LMFDB - Embedded newform 512.2.o.a.149.56

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			149.56
Character	$\chi$	$=$	512.149
Dual form			512.2.o.a.189.56

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.33284 - 0.472809i) q^{2} +(-3.40889 - 0.591499i) q^{3} +(1.55290 - 1.26035i) q^{4} +(-0.302430 + 0.915468i) q^{5} +(-4.82316 + 0.823385i) q^{6} +(-0.128376 + 2.61316i) q^{7} +(1.47386 - 2.41407i) q^{8} +(8.44603 + 3.02204i) q^{9} +O(q^{10})$	\(q+(1.33284 - 0.472809i) q^{2} +(-3.40889 - 0.591499i) q^{3} +(1.55290 - 1.26035i) q^{4} +(-0.302430 + 0.915468i) q^{5} +(-4.82316 + 0.823385i) q^{6} +(-0.128376 + 2.61316i) q^{7} +(1.47386 - 2.41407i) q^{8} +(8.44603 + 3.02204i) q^{9} +(0.0297526 + 1.36316i) q^{10} +(-0.403793 - 0.178989i) q^{11} +(-6.03917 + 3.37787i) q^{12} +(2.88177 - 2.48583i) q^{13} +(1.06442 + 3.54361i) q^{14} +(1.57245 - 2.94184i) q^{15} +(0.823013 - 3.91442i) q^{16} +(-3.05380 + 1.63229i) q^{17} +(12.6860 + 0.0345180i) q^{18} +(6.89694 - 3.90707i) q^{19} +(0.684170 + 1.80280i) q^{20} +(1.98330 - 8.83204i) q^{21} +(-0.622818 - 0.0476460i) q^{22} +(-0.182654 - 0.729197i) q^{23} +(-6.45214 + 7.35752i) q^{24} +(3.26942 + 2.42477i) q^{25} +(2.66560 - 4.67573i) q^{26} +(-17.9730 - 10.1816i) q^{27} +(3.09415 + 4.21978i) q^{28} +(6.51159 - 0.159851i) q^{29} +(0.704884 - 4.66446i) q^{30} +(-0.538158 + 0.359586i) q^{31} +(-0.753832 - 5.60640i) q^{32} +(1.27061 + 0.848998i) q^{33} +(-3.29845 + 3.61944i) q^{34} +(-2.35344 - 0.907822i) q^{35} +(16.9247 - 5.95206i) q^{36} +(4.53032 + 0.558762i) q^{37} +(7.34519 - 8.46841i) q^{38} +(-11.2940 + 6.76936i) q^{39} +(1.76427 + 2.07936i) q^{40} +(3.58576 - 2.65938i) q^{41} +(-1.53246 - 12.7094i) q^{42} +(1.30117 - 1.84752i) q^{43} +(-0.852641 + 0.230970i) q^{44} +(-5.32091 + 6.81812i) q^{45} +(-0.588220 - 0.885539i) q^{46} +(1.10035 + 11.1720i) q^{47} +(-5.12093 + 12.8570i) q^{48} +(0.154172 + 0.0151846i) q^{49} +(5.50405 + 1.68600i) q^{50} +(11.3756 - 3.75798i) q^{51} +(1.34208 - 7.49230i) q^{52} +(-4.21982 - 0.103591i) q^{53} +(-28.7690 - 5.07257i) q^{54} +(0.285978 - 0.315528i) q^{55} +(6.11915 + 4.16133i) q^{56} +(-25.8219 + 9.23923i) q^{57} +(8.60331 - 3.29180i) q^{58} +(-5.40785 + 6.26920i) q^{59} +(-1.26591 - 6.55024i) q^{60} +(-9.83831 + 2.20927i) q^{61} +(-0.547261 + 0.733715i) q^{62} +(-8.98134 + 21.6829i) q^{63} +(-3.65549 - 7.11599i) q^{64} +(1.40417 + 3.38995i) q^{65} +(2.09494 + 0.530816i) q^{66} +(1.90272 + 1.20488i) q^{67} +(-2.68499 + 6.38365i) q^{68} +(0.191330 + 2.59379i) q^{69} +(-3.56597 - 0.0972491i) q^{70} +(10.0890 + 4.77173i) q^{71} +(19.7437 - 15.9353i) q^{72} +(-0.0988353 - 2.01184i) q^{73} +(6.30236 - 1.39724i) q^{74} +(-9.71085 - 10.1996i) q^{75} +(5.78598 - 14.7599i) q^{76} +(0.519565 - 1.03220i) q^{77} +(-11.8524 + 14.3623i) q^{78} +(-2.55500 - 3.11328i) q^{79} +(3.33462 + 1.93728i) q^{80} +(34.4430 + 28.2666i) q^{81} +(3.52185 - 5.23990i) q^{82} +(4.72070 - 0.582243i) q^{83} +(-8.05163 - 16.2150i) q^{84} +(-0.570749 - 3.28931i) q^{85} +(0.860721 - 3.07764i) q^{86} +(-22.2919 - 3.30669i) q^{87} +(-1.02723 + 0.710982i) q^{88} +(2.96297 - 11.8288i) q^{89} +(-3.86823 + 11.6032i) q^{90} +(6.12592 + 7.84964i) q^{91} +(-1.20269 - 0.902163i) q^{92} +(2.04722 - 0.907468i) q^{93} +(6.74882 + 14.3702i) q^{94} +(1.49096 + 7.49554i) q^{95} +(-0.746450 + 19.5575i) q^{96} +(-0.838412 + 4.21498i) q^{97} +(0.212665 - 0.0526553i) q^{98} +(-2.86954 - 2.73203i) 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 $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{77}{128}\right)$	$1$

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 $

$2$	1.33284	−	0.472809i	0.942457	−	0.334327i
$2$	1.33284	−	0.472809i	0.942457	−	0.334327i
$3$	−3.40889	−	0.591499i	−1.96812	−	0.341502i	−0.992552	−	0.121819i	$-0.961127\pi$
$3$	−3.40889	−	0.591499i	−1.96812	−	0.341502i	−0.975571	−	0.219683i	$-0.929498\pi$
$4$	1.55290	−	1.26035i	0.776451	−	0.630177i
$5$	−0.302430	+	0.915468i	−0.135251	+	0.409410i	−0.994825	−	0.101601i	$-0.967604\pi$
$5$	−0.302430	+	0.915468i	−0.135251	+	0.409410i	0.859575	+	0.511010i	$0.170729\pi$
$6$	−4.82316	+	0.823385i	−1.96905	+	0.336145i
$7$	−0.128376	+	2.61316i	−0.0485217	+	0.987681i	0.843906	+	0.536491i	$0.180250\pi$
$7$	−0.128376	+	2.61316i	−0.0485217	+	0.987681i	−0.892428	+	0.451190i	$0.851000\pi$
$8$	1.47386	−	2.41407i	0.521087	−	0.853504i
$9$	8.44603	+	3.02204i	2.81534	+	1.00735i
$10$	0.0297526	+	1.36316i	0.00940861	+	0.431069i
$11$	−0.403793	−	0.178989i	−0.121748	−	0.0539673i	0.343468	−	0.939164i	$-0.388398\pi$
$11$	−0.403793	−	0.178989i	−0.121748	−	0.0539673i	−0.465216	+	0.885197i	$0.654023\pi$
$12$	−6.03917	+	3.37787i	−1.74336	+	0.975107i
$13$	2.88177	−	2.48583i	0.799258	−	0.689445i	−0.155169	−	0.987888i	$-0.549592\pi$
$13$	2.88177	−	2.48583i	0.799258	−	0.689445i	0.954427	+	0.298443i	$0.0964673\pi$
$14$	1.06442	+	3.54361i	0.284479	+	0.947070i
$15$	1.57245	−	2.94184i	0.406004	−	0.759581i
$16$	0.823013	−	3.91442i	0.205753	−	0.978604i
$17$	−3.05380	+	1.63229i	−0.740655	+	0.395888i	−0.798151	−	0.602457i	$-0.794188\pi$
$17$	−3.05380	+	1.63229i	−0.740655	+	0.395888i	0.0574961	+	0.998346i	$0.481688\pi$
$18$	12.6860	+	0.0345180i	2.99012	+	0.00813598i
$19$	6.89694	−	3.90707i	1.58227	−	0.896342i	0.585971	−	0.810332i	$-0.300713\pi$
$19$	6.89694	−	3.90707i	1.58227	−	0.896342i	0.996294	−	0.0860106i	$-0.0274119\pi$
$20$	0.684170	+	1.80280i	0.152985	+	0.403119i
$21$	1.98330	−	8.83204i	0.432792	−	1.92731i
$22$	−0.622818	−	0.0476460i	−0.132785	−	0.0101582i
$23$	−0.182654	−	0.729197i	−0.0380861	−	0.152048i	0.948005	−	0.318257i	$-0.103097\pi$
$23$	−0.182654	−	0.729197i	−0.0380861	−	0.152048i	−0.986091	+	0.166209i	$0.946847\pi$
$24$	−6.45214	+	7.35752i	−1.31704	+	1.50185i
$25$	3.26942	+	2.42477i	0.653884	+	0.484953i
$26$	2.66560	−	4.67573i	0.522767	−	0.916986i
$27$	−17.9730	−	10.1816i	−3.45891	−	1.95945i
$28$	3.09415	+	4.21978i	0.584740	+	0.797464i
$29$	6.51159	−	0.159851i	1.20917	−	0.0296835i	0.585042	−	0.811003i	$-0.301078\pi$
$29$	6.51159	−	0.159851i	1.20917	−	0.0296835i	0.624131	+	0.781320i	$0.285453\pi$
$30$	0.704884	−	4.66446i	0.128694	−	0.851610i
$31$	−0.538158	+	0.359586i	−0.0966560	+	0.0645835i	−0.602959	−	0.797772i	$-0.706012\pi$
$31$	−0.538158	+	0.359586i	−0.0966560	+	0.0645835i	0.506303	+	0.862356i	$0.331012\pi$
$32$	−0.753832	−	5.60640i	−0.133260	−	0.991081i
$33$	1.27061	+	0.848998i	0.221186	+	0.147792i
$34$	−3.29845	+	3.61944i	−0.565680	+	0.620728i
$35$	−2.35344	−	0.907822i	−0.397804	−	0.153450i
$36$	16.9247	−	5.95206i	2.82078	−	0.992010i
$37$	4.53032	+	0.558762i	0.744780	+	0.0918599i	0.485857	−	0.874038i	$-0.338507\pi$
$37$	4.53032	+	0.558762i	0.744780	+	0.0918599i	0.258923	+	0.965898i	$0.416632\pi$
$38$	7.34519	−	8.46841i	1.19155	−	1.37376i
$39$	−11.2940	+	6.76936i	−1.80849	+	1.08396i
$40$	1.76427	+	2.07936i	0.278955	+	0.328775i
$41$	3.58576	−	2.65938i	0.560002	−	0.415325i	−0.278331	−	0.960485i	$-0.589781\pi$
$41$	3.58576	−	2.65938i	0.560002	−	0.415325i	0.838332	+	0.545160i	$0.183531\pi$
$42$	−1.53246	−	12.7094i	−0.236463	−	1.96110i
$43$	1.30117	−	1.84752i	0.198426	−	0.281744i	−0.706144	−	0.708068i	$-0.749567\pi$
$43$	1.30117	−	1.84752i	0.198426	−	0.281744i	0.904570	+	0.426324i	$0.140192\pi$
$44$	−0.852641	+	0.230970i	−0.128541	+	0.0348200i
$45$	−5.32091	+	6.81812i	−0.793195	+	1.01638i
$46$	−0.588220	−	0.885539i	−0.0867282	−	0.130566i
$47$	1.10035	+	11.1720i	0.160502	+	1.62961i	0.651643	+	0.758526i	$0.274080\pi$
$47$	1.10035	+	11.1720i	0.160502	+	1.62961i	−0.491140	+	0.871080i	$0.663420\pi$
$48$	−5.12093	+	12.8570i	−0.739143	+	1.85575i
$49$	0.154172	+	0.0151846i	0.0220246	+	0.00216923i
$50$	5.50405	+	1.68600i	0.778390	+	0.238437i
$51$	11.3756	−	3.75798i	1.59290	−	0.526222i
$52$	1.34208	−	7.49230i	0.186113	−	1.03899i
$53$	−4.21982	−	0.103591i	−0.579637	−	0.0142293i	−0.266331	−	0.963882i	$-0.585812\pi$
$53$	−4.21982	−	0.103591i	−0.579637	−	0.0142293i	−0.313306	+	0.949652i	$0.601437\pi$
$54$	−28.7690	−	5.07257i	−3.91497	−	0.690290i
$55$	0.285978	−	0.315528i	0.0385613	−	0.0425458i
$56$	6.11915	+	4.16133i	0.817706	+	0.556081i
$57$	−25.8219	+	9.23923i	−3.42020	+	1.22377i
$58$	8.60331	−	3.29180i	1.12967	−	0.432234i
$59$	−5.40785	+	6.26920i	−0.704042	+	0.816181i	−0.989851	−	0.142106i	$-0.954613\pi$
$59$	−5.40785	+	6.26920i	−0.704042	+	0.816181i	0.285809	+	0.958287i	$0.407738\pi$
$60$	−1.26591	−	6.55024i	−0.163428	−	0.845632i
$61$	−9.83831	+	2.20927i	−1.25967	+	0.282868i	−0.797171	−	0.603754i	$-0.793671\pi$
$61$	−9.83831	+	2.20927i	−1.25967	+	0.282868i	−0.462496	+	0.886621i	$0.653046\pi$
$62$	−0.547261	+	0.733715i	−0.0695022	+	0.0931819i
$63$	−8.98134	+	21.6829i	−1.13154	+	2.73178i
$64$	−3.65549	−	7.11599i	−0.456937	−	0.889499i
$65$	1.40417	+	3.38995i	0.174165	+	0.420472i
$66$	2.09494	+	0.530816i	0.257869	+	0.0653389i
$67$	1.90272	+	1.20488i	0.232454	+	0.147200i	0.646138	−	0.763221i	$-0.276383\pi$
$67$	1.90272	+	1.20488i	0.232454	+	0.147200i	−0.413684	+	0.910421i	$0.635758\pi$
$68$	−2.68499	+	6.38365i	−0.325603	+	0.774132i
$69$	0.191330	+	2.59379i	0.0230334	+	0.312256i
$70$	−3.56597	−	0.0972491i	−0.426216	−	0.0116235i
$71$	10.0890	+	4.77173i	1.19734	+	0.566301i	0.919029	−	0.394190i	$-0.128975\pi$
$71$	10.0890	+	4.77173i	1.19734	+	0.566301i	0.278313	+	0.960490i	$0.410225\pi$
$72$	19.7437	−	15.9353i	2.32681	−	1.87799i
$73$	−0.0988353	−	2.01184i	−0.0115678	−	0.235468i	−0.997616	−	0.0690084i	$-0.978016\pi$
