LMFDB - Embedded newform 425.2.n.e.49.3

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 = [24,0,4] 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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			49.3
Character	$\chi$	$=$	425.49
Dual form			425.2.n.e.399.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.639117 + 0.639117i) q^{2} +(2.66226 - 1.10274i) q^{3} +1.18306i q^{4} +(-0.996713 + 2.40628i) q^{6} +(-0.278207 + 0.671652i) q^{7} +(-2.03435 - 2.03435i) q^{8} +(3.75027 - 3.75027i) q^{9} +(-0.958080 + 2.31301i) q^{11} +(1.30461 + 3.14961i) q^{12} +6.29663 q^{13} +(-0.251457 - 0.607071i) q^{14} +0.234252 q^{16} +(3.55925 + 2.08128i) q^{17} +4.79372i q^{18} +(0.143443 + 0.143443i) q^{19} +2.09490i q^{21} +(-0.865959 - 2.09061i) q^{22} +(0.616148 + 0.255217i) q^{23} +(-7.65933 - 3.17260i) q^{24} +(-4.02428 + 4.02428i) q^{26} +(2.54037 - 6.13299i) q^{27} +(-0.794604 - 0.329136i) q^{28} +(-7.33161 + 3.03685i) q^{29} +(-2.12864 - 5.13900i) q^{31} +(3.91898 - 3.91898i) q^{32} +7.21436i q^{33} +(-3.60496 + 0.944595i) q^{34} +(4.43679 + 4.43679i) q^{36} +(7.34010 - 3.04037i) q^{37} -0.183354 q^{38} +(16.7633 - 6.94358i) q^{39} +(-4.73632 - 1.96185i) q^{41} +(-1.33889 - 1.33889i) q^{42} +(-8.45426 - 8.45426i) q^{43} +(-2.73643 - 1.13347i) q^{44} +(-0.556904 + 0.230677i) q^{46} -10.9207 q^{47} +(0.623640 - 0.258320i) q^{48} +(4.57603 + 4.57603i) q^{49} +(11.7708 + 1.61597i) q^{51} +7.44929i q^{52} +(-2.74061 + 2.74061i) q^{53} +(2.29611 + 5.54329i) q^{54} +(1.93234 - 0.800403i) q^{56} +(0.540065 + 0.223702i) q^{57} +(2.74485 - 6.62666i) q^{58} +(2.38470 - 2.38470i) q^{59} +(-1.04828 - 0.434212i) q^{61} +(4.64487 + 1.92397i) q^{62} +(1.47552 + 3.56223i) q^{63} +5.47788i q^{64} +(-4.61082 - 4.61082i) q^{66} +5.61946i q^{67} +(-2.46228 + 4.21081i) q^{68} +1.92179 q^{69} +(-1.51683 - 3.66196i) q^{71} -15.2587 q^{72} +(-1.98578 - 4.79409i) q^{73} +(-2.74803 + 6.63433i) q^{74} +(-0.169702 + 0.169702i) q^{76} +(-1.28699 - 1.28699i) q^{77} +(-6.27594 + 15.1514i) q^{78} +(-5.37312 + 12.9718i) q^{79} -3.21797i q^{81} +(4.28091 - 1.77321i) q^{82} +(8.73235 - 8.73235i) q^{83} -2.47840 q^{84} +10.8065 q^{86} +(-16.1698 + 16.1698i) q^{87} +(6.65453 - 2.75640i) q^{88} -13.0419i q^{89} +(-1.75177 + 4.22914i) q^{91} +(-0.301937 + 0.728940i) q^{92} +(-11.3340 - 11.3340i) q^{93} +(6.97959 - 6.97959i) q^{94} +(6.11171 - 14.7550i) q^{96} +(-4.56330 - 11.0168i) q^{97} -5.84924 q^{98} +(5.08135 + 12.2675i) 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 $

$2$	−0.639117	+	0.639117i	−0.451924	+	0.451924i	−0.895993	−	0.444069i	$-0.853535\pi$
$2$	−0.639117	+	0.639117i	−0.451924	+	0.451924i	0.444069	+	0.895993i	$0.353535\pi$
$3$	2.66226	−	1.10274i	1.53706	−	0.636670i	0.556139	−	0.831090i	$-0.312282\pi$
$3$	2.66226	−	1.10274i	1.53706	−	0.636670i	0.980918	+	0.194420i	$0.0622824\pi$
$4$			1.18306i			0.591530i
$5$		0			0
$5$		0			0
$6$	−0.996713	+	2.40628i	−0.406906	+	0.982359i
$7$	−0.278207	+	0.671652i	−0.105152	+	0.253861i	−0.967695	−	0.252124i	$-0.918871\pi$
$7$	−0.278207	+	0.671652i	−0.105152	+	0.253861i	0.862542	+	0.505985i	$0.168871\pi$
$8$	−2.03435	−	2.03435i	−0.719250	−	0.719250i
$9$	3.75027	−	3.75027i	1.25009	−	1.25009i
$10$		0			0
$11$	−0.958080	+	2.31301i	−0.288872	+	0.697399i	−0.999984	−	0.00567999i	$-0.998192\pi$
$11$	−0.958080	+	2.31301i	−0.288872	+	0.697399i	0.711112	+	0.703079i	$0.248192\pi$
$12$	1.30461	+	3.14961i	0.376609	+	0.909215i
$13$	6.29663			1.74637			0.873186	−	0.487388i	$-0.162050\pi$
$13$	6.29663			1.74637			0.873186	+	0.487388i	$0.162050\pi$
$14$	−0.251457	−	0.607071i	−0.0672047	−	0.162247i
$15$		0			0
$16$	0.234252			0.0585630
$17$	3.55925	+	2.08128i	0.863245	+	0.504785i
$17$	3.55925	+	2.08128i	0.863245	+	0.504785i
$18$			4.79372i			1.12989i
$19$	0.143443	+	0.143443i	0.0329081	+	0.0329081i	0.723369	−	0.690461i	$-0.242592\pi$
$19$	0.143443	+	0.143443i	0.0329081	+	0.0329081i	−0.690461	+	0.723369i	$0.742592\pi$
$20$		0			0
$21$			2.09490i			0.457146i
$22$	−0.865959	−	2.09061i	−0.184623	−	0.445719i
$23$	0.616148	+	0.255217i	0.128476	+	0.0532164i	0.445995	−	0.895035i	$-0.352850\pi$
$23$	0.616148	+	0.255217i	0.128476	+	0.0532164i	−0.317519	+	0.948252i	$0.602850\pi$
$24$	−7.65933	−	3.17260i	−1.56345	−	0.647604i
$25$		0			0
$26$	−4.02428	+	4.02428i	−0.789227	+	0.789227i
$27$	2.54037	−	6.13299i	0.488894	−	1.18030i
$28$	−0.794604	−	0.329136i	−0.150166	−	0.0622008i
$29$	−7.33161	+	3.03685i	−1.36145	+	0.563929i	−0.939455	−	0.342671i	$-0.888668\pi$
$29$	−7.33161	+	3.03685i	−1.36145	+	0.563929i	−0.421990	+	0.906600i	$0.638668\pi$
$30$		0			0
$31$	−2.12864	−	5.13900i	−0.382315	−	0.922991i	−0.991517	−	0.129976i	$-0.958510\pi$
$31$	−2.12864	−	5.13900i	−0.382315	−	0.922991i	0.609202	−	0.793015i	$-0.291490\pi$
$32$	3.91898	−	3.91898i	0.692784	−	0.692784i
$33$			7.21436i			1.25586i
$34$	−3.60496	+	0.944595i	−0.618245	+	0.161997i
$35$		0			0
$36$	4.43679	+	4.43679i	0.739465	+	0.739465i
$37$	7.34010	−	3.04037i	1.20670	−	0.499834i	0.313545	−	0.949573i	$-0.398483\pi$
$37$	7.34010	−	3.04037i	1.20670	−	0.499834i	0.893160	+	0.449740i	$0.148483\pi$
$38$	−0.183354			−0.0297439
$39$	16.7633	−	6.94358i	2.68427	−	1.11186i
$40$		0			0
$41$	−4.73632	−	1.96185i	−0.739688	−	0.306389i	−0.0191619	−	0.999816i	$-0.506100\pi$
$41$	−4.73632	−	1.96185i	−0.739688	−	0.306389i	−0.720526	+	0.693427i	$0.756100\pi$
$42$	−1.33889	−	1.33889i	−0.206595	−	0.206595i
$43$	−8.45426	−	8.45426i	−1.28926	−	1.28926i	−0.935235	−	0.354028i	$-0.884812\pi$
$43$	−8.45426	−	8.45426i	−1.28926	−	1.28926i	−0.354028	−	0.935235i	$-0.615188\pi$
$44$	−2.73643	−	1.13347i	−0.412532	−	0.170876i
$45$		0			0
$46$	−0.556904	+	0.230677i	−0.0821110	+	0.0340115i
$47$	−10.9207			−1.59294			−0.796472	−	0.604675i	$-0.793303\pi$
$47$	−10.9207			−1.59294			−0.796472	+	0.604675i	$0.793303\pi$
$48$	0.623640	−	0.258320i	0.0900147	−	0.0372853i
$49$	4.57603	+	4.57603i	0.653719	+	0.653719i
$50$		0			0
$51$	11.7708	+	1.61597i	1.64824	+	0.226281i
$52$			7.44929i			1.03303i
$53$	−2.74061	+	2.74061i	−0.376451	+	0.376451i	−0.869820	−	0.493369i	$-0.835765\pi$
$53$	−2.74061	+	2.74061i	−0.376451	+	0.376451i	0.493369	+	0.869820i	$0.335765\pi$
$54$	2.29611	+	5.54329i	0.312461	+	0.754347i
$55$		0			0
$56$	1.93234	−	0.800403i	0.258220	−	0.106958i
$57$	0.540065	+	0.223702i	0.0715333	+	0.0296301i
$58$	2.74485	−	6.62666i	0.360417	−	0.870123i
$59$	2.38470	−	2.38470i	0.310462	−	0.310462i	−0.534626	−	0.845088i	$-0.679548\pi$
$59$	2.38470	−	2.38470i	0.310462	−	0.310462i	0.845088	+	0.534626i	$0.179548\pi$
$60$		0			0
$61$	−1.04828	−	0.434212i	−0.134219	−	0.0555952i	0.314563	−	0.949237i	$-0.398142\pi$
$61$	−1.04828	−	0.434212i	−0.134219	−	0.0555952i	−0.448782	+	0.893641i	$0.648142\pi$
$62$	4.64487	+	1.92397i	0.589899	+	0.244344i
$63$	1.47552	+	3.56223i	0.185898	+	0.448798i
$64$			5.47788i			0.684734i
$65$		0			0
$66$	−4.61082	−	4.61082i	−0.567552	−	0.567552i
$67$			5.61946i			0.686526i	0.939239	+	0.343263i	$0.111532\pi$
$67$			5.61946i			0.686526i	−0.939239	+	0.343263i	$0.888468\pi$
$68$	−2.46228	+	4.21081i	−0.298595	+	0.510635i
$69$	1.92179			0.231356
$70$		0			0
$71$	−1.51683	−	3.66196i	−0.180015	−	0.434595i	0.807954	−	0.589245i	$-0.200575\pi$
$71$	−1.51683	−	3.66196i	−0.180015	−	0.434595i	−0.987969	+	0.154650i	$0.950575\pi$
$72$	−15.2587			−1.79825
$73$	−1.98578	−	4.79409i	−0.232417	−	0.561105i	0.764043	−	0.645165i	$-0.223211\pi$
$73$	−1.98578	−	4.79409i	−0.232417	−	0.561105i	−0.996461	+	0.0840596i	$0.973211\pi$
$74$	−2.74803	+	6.63433i	−0.319452	+	0.771225i
$75$		0			0
$76$	−0.169702	+	0.169702i	−0.0194661	+	0.0194661i
$77$	−1.28699	−	1.28699i	−0.146666	−	0.146666i
$78$	−6.27594	+	15.1514i	−0.710610	+	1.71556i
$79$	−5.37312	+	12.9718i	−0.604523	+	1.45945i	0.264358	+	0.964425i	$0.414840\pi$
