LMFDB - Embedded newform 475.2.j.c.49.7

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			49.7
Root			$1.87040 - 1.07988i$ of defining polynomial
Character	$\chi$	$=$	475.49
Dual form			475.2.j.c.349.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.44154 + 0.832272i) q^{2} +(-1.00438 - 0.579878i) q^{3} +(0.385355 + 0.667454i) q^{4} +(-0.965233 - 1.67183i) q^{6} -2.43525i q^{7} -2.04621i q^{8} +(-0.827483 - 1.43324i) q^{9} -5.75477 q^{11} -0.893835i q^{12} +(1.38132 - 0.797505i) q^{13} +(2.02680 - 3.51051i) q^{14} +(2.47371 - 4.28460i) q^{16} +(5.18234 + 2.99203i) q^{17} -2.75477i q^{18} +(-0.149412 - 4.35634i) q^{19} +(-1.41215 + 2.44592i) q^{21} +(-8.29572 - 4.78953i) q^{22} +(0.814102 - 0.470022i) q^{23} +(-1.18655 + 2.05517i) q^{24} +2.65497 q^{26} +5.39862i q^{27} +(1.62542 - 0.938437i) q^{28} +(1.30917 + 2.26755i) q^{29} -5.26913 q^{31} +(3.58777 - 2.07140i) q^{32} +(5.77996 + 3.33706i) q^{33} +(4.98037 + 8.62625i) q^{34} +(0.637749 - 1.10461i) q^{36} -2.89384i q^{37} +(3.41028 - 6.40418i) q^{38} -1.84982 q^{39} +(3.15767 - 5.46925i) q^{41} +(-4.07134 + 2.35059i) q^{42} +(3.93108 + 2.26961i) q^{43} +(-2.21763 - 3.84104i) q^{44} +1.56475 q^{46} +(7.75471 - 4.47718i) q^{47} +(-4.96909 + 2.86890i) q^{48} +1.06953 q^{49} +(-3.47002 - 6.01025i) q^{51} +(1.06460 + 0.614645i) q^{52} +(1.90213 - 1.09819i) q^{53} +(-4.49313 + 7.78232i) q^{54} -4.98304 q^{56} +(-2.37608 + 4.46205i) q^{57} +4.35834i q^{58} +(-5.39939 + 9.35202i) q^{59} +(5.26434 + 9.11811i) q^{61} +(-7.59566 - 4.38535i) q^{62} +(-3.49031 + 2.01513i) q^{63} -2.99898 q^{64} +(5.55469 + 9.62100i) q^{66} +(0.874320 - 0.504789i) q^{67} +4.61197i q^{68} -1.09022 q^{69} +(-4.41694 + 7.65036i) q^{71} +(-2.93271 + 1.69320i) q^{72} +(-8.87674 - 5.12499i) q^{73} +(2.40846 - 4.17157i) q^{74} +(2.85008 - 1.77846i) q^{76} +14.0143i q^{77} +(-2.66659 - 1.53956i) q^{78} +(3.80229 - 6.58577i) q^{79} +(0.648093 - 1.12253i) q^{81} +(9.10381 - 5.25609i) q^{82} -3.11355i q^{83} -2.17672 q^{84} +(3.77787 + 6.54346i) q^{86} -3.03663i q^{87} +11.7755i q^{88} +(-5.55706 - 9.62511i) q^{89} +(-1.94213 - 3.36387i) q^{91} +(0.627436 + 0.362251i) q^{92} +(5.29220 + 3.05545i) q^{93} +14.9049 q^{94} -4.80463 q^{96} +(-3.51412 - 2.02888i) q^{97} +(1.54177 + 0.890144i) q^{98} +(4.76197 + 8.24798i) 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 $

$2$	1.44154	+	0.832272i	1.01932	+	0.588506i	0.913907	−	0.405923i	$-0.133050\pi$
$2$	1.44154	+	0.832272i	1.01932	+	0.588506i	0.105414	+	0.994428i	$0.466383\pi$
$3$	−1.00438	−	0.579878i	−0.579878	−	0.334793i	0.181207	−	0.983445i	$-0.442000\pi$
$3$	−1.00438	−	0.579878i	−0.579878	−	0.334793i	−0.761085	+	0.648652i	$0.775333\pi$
$4$	0.385355	+	0.667454i	0.192677	+	0.333727i
$5$		0			0
$5$		0			0
$6$	−0.965233	−	1.67183i	−0.394055	−	0.682523i
$7$		−	2.43525i		−	0.920440i	−0.887805	−	0.460220i	$-0.847771\pi$
$7$		−	2.43525i		−	0.920440i	0.887805	−	0.460220i	$-0.152229\pi$
$8$		−	2.04621i		−	0.723444i
$9$	−0.827483	−	1.43324i	−0.275828	−	0.477748i
$10$		0			0
$11$	−5.75477			−1.73513			−0.867564	−	0.497326i	$-0.834315\pi$
$11$	−5.75477			−1.73513			−0.867564	+	0.497326i	$0.834315\pi$
$12$		−	0.893835i		−	0.258028i
$13$	1.38132	−	0.797505i	0.383109	−	0.221188i	−0.296061	−	0.955169i	$-0.595673\pi$
$13$	1.38132	−	0.797505i	0.383109	−	0.221188i	0.679170	+	0.733981i	$0.262340\pi$
$14$	2.02680	−	3.51051i	0.541684	−	0.938224i
$15$		0			0
$16$	2.47371	−	4.28460i	0.618428	−	1.07115i
$17$	5.18234	+	2.99203i	1.25690	+	0.725673i	0.972471	−	0.233023i	$-0.0748617\pi$
$17$	5.18234	+	2.99203i	1.25690	+	0.725673i	0.284432	+	0.958696i	$0.408195\pi$
$18$		−	2.75477i		−	0.649305i
$19$	−0.149412	−	4.35634i	−0.0342775	−	0.999412i
$19$	−0.149412	−	4.35634i	−0.0342775	−	0.999412i
$20$		0			0
$21$	−1.41215	+	2.44592i	−0.308156	+	0.533743i
$22$	−8.29572	−	4.78953i	−1.76865	−	1.02113i
$23$	0.814102	−	0.470022i	0.169752	−	0.0980064i	−0.412717	−	0.910859i	$-0.635420\pi$
$23$	0.814102	−	0.470022i	0.169752	−	0.0980064i	0.582469	+	0.812853i	$0.302087\pi$
$24$	−1.18655	+	2.05517i	−0.242204	+	0.419509i
$25$		0			0
$26$	2.65497			0.520682
$27$			5.39862i			1.03897i
$28$	1.62542	−	0.938437i	0.307176	−	0.177348i
$29$	1.30917	+	2.26755i	0.243106	+	0.421073i	0.961598	−	0.274463i	$-0.0885002\pi$
$29$	1.30917	+	2.26755i	0.243106	+	0.421073i	−0.718491	+	0.695536i	$0.755167\pi$
$30$		0			0
$31$	−5.26913			−0.946364			−0.473182	−	0.880965i	$-0.656895\pi$
$31$	−5.26913			−0.946364			−0.473182	+	0.880965i	$0.656895\pi$
$32$	3.58777	−	2.07140i	0.634233	−	0.366175i
$33$	5.77996	+	3.33706i	1.00616	+	0.580908i
$34$	4.98037	+	8.62625i	0.854126	+	1.47939i
$35$		0			0
$36$	0.637749	−	1.10461i	0.106292	−	0.184102i
$37$		−	2.89384i		−	0.475744i	−0.971297	−	0.237872i	$-0.923550\pi$
$37$		−	2.89384i		−	0.475744i	0.971297	−	0.237872i	$-0.0764498\pi$
$38$	3.41028	−	6.40418i	0.553220	−	1.03889i
$39$	−1.84982			−0.296209
$40$		0			0
$41$	3.15767	−	5.46925i	0.493145	−	0.854153i	−0.506823	−	0.862050i	$-0.669180\pi$
$41$	3.15767	−	5.46925i	0.493145	−	0.854153i	0.999969	+	0.00789701i	$0.00251372\pi$
$42$	−4.07134	+	2.35059i	−0.628221	+	0.362704i
$43$	3.93108	+	2.26961i	0.599485	+	0.346113i	0.768839	−	0.639443i	$-0.220835\pi$
$43$	3.93108	+	2.26961i	0.599485	+	0.346113i	−0.169354	+	0.985555i	$0.554168\pi$
$44$	−2.21763	−	3.84104i	−0.334320	−	0.579059i
$45$		0			0
$46$	1.56475			0.230709
$47$	7.75471	−	4.47718i	1.13114	−	0.653064i	0.186919	−	0.982375i	$-0.440150\pi$
$47$	7.75471	−	4.47718i	1.13114	−	0.653064i	0.944221	+	0.329311i	$0.106816\pi$
$48$	−4.96909	+	2.86890i	−0.717226	+	0.414090i
$49$	1.06953			0.152791
$50$		0			0
$51$	−3.47002	−	6.01025i	−0.485900	−	0.841604i
$52$	1.06460	+	0.614645i	0.147633	+	0.0852359i
$53$	1.90213	−	1.09819i	0.261277	−	0.150848i	−0.363640	−	0.931540i	$-0.618466\pi$
$53$	1.90213	−	1.09819i	0.261277	−	0.150848i	0.624917	+	0.780691i	$0.285133\pi$
$54$	−4.49313	+	7.78232i	−0.611437	+	1.05904i
$55$		0			0
$56$	−4.98304			−0.665887
$57$	−2.37608	+	4.46205i	−0.314719	+	0.591013i
$58$			4.35834i			0.572278i
$59$	−5.39939	+	9.35202i	−0.702941	+	1.21753i	0.264489	+	0.964389i	$0.414797\pi$
$59$	−5.39939	+	9.35202i	−0.702941	+	1.21753i	−0.967430	+	0.253140i	$0.918537\pi$
$60$		0			0
$61$	5.26434	+	9.11811i	0.674030	+	1.16745i	0.976751	+	0.214375i	$0.0687716\pi$
$61$	5.26434	+	9.11811i	0.674030	+	1.16745i	−0.302721	+	0.953079i	$0.597895\pi$
$62$	−7.59566	−	4.38535i	−0.964649	−	0.556941i
$63$	−3.49031	+	2.01513i	−0.439738	+	0.253883i
$64$	−2.99898			−0.374873
$65$		0			0
$66$	5.55469	+	9.62100i	0.683735	+	1.18426i
$67$	0.874320	−	0.504789i	0.106815	−	0.0616698i	−0.445641	−	0.895212i	$-0.647024\pi$
$67$	0.874320	−	0.504789i	0.106815	−	0.0616698i	0.552456	+	0.833542i	$0.313691\pi$
$68$			4.61197i			0.559284i
$69$	−1.09022			−0.131247
$70$		0			0
$71$	−4.41694	+	7.65036i	−0.524194	+	0.907931i	0.475409	+	0.879765i	$0.342300\pi$
$71$	−4.41694	+	7.65036i	−0.524194	+	0.907931i	−0.999603	+	0.0281662i	$0.991033\pi$
$72$	−2.93271	+	1.69320i	−0.345624	+	0.199546i
$73$	−8.87674	−	5.12499i	−1.03894	−	0.599835i	−0.119410	−	0.992845i	$-0.538100\pi$
$73$	−8.87674	−	5.12499i	−1.03894	−	0.599835i	−0.919534	+	0.393011i	$0.871434\pi$
$74$	2.40846	−	4.17157i	0.279978	−	0.484936i
$75$		0			0
$76$	2.85008	−	1.77846i	0.326927	−	0.204004i
$77$			14.0143i			1.59708i
$78$	−2.66659	−	1.53956i	−0.301932	−	0.174320i
$79$	3.80229	−	6.58577i	0.427792	−	0.740957i	−0.568885	−	0.822417i	$-0.692625\pi$
$79$	3.80229	−	6.58577i	0.427792	−	0.740957i	0.996677	+	0.0814604i	$0.0259584\pi$
$80$		0			0
$81$	0.648093	−	1.12253i	0.0720103	−	0.124726i
