LMFDB - Embedded newform 975.2.bb.j.724.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(724,975)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("975.724");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bb (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			724.4
Root			$-1.16746 + 0.312819i$ of defining polynomial
Character	$\chi$	$=$	975.724
Dual form			975.2.bb.j.874.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.466951 + 0.269594i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.854638 - 1.48028i) q^{4} +(-0.269594 - 0.466951i) q^{6} +(-4.15777 + 2.40049i) q^{7} -2.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.466951 + 0.269594i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.854638 - 1.48028i) q^{4} +(-0.269594 - 0.466951i) q^{6} +(-4.15777 + 2.40049i) q^{7} -2.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.70928 - 2.96055i) q^{11} +1.70928i q^{12} +(-2.81325 + 2.25513i) q^{13} -2.58864 q^{14} +(-1.17009 + 2.02665i) q^{16} +(2.49360 - 1.43968i) q^{17} +0.539189i q^{18} +(2.48554 + 4.30507i) q^{19} +4.80098 q^{21} +(1.59630 - 0.921622i) q^{22} +(7.35856 + 4.24846i) q^{23} +(-1.00000 + 1.73205i) q^{24} +(-1.92162 + 0.294598i) q^{26} -1.00000i q^{27} +(7.10678 + 4.10310i) q^{28} +(-1.75513 + 3.03997i) q^{29} +3.04945 q^{31} +(-4.55685 + 2.63090i) q^{32} +(-2.96055 + 1.70928i) q^{33} +1.55252 q^{34} +(0.854638 - 1.48028i) q^{36} +(-2.32125 - 1.34017i) q^{37} +2.68035i q^{38} +(3.56391 - 0.546373i) q^{39} +(1.87577 - 3.24893i) q^{41} +(2.24183 + 1.29432i) q^{42} +(-1.37580 + 0.794319i) q^{43} -5.84324 q^{44} +(2.29072 + 3.96765i) q^{46} -0.539189i q^{47} +(2.02665 - 1.17009i) q^{48} +(8.02472 - 13.8992i) q^{49} -2.87936 q^{51} +(5.74253 + 2.23707i) q^{52} +13.7587i q^{53} +(0.269594 - 0.466951i) q^{54} +(4.80098 + 8.31555i) q^{56} -4.97107i q^{57} +(-1.63912 + 0.946346i) q^{58} +(4.20261 + 7.27913i) q^{59} +(1.52472 + 2.64090i) q^{61} +(1.42394 + 0.822114i) q^{62} +(-4.15777 - 2.40049i) q^{63} +1.84324 q^{64} -1.84324 q^{66} +(11.1288 + 6.42522i) q^{67} +(-4.26225 - 2.46081i) q^{68} +(-4.24846 - 7.35856i) q^{69} +(-1.04585 - 1.81147i) q^{71} +(1.73205 - 1.00000i) q^{72} +5.53919i q^{73} +(-0.722606 - 1.25159i) q^{74} +(4.24846 - 7.35856i) q^{76} +16.4124i q^{77} +(1.81147 + 0.705681i) q^{78} -2.21235 q^{79} +(-0.500000 + 0.866025i) q^{81} +(1.75178 - 1.01139i) q^{82} -4.34017i q^{83} +(-4.10310 - 7.10678i) q^{84} -0.856576 q^{86} +(3.03997 - 1.75513i) q^{87} +(-5.92110 - 3.41855i) q^{88} +(-3.50667 + 6.07372i) q^{89} +(6.28345 - 16.1295i) q^{91} -14.5236i q^{92} +(-2.64090 - 1.52472i) q^{93} +(0.145362 - 0.251775i) q^{94} +5.26180 q^{96} +(-12.3573 + 7.13449i) q^{97} +(7.49431 - 4.32684i) q^{98} +3.41855 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} + 6 q^{9}+O(q^{10}) $ 12 * q + 4 * q^4 + 6 * q^9	$ 12 q + 4 q^{4} + 6 q^{9} - 8 q^{11} + 48 q^{14} + 8 q^{16} + 20 q^{21} - 12 q^{24} - 36 q^{26} + 12 q^{29} - 36 q^{31} + 16 q^{34} - 4 q^{36} + 40 q^{41} - 96 q^{44} + 56 q^{46} + 60 q^{49} + 16 q^{51} + 20 q^{56} + 20 q^{59} - 18 q^{61} + 48 q^{64} - 48 q^{66} - 16 q^{69} - 8 q^{71} + 16 q^{74} + 16 q^{76} - 68 q^{79} - 6 q^{81} - 40 q^{86} - 44 q^{89} - 62 q^{91} + 16 q^{94} + 32 q^{96} - 16 q^{99}+O(q^{100}) $ 12 * q + 4 * q^4 + 6 * q^9 - 8 * q^11 + 48 * q^14 + 8 * q^16 + 20 * q^21 - 12 * q^24 - 36 * q^26 + 12 * q^29 - 36 * q^31 + 16 * q^34 - 4 * q^36 + 40 * q^41 - 96 * q^44 + 56 * q^46 + 60 * q^49 + 16 * q^51 + 20 * q^56 + 20 * q^59 - 18 * q^61 + 48 * q^64 - 48 * q^66 - 16 * q^69 - 8 * q^71 + 16 * q^74 + 16 * q^76 - 68 * q^79 - 6 * q^81 - 40 * q^86 - 44 * q^89 - 62 * q^91 + 16 * q^94 + 32 * q^96 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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 $

$2$	0.466951	+	0.269594i	0.330184	+	0.190632i	0.655923	−	0.754828i	$-0.272280\pi$
$2$	0.466951	+	0.269594i	0.330184	+	0.190632i	−0.325739	+	0.945460i	$0.605613\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−0.854638	−	1.48028i	−0.427319	−	0.740138i
$5$		0			0
$5$		0			0
$6$	−0.269594	−	0.466951i	−0.110061	−	0.190632i
$7$	−4.15777	+	2.40049i	−1.57149	+	0.907301i	−0.575504	+	0.817799i	$0.695194\pi$
$7$	−4.15777	+	2.40049i	−1.57149	+	0.907301i	−0.995987	+	0.0895019i	$0.971472\pi$
$8$		−	2.00000i		−	0.707107i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	1.70928	−	2.96055i	0.515366	−	0.892640i	−0.484475	−	0.874805i	$-0.660989\pi$
$11$	1.70928	−	2.96055i	0.515366	−	0.892640i	0.999841	−	0.0178349i	$-0.00567731\pi$
$12$			1.70928i			0.493425i
$13$	−2.81325	+	2.25513i	−0.780256	+	0.625460i
$13$	−2.81325	+	2.25513i	−0.780256	+	0.625460i
$14$	−2.58864			−0.691842
$15$		0			0
$16$	−1.17009	+	2.02665i	−0.292522	+	0.506662i
$17$	2.49360	−	1.43968i	0.604787	−	0.349174i	−0.166135	−	0.986103i	$-0.553129\pi$
$17$	2.49360	−	1.43968i	0.604787	−	0.349174i	0.770922	+	0.636929i	$0.219796\pi$
$18$			0.539189i			0.127088i
$19$	2.48554	+	4.30507i	0.570221	+	0.987652i	0.996543	+	0.0830801i	$0.0264757\pi$
$19$	2.48554	+	4.30507i	0.570221	+	0.987652i	−0.426322	+	0.904571i	$0.640191\pi$
$20$		0			0
$21$	4.80098			1.04766
$22$	1.59630	−	0.921622i	0.340332	−	0.196491i
$23$	7.35856	+	4.24846i	1.53436	+	0.885866i	0.999153	+	0.0411482i	$0.0131016\pi$
$23$	7.35856	+	4.24846i	1.53436	+	0.885866i	0.535212	+	0.844718i	$0.320232\pi$
$24$	−1.00000	+	1.73205i	−0.204124	+	0.353553i
$25$		0			0
$26$	−1.92162	+	0.294598i	−0.376861	+	0.0577755i
$27$		−	1.00000i		−	0.192450i
$28$	7.10678	+	4.10310i	1.34306	+	0.775413i
$29$	−1.75513	+	3.03997i	−0.325919	+	0.564509i	−0.981698	−	0.190444i	$-0.939007\pi$
$29$	−1.75513	+	3.03997i	−0.325919	+	0.564509i	0.655779	+	0.754953i	$0.272340\pi$
$30$		0			0
$31$	3.04945			0.547697			0.273849	−	0.961773i	$-0.411703\pi$
$31$	3.04945			0.547697			0.273849	+	0.961773i	$0.411703\pi$
$32$	−4.55685	+	2.63090i	−0.805545	+	0.465081i
$33$	−2.96055	+	1.70928i	−0.515366	+	0.297547i
$34$	1.55252			0.266255
$35$		0			0
$36$	0.854638	−	1.48028i	0.142440	−	0.246713i
$37$	−2.32125	−	1.34017i	−0.381611	−	0.220323i	0.296908	−	0.954906i	$-0.404044\pi$
$37$	−2.32125	−	1.34017i	−0.381611	−	0.220323i	−0.678519	+	0.734583i	$0.737378\pi$
$38$			2.68035i			0.434810i
$39$	3.56391	−	0.546373i	0.570683	−	0.0874898i
$40$		0			0
$41$	1.87577	−	3.24893i	0.292946	−	0.507397i	−0.681559	−	0.731763i	$-0.738698\pi$
$41$	1.87577	−	3.24893i	0.292946	−	0.507397i	0.974505	+	0.224366i	$0.0720311\pi$
$42$	2.24183	+	1.29432i	0.345921	+	0.199718i
$43$	−1.37580	+	0.794319i	−0.209808	+	0.121132i	−0.601222	−	0.799082i	$-0.705319\pi$
$43$	−1.37580	+	0.794319i	−0.209808	+	0.121132i	0.391414	+	0.920215i	$0.371986\pi$
$44$	−5.84324			−0.880902
$45$		0			0
$46$	2.29072	+	3.96765i	0.337749	+	0.584998i
$47$		−	0.539189i		−	0.0786488i	−0.999226	−	0.0393244i	$-0.987479\pi$
$47$		−	0.539189i		−	0.0786488i	0.999226	−	0.0393244i	$-0.0125206\pi$
$48$	2.02665	−	1.17009i	0.292522	−	0.168887i
$49$	8.02472	−	13.8992i	1.14639	−	1.98560i
$50$		0			0
$51$	−2.87936			−0.403191
$52$	5.74253	+	2.23707i	0.796345	+	0.310226i
$53$			13.7587i			1.88991i	0.327206	+	0.944953i	$0.393893\pi$
$53$			13.7587i			1.88991i	−0.327206	+	0.944953i	$0.606107\pi$
$54$	0.269594	−	0.466951i	0.0366872	−	0.0635440i
$55$		0			0
$56$	4.80098	+	8.31555i	0.641558	+	1.11121i
$57$		−	4.97107i		−	0.658434i
$58$	−1.63912	+	0.946346i	−0.215227	+	0.124261i
$59$	4.20261	+	7.27913i	0.547133	+	0.947663i	0.998469	+	0.0553085i	$0.0176142\pi$
$59$	4.20261	+	7.27913i	0.547133	+	0.947663i	−0.451336	+	0.892354i	$0.649052\pi$
$60$		0			0
$61$	1.52472	+	2.64090i	0.195221	+	0.338133i	0.946973	−	0.321313i	$-0.104124\pi$
$61$	1.52472	+	2.64090i	0.195221	+	0.338133i	−0.751752	+	0.659446i	$0.770791\pi$
$62$	1.42394	+	0.822114i	0.180841	+	0.104409i
$63$	−4.15777	−	2.40049i	−0.523830	−	0.302434i
$64$	1.84324			0.230406
$65$		0			0
$66$	−1.84324			−0.226888
$67$	11.1288	+	6.42522i	1.35960	+	0.784965i	0.989570	−	0.144055i	$-0.0460142\pi$
