LMFDB - Embedded newform 475.2.j.c.49.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [475,2,Mod(49,475)] 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("475.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(475, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.1387535264013605949997056.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 11x^{14} + 82x^{12} - 337x^{10} + 1006x^{8} - 1596x^{6} + 1765x^{4} - 414x^{2} + 81 $ x^16 - 11x^14 + 82x^12 - 337x^10 + 1006x^8 - 1596x^6 + 1765x^4 - 414*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.3
Root			$1.77290 - 1.02359i$ of defining polynomial
Character	$\chi$	$=$	475.49
Dual form			475.2.j.c.349.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.03136 - 0.595455i) q^{2} +(-2.63893 - 1.52359i) q^{3} +(-0.290867 - 0.503797i) q^{4} +(1.81445 + 3.14272i) q^{6} +0.609175i q^{7} +3.07461i q^{8} +(3.14263 + 5.44319i) q^{9} +4.48517 q^{11} +1.77264i q^{12} +(3.84342 - 2.21900i) q^{13} +(0.362736 - 0.628278i) q^{14} +(1.24906 - 2.16343i) q^{16} +(2.51445 + 1.45172i) q^{17} -7.48517i q^{18} +(-3.60532 + 2.44983i) q^{19} +(0.928131 - 1.60757i) q^{21} +(-4.62581 - 2.67071i) q^{22} +(-2.46580 + 1.42363i) q^{23} +(4.68443 - 8.11368i) q^{24} -5.28525 q^{26} -10.0107i q^{27} +(0.306901 - 0.177189i) q^{28} +(0.558149 + 0.966742i) q^{29} -6.22908 q^{31} +(2.74893 - 1.58710i) q^{32} +(-11.8360 - 6.83354i) q^{33} +(-1.72886 - 2.99448i) q^{34} +(1.82817 - 3.16649i) q^{36} +3.77264i q^{37} +(5.17714 - 0.379847i) q^{38} -13.5233 q^{39} +(4.15184 - 7.19120i) q^{41} +(-1.91447 + 1.10532i) q^{42} +(8.65053 + 4.99438i) q^{43} +(-1.30459 - 2.25961i) q^{44} +3.39082 q^{46} +(5.09656 - 2.94250i) q^{47} +(-6.59235 + 3.80609i) q^{48} +6.62891 q^{49} +(-4.42363 - 7.66195i) q^{51} +(-2.23585 - 1.29087i) q^{52} +(7.31681 - 4.22436i) q^{53} +(-5.96093 + 10.3246i) q^{54} -1.87298 q^{56} +(13.2467 - 0.971912i) q^{57} -1.32941i q^{58} +(5.11793 - 8.86451i) q^{59} +(2.49099 + 4.31453i) q^{61} +(6.42441 + 3.70913i) q^{62} +(-3.31586 + 1.91441i) q^{63} -8.77641 q^{64} +(8.13812 + 14.0956i) q^{66} +(-7.34057 + 4.23808i) q^{67} -1.68903i q^{68} +8.67608 q^{69} +(-5.80995 + 10.0631i) q^{71} +(-16.7357 + 9.66236i) q^{72} +(-3.22443 - 1.86162i) q^{73} +(2.24644 - 3.89095i) q^{74} +(2.28289 + 1.10377i) q^{76} +2.73225i q^{77} +(13.9474 + 8.05253i) q^{78} +(4.51908 - 7.82728i) q^{79} +(-5.82432 + 10.0880i) q^{81} +(-8.56407 + 4.94447i) q^{82} -2.12178i q^{83} -1.07985 q^{84} +(-5.94786 - 10.3020i) q^{86} -3.40155i q^{87} +13.7901i q^{88} +(3.96608 + 6.86946i) q^{89} +(1.35176 + 2.34131i) q^{91} +(1.43444 + 0.828173i) q^{92} +(16.4381 + 9.49053i) q^{93} -7.00850 q^{94} -9.67231 q^{96} +(-8.37668 - 4.83628i) q^{97} +(-6.83677 - 3.94721i) q^{98} +(14.0952 + 24.4136i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 10 q^{4} - 4 q^{6} + 2 q^{9} - 8 q^{11} - 2 q^{14} - 14 q^{16} - 10 q^{19} + 8 q^{21} + 46 q^{24} + 12 q^{26} - 2 q^{29} + 30 q^{34} + 14 q^{36} - 60 q^{39} + 16 q^{41} - 24 q^{44} + 48 q^{46} + 40 q^{49}+ \cdots + 76 q^{99}+O(q^{100}) $ 16 * q + 10 * q^4 - 4 * q^6 + 2 * q^9 - 8 * q^11 - 2 * q^14 - 14 * q^16 - 10 * q^19 + 8 * q^21 + 46 * q^24 + 12 * q^26 - 2 * q^29 + 30 * q^34 + 14 * q^36 - 60 * q^39 + 16 * q^41 - 24 * q^44 + 48 * q^46 + 40 * q^49 - 44 * q^51 - 68 * q^54 - 164 * q^56 - 10 * q^59 - 224 * q^64 + 62 * q^66 + 36 * q^69 - 40 * q^71 + 50 * q^74 + 126 * q^76 + 34 * q^79 - 24 * q^81 + 80 * q^84 - 16 * q^86 + 22 * q^89 - 12 * q^91 + 124 * q^94 + 84 * q^96 + 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.03136	−	0.595455i	−0.729280	−	0.421050i	0.0888786	−	0.996042i	$-0.471672\pi$
$2$	−1.03136	−	0.595455i	−0.729280	−	0.421050i	−0.818159	+	0.574992i	$0.805005\pi$
$3$	−2.63893	−	1.52359i	−1.52359	−	0.879643i	−0.999610	−	0.0279089i	$-0.991115\pi$
$3$	−2.63893	−	1.52359i	−1.52359	−	0.879643i	−0.523975	−	0.851734i	$-0.675552\pi$
$4$	−0.290867	−	0.503797i	−0.145434	−	0.251898i
$5$		0			0
$5$		0			0
$6$	1.81445	+	3.14272i	0.740747	+	1.28301i
$7$			0.609175i			0.230247i	0.993351	+	0.115123i	$0.0367263\pi$
$7$			0.609175i			0.230247i	−0.993351	+	0.115123i	$0.963274\pi$
$8$			3.07461i			1.08704i
$9$	3.14263	+	5.44319i	1.04754	+	1.81440i
$10$		0			0
$11$	4.48517			1.35233			0.676164	−	0.736751i	$-0.263641\pi$
$11$	4.48517			1.35233			0.676164	+	0.736751i	$0.263641\pi$
$12$			1.77264i			0.511718i
$13$	3.84342	−	2.21900i	1.06597	−	0.615439i	0.138894	−	0.990307i	$-0.455645\pi$
$13$	3.84342	−	2.21900i	1.06597	−	0.615439i	0.927078	+	0.374868i	$0.122312\pi$
$14$	0.362736	−	0.628278i	0.0969454	−	0.167914i
$15$		0			0
$16$	1.24906	−	2.16343i	0.312265	−	0.540858i
$17$	2.51445	+	1.45172i	0.609843	+	0.352093i	0.772904	−	0.634523i	$-0.218803\pi$
$17$	2.51445	+	1.45172i	0.609843	+	0.352093i	−0.163061	+	0.986616i	$0.552137\pi$
$18$		−	7.48517i		−	1.76427i
$19$	−3.60532	+	2.44983i	−0.827117	+	0.562030i
$19$	−3.60532	+	2.44983i	−0.827117	+	0.562030i
$20$		0			0
$21$	0.928131	−	1.60757i	0.202535	−	0.350800i
$22$	−4.62581	−	2.67071i	−0.986227	−	0.569398i
$23$	−2.46580	+	1.42363i	−0.514154	+	0.296847i	−0.734540	−	0.678566i	$-0.762602\pi$
$23$	−2.46580	+	1.42363i	−0.514154	+	0.296847i	0.220386	+	0.975413i	$0.429268\pi$
$24$	4.68443	−	8.11368i	0.956206	−	1.65620i
$25$		0			0
$26$	−5.28525			−1.03652
$27$		−	10.0107i		−	1.92656i
$28$	0.306901	−	0.177189i	0.0579987	−	0.0334856i
$29$	0.558149	+	0.966742i	0.103646	+	0.179519i	0.913184	−	0.407547i	$-0.133616\pi$
$29$	0.558149	+	0.966742i	0.103646	+	0.179519i	−0.809538	+	0.587067i	$0.800283\pi$
$30$		0			0
$31$	−6.22908			−1.11877			−0.559387	−	0.828906i	$-0.688964\pi$
$31$	−6.22908			−1.11877			−0.559387	+	0.828906i	$0.688964\pi$
$32$	2.74893	−	1.58710i	0.485947	−	0.280562i
$33$	−11.8360	−	6.83354i	−2.06039	−	1.18957i
$34$	−1.72886	−	2.99448i	−0.296498	−	0.513549i
$35$		0			0
$36$	1.82817	−	3.16649i	0.304696	−	0.527748i
$37$			3.77264i			0.620219i	0.950701	+	0.310109i	$0.100366\pi$
$37$			3.77264i			0.620219i	−0.950701	+	0.310109i	$0.899634\pi$
$38$	5.17714	−	0.379847i	0.839843	−	0.0616193i
$39$	−13.5233			−2.16547
$40$		0			0
$41$	4.15184	−	7.19120i	0.648409	−	1.12308i	−0.335094	−	0.942185i	$-0.608768\pi$
$41$	4.15184	−	7.19120i	0.648409	−	1.12308i	0.983503	−	0.180893i	$-0.0578987\pi$
$42$	−1.91447	+	1.10532i	−0.295409	+	0.170555i
$43$	8.65053	+	4.99438i	1.31919	+	0.761637i	0.983599	−	0.180370i	$-0.0577295\pi$
$43$	8.65053	+	4.99438i	1.31919	+	0.761637i	0.335594	+	0.942007i	$0.391063\pi$
$44$	−1.30459	−	2.25961i	−0.196674	−	0.340649i
$45$		0			0
$46$	3.39082			0.499950
$47$	5.09656	−	2.94250i	0.743409	−	0.429208i	−0.0798983	−	0.996803i	$-0.525460\pi$
$47$	5.09656	−	2.94250i	0.743409	−	0.429208i	0.823308	+	0.567595i	$0.192126\pi$
$48$	−6.59235	+	3.80609i	−0.951524	+	0.549362i
$49$	6.62891			0.946986
$50$		0			0
$51$	−4.42363	−	7.66195i	−0.619432	−	1.07289i
$52$	−2.23585	−	1.29087i	−0.310056	−	0.179011i
$53$	7.31681	−	4.22436i	1.00504	−	0.580261i	0.0953049	−	0.995448i	$-0.469617\pi$
$53$	7.31681	−	4.22436i	1.00504	−	0.580261i	0.909736	+	0.415188i	$0.136284\pi$
$54$	−5.96093	+	10.3246i	−0.811180	+	1.40501i
$55$		0			0
$56$	−1.87298			−0.250287
$57$	13.2467	−	0.971912i	1.75457	−	0.128733i
$58$		−	1.32941i		−	0.174560i
$59$	5.11793	−	8.86451i	0.666297	−	1.15406i	−0.312634	−	0.949874i	$-0.601211\pi$
$59$	5.11793	−	8.86451i	0.666297	−	1.15406i	0.978932	−	0.204187i	$-0.0654552\pi$
$60$		0			0
$61$	2.49099	+	4.31453i	0.318939	+	0.552419i	0.980267	−	0.197678i	$-0.0633401\pi$
$61$	2.49099	+	4.31453i	0.318939	+	0.552419i	−0.661328	+	0.750097i	$0.730007\pi$
$62$	6.42441	+	3.70913i	0.815900	+	0.471060i
$63$	−3.31586	+	1.91441i	−0.417759	+	0.241193i
$64$	−8.77641			−1.09705
$65$		0			0
$66$	8.13812	+	14.0956i	1.00173	+	1.73505i
$67$	−7.34057	+	4.23808i	−0.896794	+	0.517764i	−0.876159	−	0.482023i	$-0.839902\pi$