$82$	9.10381	−	5.25609i	1.00535	−	0.580438i
$83$		−	3.11355i		−	0.341756i	−0.985292	−	0.170878i	$-0.945340\pi$
$83$		−	3.11355i		−	0.341756i	0.985292	−	0.170878i	$-0.0546604\pi$
$84$	−2.17672			−0.237499
$85$		0			0
$86$	3.77787	+	6.54346i	0.407378	+	0.705600i
$87$		−	3.03663i		−	0.325561i
$88$			11.7755i			1.25527i
$89$	−5.55706	−	9.62511i	−0.589047	−	1.02026i	−0.994358	−	0.106081i	$-0.966170\pi$
$89$	−5.55706	−	9.62511i	−0.589047	−	1.02026i	0.405310	−	0.914179i	$-0.367163\pi$
$90$		0			0
$91$	−1.94213	−	3.36387i	−0.203590	−	0.352629i
$92$	0.627436	+	0.362251i	0.0654148	+	0.0377672i
$93$	5.29220	+	3.05545i	0.548776	+	0.316836i
$94$	14.9049			1.53733
$95$		0			0
$96$	−4.80463			−0.490371
$97$	−3.51412	−	2.02888i	−0.356805	−	0.206002i	0.310873	−	0.950451i	$-0.399379\pi$
$97$	−3.51412	−	2.02888i	−0.356805	−	0.206002i	−0.667678	+	0.744450i	$0.732712\pi$
$98$	1.54177	+	0.890144i	0.155743	+	0.0899181i
$99$	4.76197	+	8.24798i	0.478596	+	0.828953i
$100$		0			0
$101$	5.56503	+	9.63892i	0.553741	+	0.959108i	0.998000	+	0.0632098i	$0.0201337\pi$
$101$	5.56503	+	9.63892i	0.553741	+	0.959108i	−0.444259	+	0.895898i	$0.646533\pi$
$102$		−	11.5520i		−	1.14382i
$103$		−	11.5791i		−	1.14092i	−0.821326	−	0.570460i	$-0.806765\pi$
$103$		−	11.5791i		−	1.14092i	0.821326	−	0.570460i	$-0.193235\pi$
$104$	−1.63186	−	2.82647i	−0.160017	−	0.277158i
$105$		0			0
$106$	3.65598			0.355101
$107$			17.9177i			1.73217i	0.499894	+	0.866086i	$0.333372\pi$
$107$			17.9177i			1.73217i	−0.499894	+	0.866086i	$0.666628\pi$
$108$	−3.60333	+	2.08039i	−0.346731	+	0.200185i
$109$	2.81235	−	4.87113i	0.269374	−	0.466570i	−0.699326	−	0.714803i	$-0.746516\pi$
$109$	2.81235	−	4.87113i	0.269374	−	0.466570i	0.968700	+	0.248233i	$0.0798498\pi$
$110$		0			0
$111$	−1.67807	+	2.90650i	−0.159275	+	0.275873i
$112$	−10.4341	−	6.02412i	−0.985928	−	0.569226i
$113$			15.6789i			1.47494i	0.675378	+	0.737472i	$0.263981\pi$
$113$			15.6789i			1.47494i	−0.675378	+	0.737472i	$0.736019\pi$
$114$	−7.13885	+	4.45467i	−0.668614	+	0.417218i
$115$		0			0
$116$	−1.00899	+	1.74762i	−0.0936822	+	0.162262i
$117$	−2.28604	−	1.31984i	−0.211344	−	0.122020i
$118$	−15.5669	+	8.98753i	−1.43304	+	0.827369i
$119$	7.28635	−	12.6203i	0.667939	−	1.15690i
$120$		0			0
$121$	22.1173			2.01067
$122$			17.5255i			1.58668i
$123$	−6.34299	+	3.66213i	−0.571928	+	0.330203i
$124$	−2.03049	−	3.51691i	−0.182343	−	0.315827i
$125$		0			0
$126$	−6.70856			−0.597646
$127$	5.30000	−	3.05996i	0.470299	−	0.271527i	−0.246066	−	0.969253i	$-0.579138\pi$
$127$	5.30000	−	3.05996i	0.470299	−	0.271527i	0.716365	+	0.697726i	$0.245805\pi$
$128$	−11.4987	−	6.63877i	−1.01635	−	0.586790i
$129$	−2.63220	−	4.55910i	−0.231752	−	0.401406i
$130$		0			0
$131$	7.44055	−	12.8874i	0.650084	−	1.12598i	−0.333018	−	0.942920i	$-0.608067\pi$
$131$	7.44055	−	12.8874i	0.650084	−	1.12598i	0.983102	−	0.183058i	$-0.0585997\pi$
$132$			5.14381i			0.447711i
$133$	−10.6088	+	0.363857i	−0.919899	+	0.0315504i
$134$	1.68049			0.145172
$135$		0			0
$136$	6.12231	−	10.6042i	0.524984	−	0.909299i
$137$	15.0258	−	8.67518i	1.28374	−	0.741170i	0.306214	−	0.951963i	$-0.400938\pi$
$137$	15.0258	−	8.67518i	1.28374	−	0.741170i	0.977531	+	0.210793i	$0.0676044\pi$
$138$	−1.57160	−	0.907361i	−0.133783	−	0.0772397i
$139$	−3.35267	−	5.80700i	−0.284370	−	0.492543i	0.688086	−	0.725629i	$-0.258451\pi$
$139$	−3.35267	−	5.80700i	−0.284370	−	0.492543i	−0.972456	+	0.233086i	$0.925118\pi$
$140$		0			0
$141$	−10.3849			−0.874564
$142$	−12.7344	+	7.35219i	−1.06864	+	0.616982i
$143$	−7.94917	+	4.58946i	−0.664743	+	0.383790i
$144$	−8.18782			−0.682319
$145$		0			0
$146$	−8.53077	−	14.7757i	−0.706012	−	1.22285i
$147$	−1.07422	−	0.620199i	−0.0885999	−	0.0511532i
$148$	1.93150	−	1.11515i	0.158769	−	0.0916651i
$149$	7.19642	−	12.4646i	0.589553	−	1.02114i	−0.404737	−	0.914433i	$-0.632637\pi$
$149$	7.19642	−	12.4646i	0.589553	−	1.02114i	0.994291	−	0.106704i	$-0.0340296\pi$
$150$		0			0
$151$	12.7219			1.03529			0.517645	−	0.855595i	$-0.326809\pi$
$151$	12.7219			1.03529			0.517645	+	0.855595i	$0.326809\pi$
$152$	−8.91398	+	0.305729i	−0.723019	+	0.0247979i
$153$		−	9.90341i		−	0.800644i
$154$	−11.6637	+	20.2022i	−0.939890	+	1.62794i
$155$		0			0
$156$	−0.712838	−	1.23467i	−0.0570727	−	0.0988529i
$157$	2.92309	+	1.68765i	0.233288	+	0.134689i	0.612088	−	0.790790i	$-0.290330\pi$
$157$	2.92309	+	1.68765i	0.233288	+	0.134689i	−0.378800	+	0.925479i	$0.623663\pi$
$158$	10.9623	−	6.32909i	0.872114	−	0.503515i
$159$	−2.54727			−0.202012
$160$		0			0
$161$	−1.14462	−	1.98255i	−0.0902089	−	0.156246i
$162$	1.86850	−	1.07878i	0.146803	−	0.0847569i
$163$		−	0.307960i		−	0.0241213i	−0.999927	−	0.0120607i	$-0.996161\pi$
$163$		−	0.307960i		−	0.0241213i	0.999927	−	0.0120607i	$-0.00383912\pi$
$164$	4.86730			0.380072
$165$		0			0
$166$	2.59132	−	4.48830i	0.201125	−	0.348359i
$167$	12.3532	−	7.13215i	0.955923	−	0.551902i	0.0610070	−	0.998137i	$-0.480569\pi$
$167$	12.3532	−	7.13215i	0.955923	−	0.551902i	0.894916	+	0.446235i	$0.147235\pi$
$168$	5.00486	+	2.88955i	0.386133	+	0.222934i
$169$	−5.22797	+	9.05511i	−0.402152	+	0.696547i
$170$		0			0
$171$	−6.12005	+	3.81894i	−0.468012	+	0.292042i
$172$			3.49842i			0.266752i
$173$	11.5590	+	6.67357i	0.878811	+	0.507382i	0.870266	−	0.492581i	$-0.163947\pi$
$173$	11.5590	+	6.67357i	0.878811	+	0.507382i	0.00854514	+	0.999963i	$0.497280\pi$
$174$	2.52730	−	4.37742i	0.191594	−	0.331851i
$175$		0			0
$176$	−14.2356	+	24.6569i	−1.07305	+	1.85858i
$177$	10.8461	−	6.26197i	0.815239	−	0.470679i
$178$		−	18.5000i		−	1.38663i
$179$	14.2207			1.06291			0.531454	−	0.847087i	$-0.321646\pi$
$179$	14.2207			1.06291			0.531454	+	0.847087i	$0.321646\pi$
$180$		0			0
$181$	−4.94132	−	8.55861i	−0.367285	−	0.636157i	0.621855	−	0.783133i	$-0.286379\pi$
$181$	−4.94132	−	8.55861i	−0.367285	−	0.636157i	−0.989140	+	0.146976i	$0.953046\pi$
$182$		−	6.46552i		−	0.479256i
$183$		−	12.2107i		−	0.902641i
$184$	−0.961763	−	1.66582i	−0.0709021	−	0.122806i
$185$		0			0
$186$	5.08594	+	8.80911i	0.372919	+	0.645915i
$187$	−29.8232	−	17.2184i	−2.18089	−	1.25914i
$188$	5.97663	+	3.45061i	0.435891	+	0.251661i
$189$	13.1470			0.956305
$190$		0			0
$191$	−12.9942			−0.940228			−0.470114	−	0.882606i	$-0.655787\pi$
$191$	−12.9942			−0.940228			−0.470114	+	0.882606i	$0.655787\pi$
$192$	3.01211	+	1.73904i	0.217380	+	0.125505i
$193$	12.5711	+	7.25795i	0.904890	+	0.522439i	0.878784	−	0.477221i	$-0.158356\pi$
$193$	12.5711	+	7.25795i	0.904890	+	0.522439i	0.0261066	+	0.999659i	$0.491689\pi$
$194$	−3.37716	−	5.84942i	−0.242466	−	0.419964i
$195$		0			0
$196$	0.412150	+	0.713865i	0.0294393	+	0.0509904i
$197$		−	25.0010i		−	1.78125i	−0.454740	−	0.890624i	$-0.650268\pi$
$197$		−	25.0010i		−	1.78125i	0.454740	−	0.890624i	$-0.349732\pi$
$198$			15.8530i			1.12663i
$199$	−1.12769	−	1.95322i	−0.0799401	−	0.138460i	0.823284	−	0.567630i	$-0.192140\pi$
$199$	−1.12769	−	1.95322i	−0.0799401	−	0.138460i	−0.903224	+	0.429170i	$0.858806\pi$
$200$		0			0
$201$	−1.17086			−0.0825864
$202$			18.5265i			1.30352i
$203$	5.52205	−	3.18816i	0.387572	−	0.223765i
$204$	2.67438	−	4.63216i	0.187244	−	0.324316i
$205$		0			0
$206$	9.63694	−	16.6917i	0.671437	−	1.16296i
$207$	−1.34731	−	0.777871i	−0.0936446	−	0.0540657i
$208$		−	7.89120i		−	0.547156i
$209$	0.859833	+	25.0697i	0.0594759	+	1.73411i
$210$		0			0
$211$	−11.1081	+	19.2397i	−0.764710	+	1.32452i	0.175689	+	0.984446i	$0.443785\pi$
$211$	−11.1081	+	19.2397i	−0.764710	+	1.32452i	−0.940400	+	0.340071i	$0.889549\pi$
$212$	1.46599	+	0.846388i	0.100684	+	0.0581302i
$213$	8.87255	−	5.12257i	0.607937	−	0.350993i
