LMFDB - Embedded newform 538.3.c.b.187.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [538,3,Mod(187,538)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(538, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("538.187");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 538 = 2 \cdot 269 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	538.c (of order $4$, degree $2$, 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:	$14.6594382226$
Analytic rank:	$0$
Dimension:	$46$
Relative dimension:	$23$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			187.17
Character	$\chi$	$=$	538.187
Dual form			538.3.c.b.351.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.00000i) q^{2} +(1.35493 + 1.35493i) q^{3} +2.00000i q^{4} +4.13408 q^{5} -2.70986i q^{6} +(1.20624 - 1.20624i) q^{7} +(2.00000 - 2.00000i) q^{8} -5.32832i q^{9} +(-4.13408 - 4.13408i) q^{10} -19.3005i q^{11} +(-2.70986 + 2.70986i) q^{12} +6.76777i q^{13} -2.41248 q^{14} +(5.60140 + 5.60140i) q^{15} -4.00000 q^{16} +(-16.6705 - 16.6705i) q^{17} +(-5.32832 + 5.32832i) q^{18} +(1.42205 - 1.42205i) q^{19} +8.26816i q^{20} +3.26874 q^{21} +(-19.3005 + 19.3005i) q^{22} -16.5872 q^{23} +5.41973 q^{24} -7.90939 q^{25} +(6.76777 - 6.76777i) q^{26} +(19.4139 - 19.4139i) q^{27} +(2.41248 + 2.41248i) q^{28} +(15.5072 - 15.5072i) q^{29} -11.2028i q^{30} +(-4.83725 + 4.83725i) q^{31} +(4.00000 + 4.00000i) q^{32} +(26.1509 - 26.1509i) q^{33} +33.3410i q^{34} +(4.98668 - 4.98668i) q^{35} +10.6566 q^{36} +70.2767 q^{37} -2.84410 q^{38} +(-9.16986 + 9.16986i) q^{39} +(8.26816 - 8.26816i) q^{40} -70.2396 q^{41} +(-3.26874 - 3.26874i) q^{42} -8.53548i q^{43} +38.6011 q^{44} -22.0277i q^{45} +(16.5872 + 16.5872i) q^{46} +42.1035 q^{47} +(-5.41973 - 5.41973i) q^{48} +46.0900i q^{49} +(7.90939 + 7.90939i) q^{50} -45.1748i q^{51} -13.5355 q^{52} -14.6327 q^{53} -38.8278 q^{54} -79.7899i q^{55} -4.82495i q^{56} +3.85356 q^{57} -31.0143 q^{58} +(73.5545 - 73.5545i) q^{59} +(-11.2028 + 11.2028i) q^{60} +9.57289 q^{61} +9.67450 q^{62} +(-6.42722 - 6.42722i) q^{63} -8.00000i q^{64} +27.9785i q^{65} -52.3018 q^{66} +46.8008 q^{67} +(33.3410 - 33.3410i) q^{68} +(-22.4745 - 22.4745i) q^{69} -9.97337 q^{70} +(-55.1124 + 55.1124i) q^{71} +(-10.6566 - 10.6566i) q^{72} -140.193i q^{73} +(-70.2767 - 70.2767i) q^{74} +(-10.7167 - 10.7167i) q^{75} +(2.84410 + 2.84410i) q^{76} +(-23.2810 - 23.2810i) q^{77} +18.3397 q^{78} +138.548i q^{79} -16.5363 q^{80} +4.65415 q^{81} +(70.2396 + 70.2396i) q^{82} +(-31.5887 + 31.5887i) q^{83} +6.53748i q^{84} +(-68.9172 - 68.9172i) q^{85} +(-8.53548 + 8.53548i) q^{86} +42.0223 q^{87} +(-38.6011 - 38.6011i) q^{88} -90.2303i q^{89} +(-22.0277 + 22.0277i) q^{90} +(8.16354 + 8.16354i) q^{91} -33.1744i q^{92} -13.1083 q^{93} +(-42.1035 - 42.1035i) q^{94} +(5.87887 - 5.87887i) q^{95} +10.8395i q^{96} -70.9662i