LMFDB - Embedded newform 126.2.h.c.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(67,126)]

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([2, 4]))

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

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

chi := DirichletCharacter("126.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.h (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			79.1
Root			$0.500000 + 0.224437i$ of defining polynomial
Character	$\chi$	$=$	126.79
Dual form			126.2.h.c.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.349814 - 1.69636i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.69963 q^{5} +(-1.29418 + 1.15113i) q^{6} +(-1.40545 - 2.24159i) q^{7} +1.00000 q^{8} +(-2.75526 + 1.18682i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.349814 - 1.69636i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.69963 q^{5} +(-1.29418 + 1.15113i) q^{6} +(-1.40545 - 2.24159i) q^{7} +1.00000 q^{8} +(-2.75526 + 1.18682i) q^{9} +(-1.84981 - 3.20397i) q^{10} -1.47710 q^{11} +(1.64400 + 0.545231i) q^{12} +(-1.34981 - 2.33795i) q^{13} +(-1.23855 + 2.33795i) q^{14} +(-1.29418 - 6.27589i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.28799 + 5.69497i) q^{17} +(2.40545 + 1.79272i) q^{18} +(-0.444368 + 0.769668i) q^{19} +(-1.84981 + 3.20397i) q^{20} +(-3.31089 + 3.16828i) q^{21} +(0.738550 + 1.27921i) q^{22} +6.28799 q^{23} +(-0.349814 - 1.69636i) q^{24} +8.68725 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} +(-4.78799 + 4.25874i) q^{30} +(-3.40545 + 5.89841i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.516710 + 2.50569i) 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} +0.888736 q^{38} +(-3.49381 + 3.10761i) q^{39} +3.69963 q^{40} +(-2.05563 - 3.56046i) q^{41} +(4.39926 + 1.28318i) q^{42} +(0.00618986 - 0.0107211i) q^{43} +(0.738550 - 1.27921i) q^{44} +(-10.1934 + 4.39079i) q^{45} +(-3.14400 - 5.44556i) q^{46} +(3.49381 + 6.05146i) q^{47} +(-1.29418 + 1.15113i) q^{48} +(-3.04944 + 6.30087i) q^{49} +(-4.34362 - 7.52338i) q^{50} +(8.51052 - 7.56979i) q^{51} +2.69963 q^{52} +(-1.60507 - 2.78007i) q^{53} +(2.19963 - 4.70761i) q^{54} -5.46472 q^{55} +(-1.40545 - 2.24159i) q^{56} +(1.46108 + 0.484566i) q^{57} -2.51052 q^{58} +(-3.45489 + 5.98404i) q^{59} +(6.08217 + 2.01715i) q^{60} +(2.86652 + 4.96497i) q^{61} +6.81089 q^{62} +(6.53273 + 4.50815i) q^{63} +1.00000 q^{64} +(-4.99381 - 8.64953i) q^{65} +(1.91164 - 1.70033i) q^{66} +(4.73236 - 8.19669i) q^{67} -6.57598 q^{68} +(-2.19963 - 10.6667i) q^{69} +(-4.58217 + 8.64953i) q^{70} -5.46472 q^{71} +(-2.75526 + 1.18682i) q^{72} +(-6.03273 - 10.4490i) q^{73} +2.77747 q^{74} +(-3.03892 - 14.7367i) q^{75} +(-0.444368 - 0.769668i) q^{76} +(2.07598 + 3.31105i) q^{77} +(4.43818 + 1.47192i) q^{78} +(-5.72617 - 9.91802i) q^{79} +(-1.84981 - 3.20397i) q^{80} +(6.18292 - 6.53999i) q^{81} +(-2.05563 + 3.56046i) q^{82} +(2.23855 - 3.87728i) q^{83} +(-1.08836 - 4.45146i) q^{84} +(12.1643 + 21.0693i) q^{85} -0.0123797 q^{86} +(-4.12729 - 1.36881i) q^{87} -1.47710 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} +(11.1971 + 3.71351i) q^{93} +(3.49381 - 6.05146i) q^{94} +(-1.64400 + 2.84748i) q^{95} +(1.64400 + 0.545231i) 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 - 3 q^{2} + 4 q^{3} - 3 q^{4} + 10 q^{5} - 2 q^{6} - 2 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 + 4 * q^3 - 3 * q^4 + 10 * q^5 - 2 * q^6 - 2 * q^7 + 6 * q^8 - 4 * q^9	\( 6 q - 3 q^{2} + 4 q^{3} - 3 q^{4} + 10 q^{5} - 2 q^{6} - 2 q^{7} + 6 q^{8} - 4 q^{9} - 5 q^{10} + 2 q^{11} - 2 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} - 3 q^{16} - 4 q^{17} + 8 q^{18} - 3 q^{19} - 5 q^{20} - 7 q^{21} - q^{22} + 14 q^{23} + 4 q^{24} + 4 q^{25} - 2 q^{26} + 7 q^{27} + 4 q^{28} - 5 q^{29} - 5 q^{30} - 14 q^{31} - 3 q^{32} - 4 q^{33} - 4 q^{34} - 19 q^{35} - 4 q^{36} - 9 q^{37} + 6 q^{38} - 3 q^{39} + 10 q^{40} - 12 q^{41} + 2 q^{42} + 18 q^{43} - q^{44} - 31 q^{45} - 7 q^{46} + 3 q^{47} - 2 q^{48} - 2 q^{50} + 26 q^{51} + 4 q^{52} + 9 q^{53} + q^{54} + 14 q^{55} - 2 q^{56} + 2 q^{57} + 10 q^{58} + 4 q^{59} + 7 q^{60} + 4 q^{61} + 28 q^{62} + 28 q^{63} + 6 q^{64} - 12 q^{65} + 23 q^{66} + 5 q^{67} + 8 q^{68} - q^{69} + 2 q^{70} + 14 q^{71} - 4 q^{72} - 25 q^{73} + 18 q^{74} - 25 q^{75} - 3 q^{76} - 35 q^{77} + 9 q^{78} + 7 q^{79} - 5 q^{80} + 32 q^{81} - 12 q^{82} + 8 q^{83} + 5 q^{84} + 14 q^{85} - 36 q^{86} - 20 q^{87} + 2 q^{88} - 9 q^{89} + 29 q^{90} + 4 q^{91} - 7 q^{92} - 3 q^{93} + 3 q^{94} + 2 q^{95} - 2 q^{96} - 28 q^{97} - 12 q^{98} - 41 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + 4 * q^3 - 3 * q^4 + 10 * q^5 - 2 * q^6 - 2 * q^7 + 6 * q^8 - 4 * q^9 - 5 * q^10 + 2 * q^11 - 2 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 - 3 * q^16 - 4 * q^17 + 8 * q^18 - 3 * q^19 - 5 * q^20 - 7 * q^21 - q^22 + 14 * q^23 + 4 * q^24 + 4 * q^25 - 2 * q^26 + 7 * q^27 + 4 * q^28 - 5 * q^29 - 5 * q^30 - 14 * q^31 - 3 * q^32 - 4 * q^33 - 4 * q^34 - 19 * q^35 - 4 * q^36 - 9 * q^37 + 6 * q^38 - 3 * q^39 + 10 * q^40 - 12 * q^41 + 2 * q^42 + 18 * q^43 - q^44 - 31 * q^45 - 7 * q^46 + 3 * q^47 - 2 * q^48 - 2 * q^50 + 26 * q^51 + 4 * q^52 + 9 * q^53 + q^54 + 14 * q^55 - 2 * q^56 + 2 * q^57 + 10 * q^58 + 4 * q^59 + 7 * q^60 + 4 * q^61 + 28 * q^62 + 28 * q^63 + 6 * q^64 - 12 * q^65 + 23 * q^66 + 5 * q^67 + 8 * q^68 - q^69 + 2 * q^70 + 14 * q^71 - 4 * q^72 - 25 * q^73 + 18 * q^74 - 25 * q^75 - 3 * q^76 - 35 * q^77 + 9 * q^78 + 7 * q^79 - 5 * q^80 + 32 * q^81 - 12 * q^82 + 8 * q^83 + 5 * q^84 + 14 * q^85 - 36 * q^86 - 20 * q^87 + 2 * q^88 - 9 * q^89 + 29 * q^90 + 4 * q^91 - 7 * q^92 - 3 * q^93 + 3 * q^94 + 2 * 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 $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.349814	−	1.69636i	−0.201965	−	0.979393i
$3$	−0.349814	−	1.69636i	−0.201965	−	0.979393i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	3.69963			1.65452			0.827262	−	0.561816i	$-0.189897\pi$
$5$	3.69963			1.65452			0.827262	+	0.561816i	$0.189897\pi$
$6$	−1.29418	+	1.15113i	−0.528348	+	0.469946i
$7$	−1.40545	−	2.24159i	−0.531209	−	0.847241i
$7$	−1.40545	−	2.24159i	−0.531209	−	0.847241i
$8$	1.00000			0.353553
$9$	−2.75526	+	1.18682i	−0.918420	+	0.395607i
$10$	−1.84981	−	3.20397i	−0.584963	−	1.01318i
$11$	−1.47710			−0.445362			−0.222681	−	0.974891i	$-0.571481\pi$
$11$	−1.47710			−0.445362			−0.222681	+	0.974891i	$0.571481\pi$
$12$	1.64400	+	0.545231i	0.474581	+	0.157395i
$13$	−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	$0.955475\pi$
$14$	−1.23855	+	2.33795i	−0.331016	+	0.624843i
$15$	−1.29418	−	6.27589i	−0.334156	−	1.62043i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.28799	+	5.69497i	0.797455	+	1.38123i	0.921268	+	0.388927i	$0.127154\pi$
$17$	3.28799	+	5.69497i	0.797455	+	1.38123i	−0.123813	+	0.992306i	$0.539512\pi$
$18$	2.40545	+	1.79272i	0.566969	+	0.422547i
$19$	−0.444368	+	0.769668i	−0.101945	+	0.176574i	−0.912486	−	0.409108i	$-0.865840\pi$
$19$	−0.444368	+	0.769668i	−0.101945	+	0.176574i	0.810541	+	0.585682i	$0.199173\pi$
$20$	−1.84981	+	3.20397i	−0.413631	+	0.716430i
$21$	−3.31089	+	3.16828i	−0.722496	+	0.691375i
$22$	0.738550	+	1.27921i	0.157459	+	0.272728i
$23$	6.28799			1.31114			0.655568	−	0.755136i	$-0.272429\pi$
$23$	6.28799			1.31114			0.655568	+	0.755136i	$0.272429\pi$
$24$	−0.349814	−	1.69636i	−0.0714055	−	0.346268i
$25$	8.68725			1.73745
$26$	−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	$0.0917810\pi$
$30$	−4.78799	+	4.25874i	−0.874164	+	0.777536i
$31$	−3.40545	+	5.89841i	−0.611636	+	1.05938i	0.379329	+	0.925262i	$0.376155\pi$
$31$	−3.40545	+	5.89841i	−0.611636	+	1.05938i	−0.990965	+	0.134123i	$0.957178\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	0.516710	+	2.50569i	0.0899477	+	0.436185i
$34$	3.28799	−	5.69497i	0.563886	−	0.976679i
$35$	−5.19963	−	8.29305i	−0.878898	−	1.40178i
$36$	0.349814	−	2.97954i	0.0583023	−	0.496589i
$37$	−1.38874	+	2.40536i	−0.228307	+	0.395439i	−0.957306	−	0.289075i	$-0.906652\pi$
$37$	−1.38874	+	2.40536i	−0.228307	+	0.395439i	0.729000	+	0.684514i	$0.239986\pi$
$38$	0.888736			0.144172
$39$	−3.49381	+	3.10761i	−0.559457	+	0.497617i
$40$	3.69963			0.584963
$41$	−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	$0.937364\pi$
$42$	4.39926	+	1.28318i	0.678820	+	0.197999i
$43$	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
$45$	−10.1934	+	4.39079i	−1.51955	+	0.654541i
$46$	−3.14400	−	5.44556i	−0.463557	−	0.802904i
$47$	3.49381	+	6.05146i	0.509625	+	0.882696i	0.999938	+	0.0111494i	$0.00354904\pi$
$47$	3.49381	+	6.05146i	0.509625	+	0.882696i	−0.490313	+	0.871546i	$0.663118\pi$
$48$	−1.29418	+	1.15113i	−0.186799	+	0.166151i
$49$	−3.04944	+	6.30087i	−0.435635	+	0.900124i
