LMFDB - Embedded newform 115.2.g.a.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(6,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("115.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.g (of order $11$, degree $10$, 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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			16.1
Root			$-0.841254 - 0.540641i$ of defining polynomial
Character	$\chi$	$=$	115.16
Dual form			115.2.g.a.36.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.57028 - 1.81219i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.533654 - 3.71165i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(-0.341254 + 2.37347i) q^{6} +(1.31718 - 0.386758i) q^{7} +(-3.52977 - 2.26844i) q^{8} +(-0.830830 + 1.81926i) q^{9} +O(q^{10})$	\(q+(1.57028 - 1.81219i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.533654 - 3.71165i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(-0.341254 + 2.37347i) q^{6} +(1.31718 - 0.386758i) q^{7} +(-3.52977 - 2.26844i) q^{8} +(-0.830830 + 1.81926i) q^{9} +(-2.30075 - 0.675560i) q^{10} +(1.49103 + 1.72073i) q^{11} +(2.45561 + 2.83392i) q^{12} +(-0.817178 - 0.239945i) q^{13} +(1.36745 - 2.99430i) q^{14} +(0.841254 + 0.540641i) q^{15} +(-2.45773 + 0.721655i) q^{16} +(-0.581014 + 4.04104i) q^{17} +(1.99223 + 4.36237i) q^{18} +(0.384487 + 2.67417i) q^{19} +(-3.15455 + 2.02730i) q^{20} +(-0.898983 + 1.03748i) q^{21} +5.45963 q^{22} +(-1.93440 - 4.38840i) q^{23} +4.19584 q^{24} +(-0.654861 + 0.755750i) q^{25} +(-1.71802 + 1.10411i) q^{26} +(-0.711574 - 4.94911i) q^{27} +(-2.13843 - 4.68251i) q^{28} +(-0.951362 + 6.61687i) q^{29} +(2.30075 - 0.675560i) q^{30} +(-8.68043 - 5.57857i) q^{31} +(0.934499 - 2.04627i) q^{32} +(-2.18463 - 0.641465i) q^{33} +(6.41080 + 7.39846i) q^{34} +(-0.898983 - 1.03748i) q^{35} +(7.19584 + 2.11289i) q^{36} +(4.36764 - 9.56379i) q^{37} +(5.44986 + 3.50241i) q^{38} +(0.817178 - 0.239945i) q^{39} +(-0.597131 + 4.15314i) q^{40} +(2.86653 + 6.27683i) q^{41} +(0.468468 + 3.25827i) q^{42} +(5.91232 - 3.79962i) q^{43} +(5.59107 - 6.45244i) q^{44} +2.00000 q^{45} +(-10.9902 - 3.38549i) q^{46} -8.71406 q^{47} +(1.67742 - 1.93584i) q^{48} +(-4.30340 + 2.76563i) q^{49} +(0.341254 + 2.37347i) q^{50} +(-1.69597 - 3.71366i) q^{51} +(-0.454501 + 3.16113i) q^{52} +(-6.55432 + 1.92452i) q^{53} +(-10.0861 - 6.48195i) q^{54} +(0.945841 - 2.07110i) q^{55} +(-5.52667 - 1.62278i) q^{56} +(-1.76921 - 2.04178i) q^{57} +(10.4972 + 12.1144i) q^{58} +(-2.60598 - 0.765186i) q^{59} +(1.55773 - 3.41095i) q^{60} +(0.764538 + 0.491338i) q^{61} +(-23.7401 + 6.97073i) q^{62} +(-0.390736 + 2.71763i) q^{63} +(-4.36897 - 9.56672i) q^{64} +(0.121206 + 0.843008i) q^{65} +(-4.59293 + 2.95170i) q^{66} +(6.49469 - 7.49528i) q^{67} +15.3090 q^{68} +(3.99987 + 2.64594i) q^{69} -3.29177 q^{70} +(-1.29740 + 1.49728i) q^{71} +(7.05954 - 4.53689i) q^{72} +(1.15457 + 8.03022i) q^{73} +(-10.4731 - 22.9328i) q^{74} +(0.142315 - 0.989821i) q^{75} +(9.72038 - 2.85416i) q^{76} +(2.62945 + 1.68985i) q^{77} +(0.848368 - 1.85767i) q^{78} +(14.1009 + 4.14039i) q^{79} +(1.67742 + 1.93584i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(15.8761 + 4.66164i) q^{82} +(-0.727055 + 1.59203i) q^{83} +(4.33052 + 2.78305i) q^{84} +(3.91722 - 1.15020i) q^{85} +(2.39833 - 16.6807i) q^{86} +(-2.77701 - 6.08081i) q^{87} +(-1.35958 - 9.45610i) q^{88} +(4.47262 - 2.87438i) q^{89} +(3.14055 - 3.62439i) q^{90} -1.16917 q^{91} +(-15.2559 + 9.52171i) q^{92} +10.3184 q^{93} +(-13.6835 + 15.7916i) q^{94} +(2.27279 - 1.46063i) q^{95} +(0.320145 + 2.22666i) q^{96} +(4.52967 + 9.91860i) q^{97} +(-1.74567 + 12.1414i) q^{98} +(-4.36926 + 1.28293i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{2} + q^{3} - q^{4} + q^{5} + 6 q^{6} + 5 q^{7} - 16 q^{8} + 2 q^{9}+O(q^{10}) $ 10 * q + 5 * q^2 + q^3 - q^4 + q^5 + 6 * q^6 + 5 * q^7 - 16 * q^8 + 2 * q^9	\( 10 q + 5 q^{2} + q^{3} - q^{4} + q^{5} + 6 q^{6} + 5 q^{7} - 16 q^{8} + 2 q^{9} - 5 q^{10} + 8 q^{11} + q^{12} - 3 q^{14} - q^{15} + 5 q^{16} - 23 q^{17} - 10 q^{18} - 13 q^{19} + q^{20} + 6 q^{21} + 4 q^{22} - 21 q^{23} - 6 q^{24} - q^{25} + 11 q^{26} - 5 q^{27} - 6 q^{28} + 2 q^{29} + 5 q^{30} - 20 q^{31} - 15 q^{32} + 3 q^{33} + 16 q^{34} + 6 q^{35} + 24 q^{36} + 13 q^{37} + 21 q^{38} - 6 q^{40} - 5 q^{41} + 3 q^{42} + 15 q^{43} + 19 q^{44} + 20 q^{45} - 16 q^{46} - 52 q^{47} + 6 q^{48} + 4 q^{49} - 6 q^{50} - 10 q^{51} + 22 q^{52} + 6 q^{53} - 30 q^{54} + 3 q^{55} + 3 q^{56} + 2 q^{57} + 45 q^{58} + 5 q^{59} + 10 q^{60} - 3 q^{61} - 54 q^{62} - 10 q^{63} - 34 q^{64} - 4 q^{66} + 20 q^{67} + 32 q^{68} - q^{69} - 8 q^{70} - 22 q^{71} + 32 q^{72} + 43 q^{73} + q^{74} + q^{75} - 2 q^{76} + 4 q^{77} + 11 q^{78} + 51 q^{79} + 6 q^{80} - q^{81} + 58 q^{82} - 17 q^{83} + 6 q^{84} + q^{85} - 9 q^{86} - 2 q^{87} + 7 q^{88} + 57 q^{89} + 10 q^{90} - 22 q^{91} - 43 q^{92} + 20 q^{93} - 81 q^{94} - 9 q^{95} - 7 q^{96} + 52 q^{97} + 24 q^{98} + 6 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 + q^3 - q^4 + q^5 + 6 * q^6 + 5 * q^7 - 16 * q^8 + 2 * q^9 - 5 * q^10 + 8 * q^11 + q^12 - 3 * q^14 - q^15 + 5 * q^16 - 23 * q^17 - 10 * q^18 - 13 * q^19 + q^20 + 6 * q^21 + 4 * q^22 - 21 * q^23 - 6 * q^24 - q^25 + 11 * q^26 - 5 * q^27 - 6 * q^28 + 2 * q^29 + 5 * q^30 - 20 * q^31 - 15 * q^32 + 3 * q^33 + 16 * q^34 + 6 * q^35 + 24 * q^36 + 13 * q^37 + 21 * q^38 - 6 * q^40 - 5 * q^41 + 3 * q^42 + 15 * q^43 + 19 * q^44 + 20 * q^45 - 16 * q^46 - 52 * q^47 + 6 * q^48 + 4 * q^49 - 6 * q^50 - 10 * q^51 + 22 * q^52 + 6 * q^53 - 30 * q^54 + 3 * q^55 + 3 * q^56 + 2 * q^57 + 45 * q^58 + 5 * q^59 + 10 * q^60 - 3 * q^61 - 54 * q^62 - 10 * q^63 - 34 * q^64 - 4 * q^66 + 20 * q^67 + 32 * q^68 - q^69 - 8 * q^70 - 22 * q^71 + 32 * q^72 + 43 * q^73 + q^74 + q^75 - 2 * q^76 + 4 * q^77 + 11 * q^78 + 51 * q^79 + 6 * q^80 - q^81 + 58 * q^82 - 17 * q^83 + 6 * q^84 + q^85 - 9 * q^86 - 2 * q^87 + 7 * q^88 + 57 * q^89 + 10 * q^90 - 22 * q^91 - 43 * q^92 + 20 * q^93 - 81 * q^94 - 9 * q^95 - 7 * q^96 + 52 * q^97 + 24 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	1.57028	−	1.81219i	1.11035	−	1.28142i	0.154363	−	0.988014i	$-0.450667\pi$
$2$	1.57028	−	1.81219i	1.11035	−	1.28142i	0.955989	−	0.293401i	$-0.0947871\pi$
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i	−0.760473	−	0.649369i	$-0.775033\pi$
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i	0.274775	+	0.961508i	$0.411397\pi$
$4$	−0.533654	−	3.71165i	−0.266827	−	1.85582i
$5$	−0.415415	−	0.909632i	−0.185779	−	0.406800i
$5$	−0.415415	−	0.909632i	−0.185779	−	0.406800i
$6$	−0.341254	+	2.37347i	−0.139316	+	0.968965i
$7$	1.31718	−	0.386758i	0.497847	−	0.146181i	−0.0231631	−	0.999732i	$-0.507374\pi$
$7$	1.31718	−	0.386758i	0.497847	−	0.146181i	0.521010	+	0.853551i	$0.325556\pi$
$8$	−3.52977	−	2.26844i	−1.24796	−	0.802016i
$9$	−0.830830	+	1.81926i	−0.276943	+	0.606421i
$10$	−2.30075	−	0.675560i	−0.727560	−	0.213631i
$11$	1.49103	+	1.72073i	0.449561	+	0.518821i	0.934614	−	0.355664i	$-0.115745\pi$
$11$	1.49103	+	1.72073i	0.449561	+	0.518821i	−0.485053	+	0.874485i	$0.661200\pi$
$12$	2.45561	+	2.83392i	0.708873	+	0.818083i
$13$	−0.817178	−	0.239945i	−0.226644	−	0.0665488i	0.166438	−	0.986052i	$-0.446773\pi$
$13$	−0.817178	−	0.239945i	−0.226644	−	0.0665488i	−0.393083	+	0.919503i	$0.628591\pi$
$14$	1.36745	−	2.99430i	0.365467	−	0.800261i
$15$	0.841254	+	0.540641i	0.217211	+	0.139593i
$16$	−2.45773	+	0.721655i	−0.614432	+	0.180414i
$17$	−0.581014	+	4.04104i	−0.140917	+	0.980097i	0.789541	+	0.613698i	$0.210319\pi$
$17$	−0.581014	+	4.04104i	−0.140917	+	0.980097i	−0.930458	+	0.366399i	$0.880591\pi$
$18$	1.99223	+	4.36237i	0.469573	+	1.02822i
$19$	0.384487	+	2.67417i	0.0882074	+	0.613496i	0.985195	+	0.171439i	$0.0548418\pi$
$19$	0.384487	+	2.67417i	0.0882074	+	0.613496i	−0.896987	+	0.442056i	$0.854249\pi$
$20$	−3.15455	+	2.02730i	−0.705378	+	0.453319i
$21$	−0.898983	+	1.03748i	−0.196174	+	0.226397i
$22$	5.45963			1.16400
$23$	−1.93440	−	4.38840i	−0.403351	−	0.915046i
$23$	−1.93440	−	4.38840i	−0.403351	−	0.915046i
$24$	4.19584			0.856473
$25$	−0.654861	+	0.755750i	−0.130972	+	0.151150i
$26$	−1.71802	+	1.10411i	−0.336932	+	0.216533i
$27$	−0.711574	−	4.94911i	−0.136943	−	0.952456i
$28$	−2.13843	−	4.68251i	−0.404125	−	0.884911i
$29$	−0.951362	+	6.61687i	−0.176664	+	1.22872i	0.687753	+	0.725945i	$0.258597\pi$
$29$	−0.951362	+	6.61687i	−0.176664	+	1.22872i	−0.864416	+	0.502777i	$0.832312\pi$
$30$	2.30075	−	0.675560i	0.420057	−	0.123340i
$31$	−8.68043	−	5.57857i	−1.55905	−	1.00194i	−0.982801	−	0.184668i	$-0.940879\pi$
$31$	−8.68043	−	5.57857i	−1.55905	−	1.00194i	−0.576250	−	0.817273i	$-0.695485\pi$
$32$	0.934499	−	2.04627i	0.165198	−	0.361732i
$33$	−2.18463	−	0.641465i	−0.380295	−	0.111665i
$34$	6.41080	+	7.39846i	1.09944	+	1.26883i
$35$	−0.898983	−	1.03748i	−0.151956	−	0.175366i
$36$	7.19584	+	2.11289i	1.19931	+	0.352148i
$37$	4.36764	−	9.56379i	0.718035	−	1.57228i	−0.0986020	−	0.995127i	$-0.531437\pi$
$37$	4.36764	−	9.56379i	0.718035	−	1.57228i	0.816637	−	0.577151i	$-0.195836\pi$
$38$	5.44986	+	3.50241i	0.884084	+	0.568166i
$39$	0.817178	−	0.239945i	0.130853	−	0.0384220i
$40$	−0.597131	+	4.15314i	−0.0944147	+	0.656669i
$41$	2.86653	+	6.27683i	0.447677	+	0.980276i	0.990125	+	0.140187i	$0.0447703\pi$
$41$	2.86653	+	6.27683i	0.447677	+	0.980276i	−0.542448	+	0.840089i	$0.682502\pi$
$42$	0.468468	+	3.25827i	0.0722862	+	0.502761i
$43$	5.91232	−	3.79962i	0.901620	−	0.579436i	−0.00564997	−	0.999984i	$-0.501798\pi$
$43$	5.91232	−	3.79962i	0.901620	−	0.579436i	0.907270	+	0.420548i	$0.138162\pi$
$44$	5.59107	−	6.45244i	0.842885	−	0.972742i
$45$	2.00000			0.298142
$46$	−10.9902	−	3.38549i	−1.62041	−	0.499164i
$47$	−8.71406			−1.27108			−0.635538	−	0.772070i	$-0.719222\pi$
$47$	−8.71406			−1.27108			−0.635538	+	0.772070i	$0.719222\pi$