$73$	−0.0988353	−	2.01184i	−0.0115678	−	0.235468i	0.986048	−	0.166460i	$-0.0532335\pi$
$74$	6.30236	−	1.39724i	0.732635	−	0.162426i
$75$	−9.71085	−	10.1996i	−1.12131	−	1.17775i
$76$	5.78598	−	14.7599i	0.663698	−	1.69307i
$77$	0.519565	−	1.03220i	0.0592099	−	0.117630i
$78$	−11.8524	+	14.3623i	−1.34202	+	1.62622i
$79$	−2.55500	−	3.11328i	−0.287460	−	0.350271i	0.609180	−	0.793032i	$-0.291499\pi$
$79$	−2.55500	−	3.11328i	−0.287460	−	0.350271i	−0.896639	+	0.442761i	$0.853999\pi$
$80$	3.33462	+	1.93728i	0.372822	+	0.216594i
$81$	34.4430	+	28.2666i	3.82700	+	3.14073i
$82$	3.52185	−	5.23990i	0.388923	−	0.578650i
$83$	4.72070	−	0.582243i	0.518165	−	0.0639095i	0.140916	−	0.990022i	$-0.454995\pi$
$83$	4.72070	−	0.582243i	0.518165	−	0.0639095i	0.377249	+	0.926112i	$0.376870\pi$
$84$	−8.05163	−	16.2150i	−0.878505	−	1.76920i
$85$	−0.570749	−	3.28931i	−0.0619064	−	0.356776i
$86$	0.860721	−	3.07764i	0.0928139	−	0.331871i
$87$	−22.2919	−	3.30669i	−2.38994	−	0.354514i
$88$	−1.02723	+	0.710982i	−0.109503	+	0.0757909i
$89$	2.96297	−	11.8288i	0.314074	−	1.25385i	−0.583182	−	0.812341i	$-0.698193\pi$
$89$	2.96297	−	11.8288i	0.314074	−	1.25385i	0.897256	−	0.441511i	$-0.145557\pi$
$90$	−3.86823	+	11.6032i	−0.407747	+	1.22309i
$91$	6.12592	+	7.84964i	0.642171	+	0.822866i
$92$	−1.20269	−	0.902163i	−0.125389	−	0.0940570i
$93$	2.04722	−	0.907468i	0.212286	−	0.0941001i
$94$	6.74882	+	14.3702i	0.696088	+	1.48217i
$95$	1.49096	+	7.49554i	0.152969	+	0.769026i
$96$	−0.746450	+	19.5575i	−0.0761842	+	1.99608i
$97$	−0.838412	+	4.21498i	−0.0851279	+	0.427967i	0.914594	+	0.404374i	$0.132511\pi$
$97$	−0.838412	+	4.21498i	−0.0851279	+	0.427967i	−0.999722	+	0.0235928i	$0.992489\pi$
$98$	0.212665	−	0.0526553i	0.0214824	−	0.00531899i
$99$	−2.86954	−	2.73203i	−0.288399	−	0.274579i
$100$	8.13316	−	0.355201i	0.813316	−	0.0355201i
$101$	−15.7928	+	4.37045i	−1.57144	+	0.434876i	−0.940175	−	0.340692i	$-0.889339\pi$
$101$	−15.7928	+	4.37045i	−1.57144	+	0.434876i	−0.631264	+	0.775568i	$0.717464\pi$
$102$	13.3849	−	10.3872i	1.32531	−	1.02849i
$103$	−2.03243	−	13.7015i	−0.200261	−	1.35005i	−0.823187	−	0.567770i	$-0.807806\pi$
$103$	−2.03243	−	13.7015i	−0.200261	−	1.35005i	0.622926	−	0.782280i	$-0.285944\pi$
$104$	−1.75366	−	10.6206i	−0.171961	−	1.04143i
$105$	7.48564	+	4.48672i	0.730524	+	0.437859i
$106$	−5.67331	+	1.85710i	−0.551041	+	0.180378i
$107$	−5.37772	+	3.40541i	−0.519884	+	0.329213i	−0.768987	−	0.639264i	$-0.779239\pi$
$107$	−5.37772	+	3.40541i	−0.519884	+	0.329213i	0.249103	+	0.968477i	$0.419864\pi$
$108$	−40.7427	+	6.84135i	−3.92047	+	0.658310i
$109$	−2.73154	+	9.87051i	−0.261634	+	0.945423i	0.709069	+	0.705139i	$0.249116\pi$
$109$	−2.73154	+	9.87051i	−0.261634	+	0.945423i	−0.970703	+	0.240284i	$0.922759\pi$
$110$	0.231977	−	0.555760i	0.0221182	−	0.0529897i
$111$	−15.1129	−	4.58443i	−1.43445	−	0.435135i
$112$	10.1233	+	2.65318i	0.956565	+	0.250702i
$113$	−4.44454	−	14.6517i	−0.418107	−	1.37831i	−0.872979	−	0.487757i	$-0.837815\pi$
$113$	−4.44454	−	14.6517i	−0.418107	−	1.37831i	0.454872	−	0.890557i	$-0.349685\pi$
$114$	−30.0480	+	24.5232i	−2.81425	+	2.29681i
$115$	0.722797	+	0.0533167i	0.0674012	+	0.00497181i
$116$	9.91040	−	8.45515i	0.920158	−	0.785041i
$117$	31.8518	−	12.2866i	2.94470	−	1.13589i
$118$	−4.24364	+	10.9127i	−0.390659	+	1.00460i
$119$	−3.87340	−	8.18961i	−0.355074	−	0.750740i
$120$	−4.78426	−	8.13186i	−0.436741	−	0.742334i
$121$	−7.25614	−	8.00591i	−0.659649	−	0.727810i
$122$	−12.0683	+	7.59624i	−1.09261	+	0.687731i
$123$	−13.7965	+	6.94456i	−1.24399	+	0.626170i
$124$	−0.382501	+	1.23667i	−0.0343496	+	0.111056i
$125$	−7.14986	+	5.03550i	−0.639502	+	0.450388i
$126$	−1.71879	+	33.1462i	−0.153122	+	2.95289i
$127$	3.25825	+	3.25825i	0.289123	+	0.289123i	0.836734	−	0.547610i	$-0.184462\pi$
$127$	3.25825	+	3.25825i	0.289123	+	0.289123i	−0.547610	+	0.836734i	$0.684462\pi$
$128$	−8.23668	−	7.75610i	−0.728027	−	0.685549i
$129$	−5.52835	+	5.52835i	−0.486744	+	0.486744i
$130$	3.47432	+	3.85435i	0.304718	+	0.338049i
$131$	−2.29487	−	3.25847i	−0.200504	−	0.284694i	0.704846	−	0.709361i	$-0.251016\pi$
$131$	−2.29487	−	3.25847i	−0.200504	−	0.284694i	−0.905350	+	0.424667i	$0.860391\pi$
$132$	3.04318	−	0.283015i	0.264875	−	0.0246333i
$133$	9.32438	+	18.5244i	0.808526	+	1.60627i
$134$	3.10569	+	0.706288i	0.268291	+	0.0610140i
$135$	14.7565	−	13.3745i	1.27004	−	1.15109i
$136$	−0.560396	+	9.77785i	−0.0480536	+	0.838444i
$137$	−5.43666	+	2.57135i	−0.464485	+	0.219685i	−0.645447	−	0.763805i	$-0.723329\pi$
$137$	−5.43666	+	2.57135i	−0.464485	+	0.219685i	0.180962	+	0.983490i	$0.442079\pi$
$138$	1.48138	+	3.36664i	0.126103	+	0.286587i
$139$	−0.545224	−	1.41344i	−0.0462453	−	0.119886i	0.907943	−	0.419095i	$-0.137652\pi$
$139$	−0.545224	−	1.41344i	−0.0462453	−	0.119886i	−0.954188	+	0.299208i	$0.903277\pi$
$140$	−4.79884	+	1.55641i	−0.405576	+	0.131541i
$141$	2.85727	−	38.7350i	0.240625	−	3.26208i
$142$	15.7031	+	1.58977i	1.31777	+	0.133411i
$143$	−1.60857	+	0.487956i	−0.134516	+	0.0408049i
$144$	18.7807	−	30.5741i	1.56506	−	2.54784i
$145$	−1.82296	+	6.00950i	−0.151389	+	0.499062i
$146$	−1.08295	−	2.63472i	−0.0896254	−	0.218051i
$147$	−0.516574	−	0.142955i	−0.0426063	−	0.0117907i
$148$	7.73938	−	4.84211i	0.636173	−	0.398019i
$149$	0.327178	+	0.516670i	0.0268034	+	0.0423273i	0.857990	−	0.513666i	$-0.171713\pi$
$149$	0.327178	+	0.516670i	0.0268034	+	0.0423273i	−0.831187	+	0.555993i	$0.812338\pi$
$150$	−17.7654	−	9.00304i	−1.45054	−	0.735095i
$151$	10.2218	−	17.0540i	0.831835	−	1.38783i	−0.0882443	−	0.996099i	$-0.528126\pi$
$151$	10.2218	−	17.0540i	0.831835	−	1.38783i	0.920079	−	0.391733i	$-0.128124\pi$
$152$	0.733154	−	22.4082i	0.0594667	−	1.81754i
$153$	−30.7253	+	4.55767i	−2.48399	+	0.368466i
$154$	0.204462	−	1.62141i	0.0164760	−	0.130657i
$155$	−0.166434	−	0.601416i	−0.0133683	−	0.0483069i
$156$	−9.00668	+	24.7466i	−0.721111	+	1.98131i
$157$	−10.6527	+	11.1889i	−0.850179	+	0.892971i	−0.995339	−	0.0964371i	$-0.969255\pi$
$157$	−10.6527	+	11.1889i	−0.850179	+	0.892971i	0.145160	+	0.989408i	$0.453630\pi$
$158$	−4.87738	−	2.94146i	−0.388024	−	0.234010i
$159$	14.3236	+	2.84915i	1.13594	+	0.225952i
$160$	5.36046	+	1.00543i	0.423782	+	0.0794866i
$161$	1.92896	−	0.383693i	0.152023	−	0.0302393i
$162$	59.2715	+	21.3898i	4.65681	+	1.68054i
$163$	−1.49088	−	3.36337i	−0.116775	−	0.263439i	0.846284	−	0.532733i	$-0.178835\pi$
$163$	−1.49088	−	3.36337i	−0.116775	−	0.263439i	−0.963058	+	0.269293i	$0.913210\pi$
$164$	2.21657	−	8.64909i	0.173085	−	0.675380i
$165$	−1.16150	+	0.906445i	−0.0904228	+	0.0705667i
$166$	6.01663	−	3.00803i	0.466981	−	0.233468i
$167$	13.4600	+	3.37156i	1.04157	+	0.260899i	0.725777	−	0.687930i	$-0.241480\pi$
$167$	13.4600	+	3.37156i	1.04157	+	0.260899i	0.315790	+	0.948829i	$0.397730\pi$
$168$	−18.3981	−	17.8050i	−1.41944	−	1.37368i
$169$	0.217737	−	1.46787i	0.0167490	−	0.112913i
$170$	−2.31593	−	4.11425i	−0.177624	−	0.315549i
$171$	70.0590	−	12.1564i	5.35755	−	0.929623i
$172$	−0.307939	−	4.50895i	−0.0234801	−	0.343804i
$173$	0.423168	+	3.43095i	0.0321728	+	0.260850i	0.999959	+	0.00907613i	$0.00288906\pi$
$173$	0.423168	+	3.43095i	0.0321728	+	0.260850i	−0.967786	+	0.251774i	$0.918986\pi$
$174$	−31.2748	+	6.13253i	−2.37094	+	0.464906i
$175$	−6.75602	+	8.23223i	−0.510707	+	0.622298i
$176$	−1.03297	+	1.43330i	−0.0778627	+	0.108039i
$177$	22.1430	−	18.1723i	1.66437	−	1.36591i
$178$	−1.64363	−	17.1668i	−0.123195	−	1.28671i
$179$	−10.9135	−	5.49338i	−0.815712	−	0.410595i	−0.00785165	−	0.999969i	$-0.502499\pi$
$179$	−10.9135	−	5.49338i	−0.815712	−	0.410595i	−0.807860	+	0.589374i	$0.799374\pi$
$180$	0.330389	+	17.2941i	0.0246257	+	1.28903i
$181$	6.48534	−	6.17456i	0.482052	−	0.458951i	−0.409210	−	0.912440i	$-0.634196\pi$
$181$	6.48534	−	6.17456i	0.482052	−	0.458951i	0.891262	+	0.453489i	$0.149821\pi$
$182$	11.8762	+	7.56589i	0.880324	+	0.560821i
$183$	34.8445	−	1.71180i	2.57578	−	0.126540i
$184$	−2.02954	−	0.633791i	−0.149620	−	0.0467237i
$185$	−1.88163	+	3.97838i	−0.138340	+	0.292496i
$186$	2.29954	−	2.17745i	0.168611	−	0.159658i
$187$	1.52527	−	0.112510i	0.111538	−	0.00822757i
$188$	15.7894	+	15.9622i	1.15156	+	1.16417i
$189$	28.9134	−	45.6593i	2.10314	−	3.32122i
$190$	5.53116	+	9.28538i	0.401272	+	0.673633i
$191$	1.71866	−	0.711894i	0.124358	−	0.0515108i	−0.319637	−	0.947540i	$-0.603561\pi$
$191$	1.71866	−	0.711894i	0.124358	−	0.0515108i	0.443995	+	0.896029i	$0.353561\pi$
$192$	8.25207	+	26.4199i	0.595542	+	1.90669i
$193$	−8.80278	−	3.64623i	−0.633638	−	0.262461i	0.0426601	−	0.999090i	$-0.486417\pi$
$193$	−8.80278	−	3.64623i	−0.633638	−	0.262461i	−0.676298	+	0.736628i	$0.736417\pi$
$194$	0.875418	+	6.01429i	0.0628513	+	0.431801i
$195$	−2.78149	−	12.3865i	−0.199187	−	0.887019i
$196$	0.258552	−	0.170731i	0.0184680	−	0.0121951i
$197$	−2.39729	−	2.06792i	−0.170800	−	0.147333i	0.563605	−	0.826044i	$-0.309414\pi$
$197$	−2.39729	−	2.06792i	−0.170800	−	0.147333i	−0.734405	+	0.678711i	$0.762539\pi$
$198$	−5.11635	−	2.28460i	−0.363603	−	0.162359i
$199$	4.57011	+	12.7726i	0.323966	+	0.905425i	0.987548	+	0.157321i	$0.0502857\pi$
$199$	4.57011	+	12.7726i	0.323966	+	0.905425i	−0.663581	+	0.748104i	$0.730964\pi$
$200$	10.6722	−	4.31886i	0.754640	−	0.305389i
$201$	−5.77347	−	5.23276i	−0.407229	−	0.369091i
$202$	−18.9828	+	13.2921i	−1.33562	+	0.935226i
$203$	−0.418219	+	17.0364i	−0.0293532	+	1.19572i
$204$	12.9288	−	20.1730i	0.905194	−	1.41239i
$205$	1.35014	+	4.08692i	0.0942977	+	0.285443i
