LMFDB - Embedded newform 87.3.b.a.59.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [87,3,Mod(59,87)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(87, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("87.59");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	87.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.37057829993$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 54 x^{16} + 1187 x^{14} + 13673 x^{12} + 88449 x^{10} + 318861 x^{8} + 593533 x^{6} + \cdots + 15341 $ x^18 + 54x^16 + 1187x^14 + 13673x^12 + 88449x^10 + 318861x^8 + 593533x^6 + 482583x^4 + 152462x^2 + 15341
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			59.9
Root			$-0.441441i$ of defining polynomial
Character	$\chi$	$=$	87.59
Dual form			87.3.b.a.59.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.441441i q^{2} +(1.48935 - 2.60419i) q^{3} +3.80513 q^{4} +7.32676i q^{5} +(-1.14960 - 0.657462i) q^{6} +4.23094 q^{7} -3.44551i q^{8} +(-4.56366 - 7.75713i) q^{9} +O(q^{10})$	\(q-0.441441i q^{2} +(1.48935 - 2.60419i) q^{3} +3.80513 q^{4} +7.32676i q^{5} +(-1.14960 - 0.657462i) q^{6} +4.23094 q^{7} -3.44551i q^{8} +(-4.56366 - 7.75713i) q^{9} +3.23433 q^{10} -5.69130i q^{11} +(5.66718 - 9.90930i) q^{12} -22.0660 q^{13} -1.86771i q^{14} +(19.0803 + 10.9121i) q^{15} +13.6995 q^{16} -3.36182i q^{17} +(-3.42432 + 2.01459i) q^{18} -0.875689 q^{19} +27.8793i q^{20} +(6.30136 - 11.0182i) q^{21} -2.51237 q^{22} +31.2196i q^{23} +(-8.97277 - 5.13157i) q^{24} -28.6814 q^{25} +9.74082i q^{26} +(-26.9980 + 0.331543i) q^{27} +16.0993 q^{28} -5.38516i q^{29} +(4.81707 - 8.42283i) q^{30} -44.7335 q^{31} -19.8296i q^{32} +(-14.8212 - 8.47635i) q^{33} -1.48405 q^{34} +30.9991i q^{35} +(-17.3653 - 29.5169i) q^{36} +15.6339 q^{37} +0.386565i q^{38} +(-32.8640 + 57.4640i) q^{39} +25.2444 q^{40} -14.0863i q^{41} +(-4.86388 - 2.78168i) q^{42} +81.6804 q^{43} -21.6561i q^{44} +(56.8346 - 33.4368i) q^{45} +13.7816 q^{46} +36.9933i q^{47} +(20.4034 - 35.6762i) q^{48} -31.0991 q^{49} +12.6612i q^{50} +(-8.75484 - 5.00694i) q^{51} -83.9638 q^{52} +68.5629i q^{53} +(0.146357 + 11.9180i) q^{54} +41.6988 q^{55} -14.5777i q^{56} +(-1.30421 + 2.28046i) q^{57} -2.37723 q^{58} -109.129i q^{59} +(72.6031 + 41.5221i) q^{60} +27.5344 q^{61} +19.7472i q^{62} +(-19.3086 - 32.8199i) q^{63} +46.0445 q^{64} -161.672i q^{65} +(-3.74181 + 6.54271i) q^{66} -41.8242 q^{67} -12.7922i q^{68} +(81.3019 + 46.4970i) q^{69} +13.6843 q^{70} -14.3032i q^{71} +(-26.7272 + 15.7241i) q^{72} -25.3387 q^{73} -6.90145i q^{74} +(-42.7168 + 74.6920i) q^{75} -3.33211 q^{76} -24.0795i q^{77} +(25.3670 + 14.5075i) q^{78} +42.1483 q^{79} +100.373i q^{80} +(-39.3461 + 70.8017i) q^{81} -6.21829 q^{82} -12.9517i q^{83} +(23.9775 - 41.9256i) q^{84} +24.6313 q^{85} -36.0571i q^{86} +(-14.0240 - 8.02041i) q^{87} -19.6094 q^{88} -107.318i q^{89} +(-14.7604 - 25.0891i) q^{90} -93.3597 q^{91} +118.795i q^{92} +(-66.6239 + 116.495i) q^{93} +16.3304 q^{94} -6.41596i q^{95} +(-51.6400 - 29.5332i) q^{96} +42.9570 q^{97} +13.7284i q^{98} +(-44.1481 + 25.9731i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{3} - 36 q^{4} + 8 q^{6} - 12 q^{7} - 22 q^{9}+O(q^{10}) $ 18 * q - 2 * q^3 - 36 * q^4 + 8 * q^6 - 12 * q^7 - 22 * q^9	$ 18 q - 2 q^{3} - 36 q^{4} + 8 q^{6} - 12 q^{7} - 22 q^{9} + 12 q^{10} + 18 q^{12} + 32 q^{13} + 30 q^{15} + 76 q^{16} - 50 q^{18} - 24 q^{19} + 32 q^{21} - 94 q^{22} + 38 q^{24} - 114 q^{25} - 68 q^{27} + 94 q^{28} - 88 q^{30} + 24 q^{31} - 20 q^{33} + 70 q^{34} + 168 q^{36} - 40 q^{37} + 38 q^{39} + 160 q^{40} - 118 q^{42} - 36 q^{43} + 32 q^{45} - 228 q^{46} + 94 q^{48} + 190 q^{49} + 204 q^{51} - 386 q^{52} - 32 q^{54} + 188 q^{55} - 140 q^{57} - 354 q^{60} - 8 q^{61} - 340 q^{63} + 86 q^{64} + 178 q^{66} + 136 q^{67} + 4 q^{69} + 252 q^{70} + 358 q^{72} - 68 q^{73} + 244 q^{75} + 120 q^{76} + 66 q^{78} - 96 q^{79} + 366 q^{81} - 548 q^{82} - 664 q^{84} - 320 q^{85} + 504 q^{88} + 562 q^{90} - 156 q^{91} - 40 q^{93} - 174 q^{94} - 504 q^{96} - 12 q^{97} - 198 q^{99}+O(q^{100}) $ 18 * q - 2 * q^3 - 36 * q^4 + 8 * q^6 - 12 * q^7 - 22 * q^9 + 12 * q^10 + 18 * q^12 + 32 * q^13 + 30 * q^15 + 76 * q^16 - 50 * q^18 - 24 * q^19 + 32 * q^21 - 94 * q^22 + 38 * q^24 - 114 * q^25 - 68 * q^27 + 94 * q^28 - 88 * q^30 + 24 * q^31 - 20 * q^33 + 70 * q^34 + 168 * q^36 - 40 * q^37 + 38 * q^39 + 160 * q^40 - 118 * q^42 - 36 * q^43 + 32 * q^45 - 228 * q^46 + 94 * q^48 + 190 * q^49 + 204 * q^51 - 386 * q^52 - 32 * q^54 + 188 * q^55 - 140 * q^57 - 354 * q^60 - 8 * q^61 - 340 * q^63 + 86 * q^64 + 178 * q^66 + 136 * q^67 + 4 * q^69 + 252 * q^70 + 358 * q^72 - 68 * q^73 + 244 * q^75 + 120 * q^76 + 66 * q^78 - 96 * q^79 + 366 * q^81 - 548 * q^82 - 664 * q^84 - 320 * q^85 + 504 * q^88 + 562 * q^90 - 156 * q^91 - 40 * q^93 - 174 * q^94 - 504 * q^96 - 12 * q^97 - 198 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	0.441441i		−	0.220721i	−0.993892	−	0.110360i	$-0.964800\pi$
$2$		−	0.441441i		−	0.220721i	0.993892	−	0.110360i	$-0.0352005\pi$
$3$	1.48935	−	2.60419i	0.496451	−	0.868065i
$3$	1.48935	−	2.60419i	0.496451	−	0.868065i
$4$	3.80513			0.951282
$5$			7.32676i			1.46535i	0.680577	+	0.732676i	$0.261729\pi$
$5$			7.32676i			1.46535i	−0.680577	+	0.732676i	$0.738271\pi$
$6$	−1.14960	−	0.657462i	−0.191600	−	0.109577i
$7$	4.23094			0.604420			0.302210	−	0.953241i	$-0.402276\pi$
$7$	4.23094			0.604420			0.302210	+	0.953241i	$0.402276\pi$
$8$		−	3.44551i		−	0.430688i
$9$	−4.56366	−	7.75713i	−0.507073	−	0.861903i
$10$	3.23433			0.323433
$11$		−	5.69130i		−	0.517391i	−0.965959	−	0.258695i	$-0.916707\pi$
$11$		−	5.69130i		−	0.517391i	0.965959	−	0.258695i	$-0.0832925\pi$
$12$	5.66718	−	9.90930i	0.472265	−	0.825775i
$13$	−22.0660			−1.69738			−0.848691	−	0.528890i	$-0.822609\pi$
$13$	−22.0660			−1.69738			−0.848691	+	0.528890i	$0.822609\pi$
$14$		−	1.86771i		−	0.133408i
$15$	19.0803	+	10.9121i	1.27202	+	0.727476i
$16$	13.6995			0.856221
$17$		−	3.36182i		−	0.197754i	−0.995100	−	0.0988772i	$-0.968475\pi$
$17$		−	3.36182i		−	0.197754i	0.995100	−	0.0988772i	$-0.0315251\pi$
$18$	−3.42432	+	2.01459i	−0.190240	+	0.111921i
$19$	−0.875689			−0.0460889			−0.0230444	−	0.999734i	$-0.507336\pi$
$19$	−0.875689			−0.0460889			−0.0230444	+	0.999734i	$0.507336\pi$
$20$			27.8793i			1.39396i
$21$	6.30136	−	11.0182i	0.300065	−	0.524676i
$22$	−2.51237			−0.114199
$23$			31.2196i			1.35737i	0.734428	+	0.678687i	$0.237451\pi$
$23$			31.2196i			1.35737i	−0.734428	+	0.678687i	$0.762549\pi$
$24$	−8.97277	−	5.13157i	−0.373865	−	0.213816i
$25$	−28.6814			−1.14726
$26$			9.74082i			0.374647i
$27$	−26.9980	+	0.331543i	−0.999925	+	0.0122794i
$28$	16.0993			0.574974
$29$		−	5.38516i		−	0.185695i
$29$		−	5.38516i		−	0.185695i
$30$	4.81707	−	8.42283i	0.160569	−	0.280761i
$31$	−44.7335			−1.44302			−0.721508	−	0.692406i	$-0.756551\pi$
$31$	−44.7335			−1.44302			−0.721508	+	0.692406i	$0.756551\pi$
$32$		−	19.8296i		−	0.619674i
$33$	−14.8212	−	8.47635i	−0.449128	−	0.256859i
$34$	−1.48405			−0.0436484
$35$			30.9991i			0.885688i
$36$	−17.3653	−	29.5169i	−0.482369	−	0.819913i
$37$	15.6339			0.422538			0.211269	−	0.977428i	$-0.432240\pi$
$37$	15.6339			0.422538			0.211269	+	0.977428i	$0.432240\pi$
$38$			0.386565i			0.0101728i
$39$	−32.8640	+	57.4640i	−0.842667	+	1.47344i
$40$	25.2444			0.631110
$41$		−	14.0863i		−	0.343569i	−0.985135	−	0.171785i	$-0.945047\pi$
$41$		−	14.0863i		−	0.343569i	0.985135	−	0.171785i	$-0.0549533\pi$
$42$	−4.86388	−	2.78168i	−0.115807	−	0.0662305i
$43$	81.6804			1.89954			0.949772	−	0.312944i	$-0.101315\pi$
$43$	81.6804			1.89954			0.949772	+	0.312944i	$0.101315\pi$
$44$		−	21.6561i		−	0.492185i
