LMFDB - Embedded newform 261.2.k.a.199.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [261,2,Mod(82,261)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(261, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("261.82"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.k (of order $7$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			199.1
Root			$0.900969 + 0.433884i$ of defining polynomial
Character	$\chi$	$=$	261.199
Dual form			261.2.k.a.181.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.277479 - 1.21572i) q^{2} +(0.400969 + 0.193096i) q^{4} +(-0.900969 + 3.94740i) q^{5} +(-0.623490 + 0.300257i) q^{7} +(1.90097 - 2.38374i) q^{8} +(4.54892 + 2.19064i) q^{10} +(1.77748 + 2.22889i) q^{11} +(0.914542 + 1.14680i) q^{13} +(0.192021 + 0.841301i) q^{14} +(-1.81551 - 2.27658i) q^{16} +1.60388 q^{17} +(2.42543 + 1.16802i) q^{19} +(-1.12349 + 1.40881i) q^{20} +(3.20291 - 1.54244i) q^{22} +(-1.14795 - 5.02949i) q^{23} +(-10.2654 - 4.94355i) q^{25} +(1.64795 - 0.793610i) q^{26} -0.307979 q^{28} +(-3.71379 - 3.89971i) q^{29} +(0.434157 - 1.90216i) q^{31} +(2.22252 - 1.07031i) q^{32} +(0.445042 - 1.94986i) q^{34} +(-0.623490 - 2.73169i) q^{35} +(1.77748 - 2.22889i) q^{37} +(2.09299 - 2.62453i) q^{38} +(7.69687 + 9.65156i) q^{40} -6.49396 q^{41} +(-0.147948 - 0.648205i) q^{43} +(0.282323 + 1.23694i) q^{44} -6.43296 q^{46} +(2.96346 + 3.71606i) q^{47} +(-4.06584 + 5.09841i) q^{49} +(-8.85839 + 11.1081i) q^{50} +(0.145260 + 0.636426i) q^{52} +(0.0108851 - 0.0476909i) q^{53} +(-10.3998 + 5.00827i) q^{55} +(-0.469501 + 2.05702i) q^{56} +(-5.77144 + 3.43282i) q^{58} +6.39612 q^{59} +(1.17845 - 0.567511i) q^{61} +(-2.19202 - 1.05562i) q^{62} +(-1.98039 - 8.67664i) q^{64} +(-5.35086 + 2.57684i) q^{65} +(9.32036 - 11.6874i) q^{67} +(0.643104 + 0.309703i) q^{68} -3.49396 q^{70} +(1.40850 + 1.76621i) q^{71} +(-1.85205 - 8.11437i) q^{73} +(-2.21648 - 2.77938i) q^{74} +(0.746980 + 0.936683i) q^{76} +(-1.77748 - 0.855989i) q^{77} +(-6.07338 + 7.61577i) q^{79} +(10.6223 - 5.11543i) q^{80} +(-1.80194 + 7.89481i) q^{82} +(-3.62349 - 1.74498i) q^{83} +(-1.44504 + 6.33114i) q^{85} -0.829085 q^{86} +8.69202 q^{88} +(2.50484 - 10.9744i) q^{89} +(-0.914542 - 0.440420i) q^{91} +(0.510885 - 2.23833i) q^{92} +(5.33997 - 2.57159i) q^{94} +(-6.79590 + 8.52179i) q^{95} +(4.11745 + 1.98286i) q^{97} +(5.07002 + 6.35761i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 2 q^{4} - q^{5} + q^{7} + 7 q^{8} + 9 q^{10} + 11 q^{11} - 5 q^{13} - 9 q^{14} + 4 q^{16} - 8 q^{17} + q^{19} - 2 q^{20} + 6 q^{22} + 7 q^{23} - 24 q^{25} - 4 q^{26} - 12 q^{28} - 6 q^{29}+ \cdots - 19 q^{98}+O(q^{100}) $ 6 * q + 2 * q^2 - 2 * q^4 - q^5 + q^7 + 7 * q^8 + 9 * q^10 + 11 * q^11 - 5 * q^13 - 9 * q^14 + 4 * q^16 - 8 * q^17 + q^19 - 2 * q^20 + 6 * q^22 + 7 * q^23 - 24 * q^25 - 4 * q^26 - 12 * q^28 - 6 * q^29 + 5 * q^31 + 13 * q^32 + 2 * q^34 + q^35 + 11 * q^37 - 2 * q^38 + 14 * q^40 - 20 * q^41 + 13 * q^43 - 20 * q^44 - 11 * q^47 - 22 * q^49 - q^50 - 10 * q^52 - 3 * q^53 - 17 * q^55 + 7 * q^56 - 16 * q^58 + 56 * q^59 + 3 * q^61 - 3 * q^62 + q^64 - 5 * q^65 + 19 * q^67 + 12 * q^68 - 2 * q^70 - 21 * q^71 - 25 * q^73 + 6 * q^74 - 5 * q^76 - 11 * q^77 - 9 * q^79 + 18 * q^80 - 2 * q^82 - 17 * q^83 - 8 * q^85 + 16 * q^86 + 42 * q^88 - 7 * q^89 + 5 * q^91 + 8 * q^94 - 13 * q^95 + q^97 - 19 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{4}{7}\right)$	$1$

Coefficient data

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

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

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

$2$	0.277479	−	1.21572i	0.196207	−	0.859640i	−0.776961	−	0.629548i	$-0.783240\pi$
$2$	0.277479	−	1.21572i	0.196207	−	0.859640i	0.973169	−	0.230092i	$-0.0739028\pi$
$3$		0			0
$3$		0			0
$4$	0.400969	+	0.193096i	0.200484	+	0.0965482i
$5$	−0.900969	+	3.94740i	−0.402926	+	1.76533i	0.212524	+	0.977156i	$0.431832\pi$
$5$	−0.900969	+	3.94740i	−0.402926	+	1.76533i	−0.615450	+	0.788176i	$0.711026\pi$
$6$		0			0
$7$	−0.623490	+	0.300257i	−0.235657	+	0.113486i	−0.547986	−	0.836488i	$-0.684605\pi$
$7$	−0.623490	+	0.300257i	−0.235657	+	0.113486i	0.312329	+	0.949974i	$0.398891\pi$
$8$	1.90097	−	2.38374i	0.672094	−	0.842779i
$9$		0			0
$10$	4.54892	+	2.19064i	1.43849	+	0.692742i
$11$	1.77748	+	2.22889i	0.535930	+	0.672035i	0.973906	−	0.226952i	$-0.0728759\pi$
$11$	1.77748	+	2.22889i	0.535930	+	0.672035i	−0.437976	+	0.898987i	$0.644304\pi$
$12$		0			0
$13$	0.914542	+	1.14680i	0.253648	+	0.318065i	0.892310	−	0.451422i	$-0.149083\pi$
$13$	0.914542	+	1.14680i	0.253648	+	0.318065i	−0.638662	+	0.769487i	$0.720512\pi$
$14$	0.192021	+	0.841301i	0.0513199	+	0.224847i
$15$		0			0
$16$	−1.81551	−	2.27658i	−0.453878	−	0.569145i
$17$	1.60388			0.388997			0.194498	−	0.980903i	$-0.437692\pi$
$17$	1.60388			0.388997			0.194498	+	0.980903i	$0.437692\pi$
$18$		0			0
$19$	2.42543	+	1.16802i	0.556431	+	0.267963i	0.690895	−	0.722955i	$-0.257217\pi$
$19$	2.42543	+	1.16802i	0.556431	+	0.267963i	−0.134463	+	0.990919i	$0.542931\pi$
$20$	−1.12349	+	1.40881i	−0.251220	+	0.315020i
$21$		0			0
$22$	3.20291	−	1.54244i	0.682862	−	0.328849i
$23$	−1.14795	−	5.02949i	−0.239364	−	1.04872i	−0.941588	−	0.336766i	$-0.890667\pi$
$23$	−1.14795	−	5.02949i	−0.239364	−	1.04872i	0.702225	−	0.711955i	$-0.252190\pi$
$24$		0			0
$25$	−10.2654	−	4.94355i	−2.05308	−	0.988711i
$26$	1.64795	−	0.793610i	0.323189	−	0.155640i
$27$		0			0
$28$	−0.307979			−0.0582025
$29$	−3.71379	−	3.89971i	−0.689634	−	0.724158i
$29$	−3.71379	−	3.89971i	−0.689634	−	0.724158i
$30$		0			0
$31$	0.434157	−	1.90216i	0.0779769	−	0.341639i	−0.920858	−	0.389898i	$-0.872510\pi$
$31$	0.434157	−	1.90216i	0.0779769	−	0.341639i	0.998835	+	0.0482592i	$0.0153674\pi$
$32$	2.22252	−	1.07031i	0.392890	−	0.189206i
$33$		0			0
$34$	0.445042	−	1.94986i	0.0763241	−	0.334398i
$35$	−0.623490	−	2.73169i	−0.105389	−	0.461739i
$36$		0			0
$37$	1.77748	−	2.22889i	0.292216	−	0.366427i	−0.613953	−	0.789342i	$-0.710422\pi$
$37$	1.77748	−	2.22889i	0.292216	−	0.366427i	0.906169	+	0.422915i	$0.138993\pi$
$38$	2.09299	−	2.62453i	0.339528	−	0.425754i
$39$		0			0
$40$	7.69687	+	9.65156i	1.21698	+	1.52605i
$41$	−6.49396			−1.01419			−0.507093	−	0.861891i	$-0.669280\pi$
$41$	−6.49396			−1.01419			−0.507093	+	0.861891i	$0.669280\pi$
$42$		0			0
$43$	−0.147948	−	0.648205i	−0.0225619	−	0.0988503i	0.962393	−	0.271660i	$-0.0875726\pi$
$43$	−0.147948	−	0.648205i	−0.0225619	−	0.0988503i	−0.984955	+	0.172810i	$0.944715\pi$
$44$	0.282323	+	1.23694i	0.0425619	+	0.186476i
$45$		0			0
$46$	−6.43296			−0.948488
$47$	2.96346	+	3.71606i	0.432265	+	0.542043i	0.949486	−	0.313809i	$-0.101605\pi$
$47$	2.96346	+	3.71606i	0.432265	+	0.542043i	−0.517221	+	0.855852i	$0.673034\pi$
$48$		0			0
$49$	−4.06584	+	5.09841i	−0.580835	+	0.728344i
$50$	−8.85839	+	11.1081i	−1.25277	+	1.57092i
$51$		0			0
$52$	0.145260	+	0.636426i	0.0201439	+	0.0882564i
$53$	0.0108851	−	0.0476909i	0.00149519	−	0.00655085i	−0.974175	−	0.225795i	$-0.927502\pi$
$53$	0.0108851	−	0.0476909i	0.00149519	−	0.00655085i	0.975670	+	0.219244i	$0.0703592\pi$
$54$		0			0
$55$	−10.3998	+	5.00827i	−1.40231	+	0.675315i
$56$	−0.469501	+	2.05702i	−0.0627396	+	0.274880i
$57$		0			0
$58$	−5.77144	+	3.43282i	−0.757827	+	0.450752i
$59$	6.39612			0.832704			0.416352	−	0.909203i	$-0.363308\pi$
$59$	6.39612			0.832704			0.416352	+	0.909203i	$0.363308\pi$
$60$		0			0
$61$	1.17845	−	0.567511i	0.150885	−	0.0726623i	−0.356918	−	0.934136i	$-0.616172\pi$
$61$	1.17845	−	0.567511i	0.150885	−	0.0726623i	0.507802	+	0.861474i	$0.330458\pi$
$62$	−2.19202	−	1.05562i	−0.278387	−	0.134064i
$63$		0			0
$64$	−1.98039	−	8.67664i	−0.247548	−	1.08458i
$65$	−5.35086	+	2.57684i	−0.663692	+	0.319617i
$66$		0			0
$67$	9.32036	−	11.6874i	1.13866	−	1.42784i	0.250615	−	0.968087i	$-0.419367\pi$
$67$	9.32036	−	11.6874i	1.13866	−	1.42784i	0.888048	−	0.459751i	$-0.152061\pi$
$68$	0.643104	+	0.309703i	0.0779878	+	0.0375570i
