LMFDB - Embedded newform 756.2.ci.a.95.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(95,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 17, 12]))

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

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

chi := DirichletCharacter("756.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ci (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$840$
Relative dimension:	$140$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			95.12
Character	$\chi$	$=$	756.95
Dual form			756.2.ci.a.191.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36638 + 0.364685i) q^{2} +(1.60153 - 0.659617i) q^{3} +(1.73401 - 0.996600i) q^{4} +(-2.53354 - 0.446731i) q^{5} +(-1.94776 + 1.48535i) q^{6} +(2.18735 + 1.48846i) q^{7} +(-2.00588 + 1.99411i) q^{8} +(2.12981 - 2.11280i) q^{9} +O(q^{10})$	\(q+(-1.36638 + 0.364685i) q^{2} +(1.60153 - 0.659617i) q^{3} +(1.73401 - 0.996600i) q^{4} +(-2.53354 - 0.446731i) q^{5} +(-1.94776 + 1.48535i) q^{6} +(2.18735 + 1.48846i) q^{7} +(-2.00588 + 1.99411i) q^{8} +(2.12981 - 2.11280i) q^{9} +(3.62470 - 0.313538i) q^{10} +(-0.661535 - 3.75175i) q^{11} +(2.11970 - 2.73987i) q^{12} +(0.440282 - 2.49696i) q^{13} +(-3.53158 - 1.23611i) q^{14} +(-4.35221 + 0.955709i) q^{15} +(2.01358 - 3.45623i) q^{16} +(-2.01868 + 1.16548i) q^{17} +(-2.13963 + 3.66360i) q^{18} +(-2.70911 - 1.56410i) q^{19} +(-4.83839 + 1.75029i) q^{20} +(4.48492 + 0.941000i) q^{21} +(2.27212 + 4.88508i) q^{22} +(-1.98792 - 1.66806i) q^{23} +(-1.89713 + 4.51674i) q^{24} +(1.52078 + 0.553518i) q^{25} +(0.309012 + 3.57238i) q^{26} +(2.01733 - 4.78857i) q^{27} +(5.27628 + 0.401085i) q^{28} +(10.4928 - 1.85016i) q^{29} +(5.59826 - 2.89305i) q^{30} +(4.72569 + 0.833266i) q^{31} +(-1.49088 + 5.45686i) q^{32} +(-3.53419 - 5.57220i) q^{33} +(2.33325 - 2.32868i) q^{34} +(-4.87679 - 4.74822i) q^{35} +(1.58750 - 5.78618i) q^{36} -3.29525 q^{37} +(4.27209 + 1.14919i) q^{38} +(-0.941913 - 4.28939i) q^{39} +(5.97279 - 4.15605i) q^{40} +(0.865976 + 0.152695i) q^{41} +(-6.47129 + 0.349818i) q^{42} +(-4.14322 - 4.93770i) q^{43} +(-4.88611 - 5.84629i) q^{44} +(-6.33981 + 4.40139i) q^{45} +(3.32457 + 1.55425i) q^{46} +(-1.60801 - 9.11946i) q^{47} +(0.945020 - 6.86345i) q^{48} +(2.56899 + 6.51155i) q^{49} +(-2.27983 - 0.201712i) q^{50} +(-2.46420 + 3.19811i) q^{51} +(-1.72502 - 4.76854i) q^{52} +(2.12029 + 1.22415i) q^{53} +(-1.01012 + 7.27871i) q^{54} +9.80074i q^{55} +(-7.35569 + 1.37615i) q^{56} +(-5.37043 - 0.717990i) q^{57} +(-13.6624 + 6.35459i) q^{58} +(1.82437 - 0.664017i) q^{59} +(-6.59432 + 5.99463i) q^{60} +(-0.495987 - 2.81288i) q^{61} +(-6.76098 + 0.584827i) q^{62} +(7.80345 - 1.45129i) q^{63} +(0.0470807 - 7.99986i) q^{64} +(-2.23094 + 6.12946i) q^{65} +(6.86116 + 6.32489i) q^{66} +(7.82394 - 9.32421i) q^{67} +(-2.33888 + 4.03277i) q^{68} +(-4.28399 - 1.36019i) q^{69} +(8.39517 + 4.70939i) q^{70} +(-1.40440 + 2.43249i) q^{71} +(-0.0590006 + 8.48508i) q^{72} -10.3815 q^{73} +(4.50258 - 1.20173i) q^{74} +(2.80068 - 0.116654i) q^{75} +(-6.25640 - 0.0122732i) q^{76} +(4.13732 - 9.19106i) q^{77} +(2.85129 + 5.51745i) q^{78} +(1.90994 + 2.27618i) q^{79} +(-6.64547 + 7.85696i) q^{80} +(0.0721933 - 8.99971i) q^{81} +(-1.23894 + 0.107169i) q^{82} +(-1.83902 - 10.4296i) q^{83} +(8.71470 - 2.83797i) q^{84} +(5.63505 - 2.05099i) q^{85} +(7.46194 + 5.23582i) q^{86} +(15.5841 - 9.88431i) q^{87} +(8.80835 + 6.20638i) q^{88} +(-7.27868 - 4.20235i) q^{89} +(7.05749 - 8.32603i) q^{90} +(4.67967 - 4.80639i) q^{91} +(-5.10945 - 0.911273i) q^{92} +(8.11797 - 1.78264i) q^{93} +(5.52289 + 11.8743i) q^{94} +(6.16489 + 5.17296i) q^{95} +(1.21174 + 9.72274i) q^{96} +(-9.98509 + 8.37848i) q^{97} +(-5.88490 - 7.96040i) q^{98} +(-9.33563 - 6.59284i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} + 3 q^{10} - 3 q^{12} - 24 q^{13} + 24 q^{14} - 3 q^{16} - 18 q^{17} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} + 48 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} - 21 q^{30} - 63 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} - 12 q^{37} + 45 q^{38} - 33 q^{40} - 24 q^{41} - 21 q^{42} + 6 q^{45} - 6 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} - 63 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} - 54 q^{65} - 3 q^{66} - 12 q^{68} - 48 q^{69} - 21 q^{70} - 9 q^{72} - 12 q^{73} + 15 q^{74} + 12 q^{77} + 6 q^{78} - 54 q^{81} - 6 q^{82} - 39 q^{84} + 6 q^{85} - 9 q^{86} - 27 q^{88} - 18 q^{89} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} + 213 q^{96} - 24 q^{97} + 162 q^{98}+O(q^{100}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 + 3 * q^10 - 3 * q^12 - 24 * q^13 + 24 * q^14 - 3 * q^16 - 18 * q^17 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 + 48 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 - 21 * q^30 - 63 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 - 12 * q^37 + 45 * q^38 - 33 * q^40 - 24 * q^41 - 21 * q^42 + 6 * q^45 - 6 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 - 63 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 - 54 * q^65 - 3 * q^66 - 12 * q^68 - 48 * q^69 - 21 * q^70 - 9 * q^72 - 12 * q^73 + 15 * q^74 + 12 * q^77 + 6 * q^78 - 54 * q^81 - 6 * q^82 - 39 * q^84 + 6 * q^85 - 9 * q^86 - 27 * q^88 - 18 * q^89 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 + 213 * q^96 - 24 * q^97 + 162 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.36638	+	0.364685i	−0.966179	+	0.257871i
$2$	−1.36638	+	0.364685i	−0.966179	+	0.257871i
$3$	1.60153	−	0.659617i	0.924645	−	0.380830i
$3$	1.60153	−	0.659617i	0.924645	−	0.380830i
$4$	1.73401	−	0.996600i	0.867005	−	0.498300i
$5$	−2.53354	−	0.446731i	−1.13303	−	0.199784i	−0.424476	−	0.905439i	$-0.639542\pi$
$5$	−2.53354	−	0.446731i	−1.13303	−	0.199784i	−0.708556	+	0.705655i	$0.750653\pi$
$6$	−1.94776	+	1.48535i	−0.795168	+	0.606390i
$7$	2.18735	+	1.48846i	0.826740	+	0.562584i
$7$	2.18735	+	1.48846i	0.826740	+	0.562584i
$8$	−2.00588	+	1.99411i	−0.709184	+	0.705023i
$9$	2.12981	−	2.11280i	0.709937	−	0.704265i
$10$	3.62470	−	0.313538i	1.14623	−	0.0991494i
$11$	−0.661535	−	3.75175i	−0.199460	−	1.13120i	−0.905922	−	0.423445i	$-0.860821\pi$
$11$	−0.661535	−	3.75175i	−0.199460	−	1.13120i	0.706461	−	0.707752i	$-0.250290\pi$
$12$	2.11970	−	2.73987i	0.611904	−	0.790932i
$13$	0.440282	−	2.49696i	0.122112	−	0.692533i	−0.860869	−	0.508827i	$-0.830079\pi$
$13$	0.440282	−	2.49696i	0.122112	−	0.692533i	0.982981	−	0.183706i	$-0.0588096\pi$
$14$	−3.53158	−	1.23611i	−0.943854	−	0.330364i
$15$	−4.35221	+	0.955709i	−1.12374	+	0.246763i
$16$	2.01358	−	3.45623i	0.503394	−	0.864057i
$17$	−2.01868	+	1.16548i	−0.489601	+	0.282671i	−0.724409	−	0.689371i	$-0.757887\pi$
$17$	−2.01868	+	1.16548i	−0.489601	+	0.282671i	0.234808	+	0.972042i	$0.424554\pi$
$18$	−2.13963	+	3.66360i	−0.504317	+	0.863519i
$19$	−2.70911	−	1.56410i	−0.621512	−	0.358830i	0.155946	−	0.987766i	$-0.450158\pi$
$19$	−2.70911	−	1.56410i	−0.621512	−	0.358830i	−0.777457	+	0.628936i	$0.783491\pi$
$20$	−4.83839	+	1.75029i	−1.08190	+	0.391376i
$21$	4.48492	+	0.941000i	0.978690	+	0.205343i
$22$	2.27212	+	4.88508i	0.484418	+	1.04150i
$23$	−1.98792	−	1.66806i	−0.414509	−	0.347814i	0.411561	−	0.911382i	$-0.364984\pi$
$23$	−1.98792	−	1.66806i	−0.414509	−	0.347814i	−0.826070	+	0.563568i	$0.809428\pi$
$24$	−1.89713	+	4.51674i	−0.387250	+	0.921975i
$25$	1.52078	+	0.553518i	0.304156	+	0.110704i
$26$	0.309012	+	3.57238i	0.0606022	+	0.700601i
$27$	2.01733	−	4.78857i	0.388235	−	0.921561i
$28$	5.27628	+	0.401085i	0.997123	+	0.0757980i
$29$	10.4928	−	1.85016i	1.94846	−	0.343566i	0.948849	−	0.315731i	$-0.102250\pi$
$29$	10.4928	−	1.85016i	1.94846	−	0.343566i	0.999613	−	0.0278350i	$-0.00886130\pi$
$30$	5.59826	−	2.89305i	1.02210	−	0.528197i
$31$	4.72569	+	0.833266i	0.848758	+	0.149659i	0.581077	−	0.813849i	$-0.302632\pi$
$31$	4.72569	+	0.833266i	0.848758	+	0.149659i	0.267681	+	0.963508i	$0.413743\pi$
$32$	−1.49088	+	5.45686i	−0.263553	+	0.964645i
$33$	−3.53419	−	5.57220i	−0.615224	−	0.969995i
$34$	2.33325	−	2.32868i	0.400149	−	0.399365i
$35$	−4.87679	−	4.74822i	−0.824328	−	0.802595i
$36$	1.58750	−	5.78618i	0.264583	−	0.964363i
$37$	−3.29525			−0.541736			−0.270868	−	0.962617i	$-0.587311\pi$
$37$	−3.29525			−0.541736			−0.270868	+	0.962617i	$0.587311\pi$
$38$	4.27209	+	1.14919i	0.693024	+	0.186424i
$39$	−0.941913	−	4.28939i	−0.150827	−	0.686851i
$40$	5.97279	−	4.15605i	0.944381	−	0.657130i
$41$	0.865976	+	0.152695i	0.135243	+	0.0238469i	0.240860	−	0.970560i	$-0.422571\pi$
$41$	0.865976	+	0.152695i	0.135243	+	0.0238469i	−0.105617	+	0.994407i	$0.533682\pi$
$42$	−6.47129	+	0.349818i	−0.998542	+	0.0539781i
$43$	−4.14322	−	4.93770i	−0.631836	−	0.752993i	0.351221	−	0.936292i	$-0.385766\pi$
$43$	−4.14322	−	4.93770i	−0.631836	−	0.752993i	−0.983057	+	0.183300i	$0.941322\pi$
$44$	−4.88611	−	5.84629i	−0.736608	−	0.881361i
$45$	−6.33981	+	4.40139i	−0.945083	+	0.656121i
$46$	3.32457	+	1.55425i	0.490181	+	0.229161i
$47$	−1.60801	−	9.11946i	−0.234552	−	1.33021i	−0.843555	−	0.537043i	$-0.819541\pi$
$47$	−1.60801	−	9.11946i	−0.234552	−	1.33021i	0.609003	−	0.793168i	$-0.291570\pi$
$48$	0.945020	−	6.86345i	0.136402	−	0.990654i
$49$	2.56899	+	6.51155i	0.366999	+	0.930221i
$50$	−2.27983	−	0.201712i	−0.322416	−	0.0285264i
$51$	−2.46420	+	3.19811i	−0.345057	+	0.447825i
$52$	−1.72502	−	4.76854i	−0.239218	−	0.661278i
$53$	2.12029	+	1.22415i	0.291244	+	0.168150i	0.638503	−	0.769619i	$-0.279554\pi$
$53$	2.12029	+	1.22415i	0.291244	+	0.168150i	−0.347259	+	0.937769i	$0.612887\pi$
$54$	−1.01012	+	7.27871i	−0.137460	+	0.990507i
$55$			9.80074i			1.32153i
$56$	−7.35569	+	1.37615i	−0.982946	+	0.183895i
$57$	−5.37043	−	0.717990i	−0.711331	−	0.0951001i
$58$	−13.6624	+	6.35459i	−1.79397	+	0.834399i