$50$	−4.34362	−	7.52338i	−0.614281	−	1.06397i
$51$	8.51052	−	7.56979i	1.19171	−	1.05998i
$52$	2.69963			0.374371
$53$	−1.60507	−	2.78007i	−0.220474	−	0.381872i	0.734478	−	0.678632i	$-0.237427\pi$
$53$	−1.60507	−	2.78007i	−0.220474	−	0.381872i	−0.954952	+	0.296760i	$0.904094\pi$
$54$	2.19963	−	4.70761i	0.299331	−	0.640625i
$55$	−5.46472			−0.736863
$56$	−1.40545	−	2.24159i	−0.187811	−	0.299545i
$57$	1.46108	+	0.484566i	0.193525	+	0.0641824i
$58$	−2.51052			−0.329647
$59$	−3.45489	+	5.98404i	−0.449788	+	0.779056i	−0.998372	−	0.0570397i	$-0.981834\pi$
$59$	−3.45489	+	5.98404i	−0.449788	+	0.779056i	0.548584	+	0.836096i	$0.315167\pi$
$60$	6.08217	+	2.01715i	0.785205	+	0.260413i
$61$	2.86652	+	4.96497i	0.367021	+	0.635699i	0.989098	−	0.147257i	$-0.0470444\pi$
$61$	2.86652	+	4.96497i	0.367021	+	0.635699i	−0.622077	+	0.782956i	$0.713711\pi$
$62$	6.81089			0.864984
$63$	6.53273	+	4.50815i	0.823047	+	0.567973i
$64$	1.00000			0.125000
$65$	−4.99381	−	8.64953i	−0.619406	−	1.07284i
$66$	1.91164	−	1.70033i	0.235306	−	0.209296i
$67$	4.73236	−	8.19669i	0.578150	−	1.00138i	−0.417542	−	0.908658i	$-0.637108\pi$
$67$	4.73236	−	8.19669i	0.578150	−	1.00138i	0.995692	−	0.0927271i	$-0.0295584\pi$
$68$	−6.57598			−0.797455
$69$	−2.19963	−	10.6667i	−0.264804	−	1.28412i
$70$	−4.58217	+	8.64953i	−0.547675	+	1.03382i
$71$	−5.46472			−0.648543			−0.324271	−	0.945964i	$-0.605119\pi$
$71$	−5.46472			−0.648543			−0.324271	+	0.945964i	$0.605119\pi$
$72$	−2.75526	+	1.18682i	−0.324711	+	0.139868i
$73$	−6.03273	−	10.4490i	−0.706078	−	1.22296i	−0.966301	−	0.257414i	$-0.917130\pi$
$73$	−6.03273	−	10.4490i	−0.706078	−	1.22296i	0.260223	−	0.965548i	$-0.416204\pi$
$74$	2.77747			0.322875
$75$	−3.03892	−	14.7367i	−0.350904	−	1.70165i
$76$	−0.444368	−	0.769668i	−0.0509725	−	0.0882870i
$77$	2.07598	+	3.31105i	0.236580	+	0.377329i
$78$	4.43818	+	1.47192i	0.502525	+	0.166662i
$79$	−5.72617	−	9.91802i	−0.644244	−	1.11586i	−0.984475	−	0.175522i	$-0.943839\pi$
$79$	−5.72617	−	9.91802i	−0.644244	−	1.11586i	0.340231	−	0.940342i	$-0.389495\pi$
$80$	−1.84981	−	3.20397i	−0.206816	−	0.358215i
$81$	6.18292	−	6.53999i	0.686991	−	0.726666i
$82$	−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	$0.0876447\pi$
$84$	−1.08836	−	4.45146i	−0.118750	−	0.485694i
$85$	12.1643	+	21.0693i	1.31941	+	2.28528i
$86$	−0.0123797			−0.00133494
$87$	−4.12729	−	1.36881i	−0.442491	−	0.146752i
$88$	−1.47710			−0.157459
$89$	−4.43818	+	7.68715i	−0.470446	+	0.814836i	−0.999429	−	0.0337963i	$-0.989240\pi$
$89$	−4.43818	+	7.68715i	−0.470446	+	0.814836i	0.528983	+	0.848633i	$0.322574\pi$
$90$	8.89926	+	6.63238i	0.938064	+	0.699114i
$91$	−3.34362	+	6.31159i	−0.350507	+	0.661634i
$92$	−3.14400	+	5.44556i	−0.327784	+	0.567739i
$93$	11.1971	+	3.71351i	1.16108	+	0.385073i
$94$	3.49381	−	6.05146i	0.360359	−	0.624160i
$95$	−1.64400	+	2.84748i	−0.168670	+	0.292146i
$96$	1.64400	+	0.545231i	0.167790	+	0.0556474i
$97$	−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
$101$	5.25457			0.522849			0.261425	−	0.965224i	$-0.415808\pi$
$101$	5.25457			0.522849			0.261425	+	0.965224i	$0.415808\pi$
$102$	−10.8109	−	3.58543i	−1.07044	−	0.355011i
$103$	1.66621			0.164176			0.0820882	−	0.996625i	$-0.473841\pi$
$103$	1.66621			0.164176			0.0820882	+	0.996625i	$0.473841\pi$
$104$	−1.34981	−	2.33795i	−0.132360	−	0.229255i
$105$	−12.2491	+	11.7215i	−1.19539	+	1.14390i
$106$	−1.60507	+	2.78007i	−0.155899	+	0.270024i
$107$	−5.38255	+	9.32284i	−0.520350	+	0.901273i	0.479370	+	0.877613i	$0.340865\pi$
$107$	−5.38255	+	9.32284i	−0.520350	+	0.901273i	−0.999720	+	0.0236602i	$0.992468\pi$
$108$	−5.17673	+	0.448873i	−0.498131	+	0.0431929i
$109$	−0.0945538	−	0.163772i	−0.00905662	−	0.0156865i	0.861462	−	0.507823i	$-0.169550\pi$
$109$	−0.0945538	−	0.163772i	−0.00905662	−	0.0156865i	−0.870518	+	0.492136i	$0.836216\pi$
$110$	2.73236	+	4.73259i	0.260520	+	0.451234i
$111$	4.56615	+	1.51436i	0.433400	+	0.143737i
$112$	−1.23855	+	2.33795i	−0.117032	+	0.220915i
$113$	−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	$-0.386896\pi$
$114$	−0.310892	−	1.50761i	−0.0291177	−	0.141201i
$115$	23.2632			2.16931
$116$	1.25526	+	2.17417i	0.116548	+	0.201867i
$117$	6.49381	+	4.83967i	0.600353	+	0.447427i
$118$	6.90978			0.636097
$119$	8.14468	−	15.3743i	0.746622	−	1.40936i
$120$	−1.29418	−	6.27589i	−0.118142	−	0.572908i
$121$	−8.81818			−0.801652
$122$	2.86652	−	4.96497i	0.259523	−	0.449507i
$123$	−5.32072	+	4.73259i	−0.479754	+	0.426723i
$124$	−3.40545	−	5.89841i	−0.305818	−	0.529692i
$125$	13.6414			1.22013
$126$	0.637806	−	7.91159i	0.0568203	−	0.704820i
$127$	−2.85669			−0.253490			−0.126745	−	0.991935i	$-0.540453\pi$
$127$	−2.85669			−0.253490			−0.126745	+	0.991935i	$0.540453\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−0.0203522	−	0.00674980i	−0.00179191	−	0.000594287i
$130$	−4.99381	+	8.64953i	−0.437986	+	0.758614i
$131$	0.155687			0.0136024			0.00680122	−	0.999977i	$-0.497835\pi$
$131$	0.155687			0.0136024			0.00680122	+	0.999977i	$0.497835\pi$
$132$	−2.42835	−	0.805361i	−0.211360	−	0.0700977i
$133$	2.34981	−	0.0856364i	0.203755	−	0.00742562i
$134$	−9.46472			−0.817627
$135$	11.0142	+	15.7558i	0.947948	+	1.35604i
$136$	3.28799	+	5.69497i	0.281943	+	0.488340i
$137$	−3.41164			−0.291476			−0.145738	−	0.989323i	$-0.546556\pi$
$137$	−3.41164			−0.291476			−0.145738	+	0.989323i	$0.546556\pi$
$138$	−8.13781	+	7.23828i	−0.692736	+	0.616163i
$139$	−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	$-0.360877\pi$
$140$	9.78180	−	0.356487i	0.826713	−	0.0301287i
$141$	9.04325	−	8.04364i	0.761579	−	0.677396i
$142$	2.73236	+	4.73259i	0.229295	+	0.397150i
$143$	1.99381	+	3.45338i	0.166731	+	0.288786i
$144$	2.40545	+	1.79272i	0.200454	+	0.149393i
$145$	4.64400	−	8.04364i	0.385663	−	0.667988i
$146$	−6.03273	+	10.4490i	−0.499272	+	0.864765i
$147$	11.7553	+	2.96881i	0.969558	+	0.244864i
$148$	−1.38874	−	2.40536i	−0.114153	−	0.197719i
$149$	0.333792			0.0273453			0.0136727	−	0.999907i	$-0.495648\pi$
$149$	0.333792			0.0273453			0.0136727	+	0.999907i	$0.495648\pi$
$150$	−11.2429	+	10.0001i	−0.917977	+	0.816507i
$151$	−19.9098			−1.62023			−0.810117	−	0.586268i	$-0.800597\pi$
$151$	−19.9098			−1.62023			−0.810117	+	0.586268i	$0.800597\pi$
$152$	−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
$156$	−0.944368	−	4.57954i	−0.0756099	−	0.366656i
$157$	3.48143	−	6.03001i	0.277848	−	0.481248i	−0.693001	−	0.720936i	$-0.743712\pi$
$157$	3.48143	−	6.03001i	0.277848	−	0.481248i	0.970850	+	0.239689i	$0.0770454\pi$
$158$	−5.72617	+	9.91802i	−0.455550	+	0.789035i
$159$	−4.15452	+	3.69529i	−0.329475	+	0.293055i
$160$	−1.84981	+	3.20397i	−0.146241	+	0.253296i
$161$	−8.83743	−	14.0951i	−0.696487	−	1.11085i
$162$	−8.75526	−	2.08457i	−0.687878	−	0.163779i
$163$	4.03706	−	6.99240i	0.316207	−	0.547687i	−0.663486	−	0.748189i	$-0.730924\pi$
$163$	4.03706	−	6.99240i	0.316207	−	0.547687i	0.979693	+	0.200502i	$0.0642572\pi$
$164$	4.11126			0.321036
$165$	1.91164	+	9.27012i	0.148821	+	0.721678i
$166$	−4.47710			−0.347490
$167$	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	$0.561491\pi$
$168$	−3.31089	+	3.16828i	−0.255441	+	0.244438i
$169$	2.85600	−	4.94674i	0.219693	−	0.380519i
$170$	12.1643	−	21.0693i	0.932963	−	1.61594i
$171$	0.310892	−	2.64802i	0.0237745	−	0.202499i
$172$	0.00618986	+	0.0107211i	0.000471972	+	0.000817480i
$173$	−11.2818	−	19.5407i	−0.857740	−	1.48565i	−0.874080	−	0.485782i	$-0.838535\pi$
$173$	−11.2818	−	19.5407i	−0.857740	−	1.48565i	0.0163405	−	0.999866i	$-0.494798\pi$
$174$	0.878215	+	4.25874i	0.0665773	+	0.322854i
$175$	−12.2095	−	19.4732i	−0.922948	−	1.47204i
$176$	0.738550	+	1.27921i	0.0556703	+	0.0964238i
$177$	11.3596	+	3.76742i	0.853843	+	0.283177i
$178$	8.87636			0.665311
$179$	0.166896	+	0.289073i	0.0124744	+	0.0216063i	0.872195	−	0.489158i	$-0.162696\pi$
$179$	0.166896	+	0.289073i	0.0124744	+	0.0216063i	−0.859721	+	0.510764i	$0.829363\pi$
$180$	1.29418	−	11.0232i	0.0964626	−	0.821619i
$181$	23.2422			1.72758			0.863789	−	0.503853i	$-0.168085\pi$
$181$	23.2422			1.72758			0.863789	+	0.503853i	$0.168085\pi$
$182$	7.13781	−	0.260130i	0.529089	−	0.0192821i
$183$	7.41961	−	6.59947i	0.548473	−	0.487847i
$184$	6.28799			0.463557
$185$	−5.13781	+	8.89894i	−0.377739	+	0.654263i
$186$	−2.38255	−	11.5537i	−0.174697	−	0.847159i
$187$	−4.85669	−	8.41204i	−0.355157	−	0.615149i
$188$	−6.98762			−0.509625
$189$	5.36219	−	12.6589i	0.390042	−	0.920797i
$190$	3.28799			0.238536
$191$	8.16071	+	14.1348i	0.590488	+	1.02276i	0.994167	+	0.107854i	$0.0343980\pi$
$191$	8.16071	+	14.1348i	0.590488	+	1.02276i	−0.403679	+	0.914901i	$0.632269\pi$
$192$	−0.349814	−	1.69636i	−0.0252457	−	0.122424i
$193$	7.16071	−	12.4027i	0.515439	−	0.892766i	−0.484400	−	0.874846i	$-0.660962\pi$
