LMFDB - Embedded newform 126.2.e.d.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(25,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 4]))

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

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

chi := DirichletCharacter("126.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.e (of order $3$, 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:	$1.00611506547$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$0.500000 + 0.224437i$ of defining polynomial
Character	$\chi$	$=$	126.121
Dual form			126.2.e.d.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.29418 - 1.15113i) q^{3} +1.00000 q^{4} +(-1.84981 - 3.20397i) q^{5} +(-1.29418 - 1.15113i) q^{6} +(2.64400 - 0.0963576i) q^{7} +1.00000 q^{8} +(0.349814 + 2.97954i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.29418 - 1.15113i) q^{3} +1.00000 q^{4} +(-1.84981 - 3.20397i) q^{5} +(-1.29418 - 1.15113i) q^{6} +(2.64400 - 0.0963576i) q^{7} +1.00000 q^{8} +(0.349814 + 2.97954i) q^{9} +(-1.84981 - 3.20397i) q^{10} +(0.738550 - 1.27921i) q^{11} +(-1.29418 - 1.15113i) q^{12} +(-1.34981 + 2.33795i) q^{13} +(2.64400 - 0.0963576i) q^{14} +(-1.29418 + 6.27589i) q^{15} +1.00000 q^{16} +(3.28799 + 5.69497i) q^{17} +(0.349814 + 2.97954i) q^{18} +(-0.444368 + 0.769668i) q^{19} +(-1.84981 - 3.20397i) q^{20} +(-3.53273 - 2.91887i) q^{21} +(0.738550 - 1.27921i) q^{22} +(-3.14400 - 5.44556i) q^{23} +(-1.29418 - 1.15113i) q^{24} +(-4.34362 + 7.52338i) q^{25} +(-1.34981 + 2.33795i) q^{26} +(2.97710 - 4.25874i) q^{27} +(2.64400 - 0.0963576i) q^{28} +(1.25526 + 2.17417i) q^{29} +(-1.29418 + 6.27589i) q^{30} +6.81089 q^{31} +1.00000 q^{32} +(-2.42835 + 0.805361i) q^{33} +(3.28799 + 5.69497i) q^{34} +(-5.19963 - 8.29305i) q^{35} +(0.349814 + 2.97954i) q^{36} +(-1.38874 + 2.40536i) q^{37} +(-0.444368 + 0.769668i) q^{38} +(4.43818 - 1.47192i) q^{39} +(-1.84981 - 3.20397i) q^{40} +(-2.05563 + 3.56046i) q^{41} +(-3.53273 - 2.91887i) q^{42} +(0.00618986 + 0.0107211i) q^{43} +(0.738550 - 1.27921i) q^{44} +(8.89926 - 6.63238i) q^{45} +(-3.14400 - 5.44556i) q^{46} -6.98762 q^{47} +(-1.29418 - 1.15113i) q^{48} +(6.98143 - 0.509538i) q^{49} +(-4.34362 + 7.52338i) q^{50} +(2.30037 - 11.1552i) q^{51} +(-1.34981 + 2.33795i) q^{52} +(-1.60507 - 2.78007i) q^{53} +(2.97710 - 4.25874i) q^{54} -5.46472 q^{55} +(2.64400 - 0.0963576i) q^{56} +(1.46108 - 0.484566i) q^{57} +(1.25526 + 2.17417i) q^{58} +6.90978 q^{59} +(-1.29418 + 6.27589i) q^{60} -5.73305 q^{61} +6.81089 q^{62} +(1.21201 + 7.84417i) q^{63} +1.00000 q^{64} +9.98762 q^{65} +(-2.42835 + 0.805361i) q^{66} -9.46472 q^{67} +(3.28799 + 5.69497i) q^{68} +(-2.19963 + 10.6667i) q^{69} +(-5.19963 - 8.29305i) q^{70} -5.46472 q^{71} +(0.349814 + 2.97954i) q^{72} +(-6.03273 - 10.4490i) q^{73} +(-1.38874 + 2.40536i) q^{74} +(14.2818 - 4.73656i) q^{75} +(-0.444368 + 0.769668i) q^{76} +(1.82946 - 3.45338i) q^{77} +(4.43818 - 1.47192i) q^{78} +11.4523 q^{79} +(-1.84981 - 3.20397i) q^{80} +(-8.75526 + 2.08457i) q^{81} +(-2.05563 + 3.56046i) q^{82} +(2.23855 + 3.87728i) q^{83} +(-3.53273 - 2.91887i) q^{84} +(12.1643 - 21.0693i) q^{85} +(0.00618986 + 0.0107211i) q^{86} +(0.878215 - 4.25874i) q^{87} +(0.738550 - 1.27921i) q^{88} +(-4.43818 + 7.68715i) q^{89} +(8.89926 - 6.63238i) q^{90} +(-3.34362 + 6.31159i) q^{91} +(-3.14400 - 5.44556i) q^{92} +(-8.81453 - 7.84020i) q^{93} -6.98762 q^{94} +3.28799 q^{95} +(-1.29418 - 1.15113i) q^{96} +(-6.58836 - 11.4114i) q^{97} +(6.98143 - 0.509538i) q^{98} +(4.06979 + 1.75305i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 2 q^{3} + 6 q^{4} - 5 q^{5} - 2 q^{6} + 4 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 - 2 * q^3 + 6 * q^4 - 5 * q^5 - 2 * q^6 + 4 * q^7 + 6 * q^8 - 4 * q^9	\( 6 q + 6 q^{2} - 2 q^{3} + 6 q^{4} - 5 q^{5} - 2 q^{6} + 4 q^{7} + 6 q^{8} - 4 q^{9} - 5 q^{10} - q^{11} - 2 q^{12} - 2 q^{13} + 4 q^{14} - 2 q^{15} + 6 q^{16} - 4 q^{17} - 4 q^{18} - 3 q^{19} - 5 q^{20} - 10 q^{21} - q^{22} - 7 q^{23} - 2 q^{24} - 2 q^{25} - 2 q^{26} + 7 q^{27} + 4 q^{28} - 5 q^{29} - 2 q^{30} + 28 q^{31} + 6 q^{32} - 19 q^{33} - 4 q^{34} - 19 q^{35} - 4 q^{36} - 9 q^{37} - 3 q^{38} + 9 q^{39} - 5 q^{40} - 12 q^{41} - 10 q^{42} + 18 q^{43} - q^{44} + 29 q^{45} - 7 q^{46} - 6 q^{47} - 2 q^{48} - 12 q^{49} - 2 q^{50} + 26 q^{51} - 2 q^{52} + 9 q^{53} + 7 q^{54} + 14 q^{55} + 4 q^{56} + 2 q^{57} - 5 q^{58} - 8 q^{59} - 2 q^{60} - 8 q^{61} + 28 q^{62} + 31 q^{63} + 6 q^{64} + 24 q^{65} - 19 q^{66} - 10 q^{67} - 4 q^{68} - q^{69} - 19 q^{70} + 14 q^{71} - 4 q^{72} - 25 q^{73} - 9 q^{74} + 44 q^{75} - 3 q^{76} + 52 q^{77} + 9 q^{78} - 14 q^{79} - 5 q^{80} - 40 q^{81} - 12 q^{82} + 8 q^{83} - 10 q^{84} + 14 q^{85} + 18 q^{86} + 31 q^{87} - q^{88} - 9 q^{89} + 29 q^{90} + 4 q^{91} - 7 q^{92} - 6 q^{94} - 4 q^{95} - 2 q^{96} - 28 q^{97} - 12 q^{98} - 41 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 2 * q^3 + 6 * q^4 - 5 * q^5 - 2 * q^6 + 4 * q^7 + 6 * q^8 - 4 * q^9 - 5 * q^10 - q^11 - 2 * q^12 - 2 * q^13 + 4 * q^14 - 2 * q^15 + 6 * q^16 - 4 * q^17 - 4 * q^18 - 3 * q^19 - 5 * q^20 - 10 * q^21 - q^22 - 7 * q^23 - 2 * q^24 - 2 * q^25 - 2 * q^26 + 7 * q^27 + 4 * q^28 - 5 * q^29 - 2 * q^30 + 28 * q^31 + 6 * q^32 - 19 * q^33 - 4 * q^34 - 19 * q^35 - 4 * q^36 - 9 * q^37 - 3 * q^38 + 9 * q^39 - 5 * q^40 - 12 * q^41 - 10 * q^42 + 18 * q^43 - q^44 + 29 * q^45 - 7 * q^46 - 6 * q^47 - 2 * q^48 - 12 * q^49 - 2 * q^50 + 26 * q^51 - 2 * q^52 + 9 * q^53 + 7 * q^54 + 14 * q^55 + 4 * q^56 + 2 * q^57 - 5 * q^58 - 8 * q^59 - 2 * q^60 - 8 * q^61 + 28 * q^62 + 31 * q^63 + 6 * q^64 + 24 * q^65 - 19 * q^66 - 10 * q^67 - 4 * q^68 - q^69 - 19 * q^70 + 14 * q^71 - 4 * q^72 - 25 * q^73 - 9 * q^74 + 44 * q^75 - 3 * q^76 + 52 * q^77 + 9 * q^78 - 14 * q^79 - 5 * q^80 - 40 * q^81 - 12 * q^82 + 8 * q^83 - 10 * q^84 + 14 * q^85 + 18 * q^86 + 31 * q^87 - q^88 - 9 * q^89 + 29 * q^90 + 4 * q^91 - 7 * q^92 - 6 * q^94 - 4 * q^95 - 2 * q^96 - 28 * q^97 - 12 * q^98 - 41 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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
$3$	−1.29418	−	1.15113i	−0.747196	−	0.664603i
$3$	−1.29418	−	1.15113i	−0.747196	−	0.664603i
$4$	1.00000			0.500000
$5$	−1.84981	−	3.20397i	−0.827262	−	1.43286i	−0.900178	−	0.435522i	$-0.856564\pi$
$5$	−1.84981	−	3.20397i	−0.827262	−	1.43286i	0.0729162	−	0.997338i	$-0.476769\pi$
$6$	−1.29418	−	1.15113i	−0.528348	−	0.469946i
$7$	2.64400	−	0.0963576i	0.999337	−	0.0364197i
$7$	2.64400	−	0.0963576i	0.999337	−	0.0364197i
$8$	1.00000			0.353553
$9$	0.349814	+	2.97954i	0.116605	+	0.993178i
$10$	−1.84981	−	3.20397i	−0.584963	−	1.01318i
$11$	0.738550	−	1.27921i	0.222681	−	0.385695i	−0.732940	−	0.680293i	$-0.761852\pi$
$11$	0.738550	−	1.27921i	0.222681	−	0.385695i	0.955621	+	0.294598i	$0.0951858\pi$
$12$	−1.29418	−	1.15113i	−0.373598	−	0.332302i
$13$	−1.34981	+	2.33795i	−0.374371	+	0.648430i	−0.990233	−	0.139425i	$-0.955475\pi$
$13$	−1.34981	+	2.33795i	−0.374371	+	0.648430i	0.615862	+	0.787854i	$0.288808\pi$
$14$	2.64400	−	0.0963576i	0.706638	−	0.0257526i
$15$	−1.29418	+	6.27589i	−0.334156	+	1.62043i
$16$	1.00000			0.250000
$17$	3.28799	+	5.69497i	0.797455	+	1.38123i	0.921268	+	0.388927i	$0.127154\pi$
$17$	3.28799	+	5.69497i	0.797455	+	1.38123i	−0.123813	+	0.992306i	$0.539512\pi$
$18$	0.349814	+	2.97954i	0.0824520	+	0.702283i
$19$	−0.444368	+	0.769668i	−0.101945	+	0.176574i	−0.912486	−	0.409108i	$-0.865840\pi$
$19$	−0.444368	+	0.769668i	−0.101945	+	0.176574i	0.810541	+	0.585682i	$0.199173\pi$
$20$	−1.84981	−	3.20397i	−0.413631	−	0.716430i
$21$	−3.53273	−	2.91887i	−0.770905	−	0.636950i
$22$	0.738550	−	1.27921i	0.157459	−	0.272728i
$23$	−3.14400	−	5.44556i	−0.655568	−	1.13548i	−0.981751	−	0.190171i	$-0.939096\pi$
$23$	−3.14400	−	5.44556i	−0.655568	−	1.13548i	0.326182	−	0.945307i	$-0.394238\pi$
$24$	−1.29418	−	1.15113i	−0.264174	−	0.234973i
$25$	−4.34362	+	7.52338i	−0.868725	+	1.50468i
$26$	−1.34981	+	2.33795i	−0.264720	+	0.458509i
$27$	2.97710	−	4.25874i	0.572943	−	0.819595i
$28$	2.64400	−	0.0963576i	0.499668	−	0.0182099i
$29$	1.25526	+	2.17417i	0.233096	+	0.403734i	0.958718	−	0.284360i	$-0.0917810\pi$
$29$	1.25526	+	2.17417i	0.233096	+	0.403734i	−0.725622	+	0.688094i	$0.758448\pi$
$30$	−1.29418	+	6.27589i	−0.236284	+	1.14582i
$31$	6.81089			1.22327			0.611636	−	0.791139i	$-0.290512\pi$
$31$	6.81089			1.22327			0.611636	+	0.791139i	$0.290512\pi$
$32$	1.00000			0.176777
$33$	−2.42835	+	0.805361i	−0.422721	+	0.140195i
$34$	3.28799	+	5.69497i	0.563886	+	0.976679i
$35$	−5.19963	−	8.29305i	−0.878898	−	1.40178i
$36$	0.349814	+	2.97954i	0.0583023	+	0.496589i
$37$	−1.38874	+	2.40536i	−0.228307	+	0.395439i	−0.957306	−	0.289075i	$-0.906652\pi$
$37$	−1.38874	+	2.40536i	−0.228307	+	0.395439i	0.729000	+	0.684514i	$0.239986\pi$
$38$	−0.444368	+	0.769668i	−0.0720860	+	0.124857i
$39$	4.43818	−	1.47192i	0.710677	−	0.235696i
$40$	−1.84981	−	3.20397i	−0.292481	−	0.506592i
$41$	−2.05563	+	3.56046i	−0.321036	+	0.556050i	−0.980702	−	0.195508i	$-0.937364\pi$
$41$	−2.05563	+	3.56046i	−0.321036	+	0.556050i	0.659666	+	0.751559i	$0.270698\pi$
$42$	−3.53273	−	2.91887i	−0.545112	−	0.450392i
$43$	0.00618986	+	0.0107211i	0.000943944	+	0.00163496i	0.866497	−	0.499182i	$-0.166366\pi$
$43$	0.00618986	+	0.0107211i	0.000943944	+	0.00163496i	−0.865553	+	0.500817i	$0.833033\pi$
$44$	0.738550	−	1.27921i	0.111341	−	0.192848i
$45$	8.89926	−	6.63238i	1.32662	−	0.988697i
$46$	−3.14400	−	5.44556i	−0.463557	−	0.802904i
$47$	−6.98762			−1.01925			−0.509625	−	0.860397i	$-0.670216\pi$
$47$	−6.98762			−1.01925			−0.509625	+	0.860397i	$0.670216\pi$
$48$	−1.29418	−	1.15113i	−0.186799	−	0.166151i
