LMFDB - Embedded newform 115.2.g.b.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(6,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("115.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.g (of order $11$, degree $10$, 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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 12 x^{18} - 12 x^{17} + 56 x^{16} - 155 x^{15} + 551 x^{14} - 1189 x^{13} + \cdots + 1437601 $ x^20 - x^19 + 12x^18 - 12x^17 + 56x^16 - 155x^15 + 551x^14 - 1189x^13 + 3851x^12 - 10594x^11 + 18470x^10 - 22715x^9 + 56089x^8 + 1474x^7 - 31240x^6 + 12001x^5 + 243089x^4 + 225907x^3 + 23958x^2 + 857285x + 1437601
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			16.2
Root			$-0.932866 + 1.07658i$ of defining polynomial
Character	$\chi$	$=$	115.16
Dual form			115.2.g.b.36.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.186393 - 0.215109i) q^{2} +(1.19839 - 0.770157i) q^{3} +(0.273100 + 1.89945i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.0577033 - 0.401335i) q^{6} +(1.34020 - 0.393517i) q^{7} +(0.938384 + 0.603063i) q^{8} +(-0.403254 + 0.883004i) q^{9} +O(q^{10})$	\(q+(0.186393 - 0.215109i) q^{2} +(1.19839 - 0.770157i) q^{3} +(0.273100 + 1.89945i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.0577033 - 0.401335i) q^{6} +(1.34020 - 0.393517i) q^{7} +(0.938384 + 0.603063i) q^{8} +(-0.403254 + 0.883004i) q^{9} +(-0.273100 - 0.0801894i) q^{10} +(-3.15749 - 3.64393i) q^{11} +(1.79016 + 2.06595i) q^{12} +(0.273857 + 0.0804117i) q^{13} +(0.165154 - 0.361637i) q^{14} +(-1.19839 - 0.770157i) q^{15} +(-3.37787 + 0.991834i) q^{16} +(0.0679951 - 0.472917i) q^{17} +(0.114778 + 0.251329i) q^{18} +(0.140789 + 0.979208i) q^{19} +(1.61435 - 1.03748i) q^{20} +(1.30300 - 1.50375i) q^{21} -1.37237 q^{22} +(-4.63898 + 1.21649i) q^{23} +1.58900 q^{24} +(-0.654861 + 0.755750i) q^{25} +(0.0683422 - 0.0439209i) q^{26} +(0.804990 + 5.59883i) q^{27} +(1.11347 + 2.43817i) q^{28} +(0.0219083 - 0.152376i) q^{29} +(-0.389038 + 0.114232i) q^{30} +(-3.01445 - 1.93727i) q^{31} +(-1.34302 + 2.94080i) q^{32} +(-6.59029 - 1.93508i) q^{33} +(-0.0890547 - 0.102775i) q^{34} +(-0.914693 - 1.05561i) q^{35} +(-1.78735 - 0.524814i) q^{36} +(-1.70809 + 3.74020i) q^{37} +(0.236878 + 0.152232i) q^{38} +(0.390116 - 0.114549i) q^{39} +(0.158746 - 1.10411i) q^{40} +(-2.86572 - 6.27505i) q^{41} +(-0.0805985 - 0.560575i) q^{42} +(9.05086 - 5.81663i) q^{43} +(6.05917 - 6.99266i) q^{44} +0.970726 q^{45} +(-0.602996 + 1.22463i) q^{46} +9.42683 q^{47} +(-3.28414 + 3.79009i) q^{48} +(-4.24751 + 2.72971i) q^{49} +(0.0405070 + 0.281733i) q^{50} +(-0.282735 - 0.619104i) q^{51} +(-0.0779478 + 0.542139i) q^{52} +(4.62159 - 1.35702i) q^{53} +(1.35440 + 0.870421i) q^{54} +(-2.00297 + 4.38589i) q^{55} +(1.49493 + 0.438952i) q^{56} +(0.922863 + 1.06504i) q^{57} +(-0.0286938 - 0.0331144i) q^{58} +(6.57113 + 1.92946i) q^{59} +(1.13560 - 2.48661i) q^{60} +(9.16678 + 5.89113i) q^{61} +(-0.978595 + 0.287342i) q^{62} +(-0.192963 + 1.34208i) q^{63} +(-2.54266 - 5.56764i) q^{64} +(-0.0406193 - 0.282513i) q^{65} +(-1.64464 + 1.05694i) q^{66} +(4.62121 - 5.33316i) q^{67} +0.916853 q^{68} +(-4.62241 + 5.03057i) q^{69} -0.397564 q^{70} +(7.91831 - 9.13822i) q^{71} +(-0.910914 + 0.585409i) q^{72} +(0.970698 + 6.75135i) q^{73} +(0.486174 + 1.06457i) q^{74} +(-0.202731 + 1.41003i) q^{75} +(-1.82151 + 0.534844i) q^{76} +(-5.66560 - 3.64106i) q^{77} +(0.0480745 - 0.105268i) q^{78} +(-11.4955 - 3.37537i) q^{79} +(2.30542 + 2.66060i) q^{80} +(3.36959 + 3.88872i) q^{81} +(-1.88397 - 0.553183i) q^{82} +(2.70337 - 5.91956i) q^{83} +(3.21215 + 2.06432i) q^{84} +(-0.458426 + 0.134606i) q^{85} +(0.435806 - 3.03110i) q^{86} +(-0.0910986 - 0.199478i) q^{87} +(-0.765414 - 5.32357i) q^{88} +(-9.20422 + 5.91519i) q^{89} +(0.180936 - 0.208812i) q^{90} +0.398665 q^{91} +(-3.57757 - 8.47931i) q^{92} -5.10448 q^{93} +(1.75709 - 2.02779i) q^{94} +(0.832233 - 0.534844i) q^{95} +(0.655420 + 4.55855i) q^{96} +(-6.50117 - 14.2356i) q^{97} +(-0.204521 + 1.42247i) q^{98} +(4.49088 - 1.31864i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} + q^{3} - 4 q^{4} + 2 q^{5} - 9 q^{6} - 4 q^{7} - 17 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 + q^3 - 4 * q^4 + 2 * q^5 - 9 * q^6 - 4 * q^7 - 17 * q^9	\( 20 q - 4 q^{2} + q^{3} - 4 q^{4} + 2 q^{5} - 9 q^{6} - 4 q^{7} - 17 q^{9} + 4 q^{10} - 8 q^{11} + 2 q^{12} + 10 q^{13} + 3 q^{14} - q^{15} - 36 q^{16} - 9 q^{17} + 10 q^{18} + 24 q^{19} + 4 q^{20} + 25 q^{21} + 6 q^{22} + 11 q^{23} - 2 q^{25} - 2 q^{26} + 28 q^{27} - 8 q^{28} + 12 q^{29} - 2 q^{30} + 10 q^{31} - 50 q^{32} - 49 q^{33} - 7 q^{34} + 4 q^{35} + 43 q^{36} - 18 q^{37} - 29 q^{38} - 52 q^{39} + 22 q^{40} + 10 q^{41} - 5 q^{42} + 35 q^{43} + 6 q^{44} - 38 q^{45} - 33 q^{46} - 2 q^{47} - 4 q^{48} + 4 q^{49} + 18 q^{50} + 50 q^{51} + 9 q^{52} - 5 q^{53} + 23 q^{54} + 8 q^{55} + 33 q^{57} + 35 q^{58} + 41 q^{59} - 2 q^{60} - 13 q^{61} - 2 q^{62} - 46 q^{63} + 16 q^{64} - 10 q^{65} + 56 q^{66} - 9 q^{67} + 26 q^{68} - 45 q^{69} + 8 q^{70} - 19 q^{71} - 27 q^{73} + 8 q^{74} + q^{75} + 4 q^{76} - 64 q^{77} - 27 q^{78} - 83 q^{79} - 8 q^{80} + 12 q^{81} + 31 q^{82} + 67 q^{83} + 28 q^{84} - 13 q^{85} - 73 q^{86} + 69 q^{87} + 22 q^{88} - 5 q^{89} - 10 q^{90} - 84 q^{91} + 11 q^{92} + 28 q^{93} - 37 q^{94} - 2 q^{95} + 14 q^{96} + 18 q^{97} + 8 q^{98} + 62 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 + q^3 - 4 * q^4 + 2 * q^5 - 9 * q^6 - 4 * q^7 - 17 * q^9 + 4 * q^10 - 8 * q^11 + 2 * q^12 + 10 * q^13 + 3 * q^14 - q^15 - 36 * q^16 - 9 * q^17 + 10 * q^18 + 24 * q^19 + 4 * q^20 + 25 * q^21 + 6 * q^22 + 11 * q^23 - 2 * q^25 - 2 * q^26 + 28 * q^27 - 8 * q^28 + 12 * q^29 - 2 * q^30 + 10 * q^31 - 50 * q^32 - 49 * q^33 - 7 * q^34 + 4 * q^35 + 43 * q^36 - 18 * q^37 - 29 * q^38 - 52 * q^39 + 22 * q^40 + 10 * q^41 - 5 * q^42 + 35 * q^43 + 6 * q^44 - 38 * q^45 - 33 * q^46 - 2 * q^47 - 4 * q^48 + 4 * q^49 + 18 * q^50 + 50 * q^51 + 9 * q^52 - 5 * q^53 + 23 * q^54 + 8 * q^55 + 33 * q^57 + 35 * q^58 + 41 * q^59 - 2 * q^60 - 13 * q^61 - 2 * q^62 - 46 * q^63 + 16 * q^64 - 10 * q^65 + 56 * q^66 - 9 * q^67 + 26 * q^68 - 45 * q^69 + 8 * q^70 - 19 * q^71 - 27 * q^73 + 8 * q^74 + q^75 + 4 * q^76 - 64 * q^77 - 27 * q^78 - 83 * q^79 - 8 * q^80 + 12 * q^81 + 31 * q^82 + 67 * q^83 + 28 * q^84 - 13 * q^85 - 73 * q^86 + 69 * q^87 + 22 * q^88 - 5 * q^89 - 10 * q^90 - 84 * q^91 + 11 * q^92 + 28 * q^93 - 37 * q^94 - 2 * q^95 + 14 * q^96 + 18 * q^97 + 8 * q^98 + 62 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	0.186393	−	0.215109i	0.131800	−	0.152105i	−0.686013	−	0.727589i	$-0.740641\pi$
$2$	0.186393	−	0.215109i	0.131800	−	0.152105i	0.817813	+	0.575484i	$0.195186\pi$
$3$	1.19839	−	0.770157i	0.691889	−	0.444650i	−0.146868	−	0.989156i	$-0.546919\pi$
$3$	1.19839	−	0.770157i	0.691889	−	0.444650i	0.838757	+	0.544506i	$0.183283\pi$
$4$	0.273100	+	1.89945i	0.136550	+	0.949727i
$5$	−0.415415	−	0.909632i	−0.185779	−	0.406800i
$5$	−0.415415	−	0.909632i	−0.185779	−	0.406800i
$6$	0.0577033	−	0.401335i	0.0235573	−	0.163844i
$7$	1.34020	−	0.393517i	0.506546	−	0.148735i	−0.0184669	−	0.999829i	$-0.505879\pi$
$7$	1.34020	−	0.393517i	0.506546	−	0.148735i	0.525013	+	0.851094i	$0.324060\pi$
$8$	0.938384	+	0.603063i	0.331769	+	0.213215i
$9$	−0.403254	+	0.883004i	−0.134418	+	0.294335i
$10$	−0.273100	−	0.0801894i	−0.0863619	−	0.0253581i
$11$	−3.15749	−	3.64393i	−0.952018	−	1.09869i	−0.995026	−	0.0996124i	$-0.968240\pi$
$11$	−3.15749	−	3.64393i	−0.952018	−	1.09869i	0.0430085	−	0.999075i	$-0.486306\pi$
$12$	1.79016	+	2.06595i	0.516774	+	0.596389i
$13$	0.273857	+	0.0804117i	0.0759543	+	0.0223022i	0.319489	−	0.947590i	$-0.396489\pi$
$13$	0.273857	+	0.0804117i	0.0759543	+	0.0223022i	−0.243535	+	0.969892i	$0.578307\pi$
$14$	0.165154	−	0.361637i	0.0441392	−	0.0966514i
$15$	−1.19839	−	0.770157i	−0.309422	−	0.198854i
$16$	−3.37787	+	0.991834i	−0.844469	+	0.247958i
$17$	0.0679951	−	0.472917i	0.0164912	−	0.114699i	−0.979913	−	0.199425i	$-0.936092\pi$
$17$	0.0679951	−	0.472917i	0.0164912	−	0.114699i	0.996404	+	0.0847262i	$0.0270016\pi$
$18$	0.114778	+	0.251329i	0.0270535	+	0.0592388i
$19$	0.140789	+	0.979208i	0.0322992	+	0.224646i	0.999577	−	0.0290727i	$-0.00925544\pi$
$19$	0.140789	+	0.979208i	0.0322992	+	0.224646i	−0.967278	+	0.253718i	$0.918346\pi$
$20$	1.61435	−	1.03748i	0.360980	−	0.231988i
$21$	1.30300	−	1.50375i	0.284339	−	0.328144i
$22$	−1.37237			−0.292591
$23$	−4.63898	+	1.21649i	−0.967295	+	0.253655i
$23$	−4.63898	+	1.21649i	−0.967295	+	0.253655i
$24$	1.58900			0.324354
$25$	−0.654861	+	0.755750i	−0.130972	+	0.151150i
$26$	0.0683422	−	0.0439209i	0.0134030	−	0.00861359i
$27$	0.804990	+	5.59883i	0.154920	+	1.07749i
$28$	1.11347	+	2.43817i	0.210427	+	0.460771i
$29$	0.0219083	−	0.152376i	0.00406828	−	0.0282955i	−0.987686	−	0.156448i	$-0.949996\pi$
$29$	0.0219083	−	0.152376i	0.00406828	−	0.0282955i	0.991754	+	0.128153i	$0.0409047\pi$
$30$	−0.389038	+	0.114232i	−0.0710283	+	0.0208558i
$31$	−3.01445	−	1.93727i	−0.541411	−	0.347944i	0.241179	−	0.970481i	$-0.422466\pi$
$31$	−3.01445	−	1.93727i	−0.541411	−	0.347944i	−0.782591	+	0.622537i	$0.786102\pi$
$32$	−1.34302	+	2.94080i	−0.237414	+	0.519864i
$33$	−6.59029	−	1.93508i	−1.14722	−	0.336855i
$34$	−0.0890547	−	0.102775i	−0.0152728	−	0.0176257i
$35$	−0.914693	−	1.05561i	−0.154611	−	0.178431i
$36$	−1.78735	−	0.524814i	−0.297892	−	0.0874690i
$37$	−1.70809	+	3.74020i	−0.280809	+	0.614886i	−0.996506	−	0.0835254i	$-0.973382\pi$
$37$	−1.70809	+	3.74020i	−0.280809	+	0.614886i	0.715697	+	0.698411i	$0.246109\pi$
$38$	0.236878	+	0.152232i	0.0384267	+	0.0246953i
$39$	0.390116	−	0.114549i	0.0624686	−	0.0183424i
$40$	0.158746	−	1.10411i	0.0251000	−	0.174574i
$41$	−2.86572	−	6.27505i	−0.447550	−	0.979998i	−0.990150	−	0.140007i	$-0.955287\pi$
$41$	−2.86572	−	6.27505i	−0.447550	−	0.979998i	0.542600	−	0.839991i	$-0.317440\pi$
$42$	−0.0805985	−	0.560575i	−0.0124366	−	0.0864986i
$43$	9.05086	−	5.81663i	1.38024	−	0.887028i	0.380949	−	0.924596i	$-0.375597\pi$
