LMFDB - Embedded newform 650.2.m.e.101.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(101,650)] 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("650.101"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.m (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,8,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 8 x^{14} - 60 x^{13} + 92 x^{12} + 292 x^{11} - 104 x^{10} + 936 x^{9} + 664 x^{8} + \cdots + 256 $ x^16 - 4x^15 + 8x^14 - 60x^13 + 92x^12 + 292x^11 - 104x^10 + 936x^9 + 664x^8 - 2376x^7 + 232x^6 - 4216x^5 + 3812x^4 + 3408x^3 + 800x^2 + 640*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.7
Root			$0.478758 - 1.78675i$ of defining polynomial
Character	$\chi$	$=$	650.101
Dual form			650.2.m.e.251.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(0.588222 + 1.01883i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.01883 + 0.588222i) q^{6} +(-1.80732 - 1.04346i) q^{7} -1.00000i q^{8} +(0.807991 - 1.39948i) q^{9} +(2.59135 - 1.49612i) q^{11} +1.17644 q^{12} +(3.27004 - 1.51883i) q^{13} -2.08692 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.630092 + 1.09135i) q^{17} -1.61598i q^{18} +(3.37028 + 1.94583i) q^{19} -2.45514i q^{21} +(1.49612 - 2.59135i) q^{22} +(-0.449714 - 0.778928i) q^{23} +(1.01883 - 0.588222i) q^{24} +(2.07252 - 2.95036i) q^{26} +5.43044 q^{27} +(-1.80732 + 1.04346i) q^{28} +(0.235468 + 0.407843i) q^{29} -0.277015i q^{31} +(-0.866025 - 0.500000i) q^{32} +(3.04858 + 1.76010i) q^{33} +1.26018i q^{34} +(-0.807991 - 1.39948i) q^{36} +(-6.09479 + 3.51883i) q^{37} +3.89166 q^{38} +(3.47094 + 2.43820i) q^{39} +(9.66804 - 5.58184i) q^{41} +(-1.22757 - 2.12621i) q^{42} +(-3.89166 + 6.74056i) q^{43} -2.99224i q^{44} +(-0.778928 - 0.449714i) q^{46} +11.3189i q^{47} +(0.588222 - 1.01883i) q^{48} +(-1.32239 - 2.29044i) q^{49} -1.48254 q^{51} +(0.319674 - 3.59135i) q^{52} -12.0148 q^{53} +(4.70290 - 2.71522i) q^{54} +(-1.04346 + 1.80732i) q^{56} +4.57832i q^{57} +(0.407843 + 0.235468i) q^{58} +(-10.7029 - 6.17932i) q^{59} +(-3.82102 + 6.61820i) q^{61} +(-0.138508 - 0.239902i) q^{62} +(-2.92060 + 1.68621i) q^{63} -1.00000 q^{64} +3.52020 q^{66} +(3.46410 - 2.00000i) q^{67} +(0.630092 + 1.09135i) q^{68} +(0.529063 - 0.916364i) q^{69} +(4.07532 + 2.35289i) q^{71} +(-1.39948 - 0.807991i) q^{72} -15.2984i q^{73} +(-3.51883 + 6.09479i) q^{74} +(3.37028 - 1.94583i) q^{76} -6.24455 q^{77} +(4.22502 + 0.376079i) q^{78} +1.63645 q^{79} +(0.770331 + 1.33425i) q^{81} +(5.58184 - 9.66804i) q^{82} +11.1943i q^{83} +(-2.12621 - 1.22757i) q^{84} +7.78333i q^{86} +(-0.277015 + 0.479805i) q^{87} +(-1.49612 - 2.59135i) q^{88} +(5.98533 - 3.45563i) q^{89} +(-7.49486 - 0.667134i) q^{91} -0.899428 q^{92} +(0.282231 - 0.162946i) q^{93} +(5.65944 + 9.80244i) q^{94} -1.17644i q^{96} +(-2.23289 - 1.28916i) q^{97} +(-2.29044 - 1.32239i) q^{98} -4.83540i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 16 q^{9} - 6 q^{11} + 20 q^{14} - 8 q^{16} - 18 q^{19} + 2 q^{26} + 6 q^{29} + 16 q^{36} + 60 q^{39} + 42 q^{41} + 12 q^{46} + 30 q^{49} - 40 q^{51} - 36 q^{54} + 10 q^{56} - 60 q^{59}+ \cdots + 6 q^{94}+O(q^{100}) $ 16 * q + 8 * q^4 - 16 * q^9 - 6 * q^11 + 20 * q^14 - 8 * q^16 - 18 * q^19 + 2 * q^26 + 6 * q^29 + 16 * q^36 + 60 * q^39 + 42 * q^41 + 12 * q^46 + 30 * q^49 - 40 * q^51 - 36 * q^54 + 10 * q^56 - 60 * q^59 - 10 * q^61 - 16 * q^64 + 40 * q^66 + 4 * q^69 - 40 * q^74 - 18 * q^76 - 8 * q^79 + 16 * q^81 + 12 * q^84 + 78 * q^89 + 38 * q^91 + 6 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	0.588222	+	1.01883i	0.339610	+	0.588222i	0.984359	−	0.176172i	$-0.0563716\pi$
$3$	0.588222	+	1.01883i	0.339610	+	0.588222i	−0.644749	+	0.764394i	$0.723038\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	1.01883	+	0.588222i	0.415936	+	0.240140i
$7$	−1.80732	−	1.04346i	−0.683104	−	0.394390i	0.117919	−	0.993023i	$-0.462378\pi$
$7$	−1.80732	−	1.04346i	−0.683104	−	0.394390i	−0.801024	+	0.598633i	$0.795711\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.807991	−	1.39948i	0.269330	−	0.466494i
$10$		0			0
$11$	2.59135	−	1.49612i	0.781322	−	0.451096i	−0.0555766	−	0.998454i	$-0.517700\pi$
$11$	2.59135	−	1.49612i	0.781322	−	0.451096i	0.836899	+	0.547358i	$0.184366\pi$
$12$	1.17644			0.339610
$13$	3.27004	−	1.51883i	0.906946	−	0.421248i
$13$	3.27004	−	1.51883i	0.906946	−	0.421248i
$14$	−2.08692			−0.557752
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.630092	+	1.09135i	−0.152820	+	0.264692i	−0.932263	−	0.361781i	$-0.882169\pi$
$17$	−0.630092	+	1.09135i	−0.152820	+	0.264692i	0.779443	+	0.626473i	$0.215502\pi$
$18$		−	1.61598i		−	0.380890i
$19$	3.37028	+	1.94583i	0.773195	+	0.446404i	0.834013	−	0.551744i	$-0.186038\pi$
$19$	3.37028	+	1.94583i	0.773195	+	0.446404i	−0.0608181	+	0.998149i	$0.519371\pi$
$20$		0			0
$21$		−	2.45514i		−	0.535756i
$22$	1.49612	−	2.59135i	0.318973	−	0.552478i
$23$	−0.449714	−	0.778928i	−0.0937719	−	0.162418i	0.815324	−	0.579006i	$-0.196559\pi$
$23$	−0.449714	−	0.778928i	−0.0937719	−	0.162418i	−0.909095	+	0.416588i	$0.863226\pi$
$24$	1.01883	−	0.588222i	0.207968	−	0.120070i
$25$		0			0
$26$	2.07252	−	2.95036i	0.406455	−	0.578614i
$27$	5.43044			1.04509
$28$	−1.80732	+	1.04346i	−0.341552	+	0.197195i
$29$	0.235468	+	0.407843i	0.0437254	+	0.0757346i	0.887060	−	0.461654i	$-0.152744\pi$
$29$	0.235468	+	0.407843i	0.0437254	+	0.0757346i	−0.843334	+	0.537389i	$0.819411\pi$
$30$		0			0
$31$		−	0.277015i		−	0.0497534i	−0.999691	−	0.0248767i	$-0.992081\pi$
$31$		−	0.277015i		−	0.0497534i	0.999691	−	0.0248767i	$-0.00791932\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	3.04858	+	1.76010i	0.530689	+	0.306394i
$34$			1.26018i			0.216120i
$35$		0			0
$36$	−0.807991	−	1.39948i	−0.134665	−	0.233247i
$37$	−6.09479	+	3.51883i	−1.00198	+	0.578492i	−0.908833	−	0.417161i	$-0.863025\pi$
$37$	−6.09479	+	3.51883i	−1.00198	+	0.578492i	−0.0931448	+	0.995653i	$0.529692\pi$
$38$	3.89166			0.631311
$39$	3.47094	+	2.43820i	0.555795	+	0.390425i
$40$		0			0
$41$	9.66804	−	5.58184i	1.50989	−	0.871738i	0.509960	−	0.860198i	$-0.329660\pi$
$41$	9.66804	−	5.58184i	1.50989	−	0.871738i	0.999933	−	0.0115395i	$-0.00367323\pi$
$42$	−1.22757	−	2.12621i	−0.189418	−	0.328082i
$43$	−3.89166	+	6.74056i	−0.593473	+	1.02793i	0.400287	+	0.916390i	$0.368910\pi$
$43$	−3.89166	+	6.74056i	−0.593473	+	1.02793i	−0.993760	+	0.111536i	$0.964423\pi$
$44$		−	2.99224i		−	0.451096i
$45$		0			0
$46$	−0.778928	−	0.449714i	−0.114847	−	0.0663067i
$47$			11.3189i			1.65103i	0.564381	+	0.825514i	$0.309115\pi$
$47$			11.3189i			1.65103i	−0.564381	+	0.825514i	$0.690885\pi$
$48$	0.588222	−	1.01883i	0.0849025	−	0.147055i
$49$	−1.32239	−	2.29044i	−0.188912	−	0.327206i
$50$		0			0
$51$	−1.48254			−0.207597
$52$	0.319674	−	3.59135i	0.0443309	−	0.498031i
$53$	−12.0148			−1.65036			−0.825181	−	0.564868i	$-0.808927\pi$
$53$	−12.0148			−1.65036			−0.825181	+	0.564868i	$0.808927\pi$
$54$	4.70290	−	2.71522i	0.639984	−	0.369495i
$55$		0			0
$56$	−1.04346	+	1.80732i	−0.139438	+	0.241514i
$57$			4.57832i			0.606413i
$58$	0.407843	+	0.235468i	0.0535525	+	0.0309185i
$59$	−10.7029	−	6.17932i	−1.39340	−	0.804479i	−0.399709	−	0.916642i	$-0.630889\pi$
$59$	−10.7029	−	6.17932i	−1.39340	−	0.804479i	−0.993690	+	0.112163i	$0.964222\pi$
$60$		0			0
$61$	−3.82102	+	6.61820i	−0.489232	+	0.847374i	−0.999923	−	0.0123900i	$-0.996056\pi$
$61$	−3.82102	+	6.61820i	−0.489232	+	0.847374i	0.510692	+	0.859764i	$0.329389\pi$
$62$	−0.138508	−	0.239902i	−0.0175905	−	0.0304676i
$63$	−2.92060	+	1.68621i	−0.367961	+	0.212442i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	3.52020			0.433306
$67$	3.46410	−	2.00000i	0.423207	−	0.244339i	−0.273241	−	0.961946i	$-0.588096\pi$
$67$	3.46410	−	2.00000i	0.423207	−	0.244339i	0.696449	+	0.717607i	$0.254762\pi$
$68$	0.630092	+	1.09135i	0.0764099	+	0.132346i
$69$	0.529063	−	0.916364i	0.0636917	−	0.110317i
$70$		0			0
$71$	4.07532	+	2.35289i	0.483651	+	0.279236i	0.721937	−	0.691959i	$-0.243252\pi$