$48$	1.67742	−	1.93584i	0.242114	−	0.279415i
$49$	−4.30340	+	2.76563i	−0.614771	+	0.395089i
$50$	0.341254	+	2.37347i	0.0482605	+	0.335659i
$51$	−1.69597	−	3.71366i	−0.237484	−	0.520016i
$52$	−0.454501	+	3.16113i	−0.0630280	+	0.438369i
$53$	−6.55432	+	1.92452i	−0.900305	+	0.264353i	−0.698955	−	0.715166i	$-0.746351\pi$
$53$	−6.55432	+	1.92452i	−0.900305	+	0.264353i	−0.201350	+	0.979519i	$0.564533\pi$
$54$	−10.0861	−	6.48195i	−1.37255	−	0.882082i
$55$	0.945841	−	2.07110i	0.127537	−	0.279267i
$56$	−5.52667	−	1.62278i	−0.738533	−	0.216853i
$57$	−1.76921	−	2.04178i	−0.234338	−	0.270441i
$58$	10.4972	+	12.1144i	1.37834	+	1.59069i
$59$	−2.60598	−	0.765186i	−0.339270	−	0.0996187i	0.107660	−	0.994188i	$-0.465664\pi$
$59$	−2.60598	−	0.765186i	−0.339270	−	0.0996187i	−0.446930	+	0.894569i	$0.647483\pi$
$60$	1.55773	−	3.41095i	0.201102	−	0.440352i
$61$	0.764538	+	0.491338i	0.0978890	+	0.0629094i	0.588670	−	0.808374i	$-0.299652\pi$
$61$	0.764538	+	0.491338i	0.0978890	+	0.0629094i	−0.490781	+	0.871283i	$0.663288\pi$
$62$	−23.7401	+	6.97073i	−3.01500	+	0.885284i
$63$	−0.390736	+	2.71763i	−0.0492280	+	0.342389i
$64$	−4.36897	−	9.56672i	−0.546122	−	1.19584i
$65$	0.121206	+	0.843008i	0.0150338	+	0.104562i
$66$	−4.59293	+	2.95170i	−0.565351	+	0.363329i
$67$	6.49469	−	7.49528i	0.793453	−	0.915694i	−0.204550	−	0.978856i	$-0.565573\pi$
$67$	6.49469	−	7.49528i	0.793453	−	0.915694i	0.998003	+	0.0631624i	$0.0201186\pi$
$68$	15.3090			1.85649
$69$	3.99987	+	2.64594i	0.481528	+	0.318534i
$70$	−3.29177			−0.393442
$71$	−1.29740	+	1.49728i	−0.153973	+	0.177694i	−0.827495	−	0.561472i	$-0.810235\pi$
$71$	−1.29740	+	1.49728i	−0.153973	+	0.177694i	0.673522	+	0.739167i	$0.264781\pi$
$72$	7.05954	−	4.53689i	0.831974	−	0.534678i
$73$	1.15457	+	8.03022i	0.135132	+	0.939866i	0.938720	+	0.344680i	$0.112013\pi$
$73$	1.15457	+	8.03022i	0.135132	+	0.939866i	−0.803588	+	0.595186i	$0.797078\pi$
$74$	−10.4731	−	22.9328i	−1.21747	−	2.66588i
$75$	0.142315	−	0.989821i	0.0164331	−	0.114295i
$76$	9.72038	−	2.85416i	1.11500	−	0.327395i
$77$	2.62945	+	1.68985i	0.299654	+	0.192576i
$78$	0.848368	−	1.85767i	0.0960587	−	0.210339i
$79$	14.1009	+	4.14039i	1.58647	+	0.465830i	0.951741	−	0.306904i	$-0.0992929\pi$
$79$	14.1009	+	4.14039i	1.58647	+	0.465830i	0.634730	+	0.772734i	$0.281111\pi$
$80$	1.67742	+	1.93584i	0.187541	+	0.216434i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	15.8761	+	4.66164i	1.75322	+	0.514792i
$83$	−0.727055	+	1.59203i	−0.0798047	+	0.174748i	−0.945328	−	0.326120i	$-0.894259\pi$
$83$	−0.727055	+	1.59203i	−0.0798047	+	0.174748i	0.865524	+	0.500868i	$0.166986\pi$
$84$	4.33052	+	2.78305i	0.472498	+	0.303656i
$85$	3.91722	−	1.15020i	0.424882	−	0.124757i
$86$	2.39833	−	16.6807i	0.258618	−	1.79873i
$87$	−2.77701	−	6.08081i	−0.297727	−	0.651931i
$88$	−1.35958	−	9.45610i	−0.144932	−	1.00802i
$89$	4.47262	−	2.87438i	0.474096	−	0.304683i	−0.281685	−	0.959507i	$-0.590893\pi$
$89$	4.47262	−	2.87438i	0.474096	−	0.304683i	0.755782	+	0.654824i	$0.227257\pi$
$90$	3.14055	−	3.62439i	0.331043	−	0.382044i
$91$	−1.16917			−0.122562
$92$	−15.2559	+	9.52171i	−1.59054	+	0.992707i
$93$	10.3184			1.06997
$94$	−13.6835	+	15.7916i	−1.41134	+	1.62878i
$95$	2.27279	−	1.46063i	0.233183	−	0.149858i
$96$	0.320145	+	2.22666i	0.0326747	+	0.227257i
$97$	4.52967	+	9.91860i	0.459918	+	1.00708i	0.987506	+	0.157580i	$0.0503693\pi$
$97$	4.52967	+	9.91860i	0.459918	+	1.00708i	−0.527588	+	0.849501i	$0.676903\pi$
$98$	−1.74567	+	12.1414i	−0.176339	+	1.22647i
$99$	−4.36926	+	1.28293i	−0.439127	+	0.128939i
$100$	3.15455	+	2.02730i	0.315455	+	0.202730i
$101$	4.32298	−	9.46600i	0.430152	−	0.941902i	−0.563150	−	0.826355i	$-0.690411\pi$
$101$	4.32298	−	9.46600i	0.430152	−	0.941902i	0.993302	−	0.115547i	$-0.0368622\pi$
$102$	−9.39302	−	2.75804i	−0.930048	−	0.273087i
$103$	−8.32837	−	9.61145i	−0.820619	−	0.947045i	0.178702	−	0.983903i	$-0.442810\pi$
$103$	−8.32837	−	9.61145i	−0.820619	−	0.947045i	−0.999320	+	0.0368586i	$0.988265\pi$
$104$	2.34015	+	2.70067i	0.229470	+	0.264823i
$105$	1.31718	+	0.386758i	0.128543	+	0.0377438i
$106$	−6.80448	+	14.8997i	−0.660910	+	1.44719i
$107$	9.55833	+	6.14277i	0.924039	+	0.593844i	0.913827	−	0.406104i	$-0.133113\pi$
$107$	9.55833	+	6.14277i	0.924039	+	0.593844i	0.0102120	+	0.999948i	$0.496749\pi$
$108$	−17.9896	+	5.28223i	−1.73105	+	0.508282i
$109$	−0.608596	+	4.23288i	−0.0582930	+	0.405436i	0.939694	+	0.342016i	$0.111110\pi$
$109$	−0.608596	+	4.23288i	−0.0582930	+	0.405436i	−0.997987	+	0.0634200i	$0.979799\pi$
$110$	−2.26801	−	4.96625i	−0.216246	−	0.473513i
$111$	1.49629	+	10.4069i	0.142021	+	0.987779i
$112$	−2.95816	+	1.90110i	−0.279520	+	0.179637i
$113$	1.61271	−	1.86116i	0.151711	−	0.175084i	−0.674807	−	0.737994i	$-0.735773\pi$
$113$	1.61271	−	1.86116i	0.151711	−	0.175084i	0.826518	+	0.562911i	$0.190319\pi$
$114$	−6.47826			−0.606745
$115$	−3.18825	+	3.58260i	−0.297306	+	0.334079i
$116$	25.0672			2.32743
$117$	1.11546	−	1.28731i	0.103124	−	0.119012i
$118$	−5.47878	+	3.52100i	−0.504362	+	0.324134i
$119$	0.797608	+	5.54748i	0.0731166	+	0.508537i
$120$	−1.74302	−	3.81667i	−0.159115	−	0.348413i
$121$	0.827691	−	5.75672i	0.0752447	−	0.523338i
$122$	2.09094	−	0.613954i	0.189304	−	0.0555848i
$123$	−5.80499	−	3.73064i	−0.523418	−	0.336381i
$124$	−16.0734	+	35.1957i	−1.44343	+	3.16067i
$125$	0.959493	+	0.281733i	0.0858197	+	0.0251989i
$126$	4.31130	+	4.97551i	0.384081	+	0.443254i
$127$	−4.90692	−	5.66288i	−0.435418	−	0.502500i	0.495054	−	0.868862i	$-0.335148\pi$
$127$	−4.90692	−	5.66288i	−0.435418	−	0.502500i	−0.930472	+	0.366363i	$0.880603\pi$
$128$	−19.8804	−	5.83741i	−1.75719	−	0.515959i
$129$	−2.91953	+	6.39288i	−0.257050	+	0.562862i
$130$	1.71802	+	1.10411i	0.150681	+	0.0968365i
$131$	−0.778878	+	0.228699i	−0.0680509	+	0.0199816i	−0.315581	−	0.948899i	$-0.602199\pi$
$131$	−0.778878	+	0.228699i	−0.0680509	+	0.0199816i	0.247530	+	0.968880i	$0.420381\pi$
$132$	−1.21506	+	8.45090i	−0.105757	+	0.735556i
$133$	1.54069	+	3.37365i	0.133595	+	0.292533i
$134$	−3.38444	−	23.5393i	−0.292371	−	2.03349i
$135$	−4.20627	+	2.70320i	−0.362018	+	0.232655i
$136$	11.2177	−	12.9459i	0.961912	−	1.11011i
$137$	−12.2439			−1.04607			−0.523034	−	0.852312i	$-0.675200\pi$
$137$	−12.2439			−1.04607			−0.523034	+	0.852312i	$0.675200\pi$
$138$	11.0759	−	3.09369i	0.942841	−	0.263352i
$139$	17.2791			1.46559			0.732795	−	0.680449i	$-0.238215\pi$
$139$	17.2791			1.46559			0.732795	+	0.680449i	$0.238215\pi$
$140$	−3.37102	+	3.89037i	−0.284903	+	0.328796i
$141$	7.33073	−	4.71117i	0.617359	−	0.396752i
$142$	0.676087	+	4.70229i	0.0567359	+	0.394607i
$143$	−0.805551	−	1.76391i	−0.0673636	−	0.147506i
$144$	0.729075	−	5.07083i	0.0607563	−	0.422569i
$145$	6.41413	−	1.88336i	0.532664	−	0.156404i
$146$	16.3653	+	10.5174i	1.35440	+	0.870422i
$147$	2.12504	−	4.65319i	0.175270	−	0.383788i
$148$	−37.8282	−	11.1074i	−3.10946	−	0.913021i
$149$	9.28868	+	10.7197i	0.760958	+	0.878193i	0.995582	−	0.0938936i	$-0.0299314\pi$
$149$	9.28868	+	10.7197i	0.760958	+	0.878193i	−0.234624	+	0.972086i	$0.575386\pi$
$150$	−1.57028	−	1.81219i	−0.128212	−	0.147965i
$151$	9.03415	+	2.65266i	0.735188	+	0.215871i	0.627831	−	0.778350i	$-0.283943\pi$
$151$	9.03415	+	2.65266i	0.735188	+	0.215871i	0.107357	+	0.994220i	$0.465761\pi$
$152$	4.70905	−	10.3114i	0.381954	−	0.836363i
$153$	−6.86900	−	4.41444i	−0.555326	−	0.356886i
$154$	7.19130	−	2.11156i	0.579492	−	0.170154i
$155$	−1.46847	+	10.2134i	−0.117950	+	0.820362i
$156$	−1.32668	−	2.90503i	−0.106220	−	0.232589i
$157$	2.10172	+	14.6178i	0.167735	+	1.16663i	0.883551	+	0.468336i	$0.155146\pi$
$157$	2.10172	+	14.6178i	0.167735	+	1.16663i	−0.715815	+	0.698290i	$0.753945\pi$
$158$	29.6454	−	19.0520i	2.35846	−	1.51569i
$159$	4.47337	−	5.16254i	0.354761	−	0.409416i
$160$	−2.24955			−0.177843
$161$	−4.24520	−	5.03216i	−0.334569	−	0.396590i
$162$	−2.39788			−0.188395
$163$	3.95116	−	4.55988i	0.309478	−	0.357157i	−0.579609	−	0.814895i	$-0.696795\pi$
$163$	3.95116	−	4.55988i	0.309478	−	0.357157i	0.889087	+	0.457738i	$0.151340\pi$
$164$	21.7676	−	13.9892i	1.69977	−	1.09237i
$165$	0.324031	+	2.25368i	0.0252258	+	0.175449i
$166$	1.74339	+	3.81749i	0.135313	+	0.296295i
$167$	−0.396910	+	2.76057i	−0.0307138	+	0.213619i	−0.999399	−	0.0346742i	$-0.988961\pi$
$167$	−0.396910	+	2.76057i	−0.0307138	+	0.213619i	0.968685	+	0.248293i	$0.0798697\pi$
$168$	5.52667	−	1.62278i	0.426392	−	0.125200i
$169$	−10.3261	−	6.63617i	−0.794315	−	0.510475i
$170$	4.06673	−	8.90490i	0.311904	−	0.682975i
$171$	−5.18446	−	1.52229i	−0.396465	−	0.116413i
$172$	−17.2580	−	19.9168i	−1.31591	−	1.51864i
$173$	−10.0300	−	11.5753i	−0.762570	−	0.880053i	0.233153	−	0.972440i	$-0.425096\pi$
$173$	−10.0300	−	11.5753i	−0.762570	−	0.880053i	−0.995723	+	0.0923874i	$0.970550\pi$
$174$	−15.3803	−	4.51606i	−1.16598	−	0.342362i
$175$	−0.570276	+	1.24873i	−0.0431088	+	0.0943951i
$176$	−4.90631	−	3.15310i	−0.369827	−	0.237674i
$177$	2.60598	−	0.765186i	0.195878	−	0.0575149i
$178$	1.81431	−	12.6188i	0.135988	−	0.945820i
$179$	−5.37512	−	11.7699i	−0.401755	−	0.879721i	−0.997089	−	0.0762427i	$-0.975708\pi$
$179$	−5.37512	−	11.7699i	−0.401755	−	0.879721i	0.595334	−	0.803478i	$-0.297020\pi$
$180$	−1.06731	−	7.42330i	−0.0795525	−	0.553300i
$181$	13.0593	−	8.39272i	0.970692	−	0.623826i	0.0437545	−	0.999042i	$-0.486068\pi$
$181$	13.0593	−	8.39272i	0.970692	−	0.623826i	0.926937	+	0.375217i	$0.122432\pi$
$182$	−1.83592	+	2.11876i	−0.136087	+	0.157053i
$183$	−0.908807			−0.0671810
$184$	−3.12686	+	19.8781i	−0.230515	+	1.46544i
$185$	−10.5139			−0.772998
$186$	16.2028	−	18.6990i	1.18805	−	1.37108i
$187$	−7.81987	+	5.02552i	−0.571845	+	0.367503i
$188$	4.65029	+	32.3435i	0.339158	+	2.35889i
$189$	−2.85138	−	6.24365i	−0.207407	−	0.454159i
$190$	0.921953	−	6.41232i	0.0668855	−	0.465199i