$45$	56.8346	−	33.4368i	1.26299	−	0.743040i
$46$	13.7816			0.299600
$47$			36.9933i			0.787091i	0.919305	+	0.393546i	$0.128752\pi$
$47$			36.9933i			0.787091i	−0.919305	+	0.393546i	$0.871248\pi$
$48$	20.4034	−	35.6762i	0.425072	−	0.743255i
$49$	−31.0991			−0.634676
$50$			12.6612i			0.253223i
$51$	−8.75484	−	5.00694i	−0.171664	−	0.0981753i
$52$	−83.9638			−1.61469
$53$			68.5629i			1.29364i	0.762642	+	0.646820i	$0.223902\pi$
$53$			68.5629i			1.29364i	−0.762642	+	0.646820i	$0.776098\pi$
$54$	0.146357	+	11.9180i	0.00271031	+	0.220704i
$55$	41.6988			0.758159
$56$		−	14.5777i		−	0.260317i
$57$	−1.30421	+	2.28046i	−0.0228809	+	0.0400081i
$58$	−2.37723			−0.0409868
$59$		−	109.129i		−	1.84964i	−0.380403	−	0.924821i	$-0.624215\pi$
$59$		−	109.129i		−	1.84964i	0.380403	−	0.924821i	$-0.375785\pi$
$60$	72.6031	+	41.5221i	1.21005	+	0.692035i
$61$	27.5344			0.451384			0.225692	−	0.974199i	$-0.427536\pi$
$61$	27.5344			0.451384			0.225692	+	0.974199i	$0.427536\pi$
$62$			19.7472i			0.318503i
$63$	−19.3086	−	32.8199i	−0.306485	−	0.520952i
$64$	46.0445			0.719446
$65$		−	161.672i		−	2.48726i
$66$	−3.74181	+	6.54271i	−0.0566941	+	0.0991319i
$67$	−41.8242			−0.624242			−0.312121	−	0.950042i	$-0.601040\pi$
$67$	−41.8242			−0.624242			−0.312121	+	0.950042i	$0.601040\pi$
$68$		−	12.7922i		−	0.188120i
$69$	81.3019	+	46.4970i	1.17829	+	0.673869i
$70$	13.6843			0.195490
$71$		−	14.3032i		−	0.201453i	−0.994914	−	0.100726i	$-0.967883\pi$
$71$		−	14.3032i		−	0.201453i	0.994914	−	0.100726i	$-0.0321167\pi$
$72$	−26.7272	+	15.7241i	−0.371212	+	0.218390i
$73$	−25.3387			−0.347106			−0.173553	−	0.984825i	$-0.555525\pi$
$73$	−25.3387			−0.347106			−0.173553	+	0.984825i	$0.555525\pi$
$74$		−	6.90145i		−	0.0932629i
$75$	−42.7168	+	74.6920i	−0.569557	+	0.995894i
$76$	−3.33211			−0.0438435
$77$		−	24.0795i		−	0.312721i
$78$	25.3670	+	14.5075i	0.325218	+	0.185994i
$79$	42.1483			0.533523			0.266761	−	0.963763i	$-0.414046\pi$
$79$	42.1483			0.533523			0.266761	+	0.963763i	$0.414046\pi$
$80$			100.373i			1.25466i
$81$	−39.3461	+	70.8017i	−0.485754	+	0.874095i
$82$	−6.21829			−0.0758328
$83$		−	12.9517i		−	0.156045i	−0.996952	−	0.0780224i	$-0.975139\pi$
$83$		−	12.9517i		−	0.156045i	0.996952	−	0.0780224i	$-0.0248606\pi$
$84$	23.9775	−	41.9256i	0.285446	−	0.499115i
$85$	24.6313			0.289780
$86$		−	36.0571i		−	0.419268i
$87$	−14.0240	−	8.02041i	−0.161196	−	0.0921886i
$88$	−19.6094			−0.222834
$89$		−	107.318i		−	1.20582i	−0.797810	−	0.602909i	$-0.794008\pi$
$89$		−	107.318i		−	1.20582i	0.797810	−	0.602909i	$-0.205992\pi$
$90$	−14.7604	−	25.0891i	−0.164004	−	0.278768i
$91$	−93.3597			−1.02593
$92$			118.795i			1.29125i
$93$	−66.6239	+	116.495i	−0.716386	+	1.25263i
$94$	16.3304			0.173727
$95$		−	6.41596i		−	0.0675364i
$96$	−51.6400	−	29.5332i	−0.537917	−	0.307638i
$97$	42.9570			0.442856			0.221428	−	0.975177i	$-0.428928\pi$
$97$	42.9570			0.442856			0.221428	+	0.975177i	$0.428928\pi$
$98$			13.7284i			0.140086i
$99$	−44.1481	+	25.9731i	−0.445941	+	0.262355i
$100$	−109.137			−1.09137
$101$		−	117.873i		−	1.16706i	−0.812092	−	0.583530i	$-0.801671\pi$
$101$		−	117.873i		−	1.16706i	0.812092	−	0.583530i	$-0.198329\pi$
$102$	−2.21027	+	3.86475i	−0.0216693	+	0.0378897i
$103$	−28.1802			−0.273594			−0.136797	−	0.990599i	$-0.543681\pi$
$103$	−28.1802			−0.273594			−0.136797	+	0.990599i	$0.543681\pi$
$104$			76.0284i			0.731042i
$105$	80.7277	+	46.1686i	0.768835	+	0.439701i
$106$	30.2665			0.285533
$107$		−	54.7666i		−	0.511837i	−0.966698	−	0.255919i	$-0.917622\pi$
$107$		−	54.7666i		−	0.511837i	0.966698	−	0.255919i	$-0.0823779\pi$
$108$	−102.731	+	1.26156i	−0.951211	+	0.0116812i
$109$	140.962			1.29323			0.646616	−	0.762816i	$-0.276184\pi$
$109$	140.962			1.29323			0.646616	+	0.762816i	$0.276184\pi$
$110$		−	18.4076i		−	0.167341i
$111$	23.2844	−	40.7137i	0.209769	−	0.366790i
$112$	57.9619			0.517517
$113$			192.153i			1.70047i	0.526403	+	0.850235i	$0.323540\pi$
$113$			192.153i			1.70047i	−0.526403	+	0.850235i	$0.676460\pi$
$114$	1.00669	+	0.575732i	0.00883062	+	0.00505028i
$115$	−228.738			−1.98903
$116$		−	20.4913i		−	0.176649i
$117$	100.701	+	171.168i	0.860696	+	1.46298i
$118$	−48.1740			−0.408254
$119$		−	14.2237i		−	0.119527i
$120$	37.5978	−	65.7413i	0.313315	−	0.547844i
$121$	88.6092			0.732307
$122$		−	12.1548i		−	0.0996298i
$123$	−36.6836	−	20.9795i	−0.298240	−	0.170565i
$124$	−170.217			−1.37272
$125$		−	26.9730i		−	0.215784i
$126$	−14.4881	+	8.52359i	−0.114985	+	0.0676475i
$127$	9.67891			0.0762119			0.0381059	−	0.999274i	$-0.487868\pi$
$127$	9.67891			0.0762119			0.0381059	+	0.999274i	$0.487868\pi$
$128$		−	99.6442i		−	0.778470i
$129$	121.651	−	212.712i	0.943030	−	1.64893i
$130$	−71.3687			−0.548990
$131$			231.267i			1.76540i	0.469938	+	0.882699i	$0.344276\pi$
$131$			231.267i			1.76540i	−0.469938	+	0.882699i	$0.655724\pi$
$132$	−56.3967	−	32.2536i	−0.427248	−	0.244345i
$133$	−3.70499			−0.0278570
$134$			18.4629i			0.137783i
$135$	−2.42914	−	197.808i	−0.0179936	−	1.46524i
$136$	−11.5832			−0.0851704
$137$		−	207.823i		−	1.51696i	−0.651698	−	0.758479i	$-0.725943\pi$
$137$		−	207.823i		−	1.51696i	0.651698	−	0.758479i	$-0.274057\pi$
$138$	20.5257	−	35.8900i	0.148737	−	0.260072i
$139$	208.114			1.49722			0.748611	−	0.663009i	$-0.230721\pi$
$139$	208.114			1.49722			0.748611	+	0.663009i	$0.230721\pi$
$140$			117.956i			0.842540i
$141$	96.3377	+	55.0961i	0.683246	+	0.390752i
$142$	−6.31400			−0.0444648
$143$			125.584i			0.878209i
$144$	−62.5199	−	106.269i	−0.434166	−	0.737979i
$145$	39.4558			0.272109
$146$			11.1856i			0.0766134i
$147$	−46.3176	+	80.9882i	−0.315086	+	0.550940i
$148$	59.4891			0.401953
$149$			1.05418i			0.00707504i	0.999994	+	0.00353752i	$0.00112603\pi$
$149$			1.05418i			0.00707504i	−0.999994	+	0.00353752i	$0.998874\pi$
$150$	32.9721	+	18.8569i	0.219814	+	0.125713i
$151$	−107.353			−0.710947			−0.355473	−	0.934686i	$-0.615680\pi$
$151$	−107.353			−0.710947			−0.355473	+	0.934686i	$0.615680\pi$
$152$			3.01719i			0.0198499i
$153$	−26.0781	+	15.3422i	−0.170445	+	0.100276i
$154$	−10.6297			−0.0690240
$155$		−	327.752i		−	2.11453i
$156$	−125.052	+	218.658i	−0.801614	+	1.40165i
$157$	150.300			0.957324			0.478662	−	0.877999i	$-0.341122\pi$
$157$	150.300			0.957324			0.478662	+	0.877999i	$0.341122\pi$
$158$		−	18.6060i		−	0.117759i
$159$	178.551	+	102.114i	1.12296	+	0.642229i
$160$	145.286			0.908040
$161$			132.088i			0.820424i
$162$	31.2548	+	17.3690i	0.192931	+	0.107216i
$163$	53.5303			0.328407			0.164203	−	0.986427i	$-0.447495\pi$
$163$	53.5303			0.328407			0.164203	+	0.986427i	$0.447495\pi$
$164$		−	53.6003i		−	0.326831i
$165$	62.1042	−	108.592i	0.376389	−	0.658131i
$166$	−5.71742			−0.0344423
$167$			205.350i			1.22964i	0.788668	+	0.614819i	$0.210771\pi$
$167$			205.350i			1.22964i	−0.788668	+	0.614819i	$0.789229\pi$
$168$	−37.9632	−	21.7114i	−0.225972	−	0.129234i
$169$	317.906			1.88110
$170$		−	10.8733i		−	0.0639604i
$171$	3.99634	+	6.79283i	0.0233704	+	0.0397241i
$172$	310.804			1.80700
$173$		−	80.5035i		−	0.465338i	−0.972556	−	0.232669i	$-0.925254\pi$
$173$		−	80.5035i		−	0.465338i	0.972556	−	0.232669i	$-0.0747459\pi$
$174$	−3.54054	+	6.19078i	−0.0203479	+	0.0355792i
$175$	−121.349			−0.693425
$176$		−	77.9681i		−	0.443000i
$177$	−284.193	−	162.531i	−1.60561	−	0.918256i
$178$	−47.3745			−0.266149
$179$			20.3960i			0.113944i	0.998376	+	0.0569720i	$0.0181446\pi$
$179$			20.3960i			0.113944i	−0.998376	+	0.0569720i	$0.981855\pi$
$180$	216.263	−	127.231i	1.20146	−	0.706841i
$181$	−261.826			−1.44655			−0.723275	−	0.690560i	$-0.757364\pi$
$181$	−261.826			−1.44655			−0.723275	+	0.690560i	$0.757364\pi$
$182$			41.2128i			0.226444i
$183$	41.0085	−	71.7050i	0.224090	−	0.391831i