$71$	4.07532	+	2.35289i	0.483651	+	0.279236i	−0.238286	+	0.971195i	$0.576585\pi$
$72$	−1.39948	−	0.807991i	−0.164930	−	0.0952226i
$73$		−	15.2984i		−	1.79054i	−0.445520	−	0.895272i	$-0.646981\pi$
$73$		−	15.2984i		−	1.79054i	0.445520	−	0.895272i	$-0.353019\pi$
$74$	−3.51883	+	6.09479i	−0.409056	+	0.708505i
$75$		0			0
$76$	3.37028	−	1.94583i	0.386598	−	0.223202i
$77$	−6.24455			−0.711633
$78$	4.22502	+	0.376079i	0.478390	+	0.0425825i
$79$	1.63645			0.184115			0.0920574	−	0.995754i	$-0.470656\pi$
$79$	1.63645			0.184115			0.0920574	+	0.995754i	$0.470656\pi$
$80$		0			0
$81$	0.770331	+	1.33425i	0.0855923	+	0.148250i
$82$	5.58184	−	9.66804i	0.616412	−	1.06766i
$83$			11.1943i			1.22873i	0.789020	+	0.614367i	$0.210589\pi$
$83$			11.1943i			1.22873i	−0.789020	+	0.614367i	$0.789411\pi$
$84$	−2.12621	−	1.22757i	−0.231989	−	0.133939i
$85$		0			0
$86$			7.78333i			0.839298i
$87$	−0.277015	+	0.479805i	−0.0296992	+	0.0514405i
$88$	−1.49612	−	2.59135i	−0.159487	−	0.276239i
$89$	5.98533	−	3.45563i	0.634444	−	0.366296i	−0.148027	−	0.988983i	$-0.547292\pi$
$89$	5.98533	−	3.45563i	0.634444	−	0.366296i	0.782471	+	0.622687i	$0.213959\pi$
$90$		0			0
$91$	−7.49486	−	0.667134i	−0.785674	−	0.0699347i
$92$	−0.899428			−0.0937719
$93$	0.282231	−	0.162946i	0.0292660	−	0.0168968i
$94$	5.65944	+	9.80244i	0.583727	+	1.01104i
$95$		0			0
$96$		−	1.17644i		−	0.120070i
$97$	−2.23289	−	1.28916i	−0.226716	−	0.130894i	0.382340	−	0.924022i	$-0.375118\pi$
$97$	−2.23289	−	1.28916i	−0.226716	−	0.130894i	−0.609056	+	0.793127i	$0.708452\pi$
$98$	−2.29044	−	1.32239i	−0.231369	−	0.133581i
$99$		−	4.83540i		−	0.485976i
$100$		0			0
$101$	−0.783361	−	1.35682i	−0.0779474	−	0.135009i	0.824417	−	0.565983i	$-0.191503\pi$
$101$	−0.783361	−	1.35682i	−0.0779474	−	0.135009i	−0.902364	+	0.430974i	$0.858170\pi$
$102$	−1.28391	+	0.741268i	−0.127126	+	0.0733965i
$103$	0.916364			0.0902920			0.0451460	−	0.998980i	$-0.485625\pi$
$103$	0.916364			0.0902920			0.0451460	+	0.998980i	$0.485625\pi$
$104$	−1.51883	−	3.27004i	−0.148934	−	0.320654i
$105$		0			0
$106$	−10.4051	+	6.00741i	−1.01064	+	0.583491i
$107$	−5.85118	−	10.1345i	−0.565655	−	0.979743i	−0.996988	−	0.0775504i	$-0.975290\pi$
$107$	−5.85118	−	10.1345i	−0.565655	−	0.979743i	0.431334	−	0.902193i	$-0.358043\pi$
$108$	2.71522	−	4.70290i	0.261272	−	0.452537i
$109$			15.9902i			1.53159i	0.643087	+	0.765793i	$0.277653\pi$
$109$			15.9902i			1.53159i	−0.643087	+	0.765793i	$0.722347\pi$
$110$		0			0
$111$	−7.17018	−	4.13970i	−0.680563	−	0.392923i
$112$			2.08692i			0.197195i
$113$	−1.39101	+	2.40930i	−0.130855	+	0.226648i	−0.924007	−	0.382377i	$-0.875106\pi$
$113$	−1.39101	+	2.40930i	−0.130855	+	0.226648i	0.793151	+	0.609025i	$0.208439\pi$
$114$	2.28916	+	3.96494i	0.214400	+	0.371351i
$115$		0			0
$116$	0.470937			0.0437254
$117$	0.516588	−	5.80356i	0.0477586	−	0.536539i
$118$	−12.3586			−1.13771
$119$	2.27756	−	1.31495i	0.208784	−	0.120541i
$120$		0			0
$121$	−1.02326	+	1.77234i	−0.0930240	+	0.161122i
$122$			7.64204i			0.691878i
$123$	11.3739	+	6.56672i	1.02555	+	0.592101i
$124$	−0.239902	−	0.138508i	−0.0215439	−	0.0124384i
$125$		0			0
$126$	−1.68621	+	2.92060i	−0.150220	+	0.260188i
$127$	4.34985	+	7.53415i	0.385986	+	0.668548i	0.991906	−	0.126978i	$-0.0405278\pi$
$127$	4.34985	+	7.53415i	0.385986	+	0.668548i	−0.605919	+	0.795526i	$0.707195\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−9.15664			−0.806197
$130$		0			0
$131$	−15.8740			−1.38692			−0.693459	−	0.720496i	$-0.743914\pi$
$131$	−15.8740			−1.38692			−0.693459	+	0.720496i	$0.743914\pi$
$132$	3.04858	−	1.76010i	0.265345	−	0.153197i
$133$	−4.06079	−	7.03350i	−0.352115	−	0.609882i
$134$	2.00000	−	3.46410i	0.172774	−	0.299253i
$135$		0			0
$136$	1.09135	+	0.630092i	0.0935827	+	0.0540300i
$137$	6.25538	+	3.61155i	0.534433	+	0.308555i	0.742820	−	0.669491i	$-0.233488\pi$
$137$	6.25538	+	3.61155i	0.534433	+	0.308555i	−0.208386	+	0.978047i	$0.566821\pi$
$138$		−	1.05813i		−	0.0900737i
$139$	−9.93700	+	17.2114i	−0.842846	+	1.45985i	0.0446337	+	0.999003i	$0.485788\pi$
$139$	−9.93700	+	17.2114i	−0.842846	+	1.45985i	−0.887479	+	0.460848i	$0.847545\pi$
$140$		0			0
$141$	−11.5320	+	6.65801i	−0.971171	+	0.560706i
$142$	4.70577			0.394900
$143$	6.20147	−	8.82819i	0.518593	−	0.738250i
$144$	−1.61598			−0.134665
$145$		0			0
$146$	−7.64921	−	13.2488i	−0.633053	−	1.09648i
$147$	1.55571	−	2.69457i	0.128313	−	0.222245i
$148$			7.03766i			0.578492i
$149$	0.851450	+	0.491585i	0.0697535	+	0.0402722i	0.534471	−	0.845187i	$-0.320511\pi$
$149$	0.851450	+	0.491585i	0.0697535	+	0.0402722i	−0.464718	+	0.885459i	$0.653844\pi$
$150$		0			0
$151$			8.06034i			0.655941i	0.944688	+	0.327971i	$0.106365\pi$
$151$			8.06034i			0.655941i	−0.944688	+	0.327971i	$0.893635\pi$
$152$	1.94583	−	3.37028i	0.157828	−	0.273366i
$153$	1.01822	+	1.76360i	0.0823180	+	0.142579i
$154$	−5.40794	+	3.12228i	−0.435784	+	0.251600i
$155$		0			0
$156$	3.84702	−	1.78682i	0.308008	−	0.143060i
$157$	−2.73373			−0.218176			−0.109088	−	0.994032i	$-0.534793\pi$
$157$	−2.73373			−0.218176			−0.109088	+	0.994032i	$0.534793\pi$
$158$	1.41721	−	0.818224i	0.112747	−	0.0650944i
$159$	−7.06738	−	12.2411i	−0.560480	−	0.970779i
$160$		0			0
$161$			1.87703i			0.147931i
$162$	1.33425	+	0.770331i	0.104829	+	0.0605229i
$163$	21.2842	+	12.2885i	1.66711	+	0.962506i	0.969185	+	0.246334i	$0.0792260\pi$
$163$	21.2842	+	12.2885i	1.66711	+	0.962506i	0.697924	+	0.716172i	$0.254107\pi$
$164$		−	11.1637i		−	0.871738i
$165$		0			0
$166$	5.59715	+	9.69455i	0.434423	+	0.752443i
$167$	−11.9826	+	6.91817i	−0.927243	+	0.535344i	−0.885939	−	0.463802i	$-0.846485\pi$
$167$	−11.9826	+	6.91817i	−0.927243	+	0.535344i	−0.0413047	+	0.999147i	$0.513151\pi$
$168$	−2.45514			−0.189418
$169$	8.38631	−	9.93327i	0.645101	−	0.764097i
$170$		0			0
$171$	5.44631	−	3.14443i	0.416490	−	0.240460i
$172$	3.89166	+	6.74056i	0.296737	+	0.513963i
$173$	6.58638	−	11.4079i	0.500753	−	0.867330i	−0.499247	−	0.866460i	$-0.666390\pi$
$173$	6.58638	−	11.4079i	0.500753	−	0.867330i	1.00000		0.000869643i	$-0.000276816\pi$
$174$			0.554031i			0.0420010i
$175$		0			0
$176$	−2.59135	−	1.49612i	−0.195330	−	0.112774i
$177$		−	14.5392i		−	1.09284i
$178$	3.45563	−	5.98533i	0.259011	−	0.448620i
$179$	1.55786	+	2.69828i	0.116440	+	0.201679i	0.918354	−	0.395759i	$-0.129519\pi$
$179$	1.55786	+	2.69828i	0.116440	+	0.201679i	−0.801915	+	0.597438i	$0.796185\pi$
$180$		0			0
$181$	7.91439			0.588272			0.294136	−	0.955764i	$-0.404968\pi$
$181$	7.91439			0.588272			0.294136	+	0.955764i	$0.404968\pi$
$182$	−6.82430	+	3.16967i	−0.505851	+	0.234952i
$183$	−8.99043			−0.664592
$184$	−0.778928	+	0.449714i	−0.0574233	+	0.0331534i
$185$		0			0
$186$	0.162946	−	0.282231i	0.0119478	−	0.0206942i
$187$			3.77077i			0.275746i
$188$	9.80244	+	5.65944i	0.714916	+	0.412757i
$189$	−9.81457	−	5.66644i	−0.713905	−	0.412173i
$190$		0			0
$191$	−6.98046	+	12.0905i	−0.505088	+	0.874839i	0.494894	+	0.868953i	$0.335207\pi$
$191$	−6.98046	+	12.0905i	−0.505088	+	0.874839i	−0.999983	+	0.00588562i	$0.998127\pi$
$192$	−0.588222	−	1.01883i	−0.0424512	−	0.0735277i
$193$	−11.8018	+	6.81379i	−0.849514	+	0.490467i	−0.860487	−	0.509472i	$-0.829841\pi$
$193$	−11.8018	+	6.81379i	−0.849514	+	0.490467i	0.0109726	+	0.999940i	$0.496507\pi$
$194$	−2.57832			−0.185113
$195$		0			0
$196$	−2.64477			−0.188912
$197$	15.3477	−	8.86097i	1.09348	−	0.631318i	0.158976	−	0.987282i	$-0.449181\pi$
$197$	15.3477	−	8.86097i	1.09348	−	0.631318i	0.934500	+	0.355964i	$0.115848\pi$
$198$	−2.41770	−	4.18758i	−0.171818	−	0.297598i
$199$	−7.18270	+	12.4408i	−0.509168	+	0.881905i	0.490775	+	0.871286i	$0.336714\pi$
$199$	−7.18270	+	12.4408i	−0.509168	+	0.881905i	−0.999944	+	0.0106193i	$0.996620\pi$
$200$		0			0
$201$	4.07532	+	2.35289i	0.287451	+	0.165960i
$202$	−1.35682	−	0.783361i	−0.0954656	−	0.0551171i
$203$		−	0.982807i		−	0.0689795i
$204$	−0.741268	+	1.28391i	−0.0518991	+	0.0898919i
$205$		0			0
$206$	0.793595	−	0.458182i	0.0552924	−	0.0319231i
$207$	−1.45346			−0.101022
