LMFDB - Embedded newform 275.3.q.g.149.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(24,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.24"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.q (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [56,0,0,-18,0,60] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			149.12
Character	$\chi$	$=$	275.149
Dual form			275.3.q.g.24.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.793893 + 2.44335i) q^{2} +(-0.424261 + 0.583945i) q^{3} +(-2.10363 + 1.52838i) q^{4} +(-1.76360 - 0.573029i) q^{6} +(10.6625 - 7.74676i) q^{7} +(2.90933 + 2.11375i) q^{8} +(2.62016 + 8.06402i) q^{9} +(8.18023 - 7.35417i) q^{11} -1.87684i q^{12} +(-2.50134 - 7.69834i) q^{13} +(27.3929 + 19.9021i) q^{14} +(-6.06901 + 18.6785i) q^{16} +(2.55378 - 7.85972i) q^{17} +(-17.6231 + 12.8039i) q^{18} +(-15.2188 + 20.9469i) q^{19} +9.51297i q^{21} +(24.4631 + 14.1488i) q^{22} +5.34212i q^{23} +(-2.46863 + 0.802107i) q^{24} +(16.8240 - 12.2233i) q^{26} +(-11.9988 - 3.89865i) q^{27} +(-10.5900 + 32.5927i) q^{28} +(-18.9800 - 26.1237i) q^{29} +(13.4739 + 41.4685i) q^{31} -36.0717 q^{32} +(0.823881 + 7.89690i) q^{33} +21.2315 q^{34} +(-17.8367 - 12.9591i) q^{36} +(8.28194 + 11.3991i) q^{37} +(-63.2626 - 20.5553i) q^{38} +(5.55664 + 1.80546i) q^{39} +(-3.92574 + 5.40332i) q^{41} +(-23.2435 + 7.55228i) q^{42} -13.9858 q^{43} +(-5.96824 + 27.9730i) q^{44} +(-13.0527 + 4.24108i) q^{46} +(47.8694 - 65.8866i) q^{47} +(-8.33237 - 11.4685i) q^{48} +(38.5348 - 118.598i) q^{49} +(3.50618 + 4.82584i) q^{51} +(17.0279 + 12.3715i) q^{52} +(-48.7128 + 15.8277i) q^{53} -32.4124i q^{54} +47.3954 q^{56} +(-5.77508 - 17.7739i) q^{57} +(48.7613 - 67.1142i) q^{58} +(-43.5007 + 31.6051i) q^{59} +(-3.81411 - 1.23928i) q^{61} +(-90.6252 + 65.8431i) q^{62} +(90.4074 + 65.6849i) q^{63} +(-4.36107 - 13.4220i) q^{64} +(-18.6408 + 8.28232i) q^{66} +87.7170i q^{67} +(6.64042 + 20.4371i) q^{68} +(-3.11951 - 2.26646i) q^{69} +(10.5932 - 32.6025i) q^{71} +(-9.42243 + 28.9992i) q^{72} +(50.5378 - 36.7178i) q^{73} +(-21.2771 + 29.2854i) q^{74} -67.3246i q^{76} +(30.2507 - 141.784i) q^{77} +15.0102i q^{78} +(-119.320 + 38.7694i) q^{79} +(-54.3698 + 39.5019i) q^{81} +(-16.3188 - 5.30231i) q^{82} +(39.2492 - 120.797i) q^{83} +(-14.5394 - 20.0118i) q^{84} +(-11.1032 - 34.1723i) q^{86} +23.3073 q^{87} +(39.3439 - 4.10473i) q^{88} -43.7087 q^{89} +(-86.3078 - 62.7063i) q^{91} +(-8.16479 - 11.2379i) q^{92} +(-29.9318 - 9.72543i) q^{93} +(198.987 + 64.6549i) q^{94} +(15.3038 - 21.0639i) q^{96} +(29.0276 - 9.43164i) q^{97} +320.369 q^{98} +(80.7377 + 46.6964i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 18 q^{4} + 60 q^{6} + 62 q^{9} - 10 q^{11} - 74 q^{14} - 70 q^{16} - 160 q^{19} - 26 q^{26} + 190 q^{29} + 190 q^{31} + 296 q^{34} - 694 q^{36} + 130 q^{39} - 580 q^{41} + 506 q^{44} - 220 q^{46}+ \cdots + 1218 q^{99}+O(q^{100}) $ 56 * q - 18 * q^4 + 60 * q^6 + 62 * q^9 - 10 * q^11 - 74 * q^14 - 70 * q^16 - 160 * q^19 - 26 * q^26 + 190 * q^29 + 190 * q^31 + 296 * q^34 - 694 * q^36 + 130 * q^39 - 580 * q^41 + 506 * q^44 - 220 * q^46 - 448 * q^49 + 800 * q^51 + 1768 * q^56 - 134 * q^59 + 270 * q^61 + 238 * q^64 + 500 * q^66 - 622 * q^69 - 378 * q^71 - 1880 * q^74 - 1130 * q^79 - 1166 * q^81 + 2100 * q^84 + 414 * q^86 - 292 * q^89 - 1566 * q^91 + 1690 * q^94 - 2420 * q^96 + 1218 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$-1$

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 $

$2$	0.793893	+	2.44335i	0.396947	+	1.22168i	0.927435	+	0.373984i	$0.122008\pi$
$2$	0.793893	+	2.44335i	0.396947	+	1.22168i	−0.530489	+	0.847692i	$0.677992\pi$
$3$	−0.424261	+	0.583945i	−0.141420	+	0.194648i	−0.873852	−	0.486192i	$-0.838385\pi$
$3$	−0.424261	+	0.583945i	−0.141420	+	0.194648i	0.732431	+	0.680841i	$0.238385\pi$
$4$	−2.10363	+	1.52838i	−0.525908	+	0.382095i
$5$		0			0
$5$		0			0
$6$	−1.76360	−	0.573029i	−0.293934	−	0.0955048i
$7$	10.6625	−	7.74676i	1.52321	−	1.10668i	0.563349	−	0.826219i	$-0.309513\pi$
$7$	10.6625	−	7.74676i	1.52321	−	1.10668i	0.959866	−	0.280461i	$-0.0904872\pi$
$8$	2.90933	+	2.11375i	0.363666	+	0.264219i
$9$	2.62016	+	8.06402i	0.291129	+	0.896002i
$10$		0			0
$11$	8.18023	−	7.35417i	0.743657	−	0.668561i
$11$	8.18023	−	7.35417i	0.743657	−	0.668561i
$12$		−	1.87684i		−	0.156403i
$13$	−2.50134	−	7.69834i	−0.192411	−	0.592180i	−0.999997	−	0.00243053i	$-0.999226\pi$
$13$	−2.50134	−	7.69834i	−0.192411	−	0.592180i	0.807586	−	0.589750i	$-0.200774\pi$
$14$	27.3929	+	19.9021i	1.95664	+	1.42158i
$15$		0			0
$16$	−6.06901	+	18.6785i	−0.379313	+	1.16741i
$17$	2.55378	−	7.85972i	0.150222	−	0.462336i	−0.847423	−	0.530918i	$-0.821847\pi$
$17$	2.55378	−	7.85972i	0.150222	−	0.462336i	0.997646	+	0.0685815i	$0.0218473\pi$
$18$	−17.6231	+	12.8039i	−0.979061	+	0.711330i
$19$	−15.2188	+	20.9469i	−0.800989	+	1.10247i	0.191663	+	0.981461i	$0.438612\pi$
$19$	−15.2188	+	20.9469i	−0.800989	+	1.10247i	−0.992652	+	0.121006i	$0.961388\pi$
$20$		0			0
$21$			9.51297i			0.452998i
$22$	24.4631	+	14.1488i	1.11196	+	0.643125i
$23$			5.34212i			0.232266i	0.993234	+	0.116133i	$0.0370499\pi$
$23$			5.34212i			0.232266i	−0.993234	+	0.116133i	$0.962950\pi$
$24$	−2.46863	+	0.802107i	−0.102860	+	0.0334211i
$25$		0			0
$26$	16.8240	−	12.2233i	0.647076	−	0.470128i
$27$	−11.9988	−	3.89865i	−0.444400	−	0.144394i
$28$	−10.5900	+	32.5927i	−0.378214	+	1.16402i
$29$	−18.9800	−	26.1237i	−0.654482	−	0.900818i	0.344801	−	0.938676i	$-0.387947\pi$
$29$	−18.9800	−	26.1237i	−0.654482	−	0.900818i	−0.999283	+	0.0378581i	$0.987947\pi$
$30$		0			0
$31$	13.4739	+	41.4685i	0.434643	+	1.33769i	0.893452	+	0.449158i	$0.148276\pi$
$31$	13.4739	+	41.4685i	0.434643	+	1.33769i	−0.458809	+	0.888535i	$0.651724\pi$
$32$	−36.0717			−1.12724
$33$	0.823881	+	7.89690i	0.0249661	+	0.239300i
$34$	21.2315			0.624455
$35$		0			0
$36$	−17.8367	−	12.9591i	−0.495465	−	0.359976i
$37$	8.28194	+	11.3991i	0.223836	+	0.308084i	0.906134	−	0.422990i	$-0.139019\pi$
$37$	8.28194	+	11.3991i	0.223836	+	0.308084i	−0.682298	+	0.731074i	$0.739019\pi$
$38$	−63.2626	−	20.5553i	−1.66481	−	0.540928i
$39$	5.55664	+	1.80546i	0.142478	+	0.0462939i
$40$		0			0
$41$	−3.92574	+	5.40332i	−0.0957498	+	0.131788i	−0.854204	−	0.519938i	$-0.825955\pi$
$41$	−3.92574	+	5.40332i	−0.0957498	+	0.131788i	0.758454	+	0.651726i	$0.225955\pi$
$42$	−23.2435	+	7.55228i	−0.553417	+	0.179816i
$43$	−13.9858			−0.325252			−0.162626	−	0.986688i	$-0.551996\pi$
$43$	−13.9858			−0.325252			−0.162626	+	0.986688i	$0.551996\pi$
$44$	−5.96824	+	27.9730i	−0.135642	+	0.635749i
$45$		0			0
$46$	−13.0527	+	4.24108i	−0.283754	+	0.0921973i
$47$	47.8694	−	65.8866i	1.01850	−	1.40184i	0.105247	−	0.994446i	$-0.466437\pi$
$47$	47.8694	−	65.8866i	1.01850	−	1.40184i	0.913252	−	0.407396i	$-0.133563\pi$
$48$	−8.33237	−	11.4685i	−0.173591	−	0.238928i
$49$	38.5348	−	118.598i	0.786424	−	2.42036i
$50$		0			0
$51$	3.50618	+	4.82584i	0.0687486	+	0.0946243i
$52$	17.0279	+	12.3715i	0.327460	+	0.237913i
$53$	−48.7128	+	15.8277i	−0.919109	+	0.298636i	−0.730101	−	0.683339i	$-0.760527\pi$
$53$	−48.7128	+	15.8277i	−0.919109	+	0.298636i	−0.189008	+	0.981976i	$0.560527\pi$
$54$		−	32.4124i		−	0.600229i
$55$		0			0
$56$	47.3954			0.846347
$57$	−5.77508	−	17.7739i	−0.101317	−	0.311822i
$58$	48.7613	−	67.1142i	0.840713	−	1.15714i
$59$	−43.5007	+	31.6051i	−0.737300	+	0.535680i	−0.891865	−	0.452303i	$-0.850603\pi$
$59$	−43.5007	+	31.6051i	−0.737300	+	0.535680i	0.154564	+	0.987983i	$0.450603\pi$
$60$		0			0
$61$	−3.81411	−	1.23928i	−0.0625264	−	0.0203161i	0.277587	−	0.960701i	$-0.410465\pi$
$61$	−3.81411	−	1.23928i	−0.0625264	−	0.0203161i	−0.340113	+	0.940385i	$0.610465\pi$
$62$	−90.6252	+	65.8431i	−1.46170	+	1.06199i
$63$	90.4074	+	65.6849i	1.43504	+	1.04262i
$64$	−4.36107	−	13.4220i	−0.0681417	−	0.209719i
$65$		0			0
$66$	−18.6408	+	8.28232i	−0.282437	+	0.125490i
$67$			87.7170i			1.30921i	0.755972	+	0.654604i	$0.227165\pi$
$67$			87.7170i			1.30921i	−0.755972	+	0.654604i	$0.772835\pi$
$68$	6.64042	+	20.4371i	0.0976532	+	0.300546i
$69$	−3.11951	−	2.26646i	−0.0452103	−	0.0328472i
$70$		0			0
