LMFDB - Embedded newform 275.3.x.h.101.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(51,275)] 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([0, 7])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.51"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.x (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,-5,14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			101.6
Character	$\chi$	$=$	275.101
Dual form			275.3.x.h.226.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.44335 + 0.793893i) q^{2} +(-0.583945 + 0.424261i) q^{3} +(2.10363 + 1.52838i) q^{4} +(-1.76360 + 0.573029i) q^{6} +(-7.74676 + 10.6625i) q^{7} +(-2.11375 - 2.90933i) q^{8} +(-2.62016 + 8.06402i) q^{9} +(8.18023 + 7.35417i) q^{11} -1.87684 q^{12} +(7.69834 + 2.50134i) q^{13} +(-27.3929 + 19.9021i) q^{14} +(-6.06901 - 18.6785i) q^{16} +(-7.85972 + 2.55378i) q^{17} +(-12.8039 + 17.6231i) q^{18} +(15.2188 + 20.9469i) q^{19} -9.51297i q^{21} +(14.1488 + 24.4631i) q^{22} -5.34212 q^{23} +(2.46863 + 0.802107i) q^{24} +(16.8240 + 12.2233i) q^{26} +(-3.89865 - 11.9988i) q^{27} +(-32.5927 + 10.5900i) q^{28} +(18.9800 - 26.1237i) q^{29} +(13.4739 - 41.4685i) q^{31} -36.0717i q^{32} +(-7.89690 - 0.823881i) q^{33} -21.2315 q^{34} +(-17.8367 + 12.9591i) q^{36} +(11.3991 + 8.28194i) q^{37} +(20.5553 + 63.2626i) q^{38} +(-5.55664 + 1.80546i) q^{39} +(-3.92574 - 5.40332i) q^{41} +(7.55228 - 23.2435i) q^{42} +13.9858i q^{43} +(5.96824 + 27.9730i) q^{44} +(-13.0527 - 4.24108i) q^{46} +(-65.8866 + 47.8694i) q^{47} +(11.4685 + 8.33237i) q^{48} +(-38.5348 - 118.598i) q^{49} +(3.50618 - 4.82584i) q^{51} +(12.3715 + 17.0279i) q^{52} +(-15.8277 + 48.7128i) q^{53} -32.4124i q^{54} +47.3954 q^{56} +(-17.7739 - 5.77508i) q^{57} +(67.1142 - 48.7613i) q^{58} +(43.5007 + 31.6051i) q^{59} +(-3.81411 + 1.23928i) q^{61} +(65.8431 - 90.6252i) q^{62} +(-65.6849 - 90.4074i) q^{63} +(4.36107 - 13.4220i) q^{64} +(-18.6408 - 8.28232i) q^{66} +87.7170 q^{67} +(-20.4371 - 6.64042i) q^{68} +(3.11951 - 2.26646i) q^{69} +(10.5932 + 32.6025i) q^{71} +(28.9992 - 9.42243i) q^{72} +(36.7178 - 50.5378i) q^{73} +(21.2771 + 29.2854i) q^{74} +67.3246i q^{76} +(-141.784 + 30.2507i) q^{77} -15.0102 q^{78} +(119.320 + 38.7694i) q^{79} +(-54.3698 - 39.5019i) q^{81} +(-5.30231 - 16.3188i) q^{82} +(120.797 - 39.2492i) q^{83} +(14.5394 - 20.0118i) q^{84} +(-11.1032 + 34.1723i) q^{86} +23.3073i q^{87} +(4.10473 - 39.3439i) q^{88} +43.7087 q^{89} +(-86.3078 + 62.7063i) q^{91} +(-11.2379 - 8.16479i) q^{92} +(9.72543 + 29.9318i) q^{93} +(-198.987 + 64.6549i) q^{94} +(15.3038 + 21.0639i) q^{96} +(-9.43164 + 29.0276i) q^{97} -320.369i q^{98} +(-80.7377 + 46.6964i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 5 q^{2} + 14 q^{3} + 9 q^{4} + 30 q^{6} + 5 q^{7} + 15 q^{8} - 31 q^{9} - 5 q^{11} - 4 q^{12} - 45 q^{13} + 37 q^{14} - 35 q^{16} + 5 q^{17} + 35 q^{18} + 80 q^{19} - 50 q^{22} + 34 q^{23} - 13 q^{26}+ \cdots - 609 q^{99}+O(q^{100}) $ 28 * q - 5 * q^2 + 14 * q^3 + 9 * q^4 + 30 * q^6 + 5 * q^7 + 15 * q^8 - 31 * q^9 - 5 * q^11 - 4 * q^12 - 45 * q^13 + 37 * q^14 - 35 * q^16 + 5 * q^17 + 35 * q^18 + 80 * q^19 - 50 * q^22 + 34 * q^23 - 13 * q^26 - 118 * q^27 - 145 * q^28 - 95 * q^29 + 95 * q^31 - 381 * q^33 - 148 * q^34 - 347 * q^36 + 146 * q^37 - 10 * q^38 - 65 * q^39 - 290 * q^41 + 615 * q^42 - 253 * q^44 - 110 * q^46 - 179 * q^47 + 364 * q^48 + 224 * q^49 + 400 * q^51 - 185 * q^52 + 344 * q^53 + 884 * q^56 - 430 * q^57 + 265 * q^58 + 67 * q^59 + 135 * q^61 + 155 * q^62 + 220 * q^63 - 119 * q^64 + 250 * q^66 - 204 * q^67 + 45 * q^68 + 311 * q^69 - 189 * q^71 - 235 * q^72 - 5 * q^73 + 940 * q^74 - 215 * q^77 + 290 * q^78 + 565 * q^79 - 583 * q^81 - 195 * q^82 - 530 * q^83 - 1050 * q^84 + 207 * q^86 - 1930 * q^88 + 146 * q^89 - 783 * q^91 + 521 * q^92 - 57 * q^93 - 845 * q^94 - 1210 * q^96 + 506 * q^97 - 609 * 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 $

$2$	2.44335	+	0.793893i	1.22168	+	0.396947i	0.847692	−	0.530489i	$-0.177992\pi$
$2$	2.44335	+	0.793893i	1.22168	+	0.396947i	0.373984	+	0.927435i	$0.377992\pi$
$3$	−0.583945	+	0.424261i	−0.194648	+	0.141420i	−0.680841	−	0.732431i	$-0.738385\pi$
$3$	−0.583945	+	0.424261i	−0.194648	+	0.141420i	0.486192	+	0.873852i	$0.338385\pi$
$4$	2.10363	+	1.52838i	0.525908	+	0.382095i
$5$		0			0
$5$		0			0
$6$	−1.76360	+	0.573029i	−0.293934	+	0.0955048i
$7$	−7.74676	+	10.6625i	−1.10668	+	1.52321i	−0.280461	+	0.959866i	$0.590487\pi$
$7$	−7.74676	+	10.6625i	−1.10668	+	1.52321i	−0.826219	+	0.563349i	$0.809513\pi$
$8$	−2.11375	−	2.90933i	−0.264219	−	0.363666i
$9$	−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
$12$	−1.87684			−0.156403
$13$	7.69834	+	2.50134i	0.592180	+	0.192411i	0.589750	−	0.807586i	$-0.299226\pi$
$13$	7.69834	+	2.50134i	0.592180	+	0.192411i	0.00243053	+	0.999997i	$0.499226\pi$
$14$	−27.3929	+	19.9021i	−1.95664	+	1.42158i
$15$		0			0
$16$	−6.06901	−	18.6785i	−0.379313	−	1.16741i
$17$	−7.85972	+	2.55378i	−0.462336	+	0.150222i	−0.530918	−	0.847423i	$-0.678153\pi$
$17$	−7.85972	+	2.55378i	−0.462336	+	0.150222i	0.0685815	+	0.997646i	$0.478153\pi$
$18$	−12.8039	+	17.6231i	−0.711330	+	0.979061i
$19$	15.2188	+	20.9469i	0.800989	+	1.10247i	0.992652	+	0.121006i	$0.0386119\pi$
$19$	15.2188	+	20.9469i	0.800989	+	1.10247i	−0.191663	+	0.981461i	$0.561388\pi$
$20$		0			0
$21$		−	9.51297i		−	0.452998i
$22$	14.1488	+	24.4631i	0.643125	+	1.11196i
$23$	−5.34212			−0.232266			−0.116133	−	0.993234i	$-0.537050\pi$
$23$	−5.34212			−0.232266			−0.116133	+	0.993234i	$0.537050\pi$
$24$	2.46863	+	0.802107i	0.102860	+	0.0334211i
$25$		0			0
$26$	16.8240	+	12.2233i	0.647076	+	0.470128i
$27$	−3.89865	−	11.9988i	−0.144394	−	0.444400i
$28$	−32.5927	+	10.5900i	−1.16402	+	0.378214i
$29$	18.9800	−	26.1237i	0.654482	−	0.900818i	−0.344801	−	0.938676i	$-0.612053\pi$
$29$	18.9800	−	26.1237i	0.654482	−	0.900818i	0.999283	+	0.0378581i	$0.0120535\pi$
$30$		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	$-0.148276\pi$
$32$		−	36.0717i		−	1.12724i
$33$	−7.89690	−	0.823881i	−0.239300	−	0.0249661i
$34$	−21.2315			−0.624455
$35$		0			0
$36$	−17.8367	+	12.9591i	−0.495465	+	0.359976i
$37$	11.3991	+	8.28194i	0.308084	+	0.223836i	0.731074	−	0.682298i	$-0.239019\pi$
$37$	11.3991	+	8.28194i	0.308084	+	0.223836i	−0.422990	+	0.906134i	$0.639019\pi$
$38$	20.5553	+	63.2626i	0.540928	+	1.66481i
$39$	−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	$0.825955\pi$
$42$	7.55228	−	23.2435i	0.179816	−	0.553417i
$43$			13.9858i			0.325252i	0.986688	+	0.162626i	$0.0519963\pi$
$43$			13.9858i			0.325252i	−0.986688	+	0.162626i	$0.948004\pi$
$44$	5.96824	+	27.9730i	0.135642	+	0.635749i
$45$		0			0
$46$	−13.0527	−	4.24108i	−0.283754	−	0.0921973i
$47$	−65.8866	+	47.8694i	−1.40184	+	1.01850i	−0.407396	+	0.913252i	$0.633563\pi$
$47$	−65.8866	+	47.8694i	−1.40184	+	1.01850i	−0.994446	+	0.105247i	$0.966437\pi$
$48$	11.4685	+	8.33237i	0.238928	+	0.173591i
$49$	−38.5348	−	118.598i	−0.786424	−	2.42036i
$50$		0			0
$51$	3.50618	−	4.82584i	0.0687486	−	0.0946243i
$52$	12.3715	+	17.0279i	0.237913	+	0.327460i
$53$	−15.8277	+	48.7128i	−0.298636	+	0.919109i	0.683339	+	0.730101i	$0.260527\pi$
$53$	−15.8277	+	48.7128i	−0.298636	+	0.919109i	−0.981976	+	0.189008i	$0.939473\pi$
$54$		−	32.4124i		−	0.600229i
$55$		0			0
$56$	47.3954			0.846347
$57$	−17.7739	−	5.77508i	−0.311822	−	0.101317i
$58$	67.1142	−	48.7613i	1.15714	−	0.840713i
$59$	43.5007	+	31.6051i	0.737300	+	0.535680i	0.891865	−	0.452303i	$-0.149397\pi$