$208$	−2.95036	−	2.07252i	−0.204571	−	0.143704i
$209$	11.6448			0.805486
$210$		0			0
$211$	10.1115	+	17.5137i	0.696108	+	1.20569i	0.969806	+	0.243878i	$0.0784197\pi$
$211$	10.1115	+	17.5137i	0.696108	+	1.20569i	−0.273698	+	0.961816i	$0.588247\pi$
$212$	−6.00741	+	10.4051i	−0.412591	+	0.714628i
$213$			5.53608i			0.379326i
$214$	−10.1345	−	5.85118i	−0.692783	−	0.399978i
$215$		0			0
$216$		−	5.43044i		−	0.369495i
$217$	−0.289054	+	0.500656i	−0.0196223	+	0.0339868i
$218$	7.99511	+	13.8479i	0.541497	+	0.937901i
$219$	15.5865	−	8.99886i	1.05324	−	0.608086i
$220$		0			0
$221$	−0.402849	+	4.52577i	−0.0270985	+	0.304436i
$222$	−8.27941			−0.555677
$223$	9.65189	−	5.57252i	0.646338	−	0.373164i	−0.140714	−	0.990050i	$-0.544940\pi$
$223$	9.65189	−	5.57252i	0.646338	−	0.373164i	0.787052	+	0.616887i	$0.211606\pi$
$224$	1.04346	+	1.80732i	0.0697190	+	0.120757i
$225$		0			0
$226$			2.78203i			0.185058i
$227$	14.9885	+	8.65364i	0.994825	+	0.574362i	0.906713	−	0.421748i	$-0.138583\pi$
$227$	14.9885	+	8.65364i	0.994825	+	0.574362i	0.0881117	+	0.996111i	$0.471917\pi$
$228$	3.96494	+	2.28916i	0.262585	+	0.151603i
$229$			9.90350i			0.654442i	0.944948	+	0.327221i	$0.106112\pi$
$229$			9.90350i			0.654442i	−0.944948	+	0.327221i	$0.893888\pi$
$230$		0			0
$231$	−3.67318	−	6.36213i	−0.241677	−	0.418598i
$232$	0.407843	−	0.235468i	0.0267762	−	0.0154593i
$233$	−19.1742			−1.25614			−0.628070	−	0.778156i	$-0.716155\pi$
$233$	−19.1742			−1.25614			−0.628070	+	0.778156i	$0.716155\pi$
$234$	−2.45440	−	5.28432i	−0.160449	−	0.345447i
$235$		0			0
$236$	−10.7029	+	6.17932i	−0.696699	+	0.402240i
$237$	0.962594	+	1.66726i	0.0625272	+	0.108300i
$238$	1.31495	−	2.27756i	0.0852356	−	0.147632i
$239$			2.16448i			0.140009i	0.997547	+	0.0700043i	$0.0223013\pi$
$239$			2.16448i			0.140009i	−0.997547	+	0.0700043i	$0.977699\pi$
$240$		0			0
$241$	−13.9442	−	8.05067i	−0.898223	−	0.518589i	−0.0215996	−	0.999767i	$-0.506876\pi$
$241$	−13.9442	−	8.05067i	−0.898223	−	0.518589i	−0.876623	+	0.481178i	$0.840209\pi$
$242$			2.04653i			0.131556i
$243$	7.23941	−	12.5390i	0.464408	−	0.804379i
$244$	3.82102	+	6.61820i	0.244616	+	0.423687i
$245$		0			0
$246$	13.1334			0.837358
$247$	13.9763	+	1.24407i	0.889293	+	0.0791580i
$248$	−0.277015			−0.0175905
$249$	−11.4051	+	6.58473i	−0.722768	+	0.417290i
$250$		0			0
$251$	9.04439	−	15.6653i	0.570877	−	0.988787i	−0.425600	−	0.904912i	$-0.639937\pi$
$251$	9.04439	−	15.6653i	0.570877	−	0.988787i	0.996476	−	0.0838757i	$-0.0267299\pi$
$252$			3.37242i			0.212442i
$253$	−2.33073	−	1.34565i	−0.146532	−	0.0846003i
$254$	7.53415	+	4.34985i	0.472735	+	0.272934i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.02260	−	8.69939i	−0.313301	−	0.542653i	0.665774	−	0.746154i	$-0.268102\pi$
$257$	−5.02260	−	8.69939i	−0.313301	−	0.542653i	−0.979075	+	0.203500i	$0.934768\pi$
$258$	−7.92989	+	4.57832i	−0.493693	+	0.285034i
$259$	14.6870			0.912607
$260$		0			0
$261$	0.761025			0.0471063
$262$	−13.7473	+	7.93700i	−0.849310	+	0.490350i
$263$	−7.90133	−	13.6855i	−0.487217	−	0.843884i	0.512675	−	0.858583i	$-0.328654\pi$
$263$	−7.90133	−	13.6855i	−0.487217	−	0.843884i	−0.999892	+	0.0146985i	$0.995321\pi$
$264$	1.76010	−	3.04858i	0.108327	−	0.187627i
$265$		0			0
$266$	−7.03350	−	4.06079i	−0.431251	−	0.248983i
$267$	7.04141	+	4.06536i	0.430927	+	0.248796i
$268$		−	4.00000i		−	0.244339i
$269$	3.69294	−	6.39635i	0.225162	−	0.389993i	−0.731206	−	0.682157i	$-0.761042\pi$
$269$	3.69294	−	6.39635i	0.225162	−	0.389993i	0.956368	+	0.292164i	$0.0943754\pi$
$270$		0			0
$271$	26.8493	−	15.5014i	1.63098	−	0.941645i	0.647184	−	0.762334i	$-0.275947\pi$
$271$	26.8493	−	15.5014i	1.63098	−	0.941645i	0.983793	−	0.179310i	$-0.0573866\pi$
$272$	1.26018			0.0764099
$273$	−3.72894	−	8.02841i	−0.225686	−	0.485901i
$274$	7.22309			0.436363
$275$		0			0
$276$	−0.529063	−	0.916364i	−0.0318459	−	0.0551586i
$277$	2.35368	−	4.07668i	0.141419	−	0.244944i	−0.786612	−	0.617447i	$-0.788167\pi$
$277$	2.35368	−	4.07668i	0.141419	−	0.244944i	0.928031	+	0.372503i	$0.121500\pi$
$278$			19.8740i			1.19196i
$279$	−0.387678	−	0.223826i	−0.0232097	−	0.0134001i
$280$		0			0
$281$		−	10.7771i		−	0.642910i	−0.946925	−	0.321455i	$-0.895828\pi$
$281$		−	10.7771i		−	0.642910i	0.946925	−	0.321455i	$-0.104172\pi$
$282$	−6.65801	+	11.5320i	−0.396479	+	0.686721i
$283$	14.5610	+	25.2204i	0.865561	+	1.49919i	0.866489	+	0.499195i	$0.166371\pi$
$283$	14.5610	+	25.2204i	0.865561	+	1.49919i	−0.000928800		1.00000i	$0.500296\pi$
$284$	4.07532	−	2.35289i	0.241826	−	0.139618i
$285$		0			0
$286$	0.956541	−	10.7462i	0.0565615	−	0.635434i
$287$	−23.2977			−1.37522
$288$	−1.39948	+	0.807991i	−0.0824652	+	0.0476113i
$289$	7.70597	+	13.3471i	0.453292	+	0.785125i
$290$		0			0
$291$		−	3.03325i		−	0.177812i
$292$	−13.2488	−	7.64921i	−0.775328	−	0.447636i
$293$	−22.0186	−	12.7124i	−1.28634	−	0.742668i	−0.308339	−	0.951277i	$-0.599773\pi$
$293$	−22.0186	−	12.7124i	−1.28634	−	0.742668i	−0.977999	+	0.208609i	$0.933106\pi$
$294$		−	3.11143i		−	0.181462i
$295$		0			0
$296$	3.51883	+	6.09479i	0.204528	+	0.354253i
$297$	14.0722	−	8.12458i	0.816551	−	0.471436i
$298$	0.983169			0.0569535
$299$	−2.65364	−	1.86408i	−0.153464	−	0.107803i
$300$		0			0
$301$	14.0670	−	8.12158i	0.810808	−	0.468120i
$302$	4.03017	+	6.98046i	0.231910	+	0.401680i
$303$	0.921580	−	1.59622i	0.0529434	−	0.0917007i
$304$		−	3.89166i		−	0.223202i
$305$		0			0
$306$	1.76360	+	1.01822i	0.100819	+	0.0582076i
$307$		−	25.3305i		−	1.44569i	−0.691012	−	0.722843i	$-0.742835\pi$
$307$		−	25.3305i		−	1.44569i	0.691012	−	0.722843i	$-0.257165\pi$
$308$	−3.12228	+	5.40794i	−0.177908	+	0.308146i
$309$	0.539025	+	0.933619i	0.0306641	+	0.0531117i
$310$		0			0
$311$	−24.3495			−1.38074			−0.690368	−	0.723459i	$-0.742551\pi$
$311$	−24.3495			−1.38074			−0.690368	+	0.723459i	$0.742551\pi$
$312$	2.43820	−	3.47094i	0.138036	−	0.196503i
$313$	−15.6891			−0.886802			−0.443401	−	0.896323i	$-0.646228\pi$
$313$	−15.6891			−0.886802			−0.443401	+	0.896323i	$0.646228\pi$
$314$	−2.36748	+	1.36687i	−0.133605	+	0.0771367i
$315$		0			0
$316$	0.818224	−	1.41721i	0.0460287	−	0.0797240i
$317$		−	19.4607i		−	1.09302i	−0.837453	−	0.546510i	$-0.815956\pi$
$317$		−	19.4607i		−	1.09302i	0.837453	−	0.546510i	$-0.184044\pi$
$318$	−12.2411	−	7.06738i	−0.686445	−	0.396319i
$319$	1.22036	+	0.704577i	0.0683272	+	0.0394487i
$320$		0			0
$321$	6.88358	−	11.9227i	0.384204	−	0.665461i
$322$	0.938516	+	1.62556i	0.0523015	+	0.0905888i
$323$	−4.24717	+	2.45211i	−0.236319	+	0.136439i
$324$	1.54066			0.0855923
$325$		0			0
$326$	24.5769			1.36119
$327$	−16.2913	+	9.40580i	−0.900912	+	0.520142i
$328$	−5.58184	−	9.66804i	−0.308206	−	0.533828i
$329$	11.8108	−	20.4569i	0.651150	−	1.12782i
$330$		0			0
$331$	5.73925	+	3.31356i	0.315457	+	0.182129i	0.649366	−	0.760476i	$-0.275034\pi$
$331$	5.73925	+	3.31356i	0.315457	+	0.182129i	−0.333909	+	0.942605i	$0.608368\pi$
$332$	9.69455	+	5.59715i	0.532058	+	0.307184i
$333$			11.3727i			0.623221i
$334$	−6.91817	+	11.9826i	−0.378546	+	0.655660i
$335$		0			0
$336$	−2.12621	+	1.22757i	−0.115995	+	0.0669695i
$337$	−11.0614			−0.602555			−0.301277	−	0.953537i	$-0.597413\pi$
$337$	−11.0614			−0.602555			−0.301277	+	0.953537i	$0.597413\pi$
$338$	2.29613	−	12.7956i	0.124893	−	0.695990i
$339$	−3.27290			−0.177759
$340$		0			0
$341$	−0.414448	−	0.717844i	−0.0224436	−	0.0388734i
$342$	3.14443	−	5.44631i	0.170031	−	0.294503i
$343$			20.1279i			1.08680i
$344$	6.74056	+	3.89166i	0.363427	+	0.209824i
$345$		0			0
$346$		−	13.1728i		−	0.708172i
$347$	8.86035	−	15.3466i	0.475649	−	0.823847i	−0.523962	−	0.851741i	$-0.675547\pi$
$347$	8.86035	−	15.3466i	0.475649	−	0.823847i	0.999611	+	0.0278940i	$0.00888008\pi$
$348$	0.277015	+	0.479805i	0.0148496	+	0.0257202i
$349$	−15.3172	+	8.84341i	−0.819913	+	0.473377i	−0.850387	−	0.526158i	$-0.823632\pi$
$349$	−15.3172	+	8.84341i	−0.819913	+	0.473377i	0.0304733	+	0.999536i	$0.490299\pi$
$350$		0			0
$351$	17.7578	−	8.24791i	0.947839	−	0.440241i
$352$	−2.99224			−0.159487
