LMFDB - Embedded newform 225.2.q.a.121.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [225,2,Mod(16,225)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("225.16"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(225, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([20, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			121.10
Character	$\chi$	$=$	225.121
Dual form			225.2.q.a.106.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.05398 + 0.224029i) q^{2} +(1.71250 + 0.259519i) q^{3} +(-0.766416 + 0.341231i) q^{4} +(-1.13834 - 1.92462i) q^{5} +(-1.86307 + 0.110124i) q^{6} +(0.316483 + 0.548165i) q^{7} +(2.47480 - 1.79805i) q^{8} +(2.86530 + 0.888850i) q^{9} +(1.63096 + 1.77348i) q^{10} +(5.10644 - 1.08541i) q^{11} +(-1.40104 + 0.385457i) q^{12} +(3.72319 + 0.791388i) q^{13} +(-0.456370 - 0.506851i) q^{14} +(-1.44993 - 3.59134i) q^{15} +(-1.08284 + 1.20261i) q^{16} +(-0.365368 + 0.265455i) q^{17} +(-3.21908 - 0.294915i) q^{18} +(-3.97313 + 2.88665i) q^{19} +(1.52918 + 1.08663i) q^{20} +(0.399718 + 1.02086i) q^{21} +(-5.13890 + 2.28798i) q^{22} +(-0.0686557 - 0.0762499i) q^{23} +(4.70473 - 2.43690i) q^{24} +(-2.40836 + 4.38176i) q^{25} -4.10144 q^{26} +(4.67615 + 2.26575i) q^{27} +(-0.429608 - 0.312129i) q^{28} +(1.04992 - 9.98932i) q^{29} +(2.33276 + 3.46035i) q^{30} +(-0.422249 - 4.01743i) q^{31} +(-2.18716 + 3.78828i) q^{32} +(9.02645 - 0.533542i) q^{33} +(0.325619 - 0.361636i) q^{34} +(0.694745 - 1.23311i) q^{35} +(-2.49932 + 0.296499i) q^{36} +(0.0800637 + 0.246411i) q^{37} +(3.54089 - 3.93256i) q^{38} +(6.17057 + 2.32149i) q^{39} +(-6.27775 - 2.71627i) q^{40} +(-7.65841 - 1.62785i) q^{41} +(-0.649996 - 0.986417i) q^{42} +(3.68846 + 6.38860i) q^{43} +(-3.54328 + 2.57435i) q^{44} +(-1.55099 - 6.52644i) q^{45} +(0.0894437 + 0.0649846i) q^{46} +(-1.10730 + 10.5353i) q^{47} +(-2.16646 + 1.77845i) q^{48} +(3.29968 - 5.71521i) q^{49} +(1.55670 - 5.15781i) q^{50} +(-0.694582 + 0.359772i) q^{51} +(-3.12356 + 0.663933i) q^{52} +(-4.56626 - 3.31758i) q^{53} +(-5.43614 - 1.34045i) q^{54} +(-7.90187 - 8.59241i) q^{55} +(1.76886 + 0.787548i) q^{56} +(-7.55312 + 3.91228i) q^{57} +(1.13131 + 10.7637i) q^{58} +(-7.00744 - 1.48948i) q^{59} +(2.33673 + 2.25770i) q^{60} +(-4.51000 + 0.958629i) q^{61} +(1.34506 + 4.13967i) q^{62} +(0.419583 + 1.85196i) q^{63} +(2.45668 - 7.56088i) q^{64} +(-2.71514 - 8.06661i) q^{65} +(-9.39412 + 2.58453i) q^{66} +(-0.364553 - 3.46849i) q^{67} +(0.189442 - 0.328124i) q^{68} +(-0.0977846 - 0.148395i) q^{69} +(-0.455991 + 1.45531i) q^{70} +(-3.47832 - 2.52715i) q^{71} +(8.68926 - 2.95223i) q^{72} +(-4.75735 + 14.6416i) q^{73} +(-0.139588 - 0.241774i) q^{74} +(-5.26145 + 6.87874i) q^{75} +(2.06006 - 3.56813i) q^{76} +(2.21108 + 2.45566i) q^{77} +(-7.02371 - 1.06440i) q^{78} +(-0.142656 + 1.35728i) q^{79} +(3.54721 + 0.715070i) q^{80} +(7.41989 + 5.09364i) q^{81} +8.43646 q^{82} +(1.95429 + 0.870105i) q^{83} +(-0.654700 - 0.646011i) q^{84} +(0.926814 + 0.401017i) q^{85} +(-5.31878 - 5.90711i) q^{86} +(4.39040 - 16.8342i) q^{87} +(10.6858 - 11.8678i) q^{88} +(-5.42929 + 16.7096i) q^{89} +(3.09682 + 6.53124i) q^{90} +(0.744515 + 2.29138i) q^{91} +(0.0786377 + 0.0350118i) q^{92} +(0.319497 - 6.98942i) q^{93} +(-1.19314 - 11.3520i) q^{94} +(10.0785 + 4.36079i) q^{95} +(-4.72864 + 5.91981i) q^{96} +(0.637304 - 6.06354i) q^{97} +(-2.19740 + 6.76291i) q^{98} +(15.5962 + 1.42884i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20}+ \cdots - 20 q^{99}+O(q^{100}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−1.05398	+	0.224029i	−0.745273	+	0.158413i	−0.564870	−	0.825180i	$-0.691074\pi$
$2$	−1.05398	+	0.224029i	−0.745273	+	0.158413i	−0.180403	+	0.983593i	$0.557740\pi$
$3$	1.71250	+	0.259519i	0.988711	+	0.149833i
$3$	1.71250	+	0.259519i	0.988711	+	0.149833i
$4$	−0.766416	+	0.341231i	−0.383208	+	0.170615i
$5$	−1.13834	−	1.92462i	−0.509082	−	0.860718i
$5$	−1.13834	−	1.92462i	−0.509082	−	0.860718i
$6$	−1.86307	+	0.110124i	−0.760595	+	0.0449578i
$7$	0.316483	+	0.548165i	0.119619	+	0.207187i	0.919617	−	0.392817i	$-0.128499\pi$
$7$	0.316483	+	0.548165i	0.119619	+	0.207187i	−0.799998	+	0.600003i	$0.795166\pi$
$8$	2.47480	−	1.79805i	0.874976	−	0.635707i
$9$	2.86530	+	0.888850i	0.955100	+	0.296283i
$10$	1.63096	+	1.77348i	0.515754	+	0.560825i
$11$	5.10644	−	1.08541i	1.53965	−	0.327262i	0.641559	−	0.767074i	$-0.278288\pi$
$11$	5.10644	−	1.08541i	1.53965	−	0.327262i	0.898090	+	0.439811i	$0.144955\pi$
$12$	−1.40104	+	0.385457i	−0.404446	+	0.111272i
$13$	3.72319	+	0.791388i	1.03263	+	0.219492i	0.692901	−	0.721033i	$-0.256332\pi$
$13$	3.72319	+	0.791388i	1.03263	+	0.219492i	0.339726	+	0.940524i	$0.389666\pi$
$14$	−0.456370	−	0.506851i	−0.121970	−	0.135461i
$15$	−1.44993	−	3.59134i	−0.374371	−	0.927279i
$16$	−1.08284	+	1.20261i	−0.270709	+	0.300653i
$17$	−0.365368	+	0.265455i	−0.0886146	+	0.0643823i	−0.631210	−	0.775612i	$-0.717442\pi$
$17$	−0.365368	+	0.265455i	−0.0886146	+	0.0643823i	0.542596	+	0.839994i	$0.317442\pi$
$18$	−3.21908	−	0.294915i	−0.758745	−	0.0695120i
$19$	−3.97313	+	2.88665i	−0.911499	+	0.662243i	−0.941394	−	0.337310i	$-0.890483\pi$
$19$	−3.97313	+	2.88665i	−0.911499	+	0.662243i	0.0298945	+	0.999553i	$0.490483\pi$
$20$	1.52918	+	1.08663i	0.341936	+	0.242977i
$21$	0.399718	+	1.02086i	0.0872256	+	0.222771i
$22$	−5.13890	+	2.28798i	−1.09562	+	0.487800i
$23$	−0.0686557	−	0.0762499i	−0.0143157	−	0.0158992i	0.735944	−	0.677042i	$-0.236738\pi$
$23$	−0.0686557	−	0.0762499i	−0.0143157	−	0.0158992i	−0.750260	+	0.661143i	$0.770072\pi$
$24$	4.70473	−	2.43690i	0.960348	−	0.497430i
$25$	−2.40836	+	4.38176i	−0.481671	+	0.876352i
$26$	−4.10144			−0.804359
$27$	4.67615	+	2.26575i	0.899925	+	0.436044i
$28$	−0.429608	−	0.312129i	−0.0811883	−	0.0589868i
$29$	1.04992	−	9.98932i	0.194965	−	1.85497i	−0.261467	−	0.965212i	$-0.584206\pi$
$29$	1.04992	−	9.98932i	0.194965	−	1.85497i	0.456433	−	0.889758i	$-0.349127\pi$
$30$	2.33276	+	3.46035i	0.425901	+	0.631771i
$31$	−0.422249	−	4.01743i	−0.0758381	−	0.721551i	−0.964696	−	0.263367i	$-0.915167\pi$
$31$	−0.422249	−	4.01743i	−0.0758381	−	0.721551i	0.888858	−	0.458184i	$-0.151500\pi$
$32$	−2.18716	+	3.78828i	−0.386640	+	0.669680i
$33$	9.02645	−	0.533542i	1.57130	−	0.0928777i
$34$	0.325619	−	0.361636i	0.0558431	−	0.0620201i
$35$	0.694745	−	1.23311i	0.117433	−	0.208434i
$36$	−2.49932	+	0.296499i	−0.416553	+	0.0494164i
$37$	0.0800637	+	0.246411i	0.0131624	+	0.0405097i	0.957422	−	0.288692i	$-0.0932204\pi$
$37$	0.0800637	+	0.246411i	0.0131624	+	0.0405097i	−0.944260	+	0.329202i	$0.893220\pi$
$38$	3.54089	−	3.93256i	0.574408	−	0.637945i
$39$	6.17057	+	2.32149i	0.988083	+	0.371735i
$40$	−6.27775	−	2.71627i	−0.992599	−	0.429480i
$41$	−7.65841	−	1.62785i	−1.19604	−	0.254227i	−0.433493	−	0.901157i	$-0.642719\pi$
$41$	−7.65841	−	1.62785i	−1.19604	−	0.254227i	−0.762549	+	0.646930i	$0.776053\pi$
$42$	−0.649996	−	0.986417i	−0.100297	−	0.152207i
$43$	3.68846	+	6.38860i	0.562485	+	0.974253i	0.997279	+	0.0737227i	$0.0234880\pi$
$43$	3.68846	+	6.38860i	0.562485	+	0.974253i	−0.434794	+	0.900530i	$0.643179\pi$
$44$	−3.54328	+	2.57435i	−0.534170	+	0.388097i
$45$	−1.55099	−	6.52644i	−0.231208	−	0.972904i
$46$	0.0894437	+	0.0649846i	0.0131878	+	0.00958146i
$47$	−1.10730	+	10.5353i	−0.161517	+	1.53673i	0.550660	+	0.834730i	$0.314376\pi$
$47$	−1.10730	+	10.5353i	−0.161517	+	1.53673i	−0.712177	+	0.702000i	$0.752291\pi$
$48$	−2.16646	+	1.77845i	−0.312701	+	0.256698i
$49$	3.29968	−	5.71521i	0.471382	−	0.816458i
$50$	1.55670	−	5.15781i	0.220151	−	0.729424i
$51$	−0.694582	+	0.359772i	−0.0972609	+	0.0503781i
$52$	−3.12356	+	0.663933i	−0.433160	+	0.0920709i
$53$	−4.56626	−	3.31758i	−0.627224	−	0.455705i	0.228213	−	0.973611i	$-0.426712\pi$
$53$	−4.56626	−	3.31758i	−0.627224	−	0.455705i	−0.855437	+	0.517906i	$0.826712\pi$
$54$	−5.43614	−	1.34045i	−0.739765	−	0.182413i
$55$	−7.90187	−	8.59241i	−1.06549	−	1.15860i
$56$	1.76886	+	0.787548i	0.236374	+	0.105241i
$57$	−7.55312	+	3.91228i	−1.00044	+	0.518194i
$58$	1.13131	+	10.7637i	0.148548	+	1.41334i
$59$	−7.00744	−	1.48948i	−0.912291	−	0.193913i	−0.272225	−	0.962234i	$-0.587760\pi$
$59$	−7.00744	−	1.48948i	−0.912291	−	0.193913i	−0.640066	+	0.768320i	$0.721093\pi$
$60$	2.33673	+	2.25770i	0.301670	+	0.291467i
$61$	−4.51000	+	0.958629i	−0.577446	+	0.122740i	−0.487371	−	0.873195i	$-0.662044\pi$
$61$	−4.51000	+	0.958629i	−0.577446	+	0.122740i	−0.0900749	+	0.995935i	$0.528711\pi$
$62$	1.34506	+	4.13967i	0.170823	+	0.525739i
$63$	0.419583	+	1.85196i	0.0528624	+	0.233325i
$64$	2.45668	−	7.56088i	0.307085	−	0.945110i
$65$	−2.71514	−	8.06661i	−0.336771	−	1.00054i
$66$	−9.39412	+	2.58453i	−1.15634	+	0.318134i
$67$	−0.364553	−	3.46849i	−0.0445372	−	0.423743i	−0.993960	−	0.109743i	$-0.964997\pi$
$67$	−0.364553	−	3.46849i	−0.0445372	−	0.423743i	0.949423	−	0.314001i	$-0.101669\pi$
$68$	0.189442	−	0.328124i	0.0229732	−	0.0397908i
$69$	−0.0977846	−	0.148395i	−0.0117719	−	0.0178647i
$70$	−0.455991	+	1.45531i	−0.0545014	+	0.173943i
$71$	−3.47832	−	2.52715i	−0.412801	−	0.299917i	0.361934	−	0.932204i	$-0.382117\pi$
$71$	−3.47832	−	2.52715i	−0.412801	−	0.299917i	−0.774735	+	0.632286i	$0.782117\pi$
$72$	8.68926	−	2.95223i	1.02404	−	0.347923i
$73$	−4.75735	+	14.6416i	−0.556806	+	1.71367i	0.134320	+	0.990938i	$0.457115\pi$
$73$	−4.75735	+	14.6416i	−0.556806	+	1.71367i	−0.691126	+	0.722734i	$0.742885\pi$
$74$	−0.139588	−	0.241774i	−0.0162268	−	0.0281057i