$69$		0			0
$70$	−3.49396			−0.417608
$71$	1.40850	+	1.76621i	0.167158	+	0.209610i	0.858354	−	0.513057i	$-0.171487\pi$
$71$	1.40850	+	1.76621i	0.167158	+	0.209610i	−0.691196	+	0.722667i	$0.742916\pi$
$72$		0			0
$73$	−1.85205	−	8.11437i	−0.216766	−	0.949715i	−0.959849	−	0.280516i	$-0.909494\pi$
$73$	−1.85205	−	8.11437i	−0.216766	−	0.949715i	0.743083	−	0.669199i	$-0.233363\pi$
$74$	−2.21648	−	2.77938i	−0.257661	−	0.323096i
$75$		0			0
$76$	0.746980	+	0.936683i	0.0856844	+	0.107445i
$77$	−1.77748	−	0.855989i	−0.202563	−	0.0975490i
$78$		0			0
$79$	−6.07338	+	7.61577i	−0.683308	+	0.856841i	−0.995654	−	0.0931270i	$-0.970314\pi$
$79$	−6.07338	+	7.61577i	−0.683308	+	0.856841i	0.312346	+	0.949968i	$0.398885\pi$
$80$	10.6223	−	5.11543i	1.18761	−	0.571922i
$81$		0			0
$82$	−1.80194	+	7.89481i	−0.198991	+	0.871835i
$83$	−3.62349	−	1.74498i	−0.397730	−	0.191537i	0.224318	−	0.974516i	$-0.427985\pi$
$83$	−3.62349	−	1.74498i	−0.397730	−	0.191537i	−0.622047	+	0.782980i	$0.713699\pi$
$84$		0			0
$85$	−1.44504	+	6.33114i	−0.156737	+	0.686709i
$86$	−0.829085			−0.0894025
$87$		0			0
$88$	8.69202			0.926573
$89$	2.50484	−	10.9744i	0.265513	−	1.16329i	−0.649659	−	0.760225i	$-0.725088\pi$
$89$	2.50484	−	10.9744i	0.265513	−	1.16329i	0.915172	−	0.403063i	$-0.132054\pi$
$90$		0			0
$91$	−0.914542	−	0.440420i	−0.0958701	−	0.0461686i
$92$	0.510885	−	2.23833i	0.0532635	−	0.233362i
$93$		0			0
$94$	5.33997	−	2.57159i	0.550776	−	0.265240i
$95$	−6.79590	+	8.52179i	−0.697244	+	0.874317i
$96$		0			0
$97$	4.11745	+	1.98286i	0.418064	+	0.201329i	0.631077	−	0.775721i	$-0.282613\pi$
$97$	4.11745	+	1.98286i	0.418064	+	0.201329i	−0.213013	+	0.977049i	$0.568328\pi$
$98$	5.07002	+	6.35761i	0.512150	+	0.642215i
$99$		0			0
$100$	−3.16152	−	3.96442i	−0.316152	−	0.396442i
$101$	0.714988	+	3.13257i	0.0711440	+	0.311702i	0.997962	−	0.0638082i	$-0.0203246\pi$
$101$	0.714988	+	3.13257i	0.0711440	+	0.311702i	−0.926818	+	0.375510i	$0.877467\pi$
$102$		0			0
$103$	−4.07338	−	5.10785i	−0.401362	−	0.503292i	0.539545	−	0.841957i	$-0.318596\pi$
$103$	−4.07338	−	5.10785i	−0.401362	−	0.503292i	−0.940907	+	0.338665i	$0.890025\pi$
$104$	4.47219			0.438534
$105$		0			0
$106$	−0.0549581	−	0.0264664i	−0.00533801	−	0.00257065i
$107$	3.60656	−	4.52249i	0.348660	−	0.437205i	−0.576319	−	0.817225i	$-0.695511\pi$
$107$	3.60656	−	4.52249i	0.348660	−	0.437205i	0.924978	+	0.380020i	$0.124083\pi$
$108$		0			0
$109$	−8.27628	+	3.98565i	−0.792724	+	0.381756i	−0.786004	−	0.618222i	$-0.787853\pi$
$109$	−8.27628	+	3.98565i	−0.792724	+	0.381756i	−0.00672026	+	0.999977i	$0.502139\pi$
$110$	3.20291	+	14.0329i	0.305385	+	1.33798i
$111$		0			0
$112$	1.81551	+	0.874304i	0.171550	+	0.0826140i
$113$	−8.07822	+	3.89027i	−0.759935	+	0.365965i	−0.773379	−	0.633944i	$-0.781435\pi$
$113$	−8.07822	+	3.89027i	−0.759935	+	0.365965i	0.0134437	+	0.999910i	$0.495721\pi$
$114$		0			0
$115$	20.8877			1.94779
$116$	−0.736094	−	2.28078i	−0.0683447	−	0.211765i
$117$		0			0
$118$	1.77479	−	7.77587i	0.163383	−	0.715826i
$119$	−1.00000	+	0.481575i	−0.0916698	+	0.0441459i
$120$		0			0
$121$	0.639219	−	2.80060i	0.0581108	−	0.254600i
$122$	−0.362937	−	1.59013i	−0.0328587	−	0.143964i
$123$		0			0
$124$	0.541385	−	0.678875i	0.0486178	−	0.0609648i
$125$	16.1407	−	20.2398i	1.44367	−	1.81030i
$126$		0			0
$127$	9.70440	+	12.1689i	0.861126	+	1.07982i	0.996035	+	0.0889600i	$0.0283543\pi$
$127$	9.70440	+	12.1689i	0.861126	+	1.07982i	−0.134909	+	0.990858i	$0.543074\pi$
$128$	−6.16421			−0.544844
$129$		0			0
$130$	1.64795	+	7.22013i	0.144535	+	0.633248i
$131$	2.98911	+	13.0962i	0.261160	+	1.14422i	0.919995	+	0.391930i	$0.128192\pi$
$131$	2.98911	+	13.0962i	0.261160	+	1.14422i	−0.658835	+	0.752288i	$0.728950\pi$
$132$		0			0
$133$	−1.86294			−0.161537
$134$	−11.6223	−	14.5739i	−1.00401	−	1.25899i
$135$		0			0
$136$	3.04892	−	3.82322i	0.261443	−	0.327839i
$137$	10.5945	−	13.2851i	0.905148	−	1.13502i	−0.0851931	−	0.996364i	$-0.527151\pi$
$137$	10.5945	−	13.2851i	0.905148	−	1.13502i	0.990341	−	0.138655i	$-0.0442779\pi$
$138$		0			0
$139$	−2.77359	−	12.1519i	−0.235253	−	1.03071i	−0.945209	−	0.326465i	$-0.894142\pi$
$139$	−2.77359	−	12.1519i	−0.235253	−	1.03071i	0.709956	−	0.704246i	$-0.248715\pi$
$140$	0.277479	−	1.21572i	0.0234513	−	0.102747i
$141$		0			0
$142$	2.53803	−	1.22225i	0.212987	−	0.102569i
$143$	−0.930509	+	4.07683i	−0.0778131	+	0.340921i
$144$		0			0
$145$	18.7397	−	11.1463i	1.55625	−	0.925651i
$146$	−10.3787			−0.858945
$147$		0			0
$148$	1.14310	−	0.550490i	0.0939626	−	0.0452500i
$149$	−16.5015	−	7.94670i	−1.35185	−	0.651019i	−0.389050	−	0.921217i	$-0.627197\pi$
$149$	−16.5015	−	7.94670i	−1.35185	−	0.651019i	−0.962805	+	0.270198i	$0.912911\pi$
$150$		0			0
$151$	4.23609	+	18.5595i	0.344728	+	1.51035i	0.788961	+	0.614443i	$0.210619\pi$
$151$	4.23609	+	18.5595i	0.344728	+	1.51035i	−0.444233	+	0.895911i	$0.646524\pi$
$152$	7.39493	−	3.56121i	0.599808	−	0.288852i
$153$		0			0
$154$	−1.53385	+	1.92339i	−0.123601	+	0.154991i
$155$	7.11745	+	3.42758i	0.571687	+	0.275310i
$156$		0			0
$157$	−11.4383			−0.912879			−0.456439	−	0.889755i	$-0.650875\pi$
$157$	−11.4383			−0.912879			−0.456439	+	0.889755i	$0.650875\pi$
$158$	7.57338	+	9.49671i	0.602505	+	0.755518i
$159$		0			0
$160$	2.22252	+	9.73750i	0.175706	+	0.769817i
$161$	2.22587	+	2.79116i	0.175423	+	0.219974i
$162$		0			0
$163$	−4.16152	−	5.21838i	−0.325956	−	0.408735i	0.591671	−	0.806180i	$-0.298469\pi$
$163$	−4.16152	−	5.21838i	−0.325956	−	0.408735i	−0.917626	+	0.397444i	$0.869897\pi$
$164$	−2.60388	−	1.25396i	−0.203329	−	0.0979179i
$165$		0			0
$166$	−3.12684	+	3.92094i	−0.242690	+	0.304324i
$167$	−13.2153	+	6.36415i	−1.02263	+	0.492472i	−0.868558	−	0.495587i	$-0.834953\pi$
$167$	−13.2153	+	6.36415i	−1.02263	+	0.492472i	−0.154071	+	0.988060i	$0.549239\pi$
$168$		0			0
$169$	2.41401	−	10.5765i	0.185693	−	0.813575i
$170$	7.29590	+	3.51352i	0.559570	+	0.269475i
$171$		0			0
$172$	0.0658433	−	0.288478i	0.00502050	−	0.0219963i
$173$	23.3599			1.77602			0.888009	−	0.459825i	$-0.152088\pi$
$173$	23.3599			1.77602			0.888009	+	0.459825i	$0.152088\pi$
$174$		0			0
$175$	7.88471			0.596028
$176$	1.84721	−	8.09314i	0.139238	−	0.610044i
$177$		0			0
$178$	−12.6468	−	6.09035i	−0.947914	−	0.456491i
$179$	−0.147948	+	0.648205i	−0.0110582	+	0.0484491i	−0.980156	−	0.198228i	$-0.936481\pi$
$179$	−0.147948	+	0.648205i	−0.0110582	+	0.0484491i	0.969098	+	0.246677i	$0.0793386\pi$
$180$		0			0
$181$	−9.88016	+	4.75803i	−0.734386	+	0.353662i	−0.763408	−	0.645917i	$-0.776475\pi$
$181$	−9.88016	+	4.75803i	−0.734386	+	0.353662i	0.0290213	+	0.999579i	$0.490761\pi$
$182$	−0.789192	+	0.989616i	−0.0584988	+	0.0733552i
$183$		0			0
$184$	−14.1712	−	6.82450i	−1.04472	−	0.503108i
$185$	7.19687	+	9.02458i	0.529124	+	0.663501i
$186$		0			0
$187$	2.85086	+	3.57486i	0.208475	+	0.261420i
$188$	0.470697	+	2.06226i	0.0343291	+	0.150406i
$189$		0			0
$190$	8.47434	+	10.6265i	0.614794	+	0.770927i
$191$	0.518122			0.0374900			0.0187450	−	0.999824i	$-0.494033\pi$
$191$	0.518122			0.0374900			0.0187450	+	0.999824i	$0.494033\pi$
$192$		0			0
$193$	−1.24914	−	0.601552i	−0.0899147	−	0.0433007i	0.388386	−	0.921497i	$-0.373033\pi$
$193$	−1.24914	−	0.601552i	−0.0899147	−	0.0433007i	−0.478301	+	0.878196i	$0.658747\pi$
$194$	3.55310	−	4.45544i	0.255098	−	0.319882i
$195$		0			0
$196$	−2.61476	+	1.25920i	−0.186769	+	0.0899430i
$197$	2.88351	+	12.6335i	0.205442	+	0.900099i	0.967556	+	0.252656i	$0.0813042\pi$
$197$	2.88351	+	12.6335i	0.205442	+	0.900099i	−0.762114	+	0.647442i	$0.775839\pi$
$198$		0			0
$199$	17.5722	+	8.46232i	1.24566	+	0.599878i	0.936345	−	0.351082i	$-0.114186\pi$
$199$	17.5722	+	8.46232i	1.24566	+	0.599878i	0.309314	+	0.950960i	$0.399901\pi$
$200$	−31.2983	+	15.0725i	−2.21313	+	1.06579i
$201$		0			0
$202$	4.00670			0.281911
$203$	3.48643	+	1.31634i	0.244699	+	0.0923889i
$204$		0			0
$205$	5.85086	−	25.6343i	0.408641	−	1.79038i