$353$	29.1183	−	16.8114i	1.54981	−	0.894783i	0.551654	−	0.834073i	$-0.313997\pi$
$353$	29.1183	−	16.8114i	1.54981	−	0.894783i	0.998155	−	0.0607098i	$-0.0193364\pi$
$354$	−7.26962	−	12.5914i	−0.386376	−	0.669223i
$355$		0			0
$356$		−	6.91127i		−	0.366296i
$357$	2.67942	+	1.54697i	0.141810	+	0.0818741i
$358$	2.69828	+	1.55786i	0.142609	+	0.0823352i
$359$		−	17.4880i		−	0.922981i	−0.887145	−	0.461490i	$-0.847315\pi$
$359$		−	17.4880i		−	0.922981i	0.887145	−	0.461490i	$-0.152685\pi$
$360$		0			0
$361$	−1.92748	−	3.33849i	−0.101446	−	0.175710i
$362$	6.85407	−	3.95720i	0.360242	−	0.207986i
$363$	−2.40762			−0.126367
$364$	−4.32518	+	6.15717i	−0.226701	+	0.322723i
$365$		0			0
$366$	−7.78594	+	4.49521i	−0.406978	+	0.234969i
$367$	−3.67988	−	6.37373i	−0.192088	−	0.332706i	0.753854	−	0.657042i	$-0.228193\pi$
$367$	−3.67988	−	6.37373i	−0.192088	−	0.332706i	−0.945942	+	0.324336i	$0.894859\pi$
$368$	−0.449714	+	0.778928i	−0.0234430	+	0.0406044i
$369$		−	18.0403i		−	0.939141i
$370$		0			0
$371$	21.7147	+	12.5370i	1.12737	+	0.650887i
$372$		−	0.325893i		−	0.0168968i
$373$	14.6008	−	25.2893i	0.756000	−	1.30943i	−0.188875	−	0.982001i	$-0.560484\pi$
$373$	14.6008	−	25.2893i	0.756000	−	1.30943i	0.944875	−	0.327430i	$-0.106183\pi$
$374$	1.88538	+	3.26558i	0.0974909	+	0.168859i
$375$		0			0
$376$	11.3189			0.583727
$377$	1.38944	+	0.976027i	0.0715596	+	0.0502680i
$378$	−11.3329			−0.582901
$379$	13.2943	−	7.67544i	0.682880	−	0.394261i	−0.118059	−	0.993007i	$-0.537667\pi$
$379$	13.2943	−	7.67544i	0.682880	−	0.394261i	0.800939	+	0.598746i	$0.204334\pi$
$380$		0			0
$381$	−5.11735	+	8.86350i	−0.262170	+	0.454091i
$382$			13.9609i			0.714303i
$383$	2.76474	+	1.59622i	0.141272	+	0.0815632i	0.568970	−	0.822358i	$-0.307342\pi$
$383$	2.76474	+	1.59622i	0.141272	+	0.0815632i	−0.427698	+	0.903922i	$0.640675\pi$
$384$	−1.01883	−	0.588222i	−0.0519919	−	0.0300176i
$385$		0			0
$386$	−6.81379	+	11.8018i	−0.346813	+	0.600697i
$387$	6.28885	+	10.8926i	0.319680	+	0.553703i
$388$	−2.23289	+	1.28916i	−0.113358	+	0.0654472i
$389$	−28.9316			−1.46689			−0.733445	−	0.679749i	$-0.762089\pi$
$389$	−28.9316			−1.46689			−0.733445	+	0.679749i	$0.762089\pi$
$390$		0			0
$391$	1.13345			0.0573208
$392$	−2.29044	+	1.32239i	−0.115685	+	0.0667906i
$393$	−9.33743	−	16.1729i	−0.471011	−	0.815815i
$394$	8.86097	−	15.3477i	0.446409	−	0.773204i
$395$		0			0
$396$	−4.18758	−	2.41770i	−0.210434	−	0.121494i
$397$	4.32245	+	2.49557i	0.216937	+	0.125249i	0.604531	−	0.796581i	$-0.293360\pi$
$397$	4.32245	+	2.49557i	0.216937	+	0.125249i	−0.387594	+	0.921830i	$0.626694\pi$
$398$			14.3654i			0.720073i
$399$	4.77729	−	8.27451i	0.239164	−	0.414244i
$400$		0			0
$401$	3.46032	−	1.99782i	0.172800	−	0.0997662i	−0.411105	−	0.911588i	$-0.634857\pi$
$401$	3.46032	−	1.99782i	0.172800	−	0.0997662i	0.583905	+	0.811822i	$0.301524\pi$
$402$	4.70577			0.234703
$403$	−0.420739	−	0.905851i	−0.0209585	−	0.0451236i
$404$	−1.56672			−0.0779474
$405$		0			0
$406$	−0.491403	−	0.851136i	−0.0243879	−	0.0422412i
$407$	−10.5292	+	18.2371i	−0.521911	+	0.903977i
$408$			1.48254i			0.0733965i
$409$	−2.53695	−	1.46471i	−0.125444	−	0.0724252i	0.435965	−	0.899964i	$-0.356407\pi$
$409$	−2.53695	−	1.46471i	−0.125444	−	0.0724252i	−0.561409	+	0.827538i	$0.689741\pi$
$410$		0			0
$411$			8.49756i			0.419154i
$412$	0.458182	−	0.793595i	0.0225730	−	0.0390976i
$413$	12.8957	+	22.3361i	0.634558	+	1.09909i
$414$	−1.25873	+	0.726729i	−0.0618633	+	0.0357168i
$415$		0			0
$416$	−3.59135	−	0.319674i	−0.176081	−	0.0156733i
$417$	−23.3806			−1.14495
$418$	10.0847	−	5.82239i	0.493257	−	0.284782i
$419$	4.85425	+	8.40780i	0.237145	+	0.410748i	0.959894	−	0.280363i	$-0.0904549\pi$
$419$	4.85425	+	8.40780i	0.237145	+	0.410748i	−0.722749	+	0.691111i	$0.757122\pi$
$420$		0			0
$421$			22.8217i			1.11226i	0.831094	+	0.556132i	$0.187715\pi$
$421$			22.8217i			1.11226i	−0.831094	+	0.556132i	$0.812285\pi$
$422$	17.5137	+	10.1115i	0.852554	+	0.492222i
$423$	15.8406	+	9.14555i	0.770194	+	0.444672i
$424$			12.0148i			0.583491i
$425$		0			0
$426$	2.76804	+	4.79438i	0.134112	+	0.232289i
$427$	13.8116	−	7.97416i	0.668392	−	0.385897i
$428$	−11.7024			−0.565655
$429$	12.6423	+	1.12532i	0.610374	+	0.0543308i
$430$		0			0
$431$	10.0125	−	5.78073i	0.482286	−	0.278448i	−0.239082	−	0.970999i	$-0.576847\pi$
$431$	10.0125	−	5.78073i	0.482286	−	0.278448i	0.721369	+	0.692551i	$0.243513\pi$
$432$	−2.71522	−	4.70290i	−0.130636	−	0.226268i
$433$	6.28278	−	10.8821i	0.301931	−	0.522960i	−0.674642	−	0.738145i	$-0.735702\pi$
$433$	6.28278	−	10.8821i	0.301931	−	0.522960i	0.976573	+	0.215185i	$0.0690354\pi$
$434$			0.578108i			0.0277501i
$435$		0			0
$436$	13.8479	+	7.99511i	0.663196	+	0.382897i
$437$		−	3.50027i		−	0.167441i
$438$	8.99886	−	15.5865i	0.429982	−	0.744751i
$439$	0.905142	+	1.56775i	0.0432001	+	0.0748247i	0.886817	−	0.462121i	$-0.152911\pi$
$439$	0.905142	+	1.56775i	0.0432001	+	0.0748247i	−0.843617	+	0.536946i	$0.819578\pi$
$440$		0			0
$441$	−4.27390			−0.203519
$442$	1.91401	+	4.12085i	0.0910400	+	0.196009i
$443$	−16.7633			−0.796450			−0.398225	−	0.917288i	$-0.630374\pi$
$443$	−16.7633			−0.796450			−0.398225	+	0.917288i	$0.630374\pi$
$444$	−7.17018	+	4.13970i	−0.340282	+	0.196462i
$445$		0			0
$446$	5.57252	−	9.65189i	0.263867	−	0.457030i
$447$			1.15664i			0.0547073i
$448$	1.80732	+	1.04346i	0.0853880	+	0.0492988i
$449$	−6.13311	−	3.54095i	−0.289439	−	0.167108i	0.348250	−	0.937402i	$-0.386776\pi$
$449$	−6.13311	−	3.54095i	−0.289439	−	0.167108i	−0.637689	+	0.770294i	$0.720109\pi$
$450$		0			0
$451$	16.7022	−	28.9290i	0.786475	−	1.36222i
$452$	1.39101	+	2.40930i	0.0654277	+	0.113324i
$453$	−8.21212	+	4.74127i	−0.385839	+	0.222764i
$454$	17.3073			0.812271
$455$		0			0
$456$	4.57832			0.214400
$457$	−0.944133	+	0.545096i	−0.0441647	+	0.0254985i	−0.521920	−	0.852995i	$-0.674784\pi$
$457$	−0.944133	+	0.545096i	−0.0441647	+	0.0254985i	0.477755	+	0.878493i	$0.341451\pi$
$458$	4.95175	+	8.57668i	0.231380	+	0.400762i
$459$	−3.42168	+	5.92652i	−0.159710	+	0.276626i
$460$		0			0
$461$	−13.5007	−	7.79465i	−0.628791	−	0.363033i	0.151493	−	0.988458i	$-0.451592\pi$
$461$	−13.5007	−	7.79465i	−0.628791	−	0.363033i	−0.780284	+	0.625426i	$0.784925\pi$
$462$	−6.36213	−	3.67318i	−0.295993	−	0.170892i
$463$			19.1896i			0.891817i	0.895079	+	0.445908i	$0.147119\pi$
$463$			19.1896i			0.891817i	−0.895079	+	0.445908i	$0.852881\pi$
$464$	0.235468	−	0.407843i	0.0109313	−	0.0189337i
$465$		0			0
$466$	−16.6053	+	9.58708i	−0.769226	+	0.444113i
$467$	23.1857			1.07290			0.536452	−	0.843931i	$-0.319764\pi$
$467$	23.1857			1.07290			0.536452	+	0.843931i	$0.319764\pi$
$468$	−4.76773	−	3.34916i	−0.220389	−	0.154815i
$469$	−8.34767			−0.385460
$470$		0			0
$471$	−1.60804	−	2.78521i	−0.0740946	−	0.128336i
$472$	−6.17932	+	10.7029i	−0.284426	+	0.492641i
$473$			23.2895i			1.07085i
$474$	1.66726	+	0.962594i	0.0765799	+	0.0442134i
$475$		0			0
$476$		−	2.62990i		−	0.120541i
$477$	−9.70786	+	16.8145i	−0.444493	+	0.769884i
$478$	1.08224	+	1.87449i	0.0495005	+	0.0857374i
$479$	−3.01812	+	1.74251i	−0.137901	+	0.0796174i	−0.567363	−	0.823467i	$-0.692037\pi$
$479$	−3.01812	+	1.74251i	−0.137901	+	0.0796174i	0.429462	+	0.903085i	$0.358703\pi$
$480$		0			0
$481$	−14.5857	+	20.7637i	−0.665051	+	0.946742i
$482$	−16.1013			−0.733396
$483$	−1.91238	+	1.10411i	−0.0870162	+	0.0502388i
$484$	1.02326	+	1.77234i	0.0465120	+	0.0805611i
$485$		0			0
$486$		−	14.4788i		−	0.656773i
$487$	−1.85369	−	1.07023i	−0.0839988	−	0.0484967i	0.457412	−	0.889255i	$-0.348776\pi$
$487$	−1.85369	−	1.07023i	−0.0839988	−	0.0484967i	−0.541411	+	0.840758i	$0.682110\pi$
$488$	6.61820	+	3.82102i	0.299592	+	0.172969i
$489$			28.9133i			1.30751i
$490$		0			0
$491$	−13.6201	−	23.5908i	−0.614668	−	1.06464i	−0.990443	−	0.137926i	$-0.955956\pi$
$491$	−13.6201	−	23.5908i	−0.614668	−	1.06464i	0.375774	−	0.926711i	$-0.377377\pi$
$492$	11.3739	−	6.56672i	0.512775	−	0.296051i
$493$	−0.593468			−0.0267284