$75$	−5.26145	+	6.87874i	−0.607540	+	0.794289i
$76$	2.06006	−	3.56813i	0.236305	−	0.409292i
$77$	2.21108	+	2.45566i	0.251976	+	0.279848i
$78$	−7.02371	−	1.06440i	−0.795279	−	0.120520i
$79$	−0.142656	+	1.35728i	−0.0160501	+	0.152706i	−0.999612	−	0.0278667i	$-0.991129\pi$
$79$	−0.142656	+	1.35728i	−0.0160501	+	0.152706i	0.983562	+	0.180573i	$0.0577953\pi$
$80$	3.54721	+	0.715070i	0.396591	+	0.0799473i
$81$	7.41989	+	5.09364i	0.824432	+	0.565961i
$82$	8.43646			0.931651
$83$	1.95429	+	0.870105i	0.214511	+	0.0955065i	0.511179	−	0.859474i	$-0.329209\pi$
$83$	1.95429	+	0.870105i	0.214511	+	0.0955065i	−0.296668	+	0.954981i	$0.595876\pi$
$84$	−0.654700	−	0.646011i	−0.0714336	−	0.0704856i
$85$	0.926814	+	0.401017i	0.100527	+	0.0434964i
$86$	−5.31878	−	5.90711i	−0.573539	−	0.636980i
$87$	4.39040	−	16.8342i	0.470700	−	1.80482i
$88$	10.6858	−	11.8678i	1.13911	−	1.26511i
$89$	−5.42929	+	16.7096i	−0.575504	+	1.77122i	0.0589537	+	0.998261i	$0.481224\pi$
$89$	−5.42929	+	16.7096i	−0.575504	+	1.77122i	−0.634457	+	0.772958i	$0.718776\pi$
$90$	3.09682	+	6.53124i	0.326433	+	0.688453i
$91$	0.744515	+	2.29138i	0.0780464	+	0.240202i
$92$	0.0786377	+	0.0350118i	0.00819855	+	0.00365023i
$93$	0.319497	−	6.98942i	0.0331303	−	0.724769i
$94$	−1.19314	−	11.3520i	−0.123063	−	1.17087i
$95$	10.0785	+	4.36079i	1.03403	+	0.447408i
$96$	−4.72864	+	5.91981i	−0.482615	+	0.604188i
$97$	0.637304	−	6.06354i	0.0647084	−	0.615659i	−0.913328	−	0.407225i	$-0.866497\pi$
$97$	0.637304	−	6.06354i	0.0647084	−	0.615659i	0.978036	−	0.208434i	$-0.0668368\pi$
$98$	−2.19740	+	6.76291i	−0.221971	+	0.683157i
$99$	15.5962	+	1.42884i	1.56748	+	0.143604i
$100$	0.350613	−	4.18006i	0.0350613	−	0.418006i
$101$	1.98334	+	3.43524i	0.197350	+	0.341820i	0.947668	−	0.319257i	$-0.103433\pi$
$101$	1.98334	+	3.43524i	0.197350	+	0.341820i	−0.750319	+	0.661076i	$0.770100\pi$
$102$	0.651473	−	0.534797i	0.0645054	−	0.0529528i
$103$	1.04871	−	0.466917i	0.103333	−	0.0460067i	−0.354419	−	0.935087i	$-0.615321\pi$
$103$	1.04871	−	0.466917i	0.103333	−	0.0460067i	0.457752	+	0.889080i	$0.348655\pi$
$104$	10.6371	−	4.73595i	1.04306	−	0.464398i
$105$	1.50976	−	1.93140i	0.147338	−	0.188485i
$106$	5.55596	+	2.47367i	0.539643	+	0.240264i
$107$	4.10301			0.396653			0.198326	−	0.980136i	$-0.436449\pi$
$107$	4.10301			0.396653			0.198326	+	0.980136i	$0.436449\pi$
$108$	−4.35702	−	0.140865i	−0.419254	−	0.0135548i
$109$	0.0306236	+	0.0942499i	0.00293321	+	0.00902750i	0.952512	−	0.304500i	$-0.0984893\pi$
$109$	0.0306236	+	0.0942499i	0.00293321	+	0.00902750i	−0.949579	+	0.313527i	$0.898489\pi$
$110$	10.2533	+	7.28594i	0.977617	+	0.694687i
$111$	0.0731608	+	0.442756i	0.00694411	+	0.0420245i
$112$	−1.00193	−	0.212967i	−0.0946734	−	0.0201234i
$113$	−13.0049	−	2.76428i	−1.22340	−	0.260041i	−0.449459	−	0.893301i	$-0.648383\pi$
$113$	−13.0049	−	2.76428i	−1.22340	−	0.260041i	−0.773939	+	0.633260i	$0.781716\pi$
$114$	7.08434	−	5.81557i	0.663509	−	0.544678i
$115$	−0.0685988	+	0.218935i	−0.00639687	+	0.0204158i
$116$	2.60399	+	8.01424i	0.241774	+	0.744104i
$117$	9.96463	+	5.57692i	0.921230	+	0.515587i
$118$	7.71936			0.710624
$119$	−0.261146	−	0.116270i	−0.0239392	−	0.0106584i
$120$	−10.0457	−	6.28080i	−0.917043	−	0.573356i
$121$	14.8486	−	6.61102i	1.34987	−	0.601002i
$122$	4.53866	−	2.02074i	0.410911	−	0.182949i
$123$	−12.6926	−	4.77518i	−1.14445	−	0.430564i
$124$	1.69449	+	2.93494i	0.152169	+	0.263565i
$125$	11.1748	−	0.352760i	0.999502	−	0.0315518i
$126$	−0.857124	−	1.85792i	−0.0763586	−	0.165517i
$127$	1.73383	−	5.33620i	0.153853	−	0.473511i	−0.844190	−	0.536044i	$-0.819918\pi$
$127$	1.73383	−	5.33620i	0.153853	−	0.473511i	0.998043	+	0.0625335i	$0.0199180\pi$
$128$	0.0190639	−	0.181381i	0.00168503	−	0.0160320i
$129$	4.65852	+	11.8977i	0.410160	+	1.04753i
$130$	4.66884	+	7.89374i	0.409485	+	0.692326i
$131$	0.574155	+	5.46272i	0.0501641	+	0.477280i	0.990548	+	0.137165i	$0.0437991\pi$
$131$	0.574155	+	5.46272i	0.0501641	+	0.477280i	−0.940384	+	0.340114i	$0.889534\pi$
$132$	−6.73596	+	3.48902i	−0.586290	+	0.303680i
$133$	−2.83979	−	1.26436i	−0.246241	−	0.109633i
$134$	1.16127	+	3.57403i	0.100319	+	0.308749i
$135$	−0.962332	−	11.5790i	−0.0828244	−	0.996564i
$136$	−0.426912	+	1.31390i	−0.0366074	+	0.112666i
$137$	−6.65616	+	7.39241i	−0.568674	+	0.631576i	−0.957049	−	0.289925i	$-0.906370\pi$
$137$	−6.65616	+	7.39241i	−0.568674	+	0.631576i	0.388376	+	0.921501i	$0.373036\pi$
$138$	0.136307	+	0.134498i	0.0116033	+	0.0114493i
$139$	2.88198	+	3.20077i	0.244447	+	0.271486i	0.852866	−	0.522130i	$-0.174863\pi$
$139$	2.88198	+	3.20077i	0.244447	+	0.271486i	−0.608419	+	0.793616i	$0.708196\pi$
$140$	−0.111689	+	1.18214i	−0.00943947	+	0.0999094i
$141$	−4.63036	+	17.7543i	−0.389947	+	1.49518i
$142$	4.23222	+	1.88431i	0.355160	+	0.158127i
$143$	19.8712			1.66171
$144$	−4.17159	+	2.48336i	−0.347633	+	0.206947i
$145$	−20.4209	+	9.35056i	−1.69586	+	0.776522i
$146$	1.73398	−	16.4977i	0.143505	−	1.36536i
$147$	7.13389	−	8.93096i	0.588394	−	0.736613i
$148$	−0.145445	−	0.161533i	−0.0119555	−	0.0132779i
$149$	−0.0389321	+	0.0674323i	−0.00318944	+	0.00552427i	−0.867616	−	0.497235i	$-0.834349\pi$
$149$	−0.0389321	+	0.0674323i	−0.00318944	+	0.00552427i	0.864426	+	0.502760i	$0.167682\pi$
$150$	4.00440	−	8.42874i	0.326958	−	0.688204i
$151$	−8.59717	−	14.8907i	−0.699628	−	1.21179i	−0.968595	−	0.248642i	$-0.920016\pi$
$151$	−8.59717	−	14.8907i	−0.699628	−	1.21179i	0.268968	−	0.963149i	$-0.413318\pi$
$152$	−4.64238	+	14.2878i	−0.376547	+	1.15889i
$153$	−1.28284	+	0.435851i	−0.103711	+	0.0352365i
$154$	−2.88057	−	2.09285i	−0.232123	−	0.168647i
$155$	−7.25137	+	5.38587i	−0.582444	+	0.432604i
$156$	−5.52139	+	0.326362i	−0.442065	+	0.0261299i
$157$	−5.71800	+	9.90387i	−0.456346	+	0.790415i	−0.998765	−	0.0496936i	$-0.984176\pi$
$157$	−5.71800	+	9.90387i	−0.456346	+	0.790415i	0.542418	+	0.840109i	$0.317509\pi$
$158$	−0.153715	−	1.46250i	−0.0122289	−	0.116351i
$159$	−6.95874	−	6.86638i	−0.551864	−	0.544539i
$160$	9.78076	−	0.102888i	0.773237	−	0.00813398i
$161$	0.0200691	−	0.0617665i	0.00158167	−	0.00486788i
$162$	−8.96151	−	3.70630i	−0.704083	−	0.291195i
$163$	1.40825	+	4.33413i	0.110302	+	0.339476i	0.990938	−	0.134318i	$-0.0428843\pi$
$163$	1.40825	+	4.33413i	0.110302	+	0.339476i	−0.880636	+	0.473793i	$0.842884\pi$
$164$	6.42500	−	1.36568i	0.501708	−	0.106641i
$165$	−11.3021	−	16.7652i	−0.879864	−	1.30517i
$166$	−2.25470	−	0.479251i	−0.174999	−	0.0371971i
$167$	−1.56503	−	14.8903i	−0.121106	−	1.15225i	−0.871205	−	0.490920i	$-0.836661\pi$
$167$	−1.56503	−	14.8903i	−0.121106	−	1.15225i	0.750099	−	0.661326i	$-0.230006\pi$
$168$	2.82479	+	1.80773i	0.217937	+	0.139469i
$169$	1.35975	+	0.605399i	0.104596	+	0.0465691i
$170$	−1.06668	−	0.215028i	−0.0818105	−	0.0164919i
$171$	−13.9500	+	4.73960i	−1.06678	+	0.362446i
$172$	−5.00688	−	3.63771i	−0.381771	−	0.277373i
$173$	−3.49543	+	0.742976i	−0.265753	+	0.0564874i	−0.338861	−	0.940837i	$-0.610042\pi$
$173$	−3.49543	+	0.742976i	−0.265753	+	0.0564874i	0.0731081	+	0.997324i	$0.476708\pi$
$174$	−0.856013	+	18.7264i	−0.0648942	+	1.41965i
$175$	−3.16413	+	0.0665768i	−0.239186	+	0.00503274i
$176$	−4.22411	+	7.31638i	−0.318405	+	0.551493i
$177$	−11.6137	−	4.36929i	−0.872938	−	0.328416i
$178$	1.97889	−	18.8279i	0.148324	−	1.41121i
$179$	−17.6257	−	12.8058i	−1.31741	−	0.957151i	−0.999961	−	0.00887412i	$-0.997175\pi$
$179$	−17.6257	−	12.8058i	−1.31741	−	0.957151i	−0.317445	−	0.948277i	$-0.602825\pi$
$180$	3.41572	+	4.47273i	0.254593	+	0.333377i
$181$	14.5760	−	10.5901i	1.08343	−	0.787155i	0.105148	−	0.994457i	$-0.466468\pi$
$181$	14.5760	−	10.5901i	1.08343	−	0.787155i	0.978277	+	0.207302i	$0.0664682\pi$
$182$	−1.29804	−	2.24827i	−0.0962169	−	0.166653i
$183$	−7.97214	+	0.471223i	−0.589318	+	0.0348338i
$184$	−0.307011	−	0.0652572i	−0.0226331	−	0.00481082i
$185$	0.383108	−	0.434592i	0.0281667	−	0.0319519i
$186$	1.22909	+	7.43825i	0.0901215	+	0.545399i
$187$	−1.57760	+	1.75210i	−0.115366	+	0.128126i
$188$	−2.74631	−	8.45226i	−0.200295	−	0.616445i
$189$	0.237916	+	3.28037i	0.0173058	+	0.238612i
$190$	−11.5994	−	2.33829i	−0.841511	−	0.169637i
$191$	6.83360	−	7.58948i	0.494462	−	0.549156i	−0.443328	−	0.896360i	$-0.646202\pi$
$191$	6.83360	−	7.58948i	0.494462	−	0.549156i	0.937790	+	0.347204i	$0.112869\pi$
$192$	6.16925	−	12.3104i	0.445227	−	0.888430i
$193$	−6.35646	+	11.0097i	−0.457548	+	0.792496i	−0.998831	−	0.0483444i	$-0.984605\pi$
$193$	−6.35646	+	11.0097i	−0.457548	+	0.792496i	0.541283	+	0.840841i	$0.317939\pi$
$194$	0.686709	+	6.53360i	0.0493028	+	0.469085i
$195$	−2.55623	−	14.5187i	−0.183056	−	1.03970i
$196$	−0.578723	+	5.50618i	−0.0413373	+	0.393299i
$197$	5.47291	+	3.97630i	0.389929	+	0.283300i	0.765426	−	0.643524i	$-0.222528\pi$
$197$	5.47291	+	3.97630i	0.389929	+	0.283300i	−0.375498	+	0.926823i	$0.622528\pi$
$198$	−16.7582	+	1.98805i	−1.19095	+	0.141285i
$199$	7.09600			0.503022			0.251511	−	0.967854i	$-0.419073\pi$
$199$	7.09600			0.503022			0.251511	+	0.967854i	$0.419073\pi$
$200$	1.91842	+	15.1743i	0.135653	+	1.07299i
$201$	0.275841	−	6.03439i	0.0194563	−	0.425633i
$202$	−2.85999	−	3.17634i	−0.201228	−	0.223486i
$203$	5.80807	−	2.58592i	0.407647	−	0.181496i
$204$	0.409574	−	0.512747i	0.0286759	−	0.0358995i
$205$	5.58490	+	16.5926i	0.390066	+	1.15888i
$206$	−1.00071	+	0.727061i	−0.0697230	+	0.0506567i
$207$	−0.128945	−	0.279504i	−0.00896227	−	0.0194268i