$206$	−7.33997	+	3.53474i	−0.511400	+	0.246277i
$207$		0			0
$208$	0.950419	−	4.16406i	0.0658997	−	0.288725i
$209$	1.70775	+	7.48215i	0.118128	+	0.517551i
$210$		0			0
$211$	−12.8632	+	16.1300i	−0.885541	+	1.11043i	0.107679	+	0.994186i	$0.465658\pi$
$211$	−12.8632	+	16.1300i	−0.885541	+	1.11043i	−0.993220	+	0.116248i	$0.962913\pi$
$212$	0.0135735	−	0.0170207i	0.000932234	−	0.00116898i
$213$		0			0
$214$	−4.49731	−	5.63945i	−0.307430	−	0.385505i
$215$	2.69202			0.183594
$216$		0			0
$217$	0.300446	+	1.31634i	0.0203956	+	0.0893589i
$218$	2.54892	+	11.1675i	0.172634	+	0.756361i
$219$		0			0
$220$	−5.13706			−0.346341
$221$	1.46681	+	1.83932i	0.0986685	+	0.123726i
$222$		0			0
$223$	−13.1561	+	16.4973i	−0.881001	+	1.10474i	0.112806	+	0.993617i	$0.464016\pi$
$223$	−13.1561	+	16.4973i	−0.881001	+	1.10474i	−0.993807	+	0.111123i	$0.964555\pi$
$224$	−1.06435	+	1.33465i	−0.0711150	+	0.0891753i
$225$		0			0
$226$	2.48792	+	10.9003i	0.165494	+	0.725076i
$227$	1.58761	−	6.95579i	0.105374	−	0.461672i	−0.894519	−	0.447030i	$-0.852482\pi$
$227$	1.58761	−	6.95579i	0.105374	−	0.461672i	0.999893	−	0.0146424i	$-0.00466098\pi$
$228$		0			0
$229$	2.02930	−	0.977261i	0.134100	−	0.0645792i	−0.365631	−	0.930760i	$-0.619147\pi$
$229$	2.02930	−	0.977261i	0.134100	−	0.0645792i	0.499731	+	0.866181i	$0.333432\pi$
$230$	5.79590	−	25.3935i	0.382170	−	1.67440i
$231$		0			0
$232$	−16.3557	+	1.43948i	−1.07380	+	0.0945066i
$233$	−18.9095			−1.23880			−0.619400	−	0.785076i	$-0.712624\pi$
$233$	−18.9095			−1.23880			−0.619400	+	0.785076i	$0.712624\pi$
$234$		0			0
$235$	−17.3388	+	8.34991i	−1.13106	+	0.544688i
$236$	2.56465	+	1.23507i	0.166944	+	0.0803961i
$237$		0			0
$238$	0.307979	+	1.34934i	0.0199633	+	0.0874649i
$239$	−18.4448	+	8.88255i	−1.19310	+	0.574564i	−0.921700	−	0.387904i	$-0.873199\pi$
$239$	−18.4448	+	8.88255i	−1.19310	+	0.574564i	−0.271395	+	0.962468i	$0.587485\pi$
$240$		0			0
$241$	4.59448	−	5.76130i	0.295957	−	0.371118i	−0.611514	−	0.791234i	$-0.709439\pi$
$241$	4.59448	−	5.76130i	0.295957	−	0.371118i	0.907470	+	0.420116i	$0.138011\pi$
$242$	−3.22737	−	1.55422i	−0.207463	−	0.0999089i
$243$		0			0
$244$	0.582105			0.0372655
$245$	−16.4623	−	20.6430i	−1.05174	−	1.31883i
$246$		0			0
$247$	0.878666	+	3.84969i	0.0559082	+	0.244950i
$248$	−3.70895	−	4.65087i	−0.235518	−	0.295331i
$249$		0			0
$250$	−20.1271	−	25.2386i	−1.27295	−	1.59623i
$251$	11.6724	+	5.62114i	0.736756	+	0.354803i	0.764337	−	0.644817i	$-0.223066\pi$
$251$	11.6724	+	5.62114i	0.736756	+	0.354803i	−0.0275815	+	0.999620i	$0.508781\pi$
$252$		0			0
$253$	9.16972	−	11.4985i	0.576495	−	0.722902i
$254$	17.4867	−	8.42116i	1.09721	−	0.528391i
$255$		0			0
$256$	2.25033	−	9.85935i	0.140646	−	0.616209i
$257$	15.0390	+	7.24240i	0.938107	+	0.451768i	0.839501	−	0.543358i	$-0.182847\pi$
$257$	15.0390	+	7.24240i	0.938107	+	0.451768i	0.0986056	+	0.995127i	$0.468562\pi$
$258$		0			0
$259$	−0.439001	+	1.92339i	−0.0272782	+	0.119514i
$260$	−2.64310			−0.163918
$261$		0			0
$262$	16.7506			1.03486
$263$	3.91843	−	17.1678i	0.241621	−	1.05861i	−0.697921	−	0.716175i	$-0.745891\pi$
$263$	3.91843	−	17.1678i	0.241621	−	1.05861i	0.939542	−	0.342434i	$-0.111251\pi$
$264$		0			0
$265$	0.178448	+	0.0859360i	0.0109620	+	0.00527901i
$266$	−0.516926	+	2.26480i	−0.0316948	+	0.138864i
$267$		0			0
$268$	5.99396	−	2.88654i	0.366139	−	0.176323i
$269$	−4.18329	+	5.24568i	−0.255060	+	0.319835i	−0.892832	−	0.450390i	$-0.851285\pi$
$269$	−4.18329	+	5.24568i	−0.255060	+	0.319835i	0.637772	+	0.770225i	$0.279856\pi$
$270$		0			0
$271$	−11.4133	−	5.49638i	−0.693311	−	0.333881i	0.0538264	−	0.998550i	$-0.482858\pi$
$271$	−11.4133	−	5.49638i	−0.693311	−	0.333881i	−0.747138	+	0.664669i	$0.768573\pi$
$272$	−2.91185	−	3.65135i	−0.176557	−	0.221396i
$273$		0			0
$274$	−13.2111	−	16.5662i	−0.798112	−	1.00080i
$275$	−7.22790	−	31.6675i	−0.435859	−	1.90962i
$276$		0			0
$277$	9.81431	+	12.3068i	0.589685	+	0.739442i	0.983731	−	0.179649i	$-0.0574963\pi$
$277$	9.81431	+	12.3068i	0.589685	+	0.739442i	−0.394046	+	0.919091i	$0.628925\pi$
$278$	−15.5429			−0.932200
$279$		0			0
$280$	−7.69687	−	3.70662i	−0.459976	−	0.221513i
$281$	−7.36629	+	9.23703i	−0.439436	+	0.551035i	−0.951394	−	0.307975i	$-0.900349\pi$
$281$	−7.36629	+	9.23703i	−0.439436	+	0.551035i	0.511959	+	0.859010i	$0.328920\pi$
$282$		0			0
$283$	1.98039	−	0.953703i	0.117722	−	0.0566918i	−0.374096	−	0.927390i	$-0.622047\pi$
$283$	1.98039	−	0.953703i	0.117722	−	0.0566918i	0.491818	+	0.870698i	$0.336333\pi$
$284$	0.223717	+	0.980170i	0.0132752	+	0.0581624i
$285$		0			0
$286$	4.69806	+	2.26247i	0.277802	+	0.133783i
$287$	4.04892	−	1.94986i	0.239000	−	0.115096i
$288$		0			0
$289$	−14.4276			−0.848681
$290$	−8.35086	−	25.8751i	−0.490379	−	1.51944i
$291$		0			0
$292$	0.824240	−	3.61123i	0.0482350	−	0.211331i
$293$	−18.5993	+	8.95696i	−1.08658	+	0.523271i	−0.889416	−	0.457098i	$-0.848889\pi$
$293$	−18.5993	+	8.95696i	−1.08658	+	0.523271i	−0.197168	+	0.980370i	$0.563174\pi$
$294$		0			0
$295$	−5.76271	+	25.2481i	−0.335518	+	1.47000i
$296$	−1.93416	−	8.47409i	−0.112421	−	0.492547i
$297$		0			0
$298$	−14.2397	+	17.8561i	−0.824886	+	1.03437i
$299$	4.71797	−	5.91615i	0.272847	−	0.342140i
$300$		0			0
$301$	0.286872	+	0.359726i	0.0165350	+	0.0207343i
$302$	23.7385			1.36600
$303$		0			0
$304$	−1.74429	−	7.64224i	−0.100042	−	0.438312i
$305$	1.17845	+	5.16312i	0.0674777	+	0.295639i
$306$		0			0
$307$	22.8116			1.30193			0.650964	−	0.759108i	$-0.274365\pi$
$307$	22.8116			1.30193			0.650964	+	0.759108i	$0.274365\pi$
$308$	−0.547425	−	0.686450i	−0.0311925	−	0.0391141i
$309$		0			0
$310$	6.14191	−	7.70171i	0.348837	−	0.437428i
$311$	−19.3843	+	24.3072i	−1.09918	+	1.37833i	−0.180392	+	0.983595i	$0.557737\pi$
$311$	−19.3843	+	24.3072i	−1.09918	+	1.37833i	−0.918793	+	0.394740i	$0.870835\pi$
$312$		0			0
$313$	2.49947	+	10.9509i	0.141278	+	0.618980i	0.995139	+	0.0984792i	$0.0313978\pi$
$313$	2.49947	+	10.9509i	0.141278	+	0.618980i	−0.853861	+	0.520501i	$0.825745\pi$
$314$	−3.17390	+	13.9058i	−0.179113	+	0.784747i
$315$		0			0
$316$	−3.90581	+	1.88094i	−0.219719	+	0.105811i
$317$	−1.31886	+	5.77832i	−0.0740748	+	0.324543i	−0.998366	−	0.0571456i	$-0.981800\pi$
$317$	−1.31886	+	5.77832i	−0.0740748	+	0.324543i	0.924291	+	0.381688i	$0.124657\pi$
$318$		0			0
$319$	2.09083	−	15.2093i	0.117064	−	0.851556i
$320$	36.0344			2.01439
$321$		0			0
$322$	4.01089	−	1.93154i	0.223518	−	0.107641i
$323$	3.89008	+	1.87337i	0.216450	+	0.104237i
$324$		0			0
$325$	−3.71887	−	16.2934i	−0.206286	−	0.903798i
$326$	−7.49880	+	3.61123i	−0.415320	+	0.200008i
$327$		0			0
$328$	−12.3448	+	15.4799i	−0.681628	+	0.854735i
$329$	−2.96346	−	1.42713i	−0.163381	−	0.0786801i
$330$		0			0
$331$	30.9095			1.69894			0.849469	−	0.527639i	$-0.176923\pi$
$331$	30.9095			1.69894			0.849469	+	0.527639i	$0.176923\pi$
$332$	−1.11596	−	1.39937i	−0.0612461	−	0.0768002i
$333$		0			0
$334$	4.07002	+	17.8319i	0.222702	+	0.975720i
$335$	37.7373	+	47.3211i	2.06181	+	2.58543i
$336$		0			0
$337$	4.99731	+	6.26643i	0.272221	+	0.341354i	0.899085	−	0.437775i	$-0.144233\pi$
$337$	4.99731	+	6.26643i	0.272221	+	0.341354i	−0.626864	+	0.779129i	$0.715662\pi$
$338$	−12.1881	−	5.86950i	−0.662947	−	0.319259i
$339$		0			0
$340$	−1.80194	+	2.25956i	−0.0977238	+	0.122542i
$341$	5.01142	−	2.41337i	0.271383	−	0.130691i
$342$		0			0
$343$	2.08211	−	9.12230i	0.112423	−	0.492558i
$344$	−1.82640	−	0.879546i	−0.0984727	−	0.0474220i
$345$		0			0
$346$	6.48188	−	28.3990i	0.348468	−	1.52674i
$347$	2.26337			0.121504			0.0607521	−	0.998153i	$-0.480650\pi$
$347$	2.26337			0.121504			0.0607521	+	0.998153i	$0.480650\pi$
$348$		0			0
$349$	−23.5690			−1.26162			−0.630809	−	0.775938i	$-0.717277\pi$
$349$	−23.5690			−1.26162			−0.630809	+	0.775938i	$0.717277\pi$
$350$	2.18784	−	9.58556i	0.116945	−	0.512370i
$351$		0			0
$352$	6.33609	+	3.05130i	0.337714	+	0.162635i
$353$	−0.218636	+	0.957907i	−0.0116368	+	0.0509843i	−0.980413	−	0.196953i	$-0.936895\pi$