q^{97} +(46.0900 - 46.0900i) q^{98} -102.839 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 46 q^{2} - 6 q^{3} - 32 q^{5} + 4 q^{7} + 92 q^{8} + 32 q^{10} + 12 q^{12} - 8 q^{14} - 10 q^{15} - 184 q^{16} - 50 q^{17} + 118 q^{18} + 10 q^{19} + 16 q^{21} + 8 q^{22} - 124 q^{23} - 24 q^{24}+ \cdots + 508 q^{99}+O(q^{100}) $ 46 * q - 46 * q^2 - 6 * q^3 - 32 * q^5 + 4 * q^7 + 92 * q^8 + 32 * q^10 + 12 * q^12 - 8 * q^14 - 10 * q^15 - 184 * q^16 - 50 * q^17 + 118 * q^18 + 10 * q^19 + 16 * q^21 + 8 * q^22 - 124 * q^23 - 24 * q^24 + 178 * q^25 + 4 * q^26 + 90 * q^27 + 8 * q^28 + 40 * q^29 + 40 * q^31 + 184 * q^32 - 64 * q^33 - 14 * q^35 - 236 * q^36 - 32 * q^37 - 20 * q^38 - 54 * q^39 - 64 * q^40 - 132 * q^41 - 16 * q^42 - 16 * q^44 + 124 * q^46 - 60 * q^47 + 24 * q^48 - 178 * q^50 - 8 * q^52 - 188 * q^53 - 180 * q^54 - 40 * q^57 - 80 * q^58 + 190 * q^59 + 20 * q^60 - 80 * q^62 - 266 * q^63 + 128 * q^66 - 164 * q^67 + 100 * q^68 + 170 * q^69 + 28 * q^70 - 92 * q^71 + 236 * q^72 + 32 * q^74 - 190 * q^75 + 20 * q^76 + 20 * q^77 + 108 * q^78 + 128 * q^80 - 298 * q^81 + 132 * q^82 + 190 * q^83 + 298 * q^85 + 228 * q^86 - 92 * q^87 + 16 * q^88 - 528 * q^90 + 2 * q^91 + 232 * q^93 + 60 * q^94 - 280 * q^95 - 226 * q^98 + 508 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/538\mathbb{Z}\right)^\times$.

$n$	$271$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	1.35493	+	1.35493i	0.451644	+	0.451644i	0.895900	−	0.444256i	$-0.146532\pi$
$3$	1.35493	+	1.35493i	0.451644	+	0.451644i	−0.444256	+	0.895900i	$0.646532\pi$
$4$			2.00000i			0.500000i
$5$	4.13408			0.826816			0.413408	−	0.910546i	$-0.364338\pi$
$5$	4.13408			0.826816			0.413408	+	0.910546i	$0.364338\pi$
$6$		−	2.70986i		−	0.451644i
$7$	1.20624	−	1.20624i	0.172320	−	0.172320i	−0.615678	−	0.787998i	$-0.711118\pi$
$7$	1.20624	−	1.20624i	0.172320	−	0.172320i	0.787998	+	0.615678i	$0.211118\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$		−	5.32832i		−	0.592035i
$10$	−4.13408	−	4.13408i	−0.413408	−	0.413408i
$11$		−	19.3005i		−	1.75459i	−0.479948	−	0.877297i	$-0.659345\pi$
$11$		−	19.3005i		−	1.75459i	0.479948	−	0.877297i	$-0.340655\pi$
$12$	−2.70986	+	2.70986i	−0.225822	+	0.225822i
$13$			6.76777i			0.520597i	0.965528	+	0.260299i	$0.0838210\pi$
$13$			6.76777i			0.520597i	−0.965528	+	0.260299i	$0.916179\pi$
$14$	−2.41248			−0.172320
$15$	5.60140	+	5.60140i	0.373426	+	0.373426i
$16$	−4.00000			−0.250000
$17$	−16.6705	−	16.6705i	−0.980618	−	0.980618i	0.0191973	−	0.999816i	$-0.493889\pi$
$17$	−16.6705	−	16.6705i	−0.980618	−	0.980618i	−0.999816	+	0.0191973i	$0.993889\pi$
$18$	−5.32832	+	5.32832i	−0.296018	+	0.296018i
$19$	1.42205	−	1.42205i	0.0748448	−	0.0748448i	−0.668693	−	0.743538i	$-0.733146\pi$
$19$	1.42205	−	1.42205i	0.0748448	−	0.0748448i	0.743538	+	0.668693i	$0.233146\pi$
$20$			8.26816i			0.413408i
$21$	3.26874			0.155654