$59$	1.82437	−	0.664017i	0.237513	−	0.0864477i	−0.220521	−	0.975382i	$-0.570776\pi$
$59$	1.82437	−	0.664017i	0.237513	−	0.0864477i	0.458034	+	0.888934i	$0.348554\pi$
$60$	−6.59432	+	5.99463i	−0.851323	+	0.773903i
$61$	−0.495987	−	2.81288i	−0.0635046	−	0.360153i	−0.999956	−	0.00935589i	$-0.997022\pi$
$61$	−0.495987	−	2.81288i	−0.0635046	−	0.360153i	0.936452	−	0.350797i	$-0.114089\pi$
$62$	−6.76098	+	0.584827i	−0.858645	+	0.0742731i
$63$	7.80345	−	1.45129i	0.983142	−	0.182845i
$64$	0.0470807	−	7.99986i	0.00588508	−	0.999983i
$65$	−2.23094	+	6.12946i	−0.276714	+	0.760266i
$66$	6.86116	+	6.32489i	0.844550	+	0.778540i
$67$	7.82394	−	9.32421i	0.955846	−	1.13913i	−0.0343442	−	0.999410i	$-0.510934\pi$
$67$	7.82394	−	9.32421i	0.955846	−	1.13913i	0.990191	−	0.139723i	$-0.0446213\pi$
$68$	−2.33888	+	4.03277i	−0.283631	+	0.489046i
$69$	−4.28399	−	1.36019i	−0.515732	−	0.163747i
$70$	8.39517	+	4.70939i	1.00341	+	0.562880i
$71$	−1.40440	+	2.43249i	−0.166671	+	0.288683i	−0.937248	−	0.348665i	$-0.886635\pi$
$71$	−1.40440	+	2.43249i	−0.166671	+	0.288683i	0.770576	+	0.637348i	$0.219969\pi$
$72$	−0.0590006	+	8.48508i	−0.00695328	+	0.999976i
$73$	−10.3815			−1.21507			−0.607533	−	0.794294i	$-0.707841\pi$
$73$	−10.3815			−1.21507			−0.607533	+	0.794294i	$0.707841\pi$
$74$	4.50258	−	1.20173i	0.523414	−	0.139698i
$75$	2.80068	−	0.116654i	0.323395	−	0.0134700i
$76$	−6.25640	−	0.0122732i	−0.717659	−	0.00140784i
$77$	4.13732	−	9.19106i	0.471491	−	1.04742i
$78$	2.85129	+	5.51745i	0.322845	+	0.624728i
$79$	1.90994	+	2.27618i	0.214885	+	0.256090i	0.862710	−	0.505699i	$-0.168766\pi$
$79$	1.90994	+	2.27618i	0.214885	+	0.256090i	−0.647825	+	0.761789i	$0.724321\pi$
$80$	−6.64547	+	7.85696i	−0.742986	+	0.878434i
$81$	0.0721933	−	8.99971i	0.00802148	−	0.999968i
$82$	−1.23894	+	0.107169i	−0.136818	+	0.0118348i
$83$	−1.83902	−	10.4296i	−0.201859	−	1.14480i	−0.902307	−	0.431095i	$-0.858127\pi$
$83$	−1.83902	−	10.4296i	−0.201859	−	1.14480i	0.700448	−	0.713704i	$-0.252984\pi$
$84$	8.71470	−	2.83797i	0.950851	−	0.309648i
$85$	5.63505	−	2.05099i	0.611207	−	0.222461i
$86$	7.46194	+	5.23582i	0.804642	+	0.564593i
$87$	15.5841	−	9.88431i	1.67079	−	1.05971i
$88$	8.80835	+	6.20638i	0.938974	+	0.661603i
$89$	−7.27868	−	4.20235i	−0.771539	−	0.445448i	0.0618844	−	0.998083i	$-0.480289\pi$
$89$	−7.27868	−	4.20235i	−0.771539	−	0.445448i	−0.833423	+	0.552635i	$0.813622\pi$
$90$	7.05749	−	8.32603i	0.743924	−	0.877640i
$91$	4.67967	−	4.80639i	0.490563	−	0.503847i
$92$	−5.10945	−	0.911273i	−0.532697	−	0.0950067i
$93$	8.11797	−	1.78264i	0.841795	−	0.184851i
$94$	5.52289	+	11.8743i	0.569643	+	1.22474i
$95$	6.16489	+	5.17296i	0.632504	+	0.530734i
$96$	1.21174	+	9.72274i	0.123673	+	0.992323i
$97$	−9.98509	+	8.37848i	−1.01383	+	0.850706i	−0.988840	−	0.148981i	$-0.952401\pi$
$97$	−9.98509	+	8.37848i	−1.01383	+	0.850706i	−0.0249922	+	0.999688i	$0.507956\pi$
$98$	−5.88490	−	7.96040i	−0.594464	−	0.804122i
$99$	−9.33563	−	6.59284i	−0.938266	−	0.662605i
$100$	3.18868	−	0.555803i	0.318868	−	0.0555803i
$101$	10.1984	+	12.1540i	1.01478	+	1.20936i	0.977690	+	0.210052i	$0.0673634\pi$
$101$	10.1984	+	12.1540i	1.01478	+	1.20936i	0.0370868	+	0.999312i	$0.488192\pi$
$102$	2.20074	−	5.26851i	0.217906	−	0.521660i
$103$	−3.21266	−	0.566479i	−0.316553	−	0.0558168i	0.0131144	−	0.999914i	$-0.495825\pi$
$103$	−3.21266	−	0.566479i	−0.316553	−	0.0558168i	−0.329667	+	0.944097i	$0.606937\pi$
$104$	4.09606	+	5.88657i	0.401652	+	0.577226i
$105$	−10.9423	−	4.38761i	−1.06786	−	0.428187i
$106$	−3.34356	−	0.899420i	−0.324755	−	0.0873594i
$107$	5.01329	+	8.68327i	0.484653	+	0.839443i	0.999845	−	0.0176318i	$-0.00561266\pi$
$107$	5.01329	+	8.68327i	0.484653	+	0.839443i	−0.515192	+	0.857075i	$0.672279\pi$
$108$	−1.27423	−	10.3139i	−0.122612	−	0.992455i
$109$	4.28555	−	7.42278i	0.410481	−	0.710974i	−0.584462	−	0.811421i	$-0.698694\pi$
$109$	4.28555	−	7.42278i	0.410481	−	0.710974i	0.994942	+	0.100448i	$0.0320276\pi$
$110$	−3.57418	−	13.3916i	−0.340785	−	1.27684i
$111$	−5.27745	+	2.17360i	−0.500913	+	0.206309i
$112$	9.54884	−	4.56286i	0.902281	−	0.431149i
$113$	3.18294	−	3.79328i	0.299426	−	0.356842i	−0.595263	−	0.803531i	$-0.702952\pi$
$113$	3.18294	−	3.79328i	0.299426	−	0.356842i	0.894690	+	0.446688i	$0.147397\pi$
$114$	7.59991	−	0.977468i	0.711797	−	0.0915482i
$115$	4.29128	+	5.11415i	0.400164	+	0.476897i
$116$	16.3507	−	13.6653i	1.51813	−	1.26879i
$117$	−4.33786	−	6.24829i	−0.401035	−	0.577654i
$118$	−2.25064	+	1.57262i	−0.207188	+	0.144772i
$119$	−6.15032	−	0.455394i	−0.563799	−	0.0417459i
$120$	6.82421	−	10.5958i	0.622963	−	0.967261i
$121$	−3.30141	+	1.20161i	−0.300128	+	0.109238i
$122$	1.70353	+	3.66260i	0.154230	+	0.331596i
$123$	1.48761	−	0.326667i	0.134133	−	0.0294545i
$124$	9.02481	−	3.26473i	0.810452	−	0.293181i
$125$	7.53410	+	4.34982i	0.673871	+	0.389059i
$126$	−10.1332	+	4.82882i	−0.902741	+	0.430185i
$127$	15.2477	−	8.80324i	1.35301	−	0.781162i	0.364341	−	0.931265i	$-0.381294\pi$
$127$	15.2477	−	8.80324i	1.35301	−	0.781162i	0.988670	+	0.150104i	$0.0479608\pi$
$128$	2.85310	+	10.9481i	0.252181	+	0.967680i
$129$	−9.89250	−	5.17495i	−0.870986	−	0.455629i
$130$	0.812998	−	9.18879i	0.0713046	−	0.805910i
$131$	3.50480	+	2.94088i	0.306216	+	0.256946i	0.782926	−	0.622115i	$-0.213726\pi$
$131$	3.50480	+	2.94088i	0.306216	+	0.256946i	−0.476710	+	0.879061i	$0.658171\pi$
$132$	−11.6816	−	6.14006i	−1.01675	−	0.534424i
$133$	−3.59766	−	7.45363i	−0.311957	−	0.646312i
$134$	−7.29010	+	15.5937i	−0.629769	+	1.34709i
$135$	−7.25017	+	11.2308i	−0.623996	+	0.966595i
$136$	1.72512	−	6.36327i	0.147928	−	0.545646i
$137$	−6.35093	+	17.4490i	−0.542597	+	1.49077i	0.300910	+	0.953653i	$0.402710\pi$
$137$	−6.35093	+	17.4490i	−0.542597	+	1.49077i	−0.843506	+	0.537119i	$0.819513\pi$
$138$	6.34962	+	0.296230i	0.540515	+	0.0252168i
$139$	5.63738	+	15.4886i	0.478156	+	1.31372i	0.911056	+	0.412282i	$0.135268\pi$
$139$	5.63738	+	15.4886i	0.478156	+	1.31372i	−0.432900	+	0.901442i	$0.642510\pi$
$140$	−13.1885	−	3.37324i	−1.11463	−	0.285091i
$141$	−8.59063	−	13.5444i	−0.723461	−	1.14065i
$142$	1.03185	−	3.83587i	0.0865912	−	0.321899i
$143$	−9.65926			−0.807748
$144$	−3.01377	−	11.6154i	−0.251147	−	0.967949i
$145$	−27.4104			−2.27631
$146$	14.1852	−	3.78599i	1.17397	−	0.313331i
$147$	8.40945	+	8.73391i	0.693600	+	0.720361i
$148$	−5.71400	+	3.28405i	−0.469688	+	0.269947i
$149$	4.74728	+	13.0430i	0.388912	+	1.06853i	0.967492	+	0.252901i	$0.0813848\pi$
$149$	4.74728	+	13.0430i	0.388912	+	1.06853i	−0.578580	+	0.815626i	$0.696393\pi$
$150$	−3.78427	+	1.18076i	−0.308984	+	0.0964088i
$151$	−0.0969266	+	0.0170908i	−0.00788777	+	0.00139083i	−0.177591	−	0.984104i	$-0.556830\pi$
$151$	−0.0969266	+	0.0170908i	−0.00788777	+	0.00139083i	0.169703	+	0.985495i	$0.445719\pi$
$152$	8.55312	−	2.26485i	0.693750	−	0.183703i
$153$	−1.83697	+	6.74731i	−0.148510	+	0.545488i
$154$	−2.30131	+	14.0673i	−0.185445	+	1.13358i
$155$	−11.6005	−	4.22222i	−0.931771	−	0.339137i
$156$	−5.90809	−	6.49912i	−0.473026	−	0.520346i
$157$	11.0939	−	4.03785i	0.885389	−	0.322255i	0.141007	−	0.990009i	$-0.454966\pi$
$157$	11.0939	−	4.03785i	0.885389	−	0.322255i	0.744383	+	0.667753i	$0.232744\pi$
$158$	−3.43980	−	2.41361i	−0.273656	−	0.192016i
$159$	4.20318	+	0.561937i	0.333334	+	0.0445645i
$160$	6.21495	−	13.1591i	0.491335	−	1.04032i
$161$	−1.86543	−	6.60755i	−0.147017	−	0.520748i
$162$	3.18342	+	12.3234i	0.250113	+	0.968217i
$163$	−19.0945	+	11.0242i	−1.49560	+	0.863485i	−0.999987	−	0.00505847i	$-0.998390\pi$
$163$	−19.0945	+	11.0242i	−1.49560	+	0.863485i	−0.495613	+	0.868544i	$0.665056\pi$
$164$	1.65379	−	0.598258i	0.129139	−	0.0467161i
$165$	6.46473	+	15.6962i	0.503278	+	1.22195i
$166$	6.31634	+	13.5802i	0.490243	+	1.05403i
$167$	10.1192	+	8.49098i	0.783044	+	0.657052i	0.944013	−	0.329908i	$-0.107018\pi$
$167$	10.1192	+	8.49098i	0.783044	+	0.657052i	−0.160969	+	0.986959i	$0.551462\pi$
$168$	−10.8727	+	7.05588i	−0.838843	+	0.544373i
$169$	6.17502	+	2.24752i	0.475002	+	0.172886i
$170$	−6.95167	+	4.85746i	−0.533169	+	0.372550i
$171$	−9.07452	+	2.39254i	−0.693946	+	0.182962i
$172$	−12.1053	−	4.43288i	−0.923021	−	0.338004i
$173$	−5.57643	+	15.3211i	−0.423968	+	1.16484i	0.525449	+	0.850825i	$0.323897\pi$
$173$	−5.57643	+	15.3211i	−0.423968	+	1.16484i	−0.949417	+	0.314018i	$0.898325\pi$
$174$	−17.6892	+	19.1891i	−1.34102	+	1.45472i
$175$	2.50258	+	3.47435i	0.189178	+	0.262636i
$176$	−14.2990	−	5.26802i	−1.07783	−	0.397092i
$177$	2.48379	−	2.26683i	0.186693	−	0.170385i
$178$	11.4780	+	3.08759i	0.860313	+	0.231425i
$179$	−7.10615	−	12.3082i	−0.531139	−	0.919960i	−0.999340	−	0.0363374i	$-0.988431\pi$
$179$	−7.10615	−	12.3082i	−0.531139	−	0.919960i	0.468201	−	0.883622i	$-0.344902\pi$
$180$	−6.60685	+	13.9503i	−0.492446	+	1.03979i
$181$	9.79234	+	16.9608i	0.727859	+	1.26069i	0.957786	+	0.287481i	$0.0928177\pi$
$181$	9.79234	+	16.9608i	0.727859	+	1.26069i	−0.229928	+	0.973208i	$0.573849\pi$
$182$	−4.64141	+	8.27398i	−0.344044	+	0.613308i
$183$	−2.64976	−	4.17776i	−0.195876	−	0.308829i
$184$	7.31380	−	0.618194i	0.539180	−	0.0455739i
$185$	8.34864	+	1.47209i	0.613804	+	0.108230i
$186$	−10.4422	+	5.39628i	−0.765657	+	0.395674i
$187$	5.70803	+	6.80257i	0.417413	+	0.497453i
$188$	−11.8768	−	14.2107i	−0.866202	−	1.03642i
$189$	11.5402	−	7.47157i	0.839424	−	0.543477i
$190$	−10.3101	−	4.82000i	−0.747974	−	0.349679i
$191$	0.692103	−	0.580743i	0.0500788	−	0.0420211i	−0.617405	−	0.786646i	$-0.711816\pi$
$191$	0.692103	−	0.580743i	0.0500788	−	0.0420211i	0.667484	+	0.744625i	$0.267371\pi$
$192$	−5.20144	−	12.8431i	−0.375382	−	0.926870i
$193$	−0.578734	+	3.28216i	−0.0416582	+	0.236255i	−0.998526	−	0.0542667i	$-0.982718\pi$
$193$	−0.578734	+	3.28216i	−0.0416582	+	0.236255i	0.956868	+	0.290522i	$0.0938290\pi$
