LMFDB - Embedded newform 126.2.e.d.25.3

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			25.3
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	126.25
Dual form			126.2.e.d.121.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.09097 - 1.34528i) q^{3} +1.00000 q^{4} +(-0.880438 + 1.52496i) q^{5} +(1.09097 - 1.34528i) q^{6} +(-0.710533 + 2.54856i) q^{7} +1.00000 q^{8} +(-0.619562 - 2.93533i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.09097 - 1.34528i) q^{3} +1.00000 q^{4} +(-0.880438 + 1.52496i) q^{5} +(1.09097 - 1.34528i) q^{6} +(-0.710533 + 2.54856i) q^{7} +1.00000 q^{8} +(-0.619562 - 2.93533i) q^{9} +(-0.880438 + 1.52496i) q^{10} +(-3.06238 - 5.30420i) q^{11} +(1.09097 - 1.34528i) q^{12} +(-0.380438 - 0.658939i) q^{13} +(-0.710533 + 2.54856i) q^{14} +(1.09097 + 2.84813i) q^{15} +1.00000 q^{16} +(-3.42107 + 5.92546i) q^{17} +(-0.619562 - 2.93533i) q^{18} +(0.971410 + 1.68253i) q^{19} +(-0.880438 + 1.52496i) q^{20} +(2.65335 + 3.73627i) q^{21} +(-3.06238 - 5.30420i) q^{22} +(0.210533 - 0.364654i) q^{23} +(1.09097 - 1.34528i) q^{24} +(0.949657 + 1.64485i) q^{25} +(-0.380438 - 0.658939i) q^{26} +(-4.62476 - 2.36887i) q^{27} +(-0.710533 + 2.54856i) q^{28} +(0.732287 - 1.26836i) q^{29} +(1.09097 + 2.84813i) q^{30} +7.70370 q^{31} +1.00000 q^{32} +(-10.4766 - 1.66697i) q^{33} +(-3.42107 + 5.92546i) q^{34} +(-3.26088 - 3.32738i) q^{35} +(-0.619562 - 2.93533i) q^{36} +(1.44282 + 2.49904i) q^{37} +(0.971410 + 1.68253i) q^{38} +(-1.30150 - 0.207087i) q^{39} +(-0.880438 + 1.52496i) q^{40} +(-3.47141 - 6.01266i) q^{41} +(2.65335 + 3.73627i) q^{42} +(4.33009 - 7.49994i) q^{43} +(-3.06238 - 5.30420i) q^{44} +(5.02175 + 1.63957i) q^{45} +(0.210533 - 0.364654i) q^{46} +1.66019 q^{47} +(1.09097 - 1.34528i) q^{48} +(-5.99028 - 3.62167i) q^{49} +(0.949657 + 1.64485i) q^{50} +(4.23912 + 11.0668i) q^{51} +(-0.380438 - 0.658939i) q^{52} +(-0.112725 + 0.195246i) q^{53} +(-4.62476 - 2.36887i) q^{54} +10.7850 q^{55} +(-0.710533 + 2.54856i) q^{56} +(3.32326 + 0.528775i) q^{57} +(0.732287 - 1.26836i) q^{58} +1.98633 q^{59} +(1.09097 + 2.84813i) q^{60} -10.3502 q^{61} +7.70370 q^{62} +(7.92107 + 0.506659i) q^{63} +1.00000 q^{64} +1.33981 q^{65} +(-10.4766 - 1.66697i) q^{66} +6.78495 q^{67} +(-3.42107 + 5.92546i) q^{68} +(-0.260877 - 0.681054i) q^{69} +(-3.26088 - 3.32738i) q^{70} +10.7850 q^{71} +(-0.619562 - 2.93533i) q^{72} +(0.153353 - 0.265616i) q^{73} +(1.44282 + 2.49904i) q^{74} +(3.24884 + 0.516934i) q^{75} +(0.971410 + 1.68253i) q^{76} +(15.6940 - 4.03584i) q^{77} +(-1.30150 - 0.207087i) q^{78} -13.4451 q^{79} +(-0.880438 + 1.52496i) q^{80} +(-8.23229 + 3.63723i) q^{81} +(-3.47141 - 6.01266i) q^{82} +(-1.56238 + 2.70612i) q^{83} +(2.65335 + 3.73627i) q^{84} +(-6.02408 - 10.4340i) q^{85} +(4.33009 - 7.49994i) q^{86} +(-0.907394 - 2.36887i) q^{87} +(-3.06238 - 5.30420i) q^{88} +(1.30150 + 2.25427i) q^{89} +(5.02175 + 1.63957i) q^{90} +(1.94966 - 0.501371i) q^{91} +(0.210533 - 0.364654i) q^{92} +(8.40451 - 10.3636i) q^{93} +1.66019 q^{94} -3.42107 q^{95} +(1.09097 - 1.34528i) q^{96} +(-1.81806 + 3.14897i) q^{97} +(-5.99028 - 3.62167i) q^{98} +(-13.6722 + 12.2754i) 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
$3$	1.09097	−	1.34528i	0.629873	−	0.776698i
$3$	1.09097	−	1.34528i	0.629873	−	0.776698i
$4$	1.00000			0.500000
$5$	−0.880438	+	1.52496i	−0.393744	+	0.681985i	−0.992940	−	0.118618i	$-0.962154\pi$
$5$	−0.880438	+	1.52496i	−0.393744	+	0.681985i	0.599196	+	0.800602i	$0.295487\pi$
$6$	1.09097	−	1.34528i	0.445387	−	0.549209i
$7$	−0.710533	+	2.54856i	−0.268556	+	0.963264i
$7$	−0.710533	+	2.54856i	−0.268556	+	0.963264i
$8$	1.00000			0.353553
$9$	−0.619562	−	2.93533i	−0.206521	−	0.978442i
$10$	−0.880438	+	1.52496i	−0.278419	+	0.482236i
$11$	−3.06238	−	5.30420i	−0.923343	−	1.59928i	−0.794205	−	0.607650i	$-0.792112\pi$
$11$	−3.06238	−	5.30420i	−0.923343	−	1.59928i	−0.129138	−	0.991627i	$-0.541221\pi$
$12$	1.09097	−	1.34528i	0.314936	−	0.388349i
$13$	−0.380438	−	0.658939i	−0.105515	−	0.182757i	0.808434	−	0.588587i	$-0.200316\pi$
$13$	−0.380438	−	0.658939i	−0.105515	−	0.182757i	−0.913948	+	0.405831i	$0.866982\pi$
$14$	−0.710533	+	2.54856i	−0.189898	+	0.681130i
$15$	1.09097	+	2.84813i	0.281688	+	0.735384i
$16$	1.00000			0.250000
$17$	−3.42107	+	5.92546i	−0.829731	+	1.43714i	0.0685191	+	0.997650i	$0.478173\pi$
$17$	−3.42107	+	5.92546i	−0.829731	+	1.43714i	−0.898250	+	0.439486i	$0.855161\pi$
$18$	−0.619562	−	2.93533i	−0.146032	−	0.691863i
$19$	0.971410	+	1.68253i	0.222857	+	0.385999i	0.955674	−	0.294426i	$-0.0951285\pi$
$19$	0.971410	+	1.68253i	0.222857	+	0.385999i	−0.732818	+	0.680425i	$0.761795\pi$
$20$	−0.880438	+	1.52496i	−0.196872	+	0.340992i
$21$	2.65335	+	3.73627i	0.579009	+	0.815321i
$22$	−3.06238	−	5.30420i	−0.652902	−	1.13086i
$23$	0.210533	−	0.364654i	0.0438992	−	0.0760357i	−0.843241	−	0.537536i	$-0.819355\pi$
$23$	0.210533	−	0.364654i	0.0438992	−	0.0760357i	0.887140	+	0.461500i	$0.152689\pi$
$24$	1.09097	−	1.34528i	0.222694	−	0.274604i
$25$	0.949657	+	1.64485i	0.189931	+	0.328971i
$26$	−0.380438	−	0.658939i	−0.0746101	−	0.129228i
$27$	−4.62476	−	2.36887i	−0.890036	−	0.455890i
$28$	−0.710533	+	2.54856i	−0.134278	+	0.481632i
$29$	0.732287	−	1.26836i	0.135982	−	0.235528i	−0.789990	−	0.613120i	$-0.789914\pi$
$29$	0.732287	−	1.26836i	0.135982	−	0.235528i	0.925972	+	0.377592i	$0.123248\pi$
$30$	1.09097	+	2.84813i	0.199183	+	0.519995i
$31$	7.70370			1.38362			0.691812	−	0.722077i	$-0.256813\pi$
$31$	7.70370			1.38362			0.691812	+	0.722077i	$0.256813\pi$
$32$	1.00000			0.176777
$33$	−10.4766	−	1.66697i	−1.82374	−	0.290182i
$34$	−3.42107	+	5.92546i	−0.586708	+	1.01621i
$35$	−3.26088	−	3.32738i	−0.551189	−	0.562431i
$36$	−0.619562	−	2.93533i	−0.103260	−	0.489221i
$37$	1.44282	+	2.49904i	0.237198	+	0.410839i	0.959909	−	0.280311i	$-0.0904376\pi$
$37$	1.44282	+	2.49904i	0.237198	+	0.410839i	−0.722711	+	0.691150i	$0.757104\pi$
$38$	0.971410	+	1.68253i	0.157584	+	0.272943i
$39$	−1.30150	−	0.207087i	−0.208408	−	0.0331604i
$40$	−0.880438	+	1.52496i	−0.139210	+	0.241118i
$41$	−3.47141	−	6.01266i	−0.542143	−	0.939020i	−0.998781	−	0.0493667i	$-0.984280\pi$
$41$	−3.47141	−	6.01266i	−0.542143	−	0.939020i	0.456638	−	0.889653i	$-0.349054\pi$
$42$	2.65335	+	3.73627i	0.409421	+	0.576519i
$43$	4.33009	−	7.49994i	0.660333	−	1.14373i	−0.320195	−	0.947352i	$-0.603748\pi$
$43$	4.33009	−	7.49994i	0.660333	−	1.14373i	0.980528	−	0.196379i	$-0.0629183\pi$
$44$	−3.06238	−	5.30420i	−0.461671	−	0.799638i
$45$	5.02175	+	1.63957i	0.748599	+	0.244412i
$46$	0.210533	−	0.364654i	0.0310414	−	0.0537654i
$47$	1.66019			0.242164			0.121082	−	0.992643i	$-0.461364\pi$
$47$	1.66019			0.242164			0.121082	+	0.992643i	$0.461364\pi$
$48$	1.09097	−	1.34528i	0.157468	−	0.194175i
$49$	−5.99028	−	3.62167i	−0.855755	−	0.517381i
$50$	0.949657	+	1.64485i	0.134302	+	0.232617i
$51$	4.23912	+	11.0668i	0.593596	+	1.54966i
$52$	−0.380438	−	0.658939i	−0.0527573	−	0.0913783i
