LMFDB - Embedded newform 675.2.r.a.496.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(46,675)] 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("675.46"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([20, 18])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.r (of order $15$, degree $8$, not 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			496.19
Character	$\chi$	$=$	675.496
Dual form			675.2.r.a.181.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.05398 - 0.224029i) q^{2} +(-0.766416 + 0.341231i) q^{4} +(1.13834 + 1.92462i) q^{5} +(0.316483 + 0.548165i) q^{7} +(-2.47480 + 1.79805i) q^{8} +(1.63096 + 1.77348i) q^{10} +(-5.10644 + 1.08541i) q^{11} +(3.72319 + 0.791388i) q^{13} +(0.456370 + 0.506851i) q^{14} +(-1.08284 + 1.20261i) q^{16} +(0.365368 - 0.265455i) q^{17} +(-3.97313 + 2.88665i) q^{19} +(-1.52918 - 1.08663i) q^{20} +(-5.13890 + 2.28798i) q^{22} +(0.0686557 + 0.0762499i) q^{23} +(-2.40836 + 4.38176i) q^{25} +4.10144 q^{26} +(-0.429608 - 0.312129i) q^{28} +(-1.04992 + 9.98932i) q^{29} +(-0.422249 - 4.01743i) q^{31} +(2.18716 - 3.78828i) q^{32} +(0.325619 - 0.361636i) q^{34} +(-0.694745 + 1.23311i) q^{35} +(0.0800637 + 0.246411i) q^{37} +(-3.54089 + 3.93256i) q^{38} +(-6.27775 - 2.71627i) q^{40} +(7.65841 + 1.62785i) q^{41} +(3.68846 + 6.38860i) q^{43} +(3.54328 - 2.57435i) q^{44} +(0.0894437 + 0.0649846i) q^{46} +(1.10730 - 10.5353i) q^{47} +(3.29968 - 5.71521i) q^{49} +(-1.55670 + 5.15781i) q^{50} +(-3.12356 + 0.663933i) q^{52} +(4.56626 + 3.31758i) q^{53} +(-7.90187 - 8.59241i) q^{55} +(-1.76886 - 0.787548i) q^{56} +(1.13131 + 10.7637i) q^{58} +(7.00744 + 1.48948i) q^{59} +(-4.51000 + 0.958629i) q^{61} +(-1.34506 - 4.13967i) q^{62} +(2.45668 - 7.56088i) q^{64} +(2.71514 + 8.06661i) q^{65} +(-0.364553 - 3.46849i) q^{67} +(-0.189442 + 0.328124i) q^{68} +(-0.455991 + 1.45531i) q^{70} +(3.47832 + 2.52715i) q^{71} +(-4.75735 + 14.6416i) q^{73} +(0.139588 + 0.241774i) q^{74} +(2.06006 - 3.56813i) q^{76} +(-2.21108 - 2.45566i) q^{77} +(-0.142656 + 1.35728i) q^{79} +(-3.54721 - 0.715070i) q^{80} +8.43646 q^{82} +(-1.95429 - 0.870105i) q^{83} +(0.926814 + 0.401017i) q^{85} +(5.31878 + 5.90711i) q^{86} +(10.6858 - 11.8678i) q^{88} +(5.42929 - 16.7096i) q^{89} +(0.744515 + 2.29138i) q^{91} +(-0.0786377 - 0.0350118i) q^{92} +(-1.19314 - 11.3520i) q^{94} +(-10.0785 - 4.36079i) q^{95} +(0.637304 - 6.06354i) q^{97} +(2.19740 - 6.76291i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28}+ \cdots - 146 q^{98}+O(q^{100}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{5}\right)$

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	0.180403	−	0.983593i	$-0.442260\pi$
$2$	1.05398	−	0.224029i	0.745273	−	0.158413i	0.564870	+	0.825180i	$0.308926\pi$
$3$		0			0
$3$		0			0
$4$	−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
$6$		0			0
$7$	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
$9$		0			0
$10$	1.63096	+	1.77348i	0.515754	+	0.560825i
$11$	−5.10644	+	1.08541i	−1.53965	+	0.327262i	−0.898090	−	0.439811i	$-0.855045\pi$
$11$	−5.10644	+	1.08541i	−1.53965	+	0.327262i	−0.641559	+	0.767074i	$0.721712\pi$
$12$		0			0
$13$	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
$15$		0			0
$16$	−1.08284	+	1.20261i	−0.270709	+	0.300653i
$17$	0.365368	−	0.265455i	0.0886146	−	0.0643823i	−0.542596	−	0.839994i	$-0.682558\pi$
$17$	0.365368	−	0.265455i	0.0886146	−	0.0643823i	0.631210	+	0.775612i	$0.282558\pi$
$18$		0			0
$19$	−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			0
$22$	−5.13890	+	2.28798i	−1.09562	+	0.487800i
$23$	0.0686557	+	0.0762499i	0.0143157	+	0.0158992i	0.750260	−	0.661143i	$-0.229928\pi$
$23$	0.0686557	+	0.0762499i	0.0143157	+	0.0158992i	−0.735944	+	0.677042i	$0.763262\pi$
$24$		0			0
$25$	−2.40836	+	4.38176i	−0.481671	+	0.876352i
$26$	4.10144			0.804359
$27$		0			0
$28$	−0.429608	−	0.312129i	−0.0811883	−	0.0589868i
$29$	−1.04992	+	9.98932i	−0.194965	+	1.85497i	0.261467	+	0.965212i	$0.415794\pi$
$29$	−1.04992	+	9.98932i	−0.194965	+	1.85497i	−0.456433	+	0.889758i	$0.650873\pi$
$30$		0			0
$31$	−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
$33$		0			0
$34$	0.325619	−	0.361636i	0.0558431	−	0.0620201i
$35$	−0.694745	+	1.23311i	−0.117433	+	0.208434i
$36$		0			0
$37$	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
$39$		0			0
$40$	−6.27775	−	2.71627i	−0.992599	−	0.429480i
$41$	7.65841	+	1.62785i	1.19604	+	0.254227i	0.762549	−	0.646930i	$-0.223947\pi$
$41$	7.65841	+	1.62785i	1.19604	+	0.254227i	0.433493	+	0.901157i	$0.357281\pi$
$42$		0			0
$43$	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
$45$		0			0
$46$	0.0894437	+	0.0649846i	0.0131878	+	0.00958146i
$47$	1.10730	−	10.5353i	0.161517	−	1.53673i	−0.550660	−	0.834730i	$-0.685624\pi$
$47$	1.10730	−	10.5353i	0.161517	−	1.53673i	0.712177	−	0.702000i	$-0.247709\pi$
$48$		0			0
$49$	3.29968	−	5.71521i	0.471382	−	0.816458i
$50$	−1.55670	+	5.15781i	−0.220151	+	0.729424i
$51$		0			0
$52$	−3.12356	+	0.663933i	−0.433160	+	0.0920709i
$53$	4.56626	+	3.31758i	0.627224	+	0.455705i	0.855437	−	0.517906i	$-0.173288\pi$
$53$	4.56626	+	3.31758i	0.627224	+	0.455705i	−0.228213	+	0.973611i	$0.573288\pi$
$54$		0			0
$55$	−7.90187	−	8.59241i	−1.06549	−	1.15860i
$56$	−1.76886	−	0.787548i	−0.236374	−	0.105241i
$57$		0			0
$58$	1.13131	+	10.7637i	0.148548	+	1.41334i
$59$	7.00744	+	1.48948i	0.912291	+	0.193913i	0.640066	−	0.768320i	$-0.278907\pi$
$59$	7.00744	+	1.48948i	0.912291	+	0.193913i	0.272225	+	0.962234i	$0.412240\pi$
$60$		0			0
$61$	−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			0
$64$	2.45668	−	7.56088i	0.307085	−	0.945110i
$65$	2.71514	+	8.06661i	0.336771	+	1.00054i
$66$		0			0
$67$	−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			0
$70$	−0.455991	+	1.45531i	−0.0545014	+	0.173943i
$71$	3.47832	+	2.52715i	0.412801	+	0.299917i	0.774735	−	0.632286i	$-0.217883\pi$
$71$	3.47832	+	2.52715i	0.412801	+	0.299917i	−0.361934	+	0.932204i	$0.617883\pi$
$72$		0			0
$73$	−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
$75$		0			0