$67$	11.1288	+	6.42522i	1.35960	+	0.784965i	0.370030	+	0.929020i	$0.379347\pi$
$68$	−4.26225	−	2.46081i	−0.516874	−	0.298417i
$69$	−4.24846	−	7.35856i	−0.511455	−	0.885866i
$70$		0			0
$71$	−1.04585	−	1.81147i	−0.124120	−	0.214982i	0.797269	−	0.603625i	$-0.206277\pi$
$71$	−1.04585	−	1.81147i	−0.124120	−	0.214982i	−0.921389	+	0.388642i	$0.872944\pi$
$72$	1.73205	−	1.00000i	0.204124	−	0.117851i
$73$			5.53919i			0.648313i	0.946003	+	0.324157i	$0.105080\pi$
$73$			5.53919i			0.648313i	−0.946003	+	0.324157i	$0.894920\pi$
$74$	−0.722606	−	1.25159i	−0.0840013	−	0.145494i
$75$		0			0
$76$	4.24846	−	7.35856i	0.487332	−	0.844084i
$77$			16.4124i			1.87037i
$78$	1.81147	+	0.705681i	0.205109	+	0.0799027i
$79$	−2.21235			−0.248908			−0.124454	−	0.992225i	$-0.539718\pi$
$79$	−2.21235			−0.248908			−0.124454	+	0.992225i	$0.539718\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.75178	−	1.01139i	0.193452	−	0.111690i
$83$		−	4.34017i		−	0.476396i	−0.971217	−	0.238198i	$-0.923443\pi$
$83$		−	4.34017i		−	0.476396i	0.971217	−	0.238198i	$-0.0765567\pi$
$84$	−4.10310	−	7.10678i	−0.447685	−	0.775413i
$85$		0			0
$86$	−0.856576			−0.0923669
$87$	3.03997	−	1.75513i	0.325919	−	0.188170i
$88$	−5.92110	−	3.41855i	−0.631192	−	0.364419i
$89$	−3.50667	+	6.07372i	−0.371706	+	0.643813i	−0.989828	−	0.142269i	$-0.954560\pi$
$89$	−3.50667	+	6.07372i	−0.371706	+	0.643813i	0.618122	+	0.786082i	$0.287894\pi$
$90$		0			0
$91$	6.28345	−	16.1295i	0.658684	−	1.69083i
$92$		−	14.5236i		−	1.51419i
$93$	−2.64090	−	1.52472i	−0.273849	−	0.158107i
$94$	0.145362	−	0.251775i	0.0149930	−	0.0259686i
$95$		0			0
$96$	5.26180			0.537030
$97$	−12.3573	+	7.13449i	−1.25469	+	0.724398i	−0.972038	−	0.234824i	$-0.924549\pi$
$97$	−12.3573	+	7.13449i	−1.25469	+	0.724398i	−0.282656	+	0.959221i	$0.591215\pi$
$98$	7.49431	−	4.32684i	0.757040	−	0.437077i
$99$	3.41855			0.343577
$100$		0			0
$101$	−6.24846	+	10.8227i	−0.621745	+	1.07689i	0.367415	+	0.930057i	$0.380243\pi$
$101$	−6.24846	+	10.8227i	−0.621745	+	1.07689i	−0.989161	+	0.146838i	$0.953091\pi$
$102$	−1.34452	−	0.776260i	−0.133127	−	0.0768612i
$103$		−	6.85043i		−	0.674993i	−0.941327	−	0.337497i	$-0.890420\pi$
$103$		−	6.85043i		−	0.674993i	0.941327	−	0.337497i	$-0.109580\pi$
$104$	4.51026	+	5.62651i	0.442267	+	0.551724i
$105$		0			0
$106$	−3.70928	+	6.42465i	−0.360277	+	0.624018i
$107$	−13.4751	−	7.77985i	−1.30269	−	0.752107i	−0.321823	−	0.946800i	$-0.604296\pi$
$107$	−13.4751	−	7.77985i	−1.30269	−	0.752107i	−0.980864	+	0.194693i	$0.937629\pi$
$108$	−1.48028	+	0.854638i	−0.142440	+	0.0822375i
$109$	−15.8371			−1.51692			−0.758460	−	0.651720i	$-0.774048\pi$
$109$	−15.8371			−1.51692			−0.758460	+	0.651720i	$0.774048\pi$
$110$		0			0
$111$	1.34017	+	2.32125i	0.127204	+	0.220323i
$112$		−	11.2351i		−	1.06162i
$113$	2.66595	−	1.53919i	0.250792	−	0.144795i	−0.369335	−	0.929296i	$-0.620414\pi$
$113$	2.66595	−	1.53919i	0.250792	−	0.144795i	0.620127	+	0.784502i	$0.287081\pi$
$114$	1.34017	−	2.32125i	0.125519	−	0.217405i
$115$		0			0
$116$	6.00000			0.557086
$117$	−3.35963	−	1.30878i	−0.310598	−	0.120997i
$118$			4.53200i			0.417205i
$119$	−6.91189	+	11.9717i	−0.633611	+	1.09745i
$120$		0			0
$121$	−0.343245	−	0.594517i	−0.0312040	−	0.0540470i
$122$			1.64423i			0.148861i
$123$	−3.24893	+	1.87577i	−0.292946	+	0.169132i
$124$	−2.60617	−	4.51402i	−0.234041	−	0.405371i
$125$		0			0
$126$	−1.29432	−	2.24183i	−0.115307	−	0.199718i
$127$	6.45593	+	3.72733i	0.572871	+	0.330747i	0.758295	−	0.651911i	$-0.226033\pi$
$127$	6.45593	+	3.72733i	0.572871	+	0.330747i	−0.185424	+	0.982659i	$0.559366\pi$
$128$	9.97440	+	5.75872i	0.881621	+	0.509004i
$129$	1.58864			0.139872
$130$		0			0
$131$	11.6937			1.02168			0.510841	−	0.859675i	$-0.329334\pi$
$131$	11.6937			1.02168			0.510841	+	0.859675i	$0.329334\pi$
$132$	5.06040	+	2.92162i	0.440451	+	0.254295i
$133$	−20.6686	−	11.9330i	−1.79219	−	1.03472i
$134$	3.46441	+	6.00053i	0.299279	+	0.518366i
$135$		0			0
$136$	−2.87936	−	4.98720i	−0.246903	−	0.427649i
$137$	−8.03446	+	4.63870i	−0.686430	+	0.396311i	−0.802273	−	0.596957i	$-0.796376\pi$
$137$	−8.03446	+	4.63870i	−0.686430	+	0.396311i	0.115843	+	0.993268i	$0.463043\pi$
$138$		−	4.58145i		−	0.389999i
$139$	6.45774	+	11.1851i	0.547738	+	0.948711i	0.998429	+	0.0560304i	$0.0178444\pi$
$139$	6.45774	+	11.1851i	0.547738	+	0.948711i	−0.450691	+	0.892680i	$0.648822\pi$
$140$		0			0
$141$	−0.269594	+	0.466951i	−0.0227039	+	0.0393244i
$142$		−	1.12783i		−	0.0946451i
$143$	1.86781	+	12.1834i	0.156194	+	1.01883i
$144$	−2.34017			−0.195014
$145$		0			0
$146$	−1.49333	+	2.58653i	−0.123589	+	0.214063i
$147$	−13.8992	+	8.02472i	−1.14639	+	0.661868i
$148$			4.58145i			0.376593i
$149$	−1.00000	−	1.73205i	−0.0819232	−	0.141895i	0.822153	−	0.569267i	$-0.192773\pi$
$149$	−1.00000	−	1.73205i	−0.0819232	−	0.141895i	−0.904076	+	0.427372i	$0.859440\pi$
$150$		0			0
$151$	−8.60424			−0.700203			−0.350101	−	0.936712i	$-0.613853\pi$
$151$	−8.60424			−0.700203			−0.350101	+	0.936712i	$0.613853\pi$
$152$	8.61015	−	4.97107i	0.698375	−	0.403207i
$153$	2.49360	+	1.43968i	0.201596	+	0.116391i
$154$	−4.42469	+	7.66379i	−0.356552	+	0.617566i
$155$		0			0
$156$	−3.85464	−	4.80862i	−0.308618	−	0.384998i
$157$			0.908291i			0.0724895i	0.999343	+	0.0362448i	$0.0115396\pi$
$157$			0.908291i			0.0724895i	−0.999343	+	0.0362448i	$0.988460\pi$
$158$	−1.03306	−	0.596436i	−0.0821857	−	0.0474499i
$159$	6.87936	−	11.9154i	0.545569	−	0.944953i
$160$		0			0
$161$	−40.7936			−3.21499
$162$	−0.466951	+	0.269594i	−0.0366872	+	0.0211813i
$163$	12.6823	−	7.32211i	0.993352	−	0.573512i	0.0870777	−	0.996202i	$-0.472247\pi$
$163$	12.6823	−	7.32211i	0.993352	−	0.573512i	0.906275	+	0.422689i	$0.138914\pi$
$164$	−6.41241			−0.500725
$165$		0			0
$166$	1.17009	−	2.02665i	0.0908163	−	0.157298i
$167$	4.23916	+	2.44748i	0.328036	+	0.189392i	0.654969	−	0.755656i	$-0.272682\pi$
$167$	4.23916	+	2.44748i	0.328036	+	0.189392i	−0.326933	+	0.945048i	$0.606015\pi$
$168$		−	9.60197i		−	0.740808i
$169$	2.82878	−	12.6885i	0.217598	−	0.976038i
$170$		0			0
$171$	−2.48554	+	4.30507i	−0.190074	+	0.329217i
$172$	2.35162	+	1.35771i	0.179309	+	0.103524i
$173$	15.2072	−	8.77985i	1.15618	−	0.667520i	0.205793	−	0.978595i	$-0.434023\pi$
$173$	15.2072	−	8.77985i	1.15618	−	0.667520i	0.950385	+	0.311076i	$0.100689\pi$
$174$	1.89269			0.143485
$175$		0			0
$176$	4.00000	+	6.92820i	0.301511	+	0.522233i
$177$		−	8.40522i		−	0.631775i
$178$	−3.27488	+	1.89076i	−0.245463	+	0.141718i
$179$	0.692350	−	1.19919i	0.0517487	−	0.0896314i	−0.838991	−	0.544146i	$-0.816854\pi$
$179$	0.692350	−	1.19919i	0.0517487	−	0.0896314i	0.890739	+	0.454514i	$0.150187\pi$
$180$		0			0
$181$	−7.46800			−0.555092			−0.277546	−	0.960712i	$-0.589521\pi$
$181$	−7.46800			−0.555092			−0.277546	+	0.960712i	$0.589521\pi$
$182$	7.28249	−	5.83771i	0.539814	−	0.432720i
$183$		−	3.04945i		−	0.225422i
$184$	8.49693	−	14.7171i	0.626402	−	1.08496i
$185$		0			0
$186$	−0.822114	−	1.42394i	−0.0602803	−	0.104409i
$187$		−	9.84324i		−	0.719809i
$188$	−0.798148	+	0.460811i	−0.0582109	+	0.0336081i
$189$	2.40049	+	4.15777i	0.174610	+	0.302434i
$190$		0			0
$191$	1.20261	+	2.08298i	0.0870178	+	0.150719i	0.906249	−	0.422744i	$-0.138933\pi$
$191$	1.20261	+	2.08298i	0.0870178	+	0.150719i	−0.819231	+	0.573463i	$0.805600\pi$
$192$	−1.59630	−	0.921622i	−0.115203	−	0.0665124i
$193$	−13.7018	−	7.91075i	−0.986279	−	0.569428i	−0.0821189	−	0.996623i	$-0.526169\pi$
$193$	−13.7018	−	7.91075i	−0.986279	−	0.569428i	−0.904160	+	0.427194i	$0.859502\pi$
$194$	−7.69368			−0.552374
$195$		0			0
$196$	−27.4329			−1.95949
$197$	−15.9918	−	9.23287i	−1.13937	−	0.657814i	−0.193094	−	0.981180i	$-0.561852\pi$
$197$	−15.9918	−	9.23287i	−1.13937	−	0.657814i	−0.946274	+	0.323366i	$0.895186\pi$
$198$	1.59630	+	0.921622i	0.113444	+	0.0654968i
$199$	5.47107	+	9.47617i	0.387834	+	0.671748i	0.992158	−	0.124991i	$-0.0398901\pi$
