LMFDB - Embedded newform 126.2.e.d.25.1

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			25.1
Root			$0.500000 - 0.224437i$ of defining polynomial
Character	$\chi$	$=$	126.25
Dual form			126.2.e.d.121.1

$q$-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 $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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	0.0729162	+	0.997338i	$0.476769\pi$
$5$	−1.84981	+	3.20397i	−0.827262	+	1.43286i	−0.900178	+	0.435522i	$0.856564\pi$
$6$	−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	0.955621	−	0.294598i	$-0.0951858\pi$
$11$	0.738550	+	1.27921i	0.222681	+	0.385695i	−0.732940	+	0.680293i	$0.761852\pi$
$12$	−1.29418	+	1.15113i	−0.373598	+	0.332302i
$13$	−1.34981	−	2.33795i	−0.374371	−	0.648430i	0.615862	−	0.787854i	$-0.288808\pi$
$13$	−1.34981	−	2.33795i	−0.374371	−	0.648430i	−0.990233	+	0.139425i	$0.955475\pi$
$14$	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	−0.123813	−	0.992306i	$-0.539512\pi$
$17$	3.28799	−	5.69497i	0.797455	−	1.38123i	0.921268	−	0.388927i	$-0.127154\pi$
$18$	0.349814	−	2.97954i	0.0824520	−	0.702283i
$19$	−0.444368	−	0.769668i	−0.101945	−	0.176574i	0.810541	−	0.585682i	$-0.199173\pi$
$19$	−0.444368	−	0.769668i	−0.101945	−	0.176574i	−0.912486	+	0.409108i	$0.865840\pi$
$20$	−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	0.326182	+	0.945307i	$0.394238\pi$
$23$	−3.14400	+	5.44556i	−0.655568	+	1.13548i	−0.981751	+	0.190171i	$0.939096\pi$
$24$	−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	−0.725622	−	0.688094i	$-0.758448\pi$
$29$	1.25526	−	2.17417i	0.233096	−	0.403734i	0.958718	+	0.284360i	$0.0917810\pi$
$30$	−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	0.729000	−	0.684514i	$-0.239986\pi$
$37$	−1.38874	−	2.40536i	−0.228307	−	0.395439i	−0.957306	+	0.289075i	$0.906652\pi$
$38$	−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	0.659666	−	0.751559i	$-0.270698\pi$
$41$	−2.05563	−	3.56046i	−0.321036	−	0.556050i	−0.980702	+	0.195508i	$0.937364\pi$
$42$	−3.53273	+	2.91887i	−0.545112	+	0.450392i
$43$	0.00618986	−	0.0107211i	0.000943944	−	0.00163496i	−0.865553	−	0.500817i	$-0.833033\pi$
$43$	0.00618986	−	0.0107211i	0.000943944	−	0.00163496i	0.866497	+	0.499182i	$0.166366\pi$
$44$	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	−0.954952	−	0.296760i	$-0.904094\pi$
$53$	−1.60507	+	2.78007i	−0.220474	+	0.381872i	0.734478	+	0.678632i	$0.237427\pi$
$54$	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	0.260223	+	0.965548i	$0.416204\pi$
$73$	−6.03273	+	10.4490i	−0.706078	+	1.22296i	−0.966301	+	0.257414i	$0.917130\pi$
$74$	−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	−0.716619	−	0.697465i	$-0.754311\pi$
$83$	2.23855	−	3.87728i	0.245713	−	0.425587i	0.962332	+	0.271878i	$0.0876447\pi$
$84$	−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	0.528983	−	0.848633i	$-0.322574\pi$
$89$	−4.43818	−	7.68715i	−0.470446	−	0.814836i	−0.999429	+	0.0337963i	$0.989240\pi$
$90$	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	0.309252	+	0.950980i	$0.399921\pi$
$97$	−6.58836	+	11.4114i	−0.668947	+	1.15865i	−0.978199	+	0.207670i	$0.933412\pi$
$98$	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	0.705196	−	0.709012i	$-0.250859\pi$
$101$	−2.62729	−	4.55059i	−0.261425	−	0.452801i	−0.966621	+	0.256212i	$0.917526\pi$
$102$	2.30037	+	11.1552i	0.227771	+	1.10453i
$103$	−0.833104	+	1.44298i	−0.0820882	+	0.142181i	−0.904147	−	0.427222i	$-0.859492\pi$
$103$	−0.833104	+	1.44298i	−0.0820882	+	0.142181i	0.822059	+	0.569403i	$0.192826\pi$