$71$	10.5932	−	32.6025i	0.149200	−	0.459191i	−0.848327	−	0.529473i	$-0.822390\pi$
$71$	10.5932	−	32.6025i	0.149200	−	0.459191i	0.997527	+	0.0702818i	$0.0223899\pi$
$72$	−9.42243	+	28.9992i	−0.130867	+	0.402767i
$73$	50.5378	−	36.7178i	0.692298	−	0.502984i	−0.185116	−	0.982717i	$-0.559266\pi$
$73$	50.5378	−	36.7178i	0.692298	−	0.502984i	0.877415	+	0.479732i	$0.159266\pi$
$74$	−21.2771	+	29.2854i	−0.287528	+	0.395748i
$75$		0			0
$76$		−	67.3246i		−	0.885850i
$77$	30.2507	−	141.784i	0.392866	−	1.84135i
$78$			15.0102i			0.192438i
$79$	−119.320	+	38.7694i	−1.51038	+	0.490751i	−0.943024	−	0.332724i	$-0.892032\pi$
$79$	−119.320	+	38.7694i	−1.51038	+	0.490751i	−0.567353	+	0.823475i	$0.692032\pi$
$80$		0			0
$81$	−54.3698	+	39.5019i	−0.671231	+	0.487678i
$82$	−16.3188	−	5.30231i	−0.199010	−	0.0646623i
$83$	39.2492	−	120.797i	0.472882	−	1.45538i	−0.375910	−	0.926656i	$-0.622670\pi$
$83$	39.2492	−	120.797i	0.472882	−	1.45538i	0.848793	−	0.528726i	$-0.177330\pi$
$84$	−14.5394	−	20.0118i	−0.173088	−	0.238236i
$85$		0			0
$86$	−11.1032	−	34.1723i	−0.129107	−	0.397352i
$87$	23.3073			0.267900
$88$	39.3439	−	4.10473i	0.447089	−	0.0466447i
$89$	−43.7087			−0.491109			−0.245555	−	0.969383i	$-0.578970\pi$
$89$	−43.7087			−0.491109			−0.245555	+	0.969383i	$0.578970\pi$
$90$		0			0
$91$	−86.3078	−	62.7063i	−0.948437	−	0.689080i
$92$	−8.16479	−	11.2379i	−0.0887477	−	0.122151i
$93$	−29.9318	−	9.72543i	−0.321847	−	0.104574i
$94$	198.987	+	64.6549i	2.11689	+	0.687818i
$95$		0			0
$96$	15.3038	−	21.0639i	0.159415	−	0.219416i
$97$	29.0276	−	9.43164i	0.299253	−	0.0972334i	−0.155542	−	0.987829i	$-0.549712\pi$
$97$	29.0276	−	9.43164i	0.299253	−	0.0972334i	0.454795	+	0.890596i	$0.349712\pi$
$98$	320.369			3.26907
$99$	80.7377	+	46.6964i	0.815532	+	0.471681i
$100$		0			0
$101$	49.2339	−	15.9971i	0.487464	−	0.158387i	−0.0549650	−	0.998488i	$-0.517505\pi$
$101$	49.2339	−	15.9971i	0.487464	−	0.158387i	0.542429	+	0.840102i	$0.317505\pi$
$102$	−9.00769	+	12.3980i	−0.0883107	+	0.121549i
$103$	−40.6532	−	55.9544i	−0.394691	−	0.543246i	0.564710	−	0.825289i	$-0.308988\pi$
$103$	−40.6532	−	55.9544i	−0.394691	−	0.543246i	−0.959402	+	0.282043i	$0.908988\pi$
$104$	8.99515	−	27.6842i	0.0864919	−	0.266195i
$105$		0			0
$106$	−77.3454	−	106.457i	−0.729674	−	1.00431i
$107$	−48.0376	−	34.9014i	−0.448950	−	0.326181i	0.340231	−	0.940342i	$-0.389495\pi$
$107$	−48.0376	−	34.9014i	−0.448950	−	0.326181i	−0.789181	+	0.614161i	$0.789495\pi$
$108$	31.1997	−	10.1374i	0.288886	−	0.0938647i
$109$			80.9083i			0.742278i	0.928577	+	0.371139i	$0.121033\pi$
$109$			80.9083i			0.742278i	−0.928577	+	0.371139i	$0.878967\pi$
$110$		0			0
$111$	−10.1702			−0.0916232
$112$	79.9869	+	246.174i	0.714169	+	2.19799i
$113$	10.3903	−	14.3011i	0.0919498	−	0.126558i	−0.760564	−	0.649263i	$-0.775077\pi$
$113$	10.3903	−	14.3011i	0.0919498	−	0.126558i	0.852513	+	0.522705i	$0.175077\pi$
$114$	38.8430	−	28.2211i	0.340728	−	0.247554i
$115$		0			0
$116$	79.8539	+	25.9461i	0.688395	+	0.223673i
$117$	55.5257	−	40.3418i	0.474578	−	0.344801i
$118$	−111.757	−	81.1965i	−0.947096	−	0.688106i
$119$	−33.6577	−	103.588i	−0.282838	−	0.870485i
$120$		0			0
$121$	12.8323	−	120.318i	0.106052	−	0.994361i
$122$		−	10.3031i		−	0.0844514i
$123$	−1.48970	−	4.58484i	−0.0121114	−	0.0372751i
$124$	−91.7238	−	66.6412i	−0.739708	−	0.537429i
$125$		0			0
$126$	−88.7174	+	273.044i	−0.704106	+	2.16702i
$127$	36.6413	−	112.770i	0.288514	−	0.887955i	−0.696809	−	0.717257i	$-0.745398\pi$
$127$	36.6413	−	112.770i	0.288514	−	0.887955i	0.985323	−	0.170699i	$-0.0546024\pi$
$128$	−87.3982	+	63.4985i	−0.682798	+	0.496082i
$129$	5.93364	−	8.16695i	0.0459972	−	0.0633097i
$130$		0			0
$131$		−	175.467i		−	1.33944i	−0.742612	−	0.669722i	$-0.766413\pi$
$131$		−	175.467i		−	1.33944i	0.742612	−	0.669722i	$-0.233587\pi$
$132$	−13.8026	−	15.3530i	−0.104565	−	0.116310i
$133$			341.242i			2.56573i
$134$	−214.323	+	69.6379i	−1.59943	+	0.519686i
$135$		0			0
$136$	24.0433	−	17.4685i	0.176789	−	0.128444i
$137$	−151.765	−	49.3113i	−1.10777	−	0.359936i	−0.302682	−	0.953092i	$-0.597882\pi$
$137$	−151.765	−	49.3113i	−1.10777	−	0.359936i	−0.805088	+	0.593155i	$0.797882\pi$
$138$	3.06119	−	9.42138i	0.0221825	−	0.0682709i
$139$	−108.452	−	149.272i	−0.780232	−	1.07390i	−0.995256	−	0.0972881i	$-0.968983\pi$
$139$	−108.452	−	149.272i	−0.780232	−	1.07390i	0.215025	−	0.976609i	$-0.431017\pi$
$140$		0			0
$141$	18.1650	+	55.9062i	0.128830	+	0.396498i
$142$	88.0693			0.620207
$143$	−77.0765	−	44.5789i	−0.538997	−	0.311741i
$144$	−166.525			−1.15643
$145$		0			0
$146$	129.836	+	94.3315i	0.889289	+	0.646106i
$147$	52.9059	+	72.8187i	0.359904	+	0.495365i
$148$	−34.8443	−	11.3216i	−0.235435	−	0.0764974i
$149$	157.999	+	51.3369i	1.06039	+	0.344543i	0.786740	−	0.617285i	$-0.211767\pi$
$149$	157.999	+	51.3369i	1.06039	+	0.344543i	0.273655	+	0.961828i	$0.411767\pi$
$150$		0			0
$151$	−96.3065	+	132.555i	−0.637792	+	0.877845i	−0.998495	−	0.0548355i	$-0.982537\pi$
$151$	−96.3065	+	132.555i	−0.637792	+	0.877845i	0.360704	+	0.932680i	$0.382537\pi$
$152$	−88.5529	+	28.7726i	−0.582585	+	0.189293i
$153$	70.0722			0.457988
$154$	370.444	−	38.6483i	2.40548	−	0.250963i
$155$		0			0
$156$	−14.4486	+	4.69462i	−0.0926189	+	0.0300937i
$157$	−109.453	+	150.650i	−0.697156	+	0.959552i	0.302823	+	0.953047i	$0.402071\pi$
$157$	−109.453	+	150.650i	−0.697156	+	0.959552i	−0.999979	+	0.00650560i	$0.997929\pi$
$158$	−189.454	−	260.762i	−1.19908	−	1.65039i
$159$	11.4244	−	35.1607i	0.0718516	−	0.221136i
$160$		0			0
$161$	41.3841	+	56.9604i	0.257044	+	0.353791i
$162$	−139.681	−	101.484i	−0.862228	−	0.626445i
$163$	−231.995	+	75.3797i	−1.42328	+	0.462452i	−0.916643	−	0.399706i	$-0.869112\pi$
$163$	−231.995	+	75.3797i	−1.42328	+	0.462452i	−0.506639	+	0.862159i	$0.669112\pi$
$164$		−	17.3666i		−	0.105894i
$165$		0			0
$166$	326.309			1.96571
$167$	7.53588	+	23.1931i	0.0451250	+	0.138881i	0.971081	−	0.238752i	$-0.0767383\pi$
$167$	7.53588	+	23.1931i	0.0451250	+	0.138881i	−0.925956	+	0.377632i	$0.876738\pi$
$168$	−20.1080	+	27.6764i	−0.119691	+	0.164740i
$169$	83.7161	−	60.8233i	0.495361	−	0.359901i
$170$		0			0
$171$	−208.792	−	67.8405i	−1.22100	−	0.396728i
$172$	29.4210	−	21.3756i	0.171053	−	0.124277i
$173$	46.8713	+	34.0540i	0.270932	+	0.196844i	0.714953	−	0.699173i	$-0.246448\pi$
$173$	46.8713	+	34.0540i	0.270932	+	0.196844i	−0.444020	+	0.896017i	$0.646448\pi$
$174$	18.5035	+	56.9479i	0.106342	+	0.327287i
$175$		0			0
$176$	87.7189	+	197.427i	0.498403	+	1.12174i
$177$		−	38.8109i		−	0.219270i
$178$	−34.7000	−	106.796i	−0.194944	−	0.599976i
$179$	0.0910781	+	0.0661721i	0.000508816	+	0.000369677i	0.588040	−	0.808832i	$-0.299900\pi$
$179$	0.0910781	+	0.0661721i	0.000508816	+	0.000369677i	−0.587531	+	0.809202i	$0.699900\pi$
$180$		0			0
$181$	−8.38500	+	25.8064i	−0.0463260	+	0.142577i	−0.971544	−	0.236859i	$-0.923882\pi$
$181$	−8.38500	+	25.8064i	−0.0463260	+	0.142577i	0.925218	+	0.379436i	$0.123882\pi$
$182$	84.6944	−	260.662i	0.465354	−	1.43221i
$183$	2.34185	−	1.70145i	0.0127970	−	0.00929756i
$184$	−11.2919	+	15.5420i	−0.0613691	+	0.0844674i
$185$		0			0
$186$		−	80.8548i		−	0.434703i
$187$	−36.9112	−	83.0752i	−0.197386	−	0.444252i
$188$			211.764i			1.12640i
$189$	−158.139	+	51.3825i	−0.836715	+	0.271865i
$190$		0			0
$191$	−265.764	+	193.089i	−1.39143	+	1.01093i	−0.395726	+	0.918369i	$0.629507\pi$
$191$	−265.764	+	193.089i	−1.39143	+	1.01093i	−0.995707	+	0.0925661i	$0.970493\pi$
$192$	9.68794	+	3.14780i	0.0504580	+	0.0163948i
$193$	−69.2444	+	213.112i	−0.358779	+	1.10421i	0.595006	+	0.803721i	$0.297150\pi$
$193$	−69.2444	+	213.112i	−0.358779	+	1.10421i	−0.953785	+	0.300488i	$0.902850\pi$
$194$	46.0896	+	63.4369i	0.237575	+	0.326994i
$195$		0			0
$196$	100.199	+	308.382i	0.511222	+	1.57338i
$197$	1.50117			0.00762015			0.00381008	−	0.999993i	$-0.498787\pi$
$197$	1.50117			0.00762015			0.00381008	+	0.999993i	$0.498787\pi$
$198$	−49.9987	+	234.342i	−0.252519	+	1.18355i
$199$	65.2808			0.328044			0.164022	−	0.986457i	$-0.447553\pi$
$199$	65.2808			0.328044			0.164022	+	0.986457i	$0.447553\pi$
$200$		0			0
$201$	−51.2219	−	37.2149i	−0.254835	−	0.185149i
