LMFDB - Embedded newform 425.2.n.c.399.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(49,425)] 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("425.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.n (of order $8$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			399.5
Character	$\chi$	$=$	425.399
Dual form			425.2.n.c.49.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.528855 + 0.528855i) q^{2} +(2.84096 + 1.17676i) q^{3} -1.44062i q^{4} +(0.880118 + 2.12479i) q^{6} +(-1.23707 - 2.98655i) q^{7} +(1.81959 - 1.81959i) q^{8} +(4.56494 + 4.56494i) q^{9} +(1.04667 + 2.52689i) q^{11} +(1.69527 - 4.09275i) q^{12} -4.31833 q^{13} +(0.925222 - 2.23368i) q^{14} -0.956646 q^{16} +(2.22453 + 3.47152i) q^{17} +4.82839i q^{18} +(0.897260 - 0.897260i) q^{19} -9.94040i q^{21} +(-0.782821 + 1.88990i) q^{22} +(0.454888 - 0.188421i) q^{23} +(7.31061 - 3.02815i) q^{24} +(-2.28377 - 2.28377i) q^{26} +(4.06666 + 9.81779i) q^{27} +(-4.30250 + 1.78215i) q^{28} +(0.410535 + 0.170049i) q^{29} +(-2.11561 + 5.10754i) q^{31} +(-4.14511 - 4.14511i) q^{32} +8.41047i q^{33} +(-0.659477 + 3.01239i) q^{34} +(6.57637 - 6.57637i) q^{36} +(-9.88545 - 4.09469i) q^{37} +0.949042 q^{38} +(-12.2682 - 5.08165i) q^{39} +(-2.00526 + 0.830608i) q^{41} +(5.25703 - 5.25703i) q^{42} +(-1.52864 + 1.52864i) q^{43} +(3.64030 - 1.50786i) q^{44} +(0.340217 + 0.140922i) q^{46} -8.39597 q^{47} +(-2.71779 - 1.12575i) q^{48} +(-2.43940 + 2.43940i) q^{49} +(2.23464 + 12.4802i) q^{51} +6.22109i q^{52} +(1.28480 + 1.28480i) q^{53} +(-3.04152 + 7.34287i) q^{54} +(-7.68527 - 3.18334i) q^{56} +(3.60494 - 1.49321i) q^{57} +(0.127182 + 0.307045i) q^{58} +(2.13537 + 2.13537i) q^{59} +(11.2928 - 4.67764i) q^{61} +(-3.82000 + 1.58230i) q^{62} +(7.98628 - 19.2806i) q^{63} -2.47104i q^{64} +(-4.44792 + 4.44792i) q^{66} +4.21389i q^{67} +(5.00116 - 3.20471i) q^{68} +1.51404 q^{69} +(-1.48927 + 3.59542i) q^{71} +16.6127 q^{72} +(2.47620 - 5.97807i) q^{73} +(-3.06247 - 7.39347i) q^{74} +(-1.29261 - 1.29261i) q^{76} +(6.25188 - 6.25188i) q^{77} +(-3.80064 - 9.17555i) q^{78} +(2.76355 + 6.67180i) q^{79} +13.3100i q^{81} +(-1.49977 - 0.621223i) q^{82} +(0.160866 + 0.160866i) q^{83} -14.3204 q^{84} -1.61686 q^{86} +(0.966206 + 0.966206i) q^{87} +(6.50243 + 2.69339i) q^{88} -13.3408i q^{89} +(5.34208 + 12.8969i) q^{91} +(-0.271443 - 0.655322i) q^{92} +(-12.0207 + 12.0207i) q^{93} +(-4.44025 - 4.44025i) q^{94} +(-6.89827 - 16.6539i) q^{96} +(-5.66657 + 13.6803i) q^{97} -2.58018 q^{98} +(-6.75711 + 16.3131i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{3} - 8 q^{6} + 24 q^{9} - 8 q^{11} + 40 q^{12} + 16 q^{13} - 24 q^{16} + 8 q^{19} - 24 q^{22} + 8 q^{23} + 8 q^{24} + 16 q^{26} + 16 q^{27} - 40 q^{28} + 8 q^{29} - 16 q^{34} - 24 q^{36} - 16 q^{37}+ \cdots + 8 q^{99}+O(q^{100}) $ 24 * q - 8 * q^3 - 8 * q^6 + 24 * q^9 - 8 * q^11 + 40 * q^12 + 16 * q^13 - 24 * q^16 + 8 * q^19 - 24 * q^22 + 8 * q^23 + 8 * q^24 + 16 * q^26 + 16 * q^27 - 40 * q^28 + 8 * q^29 - 16 * q^34 - 24 * q^36 - 16 * q^37 - 48 * q^38 - 8 * q^39 + 16 * q^41 - 24 * q^42 - 8 * q^43 - 16 * q^44 + 8 * q^46 - 64 * q^47 - 8 * q^48 - 56 * q^51 + 24 * q^53 + 32 * q^54 + 64 * q^56 + 16 * q^57 + 56 * q^58 - 32 * q^59 + 32 * q^61 - 32 * q^62 + 80 * q^63 + 96 * q^66 + 24 * q^68 - 96 * q^69 - 24 * q^71 - 24 * q^72 - 64 * q^73 + 64 * q^74 - 8 * q^76 + 24 * q^77 + 8 * q^78 - 16 * q^82 - 96 * q^83 + 64 * q^84 - 16 * q^86 + 48 * q^87 + 8 * q^88 - 24 * q^91 + 112 * q^92 - 64 * q^93 - 56 * q^94 - 168 * q^96 + 48 * q^97 + 120 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$-1$	$e\left(\frac{5}{8}\right)$

Coefficient data

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

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

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

$2$	0.528855	+	0.528855i	0.373957	+	0.373957i	0.868916	−	0.494959i	$-0.164817\pi$
$2$	0.528855	+	0.528855i	0.373957	+	0.373957i	−0.494959	+	0.868916i	$0.664817\pi$
$3$	2.84096	+	1.17676i	1.64023	+	0.679404i	0.996321	−	0.0857002i	$-0.0273127\pi$
$3$	2.84096	+	1.17676i	1.64023	+	0.679404i	0.643906	+	0.765105i	$0.277313\pi$
$4$		−	1.44062i		−	0.720312i
$5$		0			0
$5$		0			0
$6$	0.880118	+	2.12479i	0.359307	+	0.867443i
$7$	−1.23707	−	2.98655i	−0.467569	−	1.12881i	−0.965221	−	0.261434i	$-0.915805\pi$
$7$	−1.23707	−	2.98655i	−0.467569	−	1.12881i	0.497653	−	0.867376i	$-0.334195\pi$
$8$	1.81959	−	1.81959i	0.643323	−	0.643323i
$9$	4.56494	+	4.56494i	1.52165	+	1.52165i
$10$		0			0
$11$	1.04667	+	2.52689i	0.315584	+	0.761886i	0.999478	+	0.0323052i	$0.0102849\pi$
$11$	1.04667	+	2.52689i	0.315584	+	0.761886i	−0.683894	+	0.729581i	$0.739715\pi$
$12$	1.69527	−	4.09275i	0.489383	−	1.18148i
$13$	−4.31833			−1.19769			−0.598845	−	0.800865i	$-0.704373\pi$
$13$	−4.31833			−1.19769			−0.598845	+	0.800865i	$0.704373\pi$
$14$	0.925222	−	2.23368i	0.247276	−	0.596977i
$15$		0			0
$16$	−0.956646			−0.239162
$17$	2.22453	+	3.47152i	0.539528	+	0.841968i
$17$	2.22453	+	3.47152i	0.539528	+	0.841968i
$18$			4.82839i			1.13806i
$19$	0.897260	−	0.897260i	0.205846	−	0.205846i	−0.596653	−	0.802499i	$-0.703503\pi$
$19$	0.897260	−	0.897260i	0.205846	−	0.205846i	0.802499	+	0.596653i	$0.203503\pi$
$20$		0			0
$21$		−	9.94040i		−	2.16917i
$22$	−0.782821	+	1.88990i	−0.166898	+	0.402928i
$23$	0.454888	−	0.188421i	0.0948506	−	0.0392884i	−0.334754	−	0.942306i	$-0.608653\pi$
$23$	0.454888	−	0.188421i	0.0948506	−	0.0392884i	0.429604	+	0.903017i	$0.358653\pi$
$24$	7.31061	−	3.02815i	1.49227	−	0.618119i
$25$		0			0
$26$	−2.28377	−	2.28377i	−0.447884	−	0.447884i
$27$	4.06666	+	9.81779i	0.782630	+	1.88943i
$28$	−4.30250	+	1.78215i	−0.813096	+	0.336795i
$29$	0.410535	+	0.170049i	0.0762345	+	0.0315774i	0.420475	−	0.907304i	$-0.361863\pi$
$29$	0.410535	+	0.170049i	0.0762345	+	0.0315774i	−0.344240	+	0.938882i	$0.611863\pi$
$30$		0			0
$31$	−2.11561	+	5.10754i	−0.379975	+	0.917342i	0.611994	+	0.790862i	$0.290368\pi$
$31$	−2.11561	+	5.10754i	−0.379975	+	0.917342i	−0.991969	+	0.126479i	$0.959632\pi$
$32$	−4.14511	−	4.14511i	−0.732759	−	0.732759i
$33$			8.41047i			1.46408i
$34$	−0.659477	+	3.01239i	−0.113099	+	0.516620i
$35$		0			0
$36$	6.57637	−	6.57637i	1.09606	−	1.09606i
$37$	−9.88545	−	4.09469i	−1.62516	−	0.673162i	−0.630481	−	0.776205i	$-0.717142\pi$
$37$	−9.88545	−	4.09469i	−1.62516	−	0.673162i	−0.994677	+	0.103043i	$0.967142\pi$
$38$	0.949042			0.153955
$39$	−12.2682	−	5.08165i	−1.96448	−	0.813715i
$40$		0			0
$41$	−2.00526	+	0.830608i	−0.313170	+	0.129719i	−0.533732	−	0.845654i	$-0.679211\pi$
$41$	−2.00526	+	0.830608i	−0.313170	+	0.129719i	0.220562	+	0.975373i	$0.429211\pi$
$42$	5.25703	−	5.25703i	0.811178	−	0.811178i
$43$	−1.52864	+	1.52864i	−0.233115	+	0.233115i	−0.813992	−	0.580876i	$-0.802710\pi$
$43$	−1.52864	+	1.52864i	−0.233115	+	0.233115i	0.580876	+	0.813992i	$0.302710\pi$
$44$	3.64030	−	1.50786i	0.548796	−	0.227319i
$45$		0			0
$46$	0.340217	+	0.140922i	0.0501622	+	0.0207779i
$47$	−8.39597			−1.22468			−0.612339	−	0.790595i	$-0.709771\pi$
$47$	−8.39597			−1.22468			−0.612339	+	0.790595i	$0.709771\pi$
$48$	−2.71779	−	1.12575i	−0.392279	−	0.162487i
$49$	−2.43940	+	2.43940i	−0.348485	+	0.348485i
$50$		0			0
$51$	2.23464	+	12.4802i	0.312912	+	1.74758i
$52$			6.22109i			0.862710i
$53$	1.28480	+	1.28480i	0.176481	+	0.176481i	0.789820	−	0.613339i	$-0.210174\pi$
$53$	1.28480	+	1.28480i	0.176481	+	0.176481i	−0.613339	+	0.789820i	$0.710174\pi$
$54$	−3.04152	+	7.34287i	−0.413898	+	0.999238i
$55$		0			0
$56$	−7.68527	−	3.18334i	−1.02699	−	0.425392i
$57$	3.60494	−	1.49321i	0.477486	−	0.197781i
$58$	0.127182	+	0.307045i	0.0166999	+	0.0403170i
$59$	2.13537	+	2.13537i	0.278001	+	0.278001i	0.832311	−	0.554309i	$-0.187018\pi$
$59$	2.13537	+	2.13537i	0.278001	+	0.278001i	−0.554309	+	0.832311i	$0.687018\pi$
$60$		0			0
$61$	11.2928	−	4.67764i	1.44590	−	0.598910i	0.484677	−	0.874693i	$-0.338937\pi$
$61$	11.2928	−	4.67764i	1.44590	−	0.598910i	0.961220	+	0.275783i	$0.0889371\pi$
$62$	−3.82000	+	1.58230i	−0.485141	+	0.200952i
$63$	7.98628	−	19.2806i	1.00618	−	2.42913i
$64$		−	2.47104i		−	0.308880i
$65$		0			0