$79$	−5.37312	+	12.9718i	−0.604523	+	1.45945i	−0.868880	+	0.495022i	$0.835160\pi$
$80$		0			0
$81$		−	3.21797i		−	0.357552i
$82$	4.28091	−	1.77321i	0.472747	−	0.195818i
$83$	8.73235	−	8.73235i	0.958500	−	0.958500i	−0.0406730	−	0.999173i	$-0.512950\pi$
$83$	8.73235	−	8.73235i	0.958500	−	0.958500i	0.999173	+	0.0406730i	$0.0129502\pi$
$84$	−2.47840			−0.270415
$85$		0			0
$86$	10.8065			1.16530
$87$	−16.1698	+	16.1698i	−1.73358	+	1.73358i
$88$	6.65453	−	2.75640i	0.709376	−	0.293833i
$89$		−	13.0419i		−	1.38244i	−0.722644	−	0.691221i	$-0.757073\pi$
$89$		−	13.0419i		−	1.38244i	0.722644	−	0.691221i	$-0.242927\pi$
$90$		0			0
$91$	−1.75177	+	4.22914i	−0.183635	+	0.443335i
$92$	−0.301937	+	0.728940i	−0.0314791	+	0.0759972i
$93$	−11.3340	−	11.3340i	−1.17528	−	1.17528i
$94$	6.97959	−	6.97959i	0.719890	−	0.719890i
$95$		0			0
$96$	6.11171	−	14.7550i	0.623774	−	1.50592i
$97$	−4.56330	−	11.0168i	−0.463333	−	1.11858i	−0.967020	−	0.254699i	$-0.918024\pi$
$97$	−4.56330	−	11.0168i	−0.463333	−	1.11858i	0.503688	−	0.863886i	$-0.331976\pi$
$98$	−5.84924			−0.590862
$99$	5.08135	+	12.2675i	0.510695	+	1.23293i
$100$		0			0
$101$	−10.0642			−1.00143			−0.500713	−	0.865613i	$-0.666929\pi$
$101$	−10.0642			−1.00143			−0.500713	+	0.865613i	$0.666929\pi$
$102$	−8.55569	+	6.49011i	−0.847140	+	0.642617i
$103$		−	9.80719i		−	0.966331i	−0.875529	−	0.483166i	$-0.839487\pi$
$103$		−	9.80719i		−	0.966331i	0.875529	−	0.483166i	$-0.160513\pi$
$104$	−12.8095	−	12.8095i	−1.25608	−	1.25608i
$105$		0			0
$106$		−	3.50314i		−	0.340255i
$107$	−1.45993	−	3.52458i	−0.141137	−	0.340734i	0.837467	−	0.546488i	$-0.184035\pi$
$107$	−1.45993	−	3.52458i	−0.141137	−	0.340734i	−0.978604	+	0.205754i	$0.934035\pi$
$108$	7.25570	+	3.00541i	0.698180	+	0.289195i
$109$	2.96319	+	1.22739i	0.283822	+	0.117563i	0.520053	−	0.854134i	$-0.325912\pi$
$109$	2.96319	+	1.22739i	0.283822	+	0.117563i	−0.236231	+	0.971697i	$0.575912\pi$
$110$		0			0
$111$	16.1885	−	16.1885i	1.53655	−	1.53655i
$112$	−0.0651706	+	0.157336i	−0.00615805	+	0.0148668i
$113$	0.372584	+	0.154329i	0.0350498	+	0.0145181i	0.400139	−	0.916454i	$-0.368962\pi$
$113$	0.372584	+	0.154329i	0.0350498	+	0.0145181i	−0.365090	+	0.930972i	$0.618962\pi$
$114$	−0.488136	+	0.202193i	−0.0457181	+	0.0189371i
$115$		0			0
$116$	−3.59278	−	8.67373i	−0.333581	−	0.805335i
$117$	23.6141	−	23.6141i	2.18312	−	2.18312i
$118$			3.04821i			0.280610i
$119$	−2.38811	+	1.81155i	−0.218917	+	0.166065i
$120$		0			0
$121$	3.34607	+	3.34607i	0.304188	+	0.304188i
$122$	0.947487	−	0.392462i	0.0857814	−	0.0355318i
$123$	−14.7727			−1.33201
$124$	6.07974	−	2.51831i	0.545976	−	0.226151i
$125$		0			0
$126$	−3.21971	−	1.33365i	−0.286835	−	0.118811i
$127$	1.52815	+	1.52815i	0.135601	+	0.135601i	0.771649	−	0.636048i	$-0.219432\pi$
$127$	1.52815	+	1.52815i	0.135601	+	0.135601i	−0.636048	+	0.771649i	$0.719432\pi$
$128$	4.33696	+	4.33696i	0.383336	+	0.383336i
$129$	−31.8303	−	13.1846i	−2.80251	−	1.16084i
$130$		0			0
$131$	−7.43241	+	3.07860i	−0.649372	+	0.268979i	−0.682959	−	0.730457i	$-0.739307\pi$
$131$	−7.43241	+	3.07860i	−0.649372	+	0.268979i	0.0335863	+	0.999436i	$0.489307\pi$
$132$	−8.53501			−0.742877
$133$	−0.136251	+	0.0564370i	−0.0118144	+	0.00489371i
$134$	−3.59149	−	3.59149i	−0.310258	−	0.310258i
$135$		0			0
$136$	−3.00670	−	11.4748i	−0.257823	−	0.983956i
$137$		−	7.87082i		−	0.672450i	−0.941782	−	0.336225i	$-0.890850\pi$
$137$		−	7.87082i		−	0.672450i	0.941782	−	0.336225i	$-0.109150\pi$
$138$	−1.22825	+	1.22825i	−0.104555	+	0.104555i
$139$	6.68268	+	16.1334i	0.566818	+	1.36842i	0.904223	+	0.427060i	$0.140451\pi$
$139$	6.68268	+	16.1334i	0.566818	+	1.36842i	−0.337405	+	0.941359i	$0.609549\pi$
$140$		0			0
$141$	−29.0737	+	12.0427i	−2.44845	+	1.01418i
$142$	3.30986	+	1.37099i	0.277757	+	0.115051i
$143$	−6.03268	+	14.5642i	−0.504478	+	1.21792i
$144$	0.878508	−	0.878508i	0.0732090	−	0.0732090i
$145$		0			0
$146$	4.33312	+	1.79484i	0.358612	+	0.148542i
$147$	17.2288	+	7.13639i	1.42101	+	0.588600i
$148$	3.59694	+	8.68377i	0.295666	+	0.713802i
$149$			7.42906i			0.608613i	0.952574	+	0.304306i	$0.0984246\pi$
$149$			7.42906i			0.608613i	−0.952574	+	0.304306i	$0.901575\pi$
$150$		0			0
$151$	−9.55527	−	9.55527i	−0.777597	−	0.777597i	0.201825	−	0.979422i	$-0.435313\pi$
$151$	−9.55527	−	9.55527i	−0.777597	−	0.777597i	−0.979422	+	0.201825i	$0.935313\pi$
$152$		−	0.583627i		−	0.0473384i
$153$	21.1535	−	5.54278i	1.71016	−	0.448107i
$154$	1.64508			0.132564
$155$		0			0
$156$	8.21466	+	19.8320i	0.657699	+	1.58783i
$157$	−2.75786			−0.220101			−0.110051	−	0.993926i	$-0.535101\pi$
$157$	−2.75786			−0.220101			−0.110051	+	0.993926i	$0.535101\pi$
$158$	−4.85648	−	11.7246i	−0.386361	−	0.932757i
$159$	−4.27402	+	10.3184i	−0.338952	+	0.818303i
$160$		0			0
$161$	−0.342834	+	0.342834i	−0.0270191	+	0.0270191i
$162$	2.05666	+	2.05666i	0.161586	+	0.161586i
$163$	−0.529525	+	1.27839i	−0.0414756	+	0.100131i	−0.943260	−	0.332056i	$-0.892258\pi$
$163$	−0.529525	+	1.27839i	−0.0414756	+	0.100131i	0.901784	+	0.432187i	$0.142258\pi$
$164$	2.32098	−	5.60334i	0.181238	−	0.437548i
$165$		0			0
$166$			11.1620i			0.866338i
$167$	−13.5665	+	5.61942i	−1.04981	+	0.434844i	−0.839822	−	0.542861i	$-0.817341\pi$
$167$	−13.5665	+	5.61942i	−1.04981	+	0.434844i	−0.209983	+	0.977705i	$0.567341\pi$
$168$	4.26176	−	4.26176i	0.328802	−	0.328802i
$169$	26.6476			2.04981
$170$		0			0
$171$	1.07590			0.0822762
$172$	10.0019	−	10.0019i	0.762637	−	0.762637i
$173$	−13.6265	+	5.64428i	−1.03600	+	0.429127i	−0.834876	−	0.550439i	$-0.814461\pi$
$173$	−13.6265	+	5.64428i	−1.03600	+	0.429127i	−0.201127	+	0.979565i	$0.564461\pi$
$174$		−	20.6688i		−	1.56689i
$175$		0			0
$176$	−0.224432	+	0.541828i	−0.0169172	+	0.0408418i
$177$	3.71899	−	8.97842i	0.279536	−	0.674860i
$178$	8.33531	+	8.33531i	0.624758	+	0.624758i
$179$	10.0949	−	10.0949i	0.754531	−	0.754531i	−0.220790	−	0.975321i	$-0.570864\pi$
$179$	10.0949	−	10.0949i	0.754531	−	0.754531i	0.975321	+	0.220790i	$0.0708636\pi$
$180$		0			0
$181$	2.30531	−	5.56552i	0.171353	−	0.413682i	−0.814752	−	0.579810i	$-0.803127\pi$
$181$	2.30531	−	5.56552i	0.171353	−	0.413682i	0.986104	+	0.166129i	$0.0531267\pi$
$182$	−1.58333	−	3.82250i	−0.117364	−	0.283343i
$183$	−3.26962			−0.241698
$184$	−0.734259	−	1.77266i	−0.0541303	−	0.130682i
$185$		0			0
$186$	14.4875			1.06227
$187$	−8.22408	+	6.23855i	−0.601404	+	0.456208i
$188$		−	12.9198i		−	0.942274i
$189$	3.41249	+	3.41249i	0.248222	+	0.248222i
$190$		0			0
$191$			14.1379i			1.02298i	0.859288	+	0.511492i	$0.170907\pi$
$191$			14.1379i			1.02298i	−0.859288	+	0.511492i	$0.829093\pi$
$192$	6.04070	+	14.5835i	0.435950	+	1.05248i
$193$	21.5052	+	8.90773i	1.54797	+	0.641192i	0.982949	−	0.183881i	$-0.0588661\pi$
$193$	21.5052	+	8.90773i	1.54797	+	0.641192i	0.565026	+	0.825073i	$0.308866\pi$
$194$	9.95749	+	4.12453i	0.714906	+	0.296124i
$195$		0			0
$196$	−5.41372	+	5.41372i	−0.386694	+	0.386694i
$197$	−3.55817	+	8.59019i	−0.253509	+	0.612026i	−0.998483	−	0.0550686i	$-0.982462\pi$
$197$	−3.55817	+	8.59019i	−0.253509	+	0.612026i	0.744973	+	0.667094i	$0.232462\pi$
$198$	−11.0879	−	4.59277i	−0.787984	−	0.326394i
$199$	−6.98662	+	2.89395i	−0.495268	+	0.205147i	−0.616315	−	0.787500i	$-0.711375\pi$
$199$	−6.98662	+	2.89395i	−0.495268	+	0.205147i	0.121046	+	0.992647i	$0.461375\pi$
$200$		0			0
$201$	6.19683	+	14.9605i	0.437090	+	1.05523i
$202$	6.43221	−	6.43221i	0.452569	−	0.452569i
$203$		−	5.76916i		−	0.404916i
$204$	−1.91179	+	13.9255i	−0.133852	+	0.974982i
$205$		0			0
$206$	6.26794	+	6.26794i	0.436708	+	0.436708i
$207$	3.26785	−	1.35359i	0.227131	−	0.0940809i
$208$	1.47500			0.102273
$209$	−0.469216	+	0.194356i	−0.0324563	+	0.0134439i
$210$		0			0
$211$	23.0644	+	9.55359i	1.58782	+	0.657697i	0.989628	−	0.143656i	$-0.0458859\pi$
