LMFDB - Embedded newform 512.2.o.a.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(5,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(128))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("512.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.o (of order $128$, degree $64$, 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:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$4032$
Relative dimension:	$63$ over $\Q(\zeta_{128})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{128}]$

Embedding invariants

Embedding label			109.1
Character	$\chi$	$=$	512.109
Dual form			512.2.o.a.357.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41253 - 0.0689831i) q^{2} +(0.145016 - 1.17576i) q^{3} +(1.99048 + 0.194882i) q^{4} +(1.12458 - 0.252532i) q^{5} +(-0.285948 + 1.65079i) q^{6} +(0.487809 - 0.361784i) q^{7} +(-2.79817 - 0.412586i) q^{8} +(1.54871 + 0.387932i) q^{9} +O(q^{10})$	\(q+(-1.41253 - 0.0689831i) q^{2} +(0.145016 - 1.17576i) q^{3} +(1.99048 + 0.194882i) q^{4} +(1.12458 - 0.252532i) q^{5} +(-0.285948 + 1.65079i) q^{6} +(0.487809 - 0.361784i) q^{7} +(-2.79817 - 0.412586i) q^{8} +(1.54871 + 0.387932i) q^{9} +(-1.60592 + 0.279132i) q^{10} +(4.01223 + 0.295960i) q^{11} +(0.517786 - 2.31207i) q^{12} +(-2.70328 - 1.90386i) q^{13} +(-0.714002 + 0.477380i) q^{14} +(-0.133835 - 1.35885i) q^{15} +(3.92404 + 0.775817i) q^{16} +(0.966673 + 0.0952090i) q^{17} +(-2.16084 - 0.654800i) q^{18} +(2.08289 + 5.39968i) q^{19} +(2.28766 - 0.283501i) q^{20} +(-0.354631 - 0.626012i) q^{21} +(-5.64697 - 0.694828i) q^{22} +(4.15914 + 0.204326i) q^{23} +(-0.890883 + 3.23015i) q^{24} +(-3.31905 + 1.56979i) q^{25} +(3.68713 + 2.87574i) q^{26} +(1.95977 - 5.08052i) q^{27} +(1.04148 - 0.625060i) q^{28} +(-1.38674 - 2.75497i) q^{29} +(0.0953085 + 1.92865i) q^{30} +(-0.0787648 - 0.395977i) q^{31} +(-5.48931 - 1.36656i) q^{32} +(0.929816 - 4.67450i) q^{33} +(-1.35889 - 0.201170i) q^{34} +(0.457216 - 0.530041i) q^{35} +(3.00708 + 1.07399i) q^{36} +(-2.71410 - 2.58404i) q^{37} +(-2.56965 - 7.77089i) q^{38} +(-2.63051 + 2.90232i) q^{39} +(-3.25095 + 0.242644i) q^{40} +(-2.66987 - 1.26275i) q^{41} +(0.457743 + 0.908724i) q^{42} +(0.307743 - 0.394337i) q^{43} +(7.92859 + 1.37101i) q^{44} +(1.83961 + 0.0451598i) q^{45} +(-5.86082 - 0.575527i) q^{46} +(10.1077 - 3.06612i) q^{47} +(1.48122 - 4.50123i) q^{48} +(-1.92492 + 6.34562i) q^{49} +(4.79655 - 1.98842i) q^{50} +(0.252126 - 1.12277i) q^{51} +(-5.00980 - 4.31642i) q^{52} +(6.39154 - 12.6978i) q^{53} +(-3.11871 + 7.04120i) q^{54} +(4.58679 - 0.680386i) q^{55} +(-1.51424 + 0.811071i) q^{56} +(6.65078 - 1.66593i) q^{57} +(1.76876 + 3.98714i) q^{58} +(-3.20560 - 4.55160i) q^{59} +(-0.00158158 - 2.73086i) q^{60} +(-0.808706 - 0.458126i) q^{61} +(0.0839419 + 0.564763i) q^{62} +(0.895823 - 0.371062i) q^{63} +(7.65955 + 2.30897i) q^{64} +(-3.52082 - 1.45837i) q^{65} +(-1.63585 + 6.53873i) q^{66} +(3.98803 - 1.10364i) q^{67} +(1.90559 + 0.377898i) q^{68} +(0.843381 - 4.86053i) q^{69} +(-0.682396 + 0.717159i) q^{70} +(-0.208023 + 0.347066i) q^{71} +(-4.17350 - 1.72448i) q^{72} +(-6.19663 - 4.59574i) q^{73} +(3.65549 + 3.83726i) q^{74} +(1.36439 + 4.13005i) q^{75} +(3.09365 + 11.1539i) q^{76} +(2.06428 - 1.30719i) q^{77} +(3.91588 - 3.91815i) q^{78} +(-2.94827 - 5.51582i) q^{79} +(4.60880 - 0.118481i) q^{80} +(-1.46517 - 0.783148i) q^{81} +(3.68416 + 1.96785i) q^{82} +(-5.12862 + 4.88285i) q^{83} +(-0.583889 - 1.31518i) q^{84} +(1.11114 - 0.137046i) q^{85} +(-0.461900 + 0.535784i) q^{86} +(-3.44029 + 1.23095i) q^{87} +(-11.1048 - 2.48353i) q^{88} +(7.40307 - 0.363689i) q^{89} +(-2.59538 - 0.190691i) q^{90} +(-2.00747 + 0.0492806i) q^{91} +(8.23888 + 1.21725i) q^{92} +(-0.476997 + 0.0351854i) q^{93} +(-14.4889 + 3.63374i) q^{94} +(3.70595 + 5.54635i) q^{95} +(-2.40278 + 6.25594i) q^{96} +(-8.11369 + 12.1430i) q^{97} +(3.15675 - 8.83059i) q^{98} +(6.09896 + 2.01483i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) $ 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{119}{128}\right)$	$1$

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 $

$2$	−1.41253	−	0.0689831i	−0.998810	−	0.0487784i
$2$	−1.41253	−	0.0689831i	−0.998810	−	0.0487784i
$3$	0.145016	−	1.17576i	0.0837252	−	0.678826i	−0.890776	−	0.454443i	$-0.849838\pi$
$3$	0.145016	−	1.17576i	0.0837252	−	0.678826i	0.974501	−	0.224383i	$-0.0720366\pi$
$4$	1.99048	+	0.194882i	0.995241	+	0.0974408i
$5$	1.12458	−	0.252532i	0.502925	−	0.112936i	0.0397631	−	0.999209i	$-0.487340\pi$
$5$	1.12458	−	0.252532i	0.502925	−	0.112936i	0.463162	+	0.886273i	$0.346715\pi$
$6$	−0.285948	+	1.65079i	−0.116738	+	0.673934i
$7$	0.487809	−	0.361784i	0.184375	−	0.136742i	−0.499575	−	0.866270i	$-0.666511\pi$
$7$	0.487809	−	0.361784i	0.184375	−	0.136742i	0.683950	+	0.729529i	$0.260261\pi$
$8$	−2.79817	−	0.412586i	−0.989304	−	0.145871i
$9$	1.54871	+	0.387932i	0.516237	+	0.129311i
$10$	−1.60592	+	0.279132i	−0.507836	+	0.0882693i
$11$	4.01223	+	0.295960i	1.20973	+	0.0892352i	0.663355	−	0.748305i	$-0.269132\pi$
$11$	4.01223	+	0.295960i	1.20973	+	0.0892352i	0.546376	+	0.837540i	$0.316007\pi$
$12$	0.517786	−	2.31207i	0.149472	−	0.667437i
$13$	−2.70328	−	1.90386i	−0.749754	−	0.528036i	0.136835	−	0.990594i	$-0.456307\pi$
$13$	−2.70328	−	1.90386i	−0.749754	−	0.528036i	−0.886589	+	0.462557i	$0.846932\pi$
$14$	−0.714002	+	0.477380i	−0.190825	+	0.127585i
$15$	−0.133835	−	1.35885i	−0.0345561	−	0.350854i
$16$	3.92404	+	0.775817i	0.981011	+	0.193954i
$17$	0.966673	+	0.0952090i	0.234453	+	0.0230916i	0.214561	−	0.976711i	$-0.431168\pi$
$17$	0.966673	+	0.0952090i	0.234453	+	0.0230916i	0.0198916	+	0.999802i	$0.493668\pi$
$18$	−2.16084	−	0.654800i	−0.509315	−	0.154338i
$19$	2.08289	+	5.39968i	0.477847	+	1.23877i	0.936661	+	0.350238i	$0.113899\pi$
$19$	2.08289	+	5.39968i	0.477847	+	1.23877i	−0.458814	+	0.888532i	$0.651726\pi$
$20$	2.28766	−	0.283501i	0.511537	−	0.0633928i
$21$	−0.354631	−	0.626012i	−0.0773869	−	0.136607i
$22$	−5.64697	−	0.694828i	−1.20394	−	0.148138i
$23$	4.15914	+	0.204326i	0.867241	+	0.0426048i	0.477823	−	0.878456i	$-0.341426\pi$
$23$	4.15914	+	0.204326i	0.867241	+	0.0426048i	0.389418	+	0.921061i	$0.372676\pi$
$24$	−0.890883	+	3.23015i	−0.181851	+	0.659352i
$25$	−3.31905	+	1.56979i	−0.663810	+	0.313959i
$26$	3.68713	+	2.87574i	0.723105	+	0.563980i
$27$	1.95977	−	5.08052i	0.377159	−	0.977747i
$28$	1.04148	−	0.625060i	0.196821	−	0.118125i
$29$	−1.38674	−	2.75497i	−0.257511	−	0.511586i	0.727060	−	0.686574i	$-0.240886\pi$
$29$	−1.38674	−	2.75497i	−0.257511	−	0.511586i	−0.984570	+	0.174988i	$0.944011\pi$
$30$	0.0953085	+	1.92865i	0.0174009	+	0.352122i
$31$	−0.0787648	−	0.395977i	−0.0141466	−	0.0711196i	0.973067	−	0.230522i	$-0.0740433\pi$
$31$	−0.0787648	−	0.395977i	−0.0141466	−	0.0711196i	−0.987214	+	0.159402i	$0.949043\pi$
$32$	−5.48931	−	1.36656i	−0.970382	−	0.241575i
$33$	0.929816	−	4.67450i	0.161860	−	0.813726i
$34$	−1.35889	−	0.201170i	−0.233047	−	0.0345003i
$35$	0.457216	−	0.530041i	0.0772837	−	0.0895933i
$36$	3.00708	+	1.07399i	0.501180	+	0.178998i
$37$	−2.71410	−	2.58404i	−0.446195	−	0.424813i	0.432913	−	0.901436i	$-0.357486\pi$
$37$	−2.71410	−	2.58404i	−0.446195	−	0.424813i	−0.879108	+	0.476623i	$0.841861\pi$
$38$	−2.56965	−	7.77089i	−0.416852	−	1.26060i
$39$	−2.63051	+	2.90232i	−0.421218	+	0.464743i
$40$	−3.25095	+	0.242644i	−0.514020	+	0.0383654i
$41$	−2.66987	−	1.26275i	−0.416964	−	0.197209i	0.207548	−	0.978225i	$-0.433452\pi$
$41$	−2.66987	−	1.26275i	−0.416964	−	0.197209i	−0.624511	+	0.781016i	$0.714702\pi$
$42$	0.457743	+	0.908724i	0.0706313	+	0.140219i
$43$	0.307743	−	0.394337i	0.0469304	−	0.0601358i	−0.764308	−	0.644852i	$-0.776919\pi$
$43$	0.307743	−	0.394337i	0.0469304	−	0.0601358i	0.811238	+	0.584716i	$0.198794\pi$
$44$	7.92859	+	1.37101i	1.19528	+	0.206688i
$45$	1.83961	+	0.0451598i	0.274232	+	0.00673203i
$46$	−5.86082	−	0.575527i	−0.864131	−	0.0848568i
$47$	10.1077	−	3.06612i	1.47435	−	0.447240i	0.552084	−	0.833788i	$-0.313833\pi$
$47$	10.1077	−	3.06612i	1.47435	−	0.447240i	0.922269	+	0.386548i	$0.126333\pi$
$48$	1.48122	−	4.50123i	0.213796	−	0.649696i
$49$	−1.92492	+	6.34562i	−0.274989	+	0.906517i
$50$	4.79655	−	1.98842i	0.678334	−	0.281205i
$51$	0.252126	−	1.12277i	0.0353047	−	0.157219i
$52$	−5.00980	−	4.31642i	−0.694734	−	0.598580i
$53$	6.39154	−	12.6978i	0.877946	−	1.74418i	0.245816	−	0.969317i	$-0.420944\pi$
$53$	6.39154	−	12.6978i	0.877946	−	1.74418i	0.632130	−	0.774862i	$-0.282181\pi$
$54$	−3.11871	+	7.04120i	−0.424403	+	0.958186i
$55$	4.58679	−	0.680386i	0.618483	−	0.0917432i
$56$	−1.51424	+	0.811071i	−0.202349	+	0.108384i
$57$	6.65078	−	1.66593i	0.880917	−	0.220658i
$58$	1.76876	+	3.98714i	0.232250	+	0.523538i
$59$	−3.20560	−	4.55160i	−0.417333	−	0.592568i	0.553344	−	0.832953i	$-0.313351\pi$
$59$	−3.20560	−	4.55160i	−0.417333	−	0.592568i	−0.970678	+	0.240385i	$0.922726\pi$
$60$	−0.00158158	−	2.73086i	−0.000204182	−	0.352552i
$61$	−0.808706	−	0.458126i	−0.103544	−	0.0586571i	0.440253	−	0.897874i	$-0.354889\pi$
$61$	−0.808706	−	0.458126i	−0.103544	−	0.0586571i	−0.543797	+	0.839217i	$0.683014\pi$
$62$	0.0839419	+	0.564763i	0.0106606	+	0.0717250i
$63$	0.895823	−	0.371062i	0.112863	−	0.0467494i
$64$	7.65955	+	2.30897i	0.957443	+	0.288622i
$65$	−3.52082	−	1.45837i	−0.436705	−	0.180889i
$66$	−1.63585	+	6.53873i	−0.201360	+	0.804862i
$67$	3.98803	−	1.10364i	0.487215	−	0.134831i	−0.0144447	−	0.999896i	$-0.504598\pi$
$67$	3.98803	−	1.10364i	0.487215	−	0.134831i	0.501660	+	0.865065i	$0.332723\pi$
$68$	1.90559	+	0.377898i	0.231087	+	0.0458269i
$69$	0.843381	−	4.86053i	0.101531	−	0.585139i