$208$	−4.98334	+	3.62061i	−0.345532	+	0.251044i
$209$	−17.1554	+	19.0530i	−1.18666	+	1.31792i
$210$	−1.15856	+	2.37388i	−0.0799485	+	0.163813i
$211$	17.7288	+	19.6898i	1.22050	+	1.35550i	0.915072	+	0.403289i	$0.132133\pi$
$211$	17.7288	+	19.6898i	1.22050	+	1.35550i	0.305429	+	0.952215i	$0.401200\pi$
$212$	4.63172	+	0.984502i	0.318108	+	0.0676158i
$213$	−5.30078	−	5.23043i	−0.363203	−	0.358383i
$214$	−4.32447	+	0.919195i	−0.295615	+	0.0628349i
$215$	8.09693	−	14.3713i	0.552206	−	0.980116i
$216$	15.6465	−	2.80066i	1.06461	−	0.190561i
$217$	2.06858	−	1.50291i	0.140424	−	0.102024i
$218$	−0.0533913	−	0.0924764i	−0.00361611	−	0.00626329i
$219$	−11.9467	+	23.8391i	−0.807285	+	1.61090i
$220$	8.98812	+	3.88900i	0.605979	+	0.262197i
$221$	−1.57041	+	0.699192i	−0.105637	+	0.0470327i
$222$	−0.176300	−	0.450264i	−0.0118325	−	0.0302197i
$223$	−3.85158	+	0.818679i	−0.257921	+	0.0548228i	−0.335057	−	0.942198i	$-0.608756\pi$
$223$	−3.85158	+	0.818679i	−0.257921	+	0.0548228i	0.0771363	+	0.997021i	$0.475422\pi$
$224$	−2.76880			−0.184998
$225$	−10.7954	+	10.4144i	−0.719693	+	0.694293i
$226$	14.3261			0.952959
$227$	23.6286	−	5.02242i	1.56829	−	0.333350i	0.659858	−	0.751390i	$-0.270616\pi$
$227$	23.6286	−	5.02242i	1.56829	−	0.333350i	0.908428	+	0.418041i	$0.137283\pi$
$228$	4.45384	−	5.57579i	0.294963	−	0.369266i
$229$	−13.8340	+	6.15929i	−0.914175	+	0.407017i	−0.809251	−	0.587463i	$-0.800127\pi$
$229$	−13.8340	+	6.15929i	−0.914175	+	0.407017i	−0.104924	+	0.994480i	$0.533460\pi$
$230$	0.0232535	−	0.246120i	0.00153329	−	0.0162287i
$231$	3.14919	+	4.77912i	0.207201	+	0.314443i
$232$	−15.3630	−	26.6094i	−1.00863	−	1.74699i
$233$	10.3302	−	7.50529i	0.676751	−	0.491688i	−0.195527	−	0.980698i	$-0.562642\pi$
$233$	10.3302	−	7.50529i	0.676751	−	0.491688i	0.872278	+	0.489010i	$0.162642\pi$
$234$	−11.7519	−	3.64557i	−0.768243	−	0.238318i
$235$	21.5370	−	9.86162i	1.40492	−	0.643301i
$236$	5.87887	−	1.24959i	0.382682	−	0.0813416i
$237$	−0.596539	+	2.28733i	−0.0387494	+	0.148578i
$238$	0.301289	+	0.0640409i	0.0195297	+	0.00415116i
$239$	−8.58195	−	9.53122i	−0.555120	−	0.616524i	0.398634	−	0.917110i	$-0.369484\pi$
$239$	−8.58195	−	9.53122i	−0.555120	−	0.616524i	−0.953755	+	0.300586i	$0.902818\pi$
$240$	5.88902	+	2.14512i	0.380135	+	0.138467i
$241$	18.4961	−	20.5420i	1.19144	−	1.32323i	0.257293	−	0.966334i	$-0.417170\pi$
$241$	18.4961	−	20.5420i	1.19144	−	1.32323i	0.934145	−	0.356892i	$-0.116164\pi$
$242$	−14.1690	+	10.2944i	−0.910817	+	0.661748i
$243$	11.3847	+	10.6485i	0.730326	+	0.683099i
$244$	3.12942	−	2.27366i	0.200341	−	0.145556i
$245$	−14.7558	+	0.155222i	−0.942713	+	0.00991677i
$246$	14.4474	+	2.18942i	0.921134	+	0.139592i
$247$	−17.0772	+	7.60325i	−1.08659	+	0.483783i
$248$	−8.26852	−	9.18312i	−0.525052	−	0.583129i
$249$	3.12091	+	1.99723i	0.197779	+	0.126569i
$250$	−11.6989	+	2.87528i	−0.739904	+	0.181848i
$251$	−2.88989			−0.182408			−0.0912042	−	0.995832i	$-0.529072\pi$
$251$	−2.88989			−0.182408			−0.0912042	+	0.995832i	$0.529072\pi$
$252$	−0.953521	−	1.27620i	−0.0600662	−	0.0803930i
$253$	−0.433349	−	0.314846i	−0.0272444	−	0.0197942i
$254$	−0.631955	+	6.01265i	−0.0396524	+	0.377267i
$255$	1.48310	+	0.927266i	0.0928751	+	0.0580676i
$256$	1.68254	+	16.0083i	0.105159	+	1.00052i
$257$	3.00243	−	5.20037i	0.187287	−	0.324390i	−0.757058	−	0.653348i	$-0.773364\pi$
$257$	3.00243	−	5.20037i	0.187287	−	0.324390i	0.944345	+	0.328958i	$0.106697\pi$
$258$	−7.57540	−	11.4962i	−0.471624	−	0.715724i
$259$	−0.109735	+	0.121873i	−0.00681859	+	0.00757281i
$260$	4.83350	+	5.25589i	0.299761	+	0.325957i
$261$	11.8873	−	27.6892i	0.735808	−	1.71392i
$262$	−1.82895	−	5.62894i	−0.112993	−	0.347757i
$263$	9.16815	−	10.1823i	0.565332	−	0.627865i	−0.390914	−	0.920427i	$-0.627841\pi$
$263$	9.16815	−	10.1823i	0.565332	−	0.627865i	0.956247	+	0.292562i	$0.0945078\pi$
$264$	21.3794	−	17.5504i	1.31581	−	1.08015i
$265$	−1.18713	+	12.5649i	−0.0729251	+	0.771854i
$266$	3.27632	+	0.696403i	0.200884	+	0.0426992i
$267$	−13.6341	+	27.2062i	−0.834394	+	1.66499i
$268$	1.46295	+	2.53391i	0.0893641	+	0.154783i
$269$	−13.3513	+	9.70027i	−0.814041	+	0.591436i	−0.915000	−	0.403455i	$-0.867809\pi$
$269$	−13.3513	+	9.70027i	−0.814041	+	0.591436i	0.100958	+	0.994891i	$0.467809\pi$
$270$	3.60832	+	11.9884i	0.219595	+	0.729592i
$271$	−4.70284	−	3.41681i	−0.285677	−	0.207557i	0.435713	−	0.900086i	$-0.356496\pi$
$271$	−4.70284	−	3.41681i	−0.285677	−	0.207557i	−0.721390	+	0.692529i	$0.756496\pi$
$272$	0.0763939	−	0.726840i	0.00463206	−	0.0440711i
$273$	0.680325	+	4.11720i	0.0411751	+	0.249184i
$274$	5.35931	−	9.28259i	0.323768	−	0.560782i
$275$	−7.54213	+	24.9892i	−0.454807	+	1.50691i
$276$	0.125581	+	0.0803655i	0.00755907	+	0.00483743i
$277$	−21.9583	+	4.66738i	−1.31935	+	0.280436i	−0.813186	−	0.582004i	$-0.802269\pi$
$277$	−21.9583	+	4.66738i	−1.31935	+	0.280436i	−0.506160	+	0.862440i	$0.668935\pi$
$278$	−3.75461	−	2.72788i	−0.225186	−	0.163607i
$279$	2.36102	−	11.8864i	0.141351	−	0.711623i
$280$	−0.497835	−	4.30089i	−0.0297513	−	0.257027i
$281$	−21.1347	−	9.40979i	−1.26079	−	0.561341i	−0.336018	−	0.941856i	$-0.609080\pi$
$281$	−21.1347	−	9.40979i	−1.26079	−	0.561341i	−0.924775	+	0.380514i	$0.875747\pi$
$282$	0.902799	−	19.7499i	0.0537609	−	1.17609i
$283$	−1.95792	−	18.6284i	−0.116386	−	1.10734i	−0.884342	−	0.466840i	$-0.845392\pi$
$283$	−1.95792	−	18.6284i	−0.116386	−	1.10734i	0.767955	−	0.640503i	$-0.221274\pi$
$284$	3.52818	+	0.749938i	0.209359	+	0.0445007i
$285$	16.1277	+	10.0834i	0.955323	+	0.597289i
$286$	−20.9438	+	4.45173i	−1.23843	+	0.263237i
$287$	−1.53143	−	4.71326i	−0.0903974	−	0.278215i
$288$	−9.63410	+	8.91050i	−0.567695	+	0.525056i
$289$	−5.19026	+	15.9740i	−0.305310	+	0.939646i
$290$	19.4283	−	14.4301i	1.14087	−	0.847366i
$291$	2.66498	−	10.2184i	0.156224	−	0.599014i
$292$	−1.35006	−	12.8449i	−0.0790061	−	0.751693i
$293$	−7.31930	+	12.6774i	−0.427598	+	0.740622i	−0.996659	−	0.0816737i	$-0.973973\pi$
$293$	−7.31930	+	12.6774i	−0.427598	+	0.740622i	0.569061	+	0.822295i	$0.307307\pi$
$294$	−5.51815	+	11.0112i	−0.321825	+	0.642187i
$295$	5.11018	+	15.1822i	0.297526	+	0.883943i
$296$	0.641201	+	0.465860i	0.0372691	+	0.0270776i
$297$	26.3377	+	6.49440i	1.52827	+	0.376843i
$298$	0.0259266	−	0.0797939i	0.00150189	−	0.00462234i
$299$	−0.195275	−	0.338226i	−0.0112930	−	0.0195601i
$300$	1.68523	−	7.06735i	0.0972966	−	0.408034i
$301$	−2.33467	+	4.04377i	−0.134568	+	0.233079i
$302$	12.3972	+	13.7685i	0.713377	+	0.792285i
$303$	2.50496	+	6.39756i	0.143906	+	0.367530i
$304$	0.830734	−	7.90390i	0.0476459	−	0.453320i
$305$	6.97892	+	7.58880i	0.399612	+	0.434533i
$306$	1.25444	−	0.746770i	0.0717113	−	0.0426900i
$307$	33.9350			1.93677			0.968386	−	0.249455i	$-0.0802515\pi$
$307$	33.9350			1.93677			0.968386	+	0.249455i	$0.0802515\pi$
$308$	−2.53255	−	1.12757i	−0.144306	−	0.0642490i
$309$	1.91709	−	0.527434i	0.109059	−	0.0300047i
$310$	6.43617	−	7.30110i	0.365550	−	0.414675i
$311$	6.10247	+	6.77748i	0.346040	+	0.384316i	0.890891	−	0.454217i	$-0.150081\pi$
$311$	6.10247	+	6.77748i	0.346040	+	0.384316i	−0.544852	+	0.838532i	$0.683414\pi$
$312$	19.4451	−	5.34978i	1.10086	−	0.302872i
$313$	−15.8589	+	17.6131i	−0.896398	+	0.995551i	0.103601	+	0.994619i	$0.466963\pi$
$313$	−15.8589	+	17.6131i	−0.896398	+	0.995551i	−1.00000		0.000932210i	$0.999703\pi$
$314$	3.80788	−	11.7194i	0.214891	−	0.661366i
$315$	3.08670	−	2.91570i	0.173916	−	0.164281i
$316$	−0.353813	−	1.08892i	−0.0199035	−	0.0612567i
$317$	−26.3835	−	11.7467i	−1.48184	−	0.659759i	−0.502985	−	0.864295i	$-0.667765\pi$
$317$	−26.3835	−	11.7467i	−1.48184	−	0.659759i	−0.978859	+	0.204536i	$0.934432\pi$
$318$	8.87261	+	5.67803i	0.497551	+	0.318408i
$319$	−5.48113	−	52.1494i	−0.306884	−	2.91981i
$320$	−17.3484	+	3.87868i	−0.969805	+	0.216825i
$321$	7.02640	+	1.06481i	0.392175	+	0.0594317i
$322$	−0.00731488	+	0.0695964i	−0.000407642	+	0.00387846i
$323$	0.685378	−	2.10938i	0.0381354	−	0.117369i
$324$	−7.42483	−	1.37196i	−0.412491	−	0.0762200i
$325$	−12.4344	+	14.4082i	−0.689739	+	0.799222i
$326$	−2.45523	−	4.25258i	−0.135983	−	0.235529i
$327$	0.0279833	+	0.169350i	0.00154748	+	0.00936508i
$328$	−21.8800	+	9.74161i	−1.20812	+	0.537891i
$329$	−6.12552	+	2.72726i	−0.337711	+	0.150358i
$330$	15.6680	+	15.1381i	0.862493	+	0.833324i
$331$	−22.2886	−	9.92350i	−1.22509	−	0.545445i	−0.310788	−	0.950479i	$-0.600593\pi$
$331$	−22.2886	−	9.92350i	−1.22509	−	0.545445i	−0.914302	+	0.405034i	$0.867260\pi$
$332$	−1.79470			−0.0984972
$333$	0.0103843	+	0.777205i	0.000569058	+	0.0425906i
$334$	4.98537	+	15.3434i	0.272787	+	0.839553i
$335$	−6.26055	+	4.64995i	−0.342051	+	0.254054i
$336$	−1.66053	−	0.624724i	−0.0905895	−	0.0340815i
$337$	1.26985	+	0.269916i	0.0691734	+	0.0147033i	0.242368	−	0.970184i	$-0.422076\pi$
$337$	1.26985	+	0.269916i	0.0691734	+	0.0147033i	−0.173195	+	0.984888i	$0.555409\pi$
$338$	−1.56877	−	0.333452i	−0.0853297	−	0.0181374i
$339$	−21.5535	−	8.10883i	−1.17062	−	0.440411i
$340$	−0.847165	+	0.00891166i	−0.0459440	+	0.000483303i
$341$	−6.51673	−	20.0564i	−0.352901	−	1.08612i
$342$	13.6412	−	8.12063i	0.737629	−	0.439113i
$343$	8.60793			0.464784
$344$	20.6153	+	9.17850i	1.11150	+	0.494872i
$345$	−0.174293	+	0.357123i	−0.00938362	+	0.0192269i
$346$	3.51765	−	1.56616i	0.189110	−	0.0841971i
$347$	15.7936	−	7.03179i	0.847847	−	0.377486i	0.0636311	−	0.997973i	$-0.479732\pi$
$347$	15.7936	−	7.03179i	0.847847	−	0.377486i	0.784216	+	0.620487i	$0.213065\pi$
