LMFDB - Embedded newform 115.2.g.b.36.2

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			36.2
Root			$-0.932866 - 1.07658i$ of defining polynomial
Character	$\chi$	$=$	115.36
Dual form			115.2.g.b.16.2

$q$-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 $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{7}{11}\right)$

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	0.817813	−	0.575484i	$-0.195186\pi$
$2$	0.186393	+	0.215109i	0.131800	+	0.152105i	−0.686013	+	0.727589i	$0.740641\pi$
$3$	1.19839	+	0.770157i	0.691889	+	0.444650i	0.838757	−	0.544506i	$-0.183283\pi$
$3$	1.19839	+	0.770157i	0.691889	+	0.444650i	−0.146868	+	0.989156i	$0.546919\pi$
$4$	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	0.525013	−	0.851094i	$-0.324060\pi$
$7$	1.34020	+	0.393517i	0.506546	+	0.148735i	−0.0184669	+	0.999829i	$0.505879\pi$
$8$	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	0.0430085	+	0.999075i	$0.486306\pi$
$11$	−3.15749	+	3.64393i	−0.952018	+	1.09869i	−0.995026	+	0.0996124i	$0.968240\pi$
$12$	1.79016	−	2.06595i	0.516774	−	0.596389i
$13$	0.273857	−	0.0804117i	0.0759543	−	0.0223022i	−0.243535	−	0.969892i	$-0.578307\pi$
$13$	0.273857	−	0.0804117i	0.0759543	−	0.0223022i	0.319489	+	0.947590i	$0.396489\pi$
$14$	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	0.996404	−	0.0847262i	$-0.0270016\pi$
$17$	0.0679951	+	0.472917i	0.0164912	+	0.114699i	−0.979913	+	0.199425i	$0.936092\pi$
$18$	0.114778	−	0.251329i	0.0270535	−	0.0592388i
$19$	0.140789	−	0.979208i	0.0322992	−	0.224646i	−0.967278	−	0.253718i	$-0.918346\pi$
$19$	0.140789	−	0.979208i	0.0322992	−	0.224646i	0.999577	+	0.0290727i	$0.00925544\pi$
$20$	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	0.991754	−	0.128153i	$-0.0409047\pi$
$29$	0.0219083	+	0.152376i	0.00406828	+	0.0282955i	−0.987686	+	0.156448i	$0.949996\pi$
$30$	−0.389038	−	0.114232i	−0.0710283	−	0.0208558i
$31$	−3.01445	+	1.93727i	−0.541411	+	0.347944i	−0.782591	−	0.622537i	$-0.786102\pi$
$31$	−3.01445	+	1.93727i	−0.541411	+	0.347944i	0.241179	+	0.970481i	$0.422466\pi$
$32$	−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	0.715697	−	0.698411i	$-0.246109\pi$
$37$	−1.70809	−	3.74020i	−0.280809	−	0.614886i	−0.996506	+	0.0835254i	$0.973382\pi$
$38$	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	0.542600	+	0.839991i	$0.317440\pi$
$41$	−2.86572	+	6.27505i	−0.447550	+	0.979998i	−0.990150	+	0.140007i	$0.955287\pi$
$42$	−0.0805985	+	0.560575i	−0.0124366	+	0.0864986i
$43$	9.05086	+	5.81663i	1.38024	+	0.887028i	0.999294	−	0.0375681i	$-0.0119611\pi$
$43$	9.05086	+	5.81663i	1.38024	+	0.887028i	0.380949	+	0.924596i	$0.375597\pi$
$44$	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	0.583282	−	0.812270i	$-0.301768\pi$
$53$	4.62159	+	1.35702i	0.634824	+	0.186401i	0.0515417	+	0.998671i	$0.483586\pi$
$54$	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	0.175556	−	0.984469i	$-0.443828\pi$
$59$	6.57113	−	1.92946i	0.855488	−	0.251194i	0.679932	+	0.733275i	$0.262009\pi$
$60$	1.13560	+	2.48661i	0.146605	+	0.321020i
$61$	9.16678	−	5.89113i	1.17369	−	0.754282i	0.199471	−	0.979904i	$-0.436078\pi$
$61$	9.16678	−	5.89113i	1.17369	−	0.754282i	0.974215	+	0.225621i	$0.0724412\pi$
$62$	−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	0.964215	−	0.265121i	$-0.0854118\pi$
$67$	4.62121	+	5.33316i	0.564571	+	0.651550i	−0.399644	+	0.916670i	$0.630866\pi$
$68$	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	0.996286	+	0.0861075i	$0.0274428\pi$
$71$	7.91831	+	9.13822i	0.939731	+	1.08451i	−0.0565552	+	0.998399i	$0.518012\pi$
$72$	−0.910914	−	0.585409i	−0.107352	−	0.0689911i
$73$	0.970698	−	6.75135i	0.113612	−	0.790186i	−0.850745	−	0.525579i	$-0.823849\pi$