$202$	78.1729	+	107.596i	0.386994	+	0.532652i
$203$	−404.748	−	131.511i	−1.99383	−	0.647836i
$204$	−14.7514	−	4.79303i	−0.0723109	−	0.0234952i
$205$		0			0
$206$	104.442	−	143.752i	0.506999	−	0.697825i
$207$	−43.0790	+	13.9972i	−0.208111	+	0.0676194i
$208$	158.974			0.764298
$209$	29.5536	+	283.272i	0.141405	+	1.35537i
$210$		0			0
$211$	235.285	−	76.4488i	1.11510	−	0.362317i	0.307202	−	0.951644i	$-0.400607\pi$
$211$	235.285	−	76.4488i	1.11510	−	0.362317i	0.807894	+	0.589328i	$0.200607\pi$
$212$	78.2830	−	107.747i	0.369259	−	0.508242i
$213$	14.5438	+	20.0178i	0.0682808	+	0.0939805i
$214$	47.1396	−	145.081i	0.220278	−	0.677947i
$215$		0			0
$216$	−26.6677	−	36.7049i	−0.123462	−	0.169930i
$217$	464.912	+	337.778i	2.14245	+	1.55658i
$218$	−197.688	+	64.2326i	−0.906824	+	0.294645i
$219$			45.0893i			0.205887i
$220$		0			0
$221$	−66.8947			−0.302691
$222$	−8.07403	−	24.8493i	−0.0363695	−	0.111934i
$223$	155.787	−	214.422i	0.698594	−	0.961533i	−0.301373	−	0.953506i	$-0.597445\pi$
$223$	155.787	−	214.422i	0.698594	−	0.961533i	0.999968	−	0.00802651i	$-0.00255495\pi$
$224$	−384.615	+	279.439i	−1.71703	+	1.24750i
$225$		0			0
$226$	43.1913	+	14.0337i	0.191112	+	0.0620961i
$227$	−298.667	+	216.994i	−1.31571	+	0.955922i	−0.315739	+	0.948846i	$0.602253\pi$
$227$	−298.667	+	216.994i	−1.31571	+	0.955922i	−0.999975	+	0.00707657i	$0.997747\pi$
$228$	39.3139	+	28.5632i	0.172429	+	0.125277i
$229$	24.0332	+	73.9665i	0.104948	+	0.322998i	0.989718	−	0.143030i	$-0.0456846\pi$
$229$	24.0332	+	73.9665i	0.104948	+	0.322998i	−0.884770	+	0.466028i	$0.845685\pi$
$230$		0			0
$231$	69.9600	+	77.8183i	0.302857	+	0.336876i
$232$		−	116.121i		−	0.500524i
$233$	67.2970	+	207.119i	0.288828	+	0.888922i	0.985225	+	0.171265i	$0.0547854\pi$
$233$	67.2970	+	207.119i	0.288828	+	0.888922i	−0.696397	+	0.717657i	$0.745215\pi$
$234$	142.651	+	103.642i	0.609618	+	0.442913i
$235$		0			0
$236$	43.2050	−	132.971i	0.183072	−	0.563437i
$237$	27.9836	−	86.1246i	0.118074	−	0.363395i
$238$	226.381	−	164.475i	0.951179	−	0.691072i
$239$	82.7232	−	113.859i	0.346122	−	0.476396i	−0.600095	−	0.799929i	$-0.704871\pi$
$239$	82.7232	−	113.859i	0.346122	−	0.476396i	0.946217	+	0.323533i	$0.104871\pi$
$240$		0			0
$241$		−	265.314i		−	1.10089i	−0.834872	−	0.550444i	$-0.814458\pi$
$241$		−	265.314i		−	1.10089i	0.834872	−	0.550444i	$-0.185542\pi$
$242$	304.166	−	64.1655i	1.25688	−	0.265146i
$243$		−	162.055i		−	0.666892i
$244$	9.91758	−	3.22242i	0.0406458	−	0.0132066i
$245$		0			0
$246$	10.0197	−	7.27974i	0.0407305	−	0.0295924i
$247$	199.324	+	64.7642i	0.806978	+	0.262203i
$248$	−48.4540	+	149.126i	−0.195379	+	0.601315i
$249$	53.8868	+	74.1687i	0.216413	+	0.297866i
$250$		0			0
$251$	−81.5281	−	250.918i	−0.324813	−	0.999672i	−0.971525	−	0.236937i	$-0.923856\pi$
$251$	−81.5281	−	250.918i	−0.324813	−	0.999672i	0.646712	−	0.762734i	$-0.276144\pi$
$252$	−290.575			−1.15308
$253$	39.2869	+	43.6998i	0.155284	+	0.172726i
$254$	304.627			1.19932
$255$		0			0
$256$	−270.204	−	196.314i	−1.05548	−	0.766853i
$257$	−186.254	−	256.357i	−0.724725	−	0.997499i	−0.999354	−	0.0359483i	$-0.988555\pi$
$257$	−186.254	−	256.357i	−0.724725	−	0.997499i	0.274628	−	0.961550i	$-0.411445\pi$
$258$	24.6654	+	8.01428i	0.0956024	+	0.0310631i
$259$	176.612	+	57.3849i	0.681901	+	0.221563i
$260$		0			0
$261$	160.932	−	221.503i	0.616596	−	0.848672i
$262$	428.728	−	139.302i	1.63637	−	0.531688i
$263$	415.617			1.58029			0.790145	−	0.612919i	$-0.210005\pi$
$263$	415.617			1.58029			0.790145	+	0.612919i	$0.210005\pi$
$264$	−14.2951	+	24.7162i	−0.0541482	+	0.0936218i
$265$		0			0
$266$	−833.775	+	270.910i	−3.13449	+	1.01846i
$267$	18.5439	−	25.5235i	0.0694528	−	0.0955936i
$268$	−134.065	−	184.524i	−0.500242	−	0.688524i
$269$	−21.6814	+	66.7285i	−0.0806000	+	0.248061i	−0.983234	−	0.182347i	$-0.941631\pi$
$269$	−21.6814	+	66.7285i	−0.0806000	+	0.248061i	0.902634	+	0.430409i	$0.141631\pi$
$270$		0			0
$271$	253.032	+	348.269i	0.933698	+	1.28513i	0.958399	+	0.285430i	$0.0921365\pi$
$271$	253.032	+	348.269i	0.933698	+	1.28513i	−0.0247014	+	0.999695i	$0.507863\pi$
$272$	131.309	+	95.4013i	0.482752	+	0.350740i
$273$	73.2341	−	23.7952i	0.268257	−	0.0871619i
$274$		−	409.962i		−	1.49621i
$275$		0			0
$276$	10.0263			0.0363272
$277$	−24.9552	−	76.8041i	−0.0900909	−	0.277271i	0.895852	−	0.444352i	$-0.146566\pi$
$277$	−24.9552	−	76.8041i	−0.0900909	−	0.277271i	−0.985943	+	0.167081i	$0.946566\pi$
$278$	278.624	−	383.493i	1.00224	−	1.37947i
$279$	−299.099	+	217.308i	−1.07204	+	0.778882i
$280$		0			0
$281$	411.029	+	133.551i	1.46274	+	0.475272i	0.928905	−	0.370318i	$-0.120751\pi$
$281$	411.029	+	133.551i	1.46274	+	0.475272i	0.533832	+	0.845590i	$0.320751\pi$
$282$	−122.178	+	88.7672i	−0.433254	+	0.314777i
$283$	−104.648	−	76.0310i	−0.369780	−	0.268661i	0.387340	−	0.921937i	$-0.373394\pi$
$283$	−104.648	−	76.0310i	−0.369780	−	0.268661i	−0.757120	+	0.653276i	$0.773394\pi$
$284$	27.5448	+	84.7742i	0.0969888	+	0.298501i
$285$		0			0
$286$	47.7315	−	223.716i	0.166893	−	0.782224i
$287$			88.0247i			0.306706i
$288$	−94.5136	−	290.883i	−0.328172	−	1.01001i
$289$	178.553	+	129.726i	0.617829	+	0.448879i
$290$		0			0
$291$	−6.80772	+	20.9520i	−0.0233942	+	0.0720000i
$292$	−50.1942	+	154.482i	−0.171898	+	0.529047i
$293$	220.293	−	160.052i	0.751853	−	0.546253i	−0.144548	−	0.989498i	$-0.546173\pi$
$293$	220.293	−	160.052i	0.751853	−	0.546253i	0.896401	+	0.443245i	$0.146173\pi$
$294$	−135.920	+	187.078i	−0.462313	+	0.636319i
$295$		0			0
$296$			50.6698i			0.171182i
$297$	−126.824	+	56.3494i	−0.427018	+	0.189729i
$298$			426.803i			1.43222i
$299$	41.1255	−	13.3625i	0.137544	−	0.0446906i
$300$		0			0
$301$	−149.124	+	108.345i	−0.495428	+	0.359949i
$302$	−400.335	−	130.077i	−1.32561	−	0.430717i
$303$	−11.5466	+	35.5368i	−0.0381076	+	0.117283i
$304$	−298.893	−	411.391i	−0.983200	−	1.35326i
$305$		0			0
$306$	55.6298	+	171.211i	0.181797	+	0.559513i
$307$	−341.863			−1.11356			−0.556780	−	0.830660i	$-0.687963\pi$
$307$	−341.863			−1.11356			−0.556780	+	0.830660i	$0.687963\pi$
$308$	153.063	+	344.496i	0.496959	+	1.11849i
$309$	49.9219			0.161559
$310$		0			0
$311$	−124.438	−	90.4098i	−0.400123	−	0.290707i	0.369468	−	0.929244i	$-0.379540\pi$
$311$	−124.438	−	90.4098i	−0.400123	−	0.290707i	−0.769591	+	0.638537i	$0.779540\pi$
$312$	12.3498	+	16.9980i	0.0395827	+	0.0544809i
$313$	−8.95868	−	2.91085i	−0.0286220	−	0.00929984i	0.294671	−	0.955599i	$-0.404790\pi$
$313$	−8.95868	−	2.91085i	−0.0286220	−	0.00929984i	−0.323293	+	0.946299i	$0.604790\pi$
$314$	−454.985	−	147.833i	−1.44900	−	0.470807i
$315$		0			0
$316$	191.751	−	263.922i	0.606806	−	0.835197i
$317$	−214.652	+	69.7448i	−0.677137	+	0.220015i	−0.627341	−	0.778744i	$-0.715857\pi$
$317$	−214.652	+	69.7448i	−0.677137	+	0.220015i	−0.0497954	+	0.998759i	$0.515857\pi$
$318$	94.9797			0.298678
$319$	−347.379	−	74.1159i	−1.08896	−	0.232338i
$320$		0			0
$321$	40.7610	−	13.2440i	0.126981	−	0.0412587i
$322$	−106.320	+	146.336i	−0.330185	+	0.454461i
$323$	125.771	+	173.109i	0.389384	+	0.535941i
$324$	54.0001	−	166.195i	0.166667	−	0.512948i
$325$		0			0
$326$	−368.358	−	507.002i	−1.12993	−	1.55522i
$327$	−47.2461	−	34.3263i	−0.144483	−	0.104973i
$328$	−22.8426	+	7.42199i	−0.0696419	+	0.0226280i
$329$		−	1073.35i		−	3.26246i
$330$		0			0
$331$	176.158			0.532198			0.266099	−	0.963946i	$-0.414265\pi$
$331$	176.158			0.532198			0.266099	+	0.963946i	$0.414265\pi$
$332$	102.057	+	314.100i	0.307401	+	0.946083i
$333$	−70.2227	+	96.6532i	−0.210879	+	0.290250i
$334$	−50.6861	+	36.8256i	−0.151755	+	0.110256i
$335$		0			0
$336$	−177.688	−	57.7343i	−0.528833	−	0.171828i
$337$	154.436	−	112.204i	0.458267	−	0.332951i	−0.334584	−	0.942366i	$-0.608596\pi$
$337$	154.436	−	112.204i	0.458267	−	0.332951i	0.792851	+	0.609415i	$0.208596\pi$
$338$	215.074	+	156.261i	0.636315	+	0.462310i
$339$	3.94282	+	12.1348i	0.0116307	+	0.0357958i
$340$		0			0
$341$	415.186	+	240.132i	1.21755	+	0.704200i
$342$		−	564.009i		−	1.64915i
$343$	−308.309	−	948.878i	−0.898860	−	2.76641i
$344$	−40.6894	−	29.5625i	−0.118283	−	0.0859376i
$345$		0			0
$346$	−45.9951	+	141.558i	−0.132934	+	0.409128i