$49$	6.98143	−	0.509538i	0.997347	−	0.0727912i
$50$	−4.34362	+	7.52338i	−0.614281	+	1.06397i
$51$	2.30037	−	11.1552i	0.322116	−	1.56204i
$52$	−1.34981	+	2.33795i	−0.187186	+	0.324215i
$53$	−1.60507	−	2.78007i	−0.220474	−	0.381872i	0.734478	−	0.678632i	$-0.237427\pi$
$53$	−1.60507	−	2.78007i	−0.220474	−	0.381872i	−0.954952	+	0.296760i	$0.904094\pi$
$54$	2.97710	−	4.25874i	0.405132	−	0.579541i
$55$	−5.46472			−0.736863
$56$	2.64400	−	0.0963576i	0.353319	−	0.0128763i
$57$	1.46108	−	0.484566i	0.193525	−	0.0641824i
$58$	1.25526	+	2.17417i	0.164824	+	0.285483i
$59$	6.90978			0.899576			0.449788	−	0.893135i	$-0.351499\pi$
$59$	6.90978			0.899576			0.449788	+	0.893135i	$0.351499\pi$
$60$	−1.29418	+	6.27589i	−0.167078	+	0.810214i
$61$	−5.73305			−0.734042			−0.367021	−	0.930213i	$-0.619622\pi$
$61$	−5.73305			−0.734042			−0.367021	+	0.930213i	$0.619622\pi$
$62$	6.81089			0.864984
$63$	1.21201	+	7.84417i	0.152699	+	0.988273i
$64$	1.00000			0.125000
$65$	9.98762			1.23881
$66$	−2.42835	+	0.805361i	−0.298909	+	0.0991331i
$67$	−9.46472			−1.15630			−0.578150	−	0.815931i	$-0.696225\pi$
$67$	−9.46472			−1.15630			−0.578150	+	0.815931i	$0.696225\pi$
$68$	3.28799	+	5.69497i	0.398728	+	0.690616i
$69$	−2.19963	+	10.6667i	−0.264804	+	1.28412i
$70$	−5.19963	−	8.29305i	−0.621474	−	0.991209i
$71$	−5.46472			−0.648543			−0.324271	−	0.945964i	$-0.605119\pi$
$71$	−5.46472			−0.648543			−0.324271	+	0.945964i	$0.605119\pi$
$72$	0.349814	+	2.97954i	0.0412260	+	0.351142i
$73$	−6.03273	−	10.4490i	−0.706078	−	1.22296i	−0.966301	−	0.257414i	$-0.917130\pi$
$73$	−6.03273	−	10.4490i	−0.706078	−	1.22296i	0.260223	−	0.965548i	$-0.416204\pi$
$74$	−1.38874	+	2.40536i	−0.161437	+	0.279618i
$75$	14.2818	−	4.73656i	1.64912	−	0.546931i
$76$	−0.444368	+	0.769668i	−0.0509725	+	0.0882870i
$77$	1.82946	−	3.45338i	0.208487	−	0.393549i
$78$	4.43818	−	1.47192i	0.502525	−	0.166662i
$79$	11.4523			1.28849			0.644244	−	0.764820i	$-0.277172\pi$
$79$	11.4523			1.28849			0.644244	+	0.764820i	$0.277172\pi$
$80$	−1.84981	−	3.20397i	−0.206816	−	0.358215i
$81$	−8.75526	+	2.08457i	−0.972807	+	0.231619i
$82$	−2.05563	+	3.56046i	−0.227007	+	0.393187i
$83$	2.23855	+	3.87728i	0.245713	+	0.425587i	0.962332	−	0.271878i	$-0.0876447\pi$
$83$	2.23855	+	3.87728i	0.245713	+	0.425587i	−0.716619	+	0.697465i	$0.754311\pi$
$84$	−3.53273	−	2.91887i	−0.385453	−	0.318475i
$85$	12.1643	−	21.0693i	1.31941	−	2.28528i
$86$	0.00618986	+	0.0107211i	0.000667469	+	0.00115609i
$87$	0.878215	−	4.25874i	0.0941546	−	0.456585i
$88$	0.738550	−	1.27921i	0.0787297	−	0.136364i
$89$	−4.43818	+	7.68715i	−0.470446	+	0.814836i	−0.999429	−	0.0337963i	$-0.989240\pi$
$89$	−4.43818	+	7.68715i	−0.470446	+	0.814836i	0.528983	+	0.848633i	$0.322574\pi$
$90$	8.89926	−	6.63238i	0.938064	−	0.699114i
$91$	−3.34362	+	6.31159i	−0.350507	+	0.661634i
$92$	−3.14400	−	5.44556i	−0.327784	−	0.567739i
$93$	−8.81453	−	7.84020i	−0.914025	−	0.812991i
$94$	−6.98762			−0.720718
$95$	3.28799			0.337341
$96$	−1.29418	−	1.15113i	−0.132087	−	0.117486i
$97$	−6.58836	−	11.4114i	−0.668947	−	1.15865i	−0.978199	−	0.207670i	$-0.933412\pi$
$97$	−6.58836	−	11.4114i	−0.668947	−	1.15865i	0.309252	−	0.950980i	$-0.399921\pi$
$98$	6.98143	−	0.509538i	0.705231	−	0.0514711i
$99$	4.06979	+	1.75305i	0.409030	+	0.176188i
$100$	−4.34362	+	7.52338i	−0.434362	+	0.752338i
$101$	−2.62729	+	4.55059i	−0.261425	+	0.452801i	−0.966621	−	0.256212i	$-0.917526\pi$
$101$	−2.62729	+	4.55059i	−0.261425	+	0.452801i	0.705196	+	0.709012i	$0.250859\pi$
$102$	2.30037	−	11.1552i	0.227771	−	1.10453i
$103$	−0.833104	−	1.44298i	−0.0820882	−	0.142181i	0.822059	−	0.569403i	$-0.192826\pi$
$103$	−0.833104	−	1.44298i	−0.0820882	−	0.142181i	−0.904147	+	0.427222i	$0.859492\pi$
$104$	−1.34981	+	2.33795i	−0.132360	+	0.229255i
$105$	−2.81708	+	16.7181i	−0.274919	+	1.63152i
$106$	−1.60507	−	2.78007i	−0.155899	−	0.270024i
$107$	−5.38255	+	9.32284i	−0.520350	+	0.901273i	0.479370	+	0.877613i	$0.340865\pi$
$107$	−5.38255	+	9.32284i	−0.520350	+	0.901273i	−0.999720	+	0.0236602i	$0.992468\pi$
$108$	2.97710	−	4.25874i	0.286472	−	0.409798i
$109$	−0.0945538	−	0.163772i	−0.00905662	−	0.0156865i	0.861462	−	0.507823i	$-0.169550\pi$
$109$	−0.0945538	−	0.163772i	−0.00905662	−	0.0156865i	−0.870518	+	0.492136i	$0.836216\pi$
$110$	−5.46472			−0.521041
$111$	4.56615	−	1.51436i	0.433400	−	0.143737i
$112$	2.64400	−	0.0963576i	0.249834	−	0.00910494i
$113$	−6.78180	+	11.7464i	−0.637978	+	1.10501i	0.347897	+	0.937533i	$0.386896\pi$
$113$	−6.78180	+	11.7464i	−0.637978	+	1.10501i	−0.985876	+	0.167478i	$0.946438\pi$
$114$	1.46108	−	0.484566i	0.136843	−	0.0453838i
$115$	−11.6316	+	20.1466i	−1.08465	+	1.87868i
$116$	1.25526	+	2.17417i	0.116548	+	0.201867i
$117$	−7.43818	−	3.20397i	−0.687660	−	0.296207i
$118$	6.90978			0.636097
$119$	9.24219	+	14.7407i	0.847230	+	1.35127i
$120$	−1.29418	+	6.27589i	−0.118142	+	0.572908i
$121$	4.40909	+	7.63676i	0.400826	+	0.694251i
$122$	−5.73305			−0.519046
$123$	6.75890	−	2.24159i	0.609430	−	0.202117i
$124$	6.81089			0.611636
$125$	13.6414			1.22013
$126$	1.21201	+	7.84417i	0.107974	+	0.698814i
$127$	−2.85669			−0.253490			−0.126745	−	0.991935i	$-0.540453\pi$
$127$	−2.85669			−0.253490			−0.126745	+	0.991935i	$0.540453\pi$
$128$	1.00000			0.0883883
$129$	0.00433060	−	0.0210004i	0.000381288	−	0.00184898i
$130$	9.98762			0.875972
$131$	−0.0778435	−	0.134829i	−0.00680122	−	0.0117801i	0.862605	−	0.505878i	$-0.168832\pi$
$131$	−0.0778435	−	0.134829i	−0.00680122	−	0.0117801i	−0.869406	+	0.494098i	$0.835498\pi$
$132$	−2.42835	+	0.805361i	−0.211360	+	0.0700977i
$133$	−1.10074	+	2.07782i	−0.0954466	+	0.180170i
$134$	−9.46472			−0.817627
$135$	−19.1520	−	1.66066i	−1.64834	−	0.142927i
$136$	3.28799	+	5.69497i	0.281943	+	0.488340i
$137$	1.70582	−	2.95456i	0.145738	−	0.252425i	−0.783910	−	0.620874i	$-0.786778\pi$
$137$	1.70582	−	2.95456i	0.145738	−	0.252425i	0.929648	+	0.368449i	$0.120111\pi$
$138$	−2.19963	+	10.6667i	−0.187245	+	0.908009i
$139$	−6.75526	+	11.7005i	−0.572974	+	0.992420i	0.423285	+	0.905997i	$0.360877\pi$
$139$	−6.75526	+	11.7005i	−0.572974	+	0.992420i	−0.996259	+	0.0864229i	$0.972456\pi$
$140$	−5.19963	−	8.29305i	−0.439449	−	0.700890i
$141$	9.04325	+	8.04364i	0.761579	+	0.677396i
$142$	−5.46472			−0.458589
$143$	1.99381	+	3.45338i	0.166731	+	0.288786i
$144$	0.349814	+	2.97954i	0.0291512	+	0.248295i
$145$	4.64400	−	8.04364i	0.385663	−	0.667988i
$146$	−6.03273	−	10.4490i	−0.499272	−	0.864765i
$147$	−9.62178	−	7.37708i	−0.793591	−	0.608451i
$148$	−1.38874	+	2.40536i	−0.114153	+	0.197719i
$149$	−0.166896	−	0.289073i	−0.0136727	−	0.0236818i	0.859108	−	0.511794i	$-0.171019\pi$
$149$	−0.166896	−	0.289073i	−0.0136727	−	0.0236818i	−0.872781	+	0.488112i	$0.837686\pi$
$150$	14.2818	−	4.73656i	1.16610	−	0.386738i
$151$	9.95489	−	17.2424i	0.810117	−	1.40316i	−0.102664	−	0.994716i	$-0.532737\pi$
$151$	9.95489	−	17.2424i	0.810117	−	1.40316i	0.912781	−	0.408448i	$-0.133930\pi$
$152$	−0.444368	+	0.769668i	−0.0360430	+	0.0624283i
$153$	−15.8182	+	11.7889i	−1.27882	+	0.953074i
$154$	1.82946	−	3.45338i	0.147422	−	0.278281i
$155$	−12.5989	−	21.8219i	−1.01197	−	1.75278i
$156$	4.43818	−	1.47192i	0.355339	−	0.117848i
$157$	−6.96286			−0.555697			−0.277848	−	0.960625i	$-0.589621\pi$
$157$	−6.96286			−0.555697			−0.277848	+	0.960625i	$0.589621\pi$
$158$	11.4523			0.911099
$159$	−1.12296	+	5.44556i	−0.0890561	+	0.431861i
$160$	−1.84981	−	3.20397i	−0.146241	−	0.253296i
$161$	−8.83743	−	14.0951i	−0.696487	−	1.11085i
$162$	−8.75526	+	2.08457i	−0.687878	+	0.163779i
$163$	4.03706	−	6.99240i	0.316207	−	0.547687i	−0.663486	−	0.748189i	$-0.730924\pi$
$163$	4.03706	−	6.99240i	0.316207	−	0.547687i	0.979693	+	0.200502i	$0.0642572\pi$
$164$	−2.05563	+	3.56046i	−0.160518	+	0.278025i
$165$	7.07234	+	6.29059i	0.550581	+	0.489721i
$166$	2.23855	+	3.87728i	0.173745	+	0.300935i
$167$	9.74288	−	16.8752i	0.753927	−	1.30584i	−0.191979	−	0.981399i	$-0.561491\pi$
$167$	9.74288	−	16.8752i	0.753927	−	1.30584i	0.945906	−	0.324440i	$-0.105176\pi$
$168$	−3.53273	−	2.91887i	−0.272556	−	0.225196i
$169$	2.85600	+	4.94674i	0.219693	+	0.380519i
$170$	12.1643	−	21.0693i	0.932963	−	1.61594i
$171$	−2.44870	−	1.05477i	−0.187257	−	0.0806602i
$172$	0.00618986	+	0.0107211i	0.000471972	+	0.000817480i
$173$	22.5636			1.71548			0.857740	−	0.514085i	$-0.171868\pi$
$173$	22.5636			1.71548			0.857740	+	0.514085i	$0.171868\pi$
$174$	0.878215	−	4.25874i	0.0665773	−	0.322854i
$175$	−10.7596	+	20.3103i	−0.813349	+	1.53532i
$176$	0.738550	−	1.27921i	0.0556703	−	0.0964238i
$177$	−8.94251	−	7.95403i	−0.672160	−	0.597861i
$178$	−4.43818	+	7.68715i	−0.332656	+	0.576176i
$179$	0.166896	+	0.289073i	0.0124744	+	0.0216063i	0.872195	−	0.489158i	$-0.162696\pi$
$179$	0.166896	+	0.289073i	0.0124744	+	0.0216063i	−0.859721	+	0.510764i	$0.829363\pi$
$180$	8.89926	−	6.63238i	0.663311	−	0.494348i
$181$	23.2422			1.72758			0.863789	−	0.503853i	$-0.168085\pi$
$181$	23.2422			1.72758			0.863789	+	0.503853i	$0.168085\pi$
$182$	−3.34362	+	6.31159i	−0.247846	+	0.467846i
$183$	7.41961	+	6.59947i	0.548473	+	0.487847i
$184$	−3.14400	−	5.44556i	−0.231778	−	0.401452i
$185$	10.2756			0.755478
$186$	−8.81453	−	7.84020i	−0.646313	−	0.574871i
$187$	9.71339			0.710313
$188$	−6.98762			−0.509625
$189$	7.46108	−	11.5470i	0.542714	−	0.839918i
$190$	3.28799			0.238536
$191$	−16.3214			−1.18098			−0.590488	−	0.807046i	$-0.701065\pi$
$191$	−16.3214			−1.18098			−0.590488	+	0.807046i	$0.701065\pi$
$192$	−1.29418	−	1.15113i	−0.0933995	−	0.0830754i
$193$	−14.3214			−1.03088			−0.515439	−	0.856926i	$-0.672371\pi$
$193$	−14.3214			−1.03088			−0.515439	+	0.856926i	$0.672371\pi$
$194$	−6.58836	−	11.4114i	−0.473017	−	0.819289i
$195$	−12.9258	−	11.4970i	−0.925636	−	0.823319i