$73$	0.970698	−	6.75135i	0.113612	−	0.790186i	0.964356	−	0.264607i	$-0.0852423\pi$
$74$	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	−0.854802	−	0.518954i	$-0.826322\pi$
$79$	−11.4955	+	3.37537i	−1.29334	+	0.379759i	−0.438537	+	0.898713i	$0.644503\pi$
$80$	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	0.998005	−	0.0631388i	$-0.0201111\pi$
$83$	2.70337	+	5.91956i	0.296733	+	0.649756i	−0.701271	+	0.712895i	$0.747384\pi$
$84$	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	−0.0473599	−	0.998878i	$-0.515081\pi$
$89$	−9.20422	−	5.91519i	−0.975645	−	0.627009i	−0.928285	+	0.371869i	$0.878717\pi$
$90$	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	0.222341	+	0.974969i	$0.428630\pi$
$97$	−6.50117	+	14.2356i	−0.660094	+	1.44540i	−0.882435	+	0.470434i	$0.844097\pi$
$98$	−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	−0.745123	−	0.666927i	$-0.767609\pi$
$101$	−7.64997	−	16.7511i	−0.761201	−	1.66680i	−0.0160775	−	0.999871i	$-0.505118\pi$
$102$	−0.185875	+	0.0545777i	−0.0184043	+	0.00540400i
$103$	8.68070	−	10.0181i	0.855335	−	0.987109i	−0.144662	−	0.989481i	$-0.546210\pi$
$103$	8.68070	−	10.0181i	0.855335	−	0.987109i	0.999997	+	0.00237206i	$0.000755052\pi$
$104$	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	−0.737360	−	0.675500i	$-0.763928\pi$
$107$	−4.43983	+	2.85330i	−0.429214	+	0.275839i	0.308146	+	0.951339i	$0.400292\pi$
$108$	−10.4149	−	3.05808i	−1.00217	−	0.294264i
$109$	−1.42192	−	9.88966i	−0.136195	−	0.947258i	−0.937248	−	0.348664i	$-0.886635\pi$
$109$	−1.42192	−	9.88966i	−0.136195	−	0.947258i	0.801053	−	0.598594i	$-0.204274\pi$
$110$	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	0.858079	−	0.513518i	$-0.171658\pi$
$113$	2.42018	+	2.79303i	0.227671	+	0.262746i	−0.630408	+	0.776264i	$0.717112\pi$
$114$	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	−0.195406	−	0.980722i	$-0.562602\pi$
$127$	9.05096	−	10.4454i	0.803143	−	0.926877i	0.998549	+	0.0538457i	$0.0171479\pi$
$128$	−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	0.0460199	−	0.998941i	$-0.485346\pi$
$131$	−5.21153	−	1.53024i	−0.455334	−	0.133698i	−0.501354	+	0.865242i	$0.667164\pi$
$132$	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	−0.423750	−	0.905779i	$-0.639286\pi$
$149$	6.50751	−	7.51007i	0.533116	−	0.615249i	0.956866	+	0.290531i	$0.0938318\pi$
$150$	0.265521	−	0.306428i	0.0216797	−	0.0250197i
$151$	19.4770	−	5.71897i	1.58502	−	0.465403i	0.633691	−	0.773586i	$-0.281539\pi$
$151$	19.4770	−	5.71897i	1.58502	−	0.465403i	0.951327	+	0.308182i	$0.0997207\pi$
$152$	−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	0.670752	+	0.741682i	$0.265972\pi$
$157$	−2.27777	+	15.8422i	−0.181786	+	1.26435i	−0.852537	+	0.522666i	$0.824937\pi$
$158$	−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	0.998516	−	0.0544617i	$-0.0173443\pi$
$163$	10.2457	+	11.8242i	0.802505	+	0.926140i	−0.196011	+	0.980602i	$0.562799\pi$
$164$	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	−0.965951	−	0.258724i	$-0.916698\pi$
$167$	−1.44760	−	10.0683i	−0.112019	−	0.779108i	0.853932	−	0.520384i	$-0.174211\pi$
$168$	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	−0.632191	−	0.774813i	$-0.717844\pi$
$173$	2.95554	−	3.41088i	0.224706	−	0.259324i	0.856896	+	0.515489i	$0.172390\pi$
$174$	−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	−0.900156	−	0.435567i	$-0.856548\pi$
$179$	0.247518	−	0.541990i	0.0185004	−	0.0405102i	0.918657	+	0.395057i	$0.129275\pi$
$180$	0.265105	−	1.84385i	0.0197598	−	0.137432i
$181$	2.38858	+	1.53505i	0.177542	+	0.114099i	0.626393	−	0.779507i	$-0.284530\pi$
$181$	2.38858	+	1.53505i	0.177542	+	0.114099i	−0.448852	+	0.893606i	$0.648167\pi$
$182$	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	−0.313774	−	0.949498i	$-0.601593\pi$