$66$	−4.44792	+	4.44792i	−0.547501	+	0.547501i
$67$			4.21389i			0.514808i	0.966304	+	0.257404i	$0.0828672\pi$
$67$			4.21389i			0.514808i	−0.966304	+	0.257404i	$0.917133\pi$
$68$	5.00116	−	3.20471i	0.606479	−	0.388629i
$69$	1.51404			0.182269
$70$		0			0
$71$	−1.48927	+	3.59542i	−0.176744	+	0.426698i	−0.987280	−	0.158991i	$-0.949176\pi$
$71$	−1.48927	+	3.59542i	−0.176744	+	0.426698i	0.810536	+	0.585689i	$0.199176\pi$
$72$	16.6127			1.95782
$73$	2.47620	−	5.97807i	0.289817	−	0.699680i	−0.710173	−	0.704027i	$-0.751383\pi$
$73$	2.47620	−	5.97807i	0.289817	−	0.699680i	0.999991	+	0.00434632i	$0.00138348\pi$
$74$	−3.06247	−	7.39347i	−0.356005	−	0.859473i
$75$		0			0
$76$	−1.29261	−	1.29261i	−0.148273	−	0.148273i
$77$	6.25188	−	6.25188i	0.712468	−	0.712468i
$78$	−3.80064	−	9.17555i	−0.430338	−	1.03893i
$79$	2.76355	+	6.67180i	0.310923	+	0.750636i	0.999671	+	0.0256347i	$0.00816068\pi$
$79$	2.76355	+	6.67180i	0.310923	+	0.750636i	−0.688748	+	0.725001i	$0.741839\pi$
$80$		0			0
$81$			13.3100i			1.47889i
$82$	−1.49977	−	0.621223i	−0.165621	−	0.0686026i
$83$	0.160866	+	0.160866i	0.0176574	+	0.0176574i	0.715880	−	0.698223i	$-0.246026\pi$
$83$	0.160866	+	0.160866i	0.0176574	+	0.0176574i	−0.698223	+	0.715880i	$0.746026\pi$
$84$	−14.3204			−1.56248
$85$		0			0
$86$	−1.61686			−0.174350
$87$	0.966206	+	0.966206i	0.103588	+	0.103588i
$88$	6.50243	+	2.69339i	0.693161	+	0.287117i
$89$		−	13.3408i		−	1.41413i	−0.707150	−	0.707064i	$-0.750019\pi$
$89$		−	13.3408i		−	1.41413i	0.707150	−	0.707064i	$-0.249981\pi$
$90$		0			0
$91$	5.34208	+	12.8969i	0.560002	+	1.35196i
$92$	−0.271443	−	0.655322i	−0.0282999	−	0.0683220i
$93$	−12.0207	+	12.0207i	−1.24649	+	1.24649i
$94$	−4.44025	−	4.44025i	−0.457977	−	0.457977i
$95$		0			0
$96$	−6.89827	−	16.6539i	−0.704052	−	1.69973i
$97$	−5.66657	+	13.6803i	−0.575353	+	1.38902i	0.321591	+	0.946879i	$0.395782\pi$
$97$	−5.66657	+	13.6803i	−0.575353	+	1.38902i	−0.896943	+	0.442145i	$0.854218\pi$
$98$	−2.58018			−0.260637
$99$	−6.75711	+	16.3131i	−0.679115	+	1.63953i
$100$		0			0
$101$	−0.284213			−0.0282803			−0.0141401	−	0.999900i	$-0.504501\pi$
$101$	−0.284213			−0.0282803			−0.0141401	+	0.999900i	$0.504501\pi$
$102$	−5.41841	+	7.78201i	−0.536503	+	0.770534i
$103$		−	14.0842i		−	1.38775i	−0.720093	−	0.693877i	$-0.755901\pi$
$103$		−	14.0842i		−	1.38775i	0.720093	−	0.693877i	$-0.244099\pi$
$104$	−7.85760	+	7.85760i	−0.770501	+	0.770501i
$105$		0			0
$106$			1.35894i			0.131992i
$107$	7.15995	−	17.2857i	0.692179	−	1.67107i	−0.0481649	−	0.998839i	$-0.515337\pi$
$107$	7.15995	−	17.2857i	0.692179	−	1.67107i	0.740344	−	0.672228i	$-0.234663\pi$
$108$	14.1437	−	5.85853i	1.36098	−	0.563738i
$109$	3.26202	−	1.35117i	0.312444	−	0.129419i	−0.220951	−	0.975285i	$-0.570916\pi$
$109$	3.26202	−	1.35117i	0.312444	−	0.129419i	0.533395	+	0.845866i	$0.320916\pi$
$110$		0			0
$111$	−23.2657	−	23.2657i	−2.20828	−	2.20828i
$112$	1.18344	+	2.85707i	0.111824	+	0.269968i
$113$	−2.62525	+	1.08741i	−0.246963	+	0.102295i	−0.502731	−	0.864443i	$-0.667671\pi$
$113$	−2.62525	+	1.08741i	−0.246963	+	0.102295i	0.255769	+	0.966738i	$0.417671\pi$
$114$	2.69619	+	1.11680i	0.252521	+	0.104598i
$115$		0			0
$116$	0.244977	−	0.591427i	0.0227456	−	0.0549126i
$117$	−19.7129	−	19.7129i	−1.82246	−	1.82246i
$118$			2.25860i			0.207921i
$119$	7.61598	−	10.9382i	0.698155	−	1.00270i
$120$		0			0
$121$	2.48852	−	2.48852i	0.226229	−	0.226229i
$122$	8.44606	+	3.49847i	0.764670	+	0.316737i
$123$	−6.67430			−0.601801
$124$	7.35805	+	3.04780i	0.660772	+	0.273701i
$125$		0			0
$126$	14.4202	−	5.97306i	1.28466	−	0.532122i
$127$	3.86444	−	3.86444i	0.342914	−	0.342914i	−0.514548	−	0.857462i	$-0.672040\pi$
$127$	3.86444	−	3.86444i	0.342914	−	0.342914i	0.857462	+	0.514548i	$0.172040\pi$
$128$	−6.98340	+	6.98340i	−0.617251	+	0.617251i
$129$	−6.14164	+	2.54395i	−0.540742	+	0.223983i
$130$		0			0
$131$	9.21986	+	3.81899i	0.805543	+	0.333667i	0.747174	−	0.664628i	$-0.231410\pi$
$131$	9.21986	+	3.81899i	0.805543	+	0.333667i	0.0583689	+	0.998295i	$0.481410\pi$
$132$	12.1163			1.05459
$133$	−3.78969	−	1.56974i	−0.328608	−	0.136114i
$134$	−2.22854	+	2.22854i	−0.192516	+	0.192516i
$135$		0			0
$136$	10.3645	+	2.26901i	0.888748	+	0.194566i
$137$			3.07772i			0.262947i	0.991320	+	0.131474i	$0.0419709\pi$
$137$			3.07772i			0.262947i	−0.991320	+	0.131474i	$0.958029\pi$
$138$	0.800709	+	0.800709i	0.0681609	+	0.0681609i
$139$	2.56777	−	6.19915i	0.217796	−	0.525805i	−0.776786	−	0.629765i	$-0.783151\pi$
$139$	2.56777	−	6.19915i	0.217796	−	0.525805i	0.994582	+	0.103960i	$0.0331513\pi$
$140$		0			0
$141$	−23.8526	−	9.88006i	−2.00875	−	0.832051i
$142$	−2.68907	+	1.11385i	−0.225661	+	0.0934720i
$143$	−4.51988	−	10.9119i	−0.377971	−	0.912503i
$144$	−4.36704	−	4.36704i	−0.363920	−	0.363920i
$145$		0			0
$146$	4.47109	−	1.85198i	0.370030	−	0.153271i
$147$	−9.80082	+	4.05963i	−0.808358	+	0.334833i
$148$	−5.89890	+	14.2412i	−0.484887	+	1.17062i
$149$			22.9914i			1.88353i	0.336276	+	0.941764i	$0.390833\pi$
$149$			22.9914i			1.88353i	−0.336276	+	0.941764i	$0.609167\pi$
$150$		0			0
$151$	0.138411	−	0.138411i	0.0112638	−	0.0112638i	−0.701452	−	0.712716i	$-0.747465\pi$
$151$	0.138411	−	0.138411i	0.0112638	−	0.0112638i	0.712716	+	0.701452i	$0.247465\pi$
$152$		−	3.26530i		−	0.264850i
$153$	−5.69244	+	26.0022i	−0.460207	+	2.10215i
$154$	6.61268			0.532865
$155$		0			0
$156$	−7.32075	+	17.6738i	−0.586129	+	1.41504i
$157$	−11.8582			−0.946391			−0.473196	−	0.880957i	$-0.656900\pi$
$157$	−11.8582			−0.946391			−0.473196	+	0.880957i	$0.656900\pi$
$158$	−2.06690	+	4.98993i	−0.164434	+	0.396978i
$159$	2.13815	+	5.16196i	0.169567	+	0.409370i
$160$		0			0
$161$	−1.12546	−	1.12546i	−0.0886983	−	0.0886983i
$162$	−7.03907	+	7.03907i	−0.553041	+	0.553041i
$163$	−2.04533	−	4.93787i	−0.160203	−	0.386764i	0.823312	−	0.567588i	$-0.192123\pi$
$163$	−2.04533	−	4.93787i	−0.160203	−	0.386764i	−0.983515	+	0.180824i	$0.942123\pi$
$164$	1.19659	+	2.88883i	0.0934382	+	0.225580i
$165$		0			0
$166$			0.170150i			0.0132062i
$167$	10.7077	+	4.43529i	0.828589	+	0.343213i	0.756344	−	0.654174i	$-0.226984\pi$
$167$	10.7077	+	4.43529i	0.828589	+	0.343213i	0.0722453	+	0.997387i	$0.476984\pi$
$168$	−18.0875	−	18.0875i	−1.39548	−	1.39548i
$169$	5.64797			0.434459
$170$		0			0
$171$	8.19188			0.626449
$172$	2.20220	+	2.20220i	0.167916	+	0.167916i
$173$	10.1877	+	4.21988i	0.774556	+	0.320832i	0.734716	−	0.678375i	$-0.237315\pi$
$173$	10.1877	+	4.21988i	0.774556	+	0.320832i	0.0398396	+	0.999206i	$0.487315\pi$
$174$			1.02197i			0.0774750i
$175$		0			0
$176$	−1.00130	−	2.41734i	−0.0754755	−	0.182214i
$177$	3.55367	+	8.57932i	0.267110	+	0.644861i
$178$	7.05538	−	7.05538i	0.528823	−	0.528823i
$179$	−14.9009	−	14.9009i	−1.11375	−	1.11375i	−0.992639	−	0.121109i	$-0.961355\pi$
$179$	−14.9009	−	14.9009i	−1.11375	−	1.11375i	−0.121109	−	0.992639i	$-0.538645\pi$
$180$		0			0
$181$	8.67131	+	20.9344i	0.644533	+	1.55604i	0.820501	+	0.571645i	$0.193695\pi$
$181$	8.67131	+	20.9344i	0.644533	+	1.55604i	−0.175968	+	0.984396i	$0.556305\pi$
$182$	−3.99542	+	9.64579i	−0.296160	+	0.714993i
$183$	37.5869			2.77850
$184$	0.484861	−	1.17056i	0.0357444	−	0.0862947i
$185$		0			0
$186$	−12.7145			−0.932269
$187$	−6.44380	+	9.25469i	−0.471217	+	0.676770i
$188$			12.0954i			0.882150i
$189$	24.2906	−	24.2906i	1.76688	−	1.76688i
$190$		0			0
$191$			3.50162i			0.253368i	0.991943	+	0.126684i	$0.0404335\pi$
$191$			3.50162i			0.253368i	−0.991943	+	0.126684i	$0.959567\pi$
$192$	2.90782	−	7.02011i	0.209854	−	0.506633i
$193$	11.3584	−	4.70480i	0.817595	−	0.338659i	0.0656152	−	0.997845i	$-0.479099\pi$
$193$	11.3584	−	4.70480i	0.817595	−	0.338659i	0.751980	+	0.659186i	$0.229099\pi$
$194$	−10.2317	+	4.23811i	−0.734593	+	0.304278i
$195$		0			0
$196$	3.51426	+	3.51426i	0.251018	+	0.251018i
$197$	−6.49632	−	15.6835i	−0.462843	−	1.11740i	−0.967225	−	0.253922i	$-0.918279\pi$
$197$	−6.49632	−	15.6835i	−0.462843	−	1.11740i	0.504381	−	0.863481i	$-0.331721\pi$
$198$	−12.2008	+	5.05374i	−0.867074	+	0.359154i
$199$	−10.6966	−	4.43067i	−0.758260	−	0.314082i	−0.0301533	−	0.999545i	$-0.509600\pi$