$494$	12.7259	−	5.91077i	0.572565	−	0.265938i
$495$		0			0
$496$	−0.239902	+	0.138508i	−0.0107719	+	0.00621918i
$497$	−4.91028	−	8.50486i	−0.220256	−	0.381495i
$498$	−6.58473	+	11.4051i	−0.295069	+	0.511074i
$499$			22.7855i			1.02002i	0.860169	+	0.510010i	$0.170358\pi$
$499$			22.7855i			1.02002i	−0.860169	+	0.510010i	$0.829642\pi$
$500$		0			0
$501$	−14.0969	−	8.13884i	−0.629802	−	0.363616i
$502$		−	18.0888i		−	0.807341i
$503$	4.80162	−	8.31665i	0.214094	−	0.370821i	−0.738898	−	0.673817i	$-0.764654\pi$
$503$	4.80162	−	8.31665i	0.214094	−	0.370821i	0.952992	+	0.302996i	$0.0979869\pi$
$504$	1.68621	+	2.92060i	0.0751098	+	0.130094i
$505$		0			0
$506$	−2.69130			−0.119643
$507$	15.0533	+	2.70126i	0.668541	+	0.119967i
$508$	8.69969			0.385986
$509$	13.5627	−	7.83041i	0.601155	−	0.347077i	−0.168341	−	0.985729i	$-0.553841\pi$
$509$	13.5627	−	7.83041i	0.601155	−	0.347077i	0.769496	+	0.638652i	$0.220508\pi$
$510$		0			0
$511$	−15.9633	+	27.6492i	−0.706173	+	1.22313i
$512$			1.00000i			0.0441942i
$513$	18.3021	+	10.5667i	0.808057	+	0.466532i
$514$	−8.69939	−	5.02260i	−0.383714	−	0.221537i
$515$		0			0
$516$	−4.57832	+	7.92989i	−0.201549	+	0.349094i
$517$	16.9344	+	29.3312i	0.744773	+	1.28998i
$518$	12.7193	−	7.34351i	0.558855	−	0.322655i
$519$	15.4970			0.680243
$520$		0			0
$521$	3.26689			0.143125			0.0715625	−	0.997436i	$-0.477201\pi$
$521$	3.26689			0.143125			0.0715625	+	0.997436i	$0.477201\pi$
$522$	0.659067	−	0.380513i	0.0288466	−	0.0166546i
$523$	−7.99511	−	13.8479i	−0.349602	−	0.605528i	0.636577	−	0.771213i	$-0.280350\pi$
$523$	−7.99511	−	13.8479i	−0.349602	−	0.605528i	−0.986179	+	0.165685i	$0.947016\pi$
$524$	−7.93700	+	13.7473i	−0.346730	+	0.600553i
$525$		0			0
$526$	−13.6855	−	7.90133i	−0.596716	−	0.344514i
$527$	0.302321	+	0.174545i	0.0131693	+	0.00760331i
$528$		−	3.52020i		−	0.153197i
$529$	11.0955	−	19.2180i	0.482414	−	0.835565i
$530$		0			0
$531$	−17.2957	+	9.98567i	−0.750569	+	0.433341i
$532$	−8.12158			−0.352115
$533$	23.1370	−	32.9369i	1.00217	−	1.42666i
$534$	8.13071			0.351850
$535$		0			0
$536$	−2.00000	−	3.46410i	−0.0863868	−	0.149626i
$537$	−1.83273	+	3.17438i	−0.0790881	+	0.136985i
$538$		−	7.38587i		−	0.318428i
$539$	−6.85354	−	3.95689i	−0.295203	−	0.170435i
$540$		0			0
$541$		−	7.38554i		−	0.317529i	−0.987316	−	0.158765i	$-0.949249\pi$
$541$		−	7.38554i		−	0.317529i	0.987316	−	0.158765i	$-0.0507511\pi$
$542$	15.5014	−	26.8493i	0.665843	−	1.15327i
$543$	4.65542	+	8.06342i	0.199783	+	0.346035i
$544$	1.09135	−	0.630092i	0.0467913	−	0.0270150i
$545$		0			0
$546$	−7.24356	−	5.08833i	−0.309996	−	0.217761i
$547$	11.4488			0.489515			0.244757	−	0.969584i	$-0.421292\pi$
$547$	11.4488			0.489515			0.244757	+	0.969584i	$0.421292\pi$
$548$	6.25538	−	3.61155i	0.267217	−	0.154278i
$549$	6.17470	+	10.6949i	0.263530	+	0.456447i
$550$		0			0
$551$			1.83273i			0.0780768i
$552$	−0.916364	−	0.529063i	−0.0390030	−	0.0225184i
$553$	−2.95759	−	1.70757i	−0.125770	−	0.0726131i
$554$		−	4.70735i		−	0.199996i
$555$		0			0
$556$	9.93700	+	17.2114i	0.421423	+	0.729926i
$557$	−16.8071	+	9.70356i	−0.712138	+	0.411153i	−0.811852	−	0.583863i	$-0.801540\pi$
$557$	−16.8071	+	9.70356i	−0.712138	+	0.411153i	0.0997144	+	0.995016i	$0.468207\pi$
$558$	−0.447652			−0.0189506
$559$	−2.48813	+	27.9527i	−0.105237	+	1.18227i
$560$		0			0
$561$	−3.84177	+	2.21805i	−0.162200	+	0.0936461i
$562$	−5.38857	−	9.33328i	−0.227303	−	0.393700i
$563$	4.44885	−	7.70563i	0.187497	−	0.324754i	−0.756918	−	0.653509i	$-0.773296\pi$
$563$	4.44885	−	7.70563i	0.187497	−	0.324754i	0.944415	+	0.328756i	$0.106629\pi$
$564$			13.3160i			0.560706i
$565$		0			0
$566$	25.2204	+	14.5610i	1.06009	+	0.612044i
$567$		−	3.21524i		−	0.135027i
$568$	2.35289	−	4.07532i	0.0987249	−	0.170997i
$569$	−3.44997	−	5.97552i	−0.144630	−	0.250507i	0.784605	−	0.619996i	$-0.212866\pi$
$569$	−3.44997	−	5.97552i	−0.144630	−	0.250507i	−0.929235	+	0.369490i	$0.879533\pi$
$570$		0			0
$571$	−32.4491			−1.35795			−0.678975	−	0.734161i	$-0.737576\pi$
$571$	−32.4491			−1.35795			−0.678975	+	0.734161i	$0.737576\pi$
$572$	−4.54470	−	9.78473i	−0.190023	−	0.409120i
$573$	−16.4242			−0.686132
$574$	−20.1764	+	11.6489i	−0.842147	+	0.486214i
$575$		0			0
$576$	−0.807991	+	1.39948i	−0.0336663	+	0.0583117i
$577$			25.3915i			1.05706i	0.848914	+	0.528530i	$0.177257\pi$
$577$			25.3915i			1.05706i	−0.848914	+	0.528530i	$0.822743\pi$
$578$	13.3471	+	7.70597i	0.555167	+	0.320526i
$579$	−13.8842	−	8.01604i	−0.577007	−	0.333135i
$580$		0			0
$581$	11.6808	−	20.2317i	0.484601	−	0.839354i
$582$	−1.51662	−	2.62687i	−0.0628661	−	0.108887i
$583$	−31.1346	+	17.9756i	−1.28946	+	0.744473i
$584$	−15.2984			−0.633053
$585$		0			0
$586$	−25.4248			−1.05029
$587$	−2.13382	+	1.23196i	−0.0880722	+	0.0508485i	−0.543389	−	0.839481i	$-0.682859\pi$
$587$	−2.13382	+	1.23196i	−0.0880722	+	0.0508485i	0.455317	+	0.890329i	$0.349526\pi$
$588$	−1.55571	−	2.69457i	−0.0641565	−	0.111122i
$589$	0.539025	−	0.933619i	0.0222101	−	0.0384691i
$590$		0			0
$591$	18.0556	+	10.4244i	0.742710	+	0.428804i
$592$	6.09479	+	3.51883i	0.250494	+	0.144623i
$593$		−	40.6651i		−	1.66992i	−0.550313	−	0.834958i	$-0.685492\pi$
$593$		−	40.6651i		−	1.66992i	0.550313	−	0.834958i	$-0.314508\pi$
$594$	8.12458	−	14.0722i	0.333355	−	0.577389i
$595$		0			0
$596$	0.851450	−	0.491585i	0.0348767	−	0.0201361i
$597$	−16.9001			−0.691675
$598$	−3.23016	−	0.287524i	−0.132091	−	0.0117577i
$599$	−26.1916			−1.07016			−0.535079	−	0.844802i	$-0.679718\pi$
$599$	−26.1916			−1.07016			−0.535079	+	0.844802i	$0.679718\pi$
$600$		0			0
$601$	6.74916	+	11.6899i	0.275304	+	0.476840i	0.970212	−	0.242259i	$-0.0778882\pi$
$601$	6.74916	+	11.6899i	0.275304	+	0.476840i	−0.694908	+	0.719099i	$0.744555\pi$
$602$	8.12158	−	14.0670i	0.331011	−	0.573328i
$603$		−	6.46392i		−	0.263231i
$604$	6.98046	+	4.03017i	0.284031	+	0.163985i
$605$		0			0
$606$		−	1.84316i		−	0.0748733i
$607$	4.91431	−	8.51183i	0.199466	−	0.345485i	−0.748890	−	0.662695i	$-0.769413\pi$
$607$	4.91431	−	8.51183i	0.199466	−	0.345485i	0.948355	+	0.317210i	$0.102746\pi$
$608$	−1.94583	−	3.37028i	−0.0789139	−	0.136683i
$609$	1.00131	−	0.578108i	0.0405752	−	0.0234261i
$610$		0			0
$611$	17.1915	+	37.0132i	0.695492	+	1.49739i
$612$	2.03643			0.0823180
$613$	−17.8551	+	10.3086i	−0.721161	+	0.416362i	−0.815180	−	0.579208i	$-0.803362\pi$
$613$	−17.8551	+	10.3086i	−0.721161	+	0.416362i	0.0940190	+	0.995570i	$0.470029\pi$
$614$	−12.6652	−	21.9368i	−0.511127	−	0.885299i
$615$		0			0
$616$			6.24455i			0.251600i
$617$	15.4318	+	8.90958i	0.621262	+	0.358686i	0.777360	−	0.629056i	$-0.216558\pi$
$617$	15.4318	+	8.90958i	0.621262	+	0.358686i	−0.156098	+	0.987742i	$0.549892\pi$
$618$	0.933619	+	0.539025i	0.0375557	+	0.0216828i
$619$		−	29.3377i		−	1.17918i	−0.807701	−	0.589592i	$-0.799289\pi$
$619$		−	29.3377i		−	1.17918i	0.807701	−	0.589592i	$-0.200711\pi$
$620$		0			0
$621$	−2.44214	−	4.22992i	−0.0979999	−	0.169741i
$622$	−21.0873	+	12.1748i	−0.845524	+	0.488164i
$623$	−14.4232			−0.577855
$624$	0.376079	−	4.22502i	0.0150552	−	0.169136i
$625$		0			0
$626$	−13.5872	+	7.84457i	−0.543053	+	0.313532i
$627$	6.84971	+	11.8640i	0.273551	+	0.473804i
$628$	−1.36687	+	2.36748i	−0.0545439	+	0.0944728i
$629$		−	8.86875i		−	0.353620i
$630$		0			0
$631$	−15.5662	−	8.98714i	−0.619680	−	0.357772i	0.157064	−	0.987588i	$-0.449797\pi$
$631$	−15.5662	−	8.98714i	−0.619680	−	0.357772i	−0.776744	+	0.629816i	$0.783130\pi$
$632$		−	1.63645i		−	0.0650944i
$633$	−11.8957	+	20.6039i	−0.472810	+	0.818931i
$634$	−9.73033	−	16.8534i	−0.386441	−	0.669335i
$635$		0			0
$636$	−14.1348			−0.560480
$637$	−7.80305	−	5.48135i	−0.309168	−	0.217179i
$638$	1.40915			0.0557890
$639$	6.58564	−	3.80222i	0.260524	−	0.150414i
$640$		0			0
$641$	−12.7805	+	22.1365i	−0.504800	+	0.874339i	0.495185	+	0.868788i	$0.335100\pi$
$641$	−12.7805	+	22.1365i	−0.504800	+	0.874339i	−0.999985	+	0.00555129i	$0.998233\pi$
$642$		−	13.7672i		−	0.543347i
$643$	19.0376	+	10.9914i	0.750769	+	0.433457i	0.825972	−	0.563712i	$-0.190627\pi$