$59$	43.5007	+	31.6051i	0.737300	+	0.535680i	−0.154564	+	0.987983i	$0.549397\pi$
$60$		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	$0.410465\pi$
$62$	65.8431	−	90.6252i	1.06199	−	1.46170i
$63$	−65.6849	−	90.4074i	−1.04262	−	1.43504i
$64$	4.36107	−	13.4220i	0.0681417	−	0.209719i
$65$		0			0
$66$	−18.6408	−	8.28232i	−0.282437	−	0.125490i
$67$	87.7170			1.30921			0.654604	−	0.755972i	$-0.272835\pi$
$67$	87.7170			1.30921			0.654604	+	0.755972i	$0.272835\pi$
$68$	−20.4371	−	6.64042i	−0.300546	−	0.0976532i
$69$	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	$0.822390\pi$
$72$	28.9992	−	9.42243i	0.402767	−	0.130867i
$73$	36.7178	−	50.5378i	0.502984	−	0.692298i	−0.479732	−	0.877415i	$-0.659266\pi$
$73$	36.7178	−	50.5378i	0.502984	−	0.692298i	0.982717	+	0.185116i	$0.0592662\pi$
$74$	21.2771	+	29.2854i	0.287528	+	0.395748i
$75$		0			0
$76$			67.3246i			0.885850i
$77$	−141.784	+	30.2507i	−1.84135	+	0.392866i
$78$	−15.0102			−0.192438
$79$	119.320	+	38.7694i	1.51038	+	0.490751i	0.943024	−	0.332724i	$-0.107968\pi$
$79$	119.320	+	38.7694i	1.51038	+	0.490751i	0.567353	+	0.823475i	$0.307968\pi$
$80$		0			0
$81$	−54.3698	−	39.5019i	−0.671231	−	0.487678i
$82$	−5.30231	−	16.3188i	−0.0646623	−	0.199010i
$83$	120.797	−	39.2492i	1.45538	−	0.472882i	0.528726	−	0.848793i	$-0.322670\pi$
$83$	120.797	−	39.2492i	1.45538	−	0.472882i	0.926656	+	0.375910i	$0.122670\pi$
$84$	14.5394	−	20.0118i	0.173088	−	0.238236i
$85$		0			0
$86$	−11.1032	+	34.1723i	−0.129107	+	0.397352i
$87$			23.3073i			0.267900i
$88$	4.10473	−	39.3439i	0.0466447	−	0.447089i
$89$	43.7087			0.491109			0.245555	−	0.969383i	$-0.421030\pi$
$89$	43.7087			0.491109			0.245555	+	0.969383i	$0.421030\pi$
$90$		0			0
$91$	−86.3078	+	62.7063i	−0.948437	+	0.689080i
$92$	−11.2379	−	8.16479i	−0.122151	−	0.0887477i
$93$	9.72543	+	29.9318i	0.104574	+	0.321847i
$94$	−198.987	+	64.6549i	−2.11689	+	0.687818i
$95$		0			0
$96$	15.3038	+	21.0639i	0.159415	+	0.219416i
$97$	−9.43164	+	29.0276i	−0.0972334	+	0.299253i	−0.987829	−	0.155542i	$-0.950288\pi$
$97$	−9.43164	+	29.0276i	−0.0972334	+	0.299253i	0.890596	+	0.454795i	$0.150288\pi$
$98$		−	320.369i		−	3.26907i
$99$	−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	$0.517505\pi$
$102$	12.3980	−	9.00769i	0.121549	−	0.0883107i
$103$	55.9544	+	40.6532i	0.543246	+	0.394691i	0.825289	−	0.564710i	$-0.191012\pi$
$103$	55.9544	+	40.6532i	0.543246	+	0.394691i	−0.282043	+	0.959402i	$0.591012\pi$
$104$	−8.99515	−	27.6842i	−0.0864919	−	0.266195i
$105$		0			0
$106$	−77.3454	+	106.457i	−0.729674	+	1.00431i
$107$	−34.9014	−	48.0376i	−0.326181	−	0.448950i	0.614161	−	0.789181i	$-0.289495\pi$
$107$	−34.9014	−	48.0376i	−0.326181	−	0.448950i	−0.940342	+	0.340231i	$0.889495\pi$
$108$	10.1374	−	31.1997i	0.0938647	−	0.288886i
$109$			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
$112$	246.174	+	79.9869i	2.19799	+	0.714169i
$113$	14.3011	−	10.3903i	0.126558	−	0.0919498i	−0.522705	−	0.852513i	$-0.675077\pi$
$113$	14.3011	−	10.3903i	0.126558	−	0.0919498i	0.649263	+	0.760564i	$0.275077\pi$
$114$	−38.8430	−	28.2211i	−0.340728	−	0.247554i
$115$		0			0
$116$	79.8539	−	25.9461i	0.688395	−	0.223673i
$117$	−40.3418	+	55.5257i	−0.344801	+	0.474578i
$118$	81.1965	+	111.757i	0.688106	+	0.947096i
$119$	33.6577	−	103.588i	0.282838	−	0.870485i
$120$		0			0
$121$	12.8323	+	120.318i	0.106052	+	0.994361i
$122$	−10.3031			−0.0844514
$123$	4.58484	+	1.48970i	0.0372751	+	0.0121114i
$124$	91.7238	−	66.6412i	0.739708	−	0.537429i
$125$		0			0
$126$	−88.7174	−	273.044i	−0.704106	−	2.16702i
$127$	−112.770	+	36.6413i	−0.887955	+	0.288514i	−0.717257	−	0.696809i	$-0.754602\pi$
$127$	−112.770	+	36.6413i	−0.887955	+	0.288514i	−0.170699	+	0.985323i	$0.554602\pi$
$128$	−63.4985	+	87.3982i	−0.496082	+	0.682798i
$129$	−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	$0.766413\pi$
$132$	−15.3530	−	13.8026i	−0.116310	−	0.104565i
$133$	−341.242			−2.56573
$134$	214.323	+	69.6379i	1.59943	+	0.519686i
$135$		0			0
$136$	24.0433	+	17.4685i	0.176789	+	0.128444i
$137$	−49.3113	−	151.765i	−0.359936	−	1.10777i	−0.953092	−	0.302682i	$-0.902118\pi$
$137$	−49.3113	−	151.765i	−0.359936	−	1.10777i	0.593155	−	0.805088i	$-0.297882\pi$
$138$	9.42138	−	3.06119i	0.0682709	−	0.0221825i
$139$	108.452	−	149.272i	0.780232	−	1.07390i	−0.215025	−	0.976609i	$-0.568983\pi$
$139$	108.452	−	149.272i	0.780232	−	1.07390i	0.995256	−	0.0972881i	$-0.0310168\pi$
$140$		0			0
$141$	18.1650	−	55.9062i	0.128830	−	0.396498i
$142$			88.0693i			0.620207i
$143$	44.5789	+	77.0765i	0.311741	+	0.538997i
$144$	166.525			1.15643
$145$		0			0
$146$	129.836	−	94.3315i	0.889289	−	0.646106i
$147$	72.8187	+	52.9059i	0.495365	+	0.359904i
$148$	11.3216	+	34.8443i	0.0764974	+	0.235435i
$149$	−157.999	+	51.3369i	−1.06039	+	0.344543i	−0.786740	−	0.617285i	$-0.788233\pi$
$149$	−157.999	+	51.3369i	−1.06039	+	0.344543i	−0.273655	+	0.961828i	$0.588233\pi$
$150$		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	$0.982537\pi$
$152$	28.7726	−	88.5529i	0.189293	−	0.582585i
$153$		−	70.0722i		−	0.457988i
$154$	−370.444	−	38.6483i	−2.40548	−	0.250963i
$155$		0			0
$156$	−14.4486	−	4.69462i	−0.0926189	−	0.0300937i
$157$	150.650	−	109.453i	0.959552	−	0.697156i	0.00650560	−	0.999979i	$-0.497929\pi$
$157$	150.650	−	109.453i	0.959552	−	0.697156i	0.953047	+	0.302823i	$0.0979292\pi$
$158$	260.762	+	189.454i	1.65039	+	1.19908i
$159$	−11.4244	−	35.1607i	−0.0718516	−	0.221136i
$160$		0			0
$161$	41.3841	−	56.9604i	0.257044	−	0.353791i
$162$	−101.484	−	139.681i	−0.626445	−	0.862228i
$163$	−75.3797	+	231.995i	−0.462452	+	1.42328i	0.399706	+	0.916643i	$0.369112\pi$
$163$	−75.3797	+	231.995i	−0.462452	+	1.42328i	−0.862159	+	0.506639i	$0.830888\pi$
$164$		−	17.3666i		−	0.105894i
$165$		0			0
$166$	326.309			1.96571
$167$	23.1931	+	7.53588i	0.138881	+	0.0451250i	0.377632	−	0.925956i	$-0.376738\pi$
$167$	23.1931	+	7.53588i	0.138881	+	0.0451250i	−0.238752	+	0.971081i	$0.576738\pi$
$168$	−27.6764	+	20.1080i	−0.164740	+	0.119691i
$169$	−83.7161	−	60.8233i	−0.495361	−	0.359901i
$170$		0			0
$171$	−208.792	+	67.8405i	−1.22100	+	0.396728i
$172$	−21.3756	+	29.4210i	−0.124277	+	0.171053i
$173$	−34.0540	−	46.8713i	−0.196844	−	0.270932i	0.699173	−	0.714953i	$-0.253552\pi$
$173$	−34.0540	−	46.8713i	−0.196844	−	0.270932i	−0.896017	+	0.444020i	$0.853552\pi$
$174$	−18.5035	+	56.9479i	−0.106342	+	0.327287i
$175$		0			0
$176$	87.7189	−	197.427i	0.498403	−	1.12174i
$177$	−38.8109			−0.219270
$178$	106.796	+	34.7000i	0.599976	+	0.194944i
$179$	−0.0910781	+	0.0661721i	−0.000508816	+	0.000369677i	−0.588040	−	0.808832i	$-0.700100\pi$
$179$	−0.0910781	+	0.0661721i	−0.000508816	+	0.000369677i	0.587531	+	0.809202i	$0.300100\pi$
$180$		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	$0.923882\pi$
$182$	−260.662	+	84.6944i	−1.43221	+	0.465354i
$183$	1.70145	−	2.34185i	0.00929756	−	0.0127970i
$184$	11.2919	+	15.5420i	0.0613691	+	0.0844674i
$185$		0			0
$186$			80.8548i			0.434703i
$187$	−83.0752	−	36.9112i	−0.444252	−	0.197386i
$188$	−211.764			−1.12640
$189$	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	$-0.629507\pi$
$192$	3.14780	+	9.68794i	0.0163948	+	0.0504580i
$193$	−213.112	+	69.2444i	−1.10421	+	0.358779i	−0.803721	−	0.595006i	$-0.797150\pi$
$193$	−213.112	+	69.2444i	−1.10421	+	0.358779i	−0.300488	+	0.953785i	$0.597150\pi$
$194$	−46.0896	+	63.4369i	−0.237575	+	0.326994i
$195$		0			0
$196$	100.199	−	308.382i	0.511222	−	1.57338i
$197$			1.50117i			0.00762015i	0.999993	+	0.00381008i	$0.00121279\pi$