$184$	107.567			0.584605
$185$			114.546i			0.619167i
$186$	51.4255	+	29.4105i	0.276481	+	0.158121i
$187$	−19.1331			−0.102316
$188$			140.764i			0.748746i
$189$	−114.227	+	1.40274i	−0.604374	+	0.00742190i
$190$	−2.83227			−0.0149067
$191$			105.816i			0.554012i	0.960868	+	0.277006i	$0.0893422\pi$
$191$			105.816i			0.554012i	−0.960868	+	0.277006i	$0.910658\pi$
$192$	68.5766	−	119.909i	0.357170	−	0.624526i
$193$	−313.905			−1.62645			−0.813226	−	0.581948i	$-0.802291\pi$
$193$	−313.905			−1.62645			−0.813226	+	0.581948i	$0.802291\pi$
$194$		−	18.9630i		−	0.0977474i
$195$	−421.025	−	240.787i	−2.15910	−	1.23480i
$196$	−118.336			−0.603757
$197$		−	350.630i		−	1.77985i	−0.456110	−	0.889923i	$-0.650758\pi$
$197$		−	350.630i		−	1.77985i	0.456110	−	0.889923i	$-0.349242\pi$
$198$	11.4656	+	19.4888i	0.0579071	+	0.0984283i
$199$	−37.8726			−0.190315			−0.0951573	−	0.995462i	$-0.530335\pi$
$199$	−37.8726			−0.190315			−0.0951573	+	0.995462i	$0.530335\pi$
$200$			98.8220i			0.494110i
$201$	−62.2911	+	108.918i	−0.309906	+	0.541883i
$202$	−52.0340			−0.257594
$203$		−	22.7843i		−	0.112238i
$204$	−33.3133	−	19.0521i	−0.163301	−	0.0933925i
$205$	103.207			0.503450
$206$			12.4399i			0.0603878i
$207$	242.174	−	142.475i	1.16992	−	0.688287i
$208$	−302.293			−1.45333
$209$			4.98380i			0.0238459i
$210$	20.3807	−	35.6365i	0.0970510	−	0.169698i
$211$	−41.4281			−0.196342			−0.0981709	−	0.995170i	$-0.531299\pi$
$211$	−41.4281			−0.196342			−0.0981709	+	0.995170i	$0.531299\pi$
$212$			260.891i			1.23062i
$213$	−37.2482	−	21.3024i	−0.174874	−	0.100011i
$214$	−24.1762			−0.112973
$215$			598.453i			2.78350i
$216$	1.14233	+	93.0216i	0.00528858	+	0.430656i
$217$	−189.265			−0.872187
$218$		−	62.2265i		−	0.285443i
$219$	−37.7383	+	65.9869i	−0.172321	+	0.301310i
$220$	158.669			0.721224
$221$			74.1818i			0.335664i
$222$	−17.9727	−	10.2787i	−0.0809582	−	0.0463004i
$223$	−176.378			−0.790931			−0.395465	−	0.918481i	$-0.629417\pi$
$223$	−176.378			−0.790931			−0.395465	+	0.918481i	$0.629417\pi$
$224$		−	83.8977i		−	0.374543i
$225$	130.892	+	222.486i	0.581743	+	0.988825i
$226$	84.8243			0.375329
$227$			346.393i			1.52596i	0.646421	+	0.762981i	$0.276265\pi$
$227$			346.393i			1.52596i	−0.646421	+	0.762981i	$0.723735\pi$
$228$	−4.96269	+	8.67746i	−0.0217662	+	0.0380590i
$229$	156.940			0.685330			0.342665	−	0.939458i	$-0.388670\pi$
$229$	156.940			0.685330			0.342665	+	0.939458i	$0.388670\pi$
$230$			100.975i			0.439020i
$231$	−62.7078	−	35.8629i	−0.271462	−	0.155251i
$232$	−18.5546			−0.0799768
$233$			10.3189i			0.0442873i	0.999755	+	0.0221436i	$0.00704911\pi$
$233$			10.3189i			0.0442873i	−0.999755	+	0.0221436i	$0.992951\pi$
$234$	75.5608	−	44.4538i	0.322909	−	0.189973i
$235$	−271.041			−1.15337
$236$		−	415.249i		−	1.75953i
$237$	62.7737	−	109.762i	0.264868	−	0.463132i
$238$	−6.27892			−0.0263820
$239$		−	155.478i		−	0.650536i	−0.945622	−	0.325268i	$-0.894545\pi$
$239$		−	155.478i		−	0.650536i	0.945622	−	0.325268i	$-0.105455\pi$
$240$	261.391	+	149.491i	1.08913	+	0.622880i
$241$	130.357			0.540900			0.270450	−	0.962734i	$-0.412828\pi$
$241$	130.357			0.540900			0.270450	+	0.962734i	$0.412828\pi$
$242$		−	39.1157i		−	0.161635i
$243$	125.781	+	207.914i	0.517618	+	0.855612i
$244$	104.772			0.429394
$245$		−	227.856i		−	0.930025i
$246$	−9.26123	+	16.1936i	−0.0376473	+	0.0658278i
$247$	19.3229			0.0782304
$248$			154.129i			0.621490i
$249$	−33.7288	−	19.2897i	−0.135457	−	0.0774686i
$250$	−11.9070			−0.0476280
$251$			100.309i			0.399637i	0.979833	+	0.199819i	$0.0640353\pi$
$251$			100.309i			0.399637i	−0.979833	+	0.199819i	$0.935965\pi$
$252$	−73.4716	−	124.884i	−0.291554	−	0.495572i
$253$	177.680			0.702292
$254$		−	4.27267i		−	0.0168215i
$255$	36.6847	−	64.1446i	0.143861	−	0.251548i
$256$	140.191			0.547622
$257$			232.677i			0.905358i	0.891674	+	0.452679i	$0.149532\pi$
$257$			232.677i			0.905358i	−0.891674	+	0.452679i	$0.850468\pi$
$258$	−93.8996	−	53.7017i	−0.363952	−	0.208146i
$259$	66.1461			0.255391
$260$		−	615.183i		−	2.36609i
$261$	−41.7734	+	24.5760i	−0.160051	+	0.0941611i
$262$	102.091			0.389660
$263$		−	62.3829i		−	0.237197i	−0.992942	−	0.118599i	$-0.962160\pi$
$263$		−	62.3829i		−	0.237197i	0.992942	−	0.118599i	$-0.0378402\pi$
$264$	−29.2053	+	51.0667i	−0.110626	+	0.193434i
$265$	−502.344			−1.89564
$266$			1.63553i			0.00614862i
$267$	−279.476	−	159.834i	−1.04673	−	0.598630i
$268$	−159.147			−0.593831
$269$		−	259.279i		−	0.963861i	−0.876210	−	0.481930i	$-0.839936\pi$
$269$		−	259.279i		−	0.963861i	0.876210	−	0.481930i	$-0.160064\pi$
$270$	−87.3204	+	1.07232i	−0.323409	+	0.00397156i
$271$	−209.892			−0.774509			−0.387254	−	0.921973i	$-0.626576\pi$
$271$	−209.892			−0.774509			−0.387254	+	0.921973i	$0.626576\pi$
$272$		−	46.0554i		−	0.169321i
$273$	−139.046	+	243.127i	−0.509325	+	0.890575i
$274$	−91.7417			−0.334824
$275$			163.235i			0.593580i
$276$	309.364	+	176.927i	1.12088	+	0.641040i
$277$	82.1661			0.296628			0.148314	−	0.988940i	$-0.452615\pi$
$277$	82.1661			0.296628			0.148314	+	0.988940i	$0.452615\pi$
$278$		−	91.8701i		−	0.330468i
$279$	204.148	+	347.003i	0.731714	+	1.24374i
$280$	106.808			0.381455
$281$		−	12.8968i		−	0.0458961i	−0.999737	−	0.0229481i	$-0.992695\pi$
$281$		−	12.8968i		−	0.0458961i	0.999737	−	0.0229481i	$-0.00730524\pi$
$282$	24.3217	−	42.5274i	0.0862471	−	0.150807i
$283$	70.0813			0.247637			0.123819	−	0.992305i	$-0.460486\pi$
$283$	70.0813			0.247637			0.123819	+	0.992305i	$0.460486\pi$
$284$		−	54.4254i		−	0.191639i
$285$	−16.7084	−	9.55563i	−0.0586260	−	0.0335285i
$286$	55.4379			0.193839
$287$		−	59.5984i		−	0.207660i
$288$	−153.820	+	90.4953i	−0.534099	+	0.314220i
$289$	277.698			0.960893
$290$		−	17.4174i		−	0.0600601i
$291$	63.9782	−	111.868i	0.219856	−	0.384428i
$292$	−96.4171			−0.330196
$293$		−	290.998i		−	0.993166i	−0.867989	−	0.496583i	$-0.834588\pi$
$293$		−	290.998i		−	0.993166i	0.867989	−	0.496583i	$-0.165412\pi$
$294$	35.7515	+	20.4465i	0.121604	+	0.0695459i
$295$	799.561			2.71038
$296$		−	53.8667i		−	0.181982i
$297$	1.88691	+	153.653i	0.00635323	+	0.517352i
$298$	0.465359			0.00156161
$299$		−	688.890i		−	2.30398i
$300$	−162.543	+	284.213i	−0.541810	+	0.947376i
$301$	345.585			1.14812
$302$			47.3900i			0.156921i
$303$	−306.964	−	175.555i	−1.01308	−	0.579388i
$304$	−11.9965			−0.0394622
$305$			201.738i			0.661437i
$306$	6.77268	+	11.5119i	0.0221329	+	0.0376207i
$307$	264.495			0.861546			0.430773	−	0.902460i	$-0.358241\pi$
$307$	264.495			0.861546			0.430773	+	0.902460i	$0.358241\pi$
$308$		−	91.6257i		−	0.297486i
$309$	−41.9702	+	73.3866i	−0.135826	+	0.237497i
$310$	−144.683			−0.466719
$311$		−	369.447i		−	1.18793i	−0.804490	−	0.593967i	$-0.797561\pi$
$311$		−	369.447i		−	1.18793i	0.804490	−	0.593967i	$-0.202439\pi$
$312$	197.993	+	113.233i	0.634592	+	0.362927i
$313$	−376.681			−1.20345			−0.601726	−	0.798702i	$-0.705520\pi$
$313$	−376.681			−1.20345			−0.601726	+	0.798702i	$0.705520\pi$
$314$		−	66.3486i		−	0.211301i
$315$	240.464	−	141.469i	0.763378	−	0.449108i
$316$	160.380			0.507531
$317$			385.773i			1.21695i	0.793573	+	0.608475i	$0.208218\pi$
$317$			385.773i			1.21695i	−0.793573	+	0.608475i	$0.791782\pi$
$318$	45.0775	−	78.8199i	0.141753	−	0.247861i
$319$	−30.6486			−0.0960770
$320$			337.357i			1.05424i
$321$	−142.623	−	81.5668i	−0.444308	−	0.254102i
$322$	58.3092			0.181084
$323$			2.94391i			0.00911427i
$324$	−149.717	+	269.410i	−0.462089	+	0.831512i
$325$	632.883			1.94733
$326$		−	23.6305i		−	0.0724861i
$327$	209.943	−	367.093i	0.642026	−	1.12261i
$328$	−48.5346			−0.147971
$329$			156.516i			0.475734i
$330$	−47.9368	−	27.4153i	−0.145263	−	0.0830768i