$22$	−19.3005	+	19.3005i	−0.877297	+	0.877297i
$23$	−16.5872			−0.721182			−0.360591	−	0.932724i	$-0.617425\pi$
$23$	−16.5872			−0.721182			−0.360591	+	0.932724i	$0.617425\pi$
$24$	5.41973			0.225822
$25$	−7.90939			−0.316376
$26$	6.76777	−	6.76777i	0.260299	−	0.260299i
$27$	19.4139	−	19.4139i	0.719033	−	0.719033i
$28$	2.41248	+	2.41248i	0.0861599	+	0.0861599i
$29$	15.5072	−	15.5072i	0.534730	−	0.534730i	−0.387247	−	0.921976i	$-0.626574\pi$
$29$	15.5072	−	15.5072i	0.534730	−	0.534730i	0.921976	+	0.387247i	$0.126574\pi$
$30$		−	11.2028i		−	0.373426i
$31$	−4.83725	+	4.83725i	−0.156040	+	0.156040i	−0.780810	−	0.624769i	$-0.785193\pi$
$31$	−4.83725	+	4.83725i	−0.156040	+	0.156040i	0.624769	+	0.780810i	$0.285193\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	26.1509	−	26.1509i	0.792452	−	0.792452i
$34$			33.3410i			0.980618i
$35$	4.98668	−	4.98668i	0.142477	−	0.142477i
$36$	10.6566			0.296018
$37$	70.2767			1.89937			0.949685	−	0.313206i	$-0.101403\pi$
$37$	70.2767			1.89937			0.949685	+	0.313206i	$0.101403\pi$
$38$	−2.84410			−0.0748448
$39$	−9.16986	+	9.16986i	−0.235125	+	0.235125i
$40$	8.26816	−	8.26816i	0.206704	−	0.206704i
$41$	−70.2396			−1.71316			−0.856581	−	0.516013i	$-0.827416\pi$
$41$	−70.2396			−1.71316			−0.856581	+	0.516013i	$0.827416\pi$
$42$	−3.26874	−	3.26874i	−0.0778272	−	0.0778272i
$43$		−	8.53548i		−	0.198500i	−0.995063	−	0.0992498i	$-0.968356\pi$
$43$		−	8.53548i		−	0.198500i	0.995063	−	0.0992498i	$-0.0316443\pi$
$44$	38.6011			0.877297
$45$		−	22.0277i		−	0.489504i
$46$	16.5872	+	16.5872i	0.360591	+	0.360591i
$47$	42.1035			0.895819			0.447909	−	0.894079i	$-0.352169\pi$
$47$	42.1035			0.895819			0.447909	+	0.894079i	$0.352169\pi$
$48$	−5.41973	−	5.41973i	−0.112911	−	0.112911i
$49$			46.0900i			0.940612i
$50$	7.90939	+	7.90939i	0.158188	+	0.158188i
$51$		−	45.1748i		−	0.885781i
$52$	−13.5355			−0.260299
$53$	−14.6327			−0.276089			−0.138044	−	0.990426i	$-0.544082\pi$
$53$	−14.6327			−0.276089			−0.138044	+	0.990426i	$0.544082\pi$
$54$	−38.8278			−0.719033
$55$		−	79.7899i		−	1.45073i
$56$		−	4.82495i		−	0.0861599i
$57$	3.85356			0.0676064
$58$	−31.0143			−0.534730
$59$	73.5545	−	73.5545i	1.24669	−	1.24669i	0.289511	−	0.957175i	$-0.406507\pi$
$59$	73.5545	−	73.5545i	1.24669	−	1.24669i	0.957175	−	0.289511i	$-0.0934927\pi$
$60$	−11.2028	+	11.2028i	−0.186713	+	0.186713i
$61$	9.57289			0.156933			0.0784663	−	0.996917i	$-0.474998\pi$
$61$	9.57289			0.156933			0.0784663	+	0.996917i	$0.474998\pi$
$62$	9.67450			0.156040
$63$	−6.42722	−	6.42722i	−0.102019	−	0.102019i
$64$		−	8.00000i		−	0.125000i
$65$			27.9785i			0.430438i
$66$	−52.3018			−0.792452
$67$	46.8008			0.698519			0.349260	−	0.937026i	$-0.386433\pi$
$67$	46.8008			0.698519			0.349260	+	0.937026i	$0.386433\pi$
$68$	33.3410	−	33.3410i	0.490309	−	0.490309i
$69$	−22.4745	−	22.4745i	−0.325718	−	0.325718i