$199$	5.47107	+	9.47617i	0.387834	+	0.671748i	−0.604324	+	0.796739i	$0.706557\pi$
$200$		0			0
$201$	−6.42522	−	11.1288i	−0.453200	−	0.784965i
$202$	−5.83546	+	3.36910i	−0.410581	+	0.237049i
$203$		−	16.8527i		−	1.18283i
$204$	2.46081	+	4.26225i	0.172291	+	0.298417i
$205$		0			0
$206$	1.84684	−	3.19882i	0.128675	−	0.222872i
$207$			8.49693i			0.590577i
$208$	−1.27861	−	8.34017i	−0.0886555	−	0.578287i
$209$	16.9939			1.17549
$210$		0			0
$211$	7.08864	−	12.2779i	0.488002	−	0.845244i	−0.511903	−	0.859043i	$-0.671059\pi$
$211$	7.08864	−	12.2779i	0.488002	−	0.845244i	0.999905	+	0.0137992i	$0.00439257\pi$
$212$	20.3667	−	11.7587i	1.39879	−	0.807592i
$213$			2.09171i			0.143322i
$214$	−4.19481	−	7.26563i	−0.286751	−	0.496668i
$215$		0			0
$216$	−2.00000			−0.136083
$217$	−12.6789	+	7.32018i	−0.860701	+	0.496926i
$218$	−7.39515	−	4.26959i	−0.500863	−	0.289173i
$219$	2.76959	−	4.79708i	0.187152	−	0.324157i
$220$		0			0
$221$	−3.76846	+	9.67358i	−0.253494	+	0.650715i
$222$			1.44521i			0.0969963i
$223$	−4.90155	−	2.82991i	−0.328232	−	0.189505i	0.326824	−	0.945085i	$-0.394022\pi$
$223$	−4.90155	−	2.82991i	−0.328232	−	0.189505i	−0.655056	+	0.755580i	$0.727355\pi$
$224$	12.6309	−	21.8774i	0.843937	−	1.46174i
$225$		0			0
$226$	1.65983			0.110410
$227$	18.0821	−	10.4397i	1.20015	−	0.692906i	0.239560	−	0.970882i	$-0.422997\pi$
$227$	18.0821	−	10.4397i	1.20015	−	0.692906i	0.960588	+	0.277976i	$0.0896634\pi$
$228$	−7.35856	+	4.24846i	−0.487332	+	0.281361i
$229$	11.5525			0.763412			0.381706	−	0.924284i	$-0.375337\pi$
$229$	11.5525			0.763412			0.381706	+	0.924284i	$0.375337\pi$
$230$		0			0
$231$	8.20620	−	14.2136i	0.539929	−	0.935184i
$232$	6.07995	+	3.51026i	0.399168	+	0.230460i
$233$			3.73206i			0.244495i	0.992500	+	0.122248i	$0.0390102\pi$
$233$			3.73206i			0.244495i	−0.992500	+	0.122248i	$0.960990\pi$
$234$	−1.21594	−	1.51687i	−0.0794885	−	0.0991612i
$235$		0			0
$236$	7.18342	−	12.4420i	0.467601	−	0.809908i
$237$	1.91595	+	1.10617i	0.124454	+	0.0718537i
$238$	−6.45503	+	3.72681i	−0.418417	+	0.241573i
$239$	−27.0928			−1.75248			−0.876242	−	0.481871i	$-0.839957\pi$
$239$	−27.0928			−1.75248			−0.876242	+	0.481871i	$0.839957\pi$
$240$		0			0
$241$	11.7990	+	20.4365i	0.760043	+	1.31643i	0.942828	+	0.333281i	$0.108156\pi$
$241$	11.7990	+	20.4365i	0.760043	+	1.31643i	−0.182784	+	0.983153i	$0.558511\pi$
$242$		−	0.370147i		−	0.0237940i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	2.60617	−	4.51402i	0.166843	−	0.288981i
$245$		0			0
$246$	−2.02279			−0.128968
$247$	−16.7009	−	6.50605i	−1.06266	−	0.413970i
$248$		−	6.09890i		−	0.387280i
$249$	−2.17009	+	3.75870i	−0.137524	+	0.238198i
$250$		0			0
$251$	13.4319	+	23.2647i	0.847813	+	1.46845i	0.883156	+	0.469080i	$0.155414\pi$
$251$	13.4319	+	23.2647i	0.847813	+	1.46845i	−0.0353430	+	0.999375i	$0.511252\pi$
$252$			8.20620i			0.516942i
$253$	25.1556	−	14.5236i	1.58152	−	0.913090i
$254$	2.00974	+	3.48097i	0.126102	+	0.218415i
$255$		0			0
$256$	1.26180	+	2.18549i	0.0788622	+	0.136593i
$257$	3.04726	+	1.75933i	0.190083	+	0.109744i	0.592021	−	0.805922i	$-0.298330\pi$
$257$	3.04726	+	1.75933i	0.190083	+	0.109744i	−0.401939	+	0.915667i	$0.631663\pi$
$258$	0.741816	+	0.428288i	0.0461835	+	0.0266640i
$259$	12.8683			0.799597
$260$		0			0
$261$	−3.51026			−0.217280
$262$	5.46038	+	3.15255i	0.337343	+	0.194765i
$263$	−7.66666	−	4.42635i	−0.472747	−	0.272940i	0.244642	−	0.969613i	$-0.421330\pi$
$263$	−7.66666	−	4.42635i	−0.472747	−	0.272940i	−0.717389	+	0.696673i	$0.754663\pi$
$264$	3.41855	+	5.92110i	0.210397	+	0.364419i
$265$		0			0
$266$	−6.43415	−	11.1443i	−0.394503	−	0.683299i
$267$	6.07372	−	3.50667i	0.371706	−	0.214604i
$268$		−	21.9649i		−	1.34172i
$269$	13.6212	+	23.5925i	0.830497	+	1.43846i	0.897645	+	0.440720i	$0.145277\pi$
$269$	13.6212	+	23.5925i	0.830497	+	1.43846i	−0.0671480	+	0.997743i	$0.521390\pi$
$270$		0			0
$271$	−6.93188	+	12.0064i	−0.421082	+	0.729335i	−0.996046	−	0.0888438i	$-0.971683\pi$
$271$	−6.93188	+	12.0064i	−0.421082	+	0.729335i	0.574964	+	0.818179i	$0.305016\pi$
$272$			6.73820i			0.408564i
$273$	−13.5064	+	10.8268i	−0.817443	+	0.655270i
$274$	−5.00227			−0.302198
$275$		0			0
$276$	−7.26180	+	12.5778i	−0.437109	+	0.757094i
$277$	2.23560	−	1.29072i	0.134324	−	0.0775521i	−0.431332	−	0.902193i	$-0.641956\pi$
$277$	2.23560	−	1.29072i	0.134324	−	0.0775521i	0.565656	+	0.824641i	$0.308623\pi$
$278$			6.96388i			0.417666i
$279$	1.52472	+	2.64090i	0.0912828	+	0.158107i
$280$		0			0
$281$	−5.35350			−0.319363			−0.159682	−	0.987169i	$-0.551047\pi$
$281$	−5.35350			−0.319363			−0.159682	+	0.987169i	$0.551047\pi$
$282$	−0.251775	+	0.145362i	−0.0149930	+	0.00865620i
$283$	13.7644	+	7.94687i	0.818207	+	0.472392i	0.849798	−	0.527109i	$-0.176724\pi$
$283$	13.7644	+	7.94687i	0.818207	+	0.472392i	−0.0315904	+	0.999501i	$0.510057\pi$
$284$	−1.78765	+	3.09631i	−0.106078	+	0.183732i
$285$		0			0
$286$	−2.41241	+	6.19261i	−0.142649	+	0.366177i
$287$			18.0111i			1.06316i
$288$	−4.55685	−	2.63090i	−0.268515	−	0.155027i
$289$	−4.35464	+	7.54245i	−0.256155	+	0.443674i
$290$		0			0
$291$	14.2690			0.836463
$292$	8.19953	−	4.73400i	0.479841	−	0.277036i
$293$	2.14889	−	1.24067i	0.125540	−	0.0724804i	−0.435915	−	0.899988i	$-0.643575\pi$
$293$	2.14889	−	1.24067i	0.125540	−	0.0724804i	0.561455	+	0.827507i	$0.310242\pi$
$294$	−8.65368			−0.504693
$295$		0			0
$296$	−2.68035	+	4.64250i	−0.155792	+	0.269840i
$297$	−2.96055	−	1.70928i	−0.171789	−	0.0991822i
$298$		−	1.07838i		−	0.0624687i
$299$	−30.2823	+	4.64250i	−1.75127	+	0.268482i
$300$		0			0
$301$	3.81351	−	6.60519i	0.219807	−	0.380717i
$302$	−4.01776	−	2.31965i	−0.231196	−	0.133481i
$303$	10.8227	−	6.24846i	0.621745	−	0.358965i
$304$	−11.6332			−0.667208
$305$		0			0
$306$	0.776260	+	1.34452i	0.0443758	+	0.0768612i
$307$		−	22.2423i		−	1.26944i	−0.772744	−	0.634718i	$-0.781116\pi$
$307$		−	22.2423i		−	1.26944i	0.772744	−	0.634718i	$-0.218884\pi$
$308$	24.2949	−	14.0267i	1.38433	−	0.799243i
$309$	−3.42522	+	5.93265i	−0.194854	+	0.337497i
$310$		0			0
$311$	−0.405220			−0.0229779			−0.0114890	−	0.999934i	$-0.503657\pi$
$311$	−0.405220			−0.0229779			−0.0114890	+	0.999934i	$0.503657\pi$
$312$	−1.09275	−	7.12783i	−0.0618646	−	0.403534i
$313$			0.353504i			0.0199812i	0.999950	+	0.00999061i	$0.00318016\pi$
$313$			0.353504i			0.0199812i	−0.999950	+	0.00999061i	$0.996820\pi$
$314$	−0.244870	+	0.424128i	−0.0138188	+	0.0239349i
$315$		0			0
$316$	1.89076	+	3.27488i	0.106363	+	0.184227i
$317$			25.3028i			1.42115i	0.703622	+	0.710574i	$0.251565\pi$
$317$			25.3028i			1.42115i	−0.703622	+	0.710574i	$0.748435\pi$
$318$	6.42465	−	3.70928i	0.360277	−	0.208006i
$319$	6.00000	+	10.3923i	0.335936	+	0.581857i
$320$		0			0
$321$	7.77985	+	13.4751i	0.434229	+	0.752107i
$322$	−19.0486	−	10.9977i	−1.06154	−	0.612880i
$323$	12.3959	+	7.15676i	0.689724	+	0.398213i
$324$	1.70928			0.0949597
$325$		0			0
$326$	7.89601			0.437319
$327$	13.7153	+	7.91855i	0.758460	+	0.437897i
$328$	−6.49785	−	3.75154i	−0.358784	−	0.207144i
$329$	1.29432	+	2.24183i	0.0713581	+	0.123596i
$330$		0			0
$331$	−2.30098	−	3.98542i	−0.126474	−	0.219059i	0.795834	−	0.605514i	$-0.207033\pi$
$331$	−2.30098	−	3.98542i	−0.126474	−	0.219059i	−0.922308	+	0.386456i	$0.873699\pi$
$332$	−6.42465	+	3.70928i	−0.352599	+	0.203573i
$333$		−	2.68035i		−	0.146882i
$334$	1.31965	+	2.28571i	0.0722083	+	0.125068i
$335$		0			0
$336$	−5.61757	+	9.72991i	−0.306463	+	0.530810i
$337$		−	31.0338i		−	1.69052i	−0.534354	−	0.845261i	$-0.679445\pi$
$337$		−	31.0338i		−	1.69052i	0.534354	−	0.845261i	$-0.320555\pi$
$338$	4.74165	−	5.16229i	0.257912	−	0.280791i
$339$	−3.07838			−0.167195
$340$		0			0
$341$	5.21235	−	9.02805i	0.282264	−	0.488896i
$342$	−2.32125	+	1.34017i	−0.125519	+	0.0724683i
$343$			43.4463i			2.34588i
$344$	1.58864	+	2.75160i	0.0856536	+	0.148356i
$345$		0			0
$346$	9.46800			0.509003
$347$	−15.5508	+	8.97826i	−0.834811	+	0.481978i	−0.855497	−	0.517808i	$-0.826748\pi$