$70$	−0.682396	+	0.717159i	−0.0815619	+	0.0857168i
$71$	−0.208023	+	0.347066i	−0.0246878	+	0.0411892i	−0.869825	−	0.493360i	$-0.835769\pi$
$71$	−0.208023	+	0.347066i	−0.0246878	+	0.0411892i	0.845137	+	0.534549i	$0.179519\pi$
$72$	−4.17350	−	1.72448i	−0.491852	−	0.203231i
$73$	−6.19663	−	4.59574i	−0.725261	−	0.537890i	0.168901	−	0.985633i	$-0.445978\pi$
$73$	−6.19663	−	4.59574i	−0.725261	−	0.537890i	−0.894162	+	0.447743i	$0.852228\pi$
$74$	3.65549	+	3.83726i	0.424942	+	0.446072i
$75$	1.36439	+	4.13005i	0.157546	+	0.476897i
$76$	3.09365	+	11.1539i	0.354866	+	1.27944i
$77$	2.06428	−	1.30719i	0.235246	−	0.148968i
$78$	3.91588	−	3.91815i	0.443386	−	0.443643i
$79$	−2.94827	−	5.51582i	−0.331706	−	0.620579i	0.659680	−	0.751546i	$-0.270692\pi$
$79$	−2.94827	−	5.51582i	−0.331706	−	0.620579i	−0.991387	+	0.130968i	$0.958192\pi$
$80$	4.60880	−	0.118481i	0.515280	−	0.0132466i
$81$	−1.46517	−	0.783148i	−0.162796	−	0.0870165i
$82$	3.68416	+	1.96785i	0.406848	+	0.217313i
$83$	−5.12862	+	4.88285i	−0.562939	+	0.535963i	−0.916806	−	0.399333i	$-0.869242\pi$
$83$	−5.12862	+	4.88285i	−0.562939	+	0.535963i	0.353867	+	0.935296i	$0.384867\pi$
$84$	−0.583889	−	1.31518i	−0.0637075	−	0.143498i
$85$	1.11114	−	0.137046i	0.120520	−	0.0148647i
$86$	−0.461900	+	0.535784i	−0.0498079	+	0.0577750i
$87$	−3.44029	+	1.23095i	−0.368838	+	0.131972i
$88$	−11.1048	−	2.48353i	−1.18378	−	0.264746i
$89$	7.40307	−	0.363689i	0.784723	−	0.0385510i	0.347239	−	0.937777i	$-0.387119\pi$
$89$	7.40307	−	0.363689i	0.784723	−	0.0385510i	0.437485	+	0.899226i	$0.355869\pi$
$90$	−2.59538	−	0.190691i	−0.273578	−	0.0201006i
$91$	−2.00747	+	0.0492806i	−0.210440	+	0.00516602i
$92$	8.23888	+	1.21725i	0.858963	+	0.126907i
$93$	−0.476997	+	0.0351854i	−0.0494623	+	0.00364856i
$94$	−14.4889	+	3.63374i	−1.49441	+	0.374791i
$95$	3.70595	+	5.54635i	0.380223	+	0.569043i
$96$	−2.40278	+	6.25594i	−0.245233	+	0.638494i
$97$	−8.11369	+	12.1430i	−0.823821	+	1.23293i	0.146041	+	0.989279i	$0.453347\pi$
$97$	−8.11369	+	12.1430i	−0.823821	+	1.23293i	−0.969862	+	0.243656i	$0.921653\pi$
$98$	3.15675	−	8.83059i	0.318880	−	0.892024i
$99$	6.09896	+	2.01483i	0.612969	+	0.202498i
$100$	−6.91243	+	2.47782i	−0.691243	+	0.247782i
$101$	−2.91082	+	1.29028i	−0.289637	+	0.128387i	−0.544943	−	0.838473i	$-0.683449\pi$
$101$	−2.91082	+	1.29028i	−0.289637	+	0.128387i	0.255306	+	0.966860i	$0.417824\pi$
$102$	−0.433588	+	1.56855i	−0.0429316	+	0.155310i
$103$	−4.63621	+	12.9573i	−0.456819	+	1.27672i	0.463688	+	0.885999i	$0.346526\pi$
$103$	−4.63621	+	12.9573i	−0.456819	+	1.27672i	−0.920507	+	0.390726i	$0.872224\pi$
$104$	6.77873	+	6.44267i	0.664709	+	0.631756i
$105$	−0.556898	−	0.614442i	−0.0543476	−	0.0599634i
$106$	−9.90418	+	17.4951i	−0.961979	+	1.69928i
$107$	−0.337797	−	0.0934811i	−0.0326561	−	0.00903716i	0.250346	−	0.968156i	$-0.419455\pi$
$107$	−0.337797	−	0.0934811i	−0.0326561	−	0.00903716i	−0.283003	+	0.959119i	$0.591330\pi$
$108$	4.89100	−	9.73077i	0.470636	−	0.936344i
$109$	−1.96972	+	4.44362i	−0.188665	+	0.425622i	−0.983428	−	0.181298i	$-0.941970\pi$
$109$	−1.96972	+	4.44362i	−0.188665	+	0.425622i	0.794763	+	0.606920i	$0.207595\pi$
$110$	−6.52591	+	0.644655i	−0.622222	+	0.0614654i
$111$	−3.43180	+	2.81640i	−0.325732	+	0.267321i
$112$	2.19486	−	1.04121i	0.207395	−	0.0983847i
$113$	−9.41992	+	11.4782i	−0.886152	+	1.07978i	0.110155	+	0.993914i	$0.464865\pi$
$113$	−9.41992	+	11.4782i	−0.886152	+	1.07978i	−0.996307	+	0.0858648i	$0.972635\pi$
$114$	−9.50935	+	1.89439i	−0.890632	+	0.177426i
$115$	4.72887	−	0.820537i	0.440969	−	0.0765154i
$116$	−2.22338	−	5.75397i	−0.206436	−	0.534243i
$117$	−3.44802	−	3.99722i	−0.318770	−	0.369543i
$118$	4.21402	+	6.65041i	0.387932	+	0.612220i
$119$	0.505997	−	0.303283i	0.0463847	−	0.0278019i
$120$	−0.186149	+	3.85752i	−0.0169930	+	0.352142i
$121$	5.12943	+	0.760879i	0.466312	+	0.0691708i
$122$	1.11072	+	0.702904i	0.100560	+	0.0636380i
$123$	−1.87187	+	2.95601i	−0.168781	+	0.266534i
$124$	−0.0796113	−	0.803536i	−0.00714931	−	0.0721597i
$125$	−7.87926	+	6.14904i	−0.704743	+	0.549987i
$126$	−1.29097	+	0.462340i	−0.115009	+	0.0411885i
$127$	−14.2567	+	14.2567i	−1.26507	+	1.26507i	−0.316472	+	0.948602i	$0.602498\pi$
$127$	−14.2567	+	14.2567i	−1.26507	+	1.26507i	−0.948602	+	0.316472i	$0.897502\pi$
$128$	−10.6601	−	3.78987i	−0.942225	−	0.334981i
$129$	−0.419018	−	0.419018i	−0.0368925	−	0.0368925i
$130$	4.87267	+	2.30287i	0.427361	+	0.201975i
$131$	4.29112	+	5.49856i	0.374917	+	0.480411i	0.938319	−	0.345772i	$-0.112383\pi$
$131$	4.29112	+	5.49856i	0.374917	+	0.480411i	−0.563402	+	0.826183i	$0.690508\pi$
$132$	2.76176	−	9.12331i	0.240380	−	0.794082i
$133$	2.96957	+	1.88046i	0.257494	+	0.163056i
$134$	−5.70934	+	1.28381i	−0.493212	+	0.110904i
$135$	0.920920	−	6.20834i	0.0792601	−	0.534328i
$136$	−2.66564	−	0.665247i	−0.228576	−	0.0570444i
$137$	−0.104356	−	0.174108i	−0.00891575	−	0.0148750i	0.853238	−	0.521521i	$-0.174635\pi$
$137$	−0.104356	−	0.174108i	−0.00891575	−	0.0148750i	−0.862154	+	0.506646i	$0.830885\pi$
$138$	−1.52660	+	6.80746i	−0.129952	+	0.579490i
$139$	6.06144	−	5.22863i	0.514124	−	0.443487i	−0.357319	−	0.933982i	$-0.616309\pi$
$139$	6.06144	−	5.22863i	0.514124	−	0.443487i	0.871444	+	0.490496i	$0.163184\pi$
$140$	1.01338	−	0.965934i	0.0856460	−	0.0816363i
$141$	−2.13925	−	12.3288i	−0.180158	−	1.03827i
$142$	0.317781	−	0.475891i	0.0266676	−	0.0399359i
$143$	−10.2827	−	8.43879i	−0.859882	−	0.705687i
$144$	5.77624	+	2.72378i	0.481353	+	0.226981i
$145$	−2.25521	−	2.74798i	−0.187285	−	0.228207i
$146$	8.43590	+	6.91908i	0.698160	+	0.572627i
$147$	7.18179	+	3.18347i	0.592344	+	0.262568i
$148$	−4.89879	−	5.67241i	−0.402678	−	0.466269i
$149$	−2.23814	+	8.08761i	−0.183356	+	0.662563i	0.813373	+	0.581743i	$0.197629\pi$
$149$	−2.23814	+	8.08761i	−0.183356	+	0.662563i	−0.996729	+	0.0808200i	$0.974246\pi$
$150$	−1.64233	−	5.92794i	−0.134096	−	0.484015i
$151$	2.50862	−	2.27368i	0.204148	−	0.185029i	−0.563082	−	0.826401i	$-0.690384\pi$
$151$	2.50862	−	2.27368i	0.204148	−	0.185029i	0.767230	+	0.641372i	$0.221634\pi$
$152$	−3.60044	−	15.9686i	−0.292035	−	1.29522i
$153$	1.46016	+	0.522454i	0.118047	+	0.0422379i
$154$	−3.00602	+	1.70404i	−0.242232	+	0.137316i
$155$	−0.188574	−	0.425416i	−0.0151466	−	0.0341702i
$156$	−5.80158	+	5.26437i	−0.464498	+	0.421487i
$157$	7.14480	−	21.6276i	0.570217	−	1.72607i	−0.110837	−	0.993839i	$-0.535353\pi$
$157$	7.14480	−	21.6276i	0.570217	−	1.72607i	0.681054	−	0.732233i	$-0.261522\pi$
$158$	3.78402	+	7.99465i	0.301040	+	0.636020i
$159$	−14.0027	−	9.35631i	−1.11049	−	0.742004i
$160$	−6.51824	−	0.150571i	−0.515312	−	0.0119037i
$161$	2.10279	−	1.40504i	0.165723	−	0.110733i
$162$	2.01557	+	1.20729i	0.158358	+	0.0948539i
$163$	1.51409	+	20.5260i	0.118593	+	1.60772i	0.649548	+	0.760321i	$0.274958\pi$
$163$	1.51409	+	20.5260i	0.118593	+	1.60772i	−0.530955	+	0.847400i	$0.678167\pi$
$164$	−5.06824	−	3.03380i	−0.395763	−	0.236900i
$165$	−0.134812	−	5.49164i	−0.0104951	−	0.427523i
$166$	7.58116	−	6.54339i	0.588412	−	0.507865i
$167$	0.487045	+	9.91402i	0.0376886	+	0.767170i	0.941045	+	0.338280i	$0.109845\pi$
$167$	0.487045	+	9.91402i	0.0376886	+	0.767170i	−0.903357	+	0.428890i	$0.858905\pi$
$168$	0.734036	+	1.89801i	0.0566321	+	0.146434i
$169$	−0.696554	−	1.94674i	−0.0535811	−	0.149749i
$170$	−1.57897	+	0.116932i	−0.121102	+	0.00896825i
$171$	1.13108	+	9.17055i	0.0864958	+	0.701290i
$172$	0.689407	−	0.724947i	0.0525668	−	0.0552767i
$173$	−12.8194	−	13.4647i	−0.974644	−	1.02370i	−0.999712	−	0.0240146i	$-0.992355\pi$
$173$	−12.8194	−	13.4647i	−0.974644	−	1.02370i	0.0250679	−	0.999686i	$-0.492020\pi$
$174$	4.94443	−	1.50144i	0.374836	−	0.113824i
$175$	−1.05114	+	1.96654i	−0.0794585	+	0.148656i
$176$	15.5145	+	4.27411i	1.16945	+	0.322173i
$177$	−5.81646	+	3.10896i	−0.437192	+	0.233684i
$178$	−10.4821	+	0.00303538i	−0.785670	+	0.000227512i
$179$	11.7939	+	18.6246i	0.881515	+	1.39206i	0.919628	+	0.392791i	$0.128490\pi$
$179$	11.7939	+	18.6246i	0.881515	+	1.39206i	−0.0381125	+	0.999273i	$0.512135\pi$
$180$	3.65290	+	0.448395i	0.272271	+	0.0334214i
$181$	−10.0654	+	3.32515i	−0.748153	+	0.247157i	−0.662390	−	0.749159i	$-0.730458\pi$
$181$	−10.0654	+	3.32515i	−0.748153	+	0.247157i	−0.0857633	+	0.996316i	$0.527333\pi$
$182$	2.83901	+	0.0688713i	0.210442	+	0.00510508i
$183$	−0.655923	+	0.884409i	−0.0484872	+	0.0653774i
$184$	−11.5537	−	2.28774i	−0.851750	−	0.168655i
$185$	−3.70476	−	2.22055i	−0.272380	−	0.163258i
$186$	0.676200	−	0.0167957i	0.0495814	−	0.00123152i
$187$	3.85033	+	0.668096i	0.281564	+	0.0488560i
$188$	20.7166	−	4.13327i	1.51092	−	0.301450i
$189$	−0.882056	−	3.18734i	−0.0641601	−	0.231845i
$190$	−4.85216	−	8.09003i	−0.352013	−	0.586913i
$191$	−1.47308	+	3.55632i	−0.106588	+	0.257327i	−0.968171	−	0.250291i	$-0.919474\pi$
$191$	−1.47308	+	3.55632i	−0.106588	+	0.257327i	0.861583	+	0.507618i	$0.169474\pi$
$192$	3.82556	−	8.67096i	0.276086	−	0.625772i
$193$	9.95526	+	24.0341i	0.716595	+	1.73001i	0.682822	+	0.730584i	$0.260752\pi$
$193$	9.95526	+	24.0341i	0.716595	+	1.73001i	0.0337729	+	0.999430i	$0.489248\pi$
$194$	12.2985	−	16.5926i	0.882981	−	1.19128i
$195$	−2.22528	+	3.92816i	−0.159355	+	0.281301i
$196$	−5.06817	+	12.2557i	−0.362012	+	0.875408i
$197$	10.6152	−	7.47610i	0.756305	−	0.532650i	−0.132363	−	0.991201i	$-0.542256\pi$
$197$	10.6152	−	7.47610i	0.756305	−	0.532650i	0.888668	+	0.458551i	$0.151631\pi$
$198$	−8.47598	−	3.26673i	−0.602362	−	0.232156i
$199$	0.421203	+	1.68154i	0.0298583	+	0.119201i	0.983128	−	0.182921i	$-0.0585551\pi$
$199$	0.421203	+	1.68154i	0.0298583	+	0.119201i	−0.953269	+	0.302122i	$0.902305\pi$