$76$	2.06006	−	3.56813i	0.236305	−	0.409292i
$77$	−2.21108	−	2.45566i	−0.251976	−	0.279848i
$78$		0			0
$79$	−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
$81$		0			0
$82$	8.43646			0.931651
$83$	−1.95429	−	0.870105i	−0.214511	−	0.0955065i	0.296668	−	0.954981i	$-0.404124\pi$
$83$	−1.95429	−	0.870105i	−0.214511	−	0.0955065i	−0.511179	+	0.859474i	$0.670791\pi$
$84$		0			0
$85$	0.926814	+	0.401017i	0.100527	+	0.0434964i
$86$	5.31878	+	5.90711i	0.573539	+	0.636980i
$87$		0			0
$88$	10.6858	−	11.8678i	1.13911	−	1.26511i
$89$	5.42929	−	16.7096i	0.575504	−	1.77122i	−0.0589537	−	0.998261i	$-0.518776\pi$
$89$	5.42929	−	16.7096i	0.575504	−	1.77122i	0.634457	−	0.772958i	$-0.281224\pi$
$90$		0			0
$91$	0.744515	+	2.29138i	0.0780464	+	0.240202i
$92$	−0.0786377	−	0.0350118i	−0.00819855	−	0.00365023i
$93$		0			0
$94$	−1.19314	−	11.3520i	−0.123063	−	1.17087i
$95$	−10.0785	−	4.36079i	−1.03403	−	0.447408i
$96$		0			0
$97$	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
$99$		0			0
$100$	0.350613	−	4.18006i	0.0350613	−	0.418006i
$101$	−1.98334	−	3.43524i	−0.197350	−	0.341820i	0.750319	−	0.661076i	$-0.229900\pi$
$101$	−1.98334	−	3.43524i	−0.197350	−	0.341820i	−0.947668	+	0.319257i	$0.896567\pi$
$102$		0			0
$103$	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
$105$		0			0
$106$	5.55596	+	2.47367i	0.539643	+	0.240264i
$107$	−4.10301			−0.396653			−0.198326	−	0.980136i	$-0.563551\pi$
$107$	−4.10301			−0.396653			−0.198326	+	0.980136i	$0.563551\pi$
$108$		0			0
$109$	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			0
$112$	−1.00193	−	0.212967i	−0.0946734	−	0.0201234i
$113$	13.0049	+	2.76428i	1.22340	+	0.260041i	0.773939	−	0.633260i	$-0.218284\pi$
$113$	13.0049	+	2.76428i	1.22340	+	0.260041i	0.449459	+	0.893301i	$0.351617\pi$
$114$		0			0
$115$	−0.0685988	+	0.218935i	−0.00639687	+	0.0204158i
$116$	−2.60399	−	8.01424i	−0.241774	−	0.744104i
$117$		0			0
$118$	7.71936			0.710624
$119$	0.261146	+	0.116270i	0.0239392	+	0.0106584i
$120$		0			0
$121$	14.8486	−	6.61102i	1.34987	−	0.601002i
$122$	−4.53866	+	2.02074i	−0.410911	+	0.182949i
$123$		0			0
$124$	1.69449	+	2.93494i	0.152169	+	0.263565i
$125$	−11.1748	+	0.352760i	−0.999502	+	0.0315518i
$126$		0			0
$127$	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
$129$		0			0
$130$	4.66884	+	7.89374i	0.409485	+	0.692326i
$131$	−0.574155	−	5.46272i	−0.0501641	−	0.477280i	−0.990548	−	0.137165i	$-0.956201\pi$
$131$	−0.574155	−	5.46272i	−0.0501641	−	0.477280i	0.940384	−	0.340114i	$-0.110466\pi$
$132$		0			0
$133$	−2.83979	−	1.26436i	−0.246241	−	0.109633i
$134$	−1.16127	−	3.57403i	−0.100319	−	0.308749i
$135$		0			0
$136$	−0.426912	+	1.31390i	−0.0366074	+	0.112666i
$137$	6.65616	−	7.39241i	0.568674	−	0.631576i	−0.388376	−	0.921501i	$-0.626964\pi$
$137$	6.65616	−	7.39241i	0.568674	−	0.631576i	0.957049	+	0.289925i	$0.0936304\pi$
$138$		0			0
$139$	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
$141$		0			0
$142$	4.23222	+	1.88431i	0.355160	+	0.158127i
$143$	−19.8712			−1.66171
$144$		0			0
$145$	−20.4209	+	9.35056i	−1.69586	+	0.776522i
$146$	−1.73398	+	16.4977i	−0.143505	+	1.36536i
$147$		0			0
$148$	−0.145445	−	0.161533i	−0.0119555	−	0.0132779i
$149$	0.0389321	−	0.0674323i	0.00318944	−	0.00552427i	−0.864426	−	0.502760i	$-0.832318\pi$
$149$	0.0389321	−	0.0674323i	0.00318944	−	0.00552427i	0.867616	+	0.497235i	$0.165651\pi$
$150$		0			0
$151$	−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
$153$		0			0
$154$	−2.88057	−	2.09285i	−0.232123	−	0.168647i
$155$	7.25137	−	5.38587i	0.582444	−	0.432604i
$156$		0			0
$157$	−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
$159$		0			0
$160$	9.78076	−	0.102888i	0.773237	−	0.00813398i
$161$	−0.0200691	+	0.0617665i	−0.00158167	+	0.00486788i
$162$		0			0
$163$	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
$165$		0			0
$166$	−2.25470	−	0.479251i	−0.174999	−	0.0371971i
$167$	1.56503	+	14.8903i	0.121106	+	1.15225i	0.871205	+	0.490920i	$0.163339\pi$
$167$	1.56503	+	14.8903i	0.121106	+	1.15225i	−0.750099	+	0.661326i	$0.769994\pi$
$168$		0			0
$169$	1.35975	+	0.605399i	0.104596	+	0.0465691i
$170$	1.06668	+	0.215028i	0.0818105	+	0.0164919i
$171$		0			0
$172$	−5.00688	−	3.63771i	−0.381771	−	0.277373i
$173$	3.49543	−	0.742976i	0.265753	−	0.0564874i	−0.0731081	−	0.997324i	$-0.523292\pi$
$173$	3.49543	−	0.742976i	0.265753	−	0.0564874i	0.338861	+	0.940837i	$0.389958\pi$
$174$		0			0
$175$	−3.16413	+	0.0665768i	−0.239186	+	0.00503274i
$176$	4.22411	−	7.31638i	0.318405	−	0.551493i
$177$		0			0
$178$	1.97889	−	18.8279i	0.148324	−	1.41121i
$179$	17.6257	+	12.8058i	1.31741	+	0.957151i	0.999961	+	0.00887412i	$0.00282476\pi$
$179$	17.6257	+	12.8058i	1.31741	+	0.957151i	0.317445	+	0.948277i	$0.397175\pi$
$180$		0			0
$181$	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
$183$		0			0
$184$	−0.307011	−	0.0652572i	−0.0226331	−	0.00481082i
$185$	−0.383108	+	0.434592i	−0.0281667	+	0.0319519i
$186$		0			0
$187$	−1.57760	+	1.75210i	−0.115366	+	0.128126i
$188$	2.74631	+	8.45226i	0.200295	+	0.616445i
$189$		0			0
$190$	−11.5994	−	2.33829i	−0.841511	−	0.169637i
$191$	−6.83360	+	7.58948i	−0.494462	+	0.549156i	−0.937790	−	0.347204i	$-0.887131\pi$
$191$	−6.83360	+	7.58948i	−0.494462	+	0.549156i	0.443328	+	0.896360i	$0.353798\pi$
$192$		0			0
$193$	−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
$195$		0			0
$196$	−0.578723	+	5.50618i	−0.0413373	+	0.393299i
$197$	−5.47291	−	3.97630i	−0.389929	−	0.283300i	0.375498	−	0.926823i	$-0.377472\pi$
$197$	−5.47291	−	3.97630i	−0.389929	−	0.283300i	−0.765426	+	0.643524i	$0.777472\pi$
$198$		0			0
$199$	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			0
$202$	−2.85999	−	3.17634i	−0.201228	−	0.223486i
$203$	−5.80807	+	2.58592i	−0.407647	+	0.181496i
$204$		0			0
$205$	5.58490	+	16.5926i	0.390066	+	1.15888i
$206$	1.00071	−	0.727061i	0.0697230	−	0.0506567i
$207$		0			0
$208$	−4.98334	+	3.62061i	−0.345532	+	0.251044i
$209$	17.1554	−	19.0530i	1.18666	−	1.31792i
$210$		0			0
$211$	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
$213$		0			0
