LMFDB - Embedded newform 275.3.q.g.24.12

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			24.12
Character	$\chi$	$=$	275.24
Dual form			275.3.q.g.149.12

$q$-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 $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

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

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	−0.530489	−	0.847692i	$-0.677992\pi$
$2$	0.793893	−	2.44335i	0.396947	−	1.22168i	0.927435	−	0.373984i	$-0.122008\pi$
$3$	−0.424261	−	0.583945i	−0.141420	−	0.194648i	0.732431	−	0.680841i	$-0.238385\pi$
$3$	−0.424261	−	0.583945i	−0.141420	−	0.194648i	−0.873852	+	0.486192i	$0.838385\pi$
$4$	−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	0.959866	+	0.280461i	$0.0904872\pi$
$7$	10.6625	+	7.74676i	1.52321	+	1.10668i	0.563349	+	0.826219i	$0.309513\pi$
$8$	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	0.807586	+	0.589750i	$0.200774\pi$
$13$	−2.50134	+	7.69834i	−0.192411	+	0.592180i	−0.999997	+	0.00243053i	$0.999226\pi$
$14$	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	0.997646	−	0.0685815i	$-0.0218473\pi$
$17$	2.55378	+	7.85972i	0.150222	+	0.462336i	−0.847423	+	0.530918i	$0.821847\pi$
$18$	−17.6231	−	12.8039i	−0.979061	−	0.711330i
$19$	−15.2188	−	20.9469i	−0.800989	−	1.10247i	−0.992652	−	0.121006i	$-0.961388\pi$
$19$	−15.2188	−	20.9469i	−0.800989	−	1.10247i	0.191663	−	0.981461i	$-0.438612\pi$
$20$		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	$-0.962950\pi$
$23$		−	5.34212i		−	0.232266i	0.993234	−	0.116133i	$-0.0370499\pi$
$24$	−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	−0.999283	−	0.0378581i	$-0.987947\pi$
$29$	−18.9800	+	26.1237i	−0.654482	+	0.900818i	0.344801	+	0.938676i	$0.387947\pi$
$30$		0			0
$31$	13.4739	−	41.4685i	0.434643	−	1.33769i	−0.458809	−	0.888535i	$-0.651724\pi$
$31$	13.4739	−	41.4685i	0.434643	−	1.33769i	0.893452	−	0.449158i	$-0.148276\pi$
$32$	−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	−0.682298	−	0.731074i	$-0.739019\pi$
$37$	8.28194	−	11.3991i	0.223836	−	0.308084i	0.906134	+	0.422990i	$0.139019\pi$
$38$	−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	0.758454	−	0.651726i	$-0.225955\pi$
$41$	−3.92574	−	5.40332i	−0.0957498	−	0.131788i	−0.854204	+	0.519938i	$0.825955\pi$
$42$	−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	0.913252	+	0.407396i	$0.133563\pi$
$47$	47.8694	+	65.8866i	1.01850	+	1.40184i	0.105247	+	0.994446i	$0.466437\pi$
$48$	−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	−0.189008	−	0.981976i	$-0.560527\pi$
$53$	−48.7128	−	15.8277i	−0.919109	−	0.298636i	−0.730101	+	0.683339i	$0.760527\pi$
$54$			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	0.154564	−	0.987983i	$-0.450603\pi$
$59$	−43.5007	−	31.6051i	−0.737300	−	0.535680i	−0.891865	+	0.452303i	$0.850603\pi$
$60$		0			0
$61$	−3.81411	+	1.23928i	−0.0625264	+	0.0203161i	−0.340113	−	0.940385i	$-0.610465\pi$
$61$	−3.81411	+	1.23928i	−0.0625264	+	0.0203161i	0.277587	+	0.960701i	$0.410465\pi$
$62$	−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	$-0.772835\pi$
$67$		−	87.7170i		−	1.30921i	0.755972	−	0.654604i	$-0.227165\pi$
$68$	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	0.997527	−	0.0702818i	$-0.0223899\pi$
$71$	10.5932	+	32.6025i	0.149200	+	0.459191i	−0.848327	+	0.529473i	$0.822390\pi$
$72$	−9.42243	−	28.9992i	−0.130867	−	0.402767i
$73$	50.5378	+	36.7178i	0.692298	+	0.502984i	0.877415	−	0.479732i	$-0.159266\pi$
$73$	50.5378	+	36.7178i	0.692298	+	0.502984i	−0.185116	+	0.982717i	$0.559266\pi$
