LMFDB - Embedded newform 425.2.n.e.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(49,425)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			49.4
Character	$\chi$	$=$	425.49
Dual form			425.2.n.e.399.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.187572 + 0.187572i) q^{2} +(-1.67148 + 0.692349i) q^{3} +1.92963i q^{4} +(0.183657 - 0.443388i) q^{6} +(-1.88562 + 4.55230i) q^{7} +(-0.737090 - 0.737090i) q^{8} +(0.193173 - 0.193173i) q^{9} +(1.50174 - 3.62553i) q^{11} +(-1.33598 - 3.22534i) q^{12} +2.07286 q^{13} +(-0.500194 - 1.20758i) q^{14} -3.58275 q^{16} +(-3.19465 - 2.60657i) q^{17} +0.0724676i q^{18} +(2.08750 + 2.08750i) q^{19} -8.91458i q^{21} +(0.398363 + 0.961734i) q^{22} +(-3.58060 - 1.48313i) q^{23} +(1.74235 + 0.721707i) q^{24} +(-0.388810 + 0.388810i) q^{26} +(1.88791 - 4.55781i) q^{27} +(-8.78427 - 3.63856i) q^{28} +(-3.22121 + 1.33427i) q^{29} +(2.23739 + 5.40154i) q^{31} +(2.14620 - 2.14620i) q^{32} +7.09972i q^{33} +(1.08815 - 0.110307i) q^{34} +(0.372752 + 0.372752i) q^{36} +(-1.88698 + 0.781612i) q^{37} -0.783113 q^{38} +(-3.46473 + 1.43514i) q^{39} +(-10.9410 - 4.53193i) q^{41} +(1.67213 + 1.67213i) q^{42} +(3.91060 + 3.91060i) q^{43} +(6.99594 + 2.89781i) q^{44} +(0.949815 - 0.393426i) q^{46} -0.453534 q^{47} +(5.98849 - 2.48051i) q^{48} +(-12.2181 - 12.2181i) q^{49} +(7.14444 + 2.14502i) q^{51} +3.99985i q^{52} +(4.60644 - 4.60644i) q^{53} +(0.500800 + 1.20904i) q^{54} +(4.74533 - 1.96558i) q^{56} +(-4.93448 - 2.04393i) q^{57} +(0.353938 - 0.854483i) q^{58} +(-4.92683 + 4.92683i) q^{59} +(-0.0429157 - 0.0177763i) q^{61} +(-1.43285 - 0.593507i) q^{62} +(0.515129 + 1.24363i) q^{63} -6.36037i q^{64} +(-1.33171 - 1.33171i) q^{66} +10.0472i q^{67} +(5.02973 - 6.16450i) q^{68} +7.01174 q^{69} +(5.85587 + 14.1373i) q^{71} -0.284771 q^{72} +(3.36399 + 8.12139i) q^{73} +(0.207336 - 0.500554i) q^{74} +(-4.02810 + 4.02810i) q^{76} +(13.6728 + 13.6728i) q^{77} +(0.380696 - 0.919080i) q^{78} +(0.991282 - 2.39317i) q^{79} +9.74493i q^{81} +(2.90230 - 1.20217i) q^{82} +(-1.09508 + 1.09508i) q^{83} +17.2019 q^{84} -1.46704 q^{86} +(4.46041 - 4.46041i) q^{87} +(-3.77926 + 1.56542i) q^{88} +10.2523i q^{89} +(-3.90863 + 9.43626i) q^{91} +(2.86190 - 6.90924i) q^{92} +(-7.47951 - 7.47951i) q^{93} +(0.0850703 - 0.0850703i) q^{94} +(-2.10141 + 5.07326i) q^{96} +(-4.07387 - 9.83519i) q^{97} +4.58356 q^{98} +(-0.410257 - 0.990448i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3} - 8 q^{6} - 12 q^{9} + 4 q^{11} - 20 q^{12} + 16 q^{13} + 24 q^{14} - 24 q^{16} + 20 q^{19} + 12 q^{22} + 8 q^{23} - 16 q^{24} + 16 q^{26} + 16 q^{27} + 20 q^{28} - 4 q^{29} + 24 q^{31} + 60 q^{32}+ \cdots + 80 q^{99}+O(q^{100}) $ 24 * q + 4 * q^3 - 8 * q^6 - 12 * q^9 + 4 * q^11 - 20 * q^12 + 16 * q^13 + 24 * q^14 - 24 * q^16 + 20 * q^19 + 12 * q^22 + 8 * q^23 - 16 * q^24 + 16 * q^26 + 16 * q^27 + 20 * q^28 - 4 * q^29 + 24 * q^31 + 60 * q^32 - 16 * q^34 + 60 * q^36 - 16 * q^37 - 48 * q^38 - 8 * q^39 - 20 * q^41 + 12 * q^42 - 32 * q^43 - 64 * q^44 - 40 * q^46 - 88 * q^47 + 4 * q^48 - 24 * q^49 + 16 * q^51 - 12 * q^53 + 20 * q^54 - 32 * q^56 - 56 * q^57 - 28 * q^58 + 16 * q^59 - 64 * q^61 + 16 * q^62 - 40 * q^63 - 72 * q^66 + 48 * q^68 + 48 * q^69 - 24 * q^71 + 120 * q^72 + 20 * q^73 - 32 * q^74 + 52 * q^76 + 24 * q^77 - 100 * q^78 + 48 * q^79 + 8 * q^82 + 12 * q^83 + 40 * q^84 - 16 * q^86 - 24 * q^87 + 80 * q^88 + 24 * q^91 - 56 * q^92 + 32 * q^93 + 40 * q^94 + 132 * q^96 - 24 * q^97 + 48 * q^98 + 80 * q^99

Character values

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

$n$	$52$	$326$
$\chi(n)$	$-1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	−0.187572	+	0.187572i	−0.132634	+	0.132634i	−0.770307	−	0.637673i	$-0.779897\pi$
$2$	−0.187572	+	0.187572i	−0.132634	+	0.132634i	0.637673	+	0.770307i	$0.279897\pi$
$3$	−1.67148	+	0.692349i	−0.965029	+	0.399728i	−0.808859	−	0.588002i	$-0.799915\pi$
$3$	−1.67148	+	0.692349i	−0.965029	+	0.399728i	−0.156169	+	0.987730i	$0.549915\pi$
$4$			1.92963i			0.964817i
$5$		0			0
$5$		0			0
$6$	0.183657	−	0.443388i	0.0749778	−	0.181013i
$7$	−1.88562	+	4.55230i	−0.712699	+	1.72061i	−0.0195547	+	0.999809i	$0.506225\pi$
$7$	−1.88562	+	4.55230i	−0.712699	+	1.72061i	−0.693144	+	0.720799i	$0.743775\pi$
$8$	−0.737090	−	0.737090i	−0.260601	−	0.260601i
$9$	0.193173	−	0.193173i	0.0643909	−	0.0643909i
$10$		0			0
$11$	1.50174	−	3.62553i	0.452793	−	1.09314i	−0.518463	−	0.855100i	$-0.673496\pi$
$11$	1.50174	−	3.62553i	0.452793	−	1.09314i	0.971256	−	0.238038i	$-0.0765043\pi$
$12$	−1.33598	−	3.22534i	−0.385664	−	0.931076i
$13$	2.07286			0.574907			0.287453	−	0.957795i	$-0.407191\pi$
$13$	2.07286			0.574907			0.287453	+	0.957795i	$0.407191\pi$
$14$	−0.500194	−	1.20758i	−0.133683	−	0.322738i
$15$		0			0
$16$	−3.58275			−0.895688
$17$	−3.19465	−	2.60657i	−0.774816	−	0.632186i
$17$	−3.19465	−	2.60657i	−0.774816	−	0.632186i
$18$			0.0724676i			0.0170808i
$19$	2.08750	+	2.08750i	0.478905	+	0.478905i	0.904781	−	0.425877i	$-0.140034\pi$
$19$	2.08750	+	2.08750i	0.478905	+	0.478905i	−0.425877	+	0.904781i	$0.640034\pi$
$20$		0			0
$21$		−	8.91458i		−	1.94532i
$22$	0.398363	+	0.961734i	0.0849313	+	0.205042i
$23$	−3.58060	−	1.48313i	−0.746606	−	0.309254i	−0.0232502	−	0.999730i	$-0.507401\pi$
$23$	−3.58060	−	1.48313i	−0.746606	−	0.309254i	−0.723356	+	0.690475i	$0.757401\pi$
$24$	1.74235	+	0.721707i	0.355656	+	0.147318i
$25$		0			0
$26$	−0.388810	+	0.388810i	−0.0762520	+	0.0762520i
$27$	1.88791	−	4.55781i	0.363328	−	0.877151i
$28$	−8.78427	−	3.63856i	−1.66007	−	0.687624i
$29$	−3.22121	+	1.33427i	−0.598165	+	0.247768i	−0.661159	−	0.750246i	$-0.729935\pi$
$29$	−3.22121	+	1.33427i	−0.598165	+	0.247768i	0.0629942	+	0.998014i	$0.479935\pi$
$30$		0			0
$31$	2.23739	+	5.40154i	0.401847	+	0.970146i	0.987217	+	0.159379i	$0.0509493\pi$
$31$	2.23739	+	5.40154i	0.401847	+	0.970146i	−0.585370	+	0.810766i	$0.699051\pi$
$32$	2.14620	−	2.14620i	0.379399	−	0.379399i
$33$			7.09972i			1.23590i
$34$	1.08815	−	0.110307i	0.186616	−	0.0189175i
$35$		0			0
$36$	0.372752	+	0.372752i	0.0621254	+	0.0621254i
$37$	−1.88698	+	0.781612i	−0.310218	+	0.128496i	−0.532360	−	0.846518i	$-0.678695\pi$
$37$	−1.88698	+	0.781612i	−0.310218	+	0.128496i	0.222143	+	0.975014i	$0.428695\pi$
$38$	−0.783113			−0.127038
$39$	−3.46473	+	1.43514i	−0.554802	+	0.229806i
$40$		0			0
$41$	−10.9410	−	4.53193i	−1.70870	−	0.707768i	−0.999997	−	0.00226326i	$-0.999280\pi$
$41$	−10.9410	−	4.53193i	−1.70870	−	0.707768i	−0.708705	−	0.705505i	$-0.750720\pi$
$42$	1.67213	+	1.67213i	0.258015	+	0.258015i
$43$	3.91060	+	3.91060i	0.596361	+	0.596361i	0.939342	−	0.342981i	$-0.111437\pi$
$43$	3.91060	+	3.91060i	0.596361	+	0.596361i	−0.342981	+	0.939342i	$0.611437\pi$
$44$	6.99594	+	2.89781i	1.05468	+	0.436862i
$45$		0			0
$46$	0.949815	−	0.393426i	0.140043	−	0.0580075i
$47$	−0.453534			−0.0661547			−0.0330773	−	0.999453i	$-0.510531\pi$
$47$	−0.453534			−0.0661547			−0.0330773	+	0.999453i	$0.510531\pi$
$48$	5.98849	−	2.48051i	0.864364	−	0.358031i
$49$	−12.2181	−	12.2181i	−1.74544	−	1.74544i
$50$		0			0
$51$	7.14444	+	2.14502i	1.00042	+	0.300362i
$52$			3.99985i			0.554680i
$53$	4.60644	−	4.60644i	0.632743	−	0.632743i	−0.316012	−	0.948755i	$-0.602344\pi$
$53$	4.60644	−	4.60644i	0.632743	−	0.632743i	0.948755	+	0.316012i	$0.102344\pi$
$54$	0.500800	+	1.20904i	0.0681502	+	0.164529i
$55$		0			0
$56$	4.74533	−	1.96558i	0.634121	−	0.262662i
$57$	−4.93448	−	2.04393i	−0.653588	−	0.270725i
$58$	0.353938	−	0.854483i	0.0464744	−	0.112199i
$59$	−4.92683	+	4.92683i	−0.641418	+	0.641418i	−0.950904	−	0.309486i	$-0.899843\pi$
$59$	−4.92683	+	4.92683i	−0.641418	+	0.641418i	0.309486	+	0.950904i	$0.399843\pi$
$60$		0			0
$61$	−0.0429157	−	0.0177763i	−0.00549480	−	0.00227602i	0.379934	−	0.925013i	$-0.375947\pi$
$61$	−0.0429157	−	0.0177763i	−0.00549480	−	0.00227602i	−0.385429	+	0.922737i	$0.625947\pi$
$62$	−1.43285	−	0.593507i	−0.181972	−	0.0753754i
$63$	0.515129	+	1.24363i	0.0649001	+	0.156683i
$64$		−	6.36037i		−	0.795046i
$65$		0			0
$66$	−1.33171	−	1.33171i	−0.163922	−	0.163922i
$67$			10.0472i			1.22746i	0.789515	+	0.613731i	$0.210332\pi$