$199$	−10.6966	−	4.43067i	−0.758260	−	0.314082i	−0.728107	+	0.685464i	$0.759600\pi$
$200$		0			0
$201$	−4.95875	+	11.9715i	−0.349763	+	0.844403i
$202$	−0.150308	−	0.150308i	−0.0105756	−	0.0105756i
$203$		−	1.43645i		−	0.100819i
$204$	17.9793	−	3.21928i	1.25880	−	0.225394i
$205$		0			0
$206$	7.44849	−	7.44849i	0.518961	−	0.518961i
$207$	2.93667	+	1.21641i	0.204112	+	0.0845461i
$208$	4.13111			0.286441
$209$	3.20642	+	1.32814i	0.221792	+	0.0918694i
$210$		0			0
$211$	6.15655	−	2.55013i	0.423834	−	0.175558i	−0.160563	−	0.987026i	$-0.551331\pi$
$211$	6.15655	−	2.55013i	0.423834	−	0.175558i	0.584397	+	0.811468i	$0.301331\pi$
$212$	1.85091	−	1.85091i	0.127121	−	0.127121i
$213$	−8.46191	+	8.46191i	−0.579800	+	0.579800i
$214$	12.9282	−	5.35503i	0.883753	−	0.366063i
$215$		0			0
$216$	25.2640	+	10.4647i	1.71900	+	0.712033i
$217$	17.8711			1.21317
$218$	2.43971	+	1.01056i	0.165238	+	0.0684438i
$219$	14.0695	−	14.0695i	0.950732	−	0.950732i
$220$		0			0
$221$	−9.60626	−	14.9912i	−0.646187	−	1.00842i
$222$		−	24.6083i		−	1.65160i
$223$	8.90442	+	8.90442i	0.596284	+	0.596284i	0.939322	−	0.343037i	$-0.111456\pi$
$223$	8.90442	+	8.90442i	0.596284	+	0.596284i	−0.343037	+	0.939322i	$0.611456\pi$
$224$	−7.25180	+	17.5074i	−0.484531	+	1.16976i
$225$		0			0
$226$	−1.96346	−	0.813292i	−0.130607	−	0.0540994i
$227$	7.43044	−	3.07779i	0.493176	−	0.204280i	−0.122213	−	0.992504i	$-0.538999\pi$
$227$	7.43044	−	3.07779i	0.493176	−	0.204280i	0.615389	+	0.788224i	$0.288999\pi$
$228$	−2.15116	−	5.19336i	−0.142464	−	0.343939i
$229$	15.2944	+	15.2944i	1.01068	+	1.01068i	0.999942	+	0.0107373i	$0.00341786\pi$
$229$	15.2944	+	15.2944i	1.01068	+	1.01068i	0.0107373	+	0.999942i	$0.496582\pi$
$230$		0			0
$231$	25.1183	−	10.4043i	1.65266	−	0.684555i
$232$	1.05643	−	0.437587i	0.0693579	−	0.0287290i
$233$	8.40011	−	20.2797i	0.550310	−	1.32857i	−0.366937	−	0.930246i	$-0.619594\pi$
$233$	8.40011	−	20.2797i	0.550310	−	1.32857i	0.917247	−	0.398320i	$-0.130406\pi$
$234$		−	20.8506i		−	1.36304i
$235$		0			0
$236$	3.07626	−	3.07626i	0.200248	−	0.200248i
$237$			22.2063i			1.44246i
$238$	9.81247	−	1.75697i	0.636048	−	0.113888i
$239$	−5.90132			−0.381725			−0.190862	−	0.981617i	$-0.561128\pi$
$239$	−5.90132			−0.381725			−0.190862	+	0.981617i	$0.561128\pi$
$240$		0			0
$241$	5.09407	−	12.2982i	0.328138	−	0.792195i	−0.670593	−	0.741826i	$-0.733960\pi$
$241$	5.09407	−	12.2982i	0.328138	−	0.792195i	0.998731	−	0.0503696i	$-0.0160399\pi$
$242$	2.63214			0.169200
$243$	−3.46273	+	8.35977i	−0.222134	+	0.536279i
$244$	−6.73872	−	16.2687i	−0.431402	−	1.04150i
$245$		0			0
$246$	−3.52974	−	3.52974i	−0.225048	−	0.225048i
$247$	−3.87467	+	3.87467i	−0.246539	+	0.246539i
$248$	5.44409	+	13.1432i	0.345700	+	0.834594i
$249$	0.267712	+	0.646315i	0.0169656	+	0.0409586i
$250$		0			0
$251$			3.59367i			0.226831i	0.993548	+	0.113415i	$0.0361790\pi$
$251$			3.59367i			0.226831i	−0.993548	+	0.113415i	$0.963821\pi$
$252$	−27.7761	−	11.5052i	−1.74973	−	0.724761i
$253$	0.952236	+	0.952236i	0.0598666	+	0.0598666i
$254$	4.08746			0.256470
$255$		0			0
$256$	−12.3285			−0.770531
$257$	17.3588	+	17.3588i	1.08281	+	1.08281i	0.996246	+	0.0865680i	$0.0275900\pi$
$257$	17.3588	+	17.3588i	1.08281	+	1.08281i	0.0865680	+	0.996246i	$0.472410\pi$
$258$	−4.59342	−	1.90266i	−0.285974	−	0.118454i
$259$			34.5888i			2.14924i
$260$		0			0
$261$	1.09781	+	2.65034i	0.0679524	+	0.164052i
$262$	2.85628	+	6.89567i	0.176462	+	0.426016i
$263$	−10.3521	+	10.3521i	−0.638340	+	0.638340i	−0.950146	−	0.311806i	$-0.899066\pi$
$263$	−10.3521	+	10.3521i	−0.638340	+	0.638340i	0.311806	+	0.950146i	$0.399066\pi$
$264$	15.3036	+	15.3036i	0.941873	+	0.941873i
$265$		0			0
$266$	−1.17403	−	2.83436i	−0.0719845	−	0.173786i
$267$	15.6990	−	37.9008i	0.960764	−	2.31949i
$268$	6.07063			0.370823
$269$	7.17904	−	17.3317i	0.437714	−	1.05673i	−0.539023	−	0.842291i	$-0.681206\pi$
$269$	7.17904	−	17.3317i	0.437714	−	1.05673i	0.976736	−	0.214443i	$-0.0687936\pi$
$270$		0			0
$271$	5.76388			0.350131			0.175065	−	0.984557i	$-0.443986\pi$
$271$	5.76388			0.350131			0.175065	+	0.984557i	$0.443986\pi$
$272$	−2.12809	−	3.32102i	−0.129034	−	0.201366i
$273$			42.9259i			2.59800i
$274$	−1.62767	+	1.62767i	−0.0983311	+	0.0983311i
$275$		0			0
$276$		−	2.18117i		−	0.131291i
$277$	0.0471663	−	0.113870i	0.00283395	−	0.00684176i	−0.922456	−	0.386102i	$-0.873821\pi$
$277$	0.0471663	−	0.113870i	0.00283395	−	0.00684176i	0.925290	+	0.379260i	$0.123821\pi$
$278$	4.63643	−	1.92047i	0.278075	−	0.115182i
$279$	−32.9733	+	13.6580i	−1.97406	+	0.817682i
$280$		0			0
$281$	−1.28950	−	1.28950i	−0.0769253	−	0.0769253i	0.667597	−	0.744523i	$-0.267323\pi$
$281$	−1.28950	−	1.28950i	−0.0769253	−	0.0769253i	−0.744523	+	0.667597i	$0.767323\pi$
$282$	−7.38944	−	17.8397i	−0.440035	−	1.06234i
$283$	−26.4486	+	10.9554i	−1.57221	+	0.651229i	−0.987155	−	0.159767i	$-0.948926\pi$
$283$	−26.4486	+	10.9554i	−1.57221	+	0.651229i	−0.585052	+	0.810996i	$0.698926\pi$
$284$	5.17965	+	2.14548i	0.307355	+	0.127311i
$285$		0			0
$286$	3.38048	−	8.16120i	0.199892	−	0.482582i
$287$	4.96130	+	4.96130i	0.292856	+	0.292856i
$288$		−	37.8444i		−	2.23000i
$289$	−7.10292	+	15.4450i	−0.417819	+	0.908530i
$290$		0			0
$291$	−32.1969	+	32.1969i	−1.88742	+	1.88742i
$292$	−8.61216	−	3.56727i	−0.503988	−	0.208759i
$293$	−1.41607			−0.0827278			−0.0413639	−	0.999144i	$-0.513170\pi$
$293$	−1.41607			−0.0827278			−0.0413639	+	0.999144i	$0.513170\pi$
$294$	−7.33017	−	3.03626i	−0.427504	−	0.177078i
$295$		0			0
$296$	−25.4381	+	10.5368i	−1.47856	+	0.612440i
$297$	−20.5520	+	20.5520i	−1.19255	+	1.19255i
$298$	−12.1591	+	12.1591i	−0.704358	+	0.704358i
$299$	−1.96435	+	0.813662i	−0.113602	+	0.0470553i
$300$		0			0
$301$	6.45639	+	2.67433i	0.372140	+	0.154146i
$302$	0.146399			0.00842433
$303$	−0.807438	−	0.334452i	−0.0463861	−	0.0192138i
$304$	−0.858361	+	0.858361i	−0.0492304	+	0.0492304i
$305$		0			0
$306$	−16.7619	+	10.7409i	−0.958212	+	0.614017i
$307$			21.7364i			1.24056i	0.784379	+	0.620281i	$0.212982\pi$
$307$			21.7364i			1.24056i	−0.784379	+	0.620281i	$0.787018\pi$
$308$	−9.00661	−	9.00661i	−0.513199	−	0.513199i
$309$	16.5737	−	40.0125i	0.942846	−	2.27623i
$310$		0			0
$311$	7.99250	+	3.31060i	0.453213	+	0.187727i	0.597600	−	0.801794i	$-0.296121\pi$
$311$	7.99250	+	3.31060i	0.453213	+	0.187727i	−0.144387	+	0.989521i	$0.546121\pi$
$312$	−31.5696	+	13.0766i	−1.78728	+	0.740315i
$313$	3.93476	+	9.49936i	0.222406	+	0.536936i	0.995216	−	0.0977022i	$-0.0311493\pi$
$313$	3.93476	+	9.49936i	0.222406	+	0.536936i	−0.772810	+	0.634638i	$0.781149\pi$
$314$	−6.27130	−	6.27130i	−0.353910	−	0.353910i
$315$		0			0
$316$	9.61155	−	3.98123i	0.540692	−	0.223962i
$317$	−1.04183	+	0.431538i	−0.0585147	+	0.0242376i	−0.411749	−	0.911297i	$-0.635082\pi$
$317$	−1.04183	+	0.431538i	−0.0585147	+	0.0242376i	0.353234	+	0.935535i	$0.385082\pi$
$318$	−1.59916	+	3.86070i	−0.0896762	+	0.216497i
$319$			1.21536i			0.0680473i
$320$		0			0
$321$	40.6822	−	40.6822i	2.27066	−	2.27066i
$322$		−	1.19041i		−	0.0663387i
$323$	5.11084	+	1.11887i	0.284375	+	0.0622559i
$324$	19.1747			1.06526
$325$		0			0
$326$	1.52974	−	3.69311i	0.0847242	−	0.204542i
$327$	10.8573			0.600407
$328$	−2.13740	+	5.16013i	−0.118018	+	0.284921i
$329$	10.3864	+	25.0750i	0.572621	+	1.38243i
$330$		0			0
$331$	−24.2254	−	24.2254i	−1.33155	−	1.33155i	−0.903984	−	0.427567i	$-0.859371\pi$
$331$	−24.2254	−	24.2254i	−1.33155	−	1.33155i	−0.427567	−	0.903984i	$-0.640629\pi$
$332$	0.231748	−	0.231748i	0.0127188	−	0.0127188i
$333$	−26.4345	−	63.8185i	−1.44860	−	3.49723i
$334$	3.31722	+	8.00847i	0.181510	+	0.438204i
$335$		0			0
$336$			9.50945i			0.518783i
$337$	12.6999	+	5.26046i	0.691807	+	0.286556i	0.700753	−	0.713404i	$-0.252848\pi$
$337$	12.6999	+	5.26046i	0.691807	+	0.286556i	−0.00894611	+	0.999960i	$0.502848\pi$
$338$	2.98696	+	2.98696i	0.162469	+	0.162469i
$339$	−8.73784			−0.474574
$340$		0			0
$341$	−15.1206			−0.818824
$342$	4.33232	+	4.33232i	0.234265	+	0.234265i
$343$	−10.6028	−	4.39181i	−0.572495	−	0.237135i
$344$			5.56300i			0.299937i
$345$		0			0
$346$	3.15611	+	7.61952i	0.169673	+	0.409628i
$347$	−7.22453	−	17.4415i	−0.387833	−	0.936311i	−0.990398	−	0.138242i	$-0.955855\pi$