$194$	10.5880	−	15.0896i	0.760171	−	1.08337i
$195$	0.470171	+	11.2881i	0.0336696	+	0.808358i
$196$	10.9441	+	8.73083i	0.781719	+	0.623631i
$197$	−11.0375	+	6.37251i	−0.786390	+	0.454023i	−0.838690	−	0.544609i	$-0.816678\pi$
$197$	−11.0375	+	6.37251i	−0.786390	+	0.454023i	0.0523001	+	0.998631i	$0.483345\pi$
$198$	15.1604	+	5.60378i	1.07740	+	0.398243i
$199$	−22.9079	+	13.2259i	−1.62390	+	0.937558i	−0.638035	+	0.770007i	$0.720253\pi$
$199$	−22.9079	+	13.2259i	−1.62390	+	0.937558i	−0.985863	+	0.167551i	$0.946414\pi$
$200$	−4.15427	+	1.92230i	−0.293751	+	0.135927i
$201$	6.37989	−	20.0938i	0.450003	−	1.41731i
$202$	−18.3673	−	12.8878i	−1.29232	−	0.906780i
$203$	25.7053	+	11.5711i	1.80416	+	0.812133i
$204$	−1.08571	+	8.00138i	−0.0760150	+	0.560209i
$205$	−2.12577	−	0.773717i	−0.148470	−	0.0540387i
$206$	4.59631	−	0.397583i	0.320240	−	0.0277009i
$207$	−7.75815	+	0.647407i	−0.539229	+	0.0449979i
$208$	−7.74354	−	6.54954i	−0.536918	−	0.454129i
$209$	−4.07596	+	11.1986i	−0.281940	+	0.774624i
$210$	16.5515	+	2.00465i	1.14216	+	0.138334i
$211$	17.9208	−	21.3572i	1.23372	−	1.47029i	0.401482	−	0.915867i	$-0.368495\pi$
$211$	17.9208	−	21.3572i	1.23372	−	1.47029i	0.832236	−	0.554421i	$-0.187060\pi$
$212$	4.89659	+	0.00960568i	0.336299	+	0.000659721i
$213$	−0.644678	+	4.82207i	−0.0441726	+	0.330403i
$214$	−10.0167	−	10.0364i	−0.684730	−	0.686074i
$215$	8.29119	+	14.3608i	0.565454	+	0.979395i
$216$	5.50241	+	13.6280i	0.374391	+	0.927271i
$217$	9.09644	+	8.85662i	0.617507	+	0.601227i
$218$	−3.14872	+	11.7052i	−0.213258	+	0.792779i
$219$	−16.6264	+	6.84783i	−1.12351	+	0.462734i
$220$	9.76742	+	16.9946i	0.658519	+	1.14577i
$221$	2.02138	+	5.55370i	0.135973	+	0.373583i
$222$	6.41834	−	4.89458i	0.430771	−	0.328503i
$223$	−2.91098	+	7.99785i	−0.194934	+	0.535576i	−0.998195	−	0.0600505i	$-0.980874\pi$
$223$	−2.91098	+	7.99785i	−0.194934	+	0.535576i	0.803262	+	0.595626i	$0.203096\pi$
$224$	−11.3834	+	9.71694i	−0.760584	+	0.649240i
$225$	4.40844	−	2.03420i	0.293896	−	0.135614i
$226$	−2.96577	+	6.34386i	−0.197280	+	0.421987i
$227$	−0.265707	−	1.50690i	−0.0176356	−	0.100016i	0.974719	−	0.223432i	$-0.0717262\pi$
$227$	−0.265707	−	1.50690i	−0.0176356	−	0.100016i	−0.992355	+	0.123416i	$0.960615\pi$
$228$	−10.0279	+	4.10717i	−0.664116	+	0.272004i
$229$	−10.7099	+	3.89807i	−0.707727	+	0.257592i	−0.670706	−	0.741723i	$-0.734009\pi$
$229$	−10.7099	+	3.89807i	−0.707727	+	0.257592i	−0.0370207	+	0.999314i	$0.511787\pi$
$230$	−7.72860	−	5.42293i	−0.509609	−	0.357577i
$231$	0.563465	−	17.4488i	0.0370733	−	1.14805i
$232$	−17.3578	+	24.6349i	−1.13960	+	1.61736i
$233$			8.98651i			0.588726i	0.955694	+	0.294363i	$0.0951074\pi$
$233$			8.98651i			0.588726i	−0.955694	+	0.294363i	$0.904893\pi$
$234$	8.20584	+	6.95561i	0.536432	+	0.454702i
$235$			23.8228i			1.55403i
$236$	2.50172	−	2.96958i	0.162848	−	0.193303i
$237$	4.56024	+	2.38554i	0.296219	+	0.154958i
$238$	8.56978	−	1.62069i	0.555496	−	0.105054i
$239$	1.53004	−	0.556890i	0.0989703	−	0.0360222i	−0.292060	−	0.956400i	$-0.594341\pi$
$239$	1.53004	−	0.556890i	0.0989703	−	0.0360222i	0.391031	+	0.920378i	$0.372119\pi$
$240$	−5.46036	+	16.9666i	−0.352465	+	1.09519i
$241$	22.9482	+	8.35247i	1.47823	+	0.538030i	0.950320	−	0.311273i	$-0.100755\pi$
$241$	22.9482	+	8.35247i	1.47823	+	0.538030i	0.527905	+	0.849303i	$0.322978\pi$
$242$	4.07278	−	2.84584i	0.261808	−	0.182938i
$243$	−5.82074	−	14.4609i	−0.373401	−	0.927670i
$244$	−3.66337	−	4.38326i	−0.234523	−	0.280610i
$245$	−3.59972	−	17.6449i	−0.229978	−	1.12729i
$246$	−1.91351	+	0.988861i	−0.122001	+	0.0630475i
$247$	−5.09828	+	6.07590i	−0.324396	+	0.386600i
$248$	−11.1408	+	7.75209i	−0.707439	+	0.492258i
$249$	−9.82480	−	15.4903i	−0.622622	−	0.981659i
$250$	−11.8808	−	3.19594i	−0.751407	−	0.202129i
$251$	−12.8315	−	22.2248i	−0.809918	−	1.40282i	−0.912920	−	0.408138i	$-0.866178\pi$
$251$	−12.8315	−	22.2248i	−0.809918	−	1.40282i	0.103002	−	0.994681i	$-0.467155\pi$
$252$	12.0849	−	10.2935i	0.761277	−	0.648427i
$253$	−4.94307	+	8.56165i	−0.310768	+	0.538266i
$254$	−17.6237	+	17.5892i	−1.10581	+	1.10365i
$255$	7.67185	−	7.00170i	0.480430	−	0.438463i
$256$	−7.89103	−	13.9188i	−0.493189	−	0.869922i
$257$	10.1519	+	27.8921i	0.633258	+	1.73986i	0.671934	+	0.740611i	$0.265464\pi$
$257$	10.1519	+	27.8921i	0.633258	+	1.73986i	−0.0386757	+	0.999252i	$0.512314\pi$
$258$	15.4042	+	3.46332i	0.959022	+	0.215617i
$259$	−7.20786	−	4.90484i	−0.447875	−	0.304772i
$260$	2.24015	+	12.8519i	0.138928	+	0.797041i
$261$	18.4386	−	26.1096i	1.14132	−	1.61614i
$262$	−5.86140	−	2.74022i	−0.362119	−	0.169291i
$263$	14.0016	−	11.7488i	0.863377	−	0.724460i	−0.0993156	−	0.995056i	$-0.531665\pi$
$263$	14.0016	−	11.7488i	0.863377	−	0.724460i	0.962693	+	0.270596i	$0.0872209\pi$
$264$	18.2007	+	4.12958i	1.12018	+	0.254158i
$265$	−4.82497	−	4.04863i	−0.296395	−	0.248705i
$266$	7.63402	+	8.87251i	0.468072	+	0.544008i
$267$	−14.4290	−	1.92906i	−0.883040	−	0.118056i
$268$	4.27427	−	23.9656i	0.261093	−	1.46393i
$269$	−8.35742	−	4.82516i	−0.509561	−	0.294195i	0.223092	−	0.974797i	$-0.428385\pi$
$269$	−8.35742	−	4.82516i	−0.509561	−	0.294195i	−0.732653	+	0.680602i	$0.761718\pi$
$270$	5.81081	−	17.9896i	0.353634	−	1.09481i
$271$	14.2072	−	8.20253i	0.863026	−	0.498268i	−0.00199839	−	0.999998i	$-0.500636\pi$
$271$	14.2072	−	8.20253i	0.863026	−	0.498268i	0.865024	+	0.501730i	$0.167303\pi$
$272$	−0.0365813	+	9.32380i	−0.00221807	+	0.565338i
$273$	4.32427	−	10.7844i	0.261717	−	0.652701i
$274$	2.31440	−	26.1582i	0.139818	−	1.58027i
$275$	1.07061	−	6.07176i	0.0645605	−	0.366141i
$276$	−8.78404	+	1.91085i	−0.528737	+	0.115020i
$277$	−7.53223	+	6.32029i	−0.452568	+	0.379749i	−0.840388	−	0.541986i	$-0.817673\pi$
$277$	−7.53223	+	6.32029i	−0.452568	+	0.379749i	0.387820	+	0.921735i	$0.373228\pi$
$278$	−13.3513	−	19.1075i	−0.800757	−	1.14599i
$279$	11.8253	−	8.20971i	0.707964	−	0.491502i
$280$	19.2507	−	0.200500i	1.15045	−	0.0119822i
$281$	−4.14273	−	4.93712i	−0.247135	−	0.294524i	0.628189	−	0.778061i	$-0.283796\pi$
$281$	−4.14273	−	4.93712i	−0.247135	−	0.294524i	−0.875324	+	0.483537i	$0.839352\pi$
$282$	16.6776	+	15.3740i	0.993134	+	0.915511i
$283$	−13.9515	+	16.6267i	−0.829329	+	0.988356i	0.170666	+	0.985329i	$0.445408\pi$
$283$	−13.9515	+	16.6267i	−0.829329	+	0.988356i	−0.999995	+	0.00302717i	$0.999036\pi$
$284$	−0.0110201	+	5.61758i	−0.000653920	+	0.333342i
$285$	13.2854	+	4.21819i	0.786962	+	0.249864i
$286$	13.1983	−	3.52259i	0.780429	−	0.208295i
$287$	1.66691	+	1.62297i	0.0983947	+	0.0958006i
$288$	8.35392	+	14.7720i	0.492260	+	0.870448i
$289$	−5.78330	+	10.0170i	−0.340194	+	0.589233i
$290$	37.4531	−	9.99616i	2.19932	−	0.586995i
$291$	−10.4649	+	20.0047i	−0.613461	+	1.17270i
$292$	−18.0017	+	10.3462i	−1.05347	+	0.605468i
$293$	−6.51340	−	17.8954i	−0.380517	−	1.04546i	−0.971139	−	0.238513i	$-0.923340\pi$
$293$	−6.51340	−	17.8954i	−0.380517	−	1.04546i	0.590622	−	0.806948i	$-0.298882\pi$
$294$	−14.6757	−	8.86707i	−0.855902	−	0.517138i
$295$	−4.91875	+	0.867309i	−0.286381	+	0.0504967i
$296$	6.60987	−	6.57108i	0.384191	−	0.381936i
$297$	−19.3001	−	4.40070i	−1.11990	−	0.255355i
$298$	−11.2432	−	16.0905i	−0.651301	−	0.932099i
$299$	−5.04033	+	4.22934i	−0.291490	+	0.244589i
$300$	4.74015	−	2.99344i	0.273673	−	0.172826i
$301$	−1.71312	−	16.9675i	−0.0987426	−	0.977990i
$302$	0.126206	−	0.0587003i	0.00726235	−	0.00337782i
$303$	24.3500	+	12.7379i	1.39887	+	0.731775i
$304$	−10.8609	+	6.21385i	−0.622915	+	0.356389i
$305$			7.34811i			0.420752i
$306$	0.0493643	−	9.88933i	0.00282197	−	0.565335i
$307$	−8.21437	−	4.74257i	−0.468819	−	0.270673i	0.246926	−	0.969034i	$-0.420579\pi$
$307$	−8.21437	−	4.74257i	−0.468819	−	0.270673i	−0.715745	+	0.698362i	$0.753913\pi$
$308$	−1.98567	−	20.0606i	−0.113144	−	1.14306i
$309$	−5.51884	+	1.21189i	−0.313956	+	0.0689420i
$310$	17.3905	+	1.53866i	0.987711	+	0.0873898i
$311$	13.2569	+	11.1238i	0.751727	+	0.630774i	0.935959	−	0.352109i	$-0.114535\pi$
$311$	13.2569	+	11.1238i	0.751727	+	0.630774i	−0.184232	+	0.982883i	$0.558980\pi$
$312$	10.4429	+	6.72570i	0.591210	+	0.380768i
$313$	−2.25199	−	0.819656i	−0.127290	−	0.0463297i	0.277590	−	0.960700i	$-0.410464\pi$
$313$	−2.25199	−	0.819656i	−0.127290	−	0.0463297i	−0.404880	+	0.914370i	$0.632687\pi$
$314$	−13.6860	+	9.56303i	−0.772344	+	0.539673i
$315$	−20.4187	+	0.190851i	−1.15046	+	0.0107532i
$316$	5.58029	+	2.04347i	0.313916	+	0.114954i
$317$	24.3252	−	4.28919i	1.36624	−	0.240905i	0.558040	−	0.829814i	$-0.311554\pi$
$317$	24.3252	−	4.28919i	1.36624	−	0.240905i	0.808199	+	0.588910i	$0.200443\pi$
$318$	−5.94809	+	0.765018i	−0.333552	+	0.0429001i
$319$	−13.8827	−	38.1424i	−0.777282	−	2.13556i
$320$	−3.69307	+	20.2469i	−0.206449	+	1.13184i
$321$	13.7566	+	10.5997i	0.767817	+	0.591617i
$322$	4.95857	+	8.34816i	0.276330	+	0.465225i
$323$	7.29175			0.405724
$324$	−8.84393	−	15.6775i	−0.491329	−	0.870974i
$325$	2.05169	−	3.55362i	0.113807	−	0.197120i
$326$	22.0701	−	22.0268i	1.22235	−	1.21995i
$327$	1.96725	−	14.7146i	0.108789	−	0.813722i
$328$	−2.04153	+	1.42056i	−0.112725	+	0.0784374i
$329$	10.0567	−	22.3409i	0.554441	−	1.23169i
$330$	−14.5575	−	19.0894i	−0.801363	−	1.05084i
$331$	14.5124	−	2.55893i	0.797674	−	0.140651i	0.240067	−	0.970756i	$-0.422831\pi$
$331$	14.5124	−	2.55893i	0.797674	−	0.140651i	0.557607	+	0.830105i	$0.311720\pi$
$332$	−13.5830	−	16.2523i	−0.745466	−	0.891960i
$333$	−7.01826	+	6.96219i	−0.384598	+	0.381526i
$334$	−16.9232	−	7.91163i	−0.925995	−	0.432905i
$335$	−23.9877	+	20.1280i	−1.31059	+	1.09971i
$336$	12.2830	−	13.6061i	0.670095	−	0.742276i
$337$	4.61783	−	26.1890i	0.251549	−	1.42661i	−0.553228	−	0.833030i	$-0.686604\pi$
$337$	4.61783	−	26.1890i	0.251549	−	1.42661i	0.804777	−	0.593577i	$-0.202285\pi$
$338$	−9.25709	−	0.819041i	−0.503519	−	0.0445499i
