216216	−	0.124833i
$79$	−7.72926	−	4.46249i	−0.869610	−	0.502069i	−0.00239128	−	0.999997i	$-0.500761\pi$
$79$	−7.72926	−	4.46249i	−0.869610	−	0.502069i	−0.867219	+	0.497928i	$0.834095\pi$
$80$	1.66117	+	1.49683i	0.185725	+	0.167351i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	3.36348			0.371435
$83$	3.38588	−	1.95484i	0.371649	−	0.214571i	−0.302530	−	0.953140i	$-0.597831\pi$
$83$	3.38588	−	1.95484i	0.371649	−	0.214571i	0.674178	+	0.738568i	$0.264498\pi$
$84$	−4.49736			−0.490702
$85$	5.42430	+	4.88768i	0.588348	+	0.530143i
$86$	4.66058	+	8.07236i	0.502563	+	0.870465i
$87$	−4.58129	+	7.93502i	−0.491165	+	0.850723i
$88$	0.412574			0.0439805
$89$	−2.49674	+	1.44149i	−0.264654	+	0.152798i	−0.626456	−	0.779457i	$-0.715495\pi$
$89$	−2.49674	+	1.44149i	−0.264654	+	0.152798i	0.361802	+	0.932255i	$0.382162\pi$
$90$	−0.465711	+	2.18703i	−0.0490902	+	0.230534i
$91$	8.58804	−	4.95830i	0.900271	−	0.519772i
$92$	0.817829	−	1.41652i	0.0852646	−	0.147683i
$93$	−3.25680	+	5.64095i	−0.337715	+	0.584939i
$94$	5.81550	−	3.35758i	0.599823	−	0.346308i
$95$	−5.21275	−	1.11001i	−0.534817	−	0.113885i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	10.9274			1.10951			0.554753	−	0.832015i	$-0.312813\pi$
$97$	10.9274			1.10951			0.554753	+	0.832015i	$0.312813\pi$
$98$	6.61313	−	11.4543i	0.668027	−	1.15706i
$99$	0.206287	+	0.357299i	0.0207326	+	0.0359099i
$100$	0.518977	+	4.97299i	0.0518977	+	0.497299i
$101$	−17.2184			−1.71329			−0.856647	−	0.515903i	$-0.827457\pi$
$101$	−17.2184			−1.71329			−0.856647	+	0.515903i	$0.827457\pi$
$102$	−2.82787	+	1.63267i	−0.280001	+	0.161659i
$103$	−16.9033			−1.66554			−0.832768	−	0.553622i	$-0.813245\pi$
$103$	−16.9033			−1.66554			−0.832768	+	0.553622i	$0.813245\pi$
$104$	1.10249	−	1.90957i	0.108108	−	0.187249i
$105$	−7.47088	−	6.73180i	−0.729084	−	0.656957i
$106$	−10.0924	−	5.82686i	−0.980262	−	0.565954i
$107$	7.58132	+	4.37708i	0.732914	+	0.423148i	0.819487	−	0.573097i	$-0.194258\pi$
$107$	7.58132	+	4.37708i	0.732914	+	0.423148i	−0.0865732	+	0.996245i	$0.527592\pi$
$108$	−0.866025	−	0.500000i	−0.0833333	−	0.0481125i
$109$	9.65596	−	5.57487i	0.924873	−	0.533976i	0.0396866	−	0.999212i	$-0.487364\pi$
$109$	9.65596	−	5.57487i	0.924873	−	0.533976i	0.885186	+	0.465236i	$0.154031\pi$
$110$	0.685356	+	0.617555i	0.0653461	+	0.0588815i
$111$	3.33100	+	5.08964i	0.316164	+	0.483087i
$112$		−	4.49736i		−	0.424961i
$113$	0.817025	+	1.41513i	0.0768593	+	0.133124i	0.901893	−	0.431959i	$-0.142177\pi$
$113$	0.817025	+	1.41513i	0.0768593	+	0.133124i	−0.825034	+	0.565083i	$0.808844\pi$
$114$	1.19174	−	2.06416i	0.111617	−	0.193326i
$115$	3.47885	−	1.12893i	0.324404	−	0.105273i
$116$	−7.93502	−	4.58129i	−0.736748	−	0.425362i
$117$	2.20498			0.203851
$118$	−4.76276	−	2.74978i	−0.438447	−	0.253138i
$119$		−	14.6854i		−	1.34621i
$120$	−2.18703	−	0.465711i	−0.199648	−	0.0425134i
$121$	−10.8298			−0.984526
$122$		−	7.47071i		−	0.676366i
$123$	−2.91286	+	1.68174i	−0.262644	+	0.151638i
$124$	−5.64095	−	3.25680i	−0.506572	−	0.292469i
$125$	−6.58164	+	9.03781i	−0.588679	+	0.808367i
$126$	3.89483	−	2.24868i	0.346979	−	0.200328i
$127$	7.90697	−	4.56509i	0.701630	−	0.405086i	−0.106324	−	0.994332i	$-0.533908\pi$
$127$	7.90697	−	4.56509i	0.701630	−	0.405086i	0.807954	+	0.589245i	$0.200575\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−8.07236	−	4.66058i	−0.710732	−	0.410341i
$130$	4.68974	−	1.52188i	0.411317	−	0.133478i
$131$	−9.85183	+	5.68796i	−0.860758	+	0.496959i	−0.864266	−	0.503035i	$-0.832217\pi$
$131$	−9.85183	+	5.68796i	−0.860758	+	0.496959i	0.00350776	+	0.999994i	$0.498883\pi$
$132$	−0.357299	+	0.206287i	−0.0310989	+	0.0179550i
$133$	5.35969	+	9.28325i	0.464744	+	0.804960i
$134$		−	3.13591i		−	0.270902i
$135$	−0.690199	−	2.12688i	−0.0594029	−	0.183053i
$136$	−1.63267	−	2.82787i	−0.140001	−	0.242488i
$137$			2.47409i			0.211376i	0.994399	+	0.105688i	$0.0337044\pi$
$137$			2.47409i			0.211376i	−0.994399	+	0.105688i	$0.966296\pi$
$138$			1.63566i			0.139236i
$139$	9.45191	+	16.3712i	0.801701	+	1.38859i	0.918496	+	0.395431i	$0.129405\pi$
$139$	9.45191	+	16.3712i	0.801701	+	1.38859i	−0.116795	+	0.993156i	$0.537262\pi$
$140$	6.73180	−	7.47088i	0.568941	−	0.631405i
$141$	−3.35758	+	5.81550i	−0.282759	+	0.489753i
$142$	2.02978			0.170335
$143$	0.454859	−	0.787840i	0.0380373	−	0.0658825i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	−6.32400	−	19.4877i	−0.525180	−	1.61837i
$146$	−5.69391	+	3.28738i	−0.471231	+	0.272065i
$147$			13.2263i			1.09088i
$148$	−5.08964	+	3.33100i	−0.418366	+	0.273806i
$149$	7.98719			0.654336			0.327168	−	0.944966i	$-0.393906\pi$
$149$	7.98719			0.654336			0.327168	+	0.944966i	$0.393906\pi$
$150$	−2.93594	−	4.04725i	−0.239719	−	0.330457i
$151$	−2.15436	+	3.73146i	−0.175319	+	0.303662i	−0.940272	−	0.340425i	$-0.889429\pi$
$151$	−2.15436	+	3.73146i	−0.175319	+	0.303662i	0.764952	+	0.644087i	$0.222762\pi$
$152$	2.06416	+	1.19174i	0.167425	+	0.0966630i
$153$	1.63267	−	2.82787i	0.131994	−	0.228620i
$154$		−	1.85549i		−	0.149520i
$155$	−4.49568	−	13.8537i	−0.361102	−	1.11275i
$156$			2.20498i			0.176540i
$157$	−3.79620	+	2.19174i	−0.302970	+	0.174920i	−0.643776	−	0.765214i	$-0.722633\pi$
$157$	−3.79620	+	2.19174i	−0.302970	+	0.174920i	0.340806	+	0.940133i	$0.389300\pi$
$158$			8.92498i			0.710033i
$159$	11.6537			0.924199
$160$	0.465711	−	2.18703i	0.0368177	−	0.172900i
$161$	−6.37061	−	3.67807i	−0.502074	−	0.289873i
$162$	1.00000			0.0785674
$163$	−8.00959	−	13.8730i	−0.627360	−	1.08662i	−0.988079	−	0.153945i	$-0.950802\pi$
$163$	−8.00959	−	13.8730i	−0.627360	−	1.08662i	0.360720	−	0.932674i	$-0.382531\pi$
$164$	−1.68174	−	2.91286i	−0.131322	−	0.227456i
$165$	−0.902313	−	0.192140i	−0.0702450	−	0.0149581i
$166$	−3.38588	−	1.95484i	−0.262795	−	0.151725i
$167$	6.66540	−	11.5448i	0.515784	−	0.893365i	−0.484048	−	0.875042i	$-0.660834\pi$
$167$	6.66540	−	11.5448i	0.515784	−	0.893365i	0.999832	−	0.0183231i	$-0.00583275\pi$
$168$	2.24868	+	3.89483i	0.173489	+	0.300493i
$169$	4.06902	+	7.04775i	0.313002	+	0.542135i
$170$	1.52071	−	7.14142i	0.116633	−	0.547722i
$171$			2.38348i			0.182269i
$172$	4.66058	−	8.07236i	0.355366	−	0.615512i
$173$	22.0473	−	12.7290i	1.67622	−	0.967768i	0.712190	−	0.701987i	$-0.247703\pi$
$173$	22.0473	−	12.7290i	1.67622	−	0.967768i	0.964033	−	0.265781i	$-0.0856299\pi$
$174$	9.16257			0.694613
$175$	22.3653	−	2.33403i	1.69066	−	0.176436i
$176$	−0.206287	−	0.357299i	−0.0155495	−	0.0269325i
$177$	5.49956			0.413372
$178$	2.49674	+	1.44149i	0.187138	+	0.108044i
$179$		−	3.35687i		−	0.250904i	−0.992100	−	0.125452i	$-0.959962\pi$
$179$		−	3.35687i		−	0.250904i	0.992100	−	0.125452i	$-0.0400382\pi$
$180$	2.12688	−	0.690199i	0.158528	−	0.0514444i
$181$	4.85498	−	8.40907i	0.360868	−	0.625041i	−0.627236	−	0.778829i	$-0.715814\pi$
$181$	4.85498	−	8.40907i	0.360868	−	0.625041i	0.988104	+	0.153788i	$0.0491472\pi$
$182$	−8.58804	−	4.95830i	−0.636588	−	0.367534i
$183$	3.73535	+	6.46982i	0.276125	+	0.478263i
$184$	−1.63566			−0.120582
$185$	−13.4407	−	2.08499i	−0.988181	−	0.153292i
$186$	6.51360			0.477601
$187$	−0.673598	−	1.16671i	−0.0492584	−	0.0853180i
$188$	−5.81550	−	3.35758i	−0.424139	−	0.244877i
$189$	−2.24868	+	3.89483i	−0.163567	+	0.283307i
$190$	1.64508	+	5.06938i	0.119346	+	0.367772i
$191$		−	18.7526i		−	1.35689i	−0.734651	−	0.678446i	$-0.762654\pi$
$191$		−	18.7526i		−	1.35689i	0.734651	−	0.678446i	$-0.237346\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	−25.6781			−1.84835			−0.924174	−	0.381971i	$-0.875245\pi$