$200$	9.93495	−	3.02316i	0.702507	−	0.213770i
$201$	−0.719283	−	4.84901i	−0.0507343	−	0.342023i
$202$	4.20062	−	1.62176i	0.295555	−	0.114106i
$203$	−1.67317	−	0.842202i	−0.117433	−	0.0591110i
$204$	0.720660	−	2.18572i	0.0504563	−	0.153031i
$205$	−3.32136	−	0.745835i	−0.231974	−	0.0520914i
$206$	7.44262	−	17.9828i	0.518552	−	1.25292i
$207$	6.36204	+	1.92990i	0.442192	+	0.134138i
$208$	−9.13073	−	9.56808i	−0.633102	−	0.663427i
$209$	6.75892	+	22.2812i	0.467524	+	1.54122i
$210$	0.744248	+	0.906334i	0.0513580	+	0.0625430i
$211$	0.563707	−	22.9629i	0.0388072	−	1.58083i	−0.592677	−	0.805440i	$-0.701929\pi$
$211$	0.563707	−	22.9629i	0.0388072	−	1.58083i	0.631484	−	0.775389i	$-0.282446\pi$
$212$	15.1968	−	24.0292i	1.04372	−	1.65033i
$213$	0.377900	+	0.294916i	0.0258933	+	0.0202073i
$214$	0.470700	+	0.155347i	0.0321764	+	0.0106193i
$215$	0.246498	−	0.521177i	0.0168110	−	0.0355439i
$216$	−7.57994	+	13.4076i	−0.515749	+	0.912272i
$217$	−0.181681	−	0.164666i	−0.0123333	−	0.0111782i
$218$	3.08883	−	6.14088i	0.209202	−	0.415913i
$219$	−6.30210	+	6.61930i	−0.425856	+	0.447291i
$220$	9.26252	−	0.460416i	0.624479	−	0.0310412i
$221$	−2.43192	−	2.09779i	−0.163589	−	0.141113i
$222$	5.04180	−	3.74152i	0.338384	−	0.251114i
$223$	−17.9124	−	3.56299i	−1.19950	−	0.238596i	−0.445387	−	0.895338i	$-0.646934\pi$
$223$	−17.9124	−	3.56299i	−1.19950	−	0.238596i	−0.754115	+	0.656743i	$0.771934\pi$
$224$	−3.17214	+	1.31933i	−0.211947	+	0.0881512i
$225$	−5.74922	+	1.14359i	−0.383281	+	0.0762394i
$226$	14.0977	−	15.5635i	0.937767	−	1.03527i
$227$	8.60817	−	4.33299i	0.571344	−	0.287591i	−0.140325	−	0.990106i	$-0.544815\pi$
$227$	8.60817	−	4.33299i	0.571344	−	0.287591i	0.711669	+	0.702515i	$0.247940\pi$
$228$	13.5629	−	2.01990i	0.898227	−	0.133771i
$229$	11.1356	+	4.29547i	0.735861	+	0.283853i	0.698659	−	0.715455i	$-0.253781\pi$
$229$	11.1356	+	4.29547i	0.735861	+	0.283853i	0.0372018	+	0.999308i	$0.488156\pi$
$230$	−6.73627	+	0.832820i	−0.444177	+	0.0549146i
$231$	−1.23759	−	2.61666i	−0.0814272	−	0.172163i
$232$	2.74367	+	8.28104i	0.180131	+	0.543677i
$233$	−0.228325	+	4.64767i	−0.0149581	+	0.304479i	0.979646	+	0.200734i	$0.0643326\pi$
$233$	−0.228325	+	4.64767i	−0.0149581	+	0.304479i	−0.994604	+	0.103745i	$0.966917\pi$
$234$	4.59470	+	5.88405i	0.300365	+	0.384652i
$235$	10.5925	−	6.00059i	0.690980	−	0.391436i
$236$	−5.49367	−	9.68460i	−0.357607	−	0.630413i
$237$	−6.91284	+	2.66657i	−0.449037	+	0.173213i
$238$	−0.735658	+	0.393491i	−0.0476856	+	0.0255062i
$239$	−1.18965	+	12.0788i	−0.0769524	+	0.781311i	0.876828	+	0.480805i	$0.159655\pi$
$239$	−1.18965	+	12.0788i	−0.0769524	+	0.781311i	−0.953780	+	0.300506i	$0.902845\pi$
$240$	0.529045	−	5.43603i	0.0341497	−	0.350894i
$241$	−0.501807	+	0.0494237i	−0.0323242	+	0.00318366i	−0.114166	−	0.993462i	$-0.536420\pi$
$241$	−0.501807	+	0.0494237i	−0.0323242	+	0.00318366i	0.0818421	+	0.996645i	$0.473920\pi$
$242$	−7.19298	−	1.42861i	−0.462382	−	0.0918344i
$243$	8.27326	−	11.7471i	0.530730	−	0.753578i
$244$	−1.52044	−	1.06949i	−0.0973359	−	0.0684674i
$245$	−0.562250	+	7.62223i	−0.0359208	+	0.486967i
$246$	2.84799	−	4.04632i	0.181581	−	0.257984i
$247$	4.64963	−	18.5623i	0.295849	−	1.18109i
$248$	0.0570229	+	1.14051i	0.00362096	+	0.0724225i
$249$	4.99733	+	6.73812i	0.316693	+	0.427011i
$250$	11.5539	−	8.14216i	0.730731	−	0.514956i
$251$	−1.45979	−	6.50075i	−0.0921413	−	0.410324i	0.907818	−	0.419365i	$-0.137747\pi$
$251$	−1.45979	−	6.50075i	−0.0921413	−	0.410324i	−0.999959	+	0.00904084i	$0.997122\pi$
$252$	1.85543	−	0.564013i	0.116881	−	0.0355295i
$253$	16.6270	+	2.05074i	1.04533	+	0.128929i
$254$	21.1214	−	19.1545i	1.32528	−	1.20186i
$255$		−	1.32631i		−	0.0830567i
$256$	14.7962	+	6.08867i	0.924764	+	0.380542i
$257$		−	16.2524i		−	1.01380i	−0.862006	−	0.506899i	$-0.830792\pi$
$257$		−	16.2524i		−	1.01380i	0.862006	−	0.506899i	$-0.169208\pi$
$258$	0.562970	+	0.620781i	0.0350490	+	0.0386481i
$259$	−2.25883	−	0.278600i	−0.140357	−	0.0173113i
$260$	−6.72393	−	3.58901i	−0.417000	−	0.222581i
$261$	−1.07891	−	4.80461i	−0.0667830	−	0.297398i
$262$	−5.68203	−	8.06290i	−0.351037	−	0.498127i
$263$	6.39695	+	8.62529i	0.394453	+	0.531858i	0.955134	−	0.296174i	$-0.0957107\pi$
$263$	6.39695	+	8.62529i	0.394453	+	0.531858i	−0.560681	+	0.828032i	$0.689461\pi$
$264$	−4.53042	+	12.6964i	−0.278828	+	0.781411i
$265$	3.98117	−	15.8937i	0.244561	−	0.976343i
$266$	−4.06488	−	2.86105i	−0.249234	−	0.175422i
$267$	0.645953	−	8.75698i	0.0395317	−	0.535918i
$268$	8.15317	−	1.41957i	0.498034	−	0.0867143i
$269$	−14.5603	+	20.6741i	−0.887759	+	1.26052i	0.0769052	+	0.997038i	$0.475496\pi$
$269$	−14.5603	+	20.6741i	−0.887759	+	1.26052i	−0.964664	+	0.263482i	$0.915129\pi$
$270$	−1.72910	+	8.70593i	−0.105229	+	0.529826i
$271$	−26.6754	+	2.62730i	−1.62041	+	0.159597i	−0.867124	−	0.498092i	$-0.834034\pi$
$271$	−26.6754	+	2.62730i	−1.62041	+	0.159597i	−0.753290	+	0.657688i	$0.771534\pi$
$272$	3.71940	+	1.12356i	0.225522	+	0.0681261i
$273$	−0.233174	+	2.36745i	−0.0141123	+	0.143285i
$274$	0.135396	+	0.253131i	0.00817956	+	0.0152922i
$275$	−13.7814	+	5.31606i	−0.831048	+	0.320571i
$276$	2.62596	−	9.51043i	0.158064	−	0.572461i
$277$	16.5506	−	9.37577i	0.994427	−	0.563336i	0.0927236	−	0.995692i	$-0.470443\pi$
$277$	16.5506	−	9.37577i	0.994427	−	0.563336i	0.901703	+	0.432356i	$0.142318\pi$
$278$	−8.92265	+	6.96746i	−0.535145	+	0.417881i
$279$	0.0316283	−	0.643810i	0.00189354	−	0.0385439i
$280$	−1.49806	+	1.29451i	−0.0895261	+	0.0773615i
$281$	1.80142	+	3.80878i	0.107464	+	0.227212i	0.950554	−	0.310559i	$-0.100516\pi$
$281$	1.80142	+	3.80878i	0.107464	+	0.227212i	−0.843091	+	0.537772i	$0.819266\pi$
$282$	2.17128	+	17.5624i	0.129298	+	1.04583i
$283$	−7.94996	−	3.06664i	−0.472576	−	0.182293i	0.111874	−	0.993722i	$-0.464315\pi$
$283$	−7.94996	−	3.06664i	−0.472576	−	0.182293i	−0.584450	+	0.811430i	$0.698690\pi$
$284$	−0.481704	+	0.650289i	−0.0285839	+	0.0385876i
$285$	7.05860	−	3.55300i	0.418116	−	0.210462i
$286$	13.9425	+	12.6294i	0.824436	+	0.746791i
$287$	−1.75923	+	0.349933i	−0.103844	+	0.0206559i
$288$	−7.97122	−	4.24588i	−0.469709	−	0.250191i
$289$	−15.7480	−	3.13246i	−0.926350	−	0.184263i
$290$	2.99599	+	4.03717i	0.175930	+	0.237071i
$291$	13.1006	+	11.3007i	0.767974	+	0.662459i
$292$	−11.4387	−	10.3553i	−0.669397	−	0.606001i
$293$	−4.24240	+	4.45593i	−0.247843	+	0.260318i	−0.836377	−	0.548155i	$-0.815330\pi$
$293$	−4.24240	+	4.45593i	−0.247843	+	0.260318i	0.588534	+	0.808473i	$0.299705\pi$
$294$	−9.92488	−	4.99216i	−0.578831	−	0.291149i
$295$	−4.75436	−	4.30910i	−0.276810	−	0.250886i
$296$	6.52838	+	8.35038i	0.379455	+	0.485356i
$297$	9.36668	−	19.8042i	0.543510	−	1.14916i
$298$	3.71935	−	11.2696i	0.215456	−	0.652830i
$299$	−10.8543	−	8.47078i	−0.627721	−	0.489878i
$300$	1.91091	+	8.48669i	0.110327	+	0.489979i
$301$	0.00745537	−	0.303698i	0.000429720	−	0.0175049i
$302$	−3.70034	+	3.03859i	−0.212931	+	0.174851i
$303$	1.09494	+	3.60953i	0.0629027	+	0.207362i
$304$	3.98417	+	22.8045i	0.228508	+	1.30793i
$305$	−1.02514	−	0.310974i	−0.0586995	−	0.0178063i
$306$	−2.02648	−	0.838709i	−0.115846	−	0.0479458i
$307$	−1.06409	−	0.238948i	−0.0607306	−	0.0136375i	0.188630	−	0.982048i	$-0.439595\pi$
$307$	−1.06409	−	0.238948i	−0.0607306	−	0.0136375i	−0.249360	+	0.968411i	$0.580220\pi$
$308$	4.36365	−	2.19965i	0.248642	−	0.125336i
$309$	14.5624	+	7.33010i	0.828426	+	0.416995i
$310$	0.237020	+	0.613921i	0.0134618	+	0.0348684i
$311$	−3.86482	−	26.0545i	−0.219154	−	1.47742i	−0.767437	−	0.641124i	$-0.778468\pi$
$311$	−3.86482	−	26.0545i	−0.219154	−	1.47742i	0.548283	−	0.836293i	$-0.315282\pi$
$312$	8.55807	−	7.03587i	0.484505	−	0.398328i
$313$	5.52024	+	22.0380i	0.312023	+	1.24566i	0.899679	+	0.436553i	$0.143801\pi$
$313$	5.52024	+	22.0380i	0.312023	+	1.24566i	−0.587656	+	0.809111i	$0.699949\pi$
$314$	−11.5842	+	30.0568i	−0.653733	+	1.69620i
$315$	0.913715	−	0.643511i	0.0514820	−	0.0362577i
$316$	−4.79355	−	11.5537i	−0.269658	−	0.649947i
$317$	−2.97189	+	5.24613i	−0.166918	+	0.294652i	−0.940983	−	0.338455i	$-0.890096\pi$
$317$	−2.97189	+	5.24613i	−0.166918	+	0.294652i	0.774064	+	0.633107i	$0.218221\pi$
$318$	19.1338	+	14.1820i	1.07297	+	0.795289i
$319$	−4.74854	−	11.4640i	−0.265867	−	0.641860i
$320$	9.19683	+	0.662335i	0.514118	+	0.0370256i
$321$	−0.158898	+	0.383613i	−0.00886880	+	0.0214112i
$322$	−3.06718	+	1.83960i	−0.170927	+	0.102517i
$323$	1.49937	+	5.41803i	0.0834272	+	0.301467i
$324$	−2.76377	−	1.84438i	−0.153543	−	0.102465i
$325$	11.9610	+	2.07543i	0.663476	+	0.115124i
$326$	−0.722748	−	29.0980i	−0.0400293	−	1.61159i
$327$	4.93900	+	2.96032i	0.273127	+	0.163706i
$328$	6.94976	+	4.63496i	0.383737	+	0.255923i
$329$	3.82134	−	5.15247i	0.210677	−	0.284065i
$330$	−0.188404	+	7.76640i	−0.0103713	+	0.427526i
$331$	30.1902	−	9.97351i	1.65941	−	0.548194i	0.677167	−	0.735829i	$-0.263207\pi$
$331$	30.1902	−	9.97351i	1.65941	−	0.548194i	0.982239	+	0.187636i	$0.0600825\pi$
$332$	−11.1600	+	8.71976i	−0.612485	+	0.478559i
$333$	−3.20092	−	5.05481i	−0.175410	−	0.277002i
$334$	−0.00406492	−	14.0375i	−0.000222422	−	0.768095i
$335$	4.20613	−	2.24822i	0.229806	−	0.122834i
$336$	−0.905918	−	2.73163i	−0.0494219	−	0.149022i
$337$	−7.54383	+	14.1135i	−0.410938	+	0.768812i	−0.999205	−	0.0398550i	$-0.987310\pi$
$337$	−7.54383	+	14.1135i	−0.410938	+	0.768812i	0.588267	+	0.808667i	$0.299810\pi$
$338$	0.849611	+	2.79788i	0.0462128	+	0.152184i
$339$	12.1296	+	12.7401i	0.658789	+	0.691948i
$340$	2.23841	−	0.0562471i	0.121395	−	0.00305043i
$341$	−0.198829	−	1.61206i	−0.0107672	−	0.0872981i
$342$	−0.965071	−	13.0317i	−0.0521850	−	0.704674i