$211$	23.0644	+	9.55359i	1.58782	+	0.657697i	0.598192	+	0.801353i	$0.295886\pi$
$212$	−3.24230	−	3.24230i	−0.222682	−	0.222682i
$213$	−8.07642	−	8.07642i	−0.553387	−	0.553387i
$214$	3.18568	+	1.31955i	0.217769	+	0.0902028i
$215$		0			0
$216$	−17.6446	+	7.30864i	−1.20056	+	0.497290i
$217$	4.04382			0.274512
$218$	−2.67827	+	1.10938i	−0.181395	+	0.0751364i
$219$	−10.5733	−	10.5733i	−0.714478	−	0.714478i
$220$		0			0
$221$	22.4113	+	13.1051i	1.50755	+	0.881542i
$222$			20.6927i			1.38880i
$223$	8.60440	−	8.60440i	0.576193	−	0.576193i	−0.357659	−	0.933852i	$-0.616425\pi$
$223$	8.60440	−	8.60440i	0.576193	−	0.576193i	0.933852	+	0.357659i	$0.116425\pi$
$224$	1.54190	+	3.72248i	0.103023	+	0.248719i
$225$		0			0
$226$	−0.336759	+	0.139490i	−0.0224009	+	0.00927876i
$227$	−1.83530	−	0.760206i	−0.121813	−	0.0504566i	0.320944	−	0.947098i	$-0.396000\pi$
$227$	−1.83530	−	0.760206i	−0.121813	−	0.0504566i	−0.442757	+	0.896641i	$0.646000\pi$
$228$	−0.264653	+	0.638928i	−0.0175271	+	0.0423141i
$229$	−1.62070	+	1.62070i	−0.107099	+	0.107099i	−0.758626	−	0.651527i	$-0.774129\pi$
$229$	−1.62070	+	1.62070i	−0.107099	+	0.107099i	0.651527	+	0.758626i	$0.274129\pi$
$230$		0			0
$231$	−4.84554	−	2.00709i	−0.318813	−	0.132057i
$232$	21.0930	+	8.73703i	1.38483	+	0.573614i
$233$	8.68807	+	20.9749i	0.569174	+	1.37411i	0.902252	+	0.431209i	$0.141913\pi$
$233$	8.68807	+	20.9749i	0.569174	+	1.37411i	−0.333078	+	0.942899i	$0.608087\pi$
$234$			30.1843i			1.97321i
$235$		0			0
$236$	2.82125	+	2.82125i	0.183647	+	0.183647i
$237$			40.4596i			2.62813i
$238$	0.368487	−	2.68407i	0.0238854	−	0.173982i
$239$	−13.2285			−0.855683			−0.427841	−	0.903854i	$-0.640726\pi$
$239$	−13.2285			−0.855683			−0.427841	+	0.903854i	$0.640726\pi$
$240$		0			0
$241$	1.10950	+	2.67856i	0.0714689	+	0.172541i	0.955577	−	0.294741i	$-0.0952333\pi$
$241$	1.10950	+	2.67856i	0.0714689	+	0.172541i	−0.884108	+	0.467282i	$0.845233\pi$
$242$	−4.27706			−0.274940
$243$	4.07251	+	9.83190i	0.261251	+	0.630717i
$244$	0.513699	−	1.24018i	0.0328862	−	0.0793943i
$245$		0			0
$246$	9.44150	−	9.44150i	0.601968	−	0.601968i
$247$	0.903209	+	0.903209i	0.0574698	+	0.0574698i
$248$	−6.12410	+	14.7849i	−0.388881	+	0.938842i
$249$	13.6182	−	32.8773i	0.863021	−	2.08352i
$250$		0			0
$251$		−	9.85445i		−	0.622008i	−0.950409	−	0.311004i	$-0.899335\pi$
$251$		−	9.85445i		−	0.622008i	0.950409	−	0.311004i	$-0.100665\pi$
$252$	−4.21432	+	1.74563i	−0.265477	+	0.109964i
$253$	−1.18064	+	1.18064i	−0.0742261	+	0.0742261i
$254$	−1.95333			−0.122563
$255$		0			0
$256$	−16.4994			−1.03121
$257$	3.74014	−	3.74014i	0.233303	−	0.233303i	−0.580767	−	0.814070i	$-0.697247\pi$
$257$	3.74014	−	3.74014i	0.233303	−	0.233303i	0.814070	+	0.580767i	$0.197247\pi$
$258$	28.7698	−	11.9168i	1.79113	−	0.741910i
$259$			5.77584i			0.358893i
$260$		0			0
$261$	−16.1065	+	38.8845i	−0.996967	+	2.40689i
$262$	2.78259	−	6.71776i	0.171909	−	0.415025i
$263$	8.89552	+	8.89552i	0.548521	+	0.548521i	0.926013	−	0.377492i	$-0.123213\pi$
$263$	8.89552	+	8.89552i	0.548521	+	0.548521i	−0.377492	+	0.926013i	$0.623213\pi$
$264$	14.6765	−	14.6765i	0.903276	−	0.903276i
$265$		0			0
$266$	0.0510104	−	0.123150i	0.00312765	−	0.00755081i
$267$	−14.3819	−	34.7210i	−0.880159	−	2.12489i
$268$	−6.64815			−0.406101
$269$	−3.52167	−	8.50207i	−0.214720	−	0.518380i	0.779417	−	0.626505i	$-0.215515\pi$
$269$	−3.52167	−	8.50207i	−0.214720	−	0.518380i	−0.994137	+	0.108125i	$0.965515\pi$
$270$		0			0
$271$	−14.6023			−0.887028			−0.443514	−	0.896267i	$-0.646268\pi$
$271$	−14.6023			−0.887028			−0.443514	+	0.896267i	$0.646268\pi$
$272$	0.833762	+	0.487545i	0.0505543	+	0.0295617i
$273$			13.1908i			0.798346i
$274$	5.03038	+	5.03038i	0.303896	+	0.303896i
$275$		0			0
$276$			2.27359i			0.136854i
$277$	−5.00008	−	12.0713i	−0.300425	−	0.725291i	−0.999943	−	0.0106758i	$-0.996602\pi$
$277$	−5.00008	−	12.0713i	−0.300425	−	0.725291i	0.699518	−	0.714615i	$-0.253398\pi$
$278$	−14.5822	−	6.04013i	−0.874580	−	0.362263i
$279$	−27.2556	−	11.2896i	−1.63175	−	0.675892i
$280$		0			0
$281$	5.34654	−	5.34654i	0.318948	−	0.318948i	−0.529415	−	0.848363i	$-0.677589\pi$
$281$	5.34654	−	5.34654i	0.318948	−	0.318948i	0.848363	+	0.529415i	$0.177589\pi$
$282$	10.8848	−	26.2782i	0.648179	−	1.56484i
$283$	3.80456	+	1.57590i	0.226157	+	0.0936775i	0.492885	−	0.870095i	$-0.335942\pi$
$283$	3.80456	+	1.57590i	0.226157	+	0.0936775i	−0.266727	+	0.963772i	$0.585942\pi$
$284$	4.33232	−	1.79450i	0.257076	−	0.106484i
$285$		0			0
$286$	−5.45262	−	13.1638i	−0.322420	−	0.778392i
$287$	2.63536	−	2.63536i	0.155560	−	0.155560i
$288$		−	29.3944i		−	1.73208i
$289$	8.33654	+	14.8156i	0.490385	+	0.871506i
$290$		0			0
$291$	−24.2974	−	24.2974i	−1.42434	−	1.42434i
$292$	5.67169	−	2.34929i	0.331911	−	0.137482i
$293$	18.5803			1.08547			0.542736	−	0.839903i	$-0.317388\pi$
$293$	18.5803			1.08547			0.542736	+	0.839903i	$0.317388\pi$
$294$	−15.5722	+	6.45021i	−0.908189	+	0.376184i
$295$		0			0
$296$	−21.1175	−	8.74714i	−1.22743	−	0.508417i
$297$	11.7518	+	11.7518i	0.681909	+	0.681909i
$298$	−4.74804	−	4.74804i	−0.275047	−	0.275047i
$299$	3.87966	+	1.60701i	0.224366	+	0.0929356i
$300$		0			0
$301$	8.03036	−	3.32628i	0.462862	−	0.191724i
$302$	12.2139			0.702829
$303$	−26.7936	+	11.0983i	−1.53925	+	0.637578i
$304$	0.0336019	+	0.0336019i	0.00192720	+	0.00192720i
$305$		0			0
$306$	−9.97708	+	17.0620i	−0.570351	+	0.975372i
$307$		−	9.82624i		−	0.560813i	−0.959881	−	0.280407i	$-0.909531\pi$
$307$		−	9.82624i		−	0.560813i	0.959881	−	0.280407i	$-0.0904693\pi$
$308$	1.52259	−	1.52259i	0.0867576	−	0.0867576i
$309$	−10.8148	−	26.1093i	−0.615234	−	1.48531i
$310$		0			0
$311$	26.5045	−	10.9785i	1.50293	−	0.622536i	0.528849	−	0.848716i	$-0.322624\pi$
$311$	26.5045	−	10.9785i	1.50293	−	0.622536i	0.974086	+	0.226180i	$0.0726237\pi$
$312$	−48.2280	−	19.9767i	−2.73037	−	1.13096i
$313$	0.370684	−	0.894911i	0.0209523	−	0.0505834i	−0.913057	−	0.407832i	$-0.866285\pi$
$313$	0.370684	−	0.894911i	0.0209523	−	0.0505834i	0.934009	+	0.357248i	$0.116285\pi$
$314$	1.76259	−	1.76259i	0.0994689	−	0.0994689i
$315$		0			0
$316$	−15.3465	−	6.35671i	−0.863306	−	0.357593i
$317$	24.5058	+	10.1506i	1.37638	+	0.570116i	0.943511	−	0.331341i	$-0.107501\pi$
$317$	24.5058	+	10.1506i	1.37638	+	0.570116i	0.432870	+	0.901456i	$0.357501\pi$
$318$	−3.86307	−	9.32626i	−0.216630	−	0.522991i
$319$		−	19.8676i		−	1.11237i
$320$		0			0
$321$	−7.77342	−	7.77342i	−0.433870	−	0.433870i
$322$		−	0.438222i		−	0.0244211i
$323$	0.212005	+	0.809096i	0.0117963	+	0.0450193i
$324$	3.80705			0.211503
$325$		0			0
$326$	−0.478610	−	1.15547i	−0.0265077	−	0.0639953i
$327$	9.24228			0.511099
$328$	5.64423	+	13.6264i	0.311651	+	0.752391i
$329$	3.03821	−	7.33489i	0.167502	−	0.404386i
$330$		0			0
$331$	4.33174	−	4.33174i	0.238094	−	0.238094i	−0.577967	−	0.816060i	$-0.696154\pi$
$331$	4.33174	−	4.33174i	0.238094	−	0.238094i	0.816060	+	0.577967i	$0.196154\pi$
$332$	10.3309	+	10.3309i	0.566981	+	0.566981i
$333$	16.1251	−	38.9295i	0.883652	−	2.13333i
$334$	5.07910	−	12.2620i	0.277916	−	0.670949i
$335$		0			0
$336$			0.490736i			0.0267718i
$337$	−14.6668	+	6.07517i	−0.798950	+	0.330936i	−0.744536	−	0.667583i	$-0.767329\pi$
$337$	−14.6668	+	6.07517i	−0.798950	+	0.330936i	−0.0544140	+	0.998518i	$0.517329\pi$
$338$	−17.0309	+	17.0309i	−0.926360	+	0.926360i
$339$	1.16210			0.0631167
$340$		0			0
$341$	13.9260			0.754133
$342$	−0.687626	+	0.687626i	−0.0371826	+	0.0371826i
$343$	−9.04815	+	3.74787i	−0.488554	+	0.202366i
$344$			34.3978i			1.85461i
$345$		0			0
$346$	5.10157	−	12.3163i	0.274262	−	0.662127i
$347$	−0.651859	+	1.57373i	−0.0349936	+	0.0844821i	−0.940410	−	0.340042i	$-0.889559\pi$
$347$	−0.651859	+	1.57373i	−0.0349936	+	0.0844821i	0.905417	+	0.424524i	$0.139559\pi$