$353$	−0.218636	+	0.957907i	−0.0116368	+	0.0509843i	0.968776	+	0.247937i	$0.0797526\pi$
$354$		0			0
$355$	−8.24094	+	3.96863i	−0.437384	+	0.210633i
$356$	3.12349	−	3.91673i	0.165545	−	0.207586i
$357$		0			0
$358$	0.746980	+	0.359726i	0.0394791	+	0.0190121i
$359$	4.91454	+	6.16264i	0.259380	+	0.325252i	0.894421	−	0.447227i	$-0.147588\pi$
$359$	4.91454	+	6.16264i	0.259380	+	0.325252i	−0.635041	+	0.772478i	$0.719017\pi$
$360$		0			0
$361$	−7.32789	−	9.18888i	−0.385678	−	0.483625i
$362$	3.04288	+	13.3317i	0.159930	+	0.700699i
$363$		0			0
$364$	−0.281659	−	0.353190i	−0.0147630	−	0.0185122i
$365$	33.6993			1.76390
$366$		0			0
$367$	26.4056	+	12.7163i	1.37836	+	0.663783i	0.968649	−	0.248432i	$-0.0799154\pi$
$367$	26.4056	+	12.7163i	1.37836	+	0.663783i	0.409711	+	0.912216i	$0.365630\pi$
$368$	−9.36592	+	11.7445i	−0.488232	+	0.612224i
$369$		0			0
$370$	12.9683	−	6.24521i	0.674190	−	0.324673i
$371$	0.00753275	+	0.0330031i	0.000391081	+	0.00171344i
$372$		0			0
$373$	3.43512	+	1.65426i	0.177864	+	0.0856546i	0.520697	−	0.853742i	$-0.325672\pi$
$373$	3.43512	+	1.65426i	0.177864	+	0.0856546i	−0.342833	+	0.939396i	$0.611387\pi$
$374$	5.13706	−	2.47388i	0.265631	−	0.127921i
$375$		0			0
$376$	14.4916			0.747345
$377$	1.07577	−	7.82543i	0.0554049	−	0.403030i
$378$		0			0
$379$	−2.00849	+	8.79978i	−0.103169	+	0.452014i	0.896785	+	0.442466i	$0.145896\pi$
$379$	−2.00849	+	8.79978i	−0.103169	+	0.452014i	−0.999954	+	0.00954794i	$0.996961\pi$
$380$	−4.37047	+	2.10471i	−0.224200	+	0.107969i
$381$		0			0
$382$	0.143768	−	0.629889i	0.00735582	−	0.0322279i
$383$	−7.38524	−	32.3568i	−0.377368	−	1.65336i	−0.705488	−	0.708722i	$-0.749272\pi$
$383$	−7.38524	−	32.3568i	−0.377368	−	1.65336i	0.328120	−	0.944636i	$-0.393585\pi$
$384$		0			0
$385$	4.98039	−	6.24521i	0.253824	−	0.318285i
$386$	−1.07792	+	1.35168i	−0.0548649	+	0.0687984i
$387$		0			0
$388$	1.26809	+	1.59013i	0.0643773	+	0.0807266i
$389$	−27.5362			−1.39614			−0.698070	−	0.716030i	$-0.745957\pi$
$389$	−27.5362			−1.39614			−0.698070	+	0.716030i	$0.745957\pi$
$390$		0			0
$391$	−1.84117	−	8.06668i	−0.0931118	−	0.407949i
$392$	4.42423	+	19.3838i	0.223457	+	0.979031i
$393$		0			0
$394$	16.1588			0.814070
$395$	−24.5906	−	30.8356i	−1.23729	−	1.55151i
$396$		0			0
$397$	−11.9852	+	15.0290i	−0.601521	+	0.754284i	−0.985614	−	0.169010i	$-0.945943\pi$
$397$	−11.9852	+	15.0290i	−0.601521	+	0.754284i	0.384093	+	0.923294i	$0.374514\pi$
$398$	15.1637	−	19.0147i	0.760086	−	0.953118i
$399$		0			0
$400$	7.38255	+	32.3451i	0.369128	+	1.61725i
$401$	2.45353	−	10.7496i	0.122524	−	0.536811i	−0.875991	−	0.482327i	$-0.839792\pi$
$401$	2.45353	−	10.7496i	0.122524	−	0.536811i	0.998515	−	0.0544837i	$-0.0173513\pi$
$402$		0			0
$403$	2.57846	−	1.24172i	0.128442	−	0.0618545i
$404$	−0.318200	+	1.39412i	−0.0158310	+	0.0693603i
$405$		0			0
$406$	2.56770	−	3.87325i	0.127433	−	0.192226i
$407$	8.12737			0.402859
$408$		0			0
$409$	−30.4720	+	14.6745i	−1.50674	+	0.725608i	−0.991337	−	0.131339i	$-0.958072\pi$
$409$	−30.4720	+	14.6745i	−1.50674	+	0.725608i	−0.515404	+	0.856948i	$0.672358\pi$
$410$	−29.5405	−	14.2259i	−1.45890	−	0.702569i
$411$		0			0
$412$	−0.646989	−	2.83464i	−0.0318749	−	0.139653i
$413$	−3.98792	+	1.92048i	−0.196233	+	0.0945007i
$414$		0			0
$415$	10.1528	−	12.7312i	0.498381	−	0.624950i
$416$	3.26002	+	1.56994i	0.159836	+	0.0769728i
$417$		0			0
$418$	9.57002			0.468085
$419$	22.2080	+	27.8480i	1.08493	+	1.36046i	0.927882	+	0.372874i	$0.121628\pi$
$419$	22.2080	+	27.8480i	1.08493	+	1.36046i	0.157052	+	0.987590i	$0.449801\pi$
$420$		0			0
$421$	2.10441	+	9.22001i	0.102563	+	0.449356i	0.999967	+	0.00814670i	$0.00259320\pi$
$421$	2.10441	+	9.22001i	0.102563	+	0.449356i	−0.897404	+	0.441209i	$0.854550\pi$
$422$	16.0402	+	20.1138i	0.780824	+	0.979123i
$423$		0			0
$424$	−0.0929903	−	0.116606i	−0.00451601	−	0.00566290i
$425$	−16.4644	−	7.92885i	−0.798642	−	0.384606i
$426$		0			0
$427$	−0.564351	+	0.707674i	−0.0273109	+	0.0342468i
$428$	2.31940	−	1.11696i	0.112112	−	0.0539904i
$429$		0			0
$430$	0.746980	−	3.27273i	0.0360226	−	0.157825i
$431$	0.887928	+	0.427603i	0.0427700	+	0.0205969i	0.455146	−	0.890417i	$-0.349587\pi$
$431$	0.887928	+	0.427603i	0.0427700	+	0.0205969i	−0.412377	+	0.911014i	$0.635301\pi$
$432$		0			0
$433$	6.38285	−	27.9651i	0.306740	−	1.34392i	−0.552999	−	0.833182i	$-0.686517\pi$
$433$	6.38285	−	27.9651i	0.306740	−	1.34392i	0.859739	−	0.510734i	$-0.170626\pi$
$434$	1.68366			0.0808183
$435$		0			0
$436$	−4.08815			−0.195787
$437$	3.09030	−	13.5395i	0.147829	−	0.647682i
$438$		0			0
$439$	5.94116	+	2.86111i	0.283556	+	0.136553i	0.570256	−	0.821467i	$-0.306844\pi$
$439$	5.94116	+	2.86111i	0.283556	+	0.136553i	−0.286700	+	0.958020i	$0.592558\pi$
$440$	−7.83124	+	34.3109i	−0.373340	+	1.63571i
$441$		0			0
$442$	2.64310	−	1.27285i	0.125720	−	0.0605434i
$443$	13.3354	−	16.7221i	0.633585	−	0.794490i	−0.356599	−	0.934257i	$-0.616064\pi$
$443$	13.3354	−	16.7221i	0.633585	−	0.794490i	0.990184	+	0.139767i	$0.0446353\pi$
$444$		0			0
$445$	41.0637	+	19.7753i	1.94661	+	0.937437i
$446$	16.4054	+	20.5718i	0.776820	+	0.974102i
$447$		0			0
$448$	3.83997	+	4.81517i	0.181422	+	0.227495i
$449$	6.51022	+	28.5231i	0.307236	+	1.34609i	0.858951	+	0.512058i	$0.171117\pi$
$449$	6.51022	+	28.5231i	0.307236	+	1.34609i	−0.551715	+	0.834033i	$0.686026\pi$
$450$		0			0
$451$	−11.5429	−	14.4743i	−0.543533	−	0.681569i
$452$	−3.99031			−0.187688
$453$		0			0
$454$	−8.01573	−	3.86017i	−0.376197	−	0.181167i
$455$	2.56249	−	3.21326i	0.120131	−	0.150640i
$456$		0			0
$457$	0.217677	−	0.104828i	0.0101825	−	0.00490362i	−0.428786	−	0.903406i	$-0.641058\pi$
$457$	0.217677	−	0.104828i	0.0101825	−	0.00490362i	0.438968	+	0.898503i	$0.355344\pi$
$458$	−0.624982	−	2.73822i	−0.0292035	−	0.127949i
$459$		0			0
$460$	8.37531	+	4.03334i	0.390501	+	0.188055i
$461$	15.6211	−	7.52272i	0.727547	−	0.350368i	−0.0331719	−	0.999450i	$-0.510561\pi$
$461$	15.6211	−	7.52272i	0.727547	−	0.350368i	0.760719	+	0.649081i	$0.224847\pi$
$462$		0			0
$463$	4.24996			0.197513			0.0987563	−	0.995112i	$-0.468514\pi$
$463$	4.24996			0.197513			0.0987563	+	0.995112i	$0.468514\pi$
$464$	−2.13557	+	15.5347i	−0.0991414	+	0.721181i
$465$		0			0
$466$	−5.24698	+	22.9885i	−0.243062	+	1.06492i
$467$	−25.9780	+	12.5103i	−1.20212	+	0.578910i	−0.924279	−	0.381718i	$-0.875333\pi$
$467$	−25.9780	+	12.5103i	−1.20212	+	0.578910i	−0.277839	+	0.960628i	$0.589618\pi$
$468$		0			0
$469$	−2.30194	+	10.0854i	−0.106294	+	0.465703i
$470$	5.33997	+	23.3959i	0.246314	+	1.07917i
$471$		0			0
$472$	12.1588	−	15.2467i	0.559656	−	0.701786i
$473$	1.18180	−	1.48193i	0.0543392	−	0.0681392i
$474$		0			0
$475$	−19.1238	−	23.9805i	−0.877459	−	1.10030i
$476$	−0.493959			−0.0226406
$477$		0			0
$478$	5.68060	+	24.8884i	0.259825	+	1.13837i
$479$	−5.37986	−	23.5707i	−0.245812	−	1.07697i	−0.935628	−	0.352988i	$-0.885166\pi$
$479$	−5.37986	−	23.5707i	−0.245812	−	1.07697i	0.689816	−	0.723985i	$-0.257692\pi$
$480$		0			0
$481$	4.18167			0.190668
$482$	−5.72923	−	7.18422i	−0.260959	−	0.327232i
$483$		0			0
$484$	0.797093	−	0.999524i	0.0362315	−	0.0454329i
$485$	−11.5368	+	14.4667i	−0.523861	+	0.656901i
$486$		0			0
$487$	−4.29709	−	18.8268i	−0.194720	−	0.853124i	−0.974018	−	0.226470i	$-0.927281\pi$
$487$	−4.29709	−	18.8268i	−0.194720	−	0.853124i	0.779298	−	0.626653i	$-0.215576\pi$
$488$	0.887395	−	3.88793i	0.0401705	−	0.175998i
$489$		0			0
$490$	−29.6640	+	14.2854i	−1.34008	+	0.645349i
$491$	8.20895	−	35.9657i	0.370465	−	1.62311i	−0.355010	−	0.934863i	$-0.615523\pi$
$491$	8.20895	−	35.9657i	0.370465	−	1.62311i	0.725475	−	0.688249i	$-0.241620\pi$
$492$		0			0
$493$	−5.95646	−	6.25465i	−0.268265	−	0.281695i
$494$	4.92394			0.221538
$495$		0			0
$496$	−5.11865	+	2.46501i	−0.229834	+	0.110682i
$497$	−1.40850	−	0.678299i	−0.0631799	−	0.0304259i
$498$		0			0
$499$	−8.39254	−	36.7701i	−0.375701	−	1.64606i	−0.710450	−	0.703748i	$-0.751508\pi$