$70$	−9.97337			−0.142477
$71$	−55.1124	+	55.1124i	−0.776231	+	0.776231i	−0.979188	−	0.202957i	$-0.934945\pi$
$71$	−55.1124	+	55.1124i	−0.776231	+	0.776231i	0.202957	+	0.979188i	$0.434945\pi$
$72$	−10.6566	−	10.6566i	−0.148009	−	0.148009i
$73$		−	140.193i		−	1.92045i	−0.279225	−	0.960226i	$-0.590078\pi$
$73$		−	140.193i		−	1.92045i	0.279225	−	0.960226i	$-0.409922\pi$
$74$	−70.2767	−	70.2767i	−0.949685	−	0.949685i
$75$	−10.7167	−	10.7167i	−0.142889	−	0.142889i
$76$	2.84410	+	2.84410i	0.0374224	+	0.0374224i
$77$	−23.2810	−	23.2810i	−0.302351	−	0.302351i
$78$	18.3397			0.235125
$79$			138.548i			1.75377i	0.480697	+	0.876887i	$0.340384\pi$
$79$			138.548i			1.75377i	−0.480697	+	0.876887i	$0.659616\pi$
$80$	−16.5363			−0.206704
$81$	4.65415			0.0574586
$82$	70.2396	+	70.2396i	0.856581	+	0.856581i
$83$	−31.5887	+	31.5887i	−0.380587	+	0.380587i	−0.871314	−	0.490727i	$-0.836731\pi$
$83$	−31.5887	+	31.5887i	−0.380587	+	0.380587i	0.490727	+	0.871314i	$0.336731\pi$
$84$			6.53748i			0.0778272i
$85$	−68.9172	−	68.9172i	−0.810791	−	0.810791i
$86$	−8.53548	+	8.53548i	−0.0992498	+	0.0992498i
$87$	42.0223			0.483015
$88$	−38.6011	−	38.6011i	−0.438648	−	0.438648i
$89$		−	90.2303i		−	1.01382i	−0.861998	−	0.506912i	$-0.830787\pi$
$89$		−	90.2303i		−	1.01382i	0.861998	−	0.506912i	$-0.169213\pi$
$90$	−22.0277	+	22.0277i	−0.244752	+	0.244752i
$91$	8.16354	+	8.16354i	0.0897092	+	0.0897092i
$92$		−	33.1744i		−	0.360591i
$93$	−13.1083			−0.140949
$94$	−42.1035	−	42.1035i	−0.447909	−	0.447909i
$95$	5.87887	−	5.87887i	0.0618828	−	0.0618828i
$96$			10.8395i			0.112911i
$97$		−	70.9662i		−	0.731610i	−0.930691	−	0.365805i	$-0.880794\pi$
$97$		−	70.9662i		−	0.731610i	0.930691	−	0.365805i	$-0.119206\pi$
$98$	46.0900	−	46.0900i	0.470306	−	0.470306i
$99$	−102.839			−1.03878
$100$		−	15.8188i		−	0.158188i
$101$	117.416	+	117.416i	1.16253	+	1.16253i	0.983920	+	0.178611i	$0.0571603\pi$
$101$	117.416	+	117.416i	1.16253	+	1.16253i	0.178611	+	0.983920i	$0.442840\pi$
$102$	−45.1748	+	45.1748i	−0.442890	+	0.442890i
$103$			118.609i			1.15154i	0.817612	+	0.575770i	$0.195297\pi$
$103$			118.609i			1.15154i	−0.817612	+	0.575770i	$0.804703\pi$
$104$	13.5355	+	13.5355i	0.130149	+	0.130149i
$105$	13.5132			0.128697
$106$	14.6327	+	14.6327i	0.138044	+	0.138044i
$107$	84.5300	−	84.5300i	0.790000	−	0.790000i	−0.191494	−	0.981494i	$-0.561333\pi$
$107$	84.5300	−	84.5300i	0.790000	−	0.790000i	0.981494	+	0.191494i	$0.0613333\pi$
$108$	38.8278	+	38.8278i	0.359517	+	0.359517i
$109$	77.6544	−	77.6544i	0.712426	−	0.712426i	−0.254616	−	0.967042i	$-0.581949\pi$
$109$	77.6544	−	77.6544i	0.712426	−	0.712426i	0.967042	+	0.254616i	$0.0819492\pi$
$110$	−79.7899	+	79.7899i	−0.725363	+	0.725363i
$111$	95.2202	+	95.2202i	0.857839	+	0.857839i
$112$	−4.82495	+	4.82495i	−0.0430799	+	0.0430799i
$113$	91.0299	−	91.0299i	0.805574	−	0.805574i	−0.178387	−	0.983960i	$-0.557088\pi$
