LMFDB - Embedded newform 546.2.bi.f.257.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(17,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 1]))

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

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

chi := DirichletCharacter("546.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.13
Character	$\chi$	$=$	546.257
Dual form			546.2.bi.f.17.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.13542 - 1.30799i) q^{3} +1.00000 q^{4} +(-1.26448 - 0.730045i) q^{5} +(1.13542 - 1.30799i) q^{6} +(-1.08820 - 2.41160i) q^{7} +1.00000 q^{8} +(-0.421657 - 2.97022i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.13542 - 1.30799i) q^{3} +1.00000 q^{4} +(-1.26448 - 0.730045i) q^{5} +(1.13542 - 1.30799i) q^{6} +(-1.08820 - 2.41160i) q^{7} +1.00000 q^{8} +(-0.421657 - 2.97022i) q^{9} +(-1.26448 - 0.730045i) q^{10} +(-1.75974 + 3.04796i) q^{11} +(1.13542 - 1.30799i) q^{12} +(0.214878 - 3.59914i) q^{13} +(-1.08820 - 2.41160i) q^{14} +(-2.39060 + 0.825011i) q^{15} +1.00000 q^{16} +7.58718 q^{17} +(-0.421657 - 2.97022i) q^{18} +(-1.72681 - 2.99093i) q^{19} +(-1.26448 - 0.730045i) q^{20} +(-4.38990 - 1.31482i) q^{21} +(-1.75974 + 3.04796i) q^{22} +3.60696i q^{23} +(1.13542 - 1.30799i) q^{24} +(-1.43407 - 2.48388i) q^{25} +(0.214878 - 3.59914i) q^{26} +(-4.36376 - 2.82092i) q^{27} +(-1.08820 - 2.41160i) q^{28} +(0.170773 - 0.0985961i) q^{29} +(-2.39060 + 0.825011i) q^{30} +(5.34484 + 9.25753i) q^{31} +1.00000 q^{32} +(1.98865 + 5.76241i) q^{33} +7.58718 q^{34} +(-0.384576 + 3.84385i) q^{35} +(-0.421657 - 2.97022i) q^{36} +5.56471i q^{37} +(-1.72681 - 2.99093i) q^{38} +(-4.46365 - 4.36759i) q^{39} +(-1.26448 - 0.730045i) q^{40} +(-2.60543 + 1.50425i) q^{41} +(-4.38990 - 1.31482i) q^{42} +(5.61139 - 9.71922i) q^{43} +(-1.75974 + 3.04796i) q^{44} +(-1.63522 + 4.06360i) q^{45} +3.60696i q^{46} +(11.0787 + 6.39629i) q^{47} +(1.13542 - 1.30799i) q^{48} +(-4.63164 + 5.24861i) q^{49} +(-1.43407 - 2.48388i) q^{50} +(8.61461 - 9.92393i) q^{51} +(0.214878 - 3.59914i) q^{52} +(-4.21555 + 2.43385i) q^{53} +(-4.36376 - 2.82092i) q^{54} +(4.45029 - 2.56938i) q^{55} +(-1.08820 - 2.41160i) q^{56} +(-5.87274 - 1.13730i) q^{57} +(0.170773 - 0.0985961i) q^{58} +1.30815i q^{59} +(-2.39060 + 0.825011i) q^{60} +(0.865717 - 0.499822i) q^{61} +(5.34484 + 9.25753i) q^{62} +(-6.70414 + 4.24906i) q^{63} +1.00000 q^{64} +(-2.89925 + 4.39416i) q^{65} +(1.98865 + 5.76241i) q^{66} +(4.78794 + 2.76432i) q^{67} +7.58718 q^{68} +(4.71786 + 4.09541i) q^{69} +(-0.384576 + 3.84385i) q^{70} +(-5.33718 + 9.24427i) q^{71} +(-0.421657 - 2.97022i) q^{72} +(-2.94410 - 5.09933i) q^{73} +5.56471i q^{74} +(-4.87714 - 0.944496i) q^{75} +(-1.72681 - 2.99093i) q^{76} +(9.26540 + 0.927001i) q^{77} +(-4.46365 - 4.36759i) q^{78} +(0.174645 - 0.302494i) q^{79} +(-1.26448 - 0.730045i) q^{80} +(-8.64441 + 2.50483i) q^{81} +(-2.60543 + 1.50425i) q^{82} -3.72979i q^{83} +(-4.38990 - 1.31482i) q^{84} +(-9.59380 - 5.53898i) q^{85} +(5.61139 - 9.71922i) q^{86} +(0.0649367 - 0.335317i) q^{87} +(-1.75974 + 3.04796i) q^{88} -14.4601i q^{89} +(-1.63522 + 4.06360i) q^{90} +(-8.91353 + 3.39839i) q^{91} +3.60696i q^{92} +(18.1773 + 3.52018i) q^{93} +(11.0787 + 6.39629i) q^{94} +5.04260i q^{95} +(1.13542 - 1.30799i) q^{96} +(-1.72747 + 2.99206i) q^{97} +(-4.63164 + 5.24861i) q^{98} +(9.79510 + 3.94162i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9}+O(q^{10}) $ 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9	$ 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20} - 7 q^{21} + 9 q^{22} + 6 q^{24} + 16 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} + 27 q^{29} - 17 q^{30} - q^{31} + 34 q^{32} + 12 q^{34} - 3 q^{35} + 4 q^{36} - 5 q^{38} - 10 q^{39} + 9 q^{40} - 3 q^{41} - 7 q^{42} - 3 q^{43} + 9 q^{44} + 9 q^{45} - 27 q^{47} + 6 q^{48} - 2 q^{49} + 16 q^{50} - 36 q^{51} + 8 q^{52} - 21 q^{53} - 18 q^{54} - 57 q^{55} + 4 q^{56} - 17 q^{57} + 27 q^{58} - 17 q^{60} - 51 q^{61} - q^{62} - 24 q^{63} + 34 q^{64} - 21 q^{65} - 21 q^{67} + 12 q^{68} + 30 q^{69} - 3 q^{70} - 15 q^{71} + 4 q^{72} - 19 q^{73} - 54 q^{75} - 5 q^{76} + 9 q^{77} - 10 q^{78} - 9 q^{79} + 9 q^{80} + 28 q^{81} - 3 q^{82} - 7 q^{84} - 42 q^{85} - 3 q^{86} - 81 q^{87} + 9 q^{88} + 9 q^{90} - 72 q^{91} - 17 q^{93} - 27 q^{94} + 6 q^{96} + 19 q^{97} - 2 q^{98} - 27 q^{99}+O(q^{100}) $ 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9 + 9 * q^10 + 9 * q^11 + 6 * q^12 + 8 * q^13 + 4 * q^14 - 17 * q^15 + 34 * q^16 + 12 * q^17 + 4 * q^18 - 5 * q^19 + 9 * q^20 - 7 * q^21 + 9 * q^22 + 6 * q^24 + 16 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 + 27 * q^29 - 17 * q^30 - q^31 + 34 * q^32 + 12 * q^34 - 3 * q^35 + 4 * q^36 - 5 * q^38 - 10 * q^39 + 9 * q^40 - 3 * q^41 - 7 * q^42 - 3 * q^43 + 9 * q^44 + 9 * q^45 - 27 * q^47 + 6 * q^48 - 2 * q^49 + 16 * q^50 - 36 * q^51 + 8 * q^52 - 21 * q^53 - 18 * q^54 - 57 * q^55 + 4 * q^56 - 17 * q^57 + 27 * q^58 - 17 * q^60 - 51 * q^61 - q^62 - 24 * q^63 + 34 * q^64 - 21 * q^65 - 21 * q^67 + 12 * q^68 + 30 * q^69 - 3 * q^70 - 15 * q^71 + 4 * q^72 - 19 * q^73 - 54 * q^75 - 5 * q^76 + 9 * q^77 - 10 * q^78 - 9 * q^79 + 9 * q^80 + 28 * q^81 - 3 * q^82 - 7 * q^84 - 42 * q^85 - 3 * q^86 - 81 * q^87 + 9 * q^88 + 9 * q^90 - 72 * q^91 - 17 * q^93 - 27 * q^94 + 6 * q^96 + 19 * q^97 - 2 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.13542	−	1.30799i	0.655533	−	0.755166i
$3$	1.13542	−	1.30799i	0.655533	−	0.755166i
$4$	1.00000			0.500000
$5$	−1.26448	−	0.730045i	−0.565491	−	0.326486i	0.189856	−	0.981812i	$-0.439198\pi$
$5$	−1.26448	−	0.730045i	−0.565491	−	0.326486i	−0.755346	+	0.655326i	$0.772531\pi$
$6$	1.13542	−	1.30799i	0.463532	−	0.533983i
$7$	−1.08820	−	2.41160i	−0.411301	−	0.911500i
$7$	−1.08820	−	2.41160i	−0.411301	−	0.911500i
$8$	1.00000			0.353553
$9$	−0.421657	−	2.97022i	−0.140552	−	0.990073i
$10$	−1.26448	−	0.730045i	−0.399862	−	0.230861i
$11$	−1.75974	+	3.04796i	−0.530581	+	0.918993i	0.468782	+	0.883314i	$0.344693\pi$
$11$	−1.75974	+	3.04796i	−0.530581	+	0.918993i	−0.999363	+	0.0356795i	$0.988640\pi$
$12$	1.13542	−	1.30799i	0.327767	−	0.377583i
$13$	0.214878	−	3.59914i	0.0595966	−	0.998223i
$13$	0.214878	−	3.59914i	0.0595966	−	0.998223i
$14$	−1.08820	−	2.41160i	−0.290834	−	0.644528i
$15$	−2.39060	+	0.825011i	−0.617249	+	0.213017i
$16$	1.00000			0.250000
$17$	7.58718			1.84016			0.920080	−	0.391729i	$-0.128123\pi$
$17$	7.58718			1.84016			0.920080	+	0.391729i	$0.128123\pi$
$18$	−0.421657	−	2.97022i	−0.0993855	−	0.700088i
$19$	−1.72681	−	2.99093i	−0.396158	−	0.686165i	0.597090	−	0.802174i	$-0.296323\pi$
$19$	−1.72681	−	2.99093i	−0.396158	−	0.686165i	−0.993248	+	0.116008i	$0.962990\pi$
$20$	−1.26448	−	0.730045i	−0.282745	−	0.163243i
$21$	−4.38990	−	1.31482i	−0.957955	−	0.286918i
$22$	−1.75974	+	3.04796i	−0.375177	+	0.649826i
$23$			3.60696i			0.752104i	0.926599	+	0.376052i	$0.122719\pi$
$23$			3.60696i			0.752104i	−0.926599	+	0.376052i	$0.877281\pi$
$24$	1.13542	−	1.30799i	0.231766	−	0.266992i
$25$	−1.43407	−	2.48388i	−0.286814	−	0.496776i
$26$	0.214878	−	3.59914i	0.0421411	−	0.705850i
$27$	−4.36376	−	2.82092i	−0.839807	−	0.542885i
$28$	−1.08820	−	2.41160i	−0.205650	−	0.455750i
$29$	0.170773	−	0.0985961i	0.0317118	−	0.0183088i	−0.484060	−	0.875035i	$-0.660838\pi$
$29$	0.170773	−	0.0985961i	0.0317118	−	0.0183088i	0.515772	+	0.856726i	$0.327505\pi$
$30$	−2.39060	+	0.825011i	−0.436461	+	0.150626i
$31$	5.34484	+	9.25753i	0.959961	+	1.66270i	0.722584	+	0.691283i	$0.242954\pi$
$31$	5.34484	+	9.25753i	0.959961	+	1.66270i	0.237377	+	0.971418i	$0.423712\pi$
$32$	1.00000			0.176777
$33$	1.98865	+	5.76241i	0.346179	+	1.00311i
$34$	7.58718			1.30119
$35$	−0.384576	+	3.84385i	−0.0650052	+	0.649729i
$36$	−0.421657	−	2.97022i	−0.0702762	−	0.495037i
$37$			5.56471i			0.914833i	0.889252	+	0.457417i	$0.151225\pi$
$37$			5.56471i			0.914833i	−0.889252	+	0.457417i	$0.848775\pi$
$38$	−1.72681	−	2.99093i	−0.280126	−	0.485192i
$39$	−4.46365	−	4.36759i	−0.714757	−	0.699373i
$40$	−1.26448	−	0.730045i	−0.199931	−	0.115430i
$41$	−2.60543	+	1.50425i	−0.406900	+	0.234924i	−0.689457	−	0.724327i	$-0.742151\pi$
$41$	−2.60543	+	1.50425i	−0.406900	+	0.234924i	0.282557	+	0.959250i	$0.408817\pi$
$42$	−4.38990	−	1.31482i	−0.677377	−	0.202881i
$43$	5.61139	−	9.71922i	0.855730	−	1.48217i	−0.0202369	−	0.999795i	$-0.506442\pi$
$43$	5.61139	−	9.71922i	0.855730	−	1.48217i	0.875967	−	0.482372i	$-0.160225\pi$
$44$	−1.75974	+	3.04796i	−0.265291	+	0.459497i
$45$	−1.63522	+	4.06360i	−0.243764	+	0.605766i
$46$			3.60696i			0.531818i
$47$	11.0787	+	6.39629i	1.61599	+	0.932994i	0.987942	+	0.154822i	$0.0494803\pi$
$47$	11.0787	+	6.39629i	1.61599	+	0.932994i	0.628051	+	0.778172i	$0.283853\pi$
$48$	1.13542	−	1.30799i	0.163883	−	0.188792i
$49$	−4.63164	+	5.24861i	−0.661663	+	0.749801i
$50$	−1.43407	−	2.48388i	−0.202808	−	0.351273i
$51$	8.61461	−	9.92393i	1.20629	−	1.38963i
$52$	0.214878	−	3.59914i	0.0297983	−	0.499111i
$53$	−4.21555	+	2.43385i	−0.579051	+	0.334315i	−0.760756	−	0.649038i	$-0.775172\pi$
$53$	−4.21555	+	2.43385i	−0.579051	+	0.334315i	0.181705	+	0.983353i	$0.441838\pi$
$54$	−4.36376	−	2.82092i	−0.593833	−	0.383878i
$55$	4.45029	−	2.56938i	0.600077	−	0.346455i
$56$	−1.08820	−	2.41160i	−0.145417	−	0.322264i
$57$	−5.87274	−	1.13730i	−0.777864	−	0.150639i