$193$	−25.6781			−1.84835			−0.924174	+	0.381971i	$0.875245\pi$
$194$	−5.46368	−	9.46337i	−0.392269	−	0.679431i
$195$	−3.30049	+	3.66286i	−0.236353	+	0.262303i
$196$	−13.2263			−0.944732
$197$	15.5562	−	8.98138i	1.10833	−	0.639897i	0.169936	−	0.985455i	$-0.445644\pi$
$197$	15.5562	−	8.98138i	1.10833	−	0.639897i	0.938397	+	0.345558i	$0.112311\pi$
$198$	0.206287	−	0.357299i	0.0146602	−	0.0253922i
$199$			8.12120i			0.575697i	0.957676	+	0.287848i	$0.0929399\pi$
$199$			8.12120i			0.575697i	−0.957676	+	0.287848i	$0.907060\pi$
$200$	4.04725	−	2.93594i	0.286184	−	0.207603i
$201$	1.56796	+	2.71578i	0.110595	+	0.191556i
$202$	8.60920	+	14.9116i	0.605741	+	1.04917i
$203$	−20.6037	+	35.6866i	−1.44610	+	2.50471i
$204$	2.82787	+	1.63267i	0.197991	+	0.114310i
$205$	1.56641	−	7.35605i	0.109403	−	0.513769i
$206$	8.45167	+	14.6387i	0.588856	+	1.01993i
$207$	−0.817829	−	1.41652i	−0.0568430	−	0.0984550i
$208$	−2.20498			−0.152888
$209$	0.851617	+	0.491681i	0.0589076	+	0.0340103i
$210$	−2.09447	+	9.83588i	−0.144532	+	0.678740i
$211$	−8.47435			−0.583399			−0.291699	−	0.956510i	$-0.594221\pi$
$211$	−8.47435			−0.583399			−0.291699	+	0.956510i	$0.594221\pi$
$212$			11.6537i			0.800380i
$213$	−1.75784	+	1.01489i	−0.120445	+	0.0695391i
$214$		−	8.75416i		−	0.598422i
$215$	19.8250	−	6.43346i	1.35205	−	0.438758i
$216$			1.00000i			0.0680414i
$217$	−14.6470	+	25.3694i	−0.994304	+	1.72219i
$218$	−9.65596	−	5.57487i	−0.653984	−	0.377578i
$219$	3.28738	−	5.69391i	0.222140	−	0.384759i
$220$	0.192140	−	0.902313i	0.0129541	−	0.0608339i
$221$	−7.20004			−0.484327
$222$	2.74226	−	5.42955i	0.184048	−	0.364408i
$223$			18.7191i			1.25352i	0.779212	+	0.626761i	$0.215620\pi$
$223$			18.7191i			1.25352i	−0.779212	+	0.626761i	$0.784380\pi$
$224$	−3.89483	+	2.24868i	−0.260234	+	0.150246i
$225$	4.56623	+	2.03705i	0.304415	+	0.135803i
$226$	0.817025	−	1.41513i	0.0543477	−	0.0941330i
$227$	2.24825	−	3.89408i	0.149222	−	0.258459i	−0.781718	−	0.623632i	$-0.785657\pi$
$227$	2.24825	−	3.89408i	0.149222	−	0.258459i	0.930940	+	0.365172i	$0.118990\pi$
$228$	−2.38348			−0.157850
$229$	10.1818	−	17.6353i	0.672829	−	1.16537i	−0.304269	−	0.952586i	$-0.598412\pi$
$229$	10.1818	−	17.6353i	0.672829	−	1.16537i	0.977098	−	0.212788i	$-0.0682545\pi$
$230$	−2.71711	−	2.44831i	−0.179161	−	0.161437i
$231$	0.927747	+	1.60690i	0.0610413	+	0.105727i
$232$			9.16257i			0.601552i
$233$			2.94072i			0.192653i	0.995350	+	0.0963266i	$0.0307093\pi$
$233$			2.94072i			0.192653i	−0.995350	+	0.0963266i	$0.969291\pi$
$234$	−1.10249	−	1.90957i	−0.0720722	−	0.124833i
$235$	−4.63480	−	14.2823i	−0.302341	−	0.931678i
$236$			5.49956i			0.357991i
$237$	−4.46249	−	7.72926i	−0.289870	−	0.502069i
$238$	−12.7180	+	7.34272i	−0.824383	+	0.475958i
$239$	−8.01145	+	4.62541i	−0.518218	+	0.299193i	−0.736205	−	0.676758i	$-0.763384\pi$
$239$	−8.01145	+	4.62541i	−0.518218	+	0.299193i	0.217987	+	0.975952i	$0.430051\pi$
$240$	0.690199	+	2.12688i	0.0445522	+	0.137290i
$241$	0.691167	+	0.399045i	0.0445220	+	0.0257048i	0.522096	−	0.852887i	$-0.325150\pi$
$241$	0.691167	+	0.399045i	0.0445220	+	0.0257048i	−0.477574	+	0.878592i	$0.658484\pi$
$242$	5.41489	+	9.37887i	0.348082	+	0.602896i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−6.46982	+	3.73535i	−0.414188	+	0.239132i
$245$	−21.9711	−	19.7975i	−1.40368	−	1.26482i
$246$	2.91286	+	1.68174i	0.185717	+	0.107224i
$247$	4.55143	−	2.62777i	0.289601	−	0.167201i
$248$			6.51360i			0.413614i
$249$	3.90968			0.247766
$250$	11.1178	+	1.18096i	0.703151	+	0.0746902i
$251$		−	13.7566i		−	0.868306i	−0.900839	−	0.434153i	$-0.857048\pi$
$251$		−	13.7566i		−	0.868306i	0.900839	−	0.434153i	$-0.142952\pi$
$252$	−3.89483	−	2.24868i	−0.245351	−	0.141654i
$253$	−0.674830			−0.0424262
$254$	−7.90697	−	4.56509i	−0.496127	−	0.286439i
$255$	2.25374	+	6.94500i	0.141135	+	0.434913i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−9.61645	−	16.6562i	−0.599858	−	1.03898i	−0.992842	−	0.119439i	$-0.961890\pi$
$257$	−9.61645	−	16.6562i	−0.599858	−	1.03898i	0.392984	−	0.919545i	$-0.371443\pi$
$258$			9.32116i			0.580310i
$259$	14.9807	+	22.8900i	0.930856	+	1.42231i
$260$	−3.66286	−	3.30049i	−0.227161	−	0.204688i
$261$	−7.93502	+	4.58129i	−0.491165	+	0.283574i
$262$	9.85183	+	5.68796i	0.608648	+	0.351403i
$263$	5.05664	+	2.91945i	0.311806	+	0.180021i	0.647734	−	0.761866i	$-0.275717\pi$
$263$	5.05664	+	2.91945i	0.311806	+	0.180021i	−0.335929	+	0.941887i	$0.609050\pi$
$264$	0.357299	+	0.206287i	0.0219903	+	0.0126961i
$265$	−17.4437	+	19.3588i	−1.07156	+	1.18920i
$266$	5.35969	−	9.28325i	0.328624	−	0.569193i
$267$	−2.88298			−0.176436
$268$	−2.71578	+	1.56796i	−0.165893	+	0.0957782i
$269$	−21.9627			−1.33909			−0.669545	−	0.742771i	$-0.733511\pi$
$269$	−21.9627			−1.33909			−0.669545	+	0.742771i	$0.733511\pi$
$270$	−1.49683	+	1.66117i	−0.0910944	+	0.101096i
$271$	−1.50615	−	2.60873i	−0.0914920	−	0.158469i	0.816647	−	0.577137i	$-0.195830\pi$
$271$	−1.50615	−	2.60873i	−0.0914920	−	0.158469i	−0.908139	+	0.418668i	$0.862497\pi$
$272$	−1.63267	+	2.82787i	−0.0989953	+	0.171465i
$273$	9.91661			0.600180
$274$	2.14262	−	1.23704i	0.129441	−	0.0747325i
$275$	1.66979	−	1.21129i	0.100692	−	0.0730438i
$276$	1.41652	−	0.817829i	0.0852646	−	0.0492275i
$277$	7.28820	−	12.6235i	0.437905	−	0.758475i	−0.559622	−	0.828748i	$-0.689054\pi$
$277$	7.28820	−	12.6235i	0.437905	−	0.758475i	0.997528	+	0.0702733i	$0.0223871\pi$
$278$	9.45191	−	16.3712i	0.566888	−	0.981879i
$279$	−5.64095	+	3.25680i	−0.337715	+	0.194980i
$280$	−9.83588	−	2.09447i	−0.587806	−	0.125168i
$281$	12.4391	−	7.18169i	0.742052	−	0.428424i	−0.0807631	−	0.996733i	$-0.525736\pi$
$281$	12.4391	−	7.18169i	0.742052	−	0.428424i	0.822815	+	0.568310i	$0.192402\pi$
$282$	6.71516			0.399882
$283$	13.5334	−	23.4405i	0.804478	−	1.39340i	−0.112166	−	0.993690i	$-0.535779\pi$
$283$	13.5334	−	23.4405i	0.804478	−	1.39340i	0.916643	−	0.399706i	$-0.130888\pi$
$284$	−1.01489	−	1.75784i	−0.0602227	−	0.104309i
$285$	−3.95937	−	3.56768i	−0.234533	−	0.211331i
$286$	−0.909719			−0.0537928
$287$	−13.1002	+	7.56340i	−0.773280	+	0.446453i
$288$	−1.00000			−0.0589256
$289$	3.16876	−	5.48845i	0.186397	−	0.322850i
$290$	−13.7148	+	15.2206i	−0.805364	+	0.893784i
$291$	9.46337	+	5.46368i	0.554753	+	0.320287i
$292$	5.69391	+	3.28738i	0.333211	+	0.192379i
$293$	−15.0447	−	8.68606i	−0.878920	−	0.507445i	−0.00861800	−	0.999963i	$-0.502743\pi$
$293$	−15.0447	−	8.68606i	−0.878920	−	0.507445i	−0.870302	+	0.492518i	$0.836077\pi$
$294$	11.4543	−	6.61313i	0.668027	−	0.385685i
$295$	−8.23192	+	9.13570i	−0.479281	+	0.531901i
$296$	5.42955	+	2.74226i	0.315586	+	0.159391i
$297$			0.412574i			0.0239400i
$298$	−3.99360	−	6.91711i	−0.231343	−	0.400697i
$299$	−1.80330	+	3.12341i	−0.104288	+	0.180631i
$300$	−2.03705	+	4.56623i	−0.117609	+	0.263631i
$301$	−36.3043	−	20.9603i	−2.09255	−	1.20813i
$302$	4.30872			0.247939
$303$	−14.9116	−	8.60920i	−0.856647	−	0.494585i
$304$		−	2.38348i		−	0.136702i
$305$	−16.3387	−	3.47919i	−0.935551	−	0.199218i
$306$	−3.26535			−0.186667
$307$			19.0895i			1.08949i	0.838600	+	0.544747i	$0.183374\pi$
$307$			19.0895i			1.08949i	−0.838600	+	0.544747i	$0.816626\pi$
$308$	−1.60690	+	0.927747i	−0.0915619	+	0.0528633i
$309$	−14.6387	−	8.45167i	−0.832768	−	0.480799i
$310$	−9.74978	+	10.8202i	−0.553750	+	0.614547i
$311$	1.51782	−	0.876316i	0.0860679	−	0.0496913i	−0.456348	−	0.889801i	$-0.650843\pi$
$311$	1.51782	−	0.876316i	0.0860679	−	0.0496913i	0.542416	+	0.840110i	$0.317510\pi$