$67$	−7.34057	+	4.23808i	−0.896794	+	0.517764i	−0.0206350	+	0.999787i	$0.506569\pi$
$68$		−	1.68903i		−	0.204825i
$69$	8.67608			1.04448
$70$		0			0
$71$	−5.80995	+	10.0631i	−0.689514	+	1.19427i	0.282481	+	0.959273i	$0.408843\pi$
$71$	−5.80995	+	10.0631i	−0.689514	+	1.19427i	−0.971995	+	0.235001i	$0.924491\pi$
$72$	−16.7357	+	9.66236i	−1.97232	+	1.13872i
$73$	−3.22443	−	1.86162i	−0.377391	−	0.217887i	0.299292	−	0.954162i	$-0.403250\pi$
$73$	−3.22443	−	1.86162i	−0.377391	−	0.217887i	−0.676682	+	0.736275i	$0.736583\pi$
$74$	2.24644	−	3.89095i	0.261143	−	0.452313i
$75$		0			0
$76$	2.28289	+	1.10377i	0.261865	+	0.126611i
$77$			2.73225i			0.311369i
$78$	13.9474	+	8.05253i	1.57923	+	0.911770i
$79$	4.51908	−	7.82728i	0.508437	−	0.880638i	−0.491516	−	0.870869i	$-0.663557\pi$
$79$	4.51908	−	7.82728i	0.508437	−	0.880638i	0.999952	−	0.00976923i	$-0.00310969\pi$
$80$		0			0
$81$	−5.82432	+	10.0880i	−0.647146	+	1.12089i
$82$	−8.56407	+	4.94447i	−0.945744	+	0.546025i
$83$		−	2.12178i		−	0.232896i	−0.993197	−	0.116448i	$-0.962849\pi$
$83$		−	2.12178i		−	0.232896i	0.993197	−	0.116448i	$-0.0371508\pi$
$84$	−1.07985			−0.117821
$85$		0			0
$86$	−5.94786	−	10.3020i	−0.641374	−	1.11089i
$87$		−	3.40155i		−	0.364684i
$88$			13.7901i			1.47003i
$89$	3.96608	+	6.86946i	0.420404	+	0.728161i	0.995979	−	0.0895879i	$-0.0285550\pi$
$89$	3.96608	+	6.86946i	0.420404	+	0.728161i	−0.575575	+	0.817749i	$0.695222\pi$
$90$		0			0
$91$	1.35176	+	2.34131i	0.141703	+	0.245436i
$92$	1.43444	+	0.828173i	0.149551	+	0.0863430i
$93$	16.4381	+	9.49053i	1.70455	+	0.984122i
$94$	−7.00850			−0.722872
$95$		0			0
$96$	−9.67231			−0.987176
$97$	−8.37668	−	4.83628i	−0.850523	−	0.491050i	0.0103043	−	0.999947i	$-0.496720\pi$
$97$	−8.37668	−	4.83628i	−0.850523	−	0.491050i	−0.860827	+	0.508897i	$0.830053\pi$
$98$	−6.83677	−	3.94721i	−0.690619	−	0.398729i
$99$	14.0952	+	24.4136i	1.41662	+	2.45366i
$100$		0			0
$101$	0.485632	+	0.841140i	0.0483222	+	0.0836965i	0.889175	−	0.457568i	$-0.151279\pi$
$101$	0.485632	+	0.841140i	0.0483222	+	0.0836965i	−0.840853	+	0.541264i	$0.817946\pi$
$102$			10.5363i			1.04325i
$103$		−	3.34143i		−	0.329241i	−0.986357	−	0.164620i	$-0.947360\pi$
$103$		−	3.34143i		−	0.329241i	0.986357	−	0.164620i	$-0.0526399\pi$
$104$	6.82256	+	11.8170i	0.669007	+	1.15875i
$105$		0			0
$106$	−10.0617			−0.977275
$107$		−	9.51655i		−	0.920000i	−0.887919	−	0.460000i	$-0.847849\pi$
$107$		−	9.51655i		−	0.920000i	0.887919	−	0.460000i	$-0.152151\pi$
$108$	−5.04337	+	2.91179i	−0.485298	+	0.280187i
$109$	2.77178	−	4.80087i	0.265489	−	0.459840i	−0.702203	−	0.711977i	$-0.747800\pi$
$109$	2.77178	−	4.80087i	0.265489	−	0.459840i	0.967692	+	0.252137i	$0.0811333\pi$
$110$		0			0
$111$	5.74795	−	9.95573i	0.545571	−	0.944956i
$112$	1.31791	+	0.760896i	0.124531	+	0.0718979i
$113$			1.54134i			0.144997i	0.997369	+	0.0724987i	$0.0230973\pi$
$113$			1.54134i			0.144997i	−0.997369	+	0.0724987i	$0.976903\pi$
$114$	−14.2408	−	6.88542i	−1.33378	−	0.644879i
$115$		0			0
$116$	0.324694	−	0.562387i	0.0301471	−	0.0522163i
$117$	24.1568	+	13.9470i	2.23330	+	1.28940i
$118$	−10.5568	+	6.09499i	−0.971835	+	0.561089i
$119$	−0.884350	+	1.53174i	−0.0810682	+	0.140414i
$120$		0			0
$121$	9.11672			0.828793
$122$		−	5.93310i		−	0.537158i
$123$	−21.9128	+	12.6514i	−1.97581	+	1.14074i
$124$	1.81183	+	3.13819i	0.162707	+	0.281818i
$125$		0			0
$126$	4.55978			0.406217
$127$	−1.99661	+	1.15274i	−0.177171	+	0.102289i	−0.585963	−	0.810338i	$-0.699283\pi$
$127$	−1.99661	+	1.15274i	−0.177171	+	0.102289i	0.408792	+	0.912628i	$0.365950\pi$
$128$	3.55376	+	2.05176i	0.314111	+	0.181352i
$129$	−15.2187	−	26.3596i	−1.33994	−	2.32084i
$130$		0			0
$131$	6.45905	−	11.1874i	0.564330	−	0.977448i	−0.432782	−	0.901499i	$-0.642468\pi$
$131$	6.45905	−	11.1874i	0.564330	−	0.977448i	0.997112	−	0.0759493i	$-0.0241987\pi$
$132$			7.95060i			0.692011i
$133$	−1.49238	−	2.19627i	−0.129405	−	0.190441i
$134$	10.0943			0.872018
$135$		0			0
$136$	−4.46346	+	7.73095i	−0.382739	+	0.662923i
$137$	11.0276	−	6.36677i	0.942149	−	0.543950i	0.0515159	−	0.998672i	$-0.483595\pi$
$137$	11.0276	−	6.36677i	0.942149	−	0.543950i	0.890633	+	0.454722i	$0.150261\pi$
$138$	−8.94814	−	5.16621i	−0.761716	−	0.439777i
$139$	5.30433	+	9.18738i	0.449908	+	0.779263i	0.998380	−	0.0569059i	$-0.0181235\pi$
$139$	5.30433	+	9.18738i	0.449908	+	0.779263i	−0.548472	+	0.836169i	$0.684790\pi$
$140$		0			0
$141$	−17.9326			−1.51020
$142$	11.9843	−	6.91913i	1.00570	−	0.580640i
$143$	17.2384	−	9.95258i	1.44154	−	0.832276i
$144$	15.7013			1.30844
$145$		0			0
$146$	2.21703	+	3.84000i	0.183482	+	0.317801i
$147$	−17.4932	−	10.0997i	−1.44281	−	0.833010i
$148$	1.90065	−	1.09734i	0.156232	−	0.0902006i
$149$	1.88653	−	3.26757i	0.154551	−	0.267690i	−0.778344	−	0.627837i	$-0.783940\pi$
$149$	1.88653	−	3.26757i	0.154551	−	0.267690i	0.932895	+	0.360147i	$0.117274\pi$
$150$		0			0
$151$	−9.51562			−0.774370			−0.387185	−	0.922002i	$-0.626553\pi$
$151$	−9.51562			−0.774370			−0.387185	+	0.922002i	$0.626553\pi$
$152$	−7.53228	−	11.0850i	−0.610948	−	0.899109i
$153$			18.2488i			1.47533i
$154$	1.62693	−	2.81793i	0.131102	−	0.227075i
$155$		0			0
$156$	3.93349	+	6.81301i	0.314931	+	0.545477i
$157$	−2.99336	−	1.72822i	−0.238896	−	0.137927i	0.375773	−	0.926712i	$-0.377377\pi$
$157$	−2.99336	−	1.72822i	−0.238896	−	0.137927i	−0.614669	+	0.788785i	$0.710710\pi$
$158$	−9.32158	+	5.38182i	−0.741585	+	0.428155i
$159$	−25.7447			−2.04169
$160$		0			0
$161$	−0.867239	−	1.50210i	−0.0683480	−	0.118382i
$162$	12.0139	−	6.93624i	0.943902	−	0.544962i
$163$			6.65283i			0.521090i	0.965462	+	0.260545i	$0.0839022\pi$
$163$			6.65283i			0.521090i	−0.965462	+	0.260545i	$0.916098\pi$
$164$	−4.83054			−0.377202
$165$		0			0
$166$	−1.26343	+	2.18832i	−0.0980609	+	0.169846i
$167$	14.2509	−	8.22775i	1.10277	−	0.636682i	0.165820	−	0.986156i	$-0.446973\pi$
$167$	14.2509	−	8.22775i	1.10277	−	0.636682i	0.936946	+	0.349474i	$0.113640\pi$
$168$	4.94265	+	2.85364i	0.381334	+	0.220163i
$169$	3.34790	−	5.79874i	0.257531	−	0.446057i
$170$		0			0
$171$	−24.6651	−	11.9255i	−1.88618	−	0.911968i
$172$		−	5.81081i		−	0.443070i
$173$	19.7302	+	11.3912i	1.50006	+	0.866058i	1.00000		6.58713e-5i	$2.09675e-5\pi$
$173$	19.7302	+	11.3912i	1.50006	+	0.866058i	0.500057	+	0.865992i	$0.333312\pi$
$174$	−2.02547	+	3.50822i	−0.153550	+	0.265957i
$175$		0			0
$176$	5.60224	−	9.70336i	0.422284	−	0.731418i
$177$	−27.0117	+	15.5952i	−2.03032	+	1.17221i
$178$		−	9.44650i		−	0.708045i
$179$	2.32916			0.174090			0.0870449	−	0.996204i	$-0.472258\pi$
$179$	2.32916			0.174090			0.0870449	+	0.996204i	$0.472258\pi$
$180$		0			0
$181$	11.1696	+	19.3463i	0.830230	+	1.43800i	0.897856	+	0.440290i	$0.145124\pi$
$181$	11.1696	+	19.3463i	0.830230	+	1.43800i	−0.0676258	+	0.997711i	$0.521542\pi$
$182$		−	3.21965i		−	0.238656i
$183$		−	15.1810i		−	1.12221i
$184$	−4.37710	−	7.58137i	−0.322684	−	0.558906i
$185$		0			0
$186$	−11.3024	−	19.5763i	−0.828729	−	1.43540i
$187$	11.2777	+	6.51119i	0.824708	+	0.476145i
$188$	−2.96484	−	1.71175i	−0.216233	−	0.124842i
$189$	6.09829			0.443585
$190$		0			0
$191$	2.23766			0.161911			0.0809556	−	0.996718i	$-0.474203\pi$
$191$	2.23766			0.161911			0.0809556	+	0.996718i	$0.474203\pi$
$192$	23.1603	+	13.3716i	1.67145	+	0.965013i
$193$	3.93441	+	2.27153i	0.283205	+	0.163508i	0.634873	−	0.772616i	$-0.281052\pi$
$193$	3.93441	+	2.27153i	0.283205	+	0.163508i	−0.351669	+	0.936125i	$0.614386\pi$
$194$	5.75957	+	9.97587i	0.413513	+	0.716226i
$195$		0			0
$196$	−1.92813	−	3.33962i	−0.137724	−	0.238544i
$197$			19.2236i			1.36962i	0.728720	+	0.684812i	$0.240116\pi$
$197$			19.2236i			1.36962i	−0.728720	+	0.684812i	$0.759884\pi$
$198$		−	33.5722i		−	2.38587i
$199$	−3.07547	−	5.32687i	−0.218014	−	0.377612i	0.736186	−	0.676779i	$-0.236625\pi$