$74$	−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	−0.567353	−	0.823475i	$-0.692032\pi$
$79$	−119.320	−	38.7694i	−1.51038	−	0.490751i	−0.943024	+	0.332724i	$0.892032\pi$
$80$		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	0.848793	+	0.528726i	$0.177330\pi$
$83$	39.2492	+	120.797i	0.472882	+	1.45538i	−0.375910	+	0.926656i	$0.622670\pi$
$84$	−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	0.454795	−	0.890596i	$-0.349712\pi$
$97$	29.0276	+	9.43164i	0.299253	+	0.0972334i	−0.155542	+	0.987829i	$0.549712\pi$
$98$	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	0.542429	−	0.840102i	$-0.317505\pi$
$101$	49.2339	+	15.9971i	0.487464	+	0.158387i	−0.0549650	+	0.998488i	$0.517505\pi$
$102$	−9.00769	−	12.3980i	−0.0883107	−	0.121549i
$103$	−40.6532	+	55.9544i	−0.394691	+	0.543246i	−0.959402	−	0.282043i	$-0.908988\pi$
$103$	−40.6532	+	55.9544i	−0.394691	+	0.543246i	0.564710	+	0.825289i	$0.308988\pi$
$104$	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	−0.789181	−	0.614161i	$-0.789495\pi$
$107$	−48.0376	+	34.9014i	−0.448950	+	0.326181i	0.340231	+	0.940342i	$0.389495\pi$
$108$	31.1997	+	10.1374i	0.288886	+	0.0938647i
$109$		−	80.9083i		−	0.742278i	−0.928577	−	0.371139i	$-0.878967\pi$
$109$		−	80.9083i		−	0.742278i	0.928577	−	0.371139i	$-0.121033\pi$
$110$		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	0.852513	−	0.522705i	$-0.175077\pi$
$113$	10.3903	+	14.3011i	0.0919498	+	0.126558i	−0.760564	+	0.649263i	$0.775077\pi$
$114$	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	0.985323	+	0.170699i	$0.0546024\pi$
$127$	36.6413	+	112.770i	0.288514	+	0.887955i	−0.696809	+	0.717257i	$0.745398\pi$
$128$	−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	$0.233587\pi$
$131$			175.467i			1.33944i	−0.742612	+	0.669722i	$0.766413\pi$
$132$	−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	−0.805088	−	0.593155i	$-0.797882\pi$
$137$	−151.765	+	49.3113i	−1.10777	+	0.359936i	−0.302682	+	0.953092i	$0.597882\pi$
$138$	3.06119	+	9.42138i	0.0221825	+	0.0682709i
$139$	−108.452	+	149.272i	−0.780232	+	1.07390i	0.215025	+	0.976609i	$0.431017\pi$
$139$	−108.452	+	149.272i	−0.780232	+	1.07390i	−0.995256	+	0.0972881i	$0.968983\pi$
$140$		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	0.273655	−	0.961828i	$-0.411767\pi$
$149$	157.999	−	51.3369i	1.06039	−	0.344543i	0.786740	+	0.617285i	$0.211767\pi$
$150$		0			0
$151$	−96.3065	−	132.555i	−0.637792	−	0.877845i	0.360704	−	0.932680i	$-0.382537\pi$
$151$	−96.3065	−	132.555i	−0.637792	−	0.877845i	−0.998495	+	0.0548355i	$0.982537\pi$
$152$	−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	−0.999979	−	0.00650560i	$-0.997929\pi$
$157$	−109.453	−	150.650i	−0.697156	−	0.959552i	0.302823	−	0.953047i	$-0.402071\pi$
$158$	−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	−0.506639	−	0.862159i	$-0.669112\pi$
$163$	−231.995	−	75.3797i	−1.42328	−	0.462452i	−0.916643	+	0.399706i	$0.869112\pi$
$164$			17.3666i			0.105894i
$165$		0			0
$166$	326.309			1.96571
$167$	7.53588	−	23.1931i	0.0451250	−	0.138881i	−0.925956	−	0.377632i	$-0.876738\pi$
$167$	7.53588	−	23.1931i	0.0451250	−	0.138881i	0.971081	+	0.238752i	$0.0767383\pi$
$168$	−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	−0.444020	−	0.896017i	$-0.646448\pi$
$173$	46.8713	−	34.0540i	0.270932	−	0.196844i	0.714953	+	0.699173i	$0.246448\pi$
$174$	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	−0.587531	−	0.809202i	$-0.699900\pi$
$179$	0.0910781	−	0.0661721i	0.000508816	−	0.000369677i	0.588040	+	0.808832i	$0.299900\pi$
$180$		0			0