$193$	7.16071	−	12.4027i	0.515439	−	0.892766i	0.999839	−	0.0179200i	$-0.00570443\pi$
$194$	13.1767			0.946034
$195$	−12.9258	+	11.4970i	−0.925636	+	0.823319i
$196$	−3.93199	−	5.79133i	−0.280856	−	0.413666i
$197$	2.42402			0.172704			0.0863520	−	0.996265i	$-0.472479\pi$
$197$	2.42402			0.172704			0.0863520	+	0.996265i	$0.472479\pi$
$198$	−3.55308	−	2.64802i	−0.252507	−	0.188187i
$199$	−3.05563	−	5.29251i	−0.216608	−	0.375176i	0.737161	−	0.675717i	$-0.236166\pi$
$199$	−3.05563	−	5.29251i	−0.216608	−	0.375176i	−0.953769	+	0.300541i	$0.902833\pi$
$200$	8.68725			0.614281
$201$	−15.5600	−	5.16046i	−1.09752	−	0.363991i
$202$	−2.62729	−	4.55059i	−0.184855	−	0.320179i
$203$	−6.63781	+	0.241908i	−0.465883	+	0.0169786i
$204$	2.30037	+	11.1552i	0.161058	+	0.781022i
$205$	−7.60507	−	13.1724i	−0.531161	−	0.919999i
$206$	−0.833104	−	1.44298i	−0.0580451	−	0.100537i
$207$	−17.3251	+	7.46271i	−1.20417	+	0.518694i
$208$	−1.34981	+	2.33795i	−0.0935928	+	0.162107i
$209$	0.656376	−	1.13688i	0.0454025	−	0.0786394i
$210$	16.2756	+	4.74728i	1.12312	+	0.327593i
$211$	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	$0.704440\pi$
$212$	3.21015			0.220474
$213$	1.91164	+	9.27012i	0.130983	+	0.635178i
$214$	10.7651			0.735887
$215$	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
$219$	−15.6149	+	13.8889i	−1.05516	+	0.938523i
$220$	2.73236	−	4.73259i	0.184216	−	0.319071i
$221$	8.87636	−	15.3743i	0.597088	−	1.03419i
$222$	−0.971599	−	4.71159i	−0.0652094	−	0.316221i
$223$	−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
$227$	13.6552			0.906328			0.453164	−	0.891427i	$-0.350295\pi$
$227$	13.6552			0.906328			0.453164	+	0.891427i	$0.350295\pi$
$228$	−1.15019	+	1.02305i	−0.0761729	+	0.0677530i
$229$	17.3745			1.14814			0.574070	−	0.818807i	$-0.305364\pi$
$229$	17.3745			1.14814			0.574070	+	0.818807i	$0.305364\pi$
$230$	−11.6316	−	20.1466i	−0.766966	−	1.32842i
$231$	4.89052	−	4.67986i	0.321772	−	0.307912i
$232$	1.25526	−	2.17417i	0.0824119	−	0.142742i
$233$	7.62110	−	13.2001i	0.499275	−	0.864769i	−0.500725	−	0.865606i	$-0.666933\pi$
$233$	7.62110	−	13.2001i	0.499275	−	0.864769i	1.00000		0.000837426i	$0.000266561\pi$
$234$	0.944368	−	8.04364i	0.0617353	−	0.525829i
$235$	12.9258	+	22.3881i	0.843186	+	1.46044i
$236$	−3.45489	−	5.98404i	−0.224894	−	0.389528i
$237$	−14.8214	+	13.1831i	−0.962754	+	0.856334i
$238$	−17.3869	+	0.633646i	−1.12702	+	0.0410732i
$239$	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	$0.623335\pi$
$240$	−4.78799	+	4.25874i	−0.309064	+	0.274901i
$241$	−24.5054			−1.57853			−0.789267	−	0.614051i	$-0.789539\pi$
$241$	−24.5054			−1.57853			−0.789267	+	0.614051i	$0.789539\pi$
$242$	4.40909	+	7.63676i	0.283427	+	0.490910i
$243$	−13.2570	−	8.20066i	−0.850440	−	0.526073i
$244$	−5.73305			−0.367021
$245$	−11.2818	+	23.3109i	−0.720768	+	1.48928i
$246$	6.75890	+	2.24159i	0.430932	+	0.142918i
$247$	2.39926			0.152661
$248$	−3.40545	+	5.89841i	−0.216246	+	0.374549i
$249$	−7.36033	−	2.44105i	−0.466442	−	0.154696i
$250$	−6.82072	−	11.8138i	−0.431380	−	0.747173i
$251$	−12.1236			−0.765238			−0.382619	−	0.923906i	$-0.624978\pi$
$251$	−12.1236			−0.765238			−0.382619	+	0.923906i	$0.624978\pi$
$252$	−7.17054	+	3.40344i	−0.451701	+	0.214396i
$253$	−9.28799			−0.583931
$254$	1.42835	+	2.47397i	0.0896224	+	0.155231i
$255$	31.4858	−	28.0054i	1.97171	−	1.75377i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−8.20877			−0.512049			−0.256025	−	0.966670i	$-0.582413\pi$
$257$	−8.20877			−0.512049			−0.256025	+	0.966670i	$0.582413\pi$
$258$	0.00433060	+	0.0210004i	0.000269611	+	0.00130743i
$259$	7.34362	−	0.267630i	0.456311	−	0.0166297i
$260$	9.98762			0.619406
$261$	−0.878215	+	7.48018i	−0.0543602	+	0.463012i
$262$	−0.0778435	−	0.134829i	−0.00480919	−	0.00832976i
$263$	−5.34617			−0.329659			−0.164830	−	0.986322i	$-0.552707\pi$
$263$	−5.34617			−0.329659			−0.164830	+	0.986322i	$0.552707\pi$
$264$	0.516710	+	2.50569i	0.0318013	+	0.154215i
$265$	−5.93818	−	10.2852i	−0.364779	−	0.631816i
$266$	−1.24907	−	1.99218i	−0.0765854	−	0.122148i
$267$	14.5927	+	4.83967i	0.893058	+	0.296183i
$268$	4.73236	+	8.19669i	0.289075	+	0.500692i
$269$	9.24219	+	16.0079i	0.563506	+	0.976022i	0.997187	+	0.0749550i	$0.0238813\pi$
$269$	9.24219	+	16.0079i	0.563506	+	0.976022i	−0.433681	+	0.901067i	$0.642785\pi$
$270$	8.13781	−	17.4164i	0.495251	−	1.05993i
$271$	−3.67742	+	6.36947i	−0.223387	+	0.386918i	−0.955834	−	0.293906i	$-0.905045\pi$
$271$	−3.67742	+	6.36947i	−0.223387	+	0.386918i	0.732447	+	0.680824i	$0.238378\pi$
$272$	3.28799	−	5.69497i	0.199364	−	0.345308i
$273$	11.8764	+	3.46410i	0.718790	+	0.209657i
$274$	1.70582	+	2.95456i	0.103052	+	0.178492i
$275$	−12.8319			−0.773795
$276$	10.3374	+	3.42841i	0.622240	+	0.206366i
$277$	−9.09888			−0.546699			−0.273349	−	0.961915i	$-0.588132\pi$
$277$	−9.09888			−0.546699			−0.273349	+	0.961915i	$0.588132\pi$
$278$	−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	$0.0500612\pi$
$282$	−11.4876	−	3.80987i	−0.684078	−	0.226874i
$283$	−4.92147	+	8.52423i	−0.292551	+	0.506713i	−0.974412	−	0.224768i	$-0.927837\pi$
$283$	−4.92147	+	8.52423i	−0.292551	+	0.506713i	0.681861	+	0.731481i	$0.261171\pi$
$284$	2.73236	−	4.73259i	0.162136	−	0.280827i
$285$	5.40545	+	1.79272i	0.320191	+	0.106191i
$286$	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
$290$	−9.28799			−0.545410
$291$	21.6625	+	7.18436i	1.26988	+	0.421155i
$292$	12.0655			0.706078
$293$	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	$0.618149\pi$
$294$	−3.30656	−	11.6648i	−0.192843	−	0.680303i
$295$	−12.7818	+	22.1387i	−0.744185	+	1.28897i
$296$	−1.38874	+	2.40536i	−0.0807186	+	0.139809i
$297$	−4.39747	−	6.29059i	−0.255167	−	0.365017i
$298$	−0.166896	−	0.289073i	−0.00966804	−	0.0167455i
$299$	−8.48762	−	14.7010i	−0.490852	−	0.850180i
$300$	14.2818	+	4.73656i	0.824560	+	0.273465i
$301$	−0.0327319	+	0.00119288i	−0.00188664	+	6.87564e-5i
$302$	9.95489	+	17.2424i	0.572839	+	0.992187i
$303$	−1.83812	−	8.91363i	−0.105597	−	0.512075i
$304$	0.888736			0.0509725
$305$	10.6051	+	18.3685i	0.607245	+	1.05178i
$306$	−2.30037	+	19.5934i	−0.131504	+	1.12008i
$307$	−5.68725			−0.324588			−0.162294	−	0.986742i	$-0.551889\pi$
$307$	−5.68725			−0.324588			−0.162294	+	0.986742i	$0.551889\pi$
$308$	−3.90545	+	0.142330i	−0.222533	+	0.00810999i
$309$	−0.582863	−	2.82648i	−0.0331579	−	0.160793i
$310$	25.1978			1.43114
$311$	5.86033	−	10.1504i	0.332309	−	0.575576i	−0.650655	−	0.759373i	$-0.725506\pi$
$311$	5.86033	−	10.1504i	0.332309	−	0.575576i	0.982964	+	0.183797i	$0.0588390\pi$
$312$	−3.49381	+	3.10761i	−0.197798	+	0.175934i
$313$	13.3869	+	23.1868i	0.756671	+	1.31059i	0.944539	+	0.328398i	$0.106509\pi$
$313$	13.3869	+	23.1868i	0.756671	+	1.31059i	−0.187868	+	0.982194i	$0.560158\pi$
$314$	−6.96286			−0.392937
$315$	24.1687	+	16.6785i	1.36175	+	0.939726i
$316$	11.4523			0.644244
$317$	−0.951246	−	1.64761i	−0.0534273	−	0.0925388i	0.838075	−	0.545555i	$-0.183681\pi$
$317$	−0.951246	−	1.64761i	−0.0534273	−	0.0925388i	−0.891502	+	0.453016i	$0.850348\pi$
$318$	5.27747	+	1.75027i	0.295946	+	0.0981504i
$319$	−1.85414	+	3.21147i	−0.103812	+	0.179808i
$320$	3.69963			0.206816
$321$	17.6978	+	5.86946i	0.987793	+	0.327601i
$322$	−7.78799	+	14.7010i	−0.434008	+	0.819254i
$323$	−5.84431			−0.325186
$324$	2.57234	+	8.62456i	0.142908	+	0.479142i
$325$	−11.7262	−	20.3103i	−0.650451	−	1.12661i
$326$	−8.07413			−0.447184
$327$	−0.244740	+	0.217687i	−0.0135341	+	0.0120381i
$328$	−2.05563	−	3.56046i	−0.113503	−	0.196593i
$329$	8.65452	−	16.3367i	0.477139	−	0.900670i
$330$	7.07234	−	6.29059i	0.389320	−	0.346285i
$331$	−2.78366	−	4.82144i	−0.153004	−	0.265010i	0.779327	−	0.626618i	$-0.215561\pi$
$331$	−2.78366	−	4.82144i	−0.153004	−	0.265010i	−0.932330	+	0.361608i	$0.882228\pi$
$332$	2.23855	+	3.87728i	0.122856	+	0.212794i
$333$	0.971599	−	8.27557i	0.0532433	−	0.453499i
$334$	9.74288	−	16.8752i	0.533107	−	0.923368i
$335$	17.5080	−	30.3247i	0.956563	−	1.65682i
$336$	4.39926	+	1.28318i	0.239999	+	0.0700031i
$337$	−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	$-0.538386\pi$
$338$	−5.71201			−0.310692
$339$	−17.5538	+	15.6134i	−0.953390	+	0.848005i
$340$	−24.3287			−1.31941
$341$	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
$345$	−8.13781	−	39.4628i	−0.438125	−	2.12460i
$346$	−11.2818	+	19.5407i	−0.606513	+	1.05051i
$347$	15.2033	−	26.3328i	0.816154	−	1.41362i	−0.0923418	−	0.995727i	$-0.529435\pi$
$347$	15.2033	−	26.3328i	0.816154	−	1.41362i	0.908496	−	0.417893i	$-0.137231\pi$
$348$	3.24907	−	2.88993i	0.174168	−	0.154916i
$349$	−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
$353$	−7.53156			−0.400865			−0.200432	−	0.979708i	$-0.564235\pi$