$312$	1.90957	−	1.10249i	0.108108	−	0.0624163i
$313$	−3.08712	−	5.34705i	−0.174495	−	0.302233i	0.765492	−	0.643446i	$-0.222496\pi$
$313$	−3.08712	−	5.34705i	−0.174495	−	0.302233i	−0.939986	+	0.341212i	$0.889162\pi$
$314$	3.79620	+	2.19174i	0.214232	+	0.123687i
$315$	−3.10407	−	9.56535i	−0.174895	−	0.538947i
$316$	7.72926	−	4.46249i	0.434805	−	0.251035i
$317$	14.2460	−	8.22494i	0.800136	−	0.461959i	−0.0433825	−	0.999059i	$-0.513813\pi$
$317$	14.2460	−	8.22494i	0.800136	−	0.461959i	0.843519	+	0.537100i	$0.180480\pi$
$318$	−5.82686	−	10.0924i	−0.326754	−	0.565954i
$319$			3.78024i			0.211653i
$320$	−2.12688	+	0.690199i	−0.118896	+	0.0385833i
$321$	4.37708	+	7.58132i	0.244305	+	0.423148i
$322$			7.35614i			0.409942i
$323$		−	7.78289i		−	0.433052i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−1.14434	−	10.9654i	−0.0634764	−	0.608249i
$326$	−8.00959	+	13.8730i	−0.443610	+	0.768356i
$327$	11.1497			0.616582
$328$	−1.68174	+	2.91286i	−0.0928587	+	0.160836i
$329$	−15.1002	+	26.1544i	−0.832504	+	1.44194i
$330$	0.284758	+	0.877496i	0.0156754	+	0.0483046i
$331$	9.69676	−	5.59843i	0.532982	−	0.307717i	−0.209248	−	0.977863i	$-0.567102\pi$
$331$	9.69676	−	5.59843i	0.532982	−	0.307717i	0.742230	+	0.670145i	$0.233768\pi$
$332$			3.90968i			0.214571i
$333$	0.339909	+	6.07326i	0.0186269	+	0.332812i
$334$	−13.3308			−0.729429
$335$	−6.85834	−	1.46043i	−0.374711	−	0.0797917i
$336$	2.24868	−	3.89483i	0.122676	−	0.212480i
$337$	−26.6165	−	15.3670i	−1.44989	−	0.837095i	−0.451417	−	0.892313i	$-0.649081\pi$
$337$	−26.6165	−	15.3670i	−1.44989	−	0.837095i	−0.998474	+	0.0552182i	$0.982415\pi$
$338$	4.06902	−	7.04775i	0.221326	−	0.383347i
$339$			1.63405i			0.0887495i
$340$	−6.94500	+	2.25374i	−0.376646	+	0.122226i
$341$			2.68734i			0.145528i
$342$	2.06416	−	1.19174i	0.111617	−	0.0644420i
$343$			28.0017i			1.51195i
$344$	−9.32116			−0.502563
$345$	3.57724	+	0.761743i	0.192592	+	0.0410109i
$346$	−22.0473	−	12.7290i	−1.18527	−	0.684315i
$347$	−6.51035			−0.349494			−0.174747	−	0.984613i	$-0.555911\pi$
$347$	−6.51035			−0.349494			−0.174747	+	0.984613i	$0.555911\pi$
$348$	−4.58129	−	7.93502i	−0.245583	−	0.425362i
$349$	−5.75901	−	9.97489i	−0.308273	−	0.533944i	0.669712	−	0.742621i	$-0.266418\pi$
$349$	−5.75901	−	9.97489i	−0.308273	−	0.533944i	−0.977985	+	0.208677i	$0.933084\pi$
$350$	−13.2040	−	18.2019i	−0.705783	−	0.972935i
$351$	1.90957	+	1.10249i	0.101925	+	0.0588467i
$352$	−0.206287	+	0.357299i	−0.0109951	+	0.0190441i
$353$	−13.7639	−	23.8398i	−0.732580	−	1.26887i	−0.955777	−	0.294093i	$-0.904983\pi$
$353$	−13.7639	−	23.8398i	−0.732580	−	1.26887i	0.223197	−	0.974773i	$-0.428351\pi$
$354$	−2.74978	−	4.76276i	−0.146149	−	0.253138i
$355$	0.945290	−	4.43920i	0.0501708	−	0.235608i
$356$		−	2.88298i		−	0.152798i
$357$	7.34272	−	12.7180i	0.388618	−	0.673106i
$358$	−2.90714	+	1.67844i	−0.153647	+	0.0887081i
$359$	−10.4314			−0.550546			−0.275273	−	0.961366i	$-0.588768\pi$
$359$	−10.4314			−0.550546			−0.275273	+	0.961366i	$0.588768\pi$
$360$	−1.66117	−	1.49683i	−0.0875514	−	0.0788901i
$361$	−6.65951	−	11.5346i	−0.350500	−	0.607084i
$362$	−9.70996			−0.510344
$363$	−9.37887	−	5.41489i	−0.492263	−	0.284208i
$364$			9.91661i			0.519772i
$365$	4.53789	+	13.9837i	0.237524	+	0.731942i
$366$	3.73535	−	6.46982i	0.195250	−	0.338183i
$367$	−6.94787	−	4.01136i	−0.362676	−	0.209391i	0.307578	−	0.951523i	$-0.400481\pi$
$367$	−6.94787	−	4.01136i	−0.362676	−	0.209391i	−0.670254	+	0.742132i	$0.733815\pi$
$368$	0.817829	+	1.41652i	0.0426323	+	0.0738413i
$369$	−3.36348			−0.175096
$370$	4.91470	+	12.6825i	0.255503	+	0.659332i
$371$	52.4109			2.72104
$372$	−3.25680	−	5.64095i	−0.168857	−	0.292469i
$373$	20.3157	+	11.7293i	1.05191	+	0.607318i	0.923182	−	0.384362i	$-0.125579\pi$
$373$	20.3157	+	11.7293i	1.05191	+	0.607318i	0.128724	+	0.991680i	$0.458912\pi$
$374$	−0.673598	+	1.16671i	−0.0348309	+	0.0603290i
$375$	−10.2188	+	4.53616i	−0.527695	+	0.234246i
$376$			6.71516i			0.346308i
$377$	17.4966	+	10.1017i	0.901120	+	0.520262i
$378$	4.49736			0.231319
$379$	−8.83500	−	15.3027i	−0.453823	−	0.786045i	0.544796	−	0.838568i	$-0.316607\pi$
$379$	−8.83500	−	15.3027i	−0.453823	−	0.786045i	−0.998620	+	0.0525234i	$0.983274\pi$
$380$	3.56768	−	3.95937i	0.183018	−	0.203111i
$381$	9.13018			0.467753
$382$	−16.2402	+	9.37630i	−0.830923	+	0.479733i
$383$	11.8360	−	20.5006i	0.604793	−	1.04753i	−0.387291	−	0.921957i	$-0.626589\pi$
$383$	11.8360	−	20.5006i	0.604793	−	1.04753i	0.992084	−	0.125575i	$-0.0400775\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−4.05803	−	0.864123i	−0.206816	−	0.0440398i
$386$	12.8390	+	22.2379i	0.653490	+	1.13188i
$387$	−4.66058	−	8.07236i	−0.236911	−	0.410341i
$388$	−5.46368	+	9.46337i	−0.277376	+	0.480430i
$389$	−12.3967	−	7.15722i	−0.628536	−	0.362886i	0.151649	−	0.988434i	$-0.451542\pi$
$389$	−12.3967	−	7.15722i	−0.628536	−	0.362886i	−0.780185	+	0.625549i	$0.784875\pi$
$390$	4.82237	+	1.02688i	0.244190	+	0.0519983i
$391$	2.67049	+	4.62543i	0.135053	+	0.233918i
$392$	6.61313	+	11.4543i	0.334013	+	0.578528i
$393$	−11.3759			−0.573839
$394$	−15.5562	−	8.98138i	−0.783710	−	0.452475i
$395$	19.5192	+	4.15646i	0.982119	+	0.209134i
$396$	−0.412574			−0.0207326
$397$		−	30.2416i		−	1.51778i	−0.651218	−	0.758891i	$-0.725742\pi$
$397$		−	30.2416i		−	1.51778i	0.651218	−	0.758891i	$-0.274258\pi$
$398$	7.03317	−	4.06060i	0.352541	−	0.203540i
$399$			10.7194i			0.536640i
$400$	−4.56623	−	2.03705i	−0.228311	−	0.101852i
$401$			3.30061i			0.164824i	0.996598	+	0.0824122i	$0.0262624\pi$
$401$			3.30061i			0.164824i	−0.996598	+	0.0824122i	$0.973738\pi$
$402$	1.56796	−	2.71578i	0.0782025	−	0.135451i
$403$	12.4382	+	7.18120i	0.619591	+	0.357721i
$404$	8.60920	−	14.9116i	0.428324	−	0.741878i
$405$	0.465711	−	2.18703i	0.0231414	−	0.108675i
$406$	41.2074			2.04509
$407$	2.24009	+	1.13138i	0.111037	+	0.0560807i
$408$		−	3.26535i		−	0.161659i
$409$	−24.6098	+	14.2085i	−1.21688	+	0.702565i	−0.964249	−	0.264998i	$-0.914629\pi$
$409$	−24.6098	+	14.2085i	−1.21688	+	0.702565i	−0.252630	+	0.967563i	$0.581295\pi$
$410$	−7.15373	+	2.32147i	−0.353298	+	0.114649i
$411$	−1.23704	+	2.14262i	−0.0610189	+	0.105688i
$412$	8.45167	−	14.6387i	0.416384	−	0.721198i
$413$	24.7335			1.21706
$414$	−0.817829	+	1.41652i	−0.0401941	+	0.0696182i
$415$	−5.85214	+	6.49464i	−0.287270	+	0.318809i
$416$	1.10249	+	1.90957i	0.0540541	+	0.0936245i
$417$			18.9038i			0.925724i
$418$		−	0.983363i		−	0.0480978i
$419$	2.15871	+	3.73900i	0.105460	+	0.182662i	0.913926	−	0.405881i	$-0.133035\pi$
$419$	2.15871	+	3.73900i	0.105460	+	0.182662i	−0.808466	+	0.588543i	$0.799702\pi$
$420$	9.56535	−	3.10407i	0.466741	−	0.151463i
$421$		−	31.2190i		−	1.52152i	−0.649034	−	0.760759i	$-0.724827\pi$
$421$		−	31.2190i		−	1.52152i	0.649034	−	0.760759i	$-0.275173\pi$
$422$	4.23718	+	7.33901i	0.206263	+	0.357257i
$423$	−5.81550	+	3.35758i	−0.282759	+	0.163251i
$424$	10.0924	−	5.82686i	0.490131	−	0.282977i
$425$	−14.9103	−	6.65167i	−0.723256	−	0.322653i
$426$	1.75784	+	1.01489i	0.0851677	+	0.0491716i
$427$	16.7992	+	29.0971i	0.812972	+	1.40811i
$428$	−7.58132	+	4.37708i	−0.366457	+	0.211574i
$429$	0.787840	−	0.454859i	0.0380373	−	0.0219608i
$430$	−15.4840	−	13.9522i	−0.746707	−	0.672836i
$431$	19.5309	+	11.2762i	0.940770	+	0.543154i	0.890202	−	0.455567i	$-0.150563\pi$
$431$	19.5309	+	11.2762i	0.940770	+	0.543154i	0.0505684	+	0.998721i	$0.483897\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$			3.06164i			0.147133i	0.997290	+	0.0735664i	$0.0234381\pi$
