LMFDB - Embedded newform 22.2.c.a.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,2,Mod(3,22)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("22.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	22.c (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.175670884447$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			3.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	22.3
Dual form			22.2.c.a.15.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(0.118034 + 0.363271i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-2.61803 - 1.90211i) q^{5} +(-0.309017 - 0.224514i) q^{6} +(-0.618034 + 1.90211i) q^{7} +(0.309017 + 0.951057i) q^{8} +(2.30902 - 1.67760i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.118034 + 0.363271i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-2.61803 - 1.90211i) q^{5} +(-0.309017 - 0.224514i) q^{6} +(-0.618034 + 1.90211i) q^{7} +(0.309017 + 0.951057i) q^{8} +(2.30902 - 1.67760i) q^{9} +3.23607 q^{10} +(0.309017 + 3.30220i) q^{11} +0.381966 q^{12} +(-1.00000 + 0.726543i) q^{13} +(-0.618034 - 1.90211i) q^{14} +(0.381966 - 1.17557i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.500000 + 0.363271i) q^{17} +(-0.881966 + 2.71441i) q^{18} +(-1.80902 - 5.56758i) q^{19} +(-2.61803 + 1.90211i) q^{20} -0.763932 q^{21} +(-2.19098 - 2.48990i) q^{22} +1.23607 q^{23} +(-0.309017 + 0.224514i) q^{24} +(1.69098 + 5.20431i) q^{25} +(0.381966 - 1.17557i) q^{26} +(1.80902 + 1.31433i) q^{27} +(1.61803 + 1.17557i) q^{28} +(1.38197 - 4.25325i) q^{29} +(0.381966 + 1.17557i) q^{30} +(-1.61803 + 1.17557i) q^{31} +1.00000 q^{32} +(-1.16312 + 0.502029i) q^{33} -0.618034 q^{34} +(5.23607 - 3.80423i) q^{35} +(-0.881966 - 2.71441i) q^{36} +(-1.14590 + 3.52671i) q^{37} +(4.73607 + 3.44095i) q^{38} +(-0.381966 - 0.277515i) q^{39} +(1.00000 - 3.07768i) q^{40} +(1.73607 + 5.34307i) q^{41} +(0.618034 - 0.449028i) q^{42} -8.56231 q^{43} +(3.23607 + 0.726543i) q^{44} -9.23607 q^{45} +(-1.00000 + 0.726543i) q^{46} +(-2.00000 - 6.15537i) q^{47} +(0.118034 - 0.363271i) q^{48} +(2.42705 + 1.76336i) q^{49} +(-4.42705 - 3.21644i) q^{50} +(-0.0729490 + 0.224514i) q^{51} +(0.381966 + 1.17557i) q^{52} +(1.23607 - 0.898056i) q^{53} -2.23607 q^{54} +(5.47214 - 9.23305i) q^{55} -2.00000 q^{56} +(1.80902 - 1.31433i) q^{57} +(1.38197 + 4.25325i) q^{58} +(-2.66312 + 8.19624i) q^{59} +(-1.00000 - 0.726543i) q^{60} +(2.00000 + 1.45309i) q^{61} +(0.618034 - 1.90211i) q^{62} +(1.76393 + 5.42882i) q^{63} +(-0.809017 + 0.587785i) q^{64} +4.00000 q^{65} +(0.645898 - 1.08981i) q^{66} +11.0902 q^{67} +(0.500000 - 0.363271i) q^{68} +(0.145898 + 0.449028i) q^{69} +(-2.00000 + 6.15537i) q^{70} +(4.23607 + 3.07768i) q^{71} +(2.30902 + 1.67760i) q^{72} +(3.20820 - 9.87384i) q^{73} +(-1.14590 - 3.52671i) q^{74} +(-1.69098 + 1.22857i) q^{75} -5.85410 q^{76} +(-6.47214 - 1.45309i) q^{77} +0.472136 q^{78} +(-10.8541 + 7.88597i) q^{79} +(1.00000 + 3.07768i) q^{80} +(2.38197 - 7.33094i) q^{81} +(-4.54508 - 3.30220i) q^{82} +(-7.54508 - 5.48183i) q^{83} +(-0.236068 + 0.726543i) q^{84} +(-0.618034 - 1.90211i) q^{85} +(6.92705 - 5.03280i) q^{86} +1.70820 q^{87} +(-3.04508 + 1.31433i) q^{88} -8.09017 q^{89} +(7.47214 - 5.42882i) q^{90} +(-0.763932 - 2.35114i) q^{91} +(0.381966 - 1.17557i) q^{92} +(-0.618034 - 0.449028i) q^{93} +(5.23607 + 3.80423i) q^{94} +(-5.85410 + 18.0171i) q^{95} +(0.118034 + 0.363271i) q^{96} +(-5.78115 + 4.20025i) q^{97} -3.00000 q^{98} +(6.25329 + 7.10642i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} + q^{6} + 2 q^{7} - q^{8} + 7 q^{9}+O(q^{10}) $ 4 * q - q^2 - 4 * q^3 - q^4 - 6 * q^5 + q^6 + 2 * q^7 - q^8 + 7 * q^9	\( 4 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} + q^{6} + 2 q^{7} - q^{8} + 7 q^{9} + 4 q^{10} - q^{11} + 6 q^{12} - 4 q^{13} + 2 q^{14} + 6 q^{15} - q^{16} + 2 q^{17} - 8 q^{18} - 5 q^{19} - 6 q^{20} - 12 q^{21} - 11 q^{22} - 4 q^{23} + q^{24} + 9 q^{25} + 6 q^{26} + 5 q^{27} + 2 q^{28} + 10 q^{29} + 6 q^{30} - 2 q^{31} + 4 q^{32} + 11 q^{33} + 2 q^{34} + 12 q^{35} - 8 q^{36} - 18 q^{37} + 10 q^{38} - 6 q^{39} + 4 q^{40} - 2 q^{41} - 2 q^{42} + 6 q^{43} + 4 q^{44} - 28 q^{45} - 4 q^{46} - 8 q^{47} - 4 q^{48} + 3 q^{49} - 11 q^{50} - 7 q^{51} + 6 q^{52} - 4 q^{53} + 4 q^{55} - 8 q^{56} + 5 q^{57} + 10 q^{58} + 5 q^{59} - 4 q^{60} + 8 q^{61} - 2 q^{62} + 16 q^{63} - q^{64} + 16 q^{65} + 16 q^{66} + 22 q^{67} + 2 q^{68} + 14 q^{69} - 8 q^{70} + 8 q^{71} + 7 q^{72} - 14 q^{73} - 18 q^{74} - 9 q^{75} - 10 q^{76} - 8 q^{77} - 16 q^{78} - 30 q^{79} + 4 q^{80} + 14 q^{81} - 7 q^{82} - 19 q^{83} + 8 q^{84} + 2 q^{85} + 21 q^{86} - 20 q^{87} - q^{88} - 10 q^{89} + 12 q^{90} - 12 q^{91} + 6 q^{92} + 2 q^{93} + 12 q^{94} - 10 q^{95} - 4 q^{96} - 3 q^{97} - 12 q^{98} - 13 q^{99}+O(q^{100}) \) 4 * q - q^2 - 4 * q^3 - q^4 - 6 * q^5 + q^6 + 2 * q^7 - q^8 + 7 * q^9 + 4 * q^10 - q^11 + 6 * q^12 - 4 * q^13 + 2 * q^14 + 6 * q^15 - q^16 + 2 * q^17 - 8 * q^18 - 5 * q^19 - 6 * q^20 - 12 * q^21 - 11 * q^22 - 4 * q^23 + q^24 + 9 * q^25 + 6 * q^26 + 5 * q^27 + 2 * q^28 + 10 * q^29 + 6 * q^30 - 2 * q^31 + 4 * q^32 + 11 * q^33 + 2 * q^34 + 12 * q^35 - 8 * q^36 - 18 * q^37 + 10 * q^38 - 6 * q^39 + 4 * q^40 - 2 * q^41 - 2 * q^42 + 6 * q^43 + 4 * q^44 - 28 * q^45 - 4 * q^46 - 8 * q^47 - 4 * q^48 + 3 * q^49 - 11 * q^50 - 7 * q^51 + 6 * q^52 - 4 * q^53 + 4 * q^55 - 8 * q^56 + 5 * q^57 + 10 * q^58 + 5 * q^59 - 4 * q^60 + 8 * q^61 - 2 * q^62 + 16 * q^63 - q^64 + 16 * q^65 + 16 * q^66 + 22 * q^67 + 2 * q^68 + 14 * q^69 - 8 * q^70 + 8 * q^71 + 7 * q^72 - 14 * q^73 - 18 * q^74 - 9 * q^75 - 10 * q^76 - 8 * q^77 - 16 * q^78 - 30 * q^79 + 4 * q^80 + 14 * q^81 - 7 * q^82 - 19 * q^83 + 8 * q^84 + 2 * q^85 + 21 * q^86 - 20 * q^87 - q^88 - 10 * q^89 + 12 * q^90 - 12 * q^91 + 6 * q^92 + 2 * q^93 + 12 * q^94 - 10 * q^95 - 4 * q^96 - 3 * q^97 - 12 * q^98 - 13 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	0.118034	+	0.363271i	0.0681470	+	0.209735i	0.979331	−	0.202265i	$-0.0648303\pi$
$3$	0.118034	+	0.363271i	0.0681470	+	0.209735i	−0.911184	+	0.412000i	$0.864830\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−2.61803	−	1.90211i	−1.17082	−	0.850651i	−0.179714	−	0.983719i	$-0.557517\pi$
$5$	−2.61803	−	1.90211i	−1.17082	−	0.850651i	−0.991107	+	0.133068i	$0.957517\pi$
$6$	−0.309017	−	0.224514i	−0.126156	−	0.0916575i
$7$	−0.618034	+	1.90211i	−0.233595	+	0.718931i	0.763710	+	0.645560i	$0.223376\pi$
$7$	−0.618034	+	1.90211i	−0.233595	+	0.718931i	−0.997305	+	0.0733714i	$0.976624\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	2.30902	−	1.67760i	0.769672	−	0.559200i
$10$	3.23607			1.02333
$11$	0.309017	+	3.30220i	0.0931721	+	0.995650i
$11$	0.309017	+	3.30220i	0.0931721	+	0.995650i
$12$	0.381966			0.110264
$13$	−1.00000	+	0.726543i	−0.277350	+	0.201507i	−0.717761	−	0.696290i	$-0.754833\pi$
$13$	−1.00000	+	0.726543i	−0.277350	+	0.201507i	0.440411	+	0.897796i	$0.354833\pi$
$14$	−0.618034	−	1.90211i	−0.165177	−	0.508361i
$15$	0.381966	−	1.17557i	0.0986232	−	0.303531i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	0.500000	+	0.363271i	0.121268	+	0.0881062i	0.646766	−	0.762688i	$-0.276121\pi$
$17$	0.500000	+	0.363271i	0.121268	+	0.0881062i	−0.525498	+	0.850795i	$0.676121\pi$
$18$	−0.881966	+	2.71441i	−0.207881	+	0.639793i
$19$	−1.80902	−	5.56758i	−0.415017	−	1.27729i	−0.912236	−	0.409666i	$-0.865645\pi$
$19$	−1.80902	−	5.56758i	−0.415017	−	1.27729i	0.497219	−	0.867625i	$-0.334355\pi$
$20$	−2.61803	+	1.90211i	−0.585410	+	0.425325i
$21$	−0.763932			−0.166704
$22$	−2.19098	−	2.48990i	−0.467119	−	0.530848i
$23$	1.23607			0.257738			0.128869	−	0.991662i	$-0.458865\pi$
$23$	1.23607			0.257738			0.128869	+	0.991662i	$0.458865\pi$
$24$	−0.309017	+	0.224514i	−0.0630778	+	0.0458287i
$25$	1.69098	+	5.20431i	0.338197	+	1.04086i
$26$	0.381966	−	1.17557i	0.0749097	−	0.230548i
$27$	1.80902	+	1.31433i	0.348145	+	0.252942i
$28$	1.61803	+	1.17557i	0.305780	+	0.222162i
$29$	1.38197	−	4.25325i	0.256625	−	0.789809i	−0.736881	−	0.676023i	$-0.763702\pi$
$29$	1.38197	−	4.25325i	0.256625	−	0.789809i	0.993505	−	0.113787i	$-0.0362980\pi$
$30$	0.381966	+	1.17557i	0.0697371	+	0.214629i
$31$	−1.61803	+	1.17557i	−0.290607	+	0.211139i	−0.723531	−	0.690292i	$-0.757482\pi$
$31$	−1.61803	+	1.17557i	−0.290607	+	0.211139i	0.432923	+	0.901431i	$0.357482\pi$
$32$	1.00000			0.176777
$33$	−1.16312	+	0.502029i	−0.202473	+	0.0873920i
$34$	−0.618034			−0.105992
$35$	5.23607	−	3.80423i	0.885057	−	0.643032i
$36$	−0.881966	−	2.71441i	−0.146994	−	0.452402i
$37$	−1.14590	+	3.52671i	−0.188384	+	0.579788i	−0.999990	−	0.00441771i	$-0.998594\pi$
$37$	−1.14590	+	3.52671i	−0.188384	+	0.579788i	0.811606	+	0.584206i	$0.198594\pi$
$38$	4.73607	+	3.44095i	0.768292	+	0.558197i
$39$	−0.381966	−	0.277515i	−0.0611635	−	0.0444379i
$40$	1.00000	−	3.07768i	0.158114	−	0.486624i
$41$	1.73607	+	5.34307i	0.271128	+	0.834447i	0.990218	+	0.139530i	$0.0445591\pi$
$41$	1.73607	+	5.34307i	0.271128	+	0.834447i	−0.719090	+	0.694917i	$0.755441\pi$
$42$	0.618034	−	0.449028i	0.0953647	−	0.0692865i
$43$	−8.56231			−1.30574			−0.652870	−	0.757470i	$-0.726435\pi$
$43$	−8.56231			−1.30574			−0.652870	+	0.757470i	$0.726435\pi$
$44$	3.23607	+	0.726543i	0.487856	+	0.109530i
$45$	−9.23607			−1.37683
$46$	−1.00000	+	0.726543i	−0.147442	+	0.107123i
$47$	−2.00000	−	6.15537i	−0.291730	−	0.897853i	−0.984300	−	0.176502i	$-0.943522\pi$
$47$	−2.00000	−	6.15537i	−0.291730	−	0.897853i	0.692570	−	0.721350i	$-0.256478\pi$
$48$	0.118034	−	0.363271i	0.0170367	−	0.0524337i
$49$	2.42705	+	1.76336i	0.346722	+	0.251908i
$50$	−4.42705	−	3.21644i	−0.626080	−	0.454873i
$51$	−0.0729490	+	0.224514i	−0.0102149	+	0.0314382i
$52$	0.381966	+	1.17557i	0.0529692	+	0.163022i