$53$	−0.112725	+	0.195246i	−0.0154840	+	0.0268190i	−0.873664	−	0.486531i	$-0.838262\pi$
$53$	−0.112725	+	0.195246i	−0.0154840	+	0.0268190i	0.858180	+	0.513350i	$0.171596\pi$
$54$	−4.62476	−	2.36887i	−0.629351	−	0.322363i
$55$	10.7850			1.45424
$56$	−0.710533	+	2.54856i	−0.0949490	+	0.340565i
$57$	3.32326	+	0.528775i	0.440176	+	0.0700379i
$58$	0.732287	−	1.26836i	0.0961540	−	0.166544i
$59$	1.98633			0.258598			0.129299	−	0.991606i	$-0.458727\pi$
$59$	1.98633			0.258598			0.129299	+	0.991606i	$0.458727\pi$
$60$	1.09097	+	2.84813i	0.140844	+	0.367692i
$61$	−10.3502			−1.32521			−0.662605	−	0.748969i	$-0.730549\pi$
$61$	−10.3502			−1.32521			−0.662605	+	0.748969i	$0.730549\pi$
$62$	7.70370			0.978370
$63$	7.92107	+	0.506659i	0.997961	+	0.0638331i
$64$	1.00000			0.125000
$65$	1.33981			0.166183
$66$	−10.4766	−	1.66697i	−1.28958	−	0.205190i
$67$	6.78495			0.828914			0.414457	−	0.910069i	$-0.363972\pi$
$67$	6.78495			0.828914			0.414457	+	0.910069i	$0.363972\pi$
$68$	−3.42107	+	5.92546i	−0.414865	+	0.718568i
$69$	−0.260877	−	0.681054i	−0.0314059	−	0.0819893i
$70$	−3.26088	−	3.32738i	−0.389749	−	0.397699i
$71$	10.7850			1.27994			0.639969	−	0.768401i	$-0.278947\pi$
$71$	10.7850			1.27994			0.639969	+	0.768401i	$0.278947\pi$
$72$	−0.619562	−	2.93533i	−0.0730160	−	0.345932i
$73$	0.153353	−	0.265616i	0.0179487	−	0.0310880i	−0.856912	−	0.515463i	$-0.827620\pi$
$73$	0.153353	−	0.265616i	0.0179487	−	0.0310880i	0.874860	+	0.484375i	$0.160953\pi$
$74$	1.44282	+	2.49904i	0.167724	+	0.290507i
$75$	3.24884	+	0.516934i	0.375144	+	0.0596904i
$76$	0.971410	+	1.68253i	0.111428	+	0.193000i
$77$	15.6940	−	4.03584i	1.78850	−	0.459927i
$78$	−1.30150	−	0.207087i	−0.147366	−	0.0234480i
$79$	−13.4451			−1.51270			−0.756348	−	0.654169i	$-0.773018\pi$
$79$	−13.4451			−1.51270			−0.756348	+	0.654169i	$0.773018\pi$
$80$	−0.880438	+	1.52496i	−0.0984360	+	0.170496i
$81$	−8.23229	+	3.63723i	−0.914699	+	0.404137i
$82$	−3.47141	−	6.01266i	−0.383353	−	0.663987i
$83$	−1.56238	+	2.70612i	−0.171494	+	0.297036i	−0.938942	−	0.344075i	$-0.888193\pi$
$83$	−1.56238	+	2.70612i	−0.171494	+	0.297036i	0.767449	+	0.641110i	$0.221526\pi$
$84$	2.65335	+	3.73627i	0.289505	+	0.407661i
$85$	−6.02408	−	10.4340i	−0.653403	−	1.13173i
$86$	4.33009	−	7.49994i	0.466926	−	0.808740i
$87$	−0.907394	−	2.36887i	−0.0972828	−	0.253970i
$88$	−3.06238	−	5.30420i	−0.326451	−	0.565430i
$89$	1.30150	+	2.25427i	0.137959	+	0.238952i	0.926724	−	0.375743i	$-0.122612\pi$
$89$	1.30150	+	2.25427i	0.137959	+	0.238952i	−0.788765	+	0.614695i	$0.789279\pi$
$90$	5.02175	+	1.63957i	0.529339	+	0.172825i
$91$	1.94966	−	0.501371i	0.204380	−	0.0525580i
$92$	0.210533	−	0.364654i	0.0219496	−	0.0380178i
$93$	8.40451	−	10.3636i	0.871508	−	1.07466i
$94$	1.66019			0.171236
$95$	−3.42107			−0.350994
$96$	1.09097	−	1.34528i	0.111347	−	0.137302i
$97$	−1.81806	+	3.14897i	−0.184596	+	0.319729i	−0.943440	−	0.331543i	$-0.892431\pi$
$97$	−1.81806	+	3.14897i	−0.184596	+	0.319729i	0.758845	+	0.651272i	$0.225764\pi$
$98$	−5.99028	−	3.62167i	−0.605110	−	0.365844i
$99$	−13.6722	+	12.2754i	−1.37411	+	1.23372i
$100$	0.949657	+	1.64485i	0.0949657	+	0.164485i
$101$	4.00520	+	6.93721i	0.398532	+	0.690278i	0.993545	−	0.113438i	$-0.0361863\pi$
$101$	4.00520	+	6.93721i	0.398532	+	0.690278i	−0.595013	+	0.803716i	$0.702853\pi$
$102$	4.23912	+	11.0668i	0.419736	+	1.09578i
$103$	3.41423	−	5.91362i	0.336414	−	0.582686i	−0.647341	−	0.762200i	$-0.724119\pi$
$103$	3.41423	−	5.91362i	0.336414	−	0.582686i	0.983755	+	0.179514i	$0.0574525\pi$
$104$	−0.380438	−	0.658939i	−0.0373051	−	0.0646142i
$105$	−8.03379	+	0.756713i	−0.784018	+	0.0738476i
$106$	−0.112725	+	0.195246i	−0.0109488	+	0.0189639i
$107$	1.77292	+	3.07078i	0.171394	+	0.296863i	0.938908	−	0.344170i	$-0.111840\pi$
$107$	1.77292	+	3.07078i	0.171394	+	0.296863i	−0.767513	+	0.641033i	$0.778506\pi$
$108$	−4.62476	−	2.36887i	−0.445018	−	0.227945i
$109$	0.351848	−	0.609419i	0.0337010	−	0.0583718i	−0.848683	−	0.528902i	$-0.822604\pi$
$109$	0.351848	−	0.609419i	0.0337010	−	0.0583718i	0.882384	+	0.470530i	$0.155937\pi$
$110$	10.7850			1.02830
$111$	4.93598	+	0.785381i	0.468503	+	0.0745451i
$112$	−0.710533	+	2.54856i	−0.0671391	+	0.240816i
$113$	4.25116	+	7.36323i	0.399916	+	0.692674i	0.993715	−	0.111939i	$-0.0357061\pi$
$113$	4.25116	+	7.36323i	0.399916	+	0.692674i	−0.593799	+	0.804613i	$0.702373\pi$
$114$	3.32326	+	0.528775i	0.311252	+	0.0495243i
$115$	0.370723	+	0.642111i	0.0345701	+	0.0598772i
$116$	0.732287	−	1.26836i	0.0679911	−	0.117764i
$117$	−1.69850	+	1.52496i	−0.157026	+	0.140983i
$118$	1.98633			0.182856
$119$	−12.6706	−	12.9290i	−1.16151	−	1.18520i
$120$	1.09097	+	2.84813i	0.0995916	+	0.259997i
$121$	−13.2564	+	22.9607i	−1.20512	+	2.08734i
$122$	−10.3502			−0.937064
$123$	−11.8759	−	1.88962i	−1.07082	−	0.170381i
$124$	7.70370			0.691812
$125$	−12.1488			−1.08663
$126$	7.92107	+	0.506659i	0.705665	+	0.0451368i
$127$	−18.9532			−1.68183			−0.840913	−	0.541170i	$-0.817982\pi$
$127$	−18.9532			−1.68183			−0.840913	+	0.541170i	$0.817982\pi$
$128$	1.00000			0.0883883
$129$	−5.36552	−	14.0074i	−0.472408	−	1.23328i
$130$	1.33981			0.117509
$131$	3.64652	−	6.31595i	0.318598	−	0.551827i	−0.661598	−	0.749859i	$-0.730121\pi$
$131$	3.64652	−	6.31595i	0.318598	−	0.551827i	0.980196	+	0.198031i	$0.0634548\pi$
$132$	−10.4766	−	1.66697i	−0.911872	−	0.145091i
$133$	−4.97825	+	1.28020i	−0.431669	+	0.111007i
$134$	6.78495			0.586131
$135$	7.68427	−	4.96695i	0.661356	−	0.427487i
$136$	−3.42107	+	5.92546i	−0.293354	+	0.508104i
$137$	4.09097	+	7.08577i	0.349515	+	0.605378i	0.986163	−	0.165776i	$-0.0530129\pi$
$137$	4.09097	+	7.08577i	0.349515	+	0.605378i	−0.636648	+	0.771154i	$0.719680\pi$
$138$	−0.260877	−	0.681054i	−0.0222073	−	0.0579752i
$139$	−6.23229	−	10.7946i	−0.528616	−	0.915589i	−0.999443	−	0.0333640i	$-0.989378\pi$
$139$	−6.23229	−	10.7946i	−0.528616	−	0.915589i	0.470828	−	0.882225i	$-0.343955\pi$
$140$	−3.26088	−	3.32738i	−0.275594	−	0.281215i
$141$	1.81122	−	2.23342i	0.152532	−	0.188088i
$142$	10.7850			0.905053
$143$	−2.33009	+	4.03584i	−0.194852	+	0.337494i
$144$	−0.619562	−	2.93533i	−0.0516301	−	0.244611i
$145$	1.28947	+	2.23342i	0.107084	+	0.185476i
$146$	0.153353	−	0.265616i	0.0126916	−	0.0219825i
$147$	−11.4074	+	4.10748i	−0.940866	+	0.338779i
$148$	1.44282	+	2.49904i	0.118599	+	0.205420i
$149$	−4.41423	+	7.64567i	−0.361628	+	0.626358i	−0.988229	−	0.152982i	$-0.951112\pi$
$149$	−4.41423	+	7.64567i	−0.361628	+	0.626358i	0.626601	+	0.779340i	$0.284446\pi$
$150$	3.24884	+	0.516934i	0.265267	+	0.0422075i
$151$	7.49316	+	12.9785i	0.609785	+	1.05618i	0.991276	+	0.131806i	$0.0420775\pi$
$151$	7.49316	+	12.9785i	0.609785	+	1.05618i	−0.381491	+	0.924373i	$0.624589\pi$
$152$	0.971410	+	1.68253i	0.0787918	+	0.136471i
$153$	19.5127	+	6.37076i	1.57751	+	0.515045i
$154$	15.6940	−	4.03584i	1.26466	−	0.325217i
$155$	−6.78263	+	11.7479i	−0.544794	+	0.943611i