$214$	−14.9124	+	25.8291i	−1.01939	+	1.76564i
$215$		0			0
$216$	11.0467			0.751634
$217$			12.8317i			0.871071i
$218$	8.10822	−	4.68128i	0.549158	−	0.317057i
$219$	5.94373	+	10.2949i	0.401640	+	0.695662i
$220$		0			0
$221$	9.54463			0.642041
$222$	−4.83801	+	2.79322i	−0.324706	+	0.187469i
$223$	8.84730	+	5.10799i	0.592459	+	0.342056i	0.766069	−	0.642758i	$-0.222210\pi$
$223$	8.84730	+	5.10799i	0.592459	+	0.342056i	−0.173610	+	0.984814i	$0.555543\pi$
$224$	−5.04438	−	8.73712i	−0.337042	−	0.583774i
$225$		0			0
$226$	−13.0491	+	22.6017i	−0.868012	+	1.50344i
$227$			4.15180i			0.275565i	0.990463	+	0.137782i	$0.0439974\pi$
$227$			4.15180i			0.275565i	−0.990463	+	0.137782i	$0.956003\pi$
$228$	−3.89385	+	0.133550i	−0.257876	+	0.00884456i
$229$	−6.53286			−0.431703			−0.215852	−	0.976426i	$-0.569253\pi$
$229$	−6.53286			−0.431703			−0.215852	+	0.976426i	$0.569253\pi$
$230$		0			0
$231$	8.12660	−	14.0757i	0.534691	−	0.926111i
$232$	4.63987	−	2.67883i	0.304623	−	0.175874i
$233$	4.45848	+	2.57410i	0.292084	+	0.168635i	0.638882	−	0.769305i	$-0.279397\pi$
$233$	4.45848	+	2.57410i	0.292084	+	0.168635i	−0.346797	+	0.937940i	$0.612731\pi$
$234$	−2.19694	−	3.80521i	−0.143618	−	0.248755i
$235$		0			0
$236$	−8.32272			−0.541763
$237$	−7.63788	+	4.40973i	−0.496134	+	0.286443i
$238$	21.0071	−	12.1285i	1.36169	−	0.786171i
$239$	−13.9962			−0.905338			−0.452669	−	0.891679i	$-0.649528\pi$
$239$	−13.9962			−0.905338			−0.452669	+	0.891679i	$0.649528\pi$
$240$		0			0
$241$	−7.61285	−	13.1858i	−0.490387	−	0.849375i	0.509552	−	0.860440i	$-0.329811\pi$
$241$	−7.61285	−	13.1858i	−0.490387	−	0.849375i	−0.999939	+	0.0110652i	$0.996478\pi$
$242$	31.8830	+	18.4076i	2.04952	+	1.18329i
$243$	12.7242	−	7.34631i	0.816256	−	0.471266i
$244$	−4.05728	+	7.02742i	−0.259741	+	0.449884i
$245$		0			0
$246$	−12.1916			−0.777305
$247$	−3.68059	−	5.89834i	−0.234190	−	0.375302i
$248$			10.7817i			0.684642i
$249$	−1.80548	+	3.12718i	−0.114417	+	0.198177i
$250$		0			0
$251$	3.05630	+	5.29366i	0.192912	+	0.334133i	0.946214	−	0.323542i	$-0.104874\pi$
$251$	3.05630	+	5.29366i	0.192912	+	0.334133i	−0.753302	+	0.657674i	$0.771540\pi$
$252$	−2.69002	−	1.55308i	−0.169455	−	0.0978350i
$253$	−4.68497	+	2.70487i	−0.294541	+	0.170053i
$254$	10.1869			0.639181
$255$		0			0
$256$	−8.05154	−	13.9457i	−0.503221	−	0.871605i
$257$	0.106246	−	0.0613414i	0.00662747	−	0.00382637i	−0.496683	−	0.867932i	$-0.665449\pi$
$257$	0.106246	−	0.0613414i	0.00662747	−	0.00382637i	0.503310	+	0.864106i	$0.332115\pi$
$258$		−	8.76281i		−	0.545549i
$259$	−7.04723			−0.437893
$260$		0			0
$261$	2.16663	−	3.75271i	0.134111	−	0.232287i
$262$	21.4517	−	12.3851i	1.32529	−	0.765156i
$263$	−8.71267	−	5.03027i	−0.537247	−	0.310179i	0.206716	−	0.978401i	$-0.433722\pi$
$263$	−8.71267	−	5.03027i	−0.537247	−	0.310179i	−0.743962	+	0.668222i	$0.767056\pi$
$264$	6.82832	−	11.8270i	0.420254	−	0.727902i
$265$		0			0
$266$	−15.5958	−	8.30489i	−0.956240	−	0.509206i
$267$			12.8897i			0.788835i
$268$	0.673847	+	0.389046i	0.0411618	+	0.0237648i
$269$	2.85614	−	4.94698i	0.174142	−	0.301623i	−0.765722	−	0.643172i	$-0.777618\pi$
$269$	2.85614	−	4.94698i	0.174142	−	0.301623i	0.939864	+	0.341549i	$0.110951\pi$
$270$		0			0
$271$	6.35560	−	11.0082i	0.386075	−	0.668702i	−0.605843	−	0.795585i	$-0.707164\pi$
$271$	6.35560	−	11.0082i	0.386075	−	0.668702i	0.991918	+	0.126883i	$0.0404972\pi$
$272$	25.6393	−	14.8028i	1.55461	−	0.897554i
$273$			4.50479i			0.272642i
$274$	28.8804			1.74473
$275$		0			0
$276$	−0.420122	−	0.727673i	−0.0252884	−	0.0438008i
$277$			17.6019i			1.05760i	0.848747	+	0.528799i	$0.177358\pi$
$277$			17.6019i			1.05760i	−0.848747	+	0.528799i	$0.822642\pi$
$278$		−	11.1613i		−	0.669413i
$279$	4.36012	+	7.55195i	0.261034	+	0.452123i
$280$		0			0
$281$	10.2502	+	17.7539i	0.611476	+	1.05911i	0.990992	+	0.133922i	$0.0427571\pi$
$281$	10.2502	+	17.7539i	0.611476	+	1.05911i	−0.379516	+	0.925185i	$0.623910\pi$
$282$	−14.9702	−	8.64305i	−0.891462	−	0.514686i
$283$	−10.2677	−	5.92805i	−0.610350	−	0.352386i	0.162752	−	0.986667i	$-0.447963\pi$
$283$	−10.2677	−	5.92805i	−0.610350	−	0.352386i	−0.773103	+	0.634281i	$0.781296\pi$
$284$	−6.80836			−0.404002
$285$		0			0
$286$	−15.2787			−0.903449
$287$	−13.3190	−	7.68973i	−0.786196	−	0.453911i
$288$	−5.93763	−	3.42809i	−0.349878	−	0.202002i
$289$	9.40447	+	16.2890i	0.553204	+	0.958177i
$290$		0			0
$291$	2.35301	+	4.07552i	0.137936	+	0.238911i
$292$		−	7.89976i		−	0.462298i
$293$			24.9814i			1.45943i	0.683751	+	0.729715i	$0.260347\pi$
$293$			24.9814i			1.45943i	−0.683751	+	0.729715i	$0.739653\pi$
$294$	−1.03235	−	1.78808i	−0.0602079	−	0.104283i
$295$		0			0
$296$	−5.92139			−0.344174
$297$		−	31.0678i		−	1.80274i
$298$	20.7478	−	11.9788i	1.20189	−	0.693911i
$299$	0.749690	−	1.29850i	0.0433557	−	0.0750943i
$300$		0			0
$301$	5.52708	−	9.57319i	0.318576	−	0.551789i
$302$	18.3391	+	10.5881i	1.05529	+	0.609274i
$303$		−	12.9082i		−	0.741554i
$304$	−19.0348	−	10.1362i	−1.09172	−	0.581348i
$305$		0			0
$306$	8.24234	−	14.2761i	0.471183	−	0.816113i
$307$	−14.6531	−	8.45997i	−0.836296	−	0.482836i	0.0197074	−	0.999806i	$-0.493727\pi$
$307$	−14.6531	−	8.45997i	−0.836296	−	0.482836i	−0.856003	+	0.516970i	$0.827060\pi$
$308$	−9.35392	+	5.40049i	−0.532989	+	0.307721i
$309$	−6.71444	+	11.6298i	−0.381971	+	0.661594i
$310$		0			0
$311$	−15.2133			−0.862670			−0.431335	−	0.902192i	$-0.641957\pi$
$311$	−15.2133			−0.862670			−0.431335	+	0.902192i	$0.641957\pi$
$312$			3.78512i			0.214290i
$313$	−21.5877	+	12.4637i	−1.22021	+	0.704488i	−0.964962	−	0.262389i	$-0.915490\pi$
$313$	−21.5877	+	12.4637i	−1.22021	+	0.704488i	−0.255246	+	0.966876i	$0.582156\pi$
$314$	2.80917	+	4.86562i	0.158531	+	0.274583i
$315$		0			0
$316$	5.86093			0.329703
$317$	−21.8502	+	12.6152i	−1.22723	+	0.708541i	−0.966449	−	0.256857i	$-0.917313\pi$
$317$	−21.8502	+	12.6152i	−1.22723	+	0.708541i	−0.260780	+	0.965398i	$0.583980\pi$
$318$	−3.67199	−	2.12002i	−0.205915	−	0.118885i
$319$	−7.53396	−	13.0492i	−0.421821	−	0.730615i
$320$		0			0
$321$	10.3901	−	17.9962i	0.579919	−	1.00445i
$322$		−	3.81055i		−	0.212354i
$323$	12.2600	−	23.0231i	0.682163	−	1.28104i
$324$	0.998983			0.0554991
$325$		0			0
$326$	0.256307	−	0.443937i	0.0141955	−	0.0245874i
$327$	−5.64933	+	3.26164i	−0.312408	+	0.180369i
$328$	−11.1912	−	6.46125i	−0.617932	−	0.356763i
$329$	−10.9031	−	18.8847i	−0.601106	−	1.04115i
$330$		0			0
$331$	−20.2063			−1.11064			−0.555320	−	0.831637i	$-0.687404\pi$
$331$	−20.2063			−1.11064			−0.555320	+	0.831637i	$0.687404\pi$
$332$	2.07815	−	1.19982i	0.114053	−	0.0658487i
$333$	−4.14757	+	2.39460i	−0.227285	+	0.131223i
$334$	23.7436			1.29919
$335$		0			0
$336$	6.98651	+	12.1010i	0.381145	+	0.660163i
$337$	27.5610	+	15.9123i	1.50134	+	0.866800i	0.999999	+	0.00155051i	$0.000493543\pi$
$337$	27.5610	+	15.9123i	1.50134	+	0.866800i	0.501342	+	0.865249i	$0.332840\pi$
$338$	−15.0726	+	8.70219i	−0.819843	+	0.473337i
$339$	9.09183	−	15.7475i	0.493800	−	0.855287i
$340$		0			0
$341$	30.3226			1.64206
$342$	−12.0007	+	0.411596i	−0.648923	+	0.0222566i
$343$		−	19.6514i		−	1.06107i
$344$	4.64410	−	8.04382i	0.250393	−	0.433693i
$345$		0			0
$346$	11.1085	+	19.2404i	0.597194	+	1.03437i
$347$	2.86009	+	1.65128i	0.153538	+	0.0886451i	0.574801	−	0.818294i	$-0.305080\pi$
$347$	2.86009	+	1.65128i	0.153538	+	0.0886451i	−0.421263	+	0.906939i	$0.638413\pi$
$348$	2.02681	−	1.17018i	0.108649	−	0.0627283i
$349$	−17.8486			−0.955416			−0.477708	−	0.878519i	$-0.658532\pi$
$349$	−17.8486			−0.955416			−0.477708	+	0.878519i	$0.658532\pi$
$350$		0			0
$351$	4.30543	+	7.45723i	0.229807	+	0.398037i