$331$	−233.205			−0.704545			−0.352273	−	0.935897i	$-0.614591\pi$
$331$	−233.205			−0.704545			−0.352273	+	0.935897i	$0.614591\pi$
$332$		−	49.2829i		−	0.148443i
$333$	−71.3478	−	121.274i	−0.214258	−	0.364187i
$334$	90.6497			0.271406
$335$		−	306.436i		−	0.914735i
$336$	86.3257	−	150.944i	0.256922	−	0.449238i
$337$	−390.479			−1.15869			−0.579346	−	0.815082i	$-0.696692\pi$
$337$	−390.479			−1.15869			−0.579346	+	0.815082i	$0.696692\pi$
$338$		−	140.337i		−	0.415198i
$339$	500.404	+	286.184i	1.47612	+	0.844200i
$340$	93.7252			0.275662
$341$			254.591i			0.746602i
$342$	2.99863	−	1.76415i	0.00876794	−	0.00515833i
$343$	−338.895			−0.988031
$344$		−	281.430i		−	0.818111i
$345$	−340.672	+	595.679i	−0.987456	+	1.72661i
$346$	−35.5376			−0.102710
$347$			40.5501i			0.116859i	0.998292	+	0.0584295i	$0.0186093\pi$
$347$			40.5501i			0.116859i	−0.998292	+	0.0584295i	$0.981391\pi$
$348$	−53.3632	−	30.5187i	−0.153343	−	0.0876974i
$349$	−256.668			−0.735438			−0.367719	−	0.929937i	$-0.619861\pi$
$349$	−256.668			−0.735438			−0.367719	+	0.929937i	$0.619861\pi$
$350$			53.5686i			0.153053i
$351$	595.736	−	7.31581i	1.69725	−	0.0208428i
$352$	−112.856			−0.320613
$353$		−	15.9229i		−	0.0451074i	−0.999746	−	0.0225537i	$-0.992820\pi$
$353$		−	15.9229i		−	0.0451074i	0.999746	−	0.0225537i	$-0.00717967\pi$
$354$	−71.7480	+	125.454i	−0.202678	+	0.354391i
$355$	104.796			0.295199
$356$		−	408.358i		−	1.14707i
$357$	−37.0412	−	21.1841i	−0.103757	−	0.0593391i
$358$	9.00362			0.0251498
$359$			633.169i			1.76370i	0.471528	+	0.881851i	$0.343703\pi$
$359$			633.169i			1.76370i	−0.471528	+	0.881851i	$0.656297\pi$
$360$	−115.207	−	195.824i	−0.320019	−	0.543956i
$361$	−360.233			−0.997876
$362$			115.581i			0.319283i
$363$	131.970	−	230.755i	0.363555	−	0.635690i
$364$	−355.246			−0.975950
$365$		−	185.651i		−	0.508632i
$366$	−31.6535	−	18.1028i	−0.0864851	−	0.0494613i
$367$	−441.257			−1.20233			−0.601167	−	0.799123i	$-0.705297\pi$
$367$	−441.257			−1.20233			−0.601167	+	0.799123i	$0.705297\pi$
$368$			427.694i			1.16221i
$369$	−109.270	+	64.2852i	−0.296123	+	0.174215i
$370$	50.5653			0.136663
$371$			290.086i			0.781902i
$372$	−253.513	+	443.277i	−0.681486	+	1.19161i
$373$	−309.317			−0.829268			−0.414634	−	0.909988i	$-0.636090\pi$
$373$	−309.317			−0.829268			−0.414634	+	0.909988i	$0.636090\pi$
$374$			8.44615i			0.0225833i
$375$	−70.2429	−	40.1723i	−0.187314	−	0.107126i
$376$	127.461			0.338991
$377$			118.829i			0.315196i
$378$	0.619227	+	50.4244i	0.00163817	+	0.133398i
$379$	−74.7665			−0.197273			−0.0986366	−	0.995124i	$-0.531448\pi$
$379$	−74.7665			−0.197273			−0.0986366	+	0.995124i	$0.531448\pi$
$380$		−	24.4136i		−	0.0642462i
$381$	14.4153	−	25.2058i	0.0378355	−	0.0661568i
$382$	46.7117			0.122282
$383$			346.389i			0.904409i	0.891914	+	0.452205i	$0.149362\pi$
$383$			346.389i			0.904409i	−0.891914	+	0.452205i	$0.850638\pi$
$384$	−259.493	−	148.405i	−0.675763	−	0.386472i
$385$	176.425			0.458247
$386$			138.571i			0.358991i
$387$	−372.761	−	633.605i	−0.963207	−	1.63722i
$388$	163.457			0.421281
$389$		−	478.407i		−	1.22984i	−0.788590	−	0.614920i	$-0.789188\pi$
$389$		−	478.407i		−	1.22984i	0.788590	−	0.614920i	$-0.210812\pi$
$390$	−106.293	+	185.858i	−0.272547	+	0.476559i
$391$	104.955			0.268426
$392$			107.152i			0.273348i
$393$	602.265	+	344.439i	1.53248	+	0.876434i
$394$	−154.782			−0.392849
$395$			308.810i			0.781799i
$396$	−167.989	+	98.8311i	−0.424215	+	0.249573i
$397$	−425.040			−1.07063			−0.535315	−	0.844652i	$-0.679807\pi$
$397$	−425.040			−1.07063			−0.535315	+	0.844652i	$0.679807\pi$
$398$			16.7185i			0.0420063i
$399$	−5.51803	+	9.64850i	−0.0138297	+	0.0241817i
$400$	−392.922			−0.982306
$401$		−	254.365i		−	0.634327i	−0.948371	−	0.317163i	$-0.897270\pi$
$401$		−	254.365i		−	0.634327i	0.948371	−	0.317163i	$-0.102730\pi$
$402$	48.0811	+	27.4978i	0.119605	+	0.0684026i
$403$	987.087			2.44935
$404$		−	448.522i		−	1.11020i
$405$	−518.747	−	288.279i	−1.28086	−	0.711801i
$406$	−10.0579			−0.0247732
$407$		−	88.9772i		−	0.218617i
$408$	−17.2514	+	30.1649i	−0.0422830	+	0.0739335i
$409$	145.150			0.354891			0.177445	−	0.984131i	$-0.443217\pi$
$409$	145.150			0.354891			0.177445	+	0.984131i	$0.443217\pi$
$410$		−	45.5599i		−	0.111122i
$411$	−541.212	−	309.522i	−1.31682	−	0.753095i
$412$	−107.229			−0.260265
$413$		−	461.718i		−	1.11796i
$414$	−62.8945	−	106.906i	−0.151919	−	0.258226i
$415$	94.8941			0.228661
$416$			437.558i			1.05182i
$417$	309.955	−	541.969i	0.743298	−	1.29969i
$418$	2.20006			0.00526329
$419$			397.971i			0.949813i	0.880036	+	0.474906i	$0.157518\pi$
$419$			397.971i			0.949813i	−0.880036	+	0.474906i	$0.842482\pi$
$420$	307.179	+	175.677i	0.731379	+	0.418280i
$421$	−589.279			−1.39971			−0.699857	−	0.714283i	$-0.746753\pi$
$421$	−589.279			−1.39971			−0.699857	+	0.714283i	$0.746753\pi$
$422$			18.2881i			0.0433367i
$423$	286.962	−	168.825i	0.678397	−	0.399113i
$424$	236.234			0.557156
$425$			96.4219i			0.226875i
$426$	−9.40377	+	16.4429i	−0.0220746	+	0.0385983i
$427$	116.497			0.272826
$428$		−	208.394i		−	0.486902i
$429$	327.045	+	187.039i	0.762342	+	0.435988i
$430$	264.182			0.614376
$431$			312.416i			0.724862i	0.932011	+	0.362431i	$0.118053\pi$
$431$			312.416i			0.724862i	−0.932011	+	0.362431i	$0.881947\pi$
$432$	−369.859	+	4.54198i	−0.856156	+	0.0105139i
$433$	69.7992			0.161199			0.0805995	−	0.996747i	$-0.474317\pi$
$433$	69.7992			0.161199			0.0805995	+	0.996747i	$0.474317\pi$
$434$			83.5492i			0.192510i
$435$	58.7636	−	102.751i	0.135089	−	0.236208i
$436$	536.380			1.23023
$437$		−	27.3386i		−	0.0625598i
$438$	29.1294	+	16.6592i	0.0665054	+	0.0380348i
$439$	74.6183			0.169973			0.0849867	−	0.996382i	$-0.472915\pi$
$439$	74.6183			0.169973			0.0849867	+	0.996382i	$0.472915\pi$
$440$		−	143.673i		−	0.326530i
$441$	141.926	+	241.240i	0.321827	+	0.547030i
$442$	32.7469			0.0740881
$443$			389.117i			0.878368i	0.898397	+	0.439184i	$0.144732\pi$
$443$			389.117i			0.878368i	−0.898397	+	0.439184i	$0.855268\pi$
$444$	88.6002	−	154.921i	0.199550	−	0.348921i
$445$	786.292			1.76695
$446$			77.8603i			0.174575i
$447$	2.74529	+	1.57005i	0.00614159	+	0.00351241i
$448$	194.812			0.434848
$449$			253.815i			0.565289i	0.959225	+	0.282644i	$0.0912117\pi$
$449$			253.815i			0.565289i	−0.959225	+	0.282644i	$0.908788\pi$
$450$	98.2143	−	57.7812i	0.218254	−	0.128403i
$451$	−80.1695			−0.177759
$452$			731.168i			1.61763i
$453$	−159.886	+	279.568i	−0.352950	+	0.617148i
$454$	152.912			0.336811
$455$		−	684.025i		−	1.50335i
$456$	7.85735	+	4.49366i	0.0172310	+	0.00985452i
$457$	−272.841			−0.597025			−0.298513	−	0.954406i	$-0.596490\pi$
$457$	−272.841			−0.597025			−0.298513	+	0.954406i	$0.596490\pi$
$458$		−	69.2800i		−	0.151266i
$459$	1.11459	+	90.7624i	0.00242830	+	0.197739i
$460$	−870.380			−1.89213
$461$		−	21.4513i		−	0.0465320i	−0.999729	−	0.0232660i	$-0.992594\pi$
$461$		−	21.4513i		−	0.0465320i	0.999729	−	0.0232660i	$-0.00740647\pi$
$462$	−15.8314	+	27.6818i	−0.0342670	+	0.0599173i
$463$	384.420			0.830280			0.415140	−	0.909757i	$-0.363733\pi$
$463$	384.420			0.830280			0.415140	+	0.909757i	$0.363733\pi$
$464$		−	73.7742i		−	0.158996i
$465$	−853.529	−	488.138i	−1.83555	−	1.04976i
$466$	4.55520			0.00977511
$467$			231.956i			0.496694i	0.968671	+	0.248347i	$0.0798873\pi$
$467$			231.956i			0.496694i	−0.968671	+	0.248347i	$0.920113\pi$
$468$	383.182	+	651.318i	0.818765	+	1.39171i
$469$	−176.956			−0.377305
$470$			119.649i			0.254572i
$471$	223.850	−	391.410i	0.475265	−	0.831020i
$472$	−376.004			−0.796619
$473$		−	464.867i		−	0.982806i
$474$	−48.4536	−	27.7109i	−0.102223	−	0.0584618i
$475$	25.1160			0.0528758
$476$		−	54.1229i		−	0.113704i