$191$	−15.0790	−	4.42758i	−1.09107	−	0.320368i	−0.777301	+	0.629129i	$0.783412\pi$
$192$	−7.33505	+	4.71395i	−0.529361	+	0.340200i
$193$	8.58667	+	18.8022i	0.618082	+	1.35341i	0.916906	+	0.399102i	$0.130678\pi$
$193$	8.58667	+	18.8022i	0.618082	+	1.35341i	−0.298825	+	0.954308i	$0.596595\pi$
$194$	−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	0.00263008	−	0.999997i	$-0.499163\pi$
$197$	7.65620	−	2.24806i	0.545482	−	0.160168i	0.542852	+	0.839829i	$0.317345\pi$
$198$	0.553416	+	1.21181i	0.0393296	+	0.0861197i
$199$	4.32669	−	2.78059i	0.306711	−	0.197111i	−0.378227	−	0.925713i	$-0.623466\pi$
$199$	4.32669	−	2.78059i	0.306711	−	0.197111i	0.684937	+	0.728602i	$0.259830\pi$
$200$	−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	0.248910	+	0.968527i	$0.419928\pi$
$211$	−3.81714	+	26.5488i	−0.262783	+	1.82769i	−0.511693	+	0.859168i	$0.670982\pi$
$212$	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	0.105835	−	0.994384i	$-0.466249\pi$
$223$	−5.11814	−	1.50282i	−0.342736	−	0.100636i	−0.448571	+	0.893747i	$0.648067\pi$
$224$	−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	0.732113	−	0.681183i	$-0.238534\pi$
$227$	6.27697	+	4.03396i	0.416617	+	0.267744i	−0.315496	+	0.948927i	$0.602171\pi$
$228$	−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	−0.346185	−	0.938166i	$-0.612523\pi$
$233$	−20.5058	−	13.1783i	−1.34338	−	0.863339i	−0.997197	+	0.0748270i	$0.976160\pi$
$234$	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	0.893200	−	0.449659i	$-0.148454\pi$
$239$	−0.487763	−	1.06805i	−0.0315508	−	0.0690865i	−0.924751	+	0.380572i	$0.875727\pi$
$240$	4.81187	−	1.41289i	0.310605	−	0.0912018i
$241$	−4.31739	+	4.98254i	−0.278108	+	0.320953i	−0.877569	−	0.479450i	$-0.840836\pi$
$241$	−4.31739	+	4.98254i	−0.278108	+	0.320953i	0.599461	+	0.800404i	$0.295382\pi$
$242$	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	0.833204	−	0.552966i	$-0.186504\pi$
$251$	2.65036	+	3.05867i	0.167289	+	0.193062i	−0.665915	+	0.746028i	$0.731959\pi$
$252$	−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	−0.986809	−	0.161891i	$-0.948241\pi$
$257$	0.0903704	−	0.628540i	0.00563715	−	0.0392072i	0.992446	+	0.122683i	$0.0391499\pi$
$258$	−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	−0.850067	−	0.526674i	$-0.823439\pi$
$263$	−20.7654	+	6.09727i	−1.28045	+	0.375974i	−0.430381	+	0.902647i	$0.641621\pi$
$264$	−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	0.299979	−	0.953946i	$-0.403020\pi$
$269$	0.600207	+	0.176237i	0.0365953	+	0.0107453i	−0.263384	+	0.964691i	$0.584839\pi$
$270$	0.229124	+	1.59359i	0.0139440	+	0.0969830i
$271$	−1.53336	+	3.35760i	−0.0931452	+	0.203959i	−0.950470	−	0.310816i	$-0.899398\pi$
$271$	−1.53336	+	3.35760i	−0.0931452	+	0.203959i	0.857325	+	0.514776i	$0.172125\pi$
$272$	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	−0.836673	−	0.547703i	$-0.815502\pi$
$281$	2.09803	−	4.59405i	0.125158	−	0.274058i	0.961831	+	0.273645i	$0.0882295\pi$
$282$	0.543959	+	3.78332i	0.0323923	+	0.225293i
$283$	0.971066	+	0.285131i	0.0577239	+	0.0169493i	0.310467	−	0.950584i	$-0.399515\pi$
$283$	0.971066	+	0.285131i	0.0577239	+	0.0169493i	−0.252743	+	0.967533i	$0.581333\pi$
$284$	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	−0.760773	−	0.649018i	$-0.775180\pi$
$293$	−3.65738	−	25.4376i	−0.213666	−	1.48608i	0.547106	−	0.837063i	$-0.315729\pi$
$294$	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	0.309351	−	0.950948i	$-0.399888\pi$
$307$	22.8282	−	14.6708i	1.30287	−	0.837305i	0.993522	+	0.113643i	$0.0362519\pi$
$308$	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	−0.0126133	+	0.999920i	$0.504015\pi$
$311$	−17.6451	+	20.3635i	−1.00056	+	1.15471i	−0.987948	+	0.154788i	$0.950530\pi$