$196$	6.98143	−	0.509538i	0.498674	−	0.0363956i
$197$	2.42402			0.172704			0.0863520	−	0.996265i	$-0.472479\pi$
$197$	2.42402			0.172704			0.0863520	+	0.996265i	$0.472479\pi$
$198$	4.06979	+	1.75305i	0.289228	+	0.124584i
$199$	−3.05563	−	5.29251i	−0.216608	−	0.375176i	0.737161	−	0.675717i	$-0.236166\pi$
$199$	−3.05563	−	5.29251i	−0.216608	−	0.375176i	−0.953769	+	0.300541i	$0.902833\pi$
$200$	−4.34362	+	7.52338i	−0.307141	+	0.531983i
$201$	12.2491	+	10.8951i	0.863983	+	0.768481i
$202$	−2.62729	+	4.55059i	−0.184855	+	0.320179i
$203$	3.52840	+	5.62755i	0.247645	+	0.394977i
$204$	2.30037	−	11.1552i	0.161058	−	0.781022i
$205$	15.2101			1.06232
$206$	−0.833104	−	1.44298i	−0.0580451	−	0.100537i
$207$	15.1254	−	11.2726i	1.05129	−	0.783499i
$208$	−1.34981	+	2.33795i	−0.0935928	+	0.162107i
$209$	0.656376	+	1.13688i	0.0454025	+	0.0786394i
$210$	−2.81708	+	16.7181i	−0.194397	+	1.15366i
$211$	5.72253	−	9.91171i	0.393955	−	0.682350i	−0.599012	−	0.800740i	$-0.704440\pi$
$211$	5.72253	−	9.91171i	0.393955	−	0.682350i	0.992967	+	0.118390i	$0.0377732\pi$
$212$	−1.60507	−	2.78007i	−0.110237	−	0.190936i
$213$	7.07234	+	6.29059i	0.484589	+	0.431024i
$214$	−5.38255	+	9.32284i	−0.367943	+	0.637296i
$215$	0.0229002	−	0.0396643i	0.00156178	−	0.00270508i
$216$	2.97710	−	4.25874i	0.202566	−	0.289771i
$217$	18.0080	−	0.656281i	1.22246	−	0.0445513i
$218$	−0.0945538	−	0.163772i	−0.00640399	−	0.0110920i
$219$	−4.22067	+	20.4673i	−0.285206	+	1.38305i
$220$	−5.46472			−0.368431
$221$	−17.7527			−1.19418
$222$	4.56615	−	1.51436i	0.306460	−	0.101637i
$223$	−3.61126	−	6.25489i	−0.241828	−	0.418859i	0.719407	−	0.694589i	$-0.244414\pi$
$223$	−3.61126	−	6.25489i	−0.241828	−	0.418859i	−0.961235	+	0.275730i	$0.911080\pi$
$224$	2.64400	−	0.0963576i	0.176659	−	0.00643816i
$225$	−23.9356	−	10.3102i	−1.59571	−	0.687347i
$226$	−6.78180	+	11.7464i	−0.451119	+	0.781361i
$227$	−6.82760	+	11.8258i	−0.453164	+	0.784903i	−0.998581	−	0.0532622i	$-0.983038\pi$
$227$	−6.82760	+	11.8258i	−0.453164	+	0.784903i	0.545417	+	0.838165i	$0.316371\pi$
$228$	1.46108	−	0.484566i	0.0967623	−	0.0320912i
$229$	−8.68725	−	15.0468i	−0.574070	−	0.994318i	−0.996142	−	0.0877555i	$-0.972031\pi$
$229$	−8.68725	−	15.0468i	−0.574070	−	0.994318i	0.422073	−	0.906562i	$-0.361303\pi$
$230$	−11.6316	+	20.1466i	−0.766966	+	1.32842i
$231$	−6.34294	+	2.36336i	−0.417335	+	0.155498i
$232$	1.25526	+	2.17417i	0.0824119	+	0.142742i
$233$	7.62110	−	13.2001i	0.499275	−	0.864769i	−0.500725	−	0.865606i	$-0.666933\pi$
$233$	7.62110	−	13.2001i	0.499275	−	0.864769i	1.00000		0.000837426i	$0.000266561\pi$
$234$	−7.43818	−	3.20397i	−0.486249	−	0.209450i
$235$	12.9258	+	22.3881i	0.843186	+	1.46044i
$236$	6.90978			0.449788
$237$	−14.8214	−	13.1831i	−0.962754	−	0.856334i
$238$	9.24219	+	14.7407i	0.599082	+	0.955495i
$239$	9.47524	−	16.4116i	0.612902	−	1.06158i	−0.377846	−	0.925868i	$-0.623335\pi$
$239$	9.47524	−	16.4116i	0.612902	−	1.06158i	0.990749	−	0.135710i	$-0.0433314\pi$
$240$	−1.29418	+	6.27589i	−0.0835391	+	0.405107i
$241$	12.2527	−	21.2223i	0.789267	−	1.36705i	−0.137150	−	0.990550i	$-0.543794\pi$
$241$	12.2527	−	21.2223i	0.789267	−	1.36705i	0.926417	−	0.376500i	$-0.122872\pi$
$242$	4.40909	+	7.63676i	0.283427	+	0.490910i
$243$	13.7305	+	7.38061i	0.880812	+	0.473466i
$244$	−5.73305			−0.367021
$245$	−14.5469	−	21.4258i	−0.929367	−	1.36884i
$246$	6.75890	−	2.24159i	0.430932	−	0.142918i
$247$	−1.19963	−	2.07782i	−0.0763305	−	0.132208i
$248$	6.81089			0.432492
$249$	1.56615	−	7.59476i	0.0992509	−	0.481299i
$250$	13.6414			0.862761
$251$	−12.1236			−0.765238			−0.382619	−	0.923906i	$-0.624978\pi$
$251$	−12.1236			−0.765238			−0.382619	+	0.923906i	$0.624978\pi$
$252$	1.21201	+	7.84417i	0.0763493	+	0.494136i
$253$	−9.28799			−0.583931
$254$	−2.85669			−0.179245
$255$	−39.9963	+	13.2648i	−2.50466	+	0.830672i
$256$	1.00000			0.0625000
$257$	4.10439	+	7.10900i	0.256025	+	0.443448i	0.965173	−	0.261611i	$-0.0842539\pi$
$257$	4.10439	+	7.10900i	0.256025	+	0.443448i	−0.709149	+	0.705059i	$0.750921\pi$
$258$	0.00433060	−	0.0210004i	0.000269611	−	0.00130743i
$259$	−3.44004	+	6.49358i	−0.213754	+	0.403491i
$260$	9.98762			0.619406
$261$	−6.03892	+	4.50065i	−0.373800	+	0.278583i
$262$	−0.0778435	−	0.134829i	−0.00480919	−	0.00832976i
$263$	2.67309	−	4.62992i	0.164830	−	0.285493i	−0.771765	−	0.635908i	$-0.780626\pi$
$263$	2.67309	−	4.62992i	0.164830	−	0.285493i	0.936595	+	0.350414i	$0.113959\pi$
$264$	−2.42835	+	0.805361i	−0.149454	+	0.0495665i
$265$	−5.93818	+	10.2852i	−0.364779	+	0.631816i
$266$	−1.10074	+	2.07782i	−0.0674909	+	0.127399i
$267$	14.5927	−	4.83967i	0.893058	−	0.296183i
$268$	−9.46472			−0.578150
$269$	9.24219	+	16.0079i	0.563506	+	0.976022i	0.997187	+	0.0749550i	$0.0238813\pi$
$269$	9.24219	+	16.0079i	0.563506	+	0.976022i	−0.433681	+	0.901067i	$0.642785\pi$
$270$	−19.1520	−	1.66066i	−1.16555	−	0.101065i
$271$	−3.67742	+	6.36947i	−0.223387	+	0.386918i	−0.955834	−	0.293906i	$-0.905045\pi$
$271$	−3.67742	+	6.36947i	−0.223387	+	0.386918i	0.732447	+	0.680824i	$0.238378\pi$
$272$	3.28799	+	5.69497i	0.199364	+	0.345308i
$273$	11.5927	−	4.31941i	0.701622	−	0.261422i
$274$	1.70582	−	2.95456i	0.103052	−	0.178492i
$275$	6.41597	+	11.1128i	0.386897	+	0.670126i
$276$	−2.19963	+	10.6667i	−0.132402	+	0.642059i
$277$	4.54944	−	7.87987i	0.273349	−	0.473455i	−0.696368	−	0.717685i	$-0.745202\pi$
$277$	4.54944	−	7.87987i	0.273349	−	0.473455i	0.969717	+	0.244230i	$0.0785351\pi$
$278$	−6.75526	+	11.7005i	−0.405154	+	0.701747i
$279$	2.38255	+	20.2933i	0.142639	+	1.21493i
$280$	−5.19963	−	8.29305i	−0.310737	−	0.495604i
$281$	6.00433	+	10.3998i	0.358188	+	0.620400i	0.987658	−	0.156624i	$-0.0500612\pi$
$281$	6.00433	+	10.3998i	0.358188	+	0.620400i	−0.629470	+	0.777025i	$0.716728\pi$
$282$	9.04325	+	8.04364i	0.538518	+	0.478992i
$283$	9.84294			0.585102			0.292551	−	0.956250i	$-0.405496\pi$
$283$	9.84294			0.585102			0.292551	+	0.956250i	$0.405496\pi$
$284$	−5.46472			−0.324271
$285$	−4.25526	−	3.78490i	−0.252060	−	0.224198i
$286$	1.99381	+	3.45338i	0.117896	+	0.204203i
$287$	−5.09201	+	9.61192i	−0.300572	+	0.567373i
$288$	0.349814	+	2.97954i	0.0206130	+	0.175571i
$289$	−13.1218	+	22.7276i	−0.771870	+	1.33692i
$290$	4.64400	−	8.04364i	0.272705	−	0.472339i
$291$	−4.60940	+	22.3524i	−0.270208	+	1.31032i
$292$	−6.03273	−	10.4490i	−0.353039	−	0.611481i
$293$	10.7101	−	18.5505i	0.625694	−	1.08373i	−0.362713	−	0.931901i	$-0.618149\pi$
$293$	10.7101	−	18.5505i	0.625694	−	1.08373i	0.988406	−	0.151832i	$-0.0485173\pi$
$294$	−9.62178	−	7.37708i	−0.561154	−	0.430240i
$295$	−12.7818	−	22.1387i	−0.744185	−	1.28897i
$296$	−1.38874	+	2.40536i	−0.0807186	+	0.139809i
$297$	−3.24907	−	6.95362i	−0.188530	−	0.403490i
$298$	−0.166896	−	0.289073i	−0.00966804	−	0.0167455i
$299$	16.9752			0.981704
$300$	14.2818	−	4.73656i	0.824560	−	0.273465i
$301$	0.0173990	+	0.0277502i	0.00100286	+	0.00159950i
$302$	9.95489	−	17.2424i	0.572839	−	0.992187i
$303$	8.63849	−	2.86496i	0.496269	−	0.164587i
$304$	−0.444368	+	0.769668i	−0.0254862	+	0.0441435i
$305$	10.6051	+	18.3685i	0.607245	+	1.05178i
$306$	−15.8182	+	11.7889i	−0.904265	+	0.673925i
$307$	−5.68725			−0.324588			−0.162294	−	0.986742i	$-0.551889\pi$
$307$	−5.68725			−0.324588			−0.162294	+	0.986742i	$0.551889\pi$
$308$	1.82946	−	3.45338i	0.104243	−	0.196775i
$309$	−0.582863	+	2.82648i	−0.0331579	+	0.160793i
$310$	−12.5989	−	21.8219i	−0.715569	−	1.23940i
$311$	−11.7207			−0.664618			−0.332309	−	0.943171i	$-0.607828\pi$
$311$	−11.7207			−0.664618			−0.332309	+	0.943171i	$0.607828\pi$
$312$	4.43818	−	1.47192i	0.251262	−	0.0833311i
$313$	−26.7738			−1.51334			−0.756671	−	0.653796i	$-0.773176\pi$
$313$	−26.7738			−1.51334			−0.756671	+	0.653796i	$0.773176\pi$
$314$	−6.96286			−0.392937
$315$	22.8905	−	18.3935i	1.28973	−	1.03636i
$316$	11.4523			0.644244
$317$	1.90249			0.106855			0.0534273	−	0.998572i	$-0.482985\pi$
$317$	1.90249			0.106855			0.0534273	+	0.998572i	$0.482985\pi$
$318$	−1.12296	+	5.44556i	−0.0629722	+	0.305372i
$319$	3.70829			0.207624
$320$	−1.84981	−	3.20397i	−0.103408	−	0.179107i
$321$	17.6978	−	5.86946i	0.987793	−	0.327601i
$322$	−8.83743	−	14.0951i	−0.492491	−	0.785489i
$323$	−5.84431			−0.325186
$324$	−8.75526	+	2.08457i	−0.486403	+	0.115809i
$325$	−11.7262	−	20.3103i	−0.650451	−	1.12661i
$326$	4.03706	−	6.99240i	0.223592	−	0.387273i
$327$	−0.0661525	+	0.320794i	−0.00365824	+	0.0177400i
$328$	−2.05563	+	3.56046i	−0.113503	+	0.196593i
$329$	−18.4752	+	0.673310i	−1.01857	+	0.0371208i
$330$	7.07234	+	6.29059i	0.389320	+	0.346285i
$331$	5.56732			0.306008			0.153004	−	0.988226i	$-0.451105\pi$
$331$	5.56732			0.306008			0.153004	+	0.988226i	$0.451105\pi$
$332$	2.23855	+	3.87728i	0.122856	+	0.212794i
$333$	−7.65266	−	3.29636i	−0.419363	−	0.180639i
$334$	9.74288	−	16.8752i	0.533107	−	0.923368i
$335$	17.5080	+	30.3247i	0.956563	+	1.65682i
$336$	−3.53273	−	2.91887i	−0.192726	−	0.159237i
$337$	−16.8869	+	29.2489i	−0.919887	+	1.59329i	−0.120302	+	0.992737i	$0.538386\pi$
$337$	−16.8869	+	29.2489i	−0.919887	+	1.59329i	−0.799585	+	0.600553i	$0.794947\pi$
$338$	2.85600	+	4.94674i	0.155346	+	0.269067i
$339$	22.2985	−	7.39530i	1.21109	−	0.401657i
$340$	12.1643	−	21.0693i	0.659704	−	1.14264i
$341$	5.03018	−	8.71253i	0.272400	−	0.471810i
$342$	−2.44870	−	1.05477i	−0.132410	−	0.0570354i
$343$	18.4098	−	2.01993i	0.994035	−	0.109066i
$344$	0.00618986	+	0.0107211i	0.000333735	+	0.000578045i
$345$	38.2447	−	12.6838i	2.05902	−	0.682875i
$346$	22.5636			1.21303
$347$	−30.4065			−1.63231			−0.816154	−	0.577834i	$-0.803898\pi$
$347$	−30.4065			−1.63231			−0.816154	+	0.577834i	$0.803898\pi$
$348$	0.878215	−	4.25874i	0.0470773	−	0.228292i