$214$	−4.32447	+	0.919195i	−0.295615	+	0.0628349i
$215$	−8.09693	+	14.3713i	−0.552206	+	0.980116i
$216$		0			0
$217$	2.06858	−	1.50291i	0.140424	−	0.102024i
$218$	0.0533913	+	0.0924764i	0.00361611	+	0.00626329i
$219$		0			0
$220$	8.98812	+	3.88900i	0.605979	+	0.262197i
$221$	1.57041	−	0.699192i	0.105637	−	0.0470327i
$222$		0			0
$223$	−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
$225$		0			0
$226$	14.3261			0.952959
$227$	−23.6286	+	5.02242i	−1.56829	+	0.333350i	−0.908428	−	0.418041i	$-0.862717\pi$
$227$	−23.6286	+	5.02242i	−1.56829	+	0.333350i	−0.659858	+	0.751390i	$0.729384\pi$
$228$		0			0
$229$	−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
$231$		0			0
$232$	−15.3630	−	26.6094i	−1.00863	−	1.74699i
$233$	−10.3302	+	7.50529i	−0.676751	+	0.491688i	−0.872278	−	0.489010i	$-0.837358\pi$
$233$	−10.3302	+	7.50529i	−0.676751	+	0.491688i	0.195527	+	0.980698i	$0.437358\pi$
$234$		0			0
$235$	21.5370	−	9.86162i	1.40492	−	0.643301i
$236$	−5.87887	+	1.24959i	−0.382682	+	0.0813416i
$237$		0			0
$238$	0.301289	+	0.0640409i	0.0195297	+	0.00415116i
$239$	8.58195	+	9.53122i	0.555120	+	0.616524i	0.953755	−	0.300586i	$-0.0971824\pi$
$239$	8.58195	+	9.53122i	0.555120	+	0.616524i	−0.398634	+	0.917110i	$0.630516\pi$
$240$		0			0
$241$	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
$243$		0			0
$244$	3.12942	−	2.27366i	0.200341	−	0.145556i
$245$	14.7558	−	0.155222i	0.942713	−	0.00991677i
$246$		0			0
$247$	−17.0772	+	7.60325i	−1.08659	+	0.483783i
$248$	8.26852	+	9.18312i	0.525052	+	0.583129i
$249$		0			0
$250$	−11.6989	+	2.87528i	−0.739904	+	0.181848i
$251$	2.88989			0.182408			0.0912042	−	0.995832i	$-0.470928\pi$
$251$	2.88989			0.182408			0.0912042	+	0.995832i	$0.470928\pi$
$252$		0			0
$253$	−0.433349	−	0.314846i	−0.0272444	−	0.0197942i
$254$	0.631955	−	6.01265i	0.0396524	−	0.377267i
$255$		0			0
$256$	1.68254	+	16.0083i	0.105159	+	1.00052i
$257$	−3.00243	+	5.20037i	−0.187287	+	0.324390i	−0.944345	−	0.328958i	$-0.893303\pi$
$257$	−3.00243	+	5.20037i	−0.187287	+	0.324390i	0.757058	+	0.653348i	$0.226636\pi$
$258$		0			0
$259$	−0.109735	+	0.121873i	−0.00681859	+	0.00757281i
$260$	−4.83350	−	5.25589i	−0.299761	−	0.325957i
$261$		0			0
$262$	−1.82895	−	5.62894i	−0.112993	−	0.347757i
$263$	−9.16815	+	10.1823i	−0.565332	+	0.627865i	−0.956247	−	0.292562i	$-0.905492\pi$
$263$	−9.16815	+	10.1823i	−0.565332	+	0.627865i	0.390914	+	0.920427i	$0.372159\pi$
$264$		0			0
$265$	−1.18713	+	12.5649i	−0.0729251	+	0.771854i
$266$	−3.27632	−	0.696403i	−0.200884	−	0.0426992i
$267$		0			0
$268$	1.46295	+	2.53391i	0.0893641	+	0.154783i
$269$	13.3513	−	9.70027i	0.814041	−	0.591436i	−0.100958	−	0.994891i	$-0.532191\pi$
$269$	13.3513	−	9.70027i	0.814041	−	0.591436i	0.915000	+	0.403455i	$0.132191\pi$
$270$		0			0
$271$	−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			0
$274$	5.35931	−	9.28259i	0.323768	−	0.560782i
$275$	7.54213	−	24.9892i	0.454807	−	1.50691i
$276$		0			0
$277$	−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
$279$		0			0
$280$	−0.497835	−	4.30089i	−0.0297513	−	0.257027i
$281$	21.1347	+	9.40979i	1.26079	+	0.561341i	0.924775	−	0.380514i	$-0.124253\pi$
$281$	21.1347	+	9.40979i	1.26079	+	0.561341i	0.336018	+	0.941856i	$0.390920\pi$
$282$		0			0
$283$	−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
$285$		0			0
$286$	−20.9438	+	4.45173i	−1.23843	+	0.263237i
$287$	1.53143	+	4.71326i	0.0903974	+	0.278215i
$288$		0			0
$289$	−5.19026	+	15.9740i	−0.305310	+	0.939646i
$290$	−19.4283	+	14.4301i	−1.14087	+	0.847366i
$291$		0			0
$292$	−1.35006	−	12.8449i	−0.0790061	−	0.751693i
$293$	7.31930	−	12.6774i	0.427598	−	0.740622i	−0.569061	−	0.822295i	$-0.692693\pi$
$293$	7.31930	−	12.6774i	0.427598	−	0.740622i	0.996659	+	0.0816737i	$0.0260265\pi$
$294$		0			0
$295$	5.11018	+	15.1822i	0.297526	+	0.883943i
$296$	−0.641201	−	0.465860i	−0.0372691	−	0.0270776i
$297$		0			0
$298$	0.0259266	−	0.0797939i	0.00150189	−	0.00462234i
$299$	0.195275	+	0.338226i	0.0112930	+	0.0195601i
$300$		0			0
$301$	−2.33467	+	4.04377i	−0.134568	+	0.233079i
$302$	−12.3972	−	13.7685i	−0.713377	−	0.792285i
$303$		0			0
$304$	0.830734	−	7.90390i	0.0476459	−	0.453320i
$305$	−6.97892	−	7.58880i	−0.399612	−	0.434533i
$306$		0			0
$307$	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
$309$		0			0
$310$	6.43617	−	7.30110i	0.365550	−	0.414675i
$311$	−6.10247	−	6.77748i	−0.346040	−	0.384316i	0.544852	−	0.838532i	$-0.316586\pi$
$311$	−6.10247	−	6.77748i	−0.346040	−	0.384316i	−0.890891	+	0.454217i	$0.849919\pi$
$312$		0			0
$313$	−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
$315$		0			0
$316$	−0.353813	−	1.08892i	−0.0199035	−	0.0612567i
$317$	26.3835	+	11.7467i	1.48184	+	0.659759i	0.978859	−	0.204536i	$-0.0655685\pi$
$317$	26.3835	+	11.7467i	1.48184	+	0.659759i	0.502985	+	0.864295i	$0.332235\pi$
$318$		0			0
$319$	−5.48113	−	52.1494i	−0.306884	−	2.91981i
$320$	17.3484	−	3.87868i	0.969805	−	0.216825i
$321$		0			0
$322$	−0.00731488	+	0.0695964i	−0.000407642	+	0.00387846i
$323$	−0.685378	+	2.10938i	−0.0381354	+	0.117369i
$324$		0			0
$325$	−12.4344	+	14.4082i	−0.689739	+	0.799222i
$326$	2.45523	+	4.25258i	0.135983	+	0.235529i
$327$		0			0
$328$	−21.8800	+	9.74161i	−1.20812	+	0.537891i
$329$	6.12552	−	2.72726i	0.337711	−	0.150358i
$330$		0			0
$331$	−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			0
$334$	4.98537	+	15.3434i	0.272787	+	0.839553i
$335$	6.26055	−	4.64995i	0.342051	−	0.254054i
$336$		0			0
$337$	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
$339$		0			0
$340$	−0.847165	+	0.00891166i	−0.0459440	+	0.000483303i
$341$	6.51673	+	20.0564i	0.352901	+	1.08612i
$342$		0			0
$343$	8.60793			0.464784
$344$	−20.6153	−	9.17850i	−1.11150	−	0.494872i
$345$		0			0
$346$	3.51765	−	1.56616i	0.189110	−	0.0841971i
$347$	−15.7936	+	7.03179i	−0.847847	+	0.377486i	−0.784216	−	0.620487i	$-0.786935\pi$
$347$	−15.7936	+	7.03179i	−0.847847	+	0.377486i	−0.0636311	+	0.997973i	$0.520268\pi$
$348$		0			0
$349$	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
$351$		0			0
$352$	−7.05679	+	21.7186i	−0.376128	+	1.15760i