$348$	2.37948	+	14.4002i	0.127553	+	0.771930i
$349$	14.5339	+	25.1734i	0.777980	+	1.34750i	0.933104	+	0.359606i	$0.117089\pi$
$349$	14.5339	+	25.1734i	0.777980	+	1.34750i	−0.155124	+	0.987895i	$0.549578\pi$
$350$	3.32000	−	0.779028i	0.177461	−	0.0416408i
$351$	15.6171	+	12.1365i	0.833579	+	0.647797i
$352$	−7.05679	+	21.7186i	−0.376128	+	1.15760i
$353$	1.95250	−	18.5768i	0.103921	−	0.988745i	−0.810982	−	0.585071i	$-0.801066\pi$
$353$	1.95250	−	18.5768i	0.103921	−	0.988745i	0.914903	−	0.403674i	$-0.132267\pi$
$354$	13.2194	+	2.00332i	0.702602	+	0.106475i
$355$	−0.904293	+	9.57122i	−0.0479949	+	0.507988i
$356$	−1.54074	−	14.6592i	−0.0816592	−	0.776935i
$357$	−0.417037	−	0.266884i	−0.0220720	−	0.0141250i
$358$	21.4459	+	9.54833i	1.13345	+	0.504645i
$359$	1.18928	+	3.66023i	0.0627679	+	0.193180i	0.977523	−	0.210829i	$-0.0676164\pi$
$359$	1.18928	+	3.66023i	0.0627679	+	0.193180i	−0.914755	+	0.404009i	$0.867616\pi$
$360$	−15.5733	−	13.3629i	−0.820783	−	0.704287i
$361$	1.58171	−	4.86800i	0.0832479	−	0.256211i
$362$	−12.9903	+	14.4271i	−0.682752	+	0.758273i
$363$	27.1439	−	7.46788i	1.42468	−	0.391962i
$364$	−1.35250	−	1.50210i	−0.0708901	−	0.0787315i
$365$	33.5951	−	7.51106i	1.75845	−	0.393147i
$366$	8.29687	−	2.28265i	0.433684	−	0.119316i
$367$	21.1594	+	9.42078i	1.10451	+	0.491761i	0.876259	−	0.481841i	$-0.160032\pi$
$367$	21.1594	+	9.42078i	1.10451	+	0.491761i	0.228254	+	0.973602i	$0.426698\pi$
$368$	0.166042			0.00865554
$369$	−20.4967	−	11.4714i	−1.06702	−	0.597180i
$370$	−0.306425	+	0.543877i	−0.0159303	+	0.0282748i
$371$	0.373437	−	3.55302i	0.0193879	−	0.184464i
$372$	2.14013	+	5.46583i	0.110961	+	0.283390i
$373$	−11.0705	−	12.2951i	−0.573210	−	0.636614i	0.384919	−	0.922950i	$-0.374229\pi$
$373$	−11.0705	−	12.2951i	−0.573210	−	0.636614i	−0.958129	+	0.286336i	$0.907563\pi$
$374$	1.27023	−	2.20010i	0.0656820	−	0.113765i
$375$	19.2283	+	2.29596i	0.992947	+	0.118563i
$376$	16.2026	+	28.0638i	0.835587	+	1.44728i
$377$	11.8145	−	36.3612i	0.608477	−	1.87270i
$378$	−0.985657	−	3.40413i	−0.0506967	−	0.175090i
$379$	−18.9711	−	13.7833i	−0.974478	−	0.708000i	−0.0180106	−	0.999838i	$-0.505733\pi$
$379$	−18.9711	−	13.7833i	−0.974478	−	0.708000i	−0.956468	+	0.291838i	$0.905733\pi$
$380$	−9.21236	+	0.0969084i	−0.472584	+	0.00497130i
$381$	4.35403	−	8.68826i	0.223064	−	0.445113i
$382$	−5.50218	+	9.53006i	−0.281516	+	0.487600i
$383$	2.27612	+	21.6559i	0.116304	+	1.10656i	0.884562	+	0.466422i	$0.154457\pi$
$383$	2.27612	+	21.6559i	0.116304	+	1.10656i	−0.768258	+	0.640140i	$0.778876\pi$
$384$	0.0797188	−	0.305668i	0.00406813	−	0.0155985i
$385$	2.20925	−	7.05088i	0.112594	−	0.359346i
$386$	4.23305	−	13.0280i	0.215457	−	0.663107i
$387$	4.89004	+	21.5838i	0.248575	+	1.09716i
$388$	1.58063	+	4.86466i	0.0802441	+	0.246966i
$389$	1.06664	−	0.226720i	0.0540805	−	0.0114952i	−0.180792	−	0.983521i	$-0.557866\pi$
$389$	1.06664	−	0.226720i	0.0540805	−	0.0114952i	0.234873	+	0.972026i	$0.424533\pi$
$390$	5.94682	+	14.7297i	0.301129	+	0.745865i
$391$	0.0453255	+	0.00963424i	0.00229221	+	0.000487224i
$392$	−2.11018	−	20.0770i	−0.106580	−	1.01404i
$393$	−0.434437	+	9.50389i	−0.0219145	+	0.479408i
$394$	−6.65912	−	2.96483i	−0.335482	−	0.149366i
$395$	2.77465	−	1.27049i	0.139608	−	0.0639255i
$396$	−12.4408	+	4.22683i	−0.625173	+	0.212406i
$397$	−15.4671	−	11.2375i	−0.776274	−	0.563996i	0.127585	−	0.991828i	$-0.459278\pi$
$397$	−15.4671	−	11.2375i	−0.776274	−	0.563996i	−0.903858	+	0.427832i	$0.859278\pi$
$398$	−7.47901	+	1.58971i	−0.374889	+	0.0796850i
$399$	−4.53501	−	2.90218i	−0.227034	−	0.145291i
$400$	−2.66170	−	7.64105i	−0.133085	−	0.382052i
$401$	0.466700	−	0.808348i	0.0233059	−	0.0403670i	−0.854137	−	0.520048i	$-0.825914\pi$
$401$	0.466700	−	0.808348i	0.0233059	−	0.0403670i	0.877443	+	0.479681i	$0.159248\pi$
$402$	1.06115	+	6.42189i	0.0529254	+	0.320295i
$403$	1.60723	−	15.2918i	0.0800620	−	0.761739i
$404$	−2.69227	−	1.95605i	−0.133946	−	0.0973172i
$405$	1.35698	−	20.0788i	0.0674289	−	0.997724i
$406$	−5.54224	+	4.02668i	−0.275057	+	0.199841i
$407$	0.676296	+	1.17138i	0.0335228	+	0.0580631i
$408$	−1.07207	+	2.13926i	−0.0530752	+	0.105909i
$409$	22.3449	+	4.74956i	1.10488	+	0.234851i	0.724019	−	0.689780i	$-0.242293\pi$
$409$	22.3449	+	4.74956i	1.10488	+	0.234851i	0.380866	+	0.924630i	$0.375626\pi$
$410$	−9.60358	−	16.2370i	−0.474287	−	0.801889i
$411$	−13.3171	+	10.9321i	−0.656885	+	0.539240i
$412$	−0.644424	+	0.715705i	−0.0317485	+	0.0352603i
$413$	−1.40126	−	4.31263i	−0.0689514	−	0.212210i
$414$	0.198521	+	0.265703i	0.00975679	+	0.0130586i
$415$	−0.550022	−	4.75175i	−0.0269995	−	0.233254i
$416$	−11.1412	+	12.3736i	−0.546244	+	0.606665i
$417$	4.10473	+	6.22924i	0.201010	+	0.305047i
$418$	13.8129	−	23.9247i	0.675611	−	1.17019i
$419$	1.10970	+	10.5580i	0.0542122	+	0.515794i	0.987607	+	0.156944i	$0.0501643\pi$
$419$	1.10970	+	10.5580i	0.0542122	+	0.515794i	−0.933395	+	0.358850i	$0.883169\pi$
$420$	−0.498056	+	1.99543i	−0.0243026	+	0.0973672i
$421$	−1.92171	+	18.2838i	−0.0936583	+	0.891099i	0.842305	+	0.539001i	$0.181198\pi$
$421$	−1.92171	+	18.2838i	−0.0936583	+	0.891099i	−0.935963	+	0.352098i	$0.885468\pi$
$422$	−23.0968	−	16.7808i	−1.12434	−	0.816878i
$423$	−12.5370	+	29.2025i	−0.609572	+	1.41988i
$424$	−17.2658			−0.838500
$425$	−0.283225	−	2.24026i	−0.0137384	−	0.108669i
$426$	6.75866	+	4.32521i	0.327458	+	0.209557i
$427$	−1.95282	−	2.16883i	−0.0945038	−	0.104957i
$428$	−3.14461	+	1.40007i	−0.152001	+	0.0676751i
$429$	34.0294	+	5.15695i	1.64296	+	0.248980i
$430$	−5.31437	+	16.9610i	−0.256282	+	0.817930i
$431$	−5.96554	+	4.33422i	−0.287350	+	0.208772i	−0.722117	−	0.691771i	$-0.756831\pi$
$431$	−5.96554	+	4.33422i	−0.287350	+	0.208772i	0.434767	+	0.900543i	$0.356831\pi$
$432$	−7.78833	+	3.17015i	−0.374716	+	0.152524i
$433$	4.26267	−	3.09701i	0.204851	−	0.148833i	−0.480630	−	0.876923i	$-0.659592\pi$
$433$	4.26267	−	3.09701i	0.204851	−	0.148833i	0.685481	+	0.728091i	$0.259592\pi$
$434$	−1.84353	+	2.04745i	−0.0884924	+	0.0982808i
$435$	−37.3973	+	10.7132i	−1.79306	+	0.513660i
$436$	−0.0556314	−	0.0617849i	−0.00266426	−	0.00295896i
$437$	0.492885	+	0.104766i	0.0235779	+	0.00501164i
$438$	7.25089	−	27.8023i	0.346461	−	1.32844i
$439$	33.0600	−	7.02713i	1.57787	−	0.335386i	0.666027	−	0.745927i	$-0.267993\pi$
$439$	33.0600	−	7.02713i	1.57787	−	0.335386i	0.911842	+	0.410541i	$0.134660\pi$
$440$	−35.0052	−	7.05657i	−1.66881	−	0.336409i
$441$	14.5345	−	13.4429i	0.692120	−	0.640137i
$442$	1.49853	−	1.08875i	0.0712780	−	0.0517865i
$443$	11.5704	+	20.0405i	0.549726	+	0.952153i	0.998293	+	0.0584042i	$0.0186012\pi$
$443$	11.5704	+	20.0405i	0.549726	+	0.952153i	−0.448567	+	0.893749i	$0.648065\pi$
$444$	−0.207153	−	0.314371i	−0.00983107	−	0.0149194i
$445$	38.3402	−	8.57194i	1.81750	−	0.406349i
$446$	3.87606	−	1.72574i	0.183537	−	0.0817159i
$447$	−0.0841710	+	0.105374i	−0.00398115	+	0.00498403i
$448$	4.92211	−	1.04623i	0.232548	−	0.0494295i
$449$	19.7430			0.931731			0.465866	−	0.884856i	$-0.345743\pi$
$449$	19.7430			0.931731			0.465866	+	0.884856i	$0.345743\pi$
$450$	9.04495	−	13.3950i	0.426383	−	0.631446i
$451$	−40.8741			−1.92469
$452$	10.9104	−	2.31908i	0.513183	−	0.109080i
$453$	−10.8582	−	27.7315i	−0.510164	−	1.30294i
$454$	−23.7788	+	10.5870i	−1.11599	+	0.496873i
$455$	3.56254	−	4.04129i	0.167014	−	0.189458i
$456$	−11.6580	+	23.2630i	−0.545937	+	1.08939i
$457$	−0.754881	−	1.30749i	−0.0353119	−	0.0611619i	0.847829	−	0.530269i	$-0.177909\pi$
$457$	−0.754881	−	1.30749i	−0.0353119	−	0.0611619i	−0.883141	+	0.469107i	$0.844576\pi$
$458$	13.2008	−	9.59095i	0.616834	−	0.448156i
$459$	−2.30997	+	0.413475i	−0.107820	+	0.0192993i
$460$	−0.0221321	−	0.191203i	−0.00103191	−	0.00891490i
$461$	−0.971865	+	0.206576i	−0.0452643	+	0.00962122i	−0.230488	−	0.973075i	$-0.574032\pi$
$461$	−0.971865	+	0.206576i	−0.0452643	+	0.00962122i	0.185224	+	0.982696i	$0.440699\pi$
$462$	−4.38983	−	4.33157i	−0.204233	−	0.201523i
$463$	−18.7069	−	3.97626i	−0.869381	−	0.184793i	−0.248438	−	0.968648i	$-0.579917\pi$
$463$	−18.7069	−	3.97626i	−0.869381	−	0.184793i	−0.620944	+	0.783855i	$0.713250\pi$
$464$	10.8764	+	12.0794i	0.504923	+	0.560774i
$465$	−13.8157	+	7.34143i	−0.640688	+	0.340451i
$466$	−9.20632	+	10.2247i	−0.426474	+	0.473648i
$467$	−7.86342	+	5.71311i	−0.363875	+	0.264371i	−0.754667	−	0.656108i	$-0.772201\pi$
$467$	−7.86342	+	5.71311i	−0.363875	+	0.264371i	0.390791	+	0.920479i	$0.372201\pi$
$468$	−9.54007	−	0.874008i	−0.440990	−	0.0404010i
$469$	1.78593	−	1.29755i	0.0824665	−	0.0599154i
$470$	−20.4901	+	15.2188i	−0.945139	+	0.701991i
$471$	−12.3623	+	15.4764i	−0.569625	+	0.713116i
$472$	−20.0202	+	8.91357i	−0.921505	+	0.410280i
$473$	25.7691	+	28.6195i	1.18487	+	1.31593i
$474$	0.116310	−	2.54443i	0.00534228	−	0.116869i
$475$	−3.07989	−	24.3614i	−0.141315	−	1.11778i
$476$	0.239821			0.0109922
$477$	−10.1349	−	13.5646i	−0.464044	−	0.621080i
$478$	11.1804	+	8.12306i	0.511381	+	0.371540i
$479$	1.61586	−	15.3739i	0.0738307	−	0.702452i	−0.893522	−	0.449019i	$-0.851774\pi$
$479$	1.61586	−	15.3739i	0.0738307	−	0.702452i	0.967353	−	0.253433i	$-0.0815597\pi$
$480$	16.7762	+	2.36209i	0.765727	+	0.107814i
$481$	0.103086	+	0.980795i	0.00470030	+	0.0447204i
$482$	−14.8924	+	25.7944i	−0.678331	+	1.17490i
$483$	0.0503979	−	0.100567i	0.00229318	−	0.00457594i
$484$	−9.12433	+	10.1336i	−0.414742	+	0.460618i
$485$	−12.3955	+	5.67581i	−0.562851	+	0.257725i