$348$	−19.1298	−	19.1298i	−1.02547	−	1.02547i
$349$	−24.9284	+	24.9284i	−1.33439	+	1.33439i	−0.432985	+	0.901401i	$0.642540\pi$
$349$	−24.9284	+	24.9284i	−1.33439	+	1.33439i	−0.901401	+	0.432985i	$0.857460\pi$
$350$		0			0
$351$	15.9958	−	38.6172i	0.853791	−	2.06123i
$352$	5.30994	+	12.8193i	0.283021	+	0.683273i
$353$	22.4928			1.19717			0.598586	−	0.801059i	$-0.295730\pi$
$353$	22.4928			1.19717			0.598586	+	0.801059i	$0.295730\pi$
$354$	3.36140	+	8.11513i	0.178656	+	0.431314i
$355$		0			0
$356$	15.4294			0.817755
$357$	−4.36008	+	7.45629i	−0.230760	+	0.394629i
$358$			12.9037i			0.681981i
$359$	12.7307	+	12.7307i	0.671898	+	0.671898i	0.958153	−	0.286255i	$-0.0924105\pi$
$359$	12.7307	+	12.7307i	0.671898	+	0.671898i	−0.286255	+	0.958153i	$0.592410\pi$
$360$		0			0
$361$		−	18.9588i		−	0.997834i
$362$	2.08365	+	5.03038i	0.109514	+	0.264391i
$363$	12.5980	+	5.21826i	0.661223	+	0.273887i
$364$	−5.00333	−	2.07245i	−0.262246	−	0.108626i
$365$		0			0
$366$	2.08967	−	2.08967i	0.109229	−	0.109229i
$367$	11.9711	−	28.9008i	0.624887	−	1.50861i	−0.221015	−	0.975271i	$-0.570937\pi$
$367$	11.9711	−	28.9008i	0.624887	−	1.50861i	0.845901	−	0.533340i	$-0.179063\pi$
$368$	0.144334	+	0.0597851i	0.00752393	+	0.00311651i
$369$	−25.1199	+	10.4050i	−1.30769	+	0.541663i
$370$		0			0
$371$	−1.07828	−	2.60319i	−0.0559814	−	0.135151i
$372$	13.4088	−	13.4088i	0.695213	−	0.695213i
$373$			24.3521i			1.26091i	0.776228	+	0.630453i	$0.217131\pi$
$373$			24.3521i			1.26091i	−0.776228	+	0.630453i	$0.782869\pi$
$374$	1.26898	−	9.24331i	0.0656175	−	0.477960i
$375$		0			0
$376$	22.2164	+	22.2164i	1.14573	+	1.14573i
$377$	−46.1644	+	19.1219i	−2.37759	+	0.984830i
$378$	−4.36196			−0.224355
$379$	−6.04944	+	2.50576i	−0.310739	+	0.128712i	−0.532603	−	0.846365i	$-0.678786\pi$
$379$	−6.04944	+	2.50576i	−0.310739	+	0.128712i	0.221864	+	0.975078i	$0.428786\pi$
$380$		0			0
$381$	5.75348	+	2.38317i	0.294760	+	0.122093i
$382$	−9.03578	−	9.03578i	−0.462311	−	0.462311i
$383$	−13.0036	−	13.0036i	−0.664451	−	0.664451i	0.291975	−	0.956426i	$-0.405688\pi$
$383$	−13.0036	−	13.0036i	−0.664451	−	0.664451i	−0.956426	+	0.291975i	$0.905688\pi$
$384$	16.3287	+	6.76355i	0.833269	+	0.345151i
$385$		0			0
$386$	−19.4374	+	8.05123i	−0.989337	+	0.409797i
$387$	−63.4115			−3.22339
$388$	13.0335	−	5.39865i	0.661676	−	0.274075i
$389$	−1.52050	−	1.52050i	−0.0770922	−	0.0770922i	0.667509	−	0.744602i	$-0.267360\pi$
$389$	−1.52050	−	1.52050i	−0.0770922	−	0.0770922i	−0.744602	+	0.667509i	$0.767360\pi$
$390$		0			0
$391$	1.66185	+	2.19076i	0.0840433	+	0.110791i
$392$		−	18.6185i		−	0.940375i
$393$	−16.3921	+	16.3921i	−0.826872	+	0.826872i
$394$	−3.21605	−	7.76423i	−0.162022	−	0.391156i
$395$		0			0
$396$	−14.5131	+	6.01154i	−0.729313	+	0.302091i
$397$	0.358143	+	0.148348i	0.0179747	+	0.00744535i	0.391653	−	0.920113i	$-0.371903\pi$
$397$	0.358143	+	0.148348i	0.0179747	+	0.00744535i	−0.373678	+	0.927558i	$0.621903\pi$
$398$	2.61569	−	6.31484i	0.131113	−	0.316534i
$399$	−0.300500	+	0.300500i	−0.0150438	+	0.0150438i
$400$		0			0
$401$	−15.4465	−	6.39816i	−0.771362	−	0.319509i	−0.0379382	−	0.999280i	$-0.512079\pi$
$401$	−15.4465	−	6.39816i	−0.771362	−	0.319509i	−0.733424	+	0.679771i	$0.762079\pi$
$402$	−13.5220	−	5.60099i	−0.674415	−	0.279352i
$403$	−13.4033	−	32.3584i	−0.667665	−	1.61188i
$404$		−	11.9066i		−	0.592374i
$405$		0			0
$406$	3.68717	+	3.68717i	0.182991	+	0.182991i
$407$			19.8906i			0.985943i
$408$	−20.6584	−	27.2333i	−1.02274	−	1.34825i
$409$	15.7306			0.777828			0.388914	−	0.921274i	$-0.372850\pi$
$409$	15.7306			0.777828			0.388914	+	0.921274i	$0.372850\pi$
$410$		0			0
$411$	−8.67951	−	20.9542i	−0.428129	−	1.03359i
$412$	11.6025			0.571613
$413$	0.938249	+	2.26513i	0.0461682	+	0.111460i
$414$	−1.22344	+	2.95364i	−0.0601287	+	0.145164i
$415$		0			0
$416$	24.6764	−	24.6764i	1.20986	−	1.20986i
$417$	35.5821	+	35.5821i	1.74246	+	1.74246i
$418$	0.175668	−	0.424100i	0.00859220	−	0.0207434i
$419$	4.06462	−	9.81286i	0.198570	−	0.479390i	−0.792959	−	0.609274i	$-0.791461\pi$
$419$	4.06462	−	9.81286i	0.198570	−	0.479390i	0.991529	+	0.129885i	$0.0414608\pi$
$420$		0			0
$421$			17.0231i			0.829656i	0.909900	+	0.414828i	$0.136158\pi$
$421$			17.0231i			0.829656i	−0.909900	+	0.414828i	$0.863842\pi$
$422$	−20.8467	+	8.63499i	−1.01480	+	0.420345i
$423$	−40.9555	+	40.9555i	−1.99132	+	1.99132i
$424$	11.1507			0.541526
$425$		0			0
$426$	10.3235			0.500178
$427$	0.583279	−	0.583279i	0.0282269	−	0.0282269i
$428$	4.16979	−	1.72718i	0.201554	−	0.0834865i
$429$			45.4261i			2.19320i
$430$		0			0
$431$	−7.53530	+	18.1918i	−0.362963	+	0.876270i	0.631901	+	0.775049i	$0.282275\pi$
$431$	−7.53530	+	18.1918i	−0.362963	+	0.876270i	−0.994864	+	0.101221i	$0.967725\pi$
$432$	0.595087	−	1.43667i	0.0286311	−	0.0691217i
$433$	15.5266	+	15.5266i	0.746159	+	0.746159i	0.973755	−	0.227597i	$-0.0730868\pi$
$433$	15.5266	+	15.5266i	0.746159	+	0.746159i	−0.227597	+	0.973755i	$0.573087\pi$
$434$	−2.58447	+	2.58447i	−0.124059	+	0.124059i
$435$		0			0
$436$	−1.45208	+	3.50563i	−0.0695419	+	0.167889i
$437$	0.0517732	+	0.124991i	0.00247665	+	0.00597915i
$438$	13.5152			0.645779
$439$	3.25235	+	7.85186i	0.155226	+	0.374749i	0.982292	−	0.187356i	$-0.0599918\pi$
$439$	3.25235	+	7.85186i	0.155226	+	0.374749i	−0.827066	+	0.562105i	$0.809992\pi$
$440$		0			0
$441$	34.3227			1.63441
$442$	−22.6991	+	5.94777i	−1.07969	+	0.282907i
$443$		−	4.70952i		−	0.223756i	−0.993722	−	0.111878i	$-0.964313\pi$
$443$		−	4.70952i		−	0.223756i	0.993722	−	0.111878i	$-0.0356866\pi$
$444$	19.1520	+	19.1520i	0.908912	+	0.908912i
$445$		0			0
$446$			10.9984i			0.520791i
$447$	8.19236	+	19.7781i	0.387485	+	0.935472i
$448$	−3.67923	−	1.52398i	−0.173827	−	0.0720015i
$449$	24.2399	+	10.0405i	1.14395	+	0.473839i	0.872500	−	0.488613i	$-0.162497\pi$
$449$	24.2399	+	10.0405i	1.14395	+	0.473839i	0.271449	+	0.962453i	$0.412497\pi$
$450$		0			0
$451$	9.07554	−	9.07554i	0.427351	−	0.427351i
$452$	−0.182581	+	0.440789i	−0.00858788	+	0.0207330i
$453$	−35.9756	−	14.9016i	−1.69028	−	0.700138i
$454$	1.65883	−	0.687110i	0.0778528	−	0.0322477i
$455$		0			0
$456$	−0.643591	−	1.55377i	−0.0301389	−	0.0727618i
$457$	−14.6247	+	14.6247i	−0.684115	+	0.684115i	−0.960925	−	0.276810i	$-0.910723\pi$
$457$	−14.6247	+	14.6247i	−0.684115	+	0.684115i	0.276810	+	0.960925i	$0.410723\pi$
$458$		−	2.07163i		−	0.0968009i
$459$	21.8063	−	16.5416i	1.01783	−	0.772098i
$460$		0			0
$461$	−1.37250	−	1.37250i	−0.0639239	−	0.0639239i	0.674422	−	0.738346i	$-0.264393\pi$
$461$	−1.37250	−	1.37250i	−0.0639239	−	0.0639239i	−0.738346	+	0.674422i	$0.764393\pi$
$462$	4.37963	−	1.81410i	0.203759	−	0.0843996i
$463$	−10.6872			−0.496676			−0.248338	−	0.968673i	$-0.579884\pi$
$463$	−10.6872			−0.496676			−0.248338	+	0.968673i	$0.579884\pi$
$464$	−1.71744	+	0.711389i	−0.0797304	+	0.0330254i
$465$		0			0
$466$	−18.9581	−	7.85269i	−0.878216	−	0.363769i
$467$	3.43207	+	3.43207i	0.158817	+	0.158817i	0.782042	−	0.623225i	$-0.214178\pi$
$467$	3.43207	+	3.43207i	0.158817	+	0.158817i	−0.623225	+	0.782042i	$0.714178\pi$
$468$	27.9368	+	27.9368i	1.29138	+	1.29138i
$469$	−3.77432	−	1.56337i	−0.174282	−	0.0721899i
$470$		0			0
$471$	−7.34214	+	3.04121i	−0.338308	+	0.140132i
$472$	−9.70263			−0.446600
$473$	27.6547	−	11.4549i	1.27156	−	0.526699i
$474$	−25.8584	−	25.8584i	−1.18772	−	1.18772i
$475$		0			0
$476$	−2.14317	−	2.82527i	−0.0982321	−	0.129496i
$477$			20.5560i			0.941196i
$478$	8.45458	−	8.45458i	0.386703	−	0.386703i
$479$	−2.91185	−	7.02983i	−0.133046	−	0.321201i	0.843291	−	0.537458i	$-0.180615\pi$
$479$	−2.91185	−	7.02983i	−0.133046	−	0.321201i	−0.976337	+	0.216256i	$0.930615\pi$
$480$		0			0
$481$	46.2179	−	19.1441i	2.10736	−	0.872895i
$482$	−2.42101	−	1.00282i	−0.110274	−	0.0456770i