$58$	0.170773	−	0.0985961i	0.0224236	−	0.0129463i
$59$			1.30815i			0.170306i	0.996368	+	0.0851532i	$0.0271380\pi$
$59$			1.30815i			0.170306i	−0.996368	+	0.0851532i	$0.972862\pi$
$60$	−2.39060	+	0.825011i	−0.308625	+	0.106508i
$61$	0.865717	−	0.499822i	0.110844	−	0.0639956i	−0.443553	−	0.896248i	$-0.646282\pi$
$61$	0.865717	−	0.499822i	0.110844	−	0.0639956i	0.554397	+	0.832252i	$0.312949\pi$
$62$	5.34484	+	9.25753i	0.678795	+	1.17571i
$63$	−6.70414	+	4.24906i	−0.844642	+	0.535331i
$64$	1.00000			0.125000
$65$	−2.89925	+	4.39416i	−0.359607	+	0.545028i
$66$	1.98865	+	5.76241i	0.244786	+	0.709304i
$67$	4.78794	+	2.76432i	0.584940	+	0.337715i	0.763094	−	0.646287i	$-0.223679\pi$
$67$	4.78794	+	2.76432i	0.584940	+	0.337715i	−0.178154	+	0.984003i	$0.557013\pi$
$68$	7.58718			0.920080
$69$	4.71786	+	4.09541i	0.567964	+	0.493029i
$70$	−0.384576	+	3.84385i	−0.0459656	+	0.459427i
$71$	−5.33718	+	9.24427i	−0.633407	+	1.09709i	0.353443	+	0.935456i	$0.385011\pi$
$71$	−5.33718	+	9.24427i	−0.633407	+	1.09709i	−0.986850	+	0.161637i	$0.948323\pi$
$72$	−0.421657	−	2.97022i	−0.0496928	−	0.350044i
$73$	−2.94410	−	5.09933i	−0.344581	−	0.596832i	0.640697	−	0.767794i	$-0.278646\pi$
$73$	−2.94410	−	5.09933i	−0.344581	−	0.596832i	−0.985278	+	0.170963i	$0.945312\pi$
$74$			5.56471i			0.646885i
$75$	−4.87714	−	0.944496i	−0.563164	−	0.109061i
$76$	−1.72681	−	2.99093i	−0.198079	−	0.343083i
$77$	9.26540	+	0.927001i	1.05589	+	0.105642i
$78$	−4.46365	−	4.36759i	−0.505409	−	0.494532i
$79$	0.174645	−	0.302494i	0.0196491	−	0.0340332i	−0.856034	−	0.516920i	$-0.827078\pi$
$79$	0.174645	−	0.302494i	0.0196491	−	0.0340332i	0.875683	+	0.482887i	$0.160412\pi$
$80$	−1.26448	−	0.730045i	−0.141373	−	0.0816215i
$81$	−8.64441	+	2.50483i	−0.960490	+	0.278314i
$82$	−2.60543	+	1.50425i	−0.287722	+	0.166116i
$83$		−	3.72979i		−	0.409398i	−0.978825	−	0.204699i	$-0.934379\pi$
$83$		−	3.72979i		−	0.409398i	0.978825	−	0.204699i	$-0.0656215\pi$
$84$	−4.38990	−	1.31482i	−0.478978	−	0.143459i
$85$	−9.59380	−	5.53898i	−1.04059	−	0.600787i
$86$	5.61139	−	9.71922i	0.605092	−	1.04805i
$87$	0.0649367	−	0.335317i	0.00696194	−	0.0359498i
$88$	−1.75974	+	3.04796i	−0.187589	+	0.324913i
$89$		−	14.4601i		−	1.53276i	−0.642385	−	0.766382i	$-0.722055\pi$
$89$		−	14.4601i		−	1.53276i	0.642385	−	0.766382i	$-0.277945\pi$
$90$	−1.63522	+	4.06360i	−0.172367	+	0.428341i
$91$	−8.91353	+	3.39839i	−0.934392	+	0.356248i
$92$			3.60696i			0.376052i
$93$	18.1773	+	3.52018i	1.88490	+	0.365026i
$94$	11.0787	+	6.39629i	1.14268	+	0.659726i
$95$			5.04260i			0.517360i
$96$	1.13542	−	1.30799i	0.115883	−	0.133496i
$97$	−1.72747	+	2.99206i	−0.175398	+	0.303798i	−0.940299	−	0.340350i	$-0.889455\pi$
$97$	−1.72747	+	2.99206i	−0.175398	+	0.303798i	0.764901	+	0.644148i	$0.222788\pi$
$98$	−4.63164	+	5.24861i	−0.467866	+	0.530190i
$99$	9.79510	+	3.94162i	0.984445	+	0.396147i
$100$	−1.43407	−	2.48388i	−0.143407	−	0.248388i
$101$	5.80861	−	10.0608i	0.577979	−	1.00109i	−0.417732	−	0.908570i	$-0.637175\pi$
$101$	5.80861	−	10.0608i	0.577979	−	1.00109i	0.995711	−	0.0925183i	$-0.0294916\pi$
$102$	8.61461	−	9.92393i	0.852973	−	0.982615i
$103$	16.2249	+	9.36744i	1.59869	+	0.923001i	0.991741	+	0.128257i	$0.0409381\pi$
$103$	16.2249	+	9.36744i	1.59869	+	0.923001i	0.606944	+	0.794745i	$0.292395\pi$
$104$	0.214878	−	3.59914i	0.0210706	−	0.352925i
$105$	4.59104	+	4.86739i	0.448040	+	0.475008i
$106$	−4.21555	+	2.43385i	−0.409451	+	0.236397i
$107$			0.350806i			0.0339137i	0.999856	+	0.0169568i	$0.00539779\pi$
$107$			0.350806i			0.0339137i	−0.999856	+	0.0169568i	$0.994602\pi$
$108$	−4.36376	−	2.82092i	−0.419903	−	0.271443i
$109$	−8.12542	+	4.69121i	−0.778274	+	0.449337i	−0.835818	−	0.549006i	$-0.815006\pi$
$109$	−8.12542	+	4.69121i	−0.778274	+	0.449337i	0.0575444	+	0.998343i	$0.481673\pi$
$110$	4.45029	−	2.56938i	0.424319	−	0.244980i
$111$	7.27857	+	6.31827i	0.690851	+	0.599704i
$112$	−1.08820	−	2.41160i	−0.102825	−	0.227875i
$113$	5.03517	+	2.90706i	0.473669	+	0.273473i	0.717774	−	0.696276i	$-0.245161\pi$
$113$	5.03517	+	2.90706i	0.473669	+	0.273473i	−0.244105	+	0.969749i	$0.578494\pi$
$114$	−5.87274	−	1.13730i	−0.550033	−	0.106518i
$115$	2.63325	−	4.56092i	0.245552	−	0.425308i
$116$	0.170773	−	0.0985961i	0.0158559	−	0.00915442i
$117$	−10.7808	+	0.879368i	−0.996690	+	0.0812976i
$118$			1.30815i			0.120425i
$119$	−8.25637	−	18.2972i	−0.756860	−	1.67731i
$120$	−2.39060	+	0.825011i	−0.218231	+	0.0753129i
$121$	−0.693357	−	1.20093i	−0.0630324	−	0.109175i
$122$	0.865717	−	0.499822i	0.0783783	−	0.0452518i
$123$	−0.990716	+	5.11581i	−0.0893298	+	0.461277i
$124$	5.34484	+	9.25753i	0.479980	+	0.831350i
$125$			11.4882i			1.02754i
$126$	−6.70414	+	4.24906i	−0.597252	+	0.378537i
$127$	−7.87940	−	13.6475i	−0.699183	−	1.21102i	−0.968750	−	0.248039i	$-0.920214\pi$
$127$	−7.87940	−	13.6475i	−0.699183	−	1.21102i	0.269567	−	0.962982i	$-0.413120\pi$
$128$	1.00000			0.0883883
$129$	−6.34134	−	18.3750i	−0.558324	−	1.61783i
$130$	−2.89925	+	4.39416i	−0.254281	+	0.385393i
$131$	−6.32520	+	10.9556i	−0.552635	+	0.957192i	0.445448	+	0.895308i	$0.353044\pi$
$131$	−6.32520	+	10.9556i	−0.552635	+	0.957192i	−0.998083	+	0.0618843i	$0.980289\pi$
$132$	1.98865	+	5.76241i	0.173090	+	0.501554i
$133$	−5.33380	+	7.41911i	−0.462499	+	0.643318i
$134$	4.78794	+	2.76432i	0.413615	+	0.238801i
$135$	3.45848	+	6.75272i	0.297658	+	0.581182i
$136$	7.58718			0.650595
$137$	−1.25158			−0.106930			−0.0534648	−	0.998570i	$-0.517026\pi$
$137$	−1.25158			−0.106930			−0.0534648	+	0.998570i	$0.517026\pi$
$138$	4.71786	+	4.09541i	0.401611	+	0.348624i
$139$	8.68419	+	5.01382i	0.736583	+	0.425267i	0.820826	−	0.571179i	$-0.193514\pi$
$139$	8.68419	+	5.01382i	0.736583	+	0.425267i	−0.0842424	+	0.996445i	$0.526847\pi$
$140$	−0.384576	+	3.84385i	−0.0325026	+	0.324864i
$141$	20.9452	−	7.22833i	1.76390	−	0.608735i
$142$	−5.33718	+	9.24427i	−0.447886	+	0.775762i
$143$	10.5919	+	6.98849i	0.885739	+	0.584407i
$144$	−0.421657	−	2.97022i	−0.0351381	−	0.247518i
$145$	−0.287918			−0.0239103
$146$	−2.94410	−	5.09933i	−0.243655	−	0.422024i
$147$	1.60627	+	12.0175i	0.132483	+	0.991185i
$148$			5.56471i			0.457417i
$149$	1.62311	+	2.81131i	0.132970	+	0.230311i	0.924820	−	0.380404i	$-0.124215\pi$
$149$	1.62311	+	2.81131i	0.132970	+	0.230311i	−0.791850	+	0.610716i	$0.790882\pi$
$150$	−4.87714	−	0.944496i	−0.398217	−	0.0771178i
$151$	−8.04225	+	4.64320i	−0.654469	+	0.377858i	−0.790166	−	0.612892i	$-0.790006\pi$
$151$	−8.04225	+	4.64320i	−0.654469	+	0.377858i	0.135697	+	0.990750i	$0.456673\pi$
$152$	−1.72681	−	2.99093i	−0.140063	−	0.242596i
$153$	−3.19919	−	22.5356i	−0.258639	−	1.82189i
$154$	9.26540	+	0.927001i	0.746627	+	0.0746999i
$155$		−	15.6079i		−	1.25366i
$156$	−4.46365	−	4.36759i	−0.357378	−	0.349687i
$157$	−16.2305	+	9.37071i	−1.29534	+	0.747864i	−0.979595	−	0.200981i	$-0.935587\pi$
$157$	−16.2305	+	9.37071i	−1.29534	+	0.747864i	−0.315743	+	0.948845i	$0.602254\pi$
$158$	0.174645	−	0.302494i	0.0138940	−	0.0240651i
$159$	−1.60297	+	8.27732i	−0.127124	+	0.656434i
$160$	−1.26448	−	0.730045i	−0.0999656	−	0.0577151i
$161$	8.69856	−	3.92510i	0.685542	−	0.309341i
$162$	−8.64441	+	2.50483i	−0.679169	+	0.196798i
$163$	0.787553	−	0.454694i	0.0616859	−	0.0356144i	−0.468840	−	0.883283i	$-0.655328\pi$
$163$	0.787553	−	0.454694i	0.0616859	−	0.0356144i	0.530526	+	0.847669i	$0.321995\pi$
$164$	−2.60543	+	1.50425i	−0.203450	+	0.117462i
$165$	1.69223	−	8.73824i	0.131740	−	0.680271i
$166$		−	3.72979i		−	0.289488i
$167$	−11.6602	+	6.73204i	−0.902297	+	0.520941i	−0.877945	−	0.478762i	$-0.841086\pi$
$167$	−11.6602	+	6.73204i	−0.902297	+	0.520941i	−0.0243520	+	0.999703i	$0.507752\pi$
$168$	−4.38990	−	1.31482i	−0.338688	−	0.101441i
$169$	−12.9077	−	1.54676i	−0.992896	−	0.118981i
$170$	−9.59380	−	5.53898i	−0.735811	−	0.424821i
$171$	−8.15558	+	6.39016i	−0.623673	+	0.488667i
$172$	5.61139	−	9.71922i	0.427865	−	0.741084i
$173$	5.08435	+	8.80635i	0.386556	+	0.669534i	0.991984	−	0.126366i	$-0.0403314\pi$
$173$	5.08435	+	8.80635i	0.386556	+	0.669534i	−0.605428	+	0.795900i	$0.706998\pi$
$174$	0.0649367	−	0.335317i	0.00492284	−	0.0254203i
$175$	−4.42957	+	6.16136i	−0.334844	+	0.465755i
$176$	−1.75974	+	3.04796i	−0.132645	+	0.229748i
$177$	1.71104	+	1.48529i	0.128610	+	0.111641i
$178$		−	14.4601i		−	1.08383i
$179$	7.39608	+	4.27013i	0.552809	+	0.319164i	0.750254	−	0.661150i	$-0.229931\pi$
$179$	7.39608	+	4.27013i	0.552809	+	0.319164i	−0.197445	+	0.980314i	$0.563264\pi$
$180$	−1.63522	+	4.06360i	−0.121882	+	0.302883i
$181$		−	25.4759i		−	1.89361i	−0.321810	−	0.946804i	$-0.604291\pi$
$181$		−	25.4759i		−	1.89361i	0.321810	−	0.946804i	$-0.395709\pi$
$182$	−8.91353	+	3.39839i	−0.660715	+	0.251905i
$183$	0.329189	−	1.69985i	0.0243344	−	0.125657i
$184$			3.60696i			0.265909i
$185$	4.06249	−	7.03645i	0.298680	−	0.517330i
$186$	18.1773	+	3.52018i	1.33283	+	0.258112i
$187$	−13.3514	+	23.1254i	−0.976354	+	1.69110i
$188$	11.0787	+	6.39629i	0.807997	+	0.466497i
$189$	−2.05428	+	13.5934i	−0.149427	+	0.988773i
$190$			5.04260i			0.365829i
$191$	−17.9487	+	10.3627i	−1.29873	+	0.749819i	−0.980184	−	0.198089i	$-0.936526\pi$
$191$	−17.9487	+	10.3627i	−1.29873	+	0.749819i	−0.318541	+	0.947909i	$0.603193\pi$
$192$	1.13542	−	1.30799i	0.0819417	−	0.0943958i
$193$	−8.21554	−	4.74324i	−0.591367	−	0.341426i	0.174271	−	0.984698i	$-0.444243\pi$