$486$	−14.3847	−	8.67271i	−0.652504	−	0.393402i
$487$	4.43743	+	13.6570i	0.201079	+	0.618858i	0.999852	+	0.0172246i	$0.00548302\pi$
$487$	4.43743	+	13.6570i	0.201079	+	0.618858i	−0.798773	+	0.601633i	$0.794517\pi$
$488$	−9.43769	+	10.4816i	−0.427224	+	0.474481i
$489$	1.28683	+	7.78766i	0.0581925	+	0.352170i
$490$	15.5175	−	3.46933i	0.701007	−	0.156728i
$491$	3.67039	+	0.780165i	0.165642	+	0.0352084i	0.289986	−	0.957031i	$-0.406349\pi$
$491$	3.67039	+	0.780165i	0.165642	+	0.0352084i	−0.124344	+	0.992239i	$0.539683\pi$
$492$	11.3572	−	0.671311i	0.512023	−	0.0302650i
$493$	2.26811	+	3.92848i	0.102150	+	0.176930i
$494$	16.2956	−	11.8394i	0.733173	−	0.532681i
$495$	−15.0039	−	31.6434i	−0.674374	−	1.42227i
$496$	5.28863	+	3.84242i	0.237467	+	0.172530i
$497$	0.284464	−	2.70649i	0.0127599	−	0.121403i
$498$	−3.73680	−	1.40585i	−0.167450	−	0.0629978i
$499$	−1.24260	+	2.15224i	−0.0556263	+	0.0963476i	−0.892498	−	0.451052i	$-0.851049\pi$
$499$	−1.24260	+	2.15224i	−0.0556263	+	0.0963476i	0.836871	+	0.547400i	$0.184382\pi$
$500$	−8.44416	+	4.08353i	−0.377634	+	0.182621i
$501$	1.18419	−	25.9058i	0.0529058	−	1.15738i
$502$	3.04587	−	0.647421i	0.135944	−	0.0288958i
$503$	−2.61295	−	1.89842i	−0.116506	−	0.0846463i	0.528007	−	0.849240i	$-0.322940\pi$
$503$	−2.61295	−	1.89842i	−0.116506	−	0.0846463i	−0.644512	+	0.764594i	$0.722940\pi$
$504$	4.36831	+	3.82881i	0.194580	+	0.170549i
$505$	4.35384	−	7.72766i	0.193743	−	0.343877i
$506$	0.527273	+	0.234757i	0.0234402	+	0.0104362i
$507$	2.17145	+	1.38962i	0.0964376	+	0.0617154i
$508$	0.492033	+	4.68138i	0.0218304	+	0.207703i
$509$	−12.1415	−	2.58076i	−0.538163	−	0.114390i	−0.0691916	−	0.997603i	$-0.522042\pi$
$509$	−12.1415	−	2.58076i	−0.538163	−	0.114390i	−0.468972	+	0.883213i	$0.655375\pi$
$510$	−1.77088	−	0.645058i	−0.0784160	−	0.0285636i
$511$	−9.53164	+	2.02601i	−0.421655	+	0.0896255i
$512$	−5.24697	−	16.1485i	−0.231885	−	0.713670i
$513$	−25.1194	+	4.49627i	−1.10905	+	0.198515i
$514$	−1.99946	+	6.15369i	−0.0881922	+	0.271428i
$515$	−2.09243	−	1.48687i	−0.0922036	−	0.0655191i
$516$	−7.63022	−	7.52896i	−0.335902	−	0.331444i
$517$	5.78070	+	54.9997i	0.254235	+	2.41888i
$518$	0.0883547	−	0.153035i	0.00388208	−	0.00672397i
$519$	−6.17873	+	0.365217i	−0.271216	+	0.0160312i
$520$	−21.2236	−	15.0813i	−0.930717	−	0.661360i
$521$	18.5974	+	13.5118i	0.814765	+	0.591962i	0.915208	−	0.402981i	$-0.132026\pi$
$521$	18.5974	+	13.5118i	0.814765	+	0.591962i	−0.100443	+	0.994943i	$0.532026\pi$
$522$	−6.32578	+	31.8468i	−0.276872	+	1.39390i
$523$	−6.02620	+	18.5468i	−0.263508	+	0.810993i	0.728526	+	0.685018i	$0.240206\pi$
$523$	−6.02620	+	18.5468i	−0.263508	+	0.810993i	−0.992033	+	0.125975i	$0.959794\pi$
$524$	−2.30409	−	3.99080i	−0.100654	−	0.174339i
$525$	−5.43584	−	0.707138i	−0.237240	−	0.0308620i
$526$	−7.38188	+	12.7858i	−0.321865	+	0.557487i
$527$	1.22072	+	1.35575i	0.0531755	+	0.0590574i
$528$	−9.13252	+	11.4331i	−0.397442	+	0.497560i
$529$	2.40305	−	22.8635i	0.104481	−	0.994067i
$530$	−1.56369	−	13.5090i	−0.0679224	−	0.586794i
$531$	−18.7545	−	10.4964i	−0.813876	−	0.455503i
$532$	2.60790			0.113067
$533$	−27.2255	−	12.1216i	−1.17927	−	0.525043i
$534$	8.27502	−	31.7291i	0.358095	−	1.37305i
$535$	−4.67063	−	7.89675i	−0.201929	−	0.341406i
$536$	−7.13872	−	7.92835i	−0.308346	−	0.342453i
$537$	−26.8606	−	26.5041i	−1.15912	−	1.14374i
$538$	11.8988	−	13.2149i	0.512992	−	0.569736i
$539$	10.6463	−	32.7658i	0.458567	−	1.41132i
$540$	4.68867	+	8.54598i	0.201768	+	0.367760i
$541$	−4.92323	−	15.1521i	−0.211666	−	0.651442i	−0.999374	−	0.0353920i	$-0.988732\pi$
$541$	−4.92323	−	15.1521i	−0.211666	−	0.651442i	0.787707	−	0.616050i	$-0.211268\pi$
$542$	5.72214	+	2.54766i	0.245787	+	0.109431i
$543$	27.7097	−	14.3528i	1.18914	−	0.615936i
$544$	−0.206499	−	1.96471i	−0.00885358	−	0.0842362i
$545$	0.146535	−	0.166228i	0.00627689	−	0.00712041i
$546$	−1.63942	−	4.18702i	−0.0701607	−	0.179188i
$547$	1.52095	−	14.4708i	0.0650310	−	0.618729i	−0.912666	−	0.408707i	$-0.865980\pi$
$547$	1.52095	−	14.4708i	0.0650310	−	0.618729i	0.977697	−	0.210022i	$-0.0673535\pi$
$548$	2.57887	−	7.93695i	0.110164	−	0.339050i
$549$	−13.7746	−	1.26195i	−0.587884	−	0.0538587i
$550$	2.35090	−	28.0277i	0.100243	−	1.19510i
$551$	24.6642	+	42.7196i	1.05073	+	1.81992i
$552$	−0.508820	−	0.191428i	−0.0216568	−	0.00814771i
$553$	−0.789164	+	0.351358i	−0.0335587	+	0.0149413i
$554$	22.0979	−	9.83860i	0.938848	−	0.418002i
$555$	0.768857	−	0.644815i	0.0326362	−	0.0273709i
$556$	−3.30100	−	1.46970i	−0.139994	−	0.0623291i
$557$	31.2370			1.32355			0.661776	−	0.749701i	$-0.269803\pi$
$557$	31.2370			1.32355			0.661776	+	0.749701i	$0.269803\pi$
$558$	0.174456	+	13.0570i	0.00738530	+	0.552745i
$559$	8.67697	+	26.7050i	0.366997	+	1.12950i
$560$	0.730657	+	2.17076i	0.0308759	+	0.0917316i
$561$	−3.15634	+	2.59106i	−0.133261	+	0.109394i
$562$	24.3836	+	5.18289i	1.02856	+	0.218627i
$563$	39.2819	+	8.34963i	1.65554	+	0.351895i	0.938537	−	0.345179i	$-0.112182\pi$
$563$	39.2819	+	8.34963i	1.65554	+	0.351895i	0.716999	+	0.697074i	$0.245515\pi$
$564$	−2.50953	−	15.1872i	−0.105670	−	0.639497i
$565$	9.48382	+	28.1762i	0.398987	+	1.18538i
$566$	6.23691	+	19.1952i	0.262157	+	0.806836i
$567$	−0.443887	+	5.67937i	−0.0186415	+	0.238511i
$568$	−13.1521			−0.551850
$569$	29.0226	+	12.9217i	1.21669	+	0.541706i	0.911782	−	0.410675i	$-0.134707\pi$
$569$	29.0226	+	12.9217i	1.21669	+	0.541706i	0.304910	+	0.952381i	$0.401374\pi$
$570$	−19.2572	−	7.01458i	−0.806594	−	0.293808i
$571$	−17.6053	+	7.83839i	−0.736759	+	0.328026i	−0.740582	−	0.671966i	$-0.765450\pi$
$571$	−17.6053	+	7.83839i	−0.736759	+	0.328026i	0.00382238	+	0.999993i	$0.498783\pi$
$572$	−15.2296	+	6.78066i	−0.636782	+	0.283514i
$573$	13.6721	−	11.2235i	0.571162	−	0.468870i
$574$	2.67000	+	4.62457i	0.111444	+	0.193026i
$575$	0.499456	−	0.117196i	0.0208288	−	0.00488741i
$576$	13.7596	−	19.4806i	0.573317	−	0.811691i
$577$	9.95121	−	30.6267i	0.414274	−	1.27500i	−0.498624	−	0.866818i	$-0.666161\pi$
$577$	9.95121	−	30.6267i	0.414274	−	1.27500i	0.912898	−	0.408187i	$-0.133839\pi$
$578$	1.89177	−	17.9990i	0.0786871	−	0.748658i
$579$	−13.7426	+	17.2045i	−0.571125	+	0.714994i
$580$	12.4602	−	14.1346i	0.517381	−	0.586909i
$581$	0.141538	+	1.34665i	0.00587199	+	0.0558683i
$582$	−0.519602	+	11.3670i	−0.0215382	+	0.471177i
$583$	−26.9182	−	11.9848i	−1.11484	−	0.496359i
$584$	14.5529	+	44.7891i	0.602202	+	1.85339i
$585$	−0.609674	−	25.5266i	−0.0252069	−	1.05540i
$586$	4.87425	−	15.0014i	0.201353	−	0.619702i
$587$	−7.74963	+	8.60684i	−0.319862	+	0.355242i	−0.881537	−	0.472116i	$-0.843490\pi$
$587$	−7.74963	+	8.60684i	−0.319862	+	0.355242i	0.561675	+	0.827358i	$0.310157\pi$
$588$	−2.42002	+	9.27913i	−0.0997998	+	0.382665i
$589$	13.2746	+	14.7429i	0.546968	+	0.607470i
$590$	−8.78726	−	14.8569i	−0.361766	−	0.611647i
$591$	8.34042	+	8.22973i	0.343079	+	0.338526i
$592$	−0.383032	−	0.170537i	−0.0157425	−	0.00700903i
$593$	−22.3537			−0.917955			−0.458977	−	0.888448i	$-0.651784\pi$
$593$	−22.3537			−0.917955			−0.458977	+	0.888448i	$0.651784\pi$
$594$	−29.2142	−	0.944516i	−1.19868	−	0.0387539i
$595$	0.0734979	+	0.634962i	0.00301312	+	0.0260309i
$596$	0.00682821	−	0.0649660i	0.000279694	−	0.00266111i
$597$	12.1519	+	1.84154i	0.497343	+	0.0753693i
$598$	0.281588	+	0.312735i	0.0115150	+	0.0127887i
$599$	−2.18765	+	3.78911i	−0.0893848	+	0.154819i	−0.907251	−	0.420589i	$-0.861823\pi$
$599$	−2.18765	+	3.78911i	−0.0893848	+	0.154819i	0.817866	+	0.575408i	$0.195157\pi$
$600$	−0.652741	+	26.4839i	−0.0266480	+	1.08120i
$601$	−7.07808	−	12.2596i	−0.288721	−	0.500079i	0.684784	−	0.728746i	$-0.259897\pi$
$601$	−7.07808	−	12.2596i	−0.288721	−	0.500079i	−0.973505	+	0.228667i	$0.926563\pi$
$602$	1.55476	−	4.78507i	0.0633674	−	0.195025i
$603$	2.03841	−	10.2623i	0.0830106	−	0.417913i
$604$	11.6702	+	8.47889i	0.474853	+	0.345001i
$605$	−29.6265	−	21.0524i	−1.20449	−	0.855901i
$606$	−4.07340	−	6.18169i	−0.165471	−	0.251114i
$607$	17.2199	−	29.8257i	0.698933	−	1.21059i	−0.269904	−	0.962887i	$-0.586992\pi$
$607$	17.2199	−	29.8257i	0.698933	−	1.21059i	0.968837	−	0.247700i	$-0.0796748\pi$
$608$	−2.24554	−	21.3649i	−0.0910688	−	0.866462i
$609$	10.6174	−	2.92108i	0.430239	−	0.118368i
$610$	−9.05572	−	6.43492i	−0.366655	−	0.260542i
$611$	−12.4602	+	38.3486i	−0.504086	+	1.55142i
$612$	0.834462	−	0.771787i	0.0337311	−	0.0311976i
$613$	−2.88297	−	8.87288i	−0.116442	−	0.358372i	0.875803	−	0.482669i	$-0.160333\pi$
$613$	−2.88297	−	8.87288i	−0.116442	−	0.358372i	−0.992245	+	0.124297i	$0.960333\pi$
$614$	−35.7667	+	7.60244i	−1.44342	+	0.306809i
$615$	5.25804	+	29.8642i	0.212025	+	1.20424i
$616$	9.88739	+	2.10163i	0.398374	+	0.0846771i
$617$	2.26139	+	21.5157i	0.0910401	+	0.866189i	0.940787	+	0.338998i	$0.110088\pi$
$617$	2.26139	+	21.5157i	0.0910401	+	0.866189i	−0.849747	+	0.527191i	$0.823245\pi$
$618$	−1.90241	+	0.985387i	−0.0765260	+	0.0396381i
$619$	14.6861	+	6.53867i	0.590284	+	0.262811i	0.680067	−	0.733150i	$-0.261951\pi$
$619$	14.6861	+	6.53867i	0.590284	+	0.262811i	−0.0897832	+	0.995961i	$0.528617\pi$
$620$	3.71975	−	6.60221i	0.149389	−	0.265151i
$621$	−0.148281	−	0.512113i	−0.00595031	−	0.0205504i
$622$	−7.95021	−	5.77617i	−0.318774	−	0.231603i
$623$	−10.8779	+	2.31217i	−0.435814	+	0.0926352i
$624$	−9.47357	+	4.90701i	−0.379246	+	0.196438i
$625$	−13.3996	−	21.1057i	−0.535986	−	0.844227i
$626$	12.7690	−	22.1166i	0.510354	−	0.883958i