$353$	−7.53156			−0.400865			−0.200432	+	0.979708i	$0.564235\pi$
$354$	−2.41714	−	11.7215i	−0.128469	−	0.622988i
$355$	−20.2174			−1.07303
$356$	−4.43818	−	7.68715i	−0.235223	−	0.407418i
$357$	−28.9294	−	8.43815i	−1.53111	−	0.446594i
$358$	0.166896	−	0.289073i	0.00882074	−	0.0152780i
$359$	−3.44801	+	5.97213i	−0.181979	+	0.315197i	−0.942554	−	0.334053i	$-0.891584\pi$
$359$	−3.44801	+	5.97213i	−0.181979	+	0.315197i	0.760575	+	0.649250i	$0.224917\pi$
$360$	−10.1934	+	4.39079i	−0.537241	+	0.231415i
$361$	9.10507	+	15.7705i	0.479214	+	0.830024i
$362$	−11.6211	−	20.1283i	−0.610791	−	1.05792i
$363$	3.08472	+	14.9588i	0.161906	+	0.785132i
$364$	−3.79418	−	6.05146i	−0.198869	−	0.317183i
$365$	−22.3189	−	38.6574i	−1.16822	−	2.02342i
$366$	−9.42511	−	3.12584i	−0.492658	−	0.163390i
$367$	23.1236			1.20704			0.603522	−	0.797346i	$-0.293763\pi$
$367$	23.1236			1.20704			0.603522	+	0.797346i	$0.293763\pi$
$368$	−3.14400	−	5.44556i	−0.163892	−	0.283869i
$369$	9.88942	+	7.37033i	0.514823	+	0.383684i
$370$	10.2756			0.534204
$371$	−3.97593	+	7.50516i	−0.206420	+	0.389648i
$372$	−8.81453	+	7.84020i	−0.457012	+	0.406495i
$373$	29.1643			1.51007			0.755036	−	0.655683i	$-0.227619\pi$
$373$	29.1643			1.51007			0.755036	+	0.655683i	$0.227619\pi$
$374$	−4.85669	+	8.41204i	−0.251134	+	0.434976i
$375$	−4.77197	−	23.1408i	−0.246423	−	1.19498i
$376$	3.49381	+	6.05146i	0.180180	+	0.312080i
$377$	−6.77747			−0.349058
$378$	−13.6440	+	1.68564i	−0.701771	+	0.0866998i
$379$	−13.5622			−0.696645			−0.348322	−	0.937375i	$-0.613249\pi$
$379$	−13.5622			−0.696645			−0.348322	+	0.937375i	$0.613249\pi$
$380$	−1.64400	−	2.84748i	−0.0843352	−	0.146073i
$381$	0.999311	+	4.84597i	0.0511963	+	0.248267i
$382$	8.16071	−	14.1348i	0.417538	−	0.723197i
$383$	−2.83565			−0.144895			−0.0724475	−	0.997372i	$-0.523081\pi$
$383$	−2.83565			−0.144895			−0.0724475	+	0.997372i	$0.523081\pi$
$384$	−1.29418	+	1.15113i	−0.0660434	+	0.0587432i
$385$	7.68037	+	12.2497i	0.391428	+	0.624300i
$386$	−14.3214			−0.728941
$387$	−0.00433060	+	0.0368858i	−0.000220137	+	0.00187501i
$388$	−6.58836	−	11.4114i	−0.334474	−	0.579325i
$389$	−18.6080			−0.943464			−0.471732	−	0.881742i	$-0.656371\pi$
$389$	−18.6080			−0.943464			−0.471732	+	0.881742i	$0.656371\pi$
$390$	16.4196	+	5.44556i	0.831439	+	0.275747i
$391$	20.6749	+	35.8099i	1.04557	+	1.81099i
$392$	−3.04944	+	6.30087i	−0.154020	+	0.318242i
$393$	−0.0544615	−	0.264101i	−0.00274722	−	0.0133221i
$394$	−1.21201	−	2.09926i	−0.0610601	−	0.105759i
$395$	−21.1847	−	36.6930i	−1.06592	−	1.84622i
$396$	−0.516710	+	4.40107i	−0.0259657	+	0.221162i
$397$	−10.2880	+	17.8193i	−0.516340	+	0.894326i	0.483481	+	0.875355i	$0.339372\pi$
$397$	−10.2880	+	17.8193i	−0.516340	+	0.894326i	−0.999820	+	0.0189712i	$0.993961\pi$
$398$	−3.05563	+	5.29251i	−0.153165	+	0.265290i
$399$	−0.967268	−	3.95617i	−0.0484240	−	0.198056i
$400$	−4.34362	−	7.52338i	−0.217181	−	0.376169i
$401$	−6.75409			−0.337283			−0.168642	−	0.985677i	$-0.553938\pi$
$401$	−6.75409			−0.337283			−0.168642	+	0.985677i	$0.553938\pi$
$402$	3.31089	+	16.0556i	0.165132	+	0.800778i
$403$	18.3869			0.915916
$404$	−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
$408$	8.51052	−	7.56979i	0.421334	−	0.374761i
$409$	−7.66071	+	13.2687i	−0.378798	+	0.656097i	−0.990888	−	0.134691i	$-0.956996\pi$
$409$	−7.66071	+	13.2687i	−0.378798	+	0.656097i	0.612090	+	0.790788i	$0.290329\pi$
$410$	−7.60507	+	13.1724i	−0.375588	+	0.650537i
$411$	1.19344	+	5.78736i	0.0588680	+	0.285469i
$412$	−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
$416$	2.69963			0.132360
$417$	−17.4851	+	15.5523i	−0.856248	+	0.761601i
$418$	−1.31275			−0.0642088
$419$	−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	$0.901043\pi$
$420$	−4.02654	−	16.4687i	−0.196475	−	0.803592i
$421$	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
$423$	−16.8083	−	12.5268i	−0.817250	−	0.609075i
$424$	−1.60507	−	2.78007i	−0.0779493	−	0.135012i
$425$	28.5636	+	49.4736i	1.38554	+	2.39982i
$426$	7.07234	−	6.29059i	0.342656	−	0.304780i
$427$	7.10067	−	13.4036i	0.343625	−	0.648644i
$428$	−5.38255	−	9.32284i	−0.260175	−	0.450637i
$429$	5.16071	−	4.59026i	0.249161	−	0.221620i
$430$	−0.0458003			−0.00220869
$431$	−4.71015	−	8.15822i	−0.226880	−	0.392967i	0.730002	−	0.683445i	$-0.239519\pi$
$431$	−4.71015	−	8.15822i	−0.226880	−	0.392967i	−0.956882	+	0.290478i	$0.906186\pi$
$432$	2.19963	−	4.70761i	0.105830	−	0.226495i
$433$	−0.208771			−0.0100329			−0.00501645	−	0.999987i	$-0.501597\pi$
$433$	−0.208771			−0.0100329			−0.00501645	+	0.999987i	$0.501597\pi$
$434$	−9.57234	−	15.2672i	−0.459487	−	0.732850i
$435$	−15.2694	−	5.06410i	−0.732113	−	0.242805i
$436$	0.189108			0.00905662
$437$	−2.79418	+	4.83967i	−0.133664	+	0.231513i
$438$	19.8356	+	6.57847i	0.947780	+	0.314331i
$439$	4.98398	+	8.63250i	0.237872	+	0.412007i	0.960104	−	0.279645i	$-0.0902167\pi$
$439$	4.98398	+	8.63250i	0.237872	+	0.412007i	−0.722231	+	0.691652i	$0.756883\pi$
$440$	−5.46472			−0.260520
$441$	0.924016	−	20.9797i	0.0440007	−	0.999031i
$442$	−17.7527			−0.844410
$443$	7.84981	+	13.5963i	0.372956	+	0.645979i	0.990019	−	0.140935i	$-0.0450109\pi$
$443$	7.84981	+	13.5963i	0.372956	+	0.645979i	−0.617063	+	0.786914i	$0.711678\pi$
$444$	−3.59455	+	3.19722i	−0.170590	+	0.151733i
$445$	−16.4196	+	28.4396i	−0.778364	+	1.34817i
$446$	7.22253			0.341997
$447$	−0.116765	−	0.566231i	−0.00552281	−	0.0267818i
$448$	−1.40545	−	2.24159i	−0.0664011	−	0.105905i
$449$	33.6253			1.58688			0.793439	−	0.608650i	$-0.208288\pi$
$449$	33.6253			1.58688			0.793439	+	0.608650i	$0.208288\pi$
$450$	20.8967	+	15.5738i	0.985080	+	0.734154i
$451$	3.03637	+	5.25915i	0.142977	+	0.247644i
$452$	13.5636			0.637978
$453$	6.96472	+	33.7741i	0.327231	+	1.58685i
$454$	−6.82760	−	11.8258i	−0.320435	−	0.555010i
$455$	−12.3702	+	23.3505i	−0.579922	+	1.09469i
$456$	1.46108	+	0.484566i	0.0684213	+	0.0226919i
$457$	−16.3541	−	28.3262i	−0.765015	−	1.32504i	−0.940239	−	0.340516i	$-0.889398\pi$
$457$	−16.3541	−	28.3262i	−0.765015	−	1.32504i	0.175224	−	0.984529i	$-0.443935\pi$
$458$	−8.68725	−	15.0468i	−0.405928	−	0.703089i
$459$	−14.4647	+	30.9572i	−0.675155	+	1.44496i
$460$	−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	$0.197427\pi$
$462$	−6.49814	−	1.89538i	−0.302321	−	0.0881811i
$463$	−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	$0.960055\pi$
$464$	−2.51052			−0.116548
$465$	41.4250	+	13.7386i	1.92104	+	0.637113i
$466$	−15.2422			−0.706081
$467$	14.9585	−	25.9089i	0.692198	−	1.19892i	−0.278918	−	0.960315i	$-0.589976\pi$
$467$	14.9585	−	25.9089i	0.692198	−	1.19892i	0.971116	−	0.238608i	$-0.0766909\pi$
$468$	−7.43818	+	3.20397i	−0.343830	+	0.148104i
$469$	−25.0247	+	0.911998i	−1.15553	+	0.0421121i
$470$	12.9258	−	22.3881i	0.596223	−	1.03269i
$471$	−11.4469	−	3.79637i	−0.527446	−	0.174927i
$472$	−3.45489	+	5.98404i	−0.159024	+	0.275438i
$473$	−0.00914304	+	0.0158362i	−0.000420397	+	0.000728149i
$474$	18.8276	+	6.24417i	0.864780	+	0.286804i
$475$	−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
$479$	−2.95930			−0.135214			−0.0676068	−	0.997712i	$-0.521536\pi$
$479$	−2.95930			−0.135214			−0.0676068	+	0.997712i	$0.521536\pi$
$480$	6.08217	+	2.01715i	0.277612	+	0.0920700i
$481$	7.49814			0.341886
$482$	12.2527	+	21.2223i	0.558096	+	0.966650i
$483$	−20.8189	+	19.9221i	−0.947291	+	0.906488i
$484$	4.40909	−	7.63676i	0.200413	−	0.347126i
$485$	−24.3745	+	42.2179i	−1.10679	+	1.91701i
$486$	−0.473458	+	15.5813i	−0.0214765	+	0.706781i
$487$	−14.0309	−	24.3022i	−0.635800	−	1.10124i	−0.986345	−	0.164691i	$-0.947337\pi$
$487$	−14.0309	−	24.3022i	−0.635800	−	1.10124i	0.350546	−	0.936546i	$-0.385996\pi$
$488$	2.86652	+	4.96497i	0.129761	+	0.224753i
$489$	−13.2738	−	4.40226i	−0.600263	−	0.199077i
$490$	25.8287	−	1.88510i	1.16682	−	0.0851602i
$491$	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	$0.553333\pi$
$492$	−1.43818	−	6.97418i	−0.0648381	−	0.314420i
$493$	16.5091			0.743534
$494$	−1.19963	−	2.07782i	−0.0539738	−	0.0934854i
$495$	15.0567	−	6.48564i	0.676750	−	0.291508i
$496$	6.81089			0.305818
$497$	7.68037	+	12.2497i	0.344512	+	0.549472i
$498$	1.56615	+	7.59476i	0.0701810	+	0.340329i
$499$	−2.28071			−0.102099			−0.0510493	−	0.998696i	$-0.516257\pi$
$499$	−2.28071			−0.102099			−0.0510493	+	0.998696i	$0.516257\pi$
$500$	−6.82072	+	11.8138i	−0.305032	+	0.528331i
$501$	25.2181	−	22.4306i	1.12666	−	1.00212i
$502$	6.06182	+	10.4994i	0.270552	+	0.468610i
$503$	13.9890			0.623739			0.311869	−	0.950125i	$-0.399045\pi$
$503$	13.9890			0.623739			0.311869	+	0.950125i	$0.399045\pi$
$504$	6.53273	+	4.50815i	0.290991	+	0.200809i
$505$	19.4400			0.865067
$506$	4.64400	+	8.04364i	0.206451	+	0.357583i
$507$	−9.39052	−	3.11436i	−0.417048	−	0.138314i
$508$	1.42835	−	2.47397i	0.0633726	−	0.109765i
