LMFDB - Embedded newform 775.2.o.f.749.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [775,2,Mod(149,775)] 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("775.149"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(775, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,4,0,-4] 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:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.118796048409600000000.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{14} + 36x^{12} - 77x^{10} + 119x^{8} - 77x^{6} + 36x^{4} - 7x^{2} + 1 $ x^16 - 7x^14 + 36x^12 - 77x^10 + 119x^8 - 77x^6 + 36x^4 - 7*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 155)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			749.4
Root			$0.413319 - 0.238630i$ of defining polynomial
Character	$\chi$	$=$	775.749
Dual form			775.2.o.f.149.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.477260i q^{2} +(-2.34981 - 1.35666i) q^{3} +1.77222 q^{4} +(-0.647481 + 1.12147i) q^{6} +(0.157874 + 0.0911485i) q^{7} -1.80033i q^{8} +(2.18107 + 3.77773i) q^{9} +(-1.57453 - 2.72717i) q^{11} +(-4.16439 - 2.40431i) q^{12} +(0.133532 - 0.0770945i) q^{13} +(0.0435016 - 0.0753469i) q^{14} +2.68522 q^{16} +(-0.881070 - 0.508686i) q^{17} +(1.80296 - 1.04094i) q^{18} +(0.379404 - 0.657147i) q^{19} +(-0.247316 - 0.428364i) q^{21} +(-1.30157 + 0.751461i) q^{22} -7.06719i q^{23} +(-2.44244 + 4.23044i) q^{24} +(-0.0367941 - 0.0637292i) q^{26} -3.69596i q^{27} +(0.279788 + 0.161536i) q^{28} -8.35947 q^{29} +(4.52783 - 3.24018i) q^{31} -4.88221i q^{32} +8.54445i q^{33} +(-0.242775 + 0.420499i) q^{34} +(3.86535 + 6.69498i) q^{36} +(-7.15862 - 4.13303i) q^{37} +(-0.313630 - 0.181074i) q^{38} -0.418365 q^{39} +(-0.803649 - 1.39196i) q^{41} +(-0.204441 + 0.118034i) q^{42} +(8.55270 + 4.93790i) q^{43} +(-2.79042 - 4.83315i) q^{44} -3.37289 q^{46} +6.97506i q^{47} +(-6.30976 - 3.64294i) q^{48} +(-3.48338 - 6.03340i) q^{49} +(1.38023 + 2.39063i) q^{51} +(0.236648 - 0.136629i) q^{52} +(-8.21261 + 4.74155i) q^{53} -1.76393 q^{54} +(0.164098 - 0.284225i) q^{56} +(-1.78306 + 1.02945i) q^{57} +3.98964i q^{58} +(-1.66312 + 2.88061i) q^{59} -14.3159 q^{61} +(-1.54641 - 2.16095i) q^{62} +0.795207i q^{63} +3.04036 q^{64} +4.07792 q^{66} +(-3.83803 + 2.21589i) q^{67} +(-1.56145 - 0.901505i) q^{68} +(-9.58780 + 16.6066i) q^{69} +(-6.81335 - 11.8011i) q^{71} +(6.80117 - 3.92666i) q^{72} +(-3.92167 + 2.26418i) q^{73} +(-1.97253 + 3.41652i) q^{74} +(0.672388 - 1.16461i) q^{76} -0.574065i q^{77} +0.199669i q^{78} +(-1.20440 + 2.08608i) q^{79} +(1.52905 - 2.64840i) q^{81} +(-0.664327 + 0.383549i) q^{82} +(13.9865 - 8.07508i) q^{83} +(-0.438299 - 0.759156i) q^{84} +(2.35666 - 4.08186i) q^{86} +(19.6432 + 11.3410i) q^{87} +(-4.90981 + 2.83468i) q^{88} +4.99092 q^{89} +0.0281082 q^{91} -12.5246i q^{92} +(-15.0354 + 1.47106i) q^{93} +3.32892 q^{94} +(-6.62352 + 11.4723i) q^{96} +3.08456i q^{97} +(-2.87950 + 1.66248i) q^{98} +(6.86834 - 11.8963i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 4 q^{6} + 10 q^{9} + 8 q^{11} + 16 q^{14} - 12 q^{16} - 6 q^{19} - 6 q^{21} - 20 q^{24} - 16 q^{26} - 76 q^{29} - 10 q^{31} + 32 q^{34} + 46 q^{36} + 28 q^{39} - 8 q^{41} + 6 q^{44} + 4 q^{46}+ \cdots + 14 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 - 4 * q^6 + 10 * q^9 + 8 * q^11 + 16 * q^14 - 12 * q^16 - 6 * q^19 - 6 * q^21 - 20 * q^24 - 16 * q^26 - 76 * q^29 - 10 * q^31 + 32 * q^34 + 46 * q^36 + 28 * q^39 - 8 * q^41 + 6 * q^44 + 4 * q^46 - 22 * q^49 - 32 * q^51 - 64 * q^54 + 30 * q^56 + 36 * q^59 - 20 * q^61 + 12 * q^64 + 20 * q^66 + 12 * q^69 - 24 * q^71 - 28 * q^74 - 22 * q^76 - 28 * q^79 - 32 * q^81 - 18 * q^84 + 14 * q^86 + 4 * q^89 + 8 * q^91 - 64 * q^94 - 62 * q^96 + 14 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$		−	0.477260i		−	0.337474i	−0.985661	−	0.168737i	$-0.946031\pi$
$2$		−	0.477260i		−	0.337474i	0.985661	−	0.168737i	$-0.0539688\pi$
$3$	−2.34981	−	1.35666i	−1.35666	−	0.783270i	−0.367491	−	0.930027i	$-0.619783\pi$
$3$	−2.34981	−	1.35666i	−1.35666	−	0.783270i	−0.989173	+	0.146757i	$0.953117\pi$
$4$	1.77222			0.886111
$5$		0			0
$5$		0			0
$6$	−0.647481	+	1.12147i	−0.264333	+	0.457839i
$7$	0.157874	+	0.0911485i	0.0596707	+	0.0344509i	0.529539	−	0.848286i	$-0.322365\pi$
$7$	0.157874	+	0.0911485i	0.0596707	+	0.0344509i	−0.469868	+	0.882737i	$0.655698\pi$
$8$		−	1.80033i		−	0.636513i
$9$	2.18107	+	3.77773i	0.727025	+	1.25924i
$10$		0			0
$11$	−1.57453	−	2.72717i	−0.474739	−	0.822273i	0.524842	−	0.851200i	$-0.324124\pi$
$11$	−1.57453	−	2.72717i	−0.474739	−	0.822273i	−0.999582	+	0.0289268i	$0.990791\pi$
$12$	−4.16439	−	2.40431i	−1.20216	−	0.694065i
$13$	0.133532	−	0.0770945i	0.0370350	−	0.0213822i	−0.481368	−	0.876518i	$-0.659860\pi$
$13$	0.133532	−	0.0770945i	0.0370350	−	0.0213822i	0.518403	+	0.855136i	$0.326527\pi$
$14$	0.0435016	−	0.0753469i	0.0116263	−	0.0201373i
$15$		0			0
$16$	2.68522			0.671305
$17$	−0.881070	−	0.508686i	−0.213691	−	0.123374i	0.389335	−	0.921096i	$-0.372705\pi$
$17$	−0.881070	−	0.508686i	−0.213691	−	0.123374i	−0.603026	+	0.797722i	$0.706038\pi$
$18$	1.80296	−	1.04094i	0.424962	−	0.245352i
$19$	0.379404	−	0.657147i	0.0870412	−	0.150760i	−0.819218	−	0.573482i	$-0.805592\pi$
$19$	0.379404	−	0.657147i	0.0870412	−	0.150760i	0.906259	+	0.422722i	$0.138925\pi$
$20$		0			0
$21$	−0.247316	−	0.428364i	−0.0539688	−	0.0934766i
$22$	−1.30157	+	0.751461i	−0.277495	+	0.160212i
$23$		−	7.06719i		−	1.47361i	−0.676105	−	0.736805i	$-0.736334\pi$
$23$		−	7.06719i		−	1.47361i	0.676105	−	0.736805i	$-0.263666\pi$
$24$	−2.44244	+	4.23044i	−0.498562	+	0.863534i
$25$		0			0
$26$	−0.0367941	−	0.0637292i	−0.00721592	−	0.0124983i
$27$		−	3.69596i		−	0.711287i
$28$	0.279788	+	0.161536i	0.0528749	+	0.0305273i
$29$	−8.35947			−1.55231			−0.776157	−	0.630539i	$-0.782834\pi$
$29$	−8.35947			−1.55231			−0.776157	+	0.630539i	$0.782834\pi$
$30$		0			0
$31$	4.52783	−	3.24018i	0.813222	−	0.581953i
$31$	4.52783	−	3.24018i	0.813222	−	0.581953i
$32$		−	4.88221i		−	0.863061i
$33$			8.54445i			1.48740i
$34$	−0.242775	+	0.420499i	−0.0416356	+	0.0721151i
$35$		0			0
$36$	3.86535	+	6.69498i	0.644225	+	1.11583i
$37$	−7.15862	−	4.13303i	−1.17687	−	0.679466i	−0.221582	−	0.975142i	$-0.571122\pi$
$37$	−7.15862	−	4.13303i	−1.17687	−	0.679466i	−0.955288	+	0.295675i	$0.904455\pi$
$38$	−0.313630	−	0.181074i	−0.0508775	−	0.0293741i
$39$	−0.418365			−0.0669920
$40$		0			0
$41$	−0.803649	−	1.39196i	−0.125509	−	0.217388i	0.796423	−	0.604740i	$-0.206723\pi$
$41$	−0.803649	−	1.39196i	−0.125509	−	0.217388i	−0.921932	+	0.387352i	$0.873390\pi$
$42$	−0.204441	+	0.118034i	−0.0315459	+	0.0182130i
$43$	8.55270	+	4.93790i	1.30427	+	0.753023i	0.981134	−	0.193328i	$-0.0619281\pi$
$43$	8.55270	+	4.93790i	1.30427	+	0.753023i	0.323140	+	0.946351i	$0.395261\pi$
$44$	−2.79042	−	4.83315i	−0.420672	−	0.728625i
$45$		0			0
$46$	−3.37289			−0.497305
$47$			6.97506i			1.01742i	0.860939	+	0.508708i	$0.169877\pi$
$47$			6.97506i			1.01742i	−0.860939	+	0.508708i	$0.830123\pi$
$48$	−6.30976	−	3.64294i	−0.910735	−	0.525813i
$49$	−3.48338	−	6.03340i	−0.497626	−	0.861914i
$50$		0			0
$51$	1.38023	+	2.39063i	0.193271	+	0.334755i
$52$	0.236648	−	0.136629i	0.0328171	−	0.0189470i
$53$	−8.21261	+	4.74155i	−1.12809	+	0.651302i	−0.943454	−	0.331505i	$-0.892444\pi$
$53$	−8.21261	+	4.74155i	−1.12809	+	0.651302i	−0.184635	+	0.982807i	$0.559110\pi$
$54$	−1.76393			−0.240041
$55$		0			0
$56$	0.164098	−	0.284225i	0.0219285	−	0.0379812i
$57$	−1.78306	+	1.02945i	−0.236171	+	0.136354i
$58$			3.98964i			0.523865i
$59$	−1.66312	+	2.88061i	−0.216520	+	0.375023i	−0.953742	−	0.300628i	$-0.902804\pi$
$59$	−1.66312	+	2.88061i	−0.216520	+	0.375023i	0.737222	+	0.675651i	$0.236137\pi$
$60$		0			0
$61$	−14.3159			−1.83296			−0.916480	−	0.400080i	$-0.868982\pi$
$61$	−14.3159			−1.83296			−0.916480	+	0.400080i	$0.868982\pi$