$206$	−9.18710	−	17.3009i	−0.640095	−	1.20541i
$207$	0.660957	−	6.71081i	0.0459397	−	0.466433i
$208$	−7.35884	−	13.3263i	−0.510244	−	0.924013i
$209$	−3.48426	+	0.343170i	−0.241011	+	0.0237375i
$210$	12.0985	+	2.44078i	0.834875	+	0.168430i
$211$	−2.06569	−	1.61208i	−0.142208	−	0.110980i	0.541620	−	0.840623i	$-0.317811\pi$
$211$	−2.06569	−	1.61208i	−0.142208	−	0.110980i	−0.683828	+	0.729643i	$0.739686\pi$
$212$	−6.68354	+	5.15761i	−0.459027	+	0.354226i
$213$	−31.5698	−	22.2339i	−2.16312	−	1.52344i
$214$	−5.55751	+	7.08148i	−0.379904	+	0.484080i
$215$	1.29783	+	1.74992i	0.0885114	+	0.119344i
$216$	−51.0687	+	28.3819i	−3.47479	+	1.93115i
$217$	−0.870568	−	1.45245i	−0.0590980	−	0.0985991i
$218$	1.02618	+	14.4473i	0.0695015	+	0.978492i
$219$	−0.853081	+	6.91660i	−0.0576459	+	0.467380i
$220$	0.0464187	−	0.850418i	0.00312955	−	0.0573352i
$221$	−4.74274	+	12.2951i	−0.319031	+	0.827058i
$222$	−22.3105	+	1.03520i	−1.49738	+	0.0694782i
$223$	−2.93107	+	4.38666i	−0.196279	+	0.293753i	−0.916534	−	0.399957i	$-0.869025\pi$
$223$	−2.93107	+	4.38666i	−0.196279	+	0.293753i	0.720255	+	0.693710i	$0.244025\pi$
$224$	14.7472	−	1.25015i	0.985338	−	0.0835294i
$225$	20.2859	+	30.3600i	1.35239	+	2.02400i
$226$	−12.8513	−	17.4269i	−0.854855	−	1.15922i
$227$	0.346952	+	14.1333i	0.0230280	+	0.938057i	0.894356	+	0.447356i	$0.147634\pi$
$227$	0.346952	+	14.1333i	0.0230280	+	0.938057i	−0.871328	+	0.490701i	$0.836741\pi$
$228$	−28.4542	+	46.8924i	−1.88443	+	3.10553i
$229$	9.99770	−	17.6484i	0.660667	−	1.16624i	−0.315440	−	0.948946i	$-0.602152\pi$
$229$	9.99770	−	17.6484i	0.660667	−	1.16624i	0.976106	−	0.217294i	$-0.0697231\pi$
$230$	0.988578	−	0.270683i	0.0651849	−	0.0178483i
$231$	−2.38168	+	3.21133i	−0.156703	+	0.211290i
$232$	9.21127	−	15.9551i	0.604749	−	1.04750i
$233$	−21.2878	+	5.33232i	−1.39461	+	0.349332i	−0.866217	−	0.499668i	$-0.833455\pi$
$233$	−21.2878	+	5.33232i	−1.39461	+	0.349332i	−0.528393	+	0.849000i	$0.677205\pi$
$234$	36.6440	−	31.4358i	2.39549	−	2.05502i
$235$	−10.5604	−	2.37142i	−0.688885	−	0.154694i
$236$	−0.496448	+	16.5513i	−0.0323160	+	1.07740i
$237$	6.86822	+	12.1241i	0.446139	+	0.787545i
$238$	−9.03473	−	9.08403i	−0.585634	−	0.588830i
$239$	6.34167	+	11.8644i	0.410208	+	0.767446i	0.999171	−	0.0407146i	$-0.0129635\pi$
$239$	6.34167	+	11.8644i	0.410208	+	0.767446i	−0.588963	+	0.808160i	$0.700463\pi$
$240$	−10.2215	−	8.57639i	−0.659792	−	0.553604i
$241$	2.74554	+	1.46752i	0.176856	+	0.0945315i	0.557449	−	0.830211i	$-0.311780\pi$
$241$	2.74554	+	1.46752i	0.176856	+	0.0945315i	−0.380593	+	0.924743i	$0.624280\pi$
$242$	−13.4565	−	7.23980i	−0.865017	−	0.465392i
$243$	−60.2157	−	69.8067i	−3.86284	−	4.47810i
$244$	−12.4935	+	15.8305i	−0.799813	+	1.01345i
$245$	−0.0605272	+	0.136547i	−0.00386694	+	0.00872368i
$246$	−15.1050	+	15.7791i	−0.963059	+	1.00604i
$247$	10.1631	−	28.4039i	0.646660	−	1.80729i
$248$	0.0748982	+	1.82913i	0.00475604	+	0.116150i
$249$	−16.4368	−	0.807486i	−1.04164	−	0.0511724i
$250$	−7.14875	+	10.0920i	−0.452127	+	0.638275i
$251$	−18.0568	−	5.96516i	−1.13974	−	0.376518i	−0.318960	−	0.947768i	$-0.603333\pi$
$251$	−18.0568	−	5.96516i	−1.13974	−	0.376518i	−0.820776	+	0.571251i	$0.806458\pi$
$252$	13.3810	+	44.9910i	0.842921	+	2.83417i
$253$	−0.0567638	+	0.327138i	−0.00356871	+	0.0205670i
$254$	5.88325	+	2.80219i	0.369148	+	0.175825i
$255$			11.5505i			0.723320i
$256$	−14.6453	−	6.44323i	−0.915331	−	0.402702i
$257$			7.85095i			0.489729i	0.969557	+	0.244864i	$0.0787434\pi$
$257$			7.85095i			0.489729i	−0.969557	+	0.244864i	$0.921257\pi$
$258$	−4.75453	+	9.98224i	−0.296004	+	0.621467i
$259$	−2.04172	+	11.7667i	−0.126866	+	0.731148i
$260$	6.45308	+	3.49452i	0.400203	+	0.216721i
$261$	55.4802	+	18.3282i	3.43414	+	1.13449i
$262$	−4.59932	−	3.25797i	−0.284147	−	0.201278i
$263$	7.40321	+	0.363696i	0.456501	+	0.0224265i	0.276020	−	0.961152i	$-0.410984\pi$
$263$	7.40321	+	0.363696i	0.456501	+	0.0224265i	0.180481	+	0.983578i	$0.442234\pi$
$264$	3.92225	−	1.81606i	0.241398	−	0.111771i
$265$	1.37103	−	3.83178i	0.0842220	−	0.235385i
$266$	21.1864	+	20.2813i	1.29902	+	1.24353i
$267$	−17.0972	+	38.5706i	−1.04633	+	2.36048i
$268$	4.47331	−	0.527033i	0.273251	−	0.0321937i
$269$	−16.8209	−	19.5001i	−1.02559	−	1.18894i	−0.981803	−	0.189904i	$-0.939182\pi$
$269$	−16.8209	−	19.5001i	−1.02559	−	1.18894i	−0.0437883	−	0.999041i	$-0.513943\pi$
$270$	13.3444	−	24.8030i	0.812113	−	1.50946i
$271$	21.4577	+	11.4694i	1.30346	+	0.696715i	0.969319	−	0.245807i	$-0.0790530\pi$
$271$	21.4577	+	11.4694i	1.30346	+	0.696715i	0.334144	+	0.942522i	$0.391553\pi$
$272$	3.87614	+	13.2972i	0.235026	+	0.806263i
$273$	−16.2395	−	30.3820i	−0.982861	−	1.83880i
$274$	−6.03042	+	5.99769i	−0.364311	+	0.362334i
$275$	−0.886162	−	1.56430i	−0.0534376	−	0.0943306i
$276$	3.56622	+	3.78676i	0.214661	+	0.227936i
$277$	5.63646	+	1.26571i	0.338662	+	0.0760491i	0.385108	−	0.922872i	$-0.374164\pi$
$277$	5.63646	+	1.26571i	0.338662	+	0.0760491i	−0.0464454	+	0.998921i	$0.514789\pi$
$278$	−1.39498	−	1.62610i	−0.0836655	−	0.0975268i
$279$	−5.63198	+	1.41074i	−0.337178	+	0.0844586i
$280$	−5.66018	+	4.34337i	−0.338260	+	0.259566i
$281$	−5.04649	+	6.80440i	−0.301048	+	0.405917i	−0.927667	−	0.373410i	$-0.878189\pi$
$281$	−5.04649	+	6.80440i	−0.301048	+	0.405917i	0.626618	+	0.779326i	$0.284439\pi$
$282$	−14.5060	−	52.9784i	−0.863821	−	3.15482i
$283$	11.7995	−	20.8291i	0.701409	−	1.23816i	−0.260681	−	0.965425i	$-0.583947\pi$
$283$	11.7995	−	20.8291i	0.701409	−	1.23816i	0.962089	−	0.272735i	$-0.0879281\pi$
$284$	21.6813	−	5.30566i	1.28655	−	0.314833i
$285$	−0.648903	−	26.4334i	−0.0384377	−	1.56578i
$286$	−1.91326	+	1.41091i	−0.113133	+	0.0834291i
$287$	6.48906	+	9.71156i	0.383037	+	0.573255i
$288$	10.5759	−	49.6299i	0.623189	−	2.92447i
$289$	−2.78338	+	4.16562i	−0.163728	+	0.245036i
$290$	0.411639	+	8.87159i	0.0241723	+	0.520958i
$291$	5.35121	−	13.8725i	0.313694	−	0.813220i
$292$	−2.68911	−	2.99962i	−0.157368	−	0.175540i
$293$	0.0336870	−	0.273127i	0.00196802	−	0.0159563i	−0.991463	−	0.130385i	$-0.958379\pi$
$293$	0.0336870	−	0.273127i	0.00196802	−	0.0159563i	0.993431	+	0.114429i	$0.0365037\pi$
$294$	−0.756098	+	0.0537051i	−0.0440965	+	0.00313214i
$295$	−4.10376	−	6.84671i	−0.238930	−	0.398631i
$296$	8.02593	−	10.1130i	0.466498	−	0.587805i
$297$	5.43498	+	7.32823i	0.315370	+	0.425227i
$298$	0.680361	+	0.533944i	0.0394122	+	0.0309305i
$299$	−2.33903	−	1.64733i	−0.135269	−	0.0952675i
$300$	−27.9351	−	3.59991i	−1.61284	−	0.207841i
$301$	4.66082	+	3.63734i	0.268645	+	0.209653i
$302$	5.56064	−	27.5631i	0.319979	−	1.58608i
$303$	56.4209	−	5.55698i	3.24130	−	0.319240i
$304$	−9.61761	−	30.2130i	−0.551608	−	1.73284i
$305$	0.952886	−	9.67481i	0.0545621	−	0.553978i
$306$	−38.7969	+	20.6018i	−2.21787	+	1.17773i
$307$	4.67380	+	14.1478i	0.266748	+	0.807458i	0.992796	+	0.119814i	$0.0382299\pi$
$307$	4.67380	+	14.1478i	0.266748	+	0.807458i	−0.726048	+	0.687644i	$0.758645\pi$
$308$	−0.494102	−	2.25774i	−0.0281541	−	0.128647i
$309$	−1.17610	+	47.9091i	−0.0669062	+	2.72546i
$310$	−0.506185	−	0.722897i	−0.0287494	−	0.0410578i
$311$	−1.08268	−	0.981283i	−0.0613931	−	0.0556435i	0.640286	−	0.768137i	$-0.278816\pi$
$311$	−1.08268	−	0.981283i	−0.0613931	−	0.0556435i	−0.701679	+	0.712493i	$0.747566\pi$
$312$	−0.304003	+	37.2416i	−0.0172108	+	2.10839i
$313$	−4.99484	−	13.9596i	−0.282325	−	0.789045i	−0.996064	−	0.0886340i	$-0.971750\pi$
$313$	−4.99484	−	13.9596i	−0.282325	−	0.789045i	0.713739	−	0.700411i	$-0.247000\pi$
$314$	−8.90810	+	19.9497i	−0.502713	+	1.12582i
$315$	−17.1337	−	14.7797i	−0.965377	−	0.832740i
$316$	−7.89150	−	1.61441i	−0.443932	−	0.0908176i
$317$	4.58180	+	20.4037i	0.257339	+	1.14598i	0.918401	+	0.395652i	$0.129481\pi$
$317$	4.58180	+	20.4037i	0.257339	+	1.14598i	−0.661061	+	0.750332i	$0.729894\pi$
$318$	20.4382	−	2.97490i	1.14612	−	0.166824i
$319$	−2.65795	−	1.10096i	−0.148817	−	0.0616418i
$320$	7.62000	−	1.19440i	0.425971	−	0.0667689i
$321$	20.3464	−	8.42774i	1.13562	−	0.470390i
$322$	2.38957	−	1.42343i	0.133165	−	0.0793246i
$323$	−14.6844	+	23.1892i	−0.817061	+	1.29028i
$324$	89.1125	+	0.484945i	4.95070	+	0.0269414i
$325$	15.4493	−	1.13961i	0.856971	−	0.0632140i
$326$	−3.57733	−	3.77791i	−0.198130	−	0.209239i
$327$	15.1499	−	32.0318i	0.837791	−	1.77136i
$328$	−1.13504	−	12.5758i	−0.0626722	−	0.694384i
$329$	−29.3355	+	1.44116i	−1.61732	+	0.0794538i
$330$	−1.11952	+	1.75731i	−0.0616273	+	0.0967368i
$331$	−21.2845	+	20.2646i	−1.16990	+	1.11384i	−0.178374	+	0.983963i	$0.557084\pi$
$331$	−21.2845	+	20.2646i	−1.16990	+	1.11384i	−0.991530	+	0.129878i	$0.958541\pi$
$332$	6.59696	−	6.85393i	0.362055	−	0.376158i
$333$	36.5746	+	18.4101i	2.00428	+	1.00887i
$334$	19.5341	−	1.87029i	1.06886	−	0.102338i
$335$	−1.67847	+	1.37748i	−0.0917046	+	0.0752600i
$336$	−32.9400	−	15.0323i	−1.79702	−	0.820082i
$337$	−12.0026	+	14.6252i	−0.653821	+	0.796683i	−0.989382	−	0.145335i	$-0.953574\pi$
$337$	−12.0026	+	14.6252i	−0.653821	+	0.796683i	0.335561	+	0.942018i	$0.391074\pi$
$338$	−0.403813	−	2.05937i	−0.0219645	−	0.112015i
$339$	6.48449	+	52.5749i	0.352189	+	2.85548i
$340$	−5.03201	−	4.38863i	−0.272899	−	0.238007i
$341$	0.281667	−	0.0488738i	0.0152531	−	0.00264666i
$342$	87.6295	−	49.3270i	4.73846	−	2.66730i
$343$	−2.74672	+	18.5169i	−0.148309	+	0.999817i
$344$	−2.54231	−	5.86409i	−0.137072	−	0.316171i
$345$	−2.43240	−	0.609284i	−0.130956	−	0.0328028i
$346$	2.18620	+	4.37282i	0.117531	+	0.235084i