$352$	−20.6468	+	11.9204i	−1.10048	+	0.635360i
$353$			8.29523i			0.441511i	0.975329	+	0.220755i	$0.0708522\pi$
$353$			8.29523i			0.441511i	−0.975329	+	0.220755i	$0.929148\pi$
$354$	20.8467			1.10799
$355$		0			0
$356$	4.28288	−	7.41817i	0.226992	−	0.393162i
$357$	−14.6365	+	8.45039i	−0.774646	+	0.447242i
$358$	20.4997	+	11.8355i	1.08344	+	0.625527i
$359$	4.17511	−	7.23150i	0.220354	−	0.381664i	−0.734562	−	0.678542i	$-0.762612\pi$
$359$	4.17511	−	7.23150i	0.220354	−	0.381664i	0.954915	+	0.296878i	$0.0959455\pi$
$360$		0			0
$361$	−18.9554	+	1.30178i	−0.997650	+	0.0685148i
$362$		−	16.4501i		−	0.864598i
$363$	−22.2142	−	12.8254i	−1.16594	−	0.673156i
$364$	1.49682	−	2.59256i	0.0784545	−	0.135887i
$365$		0			0
$366$	10.1626	−	17.6022i	0.531209	−	0.920082i
$367$	12.4879	−	7.20988i	0.651862	−	0.376353i	−0.137307	−	0.990528i	$-0.543845\pi$
$367$	12.4879	−	7.20988i	0.651862	−	0.376353i	0.789169	+	0.614176i	$0.210511\pi$
$368$		−	4.65080i		−	0.242440i
$369$	−10.4517			−0.544093
$370$		0			0
$371$	−2.67438	−	4.63216i	−0.138847	−	0.240490i
$372$			4.70974i			0.244188i
$373$			24.1157i			1.24866i	0.781159	+	0.624332i	$0.214629\pi$
$373$			24.1157i			1.24866i	−0.781159	+	0.624332i	$0.785371\pi$
$374$	−28.6608	−	49.6420i	−1.48202	−	2.56693i
$375$		0			0
$376$	−9.16125	−	15.8678i	−0.472455	−	0.818317i
$377$	3.61676	+	2.08814i	0.186273	+	0.107545i
$378$	18.9519	+	10.9419i	0.974783	+	0.562791i
$379$	−16.6757			−0.856571			−0.428285	−	0.903644i	$-0.640882\pi$
$379$	−16.6757			−0.856571			−0.428285	+	0.903644i	$0.640882\pi$
$380$		0			0
$381$	−7.09760			−0.363621
$382$	−18.7316	−	10.8147i	−0.958395	−	0.553329i
$383$	−9.42053	−	5.43895i	−0.481367	−	0.277917i	0.239619	−	0.970867i	$-0.422977\pi$
$383$	−9.42053	−	5.43895i	−0.481367	−	0.277917i	−0.720986	+	0.692950i	$0.756311\pi$
$384$	7.69935	+	13.3357i	0.392906	+	0.680533i
$385$		0			0
$386$	12.0812	+	20.9252i	0.614916	+	1.06507i
$387$		−	7.51226i		−	0.381870i
$388$		−	3.12736i		−	0.158767i
$389$	18.2272	+	31.5704i	0.924154	+	1.60068i	0.792917	+	0.609330i	$0.208562\pi$
$389$	18.2272	+	31.5704i	0.924154	+	1.60068i	0.131237	+	0.991351i	$0.458105\pi$
$390$		0			0
$391$	5.62528			0.284482
$392$		−	2.18849i		−	0.110535i
$393$	−14.9463	+	8.62922i	−0.753939	+	0.435287i
$394$	20.8077	−	36.0399i	1.04827	−	1.81566i
$395$		0			0
$396$	−3.67010	+	6.35680i	−0.184429	+	0.319441i
$397$	−7.43380	−	4.29191i	−0.373092	−	0.215405i	0.301717	−	0.953398i	$-0.402440\pi$
$397$	−7.43380	−	4.29191i	−0.373092	−	0.215405i	−0.674808	+	0.737993i	$0.735774\pi$
$398$		−	3.75419i		−	0.188181i
$399$	10.8662	+	5.78635i	0.543992	+	0.289680i
$400$		0			0
$401$	8.52785	−	14.7707i	0.425860	−	0.737612i	−0.570640	−	0.821200i	$-0.693305\pi$
$401$	8.52785	−	14.7707i	0.425860	−	0.737612i	0.996500	+	0.0835885i	$0.0266381\pi$
$402$	−1.68785	−	0.974478i	−0.0841821	−	0.0486026i
$403$	−7.27836	+	4.20216i	−0.362561	+	0.209325i
$404$	−4.28903	+	7.42881i	−0.213387	+	0.369597i
$405$		0			0
$406$	10.6137			0.526747
$407$			16.6533i			0.825476i
$408$	−12.2982	+	7.10039i	−0.608853	+	0.351522i
$409$	−5.89702	−	10.2139i	−0.291589	−	0.505047i	0.682597	−	0.730795i	$-0.260851\pi$
$409$	−5.89702	−	10.2139i	−0.291589	−	0.505047i	−0.974186	+	0.225749i	$0.927517\pi$
$410$		0			0
$411$	−20.1222			−0.992553
$412$	7.72850	−	4.46205i	0.380756	−	0.219829i
$413$	22.7745	+	13.1489i	1.12066	+	0.647015i
$414$	−1.29480	−	2.24266i	−0.0636360	−	0.110221i
$415$		0			0
$416$	3.30390	−	5.72252i	0.161987	−	0.280570i
$417$			7.77656i			0.380820i
$418$	−19.6253	+	36.8546i	−0.959907	+	1.80261i
$419$	−1.14280			−0.0558292			−0.0279146	−	0.999610i	$-0.508887\pi$
$419$	−1.14280			−0.0558292			−0.0279146	+	0.999610i	$0.508887\pi$
$420$		0			0
$421$	−9.75944	+	16.9039i	−0.475646	+	0.823843i	−0.999611	−	0.0278967i	$-0.991119\pi$
$421$	−9.75944	+	16.9039i	−0.475646	+	0.823843i	0.523965	+	0.851740i	$0.324452\pi$
$422$	−32.0254	+	18.4899i	−1.55897	+	0.900072i
$423$	−12.8338	−	7.40959i	−0.624000	−	0.360266i
$424$	−2.24713	−	3.89215i	−0.109130	−	0.189019i
$425$		0			0
$426$	17.0535			0.826245
$427$	22.2049	−	12.8200i	1.07457	−	0.620404i
$428$	−11.9593	+	6.90469i	−0.578073	+	0.333751i
$429$	10.6453			0.513960
$430$		0			0
$431$	18.4392	+	31.9377i	0.888187	+	1.53838i	0.842017	+	0.539451i	$0.181368\pi$
$431$	18.4392	+	31.9377i	0.888187	+	1.53838i	0.0461694	+	0.998934i	$0.485299\pi$
$432$	23.1309	+	13.3546i	1.11289	+	0.642526i
$433$	−0.319506	+	0.184467i	−0.0153545	+	0.00886490i	−0.507658	−	0.861559i	$-0.669488\pi$
$433$	−0.319506	+	0.184467i	−0.0153545	+	0.00886490i	0.492303	+	0.870424i	$0.336155\pi$
$434$	−10.6795	+	18.4974i	−0.512630	+	0.887902i
$435$		0			0
$436$	4.33501			0.207609
$437$	−2.16921	−	3.47628i	−0.103767	−	0.166293i
$438$			19.7872i			0.945470i
$439$	−1.13220	+	1.96102i	−0.0540367	+	0.0935944i	−0.891778	−	0.452472i	$-0.850542\pi$
$439$	−1.13220	+	1.96102i	−0.0540367	+	0.0935944i	0.837742	+	0.546067i	$0.183875\pi$
$440$		0			0
$441$	−0.885022	−	1.53290i	−0.0421439	−	0.0729954i
$442$	13.7590	+	7.94373i	0.654447	+	0.377845i
$443$	14.2572	−	8.23137i	0.677378	−	0.391084i	−0.121488	−	0.992593i	$-0.538767\pi$
$443$	14.2572	−	8.23137i	0.677378	−	0.391084i	0.798866	+	0.601508i	$0.205433\pi$
$444$	−2.58661			−0.122755
$445$		0			0
$446$	8.50248	+	14.7267i	0.402604	+	0.697331i
$447$	−14.4558	+	8.34609i	−0.683738	+	0.394756i
$448$			7.30329i			0.345048i
$449$	−14.1613			−0.668315			−0.334158	−	0.942517i	$-0.608452\pi$
$449$	−14.1613			−0.668315			−0.334158	+	0.942517i	$0.608452\pi$
$450$		0			0
$451$	−18.1717	+	31.4742i	−0.855670	+	1.48206i
$452$	−10.4649	+	6.04193i	−0.492229	+	0.284188i
$453$	−12.7776	−	7.37713i	−0.600342	−	0.346608i
$454$	−3.45543	+	5.98498i	−0.162171	+	0.280889i
$455$		0			0
$456$	9.13029	+	4.86195i	0.427565	+	0.227682i
$457$			1.22073i			0.0571033i	0.999592	+	0.0285516i	$0.00908950\pi$
$457$			1.22073i			0.0571033i	−0.999592	+	0.0285516i	$0.990910\pi$
$458$	−9.41736	−	5.43712i	−0.440045	−	0.254060i
$459$	−16.1528	+	27.9775i	−0.753950	+	1.30588i
$460$		0			0
$461$	4.34580	−	7.52714i	0.202404	−	0.350574i	−0.746898	−	0.664938i	$-0.768458\pi$
$461$	4.34580	−	7.52714i	0.202404	−	0.350574i	0.949303	+	0.314364i	$0.101791\pi$
$462$	23.4296	−	13.5271i	1.09004	−	0.629337i
$463$			19.7149i			0.916229i	0.888893	+	0.458114i	$0.151475\pi$
$463$			19.7149i			0.916229i	−0.888893	+	0.458114i	$0.848525\pi$
$464$	12.9540			0.601375
$465$		0			0
$466$	4.28471	+	7.42133i	0.198485	+	0.343787i
$467$		−	11.4795i		−	0.531207i	−0.964082	−	0.265604i	$-0.914429\pi$
$467$		−	11.4795i		−	0.531207i	0.964082	−	0.265604i	$-0.0855713\pi$
$468$		−	2.03443i		−	0.0940418i
$469$	−1.22929	−	2.12919i	−0.0567633	−	0.0983170i
$470$		0			0
$471$	−1.95726	−	3.39008i	−0.0901858	−	0.156206i
$472$	19.1362	+	11.0483i	0.880814	+	0.508538i
$473$	−22.6225	−	13.0611i	−1.04018	−	0.600549i
$474$	−14.6804			−0.674293
$475$		0			0
$476$	11.2313			0.514787
$477$	−3.14796	−	1.81747i	−0.144135	−	0.0832164i
$478$	−20.1760	−	11.6486i	−0.922830	−	0.532796i
$479$	19.6316	+	34.0029i	0.896989	+	1.55363i	0.831324	+	0.555789i	$0.187584\pi$
$479$	19.6316	+	34.0029i	0.896989	+	1.55363i	0.0656652	+	0.997842i	$0.479083\pi$
$480$		0			0
$481$	−2.30785	−	3.99731i	−0.105229	−	0.182262i
$482$		−	25.3439i		−	1.15438i
$483$			2.65497i			0.120805i
$484$	8.52302	+	14.7623i	0.387410	+	0.671014i
$485$		0			0
$486$	24.4565			1.10937
$487$			31.5943i			1.43168i	0.698266	+	0.715838i	$0.253955\pi$
$487$			31.5943i			1.43168i	−0.698266	+	0.715838i	$0.746045\pi$
$488$	18.6576	−	10.7719i	0.844588	−	0.487623i
$489$	−0.178579	+	0.309309i	−0.00807564	+	0.0139874i