$62$	−1.54641	−	2.16095i	−0.196394	−	0.274441i
$63$			0.795207i			0.100187i
$64$	3.04036			0.380044
$65$		0			0
$66$	4.07792			0.501958
$67$	−3.83803	+	2.21589i	−0.468890	+	0.270714i	−0.715775	−	0.698331i	$-0.753926\pi$
$67$	−3.83803	+	2.21589i	−0.468890	+	0.270714i	0.246885	+	0.969045i	$0.420593\pi$
$68$	−1.56145	−	0.901505i	−0.189354	−	0.109324i
$69$	−9.58780	+	16.6066i	−1.15424	+	1.99919i
$70$		0			0
$71$	−6.81335	−	11.8011i	−0.808596	−	1.40053i	−0.913836	−	0.406083i	$-0.866895\pi$
$71$	−6.81335	−	11.8011i	−0.808596	−	1.40053i	0.105240	−	0.994447i	$-0.466439\pi$
$72$	6.80117	−	3.92666i	0.801525	−	0.462761i
$73$	−3.92167	+	2.26418i	−0.458997	+	0.265002i	−0.711622	−	0.702562i	$-0.752039\pi$
$73$	−3.92167	+	2.26418i	−0.458997	+	0.265002i	0.252626	+	0.967564i	$0.418706\pi$
$74$	−1.97253	+	3.41652i	−0.229302	+	0.397163i
$75$		0			0
$76$	0.672388	−	1.16461i	0.0771282	−	0.133590i
$77$		−	0.574065i		−	0.0654208i
$78$			0.199669i			0.0226081i
$79$	−1.20440	+	2.08608i	−0.135505	+	0.234702i	−0.925790	−	0.378037i	$-0.876599\pi$
$79$	−1.20440	+	2.08608i	−0.135505	+	0.234702i	0.790285	+	0.612739i	$0.209932\pi$
$80$		0			0
$81$	1.52905	−	2.64840i	0.169895	−	0.294266i
$82$	−0.664327	+	0.383549i	−0.0733627	+	0.0423559i
$83$	13.9865	−	8.07508i	1.53521	−	0.886355i	0.536103	−	0.844152i	$-0.319896\pi$
$83$	13.9865	−	8.07508i	1.53521	−	0.886355i	0.999109	−	0.0422031i	$-0.0134376\pi$
$84$	−0.438299	−	0.759156i	−0.0478223	−	0.0828307i
$85$		0			0
$86$	2.35666	−	4.08186i	0.254126	−	0.440158i
$87$	19.6432	+	11.3410i	2.10597	+	1.21588i
$88$	−4.90981	+	2.83468i	−0.523387	+	0.302178i
$89$	4.99092			0.529036			0.264518	−	0.964381i	$-0.414787\pi$
$89$	4.99092			0.529036			0.264518	+	0.964381i	$0.414787\pi$
$90$		0			0
$91$	0.0281082			0.00294654
$92$		−	12.5246i		−	1.30578i
$93$	−15.0354	+	1.47106i	−1.55910	+	0.152542i
$94$	3.32892			0.343352
$95$		0			0
$96$	−6.62352	+	11.4723i	−0.676010	+	1.17088i
$97$			3.08456i			0.313189i	0.987663	+	0.156595i	$0.0500516\pi$
$97$			3.08456i			0.313189i	−0.987663	+	0.156595i	$0.949948\pi$
$98$	−2.87950	+	1.66248i	−0.290873	+	0.167936i
$99$	6.86834	−	11.8963i	0.690295	−	1.19563i
$100$		0			0
$101$	4.98659			0.496184			0.248092	−	0.968737i	$-0.420197\pi$
$101$	4.98659			0.496184			0.248092	+	0.968737i	$0.420197\pi$
$102$	1.14095	−	0.658729i	0.112971	−	0.0652239i
$103$	9.57680	−	5.52917i	0.943630	−	0.544805i	0.0525338	−	0.998619i	$-0.483270\pi$
$103$	9.57680	−	5.52917i	0.943630	−	0.544805i	0.891096	+	0.453814i	$0.149937\pi$
$104$	−0.138796	−	0.240401i	−0.0136100	−	0.0235733i
$105$		0			0
$106$	2.26295	+	3.91955i	0.219797	+	0.380700i
$107$	−5.70329	−	3.29280i	−0.551358	−	0.318327i	0.198312	−	0.980139i	$-0.436454\pi$
$107$	−5.70329	−	3.29280i	−0.551358	−	0.318327i	−0.749669	+	0.661812i	$0.769788\pi$
$108$		−	6.55006i		−	0.630280i
$109$	15.2744			1.46302			0.731509	−	0.681832i	$-0.238816\pi$
$109$	15.2744			1.46302			0.731509	+	0.681832i	$0.238816\pi$
$110$		0			0
$111$	11.2143	+	19.4237i	1.06441	+	1.84361i
$112$	0.423926	+	0.244754i	0.0400573	+	0.0231271i
$113$	8.65957	−	4.99960i	0.814624	−	0.470323i	−0.0339352	−	0.999424i	$-0.510804\pi$
$113$	8.65957	−	4.99960i	0.814624	−	0.470323i	0.848559	+	0.529101i	$0.177471\pi$
$114$	0.491314	+	0.850981i	0.0460158	+	0.0797017i
$115$		0			0
$116$	−14.8148			−1.37552
$117$	0.582484	+	0.336297i	0.0538507	+	0.0310907i
$118$	1.37480	+	0.793740i	0.126560	+	0.0730697i
$119$	−0.0927320	−	0.160616i	−0.00850073	−	0.0147237i
$120$		0			0
$121$	0.541695	−	0.938244i	0.0492450	−	0.0852949i
$122$			6.83240i			0.618576i
$123$			4.36113i			0.393229i
$124$	8.02432	−	5.74232i	0.720606	−	0.515675i
$125$		0			0
$126$	0.379521			0.0338104
$127$	−8.25855	−	4.76808i	−0.732828	−	0.423098i	0.0866278	−	0.996241i	$-0.472391\pi$
$127$	−8.25855	−	4.76808i	−0.732828	−	0.423098i	−0.819456	+	0.573142i	$0.805724\pi$
$128$		−	11.2155i		−	0.991316i
$129$	−13.3982	−	23.2063i	−1.17964	−	2.04320i
$130$		0			0
$131$	−4.96128	+	8.59319i	−0.433469	+	0.750791i	−0.997169	−	0.0751887i	$-0.976044\pi$
$131$	−4.96128	+	8.59319i	−0.433469	+	0.750791i	0.563700	+	0.825980i	$0.309377\pi$
$132$			15.1427i			1.31800i
$133$	0.119796	−	0.0691642i	0.0103876	−	0.00599730i
$134$	1.05756	+	1.83174i	0.0913589	+	0.158238i
$135$		0			0
$136$	−0.915803	+	1.58622i	−0.0785295	+	0.136017i
$137$	12.8657	−	7.42800i	1.09919	−	0.634616i	0.163180	−	0.986596i	$-0.447825\pi$
$137$	12.8657	−	7.42800i	1.09919	−	0.634616i	0.936008	+	0.351980i	$0.114491\pi$
$138$	7.92564	+	4.57587i	0.674675	+	0.389524i
$139$	11.7470			0.996372			0.498186	−	0.867070i	$-0.334000\pi$
$139$	11.7470			0.996372			0.498186	+	0.867070i	$0.334000\pi$
$140$		0			0
$141$	9.46281	−	16.3901i	0.796912	−	1.38029i
$142$	−5.63218	+	3.25174i	−0.472642	+	0.272880i
$143$	−0.420499	−	0.242775i	−0.0351639	−	0.0203019i
$144$	5.85666	+	10.1440i	0.488055	+	0.845337i
$145$		0			0
$146$	1.08060	+	1.87166i	0.0894312	+	0.154899i
$147$			18.9031i			1.55910i
$148$	−12.6867	−	7.32465i	−1.04284	−	0.602083i
$149$	−1.38413	+	2.39739i	−0.113393	+	0.196402i	−0.917136	−	0.398574i	$-0.869505\pi$
$149$	−1.38413	+	2.39739i	−0.113393	+	0.196402i	0.803743	+	0.594976i	$0.202838\pi$
$150$		0			0
$151$	18.0145			1.46600			0.733000	−	0.680228i	$-0.238119\pi$
$151$	18.0145			1.46600			0.733000	+	0.680228i	$0.238119\pi$
$152$	−1.18308	−	0.683053i	−0.0959606	−	0.0554029i
$153$		−	4.43793i		−	0.358785i
$154$	−0.273978			−0.0220778
$155$		0			0
$156$	−0.741436			−0.0593624
$157$			9.94733i			0.793883i	0.917844	+	0.396942i	$0.129928\pi$
$157$			9.94733i			0.793883i	−0.917844	+	0.396942i	$0.870072\pi$
$158$	0.995602	+	0.574811i	0.0792058	+	0.0457295i
$159$	25.7308			2.04058
$160$		0			0
$161$	0.644164	−	1.11572i	0.0507672	−	0.0879314i
$162$	−1.26397	−	0.729756i	−0.0993072	−	0.0573350i
$163$			0.646932i			0.0506716i	0.999679	+	0.0253358i	$0.00806551\pi$
$163$			0.646932i			0.0506716i	−0.999679	+	0.0253358i	$0.991934\pi$
$164$	−1.42424	−	2.46686i	−0.111215	−	0.192630i
$165$		0			0
$166$	−3.85391	−	6.67517i	−0.299122	−	0.518094i
$167$	1.70902	+	0.986702i	0.132248	+	0.0763533i	0.564664	−	0.825321i	$-0.309006\pi$
$167$	1.70902	+	0.986702i	0.132248	+	0.0763533i	−0.432417	+	0.901674i	$0.642339\pi$
$168$	−0.771197	+	0.445251i	−0.0594991	+	0.0343518i
$169$	−6.48811	+	11.2377i	−0.499086	+	0.864442i
$170$		0			0
$171$	3.31003			0.253125
$172$	15.1573	+	8.75107i	1.15573	+	0.667263i
$173$	9.12843	−	5.27030i	0.694021	−	0.400693i	−0.111095	−	0.993810i	$-0.535436\pi$
$173$	9.12843	−	5.27030i	0.694021	−	0.400693i	0.805117	+	0.593116i	$0.202103\pi$
$174$	5.41260	−	9.37490i	0.410328	−	0.710709i
$175$		0			0
$176$	−4.22797	−	7.32305i	−0.318695	−	0.551996i
$177$	7.81603	−	4.51259i	0.587489	−	0.339187i
$178$		−	2.38197i		−	0.178536i
$179$	10.6208	−	18.3957i	0.793832	−	1.37496i	−0.129746	−	0.991547i	$-0.541416\pi$
$179$	10.6208	−	18.3957i	0.793832	−	1.37496i	0.923578	−	0.383410i	$-0.125250\pi$
$180$		0			0
$181$	5.01558	+	8.68724i	0.372805	+	0.645718i	0.989996	−	0.141096i	$-0.0450626\pi$
$181$	5.01558	+	8.68724i	0.372805	+	0.645718i	−0.617191	+	0.786814i	$0.711729\pi$
$182$		−	0.0134149i		−	0.000994380i
$183$	33.6396	+	19.4218i	2.48671	+	1.43570i
$184$	−12.7233			−0.937972
$185$		0			0
$186$	0.702080	+	7.17578i	0.0514790	+	0.526154i
$187$			3.20377i			0.234283i
$188$			12.3614i			0.901545i
$189$	0.336881	−	0.583495i	0.0245045	−	0.0424430i
$190$		0			0
$191$	−6.70623	−	11.6155i	−0.485245	−	0.840470i	0.514611	−	0.857424i	$-0.327936\pi$
$191$	−6.70623	−	11.6155i	−0.485245	−	0.840470i	−0.999856	+	0.0169541i	$0.994603\pi$
$192$	−7.14426	−	4.12474i	−0.515593	−	0.297678i
$193$	16.4397	+	9.49147i	1.18336	+	0.683211i	0.956789	−	0.290785i	$-0.0939163\pi$
$193$	16.4397	+	9.49147i	1.18336	+	0.683211i	0.226567	+	0.973995i	$0.427250\pi$
$194$	1.47214			0.105693
$195$		0			0
$196$	−6.17333	−	10.6925i	−0.440952	−	0.763752i
$197$	8.58181	−	4.95471i	0.611428	−	0.353008i	−0.162096	−	0.986775i	$-0.551825\pi$