$499$	−8.39254	−	36.7701i	−0.375701	−	1.64606i	0.334748	−	0.942308i	$-0.391349\pi$
$500$	10.3802	−	4.99882i	0.464215	−	0.223554i
$501$		0			0
$502$	10.0725	−	12.6306i	0.449560	−	0.563730i
$503$	−6.31551	−	3.04139i	−0.281595	−	0.135609i	0.287756	−	0.957704i	$-0.407091\pi$
$503$	−6.31551	−	3.04139i	−0.281595	−	0.135609i	−0.569350	+	0.822095i	$0.692805\pi$
$504$		0			0
$505$	−13.0097			−0.578924
$506$	−11.4345	−	14.3383i	−0.508323	−	0.637417i
$507$		0			0
$508$	1.54138	+	6.75325i	0.0683879	+	0.299627i
$509$	−11.4641	−	14.3756i	−0.508138	−	0.637185i	0.459905	−	0.887968i	$-0.347883\pi$
$509$	−11.4641	−	14.3756i	−0.508138	−	0.637185i	−0.968043	+	0.250783i	$0.919312\pi$
$510$		0			0
$511$	3.59113	+	4.50313i	0.158862	+	0.199207i
$512$	−22.4693	−	10.8206i	−0.993011	−	0.478209i
$513$		0			0
$514$	12.9777	−	16.2735i	0.572422	−	0.717794i
$515$	23.8327	−	11.4772i	1.05020	−	0.505748i
$516$		0			0
$517$	−3.01520	+	13.2104i	−0.132608	+	0.580995i
$518$	2.21648	+	1.06740i	0.0973865	+	0.0468989i
$519$		0			0
$520$	−4.02930	+	17.6535i	−0.176697	+	0.774159i
$521$	−3.94571			−0.172865			−0.0864323	−	0.996258i	$-0.527547\pi$
$521$	−3.94571			−0.172865			−0.0864323	+	0.996258i	$0.527547\pi$
$522$		0			0
$523$	−33.9952			−1.48651			−0.743253	−	0.669010i	$-0.766718\pi$
$523$	−33.9952			−1.48651			−0.743253	+	0.669010i	$0.766718\pi$
$524$	−1.33028	+	5.82834i	−0.0581136	+	0.254612i
$525$		0			0
$526$	−19.7838	−	9.52738i	−0.862615	−	0.415414i
$527$	0.696333	−	3.05084i	0.0303328	−	0.132896i
$528$		0			0
$529$	−3.25571	+	1.56787i	−0.141553	+	0.0681681i
$530$	0.153989	−	0.193096i	0.00668887	−	0.00838757i
$531$		0			0
$532$	−0.746980	−	0.359726i	−0.0323857	−	0.0155961i
$533$	−5.93900	−	7.44727i	−0.257247	−	0.322577i
$534$		0			0
$535$	14.6027	+	18.3112i	0.631329	+	0.791661i
$536$	−10.1419	−	44.4346i	−0.438064	−	1.91928i
$537$		0			0
$538$	5.21648	+	6.54126i	0.224898	+	0.282014i
$539$	−18.5907			−0.800759
$540$		0			0
$541$	−21.1151	−	10.1685i	−0.907807	−	0.437177i	−0.0791047	−	0.996866i	$-0.525206\pi$
$541$	−21.1151	−	10.1685i	−0.907807	−	0.437177i	−0.828702	+	0.559689i	$0.810920\pi$
$542$	−9.84899	+	12.3502i	−0.423051	+	0.530489i
$543$		0			0
$544$	3.56465	−	1.71664i	0.152833	−	0.0736005i
$545$	−8.27628	−	36.2608i	−0.354517	−	1.55324i
$546$		0			0
$547$	−29.0976	−	14.0127i	−1.24412	−	0.599138i	−0.308193	−	0.951324i	$-0.599724\pi$
$547$	−29.0976	−	14.0127i	−1.24412	−	0.599138i	−0.935930	+	0.352186i	$0.885439\pi$
$548$	6.81336	−	3.28114i	0.291052	−	0.140163i
$549$		0			0
$550$	−40.5042			−1.72711
$551$	−4.45257	−	13.7963i	−0.189686	−	0.587741i
$552$		0			0
$553$	1.50000	−	6.57193i	0.0637865	−	0.279467i
$554$	17.6848	−	8.51654i	0.751354	−	0.361833i
$555$		0			0
$556$	1.23437	−	5.40811i	0.0523488	−	0.229355i
$557$	3.61045	+	15.8184i	0.152980	+	0.670248i	0.992010	+	0.126162i	$0.0402660\pi$
$557$	3.61045	+	15.8184i	0.152980	+	0.670248i	−0.839030	+	0.544085i	$0.816877\pi$
$558$		0			0
$559$	0.608056	−	0.762478i	0.0257180	−	0.0322494i
$560$	−5.08695	+	6.37883i	−0.214963	+	0.269555i
$561$		0			0
$562$	9.18561	+	11.5184i	0.387472	+	0.485874i
$563$	21.9168			0.923681			0.461841	−	0.886963i	$-0.347189\pi$
$563$	21.9168			0.923681			0.461841	+	0.886963i	$0.347189\pi$
$564$		0			0
$565$	−8.07822	−	35.3930i	−0.339853	−	1.48899i
$566$	−0.609916	−	2.67222i	−0.0256367	−	0.112322i
$567$		0			0
$568$	6.88769			0.289001
$569$	23.3790	+	29.3163i	0.980097	+	1.22900i	0.973421	+	0.229025i	$0.0735538\pi$
$569$	23.3790	+	29.3163i	0.980097	+	1.22900i	0.00667655	+	0.999978i	$0.497875\pi$
$570$		0			0
$571$	17.2201	−	21.5934i	0.720640	−	0.903654i	−0.277734	−	0.960658i	$-0.589583\pi$
$571$	17.2201	−	21.5934i	0.720640	−	0.903654i	0.998374	+	0.0570041i	$0.0181548\pi$
$572$	−1.16033	+	1.45500i	−0.0485156	+	0.0608367i
$573$		0			0
$574$	−1.24698	−	5.46337i	−0.0520479	−	0.228037i
$575$	−13.0794	+	57.3047i	−0.545449	+	2.38977i
$576$		0			0
$577$	5.70387	−	2.74684i	0.237455	−	0.114352i	−0.311372	−	0.950288i	$-0.600789\pi$
$577$	5.70387	−	2.74684i	0.237455	−	0.114352i	0.548827	+	0.835936i	$0.315074\pi$
$578$	−4.00335	+	17.5398i	−0.166518	+	0.729561i
$579$		0			0
$580$	9.66637	−	0.850747i	0.401374	−	0.0353253i
$581$	2.78315			0.115465
$582$		0			0
$583$	0.125646	−	0.0605078i	0.00520371	−	0.00250598i
$584$	−22.8632	−	11.0104i	−0.946087	−	0.455612i
$585$		0			0
$586$	5.72819	+	25.0969i	0.236629	+	1.03674i
$587$	−17.5939	+	8.47280i	−0.726180	+	0.349710i	−0.760180	−	0.649712i	$-0.774890\pi$
$587$	−17.5939	+	8.47280i	−0.726180	+	0.349710i	0.0340005	+	0.999422i	$0.489175\pi$
$588$		0			0
$589$	3.27479	−	4.10646i	0.134935	−	0.169204i
$590$	29.0954	+	14.0116i	1.19784	+	0.576850i
$591$		0			0
$592$	−8.30127			−0.341180
$593$	1.53720	+	1.92759i	0.0631254	+	0.0791568i	0.812392	−	0.583112i	$-0.198165\pi$
$593$	1.53720	+	1.92759i	0.0631254	+	0.0791568i	−0.749266	+	0.662269i	$0.769594\pi$
$594$		0			0
$595$	−1.00000	−	4.38129i	−0.0409960	−	0.179615i
$596$	−5.08211	−	6.37276i	−0.208171	−	0.261038i
$597$		0			0
$598$	−5.88321	−	7.37732i	−0.240583	−	0.301681i
$599$	−4.65064	−	2.23963i	−0.190020	−	0.0915087i	0.336455	−	0.941700i	$-0.390772\pi$
$599$	−4.65064	−	2.23963i	−0.190020	−	0.0915087i	−0.526474	+	0.850191i	$0.676486\pi$
$600$		0			0
$601$	−18.3723	+	23.0381i	−0.749420	+	0.939743i	−0.999595	−	0.0284577i	$-0.990940\pi$
$601$	−18.3723	+	23.0381i	−0.749420	+	0.939743i	0.250175	+	0.968201i	$0.419512\pi$
$602$	0.516926	−	0.248938i	0.0210683	−	0.0101460i
$603$		0			0
$604$	−1.88524	+	8.25977i	−0.0767093	+	0.336085i
$605$	10.4792	+	5.04651i	0.426040	+	0.205170i
$606$		0			0
$607$	−7.71068	+	33.7827i	−0.312967	+	1.37120i	0.536654	+	0.843802i	$0.319688\pi$
$607$	−7.71068	+	33.7827i	−0.312967	+	1.37120i	−0.849621	+	0.527394i	$0.823169\pi$
$608$	6.64071			0.269316
$609$		0			0
$610$	6.60388			0.267383
$611$	−1.55137	+	6.79699i	−0.0627617	+	0.274977i
$612$		0			0
$613$	−24.7407	−	11.9145i	−0.999268	−	0.481222i	−0.138578	−	0.990352i	$-0.544253\pi$
$613$	−24.7407	−	11.9145i	−0.999268	−	0.481222i	−0.860690	+	0.509130i	$0.829967\pi$
$614$	6.32975	−	27.7324i	0.255448	−	1.11919i
$615$		0			0
$616$	−5.41939	+	2.60984i	−0.218353	+	0.105153i
$617$	−21.3723	+	26.8000i	−0.860415	+	1.07893i	0.135690	+	0.990751i	$0.456675\pi$
$617$	−21.3723	+	26.8000i	−0.860415	+	1.07893i	−0.996105	+	0.0881746i	$0.971897\pi$
$618$		0			0
$619$	−23.1247	−	11.1363i	−0.929462	−	0.447605i	−0.0930221	−	0.995664i	$-0.529653\pi$
$619$	−23.1247	−	11.1363i	−0.929462	−	0.447605i	−0.836440	+	0.548059i	$0.815367\pi$
$620$	2.19202	+	2.74871i	0.0880337	+	0.110391i
$621$		0			0
$622$	24.1719	+	30.3106i	0.969204	+	1.21534i
$623$	1.73341	+	7.59455i	0.0694474	+	0.304269i
$624$		0			0
$625$	29.8330	+	37.4094i	1.19332	+	1.49638i
$626$	14.0067			0.559821
$627$		0			0
$628$	−4.58642	−	2.20870i	−0.183018	−	0.0881368i
$629$	2.85086	−	3.57486i	0.113671	−	0.142539i
$630$		0			0
$631$	26.4894	−	12.7566i	1.05453	−	0.507833i	0.175438	−	0.984491i	$-0.443866\pi$
$631$	26.4894	−	12.7566i	1.05453	−	0.507833i	0.879089	+	0.476657i	$0.158152\pi$
$632$	6.60872	+	28.9547i	0.262881	+	1.15176i
$633$		0			0
$634$	6.65883	+	3.20673i	0.264456	+	0.127355i
$635$	−56.7790	+	27.3433i	−2.25321	+	1.08509i
$636$		0			0
$637$	−9.56524			−0.378989
$638$	−17.9100	−	6.76212i	−0.709063	−	0.267715i
$639$		0			0
$640$	5.55376	−	24.3326i	0.219532	−	0.961831i
$641$	−9.43080	+	4.54164i	−0.372494	+	0.179384i	−0.610759	−	0.791816i	$-0.709136\pi$
$641$	−9.43080	+	4.54164i	−0.372494	+	0.179384i	0.238265	+	0.971200i	$0.423421\pi$
$642$		0			0
$643$	−0.678743	+	2.97377i	−0.0267670	+	0.117274i	−0.986546	−	0.163481i	$-0.947728\pi$
$643$	−0.678743	+	2.97377i	−0.0267670	+	0.117274i	0.959779	+	0.280755i	$0.0905849\pi$
$644$	0.353543	+	1.54898i	0.0139316	+	0.0610382i
$645$		0			0
$646$	3.35690	−	4.20941i	0.132075	−	0.165617i
$647$	18.5824	−	23.3016i	0.730550	−	0.916080i	−0.268334	−	0.963326i	$-0.586473\pi$
$647$	18.5824	−	23.3016i	0.730550	−	0.916080i	0.998883	+	0.0472458i	$0.0150444\pi$