$347$	−12.5068	+	9.76043i	−0.671402	+	0.523967i	−0.892365	−	0.451315i	$-0.850955\pi$
$347$	−12.5068	+	9.76043i	−0.671402	+	0.523967i	0.220963	+	0.975282i	$0.429080\pi$
$348$	−38.7847	+	22.9607i	−2.07908	+	1.23082i
$349$	1.78414	+	4.02494i	0.0955026	+	0.215450i	0.955592	−	0.294693i	$-0.0952174\pi$
$349$	1.78414	+	4.02494i	0.0955026	+	0.215450i	−0.860089	+	0.510143i	$0.829592\pi$
$350$	−5.11239	+	14.1665i	−0.273269	+	0.757232i
$351$	−77.1037	+	15.3369i	−4.11549	+	0.818622i
$352$	−0.699093	+	2.39875i	−0.0372618	+	0.127854i
$353$	−27.5050	−	5.47108i	−1.46394	−	0.291196i	−0.602119	−	0.798406i	$-0.705677\pi$
$353$	−27.5050	−	5.47108i	−1.46394	−	0.291196i	−0.861823	+	0.507210i	$0.830677\pi$
$354$	20.9210	−	34.6901i	1.11194	−	1.84376i
$355$	−7.41958	+	7.79303i	−0.393790	+	0.413611i
$356$	−10.3073	−	22.1034i	−0.546286	−	1.17148i
$357$	8.35984	+	30.2086i	0.442450	+	1.59881i
$358$	−17.1432	−	2.16178i	−0.906046	−	0.114254i
$359$	−23.9800	+	3.55710i	−1.26562	+	0.187737i	−0.745586	−	0.666410i	$-0.767830\pi$
$359$	−23.9800	+	3.55710i	−1.26562	+	0.187737i	−0.520032	+	0.854147i	$0.674080\pi$
$360$	8.61717	+	22.8940i	0.454165	+	1.20662i
$361$	22.5346	−	37.5967i	1.18603	−	1.97877i
$362$	5.72451	−	11.2960i	0.300873	−	0.593705i
$363$	19.9999	+	31.5833i	1.04972	+	1.65769i
$364$	19.4063	+	4.46889i	1.01717	+	0.234234i
$365$	1.87166	+	0.517959i	0.0979674	+	0.0271112i
$366$	45.6326	−	18.7564i	2.38526	−	0.980411i
$367$	9.30236	−	30.6658i	0.485579	−	1.60074i	−0.281750	−	0.959488i	$-0.590915\pi$
$367$	9.30236	−	30.6658i	0.485579	−	1.60074i	0.767329	−	0.641253i	$-0.221585\pi$
$368$	−3.00471	+	0.114847i	−0.156631	+	0.00598679i
$369$	38.3222	−	11.6249i	1.99497	−	0.605168i
$370$	−0.626893	+	6.19218i	−0.0325906	+	0.321916i
$371$	0.812425	−	11.0138i	0.0421790	−	0.571807i
$372$	2.03539	−	3.98943i	0.105530	−	0.206842i
$373$	−12.8973	−	33.4350i	−0.667798	−	1.73120i	−0.682053	−	0.731303i	$-0.738913\pi$
$373$	−12.8973	−	33.4350i	−0.667798	−	1.73120i	0.0142552	−	0.999898i	$-0.495462\pi$
$374$	1.97973	−	0.871118i	0.102370	−	0.0450444i
$375$	27.3516	−	12.9363i	1.41243	−	0.668029i
$376$	28.5918	+	13.8096i	1.47451	+	0.712178i
$377$	18.3675	−	16.6474i	0.945976	−	0.857383i
$378$	16.9487	−	74.5268i	0.871747	−	3.83325i
$379$	−5.36577	−	10.6599i	−0.275621	−	0.547565i	0.712421	−	0.701753i	$-0.247599\pi$
$379$	−5.36577	−	10.6599i	−0.275621	−	0.547565i	−0.988042	+	0.154188i	$0.950724\pi$
$380$	11.7623	+	9.76071i	0.603396	+	0.500714i
$381$	−9.17978	−	13.0343i	−0.470294	−	0.667767i
$382$	1.95411	−	1.76144i	0.0999808	−	0.0901230i
$383$	−7.91449	+	7.91449i	−0.404412	+	0.404412i	−0.879784	−	0.475373i	$-0.842313\pi$
$383$	−7.91449	+	7.91449i	−0.404412	+	0.404412i	0.475373	+	0.879784i	$0.342313\pi$
$384$	23.4902	+	31.3117i	1.19873	+	1.59787i
$385$	0.787813	+	0.787813i	0.0401506	+	0.0401506i
$386$	−13.4566	−	0.697790i	−0.684924	−	0.0355166i
$387$	16.5730	−	11.6720i	0.842452	−	0.593322i
$388$	4.01040	+	7.60215i	0.203597	+	0.385941i
$389$	18.4928	−	9.30847i	0.937620	−	0.471958i	0.0861037	−	0.996286i	$-0.472558\pi$
$389$	18.4928	−	9.30847i	0.937620	−	0.471958i	0.851516	+	0.524328i	$0.175683\pi$
$390$	−9.56375	−	15.1941i	−0.484279	−	0.769384i
$391$	1.74805	+	1.92868i	0.0884027	+	0.0975374i
$392$	0.263884	−	0.349802i	0.0133282	−	0.0176677i
$393$	5.89559	+	12.4652i	0.297393	+	0.628785i
$394$	−4.17292	−	1.62273i	−0.210229	−	0.0817521i
$395$	3.62281	−	1.39747i	0.182284	−	0.0703145i
$396$	−7.89943	−	0.625937i	−0.396962	−	0.0314545i
$397$	16.7954	+	1.23890i	0.842936	+	0.0621787i	0.488140	−	0.872765i	$-0.337676\pi$
$397$	16.7954	+	1.23890i	0.842936	+	0.0621787i	0.354795	+	0.934944i	$0.384551\pi$
$398$	12.1302	+	14.8630i	0.608032	+	0.745014i
$399$	−20.8287	−	68.6629i	−1.04274	−	3.43744i
$400$	12.1823	−	10.8023i	0.609116	−	0.540113i
$401$	6.72875	+	2.04115i	0.336018	+	0.101930i	0.453785	−	0.891111i	$-0.350074\pi$
$401$	6.72875	+	2.04115i	0.336018	+	0.101930i	−0.117767	+	0.993041i	$0.537574\pi$
$402$	−10.1692	−	4.24467i	−0.507193	−	0.211705i
$403$	−0.656977	+	2.37401i	−0.0327264	+	0.118258i
$404$	−19.0163	+	26.6914i	−0.946097	+	1.32795i
$405$	−36.2938	+	22.9828i	−1.80345	+	1.14202i
$406$	7.49753	+	22.9044i	0.372096	+	1.13673i
$407$	−1.72930	−	1.03650i	−0.0857182	−	0.0513775i
$408$	7.69391	−	33.0001i	0.380906	−	1.63375i
$409$	4.23402	+	28.5435i	0.209359	+	1.41138i	0.797838	+	0.602871i	$0.205977\pi$
$409$	4.23402	+	28.5435i	0.209359	+	1.41138i	−0.588480	+	0.808512i	$0.700273\pi$
$410$	3.73185	+	4.80884i	0.184303	+	0.237492i
$411$	20.0539	−	5.54967i	0.989188	−	0.273745i
$412$	−20.4249	−	18.7155i	−1.00626	−	0.922048i
$413$	−15.6882	−	14.9364i	−0.771965	−	0.734972i
$414$	−2.29199	−	9.25691i	−0.112645	−	0.454952i
$415$	−0.894657	+	4.49774i	−0.0439170	+	0.220785i
$416$	−16.1089	−	14.2824i	−0.789805	−	0.700255i
$417$	1.02256	+	5.14076i	0.0500750	+	0.251744i
$418$	−4.48169	+	2.10478i	−0.219207	+	0.102948i
$419$	22.4239	−	9.93985i	1.09548	−	0.485594i	0.223287	−	0.974753i	$-0.428321\pi$
$419$	22.4239	−	9.93985i	1.09548	−	0.485594i	0.872195	+	0.489159i	$0.162696\pi$
$420$	17.2793	−	2.46712i	0.843145	−	0.120383i
$421$	15.5083	+	19.8720i	0.755826	+	0.968502i	0.999999	−	0.00122984i	$-0.000391471\pi$
$421$	15.5083	+	19.8720i	0.755826	+	0.968502i	−0.244173	+	0.969732i	$0.578516\pi$
$422$	−3.51543	−	1.17196i	−0.171128	−	0.0570501i
$423$	−24.4687	+	97.6845i	−1.18971	+	4.74958i
$424$	−6.46949	+	10.0343i	−0.314186	+	0.487308i
$425$	−13.9421	−	2.06811i	−0.676290	−	0.100318i
$426$	−52.5897	−	14.7077i	−2.54798	−	0.712591i
$427$	−4.51016	−	25.9927i	−0.218262	−	1.25787i
$428$	−4.05906	+	12.0661i	−0.196202	+	0.583237i
$429$	5.77208	−	0.711918i	0.278679	−	0.0343717i
$430$	2.55718	+	1.71873i	0.123318	+	0.0828847i
$431$	−12.9259	−	10.6080i	−0.622617	−	0.510968i	0.269366	−	0.963038i	$-0.413186\pi$
$431$	−12.9259	−	10.6080i	−0.622617	−	0.510968i	−0.891983	+	0.452069i	$0.850686\pi$
$432$	−54.6470	+	61.9742i	−2.62920	+	2.98174i
$433$	−17.7078	−	21.5770i	−0.850982	−	1.03692i	−0.998851	−	0.0479178i	$-0.984741\pi$
$433$	−17.7078	−	21.5770i	−0.850982	−	1.03692i	0.147869	−	0.989007i	$-0.452759\pi$
$434$	−1.84706	−	1.52427i	−0.0886616	−	0.0731674i
$435$	9.76889	−	19.4074i	0.468382	−	0.930516i
$436$	8.19853	+	18.7706i	0.392638	+	0.898951i
$437$	−4.10878	−	4.31558i	−0.196549	−	0.206442i
$438$	2.13322	+	9.62203i	0.101929	+	0.459759i
$439$	1.25718	+	25.5905i	0.0600021	+	1.22137i	0.820353	+	0.571858i	$0.193777\pi$
$439$	1.25718	+	25.5905i	0.0600021	+	1.22137i	−0.760351	+	0.649513i	$0.774973\pi$
$440$	−0.340217	−	1.15542i	−0.0162192	−	0.0550823i
$441$	1.25625	+	0.594163i	0.0598215	+	0.0282935i
$442$	−0.508060	+	18.6298i	−0.0241659	+	0.886127i
$443$	−1.10778	−	15.0178i	−0.0526322	−	0.713517i	−0.957612	−	0.288062i	$-0.906989\pi$
$443$	−1.10778	−	15.0178i	−0.0526322	−	0.713517i	0.904979	−	0.425455i	$-0.139886\pi$
$444$	−29.2468	+	11.9284i	−1.38799	+	0.566096i
$445$	9.93282	+	6.28989i	0.470861	+	0.298169i
$446$	−1.83258	+	7.23254i	−0.0867754	+	0.342471i
$447$	−0.809703	−	1.95480i	−0.0382976	−	0.0924587i
$448$	19.0645	−	8.63886i	0.900713	−	0.408148i
$449$	−0.754960	+	1.82263i	−0.0356287	+	0.0860154i	−0.940692	−	0.339261i	$-0.889823\pi$
$449$	−0.754960	+	1.82263i	−0.0356287	+	0.0860154i	0.905064	+	0.425276i	$0.139823\pi$
$450$	41.3922	+	30.8735i	1.95125	+	1.45539i
$451$	−1.92391	+	0.432028i	−0.0905932	+	0.0203434i
$452$	−25.3682	−	17.1509i	−1.19322	−	0.806712i
$453$	−44.9322	+	52.0889i	−2.11110	+	2.44735i
$454$	7.14477	+	18.6733i	0.335321	+	0.876380i
$455$	−9.03875	+	3.23412i	−0.423743	+	0.151618i
$456$	−15.7536	+	75.9533i	−0.737732	+	3.55684i
$457$	−3.54190	+	3.90788i	−0.165683	+	0.182803i	−0.818133	−	0.575028i	$-0.804991\pi$
$457$	−3.54190	+	3.90788i	−0.165683	+	0.182803i	0.652451	+	0.757831i	$0.273741\pi$
$458$	4.98096	−	28.2494i	0.232745	−	1.32001i
$459$	71.5052	+	1.75535i	3.33758	+	0.0819329i
$460$	1.18963	−	0.828185i	0.0554668	−	0.0386143i
$461$	−12.0136	+	3.96875i	−0.559528	+	0.184843i	−0.579521	−	0.814957i	$-0.696761\pi$
$461$	−12.0136	+	3.96875i	−0.559528	+	0.184843i	0.0199933	+	0.999800i	$0.493636\pi$
$462$	−1.65605	+	5.40626i	−0.0770463	+	0.251522i
$463$	2.58587	+	0.254686i	0.120175	+	0.0118363i	0.157926	−	0.987451i	$-0.449519\pi$
$463$	2.58587	+	0.254686i	0.120175	+	0.0118363i	−0.0377506	+	0.999287i	$0.512019\pi$
$464$	4.73340	−	25.6206i	0.219743	−	1.18941i
$465$	0.211619	+	2.14861i	0.00981361	+	0.0996392i
$466$	−25.8520	+	17.1722i	−1.19757	+	0.795485i
$467$	12.7584	−	16.3484i	0.590389	−	0.756514i	−0.396479	−	0.918044i	$-0.629768\pi$
$467$	12.7584	−	16.3484i	0.590389	−	0.756514i	0.986868	+	0.161530i	$0.0516430\pi$
$468$	33.9772	−	59.2244i	1.57060	−	2.73765i
$469$	−3.39281	+	4.81742i	−0.156666	+	0.222448i
$470$	−15.1965	+	1.83235i	−0.700963	+	0.0845199i
$471$	42.9322	−	31.8407i	1.97821	−	1.46714i
$472$	7.16391	+	22.2949i	0.329746	+	1.02620i
$473$	−0.856089	+	0.513120i	−0.0393630	+	0.0235933i
$474$	14.8866	+	12.9121i	0.683764	+	0.593071i
$475$	32.0227	+	3.94962i	1.46930	+	0.181221i
$476$	−16.3368	−	7.83581i	−0.748797	−	0.359154i
$477$	−35.3277	−	13.6274i	−1.61754	−	0.623956i
$478$	14.0620	+	12.8149i	0.643181	+	0.586141i
$479$	−18.6830	−	12.4836i	−0.853647	−	0.570389i	0.0499601	−	0.998751i	$-0.484091\pi$
$479$	−18.6830	−	12.4836i	−0.853647	−	0.570389i	−0.903607	+	0.428363i	$0.859091\pi$
$480$	−17.6785	−	6.59812i	−0.806910	−	0.301162i
$481$	14.4443	−	9.65138i	0.658604	−	0.440065i