$312$	0.435159	−	0.127774i	0.0246360	−	0.00723379i
$313$	5.59753	+	12.2569i	0.316391	+	0.692800i	0.999289	−	0.0377142i	$-0.0120077\pi$
$313$	5.59753	+	12.2569i	0.316391	+	0.692800i	−0.682897	+	0.730514i	$0.739280\pi$
$314$	−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	−0.828565	−	0.559893i	$-0.810842\pi$
$317$	2.44221	−	5.34770i	0.137168	−	0.300357i	0.965733	+	0.259536i	$0.0835696\pi$
$318$	−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	0.667854	−	0.744293i	$-0.267213\pi$
$331$	−6.04014	−	13.2261i	−0.331996	−	0.726970i	−0.999850	+	0.0173223i	$0.994486\pi$
$332$	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	−0.862325	−	0.506355i	$-0.830992\pi$
$337$	−13.9508	+	8.96566i	−0.759951	+	0.488391i	0.102374	+	0.994746i	$0.467356\pi$
$338$	−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	0.414857	−	0.909887i	$-0.363832\pi$
$347$	−10.1487	−	11.7122i	−0.544809	−	0.628743i	−0.959666	+	0.281144i	$0.909286\pi$
$348$	0.354020	+	0.227515i	0.0189775	+	0.0121961i
$349$	−0.162561	+	1.13064i	−0.00870168	+	0.0605215i	−0.993710	−	0.111988i	$-0.964278\pi$
$349$	−0.162561	+	1.13064i	−0.00870168	+	0.0605215i	0.985008	+	0.172509i	$0.0551874\pi$
$350$	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	−0.274472	−	0.961595i	$-0.588503\pi$
$353$	9.13499	−	5.87070i	0.486206	−	0.312466i	0.760678	+	0.649129i	$0.224867\pi$
$354$	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	0.977882	−	0.209158i	$-0.0670723\pi$
$359$	3.39979	+	7.44451i	0.179434	+	0.392906i	−0.798448	+	0.602064i	$0.794345\pi$
$360$	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	0.586908	+	0.809653i	$0.300345\pi$
$373$	−7.90548	+	17.3106i	−0.409330	+	0.896308i	−0.996238	+	0.0866545i	$0.972382\pi$
$374$	−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	−0.826622	−	0.562758i	$-0.809740\pi$
$379$	−2.95818	+	3.41392i	−0.151951	+	0.175361i	0.674670	+	0.738119i	$0.264286\pi$
$380$	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	−0.624044	+	0.781389i	$0.714512\pi$
$383$	−31.1963	+	20.0487i	−1.59406	+	1.02444i	−0.970014	+	0.243050i	$0.921852\pi$
$384$	−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	0.736164	−	0.676803i	$-0.236635\pi$
$389$	−0.759670	−	0.876706i	−0.0385168	−	0.0444508i	−0.774681	+	0.632352i	$0.782090\pi$
$390$	−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	−0.984602	−	0.174814i	$-0.944068\pi$
$397$	−1.77598	−	12.3522i	−0.0891340	−	0.619940i	0.895468	−	0.445127i	$-0.146841\pi$
$398$	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	0.225082	−	0.974340i	$-0.427735\pi$
$401$	18.8475	−	5.53414i	0.941201	−	0.276362i	0.716119	+	0.697978i	$0.245917\pi$
$402$	−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	−0.984211	−	0.176997i	$-0.943362\pi$
$409$	−4.16456	+	9.11912i	−0.205924	+	0.450912i	0.778287	+	0.627909i	$0.216089\pi$
$410$	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	−0.852701	−	0.522399i	$-0.825037\pi$
$419$	2.05722	−	4.50468i	0.100502	−	0.220068i	0.953203	+	0.302330i	$0.0977646\pi$
$420$	0.543399	+	3.77942i	0.0265151	+	0.184417i
$421$	−0.214743	−	0.0630541i	−0.0104659	−	0.00307307i	0.276495	−	0.961015i	$-0.410827\pi$
$421$	−0.214743	−	0.0630541i	−0.0104659	−	0.00307307i	−0.286961	+	0.957942i	$0.592645\pi$
$422$	−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	0.999385	−	0.0350702i	$-0.0111655\pi$
$431$	0.635308	+	4.41866i	0.0306017	+	0.212840i	−0.968783	+	0.247910i	$0.920256\pi$
$432$	−8.27226	+	18.1137i	−0.397999	+	0.871497i
$433$	2.47814	−	17.2359i	0.119092	−	0.828303i	−0.839467	−	0.543410i	$-0.817133\pi$
$433$	2.47814	−	17.2359i	0.119092	−	0.828303i	0.958559	−	0.284893i	$-0.0919581\pi$
$434$	−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	0.285271	−	0.958447i	$-0.407916\pi$