$477$	531.852	−	312.898i	1.11499	−	0.655970i
$478$	−68.6344			−0.143587
$479$		−	415.289i		−	0.866992i	−0.901155	−	0.433496i	$-0.857280\pi$
$479$		−	415.289i		−	0.866992i	0.901155	−	0.433496i	$-0.142720\pi$
$480$	216.383	−	378.354i	0.450798	−	0.788238i
$481$	−344.977			−0.717208
$482$		−	57.5449i		−	0.119388i
$483$	343.983	+	196.726i	0.712181	+	0.407300i
$484$	337.169			0.696631
$485$			314.736i			0.648940i
$486$	91.7816	−	55.5250i	0.188851	−	0.114249i
$487$	167.444			0.343828			0.171914	−	0.985112i	$-0.445005\pi$
$487$	167.444			0.343828			0.171914	+	0.985112i	$0.445005\pi$
$488$		−	94.8700i		−	0.194406i
$489$	79.7255	−	139.403i	0.163038	−	0.285078i
$490$	−100.585			−0.205276
$491$		−	540.559i		−	1.10093i	−0.834857	−	0.550467i	$-0.814450\pi$
$491$		−	540.559i		−	1.10093i	0.834857	−	0.550467i	$-0.185550\pi$
$492$	−139.586	−	79.8298i	−0.283711	−	0.162256i
$493$	−18.1040			−0.0367221
$494$		−	8.52993i		−	0.0172671i
$495$	−190.299	−	323.463i	−0.384442	−	0.653460i
$496$	−612.828			−1.23554
$497$		−	60.5158i		−	0.121762i
$498$	−8.51525	+	14.8893i	−0.0170989	+	0.0298981i
$499$	−102.824			−0.206060			−0.103030	−	0.994678i	$-0.532854\pi$
$499$	−102.824			−0.206060			−0.103030	+	0.994678i	$0.532854\pi$
$500$		−	102.636i		−	0.205272i
$501$	534.770	+	305.838i	1.06741	+	0.610455i
$502$	44.2805			0.0882082
$503$			614.489i			1.22165i	0.791767	+	0.610824i	$0.209162\pi$
$503$			614.489i			1.22165i	−0.791767	+	0.610824i	$0.790838\pi$
$504$	−113.081	+	66.5277i	−0.224368	+	0.131999i
$505$	863.628			1.71015
$506$		−	78.4352i		−	0.155010i
$507$	473.475	−	827.890i	0.933876	−	1.63292i
$508$	36.8295			0.0724990
$509$			5.13770i			0.0100937i	0.999987	+	0.00504686i	$0.00160647\pi$
$509$			5.13770i			0.0100937i	−0.999987	+	0.00504686i	$0.998394\pi$
$510$	−28.3161	−	16.1941i	−0.0555217	−	0.0317532i
$511$	−107.207			−0.209798
$512$		−	460.463i		−	0.899342i
$513$	23.6418	−	0.290328i	0.0460854	−	0.000565942i
$514$	102.713			0.199831
$515$		−	206.469i		−	0.400911i
$516$	462.897	−	809.395i	0.897088	−	1.56859i
$517$	210.540			0.407234
$518$		−	29.1996i		−	0.0563699i
$519$	−209.647	−	119.898i	−0.403944	−	0.231018i
$520$	−557.042			−1.07123
$521$			693.167i			1.33046i	0.746641	+	0.665228i	$0.231665\pi$
$521$			693.167i			1.33046i	−0.746641	+	0.665228i	$0.768335\pi$
$522$	10.8489	+	18.4405i	0.0207833	+	0.0353266i
$523$	512.960			0.980804			0.490402	−	0.871496i	$-0.336850\pi$
$523$	512.960			0.980804			0.490402	+	0.871496i	$0.336850\pi$
$524$			880.002i			1.67939i
$525$	−180.732	+	316.018i	−0.344252	+	0.601938i
$526$	−27.5384			−0.0523543
$527$			150.386i			0.285363i
$528$	−203.044	−	116.122i	−0.384553	−	0.219928i
$529$	−445.663			−0.842463
$530$			221.755i			0.418407i
$531$	−846.526	+	498.026i	−1.59421	+	0.937903i
$532$	−14.0980			−0.0264999
$533$			310.828i			0.583168i
$534$	−70.5573	+	123.372i	−0.132130	+	0.231034i
$535$	401.262			0.750022
$536$			144.106i			0.268854i
$537$	53.1151	+	30.3768i	0.0989107	+	0.0565676i
$538$	−114.456			−0.212744
$539$			176.994i			0.328376i
$540$	−9.24318	−	752.684i	−0.0171170	−	1.39386i
$541$	658.522			1.21723			0.608615	−	0.793466i	$-0.291725\pi$
$541$	658.522			1.21723			0.608615	+	0.793466i	$0.291725\pi$
$542$			92.6549i			0.170950i
$543$	−389.951	+	681.845i	−0.718141	+	1.25570i
$544$	−66.6635			−0.122543
$545$			1032.80i			1.89504i
$546$	107.326	+	61.3805i	0.196568	+	0.112418i
$547$	652.360			1.19261			0.596307	−	0.802756i	$-0.296634\pi$
$547$	652.360			1.19261			0.596307	+	0.802756i	$0.296634\pi$
$548$		−	790.794i		−	1.44306i
$549$	−125.658	−	213.588i	−0.228885	−	0.389049i
$550$	72.0584			0.131015
$551$			4.71573i			0.00855849i
$552$	160.206	−	280.126i	0.290228	−	0.507475i
$553$	178.327			0.322472
$554$		−	36.2715i		−	0.0654720i
$555$	298.300	+	170.599i	0.537477	+	0.307386i
$556$	791.900			1.42428
$557$		−	382.021i		−	0.685855i	−0.939362	−	0.342927i	$-0.888582\pi$
$557$		−	382.021i		−	0.685855i	0.939362	−	0.342927i	$-0.111418\pi$
$558$	153.182	−	90.1194i	0.274519	−	0.161504i
$559$	−1802.36			−3.22425
$560$			424.673i			0.758345i
$561$	−28.4960	+	49.8264i	−0.0507950	+	0.0888171i
$562$	−5.69318			−0.0101302
$563$		−	195.678i		−	0.347564i	−0.984784	−	0.173782i	$-0.944401\pi$
$563$		−	195.678i		−	0.347564i	0.984784	−	0.173782i	$-0.0555987\pi$
$564$	366.578	+	209.648i	0.649960	+	0.371716i
$565$	−1407.86			−2.49179
$566$		−	30.9368i		−	0.0546586i
$567$	−166.471	+	299.558i	−0.293600	+	0.528321i
$568$	−49.2816			−0.0867634
$569$			51.4486i			0.0904193i	0.998978	+	0.0452096i	$0.0143956\pi$
$569$			51.4486i			0.0904193i	−0.998978	+	0.0452096i	$0.985604\pi$
$570$	−4.21825	+	7.37578i	−0.00740044	+	0.0129400i
$571$	239.593			0.419602			0.209801	−	0.977744i	$-0.432718\pi$
$571$	239.593			0.419602			0.209801	+	0.977744i	$0.432718\pi$
$572$			477.863i			0.835425i
$573$	275.566	+	157.598i	0.480918	+	0.275040i
$574$	−26.3092			−0.0458349
$575$		−	895.423i		−	1.55726i
$576$	−210.131	−	357.173i	−0.364811	−	0.620093i
$577$	−244.071			−0.423000			−0.211500	−	0.977378i	$-0.567835\pi$
$577$	−244.071			−0.423000			−0.211500	+	0.977378i	$0.567835\pi$
$578$		−	122.587i		−	0.212089i
$579$	−467.516	+	817.470i	−0.807454	+	1.41187i
$580$	150.135			0.258853
$581$		−	54.7979i		−	0.0943166i
$582$	−49.3833	−	28.2426i	−0.0848511	−	0.0485268i
$583$	390.212			0.669317
$584$			87.3047i			0.149494i
$585$	−1254.11	+	737.815i	−2.14378	+	1.26122i
$586$	−128.458			−0.219212
$587$			615.332i			1.04826i	0.851637	+	0.524132i	$0.175610\pi$
$587$			615.332i			1.04826i	−0.851637	+	0.524132i	$0.824390\pi$
$588$	−176.244	+	308.171i	−0.299736	+	0.524100i
$589$	39.1726			0.0665069
$590$		−	352.959i		−	0.598236i
$591$	−913.108	−	522.212i	−1.54502	−	0.883607i
$592$	214.177			0.361786
$593$		−	1007.29i		−	1.69864i	−0.527878	−	0.849320i	$-0.677012\pi$
$593$		−	1007.29i		−	1.69864i	0.527878	−	0.849320i	$-0.322988\pi$
$594$	67.8289	−	0.832960i	0.114190	−	0.00140229i
$595$	104.213			0.175149
$596$			4.01130i			0.00673036i
$597$	−56.4056	+	98.6276i	−0.0944818	+	0.165205i
$598$	−304.104			−0.508536
$599$		−	386.870i		−	0.645861i	−0.946423	−	0.322930i	$-0.895332\pi$
$599$		−	386.870i		−	0.645861i	0.946423	−	0.322930i	$-0.104668\pi$
$600$	257.352	+	147.181i	0.428920	+	0.245302i
$601$	−416.526			−0.693055			−0.346528	−	0.938040i	$-0.612639\pi$
$601$	−416.526			−0.693055			−0.346528	+	0.938040i	$0.612639\pi$
$602$		−	152.555i		−	0.253414i
$603$	190.871	+	324.436i	0.316536	+	0.538037i
$604$	−408.492			−0.676311
$605$			649.218i			1.07309i
$606$	−77.4970	+	135.507i	−0.127883	+	0.223608i
$607$	625.902			1.03114			0.515570	−	0.856847i	$-0.327580\pi$
$607$	625.902			1.03114			0.515570	+	0.856847i	$0.327580\pi$
$608$			17.3645i			0.0285601i
$609$	−59.3348	−	33.9339i	−0.0974298	−	0.0557207i
$610$	89.0555			0.145993
$611$		−	816.293i		−	1.33599i
$612$	−99.2305	+	58.3791i	−0.162141	+	0.0953906i
$613$	−439.362			−0.716741			−0.358370	−	0.933580i	$-0.616667\pi$
$613$	−439.362			−0.716741			−0.358370	+	0.933580i	$0.616667\pi$
$614$		−	116.759i		−	0.190161i
$615$	153.712	−	268.772i	0.249938	−	0.437027i
$616$	−82.9662			−0.134685
$617$			663.229i			1.07493i	0.843288	+	0.537463i	$0.180617\pi$
$617$			663.229i			1.07493i	−0.843288	+	0.537463i	$0.819383\pi$
$618$	32.3959	+	18.5274i	0.0524205	+	0.0299796i
$619$	595.503			0.962041			0.481020	−	0.876709i	$-0.340266\pi$
$619$	595.503			0.962041			0.481020	+	0.876709i	$0.340266\pi$
$620$		−	1247.14i		−	2.01151i
$621$	−10.3506	−	842.865i	−0.0166677	−	1.35727i
$622$	−163.089			−0.262201
$623$		−	454.055i		−	0.728821i
$624$	−450.221	+	787.230i	−0.721509	+	1.26159i
$625$	−519.411			−0.831058
$626$			166.282i			0.265627i
$627$	12.9788	+	7.42264i	0.0206998	+	0.0118383i