$193$	−8.21554	−	4.74324i	−0.591367	−	0.341426i	−0.765638	+	0.643272i	$0.777577\pi$
$194$	−1.72747	+	2.99206i	−0.124025	+	0.214818i
$195$	2.45565	+	8.78137i	0.175852	+	0.628847i
$196$	−4.63164	+	5.24861i	−0.330832	+	0.374901i
$197$	−3.21420	−	5.56716i	−0.229002	−	0.396644i	0.728510	−	0.685035i	$-0.240213\pi$
$197$	−3.21420	−	5.56716i	−0.229002	−	0.396644i	−0.957513	+	0.288391i	$0.906880\pi$
$198$	9.79510	+	3.94162i	0.696108	+	0.280118i
$199$		−	1.26513i		−	0.0896830i	−0.998994	−	0.0448415i	$-0.985722\pi$
$199$		−	1.26513i		−	0.0896830i	0.998994	−	0.0448415i	$-0.0142783\pi$
$200$	−1.43407	−	2.48388i	−0.101404	−	0.175637i
$201$	9.05200	−	3.12391i	0.638479	−	0.220343i
$202$	5.80861	−	10.0608i	0.408693	−	0.707876i
$203$	−0.423610	−	0.304545i	−0.0297316	−	0.0213749i
$204$	8.61461	−	9.92393i	0.603143	−	0.694814i
$205$	4.39267			0.306797
$206$	16.2249	+	9.36744i	1.13044	+	0.652660i
$207$	10.7135	−	1.52090i	0.744638	−	0.105710i
$208$	0.214878	−	3.59914i	0.0148991	−	0.249556i
$209$	12.1549			0.840775
$210$	4.59104	+	4.86739i	0.316812	+	0.335882i
$211$	−6.24577	−	10.8180i	−0.429977	−	0.744742i	0.566894	−	0.823791i	$-0.308145\pi$
$211$	−6.24577	−	10.8180i	−0.429977	−	0.744742i	−0.996871	+	0.0790492i	$0.974812\pi$
$212$	−4.21555	+	2.43385i	−0.289525	+	0.167158i
$213$	6.03145	+	17.4771i	0.413268	+	1.19751i
$214$			0.350806i			0.0239806i
$215$	−14.1909	+	8.19314i	−0.967814	+	0.558768i
$216$	−4.36376	−	2.82092i	−0.296917	−	0.191939i
$217$	16.5092	−	22.9637i	1.12072	−	1.55887i
$218$	−8.12542	+	4.69121i	−0.550323	+	0.317729i
$219$	−10.0126	−	1.93902i	−0.676591	−	0.131027i
$220$	4.45029	−	2.56938i	0.300039	−	0.173227i
$221$	1.63032	−	27.3073i	0.109667	−	1.83689i
$222$	7.27857	+	6.31827i	0.488506	+	0.424055i
$223$	−3.78556	−	6.55677i	−0.253500	−	0.439074i	0.710987	−	0.703205i	$-0.248248\pi$
$223$	−3.78556	−	6.55677i	−0.253500	−	0.439074i	−0.964487	+	0.264131i	$0.914915\pi$
$224$	−1.08820	−	2.41160i	−0.0727084	−	0.161132i
$225$	−6.77298	+	5.30684i	−0.451532	+	0.353789i
$226$	5.03517	+	2.90706i	0.334935	+	0.193375i
$227$		−	25.4572i		−	1.68965i	−0.535042	−	0.844826i	$-0.679704\pi$
$227$		−	25.4572i		−	1.68965i	0.535042	−	0.844826i	$-0.320296\pi$
$228$	−5.87274	−	1.13730i	−0.388932	−	0.0753196i
$229$	5.51406	−	9.55063i	0.364379	−	0.631124i	−0.624297	−	0.781187i	$-0.714614\pi$
$229$	5.51406	−	9.55063i	0.364379	−	0.631124i	0.988676	+	0.150063i	$0.0479478\pi$
$230$	2.63325	−	4.56092i	0.173631	−	0.300738i
$231$	11.7326	−	11.0665i	0.771948	−	0.728121i
$232$	0.170773	−	0.0985961i	0.0112118	−	0.00647315i
$233$	6.18721	+	3.57219i	0.405338	+	0.234022i	0.688785	−	0.724966i	$-0.258145\pi$
$233$	6.18721	+	3.57219i	0.405338	+	0.234022i	−0.283447	+	0.958988i	$0.591478\pi$
$234$	−10.7808	+	0.879368i	−0.704766	+	0.0574861i
$235$	−9.33916	−	16.1759i	−0.609219	−	1.05520i
$236$			1.30815i			0.0851532i
$237$	−0.197363	−	0.571890i	−0.0128201	−	0.0371482i
$238$	−8.25637	−	18.2972i	−0.535181	−	1.18603i
$239$	−7.32463			−0.473791			−0.236896	−	0.971535i	$-0.576130\pi$
$239$	−7.32463			−0.473791			−0.236896	+	0.971535i	$0.576130\pi$
$240$	−2.39060	+	0.825011i	−0.154312	+	0.0532542i
$241$	17.4268			1.12256			0.561280	−	0.827626i	$-0.310309\pi$
$241$	17.4268			1.12256			0.561280	+	0.827626i	$0.310309\pi$
$242$	−0.693357	−	1.20093i	−0.0445707	−	0.0771986i
$243$	−6.53873	+	14.1508i	−0.419460	+	0.907774i
$244$	0.865717	−	0.499822i	0.0554219	−	0.0319978i
$245$	9.68832	−	3.25543i	0.618964	−	0.207982i
$246$	−0.990716	+	5.11581i	−0.0631657	+	0.326172i
$247$	−11.1358	+	5.57236i	−0.708555	+	0.354561i
$248$	5.34484	+	9.25753i	0.339397	+	0.587854i
$249$	−4.87851	−	4.23487i	−0.309163	−	0.268374i
$250$			11.4882i			0.726577i
$251$	6.39321	−	11.0734i	0.403536	−	0.698944i	−0.590614	−	0.806954i	$-0.701114\pi$
$251$	6.39321	−	11.0734i	0.403536	−	0.698944i	0.994150	+	0.108010i	$0.0344478\pi$
$252$	−6.70414	+	4.24906i	−0.422321	+	0.267666i
$253$	−10.9939	−	6.34731i	−0.691178	−	0.399052i
$254$	−7.87940	−	13.6475i	−0.494397	−	0.856321i
$255$	−18.1379	+	6.25951i	−1.13584	+	0.391986i
$256$	1.00000			0.0625000
$257$	−21.3460			−1.33153			−0.665764	−	0.746163i	$-0.731894\pi$
$257$	−21.3460			−1.33153			−0.665764	+	0.746163i	$0.731894\pi$
$258$	−6.34134	−	18.3750i	−0.394794	−	1.14398i
$259$	13.4199	−	6.05552i	0.833870	−	0.376272i
$260$	−2.89925	+	4.39416i	−0.179804	+	0.272514i
$261$	−0.364860	−	0.465661i	−0.0225843	−	0.0288237i
$262$	−6.32520	+	10.9556i	−0.390772	+	0.676837i
$263$	13.7817	+	7.95686i	0.849816	+	0.490641i	0.860589	−	0.509301i	$-0.170096\pi$
$263$	13.7817	+	7.95686i	0.849816	+	0.490641i	−0.0107730	+	0.999942i	$0.503429\pi$
$264$	1.98865	+	5.76241i	0.122393	+	0.354652i
$265$	7.10729			0.436597
$266$	−5.33380	+	7.41911i	−0.327037	+	0.454895i
$267$	−18.9136	−	16.4182i	−1.15749	−	1.00478i
$268$	4.78794	+	2.76432i	0.292470	+	0.168858i
$269$	−15.4992			−0.945002			−0.472501	−	0.881330i	$-0.656649\pi$
$269$	−15.4992			−0.945002			−0.472501	+	0.881330i	$0.656649\pi$
$270$	3.45848	+	6.75272i	0.210476	+	0.410958i
$271$	14.9966			0.910977			0.455489	−	0.890242i	$-0.349465\pi$
$271$	14.9966			0.910977			0.455489	+	0.890242i	$0.349465\pi$
$272$	7.58718			0.460040
$273$	−5.67553	+	15.5174i	−0.343499	+	0.939153i
$274$	−1.25158			−0.0756107
$275$	10.0943			0.608711
$276$	4.71786	+	4.09541i	0.283982	+	0.246515i
$277$	−0.719351			−0.0432216			−0.0216108	−	0.999766i	$-0.506879\pi$
$277$	−0.719351			−0.0432216			−0.0216108	+	0.999766i	$0.506879\pi$
$278$	8.68419	+	5.01382i	0.520843	+	0.300709i
$279$	25.2432	−	19.7788i	1.51127	−	1.18413i
$280$	−0.384576	+	3.84385i	−0.0229828	+	0.229714i
$281$	−7.30448			−0.435749			−0.217874	−	0.975977i	$-0.569912\pi$
$281$	−7.30448			−0.435749			−0.217874	+	0.975977i	$0.569912\pi$
$282$	20.9452	−	7.22833i	1.24727	−	0.430441i
$283$	12.9252	+	7.46234i	0.768320	+	0.443590i	0.832275	−	0.554363i	$-0.187038\pi$
$283$	12.9252	+	7.46234i	0.768320	+	0.443590i	−0.0639547	+	0.997953i	$0.520371\pi$
$284$	−5.33718	+	9.24427i	−0.316703	+	0.548546i
$285$	6.59566	+	5.72546i	0.390693	+	0.339147i
$286$	10.5919	+	6.98849i	0.626312	+	0.413238i
$287$	6.46287	+	4.64634i	0.381491	+	0.274265i
$288$	−0.421657	−	2.97022i	−0.0248464	−	0.175022i
$289$	40.5653			2.38619
$290$	−0.287918			−0.0169072
$291$	1.95218	+	5.65675i	0.114439	+	0.331604i
$292$	−2.94410	−	5.09933i	−0.172290	−	0.298416i
$293$	−13.1158	−	7.57239i	−0.766231	−	0.442384i	0.0652973	−	0.997866i	$-0.479200\pi$
$293$	−13.1158	−	7.57239i	−0.766231	−	0.442384i	−0.831529	+	0.555482i	$0.812534\pi$
$294$	1.60627	+	12.0175i	0.0936793	+	0.700874i
$295$	0.955007	−	1.65412i	0.0556027	−	0.0963066i
$296$			5.56471i			0.323442i
$297$	16.2771	−	8.33649i	0.944494	−	0.483732i
$298$	1.62311	+	2.81131i	0.0940242	+	0.162855i
$299$	12.9820	+	0.775059i	0.750767	+	0.0448228i
$300$	−4.87714	−	0.944496i	−0.281582	−	0.0545305i
$301$	−29.5452	−	2.95599i	−1.70296	−	0.170380i
$302$	−8.04225	+	4.64320i	−0.462780	+	0.267186i
$303$	−6.56421	−	19.0208i	−0.377104	−	1.09272i
$304$	−1.72681	−	2.99093i	−0.0990395	−	0.171541i
$305$	−1.45957			−0.0835748
$306$	−3.19919	−	22.5356i	−0.182885	−	1.28827i
$307$	0.289284			0.0165103			0.00825515	−	0.999966i	$-0.497372\pi$
$307$	0.289284			0.0165103			0.00825515	+	0.999966i	$0.497372\pi$
$308$	9.26540	+	0.927001i	0.527945	+	0.0528208i
$309$	30.6745	−	10.5860i	1.74501	−	0.602215i
$310$		−	15.6079i		−	0.886468i
$311$	5.96970	+	10.3398i	0.338511	+	0.586318i	0.984153	−	0.177322i	$-0.0567435\pi$
$311$	5.96970	+	10.3398i	0.338511	+	0.586318i	−0.645642	+	0.763640i	$0.723410\pi$
$312$	−4.46365	−	4.36759i	−0.252705	−	0.247266i
$313$	−7.95301	−	4.59167i	−0.449530	−	0.259537i	0.258101	−	0.966118i	$-0.416903\pi$
$313$	−7.95301	−	4.59167i	−0.449530	−	0.259537i	−0.707632	+	0.706581i	$0.750236\pi$
$314$	−16.2305	+	9.37071i	−0.915942	+	0.528820i
$315$	11.5792	−	0.478510i	0.652416	−	0.0269610i
$316$	0.174645	−	0.302494i	0.00982454	−	0.0170166i
$317$	11.5121	−	19.9395i	0.646582	−	1.11991i	−0.337352	−	0.941379i	$-0.609531\pi$
$317$	11.5121	−	19.9395i	0.646582	−	1.11991i	0.983934	−	0.178534i	$-0.0571356\pi$
$318$	−1.60297	+	8.27732i	−0.0898899	+	0.464169i
$319$			0.694013i			0.0388573i
$320$	−1.26448	−	0.730045i	−0.0706863	−	0.0408108i
$321$	0.458849	+	0.398311i	0.0256105	+	0.0222315i
$322$	8.69856	−	3.92510i	0.484752	−	0.218737i
$323$	−13.1016	−	22.6927i	−0.728994	−	1.26265i
$324$	−8.64441	+	2.50483i	−0.480245	+	0.139157i
$325$	−9.24798	+	4.62768i	−0.512986	+	0.256698i
$326$	0.787553	−	0.454694i	0.0436185	−	0.0251832i
$327$	−3.08969	+	15.9544i	−0.170860	+	0.882281i
$328$	−2.60543	+	1.50425i	−0.143861	+	0.0830581i
$329$	3.36946	−	33.6778i	0.185764	−	1.85672i
$330$	1.69223	−	8.73824i	0.0931540	−	0.481024i
$331$	−20.4980	+	11.8345i	−1.12667	+	0.650483i	−0.943095	−	0.332522i	$-0.892100\pi$
$331$	−20.4980	+	11.8345i	−1.12667	+	0.650483i	−0.183575	+	0.983006i	$0.558767\pi$
$332$		−	3.72979i		−	0.204699i
$333$	16.5284	−	2.34640i	0.905752	−	0.128582i
$334$	−11.6602	+	6.73204i	−0.638020	+	0.368361i
$335$	−4.03616	−	6.99083i	−0.220519	−	0.381950i
$336$	−4.38990	−	1.31482i	−0.239489	−	0.0717294i
$337$	19.1537			1.04337			0.521684	−	0.853139i	$-0.325304\pi$
$337$	19.1537			1.04337			0.521684	+	0.853139i	$0.325304\pi$
$338$	−12.9077	−	1.54676i	−0.702084	−	0.0841325i
$339$	9.51941	−	3.28521i	0.517023	−	0.178428i
$340$	−9.59380	−	5.53898i	−0.520297	−	0.300394i
$341$	−37.6220			−2.03735
$342$	−8.15558	+	6.39016i	−0.441004	+	0.345540i