$156$	−1.30150	−	0.207087i	−0.104204	−	0.0165802i
$157$	18.9806			1.51481			0.757407	−	0.652943i	$-0.226466\pi$
$157$	18.9806			1.51481			0.757407	+	0.652943i	$0.226466\pi$
$158$	−13.4451			−1.06964
$159$	0.139680	+	0.364654i	0.0110774	+	0.0289190i
$160$	−0.880438	+	1.52496i	−0.0696048	+	0.120559i
$161$	0.779752	+	0.795655i	0.0614530	+	0.0627064i
$162$	−8.23229	+	3.63723i	−0.646790	+	0.285768i
$163$	−7.51887	−	13.0231i	−0.588924	−	1.02005i	−0.994374	−	0.105929i	$-0.966219\pi$
$163$	−7.51887	−	13.0231i	−0.588924	−	1.02005i	0.405450	−	0.914117i	$-0.367115\pi$
$164$	−3.47141	−	6.01266i	−0.271072	−	0.469510i
$165$	11.7661	−	14.5088i	0.915988	−	1.12951i
$166$	−1.56238	+	2.70612i	−0.121264	+	0.210036i
$167$	0.572097	+	0.990901i	0.0442702	+	0.0766782i	0.887311	−	0.461171i	$-0.152570\pi$
$167$	0.572097	+	0.990901i	0.0442702	+	0.0766782i	−0.843041	+	0.537849i	$0.819237\pi$
$168$	2.65335	+	3.73627i	0.204711	+	0.288260i
$169$	6.21053	−	10.7570i	0.477733	−	0.827458i
$170$	−6.02408	−	10.4340i	−0.462026	−	0.800252i
$171$	4.33693	−	3.89384i	0.331653	−	0.297769i
$172$	4.33009	−	7.49994i	0.330167	−	0.571865i
$173$	0.497677			0.0378377			0.0189188	−	0.999821i	$-0.493978\pi$
$173$	0.497677			0.0378377			0.0189188	+	0.999821i	$0.493978\pi$
$174$	−0.907394	−	2.36887i	−0.0687893	−	0.179584i
$175$	−4.86677	+	1.25153i	−0.367893	+	0.0946068i
$176$	−3.06238	−	5.30420i	−0.230836	−	0.399819i
$177$	2.16703	−	2.67217i	0.162884	−	0.200852i
$178$	1.30150	+	2.25427i	0.0975519	+	0.168965i
$179$	4.41423	−	7.64567i	0.329935	−	0.571464i	−0.652564	−	0.757734i	$-0.726306\pi$
$179$	4.41423	−	7.64567i	0.329935	−	0.571464i	0.982499	+	0.186270i	$0.0596398\pi$
$180$	5.02175	+	1.63957i	0.374299	+	0.122206i
$181$	1.32941			0.0988140			0.0494070	−	0.998779i	$-0.484267\pi$
$181$	1.32941			0.0988140			0.0494070	+	0.998779i	$0.484267\pi$
$182$	1.94966	−	0.501371i	0.144518	−	0.0371641i
$183$	−11.2918	+	13.9239i	−0.834713	+	1.02929i
$184$	0.210533	−	0.364654i	0.0155207	−	0.0268827i
$185$	−5.08126			−0.373581
$186$	8.40451	−	10.3636i	0.616249	−	0.759899i
$187$	41.9064			3.06450
$188$	1.66019			0.121082
$189$	9.32326	−	10.1033i	0.678167	−	0.734908i
$190$	−3.42107			−0.248190
$191$	−16.1683			−1.16989			−0.584947	−	0.811071i	$-0.698885\pi$
$191$	−16.1683			−1.16989			−0.584947	+	0.811071i	$0.698885\pi$
$192$	1.09097	−	1.34528i	0.0787341	−	0.0970873i
$193$	−14.1683			−1.01985			−0.509927	−	0.860218i	$-0.670328\pi$
$193$	−14.1683			−1.01985			−0.509927	+	0.860218i	$0.670328\pi$
$194$	−1.81806	+	3.14897i	−0.130529	+	0.226083i
$195$	1.46169	−	1.80242i	0.104674	−	0.129074i
$196$	−5.99028	−	3.62167i	−0.427877	−	0.258691i
$197$	15.8421			1.12871			0.564353	−	0.825534i	$-0.309126\pi$
$197$	15.8421			1.12871			0.564353	+	0.825534i	$0.309126\pi$
$198$	−13.6722	+	12.2754i	−0.971643	+	0.872373i
$199$	−4.47141	+	7.74471i	−0.316970	+	0.549008i	−0.979854	−	0.199714i	$-0.935999\pi$
$199$	−4.47141	+	7.74471i	−0.316970	+	0.549008i	0.662884	+	0.748722i	$0.269332\pi$
$200$	0.949657	+	1.64485i	0.0671509	+	0.116309i
$201$	7.40219	−	9.12767i	0.522110	−	0.643816i
$202$	4.00520	+	6.93721i	0.281805	+	0.488101i
$203$	2.71217	+	2.76748i	0.190357	+	0.194239i
$204$	4.23912	+	11.0668i	0.296798	+	0.774831i
$205$	12.2255			0.853862
$206$	3.41423	−	5.91362i	0.237881	−	0.412021i
$207$	−1.20082	−	0.392058i	−0.0834626	−	0.0272499i
$208$	−0.380438	−	0.658939i	−0.0263787	−	0.0456892i
$209$	5.94966	−	10.3051i	0.411546	−	0.712819i
$210$	−8.03379	+	0.756713i	−0.554384	+	0.0522181i
$211$	11.3856	+	19.7205i	0.783820	+	1.35762i	0.929702	+	0.368314i	$0.120065\pi$
$211$	11.3856	+	19.7205i	0.783820	+	1.35762i	−0.145882	+	0.989302i	$0.546602\pi$
$212$	−0.112725	+	0.195246i	−0.00774199	+	0.0134095i
$213$	11.7661	−	14.5088i	0.806198	−	0.994126i
$214$	1.77292	+	3.07078i	0.121194	+	0.209914i
$215$	7.62476	+	13.2065i	0.520005	+	0.900674i
$216$	−4.62476	−	2.36887i	−0.314675	−	0.161181i
$217$	−5.47373	+	19.6333i	−0.371581	+	1.33280i
$218$	0.351848	−	0.609419i	0.0238302	−	0.0412751i
$219$	−0.190024	−	0.496083i	−0.0128406	−	0.0335222i
$220$	10.7850			0.727121
$221$	5.20602			0.350195
$222$	4.93598	+	0.785381i	0.331282	+	0.0527113i
$223$	−6.44282	+	11.1593i	−0.431443	+	0.747281i	−0.996998	−	0.0774293i	$-0.975329\pi$
$223$	−6.44282	+	11.1593i	−0.431443	+	0.747281i	0.565555	+	0.824711i	$0.308662\pi$
$224$	−0.710533	+	2.54856i	−0.0474745	+	0.170283i
$225$	4.23981	−	3.80664i	0.282654	−	0.253776i
$226$	4.25116	+	7.36323i	0.282783	+	0.489795i
$227$	−10.9984	−	19.0497i	−0.729987	−	1.26437i	−0.956888	−	0.290457i	$-0.906193\pi$
$227$	−10.9984	−	19.0497i	−0.729987	−	1.26437i	0.226901	−	0.973918i	$-0.427141\pi$
$228$	3.32326	+	0.528775i	0.220088	+	0.0350190i
$229$	1.89931	−	3.28971i	0.125510	−	0.217390i	−0.796422	−	0.604741i	$-0.793277\pi$
$229$	1.89931	−	3.28971i	0.125510	−	0.217390i	0.921932	+	0.387351i	$0.126610\pi$
$230$	0.370723	+	0.642111i	0.0244448	+	0.0423396i
$231$	11.6923	−	25.5158i	0.769300	−	1.67882i
$232$	0.732287	−	1.26836i	0.0480770	−	0.0832718i
$233$	−3.33530	−	5.77690i	−0.218503	−	0.378458i	0.735848	−	0.677147i	$-0.236784\pi$
$233$	−3.33530	−	5.77690i	−0.218503	−	0.378458i	−0.954350	+	0.298689i	$0.903451\pi$
$234$	−1.69850	+	1.52496i	−0.111034	+	0.0996900i
$235$	−1.46169	+	2.53173i	−0.0953505	+	0.165152i
$236$	1.98633			0.129299
$237$	−14.6683	+	18.0875i	−0.952807	+	1.17491i
$238$	−12.6706	−	12.9290i	−0.821313	−	0.838064i
$239$	−7.82038	−	13.5453i	−0.505858	−	0.876172i	−0.999977	−	0.00677786i	$-0.997843\pi$
$239$	−7.82038	−	13.5453i	−0.505858	−	0.876172i	0.494119	−	0.869394i	$-0.335491\pi$
$240$	1.09097	+	2.84813i	0.0704219	+	0.183846i
$241$	−10.7060	−	18.5434i	−0.689635	−	1.19448i	−0.971956	−	0.235163i	$-0.924437\pi$
$241$	−10.7060	−	18.5434i	−0.689635	−	1.19448i	0.282320	−	0.959320i	$-0.408896\pi$
$242$	−13.2564	+	22.9607i	−0.852151	+	1.47597i
$243$	−4.08809	+	15.0429i	−0.262251	+	0.965000i
$244$	−10.3502			−0.662605
$245$	10.7970	−	5.94631i	0.689794	−	0.379896i
$246$	−11.8759	−	1.88962i	−0.757181	−	0.120478i
$247$	0.739123	−	1.28020i	0.0470293	−	0.0814571i
$248$	7.70370			0.489185
$249$	1.93598	+	5.05415i	0.122688	+	0.320294i
$250$	−12.1488			−0.768360
$251$	−23.6030			−1.48981			−0.744904	−	0.667171i	$-0.767505\pi$
$251$	−23.6030			−1.48981			−0.744904	+	0.667171i	$0.767505\pi$
$252$	7.92107	+	0.506659i	0.498980	+	0.0319165i
$253$	−2.57893			−0.162136
$254$	−18.9532			−1.18923
$255$	−20.6088	−	3.27913i	−1.29057	−	0.205347i
$256$	1.00000			0.0625000
$257$	−10.1300	+	17.5456i	−0.631890	+	1.09447i	0.355275	+	0.934762i	$0.384387\pi$
$257$	−10.1300	+	17.5456i	−0.631890	+	1.09447i	−0.987165	+	0.159704i	$0.948946\pi$
$258$	−5.36552	−	14.0074i	−0.334043	−	0.872064i
$259$	−7.39411	+	1.90146i	−0.459448	+	0.118151i
$260$	1.33981			0.0830915
$261$	−4.17674	−	1.36368i	−0.258534	−	0.0844094i
$262$	3.64652	−	6.31595i	0.225283	−	0.390201i
$263$	11.2443	+	19.4757i	0.693355	+	1.20093i	0.970732	+	0.240165i	$0.0772014\pi$