$343$	2.78896	+	7.79463i	0.150590	+	0.420871i
$344$	−1.02382	+	0.976452i	−0.0552005	+	0.0526468i
$345$	−0.278992	−	5.67901i	−0.0150204	−	0.305748i
$346$	17.1790	+	19.9036i	0.923549	+	1.07002i
$347$	−0.272367	−	11.0950i	−0.0146214	−	0.595610i	−0.961622	−	0.274378i	$-0.911528\pi$
$347$	−0.272367	−	11.0950i	−0.0146214	−	0.595610i	0.947001	−	0.321232i	$-0.104097\pi$
$348$	−7.08772	+	1.77975i	−0.379942	+	0.0954044i
$349$	0.0359472	+	0.487324i	0.00192421	+	0.0260859i	0.998167	−	0.0605153i	$-0.0192744\pi$
$349$	0.0359472	+	0.487324i	0.00192421	+	0.0260859i	−0.996243	+	0.0866012i	$0.972399\pi$
$350$	1.62042	−	2.70528i	0.0866151	−	0.144604i
$351$	−14.9704	+	10.0029i	−0.799062	+	0.533916i
$352$	−21.6199	−	7.10755i	−1.15234	−	0.378834i
$353$	−19.8730	−	13.2787i	−1.05773	−	0.706755i	−0.100168	−	0.994971i	$-0.531938\pi$
$353$	−19.8730	−	13.2787i	−1.05773	−	0.706755i	−0.957565	+	0.288216i	$0.906938\pi$
$354$	8.43039	−	3.99026i	0.448070	−	0.212080i
$355$	−0.146293	+	0.442835i	−0.00776442	+	0.0235032i
$356$	14.8066	+	0.718804i	0.784746	+	0.0380965i
$357$	−0.283211	−	0.638913i	−0.0149891	−	0.0338148i
$358$	−15.3744	−	27.1213i	−0.812563	−	1.43341i
$359$	−14.0688	−	5.03389i	−0.742521	−	0.265678i	−0.0616665	−	0.998097i	$-0.519642\pi$
$359$	−14.0688	−	5.03389i	−0.742521	−	0.265678i	−0.680855	+	0.732418i	$0.738392\pi$
$360$	−5.12890	−	0.885360i	−0.270317	−	0.0466626i
$361$	−10.7400	+	9.73419i	−0.565265	+	0.512326i
$362$	14.4470	−	4.00253i	0.759319	−	0.210369i
$363$	1.63846	−	5.92064i	0.0859969	−	0.310753i
$364$	−4.00544	−	0.293127i	−0.209942	−	0.0153640i
$365$	−8.12915	−	3.60341i	−0.425499	−	0.188611i
$366$	0.987520	−	1.20401i	0.0516185	−	0.0629345i
$367$	−5.58626	−	6.80688i	−0.291601	−	0.355316i	0.606518	−	0.795070i	$-0.292566\pi$
$367$	−5.58626	−	6.80688i	−0.291601	−	0.355316i	−0.898119	+	0.439753i	$0.855066\pi$
$368$	16.1621	+	4.02851i	0.842510	+	0.210001i
$369$	−3.64499	−	2.99137i	−0.189751	−	0.155724i
$370$	5.07991	+	3.39216i	0.264092	+	0.176350i
$371$	−1.47601	−	8.50647i	−0.0766308	−	0.441634i
$372$	−0.956311	−	0.0229219i	−0.0495824	−	0.00118845i
$373$	−18.7148	+	16.1435i	−0.969014	+	0.835877i	−0.986465	−	0.163971i	$-0.947570\pi$
$373$	−18.7148	+	16.1435i	−0.969014	+	0.835877i	0.0174513	+	0.999848i	$0.494445\pi$
$374$	−5.39262	−	1.20931i	−0.278846	−	0.0625321i
$375$	6.08718	+	10.1558i	0.314340	+	0.524445i
$376$	−29.5480	+	4.40927i	−1.52382	+	0.227391i
$377$	−1.49636	+	10.0876i	−0.0770662	+	0.519538i
$378$	1.02606	+	4.56306i	0.0527747	+	0.234699i
$379$	−10.8899	−	6.89593i	−0.559375	−	0.354220i	0.225144	−	0.974326i	$-0.427715\pi$
$379$	−10.8899	−	6.89593i	−0.559375	−	0.354220i	−0.784519	+	0.620105i	$0.787090\pi$
$380$	6.29575	+	11.7621i	0.322965	+	0.603385i
$381$	14.6950	+	18.8299i	0.752846	+	0.964683i
$382$	2.32609	−	4.92180i	0.119013	−	0.251821i
$383$	−5.58478	−	5.58478i	−0.285369	−	0.285369i	0.549877	−	0.835246i	$-0.314675\pi$
$383$	−5.58478	−	5.58478i	−0.285369	−	0.285369i	−0.835246	+	0.549877i	$0.814675\pi$
$384$	−6.00187	+	11.9841i	−0.306281	+	0.611560i
$385$	1.99133	−	1.99133i	0.101487	−	0.101487i
$386$	−12.4042	−	34.6357i	−0.631355	−	1.76291i
$387$	0.629581	−	0.491330i	0.0320034	−	0.0249757i
$388$	−18.5166	+	22.5892i	−0.940039	+	1.14679i
$389$	−5.84152	+	9.22477i	−0.296177	+	0.467714i	−0.959931	−	0.280237i	$-0.909587\pi$
$389$	−5.84152	+	9.22477i	−0.296177	+	0.467714i	0.663754	+	0.747951i	$0.268962\pi$
$390$	3.41424	−	5.39514i	0.172887	−	0.273193i
$391$	4.00108	+	0.593504i	0.202343	+	0.0300148i
$392$	8.00438	−	16.9619i	0.404282	−	0.856708i
$393$	7.08727	−	4.24795i	0.357506	−	0.214281i
$394$	−15.5101	+	9.82794i	−0.781387	+	0.495125i
$395$	−4.70847	−	5.45843i	−0.236909	−	0.274643i
$396$	11.7472	+	5.19905i	0.590320	+	0.261262i
$397$	−17.6268	+	3.05854i	−0.884664	+	0.153504i	−0.595097	−	0.803654i	$-0.702886\pi$
$397$	−17.6268	+	3.05854i	−0.884664	+	0.153504i	−0.289567	+	0.957158i	$0.593511\pi$
$398$	−0.478964	−	2.40428i	−0.0240083	−	0.120516i
$399$	2.64160	−	3.21880i	0.132246	−	0.161142i
$400$	−14.2420	+	3.58496i	−0.712098	+	0.179248i
$401$	8.82957	−	7.24624i	0.440928	−	0.361860i	−0.387581	−	0.921835i	$-0.626689\pi$
$401$	8.82957	−	7.24624i	0.440928	−	0.361860i	0.828509	+	0.559975i	$0.189189\pi$
$402$	0.681508	+	6.89899i	0.0339905	+	0.344090i
$403$	−0.540963	+	1.22039i	−0.0269473	+	0.0607922i
$404$	−6.04538	+	2.00101i	−0.300769	+	0.0995539i
$405$	−1.84546	−	0.510708i	−0.0917017	−	0.0253773i
$406$	2.30530	+	1.30506i	0.114410	+	0.0647689i
$407$	−10.1248	−	11.1710i	−0.501868	−	0.553726i
$408$	−1.16873	+	3.03768i	−0.0578608	+	0.150388i
$409$	−2.25605	+	6.30523i	−0.111554	+	0.311773i	−0.984327	−	0.176354i	$-0.943570\pi$
$409$	−2.25605	+	6.30523i	−0.111554	+	0.311773i	0.872773	+	0.488127i	$0.162320\pi$
$410$	4.64007	+	1.28263i	0.229156	+	0.0633447i
$411$	−0.219842	+	0.0974494i	−0.0108440	+	0.00480683i
$412$	−11.7534	+	24.8878i	−0.579050	+	1.22614i
$413$	−3.21042	−	1.06058i	−0.157974	−	0.0521877i
$414$	−8.85345	−	3.16492i	−0.435123	−	0.155547i
$415$	−4.53444	+	6.78627i	−0.222587	+	0.333125i
$416$	12.2374	+	14.1451i	0.599987	+	0.693519i
$417$	−5.26861	−	7.88504i	−0.258005	−	0.386132i
$418$	−8.01015	−	31.9391i	−0.391789	−	1.56219i
$419$	−17.9697	+	1.32552i	−0.877877	+	0.0647561i	−0.504995	−	0.863123i	$-0.668506\pi$
$419$	−17.9697	+	1.32552i	−0.877877	+	0.0647561i	−0.372882	+	0.927879i	$0.621631\pi$
$420$	−0.988752	−	1.33156i	−0.0482461	−	0.0649737i
$421$	21.5909	−	0.530026i	1.05228	−	0.0258319i	0.505270	−	0.862961i	$-0.331393\pi$
$421$	21.5909	−	0.530026i	1.05228	−	0.0258319i	0.547005	+	0.837129i	$0.315768\pi$
$422$	−2.38030	+	32.3969i	−0.115871	+	1.57705i
$423$	16.8433	−	0.827457i	0.818948	−	0.0402323i
$424$	−23.1236	+	32.8936i	−1.12298	+	1.59746i
$425$	−3.35789	+	1.20147i	−0.162882	+	0.0582800i
$426$	−0.513451	−	0.442647i	−0.0248768	−	0.0214463i
$427$	−0.560237	+	0.0690987i	−0.0271118	+	0.00334392i
$428$	−0.654162	−	0.251903i	−0.0316201	−	0.0121762i
$429$	−11.4132	+	10.8662i	−0.551032	+	0.524626i
$430$	−0.384138	+	0.719173i	−0.0185248	+	0.0346816i
$431$	18.2495	+	9.75454i	0.879046	+	0.469860i	0.848207	−	0.529665i	$-0.177682\pi$
$431$	18.2495	+	9.75454i	0.879046	+	0.469860i	0.0308386	+	0.999524i	$0.490182\pi$
$432$	11.6318	−	18.4158i	0.559635	−	0.886029i
$433$	15.4787	+	28.9587i	0.743860	+	1.39166i	0.913781	+	0.406206i	$0.133149\pi$
$433$	15.4787	+	28.9587i	0.743860	+	1.39166i	−0.169921	+	0.985458i	$0.554351\pi$
$434$	0.245270	+	0.245128i	0.0117733	+	0.0117665i
$435$	−3.55801	+	2.25308i	−0.170593	+	0.108027i
$436$	−4.78668	+	8.46110i	−0.229240	+	0.405213i
$437$	7.55973	+	22.8836i	0.361631	+	1.09467i
$438$	9.35853	−	8.91523i	0.447168	−	0.425986i
$439$	−4.77042	−	3.53798i	−0.227680	−	0.168859i	0.475846	−	0.879529i	$-0.342142\pi$
$439$	−4.77042	−	3.53798i	−0.227680	−	0.168859i	−0.703526	+	0.710670i	$0.748392\pi$
$440$	−13.1154	+	0.0113937i	−0.625250	+	0.000543174i
$441$	−5.44281	+	9.08079i	−0.259182	+	0.432418i
$442$	3.29045	+	3.13095i	0.156511	+	0.148924i
$443$	4.93848	−	28.4612i	0.234634	−	1.35223i	−0.599369	−	0.800473i	$-0.704582\pi$
$443$	4.93848	−	28.4612i	0.234634	−	1.35223i	0.834004	−	0.551759i	$-0.186043\pi$
$444$	−7.37980	+	4.93721i	−0.350230	+	0.234310i
$445$	8.23346	−	2.27851i	0.390304	−	0.108012i
$446$	25.0560	+	6.26849i	1.18644	+	0.296821i
$447$	9.18453	+	3.80435i	0.434413	+	0.179940i
$448$	4.57175	−	1.64476i	0.215995	−	0.0777078i
$449$	17.4150	−	7.21352i	0.821864	−	0.340427i	0.0681871	−	0.997673i	$-0.478279\pi$
$449$	17.4150	−	7.21352i	0.821864	−	0.340427i	0.753677	+	0.657245i	$0.228279\pi$
$450$	8.19983	−	1.21876i	0.386544	−	0.0574527i
$451$	−10.3384	−	5.85663i	−0.486816	−	0.275778i
$452$	−20.9871	+	21.0114i	−0.987150	+	0.988294i
$453$	−2.30951	−	3.27925i	−0.108510	−	0.154073i
$454$	−12.4582	+	5.52666i	−0.584693	+	0.259379i
$455$	−2.24511	+	0.562370i	−0.105252	+	0.0263643i
$456$	−19.2974	+	1.91755i	−0.903682	+	0.0897977i
$457$	3.49668	−	0.518684i	0.163568	−	0.0242630i	−0.0644441	−	0.997921i	$-0.520527\pi$
$457$	3.49668	−	0.518684i	0.163568	−	0.0242630i	0.228012	+	0.973658i	$0.426777\pi$
$458$	−15.4330	−	6.83565i	−0.721139	−	0.319409i
$459$	2.37817	−	4.72462i	0.111004	−	0.220526i
$460$	9.57264	−	0.711695i	0.446327	−	0.0331829i
$461$	1.22466	−	5.45366i	0.0570381	−	0.254002i	−0.938882	−	0.344238i	$-0.888137\pi$
$461$	1.22466	−	5.45366i	0.0570381	−	0.254002i	0.995920	+	0.0902362i	$0.0287622\pi$
$462$	1.56762	+	3.78148i	0.0729324	+	0.175930i
$463$	9.07527	−	29.9171i	0.421763	−	1.39037i	−0.446731	−	0.894668i	$-0.647412\pi$
$463$	9.07527	−	29.9171i	0.421763	−	1.39037i	0.868494	−	0.495699i	$-0.165088\pi$
$464$	−3.30426	−	11.8865i	−0.153396	−	0.551816i
$465$	−0.527534	+	0.160026i	−0.0244638	+	0.00742101i
$466$	0.643127	−	6.54922i	0.0297923	−	0.303387i
$467$	−33.8717	−	0.831503i	−1.56740	−	0.0384774i	−0.768461	−	0.639896i	$-0.778977\pi$
$467$	−33.8717	−	0.831503i	−1.56740	−	0.0384774i	−0.798934	+	0.601419i	$0.794602\pi$
$468$	−6.08425	−	8.62835i	−0.281244	−	0.398846i
$469$	1.54612	−	1.98117i	0.0713931	−	0.0914818i
$470$	−15.3762	+	7.74531i	−0.709252	+	0.357265i
$471$	−24.3928	−	11.5369i	−1.12396	−	0.531594i
$472$	7.09190	+	14.0588i	0.326431	+	0.647107i
$473$	1.35144	−	1.49109i	0.0621395	−	0.0685603i
$474$	9.94854	−	3.28975i	0.456951	−	0.151103i
$475$	−15.3896	−	14.6521i	−0.706122	−	0.672284i
$476$	1.06628	−	0.505070i	0.0488730	−	0.0231499i
$477$	14.8245	−	17.1857i	0.678769	−	0.786881i
$478$	2.51365	−	16.9796i	0.114972	−	0.776627i
$479$	−5.19689	+	26.1265i	−0.237452	+	1.19375i	0.659528	+	0.751680i	$0.270756\pi$
$479$	−5.19689	+	26.1265i	−0.237452	+	1.19375i	−0.896980	+	0.442071i	$0.854244\pi$