$197$	8.58181	−	4.95471i	0.611428	−	0.353008i	0.773524	+	0.633767i	$0.218492\pi$
$198$	−5.67764	−	3.27799i	−0.403492	−	0.232956i
$199$	−6.17851	−	10.7015i	−0.437983	−	0.758609i	0.559551	−	0.828796i	$-0.310974\pi$
$199$	−6.17851	−	10.7015i	−0.437983	−	0.758609i	−0.997534	+	0.0701871i	$0.977640\pi$
$200$		0			0
$201$	12.0249			0.848169
$202$		−	2.37990i		−	0.167449i
$203$	−1.31974	−	0.761954i	−0.0926278	−	0.0534787i
$204$	2.44608	+	4.23673i	0.171260	+	0.296631i
$205$		0			0
$206$	−2.63885	−	4.57062i	−0.183857	−	0.318450i
$207$	26.6979	−	15.4141i	1.85563	−	1.07135i
$208$	0.358561	−	0.207016i	0.0248618	−	0.0143539i
$209$	−2.38954			−0.165288
$210$		0			0
$211$	−1.25287	+	2.17004i	−0.0862513	+	0.149392i	−0.905924	−	0.423441i	$-0.860822\pi$
$211$	−1.25287	+	2.17004i	−0.0862513	+	0.149392i	0.819672	+	0.572833i	$0.194155\pi$
$212$	−14.5546	+	8.40309i	−0.999612	+	0.577126i
$213$			36.9737i			2.53340i
$214$	−1.57152	+	2.72195i	−0.107427	+	0.186069i
$215$		0			0
$216$	−6.65394			−0.452744
$217$	1.01016	−	0.0988346i	0.0685744	−	0.00670933i
$218$		−	7.28984i		−	0.493730i
$219$	12.2869			0.830272
$220$		0			0
$221$	−0.156867			−0.0105520
$222$	9.27015	−	5.35212i	0.622172	−	0.359211i
$223$	−16.2038	−	9.35529i	−1.08509	−	0.626477i	−0.152825	−	0.988253i	$-0.548837\pi$
$223$	−16.2038	−	9.35529i	−1.08509	−	0.626477i	−0.932265	+	0.361777i	$0.882170\pi$
$224$	0.445006	−	0.770774i	0.0297332	−	0.0514995i
$225$		0			0
$226$	−2.38611	−	4.13287i	−0.158722	−	0.274914i
$227$	−13.6689	+	7.89172i	−0.907235	+	0.523792i	−0.879540	−	0.475824i	$-0.842150\pi$
$227$	−13.6689	+	7.89172i	−0.907235	+	0.523792i	−0.0276942	+	0.999616i	$0.508816\pi$
$228$	−3.15997	+	1.82441i	−0.209274	+	0.120825i
$229$	−4.97967	+	8.62504i	−0.329066	+	0.569959i	−0.982327	−	0.187174i	$-0.940067\pi$
$229$	−4.97967	+	8.62504i	−0.329066	+	0.569959i	0.653261	+	0.757133i	$0.273401\pi$
$230$		0			0
$231$	−0.778814	+	1.34895i	−0.0512422	+	0.0887541i
$232$			15.0498i			0.988069i
$233$			3.73699i			0.244818i	0.992480	+	0.122409i	$0.0390620\pi$
$233$			3.73699i			0.244818i	−0.992480	+	0.122409i	$0.960938\pi$
$234$	0.160501	−	0.277996i	0.0104923	−	0.0181732i
$235$		0			0
$236$	−2.94742	+	5.10508i	−0.191861	+	0.332312i
$237$	5.66021	−	3.26793i	0.367670	−	0.212275i
$238$	−0.0766558	+	0.0442573i	−0.00496886	+	0.00286877i
$239$	−3.82694	−	6.62845i	−0.247544	−	0.428759i	0.715300	−	0.698818i	$-0.246290\pi$
$239$	−3.82694	−	6.62845i	−0.247544	−	0.428759i	−0.962844	+	0.270059i	$0.912957\pi$
$240$		0			0
$241$	3.67712	−	6.36895i	0.236864	−	0.410260i	−0.722949	−	0.690902i	$-0.757214\pi$
$241$	3.67712	−	6.36895i	0.236864	−	0.410260i	0.959813	+	0.280641i	$0.0905471\pi$
$242$	−0.447786	−	0.258529i	−0.0287848	−	0.0166189i
$243$	−16.7883	+	9.69275i	−1.07697	+	0.621791i
$244$	−25.3709			−1.62421
$245$		0			0
$246$	2.08139			0.132705
$247$		−	0.117000i		−	0.00744452i
$248$	−5.83339	−	8.15159i	−0.370421	−	0.517627i
$249$	−43.8207			−2.77702
$250$		0			0
$251$	−9.47442	+	16.4102i	−0.598020	+	1.03580i	0.395093	+	0.918641i	$0.370712\pi$
$251$	−9.47442	+	16.4102i	−0.598020	+	1.03580i	−0.993113	+	0.117160i	$0.962621\pi$
$252$			1.40928i			0.0887766i
$253$	−19.2734	+	11.1275i	−1.21171	+	0.699581i
$254$	−2.27561	+	3.94148i	−0.142785	+	0.247310i
$255$		0			0
$256$	0.728021			0.0455013
$257$	3.56865	−	2.06036i	0.222606	−	0.128522i	−0.384550	−	0.923104i	$-0.625643\pi$
$257$	3.56865	−	2.06036i	0.222606	−	0.128522i	0.607157	+	0.794582i	$0.292310\pi$
$258$	−11.0754	+	6.39440i	−0.689526	+	0.398098i
$259$	−0.753440	−	1.30500i	−0.0468165	−	0.0810885i
$260$		0			0
$261$	−18.2326	−	31.5798i	−1.12857	−	1.95474i
$262$	4.10119	+	2.36782i	0.253372	+	0.146285i
$263$		−	19.3874i		−	1.19548i	−0.801691	−	0.597739i	$-0.796066\pi$
$263$		−	19.3874i		−	1.19548i	0.801691	−	0.597739i	$-0.203934\pi$
$264$	15.3828			0.946748
$265$		0			0
$266$	−0.0330093	−	0.0571738i	−0.00202393	−	0.00350555i
$267$	−11.7277	−	6.77100i	−0.717725	−	0.414378i
$268$	−6.80185	+	3.92705i	−0.415489	+	0.239883i
$269$	13.5178	+	23.4135i	0.824193	+	1.42754i	0.902534	+	0.430618i	$0.141704\pi$
$269$	13.5178	+	23.4135i	0.824193	+	1.42754i	−0.0783415	+	0.996927i	$0.524962\pi$
$270$		0			0
$271$	29.5797			1.79684			0.898419	−	0.439140i	$-0.144717\pi$
$271$	29.5797			1.79684			0.898419	+	0.439140i	$0.144717\pi$
$272$	−2.36587	−	1.36593i	−0.143452	−	0.0828219i
$273$	−0.0660489	−	0.0381334i	−0.00399746	−	0.00230794i
$274$	−3.54508	−	6.14027i	−0.214166	−	0.370947i
$275$		0			0
$276$	−16.9917	+	29.4305i	−1.02278	+	1.77151i
$277$		−	13.1202i		−	0.788314i	−0.919043	−	0.394157i	$-0.871037\pi$
$277$		−	13.1202i		−	0.788314i	0.919043	−	0.394157i	$-0.128963\pi$
$278$		−	5.60640i		−	0.336249i
$279$	22.1161	+	10.0379i	1.32405	+	0.600951i
$280$		0			0
$281$	−14.1060			−0.841495			−0.420748	−	0.907178i	$-0.638232\pi$
$281$	−14.1060			−0.841495			−0.420748	+	0.907178i	$0.638232\pi$
$282$	−7.82232	−	4.51622i	−0.465813	−	0.268937i
$283$			4.40824i			0.262043i	0.991380	+	0.131021i	$0.0418256\pi$
$283$			4.40824i			0.262043i	−0.991380	+	0.131021i	$0.958174\pi$
$284$	−12.0748	−	20.9141i	−0.716506	−	1.24103i
$285$		0			0
$286$	−0.115867	+	0.200688i	−0.00685136	+	0.0118669i
$287$		−	0.293006i		−	0.0172956i
$288$	18.4437	−	10.6485i	1.08680	−	0.627467i
$289$	−7.98248	−	13.8261i	−0.469557	−	0.813297i
$290$		0			0
$291$	4.18471	−	7.24813i	0.245312	−	0.424893i
$292$	−6.95007	+	4.01262i	−0.406722	+	0.234821i
$293$	−0.403011	−	0.232678i	−0.0235441	−	0.0135932i	0.488182	−	0.872742i	$-0.337660\pi$
$293$	−0.403011	−	0.232678i	−0.0235441	−	0.0135932i	−0.511726	+	0.859149i	$0.670994\pi$
$294$	9.02171			0.526157
$295$		0			0
$296$	−7.44083	+	12.8879i	−0.432489	+	0.749093i
$297$	−10.0795	+	5.81940i	−0.584872	+	0.337676i
$298$	1.14418	+	0.660591i	0.0662804	+	0.0382670i
$299$	−0.544841	−	0.943692i	−0.0315090	−	0.0545751i
$300$		0			0
$301$	0.900166	+	1.55913i	0.0518847	+	0.0898669i
$302$		−	8.59761i		−	0.494737i
$303$	−11.7175	−	6.76512i	−0.673155	−	0.388646i
$304$	1.01878	−	1.76458i	0.0584312	−	0.101206i
$305$		0			0
$306$	−2.11805			−0.121081
$307$	18.3577	+	10.5988i	1.04773	+	0.604905i	0.922012	−	0.387161i	$-0.126544\pi$
$307$	18.3577	+	10.5988i	1.04773	+	0.604905i	0.125715	+	0.992066i	$0.459878\pi$
$308$		−	1.01737i		−	0.0579701i
$309$	−30.0049			−1.70692
$310$		0			0
$311$	18.5010			1.04909			0.524547	−	0.851382i	$-0.324235\pi$
$311$	18.5010			1.04909			0.524547	+	0.851382i	$0.324235\pi$
$312$			0.753196i			0.0426413i
$313$	17.8301	+	10.2942i	1.00782	+	0.581864i	0.910552	−	0.413394i	$-0.135657\pi$
$313$	17.8301	+	10.2942i	1.00782	+	0.581864i	0.0972662	+	0.995258i	$0.468990\pi$
$314$	4.74746			0.267915
$315$		0			0
$316$	−2.13446	+	3.69700i	−0.120073	+	0.207972i
$317$	−24.6914	−	14.2556i	−1.38681	−	0.800674i	−0.393853	−	0.919173i	$-0.628858\pi$
$317$	−24.6914	−	14.2556i	−1.38681	−	0.800674i	−0.992954	+	0.118500i	$0.962192\pi$
$318$		−	12.2803i		−	0.688643i
$319$	13.1623	+	22.7977i	0.736945	+	1.27643i
$320$		0			0
$321$	8.93444	+	15.4749i	0.498672	+	0.863724i
$322$	−0.532491	−	0.307434i	−0.0296745	−	0.0171326i
$323$	−0.668563	+	0.385995i	−0.0371998	+	0.0214773i
$324$	2.70982	−	4.69355i	0.150546	−	0.260753i
$325$		0			0
$326$	0.308755			0.0171004
$327$	−35.8918	−	20.7222i	−1.98482	−	1.14594i
$328$	−2.50599	+	1.44683i	−0.138370	+	0.0798880i
$329$	−0.635766	+	1.10118i	−0.0350509	+	0.0607100i
$330$		0			0
$331$	−2.19961	−	3.80984i	−0.120902	−	0.209408i	0.799222	−	0.601036i	$-0.205245\pi$
$331$	−2.19961	−	3.80984i	−0.120902	−	0.209408i	−0.920124	+	0.391628i	$0.871912\pi$
$332$	24.7871	−	14.3108i	1.36037	−	0.785410i
$333$		−	36.0578i		−	1.97596i
$334$	0.470913	−	0.815646i	0.0257672	−	0.0446301i
$335$		0			0
$336$	−0.664098	−	1.15025i	−0.0362295	−	0.0627513i
$337$		−	5.09585i		−	0.277589i	−0.990321	−	0.138794i	$-0.955677\pi$
$337$		−	5.09585i		−	0.277589i	0.990321	−	0.138794i	$-0.0443227\pi$