$627$	−34.3231	+	28.1760i	−1.37073	+	1.12524i
$628$	1.00287	−	9.54165i	0.0400188	−	0.380753i
$629$	−0.0946637	−	0.0687772i	−0.00377449	−	0.00274233i
$630$	−2.60011	+	3.76459i	−0.103591	+	0.149985i
$631$	36.4652	−	26.4935i	1.45165	−	1.05469i	0.466214	−	0.884672i	$-0.345618\pi$
$631$	36.4652	−	26.4935i	1.45165	−	1.05469i	0.985441	−	0.170017i	$-0.0543823\pi$
$632$	2.08742	+	3.61552i	0.0830331	+	0.143818i
$633$	25.2507	+	38.3198i	1.00362	+	1.52307i
$634$	30.4391	+	6.47004i	1.20889	+	0.256958i
$635$	−12.2439	+	2.73743i	−0.485883	+	0.108632i
$636$	7.67631	+	2.88797i	0.304385	+	0.114516i
$637$	16.8083	−	18.6675i	0.665968	−	0.739632i
$638$	17.4600	+	53.7363i	0.691247	+	2.12744i
$639$	−7.72018	−	10.3327i	−0.305406	−	0.408757i
$640$	−0.370792	+	0.169783i	−0.0146568	+	0.00671126i
$641$	−21.9255	+	24.3507i	−0.866005	+	0.961796i	−0.999572	−	0.0292433i	$-0.990690\pi$
$641$	−21.9255	+	24.3507i	−0.866005	+	0.961796i	0.133567	+	0.991040i	$0.457357\pi$
$642$	−7.64420	+	0.451839i	−0.301692	+	0.0178327i
$643$	−1.00181	+	1.73519i	−0.0395077	+	0.0684294i	−0.885103	−	0.465395i	$-0.845912\pi$
$643$	−1.00181	+	1.73519i	−0.0395077	+	0.0684294i	0.845595	+	0.533824i	$0.179246\pi$
$644$	0.00569529	+	0.0541870i	0.000224426	+	0.00213527i
$645$	17.5956	−	22.5096i	0.692826	−	0.886313i
$646$	−0.249809	+	2.37677i	−0.00982861	+	0.0935130i
$647$	8.36159	+	6.07505i	0.328728	+	0.238835i	0.739891	−	0.672727i	$-0.234877\pi$
$647$	8.36159	+	6.07505i	0.328728	+	0.238835i	−0.411163	+	0.911562i	$0.634877\pi$
$648$	27.5214	−	0.735565i	1.08114	−	0.0288957i
$649$	−37.3997			−1.46807
$650$	9.87774	−	17.9715i	0.387437	−	0.704902i
$651$	3.93247	−	2.03690i	0.154126	−	0.0798322i
$652$	−2.55824	−	2.84121i	−0.100188	−	0.111271i
$653$	11.7357	−	5.22507i	0.459253	−	0.204473i	−0.164051	−	0.986452i	$-0.552456\pi$
$653$	11.7357	−	5.22507i	0.459253	−	0.204473i	0.623305	+	0.781979i	$0.285790\pi$
$654$	−0.0674331	−	0.172222i	−0.00263684	−	0.00673440i
$655$	9.86009	−	7.32347i	0.385266	−	0.286152i
$656$	10.2505	−	7.44740i	0.400214	−	0.290772i
$657$	−26.6454	+	37.7241i	−1.03954	+	1.47176i
$658$	5.84516	−	4.24676i	0.227868	−	0.165556i
$659$	3.17399	−	3.52507i	0.123641	−	0.137317i	−0.678146	−	0.734927i	$-0.737216\pi$
$659$	3.17399	−	3.52507i	0.123641	−	0.137317i	0.801787	+	0.597610i	$0.203883\pi$
$660$	14.3829	+	8.99249i	0.559852	+	0.350032i
$661$	2.71132	+	3.01122i	0.105458	+	0.117123i	0.793563	−	0.608488i	$-0.208224\pi$
$661$	2.71132	+	3.01122i	0.105458	+	0.117123i	−0.688105	+	0.725611i	$0.741557\pi$
$662$	25.7147	+	5.46584i	0.999432	+	0.212436i
$663$	−2.87078	+	0.789814i	−0.111492	+	0.0306738i
$664$	6.40098	−	1.36057i	0.248406	−	0.0528003i
$665$	0.799241	+	6.90479i	0.0309932	+	0.267756i
$666$	−0.185062	−	0.816829i	−0.00717099	−	0.0316515i
$667$	−0.833768	+	0.605768i	−0.0322836	+	0.0234554i
$668$	6.28049	+	10.8781i	0.242999	+	0.420887i
$669$	−6.80829	+	0.402429i	−0.263224	+	0.0155588i
$670$	5.55674	−	6.30348i	0.214676	−	0.243525i
$671$	−21.9895	+	9.79036i	−0.848896	+	0.377953i
$672$	−4.74157	−	0.718555i	−0.182910	−	0.0277189i
$673$	49.3370	−	10.4869i	1.90180	−	0.404240i	0.902169	−	0.431383i	$-0.141974\pi$
$673$	49.3370	−	10.4869i	1.90180	−	0.404240i	0.999632	+	0.0271429i	$0.00864092\pi$
$674$	−1.39886			−0.0538822
$675$	−21.1898	+	15.0330i	−0.815596	+	0.578621i
$676$	−1.24871			−0.0480274
$677$	33.9900	−	7.22480i	1.30634	−	0.277672i	0.498407	−	0.866943i	$-0.333919\pi$
$677$	33.9900	−	7.22480i	1.30634	−	0.277672i	0.807935	+	0.589272i	$0.200585\pi$
$678$	24.5335	+	3.71789i	0.942202	+	0.142785i
$679$	3.52552	−	1.56966i	0.135297	−	0.0602380i
$680$	3.01473	−	0.674022i	0.115610	−	0.0258475i
$681$	41.7674	−	2.46882i	1.60053	−	0.0946053i
$682$	11.3617	+	19.6790i	0.435062	+	0.753549i
$683$	−33.1970	+	24.1191i	−1.27025	+	0.922890i	−0.999213	−	0.0396784i	$-0.987367\pi$
$683$	−33.1970	+	24.1191i	−1.27025	+	0.922890i	−0.271037	+	0.962569i	$0.587367\pi$
$684$	9.07422	−	8.39268i	0.346962	−	0.320902i
$685$	21.8046	+	4.39551i	0.833111	+	0.167944i
$686$	−9.07254	+	1.92843i	−0.346391	+	0.0736278i
$687$	−25.2891	+	6.95759i	−0.964840	+	0.265449i
$688$	−11.6770	−	2.48203i	−0.445182	−	0.0946263i
$689$	−14.3756	−	15.9657i	−0.547665	−	0.608243i
$690$	0.103694	−	0.415446i	0.00394758	−	0.0158157i
$691$	−14.7552	+	16.3873i	−0.561315	+	0.623403i	−0.955273	−	0.295725i	$-0.904439\pi$
$691$	−14.7552	+	16.3873i	−0.561315	+	0.623403i	0.393958	+	0.919128i	$0.371105\pi$
$692$	2.42543	−	1.76218i	0.0922009	−	0.0669879i
$693$	4.15271	+	9.00151i	0.157748	+	0.341939i
$694$	−15.0708	+	10.9496i	−0.572079	+	0.415640i
$695$	2.87959	−	9.19030i	0.109229	−	0.348608i
$696$	−19.4034	−	49.5556i	−0.735484	−	1.87840i
$697$	3.23025	−	1.43820i	0.122355	−	0.0544758i
$698$	−20.9579	−	23.2761i	−0.793269	−	0.881014i
$699$	19.6381	−	10.1719i	0.742782	−	0.384738i
$700$	2.40232	−	1.13072i	0.0907993	−	0.0427373i
$701$	0.897737			0.0339071			0.0169535	−	0.999856i	$-0.494603\pi$
$701$	0.897737			0.0339071			0.0169535	+	0.999856i	$0.494603\pi$
$702$	−19.1790	−	9.29286i	−0.723863	−	0.350736i
$703$	−1.02941	−	0.747907i	−0.0388247	−	0.0282078i
$704$	4.33825	−	41.2757i	0.163504	−	1.55564i
$705$	39.4413	−	11.2988i	1.48544	−	0.425536i
$706$	2.10386	+	20.0169i	0.0791800	+	0.753347i
$707$	−1.25539	+	2.17439i	−0.0472137	+	0.0817765i
$708$	10.3918	−	0.614249i	0.390550	−	0.0230849i
$709$	27.7781	−	30.8507i	1.04323	−	1.15862i	0.0561432	−	0.998423i	$-0.482120\pi$
$709$	27.7781	−	30.8507i	1.04323	−	1.15862i	0.987085	−	0.160199i	$-0.0512137\pi$
$710$	−1.19113	−	10.2904i	−0.0447024	−	0.386193i
$711$	−1.61518	+	3.76223i	−0.0605738	+	0.141095i
$712$	16.6083	+	51.1152i	0.622424	+	1.91562i
$713$	−0.277339	+	0.308016i	−0.0103864	+	0.0115353i
$714$	0.499337	+	0.187860i	0.0186872	+	0.00703049i
$715$	−22.6202	−	38.2446i	−0.845949	−	1.43027i
$716$	17.8783	+	3.80016i	0.668145	+	0.142019i
$717$	−12.2230	−	18.5494i	−0.456478	−	0.692739i
$718$	−2.07347	−	3.59136i	−0.0773813	−	0.134028i
$719$	34.2388	−	24.8759i	1.27689	−	0.927716i	0.277437	−	0.960744i	$-0.410515\pi$
$719$	34.2388	−	24.8759i	1.27689	−	0.927716i	0.999454	+	0.0330279i	$0.0105150\pi$
$720$	9.52824	+	5.20183i	0.355097	+	0.193861i
$721$	0.587847	+	0.427096i	0.0218926	+	0.0159059i
$722$	−0.576508	+	5.48510i	−0.0214554	+	0.204134i
$723$	37.0056	−	30.3780i	1.37625	−	1.12977i
$724$	−7.55762	+	13.0902i	−0.280877	+	0.486493i
$725$	41.2422	+	28.6583i	1.53170	+	1.06434i
$726$	−26.9360	+	13.9520i	−0.999687	+	0.517807i
$727$	−10.7038	+	2.27517i	−0.396983	+	0.0843814i	−0.402078	−	0.915606i	$-0.631712\pi$
$727$	−10.7038	+	2.27517i	−0.396983	+	0.0843814i	0.00509419	+	0.999987i	$0.498378\pi$
$728$	5.96255	+	4.33205i	0.220987	+	0.160556i
$729$	16.7327	+	21.1900i	0.619731	+	0.784815i
$730$	−33.7257	+	15.4428i	−1.24824	+	0.571562i
$731$	−3.04353	−	1.35507i	−0.112569	−	0.0501190i
$732$	5.94918	−	3.08149i	0.219888	−	0.113895i
$733$	−0.132815	−	1.26365i	−0.00490562	−	0.0466738i	0.991795	−	0.127837i	$-0.0408033\pi$
$733$	−0.132815	−	1.26365i	−0.00490562	−	0.0466738i	−0.996701	+	0.0811628i	$0.974137\pi$
$734$	−24.4120	−	5.18894i	−0.901065	−	0.191527i
$735$	−25.3095	−	3.56358i	−0.933557	−	0.131445i
$736$	0.439018	−	0.0933161i	0.0161824	−	0.00343968i
$737$	−5.62629	−	17.3159i	−0.207247	−	0.637841i
$738$	24.1730	+	7.49875i	0.889820	+	0.276033i
$739$	5.82472	−	17.9267i	0.214266	−	0.659443i	−0.784939	−	0.619573i	$-0.787306\pi$
$739$	5.82472	−	17.9267i	0.214266	−	0.659443i	0.999205	−	0.0398696i	$-0.0126943\pi$
$740$	−0.145324	+	0.463807i	−0.00534223	+	0.0170499i
$741$	−31.2178	+	8.58871i	−1.14682	+	0.315514i
$742$	0.402387	+	3.82846i	0.0147721	+	0.140547i
$743$	0.560250	−	0.970382i	0.0205536	−	0.0355999i	−0.855566	−	0.517694i	$-0.826790\pi$
$743$	0.560250	−	0.970382i	0.0205536	−	0.0355999i	0.876119	+	0.482094i	$0.160124\pi$
$744$	−11.7766	−	17.8719i	−0.431752	−	0.655216i
$745$	0.174100	−	0.00183143i	0.00637853	−	6.70982e-5i
$746$	14.4225	+	10.4786i	0.528046	+	0.383648i
$747$	4.82623	+	4.23018i	0.176583	+	0.154774i
$748$	0.611228	−	1.88116i	0.0223487	−	0.0687822i
$749$	1.29853	+	2.24913i	0.0474474	+	0.0821813i
$750$	−20.7805	+	1.88782i	−0.758798	+	0.0689336i
$751$	6.69286	−	11.5924i	0.244226	−	0.423012i	−0.717688	−	0.696365i	$-0.754799\pi$
$751$	6.69286	−	11.5924i	0.244226	−	0.423012i	0.961914	+	0.273353i	$0.0881328\pi$
$752$	−11.4708	−	12.7397i	−0.418298	−	0.464567i
$753$	−4.94893	−	0.749981i	−0.180349	−	0.0273308i
$754$	−4.30619	+	40.9706i	−0.156822	+	1.49206i
$755$	−18.8726	+	33.4971i	−0.686843	+	1.21908i
$756$	−1.30171	−	2.43295i	−0.0473426	−	0.0884854i
$757$	14.0336			0.510062			0.255031	−	0.966933i	$-0.417914\pi$
$757$	14.0336			0.510062			0.255031	+	0.966933i	$0.417914\pi$
$758$	23.0829	+	10.2772i	0.838409	+	0.373284i
$759$	−0.660400	−	0.651635i	−0.0239710	−	0.0236529i
$760$	32.7832	−	7.32954i	1.18917	−	0.265870i
$761$	8.86063	+	9.84073i	0.321198	+	0.356726i	0.882022	−	0.471209i	$-0.156182\pi$
$761$	8.86063	+	9.84073i	0.321198	+	0.356726i	−0.560824	+	0.827935i	$0.689516\pi$
$762$	−2.64261	+	10.1326i	−0.0957318	+	0.367067i
$763$	−0.0419726	+	0.0466153i	−0.00151951	+	0.00168759i
$764$	−2.64762	+	8.14854i	−0.0957875	+	0.294804i
$765$	2.29916	+	1.97283i	0.0831262	+	0.0713279i
$766$	−7.25052	−	22.3148i	−0.261972	−	0.806267i
$767$	−24.9113	−	11.0912i	−0.899494	−	0.400480i
$768$	−1.27310	+	27.8508i	−0.0459392	+	1.00498i
$769$	−1.19628	−	11.3819i	−0.0431390	−	0.410440i	−0.994687	−	0.102941i	$-0.967175\pi$