$43$	9.05086	−	5.81663i	1.38024	−	0.887028i	0.999294	+	0.0375681i	$0.0119611\pi$
$44$	6.05917	−	6.99266i	0.913454	−	1.05418i
$45$	0.970726			0.144707
$46$	−0.602996	+	1.22463i	−0.0889069	+	0.180562i
$47$	9.42683			1.37504			0.687522	−	0.726163i	$-0.258698\pi$
$47$	9.42683			1.37504			0.687522	+	0.726163i	$0.258698\pi$
$48$	−3.28414	+	3.79009i	−0.474024	+	0.547053i
$49$	−4.24751	+	2.72971i	−0.606787	+	0.389958i
$50$	0.0405070	+	0.281733i	0.00572856	+	0.0398430i
$51$	−0.282735	−	0.619104i	−0.0395909	−	0.0866919i
$52$	−0.0779478	+	0.542139i	−0.0108094	+	0.0751812i
$53$	4.62159	−	1.35702i	0.634824	−	0.186401i	0.0515417	−	0.998671i	$-0.483586\pi$
$53$	4.62159	−	1.35702i	0.634824	−	0.186401i	0.583282	+	0.812270i	$0.301768\pi$
$54$	1.35440	+	0.870421i	0.184311	+	0.118449i
$55$	−2.00297	+	4.38589i	−0.270081	+	0.591394i
$56$	1.49493	+	0.438952i	0.199769	+	0.0586575i
$57$	0.922863	+	1.06504i	0.122236	+	0.141068i
$58$	−0.0286938	−	0.0331144i	−0.00376768	−	0.00434814i
$59$	6.57113	+	1.92946i	0.855488	+	0.251194i	0.679932	−	0.733275i	$-0.262009\pi$
$59$	6.57113	+	1.92946i	0.855488	+	0.251194i	0.175556	+	0.984469i	$0.443828\pi$
$60$	1.13560	−	2.48661i	0.146605	−	0.321020i
$61$	9.16678	+	5.89113i	1.17369	+	0.754282i	0.974215	−	0.225621i	$-0.0724412\pi$
$61$	9.16678	+	5.89113i	1.17369	+	0.754282i	0.199471	+	0.979904i	$0.436078\pi$
$62$	−0.978595	+	0.287342i	−0.124282	+	0.0364924i
$63$	−0.192963	+	1.34208i	−0.0243110	+	0.169087i
$64$	−2.54266	−	5.56764i	−0.317832	−	0.695955i
$65$	−0.0406193	−	0.282513i	−0.00503820	−	0.0350415i
$66$	−1.64464	+	1.05694i	−0.202441	+	0.130101i
$67$	4.62121	−	5.33316i	0.564571	−	0.651550i	−0.399644	−	0.916670i	$-0.630866\pi$
$67$	4.62121	−	5.33316i	0.564571	−	0.651550i	0.964215	+	0.265121i	$0.0854118\pi$
$68$	0.916853			0.111185
$69$	−4.62241	+	5.03057i	−0.556473	+	0.605609i
$70$	−0.397564			−0.0475179
$71$	7.91831	−	9.13822i	0.939731	−	1.08451i	−0.0565552	−	0.998399i	$-0.518012\pi$
$71$	7.91831	−	9.13822i	0.939731	−	1.08451i	0.996286	−	0.0861075i	$-0.0274428\pi$
$72$	−0.910914	+	0.585409i	−0.107352	+	0.0689911i
$73$	0.970698	+	6.75135i	0.113612	+	0.790186i	0.964356	+	0.264607i	$0.0852423\pi$
$73$	0.970698	+	6.75135i	0.113612	+	0.790186i	−0.850745	+	0.525579i	$0.823849\pi$
$74$	0.486174	+	1.06457i	0.0565166	+	0.123754i
$75$	−0.202731	+	1.41003i	−0.0234094	+	0.162816i
$76$	−1.82151	+	0.534844i	−0.208942	+	0.0613508i
$77$	−5.66560	−	3.64106i	−0.645655	−	0.414937i
$78$	0.0480745	−	0.105268i	0.00544336	−	0.0119193i
$79$	−11.4955	−	3.37537i	−1.29334	−	0.379759i	−0.438537	−	0.898713i	$-0.644503\pi$
$79$	−11.4955	−	3.37537i	−1.29334	−	0.379759i	−0.854802	+	0.518954i	$0.826322\pi$
$80$	2.30542	+	2.66060i	0.257754	+	0.297464i
$81$	3.36959	+	3.88872i	0.374399	+	0.432080i
$82$	−1.88397	−	0.553183i	−0.208049	−	0.0610888i
$83$	2.70337	−	5.91956i	0.296733	−	0.649756i	−0.701271	−	0.712895i	$-0.747384\pi$
$83$	2.70337	−	5.91956i	0.296733	−	0.649756i	0.998005	+	0.0631388i	$0.0201111\pi$
$84$	3.21215	+	2.06432i	0.350474	+	0.225236i
$85$	−0.458426	+	0.134606i	−0.0497233	+	0.0146001i
$86$	0.435806	−	3.03110i	0.0469942	−	0.326852i
$87$	−0.0910986	−	0.199478i	−0.00976680	−	0.0213863i
$88$	−0.765414	−	5.32357i	−0.0815934	−	0.567495i
$89$	−9.20422	+	5.91519i	−0.975645	+	0.627009i	−0.928285	−	0.371869i	$-0.878717\pi$
$89$	−9.20422	+	5.91519i	−0.975645	+	0.627009i	−0.0473599	+	0.998878i	$0.515081\pi$
$90$	0.180936	−	0.208812i	0.0190724	−	0.0220107i
$91$	0.398665			0.0417915
$92$	−3.57757	−	8.47931i	−0.372987	−	0.884029i
$93$	−5.10448			−0.529310
$94$	1.75709	−	2.02779i	0.181230	−	0.209151i
$95$	0.832233	−	0.534844i	0.0853853	−	0.0548738i
$96$	0.655420	+	4.55855i	0.0668935	+	0.465255i
$97$	−6.50117	−	14.2356i	−0.660094	−	1.44540i	−0.882435	−	0.470434i	$-0.844097\pi$
$97$	−6.50117	−	14.2356i	−0.660094	−	1.44540i	0.222341	−	0.974969i	$-0.428630\pi$
$98$	−0.204521	+	1.42247i	−0.0206597	+	0.143692i
$99$	4.49088	−	1.31864i	0.451350	−	0.132528i
$100$	−1.61435	−	1.03748i	−0.161435	−	0.103748i
$101$	−7.64997	+	16.7511i	−0.761201	+	1.66680i	−0.0160775	+	0.999871i	$0.505118\pi$
$101$	−7.64997	+	16.7511i	−0.761201	+	1.66680i	−0.745123	+	0.666927i	$0.767609\pi$
$102$	−0.185875	−	0.0545777i	−0.0184043	−	0.00540400i
$103$	8.68070	+	10.0181i	0.855335	+	0.987109i	0.999997	−	0.00237206i	$-0.000755052\pi$
$103$	8.68070	+	10.0181i	0.855335	+	0.987109i	−0.144662	+	0.989481i	$0.546210\pi$
$104$	0.208490	+	0.240610i	0.0204441	+	0.0235938i
$105$	−1.90914	−	0.560575i	−0.186313	−	0.0547065i
$106$	0.569523	−	1.24708i	0.0553170	−	0.121127i
$107$	−4.43983	−	2.85330i	−0.429214	−	0.275839i	0.308146	−	0.951339i	$-0.400292\pi$
$107$	−4.43983	−	2.85330i	−0.429214	−	0.275839i	−0.737360	+	0.675500i	$0.763928\pi$
$108$	−10.4149	+	3.05808i	−1.00217	+	0.294264i
$109$	−1.42192	+	9.88966i	−0.136195	+	0.947258i	0.801053	+	0.598594i	$0.204274\pi$
$109$	−1.42192	+	9.88966i	−0.136195	+	0.947258i	−0.937248	+	0.348664i	$0.886635\pi$
$110$	0.570105	+	1.24836i	0.0543574	+	0.119026i
$111$	0.833586	+	5.79771i	0.0791204	+	0.550295i
$112$	−4.13671	+	2.65850i	−0.390882	+	0.251205i
$113$	2.42018	−	2.79303i	0.227671	−	0.262746i	−0.630408	−	0.776264i	$-0.717112\pi$
$113$	2.42018	−	2.79303i	0.227671	−	0.262746i	0.858079	+	0.513518i	$0.171658\pi$
$114$	0.401115			0.0375678
$115$	3.03366	+	3.71442i	0.282890	+	0.346371i
$116$	0.295414			0.0274285
$117$	−0.181438	+	0.209390i	−0.0167739	+	0.0193581i
$118$	1.63985	−	1.05387i	0.150961	−	0.0970166i
$119$	−0.0949739	−	0.660558i	−0.00870624	−	0.0605533i
$120$	−0.660095	−	1.44541i	−0.0602581	−	0.131947i
$121$	−1.74307	+	12.1233i	−0.158461	+	1.10212i
$122$	2.97586	−	0.873790i	0.269421	−	0.0791093i
$123$	−8.26701	−	5.31289i	−0.745412	−	0.479047i
$124$	2.85651	−	6.25488i	0.256522	−	0.561704i
$125$	0.959493	+	0.281733i	0.0858197	+	0.0251989i
$126$	0.252727	+	0.291663i	0.0225147	+	0.0259834i
$127$	9.05096	+	10.4454i	0.803143	+	0.926877i	0.998549	−	0.0538457i	$-0.0171479\pi$
$127$	9.05096	+	10.4454i	0.803143	+	0.926877i	−0.195406	+	0.980722i	$0.562602\pi$
$128$	−7.87557	−	2.31248i	−0.696109	−	0.204396i
$129$	6.36671	−	13.9412i	0.560558	−	1.22745i
$130$	−0.0683422	−	0.0439209i	−0.00599401	−	0.00385212i
$131$	−5.21153	+	1.53024i	−0.455334	+	0.133698i	−0.501354	−	0.865242i	$-0.667164\pi$
$131$	−5.21153	+	1.53024i	−0.455334	+	0.133698i	0.0460199	+	0.998941i	$0.485346\pi$
$132$	1.87579	−	13.0464i	0.163267	−	1.13555i
$133$	0.574019	+	1.25693i	0.0497738	+	0.108989i
$134$	−0.285849	−	1.98813i	−0.0246936	−	0.171748i
$135$	4.75847	−	3.05808i	0.409544	−	0.263198i
$136$	0.349004	−	0.402772i	0.0299269	−	0.0345374i
$137$	−19.5590			−1.67104			−0.835520	−	0.549460i	$-0.814834\pi$
$137$	−19.5590			−1.67104			−0.835520	+	0.549460i	$0.814834\pi$
$138$	0.220534	+	1.93198i	0.0187731	+	0.164461i
$139$	−11.0234			−0.934992			−0.467496	−	0.883995i	$-0.654844\pi$
$139$	−11.0234			−0.934992			−0.467496	+	0.883995i	$0.654844\pi$
$140$	1.75528	−	2.02570i	0.148348	−	0.171203i
$141$	11.2970	−	7.26014i	0.951379	−	0.611414i
$142$	−0.489795	−	3.40660i	−0.0411026	−	0.285875i
$143$	−0.571685	−	1.25182i	−0.0478067	−	0.104682i
$144$	0.486350	−	3.38264i	0.0405291	−	0.281886i
$145$	−0.147707	+	0.0433707i	−0.0122664	+	0.00360174i
$146$	1.63321	+	1.04960i	0.135165	+	0.0868654i
$147$	−2.98786	+	6.54249i	−0.246434	+	0.539616i
$148$	−7.57083	−	2.22300i	−0.622318	−	0.182729i
$149$	6.50751	+	7.51007i	0.533116	+	0.615249i	0.956866	−	0.290531i	$-0.0938318\pi$
$149$	6.50751	+	7.51007i	0.533116	+	0.615249i	−0.423750	+	0.905779i	$0.639286\pi$
$150$	0.265521	+	0.306428i	0.0216797	+	0.0250197i
$151$	19.4770	+	5.71897i	1.58502	+	0.465403i	0.951327	−	0.308182i	$-0.0997207\pi$
$151$	19.4770	+	5.71897i	1.58502	+	0.465403i	0.633691	+	0.773586i	$0.281539\pi$
$152$	−0.458410	+	1.00378i	−0.0371820	+	0.0814171i
$153$	0.390168	+	0.250746i	0.0315432	+	0.0202716i
$154$	−1.83925	+	0.540053i	−0.148211	+	0.0435187i
$155$	−0.509954	+	3.54681i	−0.0409605	+	0.284887i
$156$	0.324120	+	0.709725i	0.0259504	+	0.0568235i
$157$	−2.27777	−	15.8422i	−0.181786	−	1.26435i	−0.852537	−	0.522666i	$-0.824937\pi$
$157$	−2.27777	−	15.8422i	−0.181786	−	1.26435i	0.670752	−	0.741682i	$-0.265972\pi$
$158$	−2.86874	+	1.84363i	−0.228225	+	0.146671i
$159$	4.49333	−	5.18558i	0.356344	−	0.411243i
$160$	3.23295			0.255587
$161$	−5.73844	+	3.45585i	−0.452252	+	0.272359i
$162$	1.46457			0.115067
$163$	10.2457	−	11.8242i	0.802505	−	0.926140i	−0.196011	−	0.980602i	$-0.562799\pi$
$163$	10.2457	−	11.8242i	0.802505	−	0.926140i	0.998516	+	0.0544617i	$0.0173443\pi$
$164$	11.1365	−	7.15702i	0.869617	−	0.558869i
$165$	0.977491	+	6.79860i	0.0760976	+	0.529271i
$166$	−0.769460	−	1.68488i	−0.0597216	−	0.130772i
$167$	−1.44760	+	10.0683i	−0.112019	+	0.779108i	0.853932	+	0.520384i	$0.174211\pi$
$167$	−1.44760	+	10.0683i	−0.112019	+	0.779108i	−0.965951	+	0.258724i	$0.916698\pi$
$168$	2.12957	−	0.625299i	0.164300	−	0.0482429i
$169$	−10.8678	−	6.98429i	−0.835982	−	0.537253i
$170$	−0.0564924	+	0.123701i	−0.00433277	+	0.00948744i
$171$	−0.921418	−	0.270553i	−0.0704626	−	0.0206897i
$172$	13.5202	+	15.6032i	1.03091	+	1.18973i
$173$	2.95554	+	3.41088i	0.224706	+	0.259324i	0.856896	−	0.515489i	$-0.172390\pi$
$173$	2.95554	+	3.41088i	0.224706	+	0.259324i	−0.632191	+	0.774813i	$0.717844\pi$
$174$	−0.0598896	−	0.0175852i	−0.00454022	−	0.00133313i
$175$	−0.580241	+	1.27055i	−0.0438621	+	0.0960446i
$176$	14.2798	+	9.17705i	1.07638	+	0.691746i
$177$	9.36074	−	2.74856i	0.703597	−	0.206595i
$178$	−0.443190	+	3.08246i	−0.0332185	+	0.231040i
$179$	0.247518	+	0.541990i	0.0185004	+	0.0405102i	0.918657	−	0.395057i	$-0.129275\pi$
$179$	0.247518	+	0.541990i	0.0185004	+	0.0405102i	−0.900156	+	0.435567i	$0.856548\pi$
$180$	0.265105	+	1.84385i	0.0197598	+	0.137432i
$181$	2.38858	−	1.53505i	0.177542	−	0.114099i	−0.448852	−	0.893606i	$-0.648167\pi$
$181$	2.38858	−	1.53505i	0.177542	−	0.114099i	0.626393	+	0.779507i	$0.284530\pi$
$182$	0.0743083	−	0.0857564i	0.00550810	−	0.00635669i
$183$	15.5225			1.14745
$184$	−5.08677	−	1.65607i	−0.375001	−	0.122087i
$185$	4.11178			0.302304