$338$	5.36332	+	3.09652i	0.291726	+	0.168428i
$339$	−27.1311			−1.47356
$340$		0			0
$341$	−15.9657	−	7.24640i	−0.864593	−	0.392414i
$342$		−	1.57975i		−	0.0854229i
$343$		−	2.54610i		−	0.137477i
$344$	8.88986	−	15.3977i	0.479309	−	0.830188i
$345$		0			0
$346$	−2.51530	−	4.35663i	−0.135224	−	0.234214i
$347$	20.0381	+	11.5690i	1.07570	+	0.621057i	0.929734	−	0.368232i	$-0.120037\pi$
$347$	20.0381	+	11.5690i	1.07570	+	0.621057i	0.145969	+	0.989289i	$0.453370\pi$
$348$	34.8121	+	20.0988i	1.86612	+	1.07741i
$349$	31.4034			1.68098			0.840492	−	0.541824i	$-0.182266\pi$
$349$	31.4034			1.68098			0.840492	+	0.541824i	$0.182266\pi$
$350$		0			0
$351$	−0.284938	−	0.493527i	−0.0152089	−	0.0263425i
$352$	−13.3146	+	7.68720i	−0.709672	+	0.409729i
$353$	−4.68922	−	2.70732i	−0.249582	−	0.144096i	0.369991	−	0.929035i	$-0.379361\pi$
$353$	−4.68922	−	2.70732i	−0.249582	−	0.144096i	−0.619573	+	0.784939i	$0.712694\pi$
$354$	−2.15368	−	3.73028i	−0.114467	−	0.198262i
$355$		0			0
$356$	8.84502			0.468785
$357$			0.503224i			0.0266335i
$358$	−8.77952	−	5.06886i	−0.464012	−	0.267898i
$359$	15.3149	+	26.5262i	0.808290	+	1.40000i	0.914048	+	0.405607i	$0.132940\pi$
$359$	15.3149	+	26.5262i	0.808290	+	1.40000i	−0.105758	+	0.994392i	$0.533727\pi$
$360$		0			0
$361$	9.21211	+	15.9558i	0.484848	+	0.839781i
$362$	4.14607	−	2.39374i	0.217913	−	0.125812i
$363$	−2.54576	+	1.46980i	−0.133618	+	0.0771443i
$364$	0.0498140			0.00261096
$365$		0			0
$366$	9.26927	−	16.0548i	0.484512	−	0.839200i
$367$	18.9076	−	10.9163i	0.986968	−	0.569826i	0.0826012	−	0.996583i	$-0.473677\pi$
$367$	18.9076	−	10.9163i	0.986968	−	0.569826i	0.904367	+	0.426757i	$0.140344\pi$
$368$		−	18.9769i		−	0.989242i
$369$	3.50564	−	6.07194i	0.182496	−	0.316093i
$370$		0			0
$371$	−1.72874			−0.0897518
$372$	−26.6460	+	2.60705i	−1.38153	+	0.135169i
$373$		−	27.1661i		−	1.40661i	−0.710889	−	0.703305i	$-0.751707\pi$
$373$		−	27.1661i		−	1.40661i	0.710889	−	0.703305i	$-0.248293\pi$
$374$	1.52903			0.0790643
$375$		0			0
$376$	12.5574			0.647599
$377$	−1.11625	+	0.644469i	−0.0574899	+	0.0331918i
$378$	−0.278479	−	0.160780i	−0.0143234	−	0.00826962i
$379$	−7.98472	+	13.8299i	−0.410148	+	0.710397i	−0.994906	−	0.100811i	$-0.967856\pi$
$379$	−7.98472	+	13.8299i	−0.410148	+	0.710397i	0.584758	+	0.811208i	$0.301190\pi$
$380$		0			0
$381$	12.9374	+	22.4082i	0.662801	+	1.14800i
$382$	−5.54362	+	3.20061i	−0.283637	+	0.163758i
$383$	−5.84433	+	3.37422i	−0.298631	+	0.172415i	−0.641828	−	0.766849i	$-0.721824\pi$
$383$	−5.84433	+	3.37422i	−0.298631	+	0.172415i	0.343197	+	0.939264i	$0.388490\pi$
$384$	−15.2156	+	26.3542i	−0.776468	+	1.34488i
$385$		0			0
$386$	4.52990	−	7.84601i	0.230566	−	0.399352i
$387$			43.0797i			2.18987i
$388$			5.46652i			0.277521i
$389$	−13.4863	+	23.3590i	−0.683783	+	1.18435i	0.290035	+	0.957016i	$0.406333\pi$
$389$	−13.4863	+	23.3590i	−0.683783	+	1.18435i	−0.973818	+	0.227331i	$0.927000\pi$
$390$		0			0
$391$	−3.59498	+	6.22668i	−0.181806	+	0.314897i
$392$	−10.8621	+	6.27124i	−0.548620	+	0.316746i
$393$	23.3162	−	13.4616i	1.17614	−	0.679047i
$394$	−2.36468	−	4.09575i	−0.119131	−	0.206341i
$395$		0			0
$396$	12.1722	−	21.0829i	0.611678	−	1.05946i
$397$	−18.4795	−	10.6692i	−0.927460	−	0.535469i	−0.0414528	−	0.999140i	$-0.513199\pi$
$397$	−18.4795	−	10.6692i	−0.927460	−	0.535469i	−0.886007	+	0.463671i	$0.846532\pi$
$398$	−5.10740	+	2.94876i	−0.256011	+	0.147808i
$399$	−0.375331			−0.0187900
$400$		0			0
$401$	−24.4634			−1.22164			−0.610821	−	0.791769i	$-0.709161\pi$
$401$	−24.4634			−1.22164			−0.610821	+	0.791769i	$0.709161\pi$
$402$		−	5.73899i		−	0.286235i
$403$	0.354808	−	0.781737i	0.0176743	−	0.0389411i
$404$	8.83734			0.439674
$405$		0			0
$406$	−0.363650	+	0.629860i	−0.0180476	+	0.0312594i
$407$			26.0304i			1.29028i
$408$	4.30393	−	2.48487i	0.213076	−	0.123020i
$409$	−7.41790	+	12.8482i	−0.366791	+	0.635301i	−0.989062	−	0.147501i	$-0.952877\pi$
$409$	−7.41790	+	12.8482i	−0.366791	+	0.635301i	0.622270	+	0.782802i	$0.286210\pi$
$410$		0			0
$411$	−40.3092			−1.98830
$412$	16.9722	−	9.79892i	0.836162	−	0.482758i
$413$	−0.525126	+	0.303182i	−0.0258398	+	0.0149186i
$414$	−7.35651	−	12.7419i	−0.361553	−	0.626228i
$415$		0			0
$416$	−0.376391	−	0.651929i	−0.0184541	−	0.0319634i
$417$	−27.6033	−	15.9368i	−1.35174	−	0.780428i
$418$			1.14043i			0.0557802i
$419$	14.7454			0.720360			0.360180	−	0.932883i	$-0.382715\pi$
$419$	14.7454			0.720360			0.360180	+	0.932883i	$0.382715\pi$
$420$		0			0
$421$	3.13737	+	5.43408i	0.152906	+	0.264841i	0.932295	−	0.361700i	$-0.117804\pi$
$421$	3.13737	+	5.43408i	0.152906	+	0.264841i	−0.779389	+	0.626541i	$0.784470\pi$
$422$	1.03567	+	0.597946i	0.0504158	+	0.0291076i
$423$	−26.3499	+	15.2131i	−1.28118	+	0.739687i
$424$	8.53636	+	14.7854i	0.414563	+	0.718043i
$425$		0			0
$426$	17.6461			0.854955
$427$	−2.26010	−	1.30487i	−0.109374	−	0.0631472i
$428$	−10.1075	−	5.83557i	−0.488564	−	0.282073i
$429$	0.658729	+	1.14095i	0.0318038	+	0.0550857i
$430$		0			0
$431$	−5.84197	+	10.1186i	−0.281398	+	0.487395i	−0.971729	−	0.236098i	$-0.924131\pi$
$431$	−5.84197	+	10.1186i	−0.281398	+	0.487395i	0.690331	+	0.723493i	$0.257465\pi$
$432$		−	9.92445i		−	0.477491i
$433$			35.9341i			1.72688i	0.504447	+	0.863442i	$0.331696\pi$
$433$			35.9341i			1.72688i	−0.504447	+	0.863442i	$0.668304\pi$
$434$	−0.0471698	−	0.482111i	−0.00226422	−	0.0231421i
$435$		0			0
$436$	27.0696			1.29640
$437$	−4.64418	−	2.68132i	−0.222161	−	0.128265i
$438$		−	5.86405i		−	0.280195i
$439$	−16.6439	−	28.8281i	−0.794371	−	1.37589i	−0.923238	−	0.384229i	$-0.874467\pi$
$439$	−16.6439	−	28.8281i	−0.794371	−	1.37589i	0.128867	−	0.991662i	$-0.458866\pi$
$440$		0			0
$441$	15.1950	−	26.3186i	0.723573	−	1.25327i
$442$			0.0748666i			0.00356104i
$443$	3.38095	−	1.95199i	0.160634	−	0.0927420i	−0.417528	−	0.908664i	$-0.637104\pi$
$443$	3.38095	−	1.95199i	0.160634	−	0.0927420i	0.578162	+	0.815922i	$0.303770\pi$
$444$	19.8742	+	34.4231i	0.943187	+	1.63365i
$445$		0			0
$446$	−4.46491	+	7.73344i	−0.211419	+	0.366189i
$447$	6.50490	−	3.75561i	0.307671	−	0.177634i
$448$	0.479993	+	0.277124i	0.0226775	+	0.0130929i
$449$	27.5270			1.29908			0.649540	−	0.760328i	$-0.274962\pi$
$449$	27.5270			1.29908			0.649540	+	0.760328i	$0.274962\pi$
$450$		0			0
$451$	−2.53074	+	4.38337i	−0.119168	+	0.206405i
$452$	15.3467	−	8.86041i	0.721847	−	0.416759i
$453$	−42.3307	−	24.4396i	−1.98887	−	1.14827i
$454$	3.76640	+	6.52360i	0.176766	+	0.306168i
$455$		0			0
$456$	1.85335	+	3.21009i	0.0867909	+	0.150326i
$457$		−	21.1516i		−	0.989428i	−0.869056	−	0.494714i	$-0.835273\pi$
$457$		−	21.1516i		−	0.989428i	0.869056	−	0.494714i	$-0.164727\pi$
$458$	4.11639	+	2.37660i	0.192346	+	0.111051i
$459$	−1.88008	+	3.25640i	−0.0877547	+	0.151996i
$460$		0			0
$461$	−2.59185			−0.120714			−0.0603572	−	0.998177i	$-0.519224\pi$
$461$	−2.59185			−0.120714			−0.0603572	+	0.998177i	$0.519224\pi$
$462$	0.643798	+	0.371697i	0.0299522	+	0.0172929i
$463$			19.5917i			0.910506i	0.890362	+	0.455253i	$0.150451\pi$
$463$			19.5917i			0.910506i	−0.890362	+	0.455253i	$0.849549\pi$
$464$	−22.4470			−1.04208
$465$		0			0
$466$	1.78352			0.0826198
$467$			5.57372i			0.257921i	0.991650	+	0.128961i	$0.0411641\pi$
$467$			5.57372i			0.257921i	−0.991650	+	0.128961i	$0.958836\pi$
$468$	1.03229	+	0.595994i	0.0477177	+	0.0275498i
$469$	−0.807901			−0.0373054
$470$		0			0
$471$	13.4952	−	23.3743i	0.621825	−	1.07703i
$472$	5.18605	+	2.99416i	0.238707	+	0.137818i
$473$		−	31.0996i		−	1.42996i
$474$	−1.55965	−	2.70139i	−0.0716371	−	0.124079i
$475$		0			0
$476$	−0.164342	−	0.284648i	−0.00753259	−	0.0130468i
$477$	−35.8246	−	20.6834i	−1.64030	−	0.947026i
$478$	−3.16349	+	1.82644i	−0.144695	+	0.0835396i
$479$	8.60971	−	14.9125i	0.393388	−	0.681367i	−0.599506	−	0.800370i	$-0.704636\pi$
$479$	8.60971	−	14.9125i	0.393388	−	0.681367i	0.992894	+	0.119003i	$0.0379697\pi$