$347$	−61.4596	+	189.153i	−0.177117	+	0.545110i	−0.999724	−	0.0235005i	$-0.992519\pi$
$347$	−61.4596	+	189.153i	−0.177117	+	0.545110i	0.822607	+	0.568611i	$0.192519\pi$
$348$	−49.0300	+	35.6224i	−0.140891	+	0.102363i
$349$	120.489	−	165.839i	0.345241	−	0.475183i	−0.600722	−	0.799458i	$-0.705120\pi$
$349$	120.489	−	165.839i	0.345241	−	0.475183i	0.945963	+	0.324275i	$0.105120\pi$
$350$		0			0
$351$			102.123i			0.290948i
$352$	−295.075	+	265.278i	−0.838281	+	0.753630i
$353$		−	193.516i		−	0.548205i	−0.961701	−	0.274102i	$-0.911619\pi$
$353$		−	193.516i		−	0.548205i	0.961701	−	0.274102i	$-0.0883807\pi$
$354$	94.8286	−	30.8117i	0.267877	−	0.0870387i
$355$		0			0
$356$	91.9471	−	66.8035i	0.258278	−	0.187650i
$357$	74.7692	+	24.2940i	0.209438	+	0.0680504i
$358$	−0.0893755	+	0.275069i	−0.000249652	+	0.000768350i
$359$	−48.9531	−	67.3782i	−0.136360	−	0.187683i	0.735376	−	0.677659i	$-0.237005\pi$
$359$	−48.9531	−	67.3782i	−0.136360	−	0.187683i	−0.871736	+	0.489976i	$0.837005\pi$
$360$		0			0
$361$	−95.6045	−	294.240i	−0.264832	−	0.815070i
$362$	−69.7108			−0.192571
$363$	64.8147	+	58.5395i	0.178553	+	0.161266i
$364$	277.399			0.762085
$365$		0			0
$366$	6.01643	+	4.37119i	0.0164383	+	0.0119431i
$367$	393.044	+	540.978i	1.07096	+	1.47406i	0.869097	+	0.494642i	$0.164701\pi$
$367$	393.044	+	540.978i	1.07096	+	1.47406i	0.201867	+	0.979413i	$0.435299\pi$
$368$	−99.7828	−	32.4214i	−0.271149	−	0.0881016i
$369$	−53.8585	−	17.4997i	−0.145958	−	0.0474247i
$370$		0			0
$371$	−396.786	+	546.129i	−1.06950	+	1.47205i
$372$	77.8296	−	25.2884i	0.209219	−	0.0679795i
$373$	106.447			0.285380			0.142690	−	0.989767i	$-0.454425\pi$
$373$	106.447			0.285380			0.142690	+	0.989767i	$0.454425\pi$
$374$	173.678	−	156.140i	0.464381	−	0.417486i
$375$		0			0
$376$	278.536	−	90.5017i	0.740787	−	0.240696i
$377$	−153.634	+	211.459i	−0.407517	+	0.560899i
$378$	−251.091	−	345.597i	−0.664262	−	0.914278i
$379$	−165.105	+	508.140i	−0.435633	+	1.34074i	0.456804	+	0.889567i	$0.348994\pi$
$379$	−165.105	+	508.140i	−0.435633	+	1.34074i	−0.892437	+	0.451172i	$0.851006\pi$
$380$		0			0
$381$	50.3062	+	69.2406i	0.132037	+	0.181734i
$382$	−682.771	−	496.062i	−1.78736	−	1.29859i
$383$	−25.9749	+	8.43976i	−0.0678196	+	0.0220359i	−0.342730	−	0.939434i	$-0.611352\pi$
$383$	−25.9749	+	8.43976i	−0.0678196	+	0.0220359i	0.274911	+	0.961470i	$0.411352\pi$
$384$		−	77.9757i		−	0.203062i
$385$		0			0
$386$	−575.681			−1.49140
$387$	−36.6451	−	112.782i	−0.0946901	−	0.291426i
$388$	−46.6483	+	64.2059i	−0.120228	+	0.165479i
$389$	549.304	−	399.093i	1.41209	−	1.02595i	0.419078	−	0.907950i	$-0.362353\pi$
$389$	549.304	−	399.093i	1.41209	−	1.02595i	0.993014	−	0.117995i	$-0.0376467\pi$
$390$		0			0
$391$	41.9876	+	13.6426i	0.107385	+	0.0348915i
$392$	362.797	−	263.587i	0.925502	−	0.672417i
$393$	102.463	+	74.4439i	0.260721	+	0.189425i
$394$	1.19177	+	3.66789i	0.00302479	+	0.00930936i
$395$		0			0
$396$	−241.212	+	25.1656i	−0.609122	+	0.0635495i
$397$		−	269.778i		−	0.679542i	−0.940508	−	0.339771i	$-0.889650\pi$
$397$		−	269.778i		−	0.679542i	0.940508	−	0.339771i	$-0.110350\pi$
$398$	51.8260	+	159.504i	0.130216	+	0.400764i
$399$	−199.267	−	144.776i	−0.499416	−	0.362847i
$400$		0			0
$401$	−13.6189	+	41.9146i	−0.0339623	+	0.104525i	−0.966601	−	0.256287i	$-0.917501\pi$
$401$	−13.6189	+	41.9146i	−0.0339623	+	0.104525i	0.932638	+	0.360813i	$0.117501\pi$
$402$	50.2644	−	154.698i	0.125036	−	0.384820i
$403$	285.536	−	207.454i	0.708525	−	0.514774i
$404$	−79.1205	+	108.900i	−0.195843	+	0.269554i
$405$		0			0
$406$		−	1093.35i		−	2.69298i
$407$	151.579	+	32.3406i	0.372431	+	0.0794609i
$408$			21.4511i			0.0525763i
$409$	69.3442	−	22.5313i	0.169546	−	0.0550888i	−0.223014	−	0.974815i	$-0.571590\pi$
$409$	69.3442	−	22.5313i	0.169546	−	0.0550888i	0.392560	+	0.919726i	$0.371590\pi$
$410$		0			0
$411$	93.1829	−	67.7013i	0.226722	−	0.164723i
$412$	171.039	+	55.5739i	0.415143	+	0.134888i
$413$	−218.989	+	673.979i	−0.530240	+	1.63191i
$414$	−68.4002	−	94.1448i	−0.165218	−	0.227403i
$415$		0			0
$416$	90.2278	+	277.693i	0.216894	+	0.667530i
$417$	133.179			0.319373
$418$	−668.670	+	297.097i	−1.59969	+	0.710759i
$419$	46.3826			0.110698			0.0553491	−	0.998467i	$-0.482373\pi$
$419$	46.3826			0.110698			0.0553491	+	0.998467i	$0.482373\pi$
$420$		0			0
$421$	253.022	+	183.831i	0.601002	+	0.436653i	0.846234	−	0.532811i	$-0.178864\pi$
$421$	253.022	+	183.831i	0.601002	+	0.436653i	−0.245232	+	0.969464i	$0.578864\pi$
$422$	373.583	+	514.192i	0.885267	+	1.21847i
$423$	656.736	+	213.386i	1.55257	+	0.504460i
$424$	−175.177	−	56.9186i	−0.413154	−	0.134242i
$425$		0			0
$426$	−37.3644	+	51.4277i	−0.0877099	+	0.120722i
$427$	−50.2683	+	16.3332i	−0.117724	+	0.0382510i
$428$	154.396			0.360738
$429$	58.7322	−	26.0954i	0.136905	−	0.0608284i
$430$		0			0
$431$	−510.568	+	165.893i	−1.18461	+	0.384904i	−0.834078	−	0.551647i	$-0.814000\pi$
$431$	−510.568	+	165.893i	−1.18461	+	0.384904i	−0.350533	+	0.936550i	$0.614000\pi$
$432$	145.642	−	200.458i	0.337133	−	0.464024i
$433$	−113.734	−	156.542i	−0.262666	−	0.361529i	0.657231	−	0.753689i	$-0.271728\pi$
$433$	−113.734	−	156.542i	−0.262666	−	0.361529i	−0.919897	+	0.392161i	$0.871728\pi$
$434$	−456.221	+	1404.10i	−1.05120	+	3.23526i
$435$		0			0
$436$	−123.659	−	170.201i	−0.283621	−	0.390370i
$437$	−111.901	−	81.3006i	−0.256066	−	0.186043i
$438$	−110.169	+	35.7961i	−0.251527	+	0.0817261i
$439$			492.610i			1.12212i	0.827776	+	0.561059i	$0.189606\pi$
$439$			492.610i			1.12212i	−0.827776	+	0.561059i	$0.810394\pi$
$440$		0			0
$441$	1057.34			2.39760
$442$	−53.1072	−	163.447i	−0.120152	−	0.369790i
$443$	−43.8483	+	60.3521i	−0.0989805	+	0.136235i	−0.855634	−	0.517581i	$-0.826833\pi$
$443$	−43.8483	+	60.3521i	−0.0989805	+	0.136235i	0.756654	+	0.653816i	$0.226833\pi$
$444$	21.3943	−	15.5439i	0.0481854	−	0.0350087i
$445$		0			0
$446$	647.586	+	210.413i	1.45199	+	0.471779i
$447$	−97.0107	+	70.4824i	−0.217026	+	0.157679i
$448$	−150.477	−	109.328i	−0.335886	−	0.244035i
$449$	207.909	+	639.879i	0.463050	+	1.42512i	0.861418	+	0.507896i	$0.169577\pi$
$449$	207.909	+	639.879i	0.463050	+	1.42512i	−0.398368	+	0.917225i	$0.630423\pi$
$450$		0			0
$451$	7.62347	+	73.0710i	0.0169035	+	0.162020i
$452$			45.9645i			0.101691i
$453$	−36.5455	−	112.476i	−0.0806744	−	0.248290i
$454$	−767.303	−	557.479i	−1.69010	−	1.22793i
$455$		0			0
$456$	20.7679	−	63.9172i	0.0455437	−	0.140169i
$457$	−174.656	+	537.536i	−0.382180	+	1.17623i	0.556326	+	0.830964i	$0.312211\pi$
$457$	−174.656	+	537.536i	−0.382180	+	1.17623i	−0.938506	+	0.345264i	$0.887789\pi$
$458$	−161.646	+	117.443i	−0.352940	+	0.256426i
$459$	−61.2845	+	84.3509i	−0.133517	+	0.183771i
$460$		0			0
$461$			742.567i			1.61077i	0.592749	+	0.805387i	$0.298042\pi$
$461$			742.567i			1.61077i	−0.592749	+	0.805387i	$0.701958\pi$
$462$	−134.597	+	232.716i	−0.291335	+	0.503715i
$463$		−	279.537i		−	0.603752i	−0.953347	−	0.301876i	$-0.902387\pi$
$463$		−	279.537i		−	0.603752i	0.953347	−	0.301876i	$-0.0976128\pi$
$464$	603.141	−	195.972i	1.29987	−	0.422354i
$465$		0			0
$466$	−452.638	+	328.860i	−0.971325	+	0.705709i
$467$	726.720	+	236.126i	1.55615	+	0.505623i	0.955775	−	0.294099i	$-0.0950195\pi$
$467$	726.720	+	236.126i	1.55615	+	0.505623i	0.600371	+	0.799722i	$0.295020\pi$
$468$	−55.1481	+	169.729i	−0.117838	+	0.362668i
$469$	679.522	+	935.282i	1.44887	+	1.99420i
$470$		0			0
$471$	−41.5344	−	127.830i	−0.0881834	−	0.271401i
$472$	−193.363			−0.409668
$473$	−114.407	+	102.854i	−0.241876	+	0.217451i
$474$	232.649			0.490820
$475$		0			0
$476$	229.125	+	166.469i	0.481354	+	0.349724i
$477$	−255.270	−	351.349i	−0.535158	−	0.736581i
$478$	343.870	+	111.730i	0.719394	+	0.233745i
$479$	596.452	+	193.799i	1.24520	+	0.404591i	0.856199	−	0.516646i	$-0.172820\pi$
$479$	596.452	+	193.799i	1.24520	+	0.404591i	0.389003	+	0.921236i	$0.372820\pi$
$480$		0			0
$481$	67.0384	−	92.2704i	0.139373	−	0.191830i
$482$	648.256	−	210.631i	1.34493	−	0.436994i
$483$	−50.8194			−0.105216
$484$	156.896	+	272.717i	0.324166	+	0.563464i
$485$		0			0
$486$	395.956	−	128.654i	0.814725	−	0.264720i
$487$	98.5999	−	135.711i	0.202464	−	0.278668i	−0.695696	−	0.718336i	$-0.744904\pi$