$480$	−1.12229	+	7.64206i	−0.0512251	+	0.348811i
$481$	2.41731	+	12.1526i	0.110220	+	0.554113i
$482$	0.712227	−	0.0351962i	0.0324411	−	0.00160314i
$483$	−1.34705	−	2.67613i	−0.0612930	−	0.121768i
$484$	10.0618	+	2.51415i	0.457352	+	0.114279i
$485$	−6.05797	+	15.7047i	−0.275078	+	0.713113i
$486$	−12.4966	+	16.0224i	−0.566856	+	0.726793i
$487$	27.0296	−	12.7840i	1.22483	−	0.579300i	0.297920	−	0.954591i	$-0.403707\pi$
$487$	27.0296	−	12.7840i	1.22483	−	0.579300i	0.926907	+	0.375291i	$0.122457\pi$
$488$	2.07388	+	1.61558i	0.0938803	+	0.0731338i
$489$	24.3532	+	1.19640i	1.10129	+	0.0541030i
$490$	1.32000	−	10.7278i	0.0596315	−	0.484635i
$491$	12.6946	+	22.4091i	0.572898	+	1.01131i	0.994521	+	0.104535i	$0.0333355\pi$
$491$	12.6946	+	22.4091i	0.572898	+	1.01131i	−0.421623	+	0.906771i	$0.638539\pi$
$492$	−4.30200	+	5.51909i	−0.193949	+	0.248820i
$493$	−1.07822	−	2.79519i	−0.0485607	−	0.125889i
$494$	−7.84823	+	25.8991i	−0.353108	+	1.16526i
$495$	7.36755	+	0.725640i	0.331147	+	0.0326151i
$496$	−0.00187060	−	1.61494i	−8.39922e−5	−	0.0725129i
$497$	0.0240872	+	0.244562i	0.00108046	+	0.0109701i
$498$	−6.59406	−	9.86253i	−0.295487	−	0.441951i
$499$	18.6316	+	13.1218i	0.834064	+	0.587414i	0.912301	−	0.409520i	$-0.134304\pi$
$499$	18.6316	+	13.1218i	0.834064	+	0.587414i	−0.0782366	+	0.996935i	$0.524929\pi$
$500$	−16.8819	+	10.7040i	−0.754980	+	0.478699i
$501$	11.7271	+	0.865046i	0.523930	+	0.0386474i
$502$	1.61356	+	9.28321i	0.0720167	+	0.414330i
$503$	16.5003	+	4.13311i	0.735711	+	0.184286i	0.592687	−	0.805433i	$-0.298067\pi$
$503$	16.5003	+	4.13311i	0.735711	+	0.184286i	0.143025	+	0.989719i	$0.454317\pi$
$504$	−2.65976	+	0.668692i	−0.118475	+	0.0297859i
$505$	−2.94760	+	2.18609i	−0.131166	+	0.0972796i
$506$	−23.3446	−	4.04371i	−1.03779	−	0.179765i
$507$	−2.38991	+	0.536672i	−0.106140	+	0.0238345i
$508$	−31.1560	+	25.5993i	−1.38232	+	1.13578i
$509$	−0.818643	+	6.63739i	−0.0362857	+	0.294197i	0.963375	+	0.268157i	$0.0864147\pi$
$509$	−0.818643	+	6.63739i	−0.0362857	+	0.294197i	−0.999661	+	0.0260398i	$0.991710\pi$
$510$	−0.0914929	+	1.87345i	−0.00405138	+	0.0829578i
$511$	−4.68544			−0.207272
$512$	−20.4801	−	9.62113i	−0.905101	−	0.425198i
$513$	31.5152			1.39143
$514$	−1.12114	+	22.9570i	−0.0494515	+	1.01259i
$515$	−1.94163	+	15.7423i	−0.0855583	+	0.693688i
$516$	−0.752389	−	0.915707i	−0.0331221	−	0.0403117i
$517$	41.4617	−	9.31053i	1.82348	−	0.409477i
$518$	3.17144	+	0.549352i	0.139345	+	0.0241371i
$519$	−17.6903	+	13.1200i	−0.776516	+	0.575904i
$520$	9.25017	+	5.53342i	0.405647	+	0.242657i
$521$	−2.01497	−	0.504724i	−0.0882774	−	0.0221123i	0.198590	−	0.980083i	$-0.436364\pi$
$521$	−2.01497	−	0.504724i	−0.0882774	−	0.0221123i	−0.286867	+	0.957970i	$0.592614\pi$
$522$	1.19256	+	6.86109i	0.0521969	+	0.300302i
$523$	−20.8447	−	1.53760i	−0.911476	−	0.0672345i	−0.390304	−	0.920686i	$-0.627630\pi$
$523$	−20.8447	−	1.53760i	−0.911476	−	0.0672345i	−0.521172	+	0.853452i	$0.674505\pi$
$524$	7.46983	+	11.7810i	0.326321	+	0.514657i
$525$	2.15975	+	1.52107i	0.0942591	+	0.0663848i
$526$	−8.44088	−	12.6248i	−0.368040	−	0.550466i
$527$	−0.0384392	−	0.390280i	−0.00167444	−	0.0170009i
$528$	7.27519	−	17.6216i	0.316612	−	0.766880i
$529$	−5.63253	−	0.554755i	−0.244892	−	0.0241198i
$530$	−6.71992	+	22.1757i	−0.291895	+	0.963252i
$531$	−3.19883	−	8.29266i	−0.138818	−	0.359871i
$532$	5.54441	+	4.32173i	0.240381	+	0.187371i
$533$	4.81329	+	8.49664i	0.208487	+	0.368030i
$534$	−1.51651	+	12.3249i	−0.0656259	+	0.533352i
$535$	−0.403486	−	0.0198220i	−0.0174442	−	0.000856979i
$536$	−11.6145	+	1.44276i	−0.501671	+	0.0623177i
$537$	23.6083	−	11.1659i	1.01877	−	0.481844i
$538$	21.9931	−	28.1983i	0.948188	−	1.21572i
$539$	−9.60127	+	24.8904i	−0.413556	+	1.07210i
$540$	3.04296	−	12.1781i	0.130948	−	0.524063i
$541$	−12.3879	−	24.6106i	−0.532598	−	1.05809i	−0.985994	−	0.166782i	$-0.946663\pi$
$541$	−12.3879	−	24.6106i	−0.532598	−	1.05809i	0.453396	−	0.891309i	$-0.350212\pi$
$542$	37.8610	−	1.87098i	1.62627	−	0.0803656i
$543$	2.44994	+	12.3167i	0.105137	+	0.528559i
$544$	−5.17626	−	1.84365i	−0.221930	−	0.0790456i
$545$	−1.09295	+	5.49461i	−0.0468167	+	0.235363i
$546$	0.492679	−	3.32801i	0.0210847	−	0.142426i
$547$	−7.75988	+	8.99586i	−0.331789	+	0.384635i	−0.898273	−	0.439437i	$-0.855178\pi$
$547$	−7.75988	+	8.99586i	−0.331789	+	0.384635i	0.566485	+	0.824072i	$0.308303\pi$
$548$	−0.173789	−	0.366896i	−0.00742389	−	0.0156730i
$549$	−1.07473	−	1.02323i	−0.0458683	−	0.0436703i
$550$	19.8333	−	6.55841i	0.845696	−	0.279652i
$551$	11.9875	−	13.2262i	0.510687	−	0.563456i
$552$	−4.36531	+	13.2526i	−0.185800	+	0.564069i
$553$	−3.43373	−	1.62403i	−0.146017	−	0.0690609i
$554$	−24.0249	+	12.1019i	−1.02072	+	0.514159i
$555$	−3.14809	+	4.03390i	−0.133629	+	0.171229i
$556$	13.0842	−	9.22624i	0.554892	−	0.391280i
$557$	−15.8513	−	0.389128i	−0.671642	−	0.0164879i	−0.312706	−	0.949850i	$-0.601235\pi$
$557$	−15.8513	−	0.389128i	−0.671642	−	0.0164879i	−0.358936	+	0.933362i	$0.616860\pi$
$558$	−0.0890880	+	0.907219i	−0.00377139	+	0.0384056i
$559$	−1.58268	+	0.480100i	−0.0669402	+	0.0203061i
$560$	2.20535	−	1.72519i	0.0931931	−	0.0729025i
$561$	1.34388	−	4.43019i	0.0567387	−	0.187043i
$562$	−2.28181	−	5.50428i	−0.0962525	−	0.232184i
$563$	4.13557	−	18.4165i	0.174293	−	0.776164i	−0.808056	−	0.589106i	$-0.799480\pi$
$563$	4.13557	−	18.4165i	0.174293	−	0.776164i	0.982349	−	0.187057i	$-0.0598951\pi$
$564$	−1.85549	−	24.9572i	−0.0781301	−	1.05089i
$565$	−7.69480	+	15.2869i	−0.323723	+	0.643127i
$566$	11.0180	+	4.88013i	0.463122	+	0.205127i
$567$	−0.998053	+	0.148047i	−0.0419143	+	0.00621740i
$568$	0.725280	−	0.885324i	0.0304321	−	0.0371474i
$569$	11.1375	−	2.78980i	0.466909	−	0.116954i	−0.00238421	−	0.999997i	$-0.500759\pi$
$569$	11.1375	−	2.78980i	0.466909	−	0.116954i	0.469293	+	0.883043i	$0.344509\pi$
$570$	−10.2156	+	4.53180i	−0.427884	+	0.189816i
$571$	−23.0955	−	32.7931i	−0.966516	−	1.37235i	−0.927792	−	0.373097i	$-0.878296\pi$
$571$	−23.0955	−	32.7931i	−0.966516	−	1.37235i	−0.0387231	−	0.999250i	$-0.512329\pi$
$572$	−18.8230	−	18.8012i	−0.787027	−	0.786116i
$573$	3.96777	+	2.24771i	0.165756	+	0.0938995i
$574$	2.50911	−	0.372934i	0.104728	−	0.0155659i
$575$	−14.1251	+	5.85083i	−0.589059	+	0.243996i
$576$	10.9667	+	6.54731i	0.456945	+	0.272805i
$577$	7.14230	+	2.95844i	0.297338	+	0.123161i	0.526365	−	0.850259i	$-0.323555\pi$
$577$	7.14230	+	2.95844i	0.297338	+	0.123161i	−0.229027	+	0.973420i	$0.573555\pi$
$578$	22.0284	+	5.51104i	0.916260	+	0.229229i
$579$	29.7021	−	8.21967i	1.23438	−	0.341598i
$580$	−3.95342	−	5.90930i	−0.164157	−	0.245370i
$581$	−0.735251	+	4.23735i	−0.0305033	+	0.175795i
$582$	−17.7255	−	16.8663i	−0.734746	−	0.699131i
$583$	29.4024	−	49.0549i	1.21772	−	2.03164i
$584$	15.4431	+	15.4163i	0.639041	+	0.637932i
$585$	−4.88699	−	3.62444i	−0.202052	−	0.149852i
$586$	6.29989	−	6.00148i	0.260246	−	0.247919i
$587$	−0.439007	−	1.32889i	−0.0181197	−	0.0548493i	0.940072	−	0.340976i	$-0.110757\pi$
$587$	−0.439007	−	1.32889i	−0.0181197	−	0.0548493i	−0.958192	+	0.286126i	$0.907632\pi$
$588$	13.6748	+	7.73623i	0.563940	+	0.319037i
$589$	1.97409	−	1.25008i	0.0813410	−	0.0515086i
$590$	6.41842	+	6.41471i	0.264242	+	0.264089i
$591$	−7.25072	−	13.5651i	−0.298255	−	0.557996i
$592$	−8.64550	−	12.2455i	−0.355328	−	0.503288i
$593$	−11.3930	−	6.08969i	−0.467855	−	0.250074i	0.220584	−	0.975368i	$-0.429204\pi$
$593$	−11.3930	−	6.08969i	−0.467855	−	0.250074i	−0.688439	+	0.725294i	$0.741704\pi$
$594$	−14.5969	+	27.3279i	−0.598917	+	1.12128i
$595$	0.492443	−	0.468845i	0.0201882	−	0.0192208i
$596$	−6.03111	+	15.6621i	−0.247044	+	0.641543i
$597$	2.03817	−	0.251384i	0.0834166	−	0.0102885i
$598$	14.7477	+	12.7140i	0.603078	+	0.519914i
$599$	12.1314	−	4.34070i	0.495677	−	0.177356i	−0.0771705	−	0.997018i	$-0.524589\pi$
$599$	12.1314	−	4.34070i	0.495677	−	0.177356i	0.572848	+	0.819662i	$0.305839\pi$
$600$	−2.11379	−	12.1195i	−0.0862949	−	0.494778i
$601$	44.6781	−	2.19489i	1.82246	−	0.0895315i	0.891137	−	0.453735i	$-0.149909\pi$
$601$	44.6781	−	2.19489i	1.82246	−	0.0895315i	0.931319	+	0.364204i	$0.118659\pi$
$602$	−0.0314810	+	0.428468i	−0.00128307	+	0.0174631i
$603$	6.60443	−	0.162130i	0.268953	−	0.00660243i
$604$	5.43646	−	4.03683i	0.221206	−	0.164256i
$605$	5.96057	−	0.439678i	0.242332	−	0.0178755i
$606$	−1.29764	−	5.17411i	−0.0527130	−	0.210184i
$607$	2.20301	+	3.29704i	0.0894175	+	0.133823i	0.873482	−	0.486857i	$-0.161857\pi$
$607$	2.20301	+	3.29704i	0.0894175	+	0.133823i	−0.784064	+	0.620680i	$0.786857\pi$
$608$	−4.05464	−	32.4869i	−0.164437	−	1.31752i
$609$	−1.23287	+	1.84511i	−0.0499582	+	0.0747677i
$610$	1.42659	+	0.509977i	0.0577611	+	0.0206484i
$611$	−33.1613	−	10.9550i	−1.34156	−	0.443192i
$612$	2.80461	+	1.32449i	0.113370	+	0.0535395i
$613$	−27.7228	+	12.2887i	−1.11972	+	0.496336i	−0.880222	−	0.474562i	$-0.842606\pi$
$613$	−27.7228	+	12.2887i	−1.11972	+	0.496336i	−0.239493	+	0.970898i	$0.576981\pi$
$614$	1.48657	+	0.410926i	0.0599931	+	0.0165836i
$615$	−1.35857	+	3.79696i	−0.0547830	+	0.153108i
$616$	−6.31553	+	2.80605i	−0.254460	+	0.113059i
$617$	−28.5462	−	31.4958i	−1.14923	−	1.26797i	−0.958108	−	0.286408i	$-0.907539\pi$
$617$	−28.5462	−	31.4958i	−1.14923	−	1.26797i	−0.191118	−	0.981567i	$-0.561211\pi$
$618$	−20.0642	−	11.3585i	−0.807100	−	0.456908i
$619$	39.6375	+	10.9692i	1.59316	+	0.440888i	0.946716	−	0.322070i	$-0.104378\pi$
$619$	39.6375	+	10.9692i	1.59316	+	0.440888i	0.646449	+	0.762958i	$0.276253\pi$
$620$	−0.292447	−	0.883532i	−0.0117450	−	0.0354835i
$621$	9.18906	−	20.7302i	0.368744	−	0.831874i
$622$	3.66186	+	37.0694i	0.146827	+	1.48635i