$339$	2.59547	−	8.17459i	0.140967	−	0.443983i
$340$	7.72721	−	9.17233i	0.419067	−	0.497439i
$341$		−	18.2808i		−	0.989963i
$342$	11.5267	−	6.57848i	0.623295	−	0.355723i
$343$	−4.07288	+	18.0669i	−0.219915	+	0.975519i
$344$	18.1571	+	1.64239i	0.978965	+	0.0885518i
$345$	10.2460	+	5.35988i	0.551627	+	0.288566i
$346$	2.03216	−	22.9682i	0.109249	−	1.23478i
$347$	−2.84375	+	16.1277i	−0.152661	+	0.865781i	0.808233	+	0.588863i	$0.200424\pi$
$347$	−2.84375	+	16.1277i	−0.152661	+	0.865781i	−0.960894	+	0.276918i	$0.910687\pi$
$348$	17.1723	−	32.6706i	0.920533	−	1.75133i
$349$	−0.276734	−	1.56944i	−0.0148132	−	0.0840099i	0.976505	−	0.215495i	$-0.0691365\pi$
$349$	−0.276734	−	1.56944i	−0.0148132	−	0.0840099i	−0.991318	+	0.131485i	$0.958025\pi$
$350$	−4.68653	−	3.83464i	−0.250506	−	0.204970i
$351$	−11.0687	−	7.14551i	−0.590803	−	0.381399i
$352$	21.4590	+	1.98352i	1.14377	+	0.105722i
$353$	7.65932	−	21.0438i	0.407665	−	1.12005i	−0.550750	−	0.834670i	$-0.685658\pi$
$353$	7.65932	−	21.0438i	0.407665	−	1.12005i	0.958415	−	0.285379i	$-0.0921195\pi$
$354$	−2.56714	+	4.00316i	−0.136442	+	0.212766i
$355$	4.64476	−	5.53541i	0.246518	−	0.293789i
$356$	−16.8094	−	0.0329751i	−0.890895	−	0.00174768i
$357$	−10.1503	+	3.32753i	−0.537212	+	0.176111i
$358$	14.1984	+	14.2262i	0.750407	+	0.751880i
$359$	10.2887	−	17.8205i	0.543015	−	0.940529i	−0.455714	−	0.890126i	$-0.650616\pi$
$359$	10.2887	−	17.8205i	0.543015	−	0.940529i	0.998729	−	0.0504032i	$-0.0160506\pi$
$360$	3.94003	−	21.4709i	0.207658	−	1.13162i
$361$	−4.60716	−	7.97983i	−0.242482	−	0.419991i
$362$	−19.5655	−	19.6039i	−1.02834	−	1.03036i
$363$	−4.49471	+	4.10209i	−0.235911	+	0.215304i
$364$	3.32455	−	12.9981i	0.174254	−	0.681285i
$365$	26.3020	+	4.63775i	1.37671	+	0.242751i
$366$	5.14416	+	4.74209i	0.268890	+	0.247873i
$367$	−21.2669	+	3.74993i	−1.11012	+	0.195745i	−0.698500	−	0.715610i	$-0.746149\pi$
$367$	−21.2669	+	3.74993i	−1.11012	+	0.195745i	−0.411623	+	0.911354i	$0.635038\pi$
$368$	−9.76801	+	3.51193i	−0.509193	+	0.183072i
$369$	2.16698	−	1.50442i	0.112808	−	0.0783169i
$370$	−11.9443	+	1.03319i	−0.620954	+	0.0537128i
$371$	2.81572	+	5.83360i	0.146185	+	0.302866i
$372$	12.3001	−	11.1815i	0.637729	−	0.579733i
$373$	3.54205	−	20.0880i	0.183401	−	1.04012i	−0.744593	−	0.667519i	$-0.767356\pi$
$373$	3.54205	−	20.0880i	0.183401	−	1.04012i	0.927993	−	0.372597i	$-0.121533\pi$
$374$	−10.2802	−	7.21328i	−0.531574	−	0.372990i
$375$	14.9353	+	1.99675i	0.771257	+	0.103112i
$376$	21.4106	+	15.0860i	1.10417	+	0.778000i
$377$		−	27.0147i		−	1.39133i
$378$	−13.0435	+	14.4176i	−0.670887	+	0.741559i
$379$			28.3838i			1.45798i	0.684527	+	0.728988i	$0.260009\pi$
$379$			28.3838i			1.45798i	−0.684527	+	0.728988i	$0.739991\pi$
$380$	15.8453	+	2.82602i	0.812849	+	0.144972i
$381$	18.6129	−	24.1563i	0.953566	−	1.23756i
$382$	−0.733890	+	1.04592i	−0.0375491	+	0.0535138i
$383$	−1.70382	+	9.66286i	−0.0870613	+	0.493749i	0.909831	+	0.414978i	$0.136211\pi$
$383$	−1.70382	+	9.66286i	−0.0870613	+	0.493749i	−0.996893	+	0.0787711i	$0.974900\pi$
$384$	11.7909	+	15.6517i	0.601699	+	0.798723i
$385$	−14.5880	+	21.4376i	−0.743472	+	1.09256i
$386$	−0.406184	−	4.69575i	−0.0206742	−	0.239007i
$387$	−19.2566	−	1.76259i	−0.978870	−	0.0895975i
$388$	−8.96424	+	24.4795i	−0.455090	+	1.24276i
$389$	35.4782	−	6.25576i	1.79882	−	0.317180i	0.828676	−	0.559728i	$-0.189095\pi$
$389$	35.4782	−	6.25576i	1.79882	−	0.317180i	0.970139	+	0.242549i	$0.0779835\pi$
$390$	−4.75904	−	15.2524i	−0.240983	−	0.772336i
$391$	5.95705	+	1.05039i	0.301261	+	0.0531205i
$392$	−18.1378	−	7.93852i	−0.916097	−	0.400956i
$393$	7.55291	+	2.39809i	0.380994	+	0.120967i
$394$	12.7575	−	12.7325i	0.642714	−	0.641455i
$395$	−3.82206	−	6.62001i	−0.192309	−	0.333089i
$396$	−22.7585	−	2.12815i	−1.14366	−	0.106944i
$397$	−1.74420	+	3.02104i	−0.0875387	+	0.151622i	−0.906470	−	0.422270i	$-0.861233\pi$
$397$	−1.74420	+	3.02104i	−0.0875387	+	0.151622i	0.818931	+	0.573891i	$0.194567\pi$
$398$	26.4777	−	26.4258i	1.32721	−	1.32461i
$399$	−10.6783	−	9.56415i	−0.534584	−	0.478806i
$400$	4.97528	−	4.14160i	0.248764	−	0.207080i
$401$	−7.43527	+	8.86101i	−0.371300	+	0.442498i	−0.919048	−	0.394145i	$-0.871041\pi$
$401$	−7.43527	+	8.86101i	−0.371300	+	0.442498i	0.547748	+	0.836643i	$0.315485\pi$
$402$	−1.38945	+	29.7825i	−0.0692996	+	1.48542i
$403$	4.16127	−	11.4330i	0.207288	−	0.569518i
$404$	29.7967	+	10.9114i	1.48244	+	0.542861i
$405$	−4.20335	+	22.7688i	−0.208866	+	1.13139i
$406$	−39.3431	−	6.43624i	−1.95256	−	0.319425i
$407$	2.17993	+	12.3630i	0.108055	+	0.612810i
$408$	−1.43449	−	11.3289i	−0.0710178	−	0.560864i
$409$	−4.28017	+	24.2741i	−0.211641	+	1.20028i	0.675000	+	0.737817i	$0.264143\pi$
$409$	−4.28017	+	24.2741i	−0.211641	+	1.20028i	−0.886641	+	0.462458i	$0.846968\pi$
$410$	3.18678	+	0.281957i	0.157384	+	0.0139249i
$411$	1.33846	+	32.1344i	0.0660213	+	1.58507i
$412$	−6.13533	+	2.21946i	−0.302266	+	0.109345i
$413$	4.97890	+	1.26306i	0.244996	+	0.0621512i
$414$	10.3645	−	3.71389i	0.509388	−	0.182528i
$415$			27.2454i			1.33742i
$416$	12.9692	+	6.12523i	0.635866	+	0.300314i
$417$	19.2450	+	21.0869i	0.942430	+	1.03263i
$418$	1.48536	−	16.7880i	0.0726512	−	0.821130i
$419$	3.89825	−	22.1081i	0.190442	−	1.08005i	−0.728320	−	0.685238i	$-0.759698\pi$
$419$	3.89825	−	22.1081i	0.190442	−	1.08005i	0.918762	−	0.394813i	$-0.129191\pi$
$420$	−23.3468	+	3.29698i	−1.13921	+	0.160876i
$421$	−24.4916	+	20.5509i	−1.19365	+	1.00159i	−0.193858	+	0.981030i	$0.562100\pi$
$421$	−24.4916	+	20.5509i	−1.19365	+	1.00159i	−0.999789	+	0.0205593i	$0.993455\pi$
$422$	−16.6980	+	35.7175i	−0.812847	+	1.73870i
$423$	−22.6923	−	16.0253i	−1.10334	−	0.779179i
$424$	−6.69412	+	1.77259i	−0.325095	+	0.0860846i
$425$	−3.71507	+	0.655068i	−0.180208	+	0.0317755i
$426$	−0.877661	−	6.82391i	−0.0425228	−	0.330619i
$427$	3.10196	−	6.89101i	0.150114	−	0.333479i
$428$	17.3468	+	10.0606i	0.838491	+	0.486299i
$429$	−15.4696	+	6.37141i	−0.746880	+	0.307614i
$430$	−16.5661	−	16.5986i	−0.798888	−	0.800457i
$431$	16.2263	−	28.1048i	0.781595	−	1.35376i	−0.149417	−	0.988774i	$-0.547740\pi$
$431$	16.2263	−	28.1048i	0.781595	−	1.35376i	0.931012	−	0.364989i	$-0.118927\pi$
$432$	−12.4883	−	16.6145i	−0.600846	−	0.799365i
$433$	−0.969845			−0.0466078			−0.0233039	−	0.999728i	$-0.507419\pi$
$433$	−0.969845			−0.0466078			−0.0233039	+	0.999728i	$0.507419\pi$
$434$	−15.6591	−	8.78421i	−0.751661	−	0.421655i
$435$	−43.8986	+	18.0803i	−2.10478	+	0.866886i
$436$	0.0336279	−	17.1421i	0.00161048	−	0.820960i
$437$	2.77646	+	7.62826i	0.132816	+	0.364909i
$438$	20.2207	−	15.4202i	0.966182	−	0.736804i
$439$	13.1104	−	2.31172i	0.625727	−	0.110332i	0.148211	−	0.988956i	$-0.452649\pi$
$439$	13.1104	−	2.31172i	0.625727	−	0.110332i	0.477516	+	0.878623i	$0.341537\pi$
$440$	−19.5437	−	19.6591i	−0.931710	−	0.937209i
$441$	19.2290	+	8.44062i	0.915669	+	0.401934i
$442$	−4.78734	−	6.85132i	−0.227711	−	0.325884i
$443$	32.9069	+	11.9771i	1.56346	+	0.569051i	0.971525	−	0.236938i	$-0.0761437\pi$
$443$	32.9069	+	11.9771i	1.56346	+	0.569051i	0.591931	+	0.805989i	$0.298366\pi$
$444$	−6.98494	+	9.02856i	−0.331490	+	0.428476i
$445$	16.5635	+	13.8984i	0.785185	+	0.658848i
$446$	1.06082	−	11.9897i	0.0502311	−	0.567730i
$447$	16.2063	+	17.7575i	0.766533	+	0.839899i
$448$	12.0104	−	17.4284i	0.567440	−	0.823415i
$449$	9.51446	+	5.49318i	0.449015	+	0.259239i	0.707414	−	0.706799i	$-0.249862\pi$
$449$	9.51446	+	5.49318i	0.449015	+	0.259239i	−0.258399	+	0.966038i	$0.583195\pi$
$450$	−5.28178	+	4.38720i	−0.248985	+	0.206814i
$451$		−	3.34994i		−	0.157743i
$452$	1.73887	−	9.74971i	0.0817893	−	0.458588i
$453$	−0.143958	+	0.0913058i	−0.00676372	+	0.00428992i
$454$	0.912601	+	1.96210i	0.0428305	+	0.0920859i
$455$	−14.0033	+	10.0866i	−0.656484	+	0.472868i
$456$	12.2042	−	9.26901i	0.571513	−	0.434061i
$457$	−0.543656	+	0.456182i	−0.0254312	+	0.0213393i	−0.655415	−	0.755269i	$-0.727506\pi$
$457$	−0.543656	+	0.456182i	−0.0254312	+	0.0213393i	0.629983	+	0.776609i	$0.283062\pi$
$458$	13.2122	−	9.23198i	0.617366	−	0.431382i
$459$	1.50867	+	12.0177i	0.0704186	+	0.560940i
$460$	12.5379	+	4.59129i	0.584582	+	0.214070i
$461$	−8.25439	+	1.45547i	−0.384445	+	0.0677881i	−0.362531	−	0.931972i	$-0.618087\pi$
$461$	−8.25439	+	1.45547i	−0.384445	+	0.0677881i	−0.0219145	+	0.999760i	$0.506976\pi$
$462$	5.59342	+	24.0473i	0.260230	+	1.11878i
$463$	1.48089	+	4.06872i	0.0688229	+	0.189089i	0.969336	−	0.245740i	$-0.0790309\pi$
$463$	1.48089	+	4.06872i	0.0688229	+	0.189089i	−0.900513	+	0.434829i	$0.856809\pi$
$464$	14.7334	−	39.9909i	0.683983	−	1.85653i
$465$	−21.3635	+	0.889832i	−0.990711	+	0.0412650i
$466$	−3.27725	−	12.2790i	−0.151816	−	0.568815i
$467$	−13.0050	+	22.5253i	−0.601798	+	1.04234i	0.390751	+	0.920496i	$0.372215\pi$
$467$	−13.0050	+	22.5253i	−0.601798	+	1.04234i	−0.992549	+	0.121848i	$0.961118\pi$
$468$	−13.7489	−	6.51148i	−0.635544	−	0.300993i
$469$	30.9924	−	8.74970i	1.43109	−	0.404024i
$470$	−8.68784	−	32.5511i	−0.400740	−	1.50147i
$471$	15.1038	−	13.7845i	0.695947	−	0.635155i
$472$	−2.33534	+	4.96993i	−0.107493	+	0.228759i
$473$	−15.7842	+	18.8108i	−0.725756	+	0.864922i
$474$	−7.10100	−	1.59652i	−0.326160	−	0.0733305i
$475$	−3.25419	−	3.87819i	−0.149313	−	0.177944i
$476$	−11.1186	+	5.33976i	−0.509618	+	0.244747i
$477$	7.10220	−	1.87253i	0.325187	−	0.0857372i
$478$	−1.88754	+	1.31891i	−0.0863339	+	0.0603255i
$479$	−32.7401	+	27.4722i	−1.49593	+	1.25524i	−0.609147	+	0.793057i	$0.708488\pi$
$479$	−32.7401	+	27.4722i	−1.49593	+	1.25524i	−0.886786	+	0.462180i	$0.847067\pi$
$480$	1.27346	−	25.1742i	0.0581254	−	1.14904i
$481$	−1.45084	+	8.22812i	−0.0661526	+	0.375170i
$482$	−34.4021	−	3.04380i	−1.56697	−	0.138641i
$483$	−7.34600	−	9.35174i	−0.334255	−	0.425519i
$484$	−4.52714	+	5.37380i	−0.205779	+	0.244263i