$648$		0			0
$649$	11.3690	+	14.2562i	0.446271	+	0.559607i
$650$	−20.8401			−0.817416
$651$		0			0
$652$	−0.660990	−	2.89598i	−0.0258863	−	0.113416i
$653$	2.53438	+	11.1039i	0.0991781	+	0.434528i	1.00000		0.000338791i	$0.000107841\pi$
$653$	2.53438	+	11.1039i	0.0991781	+	0.434528i	−0.900822	+	0.434189i	$0.857035\pi$
$654$		0			0
$655$	−54.3889			−2.12515
$656$	11.7899	+	14.7840i	0.460317	+	0.577219i
$657$		0			0
$658$	−2.55728	+	3.20673i	−0.0996931	+	0.125011i
$659$	2.86025	−	3.58664i	0.111419	−	0.139716i	−0.722995	−	0.690854i	$-0.757235\pi$
$659$	2.86025	−	3.58664i	0.111419	−	0.139716i	0.834414	+	0.551138i	$0.185806\pi$
$660$		0			0
$661$	2.86712	+	12.5617i	0.111518	+	0.488592i	0.999583	+	0.0288743i	$0.00919225\pi$
$661$	2.86712	+	12.5617i	0.111518	+	0.488592i	−0.888065	+	0.459718i	$0.847951\pi$
$662$	8.57673	−	37.5771i	0.333344	−	1.46048i
$663$		0			0
$664$	−11.0477	+	5.32030i	−0.428735	+	0.206468i
$665$	1.67845	−	7.35376i	0.0650874	−	0.285167i
$666$		0			0
$667$	−15.3503	+	23.1551i	−0.594367	+	0.896571i
$668$	−6.52781			−0.252569
$669$		0			0
$670$	68.0004	−	32.7472i	2.62708	−	1.26514i
$671$	3.35958	+	1.61789i	0.129695	+	0.0624580i
$672$		0			0
$673$	−1.06518	−	4.66686i	−0.0410596	−	0.179894i	0.950240	−	0.311519i	$-0.100838\pi$
$673$	−1.06518	−	4.66686i	−0.0410596	−	0.179894i	−0.991300	+	0.131625i	$0.957981\pi$
$674$	9.00484	−	4.33650i	0.346854	−	0.167036i
$675$		0			0
$676$	3.01022	−	3.77470i	0.115778	−	0.145181i
$677$	−27.5034	−	13.2449i	−1.05704	−	0.509045i	−0.177133	−	0.984187i	$-0.556682\pi$
$677$	−27.5034	−	13.2449i	−1.05704	−	0.509045i	−0.879909	+	0.475142i	$0.842397\pi$
$678$		0			0
$679$	−3.16255			−0.121368
$680$	12.3448	+	15.4799i	0.473402	+	0.593627i
$681$		0			0
$682$	−1.54341	−	6.76212i	−0.0591002	−	0.258935i
$683$	−5.95138	−	7.46279i	−0.227723	−	0.285556i	0.654822	−	0.755783i	$-0.272743\pi$
$683$	−5.95138	−	7.46279i	−0.227723	−	0.285556i	−0.882545	+	0.470227i	$0.844172\pi$
$684$		0			0
$685$	42.8962	+	53.7901i	1.63898	+	2.05521i
$686$	−10.5124	−	5.06249i	−0.401364	−	0.193287i
$687$		0			0
$688$	−1.20709	+	1.51364i	−0.0460198	+	0.0577070i
$689$	0.0646468	−	0.0311323i	0.00246285	−	0.00118604i
$690$		0			0
$691$	3.66799	−	16.0705i	0.139537	−	0.611351i	−0.856000	−	0.516976i	$-0.827058\pi$
$691$	3.66799	−	16.0705i	0.139537	−	0.611351i	0.995537	−	0.0943750i	$-0.0300853\pi$
$692$	9.36658	+	4.51071i	0.356064	+	0.171471i
$693$		0			0
$694$	0.628039	−	2.75162i	0.0238400	−	0.104450i
$695$	50.4674			1.91434
$696$		0			0
$697$	−10.4155			−0.394515
$698$	−6.53989	+	28.6531i	−0.247539	+	1.08454i
$699$		0			0
$700$	3.16152	+	1.52251i	0.119494	+	0.0575454i
$701$	10.4288	−	45.6915i	0.393890	−	1.72574i	−0.256858	−	0.966449i	$-0.582687\pi$
$701$	10.4288	−	45.6915i	0.393890	−	1.72574i	0.650748	−	0.759294i	$-0.274456\pi$
$702$		0			0
$703$	6.91454	−	3.32987i	0.260787	−	0.125588i
$704$	15.8192	−	19.8366i	0.596207	−	0.747620i
$705$		0			0
$706$	1.10388	+	0.531598i	0.0415449	+	0.0200070i
$707$	−1.38636	−	1.73844i	−0.0521395	−	0.0653809i
$708$		0			0
$709$	6.60955	+	8.28811i	0.248227	+	0.311267i	0.890298	−	0.455379i	$-0.150496\pi$
$709$	6.60955	+	8.28811i	0.248227	+	0.311267i	−0.642071	+	0.766645i	$0.721925\pi$
$710$	2.53803	+	11.1198i	0.0952507	+	0.417320i
$711$		0			0
$712$	−21.3986	−	26.8330i	−0.801946	−	1.00561i
$713$	−10.0653			−0.376949
$714$		0			0
$715$	−15.2545	−	7.34619i	−0.570486	−	0.274732i
$716$	−0.184489	+	0.231342i	−0.00689467	+	0.00864564i
$717$		0			0
$718$	8.85570	−	4.26468i	0.330492	−	0.159156i
$719$	−2.96064	−	12.9714i	−0.110413	−	0.483752i	−0.999654	−	0.0263121i	$-0.991624\pi$
$719$	−2.96064	−	12.9714i	−0.110413	−	0.483752i	0.889241	−	0.457440i	$-0.151234\pi$
$720$		0			0
$721$	4.07338	+	1.96163i	0.151700	+	0.0730551i
$722$	−13.2044	+	6.35890i	−0.491417	+	0.236654i
$723$		0			0
$724$	−4.88040			−0.181378
$725$	18.8451	+	58.3914i	0.699890	+	2.16860i
$726$		0			0
$727$	−7.34708	+	32.1896i	−0.272488	+	1.19385i	0.634578	+	0.772859i	$0.281174\pi$
$727$	−7.34708	+	32.1896i	−0.272488	+	1.19385i	−0.907066	+	0.420989i	$0.861683\pi$
$728$	−2.78836	+	1.34281i	−0.103344	+	0.0497677i
$729$		0			0
$730$	9.35086	−	40.9688i	0.346091	−	1.51632i
$731$	−0.237291	−	1.03964i	−0.00877652	−	0.0384525i
$732$		0			0
$733$	19.8240	−	24.8585i	0.732216	−	0.918170i	−0.266744	−	0.963768i	$-0.585948\pi$
$733$	19.8240	−	24.8585i	0.732216	−	0.918170i	0.998960	+	0.0455974i	$0.0145191\pi$
$734$	22.7863	−	28.5732i	0.841059	−	1.05465i
$735$		0			0
$736$	−7.93445	−	9.94949i	−0.292468	−	0.366743i
$737$	42.6165			1.56980
$738$		0			0
$739$	5.32616	+	23.3354i	0.195926	+	0.858408i	0.973331	+	0.229407i	$0.0736786\pi$
$739$	5.32616	+	23.3354i	0.195926	+	0.858408i	−0.777405	+	0.629001i	$0.783464\pi$
$740$	1.14310	+	5.00827i	0.0420213	+	0.184108i
$741$		0			0
$742$	0.0422126			0.00154967
$743$	4.62163	+	5.79534i	0.169551	+	0.212610i	0.859346	−	0.511394i	$-0.170871\pi$
$743$	4.62163	+	5.79534i	0.169551	+	0.212610i	−0.689795	+	0.724005i	$0.742299\pi$
$744$		0			0
$745$	46.2362	−	57.9783i	1.69396	−	2.12416i
$746$	2.96429	−	3.71710i	0.108530	−	0.136093i
$747$		0			0
$748$	0.452812	+	1.98390i	0.0165564	+	0.0725385i
$749$	−0.890748	+	3.90262i	−0.0325472	+	0.142599i
$750$		0			0
$751$	17.4448	−	8.40098i	0.636570	−	0.306556i	−0.0876226	−	0.996154i	$-0.527927\pi$
$751$	17.4448	−	8.40098i	0.636570	−	0.306556i	0.724193	+	0.689598i	$0.242213\pi$
$752$	3.07971	−	13.4931i	0.112306	−	0.492043i
$753$		0			0
$754$	−9.21499	−	3.47922i	−0.335590	−	0.126706i
$755$	−77.0786			−2.80518
$756$		0			0
$757$	30.8463	−	14.8548i	1.12113	−	0.539907i	0.220887	−	0.975299i	$-0.429105\pi$
$757$	30.8463	−	14.8548i	1.12113	−	0.539907i	0.900241	+	0.435393i	$0.143390\pi$
$758$	10.1407	+	4.88351i	0.368327	+	0.177377i
$759$		0			0
$760$	7.39493	+	32.3993i	0.268242	+	1.17525i
$761$	13.1174	−	6.31703i	0.475507	−	0.228992i	−0.180751	−	0.983529i	$-0.557853\pi$
$761$	13.1174	−	6.31703i	0.475507	−	0.228992i	0.656258	+	0.754537i	$0.272138\pi$
$762$		0			0
$763$	3.96346	−	4.97002i	0.143487	−	0.179927i
$764$	0.207751	+	0.100048i	0.00751617	+	0.00361959i
$765$		0			0
$766$	−41.3860			−1.49534
$767$	5.84953	+	7.33507i	0.211214	+	0.264854i
$768$		0			0
$769$	−2.57314	−	11.2737i	−0.0927898	−	0.406539i	0.907107	−	0.420900i	$-0.138286\pi$
$769$	−2.57314	−	11.2737i	−0.0927898	−	0.406539i	−0.999897	+	0.0143613i	$0.995428\pi$
$770$	−6.21044	−	7.78764i	−0.223809	−	0.280647i
$771$		0			0
$772$	−0.384707	−	0.482407i	−0.0138459	−	0.0173622i
$773$	7.54503	+	3.63350i	0.271376	+	0.130688i	0.564623	−	0.825349i	$-0.309022\pi$
$773$	7.54503	+	3.63350i	0.271376	+	0.130688i	−0.293247	+	0.956037i	$0.594736\pi$
$774$		0			0
$775$	−13.8602	+	17.3802i	−0.497875	+	0.624315i
$776$	12.5538	−	6.04557i	0.450654	−	0.217023i
$777$		0			0
$778$	−7.64071	+	33.4761i	−0.273933	+	1.20018i
$779$	−15.7506	−	7.58510i	−0.564325	−	0.271764i
$780$		0			0
$781$	−1.43309	+	6.27879i	−0.0512801	+	0.224673i
$782$	−10.3177			−0.368959
$783$		0			0
$784$	18.9885			0.678161
$785$	10.3056	−	45.1517i	0.367822	−	1.61153i
$786$		0			0
$787$	8.76055	+	4.21886i	0.312280	+	0.150386i	0.583458	−	0.812143i	$-0.301699\pi$
$787$	8.76055	+	4.21886i	0.312280	+	0.150386i	−0.271179	+	0.962529i	$0.587413\pi$
$788$	−1.28328	+	5.62243i	−0.0457151	+	0.200291i
$789$		0			0
$790$	−44.3107	+	21.3389i	−1.57650	+	0.759205i
$791$	3.86861	−	4.85108i	0.137552	−	0.172485i
$792$		0			0
$793$	1.72856	+	0.832431i	0.0613830	+	0.0295605i
$794$	14.9453	+	18.7409i	0.530390	+	0.665088i
$795$		0			0
$796$	5.41185	+	6.78625i	0.191818	+	0.240532i
$797$	−5.87681	−	25.7480i	−0.208167	−	0.912040i	−0.965786	−	0.259342i	$-0.916494\pi$
$797$	−5.87681	−	25.7480i	−0.208167	−	0.912040i	0.757618	−	0.652698i	$-0.226363\pi$
$798$		0			0
$799$	4.75302	+	5.96010i	0.168150	+	0.210853i
$800$	−28.1062			−0.993704
$801$		0			0
$802$	−12.3877	−	5.96560i	−0.437425	−	0.210653i
$803$	14.7940	−	18.5511i	0.522070	−	0.654655i
$804$		0			0
$805$	−13.0233	+	6.27167i	−0.459010	+	0.221047i