$113$	91.0299	−	91.0299i	0.805574	−	0.805574i	0.983960	+	0.178387i	$0.0570877\pi$
$114$	−3.85356	−	3.85356i	−0.0338032	−	0.0338032i
$115$	−68.5727			−0.596285
$116$	31.0143	+	31.0143i	0.267365	+	0.267365i
$117$	36.0608			0.308212
$118$	−147.109			−1.24669
$119$	−40.2172			−0.337960
$120$	22.4056			0.186713
$121$	−251.510			−2.07860
$122$	−9.57289	−	9.57289i	−0.0784663	−	0.0784663i
$123$	−95.1699	−	95.1699i	−0.773739	−	0.773739i
$124$	−9.67450	−	9.67450i	−0.0780202	−	0.0780202i
$125$	−136.050			−1.08840
$126$			12.8544i			0.102019i
$127$			90.4399i			0.712125i	0.934462	+	0.356063i	$0.115881\pi$
$127$			90.4399i			0.712125i	−0.934462	+	0.356063i	$0.884119\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$	11.5650	−	11.5650i	0.0896511	−	0.0896511i
$130$	27.9785	−	27.9785i	0.215219	−	0.215219i
$131$	−128.918			−0.984107			−0.492053	−	0.870565i	$-0.663754\pi$
$131$	−128.918			−0.984107			−0.492053	+	0.870565i	$0.663754\pi$
$132$	52.3018	+	52.3018i	0.396226	+	0.396226i
$133$		−	3.43066i		−	0.0257945i
$134$	−46.8008	−	46.8008i	−0.349260	−	0.349260i
$135$	80.2586	−	80.2586i	0.594508	−	0.594508i
$136$	−66.6820			−0.490309
$137$	−62.2079	+	62.2079i	−0.454072	+	0.454072i	−0.896704	−	0.442631i	$-0.854045\pi$
$137$	−62.2079	+	62.2079i	−0.454072	+	0.454072i	0.442631	+	0.896704i	$0.354045\pi$
$138$			44.9490i			0.325718i
$139$	116.711	+	116.711i	0.839645	+	0.839645i	0.988812	−	0.149167i	$-0.0476591\pi$
$139$	116.711	+	116.711i	0.839645	+	0.839645i	−0.149167	+	0.988812i	$0.547659\pi$
$140$	9.97337	+	9.97337i	0.0712383	+	0.0712383i
$141$	57.0474	+	57.0474i	0.404591	+	0.404591i
$142$	110.225			0.776231
$143$	130.621			0.913437
$144$			21.3133i			0.148009i
$145$	64.1078	−	64.1078i	0.442123	−	0.442123i
$146$	−140.193	+	140.193i	−0.960226	+	0.960226i
$147$	−62.4488	+	62.4488i	−0.424822	+	0.424822i
$148$			140.553i			0.949685i
$149$			112.362i			0.754109i	0.926191	+	0.377055i	$0.123063\pi$
$149$			112.362i			0.754109i	−0.926191	+	0.377055i	$0.876937\pi$
$150$			21.4334i			0.142889i
$151$		−	214.710i		−	1.42192i	−0.703233	−	0.710959i	$-0.748261\pi$
$151$		−	214.710i		−	1.42192i	0.703233	−	0.710959i	$-0.251739\pi$
$152$		−	5.68820i		−	0.0374224i
$153$	−88.8258	+	88.8258i	−0.580561	+	0.580561i
$154$			46.5621i			0.302351i
$155$	−19.9976	+	19.9976i	−0.129017	+	0.129017i
$156$	−18.3397	−	18.3397i	−0.117562	−	0.117562i
$157$	161.118	+	161.118i	1.02623	+	1.02623i	0.999647	+	0.0265836i	$0.00846281\pi$
$157$	161.118	+	161.118i	1.02623	+	1.02623i	0.0265836	+	0.999647i	$0.491537\pi$
$158$	138.548	−	138.548i	0.876887	−	0.876887i
$159$	−19.8263	−	19.8263i	−0.124694	−	0.124694i
$160$	16.5363	+	16.5363i	0.103352	+	0.103352i
$161$	−20.0081	+	20.0081i	−0.124274	+	0.124274i
$162$	−4.65415	−	4.65415i	−0.0287293	−	0.0287293i
$163$	36.1819	−	36.1819i	0.221975	−	0.221975i	−0.587355	−	0.809330i	$-0.699831\pi$