$104$	−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	−0.999720	−	0.0236602i	$-0.992468\pi$
$107$	−5.38255	−	9.32284i	−0.520350	−	0.901273i	0.479370	−	0.877613i	$-0.340865\pi$
$108$	2.97710	+	4.25874i	0.286472	+	0.409798i
$109$	−0.0945538	+	0.163772i	−0.00905662	+	0.0156865i	−0.870518	−	0.492136i	$-0.836216\pi$
$109$	−0.0945538	+	0.163772i	−0.00905662	+	0.0156865i	0.861462	+	0.507823i	$0.169550\pi$
$110$	−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	−0.985876	−	0.167478i	$-0.946438\pi$
$113$	−6.78180	−	11.7464i	−0.637978	−	1.10501i	0.347897	−	0.937533i	$-0.386896\pi$
$114$	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	−0.869406	−	0.494098i	$-0.835498\pi$
$131$	−0.0778435	+	0.134829i	−0.00680122	+	0.0117801i	0.862605	+	0.505878i	$0.168832\pi$
$132$	−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	0.929648	−	0.368449i	$-0.120111\pi$
$137$	1.70582	+	2.95456i	0.145738	+	0.252425i	−0.783910	+	0.620874i	$0.786778\pi$
$138$	−2.19963	−	10.6667i	−0.187245	−	0.908009i
$139$	−6.75526	−	11.7005i	−0.572974	−	0.992420i	−0.996259	−	0.0864229i	$-0.972456\pi$
$139$	−6.75526	−	11.7005i	−0.572974	−	0.992420i	0.423285	−	0.905997i	$-0.360877\pi$
$140$	−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	−0.872781	−	0.488112i	$-0.837686\pi$
$149$	−0.166896	+	0.289073i	−0.0136727	+	0.0236818i	0.859108	+	0.511794i	$0.171019\pi$
$150$	14.2818	+	4.73656i	1.16610	+	0.386738i
$151$	9.95489	+	17.2424i	0.810117	+	1.40316i	0.912781	+	0.408448i	$0.133930\pi$
$151$	9.95489	+	17.2424i	0.810117	+	1.40316i	−0.102664	+	0.994716i	$0.532737\pi$
$152$	−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	0.979693	−	0.200502i	$-0.0642572\pi$
$163$	4.03706	+	6.99240i	0.316207	+	0.547687i	−0.663486	+	0.748189i	$0.730924\pi$
$164$	−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	0.945906	+	0.324440i	$0.105176\pi$
$167$	9.74288	+	16.8752i	0.753927	+	1.30584i	−0.191979	+	0.981399i	$0.561491\pi$
$168$	−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	−0.859721	−	0.510764i	$-0.829363\pi$
$179$	0.166896	−	0.289073i	0.0124744	−	0.0216063i	0.872195	+	0.489158i	$0.162696\pi$
$180$	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	−0.953769	−	0.300541i	$-0.902833\pi$
$199$	−3.05563	+	5.29251i	−0.216608	+	0.375176i	0.737161	+	0.675717i	$0.236166\pi$
$200$	−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	0.992967	−	0.118390i	$-0.0377732\pi$
$211$	5.72253	+	9.91171i	0.393955	+	0.682350i	−0.599012	+	0.800740i	$0.704440\pi$
$212$	−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	−0.961235	−	0.275730i	$-0.911080\pi$
$223$	−3.61126	+	6.25489i	−0.241828	+	0.418859i	0.719407	+	0.694589i	$0.244414\pi$
$224$	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	0.545417	−	0.838165i	$-0.316371\pi$
$227$	−6.82760	−	11.8258i	−0.453164	−	0.784903i	−0.998581	+	0.0532622i	$0.983038\pi$
$228$	1.46108	+	0.484566i	0.0967623	+	0.0320912i
$229$	−8.68725	+	15.0468i	−0.574070	+	0.994318i	0.422073	+	0.906562i	$0.361303\pi$
$229$	−8.68725	+	15.0468i	−0.574070	+	0.994318i	−0.996142	+	0.0877555i	$0.972031\pi$
$230$	−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	1.00000		0.000837426i	$-0.000266561\pi$
$233$	7.62110	+	13.2001i	0.499275	+	0.864769i	−0.500725	+	0.865606i	$0.666933\pi$
$234$	−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	0.990749	+	0.135710i	$0.0433314\pi$
$239$	9.47524	+	16.4116i	0.612902	+	1.06158i	−0.377846	+	0.925868i	$0.623335\pi$
$240$	−1.29418	−	6.27589i	−0.0835391	−	0.405107i