$353$	−1.95250	+	18.5768i	−0.103921	+	0.988745i	0.810982	+	0.585071i	$0.198934\pi$
$353$	−1.95250	+	18.5768i	−0.103921	+	0.988745i	−0.914903	+	0.403674i	$0.867733\pi$
$354$		0			0
$355$	−0.904293	+	9.57122i	−0.0479949	+	0.507988i
$356$	1.54074	+	14.6592i	0.0816592	+	0.776935i
$357$		0			0
$358$	21.4459	+	9.54833i	1.13345	+	0.504645i
$359$	−1.18928	−	3.66023i	−0.0627679	−	0.193180i	0.914755	−	0.404009i	$-0.132384\pi$
$359$	−1.18928	−	3.66023i	−0.0627679	−	0.193180i	−0.977523	+	0.210829i	$0.932384\pi$
$360$		0			0
$361$	1.58171	−	4.86800i	0.0832479	−	0.256211i
$362$	12.9903	−	14.4271i	0.682752	−	0.758273i
$363$		0			0
$364$	−1.35250	−	1.50210i	−0.0708901	−	0.0787315i
$365$	−33.5951	+	7.51106i	−1.75845	+	0.393147i
$366$		0			0
$367$	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
$369$		0			0
$370$	−0.306425	+	0.543877i	−0.0159303	+	0.0282748i
$371$	−0.373437	+	3.55302i	−0.0193879	+	0.184464i
$372$		0			0
$373$	−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
$375$		0			0
$376$	16.2026	+	28.0638i	0.835587	+	1.44728i
$377$	−11.8145	+	36.3612i	−0.608477	+	1.87270i
$378$		0			0
$379$	−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
$381$		0			0
$382$	−5.50218	+	9.53006i	−0.281516	+	0.487600i
$383$	−2.27612	−	21.6559i	−0.116304	−	1.10656i	−0.884562	−	0.466422i	$-0.845543\pi$
$383$	−2.27612	−	21.6559i	−0.116304	−	1.10656i	0.768258	−	0.640140i	$-0.221124\pi$
$384$		0			0
$385$	2.20925	−	7.05088i	0.112594	−	0.359346i
$386$	−4.23305	+	13.0280i	−0.215457	+	0.663107i
$387$		0			0
$388$	1.58063	+	4.86466i	0.0802441	+	0.246966i
$389$	−1.06664	+	0.226720i	−0.0540805	+	0.0114952i	−0.234873	−	0.972026i	$-0.575467\pi$
$389$	−1.06664	+	0.226720i	−0.0540805	+	0.0114952i	0.180792	+	0.983521i	$0.442134\pi$
$390$		0			0
$391$	0.0453255	+	0.00963424i	0.00229221	+	0.000487224i
$392$	2.11018	+	20.0770i	0.106580	+	1.01404i
$393$		0			0
$394$	−6.65912	−	2.96483i	−0.335482	−	0.149366i
$395$	−2.77465	+	1.27049i	−0.139608	+	0.0639255i
$396$		0			0
$397$	−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
$399$		0			0
$400$	−2.66170	−	7.64105i	−0.133085	−	0.382052i
$401$	−0.466700	+	0.808348i	−0.0233059	+	0.0403670i	−0.877443	−	0.479681i	$-0.840752\pi$
$401$	−0.466700	+	0.808348i	−0.0233059	+	0.0403670i	0.854137	+	0.520048i	$0.174086\pi$
$402$		0			0
$403$	1.60723	−	15.2918i	0.0800620	−	0.761739i
$404$	2.69227	+	1.95605i	0.133946	+	0.0973172i
$405$		0			0
$406$	−5.54224	+	4.02668i	−0.275057	+	0.199841i
$407$	−0.676296	−	1.17138i	−0.0335228	−	0.0580631i
$408$		0			0
$409$	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
$411$		0			0
$412$	−0.644424	+	0.715705i	−0.0317485	+	0.0352603i
$413$	1.40126	+	4.31263i	0.0689514	+	0.212210i
$414$		0			0
$415$	−0.550022	−	4.75175i	−0.0269995	−	0.233254i
$416$	11.1412	−	12.3736i	0.546244	−	0.606665i
$417$		0			0
$418$	13.8129	−	23.9247i	0.675611	−	1.17019i
$419$	−1.10970	−	10.5580i	−0.0542122	−	0.515794i	−0.987607	−	0.156944i	$-0.949836\pi$
$419$	−1.10970	−	10.5580i	−0.0542122	−	0.515794i	0.933395	−	0.358850i	$-0.116831\pi$
$420$		0			0
$421$	−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
$423$		0			0
$424$	−17.2658			−0.838500
$425$	0.283225	+	2.24026i	0.0137384	+	0.108669i
$426$		0			0
$427$	−1.95282	−	2.16883i	−0.0945038	−	0.104957i
$428$	3.14461	−	1.40007i	0.152001	−	0.0676751i
$429$		0			0
$430$	−5.31437	+	16.9610i	−0.256282	+	0.817930i
$431$	5.96554	−	4.33422i	0.287350	−	0.208772i	−0.434767	−	0.900543i	$-0.643169\pi$
$431$	5.96554	−	4.33422i	0.287350	−	0.208772i	0.722117	+	0.691771i	$0.243169\pi$
$432$		0			0
$433$	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
$435$		0			0
$436$	−0.0556314	−	0.0617849i	−0.00266426	−	0.00295896i
$437$	−0.492885	−	0.104766i	−0.0235779	−	0.00501164i
$438$		0			0
$439$	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
$441$		0			0
$442$	1.49853	−	1.08875i	0.0712780	−	0.0517865i
$443$	−11.5704	−	20.0405i	−0.549726	−	0.952153i	−0.998293	−	0.0584042i	$-0.981399\pi$
$443$	−11.5704	−	20.0405i	−0.549726	−	0.952153i	0.448567	−	0.893749i	$-0.351935\pi$
$444$		0			0
$445$	38.3402	−	8.57194i	1.81750	−	0.406349i
$446$	−3.87606	+	1.72574i	−0.183537	+	0.0817159i
$447$		0			0
$448$	4.92211	−	1.04623i	0.232548	−	0.0494295i
$449$	−19.7430			−0.931731			−0.465866	−	0.884856i	$-0.654257\pi$
$449$	−19.7430			−0.931731			−0.465866	+	0.884856i	$0.654257\pi$
$450$		0			0
$451$	−40.8741			−1.92469
$452$	−10.9104	+	2.31908i	−0.513183	+	0.109080i
$453$		0			0
$454$	−23.7788	+	10.5870i	−1.11599	+	0.496873i
$455$	−3.56254	+	4.04129i	−0.167014	+	0.189458i
$456$		0			0
$457$	−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
$459$		0			0
$460$	−0.0221321	−	0.191203i	−0.00103191	−	0.00891490i
$461$	0.971865	−	0.206576i	0.0452643	−	0.00962122i	−0.185224	−	0.982696i	$-0.559301\pi$
$461$	0.971865	−	0.206576i	0.0452643	−	0.00962122i	0.230488	+	0.973075i	$0.425968\pi$
$462$		0			0
$463$	−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
$465$		0			0
$466$	−9.20632	+	10.2247i	−0.426474	+	0.473648i
$467$	7.86342	−	5.71311i	0.363875	−	0.264371i	−0.390791	−	0.920479i	$-0.627799\pi$
$467$	7.86342	−	5.71311i	0.363875	−	0.264371i	0.754667	+	0.656108i	$0.227799\pi$
$468$		0			0
$469$	1.78593	−	1.29755i	0.0824665	−	0.0599154i
$470$	20.4901	−	15.2188i	0.945139	−	0.701991i
$471$		0			0
$472$	−20.0202	+	8.91357i	−0.921505	+	0.410280i
$473$	−25.7691	−	28.6195i	−1.18487	−	1.31593i
$474$		0			0
$475$	−3.07989	−	24.3614i	−0.141315	−	1.11778i
$476$	−0.239821			−0.0109922
$477$		0			0
$478$	11.1804	+	8.12306i	0.511381	+	0.371540i
$479$	−1.61586	+	15.3739i	−0.0738307	+	0.702452i	0.893522	+	0.449019i	$0.148226\pi$
$479$	−1.61586	+	15.3739i	−0.0738307	+	0.702452i	−0.967353	+	0.253433i	$0.918440\pi$
$480$		0			0
$481$	0.103086	+	0.980795i	0.00470030	+	0.0447204i
$482$	14.8924	−	25.7944i	0.678331	−	1.17490i
$483$		0			0
$484$	−9.12433	+	10.1336i	−0.414742	+	0.460618i
$485$	12.3955	−	5.67581i	0.562851	−	0.257725i
$486$		0			0
$487$	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
$489$		0			0
$490$	15.5175	−	3.46933i	0.701007	−	0.156728i