$480$		0			0
$481$	−1.27454			−0.0581138
$482$	−3.03965	−	1.75494i	−0.138452	−	0.0799354i
$483$	−3.02733	+	1.74783i	−0.137748	+	0.0795289i
$484$	0.960005	−	1.66278i	0.0436366	−	0.0755808i
$485$		0			0
$486$	4.62596	+	8.01241i	0.209838	+	0.363450i
$487$	27.9971	−	16.1641i	1.26867	−	0.732467i	0.293934	−	0.955826i	$-0.405036\pi$
$487$	27.9971	−	16.1641i	1.26867	−	0.732467i	0.974736	+	0.223359i	$0.0717022\pi$
$488$			25.7733i			1.16670i
$489$	0.877670	−	1.52017i	0.0396896	−	0.0687444i
$490$		0			0
$491$	−11.0239	−	19.0939i	−0.497500	−	0.861695i	0.502496	−	0.864579i	$-0.332415\pi$
$491$	−11.0239	−	19.0939i	−0.497500	−	0.861695i	−0.999996	+	0.00288473i	$0.999082\pi$
$492$			7.72889i			0.348445i
$493$	7.36528	+	4.25234i	0.331715	+	0.191516i
$494$	−0.0558393			−0.00251233
$495$		0			0
$496$	12.1582	−	8.70059i	0.545920	−	0.390668i
$497$		−	2.48411i		−	0.111427i
$498$			20.9139i			0.937173i
$499$	−8.25766	+	14.3027i	−0.369664	+	0.640276i	−0.989513	−	0.144445i	$-0.953860\pi$
$499$	−8.25766	+	14.3027i	−0.369664	+	0.640276i	0.619849	+	0.784721i	$0.287194\pi$
$500$		0			0
$501$	−2.67725	−	4.63712i	−0.119610	−	0.207171i
$502$	7.83192	+	4.52176i	0.349556	+	0.201816i
$503$	22.3505	+	12.9041i	0.996560	+	0.575364i	0.907229	−	0.420638i	$-0.138194\pi$
$503$	22.3505	+	12.9041i	0.996560	+	0.575364i	0.0893312	+	0.996002i	$0.471527\pi$
$504$	1.43164			0.0637701
$505$		0			0
$506$	5.31072	+	9.19843i	0.236090	+	0.408920i
$507$	30.4917	−	17.6044i	1.35418	−	0.781838i
$508$	−14.6360	−	8.45010i	−0.649367	−	0.374912i
$509$	−5.69876	−	9.87055i	−0.252593	−	0.437504i	0.711646	−	0.702538i	$-0.247950\pi$
$509$	−5.69876	−	9.87055i	−0.252593	−	0.437504i	−0.964239	+	0.265034i	$0.914617\pi$
$510$		0			0
$511$	−0.825505			−0.0365182
$512$		−	22.7784i		−	1.00667i
$513$	−2.42879	−	1.40226i	−0.107234	−	0.0619113i
$514$	−0.983328	−	1.70317i	−0.0433728	−	0.0751238i
$515$		0			0
$516$	−23.7445	−	41.1267i	−1.04529	−	1.81050i
$517$	19.0222	−	10.9825i	0.836594	−	0.483008i
$518$	−0.622822	+	0.359587i	−0.0273652	+	0.0157993i
$519$	−28.6001			−1.25541
$520$		0			0
$521$	−7.16994	+	12.4187i	−0.314121	+	0.544073i	−0.979250	−	0.202655i	$-0.935043\pi$
$521$	−7.16994	+	12.4187i	−0.314121	+	0.544073i	0.665129	+	0.746728i	$0.268376\pi$
$522$	−15.0718	+	8.70170i	−0.659674	+	0.380863i
$523$		−	42.0600i		−	1.83916i	−0.392909	−	0.919578i	$-0.628531\pi$
$523$		−	42.0600i		−	1.83916i	0.392909	−	0.919578i	$-0.371469\pi$
$524$	−8.79250	+	15.2291i	−0.384102	+	0.665284i
$525$		0			0
$526$	−9.25283			−0.403443
$527$	−5.63757	+	0.551581i	−0.245576	+	0.0240272i
$528$			22.9437i			0.998497i
$529$	−26.9451			−1.17153
$530$		0			0
$531$	−14.5095			−0.629661
$532$	0.212305	−	0.122574i	0.00920460	−	0.00531428i
$533$	−0.214625	−	0.123914i	−0.00929644	−	0.00536730i
$534$	−3.23153	+	5.59717i	−0.139842	+	0.242213i
$535$		0			0
$536$	3.98934	+	6.90973i	0.172313	+	0.298455i
$537$	−49.9135	+	28.8176i	−2.15393	+	1.24357i
$538$	11.1743	−	6.45149i	0.481759	−	0.278144i
$539$	−10.9694	+	18.9996i	−0.472486	+	0.818369i
$540$		0			0
$541$	−14.8641	+	25.7454i	−0.639058	+	1.10688i	0.346582	+	0.938020i	$0.387342\pi$
$541$	−14.8641	+	25.7454i	−0.639058	+	1.10688i	−0.985640	+	0.168861i	$0.945991\pi$
$542$		−	14.1172i		−	0.606386i
$543$		−	27.2178i		−	1.16803i
$544$	−2.48351	+	4.30157i	−0.106480	+	0.184428i
$545$		0			0
$546$	−0.0181995	+	0.0315225i	−0.000778868	+	0.00134904i
$547$	11.5064	−	6.64325i	0.491980	−	0.284045i	−0.233416	−	0.972377i	$-0.574990\pi$
$547$	11.5064	−	6.64325i	0.491980	−	0.284045i	0.725395	+	0.688332i	$0.241657\pi$
$548$	22.8008	−	13.1641i	0.974003	−	0.562341i
$549$	−31.2240	−	54.0815i	−1.33261	−	2.30814i
$550$		0			0
$551$	−3.17162	+	5.49340i	−0.135115	+	0.234027i
$552$	29.8973	+	17.2612i	1.27251	+	0.734686i
$553$	−0.380286	+	0.219558i	−0.0161714	+	0.00933657i
$554$	−6.26173			−0.266035
$555$		0			0
$556$	20.8184			0.882896
$557$			28.7388i			1.21770i	0.793284	+	0.608851i	$0.208369\pi$
$557$			28.7388i			1.21770i	−0.793284	+	0.608851i	$0.791631\pi$
$558$	4.79067	−	10.5551i	0.202805	−	0.446833i
$559$	1.52274			0.0644050
$560$		0			0
$561$	4.34644	−	7.52825i	0.183507	−	0.317843i
$562$			6.73224i			0.283983i
$563$	−0.177452	+	0.102452i	−0.00747872	+	0.00431784i	−0.503735	−	0.863858i	$-0.668041\pi$
$563$	−0.177452	+	0.102452i	−0.00747872	+	0.00431784i	0.496256	+	0.868176i	$0.334708\pi$
$564$	16.7702	−	29.0469i	0.706153	−	1.22309i
$565$		0			0
$566$	2.10388			0.0884325
$567$	0.482795	−	0.278742i	0.0202755	−	0.0117061i
$568$	−21.2458	+	12.2663i	−0.891455	+	0.514682i
$569$	5.93216	+	10.2748i	0.248689	+	0.430742i	0.963162	−	0.268921i	$-0.0866670\pi$
$569$	5.93216	+	10.2748i	0.248689	+	0.430742i	−0.714473	+	0.699663i	$0.753334\pi$
$570$		0			0
$571$	−9.61511	−	16.6539i	−0.402380	−	0.696942i	0.591633	−	0.806208i	$-0.298484\pi$
$571$	−9.61511	−	16.6539i	−0.402380	−	0.696942i	−0.994013	+	0.109265i	$0.965150\pi$
$572$	−0.745219	−	0.430252i	−0.0311592	−	0.0179897i
$573$			36.3924i			1.52031i
$574$	−0.139840			−0.00583680
$575$		0			0
$576$	6.63124	+	11.4856i	0.276302	+	0.478569i
$577$	−22.5574	−	13.0235i	−0.939078	−	0.542177i	−0.0494067	−	0.998779i	$-0.515733\pi$
$577$	−22.5574	−	13.0235i	−0.939078	−	0.542177i	−0.889671	+	0.456602i	$0.849066\pi$
$578$	−6.59862	+	3.80972i	−0.274467	+	0.158463i
$579$	−25.7535	−	44.6063i	−1.07028	−	1.85378i
$580$		0			0
$581$	2.94413			0.122143
$582$	−3.45924	−	1.99719i	−0.143390	−	0.0827863i
$583$	25.8620	+	14.9315i	1.07110	+	0.618398i
$584$	4.07627	+	7.06030i	0.168677	+	0.292157i
$585$		0			0
$586$	−0.111048	+	0.192341i	−0.00458735	+	0.00794553i
$587$			2.78293i			0.114864i	0.998349	+	0.0574318i	$0.0182912\pi$
$587$			2.78293i			0.114864i	−0.998349	+	0.0574318i	$0.981709\pi$
$588$			33.5006i			1.38154i
$589$	−0.411397	−	4.20479i	−0.0169513	−	0.173255i
$590$		0			0
$591$	−26.8875			−1.10600
$592$	−19.2225	−	11.0981i	−0.790039	−	0.456129i
$593$			10.0246i			0.411660i	0.978588	+	0.205830i	$0.0659893\pi$
$593$			10.0246i			0.411660i	−0.978588	+	0.205830i	$0.934011\pi$
$594$	2.77737	+	4.81054i	0.113957	+	0.197379i
$595$		0			0
$596$	−2.45299	+	4.24871i	−0.100478	+	0.174034i
$597$			33.5287i			1.37224i
$598$	−0.450386	+	0.260031i	−0.0184177	+	0.0106334i
$599$	−2.61827	−	4.53497i	−0.106979	−	0.185294i	0.807566	−	0.589778i	$-0.200785\pi$
$599$	−2.61827	−	4.53497i	−0.106979	−	0.185294i	−0.914545	+	0.404484i	$0.867451\pi$
$600$		0			0
$601$	−22.5154	+	38.9979i	−0.918424	+	1.59076i	−0.116614	+	0.993177i	$0.537204\pi$
$601$	−22.5154	+	38.9979i	−0.918424	+	1.59076i	−0.801810	+	0.597579i	$0.796129\pi$
$602$	0.744112	−	0.429613i	0.0303277	−	0.0175097i
$603$	−16.7421	−	9.66604i	−0.681790	−	0.393632i
$604$	31.9257			1.29904
$605$		0			0
$606$	−3.22872	+	5.59231i	−0.131158	+	0.227172i
$607$	−34.9034	+	20.1515i	−1.41668	+	0.817923i	−0.996006	−	0.0892866i	$-0.971541\pi$
$607$	−34.9034	+	20.1515i	−1.41668	+	0.817923i	−0.420679	+	0.907210i	$0.638208\pi$
$608$	−3.20833	−	1.85233i	−0.130115	−	0.0751219i
$609$	2.06743	+	3.58089i	0.0837765	+	0.145105i
$610$		0			0
$611$	0.537738	+	0.931390i	0.0217546	+	0.0376800i
$612$		−	7.86500i		−	0.317924i
$613$	−18.3237	−	10.5792i	−0.740086	−	0.427289i	0.0820147	−	0.996631i	$-0.473865\pi$
$613$	−18.3237	−	10.5792i	−0.740086	−	0.427289i	−0.822100	+	0.569342i	$0.807198\pi$
$614$	5.05838	−	8.76138i	0.204140	−	0.353580i
$615$		0			0
$616$	−1.03351			−0.0416412
$617$	25.8518	+	14.9256i	1.04076	+	0.600881i	0.920047	−	0.391807i	$-0.128150\pi$
$617$	25.8518	+	14.9256i	1.04076	+	0.600881i	0.120709	+	0.992688i	$0.461483\pi$
$618$			14.3201i			0.576040i
$619$	1.43250			0.0575771			0.0287885	−	0.999586i	$-0.490835\pi$
$619$	1.43250			0.0575771			0.0287885	+	0.999586i	$0.490835\pi$
$620$		0			0
$621$	−26.1200			−1.04816
$622$		−	8.82977i		−	0.354042i
$623$	0.787936	+	0.454915i	0.0315680	+	0.0182258i
$624$	−1.12340			−0.0449721
$625$		0			0