$181$	−8.38500	−	25.8064i	−0.0463260	−	0.142577i	0.925218	−	0.379436i	$-0.123882\pi$
$181$	−8.38500	−	25.8064i	−0.0463260	−	0.142577i	−0.971544	+	0.236859i	$0.923882\pi$
$182$	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	−0.995707	−	0.0925661i	$-0.970493\pi$
$191$	−265.764	−	193.089i	−1.39143	−	1.01093i	−0.395726	−	0.918369i	$-0.629507\pi$
$192$	9.68794	−	3.14780i	0.0504580	−	0.0163948i
$193$	−69.2444	−	213.112i	−0.358779	−	1.10421i	−0.953785	−	0.300488i	$-0.902850\pi$
$193$	−69.2444	−	213.112i	−0.358779	−	1.10421i	0.595006	−	0.803721i	$-0.297150\pi$
$194$	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	0.807894	−	0.589328i	$-0.200607\pi$
$211$	235.285	+	76.4488i	1.11510	+	0.362317i	0.307202	+	0.951644i	$0.400607\pi$
$212$	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	0.999968	+	0.00802651i	$0.00255495\pi$
$223$	155.787	+	214.422i	0.698594	+	0.961533i	−0.301373	+	0.953506i	$0.597445\pi$
$224$	−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	−0.999975	−	0.00707657i	$-0.997747\pi$
$227$	−298.667	−	216.994i	−1.31571	−	0.955922i	−0.315739	−	0.948846i	$-0.602253\pi$
$228$	39.3139	−	28.5632i	0.172429	−	0.125277i
$229$	24.0332	−	73.9665i	0.104948	−	0.322998i	−0.884770	−	0.466028i	$-0.845685\pi$
$229$	24.0332	−	73.9665i	0.104948	−	0.322998i	0.989718	+	0.143030i	$0.0456846\pi$
$230$		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	−0.696397	−	0.717657i	$-0.745215\pi$
$233$	67.2970	−	207.119i	0.288828	−	0.888922i	0.985225	−	0.171265i	$-0.0547854\pi$
$234$	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	0.946217	−	0.323533i	$-0.104871\pi$
$239$	82.7232	+	113.859i	0.346122	+	0.476396i	−0.600095	+	0.799929i	$0.704871\pi$
$240$		0			0
$241$			265.314i			1.10089i	0.834872	+	0.550444i	$0.185542\pi$
$241$			265.314i			1.10089i	−0.834872	+	0.550444i	$0.814458\pi$
$242$	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	0.646712	+	0.762734i	$0.276144\pi$
$251$	−81.5281	+	250.918i	−0.324813	+	0.999672i	−0.971525	+	0.236937i	$0.923856\pi$
$252$	−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	0.274628	+	0.961550i	$0.411445\pi$
$257$	−186.254	+	256.357i	−0.724725	+	0.997499i	−0.999354	+	0.0359483i	$0.988555\pi$
$258$	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	0.902634	−	0.430409i	$-0.141631\pi$
$269$	−21.6814	−	66.7285i	−0.0806000	−	0.248061i	−0.983234	+	0.182347i	$0.941631\pi$
$270$		0			0
$271$	253.032	−	348.269i	0.933698	−	1.28513i	−0.0247014	−	0.999695i	$-0.507863\pi$
$271$	253.032	−	348.269i	0.933698	−	1.28513i	0.958399	−	0.285430i	$-0.0921365\pi$
$272$	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	−0.985943	−	0.167081i	$-0.946566\pi$
$277$	−24.9552	+	76.8041i	−0.0900909	+	0.277271i	0.895852	+	0.444352i	$0.146566\pi$
$278$	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	0.533832	−	0.845590i	$-0.320751\pi$
$281$	411.029	−	133.551i	1.46274	−	0.475272i	0.928905	+	0.370318i	$0.120751\pi$
$282$	−122.178	−	88.7672i	−0.433254	−	0.314777i
$283$	−104.648	+	76.0310i	−0.369780	+	0.268661i	−0.757120	−	0.653276i	$-0.773394\pi$
$283$	−104.648	+	76.0310i	−0.369780	+	0.268661i	0.387340	+	0.921937i	$0.373394\pi$
$284$	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	0.896401	−	0.443245i	$-0.146173\pi$
$293$	220.293	+	160.052i	0.751853	+	0.546253i	−0.144548	+	0.989498i	$0.546173\pi$
$294$	−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	−0.769591	−	0.638537i	$-0.779540\pi$
$311$	−124.438	+	90.4098i	−0.400123	+	0.290707i	0.369468	+	0.929244i	$0.379540\pi$
$312$	12.3498	−	16.9980i	0.0395827	−	0.0544809i
$313$	−8.95868	+	2.91085i	−0.0286220	+	0.00929984i	−0.323293	−	0.946299i	$-0.604790\pi$