$347$	−7.22453	−	17.4415i	−0.387833	−	0.936311i	0.602566	−	0.798069i	$-0.294145\pi$
$348$	1.39194	−	1.39194i	0.0746158	−	0.0746158i
$349$	−4.98501	−	4.98501i	−0.266842	−	0.266842i	0.560985	−	0.827826i	$-0.310423\pi$
$349$	−4.98501	−	4.98501i	−0.266842	−	0.266842i	−0.827826	+	0.560985i	$0.810423\pi$
$350$		0			0
$351$	−17.5612	−	42.3965i	−0.937347	−	2.26296i
$352$	6.13567	−	14.8128i	0.327032	−	0.789526i
$353$	−8.60779			−0.458146			−0.229073	−	0.973409i	$-0.573569\pi$
$353$	−8.60779			−0.458146			−0.229073	+	0.973409i	$0.573569\pi$
$354$	−2.65784	+	6.41659i	−0.141263	+	0.341038i
$355$		0			0
$356$	−19.2191			−1.01861
$357$	34.5083	−	22.1127i	1.82637	−	1.17033i
$358$		−	15.7609i		−	0.832988i
$359$	6.49195	−	6.49195i	0.342632	−	0.342632i	−0.514724	−	0.857356i	$-0.672106\pi$
$359$	6.49195	−	6.49195i	0.342632	−	0.342632i	0.857356	+	0.514724i	$0.172106\pi$
$360$		0			0
$361$			17.3898i			0.915255i
$362$	−6.48540	+	15.6571i	−0.340865	+	0.822921i
$363$	9.99818	−	4.14138i	0.524769	−	0.217366i
$364$	18.5796	−	7.69592i	0.973836	−	0.403376i
$365$		0			0
$366$	19.8780	+	19.8780i	1.03904	+	1.03904i
$367$	2.60840	+	6.29722i	0.136157	+	0.328712i	0.977221	−	0.212223i	$-0.0680703\pi$
$367$	2.60840	+	6.29722i	0.136157	+	0.328712i	−0.841064	+	0.540935i	$0.818070\pi$
$368$	−0.435166	+	0.180252i	−0.0226846	+	0.00939628i
$369$	−12.9456	−	5.36224i	−0.673921	−	0.279147i
$370$		0			0
$371$	2.24773	−	5.42650i	0.116696	−	0.281730i
$372$	17.3174	+	17.3174i	0.897863	+	0.897863i
$373$			10.4647i			0.541841i	0.962602	+	0.270920i	$0.0873280\pi$
$373$			10.4647i			0.541841i	−0.962602	+	0.270920i	$0.912672\pi$
$374$	−8.30223	+	1.48656i	−0.429298	+	0.0768680i
$375$		0			0
$376$	−15.2772	+	15.2772i	−0.787863	+	0.787863i
$377$	−1.77283	−	0.734329i	−0.0913053	−	0.0378199i
$378$	25.6924			1.32148
$379$	−23.4129	−	9.69794i	−1.20264	−	0.498150i	−0.310789	−	0.950479i	$-0.600593\pi$
$379$	−23.4129	−	9.69794i	−1.20264	−	0.498150i	−0.891851	+	0.452330i	$0.850593\pi$
$380$		0			0
$381$	15.5263	−	6.43119i	0.795434	−	0.329480i
$382$	−1.85185	+	1.85185i	−0.0947489	+	0.0947489i
$383$	5.43799	−	5.43799i	0.277868	−	0.277868i	−0.554389	−	0.832258i	$-0.687048\pi$
$383$	5.43799	−	5.43799i	0.277868	−	0.277868i	0.832258	+	0.554389i	$0.187048\pi$
$384$	−28.0574	+	11.6217i	−1.43180	+	0.593069i
$385$		0			0
$386$	8.49511	+	3.51879i	0.432389	+	0.179102i
$387$	−13.9563			−0.709439
$388$	19.7082	+	8.16339i	1.00053	+	0.414433i
$389$	−11.1991	+	11.1991i	−0.567816	+	0.567816i	−0.931516	−	0.363700i	$-0.881513\pi$
$389$	−11.1991	+	11.1991i	−0.567816	+	0.567816i	0.363700	+	0.931516i	$0.381513\pi$
$390$		0			0
$391$	1.66602	+	1.16000i	0.0842541	+	0.0586639i
$392$			8.87742i			0.448377i
$393$	21.6992	+	21.6992i	1.09458	+	1.09458i
$394$	4.85869	−	11.7299i	0.244777	−	0.590944i
$395$		0			0
$396$	23.5011	+	9.73446i	1.18097	+	0.489175i
$397$	26.9440	−	11.1606i	1.35228	−	0.560133i	0.415355	−	0.909659i	$-0.363657\pi$
$397$	26.9440	−	11.1606i	1.35228	−	0.560133i	0.936927	+	0.349526i	$0.113657\pi$
$398$	−3.31376	−	8.00012i	−0.166104	−	0.401010i
$399$	−8.91913	−	8.91913i	−0.446515	−	0.446515i
$400$		0			0
$401$	−15.1386	+	6.27060i	−0.755984	+	0.313139i	−0.727181	−	0.686446i	$-0.759170\pi$
$401$	−15.1386	+	6.27060i	−0.755984	+	0.313139i	−0.0288034	+	0.999585i	$0.509170\pi$
$402$	−8.95364	+	3.70872i	−0.446567	+	0.184974i
$403$	9.13592	−	22.0561i	0.455092	−	1.09869i
$404$			0.409445i			0.0203706i
$405$		0			0
$406$	0.759673	−	0.759673i	0.0377019	−	0.0377019i
$407$		−	29.2652i		−	1.45062i
$408$	26.7750	+	18.6427i	1.32556	+	0.922952i
$409$	−33.9971			−1.68105			−0.840525	−	0.541772i	$-0.817753\pi$
$409$	−33.9971			−1.68105			−0.840525	+	0.541772i	$0.817753\pi$
$410$		0			0
$411$	−3.62175	+	8.74367i	−0.178648	+	0.431294i
$412$	−20.2900			−0.999616
$413$	3.73579	−	9.01899i	0.183826	−	0.443796i
$414$	0.909768	+	2.19637i	0.0447127	+	0.107946i
$415$		0			0
$416$	17.9000	+	17.9000i	0.877618	+	0.877618i
$417$	14.5899	−	14.5899i	0.714468	−	0.714468i
$418$	0.993336	+	2.39812i	0.0485856	+	0.117296i
$419$	−0.341711	−	0.824964i	−0.0166937	−	0.0403021i	0.915313	−	0.402743i	$-0.131943\pi$
$419$	−0.341711	−	0.824964i	−0.0166937	−	0.0403021i	−0.932007	+	0.362441i	$0.881943\pi$
$420$		0			0
$421$			33.6725i			1.64110i	0.571575	+	0.820550i	$0.306332\pi$
$421$			33.6725i			1.64110i	−0.571575	+	0.820550i	$0.693668\pi$
$422$	4.60457	+	1.90728i	0.224147	+	0.0928448i
$423$	−38.3271	−	38.3271i	−1.86353	−	1.86353i
$424$	4.67562			0.227068
$425$		0			0
$426$	−8.95025			−0.433641
$427$	−27.9400	−	27.9400i	−1.35211	−	1.35211i
$428$	−24.9021	−	10.3148i	−1.20369	−	0.498585i
$429$		−	36.3192i		−	1.75351i
$430$		0			0
$431$	−6.23658	−	15.0564i	−0.300405	−	0.725243i	−0.999943	−	0.0106472i	$-0.996611\pi$
$431$	−6.23658	−	15.0564i	−0.300405	−	0.725243i	0.699538	−	0.714595i	$-0.253389\pi$
$432$	−3.89036	−	9.39215i	−0.187175	−	0.451880i
$433$	24.7450	−	24.7450i	1.18917	−	1.18917i	0.211871	−	0.977298i	$-0.432044\pi$
$433$	24.7450	−	24.7450i	1.18917	−	1.18917i	0.977298	−	0.211871i	$-0.0679556\pi$
$434$	9.45122	+	9.45122i	0.453673	+	0.453673i
$435$		0			0
$436$	−1.94653	−	4.69934i	−0.0932219	−	0.225057i
$437$	0.239090	−	0.577215i	0.0114372	−	0.0276119i
$438$	14.8815			0.711066
$439$	−8.52530	+	20.5819i	−0.406891	+	0.982321i	0.579060	+	0.815285i	$0.303420\pi$
$439$	−8.52530	+	20.5819i	−0.406891	+	0.982321i	−0.985951	+	0.167036i	$0.946580\pi$
$440$		0			0
$441$	−22.2714			−1.06054
$442$	2.84784	−	13.0085i	0.135458	−	0.618750i
$443$		−	8.79907i		−	0.418056i	−0.977910	−	0.209028i	$-0.932970\pi$
$443$		−	8.79907i		−	0.418056i	0.977910	−	0.209028i	$-0.0670300\pi$
$444$	−33.5171	+	33.5171i	−1.59065	+	1.59065i
$445$		0			0
$446$			9.41830i			0.445970i
$447$	−27.0554	+	65.3175i	−1.27968	+	3.08941i
$448$	−7.37988	+	3.05685i	−0.348666	+	0.144422i
$449$	8.19189	−	3.39319i	0.386599	−	0.160135i	−0.180914	−	0.983499i	$-0.557906\pi$
$449$	8.19189	−	3.39319i	0.386599	−	0.160135i	0.567513	+	0.823364i	$0.307906\pi$
$450$		0			0
$451$	−4.19771	−	4.19771i	−0.197662	−	0.197662i
$452$	1.56655	+	3.78200i	0.0736845	+	0.177890i
$453$	0.556098	−	0.230343i	0.0261278	−	0.0108225i
$454$	5.55733	+	2.30192i	0.260819	+	0.108035i
$455$		0			0
$456$	3.84248	−	9.27656i	0.179941	−	0.434415i
$457$	13.0643	+	13.0643i	0.611120	+	0.611120i	0.943238	−	0.332118i	$-0.107763\pi$
$457$	13.0643	+	13.0643i	0.611120	+	0.611120i	−0.332118	+	0.943238i	$0.607763\pi$
$458$			16.1770i			0.755902i
$459$	−25.0363	+	35.9575i	−1.16859	+	1.67835i
$460$		0			0
$461$	17.3736	−	17.3736i	0.809169	−	0.809169i	−0.175339	−	0.984508i	$-0.556102\pi$
$461$	17.3736	−	17.3736i	0.809169	−	0.809169i	0.984508	+	0.175339i	$0.0561022\pi$
$462$	18.7863	+	7.78156i	0.874020	+	0.362031i
$463$	−9.90931			−0.460525			−0.230262	−	0.973129i	$-0.573958\pi$
$463$	−9.90931			−0.460525			−0.230262	+	0.973129i	$0.573958\pi$
$464$	−0.392737	−	0.162677i	−0.0182324	−	0.00755209i
$465$		0			0
$466$	15.1675	−	6.28257i	0.702619	−	0.291034i
$467$	−20.7918	+	20.7918i	−0.962131	+	0.962131i	−0.999309	−	0.0371777i	$-0.988163\pi$
$467$	−20.7918	+	20.7918i	−0.962131	+	0.962131i	0.0371777	+	0.999309i	$0.488163\pi$
$468$	−28.3989	+	28.3989i	−1.31274	+	1.31274i
$469$	12.5850	−	5.21287i	0.581121	−	0.240708i
$470$		0			0
$471$	−33.6888	−	13.9543i	−1.55230	−	0.642982i
$472$	7.77100			0.357689
$473$	−5.46269	−	2.26272i	−0.251175	−	0.104040i
$474$	−11.7439	+	11.7439i	−0.539417	+	0.539417i
$475$		0			0
$476$	−15.7578	−	10.9718i	−0.722259	−	0.502890i
$477$			11.7301i			0.537083i
$478$	−3.12095	−	3.12095i	−0.142749	−	0.142749i
$479$	10.9449	−	26.4232i	0.500083	−	1.20731i	−0.449354	−	0.893354i	$-0.648346\pi$
$479$	10.9449	−	26.4232i	0.500083	−	1.20731i	0.949438	−	0.313955i	$-0.101654\pi$
$480$		0			0
$481$	42.6886	+	17.6822i	1.94643	+	0.806239i
$482$	9.19799	−	3.80993i	0.418957	−	0.173538i
$483$	−1.87298	−	4.52176i	−0.0852234	−	0.205747i
$484$	−3.58503	−	3.58503i	−0.162956	−	0.162956i
$485$		0			0
$486$	−6.25239	+	2.58982i	−0.283614	+	0.117477i
$487$	−0.570849	+	0.236454i	−0.0258677	+	0.0107147i	−0.395580	−	0.918432i	$-0.629456\pi$