$186$	−0.951438	+	1.09802i	−0.0697628	+	0.0805106i
$187$	−1.93797	+	1.24546i	−0.141718	+	0.0910769i
$188$	2.57447	+	17.9058i	0.187762	+	1.30592i
$189$	3.28208	+	7.18675i	0.238736	+	0.522759i
$190$	0.0400727	−	0.278712i	0.00290718	−	0.0202199i
$191$	−15.0790	+	4.42758i	−1.09107	+	0.320368i	−0.777301	−	0.629129i	$-0.783412\pi$
$191$	−15.0790	+	4.42758i	−1.09107	+	0.320368i	−0.313774	+	0.949498i	$0.601593\pi$
$192$	−7.33505	−	4.71395i	−0.529361	−	0.340200i
$193$	8.58667	−	18.8022i	0.618082	−	1.35341i	−0.298825	−	0.954308i	$-0.596595\pi$
$193$	8.58667	−	18.8022i	0.618082	−	1.35341i	0.916906	−	0.399102i	$-0.130678\pi$
$194$	−4.27397	−	1.25495i	−0.306853	−	0.0901002i
$195$	−0.266257	−	0.307277i	−0.0190671	−	0.0220046i
$196$	−6.34494	−	7.32246i	−0.453210	−	0.523033i
$197$	7.65620	+	2.24806i	0.545482	+	0.160168i	0.542852	−	0.839829i	$-0.317345\pi$
$197$	7.65620	+	2.24806i	0.545482	+	0.160168i	0.00263008	+	0.999997i	$0.499163\pi$
$198$	0.553416	−	1.21181i	0.0393296	−	0.0861197i
$199$	4.32669	+	2.78059i	0.306711	+	0.197111i	0.684937	−	0.728602i	$-0.259830\pi$
$199$	4.32669	+	2.78059i	0.306711	+	0.197111i	−0.378227	+	0.925713i	$0.623466\pi$
$200$	−1.07028	+	0.314261i	−0.0756799	+	0.0222216i
$201$	1.43063	−	9.95025i	0.100909	−	0.701837i
$202$	2.17741	+	4.76786i	0.153202	+	0.335466i
$203$	−0.0306010	−	0.212835i	−0.00214777	−	0.0149381i
$204$	1.09874	−	0.706120i	0.0769275	−	0.0494383i
$205$	−4.51752	+	5.21350i	−0.315518	+	0.364127i
$206$	3.77299			0.262877
$207$	0.796528	−	4.58679i	0.0553625	−	0.318804i
$208$	−1.00481			−0.0696710
$209$	3.12363	−	3.60486i	0.216066	−	0.249353i
$210$	−0.476435	+	0.306186i	−0.0328771	+	0.0211289i
$211$	−3.81714	−	26.5488i	−0.262783	−	1.82769i	−0.511693	−	0.859168i	$-0.670982\pi$
$211$	−3.81714	−	26.5488i	−0.262783	−	1.82769i	0.248910	−	0.968527i	$-0.419928\pi$
$212$	3.83975	+	8.40788i	0.263715	+	0.577456i
$213$	2.45134	−	17.0495i	0.167963	−	1.16821i
$214$	−1.44132	+	0.423210i	−0.0985267	+	0.0289301i
$215$	−9.05086	−	5.81663i	−0.617263	−	0.396691i
$216$	−2.62106	+	5.73931i	−0.178340	+	0.390511i
$217$	−4.80230	−	1.41008i	−0.326001	−	0.0957226i
$218$	1.86232	+	2.14923i	0.126132	+	0.145564i
$219$	6.36287	+	7.34315i	0.429963	+	0.496204i
$220$	−8.87781	−	2.60676i	−0.598542	−	0.175748i
$221$	0.0566490	−	0.124044i	0.00381062	−	0.00834410i
$222$	1.40251	+	0.901341i	0.0941305	+	0.0604940i
$223$	−5.11814	+	1.50282i	−0.342736	+	0.100636i	−0.448571	−	0.893747i	$-0.648067\pi$
$223$	−5.11814	+	1.50282i	−0.342736	+	0.100636i	0.105835	+	0.994384i	$0.466249\pi$
$224$	−0.642652	+	4.46974i	−0.0429390	+	0.298647i
$225$	−0.403254	−	0.883004i	−0.0268836	−	0.0588669i
$226$	−0.149702	−	1.04120i	−0.00995805	−	0.0692597i
$227$	6.27697	−	4.03396i	0.416617	−	0.267744i	−0.315496	−	0.948927i	$-0.602171\pi$
$227$	6.27697	−	4.03396i	0.416617	−	0.267744i	0.732113	+	0.681183i	$0.238534\pi$
$228$	−1.77096	+	2.04380i	−0.117285	+	0.135354i
$229$	−23.1789			−1.53171			−0.765853	−	0.643016i	$-0.777683\pi$
$229$	−23.1789			−1.53171			−0.765853	+	0.643016i	$0.777683\pi$
$230$	1.36446	+	0.0397748i	0.0899696	+	0.00262267i
$231$	−9.59377			−0.631224
$232$	0.112451	−	0.129775i	0.00738275	−	0.00852015i
$233$	−20.5058	+	13.1783i	−1.34338	+	0.863339i	−0.997197	−	0.0748270i	$-0.976160\pi$
$233$	−20.5058	+	13.1783i	−1.34338	+	0.863339i	−0.346185	+	0.938166i	$0.612523\pi$
$234$	0.0112230	+	0.0780577i	0.000733671	+	0.00510279i
$235$	−3.91605	−	8.57495i	−0.255455	−	0.559368i
$236$	−1.87034	+	13.0085i	−0.121749	+	0.846781i
$237$	−16.3756	+	4.80830i	−1.06371	+	0.312333i
$238$	−0.159794	−	0.102694i	−0.0103579	−	0.00665663i
$239$	−0.487763	+	1.06805i	−0.0315508	+	0.0690865i	−0.924751	−	0.380572i	$-0.875727\pi$
$239$	−0.487763	+	1.06805i	−0.0315508	+	0.0690865i	0.893200	+	0.449659i	$0.148454\pi$
$240$	4.81187	+	1.41289i	0.310605	+	0.0912018i
$241$	−4.31739	−	4.98254i	−0.278108	−	0.320953i	0.599461	−	0.800404i	$-0.295382\pi$
$241$	−4.31739	−	4.98254i	−0.278108	−	0.320953i	−0.877569	+	0.479450i	$0.840836\pi$
$242$	2.28293	+	2.63464i	0.146752	+	0.169361i
$243$	−9.24883	−	2.71570i	−0.593313	−	0.174212i
$244$	−8.68649	+	19.0207i	−0.556095	+	1.21768i
$245$	4.24751	+	2.72971i	0.271363	+	0.174395i
$246$	−2.68376	+	0.788023i	−0.171110	+	0.0502425i
$247$	−0.0401837	+	0.279484i	−0.00255683	+	0.0177831i
$248$	−1.66042	−	3.63581i	−0.105437	−	0.230874i
$249$	−1.31930	−	9.17594i	−0.0836073	−	0.581502i
$250$	0.239446	−	0.153882i	0.0151439	−	0.00973238i
$251$	2.65036	−	3.05867i	0.167289	−	0.193062i	−0.665915	−	0.746028i	$-0.731959\pi$
$251$	2.65036	−	3.05867i	0.167289	−	0.193062i	0.833204	+	0.552966i	$0.186504\pi$
$252$	−2.60193			−0.163906
$253$	19.0803	+	13.0631i	1.19957	+	0.821270i
$254$	3.93393			0.246836
$255$	−0.445704	+	0.514370i	−0.0279111	+	0.0322111i
$256$	8.33284	−	5.35519i	0.520803	−	0.334700i
$257$	0.0903704	+	0.628540i	0.00563715	+	0.0392072i	0.992446	−	0.122683i	$-0.0391499\pi$
$257$	0.0903704	+	0.628540i	0.00563715	+	0.0392072i	−0.986809	+	0.161891i	$0.948241\pi$
$258$	−1.81216	−	3.96807i	−0.112820	−	0.247041i
$259$	−0.817347	+	5.68477i	−0.0507874	+	0.353234i
$260$	0.525528	−	0.154309i	0.0325918	−	0.00956983i
$261$	0.125714	+	0.0807914i	0.00778149	+	0.00500086i
$262$	−0.642223	+	1.40627i	−0.0396767	+	0.0868798i
$263$	−20.7654	−	6.09727i	−1.28045	−	0.375974i	−0.430381	−	0.902647i	$-0.641621\pi$
$263$	−20.7654	−	6.09727i	−1.28045	−	0.375974i	−0.850067	+	0.526674i	$0.823439\pi$
$264$	−5.01725	−	5.79021i	−0.308790	−	0.356363i
$265$	−3.15426	−	3.64022i	−0.193765	−	0.223617i
$266$	0.377369	+	0.110806i	0.0231380	+	0.00679392i
$267$	−6.47459	+	14.1774i	−0.396239	+	0.867642i
$268$	11.3921	+	7.32129i	0.695886	+	0.447219i
$269$	0.600207	−	0.176237i	0.0365953	−	0.0107453i	−0.263384	−	0.964691i	$-0.584839\pi$
$269$	0.600207	−	0.176237i	0.0365953	−	0.0107453i	0.299979	+	0.953946i	$0.403020\pi$
$270$	0.229124	−	1.59359i	0.0139440	−	0.0969830i
$271$	−1.53336	−	3.35760i	−0.0931452	−	0.203959i	0.857325	−	0.514776i	$-0.172125\pi$
$271$	−1.53336	−	3.35760i	−0.0931452	−	0.203959i	−0.950470	+	0.310816i	$0.899398\pi$
$272$	0.239375	+	1.66489i	0.0145143	+	0.100949i
$273$	0.477755	−	0.307035i	0.0289151	−	0.0185826i
$274$	−3.64566	+	4.20732i	−0.220242	+	0.254173i
$275$	4.82161			0.290754
$276$	−10.8177	−	7.40621i	−0.651149	−	0.445801i
$277$	18.1797			1.09231			0.546156	−	0.837683i	$-0.316091\pi$
$277$	18.1797			1.09231			0.546156	+	0.837683i	$0.316091\pi$
$278$	−2.05468	+	2.37123i	−0.123232	+	0.142217i
$279$	2.92621	−	1.88056i	0.175187	−	0.112586i
$280$	−0.221733	−	1.54219i	−0.0132511	−	0.0921633i
$281$	2.09803	+	4.59405i	0.125158	+	0.274058i	0.961831	−	0.273645i	$-0.0882295\pi$
$281$	2.09803	+	4.59405i	0.125158	+	0.274058i	−0.836673	+	0.547703i	$0.815502\pi$
$282$	0.543959	−	3.78332i	0.0323923	−	0.225293i
$283$	0.971066	−	0.285131i	0.0577239	−	0.0169493i	−0.252743	−	0.967533i	$-0.581333\pi$
$283$	0.971066	−	0.285131i	0.0577239	−	0.0169493i	0.310467	+	0.950584i	$0.399515\pi$
$284$	19.5201	+	12.5448i	1.15831	+	0.744398i
$285$	0.585424	−	1.28190i	0.0346775	−	0.0759332i
$286$	−0.375834	−	0.110355i	−0.0222236	−	0.00652542i
$287$	−6.30996	−	7.28209i	−0.372465	−	0.429848i
$288$	−2.05516	−	2.37178i	−0.121101	−	0.139758i
$289$	16.0924	+	4.72514i	0.946609	+	0.277949i
$290$	−0.0182021	+	0.0398571i	−0.00106886	+	0.00234049i
$291$	−18.7545	−	12.0528i	−1.09941	−	0.706548i
$292$	−12.5588	+	3.68759i	−0.734947	+	0.215800i
$293$	−3.65738	+	25.4376i	−0.213666	+	1.48608i	0.547106	+	0.837063i	$0.315729\pi$
$293$	−3.65738	+	25.4376i	−0.213666	+	1.48608i	−0.760773	+	0.649018i	$0.775180\pi$
$294$	0.850432	+	1.86219i	0.0495982	+	0.108605i
$295$	−0.974649	−	6.77884i	−0.0567463	−	0.394679i
$296$	−3.85843	+	2.47966i	−0.224267	+	0.144127i
$297$	17.8600	−	20.6116i	1.03634	−	1.19600i
$298$	2.82843			0.163847
$299$	−1.36824	−	0.0398850i	−0.0791272	−	0.00230661i
$300$	−2.73365			−0.157827
$301$	9.84097	−	11.3571i	0.567224	−	0.654612i
$302$	4.86058	−	3.12371i	0.279695	−	0.179749i
$303$	3.73335	+	25.9660i	0.214475	+	1.49171i
$304$	−1.44678	−	3.16800i	−0.0829784	−	0.181697i
$305$	1.55074	−	10.7857i	0.0887954	−	0.617585i
$306$	0.126662	−	0.0371913i	0.00724079	−	0.00212609i
$307$	22.8282	+	14.6708i	1.30287	+	0.837305i	0.993522	−	0.113643i	$-0.0362519\pi$
$307$	22.8282	+	14.6708i	1.30287	+	0.837305i	0.309351	+	0.950948i	$0.399888\pi$
$308$	5.36875	−	11.7559i	0.305913	−	0.669855i
$309$	18.1183	+	5.32002i	1.03072	+	0.302645i
$310$	0.667898	+	0.770796i	0.0379341	+	0.0437782i
$311$	−17.6451	−	20.3635i	−1.00056	−	1.15471i	−0.987948	−	0.154788i	$-0.950530\pi$
$311$	−17.6451	−	20.3635i	−1.00056	−	1.15471i	−0.0126133	−	0.999920i	$-0.504015\pi$
$312$	0.435159	+	0.127774i	0.0246360	+	0.00723379i
$313$	5.59753	−	12.2569i	0.316391	−	0.692800i	−0.682897	−	0.730514i	$-0.739280\pi$
$313$	5.59753	−	12.2569i	0.316391	−	0.692800i	0.999289	+	0.0377142i	$0.0120077\pi$
$314$	−3.83236	−	2.46291i	−0.216273	−	0.138990i
$315$	1.30096	−	0.381997i	0.0733010	−	0.0215231i
$316$	3.27195	−	22.7569i	0.184061	−	1.28018i
$317$	2.44221	+	5.34770i	0.137168	+	0.300357i	0.965733	−	0.259536i	$-0.0835696\pi$
$317$	2.44221	+	5.34770i	0.137168	+	0.300357i	−0.828565	+	0.559893i	$0.810842\pi$
$318$	−0.277939	−	1.93311i	−0.0155861	−	0.108403i
$319$	−0.624423	+	0.401292i	−0.0349610	+	0.0224680i
$320$	−4.00825	+	4.62576i	−0.224068	+	0.258588i
$321$	−7.51812			−0.419621
$322$	−0.326220	+	1.87853i	−0.0181795	+	0.104687i
$323$	0.472657			0.0262993
$324$	−6.46620	+	7.46240i	−0.359234	+	0.414578i
$325$	−0.240109	+	0.154309i	−0.0133189	+	0.00855952i
$326$	−0.633757	−	4.40788i	−0.0351006	−	0.244130i
$327$	5.91258	+	12.9467i	0.326966	+	0.715957i
$328$	1.09510	−	7.61662i	0.0604670	−	0.420557i
$329$	12.6338	−	3.70962i	0.696524	−	0.204518i
$330$	1.64464	+	1.05694i	0.0905343	+	0.0581828i
$331$	−6.04014	+	13.2261i	−0.331996	+	0.726970i	−0.999850	−	0.0173223i	$-0.994486\pi$
$331$	−6.04014	+	13.2261i	−0.331996	+	0.726970i	0.667854	+	0.744293i	$0.267213\pi$
$332$	11.9822	+	3.51830i	0.657609	+	0.193092i
$333$	−2.61382	−	3.01651i	−0.143236	−	0.165304i