$313$	−8.95868	+	2.91085i	−0.0286220	+	0.00929984i	0.294671	+	0.955599i	$0.404790\pi$
$314$	−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	−0.0497954	−	0.998759i	$-0.515857\pi$
$317$	−214.652	−	69.7448i	−0.677137	−	0.220015i	−0.627341	+	0.778744i	$0.715857\pi$
$318$	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	0.792851	−	0.609415i	$-0.208596\pi$
$337$	154.436	+	112.204i	0.458267	+	0.332951i	−0.334584	+	0.942366i	$0.608596\pi$
$338$	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	0.822607	−	0.568611i	$-0.192519\pi$
$347$	−61.4596	−	189.153i	−0.177117	−	0.545110i	−0.999724	+	0.0235005i	$0.992519\pi$
$348$	−49.0300	−	35.6224i	−0.140891	−	0.102363i
$349$	120.489	+	165.839i	0.345241	+	0.475183i	0.945963	−	0.324275i	$-0.105120\pi$
$349$	120.489	+	165.839i	0.345241	+	0.475183i	−0.600722	+	0.799458i	$0.705120\pi$
$350$		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	$0.0883807\pi$
$353$			193.516i			0.548205i	−0.961701	+	0.274102i	$0.911619\pi$
$354$	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	−0.871736	−	0.489976i	$-0.837005\pi$
$359$	−48.9531	+	67.3782i	−0.136360	+	0.187683i	0.735376	+	0.677659i	$0.237005\pi$
$360$		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	0.201867	−	0.979413i	$-0.435299\pi$
$367$	393.044	−	540.978i	1.07096	−	1.47406i	0.869097	−	0.494642i	$-0.164701\pi$
$368$	−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	−0.892437	−	0.451172i	$-0.851006\pi$
$379$	−165.105	−	508.140i	−0.435633	−	1.34074i	0.456804	−	0.889567i	$-0.348994\pi$
$380$		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	0.274911	−	0.961470i	$-0.411352\pi$
$383$	−25.9749	−	8.43976i	−0.0678196	−	0.0220359i	−0.342730	+	0.939434i	$0.611352\pi$
$384$			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	0.993014	+	0.117995i	$0.0376467\pi$
$389$	549.304	+	399.093i	1.41209	+	1.02595i	0.419078	+	0.907950i	$0.362353\pi$
$390$		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	$0.110350\pi$
$397$			269.778i			0.679542i	−0.940508	+	0.339771i	$0.889650\pi$
$398$	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	0.932638	−	0.360813i	$-0.117501\pi$
$401$	−13.6189	−	41.9146i	−0.0339623	−	0.104525i	−0.966601	+	0.256287i	$0.917501\pi$
$402$	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	0.392560	−	0.919726i	$-0.371590\pi$
$409$	69.3442	+	22.5313i	0.169546	+	0.0550888i	−0.223014	+	0.974815i	$0.571590\pi$
$410$		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	−0.245232	−	0.969464i	$-0.578864\pi$
$421$	253.022	−	183.831i	0.601002	−	0.436653i	0.846234	+	0.532811i	$0.178864\pi$
$422$	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	−0.350533	−	0.936550i	$-0.614000\pi$
$431$	−510.568	−	165.893i	−1.18461	−	0.384904i	−0.834078	+	0.551647i	$0.814000\pi$
$432$	145.642	+	200.458i	0.337133	+	0.464024i
$433$	−113.734	+	156.542i	−0.262666	+	0.361529i	−0.919897	−	0.392161i	$-0.871728\pi$
$433$	−113.734	+	156.542i	−0.262666	+	0.361529i	0.657231	+	0.753689i	$0.271728\pi$
$434$	−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	$-0.810394\pi$
$439$		−	492.610i		−	1.12212i	0.827776	−	0.561059i	$-0.189606\pi$
$440$		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	0.756654	−	0.653816i	$-0.226833\pi$
$443$	−43.8483	−	60.3521i	−0.0989805	−	0.136235i	−0.855634	+	0.517581i	$0.826833\pi$
$444$	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	−0.398368	−	0.917225i	$-0.630423\pi$
$449$	207.909	−	639.879i	0.463050	−	1.42512i	0.861418	−	0.507896i	$-0.169577\pi$