$483$	−0.534655	+	1.29077i	−0.0243276	+	0.0587321i
$484$	−3.95860	+	3.95860i	−0.179937	+	0.179937i
$485$		0			0
$486$	−8.88654	−	3.68093i	−0.403102	−	0.166970i
$487$	−0.393190	−	0.162865i	−0.0178171	−	0.00738010i	0.373757	−	0.927527i	$-0.378069\pi$
$487$	−0.393190	−	0.162865i	−0.0178171	−	0.00738010i	−0.391574	+	0.920147i	$0.628069\pi$
$488$	1.24923	+	3.01591i	0.0565500	+	0.136524i
$489$			3.98733i			0.180313i
$490$		0			0
$491$	0.197439	+	0.197439i	0.00891028	+	0.00891028i	0.711548	−	0.702638i	$-0.247994\pi$
$491$	0.197439	+	0.197439i	0.00891028	+	0.00891028i	−0.702638	+	0.711548i	$0.747994\pi$
$492$		−	17.4770i		−	0.787924i
$493$	−32.4156	−	4.45022i	−1.45992	−	0.200428i
$494$	−1.15451			−0.0519440
$495$		0			0
$496$	−0.498639	−	1.20382i	−0.0223895	−	0.0540531i
$497$	2.88156			0.129256
$498$	12.3088	+	29.7161i	0.551571	+	1.33161i
$499$	−7.08936	+	17.1152i	−0.317363	+	0.766183i	0.682029	+	0.731325i	$0.261098\pi$
$499$	−7.08936	+	17.1152i	−0.317363	+	0.766183i	−0.999392	+	0.0348579i	$0.988902\pi$
$500$		0			0
$501$	−29.9207	+	29.9207i	−1.33676	+	1.33676i
$502$	6.29815	+	6.29815i	0.281100	+	0.281100i
$503$	−3.10919	+	7.50624i	−0.138632	+	0.334687i	−0.977913	−	0.209010i	$-0.932976\pi$
$503$	−3.10919	+	7.50624i	−0.138632	+	0.334687i	0.839282	+	0.543697i	$0.182976\pi$
$504$	4.24508	−	10.2485i	0.189091	−	0.456506i
$505$		0			0
$506$		−	1.50913i		−	0.0670891i
$507$	70.9428	−	29.3855i	3.15068	−	1.30505i
$508$	−1.80789	+	1.80789i	−0.0802120	+	0.0802120i
$509$	−15.1877			−0.673181			−0.336590	−	0.941651i	$-0.609274\pi$
$509$	−15.1877			−0.673181			−0.336590	+	0.941651i	$0.609274\pi$
$510$		0			0
$511$	3.77241			0.166882
$512$	1.87113	−	1.87113i	0.0826930	−	0.0826930i
$513$	1.24414	−	0.515338i	0.0549299	−	0.0227527i
$514$			4.78077i			0.210871i
$515$		0			0
$516$	15.5981	−	37.6572i	0.686669	−	1.65777i
$517$	10.4629	−	25.2596i	0.460157	−	1.11092i
$518$	−3.69144	−	3.69144i	−0.162193	−	0.162193i
$519$	−30.0531	+	30.0531i	−1.31918	+	1.31918i
$520$		0			0
$521$	−14.2931	+	34.5065i	−0.626190	+	1.51176i	0.218131	+	0.975919i	$0.430004\pi$
$521$	−14.2931	+	34.5065i	−0.626190	+	1.51176i	−0.844321	+	0.535837i	$0.819996\pi$
$522$	−14.5578	−	35.1457i	−0.637178	−	1.53828i
$523$	−8.03541			−0.351364			−0.175682	−	0.984447i	$-0.556213\pi$
$523$	−8.03541			−0.351364			−0.175682	+	0.984447i	$0.556213\pi$
$524$	−3.64217	−	8.79298i	−0.159109	−	0.384123i
$525$		0			0
$526$	−11.3706			−0.495780
$527$	3.11932	−	22.7213i	0.135880	−	0.989754i
$528$			1.68998i			0.0735469i
$529$	−15.9490	−	15.9490i	−0.693433	−	0.693433i
$530$		0			0
$531$		−	17.8866i		−	0.776210i
$532$	−0.0667683	−	0.161193i	−0.00289477	−	0.00698860i
$533$	−29.8228	−	12.3530i	−1.29177	−	0.535069i
$534$	31.3825	+	12.9991i	1.35805	+	0.562524i
$535$		0			0
$536$	11.4319	−	11.4319i	0.493784	−	0.493784i
$537$	15.7432	−	38.0075i	0.679370	−	1.64014i
$538$	7.68457	+	3.18306i	0.331306	+	0.137231i
$539$	−14.9686	+	6.20020i	−0.644744	+	0.267062i
$540$		0			0
$541$	6.24786	+	15.0837i	0.268616	+	0.648498i	0.999419	−	0.0340917i	$-0.0108538\pi$
$541$	6.24786	+	15.0837i	0.268616	+	0.648498i	−0.730802	+	0.682589i	$0.760854\pi$
$542$	9.33259	−	9.33259i	0.400869	−	0.400869i
$543$		−	17.3590i		−	0.744947i
$544$	22.1051	−	5.79213i	0.947750	−	0.248336i
$545$		0			0
$546$	−8.43049	−	8.43049i	−0.360792	−	0.360792i
$547$	−26.6116	+	11.0229i	−1.13783	+	0.471304i	−0.870435	−	0.492283i	$-0.836162\pi$
$547$	−26.6116	+	11.0229i	−1.13783	+	0.471304i	−0.267394	+	0.963587i	$0.586162\pi$
$548$	9.31165			0.397774
$549$	−5.55975	+	2.30292i	−0.237284	+	0.0982864i
$550$		0			0
$551$	−1.48729	−	0.616054i	−0.0633605	−	0.0262448i
$552$	−3.90958	−	3.90958i	−0.166403	−	0.166403i
$553$	−7.21773	−	7.21773i	−0.306929	−	0.306929i
$554$	10.9106	+	4.51931i	0.463546	+	0.192007i
$555$		0			0
$556$	−19.0868	+	7.90601i	−0.809461	+	0.335290i
$557$	7.64838			0.324072			0.162036	−	0.986785i	$-0.448194\pi$
$557$	7.64838			0.324072			0.162036	+	0.986785i	$0.448194\pi$
$558$	24.6349	−	10.2041i	1.04288	−	0.431974i
$559$	−53.2334	−	53.2334i	−2.25153	−	2.25153i
$560$		0			0
$561$	−15.0151	+	25.6777i	−0.633938	+	1.08411i
$562$			6.83413i			0.288280i
$563$	29.9736	−	29.9736i	1.26324	−	1.26324i	0.313724	−	0.949514i	$-0.398423\pi$
$563$	29.9736	−	29.9736i	1.26324	−	1.26324i	0.949514	−	0.313724i	$-0.101577\pi$
$564$	−14.2472	−	34.3959i	−0.599917	−	1.44833i
$565$		0			0
$566$	−3.43874	+	1.42437i	−0.144541	+	0.0598709i
$567$	2.16136	+	0.895263i	0.0907684	+	0.0375975i
$568$	−4.36393	+	10.5355i	−0.183107	+	0.442058i
$569$	21.7924	−	21.7924i	0.913584	−	0.913584i	−0.0829686	−	0.996552i	$-0.526440\pi$
$569$	21.7924	−	21.7924i	0.913584	−	0.913584i	0.996552	+	0.0829686i	$0.0264401\pi$
$570$		0			0
$571$	−20.3678	−	8.43662i	−0.852366	−	0.353062i	−0.0866487	−	0.996239i	$-0.527616\pi$
$571$	−20.3678	−	8.43662i	−0.852366	−	0.353062i	−0.765717	+	0.643177i	$0.777616\pi$
$572$	−17.2303	−	7.13702i	−0.720434	−	0.298414i
$573$	15.5905	+	37.6388i	0.651303	+	1.57238i
$574$			3.36860i			0.140603i
$575$		0			0
$576$	20.5435	+	20.5435i	0.855979	+	0.855979i
$577$		−	20.2437i		−	0.842755i	−0.906885	−	0.421378i	$-0.861547\pi$
$577$		−	20.2437i		−	0.842755i	0.906885	−	0.421378i	$-0.138453\pi$
$578$	−14.7969	−	4.14088i	−0.615471	−	0.172238i
$579$	67.0753			2.78755
$580$		0			0
$581$	3.43569	+	8.29450i	0.142537	+	0.344114i
$582$	31.0577			1.28738
$583$	−3.71333	−	8.96478i	−0.153791	−	0.371283i
$584$	−5.71308	+	13.7926i	−0.236409	+	0.570742i
$585$		0			0
$586$	−11.8750	+	11.8750i	−0.490551	+	0.490551i
$587$	9.02526	+	9.02526i	0.372513	+	0.372513i	0.868392	−	0.495879i	$-0.165154\pi$
$587$	9.02526	+	9.02526i	0.372513	+	0.372513i	−0.495879	+	0.868392i	$0.665154\pi$
$588$	−8.44278	+	20.3827i	−0.348174	+	0.840567i
$589$	0.431815	−	1.04249i	0.0177926	−	0.0429552i
$590$		0			0
$591$			26.7931i			1.10212i
$592$	1.71943	−	0.712213i	0.0706683	−	0.0292718i
$593$	−2.03582	+	2.03582i	−0.0836009	+	0.0836009i	−0.747671	−	0.664070i	$-0.768828\pi$
$593$	−2.03582	+	2.03582i	−0.0836009	+	0.0836009i	0.664070	+	0.747671i	$0.268828\pi$
$594$	−15.0216			−0.616342
$595$		0			0
$596$	−8.78902			−0.360012
$597$	−15.4089	+	15.4089i	−0.630645	+	0.630645i
$598$	−3.50662	+	1.45249i	−0.143396	+	0.0593967i
$599$			12.6720i			0.517762i	0.965909	+	0.258881i	$0.0833538\pi$
$599$			12.6720i			0.517762i	−0.965909	+	0.258881i	$0.916646\pi$
$600$		0			0
$601$	−5.25226	+	12.6801i	−0.214244	+	0.517231i	−0.994067	−	0.108769i	$-0.965309\pi$
$601$	−5.25226	+	12.6801i	−0.214244	+	0.517231i	0.779823	+	0.626000i	$0.215309\pi$
$602$	−3.00645	+	7.25822i	−0.122534	+	0.295823i
$603$	21.0745	+	21.0745i	0.858219	+	0.858219i
$604$	11.3045	−	11.3045i	0.459972	−	0.459972i
$605$		0			0
$606$	10.0311	−	24.2173i	0.407487	−	0.983760i
$607$	2.98647	+	7.20998i	0.121217	+	0.292644i	0.972827	−	0.231531i	$-0.0743736\pi$
$607$	2.98647	+	7.20998i	0.121217	+	0.292644i	−0.851610	+	0.524175i	$0.824374\pi$
$608$	1.12430			0.0455965
$609$	−6.36191	−	15.3590i	−0.257798	−	0.622379i
$610$		0			0
$611$	−68.7635			−2.78187
$612$	6.55744	+	25.0258i	0.265069	+	1.01161i
$613$		−	44.7999i		−	1.80945i	−0.425994	−	0.904726i	$-0.640076\pi$
$613$		−	44.7999i		−	1.80945i	0.425994	−	0.904726i	$-0.359924\pi$
$614$	6.28011	+	6.28011i	0.253445	+	0.253445i
$615$		0			0
$616$			5.23638i			0.210980i
$617$	8.25893	+	19.9388i	0.332492	+	0.802707i	0.998393	+	0.0566667i	$0.0180472\pi$
$617$	8.25893	+	19.9388i	0.332492	+	0.802707i	−0.665901	+	0.746040i	$0.731953\pi$
$618$	23.5988	+	9.77495i	0.949284	+	0.393206i
$619$	−35.6401	−	14.7626i	−1.43250	−	0.593360i	−0.474530	−	0.880239i	$-0.657382\pi$
$619$	−35.6401	−	14.7626i	−1.43250	−	0.593360i	−0.957967	+	0.286879i	$0.907382\pi$
$620$		0			0
$621$	3.13049	−	3.13049i	0.125622	−	0.125622i
$622$	−9.92293	+	23.9561i	−0.397873	+	0.960551i