$623$	3.47971	−	2.85572i	0.139412	−	0.114412i
$624$	−12.5739	+	9.34802i	−0.503358	+	0.374220i
$625$	4.33806	−	5.28594i	0.173522	−	0.211438i
$626$	−6.27726	−	31.5102i	−0.250890	−	1.25940i
$627$	27.1775	−	4.71574i	1.08536	−	0.188329i
$628$	18.4364	−	41.6570i	0.735693	−	1.66230i
$629$	−2.37762	−	2.75633i	−0.0948020	−	0.109902i
$630$	−1.33504	+	0.845948i	−0.0531893	+	0.0337034i
$631$	14.3638	−	8.60931i	0.571813	−	0.342731i	−0.198795	−	0.980041i	$-0.563703\pi$
$631$	14.3638	−	8.60931i	0.571813	−	0.342731i	0.770608	+	0.637310i	$0.219953\pi$
$632$	5.97402	+	16.6506i	0.237634	+	0.662327i
$633$	−26.9171	−	3.99277i	−1.06986	−	0.158698i
$634$	4.55978	−	7.20530i	0.181092	−	0.286159i
$635$	−12.4324	+	19.6330i	−0.493366	+	0.779110i
$636$	−26.0488	−	21.3525i	−1.03290	−	0.846680i
$637$	17.2848	−	13.4892i	0.684848	−	0.534461i
$638$	5.91663	+	16.5208i	0.234242	+	0.654065i
$639$	−0.456806	+	0.456806i	−0.0180710	+	0.0180710i
$640$	−12.9451	−	1.56999i	−0.511700	−	0.0620594i
$641$	16.0020	+	16.0020i	0.632039	+	0.632039i	0.948579	−	0.316540i	$-0.102521\pi$
$641$	16.0020	+	16.0020i	0.632039	+	0.632039i	−0.316540	+	0.948579i	$0.602521\pi$
$642$	0.250910	−	0.530903i	0.00990264	−	0.0209531i
$643$	6.26398	+	8.02655i	0.247027	+	0.316536i	0.895810	−	0.444438i	$-0.146597\pi$
$643$	6.26398	+	8.02655i	0.247027	+	0.316536i	−0.648783	+	0.760974i	$0.724722\pi$
$644$	4.45938	−	2.38691i	0.175724	−	0.0940575i
$645$	−0.577033	−	0.365402i	−0.0227206	−	0.0143877i
$646$	−1.74415	−	7.75656i	−0.0686228	−	0.305178i
$647$	−4.45147	+	30.0094i	−0.175005	+	1.17979i	0.706534	+	0.707679i	$0.250258\pi$
$647$	−4.45147	+	30.0094i	−0.175005	+	1.17979i	−0.881539	+	0.472111i	$0.843492\pi$
$648$	3.77668	+	2.79589i	0.148362	+	0.109833i
$649$	−11.5145	−	19.2108i	−0.451984	−	0.754089i
$650$	−16.7521	−	3.75671i	−0.657070	−	0.147350i
$651$	−0.219954	+	0.189734i	−0.00862068	+	0.00743625i
$652$	−0.986371	+	41.1517i	−0.0386293	+	1.61163i
$653$	−3.97254	−	22.8943i	−0.155457	−	0.895924i	−0.955283	−	0.295692i	$-0.904450\pi$
$653$	−3.97254	−	22.8943i	−0.155457	−	0.895924i	0.799826	−	0.600232i	$-0.204925\pi$
$654$	−6.77227	−	4.52225i	−0.264817	−	0.176834i
$655$	6.21425	+	5.09990i	0.242811	+	0.199270i
$656$	−9.49702	−	7.02643i	−0.370796	−	0.274336i
$657$	−7.81396	−	9.52133i	−0.304852	−	0.371463i
$658$	−5.75319	+	7.01442i	−0.224283	+	0.273450i
$659$	−22.3507	−	9.90738i	−0.870659	−	0.385937i	−0.0789819	−	0.996876i	$-0.525167\pi$
$659$	−22.3507	−	9.90738i	−0.870659	−	0.385937i	−0.791677	+	0.610939i	$0.790792\pi$
$660$	0.801877	−	10.9573i	0.0312130	−	0.426511i
$661$	−3.70425	+	13.3854i	−0.144078	+	0.520633i	0.855915	+	0.517116i	$0.172994\pi$
$661$	−3.70425	+	13.3854i	−0.144078	+	0.520633i	−0.999994	+	0.00351672i	$0.998881\pi$
$662$	−43.3326	+	12.0053i	−1.68417	+	0.466598i
$663$	−2.81917	+	2.55514i	−0.109487	+	0.0992335i
$664$	16.3654	−	11.5471i	0.635099	−	0.448113i
$665$	3.81438	+	1.36481i	0.147915	+	0.0529249i
$666$	4.17270	+	7.36088i	0.161689	+	0.285228i
$667$	−5.20472	−	11.7417i	−0.201528	−	0.454639i
$668$	−0.962606	+	19.8286i	−0.0372443	+	0.767192i
$669$	−6.78681	+	20.5440i	−0.262393	+	0.794276i
$670$	−6.09638	+	2.88553i	−0.235524	+	0.111478i
$671$	−3.10913	−	2.07745i	−0.120026	−	0.0801991i
$672$	1.09120	+	3.92100i	0.0420940	+	0.151256i
$673$	35.7907	−	23.9146i	1.37963	−	0.921839i	0.379635	−	0.925136i	$-0.376050\pi$
$673$	35.7907	−	23.9146i	1.37963	−	0.921839i	0.999995	+	0.00329755i	$0.00104964\pi$
$674$	11.6295	−	19.4154i	0.447951	−	0.747852i
$675$	1.47078	+	19.9389i	0.0566105	+	0.767450i
$676$	−1.00710	−	4.01069i	−0.0387344	−	0.154257i
$677$	−0.0916204	−	3.73220i	−0.00352126	−	0.143440i	−0.998883	−	0.0472421i	$-0.984957\pi$
$677$	−0.0916204	−	3.73220i	−0.00352126	−	0.143440i	0.995362	−	0.0961981i	$-0.0306682\pi$
$678$	−16.2546	−	18.8325i	−0.624252	−	0.723259i
$679$	0.435209	+	8.85888i	0.0167018	+	0.339972i
$680$	−3.16571	−	0.0749620i	−0.121399	−	0.00287466i
$681$	−3.84623	−	10.7495i	−0.147388	−	0.411922i
$682$	0.169647	+	2.29080i	0.00649611	+	0.0877194i
$683$	5.92063	+	48.0032i	0.226546	+	1.83679i	0.489526	+	0.871989i	$0.337170\pi$
$683$	5.92063	+	48.0032i	0.226546	+	1.83679i	−0.262979	+	0.964801i	$0.584705\pi$
$684$	0.464223	+	18.4742i	0.0177500	+	0.706381i
$685$	−0.161324	−	0.169444i	−0.00616388	−	0.00647412i
$686$	−3.40180	−	11.2025i	−0.129881	−	0.427715i
$687$	6.66529	−	12.4699i	0.254297	−	0.475756i
$688$	1.51353	−	1.30864i	0.0577028	−	0.0498915i
$689$	−41.4530	+	22.1571i	−1.57923	+	0.844118i
$690$	0.00232849	+	8.04102i	8.86442e−5	+	0.306116i
$691$	−10.1385	−	16.0105i	−0.385688	−	0.609067i	0.595215	−	0.803566i	$-0.297067\pi$
$691$	−10.1385	−	16.0105i	−0.385688	−	0.609067i	−0.980903	+	0.194499i	$0.937692\pi$
$692$	−22.8929	−	29.2995i	−0.870256	−	1.11380i
$693$	3.70406	−	1.22366i	0.140706	−	0.0464829i
$694$	−0.380641	+	15.6908i	−0.0144489	+	0.595614i
$695$	5.49615	−	7.41070i	0.208481	−	0.281104i
$696$	10.1344	−	2.02501i	0.384143	−	0.0767578i
$697$	−2.46067	−	1.47487i	−0.0932043	−	0.0558645i
$698$	−0.0171593	−	0.690840i	−0.000649491	−	0.0261487i
$699$	5.43144	+	0.942444i	0.205436	+	0.0356465i
$700$	−2.47551	+	3.70951i	−0.0935656	+	0.140206i
$701$	−9.88664	−	35.7257i	−0.373413	−	1.34934i	−0.874953	−	0.484208i	$-0.839108\pi$
$701$	−9.88664	−	35.7257i	−0.373413	−	1.34934i	0.501540	−	0.865135i	$-0.332767\pi$
$702$	21.8362	−	13.0967i	0.824155	−	0.494304i
$703$	8.29981	−	20.0375i	0.313033	−	0.755729i
$704$	30.0485	+	11.5310i	1.13249	+	0.434592i
$705$	−5.51917	−	13.3245i	−0.207864	−	0.501828i
$706$	27.1552	+	20.1275i	1.02200	+	0.757508i
$707$	−0.953122	+	1.68250i	−0.0358458	+	0.0632768i
$708$	−12.1834	+	5.05481i	−0.457882	+	0.189972i
$709$	11.8480	−	8.34430i	0.444961	−	0.313377i	−0.331599	−	0.943420i	$-0.607588\pi$
$709$	11.8480	−	8.34430i	0.444961	−	0.313377i	0.776560	+	0.630044i	$0.216963\pi$
$710$	0.237191	−	0.615426i	0.00890162	−	0.0230965i
$711$	−2.42625	−	9.68614i	−0.0909915	−	0.363259i
$712$	−20.8651	−	2.03673i	−0.781953	−	0.0763298i
$713$	−0.246686	−	1.66302i	−0.00923845	−	0.0622806i
$714$	0.355969	+	0.922020i	0.0133218	+	0.0345057i
$715$	−13.6947	−	6.89335i	−0.512154	−	0.257797i
$716$	19.8459	+	39.3703i	0.741677	+	1.47134i
$717$	14.0292	+	3.15037i	0.523931	+	0.117653i
$718$	19.5253	+	8.08102i	0.728678	+	0.301581i
$719$	−2.72985	−	0.828091i	−0.101806	−	0.0308826i	0.238971	−	0.971027i	$-0.423190\pi$
$719$	−2.72985	−	0.828091i	−0.101806	−	0.0308826i	−0.340777	+	0.940144i	$0.610690\pi$
$720$	7.18366	+	1.60441i	0.267719	+	0.0597927i
$721$	2.42617	+	7.99802i	0.0903554	+	0.297862i
$722$	15.8421	−	13.0090i	0.589582	−	0.484143i
$723$	−0.0146598	+	0.597172i	−0.000545202	+	0.0222091i
$724$	−20.6830	+	4.65710i	−0.768676	+	0.173080i
$725$	8.92738	+	6.96700i	0.331555	+	0.258748i
$726$	−2.72280	+	8.25005i	−0.101053	+	0.306188i
$727$	2.52590	−	5.34057i	0.0936805	−	0.198071i	−0.851708	−	0.524017i	$-0.824433\pi$
$727$	2.52590	−	5.34057i	0.0936805	−	0.198071i	0.945388	+	0.325946i	$0.105683\pi$
$728$	5.63758	+	0.690358i	0.208943	+	0.0255864i
$729$	−16.3050	−	14.7779i	−0.603887	−	0.547331i
$730$	11.2341	+	5.65069i	0.415793	+	0.209142i
$731$	0.335032	−	0.351895i	0.0123916	−	0.0130153i
$732$	−1.47796	+	1.63257i	−0.0546269	+	0.0603417i
$733$	−3.47986	−	3.00175i	−0.128532	−	0.110872i	0.586550	−	0.809913i	$-0.300486\pi$
$733$	−3.47986	−	3.00175i	−0.128532	−	0.110872i	−0.715082	+	0.699041i	$0.753611\pi$
$734$	7.42120	+	10.0003i	0.273922	+	0.369117i
$735$	8.88039	+	1.76642i	0.327558	+	0.0651553i
$736$	−22.5516	−	6.80531i	−0.831263	−	0.250847i
$737$	16.3275	−	3.24774i	0.601431	−	0.119632i
$738$	4.94231	+	4.47684i	0.181929	+	0.164795i
$739$	−19.7138	+	9.92311i	−0.725185	+	0.365027i	−0.773493	−	0.633805i	$-0.781492\pi$
$739$	−19.7138	+	9.92311i	−0.725185	+	0.365027i	0.0483079	+	0.998832i	$0.484617\pi$
$740$	−6.94152	−	5.14195i	−0.255175	−	0.189022i
$741$	−21.1506	−	8.15869i	−0.776987	−	0.299717i
$742$	1.49811	+	12.1175i	0.0549973	+	0.444846i
$743$	20.7970	+	43.9716i	0.762969	+	1.61316i	0.789679	+	0.613520i	$0.210247\pi$
$743$	20.7970	+	43.9716i	0.762969	+	1.61316i	−0.0267101	+	0.999643i	$0.508503\pi$
$744$	1.34924	+	0.0983473i	0.0494654	+	0.00360559i
$745$	−0.474581	+	9.66033i	−0.0173873	+	0.353927i
$746$	27.5488	−	21.5121i	1.00863	−	0.787615i
$747$	−9.83696	+	5.57257i	−0.359915	+	0.203890i
$748$	7.53382	+	2.08019i	0.275464	+	0.0760594i
$749$	−0.198601	+	0.0766088i	−0.00725671	+	0.00279922i
$750$	−7.89774	−	14.7653i	−0.288385	−	0.539154i
$751$	−1.00957	+	10.2504i	−0.0368398	+	0.374041i	0.959034	+	0.283291i	$0.0914263\pi$
$751$	−1.00957	+	10.2504i	−0.0368398	+	0.374041i	−0.995874	+	0.0907496i	$0.971074\pi$
$752$	42.0416	−	4.18991i	1.53310	−	0.152790i
$753$	−7.85503	+	0.773652i	−0.286253	+	0.0281935i
$754$	2.80952	−	14.1458i	0.102317	−	0.515161i
$755$	2.24695	−	3.19043i	0.0817750	−	0.116112i
$756$	−1.13456	−	6.51624i	−0.0412637	−	0.236994i
$757$	−2.42327	+	32.8514i	−0.0880751	+	1.19400i	0.754822	+	0.655930i	$0.227723\pi$
$757$	−2.42327	+	32.8514i	−0.0880751	+	1.19400i	−0.842897	+	0.538075i	$0.819152\pi$
$758$	14.9066	+	10.4919i	0.541431	+	0.381084i
$759$	4.82236	−	19.2519i	0.175040	−	0.698801i
$760$	−8.08155	−	17.0487i	−0.293149	−	0.618420i
$761$	−2.93950	−	3.96346i	−0.106557	−	0.143675i	0.746710	−	0.665150i	$-0.231632\pi$
$761$	−2.93950	−	3.96346i	−0.106557	−	0.143675i	−0.853267	+	0.521474i	$0.825382\pi$
$762$	−19.4582	−	27.6115i	−0.704894	−	1.00026i
$763$	0.646783	+	2.88026i	0.0234151	+	0.104272i
$764$	−3.62520	+	6.79173i	−0.131155	+	0.245716i
$765$	1.77400	+	0.218802i	0.0641390	+	0.00791080i
$766$	7.50341	+	8.27392i	0.271109	+	0.298949i
$767$			18.4073i			0.664648i