$433$			3.06164i			0.147133i	−0.997290	+	0.0735664i	$0.976562\pi$
$434$	29.2940			1.40616
$435$	4.26711	−	20.0388i	0.204592	−	0.960789i
$436$			11.1497i			0.533976i
$437$	−3.37625	−	1.94928i	−0.161508	−	0.0932467i
$438$	−6.57476			−0.314154
$439$	3.33982	+	1.92824i	0.159401	+	0.0920301i	0.577579	−	0.816335i	$-0.303998\pi$
$439$	3.33982	+	1.92824i	0.159401	+	0.0920301i	−0.418178	+	0.908365i	$0.637331\pi$
$440$	−0.877496	+	0.284758i	−0.0418330	+	0.0135753i
$441$	−6.61313	+	11.4543i	−0.314911	+	0.545442i
$442$	3.60002	+	6.23541i	0.171235	+	0.296588i
$443$			25.4109i			1.20731i	0.797247	+	0.603654i	$0.206289\pi$
$443$			25.4109i			1.20731i	−0.797247	+	0.603654i	$0.793711\pi$
$444$	−6.07326	+	0.339909i	−0.288224	+	0.0161313i
$445$	4.31535	−	4.78913i	0.204567	−	0.227026i
$446$	16.2112	−	9.35953i	0.767622	−	0.443187i
$447$	6.91711	+	3.99360i	0.327168	+	0.188891i
$448$	3.89483	+	2.24868i	0.184013	+	0.106240i
$449$	29.8241	+	17.2189i	1.40749	+	0.812612i	0.995145	−	0.0984178i	$-0.0313782\pi$
$449$	29.8241	+	17.2189i	1.40749	+	0.812612i	0.412340	+	0.911030i	$0.364712\pi$
$450$	−0.518977	−	4.97299i	−0.0244648	−	0.234429i
$451$	−0.693843	+	1.20177i	−0.0326718	+	0.0565892i
$452$	−1.63405			−0.0768593
$453$	−3.73146	+	2.15436i	−0.175319	+	0.101221i
$454$	−4.49650			−0.211031
$455$	−14.8435	+	16.4732i	−0.695875	+	0.772275i
$456$	1.19174	+	2.06416i	0.0558084	+	0.0966630i
$457$	−0.681427	+	1.18027i	−0.0318758	+	0.0552105i	−0.881523	−	0.472141i	$-0.843481\pi$
$457$	−0.681427	+	1.18027i	−0.0318758	+	0.0552105i	0.849647	+	0.527351i	$0.176815\pi$
$458$	−20.3635			−0.951524
$459$	2.82787	−	1.63267i	0.131994	−	0.0762067i
$460$	−0.761743	+	3.57724i	−0.0355165	+	0.166790i
$461$	−10.7687	+	6.21733i	−0.501550	+	0.289570i	−0.729353	−	0.684137i	$-0.760179\pi$
$461$	−10.7687	+	6.21733i	−0.501550	+	0.289570i	0.227803	+	0.973707i	$0.426846\pi$
$462$	0.927747	−	1.60690i	0.0431627	−	0.0747600i
$463$	−2.33045	+	4.03646i	−0.108305	+	0.187590i	−0.915084	−	0.403264i	$-0.867876\pi$
$463$	−2.33045	+	4.03646i	−0.108305	+	0.187590i	0.806778	+	0.590854i	$0.201209\pi$
$464$	7.93502	−	4.58129i	0.368374	−	0.212681i
$465$	3.03345	−	14.2455i	0.140673	−	0.660618i
$466$	2.54674	−	1.47036i	0.117975	−	0.0681132i
$467$	24.9564			1.15484			0.577422	−	0.816446i	$-0.304059\pi$
$467$	24.9564			1.15484			0.577422	+	0.816446i	$0.304059\pi$
$468$	−1.10249	+	1.90957i	−0.0509627	+	0.0882700i
$469$	7.05166	+	12.2138i	0.325616	+	0.563983i
$470$	−10.0515	+	11.1550i	−0.463640	+	0.514543i
$471$	−4.38347			−0.201980
$472$	4.76276	−	2.74978i	0.219224	−	0.126569i
$473$	−3.84567			−0.176824
$474$	−4.46249	+	7.72926i	−0.204969	+	0.355017i
$475$	11.8530	−	1.23697i	0.543855	−	0.0567562i
$476$	12.7180	+	7.34272i	0.582927	+	0.336553i
$477$	10.0924	+	5.82686i	0.462100	+	0.266793i
$478$	8.01145	+	4.62541i	0.366435	+	0.211562i
$479$	−10.0078	+	5.77801i	−0.457268	+	0.264004i	−0.710895	−	0.703298i	$-0.751710\pi$
$479$	−10.0078	+	5.77801i	−0.457268	+	0.264004i	0.253627	+	0.967302i	$0.418377\pi$
$480$	1.49683	−	1.66117i	0.0683208	−	0.0758217i
$481$	11.2226	−	7.34480i	0.511706	−	0.334894i
$482$		−	0.798091i		−	0.0363520i
$483$	−3.67807	−	6.37061i	−0.167358	−	0.289873i
$484$	5.41489	−	9.37887i	0.246131	−	0.426312i
$485$	−23.2412	+	7.54206i	−1.05533	+	0.342467i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	34.7877			1.57638			0.788190	−	0.615432i	$-0.211019\pi$
$487$	34.7877			1.57638			0.788190	+	0.615432i	$0.211019\pi$
$488$	6.46982	+	3.73535i	0.292875	+	0.169092i
$489$		−	16.0192i		−	0.724413i
$490$	−6.15961	+	28.9263i	−0.278263	+	1.30675i
$491$	4.56055			0.205815			0.102907	−	0.994691i	$-0.467186\pi$
$491$	4.56055			0.205815			0.102907	+	0.994691i	$0.467186\pi$
$492$		−	3.36348i		−	0.151638i
$493$	25.9106	−	14.9595i	1.16695	−	0.673741i
$494$	−4.55143	−	2.62777i	−0.204779	−	0.118229i
$495$	−0.685356	−	0.617555i	−0.0308044	−	0.0277570i
$496$	5.64095	−	3.25680i	0.253286	−	0.146235i
$497$	−7.90565	+	4.56433i	−0.354617	+	0.204738i
$498$	−1.95484	−	3.38588i	−0.0875984	−	0.151725i
$499$	3.45818	+	1.99658i	0.154809	+	0.0893792i	0.575404	−	0.817870i	$-0.304845\pi$
$499$	3.45818	+	1.99658i	0.154809	+	0.0893792i	−0.420594	+	0.907249i	$0.638178\pi$
$500$	−4.53616	−	10.2188i	−0.202863	−	0.456997i
$501$	11.5448	−	6.66540i	0.515784	−	0.297788i
$502$	−11.9135	+	6.87828i	−0.531727	+	0.306993i
$503$	11.2212	+	19.4356i	0.500327	+	0.866593i	1.00000		0.000378200i	$0.000120385\pi$
$503$	11.2212	+	19.4356i	0.500327	+	0.866593i	−0.499672	+	0.866214i	$0.666546\pi$
$504$			4.49736i			0.200328i
$505$	36.6215	−	11.8841i	1.62963	−	0.528836i
$506$	0.337415	+	0.584420i	0.0149999	+	0.0259806i
$507$			8.13804i			0.361423i
$508$			9.13018i			0.405086i
$509$	16.6264	+	28.7978i	0.736952	+	1.27644i	0.953862	+	0.300246i	$0.0970689\pi$
$509$	16.6264	+	28.7978i	0.736952	+	1.27644i	−0.216910	+	0.976192i	$0.569598\pi$
$510$	4.88768	−	5.42430i	0.216430	−	0.240192i
$511$	14.7845	−	25.6076i	0.654029	−	1.13281i
$512$	1.00000			0.0441942
$513$	−1.19174	+	2.06416i	−0.0526167	+	0.0911347i
$514$	−9.61645	+	16.6562i	−0.424164	+	0.734673i
$515$	35.9514	−	11.6667i	1.58421	−	0.514095i
$516$	8.07236	−	4.66058i	0.355366	−	0.205171i
$517$			2.77050i			0.121846i
$518$	12.3329	−	24.4186i	0.541878	−	1.07289i
$519$	25.4580			1.11748
$520$	−1.02688	+	4.82237i	−0.0450319	+	0.211475i
$521$	−7.83325	+	13.5676i	−0.343181	+	0.594407i	−0.985022	−	0.172431i	$-0.944838\pi$
$521$	−7.83325	+	13.5676i	−0.343181	+	0.594407i	0.641841	+	0.766838i	$0.278171\pi$
$522$	7.93502	+	4.58129i	0.347306	+	0.200517i
$523$	9.39805	−	16.2779i	0.410948	−	0.711783i	−0.584046	−	0.811721i	$-0.698531\pi$
$523$	9.39805	−	16.2779i	0.410948	−	0.711783i	0.994994	+	0.0999381i	$0.0318645\pi$
$524$		−	11.3759i		−	0.496959i
$525$	20.5360	+	9.16135i	0.896263	+	0.399834i
$526$		−	5.83890i		−	0.254588i
$527$	18.4196	−	10.6346i	0.802372	−	0.463250i
$528$		−	0.412574i		−	0.0179550i
$529$	−20.3246			−0.883679
$530$	25.4871	+	5.42726i	1.10709	+	0.235745i
$531$	4.76276	+	2.74978i	0.206686	+	0.119330i
$532$	−10.7194			−0.464744
$533$	3.70821	+	6.42282i	0.160621	+	0.278203i
$534$	1.44149	+	2.49674i	0.0623795	+	0.108044i
$535$	−19.1456	−	4.07690i	−0.827738	−	0.176260i
$536$	2.71578	+	1.56796i	0.117304	+	0.0677254i
$537$	1.67844	−	2.90714i	0.0724299	−	0.125452i
$538$	10.9814	+	19.0203i	0.473440	+	0.820022i
$539$	2.72840	+	4.72573i	0.117521	+	0.203552i
$540$	2.18703	+	0.465711i	0.0941149	+	0.0200410i
$541$		−	21.1376i		−	0.908776i	−0.890804	−	0.454388i	$-0.849858\pi$
$541$		−	21.1376i		−	0.908776i	0.890804	−	0.454388i	$-0.150142\pi$
$542$	−1.50615	+	2.60873i	−0.0646946	+	0.112054i
$543$	8.40907	−	4.85498i	0.360868	−	0.208347i
$544$	3.26535			0.140001
$545$	−16.6893	+	18.5216i	−0.714891	+	0.793379i
$546$	−4.95830	−	8.58804i	−0.212196	−	0.367534i
$547$	12.0432			0.514932			0.257466	−	0.966287i	$-0.417112\pi$
$547$	12.0432			0.514932			0.257466	+	0.966287i	$0.417112\pi$
$548$	−2.14262	−	1.23704i	−0.0915283	−	0.0528439i
$549$			7.47071i			0.318842i
$550$	−1.88391	−	0.840433i	−0.0803300	−	0.0358362i
$551$	−10.9194	+	18.9130i	−0.465183	+	0.805720i
$552$	−1.41652	−	0.817829i	−0.0602911	−	0.0348091i
$553$	−20.0694	−	34.7613i	−0.853439	−	1.47820i
$554$	−14.5764			−0.619292
$555$	−10.5975	−	8.52601i	−0.449839	−	0.361909i
$556$	−18.9038			−0.801701
$557$	9.83047	+	17.0269i	0.416530	+	0.721452i	0.995588	−	0.0938350i	$-0.0299126\pi$
$557$	9.83047	+	17.0269i	0.416530	+	0.721452i	−0.579057	+	0.815287i	$0.696579\pi$