$487$	98.5999	−	135.711i	0.202464	−	0.278668i	0.898160	+	0.439668i	$0.144904\pi$
$488$	−8.47697	−	11.6676i	−0.0173708	−	0.0239089i
$489$	54.4088	−	167.453i	0.111265	−	0.342440i
$490$		0			0
$491$	−194.221	−	267.323i	−0.395563	−	0.544446i	0.564060	−	0.825734i	$-0.309238\pi$
$491$	−194.221	−	267.323i	−0.395563	−	0.544446i	−0.959623	+	0.281288i	$0.909238\pi$
$492$	10.1412	+	7.36798i	0.0206121	+	0.0149756i
$493$	−253.796	+	82.4632i	−0.514798	+	0.167268i
$494$			538.433i			1.08995i
$495$		0			0
$496$	−856.342			−1.72650
$497$	−139.614	−	429.688i	−0.280913	−	0.864563i
$498$	−138.440	+	190.546i	−0.277992	+	0.382623i
$499$	−630.351	+	457.977i	−1.26323	+	0.917789i	−0.998911	−	0.0466466i	$-0.985147\pi$
$499$	−630.351	+	457.977i	−1.26323	+	0.917789i	−0.264317	+	0.964436i	$0.585147\pi$
$500$		0			0
$501$	−16.7407	−	5.43937i	−0.0334145	−	0.0108570i
$502$	548.355	−	398.404i	1.09234	−	0.793633i
$503$	−336.060	−	244.162i	−0.668112	−	0.485412i	0.201281	−	0.979534i	$-0.435490\pi$
$503$	−336.060	−	244.162i	−0.668112	−	0.485412i	−0.869393	+	0.494122i	$0.835490\pi$
$504$	124.184	+	382.198i	0.246396	+	0.758329i
$505$		0			0
$506$	−75.5844	+	130.685i	−0.149376	+	0.258270i
$507$			74.6906i			0.147319i
$508$	95.2759	+	293.229i	0.187551	+	0.577223i
$509$	−570.074	−	414.183i	−1.11999	−	0.813719i	−0.135781	−	0.990739i	$-0.543354\pi$
$509$	−570.074	−	414.183i	−1.11999	−	0.813719i	−0.984207	+	0.177019i	$0.943354\pi$
$510$		0			0
$511$	254.415	−	783.008i	0.497876	−	1.53231i
$512$	131.620	−	405.084i	0.257070	−	0.791180i
$513$	264.272	−	192.005i	0.515149	−	0.374278i
$514$	478.505	−	658.605i	0.930943	−	1.28133i
$515$		0			0
$516$			26.2491i			0.0508704i
$517$	−92.9585	−	891.007i	−0.179804	−	1.72342i
$518$			477.084i			0.921011i
$519$	−39.7714	+	12.9225i	−0.0766307	+	0.0248988i
$520$		0			0
$521$	−141.580	+	102.864i	−0.271747	+	0.197436i	−0.715310	−	0.698808i	$-0.753714\pi$
$521$	−141.580	+	102.864i	−0.271747	+	0.197436i	0.443563	+	0.896243i	$0.353714\pi$
$522$	668.973	+	217.362i	1.28156	+	0.416403i
$523$	270.629	−	832.911i	0.517455	−	1.59256i	−0.261314	−	0.965254i	$-0.584156\pi$
$523$	270.629	−	832.911i	0.517455	−	1.59256i	0.778769	−	0.627310i	$-0.215844\pi$
$524$	268.180	+	369.119i	0.511795	+	0.704425i
$525$		0			0
$526$	329.955	+	1015.50i	0.627291	+	1.93060i
$527$	360.340			0.683757
$528$	−152.502	−	32.5375i	−0.288830	−	0.0616240i
$529$	500.462			0.946052
$530$		0			0
$531$	−368.843	−	267.980i	−0.694620	−	0.504671i
$532$	−521.547	−	717.848i	−0.980352	−	1.34934i
$533$	51.4163	+	16.7062i	0.0964658	+	0.0313436i
$534$	77.0847	+	25.0464i	0.144353	+	0.0469033i
$535$		0			0
$536$	−185.412	+	255.198i	−0.345918	+	0.476115i
$537$	−0.0772818	+	0.0251104i	−0.000143914	+	4.67605e-5i
$538$	−180.254			−0.335044
$539$	−556.966	−	1253.55i	−1.03333	−	2.32569i
$540$		0			0
$541$	−125.231	+	40.6901i	−0.231481	+	0.0752128i	−0.422461	−	0.906381i	$-0.638834\pi$
$541$	−125.231	+	40.6901i	−0.231481	+	0.0752128i	0.190980	+	0.981594i	$0.438834\pi$
$542$	−650.063	+	894.735i	−1.19938	+	1.65080i
$543$	−11.5121	−	15.8450i	−0.0212009	−	0.0291805i
$544$	−92.1191	+	283.514i	−0.169337	+	0.521165i
$545$		0			0
$546$	116.280	+	160.046i	0.212967	+	0.293124i
$547$	1.32090	+	0.959689i	0.00241481	+	0.00175446i	0.588992	−	0.808139i	$-0.299525\pi$
$547$	1.32090	+	0.959689i	0.00241481	+	0.00175446i	−0.586577	+	0.809893i	$0.699525\pi$
$548$	394.623	−	128.221i	0.720115	−	0.233980i
$549$		−	34.0042i		−	0.0619384i
$550$		0			0
$551$	836.062			1.51735
$552$	−4.28495	−	13.1877i	−0.00776260	−	0.0238908i
$553$	−971.910	+	1337.72i	−1.75752	+	2.41902i
$554$	167.848	−	121.949i	0.302974	−	0.220124i
$555$		0			0
$556$	456.287	+	148.257i	0.820661	+	0.266649i
$557$	−464.666	+	337.599i	−0.834229	+	0.606103i	−0.920753	−	0.390147i	$-0.872424\pi$
$557$	−464.666	+	337.599i	−0.834229	+	0.606103i	0.0865234	+	0.996250i	$0.472424\pi$
$558$	−768.412	−	558.284i	−1.37708	−	1.00051i
$559$	34.9833	+	107.668i	0.0625820	+	0.192608i
$560$		0			0
$561$	64.1714	+	13.6914i	0.114387	+	0.0244054i
$562$			1110.31i			1.97565i
$563$	−54.1325	−	166.603i	−0.0961502	−	0.295920i	0.891402	−	0.453214i	$-0.149723\pi$
$563$	−54.1325	−	166.603i	−0.0961502	−	0.295920i	−0.987552	+	0.157295i	$0.949723\pi$
$564$	−123.658	−	89.8432i	−0.219253	−	0.159296i
$565$		0			0
$566$	102.691	−	316.052i	0.181434	−	0.558395i
$567$	−273.705	+	842.379i	−0.482726	+	1.48568i
$568$	99.7328	−	72.4601i	0.175586	−	0.127571i
$569$	172.026	−	236.774i	0.302331	−	0.416122i	−0.630640	−	0.776076i	$-0.717207\pi$
$569$	172.026	−	236.774i	0.302331	−	0.416122i	0.932970	+	0.359953i	$0.117207\pi$
$570$		0			0
$571$			836.204i			1.46446i	0.681060	+	0.732228i	$0.261519\pi$
$571$			836.204i			1.46446i	−0.681060	+	0.732228i	$0.738481\pi$
$572$	230.274	−	24.0244i	0.402577	−	0.0420008i
$573$		−	237.111i		−	0.413807i
$574$	−215.075	+	69.8822i	−0.374696	+	0.121746i
$575$		0			0
$576$	96.8085	−	70.3355i	0.168070	−	0.122110i
$577$	876.557	+	284.811i	1.51916	+	0.493606i	0.945538	−	0.325511i	$-0.105536\pi$
$577$	876.557	+	284.811i	1.51916	+	0.493606i	0.573626	+	0.819118i	$0.305536\pi$
$578$	−175.215	+	539.255i	−0.303140	+	0.932968i
$579$	−95.0683	−	130.850i	−0.164194	−	0.225994i
$580$		0			0
$581$	−517.288	−	1592.05i	−0.890341	−	2.74019i
$582$	−56.5977			−0.0972469
$583$	−282.082	+	487.716i	−0.483845	+	0.836563i
$584$	224.643			0.384663
$585$		0			0
$586$	565.953	+	411.189i	0.965790	+	0.701688i
$587$	−154.537	−	212.702i	−0.263266	−	0.362354i	0.656836	−	0.754033i	$-0.271894\pi$
$587$	−154.537	−	212.702i	−0.263266	−	0.362354i	−0.920102	+	0.391679i	$0.871894\pi$
$588$	−222.589	−	72.3236i	−0.378553	−	0.122999i
$589$	−1073.69	−	348.863i	−1.82291	−	0.592298i
$590$		0			0
$591$	−0.636888	+	0.876602i	−0.00107765	+	0.00148325i
$592$	−263.181	+	85.5128i	−0.444563	+	0.144447i
$593$	124.297			0.209606			0.104803	−	0.994493i	$-0.466579\pi$
$593$	124.297			0.209606			0.104803	+	0.994493i	$0.466579\pi$
$594$	−238.366	−	265.141i	−0.401290	−	0.446365i
$595$		0			0
$596$	−410.834	+	133.488i	−0.689318	+	0.223973i
$597$	−27.6961	+	38.1204i	−0.0463921	+	0.0638533i
$598$	65.2985	+	89.8757i	0.109195	+	0.150294i
$599$	−24.5601	+	75.5882i	−0.0410018	+	0.126191i	−0.969462	−	0.245241i	$-0.921133\pi$
$599$	−24.5601	+	75.5882i	−0.0410018	+	0.126191i	0.928460	+	0.371432i	$0.121133\pi$
$600$		0			0
$601$	337.300	+	464.254i	0.561232	+	0.772469i	0.991482	−	0.130240i	$-0.0415749\pi$
$601$	337.300	+	464.254i	0.561232	+	0.772469i	−0.430251	+	0.902709i	$0.641575\pi$
$602$	−383.113	−	278.348i	−0.636400	−	0.462372i
$603$	−707.351	+	229.832i	−1.17305	+	0.381148i
$604$		−	426.039i		−	0.705363i
$605$		0			0
$606$	−95.9957			−0.158409
$607$	−146.723	−	451.568i	−0.241719	−	0.743934i	−0.996159	−	0.0875652i	$-0.972091\pi$
$607$	−146.723	−	451.568i	−0.241719	−	0.743934i	0.754440	−	0.656369i	$-0.227909\pi$
$608$	548.968	−	755.590i	0.902908	−	1.24275i
$609$	248.514	−	180.556i	0.408069	−	0.296480i
$610$		0			0
$611$	−626.956	−	203.710i	−1.02611	−	0.333405i
$612$	−147.406	+	107.097i	−0.240860	+	0.174995i
$613$	709.576	+	515.537i	1.15755	+	0.841007i	0.989466	−	0.144766i	$-0.0462431\pi$
$613$	709.576	+	515.537i	1.15755	+	0.841007i	0.168081	+	0.985773i	$0.446243\pi$
$614$	−271.403	−	835.291i	−0.442024	−	1.36041i
$615$		0			0
$616$	387.706	−	348.554i	0.629392	−	0.565835i
$617$		−	401.953i		−	0.651464i	−0.945462	−	0.325732i	$-0.894389\pi$
$617$		−	401.953i		−	0.651464i	0.945462	−	0.325732i	$-0.105611\pi$
$618$	39.6326	+	121.977i	0.0641305	+	0.197373i
$619$	165.411	+	120.178i	0.267223	+	0.194149i	0.713325	−	0.700833i	$-0.247188\pi$
$619$	165.411	+	120.178i	0.267223	+	0.194149i	−0.446102	+	0.894982i	$0.647188\pi$
$620$		0			0
$621$	20.8270	−	64.0991i	0.0335379	−	0.103219i
$622$	122.112	−	375.822i	0.196322	−	0.604216i
$623$	−466.044	+	338.601i	−0.748064	+	0.543500i
$624$	−67.4465	+	92.8322i	−0.108087	+	0.148770i
$625$		0			0
$626$		−	24.2001i		−	0.0386583i
$627$	−177.954	−	102.923i	−0.283818	−	0.164152i
$628$		−	484.198i		−	0.771016i
$629$	110.744	−	35.9829i	0.176064	−	0.0572066i
$630$		0			0
$631$	−418.233	+	303.864i	−0.662810	+	0.481560i	−0.867611	−	0.497244i	$-0.834345\pi$