$53$	1.23607	−	0.898056i	0.169787	−	0.123357i	−0.499647	−	0.866229i	$-0.666537\pi$
$53$	1.23607	−	0.898056i	0.169787	−	0.123357i	0.669434	+	0.742872i	$0.266537\pi$
$54$	−2.23607			−0.304290
$55$	5.47214	−	9.23305i	0.737863	−	1.24498i
$56$	−2.00000			−0.267261
$57$	1.80902	−	1.31433i	0.239610	−	0.174087i
$58$	1.38197	+	4.25325i	0.181461	+	0.558480i
$59$	−2.66312	+	8.19624i	−0.346709	+	1.06706i	0.613954	+	0.789342i	$0.289578\pi$
$59$	−2.66312	+	8.19624i	−0.346709	+	1.06706i	−0.960663	+	0.277718i	$0.910422\pi$
$60$	−1.00000	−	0.726543i	−0.129099	−	0.0937962i
$61$	2.00000	+	1.45309i	0.256074	+	0.186048i	0.708414	−	0.705797i	$-0.249411\pi$
$61$	2.00000	+	1.45309i	0.256074	+	0.186048i	−0.452341	+	0.891845i	$0.649411\pi$
$62$	0.618034	−	1.90211i	0.0784904	−	0.241569i
$63$	1.76393	+	5.42882i	0.222235	+	0.683968i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	4.00000			0.496139
$66$	0.645898	−	1.08981i	0.0795046	−	0.134147i
$67$	11.0902			1.35488			0.677440	−	0.735578i	$-0.263089\pi$
$67$	11.0902			1.35488			0.677440	+	0.735578i	$0.263089\pi$
$68$	0.500000	−	0.363271i	0.0606339	−	0.0440531i
$69$	0.145898	+	0.449028i	0.0175641	+	0.0540566i
$70$	−2.00000	+	6.15537i	−0.239046	+	0.735707i
$71$	4.23607	+	3.07768i	0.502729	+	0.365254i	0.810058	−	0.586349i	$-0.199435\pi$
$71$	4.23607	+	3.07768i	0.502729	+	0.365254i	−0.307330	+	0.951603i	$0.599435\pi$
$72$	2.30902	+	1.67760i	0.272120	+	0.197707i
$73$	3.20820	−	9.87384i	0.375492	−	1.15565i	−0.567654	−	0.823267i	$-0.692149\pi$
$73$	3.20820	−	9.87384i	0.375492	−	1.15565i	0.943146	−	0.332378i	$-0.107851\pi$
$74$	−1.14590	−	3.52671i	−0.133208	−	0.409972i
$75$	−1.69098	+	1.22857i	−0.195258	+	0.141863i
$76$	−5.85410			−0.671512
$77$	−6.47214	−	1.45309i	−0.737568	−	0.165594i
$78$	0.472136			0.0534589
$79$	−10.8541	+	7.88597i	−1.22118	+	0.887241i	−0.996198	−	0.0871218i	$-0.972233\pi$
$79$	−10.8541	+	7.88597i	−1.22118	+	0.887241i	−0.224984	+	0.974362i	$0.572233\pi$
$80$	1.00000	+	3.07768i	0.111803	+	0.344095i
$81$	2.38197	−	7.33094i	0.264663	−	0.814549i
$82$	−4.54508	−	3.30220i	−0.501921	−	0.364667i
$83$	−7.54508	−	5.48183i	−0.828181	−	0.601708i	0.0908634	−	0.995863i	$-0.471037\pi$
$83$	−7.54508	−	5.48183i	−0.828181	−	0.601708i	−0.919044	+	0.394155i	$0.871037\pi$
$84$	−0.236068	+	0.726543i	−0.0257571	+	0.0792723i
$85$	−0.618034	−	1.90211i	−0.0670352	−	0.206313i
$86$	6.92705	−	5.03280i	0.746963	−	0.542700i
$87$	1.70820			0.183139
$88$	−3.04508	+	1.31433i	−0.324607	+	0.140108i
$89$	−8.09017			−0.857556			−0.428778	−	0.903410i	$-0.641056\pi$
$89$	−8.09017			−0.857556			−0.428778	+	0.903410i	$0.641056\pi$
$90$	7.47214	−	5.42882i	0.787632	−	0.572248i
$91$	−0.763932	−	2.35114i	−0.0800818	−	0.246467i
$92$	0.381966	−	1.17557i	0.0398227	−	0.122562i
$93$	−0.618034	−	0.449028i	−0.0640871	−	0.0465620i
$94$	5.23607	+	3.80423i	0.540059	+	0.392376i
$95$	−5.85410	+	18.0171i	−0.600618	+	1.84851i
$96$	0.118034	+	0.363271i	0.0120468	+	0.0370762i
$97$	−5.78115	+	4.20025i	−0.586987	+	0.426471i	−0.841236	−	0.540668i	$-0.818172\pi$
$97$	−5.78115	+	4.20025i	−0.586987	+	0.426471i	0.254249	+	0.967139i	$0.418172\pi$
$98$	−3.00000			−0.303046
$99$	6.25329	+	7.10642i	0.628479	+	0.714222i
$100$	5.47214			0.547214
$101$	3.38197	−	2.45714i	0.336518	−	0.244495i	−0.406673	−	0.913574i	$-0.633311\pi$
$101$	3.38197	−	2.45714i	0.336518	−	0.244495i	0.743191	+	0.669079i	$0.233311\pi$
$102$	−0.0729490	−	0.224514i	−0.00722303	−	0.0222302i
$103$	4.85410	−	14.9394i	0.478289	−	1.47202i	−0.363181	−	0.931718i	$-0.618309\pi$
$103$	4.85410	−	14.9394i	0.478289	−	1.47202i	0.841470	−	0.540303i	$-0.181691\pi$
$104$	−1.00000	−	0.726543i	−0.0980581	−	0.0712434i
$105$	2.00000	+	1.45309i	0.195180	+	0.141807i
$106$	−0.472136	+	1.45309i	−0.0458579	+	0.141136i
$107$	−0.354102	−	1.08981i	−0.0342323	−	0.105356i	0.932480	−	0.361221i	$-0.117640\pi$
$107$	−0.354102	−	1.08981i	−0.0342323	−	0.105356i	−0.966713	+	0.255864i	$0.917640\pi$
$108$	1.80902	−	1.31433i	0.174073	−	0.126471i
$109$	18.9443			1.81453			0.907266	−	0.420557i	$-0.138165\pi$
$109$	18.9443			1.81453			0.907266	+	0.420557i	$0.138165\pi$
$110$	1.00000	+	10.6861i	0.0953463	+	1.01888i
$111$	−1.41641			−0.134439
$112$	1.61803	−	1.17557i	0.152890	−	0.111081i
$113$	−0.572949	−	1.76336i	−0.0538985	−	0.165883i	0.920484	−	0.390781i	$-0.127795\pi$
$113$	−0.572949	−	1.76336i	−0.0538985	−	0.165883i	−0.974382	+	0.224898i	$0.927795\pi$
$114$	−0.690983	+	2.12663i	−0.0647165	+	0.199177i
$115$	−3.23607	−	2.35114i	−0.301765	−	0.219245i
$116$	−3.61803	−	2.62866i	−0.335926	−	0.244065i
$117$	−1.09017	+	3.35520i	−0.100786	+	0.310188i
$118$	−2.66312	−	8.19624i	−0.245160	−	0.754525i
$119$	−1.00000	+	0.726543i	−0.0916698	+	0.0666020i
$120$	1.23607			0.112837
$121$	−10.8090	+	2.04087i	−0.982638	+	0.185534i
$122$	−2.47214			−0.223817
$123$	−1.73607	+	1.26133i	−0.156536	+	0.113730i
$124$	0.618034	+	1.90211i	0.0555011	+	0.170815i
$125$	0.472136	−	1.45309i	0.0422291	−	0.129968i
$126$	−4.61803	−	3.35520i	−0.411407	−	0.298905i
$127$	8.85410	+	6.43288i	0.785675	+	0.570826i	0.906677	−	0.421826i	$-0.138611\pi$
$127$	8.85410	+	6.43288i	0.785675	+	0.570826i	−0.121002	+	0.992652i	$0.538611\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−1.01064	−	3.11044i	−0.0889822	−	0.273859i
$130$	−3.23607	+	2.35114i	−0.283822	+	0.206209i
$131$	6.79837			0.593977			0.296988	−	0.954881i	$-0.404018\pi$
$131$	6.79837			0.593977			0.296988	+	0.954881i	$0.404018\pi$
$132$	0.118034	+	1.26133i	0.0102735	+	0.109784i
$133$	11.7082			1.01523
$134$	−8.97214	+	6.51864i	−0.775074	+	0.563125i
$135$	−2.23607	−	6.88191i	−0.192450	−	0.592300i
$136$	−0.190983	+	0.587785i	−0.0163767	+	0.0504022i
$137$	−13.0172	−	9.45756i	−1.11214	−	0.808014i	−0.129138	−	0.991627i	$-0.541221\pi$
$137$	−13.0172	−	9.45756i	−1.11214	−	0.808014i	−0.982999	+	0.183612i	$0.941221\pi$
$138$	−0.381966	−	0.277515i	−0.0325151	−	0.0236236i
$139$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$139$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$140$	−2.00000	−	6.15537i	−0.169031	−	0.520223i
$141$	2.00000	−	1.45309i	0.168430	−	0.122372i
$142$	−5.23607			−0.439401
$143$	−2.70820	−	3.07768i	−0.226471	−	0.257369i
$144$	−2.85410			−0.237842
$145$	−11.7082	+	8.50651i	−0.972313	+	0.706427i
$146$	3.20820	+	9.87384i	0.265513	+	0.817165i
$147$	−0.354102	+	1.08981i	−0.0292058	+	0.0898863i
$148$	3.00000	+	2.17963i	0.246598	+	0.179164i
$149$	5.00000	+	3.63271i	0.409616	+	0.297603i	0.773446	−	0.633862i	$-0.218531\pi$
$149$	5.00000	+	3.63271i	0.409616	+	0.297603i	−0.363830	+	0.931465i	$0.618531\pi$
$150$	0.645898	−	1.98787i	0.0527374	−	0.162309i
$151$	−2.47214	−	7.60845i	−0.201180	−	0.619167i	−0.999849	−	0.0173966i	$-0.994462\pi$
$151$	−2.47214	−	7.60845i	−0.201180	−	0.619167i	0.798669	−	0.601770i	$-0.205538\pi$
$152$	4.73607	−	3.44095i	0.384146	−	0.279098i
$153$	1.76393			0.142605
$154$	6.09017	−	2.62866i	0.490760	−	0.211823i
$155$	6.47214			0.519854
$156$	−0.381966	+	0.277515i	−0.0305818	+	0.0222189i
$157$	3.00000	+	9.23305i	0.239426	+	0.736878i	0.996503	+	0.0835524i	$0.0266266\pi$
$157$	3.00000	+	9.23305i	0.239426	+	0.736878i	−0.757077	+	0.653325i	$0.773373\pi$
$158$	4.14590	−	12.7598i	0.329830	−	1.01511i
$159$	0.472136	+	0.343027i	0.0374428	+	0.0272038i
$160$	−2.61803	−	1.90211i	−0.206974	−	0.150375i
$161$	−0.763932	+	2.35114i	−0.0602063	+	0.185296i
$162$	2.38197	+	7.33094i	0.187145	+	0.575973i
$163$	−0.736068	+	0.534785i	−0.0576533	+	0.0418876i	−0.616239	−	0.787559i	$-0.711344\pi$
$163$	−0.736068	+	0.534785i	−0.0576533	+	0.0418876i	0.558585	+	0.829447i	$0.311344\pi$
$164$	5.61803			0.438695
$165$	4.00000	+	0.898056i	0.311400	+	0.0699136i
$166$	9.32624			0.723856
$167$	11.9443	−	8.67802i	0.924276	−	0.671525i	−0.0203090	−	0.999794i	$-0.506465\pi$
$167$	11.9443	−	8.67802i	0.924276	−	0.671525i	0.944585	+	0.328268i	$0.106465\pi$
$168$	−0.236068	−	0.726543i	−0.0182130	−	0.0560540i
$169$	−3.54508	+	10.9106i	−0.272699	+	0.839281i
$170$	1.61803	+	1.17557i	0.124098	+	0.0901621i
$171$	−13.5172	−	9.82084i	−1.03369	−	0.751018i
$172$	−2.64590	+	8.14324i	−0.201748	+	0.620916i
$173$	6.76393	+	20.8172i	0.514252	+	1.58271i	0.784638	+	0.619954i	$0.212849\pi$
$173$	6.76393	+	20.8172i	0.514252	+	1.58271i	−0.270386	+	0.962752i	$0.587151\pi$
$174$	−1.38197	+	1.00406i	−0.104767	+	0.0761174i
$175$	−10.9443			−0.827309
$176$	1.69098	−	2.85317i	0.127463	−	0.215066i
$177$	−3.29180			−0.247427
$178$	6.54508	−	4.75528i	0.490575	−	0.356423i
$179$	−2.66312	−	8.19624i	−0.199051	−	0.612616i	−0.999905	−	0.0137566i	$-0.995621\pi$
$179$	−2.66312	−	8.19624i	−0.199051	−	0.612616i	0.800855	−	0.598859i	$-0.204379\pi$
$180$	−2.85410	+	8.78402i	−0.212732	+	0.654722i
$181$	3.38197	+	2.45714i	0.251380	+	0.182638i	0.706338	−	0.707875i	$-0.250346\pi$
$181$	3.38197	+	2.45714i	0.251380	+	0.182638i	−0.454958	+	0.890513i	$0.650346\pi$
$182$	2.00000	+	1.45309i	0.148250	+	0.107710i
$183$	−0.291796	+	0.898056i	−0.0215702	+	0.0663862i
$184$	0.381966	+	1.17557i	0.0281589	+	0.0866642i
$185$	9.70820	−	7.05342i	0.713761	−	0.518578i
$186$	0.763932			0.0560142
$187$	−1.04508	+	1.76336i	−0.0764242	+	0.128949i
$188$	−6.47214			−0.472029
$189$	−3.61803	+	2.62866i	−0.263173	+	0.191207i
$190$	−5.85410	−	18.0171i	−0.424701	−	1.30710i
$191$	1.47214	−	4.53077i	0.106520	−	0.327835i	−0.883564	−	0.468310i	$-0.844863\pi$
$191$	1.47214	−	4.53077i	0.106520	−	0.327835i	0.990084	+	0.140475i	$0.0448630\pi$
$192$	−0.309017	−	0.224514i	−0.0223014	−	0.0162029i
$193$	−14.0902	−	10.2371i	−1.01423	−	0.736883i	−0.0491400	−	0.998792i	$-0.515648\pi$
$193$	−14.0902	−	10.2371i	−1.01423	−	0.736883i	−0.965093	+	0.261909i	$0.915648\pi$
$194$	2.20820	−	6.79615i	0.158540	−	0.487935i