$349$	−6.29782	−	10.9082i	−0.337115	−	0.583900i	0.646774	−	0.762682i	$-0.276118\pi$
$349$	−6.29782	−	10.9082i	−0.337115	−	0.583900i	−0.983889	+	0.178782i	$0.942784\pi$
$350$	−10.7596	+	20.3103i	−0.575124	+	1.08563i
$351$	5.93818	+	12.7088i	0.316956	+	0.678346i
$352$	0.738550	−	1.27921i	0.0393648	−	0.0681819i
$353$	3.76578	−	6.52252i	0.200432	−	0.347159i	−0.748235	−	0.663433i	$-0.769099\pi$
$353$	3.76578	−	6.52252i	0.200432	−	0.347159i	0.948668	+	0.316274i	$0.102432\pi$
$354$	−8.94251	−	7.95403i	−0.475289	−	0.422752i
$355$	10.1087	+	17.5088i	0.536515	+	0.929271i
$356$	−4.43818	+	7.68715i	−0.235223	+	0.407418i
$357$	5.00728	−	29.7160i	0.265014	−	1.57274i
$358$	0.166896	+	0.289073i	0.00882074	+	0.0152780i
$359$	−3.44801	+	5.97213i	−0.181979	+	0.315197i	−0.942554	−	0.334053i	$-0.891584\pi$
$359$	−3.44801	+	5.97213i	−0.181979	+	0.315197i	0.760575	+	0.649250i	$0.224917\pi$
$360$	8.89926	−	6.63238i	0.469032	−	0.349557i
$361$	9.10507	+	15.7705i	0.479214	+	0.830024i
$362$	23.2422			1.22158
$363$	3.08472	−	14.9588i	0.161906	−	0.785132i
$364$	−3.34362	+	6.31159i	−0.175254	+	0.330817i
$365$	−22.3189	+	38.6574i	−1.16822	+	2.02342i
$366$	7.41961	+	6.59947i	0.387829	+	0.344960i
$367$	−11.5618	+	20.0257i	−0.603522	+	1.04533i	0.388761	+	0.921339i	$0.372903\pi$
$367$	−11.5618	+	20.0257i	−0.603522	+	1.04533i	−0.992283	+	0.123992i	$0.960430\pi$
$368$	−3.14400	−	5.44556i	−0.163892	−	0.283869i
$369$	−11.3276	−	4.87933i	−0.589691	−	0.254008i
$370$	10.2756			0.534204
$371$	−4.51169	−	7.19583i	−0.234235	−	0.373589i
$372$	−8.81453	−	7.84020i	−0.457012	−	0.406495i
$373$	−14.5822	−	25.2571i	−0.755036	−	1.30776i	−0.945356	−	0.326039i	$-0.894286\pi$
$373$	−14.5822	−	25.2571i	−0.755036	−	1.30776i	0.190320	−	0.981722i	$-0.439047\pi$
$374$	9.71339			0.502267
$375$	−17.6545	−	15.7030i	−0.911675	−	0.810901i
$376$	−6.98762			−0.360359
$377$	−6.77747			−0.349058
$378$	7.46108	−	11.5470i	0.383756	−	0.593912i
$379$	−13.5622			−0.696645			−0.348322	−	0.937375i	$-0.613249\pi$
$379$	−13.5622			−0.696645			−0.348322	+	0.937375i	$0.613249\pi$
$380$	3.28799			0.168670
$381$	3.69708	+	3.28842i	0.189407	+	0.168471i
$382$	−16.3214			−0.835076
$383$	1.41783	+	2.45575i	0.0724475	+	0.125483i	0.899973	−	0.435945i	$-0.143586\pi$
$383$	1.41783	+	2.45575i	0.0724475	+	0.125483i	−0.827526	+	0.561428i	$0.810252\pi$
$384$	−1.29418	−	1.15113i	−0.0660434	−	0.0587432i
$385$	−14.4487	+	0.526567i	−0.736374	+	0.0268364i
$386$	−14.3214			−0.728941
$387$	−0.0297787	+	0.0221933i	−0.00151374	+	0.00112815i
$388$	−6.58836	−	11.4114i	−0.334474	−	0.579325i
$389$	9.30401	−	16.1150i	0.471732	−	0.817064i	−0.527745	−	0.849403i	$-0.676962\pi$
$389$	9.30401	−	16.1150i	0.471732	−	0.817064i	0.999477	+	0.0323388i	$0.0102956\pi$
$390$	−12.9258	−	11.4970i	−0.654523	−	0.582174i
$391$	20.6749	−	35.8099i	1.04557	−	1.81099i
$392$	6.98143	−	0.509538i	0.352615	−	0.0257356i
$393$	−0.0544615	+	0.264101i	−0.00274722	+	0.0133221i
$394$	2.42402			0.122120
$395$	−21.1847	−	36.6930i	−1.06592	−	1.84622i
$396$	4.06979	+	1.75305i	0.204515	+	0.0880941i
$397$	−10.2880	+	17.8193i	−0.516340	+	0.894326i	0.483481	+	0.875355i	$0.339372\pi$
$397$	−10.2880	+	17.8193i	−0.516340	+	0.894326i	−0.999820	+	0.0189712i	$0.993961\pi$
$398$	−3.05563	−	5.29251i	−0.153165	−	0.265290i
$399$	3.81639	−	1.42198i	0.191059	−	0.0711879i
$400$	−4.34362	+	7.52338i	−0.217181	+	0.376169i
$401$	3.37704	+	5.84921i	0.168642	+	0.292096i	0.937942	−	0.346791i	$-0.112729\pi$
$401$	3.37704	+	5.84921i	0.168642	+	0.292096i	−0.769301	+	0.638887i	$0.779395\pi$
$402$	12.2491	+	10.8951i	0.610928	+	0.543398i
$403$	−9.19344	+	15.9235i	−0.457958	+	0.793206i
$404$	−2.62729	+	4.55059i	−0.130712	+	0.226400i
$405$	22.8745	+	24.1955i	1.13664	+	1.20229i
$406$	3.52840	+	5.62755i	0.175112	+	0.279291i
$407$	2.05130	+	3.55296i	0.101679	+	0.176114i
$408$	2.30037	−	11.1552i	0.113885	−	0.552266i
$409$	15.3214			0.757595			0.378798	−	0.925480i	$-0.376338\pi$
$409$	15.3214			0.757595			0.378798	+	0.925480i	$0.376338\pi$
$410$	15.2101			0.751176
$411$	−5.60872	+	1.86013i	−0.276658	+	0.0917534i
$412$	−0.833104	−	1.44298i	−0.0410441	−	0.0710904i
$413$	18.2694	−	0.665809i	0.898980	−	0.0327623i
$414$	15.1254	−	11.2726i	0.743374	−	0.554017i
$415$	8.28180	−	14.3445i	0.406538	−	0.704144i
$416$	−1.34981	+	2.33795i	−0.0661801	+	0.114627i
$417$	22.2112	−	7.36636i	1.08769	−	0.360732i
$418$	0.656376	+	1.13688i	0.0321044	+	0.0556064i
$419$	−4.32141	+	7.48491i	−0.211115	+	0.365662i	−0.952064	−	0.305900i	$-0.901043\pi$
$419$	−4.32141	+	7.48491i	−0.211115	+	0.365662i	0.740949	+	0.671561i	$0.234376\pi$
$420$	−2.81708	+	16.7181i	−0.137460	+	0.815762i
$421$	18.5636	+	32.1531i	0.904735	+	1.56705i	0.821273	+	0.570536i	$0.193264\pi$
$421$	18.5636	+	32.1531i	0.904735	+	1.56705i	0.0834618	+	0.996511i	$0.473402\pi$
$422$	5.72253	−	9.91171i	0.278568	−	0.482494i
$423$	−2.44437	−	20.8199i	−0.118849	−	1.01230i
$424$	−1.60507	−	2.78007i	−0.0779493	−	0.135012i
$425$	−57.1272			−2.77108
$426$	7.07234	+	6.29059i	0.342656	+	0.304780i
$427$	−15.1582	+	0.552423i	−0.733555	+	0.0267336i
$428$	−5.38255	+	9.32284i	−0.260175	+	0.450637i
$429$	1.39493	−	6.76443i	0.0673476	−	0.326590i
$430$	0.0229002	−	0.0396643i	0.00110434	−	0.00191278i
$431$	−4.71015	−	8.15822i	−0.226880	−	0.392967i	0.730002	−	0.683445i	$-0.239519\pi$
$431$	−4.71015	−	8.15822i	−0.226880	−	0.392967i	−0.956882	+	0.290478i	$0.906186\pi$
$432$	2.97710	−	4.25874i	0.143236	−	0.204899i
$433$	−0.208771			−0.0100329			−0.00501645	−	0.999987i	$-0.501597\pi$
$433$	−0.208771			−0.0100329			−0.00501645	+	0.999987i	$0.501597\pi$
$434$	18.0080	−	0.656281i	0.864410	−	0.0315025i
$435$	−15.2694	+	5.06410i	−0.732113	+	0.242805i
$436$	−0.0945538	−	0.163772i	−0.00452831	−	0.00784326i
$437$	5.58836			0.267328
$438$	−4.22067	+	20.4673i	−0.201671	+	0.977968i
$439$	−9.96796			−0.475745			−0.237872	−	0.971296i	$-0.576450\pi$
$439$	−9.96796			−0.475745			−0.237872	+	0.971296i	$0.576450\pi$
$440$	−5.46472			−0.260520
$441$	3.96039	+	20.6232i	0.188590	+	0.982056i
$442$	−17.7527			−0.844410
$443$	−15.6996			−0.745912			−0.372956	−	0.927849i	$-0.621656\pi$
$443$	−15.6996			−0.745912			−0.372956	+	0.927849i	$0.621656\pi$
$444$	4.56615	−	1.51436i	0.216700	−	0.0718685i
$445$	32.8392			1.55673
$446$	−3.61126	−	6.25489i	−0.170998	−	0.296178i
$447$	−0.116765	+	0.566231i	−0.00552281	+	0.0267818i
$448$	2.64400	−	0.0963576i	0.124917	−	0.00455247i
$449$	33.6253			1.58688			0.793439	−	0.608650i	$-0.208288\pi$
$449$	33.6253			1.58688			0.793439	+	0.608650i	$0.208288\pi$
$450$	−23.9356	−	10.3102i	−1.12834	−	0.486027i
$451$	3.03637	+	5.25915i	0.142977	+	0.247644i
$452$	−6.78180	+	11.7464i	−0.318989	+	0.552505i
$453$	−32.7316	+	10.8554i	−1.53786	+	0.510033i
$454$	−6.82760	+	11.8258i	−0.320435	+	0.555010i
$455$	26.4072	−	0.962383i	1.23799	−	0.0451172i
$456$	1.46108	−	0.484566i	0.0684213	−	0.0226919i
$457$	32.7083			1.53003			0.765015	−	0.644013i	$-0.222732\pi$
$457$	32.7083			1.53003			0.765015	+	0.644013i	$0.222732\pi$
$458$	−8.68725	−	15.0468i	−0.405928	−	0.703089i
$459$	34.0421	+	2.95178i	1.58895	+	0.137778i
$460$	−11.6316	+	20.1466i	−0.542327	+	0.939338i
$461$	−2.07165	−	3.58821i	−0.0964865	−	0.167120i	0.813742	−	0.581227i	$-0.197427\pi$
$461$	−2.07165	−	3.58821i	−0.0964865	−	0.167120i	−0.910228	+	0.414107i	$0.864094\pi$
$462$	−6.34294	+	2.36336i	−0.295100	+	0.109953i
$463$	−8.34176	+	14.4484i	−0.387675	+	0.671472i	−0.992136	−	0.125162i	$-0.960055\pi$
$463$	−8.34176	+	14.4484i	−0.387675	+	0.671472i	0.604462	+	0.796634i	$0.293388\pi$
$464$	1.25526	+	2.17417i	0.0582740	+	0.100934i
$465$	−8.81453	+	42.7444i	−0.408764	+	1.98223i
$466$	7.62110	−	13.2001i	0.353040	−	0.611484i
$467$	14.9585	−	25.9089i	0.692198	−	1.19892i	−0.278918	−	0.960315i	$-0.589976\pi$
$467$	14.9585	−	25.9089i	0.692198	−	1.19892i	0.971116	−	0.238608i	$-0.0766909\pi$
$468$	−7.43818	−	3.20397i	−0.343830	−	0.148104i
$469$	−25.0247	+	0.911998i	−1.15553	+	0.0421121i
$470$	12.9258	+	22.3881i	0.596223	+	1.03269i
$471$	9.01121	+	8.01514i	0.415215	+	0.369318i
$472$	6.90978			0.318048
$473$	0.0182861			0.000840794
$474$	−14.8214	−	13.1831i	−0.680770	−	0.605520i
$475$	−3.86033	−	6.68630i	−0.177124	−	0.306788i
$476$	9.24219	+	14.7407i	0.423615	+	0.675637i
$477$	7.72184	−	5.75488i	0.353559	−	0.263498i
$478$	9.47524	−	16.4116i	0.433387	−	0.750649i
$479$	1.47965	−	2.56283i	0.0676068	−	0.117098i	−0.830241	−	0.557405i	$-0.811797\pi$
$479$	1.47965	−	2.56283i	0.0676068	−	0.117098i	0.897847	+	0.440307i	$0.145130\pi$
$480$	−1.29418	+	6.27589i	−0.0590711	+	0.286454i
$481$	−3.74907	−	6.49358i	−0.170943	−	0.296082i
$482$	12.2527	−	21.2223i	0.558096	−	0.966650i
$483$	−4.78799	+	28.4146i	−0.217861	+	1.29291i
$484$	4.40909	+	7.63676i	0.200413	+	0.347126i
$485$	−24.3745	+	42.2179i	−1.10679	+	1.91701i
$486$	13.7305	+	7.38061i	0.622828	+	0.334791i
$487$	−14.0309	−	24.3022i	−0.635800	−	1.10124i	−0.986345	−	0.164691i	$-0.947337\pi$
$487$	−14.0309	−	24.3022i	−0.635800	−	1.10124i	0.350546	−	0.936546i	$-0.385996\pi$
$488$	−5.73305			−0.259523
$489$	−13.2738	+	4.40226i	−0.600263	+	0.199077i
$490$	−14.5469	−	21.4258i	−0.657162	−	0.967917i
$491$	17.0734	−	29.5721i	0.770513	−	1.33457i	−0.166769	−	0.985996i	$-0.553333\pi$
$491$	17.0734	−	29.5721i	0.770513	−	1.33457i	0.937282	−	0.348572i	$-0.113333\pi$
$492$	6.75890	−	2.24159i	0.304715	−	0.101059i
$493$	−8.25457	+	14.2973i	−0.371767	+	0.643920i
$494$	−1.19963	−	2.07782i	−0.0539738	−	0.0934854i
$495$	−1.91164	−	16.2823i	−0.0859216	−	0.731836i
$496$	6.81089			0.305818
$497$	−14.4487	+	0.526567i	−0.648113	+	0.0236198i
$498$	1.56615	−	7.59476i	0.0701810	−	0.340329i
$499$	1.14035	+	1.97515i	0.0510493	+	0.0884199i	0.890421	−	0.455138i	$-0.150410\pi$
$499$	1.14035	+	1.97515i	0.0510493	+	0.0884199i	−0.839372	+	0.543558i	$0.817077\pi$