$241$	12.2527	+	21.2223i	0.789267	+	1.36705i	0.926417	+	0.376500i	$0.122872\pi$
$241$	12.2527	+	21.2223i	0.789267	+	1.36705i	−0.137150	+	0.990550i	$0.543794\pi$
$242$	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	−0.709149	−	0.705059i	$-0.750921\pi$
$257$	4.10439	−	7.10900i	0.256025	−	0.443448i	0.965173	+	0.261611i	$0.0842539\pi$
$258$	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	0.936595	−	0.350414i	$-0.113959\pi$
$263$	2.67309	+	4.62992i	0.164830	+	0.285493i	−0.771765	+	0.635908i	$0.780626\pi$
$264$	−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	−0.433681	−	0.901067i	$-0.642785\pi$
$269$	9.24219	−	16.0079i	0.563506	−	0.976022i	0.997187	−	0.0749550i	$-0.0238813\pi$
$270$	−19.1520	+	1.66066i	−1.16555	+	0.101065i
$271$	−3.67742	−	6.36947i	−0.223387	−	0.386918i	0.732447	−	0.680824i	$-0.238378\pi$
$271$	−3.67742	−	6.36947i	−0.223387	−	0.386918i	−0.955834	+	0.293906i	$0.905045\pi$
$272$	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	0.969717	−	0.244230i	$-0.0785351\pi$
$277$	4.54944	+	7.87987i	0.273349	+	0.473455i	−0.696368	+	0.717685i	$0.745202\pi$
$278$	−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	−0.629470	−	0.777025i	$-0.716728\pi$
$281$	6.00433	−	10.3998i	0.358188	−	0.620400i	0.987658	+	0.156624i	$0.0500612\pi$
$282$	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	0.988406	+	0.151832i	$0.0485173\pi$
$293$	10.7101	+	18.5505i	0.625694	+	1.08373i	−0.362713	+	0.931901i	$0.618149\pi$
$294$	−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	−0.799585	−	0.600553i	$-0.794947\pi$
$337$	−16.8869	−	29.2489i	−0.919887	−	1.59329i	−0.120302	−	0.992737i	$-0.538386\pi$
$338$	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	−0.983889	−	0.178782i	$-0.942784\pi$
$349$	−6.29782	+	10.9082i	−0.337115	+	0.583900i	0.646774	+	0.762682i	$0.276118\pi$
$350$	−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	0.948668	−	0.316274i	$-0.102432\pi$
$353$	3.76578	+	6.52252i	0.200432	+	0.347159i	−0.748235	+	0.663433i	$0.769099\pi$
$354$	−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	0.760575	−	0.649250i	$-0.224917\pi$
$359$	−3.44801	−	5.97213i	−0.181979	−	0.315197i	−0.942554	+	0.334053i	$0.891584\pi$
$360$	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	−0.992283	−	0.123992i	$-0.960430\pi$
$367$	−11.5618	−	20.0257i	−0.603522	−	1.04533i	0.388761	−	0.921339i	$-0.372903\pi$
$368$	−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	0.190320	+	0.981722i	$0.439047\pi$
$373$	−14.5822	+	25.2571i	−0.755036	+	1.30776i	−0.945356	+	0.326039i	$0.894286\pi$
$374$	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	−0.827526	−	0.561428i	$-0.810252\pi$
$383$	1.41783	−	2.45575i	0.0724475	−	0.125483i	0.899973	+	0.435945i	$0.143586\pi$
$384$	−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	0.999477	−	0.0323388i	$-0.0102956\pi$
$389$	9.30401	+	16.1150i	0.471732	+	0.817064i	−0.527745	+	0.849403i	$0.676962\pi$
$390$	−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	−0.999820	−	0.0189712i	$-0.993961\pi$
$397$	−10.2880	−	17.8193i	−0.516340	−	0.894326i	0.483481	−	0.875355i	$-0.339372\pi$
$398$	−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	−0.769301	−	0.638887i	$-0.779395\pi$
$401$	3.37704	−	5.84921i	0.168642	−	0.292096i	0.937942	+	0.346791i	$0.112729\pi$
$402$	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	0.740949	−	0.671561i	$-0.234376\pi$
$419$	−4.32141	−	7.48491i	−0.211115	−	0.365662i	−0.952064	+	0.305900i	$0.901043\pi$
$420$	−2.81708	−	16.7181i	−0.137460	−	0.815762i