$450$		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	−0.938506	−	0.345264i	$-0.887789\pi$
$457$	−174.656	−	537.536i	−0.382180	−	1.17623i	0.556326	−	0.830964i	$-0.312211\pi$
$458$	−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	$-0.701958\pi$
$461$		−	742.567i		−	1.61077i	0.592749	−	0.805387i	$-0.298042\pi$
$462$	−134.597	−	232.716i	−0.291335	−	0.503715i
$463$			279.537i			0.603752i	0.953347	+	0.301876i	$0.0976128\pi$
$463$			279.537i			0.603752i	−0.953347	+	0.301876i	$0.902387\pi$
$464$	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	0.600371	−	0.799722i	$-0.295020\pi$
$467$	726.720	−	236.126i	1.55615	−	0.505623i	0.955775	+	0.294099i	$0.0950195\pi$
$468$	−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	0.389003	−	0.921236i	$-0.372820\pi$
$479$	596.452	−	193.799i	1.24520	−	0.404591i	0.856199	+	0.516646i	$0.172820\pi$
$480$		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	0.898160	−	0.439668i	$-0.144904\pi$
$487$	98.5999	+	135.711i	0.202464	+	0.278668i	−0.695696	+	0.718336i	$0.744904\pi$
$488$	−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	−0.959623	−	0.281288i	$-0.909238\pi$
$491$	−194.221	+	267.323i	−0.395563	+	0.544446i	0.564060	+	0.825734i	$0.309238\pi$
$492$	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	−0.264317	−	0.964436i	$-0.585147\pi$
$499$	−630.351	−	457.977i	−1.26323	−	0.917789i	−0.998911	+	0.0466466i	$0.985147\pi$
$500$		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	−0.869393	−	0.494122i	$-0.835490\pi$
$503$	−336.060	+	244.162i	−0.668112	+	0.485412i	0.201281	+	0.979534i	$0.435490\pi$
$504$	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	−0.984207	−	0.177019i	$-0.943354\pi$
$509$	−570.074	+	414.183i	−1.11999	+	0.813719i	−0.135781	+	0.990739i	$0.543354\pi$
$510$		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	0.443563	−	0.896243i	$-0.353714\pi$
$521$	−141.580	−	102.864i	−0.271747	−	0.197436i	−0.715310	+	0.698808i	$0.753714\pi$
$522$	668.973	−	217.362i	1.28156	−	0.416403i
$523$	270.629	+	832.911i	0.517455	+	1.59256i	0.778769	+	0.627310i	$0.215844\pi$
$523$	270.629	+	832.911i	0.517455	+	1.59256i	−0.261314	+	0.965254i	$0.584156\pi$
$524$	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	0.190980	−	0.981594i	$-0.438834\pi$
$541$	−125.231	−	40.6901i	−0.231481	−	0.0752128i	−0.422461	+	0.906381i	$0.638834\pi$
$542$	−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	−0.586577	−	0.809893i	$-0.699525\pi$
$547$	1.32090	−	0.959689i	0.00241481	−	0.00175446i	0.588992	+	0.808139i	$0.299525\pi$
$548$	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	0.0865234	−	0.996250i	$-0.472424\pi$
$557$	−464.666	−	337.599i	−0.834229	−	0.606103i	−0.920753	+	0.390147i	$0.872424\pi$
$558$	−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	−0.987552	−	0.157295i	$-0.949723\pi$
$563$	−54.1325	+	166.603i	−0.0961502	+	0.295920i	0.891402	+	0.453214i	$0.149723\pi$
$564$	−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	0.932970	−	0.359953i	$-0.117207\pi$
$569$	172.026	+	236.774i	0.302331	+	0.416122i	−0.630640	+	0.776076i	$0.717207\pi$
$570$		0			0
$571$		−	836.204i		−	1.46446i	−0.681060	−	0.732228i	$-0.738481\pi$
$571$		−	836.204i		−	1.46446i	0.681060	−	0.732228i	$-0.261519\pi$
$572$	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	0.573626	−	0.819118i	$-0.305536\pi$
$577$	876.557	−	284.811i	1.51916	−	0.493606i	0.945538	+	0.325511i	$0.105536\pi$
$578$	−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	−0.920102	−	0.391679i	$-0.871894\pi$
$587$	−154.537	+	212.702i	−0.263266	+	0.362354i	0.656836	+	0.754033i	$0.271894\pi$