$199$	−3.07547	−	5.32687i	−0.218014	−	0.377612i	−0.954201	+	0.299167i	$0.903291\pi$
$200$		0			0
$201$	25.8283			1.82179
$202$		−	1.15669i		−	0.0813843i
$203$	−0.588915	+	0.340010i	−0.0413338	+	0.0238641i
$204$	−2.57338	+	4.45722i	−0.180172	+	0.312068i
$205$		0			0
$206$	−1.98967	+	3.44621i	−0.138627	+	0.240109i
$207$	−15.4981	−	8.94786i	−1.07720	−	0.621919i
$208$		−	11.0866i		−	0.768720i
$209$	−16.1705	+	10.9879i	−1.11853	+	0.760049i
$210$		0			0
$211$	−6.34661	+	10.9926i	−0.436919	+	0.756765i	−0.997450	−	0.0713679i	$-0.977264\pi$
$211$	−6.34661	+	10.9926i	−0.436919	+	0.756765i	0.560531	+	0.828133i	$0.310597\pi$
$212$	−4.25644	−	2.45746i	−0.292333	−	0.168779i
$213$	30.6641	−	17.7039i	2.10107	−	1.21305i
$214$	−5.66668	+	9.81497i	−0.387366	+	0.670938i
$215$		0			0
$216$	30.7791			2.09425
$217$		−	3.79460i		−	0.257594i
$218$	−5.71740	+	3.30094i	−0.387231	+	0.223568i
$219$	5.67269	+	9.82538i	0.383325	+	0.663938i
$220$		0			0
$221$	12.8854			0.866767
$222$	−11.8564	+	6.84528i	−0.795748	+	0.459425i
$223$	−19.5181	−	11.2688i	−1.30703	−	0.754614i	−0.325430	−	0.945566i	$-0.605509\pi$
$223$	−19.5181	−	11.2688i	−1.30703	−	0.754614i	−0.981599	+	0.190952i	$0.938842\pi$
$224$	0.966820	+	1.67458i	0.0645984	+	0.111888i
$225$		0			0
$226$	0.917800	−	1.58968i	0.0610512	−	0.105744i
$227$		−	18.1124i		−	1.20216i	−0.799189	−	0.601080i	$-0.794737\pi$
$227$		−	18.1124i		−	1.20216i	0.799189	−	0.601080i	$-0.205263\pi$
$228$	−4.34268	−	6.39095i	−0.287601	−	0.423251i
$229$	9.41604			0.622229			0.311115	−	0.950372i	$-0.399298\pi$
$229$	9.41604			0.622229			0.311115	+	0.950372i	$0.399298\pi$
$230$		0			0
$231$	4.16282	−	7.21022i	0.273894	−	0.474398i
$232$	−2.97236	+	1.71609i	−0.195145	+	0.112667i
$233$	−13.5966	−	7.85000i	−0.890743	−	0.514271i	−0.0165573	−	0.999863i	$-0.505271\pi$
$233$	−13.5966	−	7.85000i	−0.890743	−	0.514271i	−0.874185	+	0.485592i	$0.838604\pi$
$234$	−16.6096	−	28.7686i	−1.08580	−	1.88066i
$235$		0			0
$236$	−5.95455			−0.387608
$237$	−23.8511	+	13.7704i	−1.54929	+	0.894485i
$238$	1.82416	−	1.05318i	0.118243	−	0.0682676i
$239$	23.4610			1.51757			0.758783	−	0.651344i	$-0.225795\pi$
$239$	23.4610			1.51757			0.758783	+	0.651344i	$0.225795\pi$
$240$		0			0
$241$	−6.58469	−	11.4050i	−0.424157	−	0.734662i	0.572184	−	0.820125i	$-0.306096\pi$
$241$	−6.58469	−	11.4050i	−0.424157	−	0.734662i	−0.996341	+	0.0854634i	$0.972763\pi$
$242$	−9.40260	−	5.42860i	−0.604422	−	0.348963i
$243$	4.73128	−	2.73161i	0.303512	−	0.175233i
$244$	1.44910	−	2.50991i	0.0927689	−	0.160680i
$245$		0			0
$246$	30.1333			1.92123
$247$	−8.42058	+	17.4159i	−0.535789	+	1.10815i
$248$		−	19.1520i		−	1.21615i
$249$	−3.23272	+	5.59923i	−0.204865	+	0.354837i
$250$		0			0
$251$	8.66257	+	15.0040i	0.546776	+	0.947045i	0.998493	+	0.0548830i	$0.0174786\pi$
$251$	8.66257	+	15.0040i	0.546776	+	0.947045i	−0.451716	+	0.892162i	$0.649188\pi$
$252$	1.92895	+	1.11368i	0.121512	+	0.0701551i
$253$	−11.0595	+	6.38521i	−0.695305	+	0.401435i
$254$	2.74563			0.172276
$255$		0			0
$256$	6.33295	+	10.9690i	0.395809	+	0.685562i
$257$	4.91867	−	2.83980i	0.306818	−	0.177142i	−0.338683	−	0.940900i	$-0.609982\pi$
$257$	4.91867	−	2.83980i	0.306818	−	0.177142i	0.645502	+	0.763759i	$0.276648\pi$
$258$			36.2483i			2.25672i
$259$	−2.29820			−0.142803
$260$		0			0
$261$	−3.50811	+	6.07622i	−0.217146	+	0.376108i
$262$	−13.3232	+	7.69215i	−0.823109	+	0.475222i
$263$	−4.89966	−	2.82882i	−0.302126	−	0.174433i	0.341272	−	0.939965i	$-0.389142\pi$
$263$	−4.89966	−	2.82882i	−0.302126	−	0.174433i	−0.643398	+	0.765532i	$0.722476\pi$
$264$	21.0105	−	36.3912i	1.29311	−	2.23972i
$265$		0			0
$266$	0.231393	+	3.15379i	0.0141876	+	0.193371i
$267$		−	24.1707i		−	1.47922i
$268$	4.27026	+	2.46544i	0.260848	+	0.150601i
$269$	−11.9959	+	20.7775i	−0.731402	+	1.26683i	0.224881	+	0.974386i	$0.427801\pi$
$269$	−11.9959	+	20.7775i	−0.731402	+	1.26683i	−0.956284	+	0.292440i	$0.905533\pi$
$270$		0			0
$271$	10.6497	−	18.4459i	0.646926	−	1.12051i	−0.336927	−	0.941531i	$-0.609388\pi$
$271$	10.6497	−	18.4459i	0.646926	−	1.12051i	0.983853	−	0.178978i	$-0.0572791\pi$
$272$	6.28138	−	3.62656i	0.380865	−	0.219892i
$273$		−	8.23808i		−	0.498591i
$274$	−15.1645			−0.916121
$275$		0			0
$276$	−2.52359	−	4.37098i	−0.151902	−	0.263102i
$277$			0.821109i			0.0493357i	0.999696	+	0.0246678i	$0.00785281\pi$
$277$			0.821109i			0.0493357i	−0.999696	+	0.0246678i	$0.992147\pi$
$278$		−	12.6340i		−	0.757735i
$279$	−19.5757	−	33.9060i	−1.17196	−	2.02990i
$280$		0			0
$281$	0.293739	+	0.508772i	0.0175230	+	0.0303508i	0.874654	−	0.484748i	$-0.161089\pi$
$281$	0.293739	+	0.508772i	0.0175230	+	0.0303508i	−0.857131	+	0.515099i	$0.827755\pi$
$282$	18.4949	+	10.6780i	1.10136	+	0.635869i
$283$	−26.7969	−	15.4712i	−1.59291	−	0.919667i	−0.992805	−	0.119746i	$-0.961792\pi$
$283$	−26.7969	−	15.4712i	−1.59291	−	0.919667i	−0.600105	−	0.799921i	$-0.704875\pi$
$284$	6.75969			0.401114
$285$		0			0
$286$	−23.7052			−1.40172
$287$	4.38070	+	2.52920i	0.258585	+	0.149294i
$288$	17.2777	+	9.97530i	1.01810	+	0.587800i
$289$	−4.28504	−	7.42191i	−0.252061	−	0.436583i
$290$		0			0
$291$	14.7370	+	25.5252i	0.863896	+	1.49631i
$292$			2.16594i			0.126752i
$293$			3.76271i			0.219820i	0.993942	+	0.109910i	$0.0350562\pi$
$293$			3.76271i			0.219820i	−0.993942	+	0.109910i	$0.964944\pi$
$294$	12.0278	+	20.8328i	0.701478	+	1.21499i
$295$		0			0
$296$	−11.5994			−0.674202
$297$		−	44.8998i		−	2.60535i
$298$	−3.89138	+	2.24669i	−0.225422	+	0.130147i
$299$	−6.31806	+	10.9432i	−0.365383	+	0.632861i
$300$		0			0
$301$	−3.04246	+	5.26969i	−0.175364	+	0.303740i
$302$	9.81401	+	5.66612i	0.564733	+	0.326049i
$303$		−	2.95961i		−	0.170025i
$304$	0.796788	+	10.8598i	0.0456989	+	0.622855i
$305$		0			0
$306$	10.8663	−	18.8211i	0.621187	−	1.07593i
$307$	17.6166	+	10.1709i	1.00543	+	0.580485i	0.909850	−	0.414936i	$-0.136196\pi$
$307$	17.6166	+	10.1709i	1.00543	+	0.580485i	0.0955798	+	0.995422i	$0.469529\pi$
$308$	1.37650	−	0.794723i	0.0784334	−	0.0452835i
$309$	−5.09095	+	8.81779i	−0.289614	+	0.501626i
$310$		0			0
$311$	−7.67830			−0.435397			−0.217698	−	0.976016i	$-0.569855\pi$
$311$	−7.67830			−0.435397			−0.217698	+	0.976016i	$0.569855\pi$
$312$		−	41.5790i		−	2.35395i
$313$	20.7783	−	11.9964i	1.17446	−	0.678074i	0.219733	−	0.975560i	$-0.429481\pi$
$313$	20.7783	−	11.9964i	1.17446	−	0.678074i	0.954726	+	0.297486i	$0.0961481\pi$
$314$	2.05815	+	3.56482i	0.116148	+	0.201174i
$315$		0			0
$316$	−5.25781			−0.295775
$317$	−0.899831	+	0.519518i	−0.0505395	+	0.0291790i	−0.525057	−	0.851067i	$-0.675956\pi$
$317$	−0.899831	+	0.519518i	−0.0505395	+	0.0291790i	0.474517	+	0.880246i	$0.342623\pi$
$318$	26.5520	+	15.3298i	1.48896	+	0.859653i
$319$	2.50339	+	4.33600i	0.140163	+	0.242769i
$320$		0			0
$321$	−14.4993	+	25.1135i	−0.809271	+	1.40170i
$322$			2.06561i			0.115112i
$323$	−12.6218	+	0.926066i	−0.702298	+	0.0515277i
$324$	6.77641			0.376467
$325$		0			0
$326$	3.96146	−	6.86145i	0.219405	−	0.380020i
$327$	−14.6291	+	8.44610i	−0.808990	+	0.467070i
$328$	22.1102	+	12.7653i	1.22083	+	0.704846i
$329$	1.79250	+	3.10470i	0.0988236	+	0.171167i
$330$		0			0
$331$	30.8316			1.69466			0.847328	−	0.531069i	$-0.178210\pi$
$331$	30.8316			1.69466			0.847328	+	0.531069i	$0.178210\pi$
$332$	−1.06895	+	0.617157i	−0.0586661	+	0.0338709i
$333$	−20.5352	+	11.8560i	−1.12532	+	0.649705i
$334$	−19.5970			−1.07230
$335$		0			0
$336$	−2.31858	−	4.01590i	−0.126489	−	0.219085i
$337$	17.9400	+	10.3576i	0.977252	+	0.564217i	0.901439	−	0.432906i	$-0.142512\pi$
$337$	17.9400	+	10.3576i	0.977252	+	0.564217i	0.0758124	+	0.997122i	$0.475845\pi$
$338$	−6.90577	+	3.98705i	−0.375625	+	0.216867i
$339$	2.34837	−	4.06749i	0.127546	−	0.220916i
$340$		0			0
$341$	−27.9384			−1.51295
$342$	18.3374	+	26.9864i	0.991572	+	1.45926i
$343$			8.30239i			0.448287i
$344$	−15.3558	+	26.5970i	−0.827929	+	1.43402i