$439$	−14.7508	−	17.0234i	−0.704018	−	0.812481i	−0.989290	+	0.145966i	$0.953371\pi$
$440$	−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	0.878568	+	0.477617i	$0.158499\pi$
$443$	3.58121	+	24.9079i	0.170149	+	1.18341i	−0.708419	+	0.705792i	$0.750591\pi$
$444$	−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	−0.998266	−	0.0588666i	$-0.981251\pi$
$449$	−16.9078	+	19.5127i	−0.797930	+	0.920861i	0.200335	+	0.979727i	$0.435797\pi$
$450$	−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	−0.382363	−	0.924012i	$-0.624889\pi$
$457$	−29.5376	−	18.9827i	−1.38171	−	0.887973i	−0.999350	+	0.0360394i	$0.988526\pi$
$458$	−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	0.259835	−	0.965653i	$-0.416332\pi$
$463$	−10.9871	−	7.06099i	−0.510614	−	0.328152i	−0.770449	+	0.637501i	$0.779968\pi$
$464$	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	0.194391	−	0.980924i	$-0.437727\pi$
$467$	−3.72568	−	1.09396i	−0.172404	−	0.0506224i	−0.366795	+	0.930302i	$0.619545\pi$
$468$	−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	−0.819446	−	0.573156i	$-0.805719\pi$
$479$	2.80762	−	19.5274i	0.128283	−	0.892231i	0.947730	−	0.319075i	$-0.103372\pi$
$480$	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	0.391711	+	0.920088i	$0.371883\pi$
$487$	−5.37031	+	37.3513i	−0.243352	+	1.69255i	−0.635063	+	0.772460i	$0.719026\pi$
$488$	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	−0.660721	−	0.750632i	$-0.729749\pi$
$491$	−5.59270	+	3.59421i	−0.252395	+	0.162204i	0.408326	+	0.912836i	$0.366113\pi$
$492$	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	0.821226	−	0.570603i	$-0.193291\pi$
$499$	26.8862	+	7.89451i	1.20359	+	0.353407i	0.382368	+	0.924010i	$0.375109\pi$
$500$	−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	0.990499	−	0.137520i	$-0.0439132\pi$
$503$	28.6373	+	18.4041i	1.27687	+	0.820597i	0.286375	+	0.958117i	$0.407550\pi$
$504$	−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	0.0942670	−	0.995547i	$-0.469949\pi$
$509$	−17.4206	−	11.1955i	−0.772154	−	0.496234i	−0.866421	+	0.499313i	$0.833586\pi$
$510$	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	−0.156043	−	0.987750i	$-0.549874\pi$
$521$	15.4670	−	9.94007i	0.677624	−	0.435482i	0.833667	+	0.552268i	$0.186237\pi$
$522$	0.0408111	+	0.0119832i	0.00178625	+	0.000524491i
$523$	−4.30323	−	29.9296i	−0.188167	−	1.30873i	−0.836750	−	0.547585i	$-0.815547\pi$
$523$	−4.30323	−	29.9296i	−0.188167	−	1.30873i	0.648583	−	0.761144i	$-0.275362\pi$
$524$	−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	0.231593	−	0.972813i	$-0.425606\pi$
$541$	27.0168	−	31.1791i	1.16154	−	1.34049i	0.929952	−	0.367681i	$-0.119848\pi$
$542$	−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	−0.950295	−	0.311351i	$-0.899219\pi$
$547$	−2.16762	+	4.74643i	−0.0926809	+	0.202943i	0.857614	+	0.514294i	$0.171946\pi$
$548$	−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	−0.638911	−	0.769280i	$-0.720615\pi$
$557$	8.51684	−	18.6493i	0.360870	−	0.790195i	0.999781	−	0.0209146i	$-0.00665782\pi$
$558$	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	0.253978	−	0.967210i	$-0.418261\pi$
$563$	27.8847	−	32.1806i	1.17520	−	1.35625i	0.921220	−	0.389042i	$-0.127194\pi$
$564$	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	0.829870	+	0.557957i	$0.188414\pi$
$569$	4.55153	+	31.6566i	0.190810	+	1.32711i	−0.639060	+	0.769157i	$0.720676\pi$
$570$	−0.166629	+	0.364867i	−0.00697932	+	0.0152826i
$571$	2.19537	−	15.2691i	0.0918734	−	0.638994i	−0.890903	−	0.454194i	$-0.849927\pi$
$571$	2.19537	−	15.2691i	0.0918734	−	0.638994i	0.982776	−	0.184800i	$-0.0591636\pi$
$572$	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	0.972197	+	0.234166i	$0.0752360\pi$