$588$	−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	0.928460	−	0.371432i	$-0.121133\pi$
$599$	−24.5601	−	75.5882i	−0.0410018	−	0.126191i	−0.969462	+	0.245241i	$0.921133\pi$
$600$		0			0
$601$	337.300	−	464.254i	0.561232	−	0.772469i	−0.430251	−	0.902709i	$-0.641575\pi$
$601$	337.300	−	464.254i	0.561232	−	0.772469i	0.991482	+	0.130240i	$0.0415749\pi$
$602$	−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	0.754440	+	0.656369i	$0.227909\pi$
$607$	−146.723	+	451.568i	−0.241719	+	0.743934i	−0.996159	+	0.0875652i	$0.972091\pi$
$608$	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	0.168081	−	0.985773i	$-0.446243\pi$
$613$	709.576	−	515.537i	1.15755	−	0.841007i	0.989466	+	0.144766i	$0.0462431\pi$
$614$	−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	$0.105611\pi$
$617$			401.953i			0.651464i	−0.945462	+	0.325732i	$0.894389\pi$
$618$	39.6326	−	121.977i	0.0641305	−	0.197373i
$619$	165.411	−	120.178i	0.267223	−	0.194149i	−0.446102	−	0.894982i	$-0.647188\pi$
$619$	165.411	−	120.178i	0.267223	−	0.194149i	0.713325	+	0.700833i	$0.247188\pi$
$620$		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	0.204801	−	0.978804i	$-0.434345\pi$
$631$	−418.233	−	303.864i	−0.662810	−	0.481560i	−0.867611	+	0.497244i	$0.834345\pi$
$632$	−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	−0.746820	−	0.665026i	$-0.768421\pi$
$641$	−221.224	+	160.729i	−0.345124	+	0.250747i	0.401697	+	0.915773i	$0.368421\pi$
$642$	64.7197	−	89.0791i	0.100810	−	0.138752i
$643$	150.697	−	48.9645i	0.234366	−	0.0761501i	−0.189479	−	0.981885i	$-0.560680\pi$
$643$	150.697	−	48.9645i	0.234366	−	0.0761501i	0.423845	+	0.905735i	$0.360680\pi$
$644$	−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	−0.560664	−	0.828044i	$-0.689454\pi$
$647$	−971.123	−	315.537i	−1.50096	−	0.487692i	−0.940298	+	0.340351i	$0.889454\pi$
$648$	−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	−0.760282	−	0.649593i	$-0.774939\pi$
$653$	60.3750	−	83.0990i	0.0924579	−	0.127257i	0.852740	+	0.522336i	$0.174939\pi$
$654$	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	$0.0918517\pi$
$659$			375.067i			0.569145i	−0.958655	+	0.284573i	$0.908148\pi$
$660$		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	−0.951594	−	0.307358i	$-0.900555\pi$
$673$	−0.725514	+	2.23290i	−0.00107803	+	0.00331783i	0.950516	+	0.310675i	$0.100555\pi$
$674$	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	0.954778	−	0.297321i	$-0.0960931\pi$
$677$	5.13532	+	15.8049i	0.00758541	+	0.0233455i	−0.947192	+	0.320666i	$0.896093\pi$
$678$	−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	$0.134576\pi$
$683$			560.470i			0.820600i	−0.911951	+	0.410300i	$0.865424\pi$
$684$	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	−0.812110	−	0.583504i	$-0.801681\pi$
$691$	129.822	−	399.551i	0.187876	−	0.578222i	0.999986	+	0.00528214i	$0.00168136\pi$
$692$	−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	0.853072	−	0.521794i	$-0.174737\pi$
$701$	65.3351	+	89.9261i	0.0932027	+	0.128283i	−0.759869	+	0.650076i	$0.774737\pi$
$702$	−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	0.924203	−	0.381902i	$-0.124731\pi$
$709$	−34.0103	−	104.673i	−0.0479694	−	0.147634i	−0.972172	+	0.234268i	$0.924731\pi$
$710$		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	0.235676	−	0.971832i	$-0.424270\pi$
$719$	−442.734	−	321.665i	−0.615763	−	0.447378i	−0.851439	+	0.524453i	$0.824270\pi$
$720$		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	$0.0709714\pi$
$727$			321.509i			0.442241i	−0.975246	+	0.221121i	$0.929029\pi$