$191$	−17.6968	+	5.19625i	−1.28050	+	0.375987i	−0.850085	−	0.526646i	$-0.823449\pi$
$191$	−17.6968	+	5.19625i	−1.28050	+	0.375987i	−0.430411	+	0.902633i	$0.641631\pi$
$192$	8.84757	+	5.68599i	0.638519	+	0.410351i
$193$	−3.16959	+	6.94043i	−0.228152	+	0.499583i	−0.988739	−	0.149653i	$-0.952184\pi$
$193$	−3.16959	+	6.94043i	−0.228152	+	0.499583i	0.760587	+	0.649237i	$0.224911\pi$
$194$	25.0873	+	7.36628i	1.80116	+	0.528868i
$195$	−0.557730	−	0.643655i	−0.0399399	−	0.0460931i
$196$	12.5616	+	14.4968i	0.897254	+	1.03549i
$197$	10.6614	+	3.13046i	0.759590	+	0.223036i	0.638517	−	0.769608i	$-0.279548\pi$
$197$	10.6614	+	3.13046i	0.759590	+	0.223036i	0.121073	+	0.992644i	$0.461366\pi$
$198$	−4.53602	+	9.93250i	−0.322361	+	0.705872i
$199$	−11.6074	−	7.45964i	−0.822828	−	0.528800i	0.0601633	−	0.998189i	$-0.480838\pi$
$199$	−11.6074	−	7.45964i	−0.822828	−	0.528800i	−0.882992	+	0.469389i	$0.844474\pi$
$200$	4.02588	−	1.18211i	0.284673	−	0.0835875i
$201$	−1.41143	+	9.81672i	−0.0995547	+	0.692418i
$202$	−10.3660	−	22.6983i	−0.729347	−	1.59705i
$203$	1.30602	+	9.08355i	0.0916644	+	0.637540i
$204$	−12.8787	+	8.27666i	−0.901692	+	0.579482i
$205$	4.51881	−	5.21498i	0.315607	−	0.364230i
$206$	−30.4957			−2.12473
$207$	9.59082	+	0.126832i	0.666608	+	0.00881541i
$208$	2.18156			0.151264
$209$	−4.02825	+	4.64885i	−0.278640	+	0.321568i
$210$	2.76921	−	1.77967i	0.191094	−	0.122809i
$211$	−0.279793	−	1.94601i	−0.0192618	−	0.133969i	0.977921	−	0.208973i	$-0.0670120\pi$
$211$	−0.279793	−	1.94601i	−0.0192618	−	0.133969i	−0.997183	+	0.0750043i	$0.976103\pi$
$212$	10.6409	+	23.3003i	0.730819	+	1.60027i
$213$	0.281952	−	1.96102i	0.0193190	−	0.134367i
$214$	26.1411	−	7.67572i	1.78697	−	0.524702i
$215$	−5.91232	−	3.79962i	−0.403217	−	0.259132i
$216$	−8.71508	+	19.0834i	−0.592986	+	1.29846i
$217$	−13.5912	−	3.99075i	−0.922633	−	0.270909i
$218$	6.71514	+	7.74968i	0.454807	+	0.524875i
$219$	−5.31275	−	6.13124i	−0.359003	−	0.414311i
$220$	−8.19196	−	2.40538i	−0.552302	−	0.162170i
$221$	1.44442	−	3.16284i	0.0971622	−	0.212756i
$222$	21.2089	+	13.6301i	1.42345	+	0.914795i
$223$	17.0728	−	5.01302i	1.14328	−	0.335697i	0.345364	−	0.938469i	$-0.387755\pi$
$223$	17.0728	−	5.01302i	1.14328	−	0.335697i	0.797913	+	0.602772i	$0.205937\pi$
$224$	0.439490	−	3.05672i	0.0293647	−	0.204236i
$225$	−0.830830	−	1.81926i	−0.0553887	−	0.121284i
$226$	−0.840396	−	5.84508i	−0.0559023	−	0.388809i
$227$	−5.64953	+	3.63073i	−0.374972	+	0.240980i	−0.714529	−	0.699605i	$-0.753359\pi$
$227$	−5.64953	+	3.63073i	−0.374972	+	0.240980i	0.339557	+	0.940585i	$0.389723\pi$
$228$	−6.63423	+	7.65631i	−0.439363	+	0.507051i
$229$	−22.1302			−1.46240			−0.731201	−	0.682162i	$-0.761040\pi$
$229$	−22.1302			−1.46240			−0.731201	+	0.682162i	$0.761040\pi$
$230$	1.48594	+	11.4034i	0.0979797	+	0.751919i
$231$	−3.12564			−0.205652
$232$	18.3681	−	21.1979i	1.20592	−	1.39171i
$233$	−13.5862	+	8.73132i	−0.890062	+	0.572008i	−0.903827	−	0.427897i	$-0.859255\pi$
$233$	−13.5862	+	8.73132i	−0.890062	+	0.572008i	0.0137656	+	0.999905i	$0.495618\pi$
$234$	−0.581276	−	4.04286i	−0.0379992	−	0.264290i
$235$	3.61995	+	7.92658i	0.236139	+	0.517073i
$236$	−1.44941	+	10.0808i	−0.0943483	+	0.656207i
$237$	−14.1009	+	4.14039i	−0.915950	+	0.268947i
$238$	11.3056	+	7.26566i	0.732832	+	0.470963i
$239$	−2.98866	+	6.54426i	−0.193320	+	0.423313i	−0.981325	−	0.192356i	$-0.938387\pi$
$239$	−2.98866	+	6.54426i	−0.193320	+	0.423313i	0.788005	+	0.615669i	$0.211114\pi$
$240$	−2.45773	−	0.721655i	−0.158646	−	0.0465826i
$241$	−12.2335	−	14.1182i	−0.788027	−	0.909432i	0.209634	−	0.977780i	$-0.432773\pi$
$241$	−12.2335	−	14.1182i	−0.788027	−	0.909432i	−0.997662	+	0.0683477i	$0.978227\pi$
$242$	−9.13259	−	10.5396i	−0.587065	−	0.677509i
$243$	15.3519	+	4.50772i	0.984824	+	0.289170i
$244$	1.41568	−	3.09990i	0.0906294	−	0.198451i
$245$	4.30340	+	2.76563i	0.274934	+	0.176689i
$246$	−15.8761	+	4.66164i	−1.01222	+	0.297215i
$247$	0.327459	−	2.27753i	0.0208357	−	0.144916i
$248$	17.9852	+	39.3821i	1.14206	+	2.50077i
$249$	−0.249078	−	1.73238i	−0.0157847	−	0.109785i
$250$	2.01722	−	1.29639i	0.127580	−	0.0819909i
$251$	0.611145	−	0.705299i	0.0385751	−	0.0445181i	−0.736134	−	0.676836i	$-0.763351\pi$
$251$	0.611145	−	0.705299i	0.0385751	−	0.0445181i	0.774709	+	0.632318i	$0.217896\pi$
$252$	10.2954			0.648548
$253$	4.66704	−	9.87181i	0.293414	−	0.620635i
$254$	−17.9675			−1.12738
$255$	−2.67353	+	3.08542i	−0.167423	+	0.193217i
$256$	−24.1011	+	15.4888i	−1.50632	+	0.968051i
$257$	1.86011	+	12.9374i	0.116031	+	0.807011i	0.961857	+	0.273553i	$0.0881988\pi$
$257$	1.86011	+	12.9374i	0.116031	+	0.807011i	−0.845826	+	0.533458i	$0.820892\pi$
$258$	7.00068	+	15.3294i	0.435843	+	0.954364i
$259$	2.05408	−	14.2864i	0.127634	−	0.887716i
$260$	3.06427	−	0.899750i	0.190038	−	0.0558001i
$261$	−11.2474	−	7.22827i	−0.696198	−	0.447419i
$262$	−0.808606	+	1.77060i	−0.0499559	+	0.109388i
$263$	−2.56657	−	0.753613i	−0.158262	−	0.0464698i	0.201642	−	0.979459i	$-0.435372\pi$
$263$	−2.56657	−	0.753613i	−0.158262	−	0.0464698i	−0.359904	+	0.932990i	$0.617190\pi$
$264$	6.25611	+	7.21993i	0.385037	+	0.444356i
$265$	4.47337	+	5.16254i	0.274797	+	0.317133i
$266$	8.53302	+	2.50552i	0.523193	+	0.153623i
$267$	−2.20860	+	4.83616i	−0.135164	+	0.295968i
$268$	−31.2857	−	20.1061i	−1.91108	−	1.22818i
$269$	30.9014	−	9.07347i	1.88409	−	0.553219i	0.888565	−	0.458751i	$-0.151703\pi$
$269$	30.9014	−	9.07347i	1.88409	−	0.553219i	0.995528	−	0.0944681i	$-0.0301150\pi$
$270$	−1.70627	+	11.8674i	−0.103840	+	0.722224i
$271$	−2.34923	−	5.14409i	−0.142705	−	0.312481i	0.824761	−	0.565482i	$-0.191310\pi$
$271$	−2.34923	−	5.14409i	−0.142705	−	0.312481i	−0.967466	+	0.253001i	$0.918582\pi$
$272$	−1.48826	−	10.3511i	−0.0902390	−	0.627626i
$273$	0.983568	−	0.632101i	0.0595283	−	0.0382565i
$274$	−19.2263	+	22.1883i	−1.16150	+	1.34045i
$275$	−2.27686			−0.137300
$276$	7.68627	−	16.2581i	0.462659	−	0.978625i
$277$	−25.9793			−1.56095			−0.780473	−	0.625189i	$-0.785022\pi$
$277$	−25.9793			−1.56095			−0.780473	+	0.625189i	$0.785022\pi$
$278$	27.1329	−	31.3130i	1.62732	−	1.87803i
$279$	17.3609	−	11.1571i	1.03937	−	0.667961i
$280$	0.819733	+	5.70137i	0.0489884	+	0.340722i
$281$	12.1690	+	26.6463i	0.725940	+	1.58959i	0.805389	+	0.592747i	$0.201957\pi$
$281$	12.1690	+	26.6463i	0.725940	+	1.58959i	−0.0794493	+	0.996839i	$0.525316\pi$
$282$	2.97370	−	20.6826i	0.177081	−	1.23163i
$283$	−3.38658	+	0.994391i	−0.201312	+	0.0591104i	−0.380834	−	0.924644i	$-0.624363\pi$
$283$	−3.38658	+	0.994391i	−0.201312	+	0.0591104i	0.179522	+	0.983754i	$0.442545\pi$
$284$	6.24974	+	4.01646i	0.370854	+	0.238333i
$285$	−1.12231	+	2.45752i	−0.0664800	+	0.145571i
$286$	−4.46149	−	1.31001i	−0.263813	−	0.0774626i
$287$	6.20335	+	7.15905i	0.366172	+	0.422585i
$288$	2.94629	+	3.40020i	0.173612	+	0.200359i
$289$	0.318941	+	0.0936497i	0.0187613	+	0.00550880i
$290$	6.65894	−	14.5810i	0.391026	−	0.856228i
$291$	−9.17300	−	5.89513i	−0.537731	−	0.345579i
$292$	29.1892	−	8.57073i	1.70817	−	0.501564i
$293$	3.35152	−	23.3104i	0.195798	−	1.36181i	−0.620514	−	0.784195i	$-0.713076\pi$
$293$	3.35152	−	23.3104i	0.195798	−	1.36181i	0.816312	−	0.577611i	$-0.196015\pi$
$294$	−5.09558	−	11.1578i	−0.297180	−	0.650734i
$295$	0.386527	+	2.68835i	0.0225045	+	0.156522i
$296$	−37.1117	+	23.8502i	−2.15707	+	1.38627i
$297$	7.45513	−	8.60367i	0.432590	−	0.499236i
$298$	34.0120			1.97026
$299$	0.527774	+	4.05026i	0.0305220	+	0.234232i
$300$	−3.74982			−0.216496
$301$	6.31805	−	7.29141i	0.364166	−	0.420270i
$302$	18.9932	−	12.2062i	1.09294	−	0.702389i
$303$	1.48099	+	10.3005i	0.0850804	+	0.591747i
$304$	−2.87479	−	6.29491i	−0.164880	−	0.361038i
$305$	0.129337	−	0.899557i	0.00740580	−	0.0515085i
$306$	−18.7860	+	5.51608i	−1.07393	+	0.315333i
$307$	−2.75476	−	1.77038i	−0.157223	−	0.101041i	0.459664	−	0.888093i	$-0.347970\pi$
$307$	−2.75476	−	1.77038i	−0.157223	−	0.101041i	−0.616886	+	0.787052i	$0.711606\pi$
$308$	4.86890	−	10.6614i	0.277431	−	0.607490i
$309$	12.2026	+	3.58301i	0.694183	+	0.203830i
$310$	16.2028	+	18.6990i	0.920257	+	1.06203i
$311$	14.6980	+	16.9624i	0.833448	+	0.961850i	0.999706	−	0.0242323i	$-0.00771414\pi$
$311$	14.6980	+	16.9624i	0.833448	+	0.961850i	−0.166259	+	0.986082i	$0.553169\pi$
$312$	−3.42875	−	1.00677i	−0.194115	−	0.0569973i
$313$	4.98954	−	10.9256i	0.282026	−	0.617550i	−0.714609	−	0.699524i	$-0.753395\pi$
$313$	4.98954	−	10.9256i	0.282026	−	0.617550i	0.996634	+	0.0819743i	$0.0261225\pi$
$314$	29.7905	+	19.1452i	1.68118	+	1.08043i
$315$	2.63436	−	0.773517i	0.148429	−	0.0435827i
$316$	7.84267	−	54.5470i	0.441185	−	3.06851i
$317$	11.8650	+	25.9807i	0.666405	+	1.45922i	0.876431	+	0.481528i	$0.159918\pi$
$317$	11.8650	+	25.9807i	0.666405	+	1.45922i	−0.210026	+	0.977696i	$0.567355\pi$
$318$	−2.33111	−	16.2132i	−0.130722	−	0.909193i
$319$	−12.8044	+	8.22888i	−0.716908	+	0.460729i
$320$	−6.88726	+	7.94832i	−0.385009	+	0.444324i
$321$	−11.3620			−0.634166
$322$	−15.7854	−	0.208750i	−0.879686	−	0.0116332i
$323$	−11.0298			−0.613715
$324$	−2.45561	+	2.83392i	−0.136423	+	0.157440i
$325$	0.716476	−	0.460451i	0.0397430	−	0.0255412i
$326$	−2.05898	−	14.3205i	−0.114036	−	0.793141i
$327$	−1.77648	−	3.88996i	−0.0982398	−	0.215115i
$328$	4.12045	−	28.6583i	0.227514	−	1.58239i
$329$	−11.4780	+	3.37023i	−0.632801	+	0.185807i
$330$	4.59293	+	2.95170i	0.252832	+	0.162486i
$331$	−11.3489	+	24.8506i	−0.623792	+	1.36591i	0.288936	+	0.957348i	$0.406698\pi$
$331$	−11.3489	+	24.8506i	−0.623792	+	1.36591i	−0.912729	+	0.408566i	$0.866029\pi$
$332$	6.29705	+	1.84898i	0.345595	+	0.101476i
$333$	13.7703	+	15.8918i	0.754608	+	0.870864i
$334$	4.37943	+	5.05413i	0.239632	+	0.276550i
$335$	−9.51594	−	2.79413i	−0.519911	−	0.152660i
$336$	1.46075	−	3.19861i	0.0796907	−	0.174498i
$337$	−9.69442	−	6.23022i	−0.528089	−	0.339382i	0.249276	−	0.968433i	$-0.419807\pi$