$197$			1.50117i			0.00762015i	−0.999993	+	0.00381008i	$0.998787\pi$
$198$	−234.342	+	49.9987i	−1.18355	+	0.252519i
$199$	−65.2808			−0.328044			−0.164022	−	0.986457i	$-0.552447\pi$
$199$	−65.2808			−0.328044			−0.164022	+	0.986457i	$0.552447\pi$
$200$		0			0
$201$	−51.2219	+	37.2149i	−0.254835	+	0.185149i
$202$	107.596	+	78.1729i	0.532652	+	0.386994i
$203$	131.511	+	404.748i	0.647836	+	1.99383i
$204$	14.7514	−	4.79303i	0.0723109	−	0.0234952i
$205$		0			0
$206$	104.442	+	143.752i	0.506999	+	0.697825i
$207$	13.9972	−	43.0790i	0.0676194	−	0.208111i
$208$		−	158.974i		−	0.764298i
$209$	−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	$0.400607\pi$
$212$	−107.747	+	78.2830i	−0.508242	+	0.369259i
$213$	−20.0178	−	14.5438i	−0.0939805	−	0.0682808i
$214$	−47.1396	−	145.081i	−0.220278	−	0.677947i
$215$		0			0
$216$	−26.6677	+	36.7049i	−0.123462	+	0.169930i
$217$	337.778	+	464.912i	1.55658	+	2.14245i
$218$	−64.2326	+	197.688i	−0.294645	+	0.906824i
$219$			45.0893i			0.205887i
$220$		0			0
$221$	−66.8947			−0.302691
$222$	−24.8493	−	8.07403i	−0.111934	−	0.0363695i
$223$	214.422	−	155.787i	0.961533	−	0.698594i	0.00802651	−	0.999968i	$-0.497445\pi$
$223$	214.422	−	155.787i	0.961533	−	0.698594i	0.953506	+	0.301373i	$0.0974451\pi$
$224$	384.615	+	279.439i	1.71703	+	1.24750i
$225$		0			0
$226$	43.1913	−	14.0337i	0.191112	−	0.0620961i
$227$	216.994	−	298.667i	0.955922	−	1.31571i	0.00707657	−	0.999975i	$-0.497747\pi$
$227$	216.994	−	298.667i	0.955922	−	1.31571i	0.948846	−	0.315739i	$-0.102253\pi$
$228$	−28.5632	−	39.3139i	−0.125277	−	0.172429i
$229$	−24.0332	+	73.9665i	−0.104948	+	0.322998i	−0.989718	−	0.143030i	$-0.954315\pi$
$229$	−24.0332	+	73.9665i	−0.104948	+	0.322998i	0.884770	+	0.466028i	$0.154315\pi$
$230$		0			0
$231$	69.9600	−	77.8183i	0.302857	−	0.336876i
$232$	−116.121			−0.500524
$233$	−207.119	−	67.2970i	−0.888922	−	0.288828i	−0.171265	−	0.985225i	$-0.554785\pi$
$233$	−207.119	−	67.2970i	−0.888922	−	0.288828i	−0.717657	+	0.696397i	$0.754785\pi$
$234$	−142.651	+	103.642i	−0.609618	+	0.442913i
$235$		0			0
$236$	43.2050	+	132.971i	0.183072	+	0.563437i
$237$	−86.1246	+	27.9836i	−0.363395	+	0.118074i
$238$	164.475	−	226.381i	0.691072	−	0.951179i
$239$	−82.7232	−	113.859i	−0.346122	−	0.476396i	0.600095	−	0.799929i	$-0.295129\pi$
$239$	−82.7232	−	113.859i	−0.346122	−	0.476396i	−0.946217	+	0.323533i	$0.895129\pi$
$240$		0			0
$241$			265.314i			1.10089i	0.834872	+	0.550444i	$0.185542\pi$
$241$			265.314i			1.10089i	−0.834872	+	0.550444i	$0.814458\pi$
$242$	−64.1655	+	304.166i	−0.265146	+	1.25688i
$243$	162.055			0.666892
$244$	−9.91758	−	3.22242i	−0.0406458	−	0.0132066i
$245$		0			0
$246$	10.0197	+	7.27974i	0.0407305	+	0.0295924i
$247$	64.7642	+	199.324i	0.262203	+	0.806978i
$248$	−149.126	+	48.4540i	−0.601315	+	0.195379i
$249$	−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	$0.923856\pi$
$252$		−	290.575i		−	1.15308i
$253$	−43.6998	−	39.2869i	−0.172726	−	0.155284i
$254$	−304.627			−1.19932
$255$		0			0
$256$	−270.204	+	196.314i	−1.05548	+	0.766853i
$257$	−256.357	−	186.254i	−0.997499	−	0.724725i	−0.0359483	−	0.999354i	$-0.511445\pi$
$257$	−256.357	−	186.254i	−0.997499	−	0.724725i	−0.961550	+	0.274628i	$0.911445\pi$
$258$	−8.01428	−	24.6654i	−0.0310631	−	0.0956024i
$259$	−176.612	+	57.3849i	−0.681901	+	0.221563i
$260$		0			0
$261$	160.932	+	221.503i	0.616596	+	0.848672i
$262$	−139.302	+	428.728i	−0.531688	+	1.63637i
$263$		−	415.617i		−	1.58029i	−0.612919	−	0.790145i	$-0.710005\pi$
$263$		−	415.617i		−	1.58029i	0.612919	−	0.790145i	$-0.289995\pi$
$264$	14.2951	+	24.7162i	0.0541482	+	0.0936218i
$265$		0			0
$266$	−833.775	−	270.910i	−3.13449	−	1.01846i
$267$	−25.5235	+	18.5439i	−0.0955936	+	0.0694528i
$268$	184.524	+	134.065i	0.688524	+	0.500242i
$269$	21.6814	+	66.7285i	0.0806000	+	0.248061i	0.983234	−	0.182347i	$-0.0583695\pi$
$269$	21.6814	+	66.7285i	0.0806000	+	0.248061i	−0.902634	+	0.430409i	$0.858369\pi$
$270$		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	$-0.0921365\pi$
$272$	95.4013	+	131.309i	0.350740	+	0.482752i
$273$	23.7952	−	73.2341i	0.0871619	−	0.268257i
$274$		−	409.962i		−	1.49621i
$275$		0			0
$276$	10.0263			0.0363272
$277$	−76.8041	−	24.9552i	−0.277271	−	0.0900909i	0.167081	−	0.985943i	$-0.446566\pi$
$277$	−76.8041	−	24.9552i	−0.277271	−	0.0900909i	−0.444352	+	0.895852i	$0.646566\pi$
$278$	383.493	−	278.624i	1.37947	−	1.00224i
$279$	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	$0.120751\pi$
$282$	88.7672	−	122.178i	0.314777	−	0.433254i
$283$	76.0310	+	104.648i	0.268661	+	0.369780i	0.921937	−	0.387340i	$-0.126606\pi$
$283$	76.0310	+	104.648i	0.268661	+	0.369780i	−0.653276	+	0.757120i	$0.726606\pi$
$284$	−27.5448	+	84.7742i	−0.0969888	+	0.298501i
$285$		0			0
$286$	47.7315	+	223.716i	0.166893	+	0.782224i
$287$	88.0247			0.306706
$288$	290.883	+	94.5136i	1.01001	+	0.328172i
$289$	−178.553	+	129.726i	−0.617829	+	0.448879i
$290$		0			0
$291$	−6.80772	−	20.9520i	−0.0233942	−	0.0720000i
$292$	154.482	−	50.1942i	0.529047	−	0.171898i
$293$	160.052	−	220.293i	0.546253	−	0.751853i	−0.443245	−	0.896401i	$-0.646173\pi$
$293$	160.052	−	220.293i	0.546253	−	0.751853i	0.989498	+	0.144548i	$0.0461727\pi$
$294$	135.920	+	187.078i	0.462313	+	0.636319i
$295$		0			0
$296$		−	50.6698i		−	0.171182i
$297$	56.3494	−	126.824i	0.189729	−	0.427018i
$298$	−426.803			−1.43222
$299$	−41.1255	−	13.3625i	−0.137544	−	0.0446906i
$300$		0			0
$301$	−149.124	−	108.345i	−0.495428	−	0.359949i
$302$	−130.077	−	400.335i	−0.430717	−	1.32561i
$303$	−35.5368	+	11.5466i	−0.117283	+	0.0381076i
$304$	298.893	−	411.391i	0.983200	−	1.35326i
$305$		0			0
$306$	55.6298	−	171.211i	0.181797	−	0.559513i
$307$		−	341.863i		−	1.11356i	−0.830660	−	0.556780i	$-0.812037\pi$
$307$		−	341.863i		−	1.11356i	0.830660	−	0.556780i	$-0.187963\pi$
$308$	−344.496	−	153.063i	−1.11849	−	0.496959i
$309$	−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	$0.379540\pi$
$312$	16.9980	+	12.3498i	0.0544809	+	0.0395827i
$313$	2.91085	+	8.95868i	0.00929984	+	0.0286220i	0.955599	−	0.294671i	$-0.0952101\pi$
$313$	2.91085	+	8.95868i	0.00929984	+	0.0286220i	−0.946299	+	0.323293i	$0.895210\pi$
$314$	454.985	−	147.833i	1.44900	−	0.470807i
$315$		0			0
$316$	191.751	+	263.922i	0.606806	+	0.835197i
$317$	69.7448	−	214.652i	0.220015	−	0.677137i	−0.778744	−	0.627341i	$-0.784143\pi$
$317$	69.7448	−	214.652i	0.220015	−	0.677137i	0.998759	−	0.0497954i	$-0.0158569\pi$
$318$		−	94.9797i		−	0.298678i
$319$	347.379	−	74.1159i	1.08896	−	0.232338i
$320$		0			0
$321$	40.7610	+	13.2440i	0.126981	+	0.0412587i
$322$	146.336	−	106.320i	0.454461	−	0.330185i
$323$	−173.109	−	125.771i	−0.535941	−	0.389384i
$324$	−54.0001	−	166.195i	−0.166667	−	0.512948i
$325$		0			0
$326$	−368.358	+	507.002i	−1.12993	+	1.55522i
$327$	−34.3263	−	47.2461i	−0.104973	−	0.144483i
$328$	−7.42199	+	22.8426i	−0.0226280	+	0.0696419i
$329$		−	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	$0.414265\pi$
$332$	314.100	+	102.057i	0.946083	+	0.307401i
$333$	−96.6532	+	70.2227i	−0.290250	+	0.210879i
$334$	50.6861	+	36.8256i	0.151755	+	0.110256i
$335$		0			0
$336$	−177.688	+	57.7343i	−0.528833	+	0.171828i
$337$	−112.204	+	154.436i	−0.332951	+	0.458267i	−0.942366	−	0.334584i	$-0.891404\pi$
$337$	−112.204	+	154.436i	−0.332951	+	0.458267i	0.609415	+	0.792851i	$0.291404\pi$
$338$	−156.261	−	215.074i	−0.462310	−	0.636315i
$339$	−3.94282	+	12.1348i	−0.0116307	+	0.0357958i
$340$		0			0
$341$	415.186	−	240.132i	1.21755	−	0.704200i