$345$		0			0
$346$	−13.5659	−	23.4968i	−0.729308	−	1.26320i
$347$	7.11991	+	4.11068i	0.382217	+	0.220673i	0.678782	−	0.734340i	$-0.262508\pi$
$347$	7.11991	+	4.11068i	0.382217	+	0.220673i	−0.296566	+	0.955013i	$0.595841\pi$
$348$	−1.71369	+	0.989399i	−0.0918634	+	0.0530373i
$349$	−11.9216			−0.638150			−0.319075	−	0.947730i	$-0.603372\pi$
$349$	−11.9216			−0.638150			−0.319075	+	0.947730i	$0.603372\pi$
$350$		0			0
$351$	−22.2138	−	38.4754i	−1.18568	−	2.05366i
$352$	12.3294	−	7.11839i	0.657160	−	0.379412i
$353$		−	11.7983i		−	0.627959i	−0.949430	−	0.313980i	$-0.898338\pi$
$353$		−	11.7983i		−	0.627959i	0.949430	−	0.313980i	$-0.101662\pi$
$354$	37.1450			1.97423
$355$		0			0
$356$	2.30721	−	3.99620i	0.122282	−	0.211798i
$357$	4.66747	−	2.69477i	0.247029	−	0.142622i
$358$	−2.40220	−	1.38691i	−0.126960	−	0.0733005i
$359$	0.0554058	−	0.0959656i	0.00292420	−	0.00506487i	−0.864560	−	0.502530i	$-0.832403\pi$
$359$	0.0554058	−	0.0959656i	0.00292420	−	0.00506487i	0.867484	+	0.497465i	$0.165736\pi$
$360$		0			0
$361$	6.99666	−	17.6648i	0.368245	−	0.929729i
$362$		−	26.6040i		−	1.39827i
$363$	−24.0584	−	13.8901i	−1.26274	−	0.729042i
$364$	0.786364	−	1.36202i	0.0412167	−	0.0713894i
$365$		0			0
$366$	−9.03958	+	15.6570i	−0.472507	+	0.818405i
$367$	−10.1669	+	5.86986i	−0.530708	+	0.306404i	−0.741305	−	0.671169i	$-0.765793\pi$
$367$	−10.1669	+	5.86986i	−0.530708	+	0.306404i	0.210597	+	0.977573i	$0.432459\pi$
$368$			7.11278i			0.370779i
$369$	52.1908			2.71694
$370$		0			0
$371$	2.57338	+	4.45722i	0.133603	+	0.231407i
$372$		−	11.0419i		−	0.572498i
$373$			14.5190i			0.751763i	0.926668	+	0.375882i	$0.122660\pi$
$373$			14.5190i			0.751763i	−0.926668	+	0.375882i	$0.877340\pi$
$374$	−7.75424	−	13.4307i	−0.400962	−	0.694487i
$375$		0			0
$376$	9.04704	+	15.6699i	0.466566	+	0.808115i
$377$	4.29040	+	2.47706i	0.220967	+	0.127575i
$378$	−6.28952	−	3.63125i	−0.323498	−	0.186772i
$379$	6.59023			0.338518			0.169259	−	0.985572i	$-0.445863\pi$
$379$	6.59023			0.338518			0.169259	+	0.985572i	$0.445863\pi$
$380$		0			0
$381$	7.02522			0.359913
$382$	−2.30782	−	1.33242i	−0.118079	−	0.0681727i
$383$	2.48481	+	1.43461i	0.126968	+	0.0733049i	0.562139	−	0.827043i	$-0.309979\pi$
$383$	2.48481	+	1.43461i	0.126968	+	0.0733049i	−0.435171	+	0.900348i	$0.643312\pi$
$384$	−6.25207	−	10.8289i	−0.319050	−	0.552610i
$385$		0			0
$386$	−2.70519	−	4.68552i	−0.137690	−	0.238487i
$387$			62.7819i			3.19138i
$388$			5.62686i			0.285660i
$389$	−3.16575	−	5.48323i	−0.160510	−	0.278011i	0.774542	−	0.632523i	$-0.217980\pi$
$389$	−3.16575	−	5.48323i	−0.160510	−	0.278011i	−0.935052	+	0.354512i	$0.884647\pi$
$390$		0			0
$391$	−8.26682			−0.418071
$392$			20.3813i			1.02941i
$393$	−34.0899	+	19.6818i	−1.71961	+	0.992817i
$394$	11.4468	−	19.8264i	0.576680	−	0.998840i
$395$		0			0
$396$	8.19966	−	14.2022i	0.412049	−	0.713689i
$397$	−26.4569	−	15.2749i	−1.32784	−	0.766626i	−0.342871	−	0.939382i	$-0.611399\pi$
$397$	−26.4569	−	15.2749i	−1.32784	−	0.766626i	−0.984965	+	0.172756i	$0.944733\pi$
$398$			7.32522i			0.367180i
$399$	0.592065	+	8.06957i	0.0296403	+	0.403984i
$400$		0			0
$401$	−15.1711	+	26.2771i	−0.757609	+	1.31222i	0.186458	+	0.982463i	$0.440299\pi$
$401$	−15.1711	+	26.2771i	−0.757609	+	1.31222i	−0.944067	+	0.329754i	$0.893034\pi$
$402$	−26.6382	−	15.3796i	−1.32859	−	0.767064i
$403$	−23.9409	+	13.8223i	−1.19258	+	0.688538i
$404$	0.282509	−	0.489320i	0.0140553	−	0.0243446i
$405$		0			0
$406$	0.809843			0.0401919
$407$			16.9209i			0.838740i
$408$	23.5575	−	13.6009i	1.16627	−	0.673347i
$409$	−7.48628	−	12.9666i	−0.370173	−	0.641158i	0.619419	−	0.785060i	$-0.287368\pi$
$409$	−7.48628	−	12.9666i	−0.370173	−	0.641158i	−0.989592	+	0.143903i	$0.954035\pi$
$410$		0			0
$411$	−38.8013			−1.91393
$412$	−1.68340	+	0.971912i	−0.0829352	+	0.0478827i
$413$	5.40004	+	3.11772i	0.265719	+	0.153413i
$414$	10.6561	+	18.4569i	0.523718	+	0.907107i
$415$		0			0
$416$	7.04353	−	12.1997i	0.345337	−	0.598142i
$417$		−	32.3264i		−	1.58303i
$418$	23.2203	−	1.70368i	1.13574	−	0.0833296i
$419$	6.17419			0.301629			0.150815	−	0.988562i	$-0.451810\pi$
$419$	6.17419			0.301629			0.150815	+	0.988562i	$0.451810\pi$
$420$		0			0
$421$	13.7714	−	23.8528i	0.671177	−	1.16251i	−0.306394	−	0.951905i	$-0.599122\pi$
$421$	13.7714	−	23.8528i	0.671177	−	1.16251i	0.977571	−	0.210608i	$-0.0675443\pi$
$422$	13.0913	−	7.55824i	0.637272	−	0.367929i
$423$	32.0331	+	18.4943i	1.55750	+	0.899226i
$424$	12.9883	+	22.4963i	0.630766	+	1.09252i
$425$		0			0
$426$	−42.1675			−2.04302
$427$	−2.62830	+	1.51745i	−0.127193	+	0.0734347i
$428$	−4.79441	+	2.76805i	−0.231746	+	0.133799i
$429$	−60.6544			−2.92842
$430$		0			0
$431$	7.52941	+	13.0413i	0.362679	+	0.628179i	0.988401	−	0.151868i	$-0.0485288\pi$
$431$	7.52941	+	13.0413i	0.362679	+	0.628179i	−0.625722	+	0.780046i	$0.715195\pi$
$432$	−21.6575	−	12.5040i	−1.04200	−	0.601598i
$433$	−0.840772	+	0.485420i	−0.0404049	+	0.0233278i	−0.520066	−	0.854126i	$-0.674093\pi$
$433$	−0.840772	+	0.485420i	−0.0404049	+	0.0233278i	0.479661	+	0.877454i	$0.340759\pi$
$434$	−2.25951	+	3.91359i	−0.108460	+	0.187858i
$435$		0			0
$436$	−3.22488			−0.154444
$437$	5.40234	−	11.1734i	0.258429	−	0.534497i
$438$		−	13.5113i		−	0.645596i
$439$	−13.7187	+	23.7616i	−0.654760	+	1.13408i	0.327194	+	0.944957i	$0.393897\pi$
$439$	−13.7187	+	23.7616i	−0.654760	+	1.13408i	−0.981954	+	0.189120i	$0.939436\pi$
$440$		0			0
$441$	20.8322	+	36.0824i	0.992008	+	1.71821i
$442$	−13.2895	−	7.67269i	−0.632116	−	0.364952i
$443$	−7.59109	+	4.38272i	−0.360664	+	0.208229i	−0.669372	−	0.742928i	$-0.733437\pi$
$443$	−7.59109	+	4.38272i	−0.360664	+	0.208229i	0.308708	+	0.951157i	$0.400103\pi$
$444$	−6.68755			−0.317377
$445$		0			0
$446$	13.4201	+	23.2443i	0.635461	+	1.10065i
$447$	−9.95686	+	5.74859i	−0.470943	+	0.271899i
$448$		−	5.34637i		−	0.252592i
$449$	9.63397			0.454655			0.227327	−	0.973818i	$-0.427001\pi$
$449$	9.63397			0.454655			0.227327	+	0.973818i	$0.427001\pi$
$450$		0			0
$451$	18.6217	−	32.2538i	0.876862	−	1.51877i
$452$	0.776524	−	0.448326i	0.0365246	−	0.0210875i
$453$	25.1110	+	14.4979i	1.17982	+	0.681169i
$454$	−10.7851	+	18.6803i	−0.506169	+	0.876711i
$455$		0			0
$456$	2.98825	+	40.7285i	0.139938	+	1.90729i
$457$			10.6708i			0.499161i	0.968354	+	0.249580i	$0.0802927\pi$
$457$			10.6708i			0.499161i	−0.968354	+	0.249580i	$0.919707\pi$
$458$	−9.71131	−	5.60683i	−0.453780	−	0.261990i
$459$	14.5327	−	25.1714i	0.678330	−	1.17490i
$460$		0			0
$461$	−2.84340	+	4.92491i	−0.132430	+	0.229376i	−0.924613	−	0.380908i	$-0.875611\pi$
$461$	−2.84340	+	4.92491i	−0.132430	+	0.229376i	0.792183	+	0.610284i	$0.208945\pi$
$462$	−8.58672	+	4.95754i	−0.399490	+	0.230646i
$463$			35.3550i			1.64309i	0.570147	+	0.821543i	$0.306886\pi$
$463$			35.3550i			1.64309i	−0.570147	+	0.821543i	$0.693114\pi$
$464$	2.78864			0.129459
$465$		0			0
$466$	9.34864	+	16.1923i	0.433067	+	0.750095i
$467$			32.9071i			1.52276i	0.648306	+	0.761380i	$0.275478\pi$
$467$			32.9071i			1.52276i	−0.648306	+	0.761380i	$0.724522\pi$
$468$		−	16.2269i		−	0.750086i
$469$	−2.58173	−	4.47169i	−0.119213	−	0.206484i
$470$		0			0
$471$	5.26617	+	9.12127i	0.242652	+	0.420286i
$472$	27.2549	+	15.7356i	1.25451	+	0.724292i
$473$	38.7991	+	22.4006i	1.78398	+	1.02998i
$474$	32.7986			1.50649
$475$		0			0
$476$	1.02891			0.0471602
$477$	45.9880	+	26.5512i	2.10564	+	1.21569i
$478$	−24.1967	−	13.9700i	−1.10673	−	0.638971i
$479$	−4.52861	−	7.84378i	−0.206917	−	0.358391i	0.743825	−	0.668375i	$-0.233010\pi$
$479$	−4.52861	−	7.84378i	−0.206917	−	0.358391i	−0.950742	+	0.309984i	$0.899676\pi$
$480$		0			0
$481$	8.37149	+	14.4998i	0.381707	+	0.661136i
$482$			15.6835i			0.714366i
$483$			5.28525i			0.240487i
$484$	−2.65175	−	4.59297i	−0.120534	−	0.208772i
$485$		0			0
$486$	−6.50619			−0.295127