$485$	29.0405	−	16.7666i	1.31866	−	0.761330i
$486$	13.2271	+	17.6365i	0.599992	+	0.800006i
$487$	23.9371	+	13.8201i	1.08470	+	0.626249i	0.932159	−	0.362049i	$-0.117923\pi$
$487$	23.9371	+	13.8201i	1.08470	+	0.626249i	0.152536	+	0.988298i	$0.451256\pi$
$488$	6.60408	+	4.65324i	0.298952	+	0.210642i
$489$	−23.3088	+	30.2508i	−1.05406	+	1.36799i
$490$	11.3534	+	22.7969i	0.512896	+	1.02986i
$491$	12.9259	+	10.8462i	0.583340	+	0.489480i	0.886042	−	0.463605i	$-0.153444\pi$
$491$	12.9259	+	10.8462i	0.583340	+	0.489480i	−0.302702	+	0.953085i	$0.597889\pi$
$492$	2.25397	−	2.04899i	0.101617	−	0.0923758i
$493$	−19.0252	+	15.9640i	−0.856852	+	0.718984i
$494$	4.75042	−	10.1613i	0.213732	−	0.457177i
$495$	20.7069	+	20.8737i	0.930708	+	0.938204i
$496$	12.3955	−	14.6552i	0.556574	−	0.658038i
$497$	−6.69256	+	3.23031i	−0.300202	+	0.144899i
$498$	19.0735	+	17.5828i	0.854706	+	0.787902i
$499$	−7.37180	−	20.2539i	−0.330007	−	0.906687i	−0.988109	−	0.153758i	$-0.950862\pi$
$499$	−7.37180	−	20.2539i	−0.330007	−	0.906687i	0.658101	−	0.752929i	$-0.271360\pi$
$500$	17.3992	+	0.0341322i	0.778117	+	0.00152644i
$501$	21.8069	+	6.92381i	0.974262	+	0.309333i
$502$	25.6378	+	25.6882i	1.14427	+	1.14652i
$503$	17.2098	−	29.8083i	0.767348	−	1.32909i	−0.171649	−	0.985158i	$-0.554909\pi$
$503$	17.2098	−	29.8083i	0.767348	−	1.32909i	0.938996	−	0.343927i	$-0.111757\pi$
$504$	−12.7587	+	18.4720i	−0.568319	+	0.822808i
$505$	−20.4084	−	35.3484i	−0.908163	−	1.57298i
$506$	3.63182	−	13.5012i	0.161454	−	0.600200i
$507$	11.3720	−	0.473666i	0.505048	−	0.0210362i
$508$	17.6663	−	30.4607i	0.783814	−	1.35148i
$509$	−15.1241	+	18.0242i	−0.670362	+	0.798907i	−0.988833	−	0.149026i	$-0.952386\pi$
$509$	−15.1241	+	18.0242i	−0.670362	+	0.798907i	0.318471	+	0.947933i	$0.396831\pi$
$510$	−7.92927	+	12.3648i	−0.351114	+	0.547523i
$511$	−22.7080	−	15.4525i	−1.00454	−	0.683577i
$512$	15.8581	+	16.1406i	0.700837	+	0.713321i
$513$	−12.9550	+	9.81744i	−0.571976	+	0.433451i
$514$	−24.0432	−	34.4091i	−1.06050	−	1.51772i
$515$	7.88633	+	2.87039i	0.347513	+	0.126484i
$516$	−22.3110	+	0.885457i	−0.982189	+	0.0389801i
$517$	−33.1502	+	12.0657i	−1.45795	+	0.530649i
$518$	11.6374	+	4.07329i	0.511319	+	0.178970i
$519$	1.17523	+	28.2156i	0.0515870	+	1.23853i
$520$	−7.74781	−	16.7437i	−0.339764	−	0.734259i
$521$		−	42.3214i		−	1.85414i	−0.374894	−	0.927068i	$-0.622321\pi$
$521$		−	42.3214i		−	1.85414i	0.374894	−	0.927068i	$-0.377679\pi$
$522$	−15.6725	+	42.4000i	−0.685965	+	1.85580i
$523$		−	20.5075i		−	0.896732i	−0.893850	−	0.448366i	$-0.852006\pi$
$523$		−	20.5075i		−	0.896732i	0.893850	−	0.448366i	$-0.147994\pi$
$524$	9.00824	+	1.60662i	0.393527	+	0.0701857i
$525$	6.29971	+	3.91354i	0.274942	+	0.170801i
$526$	−14.8470	+	21.1595i	−0.647360	+	0.922598i
$527$	−10.5108	+	3.82561i	−0.457857	+	0.166646i
$528$	−26.3751	+	0.994931i	−1.14783	+	0.0432988i
$529$	−2.82452	−	16.0187i	−0.122805	−	0.696463i
$530$	8.06923	+	3.77238i	0.350505	+	0.163862i
$531$	2.48264	−	5.26876i	0.107737	−	0.228645i
$532$	−13.6667	−	9.33923i	−0.592525	−	0.404907i
$533$	0.762548	−	2.09508i	0.0330296	−	0.0907481i
$534$	20.4190	−	2.62621i	0.883618	−	0.113647i
$535$	−8.82226	−	24.2390i	−0.381420	−	1.04794i
$536$	2.89961	+	34.3050i	0.125244	+	1.48175i
$537$	−19.4994	−	15.0247i	−0.841463	−	0.648363i
$538$	13.1791	+	3.54519i	0.568192	+	0.152844i
$539$	22.7303	−	13.9458i	0.979061	−	0.600690i
$540$	−1.37923	+	26.6999i	−0.0593528	+	1.14898i
$541$	−7.39837	−	12.8144i	−0.318081	−	0.550932i	0.662007	−	0.749498i	$-0.269705\pi$
$541$	−7.39837	−	12.8144i	−0.318081	−	0.550932i	−0.980088	+	0.198566i	$0.936372\pi$
$542$	−16.4211	+	16.3890i	−0.705349	+	0.703966i
$543$	26.8704	+	20.7041i	1.15312	+	0.888499i
$544$	−3.35027	−	12.7532i	−0.143642	−	0.546790i
$545$	−14.1736	+	16.8914i	−0.607129	+	0.723548i
$546$	−1.97571	+	16.3126i	−0.0845526	+	0.698115i
$547$	6.22500	−	17.1031i	0.266162	−	0.731274i	−0.732559	−	0.680704i	$-0.761674\pi$
$547$	6.22500	−	17.1031i	0.266162	−	0.731274i	0.998721	−	0.0505699i	$-0.0161038\pi$
$548$	6.37714	+	36.5861i	0.272418	+	1.56288i
$549$	−6.99940	−	4.94299i	−0.298727	−	0.210962i
$550$	0.751410	+	8.68679i	0.0320402	+	0.370406i
$551$	−31.3199	−	11.3995i	−1.33427	−	0.485636i
$552$	11.3055	−	5.81436i	0.481195	−	0.247476i
$553$	0.789713	+	7.82166i	0.0335820	+	0.332611i
$554$	7.98699	−	11.3828i	0.339335	−	0.483610i
$555$	14.3416	−	3.14930i	0.608768	−	0.133680i
$556$	25.2112	+	21.2391i	1.06919	+	0.900739i
$557$	−28.7308	+	16.5877i	−1.21736	+	0.702846i	−0.964353	−	0.264618i	$-0.914754\pi$
$557$	−28.7308	+	16.5877i	−1.21736	+	0.702846i	−0.253011	+	0.967463i	$0.581421\pi$
$558$	−13.1640	+	15.5301i	−0.557276	+	0.657443i
$559$	−14.1535	+	8.17150i	−0.598627	+	0.345618i
$560$	−26.2307	+	7.29440i	−1.10845	+	0.308245i
$561$	13.6287	+	7.12942i	0.575404	+	0.301004i
$562$	7.46106	+	5.23520i	0.314726	+	0.220834i
$563$	4.75439	−	26.9635i	0.200374	−	1.13638i	−0.704182	−	0.710020i	$-0.748686\pi$
$563$	4.75439	−	26.9635i	0.200374	−	1.13638i	0.904555	−	0.426356i	$-0.140203\pi$
$564$	−28.3946	−	14.9248i	−1.19563	−	0.628446i
$565$	−9.75868	+	8.18851i	−0.410551	+	0.344493i
$566$	12.9995	−	27.8064i	0.546412	−	1.16879i
$567$	13.5536	−	19.5781i	0.569197	−	0.822201i
$568$	−2.03359	−	7.67979i	−0.0853276	−	0.322237i
$569$	21.2730	+	25.3521i	0.891809	+	1.06282i	0.997656	+	0.0684341i	$0.0218003\pi$
$569$	21.2730	+	25.3521i	0.891809	+	1.06282i	−0.105847	+	0.994382i	$0.533755\pi$
$570$	−19.6913	−	0.918665i	−0.824779	−	0.0384786i
$571$	−4.95256	−	0.873270i	−0.207258	−	0.0365452i	0.0690550	−	0.997613i	$-0.478002\pi$
$571$	−4.95256	−	0.873270i	−0.207258	−	0.0365452i	−0.276313	+	0.961068i	$0.589113\pi$
$572$	−16.7492	+	9.62642i	−0.700321	+	0.402501i
$573$	0.725357	−	1.38660i	0.0303022	−	0.0579261i
$574$	−2.86951	−	1.60970i	−0.119771	−	0.0671874i
$575$	−2.09988	−	3.63709i	−0.0875709	−	0.151677i
$576$	−16.8018	−	17.1377i	−0.700075	−	0.714070i
$577$	12.7319	+	22.0523i	0.530037	+	0.918050i	0.999386	+	0.0350377i	$0.0111551\pi$
$577$	12.7319	+	22.0523i	0.530037	+	0.918050i	−0.469349	+	0.883013i	$0.655512\pi$
$578$	4.24916	−	15.7961i	0.176742	−	0.657031i
$579$	1.23811	+	5.63824i	0.0514541	+	0.234317i
$580$	−47.5299	+	27.3172i	−1.97357	+	1.13428i
$581$	11.5014	−	25.5505i	0.477160	−	1.06001i
$582$	7.00357	−	31.1505i	0.290307	−	1.29123i
$583$	3.19006	−	8.76462i	0.132119	−	0.362994i
$584$	20.8241	−	20.7019i	0.861706	−	0.856650i
$585$	8.19881	+	17.7681i	0.338979	+	0.734622i
$586$	15.4260	+	22.0767i	0.637242	+	0.911979i
$587$	−5.56147	−	2.02421i	−0.229546	−	0.0835480i	0.224686	−	0.974431i	$-0.427864\pi$
$587$	−5.56147	−	2.02421i	−0.229546	−	0.0835480i	−0.454233	+	0.890883i	$0.650086\pi$
$588$	23.2863	+	6.76381i	0.960310	+	0.278935i
$589$	−11.4991	−	9.64887i	−0.473811	−	0.397575i
$590$	6.40461	−	2.97887i	0.263673	−	0.122638i
$591$	−13.4735	+	17.4863i	−0.554226	+	0.719291i
$592$	−6.63524	+	11.3891i	−0.272707	+	0.468091i
$593$	3.57798	−	2.06575i	0.146930	−	0.0848300i	−0.424733	−	0.905319i	$-0.639632\pi$
$593$	3.57798	−	2.06575i	0.146930	−	0.0848300i	0.571663	+	0.820489i	$0.306299\pi$
$594$	27.9762	−	1.02540i	1.14788	−	0.0420727i
$595$	15.3786	+	3.90130i	0.630462	+	0.159938i
$596$	21.2305	+	17.8856i	0.869636	+	0.732623i
$597$	−27.9637	+	36.2921i	−1.14448	+	1.48534i
$598$	5.34464	−	7.61703i	0.218559	−	0.311484i
$599$	13.9819	−	5.08899i	0.571284	−	0.207930i	−0.0401940	−	0.999192i	$-0.512798\pi$
$599$	13.9819	−	5.08899i	0.571284	−	0.207930i	0.611478	+	0.791262i	$0.290575\pi$
$600$	−5.38521	+	5.81886i	−0.219850	+	0.237554i
$601$	−23.1357	−	8.42071i	−0.943725	−	0.343488i	−0.176089	−	0.984374i	$-0.556345\pi$
$601$	−23.1357	−	8.42071i	−0.943725	−	0.343488i	−0.767636	+	0.640886i	$0.778567\pi$
$602$	8.52857	+	22.5594i	0.347599	+	0.919451i
$603$	−3.03663	−	36.3892i	−0.123661	−	1.48188i
$604$	−0.151039	+	0.126233i	−0.00614569	+	0.00513633i
$605$	8.90104	−	1.56949i	0.361879	−	0.0638090i
$606$	−37.9168	−	8.52482i	−1.54026	−	0.346297i
$607$	1.21417	+	3.33590i	0.0492816	+	0.135400i	0.961892	−	0.273431i	$-0.0881586\pi$
$607$	1.21417	+	3.33590i	0.0492816	+	0.135400i	−0.912610	+	0.408831i	$0.865936\pi$
$608$	12.5740	−	12.4513i	0.509945	−	0.504967i
$609$	48.8003	+	1.57588i	1.97749	+	0.0638579i
$610$	−2.67975	−	10.0403i	−0.108500	−	0.406522i
$611$	−23.4790			−0.949857
$612$	3.53904	+	13.5306i	0.143057	+	0.546943i
$613$	38.3917			1.55063			0.775313	−	0.631577i	$-0.217592\pi$
$613$	38.3917			1.55063			0.775313	+	0.631577i	$0.217592\pi$
$614$	12.9535	+	3.48451i	0.522762	+	0.140623i
$615$	−3.91484	+	0.163061i	−0.157862	+	0.00657524i
$616$	10.0290	+	26.6864i	0.404080	+	1.07522i
$617$	−13.5767	−	37.3017i	−0.546577	−	1.50171i	−0.838302	−	0.545207i	$-0.816451\pi$
$617$	−13.5767	−	37.3017i	−0.546577	−	1.50171i	0.291724	−	0.956502i	$-0.405771\pi$
$618$	7.09889	−	3.66855i	0.285559	−	0.147571i
$619$	1.93031	−	5.30350i	0.0775859	−	0.213166i	−0.894836	−	0.446396i	$-0.852707\pi$
$619$	1.93031	−	5.30350i	0.0775859	−	0.213166i	0.972422	+	0.233230i	$0.0749296\pi$
$620$	−24.3232	+	4.23965i	−0.976841	+	0.170268i
$621$	−11.9979	+	6.15425i	−0.481459	+	0.246962i
$622$	−22.1707	−	10.3648i	−0.888962	−	0.415592i
$623$	−9.66600	−	20.0260i	−0.387260	−	0.802325i
$624$	−16.7217	−	5.38154i	−0.669404	−	0.215434i
$625$	−23.3435	−	19.5875i	−0.933739	−	0.783500i
$626$	3.37599	+	0.298698i	0.134932	+	0.0119384i
$627$	0.859009	+	20.6235i	0.0343055	+	0.823624i
$628$	15.2128	−	18.0578i	0.607057	−	0.720587i
$629$	6.65205	−	3.84056i	0.265234	−	0.153133i
$630$	27.8301	−	7.70716i	1.10878	−	0.307061i
$631$	15.3983	+	8.89022i	0.612997	+	0.353914i	0.774138	−	0.633017i	$-0.218184\pi$
$631$	15.3983	+	8.89022i	0.612997	+	0.353914i	−0.161140	+	0.986932i	$0.551517\pi$
$632$	−8.37004	−	0.757108i	−0.332942	−	0.0301161i
$633$	14.6132	−	46.0250i	0.580822	−	1.82933i