$195$	0.472136	+	1.45309i	0.0338104	+	0.104058i
$196$	2.42705	−	1.76336i	0.173361	−	0.125954i
$197$	−20.9443			−1.49222			−0.746109	−	0.665824i	$-0.768080\pi$
$197$	−20.9443			−1.49222			−0.746109	+	0.665824i	$0.768080\pi$
$198$	−9.23607	−	2.07363i	−0.656379	−	0.147366i
$199$	−18.9443			−1.34292			−0.671462	−	0.741039i	$-0.734333\pi$
$199$	−18.9443			−1.34292			−0.671462	+	0.741039i	$0.734333\pi$
$200$	−4.42705	+	3.21644i	−0.313040	+	0.227437i
$201$	1.30902	+	4.02874i	0.0923309	+	0.284165i
$202$	−1.29180	+	3.97574i	−0.0908905	+	0.279732i
$203$	7.23607	+	5.25731i	0.507872	+	0.368991i
$204$	0.190983	+	0.138757i	0.0133715	+	0.00971495i
$205$	5.61803	−	17.2905i	0.392381	−	1.20762i
$206$	4.85410	+	14.9394i	0.338201	+	1.04088i
$207$	2.85410	−	2.07363i	0.198374	−	0.144127i
$208$	1.23607			0.0857059
$209$	17.8262	−	7.69421i	1.23307	−	0.532220i
$210$	−2.47214			−0.170594
$211$	4.92705	−	3.57971i	0.339192	−	0.246438i	−0.405129	−	0.914260i	$-0.632773\pi$
$211$	4.92705	−	3.57971i	0.339192	−	0.246438i	0.744321	+	0.667822i	$0.232773\pi$
$212$	−0.472136	−	1.45309i	−0.0324264	−	0.0997983i
$213$	−0.618034	+	1.90211i	−0.0423470	+	0.130331i
$214$	0.927051	+	0.673542i	0.0633719	+	0.0460424i
$215$	22.4164	+	16.2865i	1.52879	+	1.11073i
$216$	−0.690983	+	2.12663i	−0.0470154	+	0.144699i
$217$	−1.23607	−	3.80423i	−0.0839098	−	0.258248i
$218$	−15.3262	+	11.1352i	−1.03802	+	0.754168i
$219$	3.96556			0.267968
$220$	−7.09017	−	8.05748i	−0.478019	−	0.543235i
$221$	−0.763932			−0.0513876
$222$	1.14590	−	0.832544i	0.0769076	−	0.0558767i
$223$	7.94427	+	24.4500i	0.531988	+	1.63729i	0.750069	+	0.661359i	$0.230020\pi$
$223$	7.94427	+	24.4500i	0.531988	+	1.63729i	−0.218081	+	0.975931i	$0.569980\pi$
$224$	−0.618034	+	1.90211i	−0.0412941	+	0.127090i
$225$	12.6353	+	9.18005i	0.842350	+	0.612003i
$226$	1.50000	+	1.08981i	0.0997785	+	0.0724933i
$227$	4.48278	−	13.7966i	0.297532	−	0.915711i	−0.684827	−	0.728706i	$-0.740122\pi$
$227$	4.48278	−	13.7966i	0.297532	−	0.915711i	0.982359	−	0.187005i	$-0.0598780\pi$
$228$	−0.690983	−	2.12663i	−0.0457615	−	0.140839i
$229$	−1.38197	+	1.00406i	−0.0913229	+	0.0663500i	−0.632510	−	0.774552i	$-0.717975\pi$
$229$	−1.38197	+	1.00406i	−0.0913229	+	0.0663500i	0.541187	+	0.840902i	$0.317975\pi$
$230$	4.00000			0.263752
$231$	−0.236068	−	2.52265i	−0.0155321	−	0.165978i
$232$	4.47214			0.293610
$233$	7.78115	−	5.65334i	0.509760	−	0.370363i	−0.302972	−	0.952999i	$-0.597979\pi$
$233$	7.78115	−	5.65334i	0.509760	−	0.370363i	0.812733	+	0.582637i	$0.197979\pi$
$234$	−1.09017	−	3.35520i	−0.0712666	−	0.219336i
$235$	−6.47214	+	19.9192i	−0.422196	+	1.29938i
$236$	6.97214	+	5.06555i	0.453847	+	0.329739i
$237$	−4.14590	−	3.01217i	−0.269305	−	0.195662i
$238$	0.381966	−	1.17557i	0.0247592	−	0.0762009i
$239$	−6.70820	−	20.6457i	−0.433918	−	1.33546i	−0.894192	−	0.447684i	$-0.852249\pi$
$239$	−6.70820	−	20.6457i	−0.433918	−	1.33546i	0.460274	−	0.887777i	$-0.347751\pi$
$240$	−1.00000	+	0.726543i	−0.0645497	+	0.0468981i
$241$	−11.0902			−0.714381			−0.357190	−	0.934032i	$-0.616265\pi$
$241$	−11.0902			−0.714381			−0.357190	+	0.934032i	$0.616265\pi$
$242$	7.54508	−	8.00448i	0.485016	−	0.514547i
$243$	9.65248			0.619207
$244$	2.00000	−	1.45309i	0.128037	−	0.0930242i
$245$	−3.00000	−	9.23305i	−0.191663	−	0.589878i
$246$	0.663119	−	2.04087i	0.0422789	−	0.130121i
$247$	5.85410	+	4.25325i	0.372488	+	0.270628i
$248$	−1.61803	−	1.17557i	−0.102745	−	0.0746488i
$249$	1.10081	−	3.38795i	0.0697612	−	0.214703i
$250$	0.472136	+	1.45309i	0.0298605	+	0.0919012i
$251$	−16.9443	+	12.3107i	−1.06951	+	0.777047i	−0.975825	−	0.218555i	$-0.929866\pi$
$251$	−16.9443	+	12.3107i	−1.06951	+	0.777047i	−0.0936883	+	0.995602i	$0.529866\pi$
$252$	5.70820			0.359583
$253$	0.381966	+	4.08174i	0.0240140	+	0.256617i
$254$	−10.9443			−0.686705
$255$	0.618034	−	0.449028i	0.0387028	−	0.0281192i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−1.73607	+	5.34307i	−0.108293	+	0.333291i	−0.990489	−	0.137590i	$-0.956064\pi$
$257$	−1.73607	+	5.34307i	−0.108293	+	0.333291i	0.882196	+	0.470882i	$0.156064\pi$
$258$	2.64590	+	1.92236i	0.164726	+	0.119681i
$259$	−6.00000	−	4.35926i	−0.372822	−	0.270871i
$260$	1.23607	−	3.80423i	0.0766577	−	0.235928i
$261$	−3.94427	−	12.1392i	−0.244144	−	0.751399i
$262$	−5.50000	+	3.99598i	−0.339791	+	0.246873i
$263$	−23.2361			−1.43280			−0.716399	−	0.697691i	$-0.754211\pi$
$263$	−23.2361			−1.43280			−0.716399	+	0.697691i	$0.754211\pi$
$264$	−0.836881	−	0.951057i	−0.0515065	−	0.0585335i
$265$	−4.94427			−0.303724
$266$	−9.47214	+	6.88191i	−0.580774	+	0.421957i
$267$	−0.954915	−	2.93893i	−0.0584399	−	0.179859i
$268$	3.42705	−	10.5474i	0.209340	−	0.644284i
$269$	−5.00000	−	3.63271i	−0.304855	−	0.221490i	0.424830	−	0.905273i	$-0.360334\pi$
$269$	−5.00000	−	3.63271i	−0.304855	−	0.221490i	−0.729686	+	0.683783i	$0.760334\pi$
$270$	5.85410	+	4.25325i	0.356269	+	0.258845i
$271$	0.618034	−	1.90211i	0.0375429	−	0.115545i	−0.930529	−	0.366219i	$-0.880652\pi$
$271$	0.618034	−	1.90211i	0.0375429	−	0.115545i	0.968072	+	0.250674i	$0.0806521\pi$
$272$	−0.190983	−	0.587785i	−0.0115800	−	0.0356397i
$273$	0.763932	−	0.555029i	0.0462353	−	0.0335919i
$274$	16.0902			0.972043
$275$	−16.6631	+	7.19218i	−1.00482	+	0.433705i
$276$	0.472136			0.0284192
$277$	19.1803	−	13.9353i	1.15243	−	0.837293i	0.163632	−	0.986521i	$-0.447679\pi$
$277$	19.1803	−	13.9353i	1.15243	−	0.837293i	0.988803	+	0.149228i	$0.0476790\pi$
$278$		0			0
$279$	−1.76393	+	5.42882i	−0.105604	+	0.325015i
$280$	5.23607	+	3.80423i	0.312915	+	0.227346i
$281$	13.0172	+	9.45756i	0.776542	+	0.564191i	0.903939	−	0.427661i	$-0.140662\pi$
$281$	13.0172	+	9.45756i	0.776542	+	0.564191i	−0.127397	+	0.991852i	$0.540662\pi$
$282$	−0.763932	+	2.35114i	−0.0454915	+	0.140008i
$283$	7.41641	+	22.8254i	0.440860	+	1.35683i	0.886961	+	0.461844i	$0.152812\pi$
$283$	7.41641	+	22.8254i	0.440860	+	1.35683i	−0.446101	+	0.894982i	$0.647188\pi$
$284$	4.23607	−	3.07768i	0.251364	−	0.182627i
$285$	−7.23607			−0.428628
$286$	4.00000	+	0.898056i	0.236525	+	0.0531032i
$287$	−11.2361			−0.663244
$288$	2.30902	−	1.67760i	0.136060	−	0.0988535i
$289$	−5.13525	−	15.8047i	−0.302074	−	0.929688i
$290$	4.47214	−	13.7638i	0.262613	−	0.808239i
$291$	−2.20820	−	1.60435i	−0.129447	−	0.0940489i
$292$	−8.39919	−	6.10237i	−0.491525	−	0.357114i
$293$	−8.76393	+	26.9726i	−0.511994	+	1.57576i	0.276691	+	0.960959i	$0.410762\pi$
$293$	−8.76393	+	26.9726i	−0.511994	+	1.57576i	−0.788685	+	0.614798i	$0.789238\pi$
$294$	−0.354102	−	1.08981i	−0.0206516	−	0.0635592i
$295$	22.5623	−	16.3925i	1.31363	−	0.954407i
$296$	−3.70820			−0.215535
$297$	−3.78115	+	6.37988i	−0.219405	+	0.370198i
$298$	−6.18034			−0.358017
$299$	−1.23607	+	0.898056i	−0.0714837	+	0.0519359i
$300$	0.645898	+	1.98787i	0.0372909	+	0.114770i
$301$	5.29180	−	16.2865i	0.305014	−	0.938737i
$302$	6.47214	+	4.70228i	0.372430	+	0.270586i
$303$	1.29180	+	0.938545i	0.0742117	+	0.0539180i
$304$	−1.80902	+	5.56758i	−0.103754	+	0.319323i
$305$	−2.47214	−	7.60845i	−0.141554	−	0.435659i
$306$	−1.42705	+	1.03681i	−0.0815791	+	0.0592707i
$307$	27.7984			1.58654			0.793268	−	0.608872i	$-0.208378\pi$
$307$	27.7984			1.58654			0.793268	+	0.608872i	$0.208378\pi$
$308$	−3.38197	+	5.70634i	−0.192705	+	0.325149i
$309$	6.00000			0.341328
$310$	−5.23607	+	3.80423i	−0.297389	+	0.216066i
$311$	8.05573	+	24.7930i	0.456798	+	1.40588i	0.869011	+	0.494793i	$0.164756\pi$
$311$	8.05573	+	24.7930i	0.456798	+	1.40588i	−0.412212	+	0.911088i	$0.635244\pi$
$312$	0.145898	−	0.449028i	0.00825985	−	0.0254212i
$313$	−3.50000	−	2.54290i	−0.197832	−	0.143733i	0.484459	−	0.874814i	$-0.339016\pi$
$313$	−3.50000	−	2.54290i	−0.197832	−	0.143733i	−0.682291	+	0.731081i	$0.739016\pi$
$314$	−7.85410	−	5.70634i	−0.443233	−	0.322027i
$315$	5.70820	−	17.5680i	0.321621	−	0.989847i
$316$	4.14590	+	12.7598i	0.233225	+	0.717793i
$317$	3.00000	−	2.17963i	0.168497	−	0.122420i	−0.500341	−	0.865828i	$-0.666792\pi$
$317$	3.00000	−	2.17963i	0.168497	−	0.122420i	0.668838	+	0.743408i	$0.266792\pi$
$318$	−0.583592			−0.0327262
$319$	14.4721	+	3.24920i	0.810284	+	0.181920i
$320$	3.23607			0.180902
$321$	0.354102	−	0.257270i	0.0197640	−	0.0143594i
$322$	−0.763932	−	2.35114i	−0.0425723	−	0.131024i
$323$	1.11803	−	3.44095i	0.0622091	−	0.191460i
$324$	−6.23607	−	4.53077i	−0.346448	−	0.251709i
$325$	−5.47214	−	3.97574i	−0.303539	−	0.220534i
$326$	0.281153	−	0.865300i	0.0155716	−	0.0479245i
$327$	2.23607	+	6.88191i	0.123655	+	0.380570i
$328$	−4.54508	+	3.30220i	−0.250960	+	0.182333i
$329$	12.9443			0.713641
$330$	−3.76393	+	1.62460i	−0.207198	+	0.0894312i
$331$	6.27051			0.344658			0.172329	−	0.985039i	$-0.444871\pi$
$331$	6.27051			0.344658			0.172329	+	0.985039i	$0.444871\pi$
$332$	−7.54508	+	5.48183i	−0.414090	+	0.300854i
$333$	3.27051	+	10.0656i	0.179223	+	0.551591i
$334$	−4.56231	+	14.0413i	−0.249638	+	0.768308i
$335$	−29.0344	−	21.0948i	−1.58632	−	1.15253i
$336$	0.618034	+	0.449028i	0.0337165	+	0.0244965i
$337$	−8.28115	+	25.4868i	−0.451103	+	1.38835i	0.424547	+	0.905406i	$0.360433\pi$
$337$	−8.28115	+	25.4868i	−0.451103	+	1.38835i	−0.875650	+	0.482947i	$0.839567\pi$
$338$	−3.54508	−	10.9106i	−0.192827	−	0.593461i
$339$	0.572949	−	0.416272i	0.0311183	−	0.0226088i
$340$	−2.00000			−0.108465
$341$	−4.38197	−	4.97980i	−0.237297	−	0.269671i
$342$	16.7082			0.903476
$343$	−16.1803	+	11.7557i	−0.873656	+	0.634748i
$344$	−2.64590	−	8.14324i	−0.142657	−	0.439054i
$345$	0.472136	−	1.45309i	0.0254189	−	0.0782315i
$346$	−17.7082	−	12.8658i	−0.951999	−	0.691668i
$347$	−13.4443	−	9.76784i	−0.721726	−	0.524365i	0.165209	−	0.986259i	$-0.447170\pi$
$347$	−13.4443	−	9.76784i	−0.721726	−	0.524365i	−0.886935	+	0.461894i	$0.847170\pi$