$631$	−418.233	+	303.864i	−0.662810	+	0.481560i	0.204801	+	0.978804i	$0.434345\pi$
$632$	−429.089	−	139.420i	−0.678939	−	0.220601i
$633$	−55.1804	+	169.828i	−0.0871729	+	0.268291i
$634$	−340.822	−	469.101i	−0.537574	−	0.739907i
$635$		0			0
$636$	29.7061	+	91.4260i	0.0467077	+	0.143752i
$637$	−1009.40			−1.58461
$638$	−94.6906	−	907.609i	−0.148418	−	1.42258i
$639$	290.663			0.454872
$640$		0			0
$641$	−221.224	−	160.729i	−0.345124	−	0.250747i	0.401697	−	0.915773i	$-0.368421\pi$
$641$	−221.224	−	160.729i	−0.345124	−	0.250747i	−0.746820	+	0.665026i	$0.768421\pi$
$642$	64.7197	+	89.0791i	0.100810	+	0.138752i
$643$	150.697	+	48.9645i	0.234366	+	0.0761501i	0.423845	−	0.905735i	$-0.360680\pi$
$643$	150.697	+	48.9645i	0.234366	+	0.0761501i	−0.189479	+	0.981885i	$0.560680\pi$
$644$	−174.114	−	56.5731i	−0.270364	−	0.0878464i
$645$		0			0
$646$	−323.117	+	444.733i	−0.500182	+	0.688441i
$647$	−971.123	+	315.537i	−1.50096	+	0.487692i	−0.940298	−	0.340351i	$-0.889454\pi$
$647$	−971.123	+	315.537i	−1.50096	+	0.487692i	−0.560664	+	0.828044i	$0.689454\pi$
$648$	−241.677			−0.372958
$649$	−123.416	+	578.449i	−0.190164	+	0.891293i
$650$		0			0
$651$	−394.488	+	128.177i	−0.605973	+	0.196892i
$652$	372.823	−	513.147i	0.571815	−	0.787036i
$653$	60.3750	+	83.0990i	0.0924579	+	0.127257i	0.852740	−	0.522336i	$-0.174939\pi$
$653$	60.3750	+	83.0990i	0.0924579	+	0.127257i	−0.760282	+	0.649593i	$0.774939\pi$
$654$	46.3628	−	142.690i	0.0708912	−	0.218181i
$655$		0			0
$656$	−77.1005	−	106.120i	−0.117531	−	0.161768i
$657$	428.510	+	311.331i	0.652223	+	0.473868i
$658$	2622.57	−	852.124i	3.98567	−	1.29502i
$659$		−	375.067i		−	0.569145i	−0.958655	−	0.284573i	$-0.908148\pi$
$659$		−	375.067i		−	0.569145i	0.958655	−	0.284573i	$-0.0918517\pi$
$660$		0			0
$661$	−1095.09			−1.65671			−0.828356	−	0.560203i	$-0.810723\pi$
$661$	−1095.09			−1.65671			−0.828356	+	0.560203i	$0.810723\pi$
$662$	139.850	+	430.415i	0.211254	+	0.650174i
$663$	28.3808	−	39.0628i	0.0428067	−	0.0589183i
$664$	369.523	−	268.474i	0.556511	−	0.404329i
$665$		0			0
$666$	−291.907	−	94.8464i	−0.438299	−	0.142412i
$667$	139.556	−	101.393i	0.209230	−	0.152014i
$668$	−51.3005	−	37.2720i	−0.0767971	−	0.0557964i
$669$	59.1164	+	181.942i	0.0883654	+	0.271961i
$670$		0			0
$671$	−40.3142	+	17.9120i	−0.0600807	+	0.0266945i
$672$		−	343.149i		−	0.510639i
$673$	−0.725514	−	2.23290i	−0.00107803	−	0.00331783i	0.950516	−	0.310675i	$-0.100555\pi$
$673$	−0.725514	−	2.23290i	−0.00107803	−	0.00331783i	−0.951594	+	0.307358i	$0.900555\pi$
$674$	396.760	+	288.263i	0.588665	+	0.427690i
$675$		0			0
$676$	−83.1469	+	255.900i	−0.122998	+	0.378550i
$677$	5.13532	−	15.8049i	0.00758541	−	0.0233455i	−0.947192	−	0.320666i	$-0.896093\pi$
$677$	5.13532	−	15.8049i	0.00758541	−	0.0233455i	0.954778	+	0.297321i	$0.0960931\pi$
$678$	−26.5193	+	19.2674i	−0.0391140	+	0.0284180i
$679$	236.442	−	325.435i	0.348221	−	0.479285i
$680$		0			0
$681$		−	266.468i		−	0.391289i
$682$	−257.114	+	1205.09i	−0.377000	+	1.76699i
$683$		−	560.470i		−	0.820600i	−0.911951	−	0.410300i	$-0.865424\pi$
$683$		−	560.470i		−	0.820600i	0.911951	−	0.410300i	$-0.134576\pi$
$684$	542.907	−	176.401i	0.793723	−	0.257896i
$685$		0			0
$686$	2073.68	−	1506.62i	3.02285	−	2.19623i
$687$	−53.3887	−	17.3470i	−0.0777128	−	0.0252504i
$688$	84.8800	−	261.234i	0.123372	−	0.379700i
$689$	243.695	+	335.417i	0.353693	+	0.486817i
$690$		0			0
$691$	129.822	+	399.551i	0.187876	+	0.578222i	0.999986	−	0.00528214i	$-0.00168136\pi$
$691$	129.822	+	399.551i	0.187876	+	0.578222i	−0.812110	+	0.583504i	$0.801681\pi$
$692$	−150.647			−0.217699
$693$	1222.61	−	127.555i	1.76423	−	0.184062i
$694$	−510.960			−0.736254
$695$		0			0
$696$	67.8086	+	49.2658i	0.0974261	+	0.0707842i
$697$	32.4431	+	44.6541i	0.0465468	+	0.0640661i
$698$	500.858	+	162.739i	0.717562	+	0.233150i
$699$	−149.498	−	48.5747i	−0.213874	−	0.0694917i
$700$		0			0
$701$	65.3351	−	89.9261i	0.0932027	−	0.128283i	−0.759869	−	0.650076i	$-0.774737\pi$
$701$	65.3351	−	89.9261i	0.0932027	−	0.128283i	0.853072	+	0.521794i	$0.174737\pi$
$702$	−249.522	+	81.0745i	−0.355444	+	0.115491i
$703$	−364.817			−0.518943
$704$	−134.382	−	77.7229i	−0.190884	−	0.110402i
$705$		0			0
$706$	472.828	−	153.631i	0.669729	−	0.217608i
$707$	401.031	−	551.972i	0.567229	−	0.780724i
$708$	59.3177	+	81.6438i	0.0837821	+	0.115316i
$709$	−34.0103	+	104.673i	−0.0479694	+	0.147634i	−0.972172	−	0.234268i	$-0.924731\pi$
$709$	−34.0103	+	104.673i	−0.0479694	+	0.147634i	0.924203	+	0.381902i	$0.124731\pi$
$710$		0			0
$711$	−625.273	−	860.615i	−0.879428	−	1.21043i
$712$	−127.163	−	92.3893i	−0.178600	−	0.129760i
$713$	−221.530	+	71.9794i	−0.310701	+	0.100953i
$714$			201.974i			0.282877i
$715$		0			0
$716$	−0.292731			−0.000408842
$717$	31.3910	+	96.6117i	0.0437811	+	0.134744i
$718$	125.765	−	173.101i	0.175160	−	0.241087i
$719$	−442.734	+	321.665i	−0.615763	+	0.447378i	−0.851439	−	0.524453i	$-0.824270\pi$
$719$	−442.734	+	321.665i	−0.615763	+	0.447378i	0.235676	+	0.971832i	$0.424270\pi$
$720$		0			0
$721$	−866.930	−	281.683i	−1.20240	−	0.390683i
$722$	643.033	−	467.191i	0.890627	−	0.647078i
$723$	154.929	+	112.563i	0.214286	+	0.155688i
$724$	−21.8030	−	67.1026i	−0.0301146	−	0.0926831i
$725$		0			0
$726$	−91.5766	+	204.839i	−0.126139	+	0.282148i
$727$		−	321.509i		−	0.442241i	−0.975246	−	0.221121i	$-0.929029\pi$
$727$		−	321.509i		−	0.442241i	0.975246	−	0.221121i	$-0.0709714\pi$
$728$	−118.552	−	364.866i	−0.162847	−	0.501190i
$729$	−394.697	−	286.764i	−0.541422	−	0.393366i
$730$		0			0
$731$	−35.7167	+	109.925i	−0.0488600	+	0.150376i
$732$	−2.32593	+	7.15847i	−0.00317750	+	0.00977933i
$733$	−54.3778	+	39.5078i	−0.0741853	+	0.0538988i	−0.624260	−	0.781217i	$-0.714599\pi$
$733$	−54.3778	+	39.5078i	−0.0741853	+	0.0538988i	0.550074	+	0.835116i	$0.314599\pi$
$734$	−1009.77	+	1389.82i	−1.37570	+	1.89349i
$735$		0			0
$736$		−	192.700i		−	0.261820i
$737$	645.086	+	717.545i	0.875286	+	0.973602i
$738$		−	145.488i		−	0.197139i
$739$	143.429	−	46.6030i	0.194086	−	0.0630622i	−0.210361	−	0.977624i	$-0.567464\pi$
$739$	143.429	−	46.6030i	0.194086	−	0.0630622i	0.404447	+	0.914561i	$0.367464\pi$
$740$		0			0
$741$	−122.384	+	88.9172i	−0.165161	+	0.119996i
$742$	−1649.39	−	535.920i	−2.22290	−	0.722264i
$743$	57.7178	−	177.637i	0.0776820	−	0.239081i	−0.904673	−	0.426107i	$-0.859885\pi$
$743$	57.7178	−	177.637i	0.0776820	−	0.239081i	0.982355	+	0.187026i	$0.0598848\pi$
$744$	−66.5243	−	91.5628i	−0.0894144	−	0.123068i
$745$		0			0
$746$	84.5073	+	260.087i	0.113281	+	0.348642i
$747$	1076.95			1.44169
$748$	204.618	+	118.345i	0.273554	+	0.158216i
$749$	−782.573			−1.04482
$750$		0			0
$751$	−635.190	−	461.493i	−0.845793	−	0.614504i	0.0781901	−	0.996938i	$-0.475086\pi$
$751$	−635.190	−	461.493i	−0.845793	−	0.614504i	−0.923983	+	0.382434i	$0.875086\pi$
$752$	940.142	+	1293.99i	1.25019	+	1.72074i
$753$	181.111	+	58.8467i	0.240520	+	0.0781496i
$754$	−638.637	−	207.506i	−0.846999	−	0.275207i
$755$		0			0
$756$	254.135	−	349.786i	0.336157	−	0.462680i
$757$	817.184	−	265.519i	1.07950	−	0.350752i	0.285322	−	0.958432i	$-0.407900\pi$
$757$	817.184	−	265.519i	1.07950	−	0.350752i	0.794182	+	0.607680i	$0.207900\pi$
$758$	−1372.64			−1.81087
$759$	−42.1862	+	4.40127i	−0.0555813	+	0.00579878i
$760$		0			0
$761$	1125.43	−	365.675i	1.47888	−	0.480519i	0.545105	−	0.838368i	$-0.316490\pi$
$761$	1125.43	−	365.675i	1.47888	−	0.480519i	0.933779	+	0.357849i	$0.116490\pi$
$762$	−129.241	+	177.885i	−0.169608	+	0.233445i
$763$	626.778	+	862.685i	0.821465	+	1.13065i
$764$	263.957	−	812.375i	0.345493	−	1.06332i
$765$		0			0
$766$	−41.2426	−	56.7656i	−0.0538415	−	0.0741065i
$767$	352.117	+	255.828i	0.459084	+	0.333544i
$768$	229.274	−	74.4956i	0.298534	−	0.0969994i
$769$			617.014i			0.802359i	0.915999	+	0.401179i	$0.131400\pi$
$769$			617.014i			0.802359i	−0.915999	+	0.401179i	$0.868600\pi$
$770$		0			0
$771$	228.719			0.296653
$772$	−180.052	−	554.142i	−0.233228	−	0.717801i
$773$	719.122	−	989.787i	0.930300	−	1.28045i	−0.0294422	−	0.999566i	$-0.509373\pi$
$773$	719.122	−	989.787i	0.930300	−	1.28045i	0.959742	−	0.280882i	$-0.0906269\pi$