$487$	−0.570849	+	0.236454i	−0.0258677	+	0.0107147i	0.369712	+	0.929146i	$0.379456\pi$
$488$	12.0369	−	29.0597i	0.544886	−	1.31547i
$489$		−	16.4352i		−	0.743224i
$490$		0			0
$491$	18.0077	−	18.0077i	0.812675	−	0.812675i	−0.172359	−	0.985034i	$-0.555139\pi$
$491$	18.0077	−	18.0077i	0.812675	−	0.812675i	0.985034	+	0.172359i	$0.0551390\pi$
$492$			9.61515i			0.433485i
$493$	0.322919	+	1.80346i	0.0145435	+	0.0812239i
$494$	−4.09827			−0.184390
$495$		0			0
$496$	2.02389	−	4.88611i	0.0908755	−	0.219393i
$497$	12.5802			0.564301
$498$	−0.200226	+	0.483388i	−0.00897234	+	0.0216611i
$499$	−13.9527	−	33.6849i	−0.624611	−	1.50794i	−0.846234	−	0.532811i	$-0.821136\pi$
$499$	−13.9527	−	33.6849i	−0.624611	−	1.50794i	0.221624	−	0.975132i	$-0.428864\pi$
$500$		0			0
$501$	25.2009	+	25.2009i	1.12589	+	1.12589i
$502$	−1.90053	+	1.90053i	−0.0848249	+	0.0848249i
$503$	11.5525	+	27.8902i	0.515100	+	1.24356i	0.940881	+	0.338736i	$0.109999\pi$
$503$	11.5525	+	27.8902i	0.515100	+	1.24356i	−0.425781	+	0.904826i	$0.640001\pi$
$504$	−20.5510	−	49.6146i	−0.915416	−	2.21001i
$505$		0			0
$506$			1.00719i			0.0447751i
$507$	16.0456	+	6.64632i	0.712612	+	0.295174i
$508$	−5.56721	−	5.56721i	−0.247005	−	0.247005i
$509$	40.1857			1.78120			0.890600	−	0.454787i	$-0.150285\pi$
$509$	40.1857			1.78120			0.890600	+	0.454787i	$0.150285\pi$
$510$		0			0
$511$	−20.9171			−0.925316
$512$	7.44682	+	7.44682i	0.329106	+	0.329106i
$513$	12.4580	+	5.16026i	0.550033	+	0.227831i
$514$			18.3606i			0.809852i
$515$		0			0
$516$	3.66488	+	8.84780i	0.161337	+	0.389503i
$517$	−8.78783	−	21.2157i	−0.386488	−	0.933065i
$518$	−18.2925	+	18.2925i	−0.803725	+	0.803725i
$519$	23.9770	+	23.9770i	1.05247	+	1.05247i
$520$		0			0
$521$	−13.5302	−	32.6647i	−0.592767	−	1.43107i	−0.880820	−	0.473451i	$-0.843008\pi$
$521$	−13.5302	−	32.6647i	−0.592767	−	1.43107i	0.288053	−	0.957614i	$-0.406992\pi$
$522$	−0.821064	+	1.98222i	−0.0359370	+	0.0867596i
$523$	−24.5035			−1.07146			−0.535732	−	0.844388i	$-0.679964\pi$
$523$	−24.5035			−1.07146			−0.535732	+	0.844388i	$0.679964\pi$
$524$	5.50173	−	13.2824i	0.240344	−	0.580243i
$525$		0			0
$526$	−10.9496			−0.477424
$527$	−22.4372	+	4.01749i	−0.977379	+	0.175005i
$528$		−	8.04585i		−	0.350150i
$529$	−16.0920	+	16.0920i	−0.699654	+	0.699654i
$530$		0			0
$531$			19.4957i			0.846041i
$532$	−2.26140	+	5.45951i	−0.0980443	+	0.236700i
$533$	8.65939	−	3.58684i	0.375080	−	0.155363i
$534$	28.3465	−	11.7415i	1.22667	−	0.508105i
$535$		0			0
$536$	7.66756	+	7.66756i	0.331188	+	0.331188i
$537$	−24.7981	−	59.8678i	−1.07011	−	2.58349i
$538$	12.9626	−	5.36930i	0.558859	−	0.231487i
$539$	−8.71734	−	3.61084i	−0.375483	−	0.155530i
$540$		0			0
$541$	9.77786	−	23.6058i	0.420383	−	1.01489i	−0.561852	−	0.827238i	$-0.689911\pi$
$541$	9.77786	−	23.6058i	0.420383	−	1.01489i	0.982235	−	0.187657i	$-0.0600892\pi$
$542$	3.04826	+	3.04826i	0.130934	+	0.130934i
$543$			69.6778i			2.99016i
$544$	5.16891	−	23.6108i	0.221615	−	1.01230i
$545$		0			0
$546$	−22.7016	+	22.7016i	−0.971539	+	0.971539i
$547$	10.8664	+	4.50103i	0.464616	+	0.192450i	0.602696	−	0.797971i	$-0.294093\pi$
$547$	10.8664	+	4.50103i	0.464616	+	0.192450i	−0.138080	+	0.990421i	$0.544093\pi$
$548$	4.43384			0.189404
$549$	72.9042	+	30.1979i	3.11148	+	1.28882i
$550$		0			0
$551$	0.520936	−	0.215779i	0.0221926	−	0.00919248i
$552$	2.75494	−	2.75494i	0.117258	−	0.117258i
$553$	16.5070	−	16.5070i	0.701947	−	0.701947i
$554$	0.0851647	−	0.0352764i	0.00361830	−	0.00149875i
$555$		0			0
$556$	−8.93065	−	3.69919i	−0.378744	−	0.156881i
$557$	−35.6812			−1.51186			−0.755931	−	0.654651i	$-0.772816\pi$
$557$	−35.6812			−1.51186			−0.755931	+	0.654651i	$0.772816\pi$
$558$	−24.6612	−	10.2150i	−1.04399	−	0.432436i
$559$	6.60117	−	6.60117i	0.279200	−	0.279200i
$560$		0			0
$561$	−29.1971	+	18.7094i	−1.23270	+	0.789910i
$562$		−	1.36392i		−	0.0575335i
$563$	−21.3003	−	21.3003i	−0.897702	−	0.897702i	0.0975306	−	0.995233i	$-0.468906\pi$
$563$	−21.3003	−	21.3003i	−0.897702	−	0.897702i	−0.995233	+	0.0975306i	$0.968906\pi$
$564$	−14.2335	+	34.3626i	−0.599337	+	1.44693i
$565$		0			0
$566$	−19.7813	−	8.19368i	−0.831470	−	0.344406i
$567$	39.7510	−	16.4654i	1.66939	−	0.691482i
$568$	3.83233	+	9.25206i	0.160801	+	0.388208i
$569$	17.2524	+	17.2524i	0.723257	+	0.723257i	0.969267	−	0.246010i	$-0.0791197\pi$
$569$	17.2524	+	17.2524i	0.723257	+	0.723257i	−0.246010	+	0.969267i	$0.579120\pi$
$570$		0			0
$571$	−30.7483	+	12.7364i	−1.28678	+	0.533001i	−0.918024	−	0.396526i	$-0.870216\pi$
$571$	−30.7483	+	12.7364i	−1.28678	+	0.533001i	−0.368755	+	0.929527i	$0.620216\pi$
$572$	−15.7200	+	6.51144i	−0.657287	+	0.272257i
$573$	−4.12058	+	9.94795i	−0.172140	+	0.415582i
$574$			5.24762i			0.219032i
$575$		0			0
$576$	11.2801	−	11.2801i	0.470006	−	0.470006i
$577$			18.0611i			0.751895i	0.926641	+	0.375947i	$0.122683\pi$
$577$			18.0611i			0.751895i	−0.926641	+	0.375947i	$0.877317\pi$
$578$	−11.9246	+	4.41176i	−0.495998	+	0.183505i
$579$	37.8051			1.57113
$580$		0			0
$581$	0.281432	−	0.679438i	0.0116758	−	0.0281878i
$582$	−34.0550			−1.41163
$583$	−1.90178	+	4.59131i	−0.0787637	+	0.190152i
$584$	−6.37198	−	15.3833i	−0.263675	−	0.636567i
$585$		0			0
$586$	−0.748897	−	0.748897i	−0.0309366	−	0.0309366i
$587$	−29.5785	+	29.5785i	−1.22084	+	1.22084i	−0.253500	+	0.967335i	$0.581582\pi$
$587$	−29.5785	+	29.5785i	−1.22084	+	1.22084i	−0.967335	+	0.253500i	$0.918418\pi$
$588$	5.84840	+	14.1193i	0.241184	+	0.582270i
$589$	2.68454	+	6.48105i	0.110614	+	0.267047i
$590$		0			0
$591$		−	52.2008i		−	2.14725i
$592$	9.45688	+	3.91717i	0.388675	+	0.160995i
$593$	14.6130	+	14.6130i	0.600085	+	0.600085i	0.940335	−	0.340250i	$-0.110512\pi$
$593$	14.6130	+	14.6130i	0.600085	+	0.600085i	−0.340250	+	0.940335i	$0.610512\pi$
$594$	−21.7381			−0.891925
$595$		0			0
$596$	33.1219			1.35673
$597$	−25.1747	−	25.1747i	−1.03033	−	1.03033i
$598$	−1.46917	−	0.608550i	−0.0600788	−	0.0248854i
$599$			9.21817i			0.376644i	0.982107	+	0.188322i	$0.0603049\pi$
$599$			9.21817i			0.376644i	−0.982107	+	0.188322i	$0.939695\pi$
$600$		0			0
$601$	−0.620216	−	1.49733i	−0.0252991	−	0.0610775i	0.910725	−	0.413013i	$-0.135524\pi$
$601$	−0.620216	−	1.49733i	−0.0252991	−	0.0610775i	−0.936024	+	0.351936i	$0.885524\pi$
$602$	2.00017	+	4.82883i	0.0815207	+	0.196808i
$603$	−19.2362	+	19.2362i	−0.783357	+	0.783357i
$604$	−0.199399	−	0.199399i	−0.00811342	−	0.00811342i
$605$		0			0
$606$	−0.250141	−	0.603894i	−0.0101613	−	0.0245315i
$607$	9.57311	−	23.1115i	0.388560	−	0.938068i	−0.601685	−	0.798733i	$-0.705504\pi$
$607$	9.57311	−	23.1115i	0.388560	−	0.938068i	0.990245	−	0.139334i	$-0.0444963\pi$
$608$	−7.43849			−0.301671
$609$	1.69036	−	4.08089i	0.0684968	−	0.165366i
$610$		0			0
$611$	36.2566			1.46678
$612$	37.4593	+	8.20067i	1.51420	+	0.331492i
$613$			4.83538i			0.195299i	0.995221	+	0.0976495i	$0.0311324\pi$
$613$			4.83538i			0.195299i	−0.995221	+	0.0976495i	$0.968868\pi$
$614$	−11.4954	+	11.4954i	−0.463917	+	0.463917i
$615$		0			0
$616$		−	22.7517i		−	0.916694i
$617$	6.43422	−	15.5336i	0.259032	−	0.625358i	−0.739843	−	0.672779i	$-0.765100\pi$
$617$	6.43422	−	15.5336i	0.259032	−	0.625358i	0.998875	+	0.0474212i	$0.0151003\pi$
$618$	29.9259	−	12.3957i	1.20380	−	0.498629i
$619$	−11.7540	+	4.86865i	−0.472431	+	0.195687i	−0.606179	−	0.795328i	$-0.707299\pi$
$619$	−11.7540	+	4.86865i	−0.472431	+	0.195687i	0.133748	+	0.991015i	$0.457299\pi$
$620$		0			0
$621$	3.69975	+	3.69975i	0.148466	+	0.148466i
$622$	2.47605	+	5.97771i	0.0992804	+	0.239684i
$623$	−39.8431	+	16.5036i	−1.59628	+	0.661201i
$624$	11.7363	+	4.86134i	0.469829	+	0.194609i
$625$		0			0
$626$	−2.94287	+	7.10471i	−0.117621	+	0.283961i
$627$	7.54638	+	7.54638i	0.301373	+	0.301373i
$628$			17.0833i			0.681697i
$629$	−7.77569	−	43.4263i	−0.310037	−	1.73152i
$630$		0			0
$631$	−2.99812	+	2.99812i	−0.119353	+	0.119353i	−0.764261	−	0.644907i	$-0.776896\pi$
$631$	−2.99812	+	2.99812i	−0.119353	+	0.119353i	0.644907	+	0.764261i	$0.276896\pi$
$632$	17.1685	+	7.11142i	0.682925	+	0.282877i
$633$	20.4914			0.814459
$634$	−0.779196	−	0.322754i	−0.0309458	−	0.0128182i
$635$		0			0