$491$	−3.67039	−	0.780165i	−0.165642	−	0.0352084i	0.124344	−	0.992239i	$-0.460317\pi$
$491$	−3.67039	−	0.780165i	−0.165642	−	0.0352084i	−0.289986	+	0.957031i	$0.593651\pi$
$492$		0			0
$493$	2.26811	+	3.92848i	0.102150	+	0.176930i
$494$	−16.2956	+	11.8394i	−0.733173	+	0.532681i
$495$		0			0
$496$	5.28863	+	3.84242i	0.237467	+	0.172530i
$497$	−0.284464	+	2.70649i	−0.0127599	+	0.121403i
$498$		0			0
$499$	−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
$501$		0			0
$502$	3.04587	−	0.647421i	0.135944	−	0.0288958i
$503$	2.61295	+	1.89842i	0.116506	+	0.0846463i	0.644512	−	0.764594i	$-0.277060\pi$
$503$	2.61295	+	1.89842i	0.116506	+	0.0846463i	−0.528007	+	0.849240i	$0.677060\pi$
$504$		0			0
$505$	4.35384	−	7.72766i	0.193743	−	0.343877i
$506$	−0.527273	−	0.234757i	−0.0234402	−	0.0104362i
$507$		0			0
$508$	0.492033	+	4.68138i	0.0218304	+	0.207703i
$509$	12.1415	+	2.58076i	0.538163	+	0.114390i	0.468972	−	0.883213i	$-0.344625\pi$
$509$	12.1415	+	2.58076i	0.538163	+	0.114390i	0.0691916	+	0.997603i	$0.477958\pi$
$510$		0			0
$511$	−9.53164	+	2.02601i	−0.421655	+	0.0896255i
$512$	5.24697	+	16.1485i	0.231885	+	0.713670i
$513$		0			0
$514$	−1.99946	+	6.15369i	−0.0881922	+	0.271428i
$515$	2.09243	+	1.48687i	0.0922036	+	0.0655191i
$516$		0			0
$517$	5.78070	+	54.9997i	0.254235	+	2.41888i
$518$	−0.0883547	+	0.153035i	−0.00388208	+	0.00672397i
$519$		0			0
$520$	−21.2236	−	15.0813i	−0.930717	−	0.661360i
$521$	−18.5974	−	13.5118i	−0.814765	−	0.591962i	0.100443	−	0.994943i	$-0.467974\pi$
$521$	−18.5974	−	13.5118i	−0.814765	−	0.591962i	−0.915208	+	0.402981i	$0.867974\pi$
$522$		0			0
$523$	−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
$525$		0			0
$526$	−7.38188	+	12.7858i	−0.321865	+	0.557487i
$527$	−1.22072	−	1.35575i	−0.0531755	−	0.0590574i
$528$		0			0
$529$	2.40305	−	22.8635i	0.104481	−	0.994067i
$530$	1.56369	+	13.5090i	0.0679224	+	0.586794i
$531$		0			0
$532$	2.60790			0.113067
$533$	27.2255	+	12.1216i	1.17927	+	0.525043i
$534$		0			0
$535$	−4.67063	−	7.89675i	−0.201929	−	0.341406i
$536$	7.13872	+	7.92835i	0.308346	+	0.342453i
$537$		0			0
$538$	11.8988	−	13.2149i	0.512992	−	0.569736i
$539$	−10.6463	+	32.7658i	−0.458567	+	1.41132i
$540$		0			0
$541$	−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
$543$		0			0
$544$	−0.206499	−	1.96471i	−0.00885358	−	0.0842362i
$545$	−0.146535	+	0.166228i	−0.00627689	+	0.00712041i
$546$		0			0
$547$	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
$549$		0			0
$550$	2.35090	−	28.0277i	0.100243	−	1.19510i
$551$	−24.6642	−	42.7196i	−1.05073	−	1.81992i
$552$		0			0
$553$	−0.789164	+	0.351358i	−0.0335587	+	0.0149413i
$554$	−22.0979	+	9.83860i	−0.938848	+	0.418002i
$555$		0			0
$556$	−3.30100	−	1.46970i	−0.139994	−	0.0623291i
$557$	−31.2370			−1.32355			−0.661776	−	0.749701i	$-0.730197\pi$
$557$	−31.2370			−1.32355			−0.661776	+	0.749701i	$0.730197\pi$
$558$		0			0
$559$	8.67697	+	26.7050i	0.366997	+	1.12950i
$560$	−0.730657	−	2.17076i	−0.0308759	−	0.0917316i
$561$		0			0
$562$	24.3836	+	5.18289i	1.02856	+	0.218627i
$563$	−39.2819	−	8.34963i	−1.65554	−	0.351895i	−0.716999	−	0.697074i	$-0.754485\pi$
$563$	−39.2819	−	8.34963i	−1.65554	−	0.351895i	−0.938537	+	0.345179i	$0.887818\pi$
$564$		0			0
$565$	9.48382	+	28.1762i	0.398987	+	1.18538i
$566$	−6.23691	−	19.1952i	−0.262157	−	0.806836i
$567$		0			0
$568$	−13.1521			−0.551850
$569$	−29.0226	−	12.9217i	−1.21669	−	0.541706i	−0.304910	−	0.952381i	$-0.598626\pi$
$569$	−29.0226	−	12.9217i	−1.21669	−	0.541706i	−0.911782	+	0.410675i	$0.865293\pi$
$570$		0			0
$571$	−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
$573$		0			0
$574$	2.67000	+	4.62457i	0.111444	+	0.193026i
$575$	−0.499456	+	0.117196i	−0.0208288	+	0.00488741i
$576$		0			0
$577$	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
$579$		0			0
$580$	12.4602	−	14.1346i	0.517381	−	0.586909i
$581$	−0.141538	−	1.34665i	−0.00587199	−	0.0558683i
$582$		0			0
$583$	−26.9182	−	11.9848i	−1.11484	−	0.496359i
$584$	−14.5529	−	44.7891i	−0.602202	−	1.85339i
$585$		0			0
$586$	4.87425	−	15.0014i	0.201353	−	0.619702i
$587$	7.74963	−	8.60684i	0.319862	−	0.355242i	−0.561675	−	0.827358i	$-0.689843\pi$
$587$	7.74963	−	8.60684i	0.319862	−	0.355242i	0.881537	+	0.472116i	$0.156510\pi$
$588$		0			0
$589$	13.2746	+	14.7429i	0.546968	+	0.607470i
$590$	8.78726	+	14.8569i	0.361766	+	0.611647i
$591$		0			0
$592$	−0.383032	−	0.170537i	−0.0157425	−	0.00700903i
$593$	22.3537			0.917955			0.458977	−	0.888448i	$-0.348216\pi$
$593$	22.3537			0.917955			0.458977	+	0.888448i	$0.348216\pi$
$594$		0			0
$595$	0.0734979	+	0.634962i	0.00301312	+	0.0260309i
$596$	−0.00682821	+	0.0649660i	−0.000279694	+	0.00266111i
$597$		0			0
$598$	0.281588	+	0.312735i	0.0115150	+	0.0127887i
$599$	2.18765	−	3.78911i	0.0893848	−	0.154819i	−0.817866	−	0.575408i	$-0.804843\pi$
$599$	2.18765	−	3.78911i	0.0893848	−	0.154819i	0.907251	+	0.420589i	$0.138177\pi$
$600$		0			0
$601$	−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
$603$		0			0
$604$	11.6702	+	8.47889i	0.474853	+	0.345001i
$605$	29.6265	+	21.0524i	1.20449	+	0.855901i
$606$		0			0
$607$	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
$609$		0			0
$610$	−9.05572	−	6.43492i	−0.366655	−	0.260542i
$611$	12.4602	−	38.3486i	0.504086	−	1.55142i
$612$		0			0
$613$	−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
$615$		0			0
$616$	9.88739	+	2.10163i	0.398374	+	0.0846771i
$617$	−2.26139	−	21.5157i	−0.0910401	−	0.866189i	−0.940787	−	0.338998i	$-0.889912\pi$
$617$	−2.26139	−	21.5157i	−0.0910401	−	0.866189i	0.849747	−	0.527191i	$-0.176755\pi$
$618$		0			0
$619$	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			0
$622$	−7.95021	−	5.77617i	−0.318774	−	0.231603i
$623$	10.8779	−	2.31217i	0.435814	−	0.0926352i
$624$		0			0
$625$	−13.3996	−	21.1057i	−0.535986	−	0.844227i
$626$	−12.7690	+	22.1166i	−0.510354	+	0.883958i
$627$		0			0
$628$	1.00287	−	9.54165i	0.0400188	−	0.380753i
$629$	0.0946637	+	0.0687772i	0.00377449	+	0.00274233i
$630$		0			0
$631$	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