$67$			10.0472i			1.22746i	−0.789515	+	0.613731i	$0.789668\pi$
$68$	5.02973	−	6.16450i	0.609944	−	0.747556i
$69$	7.01174			0.844114
$70$		0			0
$71$	5.85587	+	14.1373i	0.694964	+	1.67779i	0.734531	+	0.678575i	$0.237402\pi$
$71$	5.85587	+	14.1373i	0.694964	+	1.67779i	−0.0395663	+	0.999217i	$0.512598\pi$
$72$	−0.284771			−0.0335606
$73$	3.36399	+	8.12139i	0.393725	+	0.950537i	0.989121	+	0.147105i	$0.0469954\pi$
$73$	3.36399	+	8.12139i	0.393725	+	0.950537i	−0.595396	+	0.803433i	$0.703005\pi$
$74$	0.207336	−	0.500554i	0.0241023	−	0.0581882i
$75$		0			0
$76$	−4.02810	+	4.02810i	−0.462055	+	0.462055i
$77$	13.6728	+	13.6728i	1.55816	+	1.55816i
$78$	0.380696	−	0.919080i	0.0431053	−	0.104065i
$79$	0.991282	−	2.39317i	0.111528	−	0.269252i	−0.858254	−	0.513225i	$-0.828451\pi$
$79$	0.991282	−	2.39317i	0.111528	−	0.269252i	0.969782	+	0.243973i	$0.0784507\pi$
$80$		0			0
$81$			9.74493i			1.08277i
$82$	2.90230	−	1.20217i	0.320505	−	0.132758i
$83$	−1.09508	+	1.09508i	−0.120201	+	0.120201i	−0.764649	−	0.644447i	$-0.777087\pi$
$83$	−1.09508	+	1.09508i	−0.120201	+	0.120201i	0.644447	+	0.764649i	$0.277087\pi$
$84$	17.2019			1.87688
$85$		0			0
$86$	−1.46704			−0.158195
$87$	4.46041	−	4.46041i	0.478206	−	0.478206i
$88$	−3.77926	+	1.56542i	−0.402871	+	0.166874i
$89$			10.2523i			1.08674i	0.839493	+	0.543370i	$0.182852\pi$
$89$			10.2523i			1.08674i	−0.839493	+	0.543370i	$0.817148\pi$
$90$		0			0
$91$	−3.90863	+	9.43626i	−0.409736	+	0.989189i
$92$	2.86190	−	6.90924i	0.298374	−	0.720338i
$93$	−7.47951	−	7.47951i	−0.775589	−	0.775589i
$94$	0.0850703	−	0.0850703i	0.00877434	−	0.00877434i
$95$		0			0
$96$	−2.10141	+	5.07326i	−0.214474	+	0.517787i
$97$	−4.07387	−	9.83519i	−0.413639	−	0.998612i	−0.984153	−	0.177324i	$-0.943256\pi$
$97$	−4.07387	−	9.83519i	−0.413639	−	0.998612i	0.570514	−	0.821288i	$-0.306744\pi$
$98$	4.58356			0.463009
$99$	−0.410257	−	0.990448i	−0.0412324	−	0.0995438i
$100$		0			0
$101$	9.59803			0.955040			0.477520	−	0.878621i	$-0.341536\pi$
$101$	9.59803			0.955040			0.477520	+	0.878621i	$0.341536\pi$
$102$	−1.74244	+	0.937754i	−0.172528	+	0.0928515i
$103$			0.147643i			0.0145477i	0.999974	+	0.00727384i	$0.00231536\pi$
$103$			0.147643i			0.0145477i	−0.999974	+	0.00727384i	$0.997685\pi$
$104$	−1.52788	−	1.52788i	−0.149821	−	0.149821i
$105$		0			0
$106$			1.72808i			0.167846i
$107$	2.40932	+	5.81660i	0.232917	+	0.562312i	0.996518	−	0.0833763i	$-0.0265704\pi$
$107$	2.40932	+	5.81660i	0.232917	+	0.562312i	−0.763601	+	0.645689i	$0.776570\pi$
$108$	8.79490	+	3.64297i	0.846290	+	0.350545i
$109$	−10.5342	−	4.36339i	−1.00899	−	0.417937i	−0.183904	−	0.982944i	$-0.558873\pi$
$109$	−10.5342	−	4.36339i	−1.00899	−	0.417937i	−0.825086	+	0.565007i	$0.808873\pi$
$110$		0			0
$111$	2.61290	−	2.61290i	0.248005	−	0.248005i
$112$	6.75572	−	16.3098i	0.638356	−	1.54113i
$113$	−5.92270	−	2.45326i	−0.557160	−	0.230783i	0.0862915	−	0.996270i	$-0.472498\pi$
$113$	−5.92270	−	2.45326i	−0.557160	−	0.230783i	−0.643452	+	0.765487i	$0.722498\pi$
$114$	1.30896	−	0.542187i	0.122595	−	0.0507805i
$115$		0			0
$116$	−2.57465	−	6.21576i	−0.239051	−	0.577119i
$117$	0.400419	−	0.400419i	0.0370188	−	0.0370188i
$118$		−	1.84827i		−	0.170147i
$119$	17.8898	−	9.62799i	1.63996	−	0.882596i
$120$		0			0
$121$	−3.11105	−	3.11105i	−0.282823	−	0.282823i
$122$	0.0113841	−	0.00471546i	0.00103067	−	0.000426918i
$123$	21.4254			1.93186
$124$	−10.4230	+	4.31735i	−0.936013	+	0.387709i
$125$		0			0
$126$	−0.329894	−	0.136647i	−0.0293893	−	0.0121735i
$127$	3.78861	+	3.78861i	0.336185	+	0.336185i	0.854929	−	0.518745i	$-0.173600\pi$
$127$	3.78861	+	3.78861i	0.336185	+	0.336185i	−0.518745	+	0.854929i	$0.673600\pi$
$128$	5.48544	+	5.48544i	0.484849	+	0.484849i
$129$	−9.24398	−	3.82898i	−0.813887	−	0.337123i
$130$		0			0
$131$	−12.9546	+	5.36598i	−1.13185	+	0.468827i	−0.868409	−	0.495848i	$-0.834857\pi$
$131$	−12.9546	+	5.36598i	−1.13185	+	0.468827i	−0.263440	+	0.964676i	$0.584857\pi$
$132$	−13.6999			−1.19242
$133$	−13.4391	+	5.56668i	−1.16532	+	0.482692i
$134$	−1.88458	−	1.88458i	−0.162803	−	0.162803i
$135$		0			0
$136$	0.433466	+	4.27602i	0.0371694	+	0.366666i
$137$		−	5.83746i		−	0.498728i	−0.968410	−	0.249364i	$-0.919778\pi$
$137$		−	5.83746i		−	0.498728i	0.968410	−	0.249364i	$-0.0802216\pi$
$138$	−1.31521	+	1.31521i	−0.111958	+	0.111958i
$139$	−5.82739	−	14.0686i	−0.494273	−	1.19328i	−0.952526	−	0.304459i	$-0.901524\pi$
$139$	−5.82739	−	14.0686i	−0.494273	−	1.19328i	0.458252	−	0.888822i	$-0.348476\pi$
$140$		0			0
$141$	0.758072	−	0.314004i	0.0638412	−	0.0264439i
$142$	−3.75017	−	1.55337i	−0.314707	−	0.130356i
$143$	3.11290	−	7.51520i	0.260314	−	0.628452i
$144$	−0.692089	+	0.692089i	−0.0576741	+	0.0576741i
$145$		0			0
$146$	−2.15434	−	0.892357i	−0.178294	−	0.0738520i
$147$	28.8815	+	11.9631i	2.38211	+	0.986701i
$148$	−1.50823	−	3.64118i	−0.123975	−	0.299303i
$149$			20.6226i			1.68947i	0.535188	+	0.844733i	$0.320241\pi$
$149$			20.6226i			1.68947i	−0.535188	+	0.844733i	$0.679759\pi$
$150$		0			0
$151$	−3.64333	−	3.64333i	−0.296490	−	0.296490i	0.543148	−	0.839637i	$-0.317232\pi$
$151$	−3.64333	−	3.64333i	−0.296490	−	0.296490i	−0.839637	+	0.543148i	$0.817232\pi$
$152$		−	3.07735i		−	0.249606i
$153$	−1.12064	+	0.113601i	−0.0905981	+	0.00918406i
$154$	−5.12926			−0.413328
$155$		0			0
$156$	−2.76929	−	6.68567i	−0.221721	−	0.535282i
$157$	−2.57467			−0.205481			−0.102741	−	0.994708i	$-0.532761\pi$
$157$	−2.57467			−0.205481			−0.102741	+	0.994708i	$0.532761\pi$
$158$	0.262955	+	0.634828i	0.0209195	+	0.0505042i
$159$	−4.51030	+	10.8888i	−0.357690	+	0.863540i
$160$		0			0
$161$	13.5033	−	13.5033i	1.06421	−	1.06421i
$162$	−1.82788	−	1.82788i	−0.143612	−	0.143612i
$163$	−5.90686	+	14.2604i	−0.462661	+	1.11696i	0.504640	+	0.863330i	$0.331625\pi$
$163$	−5.90686	+	14.2604i	−0.462661	+	1.11696i	−0.967301	+	0.253632i	$0.918375\pi$
$164$	8.74495	−	21.1122i	0.682866	−	1.64858i
$165$		0			0
$166$		−	0.410815i		−	0.0318854i
$167$	−18.2229	+	7.54817i	−1.41013	+	0.584095i	−0.952360	−	0.304975i	$-0.901352\pi$
$167$	−18.2229	+	7.54817i	−1.41013	+	0.584095i	−0.457770	+	0.889070i	$0.651352\pi$
$168$	−6.57085	+	6.57085i	−0.506952	+	0.506952i
$169$	−8.70327			−0.669482
$170$		0			0
$171$	0.806495			0.0616742
$172$	−7.54602	+	7.54602i	−0.575379	+	0.575379i
$173$	−10.8573	+	4.49724i	−0.825466	+	0.341919i	−0.755106	−	0.655602i	$-0.772415\pi$
$173$	−10.8573	+	4.49724i	−0.825466	+	0.341919i	−0.0703598	+	0.997522i	$0.522415\pi$
$174$			1.67330i			0.126852i
$175$		0			0
$176$	−5.38037	+	12.9894i	−0.405561	+	0.979110i
$177$	4.82400	−	11.6462i	0.362594	−	0.875380i
$178$	−1.92304	−	1.92304i	−0.144138	−	0.144138i
$179$	−5.77603	+	5.77603i	−0.431721	+	0.431721i	−0.889213	−	0.457493i	$-0.848748\pi$
$179$	−5.77603	+	5.77603i	−0.431721	+	0.431721i	0.457493	+	0.889213i	$0.348748\pi$
$180$		0			0
$181$	3.88138	−	9.37049i	0.288501	−	0.696503i	−0.711480	−	0.702707i	$-0.751975\pi$
$181$	3.88138	−	9.37049i	0.288501	−	0.696503i	0.999981	+	0.00620363i	$0.00197469\pi$
$182$	−1.03683	−	2.50313i	−0.0768550	−	0.185544i
$183$	0.0840401			0.00621243
$184$	1.54602	+	3.73242i	0.113974	+	0.275158i
$185$		0			0
$186$	2.80589			0.205738
$187$	−14.2477	+	7.66789i	−1.04190	+	0.560732i
$188$		−	0.875154i		−	0.0638272i
$189$	17.1886	+	17.1886i	1.25029	+	1.25029i
$190$		0			0
$191$			13.6729i			0.989338i	0.869082	+	0.494669i	$0.164711\pi$
$191$			13.6729i			0.989338i	−0.869082	+	0.494669i	$0.835289\pi$
$192$	4.40359	+	10.6312i	0.317802	+	0.767242i
$193$	−1.38495	−	0.573664i	−0.0996906	−	0.0412932i	0.332281	−	0.943181i	$-0.392182\pi$
$193$	−1.38495	−	0.573664i	−0.0996906	−	0.0412932i	−0.431971	+	0.901887i	$0.642182\pi$
$194$	2.60895	+	1.08066i	0.187312	+	0.0775871i
$195$		0			0
$196$	23.5765	−	23.5765i	1.68403	−	1.68403i
$197$	3.84727	−	9.28813i	0.274107	−	0.661752i	−0.725544	−	0.688176i	$-0.758412\pi$
$197$	3.84727	−	9.28813i	0.274107	−	0.661752i	0.999651	+	0.0264236i	$0.00841187\pi$
$198$	0.262733	+	0.108828i	0.0186717	+	0.00773405i
$199$	4.76877	−	1.97529i	0.338049	−	0.140024i	−0.207200	−	0.978299i	$-0.566435\pi$
$199$	4.76877	−	1.97529i	0.338049	−	0.140024i	0.545249	+	0.838274i	$0.316435\pi$
$200$		0			0