$636$	7.43644	−	3.08028i	0.294874	−	0.122141i
$637$	10.5341	−	10.5341i	0.417377	−	0.417377i
$638$	−0.642752	+	0.642752i	−0.0254468	+	0.0254468i
$639$	−23.2113	+	9.61444i	−0.918226	+	0.380342i
$640$		0			0
$641$	19.6050	+	8.12065i	0.774350	+	0.320746i	0.734633	−	0.678465i	$-0.237354\pi$
$641$	19.6050	+	8.12065i	0.774350	+	0.320746i	0.0397171	+	0.999211i	$0.487354\pi$
$642$	43.0300			1.69826
$643$	−7.54502	−	3.12525i	−0.297547	−	0.123248i	0.228916	−	0.973446i	$-0.426482\pi$
$643$	−7.54502	−	3.12525i	−0.297547	−	0.123248i	−0.526462	+	0.850198i	$0.676482\pi$
$644$	−1.62136	+	1.62136i	−0.0638905	+	0.0638905i
$645$		0			0
$646$	2.11117	+	3.29462i	0.0830630	+	0.129625i
$647$		−	23.4331i		−	0.921249i	−0.887595	−	0.460624i	$-0.847626\pi$
$647$		−	23.4331i		−	0.921249i	0.887595	−	0.460624i	$-0.152374\pi$
$648$	24.2188	+	24.2188i	0.951404	+	0.951404i
$649$	−3.16081	+	7.63088i	−0.124073	+	0.299538i
$650$		0			0
$651$	50.7710	+	21.0300i	1.98987	+	0.824232i
$652$	−7.11362	+	2.94656i	−0.278591	+	0.115396i
$653$	6.43188	+	15.5279i	0.251699	+	0.607655i	0.998341	−	0.0575706i	$-0.0183354\pi$
$653$	6.43188	+	15.5279i	0.251699	+	0.607655i	−0.746643	+	0.665225i	$0.768335\pi$
$654$	5.74192	+	5.74192i	0.224527	+	0.224527i
$655$		0			0
$656$	1.91833	−	0.794598i	0.0748981	−	0.0310238i
$657$	38.5933	−	15.9859i	1.50567	−	0.623668i
$658$	−7.76814	+	18.7539i	−0.302833	+	0.731105i
$659$		−	14.0972i		−	0.549150i	−0.961566	−	0.274575i	$-0.911463\pi$
$659$		−	14.0972i		−	0.549150i	0.961566	−	0.274575i	$-0.0885371\pi$
$660$		0			0
$661$	−7.34734	+	7.34734i	−0.285779	+	0.285779i	−0.835408	−	0.549630i	$-0.814769\pi$
$661$	−7.34734	+	7.34734i	−0.285779	+	0.285779i	0.549630	+	0.835408i	$0.314769\pi$
$662$		−	25.6235i		−	0.995886i
$663$	−9.64991	−	53.8936i	−0.374771	−	2.09305i
$664$	0.585422			0.0227188
$665$		0			0
$666$	19.7707	−	47.7308i	0.766101	−	1.84953i
$667$	0.218788			0.00847151
$668$	6.38959	−	15.4258i	0.247220	−	0.596843i
$669$	14.8187	+	35.7755i	0.572923	+	1.38316i
$670$		0			0
$671$	23.6398	+	23.6398i	0.912603	+	0.912603i
$672$	−41.2041	+	41.2041i	−1.58948	+	1.58948i
$673$	−7.58646	−	18.3153i	−0.292437	−	0.706005i	0.707563	−	0.706650i	$-0.249795\pi$
$673$	−7.58646	−	18.3153i	−0.292437	−	0.706005i	−1.00000		0.000645530i	$0.999795\pi$
$674$	3.93438	+	9.49842i	0.151546	+	0.365866i
$675$		0			0
$676$		−	8.13660i		−	0.312946i
$677$	−3.09124	−	1.28043i	−0.118806	−	0.0492111i	0.322489	−	0.946573i	$-0.395481\pi$
$677$	−3.09124	−	1.28043i	−0.118806	−	0.0492111i	−0.441295	+	0.897362i	$0.645481\pi$
$678$	−4.62105	−	4.62105i	−0.177471	−	0.177471i
$679$	47.8669			1.83696
$680$		0			0
$681$	24.7314			0.947709
$682$	−7.99658	−	7.99658i	−0.306205	−	0.306205i
$683$	46.4553	+	19.2424i	1.77756	+	0.736290i	0.993260	+	0.115910i	$0.0369785\pi$
$683$	46.4553	+	19.2424i	1.77756	+	0.736290i	0.784302	+	0.620380i	$0.213022\pi$
$684$		−	11.8014i		−	0.451239i
$685$		0			0
$686$	−3.28470	−	7.92996i	−0.125410	−	0.302767i
$687$	25.4528	+	61.4484i	0.971084	+	2.34440i
$688$	1.46237	−	1.46237i	0.0557522	−	0.0557522i
$689$	−5.54818	−	5.54818i	−0.211369	−	0.211369i
$690$		0			0
$691$	−14.8926	−	35.9539i	−0.566540	−	1.36775i	−0.904454	−	0.426572i	$-0.859721\pi$
$691$	−14.8926	−	35.9539i	−0.566540	−	1.36775i	0.337913	−	0.941177i	$-0.390279\pi$
$692$	6.07926	−	14.6766i	0.231099	−	0.557922i
$693$	57.0790			2.16825
$694$	5.40333	−	13.0448i	0.205107	−	0.495173i
$695$		0			0
$696$	3.51620			0.133281
$697$	−7.34424	−	5.11360i	−0.278183	−	0.193692i
$698$		−	5.27270i		−	0.199575i
$699$	47.7287	−	47.7287i	1.80527	−	1.80527i
$700$		0			0
$701$			37.5419i			1.41794i	0.705239	+	0.708969i	$0.250840\pi$
$701$			37.5419i			1.41794i	−0.705239	+	0.708969i	$0.749160\pi$
$702$	13.1343	−	31.7089i	0.495721	−	1.19678i
$703$	−12.5438	+	5.19582i	−0.473099	+	0.195964i
$704$	6.24404	−	2.58637i	0.235331	−	0.0974773i
$705$		0			0
$706$	−4.55227	−	4.55227i	−0.171327	−	0.171327i
$707$	0.351592	+	0.848818i	0.0132230	+	0.0319231i
$708$	12.3596	−	5.11950i	0.464501	−	0.192403i
$709$	−12.7076	−	5.26367i	−0.477245	−	0.197681i	0.131076	−	0.991372i	$-0.458157\pi$
$709$	−12.7076	−	5.26367i	−0.477245	−	0.197681i	−0.608321	+	0.793691i	$0.708157\pi$
$710$		0			0
$711$	−17.8409	+	43.0718i	−0.669087	+	1.61532i
$712$	−24.2749	−	24.2749i	−0.909741	−	0.909741i
$713$			2.72198i			0.101939i
$714$	29.9443	+	6.55547i	1.12064	+	0.245332i
$715$		0			0
$716$	−21.4667	+	21.4667i	−0.802246	+	0.802246i
$717$	−16.7654	−	6.94446i	−0.626116	−	0.259346i
$718$	6.86660			0.256259
$719$	0.488717	+	0.202433i	0.0182261	+	0.00754949i	0.391778	−	0.920060i	$-0.371860\pi$
$719$	0.488717	+	0.202433i	0.0182261	+	0.00754949i	−0.373552	+	0.927609i	$0.621860\pi$
$720$		0			0
$721$	−42.0631	+	17.4231i	−1.56651	+	0.648870i
$722$	−9.19671	+	9.19671i	−0.342266	+	0.342266i
$723$	28.9441	−	28.9441i	1.07644	−	1.07644i
$724$	30.1586	−	12.4921i	1.12084	−	0.464265i
$725$		0			0
$726$	7.47778	+	3.09740i	0.277527	+	0.114955i
$727$	26.7632			0.992591			0.496296	−	0.868154i	$-0.334693\pi$
$727$	26.7632			0.992591			0.496296	+	0.868154i	$0.334693\pi$
$728$	33.1875	+	13.7467i	1.23001	+	0.509487i
$729$	8.55986	−	8.55986i	0.317032	−	0.317032i
$730$		0			0
$731$	−8.70721	−	1.90620i	−0.322048	−	0.0705033i
$732$		−	54.1486i		−	2.00139i
$733$	−12.2673	−	12.2673i	−0.453105	−	0.453105i	0.443279	−	0.896384i	$-0.353815\pi$
$733$	−12.2673	−	12.2673i	−0.453105	−	0.453105i	−0.896384	+	0.443279i	$0.853815\pi$
$734$	−1.95086	+	4.70978i	−0.0720074	+	0.173841i
$735$		0			0
$736$	−2.66658	−	1.10454i	−0.0982916	−	0.0407137i
$737$	−10.6480	+	4.41056i	−0.392225	+	0.162465i
$738$	−4.01050	−	9.68219i	−0.147628	−	0.356407i
$739$	−21.3876	−	21.3876i	−0.786757	−	0.786757i	0.194204	−	0.980961i	$-0.437788\pi$
$739$	−21.3876	−	21.3876i	−0.786757	−	0.786757i	−0.980961	+	0.194204i	$0.937788\pi$
$740$		0			0
$741$	−15.5673	+	6.44819i	−0.571880	+	0.236880i
$742$	4.05856	−	1.68111i	0.148994	−	0.0617155i
$743$	−2.74796	+	6.63416i	−0.100813	+	0.243384i	−0.966236	−	0.257657i	$-0.917049\pi$
$743$	−2.74796	+	6.63416i	−0.100813	+	0.243384i	0.865424	+	0.501041i	$0.167049\pi$
$744$			43.7457i			1.60379i
$745$		0			0
$746$	−5.53430	+	5.53430i	−0.202625	+	0.202625i
$747$			1.46869i			0.0537366i
$748$	13.3325	+	9.28309i	0.487486	+	0.339423i
$749$	−60.4819			−2.20996
$750$		0			0
$751$	11.9767	−	28.9144i	0.437037	−	1.05510i	−0.539930	−	0.841710i	$-0.681549\pi$
$751$	11.9767	−	28.9144i	0.437037	−	1.05510i	0.976967	−	0.213390i	$-0.0684505\pi$
$752$	8.03197			0.292896
$753$	−4.22890	+	10.2095i	−0.154110	+	0.372054i
$754$	−0.549215	−	1.32592i	−0.0200012	−	0.0482873i
$755$		0			0
$756$	−34.9936	−	34.9936i	−1.27271	−	1.27271i
$757$	−7.61956	+	7.61956i	−0.276938	+	0.276938i	−0.831885	−	0.554948i	$-0.812738\pi$
$757$	−7.61956	+	7.61956i	−0.276938	+	0.276938i	0.554948	+	0.831885i	$0.312738\pi$
$758$	−7.25323	−	17.5108i	−0.263449	−	0.636022i
$759$	1.58471	+	3.82582i	0.0575212	+	0.138868i
$760$		0			0
$761$			33.1409i			1.20136i	0.799491	+	0.600678i	$0.205102\pi$
$761$			33.1409i			1.20136i	−0.799491	+	0.600678i	$0.794898\pi$
$762$	11.6123	+	4.80998i	0.420670	+	0.174247i
$763$	−8.07068	−	8.07068i	−0.292178	−	0.292178i
$764$	5.04452			0.182504
$765$		0			0
$766$	5.75182			0.207822
$767$	−9.22123	−	9.22123i	−0.332959	−	0.332959i
$768$	−35.0247	−	14.5077i	−1.26385	−	0.523502i
$769$		−	11.4864i		−	0.414210i	−0.978319	−	0.207105i	$-0.933596\pi$
$769$		−	11.4864i		−	0.414210i	0.978319	−	0.207105i	$-0.0664042\pi$
$770$		0			0
$771$	28.8885	+	69.7429i	1.04039	+	2.51173i
$772$	−6.77785	−	16.3632i	−0.243940	−	0.588924i
$773$	2.26913	−	2.26913i	0.0816149	−	0.0816149i	−0.665121	−	0.746736i	$-0.731620\pi$
$773$	2.26913	−	2.26913i	0.0816149	−	0.0816149i	0.746736	+	0.665121i	$0.231620\pi$
$774$	−7.38087	−	7.38087i	−0.265300	−	0.265300i
$775$		0			0
$776$	14.5817	+	35.2034i	0.523454	+	1.26373i
$777$	−40.7028	+	98.2653i	−1.46021	+	3.52525i
$778$	−11.8454			−0.424678
$779$	−1.05397	+	2.54451i	−0.0377625	+	0.0911667i
$780$		0			0
$781$	−10.6440			−0.380873
$782$	0.267608	+	1.49456i	0.00956963	+	0.0534452i
$783$			4.72208i			0.168754i
$784$	2.33364	−	2.33364i	0.0833443	−	0.0833443i
$785$		0			0