$643$	19.0376	+	10.9914i	0.750769	+	0.433457i	−0.0752028	+	0.997168i	$0.523960\pi$
$644$	1.62556	+	0.938516i	0.0640560	+	0.0369827i
$645$		0			0
$646$	−2.45211	+	4.24717i	−0.0964769	+	0.167103i
$647$	−15.5751	−	26.9769i	−0.612321	−	1.06057i	−0.990848	−	0.134981i	$-0.956903\pi$
$647$	−15.5751	−	26.9769i	−0.612321	−	1.06057i	0.378527	−	0.925590i	$-0.376431\pi$
$648$	1.33425	−	0.770331i	0.0524144	−	0.0302615i
$649$	−36.9800			−1.45159
$650$		0			0
$651$	−0.680112			−0.0266557
$652$	21.2842	−	12.2885i	0.833554	−	0.481253i
$653$	8.91711	+	15.4449i	0.348954	+	0.604405i	0.986064	−	0.166367i	$-0.0532038\pi$
$653$	8.91711	+	15.4449i	0.348954	+	0.604405i	−0.637110	+	0.770773i	$0.719870\pi$
$654$	−9.40580	+	16.2913i	−0.367796	+	0.637041i
$655$		0			0
$656$	−9.66804	−	5.58184i	−0.377473	−	0.217934i
$657$	−21.4098	−	12.3610i	−0.835277	−	0.482248i
$658$		−	23.6216i		−	0.920865i
$659$	−9.89464	+	17.1380i	−0.385440	+	0.667602i	−0.991830	−	0.127565i	$-0.959284\pi$
$659$	−9.89464	+	17.1380i	−0.385440	+	0.667602i	0.606390	+	0.795168i	$0.292617\pi$
$660$		0			0
$661$	−15.7895	+	9.11607i	−0.614140	+	0.354574i	−0.774584	−	0.632471i	$-0.782041\pi$
$661$	−15.7895	+	9.11607i	−0.614140	+	0.354574i	0.160444	+	0.987045i	$0.448707\pi$
$662$	6.62711			0.257570
$663$	−4.84795	+	2.25172i	−0.188279	+	0.0874495i
$664$	11.1943			0.434423
$665$		0			0
$666$	5.68636	+	9.84907i	0.220342	+	0.381644i
$667$	0.211787	−	0.366826i	0.00820042	−	0.0142035i
$668$			13.8363i			0.535344i
$669$	11.3549	+	6.55576i	0.439006	+	0.253460i
$670$		0			0
$671$			22.8668i			0.882763i
$672$	−1.22757	+	2.12621i	−0.0473546	+	0.0820205i
$673$	9.92322	+	17.1875i	0.382512	+	0.662530i	0.991421	−	0.130710i	$-0.0417257\pi$
$673$	9.92322	+	17.1875i	0.382512	+	0.662530i	−0.608909	+	0.793240i	$0.708392\pi$
$674$	−9.57948	+	5.53072i	−0.368988	+	0.213035i
$675$		0			0
$676$	−4.40930	−	12.2294i	−0.169589	−	0.470361i
$677$	−4.02129			−0.154551			−0.0772753	−	0.997010i	$-0.524622\pi$
$677$	−4.02129			−0.154551			−0.0772753	+	0.997010i	$0.524622\pi$
$678$	−2.83441	+	1.63645i	−0.108855	+	0.0628474i
$679$	2.69037	+	4.65986i	0.103247	+	0.178829i
$680$		0			0
$681$			20.3610i			0.780237i
$682$	−0.717844	−	0.414448i	−0.0274877	−	0.0158700i
$683$	−8.99680	−	5.19430i	−0.344253	−	0.198754i	0.317898	−	0.948125i	$-0.397023\pi$
$683$	−8.99680	−	5.19430i	−0.344253	−	0.198754i	−0.662151	+	0.749370i	$0.730356\pi$
$684$		−	6.28885i		−	0.240460i
$685$		0			0
$686$	10.0639	+	17.4312i	0.384242	+	0.665527i
$687$	−10.0900	+	5.82545i	−0.384957	+	0.222255i
$688$	7.78333			0.296737
$689$	−39.2889	+	18.2485i	−1.49679	+	0.695211i
$690$		0			0
$691$	−24.5864	+	14.1949i	−0.935309	+	0.540001i	−0.888487	−	0.458902i	$-0.848243\pi$
$691$	−24.5864	+	14.1949i	−0.935309	+	0.540001i	−0.0468225	+	0.998903i	$0.514910\pi$
$692$	−6.58638	−	11.4079i	−0.250376	−	0.433665i
$693$	−5.04554	+	8.73913i	−0.191664	+	0.331972i
$694$		−	17.7207i		−	0.672669i
$695$		0			0
$696$	0.479805	+	0.277015i	0.0181869	+	0.0105002i
$697$			14.0683i			0.532875i
$698$	−8.84341	+	15.3172i	−0.334728	+	0.579766i
$699$	−11.2787	−	19.5352i	−0.426598	−	0.738889i
$700$		0			0
$701$	16.7917			0.634213			0.317106	−	0.948390i	$-0.397289\pi$
$701$	16.7917			0.634213			0.317106	+	0.948390i	$0.397289\pi$
$702$	11.2547	−	16.0218i	0.424782	−	0.604703i
$703$	−27.3882			−1.03297
$704$	−2.59135	+	1.49612i	−0.0976652	+	0.0563871i
$705$		0			0
$706$	16.8114	−	29.1183i	0.632707	−	1.09588i
$707$			3.26962i			0.122967i
$708$	−12.5914	−	7.26962i	−0.473212	−	0.273209i
$709$	41.9846	+	24.2398i	1.57676	+	0.910345i	0.995307	+	0.0967675i	$0.0308503\pi$
$709$	41.9846	+	24.2398i	1.57676	+	0.910345i	0.581457	+	0.813577i	$0.302483\pi$
$710$		0			0
$711$	1.32223	−	2.29018i	0.0495877	−	0.0858883i
$712$	−3.45563	−	5.98533i	−0.129505	−	0.224310i
$713$	−0.215775	+	0.124578i	−0.00808083	+	0.00466547i
$714$	3.09393			0.115787
$715$		0			0
$716$	3.11571			0.116440
$717$	−2.20524	+	1.27319i	−0.0823561	+	0.0475483i
$718$	−8.74400	−	15.1450i	−0.326323	−	0.565208i
$719$	−6.14778	+	10.6483i	−0.229273	+	0.397113i	−0.957593	−	0.288125i	$-0.906968\pi$
$719$	−6.14778	+	10.6483i	−0.229273	+	0.397113i	0.728320	+	0.685238i	$0.240302\pi$
$720$		0			0
$721$	−1.65617	−	0.956188i	−0.0616789	−	0.0356103i
$722$	−3.33849	−	1.92748i	−0.124246	−	0.0717333i
$723$		−	18.9423i		−	0.704472i
$724$	3.95720	−	6.85407i	0.147068	−	0.254729i
$725$		0			0
$726$	−2.08506	+	1.20381i	−0.0773839	+	0.0446776i
$727$	−36.1491			−1.34070			−0.670349	−	0.742046i	$-0.733855\pi$
$727$	−36.1491			−1.34070			−0.670349	+	0.742046i	$0.733855\pi$
$728$	−0.667134	+	7.49486i	−0.0247256	+	0.277778i
$729$	21.6555			0.802055
$730$		0			0
$731$	−4.90421	−	8.49435i	−0.181389	−	0.314175i
$732$	−4.49521	+	7.78594i	−0.166148	+	0.287777i
$733$			22.4789i			0.830278i	0.909758	+	0.415139i	$0.136267\pi$
$733$			22.4789i			0.830278i	−0.909758	+	0.415139i	$0.863733\pi$
$734$	−6.37373	−	3.67988i	−0.235259	−	0.135827i
$735$		0			0
$736$			0.899428i			0.0331534i
$737$	5.98447	−	10.3654i	0.220441	−	0.381815i
$738$	−9.02015	−	15.6234i	−0.332036	−	0.575104i
$739$	−10.6967	+	6.17575i	−0.393485	+	0.227179i	−0.683669	−	0.729792i	$-0.739617\pi$
$739$	−10.6967	+	6.17575i	−0.393485	+	0.227179i	0.290184	+	0.956971i	$0.406283\pi$
$740$		0			0
$741$	6.95369	+	14.9713i	0.255450	+	0.549984i
$742$	25.0740			0.920494
$743$	−19.8871	+	11.4818i	−0.729587	+	0.421227i	−0.818271	−	0.574832i	$-0.805067\pi$
$743$	−19.8871	+	11.4818i	−0.729587	+	0.421227i	0.0886839	+	0.996060i	$0.471734\pi$
$744$	−0.162946	−	0.282231i	−0.00597391	−	0.0103471i
$745$		0			0
$746$		−	29.2016i		−	1.06915i
$747$	15.6662	+	9.04489i	0.573197	+	0.330935i
$748$	3.26558	+	1.88538i	0.119401	+	0.0689365i
$749$			24.4219i			0.892355i
$750$		0			0
$751$	−16.4263	−	28.4511i	−0.599403	−	1.03820i	−0.992909	−	0.118874i	$-0.962071\pi$
$751$	−16.4263	−	28.4511i	−0.599403	−	1.03820i	0.393506	−	0.919322i	$-0.371262\pi$
$752$	9.80244	−	5.65944i	0.357458	−	0.206379i
$753$	21.2804			0.775501
$754$	1.69130	+	0.150546i	0.0615935	+	0.00548258i
$755$		0			0
$756$	−9.81457	+	5.66644i	−0.356952	+	0.206086i
$757$	16.5309	+	28.6323i	0.600826	+	1.04066i	0.992696	+	0.120640i	$0.0384947\pi$
$757$	16.5309	+	28.6323i	0.600826	+	1.04066i	−0.391871	+	0.920020i	$0.628172\pi$
$758$	7.67544	−	13.2943i	0.278785	−	0.482869i
$759$		−	3.16616i		−	0.114924i
$760$		0			0
$761$	−27.3347	−	15.7817i	−0.990882	−	0.572086i	−0.0853441	−	0.996352i	$-0.527199\pi$
$761$	−27.3347	−	15.7817i	−0.990882	−	0.572086i	−0.905538	+	0.424266i	$0.860532\pi$
$762$			10.2347i			0.370764i
$763$	16.6851	−	28.8995i	0.604043	−	1.04623i
$764$	6.98046	+	12.0905i	0.252544	+	0.437419i
$765$		0			0
$766$	3.19245			0.115348
$767$	−44.3842	−	3.95074i	−1.60262	−	0.142653i
$768$	−1.17644			−0.0424512
$769$	36.8445	−	21.2722i	1.32865	−	0.767095i	0.343556	−	0.939132i	$-0.388368\pi$
$769$	36.8445	−	21.2722i	1.32865	−	0.767095i	0.985090	+	0.172037i	$0.0550350\pi$
$770$		0			0
$771$	5.90880	−	10.2343i	0.212800	−	0.368581i
$772$			13.6276i			0.490467i
$773$	−0.923574	−	0.533226i	−0.0332187	−	0.0191788i	0.483299	−	0.875456i	$-0.339439\pi$
$773$	−0.923574	−	0.533226i	−0.0332187	−	0.0191788i	−0.516517	+	0.856277i	$0.672772\pi$
$774$	10.8926	+	6.28885i	0.391527	+	0.226048i
$775$		0			0
$776$	−1.28916	+	2.23289i	−0.0462782	+	0.0801561i
$777$	8.63922	+	14.9636i	0.309930	+	0.536815i
$778$	−25.0555	+	14.4658i	−0.898283	+	0.518624i
$779$	43.4453			1.55659
$780$		0			0
$781$	14.0808			0.503850
$782$	0.981592	−	0.566723i	0.0351017	−	0.0202660i
$783$	1.27870	+	2.21477i	0.0456969	+	0.0791494i
$784$	−1.32239	+	2.29044i	−0.0472281	+	0.0818015i
$785$		0			0
$786$	−16.1729	−	9.33743i	−0.576869	−	0.333055i
$787$	−0.0373447	−	0.0215610i	−0.00133119	−	0.000768565i	0.499334	−	0.866409i	$-0.333578\pi$
$787$	−0.0373447	−	0.0215610i	−0.00133119	−	0.000768565i	−0.500665	+	0.865641i	$0.666911\pi$
$788$		−	17.7219i		−	0.631318i
$789$	9.29546	−	16.1002i	0.330927	−	0.573183i
$790$		0			0