$342$	−564.009			−1.64915
$343$	948.878	+	308.309i	2.76641	+	0.898860i
$344$	40.6894	−	29.5625i	0.118283	−	0.0859376i
$345$		0			0
$346$	−45.9951	−	141.558i	−0.132934	−	0.409128i
$347$	189.153	−	61.4596i	0.545110	−	0.177117i	−0.0235005	−	0.999724i	$-0.507481\pi$
$347$	189.153	−	61.4596i	0.545110	−	0.177117i	0.568611	+	0.822607i	$0.307481\pi$
$348$	−35.6224	+	49.0300i	−0.102363	+	0.140891i
$349$	−120.489	−	165.839i	−0.345241	−	0.475183i	0.600722	−	0.799458i	$-0.294880\pi$
$349$	−120.489	−	165.839i	−0.345241	−	0.475183i	−0.945963	+	0.324275i	$0.894880\pi$
$350$		0			0
$351$		−	102.123i		−	0.290948i
$352$	265.278	−	295.075i	0.753630	−	0.838281i
$353$	193.516			0.548205			0.274102	−	0.961701i	$-0.411619\pi$
$353$	193.516			0.548205			0.274102	+	0.961701i	$0.411619\pi$
$354$	−94.8286	−	30.8117i	−0.267877	−	0.0870387i
$355$		0			0
$356$	91.9471	+	66.8035i	0.258278	+	0.187650i
$357$	24.2940	+	74.7692i	0.0680504	+	0.209438i
$358$	−0.275069	+	0.0893755i	−0.000768350	+	0.000249652i
$359$	48.9531	−	67.3782i	0.136360	−	0.187683i	−0.735376	−	0.677659i	$-0.762995\pi$
$359$	48.9531	−	67.3782i	0.136360	−	0.187683i	0.871736	+	0.489976i	$0.162995\pi$
$360$		0			0
$361$	−95.6045	+	294.240i	−0.264832	+	0.815070i
$362$		−	69.7108i		−	0.192571i
$363$	−58.5395	−	64.8147i	−0.161266	−	0.178553i
$364$	−277.399			−0.762085
$365$		0			0
$366$	6.01643	−	4.37119i	0.0164383	−	0.0119431i
$367$	540.978	+	393.044i	1.47406	+	1.07096i	0.979413	+	0.201867i	$0.0647009\pi$
$367$	540.978	+	393.044i	1.47406	+	1.07096i	0.494642	+	0.869097i	$0.335299\pi$
$368$	32.4214	+	99.7828i	0.0881016	+	0.271149i
$369$	53.8585	−	17.4997i	0.145958	−	0.0474247i
$370$		0			0
$371$	−396.786	−	546.129i	−1.06950	−	1.47205i
$372$	−25.2884	+	77.8296i	−0.0679795	+	0.209219i
$373$		−	106.447i		−	0.285380i	−0.989767	−	0.142690i	$-0.954425\pi$
$373$		−	106.447i		−	0.285380i	0.989767	−	0.142690i	$-0.0455752\pi$
$374$	−173.678	−	156.140i	−0.464381	−	0.417486i
$375$		0			0
$376$	278.536	+	90.5017i	0.740787	+	0.240696i
$377$	211.459	−	153.634i	0.560899	−	0.407517i
$378$	345.597	+	251.091i	0.914278	+	0.664262i
$379$	165.105	+	508.140i	0.435633	+	1.34074i	0.892437	+	0.451172i	$0.148994\pi$
$379$	165.105	+	508.140i	0.435633	+	1.34074i	−0.456804	+	0.889567i	$0.651006\pi$
$380$		0			0
$381$	50.3062	−	69.2406i	0.132037	−	0.181734i
$382$	−496.062	−	682.771i	−1.29859	−	1.78736i
$383$	−8.43976	+	25.9749i	−0.0220359	+	0.0678196i	−0.961470	−	0.274911i	$-0.911352\pi$
$383$	−8.43976	+	25.9749i	−0.0220359	+	0.0678196i	0.939434	+	0.342730i	$0.111352\pi$
$384$		−	77.9757i		−	0.203062i
$385$		0			0
$386$	−575.681			−1.49140
$387$	−112.782	−	36.6451i	−0.291426	−	0.0946901i
$388$	−64.2059	+	46.6483i	−0.165479	+	0.120228i
$389$	−549.304	−	399.093i	−1.41209	−	1.02595i	−0.993014	−	0.117995i	$-0.962353\pi$
$389$	−549.304	−	399.093i	−1.41209	−	1.02595i	−0.419078	−	0.907950i	$-0.637647\pi$
$390$		0			0
$391$	41.9876	−	13.6426i	0.107385	−	0.0348915i
$392$	−263.587	+	362.797i	−0.672417	+	0.925502i
$393$	−74.4439	−	102.463i	−0.189425	−	0.260721i
$394$	−1.19177	+	3.66789i	−0.00302479	+	0.00930936i
$395$		0			0
$396$	−241.212	−	25.1656i	−0.609122	−	0.0635495i
$397$	−269.778			−0.679542			−0.339771	−	0.940508i	$-0.610350\pi$
$397$	−269.778			−0.679542			−0.339771	+	0.940508i	$0.610350\pi$
$398$	−159.504	−	51.8260i	−0.400764	−	0.130216i
$399$	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	$0.917501\pi$
$402$	−154.698	+	50.2644i	−0.384820	+	0.125036i
$403$	207.454	−	285.536i	0.514774	−	0.708525i
$404$	79.1205	+	108.900i	0.195843	+	0.269554i
$405$		0			0
$406$			1093.35i			2.69298i
$407$	32.3406	+	151.579i	0.0794609	+	0.372431i
$408$	−21.4511			−0.0525763
$409$	−69.3442	−	22.5313i	−0.169546	−	0.0550888i	0.223014	−	0.974815i	$-0.428410\pi$
$409$	−69.3442	−	22.5313i	−0.169546	−	0.0550888i	−0.392560	+	0.919726i	$0.628410\pi$
$410$		0			0
$411$	93.1829	+	67.7013i	0.226722	+	0.164723i
$412$	55.5739	+	171.039i	0.134888	+	0.415143i
$413$	−673.979	+	218.989i	−1.63191	+	0.530240i
$414$	68.4002	−	94.1448i	0.165218	−	0.227403i
$415$		0			0
$416$	90.2278	−	277.693i	0.216894	−	0.667530i
$417$			133.179i			0.319373i
$418$	−297.097	+	668.670i	−0.710759	+	1.59969i
$419$	−46.3826			−0.110698			−0.0553491	−	0.998467i	$-0.517627\pi$
$419$	−46.3826			−0.110698			−0.0553491	+	0.998467i	$0.517627\pi$
$420$		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	$0.178864\pi$
$422$	514.192	+	373.583i	1.21847	+	0.885267i
$423$	−213.386	−	656.736i	−0.504460	−	1.55257i
$424$	175.177	−	56.9186i	0.413154	−	0.134242i
$425$		0			0
$426$	−37.3644	−	51.4277i	−0.0877099	−	0.120722i
$427$	16.3332	−	50.2683i	0.0382510	−	0.117724i
$428$		−	154.396i		−	0.360738i
$429$	−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	$0.814000\pi$
$432$	−200.458	+	145.642i	−0.464024	+	0.337133i
$433$	156.542	+	113.734i	0.361529	+	0.262666i	0.753689	−	0.657231i	$-0.228272\pi$
$433$	156.542	+	113.734i	0.361529	+	0.262666i	−0.392161	+	0.919897i	$0.628272\pi$
$434$	456.221	+	1404.10i	1.05120	+	3.23526i
$435$		0			0
$436$	−123.659	+	170.201i	−0.283621	+	0.390370i
$437$	−81.3006	−	111.901i	−0.186043	−	0.256066i
$438$	−35.7961	+	110.169i	−0.0817261	+	0.251527i
$439$			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
$442$	−163.447	−	53.1072i	−0.369790	−	0.120152i
$443$	−60.3521	+	43.8483i	−0.136235	+	0.0989805i	−0.653816	−	0.756654i	$-0.726833\pi$
$443$	−60.3521	+	43.8483i	−0.136235	+	0.0989805i	0.517581	+	0.855634i	$0.326833\pi$
$444$	−21.3943	−	15.5439i	−0.0481854	−	0.0350087i
$445$		0			0
$446$	647.586	−	210.413i	1.45199	−	0.471779i
$447$	70.4824	−	97.0107i	0.157679	−	0.217026i
$448$	109.328	+	150.477i	0.244035	+	0.335886i
$449$	−207.909	+	639.879i	−0.463050	+	1.42512i	0.398368	+	0.917225i	$0.369577\pi$
$449$	−207.909	+	639.879i	−0.463050	+	1.42512i	−0.861418	+	0.507896i	$0.830423\pi$
$450$		0			0
$451$	7.62347	−	73.0710i	0.0169035	−	0.162020i
$452$	45.9645			0.101691
$453$	112.476	+	36.5455i	0.248290	+	0.0806744i
$454$	767.303	−	557.479i	1.69010	−	1.22793i
$455$		0			0
$456$	20.7679	+	63.9172i	0.0455437	+	0.140169i
$457$	537.536	−	174.656i	1.17623	−	0.382180i	0.345264	−	0.938506i	$-0.387789\pi$
$457$	537.536	−	174.656i	1.17623	−	0.382180i	0.830964	+	0.556326i	$0.187789\pi$
$458$	−117.443	+	161.646i	−0.256426	+	0.352940i
$459$	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	$-0.298042\pi$
$462$	232.716	−	134.597i	0.503715	−	0.291335i
$463$	279.537			0.603752			0.301876	−	0.953347i	$-0.402387\pi$
$463$	279.537			0.603752			0.301876	+	0.953347i	$0.402387\pi$
$464$	−603.141	−	195.972i	−1.29987	−	0.422354i
$465$		0			0
$466$	−452.638	−	328.860i	−0.971325	−	0.705709i
$467$	236.126	+	726.720i	0.505623	+	1.55615i	0.799722	+	0.600371i	$0.204980\pi$
$467$	236.126	+	726.720i	0.505623	+	1.55615i	−0.294099	+	0.955775i	$0.595020\pi$
$468$	−169.729	+	55.1481i	−0.362668	+	0.117838i
$469$	−679.522	+	935.282i	−1.44887	+	1.99420i
$470$		0			0
$471$	−41.5344	+	127.830i	−0.0881834	+	0.271401i
$472$		−	193.363i		−	0.409668i
$473$	−102.854	+	114.407i	−0.217451	+	0.241876i
$474$	−232.649			−0.490820
$475$		0			0
$476$	229.125	−	166.469i	0.481354	−	0.349724i
$477$	−351.349	−	255.270i	−0.736581	−	0.535158i
$478$	−111.730	−	343.870i	−0.233745	−	0.719394i
$479$	−596.452	+	193.799i	−1.24520	+	0.404591i	−0.856199	−	0.516646i	$-0.827180\pi$
$479$	−596.452	+	193.799i	−1.24520	+	0.404591i	−0.389003	+	0.921236i	$0.627180\pi$
$480$		0			0
$481$	67.0384	+	92.2704i	0.139373	+	0.191830i
$482$	−210.631	+	648.256i	−0.436994	+	1.34493i