$626$	4.91302	−	8.50961i	0.196364	−	0.340112i
$627$	5.61496	+	3.24180i	0.224240	+	0.129465i
$628$			17.6289i			0.703469i
$629$	4.20483	+	7.28298i	0.167658	+	0.290391i
$630$		0			0
$631$	4.78914	+	8.29504i	0.190653	+	0.330220i	0.945467	−	0.325719i	$-0.105606\pi$
$631$	4.78914	+	8.29504i	0.190653	+	0.330220i	−0.754814	+	0.655939i	$0.772273\pi$
$632$	3.75563	+	2.16832i	0.149391	+	0.0862509i
$633$	5.88803	−	3.39945i	0.234028	−	0.135116i
$634$	−6.80362	+	11.7842i	−0.270206	+	0.468011i
$635$		0			0
$636$	45.6007			1.80818
$637$	−0.930283	−	0.537099i	−0.0368592	−	0.0212806i
$638$	10.8804	−	6.28182i	0.430760	−	0.248700i
$639$	29.7209	−	51.4780i	1.17574	−	2.03644i
$640$		0			0
$641$	5.31970	+	9.21399i	0.210115	+	0.363931i	0.951750	−	0.306873i	$-0.0992827\pi$
$641$	5.31970	+	9.21399i	0.210115	+	0.363931i	−0.741635	+	0.670804i	$0.765949\pi$
$642$	7.38555	−	4.26405i	0.291484	−	0.168289i
$643$			14.2242i			0.560946i	0.959862	+	0.280473i	$0.0904914\pi$
$643$			14.2242i			0.560946i	−0.959862	+	0.280473i	$0.909509\pi$
$644$	1.14160	−	1.97731i	0.0449854	−	0.0779170i
$645$		0			0
$646$	0.184220	+	0.319078i	0.00724804	+	0.0125540i
$647$		−	32.9960i		−	1.29721i	−0.761127	−	0.648603i	$-0.775354\pi$
$647$		−	32.9960i		−	1.29721i	0.761127	−	0.648603i	$-0.224646\pi$
$648$	−4.76799	−	2.75280i	−0.187304	−	0.108140i
$649$	10.4745			0.411162
$650$		0			0
$651$	−2.50778	−	1.13821i	−0.0982876	−	0.0446100i
$652$			1.14651i			0.0449007i
$653$		−	30.7443i		−	1.20312i	−0.798829	−	0.601559i	$-0.794547\pi$
$653$		−	30.7443i		−	1.20312i	0.798829	−	0.601559i	$-0.205453\pi$
$654$	−9.88986	+	17.1297i	−0.386724	+	0.669826i
$655$		0			0
$656$	−2.15797	−	3.73772i	−0.0842547	−	0.145933i
$657$	−17.1069	−	9.87667i	−0.667404	−	0.385326i
$658$	0.525549	+	0.303426i	0.0204880	+	0.0118288i
$659$	14.4489			0.562850			0.281425	−	0.959583i	$-0.409193\pi$
$659$	14.4489			0.562850			0.281425	+	0.959583i	$0.409193\pi$
$660$		0			0
$661$	3.35678	+	5.81411i	0.130564	+	0.226143i	0.923894	−	0.382649i	$-0.124988\pi$
$661$	3.35678	+	5.81411i	0.130564	+	0.226143i	−0.793330	+	0.608791i	$0.791655\pi$
$662$	−1.81829	+	1.04979i	−0.0706697	+	0.0408011i
$663$	0.368609	+	0.212816i	0.0143156	+	0.00826510i
$664$	−14.5378	−	25.1802i	−0.564177	−	0.977183i
$665$		0			0
$666$	−17.2089			−0.666833
$667$			59.0779i			2.28751i
$668$	3.02876	+	1.74866i	0.117186	+	0.0676575i
$669$	25.3840	+	43.9663i	0.981401	+	1.69984i
$670$		0			0
$671$	22.5408	+	39.0418i	0.870179	+	1.50719i
$672$	−2.09136	+	1.20745i	−0.0806760	+	0.0465783i
$673$	1.53669	−	0.887207i	0.0592349	−	0.0341993i	−0.470090	−	0.882618i	$-0.655779\pi$
$673$	1.53669	−	0.887207i	0.0592349	−	0.0341993i	0.529325	+	0.848419i	$0.322445\pi$
$674$	−2.43205			−0.0936789
$675$		0			0
$676$	−11.4984	+	19.9158i	−0.442245	+	0.765992i
$677$	8.73322	−	5.04213i	0.335645	−	0.193785i	−0.322700	−	0.946501i	$-0.604590\pi$
$677$	8.73322	−	5.04213i	0.335645	−	0.193785i	0.658345	+	0.752717i	$0.271257\pi$
$678$			12.9486i			0.497288i
$679$	−0.281153	+	0.486971i	−0.0107897	+	0.0186882i
$680$		0			0
$681$	42.8257			1.64108
$682$	−3.45841	+	7.61981i	−0.132430	+	0.291777i
$683$			6.84051i			0.261745i	0.991399	+	0.130872i	$0.0417778\pi$
$683$			6.84051i			0.261745i	−0.991399	+	0.130872i	$0.958222\pi$
$684$	5.86612			0.224297
$685$		0			0
$686$	−1.21515			−0.0463947
$687$	23.4026	−	13.5115i	0.892864	−	0.515495i
$688$	22.9659	+	13.2594i	0.875566	+	0.505508i
$689$	−0.731095	+	1.26629i	−0.0278525	+	0.0482419i
$690$		0			0
$691$	−4.35710	−	7.54671i	−0.165752	−	0.287090i	0.771170	−	0.636629i	$-0.219672\pi$
$691$	−4.35710	−	7.54671i	−0.165752	−	0.287090i	−0.936922	+	0.349539i	$0.886338\pi$
$692$	16.1776	−	9.34015i	0.614980	−	0.355059i
$693$	2.16866	−	1.25208i	0.0823808	−	0.0475626i
$694$	5.52143	−	9.56339i	0.209591	−	0.363021i
$695$		0			0
$696$	20.4175	−	35.3642i	0.773925	−	1.34048i
$697$			1.63522i			0.0619383i
$698$		−	14.9876i		−	0.567288i
$699$	5.06984	−	8.78122i	0.191759	−	0.332136i
$700$		0			0
$701$	14.9266	−	25.8537i	0.563771	−	0.976480i	−0.433392	−	0.901205i	$-0.642683\pi$
$701$	14.9266	−	25.8537i	0.563771	−	0.976480i	0.997163	−	0.0752741i	$-0.0239832\pi$
$702$	−0.235541	+	0.135989i	−0.00888990	+	0.00513259i
$703$	−5.43202	+	3.13618i	−0.204872	+	0.118283i
$704$	−4.78714	−	8.29157i	−0.180422	−	0.312500i
$705$		0			0
$706$	−1.29210	+	2.23798i	−0.0486287	+	0.0842273i
$707$	0.787252	+	0.454520i	0.0296076	+	0.0170940i
$708$	13.8517	−	7.99731i	0.520581	−	0.300557i
$709$	15.2001			0.570851			0.285426	−	0.958401i	$-0.407865\pi$
$709$	15.2001			0.570851			0.285426	+	0.958401i	$0.407865\pi$
$710$		0			0
$711$	−10.5075			−0.394063
$712$		−	8.98531i		−	0.336739i
$713$	−22.8989	−	31.9990i	−0.857572	−	1.19837i
$714$	0.240169			0.00898810
$715$		0			0
$716$	18.8223	−	32.6012i	0.703424	−	1.21837i
$717$			20.7675i			0.775576i
$718$	12.6599	−	7.30919i	0.472463	−	0.272777i
$719$	4.05968	−	7.03157i	0.151400	−	0.262233i	−0.780342	−	0.625353i	$-0.784955\pi$
$719$	4.05968	−	7.03157i	0.151400	−	0.262233i	0.931743	+	0.363120i	$0.118288\pi$
$720$		0			0
$721$	2.01590			0.0750761
$722$	7.61508	−	4.39657i	0.283404	−	0.163623i
$723$	−17.2811	+	9.97723i	−0.642690	+	0.371057i
$724$	8.88873	+	15.3957i	0.330347	+	0.572178i
$725$		0			0
$726$	0.701475	+	1.21499i	0.0260342	+	0.0450925i
$727$	21.3838	+	12.3460i	0.793083	+	0.457887i	0.841047	−	0.540963i	$-0.181940\pi$
$727$	21.3838	+	12.3460i	0.793083	+	0.457887i	−0.0479640	+	0.998849i	$0.515273\pi$
$728$		−	0.0506040i		−	0.00187551i
$729$	43.4249			1.60833
$730$		0			0
$731$	−5.02368	−	8.70128i	−0.185808	−	0.321828i
$732$	59.6169	+	34.4198i	2.20350	+	1.27219i
$733$	9.39212	−	5.42254i	0.346906	−	0.200286i	−0.316416	−	0.948621i	$-0.602479\pi$
$733$	9.39212	−	5.42254i	0.346906	−	0.200286i	0.663322	+	0.748334i	$0.269146\pi$
$734$	−5.20991	−	9.02383i	−0.192301	−	0.333076i
$735$		0			0
$736$	−34.5035			−1.27182
$737$	12.0862	+	6.97798i	0.445202	+	0.257037i
$738$	−2.89789	−	1.67310i	−0.106673	−	0.0615876i
$739$	−2.11738	−	3.66741i	−0.0778890	−	0.134908i	0.824450	−	0.565935i	$-0.191485\pi$
$739$	−2.11738	−	3.66741i	−0.0778890	−	0.134908i	−0.902339	+	0.431027i	$0.858151\pi$
$740$		0			0
$741$	−0.158729	+	0.274927i	−0.00583107	+	0.0100997i
$742$			0.825060i			0.0302889i
$743$			2.91165i			0.106818i	0.998573	+	0.0534090i	$0.0170087\pi$
$743$			2.91165i			0.106818i	−0.998573	+	0.0534090i	$0.982991\pi$
$744$	2.64840	+	27.0687i	0.0970951	+	0.992385i
$745$		0			0
$746$	−12.9653			−0.474694
$747$	61.0110	+	35.2247i	2.23228	+	1.28880i
$748$			5.67779i			0.207601i
$749$	−0.600267	−	1.03969i	−0.0219333	−	0.0379896i
$750$		0			0
$751$	15.8812	−	27.5070i	0.579512	−	1.00374i	−0.416023	−	0.909354i	$-0.636576\pi$
$751$	15.8812	−	27.5070i	0.579512	−	1.00374i	0.995535	−	0.0943907i	$-0.0300903\pi$
$752$			18.7296i			0.682997i
$753$	44.5262	−	25.7072i	1.62262	−	0.936823i
$754$	0.307579	+	0.532743i	0.0112014	+	0.0194013i
$755$		0			0
$756$	0.597028	−	1.03408i	0.0217137	−	0.0376092i
$757$	2.37937	−	1.37373i	0.0864797	−	0.0499291i	−0.456137	−	0.889910i	$-0.650767\pi$
$757$	2.37937	−	1.37373i	0.0864797	−	0.0499291i	0.542616	+	0.839981i	$0.317434\pi$
$758$	6.60048	+	3.81079i	0.239740	+	0.138414i
$759$	60.3852			2.19184
$760$		0			0
$761$	17.7962	−	30.8240i	0.645113	−	1.11737i	−0.339163	−	0.940728i	$-0.610144\pi$
$761$	17.7962	−	30.8240i	0.645113	−	1.11737i	0.984276	−	0.176640i	$-0.0565229\pi$
$762$	10.6945	−	6.17448i	0.387422	−	0.223678i
$763$	2.41142	+	1.39224i	0.0872994	+	0.0504023i
$764$	−11.8849	−	20.5853i	−0.429982	−	0.744750i
$765$		0			0
$766$	1.61038	+	2.78926i	0.0581855	+	0.100780i
$767$			0.512869i			0.0185186i
$768$	−1.71071	−	0.987680i	−0.0617300	−	0.0356398i
$769$	20.2137	−	35.0111i	0.728924	−	1.26253i	−0.228414	−	0.973564i	$-0.573354\pi$
$769$	20.2137	−	35.0111i	0.728924	−	1.26253i	0.957338	−	0.288970i	$-0.0933127\pi$
$770$		0			0
$771$	−11.1809			−0.402669
$772$	29.1348	+	16.8210i	1.04859	+	0.605401i