$343$	17.6977	+	5.45814i	0.955586	+	0.294712i
$344$	5.61139	−	9.71922i	0.302546	−	0.524025i
$345$	−2.97579	−	8.62279i	−0.160211	−	0.464236i
$346$	5.08435	+	8.80635i	0.273336	+	0.473432i
$347$			31.7120i			1.70239i	0.524852	+	0.851194i	$0.324121\pi$
$347$			31.7120i			1.70239i	−0.524852	+	0.851194i	$0.675879\pi$
$348$	0.0649367	−	0.335317i	0.00348097	−	0.0179749i
$349$	−3.87835	−	6.71749i	−0.207603	−	0.359579i	0.743356	−	0.668896i	$-0.233233\pi$
$349$	−3.87835	−	6.71749i	−0.207603	−	0.359579i	−0.950959	+	0.309317i	$0.899900\pi$
$350$	−4.42957	+	6.16136i	−0.236771	+	0.329338i
$351$	−11.0906	+	15.0997i	−0.591970	+	0.805960i
$352$	−1.75974	+	3.04796i	−0.0937944	+	0.162457i
$353$	−0.491689	−	0.283877i	−0.0261700	−	0.0151092i	0.486858	−	0.873481i	$-0.338143\pi$
$353$	−0.491689	−	0.283877i	−0.0261700	−	0.0151092i	−0.513028	+	0.858372i	$0.671476\pi$
$354$	1.71104	+	1.48529i	0.0909407	+	0.0789424i
$355$	13.4975	−	7.79277i	0.716371	−	0.413597i
$356$		−	14.4601i		−	0.766382i
$357$	−33.3070	−	9.97579i	−1.76279	−	0.527975i
$358$	7.39608	+	4.27013i	0.390895	+	0.225683i
$359$	−3.12906	+	5.41969i	−0.165145	+	0.286040i	−0.936707	−	0.350115i	$-0.886143\pi$
$359$	−3.12906	+	5.41969i	−0.165145	+	0.286040i	0.771562	+	0.636155i	$0.219476\pi$
$360$	−1.63522	+	4.06360i	−0.0861837	+	0.214170i
$361$	3.53624	−	6.12495i	0.186118	−	0.322366i
$362$		−	25.4759i		−	1.33898i
$363$	−2.35805	−	0.456654i	−0.123765	−	0.0239681i
$364$	−8.91353	+	3.39839i	−0.467196	+	0.178124i
$365$			8.59731i			0.450004i
$366$	0.329189	−	1.69985i	0.0172070	−	0.0888527i
$367$	−18.6936	−	10.7928i	−0.975800	−	0.563378i	−0.0748003	−	0.997199i	$-0.523832\pi$
$367$	−18.6936	−	10.7928i	−0.975800	−	0.563378i	−0.900999	+	0.433820i	$0.857165\pi$
$368$			3.60696i			0.188026i
$369$	5.56654	+	7.10442i	0.289782	+	0.369841i
$370$	4.06249	−	7.03645i	0.211199	−	0.365807i
$371$	10.4568	+	7.51772i	0.542892	+	0.390300i
$372$	18.1773	+	3.52018i	0.942451	+	0.182513i
$373$	0.378056	+	0.654812i	0.0195750	+	0.0339049i	0.875647	−	0.482952i	$-0.160435\pi$
$373$	0.378056	+	0.654812i	0.0195750	+	0.0339049i	−0.856072	+	0.516857i	$0.827102\pi$
$374$	−13.3514	+	23.1254i	−0.690387	+	1.19579i
$375$	15.0264	+	13.0439i	0.775960	+	0.673583i
$376$	11.0787	+	6.39629i	0.571340	+	0.329863i
$377$	−0.318166	−	0.635824i	−0.0163864	−	0.0327466i
$378$	−2.05428	+	13.5934i	−0.105661	+	0.699168i
$379$	6.26101	−	3.61480i	0.321607	−	0.185680i	−0.330502	−	0.943805i	$-0.607218\pi$
$379$	6.26101	−	3.61480i	0.321607	−	0.185680i	0.652108	+	0.758126i	$0.273885\pi$
$380$			5.04260i			0.258680i
$381$	−26.7972	−	5.18947i	−1.37286	−	0.265865i
$382$	−17.9487	+	10.3627i	−0.918338	+	0.530202i
$383$	−1.16788	+	0.674277i	−0.0596760	+	0.0344540i	−0.529541	−	0.848284i	$-0.677636\pi$
$383$	−1.16788	+	0.674277i	−0.0596760	+	0.0344540i	0.469865	+	0.882738i	$0.344303\pi$
$384$	1.13542	−	1.30799i	0.0579415	−	0.0667479i
$385$	−11.0391	−	7.93633i	−0.562606	−	0.404473i
$386$	−8.21554	−	4.74324i	−0.418160	−	0.241425i
$387$	−31.2343	−	12.5689i	−1.58773	−	0.638913i
$388$	−1.72747	+	2.99206i	−0.0876989	+	0.151899i
$389$	−3.70239	+	2.13758i	−0.187719	+	0.108379i	−0.590914	−	0.806734i	$-0.701233\pi$
$389$	−3.70239	+	2.13758i	−0.187719	+	0.108379i	0.403196	+	0.915114i	$0.367899\pi$
$390$	2.45565	+	8.78137i	0.124346	+	0.444662i
$391$			27.3667i			1.38399i
$392$	−4.63164	+	5.24861i	−0.233933	+	0.265095i
$393$	7.14799	+	20.7124i	0.360569	+	1.04480i
$394$	−3.21420	−	5.56716i	−0.161929	−	0.280470i
$395$	−0.441668	+	0.254997i	−0.0222228	+	0.0128303i
$396$	9.79510	+	3.94162i	0.492223	+	0.198074i
$397$	−2.86479	−	4.96196i	−0.143780	−	0.249034i	0.785137	−	0.619322i	$-0.212592\pi$
$397$	−2.86479	−	4.96196i	−0.143780	−	0.249034i	−0.928917	+	0.370288i	$0.879259\pi$
$398$		−	1.26513i		−	0.0634155i
$399$	3.64800	+	15.4003i	0.182628	+	0.770980i
$400$	−1.43407	−	2.48388i	−0.0717034	−	0.124194i
$401$	−21.9761			−1.09743			−0.548717	−	0.836008i	$-0.684883\pi$
$401$	−21.9761			−1.09743			−0.548717	+	0.836008i	$0.684883\pi$
$402$	9.05200	−	3.12391i	0.451473	−	0.155806i
$403$	34.4676	−	17.2476i	1.71696	−	0.859163i
$404$	5.80861	−	10.0608i	0.288989	−	0.500544i
$405$	12.7593	+	3.14352i	0.634014	+	0.156203i
$406$	−0.423610	−	0.304545i	−0.0210234	−	0.0151143i
$407$	−16.9610	−	9.79244i	−0.840726	−	0.485393i
$408$	8.61461	−	9.92393i	0.426487	−	0.491308i
$409$	−8.43899			−0.417281			−0.208641	−	0.977992i	$-0.566904\pi$
$409$	−8.43899			−0.417281			−0.208641	+	0.977992i	$0.566904\pi$
$410$	4.39267			0.216938
$411$	−1.42106	+	1.63705i	−0.0700959	+	0.0807497i
$412$	16.2249	+	9.36744i	0.799343	+	0.461501i
$413$	3.15473	−	1.42353i	0.155234	−	0.0700471i
$414$	10.7135	−	1.52090i	0.526539	−	0.0747483i
$415$	−2.72292	+	4.71623i	−0.133663	+	0.231511i
$416$	0.214878	−	3.59914i	0.0105353	−	0.176462i
$417$	16.4182	−	5.66603i	0.804002	−	0.277467i
$418$	12.1549			0.594518
$419$	−12.4744	−	21.6063i	−0.609413	−	1.05553i	−0.991337	−	0.131341i	$-0.958072\pi$
$419$	−12.4744	−	21.6063i	−0.609413	−	1.05553i	0.381924	−	0.924194i	$-0.375262\pi$
$420$	4.59104	+	4.86739i	0.224020	+	0.237504i
$421$			23.2628i			1.13376i	0.823800	+	0.566881i	$0.191850\pi$
$421$			23.2628i			1.13376i	−0.823800	+	0.566881i	$0.808150\pi$
$422$	−6.24577	−	10.8180i	−0.304040	−	0.526612i
$423$	14.3270	−	35.6032i	0.696601	−	1.73109i
$424$	−4.21555	+	2.43385i	−0.204725	+	0.118198i
$425$	−10.8805	−	18.8456i	−0.527783	−	0.914147i
$426$	6.03145	+	17.4771i	0.292225	+	0.846766i
$427$	−2.14744	−	1.54386i	−0.103922	−	0.0747125i
$428$			0.350806i			0.0169568i
$429$	21.1671	−	5.91921i	1.02196	−	0.285782i
$430$	−14.1909	+	8.19314i	−0.684348	+	0.395108i
$431$	−11.3685	+	19.6908i	−0.547602	+	0.948474i	0.450837	+	0.892606i	$0.351126\pi$
$431$	−11.3685	+	19.6908i	−0.547602	+	0.948474i	−0.998438	+	0.0558673i	$0.982208\pi$
$432$	−4.36376	−	2.82092i	−0.209952	−	0.135721i
$433$	11.9025	+	6.87194i	0.572000	+	0.330244i	0.757948	−	0.652315i	$-0.226202\pi$
$433$	11.9025	+	6.87194i	0.572000	+	0.330244i	−0.185948	+	0.982560i	$0.559536\pi$
$434$	16.5092	−	22.9637i	0.792468	−	1.10229i
$435$	−0.326907	+	0.376593i	−0.0156740	+	0.0180563i
$436$	−8.12542	+	4.69121i	−0.389137	+	0.224668i
$437$	10.7882	−	6.22855i	0.516068	−	0.297952i
$438$	−10.0126	−	1.93902i	−0.478422	−	0.0926501i
$439$			12.1761i			0.581134i	0.956855	+	0.290567i	$0.0938439\pi$
$439$			12.1761i			0.581134i	−0.956855	+	0.290567i	$0.906156\pi$
$440$	4.45029	−	2.56938i	0.212159	−	0.122490i
$441$	17.5425	+	11.5439i	0.835356	+	0.549709i
$442$	1.63032	−	27.3073i	0.0775465	−	1.29888i
$443$	−1.94173	−	1.12106i	−0.0922543	−	0.0532630i	0.453163	−	0.891428i	$-0.350296\pi$
$443$	−1.94173	−	1.12106i	−0.0922543	−	0.0532630i	−0.545417	+	0.838165i	$0.683629\pi$
$444$	7.27857	+	6.31827i	0.345426	+	0.299852i
$445$	−10.5565	+	18.2844i	−0.500426	+	0.866763i
$446$	−3.78556	−	6.55677i	−0.179251	−	0.310472i
$447$	5.52006	+	1.06900i	0.261090	+	0.0505620i
$448$	−1.08820	−	2.41160i	−0.0514126	−	0.113937i
$449$	3.91929	−	6.78842i	0.184963	−	0.320365i	−0.758601	−	0.651555i	$-0.774117\pi$
$449$	3.91929	−	6.78842i	0.184963	−	0.320365i	0.943564	+	0.331190i	$0.107450\pi$
$450$	−6.77298	+	5.30684i	−0.319281	+	0.250167i
$451$		−	10.5883i		−	0.498584i
$452$	5.03517	+	2.90706i	0.236834	+	0.136736i
$453$	−3.05807	+	15.7911i	−0.143681	+	0.741932i
$454$		−	25.4572i		−	1.19476i
$455$	13.7519	+	2.21010i	0.644700	+	0.103611i
$456$	−5.87274	−	1.13730i	−0.275016	−	0.0532590i
$457$			6.54295i			0.306066i	0.988221	+	0.153033i	$0.0489041\pi$
$457$			6.54295i			0.306066i	−0.988221	+	0.153033i	$0.951096\pi$
$458$	5.51406	−	9.55063i	0.257655	−	0.446272i
$459$	−33.1087	−	21.4028i	−1.54538	−	0.998997i
$460$	2.63325	−	4.56092i	0.122776	−	0.212654i
$461$	−20.3030	−	11.7219i	−0.945606	−	0.545946i	−0.0538925	−	0.998547i	$-0.517163\pi$
$461$	−20.3030	−	11.7219i	−0.945606	−	0.545946i	−0.891713	+	0.452601i	$0.850496\pi$
$462$	11.7326	−	11.0665i	0.545850	−	0.514860i
$463$			37.3356i			1.73513i	0.497321	+	0.867567i	$0.334317\pi$
$463$			37.3356i			1.73513i	−0.497321	+	0.867567i	$0.665683\pi$
$464$	0.170773	−	0.0985961i	0.00792796	−	0.00457721i
$465$	−20.4149	−	17.7215i	−0.946719	−	0.821813i
$466$	6.18721	+	3.57219i	0.286617	+	0.165479i
$467$	3.36611	−	5.83027i	0.155765	−	0.269792i	−0.777572	−	0.628793i	$-0.783549\pi$
$467$	3.36611	−	5.83027i	0.155765	−	0.269792i	0.933337	+	0.359001i	$0.116882\pi$
$468$	−10.7808	+	0.879368i	−0.498345	+	0.0406488i
$469$	1.45620	−	14.5547i	0.0672410	−	0.672075i
$470$	−9.33916	−	16.1759i	−0.430783	−	0.746138i
$471$	−6.17167	+	31.8690i	−0.284376	+	1.46845i
$472$			1.30815i			0.0602124i
$473$	19.7492	+	34.2066i	0.908068	+	1.57282i
$474$	−0.197363	−	0.571890i	−0.00906519	−	0.0262678i
$475$	−4.95273	+	8.57838i	−0.227247	+	0.393603i
$476$	−8.25637	−	18.2972i	−0.378430	−	0.838653i
$477$	9.00659	+	11.4949i	0.412383	+	0.526314i
$478$	−7.32463			−0.335021
$479$	11.2141	+	6.47445i	0.512384	+	0.295825i	0.733813	−	0.679351i	$-0.237739\pi$
$479$	11.2141	+	6.47445i	0.512384	+	0.295825i	−0.221429	+	0.975176i	$0.571072\pi$
$480$	−2.39060	+	0.825011i	−0.109115	+	0.0376564i
$481$	20.0282	+	1.19574i	0.913207	+	0.0545209i
$482$	17.4268			0.793769
$483$	4.74252	−	15.8342i	0.215792	−	0.720482i
$484$	−0.693357	−	1.20093i	−0.0315162	−	0.0545877i
$485$	4.36868	−	2.52226i	0.198372	−	0.114530i
$486$	−6.53873	+	14.1508i	−0.296603	+	0.641893i