$201$	−6.95618	−	16.7937i	−0.490651	−	1.18454i
$202$	−1.80032	+	1.80032i	−0.126670	+	0.126670i
$203$		−	17.1799i		−	1.20579i
$204$	−4.13909	+	13.7862i	−0.289795	+	0.965224i
$205$		0			0
$206$	−0.0276937	−	0.0276937i	−0.00192951	−	0.00192951i
$207$	−0.978174	+	0.405173i	−0.0679878	+	0.0281615i
$208$	−7.42653			−0.514937
$209$	10.7032	−	4.43340i	0.740353	−	0.306664i
$210$		0			0
$211$	19.3231	+	8.00388i	1.33026	+	0.551010i	0.930728	−	0.365712i	$-0.119174\pi$
$211$	19.3231	+	8.00388i	1.33026	+	0.551010i	0.399527	+	0.916721i	$0.369174\pi$
$212$	8.88874	+	8.88874i	0.610481	+	0.610481i
$213$	−19.5759	−	19.5759i	−1.34132	−	1.34132i
$214$	−1.54295	−	0.639113i	−0.105474	−	0.0436888i
$215$		0			0
$216$	−4.75107	+	1.96796i	−0.323270	+	0.133903i
$217$	−28.8083			−1.95564
$218$	2.79437	−	1.15746i	0.189258	−	0.0783934i
$219$	−11.2457	−	11.2457i	−0.759913	−	0.759913i
$220$		0			0
$221$	−6.62205	−	5.40305i	−0.445447	−	0.363448i
$222$			0.980214i			0.0657876i
$223$	15.1525	−	15.1525i	1.01468	−	1.01468i	0.0147944	−	0.999891i	$-0.495291\pi$
$223$	15.1525	−	15.1525i	1.01468	−	1.01468i	0.999891	−	0.0147944i	$-0.00470939\pi$
$224$	5.72323	+	13.8171i	0.382399	+	0.923194i
$225$		0			0
$226$	1.57110	−	0.650770i	0.104508	−	0.0432886i
$227$	−24.6868	−	10.2256i	−1.63852	−	0.678697i	−0.642372	−	0.766393i	$-0.722050\pi$
$227$	−24.6868	−	10.2256i	−1.63852	−	0.678697i	−0.996147	+	0.0876956i	$0.972050\pi$
$228$	3.94403	−	9.52174i	0.261200	−	0.630593i
$229$	4.38424	−	4.38424i	0.289719	−	0.289719i	−0.547250	−	0.836969i	$-0.684325\pi$
$229$	4.38424	−	4.38424i	0.289719	−	0.289719i	0.836969	+	0.547250i	$0.184325\pi$
$230$		0			0
$231$	−32.3201	−	13.3874i	−2.12650	−	0.880827i
$232$	3.35780	+	1.39085i	0.220451	+	0.0913136i
$233$	9.14665	+	22.0820i	0.599217	+	1.44664i	0.874381	+	0.485241i	$0.161268\pi$
$233$	9.14665	+	22.0820i	0.599217	+	1.44664i	−0.275164	+	0.961397i	$0.588732\pi$
$234$			0.150215i			0.00981986i
$235$		0			0
$236$	−9.50697	−	9.50697i	−0.618851	−	0.618851i
$237$			4.68644i			0.304417i
$238$	−1.54969	+	5.16157i	−0.100451	+	0.334575i
$239$	14.3945			0.931105			0.465552	−	0.885020i	$-0.345856\pi$
$239$	14.3945			0.931105			0.465552	+	0.885020i	$0.345856\pi$
$240$		0			0
$241$	−0.580797	−	1.40217i	−0.0374124	−	0.0903215i	0.904069	−	0.427387i	$-0.140566\pi$
$241$	−0.580797	−	1.40217i	−0.0374124	−	0.0903215i	−0.941481	+	0.337065i	$0.890566\pi$
$242$	1.16709			0.0750236
$243$	−1.08318	−	2.61502i	−0.0694857	−	0.167753i
$244$	0.0343017	−	0.0828116i	0.00219594	−	0.00530147i
$245$		0			0
$246$	−4.01881	+	4.01881i	−0.256230	+	0.256230i
$247$	4.32708	+	4.32708i	0.275326	+	0.275326i
$248$	2.33226	−	5.63058i	0.148099	−	0.357542i
$249$	1.07223	−	2.58859i	0.0679498	−	0.164045i
$250$		0			0
$251$		−	28.3303i		−	1.78819i	−0.447874	−	0.894097i	$-0.647819\pi$
$251$		−	28.3303i		−	1.78819i	0.447874	−	0.894097i	$-0.352181\pi$
$252$	−2.39975	+	0.994010i	−0.151170	+	0.0626167i
$253$	−10.7543	+	10.7543i	−0.676115	+	0.676115i
$254$	−1.42128			−0.0891788
$255$		0			0
$256$	10.6629			0.666431
$257$	−5.96067	+	5.96067i	−0.371816	+	0.371816i	−0.868138	−	0.496322i	$-0.834684\pi$
$257$	−5.96067	+	5.96067i	−0.371816	+	0.371816i	0.496322	+	0.868138i	$0.334684\pi$
$258$	2.45212	−	1.01570i	0.152663	−	0.0632349i
$259$		−	10.0639i		−	0.625342i
$260$		0			0
$261$	−0.364506	+	0.879995i	−0.0225623	+	0.0544703i
$262$	1.42342	−	3.43643i	0.0879390	−	0.212304i
$263$	16.7208	+	16.7208i	1.03105	+	1.03105i	0.999502	+	0.0315459i	$0.0100431\pi$
$263$	16.7208	+	16.7208i	1.03105	+	1.03105i	0.0315459	+	0.999502i	$0.489957\pi$
$264$	5.23313	−	5.23313i	0.322077	−	0.322077i
$265$		0			0
$266$	1.47666	−	3.56496i	0.0905396	−	0.218582i
$267$	−7.09816	−	17.1365i	−0.434400	−	1.04873i
$268$	−19.3874			−1.18428
$269$	−0.398793	−	0.962770i	−0.0243148	−	0.0587011i	0.911256	−	0.411841i	$-0.135114\pi$
$269$	−0.398793	−	0.962770i	−0.0243148	−	0.0587011i	−0.935571	+	0.353140i	$0.885114\pi$
$270$		0			0
$271$	20.0622			1.21869			0.609345	−	0.792905i	$-0.291432\pi$
$271$	20.0622			1.21869			0.609345	+	0.792905i	$0.291432\pi$
$272$	11.4456	+	9.33870i	0.693994	+	0.566242i
$273$		−	18.4786i		−	1.11838i
$274$	1.09495	+	1.09495i	0.0661481	+	0.0661481i
$275$		0			0
$276$			13.5301i			0.814415i
$277$	3.30605	+	7.98151i	0.198641	+	0.479563i	0.991542	−	0.129789i	$-0.0414299\pi$
$277$	3.30605	+	7.98151i	0.198641	+	0.479563i	−0.792900	+	0.609351i	$0.791430\pi$
$278$	3.73193	+	1.54582i	0.223826	+	0.0927119i
$279$	1.47563	+	0.611227i	0.0883438	+	0.0365932i
$280$		0			0
$281$	4.46534	−	4.46534i	0.266380	−	0.266380i	−0.561260	−	0.827640i	$-0.689683\pi$
$281$	4.46534	−	4.46534i	0.266380	−	0.266380i	0.827640	+	0.561260i	$0.189683\pi$
$282$	−0.0832949	+	0.201092i	−0.00496014	+	0.0119748i
$283$	−1.73799	−	0.719900i	−0.103313	−	0.0427936i	0.330428	−	0.943831i	$-0.392807\pi$
$283$	−1.73799	−	0.719900i	−0.103313	−	0.0427936i	−0.433741	+	0.901037i	$0.642807\pi$
$284$	−27.2799	+	11.2997i	−1.61876	+	0.670513i
$285$		0			0
$286$	0.825749	+	1.99354i	0.0488276	+	0.117880i
$287$	41.2614	−	41.2614i	2.43558	−	2.43558i
$288$		−	0.829176i		−	0.0488597i
$289$	3.41157	+	16.6542i	0.200681	+	0.979657i
$290$		0			0
$291$	13.6188	+	13.6188i	0.798346	+	0.798346i
$292$	−15.6713	+	6.49127i	−0.917094	+	0.379873i
$293$	−1.89223			−0.110545			−0.0552726	−	0.998471i	$-0.517603\pi$
$293$	−1.89223			−0.110545			−0.0552726	+	0.998471i	$0.517603\pi$
$294$	−7.66131	+	3.17342i	−0.446817	+	0.185078i
$295$		0			0
$296$	1.96699	+	0.814755i	0.114329	+	0.0473567i
$297$	−13.6893	−	13.6893i	−0.794335	−	0.794335i
$298$	−3.86822	−	3.86822i	−0.224080	−	0.224080i
$299$	−7.42206	−	3.07432i	−0.429229	−	0.177792i
$300$		0			0
$301$	−25.1761	+	10.4283i	−1.45113	+	0.601077i
$302$	1.36677			0.0786490
$303$	−16.0429	+	6.64519i	−0.921641	+	0.381756i
$304$	−7.47898	−	7.47898i	−0.428949	−	0.428949i
$305$		0			0
$306$	0.188892	−	0.231509i	0.0107982	−	0.0132345i
$307$			18.5816i			1.06051i	0.847838	+	0.530255i	$0.177904\pi$
$307$			18.5816i			1.06051i	−0.847838	+	0.530255i	$0.822096\pi$
$308$	−26.3834	+	26.3834i	−1.50334	+	1.50334i
$309$	−0.102220	−	0.246782i	−0.00581511	−	0.0140389i
$310$		0			0
$311$	−14.7175	+	6.09618i	−0.834552	+	0.345683i	−0.758703	−	0.651436i	$-0.774167\pi$
$311$	−14.7175	+	6.09618i	−0.834552	+	0.345683i	−0.0758491	+	0.997119i	$0.524167\pi$
$312$	3.61165	+	1.49599i	0.204469	+	0.0846940i
$313$	−12.1296	+	29.2835i	−0.685608	+	1.65520i	0.0678401	+	0.997696i	$0.478389\pi$
$313$	−12.1296	+	29.2835i	−0.685608	+	1.65520i	−0.753448	+	0.657508i	$0.771611\pi$
$314$	0.482937	−	0.482937i	0.0272537	−	0.0272537i
$315$		0			0
$316$	4.61793	+	1.91281i	0.259779	+	0.107604i
$317$	4.62307	+	1.91494i	0.259658	+	0.107554i	0.508715	−	0.860935i	$-0.330121\pi$
$317$	4.62307	+	1.91494i	0.259658	+	0.107554i	−0.249057	+	0.968489i	$0.580121\pi$
$318$	−1.19643	−	2.88845i	−0.0670927	−	0.161976i
$319$			13.6823i			0.766064i
$320$		0			0
$321$	−8.05424	−	8.05424i	−0.449544	−	0.449544i
$322$			5.06570i			0.282300i
$323$	−1.22761	−	12.1100i	−0.0683061	−	0.673820i
$324$	−18.8041			−1.04467
$325$		0			0
$326$	−1.56690	−	3.78282i	−0.0867823	−	0.209511i
$327$	20.6286			1.14076
$328$	4.72409	+	11.4050i	0.260844	+	0.629734i
$329$	0.855194	−	2.06462i	0.0471484	−	0.113826i
$330$		0			0
$331$	−7.16008	+	7.16008i	−0.393553	+	0.393553i	−0.875952	−	0.482398i	$-0.839766\pi$
$331$	−7.16008	+	7.16008i	−0.393553	+	0.393553i	0.482398	+	0.875952i	$0.339766\pi$
$332$	−2.11311	−	2.11311i	−0.115972	−	0.115972i
$333$	−0.213527	+	0.515499i	−0.0117012	+	0.0282492i
$334$	2.00228	−	4.83394i	0.109560	−	0.264501i
$335$		0			0
$336$			31.9387i			1.74240i
$337$	14.8146	−	6.13639i	0.807000	−	0.334271i	0.0592439	−	0.998244i	$-0.481131\pi$
$337$	14.8146	−	6.13639i	0.807000	−	0.334271i	0.747757	+	0.663973i	$0.231131\pi$
$338$	1.63249	−	1.63249i	0.0887958	−	0.0887958i
$339$	11.5982			0.629926
$340$		0			0
$341$	22.9434			1.24246
$342$	−0.151276	+	0.151276i	−0.00818007	+	0.00818007i
$343$	46.7932	−	19.3824i	2.52659	−	1.04655i
$344$		−	5.76493i		−	0.310824i
$345$		0			0
$346$	1.19297	−	2.88009i	0.0641345	−	0.154834i
$347$	5.43890	−	13.1307i	0.291976	−	0.704891i	−0.708024	−	0.706189i	$-0.750413\pi$