$623$	8.75963	+	3.62836i	0.350947	+	0.145367i
$624$	3.92683	−	1.62655i	0.157199	−	0.0651140i
$625$		0			0
$626$	0.335042	+	0.808864i	0.0133910	+	0.0323287i
$627$	−1.03485	+	1.03485i	−0.0413280	+	0.0413280i
$628$		−	3.26271i		−	0.130196i
$629$	32.4531	+	4.45538i	1.29399	+	0.177647i
$630$		0			0
$631$	17.1283	+	17.1283i	0.681866	+	0.681866i	0.960420	−	0.278555i	$-0.0898553\pi$
$631$	17.1283	+	17.1283i	0.681866	+	0.681866i	−0.278555	+	0.960420i	$0.589855\pi$
$632$	37.3200	−	15.4585i	1.48451	−	0.614904i
$633$	71.9387			2.85931
$634$	−22.1495	+	9.17461i	−0.879668	+	0.364370i
$635$		0			0
$636$	−12.2073	−	5.05642i	−0.484050	−	0.200500i
$637$	28.8136	+	28.8136i	1.14164	+	1.14164i
$638$	12.6977	+	12.6977i	0.502708	+	0.502708i
$639$	−19.4219	−	8.04480i	−0.768317	−	0.318247i
$640$		0			0
$641$	40.1257	−	16.6206i	1.58487	−	0.656475i	0.595694	−	0.803211i	$-0.296877\pi$
$641$	40.1257	−	16.6206i	1.58487	−	0.656475i	0.989176	+	0.146737i	$0.0468770\pi$
$642$	9.93625			0.392152
$643$	−32.7815	+	13.5786i	−1.29278	+	0.535486i	−0.919812	−	0.392359i	$-0.871659\pi$
$643$	−32.7815	+	13.5786i	−1.29278	+	0.535486i	−0.372965	+	0.927845i	$0.621659\pi$
$644$	−0.405593	−	0.405593i	−0.0159826	−	0.0159826i
$645$		0			0
$646$	−0.652603	−	0.381611i	−0.0256763	−	0.0150143i
$647$			28.2269i			1.10971i	0.831946	+	0.554857i	$0.187227\pi$
$647$			28.2269i			1.10971i	−0.831946	+	0.554857i	$0.812773\pi$
$648$	−6.54647	+	6.54647i	−0.257170	+	0.257170i
$649$	3.23111	+	7.80059i	0.126832	+	0.306200i
$650$		0			0
$651$	10.7657	−	4.45930i	0.421941	−	0.174774i
$652$	−1.51241	−	0.626459i	−0.0592304	−	0.0245340i
$653$	−1.42702	+	3.44513i	−0.0558436	+	0.134818i	−0.949339	−	0.314254i	$-0.898246\pi$
$653$	−1.42702	+	3.44513i	−0.0558436	+	0.134818i	0.893495	+	0.449073i	$0.148246\pi$
$654$	−5.90689	+	5.90689i	−0.230978	+	0.230978i
$655$		0			0
$656$	−1.10949	−	0.459567i	−0.0433184	−	0.0179431i
$657$	−25.4263	−	10.5319i	−0.991974	−	0.410889i
$658$	2.74608	+	6.62962i	0.107053	+	0.258450i
$659$		−	16.0238i		−	0.624200i	−0.950049	−	0.312100i	$-0.898968\pi$
$659$		−	16.0238i		−	0.624200i	0.950049	−	0.312100i	$-0.101032\pi$
$660$		0			0
$661$	−19.4741	−	19.4741i	−0.757454	−	0.757454i	0.218404	−	0.975858i	$-0.429915\pi$
$661$	−19.4741	−	19.4741i	−0.757454	−	0.757454i	−0.975858	+	0.218404i	$0.929915\pi$
$662$			5.53698i			0.215201i
$663$	74.1162	+	10.1752i	2.87844	+	0.395171i
$664$	−35.5292			−1.37880
$665$		0			0
$666$	14.5747	+	35.1864i	0.564757	+	1.36344i
$667$	−5.29241			−0.204923
$668$	−6.64811	−	16.0500i	−0.257223	−	0.620991i
$669$	13.4187	−	32.3956i	0.518797	−	1.25249i
$670$		0			0
$671$	2.00868	−	2.00868i	0.0775441	−	0.0775441i
$672$	8.20989	+	8.20989i	0.316703	+	0.316703i
$673$	7.24825	−	17.4988i	0.279400	−	0.674530i	−0.720420	−	0.693538i	$-0.756051\pi$
$673$	7.24825	−	17.4988i	0.279400	−	0.674530i	0.999819	+	0.0190080i	$0.00605081\pi$
$674$	5.49103	−	13.2565i	0.211507	−	0.510622i
$675$		0			0
$676$			31.5257i			1.21253i
$677$	−9.78472	+	4.05297i	−0.376058	+	0.155768i	−0.562703	−	0.826659i	$-0.690238\pi$
$677$	−9.78472	+	4.05297i	−0.376058	+	0.155768i	0.186645	+	0.982427i	$0.440238\pi$
$678$	−0.742719	+	0.742719i	−0.0285240	+	0.0285240i
$679$	8.66898			0.332685
$680$		0			0
$681$	−5.72436			−0.219358
$682$	−8.90032	+	8.90032i	−0.340811	+	0.340811i
$683$	−41.6347	+	17.2457i	−1.59311	+	0.659887i	−0.990420	−	0.138090i	$-0.955904\pi$
$683$	−41.6347	+	17.2457i	−1.59311	+	0.659887i	−0.602688	+	0.797977i	$0.705904\pi$
$684$			1.27285i			0.0486688i
$685$		0			0
$686$	3.38750	−	8.17815i	0.129335	−	0.312243i
$687$	−2.52750	+	6.10193i	−0.0964303	+	0.232803i
$688$	−1.98043	−	1.98043i	−0.0755031	−	0.0755031i
$689$	−17.2566	+	17.2566i	−0.657424	+	0.657424i
$690$		0			0
$691$	−4.99288	+	12.0539i	−0.189938	+	0.458551i	−0.989947	−	0.141437i	$-0.954828\pi$
$691$	−4.99288	+	12.0539i	−0.189938	+	0.458551i	0.800009	+	0.599988i	$0.204828\pi$
$692$	−6.67752	−	16.1209i	−0.253841	−	0.612827i
$693$	−9.65314			−0.366692
$694$	−0.589181	−	1.42241i	−0.0223650	−	0.0539939i
$695$		0			0
$696$	65.7899			2.49376
$697$	−12.7746	−	16.8403i	−0.483872	−	0.637872i
$698$		−	31.8643i		−	1.20608i
$699$	46.2598	+	46.2598i	1.74971	+	1.74971i
$700$		0			0
$701$			4.42228i			0.167027i	0.996507	+	0.0835136i	$0.0266142\pi$
$701$			4.42228i			0.167027i	−0.996507	+	0.0835136i	$0.973386\pi$
$702$	14.4577	+	34.9041i	0.545672	+	1.31737i
$703$	1.48901	+	0.616767i	0.0561590	+	0.0232618i
$704$	−12.6704	−	5.24825i	−0.477533	−	0.197801i
$705$		0			0
$706$	−14.3755	+	14.3755i	−0.541030	+	0.541030i
$707$	2.79994	−	6.75965i	0.105302	−	0.254223i
$708$	10.6220	+	4.39978i	0.399200	+	0.165354i
$709$	29.6088	−	12.2644i	1.11198	−	0.460597i	0.250361	−	0.968152i	$-0.419451\pi$
$709$	29.6088	−	12.2644i	1.11198	−	0.460597i	0.861619	+	0.507555i	$0.169451\pi$
$710$		0			0
$711$	28.4973	+	68.7985i	1.06873	+	2.58015i
$712$	−26.5318	+	26.5318i	−0.994321	+	0.994321i
$713$		−	3.70965i		−	0.138927i
$714$	−1.97884	−	7.55204i	−0.0740561	−	0.282628i
$715$		0			0
$716$	11.9429	+	11.9429i	0.446327	+	0.446327i
$717$	−35.2178	+	14.5877i	−1.31523	+	0.544787i
$718$	−16.2728			−0.607294
$719$	−25.6163	+	10.6106i	−0.955329	+	0.395710i	−0.805231	−	0.592961i	$-0.797959\pi$
$719$	−25.6163	+	10.6106i	−0.955329	+	0.395710i	−0.150098	+	0.988671i	$0.547959\pi$
$720$		0			0
$721$	6.58702	+	2.72843i	0.245313	+	0.101612i
$722$	12.1169	+	12.1169i	0.450945	+	0.450945i
$723$	5.90754	+	5.90754i	0.219704	+	0.219704i
$724$	6.58434	+	2.72732i	0.244705	+	0.101360i
$725$		0			0
$726$	−11.3867	+	4.71651i	−0.422599	+	0.175046i
$727$	10.5407			0.390934			0.195467	−	0.980710i	$-0.437378\pi$
$727$	10.5407			0.390934			0.195467	+	0.980710i	$0.437378\pi$
$728$	12.1673	−	5.03984i	0.450948	−	0.186789i
$729$	28.5105	+	28.5105i	1.05594	+	1.05594i
$730$		0			0
$731$	−12.4951	−	47.6865i	−0.462150	−	1.76375i
$732$		−	3.86816i		−	0.142971i
$733$	11.6126	−	11.6126i	0.428920	−	0.428920i	−0.459340	−	0.888260i	$-0.651914\pi$
$733$	11.6126	−	11.6126i	0.428920	−	0.428920i	0.888260	+	0.459340i	$0.151914\pi$
$734$	10.8201	+	26.1219i	0.399376	+	0.964178i
$735$		0			0
$736$	3.41486	−	1.41448i	0.125873	−	0.0521385i
$737$	−12.9979	−	5.38389i	−0.478783	−	0.198318i
$738$	9.40454	−	22.7046i	0.346186	−	0.835767i
$739$	−1.27919	+	1.27919i	−0.0470556	+	0.0470556i	−0.730243	−	0.683187i	$-0.760593\pi$
$739$	−1.27919	+	1.27919i	−0.0470556	+	0.0470556i	0.683187	+	0.730243i	$0.260593\pi$
$740$		0			0
$741$	3.40059	+	1.40857i	0.124924	+	0.0517451i
$742$	2.35289	+	0.974598i	0.0863773	+	0.0357786i
$743$	−16.4954	−	39.8234i	−0.605157	−	1.46098i	−0.868210	−	0.496198i	$-0.834729\pi$
$743$	−16.4954	−	39.8234i	−0.605157	−	1.46098i	0.263052	−	0.964782i	$-0.415271\pi$
$744$			46.1146i			1.69064i
$745$		0			0
$746$	−15.5639	−	15.5639i	−0.569833	−	0.569833i
$747$		−	65.4973i		−	2.39642i
$748$	−7.38058	−	9.72957i	−0.269861	−	0.355748i
$749$	2.77345			0.101340
$750$		0			0
$751$	−11.2128	−	27.0700i	−0.409160	−	0.987799i	−0.985359	−	0.170490i	$-0.945465\pi$
$751$	−11.2128	−	27.0700i	−0.409160	−	0.987799i	0.576199	−	0.817309i	$-0.304535\pi$
$752$	−2.55819			−0.0932876
$753$	−10.8669	−	26.2351i	−0.396013	−	0.956061i
$754$	17.2833	−	41.7256i	0.629421	−	1.51956i
$755$		0			0
$756$	−4.03717	+	4.03717i	−0.146831	+	0.146831i
$757$	−7.31966	−	7.31966i	−0.266038	−	0.266038i	0.561464	−	0.827501i	$-0.310238\pi$
$757$	−7.31966	−	7.31966i	−0.266038	−	0.266038i	−0.827501	+	0.561464i	$0.810238\pi$
$758$	2.26483	−	5.46777i	0.0822622	−	0.198598i
$759$	−1.84123	+	4.44511i	−0.0668323	+	0.161347i
$760$		0			0
$761$			40.0677i			1.45245i	0.687455	+	0.726227i	$0.258728\pi$
$761$			40.0677i			1.45245i	−0.687455	+	0.726227i	$0.741272\pi$
$762$	−5.20027	+	2.15402i	−0.188386	+	0.0780319i
$763$	−1.64876	+	1.64876i	−0.0596891	+	0.0596891i