$490$		0			0
$491$	5.53187	−	9.58148i	0.249650	−	0.432406i	−0.713779	−	0.700371i	$-0.753018\pi$
$491$	5.53187	−	9.58148i	0.249650	−	0.432406i	0.963429	+	0.267965i	$0.0863511\pi$
$492$	−4.88861	−	2.82244i	−0.220395	−	0.127245i
$493$			15.6683i			0.705663i
$494$	−0.396685	−	11.5659i	−0.0178477	−	0.520376i
$495$		0			0
$496$	−13.0343	+	22.5761i	−0.585258	+	1.01370i
$497$	18.6306	+	10.7564i	0.835696	+	0.482489i
$498$	−5.20533	+	3.00530i	−0.233256	+	0.134671i
$499$	−10.1868	+	17.6440i	−0.456023	+	0.789854i	−0.998746	−	0.0500570i	$-0.984060\pi$
$499$	−10.1868	+	17.6440i	−0.456023	+	0.789854i	0.542724	+	0.839911i	$0.317393\pi$
$500$		0			0
$501$	−16.5431			−0.739091
$502$			10.1747i			0.454118i
$503$	11.8407	−	6.83622i	0.527950	−	0.304812i	−0.212231	−	0.977219i	$-0.568073\pi$
$503$	11.8407	−	6.83622i	0.527950	−	0.304812i	0.740181	+	0.672407i	$0.234740\pi$
$504$	4.12338	+	7.14191i	0.183670	+	0.318126i
$505$		0			0
$506$	−9.00474			−0.400310
$507$	10.5017	−	6.06317i	0.466398	−	0.269275i
$508$	4.08476	+	2.35834i	0.181232	+	0.104634i
$509$	−3.86196	−	6.68912i	−0.171179	−	0.296490i	0.767654	−	0.640865i	$-0.221424\pi$
$509$	−3.86196	−	6.68912i	−0.171179	−	0.296490i	−0.938832	+	0.344375i	$0.888091\pi$
$510$		0			0
$511$	−12.4807	+	21.6171i	−0.552112	+	0.956285i
$512$		−	0.249240i		−	0.0110150i
$513$	23.5182	−	0.806621i	1.03836	−	0.0356132i
$514$	0.204211			0.00900736
$515$		0			0
$516$	2.02866	−	3.51374i	0.0893067	−	0.154684i
$517$	−44.6265	+	25.7651i	−1.96267	+	1.13315i
$518$	−10.1588	−	5.86521i	−0.446354	−	0.257703i
$519$	−7.73971	−	13.4056i	−0.339736	−	0.588439i
$520$		0			0
$521$	−2.16876			−0.0950151			−0.0475075	−	0.998871i	$-0.515128\pi$
$521$	−2.16876			−0.0950151			−0.0475075	+	0.998871i	$0.515128\pi$
$522$	6.24656	−	3.60645i	0.273404	−	0.157850i
$523$	20.6921	−	11.9466i	0.904804	−	0.522389i	0.0260485	−	0.999661i	$-0.491708\pi$
$523$	20.6921	−	11.9466i	0.904804	−	0.522389i	0.878756	+	0.477272i	$0.158374\pi$
$524$	11.4690			0.501026
$525$		0			0
$526$	−8.37310	−	14.5026i	−0.365085	−	0.632345i
$527$	−27.3065	−	15.7654i	−1.18949	−	0.686751i
$528$	28.5959	−	16.5099i	1.24448	−	0.718500i
$529$	−11.0582	+	19.1533i	−0.480790	+	0.832752i
$530$		0			0
$531$	17.8716			0.775562
$532$	−4.33101	−	6.94067i	−0.187773	−	0.300916i
$533$		−	10.0730i		−	0.436312i
$534$	−10.7277	+	18.5809i	−0.464234	+	0.804076i
$535$		0			0
$536$	−1.03290	−	1.78904i	−0.0446147	−	0.0772749i
$537$	−14.2830	−	8.24629i	−0.616356	−	0.355854i
$538$	8.23448	−	4.75418i	0.355013	−	0.204967i
$539$	−6.15492			−0.265111
$540$		0			0
$541$	−21.2275	−	36.7671i	−0.912641	−	1.58074i	−0.810319	−	0.585990i	$-0.800706\pi$
$541$	−21.2275	−	36.7671i	−0.912641	−	1.58074i	−0.102323	−	0.994751i	$-0.532627\pi$
$542$	18.3237	−	10.5792i	0.787069	−	0.454415i
$543$			11.4614i			0.491858i
$544$	24.7907			1.06289
$545$		0			0
$546$	−3.74921	+	6.49383i	−0.160451	+	0.277910i
$547$	10.4189	−	6.01535i	0.445480	−	0.257198i	−0.260439	−	0.965490i	$-0.583867\pi$
$547$	10.4189	−	6.01535i	0.445480	−	0.257198i	0.705919	+	0.708292i	$0.250534\pi$
$548$	11.5806	+	6.68604i	0.494697	+	0.285614i
$549$	8.71231	−	15.0902i	0.371833	−	0.644033i
$550$		0			0
$551$	9.68259	−	6.04198i	0.412492	−	0.257397i
$552$			2.23082i			0.0949500i
$553$	−16.0380	−	9.25956i	−0.682006	−	0.393756i
$554$	−14.6496	+	25.3739i	−0.622403	+	1.07803i
$555$		0			0
$556$	2.58394	−	4.47551i	0.109583	−	0.189804i
$557$	−7.58006	+	4.37635i	−0.321178	+	0.185432i	−0.651917	−	0.758290i	$-0.726035\pi$
$557$	−7.58006	+	4.37635i	−0.321178	+	0.185432i	0.330740	+	0.943722i	$0.392702\pi$
$558$			14.5152i			0.614479i
$559$	7.24011			0.306224
$560$		0			0
$561$	19.9692	+	34.5876i	0.843099	+	1.46029i
$562$			34.1238i			1.43943i
$563$			35.9707i			1.51598i	0.652265	+	0.757991i	$0.273819\pi$
$563$			35.9707i			1.51598i	−0.652265	+	0.757991i	$0.726181\pi$
$564$	−4.00186	−	6.93143i	−0.168509	−	0.291866i
$565$		0			0
$566$	−9.86750	−	17.0910i	−0.414762	−	0.718389i
$567$	−2.73365	−	1.57827i	−0.114802	−	0.0662812i
$568$	15.6542	+	9.03798i	0.656837	+	0.379225i
$569$	20.3125			0.851543			0.425772	−	0.904831i	$-0.360003\pi$
$569$	20.3125			0.851543			0.425772	+	0.904831i	$0.360003\pi$
$570$		0			0
$571$	10.1773			0.425906			0.212953	−	0.977062i	$-0.431692\pi$
$571$	10.1773			0.425906			0.212953	+	0.977062i	$0.431692\pi$
$572$	−6.12650	−	3.53714i	−0.256162	−	0.147895i
$573$	13.0511	+	7.53505i	0.545217	+	0.314781i
$574$	−12.7999	−	22.1701i	−0.534258	−	0.925362i
$575$		0			0
$576$	2.48161	+	4.29827i	0.103400	+	0.179095i
$577$		−	32.7441i		−	1.36316i	−0.731745	−	0.681578i	$-0.761294\pi$
$577$		−	32.7441i		−	1.36316i	0.731745	−	0.681578i	$-0.238706\pi$
$578$			31.3083i			1.30225i
$579$	−8.41745	−	14.5794i	−0.349817	−	0.605901i
$580$		0			0
$581$	−7.58228			−0.314566
$582$			7.83337i			0.324703i
$583$	−10.9463	+	6.31984i	−0.453349	+	0.261741i
$584$	−10.4868	+	18.1637i	−0.433947	+	0.751618i
$585$		0			0
$586$	−20.7913	+	36.0117i	−0.858883	+	1.48763i
$587$	−7.59786	−	4.38663i	−0.313597	−	0.181056i	0.334938	−	0.942240i	$-0.391285\pi$
$587$	−7.59786	−	4.38663i	−0.313597	−	0.181056i	−0.648535	+	0.761185i	$0.724618\pi$
$588$		−	0.955987i		−	0.0394243i
$589$	0.787274	+	22.9541i	0.0324390	+	0.945808i
$590$		0			0
$591$	−14.4975	+	25.1105i	−0.596349	+	1.03291i
$592$	−12.3989	−	7.15852i	−0.509592	−	0.294213i
$593$	27.9905	−	16.1603i	1.14943	−	0.663625i	0.200684	−	0.979656i	$-0.435684\pi$
$593$	27.9905	−	16.1603i	1.14943	−	0.663625i	0.948749	+	0.316031i	$0.102350\pi$
$594$	25.8569	−	44.7855i	1.06092	−	1.83757i
$595$		0			0
$596$	11.0927			0.454375
$597$			2.61570i			0.107053i
$598$	2.16141	−	1.24789i	0.0883868	−	0.0510301i
$599$	−9.77520	−	16.9311i	−0.399404	−	0.691787i	0.594249	−	0.804281i	$-0.297449\pi$
$599$	−9.77520	−	16.9311i	−0.399404	−	0.691787i	−0.993652	+	0.112494i	$0.964116\pi$
$600$		0			0
$601$	−0.401837			−0.0163913			−0.00819564	−	0.999966i	$-0.502609\pi$
$601$	−0.401837			−0.0163913			−0.00819564	+	0.999966i	$0.502609\pi$
$602$	15.9350	−	9.20008i	0.649462	−	0.374967i
$603$	−1.44697	−	0.835409i	−0.0589252	−	0.0340205i
$604$	4.90243	+	8.49126i	0.199477	+	0.345505i
$605$		0			0
$606$	10.7431	−	18.6076i	0.436409	−	0.755882i
$607$			13.4453i			0.545727i	0.962053	+	0.272863i	$0.0879707\pi$
$607$			13.4453i			0.545727i	−0.962053	+	0.272863i	$0.912029\pi$
$608$	−9.55976	−	15.3200i	−0.387700	−	0.621309i
$609$	−7.39497			−0.299659
$610$		0			0
$611$	7.14115	−	12.3688i	0.288900	−	0.500390i
$612$	6.61008	−	3.81633i	0.267196	−	0.154266i
$613$	−17.9313	−	10.3527i	−0.724239	−	0.418140i	0.0920716	−	0.995752i	$-0.470651\pi$
$613$	−17.9313	−	10.3527i	−0.724239	−	0.418140i	−0.816311	+	0.577613i	$0.803984\pi$
$614$	−14.0820	−	24.3907i	−0.568303	−	0.984330i
$615$		0			0
$616$	28.6762			1.15540
$617$	−8.03560	+	4.63936i	−0.323501	+	0.186773i	−0.652952	−	0.757399i	$-0.726470\pi$
$617$	−8.03560	+	4.63936i	−0.323501	+	0.186773i	0.329451	+	0.944173i	$0.393136\pi$
$618$	−19.3583	+	11.1765i	−0.778703	+	0.449585i
$619$	2.89129			0.116211			0.0581053	−	0.998310i	$-0.481494\pi$
$619$	2.89129			0.116211			0.0581053	+	0.998310i	$0.481494\pi$
$620$		0			0
$621$	2.53747	+	4.39503i	0.101825	+	0.176366i
$622$	−21.9306	−	12.6616i	−0.879338	−	0.507686i
$623$	−23.4396	+	13.5329i	−0.939088	+	0.542183i
$624$	−4.57593	+	7.92574i	−0.183184	+	0.317284i
$625$		0			0
$626$	−41.4926			−1.65838
$627$	13.6738	−	25.6781i	0.546078	−	1.02548i
$628$			2.60138i			0.103806i
$629$	8.65844	−	14.9969i	0.345234	−	0.597964i
$630$		0			0
$631$	−15.2270	−	26.3740i	−0.606178	−	1.04993i	−0.991864	−	0.127301i	$-0.959369\pi$