$487$			8.67630i			0.393161i	0.980488	+	0.196580i	$0.0629837\pi$
$487$			8.67630i			0.393161i	−0.980488	+	0.196580i	$0.937016\pi$
$488$	0.865717	−	0.499822i	0.0391892	−	0.0226259i
$489$	0.299467	−	1.54638i	0.0135424	−	0.0699295i
$490$	9.68832	−	3.25543i	0.437674	−	0.147065i
$491$	−14.7725	+	8.52893i	−0.666676	+	0.384905i	−0.794816	−	0.606851i	$-0.792433\pi$
$491$	−14.7725	+	8.52893i	−0.666676	+	0.384905i	0.128140	+	0.991756i	$0.459099\pi$
$492$	−0.990716	+	5.11581i	−0.0446649	+	0.230639i
$493$	1.29569	−	0.748066i	0.0583549	−	0.0336912i
$494$	−11.1358	+	5.57236i	−0.501024	+	0.250712i
$495$	−9.50811	−	12.1349i	−0.427358	−	0.545425i
$496$	5.34484	+	9.25753i	0.239990	+	0.415675i
$497$	28.1014	+	2.81154i	1.26052	+	0.126115i
$498$	−4.87851	−	4.23487i	−0.218611	−	0.189769i
$499$	20.1546	+	11.6362i	0.902243	+	0.520910i	0.877927	−	0.478794i	$-0.158926\pi$
$499$	20.1546	+	11.6362i	0.902243	+	0.520910i	0.0243156	+	0.999704i	$0.492259\pi$
$500$			11.4882i			0.513768i
$501$	−4.43381	+	22.8951i	−0.198088	+	1.02288i
$502$	6.39321	−	11.0734i	0.285343	−	0.494228i
$503$	4.33129	−	7.50201i	0.193122	−	0.334498i	−0.753161	−	0.657836i	$-0.771472\pi$
$503$	4.33129	−	7.50201i	0.193122	−	0.334498i	0.946283	+	0.323338i	$0.104805\pi$
$504$	−6.70414	+	4.24906i	−0.298626	+	0.189268i
$505$	−14.6897	+	8.48110i	−0.653683	+	0.377404i
$506$	−10.9939	−	6.34731i	−0.488737	−	0.282172i
$507$	−16.6787	+	15.1268i	−0.740727	+	0.671806i
$508$	−7.87940	−	13.6475i	−0.349592	−	0.605511i
$509$			5.78402i			0.256372i	0.991750	+	0.128186i	$0.0409155\pi$
$509$			5.78402i			0.256372i	−0.991750	+	0.128186i	$0.959085\pi$
$510$	−18.1379	+	6.25951i	−0.803159	+	0.277176i
$511$	−9.09378	+	12.6491i	−0.402285	+	0.559563i
$512$	1.00000			0.0441942
$513$	−0.901751	+	17.9229i	−0.0398133	+	0.791315i
$514$	−21.3460			−0.941532
$515$	−13.6773	−	23.6898i	−0.602694	−	1.04390i
$516$	−6.34134	−	18.3750i	−0.279162	−	0.808914i
$517$	−38.9912	+	22.5116i	−1.71483	+	0.990058i
$518$	13.4199	−	6.05552i	0.589635	−	0.266064i
$519$	17.2914	+	3.34862i	0.759010	+	0.146988i
$520$	−2.89925	+	4.39416i	−0.127140	+	0.192697i
$521$	5.46547	+	9.46647i	0.239447	+	0.414734i	0.960556	−	0.278088i	$-0.0897007\pi$
$521$	5.46547	+	9.46647i	0.239447	+	0.414734i	−0.721109	+	0.692822i	$0.756367\pi$
$522$	−0.364860	−	0.465661i	−0.0159695	−	0.0203814i
$523$			13.6134i			0.595270i	0.954680	+	0.297635i	$0.0961979\pi$
$523$			13.6134i			0.595270i	−0.954680	+	0.297635i	$0.903802\pi$
$524$	−6.32520	+	10.9556i	−0.276318	+	0.478596i
$525$	3.02956	+	12.7895i	0.132221	+	0.558181i
$526$	13.7817	+	7.95686i	0.600910	+	0.346936i
$527$	40.5522	+	70.2385i	1.76648	+	3.05964i
$528$	1.98865	+	5.76241i	0.0865448	+	0.250777i
$529$	9.98981			0.434340
$530$	7.10729			0.308721
$531$	3.88549	−	0.551590i	0.168616	−	0.0239370i
$532$	−5.33380	+	7.41911i	−0.231250	+	0.321659i
$533$	4.85414	+	9.70054i	0.210256	+	0.420177i
$534$	−18.9136	−	16.4182i	−0.818470	−	0.710485i
$535$	0.256104	−	0.443585i	0.0110723	−	0.0191779i
$536$	4.78794	+	2.76432i	0.206808	+	0.119400i
$537$	13.9829	−	4.82560i	0.603407	−	0.208240i
$538$	−15.4992			−0.668218
$539$	−7.84705	−	23.3532i	−0.337996	−	1.00589i
$540$	3.45848	+	6.75272i	0.148829	+	0.290591i
$541$	−3.38852	−	1.95636i	−0.145684	−	0.0841105i	0.425386	−	0.905012i	$-0.360138\pi$
$541$	−3.38852	−	1.95636i	−0.145684	−	0.0841105i	−0.571070	+	0.820901i	$0.693472\pi$
$542$	14.9966			0.644158
$543$	−33.3221	−	28.9258i	−1.42999	−	1.24132i
$544$	7.58718			0.325298
$545$	13.6992			0.586809
$546$	−5.67553	+	15.5174i	−0.242890	+	0.664082i
$547$	−10.8125			−0.462308			−0.231154	−	0.972917i	$-0.574250\pi$
$547$	−10.8125			−0.462308			−0.231154	+	0.972917i	$0.574250\pi$
$548$	−1.25158			−0.0534648
$549$	−1.84962	−	2.36062i	−0.0789397	−	0.100749i
$550$	10.0943			0.430424
$551$	−0.589787	−	0.340514i	−0.0251258	−	0.0145064i
$552$	4.71786	+	4.09541i	0.200805	+	0.174312i
$553$	−0.919543	−	0.0920001i	−0.0391030	−	0.00391224i
$554$	−0.719351			−0.0305623
$555$	−4.59095	−	13.3030i	−0.194875	−	0.564680i
$556$	8.68419	+	5.01382i	0.368292	+	0.212633i
$557$	−11.6199	+	20.1263i	−0.492351	+	0.852778i	−0.999961	−	0.00880939i	$-0.997196\pi$
$557$	−11.6199	+	20.1263i	−0.492351	+	0.852778i	0.507610	+	0.861587i	$0.330529\pi$
$558$	25.2432	−	19.7788i	1.06863	−	0.837305i
$559$	−33.7751	−	22.2847i	−1.42853	−	0.942541i
$560$	−0.384576	+	3.84385i	−0.0162513	+	0.162432i
$561$	15.0882	+	43.7205i	0.637026	+	1.84588i
$562$	−7.30448			−0.308121
$563$	11.8776			0.500580			0.250290	−	0.968171i	$-0.419474\pi$
$563$	11.8776			0.500580			0.250290	+	0.968171i	$0.419474\pi$
$564$	20.9452	−	7.22833i	0.881951	−	0.304368i
$565$	−4.24457	−	7.35181i	−0.178570	−	0.309293i
$566$	12.9252	+	7.46234i	0.543285	+	0.313666i
$567$	15.4475	+	18.1211i	0.648734	+	0.761015i
$568$	−5.33718	+	9.24427i	−0.223943	+	0.387881i
$569$		−	1.93128i		−	0.0809635i	−0.999180	−	0.0404817i	$-0.987111\pi$
$569$		−	1.93128i		−	0.0809635i	0.999180	−	0.0404817i	$-0.0128893\pi$
$570$	6.59566	+	5.72546i	0.276262	+	0.239813i
$571$	6.46083	+	11.1905i	0.270377	+	0.468307i	0.968958	−	0.247224i	$-0.0795182\pi$
$571$	6.46083	+	11.1905i	0.270377	+	0.468307i	−0.698581	+	0.715531i	$0.746185\pi$
$572$	10.5919	+	6.98849i	0.442869	+	0.292203i
$573$	−6.82502	+	35.2427i	−0.285119	+	1.47229i
$574$	6.46287	+	4.64634i	0.269755	+	0.193934i
$575$	8.95926	−	5.17263i	0.373627	−	0.215714i
$576$	−0.421657	−	2.97022i	−0.0175690	−	0.123759i
$577$	18.9813	+	32.8766i	0.790203	+	1.36867i	0.925841	+	0.377913i	$0.123358\pi$
$577$	18.9813	+	32.8766i	0.790203	+	1.36867i	−0.135638	+	0.990758i	$0.543308\pi$
$578$	40.5653			1.68729
$579$	−15.5322	+	5.36025i	−0.645494	+	0.222765i
$580$	−0.287918			−0.0119552
$581$	−8.99477	+	4.05876i	−0.373166	+	0.168386i
$582$	1.95218	+	5.65675i	0.0809205	+	0.234480i
$583$		−	17.1318i		−	0.709525i
$584$	−2.94410	−	5.09933i	−0.121828	−	0.211012i
$585$	14.2741	+	6.75857i	0.590161	+	0.279432i
$586$	−13.1158	−	7.57239i	−0.541807	−	0.312813i
$587$	−3.62595	+	2.09345i	−0.149659	+	0.0864058i	−0.572960	−	0.819584i	$-0.694205\pi$
$587$	−3.62595	+	2.09345i	−0.149659	+	0.0864058i	0.423300	+	0.905989i	$0.360871\pi$
$588$	1.60627	+	12.0175i	0.0662413	+	0.495593i
$589$	18.4591	−	31.9720i	0.760592	−	1.31738i
$590$	0.955007	−	1.65412i	0.0393170	−	0.0680991i
$591$	−10.9312	−	2.11692i	−0.449651	−	0.0870783i
$592$			5.56471i			0.228708i
$593$	−25.7814	−	14.8849i	−1.05872	−	0.611250i	−0.133639	−	0.991030i	$-0.542666\pi$
$593$	−25.7814	−	14.8849i	−1.05872	−	0.611250i	−0.925077	+	0.379780i	$0.876000\pi$
$594$	16.2771	−	8.33649i	0.667858	−	0.342050i
$595$	−2.91785	+	29.1639i	−0.119620	+	1.19561i
$596$	1.62311	+	2.81131i	0.0664852	+	0.115156i
$597$	−1.65478	−	1.43645i	−0.0677256	−	0.0587902i
$598$	12.9820	+	0.775059i	0.530873	+	0.0316945i
$599$	14.8413	−	8.56865i	0.606401	−	0.350106i	−0.165155	−	0.986268i	$-0.552812\pi$
$599$	14.8413	−	8.56865i	0.606401	−	0.350106i	0.771556	+	0.636162i	$0.219479\pi$
$600$	−4.87714	−	0.944496i	−0.199109	−	0.0385589i
$601$	−17.6704	+	10.2020i	−0.720790	+	0.416149i	−0.815044	−	0.579400i	$-0.803287\pi$
$601$	−17.6704	+	10.2020i	−0.720790	+	0.416149i	0.0942531	+	0.995548i	$0.469954\pi$
$602$	−29.5452	−	2.95599i	−1.20417	−	0.120477i
$603$	6.19177	−	15.3868i	0.252148	−	0.626600i
$604$	−8.04225	+	4.64320i	−0.327235	+	0.188929i
$605$			2.02473i			0.0823169i
$606$	−6.56421	−	19.0208i	−0.266653	−	0.772667i
$607$	−9.18240	+	5.30146i	−0.372702	+	0.215180i	−0.674638	−	0.738149i	$-0.735700\pi$
$607$	−9.18240	+	5.30146i	−0.372702	+	0.215180i	0.301936	+	0.953328i	$0.402367\pi$
$608$	−1.72681	−	2.99093i	−0.0700315	−	0.121298i
$609$	−0.879315	+	0.208291i	−0.0356316	+	0.00844036i
$610$	−1.45957			−0.0590963
$611$	25.4017	−	38.4994i	1.02764	−	1.55752i
$612$	−3.19919	−	22.5356i	−0.129320	−	0.910947i
$613$	19.7900	+	11.4258i	0.799310	+	0.461482i	0.843230	−	0.537553i	$-0.180651\pi$
$613$	19.7900	+	11.4258i	0.799310	+	0.461482i	−0.0439195	+	0.999035i	$0.513985\pi$
$614$	0.289284			0.0116745
$615$	4.98751	−	5.74555i	0.201116	−	0.231683i
$616$	9.26540	+	0.927001i	0.373314	+	0.0373500i
$617$	−2.03229	+	3.52003i	−0.0818170	+	0.141711i	−0.904030	−	0.427468i	$-0.859406\pi$
$617$	−2.03229	+	3.52003i	−0.0818170	+	0.141711i	0.822213	+	0.569179i	$0.192739\pi$
$618$	30.6745	−	10.5860i	1.23391	−	0.425830i
$619$	5.71042	+	9.89074i	0.229521	+	0.397542i	0.957666	−	0.287881i	$-0.0929506\pi$
$619$	5.71042	+	9.89074i	0.229521	+	0.397542i	−0.728145	+	0.685423i	$0.759617\pi$
$620$		−	15.6079i		−	0.626828i
$621$	10.1749	−	15.7399i	0.408306	−	0.631622i
$622$	5.96970	+	10.3398i	0.239363	+	0.414589i
$623$	−34.8719	+	15.7354i	−1.39711	+	0.630427i
$624$	−4.46365	−	4.36759i	−0.178689	−	0.174843i
$625$	1.21656	−	2.10715i	0.0486624	−	0.0842858i
$626$	−7.95301	−	4.59167i	−0.317866	−	0.183520i
$627$	13.8009	−	15.8985i	0.551156	−	0.634925i
$628$	−16.2305	+	9.37071i	−0.647669	+	0.373932i
$629$			42.2205i			1.68344i
$630$	11.5792	−	0.478510i	0.461327	−	0.0190643i
$631$	−2.43600	−	1.40642i	−0.0969755	−	0.0559888i	0.450728	−	0.892661i	$-0.351164\pi$
$631$	−2.43600	−	1.40642i	−0.0969755	−	0.0559888i	−0.547703	+	0.836673i	$0.684498\pi$
$632$	0.174645	−	0.302494i	0.00694700	−	0.0120326i
$633$	−21.2414	−	4.11355i	−0.844268	−	0.163499i
$634$	11.5121	−	19.9395i	0.457203	−	0.791898i
$635$			23.0093i			0.913095i
$636$	−1.60297	+	8.27732i	−0.0635618	+	0.328217i