$764$	−16.7260			−0.605125
$765$		0			0
$766$	16.6216			0.600562
$767$	15.0156	−	15.0156i	0.542182	−	0.542182i
$768$	−43.9257	+	18.1946i	−1.58503	+	0.656542i
$769$		−	40.8532i		−	1.47320i	−0.676327	−	0.736602i	$-0.736429\pi$
$769$		−	40.8532i		−	1.47320i	0.676327	−	0.736602i	$-0.263571\pi$
$770$		0			0
$771$	5.83281	−	14.0816i	0.210063	−	0.507138i
$772$	−10.5384	+	25.4419i	−0.379284	+	0.915673i
$773$	12.0994	+	12.0994i	0.435183	+	0.435183i	0.890387	−	0.455204i	$-0.150434\pi$
$773$	12.0994	+	12.0994i	0.435183	+	0.435183i	−0.455204	+	0.890387i	$0.650434\pi$
$774$	40.5273	−	40.5273i	1.45673	−	1.45673i
$775$		0			0
$776$	−13.1286	+	31.6953i	−0.471290	+	1.13779i
$777$	6.36928	+	15.3768i	0.228497	+	0.551640i
$778$	1.94355			0.0696796
$779$	−0.397979	−	0.960806i	−0.0142591	−	0.0344245i
$780$		0			0
$781$	9.92341			0.355087
$782$	−2.46227	−	0.338036i	−0.0880504	−	0.0120881i
$783$			52.6794i			1.88261i
$784$	1.07194	+	1.07194i	0.0382837	+	0.0382837i
$785$		0			0
$786$		−	20.9529i		−	0.747366i
$787$	−7.04943	−	17.0188i	−0.251285	−	0.606655i	0.747023	−	0.664798i	$-0.231482\pi$
$787$	−7.04943	−	17.0188i	−0.251285	−	0.606655i	−0.998308	+	0.0581423i	$0.981482\pi$
$788$	−10.1627	−	4.20953i	−0.362031	−	0.149958i
$789$	33.4917	+	13.8727i	1.19234	+	0.493882i
$790$		0			0
$791$	−0.207311	+	0.207311i	−0.00737114	+	0.00737114i
$792$	14.6191	−	35.2935i	0.519465	−	1.25410i
$793$	−6.60064	−	2.73408i	−0.234396	−	0.0970899i
$794$	−0.323707	+	0.134084i	−0.0114879	+	0.00475845i
$795$		0			0
$796$	−3.42372	−	8.26559i	−0.121350	−	0.292966i
$797$	20.2228	−	20.2228i	0.716328	−	0.716328i	−0.251523	−	0.967851i	$-0.580931\pi$
$797$	20.2228	−	20.2228i	0.716328	−	0.716328i	0.967851	+	0.251523i	$0.0809314\pi$
$798$		−	0.384109i		−	0.0135973i
$799$	−38.8694	−	22.7290i	−1.37510	−	0.804094i
$800$		0			0
$801$	−48.9107	−	48.9107i	−1.72817	−	1.72817i
$802$	13.9613	−	5.78296i	0.492991	−	0.204203i
$803$	12.9913			0.458453
$804$	−17.6991	+	7.33121i	−0.624200	+	0.258552i
$805$		0			0
$806$	29.2470	+	12.1145i	1.03018	+	0.426716i
$807$	−18.7512	−	18.7512i	−0.660074	−	0.660074i
$808$	20.4741	+	20.4741i	0.720276	+	0.720276i
$809$	25.1095	+	10.4007i	0.882801	+	0.365668i	0.777583	−	0.628781i	$-0.216446\pi$
$809$	25.1095	+	10.4007i	0.882801	+	0.365668i	0.105219	+	0.994449i	$0.466446\pi$
$810$		0			0
$811$	17.5782	−	7.28112i	0.617254	−	0.255675i	−0.0520727	−	0.998643i	$-0.516583\pi$
$811$	17.5782	−	7.28112i	0.617254	−	0.255675i	0.669326	+	0.742968i	$0.266583\pi$
$812$	6.82526			0.239520
$813$	−38.8752	+	16.1026i	−1.36341	+	0.564744i
$814$	−12.7124	−	12.7124i	−0.445571	−	0.445571i
$815$		0			0
$816$	2.75733	+	0.378544i	0.0965258	+	0.0132517i
$817$		−	2.42541i		−	0.0848545i
$818$	−10.0537	+	10.0537i	−0.351519	+	0.351519i
$819$	9.29082	+	22.4300i	0.324648	+	0.783768i
$820$		0			0
$821$	−26.6213	+	11.0269i	−0.929089	+	0.384841i	−0.795333	−	0.606173i	$-0.792704\pi$
$821$	−26.6213	+	11.0269i	−0.929089	+	0.384841i	−0.133756	+	0.991014i	$0.542704\pi$
$822$	18.9394	+	7.84495i	0.660587	+	0.273624i
$823$	−15.9651	+	38.5431i	−0.556507	+	1.34353i	0.356007	+	0.934483i	$0.384138\pi$
$823$	−15.9651	+	38.5431i	−0.556507	+	1.34353i	−0.912514	+	0.409044i	$0.865862\pi$
$824$	−19.9512	+	19.9512i	−0.695034	+	0.695034i
$825$		0			0
$826$	−2.04734	−	0.848034i	−0.0712359	−	0.0295069i
$827$	25.0091	+	10.3591i	0.869650	+	0.360221i	0.772474	−	0.635046i	$-0.219019\pi$
$827$	25.0091	+	10.3591i	0.869650	+	0.360221i	0.0971760	+	0.995267i	$0.469019\pi$
$828$	1.60138	+	3.86606i	0.0556516	+	0.134355i
$829$			21.8341i			0.758331i	0.925329	+	0.379165i	$0.123789\pi$
$829$			21.8341i			0.758331i	−0.925329	+	0.379165i	$0.876211\pi$
$830$		0			0
$831$	−26.6230	−	26.6230i	−0.923542	−	0.923542i
$832$			34.4922i			1.19580i
$833$	6.76324	+	25.8112i	0.234332	+	0.894307i
$834$	−45.4822			−1.57492
$835$		0			0
$836$	−0.229934	−	0.555110i	−0.00795244	−	0.0191989i
$837$	−36.9250			−1.27631
$838$	3.67380	+	8.86933i	0.126909	+	0.306386i
$839$	−17.4844	+	42.2111i	−0.603629	+	1.45729i	0.266191	+	0.963920i	$0.414235\pi$
$839$	−17.4844	+	42.2111i	−0.603629	+	1.45729i	−0.869820	+	0.493369i	$0.835765\pi$
$840$		0			0
$841$	24.0239	−	24.0239i	0.828411	−	0.828411i
$842$	−10.8798	−	10.8798i	−0.374942	−	0.374942i
$843$	8.33802	−	20.1298i	0.287177	−	0.693305i
$844$	−11.3025	+	27.2866i	−0.389047	+	0.939243i
$845$		0			0
$846$		−	52.3506i		−	1.79985i
$847$	−3.17830	+	1.31649i	−0.109208	+	0.0452353i
$848$	−0.641993	+	0.641993i	−0.0220461	+	0.0220461i
$849$	11.8665			0.407259
$850$		0			0
$851$	5.29854			0.181632
$852$	9.55488	−	9.55488i	0.327345	−	0.327345i
$853$	0.0896578	−	0.0371375i	0.00306983	−	0.00127156i	−0.381148	−	0.924514i	$-0.624471\pi$
$853$	0.0896578	−	0.0371375i	0.00306983	−	0.00127156i	0.384218	+	0.923242i	$0.374471\pi$
$854$			0.745567i			0.0255128i
$855$		0			0
$856$	−4.20022	+	10.1402i	−0.143560	+	0.346585i
$857$	17.8974	−	43.2082i	0.611364	−	1.47596i	−0.250139	−	0.968210i	$-0.580476\pi$
$857$	17.8974	−	43.2082i	0.611364	−	1.47596i	0.861503	−	0.507753i	$-0.169524\pi$
$858$	−29.0326	−	29.0326i	−0.991157	−	0.991157i
$859$	18.6065	−	18.6065i	0.634845	−	0.634845i	−0.314434	−	0.949279i	$-0.601815\pi$
$859$	18.6065	−	18.6065i	0.634845	−	0.634845i	0.949279	+	0.314434i	$0.101815\pi$
$860$		0			0
$861$	4.10988	−	9.92213i	0.140064	−	0.338145i
$862$	−6.81077	−	16.4426i	−0.231976	−	0.560039i
$863$	33.5202			1.14104			0.570520	−	0.821284i	$-0.306742\pi$
$863$	33.5202			1.14104			0.570520	+	0.821284i	$0.306742\pi$
$864$	−14.0794	−	33.9907i	−0.478992	−	1.15639i
$865$		0			0
$866$	−19.8466			−0.674414
$867$	38.5319	+	30.2499i	1.30861	+	1.02734i
$868$			4.78408i			0.162382i
$869$	−24.8561	−	24.8561i	−0.843187	−	0.843187i
$870$		0			0
$871$			35.3837i			1.19893i
$872$	−3.53121	−	8.52509i	−0.119582	−	0.288696i
$873$	−58.4295	−	24.2023i	−1.97754	−	0.819123i
$874$	−0.112973	−	0.0467950i	−0.00382138	−	0.00158287i
$875$		0			0
$876$	12.5088	−	12.5088i	0.422635	−	0.422635i
$877$	−1.51846	+	3.66588i	−0.0512747	+	0.123788i	−0.947441	−	0.319930i	$-0.896341\pi$
$877$	−1.51846	+	3.66588i	−0.0512747	+	0.123788i	0.896167	+	0.443718i	$0.146341\pi$
$878$	−7.09689	−	2.93963i	−0.239508	−	0.0992076i
$879$	49.4656	−	20.4893i	1.66843	−	0.691088i
$880$		0			0
$881$	−17.1301	−	41.3558i	−0.577129	−	1.39331i	−0.895378	−	0.445306i	$-0.853095\pi$
$881$	−17.1301	−	41.3558i	−0.577129	−	1.39331i	0.318249	−	0.948007i	$-0.396905\pi$
$882$	−21.9362	+	21.9362i	−0.738630	+	0.738630i
$883$			6.22372i			0.209445i	0.994501	+	0.104722i	$0.0333954\pi$
$883$			6.22372i			0.209445i	−0.994501	+	0.104722i	$0.966605\pi$
$884$	−15.5041	+	26.5139i	−0.521458	+	0.891759i
$885$		0			0
$886$	3.00993	+	3.00993i	0.101121	+	0.101121i
$887$	15.5607	−	6.44546i	0.522478	−	0.216417i	−0.105827	−	0.994385i	$-0.533749\pi$
$887$	15.5607	−	6.44546i	0.522478	−	0.216417i	0.628305	+	0.777967i	$0.283749\pi$
$888$	−65.8661			−2.21032
$889$	−1.45152	+	0.601240i	−0.0486825	+	0.0201650i
$890$		0			0
$891$	7.44320	+	3.08308i	0.249357	+	0.103287i
$892$	10.1795	+	10.1795i	0.340835	+	0.340835i
$893$	−1.56650	−	1.56650i	−0.0524208	−	0.0524208i
$894$	−17.8764	−	7.40465i	−0.597876	−	0.247648i
$895$		0			0
$896$	−4.11950	+	1.70635i	−0.137623	+	0.0570052i
$897$	12.1008			0.404033
$898$	−21.9091	+	9.07506i	−0.731118	+	0.302839i
$899$	31.2127	+	31.2127i	1.04100	+	1.04100i
$900$		0			0
$901$	−15.4585	+	4.05054i	−0.514997	+	0.134943i
$902$			11.6007i			0.386260i
$903$	17.7109	−	17.7109i	0.589381	−	0.589381i
$904$	−0.444006	−	1.07193i	−0.0147674	−	0.0356517i
$905$		0			0
$906$	32.5165	−	13.4688i	1.08029	−	0.447470i
$907$	−26.7345	−	11.0738i	−0.887705	−	0.367699i	−0.108225	−	0.994126i	$-0.534517\pi$
$907$	−26.7345	−	11.0738i	−0.887705	−	0.367699i	−0.779480	+	0.626427i	$0.784517\pi$
$908$	0.899369	−	2.17127i	0.0298466	−	0.0720561i