$487$			16.5206i			0.748620i	0.927304	+	0.374310i	$0.122120\pi$
$487$			16.5206i			0.748620i	−0.927304	+	0.374310i	$0.877880\pi$
$488$	−13.2655	+	7.65884i	−0.600501	+	0.346700i
$489$	10.1362	−	17.5563i	0.458373	−	0.793925i
$490$		0			0
$491$	0.695625	−	1.20486i	0.0313931	−	0.0543745i	−0.849902	−	0.526941i	$-0.823339\pi$
$491$	0.695625	−	1.20486i	0.0313931	−	0.0543745i	0.881295	+	0.472566i	$0.156672\pi$
$492$	12.7474	+	7.35974i	0.574699	+	0.331803i
$493$			3.24109i			0.145972i
$494$	19.0550	−	12.9480i	0.857326	−	0.582557i
$495$		0			0
$496$	−7.78048	+	13.4762i	−0.349354	+	0.605099i
$497$	−6.13021	−	3.53928i	−0.274977	−	0.158758i
$498$	6.66818	−	3.84988i	0.298808	−	0.172517i
$499$	−8.33255	+	14.4324i	−0.373016	+	0.646083i	−0.990028	−	0.140871i	$-0.955010\pi$
$499$	−8.33255	+	14.4324i	−0.373016	+	0.646083i	0.617012	+	0.786954i	$0.288343\pi$
$500$		0			0
$501$	−50.1427			−2.24021
$502$		−	20.6327i		−	0.920881i
$503$	13.5439	−	7.81956i	0.603892	−	0.348657i	−0.166679	−	0.986011i	$-0.553304\pi$
$503$	13.5439	−	7.81956i	0.603892	−	0.348657i	0.770571	+	0.637354i	$0.219971\pi$
$504$	−5.88607	−	10.1950i	−0.262186	−	0.454120i
$505$		0			0
$506$	15.2084			0.676096
$507$	−17.6697	+	10.2016i	−0.784741	+	0.453070i
$508$	1.16150	+	0.670591i	0.0515331	+	0.0297526i
$509$	−9.57702	−	16.5879i	−0.424494	−	0.735245i	0.571879	−	0.820338i	$-0.306215\pi$
$509$	−9.57702	−	16.5879i	−0.424494	−	0.735245i	−0.996373	+	0.0850929i	$0.972881\pi$
$510$		0			0
$511$	1.13406	−	1.96424i	0.0501677	−	0.0868929i
$512$		−	23.2910i		−	1.02933i
$513$	24.5246	+	36.0919i	1.08279	+	1.59349i
$514$	−6.76389			−0.298342
$515$		0			0
$516$	−8.85327	+	15.3343i	−0.389743	+	0.675055i
$517$	22.8589	−	13.1976i	1.00533	−	0.580430i
$518$	2.37027	+	1.36848i	0.104144	+	0.0601273i
$519$	−34.7110	−	60.1212i	−1.52364	−	2.63903i
$520$		0			0
$521$	−19.2394			−0.842892			−0.421446	−	0.906853i	$-0.638477\pi$
$521$	−19.2394			−0.842892			−0.421446	+	0.906853i	$0.638477\pi$
$522$	7.23622	−	4.17784i	0.316721	−	0.182859i
$523$	5.74993	−	3.31973i	0.251427	−	0.145161i	−0.368990	−	0.929433i	$-0.620296\pi$
$523$	5.74993	−	3.31973i	0.251427	−	0.145161i	0.620418	+	0.784272i	$0.286963\pi$
$524$	−7.51490			−0.328290
$525$		0			0
$526$	3.36887	+	5.83505i	0.146890	+	0.254420i
$527$	−15.6627	−	9.04285i	−0.682277	−	0.393913i
$528$	−29.5678	+	17.0710i	−1.28677	+	0.742919i
$529$	−7.44657	+	12.8978i	−0.323764	+	0.560775i
$530$		0			0
$531$	64.3349			2.79190
$532$	−0.672391	+	1.39068i	−0.0291519	+	0.0602935i
$533$		−	36.8517i		−	1.59623i
$534$	−14.3925	+	24.9286i	−0.622826	+	1.07877i
$535$		0			0
$536$	−13.0305	−	22.5694i	−0.562830	−	0.974850i
$537$	−6.14649	−	3.54868i	−0.265241	−	0.153137i
$538$	24.7441	−	14.2860i	1.06679	−	0.615914i
$539$	29.7317			1.28064
$540$		0			0
$541$	−20.8756	−	36.1575i	−0.897510	−	1.55453i	−0.830667	−	0.556770i	$-0.812040\pi$
$541$	−20.8756	−	36.1575i	−0.897510	−	1.55453i	−0.0668435	−	0.997763i	$-0.521293\pi$
$542$	−21.9674	+	12.6829i	−0.943581	+	0.544777i
$543$		−	68.0714i		−	2.92122i
$544$	9.21606			0.395135
$545$		0			0
$546$	−4.90540	+	8.49641i	−0.209932	+	0.363613i
$547$	−10.5700	+	6.10258i	−0.451939	+	0.260927i	−0.708649	−	0.705561i	$-0.750695\pi$
$547$	−10.5700	+	6.10258i	−0.451939	+	0.260927i	0.256710	+	0.966489i	$0.417362\pi$
$548$	−6.41512	−	3.70377i	−0.274040	−	0.158217i
$549$	−15.6565	+	27.1179i	−0.668204	+	1.15736i
$550$		0			0
$551$	−4.38066	−	2.11804i	−0.186622	−	0.0902317i
$552$			26.6756i			1.13539i
$553$	4.76819	+	2.75291i	0.202764	+	0.117066i
$554$	0.488934	−	0.846858i	0.0207728	−	0.0359795i
$555$		0			0
$556$	3.08571	−	5.34461i	0.130863	−	0.226662i
$557$	−30.4450	+	17.5774i	−1.28999	+	0.744779i	−0.978653	−	0.205519i	$-0.934112\pi$
$557$	−30.4450	+	17.5774i	−1.28999	+	0.744779i	−0.311342	+	0.950298i	$0.600778\pi$
$558$			46.6257i			1.97382i
$559$	44.3301			1.87496
$560$		0			0
$561$	−19.8407	−	34.3651i	−0.837675	−	1.45090i
$562$		−	0.699634i		−	0.0295123i
$563$			17.8406i			0.751891i	0.926642	+	0.375945i	$0.122682\pi$
$563$			17.8406i			0.751891i	−0.926642	+	0.375945i	$0.877318\pi$
$564$	5.21600	+	9.03438i	0.219633	+	0.380416i
$565$		0			0
$566$	18.4248	+	31.9127i	0.774452	+	1.34139i
$567$	−6.14537	−	3.54803i	−0.258081	−	0.149003i
$568$	−30.9402	−	17.8633i	−1.29822	−	0.749529i
$569$	−31.6042			−1.32492			−0.662459	−	0.749098i	$-0.730487\pi$
$569$	−31.6042			−1.32492			−0.662459	+	0.749098i	$0.730487\pi$
$570$		0			0
$571$	−4.73053			−0.197967			−0.0989833	−	0.995089i	$-0.531559\pi$
$571$	−4.73053			−0.197967			−0.0989833	+	0.995089i	$0.531559\pi$
$572$	−10.0281	−	5.78975i	−0.419298	−	0.242082i
$573$	−5.90501	−	3.40926i	−0.246685	−	0.142424i
$574$	−3.01205	−	5.21702i	−0.125721	−	0.217754i
$575$		0			0
$576$	−27.5810	−	47.7717i	−1.14921	−	1.99049i
$577$		−	24.4074i		−	1.01609i	−0.861330	−	0.508047i	$-0.830368\pi$
$577$		−	24.4074i		−	1.01609i	0.861330	−	0.508047i	$-0.169632\pi$
$578$			10.2062i			0.424522i
$579$	−6.92174	−	11.9888i	−0.287658	−	0.498238i
$580$		0			0
$581$	1.29254			0.0536235
$582$		−	35.1008i		−	1.45497i
$583$	32.8171	−	18.9470i	1.35915	−	0.784703i
$584$	5.72377	−	9.91386i	0.236851	−	0.410239i
$585$		0			0
$586$	2.24052	−	3.88070i	0.0925551	−	0.160310i
$587$	−24.7817	−	14.3077i	−1.02285	−	0.590543i	−0.107922	−	0.994159i	$-0.534420\pi$
$587$	−24.7817	−	14.3077i	−1.02285	−	0.590543i	−0.914928	+	0.403616i	$0.867753\pi$
$588$			11.7507i			0.484590i
$589$	22.4578	−	15.2602i	0.925358	−	0.628785i
$590$		0			0
$591$	29.2888	−	50.7297i	1.20478	−	2.08674i
$592$	8.16186	+	4.71225i	0.335450	+	0.193672i
$593$	3.21738	−	1.85756i	0.132122	−	0.0762807i	−0.432482	−	0.901642i	$-0.642362\pi$
$593$	3.21738	−	1.85756i	0.132122	−	0.0762807i	0.564604	+	0.825362i	$0.309029\pi$
$594$	−26.7358	+	46.3077i	−1.09698	+	1.90003i
$595$		0			0
$596$	−2.19492			−0.0899076
$597$			18.7430i			0.767099i
$598$	13.0324	−	7.52423i	0.532933	−	0.307689i
$599$	3.54970	+	6.14826i	0.145037	+	0.251211i	0.929387	−	0.369108i	$-0.120337\pi$
$599$	3.54970	+	6.14826i	0.145037	+	0.251211i	−0.784350	+	0.620319i	$0.787003\pi$
$600$		0			0
$601$	−11.0596			−0.451131			−0.225566	−	0.974228i	$-0.572423\pi$
$601$	−11.0596			−0.451131			−0.225566	+	0.974228i	$0.572423\pi$
$602$	6.27572	−	3.62329i	0.255779	−	0.147674i
$603$	−46.1373	−	26.6374i	−1.87886	−	1.08476i
$604$	2.76778	+	4.79394i	0.112619	+	0.195063i
$605$		0			0
$606$	−1.76231	+	3.05242i	−0.0715891	+	0.123996i
$607$		−	27.1193i		−	1.10074i	−0.834921	−	0.550369i	$-0.814487\pi$
$607$		−	27.1193i		−	1.10074i	0.834921	−	0.550369i	$-0.185513\pi$
$608$	−6.02266	+	12.4564i	−0.244251	+	0.505174i
$609$	2.07214			0.0839673
$610$		0			0
$611$	13.0588	−	22.6185i	0.528302	−	0.915046i
$612$	9.19369	−	5.30798i	0.371633	−	0.214562i
$613$	−36.2268	−	20.9156i	−1.46319	−	0.844772i	−0.464031	−	0.885819i	$-0.653597\pi$
$613$	−36.2268	−	20.9156i	−1.46319	−	0.844772i	−0.999157	+	0.0410468i	$0.986931\pi$
$614$	−12.1127	−	20.9797i	−0.488827	−	0.846673i
$615$		0			0
$616$	−8.40062			−0.338471
$617$	15.3332	−	8.85262i	0.617291	−	0.356393i	−0.158523	−	0.987355i	$-0.550673\pi$
$617$	15.3332	−	8.85262i	0.617291	−	0.356393i	0.775813	+	0.630962i	$0.217340\pi$
$618$	10.5012	−	6.06286i	0.422420	−	0.243884i
$619$	39.8064			1.59995			0.799976	−	0.600032i	$-0.204845\pi$
$619$	39.8064			1.59995			0.799976	+	0.600032i	$0.204845\pi$
$620$		0			0
$621$	14.2515	+	24.6844i	0.571895	+	0.990551i
$622$	7.91908	+	4.57208i	0.317526	+	0.183324i
$623$	−4.18471	+	2.41604i	−0.167657	+	0.0967966i
$624$	−16.8914	+	29.2568i	−0.676198	+	1.17121i
$625$		0			0
$626$	−28.5732			−1.14201
$627$	59.4137	−	4.35919i	2.37275	−	0.174089i
$628$			2.01072i			0.0802366i
$629$	−5.47681	+	9.48611i	−0.218375	+	0.378236i
$630$		0			0
$631$	−23.0990	−	40.0087i	−0.919557	−	1.59272i	−0.800088	−	0.599882i	$-0.795214\pi$