$483$			50.8194i			0.105216i
$484$	−156.896	+	272.717i	−0.324166	+	0.563464i
$485$		0			0
$486$	395.956	+	128.654i	0.814725	+	0.264720i
$487$	−135.711	+	98.5999i	−0.278668	+	0.202464i	−0.718336	−	0.695696i	$-0.755096\pi$
$487$	−135.711	+	98.5999i	−0.278668	+	0.202464i	0.439668	+	0.898160i	$0.355096\pi$
$488$	11.6676	+	8.47697i	0.0239089	+	0.0173708i
$489$	−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	$0.309238\pi$
$492$	7.36798	+	10.1412i	0.0149756	+	0.0206121i
$493$	−82.4632	+	253.796i	−0.167268	+	0.514798i
$494$			538.433i			1.08995i
$495$		0			0
$496$	−856.342			−1.72650
$497$	−429.688	−	139.614i	−0.864563	−	0.280913i
$498$	−190.546	+	138.440i	−0.382623	+	0.277992i
$499$	630.351	+	457.977i	1.26323	+	0.917789i	0.998911	−	0.0466466i	$-0.0148535\pi$
$499$	630.351	+	457.977i	1.26323	+	0.917789i	0.264317	+	0.964436i	$0.414853\pi$
$500$		0			0
$501$	−16.7407	+	5.43937i	−0.0334145	+	0.0108570i
$502$	−398.404	+	548.355i	−0.793633	+	1.09234i
$503$	244.162	+	336.060i	0.485412	+	0.668112i	0.979534	−	0.201281i	$-0.0645103\pi$
$503$	244.162	+	336.060i	0.485412	+	0.668112i	−0.494122	+	0.869393i	$0.664510\pi$
$504$	−124.184	+	382.198i	−0.246396	+	0.758329i
$505$		0			0
$506$	−75.5844	−	130.685i	−0.149376	−	0.258270i
$507$	74.6906			0.147319
$508$	−293.229	−	95.2759i	−0.577223	−	0.187551i
$509$	570.074	−	414.183i	1.11999	−	0.813719i	0.135781	−	0.990739i	$-0.456646\pi$
$509$	570.074	−	414.183i	1.11999	−	0.813719i	0.984207	+	0.177019i	$0.0566455\pi$
$510$		0			0
$511$	254.415	+	783.008i	0.497876	+	1.53231i
$512$	−405.084	+	131.620i	−0.791180	+	0.257070i
$513$	192.005	−	264.272i	0.374278	−	0.515149i
$514$	−478.505	−	658.605i	−0.930943	−	1.28133i
$515$		0			0
$516$		−	26.2491i		−	0.0508704i
$517$	−891.007	−	92.9585i	−1.72342	−	0.179804i
$518$	−477.084			−0.921011
$519$	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	$0.753714\pi$
$522$	217.362	+	668.973i	0.416403	+	1.28156i
$523$	832.911	−	270.629i	1.59256	−	0.517455i	0.627310	−	0.778769i	$-0.284156\pi$
$523$	832.911	−	270.629i	1.59256	−	0.517455i	0.965254	+	0.261314i	$0.0841558\pi$
$524$	−268.180	+	369.119i	−0.511795	+	0.704425i
$525$		0			0
$526$	329.955	−	1015.50i	0.627291	−	1.93060i
$527$			360.340i			0.683757i
$528$	32.5375	+	152.502i	0.0616240	+	0.288830i
$529$	−500.462			−0.946052
$530$		0			0
$531$	−368.843	+	267.980i	−0.694620	+	0.504671i
$532$	−717.848	−	521.547i	−1.34934	−	0.980352i
$533$	−16.7062	−	51.4163i	−0.0313436	−	0.0964658i
$534$	−77.0847	+	25.0464i	−0.144353	+	0.0469033i
$535$		0			0
$536$	−185.412	−	255.198i	−0.345918	−	0.476115i
$537$	0.0251104	−	0.0772818i	4.67605e−5	−	0.000143914i
$538$			180.254i			0.335044i
$539$	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	$0.638834\pi$
$542$	894.735	−	650.063i	1.65080	−	1.19938i
$543$	15.8450	+	11.5121i	0.0291805	+	0.0212009i
$544$	92.1191	+	283.514i	0.169337	+	0.521165i
$545$		0			0
$546$	116.280	−	160.046i	0.212967	−	0.293124i
$547$	0.959689	+	1.32090i	0.00175446	+	0.00241481i	0.809893	−	0.586577i	$-0.199525\pi$
$547$	0.959689	+	1.32090i	0.00175446	+	0.00241481i	−0.808139	+	0.588992i	$0.799525\pi$
$548$	128.221	−	394.623i	0.233980	−	0.720115i
$549$		−	34.0042i		−	0.0619384i
$550$		0			0
$551$	836.062			1.51735
$552$	−13.1877	−	4.28495i	−0.0238908	−	0.00776260i
$553$	−1337.72	+	971.910i	−2.41902	+	1.75752i
$554$	−167.848	−	121.949i	−0.302974	−	0.220124i
$555$		0			0
$556$	456.287	−	148.257i	0.820661	−	0.266649i
$557$	337.599	−	464.666i	0.606103	−	0.834229i	−0.390147	−	0.920753i	$-0.627576\pi$
$557$	337.599	−	464.666i	0.606103	−	0.834229i	0.996250	+	0.0865234i	$0.0275757\pi$
$558$	558.284	+	768.412i	1.00051	+	1.37708i
$559$	−34.9833	+	107.668i	−0.0625820	+	0.192608i
$560$		0			0
$561$	64.1714	−	13.6914i	0.114387	−	0.0244054i
$562$	1110.31			1.97565
$563$	166.603	+	54.1325i	0.295920	+	0.0961502i	0.453214	−	0.891402i	$-0.350277\pi$
$563$	166.603	+	54.1325i	0.295920	+	0.0961502i	−0.157295	+	0.987552i	$0.550277\pi$
$564$	123.658	−	89.8432i	0.219253	−	0.159296i
$565$		0			0
$566$	102.691	+	316.052i	0.181434	+	0.558395i
$567$	842.379	−	273.705i	1.48568	−	0.482726i
$568$	72.4601	−	99.7328i	0.127571	−	0.175586i
$569$	−172.026	−	236.774i	−0.302331	−	0.416122i	0.630640	−	0.776076i	$-0.282793\pi$
$569$	−172.026	−	236.774i	−0.302331	−	0.416122i	−0.932970	+	0.359953i	$0.882793\pi$
$570$		0			0
$571$		−	836.204i		−	1.46446i	−0.681060	−	0.732228i	$-0.738481\pi$
$571$		−	836.204i		−	1.46446i	0.681060	−	0.732228i	$-0.261519\pi$
$572$	−24.0244	+	230.274i	−0.0420008	+	0.402577i
$573$	237.111			0.413807
$574$	215.075	+	69.8822i	0.374696	+	0.121746i
$575$		0			0
$576$	96.8085	+	70.3355i	0.168070	+	0.122110i
$577$	284.811	+	876.557i	0.493606	+	1.51916i	0.819118	+	0.573626i	$0.194464\pi$
$577$	284.811	+	876.557i	0.493606	+	1.51916i	−0.325511	+	0.945538i	$0.605536\pi$
$578$	−539.255	+	175.215i	−0.932968	+	0.303140i
$579$	95.0683	−	130.850i	0.164194	−	0.225994i
$580$		0			0
$581$	−517.288	+	1592.05i	−0.890341	+	2.74019i
$582$		−	56.5977i		−	0.0972469i
$583$	−487.716	+	282.082i	−0.836563	+	0.483845i
$584$	−224.643			−0.384663
$585$		0			0
$586$	565.953	−	411.189i	0.965790	−	0.701688i
$587$	−212.702	−	154.537i	−0.362354	−	0.263266i	0.391679	−	0.920102i	$-0.371894\pi$
$587$	−212.702	−	154.537i	−0.362354	−	0.263266i	−0.754033	+	0.656836i	$0.771894\pi$
$588$	72.3236	+	222.589i	0.122999	+	0.378553i
$589$	1073.69	−	348.863i	1.82291	−	0.592298i
$590$		0			0
$591$	−0.636888	−	0.876602i	−0.00107765	−	0.00148325i
$592$	85.5128	−	263.181i	0.144447	−	0.444563i
$593$		−	124.297i		−	0.209606i	−0.994493	−	0.104803i	$-0.966579\pi$
$593$		−	124.297i		−	0.209606i	0.994493	−	0.104803i	$-0.0334213\pi$
$594$	238.366	−	265.141i	0.401290	−	0.446365i
$595$		0			0
$596$	−410.834	−	133.488i	−0.689318	−	0.223973i
$597$	38.1204	−	27.6961i	0.0638533	−	0.0463921i
$598$	−89.8757	−	65.2985i	−0.150294	−	0.109195i
$599$	24.5601	+	75.5882i	0.0410018	+	0.126191i	0.969462	−	0.245241i	$-0.0788670\pi$
$599$	24.5601	+	75.5882i	0.0410018	+	0.126191i	−0.928460	+	0.371432i	$0.878867\pi$
$600$		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	$0.0415749\pi$
$602$	−278.348	−	383.113i	−0.462372	−	0.636400i
$603$	−229.832	+	707.351i	−0.381148	+	1.17305i
$604$		−	426.039i		−	0.705363i
$605$		0			0
$606$	−95.9957			−0.158409
$607$	−451.568	−	146.723i	−0.743934	−	0.241719i	−0.0875652	−	0.996159i	$-0.527909\pi$
$607$	−451.568	−	146.723i	−0.743934	−	0.241719i	−0.656369	+	0.754440i	$0.727909\pi$
$608$	755.590	−	548.968i	1.24275	−	0.902908i
$609$	−248.514	−	180.556i	−0.408069	−	0.296480i
$610$		0			0
$611$	−626.956	+	203.710i	−1.02611	+	0.333405i
$612$	107.097	−	147.406i	0.174995	−	0.240860i
$613$	−515.537	−	709.576i	−0.841007	−	1.15755i	−0.985773	−	0.168081i	$-0.946243\pi$
$613$	−515.537	−	709.576i	−0.841007	−	1.15755i	0.144766	−	0.989466i	$-0.453757\pi$
$614$	271.403	−	835.291i	0.442024	−	1.36041i
$615$		0			0
$616$	387.706	+	348.554i	0.629392	+	0.565835i
$617$	−401.953			−0.651464			−0.325732	−	0.945462i	$-0.605611\pi$
$617$	−401.953			−0.651464			−0.325732	+	0.945462i	$0.605611\pi$
$618$	−121.977	−	39.6326i	−0.197373	−	0.0641305i
$619$	−165.411	+	120.178i	−0.267223	+	0.194149i	−0.713325	−	0.700833i	$-0.752812\pi$
$619$	−165.411	+	120.178i	−0.267223	+	0.194149i	0.446102	+	0.894982i	$0.352812\pi$
$620$		0			0
$621$	20.8270	+	64.0991i	0.0335379	+	0.103219i
$622$	−375.822	+	122.112i	−0.604216	+	0.196322i
$623$	−338.601	+	466.044i	−0.543500	+	0.748064i
$624$	67.4465	+	92.8322i	0.108087	+	0.148770i