$774$	246.474	−	179.074i	0.318441	−	0.231361i
$775$		0			0
$776$	104.387	+	33.9174i	0.134519	+	0.0437080i
$777$	−108.439	+	78.7859i	−0.139562	+	0.101398i
$778$	1411.21	+	1025.31i	1.81390	+	1.31787i
$779$	−53.4376	−	164.464i	−0.0685977	−	0.211122i
$780$		0			0
$781$	−153.110	−	344.601i	−0.196043	−	0.441230i
$782$			113.421i			0.145040i
$783$	125.890	+	387.449i	0.160779	+	0.494827i
$784$	1981.36	+	1439.54i	2.52725	+	1.83615i
$785$		0			0
$786$	−100.548	+	309.454i	−0.127923	+	0.393708i
$787$	−37.0249	+	113.951i	−0.0470456	+	0.144792i	−0.971820	−	0.235725i	$-0.924254\pi$
$787$	−37.0249	+	113.951i	−0.0470456	+	0.144792i	0.924774	+	0.380516i	$0.124254\pi$
$788$	−3.15791	+	2.29436i	−0.00400750	+	0.00291162i
$789$	−176.330	+	242.697i	−0.223485	+	0.307601i
$790$		0			0
$791$		−	232.976i		−	0.294534i
$792$	136.188	+	306.515i	0.171954	+	0.387013i
$793$			32.4622i			0.0409359i
$794$	659.163	−	214.175i	0.830180	−	0.269742i
$795$		0			0
$796$	−137.327	+	99.7738i	−0.172521	+	0.125344i
$797$	−567.539	−	184.404i	−0.712094	−	0.231373i	−0.0695017	−	0.997582i	$-0.522141\pi$
$797$	−567.539	−	184.404i	−0.712094	−	0.231373i	−0.642592	+	0.766209i	$0.722141\pi$
$798$	195.542	−	601.815i	0.245040	−	0.754155i
$799$	−395.602	−	544.500i	−0.495121	−	0.681476i
$800$		0			0
$801$	−114.524	−	352.468i	−0.142976	−	0.440035i
$802$	−113.224			−0.141177
$803$	143.381	−	672.024i	0.178557	−	0.836892i
$804$	164.631			0.204764
$805$		0			0
$806$	733.568	+	532.968i	0.910134	+	0.661251i
$807$	−29.7672	−	40.9711i	−0.0368863	−	0.0507696i
$808$	177.051	+	57.5275i	0.219123	+	0.0711974i
$809$	268.262	+	87.1635i	0.331597	+	0.107742i	0.470083	−	0.882622i	$-0.344224\pi$
$809$	268.262	+	87.1635i	0.331597	+	0.107742i	−0.138487	+	0.990364i	$0.544224\pi$
$810$		0			0
$811$	72.7008	−	100.064i	0.0896434	−	0.123384i	−0.761840	−	0.647766i	$-0.775704\pi$
$811$	72.7008	−	100.064i	0.0896434	−	0.123384i	0.851483	+	0.524382i	$0.175704\pi$
$812$	1052.44	−	341.959i	1.29611	−	0.421131i
$813$	−310.722			−0.382192
$814$	41.3184	+	396.036i	0.0507596	+	0.486531i
$815$		0			0
$816$	−111.418	+	36.2020i	−0.136542	+	0.0443652i
$817$	212.847	−	292.959i	0.260523	−	0.358579i
$818$	110.104	+	151.545i	0.134601	+	0.185263i
$819$	279.525	−	860.288i	0.341300	−	1.05041i
$820$		0			0
$821$	406.944	+	560.110i	0.495668	+	0.682229i	0.981421	−	0.191868i	$-0.0614544\pi$
$821$	406.944	+	560.110i	0.495668	+	0.682229i	−0.485753	+	0.874096i	$0.661454\pi$
$822$	239.395	+	173.931i	0.291235	+	0.211595i
$823$	−1017.93	+	330.747i	−1.23686	+	0.401879i	−0.853194	−	0.521594i	$-0.825338\pi$
$823$	−1017.93	+	330.747i	−1.23686	+	0.401879i	−0.383663	+	0.923473i	$0.625338\pi$
$824$		−	248.720i		−	0.301845i
$825$		0			0
$826$	−1820.62			−2.20414
$827$	−443.516	−	1365.00i	−0.536295	−	1.65054i	−0.740835	−	0.671687i	$-0.765570\pi$
$827$	−443.516	−	1365.00i	−0.536295	−	1.65054i	0.204541	−	0.978858i	$-0.434430\pi$
$828$	69.2293	−	95.2860i	0.0836103	−	0.115080i
$829$	−75.5393	+	54.8825i	−0.0911209	+	0.0662032i	−0.632413	−	0.774631i	$-0.717935\pi$
$829$	−75.5393	+	54.8825i	−0.0911209	+	0.0662032i	0.541292	+	0.840835i	$0.317935\pi$
$830$		0			0
$831$	55.4369	+	18.0125i	0.0667111	+	0.0216757i
$832$	−92.4186	+	67.1460i	−0.111080	+	0.0807044i
$833$	−833.736	−	605.745i	−1.00088	−	0.727185i
$834$	105.730	+	325.402i	0.126774	+	0.390170i
$835$		0			0
$836$	−495.117	−	550.731i	−0.592245	−	0.658769i
$837$		−	550.102i		−	0.657231i
$838$	36.8228	+	113.329i	0.0439413	+	0.135237i
$839$	995.583	+	723.334i	1.18663	+	0.862138i	0.992904	−	0.118918i	$-0.0379425\pi$
$839$	995.583	+	723.334i	1.18663	+	0.862138i	0.193727	+	0.981056i	$0.437942\pi$
$840$		0			0
$841$	−62.3252	+	191.817i	−0.0741085	+	0.228082i
$842$	−248.292	+	764.163i	−0.294883	+	0.907558i
$843$	−252.370	+	183.358i	−0.299372	+	0.217506i
$844$	−378.111	+	520.425i	−0.447999	+	0.616617i
$845$		0			0
$846$			1774.04i			2.09698i
$847$	−795.247	−	1382.30i	−0.938899	−	1.63199i
$848$		−	1005.94i		−	1.18625i
$849$	88.7959	−	28.8515i	0.104589	−	0.0339830i
$850$		0			0
$851$	−60.8955	+	44.2432i	−0.0715576	+	0.0519896i
$852$	−61.1897	−	19.8817i	−0.0718189	−	0.0233354i
$853$	−230.655	+	709.882i	−0.270404	+	0.832218i	0.719995	+	0.693979i	$0.244144\pi$
$853$	−230.655	+	709.882i	−0.270404	+	0.832218i	−0.990399	+	0.138239i	$0.955856\pi$
$854$	−79.8154	−	109.856i	−0.0934606	−	0.128638i
$855$		0			0
$856$	−65.9844	−	203.079i	−0.0770846	−	0.237242i
$857$	1009.05			1.17742			0.588710	−	0.808344i	$-0.299636\pi$
$857$	1009.05			1.17742			0.588710	+	0.808344i	$0.299636\pi$
$858$	110.387	+	122.787i	0.128656	+	0.143108i
$859$	−666.482			−0.775882			−0.387941	−	0.921684i	$-0.626813\pi$
$859$	−666.482			−0.775882			−0.387941	+	0.921684i	$0.626813\pi$
$860$		0			0
$861$	−51.4016	−	37.3455i	−0.0596999	−	0.0433745i
$862$	−810.672	−	1115.79i	−0.940455	−	1.29443i
$863$	−302.330	−	98.2329i	−0.350324	−	0.113827i	0.128569	−	0.991701i	$-0.458962\pi$
$863$	−302.330	−	98.2329i	−0.350324	−	0.113827i	−0.478893	+	0.877873i	$0.658962\pi$
$864$	432.817	+	140.631i	0.500946	+	0.162767i
$865$		0			0
$866$	292.194	−	402.171i	0.337406	−	0.464400i
$867$	−151.506	+	49.2272i	−0.174747	+	0.0567788i
$868$	−1494.26			−1.72150
$869$	−690.947	+	1194.64i	−0.795106	+	1.37473i
$870$		0			0
$871$	675.275	−	219.410i	0.775287	−	0.251906i
$872$	−171.020	+	235.389i	−0.196124	+	0.269942i
$873$	152.114	+	209.367i	0.174243	+	0.239824i
$874$	109.809	−	337.957i	0.125639	−	0.386678i
$875$		0			0
$876$	−68.9135	−	94.8513i	−0.0786683	−	0.108278i
$877$	998.734	+	725.623i	1.13881	+	0.827392i	0.986953	−	0.161011i	$-0.0514753\pi$
$877$	998.734	+	725.623i	1.13881	+	0.827392i	0.151855	+	0.988403i	$0.451475\pi$
$878$	−1203.62	+	391.080i	−1.37087	+	0.445421i
$879$			196.543i			0.223598i
$880$		0			0
$881$	902.924			1.02488			0.512442	−	0.858722i	$-0.328741\pi$
$881$	902.924			1.02488			0.512442	+	0.858722i	$0.328741\pi$
$882$	839.417	+	2583.46i	0.951720	+	2.92909i
$883$	13.5788	−	18.6896i	0.0153780	−	0.0211660i	−0.801259	−	0.598318i	$-0.795836\pi$
$883$	13.5788	−	18.6896i	0.0153780	−	0.0211660i	0.816637	+	0.577152i	$0.195836\pi$
$884$	140.722	−	102.240i	0.159188	−	0.115657i
$885$		0			0
$886$	−182.272	−	59.2238i	−0.205725	−	0.0668441i
$887$	−1241.51	+	902.007i	−1.39967	+	1.01692i	−0.404944	+	0.914341i	$0.632709\pi$
$887$	−1241.51	+	902.007i	−1.39967	+	1.01692i	−0.994725	+	0.102578i	$0.967291\pi$
$888$	−29.5884	−	21.4972i	−0.0333202	−	0.0242086i
$889$	−482.917	−	1486.26i	−0.543213	−	1.67184i
$890$		0			0
$891$	−154.253	+	722.979i	−0.173124	+	0.811425i
$892$			689.166i			0.772607i
$893$	651.603	+	2005.43i	0.729679	+	2.24572i
$894$	−249.229	−	181.076i	−0.278780	−	0.202546i
$895$		0			0
$896$	−439.975	+	1354.10i	−0.491044	+	1.51128i
$897$	−9.64499	+	29.6842i	−0.0107525	+	0.0330928i
$898$	−1398.39	+	1015.99i	−1.55723	+	1.13139i
$899$	827.576	−	1139.06i	0.920552	−	1.26703i
$900$		0			0
$901$			423.289i			0.469799i
$902$	−172.486	+	76.6374i	−0.191226	+	0.0849638i
$903$		−	133.047i		−	0.147338i
$904$	60.4578	−	19.6439i	0.0668780	−	0.0217300i
$905$		0			0
$906$	245.804	−	178.587i	0.271307	−	0.197116i
$907$	−356.091	−	115.701i	−0.392603	−	0.127565i	0.106061	−	0.994360i	$-0.466176\pi$
$907$	−356.091	−	115.701i	−0.392603	−	0.127565i	−0.498665	+	0.866795i	$0.666176\pi$
$908$	296.636	−	912.953i	0.326692	−	1.00546i
$909$	258.001	+	355.108i	0.283830	+	0.390658i
$910$		0			0
$911$	−197.187	−	606.878i	−0.216451	−	0.666167i	−0.999047	−	0.0436379i	$-0.986105\pi$
$911$	−197.187	−	606.878i	−0.216451	−	0.666167i	0.782597	−	0.622529i	$-0.213895\pi$
$912$	367.038			0.402454
$913$	−567.292	−	1276.79i	−0.621349	−	1.39846i
$914$	−1452.05			−1.58867
$915$		0			0
$916$	−163.606	−	118.867i	−0.178609	−	0.129767i
$917$	−1359.30	−	1870.92i	−1.48234	−	2.04026i
$918$	−254.752	−	82.7740i	−0.277508	−	0.0901678i
$919$	844.869	+	274.515i	0.919335	+	0.298710i	0.730194	−	0.683240i	$-0.239430\pi$
$919$	844.869	+	274.515i	0.919335	+	0.298710i	0.189141	+	0.981950i	$0.439430\pi$
$920$		0			0
$921$	145.039	−	199.629i	0.157480	−	0.216753i
$922$	−1814.35	+	589.519i	−1.96784	+	0.639391i
$923$	−277.483			−0.300631
$924$	−266.106	−	56.7757i	−0.287993	−	0.0614455i