$348$	0.527864	−	1.62460i	0.0282965	−	0.0870876i
$349$	−6.05573	−	18.6376i	−0.324156	−	0.997649i	−0.971820	−	0.235723i	$-0.924254\pi$
$349$	−6.05573	−	18.6376i	−0.324156	−	0.997649i	0.647665	−	0.761926i	$-0.275746\pi$
$350$	8.85410	−	6.43288i	0.473272	−	0.343852i
$351$	−2.76393			−0.147528
$352$	0.309017	+	3.30220i	0.0164707	+	0.176008i
$353$	32.6180			1.73608			0.868041	−	0.496492i	$-0.165379\pi$
$353$	32.6180			1.73608			0.868041	+	0.496492i	$0.165379\pi$
$354$	2.66312	−	1.93487i	0.141543	−	0.102837i
$355$	−5.23607	−	16.1150i	−0.277902	−	0.855293i
$356$	−2.50000	+	7.69421i	−0.132500	+	0.407792i
$357$	−0.381966	−	0.277515i	−0.0202158	−	0.0146876i
$358$	6.97214	+	5.06555i	0.368489	+	0.267723i
$359$	1.58359	−	4.87380i	0.0835788	−	0.257229i	−0.900531	−	0.434793i	$-0.856822\pi$
$359$	1.58359	−	4.87380i	0.0835788	−	0.257229i	0.984109	+	0.177564i	$0.0568216\pi$
$360$	−2.85410	−	8.78402i	−0.150424	−	0.462959i
$361$	−12.3541	+	8.97578i	−0.650216	+	0.472409i
$362$	−4.18034			−0.219714
$363$	−2.01722	−	3.68571i	−0.105877	−	0.193450i
$364$	−2.47214			−0.129575
$365$	−27.1803	+	19.7477i	−1.42268	+	1.03364i
$366$	−0.291796	−	0.898056i	−0.0152524	−	0.0469421i
$367$	6.09017	−	18.7436i	0.317904	−	0.978409i	−0.656638	−	0.754206i	$-0.728022\pi$
$367$	6.09017	−	18.7436i	0.317904	−	0.978409i	0.974542	−	0.224203i	$-0.0719779\pi$
$368$	−1.00000	−	0.726543i	−0.0521286	−	0.0378736i
$369$	12.9721	+	9.42481i	0.675302	+	0.490636i
$370$	−3.70820	+	11.4127i	−0.192780	+	0.593317i
$371$	0.944272	+	2.90617i	0.0490242	+	0.150881i
$372$	−0.618034	+	0.449028i	−0.0320436	+	0.0232810i
$373$	−4.29180			−0.222221			−0.111110	−	0.993808i	$-0.535441\pi$
$373$	−4.29180			−0.222221			−0.111110	+	0.993808i	$0.535441\pi$
$374$	−0.190983	−	2.04087i	−0.00987550	−	0.105531i
$375$	0.583592			0.0301366
$376$	5.23607	−	3.80423i	0.270030	−	0.196188i
$377$	1.70820	+	5.25731i	0.0879770	+	0.270765i
$378$	1.38197	−	4.25325i	0.0710807	−	0.218764i
$379$	−11.5451	−	8.38800i	−0.593031	−	0.430862i	0.250367	−	0.968151i	$-0.419449\pi$
$379$	−11.5451	−	8.38800i	−0.593031	−	0.430862i	−0.843398	+	0.537289i	$0.819449\pi$
$380$	15.3262	+	11.1352i	0.786219	+	0.571222i
$381$	−1.29180	+	3.97574i	−0.0661807	+	0.203683i
$382$	1.47214	+	4.53077i	0.0753210	+	0.231814i
$383$	22.9443	−	16.6700i	1.17240	−	0.851797i	0.181104	−	0.983464i	$-0.442033\pi$
$383$	22.9443	−	16.6700i	1.17240	−	0.851797i	0.991294	+	0.131667i	$0.0420331\pi$
$384$	0.381966			0.0194921
$385$	14.1803	+	16.1150i	0.722697	+	0.821294i
$386$	17.4164			0.886472
$387$	−19.7705	+	14.3641i	−1.00499	+	0.730169i
$388$	2.20820	+	6.79615i	0.112105	+	0.345022i
$389$	−3.29180	+	10.1311i	−0.166901	+	0.513667i	−0.999171	−	0.0407020i	$-0.987041\pi$
$389$	−3.29180	+	10.1311i	−0.166901	+	0.513667i	0.832271	+	0.554370i	$0.187041\pi$
$390$	−1.23607	−	0.898056i	−0.0625907	−	0.0454748i
$391$	0.618034	+	0.449028i	0.0312553	+	0.0227083i
$392$	−0.927051	+	2.85317i	−0.0468231	+	0.144107i
$393$	0.802439	+	2.46965i	0.0404777	+	0.124578i
$394$	16.9443	−	12.3107i	0.853640	−	0.620206i
$395$	43.4164			2.18452
$396$	8.69098	−	3.75123i	0.436738	−	0.188506i
$397$	−17.1246			−0.859460			−0.429730	−	0.902958i	$-0.641391\pi$
$397$	−17.1246			−0.859460			−0.429730	+	0.902958i	$0.641391\pi$
$398$	15.3262	−	11.1352i	0.768235	−	0.558155i
$399$	1.38197	+	4.25325i	0.0691848	+	0.212929i
$400$	1.69098	−	5.20431i	0.0845492	−	0.260216i
$401$	14.3992	+	10.4616i	0.719061	+	0.522428i	0.886084	−	0.463525i	$-0.153415\pi$
$401$	14.3992	+	10.4616i	0.719061	+	0.522428i	−0.167023	+	0.985953i	$0.553415\pi$
$402$	−3.42705	−	2.48990i	−0.170926	−	0.124185i
$403$	0.763932	−	2.35114i	0.0380542	−	0.117119i
$404$	−1.29180	−	3.97574i	−0.0642693	−	0.197800i
$405$	−20.1803	+	14.6619i	−1.00277	+	0.728554i
$406$	−8.94427			−0.443897
$407$	−12.0000	−	2.69417i	−0.594818	−	0.133545i
$408$	−0.236068			−0.0116871
$409$	10.8541	−	7.88597i	0.536701	−	0.389936i	−0.286157	−	0.958183i	$-0.592378\pi$
$409$	10.8541	−	7.88597i	0.536701	−	0.389936i	0.822858	+	0.568247i	$0.192378\pi$
$410$	5.61803	+	17.2905i	0.277455	+	0.853918i
$411$	1.89919	−	5.84510i	0.0936800	−	0.288317i
$412$	−12.7082	−	9.23305i	−0.626088	−	0.454880i
$413$	−13.9443	−	10.1311i	−0.686153	−	0.498519i
$414$	−1.09017	+	3.35520i	−0.0535789	+	0.164899i
$415$	9.32624	+	28.7032i	0.457807	+	1.40899i
$416$	−1.00000	+	0.726543i	−0.0490290	+	0.0356217i
$417$		0			0
$418$	−9.89919	+	16.7027i	−0.484185	+	0.816958i
$419$	−10.8541			−0.530258			−0.265129	−	0.964213i	$-0.585414\pi$
$419$	−10.8541			−0.530258			−0.265129	+	0.964213i	$0.585414\pi$
$420$	2.00000	−	1.45309i	0.0975900	−	0.0709033i
$421$	−9.70820	−	29.8788i	−0.473149	−	1.45620i	−0.848438	−	0.529295i	$-0.822457\pi$
$421$	−9.70820	−	29.8788i	−0.473149	−	1.45620i	0.375289	−	0.926908i	$-0.377543\pi$
$422$	−1.88197	+	5.79210i	−0.0916127	+	0.281955i
$423$	−14.9443	−	10.8576i	−0.726615	−	0.527917i
$424$	1.23607	+	0.898056i	0.0600288	+	0.0436135i
$425$	−1.04508	+	3.21644i	−0.0506941	+	0.156020i
$426$	−0.618034	−	1.90211i	−0.0299438	−	0.0921577i
$427$	−4.00000	+	2.90617i	−0.193574	+	0.140639i
$428$	−1.14590			−0.0553891
$429$	0.798374	−	1.34708i	0.0385459	−	0.0650378i
$430$	−27.7082			−1.33621
$431$	13.7082	−	9.95959i	0.660301	−	0.479737i	−0.206464	−	0.978454i	$-0.566196\pi$
$431$	13.7082	−	9.95959i	0.660301	−	0.479737i	0.866765	+	0.498718i	$0.166196\pi$
$432$	−0.690983	−	2.12663i	−0.0332449	−	0.102317i
$433$	8.57295	−	26.3848i	0.411990	−	1.26797i	−0.502926	−	0.864329i	$-0.667743\pi$
$433$	8.57295	−	26.3848i	0.411990	−	1.26797i	0.914916	−	0.403644i	$-0.132257\pi$
$434$	3.23607	+	2.35114i	0.155336	+	0.112858i
$435$	−4.47214	−	3.24920i	−0.214423	−	0.155787i
$436$	5.85410	−	18.0171i	0.280361	−	0.862861i
$437$	−2.23607	−	6.88191i	−0.106966	−	0.329206i
$438$	−3.20820	+	2.33090i	−0.153294	+	0.111375i
$439$	−6.58359			−0.314218			−0.157109	−	0.987581i	$-0.550217\pi$
$439$	−6.58359			−0.314218			−0.157109	+	0.987581i	$0.550217\pi$
$440$	10.4721	+	2.35114i	0.499239	+	0.112086i
$441$	8.56231			0.407729
$442$	0.618034	−	0.449028i	0.0293969	−	0.0213581i
$443$	−2.64590	−	8.14324i	−0.125710	−	0.386897i	0.868319	−	0.496005i	$-0.165200\pi$
$443$	−2.64590	−	8.14324i	−0.125710	−	0.386897i	−0.994030	+	0.109109i	$0.965200\pi$
$444$	−0.437694	+	1.34708i	−0.0207720	+	0.0639298i
$445$	21.1803	+	15.3884i	1.00404	+	0.729481i
$446$	−20.7984	−	15.1109i	−0.984832	−	0.715522i
$447$	−0.729490	+	2.24514i	−0.0345037	+	0.106191i
$448$	−0.618034	−	1.90211i	−0.0291994	−	0.0898664i
$449$	−7.50000	+	5.44907i	−0.353947	+	0.257157i	−0.750523	−	0.660844i	$-0.770198\pi$
$449$	−7.50000	+	5.44907i	−0.353947	+	0.257157i	0.396576	+	0.918002i	$0.370198\pi$
$450$	−15.6180			−0.736241
$451$	−17.1074	+	7.38394i	−0.805556	+	0.347696i
$452$	−1.85410			−0.0872096
$453$	2.47214	−	1.79611i	0.116151	−	0.0843887i
$454$	4.48278	+	13.7966i	0.210387	+	0.647505i
$455$	−2.47214	+	7.60845i	−0.115896	+	0.356690i
$456$	1.80902	+	1.31433i	0.0847150	+	0.0615490i
$457$	7.63525	+	5.54734i	0.357162	+	0.259493i	0.751867	−	0.659314i	$-0.229153\pi$
$457$	7.63525	+	5.54734i	0.357162	+	0.259493i	−0.394705	+	0.918808i	$0.629153\pi$
$458$	0.527864	−	1.62460i	0.0246655	−	0.0759125i
$459$	0.427051	+	1.31433i	0.0199330	+	0.0613476i
$460$	−3.23607	+	2.35114i	−0.150882	+	0.109623i
$461$	1.34752			0.0627605			0.0313802	−	0.999508i	$-0.490010\pi$
$461$	1.34752			0.0627605			0.0313802	+	0.999508i	$0.490010\pi$
$462$	1.67376	+	1.90211i	0.0778705	+	0.0884943i
$463$	−19.4164			−0.902357			−0.451178	−	0.892434i	$-0.648996\pi$
$463$	−19.4164			−0.902357			−0.451178	+	0.892434i	$0.648996\pi$
$464$	−3.61803	+	2.62866i	−0.167963	+	0.122032i
$465$	0.763932	+	2.35114i	0.0354265	+	0.109032i
$466$	−2.97214	+	9.14729i	−0.137682	+	0.423740i
$467$	26.9443	+	19.5762i	1.24683	+	0.905877i	0.998034	−	0.0626787i	$-0.0199643\pi$
$467$	26.9443	+	19.5762i	1.24683	+	0.905877i	0.248798	+	0.968555i	$0.419964\pi$
$468$	2.85410	+	2.07363i	0.131931	+	0.0958534i
$469$	−6.85410	+	21.0948i	−0.316493	+	0.974065i
$470$	−6.47214	−	19.9192i	−0.298537	−	0.918804i
$471$	−3.00000	+	2.17963i	−0.138233	+	0.100432i
$472$	−8.61803			−0.396677
$473$	−2.64590	−	28.2744i	−0.121659	−	1.30006i
$474$	5.12461			0.235381
$475$	25.9164	−	18.8294i	1.18913	−	0.863951i
$476$	0.381966	+	1.17557i	0.0175074	+	0.0538822i
$477$	1.34752	−	4.14725i	0.0616989	−	0.189890i
$478$	17.5623	+	12.7598i	0.803281	+	0.583618i
$479$	27.8885	+	20.2622i	1.27426	+	0.925804i	0.999364	−	0.0356697i	$-0.0113564\pi$
$479$	27.8885	+	20.2622i	1.27426	+	0.925804i	0.274896	+	0.961474i	$0.411356\pi$
$480$	0.381966	−	1.17557i	0.0174343	−	0.0536572i
$481$	−1.41641	−	4.35926i	−0.0645826	−	0.198765i
$482$	8.97214	−	6.51864i	0.408670	−	0.296916i
$483$	−0.944272			−0.0429659
$484$	−1.39919	+	10.9106i	−0.0635994	+	0.495939i
$485$	23.1246			1.05003
$486$	−7.80902	+	5.67358i	−0.354224	+	0.257359i
$487$	−0.416408	−	1.28157i	−0.0188692	−	0.0580736i	0.941179	−	0.337910i	$-0.109720\pi$
$487$	−0.416408	−	1.28157i	−0.0188692	−	0.0580736i	−0.960048	+	0.279836i	$0.909720\pi$
$488$	−0.763932	+	2.35114i	−0.0345816	+	0.106431i
$489$	−0.281153	−	0.204270i	−0.0127142	−	0.00923739i
$490$	7.85410	+	5.70634i	0.354812	+	0.257786i
$491$	7.06231	−	21.7355i	0.318717	−	0.980911i	−0.655480	−	0.755213i	$-0.727534\pi$
$491$	7.06231	−	21.7355i	0.318717	−	0.980911i	0.974197	−	0.225699i	$-0.0724664\pi$
$492$	0.663119	+	2.04087i	0.0298957	+	0.0920095i
$493$	2.23607	−	1.62460i	0.100707	−	0.0731682i
$494$	−7.23607			−0.325566
$495$	−2.85410	−	30.4993i	−0.128282	−	1.37084i
$496$	2.00000			0.0898027
$497$	−8.47214	+	6.15537i	−0.380027	+	0.276106i
$498$	1.10081	+	3.38795i	0.0493286	+	0.151818i
$499$	−9.53444	+	29.3440i	−0.426820	+	1.31362i	0.474420	+	0.880298i	$0.342658\pi$