$337$	−9.69442	−	6.23022i	−0.528089	−	0.339382i	−0.777364	+	0.629051i	$0.783444\pi$
$338$	−28.2408	+	8.29226i	−1.53610	+	0.451040i
$339$	−0.350475	+	2.43761i	−0.0190352	+	0.132393i
$340$	−6.35958	−	13.9255i	−0.344897	−	0.755219i
$341$	−3.34349	−	23.2545i	−0.181060	−	1.25930i
$342$	−10.8997	+	7.00483i	−0.589389	+	0.378778i
$343$	−10.8916	+	12.5696i	−0.588091	+	0.678693i
$344$	−29.4883			−1.58991
$345$	0.745229	−	4.73758i	0.0401218	−	0.255063i
$346$	−36.7266			−1.97443
$347$	6.91880	−	7.98472i	0.371421	−	0.428642i	−0.539013	−	0.842297i	$-0.681203\pi$
$347$	6.91880	−	7.98472i	0.371421	−	0.428642i	0.910434	+	0.413655i	$0.135748\pi$
$348$	−21.0879	+	13.5524i	−1.13043	+	0.726482i
$349$	0.245733	+	1.70911i	0.0131538	+	0.0914865i	0.995341	−	0.0964195i	$-0.0307390\pi$
$349$	0.245733	+	1.70911i	0.0131538	+	0.0914865i	−0.982187	+	0.187906i	$0.939830\pi$
$350$	1.36745	+	2.99430i	0.0730933	+	0.160052i
$351$	−0.606031	+	4.21504i	−0.0323476	+	0.224982i
$352$	4.91444	−	1.44301i	0.261941	−	0.0769127i
$353$	−3.78577	−	2.43297i	−0.201496	−	0.129494i	0.436002	−	0.899946i	$-0.356394\pi$
$353$	−3.78577	−	2.43297i	−0.201496	−	0.129494i	−0.637498	+	0.770452i	$0.720031\pi$
$354$	2.70545	−	5.92410i	0.143793	−	0.314862i
$355$	1.90093	+	0.558165i	0.100891	+	0.0296243i
$356$	−13.0555	−	15.0669i	−0.691940	−	0.798542i
$357$	−3.67019	−	4.23562i	−0.194247	−	0.224173i
$358$	−29.7697	−	8.74117i	−1.57338	−	0.461985i
$359$	6.27544	−	13.7413i	0.331205	−	0.725238i	−0.668626	−	0.743599i	$-0.733117\pi$
$359$	6.27544	−	13.7413i	0.331205	−	0.725238i	0.999831	+	0.0183603i	$0.00584459\pi$
$360$	−7.05954	−	4.53689i	−0.372070	−	0.239115i
$361$	11.2270	−	3.29655i	0.590896	−	0.173503i
$362$	5.29750	−	36.8449i	0.278430	−	1.93653i
$363$	2.41602	+	5.29034i	0.126808	+	0.277671i
$364$	0.623933	+	4.33955i	0.0327030	+	0.227454i
$365$	6.82492	−	4.38611i	0.357233	−	0.229579i
$366$	−1.42708	+	1.64694i	−0.0745946	+	0.0860867i
$367$	25.1252			1.31152			0.655761	−	0.754968i	$-0.272348\pi$
$367$	25.1252			1.31152			0.655761	+	0.754968i	$0.272348\pi$
$368$	7.92115	+	9.38954i	0.412918	+	0.489464i
$369$	−13.8008			−0.718442
$370$	−16.5097	+	19.0533i	−0.858301	+	0.990532i
$371$	−7.88888	+	5.06988i	−0.409570	+	0.263215i
$372$	−5.50648	−	38.2984i	−0.285498	−	1.98568i
$373$	5.38922	+	11.8008i	0.279043	+	0.611020i	0.996315	−	0.0857742i	$-0.0273364\pi$
$373$	5.38922	+	11.8008i	0.279043	+	0.611020i	−0.717271	+	0.696794i	$0.754609\pi$
$374$	−3.17212	+	22.0626i	−0.164026	+	1.14083i
$375$	−0.959493	+	0.281733i	−0.0495480	+	0.0145486i
$376$	30.7586	+	19.7674i	1.58625	+	1.01942i
$377$	2.36512	−	5.17889i	0.121810	−	0.266726i
$378$	−15.7922	−	4.63700i	−0.812261	−	0.238501i
$379$	17.9375	+	20.7010i	0.921387	+	1.06334i	0.997802	+	0.0662612i	$0.0211071\pi$
$379$	17.9375	+	20.7010i	0.921387	+	1.06334i	−0.0764153	+	0.997076i	$0.524347\pi$
$380$	−6.63423	−	7.65631i	−0.340329	−	0.392760i
$381$	7.18955	+	2.11104i	0.368332	+	0.108152i
$382$	−18.3722	+	40.2296i	−0.940005	+	2.05832i
$383$	−0.449205	−	0.288687i	−0.0229533	−	0.0147512i	0.529114	−	0.848551i	$-0.322524\pi$
$383$	−0.449205	−	0.288687i	−0.0229533	−	0.0147512i	−0.552067	+	0.833800i	$0.686161\pi$
$384$	19.8804	−	5.83741i	1.01452	−	0.297889i
$385$	0.444825	−	3.09382i	0.0226704	−	0.157676i
$386$	7.60028	+	16.6423i	0.386844	+	0.847071i
$387$	2.00037	+	13.9129i	0.101685	+	0.707233i
$388$	34.3971	−	22.1056i	1.74625	−	1.12224i
$389$	10.3277	−	11.9187i	0.523633	−	0.604304i	−0.430904	−	0.902398i	$-0.641805\pi$
$389$	10.3277	−	11.9187i	0.523633	−	0.604304i	0.954537	+	0.298093i	$0.0963507\pi$
$390$	−2.04222			−0.103412
$391$	18.8576	−	5.26727i	0.953672	−	0.266377i
$392$	21.4637			1.08408
$393$	0.531590	−	0.613488i	0.0268152	−	0.0309464i
$394$	22.4143	−	14.4048i	1.12921	−	0.725702i
$395$	−2.09148	−	14.5466i	−0.105234	−	0.731918i
$396$	7.09346	+	15.5325i	0.356460	+	0.780538i
$397$	−2.12490	+	14.7790i	−0.106646	+	0.741737i	0.864393	+	0.502816i	$0.167703\pi$
$397$	−2.12490	+	14.7790i	−0.106646	+	0.741737i	−0.971039	+	0.238921i	$0.923206\pi$
$398$	−31.7452	+	9.32122i	−1.59124	+	0.467231i
$399$	−3.12005	−	2.00513i	−0.156198	−	0.100382i
$400$	1.06408	−	2.33001i	0.0532040	−	0.116501i
$401$	22.4942	+	6.60489i	1.12331	+	0.329832i	0.790073	−	0.613013i	$-0.210042\pi$
$401$	22.4942	+	6.60489i	1.12331	+	0.329832i	0.333232	+	0.942845i	$0.391861\pi$
$402$	15.5735	+	17.9728i	0.776735	+	0.896399i
$403$	5.75491	+	6.64151i	0.286672	+	0.330837i
$404$	−37.4414	−	10.9938i	−1.86278	−	0.546962i
$405$	−0.415415	+	0.909632i	−0.0206421	+	0.0452000i
$406$	18.5120	+	11.8969i	0.918733	+	0.590434i
$407$	22.9690	−	6.74431i	1.13853	−	0.334303i
$408$	−2.43784	+	16.9556i	−0.120691	+	0.839426i
$409$	−15.0275	−	32.9057i	−0.743064	−	1.62708i	−0.778447	−	0.627710i	$-0.783992\pi$
$409$	−15.0275	−	32.9057i	−0.743064	−	1.62708i	0.0353828	−	0.999374i	$-0.488735\pi$
$410$	−2.35479	−	16.3779i	−0.116295	−	0.808847i
$411$	10.3002	−	6.61955i	0.508073	−	0.326519i
$412$	−31.2299	+	36.0412i	−1.53859	+	1.77562i
$413$	−3.72849			−0.183467
$414$	15.2901	−	17.1813i	0.751467	−	0.844414i
$415$	1.75019			0.0859135
$416$	−1.25464	+	1.44794i	−0.0615140	+	0.0709909i
$417$	−14.5361	+	9.34176i	−0.711834	+	0.457468i
$418$	2.09916	+	14.5999i	0.102673	+	0.714107i
$419$	−6.10128	−	13.3599i	−0.298067	−	0.652676i	0.700045	−	0.714099i	$-0.253163\pi$
$419$	−6.10128	−	13.3599i	−0.298067	−	0.652676i	−0.998112	+	0.0614230i	$0.980436\pi$
$420$	0.732593	−	5.09530i	0.0357469	−	0.248625i
$421$	10.6043	−	3.11371i	0.516824	−	0.151753i	−0.0129109	−	0.999917i	$-0.504110\pi$
$421$	10.6043	−	3.11371i	0.516824	−	0.151753i	0.529734	+	0.848164i	$0.322292\pi$
$422$	−3.96589	−	2.54873i	−0.193057	−	0.124070i
$423$	7.23990	−	15.8532i	0.352016	−	0.770807i
$424$	27.5009	+	8.07500i	1.33556	+	0.392156i
$425$	−2.67353	−	3.08542i	−0.129685	−	0.149665i
$426$	−3.11101	−	3.59029i	−0.150729	−	0.173950i
$427$	1.19706	+	0.351489i	0.0579299	+	0.0170097i
$428$	17.6989	−	38.7553i	0.855511	−	1.87331i
$429$	1.63131	+	1.04838i	0.0787606	+	0.0506164i
$430$	−16.1696	+	4.74783i	−0.779768	+	0.228961i
$431$	−5.61640	+	39.0629i	−0.270533	+	1.88160i	0.172380	+	0.985030i	$0.444854\pi$
$431$	−5.61640	+	39.0629i	−0.270533	+	1.88160i	−0.442913	+	0.896565i	$0.646055\pi$
$432$	5.32040	+	11.6501i	0.255978	+	0.560514i
$433$	2.02462	+	14.0816i	0.0972972	+	0.676717i	0.978842	+	0.204617i	$0.0655948\pi$
$433$	2.02462	+	14.0816i	0.0972972	+	0.676717i	−0.881545	+	0.472100i	$0.843496\pi$
$434$	−28.5740	+	18.3634i	−1.37160	+	0.881471i
$435$	−4.37769	+	5.05212i	−0.209894	+	0.242231i
$436$	16.0357			0.767973
$437$	10.9916	−	6.86019i	0.525798	−	0.328168i
$438$	−19.4535			−0.929524
$439$	−0.980571	+	1.13164i	−0.0468001	+	0.0540102i	−0.778667	−	0.627437i	$-0.784104\pi$
$439$	−0.980571	+	1.13164i	−0.0468001	+	0.0540102i	0.731867	+	0.681448i	$0.238649\pi$
$440$	−8.03678	+	5.16493i	−0.383139	+	0.246228i
$441$	−1.45601	−	10.1268i	−0.0693339	−	0.482228i
$442$	−3.46354	−	7.58410i	−0.164744	−	0.360739i
$443$	2.02330	−	14.0723i	0.0961297	−	0.668597i	−0.883596	−	0.468251i	$-0.844884\pi$
$443$	2.02330	−	14.0723i	0.0961297	−	0.668597i	0.979725	−	0.200346i	$-0.0642066\pi$
$444$	37.8282	−	11.1074i	1.79525	−	0.527133i
$445$	−4.47262	−	2.87438i	−0.212022	−	0.136258i
$446$	17.7244	−	38.8110i	0.839275	−	1.83776i
$447$	−13.6096	−	3.99615i	−0.643714	−	0.189012i
$448$	−9.45473	−	10.9113i	−0.446694	−	0.515512i
$449$	−22.7717	−	26.2800i	−1.07466	−	1.24023i	−0.969323	−	0.245792i	$-0.920952\pi$
$449$	−22.7717	−	26.2800i	−1.07466	−	1.24023i	−0.105341	−	0.994436i	$-0.533593\pi$
$450$	−4.60149	−	1.35112i	−0.216916	−	0.0636924i
$451$	−6.52669	+	14.2915i	−0.307330	+	0.672958i
$452$	−7.76861	−	4.99259i	−0.365405	−	0.234831i
$453$	−9.03415	+	2.65266i	−0.424461	+	0.124633i
$454$	−2.29172	+	15.9393i	−0.107556	+	0.748068i
$455$	0.485691	+	1.06351i	0.0227695	+	0.0498583i
$456$	1.61325	+	11.2204i	0.0755472	+	0.525443i
$457$	−8.88813	+	5.71205i	−0.415769	+	0.267199i	−0.731758	−	0.681564i	$-0.761300\pi$
$457$	−8.88813	+	5.71205i	−0.415769	+	0.267199i	0.315989	+	0.948763i	$0.397664\pi$
$458$	−34.7504	+	40.1041i	−1.62378	+	1.87394i
$459$	20.4130			0.952796
$460$	14.9988	+	9.92180i	0.699322	+	0.462607i
$461$	27.8881			1.29888			0.649438	−	0.760414i	$-0.275004\pi$
$461$	27.8881			1.29888			0.649438	+	0.760414i	$0.275004\pi$
$462$	−4.90811	+	5.66427i	−0.228346	+	0.263525i
$463$	−3.36775	+	2.16432i	−0.156513	+	0.100584i	−0.616553	−	0.787314i	$-0.711471\pi$
$463$	−3.36775	+	2.16432i	−0.156513	+	0.100584i	0.460040	+	0.887898i	$0.347835\pi$
$464$	−2.43690	−	16.9490i	−0.113130	−	0.786839i
$465$	−4.28644	−	9.38599i	−0.198779	−	0.435265i
$466$	−5.51123	+	38.3314i	−0.255303	+	1.77567i
$467$	7.40548	−	2.17445i	0.342685	−	0.100621i	−0.105862	−	0.994381i	$-0.533760\pi$
$467$	7.40548	−	2.17445i	0.342685	−	0.100621i	0.448546	+	0.893760i	$0.351942\pi$
$468$	−5.37331	−	3.45322i	−0.248381	−	0.159625i
$469$	5.65581	−	12.3845i	0.261161	−	0.571863i
$470$	20.0488	+	5.88687i	0.924784	+	0.271541i
$471$	−9.67104	−	11.1610i	−0.445618	−	0.514271i
$472$	7.46274	+	8.61246i	0.343500	+	0.396420i
$473$	15.3536	+	4.50821i	0.705957	+	0.207288i
$474$	−14.6391	+	32.0551i	−0.672394	+	1.47234i
$475$	−2.27279	−	1.46063i	−0.104283	−	0.0670183i
$476$	20.1647	−	5.92088i	0.924246	−	0.271383i
$477$	1.94431	−	13.5230i	0.0890240	−	0.619175i
$478$	7.16645	+	15.6923i	0.327786	+	0.717750i
$479$	3.24698	+	22.5833i	0.148358	+	1.03186i	0.918907	+	0.394474i	$0.129073\pi$
$479$	3.24698	+	22.5833i	0.148358	+	1.03186i	−0.770549	+	0.637381i	$0.780018\pi$
$480$	1.89245	−	1.21620i	0.0863779	−	0.0555117i
$481$	−5.86392	+	6.76733i	−0.267372	+	0.308564i
$482$	−44.7948			−2.04035
$483$	6.29189	+	1.93820i	0.286291	+	0.0881910i
$484$	−21.8086			−0.991301
$485$	7.14058	−	8.24067i	0.324237	−	0.374189i
$486$	32.2756	−	20.7422i	1.46405	−	0.940887i