$637$	17.8953	+	17.7978i	0.709036	+	0.705173i
$638$			0.694013i			0.0274762i
$639$	29.7080	+	11.9547i	1.17523	+	0.472920i
$640$	−1.26448	−	0.730045i	−0.0499828	−	0.0288576i
$641$			22.9946i			0.908232i	0.890943	+	0.454116i	$0.150045\pi$
$641$			22.9946i			0.908232i	−0.890943	+	0.454116i	$0.849955\pi$
$642$	0.458849	+	0.398311i	0.0181093	+	0.0157201i
$643$	−5.08228	+	8.80277i	−0.200426	+	0.347147i	−0.948666	−	0.316281i	$-0.897566\pi$
$643$	−5.08228	+	8.80277i	−0.200426	+	0.347147i	0.748240	+	0.663428i	$0.230899\pi$
$644$	8.69856	−	3.92510i	0.342771	−	0.154671i
$645$	−5.39611	+	27.8642i	−0.212472	+	1.09715i
$646$	−13.1016	−	22.6927i	−0.515477	−	0.892832i
$647$	−21.2471	+	36.8010i	−0.835309	+	1.44680i	0.0584688	+	0.998289i	$0.481378\pi$
$647$	−21.2471	+	36.8010i	−0.835309	+	1.44680i	−0.893778	+	0.448509i	$0.851955\pi$
$648$	−8.64441	+	2.50483i	−0.339585	+	0.0983990i
$649$	−3.98718	−	2.30200i	−0.156510	−	0.0903613i
$650$	−9.24798	+	4.62768i	−0.362736	+	0.181513i
$651$	−11.2913	−	47.6671i	−0.442541	−	1.86822i
$652$	0.787553	−	0.454694i	0.0308430	−	0.0178072i
$653$			21.6406i			0.846862i	0.905928	+	0.423431i	$0.139174\pi$
$653$			21.6406i			0.846862i	−0.905928	+	0.423431i	$0.860826\pi$
$654$	−3.08969	+	15.9544i	−0.120817	+	0.623867i
$655$	15.9961	−	9.23536i	0.625020	−	0.360855i
$656$	−2.60543	+	1.50425i	−0.101725	+	0.0587309i
$657$	−13.9047	+	10.8948i	−0.542475	+	0.425046i
$658$	3.36946	−	33.6778i	0.131355	−	1.31290i
$659$	−4.44211	−	2.56466i	−0.173040	−	0.0999048i	0.410978	−	0.911645i	$-0.365187\pi$
$659$	−4.44211	−	2.56466i	−0.173040	−	0.0999048i	−0.584019	+	0.811740i	$0.698520\pi$
$660$	1.69223	−	8.73824i	0.0658698	−	0.340135i
$661$	11.9740	−	20.7396i	0.465736	−	0.806678i	−0.533499	−	0.845801i	$-0.679123\pi$
$661$	11.9740	−	20.7396i	0.465736	−	0.806678i	0.999234	+	0.0391228i	$0.0124563\pi$
$662$	−20.4980	+	11.8345i	−0.796676	+	0.459961i
$663$	−33.8665	−	33.1376i	−1.31527	−	1.28696i
$664$		−	3.72979i		−	0.144744i
$665$	12.1607	−	5.48736i	0.471574	−	0.212791i
$666$	16.5284	−	2.34640i	0.640463	−	0.0909212i
$667$	0.355633	+	0.615974i	0.0137701	+	0.0238506i
$668$	−11.6602	+	6.73204i	−0.451148	+	0.260471i
$669$	−12.8744	−	2.49322i	−0.497751	−	0.0963933i
$670$	−4.03616	−	6.99083i	−0.155930	−	0.270079i
$671$			3.51822i			0.135819i
$672$	−4.38990	−	1.31482i	−0.169344	−	0.0507204i
$673$	−8.33251	−	14.4323i	−0.321195	−	0.556326i	0.659540	−	0.751669i	$-0.270751\pi$
$673$	−8.33251	−	14.4323i	−0.321195	−	0.556326i	−0.980735	+	0.195344i	$0.937418\pi$
$674$	19.1537			0.737772
$675$	−0.748878	+	14.8844i	−0.0288243	+	0.572902i
$676$	−12.9077	−	1.54676i	−0.496448	−	0.0594906i
$677$	18.1468	−	31.4312i	0.697439	−	1.20800i	−0.271913	−	0.962322i	$-0.587656\pi$
$677$	18.1468	−	31.4312i	0.697439	−	1.20800i	0.969352	−	0.245678i	$-0.0790105\pi$
$678$	9.51941	−	3.28521i	0.365591	−	0.126168i
$679$	9.09550	+	0.910002i	0.349053	+	0.0349227i
$680$	−9.59380	−	5.53898i	−0.367905	−	0.212410i
$681$	−33.2976	−	28.9045i	−1.27597	−	1.10762i
$682$	−37.6220			−1.44062
$683$	−36.5747			−1.39949			−0.699747	−	0.714391i	$-0.746704\pi$
$683$	−36.5747			−1.39949			−0.699747	+	0.714391i	$0.746704\pi$
$684$	−8.15558	+	6.39016i	−0.311837	+	0.244334i
$685$	1.58259	+	0.913710i	0.0604677	+	0.0349110i
$686$	17.6977	+	5.45814i	0.675701	+	0.208393i
$687$	−6.23134	−	18.0563i	−0.237741	−	0.688890i
$688$	5.61139	−	9.71922i	0.213932	−	0.370542i
$689$	7.85394	+	15.6954i	0.299211	+	0.597946i
$690$	−2.97579	−	8.62279i	−0.113286	−	0.328264i
$691$	17.4627			0.664312			0.332156	−	0.943225i	$-0.392224\pi$
$691$	17.4627			0.664312			0.332156	+	0.943225i	$0.392224\pi$
$692$	5.08435	+	8.80635i	0.193278	+	0.334767i
$693$	−1.15342	−	27.9112i	−0.0438150	−	1.06026i
$694$			31.7120i			1.20377i
$695$	−7.32063	−	12.6797i	−0.277687	−	0.480969i
$696$	0.0649367	−	0.335317i	0.00246142	−	0.0127102i
$697$	−19.7679	+	11.4130i	−0.748761	+	0.432297i
$698$	−3.87835	−	6.71749i	−0.146798	−	0.254261i
$699$	11.6974	−	4.03687i	0.442438	−	0.152688i
$700$	−4.42957	+	6.16136i	−0.167422	+	0.232877i
$701$			42.7684i			1.61534i	0.589635	+	0.807670i	$0.299272\pi$
$701$			42.7684i			1.61534i	−0.589635	+	0.807670i	$0.700728\pi$
$702$	−11.0906	+	15.0997i	−0.418586	+	0.569900i
$703$	16.6436	−	9.60922i	0.627727	−	0.362418i
$704$	−1.75974	+	3.04796i	−0.0663226	+	0.114874i
$705$	−31.7617	−	6.15089i	−1.19621	−	0.231656i
$706$	−0.491689	−	0.283877i	−0.0185050	−	0.0106838i
$707$	−30.5836	−	3.05988i	−1.15021	−	0.115079i
$708$	1.71104	+	1.48529i	0.0643048	+	0.0558207i
$709$	31.6856	−	18.2937i	1.18998	−	0.687033i	0.231675	−	0.972793i	$-0.425579\pi$
$709$	31.6856	−	18.2937i	1.18998	−	0.687033i	0.958301	+	0.285760i	$0.0922459\pi$
$710$	13.4975	−	7.79277i	0.506551	−	0.292457i
$711$	−0.972114	−	0.391185i	−0.0364571	−	0.0146706i
$712$		−	14.4601i		−	0.541914i
$713$	−33.3916	+	19.2786i	−1.25052	+	0.721990i
$714$	−33.3070	−	9.97579i	−1.24648	−	0.373334i
$715$	−8.29128	−	16.5693i	−0.310076	−	0.619658i
$716$	7.39608	+	4.27013i	0.276404	+	0.159582i
$717$	−8.31651	+	9.58052i	−0.310586	+	0.357791i
$718$	−3.12906	+	5.41969i	−0.116775	+	0.202261i
$719$	9.53832	+	16.5209i	0.355719	+	0.616124i	0.987241	−	0.159234i	$-0.0509025\pi$
$719$	9.53832	+	16.5209i	0.355719	+	0.616124i	−0.631521	+	0.775358i	$0.717569\pi$
$720$	−1.63522	+	4.06360i	−0.0609410	+	0.151441i
$721$	4.93461	−	49.3216i	0.183775	−	1.83683i
$722$	3.53624	−	6.12495i	0.131605	−	0.227947i
$723$	19.7867	−	22.7940i	0.735875	−	0.847719i
$724$		−	25.4759i		−	0.946804i
$725$	−0.489801	−	0.282787i	−0.0181908	−	0.0105024i
$726$	−2.35805	−	0.456654i	−0.0875154	−	0.0169480i
$727$		−	9.70964i		−	0.360111i	−0.983656	−	0.180055i	$-0.942372\pi$
$727$		−	9.70964i		−	0.360111i	0.983656	−	0.180055i	$-0.0576277\pi$
$728$	−8.91353	+	3.39839i	−0.330357	+	0.125953i
$729$	11.0849	+	24.6196i	0.410551	+	0.911838i
$730$			8.59731i			0.318201i
$731$	42.5746	−	73.7414i	1.57468	−	2.72743i
$732$	0.329189	−	1.69985i	0.0121672	−	0.0628284i
$733$	16.1353	−	27.9472i	0.595972	−	1.03225i	−0.397437	−	0.917629i	$-0.630100\pi$
$733$	16.1353	−	27.9472i	0.595972	−	1.03225i	0.993409	−	0.114624i	$-0.0365664\pi$
$734$	−18.6936	−	10.7928i	−0.689995	−	0.398369i
$735$	6.74222	−	16.3685i	0.248691	−	0.603760i
$736$			3.60696i			0.132954i
$737$	−16.8510	+	9.72896i	−0.620716	+	0.358371i
$738$	5.56654	+	7.10442i	0.204907	+	0.261517i
$739$	19.4708	+	11.2415i	0.716246	+	0.413525i	0.813370	−	0.581747i	$-0.197631\pi$
$739$	19.4708	+	11.2415i	0.716246	+	0.413525i	−0.0971231	+	0.995272i	$0.530964\pi$
$740$	4.06249	−	7.03645i	0.149340	−	0.258665i
$741$	−5.35523	+	20.8925i	−0.196729	+	0.767503i
$742$	10.4568	+	7.51772i	0.383883	+	0.275984i
$743$	−19.9808	−	34.6077i	−0.733023	−	1.26963i	−0.955585	−	0.294715i	$-0.904775\pi$
$743$	−19.9808	−	34.6077i	−0.733023	−	1.26963i	0.222562	−	0.974919i	$-0.428558\pi$
$744$	18.1773	+	3.52018i	0.666413	+	0.129056i
$745$		−	4.73977i		−	0.173652i
$746$	0.378056	+	0.654812i	0.0138416	+	0.0239744i
$747$	−11.0783	+	1.57269i	−0.405334	+	0.0575418i
$748$	−13.3514	+	23.1254i	−0.488177	+	0.845548i
$749$	0.846003	−	0.381747i	0.0309123	−	0.0139487i
$750$	15.0264	+	13.0439i	0.548686	+	0.476295i
$751$	31.2080			1.13880			0.569399	−	0.822061i	$-0.307176\pi$
$751$	31.2080			1.13880			0.569399	+	0.822061i	$0.307176\pi$
$752$	11.0787	+	6.39629i	0.403998	+	0.233249i
$753$	−7.22485	−	20.9351i	−0.263288	−	0.762918i
$754$	−0.318166	−	0.635824i	−0.0115869	−	0.0231553i
$755$	13.5590			0.493462
$756$	−2.05428	+	13.5934i	−0.0747133	+	0.494386i
$757$	−0.452106	−	0.783071i	−0.0164321	−	0.0284612i	0.857692	−	0.514163i	$-0.171897\pi$
$757$	−0.452106	−	0.783071i	−0.0164321	−	0.0284612i	−0.874125	+	0.485702i	$0.838564\pi$
$758$	6.26101	−	3.61480i	0.227410	−	0.131295i
$759$	−20.7848	+	7.17298i	−0.754441	+	0.260363i
$760$			5.04260i			0.182914i
$761$	36.2071	−	20.9042i	1.31251	−	0.757776i	0.329996	−	0.943982i	$-0.392953\pi$
$761$	36.2071	−	20.9042i	1.31251	−	0.757776i	0.982511	+	0.186206i	$0.0596193\pi$
$762$	−26.7972	−	5.18947i	−0.970759	−	0.187995i
$763$	20.1554	+	14.4903i	0.729675	+	0.524584i
$764$	−17.9487	+	10.3627i	−0.649363	+	0.374910i
$765$	−12.4067	+	30.8312i	−0.448565	+	1.11471i
$766$	−1.16788	+	0.674277i	−0.0421973	+	0.0243626i
$767$	4.70821	+	0.281093i	0.170004	+	0.0101497i
$768$	1.13542	−	1.30799i	0.0409708	−	0.0471979i
$769$	−10.4819	−	18.1551i	−0.377986	−	0.654691i	0.612783	−	0.790251i	$-0.290050\pi$
$769$	−10.4819	−	18.1551i	−0.377986	−	0.654691i	−0.990769	+	0.135560i	$0.956717\pi$
$770$	−11.0391	−	7.93633i	−0.397822	−	0.286006i
$771$	−24.2366	+	27.9203i	−0.872861	+	1.00552i
$772$	−8.21554	−	4.74324i	−0.295684	−	0.170713i
$773$		−	23.1443i		−	0.832442i	−0.909263	−	0.416221i	$-0.863354\pi$
$773$		−	23.1443i		−	0.832442i	0.909263	−	0.416221i	$-0.136646\pi$
$774$	−31.2343	−	12.5689i	−1.12269	−	0.451780i
$775$	15.3297	−	26.5518i	0.550660	−	0.953770i
$776$	−1.72747	+	2.99206i	−0.0620125	+	0.107409i
$777$	7.31661	−	24.4286i	0.262482	−	0.876369i
$778$	−3.70239	+	2.13758i	−0.132737	+	0.0766358i
$779$	8.99817	+	5.19510i	0.322393	+	0.186134i
$780$	2.45565	+	8.78137i	0.0879262	+	0.314424i
$781$	−18.7841	−	32.5350i	−0.672147	−	1.16419i
$782$			27.3667i			0.978630i
$783$	−1.02335	−	0.0514874i	−0.0365714	−	0.00184001i
$784$	−4.63164	+	5.24861i	−0.165416	+	0.187450i
$785$	27.3642			0.976669
$786$	7.14799	+	20.7124i	0.254960	+	0.738787i
$787$	−32.3033			−1.15149			−0.575743	−	0.817630i	$-0.695287\pi$