$509$	25.6181			1.13550			0.567750	−	0.823201i	$-0.307814\pi$
$509$	25.6181			1.13550			0.567750	+	0.823201i	$0.307814\pi$
$510$	−39.9963	−	13.2648i	−1.77107	−	0.587374i
$511$	−14.9437	+	28.2084i	−0.661069	+	1.24787i
$512$	1.00000			0.0441942
$513$	−4.60074	+	0.398930i	−0.203128	+	0.0176132i
$514$	4.10439	+	7.10900i	0.181037	+	0.313565i
$515$	6.16435			0.271634
$516$	0.0160216	−	0.0142506i	0.000705312	−	0.000627349i
$517$	−5.16071	−	8.93861i	−0.226968	−	0.393119i
$518$	−3.90359	−	6.22595i	−0.171514	−	0.273553i
$519$	−29.2014	+	25.9736i	−1.28180	+	1.14011i
$520$	−4.99381	−	8.64953i	−0.218993	−	0.379307i
$521$	−20.9127	−	36.2219i	−0.916203	−	1.58691i	−0.805130	−	0.593099i	$-0.797904\pi$
$521$	−20.9127	−	36.2219i	−0.916203	−	1.58691i	−0.111073	−	0.993812i	$-0.535429\pi$
$522$	6.91714	−	2.97954i	0.302755	−	0.130411i
$523$	7.88323	−	13.6542i	0.344710	−	0.597055i	−0.640591	−	0.767882i	$-0.721311\pi$
$523$	7.88323	−	13.6542i	0.344710	−	0.597055i	0.985301	+	0.170827i	$0.0546440\pi$
$524$	−0.0778435	+	0.134829i	−0.00340061	+	0.00589003i
$525$	−28.7625	+	27.5236i	−1.25530	+	1.20123i
$526$	2.67309	+	4.62992i	0.116552	+	0.201874i
$527$	−44.7883			−1.95101
$528$	1.91164	−	1.70033i	0.0831933	−	0.0739973i
$529$	16.5388			0.719080
$530$	−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
$534$	−3.10507	−	15.0575i	−0.134370	−	0.651601i
$535$	−19.9134	+	34.4911i	−0.860932	+	1.49118i
$536$	4.73236	−	8.19669i	0.204407	−	0.354043i
$537$	0.431988	−	0.384237i	0.0186417	−	0.0165811i
$538$	9.24219	−	16.0079i	0.398459	−	0.690152i
$539$	4.50433	−	9.30701i	0.194015	−	0.400881i
$540$	−19.1520	+	1.66066i	−0.824170	+	0.0714636i
$541$	−21.0963	+	36.5399i	−0.907002	+	1.57097i	−0.0887957	+	0.996050i	$0.528302\pi$
$541$	−21.0963	+	36.5399i	−0.907002	+	1.57097i	−0.818207	+	0.574924i	$0.805031\pi$
$542$	7.35483			0.315917
$543$	−8.13045	−	39.4271i	−0.348911	−	1.69198i
$544$	−6.57598			−0.281943
$545$	−0.349814	−	0.605896i	−0.0149844	−	0.0259537i
$546$	−2.93818	−	12.0173i	−0.125742	−	0.514292i
$547$	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
$549$	−13.7905	−	10.2777i	−0.588566	−	0.438643i
$550$	6.41597	+	11.1128i	0.273578	+	0.473851i
$551$	1.11559	+	1.93227i	0.0475259	+	0.0823173i
$552$	−2.19963	−	10.6667i	−0.0936224	−	0.454004i
$553$	−14.1843	+	26.7750i	−0.603178	+	1.13859i
$554$	4.54944	+	7.87987i	0.193287	+	0.334783i
$555$	16.8931	+	5.60258i	0.717071	+	0.237816i
$556$	13.5105			0.572974
$557$	6.68794	+	11.5838i	0.283377	+	0.490823i	0.972214	−	0.234093i	$-0.0752119\pi$
$557$	6.68794	+	11.5838i	0.283377	+	0.490823i	−0.688837	+	0.724916i	$0.741879\pi$
$558$	−18.7658	+	8.08330i	−0.794419	+	0.342193i
$559$	−0.0334206			−0.00141354
$560$	−4.58217	+	8.64953i	−0.193632	+	0.365509i
$561$	−12.5709	+	11.1813i	−0.530743	+	0.472076i
$562$	−12.0087			−0.506555
$563$	16.3807	−	28.3722i	0.690364	−	1.19574i	−0.281355	−	0.959604i	$-0.590784\pi$
$563$	16.3807	−	28.3722i	0.690364	−	1.19574i	0.971719	−	0.236141i	$-0.0758828\pi$
$564$	2.44437	+	11.8535i	0.102926	+	0.499123i
$565$	−25.0901	−	43.4574i	−1.05555	−	1.82827i
$566$	9.84294			0.413729
$567$	−23.3497	−	4.66795i	−0.980597	−	0.196035i
$568$	−5.46472			−0.229295
$569$	8.36398	+	14.4868i	0.350636	+	0.607320i	0.986361	−	0.164596i	$-0.0526321\pi$
$569$	8.36398	+	14.4868i	0.350636	+	0.607320i	−0.635725	+	0.771916i	$0.719299\pi$
$570$	−1.15019	−	5.57761i	−0.0481760	−	0.233620i
$571$	13.7367	−	23.7926i	0.574863	−	0.995691i	−0.421194	−	0.906971i	$-0.638389\pi$
$571$	13.7367	−	23.7926i	0.574863	−	0.995691i	0.996057	−	0.0887207i	$-0.0282778\pi$
$572$	−3.98762			−0.166731
$573$	21.1229	−	18.7880i	0.882421	−	0.784881i
$574$	10.8702	−	0.396151i	0.453712	−	0.0165350i
$575$	54.6253			2.27803
$576$	−2.75526	+	1.18682i	−0.114803	+	0.0494508i
$577$	1.41714	+	2.45455i	0.0589962	+	0.102184i	0.894015	−	0.448037i	$-0.147877\pi$
$577$	1.41714	+	2.45455i	0.0589962	+	0.102184i	−0.835019	+	0.550221i	$0.814543\pi$
$578$	26.2436			1.09159
$579$	−23.5443	−	7.80848i	−0.978470	−	0.324509i
$580$	4.64400	+	8.04364i	0.192831	+	0.333994i
$581$	−11.8374	+	0.431403i	−0.491100	+	0.0178976i
$582$	−4.60940	−	22.3524i	−0.191066	−	0.926539i
$583$	2.37085	+	4.10644i	0.0981908	+	0.170071i
$584$	−6.03273	−	10.4490i	−0.249636	−	0.432383i
$585$	24.0247	+	17.9050i	0.993298	+	0.740279i
$586$	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	$0.197563\pi$
$588$	−8.44870	+	8.69595i	−0.348418	+	0.358615i
$589$	−3.02654	−	5.24212i	−0.124706	−	0.215998i
$590$	25.5636			1.05244
$591$	−0.847955	−	4.11200i	−0.0348802	−	0.169145i
$592$	2.77747			0.114153
$593$	0.636024	−	1.10163i	0.0261184	−	0.0452383i	−0.852671	−	0.522449i	$-0.825019\pi$
$593$	0.636024	−	1.10163i	0.0261184	−	0.0452383i	0.878789	+	0.477210i	$0.158352\pi$
$594$	−3.24907	+	6.95362i	−0.133311	+	0.285310i
$595$	30.1323	−	56.8792i	1.23530	−	2.33182i
$596$	−0.166896	+	0.289073i	−0.00683634	+	0.0118409i
$597$	−7.90909	+	7.03484i	−0.323697	+	0.287917i
$598$	−8.48762	+	14.7010i	−0.347085	+	0.601168i
$599$	−21.9258	+	37.9766i	−0.895864	+	1.55168i	−0.0631320	+	0.998005i	$0.520109\pi$
$599$	−21.9258	+	37.9766i	−0.895864	+	1.55168i	−0.832732	+	0.553676i	$0.813224\pi$
$600$	−3.03892	−	14.7367i	−0.124063	−	0.601623i
$601$	−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
$605$	−32.6240			−1.32635
$606$	−6.80037	+	6.04868i	−0.276246	+	0.245711i
$607$	−4.58465			−0.186085			−0.0930425	−	0.995662i	$-0.529659\pi$
$607$	−4.58465			−0.186085			−0.0930425	+	0.995662i	$0.529659\pi$
$608$	−0.444368	−	0.769668i	−0.0180215	−	0.0312142i
$609$	2.73236	+	11.1755i	0.110721	+	0.452853i
$610$	10.6051	−	18.3685i	0.429387	−	0.743720i
$611$	9.43199	−	16.3367i	0.381577	−	0.660911i
$612$	18.1185	−	7.80451i	0.732399	−	0.315479i
$613$	−11.0538	−	19.1457i	−0.446458	−	0.773287i	0.551695	−	0.834046i	$-0.313981\pi$
$613$	−11.0538	−	19.1457i	−0.446458	−	0.773287i	−0.998152	+	0.0607587i	$0.980648\pi$
$614$	2.84362	+	4.92530i	0.114759	+	0.198769i
$615$	−19.6847	+	17.5088i	−0.793764	+	0.706023i
$616$	2.07598	+	3.31105i	0.0836438	+	0.133406i
$617$	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	$0.755620\pi$
$618$	−2.15638	+	1.91802i	−0.0867422	+	0.0771539i
$619$	−17.5636			−0.705941			−0.352970	−	0.935634i	$-0.614828\pi$
$619$	−17.5636			−0.705941			−0.352970	+	0.935634i	$0.614828\pi$
$620$	−12.5989	−	21.8219i	−0.505983	−	0.876389i
$621$	18.7200	+	26.7789i	0.751207	+	1.07460i
$622$	−11.7207			−0.469956
$623$	23.4691	−	0.855304i	0.940268	−	0.0342670i
$624$	4.43818	+	1.47192i	0.177669	+	0.0589240i
$625$	7.03204			0.281282
$626$	13.3869	−	23.1868i	0.535047	−	0.926729i
$627$	−2.15816	−	0.715753i	−0.0861885	−	0.0285844i
$628$	3.48143	+	6.03001i	0.138924	+	0.240624i
$629$	−18.2646			−0.728258
$630$	2.35965	−	29.2699i	0.0940105	−	1.16614i
$631$	−44.9381			−1.78896			−0.894479	−	0.447110i	$-0.852453\pi$
$631$	−44.9381			−1.78896			−0.894479	+	0.447110i	$0.852453\pi$
$632$	−5.72617	−	9.91802i	−0.227775	−	0.394518i
$633$	14.8120	−	13.1747i	0.588724	−	0.523648i
$634$	−0.951246	+	1.64761i	−0.0377788	+	0.0654348i
$635$	−10.5687			−0.419406
$636$	−1.12296	−	5.44556i	−0.0445281	−	0.215931i
$637$	18.8473	−	1.37556i	0.746756	−	0.0545018i
$638$	3.70829			0.146813
$639$	15.0567	−	6.48564i	0.595635	−	0.256568i
$640$	−1.84981	−	3.20397i	−0.0731203	−	0.126648i
$641$	−28.9839			−1.14480			−0.572398	−	0.819976i	$-0.693987\pi$
$641$	−28.9839			−1.14480			−0.572398	+	0.819976i	$0.693987\pi$
$642$	−3.76578	−	18.2614i	−0.148624	−	0.720722i
$643$	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	$0.756896\pi$
$644$	16.6254	−	0.605896i	0.655134	−	0.0238756i
$645$	−0.0752956	−	0.0249718i	−0.00296476	−	0.000983262i
$646$	2.92216	+	5.06132i	0.114971	+	0.199135i
$647$	18.8825	+	32.7055i	0.742349	+	1.28579i	0.951423	+	0.307887i	$0.0996219\pi$
$647$	18.8825	+	32.7055i	0.742349	+	1.28579i	−0.209073	+	0.977900i	$0.567045\pi$
$648$	6.18292	−	6.53999i	0.242888	−	0.256915i
$649$	5.10322	−	8.83903i	0.200319	−	0.346962i
$650$	−11.7262	+	20.3103i	−0.459938	+	0.796636i
$651$	−7.41273	−	30.3184i	−0.290528	−	1.18827i
$652$	4.03706	+	6.99240i	0.158104	+	0.273843i
$653$	37.4079			1.46388			0.731942	−	0.681366i	$-0.238614\pi$
$653$	37.4079			1.46388			0.731942	+	0.681366i	$0.238614\pi$
$654$	0.310892	+	0.103107i	0.0121569	+	0.00403182i
$655$	0.575984			0.0225056
$656$	−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	$-0.0309884\pi$
$660$	−8.98398	−	2.97954i	−0.349701	−	0.115978i
$661$	−2.80401	+	4.85669i	−0.109063	+	0.188904i	−0.915391	−	0.402566i	$-0.868119\pi$
$661$	−2.80401	+	4.85669i	−0.109063	+	0.188904i	0.806328	+	0.591469i	$0.201452\pi$
$662$	−2.78366	+	4.82144i	−0.108190	+	0.187391i
$663$	−29.1854	−	9.67933i	−1.13347	−	0.375914i