$728$	−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	0.550074	−	0.835116i	$-0.314599\pi$
$733$	−54.3778	−	39.5078i	−0.0741853	−	0.0538988i	−0.624260	+	0.781217i	$0.714599\pi$
$734$	−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	0.404447	−	0.914561i	$-0.367464\pi$
$739$	143.429	+	46.6030i	0.194086	+	0.0630622i	−0.210361	+	0.977624i	$0.567464\pi$
$740$		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	0.982355	−	0.187026i	$-0.0598848\pi$
$743$	57.7178	+	177.637i	0.0776820	+	0.239081i	−0.904673	+	0.426107i	$0.859885\pi$
$744$	−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	−0.923983	−	0.382434i	$-0.875086\pi$
$751$	−635.190	+	461.493i	−0.845793	+	0.614504i	0.0781901	+	0.996938i	$0.475086\pi$
$752$	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	0.794182	−	0.607680i	$-0.207900\pi$
$757$	817.184	+	265.519i	1.07950	+	0.350752i	0.285322	+	0.958432i	$0.407900\pi$
$758$	−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	0.933779	−	0.357849i	$-0.116490\pi$
$761$	1125.43	+	365.675i	1.47888	+	0.480519i	0.545105	+	0.838368i	$0.316490\pi$
$762$	−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	$-0.868600\pi$
$769$		−	617.014i		−	0.802359i	0.915999	−	0.401179i	$-0.131400\pi$
$770$		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	0.959742	+	0.280882i	$0.0906269\pi$
$773$	719.122	+	989.787i	0.930300	+	1.28045i	−0.0294422	+	0.999566i	$0.509373\pi$
$774$	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	0.924774	−	0.380516i	$-0.124254\pi$
$787$	−37.0249	−	113.951i	−0.0470456	−	0.144792i	−0.971820	+	0.235725i	$0.924254\pi$
$788$	−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	−0.642592	−	0.766209i	$-0.722141\pi$
$797$	−567.539	+	184.404i	−0.712094	+	0.231373i	−0.0695017	+	0.997582i	$0.522141\pi$
$798$	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	−0.138487	−	0.990364i	$-0.544224\pi$
$809$	268.262	−	87.1635i	0.331597	−	0.107742i	0.470083	+	0.882622i	$0.344224\pi$
$810$		0			0
$811$	72.7008	+	100.064i	0.0896434	+	0.123384i	0.851483	−	0.524382i	$-0.175704\pi$
$811$	72.7008	+	100.064i	0.0896434	+	0.123384i	−0.761840	+	0.647766i	$0.775704\pi$
$812$	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	−0.485753	−	0.874096i	$-0.661454\pi$
$821$	406.944	−	560.110i	0.495668	−	0.682229i	0.981421	+	0.191868i	$0.0614544\pi$
$822$	239.395	−	173.931i	0.291235	−	0.211595i
$823$	−1017.93	−	330.747i	−1.23686	−	0.401879i	−0.383663	−	0.923473i	$-0.625338\pi$
$823$	−1017.93	−	330.747i	−1.23686	−	0.401879i	−0.853194	+	0.521594i	$0.825338\pi$
$824$			248.720i			0.301845i
$825$		0			0
$826$	−1820.62			−2.20414
$827$	−443.516	+	1365.00i	−0.536295	+	1.65054i	0.204541	+	0.978858i	$0.434430\pi$
$827$	−443.516	+	1365.00i	−0.536295	+	1.65054i	−0.740835	+	0.671687i	$0.765570\pi$
$828$	69.2293	+	95.2860i	0.0836103	+	0.115080i
$829$	−75.5393	−	54.8825i	−0.0911209	−	0.0662032i	0.541292	−	0.840835i	$-0.317935\pi$
$829$	−75.5393	−	54.8825i	−0.0911209	−	0.0662032i	−0.632413	+	0.774631i	$0.717935\pi$
$830$		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	0.193727	−	0.981056i	$-0.437942\pi$
$839$	995.583	−	723.334i	1.18663	−	0.862138i	0.992904	+	0.118918i	$0.0379425\pi$
$840$		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	−0.990399	−	0.138239i	$-0.955856\pi$
$853$	−230.655	−	709.882i	−0.270404	−	0.832218i	0.719995	−	0.693979i	$-0.244144\pi$
$854$	−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	−0.478893	−	0.877873i	$-0.658962\pi$
$863$	−302.330	+	98.2329i	−0.350324	+	0.113827i	0.128569	+	0.991701i	$0.458962\pi$