$768$	9.30452	−	16.5139i	0.335748	−	0.595892i
$769$			32.6763i			1.17834i	0.808011	+	0.589168i	$0.200544\pi$
$769$			32.6763i			1.17834i	−0.808011	+	0.589168i	$0.799456\pi$
$770$	−2.95018	+	2.67544i	−0.106317	+	0.0964162i
$771$	−19.1090	−	2.35686i	−0.688192	−	0.0848804i
$772$	15.1320	+	49.7796i	0.544611	+	1.79161i
$773$	−9.98947	−	44.4851i	−0.359296	−	1.60002i	−0.738199	−	0.674583i	$-0.764323\pi$
$773$	−9.98947	−	44.4851i	−0.359296	−	1.60002i	0.378903	−	0.925437i	$-0.376302\pi$
$774$	−0.923196	+	0.650588i	−0.0331836	+	0.0233849i
$775$	0.883027	+	1.19062i	0.0317193	+	0.0427685i
$776$	27.7135	−	30.6306i	0.994858	−	1.09958i
$777$	−0.655133	+	2.61544i	−0.0235028	+	0.0938284i
$778$	8.88767	−	12.6273i	0.318639	−	0.452710i
$779$	1.25743	−	17.0466i	0.0450522	−	0.610758i
$780$	−5.19490	+	7.38527i	−0.186007	+	0.264435i
$781$	−0.937355	+	1.33094i	−0.0335412	+	0.0476248i
$782$	−5.61070	−	1.11435i	−0.200638	−	0.0398490i
$783$	−16.7144	+	1.64622i	−0.597324	+	0.0588312i
$784$	−12.4765	+	23.4071i	−0.445590	+	0.835968i
$785$	2.57320	−	26.1262i	0.0918416	−	0.932483i
$786$	−10.3040	+	5.51145i	−0.367532	+	0.196587i
$787$	4.75582	−	1.83452i	0.169527	−	0.0653937i	−0.273643	−	0.961831i	$-0.588229\pi$
$787$	4.75582	−	1.83452i	0.169527	−	0.0653937i	0.443170	+	0.896438i	$0.353854\pi$
$788$	22.5864	−	12.8123i	0.804608	−	0.456420i
$789$	11.0689	−	6.27047i	0.394065	−	0.223235i
$790$	6.27432	+	8.03500i	0.223230	+	0.285872i
$791$	−0.442493	+	9.00716i	−0.0157333	+	0.320258i
$792$	−16.2347	−	8.15418i	−0.576874	−	0.289746i
$793$	1.31395	+	2.77811i	0.0466596	+	0.0986535i
$794$	25.1094	−	3.10433i	0.891099	−	0.110169i
$795$	−18.1099	−	6.98575i	−0.642291	−	0.247759i
$796$	0.510697	+	3.42916i	0.0181012	+	0.121543i
$797$	−34.6782	+	17.4556i	−1.22837	+	0.618307i	−0.940640	−	0.339406i	$-0.889774\pi$
$797$	−34.6782	+	17.4556i	−1.22837	+	0.618307i	−0.287726	+	0.957713i	$0.592899\pi$
$798$	−3.95339	+	4.36443i	−0.139948	+	0.154499i
$799$	10.0627	−	2.00160i	0.355993	−	0.0708115i
$800$	20.3645	−	4.08141i	0.719994	−	0.144300i
$801$	11.6063	+	2.30863i	0.410088	+	0.0815716i
$802$	−12.9719	+	9.62645i	−0.458054	+	0.339922i
$803$	−23.5021	−	20.2731i	−0.829373	−	0.715422i
$804$	−0.486737	−	9.79204i	−0.0171659	−	0.345339i
$805$	2.00993	−	2.11110i	0.0708407	−	0.0744063i
$806$	0.848314	−	1.68653i	0.0298806	−	0.0594053i
$807$	22.1963	+	20.1175i	0.781346	+	0.708171i
$808$	8.67732	−	2.40945i	0.305267	−	0.0847643i
$809$	−7.05633	+	14.9194i	−0.248087	+	0.524537i	−0.989152	−	0.146897i	$-0.953071\pi$
$809$	−7.05633	+	14.9194i	−0.248087	+	0.524537i	0.741064	+	0.671434i	$0.234321\pi$
$810$	2.57154	+	0.848696i	0.0903547	+	0.0298201i
$811$	−7.49052	−	5.84566i	−0.263028	−	0.205269i	0.475096	−	0.879934i	$-0.342413\pi$
$811$	−7.49052	−	5.84566i	−0.263028	−	0.205269i	−0.738124	+	0.674665i	$0.764288\pi$
$812$	−3.16628	−	2.00246i	−0.111115	−	0.0702725i
$813$	−0.779293	+	31.7449i	−0.0273310	+	1.11334i
$814$	13.5310	+	16.4778i	0.474261	+	0.577548i
$815$	6.88618	+	22.7007i	0.241212	+	0.795170i
$816$	1.86042	−	4.21019i	0.0651276	−	0.147386i
$817$	2.77029	+	0.840357i	0.0969200	+	0.0294004i
$818$	3.62169	−	8.75069i	0.126629	−	0.305961i
$819$	−3.12811	−	0.702440i	−0.109305	−	0.0245452i
$820$	−6.46575	−	2.13184i	−0.225794	−	0.0744472i
$821$	44.4826	+	22.3907i	1.55245	+	0.781440i	0.998687	−	0.0512315i	$-0.0163146\pi$
$821$	44.4826	+	22.3907i	1.55245	+	0.781440i	0.553768	+	0.832671i	$0.313190\pi$
$822$	0.317256	−	0.122485i	0.0110656	−	0.00427215i
$823$	−0.871503	−	5.87520i	−0.0303787	−	0.204796i	0.968673	−	0.248340i	$-0.0798851\pi$
$823$	−0.871503	−	5.87520i	−0.0303787	−	0.204796i	−0.999052	+	0.0435440i	$0.986135\pi$
$824$	18.3189	−	34.3440i	0.638170	−	1.19643i
$825$	4.25189	+	16.9745i	0.148032	+	0.590977i
$826$	4.46165	+	1.71956i	0.155241	+	0.0598313i
$827$	−1.43029	+	1.00733i	−0.0497362	+	0.0350282i	−0.600410	−	0.799692i	$-0.704996\pi$
$827$	−1.43029	+	1.00733i	−0.0497362	+	0.0350282i	0.550674	+	0.834721i	$0.314371\pi$
$828$	12.2874	+	5.08129i	0.427018	+	0.176587i
$829$	−5.09538	+	8.99459i	−0.176970	+	0.312395i	−0.944437	−	0.328693i	$-0.893392\pi$
$829$	−5.09538	+	8.99459i	−0.176970	+	0.312395i	0.767467	+	0.641088i	$0.221517\pi$
$830$	6.87318	−	9.27302i	0.238571	−	0.321871i
$831$	−8.62357	−	20.8191i	−0.299148	−	0.722208i
$832$	−16.3099	−	20.8245i	−0.565444	−	0.721960i
$833$	−2.46493	+	5.95087i	−0.0854048	+	0.206185i
$834$	6.89814	+	11.5013i	0.238863	+	0.398257i
$835$	3.05132	+	11.0261i	0.105595	+	0.381573i
$836$	9.11132	+	45.6675i	0.315122	+	1.57944i
$837$	−2.16613	−	0.375860i	−0.0748725	−	0.0129916i
$838$	25.4742	−	0.632737i	0.879991	−	0.0218575i
$839$	31.2321	+	18.7198i	1.07825	+	0.646280i	0.938979	−	0.343974i	$-0.111773\pi$
$839$	31.2321	+	18.7198i	1.07825	+	0.646280i	0.139273	+	0.990254i	$0.455523\pi$
$840$	1.30479	+	1.94908i	0.0450194	+	0.0672497i
$841$	11.6084	−	15.6522i	0.400291	−	0.539730i
$842$	−30.5343	−	0.740729i	−1.05228	−	0.0255272i
$843$	4.73944	−	1.56570i	0.163235	−	0.0539256i
$844$	5.59709	−	45.5973i	0.192660	−	1.56952i
$845$	−1.27494	−	2.01335i	−0.0438593	−	0.0692614i
$846$	−23.8487	+	0.00690603i	−0.819936	+	0.000237434i
$847$	2.77746	−	1.48458i	0.0954345	−	0.0510108i
$848$	34.9319	−	44.8681i	1.19956	−	1.54078i
$849$	−4.75851	+	8.90254i	−0.163311	+	0.305534i
$850$	4.82601	−	1.46548i	0.165531	−	0.0502655i
$851$	−10.7603	−	11.3019i	−0.368860	−	0.387426i
$852$	0.694730	+	0.660671i	0.0238010	+	0.0226342i
$853$	−0.748990	−	6.07265i	−0.0256449	−	0.207924i	0.974197	−	0.225699i	$-0.0724666\pi$
$853$	−0.748990	−	6.07265i	−0.0256449	−	0.207924i	−0.999842	+	0.0177755i	$0.994342\pi$
$854$	0.796119	−	0.0589570i	0.0272426	−	0.00201747i
$855$	3.58784	+	10.0273i	0.122702	+	0.342928i
$856$	0.906647	+	0.400947i	0.0309885	+	0.0137041i
$857$	−2.67049	−	54.3590i	−0.0912221	−	1.85687i	−0.413853	−	0.910344i	$-0.635817\pi$
$857$	−2.67049	−	54.3590i	−0.0912221	−	1.85687i	0.322631	−	0.946525i	$-0.395433\pi$
$858$	16.8710	−	14.5616i	0.575967	−	0.497123i
$859$	−0.600240	−	24.4511i	−0.0204799	−	0.834259i	−0.918756	−	0.394827i	$-0.870805\pi$
$859$	−0.600240	−	24.4511i	−0.0204799	−	0.834259i	0.898276	−	0.439432i	$-0.144820\pi$
$860$	0.592218	−	0.989355i	0.0201945	−	0.0337367i
$861$	0.156320	+	2.11918i	0.00532738	+	0.0722215i
$862$	−25.1050	−	15.0375i	−0.855080	−	0.512179i
$863$	−31.5175	+	21.0594i	−1.07287	+	0.716869i	−0.960915	−	0.276845i	$-0.910711\pi$
$863$	−31.5175	+	21.0594i	−1.07287	+	0.716869i	−0.111955	+	0.993713i	$0.535711\pi$
$864$	−17.7006	+	25.2104i	−0.602188	+	0.857676i
$865$	−17.8167	−	11.9047i	−0.605785	−	0.404773i
$866$	−19.8665	−	41.9727i	−0.675091	−	1.42629i
$867$	−5.96674	+	18.0616i	−0.202641	+	0.613403i
$868$	−0.329542	−	0.363170i	−0.0111854	−	0.0123268i
$869$	−10.1967	−	23.0033i	−0.345898	−	0.780333i
$870$	5.18122	−	2.93711i	0.175660	−	0.0995772i
$871$	−12.8819	−	4.60922i	−0.436487	−	0.156177i
$872$	7.34500	−	11.6214i	0.248733	−	0.393549i
$873$	−17.2764	+	15.6584i	−0.584718	+	0.529958i
$874$	−9.09976	−	32.8453i	−0.307804	−	1.11101i
$875$	−1.61895	+	5.85015i	−0.0547307	+	0.197771i
$876$	−13.8342	+	11.9474i	−0.467414	+	0.403667i
$877$	−0.298076	−	0.132128i	−0.0100653	−	0.00446164i	0.400203	−	0.916427i	$-0.368940\pi$
$877$	−0.298076	−	0.132128i	−0.0100653	−	0.00446164i	−0.410268	+	0.911965i	$0.634565\pi$
$878$	6.49430	+	5.32659i	0.219172	+	0.179764i
$879$	4.62389	+	5.63422i	0.155960	+	0.190038i
$880$	18.5266	+	0.888644i	0.624532	+	0.0299562i
$881$	4.26663	+	3.50153i	0.143746	+	0.117970i	0.703518	−	0.710677i	$-0.251611\pi$
$881$	4.26663	+	3.50153i	0.143746	+	0.117970i	−0.559772	+	0.828647i	$0.689111\pi$
$882$	8.31456	−	12.4514i	0.279966	−	0.419261i
$883$	3.74612	+	21.5894i	0.126067	+	0.726542i	0.978897	+	0.204354i	$0.0655092\pi$
$883$	3.74612	+	21.5894i	0.126067	+	0.726542i	−0.852830	+	0.522188i	$0.825116\pi$
$884$	−4.43187	−	4.64955i	−0.149060	−	0.156381i
$885$	−5.75593	+	4.96510i	−0.193484	+	0.166900i
$886$	−8.93910	+	39.8616i	−0.300315	+	1.33918i
$887$	5.17826	+	8.63941i	0.173869	+	0.290083i	0.932311	−	0.361658i	$-0.117789\pi$
$887$	5.17826	+	8.63941i	0.173869	+	0.290083i	−0.758442	+	0.651741i	$0.774039\pi$
$888$	10.7648	−	6.46488i	0.361242	−	0.216947i
$889$	−1.79670	+	12.1124i	−0.0602594	+	0.406236i
$890$	−11.7872	+	2.65049i	−0.395108	+	0.0888446i
$891$	−5.64680	−	3.57580i	−0.189175	−	0.119794i
$892$	−34.9599	−	10.5829i	−1.17054	−	0.354341i
$893$	37.6092	+	48.1917i	1.25854	+	1.61267i
$894$	−12.7110	−	6.00734i	−0.425119	−	0.200916i
$895$	17.9664	+	17.9664i	0.600550	+	0.600550i
$896$	−6.57119	+	2.00790i	−0.219528	+	0.0670794i
$897$	−11.5337	+	11.5337i	−0.385098	+	0.385098i
$898$	−25.0968	+	8.98797i	−0.837491	+	0.299933i
$899$	−0.981681	+	0.766111i	−0.0327409	+	0.0255512i
$900$	−11.6666	+	1.15588i	−0.388886	+	0.0385294i
$901$	7.38748	−	11.6661i	0.246113	−	0.388654i
$902$	14.1993	+	8.98584i	0.472785	+	0.299196i
$903$	−0.355995	−	0.0528069i	−0.0118468	−	0.00175730i
$904$	31.0943	−	28.2315i	1.03418	−	0.938966i
$905$	−10.4796	+	6.28121i	−0.348353	+	0.208795i
$906$	3.03604	+	4.79136i	0.100866	+	0.159182i
$907$	−2.43357	−	2.82118i	−0.0808054	−	0.0936759i	0.715356	−	0.698760i	$-0.246264\pi$
$907$	−2.43357	−	2.82118i	−0.0808054	−	0.0936759i	−0.796162	+	0.605084i	$0.793139\pi$
$908$	17.9788	−	6.94717i	0.596649	−	0.230550i
$909$	−5.00855	+	0.869066i	−0.166123	+	0.0288251i
$910$	3.21008	−	0.639490i	0.106413	−	0.0211989i
$911$	11.3265	−	13.8014i	0.375263	−	0.457260i	−0.550795	−	0.834641i	$-0.685675\pi$
$911$	11.3265	−	13.8014i	0.375263	−	0.457260i	0.926058	+	0.377381i	$0.123175\pi$
$912$	27.3904	−	1.37741i	0.906987	−	0.0456106i