$334$	1.89596	+	2.18805i	0.103742	+	0.119725i
$335$	−6.77094	−	1.98813i	−0.369936	−	0.108623i
$336$	−2.90992	+	6.37183i	−0.158749	+	0.347612i
$337$	−13.9508	−	8.96566i	−0.759951	−	0.488391i	0.102374	−	0.994746i	$-0.467356\pi$
$337$	−13.9508	−	8.96566i	−0.759951	−	0.488391i	−0.862325	+	0.506355i	$0.830992\pi$
$338$	−3.52805	+	1.03593i	−0.191901	+	0.0563472i
$339$	0.749236	−	5.21105i	0.0406929	−	0.283025i
$340$	−0.380874	−	0.833998i	−0.0206558	−	0.0452299i
$341$	2.45880	+	17.1014i	0.133152	+	0.926090i
$342$	−0.229944	+	0.147776i	−0.0124339	+	0.00799081i
$343$	−11.0212	+	12.7191i	−0.595086	+	0.686766i
$344$	12.0010			0.647049
$345$	6.49618	+	2.11492i	0.349743	+	0.113864i
$346$	1.28460			0.0690606
$347$	−10.1487	+	11.7122i	−0.544809	+	0.628743i	−0.959666	−	0.281144i	$-0.909286\pi$
$347$	−10.1487	+	11.7122i	−0.544809	+	0.628743i	0.414857	+	0.909887i	$0.363832\pi$
$348$	0.354020	−	0.227515i	0.0189775	−	0.0121961i
$349$	−0.162561	−	1.13064i	−0.00870168	−	0.0605215i	0.985008	−	0.172509i	$-0.0551874\pi$
$349$	−0.162561	−	1.13064i	−0.00870168	−	0.0605215i	−0.993710	+	0.111988i	$0.964278\pi$
$350$	0.165154	+	0.361637i	0.00882785	+	0.0193303i
$351$	−0.229759	+	1.59801i	−0.0122636	+	0.0852954i
$352$	14.9566	−	4.39166i	0.797191	−	0.234076i
$353$	9.13499	+	5.87070i	0.486206	+	0.312466i	0.760678	−	0.649129i	$-0.224867\pi$
$353$	9.13499	+	5.87070i	0.486206	+	0.312466i	−0.274472	+	0.961595i	$0.588503\pi$
$354$	1.15354	−	2.52589i	0.0613097	−	0.134250i
$355$	−11.6018	−	3.40660i	−0.615760	−	0.180803i
$356$	−13.7493	−	15.8675i	−0.728712	−	0.840978i
$357$	−0.622549	−	0.718460i	−0.0329488	−	0.0380249i
$358$	0.162722	+	0.0477796i	0.00860015	+	0.00252523i
$359$	3.39979	−	7.44451i	0.179434	−	0.392906i	−0.798448	−	0.602064i	$-0.794345\pi$
$359$	3.39979	−	7.44451i	0.179434	−	0.392906i	0.977882	+	0.209158i	$0.0670723\pi$
$360$	0.910914	+	0.585409i	0.0480094	+	0.0308538i
$361$	17.2913	−	5.07720i	0.910071	−	0.267221i
$362$	0.115012	−	0.799925i	0.00604489	−	0.0420431i
$363$	7.24797	+	15.8708i	0.380420	+	0.833003i
$364$	0.108876	+	0.757246i	0.00570663	+	0.0396905i
$365$	5.73801	−	3.68759i	0.300341	−	0.193017i
$366$	2.89327	−	3.33902i	0.151234	−	0.174533i
$367$	−1.28779			−0.0672223			−0.0336112	−	0.999435i	$-0.510701\pi$
$367$	−1.28779			−0.0672223			−0.0336112	+	0.999435i	$0.510701\pi$
$368$	14.4634	−	8.71024i	0.753954	−	0.454053i
$369$	6.69651			0.348606
$370$	0.766406	−	0.884479i	0.0398435	−	0.0459819i
$371$	5.65982	−	3.63734i	0.293843	−	0.188841i
$372$	−1.39403	−	9.69572i	−0.0722773	−	0.502700i
$373$	−7.90548	−	17.3106i	−0.409330	−	0.896308i	−0.996238	−	0.0866545i	$-0.972382\pi$
$373$	−7.90548	−	17.3106i	−0.409330	−	0.896308i	0.586908	−	0.809653i	$-0.300345\pi$
$374$	−0.0933148	+	0.649019i	−0.00482519	+	0.0335600i
$375$	1.36682	−	0.401335i	0.0705824	−	0.0207249i
$376$	8.84599	+	5.68497i	0.456197	+	0.293180i
$377$	0.0182526	−	0.0399675i	0.000940054	−	0.00205843i
$378$	2.15769	+	0.633554i	0.110979	+	0.0325865i
$379$	−2.95818	−	3.41392i	−0.151951	−	0.175361i	0.674670	−	0.738119i	$-0.264286\pi$
$379$	−2.95818	−	3.41392i	−0.151951	−	0.175361i	−0.826622	+	0.562758i	$0.809740\pi$
$380$	1.24319	+	1.43472i	0.0637745	+	0.0735997i
$381$	18.8911	+	5.54694i	0.967822	+	0.284178i
$382$	−1.85820	+	4.06888i	−0.0950736	+	0.208182i
$383$	−31.1963	−	20.0487i	−1.59406	−	1.02444i	−0.970014	−	0.243050i	$-0.921852\pi$
$383$	−31.1963	−	20.0487i	−1.59406	−	1.02444i	−0.624044	−	0.781389i	$-0.714512\pi$
$384$	−11.2190	+	3.29418i	−0.572515	+	0.168106i
$385$	−0.958449	+	6.66616i	−0.0488471	+	0.339739i
$386$	−2.44402	−	5.35166i	−0.124397	−	0.272392i
$387$	1.48631	+	10.3375i	0.0755534	+	0.525486i
$388$	25.2643	−	16.2364i	1.28260	−	0.824278i
$389$	−0.759670	+	0.876706i	−0.0385168	+	0.0444508i	−0.774681	−	0.632352i	$-0.782090\pi$
$389$	−0.759670	+	0.876706i	−0.0385168	+	0.0444508i	0.736164	+	0.676803i	$0.236635\pi$
$390$	−0.115726			−0.00586004
$391$	0.259868	+	2.27657i	0.0131421	+	0.115131i
$392$	−5.63198			−0.284458
$393$	−5.06691	+	5.84752i	−0.255592	+	0.294969i
$394$	1.91064	−	1.22789i	0.0962566	−	0.0618603i
$395$	1.70504	+	11.8588i	0.0857898	+	0.596681i
$396$	3.73115	+	8.17009i	0.187498	+	0.410562i
$397$	−1.77598	+	12.3522i	−0.0891340	+	0.619940i	0.895468	+	0.445127i	$0.146841\pi$
$397$	−1.77598	+	12.3522i	−0.0891340	+	0.619940i	−0.984602	+	0.174814i	$0.944068\pi$
$398$	1.40459	−	0.412426i	0.0704059	−	0.0206730i
$399$	1.65593	+	1.06420i	0.0829001	+	0.0532767i
$400$	1.46246	−	3.20234i	0.0731230	−	0.160117i
$401$	18.8475	+	5.53414i	0.941201	+	0.276362i	0.716119	−	0.697978i	$-0.245917\pi$
$401$	18.8475	+	5.53414i	0.941201	+	0.276362i	0.225082	+	0.974340i	$0.427735\pi$
$402$	−1.87373	−	2.16240i	−0.0934530	−	0.107851i
$403$	−0.669749	−	0.772932i	−0.0333626	−	0.0385025i
$404$	−33.9072	−	9.95604i	−1.68694	−	0.495331i
$405$	2.13752	−	4.68052i	0.106214	−	0.232577i
$406$	−0.0514864	−	0.0330883i	−0.00255523	−	0.00164215i
$407$	19.0223	−	5.58546i	0.942902	−	0.276861i
$408$	0.108044	−	0.751465i	0.00534899	−	0.0372031i
$409$	−4.16456	−	9.11912i	−0.205924	−	0.450912i	0.778287	−	0.627909i	$-0.216089\pi$
$409$	−4.16456	−	9.11912i	−0.205924	−	0.450912i	−0.984211	+	0.176997i	$0.943362\pi$
$410$	0.279436	+	1.94352i	0.0138003	+	0.0959835i
$411$	−23.4393	+	15.0635i	−1.15617	+	0.743028i
$412$	−16.6581	+	19.2245i	−0.820688	+	0.947124i
$413$	9.56587			0.470706
$414$	−0.838192	−	1.02628i	−0.0411949	−	0.0504392i
$415$	−6.50764			−0.319447
$416$	−0.604269	+	0.697364i	−0.0296267	+	0.0341911i
$417$	−13.2103	+	8.48974i	−0.646911	+	0.415744i
$418$	−0.193215	−	1.34384i	−0.00945045	−	0.0657293i
$419$	2.05722	+	4.50468i	0.100502	+	0.220068i	0.953203	−	0.302330i	$-0.0977646\pi$
$419$	2.05722	+	4.50468i	0.100502	+	0.220068i	−0.852701	+	0.522399i	$0.825037\pi$
$420$	0.543399	−	3.77942i	0.0265151	−	0.184417i
$421$	−0.214743	+	0.0630541i	−0.0104659	+	0.00307307i	−0.286961	−	0.957942i	$-0.592645\pi$
$421$	−0.214743	+	0.0630541i	−0.0104659	+	0.00307307i	0.276495	+	0.961015i	$0.410827\pi$
$422$	−6.42237	−	4.12740i	−0.312636	−	0.200919i
$423$	−3.80141	+	8.32393i	−0.184831	+	0.404723i
$424$	5.15519	+	1.51370i	0.250358	+	0.0735118i
$425$	0.312879	+	0.361082i	0.0151769	+	0.0175150i
$426$	−3.21058	−	3.70520i	−0.155553	−	0.179518i
$427$	14.6035	+	4.28799i	0.706715	+	0.207510i
$428$	4.20720	−	9.21248i	0.203363	−	0.445302i
$429$	−1.64919	−	1.05987i	−0.0796238	−	0.0511711i
$430$	−2.93822	+	0.862740i	−0.141694	+	0.0416050i
$431$	0.635308	−	4.41866i	0.0306017	−	0.212840i	−0.968783	−	0.247910i	$-0.920256\pi$
$431$	0.635308	−	4.41866i	0.0306017	−	0.212840i	0.999385	+	0.0350702i	$0.0111655\pi$
$432$	−8.27226	−	18.1137i	−0.397999	−	0.871497i
$433$	2.47814	+	17.2359i	0.119092	+	0.828303i	0.958559	+	0.284893i	$0.0919581\pi$
$433$	2.47814	+	17.2359i	0.119092	+	0.828303i	−0.839467	+	0.543410i	$0.817133\pi$
$434$	−1.19844	+	0.770188i	−0.0575267	+	0.0369702i
$435$	−0.143608	+	0.165732i	−0.00688548	+	0.00794626i
$436$	−19.1733			−0.918233
$437$	−1.84431	−	4.37126i	−0.0882253	−	0.209106i
$438$	2.76557			0.132144
$439$	−14.7508	+	17.0234i	−0.704018	+	0.812481i	−0.989290	−	0.145966i	$-0.953371\pi$
$439$	−14.7508	+	17.0234i	−0.704018	+	0.812481i	0.285271	+	0.958447i	$0.407916\pi$
$440$	−4.52453	+	2.90774i	−0.215698	+	0.138621i
$441$	−0.697516	−	4.85133i	−0.0332150	−	0.231016i
$442$	−0.0161240	−	0.0353066i	−0.000766939	−	0.00167936i
$443$	3.58121	−	24.9079i	0.170149	−	1.18341i	−0.708419	−	0.705792i	$-0.750591\pi$
$443$	3.58121	−	24.9079i	0.170149	−	1.18341i	0.878568	−	0.477617i	$-0.158499\pi$
$444$	−10.7848	+	3.16671i	−0.511826	+	0.150286i
$445$	9.20422	+	5.91519i	0.436322	+	0.280407i
$446$	−0.630715	+	1.38107i	−0.0298652	+	0.0653957i
$447$	13.5824	+	3.98817i	0.642428	+	0.188634i
$448$	−5.59862	−	6.46115i	−0.264510	−	0.305261i
$449$	−16.9078	−	19.5127i	−0.797930	−	0.920861i	0.200335	−	0.979727i	$-0.435797\pi$
$449$	−16.9078	−	19.5127i	−0.797930	−	0.920861i	−0.998266	+	0.0588666i	$0.981251\pi$
$450$	−0.265105	−	0.0778420i	−0.0124972	−	0.00366951i
$451$	−13.8174	+	30.2559i	−0.650636	+	1.42469i
$452$	5.96618	+	3.83423i	0.280626	+	0.180347i
$453$	27.7455	−	8.14683i	1.30360	−	0.382771i
$454$	0.302241	−	2.10213i	0.0141849	−	0.0986580i
$455$	−0.165612	−	0.362639i	−0.00776399	−	0.0170008i
$456$	0.223714	+	1.55596i	0.0104763	+	0.0728646i
$457$	−29.5376	+	18.9827i	−1.38171	+	0.887973i	−0.999350	−	0.0360394i	$-0.988526\pi$
$457$	−29.5376	+	18.9827i	−1.38171	+	0.887973i	−0.382363	+	0.924012i	$0.624889\pi$
$458$	−4.32038	+	4.98599i	−0.201878	+	0.232980i
$459$	2.70251			0.126143
$460$	−6.22688	+	6.77670i	−0.290330	+	0.315965i
$461$	26.7881			1.24765			0.623824	−	0.781565i	$-0.285578\pi$
$461$	26.7881			1.24765			0.623824	+	0.781565i	$0.285578\pi$
$462$	−1.78821	+	2.06370i	−0.0831950	+	0.0960122i
$463$	−10.9871	+	7.06099i	−0.510614	+	0.328152i	−0.770449	−	0.637501i	$-0.779968\pi$
$463$	−10.9871	+	7.06099i	−0.510614	+	0.328152i	0.259835	+	0.965653i	$0.416332\pi$
$464$	0.0771279	+	0.536436i	0.00358057	+	0.0249034i
$465$	2.12048	+	4.64320i	0.0983348	+	0.215323i
$466$	−0.987372	+	6.86732i	−0.0457391	+	0.318123i
$467$	−3.72568	+	1.09396i	−0.172404	+	0.0506224i	−0.366795	−	0.930302i	$-0.619545\pi$
$467$	−3.72568	+	1.09396i	−0.172404	+	0.0506224i	0.194391	+	0.980924i	$0.437727\pi$
$468$	−0.447278	−	0.287448i	−0.0206754	−	0.0132873i
$469$	4.09464	−	8.96601i	0.189073	−	0.414012i
$470$	−2.57447	−	0.755932i	−0.118751	−	0.0348686i
$471$	−14.9307	−	17.2309i	−0.687968	−	0.793958i
$472$	5.00266	+	5.77338i	0.230266	+	0.265741i
$473$	−49.7734	−	14.6148i	−2.28858	−	0.671988i
$474$	−2.01798	+	4.41876i	−0.0926889	+	0.202960i
$475$	−0.832233	−	0.534844i	−0.0381855	−	0.0245403i
$476$	1.22876	−	0.360797i	0.0563202	−	0.0165371i
$477$	−0.665420	+	4.62810i	−0.0304675	+	0.211906i
$478$	0.138832	+	0.303999i	0.00635002	+	0.0139046i
$479$	2.80762	+	19.5274i	0.128283	+	0.892231i	0.947730	+	0.319075i	$0.103372\pi$
$479$	2.80762	+	19.5274i	0.128283	+	0.892231i	−0.819446	+	0.573156i	$0.805719\pi$
$480$	3.87433	−	2.48988i	0.176838	−	0.113647i
$481$	−0.768530	+	0.886931i	−0.0350419	+	0.0404406i