$631$	−23.0990	−	40.0087i	−0.919557	−	1.59272i	−0.119469	−	0.992838i	$-0.538119\pi$
$632$	24.0659	+	13.8944i	0.957288	+	0.552691i
$633$	33.4965	−	19.3392i	1.33137	−	0.768664i
$634$	1.23740			0.0491433
$635$		0			0
$636$	7.48829	+	12.9701i	0.296930	+	0.514298i
$637$	25.4776	−	14.7095i	1.00946	−	0.582813i
$638$		−	5.96262i		−	0.236062i
$639$	−73.0340			−2.88918
$640$		0			0
$641$	−3.30674	+	5.72744i	−0.130608	+	0.226220i	−0.923911	−	0.382607i	$-0.875026\pi$
$641$	−3.30674	+	5.72744i	−0.130608	+	0.226220i	0.793303	+	0.608827i	$0.208360\pi$
$642$	29.9079	−	17.2673i	1.18037	−	0.681487i
$643$	26.5135	+	15.3076i	1.04559	+	0.603673i	0.921412	−	0.388587i	$-0.127037\pi$
$643$	26.5135	+	15.3076i	1.04559	+	0.603673i	0.124180	+	0.992260i	$0.460370\pi$
$644$	−0.504503	+	0.873824i	−0.0198802	+	0.0344335i
$645$		0			0
$646$	13.5691	+	6.56063i	0.533868	+	0.258125i
$647$			11.8979i			0.467753i	0.972266	+	0.233877i	$0.0751412\pi$
$647$			11.8979i			0.467753i	−0.972266	+	0.233877i	$0.924859\pi$
$648$	−31.0167	−	17.9075i	−1.21845	−	0.703474i
$649$	22.9548	−	39.7588i	0.901053	−	1.56067i
$650$		0			0
$651$	−5.78140	+	10.0137i	−0.226591	+	0.392467i
$652$	3.35167	−	1.93509i	0.131262	−	0.0757839i
$653$		−	1.42899i		−	0.0559207i	−0.999609	−	0.0279604i	$-0.991099\pi$
$653$		−	1.42899i		−	0.0559207i	0.999609	−	0.0279604i	$-0.00890122\pi$
$654$	20.1171			0.786640
$655$		0			0
$656$	−10.3718	−	17.9645i	−0.404950	−	0.701395i
$657$		−	23.4015i		−	0.912981i
$658$		−	4.26941i		−	0.166439i
$659$	−12.2485	−	21.2150i	−0.477134	−	0.826420i	0.522523	−	0.852625i	$-0.324991\pi$
$659$	−12.2485	−	21.2150i	−0.477134	−	0.826420i	−0.999657	+	0.0262051i	$0.991658\pi$
$660$		0			0
$661$	1.61303	+	2.79385i	0.0627396	+	0.108668i	0.895689	−	0.444681i	$-0.146683\pi$
$661$	1.61303	+	2.79385i	0.0627396	+	0.108668i	−0.832949	+	0.553349i	$0.813350\pi$
$662$	−31.7984	−	18.3588i	−1.23588	−	0.713535i
$663$	−34.0037	−	19.6320i	−1.32059	−	0.762445i
$664$	6.52366			0.253167
$665$		0			0
$666$	28.2389			1.09423
$667$	−2.75256	−	1.58919i	−0.106580	−	0.0615338i
$668$	−8.29023	−	4.78636i	−0.320758	−	0.185190i
$669$	34.3379	+	59.4750i	1.32758	+	2.29944i
$670$		0			0
$671$	11.1725	+	19.3514i	0.431311	+	0.747052i
$672$		−	5.89213i		−	0.227294i
$673$			37.1424i			1.43173i	0.698237	+	0.715866i	$0.253968\pi$
$673$			37.1424i			1.43173i	−0.698237	+	0.715866i	$0.746032\pi$
$674$	−12.3350	−	21.3649i	−0.475127	−	0.822944i
$675$		0			0
$676$	−3.89518			−0.149815
$677$			24.7550i			0.951412i	0.879604	+	0.475706i	$0.157807\pi$
$677$			24.7550i			0.951412i	−0.879604	+	0.475706i	$0.842193\pi$
$678$	−4.84402	+	2.79669i	−0.186033	+	0.107406i
$679$	2.94614	−	5.10287i	0.113063	−	0.195830i
$680$		0			0
$681$	−27.5957	+	47.7972i	−1.05747	+	1.83159i
$682$	28.8145	+	16.6361i	1.10337	+	0.637028i
$683$			40.1153i			1.53497i	0.641068	+	0.767484i	$0.278492\pi$
$683$			40.1153i			1.53497i	−0.641068	+	0.767484i	$0.721508\pi$
$684$	1.16621	+	15.8949i	0.0445912	+	0.607757i
$685$		0			0
$686$	4.94370	−	8.56274i	0.188751	−	0.326927i
$687$	−24.8482	−	14.3461i	−0.948020	−	0.547340i
$688$	21.6100	−	12.4766i	0.823875	−	0.475664i
$689$	18.7477	−	32.4720i	0.714230	−	1.23708i
$690$		0			0
$691$	39.4963			1.50251			0.751254	−	0.660013i	$-0.229449\pi$
$691$	39.4963			1.50251			0.751254	+	0.660013i	$0.229449\pi$
$692$		−	13.2533i		−	0.503816i
$693$	−14.8722	+	8.58645i	−0.564947	+	0.326172i
$694$	−4.89545	−	8.47917i	−0.185829	−	0.321865i
$695$		0			0
$696$	10.4584			0.396426
$697$	20.8792	−	12.0546i	0.790855	−	0.456600i
$698$	12.2955	+	7.09879i	0.465390	+	0.268693i
$699$	23.9203	+	41.4312i	0.904748	+	1.56707i
$700$		0			0
$701$	−0.0109776	+	0.0190137i	−0.000414618	+	0.000718139i	−0.866233	−	0.499641i	$-0.833465\pi$
$701$	−0.0109776	+	0.0190137i	−0.000414618	+	0.000718139i	0.865818	+	0.500359i	$0.166799\pi$
$702$			52.9092i			1.99693i
$703$	−9.24234	−	13.6016i	−0.348581	−	0.512994i
$704$	−39.3637			−1.48357
$705$		0			0
$706$	−7.02535	+	12.1683i	−0.264402	+	0.457958i
$707$	−0.512402	+	0.295835i	−0.0192708	+	0.0111260i
$708$	15.7136	+	9.07226i	0.590554	+	0.340957i
$709$	−8.90087	−	15.4168i	−0.334279	−	0.578989i	0.649067	−	0.760731i	$-0.275160\pi$
$709$	−8.90087	−	15.4168i	−0.334279	−	0.578989i	−0.983346	+	0.181743i	$0.941826\pi$
$710$		0			0
$711$	56.8071			2.13043
$712$	−21.1209	+	12.1942i	−0.791540	+	0.456996i
$713$	15.3596	−	8.86789i	0.575223	−	0.332105i
$714$	−6.41844			−0.240204
$715$		0			0
$716$	−0.677477	−	1.17342i	−0.0253185	−	0.0438529i
$717$	−61.9118	−	35.7448i	−2.31214	−	1.33491i
$718$	−0.114286	+	0.0659833i	−0.00426513	+	0.00246247i
$719$	9.40515	−	16.2902i	0.350753	−	0.607522i	−0.635629	−	0.771995i	$-0.719259\pi$
$719$	9.40515	−	16.2902i	0.350753	−	0.607522i	0.986382	+	0.164473i	$0.0525923\pi$
$720$		0			0
$721$	2.03552			0.0758066
$722$	−17.7347	+	14.0526i	−0.660016	+	0.522983i
$723$			40.1294i			1.49243i
$724$	6.49774	−	11.2544i	0.241487	−	0.418267i
$725$		0			0
$726$	16.5419	+	28.6513i	0.613926	+	1.06335i
$727$	4.33274	+	2.50151i	0.160692	+	0.0927758i	0.578190	−	0.815902i	$-0.303759\pi$
$727$	4.33274	+	2.50151i	0.160692	+	0.0927758i	−0.417497	+	0.908678i	$0.637093\pi$
$728$	−7.19864	+	4.15613i	−0.266799	+	0.154037i
$729$	18.2986			0.677725
$730$		0			0
$731$	14.5009	+	25.1162i	0.536334	+	0.928957i
$732$	−7.64812	+	4.41565i	−0.282683	+	0.163207i
$733$		−	23.5259i		−	0.868950i	−0.900684	−	0.434475i	$-0.856934\pi$
$733$		−	23.5259i		−	0.868950i	0.900684	−	0.434475i	$-0.143066\pi$
$734$	13.9809			0.516046
$735$		0			0
$736$	−4.51887	+	7.82691i	−0.166568	+	0.288504i
$737$	−32.9237	+	19.0085i	−1.21276	+	0.700187i
$738$	−53.8274	−	31.0772i	−1.98141	−	1.14397i
$739$	−18.6918	+	32.3752i	−0.687590	+	1.19094i	0.285026	+	0.958520i	$0.407998\pi$
$739$	−18.6918	+	32.3752i	−0.687590	+	1.19094i	−0.972615	+	0.232421i	$0.925335\pi$
$740$		0			0
$741$	48.7559	−	33.1299i	1.79109	−	1.21706i
$742$		−	6.12932i		−	0.225014i
$743$	−8.99679	−	5.19430i	−0.330060	−	0.190560i	0.325808	−	0.945436i	$-0.394364\pi$
$743$	−8.99679	−	5.19430i	−0.330060	−	0.190560i	−0.655868	+	0.754876i	$0.727697\pi$
$744$	−29.1797	+	50.5407i	−1.06978	+	1.85291i
$745$		0			0
$746$	8.64539	−	14.9742i	0.316530	−	0.548246i
$747$	11.5493	−	6.66797i	0.422566	−	0.243968i
$748$		−	7.57556i		−	0.276990i
$749$	5.79725			0.211827
$750$		0			0
$751$	15.6413	+	27.0915i	0.570758	+	0.988581i	0.996488	+	0.0837314i	$0.0266838\pi$
$751$	15.6413	+	27.0915i	0.570758	+	0.988581i	−0.425731	+	0.904850i	$0.639983\pi$
$752$		−	14.7014i		−	0.536105i
$753$		−	52.7927i		−	1.92387i
$754$	−2.94996	−	5.10947i	−0.107431	−	0.186076i
$755$		0			0
$756$	−1.77379	−	3.07230i	−0.0645122	−	0.111738i
$757$	−10.9328	−	6.31205i	−0.397359	−	0.229415i	0.287985	−	0.957635i	$-0.407015\pi$
$757$	−10.9328	−	6.31205i	−0.397359	−	0.229415i	−0.685344	+	0.728220i	$0.740348\pi$
$758$	−6.79689	−	3.92419i	−0.246874	−	0.142533i
$759$	38.9137			1.41248
$760$		0			0
$761$	11.5495			0.418668			0.209334	−	0.977844i	$-0.432870\pi$
$761$	11.5495			0.418668			0.209334	+	0.977844i	$0.432870\pi$
$762$	−7.24551	−	4.18320i	−0.262477	−	0.151541i
$763$	2.92457	+	1.68850i	0.105877	+	0.0611279i
$764$	−0.650861	−	1.12732i	−0.0235473	−	0.0407851i
$765$		0			0
$766$	−1.70849	−	2.95918i	−0.0617301	−	0.106920i
$767$		−	45.4267i		−	1.64026i
$768$		−	38.5951i		−	1.39268i
$769$	−13.4603	−	23.3140i	−0.485392	−	0.840724i	0.514467	−	0.857510i	$-0.327990\pi$
$769$	−13.4603	−	23.3140i	−0.485392	−	0.840724i	−0.999859	+	0.0167864i	$0.994656\pi$
$770$		0			0
$771$	−17.3067			−0.623286
$772$		−	2.64286i		−	0.0951184i
$773$	18.4750	−	10.6666i	0.664500	−	0.383649i	−0.129489	−	0.991581i	$-0.541334\pi$
$773$	18.4750	−	10.6666i	0.664500	−	0.383649i	0.793989	+	0.607932i	$0.208001\pi$
$774$	37.3838	−	64.7506i	1.34373	−	2.32741i
$775$		0			0
$776$	14.8697	−	25.7550i	0.533790	−	0.924552i
$777$	6.06479	+	3.50151i	0.217573	+	0.125616i