$482$	4.35322	+	0.657849i	0.198284	+	0.0299642i
$483$	−6.80256	+	0.166993i	−0.309527	+	0.00759846i
$484$	−21.3584	−	3.28710i	−0.970835	−	0.149414i
$485$	−3.60512	−	2.04228i	−0.163700	−	0.0927350i
$486$	−113.263	−	64.5704i	−5.13771	−	2.92897i
$487$	−22.7062	−	16.8401i	−1.02892	−	0.763098i	−0.0569899	−	0.998375i	$-0.518150\pi$
$487$	−22.7062	−	16.8401i	−1.02892	−	0.763098i	−0.971928	+	0.235277i	$0.924400\pi$
$488$	−9.16693	+	27.0065i	−0.414968	+	1.22253i
$489$	3.09281	+	12.3472i	0.139862	+	0.558359i
$490$	−0.0161120	+	0.210613i	−0.000727868	+	0.00951452i
$491$	−3.50369	+	15.6026i	−0.158119	+	0.704137i	0.830909	+	0.556409i	$0.187821\pi$
$491$	−3.50369	+	15.6026i	−0.158119	+	0.704137i	−0.989028	+	0.147728i	$0.952804\pi$
$492$	−12.6720	+	28.1727i	−0.571297	+	1.27012i
$493$	−19.6242	+	11.1170i	−0.883828	+	0.500683i
$494$	0.116084	−	42.6629i	0.00522285	−	1.91949i
$495$	3.36892	−	1.80072i	0.151422	−	0.0809365i
$496$	0.964657	+	2.40252i	0.0433144	+	0.107876i
$497$	−13.7645	+	25.7515i	−0.617422	+	1.15511i
$498$	−22.2893	+	6.69521i	−0.998807	+	0.300019i
$499$	−11.7388	+	10.1260i	−0.525501	+	0.453301i	−0.875339	−	0.483510i	$-0.839362\pi$
$499$	−11.7388	+	10.1260i	−0.525501	+	0.453301i	0.349838	+	0.936810i	$0.386237\pi$
$500$	−4.75652	+	16.8310i	−0.212718	+	0.752705i
$501$	−43.8895	−	19.4549i	−1.96084	−	0.869179i
$502$	−26.8871	+	0.586844i	−1.20003	+	0.0261922i
$503$	24.3546	+	8.71422i	1.08592	+	0.388548i	0.818191	−	0.574947i	$-0.194977\pi$
$503$	24.3546	+	8.71422i	1.08592	+	0.388548i	0.267727	+	0.963495i	$0.413727\pi$
$504$	39.1068	+	53.6390i	1.74196	+	2.38927i
$505$	0.775199	−	15.7795i	0.0344959	−	0.702180i
$506$	0.0790171	+	0.462860i	0.00351274	+	0.0205766i
$507$	−1.61048	+	4.87500i	−0.0715241	+	0.216506i
$508$	9.16631	+	0.953196i	0.406689	+	0.0422912i
$509$	−1.33506	−	0.231655i	−0.0591754	−	0.0102679i	0.141297	−	0.989967i	$-0.454873\pi$
$509$	−1.33506	−	0.231655i	−0.0591754	−	0.0102679i	−0.200473	+	0.979699i	$0.564248\pi$
$510$	5.46118	+	15.3949i	0.241825	+	0.681698i
$511$	5.26994			0.233129
$512$	−22.5662	−	1.66333i	−0.997295	−	0.0735095i
$513$	−163.739			−7.22924
$514$	3.71200	+	10.4640i	0.163729	+	0.461548i
$515$	13.1580	+	2.28312i	0.579809	+	0.100606i
$516$	−1.61731	+	15.5527i	−0.0711980	+	0.684668i
$517$	1.55536	−	4.70814i	0.0684046	−	0.207064i
$518$	2.84214	+	16.6484i	0.124876	+	0.731491i
$519$	0.586871	−	11.9460i	0.0257608	−	0.524373i
$520$	10.2531	+	1.60655i	0.449630	+	0.0704519i
$521$	23.9131	+	8.55625i	1.04765	+	0.374856i	0.803765	−	0.594947i	$-0.202827\pi$
$521$	23.9131	+	8.55625i	1.04765	+	0.374856i	0.243888	+	0.969803i	$0.421577\pi$
$522$	82.6117	−	1.80310i	3.61582	−	0.0789196i
$523$	13.5591	+	6.01033i	0.592897	+	0.262813i	0.679793	−	0.733404i	$-0.262070\pi$
$523$	13.5591	+	6.01033i	0.592897	+	0.262813i	−0.0868957	+	0.996217i	$0.527695\pi$
$524$	−7.67054	−	2.16773i	−0.335089	−	0.0946978i
$525$	27.8999	−	24.0666i	1.21765	−	1.05035i
$526$	10.0392	−	3.01556i	0.437731	−	0.131485i
$527$	1.05648	−	1.97653i	0.0460209	−	0.0860991i
$528$	4.36906	−	4.27498i	0.190139	−	0.186045i
$529$	19.7858	−	10.5757i	0.860253	−	0.459815i
$530$	0.0156601	−	5.75538i	0.000680231	−	0.249998i
$531$	−64.6207	+	36.6071i	−2.80430	+	1.58861i
$532$	37.8271	+	17.0145i	1.64001	+	0.737672i
$533$	3.72256	−	16.5773i	0.161242	−	0.718043i
$534$	−4.55118	+	59.4919i	−0.196949	+	2.57447i
$535$	−1.49116	−	5.95303i	−0.0644683	−	0.257372i
$536$	5.71300	−	2.81747i	0.246764	−	0.121696i
$537$	33.9535	+	25.1816i	1.46520	+	1.08667i
$538$	−31.6394	−	18.0374i	−1.36407	−	0.777647i
$539$	−0.0595357	−	0.0337266i	−0.00256438	−	0.00145271i
$540$	6.05877	−	39.3677i	0.260728	−	1.69412i
$541$	18.7445	−	0.460152i	0.805889	−	0.0197835i	0.380485	−	0.924787i	$-0.375757\pi$
$541$	18.7445	−	0.460152i	0.805889	−	0.0197835i	0.425404	+	0.905004i	$0.360132\pi$
$542$	34.0224	+	5.14140i	1.46139	+	0.220842i
$543$	−25.7601	+	17.2123i	−1.10547	+	0.738652i
$544$	11.4533	+	15.8903i	0.491057	+	0.681293i
$545$	−8.21004	−	5.48577i	−0.351679	−	0.234985i
$546$	−36.0095	−	32.8160i	−1.54107	−	1.40440i
$547$	−4.35149	−	1.67856i	−0.186056	−	0.0717698i	0.265073	−	0.964228i	$-0.414604\pi$
$547$	−4.35149	−	1.67856i	−0.186056	−	0.0717698i	−0.451130	+	0.892458i	$0.648979\pi$
$548$	−5.20180	+	10.8452i	−0.222210	+	0.463283i
$549$	−89.7712	−	11.0722i	−3.83134	−	0.472551i
$550$	−1.92072	−	1.66596i	−0.0818999	−	0.0710369i
$551$	44.2855	−	26.5437i	1.88663	−	1.13080i
$552$	6.54360	+	3.36100i	0.278514	+	0.143053i
$553$	8.46349	−	6.27695i	0.359904	−	0.266923i
$554$	8.11092	−	0.977989i	0.344600	−	0.0415508i
$555$	8.76748	−	12.4489i	0.372159	−	0.528425i
$556$	−2.62812	−	1.50776i	−0.111457	−	0.0639432i
$557$	−4.74380	+	6.07861i	−0.201001	+	0.257559i	−0.878258	−	0.478188i	$-0.841294\pi$
$557$	−4.74380	+	6.07861i	−0.201001	+	0.257559i	0.677256	+	0.735747i	$0.263169\pi$
$558$	−6.83949	+	4.54313i	−0.289539	+	0.192326i
$559$	−0.842949	−	8.55860i	−0.0356529	−	0.361990i
$560$	−5.49050	+	8.46519i	−0.232016	+	0.357720i
$561$	−5.26601	−	0.518657i	−0.222331	−	0.0218977i
$562$	−3.50896	+	11.4552i	−0.148016	+	0.483208i
$563$	−19.0580	+	6.29590i	−0.803197	+	0.265340i	−0.685843	−	0.727750i	$-0.740566\pi$
$563$	−19.0580	+	6.29590i	−0.803197	+	0.265340i	−0.117354	+	0.993090i	$0.537441\pi$
$564$	−44.3828	−	63.7529i	−1.86885	−	2.68448i
$565$	14.7573	+	0.362271i	0.620844	+	0.0152409i
$566$	5.87865	−	33.3407i	0.247098	−	1.40141i
$567$	−78.2868	+	86.3762i	−3.28774	+	3.62746i
$568$	26.3890	−	17.3227i	1.10726	−	0.726844i
$569$	−2.25532	+	0.806968i	−0.0945481	+	0.0338298i	−0.383739	−	0.923442i	$-0.625364\pi$
$569$	−2.25532	+	0.806968i	−0.0945481	+	0.0338298i	0.289191	+	0.957271i	$0.406614\pi$
$570$	−13.3628	−	34.9245i	−0.559707	−	1.46283i
$571$	−16.9318	+	19.6286i	−0.708572	+	0.821432i	−0.990429	−	0.138024i	$-0.955925\pi$
$571$	−16.9318	+	19.6286i	−0.708572	+	0.821432i	0.281857	+	0.959457i	$0.409050\pi$
$572$	−1.88296	+	2.78512i	−0.0787306	+	0.116452i
$573$	−6.27982	+	1.41018i	−0.262343	+	0.0589111i
$574$	13.2406	+	9.87583i	0.552651	+	0.412209i
$575$	1.17096	−	2.82695i	0.0488324	−	0.117892i
$576$	−9.36960	−	71.1489i	−0.390400	−	2.96454i
$577$	13.7713	+	33.2468i	0.573305	+	1.38408i	0.898726	+	0.438511i	$0.144494\pi$
$577$	13.7713	+	33.2468i	0.573305	+	1.38408i	−0.325421	+	0.945569i	$0.605506\pi$
$578$	−1.74024	+	6.86809i	−0.0723845	+	0.285675i
$579$	27.8510	+	17.6364i	1.15745	+	0.732945i
$580$	4.74322	+	11.6297i	0.196951	+	0.482899i
$581$	0.915468	+	12.4107i	0.0379800	+	0.514883i
$582$	0.573241	−	21.0199i	0.0237616	−	0.871301i
$583$	1.68539	+	0.797132i	0.0698019	+	0.0330138i
$584$	−5.00239	−	2.72657i	−0.207001	−	0.112826i
$585$	1.61505	+	32.8751i	0.0667741	+	1.35922i
$586$	−0.0842379	−	0.379961i	−0.00347983	−	0.0156961i
$587$	−0.501234	−	0.526463i	−0.0206881	−	0.0217294i	0.713822	−	0.700328i	$-0.246963\pi$
$587$	−0.501234	−	0.526463i	−0.0206881	−	0.0217294i	−0.734510	+	0.678598i	$0.762588\pi$
$588$	−0.982363	+	0.429070i	−0.0405120	+	0.0176946i
$589$	−2.30672	+	4.58266i	−0.0950466	+	0.188825i
$590$	−8.70683	−	7.18524i	−0.358454	−	0.295812i
$591$	6.94893	+	8.46729i	0.285841	+	0.348298i
$592$	5.91574	−	17.2737i	0.243135	−	0.709944i
$593$	5.32968	+	4.37396i	0.218864	+	0.179617i	0.737436	−	0.675417i	$-0.236036\pi$
$593$	5.32968	+	4.37396i	0.218864	+	0.179617i	−0.518572	+	0.855034i	$0.673536\pi$
$594$	10.7088	+	7.19761i	0.439387	+	0.295322i
$595$	8.66876	−	1.06919i	0.355384	−	0.0438325i
$596$	1.15926	+	0.389978i	0.0474852	+	0.0159741i
$597$	−8.02402	−	46.2436i	−0.328401	−	1.89262i
$598$	−3.89641	−	1.08970i	−0.159336	−	0.0445613i
$599$	4.45093	+	0.660233i	0.181860	+	0.0269764i	0.237039	−	0.971500i	$-0.423823\pi$
$599$	4.45093	+	0.660233i	0.181860	+	0.0269764i	−0.0551792	+	0.998476i	$0.517573\pi$
$600$	−38.9350	+	8.40991i	−1.58952	+	0.343333i
$601$	7.98583	−	31.8812i	0.325749	−	1.30046i	−0.556959	−	0.830540i	$-0.688032\pi$
$601$	7.98583	−	31.8812i	0.325749	−	1.30046i	0.882708	−	0.469923i	$-0.155718\pi$
$602$	7.93188	+	2.64430i	0.323279	+	0.107774i
$603$	12.4292	+	15.9265i	0.506156	+	0.648579i
$604$	−5.62066	−	39.3662i	−0.228701	−	1.60179i
$605$	9.52363	−	4.22154i	0.387191	−	0.171630i
$606$	72.5724	−	34.0829i	2.94805	−	1.38452i
$607$	−5.94892	−	29.9072i	−0.241459	−	1.21390i	−0.891154	−	0.453701i	$-0.850103\pi$
$607$	−5.94892	−	29.9072i	−0.241459	−	1.21390i	0.649695	−	0.760195i	$-0.274897\pi$
$608$	−27.1037	−	35.7217i	−1.09920	−	1.44871i
$609$	11.5026	−	57.8277i	0.466111	−	2.34330i
$610$	−3.30430	−	13.3455i	−0.133787	−	0.540342i
$611$	30.9427	+	29.4599i	1.25181	+	1.19182i
$612$	−41.9691	+	45.8024i	−1.69650	+	1.85145i
$613$	13.1546	−	3.64036i	0.531309	−	0.147033i	0.00927363	−	0.999957i	$-0.497048\pi$
$613$	13.1546	−	3.64036i	0.531309	−	0.147033i	0.522035	+	0.852924i	$0.325173\pi$
$614$	12.9186	+	16.6469i	0.521353	+	0.671814i
$615$	−2.18506	−	14.7305i	−0.0881101	−	0.593990i
$616$	−1.72604	−	2.77558i	−0.0695440	−	0.111831i
$617$	−32.1899	−	19.2939i	−1.29592	−	0.776742i	−0.311105	−	0.950376i	$-0.600699\pi$
$617$	−32.1899	−	19.2939i	−1.29592	−	0.776742i	−0.984810	+	0.173634i	$0.944449\pi$
$618$	21.0843	+	64.4111i	0.848136	+	2.59099i
$619$	−6.42295	+	4.06729i	−0.258160	+	0.163478i	−0.657797	−	0.753196i	$-0.728511\pi$
$619$	−6.42295	+	4.06729i	−0.258160	+	0.163478i	0.399636	+	0.916674i	$0.369136\pi$
$620$	−1.01645	−	0.724174i	−0.0408217	−	0.0290835i
$621$	−4.14153	+	14.9656i	−0.166194	+	0.600548i
$622$	−1.90699	−	0.795989i	−0.0764635	−	0.0319162i