$631$	−15.2270	−	26.3740i	−0.606178	−	1.04993i	0.385686	−	0.922630i	$-0.373965\pi$
$632$	−13.4759	−	7.78029i	−0.536041	−	0.309483i
$633$	22.3134	−	12.8826i	0.886877	−	0.512039i
$634$	−41.9972			−1.66792
$635$		0			0
$636$	−0.981604	−	1.70019i	−0.0389231	−	0.0674168i
$637$	1.47737	−	0.852959i	0.0585355	−	0.0337955i
$638$		−	25.0812i		−	0.992975i
$639$	14.6198			0.578349
$640$		0			0
$641$	10.0369	−	17.3845i	0.396434	−	0.686645i	−0.596849	−	0.802354i	$-0.703581\pi$
$641$	10.0369	−	17.3845i	0.396434	−	0.686645i	0.993283	+	0.115709i	$0.0369141\pi$
$642$	29.9554	−	17.2948i	1.18225	−	0.682571i
$643$	−1.80924	−	1.04457i	−0.0713496	−	0.0411937i	0.463901	−	0.885887i	$-0.346449\pi$
$643$	−1.80924	−	1.04457i	−0.0713496	−	0.0411937i	−0.535250	+	0.844693i	$0.679783\pi$
$644$	0.882172	−	1.52797i	0.0347625	−	0.0602103i
$645$		0			0
$646$	36.8347	−	22.9850i	1.44924	−	0.904334i
$647$		−	2.10623i		−	0.0828043i	−0.999143	−	0.0414021i	$-0.986818\pi$
$647$		−	2.10623i		−	0.0828043i	0.999143	−	0.0414021i	$-0.0131825\pi$
$648$	−2.29693	−	1.32613i	−0.0902319	−	0.0520954i
$649$	31.0722	−	53.8187i	1.21969	−	2.11257i
$650$		0			0
$651$	7.44081	−	12.8879i	0.291628	−	0.505115i
$652$	0.205549	−	0.118674i	0.00804994	−	0.00464763i
$653$		−	1.83067i		−	0.0716395i	−0.999358	−	0.0358197i	$-0.988596\pi$
$653$		−	1.83067i		−	0.0716395i	0.999358	−	0.0358197i	$-0.0114042\pi$
$654$	−10.8583			−0.424593
$655$		0			0
$656$	−15.6223	−	27.0587i	−0.609950	−	1.05646i
$657$			16.9634i			0.661804i
$658$		−	36.2973i		−	1.41502i
$659$	12.0268	+	20.8310i	0.468497	+	0.811460i	0.999352	−	0.0360024i	$-0.0114624\pi$
$659$	12.0268	+	20.8310i	0.468497	+	0.811460i	−0.530855	+	0.847463i	$0.678129\pi$
$660$		0			0
$661$	8.72110	+	15.1054i	0.339211	+	0.587531i	0.984285	−	0.176589i	$-0.0565065\pi$
$661$	8.72110	+	15.1054i	0.339211	+	0.587531i	−0.645073	+	0.764121i	$0.723173\pi$
$662$	−29.1282	−	16.8172i	−1.13210	−	0.653617i
$663$	−9.58642	−	5.53472i	−0.372306	−	0.214951i
$664$	−6.37097			−0.247241
$665$		0			0
$666$	−7.97184			−0.308902
$667$	2.13159	+	1.23068i	0.0825356	+	0.0476519i
$668$	9.52077	+	5.49682i	0.368370	+	0.212678i
$669$	−5.92402	−	10.2607i	−0.229036	−	0.396702i
$670$		0			0
$671$	−30.2951	−	52.4726i	−1.16953	−	2.02568i
$672$			11.7005i			0.451357i
$673$		−	47.5187i		−	1.83171i	−0.401506	−	0.915856i	$-0.631513\pi$
$673$		−	47.5187i		−	1.83171i	0.401506	−	0.915856i	$-0.368487\pi$
$674$	26.4868	+	45.8765i	1.02023	+	1.76709i
$675$		0			0
$676$	−8.05850			−0.309942
$677$			14.5531i			0.559321i	0.960099	+	0.279661i	$0.0902219\pi$
$677$			14.5531i			0.559321i	−0.960099	+	0.279661i	$0.909778\pi$
$678$	26.2124	−	15.1338i	1.00668	−	0.581208i
$679$	−4.94084	+	8.55778i	−0.189612	+	0.328418i
$680$		0			0
$681$	2.40754	−	4.16998i	0.0922570	−	0.159794i
$682$	43.7112	+	25.2367i	1.67379	+	0.966363i
$683$		−	3.33714i		−	0.127692i	−0.997960	−	0.0638460i	$-0.979663\pi$
$683$		−	3.33714i		−	0.127692i	0.997960	−	0.0638460i	$-0.0203367\pi$
$684$	−4.90736	−	2.61321i	−0.187638	−	0.0999185i
$685$		0			0
$686$	16.3553	−	28.3282i	0.624448	−	1.08158i
$687$	6.56146	+	3.78826i	0.250335	+	0.144531i
$688$	19.4487	−	11.2287i	0.741476	−	0.428092i
$689$	1.75163	−	3.03391i	0.0667318	−	0.115583i
$690$		0			0
$691$	−19.3318			−0.735415			−0.367708	−	0.929941i	$-0.619857\pi$
$691$	−19.3318			−0.735415			−0.367708	+	0.929941i	$0.619857\pi$
$692$			10.2868i			0.391044i
$693$	20.0859	−	11.5966i	0.763001	−	0.440519i
$694$	2.74862	+	4.76075i	0.104336	+	0.180716i
$695$		0			0
$696$	−6.21358			−0.235525
$697$	32.7283	−	18.8957i	1.23967	−	0.715725i
$698$	−25.7295	−	14.8549i	−0.973876	−	0.562268i
$699$	−2.98533	−	5.17074i	−0.112916	−	0.195575i
$700$		0			0
$701$	−4.96892	+	8.60643i	−0.187674	+	0.325060i	−0.944474	−	0.328586i	$-0.893428\pi$
$701$	−4.96892	+	8.60643i	−0.187674	+	0.325060i	0.756801	+	0.653646i	$0.226761\pi$
$702$			14.3332i			0.540971i
$703$	−12.6065	+	0.432375i	−0.475464	+	0.0163073i
$704$	17.2584			0.650452
$705$		0			0
$706$	−6.90389	+	11.9579i	−0.259831	+	0.450041i
$707$	23.4732	−	13.5523i	0.882801	−	0.509686i
$708$	8.35916	+	4.82616i	0.314157	+	0.181378i
$709$	18.6059	+	32.2264i	0.698760	+	1.21029i	0.968897	+	0.247466i	$0.0795979\pi$
$709$	18.6059	+	32.2264i	0.698760	+	1.21029i	−0.270136	+	0.962822i	$0.587069\pi$
$710$		0			0
$711$	−12.5853			−0.471987
$712$	−19.6950	+	11.3709i	−0.738101	+	0.426143i
$713$	−4.28961	+	2.47661i	−0.160647	+	0.0927497i
$714$	−28.1321			−1.05282
$715$		0			0
$716$	5.48003	+	9.49169i	0.204798	+	0.354721i
$717$	14.0575	+	8.11608i	0.524985	+	0.303100i
$718$	12.0372	−	6.94966i	0.449223	−	0.259359i
$719$	−1.32109	+	2.28819i	−0.0492683	+	0.0853351i	−0.889608	−	0.456725i	$-0.849022\pi$
$719$	−1.32109	+	2.28819i	−0.0492683	+	0.0853351i	0.840340	+	0.542060i	$0.182356\pi$
$720$		0			0
$721$	−28.1980			−1.05015
$722$	−28.4083	−	13.8995i	−1.05725	−	0.517284i
$723$			17.6581i			0.656711i
$724$	3.80832	−	6.59621i	0.141535	−	0.245146i
$725$		0			0
$726$	−21.3484	−	36.9765i	−0.792313	−	1.37233i
$727$	8.81013	+	5.08653i	0.326750	+	0.188649i	0.654397	−	0.756151i	$-0.272923\pi$
$727$	8.81013	+	5.08653i	0.326750	+	0.188649i	−0.327647	+	0.944800i	$0.606256\pi$
$728$	−6.88317	+	3.97400i	−0.255107	+	0.147286i
$729$	−20.9284			−0.775126
$730$		0			0
$731$	13.5815	+	23.5238i	0.502329	+	0.870060i
$732$	8.15009	−	4.70546i	0.301236	−	0.173919i
$733$		−	14.8222i		−	0.547472i	−0.961805	−	0.273736i	$-0.911741\pi$
$733$		−	14.8222i		−	0.547472i	0.961805	−	0.273736i	$-0.0882594\pi$
$734$	24.0023			0.885942
$735$		0			0
$736$	1.94720	−	3.37266i	0.0717749	−	0.124318i
$737$	−5.03151	+	2.90494i	−0.185338	+	0.107005i
$738$	−15.0665	−	8.69865i	−0.554605	−	0.320202i
$739$	17.7433	−	30.7323i	0.652697	−	1.13050i	−0.329769	−	0.944062i	$-0.606971\pi$
$739$	17.7433	−	30.7323i	0.652697	−	1.13050i	0.982466	−	0.186443i	$-0.0596959\pi$
$740$		0			0
$741$	0.276386	+	8.05845i	0.0101533	+	0.296035i
$742$		−	8.90325i		−	0.326849i
$743$	−7.56804	−	4.36941i	−0.277645	−	0.160298i	0.354712	−	0.934976i	$-0.384579\pi$
$743$	−7.56804	−	4.36941i	−0.277645	−	0.160298i	−0.632357	+	0.774677i	$0.717912\pi$
$744$	6.25210	−	10.8289i	0.229213	−	0.397009i
$745$		0			0
$746$	−20.0708	+	34.7637i	−0.734846	+	1.27279i
$747$	−4.46247	+	2.57641i	−0.163273	+	0.0942658i
$748$		−	26.5408i		−	0.970428i
$749$	43.6342			1.59436
$750$		0			0
$751$	−6.54957	−	11.3442i	−0.238997	−	0.413955i	0.721430	−	0.692488i	$-0.243485\pi$
$751$	−6.54957	−	11.3442i	−0.238997	−	0.413955i	−0.960427	+	0.278533i	$0.910152\pi$
$752$		−	44.3011i		−	1.61549i
$753$		−	7.08911i		−	0.258342i
$754$	3.47580	+	6.02026i	0.126581	+	0.219245i
$755$		0			0
$756$	5.06627	+	8.77504i	0.184258	+	0.319145i
$757$	14.2357	+	8.21901i	0.517407	+	0.298725i	0.735873	−	0.677119i	$-0.236772\pi$
$757$	14.2357	+	8.21901i	0.517407	+	0.298725i	−0.218466	+	0.975845i	$0.570105\pi$
$758$	−24.0386	−	13.8787i	−0.873121	−	0.504097i
$759$	6.27397			0.227731
$760$		0			0
$761$	16.3918			0.594203			0.297101	−	0.954846i	$-0.403980\pi$
$761$	16.3918			0.594203			0.297101	+	0.954846i	$0.403980\pi$
$762$	−10.2315	−	5.90714i	−0.370647	−	0.213993i
$763$	−11.8625	−	6.84879i	−0.429450	−	0.247943i
$764$	−5.00738	−	8.67304i	−0.181161	−	0.313780i
$765$		0			0
$766$	−9.05337	−	15.6809i	−0.327112	−	0.566574i
$767$			17.2242i			0.621929i
$768$			18.6756i			0.673899i
$769$	−25.0210	−	43.3377i	−0.902282	−	1.56280i	−0.824525	−	0.565825i	$-0.808558\pi$
$769$	−25.0210	−	43.3377i	−0.902282	−	1.56280i	−0.0777564	−	0.996972i	$-0.524776\pi$
$770$		0			0
$771$	−0.142282			−0.00512416
$772$			11.1875i			0.402649i
$773$	−42.1644	+	24.3436i	−1.51655	+	0.875580i	−0.516737	+	0.856144i	$0.672854\pi$