$913$	−22.0223	+	18.0732i	−0.728832	+	0.598137i
$914$	−4.97495	+	0.491445i	−0.164557	+	0.0162555i
$915$	−0.514293	+	1.16023i	−0.0170020	+	0.0383559i
$916$	21.3281	+	10.7202i	0.704700	+	0.354205i
$917$	4.08254	+	1.12979i	0.134817	+	0.0373090i
$918$	−3.68516	+	6.50961i	−0.121628	+	0.214849i
$919$	−25.7758	−	28.4392i	−0.850266	−	0.938124i	0.148443	−	0.988921i	$-0.452574\pi$
$919$	−25.7758	−	28.4392i	−0.850266	−	0.938124i	−0.998709	+	0.0507970i	$0.983824\pi$
$920$	−13.5707	+	0.344940i	−0.447414	+	0.0113723i
$921$	−0.435256	+	1.21646i	−0.0143422	+	0.0400837i
$922$	−2.10608	+	7.61897i	−0.0693600	+	0.250918i
$923$	1.22311	−	0.542168i	0.0402592	−	0.0178457i
$924$	−1.95346	−	5.44959i	−0.0642640	−	0.179278i
$925$	13.0646	+	4.31597i	0.429563	+	0.141908i
$926$	−14.8829	+	41.6328i	−0.489081	+	1.36814i
$927$	−12.2067	+	18.2686i	−0.400921	+	0.600020i
$928$	3.84740	+	17.0180i	0.126297	+	0.558642i
$929$	−18.9404	−	28.3463i	−0.621415	−	0.930013i	−0.999990	−	0.00444282i	$-0.998586\pi$
$929$	−18.9404	−	28.3463i	−0.621415	−	0.930013i	0.378575	−	0.925571i	$-0.376414\pi$
$930$	0.756196	−	0.189650i	0.0247966	−	0.00621887i
$931$	−38.2737	+	2.82324i	−1.25437	+	0.0925278i
$932$	−1.36022	+	9.20661i	−0.0445556	+	0.301573i
$933$	−31.1943	+	0.765778i	−1.02126	+	0.0250705i
$934$	47.7874	+	3.51110i	1.56365	+	0.114887i
$935$	4.49870	−	0.221007i	0.147123	−	0.00722771i
$936$	7.99897	+	12.6075i	0.261455	+	0.412089i
$937$	−50.8338	+	18.1886i	−1.66067	+	0.594196i	−0.989165	−	0.146807i	$-0.953100\pi$
$937$	−50.8338	+	18.1886i	−1.66067	+	0.594196i	−0.671501	+	0.741003i	$0.734350\pi$
$938$	−2.32061	+	2.69180i	−0.0757705	+	0.0878905i
$939$	26.7120	−	3.29461i	0.871713	−	0.107516i
$940$	22.2537	−	9.87979i	0.725834	−	0.322243i
$941$	−27.2337	+	25.9286i	−0.887792	+	0.845248i	−0.988740	−	0.149644i	$-0.952187\pi$
$941$	−27.2337	+	25.9286i	−0.887792	+	0.845248i	0.100948	+	0.994892i	$0.467812\pi$
$942$	33.6597	+	17.9790i	1.09669	+	0.585786i
$943$	−10.8464	−	5.79750i	−0.353206	−	0.188793i
$944$	−9.04770	−	20.3476i	−0.294478	−	0.662259i
$945$	−1.79684	−	3.36166i	−0.0584513	−	0.109355i
$946$	−2.01182	+	2.01298i	−0.0654098	+	0.0654477i
$947$	27.7163	−	17.5512i	0.900659	−	0.570336i	−0.00233114	−	0.999997i	$-0.500742\pi$
$947$	27.7163	−	17.5512i	0.900659	−	0.570336i	0.902990	+	0.429661i	$0.141367\pi$
$948$	−14.2795	+	3.96059i	−0.463778	+	0.128634i
$949$	8.00157	+	24.2211i	0.259742	+	0.786250i
$950$	20.7275	+	21.7581i	0.672489	+	0.705927i
$951$	5.73722	+	4.25501i	0.186042	+	0.137978i
$952$	−1.54100	+	0.639871i	−0.0499440	+	0.0207383i
$953$	12.8206	−	21.3899i	0.415301	−	0.692888i	−0.576999	−	0.816745i	$-0.695776\pi$
$953$	12.8206	−	21.3899i	0.415301	−	0.692888i	0.992300	+	0.123857i	$0.0395264\pi$
$954$	−22.1256	+	23.2527i	−0.716343	+	0.752835i
$955$	−0.758502	+	4.37135i	−0.0245445	+	0.141454i
$956$	−4.72192	+	23.8107i	−0.152718	+	0.770094i
$957$	−14.1675	+	3.92068i	−0.457971	+	0.126738i
$958$	9.14305	−	36.5460i	0.295399	−	1.18075i
$959$	−0.113895	−	0.0471770i	−0.00367787	−	0.00152342i
$960$	2.11244	−	10.7172i	0.0681786	−	0.345897i
$961$	28.4897	−	11.8008i	0.919022	−	0.380671i
$962$	−2.57620	−	17.3327i	−0.0830599	−	0.558830i
$963$	−0.486886	−	0.275817i	−0.0156897	−	0.00888809i
$964$	−1.00847		0.000584059i	−0.0324806		1.88113e-5i
$965$	17.2648	+	24.5142i	0.555774	+	0.789139i
$966$	1.71814	+	3.87304i	0.0552804	+	0.124613i
$967$	18.9856	−	4.75566i	0.610537	−	0.152932i	0.0746339	−	0.997211i	$-0.476221\pi$
$967$	18.9856	−	4.75566i	0.610537	−	0.152932i	0.535903	+	0.844279i	$0.319971\pi$
$968$	−14.0391	−	4.24540i	−0.451234	−	0.136452i
$969$	6.58774	−	0.977199i	0.211629	−	0.0313922i
$970$	9.64042	−	21.7654i	0.309535	−	0.698846i
$971$	12.7435	−	25.3170i	0.408958	−	0.812460i	−0.591025	−	0.806653i	$-0.701277\pi$
$971$	12.7435	−	25.3170i	0.408958	−	0.812460i	0.999983	−	0.00580697i	$-0.00184843\pi$
$972$	18.7571	−	21.7701i	0.601633	−	0.698277i
$973$	1.06519	−	4.74351i	0.0341484	−	0.152070i
$974$	−39.0620	+	16.1933i	−1.25163	+	0.518865i
$975$	4.17474	−	13.7623i	0.133699	−	0.440746i
$976$	−2.81798	−	2.42512i	−0.0902012	−	0.0776260i
$977$	16.1191	−	4.88969i	0.515697	−	0.156435i	−0.0216997	−	0.999765i	$-0.506908\pi$
$977$	16.1191	−	4.88969i	0.515697	−	0.156435i	0.537397	+	0.843330i	$0.319408\pi$
$978$	−34.3172	−	3.36991i	−1.09734	−	0.107758i
$979$	29.8104	+	0.731805i	0.952745	+	0.0233886i
$980$	−2.60458	+	15.0623i	−0.0832003	+	0.481149i
$981$	−4.77435	+	6.11777i	−0.152433	+	0.195325i
$982$	−16.3856	−	32.5292i	−0.522886	−	1.03805i
$983$	19.4007	+	9.17585i	0.618786	+	0.292664i	0.711127	−	0.703063i	$-0.248185\pi$
$983$	19.4007	+	9.17585i	0.618786	+	0.292664i	−0.0923409	+	0.995727i	$0.529435\pi$
$984$	6.45743	−	7.49912i	0.205855	−	0.239063i
$985$	10.0497	−	11.0881i	0.320210	−	0.353297i
$986$	1.33020	+	4.02267i	0.0423622	+	0.128108i
$987$	−5.50392	−	5.24017i	−0.175192	−	0.166796i
$988$	12.8725	−	36.0419i	0.409527	−	1.14665i
$989$	1.36052	−	1.57722i	0.0432621	−	0.0501528i
$990$	−10.3568	−	1.53323i	−0.329162	−	0.0487291i
$991$	7.56146	−	38.0140i	0.240198	−	1.20756i	−0.652813	−	0.757519i	$-0.726411\pi$
$991$	7.56146	−	38.0140i	0.240198	−	1.20756i	0.893010	−	0.450036i	$-0.148589\pi$
$992$	−0.108761	+	2.28128i	−0.00345317	+	0.0724307i
$993$	−7.34838	−	36.9428i	−0.233194	−	1.17234i
$994$	−0.0171533	−	0.347112i	−0.000544070	−	0.0110097i
$995$	0.898316	+	1.78465i	0.0284785	+	0.0565771i
$996$	8.63397	+	14.3860i	0.273578	+	0.455838i
$997$	15.7084	−	40.7226i	0.497491	−	1.28970i	−0.425529	−	0.904945i	$-0.639912\pi$
$997$	15.7084	−	40.7226i	0.497491	−	1.28970i	0.923020	−	0.384752i	$-0.125713\pi$
$998$	−25.4125	−	19.8203i	−0.804418	−	0.627400i
$999$	−18.4473	+	8.72492i	−0.583646	+	0.276044i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.o.a.109.1	✓	4032
512.357	even	128	inner	512.2.o.a.357.1	yes	4032

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
512.2.o.a.109.1	✓	4032	1.1	even	1	trivial
512.2.o.a.357.1	yes	4032	512.357	even	128	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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.o (of order \(128\), degree \(64\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41253 - 0.0689831i) q^{2} +(0.145016 - 1.17576i) q^{3} +(1.99048 + 0.194882i) q^{4} +(1.12458 - 0.252532i) q^{5} +(-0.285948 + 1.65079i) q^{6} +(0.487809 - 0.361784i) q^{7} +(-2.79817 - 0.412586i) q^{8} +(1.54871 + 0.387932i) q^{9} +O(q^{10})\)	\(q+(-1.41253 - 0.0689831i) q^{2} +(0.145016 - 1.17576i) q^{3} +(1.99048 + 0.194882i) q^{4} +(1.12458 - 0.252532i) q^{5} +(-0.285948 + 1.65079i) q^{6} +(0.487809 - 0.361784i) q^{7} +(-2.79817 - 0.412586i) q^{8} +(1.54871 + 0.387932i) q^{9} +(-1.60592 + 0.279132i) q^{10} +(4.01223 + 0.295960i) q^{11} +(0.517786 - 2.31207i) q^{12} +(-2.70328 - 1.90386i) q^{13} +(-0.714002 + 0.477380i) q^{14} +(-0.133835 - 1.35885i) q^{15} +(3.92404 + 0.775817i) q^{16} +(0.966673 + 0.0952090i) q^{17} +(-2.16084 - 0.654800i) q^{18} +(2.08289 + 5.39968i) q^{19} +(2.28766 - 0.283501i) q^{20} +(-0.354631 - 0.626012i) q^{21} +(-5.64697 - 0.694828i) q^{22} +(4.15914 + 0.204326i) q^{23} +(-0.890883 + 3.23015i) q^{24} +(-3.31905 + 1.56979i) q^{25} +(3.68713 + 2.87574i) q^{26} +(1.95977 - 5.08052i) q^{27} +(1.04148 - 0.625060i) q^{28} +(-1.38674 - 2.75497i) q^{29} +(0.0953085 + 1.92865i) q^{30} +(-0.0787648 - 0.395977i) q^{31} +(-5.48931 - 1.36656i) q^{32} +(0.929816 - 4.67450i) q^{33} +(-1.35889 - 0.201170i) q^{34} +(0.457216 - 0.530041i) q^{35} +(3.00708 + 1.07399i) q^{36} +(-2.71410 - 2.58404i) q^{37} +(-2.56965 - 7.77089i) q^{38} +(-2.63051 + 2.90232i) q^{39} +(-3.25095 + 0.242644i) q^{40} +(-2.66987 - 1.26275i) q^{41} +(0.457743 + 0.908724i) q^{42} +(0.307743 - 0.394337i) q^{43} +(7.92859 + 1.37101i) q^{44} +(1.83961 + 0.0451598i) q^{45} +(-5.86082 - 0.575527i) q^{46} +(10.1077 - 3.06612i) q^{47} +(1.48122 - 4.50123i) q^{48} +(-1.92492 + 6.34562i) q^{49} +(4.79655 - 1.98842i) q^{50} +(0.252126 - 1.12277i) q^{51} +(-5.00980 - 4.31642i) q^{52} +(6.39154 - 12.6978i) q^{53} +(-3.11871 + 7.04120i) q^{54} +(4.58679 - 0.680386i) q^{55} +(-1.51424 + 0.811071i) q^{56} +(6.65078 - 1.66593i) q^{57} +(1.76876 + 3.98714i) q^{58} +(-3.20560 - 4.55160i) q^{59} +(-0.00158158 - 2.73086i) q^{60} +(-0.808706 - 0.458126i) q^{61} +(0.0839419 + 0.564763i) q^{62} +(0.895823 - 0.371062i) q^{63} +(7.65955 + 2.30897i) q^{64} +(-3.52082 - 1.45837i) q^{65} +(-1.63585 + 6.53873i) q^{66} +(3.98803 - 1.10364i) q^{67} +(1.90559 + 0.377898i) q^{68} +(0.843381 - 4.86053i) q^{69} +(-0.682396 + 0.717159i) q^{70} +(-0.208023 + 0.347066i) q^{71} +(-4.17350 - 1.72448i) q^{72} +(-6.19663 - 4.59574i) q^{73} +(3.65549 + 3.83726i) q^{74} +(1.36439 + 4.13005i) q^{75} +(3.09365 + 11.1539i) q^{76} +(2.06428 - 1.30719i) q^{77} +(3.91588 - 3.91815i) q^{78} +(-2.94827 - 5.51582i) q^{79} +(4.60880 - 0.118481i) q^{80} +(-1.46517 - 0.783148i) q^{81} +(3.68416 + 1.96785i) q^{82} +(-5.12862 + 4.88285i) q^{83} +(-0.583889 - 1.31518i) q^{84} +(1.11114 - 0.137046i) q^{85} +(-0.461900 + 0.535784i) q^{86} +(-3.44029 + 1.23095i) q^{87} +(-11.1048 - 2.48353i) q^{88} +(7.40307 - 0.363689i) q^{89} +(-2.59538 - 0.190691i) q^{90} +(-2.00747 + 0.0492806i) q^{91} +(8.23888 + 1.21725i) q^{92} +(-0.476997 + 0.0351854i) q^{93} +(-14.4889 + 3.63374i) q^{94} +(3.70595 + 5.54635i) q^{95} +(-2.40278 + 6.25594i) q^{96} +(-8.11369 + 12.1430i) q^{97} +(3.15675 - 8.83059i) q^{98} +(6.09896 + 2.01483i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Introduction

L-functions

Modular forms

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Database

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