$482$	−1.87652			−0.0854731
$483$	−4.21532	+	8.56094i	−0.191804	+	0.389536i
$484$	−23.5037			−1.06835
$485$	−10.2484	+	11.8273i	−0.465358	+	0.537052i
$486$	−2.30809	+	1.48332i	−0.104697	+	0.0672846i
$487$	−5.37031	−	37.3513i	−0.243352	−	1.69255i	−0.635063	−	0.772460i	$-0.719026\pi$
$487$	−5.37031	−	37.3513i	−0.243352	−	1.69255i	0.391711	−	0.920088i	$-0.371883\pi$
$488$	5.04924	+	11.0563i	0.228568	+	0.500495i
$489$	3.17185	−	22.0607i	0.143436	−	0.997620i
$490$	1.37889	−	0.404878i	0.0622918	−	0.0182905i
$491$	−5.59270	−	3.59421i	−0.252395	−	0.162204i	0.408326	−	0.912836i	$-0.366113\pi$
$491$	−5.59270	−	3.59421i	−0.252395	−	0.162204i	−0.660721	+	0.750632i	$0.729749\pi$
$492$	7.83386	−	17.1538i	0.353178	−	0.773351i
$493$	−0.0705714	−	0.0207216i	−0.00317838	−	0.000933256i
$494$	0.0526295	+	0.0607377i	0.00236791	+	0.00273272i
$495$	−3.06505	−	3.53726i	−0.137764	−	0.158988i
$496$	12.1039	+	3.55402i	0.543480	+	0.159580i
$497$	7.01604	−	15.3630i	0.314712	−	0.689124i
$498$	−2.21973	−	1.42654i	−0.0994686	−	0.0639246i
$499$	26.8862	−	7.89451i	1.20359	−	0.353407i	0.382368	−	0.924010i	$-0.375109\pi$
$499$	26.8862	−	7.89451i	1.20359	−	0.353407i	0.821226	+	0.570603i	$0.193291\pi$
$500$	−0.273100	+	1.89945i	−0.0122134	+	0.0849461i
$501$	6.01938	+	13.1806i	0.268926	+	0.588866i
$502$	−0.163940	−	1.14023i	−0.00731701	−	0.0508910i
$503$	28.6373	−	18.4041i	1.27687	−	0.820597i	0.286375	−	0.958117i	$-0.407550\pi$
$503$	28.6373	−	18.4041i	1.27687	−	0.820597i	0.990499	+	0.137520i	$0.0439132\pi$
$504$	−0.990435	+	1.14302i	−0.0441175	+	0.0509143i
$505$	18.4153			0.819468
$506$	6.36642	−	1.66948i	0.283022	−	0.0742172i
$507$	−18.4028			−0.817297
$508$	−17.3687	+	20.0445i	−0.770610	+	0.889332i
$509$	−17.4206	+	11.1955i	−0.772154	+	0.496234i	−0.866421	−	0.499313i	$-0.833586\pi$
$509$	−17.4206	+	11.1955i	−0.772154	+	0.496234i	0.0942670	+	0.995547i	$0.469949\pi$
$510$	0.0275695	+	0.191750i	0.00122080	+	0.00849083i
$511$	3.95770	+	8.66615i	0.175078	+	0.383368i
$512$	2.73749	−	19.0397i	0.120981	−	0.841442i
$513$	−5.36908	+	1.57650i	−0.237051	+	0.0696044i
$514$	0.152049	+	0.0977158i	0.00670658	+	0.00431006i
$515$	5.50666	−	12.0579i	0.242652	−	0.531334i
$516$	28.2193	+	8.28594i	1.24229	+	0.364768i
$517$	−29.7651	−	34.3507i	−1.30907	−	1.51074i
$518$	1.07050	+	1.23542i	0.0470349	+	0.0542812i
$519$	6.16879	+	1.81132i	0.270780	+	0.0795082i
$520$	0.132257	−	0.289602i	0.00579985	−	0.0126999i
$521$	15.4670	+	9.94007i	0.677624	+	0.435482i	0.833667	−	0.552268i	$-0.186237\pi$
$521$	15.4670	+	9.94007i	0.677624	+	0.435482i	−0.156043	+	0.987750i	$0.549874\pi$
$522$	0.0408111	−	0.0119832i	0.00178625	−	0.000524491i
$523$	−4.30323	+	29.9296i	−0.188167	+	1.30873i	0.648583	+	0.761144i	$0.275362\pi$
$523$	−4.30323	+	29.9296i	−0.188167	+	1.30873i	−0.836750	+	0.547585i	$0.815547\pi$
$524$	−4.32990	−	9.48115i	−0.189152	−	0.414186i
$525$	0.283170	+	1.96949i	0.0123585	+	0.0859555i
$526$	−5.18209	+	3.33033i	−0.225950	+	0.145209i
$527$	−1.12113	+	1.29386i	−0.0488374	+	0.0563614i
$528$	24.1805			1.05232
$529$	20.0403	−	11.2865i	0.871318	−	0.490718i
$530$	−1.37097			−0.0595513
$531$	−4.35355	+	5.02427i	−0.188928	+	0.218035i
$532$	−2.23071	+	1.43359i	−0.0967135	+	0.0621540i
$533$	−0.280210	−	1.94890i	−0.0121372	−	0.0844164i
$534$	1.84286	+	4.03530i	0.0797484	+	0.174625i
$535$	−0.751085	+	5.22391i	−0.0324722	+	0.225849i
$536$	7.55271	−	2.21767i	0.326227	−	0.0957890i
$537$	0.714040	+	0.458886i	0.0308131	+	0.0198024i
$538$	0.0739642	−	0.161959i	0.00318882	−	0.00698255i
$539$	23.3583	+	6.85862i	1.00611	+	0.295422i
$540$	7.10822	+	8.20333i	0.305889	+	0.353015i
$541$	27.0168	+	31.1791i	1.16154	+	1.34049i	0.929952	+	0.367681i	$0.119848\pi$
$541$	27.0168	+	31.1791i	1.16154	+	1.34049i	0.231593	+	0.972813i	$0.425606\pi$
$542$	−1.00806	−	0.295992i	−0.0432997	−	0.0127139i
$543$	1.68022	−	3.67916i	0.0721049	−	0.157888i
$544$	1.29943	+	0.835095i	0.0557127	+	0.0358044i
$545$	9.58664	−	2.81489i	0.410646	−	0.120577i
$546$	0.0230043	−	0.159998i	0.000984493	−	0.00684730i
$547$	−2.16762	−	4.74643i	−0.0926809	−	0.202943i	0.857614	−	0.514294i	$-0.171946\pi$
$547$	−2.16762	−	4.74643i	−0.0926809	−	0.202943i	−0.950295	+	0.311351i	$0.899219\pi$
$548$	−5.34157	−	37.1515i	−0.228181	−	1.58703i
$549$	−8.89844	+	5.71868i	−0.379776	+	0.244067i
$550$	0.898714	−	1.03717i	0.0383213	−	0.0442251i
$551$	0.152292			0.00648786
$552$	−7.37135	+	1.93300i	−0.313745	+	0.0822739i
$553$	−16.7344			−0.711620
$554$	3.38856	−	3.91061i	0.143966	−	0.166146i
$555$	4.92750	−	3.16671i	0.209161	−	0.134420i
$556$	−3.01049	−	20.9384i	−0.127673	−	0.887987i
$557$	8.51684	+	18.6493i	0.360870	+	0.790195i	0.999781	+	0.0209146i	$0.00665782\pi$
$557$	8.51684	+	18.6493i	0.360870	+	0.790195i	−0.638911	+	0.769280i	$0.720615\pi$
$558$	0.140899	−	0.979975i	0.00596473	−	0.0414856i
$559$	2.94637	−	0.865131i	0.124618	−	0.0365911i
$560$	4.13671	+	2.65850i	0.174808	+	0.112342i
$561$	−1.36324	+	2.98508i	−0.0575561	+	0.126030i
$562$	1.37928	+	0.404992i	0.0581813	+	0.0170836i
$563$	27.8847	+	32.1806i	1.17520	+	1.35625i	0.921220	+	0.389042i	$0.127194\pi$
$563$	27.8847	+	32.1806i	1.17520	+	1.35625i	0.253978	+	0.967210i	$0.418261\pi$
$564$	16.8755	+	19.4754i	0.710587	+	0.820061i
$565$	−3.54601	−	1.04120i	−0.149182	−	0.0438037i
$566$	0.119666	−	0.262031i	0.00502992	−	0.0110140i
$567$	6.04619	+	3.88565i	0.253916	+	0.163182i
$568$	12.9413	−	3.79992i	0.543007	−	0.159441i
$569$	4.55153	−	31.6566i	0.190810	−	1.32711i	−0.639060	−	0.769157i	$-0.720676\pi$
$569$	4.55153	−	31.6566i	0.190810	−	1.32711i	0.829870	−	0.557957i	$-0.188414\pi$
$570$	−0.166629	−	0.364867i	−0.00697932	−	0.0152826i
$571$	2.19537	+	15.2691i	0.0918734	+	0.638994i	0.982776	+	0.184800i	$0.0591636\pi$
$571$	2.19537	+	15.2691i	0.0918734	+	0.638994i	−0.890903	+	0.454194i	$0.849927\pi$
$572$	2.22164	−	1.42776i	0.0928913	−	0.0596976i
$573$	−14.6605	+	16.9191i	−0.612451	+	0.706806i
$574$	−2.74257			−0.114473
$575$	2.11853	−	4.30254i	0.0883487	−	0.179428i
$576$	5.94159			0.247566
$577$	25.5971	−	29.5406i	1.06562	−	1.22979i	0.0934247	−	0.995626i	$-0.470219\pi$
$577$	25.5971	−	29.5406i	1.06562	−	1.22979i	0.972197	−	0.234166i	$-0.0752360\pi$
$578$	4.01592	−	2.58087i	0.167040	−	0.107350i
$579$	−4.19047	−	29.1454i	−0.174150	−	1.21124i
$580$	−0.122719	−	0.268718i	−0.00509565	−	0.0111579i
$581$	1.29360	−	8.99719i	0.0536676	−	0.373266i
$582$	−6.08838	+	1.78771i	−0.252371	+	0.0741029i
$583$	−19.5375	−	12.5560i	−0.809160	−	0.520015i
$584$	−3.16060	+	6.92076i	−0.130787	+	0.286383i
$585$	0.265840	+	0.0780577i	0.0109911	+	0.00322729i
$586$	4.79015	+	5.52812i	0.197879	+	0.228365i
$587$	−24.4245	−	28.1874i	−1.00811	−	1.16342i	−0.986518	−	0.163651i	$-0.947673\pi$
$587$	−24.4245	−	28.1874i	−1.00811	−	1.16342i	−0.0215889	−	0.999767i	$-0.506872\pi$
$588$	−13.2431	−	3.88854i	−0.546138	−	0.160361i
$589$	1.47259	−	3.22452i	0.0606769	−	0.132864i
$590$	−1.63985	−	1.05387i	−0.0675117	−	0.0433872i
$591$	10.9065	−	3.20242i	0.448632	−	0.131730i
$592$	2.06007	−	14.3281i	0.0846683	−	0.588881i
$593$	19.5387	+	42.7839i	0.802360	+	1.75692i	0.637263	+	0.770647i	$0.280067\pi$
$593$	19.5387	+	42.7839i	0.802360	+	1.75692i	0.165097	+	0.986277i	$0.447206\pi$
$594$	−1.10475	−	7.68369i	−0.0453283	−	0.315266i
$595$	−0.561411	+	0.360797i	−0.0230156	+	0.0147912i
$596$	−12.4878	+	14.4117i	−0.511521	+	0.590327i
$597$	7.32654			0.299855
$598$	−0.263609	+	0.286886i	−0.0107798	+	0.0117316i
$599$	26.3109			1.07503			0.537517	−	0.843253i	$-0.319363\pi$
$599$	26.3109			1.07503			0.537517	+	0.843253i	$0.319363\pi$
$600$	−1.04057	+	1.20089i	−0.0424813	+	0.0490260i
$601$	−25.2339	+	16.2168i	−1.02931	+	0.661498i	−0.942321	−	0.334711i	$-0.891361\pi$
$601$	−25.2339	+	16.2168i	−1.02931	+	0.661498i	−0.0869905	+	0.996209i	$0.527725\pi$
$602$	−0.608723	−	4.23376i	−0.0248097	−	0.172555i
$603$	2.84568	+	6.23117i	0.115885	+	0.253753i
$604$	−5.54374	+	38.5576i	−0.225572	+	1.56889i
$605$	11.7518	−	3.45065i	0.477780	−	0.140289i
$606$	6.28138	+	4.03680i	0.255164	+	0.163984i
$607$	−0.908402	+	1.98912i	−0.0368709	+	0.0807360i	−0.927171	−	0.374638i	$-0.877767\pi$
$607$	−0.908402	+	1.98912i	−0.0368709	+	0.0807360i	0.890300	+	0.455374i	$0.150494\pi$
$608$	−3.06873	−	0.901061i	−0.124454	−	0.0365429i
$609$	−0.200588	−	0.231491i	−0.00812824	−	0.00938049i
$610$	−2.03104	−	2.34395i	−0.0822345	−	0.0949037i
$611$	2.58160	+	0.758027i	0.104441	+	0.0306665i
$612$	−0.369725	+	0.809584i	−0.0149452	+	0.0327255i
$613$	−28.6930	−	18.4399i	−1.15890	−	0.744780i	−0.187508	−	0.982263i	$-0.560041\pi$
$613$	−28.6930	−	18.4399i	−1.15890	−	0.744780i	−0.971392	+	0.237483i	$0.923678\pi$
$614$	7.41082	−	2.17601i	0.299076	−	0.0878167i
$615$	−1.39853	+	9.72699i	−0.0563942	+	0.392230i
$616$	−3.12072	−	6.83343i	−0.125737	−	0.275327i
$617$	1.99096	+	13.8474i	0.0801529	+	0.557476i	0.989840	+	0.142182i	$0.0454119\pi$
$617$	1.99096	+	13.8474i	0.0801529	+	0.557476i	−0.909688	+	0.415293i	$0.863679\pi$
$618$	4.52151	−	2.90580i	0.181882	−	0.116888i
$619$	−20.8146	+	24.0213i	−0.836608	+	0.965497i	−0.999777	−	0.0211014i	$-0.993283\pi$
$619$	−20.8146	+	24.0213i	−0.836608	+	0.965497i	0.163170	+	0.986598i	$0.447828\pi$
$620$	−6.87627			−0.276158
$621$	−10.5452	−	24.9936i	−0.423166	−	1.00296i
$622$	−7.66929			−0.307510
$623$	−10.0077	+	11.5495i	−0.400951	+	0.462722i
$624$	−1.20415	+	0.773861i	−0.0482046	+	0.0309792i
$625$	−0.142315	−	0.989821i	−0.00569259	−	0.0395929i
$626$	−1.59322	−	3.48867i	−0.0636780	−	0.139435i
$627$	0.967010	−	6.72570i	0.0386187	−	0.268599i
$628$	29.4695	−	8.65303i	1.17596	−	0.345294i
$629$	1.65266	+	1.06210i	0.0658960	+	0.0423488i
$630$	0.160319	−	0.351050i	0.00638727	−	0.0139862i
$631$	28.3310	+	8.31873i	1.12784	+	0.331164i	0.791858	−	0.610705i	$-0.209114\pi$
$631$	28.3310	+	8.31873i	1.12784	+	0.331164i	0.335981	+	0.941869i	$0.390932\pi$
$632$	−8.75159	−	10.0999i	−0.348120	−	0.401752i
$633$	−25.0212	−	28.8759i	−0.994502	−	1.14772i
$634$	1.60555	+	0.471432i	0.0637645	+	0.0187229i
$635$	5.74154	−	12.5722i	0.227846	−	0.498913i
$636$	11.0769	+	7.11869i	0.439228	+	0.282274i