$263$	11.2443	+	19.4757i	0.693355	+	1.20093i	−0.277377	+	0.960761i	$0.589465\pi$
$264$	−10.4766	−	1.66697i	−0.644791	−	0.102595i
$265$	−0.198495	−	0.343803i	−0.0121935	−	0.0211197i
$266$	−4.97825	+	1.28020i	−0.305236	+	0.0784940i
$267$	4.45254	+	0.708458i	0.272491	+	0.0433569i
$268$	6.78495			0.414457
$269$	−12.6706	+	21.9461i	−0.772540	+	1.33808i	0.163627	+	0.986522i	$0.447681\pi$
$269$	−12.6706	+	21.9461i	−0.772540	+	1.33808i	−0.936167	+	0.351556i	$0.885653\pi$
$270$	7.68427	−	4.96695i	0.467650	−	0.302279i
$271$	−6.87880	−	11.9144i	−0.417858	−	0.723751i	0.577866	−	0.816132i	$-0.303886\pi$
$271$	−6.87880	−	11.9144i	−0.417858	−	0.723751i	−0.995724	+	0.0923810i	$0.970552\pi$
$272$	−3.42107	+	5.92546i	−0.207433	+	0.359284i
$273$	1.45254	−	3.16982i	0.0879114	−	0.191846i
$274$	4.09097	+	7.08577i	0.247145	+	0.428067i
$275$	5.81642	−	10.0743i	0.350743	−	0.607505i
$276$	−0.260877	−	0.681054i	−0.0157029	−	0.0409946i
$277$	1.64132	+	2.84284i	0.0986171	+	0.170810i	0.911112	−	0.412158i	$-0.135225\pi$
$277$	1.64132	+	2.84284i	0.0986171	+	0.170810i	−0.812495	+	0.582968i	$0.801891\pi$
$278$	−6.23229	−	10.7946i	−0.373788	−	0.647419i
$279$	−4.77292	−	22.6129i	−0.285747	−	1.35380i
$280$	−3.26088	−	3.32738i	−0.194875	−	0.198849i
$281$	0.634479	−	1.09895i	0.0378498	−	0.0655578i	−0.846480	−	0.532421i	$-0.821282\pi$
$281$	0.634479	−	1.09895i	0.0378498	−	0.0655578i	0.884330	+	0.466863i	$0.154616\pi$
$282$	1.81122	−	2.23342i	0.107857	−	0.132998i
$283$	−8.19235			−0.486984			−0.243492	−	0.969903i	$-0.578293\pi$
$283$	−8.19235			−0.486984			−0.243492	+	0.969903i	$0.578293\pi$
$284$	10.7850			0.639969
$285$	−3.73229	+	4.60230i	−0.221082	+	0.272616i
$286$	−2.33009	+	4.03584i	−0.137781	+	0.238644i
$287$	17.7902	−	4.57489i	1.05012	−	0.270047i
$288$	−0.619562	−	2.93533i	−0.0365080	−	0.172966i
$289$	−14.9074	−	25.8204i	−0.876906	−	1.51884i
$290$	1.28947	+	2.23342i	0.0757201	+	0.131151i
$291$	2.25280	+	5.88123i	0.132061	+	0.344764i
$292$	0.153353	−	0.265616i	0.00897433	−	0.0155440i
$293$	7.72545	+	13.3809i	0.451326	+	0.781719i	0.998469	−	0.0553202i	$-0.0176180\pi$
$293$	7.72545	+	13.3809i	0.451326	+	0.781719i	−0.547143	+	0.837039i	$0.684285\pi$
$294$	−11.4074	+	4.10748i	−0.665293	+	0.239553i
$295$	−1.74884	+	3.02908i	−0.101821	+	0.176360i
$296$	1.44282	+	2.49904i	0.0838622	+	0.145254i
$297$	1.59781	+	31.7851i	0.0927142	+	1.84436i
$298$	−4.41423	+	7.64567i	−0.255709	+	0.442902i
$299$	−0.320380			−0.0185280
$300$	3.24884	+	0.516934i	0.187572	+	0.0298452i
$301$	16.0374	+	16.3645i	0.924378	+	0.943231i
$302$	7.49316	+	12.9785i	0.431183	+	0.746831i
$303$	13.7021	+	2.18018i	0.787163	+	0.125248i
$304$	0.971410	+	1.68253i	0.0557142	+	0.0964998i
$305$	9.11273	−	15.7837i	0.521793	−	0.903772i
$306$	19.5127	+	6.37076i	1.11547	+	0.364192i
$307$	4.89931			0.279619			0.139809	−	0.990178i	$-0.455351\pi$
$307$	4.89931			0.279619			0.139809	+	0.990178i	$0.455351\pi$
$308$	15.6940	−	4.03584i	0.894248	−	0.229963i
$309$	−4.23065	−	11.0447i	−0.240673	−	0.628310i
$310$	−6.78263	+	11.7479i	−0.385228	+	0.667234i
$311$	−7.69002			−0.436061			−0.218031	−	0.975942i	$-0.569963\pi$
$311$	−7.69002			−0.436061			−0.218031	+	0.975942i	$0.569963\pi$
$312$	−1.30150	−	0.207087i	−0.0736832	−	0.0117240i
$313$	−1.72313			−0.0973969			−0.0486985	−	0.998814i	$-0.515507\pi$
$313$	−1.72313			−0.0973969			−0.0486985	+	0.998814i	$0.515507\pi$
$314$	18.9806			1.07114
$315$	−7.74665	+	11.6333i	−0.436474	+	0.655460i
$316$	−13.4451			−0.756348
$317$	33.2028			1.86485			0.932426	−	0.361361i	$-0.117688\pi$
$317$	33.2028			1.86485			0.932426	+	0.361361i	$0.117688\pi$
$318$	0.139680	+	0.364654i	0.00783288	+	0.0204488i
$319$	−8.97017			−0.502233
$320$	−0.880438	+	1.52496i	−0.0492180	+	0.0852481i
$321$	6.06526	+	0.965064i	0.338530	+	0.0538646i
$322$	0.779752	+	0.795655i	0.0434539	+	0.0443401i
$323$	−13.2930			−0.739644
$324$	−8.23229	+	3.63723i	−0.457349	+	0.202068i
$325$	0.722572	−	1.25153i	0.0400811	−	0.0694224i
$326$	−7.51887	−	13.0231i	−0.416432	−	0.721281i
$327$	−0.435984	−	1.13819i	−0.0241099	−	0.0629423i
$328$	−3.47141	−	6.01266i	−0.191677	−	0.331994i
$329$	−1.17962	+	4.23109i	−0.0650346	+	0.233267i
$330$	11.7661	−	14.5088i	0.647701	−	0.798683i
$331$	2.88891			0.158789			0.0793944	−	0.996843i	$-0.474701\pi$
$331$	2.88891			0.158789			0.0793944	+	0.996843i	$0.474701\pi$
$332$	−1.56238	+	2.70612i	−0.0857468	+	0.148518i
$333$	6.44158	−	5.78346i	0.352996	−	0.316931i
$334$	0.572097	+	0.990901i	0.0313037	+	0.0542197i
$335$	−5.97373	+	10.3468i	−0.326380	+	0.565307i
$336$	2.65335	+	3.73627i	0.144752	+	0.203830i
$337$	−4.36156	−	7.55445i	−0.237590	−	0.411517i	0.722433	−	0.691441i	$-0.243024\pi$
$337$	−4.36156	−	7.55445i	−0.237590	−	0.411517i	−0.960022	+	0.279924i	$0.909691\pi$
$338$	6.21053	−	10.7570i	0.337808	−	0.585101i
$339$	14.5435	+	2.31407i	0.789895	+	0.125683i
$340$	−6.02408	−	10.4340i	−0.326701	−	0.565863i
$341$	−23.5917	−	40.8620i	−1.27756	−	2.21280i
$342$	4.33693	−	3.89384i	0.234514	−	0.210555i
$343$	13.4863	−	12.6933i	0.728193	−	0.685372i
$344$	4.33009	−	7.49994i	0.233463	−	0.404370i
$345$	1.26827	+	0.201799i	0.0682813	+	0.0108645i
$346$	0.497677			0.0267553
$347$	9.69467			0.520437			0.260219	−	0.965550i	$-0.416205\pi$
$347$	9.69467			0.520437			0.260219	+	0.965550i	$0.416205\pi$
$348$	−0.907394	−	2.36887i	−0.0486414	−	0.126985i
$349$	14.1992	−	24.5937i	0.760065	−	1.31647i	−0.182752	−	0.983159i	$-0.558500\pi$
$349$	14.1992	−	24.5937i	0.760065	−	1.31647i	0.942817	−	0.333312i	$-0.108166\pi$
$350$	−4.86677	+	1.25153i	−0.260140	+	0.0668971i
$351$	0.198495	+	3.94865i	0.0105949	+	0.210763i
$352$	−3.06238	−	5.30420i	−0.163225	−	0.282715i
$353$	2.19686	+	3.80507i	0.116927	+	0.202524i	0.918548	−	0.395308i	$-0.129362\pi$
$353$	2.19686	+	3.80507i	0.116927	+	0.202524i	−0.801621	+	0.597832i	$0.796029\pi$
$354$	2.16703	−	2.67217i	0.115176	−	0.142024i
$355$	−9.49549	+	16.4467i	−0.503968	+	0.872898i
$356$	1.30150	+	2.25427i	0.0689796	+	0.119476i
$357$	−31.2164	+	2.94031i	−1.65215	+	0.155618i
$358$	4.41423	−	7.64567i	0.233299	−	0.404086i
$359$	16.0796	+	27.8507i	0.848650	+	1.46990i	0.882413	+	0.470475i	$0.155917\pi$
$359$	16.0796	+	27.8507i	0.848650	+	1.46990i	−0.0337633	+	0.999430i	$0.510749\pi$
$360$	5.02175	+	1.63957i	0.264670	+	0.0864127i
$361$	7.61273	−	13.1856i	0.400670	−	0.693980i
$362$	1.32941			0.0698721
$363$	16.4263	+	42.8830i	0.862155	+	2.25077i
$364$	1.94966	−	0.501371i	0.102190	−	0.0262790i
$365$	0.270036	+	0.467717i	0.0141343	+	0.0244814i
$366$	−11.2918	+	13.9239i	−0.590231	+	0.727816i
$367$	−17.3015	−	29.9671i	−0.903131	−	1.56427i	−0.823406	−	0.567452i	$-0.807929\pi$
$367$	−17.3015	−	29.9671i	−0.903131	−	1.56427i	−0.0797249	−	0.996817i	$-0.525404\pi$
$368$	0.210533	−	0.364654i	0.0109748	−	0.0190089i
$369$	−15.4984	+	13.9149i	−0.806813	+	0.724383i
$370$	−5.08126			−0.264162
$371$	−0.417500	−	0.426015i	−0.0216755	−	0.0221176i
$372$	8.40451	−	10.3636i	0.435754	−	0.537330i