$634$	−31.6733	+	14.7317i	−1.25791	+	0.585071i
$635$	−42.5632	+	15.4917i	−1.68907	+	0.614771i
$636$	7.84838	−	3.21449i	0.311209	−	0.127463i
$637$	17.3902	−	3.54776i	0.689024	−	0.140567i
$638$	32.8791	+	47.0543i	1.30169	+	1.86290i
$639$	2.14825	+	8.14794i	0.0849833	+	0.322328i
$640$	−2.33761	−	29.0119i	−0.0924020	−	1.14679i
$641$	−5.41425	−	6.45245i	−0.213850	−	0.254857i	0.648447	−	0.761260i	$-0.275419\pi$
$641$	−5.41425	−	6.45245i	−0.213850	−	0.254857i	−0.862297	+	0.506404i	$0.830975\pi$
$642$	−22.6623	−	9.46642i	−0.894410	−	0.373610i
$643$	13.6640	−	16.2842i	0.538857	−	0.642185i	−0.426074	−	0.904688i	$-0.640104\pi$
$643$	13.6640	−	16.2842i	0.538857	−	0.642185i	0.964931	+	0.262503i	$0.0845480\pi$
$644$	−9.81976	−	9.59847i	−0.386953	−	0.378233i
$645$	22.7512	+	17.5302i	0.895828	+	0.690251i
$646$	−9.96333	+	2.65919i	−0.392002	+	0.104625i
$647$	−10.8302	+	18.7585i	−0.425780	+	0.737473i	−0.996493	−	0.0836769i	$-0.973334\pi$
$647$	−10.8302	+	18.7585i	−0.425780	+	0.737473i	0.570713	+	0.821150i	$0.306667\pi$
$648$	17.8016	+	18.1963i	0.699312	+	0.714817i
$649$	−3.69812	−	6.40532i	−0.145164	−	0.251431i
$650$	−1.50744	+	5.60383i	−0.0591265	+	0.219800i
$651$	20.4102	+	8.18400i	0.799940	+	0.320756i
$652$	−22.1234	+	38.1458i	−0.866417	+	1.49390i
$653$	−40.6419	−	7.16627i	−1.59044	−	0.280438i	−0.692788	−	0.721141i	$-0.743618\pi$
$653$	−40.6419	−	7.16627i	−1.59044	−	0.280438i	−0.897653	+	0.440703i	$0.854729\pi$
$654$	2.67820	+	20.8233i	0.104726	+	0.814255i
$655$	−7.56577	−	9.01653i	−0.295619	−	0.352305i
$656$	2.27146	−	2.68555i	0.0886855	−	0.104853i
$657$	−22.1107	+	21.9341i	−0.862621	+	0.855729i
$658$	−5.59385	+	34.1938i	−0.218071	+	1.33301i
$659$	17.8969	−	15.0173i	0.697165	−	0.584991i	−0.223800	−	0.974635i	$-0.571846\pi$
$659$	17.8969	−	15.0173i	0.697165	−	0.584991i	0.920966	+	0.389644i	$0.127402\pi$
$660$	26.8527	+	20.7746i	1.04524	+	0.808650i
$661$	−12.3839	−	10.3913i	−0.481677	−	0.404175i	0.369355	−	0.929288i	$-0.379579\pi$
$661$	−12.3839	−	10.3913i	−0.481677	−	0.404175i	−0.851032	+	0.525113i	$0.824023\pi$
$662$	−18.8963	+	8.78894i	−0.734426	+	0.341592i
$663$	6.90063	+	7.56110i	0.267998	+	0.293649i
$664$	24.4866	+	17.2533i	0.950265	+	0.669558i
$665$	5.78504	+	20.4912i	0.224334	+	0.794616i
$666$	7.05063	−	12.0725i	0.273206	−	0.467799i
$667$	−23.9449	−	13.8246i	−0.927152	−	0.535291i
$668$	26.0088	+	4.63868i	1.00631	+	0.179476i
$669$	0.613489	+	14.7289i	0.0237188	+	0.569454i
$670$	25.4359	−	36.2506i	0.982676	−	1.40048i
$671$	−10.2251	+	3.72164i	−0.394737	+	0.143672i
$672$	−11.8214	+	23.0706i	−0.456020	+	0.889970i
$673$	5.75991	+	32.6661i	0.222028	+	1.25919i	0.868285	+	0.496065i	$0.165222\pi$
$673$	5.75991	+	32.6661i	0.222028	+	1.25919i	−0.646257	+	0.763120i	$0.723666\pi$
$674$	3.24102	+	37.4683i	0.124840	+	1.44323i
$675$	5.71846	−	6.16572i	0.220104	−	0.237319i
$676$	12.9474	−	2.25680i	0.497978	−	0.0868001i
$677$	−10.9483	−	13.0476i	−0.420776	−	0.501461i	0.513462	−	0.858113i	$-0.328363\pi$
$677$	−10.9483	−	13.0476i	−0.420776	−	0.501461i	−0.934238	+	0.356651i	$0.883918\pi$
$678$	−0.565259	+	12.1162i	−0.0217086	+	0.465318i
$679$	−34.3119	+	3.46430i	−1.31677	+	0.132947i
$680$	−7.21332	+	15.3509i	−0.276618	+	0.588681i
$681$	−1.41951	−	2.23808i	−0.0543958	−	0.0857634i
$682$	6.66676	+	24.9786i	0.255283	+	0.956482i
$683$	−0.306257			−0.0117186			−0.00585930	−	0.999983i	$-0.501865\pi$
$683$	−0.306257			−0.0117186			−0.00585930	+	0.999983i	$0.501865\pi$
$684$	−13.3509	+	13.1924i	−0.510484	+	0.504422i
$685$	23.8853	−	41.3706i	0.912612	−	1.58069i
$686$	−1.02360	−	26.1716i	−0.0390814	−	0.999236i
$687$	−14.5809	+	13.3073i	−0.556298	+	0.507704i
$688$	−25.4085	+	4.37749i	−0.968691	+	0.166890i
$689$	3.99018	−	4.75532i	0.152014	−	0.181163i
$690$	−15.9547	−	3.58708i	−0.607383	−	0.136558i
$691$	7.54556	−	20.7313i	0.287047	−	0.788654i	−0.709429	−	0.704776i	$-0.751047\pi$
$691$	7.54556	−	20.7313i	0.287047	−	0.788654i	0.996476	−	0.0838776i	$-0.0267305\pi$
$692$	5.59945	+	32.1244i	0.212859	+	1.22119i
$693$	−10.6071	−	28.3165i	−0.402932	−	1.07566i
$694$	−1.99589	−	23.0737i	−0.0757628	−	0.875866i
$695$	−7.36329	−	41.7593i	−0.279305	−	1.58402i
$696$	−11.5495	+	50.9031i	−0.437782	+	1.92948i
$697$	−1.92609	+	0.701039i	−0.0729558	+	0.0265538i
$698$	0.950475	+	2.04353i	0.0359760	+	0.0773488i
$699$	5.92765	+	14.3922i	0.224204	+	0.544362i
$700$	7.80204	+	3.53048i	0.294889	+	0.133439i
$701$			6.95890i			0.262834i	0.991327	+	0.131417i	$0.0419527\pi$
$701$			6.95890i			0.262834i	−0.991327	+	0.131417i	$0.958047\pi$
$702$	17.7299	+	5.72692i	0.669174	+	0.216149i
$703$	8.92719	+	5.15411i	0.336695	+	0.194391i
$704$	−30.0447	+	5.11556i	−1.13235	+	0.192800i
$705$	15.7139	+	38.1531i	0.591822	+	1.43693i
$706$	−2.79120	+	31.5472i	−0.105048	+	1.18729i
$707$	4.21678	+	41.7648i	0.158588	+	1.57073i
$708$	2.04780	−	6.40606i	0.0769609	−	0.240754i
$709$	6.99700	+	39.6820i	0.262778	+	1.49029i	0.775289	+	0.631607i	$0.217604\pi$
$709$	6.99700	+	39.6820i	0.262778	+	1.49029i	−0.512511	+	0.858681i	$0.671285\pi$
$710$	−4.32784	+	9.25737i	−0.162421	+	0.347423i
$711$	8.87691	+	0.812517i	0.332910	+	0.0304718i
$712$	22.9801	−	6.08507i	0.861215	−	0.228048i
$713$	−8.00433	−	9.53918i	−0.299764	−	0.357245i
$714$	12.6557	−	8.24835i	0.473629	−	0.308687i
$715$	24.4721	+	4.31509i	0.915204	+	0.161375i
$716$	−24.5885	−	14.2606i	−0.918916	−	0.532943i
$717$	2.08308	−	1.90112i	0.0777940	−	0.0709986i
$718$	−7.55939	+	28.1018i	−0.282114	+	1.04875i
$719$	−25.8307			−0.963324			−0.481662	−	0.876357i	$-0.659967\pi$
$719$	−25.8307			−0.963324			−0.481662	+	0.876357i	$0.659967\pi$
$720$	2.44653	+	30.7744i	0.0911769	+	1.14689i
$721$	−6.18403	−	6.02099i	−0.230305	−	0.224233i
$722$	9.20527	+	9.22335i	0.342585	+	0.343258i
$723$	42.2618	−	1.76028i	1.57173	−	0.0654656i
$724$	33.8832	+	19.6512i	1.25926	+	0.730330i
$725$	16.9813	+	2.99426i	0.630669	+	0.111204i
$726$	4.64552	−	7.24418i	0.172412	−	0.268857i
$727$	−14.2663	+	2.51554i	−0.529110	+	0.0932963i	−0.431820	−	0.901960i	$-0.642128\pi$
$727$	−14.2663	+	2.51554i	−0.529110	+	0.0932963i	−0.0972896	+	0.995256i	$0.531017\pi$
$728$	0.197606	+	18.9728i	0.00732376	+	0.703179i
$729$	−18.8608	−	19.3202i	−0.698548	−	0.715564i
$730$	−37.6299	+	3.25500i	−1.39275	+	0.120473i
$731$	14.1186	+	5.13876i	0.522197	+	0.190064i
$732$	−8.75827	−	4.60352i	−0.323715	−	0.170151i
$733$	−4.25903	−	3.57375i	−0.157311	−	0.132000i	0.560735	−	0.827995i	$-0.310519\pi$
$733$	−4.25903	−	3.57375i	−0.157311	−	0.132000i	−0.718046	+	0.695996i	$0.754963\pi$
$734$	27.6912	−	12.8796i	1.02210	−	0.475393i
$735$	−17.4039	−	25.8844i	−0.641954	−	0.954762i
$736$	12.0661	−	8.36089i	0.444762	−	0.308186i
$737$	−40.1579	−	23.1852i	−1.47924	−	0.854038i
$738$	−2.41229	+	2.84588i	−0.0887975	+	0.104758i
$739$	26.3939	−	15.2385i	0.970914	−	0.560557i	0.0713992	−	0.997448i	$-0.477254\pi$
$739$	26.3939	−	15.2385i	0.970914	−	0.560557i	0.899515	+	0.436890i	$0.143920\pi$
$740$	15.9437	−	5.76764i	0.586102	−	0.212023i
$741$	−4.15730	+	13.0937i	−0.152722	+	0.481008i
$742$	−5.97478	−	6.94409i	−0.219341	−	0.254926i
$743$	0.619166	−	3.51147i	0.0227150	−	0.128823i	−0.971342	−	0.237688i	$-0.923610\pi$
$743$	0.619166	−	3.51147i	0.0227150	−	0.128823i	0.994057	+	0.108865i	$0.0347215\pi$
$744$	−12.7289	+	19.7639i	−0.466663	+	0.724578i
$745$	−6.20067	−	35.1658i	−0.227175	−	1.28837i
$746$	2.48599	+	28.7396i	0.0910185	+	1.05223i
$747$	−25.9524	−	18.3276i	−0.949549	−	0.670573i
$748$	16.6772	+	6.10709i	0.609780	+	0.223297i
$749$	−1.95886	+	26.4554i	−0.0715752	+	0.966659i
$750$	−21.1356	+	2.71836i	−0.771762	+	0.0992606i
$751$	31.2321	+	5.50706i	1.13968	+	0.200956i	0.711464	−	0.702723i	$-0.248033\pi$
$751$	31.2321	+	5.50706i	1.13968	+	0.200956i	0.428212	+	0.903678i	$0.359144\pi$
$752$	−34.7568	−	12.8051i	−1.26745	−	0.466954i
$753$	−35.2100	−	27.1299i	−1.28312	−	0.988669i
$754$	9.85187	+	36.9124i	0.358784	+	1.34427i
$755$	0.253202			0.00921497
$756$	12.5646	−	24.4567i	0.456970	−	0.889482i
$757$	19.3596			0.703637			0.351819	−	0.936068i	$-0.385563\pi$
$757$	19.3596			0.703637			0.351819	+	0.936068i	$0.385563\pi$
$758$	−10.3511	−	38.7831i	−0.375970	−	1.40867i
$759$	−2.26908	+	16.9723i	−0.0823624	+	0.616055i
$760$	−22.6814	+	1.91713i	−0.822742	+	0.0695417i
$761$	−17.5812	−	3.10004i	−0.637318	−	0.112376i	−0.154352	−	0.988016i	$-0.549329\pi$
$761$	−17.5812	−	3.10004i	−0.637318	−	0.112376i	−0.482965	+	0.875640i	$0.660440\pi$
$762$	−16.6229	+	39.7946i	−0.602183	+	1.44161i
$763$	20.4225	−	9.85737i	0.739343	−	0.356861i
$764$	0.621344	−	1.69676i	0.0224794	−	0.0613868i
$765$	7.66827	−	16.2739i	0.277247	−	0.588385i
$766$	−1.19583	−	13.8245i	−0.0432070	−	0.499501i
$767$	−0.854789	−	4.84775i	−0.0308646	−	0.175042i
$768$	−21.8188	−	17.0863i	−0.787317	−	0.616548i
$769$	2.48785	−	14.1093i	0.0897143	−	0.508795i	−0.906525	−	0.422152i	$-0.861275\pi$
$769$	2.48785	−	14.1093i	0.0897143	−	0.508795i	0.996239	−	0.0866431i	$-0.0276140\pi$
$770$	12.1148	−	34.6120i	0.436586	−	1.24733i
$771$	34.6567	+	37.9738i	1.24813	+	1.36759i
$772$	2.26748	+	6.26807i	0.0816082	+	0.225593i
$773$	−24.2171	+	13.9818i	−0.871029	+	0.502889i	−0.867690	−	0.497106i	$-0.834396\pi$
$773$	−24.2171	+	13.9818i	−0.871029	+	0.502889i	−0.00333896	+	0.999994i	$0.501063\pi$
$774$	26.9547	−	4.61424i	0.968868	−	0.165855i
$775$	6.72549	+	3.88296i	0.241587	+	0.139480i
$776$	3.32127	−	36.7175i	0.119227	−	1.31808i
$777$	−14.7789	−	3.10083i	−0.530192	−	0.111242i
$778$	−46.1954	+	21.4861i	−1.65619	+	0.770316i
$779$	−2.10719	−	1.76814i	−0.0754980	−	0.0633503i
$780$	12.0650	+	19.1051i	0.431996	+	0.684072i
$781$	10.0552	+	3.65978i	0.359802	+	0.130957i
$782$	−8.52268	+	0.737215i	−0.304771	+	0.0263628i
$783$	12.3078	−	53.9778i	0.439843	−	1.92901i
$784$	27.6783	+	4.23248i	0.988509	+	0.151160i