$500$	13.6414			0.610064
$501$	−32.0345	+	10.6242i	−1.43120	+	0.474656i
$502$	−12.1236			−0.541105
$503$	13.9890			0.623739			0.311869	−	0.950125i	$-0.399045\pi$
$503$	13.9890			0.623739			0.311869	+	0.950125i	$0.399045\pi$
$504$	1.21201	+	7.84417i	0.0539871	+	0.349407i
$505$	19.4400			0.865067
$506$	−9.28799			−0.412902
$507$	1.99814	−	9.68961i	0.0887405	−	0.430331i
$508$	−2.85669			−0.126745
$509$	−12.8090	−	22.1859i	−0.567750	−	0.983373i	−0.996788	−	0.0800859i	$-0.974481\pi$
$509$	−12.8090	−	22.1859i	−0.567750	−	0.983373i	0.429038	−	0.903287i	$-0.358853\pi$
$510$	−39.9963	+	13.2648i	−1.77107	+	0.587374i
$511$	−16.9574	−	27.0458i	−0.750149	−	1.19644i
$512$	1.00000			0.0441942
$513$	1.95489	+	4.18383i	0.0863104	+	0.184720i
$514$	4.10439	+	7.10900i	0.181037	+	0.313565i
$515$	−3.08217	+	5.33848i	−0.135817	+	0.235242i
$516$	0.00433060	−	0.0210004i	0.000190644	−	0.000924492i
$517$	−5.16071	+	8.93861i	−0.226968	+	0.393119i
$518$	−3.44004	+	6.49358i	−0.151147	+	0.285312i
$519$	−29.2014	−	25.9736i	−1.28180	−	1.14011i
$520$	9.98762			0.437986
$521$	−20.9127	−	36.2219i	−0.916203	−	1.58691i	−0.805130	−	0.593099i	$-0.797904\pi$
$521$	−20.9127	−	36.2219i	−0.916203	−	1.58691i	−0.111073	−	0.993812i	$-0.535429\pi$
$522$	−6.03892	+	4.50065i	−0.264316	+	0.196988i
$523$	7.88323	−	13.6542i	0.344710	−	0.597055i	−0.640591	−	0.767882i	$-0.721311\pi$
$523$	7.88323	−	13.6542i	0.344710	−	0.597055i	0.985301	+	0.170827i	$0.0546440\pi$
$524$	−0.0778435	−	0.134829i	−0.00340061	−	0.00589003i
$525$	37.3046	−	13.8996i	1.62811	−	0.606628i
$526$	2.67309	−	4.62992i	0.116552	−	0.201874i
$527$	22.3942	+	38.7878i	0.975505	+	1.68962i
$528$	−2.42835	+	0.805361i	−0.105680	+	0.0350488i
$529$	−8.26942	+	14.3231i	−0.359540	+	0.622742i
$530$	−5.93818	+	10.2852i	−0.257938	+	0.446762i
$531$	2.41714	+	20.5879i	0.104895	+	0.893440i
$532$	−1.10074	+	2.07782i	−0.0477233	+	0.0900848i
$533$	−5.54944	−	9.61192i	−0.240373	−	0.416338i
$534$	14.5927	−	4.83967i	0.631488	−	0.209433i
$535$	39.8268			1.72186
$536$	−9.46472			−0.408814
$537$	0.116765	−	0.566231i	0.00503879	−	0.0244347i
$538$	9.24219	+	16.0079i	0.398459	+	0.690152i
$539$	4.50433	−	9.30701i	0.194015	−	0.400881i
$540$	−19.1520	−	1.66066i	−0.824170	−	0.0714636i
$541$	−21.0963	+	36.5399i	−0.907002	+	1.57097i	−0.0887957	+	0.996050i	$0.528302\pi$
$541$	−21.0963	+	36.5399i	−0.907002	+	1.57097i	−0.818207	+	0.574924i	$0.805031\pi$
$542$	−3.67742	+	6.36947i	−0.157959	+	0.273592i
$543$	−30.0796	−	26.7547i	−1.29084	−	1.14815i
$544$	3.28799	+	5.69497i	0.140971	+	0.244170i
$545$	−0.349814	+	0.605896i	−0.0149844	+	0.0259537i
$546$	11.5927	−	4.31941i	0.496122	−	0.184854i
$547$	20.3356	+	35.2222i	0.869486	+	1.50599i	0.862522	+	0.506019i	$0.168883\pi$
$547$	20.3356	+	35.2222i	0.869486	+	1.50599i	0.00696400	+	0.999976i	$0.497783\pi$
$548$	1.70582	−	2.95456i	0.0728689	−	0.126213i
$549$	−2.00550	−	17.0818i	−0.0855927	−	0.729034i
$550$	6.41597	+	11.1128i	0.273578	+	0.473851i
$551$	−2.23119			−0.0950519
$552$	−2.19963	+	10.6667i	−0.0936224	+	0.454004i
$553$	30.2799	−	1.10352i	1.28763	−	0.0469264i
$554$	4.54944	−	7.87987i	0.193287	−	0.334783i
$555$	−13.2985	−	11.8285i	−0.564490	−	0.502093i
$556$	−6.75526	+	11.7005i	−0.286487	+	0.496210i
$557$	6.68794	+	11.5838i	0.283377	+	0.490823i	0.972214	−	0.234093i	$-0.0752119\pi$
$557$	6.68794	+	11.5838i	0.283377	+	0.490823i	−0.688837	+	0.724916i	$0.741879\pi$
$558$	2.38255	+	20.2933i	0.100861	+	0.859084i
$559$	−0.0334206			−0.00141354
$560$	−5.19963	−	8.29305i	−0.219724	−	0.350445i
$561$	−12.5709	−	11.1813i	−0.530743	−	0.472076i
$562$	6.00433	+	10.3998i	0.253277	+	0.438689i
$563$	−32.7614			−1.38073			−0.690364	−	0.723463i	$-0.742549\pi$
$563$	−32.7614			−1.38073			−0.690364	+	0.723463i	$0.742549\pi$
$564$	9.04325	+	8.04364i	0.380790	+	0.338698i
$565$	50.1803			2.11110
$566$	9.84294			0.413729
$567$	−22.9480	+	6.35522i	−0.963726	+	0.266894i
$568$	−5.46472			−0.229295
$569$	−16.7280			−0.701272			−0.350636	−	0.936512i	$-0.614035\pi$
$569$	−16.7280			−0.701272			−0.350636	+	0.936512i	$0.614035\pi$
$570$	−4.25526	−	3.78490i	−0.178233	−	0.158532i
$571$	−27.4734			−1.14973			−0.574863	−	0.818250i	$-0.694945\pi$
$571$	−27.4734			−1.14973			−0.574863	+	0.818250i	$0.694945\pi$
$572$	1.99381	+	3.45338i	0.0833654	+	0.144393i
$573$	21.1229	+	18.7880i	0.882421	+	0.784881i
$574$	−5.09201	+	9.61192i	−0.212536	+	0.401194i
$575$	54.6253			2.27803
$576$	0.349814	+	2.97954i	0.0145756	+	0.124147i
$577$	1.41714	+	2.45455i	0.0589962	+	0.102184i	0.894015	−	0.448037i	$-0.147877\pi$
$577$	1.41714	+	2.45455i	0.0589962	+	0.102184i	−0.835019	+	0.550221i	$0.814543\pi$
$578$	−13.1218	+	22.7276i	−0.545794	+	0.945343i
$579$	18.5345	+	16.4858i	0.770268	+	0.685125i
$580$	4.64400	−	8.04364i	0.192831	−	0.333994i
$581$	6.29232	+	10.0358i	0.261050	+	0.416356i
$582$	−4.60940	+	22.3524i	−0.191066	+	0.926539i
$583$	−4.74171			−0.196382
$584$	−6.03273	−	10.4490i	−0.249636	−	0.432383i
$585$	3.49381	+	29.7585i	0.144451	+	1.23036i
$586$	10.7101	−	18.5505i	0.442432	−	0.766315i
$587$	−2.34795	−	4.06678i	−0.0969105	−	0.167854i	0.813494	−	0.581573i	$-0.197563\pi$
$587$	−2.34795	−	4.06678i	−0.0969105	−	0.167854i	−0.910404	+	0.413720i	$0.864229\pi$
$588$	−9.62178	−	7.37708i	−0.396796	−	0.304226i
$589$	−3.02654	+	5.24212i	−0.124706	+	0.215998i
$590$	−12.7818	−	22.1387i	−0.526218	−	0.911437i
$591$	−3.13712	−	2.79035i	−0.129044	−	0.114780i
$592$	−1.38874	+	2.40536i	−0.0570767	+	0.0988597i
$593$	0.636024	−	1.10163i	0.0261184	−	0.0452383i	−0.852671	−	0.522449i	$-0.825019\pi$
$593$	0.636024	−	1.10163i	0.0261184	−	0.0452383i	0.878789	+	0.477210i	$0.158352\pi$
$594$	−3.24907	−	6.95362i	−0.133311	−	0.285310i
$595$	30.1323	−	56.8792i	1.23530	−	2.33182i
$596$	−0.166896	−	0.289073i	−0.00683634	−	0.0118409i
$597$	−2.13781	+	10.3669i	−0.0874946	+	0.424289i
$598$	16.9752			0.694169
$599$	43.8516			1.79173			0.895864	−	0.444329i	$-0.146558\pi$
$599$	43.8516			1.79173			0.895864	+	0.444329i	$0.146558\pi$
$600$	14.2818	−	4.73656i	0.583052	−	0.193369i
$601$	−6.71634	−	11.6330i	−0.273965	−	0.474522i	0.695908	−	0.718131i	$-0.255002\pi$
$601$	−6.71634	−	11.6330i	−0.273965	−	0.474522i	−0.969874	+	0.243609i	$0.921669\pi$
$602$	0.0173990	+	0.0277502i	0.000709131	+	0.00113101i
$603$	−3.31089	−	28.2005i	−0.134830	−	1.14841i
$604$	9.95489	−	17.2424i	0.405059	−	0.701582i
$605$	16.3120	−	28.2532i	0.663177	−	1.14866i
$606$	8.63849	−	2.86496i	0.350915	−	0.116381i
$607$	2.29232	+	3.97042i	0.0930425	+	0.161154i	0.908790	−	0.417254i	$-0.137007\pi$
$607$	2.29232	+	3.97042i	0.0930425	+	0.161154i	−0.815747	+	0.578408i	$0.803674\pi$
$608$	−0.444368	+	0.769668i	−0.0180215	+	0.0312142i
$609$	1.91164	−	11.3447i	0.0774634	−	0.459711i
$610$	10.6051	+	18.3685i	0.429387	+	0.743720i
$611$	9.43199	−	16.3367i	0.381577	−	0.660911i
$612$	−15.8182	+	11.7889i	−0.639412	+	0.476537i
$613$	−11.0538	−	19.1457i	−0.446458	−	0.773287i	0.551695	−	0.834046i	$-0.313981\pi$
$613$	−11.0538	−	19.1457i	−0.446458	−	0.773287i	−0.998152	+	0.0607587i	$0.980648\pi$
$614$	−5.68725			−0.229519
$615$	−19.6847	−	17.5088i	−0.793764	−	0.706023i
$616$	1.82946	−	3.45338i	0.0737111	−	0.139141i
$617$	6.00433	−	10.3998i	0.241725	−	0.418680i	−0.719481	−	0.694513i	$-0.755620\pi$
$617$	6.00433	−	10.3998i	0.241725	−	0.418680i	0.961206	+	0.275832i	$0.0889534\pi$
$618$	−0.582863	+	2.82648i	−0.0234462	+	0.113698i
$619$	8.78180	−	15.2105i	0.352970	−	0.611363i	−0.633798	−	0.773499i	$-0.718505\pi$
$619$	8.78180	−	15.2105i	0.352970	−	0.611363i	0.986768	+	0.162136i	$0.0518383\pi$
$620$	−12.5989	−	21.8219i	−0.505983	−	0.876389i
$621$	−32.5512	−	2.82251i	−1.30624	−	0.113264i
$622$	−11.7207			−0.469956
$623$	−10.9938	+	20.7524i	−0.440458	+	0.831429i
$624$	4.43818	−	1.47192i	0.177669	−	0.0589240i
$625$	−3.51602	−	6.08993i	−0.140641	−	0.243597i
$626$	−26.7738			−1.07009
$627$	0.459219	−	2.22690i	0.0183394	−	0.0889337i
$628$	−6.96286			−0.277848
$629$	−18.2646			−0.728258
$630$	22.8905	−	18.3935i	0.911980	−	0.732815i
$631$	−44.9381			−1.78896			−0.894479	−	0.447110i	$-0.852453\pi$
$631$	−44.9381			−1.78896			−0.894479	+	0.447110i	$0.852453\pi$
$632$	11.4523			0.455550
$633$	−18.8156	+	6.24020i	−0.747854	+	0.248026i
$634$	1.90249			0.0755576
$635$	5.28435	+	9.15276i	0.209703	+	0.363216i
$636$	−1.12296	+	5.44556i	−0.0445281	+	0.215931i
$637$	−8.23236	+	17.0100i	−0.326178	+	0.673960i
$638$	3.70829			0.146813
$639$	−1.91164	−	16.2823i	−0.0756232	−	0.644119i
$640$	−1.84981	−	3.20397i	−0.0731203	−	0.126648i
$641$	14.4920	−	25.1008i	0.572398	−	0.991422i	−0.423921	−	0.905699i	$-0.639347\pi$
$641$	14.4920	−	25.1008i	0.572398	−	0.991422i	0.996319	−	0.0857228i	$-0.0273199\pi$
$642$	17.6978	−	5.86946i	0.698475	−	0.231649i
$643$	6.03087	−	10.4458i	0.237834	−	0.411941i	−0.722258	−	0.691623i	$-0.756896\pi$
$643$	6.03087	−	10.4458i	0.237834	−	0.411941i	0.960093	+	0.279682i	$0.0902291\pi$
$644$	−8.83743	−	14.0951i	−0.348244	−	0.555425i
$645$	−0.0752956	+	0.0249718i	−0.00296476	+	0.000983262i
$646$	−5.84431			−0.229941
$647$	18.8825	+	32.7055i	0.742349	+	1.28579i	0.951423	+	0.307887i	$0.0996219\pi$
$647$	18.8825	+	32.7055i	0.742349	+	1.28579i	−0.209073	+	0.977900i	$0.567045\pi$
$648$	−8.75526	+	2.08457i	−0.343939	+	0.0818895i
$649$	5.10322	−	8.83903i	0.200319	−	0.346962i
$650$	−11.7262	−	20.3103i	−0.459938	−	0.796636i
$651$	−24.0611	−	19.8801i	−0.943027	−	0.779163i
$652$	4.03706	−	6.99240i	0.158104	−	0.273843i
$653$	−18.7040	−	32.3962i	−0.731942	−	1.26776i	−0.956052	−	0.293198i	$-0.905281\pi$
$653$	−18.7040	−	32.3962i	−0.731942	−	1.26776i	0.224109	−	0.974564i	$-0.428053\pi$
$654$	−0.0661525	+	0.320794i	−0.00258677	+	0.0125441i
$655$	−0.287992	+	0.498817i	−0.0112528	+	0.0194904i