$487$	0.670174	+	4.66116i	0.0303685	+	0.211217i	0.999356	−	0.0358938i	$-0.0114278\pi$
$487$	0.670174	+	4.66116i	0.0303685	+	0.211217i	−0.968987	+	0.247111i	$0.920519\pi$
$488$	−1.58407	−	3.46862i	−0.0717073	−	0.157017i
$489$	−0.858668	+	5.97217i	−0.0388303	+	0.270071i
$490$	11.7694	−	3.45580i	0.531686	−	0.156117i
$491$	−13.0501	−	8.38676i	−0.588941	−	0.378489i	0.211967	−	0.977277i	$-0.432013\pi$
$491$	−13.0501	−	8.38676i	−0.588941	−	0.378489i	−0.800908	+	0.598787i	$0.795649\pi$
$492$	−10.7490	+	23.5370i	−0.484601	+	1.06113i
$493$	−26.1863	−	7.68899i	−1.17937	−	0.346295i
$494$	−3.61312	−	4.16976i	−0.162562	−	0.187606i
$495$	2.98205	+	3.44147i	0.134033	+	0.154683i
$496$	25.3599	+	7.44635i	1.13870	+	0.334351i
$497$	−1.12982	+	2.47397i	−0.0506795	+	0.110973i
$498$	−3.53052	−	2.26893i	−0.158207	−	0.101673i
$499$	−19.8125	+	5.81748i	−0.886930	+	0.260426i	−0.693301	−	0.720648i	$-0.743844\pi$
$499$	−19.8125	+	5.81748i	−0.886930	+	0.260426i	−0.193630	+	0.981075i	$0.562026\pi$
$500$	0.533654	−	3.71165i	0.0238658	−	0.165990i
$501$	−1.15857	−	2.53692i	−0.0517613	−	0.113341i
$502$	−0.318473	−	2.21503i	−0.0142141	−	0.0988615i
$503$	7.51095	−	4.82699i	0.334897	−	0.215225i	−0.362374	−	0.932033i	$-0.618034\pi$
$503$	7.51095	−	4.82699i	0.334897	−	0.215225i	0.697271	+	0.716808i	$0.254397\pi$
$504$	7.54399	−	8.70623i	0.336036	−	0.387806i
$505$	−10.4064			−0.463079
$506$	−10.5611	−	23.9590i	−0.469499	−	1.06511i
$507$	12.2746			0.545136
$508$	−18.4000	+	21.2348i	−0.816369	+	0.942141i
$509$	−24.4024	+	15.6824i	−1.08162	+	0.695112i	−0.954930	−	0.296831i	$-0.904070\pi$
$509$	−24.4024	+	15.6824i	−1.08162	+	0.695112i	−0.126685	+	0.991943i	$0.540434\pi$
$510$	1.39320	+	9.68992i	0.0616920	+	0.429077i
$511$	4.62653	+	10.1307i	0.204666	+	0.448155i
$512$	−3.87913	+	26.9800i	−0.171435	+	1.19236i
$513$	12.9611	−	3.80574i	0.572248	−	0.168027i
$514$	26.3659	+	16.9444i	1.16295	+	0.747383i
$515$	−5.28316	+	11.5685i	−0.232804	+	0.509769i
$516$	25.2862	+	7.42469i	1.11316	+	0.326854i
$517$	−12.9929	−	14.9946i	−0.571426	−	0.659461i
$518$	−22.6643	−	26.1560i	−0.995814	−	1.14923i
$519$	14.6959	+	4.31510i	0.645078	+	0.189412i
$520$	1.48449	−	3.25057i	0.0650991	−	0.142547i
$521$	−11.6208	−	7.46825i	−0.509118	−	0.327190i	0.260736	−	0.965410i	$-0.416035\pi$
$521$	−11.6208	−	7.46825i	−0.509118	−	0.327190i	−0.769854	+	0.638220i	$0.779671\pi$
$522$	−30.7606	+	9.03212i	−1.34635	+	0.395325i
$523$	−4.57967	+	31.8523i	−0.200255	+	1.39280i	0.603272	+	0.797535i	$0.293863\pi$
$523$	−4.57967	+	31.8523i	−0.200255	+	1.39280i	−0.803527	+	0.595268i	$0.797046\pi$
$524$	1.26450	+	2.76888i	0.0552401	+	0.120959i
$525$	−0.195368	−	1.35881i	−0.00852655	−	0.0593034i
$526$	−5.39592	+	3.46775i	−0.235273	+	0.151201i
$527$	27.5867	−	31.8367i	1.20170	−	1.38683i
$528$	5.83214			0.253812
$529$	−15.5162	+	16.9779i	−0.674617	+	0.738168i
$530$	16.3800			0.711500
$531$	3.55720	−	4.10523i	0.154369	−	0.178152i
$532$	11.6996	−	7.51888i	0.507242	−	0.325985i
$533$	−0.836373	−	5.81710i	−0.0362273	−	0.251967i
$534$	5.29595	+	11.5965i	0.229178	+	0.501830i
$535$	1.61698	−	11.2464i	0.0699083	−	0.486223i
$536$	−39.9274	+	11.7237i	−1.72460	+	0.506388i
$537$	10.8851	+	6.99543i	0.469727	+	0.301875i
$538$	32.0808	−	70.2472i	1.38310	−	3.02857i
$539$	−11.1754	−	3.28139i	−0.481358	−	0.141339i
$540$	12.2780	+	14.1696i	0.528363	+	0.609763i
$541$	−0.833443	−	0.961844i	−0.0358325	−	0.0413529i	0.737550	−	0.675292i	$-0.235982\pi$
$541$	−0.833443	−	0.961844i	−0.0358325	−	0.0413529i	−0.773383	+	0.633939i	$0.781437\pi$
$542$	−13.0110	−	3.82038i	−0.558871	−	0.164099i
$543$	−6.44875	+	14.1208i	−0.276743	+	0.605982i
$544$	7.72609	+	4.96526i	0.331253	+	0.212884i
$545$	4.10318	−	1.20480i	0.175761	−	0.0516081i
$546$	0.398983	−	2.77499i	0.0170749	−	0.118759i
$547$	−8.25842	−	18.0834i	−0.353104	−	0.773191i	−0.999944	−	0.0105648i	$-0.996637\pi$
$547$	−8.25842	−	18.0834i	−0.353104	−	0.773191i	0.646840	−	0.762626i	$-0.276090\pi$
$548$	6.53401	+	45.4451i	0.279119	+	1.94132i
$549$	−1.52908	+	0.982677i	−0.0652593	+	0.0419396i
$550$	−3.57530	+	4.12611i	−0.152451	+	0.175938i
$551$	−18.0604			−0.769399
$552$	−8.11645	−	18.4131i	−0.345459	−	0.783712i
$553$	20.1747			0.857915
$554$	−40.7947	+	47.0796i	−1.73320	+	2.00022i
$555$	8.84487	−	5.68425i	0.375444	−	0.241283i
$556$	−9.22104	−	64.1338i	−0.391059	−	2.71988i
$557$	−19.0488	−	41.7110i	−0.807123	−	1.76735i	−0.619308	−	0.785148i	$-0.712587\pi$
$557$	−19.0488	−	41.7110i	−0.807123	−	1.76735i	−0.187814	−	0.982205i	$-0.560140\pi$
$558$	7.04241	−	48.9811i	0.298129	−	2.07353i
$559$	−5.74312	+	1.68633i	−0.242908	+	0.0713242i
$560$	2.95816	+	1.90110i	0.125005	+	0.0803359i
$561$	3.86149	−	8.45548i	0.163032	−	0.356991i
$562$	67.3969	+	19.7895i	2.84297	+	0.834771i
$563$	−10.4097	−	12.0135i	−0.438718	−	0.506308i	0.492730	−	0.870183i	$-0.335999\pi$
$563$	−10.4097	−	12.0135i	−0.438718	−	0.506308i	−0.931448	+	0.363874i	$0.881454\pi$
$564$	−21.3983	−	24.6950i	−0.901031	−	1.03985i
$565$	−2.36292	−	0.693815i	−0.0994087	−	0.0291890i
$566$	−3.51584	+	7.69862i	−0.147782	+	0.323597i
$567$	−1.15486	−	0.742184i	−0.0484996	−	0.0311688i
$568$	7.97602	−	2.34197i	0.334666	−	0.0982669i
$569$	−4.63561	+	32.2414i	−0.194335	+	1.35163i	0.626035	+	0.779795i	$0.284677\pi$
$569$	−4.63561	+	32.2414i	−0.194335	+	1.35163i	−0.820370	+	0.571833i	$0.806232\pi$
$570$	2.69117	+	5.89283i	0.112721	+	0.246824i
$571$	0.274000	+	1.90571i	0.0114665	+	0.0797515i	0.994751	−	0.102324i	$-0.0326277\pi$
$571$	0.274000	+	1.90571i	0.0114665	+	0.0797515i	−0.983285	+	0.182075i	$0.941719\pi$
$572$	−6.11713	+	3.93124i	−0.255770	+	0.164373i
$573$	12.0782	−	13.9390i	0.504574	−	0.582309i
$574$	22.7146			0.948087
$575$	4.58330	+	1.41187i	0.191137	+	0.0588791i
$576$	21.0343			0.876428
$577$	−15.5509	+	17.9467i	−0.647394	+	0.747132i	−0.980664	−	0.195699i	$-0.937302\pi$
$577$	−15.5509	+	17.9467i	−0.647394	+	0.747132i	0.333270	+	0.942831i	$0.391848\pi$
$578$	0.670538	−	0.430928i	0.0278907	−	0.0179243i
$579$	−1.08585	−	7.55227i	−0.0451265	−	0.313862i
$580$	−10.4133	−	22.8019i	−0.432388	−	0.946798i
$581$	−0.341931	+	2.37818i	−0.0141857	+	0.0986636i
$582$	−25.0873	+	7.36628i	−1.03990	+	0.305342i
$583$	−13.0842	−	8.40874i	−0.541894	−	0.348254i
$584$	14.1407	−	30.9639i	0.585148	−	1.28130i
$585$	−1.63436	−	0.479890i	−0.0675723	−	0.0198410i
$586$	−36.9801	−	42.6773i	−1.52763	−	1.76298i
$587$	2.74755	+	3.17084i	0.113404	+	0.130875i	0.809613	−	0.586964i	$-0.199677\pi$
$587$	2.74755	+	3.17084i	0.113404	+	0.130875i	−0.696209	+	0.717839i	$0.745132\pi$
$588$	−18.4050	−	5.40420i	−0.759010	−	0.222866i
$589$	11.5805	−	25.3578i	0.477167	−	1.04485i
$590$	5.47878	+	3.52100i	0.225558	+	0.144957i
$591$	−10.6614	+	3.13046i	−0.438549	+	0.128770i
$592$	−3.83272	+	26.6571i	−0.157524	+	1.09560i
$593$	10.6921	+	23.4123i	0.439070	+	0.961429i	0.991768	+	0.128048i	$0.0408710\pi$
$593$	10.6921	+	23.4123i	0.439070	+	0.961429i	−0.552698	+	0.833382i	$0.686402\pi$
$594$	−3.88493	−	27.0203i	−0.159401	−	1.10866i
$595$	4.71483	−	3.03004i	0.193289	−	0.124219i
$596$	34.8308	−	40.1969i	1.42673	−	1.64653i
$597$	13.7978			0.564705
$598$	8.16861	+	5.40359i	0.334039	+	0.220969i
$599$	−13.1966			−0.539197			−0.269598	−	0.962973i	$-0.586891\pi$
$599$	−13.1966			−0.539197			−0.269598	+	0.962973i	$0.586891\pi$
$600$	−2.74769	+	3.17101i	−0.112174	+	0.129456i
$601$	28.3826	−	18.2404i	1.15775	−	0.744041i	0.186583	−	0.982439i	$-0.440259\pi$
$601$	28.3826	−	18.2404i	1.15775	−	0.744041i	0.971168	+	0.238398i	$0.0766222\pi$
$602$	−3.29239	−	22.8991i	−0.134188	−	0.933296i
$603$	8.23990	+	18.0429i	0.335555	+	0.734762i
$604$	5.02465	−	34.9472i	0.204450	−	1.42198i
$605$	−5.58033	+	1.63853i	−0.226873	+	0.0666158i
$606$	20.9920	+	13.4908i	0.852743	+	0.548025i
$607$	−13.6115	+	29.8050i	−0.552473	+	1.20975i	0.403144	+	0.915137i	$0.367917\pi$
$607$	−13.6115	+	29.8050i	−0.552473	+	1.20975i	−0.955617	+	0.294611i	$0.904810\pi$
$608$	5.83136	+	1.71224i	0.236493	+	0.0694406i
$609$	−6.00963	−	6.93548i	−0.243522	−	0.281040i
$610$	−1.42708	−	1.64694i	−0.0577807	−	0.0666825i
$611$	7.12094	+	2.09090i	0.288082	+	0.0845886i
$612$	−12.7192	+	27.8511i	−0.514142	+	1.12581i
$613$	−5.21401	−	3.35084i	−0.210592	−	0.135339i	0.431093	−	0.902307i	$-0.358128\pi$
$613$	−5.21401	−	3.35084i	−0.210592	−	0.135339i	−0.641685	+	0.766968i	$0.721764\pi$
$614$	−7.53400	+	2.21218i	−0.304048	+	0.0892764i
$615$	−0.982030	+	6.83017i	−0.0395993	+	0.275419i
$616$	−5.44804	−	11.9295i	−0.219508	−	0.480655i
$617$	−3.60268	−	25.0572i	−0.145038	−	1.00876i	−0.924191	−	0.381930i	$-0.875260\pi$
$617$	−3.60268	−	25.0572i	−0.145038	−	1.00876i	0.779153	−	0.626834i	$-0.215649\pi$
$618$	25.6546	−	16.4872i	1.03198	−	0.663213i
$619$	−10.8800	+	12.5562i	−0.437304	+	0.504675i	−0.931030	−	0.364942i	$-0.881089\pi$
$619$	−10.8800	+	12.5562i	−0.437304	+	0.504675i	0.493727	+	0.869617i	$0.335634\pi$
$620$	38.6923			1.55392
$621$	−20.3422	+	12.6962i	−0.816305	+	0.509482i
$622$	53.8191			2.15795
$623$	4.77954	−	5.51589i	0.191488	−	0.220989i
$624$	−1.83525	+	1.17944i	−0.0734686	+	0.0472154i
$625$	−0.142315	−	0.989821i	−0.00569259	−	0.0395929i
$626$	−11.9643	−	26.1982i	−0.478190	−	1.04709i
$627$	0.875422	−	6.08870i	0.0349610	−	0.243159i
$628$	53.1344	−	15.6017i	2.12029	−	0.622575i
$629$	36.1100	+	23.2065i	1.43980	+	0.925304i
$630$	2.73490	−	5.98860i	0.108961	−	0.238592i
$631$	−20.3715	−	5.98161i	−0.810976	−	0.238124i	−0.150150	−	0.988663i	$-0.547976\pi$
$631$	−20.3715	−	5.98161i	−0.810976	−	0.238124i	−0.660826	+	0.750539i	$0.729794\pi$
$632$	−40.3805	−	46.6016i	−1.60625	−	1.85371i
$633$	1.28747	+	1.48582i	0.0511722	+	0.0590559i
$634$	65.7135	+	19.2952i	2.60982	+	0.766311i
$635$	−3.11273	+	6.81594i	−0.123525	+	0.270482i
$636$	−21.5488	−	13.8486i	−0.854465	−	0.549131i
$637$	4.18024	−	1.22743i	0.165627	−	0.0486325i