$785$	−29.9106	+	5.27405i	−1.06756	+	0.188239i
$786$	−11.1947	−	0.522270i	−0.399302	−	0.0186288i
$787$	28.9687	+	5.10796i	1.03262	+	0.182079i	0.664181	−	0.747572i	$-0.268781\pi$
$787$	28.9687	+	5.10796i	1.03262	+	0.182079i	0.368441	+	0.929651i	$0.379892\pi$
$788$	−12.7883	+	22.0500i	−0.455564	+	0.785498i
$789$	14.6744	−	28.0517i	0.522422	−	0.998668i
$790$	7.63663	+	7.65162i	0.271699	+	0.272232i
$791$	12.6083	−	3.55956i	0.448301	−	0.126563i
$792$	31.8729	−	5.39182i	1.13256	−	0.191590i
$793$	−7.24204			−0.257172
$794$	1.28151	−	4.76398i	0.0454792	−	0.169067i
$795$	−10.3979	−	3.30138i	−0.368775	−	0.117088i
$796$	−26.5416	+	45.7638i	−0.940742	+	1.62206i
$797$	−3.28832	−	0.579820i	−0.116478	−	0.0205383i	0.115105	−	0.993353i	$-0.463280\pi$
$797$	−3.28832	−	0.579820i	−0.116478	−	0.0205383i	−0.231583	+	0.972815i	$0.574391\pi$
$798$	18.0786	+	9.17408i	0.639975	+	0.324759i
$799$	13.8746	+	16.5351i	0.490849	+	0.584971i
$800$	−5.28777	+	7.47344i	−0.186951	+	0.264226i
$801$	−24.3809	+	6.42815i	−0.861458	+	0.227128i
$802$	6.92795	−	14.8191i	0.244635	−	0.523280i
$803$	6.86775	+	38.9490i	0.242358	+	1.37448i
$804$	−8.96273	−	41.2011i	−0.316091	−	1.45305i
$805$	1.77434	+	17.5738i	0.0625372	+	0.619396i
$806$	−1.51645	+	17.1394i	−0.0534145	+	0.603710i
$807$	−16.5674	−	2.21495i	−0.583201	−	0.0779701i
$808$	−44.6930	−	4.04268i	−1.57229	−	0.142221i
$809$	−6.25527	−	3.61148i	−0.219923	−	0.126973i	0.385991	−	0.922502i	$-0.373859\pi$
$809$	−6.25527	−	3.61148i	−0.219923	−	0.126973i	−0.605915	+	0.795530i	$0.707193\pi$
$810$	−2.56007	−	32.6439i	−0.0899518	−	1.14699i
$811$		−	35.5257i		−	1.24748i	−0.781633	−	0.623739i	$-0.785613\pi$
$811$		−	35.5257i		−	1.24748i	0.781633	−	0.623739i	$-0.214387\pi$
$812$	56.1049	−	5.55347i	1.96890	−	0.194888i
$813$	17.3428	−	22.5079i	0.608237	−	0.789388i
$814$	−7.48721	−	16.0976i	−0.262427	−	0.564220i
$815$	53.3016	−	19.4002i	1.86707	−	0.679559i
$816$	6.09155	+	14.9565i	0.213247	+	0.523582i
$817$	3.50136	+	19.8572i	0.122497	+	0.694715i
$818$	−3.00404	−	34.7286i	−0.105034	−	1.21426i
$819$	−0.188096	−	20.1239i	−0.00657260	−	0.703186i
$820$	−4.45719	+	0.776910i	−0.155652	+	0.0271309i
$821$	11.2777	−	30.9851i	0.393593	−	1.08139i	−0.571755	−	0.820424i	$-0.693737\pi$
$821$	11.2777	−	30.9851i	0.393593	−	1.08139i	0.965349	−	0.260964i	$-0.0840404\pi$
$822$	−13.5478	−	43.4198i	−0.472533	−	1.51444i
$823$	13.3205	−	15.8747i	0.464323	−	0.553358i	−0.482173	−	0.876076i	$-0.660152\pi$
$823$	13.3205	−	15.8747i	0.464323	−	0.553358i	0.946495	+	0.322718i	$0.104597\pi$
$824$	7.57382	−	5.27010i	0.263846	−	0.183593i
$825$	−2.29041	−	10.4303i	−0.0797418	−	0.363137i
$826$	−7.26371	+	0.0899042i	−0.252737	+	0.00312817i
$827$	5.61833	−	9.73123i	0.195368	−	0.338388i	−0.751653	−	0.659559i	$-0.770743\pi$
$827$	5.61833	−	9.73123i	0.195368	−	0.338388i	0.947021	+	0.321171i	$0.104076\pi$
$828$	−12.8075	+	8.85439i	−0.445091	+	0.307711i
$829$	11.7737			0.408917			0.204458	−	0.978875i	$-0.434457\pi$
$829$	11.7737			0.408917			0.204458	+	0.978875i	$0.434457\pi$
$830$	−9.93598	−	37.2276i	−0.344883	−	1.29219i
$831$	−7.89413	+	15.0905i	−0.273844	+	0.523485i
$832$	−19.9546	−	3.63975i	−0.691803	−	0.126186i
$833$	−12.7751	−	10.1506i	−0.442630	−	0.351697i
$834$	−33.9861	−	21.7945i	−1.17684	−	0.754682i
$835$	−21.8441	−	26.0327i	−0.755945	−	0.900900i
$836$	4.09279	+	23.4806i	0.141552	+	0.812094i
$837$	13.5234	−	20.9483i	0.467437	−	0.724079i
$838$	2.73599	+	31.6298i	0.0945131	+	1.09263i
$839$	−1.92484	−	10.9163i	−0.0664529	−	0.376873i	−0.999838	−	0.0179970i	$-0.994271\pi$
$839$	−1.92484	−	10.9163i	−0.0664529	−	0.376873i	0.933385	−	0.358876i	$-0.116840\pi$
$840$	30.6983	−	13.0192i	1.05919	−	0.449205i
$841$	79.4243	−	28.9081i	2.73877	−	0.996831i
$842$	25.9703	−	37.0121i	0.894996	−	1.27552i
$843$	−9.89133	−	5.17434i	−0.340675	−	0.178214i
$844$	9.79026	−	54.8934i	0.336995	−	1.88951i
$845$	−14.6406	−	8.45276i	−0.503652	−	0.290784i
$846$	36.8506	+	13.6212i	1.26695	+	0.468307i
$847$	−9.00989	−	2.28565i	−0.309583	−	0.0785360i
$848$	8.50031	−	4.86329i	0.291902	−	0.167006i
$849$	−11.3765	+	35.8309i	−0.390440	+	1.22971i
$850$	4.83732	−	2.24991i	0.165919	−	0.0771712i
$851$	6.55068	+	5.49667i	0.224554	+	0.188424i
$852$	3.68780	+	9.00400i	0.126342	+	0.308472i
$853$	19.8380	−	16.6461i	0.679240	−	0.569950i	−0.236544	−	0.971621i	$-0.576015\pi$
$853$	19.8380	−	16.6461i	0.679240	−	0.569950i	0.915784	+	0.401671i	$0.131570\pi$
$854$	−1.72541	+	10.5470i	−0.0590424	+	0.360911i
$855$	24.0595	−	2.00773i	0.822816	−	0.0686628i
$856$	−27.3714	−	7.42053i	−0.935535	−	0.253629i
$857$	−9.53836	−	11.3674i	−0.325824	−	0.388302i	0.578121	−	0.815951i	$-0.303786\pi$
$857$	−9.53836	−	11.3674i	−0.325824	−	0.388302i	−0.903945	+	0.427649i	$0.859342\pi$
$858$	18.8139	−	14.3473i	0.642295	−	0.489810i
$859$	18.9233	+	3.33668i	0.645653	+	0.113846i	0.486880	−	0.873469i	$-0.338135\pi$
$859$	18.9233	+	3.33668i	0.645653	+	0.113846i	0.158773	+	0.987315i	$0.449246\pi$
$860$	28.6889	+	16.6387i	0.978284	+	0.567374i
$861$	3.74015	+	1.49971i	0.127464	+	0.0511099i
$862$	−11.9220	+	44.3195i	−0.406064	+	1.50953i
$863$	18.3101	+	31.7141i	0.623284	+	1.07956i	0.988870	+	0.148782i	$0.0475354\pi$
$863$	18.3101	+	31.7141i	0.623284	+	1.07956i	−0.365586	+	0.930778i	$0.619131\pi$
$864$	23.1229	+	18.1474i	0.786658	+	0.617389i
$865$	20.9725	−	36.3255i	0.713087	−	1.23510i
$866$	1.32518	−	0.353688i	0.0450315	−	0.0120188i
$867$	−2.65478	+	19.8572i	−0.0901610	+	0.674388i
$868$	24.5998	+	6.29195i	0.834973	+	0.213563i
$869$	7.27617	−	8.67140i	0.246827	−	0.294157i
$870$	53.3887	−	40.7139i	1.81005	−	1.38033i
$871$	−19.8375	−	23.6414i	−0.672167	−	0.801058i
$872$	6.20554	+	23.4350i	0.210146	+	0.793610i
$873$	−3.56434	+	38.9410i	−0.120634	+	1.31795i
$874$	−6.57562	−	9.41059i	−0.222424	−	0.318318i
$875$	10.0052	+	20.7288i	0.338237	+	0.700760i
$876$	−22.0057	+	28.4440i	−0.743504	+	0.961035i
$877$	5.45788	−	1.98651i	0.184300	−	0.0670796i	−0.248222	−	0.968703i	$-0.579846\pi$
$877$	5.45788	−	1.98651i	0.184300	−	0.0670796i	0.432521	+	0.901624i	$0.357624\pi$
$878$	−17.0708	+	7.93988i	−0.576112	+	0.267958i
$879$	−22.2355	−	24.3637i	−0.749986	−	0.821769i
$880$	33.8736	+	19.7345i	1.14188	+	0.665251i
$881$	21.0923	+	12.1776i	0.710616	+	0.410275i	0.811289	−	0.584645i	$-0.198766\pi$
$881$	21.0923	+	12.1776i	0.710616	+	0.410275i	−0.100673	+	0.994920i	$0.532100\pi$
$882$	−29.3524	−	4.52058i	−0.988347	−	0.152216i
$883$	−20.4217	+	11.7905i	−0.687246	+	0.396782i	−0.802580	−	0.596545i	$-0.796540\pi$
$883$	−20.4217	+	11.7905i	−0.687246	+	0.396782i	0.115333	+	0.993327i	$0.463206\pi$
$884$	9.03992	+	7.61566i	0.304045	+	0.256142i
$885$	−7.30545	+	4.63351i	−0.245570	+	0.155754i
$886$	−49.3314	−	4.36470i	−1.65732	−	0.146635i
$887$	−15.3201	−	12.8551i	−0.514398	−	0.431631i	0.348276	−	0.937392i	$-0.386767\pi$
$887$	−15.3201	−	12.8551i	−0.514398	−	0.431631i	−0.862674	+	0.505761i	$0.831212\pi$
$888$	6.25152	−	14.8838i	0.209787	−	0.499467i
$889$	46.4552	+	3.43973i	1.55806	+	0.115365i
$890$	−27.7006	−	12.9501i	−0.928527	−	0.434089i
$891$	−33.8125	+	5.68278i	−1.13276	+	0.190380i
$892$	2.92300	+	16.7694i	0.0978691	+	0.561482i
$893$	−9.90752	+	27.2207i	−0.331543	+	0.910906i
$894$	−28.6199	−	18.3533i	−0.957194	−	0.613826i
$895$	12.5052	+	34.3579i	0.418004	+	1.14846i
$896$	−10.0550	+	28.1939i	−0.335913	+	0.941893i
$897$	−5.28251	+	10.0981i	−0.176378	+	0.337166i
$898$	−15.0037	−	4.03600i	−0.500679	−	0.134683i
$899$	51.1273			1.70519
$900$	5.61699	−	7.92078i	0.187233	−	0.264026i
$901$	−5.70691			−0.190125
$902$	1.22168	+	4.57731i	0.0406773	+	0.152408i
$903$	−13.9357	−	26.0440i	−0.463750	−	0.866689i
$904$	1.17962	+	13.9560i	0.0392336	+	0.464169i
$905$	−17.2323	−	47.3454i	−0.572822	−	1.57382i
$906$	0.163404	−	0.177258i	0.00542872	−	0.00588900i
$907$	−26.4756	+	4.66836i	−0.879108	+	0.155010i	−0.594946	−	0.803766i	$-0.702827\pi$
$907$	−26.4756	+	4.66836i	−0.879108	+	0.155010i	−0.284162	+	0.958776i	$0.591715\pi$
$908$	−1.96251	−	2.34817i	−0.0651282	−	0.0779268i
$909$	47.3995	+	4.33855i	1.57214	+	0.143901i
$910$	15.4554	−	18.8890i	0.512342	−	0.626164i
$911$	−36.0407	−	13.1177i	−1.19408	−	0.434610i	−0.332926	−	0.942953i	$-0.608036\pi$
$911$	−36.0407	−	13.1177i	−1.19408	−	0.434610i	−0.861155	+	0.508343i	$0.830258\pi$
$912$	−13.2953	+	17.1157i	−0.440252	+	0.566758i
$913$	−37.9128	+	13.7991i	−1.25473	+	0.456684i
$914$	0.576480	−	0.821583i	0.0190683	−	0.0271756i
$915$	4.84694	+	11.7682i	0.160235	+	0.389046i
$916$	−14.6862	+	17.4327i	−0.485245	+	0.575994i
$917$	3.28886	+	11.6495i	0.108608	+	0.384700i
$918$	−6.44411	−	15.8706i	−0.212687	−	0.523809i
$919$	−31.2058	+	18.0167i	−1.02939	+	0.594316i	−0.916809	−	0.399327i	$-0.869244\pi$
$919$	−31.2058	+	18.0167i	−1.02939	+	0.594316i	−0.112577	+	0.993643i	$0.535911\pi$
$920$	−18.8059	−	1.70108i	−0.620014	−	0.0560830i
$921$	−16.2839	−	2.17704i	−0.536571	−	0.0717359i
$922$	10.7479	−	4.99899i	0.353963	−	0.164633i
$923$	5.45550	+	4.57771i	0.179570	+	0.150677i
$924$	−16.4125	−	30.8180i	−0.539930	−	1.01384i
$925$	−5.01134	−	1.82398i	−0.164772	−	0.0599721i
$926$	−3.50727	−	5.01937i	−0.115256	−	0.164947i
$927$	−8.03921	+	5.58120i	−0.264042	+	0.183311i
$928$	−5.54743	+	60.0160i	−0.182103	+	1.97012i
$929$	−1.78988	+	4.91764i	−0.0587239	+	0.161343i	−0.965585	−	0.260086i	$-0.916249\pi$
$929$	−1.78988	+	4.91764i	−0.0587239	+	0.161343i	0.906862	+	0.421429i	$0.138471\pi$
$930$	28.8663	−	9.00682i	0.946563	−	0.295345i
$931$	3.22507	−	21.6587i	0.105697	−	0.709834i
$932$	8.95596	+	15.5827i	0.293362	+	0.510428i
$933$	28.5687	+	9.07072i	0.935299	+	0.296962i
$934$	9.55514	−	35.5209i	0.312654	−	1.16228i
$935$	−11.4226	−	19.7845i	−0.373559	−	0.647023i
$936$	21.1610	+	3.88315i	0.691667	+	0.126925i
$937$	5.01933	+	8.69373i	0.163974	+	0.284012i	0.936291	−	0.351226i	$-0.114235\pi$