$373$	−5.48796	+	9.50543i	−0.284156	+	0.492172i	−0.972404	−	0.233303i	$-0.925047\pi$
$373$	−5.48796	+	9.50543i	−0.284156	+	0.492172i	0.688248	+	0.725475i	$0.258380\pi$
$374$	41.9064			2.16693
$375$	−13.2540	+	16.3436i	−0.684436	+	0.843980i
$376$	1.66019			0.0856178
$377$	−1.11436			−0.0573925
$378$	9.32326	−	10.1033i	0.479537	−	0.519658i
$379$	33.9877			1.74583			0.872916	−	0.487871i	$-0.162226\pi$
$379$	33.9877			1.74583			0.872916	+	0.487871i	$0.162226\pi$
$380$	−3.42107			−0.175497
$381$	−20.6774	+	25.4974i	−1.05934	+	1.30627i
$382$	−16.1683			−0.827241
$383$	10.5120	−	18.2074i	0.537140	−	0.930354i	−0.461916	−	0.886923i	$-0.652838\pi$
$383$	10.5120	−	18.2074i	0.537140	−	0.930354i	0.999056	−	0.0434304i	$-0.0138287\pi$
$384$	1.09097	−	1.34528i	0.0556734	−	0.0686511i
$385$	−7.66307	+	27.4861i	−0.390546	+	1.40082i
$386$	−14.1683			−0.721146
$387$	−24.6975	−	8.06357i	−1.25545	−	0.409894i
$388$	−1.81806	+	3.14897i	−0.0922978	+	0.159865i
$389$	−6.86909	−	11.8976i	−0.348277	−	0.603233i	0.637667	−	0.770312i	$-0.279900\pi$
$389$	−6.86909	−	11.8976i	−0.348277	−	0.603233i	−0.985943	+	0.167080i	$0.946566\pi$
$390$	1.46169	−	1.80242i	0.0740158	−	0.0912691i
$391$	1.44050	+	2.49501i	0.0728491	+	0.126178i
$392$	−5.99028	−	3.62167i	−0.302555	−	0.182922i
$393$	−4.51848	−	11.7961i	−0.227927	−	0.595035i
$394$	15.8421			0.798115
$395$	11.8376	−	20.5034i	0.595615	−	1.03164i
$396$	−13.6722	+	12.2754i	−0.687055	+	0.616861i
$397$	−3.57893	−	6.19889i	−0.179622	−	0.311114i	0.762129	−	0.647425i	$-0.224154\pi$
$397$	−3.57893	−	6.19889i	−0.179622	−	0.311114i	−0.941751	+	0.336311i	$0.890821\pi$
$398$	−4.47141	+	7.74471i	−0.224132	+	0.388207i
$399$	−3.70890	+	8.09380i	−0.185677	+	0.405197i
$400$	0.949657	+	1.64485i	0.0474828	+	0.0822427i
$401$	4.63968	−	8.03616i	0.231695	−	0.401307i	−0.726612	−	0.687048i	$-0.758906\pi$
$401$	4.63968	−	8.03616i	0.231695	−	0.401307i	0.958307	+	0.285741i	$0.0922397\pi$
$402$	7.40219	−	9.12767i	0.369188	−	0.455247i
$403$	−2.93078	−	5.07626i	−0.145993	−	0.252867i
$404$	4.00520	+	6.93721i	0.199266	+	0.345139i
$405$	1.70137	−	15.7563i	0.0845419	−	0.782937i
$406$	2.71217	+	2.76748i	0.134603	+	0.137348i
$407$	8.83693	−	15.3060i	0.438030	−	0.758691i
$408$	4.23912	+	11.0668i	0.209868	+	0.547889i
$409$	15.1683			0.750023			0.375011	−	0.927020i	$-0.377639\pi$
$409$	15.1683			0.750023			0.375011	+	0.927020i	$0.377639\pi$
$410$	12.2255			0.603772
$411$	13.9955	+	2.22687i	0.690346	+	0.109843i
$412$	3.41423	−	5.91362i	0.168207	−	0.291343i
$413$	−1.41135	+	5.06227i	−0.0694481	+	0.249098i
$414$	−1.20082	−	0.392058i	−0.0590170	−	0.0192686i
$415$	−2.75116	−	4.76515i	−0.135049	−	0.233912i
$416$	−0.380438	−	0.658939i	−0.0186525	−	0.0323071i
$417$	−21.3211	−	3.39247i	−1.04410	−	0.166130i
$418$	5.94966	−	10.3051i	0.291007	−	0.504039i
$419$	−4.16827	−	7.21966i	−0.203633	−	0.352703i	0.746063	−	0.665875i	$-0.231942\pi$
$419$	−4.16827	−	7.21966i	−0.203633	−	0.352703i	−0.949696	+	0.313172i	$0.898608\pi$
$420$	−8.03379	+	0.756713i	−0.392009	+	0.0369238i
$421$	−3.50232	+	6.06620i	−0.170693	+	0.295649i	−0.938662	−	0.344838i	$-0.887934\pi$
$421$	−3.50232	+	6.06620i	−0.170693	+	0.295649i	0.767969	+	0.640486i	$0.221267\pi$
$422$	11.3856	+	19.7205i	0.554244	+	0.959979i
$423$	−1.02859	−	4.87320i	−0.0500118	−	0.236943i
$424$	−0.112725	+	0.195246i	−0.00547442	+	0.00948197i
$425$	−12.9954			−0.630367
$426$	11.7661	−	14.5088i	0.570068	−	0.702953i
$427$	7.35417	−	26.3781i	0.355893	−	1.27653i
$428$	1.77292	+	3.07078i	0.0856971	+	0.148432i
$429$	2.88727	+	7.53762i	0.139399	+	0.363920i
$430$	7.62476	+	13.2065i	0.367699	+	0.636873i
$431$	−1.72545	+	2.98857i	−0.0831120	+	0.143954i	−0.904585	−	0.426293i	$-0.859819\pi$
$431$	−1.72545	+	2.98857i	−0.0831120	+	0.143954i	0.821473	+	0.570247i	$0.193153\pi$
$432$	−4.62476	−	2.36887i	−0.222509	−	0.113972i
$433$	28.2599			1.35809			0.679043	−	0.734099i	$-0.262395\pi$
$433$	28.2599			1.35809			0.679043	+	0.734099i	$0.262395\pi$
$434$	−5.47373	+	19.6333i	−0.262748	+	0.942429i
$435$	4.41135	+	0.701905i	0.211508	+	0.0336538i
$436$	0.351848	−	0.609419i	0.0168505	−	0.0291859i
$437$	0.818057			0.0391330
$438$	−0.190024	−	0.496083i	−0.00907968	−	0.0237037i
$439$	−28.8960			−1.37913			−0.689566	−	0.724222i	$-0.742199\pi$
$439$	−28.8960			−1.37913			−0.689566	+	0.724222i	$0.742199\pi$
$440$	10.7850			0.514152
$441$	−6.91943	+	19.8273i	−0.329497	+	0.944157i
$442$	5.20602			0.247625
$443$	−13.7609			−0.653799			−0.326899	−	0.945059i	$-0.606004\pi$
$443$	−13.7609			−0.653799			−0.326899	+	0.945059i	$0.606004\pi$
$444$	4.93598	+	0.785381i	0.234251	+	0.0372725i
$445$	−4.58358			−0.217283
$446$	−6.44282	+	11.1593i	−0.305076	+	0.528408i
$447$	5.46978	+	14.2796i	0.258711	+	0.675401i
$448$	−0.710533	+	2.54856i	−0.0335695	+	0.120408i
$449$	−20.2003			−0.953309			−0.476655	−	0.879091i	$-0.658151\pi$
$449$	−20.2003			−0.953309			−0.476655	+	0.879091i	$0.658151\pi$
$450$	4.23981	−	3.80664i	0.199867	−	0.179447i
$451$	−21.2616	+	36.8261i	−1.00117	+	1.73407i
$452$	4.25116	+	7.36323i	0.199958	+	0.346337i
$453$	25.6346	+	4.07881i	1.20442	+	0.191639i
$454$	−10.9984	−	19.0497i	−0.516179	−	0.894048i
$455$	−0.951980	+	3.41458i	−0.0446295	+	0.160078i
$456$	3.32326	+	0.528775i	0.155626	+	0.0247621i
$457$	20.0298			0.936956			0.468478	−	0.883475i	$-0.344803\pi$
$457$	20.0298			0.936956			0.468478	+	0.883475i	$0.344803\pi$
$458$	1.89931	−	3.28971i	0.0887491	−	0.153718i
$459$	29.8583	−	19.2998i	1.39367	−	0.900837i
$460$	0.370723	+	0.642111i	0.0172851	+	0.0299386i
$461$	5.97661	−	10.3518i	0.278359	−	0.482131i	−0.692618	−	0.721304i	$-0.743543\pi$
$461$	5.97661	−	10.3518i	0.278359	−	0.482131i	0.970977	+	0.239173i	$0.0768763\pi$
$462$	11.6923	−	25.5158i	0.543977	−	1.18710i
$463$	6.64527	+	11.5100i	0.308832	+	0.534913i	0.978107	−	0.208102i	$-0.0667286\pi$
$463$	6.64527	+	11.5100i	0.308832	+	0.534913i	−0.669275	+	0.743015i	$0.733395\pi$
$464$	0.732287	−	1.26836i	0.0339956	−	0.0588820i
$465$	8.40451	+	21.9411i	0.389750	+	1.01750i
$466$	−3.33530	−	5.77690i	−0.154505	−	0.267610i
$467$	−5.61505	−	9.72555i	−0.259833	−	0.450045i	0.706364	−	0.707849i	$-0.250334\pi$
$467$	−5.61505	−	9.72555i	−0.259833	−	0.450045i	−0.966197	+	0.257804i	$0.917001\pi$
$468$	−1.69850	+	1.52496i	−0.0785130	+	0.0704915i
$469$	−4.82094	+	17.2918i	−0.222610	+	0.798463i
$470$	−1.46169	+	2.53173i	−0.0674230	+	0.116780i
$471$	20.7073	−	25.5342i	0.954140	−	1.17655i
$472$	1.98633			0.0914281
$473$	−53.0416			−2.43886
$474$	−14.6683	+	18.0875i	−0.673736	+	0.830786i
$475$	−1.84501	+	3.19565i	−0.0846550	+	0.146627i
$476$	−12.6706	−	12.9290i	−0.580756	−	0.592601i
$477$	0.642950	+	0.209918i	0.0294387	+	0.00961150i
$478$	−7.82038	−	13.5453i	−0.357696	−	0.619547i
$479$	16.3135	+	28.2559i	0.745385	+	1.29104i	0.950015	+	0.312205i	$0.101068\pi$
$479$	16.3135	+	28.2559i	0.745385	+	1.29104i	−0.204630	+	0.978839i	$0.565599\pi$
$480$	1.09097	+	2.84813i	0.0497958	+	0.129999i
$481$	1.09781	−	1.90146i	0.0500557	−	0.0866991i