$499$	−9.53444	+	29.3440i	−0.426820	+	1.31362i	−0.901241	+	0.433319i	$0.857342\pi$
$500$	−1.23607	−	0.898056i	−0.0552786	−	0.0401623i
$501$	4.56231	+	3.31471i	0.203829	+	0.148090i
$502$	6.47214	−	19.9192i	0.288866	−	0.889037i
$503$	−1.00000	−	3.07768i	−0.0445878	−	0.137227i	0.926284	−	0.376825i	$-0.122984\pi$
$503$	−1.00000	−	3.07768i	−0.0445878	−	0.137227i	−0.970872	+	0.239598i	$0.922984\pi$
$504$	−4.61803	+	3.35520i	−0.205704	+	0.149452i
$505$	−13.5279			−0.601982
$506$	−2.70820	−	3.07768i	−0.120394	−	0.136820i
$507$	−4.38197			−0.194610
$508$	8.85410	−	6.43288i	0.392837	−	0.285413i
$509$	−2.56231	−	7.88597i	−0.113572	−	0.349539i	0.878074	−	0.478524i	$-0.158828\pi$
$509$	−2.56231	−	7.88597i	−0.113572	−	0.349539i	−0.991647	+	0.128985i	$0.958828\pi$
$510$	−0.236068	+	0.726543i	−0.0104533	+	0.0321718i
$511$	16.7984	+	12.2047i	0.743116	+	0.539906i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	4.04508	−	12.4495i	0.178595	−	0.549658i
$514$	−1.73607	−	5.34307i	−0.0765747	−	0.235673i
$515$	−41.1246	+	29.8788i	−1.81217	+	1.31662i
$516$	−3.27051			−0.143976
$517$	19.7082	−	8.50651i	0.866766	−	0.374116i
$518$	7.41641			0.325858
$519$	−6.76393	+	4.91428i	−0.296904	+	0.215713i
$520$	1.23607	+	3.80423i	0.0542052	+	0.166826i
$521$	−6.19098	+	19.0539i	−0.271232	+	0.834766i	0.718960	+	0.695052i	$0.244618\pi$
$521$	−6.19098	+	19.0539i	−0.271232	+	0.834766i	−0.990192	+	0.139714i	$0.955382\pi$
$522$	10.3262	+	7.50245i	0.451967	+	0.328373i
$523$	−7.44427	−	5.40858i	−0.325515	−	0.236501i	0.413010	−	0.910726i	$-0.364477\pi$
$523$	−7.44427	−	5.40858i	−0.325515	−	0.236501i	−0.738525	+	0.674226i	$0.764477\pi$
$524$	2.10081	−	6.46564i	0.0917744	−	0.282453i
$525$	−1.29180	−	3.97574i	−0.0563786	−	0.173515i
$526$	18.7984	−	13.6578i	0.819648	−	0.595509i
$527$	−1.23607			−0.0538440
$528$	1.23607	+	0.277515i	0.0537930	+	0.0120773i
$529$	−21.4721			−0.933571
$530$	4.00000	−	2.90617i	0.173749	−	0.126236i
$531$	7.60081	+	23.3929i	0.329847	+	1.01517i
$532$	3.61803	−	11.1352i	0.156862	−	0.482771i
$533$	−5.61803	−	4.08174i	−0.243344	−	0.176800i
$534$	2.50000	+	1.81636i	0.108186	+	0.0786014i
$535$	−1.14590	+	3.52671i	−0.0495415	+	0.152473i
$536$	3.42705	+	10.5474i	0.148026	+	0.455577i
$537$	2.66312	−	1.93487i	0.114922	−	0.0834958i
$538$	6.18034			0.266453
$539$	−5.07295	+	8.55951i	−0.218507	+	0.368684i
$540$	−7.23607			−0.311391
$541$	2.52786	−	1.83660i	0.108681	−	0.0789616i	−0.532117	−	0.846671i	$-0.678603\pi$
$541$	2.52786	−	1.83660i	0.108681	−	0.0789616i	0.640798	+	0.767709i	$0.278603\pi$
$542$	0.618034	+	1.90211i	0.0265468	+	0.0817028i
$543$	−0.493422	+	1.51860i	−0.0211748	+	0.0651693i
$544$	0.500000	+	0.363271i	0.0214373	+	0.0155751i
$545$	−49.5967	−	36.0341i	−2.12449	−	1.54353i
$546$	−0.291796	+	0.898056i	−0.0124877	+	0.0384332i
$547$	2.57295	+	7.91872i	0.110011	+	0.338580i	0.990874	−	0.134792i	$-0.0430366\pi$
$547$	2.57295	+	7.91872i	0.110011	+	0.338580i	−0.880863	+	0.473372i	$0.843037\pi$
$548$	−13.0172	+	9.45756i	−0.556068	+	0.404007i
$549$	7.05573			0.301131
$550$	9.25329	−	15.6129i	0.394562	−	0.665738i
$551$	−26.1803			−1.11532
$552$	−0.381966	+	0.277515i	−0.0162576	+	0.0118118i
$553$	−8.29180	−	25.5195i	−0.352603	−	1.08520i
$554$	−7.32624	+	22.5478i	−0.311262	+	0.957966i
$555$	3.70820	+	2.69417i	0.157404	+	0.114361i
$556$		0			0
$557$	10.8885	−	33.5115i	0.461362	−	1.41993i	−0.402138	−	0.915579i	$-0.631733\pi$
$557$	10.8885	−	33.5115i	0.461362	−	1.41993i	0.863500	−	0.504348i	$-0.168267\pi$
$558$	−1.76393	−	5.42882i	−0.0746732	−	0.229820i
$559$	8.56231	−	6.22088i	0.362147	−	0.263115i
$560$	−6.47214			−0.273498
$561$	−0.763932	−	0.171513i	−0.0322532	−	0.00724130i
$562$	−16.0902			−0.678723
$563$	−0.309017	+	0.224514i	−0.0130235	+	0.00946214i	−0.594278	−	0.804260i	$-0.702562\pi$
$563$	−0.309017	+	0.224514i	−0.0130235	+	0.00946214i	0.581254	+	0.813722i	$0.302562\pi$
$564$	−0.763932	−	2.35114i	−0.0321673	−	0.0990009i
$565$	−1.85410	+	5.70634i	−0.0780027	+	0.240067i
$566$	−19.4164	−	14.1068i	−0.816132	−	0.592955i
$567$	12.4721	+	9.06154i	0.523780	+	0.380549i
$568$	−1.61803	+	4.97980i	−0.0678912	+	0.208948i
$569$	11.8090	+	36.3444i	0.495060	+	1.52364i	0.816864	+	0.576831i	$0.195711\pi$
$569$	11.8090	+	36.3444i	0.495060	+	1.52364i	−0.321804	+	0.946806i	$0.604289\pi$
$570$	5.85410	−	4.25325i	0.245201	−	0.178149i
$571$	−2.47214			−0.103456			−0.0517278	−	0.998661i	$-0.516473\pi$
$571$	−2.47214			−0.103456			−0.0517278	+	0.998661i	$0.516473\pi$
$572$	−3.76393	+	1.62460i	−0.157378	+	0.0679279i
$573$	1.81966			0.0760174
$574$	9.09017	−	6.60440i	0.379416	−	0.275662i
$575$	2.09017	+	6.43288i	0.0871661	+	0.268270i
$576$	−0.881966	+	2.71441i	−0.0367486	+	0.113101i
$577$	5.50000	+	3.99598i	0.228968	+	0.166355i	0.696354	−	0.717698i	$-0.254804\pi$
$577$	5.50000	+	3.99598i	0.228968	+	0.166355i	−0.467386	+	0.884053i	$0.654804\pi$
$578$	13.4443	+	9.76784i	0.559208	+	0.406288i
$579$	2.05573	−	6.32688i	0.0854331	−	0.262936i
$580$	4.47214	+	13.7638i	0.185695	+	0.571511i
$581$	15.0902	−	10.9637i	0.626046	−	0.454849i
$582$	2.72949			0.113141
$583$	3.34752	+	3.80423i	0.138640	+	0.157555i
$584$	10.3820			0.429609
$585$	9.23607	−	6.71040i	0.381864	−	0.277441i
$586$	−8.76393	−	26.9726i	−0.362035	−	1.11423i
$587$	6.84346	−	21.0620i	0.282460	−	0.869322i	−0.704689	−	0.709517i	$-0.748913\pi$
$587$	6.84346	−	21.0620i	0.282460	−	0.869322i	0.987149	−	0.159805i	$-0.0510866\pi$
$588$	0.927051	+	0.673542i	0.0382309	+	0.0277764i
$589$	9.47214	+	6.88191i	0.390293	+	0.283564i
$590$	−8.61803	+	26.5236i	−0.354799	+	1.09196i
$591$	−2.47214	−	7.60845i	−0.101690	−	0.312970i
$592$	3.00000	−	2.17963i	0.123299	−	0.0895821i
$593$	−28.6869			−1.17803			−0.589015	−	0.808122i	$-0.700484\pi$
$593$	−28.6869			−1.17803			−0.589015	+	0.808122i	$0.700484\pi$
$594$	−0.690983	−	7.38394i	−0.0283514	−	0.302967i
$595$	4.00000			0.163984
$596$	5.00000	−	3.63271i	0.204808	−	0.148802i
$597$	−2.23607	−	6.88191i	−0.0915162	−	0.281658i
$598$	0.472136	−	1.45309i	0.0193071	−	0.0594211i
$599$	10.8541	+	7.88597i	0.443487	+	0.322212i	0.787019	−	0.616929i	$-0.211623\pi$
$599$	10.8541	+	7.88597i	0.443487	+	0.322212i	−0.343532	+	0.939141i	$0.611623\pi$
$600$	−1.69098	−	1.22857i	−0.0690341	−	0.0501562i
$601$	−8.38854	+	25.8173i	−0.342176	+	1.05311i	0.620903	+	0.783888i	$0.286766\pi$
$601$	−8.38854	+	25.8173i	−0.342176	+	1.05311i	−0.963078	+	0.269221i	$0.913234\pi$
$602$	5.29180	+	16.2865i	0.215678	+	0.663787i
$603$	25.6074	−	18.6049i	1.04281	−	0.757648i
$604$	−8.00000			−0.325515
$605$	32.1803	+	15.2169i	1.30832	+	0.618655i
$606$	−1.59675			−0.0648634
$607$	−18.7082	+	13.5923i	−0.759343	+	0.551695i	−0.898709	−	0.438546i	$-0.855494\pi$
$607$	−18.7082	+	13.5923i	−0.759343	+	0.551695i	0.139366	+	0.990241i	$0.455494\pi$
$608$	−1.80902	−	5.56758i	−0.0733653	−	0.225795i
$609$	−1.05573	+	3.24920i	−0.0427803	+	0.131664i
$610$	6.47214	+	4.70228i	0.262049	+	0.190390i
$611$	6.47214	+	4.70228i	0.261835	+	0.190234i
$612$	0.545085	−	1.67760i	0.0220338	−	0.0678129i
$613$	11.0344	+	33.9605i	0.445677	+	1.37165i	0.881740	+	0.471736i	$0.156373\pi$
$613$	11.0344	+	33.9605i	0.445677	+	1.37165i	−0.436063	+	0.899916i	$0.643627\pi$
$614$	−22.4894	+	16.3395i	−0.907597	+	0.659408i
$615$	6.94427			0.280020
$616$	−0.618034	−	6.60440i	−0.0249013	−	0.266099i
$617$	23.4508			0.944096			0.472048	−	0.881573i	$-0.343515\pi$
$617$	23.4508			0.944096			0.472048	+	0.881573i	$0.343515\pi$
$618$	−4.85410	+	3.52671i	−0.195261	+	0.141865i
$619$	1.60739	+	4.94704i	0.0646065	+	0.198838i	0.978149	−	0.207905i	$-0.0666644\pi$
$619$	1.60739	+	4.94704i	0.0646065	+	0.198838i	−0.913543	+	0.406743i	$0.866664\pi$
$620$	2.00000	−	6.15537i	0.0803219	−	0.247205i
$621$	2.23607	+	1.62460i	0.0897303	+	0.0651929i
$622$	−21.0902	−	15.3229i	−0.845639	−	0.614393i
$623$	5.00000	−	15.3884i	0.200321	−	0.616524i
$624$	0.145898	+	0.449028i	0.00584060	+	0.0179755i
$625$	18.1353	−	13.1760i	0.725410	−	0.527041i
$626$	4.32624			0.172911
$627$	4.89919	+	5.56758i	0.195655	+	0.222348i
$628$	9.70820			0.387400
$629$	−1.85410	+	1.34708i	−0.0739279	+	0.0537118i
$630$	5.70820	+	17.5680i	0.227420	+	0.699928i
$631$	7.32624	−	22.5478i	0.291653	−	0.897615i	−0.692672	−	0.721252i	$-0.743567\pi$
$631$	7.32624	−	22.5478i	0.291653	−	0.897615i	0.984325	−	0.176363i	$-0.0564332\pi$
$632$	−10.8541	−	7.88597i	−0.431753	−	0.313687i
$633$	1.88197	+	1.36733i	0.0748014	+	0.0543464i
$634$	−1.14590	+	3.52671i	−0.0455094	+	0.140064i
$635$	−10.9443	−	33.6830i	−0.434310	−	1.33667i
$636$	0.472136	−	0.343027i	0.0187214	−	0.0136019i
$637$	−3.70820			−0.146924
$638$	−13.6180	+	5.87785i	−0.539143	+	0.232706i
$639$	14.9443			0.591186
$640$	−2.61803	+	1.90211i	−0.103487	+	0.0751876i
$641$	5.15248	+	15.8577i	0.203511	+	0.626341i	0.999771	+	0.0213875i	$0.00680836\pi$
$641$	5.15248	+	15.8577i	0.203511	+	0.626341i	−0.796261	+	0.604954i	$0.793192\pi$
$642$	−0.135255	+	0.416272i	−0.00533809	+	0.0164289i
$643$	−32.3435	−	23.4989i	−1.27550	−	0.926706i	−0.276094	−	0.961131i	$-0.589040\pi$
$643$	−32.3435	−	23.4989i	−1.27550	−	0.926706i	−0.999407	+	0.0344245i	$0.989040\pi$
$644$	2.00000	+	1.45309i	0.0788110	+	0.0572596i
$645$	−3.27051	+	10.0656i	−0.128776	+	0.396332i
$646$	1.11803	+	3.44095i	0.0439885	+	0.135383i
$647$	−23.5066	+	17.0785i	−0.924139	+	0.671426i	−0.944551	−	0.328365i	$-0.893502\pi$
$647$	−23.5066	+	17.0785i	−0.924139	+	0.671426i	0.0204118	+	0.999792i	$0.493502\pi$
$648$	7.70820			0.302807
$649$	−27.8885	−	6.26137i	−1.09472	−	0.245780i
$650$	6.76393			0.265303
$651$	1.23607	−	0.898056i	0.0484453	−	0.0351976i
$652$	0.281153	+	0.865300i	0.0110108	+	0.0338878i
$653$	−4.74265	+	14.5964i	−0.185594	+	0.571200i	−0.999958	−	0.00915459i	$-0.997086\pi$