$925$		0			0
$926$	683.007	−	221.922i	0.737589	−	0.239657i
$927$	344.699	−	474.438i	0.371844	−	0.511799i
$928$	684.641	+	942.328i	0.737760	+	1.01544i
$929$	461.175	−	1419.35i	0.496421	−	1.52783i	−0.318309	−	0.947987i	$-0.603115\pi$
$929$	461.175	−	1419.35i	0.496421	−	1.52783i	0.814730	−	0.579841i	$-0.196885\pi$
$930$		0			0
$931$	1897.80	+	2612.10i	2.03845	+	2.80569i
$932$	−458.124	−	332.847i	−0.491550	−	0.357132i
$933$	105.589	−	34.3079i	0.113171	−	0.0367716i
$934$			1963.09i			2.10181i
$935$		0			0
$936$	246.815			0.263691
$937$	25.8710	+	79.6229i	0.0276105	+	0.0849764i	0.963912	−	0.266220i	$-0.0857749\pi$
$937$	25.8710	+	79.6229i	0.0276105	+	0.0849764i	−0.936302	+	0.351197i	$0.885775\pi$
$938$	−1745.75	+	2402.83i	−1.86115	+	2.56165i
$939$	5.50060	−	3.99642i	0.00585793	−	0.00425603i
$940$		0			0
$941$	1139.52	+	370.253i	1.21097	+	0.393468i	0.843785	−	0.536681i	$-0.180322\pi$
$941$	1139.52	+	370.253i	1.21097	+	0.393468i	0.367184	+	0.930148i	$0.380322\pi$
$942$	279.359	−	202.966i	0.296559	−	0.215463i
$943$	−28.8652	−	20.9718i	−0.0306100	−	0.0222394i
$944$	−326.330	−	1004.34i	−0.345688	−	1.06392i
$945$		0			0
$946$	−342.136	−	197.882i	−0.361666	−	0.209177i
$947$			934.828i			0.987147i	0.869704	+	0.493574i	$0.164310\pi$
$947$			934.828i			0.987147i	−0.869704	+	0.493574i	$0.835690\pi$
$948$	72.7638	+	223.944i	0.0767551	+	0.236228i
$949$	−409.079	−	297.213i	−0.431063	−	0.313186i
$950$		0			0
$951$	50.3415	−	154.935i	0.0529353	−	0.162918i
$952$	121.037	−	372.515i	0.127140	−	0.391297i
$953$	765.792	−	556.381i	0.803560	−	0.583820i	−0.108397	−	0.994108i	$-0.534572\pi$
$953$	765.792	−	556.381i	0.803560	−	0.583820i	0.911956	+	0.410287i	$0.134572\pi$
$954$	655.813	−	902.649i	0.687435	−	0.946173i
$955$		0			0
$956$			365.949i			0.382792i
$957$	190.659	−	171.406i	0.199226	−	0.179107i
$958$			1611.20i			1.68183i
$959$	−2000.19	+	649.902i	−2.08571	+	0.677687i
$960$		0			0
$961$	−760.623	+	552.625i	−0.791491	+	0.575052i
$962$	278.670	+	90.5455i	0.289678	+	0.0941221i
$963$	155.579	−	478.823i	0.161557	−	0.497220i
$964$	405.501	+	558.124i	0.420644	+	0.578967i
$965$		0			0
$966$	−40.3452	−	124.170i	−0.0417652	−	0.128540i
$967$	196.064			0.202755			0.101378	−	0.994848i	$-0.467675\pi$
$967$	196.064			0.202755			0.101378	+	0.994848i	$0.467675\pi$
$968$	291.655	−	322.919i	0.301297	−	0.333594i
$969$	−154.446			−0.159387
$970$		0			0
$971$	337.051	+	244.882i	0.347117	+	0.252196i	0.747659	−	0.664083i	$-0.231178\pi$
$971$	337.051	+	244.882i	0.347117	+	0.252196i	−0.400541	+	0.916279i	$0.631178\pi$
$972$	247.681	+	340.904i	0.254816	+	0.350724i
$973$	−2312.74	−	751.456i	−2.37692	−	0.772308i
$974$	409.868	+	133.174i	0.420809	+	0.136729i
$975$		0			0
$976$	46.2957	−	63.7206i	0.0474341	−	0.0652875i
$977$	1028.91	−	334.314i	1.05313	−	0.342184i	0.269237	−	0.963074i	$-0.413229\pi$
$977$	1028.91	−	334.314i	1.05313	−	0.342184i	0.783898	+	0.620890i	$0.213229\pi$
$978$	452.341			0.462517
$979$	−357.547	+	321.441i	−0.365217	+	0.328336i
$980$		0			0
$981$	−652.446	+	211.993i	−0.665083	+	0.216099i
$982$	498.973	−	686.777i	0.508119	−	0.699366i
$983$	320.324	+	440.888i	0.325863	+	0.448512i	0.940246	−	0.340496i	$-0.110595\pi$
$983$	320.324	+	440.888i	0.325863	+	0.448512i	−0.614383	+	0.789008i	$0.710595\pi$
$984$	5.35717	−	16.4877i	0.00544428	−	0.0167558i
$985$		0			0
$986$	−402.973	−	554.645i	−0.408695	−	0.562520i
$987$	626.777	+	455.380i	0.635032	+	0.461378i
$988$	−518.288	+	168.402i	−0.524583	+	0.170447i
$989$		−	74.7140i		−	0.0755450i
$990$		0			0
$991$	−1732.03			−1.74776			−0.873881	−	0.486140i	$-0.838405\pi$
$991$	−1732.03			−1.74776			−0.873881	+	0.486140i	$0.838405\pi$
$992$	−486.028	−	1495.84i	−0.489947	−	1.50790i
$993$	−74.7368	+	102.866i	−0.0752637	+	0.103592i
$994$	939.039	−	682.252i	0.944708	−	0.686370i
$995$		0			0
$996$	−226.716	−	73.6645i	−0.227626	−	0.0739603i
$997$	−449.898	+	326.870i	−0.451252	+	0.327854i	−0.790090	−	0.612991i	$-0.789966\pi$
$997$	−449.898	+	326.870i	−0.451252	+	0.327854i	0.338838	+	0.940845i	$0.389966\pi$
$998$	−1619.43	−	1176.58i	−1.62268	−	1.17894i
$999$	−54.9323	−	169.064i	−0.0549872	−	0.169233i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.q.g.149.12		56
5.2	odd	4		275.3.x.i.226.2	yes	28
5.3	odd	4		275.3.x.h.226.6	yes	28
5.4	even	2	inner	275.3.q.g.149.3		56
11.2	odd	10	inner	275.3.q.g.24.3		56
55.2	even	20		275.3.x.i.101.2	yes	28
55.13	even	20		275.3.x.h.101.6	✓	28
55.24	odd	10	inner	275.3.q.g.24.12		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.3.q.g.24.3		56	11.2	odd	10	inner
275.3.q.g.24.12		56	55.24	odd	10	inner
275.3.q.g.149.3		56	5.4	even	2	inner
275.3.q.g.149.12		56	1.1	even	1	trivial
275.3.x.h.101.6	✓	28	55.13	even	20
275.3.x.h.226.6	yes	28	5.3	odd	4
275.3.x.i.101.2	yes	28	55.2	even	20
275.3.x.i.226.2	yes	28	5.2	odd	4

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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.q (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.793893 + 2.44335i) q^{2} +(-0.424261 + 0.583945i) q^{3} +(-2.10363 + 1.52838i) q^{4} +(-1.76360 - 0.573029i) q^{6} +(10.6625 - 7.74676i) q^{7} +(2.90933 + 2.11375i) q^{8} +(2.62016 + 8.06402i) q^{9} +(8.18023 - 7.35417i) q^{11} -1.87684i q^{12} +(-2.50134 - 7.69834i) q^{13} +(27.3929 + 19.9021i) q^{14} +(-6.06901 + 18.6785i) q^{16} +(2.55378 - 7.85972i) q^{17} +(-17.6231 + 12.8039i) q^{18} +(-15.2188 + 20.9469i) q^{19} +9.51297i q^{21} +(24.4631 + 14.1488i) q^{22} +5.34212i q^{23} +(-2.46863 + 0.802107i) q^{24} +(16.8240 - 12.2233i) q^{26} +(-11.9988 - 3.89865i) q^{27} +(-10.5900 + 32.5927i) q^{28} +(-18.9800 - 26.1237i) q^{29} +(13.4739 + 41.4685i) q^{31} -36.0717 q^{32} +(0.823881 + 7.89690i) q^{33} +21.2315 q^{34} +(-17.8367 - 12.9591i) q^{36} +(8.28194 + 11.3991i) q^{37} +(-63.2626 - 20.5553i) q^{38} +(5.55664 + 1.80546i) q^{39} +(-3.92574 + 5.40332i) q^{41} +(-23.2435 + 7.55228i) q^{42} -13.9858 q^{43} +(-5.96824 + 27.9730i) q^{44} +(-13.0527 + 4.24108i) q^{46} +(47.8694 - 65.8866i) q^{47} +(-8.33237 - 11.4685i) q^{48} +(38.5348 - 118.598i) q^{49} +(3.50618 + 4.82584i) q^{51} +(17.0279 + 12.3715i) q^{52} +(-48.7128 + 15.8277i) q^{53} -32.4124i q^{54} +47.3954 q^{56} +(-5.77508 - 17.7739i) q^{57} +(48.7613 - 67.1142i) q^{58} +(-43.5007 + 31.6051i) q^{59} +(-3.81411 - 1.23928i) q^{61} +(-90.6252 + 65.8431i) q^{62} +(90.4074 + 65.6849i) q^{63} +(-4.36107 - 13.4220i) q^{64} +(-18.6408 + 8.28232i) q^{66} +87.7170i q^{67} +(6.64042 + 20.4371i) q^{68} +(-3.11951 - 2.26646i) q^{69} +(10.5932 - 32.6025i) q^{71} +(-9.42243 + 28.9992i) q^{72} +(50.5378 - 36.7178i) q^{73} +(-21.2771 + 29.2854i) q^{74} -67.3246i q^{76} +(30.2507 - 141.784i) q^{77} +15.0102i q^{78} +(-119.320 + 38.7694i) q^{79} +(-54.3698 + 39.5019i) q^{81} +(-16.3188 - 5.30231i) q^{82} +(39.2492 - 120.797i) q^{83} +(-14.5394 - 20.0118i) q^{84} +(-11.1032 - 34.1723i) q^{86} +23.3073 q^{87} +(39.3439 - 4.10473i) q^{88} -43.7087 q^{89} +(-86.3078 - 62.7063i) q^{91} +(-8.16479 - 11.2379i) q^{92} +(-29.9318 - 9.72543i) q^{93} +(198.987 + 64.6549i) q^{94} +(15.3038 - 21.0639i) q^{96} +(29.0276 - 9.43164i) q^{97} +320.369 q^{98} +(80.7377 + 46.6964i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 18 q^{4} + 60 q^{6} + 62 q^{9} - 10 q^{11} - 74 q^{14} - 70 q^{16} - 160 q^{19} - 26 q^{26} + 190 q^{29} + 190 q^{31} + 296 q^{34} - 694 q^{36} + 130 q^{39} - 580 q^{41} + 506 q^{44} - 220 q^{46}+ \cdots + 1218 q^{99}+O(q^{100}) \) 56 * q - 18 * q^4 + 60 * q^6 + 62 * q^9 - 10 * q^11 - 74 * q^14 - 70 * q^16 - 160 * q^19 - 26 * q^26 + 190 * q^29 + 190 * q^31 + 296 * q^34 - 694 * q^36 + 130 * q^39 - 580 * q^41 + 506 * q^44 - 220 * q^46 - 448 * q^49 + 800 * q^51 + 1768 * q^56 - 134 * q^59 + 270 * q^61 + 238 * q^64 + 500 * q^66 - 622 * q^69 - 378 * q^71 - 1880 * q^74 - 1130 * q^79 - 1166 * q^81 + 2100 * q^84 + 414 * q^86 - 292 * q^89 - 1566 * q^91 + 1690 * q^94 - 2420 * q^96 + 1218 * q^99

Introduction

L-functions

Modular forms

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Representations

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Database

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