$577$	25.5971	+	29.5406i	1.06562	+	1.22979i	0.0934247	+	0.995626i	$0.470219\pi$
$578$	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	−0.0215889	+	0.999767i	$0.506872\pi$
$587$	−24.4245	+	28.1874i	−1.00811	+	1.16342i	−0.986518	+	0.163651i	$0.947673\pi$
$588$	−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	0.165097	−	0.986277i	$-0.447206\pi$
$593$	19.5387	−	42.7839i	0.802360	−	1.75692i	0.637263	−	0.770647i	$-0.280067\pi$
$594$	−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	−0.0869905	−	0.996209i	$-0.527725\pi$
$601$	−25.2339	−	16.2168i	−1.02931	−	0.661498i	−0.942321	+	0.334711i	$0.891361\pi$
$602$	−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	0.890300	−	0.455374i	$-0.150494\pi$
$607$	−0.908402	−	1.98912i	−0.0368709	−	0.0807360i	−0.927171	+	0.374638i	$0.877767\pi$
$608$	−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	−0.971392	−	0.237483i	$-0.923678\pi$
$613$	−28.6930	+	18.4399i	−1.15890	+	0.744780i	−0.187508	+	0.982263i	$0.560041\pi$
$614$	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	−0.909688	−	0.415293i	$-0.863679\pi$
$617$	1.99096	−	13.8474i	0.0801529	−	0.557476i	0.989840	−	0.142182i	$-0.0454119\pi$
$618$	4.52151	+	2.90580i	0.181882	+	0.116888i
$619$	−20.8146	−	24.0213i	−0.836608	−	0.965497i	0.163170	−	0.986598i	$-0.447828\pi$
$619$	−20.8146	−	24.0213i	−0.836608	−	0.965497i	−0.999777	+	0.0211014i	$0.993283\pi$
$620$	−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	0.335981	−	0.941869i	$-0.390932\pi$
$631$	28.3310	−	8.31873i	1.12784	−	0.331164i	0.791858	+	0.610705i	$0.209114\pi$
$632$	−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	−0.334792	−	0.942292i	$-0.608666\pi$
$641$	−33.6984	−	21.6567i	−1.33101	−	0.855387i	−0.996217	+	0.0869046i	$0.972302\pi$
$642$	−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	0.903906	−	0.427730i	$-0.140687\pi$
$647$	22.6465	+	14.5540i	0.890326	+	0.572178i	−0.0135807	+	0.999908i	$0.504323\pi$
$648$	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	0.951759	+	0.306846i	$0.0992737\pi$
$653$	14.3201	+	31.3566i	0.560388	+	1.22708i	−0.391371	+	0.920233i	$0.627999\pi$
$654$	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	−0.879534	−	0.475836i	$-0.842145\pi$
$659$	−20.8466	+	13.3973i	−0.812069	+	0.521885i	0.0674645	+	0.997722i	$0.478509\pi$
$660$	−12.6467	−	3.71340i	−0.492271	−	0.144544i
$661$	−2.66397	−	18.5283i	−0.103616	−	0.720668i	−0.973712	−	0.227784i	$-0.926852\pi$
$661$	−2.66397	−	18.5283i	−0.103616	−	0.720668i	0.870095	−	0.492884i	$-0.164057\pi$
$662$	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	−0.999652	−	0.0263623i	$-0.991608\pi$
$673$	−1.24315	−	8.64633i	−0.0479201	−	0.333291i	0.951732	−	0.306929i	$-0.0993015\pi$
$674$	−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	−0.171460	−	0.985191i	$-0.554848\pi$
$677$	5.64443	−	1.65735i	0.216933	−	0.0636973i	0.388393	+	0.921494i	$0.373030\pi$
$678$	−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	0.0297560	−	0.999557i	$-0.490527\pi$
$683$	−12.6911	−	3.72646i	−0.485613	−	0.142589i	−0.515369	+	0.856968i	$0.672345\pi$
$684$	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	−0.895613	−	0.444834i	$-0.853263\pi$
$701$	−8.68025	+	10.0175i	−0.327848	+	0.378357i	0.567765	+	0.823191i	$0.307808\pi$
$702$	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	−0.994885	−	0.101009i	$-0.967793\pi$
$709$	−0.315324	+	2.19313i	−0.0118423	+	0.0823647i	0.983043	+	0.183374i	$0.0587019\pi$
$710$	−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	0.992304	+	0.123829i	$0.0395176\pi$
$719$	2.01326	+	14.0026i	0.0750820	+	0.522207i	−0.917221	+	0.398378i	$0.869573\pi$
$720$	−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	0.966272	−	0.257524i	$-0.0829066\pi$
$727$	3.74447	+	8.19925i	0.138875	+	0.304093i	−0.827397	+	0.561617i	$0.810179\pi$