$347$	−15.5508	+	8.97826i	−0.834811	+	0.481978i	0.0206863	+	0.999786i	$0.493415\pi$
$348$	−5.19615	−	3.00000i	−0.278543	−	0.160817i
$349$	0.0505820	−	0.0876107i	0.00270759	−	0.00468969i	−0.864668	−	0.502343i	$-0.832471\pi$
$349$	0.0505820	−	0.0876107i	0.00270759	−	0.00468969i	0.867376	+	0.497653i	$0.165805\pi$
$350$		0			0
$351$	2.25513	+	2.81325i	0.120370	+	0.150160i
$352$			17.9877i			0.958748i
$353$	−25.4271	−	14.6803i	−1.35335	−	0.781356i	−0.364631	−	0.931152i	$-0.618805\pi$
$353$	−25.4271	−	14.6803i	−1.35335	−	0.781356i	−0.988717	+	0.149796i	$0.952138\pi$
$354$	2.26600	−	3.92483i	0.120437	−	0.208602i
$355$		0			0
$356$	11.9877			0.635348
$357$	11.9717	−	6.91189i	0.633611	−	0.365816i
$358$	0.646588	−	0.373308i	0.0341732	−	0.0197299i
$359$	11.5369			0.608895			0.304448	−	0.952529i	$-0.401528\pi$
$359$	11.5369			0.608895			0.304448	+	0.952529i	$0.401528\pi$
$360$		0			0
$361$	−2.85577	+	4.94634i	−0.150304	+	0.260334i
$362$	−3.48719	−	2.01333i	−0.183283	−	0.105818i
$363$			0.686489i			0.0360313i
$364$	−29.2462	+	4.48365i	−1.53292	+	0.235007i
$365$		0			0
$366$	0.822114	−	1.42394i	0.0429726	−	0.0744307i
$367$	30.8562	+	17.8148i	1.61068	+	0.929927i	0.989213	+	0.146488i	$0.0467968\pi$
$367$	30.8562	+	17.8148i	1.61068	+	0.929927i	0.621468	+	0.783439i	$0.286536\pi$
$368$	−17.2203	+	9.94214i	−0.897670	+	0.518270i
$369$	3.75154			0.195297
$370$		0			0
$371$	−33.0277	−	57.2057i	−1.71471	−	2.96997i
$372$			5.21235i			0.270248i
$373$	8.32374	−	4.80571i	0.430987	−	0.248830i	−0.268780	−	0.963202i	$-0.586621\pi$
$373$	8.32374	−	4.80571i	0.430987	−	0.248830i	0.699767	+	0.714371i	$0.253287\pi$
$374$	2.65368	−	4.59632i	0.137219	−	0.237670i
$375$		0			0
$376$	−1.07838			−0.0556131
$377$	−1.91791	−	12.5103i	−0.0987775	−	0.644311i
$378$			2.58864i			0.133145i
$379$	3.51139	−	6.08191i	0.180368	−	0.312407i	−0.761638	−	0.648003i	$-0.775604\pi$
$379$	3.51139	−	6.08191i	0.180368	−	0.312407i	0.942006	+	0.335596i	$0.108938\pi$
$380$		0			0
$381$	−3.72733	−	6.45593i	−0.190957	−	0.330747i
$382$			1.29687i			0.0663535i
$383$	−17.5053	+	10.1067i	−0.894480	+	0.516428i	−0.875405	−	0.483390i	$-0.839405\pi$
$383$	−17.5053	+	10.1067i	−0.894480	+	0.516428i	−0.0190745	+	0.999818i	$0.506072\pi$
$384$	−5.75872	−	9.97440i	−0.293874	−	0.509004i
$385$		0			0
$386$	−4.26539	−	7.38787i	−0.217103	−	0.376033i
$387$	−1.37580	−	0.794319i	−0.0699359	−	0.0403775i
$388$	21.1220	+	12.1948i	1.07231	+	0.619098i
$389$	15.7587			0.798999			0.399500	−	0.916733i	$-0.369184\pi$
$389$	15.7587			0.798999			0.399500	+	0.916733i	$0.369184\pi$
$390$		0			0
$391$	24.4657			1.23729
$392$	−27.7985	−	16.0494i	−1.40403	−	0.810620i
$393$	−10.1270	−	5.84684i	−0.510841	−	0.294934i
$394$	−4.97826	−	8.62260i	−0.250801	−	0.434400i
$395$		0			0
$396$	−2.92162	−	5.06040i	−0.146817	−	0.254295i
$397$	9.82710	−	5.67368i	0.493208	−	0.284754i	−0.232696	−	0.972549i	$-0.574755\pi$
$397$	9.82710	−	5.67368i	0.493208	−	0.284754i	0.725904	+	0.687796i	$0.241421\pi$
$398$			5.89988i			0.295734i
$399$	11.9330	+	20.6686i	0.597398	+	1.03472i
$400$		0			0
$401$	−13.3268	+	23.0828i	−0.665511	+	1.15270i	0.313636	+	0.949543i	$0.398453\pi$
$401$	−13.3268	+	23.0828i	−0.665511	+	1.15270i	−0.979147	+	0.203155i	$0.934880\pi$
$402$		−	6.92881i		−	0.345578i
$403$	−8.57887	+	6.87690i	−0.427344	+	0.342563i
$404$	21.3607			1.06273
$405$		0			0
$406$	4.54339	−	7.86939i	0.225485	−	0.390551i
$407$	−7.93530	+	4.58145i	−0.393338	+	0.227094i
$408$			5.75872i			0.285099i
$409$	−15.4463	−	26.7539i	−0.763773	−	1.32289i	−0.940893	−	0.338704i	$-0.890012\pi$
$409$	−15.4463	−	26.7539i	−0.763773	−	1.32289i	0.177120	−	0.984189i	$-0.443322\pi$
$410$		0			0
$411$	9.27739			0.457620
$412$	−10.1405	+	5.85464i	−0.499588	+	0.288437i
$413$	−34.9470	−	20.1767i	−1.71963	−	0.992829i
$414$	−2.29072	+	3.96765i	−0.112583	+	0.194999i
$415$		0			0
$416$	6.88655	−	17.6777i	0.337641	−	0.866719i
$417$		−	12.9155i		−	0.632474i
$418$	7.93530	+	4.58145i	0.388128	+	0.224086i
$419$	17.1581	−	29.7187i	0.838227	−	1.45185i	−0.0531484	−	0.998587i	$-0.516926\pi$
$419$	17.1581	−	29.7187i	0.838227	−	1.45185i	0.891376	−	0.453265i	$-0.149741\pi$
$420$		0			0
$421$	−13.5320			−0.659509			−0.329755	−	0.944067i	$-0.606966\pi$
$421$	−13.5320			−0.659509			−0.329755	+	0.944067i	$0.606966\pi$
$422$	6.62010	−	3.82211i	0.322261	−	0.186058i
$423$	0.466951	−	0.269594i	0.0227039	−	0.0131081i
$424$	27.5174			1.33637
$425$		0			0
$426$	−0.563913	+	0.976726i	−0.0273217	+	0.0473225i
$427$	−12.6789	−	7.32018i	−0.613576	−	0.354248i
$428$			26.5958i			1.28556i
$429$	4.47414	−	11.4851i	0.216014	−	0.554504i
$430$		0			0
$431$	−7.63090	+	13.2171i	−0.367567	+	0.636645i	−0.989185	−	0.146676i	$-0.953143\pi$
$431$	−7.63090	+	13.2171i	−0.367567	+	0.636645i	0.621617	+	0.783321i	$0.286476\pi$
$432$	2.02665	+	1.17009i	0.0975072	+	0.0562958i
$433$	−3.35963	+	1.93968i	−0.161453	+	0.0932151i	−0.578550	−	0.815647i	$-0.696381\pi$
$433$	−3.35963	+	1.93968i	−0.161453	+	0.0932151i	0.417096	+	0.908862i	$0.363048\pi$
$434$	−7.89392			−0.378920
$435$		0			0
$436$	13.5350	+	23.4433i	0.648208	+	1.12273i
$437$			42.2388i			2.02056i
$438$	2.58653	−	1.49333i	0.123589	−	0.0713543i
$439$	−10.1556	+	17.5901i	−0.484701	+	0.839527i	−0.999846	−	0.0175761i	$-0.994405\pi$
$439$	−10.1556	+	17.5901i	−0.484701	+	0.839527i	0.515144	+	0.857104i	$0.327738\pi$
$440$		0			0
$441$	16.0494			0.764259
$442$	−4.36763	+	3.50113i	−0.207747	+	0.166532i
$443$			35.0772i			1.66657i	0.552847	+	0.833283i	$0.313542\pi$
$443$			35.0772i			1.66657i	−0.552847	+	0.833283i	$0.686458\pi$
$444$	2.29072	−	3.96765i	0.108713	−	0.188296i
$445$		0			0
$446$	−1.52586	−	2.64286i	−0.0722515	−	0.125143i
$447$			2.00000i			0.0945968i
$448$	−7.66379	+	4.42469i	−0.362080	+	0.209047i
$449$	3.98667	+	6.90511i	0.188143	+	0.325872i	0.944631	−	0.328135i	$-0.106420\pi$
$449$	3.98667	+	6.90511i	0.188143	+	0.325872i	−0.756488	+	0.654007i	$0.773087\pi$
$450$		0			0
$451$	−6.41241	−	11.1066i	−0.301948	−	0.522990i
$452$	−4.55685	−	2.63090i	−0.214336	−	0.123747i
$453$	7.45149	+	4.30212i	0.350101	+	0.202131i
$454$	11.2579			0.528360
$455$		0			0
$456$	−9.94214			−0.465583
$457$	−2.25960	−	1.30458i	−0.105699	−	0.0610256i	0.446218	−	0.894924i	$-0.352770\pi$
$457$	−2.25960	−	1.30458i	−0.105699	−	0.0610256i	−0.551918	+	0.833899i	$0.686104\pi$
$458$	5.39446	+	3.11450i	0.252067	+	0.145531i
$459$	−1.43968	−	2.49360i	−0.0671986	−	0.116391i
$460$		0			0
$461$	15.0397	+	26.0495i	0.700469	+	1.21325i	0.968302	+	0.249783i	$0.0803592\pi$
$461$	15.0397	+	26.0495i	0.700469	+	1.21325i	−0.267833	+	0.963465i	$0.586307\pi$
$462$	7.66379	−	4.42469i	0.356552	−	0.205855i
$463$			6.36788i			0.295940i	0.988992	+	0.147970i	$0.0472740\pi$
$463$			6.36788i			0.295940i	−0.988992	+	0.147970i	$0.952726\pi$
$464$	−4.10731	−	7.11406i	−0.190677	−	0.330262i
$465$		0			0
$466$	−1.00614	+	1.74269i	−0.0466087	+	0.0807286i
$467$		−	2.06892i		−	0.0957383i	−0.998854	−	0.0478692i	$-0.984757\pi$
$467$		−	2.06892i		−	0.0957383i	0.998854	−	0.0478692i	$-0.0152431\pi$
$468$	0.933903	+	6.09171i	0.0431697	+	0.281589i
$469$	−61.6947			−2.84880
$470$		0			0
$471$	0.454146	−	0.786603i	0.0209259	−	0.0362448i
$472$	14.5583	−	8.40522i	0.670099	−	0.386882i
$473$			5.43084i			0.249710i
$474$	0.596436	+	1.03306i	0.0273952	+	0.0474499i
$475$		0			0
$476$	23.6286			1.08302
$477$	−11.9154	+	6.87936i	−0.545569	+	0.314984i
$478$	−12.6510	−	7.30406i	−0.578643	−	0.334080i
$479$	5.75513	−	9.96818i	0.262959	−	0.455458i	−0.704068	−	0.710132i	$-0.748635\pi$
$479$	5.75513	−	9.96818i	0.262959	−	0.455458i	0.967027	+	0.254675i	$0.0819684\pi$
$480$		0			0
$481$	9.55252	−	1.46447i	0.435557	−	0.0667741i
$482$			12.7238i			0.579555i
$483$	35.3283	+	20.3968i	1.60749	+	0.928087i
$484$	−0.586699	+	1.01619i	−0.0266682	+	0.0461906i
$485$		0			0
$486$	0.539189			0.0244581
$487$	17.4490	−	10.0742i	0.790689	−	0.456504i	−0.0495162	−	0.998773i	$-0.515768\pi$
$487$	17.4490	−	10.0742i	0.790689	−	0.456504i	0.840205	+	0.542269i	$0.182435\pi$