$347$	5.43890	−	13.1307i	0.291976	−	0.704891i	0.999999	+	0.00129748i	$0.000413002\pi$
$348$	8.60696	+	8.60696i	0.461381	+	0.461381i
$349$	17.3032	−	17.3032i	0.926221	−	0.926221i	−0.0712379	−	0.997459i	$-0.522695\pi$
$349$	17.3032	−	17.3032i	0.926221	−	0.926221i	0.997459	+	0.0712379i	$0.0226950\pi$
$350$		0			0
$351$	3.91336	−	9.44768i	0.208880	−	0.504280i
$352$	−4.55808	−	11.0042i	−0.242946	−	0.586524i
$353$	25.3622			1.34989			0.674947	−	0.737866i	$-0.264166\pi$
$353$	25.3622			1.34989			0.674947	+	0.737866i	$0.264166\pi$
$354$	1.27965	+	3.08935i	0.0680126	+	0.164197i
$355$		0			0
$356$	−19.7831			−1.04850
$357$	−23.2365	+	28.4790i	−1.22981	+	1.50727i
$358$		−	2.16685i		−	0.114521i
$359$	−18.7611	−	18.7611i	−0.990171	−	0.990171i	0.00978160	−	0.999952i	$-0.496886\pi$
$359$	−18.7611	−	18.7611i	−0.990171	−	0.990171i	−0.999952	+	0.00978160i	$0.996886\pi$
$360$		0			0
$361$		−	10.2847i		−	0.541301i
$362$	1.02960	+	2.48568i	0.0541148	+	0.130645i
$363$	7.35398	+	3.04612i	0.385984	+	0.159880i
$364$	−18.2085	−	7.54222i	−0.954386	−	0.395320i
$365$		0			0
$366$	−0.0157636	+	0.0157636i	−0.000823976	+	0.000823976i
$367$	1.43961	−	3.47553i	0.0751471	−	0.181421i	−0.881842	−	0.471545i	$-0.843697\pi$
$367$	1.43961	−	3.47553i	0.0751471	−	0.181421i	0.956989	+	0.290124i	$0.0936965\pi$
$368$	12.8284	+	5.31369i	0.668726	+	0.276995i
$369$	−2.98895	+	1.23806i	−0.155599	+	0.0644511i
$370$		0			0
$371$	12.2839	+	29.6559i	0.637747	+	1.53966i
$372$	14.4327	−	14.4327i	0.748301	−	0.748301i
$373$		−	10.8498i		−	0.561779i	−0.959740	−	0.280890i	$-0.909370\pi$
$373$		−	10.8498i		−	0.561779i	0.959740	−	0.280890i	$-0.0906295\pi$
$374$	1.23420	−	4.11076i	0.0638188	−	0.212563i
$375$		0			0
$376$	0.334295	+	0.334295i	0.0172400	+	0.0172400i
$377$	−6.67711	+	2.76575i	−0.343889	+	0.142443i
$378$	−6.44822			−0.331661
$379$	27.7148	−	11.4798i	1.42361	−	0.589680i	0.467848	−	0.883809i	$-0.345030\pi$
$379$	27.7148	−	11.4798i	1.42361	−	0.589680i	0.955766	+	0.294129i	$0.0950295\pi$
$380$		0			0
$381$	−8.95562	−	3.70954i	−0.458810	−	0.190045i
$382$	−2.56466	−	2.56466i	−0.131219	−	0.131219i
$383$	−9.57167	−	9.57167i	−0.489089	−	0.489089i	0.418929	−	0.908019i	$-0.362405\pi$
$383$	−9.57167	−	9.57167i	−0.489089	−	0.489089i	−0.908019	+	0.418929i	$0.862405\pi$
$384$	−12.9666	−	5.37095i	−0.661700	−	0.274085i
$385$		0			0
$386$	0.367381	−	0.152174i	0.0186992	−	0.00774546i
$387$	1.51084			0.0768004
$388$	18.9783	−	7.86107i	0.963477	−	0.399085i
$389$	14.5777	+	14.5777i	0.739120	+	0.739120i	0.972408	−	0.233288i	$-0.0749485\pi$
$389$	14.5777	+	14.5777i	0.739120	+	0.739120i	−0.233288	+	0.972408i	$0.574948\pi$
$390$		0			0
$391$	7.57286	+	14.0712i	0.382976	+	0.711610i
$392$			18.0117i			0.909728i
$393$	17.9382	−	17.9382i	0.904864	−	0.904864i
$394$	1.02055	+	2.46384i	0.0514148	+	0.124126i
$395$		0			0
$396$	1.91120	−	0.791646i	0.0960415	−	0.0397817i
$397$	11.8052	+	4.88987i	0.592486	+	0.245416i	0.658720	−	0.752389i	$-0.271098\pi$
$397$	11.8052	+	4.88987i	0.592486	+	0.245416i	−0.0662339	+	0.997804i	$0.521098\pi$
$398$	−0.523979	+	1.26500i	−0.0262647	+	0.0634086i
$399$	18.6092	−	18.6092i	0.931623	−	0.931623i
$400$		0			0
$401$	−0.000809576	0	0.000335338i	−4.04283e−5	0	1.67460e-5i	0.382663	−	0.923888i	$-0.375007\pi$
$401$	−0.000809576	0	0.000335338i	−4.04283e−5	0	1.67460e-5i	−0.382704	+	0.923871i	$0.625007\pi$
$402$	4.45482	+	1.84525i	0.222186	+	0.0920325i
$403$	4.63779	+	11.1966i	0.231025	+	0.557743i
$404$			18.5207i			0.921438i
$405$		0			0
$406$	3.22247	+	3.22247i	0.159928	+	0.159928i
$407$			8.01508i			0.397293i
$408$	−3.68503	−	6.84717i	−0.182436	−	0.338985i
$409$	18.8814			0.933624			0.466812	−	0.884357i	$-0.345402\pi$
$409$	18.8814			0.933624			0.466812	+	0.884357i	$0.345402\pi$
$410$		0			0
$411$	4.04156	+	9.75719i	0.199355	+	0.481287i
$412$	−0.284896			−0.0140358
$413$	−13.1382	−	31.7185i	−0.646491	−	1.56077i
$414$	0.107479	−	0.259477i	0.00528231	−	0.0127526i
$415$		0			0
$416$	4.44877	−	4.44877i	0.218119	−	0.218119i
$417$	19.4807	+	19.4807i	0.953975	+	0.953975i
$418$	−1.17603	+	2.83920i	−0.0575217	+	0.138870i
$419$	3.53356	−	8.53078i	0.172626	−	0.416756i	−0.813760	−	0.581200i	$-0.802583\pi$
$419$	3.53356	−	8.53078i	0.172626	−	0.416756i	0.986386	+	0.164445i	$0.0525832\pi$
$420$		0			0
$421$			34.9204i			1.70192i	0.525232	+	0.850959i	$0.323979\pi$
$421$			34.9204i			1.70192i	−0.525232	+	0.850959i	$0.676021\pi$
$422$	−5.12578	+	2.12317i	−0.249519	+	0.103354i
$423$	−0.0876103	+	0.0876103i	−0.00425976	+	0.00425976i
$424$	−6.79072			−0.329787
$425$		0			0
$426$	7.34380			0.355808
$427$	0.161846	−	0.161846i	0.00783227	−	0.00783227i
$428$	−11.2239	+	4.64910i	−0.542528	+	0.224723i
$429$			14.7167i			0.710529i
$430$		0			0
$431$	−2.87069	+	6.93046i	−0.138276	+	0.333829i	−0.977815	−	0.209472i	$-0.932826\pi$
$431$	−2.87069	+	6.93046i	−0.138276	+	0.333829i	0.839538	+	0.543300i	$0.182826\pi$
$432$	−6.76390	+	16.3295i	−0.325428	+	0.785653i
$433$	−15.7011	−	15.7011i	−0.754548	−	0.754548i	0.220777	−	0.975324i	$-0.429141\pi$
$433$	−15.7011	−	15.7011i	−0.754548	−	0.754548i	−0.975324	+	0.220777i	$0.929141\pi$
$434$	5.40364	−	5.40364i	0.259383	−	0.259383i
$435$		0			0
$436$	8.41975	−	20.3271i	0.403233	−	0.973490i
$437$	−4.37845	−	10.5705i	−0.209450	−	0.505657i
$438$	4.21875			0.201580
$439$	6.43977	+	15.5470i	0.307353	+	0.742017i	0.999789	+	0.0205370i	$0.00653760\pi$
$439$	6.43977	+	15.5470i	0.307353	+	0.742017i	−0.692436	+	0.721480i	$0.743462\pi$
$440$		0			0
$441$	−4.72041			−0.224781
$442$	2.25557	−	0.228651i	0.107287	−	0.0108758i
$443$			20.2349i			0.961391i	0.876888	+	0.480696i	$0.159616\pi$
$443$			20.2349i			0.961391i	−0.876888	+	0.480696i	$0.840384\pi$
$444$	5.04193	+	5.04193i	0.239280	+	0.239280i
$445$		0			0
$446$			5.68437i			0.269163i
$447$	−14.2780	−	34.4702i	−0.675327	−	1.63038i
$448$	28.9543	+	11.9933i	1.36796	+	0.566628i
$449$	26.7110	+	11.0641i	1.26057	+	0.522145i	0.910084	−	0.414423i	$-0.136017\pi$
$449$	26.7110	+	11.0641i	1.26057	+	0.522145i	0.350485	+	0.936568i	$0.386017\pi$
$450$		0			0
$451$	−32.8612	+	32.8612i	−1.54738	+	1.54738i
$452$	4.73389	−	11.4286i	0.222664	−	0.537558i
$453$	8.61219	+	3.56729i	0.404636	+	0.167606i
$454$	6.54859	−	2.71252i	0.307341	−	0.127305i
$455$		0			0
$456$	2.13060	+	5.14372i	0.0997744	+	0.240877i
$457$	12.1223	−	12.1223i	0.567055	−	0.567055i	−0.364247	−	0.931302i	$-0.618674\pi$
$457$	12.1223	−	12.1223i	0.567055	−	0.567055i	0.931302	+	0.364247i	$0.118674\pi$
$458$			1.64472i			0.0768529i
$459$	−17.9115	+	9.63964i	−0.836035	+	0.449940i
$460$		0			0
$461$	4.21017	+	4.21017i	0.196087	+	0.196087i	0.798320	−	0.602233i	$-0.205722\pi$
$461$	4.21017	+	4.21017i	0.196087	+	0.196087i	−0.602233	+	0.798320i	$0.705722\pi$
$462$	8.57345	−	3.55124i	0.398873	−	0.165219i
$463$	−30.6161			−1.42285			−0.711425	−	0.702762i	$-0.751950\pi$
$463$	−30.6161			−1.42285			−0.711425	+	0.702762i	$0.751950\pi$
$464$	11.5408	−	4.78036i	0.535769	−	0.221923i
$465$		0			0
$466$	−5.85762	−	2.42631i	−0.271349	−	0.112396i
$467$	17.6583	+	17.6583i	0.817131	+	0.817131i	0.985691	−	0.168560i	$-0.0539118\pi$
$467$	17.6583	+	17.6583i	0.817131	+	0.817131i	−0.168560	+	0.985691i	$0.553912\pi$
$468$	0.772662	+	0.772662i	0.0357163	+	0.0357163i
$469$	−45.7379	−	18.9453i	−2.11198	−	0.874811i
$470$		0			0
$471$	4.30351	−	1.78257i	0.198295	−	0.0821366i
$472$	7.26303			0.334308
$473$	20.0507	−	8.30527i	0.921932	−	0.381877i
$474$	−0.879046	−	0.879046i	−0.0403759	−	0.0403759i
$475$		0			0
$476$	18.5785	+	34.5208i	0.851543	+	1.58226i
$477$		−	1.77968i		−	0.0814858i
$478$	−2.70001	+	2.70001i	−0.123496	+	0.123496i
$479$	0.587320	+	1.41792i	0.0268353	+	0.0647862i	0.936729	−	0.350055i	$-0.113837\pi$
$479$	0.587320	+	1.41792i	0.0268353	+	0.0647862i	−0.909894	+	0.414841i	$0.863837\pi$
$480$		0			0
$481$	−3.91144	+	1.62017i	−0.178346	+	0.0738734i
$482$	0.371949	+	0.154066i	0.0169418	+	0.00701753i
$483$	−13.2215	+	31.9195i	−0.601599	+	1.45239i
$484$	6.00318	−	6.00318i	0.272872	−	0.272872i
$485$		0			0
$486$	0.693678	+	0.287331i	0.0314659	+	0.0130336i
$487$	20.4082	+	8.45334i	0.924782	+	0.383057i	0.793697	−	0.608314i	$-0.208154\pi$