$728$	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	0.993524	−	0.113625i	$-0.0362463\pi$
$733$	35.2744	+	22.6695i	1.30289	+	0.837317i	0.309368	+	0.950943i	$0.399883\pi$
$734$	−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	0.548337	−	0.836257i	$-0.315261\pi$
$739$	0.419683	+	0.269714i	0.0154383	+	0.00992158i	−0.532899	+	0.846179i	$0.678897\pi$
$740$	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	0.281565	−	0.959542i	$-0.409147\pi$
$743$	−0.00916062	−	0.00268980i	−0.000336070	−	9.86792e-5i	−0.281901	+	0.959444i	$0.590965\pi$
$744$	−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	−0.954857	−	0.297065i	$-0.903992\pi$
$751$	−29.6324	+	19.0436i	−1.08130	+	0.694909i	−0.126443	+	0.991974i	$0.540356\pi$
$752$	−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	0.566868	−	0.823809i	$-0.308155\pi$
$757$	−9.05830	−	10.4538i	−0.329229	−	0.379951i	−0.896097	+	0.443858i	$0.853610\pi$
$758$	−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	0.930102	−	0.367301i	$-0.119718\pi$
$761$	11.9772	+	13.8224i	0.434172	+	0.501061i	−0.495930	+	0.868362i	$0.665173\pi$
$762$	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	−0.00379292	−	0.999993i	$-0.501207\pi$
$769$	14.7987	−	4.34528i	0.533653	−	0.156695i	0.537446	+	0.843298i	$0.319389\pi$
$770$	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	0.888929	−	0.458045i	$-0.151450\pi$
$773$	−1.09441	−	2.39642i	−0.0393631	−	0.0861932i	−0.928292	+	0.371852i	$0.878723\pi$
$774$	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	−0.995593	−	0.0937771i	$-0.970106\pi$
$787$	−7.65149	+	16.7544i	−0.272746	+	0.597231i	0.722847	+	0.691008i	$0.242833\pi$
$788$	−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	0.480890	−	0.876781i	$-0.340314\pi$
$797$	41.7315	−	26.8192i	1.47821	−	0.949986i	0.997317	−	0.0732048i	$-0.0233227\pi$
$798$	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	0.953966	+	0.299915i	$0.0969583\pi$
$809$	−1.30421	+	9.07096i	−0.0458535	+	0.318918i	−0.999819	+	0.0190030i	$0.993951\pi$
$810$	−0.608402	+	1.33222i	−0.0213771	+	0.0468093i
$811$	0.665879	+	4.63129i	0.0233822	+	0.162627i	0.998167	−	0.0605205i	$-0.0192761\pi$
$811$	0.665879	+	4.63129i	0.0233822	+	0.162627i	−0.974785	+	0.223147i	$0.928367\pi$
$812$	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	0.0845109	−	0.996423i	$-0.473067\pi$
$821$	−10.9770	−	3.22314i	−0.383101	−	0.112489i	−0.467612	+	0.883934i	$0.654885\pi$
$822$	−1.12862	−	7.84973i	−0.0393652	−	0.273791i
$823$	−15.1472	+	33.1678i	−0.527998	+	1.15616i	0.438323	+	0.898817i	$0.355573\pi$
$823$	−15.1472	+	33.1678i	−0.527998	+	1.15616i	−0.966322	+	0.257338i	$0.917155\pi$
$824$	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	−0.640528	−	0.767934i	$-0.721285\pi$
$839$	6.10437	−	7.04482i	0.210746	−	0.243214i	0.851275	+	0.524720i	$0.175830\pi$
$840$	−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	0.717175	−	0.696893i	$-0.245435\pi$
$853$	−2.18140	−	2.51747i	−0.0746897	−	0.0861965i	−0.791865	+	0.610697i	$0.790889\pi$
$854$	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	−0.642412	−	0.766360i	$-0.722066\pi$
$857$	−7.08241	−	49.2593i	−0.241931	−	1.68266i	0.400481	−	0.916305i	$-0.368843\pi$
$858$	−0.535386	−	0.157203i	−0.0182778	−	0.00536684i
$859$	−18.2530	+	11.7305i	−0.622784	+	0.400239i	−0.813632	−	0.581380i	$-0.802513\pi$
$859$	−18.2530	+	11.7305i	−0.622784	+	0.400239i	0.190847	+	0.981620i	$0.438876\pi$
$860$	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	−0.486137	−	0.873883i	$-0.661594\pi$
$863$	13.1619	−	15.1896i	0.448035	−	0.517060i	0.934172	+	0.356822i	$0.116140\pi$
$864$	−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	0.632768	−	0.774341i	$-0.281919\pi$