$773$	−42.1644	+	24.3436i	−1.51655	+	0.875580i	−0.999811	+	0.0194356i	$0.993813\pi$
$774$	6.25225	−	10.8292i	0.224732	−	0.389248i
$775$		0			0
$776$	−4.15151	+	7.19063i	−0.149031	+	0.258129i
$777$	7.07808	+	4.08653i	0.253925	+	0.146603i
$778$			60.6799i			2.17548i
$779$	−24.2977	−	12.9387i	−0.870555	−	0.463577i
$780$		0			0
$781$	25.4185	−	44.0261i	0.909544	−	1.57538i
$782$	8.10905	+	4.68176i	0.289979	+	0.167419i
$783$	−12.2416	+	7.06771i	−0.437480	+	0.252579i
$784$	2.64572	−	4.58252i	0.0944900	−	0.163662i
$785$		0			0
$786$	−28.7275			−1.02467
$787$			6.51678i			0.232298i	0.993232	+	0.116149i	$0.0370550\pi$
$787$			6.51678i			0.232298i	−0.993232	+	0.116149i	$0.962945\pi$
$788$	16.6870	−	9.63426i	0.594451	−	0.343206i
$789$	5.83388	+	10.1046i	0.207692	+	0.359732i
$790$		0			0
$791$	38.1820			1.35760
$792$	16.8771	−	9.74399i	0.599701	−	0.346238i
$793$	14.5435	+	8.39668i	0.516454	+	0.298175i
$794$	−7.14407	−	12.3739i	−0.253534	−	0.439133i
$795$		0			0
$796$	0.869124	−	1.50537i	0.0308053	−	0.0533563i
$797$			38.3796i			1.35947i	0.733456	+	0.679737i	$0.237906\pi$
$797$			38.3796i			1.35947i	−0.733456	+	0.679737i	$0.762094\pi$
$798$	10.8483	+	17.3849i	0.384024	+	0.615419i
$799$	53.5834			1.89565
$800$		0			0
$801$	−9.19675	+	15.9292i	−0.324951	+	0.562832i
$802$	24.5864	−	14.1950i	0.868177	−	0.501242i
$803$	51.0836	+	29.4931i	1.80270	+	1.04079i
$804$	−0.451198	−	0.781498i	−0.0159125	−	0.0275613i
$805$		0			0
$806$	−13.9894			−0.492755
$807$	−5.73729	+	3.31243i	−0.201962	+	0.116603i
$808$	19.7232	−	11.3872i	0.693861	−	0.400601i
$809$	−25.1409			−0.883906			−0.441953	−	0.897038i	$-0.645714\pi$
$809$	−25.1409			−0.883906			−0.441953	+	0.897038i	$0.645714\pi$
$810$		0			0
$811$	23.5053	+	40.7124i	0.825383	+	1.42961i	0.901626	+	0.432517i	$0.142374\pi$
$811$	23.5053	+	40.7124i	0.825383	+	1.42961i	−0.0762426	+	0.997089i	$0.524292\pi$
$812$	4.25590	+	2.45714i	0.149353	+	0.0862289i
$813$	−12.7668	+	7.37094i	−0.447753	+	0.258510i
$814$	−13.8601	+	24.0064i	−0.485797	+	0.841425i
$815$		0			0
$816$	−34.3354			−1.20198
$817$	9.29984	−	17.4642i	0.325360	−	0.610996i
$818$		−	19.6317i		−	0.686406i
$819$	−3.21416	+	5.56708i	−0.112312	+	0.194530i
$820$		0			0
$821$	9.91021	+	17.1650i	0.345869	+	0.599062i	0.985511	−	0.169610i	$-0.0542509\pi$
$821$	9.91021	+	17.1650i	0.345869	+	0.599062i	−0.639642	+	0.768673i	$0.720918\pi$
$822$	−29.0069	−	16.7471i	−1.01173	−	0.584123i
$823$	33.9627	−	19.6084i	1.18387	−	0.683505i	0.226960	−	0.973904i	$-0.427121\pi$
$823$	33.9627	−	19.6084i	1.18387	−	0.683505i	0.956906	+	0.290399i	$0.0937881\pi$
$824$	−23.6932			−0.825391
$825$		0			0
$826$	21.8869	+	37.9092i	0.761543	+	1.31903i
$827$	−10.2568	+	5.92176i	−0.356663	+	0.205920i	−0.667616	−	0.744506i	$-0.732685\pi$
$827$	−10.2568	+	5.92176i	−0.356663	+	0.205920i	0.310953	+	0.950425i	$0.399352\pi$
$828$		−	1.19903i		−	0.0416690i
$829$	−46.9321			−1.63002			−0.815010	−	0.579447i	$-0.803269\pi$
$829$	−46.9321			−1.63002			−0.815010	+	0.579447i	$0.803269\pi$
$830$		0			0
$831$	10.2070	−	17.6790i	0.354076	−	0.613278i
$832$	−4.14255	+	2.39170i	−0.143617	+	0.0829174i
$833$	5.54270	+	3.20008i	0.192043	+	0.110876i
$834$	−6.47222	+	11.2102i	−0.224115	+	0.388178i
$835$		0			0
$836$	−16.4015	+	10.2346i	−0.567259	+	0.353972i
$837$		−	28.4461i		−	0.983240i
$838$	−1.64738	−	0.951117i	−0.0569079	−	0.0328558i
$839$	−26.5669	+	46.0153i	−0.917192	+	1.58862i	−0.113532	+	0.993534i	$0.536217\pi$
$839$	−26.5669	+	46.0153i	−0.917192	+	1.58862i	−0.803660	+	0.595089i	$0.797117\pi$
$840$		0			0
$841$	11.0722	−	19.1775i	0.381799	−	0.661294i
$842$	−28.1372	+	16.2450i	−0.969673	+	0.559841i
$843$		−	23.7755i		−	0.818870i
$844$	−17.1222			−0.589370
$845$		0			0
$846$	−12.3336	−	21.3624i	−0.424038	−	0.734455i
$847$		−	53.8613i		−	1.85070i
$848$		−	10.8665i		−	0.373156i
$849$	6.87509	+	11.9080i	0.235952	+	0.408682i
$850$		0			0
$851$	−1.36017	−	2.35588i	−0.0466259	−	0.0807584i
$852$	6.83816	+	3.94802i	0.234272	+	0.135257i
$853$	36.6327	+	21.1499i	1.25428	+	0.724159i	0.971957	−	0.235160i	$-0.0755615\pi$
$853$	36.6327	+	21.1499i	1.25428	+	0.724159i	0.282324	+	0.959319i	$0.408895\pi$
$854$	42.6790			1.46045
$855$		0			0
$856$	36.6634			1.25313
$857$	−20.3849	−	11.7692i	−0.696333	−	0.402028i	0.109647	−	0.993971i	$-0.465028\pi$
$857$	−20.3849	−	11.7692i	−0.696333	−	0.402028i	−0.805980	+	0.591942i	$0.798361\pi$
$858$	15.3456	+	8.85979i	0.523890	+	0.302468i
$859$	4.74062	+	8.21099i	0.161748	+	0.280156i	0.935496	−	0.353338i	$-0.114954\pi$
$859$	4.74062	+	8.21099i	0.161748	+	0.280156i	−0.773748	+	0.633494i	$0.781620\pi$
$860$		0			0
$861$	8.91821	+	15.4468i	0.303932	+	0.526425i
$862$			61.3859i			2.09081i
$863$		−	22.8204i		−	0.776816i	−0.921487	−	0.388408i	$-0.873025\pi$
$863$		−	22.8204i		−	0.776816i	0.921487	−	0.388408i	$-0.126975\pi$
$864$	11.1827	+	19.3690i	0.380443	+	0.658947i
$865$		0			0
$866$	−0.614106			−0.0208682
$867$		−	21.8138i		−	0.740834i
$868$	−8.56456	+	4.94475i	−0.290700	+	0.167836i
$869$	−21.8813	+	37.8996i	−0.742273	+	1.28565i
$870$		0			0
$871$	0.805144	−	1.39455i	0.0272813	−	0.0472525i
$872$	−9.96736	−	5.75466i	−0.337537	−	0.194877i
$873$			6.71546i			0.227284i
$874$	−0.233792	−	6.81656i	−0.00790814	−	0.230574i
$875$		0			0
$876$	−4.58089	+	7.93434i	−0.154774	+	0.268077i
$877$	21.9054	+	12.6471i	0.739693	+	0.427062i	0.821958	−	0.569549i	$-0.192882\pi$
$877$	21.9054	+	12.6471i	0.739693	+	0.427062i	−0.0822647	+	0.996611i	$0.526215\pi$
$878$	−3.26421	+	1.88459i	−0.110162	+	0.0636018i
$879$	14.4862	−	25.0908i	0.488606	−	0.846291i
$880$		0			0
$881$	−33.2871			−1.12147			−0.560736	−	0.827995i	$-0.689482\pi$
$881$	−33.2871			−1.12147			−0.560736	+	0.827995i	$0.689482\pi$
$882$		−	2.94632i		−	0.0992077i
$883$	13.2596	−	7.65544i	0.446222	−	0.257626i	−0.260011	−	0.965606i	$-0.583726\pi$
$883$	13.2596	−	7.65544i	0.446222	−	0.257626i	0.706233	+	0.707979i	$0.250393\pi$
$884$	3.67807	+	6.37061i	0.123707	+	0.214267i
$885$		0			0
$886$	27.4030			0.920621
$887$	37.4171	−	21.6027i	1.25634	−	0.725349i	0.283980	−	0.958830i	$-0.408345\pi$
$887$	37.4171	−	21.6027i	1.25634	−	0.725349i	0.972361	+	0.233481i	$0.0750116\pi$
$888$	5.94731	+	3.43368i	0.199579	+	0.115227i
$889$	−7.45177	−	12.9068i	−0.249924	−	0.432882i
$890$		0			0
$891$	−3.72962	+	6.45990i	−0.124947	+	0.216415i
$892$			7.87356i			0.263626i
$893$	−20.6628	−	33.1132i	−0.691453	−	1.10809i
$894$	−27.7849			−0.929265
$895$		0			0
$896$	−16.1671	+	28.0022i	−0.540104	+	0.935488i
$897$	−1.50594	+	0.869457i	−0.0502820	+	0.0290303i
$898$	−20.4141	−	11.7861i	−0.681228	−	0.393307i
$899$	−6.89818	−	11.9480i	−0.230067	−	0.398488i
$900$		0			0
$901$	13.1433			0.437867
$902$	−52.3903	+	30.2475i	−1.74441	+	1.00713i
$903$	−11.1026	+	6.41007i	−0.369470	+	0.213314i
$904$	32.0822			1.06704
$905$		0			0
$906$	−12.2796	−	21.2688i	−0.407961	−	0.706609i
$907$	−12.4083	−	7.16392i	−0.412010	−	0.237874i	0.279643	−	0.960104i	$-0.409784\pi$
$907$	−12.4083	−	7.16392i	−0.412010	−	0.237874i	−0.691653	+	0.722230i	$0.743117\pi$
$908$	−2.77114	+	1.59992i	−0.0919634	+	0.0530951i
$909$	9.20994	−	15.9521i	0.305475	−	0.529097i
$910$		0			0
$911$	−4.61162			−0.152790			−0.0763949	−	0.997078i	$-0.524341\pi$
$911$	−4.61162			−0.152790			−0.0763949	+	0.997078i	$0.524341\pi$
$912$	13.2404	+	21.2184i	0.438432	+	0.702610i
$913$			17.9177i			0.592990i
$914$	−1.01598	+	1.75973i	−0.0336056	+	0.0582066i
$915$		0			0
$916$	−2.51747	−	4.36038i	−0.0831795	−	0.144071i
$917$	−31.3841	−	18.1196i	−1.03640	−	0.598363i
$918$	−46.5699	+	26.8871i	−1.53703	+	0.887407i