$628$	571.911			0.910686
$629$		−	52.5584i		−	0.0835587i
$630$	−62.4503	−	106.151i	−0.0991275	−	0.168493i
$631$	−730.221			−1.15724			−0.578622	−	0.815596i	$-0.696409\pi$
$631$	−730.221			−1.15724			−0.578622	+	0.815596i	$0.696409\pi$
$632$		−	145.222i		−	0.229782i
$633$	−61.7011	+	107.887i	−0.0974741	+	0.170437i
$634$	170.296			0.268606
$635$			70.9151i			0.111677i
$636$	679.411	+	388.559i	1.06826	+	0.610941i
$637$	686.232			1.07729
$638$			13.5295i			0.0212062i
$639$	−110.951	+	65.2747i	−0.173633	+	0.102151i
$640$	730.069			1.14073
$641$		−	270.388i		−	0.421822i	−0.977505	−	0.210911i	$-0.932357\pi$
$641$		−	270.388i		−	0.421822i	0.977505	−	0.210911i	$-0.0676430\pi$
$642$	−36.0069	+	62.9596i	−0.0560856	+	0.0980679i
$643$	511.574			0.795605			0.397803	−	0.917471i	$-0.369773\pi$
$643$	511.574			0.795605			0.397803	+	0.917471i	$0.369773\pi$
$644$			502.613i			0.780455i
$645$	1558.49	+	891.307i	2.41626	+	1.38187i
$646$	1.29956			0.00201171
$647$			659.579i			1.01944i	0.860340	+	0.509721i	$0.170251\pi$
$647$			659.579i			1.01944i	−0.860340	+	0.509721i	$0.829749\pi$
$648$	243.948	+	135.567i	0.376463	+	0.209209i
$649$	−621.085			−0.956987
$650$		−	279.381i		−	0.429817i
$651$	−281.882	+	492.882i	−0.432998	+	0.757115i
$652$	203.690			0.312407
$653$		−	356.744i		−	0.546315i	−0.961969	−	0.273157i	$-0.911932\pi$
$653$		−	356.744i		−	0.546315i	0.961969	−	0.273157i	$-0.0880680\pi$
$654$	−162.050	−	92.6773i	−0.247783	−	0.141708i
$655$	−1694.44			−2.58693
$656$		−	192.976i		−	0.294171i
$657$	115.637	+	196.556i	0.176008	+	0.299172i
$658$	69.0928			0.105004
$659$			104.518i			0.158601i	0.996851	+	0.0793007i	$0.0252687\pi$
$659$			104.518i			0.158601i	−0.996851	+	0.0793007i	$0.974731\pi$
$660$	236.314	−	413.205i	0.358052	−	0.626069i
$661$	−597.645			−0.904153			−0.452076	−	0.891979i	$-0.649317\pi$
$661$	−597.645			−0.904153			−0.452076	+	0.891979i	$0.649317\pi$
$662$			102.946i			0.155508i
$663$	193.184	+	110.483i	0.291378	+	0.166641i
$664$	−44.6252			−0.0672066
$665$		−	27.1455i		−	0.0408204i
$666$	−53.5354	+	31.4958i	−0.0803836	+	0.0472911i
$667$	168.123			0.252058
$668$			781.382i			1.16973i
$669$	−262.688	+	459.322i	−0.392658	+	0.686579i
$670$	−135.274			−0.201901
$671$		−	156.707i		−	0.233542i
$672$	−218.486	−	124.953i	−0.325128	−	0.185942i
$673$	−597.660			−0.888054			−0.444027	−	0.896013i	$-0.646451\pi$
$673$	−597.660			−0.888054			−0.444027	+	0.896013i	$0.646451\pi$
$674$			172.374i			0.255747i
$675$	774.340	−	9.50913i	1.14717	−	0.0140876i
$676$	1209.68			1.78946
$677$		−	1013.09i		−	1.49644i	−0.663452	−	0.748219i	$-0.730909\pi$
$677$		−	1013.09i		−	1.49644i	0.663452	−	0.748219i	$-0.269091\pi$
$678$	126.333	−	220.899i	0.186332	−	0.325810i
$679$	181.749			0.267671
$680$		−	84.8672i		−	0.124805i
$681$	902.075	+	515.902i	1.32463	+	0.757565i
$682$	112.387			0.164791
$683$		−	717.877i		−	1.05106i	−0.850774	−	0.525532i	$-0.823866\pi$
$683$		−	717.877i		−	1.05106i	0.850774	−	0.525532i	$-0.176134\pi$
$684$	15.2066	+	25.8476i	0.0222319	+	0.0377889i
$685$	1522.67			2.22288
$686$			149.602i			0.218079i
$687$	233.740	−	408.704i	0.340233	−	0.594911i
$688$	1118.98			1.62643
$689$		−	1512.91i		−	2.19580i
$690$	262.957	+	150.387i	0.381098	+	0.217952i
$691$	−815.035			−1.17950			−0.589751	−	0.807585i	$-0.700774\pi$
$691$	−815.035			−1.17950			−0.589751	+	0.807585i	$0.700774\pi$
$692$		−	306.326i		−	0.442668i
$693$	−186.788	+	109.891i	−0.269535	+	0.158572i
$694$	17.9005			0.0257932
$695$			1524.80i			2.19396i
$696$	−27.6344	+	48.3198i	−0.0397046	+	0.0694250i
$697$	−47.3558			−0.0679423
$698$			113.304i			0.162326i
$699$	26.8725	+	15.3685i	0.0384442	+	0.0219865i
$700$	−461.750			−0.659643
$701$			633.219i			0.903308i	0.892193	+	0.451654i	$0.149166\pi$
$701$			633.219i			0.903308i	−0.892193	+	0.451654i	$0.850834\pi$
$702$	−3.22950	−	262.982i	−0.00460043	−	0.374619i
$703$	−13.6904			−0.0194743
$704$		−	262.053i		−	0.372235i
$705$	−403.676	+	705.844i	−0.572590	+	1.00120i
$706$	−7.02903			−0.00995613
$707$		−	498.714i		−	0.705395i
$708$	−1081.39	−	618.453i	−1.52739	−	0.873521i
$709$	825.996			1.16502			0.582508	−	0.812825i	$-0.302071\pi$
$709$	825.996			1.16502			0.582508	+	0.812825i	$0.302071\pi$
$710$		−	46.2612i		−	0.0651566i
$711$	−192.350	−	326.950i	−0.270535	−	0.459845i
$712$	−369.764			−0.519332
$713$		−	1396.56i		−	1.95871i
$714$	−9.35152	+	16.3515i	−0.0130974	+	0.0229013i
$715$	−920.123			−1.28689
$716$			77.6093i			0.108393i
$717$	−404.895	−	231.562i	−0.564707	−	0.322959i
$718$	279.507			0.389285
$719$		−	3.02037i		−	0.00420080i	−0.999998	−	0.00210040i	$-0.999331\pi$
$719$		−	3.02037i		−	0.00420080i	0.999998	−	0.00210040i	$-0.000668578\pi$
$720$	778.608	−	458.069i	1.08140	−	0.636207i
$721$	−119.229			−0.165366
$722$			159.022i			0.220252i
$723$	194.147	−	339.475i	0.268530	−	0.469536i
$724$	−996.280			−1.37608
$725$			154.454i			0.213040i
$726$	−101.865	−	58.2571i	−0.140310	−	0.0802440i
$727$	390.200			0.536727			0.268363	−	0.963318i	$-0.413517\pi$
$727$	390.200			0.536727			0.268363	+	0.963318i	$0.413517\pi$
$728$			321.672i			0.441856i
$729$	728.780	−	17.9020i	0.999698	−	0.0245569i
$730$	−81.9539			−0.112266
$731$		−	274.595i		−	0.375643i
$732$	156.043	−	272.847i	0.213173	−	0.372742i
$733$	840.580			1.14677			0.573383	−	0.819287i	$-0.305631\pi$
$733$	840.580			1.14677			0.573383	+	0.819287i	$0.305631\pi$
$734$			194.789i			0.265380i
$735$	−593.381	−	339.358i	−0.807322	−	0.461712i
$736$	619.071			0.841129
$737$			238.034i			0.322977i
$738$	28.3781	+	48.2361i	0.0384527	+	0.0653605i
$739$	−561.236			−0.759453			−0.379727	−	0.925099i	$-0.623982\pi$
$739$	−561.236			−0.759453			−0.379727	+	0.925099i	$0.623982\pi$
$740$			435.862i			0.589003i
$741$	28.7786	−	50.3206i	0.0388376	−	0.0679090i
$742$	128.056			0.172582
$743$		−	1339.34i		−	1.80261i	−0.433181	−	0.901307i	$-0.642609\pi$
$743$		−	1339.34i		−	1.80261i	0.433181	−	0.901307i	$-0.357391\pi$
$744$	401.383	+	229.553i	0.539493	+	0.308539i
$745$	−7.72373			−0.0103674
$746$			136.545i			0.183037i
$747$	−100.468	+	59.1072i	−0.134495	+	0.0791260i
$748$	−72.8040			−0.0973316
$749$		−	231.714i		−	0.309365i
$750$	−17.7337	+	31.0081i	−0.0236450	+	0.0413442i
$751$	652.198			0.868439			0.434219	−	0.900807i	$-0.357024\pi$
$751$	652.198			0.868439			0.434219	+	0.900807i	$0.357024\pi$
$752$			506.791i			0.673924i
$753$	261.224	+	149.395i	0.346911	+	0.198400i
$754$	52.4559			0.0695702
$755$		−	786.549i		−	1.04179i
$756$	−434.648	+	5.33760i	−0.574931	+	0.00706032i
$757$	924.057			1.22068			0.610342	−	0.792138i	$-0.291032\pi$
$757$	924.057			1.22068			0.610342	+	0.792138i	$0.291032\pi$
$758$			33.0050i			0.0435423i
$759$	264.628	−	462.713i	0.348654	−	0.609635i
$760$	−22.1062			−0.0290871
$761$			1108.19i			1.45623i	0.685454	+	0.728116i	$0.259604\pi$
$761$			1108.19i			1.45623i	−0.685454	+	0.728116i	$0.740396\pi$
$762$	−11.1269	−	6.36351i	−0.0146022	−	0.00835106i
$763$	596.403			0.781655
$764$			402.645i			0.527022i
$765$	−112.409	−	191.068i	−0.146939	−	0.249762i
$766$	152.910			0.199622
$767$			2408.03i			3.13955i
$768$	208.794	−	365.085i	0.271867	−	0.475371i
$769$	−1020.69			−1.32730			−0.663650	−	0.748043i	$-0.730994\pi$
$769$	−1020.69			−1.32730			−0.663650	+	0.748043i	$0.730994\pi$
$770$		−	77.8813i		−	0.101144i
$771$	605.936	+	346.538i	0.785909	+	0.449466i
$772$	−1194.45			−1.54722
$773$		−	443.968i		−	0.574344i	−0.957879	−	0.287172i	$-0.907285\pi$
$773$		−	443.968i		−	0.574344i	0.957879	−	0.287172i	$-0.0927151\pi$
$774$	−279.699	+	164.552i	−0.361369	+	0.212600i
$775$	1283.02			1.65551
$776$		−	148.009i		−	0.190733i
$777$	98.5150	−	172.257i	0.126789	−	0.221696i
$778$	−211.189			−0.271451
$779$			12.3352i			0.0158347i