$877$	5.66411	+	3.64010i	0.191263	+	0.122918i	−0.441504	+	0.897259i	$0.645555\pi$
$878$	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	−0.758834	−	0.651284i	$-0.774231\pi$
$881$	−51.9226	−	15.2459i	−1.74932	−	0.513646i	−0.990483	+	0.137638i	$0.956049\pi$
$882$	−1.17358	+	0.754211i	−0.0395163	+	0.0253956i
$883$	−0.291639	−	0.638600i	−0.00981442	−	0.0214906i	0.904661	−	0.426131i	$-0.140124\pi$
$883$	−0.291639	−	0.638600i	−0.00981442	−	0.0214906i	−0.914476	+	0.404641i	$0.867397\pi$
$884$	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	0.205452	−	0.978667i	$-0.434133\pi$
$887$	27.0246	−	7.93514i	0.907397	−	0.266436i	0.701945	+	0.712231i	$0.252315\pi$
$888$	−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	−0.562871	−	0.826545i	$-0.690303\pi$
$907$	−17.7544	+	5.21316i	−0.589524	+	0.173100i	−0.0266534	+	0.999645i	$0.508485\pi$
$908$	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	−0.990474	−	0.137703i	$-0.956028\pi$
$911$	−13.4591	−	29.4714i	−0.445920	−	0.976429i	0.544553	−	0.838726i	$-0.316699\pi$
$912$	−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	0.778736	−	0.627352i	$-0.215861\pi$
$929$	−6.25892	−	13.7051i	−0.205349	−	0.449651i	−0.984084	+	0.177701i	$0.943134\pi$
$930$	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	0.983378	−	0.181572i	$-0.0581185\pi$
$937$	−0.346540	−	2.41024i	−0.0113210	−	0.0787390i	−0.994699	+	0.102833i	$0.967209\pi$
$938$	−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	0.969666	+	0.244434i	$0.0786023\pi$
$941$	32.9339	+	38.0077i	1.07361	+	1.23902i	0.103949	+	0.994583i	$0.466852\pi$
$942$	−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	0.950815	+	0.309758i	$0.100248\pi$
$947$	−1.50033	+	10.4350i	−0.0487542	+	0.339093i	−0.999570	+	0.0293348i	$0.990661\pi$
$948$	−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	0.121844	−	0.992549i	$-0.461119\pi$
$953$	23.4913	−	6.89767i	0.760958	−	0.223438i	0.639114	+	0.769112i	$0.279301\pi$
$954$	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	−0.623576	−	0.781763i	$-0.714321\pi$
$971$	11.7039	−	25.6280i	0.375596	−	0.822441i	0.999172	−	0.0406780i	$-0.0129518\pi$
$972$	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	−0.912440	−	0.409210i	$-0.865804\pi$
$977$	−11.8008	+	13.6189i	−0.377542	+	0.435706i	0.534899	+	0.844916i	$0.320350\pi$
$978$	−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	−0.989237	−	0.146320i	$-0.953257\pi$
$983$	−2.54880	−	17.7273i	−0.0812941	−	0.565413i	0.907943	−	0.419093i	$-0.137652\pi$
$984$	−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	−0.996200	−	0.0870922i	$-0.972243\pi$
$991$	−29.6112	−	34.1732i	−0.940632	−	1.08555i	0.0555684	−	0.998455i	$-0.482303\pi$
$992$	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	−0.474957	−	0.880009i	$-0.657537\pi$
$997$	4.04866	−	2.60192i	0.128222	−	0.0824036i	0.603180	+	0.797605i	$0.293900\pi$
$998$	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.36.2	yes	20
5.2	odd	4		575.2.p.c.174.2		40
5.3	odd	4		575.2.p.c.174.3		40
5.4	even	2		575.2.k.c.151.1		20
23.4	even	11		2645.2.a.t.1.6		10
23.16	even	11	inner	115.2.g.b.16.2	✓	20
23.19	odd	22		2645.2.a.u.1.6		10
115.39	even	22		575.2.k.c.476.1		20
115.62	odd	44		575.2.p.c.499.3		40
115.108	odd	44		575.2.p.c.499.2		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.b.16.2	✓	20	23.16	even	11	inner
115.2.g.b.36.2	yes	20	1.1	even	1	trivial
575.2.k.c.151.1		20	5.4	even	2
575.2.k.c.476.1		20	115.39	even	22
575.2.p.c.174.2		40	5.2	odd	4
575.2.p.c.174.3		40	5.3	odd	4
575.2.p.c.499.2		40	115.108	odd	44
575.2.p.c.499.3		40	115.62	odd	44
2645.2.a.t.1.6		10	23.4	even	11
2645.2.a.u.1.6		10	23.19	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

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