$787$	−32.3033			−1.15149			−0.575743	+	0.817630i	$0.695287\pi$
$788$	−3.21420	−	5.56716i	−0.114501	−	0.198322i
$789$	26.0554	−	8.99191i	0.927598	−	0.320121i
$790$	−0.441668	+	0.254997i	−0.0157139	+	0.00907240i
$791$	1.53139	−	15.3063i	0.0544500	−	0.544229i
$792$	9.79510	+	3.94162i	0.348054	+	0.140059i
$793$	−1.61291	−	3.22324i	−0.0572760	−	0.114461i
$794$	−2.86479	−	4.96196i	−0.101668	−	0.176094i
$795$	8.06973	−	9.29623i	0.286204	−	0.329703i
$796$		−	1.26513i		−	0.0448415i
$797$	−6.10975	+	10.5824i	−0.216418	+	0.374848i	−0.953710	−	0.300727i	$-0.902771\pi$
$797$	−6.10975	+	10.5824i	−0.216418	+	0.374848i	0.737292	+	0.675574i	$0.236104\pi$
$798$	3.64800	+	15.4003i	0.129138	+	0.545166i
$799$	84.0560	+	48.5298i	2.97369	+	1.71686i
$800$	−1.43407	−	2.48388i	−0.0507020	−	0.0878184i
$801$	−42.9496	+	6.09719i	−1.51755	+	0.215434i
$802$	−21.9761			−0.776003
$803$	20.7234			0.731312
$804$	9.05200	−	3.12391i	0.319239	−	0.110172i
$805$	−13.8646	−	1.38715i	−0.488663	−	0.0488907i
$806$	34.4676	−	17.2476i	1.21407	−	0.607520i
$807$	−17.5980	+	20.2727i	−0.619480	+	0.713634i
$808$	5.80861	−	10.0608i	0.204346	−	0.353938i
$809$	25.5113	+	14.7289i	0.896929	+	0.517842i	0.876202	−	0.481943i	$-0.160069\pi$
$809$	25.5113	+	14.7289i	0.896929	+	0.517842i	0.0207261	+	0.999785i	$0.493402\pi$
$810$	12.7593	+	3.14352i	0.448316	+	0.110452i
$811$	−36.5632			−1.28391			−0.641954	−	0.766743i	$-0.721876\pi$
$811$	−36.5632			−1.28391			−0.641954	+	0.766743i	$0.721876\pi$
$812$	−0.423610	−	0.304545i	−0.0148658	−	0.0106874i
$813$	17.0274	−	19.6153i	0.597176	−	0.687940i
$814$	−16.9610	−	9.79244i	−0.594483	−	0.343225i
$815$	−1.32779			−0.0465104
$816$	8.61461	−	9.92393i	0.301572	−	0.347407i
$817$	−38.7593			−1.35602
$818$	−8.43899			−0.295062
$819$	13.8524	+	25.0422i	0.484042	+	0.875045i
$820$	4.39267			0.153399
$821$	−23.6479			−0.825317			−0.412658	−	0.910886i	$-0.635400\pi$
$821$	−23.6479			−0.825317			−0.412658	+	0.910886i	$0.635400\pi$
$822$	−1.42106	+	1.63705i	−0.0495653	+	0.0570986i
$823$	14.2248			0.495845			0.247923	−	0.968780i	$-0.420252\pi$
$823$	14.2248			0.495845			0.247923	+	0.968780i	$0.420252\pi$
$824$	16.2249	+	9.36744i	0.565221	+	0.326330i
$825$	11.4613	−	13.2033i	0.399030	−	0.459678i
$826$	3.15473	−	1.42353i	0.109767	−	0.0495308i
$827$	38.3054			1.33201			0.666004	−	0.745948i	$-0.268003\pi$
$827$	38.3054			1.33201			0.666004	+	0.745948i	$0.268003\pi$
$828$	10.7135	−	1.52090i	0.372319	−	0.0528550i
$829$	−18.9848	−	10.9609i	−0.659368	−	0.380687i	0.132668	−	0.991161i	$-0.457646\pi$
$829$	−18.9848	−	10.9609i	−0.659368	−	0.380687i	−0.792036	+	0.610474i	$0.790979\pi$
$830$	−2.72292	+	4.71623i	−0.0945138	+	0.163703i
$831$	−0.816764	+	0.940902i	−0.0283332	+	0.0326395i
$832$	0.214878	−	3.59914i	0.00744957	−	0.124778i
$833$	−35.1411	+	39.8221i	−1.21757	+	1.37975i
$834$	16.4182	−	5.66603i	0.568515	−	0.196198i
$835$	19.6588			0.680320
$836$	12.1549			0.420388
$837$	2.79110	−	55.4750i	0.0964746	−	1.91750i
$838$	−12.4744	−	21.6063i	−0.430920	−	0.746376i
$839$	28.0544	+	16.1972i	0.968547	+	0.559191i	0.898793	−	0.438373i	$-0.144445\pi$
$839$	28.0544	+	16.1972i	0.968547	+	0.559191i	0.0697541	+	0.997564i	$0.477779\pi$
$840$	4.59104	+	4.86739i	0.158406	+	0.167941i
$841$	−14.4806	+	25.0811i	−0.499330	+	0.864864i
$842$			23.2628i			0.801690i
$843$	−8.29363	+	9.55416i	−0.285648	+	0.329063i
$844$	−6.24577	−	10.8180i	−0.214988	−	0.372371i
$845$	15.1922	+	11.3790i	0.522628	+	0.391450i
$846$	14.3270	−	35.6032i	0.492571	−	1.22406i
$847$	−2.14165	+	2.97895i	−0.0735880	+	0.102358i
$848$	−4.21555	+	2.43385i	−0.144763	+	0.0835788i
$849$	24.4361	−	8.43306i	0.838644	−	0.289422i
$850$	−10.8805	−	18.8456i	−0.373199	−	0.646400i
$851$	−20.0717			−0.688050
$852$	6.03145	+	17.4771i	0.206634	+	0.598754i
$853$	14.9608			0.512249			0.256125	−	0.966644i	$-0.417554\pi$
$853$	14.9608			0.512249			0.256125	+	0.966644i	$0.417554\pi$
$854$	−2.14744	−	1.54386i	−0.0734840	−	0.0528297i
$855$	14.9776	−	2.12625i	0.512225	−	0.0727162i
$856$			0.350806i			0.0119903i
$857$	1.02659	+	1.77810i	0.0350675	+	0.0607387i	0.883027	−	0.469323i	$-0.155502\pi$
$857$	1.02659	+	1.77810i	0.0350675	+	0.0607387i	−0.847959	+	0.530062i	$0.822169\pi$
$858$	21.1671	−	5.91921i	0.722632	−	0.202079i
$859$	−45.8673	−	26.4815i	−1.56497	−	0.903536i	−0.996741	−	0.0806667i	$-0.974295\pi$
$859$	−45.8673	−	26.4815i	−1.56497	−	0.903536i	−0.568230	−	0.822870i	$-0.692372\pi$
$860$	−14.1909	+	8.19314i	−0.483907	+	0.279384i
$861$	13.4154	−	3.17781i	0.457195	−	0.108300i
$862$	−11.3685	+	19.6908i	−0.387213	+	0.670672i
$863$	10.0096	−	17.3372i	0.340732	−	0.590165i	−0.643837	−	0.765163i	$-0.722658\pi$
$863$	10.0096	−	17.3372i	0.340732	−	0.590165i	0.984569	+	0.174998i	$0.0559918\pi$
$864$	−4.36376	−	2.82092i	−0.148458	−	0.0959695i
$865$		−	14.8472i		−	0.504820i
$866$	11.9025	+	6.87194i	0.404465	+	0.233518i
$867$	46.0585	−	53.0588i	1.56423	−	1.80197i
$868$	16.5092	−	22.9637i	0.560359	−	0.779437i
$869$	0.614659	+	1.06462i	0.0208509	+	0.0361148i
$870$	−0.326907	+	0.376593i	−0.0110832	+	0.0127677i
$871$	10.9780	−	16.6385i	0.371976	−	0.563774i
$872$	−8.12542	+	4.69121i	−0.275161	+	0.158864i
$873$	9.61549	+	3.86934i	0.325435	+	0.130957i
$874$	10.7882	−	6.22855i	0.364915	−	0.210684i
$875$	27.7049	−	12.5014i	0.936598	−	0.422626i
$876$	−10.0126	−	1.93902i	−0.338296	−	0.0655135i
$877$	−0.209887	+	0.121178i	−0.00708737	+	0.00409190i	−0.503540	−	0.863972i	$-0.667969\pi$
$877$	−0.209887	+	0.121178i	−0.00708737	+	0.00409190i	0.496452	+	0.868064i	$0.334636\pi$
$878$			12.1761i			0.410924i
$879$	−24.7964	+	8.55742i	−0.836363	+	0.288635i
$880$	4.45029	−	2.56938i	0.150019	−	0.0866137i
$881$	−13.7225	−	23.7681i	−0.462323	−	0.800768i	0.536753	−	0.843740i	$-0.319651\pi$
$881$	−13.7225	−	23.7681i	−0.462323	−	0.800768i	−0.999076	+	0.0429719i	$0.986317\pi$
$882$	17.5425	+	11.5439i	0.590686	+	0.388703i
$883$	13.7372			0.462293			0.231146	−	0.972919i	$-0.425752\pi$
$883$	13.7372			0.462293			0.231146	+	0.972919i	$0.425752\pi$
$884$	1.63032	−	27.3073i	0.0548336	−	0.918445i
$885$	−1.07924	−	3.12725i	−0.0362781	−	0.105121i
$886$	−1.94173	−	1.12106i	−0.0652336	−	0.0376626i
$887$	−50.7830			−1.70513			−0.852563	−	0.522625i	$-0.824953\pi$
$887$	−50.7830			−1.70513			−0.852563	+	0.522625i	$0.824953\pi$
$888$	7.27857	+	6.31827i	0.244253	+	0.212027i
$889$	−24.3380	+	33.8532i	−0.816271	+	1.13540i
$890$	−10.5565	+	18.2844i	−0.353855	+	0.612894i
$891$	7.57729	−	30.7556i	0.253849	−	1.03035i
$892$	−3.78556	−	6.55677i	−0.126750	−	0.219537i
$893$		−	44.1807i		−	1.47845i
$894$	5.52006	+	1.06900i	0.184618	+	0.0357528i
$895$	−6.23477	−	10.7989i	−0.208405	−	0.360969i
$896$	−1.08820	−	2.41160i	−0.0363542	−	0.0805659i
$897$	15.7537	−	16.1002i	0.526001	−	0.537571i
$898$	3.91929	−	6.78842i	0.130789	−	0.226532i
$899$	1.82551	+	1.05396i	0.0608842	+	0.0351515i
$900$	−6.77298	+	5.30684i	−0.225766	+	0.176895i
$901$	−31.9842	+	18.4661i	−1.06555	+	0.615194i
$902$		−	10.5883i		−	0.352552i
$903$	−37.4125	+	35.2884i	−1.24501	+	1.17433i
$904$	5.03517	+	2.90706i	0.167467	+	0.0966873i
$905$	−18.5986	+	32.2137i	−0.618237	+	1.07082i
$906$	−3.05807	+	15.7911i	−0.101598	+	0.524625i
$907$	−8.93711	+	15.4795i	−0.296752	+	0.513990i	−0.975391	−	0.220483i	$-0.929237\pi$
$907$	−8.93711	+	15.4795i	−0.296752	+	0.513990i	0.678639	+	0.734472i	$0.262570\pi$
$908$		−	25.4572i		−	0.844826i
$909$	−32.3321	−	13.0106i	−1.07239	−	0.431536i
$910$	13.7519	+	2.21010i	0.455871	+	0.0732642i
$911$		−	43.8367i		−	1.45238i	−0.687496	−	0.726188i	$-0.741290\pi$
$911$		−	43.8367i		−	1.45238i	0.687496	−	0.726188i	$-0.258710\pi$
$912$	−5.87274	−	1.13730i	−0.194466	−	0.0376598i
$913$	11.3682	+	6.56345i	0.376234	+	0.217219i
$914$			6.54295i			0.216421i
$915$	−1.65722	+	1.90910i	−0.0547860	+	0.0631129i
$916$	5.51406	−	9.55063i	0.182190	−	0.315562i
$917$	33.3035	+	3.33201i	1.09978	+	0.110033i
$918$	−33.1087	−	21.4028i	−1.09275	−	0.706397i
$919$	−26.8620	−	46.5264i	−0.886096	−	1.53476i	−0.844453	−	0.535630i	$-0.820074\pi$
$919$	−26.8620	−	46.5264i	−0.886096	−	1.53476i	−0.0416430	−	0.999133i	$-0.513259\pi$
$920$	2.63325	−	4.56092i	0.0868156	−	0.150369i
$921$	0.328458	−	0.378379i	0.0108230	−	0.0124680i
$922$	−20.3030	−	11.7219i	−0.668644	−	0.386042i
$923$	32.1246	+	21.1957i	1.05739	+	0.697664i
$924$	11.7326	−	11.0665i	0.385974	−	0.364061i
$925$	13.8221	−	7.98018i	0.454467	−	0.262387i
$926$			37.3356i			1.22692i
$927$	20.9820	−	52.1413i	0.689140	−	1.71255i
$928$	0.170773	−	0.0985961i	0.00560591	−	0.00323657i
$929$	6.58944	−	3.80441i	0.216193	−	0.124819i	−0.387994	−	0.921662i	$-0.626832\pi$
$929$	6.58944	−	3.80441i	0.216193	−	0.124819i	0.604186	+	0.796843i	$0.293498\pi$
$930$	−20.4149	−	17.7215i	−0.669431	−	0.581110i
$931$	23.6962	+	4.78954i	0.776611	+	0.156971i
$932$	6.18721	+	3.57219i	0.202669	+	0.117011i
$933$	20.3024	+	3.93172i	0.664672	+	0.128719i
$934$	3.36611	−	5.83027i	0.110142	−	0.190772i
$935$	33.7652	−	19.4943i	1.10424	−	0.637532i
$936$	−10.7808	+	0.879368i	−0.352383	+	0.0287430i
$937$			25.7440i			0.841020i	0.907288	+	0.420510i	$0.138149\pi$
$937$			25.7440i			0.841020i	−0.907288	+	0.420510i	$0.861851\pi$
$938$	1.45620	−	14.5547i	0.0475466	−	0.475229i
$939$	−15.0358	+	5.18896i	−0.490675	+	0.169335i
$940$	−9.33916	−	16.1759i	−0.304610	−	0.527599i
$941$	17.8743	−	10.3197i	0.582684	−	0.336413i	−0.179515	−	0.983755i	$-0.557453\pi$