$919$	−26.4921			−0.873892			−0.436946	−	0.899488i	$-0.643940\pi$
$919$	−26.4921			−0.873892			−0.436946	+	0.899488i	$0.643940\pi$
$920$		0			0
$921$	9.81149	+	16.9940i	0.323300	+	0.559972i
$922$	12.5293	−	7.23378i	0.412630	−	0.238232i
$923$			14.0901i			0.463782i
$924$	12.5265			0.412091
$925$		0			0
$926$	−16.4082	+	28.4198i	−0.539206	+	0.933932i
$927$	−16.5956	+	9.58148i	−0.545072	+	0.314697i
$928$	9.39398	+	5.42362i	0.308372	+	0.178039i
$929$	−2.37863	+	4.11990i	−0.0780402	+	0.135170i	−0.902404	−	0.430890i	$-0.858200\pi$
$929$	−2.37863	+	4.11990i	−0.0780402	+	0.135170i	0.824364	+	0.566060i	$0.191533\pi$
$930$		0			0
$931$	−0.159802	−	4.65925i	−0.00523729	−	0.152701i
$932$			3.96777i			0.129969i
$933$	15.2799	+	8.82188i	0.500243	+	0.288815i
$934$	9.55406	−	16.5481i	0.312619	−	0.541471i
$935$		0			0
$936$	−2.70068	+	4.67771i	−0.0882744	+	0.152896i
$937$	−10.3375	+	5.96833i	−0.337710	+	0.194977i	−0.659259	−	0.751916i	$-0.729130\pi$
$937$	−10.3375	+	5.96833i	−0.337710	+	0.194977i	0.321549	+	0.946893i	$0.395797\pi$
$938$		−	4.09242i		−	0.133622i
$939$	28.9096			0.943429
$940$		0			0
$941$	8.99715	+	15.5835i	0.293299	+	0.508008i	0.974588	−	0.224006i	$-0.0719136\pi$
$941$	8.99715	+	15.5835i	0.293299	+	0.508008i	−0.681289	+	0.732015i	$0.738580\pi$
$942$		−	6.51590i		−	0.212299i
$943$		−	5.93670i		−	0.193326i
$944$	26.7131	+	46.2684i	0.869437	+	1.50591i
$945$		0			0
$946$	−21.7408	−	37.6561i	−0.706853	−	1.22431i
$947$	21.8404	+	12.6096i	0.709717	+	0.409755i	0.810956	−	0.585107i	$-0.198947\pi$
$947$	21.8404	+	12.6096i	0.709717	+	0.409755i	−0.101239	+	0.994862i	$0.532281\pi$
$948$	−5.88659	−	3.39862i	−0.191188	−	0.110382i
$949$	−16.3488			−0.530705
$950$		0			0
$951$	29.2611			0.948858
$952$	−25.8238	−	14.9094i	−0.836955	−	0.483216i
$953$	36.6484	+	21.1589i	1.18716	+	0.685405i	0.957659	−	0.287904i	$-0.0929583\pi$
$953$	36.6484	+	21.1589i	1.18716	+	0.685405i	0.229498	+	0.973309i	$0.426292\pi$
$954$	−3.02527	−	5.23991i	−0.0979466	−	0.169648i
$955$		0			0
$956$	−5.39350	−	9.34181i	−0.174438	−	0.302136i
$957$			17.4751i			0.564890i
$958$			65.3552i			2.11153i
$959$	−21.1263	−	36.5918i	−0.682203	−	1.18161i
$960$		0			0
$961$	−3.23623			−0.104395
$962$		−	7.68304i		−	0.247711i
$963$	25.6805	−	14.8266i	0.827542	−	0.477781i
$964$	5.86730	−	10.1625i	0.188973	−	0.327311i
$965$		0			0
$966$	−2.20966	+	3.82724i	−0.0710945	+	0.123139i
$967$	11.8614	+	6.84820i	0.381438	+	0.220223i	0.678444	−	0.734652i	$-0.262655\pi$
$967$	11.8614	+	6.84820i	0.381438	+	0.220223i	−0.297006	+	0.954876i	$0.595988\pi$
$968$		−	45.2567i		−	1.45460i
$969$	−25.6642	+	16.0146i	−0.824454	+	0.514463i
$970$		0			0
$971$	19.2906	−	33.4123i	0.619065	−	1.07225i	−0.370591	−	0.928796i	$-0.620845\pi$
$971$	19.2906	−	33.4123i	0.619065	−	1.07225i	0.989657	−	0.143457i	$-0.0458217\pi$
$972$	9.80665	+	5.66187i	0.314548	+	0.181605i
$973$	−14.1415	+	8.16461i	−0.453356	+	0.261745i
$974$	−26.2951	+	45.5445i	−0.842549	+	1.45934i
$975$		0			0
$976$	52.0899			1.66736
$977$		−	17.4592i		−	0.558568i	−0.960209	−	0.279284i	$-0.909903\pi$
$977$		−	17.4592i		−	0.558568i	0.960209	−	0.279284i	$-0.0900971\pi$
$978$	−0.514858	+	0.297253i	−0.0164633	+	0.00950512i
$979$	31.9796	+	55.3903i	1.02207	+	1.77028i
$980$		0			0
$981$	−9.30869			−0.297204
$982$	15.9488	−	9.20805i	0.508947	−	0.293841i
$983$	38.0325	+	21.9581i	1.21305	+	0.700353i	0.963422	−	0.267989i	$-0.0863592\pi$
$983$	38.0325	+	21.9581i	1.21305	+	0.700353i	0.249625	+	0.968342i	$0.419692\pi$
$984$	7.49348	+	12.9791i	0.238883	+	0.413758i
$985$		0			0
$986$	−13.0403	+	22.5864i	−0.415287	+	0.719298i
$987$			25.2898i			0.804984i
$988$	2.51854	−	4.72958i	0.0801254	−	0.150468i
$989$	4.26707			0.135685
$990$		0			0
$991$	−23.1731	+	40.1370i	−0.736118	+	1.27499i	0.218112	+	0.975924i	$0.430010\pi$
$991$	−23.1731	+	40.1370i	−0.736118	+	1.27499i	−0.954231	+	0.299071i	$0.903323\pi$
$992$	−18.9044	+	10.9145i	−0.600216	+	0.346535i
$993$	20.2948	+	11.7172i	0.644035	+	0.371834i
$994$	17.9045	+	31.0114i	0.567895	+	0.983623i
$995$		0			0
$996$	−2.78300			−0.0881827
$997$	10.1647	−	5.86857i	0.321918	−	0.185859i	−0.330329	−	0.943866i	$-0.607160\pi$
$997$	10.1647	−	5.86857i	0.321918	−	0.185859i	0.652247	+	0.758006i	$0.273826\pi$
$998$	−29.3692	+	16.9563i	−0.929667	+	0.536744i
$999$	15.6227			0.494281

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.j.c.49.7		16
5.2	odd	4		475.2.e.e.201.1		8
5.3	odd	4		95.2.e.c.11.4	✓	8
5.4	even	2	inner	475.2.j.c.49.2		16
15.8	even	4		855.2.k.h.676.1		8
19.7	even	3	inner	475.2.j.c.349.2		16
20.3	even	4		1520.2.q.o.961.1		8
95.7	odd	12		475.2.e.e.26.1		8
95.8	even	12		1805.2.a.i.1.4		4
95.27	even	12		9025.2.a.bp.1.1		4
95.64	even	6	inner	475.2.j.c.349.7		16
95.68	odd	12		1805.2.a.o.1.1		4
95.83	odd	12		95.2.e.c.26.4	yes	8
95.87	odd	12		9025.2.a.bg.1.4		4
285.83	even	12		855.2.k.h.406.1		8
380.83	even	12		1520.2.q.o.881.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.c.11.4	✓	8	5.3	odd	4
95.2.e.c.26.4	yes	8	95.83	odd	12
475.2.e.e.26.1		8	95.7	odd	12
475.2.e.e.201.1		8	5.2	odd	4
475.2.j.c.49.2		16	5.4	even	2	inner
475.2.j.c.49.7		16	1.1	even	1	trivial
475.2.j.c.349.2		16	19.7	even	3	inner
475.2.j.c.349.7		16	95.64	even	6	inner
855.2.k.h.406.1		8	285.83	even	12
855.2.k.h.676.1		8	15.8	even	4
1520.2.q.o.881.1		8	380.83	even	12
1520.2.q.o.961.1		8	20.3	even	4
1805.2.a.i.1.4		4	95.8	even	12
1805.2.a.o.1.1		4	95.68	odd	12
9025.2.a.bg.1.4		4	95.87	odd	12
9025.2.a.bp.1.1		4	95.27	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+(1.44154 + 0.832272i) q^{2} +(-1.00438 - 0.579878i) q^{3} +(0.385355 + 0.667454i) q^{4} +(-0.965233 - 1.67183i) q^{6} -2.43525i q^{7} -2.04621i q^{8} +(-0.827483 - 1.43324i) q^{9} -5.75477 q^{11} -0.893835i q^{12} +(1.38132 - 0.797505i) q^{13} +(2.02680 - 3.51051i) q^{14} +(2.47371 - 4.28460i) q^{16} +(5.18234 + 2.99203i) q^{17} -2.75477i q^{18} +(-0.149412 - 4.35634i) q^{19} +(-1.41215 + 2.44592i) q^{21} +(-8.29572 - 4.78953i) q^{22} +(0.814102 - 0.470022i) q^{23} +(-1.18655 + 2.05517i) q^{24} +2.65497 q^{26} +5.39862i q^{27} +(1.62542 - 0.938437i) q^{28} +(1.30917 + 2.26755i) q^{29} -5.26913 q^{31} +(3.58777 - 2.07140i) q^{32} +(5.77996 + 3.33706i) q^{33} +(4.98037 + 8.62625i) q^{34} +(0.637749 - 1.10461i) q^{36} -2.89384i q^{37} +(3.41028 - 6.40418i) q^{38} -1.84982 q^{39} +(3.15767 - 5.46925i) q^{41} +(-4.07134 + 2.35059i) q^{42} +(3.93108 + 2.26961i) q^{43} +(-2.21763 - 3.84104i) q^{44} +1.56475 q^{46} +(7.75471 - 4.47718i) q^{47} +(-4.96909 + 2.86890i) q^{48} +1.06953 q^{49} +(-3.47002 - 6.01025i) q^{51} +(1.06460 + 0.614645i) q^{52} +(1.90213 - 1.09819i) q^{53} +(-4.49313 + 7.78232i) q^{54} -4.98304 q^{56} +(-2.37608 + 4.46205i) q^{57} +4.35834i q^{58} +(-5.39939 + 9.35202i) q^{59} +(5.26434 + 9.11811i) q^{61} +(-7.59566 - 4.38535i) q^{62} +(-3.49031 + 2.01513i) q^{63} -2.99898 q^{64} +(5.55469 + 9.62100i) q^{66} +(0.874320 - 0.504789i) q^{67} +4.61197i q^{68} -1.09022 q^{69} +(-4.41694 + 7.65036i) q^{71} +(-2.93271 + 1.69320i) q^{72} +(-8.87674 - 5.12499i) q^{73} +(2.40846 - 4.17157i) q^{74} +(2.85008 - 1.77846i) q^{76} +14.0143i q^{77} +(-2.66659 - 1.53956i) q^{78} +(3.80229 - 6.58577i) q^{79} +(0.648093 - 1.12253i) q^{81} +(9.10381 - 5.25609i) q^{82} -3.11355i q^{83} -2.17672 q^{84} +(3.77787 + 6.54346i) q^{86} -3.03663i q^{87} +11.7755i q^{88} +(-5.55706 - 9.62511i) q^{89} +(-1.94213 - 3.36387i) q^{91} +(0.627436 + 0.362251i) q^{92} +(5.29220 + 3.05545i) q^{93} +14.9049 q^{94} -4.80463 q^{96} +(-3.51412 - 2.02888i) q^{97} +(1.54177 + 0.890144i) q^{98} +(4.76197 + 8.24798i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more