$558$	5.64095	+	3.25680i	0.238800	+	0.137871i
$559$	−10.2765	+	17.7994i	−0.434650	+	0.752836i
$560$	3.10407	+	9.56535i	0.131171	+	0.404210i
$561$		−	1.34720i		−	0.0568787i
$562$	−12.4391	−	7.18169i	−0.524710	−	0.302941i
$563$	40.6424			1.71287			0.856436	−	0.516252i	$-0.172673\pi$
$563$	40.6424			1.71287			0.856436	+	0.516252i	$0.172673\pi$
$564$	−3.35758	−	5.81550i	−0.141380	−	0.244877i
$565$	−2.71444	−	2.44590i	−0.114197	−	0.102900i
$566$	−27.0668			−1.13770
$567$	−3.89483	+	2.24868i	−0.163567	+	0.0944357i
$568$	−1.01489	+	1.75784i	−0.0425838	+	0.0737574i
$569$			12.5423i			0.525799i	0.964823	+	0.262900i	$0.0846788\pi$
$569$			12.5423i			0.525799i	−0.964823	+	0.262900i	$0.915321\pi$
$570$	−1.11001	+	5.21275i	−0.0464933	+	0.218338i
$571$	−19.7682	−	34.2396i	−0.827275	−	1.43288i	−0.900168	−	0.435542i	$-0.856557\pi$
$571$	−19.7682	−	34.2396i	−0.827275	−	1.43288i	0.0728934	−	0.997340i	$-0.476777\pi$
$572$	0.454859	+	0.787840i	0.0190186	+	0.0329412i
$573$	9.37630	−	16.2402i	0.391701	−	0.678446i
$574$	13.1002	+	7.56340i	0.546791	+	0.315690i
$575$	−6.61992	+	4.80220i	−0.276070	+	0.200266i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−16.0103	−	27.7306i	−0.666516	−	1.15444i	−0.978872	−	0.204474i	$-0.934452\pi$
$577$	−16.0103	−	27.7306i	−0.666516	−	1.15444i	0.312356	−	0.949965i	$-0.398882\pi$
$578$	−6.33751			−0.263606
$579$	−22.2379	−	12.8390i	−0.924174	−	0.533572i
$580$	20.0388	+	4.26711i	0.832068	+	0.177182i
$581$	17.5832			0.729475
$582$		−	10.9274i		−	0.452954i
$583$	4.16386	−	2.40401i	0.172450	−	0.0995639i
$584$		−	6.57476i		−	0.272065i
$585$	−4.68974	+	1.52188i	−0.193897	+	0.0629219i
$586$			17.3721i			0.717635i
$587$	−23.6410	+	40.9474i	−0.975769	+	1.69008i	−0.298396	+	0.954442i	$0.596451\pi$
$587$	−23.6410	+	40.9474i	−0.975769	+	1.69008i	−0.677373	+	0.735639i	$0.736882\pi$
$588$	−11.4543	−	6.61313i	−0.472366	−	0.272721i
$589$	−7.76253	+	13.4451i	−0.319849	+	0.553995i
$590$	12.0277	+	2.56120i	0.495173	+	0.105443i
$591$	17.9628			0.738889
$592$	−0.339909	−	6.07326i	−0.0139702	−	0.249609i
$593$			33.0223i			1.35606i	0.735033	+	0.678032i	$0.237167\pi$
$593$			33.0223i			1.35606i	−0.735033	+	0.678032i	$0.762833\pi$
$594$	0.357299	−	0.206287i	0.0146602	−	0.00846406i
$595$	10.1359	+	31.2342i	0.415531	+	1.28048i
$596$	−3.99360	+	6.91711i	−0.163584	+	0.283336i
$597$	−4.06060	+	7.03317i	−0.166189	+	0.287848i
$598$	3.60660			0.147485
$599$	7.17181	−	12.4219i	0.293032	−	0.507547i	−0.681493	−	0.731825i	$-0.738669\pi$
$599$	7.17181	−	12.4219i	0.293032	−	0.507547i	0.974525	+	0.224278i	$0.0720024\pi$
$600$	4.97299	−	0.518977i	0.203022	−	0.0211871i
$601$	15.3756	+	26.6314i	0.627185	+	1.08632i	0.988114	+	0.153723i	$0.0491263\pi$
$601$	15.3756	+	26.6314i	0.627185	+	1.08632i	−0.360929	+	0.932593i	$0.617540\pi$
$602$			41.9206i			1.70856i
$603$			3.13591i			0.127704i
$604$	−2.15436	−	3.73146i	−0.0876597	−	0.151831i
$605$	23.0337	−	7.47471i	0.936452	−	0.303890i
$606$			17.2184i			0.699449i
$607$	−9.17110	−	15.8848i	−0.372243	−	0.644745i	0.617667	−	0.786440i	$-0.288078\pi$
$607$	−9.17110	−	15.8848i	−0.372243	−	0.644745i	−0.989910	+	0.141695i	$0.954745\pi$
$608$	−2.06416	+	1.19174i	−0.0837126	+	0.0483315i
$609$	−35.6866	+	20.6037i	−1.44610	+	0.834904i
$610$	5.15628	+	15.8893i	0.208772	+	0.643340i
$611$	12.8231	+	7.40341i	0.518766	+	0.299510i
$612$	1.63267	+	2.82787i	0.0659969	+	0.114310i
$613$	16.8714	−	9.74069i	0.681429	−	0.393423i	−0.118965	−	0.992899i	$-0.537957\pi$
$613$	16.8714	−	9.74069i	0.681429	−	0.393423i	0.800393	+	0.599476i	$0.204624\pi$
$614$	16.5320	−	9.54474i	0.667176	−	0.385194i
$615$	5.03458	−	5.58732i	0.203014	−	0.225303i
$616$	1.60690	+	0.927747i	0.0647440	+	0.0373800i
$617$	26.0408	−	15.0346i	1.04836	−	0.605272i	0.126171	−	0.992008i	$-0.459731\pi$
$617$	26.0408	−	15.0346i	1.04836	−	0.605272i	0.922190	+	0.386737i	$0.126398\pi$
$618$			16.9033i			0.679952i
$619$	−25.2132			−1.01340			−0.506702	−	0.862121i	$-0.669135\pi$
$619$	−25.2132			−1.01340			−0.506702	+	0.862121i	$0.669135\pi$
$620$	14.2455	+	3.03345i	0.572112	+	0.121826i
$621$		−	1.63566i		−	0.0656367i
$622$	−1.51782	−	0.876316i	−0.0608592	−	0.0351371i
$623$	−12.9658			−0.519465
$624$	−1.90957	−	1.10249i	−0.0764441	−	0.0441350i
$625$	7.76047	−	23.7650i	0.310419	−	0.950600i
$626$	−3.08712	+	5.34705i	−0.123386	+	0.213711i
$627$	0.491681	+	0.851617i	0.0196359	+	0.0340103i
$628$		−	4.38347i		−	0.174920i
$629$	−1.10992	−	19.8313i	−0.0442554	−	0.790725i
$630$	−6.73180	+	7.47088i	−0.268201	+	0.297647i
$631$	−3.21095	+	1.85384i	−0.127826	+	0.0738003i	−0.562549	−	0.826764i	$-0.690179\pi$
$631$	−3.21095	+	1.85384i	−0.127826	+	0.0738003i	0.434724	+	0.900564i	$0.356846\pi$
$632$	−7.72926	−	4.46249i	−0.307454	−	0.177508i
$633$	−7.33901	−	4.23718i	−0.291699	−	0.168413i
$634$	−14.2460	−	8.22494i	−0.565782	−	0.326654i
$635$	−13.6664	+	15.1668i	−0.542333	+	0.601876i
$636$	−5.82686	+	10.0924i	−0.231050	+	0.400190i
$637$	29.1637			1.15551
$638$	3.27378	−	1.89012i	0.129610	−	0.0748305i
$639$	−2.02978			−0.0802969
$640$	1.66117	+	1.49683i	0.0656635	+	0.0591676i
$641$	−21.6941	−	37.5752i	−0.856864	−	1.48413i	−0.874905	−	0.484295i	$-0.839076\pi$
$641$	−21.6941	−	37.5752i	−0.856864	−	1.48413i	0.0180408	−	0.999837i	$-0.494257\pi$
$642$	4.37708	−	7.58132i	0.172750	−	0.299211i
$643$	−20.0324			−0.790003			−0.395001	−	0.918681i	$-0.629256\pi$
$643$	−20.0324			−0.790003			−0.395001	+	0.918681i	$0.629256\pi$
$644$	6.37061	−	3.67807i	0.251037	−	0.144936i
$645$	20.3857	+	4.34097i	0.802686	+	0.170925i
$646$	−6.74018	+	3.89145i	−0.265189	+	0.153107i
$647$	−3.87468	+	6.71115i	−0.152329	+	0.263842i	−0.932083	−	0.362244i	$-0.882011\pi$
$647$	−3.87468	+	6.71115i	−0.152329	+	0.263842i	0.779754	+	0.626086i	$0.215344\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	1.96499	−	1.13449i	0.0771326	−	0.0445325i
$650$	−8.92412	+	6.47371i	−0.350033	+	0.253920i
$651$	−25.3694	+	14.6470i	−0.994304	+	0.574062i
$652$	16.0192			0.627360
$653$	−16.5210	+	28.6152i	−0.646516	+	1.11980i	0.337433	+	0.941350i	$0.390441\pi$
$653$	−16.5210	+	28.6152i	−0.646516	+	1.11980i	−0.983949	+	0.178449i	$0.942892\pi$
$654$	−5.57487	−	9.65596i	−0.217995	−	0.377578i
$655$	17.0279	−	18.8973i	0.665333	−	0.738380i
$656$	3.36348			0.131322
$657$	5.69391	−	3.28738i	0.222140	−	0.128253i
$658$	30.2005			1.17734
$659$	7.97035	−	13.8051i	0.310481	−	0.537768i	−0.667986	−	0.744174i	$-0.732843\pi$
$659$	7.97035	−	13.8051i	0.310481	−	0.537768i	0.978467	+	0.206406i	$0.0661766\pi$
$660$	0.617555	−	0.685356i	0.0240383	−	0.0266774i
$661$	22.0245	+	12.7158i	0.856653	+	0.494589i	0.862890	−	0.505392i	$-0.168652\pi$
$661$	22.0245	+	12.7158i	0.856653	+	0.494589i	−0.00623711	+	0.999981i	$0.501985\pi$
$662$	−9.69676	−	5.59843i	−0.376875	−	0.217589i
$663$	−6.23541	−	3.60002i	−0.242163	−	0.139813i
$664$	3.38588	−	1.95484i	0.131398	−	0.0758625i
$665$	−17.8067	−	16.0451i	−0.690515	−	0.622203i
$666$	5.08964	−	3.33100i	0.197220	−	0.129074i
$667$		−	14.9868i		−	0.580292i
$668$	6.66540	+	11.5448i	0.257892	+	0.446682i
$669$	−9.35953	+	16.2112i	−0.361860	+	0.626761i
$670$	2.16440	+	6.66971i	0.0836182	+	0.257674i
$671$	2.66928	+	1.54111i	0.103046	+	0.0594939i
$672$	−4.49736			−0.173489
$673$	−29.2455	−	16.8849i	−1.12733	−	0.650866i	−0.184070	−	0.982913i	$-0.558927\pi$
$673$	−29.2455	−	16.8849i	−1.12733	−	0.650866i	−0.943263	+	0.332047i	$0.892261\pi$
$674$			30.7340i			1.18383i
$675$	2.93594	+	4.04725i	0.113005	+	0.155779i
$676$	−8.13804			−0.313002