$487$	20.4082	+	8.45334i	0.924782	+	0.383057i	0.131085	+	0.991371i	$0.458154\pi$
$488$	0.0185300	+	0.0447355i	0.000838816	+	0.00202508i
$489$		−	27.9256i		−	1.26284i
$490$		0			0
$491$	−4.34204	−	4.34204i	−0.195953	−	0.195953i	0.602309	−	0.798263i	$-0.294247\pi$
$491$	−4.34204	−	4.34204i	−0.195953	−	0.195953i	−0.798263	+	0.602309i	$0.794247\pi$
$492$			41.3431i			1.86389i
$493$	13.7685	+	4.13380i	0.620103	+	0.186177i
$494$	−1.62328			−0.0730348
$495$		0			0
$496$	−8.01602	−	19.3524i	−0.359930	−	0.868948i
$497$	−75.3993			−3.38212
$498$	0.284427	+	0.686668i	0.0127455	+	0.0307703i
$499$	−12.7057	+	30.6744i	−0.568787	+	1.37317i	0.333792	+	0.942647i	$0.391672\pi$
$499$	−12.7057	+	30.6744i	−0.568787	+	1.37317i	−0.902578	+	0.430526i	$0.858328\pi$
$500$		0			0
$501$	25.2332	−	25.2332i	1.12734	−	1.12734i
$502$	5.31398	+	5.31398i	0.237174	+	0.237174i
$503$	6.96489	−	16.8147i	0.310549	−	0.749732i	−0.689136	−	0.724632i	$-0.742010\pi$
$503$	6.96489	−	16.8147i	0.310549	−	0.749732i	0.999685	−	0.0250995i	$-0.00799026\pi$
$504$	0.536972	−	1.29636i	0.0239186	−	0.0577446i
$505$		0			0
$506$		−	4.03441i		−	0.179351i
$507$	14.5473	−	6.02570i	0.646069	−	0.267611i
$508$	−7.31063	+	7.31063i	−0.324357	+	0.324357i
$509$	−11.9447			−0.529440			−0.264720	−	0.964325i	$-0.585279\pi$
$509$	−11.9447			−0.529440			−0.264720	+	0.964325i	$0.585279\pi$
$510$		0			0
$511$	−43.3142			−1.91611
$512$	−12.9709	+	12.9709i	−0.573240	+	0.573240i
$513$	13.4554	−	5.57341i	0.594071	−	0.246072i
$514$		−	2.23611i		−	0.0986307i
$515$		0			0
$516$	7.38853	−	17.8375i	0.325262	−	0.785252i
$517$	−0.681091	+	1.64430i	−0.0299544	+	0.0723162i
$518$	1.88771	+	1.88771i	0.0829413	+	0.0829413i
$519$	15.0341	−	15.0341i	0.659924	−	0.659924i
$520$		0			0
$521$	12.8513	−	31.0257i	0.563024	−	1.35926i	−0.344313	−	0.938855i	$-0.611888\pi$
$521$	12.8513	−	31.0257i	0.563024	−	1.35926i	0.907337	−	0.420404i	$-0.138112\pi$
$522$	−0.0966915	−	0.233434i	−0.00423207	−	0.0102171i
$523$	2.18257			0.0954369			0.0477185	−	0.998861i	$-0.484805\pi$
$523$	2.18257			0.0954369			0.0477185	+	0.998861i	$0.484805\pi$
$524$	−10.3544	−	24.9976i	−0.452333	−	1.09203i
$525$		0			0
$526$	−6.27271			−0.273503
$527$	6.93182	−	23.0880i	0.301955	−	1.00573i
$528$		−	25.4365i		−	1.10698i
$529$	−5.64246	−	5.64246i	−0.245324	−	0.245324i
$530$		0			0
$531$			1.90346i			0.0826030i
$532$	−10.7416	−	25.9326i	−0.465709	−	1.12432i
$533$	−22.6792	−	9.39403i	−0.982345	−	0.406901i
$534$	4.54574	+	1.88291i	0.196714	+	0.0814814i
$535$		0			0
$536$	7.40570	−	7.40570i	0.319877	−	0.319877i
$537$	5.65548	−	13.6535i	0.244052	−	0.589194i
$538$	0.255391	+	0.105787i	0.0110107	+	0.00456078i
$539$	−62.6456	+	25.9486i	−2.69833	+	1.11769i
$540$		0			0
$541$	−4.78201	−	11.5448i	−0.205595	−	0.496350i	0.787125	−	0.616793i	$-0.211568\pi$
$541$	−4.78201	−	11.5448i	−0.205595	−	0.496350i	−0.992720	+	0.120443i	$0.961568\pi$
$542$	−3.76311	+	3.76311i	−0.161639	+	0.161639i
$543$			18.3498i			0.787467i
$544$	−12.4506	+	1.26214i	−0.533815	+	0.0541136i
$545$		0			0
$546$	3.46608	+	3.46608i	0.148335	+	0.148335i
$547$	33.8409	−	14.0173i	1.44693	−	0.599338i	0.485463	−	0.874257i	$-0.338651\pi$
$547$	33.8409	−	14.0173i	1.44693	−	0.599338i	0.961468	+	0.274919i	$0.0886509\pi$
$548$	11.2642			0.481181
$549$	−0.0117240	+	0.00485626i	−0.000500370	+	0.000207260i
$550$		0			0
$551$	−9.50956	−	3.93899i	−0.405121	−	0.167807i
$552$	−5.16828	−	5.16828i	−0.219977	−	0.219977i
$553$	9.02522	+	9.02522i	0.383792	+	0.383792i
$554$	−2.11723	−	0.876987i	−0.0899526	−	0.0372596i
$555$		0			0
$556$	27.1472	−	11.2447i	1.15130	−	0.476883i
$557$	−10.2425			−0.433990			−0.216995	−	0.976173i	$-0.569626\pi$
$557$	−10.2425			−0.433990			−0.216995	+	0.976173i	$0.569626\pi$
$558$	−0.391437	+	0.162139i	−0.0165708	+	0.00686387i
$559$	8.10611	+	8.10611i	0.342852	+	0.342852i
$560$		0			0
$561$	18.5059	−	22.6811i	0.781321	−	0.957598i
$562$			1.67515i			0.0706619i
$563$	−25.6813	+	25.6813i	−1.08234	+	1.08234i	−0.0860471	+	0.996291i	$0.527424\pi$
$563$	−25.6813	+	25.6813i	−1.08234	+	1.08234i	−0.996291	+	0.0860471i	$0.972576\pi$
$564$	0.605912	+	1.46280i	0.0255135	+	0.0615950i
$565$		0			0
$566$	0.461032	−	0.190966i	0.0193786	−	0.00802689i
$567$	−44.3618	−	18.3753i	−1.86302	−	0.771689i
$568$	6.10418	−	14.7368i	0.256126	−	0.618342i
$569$	9.63858	−	9.63858i	0.404070	−	0.404070i	−0.475594	−	0.879665i	$-0.657767\pi$
$569$	9.63858	−	9.63858i	0.404070	−	0.404070i	0.879665	+	0.475594i	$0.157767\pi$
$570$		0			0
$571$	−19.4934	−	8.07442i	−0.815773	−	0.337904i	−0.0645180	−	0.997917i	$-0.520551\pi$
$571$	−19.4934	−	8.07442i	−0.815773	−	0.337904i	−0.751255	+	0.660012i	$0.770551\pi$
$572$	14.5016	+	6.00675i	0.606341	+	0.251155i
$573$	−9.46643	−	22.8540i	−0.395466	−	0.954739i
$574$			15.4790i			0.646080i
$575$		0			0
$576$	−1.22865	−	1.22865i	−0.0511937	−	0.0511937i
$577$			1.55270i			0.0646399i	0.999478	+	0.0323200i	$0.0102896\pi$
$577$			1.55270i			0.0646399i	−0.999478	+	0.0323200i	$0.989710\pi$
$578$	−3.76377	−	2.48394i	−0.156552	−	0.103318i
$579$	2.71208			0.112710
$580$		0			0
$581$	−2.92023	−	7.05007i	−0.121152	−	0.292486i
$582$	−5.10900			−0.211775
$583$	−9.78309	−	23.6185i	−0.405174	−	0.978177i
$584$	3.50663	−	8.46576i	0.145106	−	0.350316i
$585$		0			0
$586$	0.354930	−	0.354930i	0.0146620	−	0.0146620i
$587$	12.2371	+	12.2371i	0.505079	+	0.505079i	0.913012	−	0.407933i	$-0.133750\pi$
$587$	12.2371	+	12.2371i	0.505079	+	0.505079i	−0.407933	+	0.913012i	$0.633750\pi$
$588$	−23.0844	+	55.7307i	−0.951985	+	2.29830i
$589$	−6.60515	+	15.9463i	−0.272161	+	0.657054i
$590$		0			0
$591$			18.1886i			0.748178i
$592$	6.76058	−	2.80032i	0.277858	−	0.115093i
$593$	0.590524	−	0.590524i	0.0242499	−	0.0242499i	−0.694878	−	0.719128i	$-0.744542\pi$
$593$	0.590524	−	0.590524i	0.0242499	−	0.0242499i	0.719128	+	0.694878i	$0.244542\pi$
$594$	5.13547			0.210711
$595$		0			0
$596$	−39.7940			−1.63003
$597$	−6.60330	+	6.60330i	−0.270255	+	0.270255i
$598$	1.96883	−	0.815516i	0.0805114	−	0.0333489i
$599$		−	14.4579i		−	0.590732i	−0.955384	−	0.295366i	$-0.904558\pi$
$599$		−	14.4579i		−	0.590732i	0.955384	−	0.295366i	$-0.0954416\pi$
$600$		0			0
$601$	−4.16494	+	10.0551i	−0.169891	+	0.410154i	−0.985777	−	0.168059i	$-0.946250\pi$
$601$	−4.16494	+	10.0551i	−0.169891	+	0.410154i	0.815885	+	0.578214i	$0.196250\pi$
$602$	2.76628	−	6.67840i	0.112745	−	0.272191i
$603$	1.94085	+	1.94085i	0.0790374	+	0.0790374i
$604$	7.03028	−	7.03028i	0.286058	−	0.286058i
$605$		0			0
$606$	1.76275	−	4.25566i	0.0716068	−	0.172874i
$607$	2.21384	+	5.34469i	0.0898571	+	0.216934i	0.962419	−	0.271570i	$-0.0875428\pi$
$607$	2.21384	+	5.34469i	0.0898571	+	0.216934i	−0.872562	+	0.488504i	$0.837543\pi$
$608$	8.96039			0.363392
$609$	11.8945	+	28.7158i	0.481988	+	1.16362i
$610$		0			0
$611$	−0.940110			−0.0380328
$612$	−0.219207	−	2.16242i	−0.00886093	−	0.0874106i
$613$			37.2383i			1.50404i	0.659139	+	0.752021i	$0.270921\pi$
$613$			37.2383i			1.50404i	−0.659139	+	0.752021i	$0.729079\pi$
$614$	−3.48540	−	3.48540i	−0.140659	−	0.140659i
$615$		0			0
$616$		−	20.1561i		−	0.812113i
$617$	8.97567	+	21.6692i	0.361347	+	0.872369i	0.995104	+	0.0988364i	$0.0315121\pi$
$617$	8.97567	+	21.6692i	0.361347	+	0.872369i	−0.633757	+	0.773532i	$0.718488\pi$
$618$	0.0654631	+	0.0271157i	0.00263331	+	0.00109075i
$619$	8.13185	+	3.36832i	0.326847	+	0.135384i	0.540072	−	0.841619i	$-0.318397\pi$
$619$	8.13185	+	3.36832i	0.326847	+	0.135384i	−0.213225	+	0.977003i	$0.568397\pi$
$620$		0			0
$621$	−13.5197	+	13.5197i	−0.542525	+	0.542525i
$622$	1.61712	−	3.90407i	0.0648405	−	0.156539i
$623$	−46.6715	−	19.3320i	−1.86985	−	0.774518i
$624$	12.4133	−	5.14175i	0.496929	−	0.205835i
$625$		0			0
$626$	−3.21760	−	7.76796i	−0.128601	−	0.310470i
$627$	−14.8206	+	14.8206i	−0.591880	+	0.591880i
$628$		−	4.96817i		−	0.198252i
$629$	8.06557	+	2.42157i	0.321595	+	0.0965543i
$630$		0			0
$631$	2.11407	+	2.11407i	0.0841597	+	0.0841597i	0.747933	−	0.663774i	$-0.231046\pi$
$631$	2.11407	+	2.11407i	0.0841597	+	0.0841597i	−0.663774	+	0.747933i	$0.731046\pi$
$632$	−2.49464	+	1.03331i	−0.0992316	+	0.0411031i
$633$	−37.8396			−1.50399
$634$	−1.22635	+	0.507970i	−0.0487045	+	0.0201741i