$653$	−4.74265	+	14.5964i	−0.185594	+	0.571200i	0.814364	+	0.580354i	$0.197086\pi$
$654$	−5.85410	−	4.25325i	−0.228914	−	0.166315i
$655$	−17.7984	−	12.9313i	−0.695440	−	0.505267i
$656$	1.73607	−	5.34307i	0.0677821	−	0.208612i
$657$	−9.15654	−	28.1809i	−0.357231	−	1.09944i
$658$	−10.4721	+	7.60845i	−0.408246	+	0.296608i
$659$	−16.9098			−0.658713			−0.329357	−	0.944206i	$-0.606832\pi$
$659$	−16.9098			−0.658713			−0.329357	+	0.944206i	$0.606832\pi$
$660$	2.09017	−	3.52671i	0.0813598	−	0.137277i
$661$	−3.52786			−0.137218			−0.0686090	−	0.997644i	$-0.521856\pi$
$661$	−3.52786			−0.137218			−0.0686090	+	0.997644i	$0.521856\pi$
$662$	−5.07295	+	3.68571i	−0.197166	+	0.143249i
$663$	−0.0901699	−	0.277515i	−0.00350191	−	0.0107778i
$664$	2.88197	−	8.86978i	0.111842	−	0.344214i
$665$	−30.6525	−	22.2703i	−1.18865	−	0.863606i
$666$	−8.56231	−	6.22088i	−0.331783	−	0.241054i
$667$	1.70820	−	5.25731i	0.0661419	−	0.203564i
$668$	−4.56231	−	14.0413i	−0.176521	−	0.543276i
$669$	−7.94427	+	5.77185i	−0.307143	+	0.223153i
$670$	35.8885			1.38650
$671$	−4.18034	+	7.05342i	−0.161380	+	0.272294i
$672$	−0.763932			−0.0294693
$673$	−7.97214	+	5.79210i	−0.307303	+	0.223269i	−0.730738	−	0.682657i	$-0.760824\pi$
$673$	−7.97214	+	5.79210i	−0.307303	+	0.223269i	0.423435	+	0.905926i	$0.360824\pi$
$674$	−8.28115	−	25.4868i	−0.318978	−	0.981714i
$675$	−3.78115	+	11.6372i	−0.145537	+	0.447916i
$676$	9.28115	+	6.74315i	0.356967	+	0.259352i
$677$	11.6180	+	8.44100i	0.446517	+	0.324414i	0.788219	−	0.615395i	$-0.211003\pi$
$677$	11.6180	+	8.44100i	0.446517	+	0.324414i	−0.341702	+	0.939808i	$0.611003\pi$
$678$	−0.218847	+	0.673542i	−0.00840477	+	0.0258672i
$679$	−4.41641	−	13.5923i	−0.169486	−	0.521625i
$680$	1.61803	−	1.17557i	0.0620488	−	0.0450811i
$681$	5.54102			0.212332
$682$	6.47214	+	1.45309i	0.247831	+	0.0556415i
$683$	18.4721			0.706817			0.353408	−	0.935469i	$-0.385023\pi$
$683$	18.4721			0.706817			0.353408	+	0.935469i	$0.385023\pi$
$684$	−13.5172	+	9.82084i	−0.516844	+	0.375509i
$685$	16.0902	+	49.5205i	0.614774	+	1.89208i
$686$	6.18034	−	19.0211i	0.235966	−	0.726230i
$687$	−0.527864	−	0.383516i	−0.0201393	−	0.0146320i
$688$	6.92705	+	5.03280i	0.264091	+	0.191874i
$689$	−0.583592	+	1.79611i	−0.0222331	+	0.0684264i
$690$	0.472136	+	1.45309i	0.0179739	+	0.0553180i
$691$	21.2082	−	15.4087i	0.806798	−	0.586173i	−0.106102	−	0.994355i	$-0.533837\pi$
$691$	21.2082	−	15.4087i	0.806798	−	0.586173i	0.912901	+	0.408182i	$0.133837\pi$
$692$	21.8885			0.832078
$693$	−17.3820	+	7.50245i	−0.660286	+	0.284995i
$694$	16.6180			0.630812
$695$		0			0
$696$	0.527864	+	1.62460i	0.0200086	+	0.0615802i
$697$	−1.07295	+	3.30220i	−0.0406408	+	0.125080i
$698$	15.8541	+	11.5187i	0.600087	+	0.435988i
$699$	2.97214	+	2.15938i	0.112417	+	0.0816754i
$700$	−3.38197	+	10.4086i	−0.127826	+	0.393409i
$701$	−4.58359	−	14.1068i	−0.173120	−	0.532808i	0.826423	−	0.563050i	$-0.190372\pi$
$701$	−4.58359	−	14.1068i	−0.173120	−	0.532808i	−0.999543	+	0.0302419i	$0.990372\pi$
$702$	2.23607	−	1.62460i	0.0843949	−	0.0613165i
$703$	21.7082			0.818740
$704$	−2.19098	−	2.48990i	−0.0825758	−	0.0938416i
$705$	−8.00000			−0.301297
$706$	−26.3885	+	19.1724i	−0.993146	+	0.721563i
$707$	2.58359	+	7.95148i	0.0971660	+	0.299046i
$708$	−1.01722	+	3.13068i	−0.0382295	+	0.117658i
$709$	−19.7984	−	14.3844i	−0.743544	−	0.540216i	0.150275	−	0.988644i	$-0.451984\pi$
$709$	−19.7984	−	14.3844i	−0.743544	−	0.540216i	−0.893819	+	0.448428i	$0.851984\pi$
$710$	13.7082	+	9.95959i	0.514460	+	0.373777i
$711$	−11.8328	+	36.4177i	−0.443765	+	1.36577i
$712$	−2.50000	−	7.69421i	−0.0936915	−	0.288353i
$713$	−2.00000	+	1.45309i	−0.0749006	+	0.0544185i
$714$	0.472136			0.0176692
$715$	1.23607	+	13.2088i	0.0462263	+	0.493981i
$716$	−8.61803			−0.322071
$717$	6.70820	−	4.87380i	0.250522	−	0.182015i
$718$	1.58359	+	4.87380i	0.0590991	+	0.181888i
$719$	8.29180	−	25.5195i	0.309232	−	0.951718i	−0.668832	−	0.743413i	$-0.733206\pi$
$719$	8.29180	−	25.5195i	0.309232	−	0.951718i	0.978064	−	0.208304i	$-0.0667944\pi$
$720$	7.47214	+	5.42882i	0.278470	+	0.202320i
$721$	25.4164	+	18.4661i	0.946556	+	0.687714i
$722$	4.71885	−	14.5231i	0.175617	−	0.540494i
$723$	−1.30902	−	4.02874i	−0.0486829	−	0.149830i
$724$	3.38197	−	2.45714i	0.125690	−	0.0913190i
$725$	24.4721			0.908872
$726$	3.79837	+	1.79611i	0.140971	+	0.0666600i
$727$	2.87539			0.106642			0.0533211	−	0.998577i	$-0.483019\pi$
$727$	2.87539			0.106642			0.0533211	+	0.998577i	$0.483019\pi$
$728$	2.00000	−	1.45309i	0.0741249	−	0.0538549i
$729$	−6.00658	−	18.4863i	−0.222466	−	0.684679i
$730$	10.3820	−	31.9524i	0.384254	−	1.18261i
$731$	−4.28115	−	3.11044i	−0.158344	−	0.115044i
$732$	0.763932	+	0.555029i	0.0282357	+	0.0205145i
$733$	−2.90983	+	8.95554i	−0.107477	+	0.330780i	−0.990304	−	0.138918i	$-0.955637\pi$
$733$	−2.90983	+	8.95554i	−0.107477	+	0.330780i	0.882827	+	0.469699i	$0.155637\pi$
$734$	6.09017	+	18.7436i	0.224792	+	0.691839i
$735$	3.00000	−	2.17963i	0.110657	−	0.0803968i
$736$	1.23607			0.0455621
$737$	3.42705	+	36.6219i	0.126237	+	1.34899i
$738$	−16.0344			−0.590236
$739$	30.3885	−	22.0786i	1.11786	−	0.812173i	0.133977	−	0.990984i	$-0.457225\pi$
$739$	30.3885	−	22.0786i	1.11786	−	0.812173i	0.983883	+	0.178811i	$0.0572251\pi$
$740$	−3.70820	−	11.4127i	−0.136316	−	0.419538i
$741$	−0.854102	+	2.62866i	−0.0313762	+	0.0965661i
$742$	−2.47214	−	1.79611i	−0.0907550	−	0.0659373i
$743$	7.09017	+	5.15131i	0.260113	+	0.188983i	0.710197	−	0.704003i	$-0.248606\pi$
$743$	7.09017	+	5.15131i	0.260113	+	0.188983i	−0.450084	+	0.892986i	$0.648606\pi$
$744$	0.236068	−	0.726543i	0.00865467	−	0.0266363i
$745$	−6.18034	−	19.0211i	−0.226430	−	0.696880i
$746$	3.47214	−	2.52265i	0.127124	−	0.0923609i
$747$	−26.6180			−0.973903
$748$	1.35410	+	1.53884i	0.0495109	+	0.0562656i
$749$	2.29180			0.0837404
$750$	−0.472136	+	0.343027i	−0.0172400	+	0.0125256i
$751$	−10.4377	−	32.1239i	−0.380877	−	1.17222i	−0.939427	−	0.342748i	$-0.888642\pi$
$751$	−10.4377	−	32.1239i	−0.380877	−	1.17222i	0.558551	−	0.829470i	$-0.311358\pi$
$752$	−2.00000	+	6.15537i	−0.0729325	+	0.224463i
$753$	−6.47214	−	4.70228i	−0.235858	−	0.171361i
$754$	−4.47214	−	3.24920i	−0.162866	−	0.118329i
$755$	−8.00000	+	24.6215i	−0.291150	+	0.896067i
$756$	1.38197	+	4.25325i	0.0502616	+	0.154689i
$757$	2.14590	−	1.55909i	0.0779940	−	0.0566660i	−0.548105	−	0.836410i	$-0.684651\pi$
$757$	2.14590	−	1.55909i	0.0779940	−	0.0566660i	0.626099	+	0.779744i	$0.284651\pi$
$758$	14.2705			0.518328
$759$	−1.43769	+	0.620541i	−0.0521850	+	0.0225242i
$760$	−18.9443			−0.687181
$761$	3.44427	−	2.50241i	0.124855	−	0.0907123i	−0.523605	−	0.851961i	$-0.675413\pi$
$761$	3.44427	−	2.50241i	0.124855	−	0.0907123i	0.648460	+	0.761249i	$0.275413\pi$
$762$	−1.29180	−	3.97574i	−0.0467968	−	0.144026i
$763$	−11.7082	+	36.0341i	−0.423865	+	1.30452i
$764$	−3.85410	−	2.80017i	−0.139437	−	0.101307i
$765$	−4.61803	−	3.35520i	−0.166965	−	0.121307i
$766$	−8.76393	+	26.9726i	−0.316654	+	0.974560i
$767$	−3.29180	−	10.1311i	−0.118860	−	0.365813i
$768$	−0.309017	+	0.224514i	−0.0111507	+	0.00810145i
$769$	13.4164			0.483808			0.241904	−	0.970300i	$-0.422228\pi$
$769$	13.4164			0.483808			0.241904	+	0.970300i	$0.422228\pi$
$770$	−20.9443	−	4.70228i	−0.754779	−	0.169458i
$771$	−2.14590			−0.0772826
$772$	−14.0902	+	10.2371i	−0.507116	+	0.368442i
$773$	−1.20163	−	3.69822i	−0.0432195	−	0.133016i	0.927118	−	0.374768i	$-0.122278\pi$
$773$	−1.20163	−	3.69822i	−0.0432195	−	0.133016i	−0.970338	+	0.241753i	$0.922278\pi$
$774$	7.55166	−	23.2416i	0.271439	−	0.835403i
$775$	−8.85410	−	6.43288i	−0.318049	−	0.231076i
$776$	−5.78115	−	4.20025i	−0.207531	−	0.150780i
$777$	0.875388	−	2.69417i	0.0314044	−	0.0966527i
$778$	−3.29180	−	10.1311i	−0.118017	−	0.363218i
$779$	26.6074	−	19.3314i	0.953309	−	0.692619i
$780$	1.52786			0.0547063
$781$	−8.85410	+	14.9394i	−0.316825	+	0.534573i
$782$	−0.763932			−0.0273182
$783$	8.09017	−	5.87785i	0.289119	−	0.210057i
$784$	−0.927051	−	2.85317i	−0.0331090	−	0.101899i
$785$	9.70820	−	29.8788i	0.346501	−	1.06642i
$786$	−2.10081	−	1.52633i	−0.0749335	−	0.0544424i
$787$	−21.2082	−	15.4087i	−0.755991	−	0.549259i	0.141687	−	0.989911i	$-0.454747\pi$
$787$	−21.2082	−	15.4087i	−0.755991	−	0.549259i	−0.897678	+	0.440652i	$0.854747\pi$
$788$	−6.47214	+	19.9192i	−0.230560	+	0.709592i
$789$	−2.74265	−	8.44100i	−0.0976408	−	0.300507i
$790$	−35.1246	+	25.5195i	−1.24968	+	0.907944i
$791$	3.70820			0.131849
$792$	−4.82624	+	8.14324i	−0.171493	+	0.289357i
$793$	−3.05573			−0.108512
$794$	13.8541	−	10.0656i	0.491664	−	0.357215i
$795$	−0.583592	−	1.79611i	−0.0206979	−	0.0637015i
$796$	−5.85410	+	18.0171i	−0.207493	+	0.638598i
$797$	20.0344	+	14.5559i	0.709656	+	0.515596i	0.883063	−	0.469255i	$-0.155477\pi$
$797$	20.0344	+	14.5559i	0.709656	+	0.515596i	−0.173406	+	0.984850i	$0.555477\pi$
$798$	−3.61803	−	2.62866i	−0.128077	−	0.0930534i
$799$	1.23607	−	3.80423i	0.0437289	−	0.134584i
$800$	1.69098	+	5.20431i	0.0597853	+	0.184000i
$801$	−18.6803	+	13.5721i	−0.660037	+	0.479545i
$802$	−17.7984			−0.628482
$803$	33.5967	+	7.54294i	1.18560	+	0.266185i
$804$	4.23607			0.149395
$805$	6.47214	−	4.70228i	0.228113	−	0.165734i
$806$	0.763932	+	2.35114i	0.0269084	+	0.0828154i
$807$	0.729490	−	2.24514i	0.0256793	−	0.0790327i
$808$	3.38197	+	2.45714i	0.118977	+	0.0864420i
$809$	−13.6803	−	9.93935i	−0.480975	−	0.349449i	0.320728	−	0.947171i	$-0.396072\pi$
$809$	−13.6803	−	9.93935i	−0.480975	−	0.349449i	−0.801703	+	0.597722i	$0.796072\pi$
$810$	7.70820	−	23.7234i	0.270839	−	0.833556i
$811$	2.59017	+	7.97172i	0.0909532	+	0.279925i	0.986178	−	0.165690i	$-0.0529851\pi$
$811$	2.59017	+	7.97172i	0.0909532	+	0.279925i	−0.895225	+	0.445615i	$0.852985\pi$