$623$	30.5302	+	9.26124i	1.22317	+	0.371044i
$624$	17.2030	+	49.7806i	0.688670	+	1.99282i
$625$	3.46045	+	11.4076i	0.138418	+	0.456302i
$626$	−13.2575	−	16.2443i	−0.529878	−	0.649253i
$627$	12.0804	+	0.891107i	0.482446	+	0.0355874i
$628$	−2.44065	+	30.8015i	−0.0973926	+	1.22911i
$629$	−14.7467	+	5.68845i	−0.587991	+	0.226813i
$630$	−29.8244	−	11.5979i	−1.18823	−	0.462071i
$631$	12.1605	+	25.7112i	0.484101	+	1.02354i	0.987225	+	0.159331i	$0.0509337\pi$
$631$	12.1605	+	25.7112i	0.484101	+	1.02354i	−0.503125	+	0.864214i	$0.667816\pi$
$632$	−11.2814	+	1.57943i	−0.448749	+	0.0628264i
$633$	6.08816	+	6.71725i	0.241983	+	0.266987i
$634$	15.7538	+	25.0284i	0.625664	+	0.994005i
$635$	−3.96822	+	1.99744i	−0.157474	+	0.0792658i
$636$	25.8342	−	13.6284i	1.02439	−	0.540402i
$637$	0.482034	−	0.339487i	0.0190989	−	0.0134509i
$638$	−4.06315	−	0.210694i	−0.160862	−	0.00834144i
$639$	70.7915	+	70.7915i	2.80047	+	2.80047i
$640$	9.59148	−	5.19474i	0.379137	−	0.205340i
$641$	−10.0446	+	10.0446i	−0.396736	+	0.396736i	−0.877080	−	0.480344i	$-0.840512\pi$
$641$	−10.0446	+	10.0446i	−0.396736	+	0.396736i	0.480344	+	0.877080i	$0.340512\pi$
$642$	23.1336	−	20.8527i	0.913012	−	0.822992i
$643$	5.79303	+	8.22548i	0.228455	+	0.324381i	0.915563	−	0.402174i	$-0.131745\pi$
$643$	5.79303	+	8.22548i	0.228455	+	0.324381i	−0.687108	+	0.726555i	$0.741120\pi$
$644$	2.51189	−	3.02701i	0.0989824	−	0.119281i
$645$	−3.38909	−	6.73296i	−0.133445	−	0.265110i
$646$	−8.60782	+	37.8503i	−0.338670	+	1.48920i
$647$	3.07982	−	2.79139i	0.121080	−	0.109741i	−0.608773	−	0.793344i	$-0.708338\pi$
$647$	3.07982	−	2.79139i	0.121080	−	0.109741i	0.729854	+	0.683603i	$0.239588\pi$
$648$	119.002	−	41.4869i	4.67483	−	1.62976i
$649$	3.30577	−	1.56351i	0.129763	−	0.0613733i
$650$	20.0525	−	8.82346i	0.786524	−	0.346085i
$651$	2.10855	+	5.46620i	0.0826404	+	0.214237i
$652$	−6.55422	−	3.34394i	−0.256683	−	0.130959i
$653$	1.03429	−	14.0216i	0.0404750	−	0.548707i	−0.938573	−	0.345080i	$-0.887852\pi$
$653$	1.03429	−	14.0216i	0.0404750	−	0.548707i	0.979048	−	0.203627i	$-0.0652731\pi$
$654$	5.04741	−	49.8561i	0.197369	−	1.94953i
$655$	3.67706	−	1.11543i	0.143675	−	0.0435833i
$656$	−7.45879	−	16.2249i	−0.291217	−	0.633474i
$657$	5.24509	−	17.2907i	0.204630	−	0.674576i
$658$	−38.4180	+	15.7909i	−1.49769	+	0.615595i
$659$	−25.1191	−	6.95138i	−0.978499	−	0.270787i	−0.259458	−	0.965754i	$-0.583544\pi$
$659$	−25.1191	−	6.95138i	−0.978499	−	0.270787i	−0.719042	+	0.694967i	$0.755419\pi$
$660$	−0.661257	+	2.87153i	−0.0257394	+	0.111774i
$661$	11.7234	+	18.5133i	0.455988	+	0.720084i	0.992289	−	0.123942i	$-0.0395538\pi$
$661$	11.7234	+	18.5133i	0.455988	+	0.720084i	−0.536301	+	0.844027i	$0.680179\pi$
$662$	−18.7875	+	37.0729i	−0.730198	+	1.44088i
$663$	23.4400	−	39.1073i	0.910335	−	1.51880i
$664$	5.55206	−	12.2543i	0.215462	−	0.475558i
$665$	−19.7784	+	2.93385i	−0.766975	+	0.113770i
$666$	57.4524	+	7.24484i	2.22624	+	0.280732i
$667$	−1.30593	−	4.71904i	−0.0505660	−	0.182722i
$668$	25.1515	−	11.7287i	0.973139	−	0.453797i
$669$	12.5864	−	13.2199i	0.486619	−	0.511112i
$670$	−1.58584	+	2.62956i	−0.0612662	+	0.101589i
$671$	4.36808	+	0.868865i	0.168628	+	0.0335422i
$672$	−51.0110	−	4.46131i	−1.96779	−	0.172099i
$673$	14.1874	−	2.82206i	0.546886	−	0.108782i	0.0860880	−	0.996288i	$-0.472563\pi$
$673$	14.1874	−	2.82206i	0.546886	−	0.108782i	0.460798	+	0.887505i	$0.347563\pi$
$674$	−9.08253	+	25.1679i	−0.349846	+	0.969430i
$675$	−34.0733	−	76.8682i	−1.31148	−	2.95866i
$676$	−1.51191	−	2.55388i	−0.0581503	−	0.0982261i
$677$	6.68912	−	5.22024i	0.257084	−	0.200630i	−0.478456	−	0.878111i	$-0.658803\pi$
$677$	6.68912	−	5.22024i	0.257084	−	0.200630i	0.735540	+	0.677481i	$0.236928\pi$
$678$	33.5007	+	67.0078i	1.28659	+	2.57342i
$679$	−10.9068	−	2.73201i	−0.418564	−	0.104845i
$680$	−8.78183	−	3.47014i	−0.336768	−	0.133074i
$681$	7.17708	−	48.3840i	0.275026	−	1.85408i
$682$	0.352307	−	0.198315i	0.0134905	−	0.00759388i
$683$	−8.06399	+	1.39924i	−0.308560	+	0.0535403i	−0.323133	−	0.946354i	$-0.604736\pi$
$683$	−8.06399	+	1.39924i	−0.308560	+	0.0535403i	0.0145729	+	0.999894i	$0.495361\pi$
$684$	93.4735	−	107.177i	3.57405	−	4.09801i
$685$	−0.709780	−	5.75474i	−0.0271193	−	0.219877i
$686$	5.09403	+	25.9786i	0.194491	+	0.991869i
$687$	−44.5201	+	54.2479i	−1.69855	+	2.06969i
$688$	−6.16108	−	6.61385i	−0.234889	−	0.252151i
$689$	−12.4181	+	10.1912i	−0.473090	+	0.388255i
$690$	−3.53006	+	0.337985i	−0.134387	+	0.0128669i
$691$	−1.62166	−	0.816274i	−0.0616908	−	0.0310525i	0.418498	−	0.908218i	$-0.362557\pi$
$691$	−1.62166	−	0.816274i	−0.0616908	−	0.0310525i	−0.480189	+	0.877165i	$0.659432\pi$
$692$	4.98135	+	4.79459i	0.189363	+	0.182263i
$693$	7.50760	−	7.14783i	0.285190	−	0.271524i
$694$	−12.0547	+	18.9224i	−0.457592	+	0.718285i
$695$	1.45885	−	0.0716688i	0.0553374	−	0.00271855i
$696$	−40.8376	+	48.9406i	−1.54794	+	1.85509i
$697$	−6.60931	+	13.9742i	−0.250345	+	0.529311i
$698$	4.28099	+	4.52103i	0.162038	+	0.171124i
$699$	75.7218	−	5.58558i	2.86406	−	0.211266i
$700$	−0.115907	+	21.2988i	−0.00438087	+	0.805020i
$701$	22.6933	−	35.8366i	0.857114	−	1.35353i	−0.0771765	−	0.997017i	$-0.524591\pi$
$701$	22.6933	−	35.8366i	0.857114	−	1.35353i	0.934290	−	0.356513i	$-0.116034\pi$
$702$	−95.5151	+	56.8969i	−3.60499	+	2.14743i
$703$	33.4284	−	13.8465i	1.26078	−	0.522231i
$704$	0.202377	+	3.52768i	0.00762737	+	0.132955i
$705$	34.5966	+	14.3304i	1.30298	+	0.539713i
$706$	−39.2464	+	5.71256i	−1.47706	+	0.214995i
$707$	−9.39326	−	41.8301i	−0.353270	−	1.57318i
$708$	11.4824	−	56.1278i	0.431535	−	2.10941i
$709$	−34.2129	−	29.5123i	−1.28489	−	1.10836i	−0.988165	−	0.153394i	$-0.950980\pi$
$709$	−34.2129	−	29.5123i	−1.28489	−	1.10836i	−0.296728	−	0.954962i	$-0.595895\pi$
$710$	−6.20446	+	13.8949i	−0.232849	+	0.521465i
$711$	−12.1712	−	34.0161i	−0.456454	−	1.27570i
$712$	−24.1886	−	24.5868i	−0.906508	−	0.921429i
$713$	0.360506	+	0.326743i	0.0135010	+	0.0122366i
$714$	25.4252	+	36.3105i	0.951514	+	1.35889i
$715$	0.0397730	−	1.62017i	0.00148742	−	0.0605910i
$716$	−23.8712	+	5.22416i	−0.892108	+	0.195236i
$717$	−14.6003	−	44.1956i	−0.545256	−	1.65051i
$718$	−30.2796	+	16.0790i	−1.13003	+	0.600064i
$719$	−3.22501	+	32.7441i	−0.120273	+	1.22115i	0.725733	+	0.687976i	$0.241501\pi$
$719$	−3.22501	+	32.7441i	−0.120273	+	1.22115i	−0.846006	+	0.533173i	$0.820999\pi$
$720$	22.3098	+	26.4397i	0.831436	+	0.985348i
$721$	36.0652	−	3.55211i	1.34314	−	0.132287i
$722$	12.2588	−	60.7648i	0.456227	−	2.26143i
$723$	−8.49121	−	6.62661i	−0.315792	−	0.246446i
$724$	2.28897	−	17.7623i	0.0850690	−	0.660132i
$725$	21.6767	+	15.2665i	0.805054	+	0.566983i
$726$	41.5894	+	32.6392i	1.54353	+	1.21135i
$727$	−16.6770	−	22.4863i	−0.618515	−	0.833970i	0.377231	−	0.926119i	$-0.376876\pi$
$727$	−16.6770	−	22.4863i	−0.618515	−	0.833970i	−0.995745	+	0.0921490i	$0.970626\pi$
$728$	27.9783	−	3.21917i	1.03695	−	0.119310i
$729$	95.2577	+	158.928i	3.52806	+	5.88621i
$730$	2.73952	−	0.194586i	0.101394	−	0.00720195i
$731$	−0.957824	+	7.76583i	−0.0354264	+	0.287230i
$732$	51.9526	−	46.5747i	1.92023	−	1.72145i
$733$	−6.40796	+	16.6120i	−0.236683	+	0.613579i	−0.999452	−	0.0330924i	$-0.989464\pi$
$733$	−6.40796	+	16.6120i	−0.236683	+	0.613579i	0.762769	+	0.646671i	$0.223839\pi$
$734$	−2.10055	−	45.2707i	−0.0775326	−	1.67097i
$735$	0.287098	−	0.429673i	0.0105898	−	0.0158487i
$736$	−3.95048	+	1.57373i	−0.145617	+	0.0580083i
$737$	−0.552643	−	0.827089i	−0.0203569	−	0.0304662i
$738$	45.5808	−	33.6132i	1.67785	−	1.23732i
$739$	−1.26223	−	51.4177i	−0.0464321	−	1.89143i	−0.347282	−	0.937761i	$-0.612895\pi$
$739$	−1.26223	−	51.4177i	−0.0464321	−	1.89143i	0.300850	−	0.953672i	$-0.402730\pi$
$740$	2.09217	+	8.54956i	0.0769099	+	0.314288i
$741$	−51.4456	+	90.8142i	−1.88990	+	3.33614i
$742$	−4.12459	−	15.0637i	−0.151418	−	0.553005i
$743$	−31.1340	+	41.9793i	−1.14219	+	1.54007i	−0.342649	+	0.939463i	$0.611324\pi$
$743$	−31.1340	+	41.9793i	−1.14219	+	1.54007i	−0.799545	+	0.600607i	$0.794926\pi$
$744$	0.826608	−	6.27961i	0.0303049	−	0.230222i
$745$	−0.571943	+	0.143264i	−0.0209544	+	0.00524880i
$746$	−32.9984	−	38.4655i	−1.20816	−	1.40832i
$747$	41.6308	+	9.34850i	1.52319	+	0.342044i
$748$	2.22679	−	2.09709i	0.0814193	−	0.0766773i
$749$	−8.20849	−	14.4900i	−0.299932	−	0.529454i
$750$	30.3387	−	30.1741i	1.10781	−	1.10180i
$751$	−2.82192	−	5.27944i	−0.102973	−	0.192650i	0.825158	−	0.564901i	$-0.191086\pi$
$751$	−2.82192	−	5.27944i	−0.102973	−	0.192650i	−0.928132	+	0.372252i	$0.878586\pi$
$752$	44.6375	+	4.88750i	1.62776	+	0.178229i
$753$	58.0253	+	31.0152i	2.11456	+	1.13026i
$754$	16.6099	−	30.8725i	0.604896	−	1.12431i
$755$	12.5210	+	14.5153i	0.455686	+	0.528267i
$756$	−12.6471	−	107.346i	−0.459972	−	3.90412i
$757$	−19.9516	+	45.0102i	−0.725155	+	1.63592i	0.0457341	+	0.998954i	$0.485437\pi$
$757$	−19.9516	+	45.0102i	−0.725155	+	1.63592i	−0.770889	+	0.636970i	$0.780188\pi$
$758$	−12.1918	−	11.6710i	−0.442827	−	0.423909i
$759$	0.387003	−	1.08160i	0.0140473	−	0.0392597i
$760$	20.2922	+	7.44807i	0.736076	+	0.270170i
$761$	−54.9799	−	2.70099i	−1.99302	−	0.0979107i	−0.993191	−	0.116494i	$-0.962834\pi$
$761$	−54.9799	−	2.70099i	−1.99302	−	0.0979107i	−0.999827	+	0.0185836i	$0.994084\pi$
$762$	−18.3979	−	13.0323i	−0.666485	−	0.472110i
$763$	−25.4425	−	8.40508i	−0.921082	−	0.304284i
$764$	1.77168	−	3.27163i	0.0640971	−	0.118363i
$765$	5.11985	−	29.5064i	0.185109	−	1.06681i