$625$		0			0
$626$			24.2001i			0.0386583i
$627$	−102.923	−	177.954i	−0.164152	−	0.283818i
$628$	484.198			0.771016
$629$	−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	$0.834345\pi$
$632$	−139.420	−	429.089i	−0.220601	−	0.678939i
$633$	−169.828	+	55.1804i	−0.268291	+	0.0871729i
$634$	340.822	−	469.101i	0.537574	−	0.739907i
$635$		0			0
$636$	29.7061	−	91.4260i	0.0467077	−	0.143752i
$637$		−	1009.40i		−	1.58461i
$638$	907.609	+	94.6906i	1.42258	+	0.148418i
$639$	−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	$0.368421\pi$
$642$	89.0791	+	64.7197i	0.138752	+	0.100810i
$643$	−48.9645	−	150.697i	−0.0761501	−	0.234366i	0.905735	−	0.423845i	$-0.139320\pi$
$643$	−48.9645	−	150.697i	−0.0761501	−	0.234366i	−0.981885	+	0.189479i	$0.939320\pi$
$644$	174.114	−	56.5731i	0.270364	−	0.0878464i
$645$		0			0
$646$	−323.117	−	444.733i	−0.500182	−	0.688441i
$647$	315.537	−	971.123i	0.487692	−	1.50096i	−0.340351	−	0.940298i	$-0.610546\pi$
$647$	315.537	−	971.123i	0.487692	−	1.50096i	0.828044	−	0.560664i	$-0.189454\pi$
$648$			241.677i			0.372958i
$649$	123.416	+	578.449i	0.190164	+	0.891293i
$650$		0			0
$651$	−394.488	−	128.177i	−0.605973	−	0.196892i
$652$	−513.147	+	372.823i	−0.787036	+	0.571815i
$653$	−83.0990	−	60.3750i	−0.127257	−	0.0924579i	0.522336	−	0.852740i	$-0.325061\pi$
$653$	−83.0990	−	60.3750i	−0.127257	−	0.0924579i	−0.649593	+	0.760282i	$0.725061\pi$
$654$	−46.3628	−	142.690i	−0.0708912	−	0.218181i
$655$		0			0
$656$	−77.1005	+	106.120i	−0.117531	+	0.161768i
$657$	311.331	+	428.510i	0.473868	+	0.652223i
$658$	852.124	−	2622.57i	1.29502	−	3.98567i
$659$		−	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	$0.810723\pi$
$662$	430.415	+	139.850i	0.650174	+	0.211254i
$663$	39.0628	−	28.3808i	0.0589183	−	0.0428067i
$664$	−369.523	−	268.474i	−0.556511	−	0.404329i
$665$		0			0
$666$	−291.907	+	94.8464i	−0.438299	+	0.142412i
$667$	−101.393	+	139.556i	−0.152014	+	0.209230i
$668$	37.2720	+	51.3005i	0.0557964	+	0.0767971i
$669$	−59.1164	+	181.942i	−0.0883654	+	0.271961i
$670$		0			0
$671$	−40.3142	−	17.9120i	−0.0600807	−	0.0266945i
$672$	−343.149			−0.510639
$673$	2.23290	+	0.725514i	0.00331783	+	0.00107803i	0.310675	−	0.950516i	$-0.399445\pi$
$673$	2.23290	+	0.725514i	0.00331783	+	0.00107803i	−0.307358	+	0.951594i	$0.599445\pi$
$674$	−396.760	+	288.263i	−0.588665	+	0.427690i
$675$		0			0
$676$	−83.1469	−	255.900i	−0.122998	−	0.378550i
$677$	−15.8049	+	5.13532i	−0.0233455	+	0.00758541i	−0.320666	−	0.947192i	$-0.603907\pi$
$677$	−15.8049	+	5.13532i	−0.0233455	+	0.00758541i	0.297321	+	0.954778i	$0.403907\pi$
$678$	−19.2674	+	26.5193i	−0.0284180	+	0.0391140i
$679$	−236.442	−	325.435i	−0.348221	−	0.479285i
$680$		0			0
$681$			266.468i			0.391289i
$682$	1205.09	−	257.114i	1.76699	−	0.377000i
$683$	560.470			0.820600			0.410300	−	0.911951i	$-0.365424\pi$
$683$	560.470			0.820600			0.410300	+	0.911951i	$0.365424\pi$
$684$	−542.907	−	176.401i	−0.793723	−	0.257896i
$685$		0			0
$686$	2073.68	+	1506.62i	3.02285	+	2.19623i
$687$	−17.3470	−	53.3887i	−0.0252504	−	0.0777128i
$688$	261.234	−	84.8800i	0.379700	−	0.123372i
$689$	−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	$0.00168136\pi$
$692$		−	150.647i		−	0.217699i
$693$	127.555	−	1222.61i	0.184062	−	1.76423i
$694$	510.960			0.736254
$695$		0			0
$696$	67.8086	−	49.2658i	0.0974261	−	0.0707842i
$697$	44.6541	+	32.4431i	0.0640661	+	0.0465468i
$698$	−162.739	−	500.858i	−0.233150	−	0.717562i
$699$	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	$0.774737\pi$
$702$	81.0745	−	249.522i	0.115491	−	0.355444i
$703$			364.817i			0.518943i
$704$	134.382	−	77.7229i	0.190884	−	0.110402i
$705$		0			0
$706$	472.828	+	153.631i	0.669729	+	0.217608i
$707$	−551.972	+	401.031i	−0.780724	+	0.567229i
$708$	−81.6438	−	59.3177i	−0.115316	−	0.0837821i
$709$	34.0103	+	104.673i	0.0479694	+	0.147634i	0.972172	−	0.234268i	$-0.0752692\pi$
$709$	34.0103	+	104.673i	0.0479694	+	0.147634i	−0.924203	+	0.381902i	$0.875269\pi$
$710$		0			0
$711$	−625.273	+	860.615i	−0.879428	+	1.21043i
$712$	−92.3893	−	127.163i	−0.129760	−	0.178600i
$713$	−71.9794	+	221.530i	−0.100953	+	0.310701i
$714$			201.974i			0.282877i
$715$		0			0
$716$	−0.292731			−0.000408842
$717$	96.6117	+	31.3910i	0.134744	+	0.0437811i
$718$	173.101	−	125.765i	0.241087	−	0.175160i
$719$	442.734	+	321.665i	0.615763	+	0.447378i	0.851439	−	0.524453i	$-0.175730\pi$
$719$	442.734	+	321.665i	0.615763	+	0.447378i	−0.235676	+	0.971832i	$0.575730\pi$
$720$		0			0
$721$	−866.930	+	281.683i	−1.20240	+	0.390683i
$722$	−467.191	+	643.033i	−0.647078	+	0.890627i
$723$	−112.563	−	154.929i	−0.155688	−	0.214286i
$724$	21.8030	−	67.1026i	0.0301146	−	0.0926831i
$725$		0			0
$726$	−91.5766	−	204.839i	−0.126139	−	0.282148i
$727$	−321.509			−0.442241			−0.221121	−	0.975246i	$-0.570971\pi$
$727$	−321.509			−0.442241			−0.221121	+	0.975246i	$0.570971\pi$
$728$	364.866	+	118.552i	0.501190	+	0.162847i
$729$	394.697	−	286.764i	0.541422	−	0.393366i
$730$		0			0
$731$	−35.7167	−	109.925i	−0.0488600	−	0.150376i
$732$	7.15847	−	2.32593i	0.00977933	−	0.00317750i
$733$	−39.5078	+	54.3778i	−0.0538988	+	0.0741853i	−0.835116	−	0.550074i	$-0.814599\pi$
$733$	−39.5078	+	54.3778i	−0.0538988	+	0.0741853i	0.781217	+	0.624260i	$0.214599\pi$
$734$	1009.77	+	1389.82i	1.37570	+	1.89349i
$735$		0			0
$736$			192.700i			0.261820i
$737$	717.545	+	645.086i	0.973602	+	0.875286i
$738$	145.488			0.197139
$739$	−143.429	−	46.6030i	−0.194086	−	0.0630622i	0.210361	−	0.977624i	$-0.432536\pi$
$739$	−143.429	−	46.6030i	−0.194086	−	0.0630622i	−0.404447	+	0.914561i	$0.632536\pi$
$740$		0			0
$741$	−122.384	−	88.9172i	−0.165161	−	0.119996i
$742$	−535.920	−	1649.39i	−0.722264	−	2.22290i
$743$	177.637	−	57.7178i	0.239081	−	0.0776820i	−0.187026	−	0.982355i	$-0.559885\pi$
$743$	177.637	−	57.7178i	0.239081	−	0.0776820i	0.426107	+	0.904673i	$0.359885\pi$
$744$	66.5243	−	91.5628i	0.0894144	−	0.123068i
$745$		0			0
$746$	84.5073	−	260.087i	0.113281	−	0.348642i
$747$			1076.95i			1.44169i
$748$	−118.345	−	204.618i	−0.158216	−	0.273554i
$749$	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	$0.475086\pi$
$752$	1293.99	+	940.142i	1.72074	+	1.25019i
$753$	−58.8467	−	181.111i	−0.0781496	−	0.240520i
$754$	638.637	−	207.506i	0.846999	−	0.275207i
$755$		0			0
$756$	254.135	+	349.786i	0.336157	+	0.462680i
$757$	−265.519	+	817.184i	−0.350752	+	1.07950i	0.607680	+	0.794182i	$0.292100\pi$
$757$	−265.519	+	817.184i	−0.350752	+	1.07950i	−0.958432	+	0.285322i	$0.907900\pi$
$758$			1372.64i			1.81087i
$759$	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	$0.316490\pi$
$762$	177.885	−	129.241i	0.233445	−	0.169608i
$763$	−862.685	−	626.778i	−1.13065	−	0.821465i
$764$	−263.957	−	812.375i	−0.345493	−	1.06332i
$765$		0			0
$766$	−41.2426	+	56.7656i	−0.0538415	+	0.0741065i
$767$	255.828	+	352.117i	0.333544	+	0.459084i
$768$	74.4956	−	229.274i	0.0969994	−	0.298534i
$769$			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
$772$	−554.142	−	180.052i	−0.717801	−	0.233228i
$773$	989.787	−	719.122i	1.28045	−	0.930300i	0.280882	−	0.959742i	$-0.409373\pi$
$773$	989.787	−	719.122i	1.28045	−	0.930300i	0.999566	+	0.0294422i	$0.00937308\pi$
$774$	−246.474	−	179.074i	−0.318441	−	0.231361i
$775$		0			0
$776$	104.387	−	33.9174i	0.134519	−	0.0437080i
$777$	78.7859	−	108.439i	0.101398	−	0.139562i
$778$	−1025.31	−	1411.21i	−1.31787	−	1.81390i
$779$	53.4376	−	164.464i	0.0685977	−	0.211122i
$780$		0			0
$781$	−153.110	+	344.601i	−0.196043	+	0.441230i