$812$	7.23607	−	5.25731i	0.253936	−	0.184495i
$813$	0.763932			0.0267923
$814$	11.2918	−	4.87380i	0.395777	−	0.170826i
$815$	2.94427			0.103133
$816$	0.190983	−	0.138757i	0.00668574	−	0.00485748i
$817$	15.4894	+	47.6713i	0.541904	+	1.66781i
$818$	−4.14590	+	12.7598i	−0.144958	+	0.446135i
$819$	−5.70820	−	4.14725i	−0.199461	−	0.144917i
$820$	−14.7082	−	10.6861i	−0.513633	−	0.373176i
$821$	9.43769	−	29.0462i	0.329378	−	1.01372i	−0.640048	−	0.768335i	$-0.721085\pi$
$821$	9.43769	−	29.0462i	0.329378	−	1.01372i	0.969426	−	0.245386i	$-0.0789145\pi$
$822$	1.89919	+	5.84510i	0.0662418	+	0.203871i
$823$	−19.0902	+	13.8698i	−0.665441	+	0.483472i	−0.868496	−	0.495696i	$-0.834913\pi$
$823$	−19.0902	+	13.8698i	−0.665441	+	0.483472i	0.203055	+	0.979167i	$0.434913\pi$
$824$	15.7082			0.547221
$825$	−4.57953	−	5.20431i	−0.159439	−	0.181191i
$826$	17.2361			0.599720
$827$	−31.8607	+	23.1481i	−1.10790	+	0.804940i	−0.982332	−	0.187145i	$-0.940077\pi$
$827$	−31.8607	+	23.1481i	−1.10790	+	0.804940i	−0.125572	+	0.992085i	$0.540077\pi$
$828$	−1.09017	−	3.35520i	−0.0378860	−	0.116601i
$829$	9.59675	−	29.5358i	0.333309	−	1.02582i	−0.634240	−	0.773136i	$-0.718687\pi$
$829$	9.59675	−	29.5358i	0.333309	−	1.02582i	0.967549	−	0.252683i	$-0.0813130\pi$
$830$	−24.4164	−	17.7396i	−0.847506	−	0.615749i
$831$	7.32624	+	5.32282i	0.254144	+	0.184647i
$832$	0.381966	−	1.17557i	0.0132423	−	0.0407556i
$833$	0.572949	+	1.76336i	0.0198515	+	0.0610967i
$834$		0			0
$835$	−47.7771			−1.65339
$836$	−1.80902	−	19.3314i	−0.0625662	−	0.668590i
$837$	−4.47214			−0.154580
$838$	8.78115	−	6.37988i	0.303340	−	0.220389i
$839$	3.74265	+	11.5187i	0.129210	+	0.397669i	0.994645	−	0.103354i	$-0.0329573\pi$
$839$	3.74265	+	11.5187i	0.129210	+	0.397669i	−0.865434	+	0.501023i	$0.832957\pi$
$840$	−0.763932	+	2.35114i	−0.0263582	+	0.0811221i
$841$	7.28115	+	5.29007i	0.251074	+	0.182416i
$842$	25.4164	+	18.4661i	0.875907	+	0.636384i
$843$	−1.89919	+	5.84510i	−0.0654115	+	0.201316i
$844$	−1.88197	−	5.79210i	−0.0647799	−	0.199372i
$845$	30.0344	−	21.8213i	1.03322	−	0.750676i
$846$	18.4721			0.635085
$847$	2.79837	−	21.8213i	0.0961533	−	0.749789i
$848$	−1.52786			−0.0524671
$849$	−7.41641	+	5.38834i	−0.254530	+	0.184927i
$850$	−1.04508	−	3.21644i	−0.0358461	−	0.110323i
$851$	−1.41641	+	4.35926i	−0.0485538	+	0.149433i
$852$	1.61803	+	1.17557i	0.0554329	+	0.0402744i
$853$	24.6525	+	17.9111i	0.844085	+	0.613263i	0.923509	−	0.383577i	$-0.125308\pi$
$853$	24.6525	+	17.9111i	0.844085	+	0.613263i	−0.0794240	+	0.996841i	$0.525308\pi$
$854$	1.52786	−	4.70228i	0.0522824	−	0.160909i
$855$	16.7082	+	51.4226i	0.571409	+	1.75861i
$856$	0.927051	−	0.673542i	0.0316860	−	0.0230212i
$857$	−10.7426			−0.366962			−0.183481	−	0.983023i	$-0.558737\pi$
$857$	−10.7426			−0.366962			−0.183481	+	0.983023i	$0.558737\pi$
$858$	0.145898	+	1.55909i	0.00498088	+	0.0532263i
$859$	46.5066			1.58678			0.793392	−	0.608711i	$-0.208313\pi$
$859$	46.5066			1.58678			0.793392	+	0.608711i	$0.208313\pi$
$860$	22.4164	−	16.2865i	0.764393	−	0.555364i
$861$	−1.32624	−	4.08174i	−0.0451981	−	0.139105i
$862$	−5.23607	+	16.1150i	−0.178341	+	0.548878i
$863$	26.8885	+	19.5357i	0.915297	+	0.665002i	0.942349	−	0.334632i	$-0.108612\pi$
$863$	26.8885	+	19.5357i	0.915297	+	0.665002i	−0.0270522	+	0.999634i	$0.508612\pi$
$864$	1.80902	+	1.31433i	0.0615440	+	0.0447143i
$865$	21.8885	−	67.3660i	0.744233	−	2.29051i
$866$	8.57295	+	26.3848i	0.291321	+	0.896593i
$867$	5.13525	−	3.73098i	0.174402	−	0.126711i
$868$	−4.00000			−0.135769
$869$	−29.3951	−	33.4055i	−0.997161	−	1.13320i
$870$	5.52786			0.187412
$871$	−11.0902	+	8.05748i	−0.375776	+	0.273017i
$872$	5.85410	+	18.0171i	0.198245	+	0.610135i
$873$	−6.30244	+	19.3969i	−0.213305	+	0.656486i
$874$	5.85410	+	4.25325i	0.198018	+	0.143868i
$875$	2.47214	+	1.79611i	0.0835734	+	0.0607197i
$876$	1.22542	−	3.77147i	0.0414033	−	0.127426i
$877$	−8.70820	−	26.8011i	−0.294055	−	0.905009i	−0.983537	−	0.180706i	$-0.942162\pi$
$877$	−8.70820	−	26.8011i	−0.294055	−	0.905009i	0.689482	−	0.724303i	$-0.257838\pi$
$878$	5.32624	−	3.86974i	0.179752	−	0.130597i
$879$	−10.8328			−0.365382
$880$	−9.85410	+	4.25325i	−0.332182	+	0.143377i
$881$	−46.3394			−1.56121			−0.780607	−	0.625022i	$-0.785090\pi$
$881$	−46.3394			−1.56121			−0.780607	+	0.625022i	$0.785090\pi$
$882$	−6.92705	+	5.03280i	−0.233246	+	0.169463i
$883$	−1.06231	−	3.26944i	−0.0357494	−	0.110025i	0.931589	−	0.363512i	$-0.118423\pi$
$883$	−1.06231	−	3.26944i	−0.0357494	−	0.110025i	−0.967339	+	0.253487i	$0.918423\pi$
$884$	−0.236068	+	0.726543i	−0.00793983	+	0.0244363i
$885$	8.61803	+	6.26137i	0.289692	+	0.210474i
$886$	6.92705	+	5.03280i	0.232719	+	0.169080i
$887$	−11.6738	+	35.9281i	−0.391967	+	1.20635i	0.539332	+	0.842093i	$0.318677\pi$
$887$	−11.6738	+	35.9281i	−0.391967	+	1.20635i	−0.931299	+	0.364256i	$0.881323\pi$
$888$	−0.437694	−	1.34708i	−0.0146881	−	0.0452052i
$889$	−17.7082	+	12.8658i	−0.593914	+	0.431504i
$890$	−26.1803			−0.877567
$891$	24.9443	+	5.60034i	0.835665	+	0.187618i
$892$	25.7082			0.860774
$893$	−30.6525	+	22.2703i	−1.02575	+	0.745248i
$894$	−0.729490	−	2.24514i	−0.0243978	−	0.0750887i
$895$	−8.61803	+	26.5236i	−0.288069	+	0.886586i
$896$	1.61803	+	1.17557i	0.0540547	+	0.0392731i
$897$	−0.472136	−	0.343027i	−0.0157642	−	0.0114533i
$898$	2.86475	−	8.81678i	0.0955978	−	0.294220i
$899$	2.76393	+	8.50651i	0.0921823	+	0.283708i
$900$	12.6353	−	9.18005i	0.421175	−	0.306002i
$901$	0.944272			0.0314583
$902$	9.50000	−	16.0292i	0.316315	−	0.533714i
$903$	6.54102			0.217672
$904$	1.50000	−	1.08981i	0.0498893	−	0.0362467i
$905$	−4.18034	−	12.8658i	−0.138959	−	0.427672i
$906$	−0.944272	+	2.90617i	−0.0313713	+	0.0965510i
$907$	−8.44427	−	6.13512i	−0.280387	−	0.203713i	0.438699	−	0.898634i	$-0.355439\pi$
$907$	−8.44427	−	6.13512i	−0.280387	−	0.203713i	−0.719086	+	0.694921i	$0.755439\pi$
$908$	−11.7361	−	8.52675i	−0.389475	−	0.282970i
$909$	3.68692	−	11.3472i	0.122287	−	0.376362i
$910$	−2.47214	−	7.60845i	−0.0819505	−	0.252218i
$911$	−14.7082	+	10.6861i	−0.487305	+	0.354047i	−0.804147	−	0.594431i	$-0.797377\pi$
$911$	−14.7082	+	10.6861i	−0.487305	+	0.354047i	0.316842	+	0.948478i	$0.397377\pi$
$912$	−2.23607			−0.0740436
$913$	15.7705	−	26.6093i	0.521928	−	0.880641i
$914$	−9.43769			−0.312171
$915$	2.47214	−	1.79611i	0.0817263	−	0.0593776i
$916$	0.527864	+	1.62460i	0.0174411	+	0.0536782i
$917$	−4.20163	+	12.9313i	−0.138750	+	0.427028i
$918$	−1.11803	−	0.812299i	−0.0369006	−	0.0268099i
$919$	−35.1246	−	25.5195i	−1.15865	−	0.841811i	−0.169047	−	0.985608i	$-0.554069\pi$
$919$	−35.1246	−	25.5195i	−1.15865	−	0.841811i	−0.989607	+	0.143797i	$0.954069\pi$
$920$	1.23607	−	3.80423i	0.0407520	−	0.125422i
$921$	3.28115	+	10.0984i	0.108118	+	0.332752i
$922$	−1.09017	+	0.792055i	−0.0359028	+	0.0260849i
$923$	−6.47214			−0.213033
$924$	−2.47214	−	0.555029i	−0.0813273	−	0.0182591i
$925$	−20.2918			−0.667190
$926$	15.7082	−	11.4127i	0.516204	−	0.375044i
$927$	−13.8541	−	42.6385i	−0.455028	−	1.40043i
$928$	1.38197	−	4.25325i	0.0453653	−	0.139620i
$929$	13.1525	+	9.55583i	0.431519	+	0.313517i	0.782256	−	0.622957i	$-0.214069\pi$
$929$	13.1525	+	9.55583i	0.431519	+	0.313517i	−0.350737	+	0.936474i	$0.614069\pi$
$930$	−2.00000	−	1.45309i	−0.0655826	−	0.0476485i
$931$	5.42705	−	16.7027i	0.177864	−	0.547410i
$932$	−2.97214	−	9.14729i	−0.0973556	−	0.299630i
$933$	−8.05573	+	5.85283i	−0.263733	+	0.191613i
$934$	−33.3050			−1.08977
$935$	6.09017	−	2.62866i	0.199170	−	0.0859662i
$936$	−3.52786			−0.115312
$937$	30.6246	−	22.2501i	1.00046	−	0.726879i	0.0382752	−	0.999267i	$-0.487814\pi$
$937$	30.6246	−	22.2501i	1.00046	−	0.726879i	0.962187	+	0.272389i	$0.0878137\pi$
$938$	−6.85410	−	21.0948i	−0.223794	−	0.688768i
$939$	0.510643	−	1.57160i	0.0166642	−	0.0512872i
$940$	16.9443	+	12.3107i	0.552661	+	0.401532i
$941$	−38.9787	−	28.3197i	−1.27067	−	0.923196i	−0.271441	−	0.962455i	$-0.587500\pi$
$941$	−38.9787	−	28.3197i	−1.27067	−	0.923196i	−0.999229	+	0.0392595i	$0.987500\pi$
$942$	1.14590	−	3.52671i	0.0373354	−	0.114906i
$943$	2.14590	+	6.60440i	0.0698801	+	0.215069i
$944$	6.97214	−	5.06555i	0.226924	−	0.164870i
$945$	14.4721			0.470779
$946$	18.7599	+	21.3193i	0.609936	+	0.693149i
$947$	−30.2148			−0.981848			−0.490924	−	0.871202i	$-0.663341\pi$
$947$	−30.2148			−0.981848			−0.490924	+	0.871202i	$0.663341\pi$
$948$	−4.14590	+	3.01217i	−0.134653	+	0.0978308i
$949$	3.96556	+	12.2047i	0.128727	+	0.396182i
$950$	−9.89919	+	30.4666i	−0.321172	+	0.988466i
$951$	1.14590	+	0.832544i	0.0371583	+	0.0269971i
$952$	−1.00000	−	0.726543i	−0.0324102	−	0.0235474i
$953$	−3.50000	+	10.7719i	−0.113376	+	0.348936i	−0.991605	−	0.129305i	$-0.958725\pi$
$953$	−3.50000	+	10.7719i	−0.113376	+	0.348936i	0.878229	+	0.478241i	$0.158725\pi$
$954$	1.34752	+	4.14725i	0.0436277	+	0.134272i
$955$	−12.4721	+	9.06154i	−0.403589	+	0.293224i
$956$	−21.7082			−0.702093
$957$	0.527864	+	5.64083i	0.0170634	+	0.182342i
$958$	−34.4721			−1.11374
$959$	26.0344	−	18.9151i	0.840696	−	0.610801i
$960$	0.381966	+	1.17557i	0.0123279	+	0.0379414i
$961$	−8.34346	+	25.6785i	−0.269144	+	0.828340i
$962$	3.70820	+	2.69417i	0.119557	+	0.0868635i
$963$	−2.64590	−	1.92236i	−0.0852629	−	0.0619471i
$964$	−3.42705	+	10.5474i	−0.110378	+	0.339708i
$965$	17.4164	+	53.6022i	0.560654	+	1.72552i
$966$	0.763932	−	0.555029i	0.0245791	−	0.0178578i
$967$	38.0000			1.22200			0.610999	−	0.791632i	$-0.290768\pi$
$967$	38.0000			1.22200			0.610999	+	0.791632i	$0.290768\pi$
$968$	−5.28115	−	9.64932i	−0.169743	−	0.310141i
$969$	1.38197			0.0443951
$970$	−18.7082	+	13.5923i	−0.600684	+	0.436423i
$971$	−3.12461	−	9.61657i	−0.100274	−	0.308610i	0.888319	−	0.459228i	$-0.151874\pi$