$656$	−2.05563	+	3.56046i	−0.0802589	+	0.139013i
$657$	29.0228	−	21.6299i	1.13229	−	0.843864i
$658$	−18.4752	+	0.673310i	−0.720240	+	0.0262484i
$659$	14.9356	+	25.8693i	0.581810	+	1.00772i	0.995265	+	0.0971993i	$0.0309884\pi$
$659$	14.9356	+	25.8693i	0.581810	+	1.00772i	−0.413455	+	0.910524i	$0.635678\pi$
$660$	7.07234	+	6.29059i	0.275291	+	0.244861i
$661$	5.60803			0.218127			0.109063	−	0.994035i	$-0.465215\pi$
$661$	5.60803			0.218127			0.109063	+	0.994035i	$0.465215\pi$
$662$	5.56732			0.216380
$663$	22.9752	+	20.4356i	0.892284	+	0.793654i
$664$	2.23855	+	3.87728i	0.0868726	+	0.150468i
$665$	8.69344	−	0.316823i	0.337117	−	0.0122859i
$666$	−7.65266	−	3.29636i	−0.296534	−	0.127731i
$667$	7.89307	−	13.6712i	0.305621	−	0.529351i
$668$	9.74288	−	16.8752i	0.376963	−	0.652920i
$669$	−2.52654	+	12.2520i	−0.0976818	+	0.473689i
$670$	17.5080	+	30.3247i	0.676392	+	1.17155i
$671$	−4.23414	+	7.33375i	−0.163457	+	0.283116i
$672$	−3.53273	−	2.91887i	−0.136278	−	0.112598i
$673$	−4.72253	−	8.17966i	−0.182040	−	0.315303i	0.760535	−	0.649297i	$-0.224937\pi$
$673$	−4.72253	−	8.17966i	−0.182040	−	0.315303i	−0.942575	+	0.333994i	$0.891603\pi$
$674$	−16.8869	+	29.2489i	−0.650458	+	1.12663i
$675$	19.1087	+	40.8962i	0.735495	+	1.57410i
$676$	2.85600	+	4.94674i	0.109846	+	0.190259i
$677$	11.0617			0.425137			0.212569	−	0.977146i	$-0.431817\pi$
$677$	11.0617			0.425137			0.212569	+	0.977146i	$0.431817\pi$
$678$	22.2985	−	7.39530i	0.856369	−	0.284015i
$679$	−18.5192	−	29.5368i	−0.710701	−	1.13352i
$680$	12.1643	−	21.0693i	0.466481	−	0.807970i
$681$	22.4491	−	7.44524i	0.860252	−	0.285302i
$682$	5.03018	−	8.71253i	0.192616	−	0.333620i
$683$	−4.41961	−	7.65499i	−0.169112	−	0.292910i	0.768996	−	0.639253i	$-0.220757\pi$
$683$	−4.41961	−	7.65499i	−0.169112	−	0.292910i	−0.938108	+	0.346343i	$0.887423\pi$
$684$	−2.44870	−	1.05477i	−0.0936283	−	0.0403301i
$685$	−12.6218			−0.482254
$686$	18.4098	−	2.01993i	0.702889	−	0.0771213i
$687$	−6.07784	+	29.4734i	−0.231884	+	1.12448i
$688$	0.00618986	+	0.0107211i	0.000235986	+	0.000408740i
$689$	8.66621			0.330156
$690$	38.2447	−	12.6838i	1.45595	−	0.482865i
$691$	25.0617			0.953394			0.476697	−	0.879068i	$-0.341834\pi$
$691$	25.0617			0.953394			0.476697	+	0.879068i	$0.341834\pi$
$692$	22.5636			0.857740
$693$	10.9294	+	4.24290i	0.415175	+	0.161175i
$694$	−30.4065			−1.15422
$695$	49.9839			1.89600
$696$	0.878215	−	4.25874i	0.0332887	−	0.161427i
$697$	−27.0356			−1.02405
$698$	−6.29782	−	10.9082i	−0.238376	−	0.412880i
$699$	−25.0581	+	8.31052i	−0.947785	+	0.314333i
$700$	−10.7596	+	20.3103i	−0.406674	+	0.767658i
$701$	−43.4858			−1.64243			−0.821217	−	0.570616i	$-0.806705\pi$
$701$	−43.4858			−1.64243			−0.821217	+	0.570616i	$0.806705\pi$
$702$	5.93818	+	12.7088i	0.224122	+	0.479663i
$703$	−1.23422	−	2.13773i	−0.0465495	−	0.0806260i
$704$	0.738550	−	1.27921i	0.0278351	−	0.0482119i
$705$	9.04325	−	43.8536i	0.340589	−	1.65162i
$706$	3.76578	−	6.52252i	0.141727	−	0.245478i
$707$	−6.50805	+	12.2849i	−0.244760	+	0.462021i
$708$	−8.94251	−	7.95403i	−0.336080	−	0.298931i
$709$	−22.7403			−0.854031			−0.427016	−	0.904244i	$-0.640435\pi$
$709$	−22.7403			−0.854031			−0.427016	+	0.904244i	$0.640435\pi$
$710$	10.1087	+	17.5088i	0.379373	+	0.657094i
$711$	4.00619	+	34.1227i	0.150244	+	1.27970i
$712$	−4.43818	+	7.68715i	−0.166328	+	0.288088i
$713$	−21.4134	−	37.0891i	−0.801939	−	1.38900i
$714$	5.00728	−	29.7160i	0.187393	−	1.11209i
$715$	7.37636	−	12.7762i	0.275860	−	0.477804i
$716$	0.166896	+	0.289073i	0.00623721	+	0.0108032i
$717$	−31.1545	+	10.3324i	−1.16349	+	0.385870i
$718$	−3.44801	+	5.97213i	−0.128679	+	0.222878i
$719$	6.06182	−	10.4994i	0.226068	−	0.391561i	−0.730571	−	0.682836i	$-0.760746\pi$
$719$	6.06182	−	10.4994i	0.226068	−	0.391561i	0.956639	+	0.291275i	$0.0940796\pi$
$720$	8.89926	−	6.63238i	0.331656	−	0.247174i
$721$	−2.34176	−	3.73495i	−0.0872119	−	0.139097i
$722$	9.10507	+	15.7705i	0.338856	+	0.586915i
$723$	−40.2868	+	13.3611i	−1.49828	+	0.496905i
$724$	23.2422			0.863789
$725$	−21.8095			−0.809985
$726$	3.08472	−	14.9588i	0.114485	−	0.555172i
$727$	23.0908	+	39.9945i	0.856392	+	1.48331i	0.875348	+	0.483494i	$0.160632\pi$
$727$	23.0908	+	39.9945i	0.856392	+	1.48331i	−0.0189562	+	0.999820i	$0.506034\pi$
$728$	−3.34362	+	6.31159i	−0.123923	+	0.233923i
$729$	−9.27375	−	25.3574i	−0.343472	−	0.939163i
$730$	−22.3189	+	38.6574i	−0.826058	+	1.43077i
$731$	−0.0407044	+	0.0705021i	−0.00150551	+	0.00260761i
$732$	7.41961	+	6.59947i	0.274237	+	0.243923i
$733$	18.0149	+	31.2026i	0.665394	+	1.15250i	0.979178	+	0.203002i	$0.0650696\pi$
$733$	18.0149	+	31.2026i	0.665394	+	1.15250i	−0.313785	+	0.949494i	$0.601597\pi$
$734$	−11.5618	+	20.0257i	−0.426755	+	0.739161i
$735$	−5.83743	+	44.4741i	−0.215317	+	1.64045i
$736$	−3.14400	−	5.44556i	−0.115889	−	0.200726i
$737$	−6.99017	+	12.1073i	−0.257486	+	0.445979i
$738$	−11.3276	−	4.87933i	−0.416975	−	0.179611i
$739$	23.2119	+	40.2042i	0.853865	+	1.47894i	0.877694	+	0.479221i	$0.159081\pi$
$739$	23.2119	+	40.2042i	0.853865	+	1.47894i	−0.0238296	+	0.999716i	$0.507586\pi$
$740$	10.2756			0.377739
$741$	−0.839294	+	4.07000i	−0.0308322	+	0.149515i
$742$	−4.51169	−	7.19583i	−0.165629	−	0.264167i
$743$	0.598884	−	1.03730i	0.0219709	−	0.0380548i	−0.854831	−	0.518907i	$-0.826339\pi$
$743$	0.598884	−	1.03730i	0.0219709	−	0.0380548i	0.876802	+	0.480852i	$0.159673\pi$
$744$	−8.81453	−	7.84020i	−0.323157	−	0.287436i
$745$	−0.617454	+	1.06946i	−0.0226218	+	0.0391820i
$746$	−14.5822	−	25.2571i	−0.533891	−	0.924727i
$747$	−10.7694	+	8.02617i	−0.394033	+	0.293662i
$748$	9.71339			0.355157
$749$	−13.3331	+	25.1682i	−0.487181	+	0.919626i
$750$	−17.6545	−	15.7030i	−0.644652	−	0.573394i
$751$	−24.0600	−	41.6731i	−0.877961	−	1.52067i	−0.853575	−	0.520970i	$-0.825570\pi$
$751$	−24.0600	−	41.6731i	−0.877961	−	1.52067i	−0.0243853	−	0.999703i	$-0.507763\pi$
$752$	−6.98762			−0.254812
$753$	15.6902	+	13.9559i	0.571783	+	0.508580i
$754$	−6.77747			−0.246821
$755$	−73.6588			−2.68072
$756$	7.46108	−	11.5470i	0.271357	−	0.419959i
$757$	49.6006			1.80276			0.901382	−	0.433025i	$-0.142554\pi$
$757$	49.6006			1.80276			0.901382	+	0.433025i	$0.142554\pi$
$758$	−13.5622			−0.492602
$759$	12.0204	+	10.6917i	0.436311	+	0.388083i
$760$	3.28799			0.119268
$761$	18.7701	+	32.5108i	0.680416	+	1.17852i	0.974854	+	0.222845i	$0.0715342\pi$
$761$	18.7701	+	32.5108i	0.680416	+	1.17852i	−0.294438	+	0.955671i	$0.595132\pi$
$762$	3.69708	+	3.28842i	0.133931	+	0.119127i
$763$	−0.265781	−	0.423902i	−0.00962191	−	0.0153463i
$764$	−16.3214			−0.590488
$765$	67.0319	+	28.8738i	2.42354	+	1.04393i
$766$	1.41783	+	2.45575i	0.0512281	+	0.0887297i
$767$	−9.32691	+	16.1547i	−0.336775	+	0.583312i
$768$	−1.29418	−	1.15113i	−0.0466998	−	0.0415377i
$769$	−13.4592	+	23.3121i	−0.485352	+	0.840654i	−0.999858	−	0.0168324i	$-0.994642\pi$
$769$	−13.4592	+	23.3121i	−0.485352	+	0.840654i	0.514506	+	0.857486i	$0.327975\pi$
$770$	−14.4487	+	0.526567i	−0.520695	+	0.0189762i
$771$	2.87154	−	13.9250i	0.103416	−	0.501497i
$772$	−14.3214			−0.515439
$773$	25.1130	+	43.4971i	0.903254	+	1.56448i	0.823245	+	0.567687i	$0.192162\pi$
$773$	25.1130	+	43.4971i	0.903254	+	1.56448i	0.0800089	+	0.996794i	$0.474505\pi$
$774$	−0.0297787	+	0.0221933i	−0.00107037	+	0.000797722i
$775$	−29.5840	+	51.2409i	−1.06269	+	1.84063i
$776$	−6.58836	−	11.4114i	−0.236508	−	0.409645i
$777$	11.9270	−	4.44396i	0.427878	−	0.159426i
$778$	9.30401	−	16.1150i	0.333565	−	0.577752i
$779$	−1.82691	−	3.16431i	−0.0654560	−	0.113373i
$780$	−12.9258	−	11.4970i	−0.462818	−	0.411659i
$781$	−4.03597	+	6.99050i	−0.144418	+	0.250140i
$782$	20.6749	−	35.8099i	0.739332	−	1.28056i
$783$	12.9963	+	1.12691i	0.464449	+	0.0402723i
$784$	6.98143	−	0.509538i	0.249337	−	0.0181978i
$785$	12.8800	+	22.3088i	0.459707	+	0.796236i
$786$	−0.0544615	+	0.264101i	−0.00194258	+	0.00942017i
$787$	−1.65892			−0.0591342			−0.0295671	−	0.999563i	$-0.509413\pi$
$787$	−1.65892			−0.0591342			−0.0295671	+	0.999563i	$0.509413\pi$
$788$	2.42402			0.0863520
$789$	−8.78909	+	2.91490i	−0.312900	+	0.103773i
$790$	−21.1847	−	36.6930i	−0.753718	−	1.30548i
$791$	−16.7992	+	31.7110i	−0.597311	+	1.12751i
$792$	4.06979	+	1.75305i	0.144614	+	0.0622920i
$793$	7.73855	−	13.4036i	0.274804	−	0.475974i
$794$	−10.2880	+	17.8193i	−0.365107	+	0.632384i
$795$	19.5247	−	6.47536i	0.692469	−	0.229657i
$796$	−3.05563	−	5.29251i	−0.108304	−	0.187588i
$797$	−15.3702	+	26.6219i	−0.544439	+	0.942996i	0.454203	+	0.890898i	$0.349924\pi$
$797$	−15.3702	+	26.6219i	−0.544439	+	0.942996i	−0.998642	+	0.0520981i	$0.983409\pi$
$798$	3.81639	−	1.42198i	0.135099	−	0.0503375i
$799$	−22.9752	−	39.7943i	−0.812806	−	1.40782i
$800$	−4.34362	+	7.52338i	−0.153570	+	0.265992i
$801$	−24.4567	−	10.5346i	−0.864134	−	0.372223i
$802$	3.37704	+	5.84921i	0.119248	+	0.206543i
$803$	−17.8219			−0.628921
$804$	12.2491	+	10.8951i	0.431991	+	0.384240i
$805$	−28.8127	+	54.3882i	−1.01551	+	1.91693i
$806$	−9.19344	+	15.9235i	−0.323825	+	0.560881i
$807$	6.46610	−	31.3561i	0.227617	−	1.10379i
$808$	−2.62729	+	4.55059i	−0.0924276	+	0.160089i
$809$	−1.44251	−	2.49850i	−0.0507159	−	0.0878425i	0.839553	−	0.543278i	$-0.182817\pi$
$809$	−1.44251	−	2.49850i	−0.0507159	−	0.0878425i	−0.890269	+	0.455435i	$0.849484\pi$
$810$	22.8745	+	24.1955i	0.803728	+	0.850145i
$811$	28.5461			1.00239			0.501195	−	0.865334i	$-0.332894\pi$
$811$	28.5461			1.00239			0.501195	+	0.865334i	$0.332894\pi$
$812$	3.52840	+	5.62755i	0.123823	+	0.197488i
$813$	12.0913	−	4.01008i	0.424061	−	0.140640i
$814$	2.05130	+	3.55296i	0.0718981	+	0.124531i
$815$	−29.8713			−1.04634
$816$	2.30037	−	11.1552i	0.0805291	−	0.390511i
$817$	−0.0110023			−0.000384922