$635$		0			0
$636$	−21.0114	−	8.70323i	−0.833158	−	0.345105i
$637$	−25.3264	−	25.3264i	−1.00347	−	1.00347i
$638$	−2.56643	−	2.56643i	−0.101606	−	0.101606i
$639$	3.86214	+	1.59975i	0.152784	+	0.0632852i
$640$		0			0
$641$	0.688309	−	0.285107i	0.0271866	−	0.0112610i	−0.369049	−	0.929410i	$-0.620316\pi$
$641$	0.688309	−	0.285107i	0.0271866	−	0.0112610i	0.396235	+	0.918149i	$0.370316\pi$
$642$	3.02150			0.119249
$643$	−3.72024	+	1.54097i	−0.146712	+	0.0607700i	−0.454831	−	0.890578i	$-0.650300\pi$
$643$	−3.72024	+	1.54097i	−0.146712	+	0.0607700i	0.308119	+	0.951348i	$0.400300\pi$
$644$	26.0565	+	26.0565i	1.02677	+	1.02677i
$645$		0			0
$646$	2.50177	+	2.04124i	0.0984309	+	0.0803115i
$647$		−	18.7850i		−	0.738513i	−0.929328	−	0.369257i	$-0.879612\pi$
$647$		−	18.7850i		−	0.738513i	0.929328	−	0.369257i	$-0.120388\pi$
$648$	7.18289	−	7.18289i	0.282171	−	0.282171i
$649$	10.4635	+	25.2612i	0.410729	+	0.991588i
$650$		0			0
$651$	48.1525	−	19.9454i	1.88724	−	0.781722i
$652$	−27.5174	−	11.3981i	−1.07766	−	0.446383i
$653$	−8.02609	+	19.3767i	−0.314085	+	0.758268i	0.685460	+	0.728110i	$0.259601\pi$
$653$	−8.02609	+	19.3767i	−0.314085	+	0.758268i	−0.999545	+	0.0301582i	$0.990399\pi$
$654$	−3.86936	+	3.86936i	−0.151304	+	0.151304i
$655$		0			0
$656$	39.1990	+	16.2368i	1.53046	+	0.633939i
$657$	2.21866	+	0.919000i	0.0865583	+	0.0358536i
$658$	0.226855	+	0.547676i	0.00884373	+	0.0213506i
$659$			0.651672i			0.0253855i	0.999919	+	0.0126928i	$0.00404034\pi$
$659$			0.651672i			0.0253855i	−0.999919	+	0.0126928i	$0.995960\pi$
$660$		0			0
$661$	−20.9013	−	20.9013i	−0.812965	−	0.812965i	0.172112	−	0.985077i	$-0.444941\pi$
$661$	−20.9013	−	20.9013i	−0.812965	−	0.812965i	−0.985077	+	0.172112i	$0.944941\pi$
$662$		−	2.68606i		−	0.104397i
$663$	14.8094	+	4.44631i	0.575150	+	0.172680i
$664$	1.61435			0.0626490
$665$		0			0
$666$	−0.0566416	−	0.136745i	−0.00219482	−	0.00529876i
$667$	13.5128			0.523217
$668$	−14.5652	−	35.1635i	−0.563545	−	1.36052i
$669$	−14.8362	+	35.8178i	−0.573602	+	1.38480i
$670$		0			0
$671$	−0.128897	+	0.128897i	−0.00497601	+	0.00497601i
$672$	−19.1325	−	19.1325i	−0.738053	−	0.738053i
$673$	15.4136	−	37.2118i	0.594152	−	1.43441i	−0.285307	−	0.958436i	$-0.592096\pi$
$673$	15.4136	−	37.2118i	0.594152	−	1.43441i	0.879459	−	0.475974i	$-0.157904\pi$
$674$	−1.62778	+	3.92982i	−0.0626999	+	0.151371i
$675$		0			0
$676$		−	16.7941i		−	0.645927i
$677$	−10.3563	+	4.28972i	−0.398025	+	0.164867i	−0.572712	−	0.819757i	$-0.694109\pi$
$677$	−10.3563	+	4.28972i	−0.398025	+	0.164867i	0.174687	+	0.984624i	$0.444109\pi$
$678$	−2.17550	+	2.17550i	−0.0835494	+	0.0835494i
$679$	52.4545			2.01302
$680$		0			0
$681$	48.3431			1.85251
$682$	−4.30355	+	4.30355i	−0.164791	+	0.164791i
$683$	−4.04798	+	1.67673i	−0.154892	+	0.0641583i	−0.458782	−	0.888549i	$-0.651714\pi$
$683$	−4.04798	+	1.67673i	−0.154892	+	0.0641583i	0.303891	+	0.952707i	$0.401714\pi$
$684$			1.55624i			0.0595043i
$685$		0			0
$686$	−5.14150	+	12.4127i	−0.196304	+	0.473919i
$687$	−4.29274	+	10.3636i	−0.163778	+	0.395395i
$688$	−14.0107	−	14.0107i	−0.534153	−	0.534153i
$689$	9.54849	−	9.54849i	0.363768	−	0.363768i
$690$		0			0
$691$	7.05954	−	17.0432i	0.268557	−	0.648355i	−0.730858	−	0.682529i	$-0.760880\pi$
$691$	7.05954	−	17.0432i	0.268557	−	0.648355i	0.999416	+	0.0341741i	$0.0108801\pi$
$692$	−8.67803	−	20.9506i	−0.329889	−	0.796423i
$693$	5.28241			0.200662
$694$	1.44276	+	3.48314i	0.0547665	+	0.132218i
$695$		0			0
$696$	−6.57545			−0.249242
$697$	23.1400	+	42.9965i	0.876489	+	1.62861i
$698$			6.49122i			0.245696i
$699$	−30.5769	−	30.5769i	−1.15652	−	1.15652i
$700$		0			0
$701$		−	9.86753i		−	0.372692i	−0.982484	−	0.186346i	$-0.940336\pi$
$701$		−	9.86753i		−	0.372692i	0.982484	−	0.186346i	$-0.0596645\pi$
$702$	1.03809	+	2.50616i	0.0391800	+	0.0945889i
$703$	−5.57068	−	2.30745i	−0.210102	−	0.0870271i
$704$	−23.0597	−	9.55164i	−0.869095	−	0.359991i
$705$		0			0
$706$	−4.75725	+	4.75725i	−0.179041	+	0.179041i
$707$	−18.0983	+	43.6931i	−0.680656	+	1.64325i
$708$	22.4728	+	9.30855i	0.844581	+	0.349837i
$709$	40.9337	−	16.9553i	1.53730	−	0.636769i	0.556333	−	0.830960i	$-0.312208\pi$
$709$	40.9337	−	16.9553i	1.53730	−	0.636769i	0.980964	+	0.194190i	$0.0622080\pi$
$710$		0			0
$711$	−0.270806	−	0.653783i	−0.0101560	−	0.0245188i
$712$	7.55685	−	7.55685i	0.283205	−	0.283205i
$713$		−	22.6591i		−	0.848590i
$714$	−0.983341	−	9.70038i	−0.0368006	−	0.363028i
$715$		0			0
$716$	−11.1456	−	11.1456i	−0.416531	−	0.416531i
$717$	−24.0601	+	9.96604i	−0.898543	+	0.372189i
$718$	7.03811			0.262660
$719$	−3.92218	+	1.62462i	−0.146273	+	0.0605882i	−0.454619	−	0.890686i	$-0.650225\pi$
$719$	−3.92218	+	1.62462i	−0.146273	+	0.0605882i	0.308346	+	0.951274i	$0.400225\pi$
$720$		0			0
$721$	−0.672114	−	0.278399i	−0.0250308	−	0.0103681i
$722$	1.92913	+	1.92913i	0.0717946	+	0.0717946i
$723$	1.94158	+	1.94158i	0.0722081	+	0.0722081i
$724$	18.0816	+	7.48965i	0.671998	+	0.278351i
$725$		0			0
$726$	−1.95077	+	0.808036i	−0.0723999	+	0.0299890i
$727$	−18.4022			−0.682501			−0.341251	−	0.939972i	$-0.610850\pi$
$727$	−18.4022			−0.682501			−0.341251	+	0.939972i	$0.610850\pi$
$728$	9.83639	−	4.07436i	0.364561	−	0.151006i
$729$	−17.0511	−	17.0511i	−0.631523	−	0.631523i
$730$		0			0
$731$	−2.29974	−	22.6862i	−0.0850588	−	0.839081i
$732$			0.162167i			0.00599385i
$733$	0.0568626	−	0.0568626i	0.00210027	−	0.00210027i	−0.706056	−	0.708156i	$-0.749527\pi$
$733$	0.0568626	−	0.0568626i	0.00210027	−	0.00210027i	0.708156	+	0.706056i	$0.249527\pi$
$734$	0.381882	+	0.921944i	0.0140955	+	0.0340296i
$735$		0			0
$736$	−10.8678	+	4.50159i	−0.400592	+	0.165931i
$737$	36.4264	+	15.0883i	1.34179	+	0.555786i
$738$	0.328418	−	0.792871i	0.0120892	−	0.0291860i
$739$	−33.6880	+	33.6880i	−1.23923	+	1.23923i	−0.278919	+	0.960315i	$0.589976\pi$
$739$	−33.6880	+	33.6880i	−1.23923	+	1.23923i	−0.960315	+	0.278919i	$0.910024\pi$
$740$		0			0
$741$	−10.2285	−	4.23677i	−0.375752	−	0.155642i
$742$	−7.86674	−	3.25851i	−0.288797	−	0.119624i
$743$	9.24945	+	22.3302i	0.339330	+	0.819214i	0.997780	+	0.0665903i	$0.0212120\pi$
$743$	9.24945	+	22.3302i	0.339330	+	0.819214i	−0.658451	+	0.752624i	$0.728788\pi$
$744$			11.0261i			0.404238i
$745$		0			0
$746$	2.03511	+	2.03511i	0.0745108	+	0.0745108i
$747$			0.423081i			0.0154797i
$748$	−14.7962	−	27.4929i	−0.541003	−	1.00524i
$749$	−31.0220			−1.13352
$750$		0			0
$751$	5.28236	+	12.7527i	0.192756	+	0.465354i	0.990478	−	0.137671i	$-0.0439617\pi$
$751$	5.28236	+	12.7527i	0.192756	+	0.465354i	−0.797722	+	0.603025i	$0.793962\pi$
$752$	1.62490			0.0592540
$753$	19.6145	+	47.3535i	0.714791	+	1.72566i
$754$	0.733663	−	1.77122i	0.0267184	−	0.0645040i
$755$		0			0
$756$	−33.1678	+	33.1678i	−1.20630	+	1.20630i
$757$	−5.54725	−	5.54725i	−0.201618	−	0.201618i	0.599075	−	0.800693i	$-0.295535\pi$
$757$	−5.54725	−	5.54725i	−0.201618	−	0.201618i	−0.800693	+	0.599075i	$0.795535\pi$
$758$	−3.04523	+	7.35183i	−0.110608	+	0.267030i
$759$	10.5298	−	25.4212i	0.382208	−	0.922733i
$760$		0			0
$761$		−	2.34626i		−	0.0850518i	−0.999095	−	0.0425259i	$-0.986460\pi$
$761$		−	2.34626i		−	0.0850518i	0.999095	−	0.0425259i	$-0.0135405\pi$
$762$	2.37563	−	0.984019i	0.0860601	−	0.0356473i
$763$	39.7269	−	39.7269i	1.43821	−	1.43821i
$764$	−26.3837			−0.954529
$765$		0			0
$766$	3.59076			0.129739
$767$	−10.2126	+	10.2126i	−0.368756	+	0.368756i
$768$	−17.8228	+	7.38245i	−0.643125	+	0.266391i
$769$		−	7.42438i		−	0.267730i	−0.991000	−	0.133865i	$-0.957261\pi$
$769$		−	7.42438i		−	0.267730i	0.991000	−	0.133865i	$-0.0427389\pi$
$770$		0			0
$771$	5.83627	−	14.0900i	0.210188	−	0.507439i
$772$	1.10696	−	2.67244i	0.0398404	−	0.0961832i
$773$	−4.40565	−	4.40565i	−0.158460	−	0.158460i	0.623424	−	0.781884i	$-0.285741\pi$
$773$	−4.40565	−	4.40565i	−0.158460	−	0.158460i	−0.781884	+	0.623424i	$0.785741\pi$
$774$	−0.283392	+	0.283392i	−0.0101863	+	0.0101863i
$775$		0			0
$776$	−4.24661	+	10.2522i	−0.152444	+	0.368033i
$777$	6.96775	+	16.8216i	0.249967	+	0.603473i
$778$	−5.46875			−0.196064
$779$	−13.3790	−	32.2998i	−0.479352	−	1.15726i
$780$		0			0
$781$	60.0493			2.14873
$782$	−4.05982	−	1.21890i	−0.145179	−	0.0435878i