$633$		0			0
$634$	30.4391	+	6.47004i	1.20889	+	0.256958i
$635$	12.2439	−	2.73743i	0.485883	−	0.108632i
$636$		0			0
$637$	16.8083	−	18.6675i	0.665968	−	0.739632i
$638$	−17.4600	−	53.7363i	−0.691247	−	2.12744i
$639$		0			0
$640$	−0.370792	+	0.169783i	−0.0146568	+	0.00671126i
$641$	21.9255	−	24.3507i	0.866005	−	0.961796i	−0.133567	−	0.991040i	$-0.542643\pi$
$641$	21.9255	−	24.3507i	0.866005	−	0.961796i	0.999572	+	0.0292433i	$0.00930976\pi$
$642$		0			0
$643$	−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
$645$		0			0
$646$	−0.249809	+	2.37677i	−0.00982861	+	0.0935130i
$647$	−8.36159	−	6.07505i	−0.328728	−	0.238835i	0.411163	−	0.911562i	$-0.365123\pi$
$647$	−8.36159	−	6.07505i	−0.328728	−	0.238835i	−0.739891	+	0.672727i	$0.765123\pi$
$648$		0			0
$649$	−37.3997			−1.46807
$650$	−9.87774	+	17.9715i	−0.387437	+	0.704902i
$651$		0			0
$652$	−2.55824	−	2.84121i	−0.100188	−	0.111271i
$653$	−11.7357	+	5.22507i	−0.459253	+	0.204473i	−0.623305	−	0.781979i	$-0.714210\pi$
$653$	−11.7357	+	5.22507i	−0.459253	+	0.204473i	0.164051	+	0.986452i	$0.447544\pi$
$654$		0			0
$655$	9.86009	−	7.32347i	0.385266	−	0.286152i
$656$	−10.2505	+	7.44740i	−0.400214	+	0.290772i
$657$		0			0
$658$	5.84516	−	4.24676i	0.227868	−	0.165556i
$659$	−3.17399	+	3.52507i	−0.123641	+	0.137317i	−0.801787	−	0.597610i	$-0.796117\pi$
$659$	−3.17399	+	3.52507i	−0.123641	+	0.137317i	0.678146	+	0.734927i	$0.262784\pi$
$660$		0			0
$661$	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
$663$		0			0
$664$	6.40098	−	1.36057i	0.248406	−	0.0528003i
$665$	−0.799241	−	6.90479i	−0.0309932	−	0.267756i
$666$		0			0
$667$	−0.833768	+	0.605768i	−0.0322836	+	0.0234554i
$668$	−6.28049	−	10.8781i	−0.242999	−	0.420887i
$669$		0			0
$670$	5.55674	−	6.30348i	0.214676	−	0.243525i
$671$	21.9895	−	9.79036i	0.848896	−	0.377953i
$672$		0			0
$673$	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
$675$		0			0
$676$	−1.24871			−0.0480274
$677$	−33.9900	+	7.22480i	−1.30634	+	0.277672i	−0.807935	−	0.589272i	$-0.799415\pi$
$677$	−33.9900	+	7.22480i	−1.30634	+	0.277672i	−0.498407	+	0.866943i	$0.666081\pi$
$678$		0			0
$679$	3.52552	−	1.56966i	0.135297	−	0.0602380i
$680$	−3.01473	+	0.674022i	−0.115610	+	0.0258475i
$681$		0			0
$682$	11.3617	+	19.6790i	0.435062	+	0.753549i
$683$	33.1970	−	24.1191i	1.27025	−	0.922890i	0.271037	−	0.962569i	$-0.412633\pi$
$683$	33.1970	−	24.1191i	1.27025	−	0.922890i	0.999213	+	0.0396784i	$0.0126333\pi$
$684$		0			0
$685$	21.8046	+	4.39551i	0.833111	+	0.167944i
$686$	9.07254	−	1.92843i	0.346391	−	0.0736278i
$687$		0			0
$688$	−11.6770	−	2.48203i	−0.445182	−	0.0946263i
$689$	14.3756	+	15.9657i	0.547665	+	0.608243i
$690$		0			0
$691$	−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
$693$		0			0
$694$	−15.0708	+	10.9496i	−0.572079	+	0.415640i
$695$	−2.87959	+	9.19030i	−0.109229	+	0.348608i
$696$		0			0
$697$	3.23025	−	1.43820i	0.122355	−	0.0544758i
$698$	20.9579	+	23.2761i	0.793269	+	0.881014i
$699$		0			0
$700$	2.40232	−	1.13072i	0.0907993	−	0.0427373i
$701$	−0.897737			−0.0339071			−0.0169535	−	0.999856i	$-0.505397\pi$
$701$	−0.897737			−0.0339071			−0.0169535	+	0.999856i	$0.505397\pi$
$702$		0			0
$703$	−1.02941	−	0.747907i	−0.0388247	−	0.0282078i
$704$	−4.33825	+	41.2757i	−0.163504	+	1.55564i
$705$		0			0
$706$	2.10386	+	20.0169i	0.0791800	+	0.753347i
$707$	1.25539	−	2.17439i	0.0472137	−	0.0817765i
$708$		0			0
$709$	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
$711$		0			0
$712$	16.6083	+	51.1152i	0.622424	+	1.91562i
$713$	0.277339	−	0.308016i	0.0103864	−	0.0115353i
$714$		0			0
$715$	−22.6202	−	38.2446i	−0.845949	−	1.43027i
$716$	−17.8783	−	3.80016i	−0.668145	−	0.142019i
$717$		0			0
$718$	−2.07347	−	3.59136i	−0.0773813	−	0.134028i
$719$	−34.2388	+	24.8759i	−1.27689	+	0.927716i	−0.999454	−	0.0330279i	$-0.989485\pi$
$719$	−34.2388	+	24.8759i	−1.27689	+	0.927716i	−0.277437	+	0.960744i	$0.589485\pi$
$720$		0			0
$721$	0.587847	+	0.427096i	0.0218926	+	0.0159059i
$722$	0.576508	−	5.48510i	0.0214554	−	0.204134i
$723$		0			0
$724$	−7.55762	+	13.0902i	−0.280877	+	0.486493i
$725$	−41.2422	−	28.6583i	−1.53170	−	1.06434i
$726$		0			0
$727$	−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
$729$		0			0
$730$	−33.7257	+	15.4428i	−1.24824	+	0.571562i
$731$	3.04353	+	1.35507i	0.112569	+	0.0501190i
$732$		0			0
$733$	−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
$735$		0			0
$736$	0.439018	−	0.0933161i	0.0161824	−	0.00343968i
$737$	5.62629	+	17.3159i	0.207247	+	0.637841i
$738$		0			0
$739$	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
$741$		0			0
$742$	0.402387	+	3.82846i	0.0147721	+	0.140547i
$743$	−0.560250	+	0.970382i	−0.0205536	+	0.0355999i	−0.876119	−	0.482094i	$-0.839876\pi$
$743$	−0.560250	+	0.970382i	−0.0205536	+	0.0355999i	0.855566	+	0.517694i	$0.173210\pi$
$744$		0			0
$745$	0.174100	−	0.00183143i	0.00637853	−	6.70982e-5i
$746$	−14.4225	−	10.4786i	−0.528046	−	0.383648i
$747$		0			0
$748$	0.611228	−	1.88116i	0.0223487	−	0.0687822i
$749$	−1.29853	−	2.24913i	−0.0474474	−	0.0821813i
$750$		0			0
$751$	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
$753$		0			0
$754$	−4.30619	+	40.9706i	−0.156822	+	1.49206i
$755$	18.8726	−	33.4971i	0.686843	−	1.21908i
$756$		0			0
$757$	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			0
$760$	32.7832	−	7.32954i	1.18917	−	0.265870i
$761$	−8.86063	−	9.84073i	−0.321198	−	0.356726i	0.560824	−	0.827935i	$-0.310484\pi$
$761$	−8.86063	−	9.84073i	−0.321198	−	0.356726i	−0.882022	+	0.471209i	$0.843818\pi$
$762$		0			0
$763$	−0.0419726	+	0.0466153i	−0.00151951	+	0.00168759i
$764$	2.64762	−	8.14854i	0.0957875	−	0.294804i
$765$		0			0
$766$	−7.25052	−	22.3148i	−0.261972	−	0.806267i
$767$	24.9113	+	11.0912i	0.899494	+	0.400480i
$768$		0			0
$769$	−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
$771$		0			0
$772$	1.11484	−	10.6070i	0.0401241	−	0.381756i
$773$	9.74410	−	29.9892i	0.350471	−	1.07864i	−0.608119	−	0.793846i	$-0.708075\pi$
$773$	9.74410	−	29.9892i	0.350471	−	1.07864i	0.958589	−	0.284792i	$-0.0919245\pi$
$774$		0			0