$769$	−1.19628	−	11.3819i	−0.0431390	−	0.410440i	0.951548	−	0.307499i	$-0.0994920\pi$
$770$	−0.748888	+	7.92639i	−0.0269881	+	0.285647i
$771$	6.49125	−	8.12643i	0.233777	−	0.292666i
$772$	1.11484	−	10.6070i	0.0401241	−	0.381756i
$773$	−9.74410	+	29.9892i	−0.350471	+	1.07864i	0.608119	+	0.793846i	$0.291925\pi$
$773$	−9.74410	+	29.9892i	−0.350471	+	1.07864i	−0.958589	+	0.284792i	$0.908075\pi$
$774$	−9.98938	−	21.6532i	−0.359061	−	0.778309i
$775$	18.6203	+	7.82520i	0.668862	+	0.281090i
$776$	−9.32535	−	16.1520i	−0.334761	−	0.579823i
$777$	−0.219549	+	0.180229i	−0.00787628	+	0.00646568i
$778$	−1.07341	+	0.477915i	−0.0384838	+	0.0171341i
$779$	35.1269	−	15.6395i	1.25855	−	0.560343i
$780$	6.91335	+	10.2551i	0.247538	+	0.367191i
$781$	−20.5048	−	9.12933i	−0.733720	−	0.326673i
$782$	−0.0499303			−0.00178550
$783$	27.5429	−	44.3327i	0.984303	−	1.58432i
$784$	3.30017	+	10.1569i	0.117863	+	0.362745i
$785$	25.5703	−	0.268984i	0.912642	−	0.00960044i
$786$	−1.67127	−	10.1142i	−0.0596121	−	0.360761i
$787$	33.4612	+	7.11239i	1.19276	+	0.253529i	0.761178	−	0.648543i	$-0.224622\pi$
$787$	33.4612	+	7.11239i	1.19276	+	0.253529i	0.431584	+	0.902073i	$0.357955\pi$
$788$	−5.55136	−	1.17998i	−0.197759	−	0.0420350i
$789$	18.3429	−	15.0578i	0.653025	−	0.536072i
$790$	−2.63979	+	1.96067i	−0.0939195	+	0.0697576i
$791$	−2.60055	−	8.00367i	−0.0924649	−	0.284578i
$792$	41.1668	−	24.5067i	1.46280	−	0.870809i
$793$	−17.5502			−0.623226
$794$	18.8195	+	8.37899i	0.667880	+	0.297359i
$795$	−5.29378	+	21.2092i	−0.187751	+	0.752214i
$796$	−5.43849	+	2.42137i	−0.192762	+	0.0858232i
$797$	−34.2521	+	15.2500i	−1.21327	+	0.540183i	−0.910750	−	0.412959i	$-0.864495\pi$
$797$	−34.2521	+	15.2500i	−1.21327	+	0.540183i	−0.302522	+	0.953142i	$0.597829\pi$
$798$	5.42996	+	2.04285i	0.192219	+	0.0723163i
$799$	−2.39207	−	4.14319i	−0.0846255	−	0.146576i
$800$	−11.3319	−	18.7072i	−0.400642	−	0.661398i
$801$	−30.4089	+	43.0523i	−1.07445	+	1.52118i
$802$	−0.310796	+	0.956533i	−0.0109746	+	0.0337764i
$803$	−8.40100	+	79.9302i	−0.296465	+	2.82068i
$804$	1.84771	+	4.71898i	0.0651637	+	0.166426i
$805$	−0.141723	+	0.0316858i	−0.00499507	+	0.00111678i
$806$	1.73183	+	16.4772i	0.0610011	+	0.580386i
$807$	−25.3814	+	13.1468i	−0.893469	+	0.462789i
$808$	11.0851	+	4.93541i	0.389973	+	0.173627i
$809$	−2.07744	−	6.39370i	−0.0730388	−	0.224790i	0.907872	−	0.419247i	$-0.137706\pi$
$809$	−2.07744	−	6.39370i	−0.0730388	−	0.224790i	−0.980911	+	0.194456i	$0.937706\pi$
$810$	3.06802	+	21.4666i	0.107799	+	0.754258i
$811$	−0.0417238	+	0.128413i	−0.00146512	+	0.00450918i	−0.951786	−	0.306762i	$-0.900755\pi$
$811$	−0.0417238	+	0.128413i	−0.00146512	+	0.00450918i	0.950321	+	0.311271i	$0.100755\pi$
$812$	−3.56901	+	3.96378i	−0.125248	+	0.139102i
$813$	−7.16688	−	7.07176i	−0.251353	−	0.248018i
$814$	−0.975223	−	1.08309i	−0.0341815	−	0.0379625i
$815$	6.73851	−	7.64407i	0.236040	−	0.267760i
$816$	0.319453	−	1.22489i	0.0111831	−	0.0428796i
$817$	−33.0964	−	14.7355i	−1.15790	−	0.515529i
$818$	−24.6150			−0.860644
$819$	0.0965643	+	7.22726i	0.00337423	+	0.252541i
$820$	−9.94226	−	10.8111i	−0.347199	−	0.377540i
$821$	−0.235317	+	2.23889i	−0.00821263	+	0.0781380i	−0.997861	−	0.0653788i	$-0.979174\pi$
$821$	−0.235317	+	2.23889i	−0.00821263	+	0.0781380i	0.989648	+	0.143517i	$0.0458411\pi$
$822$	11.5868	−	14.5056i	0.404136	−	0.505940i
$823$	−37.4208	−	41.5600i	−1.30441	−	1.44869i	−0.818297	−	0.574795i	$-0.805082\pi$
$823$	−37.4208	−	41.5600i	−1.30441	−	1.44869i	−0.486111	−	0.873897i	$-0.661585\pi$
$824$	1.75582	−	3.04117i	0.0611668	−	0.105944i
$825$	−19.4011	+	40.8367i	−0.675458	+	1.42175i
$826$	2.44304	+	4.23148i	0.0850044	+	0.147232i
$827$	−9.90533	+	30.4855i	−0.344442	+	1.06008i	0.617440	+	0.786618i	$0.288170\pi$
$827$	−9.90533	+	30.4855i	−0.344442	+	1.06008i	−0.961882	+	0.273466i	$0.911830\pi$
$828$	0.194200	+	0.170216i	0.00674893	+	0.00591543i
$829$	−27.9759	−	20.3257i	−0.971642	−	0.705939i	−0.0158167	−	0.999875i	$-0.505035\pi$
$829$	−27.9759	−	20.3257i	−0.971642	−	0.705939i	−0.955825	+	0.293936i	$0.905035\pi$
$830$	1.64424	+	4.88500i	0.0570724	+	0.169561i
$831$	−38.8148	+	2.29429i	−1.34647	+	0.0795882i
$832$	15.1303	−	26.2064i	0.524548	−	0.908544i
$833$	0.311536	+	2.96407i	0.0107941	+	0.102699i
$834$	−5.72182	−	5.64588i	−0.198130	−	0.195501i
$835$	−26.8767	+	19.9623i	−0.930106	+	0.690825i
$836$	6.64670	−	20.4564i	0.229881	−	0.707500i
$837$	7.12800	−	19.7428i	0.246380	−	0.682411i
$838$	−3.53490	−	10.8793i	−0.122111	−	0.375820i
$839$	−29.9381	+	6.36354i	−1.03358	+	0.219694i	−0.693314	−	0.720636i	$-0.743850\pi$
$839$	−29.9381	+	6.36354i	−1.03358	+	0.219694i	−0.340264	+	0.940330i	$0.610517\pi$
$840$	0.263619	−	7.49447i	0.00909574	−	0.258584i
$841$	−70.3179	−	14.9465i	−2.42476	−	0.515398i
$842$	−2.07068	−	19.7012i	−0.0713604	−	0.678949i
$843$	−33.7512	−	21.5991i	−1.16245	−	0.743913i
$844$	−20.3064	−	9.04100i	−0.698976	−	0.311204i
$845$	−0.382693	−	3.30615i	−0.0131650	−	0.113735i
$846$	6.67151	−	33.5874i	0.229371	−	1.15476i
$847$	8.32326	+	6.04720i	0.285991	+	0.207784i
$848$	8.93427	−	1.89904i	0.306804	−	0.0652133i
$849$	1.48147	−	32.4092i	0.0508441	−	1.11228i
$850$	0.800397	+	2.29773i	0.0274534	+	0.0788115i
$851$	0.0132920	−	0.0230224i	0.000455643	−	0.000789197i
$852$	5.84738	+	2.19990i	0.200328	+	0.0753672i
$853$	−2.79308	+	26.5744i	−0.0956333	+	0.909890i	0.836547	+	0.547895i	$0.184571\pi$
$853$	−2.79308	+	26.5744i	−0.0956333	+	0.909890i	−0.932180	+	0.361995i	$0.882096\pi$
$854$	2.54411	+	1.84840i	0.0870576	+	0.0632511i
$855$	25.0018	+	21.4533i	0.855045	+	0.733686i
$856$	10.1541	−	7.37742i	0.347062	−	0.252155i
$857$	−14.7634	−	25.5710i	−0.504309	−	0.873488i	−0.999988	−	0.00498242i	$-0.998414\pi$
$857$	−14.7634	−	25.5710i	−0.504309	−	0.873488i	0.495679	−	0.868506i	$-0.334919\pi$
$858$	−37.0215	+	2.18829i	−1.26389	+	0.0747071i
$859$	−5.22423	−	1.11044i	−0.178248	−	0.0378879i	0.117923	−	0.993023i	$-0.462377\pi$
$859$	−5.22423	−	1.11044i	−0.178248	−	0.0378879i	−0.296171	+	0.955135i	$0.595710\pi$
$860$	−1.30169	+	13.7773i	−0.0443872	+	0.469803i
$861$	−1.39939	−	8.46888i	−0.0476912	−	0.288619i
$862$	5.31654	−	5.90462i	0.181082	−	0.201112i
$863$	−9.94721	−	30.6144i	−0.338607	−	1.04212i	−0.964918	−	0.262552i	$-0.915436\pi$
$863$	−9.94721	−	30.6144i	−0.338607	−	1.04212i	0.626311	−	0.779573i	$-0.284564\pi$
$864$	−18.8108	+	12.7590i	−0.639957	+	0.434070i
$865$	5.40894	+	5.88163i	0.183910	+	0.199981i
$866$	−3.79893	+	4.21914i	−0.129093	+	0.143372i
$867$	−13.0339	+	26.0084i	−0.442653	+	0.883293i
$868$	−1.07255	+	1.85772i	−0.0364048	+	0.0630550i
$869$	0.744740	+	7.08573i	0.0252636	+	0.240367i
$870$	37.0158	−	19.6696i	1.25495	−	0.666861i
$871$	1.38762	−	13.2023i	0.0470178	−	0.447344i
$872$	0.245254	+	0.178187i	0.00830533	+	0.00603418i
$873$	7.21565	−	16.8074i	0.244213	−	0.568844i
$874$	−0.542959			−0.0183659
$875$	3.73000	+	6.01397i	0.126097	+	0.203309i
$876$	1.02153	−	22.3473i	0.0345142	−	0.755045i
$877$	21.6828	+	24.0811i	0.732175	+	0.813163i	0.988145	−	0.153522i	$-0.0490616\pi$
$877$	21.6828	+	24.0811i	0.732175	+	0.813163i	−0.255970	+	0.966685i	$0.582395\pi$
$878$	−33.2702	+	14.8128i	−1.12281	+	0.499909i
$879$	−15.8243	+	19.8105i	−0.533741	+	0.668193i
$880$	18.8898	−	0.198709i	0.636774	−	0.00669848i
$881$	26.9732	−	19.5972i	0.908750	−	0.660246i	−0.0319481	−	0.999490i	$-0.510171\pi$
$881$	26.9732	−	19.5972i	0.908750	−	0.660246i	0.940699	+	0.339244i	$0.110171\pi$
$882$	−12.3074	+	17.4246i	−0.414413	+	0.586717i
$883$	8.26440	−	6.00444i	0.278119	−	0.202066i	−0.439977	−	0.898009i	$-0.645014\pi$
$883$	8.26440	−	6.00444i	0.278119	−	0.202066i	0.718097	+	0.695943i	$0.245014\pi$
$884$	0.965002	−	1.07174i	0.0324565	−	0.0360466i
$885$	4.81110	+	27.3257i	0.161723	+	0.918544i
$886$	−16.6846	−	18.5301i	−0.560529	−	0.622531i
$887$	−35.8545	−	7.62112i	−1.20388	−	0.255892i	−0.438058	−	0.898947i	$-0.644333\pi$
$887$	−35.8545	−	7.62112i	−1.20388	−	0.255892i	−0.765820	+	0.643055i	$0.777667\pi$
$888$	0.977156	+	0.964188i	0.0327912	+	0.0323560i
$889$	3.47384	−	0.738388i	0.116509	−	0.0247647i
$890$	−38.4892	+	17.6239i	−1.29016	+	0.590756i
$891$	43.4179	+	17.9568i	1.45455	+	0.601575i
$892$	2.67256	−	1.94173i	0.0894838	−	0.0650138i
$893$	−26.0122	−	45.0545i	−0.870466	−	1.50769i
$894$	0.0651073	−	0.129919i	0.00217751	−	0.00434512i
$895$	−4.58232	+	48.5002i	−0.153170	+	1.62118i
$896$	0.105460	−	0.0469539i	0.00352318	−	0.00156862i
$897$	−0.246632	−	0.629889i	−0.00823481	−	0.0210314i
$898$	−20.8087	+	4.42302i	−0.694394	+	0.147598i
$899$	−40.5747			−1.35324
$900$	4.72006	−	11.6655i	0.157335	−	0.388849i
$901$	2.54903			0.0849206
$902$	43.0803	−	9.15699i	1.43442	−	0.304895i
$903$	−5.04755	+	6.31906i	−0.167972	+	0.210285i
$904$	−37.1549	+	16.5424i	−1.23575	+	0.550193i
$905$	−36.9744	−	15.9982i	−1.22907	−	0.531798i
$906$	17.6570	+	26.7957i	0.586613	+	0.890229i
$907$	−10.3737	−	17.9678i	−0.344454	−	0.596612i	0.640800	−	0.767708i	$-0.278603\pi$
$907$	−10.3737	−	17.9678i	−0.344454	−	0.596612i	−0.985254	+	0.171095i	$0.945269\pi$
$908$	−16.3956	+	11.9121i	−0.544106	+	0.395316i
$909$	2.62945	+	11.6059i	0.0872132	+	0.384943i
$910$	−2.84946	+	5.05753i	−0.0944586	+	0.167655i
$911$	55.5454	−	11.8065i	1.84030	−	0.391168i	0.849623	−	0.527390i	$-0.176829\pi$
$911$	55.5454	−	11.8065i	1.84030	−	0.391168i	0.990678	+	0.136222i	$0.0434960\pi$
$912$	3.47384	−	13.3198i	0.115030	−	0.441064i
$913$	10.9239	+	2.32194i	0.361527	+	0.0768450i
$914$	1.08854	+	1.20895i	0.0360058	+	0.0399885i