$783$			17.2007i			0.614701i
$784$	43.7744	+	43.7744i	1.56337	+	1.56337i
$785$		0			0
$786$			6.72943i			0.240031i
$787$	−0.606819	−	1.46499i	−0.0216308	−	0.0522213i	0.912695	−	0.408641i	$-0.133997\pi$
$787$	−0.606819	−	1.46499i	−0.0216308	−	0.0522213i	−0.934326	+	0.356420i	$0.883997\pi$
$788$	17.9227	+	7.42382i	0.638469	+	0.264463i
$789$	−39.5251	−	16.3718i	−1.40713	−	0.582852i
$790$		0			0
$791$	22.3360	−	22.3360i	0.794175	−	0.794175i
$792$	−0.427653	+	1.03245i	−0.0151960	+	0.0366864i
$793$	−0.0889582	−	0.0368477i	−0.00315900	−	0.00130850i
$794$	−3.13153	+	1.29712i	−0.111134	+	0.0460332i
$795$		0			0
$796$	3.81158	+	9.20197i	0.135098	+	0.326155i
$797$	13.0147	−	13.0147i	0.461004	−	0.461004i	−0.437981	−	0.898984i	$-0.644306\pi$
$797$	13.0147	−	13.0147i	0.461004	−	0.461004i	0.898984	+	0.437981i	$0.144306\pi$
$798$			6.98112i			0.247129i
$799$	1.44888	+	1.18217i	0.0512577	+	0.0418221i
$800$		0			0
$801$	1.98046	+	1.98046i	0.0699761	+	0.0699761i
$802$	0.000214754	0	8.89540e-5i	7.58323e−6	0	3.14108e-6i
$803$	34.4962			1.21734
$804$	32.4057	−	13.4229i	1.14286	−	0.473388i
$805$		0			0
$806$	−2.97010	−	1.23025i	−0.104617	−	0.0433338i
$807$	1.33315	+	1.33315i	0.0469290	+	0.0469290i
$808$	−7.07461	−	7.07461i	−0.248884	−	0.248884i
$809$	−1.66359	−	0.689080i	−0.0584886	−	0.0242268i	0.353247	−	0.935530i	$-0.385077\pi$
$809$	−1.66359	−	0.689080i	−0.0584886	−	0.0242268i	−0.411736	+	0.911303i	$0.635077\pi$
$810$		0			0
$811$	1.60465	−	0.664668i	0.0563469	−	0.0233397i	−0.354332	−	0.935120i	$-0.615292\pi$
$811$	1.60465	−	0.664668i	0.0563469	−	0.0233397i	0.410679	+	0.911780i	$0.365292\pi$
$812$	33.1508			1.16337
$813$	−33.5335	+	13.8900i	−1.17607	+	0.487144i
$814$	−1.50341	−	1.50341i	−0.0526944	−	0.0526944i
$815$		0			0
$816$	−25.5968	−	7.68506i	−0.896066	−	0.269031i
$817$			16.3267i			0.571200i
$818$	−3.54162	+	3.54162i	−0.123830	+	0.123830i
$819$	1.06779	+	2.57787i	0.0373115	+	0.0900780i
$820$		0			0
$821$	−42.6963	+	17.6854i	−1.49011	+	0.617225i	−0.971341	−	0.237689i	$-0.923610\pi$
$821$	−42.6963	+	17.6854i	−1.49011	+	0.617225i	−0.518771	+	0.854913i	$0.673610\pi$
$822$	−2.58826	−	1.07209i	−0.0902760	−	0.0373936i
$823$	13.7041	−	33.0846i	0.477695	−	1.15326i	−0.482992	−	0.875625i	$-0.660450\pi$
$823$	13.7041	−	33.0846i	0.477695	−	1.15326i	0.960687	−	0.277633i	$-0.0895500\pi$
$824$	0.108826	−	0.108826i	0.00379113	−	0.00379113i
$825$		0			0
$826$	8.41389	+	3.48515i	0.292757	+	0.121264i
$827$	−18.8645	−	7.81395i	−0.655984	−	0.271718i	0.0297634	−	0.999557i	$-0.490525\pi$
$827$	−18.8645	−	7.81395i	−0.655984	−	0.271718i	−0.685748	+	0.727839i	$0.740525\pi$
$828$	−0.781835	−	1.88752i	−0.0271706	−	0.0655957i
$829$		−	34.9581i		−	1.21414i	−0.794647	−	0.607072i	$-0.792344\pi$
$829$		−	34.9581i		−	1.21414i	0.794647	−	0.607072i	$-0.207656\pi$
$830$		0			0
$831$	−11.0520	−	11.0520i	−0.383389	−	0.383389i
$832$		−	13.1841i		−	0.457077i
$833$	7.18520	+	70.8799i	0.248952	+	2.45584i
$834$	−7.30809			−0.253058
$835$		0			0
$836$	8.55483	+	20.6532i	0.295875	+	0.714305i
$837$	28.8432			0.996966
$838$	0.937338	+	2.26294i	0.0323798	+	0.0781718i
$839$	−2.98719	+	7.21171i	−0.103129	+	0.248976i	−0.967019	−	0.254705i	$-0.918021\pi$
$839$	−2.98719	+	7.21171i	−0.103129	+	0.248976i	0.863889	+	0.503681i	$0.168021\pi$
$840$		0			0
$841$	−11.9102	+	11.9102i	−0.410695	+	0.410695i
$842$	−6.55011	−	6.55011i	−0.225732	−	0.225732i
$843$	−4.37215	+	10.5553i	−0.150585	+	0.363544i
$844$	−15.4446	+	37.2864i	−0.531623	+	1.28345i
$845$		0			0
$846$		−	0.0328665i		−	0.00112997i
$847$	20.0287	−	8.29616i	0.688194	−	0.285059i
$848$	−16.5037	+	16.5037i	−0.566740	+	0.566740i
$849$	3.40344			0.116806
$850$		0			0
$851$	7.91575			0.271348
$852$	37.7744	−	37.7744i	1.29413	−	1.29413i
$853$	−24.7835	+	10.2657i	−0.848571	+	0.351490i	−0.764227	−	0.644947i	$-0.776879\pi$
$853$	−24.7835	+	10.2657i	−0.848571	+	0.351490i	−0.0843438	+	0.996437i	$0.526879\pi$
$854$			0.0607156i			0.00207765i
$855$		0			0
$856$	2.51148	−	6.06324i	0.0858406	−	0.207237i
$857$	−0.111900	+	0.270150i	−0.00382243	+	0.00922815i	−0.925779	−	0.378065i	$-0.876590\pi$
$857$	−0.111900	+	0.270150i	−0.00382243	+	0.00922815i	0.921957	+	0.387293i	$0.126590\pi$
$858$	−2.76044	−	2.76044i	−0.0942400	−	0.0942400i
$859$	−20.5174	+	20.5174i	−0.700046	+	0.700046i	−0.964420	−	0.264374i	$-0.914835\pi$
$859$	−20.5174	+	20.5174i	−0.700046	+	0.700046i	0.264374	+	0.964420i	$0.414835\pi$
$860$		0			0
$861$	−40.4002	+	97.5348i	−1.37684	+	3.32398i
$862$	−0.761500	−	1.83842i	−0.0259368	−	0.0626170i
$863$	6.90380			0.235008			0.117504	−	0.993072i	$-0.462511\pi$
$863$	6.90380			0.235008			0.117504	+	0.993072i	$0.462511\pi$
$864$	−5.73016	−	13.8338i	−0.194944	−	0.470636i
$865$		0			0
$866$	5.89019			0.200157
$867$	−17.2329	−	25.4751i	−0.585259	−	0.865179i
$868$		−	55.5895i		−	1.88683i
$869$	−7.18784	−	7.18784i	−0.243831	−	0.243831i
$870$		0			0
$871$			20.8264i			0.705676i
$872$	4.54841	+	10.9808i	0.154029	+	0.371858i
$873$	−2.68685	−	1.11293i	−0.0909360	−	0.0376669i
$874$	2.80401	+	1.16146i	0.0948471	+	0.0392870i
$875$		0			0
$876$	21.7000	−	21.7000i	0.733176	−	0.733176i
$877$	11.9103	−	28.7539i	0.402181	−	0.970950i	−0.584955	−	0.811066i	$-0.698888\pi$
$877$	11.9103	−	28.7539i	0.402181	−	0.970950i	0.987136	−	0.159885i	$-0.0511122\pi$
$878$	−4.12410	−	1.70826i	−0.139182	−	0.0576509i
$879$	3.16282	−	1.31008i	0.106679	−	0.0441880i
$880$		0			0
$881$	12.9485	+	31.2604i	0.436246	+	1.05319i	0.977235	+	0.212161i	$0.0680502\pi$
$881$	12.9485	+	31.2604i	0.436246	+	1.05319i	−0.540989	+	0.841030i	$0.681950\pi$
$882$	0.885417	−	0.885417i	0.0298136	−	0.0298136i
$883$			17.2493i			0.580484i	0.956953	+	0.290242i	$0.0937359\pi$
$883$			17.2493i			0.580484i	−0.956953	+	0.290242i	$0.906264\pi$
$884$	10.4259	−	12.7781i	0.350661	−	0.429775i
$885$		0			0
$886$	−3.79551	−	3.79551i	−0.127513	−	0.127513i
$887$	−5.50312	+	2.27947i	−0.184777	+	0.0765370i	−0.473153	−	0.880980i	$-0.656884\pi$
$887$	−5.50312	+	2.27947i	−0.184777	+	0.0765370i	0.288377	+	0.957517i	$0.406884\pi$
$888$	−3.85188			−0.129261
$889$	−24.3908	+	10.1030i	−0.818041	+	0.338844i
$890$		0			0
$891$	35.3305	+	14.6344i	1.18362	+	0.490270i
$892$	29.2387	+	29.2387i	0.978985	+	0.978985i
$893$	−0.946750	−	0.946750i	−0.0316818	−	0.0316818i
$894$	9.14381	+	3.78749i	0.305815	+	0.126673i
$895$		0			0
$896$	−35.3148	+	14.6279i	−1.17979	+	0.488683i
$897$	14.5343			0.485287
$898$	−7.08555	+	2.93493i	−0.236448	+	0.0979399i
$899$	−14.4142	−	14.4142i	−0.480742	−	0.480742i
$900$		0			0
$901$	−26.7230	+	2.70894i	−0.890271	+	0.0902480i
$902$		−	12.3277i		−	0.410468i
$903$	34.8613	−	34.8613i	1.16011	−	1.16011i
$904$	2.55729	+	6.17384i	0.0850541	+	0.205339i
$905$		0			0
$906$	−2.28453	+	0.946284i	−0.0758985	+	0.0314382i
$907$	28.6501	+	11.8673i	0.951312	+	0.394046i	0.803724	−	0.595003i	$-0.202849\pi$
$907$	28.6501	+	11.8673i	0.951312	+	0.394046i	0.147588	+	0.989049i	$0.452849\pi$
$908$	19.7317	−	47.6364i	0.654818	−	1.58087i
$909$	1.85408	−	1.85408i	0.0614958	−	0.0614958i
$910$		0			0
$911$	−11.0101	−	4.56054i	−0.364782	−	0.151098i	0.192761	−	0.981246i	$-0.438256\pi$
$911$	−11.0101	−	4.56054i	−0.364782	−	0.151098i	−0.557543	+	0.830148i	$0.688256\pi$
$912$	17.6790	+	7.32289i	0.585411	+	0.242485i
$913$	2.32572	+	5.61480i	0.0769702	+	0.185823i
$914$			4.54759i			0.150421i
$915$		0			0
$916$	8.45998	+	8.45998i	0.279525	+	0.279525i
$917$		−	69.0915i		−	2.28160i
$918$	1.55156	−	5.16782i	0.0512092	−	0.170563i
$919$	6.38966			0.210776			0.105388	−	0.994431i	$-0.466392\pi$
$919$	6.38966			0.210776			0.105388	+	0.994431i	$0.466392\pi$
$920$		0			0
$921$	−12.8650	−	31.0588i	−0.423916	−	1.02342i
$922$	−1.57942			−0.0520155
$923$	12.1384	+	29.3047i	0.399540	+	0.964574i
$924$	25.8328	−	62.3659i	0.849836	−	2.05169i
$925$		0			0
$926$	5.74273	−	5.74273i	0.188718	−	0.188718i
$927$	0.0285205	+	0.0285205i	0.000936738	+	0.000936738i
$928$	−4.04977	+	9.77700i	−0.132940	+	0.320946i
$929$	−3.79175	+	9.15410i	−0.124403	+	0.300336i	−0.973795	−	0.227426i	$-0.926969\pi$
$929$	−3.79175	+	9.15410i	−0.124403	+	0.300336i	0.849392	+	0.527763i	$0.176969\pi$
$930$		0			0
$931$		−	51.0105i		−	1.67180i