$909$	−37.7435	+	37.7435i	−1.25187	+	1.25187i
$910$		0			0
$911$	14.2044	+	5.88367i	0.470614	+	0.194935i	0.605370	−	0.795944i	$-0.293025\pi$
$911$	14.2044	+	5.88367i	0.470614	+	0.194935i	−0.134756	+	0.990879i	$0.543025\pi$
$912$	0.126511	+	0.0524027i	0.00418921	+	0.00173523i
$913$	11.8317	+	28.5643i	0.391573	+	0.945340i
$914$		−	18.6938i		−	0.618336i
$915$		0			0
$916$	−1.91738	−	1.91738i	−0.0633521	−	0.0633521i
$917$		−	5.84848i		−	0.193134i
$918$	−3.36473	+	24.5088i	−0.111053	+	0.808911i
$919$	−9.89298			−0.326339			−0.163170	−	0.986598i	$-0.552172\pi$
$919$	−9.89298			−0.326339			−0.163170	+	0.986598i	$0.552172\pi$
$920$		0			0
$921$	−10.8358	−	26.1600i	−0.357053	−	0.862002i
$922$	1.75438			0.0577774
$923$	−9.55095	−	23.0580i	−0.314373	−	0.758964i
$924$	2.37450	−	5.73256i	0.0781154	−	0.188587i
$925$		0			0
$926$	6.83036	−	6.83036i	0.224460	−	0.224460i
$927$	−36.7796	−	36.7796i	−1.20800	−	1.20800i
$928$	−16.8311	+	40.6338i	−0.552507	+	1.33387i
$929$	2.76136	−	6.66651i	0.0905973	−	0.218721i	−0.872085	−	0.489354i	$-0.837233\pi$
$929$	2.76136	−	6.66651i	0.0905973	−	0.218721i	0.962683	+	0.270632i	$0.0872328\pi$
$930$		0			0
$931$			1.31280i			0.0430253i
$932$	−24.8145	+	10.2785i	−0.812826	+	0.336684i
$933$	58.4555	−	58.4555i	1.91375	−	1.91375i
$934$	−4.38699			−0.143547
$935$		0			0
$936$	−96.0783			−3.14042
$937$	3.46962	−	3.46962i	0.113348	−	0.113348i	−0.648158	−	0.761506i	$-0.724460\pi$
$937$	3.46962	−	3.46962i	0.113348	−	0.113348i	0.761506	+	0.648158i	$0.224460\pi$
$938$	3.41141	−	1.41305i	0.111386	−	0.0461378i
$939$		−	2.79126i		−	0.0910892i
$940$		0			0
$941$	10.0630	−	24.2941i	0.328043	−	0.791966i	−0.670695	−	0.741734i	$-0.734004\pi$
$941$	10.0630	−	24.2941i	0.328043	−	0.791966i	0.998738	−	0.0502322i	$-0.0159961\pi$
$942$	2.74879	−	6.63617i	0.0895605	−	0.216218i
$943$	−2.41758	−	2.41758i	−0.0787271	−	0.0787271i
$944$	0.558622	−	0.558622i	0.0181816	−	0.0181816i
$945$		0			0
$946$	−10.3535	+	24.9956i	−0.336622	+	0.812677i
$947$	−12.6418	−	30.5201i	−0.410804	−	0.991770i	−0.984922	−	0.172997i	$-0.944655\pi$
$947$	−12.6418	−	30.5201i	−0.410804	−	0.991770i	0.574118	−	0.818773i	$-0.305345\pi$
$948$	−47.8661			−1.55462
$949$	−12.5037	−	30.1866i	−0.405887	−	0.979899i
$950$		0			0
$951$	76.4343			2.47855
$952$	8.54356	+	1.17292i	0.276898	+	0.0380144i
$953$			51.4399i			1.66630i	0.553046	+	0.833151i	$0.313465\pi$
$953$			51.4399i			1.66630i	−0.553046	+	0.833151i	$0.686535\pi$
$954$	−13.1377	−	13.1377i	−0.425349	−	0.425349i
$955$		0			0
$956$		−	15.6501i		−	0.506162i
$957$	−21.9089	−	52.8928i	−0.708215	−	1.70978i
$958$	6.35390	+	2.63187i	0.205285	+	0.0850319i
$959$	5.28645	+	2.18972i	0.170708	+	0.0707098i
$960$		0			0
$961$	0.0421545	−	0.0421545i	0.00135982	−	0.00135982i
$962$	−17.3033	+	41.7739i	−0.557882	+	1.34685i
$963$	−18.6932	−	7.74299i	−0.602381	−	0.249514i
$964$	−3.16890	+	1.31260i	−0.102063	+	0.0422760i
$965$		0			0
$966$	−0.483247	−	1.16666i	−0.0155482	−	0.0375367i
$967$	−21.4243	+	21.4243i	−0.688960	+	0.688960i	−0.962002	−	0.273042i	$-0.911970\pi$
$967$	−21.4243	+	21.4243i	−0.688960	+	0.688960i	0.273042	+	0.962002i	$0.411970\pi$
$968$		−	13.6141i		−	0.437575i
$969$	1.45664	+	1.92024i	0.0467940	+	0.0616869i
$970$		0			0
$971$	−24.6251	−	24.6251i	−0.790256	−	0.790256i	0.191279	−	0.981536i	$-0.438736\pi$
$971$	−24.6251	−	24.6251i	−0.790256	−	0.790256i	−0.981536	+	0.191279i	$0.938736\pi$
$972$	−11.6317	+	4.81802i	−0.373088	+	0.154538i
$973$	−12.6952			−0.406990
$974$	0.355384	−	0.147205i	0.0113872	−	0.00471675i
$975$		0			0
$976$	−0.245562	−	0.101715i	−0.00786025	−	0.00325582i
$977$	−14.6363	−	14.6363i	−0.468257	−	0.468257i	0.433092	−	0.901349i	$-0.357422\pi$
$977$	−14.6363	−	14.6363i	−0.468257	−	0.468257i	−0.901349	+	0.433092i	$0.857422\pi$
$978$	−2.54837	−	2.54837i	−0.0814878	−	0.0814878i
$979$	30.1661	+	12.4952i	0.964113	+	0.399349i
$980$		0			0
$981$	15.7158	−	6.50969i	0.501767	−	0.207839i
$982$	−0.252373			−0.00805354
$983$	40.9497	−	16.9619i	1.30609	−	0.541002i	0.382352	−	0.924017i	$-0.375114\pi$
$983$	40.9497	−	16.9619i	1.30609	−	0.541002i	0.923742	+	0.383015i	$0.125114\pi$
$984$	30.0528	+	30.0528i	0.958050	+	0.958050i
$985$		0			0
$986$	23.5616	−	17.8731i	0.750353	−	0.569196i
$987$		−	22.8778i		−	0.728207i
$988$	−1.06855	+	1.06855i	−0.0339951	+	0.0339951i
$989$	−3.05141	−	7.36675i	−0.0970291	−	0.234249i
$990$		0			0
$991$	24.1426	−	10.0002i	0.766915	−	0.317667i	0.0352929	−	0.999377i	$-0.488764\pi$
$991$	24.1426	−	10.0002i	0.766915	−	0.317667i	0.731622	+	0.681710i	$0.238764\pi$
$992$	−28.4817	−	11.7975i	−0.904295	−	0.374571i
$993$	6.75542	−	16.3090i	0.214377	−	0.517551i
$994$	−1.84165	+	1.84165i	−0.0584137	+	0.0584137i
$995$		0			0
$996$	38.8958	+	16.1112i	1.23246	+	0.510502i
$997$	24.2756	+	10.0553i	0.768816	+	0.318454i	0.732393	−	0.680882i	$-0.238404\pi$
$997$	24.2756	+	10.0553i	0.768816	+	0.318454i	0.0364232	+	0.999336i	$0.488404\pi$
$998$	−6.40770	−	15.4696i	−0.202832	−	0.489681i
$999$		−	52.7404i		−	1.66863i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.m.c.76.4	✓	24	85.8	odd	8
425.2.m.c.151.4	yes	24	5.3	odd	4
425.2.m.d.76.3	yes	24	85.42	odd	8
425.2.m.d.151.3	yes	24	5.2	odd	4
425.2.n.d.49.4		24	5.4	even	2
425.2.n.d.399.4		24	17.8	even	8
425.2.n.e.49.3		24	1.1	even	1	trivial
425.2.n.e.399.3		24	85.59	even	8	inner
7225.2.a.bx.1.11		24	85.73	even	16
7225.2.a.bx.1.12		24	85.63	even	16
7225.2.a.cb.1.13		24	85.12	even	16
7225.2.a.cb.1.14		24	85.22	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+(-0.639117 + 0.639117i) q^{2} +(2.66226 - 1.10274i) q^{3} +1.18306i q^{4} +(-0.996713 + 2.40628i) q^{6} +(-0.278207 + 0.671652i) q^{7} +(-2.03435 - 2.03435i) q^{8} +(3.75027 - 3.75027i) q^{9} +(-0.958080 + 2.31301i) q^{11} +(1.30461 + 3.14961i) q^{12} +6.29663 q^{13} +(-0.251457 - 0.607071i) q^{14} +0.234252 q^{16} +(3.55925 + 2.08128i) q^{17} +4.79372i q^{18} +(0.143443 + 0.143443i) q^{19} +2.09490i q^{21} +(-0.865959 - 2.09061i) q^{22} +(0.616148 + 0.255217i) q^{23} +(-7.65933 - 3.17260i) q^{24} +(-4.02428 + 4.02428i) q^{26} +(2.54037 - 6.13299i) q^{27} +(-0.794604 - 0.329136i) q^{28} +(-7.33161 + 3.03685i) q^{29} +(-2.12864 - 5.13900i) q^{31} +(3.91898 - 3.91898i) q^{32} +7.21436i q^{33} +(-3.60496 + 0.944595i) q^{34} +(4.43679 + 4.43679i) q^{36} +(7.34010 - 3.04037i) q^{37} -0.183354 q^{38} +(16.7633 - 6.94358i) q^{39} +(-4.73632 - 1.96185i) q^{41} +(-1.33889 - 1.33889i) q^{42} +(-8.45426 - 8.45426i) q^{43} +(-2.73643 - 1.13347i) q^{44} +(-0.556904 + 0.230677i) q^{46} -10.9207 q^{47} +(0.623640 - 0.258320i) q^{48} +(4.57603 + 4.57603i) q^{49} +(11.7708 + 1.61597i) q^{51} +7.44929i q^{52} +(-2.74061 + 2.74061i) q^{53} +(2.29611 + 5.54329i) q^{54} +(1.93234 - 0.800403i) q^{56} +(0.540065 + 0.223702i) q^{57} +(2.74485 - 6.62666i) q^{58} +(2.38470 - 2.38470i) q^{59} +(-1.04828 - 0.434212i) q^{61} +(4.64487 + 1.92397i) q^{62} +(1.47552 + 3.56223i) q^{63} +5.47788i q^{64} +(-4.61082 - 4.61082i) q^{66} +5.61946i q^{67} +(-2.46228 + 4.21081i) q^{68} +1.92179 q^{69} +(-1.51683 - 3.66196i) q^{71} -15.2587 q^{72} +(-1.98578 - 4.79409i) q^{73} +(-2.74803 + 6.63433i) q^{74} +(-0.169702 + 0.169702i) q^{76} +(-1.28699 - 1.28699i) q^{77} +(-6.27594 + 15.1514i) q^{78} +(-5.37312 + 12.9718i) q^{79} -3.21797i q^{81} +(4.28091 - 1.77321i) q^{82} +(8.73235 - 8.73235i) q^{83} -2.47840 q^{84} +10.8065 q^{86} +(-16.1698 + 16.1698i) q^{87} +(6.65453 - 2.75640i) q^{88} -13.0419i q^{89} +(-1.75177 + 4.22914i) q^{91} +(-0.301937 + 0.728940i) q^{92} +(-11.3340 - 11.3340i) q^{93} +(6.97959 - 6.97959i) q^{94} +(6.11171 - 14.7550i) q^{96} +(-4.56330 - 11.0168i) q^{97} -5.84924 q^{98} +(5.08135 + 12.2675i) 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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