$638$	−5.19408	+	36.1256i	−0.205636	+	1.43023i
$639$	−1.64603	−	3.60430i	−0.0651159	−	0.142584i
$640$	2.94872	+	20.5088i	0.116558	+	0.810681i
$641$	1.52069	−	0.977288i	0.0600636	−	0.0386006i	−0.510264	−	0.860018i	$-0.670452\pi$
$641$	1.52069	−	0.977288i	0.0600636	−	0.0386006i	0.570328	+	0.821417i	$0.306816\pi$
$642$	−17.8415	+	20.5902i	−0.704147	+	0.812629i
$643$	20.7517			0.818367			0.409184	−	0.912452i	$-0.365814\pi$
$643$	20.7517			0.818367			0.409184	+	0.912452i	$0.365814\pi$
$644$	−16.4122	+	18.4421i	−0.646729	+	0.726722i
$645$	7.02799			0.276727
$646$	−17.3198	+	19.9882i	−0.681440	+	0.786424i
$647$	−20.7845	+	13.3574i	−0.817122	+	0.525132i	−0.881162	−	0.472815i	$-0.843238\pi$
$647$	−20.7845	+	13.3574i	−0.817122	+	0.525132i	0.0640400	+	0.997947i	$0.479601\pi$
$648$	0.597131	+	4.15314i	0.0234575	+	0.163151i
$649$	−2.56890	−	5.62512i	−0.100838	−	0.220805i
$650$	0.290638	−	2.02143i	0.0113998	−	0.0792870i
$651$	13.5912	−	3.99075i	0.532682	−	0.156410i
$652$	−19.0332	−	12.2319i	−0.745398	−	0.479038i
$653$	−0.639465	+	1.40023i	−0.0250242	+	0.0547953i	−0.921731	−	0.387829i	$-0.873225\pi$
$653$	−0.639465	+	1.40023i	−0.0250242	+	0.0547953i	0.896707	+	0.442624i	$0.145952\pi$
$654$	−9.83893	−	2.88897i	−0.384733	−	0.112968i
$655$	0.531590	+	0.613488i	0.0207709	+	0.0239709i
$656$	−11.5749	−	13.3581i	−0.451923	−	0.521546i
$657$	−15.5683	−	4.57128i	−0.607379	−	0.178343i
$658$	−11.9160	+	26.0925i	−0.464536	+	1.01719i
$659$	−22.7777	−	14.6383i	−0.887293	−	0.570229i	0.0157033	−	0.999877i	$-0.495001\pi$
$659$	−22.7777	−	14.6383i	−0.887293	−	0.570229i	−0.902996	+	0.429648i	$0.858638\pi$
$660$	8.19196	−	2.40538i	0.318872	−	0.0936291i
$661$	−1.64945	+	11.4722i	−0.0641560	+	0.446215i	0.932271	+	0.361760i	$0.117824\pi$
$661$	−1.64945	+	11.4722i	−0.0641560	+	0.446215i	−0.996427	+	0.0844550i	$0.973085\pi$
$662$	27.2133	+	59.5888i	1.05767	+	2.31598i
$663$	0.494836	+	3.44166i	0.0192179	+	0.133663i
$664$	6.17777	−	3.97021i	0.239744	−	0.154074i
$665$	2.42875	−	2.80293i	0.0941830	−	0.108693i
$666$	50.4222			1.95382
$667$	30.8778	−	8.62472i	1.19559	−	0.333951i
$668$	10.4581			0.404635
$669$	−11.6523	+	13.4475i	−0.450504	+	0.519909i
$670$	−20.0062	+	12.8572i	−0.772905	+	0.496716i
$671$	0.294482	+	2.04816i	0.0113683	+	0.0790685i
$672$	1.28287	+	2.80909i	0.0494876	+	0.108363i
$673$	−4.14880	+	28.8555i	−0.159924	+	1.11230i	0.738844	+	0.673876i	$0.235372\pi$
$673$	−4.14880	+	28.8555i	−0.159924	+	1.11230i	−0.898769	+	0.438423i	$0.855537\pi$
$674$	−26.5133	+	7.78500i	−1.02125	+	0.299867i
$675$	4.20627	+	2.70320i	0.161899	+	0.104046i
$676$	−19.1206	+	41.8682i	−0.735407	+	1.61032i
$677$	18.7219	+	5.49725i	0.719541	+	0.211276i	0.620948	−	0.783851i	$-0.286748\pi$
$677$	18.7219	+	5.49725i	0.719541	+	0.211276i	0.0985929	+	0.995128i	$0.468566\pi$
$678$	3.86708	+	4.46284i	0.148514	+	0.171394i
$679$	9.80248	+	11.3127i	0.376185	+	0.434140i
$680$	−16.4361	−	4.82606i	−0.630294	−	0.185071i
$681$	2.78976	−	6.10873i	0.106904	−	0.234087i
$682$	−47.3919	−	30.4569i	−1.81473	−	1.16626i
$683$	−26.3297	+	7.73108i	−1.00748	+	0.295822i	−0.743520	−	0.668713i	$-0.766845\pi$
$683$	−26.3297	+	7.73108i	−1.00748	+	0.295822i	−0.263956	+	0.964535i	$0.585027\pi$
$684$	−2.88351	+	20.0553i	−0.110254	+	0.766832i
$685$	5.08630	+	11.1374i	0.194338	+	0.425540i
$686$	5.67570	+	39.4754i	0.216699	+	1.50718i
$687$	18.6171	−	11.9645i	0.710285	−	0.456473i
$688$	−11.7889	+	13.6051i	−0.449447	+	0.518689i
$689$	5.81783			0.221642
$690$	−7.41520	−	8.78980i	−0.282292	−	0.334622i
$691$	−24.2740			−0.923425			−0.461712	−	0.887030i	$-0.652765\pi$
$691$	−24.2740			−0.923425			−0.461712	+	0.887030i	$0.652765\pi$
$692$	−37.6108	+	43.4052i	−1.42975	+	1.65002i
$693$	−5.25891	+	3.37970i	−0.199769	+	0.128384i
$694$	−3.60545	−	25.0764i	−0.136861	−	0.951888i
$695$	−7.17798	−	15.7176i	−0.272276	−	0.596202i
$696$	−3.99177	+	27.7634i	−0.151308	+	1.05237i
$697$	−27.0304	+	7.93685i	−1.02385	+	0.300630i
$698$	3.48311	+	2.23846i	0.131838	+	0.0847268i
$699$	6.70893	−	14.6905i	0.253755	−	0.555646i
$700$	4.93918	+	1.45027i	0.186683	+	0.0548152i
$701$	0.810987	+	0.935929i	0.0306306	+	0.0353496i	0.770858	−	0.637007i	$-0.219828\pi$
$701$	0.810987	+	0.935929i	0.0306306	+	0.0353496i	−0.740228	+	0.672356i	$0.765282\pi$
$702$	6.68684	+	7.71702i	0.252378	+	0.291260i
$703$	27.2545	+	8.00264i	1.02792	+	0.301825i
$704$	9.94754	−	21.7821i	0.374912	−	0.820942i
$705$	−7.33073	−	4.71117i	−0.276091	−	0.177433i
$706$	−10.3537	+	3.04012i	−0.389667	+	0.114417i
$707$	2.03308	−	14.1404i	0.0764617	−	0.531803i
$708$	−4.23079	−	9.26415i	−0.159003	−	0.348168i
$709$	2.47319	+	17.2014i	0.0928825	+	0.646012i	0.982077	+	0.188482i	$0.0603567\pi$
$709$	2.47319	+	17.2014i	0.0928825	+	0.646012i	−0.889194	+	0.457530i	$0.848734\pi$
$710$	3.99649	−	2.56839i	0.149986	−	0.0963900i
$711$	−19.2479	+	22.2132i	−0.721852	+	0.833061i
$712$	−22.3077			−0.836015
$713$	−7.68960	+	48.8844i	−0.287978	+	1.83074i
$714$	−13.4390			−0.502941
$715$	−1.26987	+	1.46551i	−0.0474905	+	0.0548070i
$716$	−40.8171	+	26.2316i	−1.52541	+	0.980320i
$717$	−1.02387	−	7.12117i	−0.0382371	−	0.265945i
$718$	−15.0477	−	32.9500i	−0.561577	−	1.22968i
$719$	2.62249	−	18.2398i	0.0978022	−	0.680230i	−0.880652	−	0.473764i	$-0.842895\pi$
$719$	2.62249	−	18.2398i	0.0978022	−	0.680230i	0.978454	−	0.206465i	$-0.0661960\pi$
$720$	−4.91546	+	1.44331i	−0.183188	+	0.0537890i
$721$	−14.6873	−	9.43893i	−0.546982	−	0.351524i
$722$	11.6555	−	25.5221i	0.433774	−	0.949833i
$723$	17.9243	+	5.26306i	0.666613	+	0.195735i
$724$	−38.1200	−	43.9928i	−1.41672	−	1.63498i
$725$	−4.37769	−	5.05212i	−0.162583	−	0.187631i
$726$	13.3810	+	3.92900i	0.496614	+	0.145819i
$727$	5.92475	−	12.9734i	0.219737	−	0.481156i	−0.767373	−	0.641201i	$-0.778436\pi$
$727$	5.92475	−	12.9734i	0.219737	−	0.481156i	0.987110	+	0.160044i	$0.0511638\pi$
$728$	4.12690	+	2.65220i	0.152953	+	0.0982970i
$729$	−12.4734	+	3.66252i	−0.461978	+	0.135649i
$730$	2.76852	−	19.2555i	0.102468	−	0.712677i
$731$	11.9193	+	26.0996i	0.440850	+	0.965327i
$732$	0.484989	+	3.37317i	0.0179257	+	0.124676i
$733$	−25.3320	+	16.2799i	−0.935660	+	0.601312i	−0.917161	−	0.398517i	$-0.869525\pi$
$733$	−25.3320	+	16.2799i	−0.935660	+	0.601312i	−0.0184988	+	0.999829i	$0.505889\pi$
$734$	39.4534	−	45.5317i	1.45625	−	1.68060i
$735$	−5.11546			−0.188687
$736$	−10.7875	−	0.142657i	−0.397634	−	0.00525842i
$737$	22.5811			0.831787
$738$	−21.6711	+	25.0098i	−0.797724	+	0.920622i
$739$	−24.0929	+	15.4835i	−0.886270	+	0.569571i	−0.902689	−	0.430294i	$-0.858410\pi$
$739$	−24.0929	+	15.4835i	−0.886270	+	0.569571i	0.0164185	+	0.999865i	$0.494774\pi$
$740$	5.61080	+	39.0240i	0.206257	+	1.43455i
$741$	0.955848	+	2.09301i	0.0351139	+	0.0768888i
$742$	−3.20012	+	22.2573i	−0.117480	+	0.817091i
$743$	−14.0696	+	4.13119i	−0.516162	+	0.151559i	−0.529431	−	0.848353i	$-0.677594\pi$
$743$	−14.0696	+	4.13119i	−0.516162	+	0.151559i	0.0132689	+	0.999912i	$0.495776\pi$
$744$	−36.4217	−	23.4068i	−1.33529	−	0.858136i
$745$	5.89233	−	12.9024i	0.215878	−	0.472708i
$746$	29.8478	+	8.76412i	1.09281	+	0.320877i
$747$	−2.29226	−	2.64541i	−0.0838695	−	0.0967905i
$748$	22.8261	+	26.3427i	0.834604	+	0.963185i
$749$	14.9658	+	4.39435i	0.546838	+	0.160566i
$750$	−0.996114	+	2.18119i	−0.0363730	+	0.0796457i
$751$	39.3442	+	25.2850i	1.43569	+	0.922663i	0.999743	+	0.0226917i	$0.00722361\pi$
$751$	39.3442	+	25.2850i	1.43569	+	0.922663i	0.435949	+	0.899971i	$0.356413\pi$
$752$	21.4168	−	6.28854i	0.780990	−	0.229319i
$753$	−0.132815	+	0.923745i	−0.00484003	+	0.0336632i
$754$	−5.67126	−	12.4183i	−0.206535	−	0.452249i
$755$	−1.33997	−	9.31970i	−0.0487665	−	0.339179i
$756$	−21.6526	+	13.9153i	−0.787497	+	0.506093i
$757$	2.89191	−	3.33744i	0.105108	−	0.121301i	−0.700758	−	0.713399i	$-0.747155\pi$
$757$	2.89191	−	3.33744i	0.105108	−	0.121301i	0.805866	+	0.592098i	$0.201700\pi$
$758$	65.6810			2.38564
$759$	1.41094	+	10.8279i	0.0512139	+	0.393027i
$760$	−11.3358			−0.411191
$761$	13.7133	−	15.8260i	0.497108	−	0.573693i	−0.450643	−	0.892704i	$-0.648805\pi$
$761$	13.7133	−	15.8260i	0.497108	−	0.573693i	0.947751	+	0.319011i	$0.103351\pi$
$762$	15.1152	−	9.71394i	0.547566	−	0.351899i
$763$	0.835472	+	5.81084i	0.0302461	+	0.210366i
$764$	28.7306	+	62.9113i	1.03944	+	2.27605i
$765$	−1.16203	+	8.08208i	−0.0420132	+	0.292208i
$766$	−1.22853	+	0.360730i	−0.0443887	+	0.0130337i
$767$	1.94595	+	1.25059i	0.0702642	+	0.0451560i
$768$	11.9012	−	26.0600i	0.429448	−	0.940361i
$769$	1.66441	+	0.488714i	0.0600201	+	0.0176235i	0.311605	−	0.950212i	$-0.399134\pi$
$769$	1.66441	+	0.488714i	0.0600201	+	0.0176235i	−0.251585	+	0.967835i	$0.580952\pi$
$770$	−4.90811	−	5.66427i	−0.176876	−	0.204126i
$771$	−8.55930	−	9.87796i	−0.308256	−	0.355746i
$772$	27.4519	+	8.06061i	0.988016	+	0.290108i
$773$	15.6659	−	34.3035i	0.563463	−	1.23381i	−0.386742	−	0.922188i	$-0.626400\pi$
$773$	15.6659	−	34.3035i	0.563463	−	1.23381i	0.950205	−	0.311625i	$-0.100873\pi$
$774$	28.3540	+	18.2220i	1.01916	+	0.654978i
$775$	9.90048	−	2.90704i	0.355636	−	0.104424i
$776$	6.51109	−	45.2857i	0.233735	−	1.62566i
$777$	5.99583	+	13.1290i	0.215099	+	0.471002i
$778$	−5.38183	−	37.4314i	−0.192948	−	1.34198i
$779$	−15.6831	+	10.0789i	−0.561907	+	0.361116i
$780$	−2.09138	+	2.41359i	−0.0748836	+	0.0864202i
$781$	−4.51088			−0.161412
$782$	20.0664	−	42.4448i	0.717572	−	1.51782i
$783$	33.4246			1.19450
$784$	8.58076	−	9.90273i	0.306456	−	0.353669i
$785$	12.4237	−	7.98423i	0.443421	−	0.284969i
$786$	−0.277016	−	1.92669i	−0.00988084	−	0.0687227i
$787$	−22.3702	−	48.9839i	−0.797411	−	1.74609i	−0.654098	−	0.756410i	$-0.726952\pi$
$787$	−22.3702	−	48.9839i	−0.797411	−	1.74609i	−0.143313	−	0.989677i	$-0.545776\pi$
$788$	5.92967	−	41.2418i	0.211236	−	1.46918i
$789$	2.56657	−	0.753613i	0.0913723	−	0.0268293i
$790$	−29.6454	−	19.0520i	−1.05474	−	0.677838i