$677$		−	15.8792i		−	0.610288i	−0.952306	−	0.305144i	$-0.901295\pi$
$677$		−	15.8792i		−	0.610288i	0.952306	−	0.305144i	$-0.0987045\pi$
$678$	1.41513	−	0.817025i	0.0543477	−	0.0313777i
$679$	42.5602	+	24.5721i	1.63331	+	0.942992i
$680$	5.42430	+	4.88768i	0.208012	+	0.187434i
$681$	3.89408	−	2.24825i	0.149222	−	0.0861531i
$682$	2.32731	−	1.34367i	0.0891172	−	0.0514518i
$683$	−16.4618	−	28.5127i	−0.629894	−	1.09101i	−0.987572	−	0.157164i	$-0.949765\pi$
$683$	−16.4618	−	28.5127i	−0.629894	−	1.09101i	0.357678	−	0.933845i	$-0.383569\pi$
$684$	−2.06416	−	1.19174i	−0.0789250	−	0.0455674i
$685$	−1.70761	−	5.26209i	−0.0652445	−	0.201054i
$686$	24.2502	−	14.0009i	0.925877	−	0.534555i
$687$	17.6353	−	10.1818i	0.672829	−	0.388458i
$688$	4.66058	+	8.07236i	0.177683	+	0.307756i
$689$		−	25.6962i		−	0.978949i
$690$	−1.12893	−	3.47885i	−0.0429776	−	0.132438i
$691$	−18.6030	−	32.2214i	−0.707693	−	1.22576i	−0.965711	−	0.259619i	$-0.916403\pi$
$691$	−18.6030	−	32.2214i	−0.707693	−	1.22576i	0.258018	−	0.966140i	$-0.416930\pi$
$692$			25.4580i			0.967768i
$693$			1.85549i			0.0704844i
$694$	3.25518	+	5.63813i	0.123565	+	0.214020i
$695$	−31.4025	−	28.2959i	−1.19116	−	1.07332i
$696$	−4.58129	+	7.93502i	−0.173653	+	0.300776i
$697$	10.9829			0.416008
$698$	−5.75901	+	9.97489i	−0.217982	+	0.377555i
$699$	−1.47036	+	2.54674i	−0.0556142	+	0.0963266i
$700$	−9.16135	+	20.5360i	−0.346266	+	0.776187i
$701$	7.57252	−	4.37200i	0.286010	−	0.165128i	−0.350131	−	0.936701i	$-0.613863\pi$
$701$	7.57252	−	4.37200i	0.286010	−	0.165128i	0.636141	+	0.771573i	$0.280530\pi$
$702$		−	2.20498i		−	0.0832218i
$703$	7.93938	+	12.1311i	0.299439	+	0.457532i
$704$	0.412574			0.0155495
$705$	3.12732	−	14.6863i	0.117782	−	0.553117i
$706$	−13.7639	+	23.8398i	−0.518012	+	0.897224i
$707$	−67.0627	−	38.7187i	−2.52215	−	1.45617i
$708$	−2.74978	+	4.76276i	−0.103343	+	0.178995i
$709$			8.59568i			0.322817i	0.986888	+	0.161409i	$0.0516037\pi$
$709$			8.59568i			0.322817i	−0.986888	+	0.161409i	$0.948396\pi$
$710$	−4.31710	+	1.40095i	−0.162018	+	0.0525768i
$711$		−	8.92498i		−	0.334713i
$712$	−2.49674	+	1.44149i	−0.0935692	+	0.0540222i
$713$		−	10.6540i		−	0.398996i
$714$	−14.6854			−0.549589
$715$	−0.423666	+	1.98959i	−0.0158442	+	0.0744063i
$716$	2.90714	+	1.67844i	0.108645	+	0.0627261i
$717$	−9.25083			−0.345478
$718$	5.21568	+	9.03383i	0.194648	+	0.337139i
$719$	−18.9145	−	32.7608i	−0.705391	−	1.22177i	−0.966550	−	0.256477i	$-0.917438\pi$
$719$	−18.9145	−	32.7608i	−0.705391	−	1.22177i	0.261160	−	0.965296i	$-0.415895\pi$
$720$	−0.465711	+	2.18703i	−0.0173560	+	0.0815059i
$721$	−65.8356	−	38.0102i	−2.45185	−	1.41557i
$722$	−6.65951	+	11.5346i	−0.247841	+	0.429273i
$723$	0.399045	+	0.691167i	0.0148407	+	0.0257048i
$724$	4.85498	+	8.40907i	0.180434	+	0.312521i
$725$	26.9008	+	37.0832i	0.999071	+	1.37724i
$726$			10.8298i			0.401931i
$727$	11.9500	−	20.6980i	0.443200	−	0.767646i	−0.554724	−	0.832034i	$-0.687176\pi$
$727$	11.9500	−	20.6980i	0.443200	−	0.767646i	0.997925	+	0.0643884i	$0.0205096\pi$
$728$	8.58804	−	4.95830i	0.318294	−	0.183767i
$729$	−1.00000			−0.0370370
$730$	9.84132	−	10.9218i	0.364244	−	0.404234i
$731$	15.2184	+	26.3591i	0.562873	+	0.974925i
$732$	−7.47071			−0.276125
$733$	−18.4978	−	10.6797i	−0.683233	−	0.394465i	0.117839	−	0.993033i	$-0.462403\pi$
$733$	−18.4978	−	10.6797i	−0.683233	−	0.394465i	−0.801072	+	0.598568i	$0.795737\pi$
$734$			8.02271i			0.296124i
$735$	−9.12875	−	28.1307i	−0.336719	−	1.03762i
$736$	0.817829	−	1.41652i	0.0301456	−	0.0522137i
$737$	1.12046	+	0.646898i	0.0412727	+	0.0238288i
$738$	1.68174	+	2.91286i	0.0619058	+	0.107224i
$739$	40.7382			1.49858			0.749289	−	0.662243i	$-0.230396\pi$
$739$	40.7382			1.49858			0.749289	+	0.662243i	$0.230396\pi$
$740$	8.52601	−	10.5975i	0.313422	−	0.389572i
$741$	5.25554			0.193067
$742$	−26.2055	−	45.3892i	−0.962033	−	1.66629i
$743$	−17.7672	−	10.2579i	−0.651816	−	0.376326i	0.137336	−	0.990525i	$-0.456146\pi$
$743$	−17.7672	−	10.2579i	−0.651816	−	0.376326i	−0.789152	+	0.614199i	$0.789479\pi$
$744$	−3.25680	+	5.64095i	−0.119400	+	0.206807i
$745$	−16.9878	+	5.51275i	−0.622385	+	0.201972i
$746$		−	23.4585i		−	0.858878i
$747$	3.38588	+	1.95484i	0.123883	+	0.0715238i
$748$	1.34720			0.0492584
$749$	19.6853	+	34.0959i	0.719285	+	1.24584i
$750$	9.03781	+	6.58164i	0.330014	+	0.240327i
$751$	37.7421			1.37723			0.688614	−	0.725128i	$-0.258219\pi$
$751$	37.7421			1.37723			0.688614	+	0.725128i	$0.258219\pi$
$752$	5.81550	−	3.35758i	0.212069	−	0.122438i
$753$	6.87828	−	11.9135i	0.250658	−	0.434153i
$754$		−	20.2033i		−	0.735762i
$755$	2.00662	−	9.42331i	0.0730283	−	0.342949i
$756$	−2.24868	−	3.89483i	−0.0817837	−	0.141654i
$757$	16.4384	+	28.4721i	0.597462	+	1.03484i	0.993194	+	0.116469i	$0.0371576\pi$
$757$	16.4384	+	28.4721i	0.597462	+	1.03484i	−0.395732	+	0.918366i	$0.629509\pi$
$758$	−8.83500	+	15.3027i	−0.320901	+	0.555818i
$759$	−0.584420	−	0.337415i	−0.0212131	−	0.0122474i
$760$	−5.21275	−	1.11001i	−0.189086	−	0.0402644i
$761$	9.42311	+	16.3213i	0.341587	+	0.591647i	0.984728	−	0.174102i	$-0.0557021\pi$
$761$	9.42311	+	16.3213i	0.341587	+	0.591647i	−0.643140	+	0.765748i	$0.722369\pi$
$762$	−4.56509	−	7.90697i	−0.165376	−	0.286439i
$763$	50.1444			1.81535
$764$	16.2402	+	9.37630i	0.587551	+	0.339223i
$765$	−1.52071	+	7.14142i	−0.0549813	+	0.258199i
$766$	−23.6721			−0.855306
$767$		−	12.1264i		−	0.437860i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$			11.5220i			0.415493i	0.978183	+	0.207746i	$0.0666129\pi$
$769$			11.5220i			0.415493i	−0.978183	+	0.207746i	$0.933387\pi$
$770$	1.28066	+	3.94642i	0.0461518	+	0.142219i
$771$		−	19.2329i		−	0.692656i
$772$	12.8390	−	22.2379i	0.462087	−	0.800358i
$773$	−22.3027	−	12.8765i	−0.802173	−	0.463135i	0.0420574	−	0.999115i	$-0.486609\pi$
$773$	−22.3027	−	12.8765i	−0.802173	−	0.463135i	−0.844230	+	0.535980i	$0.819942\pi$
$774$	−4.66058	+	8.07236i	−0.167521	+	0.290155i
$775$	19.1236	+	26.3622i	0.686939	+	0.946958i
$776$	10.9274			0.392269
$777$	1.52869	+	27.3136i	0.0548415	+	0.979871i
$778$			14.3144i			0.513198i
$779$	−6.94276	+	4.00840i	−0.248750	+	0.143616i
$780$	−1.52188	−	4.68974i	−0.0544920	−	0.167920i
$781$	−0.418717	+	0.725240i	−0.0149829	+	0.0259511i
$782$	2.67049	−	4.62543i	0.0954967	−	0.165405i
$783$	−9.16257			−0.327444
$784$	6.61313	−	11.4543i	0.236183	−	0.409081i
$785$	6.56133	−	7.28170i	0.234184	−	0.259895i
$786$	5.68796	+	9.85183i	0.202883	+	0.351403i
$787$			44.7546i			1.59533i	0.603102	+	0.797664i	$0.293931\pi$
$787$			44.7546i			1.59533i	−0.603102	+	0.797664i	$0.706069\pi$
$788$			17.9628i			0.639897i
$789$	2.91945	+	5.05664i	0.103935	+	0.180021i
$790$	−6.16002	−	18.9824i	−0.219164	−	0.675363i
$791$			7.34892i			0.261297i
$792$	0.206287	+	0.357299i	0.00733009	+	0.0126961i
$793$	14.2659	−	8.23640i	0.506596	−	0.292483i
$794$	−26.1900	+	15.1208i	−0.929448	+	0.536617i
$795$	−24.7861	+	8.04338i	−0.879071	+	0.285269i
$796$	−7.03317	−	4.06060i	−0.249284	−	0.143924i
$797$	25.3243	+	43.8629i	0.897031	+	1.55370i	0.831270	+	0.555868i	$0.187614\pi$
$797$	25.3243	+	43.8629i	0.897031	+	1.55370i	0.0657607	+	0.997835i	$0.479053\pi$
$798$	9.28325	−	5.35969i	0.328624	−	0.189731i
$799$	18.9896	−	10.9637i	0.671804	−	0.387866i
$800$	0.518977	+	4.97299i	0.0183486	+	0.175822i
$801$	−2.49674	−	1.44149i	−0.0882179	−	0.0509326i
$802$	2.85841	−	1.65030i	0.100934	−	0.0582742i
$803$		−	2.71257i		−	0.0957246i
$804$	−3.13591			−0.110595
$805$	16.0881	+	3.42583i	0.567032	+	0.120745i