$941$	17.8743	−	10.3197i	0.582684	−	0.336413i	0.762199	+	0.647342i	$0.224120\pi$
$942$	−6.17167	+	31.8690i	−0.201084	+	1.03835i
$943$	−5.42576	−	9.39769i	−0.176687	−	0.306031i
$944$			1.30815i			0.0425766i
$945$	12.5214	−	15.6888i	0.407320	−	0.510356i
$946$	19.7492	+	34.2066i	0.642101	+	1.11215i
$947$	−60.7640			−1.97456			−0.987282	−	0.158978i	$-0.949180\pi$
$947$	−60.7640			−1.97456			−0.987282	+	0.158978i	$0.949180\pi$
$948$	−0.197363	−	0.571890i	−0.00641006	−	0.0185741i
$949$	−18.9858	+	9.50050i	−0.616307	+	0.308399i
$950$	−4.95273	+	8.57838i	−0.160688	+	0.278319i
$951$	−13.0096	−	37.6973i	−0.421865	−	1.22242i
$952$	−8.25637	−	18.2972i	−0.267590	−	0.593017i
$953$	−3.76601	−	2.17431i	−0.121993	−	0.0704328i	0.437762	−	0.899091i	$-0.355771\pi$
$953$	−3.76601	−	2.17431i	−0.121993	−	0.0704328i	−0.559755	+	0.828658i	$0.689105\pi$
$954$	9.00659	+	11.4949i	0.291599	+	0.372160i
$955$	30.2610			0.979223
$956$	−7.32463			−0.236896
$957$	0.907760	+	0.787994i	0.0293437	+	0.0254722i
$958$	11.2141	+	6.47445i	0.362310	+	0.209180i
$959$	1.36197	+	3.01831i	0.0439803	+	0.0974663i
$960$	−2.39060	+	0.825011i	−0.0771562	+	0.0266271i
$961$	−41.6345	+	72.1131i	−1.34305	+	2.32623i
$962$	20.0282	+	1.19574i	0.645735	+	0.0385521i
$963$	1.04197	−	0.147920i	0.0335770	−	0.00476665i
$964$	17.4268			0.561280
$965$	6.92556	+	11.9954i	0.222942	+	0.386146i
$966$	4.74252	−	15.8342i	0.152588	−	0.509458i
$967$		−	34.3376i		−	1.10422i	−0.833771	−	0.552111i	$-0.813823\pi$
$967$		−	34.3376i		−	1.10422i	0.833771	−	0.552111i	$-0.186177\pi$
$968$	−0.693357	−	1.20093i	−0.0222853	−	0.0385993i
$969$	−44.5575	−	8.62891i	−1.43139	−	0.277200i
$970$	4.36868	−	2.52226i	0.140270	−	0.0809849i
$971$	−0.620174	−	1.07417i	−0.0199023	−	0.0344718i	0.855903	−	0.517137i	$-0.173002\pi$
$971$	−0.620174	−	1.07417i	−0.0199023	−	0.0344718i	−0.875805	+	0.482665i	$0.839669\pi$
$972$	−6.53873	+	14.1508i	−0.209730	+	0.453887i
$973$	2.64120	−	26.3988i	0.0846729	−	0.846308i
$974$			8.67630i			0.278007i
$975$	−4.44737	+	17.3506i	−0.142430	+	0.555663i
$976$	0.865717	−	0.499822i	0.0277109	−	0.0159989i
$977$	0.286041	−	0.495437i	0.00915126	−	0.0158504i	−0.861414	−	0.507904i	$-0.830420\pi$
$977$	0.286041	−	0.495437i	0.00915126	−	0.0158504i	0.870565	+	0.492054i	$0.163754\pi$
$978$	0.299467	−	1.54638i	0.00957591	−	0.0494476i
$979$	44.0736	+	25.4459i	1.40860	+	0.813255i
$980$	9.68832	−	3.25543i	0.309482	−	0.103991i
$981$	17.3601	+	22.1562i	0.554264	+	0.707393i
$982$	−14.7725	+	8.52893i	−0.471411	+	0.272169i
$983$	−6.05482	+	3.49575i	−0.193119	+	0.111497i	−0.593442	−	0.804877i	$-0.702231\pi$
$983$	−6.05482	+	3.49575i	−0.193119	+	0.111497i	0.400323	+	0.916374i	$0.368898\pi$
$984$	−0.990716	+	5.11581i	−0.0315829	+	0.163086i
$985$			9.38605i			0.299064i
$986$	1.29569	−	0.748066i	0.0412631	−	0.0238233i
$987$	−40.2244	−	42.6456i	−1.28036	−	1.35742i
$988$	−11.1358	+	5.57236i	−0.354278	+	0.177280i
$989$	35.0569	+	20.2401i	1.11474	+	0.643598i
$990$	−9.50811	−	12.1349i	−0.302188	−	0.385674i
$991$	21.3759	−	37.0241i	0.679028	−	1.17611i	−0.296247	−	0.955112i	$-0.595735\pi$
$991$	21.3759	−	37.0241i	0.679028	−	1.17611i	0.975274	−	0.220999i	$-0.0709317\pi$
$992$	5.34484	+	9.25753i	0.169699	+	0.293927i
$993$	−7.79436	+	40.2482i	−0.247347	+	1.27724i
$994$	28.1014	+	2.81154i	0.891323	+	0.0891766i
$995$	−0.923605	+	1.59973i	−0.0292803	+	0.0507149i
$996$	−4.87851	−	4.23487i	−0.154582	−	0.134187i
$997$		−	8.93718i		−	0.283043i	−0.989935	−	0.141522i	$-0.954800\pi$
$997$		−	8.93718i		−	0.283043i	0.989935	−	0.141522i	$-0.0451995\pi$
$998$	20.1546	+	11.6362i	0.637982	+	0.368339i
$999$	15.6976	−	24.2831i	0.496650	−	0.768283i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bi.f.257.13	yes	34
3.2	odd	2		546.2.bi.e.257.7	yes	34
7.3	odd	6		546.2.bn.e.101.16	yes	34
13.4	even	6		546.2.bn.f.173.2	yes	34
21.17	even	6		546.2.bn.f.101.2	yes	34
39.17	odd	6		546.2.bn.e.173.16	yes	34
91.17	odd	6		546.2.bi.e.17.7	✓	34
273.17	even	6	inner	546.2.bi.f.17.13	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.7	✓	34	91.17	odd	6
546.2.bi.e.257.7	yes	34	3.2	odd	2
546.2.bi.f.17.13	yes	34	273.17	even	6	inner
546.2.bi.f.257.13	yes	34	1.1	even	1	trivial
546.2.bn.e.101.16	yes	34	7.3	odd	6
546.2.bn.e.173.16	yes	34	39.17	odd	6
546.2.bn.f.101.2	yes	34	21.17	even	6
546.2.bn.f.173.2	yes	34	13.4	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.13542 - 1.30799i) q^{3} +1.00000 q^{4} +(-1.26448 - 0.730045i) q^{5} +(1.13542 - 1.30799i) q^{6} +(-1.08820 - 2.41160i) q^{7} +1.00000 q^{8} +(-0.421657 - 2.97022i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.13542 - 1.30799i) q^{3} +1.00000 q^{4} +(-1.26448 - 0.730045i) q^{5} +(1.13542 - 1.30799i) q^{6} +(-1.08820 - 2.41160i) q^{7} +1.00000 q^{8} +(-0.421657 - 2.97022i) q^{9} +(-1.26448 - 0.730045i) q^{10} +(-1.75974 + 3.04796i) q^{11} +(1.13542 - 1.30799i) q^{12} +(0.214878 - 3.59914i) q^{13} +(-1.08820 - 2.41160i) q^{14} +(-2.39060 + 0.825011i) q^{15} +1.00000 q^{16} +7.58718 q^{17} +(-0.421657 - 2.97022i) q^{18} +(-1.72681 - 2.99093i) q^{19} +(-1.26448 - 0.730045i) q^{20} +(-4.38990 - 1.31482i) q^{21} +(-1.75974 + 3.04796i) q^{22} +3.60696i q^{23} +(1.13542 - 1.30799i) q^{24} +(-1.43407 - 2.48388i) q^{25} +(0.214878 - 3.59914i) q^{26} +(-4.36376 - 2.82092i) q^{27} +(-1.08820 - 2.41160i) q^{28} +(0.170773 - 0.0985961i) q^{29} +(-2.39060 + 0.825011i) q^{30} +(5.34484 + 9.25753i) q^{31} +1.00000 q^{32} +(1.98865 + 5.76241i) q^{33} +7.58718 q^{34} +(-0.384576 + 3.84385i) q^{35} +(-0.421657 - 2.97022i) q^{36} +5.56471i q^{37} +(-1.72681 - 2.99093i) q^{38} +(-4.46365 - 4.36759i) q^{39} +(-1.26448 - 0.730045i) q^{40} +(-2.60543 + 1.50425i) q^{41} +(-4.38990 - 1.31482i) q^{42} +(5.61139 - 9.71922i) q^{43} +(-1.75974 + 3.04796i) q^{44} +(-1.63522 + 4.06360i) q^{45} +3.60696i q^{46} +(11.0787 + 6.39629i) q^{47} +(1.13542 - 1.30799i) q^{48} +(-4.63164 + 5.24861i) q^{49} +(-1.43407 - 2.48388i) q^{50} +(8.61461 - 9.92393i) q^{51} +(0.214878 - 3.59914i) q^{52} +(-4.21555 + 2.43385i) q^{53} +(-4.36376 - 2.82092i) q^{54} +(4.45029 - 2.56938i) q^{55} +(-1.08820 - 2.41160i) q^{56} +(-5.87274 - 1.13730i) q^{57} +(0.170773 - 0.0985961i) q^{58} +1.30815i q^{59} +(-2.39060 + 0.825011i) q^{60} +(0.865717 - 0.499822i) q^{61} +(5.34484 + 9.25753i) q^{62} +(-6.70414 + 4.24906i) q^{63} +1.00000 q^{64} +(-2.89925 + 4.39416i) q^{65} +(1.98865 + 5.76241i) q^{66} +(4.78794 + 2.76432i) q^{67} +7.58718 q^{68} +(4.71786 + 4.09541i) q^{69} +(-0.384576 + 3.84385i) q^{70} +(-5.33718 + 9.24427i) q^{71} +(-0.421657 - 2.97022i) q^{72} +(-2.94410 - 5.09933i) q^{73} +5.56471i q^{74} +(-4.87714 - 0.944496i) q^{75} +(-1.72681 - 2.99093i) q^{76} +(9.26540 + 0.927001i) q^{77} +(-4.46365 - 4.36759i) q^{78} +(0.174645 - 0.302494i) q^{79} +(-1.26448 - 0.730045i) q^{80} +(-8.64441 + 2.50483i) q^{81} +(-2.60543 + 1.50425i) q^{82} -3.72979i q^{83} +(-4.38990 - 1.31482i) q^{84} +(-9.59380 - 5.53898i) q^{85} +(5.61139 - 9.71922i) q^{86} +(0.0649367 - 0.335317i) q^{87} +(-1.75974 + 3.04796i) q^{88} -14.4601i q^{89} +(-1.63522 + 4.06360i) q^{90} +(-8.91353 + 3.39839i) q^{91} +3.60696i q^{92} +(18.1773 + 3.52018i) q^{93} +(11.0787 + 6.39629i) q^{94} +5.04260i q^{95} +(1.13542 - 1.30799i) q^{96} +(-1.72747 + 2.99206i) q^{97} +(-4.63164 + 5.24861i) q^{98} +(9.79510 + 3.94162i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9}+O(q^{10}) \) 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9	\( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20} - 7 q^{21} + 9 q^{22} + 6 q^{24} + 16 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} + 27 q^{29} - 17 q^{30} - q^{31} + 34 q^{32} + 12 q^{34} - 3 q^{35} + 4 q^{36} - 5 q^{38} - 10 q^{39} + 9 q^{40} - 3 q^{41} - 7 q^{42} - 3 q^{43} + 9 q^{44} + 9 q^{45} - 27 q^{47} + 6 q^{48} - 2 q^{49} + 16 q^{50} - 36 q^{51} + 8 q^{52} - 21 q^{53} - 18 q^{54} - 57 q^{55} + 4 q^{56} - 17 q^{57} + 27 q^{58} - 17 q^{60} - 51 q^{61} - q^{62} - 24 q^{63} + 34 q^{64} - 21 q^{65} - 21 q^{67} + 12 q^{68} + 30 q^{69} - 3 q^{70} - 15 q^{71} + 4 q^{72} - 19 q^{73} - 54 q^{75} - 5 q^{76} + 9 q^{77} - 10 q^{78} - 9 q^{79} + 9 q^{80} + 28 q^{81} - 3 q^{82} - 7 q^{84} - 42 q^{85} - 3 q^{86} - 81 q^{87} + 9 q^{88} + 9 q^{90} - 72 q^{91} - 17 q^{93} - 27 q^{94} + 6 q^{96} + 19 q^{97} - 2 q^{98} - 27 q^{99}+O(q^{100}) \) 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9 + 9 * q^10 + 9 * q^11 + 6 * q^12 + 8 * q^13 + 4 * q^14 - 17 * q^15 + 34 * q^16 + 12 * q^17 + 4 * q^18 - 5 * q^19 + 9 * q^20 - 7 * q^21 + 9 * q^22 + 6 * q^24 + 16 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 + 27 * q^29 - 17 * q^30 - q^31 + 34 * q^32 + 12 * q^34 - 3 * q^35 + 4 * q^36 - 5 * q^38 - 10 * q^39 + 9 * q^40 - 3 * q^41 - 7 * q^42 - 3 * q^43 + 9 * q^44 + 9 * q^45 - 27 * q^47 + 6 * q^48 - 2 * q^49 + 16 * q^50 - 36 * q^51 + 8 * q^52 - 21 * q^53 - 18 * q^54 - 57 * q^55 + 4 * q^56 - 17 * q^57 + 27 * q^58 - 17 * q^60 - 51 * q^61 - q^62 - 24 * q^63 + 34 * q^64 - 21 * q^65 - 21 * q^67 + 12 * q^68 + 30 * q^69 - 3 * q^70 - 15 * q^71 + 4 * q^72 - 19 * q^73 - 54 * q^75 - 5 * q^76 + 9 * q^77 - 10 * q^78 - 9 * q^79 + 9 * q^80 + 28 * q^81 - 3 * q^82 - 7 * q^84 - 42 * q^85 - 3 * q^86 - 81 * q^87 + 9 * q^88 + 9 * q^90 - 72 * q^91 - 17 * q^93 - 27 * q^94 + 6 * q^96 + 19 * q^97 - 2 * q^98 - 27 * q^99

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