$971$	−3.12461	−	9.61657i	−0.100274	−	0.308610i	−0.988592	+	0.150617i	$0.951874\pi$
$972$	2.98278	−	9.18005i	0.0956727	−	0.294450i
$973$		0			0
$974$	1.09017	+	0.792055i	0.0349313	+	0.0253791i
$975$	0.798374	−	2.45714i	0.0255684	−	0.0786915i
$976$	−0.763932	−	2.35114i	−0.0244529	−	0.0752582i
$977$	35.0344	−	25.4540i	1.12085	−	0.814346i	0.136513	−	0.990638i	$-0.456410\pi$
$977$	35.0344	−	25.4540i	1.12085	−	0.814346i	0.984338	+	0.176292i	$0.0564104\pi$
$978$	0.347524			0.0111126
$979$	−2.50000	−	26.7153i	−0.0799003	−	0.853826i
$980$	−9.70820			−0.310117
$981$	43.7426	−	31.7809i	1.39660	−	1.01469i
$982$	7.06231	+	21.7355i	0.225367	+	0.693609i
$983$	−1.85410	+	5.70634i	−0.0591367	+	0.182004i	−0.976261	−	0.216597i	$-0.930504\pi$
$983$	−1.85410	+	5.70634i	−0.0591367	+	0.182004i	0.917124	+	0.398601i	$0.130504\pi$
$984$	−1.73607	−	1.26133i	−0.0553438	−	0.0402096i
$985$	54.8328	+	39.8384i	1.74712	+	1.26936i
$986$	−0.854102	+	2.62866i	−0.0272001	+	0.0837134i
$987$	1.52786	+	4.70228i	0.0486324	+	0.149675i
$988$	5.85410	−	4.25325i	0.186244	−	0.135314i
$989$	−10.5836			−0.336539
$990$	20.2361	+	22.9969i	0.643144	+	0.730889i
$991$	30.5410			0.970167			0.485084	−	0.874468i	$-0.338789\pi$
$991$	30.5410			0.970167			0.485084	+	0.874468i	$0.338789\pi$
$992$	−1.61803	+	1.17557i	−0.0513726	+	0.0373244i
$993$	0.740133	+	2.27790i	0.0234874	+	0.0722868i
$994$	3.23607	−	9.95959i	0.102642	−	0.315899i
$995$	49.5967	+	36.0341i	1.57232	+	1.14236i
$996$	−2.88197	−	2.09387i	−0.0913186	−	0.0663468i
$997$	2.67376	−	8.22899i	0.0846789	−	0.260615i	−0.899748	−	0.436410i	$-0.856250\pi$
$997$	2.67376	−	8.22899i	0.0846789	−	0.260615i	0.984427	+	0.175795i	$0.0562497\pi$
$998$	−9.53444	−	29.3440i	−0.301807	−	0.928868i
$999$	−6.70820	+	4.87380i	−0.212238	+	0.154200i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.2.c.a.3.1	✓	4
3.2	odd	2		198.2.f.e.91.1		4
4.3	odd	2		176.2.m.c.113.1		4
5.2	odd	4		550.2.ba.c.399.1		8
5.3	odd	4		550.2.ba.c.399.2		8
5.4	even	2		550.2.h.h.201.1		4
8.3	odd	2		704.2.m.a.641.1		4
8.5	even	2		704.2.m.h.641.1		4
11.2	odd	10		242.2.a.d.1.1		2
11.3	even	5		242.2.c.a.27.1		4
11.4	even	5	inner	22.2.c.a.15.1	yes	4
11.5	even	5		242.2.c.a.9.1		4
11.6	odd	10		242.2.c.d.9.1		4
11.7	odd	10		242.2.c.c.81.1		4
11.8	odd	10		242.2.c.d.27.1		4
11.9	even	5		242.2.a.f.1.1		2
11.10	odd	2		242.2.c.c.3.1		4
33.2	even	10		2178.2.a.x.1.1		2
33.20	odd	10		2178.2.a.p.1.1		2
33.26	odd	10		198.2.f.e.37.1		4
44.15	odd	10		176.2.m.c.81.1		4
44.31	odd	10		1936.2.a.o.1.2		2
44.35	even	10		1936.2.a.n.1.2		2
55.4	even	10		550.2.h.h.301.1		4
55.9	even	10		6050.2.a.bs.1.2		2
55.24	odd	10		6050.2.a.ci.1.2		2
55.37	odd	20		550.2.ba.c.499.2		8
55.48	odd	20		550.2.ba.c.499.1		8
88.13	odd	10		7744.2.a.bn.1.2		2
88.35	even	10		7744.2.a.cy.1.1		2
88.37	even	10		704.2.m.h.257.1		4
88.53	even	10		7744.2.a.bm.1.2		2
88.59	odd	10		704.2.m.a.257.1		4
88.75	odd	10		7744.2.a.cz.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.2.c.a.3.1	✓	4	1.1	even	1	trivial
22.2.c.a.15.1	yes	4	11.4	even	5	inner
176.2.m.c.81.1		4	44.15	odd	10
176.2.m.c.113.1		4	4.3	odd	2
198.2.f.e.37.1		4	33.26	odd	10
198.2.f.e.91.1		4	3.2	odd	2
242.2.a.d.1.1		2	11.2	odd	10
242.2.a.f.1.1		2	11.9	even	5
242.2.c.a.9.1		4	11.5	even	5
242.2.c.a.27.1		4	11.3	even	5
242.2.c.c.3.1		4	11.10	odd	2
242.2.c.c.81.1		4	11.7	odd	10
242.2.c.d.9.1		4	11.6	odd	10
242.2.c.d.27.1		4	11.8	odd	10
550.2.h.h.201.1		4	5.4	even	2
550.2.h.h.301.1		4	55.4	even	10
550.2.ba.c.399.1		8	5.2	odd	4
550.2.ba.c.399.2		8	5.3	odd	4
550.2.ba.c.499.1		8	55.48	odd	20
550.2.ba.c.499.2		8	55.37	odd	20
704.2.m.a.257.1		4	88.59	odd	10
704.2.m.a.641.1		4	8.3	odd	2
704.2.m.h.257.1		4	88.37	even	10
704.2.m.h.641.1		4	8.5	even	2
1936.2.a.n.1.2		2	44.35	even	10
1936.2.a.o.1.2		2	44.31	odd	10
2178.2.a.p.1.1		2	33.20	odd	10
2178.2.a.x.1.1		2	33.2	even	10
6050.2.a.bs.1.2		2	55.9	even	10
6050.2.a.ci.1.2		2	55.24	odd	10
7744.2.a.bm.1.2		2	88.53	even	10
7744.2.a.bn.1.2		2	88.13	odd	10
7744.2.a.cy.1.1		2	88.35	even	10
7744.2.a.cz.1.1		2	88.75	odd	10

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:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	22.c (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.118034 + 0.363271i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-2.61803 - 1.90211i) q^{5} +(-0.309017 - 0.224514i) q^{6} +(-0.618034 + 1.90211i) q^{7} +(0.309017 + 0.951057i) q^{8} +(2.30902 - 1.67760i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.118034 + 0.363271i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-2.61803 - 1.90211i) q^{5} +(-0.309017 - 0.224514i) q^{6} +(-0.618034 + 1.90211i) q^{7} +(0.309017 + 0.951057i) q^{8} +(2.30902 - 1.67760i) q^{9} +3.23607 q^{10} +(0.309017 + 3.30220i) q^{11} +0.381966 q^{12} +(-1.00000 + 0.726543i) q^{13} +(-0.618034 - 1.90211i) q^{14} +(0.381966 - 1.17557i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.500000 + 0.363271i) q^{17} +(-0.881966 + 2.71441i) q^{18} +(-1.80902 - 5.56758i) q^{19} +(-2.61803 + 1.90211i) q^{20} -0.763932 q^{21} +(-2.19098 - 2.48990i) q^{22} +1.23607 q^{23} +(-0.309017 + 0.224514i) q^{24} +(1.69098 + 5.20431i) q^{25} +(0.381966 - 1.17557i) q^{26} +(1.80902 + 1.31433i) q^{27} +(1.61803 + 1.17557i) q^{28} +(1.38197 - 4.25325i) q^{29} +(0.381966 + 1.17557i) q^{30} +(-1.61803 + 1.17557i) q^{31} +1.00000 q^{32} +(-1.16312 + 0.502029i) q^{33} -0.618034 q^{34} +(5.23607 - 3.80423i) q^{35} +(-0.881966 - 2.71441i) q^{36} +(-1.14590 + 3.52671i) q^{37} +(4.73607 + 3.44095i) q^{38} +(-0.381966 - 0.277515i) q^{39} +(1.00000 - 3.07768i) q^{40} +(1.73607 + 5.34307i) q^{41} +(0.618034 - 0.449028i) q^{42} -8.56231 q^{43} +(3.23607 + 0.726543i) q^{44} -9.23607 q^{45} +(-1.00000 + 0.726543i) q^{46} +(-2.00000 - 6.15537i) q^{47} +(0.118034 - 0.363271i) q^{48} +(2.42705 + 1.76336i) q^{49} +(-4.42705 - 3.21644i) q^{50} +(-0.0729490 + 0.224514i) q^{51} +(0.381966 + 1.17557i) q^{52} +(1.23607 - 0.898056i) q^{53} -2.23607 q^{54} +(5.47214 - 9.23305i) q^{55} -2.00000 q^{56} +(1.80902 - 1.31433i) q^{57} +(1.38197 + 4.25325i) q^{58} +(-2.66312 + 8.19624i) q^{59} +(-1.00000 - 0.726543i) q^{60} +(2.00000 + 1.45309i) q^{61} +(0.618034 - 1.90211i) q^{62} +(1.76393 + 5.42882i) q^{63} +(-0.809017 + 0.587785i) q^{64} +4.00000 q^{65} +(0.645898 - 1.08981i) q^{66} +11.0902 q^{67} +(0.500000 - 0.363271i) q^{68} +(0.145898 + 0.449028i) q^{69} +(-2.00000 + 6.15537i) q^{70} +(4.23607 + 3.07768i) q^{71} +(2.30902 + 1.67760i) q^{72} +(3.20820 - 9.87384i) q^{73} +(-1.14590 - 3.52671i) q^{74} +(-1.69098 + 1.22857i) q^{75} -5.85410 q^{76} +(-6.47214 - 1.45309i) q^{77} +0.472136 q^{78} +(-10.8541 + 7.88597i) q^{79} +(1.00000 + 3.07768i) q^{80} +(2.38197 - 7.33094i) q^{81} +(-4.54508 - 3.30220i) q^{82} +(-7.54508 - 5.48183i) q^{83} +(-0.236068 + 0.726543i) q^{84} +(-0.618034 - 1.90211i) q^{85} +(6.92705 - 5.03280i) q^{86} +1.70820 q^{87} +(-3.04508 + 1.31433i) q^{88} -8.09017 q^{89} +(7.47214 - 5.42882i) q^{90} +(-0.763932 - 2.35114i) q^{91} +(0.381966 - 1.17557i) q^{92} +(-0.618034 - 0.449028i) q^{93} +(5.23607 + 3.80423i) q^{94} +(-5.85410 + 18.0171i) q^{95} +(0.118034 + 0.363271i) q^{96} +(-5.78115 + 4.20025i) q^{97} -3.00000 q^{98} +(6.25329 + 7.10642i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} + q^{6} + 2 q^{7} - q^{8} + 7 q^{9}+O(q^{10}) \) 4 * q - q^2 - 4 * q^3 - q^4 - 6 * q^5 + q^6 + 2 * q^7 - q^8 + 7 * q^9	\( 4 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} + q^{6} + 2 q^{7} - q^{8} + 7 q^{9} + 4 q^{10} - q^{11} + 6 q^{12} - 4 q^{13} + 2 q^{14} + 6 q^{15} - q^{16} + 2 q^{17} - 8 q^{18} - 5 q^{19} - 6 q^{20} - 12 q^{21} - 11 q^{22} - 4 q^{23} + q^{24} + 9 q^{25} + 6 q^{26} + 5 q^{27} + 2 q^{28} + 10 q^{29} + 6 q^{30} - 2 q^{31} + 4 q^{32} + 11 q^{33} + 2 q^{34} + 12 q^{35} - 8 q^{36} - 18 q^{37} + 10 q^{38} - 6 q^{39} + 4 q^{40} - 2 q^{41} - 2 q^{42} + 6 q^{43} + 4 q^{44} - 28 q^{45} - 4 q^{46} - 8 q^{47} - 4 q^{48} + 3 q^{49} - 11 q^{50} - 7 q^{51} + 6 q^{52} - 4 q^{53} + 4 q^{55} - 8 q^{56} + 5 q^{57} + 10 q^{58} + 5 q^{59} - 4 q^{60} + 8 q^{61} - 2 q^{62} + 16 q^{63} - q^{64} + 16 q^{65} + 16 q^{66} + 22 q^{67} + 2 q^{68} + 14 q^{69} - 8 q^{70} + 8 q^{71} + 7 q^{72} - 14 q^{73} - 18 q^{74} - 9 q^{75} - 10 q^{76} - 8 q^{77} - 16 q^{78} - 30 q^{79} + 4 q^{80} + 14 q^{81} - 7 q^{82} - 19 q^{83} + 8 q^{84} + 2 q^{85} + 21 q^{86} - 20 q^{87} - q^{88} - 10 q^{89} + 12 q^{90} - 12 q^{91} + 6 q^{92} + 2 q^{93} + 12 q^{94} - 10 q^{95} - 4 q^{96} - 3 q^{97} - 12 q^{98} - 13 q^{99}+O(q^{100}) \) 4 * q - q^2 - 4 * q^3 - q^4 - 6 * q^5 + q^6 + 2 * q^7 - q^8 + 7 * q^9 + 4 * q^10 - q^11 + 6 * q^12 - 4 * q^13 + 2 * q^14 + 6 * q^15 - q^16 + 2 * q^17 - 8 * q^18 - 5 * q^19 - 6 * q^20 - 12 * q^21 - 11 * q^22 - 4 * q^23 + q^24 + 9 * q^25 + 6 * q^26 + 5 * q^27 + 2 * q^28 + 10 * q^29 + 6 * q^30 - 2 * q^31 + 4 * q^32 + 11 * q^33 + 2 * q^34 + 12 * q^35 - 8 * q^36 - 18 * q^37 + 10 * q^38 - 6 * q^39 + 4 * q^40 - 2 * q^41 - 2 * q^42 + 6 * q^43 + 4 * q^44 - 28 * q^45 - 4 * q^46 - 8 * q^47 - 4 * q^48 + 3 * q^49 - 11 * q^50 - 7 * q^51 + 6 * q^52 - 4 * q^53 + 4 * q^55 - 8 * q^56 + 5 * q^57 + 10 * q^58 + 5 * q^59 - 4 * q^60 + 8 * q^61 - 2 * q^62 + 16 * q^63 - q^64 + 16 * q^65 + 16 * q^66 + 22 * q^67 + 2 * q^68 + 14 * q^69 - 8 * q^70 + 8 * q^71 + 7 * q^72 - 14 * q^73 - 18 * q^74 - 9 * q^75 - 10 * q^76 - 8 * q^77 - 16 * q^78 - 30 * q^79 + 4 * q^80 + 14 * q^81 - 7 * q^82 - 19 * q^83 + 8 * q^84 + 2 * q^85 + 21 * q^86 - 20 * q^87 - q^88 - 10 * q^89 + 12 * q^90 - 12 * q^91 + 6 * q^92 + 2 * q^93 + 12 * q^94 - 10 * q^95 - 4 * q^96 - 3 * q^97 - 12 * q^98 - 13 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more