$786$			22.9515i			0.818651i
$787$	1.28976	−	3.11375i	0.0459748	−	0.110993i	−0.899224	−	0.437489i	$-0.855868\pi$
$787$	1.28976	−	3.11375i	0.0459748	−	0.110993i	0.945199	+	0.326496i	$0.105868\pi$
$788$	−22.5940	+	9.35875i	−0.804879	+	0.333392i
$789$	−41.5920	+	17.2280i	−1.48071	+	0.613332i
$790$		0			0
$791$	6.49523	+	6.49523i	0.230944	+	0.230944i
$792$	17.3880	+	41.9784i	0.617857	+	1.49164i
$793$	−48.7661	+	20.1996i	−1.73174	+	0.717308i
$794$	20.1518	+	8.34716i	0.715161	+	0.296230i
$795$		0			0
$796$	−6.38293	+	15.4097i	−0.226237	+	0.546184i
$797$	15.0966	+	15.0966i	0.534747	+	0.534747i	0.921981	−	0.387234i	$-0.126569\pi$
$797$	15.0966	+	15.0966i	0.534747	+	0.534747i	−0.387234	+	0.921981i	$0.626569\pi$
$798$		−	9.43385i		−	0.333955i
$799$	−18.6771	−	29.1468i	−0.660748	−	1.03114i
$800$		0			0
$801$	60.9002	−	60.9002i	2.15180	−	2.15180i
$802$	−11.3224	−	4.68987i	−0.399806	−	0.165605i
$803$	17.6977			0.624538
$804$	17.2464	+	7.14369i	0.608233	+	0.251939i
$805$		0			0
$806$	16.4960	−	6.83288i	0.581048	−	0.240678i
$807$	40.7907	−	40.7907i	1.43590	−	1.43590i
$808$	−0.517153	+	0.517153i	−0.0181934	+	0.0181934i
$809$	2.52190	−	1.04460i	0.0886652	−	0.0367263i	−0.337910	−	0.941178i	$-0.609720\pi$
$809$	2.52190	−	1.04460i	0.0886652	−	0.0367263i	0.426575	+	0.904452i	$0.359720\pi$
$810$		0			0
$811$	−34.4933	−	14.2876i	−1.21122	−	0.501705i	−0.316614	−	0.948554i	$-0.602546\pi$
$811$	−34.4933	−	14.2876i	−1.21122	−	0.501705i	−0.894609	+	0.446849i	$0.852546\pi$
$812$	−2.06938			−0.0726211
$813$	16.3749	+	6.78272i	0.574294	+	0.237880i
$814$	15.4771	−	15.4771i	0.542471	−	0.542471i
$815$		0			0
$816$	−2.13776	−	11.9391i	−0.0748365	−	0.417953i
$817$			2.74317i			0.0959715i
$818$	−17.9796	−	17.9796i	−0.628641	−	0.628641i
$819$	−34.4874	+	83.2600i	−1.20509	+	2.90934i
$820$		0			0
$821$	−39.0148	−	16.1605i	−1.36163	−	0.564004i	−0.422121	−	0.906540i	$-0.638714\pi$
$821$	−39.0148	−	16.1605i	−1.36163	−	0.564004i	−0.939505	+	0.342536i	$0.888714\pi$
$822$	−6.53952	+	2.70876i	−0.228092	+	0.0944788i
$823$	7.94473	+	19.1803i	0.276936	+	0.668582i	0.999748	−	0.0224627i	$-0.00715069\pi$
$823$	7.94473	+	19.1803i	0.276936	+	0.668582i	−0.722812	+	0.691045i	$0.757151\pi$
$824$	−25.6275	−	25.6275i	−0.892775	−	0.892775i
$825$		0			0
$826$	6.74543	−	2.79405i	0.234704	−	0.0972174i
$827$	−10.6314	+	4.40367i	−0.369690	+	0.153131i	−0.559791	−	0.828634i	$-0.689119\pi$
$827$	−10.6314	+	4.40367i	−0.369690	+	0.153131i	0.190101	+	0.981765i	$0.439119\pi$
$828$	1.75238	−	4.23063i	0.0608996	−	0.147025i
$829$			11.7508i			0.408121i	0.978958	+	0.204060i	$0.0654139\pi$
$829$			11.7508i			0.408121i	−0.978958	+	0.204060i	$0.934586\pi$
$830$		0			0
$831$	0.267995	−	0.267995i	0.00929664	−	0.00929664i
$832$			10.6708i			0.369942i
$833$	−13.8949	−	3.04191i	−0.481431	−	0.105396i
$834$	15.4318			0.534361
$835$		0			0
$836$	1.91335	−	4.61924i	0.0661747	−	0.159760i
$837$	−58.7483			−2.03064
$838$	0.255571	−	0.617003i	0.00882855	−	0.0213140i
$839$	14.0060	+	33.8134i	0.483540	+	1.16737i	0.957917	+	0.287046i	$0.0926733\pi$
$839$	14.0060	+	33.8134i	0.483540	+	1.16737i	−0.474377	+	0.880322i	$0.657327\pi$
$840$		0			0
$841$	−20.3665	−	20.3665i	−0.702292	−	0.702292i
$842$	−17.8079	+	17.8079i	−0.613701	+	0.613701i
$843$	−2.14598	−	5.18086i	−0.0739116	−	0.178438i
$844$	−3.67377	−	8.86927i	−0.126457	−	0.305293i
$845$		0			0
$846$		−	40.5390i		−	1.39376i
$847$	−10.5106	−	4.35362i	−0.361148	−	0.149592i
$848$	−1.22910	−	1.22910i	−0.0422074	−	0.0422074i
$849$	−88.0312			−3.02122
$850$		0			0
$851$	−5.26829			−0.180595
$852$	12.1904	+	12.1904i	0.417637	+	0.417637i
$853$	35.1787	+	14.5715i	1.20450	+	0.498918i	0.892449	−	0.451149i	$-0.148986\pi$
$853$	35.1787	+	14.5715i	1.20450	+	0.498918i	0.312046	+	0.950067i	$0.398986\pi$
$854$		−	29.5524i		−	1.01126i
$855$		0			0
$856$	−18.4247	−	44.4811i	−0.629742	−	1.52033i
$857$	7.74080	+	18.6880i	0.264421	+	0.638368i	0.999202	−	0.0399356i	$-0.0127153\pi$
$857$	7.74080	+	18.6880i	0.264421	+	0.638368i	−0.734781	+	0.678304i	$0.762715\pi$
$858$	19.2076	−	19.2076i	0.655736	−	0.655736i
$859$	−1.84360	−	1.84360i	−0.0629028	−	0.0629028i	0.674956	−	0.737858i	$-0.264163\pi$
$859$	−1.84360	−	1.84360i	−0.0629028	−	0.0629028i	−0.737858	+	0.674956i	$0.764163\pi$
$860$		0			0
$861$	8.25657	+	19.9331i	0.281383	+	0.679319i
$862$	4.66443	−	11.2609i	0.158871	−	0.383548i
$863$	−11.2563			−0.383169			−0.191584	−	0.981476i	$-0.561363\pi$
$863$	−11.2563			−0.383169			−0.191584	+	0.981476i	$0.561363\pi$
$864$	23.8391	−	57.5526i	0.811022	−	1.95798i
$865$		0			0
$866$	26.1730			0.889396
$867$	−38.3542	+	35.5202i	−1.30258	+	1.20633i
$868$		−	25.7455i		−	0.873860i
$869$	−13.9664	+	13.9664i	−0.473777	+	0.473777i
$870$		0			0
$871$		−	18.1970i		−	0.616580i
$872$	3.47696	−	8.39412i	0.117745	−	0.284261i
$873$	−88.3174	+	36.5822i	−2.98909	+	1.23812i
$874$	0.431707	−	0.178819i	0.0146027	−	0.00604864i
$875$		0			0
$876$	−20.2689	−	20.2689i	−0.684824	−	0.684824i
$877$	2.29651	+	5.54426i	0.0775476	+	0.187216i	0.957899	−	0.287106i	$-0.0926932\pi$
$877$	2.29651	+	5.54426i	0.0775476	+	0.187216i	−0.880351	+	0.474322i	$0.842693\pi$
$878$	−15.3935	+	6.37620i	−0.519506	+	0.215186i
$879$	−4.02300	−	1.66638i	−0.135692	−	0.0562056i
$880$		0			0
$881$	13.1380	−	31.7181i	0.442632	−	1.06861i	−0.532390	−	0.846499i	$-0.678706\pi$
$881$	13.1380	−	31.7181i	0.442632	−	1.06861i	0.975022	−	0.222109i	$-0.0712941\pi$
$882$	−11.7784	−	11.7784i	−0.396598	−	0.396598i
$883$		−	11.8244i		−	0.397921i	−0.980007	−	0.198961i	$-0.936243\pi$
$883$		−	11.8244i		−	0.397921i	0.980007	−	0.198961i	$-0.0637566\pi$
$884$	−21.5966	+	13.8390i	−0.726374	+	0.465456i
$885$		0			0
$886$	4.65343	−	4.65343i	0.156335	−	0.156335i
$887$	22.3904	+	9.27440i	0.751796	+	0.311404i	0.725474	−	0.688250i	$-0.241621\pi$
$887$	22.3904	+	9.27440i	0.751796	+	0.311404i	0.0263216	+	0.999654i	$0.491621\pi$
$888$	−84.6680			−2.84127
$889$	−16.3220	−	6.76077i	−0.547421	−	0.226749i
$890$		0			0
$891$	−33.6329	+	13.9312i	−1.12675	+	0.466713i
$892$	12.8279	−	12.8279i	0.429511	−	0.429511i
$893$	−7.53337	+	7.53337i	−0.252095	+	0.252095i
$894$	−48.8519	+	20.2351i	−1.63385	+	0.676764i
$895$		0			0
$896$	29.4952	+	12.2173i	0.985367	+	0.408152i
$897$	−6.53813			−0.218302
$898$	6.12683	+	2.53782i	0.204455	+	0.0846880i
$899$	−1.73707	+	1.73707i	−0.0579345	+	0.0579345i
$900$		0			0
$901$	−1.60213	+	7.31828i	−0.0533747	+	0.243807i
$902$		−	4.43996i		−	0.147835i
$903$	15.1953	+	15.1953i	0.505668	+	0.505668i
$904$	−2.79823	+	6.75553i	−0.0930678	+	0.224686i
$905$		0			0
$906$	0.415914	+	0.172277i	0.0138178	+	0.00572353i
$907$	−41.3709	+	17.1364i	−1.37370	+	0.569005i	−0.942789	−	0.333390i	$-0.891808\pi$
$907$	−41.3709	+	17.1364i	−1.37370	+	0.569005i	−0.430910	+	0.902395i	$0.641808\pi$
$908$	−4.43394	−	10.7045i	−0.147145	−	0.355240i
$909$	−1.29742	−	1.29742i	−0.0430326	−	0.0430326i
$910$		0			0
$911$	9.19129	−	3.80716i	0.304521	−	0.126137i	−0.225190	−	0.974315i	$-0.572300\pi$
$911$	9.19129	−	3.80716i	0.304521	−	0.126137i	0.529711	+	0.848178i	$0.322300\pi$
$912$	−3.44865	+	1.42848i	−0.114196	+	0.0473016i
$913$	−0.238117	+	0.574865i	−0.00788052	+	0.0190253i
$914$			13.8182i			0.457066i
$915$		0			0
$916$	22.0334	−	22.0334i	0.728005	−	0.728005i
$917$		−	32.2600i		−	1.06532i
$918$	−32.2569	+	5.77575i	−1.06464	+	0.190628i
$919$	33.3601			1.10045			0.550224	−	0.835017i	$-0.314542\pi$
$919$	33.3601			1.10045			0.550224	+	0.835017i	$0.314542\pi$
$920$		0			0
$921$	−25.5786	+	61.7522i	−0.842844	+	2.03480i
$922$	18.3762			0.605189
$923$	6.43116	−	15.5262i	0.211684	−	0.511051i
$924$	−14.9887	−	36.1860i	−0.493094	−	1.19043i
$925$		0			0
$926$	−5.24059	−	5.24059i	−0.172217	−	0.172217i
$927$	64.2934	−	64.2934i	2.11167	−	2.11167i
$928$	−0.996842	−	2.40659i	−0.0327229	−	0.0790001i
$929$	9.52731	+	23.0010i	0.312581	+	0.754637i	0.999608	+	0.0280049i	$0.00891541\pi$
$929$	9.52731	+	23.0010i	0.312581	+	0.754637i	−0.687027	+	0.726632i	$0.741085\pi$
$930$		0			0
$931$			4.37755i			0.143468i
$932$	−29.2154	−	12.1014i	−0.956982	−	0.396395i
$933$	18.8106	+	18.8106i	0.615830	+	0.615830i
$934$	−21.9917			−0.719592
$935$		0			0
$936$	−71.7390			−2.34486