$778$			7.54024i			0.270331i
$779$	2.64851	+	36.0979i	0.0948926	+	1.29334i
$780$		0			0
$781$	−26.0586	+	45.1348i	−0.932450	+	1.61505i
$782$	8.52605	+	4.92252i	0.304891	+	0.176029i
$783$	9.67779	−	5.58747i	0.345856	−	0.199680i
$784$	8.27989	−	14.3412i	0.295710	−	0.512185i
$785$		0			0
$786$	46.8786			1.67210
$787$		−	3.52489i		−	0.125649i	−0.998025	−	0.0628243i	$-0.979989\pi$
$787$		−	3.52489i		−	0.125649i	0.998025	−	0.0628243i	$-0.0200108\pi$
$788$	9.68478	−	5.59151i	0.345006	−	0.199189i
$789$	8.61990	+	14.9301i	0.306877	+	0.531526i
$790$		0			0
$791$	−0.938948			−0.0333852
$792$	−75.0624	+	43.3373i	−2.66723	+	1.53992i
$793$	19.1479	+	11.0550i	0.679961	+	0.392575i
$794$	18.1911	+	31.5078i	0.645576	+	1.11817i
$795$		0			0
$796$	−1.78911	+	3.09882i	−0.0634132	+	0.109835i
$797$			39.0084i			1.38175i	0.722974	+	0.690875i	$0.242774\pi$
$797$			39.0084i			1.38175i	−0.722974	+	0.690875i	$0.757226\pi$
$798$	4.19443	−	8.67516i	0.148481	−	0.307097i
$799$	17.0867			0.604484
$800$		0			0
$801$	−24.9278	+	43.1763i	−0.880782	+	1.52556i
$802$	31.2937	−	18.0674i	1.10502	−	0.637983i
$803$	−14.4621	−	8.34969i	−0.510356	−	0.294654i
$804$	−7.51261	−	13.0122i	−0.264949	−	0.458906i
$805$		0			0
$806$	32.9222			1.15964
$807$	63.3126	−	36.5535i	2.22871	−	1.28675i
$808$	−2.58618	+	1.49313i	−0.0909814	+	0.0525282i
$809$	−50.7196			−1.78321			−0.891604	−	0.452816i	$-0.850419\pi$
$809$	−50.7196			−1.78321			−0.891604	+	0.452816i	$0.850419\pi$
$810$		0			0
$811$	−14.5188	−	25.1473i	−0.509824	−	0.883041i	−0.999935	−	0.0113812i	$-0.996377\pi$
$811$	−14.5188	−	25.1473i	−0.509824	−	0.883041i	0.490111	−	0.871660i	$-0.336956\pi$
$812$	0.342592	+	0.197796i	0.0120226	+	0.00694127i
$813$	−56.2078	+	32.4516i	−1.97129	+	1.13813i
$814$	10.0757	−	17.4515i	0.353151	−	0.611676i
$815$		0			0
$816$	−22.1015			−0.773706
$817$	−43.4233	+	3.18597i	−1.51919	+	0.111463i
$818$			17.8310i			0.623445i
$819$	−8.49614	+	14.7158i	−0.296879	+	0.514210i
$820$		0			0
$821$	−16.4939	−	28.5682i	−0.575640	−	0.997038i	−0.995972	−	0.0896677i	$-0.971420\pi$
$821$	−16.4939	−	28.5682i	−0.575640	−	0.997038i	0.420331	−	0.907371i	$-0.361914\pi$
$822$	40.0180	+	23.1044i	1.39579	+	0.805859i
$823$	−22.9959	+	13.2767i	−0.801586	+	0.462796i	−0.844025	−	0.536303i	$-0.819820\pi$
$823$	−22.9959	+	13.2767i	−0.801586	+	0.462796i	0.0424397	+	0.999099i	$0.486487\pi$
$824$	10.2736			0.357898
$825$		0			0
$826$	−3.71292	−	6.43096i	−0.129189	−	0.223762i
$827$	28.3767	−	16.3833i	0.986754	−	0.569703i	0.0824515	−	0.996595i	$-0.473725\pi$
$827$	28.3767	−	16.3833i	0.986754	−	0.569703i	0.904302	+	0.426892i	$0.140392\pi$
$828$			10.4106i			0.361792i
$829$	−32.4548			−1.12720			−0.563601	−	0.826047i	$-0.690584\pi$
$829$	−32.4548			−1.12720			−0.563601	+	0.826047i	$0.690584\pi$
$830$		0			0
$831$	1.25103	−	2.16685i	0.0433978	−	0.0751671i
$832$	−33.7314	+	19.4748i	−1.16943	+	0.675168i
$833$	16.6680	+	9.62329i	0.577513	+	0.333427i
$834$	−19.2489	+	33.3401i	−0.666536	+	1.15447i
$835$		0			0
$836$	10.2391	+	4.95061i	0.354127	+	0.171220i
$837$			62.3576i			2.15539i
$838$	−6.36780	−	3.67645i	−0.219972	−	0.127001i
$839$	−17.6049	+	30.4926i	−0.607788	+	1.05272i	0.383816	+	0.923410i	$0.374610\pi$
$839$	−17.6049	+	30.4926i	−0.607788	+	1.05272i	−0.991604	+	0.129310i	$0.958724\pi$
$840$		0			0
$841$	13.8769	−	24.0356i	0.478515	−	0.828813i
$842$	−28.4065	+	16.4005i	−0.978952	+	0.565198i
$843$		−	1.79015i		−	0.0616560i
$844$	7.38408			0.254171
$845$		0			0
$846$	−22.0251	−	38.1486i	−0.757238	−	1.31158i
$847$			5.55368i			0.190827i
$848$		−	21.1059i		−	0.724779i
$849$	47.1434	+	81.6547i	1.61796	+	2.80238i
$850$		0			0
$851$	−5.37084	−	9.30257i	−0.184110	−	0.318888i
$852$	−17.8383	−	10.2990i	−0.611132	−	0.352837i
$853$	1.54867	+	0.894126i	0.0530255	+	0.0306143i	0.526278	−	0.850312i	$-0.323587\pi$
$853$	1.54867	+	0.894126i	0.0530255	+	0.0306143i	−0.473253	+	0.880927i	$0.656920\pi$
$854$	3.61430			0.123679
$855$		0			0
$856$	29.2597			1.00008
$857$	3.12964	+	1.80690i	0.106906	+	0.0617224i	0.552500	−	0.833513i	$-0.313674\pi$
$857$	3.12964	+	1.80690i	0.106906	+	0.0617224i	−0.445594	+	0.895235i	$0.647007\pi$
$858$	62.5564	+	36.1170i	2.13564	+	1.23301i
$859$	−12.6824	−	21.9666i	−0.432719	−	0.749491i	0.564388	−	0.825510i	$-0.309112\pi$
$859$	−12.6824	−	21.9666i	−0.432719	−	0.749491i	−0.997106	+	0.0760192i	$0.975779\pi$
$860$		0			0
$861$	−7.70691	−	13.3488i	−0.262651	−	0.454924i
$862$		−	17.9337i		−	0.610824i
$863$		−	29.9878i		−	1.02080i	−0.859939	−	0.510398i	$-0.829498\pi$
$863$		−	29.9878i		−	1.02080i	0.859939	−	0.510398i	$-0.170502\pi$
$864$	−15.8880	−	27.5188i	−0.540520	−	0.936209i
$865$		0			0
$866$	1.15618			0.0392887
$867$			26.1145i			0.886895i
$868$	−1.91171	+	1.10372i	−0.0648875	+	0.0374628i
$869$	20.2688	−	35.1067i	0.687573	−	1.19091i
$870$		0			0
$871$	−18.8086	+	32.5774i	−0.637305	+	1.10384i
$872$	14.7608	+	8.52216i	0.499864	+	0.288597i
$873$		−	60.7945i		−	2.05758i
$874$	−12.2250	+	8.30695i	−0.413517	+	0.280987i
$875$		0			0
$876$	3.30000	−	5.71576i	0.111497	−	0.193118i
$877$	9.22125	+	5.32389i	0.311380	+	0.179775i	0.647544	−	0.762028i	$-0.275796\pi$
$877$	9.22125	+	5.32389i	0.311380	+	0.179775i	−0.336164	+	0.941803i	$0.609130\pi$
$878$	28.2979	−	16.3378i	0.955007	−	0.551374i
$879$	5.73281	−	9.92951i	0.193363	−	0.334914i
$880$		0			0
$881$	−31.5797			−1.06395			−0.531973	−	0.846761i	$-0.678549\pi$
$881$	−31.5797			−1.06395			−0.531973	+	0.846761i	$0.678549\pi$
$882$		−	49.6185i		−	1.67074i
$883$	14.7375	−	8.50871i	0.495957	−	0.286341i	−0.231085	−	0.972933i	$-0.574228\pi$
$883$	14.7375	−	8.50871i	0.495957	−	0.286341i	0.727042	+	0.686593i	$0.240894\pi$
$884$	−3.74795	−	6.49163i	−0.126057	−	0.218337i
$885$		0			0
$886$	10.4388			0.350700
$887$	11.4567	−	6.61451i	0.384677	−	0.222093i	−0.295174	−	0.955443i	$-0.595378\pi$
$887$	11.4567	−	6.61451i	0.384677	−	0.222093i	0.679851	+	0.733350i	$0.262044\pi$
$888$	30.6100	+	17.6727i	1.02721	+	0.593057i
$889$	−0.702223	−	1.21629i	−0.0235518	−	0.0407929i
$890$		0			0
$891$	−26.1230	+	45.2464i	−0.875155	+	1.51581i
$892$			13.1109i			0.438985i
$893$	−11.1661	+	23.0943i	−0.373659	+	0.772823i
$894$	13.6921			0.457933
$895$		0			0
$896$	−1.24988	+	2.16486i	−0.0417557	+	0.0723229i
$897$	33.3458	−	19.2522i	1.11338	−	0.642812i
$898$	−9.93607	−	5.73659i	−0.331571	−	0.191433i
$899$	−3.47675	−	6.02191i	−0.115956	−	0.200842i
$900$		0			0
$901$	24.5303			0.817222
$902$	−38.4113	+	22.1768i	−1.27896	+	0.738406i
$903$	16.0576	−	9.27088i	0.534365	−	0.308516i
$904$	−4.73903			−0.157618
$905$		0			0
$906$	−17.2656	−	29.9050i	−0.573613	−	0.993526i
$907$	−12.8955	−	7.44520i	−0.428187	−	0.247214i	0.270387	−	0.962752i	$-0.412848\pi$
$907$	−12.8955	−	7.44520i	−0.428187	−	0.247214i	−0.698574	+	0.715538i	$0.746182\pi$
$908$	−9.12494	+	5.26829i	−0.302822	+	0.174834i
$909$	−3.05232	+	5.28678i	−0.101239	+	0.175351i
$910$		0			0
$911$	−49.5480			−1.64160			−0.820800	−	0.571216i	$-0.806472\pi$
$911$	−49.5480			−1.64160			−0.820800	+	0.571216i	$0.806472\pi$
$912$	14.4432	−	29.8723i	0.478263	−	0.989172i
$913$		−	9.51655i		−	0.314952i
$914$	6.35400	−	11.0055i	0.210172	−	0.364028i
$915$		0			0
$916$	−2.73882	−	4.74377i	−0.0904931	−	0.156739i
$917$	6.81509	+	3.93469i	0.225054	+	0.129935i
$918$	−29.9769	+	17.3072i	−0.989385	+	0.571222i
$919$	−27.3835			−0.903300			−0.451650	−	0.892195i	$-0.649164\pi$
$919$	−27.3835			−0.903300			−0.451650	+	0.892195i	$0.649164\pi$
$920$		0			0
$921$	−30.9926	−	53.6807i	−1.02124	−	1.76884i
$922$	5.86513	−	3.38623i	0.193158	−	0.111520i
$923$			51.5691i			1.69742i
$924$	−4.84331			−0.159333
$925$		0			0
$926$	21.0523	−	36.4637i	0.691821	−	1.19827i
$927$	18.1880	−	10.5009i	0.597373	−	0.344893i
$928$	3.06863	+	1.77167i	0.100733	+	0.0581580i
$929$	26.0947	−	45.1973i	0.856139	−	1.48288i	−0.0194449	−	0.999811i	$-0.506190\pi$