$664$	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
$668$	−19.4858			−0.753927
$669$	11.8738	+	3.93795i	0.459068	+	0.152250i
$670$	−35.0159			−1.35278
$671$	−4.23414	−	7.33375i	−0.163457	−	0.283116i
$672$	−1.08836	−	4.45146i	−0.0419846	−	0.171719i
$673$	−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
$675$	25.8628	+	36.9967i	0.995460	+	1.42401i
$676$	2.85600	+	4.94674i	0.109846	+	0.190259i
$677$	−5.53087	−	9.57975i	−0.212569	−	0.368180i	0.739949	−	0.672663i	$-0.234850\pi$
$677$	−5.53087	−	9.57975i	−0.212569	−	0.368180i	−0.952518	+	0.304483i	$0.901516\pi$
$678$	22.2985	+	7.39530i	0.856369	+	0.284015i
$679$	34.8392	−	1.26968i	1.33701	−	0.0487258i
$680$	12.1643	+	21.0693i	0.466481	+	0.807970i
$681$	−4.77678	−	23.1641i	−0.183047	−	0.887651i
$682$	−10.0604			−0.385231
$683$	−4.41961	−	7.65499i	−0.169112	−	0.292910i	0.768996	−	0.639253i	$-0.220757\pi$
$683$	−4.41961	−	7.65499i	−0.169112	−	0.292910i	−0.938108	+	0.346343i	$0.887423\pi$
$684$	2.13781	+	1.59325i	0.0817411	+	0.0609195i
$685$	−12.6218			−0.482254
$686$	−10.9542	−	14.9334i	−0.418233	−	0.570159i
$687$	−6.07784	−	29.4734i	−0.231884	−	1.12448i
$688$	−0.0123797			−0.000471972
$689$	−4.33310	+	7.50516i	−0.165078	+	0.285924i
$690$	−30.1069	+	26.7789i	−1.14615	+	1.01946i
$691$	−12.5309	−	21.7041i	−0.476697	−	0.825663i	0.522947	−	0.852365i	$-0.324833\pi$
$691$	−12.5309	−	21.7041i	−0.476697	−	0.825663i	−0.999643	+	0.0267023i	$0.991499\pi$
$692$	22.5636			0.857740
$693$	−9.64950	−	6.65899i	−0.366554	−	0.252954i
$694$	−30.4065			−1.15422
$695$	−24.9920	−	43.2873i	−0.947999	−	1.64198i
$696$	−4.12729	−	1.36881i	−0.156444	−	0.0518848i
$697$	13.5178	−	23.4135i	0.512023	−	0.886850i
$698$	12.5956			0.476752
$699$	−25.0581	−	8.31052i	−0.947785	−	0.314333i
$700$	22.9691	−	0.837082i	0.868149	−	0.0316387i
$701$	−43.4858			−1.64243			−0.821217	−	0.570616i	$-0.806705\pi$
$701$	−43.4858			−1.64243			−0.821217	+	0.570616i	$0.806705\pi$
$702$	−13.9752	+	1.21179i	−0.527461	+	0.0457361i
$703$	−1.23422	−	2.13773i	−0.0465495	−	0.0806260i
$704$	−1.47710			−0.0556703
$705$	33.4567	−	29.7585i	1.26005	−	1.12077i
$706$	3.76578	+	6.52252i	0.141727	+	0.245478i
$707$	−7.38502	−	11.7786i	−0.277742	−	0.442979i
$708$	−8.94251	+	7.95403i	−0.336080	+	0.298931i
$709$	11.3702	+	19.6937i	0.427016	+	0.739613i	0.996606	−	0.0823158i	$-0.0262316\pi$
$709$	11.3702	+	19.6937i	0.427016	+	0.739613i	−0.569591	+	0.821928i	$0.692898\pi$
$710$	10.1087	+	17.5088i	0.379373	+	0.657094i
$711$	27.5480	+	20.5308i	1.03313	+	0.769965i
$712$	−4.43818	+	7.68715i	−0.166328	+	0.288088i
$713$	−21.4134	+	37.0891i	−0.801939	+	1.38900i
$714$	7.15706	+	29.2727i	0.267846	+	1.09550i
$715$	7.37636	+	12.7762i	0.275860	+	0.477804i
$716$	−0.333792			−0.0124744
$717$	24.5254	−	21.8144i	0.915917	−	0.814674i
$718$	6.89602			0.257357
$719$	6.06182	−	10.4994i	0.226068	−	0.391561i	−0.730571	−	0.682836i	$-0.760746\pi$
$719$	6.06182	−	10.4994i	0.226068	−	0.391561i	0.956639	+	0.291275i	$0.0940796\pi$
$720$	8.89926	+	6.63238i	0.331656	+	0.247174i
$721$	−2.34176	−	3.73495i	−0.0872119	−	0.139097i
$722$	9.10507	−	15.7705i	0.338856	−	0.586915i
$723$	8.57234	+	41.5700i	0.318809	+	1.54600i
$724$	−11.6211	+	20.1283i	−0.431895	+	0.748063i
$725$	10.9048	−	18.8876i	0.404993	−	0.701468i
$726$	11.4123	−	10.1508i	0.423551	−	0.376733i
$727$	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
$731$	0.0814088			0.00301101
$732$	2.00550	+	9.72530i	0.0741255	+	0.359458i
$733$	−36.0297			−1.33079			−0.665394	−	0.746493i	$-0.731736\pi$
$733$	−36.0297			−1.33079			−0.665394	+	0.746493i	$0.731736\pi$
$734$	−11.5618	−	20.0257i	−0.426755	−	0.739161i
$735$	43.4901	+	10.9835i	1.60416	+	0.405133i
$736$	−3.14400	+	5.44556i	−0.115889	+	0.200726i
$737$	−6.99017	+	12.1073i	−0.257486	+	0.445979i
$738$	1.43818	−	12.2497i	0.0529401	−	0.450916i
$739$	23.2119	+	40.2042i	0.853865	+	1.47894i	0.877694	+	0.479221i	$0.159081\pi$
$739$	23.2119	+	40.2042i	0.853865	+	1.47894i	−0.0238296	+	0.999716i	$0.507586\pi$
$740$	−5.13781	−	8.89894i	−0.188870	−	0.327132i
$741$	−0.839294	−	4.07000i	−0.0308322	−	0.149515i
$742$	8.48762	−	0.309322i	0.311590	−	0.0113556i
$743$	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	$0.826339\pi$
$744$	11.1971	+	3.71351i	0.410505	+	0.136144i
$745$	1.23491			0.0452435
$746$	−14.5822	−	25.2571i	−0.533891	−	0.924727i
$747$	−1.56615	+	13.3397i	−0.0573025	+	0.488073i
$748$	9.71339			0.355157
$749$	28.4629	−	1.03730i	1.04001	−	0.0379021i
$750$	−17.6545	+	15.7030i	−0.644652	+	0.573394i
$751$	48.1199			1.75592			0.877961	−	0.478733i	$-0.158904\pi$
$751$	48.1199			1.75592			0.877961	+	0.478733i	$0.158904\pi$
$752$	3.49381	−	6.05146i	0.127406	−	0.220674i
$753$	4.24102	+	20.5660i	0.154551	+	0.749468i
$754$	3.38874	+	5.86946i	0.123410	+	0.213753i
$755$	−73.6588			−2.68072
$756$	8.28180	+	10.9732i	0.301206	+	0.399092i
$757$	49.6006			1.80276			0.901382	−	0.433025i	$-0.142554\pi$
$757$	49.6006			1.80276			0.901382	+	0.433025i	$0.142554\pi$
$758$	6.78111	+	11.7452i	0.246301	+	0.426606i
$759$	3.24907	+	15.7558i	0.117934	+	0.571898i
$760$	−1.64400	+	2.84748i	−0.0596340	+	0.103289i
$761$	−37.5402			−1.36083			−0.680416	−	0.732826i	$-0.738201\pi$
$761$	−37.5402			−1.36083			−0.680416	+	0.732826i	$0.738201\pi$
$762$	3.69708	−	3.28842i	0.133931	−	0.119127i
$763$	−0.234219	+	0.442124i	−0.00847931	+	0.0160060i
$764$	−16.3214			−0.590488
$765$	−58.5214	−	43.6144i	−2.11584	−	1.57688i
$766$	1.41783	+	2.45575i	0.0512281	+	0.0887297i
$767$	18.6538			0.673551
$768$	1.64400	+	0.545231i	0.0593226	+	0.0196743i
$769$	−13.4592	−	23.3121i	−0.485352	−	0.840654i	0.514506	−	0.857486i	$-0.327975\pi$
$769$	−13.4592	−	23.3121i	−0.485352	−	0.840654i	−0.999858	+	0.0168324i	$0.994642\pi$
$770$	6.76833	−	12.7762i	0.243914	−	0.460423i
$771$	2.87154	+	13.9250i	0.103416	+	0.501497i
$772$	7.16071	+	12.4027i	0.257719	+	0.446383i
$773$	25.1130	+	43.4971i	0.903254	+	1.56448i	0.823245	+	0.567687i	$0.192162\pi$
$773$	25.1130	+	43.4971i	0.903254	+	1.56448i	0.0800089	+	0.996794i	$0.474505\pi$
$774$	0.0341093	−	0.0146925i	0.00122603	−	0.000528111i
$775$	−29.5840	+	51.2409i	−1.06269	+	1.84063i
$776$	−6.58836	+	11.4114i	−0.236508	+	0.409645i
$777$	−3.02290	−	12.3638i	−0.108446	−	0.443549i
$778$	9.30401	+	16.1150i	0.333565	+	0.577752i
$779$	3.65383			0.130912
$780$	−3.49381	−	16.9426i	−0.125098	−	0.606642i
$781$	8.07194			0.288837
$782$	20.6749	−	35.8099i	0.739332	−	1.28056i
$783$	12.9963	−	1.12691i	0.464449	−	0.0402723i
$784$	6.98143	−	0.509538i	0.249337	−	0.0181978i
$785$	12.8800	−	22.3088i	0.459707	−	0.796236i
$786$	−0.201487	+	0.179216i	−0.00718682	+	0.00639241i
$787$	0.829462	−	1.43667i	0.0295671	−	0.0512118i	−0.850863	−	0.525387i	$-0.823920\pi$
$787$	0.829462	−	1.43667i	0.0295671	−	0.0512118i	0.880430	+	0.474176i	$0.157254\pi$
$788$	−1.21201	+	2.09926i	−0.0431760	+	0.0747830i
$789$	1.87017	+	9.06902i	0.0665797	+	0.322866i
$790$	−21.1847	+	36.6930i	−0.753718	+	1.30548i
$791$	−16.7992	+	31.7110i	−0.597311	+	1.12751i
$792$	4.06979	−	1.75305i	0.144614	−	0.0622920i
$793$	7.73855	−	13.4036i	0.274804	−	0.475974i
$794$	20.5760			0.730214
$795$	−15.3702	+	13.6712i	−0.545124	+	0.484867i
$796$	6.11126			0.216608
$797$	−15.3702	−	26.6219i	−0.544439	−	0.942996i	−0.998642	−	0.0520981i	$-0.983409\pi$
$797$	−15.3702	−	26.6219i	−0.544439	−	0.942996i	0.454203	−	0.890898i	$-0.349924\pi$
$798$	−2.94251	+	2.81576i	−0.104164	+	0.0996769i
$799$	−22.9752	+	39.7943i	−0.812806	+	1.40782i
$800$	−4.34362	+	7.52338i	−0.153570	+	0.265992i
$801$	3.10507	−	26.4474i	0.109712	−	0.934473i
$802$	3.37704	+	5.84921i	0.119248	+	0.206543i
$803$	8.91095	+	15.4342i	0.314461	+	0.544662i
$804$	12.2491	−	10.8951i	0.431991	−	0.384240i
$805$	−32.6952	−	52.1466i	−1.15236	−	1.83793i
$806$	−9.19344	−	15.9235i	−0.323825	−	0.560881i
$807$	23.9222	−	21.2779i	0.842100	−	0.749016i
$808$	5.25457			0.184855
$809$	−1.44251	−	2.49850i	−0.0507159	−	0.0878425i	0.839553	−	0.543278i	$-0.182817\pi$
$809$	−1.44251	−	2.49850i	−0.0507159	−	0.0878425i	−0.890269	+	0.455435i	$0.849484\pi$
$810$	−32.3912	−	7.71212i	−1.13811	−	0.270976i
$811$	28.5461			1.00239			0.501195	−	0.865334i	$-0.332894\pi$
$811$	28.5461			1.00239			0.501195	+	0.865334i	$0.332894\pi$
$812$	3.10940	−	5.86946i	0.109119	−	0.205978i
$813$	12.0913	+	4.01008i	0.424061	+	0.140640i
$814$	−4.10260			−0.143796
$815$	14.9356	−	25.8693i	0.523172	−	0.906161i
$816$	−10.8109	−	3.58543i	−0.378457	−	0.125515i
$817$	0.00550115	+	0.00952827i	0.000192461	+	0.000333352i
$818$	15.3214			0.535701
$819$	1.72184	−	21.3583i	0.0601659	−	0.746321i
$820$	15.2101			0.531161
$821$	−3.98329	−	6.89926i	−0.139018	−	0.240786i	0.788107	−	0.615538i	$-0.211061\pi$
$821$	−3.98329	−	6.89926i	−0.139018	−	0.240786i	−0.927125	+	0.374752i	$0.877728\pi$
$822$	4.41528	−	3.92723i	0.154001	−	0.136978i