$637$	−1.38271	+	0.406000i	−0.0547849	+	0.0160863i
$638$	−0.0300665	+	0.209117i	−0.00119034	+	0.00827901i
$639$	4.87599	+	10.6769i	0.192891	+	0.422373i
$640$	1.16813	+	8.12451i	0.0461743	+	0.321149i
$641$	−33.6984	+	21.6567i	−1.33101	+	0.855387i	−0.996217	−	0.0869046i	$-0.972302\pi$
$641$	−33.6984	+	21.6567i	−1.33101	+	0.855387i	−0.334792	+	0.942292i	$0.608666\pi$
$642$	−1.40132	+	1.61721i	−0.0553058	+	0.0638263i
$643$	29.7612			1.17367			0.586834	−	0.809707i	$-0.300374\pi$
$643$	29.7612			1.17367			0.586834	+	0.809707i	$0.300374\pi$
$644$	−8.13139	−	9.95610i	−0.320422	−	0.392325i
$645$	−15.3262			−0.603467
$646$	0.0880998	−	0.101673i	0.00346624	−	0.00400025i
$647$	22.6465	−	14.5540i	0.890326	−	0.572178i	−0.0135807	−	0.999908i	$-0.504323\pi$
$647$	22.6465	−	14.5540i	0.890326	−	0.572178i	0.903906	+	0.427730i	$0.140687\pi$
$648$	0.816832	+	5.68119i	0.0320882	+	0.223178i
$649$	−13.7174	−	30.0370i	−0.538456	−	1.17906i
$650$	−0.0115615	+	0.0804117i	−0.000453478	+	0.00315401i
$651$	−6.84100	+	2.00870i	−0.268120	+	0.0787271i
$652$	25.2576	+	16.2320i	0.989162	+	0.635696i
$653$	14.3201	−	31.3566i	0.560388	−	1.22708i	−0.391371	−	0.920233i	$-0.627999\pi$
$653$	14.3201	−	31.3566i	0.560388	−	1.22708i	0.951759	−	0.306846i	$-0.0992737\pi$
$654$	3.88702	+	1.14133i	0.151995	+	0.0446296i
$655$	3.55691	+	4.10489i	0.138980	+	0.160391i
$656$	15.9038	+	18.3540i	0.620941	+	0.716604i
$657$	−6.35291	−	1.86538i	−0.247851	−	0.0727755i
$658$	1.55688	−	3.40909i	0.0606934	−	0.132900i
$659$	−20.8466	−	13.3973i	−0.812069	−	0.521885i	0.0674645	−	0.997722i	$-0.478509\pi$
$659$	−20.8466	−	13.3973i	−0.812069	−	0.521885i	−0.879534	+	0.475836i	$0.842145\pi$
$660$	−12.6467	+	3.71340i	−0.492271	+	0.144544i
$661$	−2.66397	+	18.5283i	−0.103616	+	0.720668i	0.870095	+	0.492884i	$0.164057\pi$
$661$	−2.66397	+	18.5283i	−0.103616	+	0.720668i	−0.973712	+	0.227784i	$0.926852\pi$
$662$	1.71920	+	3.76453i	0.0668187	+	0.146313i
$663$	−0.0276459	−	0.192281i	−0.00107368	−	0.00746759i
$664$	6.10667	−	3.92452i	0.236985	−	0.152301i
$665$	0.904885	−	1.04429i	0.0350899	−	0.0404959i
$666$	−1.13607			−0.0440220
$667$	0.0837308	+	0.733520i	0.00324207	+	0.0284020i
$668$	−19.5196			−0.755236
$669$	−4.97611	+	5.74273i	−0.192387	+	0.222027i
$670$	−1.68972	+	1.08592i	−0.0652795	+	0.0419526i
$671$	−7.47709	−	52.0043i	−0.288650	−	2.00760i
$672$	2.67226	+	5.85143i	0.103085	+	0.225724i
$673$	−1.24315	+	8.64633i	−0.0479201	+	0.333291i	0.951732	+	0.306929i	$0.0993015\pi$
$673$	−1.24315	+	8.64633i	−0.0479201	+	0.333291i	−0.999652	+	0.0263623i	$0.991608\pi$
$674$	−4.52893	+	1.32981i	−0.174448	+	0.0512225i
$675$	−4.75847	−	3.05808i	−0.183154	−	0.117706i
$676$	10.2983	−	22.5502i	0.396090	−	0.867316i
$677$	5.64443	+	1.65735i	0.216933	+	0.0636973i	0.388393	−	0.921494i	$-0.373030\pi$
$677$	5.64443	+	1.65735i	0.216933	+	0.0636973i	−0.171460	+	0.985191i	$0.554848\pi$
$678$	−0.981290	−	1.13247i	−0.0376862	−	0.0434922i
$679$	−14.3148	−	16.5201i	−0.549351	−	0.633984i
$680$	−0.511356	−	0.150148i	−0.0196096	−	0.00575790i
$681$	4.41546	−	9.66850i	0.169201	−	0.370498i
$682$	4.13695	+	2.65866i	0.158412	+	0.101805i
$683$	−12.6911	+	3.72646i	−0.485613	+	0.142589i	−0.515369	−	0.856968i	$-0.672345\pi$
$683$	−12.6911	+	3.72646i	−0.485613	+	0.142589i	0.0297560	+	0.999557i	$0.490527\pi$
$684$	0.262263	−	1.82408i	0.0100279	−	0.0697454i
$685$	8.12511	+	17.7915i	0.310445	+	0.679779i
$686$	0.681724	+	4.74149i	0.0260283	+	0.181031i
$687$	−27.7773	+	17.8514i	−1.05977	+	0.681073i
$688$	−24.8035	+	28.6248i	−0.945626	+	1.09131i
$689$	1.37477			0.0523747
$690$	1.66578	−	1.00318i	0.0634152	−	0.0381904i
$691$	−9.66154			−0.367542			−0.183771	−	0.982969i	$-0.558831\pi$
$691$	−9.66154			−0.367542			−0.183771	+	0.982969i	$0.558831\pi$
$692$	−5.67164	+	6.54543i	−0.215604	+	0.248820i
$693$	5.49974	−	3.53447i	0.208918	−	0.134263i
$694$	0.627755	+	4.36613i	0.0238293	+	0.165736i
$695$	4.57928	+	10.0272i	0.173702	+	0.380355i
$696$	0.0348124	−	0.242125i	0.00131956	−	0.00917774i
$697$	−3.16243	+	0.928573i	−0.119786	+	0.0351722i
$698$	−0.273510	−	0.175774i	−0.0103525	−	0.00665315i
$699$	−14.4246	+	31.5854i	−0.545588	+	1.19467i
$700$	−2.57182	−	0.755153i	−0.0972055	−	0.0285421i
$701$	−8.68025	−	10.0175i	−0.327848	−	0.378357i	0.567765	−	0.823191i	$-0.307808\pi$
$701$	−8.68025	−	10.0175i	−0.327848	−	0.378357i	−0.895613	+	0.444834i	$0.853263\pi$
$702$	0.300920	+	0.347281i	0.0113575	+	0.0131073i
$703$	−3.90292	−	1.14600i	−0.147201	−	0.0432222i
$704$	−12.2597	+	26.8450i	−0.462055	+	1.01176i
$705$	−11.2970	−	7.26014i	−0.425469	−	0.273433i
$706$	2.96554	−	0.870760i	0.111609	−	0.0327715i
$707$	−3.66062	+	25.4602i	−0.137672	+	0.957528i
$708$	7.77719	+	17.0297i	0.292285	+	0.640014i
$709$	−0.315324	−	2.19313i	−0.0118423	−	0.0823647i	0.983043	−	0.183374i	$-0.0587019\pi$
$709$	−0.315324	−	2.19313i	−0.0118423	−	0.0823647i	−0.994885	+	0.101009i	$0.967793\pi$
$710$	−2.89528	+	1.86068i	−0.108658	+	0.0698302i
$711$	7.61605	−	8.78939i	0.285624	−	0.329628i
$712$	−12.2043			−0.457377
$713$	16.3406	+	5.31992i	0.611962	+	0.199233i
$714$	−0.270586			−0.0101264
$715$	−0.901205	+	1.04005i	−0.0337031	+	0.0388955i
$716$	−0.961887	+	0.618167i	−0.0359474	+	0.0231020i
$717$	0.238038	+	1.65559i	0.00888971	+	0.0618293i
$718$	−0.967682	−	2.11893i	−0.0361136	−	0.0790777i
$719$	2.01326	−	14.0026i	0.0750820	−	0.522207i	−0.917221	−	0.398378i	$-0.869573\pi$
$719$	2.01326	−	14.0026i	0.0750820	−	0.522207i	0.992304	−	0.123829i	$-0.0395176\pi$
$720$	−3.27899	+	0.962799i	−0.122201	+	0.0358814i
$721$	15.5761	+	10.0102i	0.580085	+	0.372798i
$722$	2.13083	−	4.66587i	0.0793014	−	0.173646i
$723$	−9.01124	−	2.64594i	−0.335132	−	0.0984036i
$724$	3.56807	+	4.11777i	0.132606	+	0.153036i
$725$	0.100811	+	0.116342i	0.00374403	+	0.00432084i
$726$	4.76493	+	1.39911i	0.176843	+	0.0519258i
$727$	3.74447	−	8.19925i	0.138875	−	0.304093i	−0.827397	−	0.561617i	$-0.810179\pi$
$727$	3.74447	−	8.19925i	0.138875	−	0.304093i	0.966272	+	0.257524i	$0.0829066\pi$
$728$	0.374101	+	0.240420i	0.0138651	+	0.00891057i
$729$	−27.9864	+	8.21756i	−1.03654	+	0.304354i
$730$	0.276290	−	1.92164i	0.0102259	−	0.0711229i
$731$	−2.13537	−	4.67580i	−0.0789794	−	0.172941i
$732$	4.23919	+	29.4842i	0.156685	+	1.08977i
$733$	35.2744	−	22.6695i	1.30289	−	0.837317i	0.309368	−	0.950943i	$-0.399883\pi$
$733$	35.2744	−	22.6695i	1.30289	−	0.837317i	0.993524	+	0.113625i	$0.0362463\pi$
$734$	−0.240036	+	0.277016i	−0.00885987	+	0.0102248i
$735$	7.19246			0.265298
$736$	2.65279	−	15.2761i	0.0977832	−	0.563083i
$737$	−34.0251			−1.25333
$738$	1.24818	−	1.44048i	0.0459462	−	0.0530247i
$739$	0.419683	−	0.269714i	0.0154383	−	0.00992158i	−0.532899	−	0.846179i	$-0.678897\pi$
$739$	0.419683	−	0.269714i	0.0154383	−	0.00992158i	0.548337	+	0.836257i	$0.315261\pi$
$740$	1.12293	+	7.81013i	0.0412796	+	0.287106i
$741$	0.167091	+	0.365878i	0.00613823	+	0.0134409i
$742$	0.272525	−	1.89545i	0.0100047	−	0.0695842i
$743$	−0.00916062	+	0.00268980i	−0.000336070	+	9.86792e-5i	−0.281901	−	0.959444i	$-0.590965\pi$
$743$	−0.00916062	+	0.00268980i	−0.000336070	+	9.86792e-5i	0.281565	+	0.959542i	$0.409147\pi$
$744$	−4.78996	−	3.07832i	−0.175609	−	0.112857i
$745$	4.12808	−	9.03924i	0.151241	−	0.331172i
$746$	−5.19718	−	1.52603i	−0.190282	−	0.0558719i
$747$	4.13684	+	4.77417i	0.151359	+	0.174678i
$748$	−2.89495	−	3.34095i	−0.105850	−	0.122157i
$749$	−7.07306	−	2.07684i	−0.258444	−	0.0758860i
$750$	0.168435	−	0.368822i	0.00615038	−	0.0134675i
$751$	−29.6324	−	19.0436i	−1.08130	−	0.694909i	−0.126443	−	0.991974i	$-0.540356\pi$
$751$	−29.6324	−	19.0436i	−1.08130	−	0.694909i	−0.954857	+	0.297065i	$0.903992\pi$
$752$	−31.8427	+	9.34985i	−1.16118	+	0.340954i
$753$	0.820495	−	5.70667i	0.0299005	−	0.207963i
$754$	−0.00519522	−	0.0113759i	−0.000189199	−	0.000414287i
$755$	−2.88889	−	20.0927i	−0.105138	−	0.731248i
$756$	−12.7546	+	8.19686i	−0.463879	+	0.298117i
$757$	−9.05830	+	10.4538i	−0.329229	+	0.379951i	−0.896097	−	0.443858i	$-0.853610\pi$
$757$	−9.05830	+	10.4538i	−0.329229	+	0.379951i	0.566868	+	0.823809i	$0.308155\pi$
$758$	−1.28575			−0.0467004
$759$	32.9263	+	0.959822i	1.19515	+	0.0348393i
$760$	1.10350			0.0400281
$761$	11.9772	−	13.8224i	0.434172	−	0.501061i	−0.495930	−	0.868362i	$-0.665173\pi$
$761$	11.9772	−	13.8224i	0.434172	−	0.501061i	0.930102	+	0.367301i	$0.119718\pi$
$762$	4.71437	−	3.02974i	0.170783	−	0.109756i
$763$	1.98610	+	13.8136i	0.0719016	+	0.500087i
$764$	−12.5280	−	27.4326i	−0.453249	−	0.992477i
$765$	0.0660047	−	0.459073i	0.00238640	−	0.0165978i
$766$	−10.1274	+	2.97368i	−0.365918	+	0.107443i
$767$	1.64440	+	1.05679i	0.0593758	+	0.0381585i
$768$	5.86164	−	12.8352i	0.211514	−	0.463150i
$769$	14.7987	+	4.34528i	0.533653	+	0.156695i	0.537446	−	0.843298i	$-0.319389\pi$
$769$	14.7987	+	4.34528i	0.533653	+	0.156695i	−0.00379292	+	0.999993i	$0.501207\pi$
$770$	1.25530	+	1.44869i	0.0452379	+	0.0522073i
$771$	0.592373	+	0.683635i	0.0213338	+	0.0246205i
$772$	38.0589	+	11.1751i	1.36977	+	0.402200i
$773$	−1.09441	+	2.39642i	−0.0393631	+	0.0861932i	−0.928292	−	0.371852i	$-0.878723\pi$
$773$	−1.09441	+	2.39642i	−0.0393631	+	0.0861932i	0.888929	+	0.458045i	$0.151450\pi$
$774$	2.50073	+	1.60712i	0.0898868	+	0.0577668i
$775$	3.43814	−	1.00953i	0.123501	−	0.0362633i
$776$	2.48435	−	17.2791i	0.0891831	−	0.620282i
$777$	3.39867	+	7.44204i	0.121926	+	0.266982i
$778$	0.0469901	+	0.326823i	0.00168468	+	0.0117172i
$779$	5.74112	−	3.68959i	0.205697	−	0.132193i
$780$	0.510944	−	0.589661i	0.0182947	−	0.0211132i
$781$	−58.3010			−2.08617
$782$	0.538147	+	0.368436i	0.0192441	+	0.0131752i
$783$	0.870762			0.0311185
$784$	11.6401	−	13.4334i	0.415719	−	0.479765i
$785$	−13.4644	+	8.65303i	−0.480565	+	0.308840i
$786$	0.313418	+	2.17987i	0.0111793	+	0.0777535i
$787$	−7.65149	−	16.7544i	−0.272746	−	0.597231i	0.722847	−	0.691008i	$-0.242833\pi$
$787$	−7.65149	−	16.7544i	−0.272746	−	0.597231i	−0.995593	+	0.0937771i	$0.970106\pi$
$788$	−2.17918	+	15.1565i	−0.0776301	+	0.539929i
$789$	−29.5808	+	8.68571i	−1.05311	+	0.309220i
$790$	2.86874	+	1.84363i	0.102065	+	0.0655933i