$791$	1.40440	−	3.07521i	0.0499348	−	0.109342i
$792$	18.3327	+	5.38298i	0.651425	+	0.191276i
$793$	−0.506869	−	0.584958i	−0.0179994	−	0.0207725i
$794$	23.4458	+	27.0578i	0.832059	+	0.960247i
$795$	−6.55432	−	1.92452i	−0.232458	−	0.0682558i
$796$	−21.4932	+	47.0635i	−0.761806	+	1.66812i
$797$	−7.14835	−	4.59397i	−0.253208	−	0.162727i	0.407880	−	0.913036i	$-0.366268\pi$
$797$	−7.14835	−	4.59397i	−0.253208	−	0.162727i	−0.661087	+	0.750309i	$0.729905\pi$
$798$	−8.53302	+	2.50552i	−0.302066	+	0.0886945i
$799$	5.06299	−	35.2139i	0.179116	−	1.24578i
$800$	0.934499	+	2.04627i	0.0330395	+	0.0723465i
$801$	1.51326	+	10.5250i	0.0534686	+	0.371882i
$802$	47.2914	−	30.3923i	1.66992	−	1.07319i
$803$	−12.0964	+	13.9600i	−0.426872	+	0.492637i
$804$	37.1894			1.31157
$805$	−2.81390	+	5.95201i	−0.0991768	+	0.209781i
$806$	21.0725			0.742247
$807$	−21.0904	+	24.3397i	−0.742418	+	0.856797i
$808$	−36.7322	+	23.6064i	−1.29223	+	0.830469i
$809$	−3.06730	−	21.3335i	−0.107840	−	0.750047i	−0.969946	−	0.243319i	$-0.921764\pi$
$809$	−3.06730	−	21.3335i	−0.107840	−	0.750047i	0.862106	−	0.506728i	$-0.169145\pi$
$810$	0.996114	+	2.18119i	0.0349999	+	0.0766391i
$811$	5.96255	−	41.4704i	0.209373	−	1.45622i	−0.565835	−	0.824519i	$-0.691446\pi$
$811$	5.96255	−	41.4704i	0.209373	−	1.45622i	0.775208	−	0.631706i	$-0.217645\pi$
$812$	33.0180	−	9.69495i	1.15870	−	0.340226i
$813$	4.75740	+	3.05739i	0.166849	+	0.107228i
$814$	23.8457	−	52.2147i	0.835791	−	1.83013i
$815$	−5.78918	−	1.69986i	−0.202786	−	0.0595434i
$816$	6.84822	+	7.90327i	0.239736	+	0.276670i
$817$	12.4340	+	14.3496i	0.435011	+	0.502030i
$818$	−83.2290	−	24.4382i	−2.91003	−	0.854463i
$819$	0.971382	−	2.12703i	0.0339428	−	0.0743244i
$820$	−21.7676	−	13.9892i	−0.760159	−	0.488525i
$821$	37.3263	−	10.9600i	1.30270	−	0.382506i	0.444478	−	0.895790i	$-0.353389\pi$
$821$	37.3263	−	10.9600i	1.30270	−	0.382506i	0.858219	+	0.513284i	$0.171571\pi$
$822$	4.17828	−	29.0605i	0.145734	−	1.01360i
$823$	−12.4876	−	27.3441i	−0.435291	−	0.953155i	−0.992439	−	0.122741i	$-0.960831\pi$
$823$	−12.4876	−	27.3441i	−0.435291	−	0.953155i	0.557148	−	0.830414i	$-0.311896\pi$
$824$	7.59418	+	52.8187i	0.264556	+	1.84003i
$825$	1.91542	−	1.23096i	0.0666862	−	0.0428566i
$826$	−5.85475	+	6.75674i	−0.203713	+	0.235097i
$827$	5.04720			0.175508			0.0877542	−	0.996142i	$-0.472031\pi$
$827$	5.04720			0.175508			0.0877542	+	0.996142i	$0.472031\pi$
$828$	−4.64743	−	35.6655i	−0.161509	−	1.23946i
$829$	19.2151			0.667367			0.333684	−	0.942685i	$-0.391708\pi$
$829$	19.2151			0.667367			0.333684	+	0.942685i	$0.391708\pi$
$830$	2.74828	−	3.17169i	0.0953942	−	0.110091i
$831$	21.8552	−	14.0455i	0.758149	−	0.487232i
$832$	1.27474	+	8.86603i	0.0441937	+	0.307374i
$833$	−8.67568	−	18.9971i	−0.300594	−	0.658210i
$834$	−5.89654	+	41.0113i	−0.204180	+	1.42011i
$835$	2.67598	−	0.785740i	0.0926063	−	0.0271917i
$836$	19.4046	+	12.4706i	0.671122	+	0.431304i
$837$	−21.4322	+	46.9299i	−0.740805	+	1.62214i
$838$	−33.7915	−	9.92209i	−1.16731	−	0.342753i
$839$	−11.1165	−	12.8291i	−0.383785	−	0.442911i	0.530683	−	0.847571i	$-0.321936\pi$
$839$	−11.1165	−	12.8291i	−0.383785	−	0.442911i	−0.914467	+	0.404659i	$0.867390\pi$
$840$	−3.77199	−	4.35311i	−0.130146	−	0.150197i
$841$	−15.0526	−	4.41984i	−0.519055	−	0.152408i
$842$	11.0091	−	24.1065i	0.379398	−	0.830765i
$843$	−24.6433	−	15.8373i	−0.848759	−	0.545464i
$844$	−7.07358	+	2.07699i	−0.243483	+	0.0714929i
$845$	−1.74686	+	12.1497i	−0.0600940	+	0.417963i
$846$	−17.3604	−	38.0140i	−0.596863	−	1.30695i
$847$	−1.13624	−	7.90274i	−0.0390418	−	0.271541i
$848$	14.7199	−	9.45991i	0.505484	−	0.324855i
$849$	2.31137	−	2.66746i	0.0793259	−	0.0915470i
$850$	−9.78957			−0.335779
$851$	−50.4186	−	0.666748i	−1.72833	−	0.0228558i
$852$	−7.42908			−0.254516
$853$	−3.20733	+	3.70146i	−0.109817	+	0.126736i	−0.807997	−	0.589187i	$-0.799448\pi$
$853$	−3.20733	+	3.70146i	−0.109817	+	0.126736i	0.698180	+	0.715923i	$0.253994\pi$
$854$	2.51668	−	1.61737i	0.0861191	−	0.0553454i
$855$	0.768974	+	5.34833i	0.0262984	+	0.182909i
$856$	−19.8042	−	43.3651i	−0.676893	−	1.48219i
$857$	−6.53414	+	45.4459i	−0.223202	+	1.55240i	0.502612	+	0.864512i	$0.332373\pi$
$857$	−6.53414	+	45.4459i	−0.223202	+	1.55240i	−0.725814	+	0.687892i	$0.758536\pi$
$858$	4.46149	−	1.31001i	0.152313	−	0.0447230i
$859$	12.0476	+	7.74251i	0.411058	+	0.264171i	0.729786	−	0.683675i	$-0.239619\pi$
$859$	12.0476	+	7.74251i	0.411058	+	0.264171i	−0.318729	+	0.947846i	$0.603256\pi$
$860$	−10.9477	+	23.9721i	−0.373314	+	0.817443i
$861$	−9.08906	−	2.66879i	−0.309754	−	0.0909521i
$862$	61.9703	+	71.5176i	2.11072	+	2.43590i
$863$	−37.3754	−	43.1336i	−1.27227	−	1.46828i	−0.815562	−	0.578669i	$-0.803572\pi$
$863$	−37.3754	−	43.1336i	−1.27227	−	1.46828i	−0.456713	−	0.889614i	$-0.650973\pi$
$864$	−10.7922	−	3.16886i	−0.367157	−	0.107807i
$865$	−6.36262	+	13.9322i	−0.216336	+	0.473709i
$866$	28.6978	+	18.4429i	0.975190	+	0.626716i
$867$	−0.318941	+	0.0936497i	−0.0108318	+	0.00318051i
$868$	−7.55922	+	52.5755i	−0.256577	+	1.78453i
$869$	13.9002	+	30.4373i	0.471533	+	1.03251i
$870$	2.28125	+	15.8664i	0.0773416	+	0.537923i
$871$	−7.10578	+	4.56661i	−0.240770	+	0.154734i
$872$	11.7503	−	13.5605i	0.397914	−	0.459217i
$873$	−21.8079			−0.738087
$874$	4.82779	−	30.6913i	0.163302	−	1.03815i
$875$	1.37279			0.0464086
$876$	−19.9218	+	22.9910i	−0.673097	+	0.776795i
$877$	−23.9354	+	15.3823i	−0.808240	+	0.519424i	−0.878295	−	0.478119i	$-0.841319\pi$
$877$	−23.9354	+	15.3823i	−0.808240	+	0.519424i	0.0700552	+	0.997543i	$0.477682\pi$
$878$	0.510984	+	3.55397i	0.0172449	+	0.119941i
$879$	9.78305	+	21.4219i	0.329974	+	0.722542i
$880$	−0.830001	+	5.77278i	−0.0279793	+	0.194600i
$881$	30.8976	−	9.07235i	1.04097	−	0.305655i	0.283804	−	0.958882i	$-0.408403\pi$
$881$	30.8976	−	9.07235i	1.04097	−	0.305655i	0.757162	+	0.653227i	$0.226585\pi$
$882$	−20.6380	−	13.2633i	−0.694919	−	0.446597i
$883$	1.85934	−	4.07138i	0.0625716	−	0.137013i	−0.875763	−	0.482742i	$-0.839641\pi$
$883$	1.85934	−	4.07138i	0.0625716	−	0.137013i	0.938334	+	0.345729i	$0.112368\pi$
$884$	−12.5102	−	3.67332i	−0.420762	−	0.123547i
$885$	−1.77860	−	2.05262i	−0.0597870	−	0.0689979i
$886$	−22.3247	−	25.7641i	−0.750012	−	0.865560i
$887$	−7.97115	−	2.34054i	−0.267645	−	0.0785877i	0.145156	−	0.989409i	$-0.453631\pi$
$887$	−7.97115	−	2.34054i	−0.267645	−	0.0785877i	−0.412801	+	0.910821i	$0.635450\pi$
$888$	18.3259	−	40.1282i	0.614978	−	1.34661i
$889$	−8.65345	−	5.56124i	−0.290227	−	0.186518i
$890$	−12.2322	+	3.59169i	−0.410023	+	0.120394i
$891$	0.324031	−	2.25368i	0.0108554	−	0.0755012i
$892$	−27.7175	−	60.6929i	−0.928052	−	2.03215i
$893$	−3.35044	−	23.3028i	−0.112118	−	0.779800i
$894$	−28.6127	+	18.3883i	−0.956952	+	0.614996i
$895$	−8.47334	+	9.77876i	−0.283233	+	0.326868i
$896$	−28.4437			−0.950237
$897$	−2.63373	−	3.12196i	−0.0879376	−	0.104239i
$898$	−83.3823			−2.78250
$899$	45.1709	−	52.1300i	1.50653	−	1.73863i
$900$	−6.30909	+	4.05461i	−0.210303	+	0.135154i
$901$	−3.96892	−	27.6045i	−0.132224	−	0.919638i
$902$	15.6502	+	34.2692i	0.521095	+	1.14104i
$903$	−1.37304	+	9.54972i	−0.0456920	+	0.317795i
$904$	−9.91443	+	2.91114i	−0.329749	+	0.0968231i
$905$	−13.0593	−	8.39272i	−0.434106	−	0.278983i
$906$	−9.37896	+	20.5370i	−0.311595	+	0.682298i
$907$	19.2618	+	5.65576i	0.639576	+	0.187796i	0.585412	−	0.810736i	$-0.300933\pi$
$907$	19.2618	+	5.65576i	0.639576	+	0.187796i	0.0541635	+	0.998532i	$0.482751\pi$
$908$	16.4909	+	19.0315i	0.547269	+	0.631582i
$909$	13.6295	+	15.7293i	0.452062	+	0.521707i
$910$	2.68996	+	0.789845i	0.0891714	+	0.0261831i
$911$	−7.07714	+	15.4968i	−0.234476	+	0.513431i	−0.989893	−	0.141813i	$-0.954707\pi$
$911$	−7.07714	+	15.4968i	−0.234476	+	0.513431i	0.755417	+	0.655244i	$0.227434\pi$
$912$	5.82171	+	3.74139i	0.192776	+	0.123890i
$913$	−3.82352	+	1.12269i	−0.126540	+	0.0371555i
$914$	−3.60546	+	25.0765i	−0.119258	+	0.829457i
$915$	0.377532	+	0.826680i	0.0124808	+	0.0273292i
$916$	11.8099	+	82.1393i	0.390209	+	2.71396i
$917$	−0.937470	+	0.602476i	−0.0309580	+	0.0198955i
$918$	32.0540	−	36.9923i	1.05794	−	1.22093i
$919$	4.71929			0.155675			0.0778376	−	0.996966i	$-0.475198\pi$
$919$	4.71929			0.155675			0.0778376	+	0.996966i	$0.475198\pi$
$920$	19.3807	−	5.41338i	0.638964	−	0.178474i
$921$	3.27459			0.107901
$922$	43.7919	−	50.5386i	1.44221	−	1.66440i
$923$	1.41947	−	0.912240i	0.0467225	−	0.0300267i
$924$	1.66801	+	11.6013i	0.0548735	+	0.381654i
$925$	4.36764	+	9.56379i	0.143607	+	0.314456i
$926$	−1.36612	+	9.50159i	−0.0448936	+	0.312242i
$927$	24.4052	−	7.16602i	0.801573	−	0.235363i
$928$	12.6508	+	8.13020i	0.415284	+	0.266887i
$929$	−5.90566	+	12.9316i	−0.193758	+	0.424271i	−0.981429	−	0.191825i	$-0.938559\pi$
$929$	−5.90566	+	12.9316i	−0.193758	+	0.424271i	0.787671	+	0.616096i	$0.211287\pi$
$930$	−23.7401	−	6.97073i	−0.778469	−	0.228579i
$931$	−9.05035	−	10.4447i	−0.296613	−	0.342310i
$932$	39.6579	+	45.7677i	1.29904	+	1.49917i
$933$	−21.5353	−	6.32334i	−0.705035	−	0.207017i
$934$	7.68813	−	16.8347i	0.251563	−	0.550847i
$935$	7.81987	+	5.02552i	0.255737	+	0.164352i
$936$	−6.85750	+	2.01354i	−0.224145	+	0.0658148i
$937$	2.42548	−	16.8696i	0.0792371	−	0.551106i	−0.911074	−	0.412242i	$-0.864746\pi$
$937$	2.42548	−	16.8696i	0.0792371	−	0.551106i	0.990311	−	0.138864i	$-0.0443451\pi$
$938$	−13.5619	−	29.6965i	−0.442813	−	0.969625i
$939$	1.70934	+	11.8887i	0.0557822	+	0.387974i
$940$	27.4889	−	17.6660i	0.896589	−	0.576203i
$941$	−22.0089	+	25.3997i	−0.717471	+	0.828005i	−0.991000	−	0.133858i	$-0.957263\pi$
$941$	−22.0089	+	25.3997i	−0.717471	+	0.828005i	0.273530	+	0.961863i	$0.411809\pi$
$942$	−35.4121			−1.15379
$943$	22.0002	−	24.7214i	0.716427	−	0.805040i
$944$	6.95700			0.226431
$945$	−4.49492	+	5.18741i	−0.146220	+	0.168746i
$946$	32.2791	−	20.7445i	1.04948	−	0.674462i