$773$		−	17.0700i		−	0.613964i	−0.951715	−	0.306982i	$-0.900681\pi$
$773$		−	17.0700i		−	0.613964i	0.951715	−	0.306982i	$-0.0993192\pi$
$774$	20.5602			0.739022
$775$		0			0
$776$	5.55322			0.199349
$777$			4.08866i			0.146680i
$778$	11.1483	+	6.43647i	0.399686	+	0.230759i
$779$	−1.21963			−0.0436978
$780$		0			0
$781$	−21.4557	+	37.1623i	−0.767745	+	1.32977i
$782$	2.97175	+	1.71574i	0.106269	+	0.0613547i
$783$			30.8962i			1.10414i
$784$	−9.35365	−	16.2010i	−0.334059	−	0.578607i
$785$		0			0
$786$	−6.42468	−	11.1279i	−0.229161	−	0.396918i
$787$	−33.8907	−	19.5668i	−1.20807	−	0.697481i	−0.245734	−	0.969337i	$-0.579029\pi$
$787$	−33.8907	−	19.5668i	−1.20807	−	0.697481i	−0.962338	+	0.271856i	$0.912362\pi$
$788$	15.2089	−	8.78085i	0.541794	−	0.312805i
$789$	−26.3022	+	45.5567i	−0.936383	+	1.62186i
$790$		0			0
$791$	1.82283			0.0648123
$792$	−21.4173	−	12.3653i	−0.761031	−	0.439382i
$793$	−1.91162	+	1.10367i	−0.0678836	+	0.0391926i
$794$	−5.09196	+	8.81953i	−0.180707	+	0.312994i
$795$		0			0
$796$	−10.9497	−	18.9654i	−0.388102	−	0.672212i
$797$	0.153698	−	0.0887374i	0.00544425	−	0.00314324i	−0.497275	−	0.867593i	$-0.665666\pi$
$797$	0.153698	−	0.0887374i	0.00544425	−	0.00314324i	0.502720	+	0.864450i	$0.332333\pi$
$798$			0.179130i			0.00634114i
$799$	3.54811	−	6.14551i	0.125523	−	0.217413i
$800$		0			0
$801$	10.8856	+	18.8544i	0.384623	+	0.666186i
$802$			11.6754i			0.412272i
$803$	12.3496	+	7.13004i	0.435807	+	0.251614i
$804$	21.3108			0.751572
$805$		0			0
$806$	−0.373092	−	0.169336i	−0.0131416	−	0.00596460i
$807$		−	73.3563i		−	2.58226i
$808$		−	8.97750i		−	0.315827i
$809$	−10.3592	+	17.9427i	−0.364211	+	0.630832i	−0.988649	−	0.150242i	$-0.951995\pi$
$809$	−10.3592	+	17.9427i	−0.364211	+	0.630832i	0.624438	+	0.781074i	$0.285328\pi$
$810$		0			0
$811$	−19.2970	−	33.4235i	−0.677611	−	1.17366i	−0.975698	−	0.219118i	$-0.929682\pi$
$811$	−19.2970	−	33.4235i	−0.677611	−	1.17366i	0.298088	−	0.954538i	$-0.403651\pi$
$812$	−2.33888	−	1.35035i	−0.0820785	−	0.0473880i
$813$	−69.5067	−	40.1297i	−2.43770	−	1.40741i
$814$	12.4233			0.435435
$815$		0			0
$816$	3.70623	+	6.41937i	0.129744	+	0.224723i
$817$	6.48986	−	3.74692i	0.227051	−	0.131088i
$818$	6.13192	+	3.54027i	0.214398	+	0.123782i
$819$	0.0613061	+	0.106185i	0.00214221	+	0.00371041i
$820$		0			0
$821$	−10.7108			−0.373808			−0.186904	−	0.982378i	$-0.559845\pi$
$821$	−10.7108			−0.373808			−0.186904	+	0.982378i	$0.559845\pi$
$822$			19.2380i			0.671001i
$823$	22.5541	+	13.0216i	0.786185	+	0.453904i	0.838618	−	0.544720i	$-0.183364\pi$
$823$	22.5541	+	13.0216i	0.786185	+	0.453904i	−0.0524328	+	0.998624i	$0.516698\pi$
$824$	−9.95433	−	17.2414i	−0.346776	−	0.600633i
$825$		0			0
$826$	0.144697	+	0.250622i	0.00503464	+	0.00872025i
$827$	−6.20259	+	3.58107i	−0.215685	+	0.124526i	−0.603951	−	0.797022i	$-0.706408\pi$
$827$	−6.20259	+	3.58107i	−0.215685	+	0.124526i	0.388266	+	0.921548i	$0.373074\pi$
$828$	47.3147	−	27.3171i	1.64430	−	0.949336i
$829$	−6.65904			−0.231278			−0.115639	−	0.993291i	$-0.536892\pi$
$829$	−6.65904			−0.231278			−0.115639	+	0.993291i	$0.536892\pi$
$830$		0			0
$831$	−17.7997	+	30.8299i	−0.617463	+	1.06948i
$832$	0.405983	−	0.234395i	0.0140749	−	0.00812617i
$833$			7.08779i			0.245577i
$834$	−7.60600	+	13.1740i	−0.263374	+	0.456177i
$835$		0			0
$836$	−4.23479			−0.146463
$837$	−11.9756	−	16.7347i	−0.413936	−	0.578434i
$838$		−	7.03739i		−	0.243102i
$839$	29.2023			1.00818			0.504088	−	0.863652i	$-0.331829\pi$
$839$	29.2023			1.00818			0.504088	+	0.863652i	$0.331829\pi$
$840$		0			0
$841$	40.8807			1.40968
$842$	2.59347	−	1.49734i	0.0893768	−	0.0516017i
$843$	33.1465	+	19.1371i	1.14163	+	0.659118i
$844$	−2.22037	+	3.84579i	−0.0764283	+	0.132378i
$845$		0			0
$846$	7.26061	+	12.5758i	0.249625	+	0.432363i
$847$	0.171039	−	0.0987495i	0.00587697	−	0.00339307i
$848$	−22.0527	+	12.7321i	−0.757292	+	0.437222i
$849$	5.98050	−	10.3585i	0.205250	−	0.355504i
$850$		0			0
$851$	−29.2089	+	50.5913i	−1.00127	+	1.73425i
$852$			65.5257i			2.24487i
$853$			24.1509i			0.826911i	0.910524	+	0.413455i	$0.135678\pi$
$853$			24.1509i			0.826911i	−0.910524	+	0.413455i	$0.864322\pi$
$854$	−0.622763	+	1.07866i	−0.0213105	+	0.0369109i
$855$		0			0
$856$	−5.92812	+	10.2678i	−0.202619	+	0.350947i
$857$	−24.2694	+	14.0119i	−0.829026	+	0.478638i	−0.853519	−	0.521062i	$-0.825536\pi$
$857$	−24.2694	+	14.0119i	−0.829026	+	0.478638i	0.0244932	+	0.999700i	$0.492203\pi$
$858$	0.544531	−	0.314385i	0.0185900	−	0.0107329i
$859$	6.39974	+	11.0847i	0.218356	+	0.378204i	0.954306	−	0.298833i	$-0.0965972\pi$
$859$	6.39974	+	11.0847i	0.218356	+	0.378204i	−0.735949	+	0.677037i	$0.763264\pi$
$860$		0			0
$861$	−0.397510	+	0.688508i	−0.0135471	+	0.0234643i
$862$	4.82920	+	2.78814i	0.164483	+	0.0949644i
$863$	−35.2042	+	20.3251i	−1.19836	+	0.691876i	−0.960190	−	0.279347i	$-0.909882\pi$
$863$	−35.2042	+	20.3251i	−1.19836	+	0.691876i	−0.238174	+	0.971223i	$0.576549\pi$
$864$	−18.0444			−0.613884
$865$		0			0
$866$	17.1499			0.582778
$867$			43.3182i			1.47116i
$868$	1.79024	−	0.175157i	0.0607645	−	0.00594521i
$869$	7.58545			0.257319
$870$		0			0
$871$	−0.341666	+	0.591782i	−0.0115769	+	0.0200518i
$872$		−	27.4989i		−	0.931230i
$873$	−11.6526	+	6.72765i	−0.394382	+	0.227696i
$874$	−1.27969	+	2.21648i	−0.0432860	+	0.0749736i
$875$		0			0
$876$	21.7751			0.735714
$877$	5.13898	−	2.96699i	0.173531	−	0.100188i	−0.410719	−	0.911762i	$-0.634722\pi$
$877$	5.13898	−	2.96699i	0.173531	−	0.100188i	0.584250	+	0.811574i	$0.301389\pi$
$878$	−13.7585	+	7.94348i	−0.464327	+	0.268079i
$879$	0.631332	+	1.09350i	0.0212943	+	0.0368828i
$880$		0			0
$881$	24.6146	+	42.6338i	0.829289	+	1.43637i	0.898597	+	0.438775i	$0.144587\pi$
$881$	24.6146	+	42.6338i	0.829289	+	1.43637i	−0.0693086	+	0.997595i	$0.522079\pi$
$882$	−12.5608	−	7.25198i	−0.422944	−	0.244187i
$883$		−	1.11132i		−	0.0373989i	−0.999825	−	0.0186994i	$-0.994047\pi$
$883$		−	1.11132i		−	0.0373989i	0.999825	−	0.0186994i	$-0.00595256\pi$
$884$	−0.278004			−0.00935029
$885$		0			0
$886$	−0.931608	−	1.61359i	−0.0312980	−	0.0542097i
$887$	4.84971	+	2.79998i	0.162837	+	0.0940141i	0.579204	−	0.815183i	$-0.303363\pi$
$887$	4.84971	+	2.79998i	0.162837	+	0.0940141i	−0.416367	+	0.909197i	$0.636697\pi$
$888$	34.9691	−	20.1894i	1.17349	−	0.677512i
$889$	−0.869207	−	1.50551i	−0.0291523	−	0.0504932i
$890$		0			0
$891$	−9.63017			−0.322623
$892$	−28.7168	−	16.5797i	−0.961510	−	0.555128i
$893$	4.58364	+	2.64637i	0.153386	+	0.0885572i
$894$	−1.79240	−	3.10453i	−0.0599469	−	0.103831i
$895$		0			0
$896$	1.02227	−	1.77063i	0.0341517	−	0.0591526i
$897$			2.95666i			0.0987201i
$898$		−	13.1375i		−	0.438405i
$899$	−37.8503	+	27.0862i	−1.26238	+	0.903375i
$900$		0			0
$901$	9.64784			0.321416
$902$	2.09201	+	1.20782i	0.0696563	+	0.0402161i
$903$		−	4.88489i		−	0.162559i
$904$	−9.00094	−	15.5901i	−0.299367	−	0.518519i
$905$		0			0
$906$	−11.6641	+	20.2028i	−0.387513	+	0.671191i
$907$		−	25.5048i		−	0.846872i	−0.905926	−	0.423436i	$-0.860824\pi$
$907$		−	25.5048i		−	0.846872i	0.905926	−	0.423436i	$-0.139176\pi$
$908$	−24.2243	+	13.9859i	−0.803911	+	0.464138i
$909$	10.8761	+	18.8380i	0.360738	+	0.624816i
$910$		0			0
$911$	17.5554	−	30.4069i	0.581637	−	1.00742i	−0.413649	−	0.910437i	$-0.635746\pi$
$911$	17.5554	−	30.4069i	0.581637	−	1.00742i	0.995286	−	0.0969880i	$-0.0309208\pi$
$912$	−4.78790	+	2.76429i	−0.158543	+	0.0915349i
$913$	−44.0442	−	25.4290i	−1.45765	−	0.841576i
$914$	−10.0948			−0.333906
$915$		0			0
$916$	−8.82509	+	15.2855i	−0.291589	+	0.505047i
$917$	−1.56651	+	0.904428i	−0.0517309	+	0.0298668i
$918$	1.55415	+	0.897287i	0.0512945	+	0.0296149i
$919$	−16.2644	−	28.1708i	−0.536515	−	0.929271i	−0.999088	−	0.0426898i	$-0.986407\pi$
$919$	−16.2644	−	28.1708i	−0.536515	−	0.929271i	0.462574	−	0.886581i	$-0.346926\pi$
$920$		0			0
$921$	−28.7580	−	49.8104i	−0.947609	−	1.64131i