$780$	−1602.06	−	916.225i	−2.05392	−	1.17465i
$781$	−81.4035			−0.104230
$782$		−	46.3313i		−	0.0592472i
$783$	1.78541	+	145.388i	0.00228022	+	0.185681i
$784$	−426.044			−0.543423
$785$			1101.21i			1.40282i
$786$	152.049	−	265.864i	0.193447	−	0.338250i
$787$	−51.9263			−0.0659800			−0.0329900	−	0.999456i	$-0.510503\pi$
$787$	−51.9263			−0.0659800			−0.0329900	+	0.999456i	$0.510503\pi$
$788$		−	1334.19i		−	1.69314i
$789$	−162.457	−	92.9102i	−0.205903	−	0.117757i
$790$	136.322			0.172559
$791$			812.989i			1.02780i
$792$	89.4905	+	152.113i	0.112993	+	0.192061i
$793$	−607.574			−0.766171
$794$			187.630i			0.236310i
$795$	−748.168	+	1308.20i	−0.941092	+	1.64554i
$796$	−144.110			−0.181043
$797$		−	1223.59i		−	1.53524i	−0.640902	−	0.767622i	$-0.721440\pi$
$797$		−	1223.59i		−	1.53524i	0.640902	−	0.767622i	$-0.278560\pi$
$798$	4.25925	+	2.43589i	0.00533740	+	0.00305249i
$799$	124.365			0.155651
$800$			568.740i			0.710925i
$801$	−832.478	+	489.761i	−1.03930	+	0.611438i
$802$	−112.287			−0.140009
$803$			144.210i			0.179589i
$804$	−237.026	+	414.449i	−0.294808	+	0.515484i
$805$	−967.779			−1.20221
$806$		−	435.741i		−	0.540621i
$807$	−675.212	−	386.157i	−0.836694	−	0.478510i
$808$	−406.132			−0.502639
$809$		−	1027.21i		−	1.26973i	−0.772622	−	0.634866i	$-0.781055\pi$
$809$		−	1027.21i		−	1.26973i	0.772622	−	0.634866i	$-0.218945\pi$
$810$	−127.258	+	228.996i	−0.157109	+	0.282712i
$811$	1452.18			1.79060			0.895302	−	0.445460i	$-0.146960\pi$
$811$	1452.18			1.79060			0.895302	+	0.445460i	$0.146960\pi$
$812$		−	86.6973i		−	0.106770i
$813$	−312.603	+	546.599i	−0.384506	+	0.672324i
$814$	−39.2782			−0.0482533
$815$			392.204i			0.481231i
$816$	−119.937	−	68.5927i	−0.146982	−	0.0840597i
$817$	−71.5266			−0.0875478
$818$		−	64.0753i		−	0.0783317i
$819$	426.062	+	724.204i	0.520222	+	0.884253i
$820$	392.717			0.478923
$821$		−	710.412i		−	0.865300i	−0.901562	−	0.432650i	$-0.857579\pi$
$821$		−	710.412i		−	0.865300i	0.901562	−	0.432650i	$-0.142421\pi$
$822$	−136.636	+	238.913i	−0.166224	+	0.290649i
$823$	−959.009			−1.16526			−0.582630	−	0.812737i	$-0.697976\pi$
$823$	−959.009			−1.16526			−0.582630	+	0.812737i	$0.697976\pi$
$824$			97.0949i			0.117834i
$825$	425.094	+	243.114i	0.515266	+	0.294683i
$826$	−203.821			−0.246757
$827$		−	1170.22i		−	1.41502i	−0.706703	−	0.707510i	$-0.749818\pi$
$827$		−	1170.22i		−	1.41502i	0.706703	−	0.707510i	$-0.250182\pi$
$828$	921.505	−	542.138i	1.11293	−	0.654756i
$829$	799.255			0.964119			0.482060	−	0.876138i	$-0.339889\pi$
$829$	799.255			0.964119			0.482060	+	0.876138i	$0.339889\pi$
$830$		−	41.8902i		−	0.0504701i
$831$	122.374	−	213.976i	0.147261	−	0.257493i
$832$	−1016.02			−1.22117
$833$			104.550i			0.125510i
$834$	−239.247	−	136.827i	−0.286867	−	0.164061i
$835$	−1504.55			−1.80185
$836$			18.9640i			0.0226842i
$837$	1207.71	−	14.8311i	1.44291	−	0.0177193i
$838$	175.681			0.209643
$839$		−	95.8347i		−	0.114225i	−0.998368	−	0.0571125i	$-0.981811\pi$
$839$		−	95.8347i		−	0.114225i	0.998368	−	0.0571125i	$-0.0181894\pi$
$840$	159.074	−	278.148i	0.189374	−	0.331128i
$841$	−29.0000			−0.0344828
$842$			260.132i			0.308946i
$843$	−33.5858	−	19.2079i	−0.0398408	−	0.0227852i
$844$	−157.639			−0.186777
$845$			2329.22i			2.75648i
$846$	−74.5262	−	126.677i	−0.0880924	−	0.149736i
$847$	374.900			0.442621
$848$			939.280i			1.10764i
$849$	104.376	−	182.505i	0.122940	−	0.214965i
$850$	42.5646			0.0500760
$851$			488.084i			0.573542i
$852$	−141.734	−	81.0586i	−0.166355	−	0.0951392i
$853$	643.037			0.753853			0.376927	−	0.926243i	$-0.376981\pi$
$853$	643.037			0.753853			0.376927	+	0.926243i	$0.376981\pi$
$854$		−	51.4264i		−	0.0602182i
$855$	−49.7694	+	29.2802i	−0.0582099	+	0.0342459i
$856$	−188.699			−0.220442
$857$			1197.69i			1.39753i	0.715349	+	0.698767i	$0.246268\pi$
$857$			1197.69i			1.39753i	−0.715349	+	0.698767i	$0.753732\pi$
$858$	82.5666	−	144.371i	0.0962315	−	0.168265i
$859$	−242.376			−0.282160			−0.141080	−	0.989998i	$-0.545058\pi$
$859$	−242.376			−0.282160			−0.141080	+	0.989998i	$0.545058\pi$
$860$			2277.19i			2.64789i
$861$	−155.206	−	88.7631i	−0.180262	−	0.103093i
$862$	137.913			0.159992
$863$			1030.16i			1.19369i	0.802356	+	0.596846i	$0.203580\pi$
$863$			1030.16i			1.19369i	−0.802356	+	0.596846i	$0.796420\pi$
$864$	6.57435	+	535.358i	0.00760920	+	0.619627i
$865$	589.830			0.681884
$866$		−	30.8122i		−	0.0355800i
$867$	413.591	−	723.180i	0.477036	−	0.834118i
$868$	−720.177			−0.829697
$869$		−	239.878i		−	0.276040i
$870$	−45.3584	−	25.9407i	−0.0521360	−	0.0298169i
$871$	922.892			1.05958
$872$		−	485.686i		−	0.556980i
$873$	−196.041	−	333.223i	−0.224560	−	0.381699i
$874$	−12.0684			−0.0138082
$875$		−	114.121i		−	0.130424i
$876$	−143.599	+	251.089i	−0.163926	+	0.286631i
$877$	−8.14318			−0.00928526			−0.00464263	−	0.999989i	$-0.501478\pi$
$877$	−8.14318			−0.00928526			−0.00464263	+	0.999989i	$0.501478\pi$
$878$		−	32.9396i		−	0.0375166i
$879$	−757.815	−	433.398i	−0.862133	−	0.493058i
$880$	571.254			0.649152
$881$		−	1281.46i		−	1.45455i	−0.686345	−	0.727276i	$-0.740786\pi$
$881$		−	1281.46i		−	1.45455i	0.686345	−	0.727276i	$-0.259214\pi$
$882$	106.493	−	62.6519i	0.120741	−	0.0710339i
$883$	−1199.52			−1.35846			−0.679228	−	0.733927i	$-0.737685\pi$
$883$	−1199.52			−1.35846			−0.679228	+	0.733927i	$0.737685\pi$
$884$			282.272i			0.319312i
$885$	1190.83	−	2082.21i	1.34557	−	2.35278i
$886$	171.772			0.193874
$887$		−	938.381i		−	1.05793i	−0.848645	−	0.528963i	$-0.822581\pi$
$887$		−	938.381i		−	1.05793i	0.848645	−	0.528963i	$-0.177419\pi$
$888$	−140.279	−	80.2266i	−0.157972	−	0.0903452i
$889$	40.9509			0.0460640
$890$		−	347.102i		−	0.390002i
$891$	402.954	+	223.930i	0.452249	+	0.251325i
$892$	−671.140			−0.752399
$893$		−	32.3946i		−	0.0362762i
$894$	0.693084	−	1.21188i	0.000775261	−	0.00135558i
$895$	−149.436			−0.166968
$896$		−	421.589i		−	0.470523i
$897$	−1794.00	−	1026.00i	−2.00000	−	1.14381i
$898$	112.044			0.124771
$899$			240.897i			0.267961i
$900$	498.062	+	846.587i	0.553402	+	0.940652i
$901$	230.497			0.255823
$902$			35.3901i			0.0392352i
$903$	514.698	−	899.970i	0.569986	−	0.996644i
$904$	662.065			0.732373
$905$		−	1918.33i		−	2.11971i
$906$	123.413	+	70.5804i	0.136217	+	0.0779034i
$907$	97.5050			0.107503			0.0537514	−	0.998554i	$-0.482882\pi$
$907$	97.5050			0.107503			0.0537514	+	0.998554i	$0.482882\pi$
$908$			1318.07i			1.45162i
$909$	−914.357	+	537.932i	−1.00589	+	0.591784i
$910$	−301.957			−0.331820
$911$			353.509i			0.388045i	0.980997	+	0.194022i	$0.0621535\pi$
$911$			353.509i			0.388045i	−0.980997	+	0.194022i	$0.937847\pi$
$912$	−17.8671	+	31.2413i	−0.0195911	+	0.0342558i
$913$	−73.7120			−0.0807361
$914$			120.443i			0.131776i
$915$	525.365	+	300.459i	0.574170	+	0.328371i
$916$	597.179			0.651942
$917$			978.478i			1.06704i
$918$	40.0663	−	0.492026i	0.0436452	−	0.000535976i
$919$	−1350.51			−1.46955			−0.734773	−	0.678313i	$-0.762711\pi$
$919$	−1350.51			−1.46955			−0.734773	+	0.678313i	$0.762711\pi$
$920$			788.120i			0.856652i
$921$	393.926	−	688.796i	0.427715	−	0.747878i
$922$	−9.46947			−0.0102706
$923$			315.613i			0.341942i
$924$	−238.611	−	136.463i	−0.258237	−	0.147687i
$925$	−448.403			−0.484760
$926$		−	169.699i		−	0.183260i
$927$	128.605	+	218.597i	0.138732	+	0.235811i
$928$	−106.785			−0.115071
$929$		−	888.991i		−	0.956933i	−0.878106	−	0.478467i	$-0.841193\pi$
$929$		−	888.991i		−	0.956933i	0.878106	−	0.478467i	$-0.158807\pi$
$930$	−215.484	+	376.783i	−0.231703	+	0.405143i
$931$	27.2332			0.0292515
$932$			39.2649i			0.0421297i
$933$	−962.113	−	550.237i	−1.03120	−	0.589751i
$934$	102.395			0.109631
$935$		−	140.184i		−	0.149929i