$806$		−	14.3624i		−	0.505894i
$807$	−19.0203	−	10.9814i	−0.669545	−	0.386562i
$808$	−17.2184			−0.605741
$809$	30.4793	+	17.5972i	1.07160	+	0.618686i	0.928617	−	0.371040i	$-0.120999\pi$
$809$	30.4793	+	17.5972i	1.07160	+	0.618686i	0.142979	+	0.989726i	$0.454332\pi$
$810$	−2.12688	+	0.690199i	−0.0747310	+	0.0242511i
$811$	−24.7519	+	42.8716i	−0.869158	+	1.50543i	−0.00629997	+	0.999980i	$0.502005\pi$
$811$	−24.7519	+	42.8716i	−0.869158	+	1.50543i	−0.862858	+	0.505446i	$0.831328\pi$
$812$	−20.6037	−	35.6866i	−0.723048	−	1.25236i
$813$		−	3.01230i		−	0.105646i
$814$	−0.140237	−	2.50567i	−0.00491532	−	0.0878236i
$815$	26.6106	+	23.9781i	0.932129	+	0.839915i
$816$	−2.82787	+	1.63267i	−0.0989953	+	0.0571550i
$817$	−19.2403	−	11.1084i	−0.673134	−	0.388634i
$818$	24.6098	+	14.2085i	0.860463	+	0.496789i
$819$	8.58804	+	4.95830i	0.300090	+	0.173257i
$820$	5.58732	+	5.03458i	0.195118	+	0.175815i
$821$	12.3439	−	21.3802i	0.430804	−	0.746174i	−0.566139	−	0.824310i	$-0.691563\pi$
$821$	12.3439	−	21.3802i	0.430804	−	0.746174i	0.996943	+	0.0781356i	$0.0248967\pi$
$822$	2.47409			0.0862937
$823$	−19.9965	+	11.5450i	−0.697036	+	0.402434i	−0.806242	−	0.591585i	$-0.798502\pi$
$823$	−19.9965	+	11.5450i	−0.697036	+	0.402434i	0.109207	+	0.994019i	$0.465169\pi$
$824$	−16.9033			−0.588856
$825$	2.05173	−	0.214116i	0.0714320	−	0.00745458i
$826$	−12.3667	−	21.4198i	−0.430294	−	0.745291i
$827$	−26.9683	+	46.7104i	−0.937779	+	1.62428i	−0.168176	+	0.985757i	$0.553788\pi$
$827$	−26.9683	+	46.7104i	−0.937779	+	1.62428i	−0.769603	+	0.638523i	$0.779546\pi$
$828$	1.63566			0.0568430
$829$	4.52451	−	2.61222i	0.157143	−	0.0907263i	−0.419367	−	0.907817i	$-0.637748\pi$
$829$	4.52451	−	2.61222i	0.157143	−	0.0907263i	0.576509	+	0.817091i	$0.304414\pi$
$830$	8.55059	+	1.82078i	0.296795	+	0.0632002i
$831$	12.6235	−	7.28820i	0.437905	−	0.252825i
$832$	1.10249	−	1.90957i	0.0382220	−	0.0662025i
$833$	21.5941	−	37.4022i	0.748193	−	1.29591i
$834$	16.3712	−	9.45191i	0.566888	−	0.327293i
$835$	−6.20830	+	29.1549i	−0.214847	+	1.00895i
$836$	−0.851617	+	0.491681i	−0.0294538	+	0.0170052i
$837$	−6.51360			−0.225143
$838$	2.15871	−	3.73900i	0.0745715	−	0.129162i
$839$	9.37644	+	16.2405i	0.323711	+	0.560684i	0.981251	−	0.192736i	$-0.0617362\pi$
$839$	9.37644	+	16.2405i	0.323711	+	0.560684i	−0.657540	+	0.753420i	$0.728403\pi$
$840$	−7.47088	−	6.73180i	−0.257770	−	0.232269i
$841$	−54.9527			−1.89492
$842$	−27.0364	+	15.6095i	−0.931736	+	0.537938i
$843$	14.3634			0.494701
$844$	4.23718	−	7.33901i	0.145850	−	0.252619i
$845$	−13.5187	−	12.1813i	−0.465057	−	0.419049i
$846$	5.81550	+	3.35758i	0.199941	+	0.115436i
$847$	−42.1801	−	24.3527i	−1.44933	−	0.836769i
$848$	−10.0924	−	5.82686i	−0.346575	−	0.200095i
$849$	23.4405	−	13.5334i	0.804478	−	0.464465i
$850$	1.69464	+	16.2385i	0.0581257	+	0.556977i
$851$	−8.88089	−	4.48540i	−0.304433	−	0.153757i
$852$		−	2.02978i		−	0.0695391i
$853$	−13.8286	−	23.9518i	−0.473482	−	0.820095i	0.526057	−	0.850449i	$-0.323670\pi$
$853$	−13.8286	−	23.9518i	−0.473482	−	0.820095i	−0.999539	+	0.0303541i	$0.990337\pi$
$854$	16.7992	−	29.0971i	0.574858	−	0.995683i
$855$	−1.64508	−	5.06938i	−0.0562605	−	0.173369i
$856$	7.58132	+	4.37708i	0.259124	+	0.149605i
$857$	45.7437			1.56257			0.781287	−	0.624172i	$-0.214563\pi$
$857$	45.7437			1.56257			0.781287	+	0.624172i	$0.214563\pi$
$858$	−0.787840	−	0.454859i	−0.0268964	−	0.0155286i
$859$			38.2079i			1.30364i	0.758375	+	0.651819i	$0.225994\pi$
$859$			38.2079i			1.30364i	−0.758375	+	0.651819i	$0.774006\pi$
$860$	−4.34097	+	20.3857i	−0.148026	+	0.695146i
$861$	−15.1268			−0.515520
$862$		−	22.5523i		−	0.768135i
$863$	0.812686	−	0.469204i	0.0276642	−	0.0159719i	−0.486104	−	0.873901i	$-0.661582\pi$
$863$	0.812686	−	0.469204i	0.0276642	−	0.0159719i	0.513768	+	0.857929i	$0.328249\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	−38.1064	+	42.2901i	−1.29566	+	1.43791i
$866$	2.65145	−	1.53082i	0.0901001	−	0.0520193i
$867$	5.48845	−	3.16876i	0.186397	−	0.107617i
$868$	−14.6470	−	25.3694i	−0.497152	−	0.861093i
$869$	−3.18889	−	1.84111i	−0.108176	−	0.0624553i
$870$	−19.4877	+	6.32400i	−0.660695	+	0.214404i
$871$	5.98825	−	3.45732i	0.202904	−	0.117147i
$872$	9.65596	−	5.57487i	0.326992	−	0.188789i
$873$	5.46368	+	9.46337i	0.184918	+	0.320287i
$874$			3.89856i			0.131871i
$875$	−45.9575	+	20.4007i	−1.55365	+	0.689671i
$876$	3.28738	+	5.69391i	0.111070	+	0.192379i
$877$		−	7.26127i		−	0.245196i	−0.992456	−	0.122598i	$-0.960877\pi$
$877$		−	7.26127i		−	0.245196i	0.992456	−	0.122598i	$-0.0391225\pi$
$878$		−	3.85649i		−	0.130150i
$879$	−8.68606	−	15.0447i	−0.292973	−	0.507445i
$880$	0.685356	+	0.617555i	0.0231033	+	0.0208178i
$881$	−20.2490	+	35.0723i	−0.682206	+	1.18161i	0.292101	+	0.956388i	$0.405646\pi$
$881$	−20.2490	+	35.0723i	−0.682206	+	1.18161i	−0.974306	+	0.225227i	$0.927688\pi$
$882$	13.2263			0.445351
$883$	20.9204	−	36.2352i	0.704028	−	1.21941i	−0.263014	−	0.964792i	$-0.584716\pi$
$883$	20.9204	−	36.2352i	0.704028	−	1.21941i	0.967041	−	0.254619i	$-0.0819502\pi$
$884$	3.60002	−	6.23541i	0.121082	−	0.209720i
$885$	−11.6969	+	3.79579i	−0.393187	+	0.127594i
$886$	22.0065	−	12.7054i	0.739322	−	0.426848i
$887$		−	45.9708i		−	1.54355i	−0.635896	−	0.771775i	$-0.719369\pi$
$887$		−	45.9708i		−	1.54355i	0.635896	−	0.771775i	$-0.280631\pi$
$888$	3.33100	+	5.08964i	0.111781	+	0.170797i
$889$	41.0617			1.37717
$890$	−6.30518	−	1.34264i	−0.211350	−	0.0450053i
$891$	−0.206287	+	0.357299i	−0.00691087	+	0.0119700i
$892$	−16.2112	−	9.35953i	−0.542791	−	0.313380i
$893$	−8.00273	+	13.8611i	−0.267801	+	0.463845i
$894$		−	7.98719i		−	0.267132i
$895$	2.31691	+	7.13967i	0.0774458	+	0.238653i
$896$		−	4.49736i		−	0.150246i
$897$	−3.12341	+	1.80330i	−0.104288	+	0.0602104i
$898$		−	34.4379i		−	1.14921i
$899$	−59.6814			−1.99048
$900$	−4.04725	+	2.93594i	−0.134908	+	0.0978648i
$901$	−32.9552	−	19.0267i	−1.09790	−	0.633871i
$902$	1.38769			0.0462049
$903$	−20.9603	−	36.3043i	−0.697516	−	1.20813i
$904$	0.817025	+	1.41513i	0.0271739	+	0.0470665i
$905$	−4.52203	+	21.2360i	−0.150317	+	0.705909i
$906$	3.73146	+	2.15436i	0.123969	+	0.0715738i
$907$	−22.9264	+	39.7096i	−0.761257	+	1.31854i	0.180945	+	0.983493i	$0.442084\pi$
$907$	−22.9264	+	39.7096i	−0.761257	+	1.31854i	−0.942203	+	0.335043i	$0.891249\pi$
$908$	2.24825	+	3.89408i	0.0746108	+	0.129230i
$909$	−8.60920	−	14.9116i	−0.285549	−	0.494585i
$910$	21.6880	+	4.61827i	0.718949	+	0.153094i
$911$			27.2436i			0.902621i	0.892367	+	0.451311i	$0.149043\pi$
$911$			27.2436i			0.902621i	−0.892367	+	0.451311i	$0.850957\pi$
$912$	1.19174	−	2.06416i	0.0394625	−	0.0683510i
$913$	1.39693	−	0.806515i	0.0462315	−	0.0266918i
$914$	1.36285			0.0450792
$915$	−12.4101	−	11.1824i	−0.410266	−	0.369679i
$916$	10.1818	+	17.6353i	0.336415	+	0.582687i
$917$	−51.1616			−1.68950
$918$	−2.82787	−	1.63267i	−0.0933337	−	0.0538862i
$919$		−	8.75052i		−	0.288653i	−0.989530	−	0.144326i	$-0.953898\pi$
$919$		−	8.75052i		−	0.288653i	0.989530	−	0.144326i	$-0.0461015\pi$
$920$	3.47885	−	1.12893i	0.114694	−	0.0372197i
$921$	−9.54474	+	16.5320i	−0.314510	+	0.544747i
$922$	10.7687	+	6.21733i	0.354649	+	0.204757i
$923$	2.23782	+	3.87601i	0.0736586	+	0.127581i
$924$	−1.85549			−0.0610413
$925$	30.0259	−	4.84224i	0.987244	−	0.159212i
$926$	4.66091			0.153167
$927$	−8.45167	−	14.6387i	−0.277589	−	0.480799i
$928$	−7.93502	−	4.58129i	−0.260480	−	0.150388i
$929$	9.61913	−	16.6608i	0.315593	−	0.546624i	−0.663970	−	0.747759i	$-0.731130\pi$