$922$			1.23699i			0.0407380i
$923$	−1.81959	−	1.05054i	−0.0598927	−	0.0345790i
$924$	−1.38023	+	2.39063i	−0.0454063	+	0.0786460i
$925$		0			0
$926$	9.35036			0.307272
$927$	41.7754	+	24.1191i	1.37209	+	0.792174i
$928$			40.8127i			1.33974i
$929$	2.86432			0.0939752			0.0469876	−	0.998895i	$-0.485038\pi$
$929$	2.86432			0.0939752			0.0469876	+	0.998895i	$0.485038\pi$
$930$		0			0
$931$	−5.28644			−0.173256
$932$			6.62278i			0.216936i
$933$	−43.4738	−	25.0996i	−1.42327	−	0.821724i
$934$	2.66011			0.0870416
$935$		0			0
$936$	0.605447	−	1.04866i	0.0197896	−	0.0342767i
$937$	1.08083	+	0.624020i	0.0353093	+	0.0203858i	0.517551	−	0.855653i	$-0.326844\pi$
$937$	1.08083	+	0.624020i	0.0353093	+	0.0203858i	−0.482241	+	0.876038i	$0.660177\pi$
$938$			0.385579i			0.0125896i
$939$	−27.9316	−	48.3790i	−0.911514	−	1.57879i
$940$		0			0
$941$	1.77944	+	3.08208i	0.0580081	+	0.100473i	0.893571	−	0.448922i	$-0.148192\pi$
$941$	1.77944	+	3.08208i	0.0580081	+	0.100473i	−0.835563	+	0.549395i	$0.814858\pi$
$942$	−11.1556	−	6.44071i	−0.363470	−	0.209850i
$943$	−9.83724	+	5.67954i	−0.320345	+	0.184951i
$944$	−4.46584	+	7.73506i	−0.145351	+	0.251755i
$945$		0			0
$946$	−14.8426			−0.482574
$947$	−7.68066	−	4.43443i	−0.249588	−	0.144100i	0.369988	−	0.929037i	$-0.379362\pi$
$947$	−7.68066	−	4.43443i	−0.249588	−	0.144100i	−0.619576	+	0.784937i	$0.712695\pi$
$948$	10.0312	−	5.79149i	0.325797	−	0.188099i
$949$	−0.349111	+	0.604678i	−0.0113326	+	0.0196287i
$950$		0			0
$951$	38.6801	+	66.9959i	1.25429	+	2.17249i
$952$	−0.289163	+	0.166948i	−0.00937182	+	0.00541082i
$953$			11.7561i			0.380816i	0.981705	+	0.190408i	$0.0609811\pi$
$953$			11.7561i			0.380816i	−0.981705	+	0.190408i	$0.939019\pi$
$954$	−9.87134	+	17.0977i	−0.319596	+	0.553557i
$955$		0			0
$956$	−6.78219	−	11.7471i	−0.219352	−	0.379928i
$957$		−	71.4270i		−	2.30891i
$958$	−7.11712	−	4.10907i	−0.229944	−	0.132758i
$959$	2.70820			0.0874525
$960$		0			0
$961$	10.0025	−	29.3420i	0.322661	−	0.946515i
$962$			0.608285i			0.0196119i
$963$		−	28.7273i		−	0.925725i
$964$	6.51667	−	11.2872i	0.209888	−	0.363536i
$965$		0			0
$966$	0.834168	+	1.44482i	0.0268389	+	0.0464864i
$967$	−2.12801	−	1.22860i	−0.0684321	−	0.0395093i	0.465394	−	0.885104i	$-0.345913\pi$
$967$	−2.12801	−	1.22860i	−0.0684321	−	0.0395093i	−0.533826	+	0.845595i	$0.679246\pi$
$968$	−1.68915	−	0.975231i	−0.0542913	−	0.0313451i
$969$	2.09466			0.0672902
$970$		0			0
$971$	−17.6046	−	30.4921i	−0.564959	−	0.978537i	−0.997054	−	0.0767092i	$-0.975559\pi$
$971$	−17.6046	−	30.4921i	−0.564959	−	0.978537i	0.432095	−	0.901828i	$-0.357775\pi$
$972$	−29.7527	+	17.1777i	−0.954318	+	0.550976i
$973$	1.85455	+	1.07073i	0.0594542	+	0.0343259i
$974$	−7.71450	−	13.3619i	−0.247188	−	0.428143i
$975$		0			0
$976$	−38.4413			−1.23048
$977$			8.97186i			0.287035i	0.989648	+	0.143518i	$0.0458414\pi$
$977$			8.97186i			0.287035i	−0.989648	+	0.143518i	$0.954159\pi$
$978$	−0.725516	−	0.418877i	−0.0231994	−	0.0133942i
$979$	−7.85836	−	13.6111i	−0.251154	−	0.435012i
$980$		0			0
$981$	33.3145	+	57.7024i	1.06365	+	1.84230i
$982$	−9.11274	+	5.26125i	−0.290799	+	0.167893i
$983$	−5.80873	+	3.35367i	−0.185270	+	0.106965i	−0.589766	−	0.807574i	$-0.700780\pi$
$983$	−5.80873	+	3.35367i	−0.185270	+	0.106965i	0.404497	+	0.914540i	$0.367447\pi$
$984$	7.85147			0.250296
$985$		0			0
$986$	2.02947	−	3.51515i	0.0646316	−	0.111945i
$987$	2.98786	−	1.72504i	0.0951047	−	0.0549087i
$988$		−	0.207350i		−	0.00659667i
$989$	34.8971	−	60.4435i	1.10966	−	1.92199i
$990$		0			0
$991$	−27.4394			−0.871643			−0.435821	−	0.900033i	$-0.643542\pi$
$991$	−27.4394			−0.871643			−0.435821	+	0.900033i	$0.643542\pi$
$992$	−15.8192	−	22.1058i	−0.502261	−	0.701860i
$993$			11.9365i			0.378795i
$994$	−1.18557			−0.0376039
$995$		0			0
$996$	−77.6600			−2.46075
$997$	33.8648	−	19.5519i	1.07251	−	0.619214i	0.143644	−	0.989629i	$-0.454118\pi$
$997$	33.8648	−	19.5519i	1.07251	−	0.619214i	0.928866	+	0.370416i	$0.120785\pi$
$998$	6.82610	+	3.94105i	0.216076	+	0.124752i
$999$	−15.2755	+	26.4580i	−0.483296	+	0.837093i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.o.f.749.4		16
5.2	odd	4		775.2.e.f.501.3		8
5.3	odd	4		155.2.e.d.36.2	✓	8
5.4	even	2	inner	775.2.o.f.749.5		16
31.25	even	3	inner	775.2.o.f.149.4		16
155.87	odd	12		775.2.e.f.676.3		8
155.88	even	12		4805.2.a.m.1.2		4
155.98	odd	12		4805.2.a.o.1.2		4
155.118	odd	12		155.2.e.d.56.2	yes	8
155.149	even	6	inner	775.2.o.f.149.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.e.d.36.2	✓	8	5.3	odd	4
155.2.e.d.56.2	yes	8	155.118	odd	12
775.2.e.f.501.3		8	5.2	odd	4
775.2.e.f.676.3		8	155.87	odd	12
775.2.o.f.149.4		16	31.25	even	3	inner
775.2.o.f.149.5		16	155.149	even	6	inner
775.2.o.f.749.4		16	1.1	even	1	trivial
775.2.o.f.749.5		16	5.4	even	2	inner
4805.2.a.m.1.2		4	155.88	even	12
4805.2.a.o.1.2		4	155.98	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:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.477260i q^{2} +(-2.34981 - 1.35666i) q^{3} +1.77222 q^{4} +(-0.647481 + 1.12147i) q^{6} +(0.157874 + 0.0911485i) q^{7} -1.80033i q^{8} +(2.18107 + 3.77773i) q^{9} +(-1.57453 - 2.72717i) q^{11} +(-4.16439 - 2.40431i) q^{12} +(0.133532 - 0.0770945i) q^{13} +(0.0435016 - 0.0753469i) q^{14} +2.68522 q^{16} +(-0.881070 - 0.508686i) q^{17} +(1.80296 - 1.04094i) q^{18} +(0.379404 - 0.657147i) q^{19} +(-0.247316 - 0.428364i) q^{21} +(-1.30157 + 0.751461i) q^{22} -7.06719i q^{23} +(-2.44244 + 4.23044i) q^{24} +(-0.0367941 - 0.0637292i) q^{26} -3.69596i q^{27} +(0.279788 + 0.161536i) q^{28} -8.35947 q^{29} +(4.52783 - 3.24018i) q^{31} -4.88221i q^{32} +8.54445i q^{33} +(-0.242775 + 0.420499i) q^{34} +(3.86535 + 6.69498i) q^{36} +(-7.15862 - 4.13303i) q^{37} +(-0.313630 - 0.181074i) q^{38} -0.418365 q^{39} +(-0.803649 - 1.39196i) q^{41} +(-0.204441 + 0.118034i) q^{42} +(8.55270 + 4.93790i) q^{43} +(-2.79042 - 4.83315i) q^{44} -3.37289 q^{46} +6.97506i q^{47} +(-6.30976 - 3.64294i) q^{48} +(-3.48338 - 6.03340i) q^{49} +(1.38023 + 2.39063i) q^{51} +(0.236648 - 0.136629i) q^{52} +(-8.21261 + 4.74155i) q^{53} -1.76393 q^{54} +(0.164098 - 0.284225i) q^{56} +(-1.78306 + 1.02945i) q^{57} +3.98964i q^{58} +(-1.66312 + 2.88061i) q^{59} -14.3159 q^{61} +(-1.54641 - 2.16095i) q^{62} +0.795207i q^{63} +3.04036 q^{64} +4.07792 q^{66} +(-3.83803 + 2.21589i) q^{67} +(-1.56145 - 0.901505i) q^{68} +(-9.58780 + 16.6066i) q^{69} +(-6.81335 - 11.8011i) q^{71} +(6.80117 - 3.92666i) q^{72} +(-3.92167 + 2.26418i) q^{73} +(-1.97253 + 3.41652i) q^{74} +(0.672388 - 1.16461i) q^{76} -0.574065i q^{77} +0.199669i q^{78} +(-1.20440 + 2.08608i) q^{79} +(1.52905 - 2.64840i) q^{81} +(-0.664327 + 0.383549i) q^{82} +(13.9865 - 8.07508i) q^{83} +(-0.438299 - 0.759156i) q^{84} +(2.35666 - 4.08186i) q^{86} +(19.6432 + 11.3410i) q^{87} +(-4.90981 + 2.83468i) q^{88} +4.99092 q^{89} +0.0281082 q^{91} -12.5246i q^{92} +(-15.0354 + 1.47106i) q^{93} +3.32892 q^{94} +(-6.62352 + 11.4723i) q^{96} +3.08456i q^{97} +(-2.87950 + 1.66248i) q^{98} +(6.86834 - 11.8963i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 4 q^{6} + 10 q^{9} + 8 q^{11} + 16 q^{14} - 12 q^{16} - 6 q^{19} - 6 q^{21} - 20 q^{24} - 16 q^{26} - 76 q^{29} - 10 q^{31} + 32 q^{34} + 46 q^{36} + 28 q^{39} - 8 q^{41} + 6 q^{44} + 4 q^{46}+ \cdots + 14 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 - 4 * q^6 + 10 * q^9 + 8 * q^11 + 16 * q^14 - 12 * q^16 - 6 * q^19 - 6 * q^21 - 20 * q^24 - 16 * q^26 - 76 * q^29 - 10 * q^31 + 32 * q^34 + 46 * q^36 + 28 * q^39 - 8 * q^41 + 6 * q^44 + 4 * q^46 - 22 * q^49 - 32 * q^51 - 64 * q^54 + 30 * q^56 + 36 * q^59 - 20 * q^61 + 12 * q^64 + 20 * q^66 + 12 * q^69 - 24 * q^71 - 28 * q^74 - 22 * q^76 - 28 * q^79 - 32 * q^81 - 18 * q^84 + 14 * q^86 + 4 * q^89 + 8 * q^91 - 64 * q^94 - 62 * q^96 + 14 * q^99

Introduction

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