$791$	2.14440	−	4.69559i	0.0762462	−	0.166956i
$792$	5.00939	+	1.47089i	0.178001	+	0.0522658i
$793$	2.03667	+	2.35044i	0.0723243	+	0.0834667i
$794$	2.32604	+	2.68440i	0.0825481	+	0.0952656i
$795$	−6.58357	−	1.93311i	−0.233495	−	0.0685603i
$796$	−4.09999	+	8.97772i	−0.145320	+	0.318207i
$797$	41.7315	+	26.8192i	1.47821	+	0.949986i	0.997317	+	0.0732048i	$0.0233227\pi$
$797$	41.7315	+	26.8192i	1.47821	+	0.949986i	0.480890	+	0.876781i	$0.340314\pi$
$798$	0.537572	−	0.157845i	0.0190298	−	0.00558767i
$799$	0.640979	−	4.45811i	0.0226762	−	0.157716i
$800$	−1.34302	−	2.94080i	−0.0474828	−	0.103973i
$801$	−1.51150	−	10.5127i	−0.0534061	−	0.371447i
$802$	4.70349	−	3.02275i	0.166086	−	0.106737i
$803$	21.5365	−	24.8545i	0.760007	−	0.877095i
$804$	19.2907			0.680332
$805$	5.52738	+	3.78425i	0.194815	+	0.133377i
$806$	−0.291101			−0.0102536
$807$	0.583551	−	0.673453i	0.0205420	−	0.0237067i
$808$	−17.2806	+	11.1056i	−0.607929	+	0.390692i
$809$	−1.30421	−	9.07096i	−0.0458535	−	0.318918i	−0.999819	−	0.0190030i	$-0.993951\pi$
$809$	−1.30421	−	9.07096i	−0.0458535	−	0.318918i	0.953966	−	0.299915i	$-0.0969583\pi$
$810$	−0.608402	−	1.33222i	−0.0213771	−	0.0468093i
$811$	0.665879	−	4.63129i	0.0233822	−	0.162627i	−0.974785	−	0.223147i	$-0.928367\pi$
$811$	0.665879	−	4.63129i	0.0233822	−	0.162627i	0.998167	+	0.0605205i	$0.0192761\pi$
$812$	0.395913	−	0.116250i	0.0138938	−	0.00407959i
$813$	−4.42344	−	2.84277i	−0.155137	−	0.0997004i
$814$	2.34415	−	5.13296i	0.0821622	−	0.179910i
$815$	−15.0119	−	4.40788i	−0.525842	−	0.154401i
$816$	1.56909	+	1.81083i	0.0549292	+	0.0633917i
$817$	6.96995	+	8.04375i	0.243848	+	0.281415i
$818$	−2.73785	−	0.803905i	−0.0957266	−	0.0281079i
$819$	−0.160763	+	0.352023i	−0.00561753	+	0.0123007i
$820$	−11.1365	−	7.15702i	−0.388905	−	0.249934i
$821$	−10.9770	+	3.22314i	−0.383101	+	0.112489i	−0.467612	−	0.883934i	$-0.654885\pi$
$821$	−10.9770	+	3.22314i	−0.383101	+	0.112489i	0.0845109	+	0.996423i	$0.473067\pi$
$822$	−1.12862	+	7.84973i	−0.0393652	+	0.273791i
$823$	−15.1472	−	33.1678i	−0.527998	−	1.15616i	−0.966322	−	0.257338i	$-0.917155\pi$
$823$	−15.1472	−	33.1678i	−0.527998	−	1.15616i	0.438323	−	0.898817i	$-0.355573\pi$
$824$	2.10431	+	14.6358i	0.0733071	+	0.509862i
$825$	5.77816	−	3.71340i	0.201170	−	0.129284i
$826$	1.78301	−	2.05770i	0.0620388	−	0.0715966i
$827$	41.7751			1.45266			0.726331	−	0.687345i	$-0.241224\pi$
$827$	41.7751			1.45266			0.726331	+	0.687345i	$0.241224\pi$
$828$	8.92993	+	0.260313i	0.310336	+	0.00904651i
$829$	44.3330			1.53975			0.769874	−	0.638196i	$-0.220319\pi$
$829$	44.3330			1.53975			0.769874	+	0.638196i	$0.220319\pi$
$830$	−1.21298	+	1.39985i	−0.0421030	+	0.0485895i
$831$	21.7863	−	14.0012i	0.755759	−	0.485697i
$832$	−0.248621	−	1.72920i	−0.00861938	−	0.0599491i
$833$	1.00211	+	2.19432i	0.0347212	+	0.0760288i
$834$	−0.636086	+	4.42408i	−0.0220259	+	0.153193i
$835$	9.75980	−	2.86574i	0.337752	−	0.0991729i
$836$	7.70033	+	4.94870i	0.266321	+	0.171154i
$837$	8.41984	−	18.4369i	0.291032	−	0.637271i
$838$	1.35245	+	0.397114i	0.0467195	+	0.0137181i
$839$	6.10437	+	7.04482i	0.210746	+	0.243214i	0.851275	−	0.524720i	$-0.175830\pi$
$839$	6.10437	+	7.04482i	0.210746	+	0.243214i	−0.640528	+	0.767934i	$0.721285\pi$
$840$	−1.45345	−	1.67737i	−0.0501487	−	0.0578747i
$841$	27.8026	+	8.16357i	0.958709	+	0.281502i
$842$	−0.0264630	+	0.0579459i	−0.000911975	+	0.00199695i
$843$	6.05239	+	3.88964i	0.208455	+	0.133966i
$844$	49.3857	−	14.5010i	1.69993	−	0.499144i
$845$	−1.83850	+	12.7870i	−0.0632463	+	0.439888i
$846$	1.08199	+	2.36924i	0.0371997	+	0.0814560i
$847$	2.43467	+	16.9335i	0.0836563	+	0.581843i
$848$	−14.2652	+	9.16769i	−0.489869	+	0.314820i
$849$	0.944117	−	1.08957i	0.0324020	−	0.0373939i
$850$	0.135990			0.00466443
$851$	3.37391	−	19.4286i	0.115656	−	0.666004i
$852$	33.0541			1.13242
$853$	−2.18140	+	2.51747i	−0.0746897	+	0.0861965i	−0.791865	−	0.610697i	$-0.790889\pi$
$853$	−2.18140	+	2.51747i	−0.0746897	+	0.0861965i	0.717175	+	0.696893i	$0.245435\pi$
$854$	3.64438	−	2.34210i	0.124708	−	0.0801450i
$855$	0.136667	+	0.950542i	0.00467393	+	0.0325079i
$856$	−2.44554	−	5.35499i	−0.0835869	−	0.183030i
$857$	−7.08241	+	49.2593i	−0.241931	+	1.68266i	0.400481	+	0.916305i	$0.368843\pi$
$857$	−7.08241	+	49.2593i	−0.241931	+	1.68266i	−0.642412	+	0.766360i	$0.722066\pi$
$858$	−0.535386	+	0.157203i	−0.0182778	+	0.00536684i
$859$	−18.2530	−	11.7305i	−0.622784	−	0.400239i	0.190847	−	0.981620i	$-0.438876\pi$
$859$	−18.2530	−	11.7305i	−0.622784	−	0.400239i	−0.813632	+	0.581380i	$0.802513\pi$
$860$	8.57663	−	18.7802i	0.292461	−	0.640400i
$861$	−13.1701	−	3.86710i	−0.448837	−	0.131790i
$862$	−0.832076	−	0.960267i	−0.0283406	−	0.0327068i
$863$	13.1619	+	15.1896i	0.448035	+	0.517060i	0.934172	−	0.356822i	$-0.116140\pi$
$863$	13.1619	+	15.1896i	0.448035	+	0.517060i	−0.486137	+	0.873883i	$0.661594\pi$
$864$	−17.5461	−	5.15201i	−0.596931	−	0.175275i
$865$	1.87487	−	4.10539i	0.0637474	−	0.139587i
$866$	4.16950	+	2.67957i	0.141685	+	0.0910556i
$867$	22.9240	−	6.73109i	0.778539	−	0.228600i
$868$	1.36688	−	9.50684i	0.0463948	−	0.322683i
$869$	23.9971	+	52.5463i	0.814046	+	1.78251i
$870$	0.00888301	+	0.0617827i	0.000301162	+	0.00209463i
$871$	1.69440	−	1.08892i	0.0574125	−	0.0368968i
$872$	−7.29839	+	8.42280i	−0.247155	+	0.285232i
$873$	15.1917			0.514161
$874$	−1.28406	−	0.418044i	−0.0434341	−	0.0141406i
$875$	1.39677			0.0472196
$876$	−12.2103	+	14.0914i	−0.412547	+	0.476104i
$877$	5.66411	−	3.64010i	0.191263	−	0.122918i	−0.441504	−	0.897259i	$-0.645555\pi$
$877$	5.66411	−	3.64010i	0.191263	−	0.122918i	0.632768	+	0.774341i	$0.281919\pi$
$878$	0.912426	+	6.34606i	0.0307929	+	0.214169i
$879$	15.2080	+	33.3009i	0.512953	+	1.12321i
$880$	2.41571	−	16.8016i	0.0814335	−	0.566382i
$881$	−51.9226	+	15.2459i	−1.74932	+	0.513646i	−0.990483	−	0.137638i	$-0.956049\pi$
$881$	−51.9226	+	15.2459i	−1.74932	+	0.513646i	−0.758834	+	0.651284i	$0.774231\pi$
$882$	−1.17358	−	0.754211i	−0.0395163	−	0.0253956i
$883$	−0.291639	+	0.638600i	−0.00981442	+	0.0214906i	−0.914476	−	0.404641i	$-0.867397\pi$
$883$	−0.291639	+	0.638600i	−0.00981442	+	0.0214906i	0.904661	+	0.426131i	$0.140124\pi$
$884$	0.251086	+	0.0737256i	0.00844495	+	0.00247966i
$885$	−6.38877	−	7.37304i	−0.214756	−	0.247842i
$886$	−4.69039	−	5.41300i	−0.157577	−	0.181853i
$887$	27.0246	+	7.93514i	0.907397	+	0.266436i	0.701945	−	0.712231i	$-0.252315\pi$
$887$	27.0246	+	7.93514i	0.907397	+	0.266436i	0.205452	+	0.978667i	$0.434133\pi$
$888$	−2.71416	+	5.94319i	−0.0910814	+	0.199440i
$889$	16.2405	+	10.4371i	0.544689	+	0.350050i
$890$	2.98801	−	0.877359i	0.100158	−	0.0294091i
$891$	3.53078	−	24.5571i	0.118286	−	0.822695i
$892$	−4.25231	−	9.31125i	−0.142378	−	0.311764i
$893$	1.32719	+	9.23083i	0.0444128	+	0.308898i
$894$	3.38956	−	2.17834i	0.113364	−	0.0728545i
$895$	0.390188	−	0.450301i	0.0130426	−	0.0150519i
$896$	−11.4648			−0.383012
$897$	−1.67040	+	1.00596i	−0.0557729	+	0.0335880i
$898$	−7.34885			−0.245234
$899$	−0.361235	+	0.416887i	−0.0120479	+	0.0139040i
$900$	1.56710	−	1.00711i	0.0522365	−	0.0335704i
$901$	−0.327512	−	2.27790i	−0.0109110	−	0.0758877i
$902$	3.93284	+	8.61172i	0.130949	+	0.286739i
$903$	3.04656	−	21.1893i	0.101383	−	0.705135i
$904$	3.95543	−	1.16142i	0.131556	−	0.0386282i
$905$	−2.38858	−	1.53505i	−0.0793990	−	0.0510266i
$906$	3.41912	−	7.48682i	0.113593	−	0.248733i
$907$	−17.7544	−	5.21316i	−0.589524	−	0.173100i	−0.0266534	−	0.999645i	$-0.508485\pi$
$907$	−17.7544	−	5.21316i	−0.589524	−	0.173100i	−0.562871	+	0.826545i	$0.690303\pi$
$908$	9.37657	+	10.8211i	0.311172	+	0.359112i
$909$	−11.7064	−	13.5099i	−0.388277	−	0.448095i
$910$	−0.108876	−	0.0319688i	−0.00360919	−	0.00105975i
$911$	−13.4591	+	29.4714i	−0.445920	+	0.976429i	0.544553	+	0.838726i	$0.316699\pi$
$911$	−13.4591	+	29.4714i	−0.445920	+	0.976429i	−0.990474	+	0.137703i	$0.956028\pi$
$912$	−4.17366	−	2.68225i	−0.138204	−	0.0888181i
$913$	−30.1063	+	8.84001i	−0.996374	+	0.292562i
$914$	−1.42226	+	9.89204i	−0.0470442	+	0.327200i
$915$	−6.44826	−	14.1197i	−0.213173	−	0.466784i
$916$	−6.33017	−	44.0273i	−0.209155	−	1.45470i
$917$	−6.38230	+	4.10165i	−0.210762	+	0.135449i
$918$	0.503729	−	0.581334i	0.0166255	−	0.0191869i
$919$	3.23843			0.106826			0.0534130	−	0.998573i	$-0.482990\pi$
$919$	3.23843			0.106826			0.0534130	+	0.998573i	$0.482990\pi$
$920$	0.606708	+	5.31504i	0.0200026	+	0.175232i
$921$	38.6558			1.27375
$922$	4.99311	−	5.76236i	0.164439	−	0.189773i
$923$	2.90330	−	1.86584i	0.0955634	−	0.0614149i
$924$	−2.62006	−	18.2229i	−0.0861936	−	0.599490i
$925$	−1.70809	−	3.74020i	−0.0561618	−	0.122977i
$926$	−0.529038	+	3.67954i	−0.0173853	+	0.120917i
$927$	−12.3465	+	3.62526i	−0.405513	+	0.119069i
$928$	0.418683	+	0.269071i	0.0137440	+	0.00883270i
$929$	−6.25892	+	13.7051i	−0.205349	+	0.449651i	−0.984084	−	0.177701i	$-0.943134\pi$
$929$	−6.25892	+	13.7051i	−0.205349	+	0.449651i	0.778736	+	0.627352i	$0.215861\pi$
$930$	1.39403	+	0.409325i	0.0457122	+	0.0134223i
$931$	−3.27095	−	3.77488i	−0.107201	−	0.123717i
$932$	−30.6317	−	35.3509i	−1.00338	−	1.15796i
$933$	−36.8287	−	10.8139i	−1.20572	−	0.354031i
$934$	−0.459120	+	1.00533i	−0.0150229	+	0.0328955i
$935$	1.93797	+	1.24546i	0.0633784	+	0.0407308i
$936$	−0.296534	+	0.0870702i	−0.00969252	+	0.00284598i
$937$	−0.346540	+	2.41024i	−0.0113210	+	0.0787390i	−0.994699	−	0.102833i	$-0.967209\pi$
$937$	−0.346540	+	2.41024i	−0.0113210	+	0.0787390i	0.983378	+	0.181572i	$0.0581185\pi$
$938$	−1.16546	−	2.55199i	−0.0380535	−	0.0833255i
$939$	−2.73171	−	18.9995i	−0.0891460	−	0.620024i
$940$	15.2182	−	9.78017i	0.496364	−	0.318994i
$941$	32.9339	−	38.0077i	1.07361	−	1.23902i	0.103949	−	0.994583i	$-0.466852\pi$
$941$	32.9339	−	38.0077i	1.07361	−	1.23902i	0.969666	−	0.244434i	$-0.0786023\pi$
$942$	−6.48948			−0.211439
$943$	20.9275	+	25.6237i	0.681494	+	0.834424i
$944$	−24.1102			−0.784719
$945$	5.17387	−	5.97097i	0.168306	−	0.194236i
$946$	−12.4212	+	7.98260i	−0.403847	+	0.259537i
$947$	−1.50033	−	10.4350i	−0.0487542	−	0.339093i	−0.999570	−	0.0293348i	$-0.990661\pi$