$163$	36.1819	−	36.1819i	0.221975	−	0.221975i	0.809330	+	0.587355i	$0.199831\pi$
$164$		−	140.479i		−	0.856581i
$165$	108.110	−	108.110i	0.655211	−	0.655211i
$166$	63.1774			0.380587
$167$	118.814	+	118.814i	0.711459	+	0.711459i	0.966840	−	0.255381i	$-0.0822010\pi$
$167$	118.814	+	118.814i	0.711459	+	0.711459i	−0.255381	+	0.966840i	$0.582201\pi$
$168$	6.53748	−	6.53748i	0.0389136	−	0.0389136i
$169$	123.197			0.728978
$170$			137.834i			0.810791i
$171$	−7.57714	−	7.57714i	−0.0443108	−	0.0443108i
$172$	17.0710			0.0992498
$173$	135.664			0.784186			0.392093	−	0.919926i	$-0.371751\pi$
$173$	135.664			0.784186			0.392093	+	0.919926i	$0.371751\pi$
$174$	−42.0223	−	42.0223i	−0.241507	−	0.241507i
$175$	−9.54061	+	9.54061i	−0.0545178	+	0.0545178i
$176$			77.2021i			0.438648i
$177$	199.323			1.12612
$178$	−90.2303	+	90.2303i	−0.506912	+	0.506912i
$179$	215.551	+	215.551i	1.20419	+	1.20419i	0.972879	+	0.231315i	$0.0743029\pi$
$179$	215.551	+	215.551i	1.20419	+	1.20419i	0.231315	+	0.972879i	$0.425697\pi$
$180$	44.0554			0.244752
$181$	−17.9617	+	17.9617i	−0.0992359	+	0.0992359i	−0.754982	−	0.655746i	$-0.772354\pi$
$181$	−17.9617	+	17.9617i	−0.0992359	+	0.0992359i	0.655746	+	0.754982i	$0.272354\pi$
$182$		−	16.3271i		−	0.0897092i
$183$	12.9706	+	12.9706i	0.0708777	+	0.0708777i
$184$	−33.1744	+	33.1744i	−0.180296	+	0.180296i
$185$	290.529			1.57043
$186$	13.1083	+	13.1083i	0.0704747	+	0.0704747i
$187$	−321.750	+	321.750i	−1.72059	+	1.72059i
$188$			84.2070i			0.447909i
$189$		−	46.8356i		−	0.247807i
$190$	−11.7577			−0.0618828
$191$			0.142693i			0.000747085i	1.00000		0.000373543i	$0.000118902\pi$
$191$			0.142693i			0.000747085i	−1.00000		0.000373543i	$0.999881\pi$
$192$	10.8395	−	10.8395i	0.0564555	−	0.0564555i
$193$	−142.103	+	142.103i	−0.736286	+	0.736286i	−0.971857	−	0.235571i	$-0.924304\pi$
$193$	−142.103	+	142.103i	−0.736286	+	0.736286i	0.235571	+	0.971857i	$0.424304\pi$
$194$	−70.9662	+	70.9662i	−0.365805	+	0.365805i
$195$	−37.9089	+	37.9089i	−0.194405	+	0.194405i
$196$	−92.1800			−0.470306
$197$	97.0567	−	97.0567i	0.492674	−	0.492674i	−0.416474	−	0.909148i	$-0.636734\pi$
$197$	97.0567	−	97.0567i	0.492674	−	0.492674i	0.909148	+	0.416474i	$0.136734\pi$
$198$	102.839	+	102.839i	0.519391	+	0.519391i
$199$			271.148i			1.36255i	0.732025	+	0.681277i	$0.238575\pi$
$199$			271.148i			1.36255i	−0.732025	+	0.681277i	$0.761425\pi$
$200$	−15.8188	+	15.8188i	−0.0790939	+	0.0790939i
$201$	63.4119	+	63.4119i	0.315482	+	0.315482i
$202$		−	234.831i		−	1.16253i
$203$		−	37.4107i		−	0.184289i
$204$	90.3496			0.442890
$205$	−290.376			−1.41647
$206$	118.609	−	118.609i	0.575770	−	0.575770i
$207$			88.3818i			0.426965i
$208$		−	27.0711i		−	0.130149i
$209$	−27.4463	−	27.4463i	−0.131322	−	0.131322i
$210$	−13.5132	−	13.5132i	−0.0643487	−	0.0643487i
$211$		−	37.2983i		−	0.176769i	−0.996086	−	0.0883845i	$-0.971830\pi$