$488$	5.28180	−	3.04945i	0.239096	−	0.138042i
$489$	−14.6442			−0.662235
$490$		0			0
$491$	10.9408	−	18.9500i	0.493752	−	0.855204i	−0.506222	−	0.862403i	$-0.668958\pi$
$491$	10.9408	−	18.9500i	0.493752	−	0.855204i	0.999974	+	0.00719955i	$0.00229171\pi$
$492$	5.55331	+	3.20620i	0.250362	+	0.144547i
$493$			10.1073i			0.455210i
$494$	−6.04453	−	7.54049i	−0.271956	−	0.339263i
$495$		0			0
$496$	−3.56812	+	6.18016i	−0.160213	+	0.277497i
$497$	8.69685	+	5.02113i	0.390107	+	0.225228i
$498$	−2.02665	+	1.17009i	−0.0908163	+	0.0524328i
$499$	23.8225			1.06644			0.533222	−	0.845975i	$-0.320981\pi$
$499$	23.8225			1.06644			0.533222	+	0.845975i	$0.320981\pi$
$500$		0			0
$501$	−2.44748	−	4.23916i	−0.109345	−	0.189392i
$502$			14.4846i			0.646481i
$503$	−3.73168	+	2.15449i	−0.166388	+	0.0960639i	−0.580881	−	0.813988i	$-0.697292\pi$
$503$	−3.73168	+	2.15449i	−0.166388	+	0.0960639i	0.414494	+	0.910052i	$0.363959\pi$
$504$	−4.80098	+	8.31555i	−0.213853	+	0.370404i
$505$		0			0
$506$	15.6619			0.696257
$507$	−8.79404	+	9.57417i	−0.390557	+	0.425204i
$508$		−	12.7421i		−	0.565338i
$509$	0.496928	−	0.860705i	0.0220260	−	0.0381501i	−0.854802	−	0.518954i	$-0.826322\pi$
$509$	0.496928	−	0.860705i	0.0220260	−	0.0381501i	0.876828	+	0.480804i	$0.159655\pi$
$510$		0			0
$511$	−13.2968	−	23.0307i	−0.588215	−	1.01882i
$512$		−	21.6742i		−	0.957873i
$513$	4.30507	−	2.48554i	0.190074	−	0.109739i
$514$	0.948614	+	1.64305i	0.0418416	+	0.0724717i
$515$		0			0
$516$	−1.35771	−	2.35162i	−0.0597698	−	0.103524i
$517$	−1.59630	−	0.921622i	−0.0702050	−	0.0405329i
$518$	6.00887	+	3.46922i	0.264015	+	0.152429i
$519$	−17.5597			−0.770786
$520$		0			0
$521$	9.75154			0.427223			0.213611	−	0.976919i	$-0.431477\pi$
$521$	9.75154			0.427223			0.213611	+	0.976919i	$0.431477\pi$
$522$	−1.63912	−	0.946346i	−0.0717423	−	0.0414205i
$523$	−9.54405	−	5.51026i	−0.417332	−	0.240947i	0.276603	−	0.960984i	$-0.410791\pi$
$523$	−9.54405	−	5.51026i	−0.417332	−	0.240947i	−0.693935	+	0.720037i	$0.744125\pi$
$524$	−9.99386	−	17.3099i	−0.436584	−	0.756185i
$525$		0			0
$526$	−2.38664	−	4.13378i	−0.104062	−	0.180241i
$527$	7.60411	−	4.39023i	0.331240	−	0.191242i
$528$		−	8.00000i		−	0.348155i
$529$	24.5989	+	42.6065i	1.06952	+	1.85246i
$530$		0			0
$531$	−4.20261	+	7.27913i	−0.182378	+	0.315888i
$532$			40.7936i			1.76863i
$533$	2.04974	+	13.3701i	0.0887841	+	0.579125i
$534$	3.78151			0.163642
$535$		0			0
$536$	12.8504	−	22.2576i	0.555054	−	0.961382i
$537$	−1.19919	+	0.692350i	−0.0517487	+	0.0298771i
$538$			14.6888i			0.633277i
$539$	−27.4329	−	47.5152i	−1.18162	−	2.04663i
$540$		0			0
$541$	−6.28846			−0.270362			−0.135181	−	0.990821i	$-0.543162\pi$
$541$	−6.28846			−0.270362			−0.135181	+	0.990821i	$0.543162\pi$
$542$	−6.47370	+	3.73759i	−0.278069	+	0.160543i
$543$	6.46748	+	3.73400i	0.277546	+	0.160241i
$544$	−7.57531	+	13.1208i	−0.324789	+	0.562550i
$545$		0			0
$546$	−9.22568	+	1.41436i	−0.394823	+	0.0605291i
$547$			27.6875i			1.18383i	0.805999	+	0.591917i	$0.201629\pi$
$547$			27.6875i			1.18383i	−0.805999	+	0.591917i	$0.798371\pi$
$548$	13.7331	+	7.92881i	0.586649	+	0.338702i
$549$	−1.52472	+	2.64090i	−0.0650736	+	0.112711i
$550$		0			0
$551$	−17.4497			−0.743384
$552$	−14.7171	+	8.49693i	−0.626402	+	0.361653i
$553$	9.19844	−	5.31072i	0.391157	−	0.225835i
$554$	1.39189			0.0591357
$555$		0			0
$556$	11.0381	−	19.1185i	0.468118	−	0.810804i
$557$	18.5885	+	10.7321i	0.787619	+	0.454732i	0.839124	−	0.543941i	$-0.183068\pi$
$557$	18.5885	+	10.7321i	0.787619	+	0.454732i	−0.0515046	+	0.998673i	$0.516402\pi$
$558$			1.64423i			0.0696057i
$559$	2.07918	−	5.33723i	0.0879400	−	0.225741i
$560$		0			0
$561$	−4.92162	+	8.52450i	−0.207791	+	0.359905i
$562$	−2.49983	−	1.44327i	−0.105449	−	0.0608809i
$563$	13.5743	−	7.83710i	0.572087	−	0.330294i	−0.185896	−	0.982570i	$-0.559519\pi$
$563$	13.5743	−	7.83710i	0.572087	−	0.330294i	0.757982	+	0.652275i	$0.226185\pi$
$564$	0.921622			0.0388073
$565$		0			0
$566$	4.28486	+	7.42160i	0.180106	+	0.311953i
$567$		−	4.80098i		−	0.201622i
$568$	−3.62295	+	2.09171i	−0.152015	+	0.0877661i
$569$	8.21594	−	14.2304i	0.344430	−	0.596571i	−0.640820	−	0.767691i	$-0.721405\pi$
$569$	8.21594	−	14.2304i	0.344430	−	0.596571i	0.985250	+	0.171121i	$0.0547388\pi$
$570$		0			0
$571$	14.6765			0.614191			0.307096	−	0.951679i	$-0.400643\pi$
$571$	14.6765			0.614191			0.307096	+	0.951679i	$0.400643\pi$
$572$	16.4385	−	13.1773i	0.687329	−	0.550970i
$573$		−	2.40522i		−	0.100479i
$574$	−4.85568	+	8.41029i	−0.202672	+	0.351039i
$575$		0			0
$576$	0.921622	+	1.59630i	0.0384009	+	0.0665124i
$577$		−	17.8622i		−	0.743611i	−0.928311	−	0.371806i	$-0.878739\pi$
$577$		−	17.8622i		−	0.743611i	0.928311	−	0.371806i	$-0.121261\pi$
$578$	−4.06681	+	2.34797i	−0.169157	+	0.0976628i
$579$	7.91075	+	13.7018i	0.328760	+	0.569428i
$580$		0			0
$581$	10.4186	+	18.0455i	0.432234	+	0.748652i
$582$	6.66292	+	3.84684i	0.276187	+	0.159457i
$583$	40.7334	+	23.5174i	1.68701	+	0.973993i
$584$	11.0784			0.458427
$585$		0			0
$586$	1.33791			0.0552684
$587$	3.83084	+	2.21174i	0.158116	+	0.0912881i	0.576970	−	0.816765i	$-0.304235\pi$
$587$	3.83084	+	2.21174i	0.158116	+	0.0912881i	−0.418854	+	0.908053i	$0.637568\pi$
$588$	23.7576	+	13.7165i	0.979747	+	0.565657i
$589$	7.57951	+	13.1281i	0.312308	+	0.540934i
$590$		0			0
$591$	9.23287	+	15.9918i	0.379789	+	0.657814i
$592$	5.43212	−	3.13624i	0.223259	−	0.128899i
$593$		−	12.5380i		−	0.514873i	−0.966295	−	0.257436i	$-0.917122\pi$
$593$		−	12.5380i		−	0.514873i	0.966295	−	0.257436i	$-0.0828777\pi$
$594$	−0.921622	−	1.59630i	−0.0378146	−	0.0654968i
$595$		0			0
$596$	−1.70928	+	2.96055i	−0.0700146	+	0.121269i
$597$		−	10.9421i		−	0.447832i
$598$	−15.3920	−	5.99612i	−0.629424	−	0.245200i
$599$	−23.5825			−0.963555			−0.481777	−	0.876294i	$-0.660009\pi$
$599$	−23.5825			−0.963555			−0.481777	+	0.876294i	$0.660009\pi$
$600$		0			0
$601$	−1.64229	+	2.84453i	−0.0669904	+	0.116031i	−0.897575	−	0.440861i	$-0.854673\pi$
$601$	−1.64229	+	2.84453i	−0.0669904	+	0.116031i	0.830585	+	0.556892i	$0.188006\pi$
$602$	3.56145	−	2.05620i	0.145154	−	0.0838046i
$603$			12.8504i			0.523310i
$604$	7.35350	+	12.7366i	0.299210	+	0.518247i
$605$		0			0
$606$	6.73820			0.273721
$607$	−5.20344	+	3.00421i	−0.211201	+	0.121937i	−0.601869	−	0.798595i	$-0.705577\pi$
$607$	−5.20344	+	3.00421i	−0.211201	+	0.121937i	0.390668	+	0.920531i	$0.372244\pi$
$608$	−22.6524	−	13.0784i	−0.918677	−	0.530398i
$609$	−8.42635	+	14.5949i	−0.341453	+	0.591414i
$610$		0			0
$611$	1.21594	+	1.51687i	0.0491917	+	0.0613662i
$612$		−	4.92162i		−	0.198945i
$613$	−4.78979	−	2.76539i	−0.193458	−	0.111693i	0.400142	−	0.916453i	$-0.368961\pi$
$613$	−4.78979	−	2.76539i	−0.193458	−	0.111693i	−0.593600	+	0.804760i	$0.702294\pi$
$614$	5.99641	−	10.3861i	0.241995	−	0.419148i
$615$		0			0
$616$	32.8248			1.32255
$617$	10.2921	−	5.94214i	0.414344	−	0.239222i	−0.278311	−	0.960491i	$-0.589774\pi$
$617$	10.2921	−	5.94214i	0.414344	−	0.239222i	0.692654	+	0.721270i	$0.256441\pi$
$618$	−3.19882	+	1.84684i	−0.128675	+	0.0742907i
$619$	−32.2183			−1.29496			−0.647482	−	0.762081i	$-0.724178\pi$
$619$	−32.2183			−1.29496			−0.647482	+	0.762081i	$0.724178\pi$
$620$		0			0
$621$	4.24846	−	7.35856i	0.170485	−	0.295289i
$622$	−0.189218	−	0.109245i	−0.00758695	−	0.00438032i
$623$		−	33.6709i		−	1.34900i
$624$	−3.06278	+	7.86211i	−0.122609	+	0.314736i
$625$		0			0
$626$	−0.0953027	+	0.165069i	−0.00380906	+	0.00659749i
$627$	−14.7171	−	8.49693i	−0.587745	−	0.339335i
$628$	1.34452	−	0.776260i	0.0536523	−	0.0309761i
$629$	−7.71769			−0.307724
$630$		0			0
$631$	9.87209	+	17.0990i	0.393002	+	0.680699i	0.992844	−	0.119420i	$-0.0381034\pi$
$631$	9.87209	+	17.0990i	0.393002	+	0.680699i	−0.599842	+	0.800118i	$0.704770\pi$
$632$			4.42469i			0.176005i
$633$	−12.2779	+	7.08864i	−0.488002	+	0.281748i
$634$	−6.82150	+	11.8152i	−0.270916	+	0.469241i
$635$		0			0