$421$	18.5636	−	32.1531i	0.904735	−	1.56705i	0.0834618	−	0.996511i	$-0.473402\pi$
$421$	18.5636	−	32.1531i	0.904735	−	1.56705i	0.821273	−	0.570536i	$-0.193264\pi$
$422$	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	−0.956882	−	0.290478i	$-0.906186\pi$
$431$	−4.71015	+	8.15822i	−0.226880	+	0.392967i	0.730002	+	0.683445i	$0.239519\pi$
$432$	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	−0.910228	−	0.414107i	$-0.864094\pi$
$461$	−2.07165	+	3.58821i	−0.0964865	+	0.167120i	0.813742	+	0.581227i	$0.197427\pi$
$462$	−6.34294	−	2.36336i	−0.295100	−	0.109953i
$463$	−8.34176	−	14.4484i	−0.387675	−	0.671472i	0.604462	−	0.796634i	$-0.293388\pi$
$463$	−8.34176	−	14.4484i	−0.387675	−	0.671472i	−0.992136	+	0.125162i	$0.960055\pi$
$464$	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	0.971116	+	0.238608i	$0.0766909\pi$
$467$	14.9585	+	25.9089i	0.692198	+	1.19892i	−0.278918	+	0.960315i	$0.589976\pi$
$468$	−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	0.897847	−	0.440307i	$-0.145130\pi$
$479$	1.47965	+	2.56283i	0.0676068	+	0.117098i	−0.830241	+	0.557405i	$0.811797\pi$
$480$	−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	0.350546	+	0.936546i	$0.385996\pi$
$487$	−14.0309	+	24.3022i	−0.635800	+	1.10124i	−0.986345	+	0.164691i	$0.947337\pi$
$488$	−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	0.937282	+	0.348572i	$0.113333\pi$
$491$	17.0734	+	29.5721i	0.770513	+	1.33457i	−0.166769	+	0.985996i	$0.553333\pi$
$492$	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	−0.839372	−	0.543558i	$-0.817077\pi$
$499$	1.14035	−	1.97515i	0.0510493	−	0.0884199i	0.890421	+	0.455138i	$0.150410\pi$
$500$	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	0.429038	+	0.903287i	$0.358853\pi$
$509$	−12.8090	+	22.1859i	−0.567750	+	0.983373i	−0.996788	+	0.0800859i	$0.974481\pi$
$510$	−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	−0.111073	+	0.993812i	$0.535429\pi$
$521$	−20.9127	+	36.2219i	−0.916203	+	1.58691i	−0.805130	+	0.593099i	$0.797904\pi$
$522$	−6.03892	−	4.50065i	−0.264316	−	0.196988i
$523$	7.88323	+	13.6542i	0.344710	+	0.597055i	0.985301	−	0.170827i	$-0.0546440\pi$
$523$	7.88323	+	13.6542i	0.344710	+	0.597055i	−0.640591	+	0.767882i	$0.721311\pi$
$524$	−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	−0.818207	−	0.574924i	$-0.805031\pi$
$541$	−21.0963	−	36.5399i	−0.907002	−	1.57097i	−0.0887957	−	0.996050i	$-0.528302\pi$
$542$	−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	0.00696400	−	0.999976i	$-0.497783\pi$
$547$	20.3356	−	35.2222i	0.869486	−	1.50599i	0.862522	−	0.506019i	$-0.168883\pi$
$548$	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	−0.688837	−	0.724916i	$-0.741879\pi$
$557$	6.68794	−	11.5838i	0.283377	−	0.490823i	0.972214	+	0.234093i	$0.0752119\pi$
$558$	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	−0.835019	−	0.550221i	$-0.814543\pi$
$577$	1.41714	−	2.45455i	0.0589962	−	0.102184i	0.894015	+	0.448037i	$0.147877\pi$
$578$	−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	−0.910404	−	0.413720i	$-0.864229\pi$
$587$	−2.34795	+	4.06678i	−0.0969105	+	0.167854i	0.813494	+	0.581573i	$0.197563\pi$
$588$	−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	0.878789	−	0.477210i	$-0.158352\pi$
$593$	0.636024	+	1.10163i	0.0261184	+	0.0452383i	−0.852671	+	0.522449i	$0.825019\pi$
$594$	−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	−0.969874	−	0.243609i	$-0.921669\pi$
$601$	−6.71634	+	11.6330i	−0.273965	+	0.474522i	0.695908	+	0.718131i	$0.255002\pi$