$791$	5.02802	−	2.90293i	0.178776	−	0.103216i
$792$	−4.83540			−0.171818
$793$	−2.44296	+	27.4453i	−0.0867522	+	0.974610i
$794$	4.99113			0.177129
$795$		0			0
$796$	7.18270	+	12.4408i	0.254584	+	0.440953i
$797$	17.2951	−	29.9559i	0.612623	−	1.06109i	−0.378174	−	0.925735i	$-0.623448\pi$
$797$	17.2951	−	29.9559i	0.612623	−	1.06109i	0.990797	−	0.135359i	$-0.0432188\pi$
$798$		−	9.55458i		−	0.338229i
$799$	−12.3529	−	7.13194i	−0.437014	−	0.252310i
$800$		0			0
$801$		−	11.1685i		−	0.394619i
$802$	1.99782	−	3.46032i	0.0705453	−	0.122188i
$803$	−22.8882	−	39.6436i	−0.807708	−	1.39899i
$804$	4.07532	−	2.35289i	0.143725	−	0.0829799i
$805$		0			0
$806$	−0.817296	−	0.574120i	−0.0287880	−	0.0202225i
$807$	8.68906			0.305869
$808$	−1.35682	+	0.783361i	−0.0477328	+	0.0275586i
$809$	3.04046	+	5.26623i	0.106897	+	0.185151i	0.914512	−	0.404560i	$-0.132575\pi$
$809$	3.04046	+	5.26623i	0.106897	+	0.185151i	−0.807615	+	0.589710i	$0.799242\pi$
$810$		0			0
$811$			5.47145i			0.192129i	0.995375	+	0.0960644i	$0.0306255\pi$
$811$			5.47145i			0.192129i	−0.995375	+	0.0960644i	$0.969375\pi$
$812$	−0.851136	−	0.491403i	−0.0298690	−	0.0172449i
$813$	31.5866	+	18.2365i	1.10779	+	0.639584i
$814$			21.0583i			0.738094i
$815$		0			0
$816$	0.741268	+	1.28391i	0.0259496	+	0.0449460i
$817$	−26.2320	+	15.1450i	−0.917741	+	0.529858i
$818$	−2.92942			−0.102425
$819$	−6.98942	+	9.94987i	−0.244230	+	0.347677i
$820$		0			0
$821$	38.1625	−	22.0331i	1.33188	−	0.768961i	0.346291	−	0.938127i	$-0.387441\pi$
$821$	38.1625	−	22.0331i	1.33188	−	0.768961i	0.985588	+	0.169166i	$0.0541075\pi$
$822$	4.24878	+	7.35910i	0.148193	+	0.256678i
$823$	−6.25823	+	10.8396i	−0.218148	+	0.377844i	−0.954242	−	0.299036i	$-0.903335\pi$
$823$	−6.25823	+	10.8396i	−0.218148	+	0.377844i	0.736094	+	0.676880i	$0.236668\pi$
$824$		−	0.916364i		−	0.0319231i
$825$		0			0
$826$	22.3361	+	12.8957i	0.777171	+	0.448700i
$827$			51.7679i			1.80015i	0.435738	+	0.900074i	$0.356488\pi$
$827$			51.7679i			1.80015i	−0.435738	+	0.900074i	$0.643512\pi$
$828$	−0.726729	+	1.25873i	−0.0252556	+	0.0437440i
$829$	−6.95883	−	12.0531i	−0.241690	−	0.418620i	0.719506	−	0.694487i	$-0.244368\pi$
$829$	−6.95883	−	12.0531i	−0.241690	−	0.418620i	−0.961196	+	0.275867i	$0.911035\pi$
$830$		0			0
$831$	5.53793			0.192109
$832$	−3.27004	+	1.51883i	−0.113368	+	0.0526559i
$833$	3.33290			0.115478
$834$	−20.2482	+	11.6903i	−0.701139	+	0.404803i
$835$		0			0
$836$	5.82239	−	10.0847i	0.201371	−	0.348786i
$837$		−	1.50432i		−	0.0519967i
$838$	8.40780	+	4.85425i	0.290443	+	0.167687i
$839$	43.3416	+	25.0233i	1.49632	+	0.863899i	0.999991	−	0.00423634i	$-0.00134847\pi$
$839$	43.3416	+	25.0233i	1.49632	+	0.863899i	0.496327	+	0.868136i	$0.334682\pi$
$840$		0			0
$841$	14.3891	−	24.9227i	0.496176	−	0.859402i
$842$	11.4109	+	19.7642i	0.393245	+	0.681120i
$843$	10.9801	−	6.33935i	0.378174	−	0.218339i
$844$	20.2231			0.696108
$845$		0			0
$846$	18.2911			0.628861
$847$	3.69874	−	2.13547i	0.127090	−	0.0733755i
$848$	6.00741	+	10.4051i	0.206295	+	0.357314i
$849$	−17.1302	+	29.6703i	−0.587906	+	1.01828i
$850$		0			0
$851$	5.48183	+	3.16493i	0.187915	+	0.108493i
$852$	4.79438	+	2.76804i	0.164253	+	0.0948314i
$853$		−	12.7392i		−	0.436183i	−0.975928	−	0.218092i	$-0.930017\pi$
$853$		−	12.7392i		−	0.436183i	0.975928	−	0.218092i	$-0.0699832\pi$
$854$	7.97416	−	13.8116i	0.272870	−	0.472625i
$855$		0			0
$856$	−10.1345	+	5.85118i	−0.346391	+	0.199989i
$857$	30.3306			1.03607			0.518036	−	0.855359i	$-0.326663\pi$
$857$	30.3306			1.03607			0.518036	+	0.855359i	$0.326663\pi$
$858$	11.5112	−	5.34658i	0.392985	−	0.182529i
$859$	−48.7446			−1.66314			−0.831572	−	0.555417i	$-0.812559\pi$
$859$	−48.7446			−1.66314			−0.831572	+	0.555417i	$0.812559\pi$
$860$		0			0
$861$	−13.7042	−	23.7364i	−0.467038	−	0.808934i
$862$	5.78073	−	10.0125i	0.196893	−	0.341028i
$863$		−	17.6100i		−	0.599451i	−0.954026	−	0.299725i	$-0.903105\pi$
$863$		−	17.6100i		−	0.599451i	0.954026	−	0.299725i	$-0.0968950\pi$
$864$	−4.70290	−	2.71522i	−0.159996	−	0.0923737i
$865$		0			0
$866$		−	12.5656i		−	0.426995i
$867$	−9.06563	+	15.7021i	−0.307885	+	0.533273i
$868$	0.289054	+	0.500656i	0.00981114	+	0.0169934i
$869$	4.24061	−	2.44832i	0.143853	−	0.0830535i
$870$		0			0
$871$	8.29009	−	11.8015i	0.280899	−	0.399877i
$872$	15.9902			0.541497
$873$	−3.60831	+	2.08326i	−0.122123	+	0.0705076i
$874$	−1.75014	−	3.03132i	−0.0591992	−	0.102536i
$875$		0			0
$876$		−	17.9977i		−	0.608086i
$877$	−36.3115	−	20.9644i	−1.22615	−	0.707918i	−0.259928	−	0.965628i	$-0.583699\pi$
$877$	−36.3115	−	20.9644i	−1.22615	−	0.707918i	−0.966222	+	0.257709i	$0.917032\pi$
$878$	1.56775	+	0.905142i	0.0529091	+	0.0305471i
$879$		−	29.9109i		−	1.00887i
$880$		0			0
$881$	14.9695	+	25.9280i	0.504336	+	0.873535i	0.999987	+	0.00501392i	$0.00159599\pi$
$881$	14.9695	+	25.9280i	0.504336	+	0.873535i	−0.495652	+	0.868521i	$0.665071\pi$
$882$	−3.70131	+	2.13695i	−0.124630	+	0.0719549i
$883$	35.3391			1.18926			0.594629	−	0.804001i	$-0.297299\pi$
$883$	35.3391			1.18926			0.594629	+	0.804001i	$0.297299\pi$
$884$	3.71800	+	2.61176i	0.125050	+	0.0878430i
$885$		0			0
$886$	−14.5175	+	8.38166i	−0.487724	+	0.281587i
$887$	−21.2859	−	36.8682i	−0.714709	−	1.23791i	−0.963071	−	0.269246i	$-0.913226\pi$
$887$	−21.2859	−	36.8682i	−0.714709	−	1.23791i	0.248362	−	0.968667i	$-0.420108\pi$
$888$	−4.13970	+	7.17018i	−0.138919	+	0.240615i
$889$		−	18.1555i		−	0.608917i
$890$		0			0
$891$	3.99240	+	2.30501i	0.133750	+	0.0772208i
$892$		−	11.1450i		−	0.373164i
$893$	−22.0246	+	38.1478i	−0.737026	+	1.27657i
$894$	0.578321	+	1.00168i	0.0193420	+	0.0335013i
$895$		0			0
$896$	2.08692			0.0697190
$897$	0.338256	−	3.80010i	0.0112940	−	0.126882i
$898$	−7.08190			−0.236326
$899$	0.112979	−	0.0652284i	0.00376806	−	0.00217549i
$900$		0			0
$901$	7.57045	−	13.1124i	0.252208	−	0.436837i
$902$		−	33.4044i		−	1.11224i
$903$	16.5490	+	9.55458i	0.550717	+	0.317957i
$904$	2.40930	+	1.39101i	0.0801323	+	0.0462644i
$905$		0			0
$906$	−4.74127	+	8.21212i	−0.157518	+	0.272829i
$907$	7.22247	+	12.5097i	0.239818	+	0.415377i	0.960662	−	0.277720i	$-0.0895788\pi$
$907$	7.22247	+	12.5097i	0.239818	+	0.415377i	−0.720844	+	0.693098i	$0.756245\pi$
$908$	14.9885	−	8.65364i	0.497412	−	0.287181i
$909$	−2.53179			−0.0839743
$910$		0			0
$911$	−42.9419			−1.42273			−0.711364	−	0.702824i	$-0.751922\pi$
$911$	−42.9419			−1.42273			−0.711364	+	0.702824i	$0.751922\pi$
$912$	3.96494	−	2.28916i	0.131292	−	0.0758017i
$913$	16.7480	+	29.0084i	0.554278	+	0.960037i
$914$	−0.545096	+	0.944133i	−0.0180302	+	0.0312292i
$915$		0			0
$916$	8.57668	+	4.95175i	0.283382	+	0.163610i
$917$	28.6895	+	16.5639i	0.947410	+	0.546987i
$918$			6.84336i			0.225864i
$919$	20.3770	−	35.2940i	0.672175	−	1.16424i	−0.305111	−	0.952317i	$-0.598693\pi$
$919$	20.3770	−	35.2940i	0.672175	−	1.16424i	0.977286	−	0.211925i	$-0.0679733\pi$
$920$		0			0
$921$	25.8074	−	14.8999i	0.850384	−	0.490970i
$922$	−15.5893			−0.513406
$923$	16.9001	+	1.50432i	0.556273	+	0.0495151i
$924$	−7.34636			−0.241677
$925$		0			0
$926$	9.59481	+	16.6187i	0.315305	+	0.546124i
$927$	0.740414	−	1.28243i	0.0243184	−	0.0421207i
$928$		−	0.470937i		−	0.0154593i
$929$	11.3326	+	6.54286i	0.371809	+	0.214664i	0.674249	−	0.738504i	$-0.264468\pi$
$929$	11.3326	+	6.54286i	0.371809	+	0.214664i	−0.302439	+	0.953169i	$0.597801\pi$
$930$		0			0
$931$		−	10.2926i		−	0.337325i
$932$	−9.58708	+	16.6053i	−0.314035	+	0.543925i
$933$	−14.3229	−	24.8080i	−0.468911	−	0.812178i
$934$	20.0794	−	11.5928i	0.657017	−	0.379329i
$935$		0			0
$936$	−5.80356	−	0.516588i	−0.189695	−	0.0168852i
$937$	41.0546			1.34120			0.670598	−	0.741821i	$-0.266038\pi$
$937$	41.0546			1.34120			0.670598	+	0.741821i	$0.266038\pi$
$938$	−7.22930	+	4.17384i	−0.236045	+	0.136281i
$939$	−9.22869	−	15.9846i	−0.301167	−	0.521636i
$940$		0			0
$941$			24.4162i			0.795945i	0.917397	+	0.397973i	$0.130286\pi$
$941$			24.4162i			0.795945i	−0.917397	+	0.397973i	$0.869714\pi$