$482$	−10.7060	−	18.5434i	−0.487646	−	0.844627i
$483$	1.92107	−	0.180948i	0.0874116	−	0.00823340i
$484$	−13.2564	+	22.9607i	−0.602562	+	1.04367i
$485$	−3.20137	−	5.54494i	−0.145367	−	0.251783i
$486$	−4.08809	+	15.0429i	−0.185440	+	0.682358i
$487$	1.84897	−	3.20251i	0.0837848	−	0.145120i	−0.821088	−	0.570802i	$-0.806632\pi$
$487$	1.84897	−	3.20251i	0.0837848	−	0.145120i	0.904873	+	0.425682i	$0.139966\pi$
$488$	−10.3502			−0.468532
$489$	−25.7226	−	4.09280i	−1.16321	−	0.185083i
$490$	10.7970	−	5.94631i	0.487758	−	0.268627i
$491$	−18.7804	−	32.5287i	−0.847549	−	1.46800i	−0.883389	−	0.468641i	$-0.844744\pi$
$491$	−18.7804	−	32.5287i	−0.847549	−	1.46800i	0.0358393	−	0.999358i	$-0.488590\pi$
$492$	−11.8759	−	1.88962i	−0.535408	−	0.0851906i
$493$	5.01040	+	8.67827i	0.225657	+	0.390850i
$494$	0.739123	−	1.28020i	0.0332547	−	0.0575989i
$495$	−6.68194	−	31.6574i	−0.300331	−	1.42289i
$496$	7.70370			0.345906
$497$	−7.66307	+	27.4861i	−0.343736	+	1.23292i
$498$	1.93598	+	5.05415i	0.0867535	+	0.226482i
$499$	15.8977	−	27.5356i	0.711678	−	1.23266i	−0.252549	−	0.967584i	$-0.581269\pi$
$499$	15.8977	−	27.5356i	0.711678	−	1.23266i	0.964227	−	0.265078i	$-0.0853977\pi$
$500$	−12.1488			−0.543313
$501$	1.95718	+	0.311414i	0.0874404	+	0.0139129i
$502$	−23.6030			−1.05345
$503$	30.8252			1.37443			0.687214	−	0.726455i	$-0.258834\pi$
$503$	30.8252			1.37443			0.687214	+	0.726455i	$0.258834\pi$
$504$	7.92107	+	0.506659i	0.352832	+	0.0225684i
$505$	−14.1053			−0.627679
$506$	−2.57893			−0.114648
$507$	−7.69562	−	20.0904i	−0.341774	−	0.892248i
$508$	−18.9532			−0.840913
$509$	−4.00808	+	6.94220i	−0.177655	+	0.307708i	−0.941077	−	0.338193i	$-0.890184\pi$
$509$	−4.00808	+	6.94220i	−0.177655	+	0.307708i	0.763422	+	0.645900i	$0.223518\pi$
$510$	−20.6088	−	3.27913i	−0.912572	−	0.145202i
$511$	0.567974	+	0.579559i	0.0251257	+	0.0256382i
$512$	1.00000			0.0441942
$513$	−0.506837	−	10.0825i	−0.0223774	−	0.445151i
$514$	−10.1300	+	17.5456i	−0.446814	+	0.773904i
$515$	6.01204	+	10.4132i	0.264922	+	0.458858i
$516$	−5.36552	−	14.0074i	−0.236204	−	0.616642i
$517$	−5.08414	−	8.80598i	−0.223600	−	0.387287i
$518$	−7.39411	+	1.90146i	−0.324879	+	0.0835453i
$519$	0.542951	−	0.669515i	0.0238329	−	0.0293885i
$520$	1.33981			0.0587546
$521$	14.8646	−	25.7462i	0.651229	−	1.12796i	−0.331596	−	0.943421i	$-0.607587\pi$
$521$	14.8646	−	25.7462i	0.651229	−	1.12796i	0.982825	−	0.184540i	$-0.0590795\pi$
$522$	−4.17674	−	1.36368i	−0.182811	−	0.0596864i
$523$	13.4698	+	23.3303i	0.588992	+	1.02016i	0.994365	+	0.106013i	$0.0338084\pi$
$523$	13.4698	+	23.3303i	0.588992	+	1.02016i	−0.405373	+	0.914152i	$0.632858\pi$
$524$	3.64652	−	6.31595i	0.159299	−	0.275914i
$525$	−3.62584	+	7.91255i	−0.158245	+	0.345332i
$526$	11.2443	+	19.4757i	0.490276	+	0.849183i
$527$	−26.3549	+	45.6480i	−1.14804	+	1.98846i
$528$	−10.4766	−	1.66697i	−0.455936	−	0.0725455i
$529$	11.4114	+	19.7650i	0.496146	+	0.859350i
$530$	−0.198495	−	0.343803i	−0.00862207	−	0.0149339i
$531$	−1.23065	−	5.83052i	−0.0534057	−	0.253023i
$532$	−4.97825	+	1.28020i	−0.215834	+	0.0555037i
$533$	−2.64132	+	4.57489i	−0.114408	+	0.198161i
$534$	4.45254	+	0.708458i	0.192680	+	0.0306580i
$535$	−6.24377			−0.269942
$536$	6.78495			0.293065
$537$	−5.46978	−	14.2796i	−0.236038	−	0.616210i
$538$	−12.6706	+	21.9461i	−0.546268	+	0.946164i
$539$	−0.865521	+	42.8646i	−0.0372806	+	1.84631i
$540$	7.68427	−	4.96695i	0.330678	−	0.213744i
$541$	7.15568	+	12.3940i	0.307647	+	0.532859i	0.977847	−	0.209321i	$-0.0671252\pi$
$541$	7.15568	+	12.3940i	0.307647	+	0.532859i	−0.670201	+	0.742180i	$0.733792\pi$
$542$	−6.87880	−	11.9144i	−0.295470	−	0.511769i
$543$	1.45034	−	1.78843i	0.0622403	−	0.0767487i
$544$	−3.42107	+	5.92546i	−0.146677	+	0.254052i
$545$	0.619562	+	1.07311i	0.0265391	+	0.0459671i
$546$	1.45254	−	3.16982i	0.0621628	−	0.135656i
$547$	1.02463	−	1.77471i	0.0438101	−	0.0758813i	−0.843289	−	0.537461i	$-0.819384\pi$
$547$	1.02463	−	1.77471i	0.0438101	−	0.0758813i	0.887099	+	0.461579i	$0.152717\pi$
$548$	4.09097	+	7.08577i	0.174758	+	0.302689i
$549$	6.41260	+	30.3813i	0.273683	+	1.29664i
$550$	5.81642	−	10.0743i	0.248013	−	0.429571i
$551$	2.84540			0.121218
$552$	−0.260877	−	0.681054i	−0.0111037	−	0.0289876i
$553$	9.55322	−	34.2657i	0.406244	−	1.45713i
$554$	1.64132	+	2.84284i	0.0697328	+	0.120781i
$555$	−5.54351	+	6.83572i	−0.235309	+	0.290160i
$556$	−6.23229	−	10.7946i	−0.264308	−	0.457795i
$557$	8.84338	−	15.3172i	0.374706	−	0.649010i	−0.615577	−	0.788077i	$-0.711077\pi$
$557$	8.84338	−	15.3172i	0.374706	−	0.649010i	0.990283	+	0.139067i	$0.0444103\pi$
$558$	−4.77292	−	22.6129i	−0.202054	−	0.957279i
$559$	−6.58934			−0.278699
$560$	−3.26088	−	3.32738i	−0.137797	−	0.140608i
$561$	45.7187	−	56.3759i	1.93025	−	2.38019i
$562$	0.634479	−	1.09895i	0.0267639	−	0.0463564i
$563$	0.937063			0.0394925			0.0197462	−	0.999805i	$-0.493714\pi$
$563$	0.937063			0.0394925			0.0197462	+	0.999805i	$0.493714\pi$
$564$	1.81122	−	2.23342i	0.0762661	−	0.0940440i
$565$	−14.9715			−0.629858
$566$	−8.19235			−0.344350
$567$	−3.42038	−	23.5648i	−0.143642	−	0.989630i
$568$	10.7850			0.452527
$569$	23.5264			0.986278			0.493139	−	0.869951i	$-0.335849\pi$
$569$	23.5264			0.986278			0.493139	+	0.869951i	$0.335849\pi$
$570$	−3.73229	+	4.60230i	−0.156328	+	0.192769i
$571$	−0.484004			−0.0202549			−0.0101275	−	0.999949i	$-0.503224\pi$
$571$	−0.484004			−0.0202549			−0.0101275	+	0.999949i	$0.503224\pi$
$572$	−2.33009	+	4.03584i	−0.0974262	+	0.168747i
$573$	−17.6391	+	21.7509i	−0.736885	+	0.908655i
$574$	17.7902	−	4.57489i	0.742547	−	0.190952i
$575$	0.799737			0.0333514
$576$	−0.619562	−	2.93533i	−0.0258151	−	0.122305i
$577$	−2.23065	+	3.86360i	−0.0928633	+	0.160844i	−0.908715	−	0.417417i	$-0.862935\pi$
$577$	−2.23065	+	3.86360i	−0.0928633	+	0.160844i	0.815852	+	0.578261i	$0.196269\pi$
$578$	−14.9074	−	25.8204i	−0.620066	−	1.07399i
$579$	−15.4572	+	19.0603i	−0.642379	+	0.792119i
$580$	1.28947	+	2.23342i	0.0535422	+	0.0927378i
$581$	−5.78659	−	5.90461i	−0.240068	−	0.244965i
$582$	2.25280	+	5.88123i	0.0933814	+	0.243785i
$583$	1.38083			0.0571881
$584$	0.153353	−	0.265616i	0.00634581	−	0.0109913i
$585$	−0.830095	−	3.93278i	−0.0343202	−	0.162600i
$586$	7.72545	+	13.3809i	0.319135	+	0.552759i
$587$	8.31518	−	14.4023i	0.343204	−	0.594447i	−0.641822	−	0.766854i	$-0.721821\pi$
$587$	8.31518	−	14.4023i	0.343204	−	0.594447i	0.985026	+	0.172407i	$0.0551544\pi$
$588$	−11.4074	+	4.10748i	−0.470433	+	0.169390i
$589$	7.48345	+	12.9617i	0.308350	+	0.534078i
$590$	−1.74884	+	3.02908i	−0.0719985	+	0.124705i
$591$	17.2833	−	21.3121i	0.710941	−	0.876663i
$592$	1.44282	+	2.49904i	0.0592995	+	0.102710i
$593$	20.7632	+	35.9629i	0.852642	+	1.47682i	0.878815	+	0.477163i	$0.158335\pi$
$593$	20.7632	+	35.9629i	0.852642	+	1.47682i	−0.0261726	+	0.999657i	$0.508332\pi$
$594$	1.59781	+	31.7851i	0.0655589	+	1.30416i
$595$	30.8720	−	7.93899i	1.26563	−	0.325467i
$596$	−4.41423	+	7.64567i	−0.180814	+	0.313179i