$766$	−6.80667	+	14.2908i	−0.245935	+	0.516346i
$767$			31.5094i			1.13774i
$768$	46.1131	+	30.6269i	1.66396	+	1.10515i
$769$		−	25.5421i		−	0.921072i	−0.887641	−	0.460536i	$-0.847657\pi$
$769$		−	25.5421i		−	0.921072i	0.887641	−	0.460536i	$-0.152343\pi$
$770$	1.42251	+	0.677540i	0.0512637	+	0.0244168i
$771$	4.64382	−	26.7630i	0.167243	−	0.963847i
$772$	−18.2654	+	5.43238i	−0.657386	+	0.195516i
$773$	32.0309	+	10.5816i	1.15207	+	0.380592i	0.825401	−	0.564547i	$-0.190949\pi$
$773$	32.0309	+	10.5816i	1.15207	+	0.380592i	0.326668	+	0.945139i	$0.394074\pi$
$774$	16.5704	−	23.3927i	0.595612	−	0.840835i
$775$	−2.63138	−	0.129271i	−0.0945218	−	0.00464356i
$776$	8.93957	+	8.23627i	0.320912	+	0.295665i
$777$	13.9200	−	38.9038i	0.499377	−	1.39566i
$778$	20.2467	−	21.1502i	0.725879	−	0.758272i
$779$	14.3404	−	32.3514i	0.513797	−	1.15911i
$780$	−19.9308	−	15.7294i	−0.713638	−	0.563204i
$781$	−3.21977	−	3.73261i	−0.115213	−	0.133563i
$782$	3.24176	+	1.74411i	0.115925	+	0.0623694i
$783$	−118.660	−	63.4253i	−4.24058	−	2.26664i
$784$	0.186324	−	0.590996i	0.00665444	−	0.0211070i
$785$	−7.02138	−	13.1361i	−0.250604	−	0.468847i
$786$	13.7515	+	13.8265i	0.490500	+	0.493177i
$787$	18.4388	+	32.5491i	0.657273	+	1.16025i	0.977102	+	0.212773i	$0.0682496\pi$
$787$	18.4388	+	32.5491i	0.657273	+	1.16025i	−0.319829	+	0.947475i	$0.603625\pi$
$788$	−6.32907	−	0.189838i	−0.225464	−	0.00676268i
$789$	−25.0216	−	5.61879i	−0.890792	−	0.200034i
$790$	4.16788	−	3.57550i	0.148286	−	0.127211i
$791$	38.8577	−	9.73336i	1.38162	−	0.346078i
$792$	−10.8246	+	2.90066i	−0.384635	+	0.103070i
$793$	−22.8599	+	30.8230i	−0.811778	+	1.09456i
$794$	22.9712	−	6.28976i	0.815219	−	0.223215i
$795$	−6.94020	+	12.2512i	−0.246144	+	0.434504i
$796$	23.1949	+	14.0746i	0.822122	+	0.498862i
$797$	0.0801289	+	3.26409i	0.00283831	+	0.115620i	0.999445	+	0.0333098i	$0.0106048\pi$
$797$	0.0801289	+	3.26409i	0.00283831	+	0.115620i	−0.996607	+	0.0823102i	$0.973770\pi$
$798$	−60.2256	−	81.6684i	−2.13196	−	2.89103i
$799$	−21.5962	−	32.3210i	−0.764019	−	1.14344i
$800$	11.1296	−	20.1575i	0.393492	−	0.712677i
$801$	60.7724	−	90.9524i	2.14729	−	3.21364i
$802$	9.93340	−	0.460907i	0.350760	−	0.0162752i
$803$	−0.320188	+	0.830057i	−0.0112992	+	0.0292921i
$804$	−15.5608	−	0.849359i	−0.548786	−	0.0299546i
$805$	−0.232115	+	1.88194i	−0.00818098	+	0.0663296i
$806$	0.246812	+	3.47479i	0.00869357	+	0.122394i
$807$	45.8064	+	76.4234i	1.61246	+	2.69023i
$808$	−12.7257	+	44.5663i	−0.447689	+	1.56784i
$809$	−11.8337	−	15.9559i	−0.416050	−	0.560979i	0.544615	−	0.838686i	$-0.316676\pi$
$809$	−11.8337	−	15.9559i	−0.416050	−	0.560979i	−0.960666	+	0.277707i	$0.910426\pi$
$810$	−37.5072	+	47.7923i	−1.31787	+	1.67925i
$811$	13.0487	+	9.18997i	0.458204	+	0.322703i	0.781841	−	0.623478i	$-0.214281\pi$
$811$	13.0487	+	9.18997i	0.458204	+	0.322703i	−0.323637	+	0.946181i	$0.604906\pi$
$812$	20.8224	+	26.9829i	0.730723	+	0.946914i
$813$	−66.3628	−	51.7900i	−2.32745	−	1.81636i
$814$	−2.79494	−	0.563858i	−0.0979626	−	0.0197632i
$815$	3.52994	−	0.347669i	0.123648	−	0.0121783i
$816$	−5.34805	−	47.6215i	−0.187219	−	1.66709i
$817$	1.75570	−	17.8260i	0.0614243	−	0.623652i
$818$	19.1389	+	36.0419i	0.669175	+	1.26017i
$819$	28.0178	+	84.8110i	0.979020	+	2.96354i
$820$	7.24761	+	4.64494i	0.253097	+	0.162208i
$821$	−0.686832	+	27.9784i	−0.0239706	+	0.976454i	0.860386	+	0.509643i	$0.170222\pi$
$821$	−0.686832	+	27.9784i	−0.0239706	+	0.976454i	−0.884357	+	0.466812i	$0.845403\pi$
$822$	24.1047	−	16.8785i	0.840747	−	0.588705i
$823$	−35.8557	−	32.4978i	−1.24985	−	1.13280i	−0.985734	−	0.168310i	$-0.946169\pi$
$823$	−35.8557	−	32.4978i	−1.24985	−	1.13280i	−0.264119	−	0.964490i	$-0.585081\pi$
$824$	−36.0720	−	15.2876i	−1.25663	−	0.532570i
$825$	2.09555	+	5.85667i	0.0729577	+	0.203903i
$826$	−27.9718	−	12.4902i	−0.973265	−	0.434591i
$827$	−23.7763	−	20.5096i	−0.826784	−	0.713189i	0.133851	−	0.991001i	$-0.457266\pi$
$827$	−23.7763	−	20.5096i	−0.826784	−	0.713189i	−0.960635	+	0.277813i	$0.910391\pi$
$828$	−7.43160	−	11.2543i	−0.258266	−	0.391113i
$829$	5.74452	+	25.5815i	0.199515	+	0.888483i	0.968460	+	0.249168i	$0.0801570\pi$
$829$	5.74452	+	25.5815i	0.199515	+	0.888483i	−0.768945	+	0.639315i	$0.779218\pi$
$830$	0.934145	+	6.41775i	0.0324246	+	0.222764i
$831$	−18.4654	−	7.64862i	−0.640558	−	0.265328i
$832$	−28.2234	−	11.4197i	−0.978471	−	0.395907i
$833$	−0.495596	+	0.205282i	−0.0171714	+	0.00711262i
$834$	3.79351	+	6.36832i	0.131358	+	0.220517i
$835$	−7.15727	+	11.3026i	−0.247687	+	0.391141i
$836$	−4.97820	+	4.92431i	−0.172175	+	0.170311i
$837$	13.3335	−	0.983536i	0.460872	−	0.0339960i
$838$	25.1878	−	23.8504i	0.870098	−	0.823900i
$839$	4.08446	−	8.63587i	0.141011	−	0.298143i	−0.821108	−	0.570773i	$-0.806643\pi$
$839$	4.08446	−	8.63587i	0.141011	−	0.298143i	0.962119	+	0.272630i	$0.0878935\pi$
$840$	21.8640	−	11.4581i	0.754381	−	0.395342i
$841$	13.4102	−	0.658803i	0.462422	−	0.0227173i
$842$	30.0656	+	19.1537i	1.03613	+	0.660079i
$843$	21.2277	−	20.2105i	0.731122	−	0.696086i
$844$	−5.23960	+	0.100098i	−0.180355	+	0.00344552i
$845$	1.27793	+	0.643258i	0.0439623	+	0.0221287i
$846$	13.5734	+	141.766i	0.466663	+	4.87403i
$847$	21.8522	−	17.9337i	0.750852	−	0.616208i
$848$	−3.87847	+	16.4329i	−0.133187	+	0.564308i
$849$	−52.5436	+	64.0246i	−1.80329	+	2.19732i
$850$	−19.5603	+	3.83549i	−0.670913	+	0.131556i
$851$	−0.420035	−	3.40556i	−0.0143986	−	0.116741i
$852$	−77.0474	+	5.26196i	−2.63960	+	0.180272i
$853$	27.7238	−	4.81053i	0.949244	−	0.164709i	0.324803	−	0.945782i	$-0.394702\pi$
$853$	27.7238	−	4.81053i	0.949244	−	0.164709i	0.624441	+	0.781072i	$0.285327\pi$
$854$	−18.3009	−	32.5115i	−0.626244	−	1.11252i
$855$	−10.0591	+	67.8133i	−0.344016	+	2.31916i
$856$	0.294903	+	18.0013i	0.0100796	+	0.615271i
$857$	23.2071	+	5.81309i	0.792741	+	0.198571i	0.618140	−	0.786068i	$-0.287887\pi$
$857$	23.2071	+	5.81309i	0.792741	+	0.198571i	0.174601	+	0.984639i	$0.444137\pi$
$858$	7.35663	−	3.67796i	0.251151	−	0.125564i
$859$	−8.92762	+	6.96718i	−0.304606	+	0.237717i	−0.755944	−	0.654636i	$-0.772822\pi$
$859$	−8.92762	+	6.96718i	−0.304606	+	0.237717i	0.451338	+	0.892353i	$0.350947\pi$
$860$	4.22093	+	1.08173i	0.143933	+	0.0368868i
$861$	−16.3761	−	36.9439i	−0.558096	−	1.25905i
$862$	−22.2436	−	8.02723i	−0.757620	−	0.273408i
$863$	7.81156	−	1.55382i	0.265908	−	0.0528925i	−0.0603353	−	0.998178i	$-0.519217\pi$
$863$	7.81156	−	1.55382i	0.265908	−	0.0528925i	0.326244	+	0.945286i	$0.394217\pi$
$864$	−43.5334	+	108.439i	−1.48104	+	3.68917i
$865$	−3.26891	−	0.650226i	−0.111146	−	0.0221083i
$866$	−33.8034	−	20.3862i	−1.14869	−	0.692751i
$867$	11.9522	−	12.5538i	0.405918	−	0.426349i
$868$	−3.18252	−	1.15830i	−0.108022	−	0.0393151i
$869$	0.474449	+	1.71444i	0.0160946	+	0.0581583i
$870$	3.84430	−	30.4858i	0.130334	−	1.03356i
$871$	8.47832	−	1.25764i	0.287277	−	0.0426135i
$872$	19.8022	+	21.1418i	0.670588	+	0.715953i
$873$	−19.8191	+	33.0662i	−0.670775	+	1.11912i
$874$	−7.51677	−	3.80930i	−0.254259	−	0.128851i
$875$	−12.2407	−	19.3301i	−0.413811	−	0.653478i
$876$	7.39261	+	11.8160i	0.249773	+	0.399225i
$877$	7.56885	+	2.09458i	0.255582	+	0.0707291i	0.392149	−	0.919902i	$-0.371732\pi$
$877$	7.56885	+	2.09458i	0.255582	+	0.0707291i	−0.136567	+	0.990631i	$0.543607\pi$
$878$	13.7751	+	33.5136i	0.464886	+	1.13103i
$879$	−0.276390	+	0.911135i	−0.00932240	+	0.0307318i
$880$	−0.999745	−	1.37912i	−0.0337014	−	0.0464902i
$881$	18.0020	−	5.46086i	0.606504	−	0.183981i	0.0279285	−	0.999610i	$-0.491109\pi$
$881$	18.0020	−	5.46086i	0.606504	−	0.183981i	0.578575	+	0.815629i	$0.303609\pi$
$882$	1.95530	+	0.197954i	0.0658385	+	0.00666546i
$883$	0.781725	−	10.5976i	0.0263071	−	0.356637i	−0.968065	−	0.250698i	$-0.919340\pi$
$883$	0.781725	−	10.5976i	0.0263071	−	0.356637i	0.994373	−	0.105940i	$-0.0337850\pi$
$884$	8.13117	+	25.0706i	0.273481	+	0.843216i
$885$	9.93945	+	25.7671i	0.334111	+	0.866150i
$886$	−8.57705	−	19.4925i	−0.288152	−	0.654863i
$887$	14.6895	−	6.94763i	0.493226	−	0.233279i	−0.164725	−	0.986340i	$-0.552674\pi$
$887$	14.6895	−	6.94763i	0.493226	−	0.233279i	0.657951	+	0.753061i	$0.271424\pi$
$888$	−33.3413	+	29.7267i	−1.11886	+	0.997564i
$889$	−8.93262	+	8.09606i	−0.299591	+	0.271533i
$890$	16.2127	+	3.68706i	0.543452	+	0.123590i
$891$	−8.84842	−	17.5788i	−0.296433	−	0.588912i
$892$	0.977077	+	10.5062i	0.0327150	+	0.351775i
$893$	51.2388	+	72.7536i	1.71464	+	2.43461i
$894$	−2.00345	−	2.22259i	−0.0670053	−	0.0743344i
$895$	8.32958	−	8.32958i	0.278427	−	0.278427i
$896$	21.3253	−	20.5281i	0.712429	−	0.685794i
$897$	6.99909	+	6.99909i	0.233693	+	0.233693i
$898$	−0.144479	+	2.78622i	−0.00482132	+	0.0929775i
$899$	−3.44679	+	2.42750i	−0.114957	+	0.0809617i
$900$	69.7663	+	21.5787i	2.32554	+	0.719289i
$901$	13.0556	−	6.57163i	0.434944	−	0.218933i
$902$	−2.35998	+	1.48546i	−0.0785789	+	0.0494605i
$903$	−13.7367	−	15.1562i	−0.457130	−	0.504366i
$904$	−41.9208	−	10.8650i	−1.39427	−	0.361366i
$905$	3.69125	+	7.80450i	0.122701	+	0.259430i
$906$	−35.2591	+	90.6704i	−1.17141	+	3.01232i
$907$	−23.8981	+	9.21852i	−0.793524	+	0.306096i	−0.722493	−	0.691378i	$-0.757004\pi$
$907$	−23.8981	+	9.21852i	−0.793524	+	0.306096i	−0.0710307	+	0.997474i	$0.522629\pi$
$908$	18.3517	+	21.5103i	0.609023	+	0.713844i
$909$	−146.594	−	10.8134i	−4.86221	−	0.358658i
$910$	−10.5181	+	8.58416i	−0.348670	+	0.284562i
$911$	13.1653	+	43.4001i	0.436185	+	1.43791i	0.849630	+	0.527380i	$0.176826\pi$