$929$	9.61913	−	16.6608i	0.315593	−	0.546624i	0.979563	+	0.201135i	$0.0644631\pi$
$930$	−13.8537	+	4.49568i	−0.454280	+	0.147419i
$931$			31.5245i			1.03318i
$932$	−2.54674	−	1.47036i	−0.0834213	−	0.0481633i
$933$	1.75263			0.0573786
$934$	−12.4782	−	21.6129i	−0.408299	−	0.707194i
$935$	2.23792	+	2.01653i	0.0731879	+	0.0659476i
$936$	2.20498			0.0720722
$937$	−22.5574	+	13.0235i	−0.736917	+	0.425459i	−0.820947	−	0.571004i	$-0.806554\pi$
$937$	−22.5574	+	13.0235i	−0.736917	+	0.425459i	0.0840301	+	0.996463i	$0.473221\pi$
$938$	7.05166	−	12.2138i	0.230245	−	0.398796i
$939$		−	6.17425i		−	0.201489i
$940$	14.6863	+	3.12732i	0.479013	+	0.102002i
$941$	−0.822234	−	1.42415i	−0.0268041	−	0.0464260i	0.852312	−	0.523033i	$-0.175200\pi$
$941$	−0.822234	−	1.42415i	−0.0268041	−	0.0464260i	−0.879116	+	0.476607i	$0.841866\pi$
$942$	2.19174	+	3.79620i	0.0714107	+	0.123687i
$943$	2.75075	−	4.76445i	0.0895769	−	0.155152i
$944$	−4.76276	−	2.74978i	−0.155015	−	0.0894977i
$945$	2.09447	−	9.83588i	0.0681331	−	0.319961i
$946$	1.92283	+	3.33045i	0.0625167	+	0.108282i
$947$	−20.1455	−	34.8931i	−0.654641	−	1.13387i	−0.981984	−	0.188966i	$-0.939486\pi$
$947$	−20.1455	−	34.8931i	−0.654641	−	1.13387i	0.327342	−	0.944906i	$-0.393847\pi$
$948$	8.92498			0.289870
$949$	−12.5550	−	7.24862i	−0.407552	−	0.235300i
$950$	−6.99777	−	9.64655i	−0.227038	−	0.312975i
$951$	16.4499			0.533424
$952$		−	14.6854i		−	0.475958i
$953$	−17.7933	+	10.2730i	−0.576381	+	0.332774i	−0.759694	−	0.650281i	$-0.774651\pi$
$953$	−17.7933	+	10.2730i	−0.576381	+	0.332774i	0.183313	+	0.983055i	$0.441318\pi$
$954$		−	11.6537i		−	0.377303i
$955$	12.9430	+	39.8846i	0.418827	+	1.29063i
$956$		−	9.25083i		−	0.299193i
$957$	−1.89012	+	3.27378i	−0.0610989	+	0.105826i
$958$	10.0078	+	5.77801i	0.323338	+	0.186679i
$959$	−5.56343	+	9.63615i	−0.179653	+	0.311167i
$960$	−2.18703	−	0.465711i	−0.0705862	−	0.0150307i
$961$	−11.4270			−0.368614
$962$	−11.9721	−	6.04664i	−0.385995	−	0.194951i
$963$			8.75416i			0.282099i
$964$	−0.691167	+	0.399045i	−0.0222610	+	0.0128524i
$965$	54.6142	−	17.7230i	1.75809	−	0.570523i
$966$	−3.67807	+	6.37061i	−0.118340	+	0.204971i
$967$	−22.3500	+	38.7114i	−0.718729	+	1.24487i	0.242775	+	0.970083i	$0.421942\pi$
$967$	−22.3500	+	38.7114i	−0.718729	+	1.24487i	−0.961504	+	0.274792i	$0.911391\pi$
$968$	−10.8298			−0.348082
$969$	3.89145	−	6.74018i	0.125011	−	0.216526i
$970$	18.1522	+	16.3564i	0.582832	+	0.525174i
$971$	−0.443756	−	0.768607i	−0.0142408	−	0.0246658i	0.858817	−	0.512282i	$-0.171200\pi$
$971$	−0.443756	−	0.768607i	−0.0142408	−	0.0246658i	−0.873058	+	0.487616i	$0.837866\pi$
$972$		−	1.00000i		−	0.0320750i
$973$			85.0173i			2.72553i
$974$	−17.3938	−	30.1270i	−0.557334	−	0.965331i
$975$	4.49166	−	10.0685i	0.143848	−	0.322449i
$976$		−	7.47071i		−	0.239132i
$977$	−7.95604	−	13.7803i	−0.254536	−	0.440870i	0.710233	−	0.703967i	$-0.248590\pi$
$977$	−7.95604	−	13.7803i	−0.254536	−	0.440870i	−0.964769	+	0.263097i	$0.915256\pi$
$978$	−13.8730	+	8.00959i	−0.443610	+	0.256119i
$979$	−1.03009	+	0.594722i	−0.0329218	+	0.0190074i
$980$	28.1307	−	9.12875i	0.898601	−	0.291607i
$981$	9.65596	+	5.57487i	0.308291	+	0.177992i
$982$	−2.28027	−	3.94955i	−0.0727664	−	0.126035i
$983$	−14.3688	+	8.29582i	−0.458293	+	0.264596i	−0.711326	−	0.702862i	$-0.751905\pi$
$983$	−14.3688	+	8.29582i	−0.458293	+	0.264596i	0.253033	+	0.967458i	$0.418572\pi$
$984$	−2.91286	+	1.68174i	−0.0928587	+	0.0536120i
$985$	−26.8873	+	29.8392i	−0.856699	+	0.950756i
$986$	−25.9106	−	14.9595i	−0.825161	−	0.476407i
$987$	−26.1544	+	15.1002i	−0.832504	+	0.480646i
$988$			5.25554i			0.167201i
$989$	15.2462			0.484802
$990$	−0.192140	+	0.902313i	−0.00610661	+	0.0286774i
$991$			12.0478i			0.382710i	0.981521	+	0.191355i	$0.0612882\pi$
$991$			12.0478i			0.382710i	−0.981521	+	0.191355i	$0.938712\pi$
$992$	−5.64095	−	3.25680i	−0.179100	−	0.103404i
$993$	11.1969			0.355321
$994$	7.90565	+	4.56433i	0.250752	+	0.144772i
$995$	−5.60525	−	17.2728i	−0.177698	−	0.547586i
$996$	−1.95484	+	3.38588i	−0.0619414	+	0.107286i
$997$	−10.4395	−	18.0817i	−0.330621	−	0.572653i	0.652013	−	0.758208i	$-0.273925\pi$
$997$	−10.4395	−	18.0817i	−0.330621	−	0.572653i	−0.982634	+	0.185555i	$0.940592\pi$
$998$		−	3.99316i		−	0.126401i
$999$	−2.74226	+	5.42955i	−0.0867613	+	0.171783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.ba.a.529.12	✓	36
5.4	even	2		1110.2.ba.b.529.7	yes	36
37.27	even	6		1110.2.ba.b.619.7	yes	36
185.64	even	6	inner	1110.2.ba.a.619.12	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.ba.a.529.12	✓	36	1.1	even	1	trivial
1110.2.ba.a.619.12	yes	36	185.64	even	6	inner
1110.2.ba.b.529.7	yes	36	5.4	even	2
1110.2.ba.b.619.7	yes	36	37.27	even	6

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.12688 + 0.690199i) q^{5} -1.00000i q^{6} +(3.89483 + 2.24868i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.12688 + 0.690199i) q^{5} -1.00000i q^{6} +(3.89483 + 2.24868i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(1.66117 + 1.49683i) q^{10} +0.412574 q^{11} +(-0.866025 + 0.500000i) q^{12} +(1.10249 - 1.90957i) q^{13} -4.49736i q^{14} +(-2.18703 - 0.465711i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.63267 - 2.82787i) q^{17} +(0.500000 - 0.866025i) q^{18} +(2.06416 + 1.19174i) q^{19} +(0.465711 - 2.18703i) q^{20} +(2.24868 + 3.89483i) q^{21} +(-0.206287 - 0.357299i) q^{22} -1.63566 q^{23} +(0.866025 + 0.500000i) q^{24} +(4.04725 - 2.93594i) q^{25} -2.20498 q^{26} +1.00000i q^{27} +(-3.89483 + 2.24868i) q^{28} +9.16257i q^{29} +(0.690199 + 2.12688i) q^{30} +6.51360i q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.357299 + 0.206287i) q^{33} +(-1.63267 + 2.82787i) q^{34} +(-9.83588 - 2.09447i) q^{35} -1.00000 q^{36} +(5.42955 + 2.74226i) q^{37} -2.38348i q^{38} +(1.90957 - 1.10249i) q^{39} +(-2.12688 + 0.690199i) q^{40} +(-1.68174 + 2.91286i) q^{41} +(2.24868 - 3.89483i) q^{42} -9.32116 q^{43} +(-0.206287 + 0.357299i) q^{44} +(-1.66117 - 1.49683i) q^{45} +(0.817829 + 1.41652i) q^{46} +6.71516i q^{47} -1.00000i q^{48} +(6.61313 + 11.4543i) q^{49} +(-4.56623 - 2.03705i) q^{50} -3.26535i q^{51} +(1.10249 + 1.90957i) q^{52} +(10.0924 - 5.82686i) q^{53} +(0.866025 - 0.500000i) q^{54} +(-0.877496 + 0.284758i) q^{55} +(3.89483 + 2.24868i) q^{56} +(1.19174 + 2.06416i) q^{57} +(7.93502 - 4.58129i) q^{58} +(4.76276 - 2.74978i) q^{59} +(1.49683 - 1.66117i) q^{60} +(6.46982 + 3.73535i) q^{61} +(5.64095 - 3.25680i) q^{62} +4.49736i q^{63} +1.00000 q^{64} +(-1.02688 + 4.82237i) q^{65} -0.412574i q^{66} +(2.71578 + 1.56796i) q^{67} +3.26535 q^{68} +(-1.41652 - 0.817829i) q^{69} +(3.10407 + 9.56535i) q^{70} +(-1.01489 + 1.75784i) q^{71} +(0.500000 + 0.866025i) q^{72} -6.57476i q^{73} +(-0.339909 - 6.07326i) q^{74} +(4.97299 - 0.518977i) q^{75} +(-2.06416 + 1.19174i) q^{76} +(1.60690 + 0.927747i) q^{77} +(-1.90957 - 1.10249i) q^{78} +(-7.72926 - 4.46249i) q^{79} +(1.66117 + 1.49683i) q^{80} +(-0.500000 + 0.866025i) q^{81} +3.36348 q^{82} +(3.38588 - 1.95484i) q^{83} -4.49736 q^{84} +(5.42430 + 4.88768i) q^{85} +(4.66058 + 8.07236i) q^{86} +(-4.58129 + 7.93502i) q^{87} +0.412574 q^{88} +(-2.49674 + 1.44149i) q^{89} +(-0.465711 + 2.18703i) q^{90} +(8.58804 - 4.95830i) q^{91} +(0.817829 - 1.41652i) q^{92} +(-3.25680 + 5.64095i) q^{93} +(5.81550 - 3.35758i) q^{94} +(-5.21275 - 1.11001i) q^{95} +(-0.866025 + 0.500000i) q^{96} +10.9274 q^{97} +(6.61313 - 11.4543i) q^{98} +(0.206287 + 0.357299i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more