$823$	−20.2731	+	35.1140i	−0.706675	+	1.22400i	0.259409	+	0.965768i	$0.416472\pi$
$823$	−20.2731	+	35.1140i	−0.706675	+	1.22400i	−0.966084	+	0.258229i	$0.916861\pi$
$824$	1.66621			0.0580451
$825$	4.48879	+	21.7676i	0.156280	+	0.757849i
$826$	−9.71132	−	15.4889i	−0.337900	−	0.538927i
$827$	1.22115			0.0424636			0.0212318	−	0.999775i	$-0.493241\pi$
$827$	1.22115			0.0424636			0.0212318	+	0.999775i	$0.493241\pi$
$828$	2.19963	−	18.7353i	0.0764424	−	0.651096i
$829$	−7.07530	−	12.2548i	−0.245735	−	0.425626i	0.716603	−	0.697481i	$-0.245696\pi$
$829$	−7.07530	−	12.2548i	−0.245735	−	0.425626i	−0.962338	+	0.271856i	$0.912363\pi$
$830$	−16.5636			−0.574931
$831$	3.18292	+	15.4350i	0.110414	+	0.535433i
$832$	−1.34981	−	2.33795i	−0.0467964	−	0.0810537i
$833$	−45.9098	+	3.35071i	−1.59068	+	0.116095i
$834$	22.2112	+	7.36636i	0.769112	+	0.255076i
$835$	36.0450	+	62.4318i	1.24739	+	2.16054i
$836$	0.656376	+	1.13688i	0.0227012	+	0.0393197i
$837$	−35.2581	+	3.05723i	−1.21870	+	0.105673i
$838$	−4.32141	+	7.48491i	−0.149281	+	0.258562i
$839$	1.19599	−	2.07151i	0.0412900	−	0.0715164i	−0.844642	−	0.535332i	$-0.820187\pi$
$839$	1.19599	−	2.07151i	0.0412900	−	0.0715164i	0.885932	+	0.463815i	$0.153520\pi$
$840$	−12.2491	+	11.7215i	−0.422633	+	0.404429i
$841$	11.3486	+	19.6564i	0.391333	+	0.677808i
$842$	−37.1272			−1.27949
$843$	−19.7422	−	6.54750i	−0.679957	−	0.225508i
$844$	−11.4451			−0.393955
$845$	10.5662	−	18.3011i	0.363487	−	0.629577i
$846$	−2.44437	+	20.8199i	−0.0840391	+	0.715802i
$847$	12.3935	+	19.7667i	0.425845	+	0.679193i
$848$	−1.60507	+	2.78007i	−0.0551185	+	0.0954680i
$849$	16.1817	+	5.36667i	0.555356	+	0.184184i
$850$	28.5636	−	49.4736i	0.979724	−	1.69693i
$851$	−8.73236	+	15.1249i	−0.299341	+	0.518475i
$852$	−8.98398	−	2.97954i	−0.307786	−	0.102077i
$853$	−8.33998	+	14.4453i	−0.285556	+	0.494597i	−0.972744	−	0.231883i	$-0.925511\pi$
$853$	−8.33998	+	14.4453i	−0.285556	+	0.494597i	0.687188	+	0.726479i	$0.258845\pi$
$854$	−15.1582	+	0.552423i	−0.518702	+	0.0189035i
$855$	1.15019	−	9.79669i	0.0393355	−	0.335040i
$856$	−5.38255	+	9.32284i	−0.183972	+	0.318648i
$857$	−13.8516			−0.473162			−0.236581	−	0.971612i	$-0.576027\pi$
$857$	−13.8516			−0.473162			−0.236581	+	0.971612i	$0.576027\pi$
$858$	−6.55563	−	2.17417i	−0.223806	−	0.0742251i
$859$	48.4944			1.65461			0.827304	−	0.561754i	$-0.189873\pi$
$859$	48.4944			1.65461			0.827304	+	0.561754i	$0.189873\pi$
$860$	0.0229002	+	0.0396643i	0.000780889	+	0.00135254i
$861$	18.0865	+	5.27548i	0.616386	+	0.179788i
$862$	−4.71015	+	8.15822i	−0.160428	+	0.277870i
$863$	2.96541	−	5.13624i	0.100944	−	0.174840i	−0.811130	−	0.584866i	$-0.801147\pi$
$863$	2.96541	−	5.13624i	0.100944	−	0.174840i	0.912074	+	0.410026i	$0.134480\pi$
$864$	−5.17673	+	0.448873i	−0.176116	+	0.0152710i
$865$	−41.7385	−	72.2932i	−1.41915	−	2.45804i
$866$	0.104386	+	0.180801i	0.00354717	+	0.00614387i
$867$	43.1443	+	14.3088i	1.46526	+	0.485953i
$868$	−8.43563	+	15.9235i	−0.286324	+	0.540479i
$869$	8.45813	+	14.6499i	0.286922	+	0.496964i
$870$	3.24907	+	15.7558i	0.110154	+	0.534170i
$871$	−25.5512			−0.865770
$872$	−0.0945538	−	0.163772i	−0.00320200	−	0.00554602i
$873$	4.60940	−	39.2605i	0.156005	−	1.32877i
$874$	5.58836			0.189029
$875$	−19.1723	−	30.5785i	−0.648143	−	1.03374i
$876$	−4.22067	−	20.4673i	−0.142603	−	0.691527i
$877$	3.92944			0.132688			0.0663439	−	0.997797i	$-0.478867\pi$
$877$	3.92944			0.132688			0.0663439	+	0.997797i	$0.478867\pi$
$878$	4.98398	−	8.63250i	0.168201	−	0.291333i
$879$	27.7218	−	24.6575i	0.935032	−	0.831676i
$880$	2.73236	+	4.73259i	0.0921078	+	0.159535i
$881$	37.6552			1.26864			0.634318	−	0.773072i	$-0.281281\pi$
$881$	37.6552			1.26864			0.634318	+	0.773072i	$0.281281\pi$
$882$	−18.6309	+	9.68961i	−0.627336	+	0.326266i
$883$	−53.2334			−1.79145			−0.895723	−	0.444613i	$-0.853341\pi$
$883$	−53.2334			−1.79145			−0.895723	+	0.444613i	$0.853341\pi$
$884$	8.87636	+	15.3743i	0.298544	+	0.517094i
$885$	42.0265	+	13.9381i	1.41270	+	0.468523i
$886$	7.84981	−	13.5963i	0.263720	−	0.456776i
$887$	−36.9876			−1.24192			−0.620961	−	0.783841i	$-0.713258\pi$
$887$	−36.9876			−1.24192			−0.620961	+	0.783841i	$0.713258\pi$
$888$	4.56615	+	1.51436i	0.153230	+	0.0508187i
$889$	4.01493	+	6.40353i	0.134656	+	0.214768i
$890$	32.8392			1.10077
$891$	−9.13279	+	9.66022i	−0.305960	+	0.323630i
$892$	−3.61126	−	6.25489i	−0.120914	−	0.209429i
$893$	−6.21015			−0.207815
$894$	−0.431988	+	0.384237i	−0.0144478	+	0.0128508i
$895$	0.617454	+	1.06946i	0.0206392	+	0.0357482i
$896$	−1.23855	+	2.33795i	−0.0413770	+	0.0781053i
$897$	−21.9691	+	19.5407i	−0.733525	+	0.652443i
$898$	−16.8127	−	29.1204i	−0.561046	−	0.971761i
$899$	8.54944	+	14.8081i	0.285140	+	0.493877i
$900$	3.03892	−	25.8840i	0.101297	−	0.862799i
$901$	10.5549	−	18.2817i	0.351636	−	0.609052i
$902$	3.03637	−	5.25915i	0.101100	−	0.175111i
$903$	0.0134736	+	0.0551078i	0.000448374	+	0.00183387i
$904$	−6.78180	−	11.7464i	−0.225559	−	0.390680i
$905$	85.9875			2.85832
$906$	25.7669	−	22.9187i	0.856047	−	0.761422i
$907$	−39.0159			−1.29550			−0.647752	−	0.761852i	$-0.724291\pi$
$907$	−39.0159			−1.29550			−0.647752	+	0.761852i	$0.724291\pi$
$908$	−6.82760	+	11.8258i	−0.226582	+	0.392451i
$909$	−14.4777	+	6.23623i	−0.480195	+	0.206843i
$910$	26.4072	−	0.962383i	0.875391	−	0.0319027i
$911$	−12.8090	+	22.1859i	−0.424382	+	0.735052i	−0.996363	−	0.0852158i	$-0.972842\pi$
$911$	−12.8090	+	22.1859i	−0.424382	+	0.735052i	0.571980	+	0.820267i	$0.306175\pi$
$912$	−0.310892	−	1.50761i	−0.0102947	−	0.0499221i
$913$	−3.30656	+	5.72713i	−0.109431	+	0.189540i
$914$	−16.3541	+	28.3262i	−0.540947	+	0.936948i
$915$	27.4498	−	24.4156i	0.907462	−	0.807154i
$916$	−8.68725	+	15.0468i	−0.287035	+	0.497159i
$917$	−0.218810	−	0.348986i	−0.00722574	−	0.0115245i
$918$	34.0421	−	2.95178i	1.12356	−	0.0974234i
$919$	10.3367	−	17.9038i	0.340978	−	0.590591i	−0.643637	−	0.765331i	$-0.722575\pi$
$919$	10.3367	−	17.9038i	0.340978	−	0.590591i	0.984615	+	0.174740i	$0.0559086\pi$
$920$	23.2632			0.766966
$921$	1.98948	+	9.64761i	0.0655556	+	0.317900i
$922$	4.14331			0.136453
$923$	7.37636	+	12.7762i	0.242796	+	0.420535i
$924$	1.60762	+	6.57525i	0.0528869	+	0.216310i
$925$	−12.0643	+	20.8960i	−0.396672	+	0.687055i
$926$	−8.34176	+	14.4484i	−0.274127	+	0.474803i
$927$	−4.59084	+	1.97749i	−0.150783	+	0.0649492i
$928$	1.25526	+	2.17417i	0.0412059	+	0.0713708i
$929$	1.87017	+	3.23922i	0.0613582	+	0.106275i	0.895073	−	0.445920i	$-0.147123\pi$
$929$	1.87017	+	3.23922i	0.0613582	+	0.106275i	−0.833715	+	0.552196i	$0.813790\pi$
$930$	−8.81453	−	42.7444i	−0.289040	−	1.40165i
$931$	−3.49450	−	5.14696i	−0.114528	−	0.168685i
$932$	7.62110	+	13.2001i	0.249637	+	0.432384i
$933$	−19.2687	−	6.39047i	−0.630830	−	0.209215i
$934$	−29.9171			−0.978916
$935$	−17.9680	−	31.1214i	−0.587615	−	1.01778i
$936$	6.49381	+	4.83967i	0.212257	+	0.158189i
$937$	−27.1345			−0.886445			−0.443223	−	0.896412i	$-0.646165\pi$
$937$	−27.1345			−0.886445			−0.443223	+	0.896412i	$0.646165\pi$
$938$	13.3022	+	21.2160i	0.434331	+	0.692727i
$939$	34.6501	−	30.8200i	1.13076	−	1.00577i
$940$	−25.8516			−0.843186
$941$	−3.16435	+	5.48081i	−0.103155	+	0.178669i	−0.912983	−	0.407998i	$-0.866227\pi$
$941$	−3.16435	+	5.48081i	−0.103155	+	0.178669i	0.809828	+	0.586667i	$0.199560\pi$
$942$	2.43571	+	11.8115i	0.0793596	+	0.384840i
$943$	−12.9258	−	22.3881i	−0.420922	−	0.729058i
$944$	6.90978			0.224894
$945$	19.8381	−	46.8331i	0.645334	−	1.52348i
$946$	0.0182861			0.000594531
$947$	−15.6396	−	27.0886i	−0.508218	−	0.880260i	−0.999955	−	0.00951587i	$-0.996971\pi$
$947$	−15.6396	−	27.0886i	−0.508218	−	0.880260i	0.491736	−	0.870744i	$-0.336362\pi$
$948$	−4.00619	−	19.4273i	−0.130115	−	0.630968i
$949$	−16.2861	+	28.2084i	−0.528670	+	0.915684i
$950$	7.72067			0.250492
$951$	−2.46217	+	2.19001i	−0.0798414	+	0.0710160i
$952$	8.14468	−	15.3743i	0.263971	−	0.498284i
$953$	4.28937			0.138946			0.0694732	−	0.997584i	$-0.477868\pi$
$953$	4.28937			0.138946			0.0694732	+	0.997584i	$0.477868\pi$
$954$	1.12296	−	9.56475i	0.0363570	−	0.309670i
$955$	30.1916	+	52.2933i	0.976977	+	1.69217i
$956$	−18.9505			−0.612902
$957$	6.09641	+	2.02187i	0.197069	+	0.0653579i
$958$	1.47965	+	2.56283i	0.0478053	+	0.0828011i
$959$	4.79487	+	7.64749i	0.154834	+	0.246950i
$960$	−1.29418	−	6.27589i	−0.0417695	−	0.202554i
$961$	−7.69413	−	13.3266i	−0.248198	−	0.429891i
$962$	−3.74907	−	6.49358i	−0.120875	−	0.209361i
$963$	3.76578	−	32.0750i	0.121351	−	1.03360i
$964$	12.2527	−	21.2223i	0.394633	−	0.683525i
$965$	26.4920	−	45.8854i	0.852806	−	1.47710i
$966$	27.6625	+	8.06861i	0.890026	+	0.259603i
$967$	−7.59201	−	13.1497i	−0.244142	−	0.422867i	0.717748	−	0.696303i	$-0.245173\pi$