$937$	5.01933	+	8.69373i	0.163974	+	0.284012i	−0.772316	+	0.635238i	$0.780902\pi$
$938$	−39.1566	+	23.2579i	−1.27851	+	0.759398i
$939$	−4.14729	+	0.172742i	−0.135342	+	0.00563723i
$940$	23.7419	+	41.3090i	0.774374	+	1.34735i
$941$	20.6485	+	3.64088i	0.673121	+	0.118689i	0.499753	−	0.866168i	$-0.333424\pi$
$941$	20.6485	+	3.64088i	0.673121	+	0.118689i	0.173368	+	0.984857i	$0.444535\pi$
$942$	−15.6106	+	24.3430i	−0.508621	+	0.793138i
$943$	−1.46678	−	1.74804i	−0.0477650	−	0.0569242i
$944$	1.37852	−	7.64249i	0.0448669	−	0.248742i
$945$	−32.5752	+	13.7741i	−1.05967	+	0.448073i
$946$	14.7072	−	31.4591i	0.478172	−	1.02282i
$947$	28.4194	−	23.8467i	0.923507	−	0.774914i	−0.0511334	−	0.998692i	$-0.516283\pi$
$947$	28.4194	−	23.8467i	0.923507	−	0.774914i	0.974640	+	0.223778i	$0.0718389\pi$
$948$	10.2849	−	0.408177i	0.334039	−	0.0132570i
$949$	−4.57080	+	25.9223i	−0.148375	+	0.841474i
$950$	5.86079	+	4.11234i	0.190149	+	0.133422i
$951$	36.1283	−	22.9146i	1.17154	−	0.743056i
$952$	13.2449	−	11.3509i	0.429269	−	0.367886i
$953$	−42.5367	+	24.5586i	−1.37790	+	0.795531i	−0.991906	−	0.126971i	$-0.959475\pi$
$953$	−42.5367	+	24.5586i	−1.37790	+	0.795531i	−0.385993	+	0.922502i	$0.626141\pi$
$954$	−9.02144	+	5.14866i	−0.292080	+	0.166694i
$955$	−2.01290	+	1.16215i	−0.0651360	+	0.0376063i
$956$	2.09811	−	2.49049i	0.0678578	−	0.0805483i
$957$	−47.3930	−	51.9290i	−1.53200	−	1.67863i
$958$	34.7168	−	49.4774i	1.12165	−	1.59854i
$959$	−39.8638	+	28.7140i	−1.28727	+	0.927225i
$960$	7.44064	+	34.8621i	0.240146	+	1.12517i
$961$	−7.49270	−	2.72712i	−0.241700	−	0.0879716i
$962$	−1.01827	−	11.7719i	−0.0328304	−	0.379540i
$963$	29.0233	+	7.90167i	0.935263	+	0.254628i
$964$	48.1165	−	8.38695i	1.54973	−	0.270125i
$965$	2.93249	−	8.05695i	0.0944001	−	0.259362i
$966$	13.4479	+	10.0991i	0.432679	+	0.324933i
$967$	−33.3478	+	39.7424i	−1.07239	+	1.27803i	−0.113724	+	0.993512i	$0.536278\pi$
$967$	−33.3478	+	39.7424i	−1.07239	+	1.27803i	−0.958671	+	0.284518i	$0.908167\pi$
$968$	4.22607	−	8.99365i	0.135831	−	0.289067i
$969$	11.6780	−	4.80976i	0.375150	−	0.154512i
$970$	−33.5660	+	33.5002i	−1.07774	+	1.07563i
$971$	6.07842	+	10.5281i	0.195066	+	0.337864i	0.946922	−	0.321463i	$-0.104175\pi$
$971$	6.07842	+	10.5281i	0.195066	+	0.337864i	−0.751856	+	0.659327i	$0.770841\pi$
$972$	−24.5050	−	19.2745i	−0.785998	−	0.618229i
$973$	−10.7232	+	42.2699i	−0.343769	+	1.35511i
$974$	−37.7473	−	10.1541i	−1.20950	−	0.325357i
$975$	0.941811	−	7.04457i	0.0301621	−	0.225607i
$976$	−10.7207	−	3.94971i	−0.343160	−	0.126427i
$977$	8.82019	+	24.2333i	0.282183	+	0.775291i	0.997101	+	0.0760833i	$0.0242415\pi$
$977$	8.82019	+	24.2333i	0.282183	+	0.775291i	−0.714919	+	0.699208i	$0.753536\pi$
$978$	20.8167	−	49.8345i	0.665645	−	1.59353i
$979$	−10.9511	+	30.0878i	−0.349998	+	0.961611i
$980$	−23.8269	−	27.0089i	−0.761121	−	0.862769i
$981$	−6.55541	−	24.8636i	−0.209298	−	0.793834i
$982$	−21.6172	−	10.1061i	−0.689834	−	0.322499i
$983$	8.33279	+	47.2576i	0.265775	+	1.50728i	0.766820	+	0.641863i	$0.221838\pi$
$983$	8.33279	+	47.2576i	0.265775	+	1.50728i	−0.501045	+	0.865421i	$0.667051\pi$
$984$	−2.33255	+	3.62170i	−0.0743591	+	0.115456i
$985$	30.8107	−	11.2142i	0.981712	−	0.357314i
$986$	20.1739	−	28.7512i	0.642467	−	0.915626i
$987$	1.36963	−	42.4132i	0.0435957	−	1.35003i
$988$	−2.78523	+	15.6166i	−0.0886099	+	0.496831i
$989$			16.7269i			0.531884i
$990$	−35.9060	−	20.9700i	−1.14117	−	0.666470i
$991$			3.05708i			0.0971114i	0.998820	+	0.0485557i	$0.0154618\pi$
$991$			3.05708i			0.0971114i	−0.998820	+	0.0485557i	$0.984538\pi$
$992$	−11.5924	+	24.5451i	−0.368061	+	0.779307i
$993$	21.5542	−	13.6708i	0.684001	−	0.433831i
$994$	7.96656	−	6.85453i	0.252684	−	0.217412i
$995$	63.9464	−	23.2746i	2.02724	−	0.737854i
$996$	−32.4739	−	17.0689i	−1.02898	−	0.540850i
$997$	45.9057	+	16.7083i	1.45385	+	0.529158i	0.943664	−	0.330906i	$-0.107354\pi$
$997$	45.9057	+	16.7083i	1.45385	+	0.529158i	0.510186	+	0.860064i	$0.329577\pi$
$998$	17.4590	+	24.9862i	0.552655	+	0.790923i
$999$	−6.64760	+	15.7795i	−0.210321	+	0.499242i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ci.a.95.12	yes	840
4.3	odd	2	inner	756.2.ci.a.95.91	yes	840
7.2	even	3		756.2.bs.a.527.106	yes	840
27.2	odd	18		756.2.bs.a.515.5	✓	840
28.23	odd	6		756.2.bs.a.527.5	yes	840
108.83	even	18		756.2.bs.a.515.106	yes	840
189.2	odd	18	inner	756.2.ci.a.191.91	yes	840
756.191	even	18	inner	756.2.ci.a.191.12	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bs.a.515.5	✓	840	27.2	odd	18
756.2.bs.a.515.106	yes	840	108.83	even	18
756.2.bs.a.527.5	yes	840	28.23	odd	6
756.2.bs.a.527.106	yes	840	7.2	even	3
756.2.ci.a.95.12	yes	840	1.1	even	1	trivial
756.2.ci.a.95.91	yes	840	4.3	odd	2	inner
756.2.ci.a.191.12	yes	840	756.191	even	18	inner
756.2.ci.a.191.91	yes	840	189.2	odd	18	inner

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ci (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36638 + 0.364685i) q^{2} +(1.60153 - 0.659617i) q^{3} +(1.73401 - 0.996600i) q^{4} +(-2.53354 - 0.446731i) q^{5} +(-1.94776 + 1.48535i) q^{6} +(2.18735 + 1.48846i) q^{7} +(-2.00588 + 1.99411i) q^{8} +(2.12981 - 2.11280i) q^{9} +O(q^{10})\)	\(q+(-1.36638 + 0.364685i) q^{2} +(1.60153 - 0.659617i) q^{3} +(1.73401 - 0.996600i) q^{4} +(-2.53354 - 0.446731i) q^{5} +(-1.94776 + 1.48535i) q^{6} +(2.18735 + 1.48846i) q^{7} +(-2.00588 + 1.99411i) q^{8} +(2.12981 - 2.11280i) q^{9} +(3.62470 - 0.313538i) q^{10} +(-0.661535 - 3.75175i) q^{11} +(2.11970 - 2.73987i) q^{12} +(0.440282 - 2.49696i) q^{13} +(-3.53158 - 1.23611i) q^{14} +(-4.35221 + 0.955709i) q^{15} +(2.01358 - 3.45623i) q^{16} +(-2.01868 + 1.16548i) q^{17} +(-2.13963 + 3.66360i) q^{18} +(-2.70911 - 1.56410i) q^{19} +(-4.83839 + 1.75029i) q^{20} +(4.48492 + 0.941000i) q^{21} +(2.27212 + 4.88508i) q^{22} +(-1.98792 - 1.66806i) q^{23} +(-1.89713 + 4.51674i) q^{24} +(1.52078 + 0.553518i) q^{25} +(0.309012 + 3.57238i) q^{26} +(2.01733 - 4.78857i) q^{27} +(5.27628 + 0.401085i) q^{28} +(10.4928 - 1.85016i) q^{29} +(5.59826 - 2.89305i) q^{30} +(4.72569 + 0.833266i) q^{31} +(-1.49088 + 5.45686i) q^{32} +(-3.53419 - 5.57220i) q^{33} +(2.33325 - 2.32868i) q^{34} +(-4.87679 - 4.74822i) q^{35} +(1.58750 - 5.78618i) q^{36} -3.29525 q^{37} +(4.27209 + 1.14919i) q^{38} +(-0.941913 - 4.28939i) q^{39} +(5.97279 - 4.15605i) q^{40} +(0.865976 + 0.152695i) q^{41} +(-6.47129 + 0.349818i) q^{42} +(-4.14322 - 4.93770i) q^{43} +(-4.88611 - 5.84629i) q^{44} +(-6.33981 + 4.40139i) q^{45} +(3.32457 + 1.55425i) q^{46} +(-1.60801 - 9.11946i) q^{47} +(0.945020 - 6.86345i) q^{48} +(2.56899 + 6.51155i) q^{49} +(-2.27983 - 0.201712i) q^{50} +(-2.46420 + 3.19811i) q^{51} +(-1.72502 - 4.76854i) q^{52} +(2.12029 + 1.22415i) q^{53} +(-1.01012 + 7.27871i) q^{54} +9.80074i q^{55} +(-7.35569 + 1.37615i) q^{56} +(-5.37043 - 0.717990i) q^{57} +(-13.6624 + 6.35459i) q^{58} +(1.82437 - 0.664017i) q^{59} +(-6.59432 + 5.99463i) q^{60} +(-0.495987 - 2.81288i) q^{61} +(-6.76098 + 0.584827i) q^{62} +(7.80345 - 1.45129i) q^{63} +(0.0470807 - 7.99986i) q^{64} +(-2.23094 + 6.12946i) q^{65} +(6.86116 + 6.32489i) q^{66} +(7.82394 - 9.32421i) q^{67} +(-2.33888 + 4.03277i) q^{68} +(-4.28399 - 1.36019i) q^{69} +(8.39517 + 4.70939i) q^{70} +(-1.40440 + 2.43249i) q^{71} +(-0.0590006 + 8.48508i) q^{72} -10.3815 q^{73} +(4.50258 - 1.20173i) q^{74} +(2.80068 - 0.116654i) q^{75} +(-6.25640 - 0.0122732i) q^{76} +(4.13732 - 9.19106i) q^{77} +(2.85129 + 5.51745i) q^{78} +(1.90994 + 2.27618i) q^{79} +(-6.64547 + 7.85696i) q^{80} +(0.0721933 - 8.99971i) q^{81} +(-1.23894 + 0.107169i) q^{82} +(-1.83902 - 10.4296i) q^{83} +(8.71470 - 2.83797i) q^{84} +(5.63505 - 2.05099i) q^{85} +(7.46194 + 5.23582i) q^{86} +(15.5841 - 9.88431i) q^{87} +(8.80835 + 6.20638i) q^{88} +(-7.27868 - 4.20235i) q^{89} +(7.05749 - 8.32603i) q^{90} +(4.67967 - 4.80639i) q^{91} +(-5.10945 - 0.911273i) q^{92} +(8.11797 - 1.78264i) q^{93} +(5.52289 + 11.8743i) q^{94} +(6.16489 + 5.17296i) q^{95} +(1.21174 + 9.72274i) q^{96} +(-9.98509 + 8.37848i) q^{97} +(-5.88490 - 7.96040i) q^{98} +(-9.33563 - 6.59284i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} + 3 q^{10} - 3 q^{12} - 24 q^{13} + 24 q^{14} - 3 q^{16} - 18 q^{17} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} + 48 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} - 21 q^{30} - 63 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} - 12 q^{37} + 45 q^{38} - 33 q^{40} - 24 q^{41} - 21 q^{42} + 6 q^{45} - 6 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} - 63 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} - 54 q^{65} - 3 q^{66} - 12 q^{68} - 48 q^{69} - 21 q^{70} - 9 q^{72} - 12 q^{73} + 15 q^{74} + 12 q^{77} + 6 q^{78} - 54 q^{81} - 6 q^{82} - 39 q^{84} + 6 q^{85} - 9 q^{86} - 27 q^{88} - 18 q^{89} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} + 213 q^{96} - 24 q^{97} + 162 q^{98}+O(q^{100}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 + 3 * q^10 - 3 * q^12 - 24 * q^13 + 24 * q^14 - 3 * q^16 - 18 * q^17 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 + 48 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 - 21 * q^30 - 63 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 - 12 * q^37 + 45 * q^38 - 33 * q^40 - 24 * q^41 - 21 * q^42 + 6 * q^45 - 6 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 - 63 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 - 54 * q^65 - 3 * q^66 - 12 * q^68 - 48 * q^69 - 21 * q^70 - 9 * q^72 - 12 * q^73 + 15 * q^74 + 12 * q^77 + 6 * q^78 - 54 * q^81 - 6 * q^82 - 39 * q^84 + 6 * q^85 - 9 * q^86 - 27 * q^88 - 18 * q^89 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 + 213 * q^96 - 24 * q^97 + 162 * q^98

Introduction

L-functions

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