$929$	26.0947	−	45.1973i	0.856139	−	1.48288i	0.875584	−	0.483066i	$-0.160477\pi$
$930$		0			0
$931$	−23.8993	+	16.2397i	−0.783269	+	0.532234i
$932$			9.13323i			0.299169i
$933$	20.2625	+	11.6985i	0.663364	+	0.382993i
$934$	19.5947	−	33.9390i	0.641158	−	1.11052i
$935$		0			0
$936$	−42.8815	+	74.2729i	−1.40163	+	2.42769i
$937$	−13.4925	+	7.78988i	−0.440780	+	0.254484i	−0.703928	−	0.710271i	$-0.748572\pi$
$937$	−13.4925	+	7.78988i	−0.440780	+	0.254484i	0.263149	+	0.964755i	$0.415239\pi$
$938$			6.14922i			0.200779i
$939$	−73.1099			−2.38585
$940$		0			0
$941$	29.3277	+	50.7970i	0.956055	+	1.65594i	0.731936	+	0.681373i	$0.238617\pi$
$941$	29.3277	+	50.7970i	0.956055	+	1.65594i	0.224119	+	0.974562i	$0.428050\pi$
$942$		−	12.5431i		−	0.408675i
$943$			23.6427i			0.769913i
$944$	−12.7852	−	22.1446i	−0.416122	−	0.720745i
$945$		0			0
$946$	−26.6771	−	46.2062i	−0.867349	−	1.50229i
$947$	10.6578	+	6.15326i	0.346331	+	0.199954i	0.663068	−	0.748559i	$-0.269254\pi$
$947$	10.6578	+	6.15326i	0.346331	+	0.199954i	−0.316737	+	0.948513i	$0.602587\pi$
$948$	13.8750	+	8.01072i	0.450638	+	0.260176i
$949$	−16.5238			−0.536384
$950$		0			0
$951$	3.16612			0.102668
$952$	−4.70950	−	2.71903i	−0.152636	−	0.0881244i
$953$	−7.16201	−	4.13499i	−0.232000	−	0.133945i	0.379494	−	0.925194i	$-0.376098\pi$
$953$	−7.16201	−	4.13499i	−0.232000	−	0.133945i	−0.611494	+	0.791249i	$0.709431\pi$
$954$	−31.6200	−	54.7675i	−1.02374	−	1.77316i
$955$		0			0
$956$	−6.82403	−	11.8196i	−0.220705	−	0.382272i
$957$		−	15.2565i		−	0.493173i
$958$			10.7863i			0.348490i
$959$	3.87848	+	6.71773i	0.125243	+	0.216927i
$960$		0			0
$961$	7.80138			0.251657
$962$		−	19.9394i		−	0.642871i
$963$	51.8004	−	29.9070i	1.66924	−	0.963738i
$964$	−3.83054	+	6.63469i	−0.123373	+	0.213689i
$965$		0			0
$966$	3.14713	−	5.45099i	0.101257	−	0.175383i
$967$	12.3190	+	7.11235i	0.396151	+	0.228718i	0.684822	−	0.728711i	$-0.259880\pi$
$967$	12.3190	+	7.11235i	0.396151	+	0.228718i	−0.288671	+	0.957428i	$0.593213\pi$
$968$			28.0304i			0.900931i
$969$	34.7191	+	16.7866i	1.11534	+	0.539264i
$970$		0			0
$971$	−4.86930	+	8.43388i	−0.156263	+	0.270656i	−0.933518	−	0.358530i	$-0.883278\pi$
$971$	−4.86930	+	8.43388i	−0.156263	+	0.270656i	0.777255	+	0.629186i	$0.216612\pi$
$972$	−2.75235	−	1.58907i	−0.0882816	−	0.0509694i
$973$	−5.59672	+	3.23127i	−0.179423	+	0.103590i
$974$	9.83727	−	17.0387i	0.315207	−	0.545954i
$975$		0			0
$976$	12.4456			0.398374
$977$			6.35308i			0.203253i	0.994823	+	0.101627i	$0.0324047\pi$
$977$			6.35308i			0.203253i	−0.994823	+	0.101627i	$0.967595\pi$
$978$	−20.9080	+	12.0712i	−0.668564	+	0.385996i
$979$	17.7885	+	30.8107i	0.568524	+	0.984713i
$980$		0			0
$981$	34.8427			1.11244
$982$	−1.43488	+	0.828426i	−0.0457887	+	0.0264361i
$983$	−8.55708	−	4.94043i	−0.272929	−	0.157575i	0.357289	−	0.933994i	$-0.383701\pi$
$983$	−8.55708	−	4.94043i	−0.272929	−	0.157575i	−0.630218	+	0.776418i	$0.717034\pi$
$984$	−38.8981	−	67.3735i	−1.24003	−	2.14779i
$985$		0			0
$986$	1.92993	−	3.34273i	0.0614613	−	0.106454i
$987$		−	10.9241i		−	0.347718i
$988$	11.2234	−	0.823458i	0.357062	−	0.0261977i
$989$	−28.4406			−0.904358
$990$		0			0
$991$	−18.6675	+	32.3331i	−0.592993	+	1.02709i	0.400834	+	0.916151i	$0.368720\pi$
$991$	−18.6675	+	32.3331i	−0.592993	+	1.02709i	−0.993827	+	0.110943i	$0.964613\pi$
$992$	−17.1233	+	9.88614i	−0.543665	+	0.313885i
$993$	−81.3623	−	46.9745i	−2.58195	−	1.49069i
$994$	4.21496	+	7.30053i	0.133690	+	0.231559i
$995$		0			0
$996$	3.76117			0.119177
$997$	37.8408	−	21.8474i	1.19843	−	0.691914i	0.238225	−	0.971210i	$-0.423434\pi$
$997$	37.8408	−	21.8474i	1.19843	−	0.691914i	0.960205	+	0.279296i	$0.0901010\pi$
$998$	17.1877	−	9.92332i	0.544067	−	0.314117i
$999$	37.7669			1.19489

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.j.c.49.3		16
5.2	odd	4		95.2.e.c.11.3	✓	8
5.3	odd	4		475.2.e.e.201.2		8
5.4	even	2	inner	475.2.j.c.49.6		16
15.2	even	4		855.2.k.h.676.2		8
19.7	even	3	inner	475.2.j.c.349.6		16
20.7	even	4		1520.2.q.o.961.4		8
95.7	odd	12		95.2.e.c.26.3	yes	8
95.8	even	12		9025.2.a.bp.1.2		4
95.27	even	12		1805.2.a.i.1.3		4
95.64	even	6	inner	475.2.j.c.349.3		16
95.68	odd	12		9025.2.a.bg.1.3		4
95.83	odd	12		475.2.e.e.26.2		8
95.87	odd	12		1805.2.a.o.1.2		4
285.197	even	12		855.2.k.h.406.2		8
380.7	even	12		1520.2.q.o.881.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.c.11.3	✓	8	5.2	odd	4
95.2.e.c.26.3	yes	8	95.7	odd	12
475.2.e.e.26.2		8	95.83	odd	12
475.2.e.e.201.2		8	5.3	odd	4
475.2.j.c.49.3		16	1.1	even	1	trivial
475.2.j.c.49.6		16	5.4	even	2	inner
475.2.j.c.349.3		16	95.64	even	6	inner
475.2.j.c.349.6		16	19.7	even	3	inner
855.2.k.h.406.2		8	285.197	even	12
855.2.k.h.676.2		8	15.2	even	4
1520.2.q.o.881.4		8	380.7	even	12
1520.2.q.o.961.4		8	20.7	even	4
1805.2.a.i.1.3		4	95.27	even	12
1805.2.a.o.1.2		4	95.87	odd	12
9025.2.a.bg.1.3		4	95.68	odd	12
9025.2.a.bp.1.2		4	95.8	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.03136 - 0.595455i) q^{2} +(-2.63893 - 1.52359i) q^{3} +(-0.290867 - 0.503797i) q^{4} +(1.81445 + 3.14272i) q^{6} +0.609175i q^{7} +3.07461i q^{8} +(3.14263 + 5.44319i) q^{9} +4.48517 q^{11} +1.77264i q^{12} +(3.84342 - 2.21900i) q^{13} +(0.362736 - 0.628278i) q^{14} +(1.24906 - 2.16343i) q^{16} +(2.51445 + 1.45172i) q^{17} -7.48517i q^{18} +(-3.60532 + 2.44983i) q^{19} +(0.928131 - 1.60757i) q^{21} +(-4.62581 - 2.67071i) q^{22} +(-2.46580 + 1.42363i) q^{23} +(4.68443 - 8.11368i) q^{24} -5.28525 q^{26} -10.0107i q^{27} +(0.306901 - 0.177189i) q^{28} +(0.558149 + 0.966742i) q^{29} -6.22908 q^{31} +(2.74893 - 1.58710i) q^{32} +(-11.8360 - 6.83354i) q^{33} +(-1.72886 - 2.99448i) q^{34} +(1.82817 - 3.16649i) q^{36} +3.77264i q^{37} +(5.17714 - 0.379847i) q^{38} -13.5233 q^{39} +(4.15184 - 7.19120i) q^{41} +(-1.91447 + 1.10532i) q^{42} +(8.65053 + 4.99438i) q^{43} +(-1.30459 - 2.25961i) q^{44} +3.39082 q^{46} +(5.09656 - 2.94250i) q^{47} +(-6.59235 + 3.80609i) q^{48} +6.62891 q^{49} +(-4.42363 - 7.66195i) q^{51} +(-2.23585 - 1.29087i) q^{52} +(7.31681 - 4.22436i) q^{53} +(-5.96093 + 10.3246i) q^{54} -1.87298 q^{56} +(13.2467 - 0.971912i) q^{57} -1.32941i q^{58} +(5.11793 - 8.86451i) q^{59} +(2.49099 + 4.31453i) q^{61} +(6.42441 + 3.70913i) q^{62} +(-3.31586 + 1.91441i) q^{63} -8.77641 q^{64} +(8.13812 + 14.0956i) q^{66} +(-7.34057 + 4.23808i) q^{67} -1.68903i q^{68} +8.67608 q^{69} +(-5.80995 + 10.0631i) q^{71} +(-16.7357 + 9.66236i) q^{72} +(-3.22443 - 1.86162i) q^{73} +(2.24644 - 3.89095i) q^{74} +(2.28289 + 1.10377i) q^{76} +2.73225i q^{77} +(13.9474 + 8.05253i) q^{78} +(4.51908 - 7.82728i) q^{79} +(-5.82432 + 10.0880i) q^{81} +(-8.56407 + 4.94447i) q^{82} -2.12178i q^{83} -1.07985 q^{84} +(-5.94786 - 10.3020i) q^{86} -3.40155i q^{87} +13.7901i q^{88} +(3.96608 + 6.86946i) q^{89} +(1.35176 + 2.34131i) q^{91} +(1.43444 + 0.828173i) q^{92} +(16.4381 + 9.49053i) q^{93} -7.00850 q^{94} -9.67231 q^{96} +(-8.37668 - 4.83628i) q^{97} +(-6.83677 - 3.94721i) q^{98} +(14.0952 + 24.4136i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 10 q^{4} - 4 q^{6} + 2 q^{9} - 8 q^{11} - 2 q^{14} - 14 q^{16} - 10 q^{19} + 8 q^{21} + 46 q^{24} + 12 q^{26} - 2 q^{29} + 30 q^{34} + 14 q^{36} - 60 q^{39} + 16 q^{41} - 24 q^{44} + 48 q^{46} + 40 q^{49}+ \cdots + 76 q^{99}+O(q^{100}) \) 16 * q + 10 * q^4 - 4 * q^6 + 2 * q^9 - 8 * q^11 - 2 * q^14 - 14 * q^16 - 10 * q^19 + 8 * q^21 + 46 * q^24 + 12 * q^26 - 2 * q^29 + 30 * q^34 + 14 * q^36 - 60 * q^39 + 16 * q^41 - 24 * q^44 + 48 * q^46 + 40 * q^49 - 44 * q^51 - 68 * q^54 - 164 * q^56 - 10 * q^59 - 224 * q^64 + 62 * q^66 + 36 * q^69 - 40 * q^71 + 50 * q^74 + 126 * q^76 + 34 * q^79 - 24 * q^81 + 80 * q^84 - 16 * q^86 + 22 * q^89 - 12 * q^91 + 124 * q^94 + 84 * q^96 + 76 * q^99

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