$636$	−23.5174			−0.932527
$637$	8.76899	+	57.1988i	0.347440	+	2.26630i
$638$			6.47027i			0.256160i
$639$	1.04585	−	1.81147i	0.0413734	−	0.0716608i
$640$		0			0
$641$	−18.0566	−	31.2750i	−0.713194	−	1.23529i	−0.963652	−	0.267161i	$-0.913914\pi$
$641$	−18.0566	−	31.2750i	−0.713194	−	1.23529i	0.250458	−	0.968128i	$-0.419419\pi$
$642$			8.38962i			0.331112i
$643$	−33.9328	+	19.5911i	−1.33818	+	0.772597i	−0.986537	−	0.163537i	$-0.947710\pi$
$643$	−33.9328	+	19.5911i	−1.33818	+	0.772597i	−0.351641	+	0.936135i	$0.614376\pi$
$644$	34.8638	+	60.3858i	1.37382	+	2.37953i
$645$		0			0
$646$	3.85884	+	6.68371i	0.151824	+	0.262967i
$647$	36.5213	+	21.0856i	1.43580	+	0.828959i	0.997554	−	0.0698964i	$-0.0222669\pi$
$647$	36.5213	+	21.0856i	1.43580	+	0.828959i	0.438245	+	0.898856i	$0.355600\pi$
$648$	1.73205	+	1.00000i	0.0680414	+	0.0392837i
$649$	28.7337			1.12790
$650$		0			0
$651$	14.6404			0.573801
$652$	−21.6775	−	12.5155i	−0.848956	−	0.490145i
$653$	−29.3120	−	16.9233i	−1.14707	−	0.662259i	−0.198896	−	0.980021i	$-0.563735\pi$
$653$	−29.3120	−	16.9233i	−1.14707	−	0.662259i	−0.948171	+	0.317762i	$0.897069\pi$
$654$	4.26959	+	7.39515i	0.166954	+	0.289173i
$655$		0			0
$656$	4.38962	+	7.60305i	0.171386	+	0.296849i
$657$	−4.79708	+	2.76959i	−0.187152	+	0.108052i
$658$			1.39576i			0.0544126i
$659$	−15.7659	−	27.3074i	−0.614153	−	1.06374i	−0.990533	−	0.137278i	$-0.956165\pi$
$659$	−15.7659	−	27.3074i	−0.614153	−	1.06374i	0.376380	−	0.926465i	$-0.377169\pi$
$660$		0			0
$661$	3.18876	−	5.52309i	0.124028	−	0.214823i	−0.797324	−	0.603551i	$-0.793752\pi$
$661$	3.18876	−	5.52309i	0.124028	−	0.214823i	0.921353	+	0.388728i	$0.127085\pi$
$662$		−	2.48133i		−	0.0964396i
$663$	8.10037	−	6.49333i	0.314592	−	0.252180i
$664$	−8.68035			−0.336863
$665$		0			0
$666$	0.722606	−	1.25159i	0.0280004	−	0.0484982i
$667$	−25.8304	+	14.9132i	−1.00016	+	0.577442i
$668$		−	8.36683i		−	0.323723i
$669$	2.82991	+	4.90155i	0.109411	+	0.189505i
$670$		0			0
$671$	10.4247			0.402441
$672$	−21.8774	+	12.6309i	−0.843937	+	0.487247i
$673$	8.42002	+	4.86130i	0.324568	+	0.187389i	0.653427	−	0.756990i	$-0.273331\pi$
$673$	8.42002	+	4.86130i	0.324568	+	0.187389i	−0.328859	+	0.944379i	$0.606664\pi$
$674$	8.36655	−	14.4913i	0.322268	−	0.558184i
$675$		0			0
$676$	−21.2001	+	6.65669i	−0.815387	+	0.256027i
$677$		−	10.0845i		−	0.387580i	−0.981043	−	0.193790i	$-0.937922\pi$
$677$		−	10.0845i		−	0.387580i	0.981043	−	0.193790i	$-0.0620780\pi$
$678$	−1.43745	−	0.829914i	−0.0552050	−	0.0318726i
$679$	34.2526	−	59.3272i	1.31449	−	2.27677i
$680$		0			0
$681$	−20.8794			−0.800099
$682$	4.86782	−	2.81044i	0.186399	−	0.107617i
$683$	5.83440	−	3.36849i	0.223247	−	0.128892i	−0.384206	−	0.923247i	$-0.625525\pi$
$683$	5.83440	−	3.36849i	0.223247	−	0.128892i	0.607453	+	0.794356i	$0.292191\pi$
$684$	8.49693			0.324888
$685$		0			0
$686$	−11.7129	+	20.2873i	−0.447199	+	0.774572i
$687$	−10.0048	−	5.77626i	−0.381706	−	0.220378i
$688$		−	3.71769i		−	0.141735i
$689$	−31.0277	−	38.7068i	−1.18206	−	1.47461i
$690$		0			0
$691$	8.97220	−	15.5403i	0.341319	−	0.591181i	−0.643359	−	0.765565i	$-0.722460\pi$
$691$	8.97220	−	15.5403i	0.341319	−	0.591181i	0.984678	+	0.174383i	$0.0557931\pi$
$692$	−25.9932	−	15.0072i	−0.988114	−	0.570488i
$693$	−14.2136	+	8.20620i	−0.539929	+	0.311728i
$694$	−9.68195			−0.367522
$695$		0			0
$696$	−3.51026	−	6.07995i	−0.133056	−	0.230460i
$697$		−	10.8020i		−	0.409156i
$698$	0.0472387	−	0.0272733i	0.00178801	−	0.00103231i
$699$	1.86603	−	3.23206i	0.0705798	−	0.122248i
$700$		0			0
$701$	41.2762			1.55898			0.779490	−	0.626415i	$-0.215478\pi$
$701$	41.2762			1.55898			0.779490	+	0.626415i	$0.215478\pi$
$702$	0.294598	+	1.92162i	0.0111189	+	0.0725270i
$703$		−	13.3242i		−	0.502531i
$704$	3.15061	−	5.45702i	0.118743	−	0.205669i
$705$		0			0
$706$	−7.91548	−	13.7100i	−0.297903	−	0.515983i
$707$		−	59.9976i		−	2.25644i
$708$	−12.4420	+	7.18342i	−0.467601	+	0.269969i
$709$	0.732866	+	1.26936i	0.0275234	+	0.0476718i	0.879459	−	0.475975i	$-0.157905\pi$
$709$	0.732866	+	1.26936i	0.0275234	+	0.0476718i	−0.851936	+	0.523647i	$0.824571\pi$
$710$		0			0
$711$	−1.10617	−	1.91595i	−0.0414847	−	0.0718537i
$712$	12.1474	+	7.01333i	0.455245	+	0.262836i
$713$	22.4395	+	12.9555i	0.840367	+	0.485186i
$714$	7.45362			0.278945
$715$		0			0
$716$	−2.36683			−0.0884528
$717$	23.4630	+	13.5464i	0.876242	+	0.505899i
$718$	5.38718	+	3.11029i	0.201048	+	0.116075i
$719$	−4.80685	−	8.32570i	−0.179265	−	0.310496i	0.762364	−	0.647149i	$-0.224039\pi$
$719$	−4.80685	−	8.32570i	−0.179265	−	0.310496i	−0.941629	+	0.336652i	$0.890705\pi$
$720$		0			0
$721$	16.4444	+	28.4826i	0.612422	+	1.06075i
$722$	−2.66701	+	1.53980i	−0.0992559	+	0.0573054i
$723$		−	23.5981i		−	0.877623i
$724$	6.38243	+	11.0547i	0.237201	+	0.410845i
$725$		0			0
$726$	−0.185074	+	0.320557i	−0.00686873	+	0.0118970i
$727$		−	42.6547i		−	1.58198i	−0.611831	−	0.790988i	$-0.709567\pi$
$727$		−	42.6547i		−	1.58198i	0.611831	−	0.790988i	$-0.290433\pi$
$728$	−32.2590	−	12.5669i	−1.19560	−	0.465760i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−2.28713	+	3.96143i	−0.0845926	+	0.146519i
$732$	−4.51402	+	2.60617i	−0.166843	+	0.0963269i
$733$			6.48360i			0.239477i	0.992805	+	0.119739i	$0.0382056\pi$
$733$			6.48360i			0.239477i	−0.992805	+	0.119739i	$0.961794\pi$
$734$	9.60556	+	16.6373i	0.354548	+	0.614095i
$735$		0			0
$736$	−44.7091			−1.64800
$737$	38.0444	−	21.9649i	1.40138	−	0.809089i
$738$	1.75178	+	1.01139i	0.0644841	+	0.0372299i
$739$	−21.1845	+	36.6926i	−0.779283	+	1.34976i	0.153072	+	0.988215i	$0.451083\pi$
$739$	−21.1845	+	36.6926i	−0.779283	+	1.34976i	−0.932355	+	0.361543i	$0.882250\pi$
$740$		0			0
$741$	11.2104	+	13.9849i	0.411825	+	0.513747i
$742$		−	35.6163i		−	1.30752i
$743$	−15.0945	−	8.71481i	−0.553763	−	0.319715i	0.196875	−	0.980429i	$-0.436921\pi$
$743$	−15.0945	−	8.71481i	−0.553763	−	0.319715i	−0.750638	+	0.660713i	$0.770254\pi$
$744$	−3.04945	+	5.28180i	−0.111798	+	0.193640i
$745$		0			0
$746$	5.18237			0.189740
$747$	3.75870	−	2.17009i	0.137524	−	0.0793993i
$748$	−14.5707	+	8.41241i	−0.532758	+	0.307588i
$749$	74.7019			2.72955
$750$		0			0
$751$	−6.68455	+	11.5780i	−0.243923	+	0.422487i	−0.961828	−	0.273654i	$-0.911768\pi$
$751$	−6.68455	+	11.5780i	−0.243923	+	0.422487i	0.717905	+	0.696141i	$0.245101\pi$
$752$	1.09275	+	0.630898i	0.0398484	+	0.0230065i
$753$		−	26.8638i		−	0.978970i
$754$	2.47712	−	6.35874i	0.0902116	−	0.231572i
$755$		0			0
$756$	4.10310	−	7.10678i	0.149228	−	0.258471i
$757$	−23.9824	−	13.8462i	−0.871654	−	0.503250i	−0.00375649	−	0.999993i	$-0.501196\pi$
$757$	−23.9824	−	13.8462i	−0.871654	−	0.503250i	−0.867898	+	0.496743i	$0.834529\pi$
$758$	3.27930	−	1.89330i	0.119110	−	0.0687679i
$759$	−29.0472			−1.05435
$760$		0			0
$761$	0.261795	+	0.453443i	0.00949007	+	0.0164373i	0.870731	−	0.491759i	$-0.163646\pi$
$761$	0.261795	+	0.453443i	0.00949007	+	0.0164373i	−0.861241	+	0.508196i	$0.830313\pi$
$762$		−	4.01947i		−	0.145610i
$763$	65.8471	−	38.0168i	2.38382	−	1.37630i
$764$	2.05559	−	3.56039i	0.0743687	−	0.128810i
$765$		0			0
$766$	−10.8988			−0.393791
$767$	−28.2384	−	11.0006i	−1.01963	−	0.397209i
$768$		−	2.52359i		−	0.0910622i
$769$	−7.08032	+	12.2635i	−0.255323	+	0.442232i	−0.964983	−	0.262312i	$-0.915515\pi$
$769$	−7.08032	+	12.2635i	−0.255323	+	0.442232i	0.709660	+	0.704544i	$0.248848\pi$
$770$		0			0
$771$	−1.75933	−	3.04726i	−0.0633609	−	0.109744i
$772$			27.0433i			0.973310i
$773$	−23.7452	+	13.7093i	−0.854054	+	0.493088i	−0.862017	−	0.506880i	$-0.830799\pi$
$773$	−23.7452	+	13.7093i	−0.854054	+	0.493088i	0.00796257	+	0.999968i	$0.497465\pi$
$774$	−0.428288	−	0.741816i	−0.0153945	−	0.0266640i
$775$		0			0
$776$	14.2690	+	24.7146i	0.512227	+	0.887203i
$777$	−11.1443	−	6.43415i	−0.399799	−	0.230824i
$778$	7.35856	+	4.24846i	0.263817	+	0.152315i
$779$	18.6491			0.668175
$780$		0			0
$781$	−7.15061			−0.255869
$782$	11.4243	+	6.59583i	0.408532	+	0.235866i