$597$	5.54063	+	14.4646i	0.226763	+	0.591995i
$598$	−0.320380			−0.0131013
$599$	15.0766			0.616014			0.308007	−	0.951384i	$-0.400338\pi$
$599$	15.0766			0.616014			0.308007	+	0.951384i	$0.400338\pi$
$600$	3.24884	+	0.516934i	0.132633	+	0.0211037i
$601$	−8.05555	+	13.9526i	−0.328593	+	0.569139i	−0.982233	−	0.187666i	$-0.939908\pi$
$601$	−8.05555	+	13.9526i	−0.328593	+	0.569139i	0.653640	+	0.756805i	$0.273241\pi$
$602$	16.0374	+	16.3645i	0.653634	+	0.666965i
$603$	−4.20370	−	19.9161i	−0.171188	−	0.811044i
$604$	7.49316	+	12.9785i	0.304892	+	0.528089i
$605$	−23.3428	−	40.4310i	−0.949021	−	1.64375i
$606$	13.7021	+	2.18018i	0.556608	+	0.0885638i
$607$	−9.78659	+	16.9509i	−0.397225	+	0.688014i	−0.993382	−	0.114853i	$-0.963360\pi$
$607$	−9.78659	+	16.9509i	−0.397225	+	0.688014i	0.596157	+	0.802868i	$0.296694\pi$
$608$	0.971410	+	1.68253i	0.0393959	+	0.0682357i
$609$	6.68194	−	0.629380i	0.270766	−	0.0255038i
$610$	9.11273	−	15.7837i	0.368963	−	0.639063i
$611$	−0.631600	−	1.09396i	−0.0255518	−	0.0442570i
$612$	19.5127	+	6.37076i	0.788755	+	0.257523i
$613$	−2.77579	+	4.80782i	−0.112113	+	0.194186i	−0.916622	−	0.399755i	$-0.869095\pi$
$613$	−2.77579	+	4.80782i	−0.112113	+	0.194186i	0.804509	+	0.593941i	$0.202429\pi$
$614$	4.89931			0.197720
$615$	13.3376	−	16.4467i	0.537825	−	0.663194i
$616$	15.6940	−	4.03584i	0.632329	−	0.162609i
$617$	0.634479	+	1.09895i	0.0255431	+	0.0442420i	0.878514	−	0.477716i	$-0.158535\pi$
$617$	0.634479	+	1.09895i	0.0255431	+	0.0442420i	−0.852971	+	0.521958i	$0.825202\pi$
$618$	−4.23065	−	11.0447i	−0.170182	−	0.444283i
$619$	−2.25116	−	3.89913i	−0.0904818	−	0.156719i	0.817232	−	0.576309i	$-0.195507\pi$
$619$	−2.25116	−	3.89913i	−0.0904818	−	0.156719i	−0.907714	+	0.419589i	$0.862174\pi$
$620$	−6.78263	+	11.7479i	−0.272397	+	0.471805i
$621$	−1.83749	+	1.18771i	−0.0737358	+	0.0476613i
$622$	−7.69002			−0.308342
$623$	−6.66991	+	1.71522i	−0.267224	+	0.0687190i
$624$	−1.30150	−	0.207087i	−0.0521019	−	0.00829011i
$625$	5.94802	−	10.3023i	0.237921	−	0.412091i
$626$	−1.72313			−0.0688700
$627$	−7.37236	−	19.2465i	−0.294424	−	0.768633i
$628$	18.9806			0.757407
$629$	−19.7439			−0.787242
$630$	−7.74665	+	11.6333i	−0.308634	+	0.463480i
$631$	−1.69905			−0.0676381			−0.0338191	−	0.999428i	$-0.510767\pi$
$631$	−1.69905			−0.0676381			−0.0338191	+	0.999428i	$0.510767\pi$
$632$	−13.4451			−0.534819
$633$	38.9510	+	6.19763i	1.54816	+	0.246334i
$634$	33.2028			1.31865
$635$	16.6871	−	28.9030i	0.662209	−	1.14698i
$636$	0.139680	+	0.364654i	0.00553868	+	0.0144595i
$637$	−0.107523	+	5.32505i	−0.00426023	+	0.210986i
$638$	−8.97017			−0.355132
$639$	−6.68194	−	31.6574i	−0.264334	−	1.25235i
$640$	−0.880438	+	1.52496i	−0.0348024	+	0.0602795i
$641$	0.474289	+	0.821492i	0.0187333	+	0.0324470i	0.875240	−	0.483689i	$-0.160703\pi$
$641$	0.474289	+	0.821492i	0.0187333	+	0.0324470i	−0.856507	+	0.516136i	$0.827370\pi$
$642$	6.06526	+	0.965064i	0.239377	+	0.0380880i
$643$	−9.84897	−	17.0589i	−0.388405	−	0.672738i	0.603830	−	0.797113i	$-0.293641\pi$
$643$	−9.84897	−	17.0589i	−0.388405	−	0.672738i	−0.992235	+	0.124375i	$0.960307\pi$
$644$	0.779752	+	0.795655i	0.0307265	+	0.0313532i
$645$	26.0848	+	4.15044i	1.02709	+	0.163424i
$646$	−13.2930			−0.523007
$647$	11.7271	−	20.3119i	0.461039	−	0.798543i	−0.537974	−	0.842962i	$-0.680810\pi$
$647$	11.7271	−	20.3119i	0.461039	−	0.798543i	0.999013	+	0.0444181i	$0.0141434\pi$
$648$	−8.23229	+	3.63723i	−0.323395	+	0.142884i
$649$	−6.08289	−	10.5359i	−0.238774	−	0.413569i
$650$	0.722572	−	1.25153i	0.0283416	−	0.0490891i
$651$	20.4406	+	28.7831i	0.801131	+	1.12810i
$652$	−7.51887	−	13.0231i	−0.294462	−	0.510023i
$653$	−11.3954	+	19.7373i	−0.445935	+	0.772382i	−0.998117	−	0.0613420i	$-0.980462\pi$
$653$	−11.3954	+	19.7373i	−0.445935	+	0.772382i	0.552182	+	0.833724i	$0.313795\pi$
$654$	−0.435984	−	1.13819i	−0.0170483	−	0.0445069i
$655$	6.42107	+	11.1216i	0.250892	+	0.434557i
$656$	−3.47141	−	6.01266i	−0.135536	−	0.234755i
$657$	−0.874681	−	0.285577i	−0.0341246	−	0.0111414i
$658$	−1.17962	+	4.23109i	−0.0459864	+	0.164945i
$659$	−13.2398	+	22.9320i	−0.515750	+	0.893305i	0.484083	+	0.875022i	$0.339153\pi$
$659$	−13.2398	+	22.9320i	−0.515750	+	0.893305i	−0.999833	+	0.0182828i	$0.994180\pi$
$660$	11.7661	−	14.5088i	0.457994	−	0.564754i
$661$	−26.7382			−1.03999			−0.519997	−	0.854168i	$-0.674067\pi$
$661$	−26.7382			−1.03999			−0.519997	+	0.854168i	$0.674067\pi$
$662$	2.88891			0.112281
$663$	5.67962	−	7.00356i	0.220578	−	0.271996i
$664$	−1.56238	+	2.70612i	−0.0606322	+	0.105018i
$665$	2.43078	−	8.71878i	0.0942617	−	0.338100i
$666$	6.44158	−	5.78346i	0.249606	−	0.224104i
$667$	−0.308342	−	0.534063i	−0.0119390	−	0.0206790i
$668$	0.572097	+	0.990901i	0.0221351	+	0.0383391i
$669$	7.98345	+	20.8419i	0.308658	+	0.805793i
$670$	−5.97373	+	10.3468i	−0.230785	+	0.399732i
$671$	31.6963	+	54.8996i	1.22362	+	2.11938i
$672$	2.65335	+	3.73627i	0.102355	+	0.144130i
$673$	−10.3856	+	17.9885i	−0.400337	+	0.693404i	−0.993766	−	0.111482i	$-0.964440\pi$
$673$	−10.3856	+	17.9885i	−0.400337	+	0.693404i	0.593429	+	0.804886i	$0.297774\pi$
$674$	−4.36156	−	7.55445i	−0.168001	−	0.290987i
$675$	−0.495487	−	9.85667i	−0.0190713	−	0.379384i
$676$	6.21053	−	10.7570i	0.238867	−	0.413729i
$677$	−20.6979			−0.795486			−0.397743	−	0.917497i	$-0.630207\pi$
$677$	−20.6979			−0.795486			−0.397743	+	0.917497i	$0.630207\pi$
$678$	14.5435	+	2.31407i	0.558540	+	0.0888712i
$679$	−6.73353	−	6.87087i	−0.258409	−	0.263680i
$680$	−6.02408	−	10.4340i	−0.231013	−	0.400126i
$681$	−37.6261	−	5.98682i	−1.44184	−	0.229416i
$682$	−23.5917	−	40.8620i	−0.903371	−	1.56469i
$683$	14.2918	−	24.7541i	0.546860	−	0.947190i	−0.451627	−	0.892207i	$-0.649156\pi$
$683$	14.2918	−	24.7541i	0.546860	−	0.947190i	0.998487	−	0.0549828i	$-0.0175104\pi$
$684$	4.33693	−	3.89384i	0.165827	−	0.148885i
$685$	−14.4074			−0.550478
$686$	13.4863	−	12.6933i	0.514910	−	0.484631i
$687$	−2.35348	−	6.14409i	−0.0897910	−	0.234412i
$688$	4.33009	−	7.49994i	0.165083	−	0.285933i
$689$	0.171540			0.00653515
$690$	1.26827	+	0.201799i	0.0482822	+	0.00768234i
$691$	−6.69794			−0.254802			−0.127401	−	0.991851i	$-0.540663\pi$
$691$	−6.69794			−0.254802			−0.127401	+	0.991851i	$0.540663\pi$
$692$	0.497677			0.0189188
$693$	−21.5699	−	43.5665i	−0.819373	−	1.65495i
$694$	9.69467			0.368005
$695$	21.9486			0.832557
$696$	−0.907394	−	2.36887i	−0.0343947	−	0.0897919i
$697$	47.5037			1.79933
$698$	14.1992	−	24.5937i	0.537447	−	0.930886i
$699$	−11.4103	−	1.81553i	−0.431576	−	0.0686695i
$700$	−4.86677	+	1.25153i	−0.183946	+	0.0473034i
$701$	−25.1442			−0.949683			−0.474842	−	0.880071i	$-0.657495\pi$
$701$	−25.1442			−0.949683			−0.474842	+	0.880071i	$0.657495\pi$
$702$	0.198495	+	3.94865i	0.00749171	+	0.149032i
$703$	−2.80314	+	4.85518i	−0.105722	+	0.183117i
$704$	−3.06238	−	5.30420i	−0.115418	−	0.199910i
$705$	1.81122	+	4.72844i	0.0682145	+	0.178083i
$706$	2.19686	+	3.80507i	0.0826799	+	0.143206i