$932$	−42.6101	+	17.6497i	−1.39574	+	0.578135i
$933$	20.3793	−	20.3793i	0.667188	−	0.667188i
$934$	−6.62443			−0.216758
$935$		0			0
$936$	−0.590290			−0.0192942
$937$	8.28441	−	8.28441i	0.270640	−	0.270640i	−0.558718	−	0.829358i	$-0.688707\pi$
$937$	8.28441	−	8.28441i	0.270640	−	0.270640i	0.829358	+	0.558718i	$0.188707\pi$
$938$	12.1328	−	5.02556i	0.396149	−	0.164090i
$939$		−	57.3448i		−	1.87138i
$940$		0			0
$941$	−5.08066	+	12.2658i	−0.165625	+	0.399853i	−0.984801	−	0.173689i	$-0.944431\pi$
$941$	−5.08066	+	12.2658i	−0.165625	+	0.399853i	0.819176	+	0.573542i	$0.194431\pi$
$942$	−0.472858	+	1.14158i	−0.0154065	+	0.0371947i
$943$	32.4540	+	32.4540i	1.05685	+	1.05685i
$944$	17.6516	−	17.6516i	0.574510	−	0.574510i
$945$		0			0
$946$	−2.20312	+	5.31879i	−0.0716295	+	0.172929i
$947$	12.6459	+	30.5299i	0.410936	+	0.992087i	0.984887	+	0.173197i	$0.0554099\pi$
$947$	12.6459	+	30.5299i	0.410936	+	0.992087i	−0.573951	+	0.818889i	$0.694590\pi$
$948$	−9.04311			−0.293706
$949$	6.97307	+	16.8345i	0.226355	+	0.546470i
$950$		0			0
$951$	−9.05317			−0.293569
$952$	−20.2831	−	6.08970i	−0.657379	−	0.197368i
$953$		−	15.7853i		−	0.511335i	−0.966765	−	0.255668i	$-0.917705\pi$
$953$		−	15.7853i		−	0.511335i	0.966765	−	0.255668i	$-0.0822953\pi$
$954$	0.333818	+	0.333818i	0.0108077	+	0.0108077i
$955$		0			0
$956$			27.7762i			0.898345i
$957$	−9.47295	−	22.8697i	−0.306217	−	0.739273i
$958$	−0.376126	−	0.155797i	−0.0121521	−	0.00503356i
$959$	26.5739	+	11.0073i	0.858115	+	0.355443i
$960$		0			0
$961$	−2.25043	+	2.25043i	−0.0725944	+	0.0725944i
$962$	0.429778	−	1.03758i	0.0138566	−	0.0334528i
$963$	1.58902	+	0.658195i	0.0512055	+	0.0212100i
$964$	2.70567	−	1.12072i	0.0871437	−	0.0360961i
$965$		0			0
$966$	−3.50723	−	8.46720i	−0.112843	−	0.272428i
$967$	−34.4173	+	34.4173i	−1.10679	+	1.10679i	−0.113215	+	0.993571i	$0.536115\pi$
$967$	−34.4173	+	34.4173i	−1.10679	+	1.10679i	−0.993571	+	0.113215i	$0.963885\pi$
$968$			4.58625i			0.147408i
$969$	10.4363	+	19.3917i	0.335262	+	0.622952i
$970$		0			0
$971$	0.0626140	+	0.0626140i	0.00200938	+	0.00200938i	0.708111	−	0.706101i	$-0.249548\pi$
$971$	0.0626140	+	0.0626140i	0.00200938	+	0.00200938i	−0.706101	+	0.708111i	$0.749548\pi$
$972$	5.04602	−	2.09013i	0.161851	−	0.0670410i
$973$	75.0326			2.40544
$974$	−5.41361	+	2.24239i	−0.173463	+	0.0718509i
$975$		0			0
$976$	0.153756	+	0.0636880i	0.00492162	+	0.00203860i
$977$	37.1283	+	37.1283i	1.18784	+	1.18784i	0.977663	+	0.210177i	$0.0674040\pi$
$977$	37.1283	+	37.1283i	1.18784	+	1.18784i	0.210177	+	0.977663i	$0.432596\pi$
$978$	5.23806	+	5.23806i	0.167495	+	0.167495i
$979$	37.1699	+	15.3963i	1.18796	+	0.492068i
$980$		0			0
$981$	−2.87780	+	1.19202i	−0.0918811	+	0.0380584i
$982$	1.62889			0.0519800
$983$	25.0939	−	10.3942i	0.800372	−	0.331525i	0.0552663	−	0.998472i	$-0.482399\pi$
$983$	25.0939	−	10.3942i	0.800372	−	0.331525i	0.745105	+	0.666947i	$0.232399\pi$
$984$	−15.7924	−	15.7924i	−0.503444	−	0.503444i
$985$		0			0
$986$	−3.35798	+	1.80721i	−0.106940	+	0.0575532i
$987$			4.04306i			0.128692i
$988$	−8.34968	+	8.34968i	−0.265639	+	0.265639i
$989$	−8.20234	−	19.8022i	−0.260819	−	0.629674i
$990$		0			0
$991$	1.25144	−	0.518363i	0.0397533	−	0.0164663i	−0.362718	−	0.931899i	$-0.618151\pi$
$991$	1.25144	−	0.518363i	0.0397533	−	0.0164663i	0.402471	+	0.915433i	$0.368151\pi$
$992$	16.3947	+	6.79091i	0.520533	+	0.215612i
$993$	7.01064	−	16.9252i	0.222476	−	0.537105i
$994$	14.1428	−	14.1428i	0.448583	−	0.448583i
$995$		0			0
$996$	4.99503	+	2.06901i	0.158274	+	0.0655591i
$997$	−5.92470	−	2.45409i	−0.187637	−	0.0777219i	0.286887	−	0.957965i	$-0.407380\pi$
$997$	−5.92470	−	2.45409i	−0.187637	−	0.0777219i	−0.474524	+	0.880243i	$0.657380\pi$
$998$	−3.37041	−	8.13690i	−0.106689	−	0.257569i
$999$			10.0761i			0.318794i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.n.e.49.4		24
5.2	odd	4		425.2.m.d.151.4	yes	24
5.3	odd	4		425.2.m.c.151.3	yes	24
5.4	even	2		425.2.n.d.49.3		24
17.8	even	8		425.2.n.d.399.3		24
85.8	odd	8		425.2.m.c.76.3	✓	24
85.12	even	16		7225.2.a.cb.1.12		24
85.22	even	16		7225.2.a.cb.1.11		24
85.42	odd	8		425.2.m.d.76.4	yes	24
85.59	even	8	inner	425.2.n.e.399.4		24
85.63	even	16		7225.2.a.bx.1.13		24
85.73	even	16		7225.2.a.bx.1.14		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.m.c.76.3	✓	24	85.8	odd	8
425.2.m.c.151.3	yes	24	5.3	odd	4
425.2.m.d.76.4	yes	24	85.42	odd	8
425.2.m.d.151.4	yes	24	5.2	odd	4
425.2.n.d.49.3		24	5.4	even	2
425.2.n.d.399.3		24	17.8	even	8
425.2.n.e.49.4		24	1.1	even	1	trivial
425.2.n.e.399.4		24	85.59	even	8	inner
7225.2.a.bx.1.13		24	85.63	even	16
7225.2.a.bx.1.14		24	85.73	even	16
7225.2.a.cb.1.11		24	85.22	even	16
7225.2.a.cb.1.12		24	85.12	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 $\F_{q}$

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+(-0.187572 + 0.187572i) q^{2} +(-1.67148 + 0.692349i) q^{3} +1.92963i q^{4} +(0.183657 - 0.443388i) q^{6} +(-1.88562 + 4.55230i) q^{7} +(-0.737090 - 0.737090i) q^{8} +(0.193173 - 0.193173i) q^{9} +(1.50174 - 3.62553i) q^{11} +(-1.33598 - 3.22534i) q^{12} +2.07286 q^{13} +(-0.500194 - 1.20758i) q^{14} -3.58275 q^{16} +(-3.19465 - 2.60657i) q^{17} +0.0724676i q^{18} +(2.08750 + 2.08750i) q^{19} -8.91458i q^{21} +(0.398363 + 0.961734i) q^{22} +(-3.58060 - 1.48313i) q^{23} +(1.74235 + 0.721707i) q^{24} +(-0.388810 + 0.388810i) q^{26} +(1.88791 - 4.55781i) q^{27} +(-8.78427 - 3.63856i) q^{28} +(-3.22121 + 1.33427i) q^{29} +(2.23739 + 5.40154i) q^{31} +(2.14620 - 2.14620i) q^{32} +7.09972i q^{33} +(1.08815 - 0.110307i) q^{34} +(0.372752 + 0.372752i) q^{36} +(-1.88698 + 0.781612i) q^{37} -0.783113 q^{38} +(-3.46473 + 1.43514i) q^{39} +(-10.9410 - 4.53193i) q^{41} +(1.67213 + 1.67213i) q^{42} +(3.91060 + 3.91060i) q^{43} +(6.99594 + 2.89781i) q^{44} +(0.949815 - 0.393426i) q^{46} -0.453534 q^{47} +(5.98849 - 2.48051i) q^{48} +(-12.2181 - 12.2181i) q^{49} +(7.14444 + 2.14502i) q^{51} +3.99985i q^{52} +(4.60644 - 4.60644i) q^{53} +(0.500800 + 1.20904i) q^{54} +(4.74533 - 1.96558i) q^{56} +(-4.93448 - 2.04393i) q^{57} +(0.353938 - 0.854483i) q^{58} +(-4.92683 + 4.92683i) q^{59} +(-0.0429157 - 0.0177763i) q^{61} +(-1.43285 - 0.593507i) q^{62} +(0.515129 + 1.24363i) q^{63} -6.36037i q^{64} +(-1.33171 - 1.33171i) q^{66} +10.0472i q^{67} +(5.02973 - 6.16450i) q^{68} +7.01174 q^{69} +(5.85587 + 14.1373i) q^{71} -0.284771 q^{72} +(3.36399 + 8.12139i) q^{73} +(0.207336 - 0.500554i) q^{74} +(-4.02810 + 4.02810i) q^{76} +(13.6728 + 13.6728i) q^{77} +(0.380696 - 0.919080i) q^{78} +(0.991282 - 2.39317i) q^{79} +9.74493i q^{81} +(2.90230 - 1.20217i) q^{82} +(-1.09508 + 1.09508i) q^{83} +17.2019 q^{84} -1.46704 q^{86} +(4.46041 - 4.46041i) q^{87} +(-3.77926 + 1.56542i) q^{88} +10.2523i q^{89} +(-3.90863 + 9.43626i) q^{91} +(2.86190 - 6.90924i) q^{92} +(-7.47951 - 7.47951i) q^{93} +(0.0850703 - 0.0850703i) q^{94} +(-2.10141 + 5.07326i) q^{96} +(-4.07387 - 9.83519i) q^{97} +4.58356 q^{98} +(-0.410257 - 0.990448i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3} - 8 q^{6} - 12 q^{9} + 4 q^{11} - 20 q^{12} + 16 q^{13} + 24 q^{14} - 24 q^{16} + 20 q^{19} + 12 q^{22} + 8 q^{23} - 16 q^{24} + 16 q^{26} + 16 q^{27} + 20 q^{28} - 4 q^{29} + 24 q^{31} + 60 q^{32}+ \cdots + 80 q^{99}+O(q^{100}) \) 24 * q + 4 * q^3 - 8 * q^6 - 12 * q^9 + 4 * q^11 - 20 * q^12 + 16 * q^13 + 24 * q^14 - 24 * q^16 + 20 * q^19 + 12 * q^22 + 8 * q^23 - 16 * q^24 + 16 * q^26 + 16 * q^27 + 20 * q^28 - 4 * q^29 + 24 * q^31 + 60 * q^32 - 16 * q^34 + 60 * q^36 - 16 * q^37 - 48 * q^38 - 8 * q^39 - 20 * q^41 + 12 * q^42 - 32 * q^43 - 64 * q^44 - 40 * q^46 - 88 * q^47 + 4 * q^48 - 24 * q^49 + 16 * q^51 - 12 * q^53 + 20 * q^54 - 32 * q^56 - 56 * q^57 - 28 * q^58 + 16 * q^59 - 64 * q^61 + 16 * q^62 - 40 * q^63 - 72 * q^66 + 48 * q^68 + 48 * q^69 - 24 * q^71 + 120 * q^72 + 20 * q^73 - 32 * q^74 + 52 * q^76 + 24 * q^77 - 100 * q^78 + 48 * q^79 + 8 * q^82 + 12 * q^83 + 40 * q^84 - 16 * q^86 - 24 * q^87 + 80 * q^88 + 24 * q^91 - 56 * q^92 + 32 * q^93 + 40 * q^94 + 132 * q^96 - 24 * q^97 + 48 * q^98 + 80 * q^99

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