$783$	3.03997	+	1.75513i	0.108640	+	0.0627232i
$784$	18.7792	+	32.5266i	0.670687	+	1.16166i
$785$		0			0
$786$	−3.15255	−	5.46038i	−0.112448	−	0.194765i
$787$	18.5071	−	10.6851i	0.659707	−	0.380882i	−0.132459	−	0.991189i	$-0.542287\pi$
$787$	18.5071	−	10.6851i	0.659707	−	0.380882i	0.792165	+	0.610307i	$0.208954\pi$
$788$			31.5630i			1.12439i
$789$	4.42635	+	7.66666i	0.157582	+	0.272940i
$790$		0			0
$791$	−7.38962	+	12.7992i	−0.262745	+	0.455087i
$792$		−	6.83710i		−	0.242946i
$793$	−10.2450	−	3.99107i	−0.363811	−	0.141727i
$794$	6.11837			0.217133
$795$		0			0
$796$	9.35157	−	16.1974i	0.331457	−	0.574101i
$797$	3.36495	−	1.94275i	0.119193	−	0.0688158i	−0.439218	−	0.898380i	$-0.644745\pi$
$797$	3.36495	−	1.94275i	0.119193	−	0.0688158i	0.558411	+	0.829564i	$0.311411\pi$
$798$			12.8683i			0.455533i
$799$	−0.776260	−	1.34452i	−0.0274621	−	0.0475658i
$800$		0			0
$801$	−7.01333			−0.247804
$802$	−12.4460	+	7.18568i	−0.439483	+	0.253735i
$803$	16.3991	+	9.46800i	0.578710	+	0.334118i
$804$	−10.9825	+	19.0222i	−0.387322	+	0.670861i
$805$		0			0
$806$	−5.85989	+	0.898363i	−0.206406	+	0.0316435i
$807$		−	27.2423i		−	0.958975i
$808$	21.6453	+	12.4969i	0.761480	+	0.439640i
$809$	−25.4524	+	44.0849i	−0.894859	+	1.54994i	−0.0608794	+	0.998145i	$0.519391\pi$
$809$	−25.4524	+	44.0849i	−0.894859	+	1.54994i	−0.833979	+	0.551796i	$0.813943\pi$
$810$		0			0
$811$	−42.5174			−1.49299			−0.746495	−	0.665391i	$-0.768265\pi$
$811$	−42.5174			−1.49299			−0.746495	+	0.665391i	$0.768265\pi$
$812$	−24.9466	+	14.4030i	−0.875456	+	0.505445i
$813$	12.0064	−	6.93188i	0.421082	−	0.243112i
$814$	−4.94053			−0.173166
$815$		0			0
$816$	3.36910	−	5.83546i	0.117942	−	0.204282i
$817$	−6.83920	−	3.94861i	−0.239273	−	0.138145i
$818$		−	16.6570i		−	0.582398i
$819$	17.1103	−	2.62313i	0.597882	−	0.0916596i
$820$		0			0
$821$	1.99773	−	3.46017i	0.0697213	−	0.120761i	−0.829057	−	0.559164i	$-0.811122\pi$
$821$	1.99773	−	3.46017i	0.0697213	−	0.120761i	0.898779	+	0.438403i	$0.144456\pi$
$822$	4.33209	+	2.50113i	0.151099	+	0.0872371i
$823$	1.36426	−	0.787653i	0.0475549	−	0.0274559i	−0.476034	−	0.879427i	$-0.657926\pi$
$823$	1.36426	−	0.787653i	0.0475549	−	0.0274559i	0.523589	+	0.851971i	$0.324593\pi$
$824$	−13.7009			−0.477292
$825$		0			0
$826$	−10.8790	−	18.8430i	−0.378530	−	0.655633i
$827$			9.17850i			0.319168i	0.987184	+	0.159584i	$0.0510152\pi$
$827$			9.17850i			0.319168i	−0.987184	+	0.159584i	$0.948985\pi$
$828$	12.5778	−	7.26180i	0.437109	−	0.252365i
$829$	24.7358	−	42.8437i	0.859112	−	1.48802i	−0.0136660	−	0.999907i	$-0.504350\pi$
$829$	24.7358	−	42.8437i	0.859112	−	1.48802i	0.872778	−	0.488118i	$-0.162317\pi$
$830$		0			0
$831$	−2.58145			−0.0895495
$832$	−5.18551	+	4.15676i	−0.179775	+	0.144110i
$833$		−	46.2122i		−	1.60116i
$834$	3.48194	−	6.03090i	0.120570	−	0.208833i
$835$		0			0
$836$	−14.5236	−	25.1556i	−0.502309	−	0.870024i
$837$		−	3.04945i		−	0.105404i
$838$	16.0240	−	9.25145i	0.553539	−	0.319586i
$839$	4.64650	+	8.04797i	0.160415	+	0.277847i	0.935018	−	0.354601i	$-0.115383\pi$
$839$	4.64650	+	8.04797i	0.160415	+	0.277847i	−0.774603	+	0.632448i	$0.782050\pi$
$840$		0			0
$841$	8.33904	+	14.4436i	0.287553	+	0.498057i
$842$	−6.31878	−	3.64815i	−0.217760	−	0.125724i
$843$	4.63627	+	2.67675i	0.159682	+	0.0921922i
$844$	−24.2329			−0.834130
$845$		0			0
$846$	0.290725			0.00999532
$847$	2.85427	+	1.64791i	0.0980738	+	0.0566229i
$848$	−27.8841	−	16.0989i	−0.957544	−	0.552838i
$849$	−7.94687	−	13.7644i	−0.272736	−	0.472392i
$850$		0			0
$851$	−11.3874	−	19.7235i	−0.390353	−	0.676112i
$852$	3.09631	−	1.78765i	0.106078	−	0.0612440i
$853$			11.0423i			0.378080i	0.981969	+	0.189040i	$0.0605376\pi$
$853$			11.0423i			0.378080i	−0.981969	+	0.189040i	$0.939462\pi$
$854$	−3.94696	−	6.83633i	−0.135062	−	0.233934i
$855$		0			0
$856$	−15.5597	+	26.9502i	−0.531820	+	0.921139i
$857$		−	8.58476i		−	0.293250i	−0.989192	−	0.146625i	$-0.953159\pi$
$857$		−	8.58476i		−	0.293250i	0.989192	−	0.146625i	$-0.0468410\pi$
$858$	5.18551	−	4.15676i	0.177030	−	0.141909i
$859$	46.6202			1.59066			0.795331	−	0.606176i	$-0.207297\pi$
$859$	46.6202			1.59066			0.795331	+	0.606176i	$0.207297\pi$
$860$		0			0
$861$	9.00553	−	15.5980i	0.306908	−	0.531580i
$862$	−7.12651	+	4.11450i	−0.242730	+	0.140140i
$863$		−	10.6947i		−	0.364053i	−0.983294	−	0.182026i	$-0.941734\pi$
$863$		−	10.6947i		−	0.364053i	0.983294	−	0.182026i	$-0.0582656\pi$
$864$	2.63090	+	4.55685i	0.0895050	+	0.155027i
$865$		0			0
$866$	−2.09171			−0.0710792
$867$	7.54245	−	4.35464i	0.256155	−	0.147891i
$868$	21.6718	+	12.5122i	0.735588	+	0.424692i
$869$	−3.78151	+	6.54977i	−0.128279	+	0.222186i
$870$		0			0
$871$	−45.7978	+	7.02113i	−1.55180	+	0.237902i
$872$			31.6742i			1.07262i
$873$	−12.3573	−	7.13449i	−0.418231	−	0.241466i
$874$	−11.3874	+	19.7235i	−0.385183	+	0.667157i
$875$		0			0
$876$	−9.46800			−0.319894
$877$	−9.17625	+	5.29791i	−0.309860	+	0.178898i	−0.646864	−	0.762605i	$-0.723920\pi$
$877$	−9.17625	+	5.29791i	−0.309860	+	0.178898i	0.337004	+	0.941503i	$0.390586\pi$
$878$	−9.48436	+	5.47580i	−0.320082	+	0.184799i
$879$	−2.48133			−0.0836932
$880$		0			0
$881$	8.11450	−	14.0547i	0.273384	−	0.473515i	−0.696342	−	0.717710i	$-0.745190\pi$
$881$	8.11450	−	14.0547i	0.273384	−	0.473515i	0.969726	+	0.244195i	$0.0785236\pi$
$882$	7.49431	+	4.32684i	0.252347	+	0.145692i
$883$		−	12.6137i		−	0.424484i	−0.977217	−	0.212242i	$-0.931923\pi$
$883$		−	12.6137i		−	0.424484i	0.977217	−	0.212242i	$-0.0680766\pi$
$884$	17.5402	−	2.68904i	0.589942	−	0.0904423i
$885$		0			0
$886$	−9.45661	+	16.3793i	−0.317701	+	0.550274i
$887$	11.5967	+	6.69533i	0.389378	+	0.224807i	0.681890	−	0.731454i	$-0.261158\pi$
$887$	11.5967	+	6.69533i	0.389378	+	0.224807i	−0.292513	+	0.956262i	$0.594491\pi$
$888$	4.64250	−	2.68035i	0.155792	−	0.0899465i
$889$	−35.7897			−1.20035
$890$		0			0
$891$	1.70928	+	2.96055i	0.0572629	+	0.0991822i
$892$			9.67420i			0.323916i
$893$	2.32125	−	1.34017i	0.0776776	−	0.0448472i
$894$	−0.539189	+	0.933903i	−0.0180332	+	0.0312344i
$895$		0			0
$896$	−55.2951			−1.84728
$897$	28.5465	+	11.1206i	0.953140	+	0.371307i
$898$			4.29914i			0.143464i
$899$	−5.35218	+	9.27024i	−0.178505	+	0.309180i
$900$		0			0
$901$	19.8082	+	34.3088i	0.659906	+	1.14299i
$902$		−	6.91500i		−	0.230244i
$903$	−6.60519	+	3.81351i	−0.219807	+	0.126906i
$904$	−3.07838	−	5.33191i	−0.102385	−	0.177337i
$905$		0			0
$906$	2.31965	+	4.01776i	0.0770653	+	0.133481i
$907$	40.1014	+	23.1526i	1.33154	+	0.768768i	0.985536	−	0.169464i	$-0.0542035\pi$
$907$	40.1014	+	23.1526i	1.33154	+	0.768768i	0.346008	+	0.938231i	$0.387537\pi$
$908$	−30.9072	−	17.8443i	−1.02569	−	0.592184i
$909$	−12.4969			−0.414497
$910$		0			0
$911$	−40.6947			−1.34828			−0.674138	−	0.738605i	$-0.735485\pi$
$911$	−40.6947			−1.34828			−0.674138	+	0.738605i	$0.735485\pi$
$912$	10.0746	+	5.81658i	0.333604	+	0.192606i
$913$	−12.8493	−	7.41855i	−0.425250	−	0.245518i
$914$	−0.703414	−	1.21835i	−0.0232669	−	0.0402994i
$915$		0			0
$916$	−9.87322	−	17.1009i	−0.326220	−	0.565030i
$917$	−48.6197	+	28.0706i	−1.60556	+	0.926972i
$918$		−	1.55252i		−	0.0512408i
$919$	−22.2937	−	38.6138i	−0.735402	−	1.27375i	−0.954547	−	0.298061i	$-0.903660\pi$
$919$	−22.2937	−	38.6138i	−0.735402	−	1.27375i	0.219145	−	0.975692i	$-0.429673\pi$
$920$		0			0
$921$	−11.1212	+	19.2624i	−0.366455	+	0.634718i
$922$			16.2185i			0.534128i
$923$	7.02736	+	2.73759i	0.231308	+	0.0901090i
$924$	−28.0533			−0.922887
$925$		0			0
$926$	−1.71674	+	2.97349i	−0.0564157	+	0.0977149i
$927$	5.93265	−	3.42522i	0.194854	−	0.112499i
$928$		−	18.4703i		−	0.606316i
$929$	14.4885	+	25.0948i	0.475353	+	0.823335i	0.999601	−	0.0282300i	$-0.00898707\pi$
$929$	14.4885	+	25.0948i	0.475353	+	0.823335i	−0.524249	+	0.851565i	$0.675654\pi$
$930$		0			0
$931$	79.7829			2.61478
$932$	5.52448	−	3.18956i	0.180960	−	0.104478i
$933$	0.350931	+	0.202610i	0.0114890	+	0.00663315i
$934$	0.557770	−	0.966086i	0.0182508	−	0.0316113i