$707$	−20.5257	+	5.27836i	−0.771949	+	0.198513i
$708$	2.16703	−	2.67217i	0.0814418	−	0.100426i
$709$	8.86621			0.332977			0.166489	−	0.986043i	$-0.446757\pi$
$709$	8.86621			0.332977			0.166489	+	0.986043i	$0.446757\pi$
$710$	−9.49549	+	16.4467i	−0.356359	+	0.617232i
$711$	8.33009	+	39.4659i	0.312403	+	1.48009i
$712$	1.30150	+	2.25427i	0.0487760	+	0.0844824i
$713$	1.62188	−	2.80919i	0.0607401	−	0.105205i
$714$	−31.2164	+	2.94031i	−1.16825	+	0.110038i
$715$	−4.10301	−	7.10662i	−0.153444	−	0.265773i
$716$	4.41423	−	7.64567i	0.164968	−	0.285732i
$717$	−26.7540	−	4.25693i	−0.999148	−	0.158978i
$718$	16.0796	+	27.8507i	0.600086	+	1.03938i
$719$	11.8015	+	20.4408i	0.440122	+	0.762313i	0.997698	−	0.0678123i	$-0.0216019\pi$
$719$	11.8015	+	20.4408i	0.440122	+	0.762313i	−0.557576	+	0.830126i	$0.688269\pi$
$720$	5.02175	+	1.63957i	0.187150	+	0.0611030i
$721$	12.6453	+	12.9032i	0.470935	+	0.480540i
$722$	7.61273	−	13.1856i	0.283316	−	0.490718i
$723$	−36.6260	−	5.82769i	−1.36214	−	0.216734i
$724$	1.32941			0.0494070
$725$	2.78168			0.103309
$726$	16.4263	+	42.8830i	0.609636	+	1.59154i
$727$	3.25692	−	5.64115i	0.120792	−	0.209219i	−0.799288	−	0.600948i	$-0.794790\pi$
$727$	3.25692	−	5.64115i	0.120792	−	0.209219i	0.920080	+	0.391730i	$0.128123\pi$
$728$	1.94966	−	0.501371i	0.0722591	−	0.0185820i
$729$	15.7769	+	21.9110i	0.584329	+	0.811517i
$730$	0.270036	+	0.467717i	0.00999449	+	0.0173110i
$731$	29.6271	+	51.3156i	1.09580	+	1.89798i
$732$	−11.2918	+	13.9239i	−0.417357	+	0.514644i
$733$	11.5991	−	20.0901i	0.428421	−	0.742047i	−0.568312	−	0.822813i	$-0.692403\pi$
$733$	11.5991	−	20.0901i	0.428421	−	0.742047i	0.996733	+	0.0807664i	$0.0257368\pi$
$734$	−17.3015	−	29.9671i	−0.638610	−	1.10611i
$735$	3.77975	−	21.0122i	0.139418	−	0.775048i
$736$	0.210533	−	0.364654i	0.00776036	−	0.0134413i
$737$	−20.7781	−	35.9888i	−0.765372	−	1.32566i
$738$	−15.4984	+	13.9149i	−0.570503	+	0.512216i
$739$	−7.57838	+	13.1261i	−0.278775	+	0.482853i	−0.971081	−	0.238752i	$-0.923262\pi$
$739$	−7.57838	+	13.1261i	−0.278775	+	0.482853i	0.692305	+	0.721605i	$0.256595\pi$
$740$	−5.08126			−0.186791
$741$	−0.915865	−	2.39099i	−0.0336451	−	0.0878352i
$742$	−0.417500	−	0.426015i	−0.0153269	−	0.0156395i
$743$	−5.21737	−	9.03675i	−0.191407	−	0.331526i	0.754310	−	0.656518i	$-0.227972\pi$
$743$	−5.21737	−	9.03675i	−0.191407	−	0.331526i	−0.945717	+	0.324992i	$0.894638\pi$
$744$	8.40451	−	10.3636i	0.308124	−	0.379949i
$745$	−7.77292	−	13.4631i	−0.284778	−	0.493249i
$746$	−5.48796	+	9.50543i	−0.200929	+	0.348018i
$747$	8.91135	+	2.90949i	0.326049	+	0.106453i
$748$	41.9064			1.53225
$749$	−9.08577	+	2.33648i	−0.331987	+	0.0853733i
$750$	−13.2540	+	16.3436i	−0.483969	+	0.596784i
$751$	−20.1059	+	34.8244i	−0.733674	+	1.27076i	0.221628	+	0.975131i	$0.428863\pi$
$751$	−20.1059	+	34.8244i	−0.733674	+	1.27076i	−0.955303	+	0.295630i	$0.904470\pi$
$752$	1.66019			0.0605409
$753$	−25.7502	+	31.7527i	−0.938390	+	1.15713i
$754$	−1.11436			−0.0405826
$755$	−26.3891			−0.960397
$756$	9.32326	−	10.1033i	0.339084	−	0.367454i
$757$	−21.5206			−0.782181			−0.391091	−	0.920352i	$-0.627902\pi$
$757$	−21.5206			−0.782181			−0.391091	+	0.920352i	$0.627902\pi$
$758$	33.9877			1.23449
$759$	−2.81354	+	3.46939i	−0.102125	+	0.125931i
$760$	−3.42107			−0.124095
$761$	11.8313	−	20.4925i	0.428886	−	0.742852i	−0.567889	−	0.823105i	$-0.692240\pi$
$761$	11.8313	−	20.4925i	0.428886	−	0.742852i	0.996774	+	0.0802535i	$0.0255730\pi$
$762$	−20.6774	+	25.4974i	−0.749064	+	0.923674i
$763$	1.30314	+	1.32972i	0.0471768	+	0.0481390i
$764$	−16.1683			−0.584947
$765$	−26.8949	+	24.1471i	−0.972388	+	0.873042i
$766$	10.5120	−	18.2074i	0.379815	−	0.657860i
$767$	−0.755675	−	1.30887i	−0.0272858	−	0.0472605i
$768$	1.09097	−	1.34528i	0.0393670	−	0.0485436i
$769$	−5.62764

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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.09097 - 1.34528i) q^{3} +1.00000 q^{4} +(-0.880438 + 1.52496i) q^{5} +(1.09097 - 1.34528i) q^{6} +(-0.710533 + 2.54856i) q^{7} +1.00000 q^{8} +(-0.619562 - 2.93533i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.09097 - 1.34528i) q^{3} +1.00000 q^{4} +(-0.880438 + 1.52496i) q^{5} +(1.09097 - 1.34528i) q^{6} +(-0.710533 + 2.54856i) q^{7} +1.00000 q^{8} +(-0.619562 - 2.93533i) q^{9} +(-0.880438 + 1.52496i) q^{10} +(-3.06238 - 5.30420i) q^{11} +(1.09097 - 1.34528i) q^{12} +(-0.380438 - 0.658939i) q^{13} +(-0.710533 + 2.54856i) q^{14} +(1.09097 + 2.84813i) q^{15} +1.00000 q^{16} +(-3.42107 + 5.92546i) q^{17} +(-0.619562 - 2.93533i) q^{18} +(0.971410 + 1.68253i) q^{19} +(-0.880438 + 1.52496i) q^{20} +(2.65335 + 3.73627i) q^{21} +(-3.06238 - 5.30420i) q^{22} +(0.210533 - 0.364654i) q^{23} +(1.09097 - 1.34528i) q^{24} +(0.949657 + 1.64485i) q^{25} +(-0.380438 - 0.658939i) q^{26} +(-4.62476 - 2.36887i) q^{27} +(-0.710533 + 2.54856i) q^{28} +(0.732287 - 1.26836i) q^{29} +(1.09097 + 2.84813i) q^{30} +7.70370 q^{31} +1.00000 q^{32} +(-10.4766 - 1.66697i) q^{33} +(-3.42107 + 5.92546i) q^{34} +(-3.26088 - 3.32738i) q^{35} +(-0.619562 - 2.93533i) q^{36} +(1.44282 + 2.49904i) q^{37} +(0.971410 + 1.68253i) q^{38} +(-1.30150 - 0.207087i) q^{39} +(-0.880438 + 1.52496i) q^{40} +(-3.47141 - 6.01266i) q^{41} +(2.65335 + 3.73627i) q^{42} +(4.33009 - 7.49994i) q^{43} +(-3.06238 - 5.30420i) q^{44} +(5.02175 + 1.63957i) q^{45} +(0.210533 - 0.364654i) q^{46} +1.66019 q^{47} +(1.09097 - 1.34528i) q^{48} +(-5.99028 - 3.62167i) q^{49} +(0.949657 + 1.64485i) q^{50} +(4.23912 + 11.0668i) q^{51} +(-0.380438 - 0.658939i) q^{52} +(-0.112725 + 0.195246i) q^{53} +(-4.62476 - 2.36887i) q^{54} +10.7850 q^{55} +(-0.710533 + 2.54856i) q^{56} +(3.32326 + 0.528775i) q^{57} +(0.732287 - 1.26836i) q^{58} +1.98633 q^{59} +(1.09097 + 2.84813i) q^{60} -10.3502 q^{61} +7.70370 q^{62} +(7.92107 + 0.506659i) q^{63} +1.00000 q^{64} +1.33981 q^{65} +(-10.4766 - 1.66697i) q^{66} +6.78495 q^{67} +(-3.42107 + 5.92546i) q^{68} +(-0.260877 - 0.681054i) q^{69} +(-3.26088 - 3.32738i) q^{70} +10.7850 q^{71} +(-0.619562 - 2.93533i) q^{72} +(0.153353 - 0.265616i) q^{73} +(1.44282 + 2.49904i) q^{74} +(3.24884 + 0.516934i) q^{75} +(0.971410 + 1.68253i) q^{76} +(15.6940 - 4.03584i) q^{77} +(-1.30150 - 0.207087i) q^{78} -13.4451 q^{79} +(-0.880438 + 1.52496i) q^{80} +(-8.23229 + 3.63723i) q^{81} +(-3.47141 - 6.01266i) q^{82} +(-1.56238 + 2.70612i) q^{83} +(2.65335 + 3.73627i) q^{84} +(-6.02408 - 10.4340i) q^{85} +(4.33009 - 7.49994i) q^{86} +(-0.907394 - 2.36887i) q^{87} +(-3.06238 - 5.30420i) q^{88} +(1.30150 + 2.25427i) q^{89} +(5.02175 + 1.63957i) q^{90} +(1.94966 - 0.501371i) q^{91} +(0.210533 - 0.364654i) q^{92} +(8.40451 - 10.3636i) q^{93} +1.66019 q^{94} -3.42107 q^{95} +(1.09097 - 1.34528i) q^{96} +(-1.81806 + 3.14897i) q^{97} +(-5.99028 - 3.62167i) q^{98} +(-13.6722 + 12.2754i) 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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