$211$		−	37.2983i		−	0.176769i	0.996086	−	0.0883845i	$-0.0281704\pi$
$212$		−	29.2654i		−	0.138044i
$213$	−149.347			−0.701160
$214$	−169.060			−0.790000
$215$		−	35.2864i		−	0.164123i
$216$		−	77.6556i		−	0.359517i
$217$			11.6698i			0.0537777i
$218$	−155.309			−0.712426
$219$	189.952	−	189.952i	0.867360	−	0.867360i
$220$	159.580			0.725363
$221$	112.822	−	112.822i	0.510507	−	0.510507i
$222$		−	190.440i		−	0.857839i
$223$	−225.529	+	225.529i	−1.01134	+	1.01134i	−0.0114070	+	0.999935i	$0.503631\pi$
$223$	−225.529	+	225.529i	−1.01134	+	1.01134i	−0.999935	+	0.0114070i	$0.996369\pi$
$224$	9.64990			0.0430799
$225$			42.1438i			0.187306i
$226$	−182.060			−0.805574
$227$	1.39544	−	1.39544i	0.00614733	−	0.00614733i	−0.704026	−	0.710174i	$-0.748616\pi$
$227$	1.39544	−	1.39544i	0.00614733	−	0.00614733i	0.710174	+	0.704026i	$0.248616\pi$
$228$			7.70713i			0.0338032i
$229$	−254.395	−	254.395i	−1.11090	−	1.11090i	−0.993029	−	0.117867i	$-0.962394\pi$
$229$	−254.395	−	254.395i	−1.11090	−	1.11090i	−0.117867	−	0.993029i	$-0.537606\pi$
$230$	68.5727	+	68.5727i	0.298142	+	0.298142i
$231$		−	63.0884i		−	0.273110i
$232$		−	62.0286i		−	0.267365i
$233$		−	189.112i		−	0.811638i	−0.913954	−	0.405819i	$-0.866986\pi$
$233$		−	189.112i		−	0.811638i	0.913954	−	0.405819i	$-0.133014\pi$
$234$	−36.0608	−	36.0608i	−0.154106	−	0.154106i
$235$	174.059			0.740677
$236$	147.109	+	147.109i	0.623343	+	0.623343i
$237$	−187.723	+	187.723i	−0.792081	+	0.792081i
$238$	40.2172	+	40.2172i	0.168980	+	0.168980i
$239$	183.675			0.768517			0.384258	−	0.923226i	$-0.374457\pi$
$239$	183.675			0.768517			0.384258	+	0.923226i	$0.374457\pi$
$240$	−22.4056	−	22.4056i	−0.0933566	−	0.0933566i
$241$	−320.027	+	320.027i	−1.32791	+	1.32791i	−0.420726	+	0.907188i	$0.638225\pi$
$241$	−320.027	+	320.027i	−1.32791	+	1.32791i	−0.907188	+	0.420726i	$0.861775\pi$
$242$	251.510	+	251.510i	1.03930	+	1.03930i
$243$	−168.419	−	168.419i	−0.693082	−	0.693082i
$244$			19.1458i			0.0784663i
$245$			190.540i			0.777713i
$246$			190.340i			0.773739i
$247$	9.62411	+	9.62411i	0.0389640	+	0.0389640i
$248$			19.3490i			0.0780202i
$249$	−85.6011			−0.343780
$250$	136.050	+	136.050i	0.544200	+	0.544200i
$251$	281.315	+	281.315i	1.12078	+	1.12078i	0.991625	+	0.129154i	$0.0412261\pi$
$251$	281.315	+	281.315i	1.12078	+	1.12078i	0.129154	+	0.991625i	$0.458774\pi$
$252$	12.8544	−	12.8544i	0.0510097	−	0.0510097i
$253$			320.142i			1.26538i
$254$	90.4399	−	90.4399i	0.356063	−	0.356063i
$255$		−	186.756i		−	0.732377i
$256$	16.0000			0.0625000
$257$	−187.404	−	187.404i	−0.729198	−	0.729198i	0.241262	−	0.970460i	$-0.422439\pi$
$257$	−187.404	−	187.404i	−0.729198	−	0.729198i	−0.970460	+	0.241262i	$0.922439\pi$
$258$	−23.1300			−0.0896511
$259$	84.7704	−	84.7704i	0.327299	−	0.327299i
$260$	−55.9570			−0.215219
$261$	−82.6271	−	82.6271i	−0.316579	−	0.316579i