$818$	15.3214			0.535701
$819$	−19.9752	−	7.75456i	−0.697991	−	0.270966i
$820$	15.2101			0.531161
$821$	7.96658			0.278036			0.139018	−	0.990290i	$-0.455605\pi$
$821$	7.96658			0.278036			0.139018	+	0.990290i	$0.455605\pi$
$822$	−5.60872	+	1.86013i	−0.195626	+	0.0648795i
$823$	40.5461			1.41335			0.706675	−	0.707539i	$-0.250194\pi$
$823$	40.5461			1.41335			0.706675	+	0.707539i	$0.250194\pi$
$824$	−0.833104	−	1.44298i	−0.0290225	−	0.0502685i
$825$	4.48879	−	21.7676i	0.156280	−	0.757849i
$826$	18.2694	−	0.665809i	0.635675	−	0.0231665i
$827$	1.22115			0.0424636			0.0212318	−	0.999775i	$-0.493241\pi$
$827$	1.22115			0.0424636			0.0212318	+	0.999775i	$0.493241\pi$
$828$	15.1254	−	11.2726i	0.525645	−	0.391749i
$829$	−7.07530	−	12.2548i	−0.245735	−	0.425626i	0.716603	−	0.697481i	$-0.245696\pi$
$829$	−7.07530	−	12.2548i	−0.245735	−	0.425626i	−0.962338	+	0.271856i	$0.912363\pi$
$830$	8.28180	−	14.3445i	0.287466	−	0.497905i
$831$	−14.9585	+	4.96099i	−0.518906	+	0.172095i
$832$	−1.34981	+	2.33795i	−0.0467964	+	0.0810537i
$833$	25.8567	+	38.0837i	0.895881	+	1.31952i
$834$	22.2112	−	7.36636i	0.769112	−	0.255076i
$835$	−72.0901			−2.49478
$836$	0.656376	+	1.13688i	0.0227012	+	0.0393197i
$837$	20.2767	−	29.0058i	0.700866	−	1.00259i
$838$	−4.32141	+	7.48491i	−0.149281	+	0.258562i
$839$	1.19599	+	2.07151i	0.0412900	+	0.0715164i	0.885932	−	0.463815i	$-0.153520\pi$
$839$	1.19599	+	2.07151i	0.0412900	+	0.0715164i	−0.844642	+	0.535332i	$0.820187\pi$
$840$	−2.81708	+	16.7181i	−0.0971986	+	0.576831i
$841$	11.3486	−	19.6564i	0.391333	−	0.677808i
$842$	18.5636	+	32.1531i	0.639744	+	1.10807i
$843$	4.20080	−	20.3710i	0.144683	−	0.701614i
$844$	5.72253	−	9.91171i	0.196978	−	0.341175i
$845$	10.5662	−	18.3011i	0.363487	−	0.629577i
$846$	−2.44437	−	20.8199i	−0.0840391	−	0.715802i
$847$	12.3935	+	19.7667i	0.425845	+	0.679193i
$848$	−1.60507	−	2.78007i	−0.0551185	−	0.0954680i
$849$	−12.7385	−	11.3305i	−0.437186	−	0.388861i
$850$	−57.1272			−1.95945
$851$	17.4647			0.598683
$852$	7.07234	+	6.29059i	0.242294	+	0.215512i
$853$	−8.33998	−	14.4453i	−0.285556	−	0.494597i	0.687188	−	0.726479i	$-0.258845\pi$
$853$	−8.33998	−	14.4453i	−0.285556	−	0.494597i	−0.972744	+	0.231883i	$0.925511\pi$
$854$	−15.1582	+	0.552423i	−0.518702	+	0.0189035i
$855$	1.15019	+	9.79669i	0.0393355	+	0.335040i
$856$	−5.38255	+	9.32284i	−0.183972	+	0.318648i
$857$	6.92580	−	11.9958i	0.236581	−	0.409770i	−0.723150	−	0.690691i	$-0.757307\pi$
$857$	6.92580	−	11.9958i	0.236581	−	0.409770i	0.959731	+	0.280921i	$0.0906399\pi$
$858$	1.39493	−	6.76443i	0.0476220	−	0.230934i
$859$	−24.2472	−	41.9974i	−0.827304	−	1.43293i	−0.900146	−	0.435589i	$-0.856540\pi$
$859$	−24.2472	−	41.9974i	−0.827304	−	1.43293i	0.0728414	−	0.997344i	$-0.476793\pi$
$860$	0.0229002	−	0.0396643i	0.000780889	−	0.00135254i
$861$	17.6545	−	6.57802i	0.601664	−	0.224178i
$862$	−4.71015	−	8.15822i	−0.160428	−	0.277870i
$863$	2.96541	−	5.13624i	0.100944	−	0.174840i	−0.811130	−	0.584866i	$-0.801147\pi$
$863$	2.96541	−	5.13624i	0.100944	−	0.174840i	0.912074	+	0.410026i	$0.134480\pi$
$864$	2.97710	−	4.25874i	0.101283	−	0.144885i
$865$	−41.7385	−	72.2932i	−1.41915	−	2.45804i
$866$	−0.208771			−0.00709433
$867$	43.1443	−	14.3088i	1.46526	−	0.485953i
$868$	18.0080	−	0.656281i	0.611230	−	0.0222756i
$869$	8.45813	−	14.6499i	0.286922	−	0.496964i
$870$	−15.2694	+	5.06410i	−0.517682	+	0.171689i
$871$	12.7756	−	22.1280i	0.432885	−	0.749779i
$872$	−0.0945538	−	0.163772i	−0.00320200	−	0.00554602i
$873$	31.6959	−	23.6221i	1.07274	−	0.799488i
$874$	5.58836			0.189029
$875$	36.0679	−	1.31446i	1.21932	−	0.0444368i
$876$	−4.22067	+	20.4673i	−0.142603	+	0.691527i
$877$	−1.96472	−	3.40300i	−0.0663439	−	0.114911i	0.830945	−	0.556354i	$-0.187800\pi$
$877$	−1.96472	−	3.40300i	−0.0663439	−	0.114911i	−0.897289	+	0.441443i	$0.854467\pi$
$878$	−9.96796			−0.336402
$879$	−35.2149	+	11.6790i	−1.18777	+	0.393923i
$880$	−5.46472			−0.184216
$881$	37.6552			1.26864			0.634318	−	0.773072i	$-0.281281\pi$
$881$	37.6552			1.26864			0.634318	+	0.773072i	$0.281281\pi$
$882$	3.96039	+	20.6232i	0.133353	+	0.694418i
$883$	−53.2334			−1.79145			−0.895723	−	0.444613i	$-0.853341\pi$
$883$	−53.2334			−1.79145			−0.895723	+	0.444613i	$0.853341\pi$
$884$	−17.7527			−0.597088
$885$	−8.94251	+	43.3650i	−0.300599	+	1.45770i
$886$	−15.6996			−0.527439
$887$	18.4938	+	32.0322i	0.620961	+	1.07554i	0.989307	+	0.145848i	$0.0465910\pi$
$887$	18.4938	+	32.0322i	0.620961	+	1.07554i	−0.368346	+	0.929689i	$0.620076\pi$
$888$	4.56615	−	1.51436i	0.153230	−	0.0508187i
$889$	−7.55308	+	0.275264i	−0.253322	+	0.00923206i
$890$	32.8392			1.10077
$891$	−3.79961	+	12.7393i	−0.127292	+	0.426784i
$892$	−3.61126	−	6.25489i	−0.120914	−	0.209429i
$893$	3.10507	−	5.37815i	0.103907	−	0.179973i
$894$	−0.116765	+	0.566231i	−0.00390522	+	0.0189376i
$895$	0.617454	−	1.06946i	0.0206392	−	0.0357482i
$896$	2.64400	−	0.0963576i	0.0883297	−	0.00321908i
$897$	−21.9691	−	19.5407i	−0.733525	−	0.652443i
$898$	33.6253			1.12209
$899$	8.54944	+	14.8081i	0.285140	+	0.493877i
$900$	−23.9356	−	10.3102i	−0.797854	−	0.343673i
$901$	10.5549	−	18.2817i	0.351636	−	0.609052i
$902$	3.03637	+	5.25915i	0.101100	+	0.175111i
$903$	0.00942653	−	0.0559423i	0.000313695	−	0.00186164i
$904$	−6.78180	+	11.7464i	−0.225559	+	0.390680i
$905$	−42.9937	−	74.4673i	−1.42916	−	2.47538i
$906$	−32.7316	+	10.8554i	−1.08743	+	0.360647i
$907$	19.5080	−	33.7888i	0.647752	−	1.12194i	−0.335907	−	0.941895i	$-0.609043\pi$
$907$	19.5080	−	33.7888i	0.647752	−	1.12194i	0.983659	−	0.180044i	$-0.0576239\pi$
$908$	−6.82760	+	11.8258i	−0.226582	+	0.392451i
$909$	−14.4777	−	6.23623i	−0.480195	−	0.206843i
$910$	26.4072	−	0.962383i	0.875391	−	0.0319027i
$911$	−12.8090	−	22.1859i	−0.424382	−	0.735052i	0.571980	−	0.820267i	$-0.306175\pi$
$911$	−12.8090	−	22.1859i	−0.424382	−	0.735052i	−0.996363	+	0.0852158i	$0.972842\pi$
$912$	1.46108	−	0.484566i	0.0483811	−	0.0160456i
$913$	6.61312			0.218862
$914$	32.7083			1.08189
$915$	7.41961	−	35.9800i	0.245285	−	1.18946i
$916$	−8.68725	−	15.0468i	−0.287035	−	0.497159i
$917$	−0.218810	−	0.348986i	−0.00722574	−	0.0115245i
$918$	34.0421	+	2.95178i	1.12356	+	0.0974234i
$919$	10.3367	−	17.9038i	0.340978	−	0.590591i	−0.643637	−	0.765331i	$-0.722575\pi$
$919$	10.3367	−	17.9038i	0.340978	−	0.590591i	0.984615	+	0.174740i	$0.0559086\pi$
$920$	−11.6316	+	20.1466i	−0.383483	+	0.664212i
$921$	7.36033	+	6.54674i	0.242531	+	0.215723i
$922$	−2.07165	−	3.58821i	−0.0682263	−	0.118171i
$923$	7.37636	−	12.7762i	0.242796	−	0.420535i
$924$	−6.34294	+	2.36336i	−0.208667	+	0.0777488i
$925$	−12.0643	−	20.8960i	−0.396672	−	0.687055i
$926$	−8.34176	+	14.4484i	−0.274127	+	0.474803i
$927$	4.00797	−	2.98704i	0.131639	−	0.0981071i
$928$	1.25526	+	2.17417i	0.0412059	+	0.0713708i
$929$	−3.74033			−0.122716			−0.0613582	−	0.998116i	$-0.519543\pi$
$929$	−3.74033			−0.122716			−0.0613582	+	0.998116i	$0.519543\pi$
$930$	−8.81453	+	42.7444i	−0.289040	+	1.40165i
$931$	−2.71015	+	5.59980i	−0.0888215	+	0.183526i
$932$	7.62110	−	13.2001i	0.249637	−	0.432384i
$933$	15.1687	+	13.4920i	0.496600	+	0.441707i
$934$	14.9585	−	25.9089i	0.489458	−	0.847766i
$935$	−17.9680	−	31.1214i	−0.587615	−	1.01778i
$936$	−7.43818	−	3.20397i	−0.243124	−	0.104725i
$937$	−27.1345			−0.886445			−0.443223	−	0.896412i	$-0.646165\pi$
$937$	−27.1345			−0.886445			−0.443223	+	0.896412i	$0.646165\pi$
$938$	−25.0247	+	0.911998i	−0.817085	+	0.0297778i
$939$	34.6501	+	30.8200i	1.13076	+	1.00577i
$940$	12.9258	+	22.3881i	0.421593	+	0.730221i
$941$	6.32870			0.206310			0.103155	−	0.994665i	$-0.467106\pi$
$941$	6.32870			0.206310			0.103155	+	0.994665i	$0.467106\pi$
$942$	9.01121	+	8.01514i	0.293601	+	0.261147i
$943$	25.8516			0.841844
$944$	6.90978			0.224894
$945$	−50.7977	−	2.54535i	−1.65245	−	0.0828004i
$946$	0.0182861			0.000594531
$947$	31.2792			1.01644			0.508218	−	0.861228i	$-0.330304\pi$
$947$	31.2792			1.01644			0.508218	+	0.861228i	$0.330304\pi$
$948$	−14.8214	−	13.1831i	−0.481377	−	0.428167i
$949$	32.5723			1.05734
$950$	−3.86033	−	6.68630i	−0.125246	−	0.216932i
$951$	−2.46217	−	2.19001i	−0.0798414	−	0.0710160i
$952$	9.24219	+	14.7407i	0.299541	+	0.477747i
$953$	4.28937			0.138946			0.0694732	−	0.997584i	$-0.477868\pi$
$953$	4.28937			0.138946			0.0694732	+	0.997584i	$0.477868\pi$
$954$	7.72184	−	5.75488i	0.250004	−	0.186321i
$955$	30.1916	+	52.2933i	0.976977	+	1.69217i
$956$	9.47524	−	16.4116i	0.306451	−	0.530789i
$957$	−4.79920	−	4.26871i	−0.155136	−	0.137988i
$958$	1.47965	−	2.56283i	0.0478053	−	0.0828011i
$959$	4.22548	−	7.97622i	0.136448	−	0.257566i
$960$	−1.29418	+	6.27589i	−0.0417695	+	0.202554i
$961$	15.3883			0.496395
$962$	−3.74907	−	6.49358i	−0.120875	−	0.209361i
$963$	−29.6606	−	12.7762i	−0.955800	−	0.411708i
$964$	12.2527	−	21.2223i	0.394633	−	0.683525i
$965$	26.4920	+	45.8854i	0.852806	+	1.47710i
$966$	−4.78799	+	28.4146i	−0.154051	+	0.914226i
$967$	−7.59201	+	13.1497i	−0.244142	+	0.422867i	−0.961890	−	0.273436i	$-0.911840\pi$
$967$	−7.59201	+	13.1497i	−0.244142	+	0.422867i	0.717748	+	0.696303i	$0.245173\pi$
$968$	4.40909	+	7.63676i	0.141713	+	0.245455i
$969$	7.56360	+	6.72755i	0.242978	+	0.216120i
$970$	−24.3745	+	42.2179i	−0.782618	+	1.35553i
$971$	1.62364	−	2.81223i	0.0521052	−	0.0902489i	−0.838796	−	0.544445i	$-0.816740\pi$
$971$	1.62364	−	2.81223i	0.0521052	−	0.0902489i	0.890902	+	0.454196i	$0.150074\pi$
$972$	13.7305	+	7.38061i	0.440406	+	0.236733i
$973$	−16.7335	+	31.5869i	−0.536450	+	1.01263i
$974$	−14.0309	−	24.3022i	−0.449578	−	0.778692i
$975$	−8.20396	+	39.7836i	−0.262737	+	1.27409i
$976$	−5.73305			−0.183510
$977$	15.5439			0.497295			0.248647	−	0.968594i	$-0.420014\pi$
$977$	15.5439			0.497295			0.248647	+	0.968594i	$0.420014\pi$