$782$	113.421			0.145040
$783$	−387.449	−	125.890i	−0.494827	−	0.160779i
$784$	−1981.36	+	1439.54i	−2.52725	+	1.83615i
$785$		0			0
$786$	−100.548	−	309.454i	−0.127923	−	0.393708i
$787$	113.951	−	37.0249i	0.144792	−	0.0470456i	−0.235725	−	0.971820i	$-0.575746\pi$
$787$	113.951	−	37.0249i	0.144792	−	0.0470456i	0.380516	+	0.924774i	$0.375746\pi$
$788$	−2.29436	+	3.15791i	−0.00291162	+	0.00400750i
$789$	176.330	+	242.697i	0.223485	+	0.307601i
$790$		0			0
$791$			232.976i			0.294534i
$792$	306.515	+	136.188i	0.387013	+	0.171954i
$793$	−32.4622			−0.0409359
$794$	−659.163	−	214.175i	−0.830180	−	0.269742i
$795$		0			0
$796$	−137.327	−	99.7738i	−0.172521	−	0.125344i
$797$	−184.404	−	567.539i	−0.231373	−	0.712094i	−0.997582	−	0.0695017i	$-0.977859\pi$
$797$	−184.404	−	567.539i	−0.231373	−	0.712094i	0.766209	−	0.642592i	$-0.222141\pi$
$798$	601.815	−	195.542i	0.754155	−	0.245040i
$799$	395.602	−	544.500i	0.495121	−	0.681476i
$800$		0			0
$801$	−114.524	+	352.468i	−0.142976	+	0.440035i
$802$		−	113.224i		−	0.141177i
$803$	672.024	−	143.381i	0.836892	−	0.178557i
$804$	−164.631			−0.204764
$805$		0			0
$806$	733.568	−	532.968i	0.910134	−	0.661251i
$807$	−40.9711	−	29.7672i	−0.0507696	−	0.0368863i
$808$	−57.5275	−	177.051i	−0.0711974	−	0.219123i
$809$	−268.262	+	87.1635i	−0.331597	+	0.107742i	−0.470083	−	0.882622i	$-0.655776\pi$
$809$	−268.262	+	87.1635i	−0.331597	+	0.107742i	0.138487	+	0.990364i	$0.455776\pi$
$810$		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	$0.775704\pi$
$812$	−341.959	+	1052.44i	−0.421131	+	1.29611i
$813$			310.722i			0.382192i
$814$	−41.3184	+	396.036i	−0.0507596	+	0.486531i
$815$		0			0
$816$	−111.418	−	36.2020i	−0.136542	−	0.0443652i
$817$	−292.959	+	212.847i	−0.358579	+	0.260523i
$818$	−151.545	−	110.104i	−0.185263	−	0.134601i
$819$	−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	$0.0614544\pi$
$822$	173.931	+	239.395i	0.211595	+	0.291235i
$823$	−330.747	+	1017.93i	−0.401879	+	1.23686i	0.521594	+	0.853194i	$0.325338\pi$
$823$	−330.747	+	1017.93i	−0.401879	+	1.23686i	−0.923473	+	0.383663i	$0.874662\pi$
$824$		−	248.720i		−	0.301845i
$825$		0			0
$826$	−1820.62			−2.20414
$827$	−1365.00	−	443.516i	−1.65054	−	0.536295i	−0.671687	−	0.740835i	$-0.734430\pi$
$827$	−1365.00	−	443.516i	−1.65054	−	0.536295i	−0.978858	+	0.204541i	$0.934430\pi$
$828$	95.2860	−	69.2293i	0.115080	−	0.0836103i
$829$	75.5393	+	54.8825i	0.0911209	+	0.0662032i	0.632413	−	0.774631i	$-0.282065\pi$
$829$	75.5393	+	54.8825i	0.0911209	+	0.0662032i	−0.541292	+	0.840835i	$0.682065\pi$
$830$		0			0
$831$	55.4369	−	18.0125i	0.0667111	−	0.0216757i
$832$	67.1460	−	92.4186i	0.0807044	−	0.111080i
$833$	605.745	+	833.736i	0.727185	+	1.00088i
$834$	−105.730	+	325.402i	−0.126774	+	0.390170i
$835$		0			0
$836$	−495.117	+	550.731i	−0.592245	+	0.658769i
$837$	−550.102			−0.657231
$838$	−113.329	−	36.8228i	−0.135237	−	0.0439413i
$839$	−995.583	+	723.334i	−1.18663	+	0.862138i	−0.992904	−	0.118918i	$-0.962058\pi$
$839$	−995.583	+	723.334i	−1.18663	+	0.862138i	−0.193727	+	0.981056i	$0.562058\pi$
$840$		0			0
$841$	−62.3252	−	191.817i	−0.0741085	−	0.228082i
$842$	764.163	−	248.292i	0.907558	−	0.294883i
$843$	−183.358	+	252.370i	−0.217506	+	0.299372i
$844$	378.111	+	520.425i	0.447999	+	0.616617i
$845$		0			0
$846$		−	1774.04i		−	2.09698i
$847$	−1382.30	−	795.247i	−1.63199	−	0.938899i
$848$	1005.94			1.18625
$849$	−88.7959	−	28.8515i	−0.104589	−	0.0339830i
$850$		0			0
$851$	−60.8955	−	44.2432i	−0.0715576	−	0.0519896i
$852$	−19.8817	−	61.1897i	−0.0233354	−	0.0718189i
$853$	−709.882	+	230.655i	−0.832218	+	0.270404i	−0.693979	−	0.719995i	$-0.744144\pi$
$853$	−709.882	+	230.655i	−0.832218	+	0.270404i	−0.138239	+	0.990399i	$0.544144\pi$
$854$	79.8154	−	109.856i	0.0934606	−	0.128638i
$855$		0			0
$856$	−65.9844	+	203.079i	−0.0770846	+	0.237242i
$857$			1009.05i			1.17742i	0.808344	+	0.588710i	$0.200364\pi$
$857$			1009.05i			1.17742i	−0.808344	+	0.588710i	$0.799636\pi$
$858$	−122.787	−	110.387i	−0.143108	−	0.128656i
$859$	666.482			0.775882			0.387941	−	0.921684i	$-0.373187\pi$
$859$	666.482			0.775882			0.387941	+	0.921684i	$0.373187\pi$
$860$		0			0
$861$	−51.4016	+	37.3455i	−0.0596999	+	0.0433745i
$862$	−1115.79	−	810.672i	−1.29443	−	0.940455i
$863$	98.2329	+	302.330i	0.113827	+	0.350324i	0.991701	−	0.128569i	$-0.0410383\pi$
$863$	98.2329	+	302.330i	0.113827	+	0.350324i	−0.877873	+	0.478893i	$0.841038\pi$
$864$	−432.817	+	140.631i	−0.500946	+	0.162767i
$865$		0			0
$866$	292.194	+	402.171i	0.337406	+	0.464400i
$867$	49.2272	−	151.506i	0.0567788	−	0.174747i
$868$			1494.26i			1.72150i
$869$	690.947	+	1194.64i	0.795106	+	1.37473i
$870$		0			0
$871$	675.275	+	219.410i	0.775287	+	0.251906i
$872$	235.389	−	171.020i	0.269942	−	0.196124i
$873$	−209.367	−	152.114i	−0.239824	−	0.174243i
$874$	−109.809	−	337.957i	−0.125639	−	0.386678i
$875$		0			0
$876$	−68.9135	+	94.8513i	−0.0786683	+	0.108278i
$877$	725.623	+	998.734i	0.827392	+	1.13881i	0.988403	+	0.151855i	$0.0485247\pi$
$877$	725.623	+	998.734i	0.827392	+	1.13881i	−0.161011	+	0.986953i	$0.551475\pi$
$878$	−391.080	+	1203.62i	−0.445421	+	1.37087i
$879$			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	$0.328741\pi$
$882$	2583.46	+	839.417i	2.92909	+	0.951720i
$883$	18.6896	−	13.5788i	0.0211660	−	0.0153780i	−0.577152	−	0.816637i	$-0.695836\pi$
$883$	18.6896	−	13.5788i	0.0211660	−	0.0153780i	0.598318	+	0.801259i	$0.295836\pi$
$884$	−140.722	−	102.240i	−0.159188	−	0.115657i
$885$		0			0
$886$	−182.272	+	59.2238i	−0.205725	+	0.0668441i
$887$	902.007	−	1241.51i	1.01692	−	1.39967i	0.102578	−	0.994725i	$-0.467291\pi$
$887$	902.007	−	1241.51i	1.01692	−	1.39967i	0.914341	−	0.404944i	$-0.132709\pi$
$888$	21.4972	+	29.5884i	0.0242086	+	0.0333202i
$889$	482.917	−	1486.26i	0.543213	−	1.67184i
$890$		0			0
$891$	−154.253	−	722.979i	−0.173124	−	0.811425i
$892$	689.166			0.772607
$893$	−2005.43	−	651.603i	−2.24572	−	0.729679i
$894$	249.229	−	181.076i	0.278780	−	0.202546i
$895$		0			0
$896$	−439.975	−	1354.10i	−0.491044	−	1.51128i
$897$	29.6842	−	9.64499i	0.0330928	−	0.0107525i
$898$	−1015.99	+	1398.39i	−1.13139	+	1.55723i
$899$	−827.576	−	1139.06i	−0.920552	−	1.26703i
$900$		0			0
$901$		−	423.289i		−	0.469799i
$902$	76.6374	−	172.486i	0.0849638	−	0.191226i
$903$	133.047			0.147338
$904$	−60.4578	−	19.6439i	−0.0668780	−	0.0217300i
$905$		0			0
$906$	245.804	+	178.587i	0.271307	+	0.197116i
$907$	−115.701	−	356.091i	−0.127565	−	0.392603i	0.866795	−	0.498665i	$-0.166176\pi$
$907$	−115.701	−	356.091i	−0.127565	−	0.392603i	−0.994360	+	0.106061i	$0.966176\pi$
$908$	912.953	−	296.636i	1.00546	−	0.326692i
$909$	−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	$0.986105\pi$
$912$			367.038i			0.402454i
$913$	1276.79	+	567.292i	1.39846	+	0.621349i
$914$	1452.05			1.58867
$915$		0			0
$916$	−163.606	+	118.867i	−0.178609	+	0.129767i
$917$	−1870.92	−	1359.30i	−2.04026	−	1.48234i
$918$	82.7740	+	254.752i	0.0901678	+	0.277508i
$919$	−844.869	+	274.515i	−0.919335	+	0.298710i	−0.730194	−	0.683240i	$-0.760570\pi$
$919$	−844.869	+	274.515i	−0.919335	+	0.298710i	−0.189141	+	0.981950i	$0.560570\pi$
$920$		0			0
$921$	145.039	+	199.629i	0.157480	+	0.216753i
$922$	589.519	−	1814.35i	0.639391	−	1.96784i
$923$			277.483i			0.300631i
$924$	266.106	−	56.7757i	0.287993	−	0.0614455i
$925$		0			0
$926$	683.007	+	221.922i	0.737589	+	0.239657i
$927$	−474.438	+	344.699i	−0.511799	+	0.371844i
$928$	−942.328	−	684.641i	−1.01544	−	0.737760i