$967$	−7.59201	−	13.1497i	−0.244142	−	0.422867i	−0.961890	+	0.273436i	$0.911840\pi$
$968$	−8.81818			−0.283427
$969$	2.04442	+	9.91405i	0.0656763	+	0.318485i
$970$	48.7490			1.56524
$971$	1.62364	−	2.81223i	0.0521052	−	0.0902489i	−0.838796	−	0.544445i	$-0.816740\pi$
$971$	1.62364	−	2.81223i	0.0521052	−	0.0902489i	0.890902	+	0.454196i	$0.150074\pi$
$972$	13.7305	−	7.38061i	0.440406	−	0.236733i
$973$	−16.7335	+	31.5869i	−0.536450	+	1.01263i
$974$	−14.0309	+	24.3022i	−0.449578	+	0.778692i
$975$	−30.3516	+	26.9966i	−0.972029	+	0.864584i
$976$	2.86652	−	4.96497i	0.0917552	−	0.158925i
$977$	−7.77197	+	13.4614i	−0.248647	+	0.430670i	−0.963151	−	0.268962i	$-0.913319\pi$
$977$	−7.77197	+	13.4614i	−0.248647	+	0.430670i	0.714503	+	0.699632i	$0.246653\pi$
$978$	2.82444	+	13.6966i	0.0903157	+	0.437969i
$979$	6.55563	−	11.3547i	0.209519	−	0.362897i
$980$	−14.5469	−	21.4258i	−0.464683	−	0.684421i
$981$	0.454888	+	0.339016i	0.0145235	+	0.0108240i
$982$	17.0734	−	29.5721i	0.544835	−	0.943682i
$983$	12.3832			0.394961			0.197481	−	0.980307i	$-0.436724\pi$
$983$	12.3832			0.394961			0.197481	+	0.980307i	$0.436724\pi$
$984$	−5.32072	+	4.73259i	−0.169618	+	0.150869i
$985$	8.96796			0.285743
$986$	−8.25457	−	14.2973i	−0.262879	−	0.455320i
$987$	−30.7403	−	8.96636i	−0.978476	−	0.285402i
$988$	−1.19963	+	2.07782i	−0.0381653	+	0.0661042i
$989$	0.0389218	−	0.0674145i	0.00123764	−	0.00214366i
$990$	−13.1451	−	9.79669i	−0.417778	−	0.311359i
$991$	−3.32760	−	5.76358i	−0.105705	−	0.183086i	0.808321	−	0.588742i	$-0.200377\pi$
$991$	−3.32760	−	5.76358i	−0.105705	−	0.183086i	−0.914026	+	0.405656i	$0.867043\pi$
$992$	−3.40545	−	5.89841i	−0.108123	−	0.187275i
$993$	−7.20513	+	6.40869i	−0.228648	+	0.203374i
$994$	6.76833	−	12.7762i	0.214678	−	0.405237i
$995$	−11.3047	−	19.5803i	−0.358383	−	0.620738i
$996$	5.79418	−	5.15371i	0.183596	−	0.163302i
$997$	4.80208			0.152083			0.0760417	−	0.997105i	$-0.475772\pi$
$997$	4.80208			0.152083			0.0760417	+	0.997105i	$0.475772\pi$
$998$	1.14035	+	1.97515i	0.0360973	+	0.0625223i
$999$	−14.3782	+	1.24673i	−0.454907	+	0.0394449i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.d.25.1	✓	6	7.4	even	3
126.2.e.d.121.1	yes	6	9.4	even	3
126.2.h.c.67.1	yes	6	63.4	even	3	inner
126.2.h.c.79.1	yes	6	1.1	even	1	trivial
378.2.e.c.37.3		6	9.5	odd	6
378.2.e.c.235.3		6	21.11	odd	6
378.2.h.d.289.1		6	3.2	odd	2
378.2.h.d.361.1		6	63.32	odd	6
882.2.e.p.373.3		6	63.13	odd	6
882.2.e.p.655.3		6	7.3	odd	6
882.2.f.l.295.3		6	7.2	even	3
882.2.f.l.589.3		6	63.58	even	3
882.2.f.m.295.1		6	7.5	odd	6
882.2.f.m.589.1		6	63.40	odd	6
882.2.h.o.67.3		6	63.31	odd	6
882.2.h.o.79.3		6	7.6	odd	2
1008.2.q.h.529.3		6	28.11	odd	6
1008.2.q.h.625.3		6	36.31	odd	6
1008.2.t.g.193.3		6	252.67	odd	6
1008.2.t.g.961.3		6	4.3	odd	2
1134.2.g.k.163.1		6	9.7	even	3
1134.2.g.k.487.1		6	63.25	even	3
1134.2.g.n.163.3		6	9.2	odd	6
1134.2.g.n.487.3		6	63.11	odd	6
2646.2.e.o.1549.1		6	63.41	even	6
2646.2.e.o.2125.1		6	21.17	even	6
2646.2.f.n.883.1		6	21.5	even	6
2646.2.f.n.1765.1		6	63.5	even	6
2646.2.f.o.883.3		6	21.2	odd	6
2646.2.f.o.1765.3		6	63.23	odd	6
2646.2.h.p.361.3		6	63.59	even	6
2646.2.h.p.667.3		6	21.20	even	2
3024.2.q.h.2305.3		6	36.23	even	6
3024.2.q.h.2881.3		6	84.11	even	6
3024.2.t.g.289.1		6	12.11	even	2
3024.2.t.g.1873.1		6	252.95	even	6
7938.2.a.bu.1.1		3	63.2	odd	6
7938.2.a.bx.1.3		3	63.47	even	6
7938.2.a.by.1.1		3	63.61	odd	6
7938.2.a.cb.1.3		3	63.16	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.349814 - 1.69636i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.69963 q^{5} +(-1.29418 + 1.15113i) q^{6} +(-1.40545 - 2.24159i) q^{7} +1.00000 q^{8} +(-2.75526 + 1.18682i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.349814 - 1.69636i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.69963 q^{5} +(-1.29418 + 1.15113i) q^{6} +(-1.40545 - 2.24159i) q^{7} +1.00000 q^{8} +(-2.75526 + 1.18682i) q^{9} +(-1.84981 - 3.20397i) q^{10} -1.47710 q^{11} +(1.64400 + 0.545231i) q^{12} +(-1.34981 - 2.33795i) q^{13} +(-1.23855 + 2.33795i) q^{14} +(-1.29418 - 6.27589i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.28799 + 5.69497i) q^{17} +(2.40545 + 1.79272i) q^{18} +(-0.444368 + 0.769668i) q^{19} +(-1.84981 + 3.20397i) q^{20} +(-3.31089 + 3.16828i) q^{21} +(0.738550 + 1.27921i) q^{22} +6.28799 q^{23} +(-0.349814 - 1.69636i) q^{24} +8.68725 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} +(-4.78799 + 4.25874i) q^{30} +(-3.40545 + 5.89841i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.516710 + 2.50569i) 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} +0.888736 q^{38} +(-3.49381 + 3.10761i) q^{39} +3.69963 q^{40} +(-2.05563 - 3.56046i) q^{41} +(4.39926 + 1.28318i) q^{42} +(0.00618986 - 0.0107211i) q^{43} +(0.738550 - 1.27921i) q^{44} +(-10.1934 + 4.39079i) q^{45} +(-3.14400 - 5.44556i) q^{46} +(3.49381 + 6.05146i) q^{47} +(-1.29418 + 1.15113i) q^{48} +(-3.04944 + 6.30087i) q^{49} +(-4.34362 - 7.52338i) q^{50} +(8.51052 - 7.56979i) q^{51} +2.69963 q^{52} +(-1.60507 - 2.78007i) q^{53} +(2.19963 - 4.70761i) q^{54} -5.46472 q^{55} +(-1.40545 - 2.24159i) q^{56} +(1.46108 + 0.484566i) q^{57} -2.51052 q^{58} +(-3.45489 + 5.98404i) q^{59} +(6.08217 + 2.01715i) q^{60} +(2.86652 + 4.96497i) q^{61} +6.81089 q^{62} +(6.53273 + 4.50815i) q^{63} +1.00000 q^{64} +(-4.99381 - 8.64953i) q^{65} +(1.91164 - 1.70033i) q^{66} +(4.73236 - 8.19669i) q^{67} -6.57598 q^{68} +(-2.19963 - 10.6667i) q^{69} +(-4.58217 + 8.64953i) q^{70} -5.46472 q^{71} +(-2.75526 + 1.18682i) q^{72} +(-6.03273 - 10.4490i) q^{73} +2.77747 q^{74} +(-3.03892 - 14.7367i) q^{75} +(-0.444368 - 0.769668i) q^{76} +(2.07598 + 3.31105i) q^{77} +(4.43818 + 1.47192i) q^{78} +(-5.72617 - 9.91802i) q^{79} +(-1.84981 - 3.20397i) q^{80} +(6.18292 - 6.53999i) q^{81} +(-2.05563 + 3.56046i) q^{82} +(2.23855 - 3.87728i) q^{83} +(-1.08836 - 4.45146i) q^{84} +(12.1643 + 21.0693i) q^{85} -0.0123797 q^{86} +(-4.12729 - 1.36881i) q^{87} -1.47710 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} +(11.1971 + 3.71351i) q^{93} +(3.49381 - 6.05146i) q^{94} +(-1.64400 + 2.84748i) q^{95} +(1.64400 + 0.545231i) q^{96} +(-6.58836 + 11.4114i) q^{97} +(6.98143 - 0.509538i) q^{98} +(4.06979 - 1.75305i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 4 q^{3} - 3 q^{4} + 10 q^{5} - 2 q^{6} - 2 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 + 4 * q^3 - 3 * q^4 + 10 * q^5 - 2 * q^6 - 2 * q^7 + 6 * q^8 - 4 * q^9	\( 6 q - 3 q^{2} + 4 q^{3} - 3 q^{4} + 10 q^{5} - 2 q^{6} - 2 q^{7} + 6 q^{8} - 4 q^{9} - 5 q^{10} + 2 q^{11} - 2 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} - 3 q^{16} - 4 q^{17} + 8 q^{18} - 3 q^{19} - 5 q^{20} - 7 q^{21} - q^{22} + 14 q^{23} + 4 q^{24} + 4 q^{25} - 2 q^{26} + 7 q^{27} + 4 q^{28} - 5 q^{29} - 5 q^{30} - 14 q^{31} - 3 q^{32} - 4 q^{33} - 4 q^{34} - 19 q^{35} - 4 q^{36} - 9 q^{37} + 6 q^{38} - 3 q^{39} + 10 q^{40} - 12 q^{41} + 2 q^{42} + 18 q^{43} - q^{44} - 31 q^{45} - 7 q^{46} + 3 q^{47} - 2 q^{48} - 2 q^{50} + 26 q^{51} + 4 q^{52} + 9 q^{53} + q^{54} + 14 q^{55} - 2 q^{56} + 2 q^{57} + 10 q^{58} + 4 q^{59} + 7 q^{60} + 4 q^{61} + 28 q^{62} + 28 q^{63} + 6 q^{64} - 12 q^{65} + 23 q^{66} + 5 q^{67} + 8 q^{68} - q^{69} + 2 q^{70} + 14 q^{71} - 4 q^{72} - 25 q^{73} + 18 q^{74} - 25 q^{75} - 3 q^{76} - 35 q^{77} + 9 q^{78} + 7 q^{79} - 5 q^{80} + 32 q^{81} - 12 q^{82} + 8 q^{83} + 5 q^{84} + 14 q^{85} - 36 q^{86} - 20 q^{87} + 2 q^{88} - 9 q^{89} + 29 q^{90} + 4 q^{91} - 7 q^{92} - 3 q^{93} + 3 q^{94} + 2 q^{95} - 2 q^{96} - 28 q^{97} - 12 q^{98} - 41 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + 4 * q^3 - 3 * q^4 + 10 * q^5 - 2 * q^6 - 2 * q^7 + 6 * q^8 - 4 * q^9 - 5 * q^10 + 2 * q^11 - 2 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 - 3 * q^16 - 4 * q^17 + 8 * q^18 - 3 * q^19 - 5 * q^20 - 7 * q^21 - q^22 + 14 * q^23 + 4 * q^24 + 4 * q^25 - 2 * q^26 + 7 * q^27 + 4 * q^28 - 5 * q^29 - 5 * q^30 - 14 * q^31 - 3 * q^32 - 4 * q^33 - 4 * q^34 - 19 * q^35 - 4 * q^36 - 9 * q^37 + 6 * q^38 - 3 * q^39 + 10 * q^40 - 12 * q^41 + 2 * q^42 + 18 * q^43 - q^44 - 31 * q^45 - 7 * q^46 + 3 * q^47 - 2 * q^48 - 2 * q^50 + 26 * q^51 + 4 * q^52 + 9 * q^53 + q^54 + 14 * q^55 - 2 * q^56 + 2 * q^57 + 10 * q^58 + 4 * q^59 + 7 * q^60 + 4 * q^61 + 28 * q^62 + 28 * q^63 + 6 * q^64 - 12 * q^65 + 23 * q^66 + 5 * q^67 + 8 * q^68 - q^69 + 2 * q^70 + 14 * q^71 - 4 * q^72 - 25 * q^73 + 18 * q^74 - 25 * q^75 - 3 * q^76 - 35 * q^77 + 9 * q^78 + 7 * q^79 - 5 * q^80 + 32 * q^81 - 12 * q^82 + 8 * q^83 + 5 * q^84 + 14 * q^85 - 36 * q^86 - 20 * q^87 + 2 * q^88 - 9 * q^89 + 29 * q^90 + 4 * q^91 - 7 * q^92 - 3 * q^93 + 3 * q^94 + 2 * q^95 - 2 * q^96 - 28 * q^97 - 12 * q^98 - 41 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more