$602$	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	−0.815747	−	0.578408i	$-0.803674\pi$
$607$	2.29232	−	3.97042i	0.0930425	−	0.161154i	0.908790	+	0.417254i	$0.137007\pi$
$608$	−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	−0.998152	−	0.0607587i	$-0.980648\pi$
$613$	−11.0538	+	19.1457i	−0.446458	+	0.773287i	0.551695	+	0.834046i	$0.313981\pi$
$614$	−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	0.961206	−	0.275832i	$-0.0889534\pi$
$617$	6.00433	+	10.3998i	0.241725	+	0.418680i	−0.719481	+	0.694513i	$0.755620\pi$
$618$	−0.582863	−	2.82648i	−0.0234462	−	0.113698i
$619$	8.78180	+	15.2105i	0.352970	+	0.611363i	0.986768	−	0.162136i	$-0.0518383\pi$
$619$	8.78180	+	15.2105i	0.352970	+	0.611363i	−0.633798	+	0.773499i	$0.718505\pi$
$620$	−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	0.996319	+	0.0857228i	$0.0273199\pi$
$641$	14.4920	+	25.1008i	0.572398	+	0.991422i	−0.423921	+	0.905699i	$0.639347\pi$
$642$	17.6978	+	5.86946i	0.698475	+	0.231649i
$643$	6.03087	+	10.4458i	0.237834	+	0.411941i	0.960093	−	0.279682i	$-0.0902291\pi$
$643$	6.03087	+	10.4458i	0.237834	+	0.411941i	−0.722258	+	0.691623i	$0.756896\pi$
$644$	−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	−0.209073	−	0.977900i	$-0.567045\pi$
$647$	18.8825	−	32.7055i	0.742349	−	1.28579i	0.951423	−	0.307887i	$-0.0996219\pi$
$648$	−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	0.224109	+	0.974564i	$0.428053\pi$
$653$	−18.7040	+	32.3962i	−0.731942	+	1.26776i	−0.956052	+	0.293198i	$0.905281\pi$
$654$	−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	−0.413455	−	0.910524i	$-0.635678\pi$
$659$	14.9356	−	25.8693i	0.581810	−	1.00772i	0.995265	−	0.0971993i	$-0.0309884\pi$
$660$	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	−0.942575	−	0.333994i	$-0.891603\pi$
$673$	−4.72253	+	8.17966i	−0.182040	+	0.315303i	0.760535	+	0.649297i	$0.224937\pi$
$674$	−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	−0.938108	−	0.346343i	$-0.887423\pi$
$683$	−4.41961	+	7.65499i	−0.169112	+	0.292910i	0.768996	+	0.639253i	$0.220757\pi$
$684$	−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	0.956639	−	0.291275i	$-0.0940796\pi$
$719$	6.06182	+	10.4994i	0.226068	+	0.391561i	−0.730571	+	0.682836i	$0.760746\pi$
$720$	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	−0.0189562	−	0.999820i	$-0.506034\pi$
$727$	23.0908	−	39.9945i	0.856392	−	1.48331i	0.875348	−	0.483494i	$-0.160632\pi$
$728$	−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	−0.313785	−	0.949494i	$-0.601597\pi$
$733$	18.0149	−	31.2026i	0.665394	−	1.15250i	0.979178	−	0.203002i	$-0.0650696\pi$
$734$	−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	−0.0238296	−	0.999716i	$-0.507586\pi$
$739$	23.2119	−	40.2042i	0.853865	−	1.47894i	0.877694	−	0.479221i	$-0.159081\pi$
$740$	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	0.876802	−	0.480852i	$-0.159673\pi$
$743$	0.598884	+	1.03730i	0.0219709	+	0.0380548i	−0.854831	+	0.518907i	$0.826339\pi$
$744$	−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	−0.0243853	+	0.999703i	$0.507763\pi$
$751$	−24.0600	+	41.6731i	−0.877961	+	1.52067i	−0.853575	+	0.520970i	$0.825570\pi$
$752$	−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	−0.294438	−	0.955671i	$-0.595132\pi$
$761$	18.7701	−	32.5108i	0.680416	−	1.17852i	0.974854	−	0.222845i	$-0.0715342\pi$
$762$	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
$769$

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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