$775$	18.6203	+	7.82520i	0.668862	+	0.281090i
$776$	9.32535	+	16.1520i	0.334761	+	0.579823i
$777$		0			0
$778$	−1.07341	+	0.477915i	−0.0384838	+	0.0171341i
$779$	−35.1269	+	15.6395i	−1.25855	+	0.560343i
$780$		0			0
$781$	−20.5048	−	9.12933i	−0.733720	−	0.326673i
$782$	0.0499303			0.00178550
$783$		0			0
$784$	3.30017	+	10.1569i	0.117863	+	0.362745i
$785$	−25.5703	+	0.268984i	−0.912642	+	0.00960044i
$786$		0			0
$787$	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
$789$		0			0
$790$	−2.63979	+	1.96067i	−0.0939195	+	0.0697576i
$791$	2.60055	+	8.00367i	0.0924649	+	0.284578i
$792$		0			0
$793$	−17.5502			−0.623226
$794$	−18.8195	−	8.37899i	−0.667880	−	0.297359i
$795$		0			0
$796$	−5.43849	+	2.42137i	−0.192762	+	0.0858232i
$797$	34.2521	−	15.2500i	1.21327	−	0.540183i	0.302522	−	0.953142i	$-0.402171\pi$
$797$	34.2521	−	15.2500i	1.21327	−	0.540183i	0.910750	+	0.412959i	$0.135505\pi$
$798$		0			0
$799$	−2.39207	−	4.14319i	−0.0846255	−	0.146576i
$800$	11.3319	+	18.7072i	0.400642	+	0.661398i
$801$		0			0
$802$	−0.310796	+	0.956533i	−0.0109746	+	0.0337764i
$803$	8.40100	−	79.9302i	0.296465	−	2.82068i
$804$		0			0
$805$	−0.141723	+	0.0316858i	−0.00499507	+	0.00111678i
$806$	−1.73183	−	16.4772i	−0.0610011	−	0.580386i
$807$		0			0
$808$	11.0851	+	4.93541i	0.389973	+	0.173627i
$809$	2.07744	+	6.39370i	0.0730388	+	0.224790i	0.980911	−	0.194456i	$-0.0622942\pi$
$809$	2.07744	+	6.39370i	0.0730388	+	0.224790i	−0.907872	+	0.419247i	$0.862294\pi$
$810$		0			0
$811$	−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
$813$		0			0
$814$	−0.975223	−	1.08309i	−0.0341815	−	0.0379625i
$815$	−6.73851	+	7.64407i	−0.236040	+	0.267760i
$816$		0			0
$817$	−33.0964	−	14.7355i	−1.15790	−	0.515529i
$818$	24.6150			0.860644
$819$		0			0
$820$	−9.94226	−	10.8111i	−0.347199	−	0.377540i
$821$	0.235317	−	2.23889i	0.00821263	−	0.0781380i	−0.989648	−	0.143517i	$-0.954159\pi$
$821$	0.235317	−	2.23889i	0.00821263	−	0.0781380i	0.997861	+	0.0653788i	$0.0208256\pi$
$822$		0			0
$823$	−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
$825$		0			0
$826$	2.44304	+	4.23148i	0.0850044	+	0.147232i
$827$	9.90533	−	30.4855i	0.344442	−	1.06008i	−0.617440	−	0.786618i	$-0.711830\pi$
$827$	9.90533	−	30.4855i	0.344442	−	1.06008i	0.961882	−	0.273466i	$-0.0881700\pi$
$828$		0			0
$829$	−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
$831$		0			0
$832$	15.1303	−	26.2064i	0.524548	−	0.908544i
$833$	−0.311536	−	2.96407i	−0.0107941	−	0.102699i
$834$		0			0
$835$	−26.8767	+	19.9623i	−0.930106	+	0.690825i
$836$	−6.64670	+	20.4564i	−0.229881	+	0.707500i
$837$		0			0
$838$	−3.53490	−	10.8793i	−0.122111	−	0.375820i
$839$	29.9381	−	6.36354i	1.03358	−	0.219694i	0.340264	−	0.940330i	$-0.389483\pi$
$839$	29.9381	−	6.36354i	1.03358	−	0.219694i	0.693314	+	0.720636i	$0.256150\pi$
$840$		0			0
$841$	−70.3179	−	14.9465i	−2.42476	−	0.515398i
$842$	2.07068	+	19.7012i	0.0713604	+	0.678949i
$843$		0			0
$844$	−20.3064	−	9.04100i	−0.698976	−	0.311204i
$845$	0.382693	+	3.30615i	0.0131650	+	0.113735i
$846$		0			0
$847$	8.32326	+	6.04720i	0.285991	+	0.207784i
$848$	−8.93427	+	1.89904i	−0.306804	+	0.0652133i
$849$		0			0
$850$	0.800397	+	2.29773i	0.0274534	+	0.0788115i
$851$	−0.0132920	+	0.0230224i	−0.000455643	+	0.000789197i
$852$		0			0
$853$	−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
$855$		0			0
$856$	10.1541	−	7.37742i	0.347062	−	0.252155i
$857$	14.7634	+	25.5710i	0.504309	+	0.873488i	0.999988	+	0.00498242i	$0.00158596\pi$
$857$	14.7634	+	25.5710i	0.504309	+	0.873488i	−0.495679	+	0.868506i	$0.665081\pi$
$858$		0			0
$859$	−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
$861$		0			0
$862$	5.31654	−	5.90462i	0.181082	−	0.201112i
$863$	9.94721	+	30.6144i	0.338607	+	1.04212i	0.964918	+	0.262552i	$0.0845640\pi$
$863$	9.94721	+	30.6144i	0.338607	+	1.04212i	−0.626311	+	0.779573i	$0.715436\pi$
$864$		0			0
$865$	5.40894	+	5.88163i	0.183910	+	0.199981i
$866$	3.79893	−	4.21914i	0.129093	−	0.143372i
$867$		0			0
$868$	−1.07255	+	1.85772i	−0.0364048	+	0.0630550i
$869$	−0.744740	−	7.08573i	−0.0252636	−	0.240367i
$870$		0			0
$871$	1.38762	−	13.2023i	0.0470178	−	0.447344i
$872$	−0.245254	−	0.178187i	−0.00830533	−	0.00603418i
$873$		0			0
$874$	−0.542959			−0.0183659
$875$	−3.73000	−	6.01397i	−0.126097	−	0.203309i
$876$		0			0
$877$	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
$879$		0			0
$880$	18.8898	−	0.198709i	0.636774	−	0.00669848i
$881$	−26.9732	+	19.5972i	−0.908750	+	0.660246i	−0.940699	−	0.339244i	$-0.889829\pi$
$881$	−26.9732	+	19.5972i	−0.908750	+	0.660246i	0.0319481	+	0.999490i	$0.489829\pi$
$882$		0			0
$883$	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
$885$		0			0
$886$	−16.6846	−	18.5301i	−0.560529	−	0.622531i
$887$	35.8545	+	7.62112i	1.20388	+	0.255892i	0.765820	−	0.643055i	$-0.222333\pi$
$887$	35.8545	+	7.62112i	1.20388	+	0.255892i	0.438058	+	0.898947i	$0.355667\pi$
$888$		0			0
$889$	3.47384	−	0.738388i	0.116509	−	0.0247647i
$890$	38.4892	−	17.6239i	1.29016	−	0.590756i
$891$		0			0
$892$	2.67256	−	1.94173i	0.0894838	−	0.0650138i
$893$	26.0122	+	45.0545i	0.870466	+	1.50769i
$894$		0			0
$895$	−4.58232	+	48.5002i	−0.153170	+	1.62118i
$896$	−0.105460	+	0.0469539i	−0.00352318	+	0.00156862i
$897$		0			0
$898$	−20.8087	+	4.42302i	−0.694394	+	0.147598i
$899$	40.5747			1.35324
$900$		0			0
$901$	2.54903			0.0849206
$902$	−43.0803	+	9.15699i	−1.43442	+	0.304895i
$903$		0			0
$904$	−37.1549	+	16.5424i	−1.23575	+	0.550193i
$905$	36.9744	+	15.9982i	1.22907	+	0.531798i
$906$		0			0
$907$	−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
$909$		0			0
$910$	−2.84946	+	5.05753i	−0.0944586	+	0.167655i
$911$	−55.5454	+	11.8065i	−1.84030	+	0.391168i	−0.990678	−	0.136222i	$-0.956504\pi$
$911$	−55.5454	+	11.8065i	−1.84030	+	0.391168i	−0.849623	+	0.527390i	$0.823171\pi$
$912$		0			0
$913$	10.9239	+	2.32194i	0.361527	+	0.0768450i
$914$	−1.08854	−	1.20895i	−0.0360058	−	0.0399885i
$915$		0			0
$916$	8.50085	−	9.44116i	0.280876	−	0.311945i
$917$	2.81276	−	2.04359i	0.0928854	−	0.0674852i
$918$		0			0