$936$	589.762	−	346.967i	0.630088	−	0.370692i
$937$	192.518			0.205462			0.102731	−	0.994709i	$-0.467242\pi$
$937$	192.518			0.205462			0.102731	+	0.994709i	$0.467242\pi$
$938$			78.1156i			0.0832789i
$939$	−561.011	+	980.950i	−0.597455	+	1.04468i
$940$	−1031.35			−1.09718
$941$			610.585i			0.648868i	0.945908	+	0.324434i	$0.105174\pi$
$941$			610.585i			0.648868i	−0.945908	+	0.324434i	$0.894826\pi$
$942$	−172.785	−	98.8164i	−0.183423	−	0.104901i
$943$	439.770			0.466352
$944$		−	1495.01i		−	1.58370i
$945$	−10.2775	−	836.912i	−0.0108757	−	0.885622i
$946$	−205.211			−0.216925
$947$			1277.08i			1.34855i	0.738481	+	0.674275i	$0.235544\pi$
$947$			1277.08i			1.34855i	−0.738481	+	0.674275i	$0.764456\pi$
$948$	238.862	−	417.660i	0.251964	−	0.440570i
$949$	559.123			0.589171
$950$		−	11.0872i		−	0.0116708i
$951$	1004.63	+	574.552i	1.05639	+	0.604156i
$952$	−49.0077			−0.0514787
$953$		−	163.858i		−	0.171939i	−0.996298	−	0.0859697i	$-0.972601\pi$
$953$		−	163.858i		−	0.171939i	0.996298	−	0.0859697i	$-0.0273988\pi$
$954$	−138.126	−	234.781i	−0.144786	−	0.246102i
$955$	−775.290			−0.811823
$956$		−	591.614i		−	0.618844i
$957$	−45.6465	+	79.8148i	−0.0476975	+	0.0834011i
$958$	−183.326			−0.191363
$959$		−	879.288i		−	0.916880i
$960$	878.544	+	502.444i	0.915150	+	0.523379i
$961$	1040.08			1.08229
$962$			152.287i			0.158303i
$963$	−424.832	+	249.936i	−0.441154	+	0.259539i
$964$	496.025			0.514548
$965$		−	2299.91i		−	2.38333i
$966$	86.8429	−	151.848i	0.0898995	−	0.157193i
$967$	819.560			0.847528			0.423764	−	0.905773i	$-0.360709\pi$
$967$	819.560			0.847528			0.423764	+	0.905773i	$0.360709\pi$
$968$		−	305.303i		−	0.315396i
$969$	7.66651	+	4.38452i	0.00791178	+	0.00452479i
$970$	138.937			0.143234
$971$		−	455.065i		−	0.468656i	−0.972158	−	0.234328i	$-0.924711\pi$
$971$		−	455.065i		−	0.468656i	0.972158	−	0.234328i	$-0.0752890\pi$
$972$	478.614	+	791.138i	0.492401	+	0.813928i
$973$	880.518			0.904951
$974$		−	73.9168i		−	0.0758899i
$975$	942.587	−	1648.15i	0.966755	−	1.69041i
$976$	377.209			0.386484
$977$			1016.69i			1.04063i	0.853975	+	0.520314i	$0.174185\pi$
$977$			1016.69i			1.04063i	−0.853975	+	0.520314i	$0.825815\pi$
$978$	−61.5383	−	35.1941i	−0.0629226	−	0.0359858i
$979$	−610.777			−0.623879
$980$		−	867.022i		−	0.884716i
$981$	−643.303	−	1093.46i	−0.655763	−	1.11464i
$982$	−238.625			−0.242999
$983$			1373.13i			1.39688i	0.715669	+	0.698439i	$0.246122\pi$
$983$			1373.13i			1.39688i	−0.715669	+	0.698439i	$0.753878\pi$
$984$	−72.2851	+	126.393i	−0.0734604	+	0.128449i
$985$	2568.98			2.60810
$986$			7.99184i			0.00810531i
$987$	407.599	+	233.108i	0.412968	+	0.236179i
$988$	73.5262			0.0744192
$989$			2550.03i			2.57839i
$990$	−142.790	+	84.0057i	−0.144232	+	0.0848543i
$991$	667.265			0.673325			0.336662	−	0.941625i	$-0.390702\pi$
$991$	667.265			0.673325			0.336662	+	0.941625i	$0.390702\pi$
$992$			887.045i			0.894199i
$993$	−347.324	+	607.310i	−0.349772	+	0.611591i
$994$	−26.7142			−0.0268754
$995$		−	277.483i		−	0.278878i
$996$	−128.342	−	73.3997i	−0.128858	−	0.0736945i
$997$	1215.89			1.21955			0.609775	−	0.792574i	$-0.291260\pi$
$997$	1215.89			1.21955			0.609775	+	0.792574i	$0.291260\pi$
$998$			45.3906i			0.0454816i
$999$	−422.084	+	5.18331i	−0.422506	+	0.00518850i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.3.b.a.59.9	✓	18
3.2	odd	2	inner	87.3.b.a.59.10	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.3.b.a.59.9	✓	18	1.1	even	1	trivial
87.3.b.a.59.10	yes	18	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	87.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.441441i q^{2} +(1.48935 - 2.60419i) q^{3} +3.80513 q^{4} +7.32676i q^{5} +(-1.14960 - 0.657462i) q^{6} +4.23094 q^{7} -3.44551i q^{8} +(-4.56366 - 7.75713i) q^{9} +O(q^{10})\)	\(q-0.441441i q^{2} +(1.48935 - 2.60419i) q^{3} +3.80513 q^{4} +7.32676i q^{5} +(-1.14960 - 0.657462i) q^{6} +4.23094 q^{7} -3.44551i q^{8} +(-4.56366 - 7.75713i) q^{9} +3.23433 q^{10} -5.69130i q^{11} +(5.66718 - 9.90930i) q^{12} -22.0660 q^{13} -1.86771i q^{14} +(19.0803 + 10.9121i) q^{15} +13.6995 q^{16} -3.36182i q^{17} +(-3.42432 + 2.01459i) q^{18} -0.875689 q^{19} +27.8793i q^{20} +(6.30136 - 11.0182i) q^{21} -2.51237 q^{22} +31.2196i q^{23} +(-8.97277 - 5.13157i) q^{24} -28.6814 q^{25} +9.74082i q^{26} +(-26.9980 + 0.331543i) q^{27} +16.0993 q^{28} -5.38516i q^{29} +(4.81707 - 8.42283i) q^{30} -44.7335 q^{31} -19.8296i q^{32} +(-14.8212 - 8.47635i) q^{33} -1.48405 q^{34} +30.9991i q^{35} +(-17.3653 - 29.5169i) q^{36} +15.6339 q^{37} +0.386565i q^{38} +(-32.8640 + 57.4640i) q^{39} +25.2444 q^{40} -14.0863i q^{41} +(-4.86388 - 2.78168i) q^{42} +81.6804 q^{43} -21.6561i q^{44} +(56.8346 - 33.4368i) q^{45} +13.7816 q^{46} +36.9933i q^{47} +(20.4034 - 35.6762i) q^{48} -31.0991 q^{49} +12.6612i q^{50} +(-8.75484 - 5.00694i) q^{51} -83.9638 q^{52} +68.5629i q^{53} +(0.146357 + 11.9180i) q^{54} +41.6988 q^{55} -14.5777i q^{56} +(-1.30421 + 2.28046i) q^{57} -2.37723 q^{58} -109.129i q^{59} +(72.6031 + 41.5221i) q^{60} +27.5344 q^{61} +19.7472i q^{62} +(-19.3086 - 32.8199i) q^{63} +46.0445 q^{64} -161.672i q^{65} +(-3.74181 + 6.54271i) q^{66} -41.8242 q^{67} -12.7922i q^{68} +(81.3019 + 46.4970i) q^{69} +13.6843 q^{70} -14.3032i q^{71} +(-26.7272 + 15.7241i) q^{72} -25.3387 q^{73} -6.90145i q^{74} +(-42.7168 + 74.6920i) q^{75} -3.33211 q^{76} -24.0795i q^{77} +(25.3670 + 14.5075i) q^{78} +42.1483 q^{79} +100.373i q^{80} +(-39.3461 + 70.8017i) q^{81} -6.21829 q^{82} -12.9517i q^{83} +(23.9775 - 41.9256i) q^{84} +24.6313 q^{85} -36.0571i q^{86} +(-14.0240 - 8.02041i) q^{87} -19.6094 q^{88} -107.318i q^{89} +(-14.7604 - 25.0891i) q^{90} -93.3597 q^{91} +118.795i q^{92} +(-66.6239 + 116.495i) q^{93} +16.3304 q^{94} -6.41596i q^{95} +(-51.6400 - 29.5332i) q^{96} +42.9570 q^{97} +13.7284i q^{98} +(-44.1481 + 25.9731i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{3} - 36 q^{4} + 8 q^{6} - 12 q^{7} - 22 q^{9}+O(q^{10}) \) 18 * q - 2 * q^3 - 36 * q^4 + 8 * q^6 - 12 * q^7 - 22 * q^9	\( 18 q - 2 q^{3} - 36 q^{4} + 8 q^{6} - 12 q^{7} - 22 q^{9} + 12 q^{10} + 18 q^{12} + 32 q^{13} + 30 q^{15} + 76 q^{16} - 50 q^{18} - 24 q^{19} + 32 q^{21} - 94 q^{22} + 38 q^{24} - 114 q^{25} - 68 q^{27} + 94 q^{28} - 88 q^{30} + 24 q^{31} - 20 q^{33} + 70 q^{34} + 168 q^{36} - 40 q^{37} + 38 q^{39} + 160 q^{40} - 118 q^{42} - 36 q^{43} + 32 q^{45} - 228 q^{46} + 94 q^{48} + 190 q^{49} + 204 q^{51} - 386 q^{52} - 32 q^{54} + 188 q^{55} - 140 q^{57} - 354 q^{60} - 8 q^{61} - 340 q^{63} + 86 q^{64} + 178 q^{66} + 136 q^{67} + 4 q^{69} + 252 q^{70} + 358 q^{72} - 68 q^{73} + 244 q^{75} + 120 q^{76} + 66 q^{78} - 96 q^{79} + 366 q^{81} - 548 q^{82} - 664 q^{84} - 320 q^{85} + 504 q^{88} + 562 q^{90} - 156 q^{91} - 40 q^{93} - 174 q^{94} - 504 q^{96} - 12 q^{97} - 198 q^{99}+O(q^{100}) \) 18 * q - 2 * q^3 - 36 * q^4 + 8 * q^6 - 12 * q^7 - 22 * q^9 + 12 * q^10 + 18 * q^12 + 32 * q^13 + 30 * q^15 + 76 * q^16 - 50 * q^18 - 24 * q^19 + 32 * q^21 - 94 * q^22 + 38 * q^24 - 114 * q^25 - 68 * q^27 + 94 * q^28 - 88 * q^30 + 24 * q^31 - 20 * q^33 + 70 * q^34 + 168 * q^36 - 40 * q^37 + 38 * q^39 + 160 * q^40 - 118 * q^42 - 36 * q^43 + 32 * q^45 - 228 * q^46 + 94 * q^48 + 190 * q^49 + 204 * q^51 - 386 * q^52 - 32 * q^54 + 188 * q^55 - 140 * q^57 - 354 * q^60 - 8 * q^61 - 340 * q^63 + 86 * q^64 + 178 * q^66 + 136 * q^67 + 4 * q^69 + 252 * q^70 + 358 * q^72 - 68 * q^73 + 244 * q^75 + 120 * q^76 + 66 * q^78 - 96 * q^79 + 366 * q^81 - 548 * q^82 - 664 * q^84 - 320 * q^85 + 504 * q^88 + 562 * q^90 - 156 * q^91 - 40 * q^93 - 174 * q^94 - 504 * q^96 - 12 * q^97 - 198 * q^99

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