$935$		0			0
$936$	−2.61757	+	6.71925i	−0.0855578	+	0.219626i
$937$		−	53.1871i		−	1.73755i	−0.495209	−	0.868774i	$-0.664909\pi$
$937$		−	53.1871i		−	1.73755i	0.495209	−	0.868774i	$-0.335091\pi$
$938$	−28.8084	−	16.6326i	−0.940629	−	0.543072i
$939$	0.176752	−	0.306143i	0.00576808	−	0.00999061i
$940$		0			0
$941$	26.3617			0.859368			0.429684	−	0.902979i	$-0.358625\pi$
$941$	26.3617			0.859368			0.429684	+	0.902979i	$0.358625\pi$
$942$	0.424128	−	0.244870i	0.0138188	−	0.00797830i
$943$	27.6059	−	15.9383i	0.898971	−	0.519021i
$944$	−19.6697			−0.640193
$945$		0			0
$946$	−1.46412	+	2.53594i	−0.0476028	+	0.0824504i
$947$	43.9751	+	25.3890i	1.42900	+	0.825032i	0.997042	−	0.0768629i	$-0.0244904\pi$
$947$	43.9751	+	25.3890i	1.42900	+	0.825032i	0.431956	+	0.901895i	$0.357824\pi$
$948$		−	3.78151i		−	0.122818i
$949$	−12.4916	−	15.5831i	−0.405494	−	0.505850i
$950$		0			0
$951$	12.6514	−	21.9129i	0.410250	−	0.710574i
$952$	23.9435	+	13.8238i	0.776012	+	0.448031i
$953$	18.0415	−	10.4163i	0.584423	−	0.337417i	−0.178466	−	0.983946i	$-0.557114\pi$
$953$	18.0415	−	10.4163i	0.584423	−	0.337417i	0.762889	+	0.646529i	$0.223780\pi$
$954$	−7.41855			−0.240184
$955$		0			0
$956$	23.1545	+	40.1047i	0.748870	+	1.29708i
$957$		−	12.0000i		−	0.387905i
$958$	5.37473	−	3.10310i	0.173650	−	0.100257i
$959$	22.2703	−	38.5733i	0.719146	−	1.24560i
$960$		0			0
$961$	−21.7009			−0.700028
$962$	4.85537	+	1.89147i	0.156544	+	0.0609834i
$963$		−	15.5597i		−	0.501405i
$964$	20.1678	−	34.9317i	0.649562	−	1.12507i
$965$		0			0
$966$	10.9977	+	19.0486i	0.353846	+	0.612880i
$967$		−	5.92777i		−	0.190624i	−0.995447	−	0.0953120i	$-0.969615\pi$
$967$		−	5.92777i		−	0.190624i	0.995447	−	0.0953120i	$-0.0303849\pi$
$968$	−1.18903	+	0.686489i	−0.0382170	+	0.0220646i
$969$	−7.15676	−	12.3959i	−0.229908	−	0.398213i
$970$		0			0
$971$	−5.24846	−	9.09061i	−0.168431	−	0.291731i	0.769437	−	0.638722i	$-0.220537\pi$
$971$	−5.24846	−	9.09061i	−0.168431	−	0.291731i	−0.937868	+	0.346991i	$0.887203\pi$
$972$	−1.48028	−	0.854638i	−0.0474799	−	0.0274125i
$973$	−53.6996	−	31.0035i	−1.72153	−	0.993927i
$974$	10.8638			0.348097
$975$		0			0
$976$	−7.13624			−0.228425
$977$	−46.1780	−	26.6609i	−1.47736	−	0.852957i	−0.477692	−	0.878528i	$-0.658526\pi$
$977$	−46.1780	−	26.6609i	−1.47736	−	0.852957i	−0.999673	+	0.0255707i	$0.991860\pi$
$978$	−6.83814	−	3.94800i	−0.218660	−	0.126243i
$979$	11.9877	+	20.7633i	0.383129	+	0.663599i
$980$		0			0
$981$	−7.91855	−	13.7153i	−0.252820	−	0.437897i
$982$	10.2177	−	5.89917i	0.326058	−	0.188250i
$983$		−	21.7275i		−	0.693000i	−0.938050	−	0.346500i	$-0.887370\pi$
$983$		−	21.7275i		−	0.693000i	0.938050	−	0.346500i	$-0.112630\pi$
$984$	3.75154	+	6.49785i	0.119595	+	0.207144i
$985$		0			0
$986$	−2.72487	+	4.71962i	−0.0867777	+	0.150303i
$987$		−	2.58864i		−	0.0823972i
$988$	4.64250	+	30.2823i	0.147697	+	0.963409i
$989$	−13.4985			−0.429228
$990$		0			0
$991$	4.37823	−	7.58331i	0.139079	−	0.240892i	−0.788069	−	0.615587i	$-0.788919\pi$
$991$	4.37823	−	7.58331i	0.139079	−	0.240892i	0.927148	+	0.374695i	$0.122252\pi$
$992$	−13.8959	+	8.02279i	−0.441194	+	0.254724i
$993$			4.60197i			0.146039i
$994$	2.70734	+	4.68925i	0.0858715	+	0.148734i
$995$		0			0
$996$	7.41855			0.235066
$997$	2.99576	−	1.72960i	0.0948766	−	0.0547770i	−0.451811	−	0.892114i	$-0.649222\pi$
$997$	2.99576	−	1.72960i	0.0948766	−	0.0547770i	0.546688	+	0.837337i	$0.315889\pi$
$998$	11.1240	+	6.42243i	0.352123	+	0.203298i
$999$	−1.34017	+	2.32125i	−0.0424012	+	0.0734410i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bb.j.724.4		12
5.2	odd	4		975.2.i.m.451.2		6
5.3	odd	4		195.2.i.e.61.2	yes	6
5.4	even	2	inner	975.2.bb.j.724.3		12
13.3	even	3	inner	975.2.bb.j.874.3		12
15.8	even	4		585.2.j.g.451.2		6
65.3	odd	12		195.2.i.e.16.2	✓	6
65.29	even	6	inner	975.2.bb.j.874.4		12
65.42	odd	12		975.2.i.m.601.2		6
65.43	odd	12		2535.2.a.z.1.2		3
65.48	odd	12		2535.2.a.y.1.2		3
195.68	even	12		585.2.j.g.406.2		6
195.113	even	12		7605.2.a.bu.1.2		3
195.173	even	12		7605.2.a.bt.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.i.e.16.2	✓	6	65.3	odd	12
195.2.i.e.61.2	yes	6	5.3	odd	4
585.2.j.g.406.2		6	195.68	even	12
585.2.j.g.451.2		6	15.8	even	4
975.2.i.m.451.2		6	5.2	odd	4
975.2.i.m.601.2		6	65.42	odd	12
975.2.bb.j.724.3		12	5.4	even	2	inner
975.2.bb.j.724.4		12	1.1	even	1	trivial
975.2.bb.j.874.3		12	13.3	even	3	inner
975.2.bb.j.874.4		12	65.29	even	6	inner
2535.2.a.y.1.2		3	65.48	odd	12
2535.2.a.z.1.2		3	65.43	odd	12
7605.2.a.bt.1.2		3	195.173	even	12
7605.2.a.bu.1.2		3	195.113	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.466951 + 0.269594i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.854638 - 1.48028i) q^{4} +(-0.269594 - 0.466951i) q^{6} +(-4.15777 + 2.40049i) q^{7} -2.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.466951 + 0.269594i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.854638 - 1.48028i) q^{4} +(-0.269594 - 0.466951i) q^{6} +(-4.15777 + 2.40049i) q^{7} -2.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.70928 - 2.96055i) q^{11} +1.70928i q^{12} +(-2.81325 + 2.25513i) q^{13} -2.58864 q^{14} +(-1.17009 + 2.02665i) q^{16} +(2.49360 - 1.43968i) q^{17} +0.539189i q^{18} +(2.48554 + 4.30507i) q^{19} +4.80098 q^{21} +(1.59630 - 0.921622i) q^{22} +(7.35856 + 4.24846i) q^{23} +(-1.00000 + 1.73205i) q^{24} +(-1.92162 + 0.294598i) q^{26} -1.00000i q^{27} +(7.10678 + 4.10310i) q^{28} +(-1.75513 + 3.03997i) q^{29} +3.04945 q^{31} +(-4.55685 + 2.63090i) q^{32} +(-2.96055 + 1.70928i) q^{33} +1.55252 q^{34} +(0.854638 - 1.48028i) q^{36} +(-2.32125 - 1.34017i) q^{37} +2.68035i q^{38} +(3.56391 - 0.546373i) q^{39} +(1.87577 - 3.24893i) q^{41} +(2.24183 + 1.29432i) q^{42} +(-1.37580 + 0.794319i) q^{43} -5.84324 q^{44} +(2.29072 + 3.96765i) q^{46} -0.539189i q^{47} +(2.02665 - 1.17009i) q^{48} +(8.02472 - 13.8992i) q^{49} -2.87936 q^{51} +(5.74253 + 2.23707i) q^{52} +13.7587i q^{53} +(0.269594 - 0.466951i) q^{54} +(4.80098 + 8.31555i) q^{56} -4.97107i q^{57} +(-1.63912 + 0.946346i) q^{58} +(4.20261 + 7.27913i) q^{59} +(1.52472 + 2.64090i) q^{61} +(1.42394 + 0.822114i) q^{62} +(-4.15777 - 2.40049i) q^{63} +1.84324 q^{64} -1.84324 q^{66} +(11.1288 + 6.42522i) q^{67} +(-4.26225 - 2.46081i) q^{68} +(-4.24846 - 7.35856i) q^{69} +(-1.04585 - 1.81147i) q^{71} +(1.73205 - 1.00000i) q^{72} +5.53919i q^{73} +(-0.722606 - 1.25159i) q^{74} +(4.24846 - 7.35856i) q^{76} +16.4124i q^{77} +(1.81147 + 0.705681i) q^{78} -2.21235 q^{79} +(-0.500000 + 0.866025i) q^{81} +(1.75178 - 1.01139i) q^{82} -4.34017i q^{83} +(-4.10310 - 7.10678i) q^{84} -0.856576 q^{86} +(3.03997 - 1.75513i) q^{87} +(-5.92110 - 3.41855i) q^{88} +(-3.50667 + 6.07372i) q^{89} +(6.28345 - 16.1295i) q^{91} -14.5236i q^{92} +(-2.64090 - 1.52472i) q^{93} +(0.145362 - 0.251775i) q^{94} +5.26180 q^{96} +(-12.3573 + 7.13449i) q^{97} +(7.49431 - 4.32684i) q^{98} +3.41855 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} + 6 q^{9}+O(q^{10}) \) 12 * q + 4 * q^4 + 6 * q^9	\( 12 q + 4 q^{4} + 6 q^{9} - 8 q^{11} + 48 q^{14} + 8 q^{16} + 20 q^{21} - 12 q^{24} - 36 q^{26} + 12 q^{29} - 36 q^{31} + 16 q^{34} - 4 q^{36} + 40 q^{41} - 96 q^{44} + 56 q^{46} + 60 q^{49} + 16 q^{51} + 20 q^{56} + 20 q^{59} - 18 q^{61} + 48 q^{64} - 48 q^{66} - 16 q^{69} - 8 q^{71} + 16 q^{74} + 16 q^{76} - 68 q^{79} - 6 q^{81} - 40 q^{86} - 44 q^{89} - 62 q^{91} + 16 q^{94} + 32 q^{96} - 16 q^{99}+O(q^{100}) \) 12 * q + 4 * q^4 + 6 * q^9 - 8 * q^11 + 48 * q^14 + 8 * q^16 + 20 * q^21 - 12 * q^24 - 36 * q^26 + 12 * q^29 - 36 * q^31 + 16 * q^34 - 4 * q^36 + 40 * q^41 - 96 * q^44 + 56 * q^46 + 60 * q^49 + 16 * q^51 + 20 * q^56 + 20 * q^59 - 18 * q^61 + 48 * q^64 - 48 * q^66 - 16 * q^69 - 8 * q^71 + 16 * q^74 + 16 * q^76 - 68 * q^79 - 6 * q^81 - 40 * q^86 - 44 * q^89 - 62 * q^91 + 16 * q^94 + 32 * q^96 - 16 * q^99

Introduction

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