$937$	22.0943	+	22.0943i	0.721788	+	0.721788i	0.968969	−	0.247181i	$-0.0795043\pi$
$937$	22.0943	+	22.0943i	0.721788	+	0.721788i	−0.247181	+	0.968969i	$0.579504\pi$
$938$	9.41250	+	3.89878i	0.307329	+	0.127300i
$939$			31.6176i			1.03180i
$940$		0			0
$941$	−0.663467	−	1.60175i	−0.0216284	−	0.0522156i	0.912696	−	0.408638i	$-0.133996\pi$
$941$	−0.663467	−	1.60175i	−0.0216284	−	0.0522156i	−0.934325	+	0.356423i	$0.883996\pi$
$942$	−10.4367	−	25.1963i	−0.340045	−	0.820940i
$943$	−0.755666	+	0.755666i	−0.0246079	+	0.0246079i
$944$	−2.04279	−	2.04279i	−0.0664873	−	0.0664873i
$945$		0			0
$946$	−1.69232	−	4.08562i	−0.0550221	−	0.132835i
$947$	4.15260	−	10.0253i	0.134941	−	0.325777i	−0.841936	−	0.539577i	$-0.818584\pi$
$947$	4.15260	−	10.0253i	0.134941	−	0.325777i	0.976877	+	0.213800i	$0.0685841\pi$
$948$	31.9910			1.03902
$949$	−10.6930	+	25.8153i	−0.347111	+	0.838000i
$950$		0			0
$951$	−3.46760			−0.112445
$952$	−6.04508	−	33.7610i	−0.195922	−	1.09420i
$953$		−	16.9007i		−	0.547466i	−0.961806	−	0.273733i	$-0.911742\pi$
$953$		−	16.9007i		−	0.547466i	0.961806	−	0.273733i	$-0.0882584\pi$
$954$	−6.20351	+	6.20351i	−0.200846	+	0.200846i
$955$		0			0
$956$			8.50159i			0.274961i
$957$	−1.43020	+	3.45280i	−0.0462316	+	0.111613i
$958$	19.7623	−	8.18582i	0.638491	−	0.264472i
$959$	9.19177	−	3.80736i	0.296818	−	0.122946i
$960$		0			0
$961$	0.309144	+	0.309144i	0.00997239	+	0.00997239i
$962$	13.2248	+	31.9274i	0.426384	+	1.02938i
$963$	111.593	−	46.2233i	3.59603	−	1.48952i
$964$	−17.7171	−	7.33864i	−0.570628	−	0.236362i
$965$		0			0
$966$	1.40083	−	3.38189i	0.0450708	−	0.108811i
$967$	−22.0869	−	22.0869i	−0.710267	−	0.710267i	0.256324	−	0.966591i	$-0.417489\pi$
$967$	−22.0869	−	22.0869i	−0.710267	−	0.710267i	−0.966591	+	0.256324i	$0.917489\pi$
$968$		−	9.05619i		−	0.291077i
$969$	13.2030	+	9.19292i	0.424142	+	0.295319i
$970$		0			0
$971$	−12.2957	+	12.2957i	−0.394589	+	0.394589i	−0.876319	−	0.481731i	$-0.840008\pi$
$971$	−12.2957	+	12.2957i	−0.394589	+	0.394589i	0.481731	+	0.876319i	$0.340008\pi$
$972$	12.0433	+	4.98849i	0.386288	+	0.160006i
$973$	−21.6906			−0.695368
$974$	−0.426947	−	0.176847i	−0.0136802	−	0.00566654i
$975$		0			0
$976$	−10.8032	+	4.47485i	−0.345803	+	0.143236i
$977$	−6.48656	+	6.48656i	−0.207523	+	0.207523i	−0.803214	−	0.595691i	$-0.796878\pi$
$977$	−6.48656	+	6.48656i	−0.207523	+	0.207523i	0.595691	+	0.803214i	$0.296878\pi$
$978$	8.69182	−	8.69182i	0.277934	−	0.277934i
$979$	33.7109	−	13.9635i	1.07740	−	0.446275i
$980$		0			0
$981$	21.0589	+	8.72290i	0.672360	+	0.278501i
$982$	19.0469			0.607811
$983$	34.4578	+	14.2729i	1.09903	+	0.455235i	0.857148	−	0.515070i	$-0.172234\pi$
$983$	34.4578	+	14.2729i	1.09903	+	0.455235i	0.241886	+	0.970305i	$0.422234\pi$
$984$	−12.1445	+	12.1445i	−0.387152	+	0.387152i
$985$		0			0
$986$	−0.782993	+	1.12455i	−0.0249356	+	0.0358129i
$987$			83.4593i			2.65654i
$988$	5.58194	+	5.58194i	0.177585	+	0.177585i
$989$	−0.407332	+	0.983386i	−0.0129524	+	0.0312699i
$990$		0			0
$991$	−32.3988	−	13.4200i	−1.02918	−	0.426301i	−0.196765	−	0.980451i	$-0.563044\pi$
$991$	−32.3988	−	13.4200i	−1.02918	−	0.426301i	−0.832417	+	0.554149i	$0.813044\pi$
$992$	29.9408	−	12.4019i	0.950621	−	0.393760i
$993$	−40.3158	−	97.3310i	−1.27938	−	3.08871i
$994$	6.65312	+	6.65312i	0.211024	+	0.211024i
$995$		0			0
$996$	0.931097	−	0.385673i	0.0295029	−	0.0122205i
$997$	34.5139	−	14.2961i	1.09307	−	0.452763i	0.237991	−	0.971267i	$-0.423511\pi$
$997$	34.5139	−	14.2961i	1.09307	−	0.452763i	0.855075	+	0.518505i	$0.173511\pi$
$998$	10.4355	−	25.1934i	0.330329	−	0.797484i
$999$		−	113.705i		−	3.59747i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.n.c.399.5		24
5.2	odd	4		85.2.l.a.76.2	yes	24
5.3	odd	4		425.2.m.b.76.5		24
5.4	even	2		425.2.n.f.399.2		24
15.2	even	4		765.2.be.b.586.5		24
17.15	even	8		425.2.n.f.49.2		24
85.7	even	16		1445.2.a.p.1.9		12
85.27	even	16		1445.2.a.q.1.9		12
85.32	odd	8		85.2.l.a.66.2	✓	24
85.49	even	8	inner	425.2.n.c.49.5		24
85.57	even	16		1445.2.d.j.866.8		24
85.58	even	16		7225.2.a.bs.1.4		12
85.62	even	16		1445.2.d.j.866.7		24
85.78	even	16		7225.2.a.bq.1.4		12
85.83	odd	8		425.2.m.b.151.5		24
255.32	even	8		765.2.be.b.406.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.66.2	✓	24	85.32	odd	8
85.2.l.a.76.2	yes	24	5.2	odd	4
425.2.m.b.76.5		24	5.3	odd	4
425.2.m.b.151.5		24	85.83	odd	8
425.2.n.c.49.5		24	85.49	even	8	inner
425.2.n.c.399.5		24	1.1	even	1	trivial
425.2.n.f.49.2		24	17.15	even	8
425.2.n.f.399.2		24	5.4	even	2
765.2.be.b.406.5		24	255.32	even	8
765.2.be.b.586.5		24	15.2	even	4
1445.2.a.p.1.9		12	85.7	even	16
1445.2.a.q.1.9		12	85.27	even	16
1445.2.d.j.866.7		24	85.62	even	16
1445.2.d.j.866.8		24	85.57	even	16
7225.2.a.bq.1.4		12	85.78	even	16
7225.2.a.bs.1.4		12	85.58	even	16

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.n (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.528855 + 0.528855i) q^{2} +(2.84096 + 1.17676i) q^{3} -1.44062i q^{4} +(0.880118 + 2.12479i) q^{6} +(-1.23707 - 2.98655i) q^{7} +(1.81959 - 1.81959i) q^{8} +(4.56494 + 4.56494i) q^{9} +(1.04667 + 2.52689i) q^{11} +(1.69527 - 4.09275i) q^{12} -4.31833 q^{13} +(0.925222 - 2.23368i) q^{14} -0.956646 q^{16} +(2.22453 + 3.47152i) q^{17} +4.82839i q^{18} +(0.897260 - 0.897260i) q^{19} -9.94040i q^{21} +(-0.782821 + 1.88990i) q^{22} +(0.454888 - 0.188421i) q^{23} +(7.31061 - 3.02815i) q^{24} +(-2.28377 - 2.28377i) q^{26} +(4.06666 + 9.81779i) q^{27} +(-4.30250 + 1.78215i) q^{28} +(0.410535 + 0.170049i) q^{29} +(-2.11561 + 5.10754i) q^{31} +(-4.14511 - 4.14511i) q^{32} +8.41047i q^{33} +(-0.659477 + 3.01239i) q^{34} +(6.57637 - 6.57637i) q^{36} +(-9.88545 - 4.09469i) q^{37} +0.949042 q^{38} +(-12.2682 - 5.08165i) q^{39} +(-2.00526 + 0.830608i) q^{41} +(5.25703 - 5.25703i) q^{42} +(-1.52864 + 1.52864i) q^{43} +(3.64030 - 1.50786i) q^{44} +(0.340217 + 0.140922i) q^{46} -8.39597 q^{47} +(-2.71779 - 1.12575i) q^{48} +(-2.43940 + 2.43940i) q^{49} +(2.23464 + 12.4802i) q^{51} +6.22109i q^{52} +(1.28480 + 1.28480i) q^{53} +(-3.04152 + 7.34287i) q^{54} +(-7.68527 - 3.18334i) q^{56} +(3.60494 - 1.49321i) q^{57} +(0.127182 + 0.307045i) q^{58} +(2.13537 + 2.13537i) q^{59} +(11.2928 - 4.67764i) q^{61} +(-3.82000 + 1.58230i) q^{62} +(7.98628 - 19.2806i) q^{63} -2.47104i q^{64} +(-4.44792 + 4.44792i) q^{66} +4.21389i q^{67} +(5.00116 - 3.20471i) q^{68} +1.51404 q^{69} +(-1.48927 + 3.59542i) q^{71} +16.6127 q^{72} +(2.47620 - 5.97807i) q^{73} +(-3.06247 - 7.39347i) q^{74} +(-1.29261 - 1.29261i) q^{76} +(6.25188 - 6.25188i) q^{77} +(-3.80064 - 9.17555i) q^{78} +(2.76355 + 6.67180i) q^{79} +13.3100i q^{81} +(-1.49977 - 0.621223i) q^{82} +(0.160866 + 0.160866i) q^{83} -14.3204 q^{84} -1.61686 q^{86} +(0.966206 + 0.966206i) q^{87} +(6.50243 + 2.69339i) q^{88} -13.3408i q^{89} +(5.34208 + 12.8969i) q^{91} +(-0.271443 - 0.655322i) q^{92} +(-12.0207 + 12.0207i) q^{93} +(-4.44025 - 4.44025i) q^{94} +(-6.89827 - 16.6539i) q^{96} +(-5.66657 + 13.6803i) q^{97} -2.58018 q^{98} +(-6.75711 + 16.3131i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{3} - 8 q^{6} + 24 q^{9} - 8 q^{11} + 40 q^{12} + 16 q^{13} - 24 q^{16} + 8 q^{19} - 24 q^{22} + 8 q^{23} + 8 q^{24} + 16 q^{26} + 16 q^{27} - 40 q^{28} + 8 q^{29} - 16 q^{34} - 24 q^{36} - 16 q^{37}+ \cdots + 8 q^{99}+O(q^{100}) \) 24 * q - 8 * q^3 - 8 * q^6 + 24 * q^9 - 8 * q^11 + 40 * q^12 + 16 * q^13 - 24 * q^16 + 8 * q^19 - 24 * q^22 + 8 * q^23 + 8 * q^24 + 16 * q^26 + 16 * q^27 - 40 * q^28 + 8 * q^29 - 16 * q^34 - 24 * q^36 - 16 * q^37 - 48 * q^38 - 8 * q^39 + 16 * q^41 - 24 * q^42 - 8 * q^43 - 16 * q^44 + 8 * q^46 - 64 * q^47 - 8 * q^48 - 56 * q^51 + 24 * q^53 + 32 * q^54 + 64 * q^56 + 16 * q^57 + 56 * q^58 - 32 * q^59 + 32 * q^61 - 32 * q^62 + 80 * q^63 + 96 * q^66 + 24 * q^68 - 96 * q^69 - 24 * q^71 - 24 * q^72 - 64 * q^73 + 64 * q^74 - 8 * q^76 + 24 * q^77 + 8 * q^78 - 16 * q^82 - 96 * q^83 + 64 * q^84 - 16 * q^86 + 48 * q^87 + 8 * q^88 - 24 * q^91 + 112 * q^92 - 64 * q^93 - 56 * q^94 - 168 * q^96 + 48 * q^97 + 120 * q^98 + 8 * q^99

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