$947$	−1.50033	−	10.4350i	−0.0487542	−	0.339093i	0.950815	−	0.309758i	$-0.100248\pi$
$948$	−13.6053	−	29.7915i	−0.441880	−	0.967582i
$949$	−0.277055	+	1.92696i	−0.00899359	+	0.0625518i
$950$	−0.270172	+	0.0793296i	−0.00876553	+	0.00257379i
$951$	7.04529	+	4.52773i	0.228459	+	0.146822i
$952$	0.309236	−	0.677133i	0.0100224	−	0.0219460i
$953$	23.4913	+	6.89767i	0.760958	+	0.223438i	0.639114	−	0.769112i	$-0.279301\pi$
$953$	23.4913	+	6.89767i	0.760958	+	0.223438i	0.121844	+	0.992549i	$0.461119\pi$
$954$	0.871515	+	1.00578i	0.0282164	+	0.0325634i
$955$	10.2915	+	11.8770i	0.333025	+	0.384331i
$956$	−2.16192	−	0.634798i	−0.0699216	−	0.0205308i
$957$	−0.439243	+	0.961807i	−0.0141987	+	0.0310908i
$958$	4.72384	+	3.03583i	0.152620	+	0.0980831i
$959$	−26.2129	+	7.69681i	−0.846459	+	0.248543i
$960$	−1.24087	+	8.63044i	−0.0400489	+	0.278546i
$961$	−7.54397	−	16.5190i	−0.243354	−	0.532871i
$962$	0.0475381	+	0.330635i	0.00153269	+	0.0106601i
$963$	4.30986	−	2.76978i	0.138883	−	0.0892548i
$964$	8.28502	−	9.56142i	0.266842	−	0.307953i
$965$	−20.6701			−0.665394
$966$	1.05583	+	2.50245i	0.0339707	+	0.0805150i
$967$	−41.3872			−1.33092			−0.665462	−	0.746432i	$-0.731765\pi$
$967$	−41.3872			−1.33092			−0.665462	+	0.746432i	$0.731765\pi$
$968$	−8.94678	+	10.3251i	−0.287560	+	0.331862i
$969$	0.566426	−	0.364020i	0.0181962	−	0.0116940i
$970$	0.633927	+	4.40906i	0.0203542	+	0.141566i
$971$	11.7039	+	25.6280i	0.375596	+	0.822441i	0.999172	+	0.0406780i	$0.0129518\pi$
$971$	11.7039	+	25.6280i	0.375596	+	0.822441i	−0.623576	+	0.781763i	$0.714321\pi$
$972$	2.63249	−	18.3094i	0.0844372	−	0.587274i
$973$	−14.7735	+	4.33789i	−0.473617	+	0.139066i
$974$	−9.03558	−	5.80681i	−0.289519	−	0.186062i
$975$	−0.168902	+	0.369844i	−0.00540919	+	0.0118445i
$976$	−36.8073	−	10.8076i	−1.17817	−	0.345943i
$977$	−11.8008	−	13.6189i	−0.377542	−	0.435706i	0.534899	−	0.844916i	$-0.320350\pi$
$977$	−11.8008	−	13.6189i	−0.377542	−	0.435706i	−0.912440	+	0.409210i	$0.865804\pi$
$978$	−4.15424	−	4.79425i	−0.132838	−	0.153303i
$979$	50.6168	+	14.8624i	1.61772	+	0.475005i
$980$	−4.02496	+	8.81342i	−0.128572	+	0.281534i
$981$	−8.15921	−	5.24361i	−0.260504	−	0.167415i
$982$	−1.81558	+	0.533104i	−0.0579376	+	0.0170120i
$983$	−2.54880	+	17.7273i	−0.0812941	+	0.565413i	0.907943	+	0.419093i	$0.137652\pi$
$983$	−2.54880	+	17.7273i	−0.0812941	+	0.565413i	−0.989237	+	0.146320i	$0.953257\pi$
$984$	−4.55363	−	9.97106i	−0.145164	−	0.317866i
$985$	−1.13559	−	7.89820i	−0.0361829	−	0.251658i
$986$	−0.0176114	+	0.0113182i	−0.000560862	+	0.000360444i
$987$	12.2832	−	14.1756i	0.390978	−	0.451213i
$988$	−0.541841			−0.0172383
$989$	−34.9109	+	37.9935i	−1.11010	+	1.20812i
$990$	−1.33220			−0.0423401
$991$	−29.6112	+	34.1732i	−0.940632	+	1.08555i	0.0555684	+	0.998455i	$0.482303\pi$
$991$	−29.6112	+	34.1732i	−0.940632	+	1.08555i	−0.996200	+	0.0870922i	$0.972243\pi$
$992$	9.74557	−	6.26310i	0.309422	−	0.198854i
$993$	2.94771	+	20.5018i	0.0935429	+	0.650605i
$994$	−1.99697	−	4.37276i	−0.0633402	−	0.138696i
$995$	0.731946	−	5.09079i	0.0232042	−	0.161389i
$996$	17.0690	−	5.01190i	0.540851	−	0.158808i
$997$	4.04866	+	2.60192i	0.128222	+	0.0824036i	0.603180	−	0.797605i	$-0.293900\pi$
$997$	4.04866	+	2.60192i	0.128222	+	0.0824036i	−0.474957	+	0.880009i	$0.657537\pi$
$998$	3.31322	−	7.25495i	0.104878	−	0.229651i
$999$	−22.3158	−	6.55250i	−0.706039	−	0.207312i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.g.b.16.2	✓	20
5.2	odd	4		575.2.p.c.499.3		40
5.3	odd	4		575.2.p.c.499.2		40
5.4	even	2		575.2.k.c.476.1		20
23.6	even	11		2645.2.a.t.1.6		10
23.13	even	11	inner	115.2.g.b.36.2	yes	20
23.17	odd	22		2645.2.a.u.1.6		10
115.13	odd	44		575.2.p.c.174.3		40
115.59	even	22		575.2.k.c.151.1		20
115.82	odd	44		575.2.p.c.174.2		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.b.16.2	✓	20	1.1	even	1	trivial
115.2.g.b.36.2	yes	20	23.13	even	11	inner
575.2.k.c.151.1		20	115.59	even	22
575.2.k.c.476.1		20	5.4	even	2
575.2.p.c.174.2		40	115.82	odd	44
575.2.p.c.174.3		40	115.13	odd	44
575.2.p.c.499.2		40	5.3	odd	4
575.2.p.c.499.3		40	5.2	odd	4
2645.2.a.t.1.6		10	23.6	even	11
2645.2.a.u.1.6		10	23.17	odd	22

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.186393 - 0.215109i) q^{2} +(1.19839 - 0.770157i) q^{3} +(0.273100 + 1.89945i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.0577033 - 0.401335i) q^{6} +(1.34020 - 0.393517i) q^{7} +(0.938384 + 0.603063i) q^{8} +(-0.403254 + 0.883004i) q^{9} +O(q^{10})\)	\(q+(0.186393 - 0.215109i) q^{2} +(1.19839 - 0.770157i) q^{3} +(0.273100 + 1.89945i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(0.0577033 - 0.401335i) q^{6} +(1.34020 - 0.393517i) q^{7} +(0.938384 + 0.603063i) q^{8} +(-0.403254 + 0.883004i) q^{9} +(-0.273100 - 0.0801894i) q^{10} +(-3.15749 - 3.64393i) q^{11} +(1.79016 + 2.06595i) q^{12} +(0.273857 + 0.0804117i) q^{13} +(0.165154 - 0.361637i) q^{14} +(-1.19839 - 0.770157i) q^{15} +(-3.37787 + 0.991834i) q^{16} +(0.0679951 - 0.472917i) q^{17} +(0.114778 + 0.251329i) q^{18} +(0.140789 + 0.979208i) q^{19} +(1.61435 - 1.03748i) q^{20} +(1.30300 - 1.50375i) q^{21} -1.37237 q^{22} +(-4.63898 + 1.21649i) q^{23} +1.58900 q^{24} +(-0.654861 + 0.755750i) q^{25} +(0.0683422 - 0.0439209i) q^{26} +(0.804990 + 5.59883i) q^{27} +(1.11347 + 2.43817i) q^{28} +(0.0219083 - 0.152376i) q^{29} +(-0.389038 + 0.114232i) q^{30} +(-3.01445 - 1.93727i) q^{31} +(-1.34302 + 2.94080i) q^{32} +(-6.59029 - 1.93508i) q^{33} +(-0.0890547 - 0.102775i) q^{34} +(-0.914693 - 1.05561i) q^{35} +(-1.78735 - 0.524814i) q^{36} +(-1.70809 + 3.74020i) q^{37} +(0.236878 + 0.152232i) q^{38} +(0.390116 - 0.114549i) q^{39} +(0.158746 - 1.10411i) q^{40} +(-2.86572 - 6.27505i) q^{41} +(-0.0805985 - 0.560575i) q^{42} +(9.05086 - 5.81663i) q^{43} +(6.05917 - 6.99266i) q^{44} +0.970726 q^{45} +(-0.602996 + 1.22463i) q^{46} +9.42683 q^{47} +(-3.28414 + 3.79009i) q^{48} +(-4.24751 + 2.72971i) q^{49} +(0.0405070 + 0.281733i) q^{50} +(-0.282735 - 0.619104i) q^{51} +(-0.0779478 + 0.542139i) q^{52} +(4.62159 - 1.35702i) q^{53} +(1.35440 + 0.870421i) q^{54} +(-2.00297 + 4.38589i) q^{55} +(1.49493 + 0.438952i) q^{56} +(0.922863 + 1.06504i) q^{57} +(-0.0286938 - 0.0331144i) q^{58} +(6.57113 + 1.92946i) q^{59} +(1.13560 - 2.48661i) q^{60} +(9.16678 + 5.89113i) q^{61} +(-0.978595 + 0.287342i) q^{62} +(-0.192963 + 1.34208i) q^{63} +(-2.54266 - 5.56764i) q^{64} +(-0.0406193 - 0.282513i) q^{65} +(-1.64464 + 1.05694i) q^{66} +(4.62121 - 5.33316i) q^{67} +0.916853 q^{68} +(-4.62241 + 5.03057i) q^{69} -0.397564 q^{70} +(7.91831 - 9.13822i) q^{71} +(-0.910914 + 0.585409i) q^{72} +(0.970698 + 6.75135i) q^{73} +(0.486174 + 1.06457i) q^{74} +(-0.202731 + 1.41003i) q^{75} +(-1.82151 + 0.534844i) q^{76} +(-5.66560 - 3.64106i) q^{77} +(0.0480745 - 0.105268i) q^{78} +(-11.4955 - 3.37537i) q^{79} +(2.30542 + 2.66060i) q^{80} +(3.36959 + 3.88872i) q^{81} +(-1.88397 - 0.553183i) q^{82} +(2.70337 - 5.91956i) q^{83} +(3.21215 + 2.06432i) q^{84} +(-0.458426 + 0.134606i) q^{85} +(0.435806 - 3.03110i) q^{86} +(-0.0910986 - 0.199478i) q^{87} +(-0.765414 - 5.32357i) q^{88} +(-9.20422 + 5.91519i) q^{89} +(0.180936 - 0.208812i) q^{90} +0.398665 q^{91} +(-3.57757 - 8.47931i) q^{92} -5.10448 q^{93} +(1.75709 - 2.02779i) q^{94} +(0.832233 - 0.534844i) q^{95} +(0.655420 + 4.55855i) q^{96} +(-6.50117 - 14.2356i) q^{97} +(-0.204521 + 1.42247i) q^{98} +(4.49088 - 1.31864i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} + q^{3} - 4 q^{4} + 2 q^{5} - 9 q^{6} - 4 q^{7} - 17 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 + q^3 - 4 * q^4 + 2 * q^5 - 9 * q^6 - 4 * q^7 - 17 * q^9	\( 20 q - 4 q^{2} + q^{3} - 4 q^{4} + 2 q^{5} - 9 q^{6} - 4 q^{7} - 17 q^{9} + 4 q^{10} - 8 q^{11} + 2 q^{12} + 10 q^{13} + 3 q^{14} - q^{15} - 36 q^{16} - 9 q^{17} + 10 q^{18} + 24 q^{19} + 4 q^{20} + 25 q^{21} + 6 q^{22} + 11 q^{23} - 2 q^{25} - 2 q^{26} + 28 q^{27} - 8 q^{28} + 12 q^{29} - 2 q^{30} + 10 q^{31} - 50 q^{32} - 49 q^{33} - 7 q^{34} + 4 q^{35} + 43 q^{36} - 18 q^{37} - 29 q^{38} - 52 q^{39} + 22 q^{40} + 10 q^{41} - 5 q^{42} + 35 q^{43} + 6 q^{44} - 38 q^{45} - 33 q^{46} - 2 q^{47} - 4 q^{48} + 4 q^{49} + 18 q^{50} + 50 q^{51} + 9 q^{52} - 5 q^{53} + 23 q^{54} + 8 q^{55} + 33 q^{57} + 35 q^{58} + 41 q^{59} - 2 q^{60} - 13 q^{61} - 2 q^{62} - 46 q^{63} + 16 q^{64} - 10 q^{65} + 56 q^{66} - 9 q^{67} + 26 q^{68} - 45 q^{69} + 8 q^{70} - 19 q^{71} - 27 q^{73} + 8 q^{74} + q^{75} + 4 q^{76} - 64 q^{77} - 27 q^{78} - 83 q^{79} - 8 q^{80} + 12 q^{81} + 31 q^{82} + 67 q^{83} + 28 q^{84} - 13 q^{85} - 73 q^{86} + 69 q^{87} + 22 q^{88} - 5 q^{89} - 10 q^{90} - 84 q^{91} + 11 q^{92} + 28 q^{93} - 37 q^{94} - 2 q^{95} + 14 q^{96} + 18 q^{97} + 8 q^{98} + 62 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 + q^3 - 4 * q^4 + 2 * q^5 - 9 * q^6 - 4 * q^7 - 17 * q^9 + 4 * q^10 - 8 * q^11 + 2 * q^12 + 10 * q^13 + 3 * q^14 - q^15 - 36 * q^16 - 9 * q^17 + 10 * q^18 + 24 * q^19 + 4 * q^20 + 25 * q^21 + 6 * q^22 + 11 * q^23 - 2 * q^25 - 2 * q^26 + 28 * q^27 - 8 * q^28 + 12 * q^29 - 2 * q^30 + 10 * q^31 - 50 * q^32 - 49 * q^33 - 7 * q^34 + 4 * q^35 + 43 * q^36 - 18 * q^37 - 29 * q^38 - 52 * q^39 + 22 * q^40 + 10 * q^41 - 5 * q^42 + 35 * q^43 + 6 * q^44 - 38 * q^45 - 33 * q^46 - 2 * q^47 - 4 * q^48 + 4 * q^49 + 18 * q^50 + 50 * q^51 + 9 * q^52 - 5 * q^53 + 23 * q^54 + 8 * q^55 + 33 * q^57 + 35 * q^58 + 41 * q^59 - 2 * q^60 - 13 * q^61 - 2 * q^62 - 46 * q^63 + 16 * q^64 - 10 * q^65 + 56 * q^66 - 9 * q^67 + 26 * q^68 - 45 * q^69 + 8 * q^70 - 19 * q^71 - 27 * q^73 + 8 * q^74 + q^75 + 4 * q^76 - 64 * q^77 - 27 * q^78 - 83 * q^79 - 8 * q^80 + 12 * q^81 + 31 * q^82 + 67 * q^83 + 28 * q^84 - 13 * q^85 - 73 * q^86 + 69 * q^87 + 22 * q^88 - 5 * q^89 - 10 * q^90 - 84 * q^91 + 11 * q^92 + 28 * q^93 - 37 * q^94 - 2 * q^95 + 14 * q^96 + 18 * q^97 + 8 * q^98 + 62 * q^99

Introduction

L-functions

Modular forms

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Database

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