$911$	13.1653	+	43.4001i	0.436185	+	1.43791i	−0.413445	+	0.910529i	$0.635674\pi$
$912$	14.9144	+	108.682i	0.493866	+	3.59881i
$913$	−2.01040	−	0.609849i	−0.0665347	−	0.0201831i
$914$	−2.87308	+	6.88320i	−0.0950332	+	0.227676i
$915$	−8.97092	+	32.4167i	−0.296569	+	1.07166i
$916$	−6.71780	−	40.0069i	−0.221962	−	1.32187i
$917$	8.80951	−	5.57856i	0.290916	−	0.184220i
$918$	96.1347	−	31.4687i	3.17292	−	1.03862i
$919$	−9.12911	−	5.47178i	−0.301142	−	0.180497i	0.355549	−	0.934658i	$-0.384294\pi$
$919$	−9.12911	−	5.47178i	−0.301142	−	0.180497i	−0.656690	+	0.754161i	$0.728044\pi$
$920$	1.19401	−	1.66630i	0.0393653	−	0.0549364i
$921$	−7.56408	−	50.9929i	−0.249245	−	1.68027i
$922$	−14.1357	+	10.9698i	−0.465533	+	0.361272i
$923$	40.9358	−	11.3285i	1.34742	−	0.372881i
$924$	0.348890	+	7.98865i	0.0114776	+	0.262807i
$925$	13.4566	+	12.8118i	0.442452	+	0.421249i
$926$	3.56696	−	0.883168i	0.117217	−	0.0290227i
$927$	24.2405	−	121.865i	0.796164	−	4.00259i
$928$	−5.80483	−	36.3861i	−0.190553	−	1.19443i
$929$	−1.58537	−	7.97018i	−0.0520142	−	0.261493i	0.946024	−	0.324096i	$-0.105060\pi$
$929$	−1.58537	−	7.97018i	−0.0520142	−	0.261493i	−0.998039	+	0.0626025i	$0.980060\pi$
$930$	1.29793	+	2.76368i	0.0425610	+	0.0906248i
$931$	1.12264	−	0.497633i	0.0367931	−	0.0163093i
$932$	−26.3373	+	35.1107i	−0.862706	+	1.15009i
$933$	3.11031	+	3.98549i	0.101827	+	0.130479i
$934$	9.27520	−	27.8220i	0.303494	−	0.910364i
$935$	−0.358286	+	1.43036i	−0.0117172	+	0.0467777i
$936$	17.2842	−	95.0011i	0.564953	−	3.10521i
$937$	14.5957	+	2.16507i	0.476822	+	0.0707298i	0.380816	−	0.924651i	$-0.375643\pi$
$937$	14.5957	+	2.16507i	0.476822	+	0.0707298i	0.0960059	+	0.995381i	$0.469393\pi$
$938$	−2.24434	+	8.02499i	−0.0732803	+	0.262025i
$939$	8.76975	+	50.5413i	0.286190	+	1.64935i
$940$	−19.3881	+	9.62727i	−0.632370	+	0.314007i
$941$	13.7952	−	1.70148i	0.449711	−	0.0554666i	0.105628	−	0.994406i	$-0.466315\pi$
$941$	13.7952	−	1.70148i	0.449711	−	0.0554666i	0.344083	+	0.938939i	$0.388190\pi$
$942$	42.1669	−	62.7371i	1.37387	−	2.04408i
$943$	−2.59417	−	2.12898i	−0.0844777	−	0.0693291i
$944$	20.0895	+	26.3282i	0.653859	+	0.856910i
$945$	33.0553	+	40.2780i	1.07529	+	1.31024i
$946$	−0.898418	+	1.08867i	−0.0292101	+	0.0353958i
$947$	13.2332	−	26.2898i	0.430021	−	0.854305i	−0.569458	−	0.822020i	$-0.692847\pi$
$947$	13.2332	−	26.2898i	0.430021	−	0.854305i	0.999479	−	0.0322841i	$-0.0102781\pi$
$948$	25.9463	+	10.1712i	0.842698	+	0.330344i
$949$	−5.28591	−	5.55196i	−0.171588	−	0.180224i
$950$	44.5484	−	9.87643i	1.44534	−	0.320434i
$951$	−3.55010	−	72.2640i	−0.115120	−	2.34332i
$952$	−25.4791	−	2.71965i	−0.825784	−	0.0881443i
$953$	16.5383	+	7.82205i	0.535729	+	0.253381i	0.676218	−	0.736701i	$-0.263618\pi$
$953$	16.5383	+	7.82205i	0.535729	+	0.253381i	−0.140489	+	0.990082i	$0.544868\pi$
$954$	−53.5292	−	1.45982i	−1.73307	−	0.0472633i
$955$	0.131941	+	1.78868i	0.00426951	+	0.0578803i
$956$	24.8014	+	10.4315i	0.802134	+	0.337380i
$957$	8.40944	+	5.32522i	0.271839	+	0.172140i
$958$	−30.8037	−	7.80506i	−0.995222	−	0.252170i
$959$	−6.02141	−	14.5370i	−0.194441	−	0.469423i
$960$	−26.6822	−	0.435643i	−0.861165	−	0.0140603i
$961$	−11.7029	+	28.2532i	−0.377512	+	0.911395i
$962$	14.6886	−	19.6931i	0.473581	−	0.634931i
$963$	−55.7117	+	12.5105i	−1.79528	+	0.403144i
$964$	6.11316	−	1.18144i	0.196892	−	0.0380515i
$965$	6.00023	−	6.95593i	0.193154	−	0.223919i
$966$	−8.98773	+	3.43889i	−0.289176	+	0.110644i
$967$	−37.9378	+	13.5744i	−1.22000	+	0.436522i	−0.866624	−	0.498961i	$-0.833715\pi$
$967$	−37.9378	+	13.5744i	−1.22000	+	0.436522i	−0.353372	+	0.935483i	$0.614965\pi$
$968$	−30.0214	+	5.71727i	−0.964923	+	0.183760i
$969$	63.7738	−	70.3636i	2.04871	−	2.26040i
$970$	−5.77064	−	1.01748i	−0.185284	−	0.0326694i
$971$	−36.7066	−	0.901096i	−1.17797	−	0.0289175i	−0.569155	−	0.822230i	$-0.692730\pi$
$971$	−36.7066	−	0.901096i	−1.17797	−	0.0289175i	−0.608815	+	0.793312i	$0.708355\pi$
$972$	−181.490	−	32.5099i	−5.82131	−	1.04276i
$973$	3.76354	−	1.24331i	0.120654	−	0.0398585i
$974$	−38.2259	−	11.7094i	−1.22484	−	0.375192i
$975$	−53.3389	−	5.25342i	−1.70821	−	0.168244i
$976$	0.550932	+	40.3295i	0.0176349	+	1.29092i
$977$	−4.24047	−	43.0542i	−0.135665	−	1.37743i	−0.786211	−	0.617959i	$-0.787960\pi$
$977$	−4.24047	−	43.0542i	−0.135665	−	1.37743i	0.650546	−	0.759467i	$-0.274540\pi$
$978$	9.96008	+	14.9945i	0.318488	+	0.479470i
$979$	−3.31366	+	4.24606i	−0.105905	+	0.135705i
$980$	0.0781050	+	0.288330i	0.00249497	+	0.00921037i
$981$	−52.8997	+	75.1118i	−1.68896	+	2.39813i
$982$	2.70723	+	22.4523i	0.0863912	+	0.716483i
$983$	37.5675	−	27.8619i	1.19822	−	0.888658i	0.202335	−	0.979316i	$-0.435147\pi$
$983$	37.5675	−	27.8619i	1.19822	−	0.888658i	0.995882	+	0.0906583i	$0.0288971\pi$
$984$	−3.56935	+	43.5410i	−0.113787	+	1.38804i
$985$	2.61812	−	1.56924i	0.0834204	−	0.0500002i
$986$	−20.8996	+	24.0956i	−0.665579	+	0.767359i
$987$	100.854	+	12.4392i	3.21022	+	0.395943i
$988$	−20.0167	−	56.9175i	−0.636816	−	1.81079i
$989$	−1.58487	−	0.611352i	−0.0503959	−	0.0194399i
$990$	3.63881	−	3.99292i	0.115649	−	0.126903i
$991$	−19.7918	−	13.2245i	−0.628708	−	0.420089i	0.199980	−	0.979800i	$-0.435912\pi$
$991$	−19.7918	−	13.2245i	−0.628708	−	0.420089i	−0.828688	+	0.559711i	$0.810912\pi$
$992$	2.42166	+	2.74606i	0.0768878	+	0.0871876i
$993$	84.5431	−	56.4899i	2.68289	−	1.79265i
$994$	−6.17023	+	40.8306i	−0.195708	+	1.29507i
$995$	−13.0750	+	0.320974i	−0.414507	+	0.0101756i
$996$	−26.5424	+	19.4622i	−0.841028	+	0.616683i
$997$	20.3236	+	11.5132i	0.643654	+	0.364625i	0.779769	−	0.626068i	$-0.215337\pi$
$997$	20.3236	+	11.5132i	0.643654	+	0.364625i	−0.136115	+	0.990693i	$0.543462\pi$
$998$	−10.8583	+	19.0465i	−0.343712	+	0.602906i
$999$	−75.7344	−	56.1684i	−2.39613	−	1.77709i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.o.a.149.56	✓	4032
512.189	even	128	inner	512.2.o.a.189.56	yes	4032

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
512.2.o.a.149.56	✓	4032	1.1	even	1	trivial
512.2.o.a.189.56	yes	4032	512.189	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)

\(f(q)\)	\(=\)	\(q+(1.33284 - 0.472809i) q^{2} +(-3.40889 - 0.591499i) q^{3} +(1.55290 - 1.26035i) q^{4} +(-0.302430 + 0.915468i) q^{5} +(-4.82316 + 0.823385i) q^{6} +(-0.128376 + 2.61316i) q^{7} +(1.47386 - 2.41407i) q^{8} +(8.44603 + 3.02204i) q^{9} +O(q^{10})\)	\(q+(1.33284 - 0.472809i) q^{2} +(-3.40889 - 0.591499i) q^{3} +(1.55290 - 1.26035i) q^{4} +(-0.302430 + 0.915468i) q^{5} +(-4.82316 + 0.823385i) q^{6} +(-0.128376 + 2.61316i) q^{7} +(1.47386 - 2.41407i) q^{8} +(8.44603 + 3.02204i) q^{9} +(0.0297526 + 1.36316i) q^{10} +(-0.403793 - 0.178989i) q^{11} +(-6.03917 + 3.37787i) q^{12} +(2.88177 - 2.48583i) q^{13} +(1.06442 + 3.54361i) q^{14} +(1.57245 - 2.94184i) q^{15} +(0.823013 - 3.91442i) q^{16} +(-3.05380 + 1.63229i) q^{17} +(12.6860 + 0.0345180i) q^{18} +(6.89694 - 3.90707i) q^{19} +(0.684170 + 1.80280i) q^{20} +(1.98330 - 8.83204i) q^{21} +(-0.622818 - 0.0476460i) q^{22} +(-0.182654 - 0.729197i) q^{23} +(-6.45214 + 7.35752i) q^{24} +(3.26942 + 2.42477i) q^{25} +(2.66560 - 4.67573i) q^{26} +(-17.9730 - 10.1816i) q^{27} +(3.09415 + 4.21978i) q^{28} +(6.51159 - 0.159851i) q^{29} +(0.704884 - 4.66446i) q^{30} +(-0.538158 + 0.359586i) q^{31} +(-0.753832 - 5.60640i) q^{32} +(1.27061 + 0.848998i) q^{33} +(-3.29845 + 3.61944i) q^{34} +(-2.35344 - 0.907822i) q^{35} +(16.9247 - 5.95206i) q^{36} +(4.53032 + 0.558762i) q^{37} +(7.34519 - 8.46841i) q^{38} +(-11.2940 + 6.76936i) q^{39} +(1.76427 + 2.07936i) q^{40} +(3.58576 - 2.65938i) q^{41} +(-1.53246 - 12.7094i) q^{42} +(1.30117 - 1.84752i) q^{43} +(-0.852641 + 0.230970i) q^{44} +(-5.32091 + 6.81812i) q^{45} +(-0.588220 - 0.885539i) q^{46} +(1.10035 + 11.1720i) q^{47} +(-5.12093 + 12.8570i) q^{48} +(0.154172 + 0.0151846i) q^{49} +(5.50405 + 1.68600i) q^{50} +(11.3756 - 3.75798i) q^{51} +(1.34208 - 7.49230i) q^{52} +(-4.21982 - 0.103591i) q^{53} +(-28.7690 - 5.07257i) q^{54} +(0.285978 - 0.315528i) q^{55} +(6.11915 + 4.16133i) q^{56} +(-25.8219 + 9.23923i) q^{57} +(8.60331 - 3.29180i) q^{58} +(-5.40785 + 6.26920i) q^{59} +(-1.26591 - 6.55024i) q^{60} +(-9.83831 + 2.20927i) q^{61} +(-0.547261 + 0.733715i) q^{62} +(-8.98134 + 21.6829i) q^{63} +(-3.65549 - 7.11599i) q^{64} +(1.40417 + 3.38995i) q^{65} +(2.09494 + 0.530816i) q^{66} +(1.90272 + 1.20488i) q^{67} +(-2.68499 + 6.38365i) q^{68} +(0.191330 + 2.59379i) q^{69} +(-3.56597 - 0.0972491i) q^{70} +(10.0890 + 4.77173i) q^{71} +(19.7437 - 15.9353i) q^{72} +(-0.0988353 - 2.01184i) q^{73} +(6.30236 - 1.39724i) q^{74} +(-9.71085 - 10.1996i) q^{75} +(5.78598 - 14.7599i) q^{76} +(0.519565 - 1.03220i) q^{77} +(-11.8524 + 14.3623i) q^{78} +(-2.55500 - 3.11328i) q^{79} +(3.33462 + 1.93728i) q^{80} +(34.4430 + 28.2666i) q^{81} +(3.52185 - 5.23990i) q^{82} +(4.72070 - 0.582243i) q^{83} +(-8.05163 - 16.2150i) q^{84} +(-0.570749 - 3.28931i) q^{85} +(0.860721 - 3.07764i) q^{86} +(-22.2919 - 3.30669i) q^{87} +(-1.02723 + 0.710982i) q^{88} +(2.96297 - 11.8288i) q^{89} +(-3.86823 + 11.6032i) q^{90} +(6.12592 + 7.84964i) q^{91} +(-1.20269 - 0.902163i) q^{92} +(2.04722 - 0.907468i) q^{93} +(6.74882 + 14.3702i) q^{94} +(1.49096 + 7.49554i) q^{95} +(-0.746450 + 19.5575i) q^{96} +(-0.838412 + 4.21498i) q^{97} +(0.212665 - 0.0526553i) q^{98} +(-2.86954 - 2.73203i) 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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