$978$	−13.2738	+	4.40226i	−0.424450	+	0.140769i
$979$	6.55563	+	11.3547i	0.209519	+	0.362897i
$980$	−14.5469	−	21.4258i	−0.464683	−	0.684421i
$981$	0.454888	−	0.339016i	0.0145235	−	0.0108240i
$982$	17.0734	−	29.5721i	0.544835	−	0.943682i
$983$	−6.19158	+	10.7241i	−0.197481	+	0.342047i	−0.947711	−	0.319130i	$-0.896609\pi$
$983$	−6.19158	+	10.7241i	−0.197481	+	0.342047i	0.750230	+	0.661177i	$0.229943\pi$
$984$	6.75890	−	2.24159i	0.215466	−	0.0714592i
$985$	−4.48398	−	7.76648i	−0.142871	−	0.247461i
$986$	−8.25457	+	14.2973i	−0.262879	+	0.455320i
$987$	24.6854	+	20.3960i	0.785745	+	0.649211i
$988$	−1.19963	−	2.07782i	−0.0381653	−	0.0661042i
$989$	0.0389218	−	0.0674145i	0.00123764	−	0.00214366i
$990$	−1.91164	−	16.2823i	−0.0607558	−	0.517486i
$991$	−3.32760	−	5.76358i	−0.105705	−	0.183086i	0.808321	−	0.588742i	$-0.200377\pi$
$991$	−3.32760	−	5.76358i	−0.105705	−	0.183086i	−0.914026	+	0.405656i	$0.867043\pi$
$992$	6.81089			0.216246
$993$	−7.20513	−	6.40869i	−0.228648	−	0.203374i
$994$	−14.4487	+	0.526567i	−0.458285	+	0.0167017i
$995$	−11.3047	+	19.5803i	−0.358383	+	0.620738i
$996$	1.56615	−	7.59476i	0.0496254	−	0.240649i
$997$	−2.40104	+	4.15872i	−0.0760417	+	0.131708i	−0.901539	−	0.432698i	$-0.857562\pi$
$997$	−2.40104	+	4.15872i	−0.0760417	+	0.131708i	0.825497	+	0.564406i	$0.190895\pi$
$998$	1.14035	+	1.97515i	0.0360973	+	0.0625223i
$999$	6.10940	+	13.0753i	0.193293	+	0.413683i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.2.e.d.121.1	yes	6
3.2	odd	2		378.2.e.c.37.3		6
4.3	odd	2		1008.2.q.h.625.3		6
7.2	even	3		882.2.f.l.589.3		6
7.3	odd	6		882.2.h.o.67.3		6
7.4	even	3		126.2.h.c.67.1	yes	6
7.5	odd	6		882.2.f.m.589.1		6
7.6	odd	2		882.2.e.p.373.3		6
9.2	odd	6		378.2.h.d.289.1		6
9.4	even	3		1134.2.g.k.163.1		6
9.5	odd	6		1134.2.g.n.163.3		6
9.7	even	3		126.2.h.c.79.1	yes	6
12.11	even	2		3024.2.q.h.2305.3		6
21.2	odd	6		2646.2.f.o.1765.3		6
21.5	even	6		2646.2.f.n.1765.1		6
21.11	odd	6		378.2.h.d.361.1		6
21.17	even	6		2646.2.h.p.361.3		6
21.20	even	2		2646.2.e.o.1549.1		6
28.11	odd	6		1008.2.t.g.193.3		6
36.7	odd	6		1008.2.t.g.961.3		6
36.11	even	6		3024.2.t.g.289.1		6
63.2	odd	6		2646.2.f.o.883.3		6
63.4	even	3		1134.2.g.k.487.1		6
63.5	even	6		7938.2.a.bx.1.3		3
63.11	odd	6		378.2.e.c.235.3		6
63.16	even	3		882.2.f.l.295.3		6
63.20	even	6		2646.2.h.p.667.3		6
63.23	odd	6		7938.2.a.bu.1.1		3
63.25	even	3	inner	126.2.e.d.25.1	✓	6
63.32	odd	6		1134.2.g.n.487.3		6
63.34	odd	6		882.2.h.o.79.3		6
63.38	even	6		2646.2.e.o.2125.1		6
63.40	odd	6		7938.2.a.by.1.1		3
63.47	even	6		2646.2.f.n.883.1		6
63.52	odd	6		882.2.e.p.655.3		6
63.58	even	3		7938.2.a.cb.1.3		3
63.61	odd	6		882.2.f.m.295.1		6
84.11	even	6		3024.2.t.g.1873.1		6
252.11	even	6		3024.2.q.h.2881.3		6
252.151	odd	6		1008.2.q.h.529.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.d.25.1	✓	6	63.25	even	3	inner
126.2.e.d.121.1	yes	6	1.1	even	1	trivial
126.2.h.c.67.1	yes	6	7.4	even	3
126.2.h.c.79.1	yes	6	9.7	even	3
378.2.e.c.37.3		6	3.2	odd	2
378.2.e.c.235.3		6	63.11	odd	6
378.2.h.d.289.1		6	9.2	odd	6
378.2.h.d.361.1		6	21.11	odd	6
882.2.e.p.373.3		6	7.6	odd	2
882.2.e.p.655.3		6	63.52	odd	6
882.2.f.l.295.3		6	63.16	even	3
882.2.f.l.589.3		6	7.2	even	3
882.2.f.m.295.1		6	63.61	odd	6
882.2.f.m.589.1		6	7.5	odd	6
882.2.h.o.67.3		6	7.3	odd	6
882.2.h.o.79.3		6	63.34	odd	6
1008.2.q.h.529.3		6	252.151	odd	6
1008.2.q.h.625.3		6	4.3	odd	2
1008.2.t.g.193.3		6	28.11	odd	6
1008.2.t.g.961.3		6	36.7	odd	6
1134.2.g.k.163.1		6	9.4	even	3
1134.2.g.k.487.1		6	63.4	even	3
1134.2.g.n.163.3		6	9.5	odd	6
1134.2.g.n.487.3		6	63.32	odd	6
2646.2.e.o.1549.1		6	21.20	even	2
2646.2.e.o.2125.1		6	63.38	even	6
2646.2.f.n.883.1		6	63.47	even	6
2646.2.f.n.1765.1		6	21.5	even	6
2646.2.f.o.883.3		6	63.2	odd	6
2646.2.f.o.1765.3		6	21.2	odd	6
2646.2.h.p.361.3		6	21.17	even	6
2646.2.h.p.667.3		6	63.20	even	6
3024.2.q.h.2305.3		6	12.11	even	2
3024.2.q.h.2881.3		6	252.11	even	6
3024.2.t.g.289.1		6	36.11	even	6
3024.2.t.g.1873.1		6	84.11	even	6
7938.2.a.bu.1.1		3	63.23	odd	6
7938.2.a.bx.1.3		3	63.5	even	6
7938.2.a.by.1.1		3	63.40	odd	6
7938.2.a.cb.1.3		3	63.58	even	3

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	126.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.29418 - 1.15113i) q^{3} +1.00000 q^{4} +(-1.84981 - 3.20397i) q^{5} +(-1.29418 - 1.15113i) q^{6} +(2.64400 - 0.0963576i) q^{7} +1.00000 q^{8} +(0.349814 + 2.97954i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.29418 - 1.15113i) q^{3} +1.00000 q^{4} +(-1.84981 - 3.20397i) q^{5} +(-1.29418 - 1.15113i) q^{6} +(2.64400 - 0.0963576i) q^{7} +1.00000 q^{8} +(0.349814 + 2.97954i) q^{9} +(-1.84981 - 3.20397i) q^{10} +(0.738550 - 1.27921i) q^{11} +(-1.29418 - 1.15113i) q^{12} +(-1.34981 + 2.33795i) q^{13} +(2.64400 - 0.0963576i) q^{14} +(-1.29418 + 6.27589i) q^{15} +1.00000 q^{16} +(3.28799 + 5.69497i) q^{17} +(0.349814 + 2.97954i) q^{18} +(-0.444368 + 0.769668i) q^{19} +(-1.84981 - 3.20397i) q^{20} +(-3.53273 - 2.91887i) q^{21} +(0.738550 - 1.27921i) q^{22} +(-3.14400 - 5.44556i) q^{23} +(-1.29418 - 1.15113i) q^{24} +(-4.34362 + 7.52338i) q^{25} +(-1.34981 + 2.33795i) q^{26} +(2.97710 - 4.25874i) q^{27} +(2.64400 - 0.0963576i) q^{28} +(1.25526 + 2.17417i) q^{29} +(-1.29418 + 6.27589i) q^{30} +6.81089 q^{31} +1.00000 q^{32} +(-2.42835 + 0.805361i) q^{33} +(3.28799 + 5.69497i) q^{34} +(-5.19963 - 8.29305i) q^{35} +(0.349814 + 2.97954i) q^{36} +(-1.38874 + 2.40536i) q^{37} +(-0.444368 + 0.769668i) q^{38} +(4.43818 - 1.47192i) q^{39} +(-1.84981 - 3.20397i) q^{40} +(-2.05563 + 3.56046i) q^{41} +(-3.53273 - 2.91887i) q^{42} +(0.00618986 + 0.0107211i) q^{43} +(0.738550 - 1.27921i) q^{44} +(8.89926 - 6.63238i) q^{45} +(-3.14400 - 5.44556i) q^{46} -6.98762 q^{47} +(-1.29418 - 1.15113i) q^{48} +(6.98143 - 0.509538i) q^{49} +(-4.34362 + 7.52338i) q^{50} +(2.30037 - 11.1552i) q^{51} +(-1.34981 + 2.33795i) q^{52} +(-1.60507 - 2.78007i) q^{53} +(2.97710 - 4.25874i) q^{54} -5.46472 q^{55} +(2.64400 - 0.0963576i) q^{56} +(1.46108 - 0.484566i) q^{57} +(1.25526 + 2.17417i) q^{58} +6.90978 q^{59} +(-1.29418 + 6.27589i) q^{60} -5.73305 q^{61} +6.81089 q^{62} +(1.21201 + 7.84417i) q^{63} +1.00000 q^{64} +9.98762 q^{65} +(-2.42835 + 0.805361i) q^{66} -9.46472 q^{67} +(3.28799 + 5.69497i) q^{68} +(-2.19963 + 10.6667i) q^{69} +(-5.19963 - 8.29305i) q^{70} -5.46472 q^{71} +(0.349814 + 2.97954i) q^{72} +(-6.03273 - 10.4490i) q^{73} +(-1.38874 + 2.40536i) q^{74} +(14.2818 - 4.73656i) q^{75} +(-0.444368 + 0.769668i) q^{76} +(1.82946 - 3.45338i) q^{77} +(4.43818 - 1.47192i) q^{78} +11.4523 q^{79} +(-1.84981 - 3.20397i) q^{80} +(-8.75526 + 2.08457i) q^{81} +(-2.05563 + 3.56046i) q^{82} +(2.23855 + 3.87728i) q^{83} +(-3.53273 - 2.91887i) q^{84} +(12.1643 - 21.0693i) q^{85} +(0.00618986 + 0.0107211i) q^{86} +(0.878215 - 4.25874i) q^{87} +(0.738550 - 1.27921i) q^{88} +(-4.43818 + 7.68715i) q^{89} +(8.89926 - 6.63238i) q^{90} +(-3.34362 + 6.31159i) q^{91} +(-3.14400 - 5.44556i) q^{92} +(-8.81453 - 7.84020i) q^{93} -6.98762 q^{94} +3.28799 q^{95} +(-1.29418 - 1.15113i) q^{96} +(-6.58836 - 11.4114i) q^{97} +(6.98143 - 0.509538i) q^{98} +(4.06979 + 1.75305i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 2 q^{3} + 6 q^{4} - 5 q^{5} - 2 q^{6} + 4 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 - 2 * q^3 + 6 * q^4 - 5 * q^5 - 2 * q^6 + 4 * q^7 + 6 * q^8 - 4 * q^9	\( 6 q + 6 q^{2} - 2 q^{3} + 6 q^{4} - 5 q^{5} - 2 q^{6} + 4 q^{7} + 6 q^{8} - 4 q^{9} - 5 q^{10} - q^{11} - 2 q^{12} - 2 q^{13} + 4 q^{14} - 2 q^{15} + 6 q^{16} - 4 q^{17} - 4 q^{18} - 3 q^{19} - 5 q^{20} - 10 q^{21} - q^{22} - 7 q^{23} - 2 q^{24} - 2 q^{25} - 2 q^{26} + 7 q^{27} + 4 q^{28} - 5 q^{29} - 2 q^{30} + 28 q^{31} + 6 q^{32} - 19 q^{33} - 4 q^{34} - 19 q^{35} - 4 q^{36} - 9 q^{37} - 3 q^{38} + 9 q^{39} - 5 q^{40} - 12 q^{41} - 10 q^{42} + 18 q^{43} - q^{44} + 29 q^{45} - 7 q^{46} - 6 q^{47} - 2 q^{48} - 12 q^{49} - 2 q^{50} + 26 q^{51} - 2 q^{52} + 9 q^{53} + 7 q^{54} + 14 q^{55} + 4 q^{56} + 2 q^{57} - 5 q^{58} - 8 q^{59} - 2 q^{60} - 8 q^{61} + 28 q^{62} + 31 q^{63} + 6 q^{64} + 24 q^{65} - 19 q^{66} - 10 q^{67} - 4 q^{68} - q^{69} - 19 q^{70} + 14 q^{71} - 4 q^{72} - 25 q^{73} - 9 q^{74} + 44 q^{75} - 3 q^{76} + 52 q^{77} + 9 q^{78} - 14 q^{79} - 5 q^{80} - 40 q^{81} - 12 q^{82} + 8 q^{83} - 10 q^{84} + 14 q^{85} + 18 q^{86} + 31 q^{87} - q^{88} - 9 q^{89} + 29 q^{90} + 4 q^{91} - 7 q^{92} - 6 q^{94} - 4 q^{95} - 2 q^{96} - 28 q^{97} - 12 q^{98} - 41 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 2 * q^3 + 6 * q^4 - 5 * q^5 - 2 * q^6 + 4 * q^7 + 6 * q^8 - 4 * q^9 - 5 * q^10 - q^11 - 2 * q^12 - 2 * q^13 + 4 * q^14 - 2 * q^15 + 6 * q^16 - 4 * q^17 - 4 * q^18 - 3 * q^19 - 5 * q^20 - 10 * q^21 - q^22 - 7 * q^23 - 2 * q^24 - 2 * q^25 - 2 * q^26 + 7 * q^27 + 4 * q^28 - 5 * q^29 - 2 * q^30 + 28 * q^31 + 6 * q^32 - 19 * q^33 - 4 * q^34 - 19 * q^35 - 4 * q^36 - 9 * q^37 - 3 * q^38 + 9 * q^39 - 5 * q^40 - 12 * q^41 - 10 * q^42 + 18 * q^43 - q^44 + 29 * q^45 - 7 * q^46 - 6 * q^47 - 2 * q^48 - 12 * q^49 - 2 * q^50 + 26 * q^51 - 2 * q^52 + 9 * q^53 + 7 * q^54 + 14 * q^55 + 4 * q^56 + 2 * q^57 - 5 * q^58 - 8 * q^59 - 2 * q^60 - 8 * q^61 + 28 * q^62 + 31 * q^63 + 6 * q^64 + 24 * q^65 - 19 * q^66 - 10 * q^67 - 4 * q^68 - q^69 - 19 * q^70 + 14 * q^71 - 4 * q^72 - 25 * q^73 - 9 * q^74 + 44 * q^75 - 3 * q^76 + 52 * q^77 + 9 * q^78 - 14 * q^79 - 5 * q^80 - 40 * q^81 - 12 * q^82 + 8 * q^83 - 10 * q^84 + 14 * q^85 + 18 * q^86 + 31 * q^87 - q^88 - 9 * q^89 + 29 * q^90 + 4 * q^91 - 7 * q^92 - 6 * q^94 - 4 * q^95 - 2 * q^96 - 28 * q^97 - 12 * q^98 - 41 * q^99

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