$919$	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
$921$		0			0
$922$	0.978042	−	0.435453i	0.0322101	−	0.0143409i
$923$	10.9505	+	12.1618i	0.360440	+	0.400309i
$924$		0			0
$925$	−1.27253	−	0.242625i	−0.0418407	−	0.00797746i
$926$	−20.6074			−0.677200
$927$		0			0
$928$	35.5460	+	25.8257i	1.16685	+	0.847769i
$929$	−4.04198	+	38.4568i	−0.132613	+	1.26173i	0.702514	+	0.711670i	$0.252061\pi$
$929$	−4.04198	+	38.4568i	−0.132613	+	1.26173i	−0.835127	+	0.550058i	$0.814606\pi$
$930$		0			0
$931$	3.38775	+	32.2323i	0.111029	+	1.05637i
$932$	5.35616	−	9.27714i	0.175447	−	0.303883i
$933$		0			0
$934$	7.00794	−	7.78311i	0.229307	−	0.254671i
$935$	−5.16799	−	1.04180i	−0.169011	−	0.0340704i
$936$		0			0
$937$	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
$939$		0			0
$940$	−13.1412	+	14.9072i	−0.428618	+	0.486218i
$941$	10.7042	+	2.27524i	0.348946	+	0.0741707i	0.379050	−	0.925376i	$-0.376251\pi$
$941$	10.7042	+	2.27524i	0.348946	+	0.0741707i	−0.0301046	+	0.999547i	$0.509584\pi$
$942$		0			0
$943$	0.401671	+	0.695714i	0.0130802	+	0.0226556i
$944$	−9.37918	+	6.81437i	−0.305266	+	0.221789i
$945$		0			0
$946$	−33.5716	−	24.3912i	−1.09151	−	0.793027i
$947$	−5.13830	+	48.8876i	−0.166972	+	1.58863i	0.514957	+	0.857216i	$0.327808\pi$
$947$	−5.13830	+	48.8876i	−0.166972	+	1.58863i	−0.681929	+	0.731418i	$0.738859\pi$
$948$		0			0
$949$	−29.2997	+	50.7486i	−0.951109	+	1.64737i
$950$	−8.70379	−	24.9863i	−0.282388	−	0.810663i
$951$		0			0
$952$	−0.855343	+	0.181809i	−0.0277218	+	0.00589246i
$953$	−13.3275	−	9.68303i	−0.431721	−	0.313664i	0.350615	−	0.936520i	$-0.385972\pi$
$953$	−13.3275	−	9.68303i	−0.431721	−	0.313664i	−0.782337	+	0.622856i	$0.785972\pi$
$954$		0			0
$955$	−22.3859	−	4.51269i	−0.724390	−	0.146027i
$956$	−9.82969	−	4.37646i	−0.317915	−	0.141545i
$957$		0			0
$958$	1.74113	+	16.5657i	0.0562533	+	0.535214i
$959$	6.15882	+	1.30910i	0.198879	+	0.0422730i
$960$		0			0
$961$	14.3612	−	3.05256i	0.463263	−	0.0984696i
$962$	0.328377	+	1.01064i	0.0105873	+	0.0325843i
$963$		0			0
$964$	−7.16615	+	22.0551i	−0.230806	+	0.710348i
$965$	−28.4254	+	0.299018i	−0.915045	+	0.00962572i
$966$		0			0
$967$	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
$969$		0			0
$970$	11.7930	−	8.75912i	0.378651	−	0.281238i
$971$	1.48662	+	1.08010i	0.0477080	+	0.0346619i	0.611384	−	0.791334i	$-0.290613\pi$
$971$	1.48662	+	1.08010i	0.0477080	+	0.0346619i	−0.563676	+	0.825996i	$0.690613\pi$
$972$		0			0
$973$	−0.842449	+	2.59279i	−0.0270077	+	0.0831211i
$974$	7.73651	+	13.4000i	0.247894	+	0.429364i
$975$		0			0
$976$	3.73073	−	6.46181i	0.119418	−	0.206838i
$977$	38.7931	+	43.0841i	1.24110	+	1.37838i	0.898542	+	0.438887i	$0.144627\pi$
$977$	38.7931	+	43.0841i	1.24110	+	1.37838i	0.342559	+	0.939496i	$0.388706\pi$
$978$		0			0
$979$	−9.58758	+	91.2197i	−0.306420	+	2.91540i
$980$	−11.2561	+	5.15409i	−0.359563	+	0.164641i
$981$		0			0
$982$	−4.04328			−0.129026
$983$	−17.6257	−	7.84748i	−0.562173	−	0.250296i	0.105918	−	0.994375i	$-0.466222\pi$
$983$	−17.6257	−	7.84748i	−0.562173	−	0.250296i	−0.668092	+	0.744079i	$0.732889\pi$
$984$		0			0
$985$	1.42284	−	15.0597i	0.0453356	−	0.479841i
$986$	3.27063	+	3.63240i	0.104158	+	0.115679i
$987$		0			0
$988$	10.4938	−	11.6545i	0.333851	−	0.370779i
$989$	−0.233896	+	0.719859i	−0.00743748	+	0.0228902i
$990$		0			0
$991$	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
$993$		0			0
$994$	0.306516	+	2.91630i	0.00972210	+	0.0924996i
$995$	8.07767	+	13.6571i	0.256079	+	0.432960i
$996$		0			0
$997$	−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			0

Twists

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

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

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.r (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.05398 - 0.224029i) q^{2} +(-0.766416 + 0.341231i) q^{4} +(1.13834 + 1.92462i) q^{5} +(0.316483 + 0.548165i) q^{7} +(-2.47480 + 1.79805i) q^{8} +(1.63096 + 1.77348i) q^{10} +(-5.10644 + 1.08541i) q^{11} +(3.72319 + 0.791388i) q^{13} +(0.456370 + 0.506851i) q^{14} +(-1.08284 + 1.20261i) q^{16} +(0.365368 - 0.265455i) q^{17} +(-3.97313 + 2.88665i) q^{19} +(-1.52918 - 1.08663i) q^{20} +(-5.13890 + 2.28798i) q^{22} +(0.0686557 + 0.0762499i) q^{23} +(-2.40836 + 4.38176i) q^{25} +4.10144 q^{26} +(-0.429608 - 0.312129i) q^{28} +(-1.04992 + 9.98932i) q^{29} +(-0.422249 - 4.01743i) q^{31} +(2.18716 - 3.78828i) q^{32} +(0.325619 - 0.361636i) q^{34} +(-0.694745 + 1.23311i) q^{35} +(0.0800637 + 0.246411i) q^{37} +(-3.54089 + 3.93256i) q^{38} +(-6.27775 - 2.71627i) q^{40} +(7.65841 + 1.62785i) q^{41} +(3.68846 + 6.38860i) q^{43} +(3.54328 - 2.57435i) q^{44} +(0.0894437 + 0.0649846i) q^{46} +(1.10730 - 10.5353i) q^{47} +(3.29968 - 5.71521i) q^{49} +(-1.55670 + 5.15781i) q^{50} +(-3.12356 + 0.663933i) q^{52} +(4.56626 + 3.31758i) q^{53} +(-7.90187 - 8.59241i) q^{55} +(-1.76886 - 0.787548i) q^{56} +(1.13131 + 10.7637i) q^{58} +(7.00744 + 1.48948i) q^{59} +(-4.51000 + 0.958629i) q^{61} +(-1.34506 - 4.13967i) q^{62} +(2.45668 - 7.56088i) q^{64} +(2.71514 + 8.06661i) q^{65} +(-0.364553 - 3.46849i) q^{67} +(-0.189442 + 0.328124i) q^{68} +(-0.455991 + 1.45531i) q^{70} +(3.47832 + 2.52715i) q^{71} +(-4.75735 + 14.6416i) q^{73} +(0.139588 + 0.241774i) q^{74} +(2.06006 - 3.56813i) q^{76} +(-2.21108 - 2.45566i) q^{77} +(-0.142656 + 1.35728i) q^{79} +(-3.54721 - 0.715070i) q^{80} +8.43646 q^{82} +(-1.95429 - 0.870105i) q^{83} +(0.926814 + 0.401017i) q^{85} +(5.31878 + 5.90711i) q^{86} +(10.6858 - 11.8678i) q^{88} +(5.42929 - 16.7096i) q^{89} +(0.744515 + 2.29138i) q^{91} +(-0.0786377 - 0.0350118i) q^{92} +(-1.19314 - 11.3520i) q^{94} +(-10.0785 - 4.36079i) q^{95} +(0.637304 - 6.06354i) q^{97} +(2.19740 - 6.76291i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28}+ \cdots - 146 q^{98}+O(q^{100}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Introduction

L-functions

Modular forms

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Database

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