$929$	−461.175	−	1419.35i	−0.496421	−	1.52783i	−0.814730	−	0.579841i	$-0.803115\pi$
$929$	−461.175	−	1419.35i	−0.496421	−	1.52783i	0.318309	−	0.947987i	$-0.396885\pi$
$930$		0			0
$931$	1897.80	−	2612.10i	2.03845	−	2.80569i
$932$	−332.847	−	458.124i	−0.357132	−	0.491550i
$933$	34.3079	−	105.589i	0.0367716	−	0.113171i
$934$			1963.09i			2.10181i
$935$		0			0
$936$	246.815			0.263691
$937$	79.6229	+	25.8710i	0.0849764	+	0.0276105i	0.351197	−	0.936302i	$-0.385775\pi$
$937$	79.6229	+	25.8710i	0.0849764	+	0.0276105i	−0.266220	+	0.963912i	$0.585775\pi$
$938$	−2402.83	+	1745.75i	−2.56165	+	1.86115i
$939$	−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	$0.180322\pi$
$942$	−202.966	+	279.359i	−0.215463	+	0.296559i
$943$	20.9718	+	28.8652i	0.0222394	+	0.0306100i
$944$	326.330	−	1004.34i	0.345688	−	1.06392i
$945$		0			0
$946$	−342.136	+	197.882i	−0.361666	+	0.209177i
$947$	934.828			0.987147			0.493574	−	0.869704i	$-0.335690\pi$
$947$	934.828			0.987147			0.493574	+	0.869704i	$0.335690\pi$
$948$	−223.944	−	72.7638i	−0.236228	−	0.0767551i
$949$	409.079	−	297.213i	0.431063	−	0.313186i
$950$		0			0
$951$	50.3415	+	154.935i	0.0529353	+	0.162918i
$952$	−372.515	+	121.037i	−0.391297	+	0.127140i
$953$	556.381	−	765.792i	0.583820	−	0.803560i	−0.410287	−	0.911956i	$-0.634572\pi$
$953$	556.381	−	765.792i	0.583820	−	0.803560i	0.994108	+	0.108397i	$0.0345716\pi$
$954$	−655.813	−	902.649i	−0.687435	−	0.946173i
$955$		0			0
$956$		−	365.949i		−	0.382792i
$957$	−171.406	+	190.659i	−0.179107	+	0.199226i
$958$	−1611.20			−1.68183
$959$	2000.19	+	649.902i	2.08571	+	0.677687i
$960$		0			0
$961$	−760.623	−	552.625i	−0.791491	−	0.575052i
$962$	90.5455	+	278.670i	0.0941221	+	0.289678i
$963$	478.823	−	155.579i	0.497220	−	0.161557i
$964$	−405.501	+	558.124i	−0.420644	+	0.578967i
$965$		0			0
$966$	−40.3452	+	124.170i	−0.0417652	+	0.128540i
$967$			196.064i			0.202755i	0.994848	+	0.101378i	$0.0323251\pi$
$967$			196.064i			0.202755i	−0.994848	+	0.101378i	$0.967675\pi$
$968$	322.919	−	291.655i	0.333594	−	0.301297i
$969$	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	$0.231178\pi$
$972$	340.904	+	247.681i	0.350724	+	0.254816i
$973$	751.456	+	2312.74i	0.772308	+	2.37692i
$974$	−409.868	+	133.174i	−0.420809	+	0.136729i
$975$		0			0
$976$	46.2957	+	63.7206i	0.0474341	+	0.0652875i
$977$	−334.314	+	1028.91i	−0.342184	+	1.05313i	0.620890	+	0.783898i	$0.286771\pi$
$977$	−334.314	+	1028.91i	−0.342184	+	1.05313i	−0.963074	+	0.269237i	$0.913229\pi$
$978$		−	452.341i		−	0.462517i
$979$	357.547	+	321.441i	0.365217	+	0.328336i
$980$		0			0
$981$	−652.446	−	211.993i	−0.665083	−	0.216099i
$982$	−686.777	+	498.973i	−0.699366	+	0.508119i
$983$	−440.888	−	320.324i	−0.448512	−	0.325863i	0.340496	−	0.940246i	$-0.389405\pi$
$983$	−440.888	−	320.324i	−0.448512	−	0.325863i	−0.789008	+	0.614383i	$0.789405\pi$
$984$	−5.35717	−	16.4877i	−0.00544428	−	0.0167558i
$985$		0			0
$986$	−402.973	+	554.645i	−0.408695	+	0.562520i
$987$	455.380	+	626.777i	0.461378	+	0.635032i
$988$	−168.402	+	518.288i	−0.170447	+	0.524583i
$989$		−	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	$0.838405\pi$
$992$	−1495.84	−	486.028i	−1.50790	−	0.489947i
$993$	−102.866	+	74.7368i	−0.103592	+	0.0752637i
$994$	−939.039	−	682.252i	−0.944708	−	0.686370i
$995$		0			0
$996$	−226.716	+	73.6645i	−0.227626	+	0.0739603i
$997$	326.870	−	449.898i	0.327854	−	0.451252i	−0.612991	−	0.790090i	$-0.710034\pi$
$997$	326.870	−	449.898i	0.327854	−	0.451252i	0.940845	+	0.338838i	$0.110034\pi$
$998$	1176.58	+	1619.43i	1.17894	+	1.62268i
$999$	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.x.h.101.6	✓	28
5.2	odd	4		275.3.q.g.24.3		56
5.3	odd	4		275.3.q.g.24.12		56
5.4	even	2		275.3.x.i.101.2	yes	28
11.6	odd	10	inner	275.3.x.h.226.6	yes	28
55.17	even	20		275.3.q.g.149.12		56
55.28	even	20		275.3.q.g.149.3		56
55.39	odd	10		275.3.x.i.226.2	yes	28

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

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.x (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.44335 + 0.793893i) q^{2} +(-0.583945 + 0.424261i) q^{3} +(2.10363 + 1.52838i) q^{4} +(-1.76360 + 0.573029i) q^{6} +(-7.74676 + 10.6625i) q^{7} +(-2.11375 - 2.90933i) q^{8} +(-2.62016 + 8.06402i) q^{9} +(8.18023 + 7.35417i) q^{11} -1.87684 q^{12} +(7.69834 + 2.50134i) q^{13} +(-27.3929 + 19.9021i) q^{14} +(-6.06901 - 18.6785i) q^{16} +(-7.85972 + 2.55378i) q^{17} +(-12.8039 + 17.6231i) q^{18} +(15.2188 + 20.9469i) q^{19} -9.51297i q^{21} +(14.1488 + 24.4631i) q^{22} -5.34212 q^{23} +(2.46863 + 0.802107i) q^{24} +(16.8240 + 12.2233i) q^{26} +(-3.89865 - 11.9988i) q^{27} +(-32.5927 + 10.5900i) q^{28} +(18.9800 - 26.1237i) q^{29} +(13.4739 - 41.4685i) q^{31} -36.0717i q^{32} +(-7.89690 - 0.823881i) q^{33} -21.2315 q^{34} +(-17.8367 + 12.9591i) q^{36} +(11.3991 + 8.28194i) q^{37} +(20.5553 + 63.2626i) q^{38} +(-5.55664 + 1.80546i) q^{39} +(-3.92574 - 5.40332i) q^{41} +(7.55228 - 23.2435i) q^{42} +13.9858i q^{43} +(5.96824 + 27.9730i) q^{44} +(-13.0527 - 4.24108i) q^{46} +(-65.8866 + 47.8694i) q^{47} +(11.4685 + 8.33237i) q^{48} +(-38.5348 - 118.598i) q^{49} +(3.50618 - 4.82584i) q^{51} +(12.3715 + 17.0279i) q^{52} +(-15.8277 + 48.7128i) q^{53} -32.4124i q^{54} +47.3954 q^{56} +(-17.7739 - 5.77508i) q^{57} +(67.1142 - 48.7613i) q^{58} +(43.5007 + 31.6051i) q^{59} +(-3.81411 + 1.23928i) q^{61} +(65.8431 - 90.6252i) q^{62} +(-65.6849 - 90.4074i) q^{63} +(4.36107 - 13.4220i) q^{64} +(-18.6408 - 8.28232i) q^{66} +87.7170 q^{67} +(-20.4371 - 6.64042i) q^{68} +(3.11951 - 2.26646i) q^{69} +(10.5932 + 32.6025i) q^{71} +(28.9992 - 9.42243i) q^{72} +(36.7178 - 50.5378i) q^{73} +(21.2771 + 29.2854i) q^{74} +67.3246i q^{76} +(-141.784 + 30.2507i) q^{77} -15.0102 q^{78} +(119.320 + 38.7694i) q^{79} +(-54.3698 - 39.5019i) q^{81} +(-5.30231 - 16.3188i) q^{82} +(120.797 - 39.2492i) q^{83} +(14.5394 - 20.0118i) q^{84} +(-11.1032 + 34.1723i) q^{86} +23.3073i q^{87} +(4.10473 - 39.3439i) q^{88} +43.7087 q^{89} +(-86.3078 + 62.7063i) q^{91} +(-11.2379 - 8.16479i) q^{92} +(9.72543 + 29.9318i) q^{93} +(-198.987 + 64.6549i) q^{94} +(15.3038 + 21.0639i) q^{96} +(-9.43164 + 29.0276i) q^{97} -320.369i q^{98} +(-80.7377 + 46.6964i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 5 q^{2} + 14 q^{3} + 9 q^{4} + 30 q^{6} + 5 q^{7} + 15 q^{8} - 31 q^{9} - 5 q^{11} - 4 q^{12} - 45 q^{13} + 37 q^{14} - 35 q^{16} + 5 q^{17} + 35 q^{18} + 80 q^{19} - 50 q^{22} + 34 q^{23} - 13 q^{26}+ \cdots - 609 q^{99}+O(q^{100}) \) 28 * q - 5 * q^2 + 14 * q^3 + 9 * q^4 + 30 * q^6 + 5 * q^7 + 15 * q^8 - 31 * q^9 - 5 * q^11 - 4 * q^12 - 45 * q^13 + 37 * q^14 - 35 * q^16 + 5 * q^17 + 35 * q^18 + 80 * q^19 - 50 * q^22 + 34 * q^23 - 13 * q^26 - 118 * q^27 - 145 * q^28 - 95 * q^29 + 95 * q^31 - 381 * q^33 - 148 * q^34 - 347 * q^36 + 146 * q^37 - 10 * q^38 - 65 * q^39 - 290 * q^41 + 615 * q^42 - 253 * q^44 - 110 * q^46 - 179 * q^47 + 364 * q^48 + 224 * q^49 + 400 * q^51 - 185 * q^52 + 344 * q^53 + 884 * q^56 - 430 * q^57 + 265 * q^58 + 67 * q^59 + 135 * q^61 + 155 * q^62 + 220 * q^63 - 119 * q^64 + 250 * q^66 - 204 * q^67 + 45 * q^68 + 311 * q^69 - 189 * q^71 - 235 * q^72 - 5 * q^73 + 940 * q^74 - 215 * q^77 + 290 * q^78 + 565 * q^79 - 583 * q^81 - 195 * q^82 - 530 * q^83 - 1050 * q^84 + 207 * q^86 - 1930 * q^88 + 146 * q^89 - 783 * q^91 + 521 * q^92 - 57 * q^93 - 845 * q^94 - 1210 * q^96 + 506 * q^97 - 609 * q^99

Introduction

L-functions

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