$942$	−2.78521	−	1.60804i	−0.0907470	−	0.0523928i
$943$	−8.69570	−	5.02047i	−0.283171	−	0.163489i
$944$			12.3586i			0.402240i
$945$		0			0
$946$	11.6448	+	20.1693i	0.378604	+	0.655762i
$947$	3.99122	−	2.30433i	0.129697	−	0.0748807i	−0.433748	−	0.901034i	$-0.642809\pi$
$947$	3.99122	−	2.30433i	0.129697	−	0.0748807i	0.563445	+	0.826154i	$0.309476\pi$
$948$	1.92519			0.0625272
$949$	−23.2357	−	50.0264i	−0.754262	−	1.62393i
$950$		0			0
$951$	19.8271	−	11.4472i	0.642937	−	0.371200i
$952$	−1.31495	−	2.27756i	−0.0426178	−	0.0738162i
$953$	−2.36493	+	4.09617i	−0.0766075	+	0.132688i	−0.901784	−	0.432187i	$-0.857742\pi$
$953$	−2.36493	+	4.09617i	−0.0766075	+	0.132688i	0.825177	+	0.564875i	$0.191075\pi$
$954$			19.4157i			0.628607i
$955$		0			0
$956$	1.87449	+	1.08224i	0.0606255	+	0.0350021i
$957$			1.65779i			0.0535887i
$958$	−1.74251	+	3.01812i	−0.0562980	+	0.0975111i
$959$	−7.53700	−	13.0545i	−0.243383	−	0.421551i
$960$		0			0
$961$	30.9233			0.997525
$962$	−2.24976	+	25.2747i	−0.0725352	+	0.814889i
$963$	−18.9108			−0.609392
$964$	−13.9442	+	8.05067i	−0.449111	+	0.259295i
$965$		0			0
$966$	−1.10411	+	1.91238i	−0.0355242	+	0.0615297i
$967$			23.8186i			0.765955i	0.923758	+	0.382977i	$0.125101\pi$
$967$			23.8186i			0.765955i	−0.923758	+	0.382977i	$0.874899\pi$
$968$	1.77234	+	1.02326i	0.0569653	+	0.0328889i
$969$	−4.99656	−	2.88477i	−0.160513	−	0.0926720i
$970$		0			0
$971$	15.8349	−	27.4269i	0.508167	−	0.880170i	−0.491789	−	0.870715i	$-0.663657\pi$
$971$	15.8349	−	27.4269i	0.508167	−	0.880170i	0.999955	−	0.00945572i	$-0.00300989\pi$
$972$	−7.23941	−	12.5390i	−0.232204	−	0.402189i
$973$	35.9188	−	20.7377i	1.15150	−	0.664820i
$974$	−2.14046			−0.0685847
$975$		0			0
$976$	7.64204			0.244616
$977$	23.2707	−	13.4354i	0.744497	−	0.429835i	−0.0792052	−	0.996858i	$-0.525238\pi$
$977$	23.2707	−	13.4354i	0.744497	−	0.429835i	0.823702	+	0.567023i	$0.191905\pi$
$978$	14.4567	+	25.0397i	0.462273	+	0.800681i
$979$	10.3401	−	17.9095i	0.330470	−	0.572391i
$980$		0			0
$981$	22.3780	+	12.9200i	0.714475	+	0.412502i
$982$	−23.5908	−	13.6201i	−0.752812	−	0.434636i
$983$		−	8.22637i		−	0.262380i	−0.991357	−	0.131190i	$-0.958120\pi$
$983$		−	8.22637i		−	0.262380i	0.991357	−	0.131190i	$-0.0418799\pi$
$984$	6.56672	−	11.3739i	0.209339	−	0.362587i
$985$		0			0
$986$	−0.513958	+	0.296734i	−0.0163678	+	0.00944993i
$987$	27.7894			0.884548
$988$	8.06556	−	11.4818i	0.256600	−	0.365286i
$989$	7.00054			0.222604
$990$		0			0
$991$	11.1157	+	19.2530i	0.353102	+	0.611591i	0.986791	−	0.161997i	$-0.0517935\pi$
$991$	11.1157	+	19.2530i	0.353102	+	0.611591i	−0.633689	+	0.773588i	$0.718460\pi$
$992$	−0.138508	+	0.239902i	−0.00439762	+	0.00761691i
$993$			7.79642i			0.247412i
$994$	−8.50486	−	4.91028i	−0.269758	−	0.155745i
$995$		0			0
$996$			13.1695i			0.417290i
$997$	11.7850	−	20.4122i	0.373234	−	0.646459i	−0.616827	−	0.787098i	$-0.711582\pi$
$997$	11.7850	−	20.4122i	0.373234	−	0.646459i	0.990061	+	0.140639i	$0.0449157\pi$
$998$	11.3928	+	19.7328i	0.360631	+	0.624632i
$999$	−33.0974	+	19.1088i	−1.04716	+	0.604576i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.m.e.101.7		16
5.2	odd	4		130.2.m.b.49.3	yes	8
5.3	odd	4		130.2.m.a.49.2	✓	8
5.4	even	2	inner	650.2.m.e.101.2		16
13.2	odd	12		8450.2.a.cs.1.4		8
13.4	even	6	inner	650.2.m.e.251.7		16
13.11	odd	12		8450.2.a.cr.1.4		8
15.2	even	4		1170.2.bj.a.829.2		8
15.8	even	4		1170.2.bj.b.829.3		8
20.3	even	4		1040.2.df.c.49.3		8
20.7	even	4		1040.2.df.a.49.2		8
65.2	even	12		1690.2.b.e.339.13		16
65.3	odd	12		1690.2.c.f.1689.4		8
65.4	even	6	inner	650.2.m.e.251.2		16
65.17	odd	12		130.2.m.a.69.2	yes	8
65.23	odd	12		1690.2.c.e.1689.4		8
65.24	odd	12		8450.2.a.cs.1.5		8
65.28	even	12		1690.2.b.e.339.4		16
65.37	even	12		1690.2.b.e.339.5		16
65.42	odd	12		1690.2.c.e.1689.5		8
65.43	odd	12		130.2.m.b.69.3	yes	8
65.54	odd	12		8450.2.a.cr.1.5		8
65.62	odd	12		1690.2.c.f.1689.5		8
65.63	even	12		1690.2.b.e.339.12		16
195.17	even	12		1170.2.bj.b.199.3		8
195.173	even	12		1170.2.bj.a.199.2		8
260.43	even	12		1040.2.df.a.849.2		8
260.147	even	12		1040.2.df.c.849.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.m.a.49.2	✓	8	5.3	odd	4
130.2.m.a.69.2	yes	8	65.17	odd	12
130.2.m.b.49.3	yes	8	5.2	odd	4
130.2.m.b.69.3	yes	8	65.43	odd	12
650.2.m.e.101.2		16	5.4	even	2	inner
650.2.m.e.101.7		16	1.1	even	1	trivial
650.2.m.e.251.2		16	65.4	even	6	inner
650.2.m.e.251.7		16	13.4	even	6	inner
1040.2.df.a.49.2		8	20.7	even	4
1040.2.df.a.849.2		8	260.43	even	12
1040.2.df.c.49.3		8	20.3	even	4
1040.2.df.c.849.3		8	260.147	even	12
1170.2.bj.a.199.2		8	195.173	even	12
1170.2.bj.a.829.2		8	15.2	even	4
1170.2.bj.b.199.3		8	195.17	even	12
1170.2.bj.b.829.3		8	15.8	even	4
1690.2.b.e.339.4		16	65.28	even	12
1690.2.b.e.339.5		16	65.37	even	12
1690.2.b.e.339.12		16	65.63	even	12
1690.2.b.e.339.13		16	65.2	even	12
1690.2.c.e.1689.4		8	65.23	odd	12
1690.2.c.e.1689.5		8	65.42	odd	12
1690.2.c.f.1689.4		8	65.3	odd	12
1690.2.c.f.1689.5		8	65.62	odd	12
8450.2.a.cr.1.4		8	13.11	odd	12
8450.2.a.cr.1.5		8	65.54	odd	12
8450.2.a.cs.1.4		8	13.2	odd	12
8450.2.a.cs.1.5		8	65.24	odd	12

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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.588222 + 1.01883i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.01883 + 0.588222i) q^{6} +(-1.80732 - 1.04346i) q^{7} -1.00000i q^{8} +(0.807991 - 1.39948i) q^{9} +(2.59135 - 1.49612i) q^{11} +1.17644 q^{12} +(3.27004 - 1.51883i) q^{13} -2.08692 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.630092 + 1.09135i) q^{17} -1.61598i q^{18} +(3.37028 + 1.94583i) q^{19} -2.45514i q^{21} +(1.49612 - 2.59135i) q^{22} +(-0.449714 - 0.778928i) q^{23} +(1.01883 - 0.588222i) q^{24} +(2.07252 - 2.95036i) q^{26} +5.43044 q^{27} +(-1.80732 + 1.04346i) q^{28} +(0.235468 + 0.407843i) q^{29} -0.277015i q^{31} +(-0.866025 - 0.500000i) q^{32} +(3.04858 + 1.76010i) q^{33} +1.26018i q^{34} +(-0.807991 - 1.39948i) q^{36} +(-6.09479 + 3.51883i) q^{37} +3.89166 q^{38} +(3.47094 + 2.43820i) q^{39} +(9.66804 - 5.58184i) q^{41} +(-1.22757 - 2.12621i) q^{42} +(-3.89166 + 6.74056i) q^{43} -2.99224i q^{44} +(-0.778928 - 0.449714i) q^{46} +11.3189i q^{47} +(0.588222 - 1.01883i) q^{48} +(-1.32239 - 2.29044i) q^{49} -1.48254 q^{51} +(0.319674 - 3.59135i) q^{52} -12.0148 q^{53} +(4.70290 - 2.71522i) q^{54} +(-1.04346 + 1.80732i) q^{56} +4.57832i q^{57} +(0.407843 + 0.235468i) q^{58} +(-10.7029 - 6.17932i) q^{59} +(-3.82102 + 6.61820i) q^{61} +(-0.138508 - 0.239902i) q^{62} +(-2.92060 + 1.68621i) q^{63} -1.00000 q^{64} +3.52020 q^{66} +(3.46410 - 2.00000i) q^{67} +(0.630092 + 1.09135i) q^{68} +(0.529063 - 0.916364i) q^{69} +(4.07532 + 2.35289i) q^{71} +(-1.39948 - 0.807991i) q^{72} -15.2984i q^{73} +(-3.51883 + 6.09479i) q^{74} +(3.37028 - 1.94583i) q^{76} -6.24455 q^{77} +(4.22502 + 0.376079i) q^{78} +1.63645 q^{79} +(0.770331 + 1.33425i) q^{81} +(5.58184 - 9.66804i) q^{82} +11.1943i q^{83} +(-2.12621 - 1.22757i) q^{84} +7.78333i q^{86} +(-0.277015 + 0.479805i) q^{87} +(-1.49612 - 2.59135i) q^{88} +(5.98533 - 3.45563i) q^{89} +(-7.49486 - 0.667134i) q^{91} -0.899428 q^{92} +(0.282231 - 0.162946i) q^{93} +(5.65944 + 9.80244i) q^{94} -1.17644i q^{96} +(-2.23289 - 1.28916i) q^{97} +(-2.29044 - 1.32239i) q^{98} -4.83540i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 16 q^{9} - 6 q^{11} + 20 q^{14} - 8 q^{16} - 18 q^{19} + 2 q^{26} + 6 q^{29} + 16 q^{36} + 60 q^{39} + 42 q^{41} + 12 q^{46} + 30 q^{49} - 40 q^{51} - 36 q^{54} + 10 q^{56} - 60 q^{59}+ \cdots + 6 q^{94}+O(q^{100}) \) 16 * q + 8 * q^4 - 16 * q^9 - 6 * q^11 + 20 * q^14 - 8 * q^16 - 18 * q^19 + 2 * q^26 + 6 * q^29 + 16 * q^36 + 60 * q^39 + 42 * q^41 + 12 * q^46 + 30 * q^49 - 40 * q^51 - 36 * q^54 + 10 * q^56 - 60 * q^59 - 10 * q^61 - 16 * q^64 + 40 * q^66 + 4 * q^69 - 40 * q^74 - 18 * q^76 - 8 * q^79 + 16 * q^81 + 12 * q^84 + 78 * q^89 + 38 * q^91 + 6 * q^94

Introduction

L-functions

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