$915$	9.98195	+	14.8070i	0.329993	+	0.489503i
$916$	8.50085	−	9.44116i	0.280876	−	0.311945i
$917$	−2.81276	+	2.04359i	−0.0928854	+	0.0674852i
$918$	2.34202	−	0.953293i	0.0772981	−	0.0314634i
$919$	6.57695	−	4.77844i	0.216954	−	0.157626i	−0.474001	−	0.880524i	$-0.657191\pi$
$919$	6.57695	−	4.77844i	0.216954	−	0.157626i	0.690954	+	0.722898i	$0.257191\pi$
$920$	0.223888	+	0.665165i	0.00738136	+	0.0219299i
$921$	58.1136	+	8.80676i	1.91491	+	0.290193i
$922$	0.978042	−	0.435453i	0.0322101	−	0.0143409i
$923$	−10.9505	−	12.1618i	−0.360440	−	0.400309i
$924$	−4.04437	−	2.58820i	−0.133050	−	0.0851455i
$925$	−1.27253	−	0.242625i	−0.0418407	−	0.00797746i
$926$	20.6074			0.677200
$927$	3.41989	−	0.405709i	0.112324	−	0.0133252i
$928$	35.5460	+	25.8257i	1.16685	+	0.847769i
$929$	4.04198	−	38.4568i	0.132613	−	1.26173i	−0.702514	−	0.711670i	$-0.747939\pi$
$929$	4.04198	−	38.4568i	0.132613	−	1.26173i	0.835127	−	0.550058i	$-0.185394\pi$
$930$	12.9167	−	10.8328i	0.423556	−	0.355222i
$931$	3.38775	+	32.2323i	0.111029	+	1.05637i
$932$	−5.35616	+	9.27714i	−0.175447	+	0.303883i
$933$	8.69159	+	13.1901i	0.284550	+	0.431826i
$934$	7.00794	−	7.78311i	0.229307	−	0.254671i
$935$	5.16799	+	1.04180i	0.169011	+	0.0340704i
$936$	34.6881	−	4.11512i	1.13382	−	0.134507i
$937$	7.87414	+	24.2341i	0.257237	+	0.791694i	0.993381	+	0.114869i	$0.0366447\pi$
$937$	7.87414	+	24.2341i	0.257237	+	0.791694i	−0.736144	+	0.676825i	$0.763355\pi$
$938$	−1.59163	+	1.76769i	−0.0519687	+	0.0577171i
$939$	−31.7293	+	26.0467i	−1.03545	+	0.850003i
$940$	−13.1412	+	14.9072i	−0.428618	+	0.486218i
$941$	−10.7042	−	2.27524i	−0.348946	−	0.0741707i	0.0301046	−	0.999547i	$-0.490416\pi$
$941$	−10.7042	−	2.27524i	−0.348946	−	0.0741707i	−0.379050	+	0.925376i	$0.623749\pi$
$942$	9.56239	−	19.0813i	0.311560	−	0.621702i
$943$	0.401671	+	0.695714i	0.0130802	+	0.0226556i
$944$	9.37918	−	6.81437i	0.305266	−	0.221789i
$945$	6.04265	−	4.19208i	0.196568	−	0.136368i
$946$	−33.5716	−	24.3912i	−1.09151	−	0.793027i
$947$	5.13830	−	48.8876i	0.166972	−	1.58863i	−0.514957	−	0.857216i	$-0.672192\pi$
$947$	5.13830	−	48.8876i	0.166972	−	1.58863i	0.681929	−	0.731418i	$-0.261141\pi$
$948$	−0.323308	−	1.95660i	−0.0105005	−	0.0635474i
$949$	−29.2997	+	50.7486i	−0.951109	+	1.64737i
$950$	8.70379	+	24.9863i	0.282388	+	0.810663i
$951$	−42.1332	−	26.9632i	−1.36626	−	0.874341i
$952$	−0.855343	+	0.181809i	−0.0277218	+	0.00589246i
$953$	13.3275	+	9.68303i	0.431721	+	0.313664i	0.782337	−	0.622856i	$-0.214028\pi$
$953$	13.3275	+	9.68303i	0.431721	+	0.313664i	−0.350615	+	0.936520i	$0.614028\pi$
$954$	13.7208	+	12.0262i	0.444226	+	0.389364i
$955$	−22.3859	−	4.51269i	−0.724390	−	0.146027i
$956$	9.82969	+	4.37646i	0.317915	+	0.141545i
$957$	4.14733	−	90.7283i	0.134064	−	2.93283i
$958$	1.74113	+	16.5657i	0.0562533	+	0.535214i
$959$	−6.15882	−	1.30910i	−0.198879	−	0.0422730i
$960$	−30.7157	+	2.14001i	−0.991345	+	0.0690684i
$961$	14.3612	−	3.05256i	0.463263	−	0.0984696i
$962$	−0.328377	−	1.01064i	−0.0105873	−	0.0325843i
$963$	11.7564	+	3.64696i	0.378843	+	0.117522i
$964$	−7.16615	+	22.0551i	−0.230806	+	0.710348i
$965$	28.4254	−	0.299018i	0.915045	−	0.00962572i
$966$	−0.0305883	+	0.117285i	−0.000984161	+	0.00377359i
$967$	4.19529	+	39.9155i	0.134911	+	1.28360i	0.827172	+	0.561949i	$0.189948\pi$
$967$	4.19529	+	39.9155i	0.134911	+	1.28360i	−0.692260	+	0.721648i	$0.743385\pi$
$968$	24.8604	−	43.0595i	0.799045	−	1.38399i
$969$	1.72113	−	3.43443i	0.0552907	−	0.110330i
$970$	11.7930	−	8.75912i	0.378651	−	0.281238i
$971$	−1.48662	−	1.08010i	−0.0477080	−	0.0346619i	0.563676	−	0.825996i	$-0.309387\pi$
$971$	−1.48662	−	1.08010i	−0.0477080	−	0.0346619i	−0.611384	+	0.791334i	$0.709387\pi$
$972$	−12.3590	−	4.27636i	−0.396414	−	0.137164i
$973$	−0.842449	+	2.59279i	−0.0270077	+	0.0831211i
$974$	−7.73651	−	13.4000i	−0.247894	−	0.429364i
$975$	−25.0331	+	21.4470i	−0.801702	+	0.686854i
$976$	3.73073	−	6.46181i	0.119418	−	0.206838i
$977$	−38.7931	−	43.0841i	−1.24110	−	1.37838i	−0.898542	−	0.438887i	$-0.855373\pi$
$977$	−38.7931	−	43.0841i	−1.24110	−	1.37838i	−0.342559	−	0.939496i	$-0.611294\pi$
$978$	−3.10095	−	7.91972i	−0.0991575	−	0.253245i
$979$	−9.58758	+	91.2197i	−0.306420	+	2.91540i
$980$	11.2561	−	5.15409i	0.359563	−	0.164641i
$981$	0.00397191	+	0.297274i	0.000126813	+	0.00949123i
$982$	−4.04328			−0.129026
$983$	17.6257	+	7.84748i	0.562173	+	0.250296i	0.668092	−	0.744079i	$-0.267111\pi$
$983$	17.6257	+	7.84748i	0.562173	+	0.250296i	−0.105918	+	0.994375i	$0.533778\pi$
$984$	−39.9976	+	11.0042i	−1.27508	+	0.350802i
$985$	1.42284	−	15.0597i	0.0453356	−	0.479841i
$986$	−3.27063	−	3.63240i	−0.104158	−	0.115679i
$987$	−11.1977	+	3.08074i	−0.356427	+	0.0980609i
$988$	10.4938	−	11.6545i	0.333851	−	0.370779i
$989$	0.233896	−	0.719859i	0.00743748	−	0.0228902i
$990$	22.9028	+	29.9901i	0.727898	+	0.953147i
$991$	12.9369	+	39.8158i	0.410956	+	1.26479i	0.915819	+	0.401592i	$0.131543\pi$
$991$	12.9369	+	39.8158i	0.410956	+	1.26479i	−0.504863	+	0.863199i	$0.668457\pi$
$992$	16.1427	+	7.18718i	0.512530	+	0.228193i
$993$	−35.5938	−	22.7783i	−1.12953	−	0.722847i
$994$	0.306516	+	2.91630i	0.00972210	+	0.0924996i
$995$	−8.07767	−	13.6571i	−0.256079	−	0.432960i
$996$	−3.07343	−	0.465759i	−0.0973853	−	0.0147581i
$997$	−3.62146	+	34.4559i	−0.114693	+	1.09123i	0.774146	+	0.633008i	$0.218180\pi$
$997$	−3.62146	+	34.4559i	−0.114693	+	1.09123i	−0.888838	+	0.458221i	$0.848487\pi$
$998$	0.827501	−	2.54679i	0.0261941	−	0.0806172i
$999$	−0.183916	+	1.33366i	−0.00581885	+	0.0421951i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.121.10	yes	224
3.2	odd	2		675.2.r.a.496.19		224
9.2	odd	6		675.2.r.a.46.10		224
9.7	even	3	inner	225.2.q.a.196.19	yes	224
25.6	even	5	inner	225.2.q.a.31.19	✓	224
75.56	odd	10		675.2.r.a.631.10		224
225.56	odd	30		675.2.r.a.181.19		224
225.106	even	15	inner	225.2.q.a.106.10	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.19	✓	224	25.6	even	5	inner
225.2.q.a.106.10	yes	224	225.106	even	15	inner
225.2.q.a.121.10	yes	224	1.1	even	1	trivial
225.2.q.a.196.19	yes	224	9.7	even	3	inner
675.2.r.a.46.10		224	9.2	odd	6
675.2.r.a.181.19		224	225.56	odd	30
675.2.r.a.496.19		224	3.2	odd	2
675.2.r.a.631.10		224	75.56	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05398 + 0.224029i) q^{2} +(1.71250 + 0.259519i) q^{3} +(-0.766416 + 0.341231i) q^{4} +(-1.13834 - 1.92462i) q^{5} +(-1.86307 + 0.110124i) q^{6} +(0.316483 + 0.548165i) q^{7} +(2.47480 - 1.79805i) q^{8} +(2.86530 + 0.888850i) q^{9} +(1.63096 + 1.77348i) q^{10} +(5.10644 - 1.08541i) q^{11} +(-1.40104 + 0.385457i) q^{12} +(3.72319 + 0.791388i) q^{13} +(-0.456370 - 0.506851i) q^{14} +(-1.44993 - 3.59134i) q^{15} +(-1.08284 + 1.20261i) q^{16} +(-0.365368 + 0.265455i) q^{17} +(-3.21908 - 0.294915i) q^{18} +(-3.97313 + 2.88665i) q^{19} +(1.52918 + 1.08663i) q^{20} +(0.399718 + 1.02086i) q^{21} +(-5.13890 + 2.28798i) q^{22} +(-0.0686557 - 0.0762499i) q^{23} +(4.70473 - 2.43690i) q^{24} +(-2.40836 + 4.38176i) q^{25} -4.10144 q^{26} +(4.67615 + 2.26575i) q^{27} +(-0.429608 - 0.312129i) q^{28} +(1.04992 - 9.98932i) q^{29} +(2.33276 + 3.46035i) q^{30} +(-0.422249 - 4.01743i) q^{31} +(-2.18716 + 3.78828i) q^{32} +(9.02645 - 0.533542i) q^{33} +(0.325619 - 0.361636i) q^{34} +(0.694745 - 1.23311i) q^{35} +(-2.49932 + 0.296499i) q^{36} +(0.0800637 + 0.246411i) q^{37} +(3.54089 - 3.93256i) q^{38} +(6.17057 + 2.32149i) q^{39} +(-6.27775 - 2.71627i) q^{40} +(-7.65841 - 1.62785i) q^{41} +(-0.649996 - 0.986417i) q^{42} +(3.68846 + 6.38860i) q^{43} +(-3.54328 + 2.57435i) q^{44} +(-1.55099 - 6.52644i) q^{45} +(0.0894437 + 0.0649846i) q^{46} +(-1.10730 + 10.5353i) q^{47} +(-2.16646 + 1.77845i) q^{48} +(3.29968 - 5.71521i) q^{49} +(1.55670 - 5.15781i) q^{50} +(-0.694582 + 0.359772i) q^{51} +(-3.12356 + 0.663933i) q^{52} +(-4.56626 - 3.31758i) q^{53} +(-5.43614 - 1.34045i) q^{54} +(-7.90187 - 8.59241i) q^{55} +(1.76886 + 0.787548i) q^{56} +(-7.55312 + 3.91228i) q^{57} +(1.13131 + 10.7637i) q^{58} +(-7.00744 - 1.48948i) q^{59} +(2.33673 + 2.25770i) q^{60} +(-4.51000 + 0.958629i) q^{61} +(1.34506 + 4.13967i) q^{62} +(0.419583 + 1.85196i) q^{63} +(2.45668 - 7.56088i) q^{64} +(-2.71514 - 8.06661i) q^{65} +(-9.39412 + 2.58453i) q^{66} +(-0.364553 - 3.46849i) q^{67} +(0.189442 - 0.328124i) q^{68} +(-0.0977846 - 0.148395i) q^{69} +(-0.455991 + 1.45531i) q^{70} +(-3.47832 - 2.52715i) q^{71} +(8.68926 - 2.95223i) q^{72} +(-4.75735 + 14.6416i) q^{73} +(-0.139588 - 0.241774i) q^{74} +(-5.26145 + 6.87874i) q^{75} +(2.06006 - 3.56813i) q^{76} +(2.21108 + 2.45566i) q^{77} +(-7.02371 - 1.06440i) q^{78} +(-0.142656 + 1.35728i) q^{79} +(3.54721 + 0.715070i) q^{80} +(7.41989 + 5.09364i) q^{81} +8.43646 q^{82} +(1.95429 + 0.870105i) q^{83} +(-0.654700 - 0.646011i) q^{84} +(0.926814 + 0.401017i) q^{85} +(-5.31878 - 5.90711i) q^{86} +(4.39040 - 16.8342i) q^{87} +(10.6858 - 11.8678i) q^{88} +(-5.42929 + 16.7096i) q^{89} +(3.09682 + 6.53124i) q^{90} +(0.744515 + 2.29138i) q^{91} +(0.0786377 + 0.0350118i) q^{92} +(0.319497 - 6.98942i) q^{93} +(-1.19314 - 11.3520i) q^{94} +(10.0785 + 4.36079i) q^{95} +(-4.72864 + 5.91981i) q^{96} +(0.637304 - 6.06354i) q^{97} +(-2.19740 + 6.76291i) q^{98} +(15.5962 + 1.42884i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20}+ \cdots - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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