$806$	−0.794109	−	3.47922i	−0.0279713	−	0.122550i
$807$		0			0
$808$	8.82640	+	4.25057i	0.310512	+	0.149534i
$809$	16.9291	−	8.15261i	0.595195	−	0.286631i	−0.111934	−	0.993716i	$-0.535704\pi$
$809$	16.9291	−	8.15261i	0.595195	−	0.286631i	0.707129	+	0.707085i	$0.249990\pi$
$810$		0			0
$811$	48.6983			1.71003			0.855013	−	0.518606i	$-0.173549\pi$
$811$	48.6983			1.71003			0.855013	+	0.518606i	$0.173549\pi$
$812$	1.14377	+	1.20103i	0.0401384	+	0.0421478i
$813$		0			0
$814$	2.25518	−	9.88057i	0.0790439	−	0.346314i
$815$	24.3485	−	11.7256i	0.852889	−	0.410730i
$816$		0			0
$817$	0.398280	−	1.74498i	0.0139341	−	0.0610491i
$818$	9.38471	+	41.1171i	0.328129	+	1.43763i
$819$		0			0
$820$	7.29590	−	9.14877i	0.254784	−	0.319489i
$821$	−3.90246	+	4.89353i	−0.136197	+	0.170785i	−0.845253	−	0.534367i	$-0.820550\pi$
$821$	−3.90246	+	4.89353i	−0.136197	+	0.170785i	0.709056	+	0.705152i	$0.249121\pi$
$822$		0			0
$823$	−9.36257	−	11.7403i	−0.326359	−	0.409241i	0.591401	−	0.806378i	$-0.298575\pi$
$823$	−9.36257	−	11.7403i	−0.326359	−	0.409241i	−0.917759	+	0.397137i	$0.870004\pi$
$824$	−19.9191			−0.693916
$825$		0			0
$826$	1.22819	+	5.38107i	0.0427343	+	0.187231i
$827$	2.66069	+	11.6573i	0.0925214	+	0.405363i	0.999888	−	0.0149778i	$-0.00476776\pi$
$827$	2.66069	+	11.6573i	0.0925214	+	0.405363i	−0.907366	+	0.420341i	$0.861911\pi$
$828$		0			0
$829$	28.6305			0.994380			0.497190	−	0.867642i	$-0.334365\pi$
$829$	28.6305			0.994380			0.497190	+	0.867642i	$0.334365\pi$
$830$	−12.6603	−	15.8755i	−0.439446	−	0.551048i
$831$		0			0
$832$	8.13922	−	10.2063i	0.282177	−	0.353838i
$833$	−6.52111	+	8.17721i	−0.225943	+	0.283323i
$834$		0			0
$835$	−13.2153	−	57.8999i	−0.457334	−	2.00371i
$836$	−0.760021	+	3.32987i	−0.0262859	+	0.115166i
$837$		0			0
$838$	40.0175	−	19.2714i	1.38238	−	0.665720i
$839$	−10.7529	+	47.1115i	−0.371231	+	1.62647i	0.352096	+	0.935964i	$0.385469\pi$
$839$	−10.7529	+	47.1115i	−0.371231	+	1.62647i	−0.723327	+	0.690505i	$0.757388\pi$
$840$		0			0
$841$	−1.41550	+	28.9654i	−0.0488104	+	0.998808i
$842$	11.7928			0.406408
$843$		0			0
$844$	−8.27240	+	3.98378i	−0.284748	+	0.137127i
$845$	39.5746	+	19.0581i	1.36141	+	0.655620i
$846$		0			0
$847$	0.442353	+	1.93808i	0.0151994	+	0.0665931i
$848$	−0.128334	+	0.0618025i	−0.00440701	+	0.00212231i
$849$		0			0
$850$	−14.2078	+	17.8160i	−0.487322	+	0.611082i
$851$	−13.2506	−	6.38117i	−0.454226	−	0.218744i
$852$		0			0
$853$	−6.40688			−0.219367			−0.109684	−	0.993967i	$-0.534984\pi$
$853$	−6.40688			−0.219367			−0.109684	+	0.993967i	$0.534984\pi$
$854$	0.703735	+	0.882455i	0.0240813	+	0.0301970i
$855$		0			0
$856$	−3.92447	−	17.1942i	−0.134136	−	0.587686i
$857$	0.447730	+	0.561436i	0.0152942	+	0.0191783i	0.789420	−	0.613854i	$-0.210382\pi$
$857$	0.447730	+	0.561436i	0.0152942	+	0.0191783i	−0.774126	+	0.633032i	$0.781810\pi$
$858$		0			0
$859$	−9.72484	−	12.1946i	−0.331807	−	0.416073i	0.587742	−	0.809049i	$-0.300017\pi$
$859$	−9.72484	−	12.1946i	−0.331807	−	0.416073i	−0.919549	+	0.392975i	$0.871446\pi$
$860$	1.07942	+	0.519820i	0.0368078	+	0.0177257i
$861$		0			0
$862$	0.766225	−	0.960816i	0.0260977	−	0.0327255i
$863$	12.1586	−	5.85527i	0.413883	−	0.199316i	−0.215342	−	0.976539i	$-0.569087\pi$
$863$	12.1586	−	5.85527i	0.413883	−	0.199316i	0.629225	+	0.777223i	$0.283372\pi$
$864$		0			0
$865$	−21.0465	+	92.2108i	−0.715603	+	3.13526i
$866$	−32.2265	−	15.5194i	−1.09510	−	0.527372i
$867$		0			0
$868$	−0.133711	+	0.585826i	−0.00453845	+	0.0198842i
$869$	−27.7700			−0.942033
$870$		0			0
$871$	21.9269			0.742965
$872$	−6.23221	+	27.3051i	−0.211049	+	0.924667i
$873$		0			0
$874$	−15.6027	−	7.51385i	−0.527768	−	0.254160i
$875$	−3.98643	+	17.4657i	−0.134766	+	0.590448i
$876$		0			0
$877$	14.1446	−	6.81168i	0.477629	−	0.230014i	−0.179550	−	0.983749i	$-0.557464\pi$
$877$	14.1446	−	6.81168i	0.477629	−	0.230014i	0.657179	+	0.753735i	$0.271750\pi$
$878$	5.12684	−	6.42886i	0.173023	−	0.216963i
$879$		0			0
$880$	30.2826	+	14.5833i	1.02083	+	0.491604i
$881$	6.75332	+	8.46839i	0.227525	+	0.285307i	0.882469	−	0.470370i	$-0.155879\pi$
$881$	6.75332	+	8.46839i	0.227525	+	0.285307i	−0.654944	+	0.755677i	$0.727308\pi$
$882$		0			0
$883$	−10.2744	−	12.8837i	−0.345762	−	0.433572i	0.578294	−	0.815828i	$-0.303719\pi$
$883$	−10.2744	−	12.8837i	−0.345762	−	0.433572i	−0.924056	+	0.382257i	$0.875147\pi$
$884$	0.232979	+	1.02075i	0.00783593	+	0.0343315i
$885$		0			0
$886$	−16.6290	−	20.8521i	−0.558662	−	0.700540i
$887$	28.5763			0.959497			0.479748	−	0.877406i	$-0.340728\pi$
$887$	28.5763			0.959497			0.479748	+	0.877406i	$0.340728\pi$
$888$		0			0
$889$	−9.70440	−	4.67339i	−0.325475	−	0.156741i
$890$	35.4354	−	44.4346i	1.18780	−	1.48945i
$891$		0			0
$892$	−8.46077	+	4.07449i	−0.283288	+	0.136424i
$893$	2.84721	+	12.4744i	0.0952782	+	0.417441i
$894$		0			0
$895$	−2.42543	−	1.16802i	−0.0810731	−	0.0390427i
$896$	3.84332	−	1.85085i	0.128396	−	0.0618324i
$897$		0			0
$898$	36.4825			1.21744
$899$	−9.03026	+	5.37116i	−0.301176	+	0.179138i
$900$		0			0
$901$	0.0174584	−	0.0764902i	0.000581624	−	0.00254826i
$902$	−20.7995	+	10.0165i	−0.692549	+	0.333514i
$903$		0			0
$904$	−6.08306	+	26.6516i	−0.202320	+	0.886421i
$905$	−9.88016	−	43.2878i	−0.328428	−	1.43894i
$906$		0			0
$907$	20.4875	−	25.6906i	0.680278	−	0.853042i	−0.315102	−	0.949058i	$-0.602039\pi$
$907$	20.4875	−	25.6906i	0.680278	−	0.853042i	0.995380	+	0.0960163i	$0.0306101\pi$
$908$	1.97972	−	2.48249i	0.0656994	−	0.0823844i
$909$		0			0
$910$	−3.19537	−	4.00687i	−0.105926	−	0.132827i
$911$	−10.9638			−0.363245			−0.181623	−	0.983368i	$-0.558135\pi$
$911$	−10.9638			−0.363245			−0.181623	+	0.983368i	$0.558135\pi$
$912$		0			0
$913$	−2.55131	−	11.1780i	−0.0844360	−	0.369938i
$914$	−0.0670397	−	0.293720i	−0.00221748	−	0.00971540i
$915$		0			0
$916$	1.00239			0.0331200
$917$	−5.79590	−	7.26782i	−0.191397	−	0.240005i
$918$		0			0
$919$	4.77748	−	5.99077i	0.157594	−	0.197617i	−0.696765	−	0.717299i	$-0.745378\pi$
$919$	4.77748	−	5.99077i	0.157594	−	0.197617i	0.854360	+	0.519682i	$0.173950\pi$
$920$	39.7068	−	49.7908i	1.30910	−	1.64155i
$921$		0			0
$922$	−4.81096	−	21.0782i	−0.158441	−	0.694174i
$923$	−0.737349	+	3.23054i	−0.0242702	+	0.106334i
$924$		0			0
$925$	−29.2652	+	14.0934i	−0.962233	+	0.463387i
$926$	1.17928	−	5.16675i	0.0387534	−	0.169790i
$927$		0			0
$928$	−12.4279	−	4.69228i	−0.407965	−	0.154032i
$929$	−9.35988			−0.307088			−0.153544	−	0.988142i	$-0.549069\pi$
$929$	−9.35988			−0.307088			−0.153544	+	0.988142i	$0.549069\pi$
$930$		0			0
$931$	−15.8165	+	7.61681i	−0.518364	+	0.249631i
$932$	−7.58211	−	3.65135i	−0.248360	−	0.119604i
$933$		0			0
$934$	8.00066	+	35.0532i	0.261790	+	1.14698i
$935$	−16.6799	+	8.03264i	−0.545492	+	0.262695i
$936$		0			0
$937$	4.86563	−	6.10130i	0.158953	−	0.199321i	−0.695977	−	0.718064i	$-0.745028\pi$
$937$	4.86563	−	6.10130i	0.158953	−	0.199321i	0.854930	+	0.518743i	$0.173600\pi$
$938$	11.6223	+	5.59700i	0.379481	+	0.182749i
$939$		0			0
$940$	−8.56465			−0.279348
$941$	17.9242	+	22.4763i	0.584313	+	0.732706i	0.982842	−	0.184450i	$-0.0590505\pi$
$941$	17.9242	+	22.4763i	0.584313	+	0.732706i	−0.398529	+	0.917156i	$0.630479\pi$
$942$		0			0
$943$	7.45473	+	32.6613i	0.242759	+	1.06360i
$944$	−11.6122	−	14.5613i	−0.377946	−	0.473929i
$945$		0			0
$946$	−1.47368	−	1.84794i	−0.0479135	−	0.0600816i
$947$	−2.08061	−	1.00197i	−0.0676108	−	0.0325597i	0.399773	−	0.916614i	$-0.369089\pi$
$947$	−2.08061	−	1.00197i	−0.0676108	−	0.0325597i	−0.467384	+	0.884055i	$0.654803\pi$
$948$		0			0
$949$	7.61178	−	9.54487i	0.247089	−	0.309839i
$950$	−34.4599	+	16.5950i	−1.11803	+	0.538413i
$951$		0			0
$952$	−0.753020	+	3.29920i	−0.0244055	+	0.106928i
$953$	−31.1107	−	14.9821i	−1.00778	−	0.485319i	−0.144206	−	0.989548i	$-0.546063\pi$
$953$	−31.1107	−	14.9821i	−1.00778	−	0.485319i	−0.863570	+	0.504228i	$0.831777\pi$
$954$		0			0
$955$	−0.466812	+	2.04524i	−0.0151057	+	0.0661823i