$947$	−1.50709	−	10.4821i	−0.0489740	−	0.340622i	−0.999546	−	0.0301184i	$-0.990412\pi$
$947$	−1.50709	−	10.4821i	−0.0489740	−	0.340622i	0.950572	−	0.310503i	$-0.100498\pi$
$948$	22.8926	+	50.1279i	0.743519	+	1.62808i
$949$	0.983322	−	6.83915i	0.0319200	−	0.222008i
$950$	−6.21585	+	1.82514i	−0.201669	+	0.0592153i
$951$	−24.0277	−	15.4417i	−0.779152	−	0.500731i
$952$	9.76879	−	21.3907i	0.316608	−	0.693275i
$953$	22.6166	+	6.64084i	0.732624	+	0.215118i	0.626705	−	0.779257i	$-0.284403\pi$
$953$	22.6166	+	6.64084i	0.732624	+	0.215118i	0.105920	+	0.994375i	$0.466221\pi$
$954$	−21.4532	−	24.7583i	−0.694573	−	0.801579i
$955$	12.0782	+	13.9390i	0.390841	+	0.451055i
$956$	25.8849	+	7.60049i	0.837177	+	0.245817i
$957$	6.32287	−	13.8451i	0.204389	−	0.447550i
$958$	46.0239	+	29.5778i	1.48697	+	0.955614i
$959$	−16.1274	+	4.73543i	−0.520781	+	0.152915i
$960$	1.49674	−	10.4101i	0.0483072	−	0.335984i
$961$	31.3515	+	68.6502i	1.01134	+	2.21452i
$962$	3.05574	+	21.2531i	0.0985211	+	0.685229i
$963$	−19.1167	+	12.2855i	−0.616026	+	0.395896i
$964$	−45.8733	+	52.9406i	−1.47748	+	1.70510i
$965$	7.62993			0.245616
$966$	13.3924	−	8.35862i	0.430893	−	0.268934i
$967$	−0.637460			−0.0204993			−0.0102497	−	0.999947i	$-0.503263\pi$
$967$	−0.637460			−0.0204993			−0.0102497	+	0.999947i	$0.503263\pi$
$968$	−15.9804	+	18.4423i	−0.513628	+	0.592758i
$969$	9.27887	−	5.96316i	0.298080	−	0.191564i
$970$	−3.72102	−	25.8802i	−0.119475	−	0.830964i
$971$	5.18090	+	11.3446i	0.166263	+	0.364065i	0.974363	−	0.224980i	$-0.0722315\pi$
$971$	5.18090	+	11.3446i	0.166263	+	0.364065i	−0.808101	+	0.589045i	$0.799504\pi$
$972$	8.53847	−	59.3864i	0.273872	−	1.90482i
$973$	22.7596	−	6.68282i	0.729639	−	0.214241i
$974$	9.49929	+	6.10482i	0.304377	+	0.195611i
$975$	−0.353799	+	0.774713i	−0.0113306	+	0.0248107i
$976$	−2.23360	−	0.655845i	−0.0714959	−	0.0209931i
$977$	11.8252	+	13.6470i	0.378321	+	0.436605i	0.912694	−	0.408643i	$-0.133998\pi$
$977$	11.8252	+	13.6470i	0.378321	+	0.436605i	−0.534374	+	0.845248i	$0.679452\pi$
$978$	9.47439	+	10.9340i	0.302957	+	0.349632i
$979$	11.6148	+	3.41042i	0.371211	+	0.108997i
$980$	7.96850	−	17.4486i	0.254545	−	0.557375i
$981$	−7.19509	−	4.62400i	−0.229721	−	0.147633i
$982$	−35.6906	+	10.4797i	−1.13893	+	0.334421i
$983$	3.87317	−	26.9385i	0.123535	−	0.859204i	−0.829966	−	0.557814i	$-0.811640\pi$
$983$	3.87317	−	26.9385i	0.123535	−	0.859204i	0.953501	−	0.301390i	$-0.0974506\pi$
$984$	12.0275	+	26.3366i	0.383423	+	0.839580i
$985$	−1.58132	−	10.9983i	−0.0503851	−	0.350436i
$986$	−55.0537	+	35.3808i	−1.75327	+	1.12676i
$987$	7.83379	−	9.04068i	0.249352	−	0.287768i
$988$	−8.62812			−0.274497
$989$	−28.1111	−	18.5957i	−0.893880	−	0.591308i
$990$	10.9193			0.347037
$991$	17.4533	−	20.1422i	0.554423	−	0.639839i	−0.407485	−	0.913212i	$-0.633594\pi$
$991$	17.4533	−	20.1422i	0.554423	−	0.639839i	0.961908	+	0.273373i	$0.0881395\pi$
$992$	−19.5271	+	12.5493i	−0.619986	+	0.398441i
$993$	−3.88796	−	27.0414i	−0.123381	−	0.858132i
$994$	2.70918	+	5.93227i	0.0859298	+	0.188160i
$995$	−1.96363	+	13.6573i	−0.0622512	+	0.432966i
$996$	−6.29705	+	1.84898i	−0.199530	+	0.0585872i
$997$	32.9143	+	21.1527i	1.04241	+	0.669913i	0.945580	−	0.325388i	$-0.105495\pi$
$997$	32.9143	+	21.1527i	1.04241	+	0.669913i	0.0968246	+	0.995301i	$0.469131\pi$
$998$	−20.5687	+	45.0392i	−0.651091	+	1.42569i
$999$	−50.4401	−	14.8106i	−1.59586	−	0.468585i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.g.a.16.1	✓	10
5.2	odd	4		575.2.p.a.499.2		20
5.3	odd	4		575.2.p.a.499.1		20
5.4	even	2		575.2.k.a.476.1		10
23.6	even	11		2645.2.a.n.1.1		5
23.13	even	11	inner	115.2.g.a.36.1	yes	10
23.17	odd	22		2645.2.a.o.1.1		5
115.13	odd	44		575.2.p.a.174.2		20
115.59	even	22		575.2.k.a.151.1		10
115.82	odd	44		575.2.p.a.174.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.a.16.1	✓	10	1.1	even	1	trivial
115.2.g.a.36.1	yes	10	23.13	even	11	inner
575.2.k.a.151.1		10	115.59	even	22
575.2.k.a.476.1		10	5.4	even	2
575.2.p.a.174.1		20	115.82	odd	44
575.2.p.a.174.2		20	115.13	odd	44
575.2.p.a.499.1		20	5.3	odd	4
575.2.p.a.499.2		20	5.2	odd	4
2645.2.a.n.1.1		5	23.6	even	11
2645.2.a.o.1.1		5	23.17	odd	22

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.57028 - 1.81219i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.533654 - 3.71165i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(-0.341254 + 2.37347i) q^{6} +(1.31718 - 0.386758i) q^{7} +(-3.52977 - 2.26844i) q^{8} +(-0.830830 + 1.81926i) q^{9} +O(q^{10})\)	\(q+(1.57028 - 1.81219i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.533654 - 3.71165i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(-0.341254 + 2.37347i) q^{6} +(1.31718 - 0.386758i) q^{7} +(-3.52977 - 2.26844i) q^{8} +(-0.830830 + 1.81926i) q^{9} +(-2.30075 - 0.675560i) q^{10} +(1.49103 + 1.72073i) q^{11} +(2.45561 + 2.83392i) q^{12} +(-0.817178 - 0.239945i) q^{13} +(1.36745 - 2.99430i) q^{14} +(0.841254 + 0.540641i) q^{15} +(-2.45773 + 0.721655i) q^{16} +(-0.581014 + 4.04104i) q^{17} +(1.99223 + 4.36237i) q^{18} +(0.384487 + 2.67417i) q^{19} +(-3.15455 + 2.02730i) q^{20} +(-0.898983 + 1.03748i) q^{21} +5.45963 q^{22} +(-1.93440 - 4.38840i) q^{23} +4.19584 q^{24} +(-0.654861 + 0.755750i) q^{25} +(-1.71802 + 1.10411i) q^{26} +(-0.711574 - 4.94911i) q^{27} +(-2.13843 - 4.68251i) q^{28} +(-0.951362 + 6.61687i) q^{29} +(2.30075 - 0.675560i) q^{30} +(-8.68043 - 5.57857i) q^{31} +(0.934499 - 2.04627i) q^{32} +(-2.18463 - 0.641465i) q^{33} +(6.41080 + 7.39846i) q^{34} +(-0.898983 - 1.03748i) q^{35} +(7.19584 + 2.11289i) q^{36} +(4.36764 - 9.56379i) q^{37} +(5.44986 + 3.50241i) q^{38} +(0.817178 - 0.239945i) q^{39} +(-0.597131 + 4.15314i) q^{40} +(2.86653 + 6.27683i) q^{41} +(0.468468 + 3.25827i) q^{42} +(5.91232 - 3.79962i) q^{43} +(5.59107 - 6.45244i) q^{44} +2.00000 q^{45} +(-10.9902 - 3.38549i) q^{46} -8.71406 q^{47} +(1.67742 - 1.93584i) q^{48} +(-4.30340 + 2.76563i) q^{49} +(0.341254 + 2.37347i) q^{50} +(-1.69597 - 3.71366i) q^{51} +(-0.454501 + 3.16113i) q^{52} +(-6.55432 + 1.92452i) q^{53} +(-10.0861 - 6.48195i) q^{54} +(0.945841 - 2.07110i) q^{55} +(-5.52667 - 1.62278i) q^{56} +(-1.76921 - 2.04178i) q^{57} +(10.4972 + 12.1144i) q^{58} +(-2.60598 - 0.765186i) q^{59} +(1.55773 - 3.41095i) q^{60} +(0.764538 + 0.491338i) q^{61} +(-23.7401 + 6.97073i) q^{62} +(-0.390736 + 2.71763i) q^{63} +(-4.36897 - 9.56672i) q^{64} +(0.121206 + 0.843008i) q^{65} +(-4.59293 + 2.95170i) q^{66} +(6.49469 - 7.49528i) q^{67} +15.3090 q^{68} +(3.99987 + 2.64594i) q^{69} -3.29177 q^{70} +(-1.29740 + 1.49728i) q^{71} +(7.05954 - 4.53689i) q^{72} +(1.15457 + 8.03022i) q^{73} +(-10.4731 - 22.9328i) q^{74} +(0.142315 - 0.989821i) q^{75} +(9.72038 - 2.85416i) q^{76} +(2.62945 + 1.68985i) q^{77} +(0.848368 - 1.85767i) q^{78} +(14.1009 + 4.14039i) q^{79} +(1.67742 + 1.93584i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(15.8761 + 4.66164i) q^{82} +(-0.727055 + 1.59203i) q^{83} +(4.33052 + 2.78305i) q^{84} +(3.91722 - 1.15020i) q^{85} +(2.39833 - 16.6807i) q^{86} +(-2.77701 - 6.08081i) q^{87} +(-1.35958 - 9.45610i) q^{88} +(4.47262 - 2.87438i) q^{89} +(3.14055 - 3.62439i) q^{90} -1.16917 q^{91} +(-15.2559 + 9.52171i) q^{92} +10.3184 q^{93} +(-13.6835 + 15.7916i) q^{94} +(2.27279 - 1.46063i) q^{95} +(0.320145 + 2.22666i) q^{96} +(4.52967 + 9.91860i) q^{97} +(-1.74567 + 12.1414i) q^{98} +(-4.36926 + 1.28293i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{2} + q^{3} - q^{4} + q^{5} + 6 q^{6} + 5 q^{7} - 16 q^{8} + 2 q^{9}+O(q^{10}) \) 10 * q + 5 * q^2 + q^3 - q^4 + q^5 + 6 * q^6 + 5 * q^7 - 16 * q^8 + 2 * q^9	\( 10 q + 5 q^{2} + q^{3} - q^{4} + q^{5} + 6 q^{6} + 5 q^{7} - 16 q^{8} + 2 q^{9} - 5 q^{10} + 8 q^{11} + q^{12} - 3 q^{14} - q^{15} + 5 q^{16} - 23 q^{17} - 10 q^{18} - 13 q^{19} + q^{20} + 6 q^{21} + 4 q^{22} - 21 q^{23} - 6 q^{24} - q^{25} + 11 q^{26} - 5 q^{27} - 6 q^{28} + 2 q^{29} + 5 q^{30} - 20 q^{31} - 15 q^{32} + 3 q^{33} + 16 q^{34} + 6 q^{35} + 24 q^{36} + 13 q^{37} + 21 q^{38} - 6 q^{40} - 5 q^{41} + 3 q^{42} + 15 q^{43} + 19 q^{44} + 20 q^{45} - 16 q^{46} - 52 q^{47} + 6 q^{48} + 4 q^{49} - 6 q^{50} - 10 q^{51} + 22 q^{52} + 6 q^{53} - 30 q^{54} + 3 q^{55} + 3 q^{56} + 2 q^{57} + 45 q^{58} + 5 q^{59} + 10 q^{60} - 3 q^{61} - 54 q^{62} - 10 q^{63} - 34 q^{64} - 4 q^{66} + 20 q^{67} + 32 q^{68} - q^{69} - 8 q^{70} - 22 q^{71} + 32 q^{72} + 43 q^{73} + q^{74} + q^{75} - 2 q^{76} + 4 q^{77} + 11 q^{78} + 51 q^{79} + 6 q^{80} - q^{81} + 58 q^{82} - 17 q^{83} + 6 q^{84} + q^{85} - 9 q^{86} - 2 q^{87} + 7 q^{88} + 57 q^{89} + 10 q^{90} - 22 q^{91} - 43 q^{92} + 20 q^{93} - 81 q^{94} - 9 q^{95} - 7 q^{96} + 52 q^{97} + 24 q^{98} + 6 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 + q^3 - q^4 + q^5 + 6 * q^6 + 5 * q^7 - 16 * q^8 + 2 * q^9 - 5 * q^10 + 8 * q^11 + q^12 - 3 * q^14 - q^15 + 5 * q^16 - 23 * q^17 - 10 * q^18 - 13 * q^19 + q^20 + 6 * q^21 + 4 * q^22 - 21 * q^23 - 6 * q^24 - q^25 + 11 * q^26 - 5 * q^27 - 6 * q^28 + 2 * q^29 + 5 * q^30 - 20 * q^31 - 15 * q^32 + 3 * q^33 + 16 * q^34 + 6 * q^35 + 24 * q^36 + 13 * q^37 + 21 * q^38 - 6 * q^40 - 5 * q^41 + 3 * q^42 + 15 * q^43 + 19 * q^44 + 20 * q^45 - 16 * q^46 - 52 * q^47 + 6 * q^48 + 4 * q^49 - 6 * q^50 - 10 * q^51 + 22 * q^52 + 6 * q^53 - 30 * q^54 + 3 * q^55 + 3 * q^56 + 2 * q^57 + 45 * q^58 + 5 * q^59 + 10 * q^60 - 3 * q^61 - 54 * q^62 - 10 * q^63 - 34 * q^64 - 4 * q^66 + 20 * q^67 + 32 * q^68 - q^69 - 8 * q^70 - 22 * q^71 + 32 * q^72 + 43 * q^73 + q^74 + q^75 - 2 * q^76 + 4 * q^77 + 11 * q^78 + 51 * q^79 + 6 * q^80 - q^81 + 58 * q^82 - 17 * q^83 + 6 * q^84 + q^85 - 9 * q^86 - 2 * q^87 + 7 * q^88 + 57 * q^89 + 10 * q^90 - 22 * q^91 - 43 * q^92 + 20 * q^93 - 81 * q^94 - 9 * q^95 - 7 * q^96 + 52 * q^97 + 24 * q^98 + 6 * q^99

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