$864$	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	0.151855	−	0.988403i	$-0.451475\pi$
$877$	998.734	−	725.623i	1.13881	−	0.827392i	0.986953	+	0.161011i	$0.0514753\pi$
$878$	−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	0.816637	−	0.577152i	$-0.195836\pi$
$883$	13.5788	+	18.6896i	0.0153780	+	0.0211660i	−0.801259	+	0.598318i	$0.795836\pi$
$884$	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	−0.994725	−	0.102578i	$-0.967291\pi$
$887$	−1241.51	−	902.007i	−1.39967	−	1.01692i	−0.404944	−	0.914341i	$-0.632709\pi$
$888$	−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	−0.498665	−	0.866795i	$-0.666176\pi$
$907$	−356.091	+	115.701i	−0.392603	+	0.127565i	0.106061	+	0.994360i	$0.466176\pi$
$908$	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	0.782597	+	0.622529i	$0.213895\pi$
$911$	−197.187	+	606.878i	−0.216451	+	0.666167i	−0.999047	+	0.0436379i	$0.986105\pi$
$912$	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	0.189141	−	0.981950i	$-0.439430\pi$
$919$	844.869	−	274.515i	0.919335	−	0.298710i	0.730194	+	0.683240i	$0.239430\pi$
$920$		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	0.814730	+	0.579841i	$0.196885\pi$
$929$	461.175	+	1419.35i	0.496421	+	1.52783i	−0.318309	+	0.947987i	$0.603115\pi$
$930$		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	−0.936302	−	0.351197i	$-0.885775\pi$
$937$	25.8710	−	79.6229i	0.0276105	−	0.0849764i	0.963912	+	0.266220i	$0.0857749\pi$
$938$	−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	0.367184	−	0.930148i	$-0.380322\pi$
$941$	1139.52	−	370.253i	1.21097	−	0.393468i	0.843785	+	0.536681i	$0.180322\pi$
$942$	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	$-0.835690\pi$
$947$		−	934.828i		−	0.987147i	0.869704	−	0.493574i	$-0.164310\pi$
$948$	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	0.911956	−	0.410287i	$-0.134572\pi$
$953$	765.792	+	556.381i	0.803560	+	0.583820i	−0.108397	+	0.994108i	$0.534572\pi$
$954$	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	−0.400541	−	0.916279i	$-0.631178\pi$
$971$	337.051	−	244.882i	0.347117	−	0.252196i	0.747659	+	0.664083i	$0.231178\pi$
$972$	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	0.783898	−	0.620890i	$-0.213229\pi$
$977$	1028.91	+	334.314i	1.05313	+	0.342184i	0.269237	+	0.963074i	$0.413229\pi$
$978$	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	−0.614383	−	0.789008i	$-0.710595\pi$
$983$	320.324	−	440.888i	0.325863	−	0.448512i	0.940246	+	0.340496i	$0.110595\pi$
$984$	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	0.338838	−	0.940845i	$-0.389966\pi$
$997$	−449.898	−	326.870i	−0.451252	−	0.327854i	−0.790090	+	0.612991i	$0.789966\pi$
$998$	−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.24.12		56
5.2	odd	4		275.3.x.h.101.6	✓	28
5.3	odd	4		275.3.x.i.101.2	yes	28
5.4	even	2	inner	275.3.q.g.24.3		56
11.6	odd	10	inner	275.3.q.g.149.3		56
55.17	even	20		275.3.x.h.226.6	yes	28
55.28	even	20		275.3.x.i.226.2	yes	28
55.39	odd	10	inner	275.3.q.g.149.12		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.3.q.g.24.3		56	5.4	even	2	inner
275.3.q.g.24.12		56	1.1	even	1	trivial
275.3.q.g.149.3		56	11.6	odd	10	inner
275.3.q.g.149.12		56	55.39	odd	10	inner
275.3.x.h.101.6	✓	28	5.2	odd	4
275.3.x.h.226.6	yes	28	55.17	even	20
275.3.x.i.101.2	yes	28	5.3	odd	4
275.3.x.i.226.2	yes	28	55.28	even	20

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

Varieties

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Representations

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Database

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