$956$	−9.11098			−0.294670
$957$		0			0
$958$	−30.1481			−0.974040
$959$	−2.61662	+	11.4642i	−0.0844951	+	0.370197i
$960$		0			0
$961$	24.5003	+	11.7987i	0.790332	+	0.380604i
$962$	1.16033	−	5.08372i	0.0374104	−	0.163906i
$963$		0			0
$964$	2.95473	−	1.42292i	0.0951655	−	0.0458293i
$965$	3.50000	−	4.38886i	0.112669	−	0.141282i
$966$		0			0
$967$	−46.4163	−	22.3529i	−1.49265	−	0.718822i	−0.503263	−	0.864134i	$-0.667867\pi$
$967$	−46.4163	−	22.3529i	−1.49265	−	0.718822i	−0.989386	+	0.145312i	$0.953581\pi$
$968$	−5.46077	−	6.84759i	−0.175516	−	0.220090i
$969$		0			0
$970$	14.3862	+	18.0397i	0.461913	+	0.579221i
$971$	1.76582	+	7.73658i	0.0566680	+	0.248279i	0.995326	−	0.0965703i	$-0.0307873\pi$
$971$	1.76582	+	7.73658i	0.0566680	+	0.248279i	−0.938658	+	0.344849i	$0.887930\pi$
$972$		0			0
$973$	5.37800	+	6.74380i	0.172411	+	0.216196i
$974$	−24.0804			−0.771585
$975$		0			0
$976$	−3.43147	−	1.65251i	−0.109839	−	0.0528955i
$977$	−17.2080	+	21.5782i	−0.550534	+	0.690348i	−0.976776	−	0.214261i	$-0.931266\pi$
$977$	−17.2080	+	21.5782i	−0.550534	+	0.690348i	0.426242	+	0.904609i	$0.359837\pi$
$978$		0			0
$979$	28.9131	−	13.9238i	0.924067	−	0.445007i
$980$	−2.61476	−	11.4560i	−0.0835255	−	0.365949i
$981$		0			0
$982$	−41.4463	−	19.9595i	−1.32260	−	0.636933i
$983$	31.8288	−	15.3280i	1.01518	−	0.488886i	0.149119	−	0.988819i	$-0.452356\pi$
$983$	31.8288	−	15.3280i	1.01518	−	0.488886i	0.866064	+	0.499933i	$0.166642\pi$
$984$		0			0
$985$	−52.4674			−1.67175
$986$	−9.25667	+	5.50582i	−0.294792	+	0.175341i
$987$		0			0
$988$	−0.391043	+	1.71327i	−0.0124407	+	0.0545065i
$989$	−3.09030	+	1.48821i	−0.0982659	+	0.0473224i
$990$		0			0
$991$	0.123194	−	0.539750i	0.00391340	−	0.0171457i	−0.972934	−	0.231085i	$-0.925772\pi$
$991$	0.123194	−	0.539750i	0.00391340	−	0.0171457i	0.976847	+	0.213939i	$0.0686295\pi$
$992$	−1.07098	−	4.69228i	−0.0340037	−	0.148980i
$993$		0			0
$994$	−1.21545	+	1.52412i	−0.0385517	+	0.0483423i
$995$	−49.2362	+	61.7402i	−1.56089	+	1.95730i
$996$		0			0
$997$	13.8699	+	17.3924i	0.439265	+	0.550821i	0.951349	−	0.308114i	$-0.0996978\pi$
$997$	13.8699	+	17.3924i	0.439265	+	0.550821i	−0.512084	+	0.858935i	$0.671126\pi$
$998$	−47.0307			−1.48873
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.k.a.199.1		6
3.2	odd	2		29.2.d.a.25.1	yes	6
12.11	even	2		464.2.u.f.257.1		6
15.2	even	4		725.2.r.b.199.1		12
15.8	even	4		725.2.r.b.199.2		12
15.14	odd	2		725.2.l.b.576.1		6
29.6	even	14		7569.2.a.p.1.3		3
29.7	even	7	inner	261.2.k.a.181.1		6
29.23	even	7		7569.2.a.r.1.1		3
87.2	even	28		841.2.e.c.651.1		12
87.5	odd	14		841.2.d.c.190.1		6
87.8	even	28		841.2.e.b.63.1		12
87.11	even	28		841.2.e.c.270.2		12
87.14	even	28		841.2.b.c.840.2		6
87.17	even	4		841.2.e.d.236.2		12
87.20	odd	14		841.2.d.e.778.1		6
87.23	odd	14		841.2.a.e.1.3		3
87.26	even	28		841.2.e.d.196.2		12
87.32	even	28		841.2.e.d.196.1		12
87.35	odd	14		841.2.a.f.1.1		3
87.38	odd	14		841.2.d.a.778.1		6
87.41	even	4		841.2.e.d.236.1		12
87.44	even	28		841.2.b.c.840.5		6
87.47	even	28		841.2.e.c.270.1		12
87.50	even	28		841.2.e.b.63.2		12
87.53	odd	14		841.2.d.b.190.1		6
87.56	even	28		841.2.e.c.651.2		12
87.62	odd	14		841.2.d.a.574.1		6
87.65	odd	14		29.2.d.a.7.1	✓	6
87.68	even	28		841.2.e.b.267.2		12
87.71	odd	14		841.2.d.c.571.1		6
87.74	odd	14		841.2.d.b.571.1		6
87.77	even	28		841.2.e.b.267.1		12
87.80	odd	14		841.2.d.d.645.1		6
87.83	odd	14		841.2.d.e.574.1		6
87.86	odd	2		841.2.d.d.605.1		6
348.239	even	14		464.2.u.f.65.1		6
435.152	even	28		725.2.r.b.674.2		12
435.239	odd	14		725.2.l.b.326.1		6
435.413	even	28		725.2.r.b.674.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.d.a.7.1	✓	6	87.65	odd	14
29.2.d.a.25.1	yes	6	3.2	odd	2
261.2.k.a.181.1		6	29.7	even	7	inner
261.2.k.a.199.1		6	1.1	even	1	trivial
464.2.u.f.65.1		6	348.239	even	14
464.2.u.f.257.1		6	12.11	even	2
725.2.l.b.326.1		6	435.239	odd	14
725.2.l.b.576.1		6	15.14	odd	2
725.2.r.b.199.1		12	15.2	even	4
725.2.r.b.199.2		12	15.8	even	4
725.2.r.b.674.1		12	435.413	even	28
725.2.r.b.674.2		12	435.152	even	28
841.2.a.e.1.3		3	87.23	odd	14
841.2.a.f.1.1		3	87.35	odd	14
841.2.b.c.840.2		6	87.14	even	28
841.2.b.c.840.5		6	87.44	even	28
841.2.d.a.574.1		6	87.62	odd	14
841.2.d.a.778.1		6	87.38	odd	14
841.2.d.b.190.1		6	87.53	odd	14
841.2.d.b.571.1		6	87.74	odd	14
841.2.d.c.190.1		6	87.5	odd	14
841.2.d.c.571.1		6	87.71	odd	14
841.2.d.d.605.1		6	87.86	odd	2
841.2.d.d.645.1		6	87.80	odd	14
841.2.d.e.574.1		6	87.83	odd	14
841.2.d.e.778.1		6	87.20	odd	14
841.2.e.b.63.1		12	87.8	even	28
841.2.e.b.63.2		12	87.50	even	28
841.2.e.b.267.1		12	87.77	even	28
841.2.e.b.267.2		12	87.68	even	28
841.2.e.c.270.1		12	87.47	even	28
841.2.e.c.270.2		12	87.11	even	28
841.2.e.c.651.1		12	87.2	even	28
841.2.e.c.651.2		12	87.56	even	28
841.2.e.d.196.1		12	87.32	even	28
841.2.e.d.196.2		12	87.26	even	28
841.2.e.d.236.1		12	87.41	even	4
841.2.e.d.236.2		12	87.17	even	4
7569.2.a.p.1.3		3	29.6	even	14
7569.2.a.r.1.1		3	29.23	even	7

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.277479 - 1.21572i) q^{2} +(0.400969 + 0.193096i) q^{4} +(-0.900969 + 3.94740i) q^{5} +(-0.623490 + 0.300257i) q^{7} +(1.90097 - 2.38374i) q^{8} +(4.54892 + 2.19064i) q^{10} +(1.77748 + 2.22889i) q^{11} +(0.914542 + 1.14680i) q^{13} +(0.192021 + 0.841301i) q^{14} +(-1.81551 - 2.27658i) q^{16} +1.60388 q^{17} +(2.42543 + 1.16802i) q^{19} +(-1.12349 + 1.40881i) q^{20} +(3.20291 - 1.54244i) q^{22} +(-1.14795 - 5.02949i) q^{23} +(-10.2654 - 4.94355i) q^{25} +(1.64795 - 0.793610i) q^{26} -0.307979 q^{28} +(-3.71379 - 3.89971i) q^{29} +(0.434157 - 1.90216i) q^{31} +(2.22252 - 1.07031i) q^{32} +(0.445042 - 1.94986i) q^{34} +(-0.623490 - 2.73169i) q^{35} +(1.77748 - 2.22889i) q^{37} +(2.09299 - 2.62453i) q^{38} +(7.69687 + 9.65156i) q^{40} -6.49396 q^{41} +(-0.147948 - 0.648205i) q^{43} +(0.282323 + 1.23694i) q^{44} -6.43296 q^{46} +(2.96346 + 3.71606i) q^{47} +(-4.06584 + 5.09841i) q^{49} +(-8.85839 + 11.1081i) q^{50} +(0.145260 + 0.636426i) q^{52} +(0.0108851 - 0.0476909i) q^{53} +(-10.3998 + 5.00827i) q^{55} +(-0.469501 + 2.05702i) q^{56} +(-5.77144 + 3.43282i) q^{58} +6.39612 q^{59} +(1.17845 - 0.567511i) q^{61} +(-2.19202 - 1.05562i) q^{62} +(-1.98039 - 8.67664i) q^{64} +(-5.35086 + 2.57684i) q^{65} +(9.32036 - 11.6874i) q^{67} +(0.643104 + 0.309703i) q^{68} -3.49396 q^{70} +(1.40850 + 1.76621i) q^{71} +(-1.85205 - 8.11437i) q^{73} +(-2.21648 - 2.77938i) q^{74} +(0.746980 + 0.936683i) q^{76} +(-1.77748 - 0.855989i) q^{77} +(-6.07338 + 7.61577i) q^{79} +(10.6223 - 5.11543i) q^{80} +(-1.80194 + 7.89481i) q^{82} +(-3.62349 - 1.74498i) q^{83} +(-1.44504 + 6.33114i) q^{85} -0.829085 q^{86} +8.69202 q^{88} +(2.50484 - 10.9744i) q^{89} +(-0.914542 - 0.440420i) q^{91} +(0.510885 - 2.23833i) q^{92} +(5.33997 - 2.57159i) q^{94} +(-6.79590 + 8.52179i) q^{95} +(4.11745 + 1.98286i) q^{97} +(5.07002 + 6.35761i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 2 q^{4} - q^{5} + q^{7} + 7 q^{8} + 9 q^{10} + 11 q^{11} - 5 q^{13} - 9 q^{14} + 4 q^{16} - 8 q^{17} + q^{19} - 2 q^{20} + 6 q^{22} + 7 q^{23} - 24 q^{25} - 4 q^{26} - 12 q^{28} - 6 q^{29}+ \cdots - 19 q^{98}+O(q^{100}) \) 6 * q + 2 * q^2 - 2 * q^4 - q^5 + q^7 + 7 * q^8 + 9 * q^10 + 11 * q^11 - 5 * q^13 - 9 * q^14 + 4 * q^16 - 8 * q^17 + q^19 - 2 * q^20 + 6 * q^22 + 7 * q^23 - 24 * q^25 - 4 * q^26 - 12 * q^28 - 6 * q^29 + 5 * q^31 + 13 * q^32 + 2 * q^34 + q^35 + 11 * q^37 - 2 * q^38 + 14 * q^40 - 20 * q^41 + 13 * q^43 - 20 * q^44 - 11 * q^47 - 22 * q^49 - q^50 - 10 * q^52 - 3 * q^53 - 17 * q^55 + 7 * q^56 - 16 * q^58 + 56 * q^59 + 3 * q^61 - 3 * q^62 + q^64 - 5 * q^65 + 19 * q^67 + 12 * q^68 - 2 * q^70 - 21 * q^71 - 25 * q^73 + 6 * q^74 - 5 * q^76 - 11 * q^77 - 9 * q^79 + 18 * q^80 - 2 * q^82 - 17 * q^83 - 8 * q^85 + 16 * q^86 + 42 * q^88 - 7 * q^89 + 5 * q^91 + 8 * q^94 - 13 * q^95 + q^97 - 19 * q^98

Introduction

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