$262$	128.918	+	128.918i	0.492053	+	0.492053i
$263$	−169.518			−0.644555			−0.322278	−	0.946645i	$-0.604448\pi$
$263$	−169.518			−0.644555			−0.322278	+	0.946645i	$0.604448\pi$
$264$		−	104.604i		−	0.396226i
$265$	−60.4927			−0.228274
$266$	−3.43066	+	3.43066i	−0.0128972	+	0.0128972i
$267$	122.256	−	122.256i	0.457887	−	0.457887i
$268$			93.6016i			0.349260i
$269$	242.167	−	117.115i	0.900250	−	0.435372i
$269$	242.167	−	117.115i	0.900250	−	0.435372i
$270$	−160.517			−0.594508
$271$	−268.648	−	268.648i	−0.991321	−	0.991321i	0.00864200	−	0.999963i	$-0.497249\pi$
$271$	−268.648	−	268.648i	−0.991321	−	0.991321i	−0.999963	+	0.00864200i	$0.997249\pi$
$272$	66.6820	+	66.6820i	0.245155	+	0.245155i
$273$			22.1221i			0.0810332i
$274$	124.416			0.454072
$275$			152.655i			0.555111i
$276$	44.9490	−	44.9490i	0.162859	−	0.162859i
$277$	−210.411	+	210.411i	−0.759606	+	0.759606i	−0.976251	−	0.216645i	$-0.930489\pi$
$277$	−210.411	+	210.411i	−0.759606	+	0.759606i	0.216645	+	0.976251i	$0.430489\pi$
$278$		−	233.421i		−	0.839645i
$279$	25.7744	+	25.7744i	0.0923814	+	0.0923814i
$280$		−	19.9467i		−	0.0712383i
$281$	232.733	−	232.733i	0.828232	−	0.828232i	−0.159040	−	0.987272i	$-0.550840\pi$
$281$	232.733	−	232.733i	0.828232	−	0.828232i	0.987272	+	0.159040i	$0.0508399\pi$
$282$		−	114.095i		−	0.404591i
$283$	125.573			0.443721			0.221860	−	0.975078i	$-0.428787\pi$
$283$	125.573			0.443721			0.221860	+	0.975078i	$0.428787\pi$
$284$	−110.225	−	110.225i	−0.388115	−	0.388115i
$285$	15.9309			0.0558980
$286$	−130.621	−	130.621i	−0.456718	−	0.456718i
$287$	−84.7257	+	84.7257i	−0.295211	+	0.295211i
$288$	21.3133	−	21.3133i	0.0740044	−	0.0740044i
$289$			266.812i			0.923225i
$290$	−128.216			−0.442123
$291$	96.1544	−	96.1544i	0.330427	−	0.330427i
$292$	280.386			0.960226
$293$	−217.883			−0.743628			−0.371814	−	0.928307i	$-0.621264\pi$
$293$	−217.883			−0.743628			−0.371814	+	0.928307i	$0.621264\pi$
$294$	124.898			0.424822
$295$	304.080	−	304.080i	1.03078	−	1.03078i
$296$	140.553	−	140.553i	0.474843	−	0.474843i
$297$	−374.698	−	374.698i	−1.26161	−	1.26161i
$298$	112.362	−	112.362i	0.377055	−	0.377055i
$299$		−	112.258i		−	0.375446i
$300$	21.4334	−	21.4334i	0.0714446	−	0.0714446i
$301$	−10.2958	−	10.2958i	−0.0342054	−	0.0342054i
$302$	−214.710	+	214.710i	−0.710959	+	0.710959i
$303$			318.180i			1.05010i
$304$	−5.68820	+	5.68820i	−0.0187112	+	0.0187112i
$305$	39.5751			0.129754
$306$	177.652			0.580561
$307$	−347.530			−1.13202			−0.566010	−	0.824399i	$-0.691513\pi$
$307$	−347.530			−1.13202			−0.566010	+	0.824399i	$0.691513\pi$
$308$	46.5621	−	46.5621i	0.151176	−	0.151176i
$309$	−160.706	+	160.706i	−0.520086	+	0.520086i
$310$	39.9951			0.129017
$311$	−71.6354	−	71.6354i	−0.230339	−	0.230339i	0.582495	−	0.812834i	$-0.302076\pi$
$311$	−71.6354	−	71.6354i	−0.230339	−	0.230339i	−0.812834	+	0.582495i	$0.802076\pi$
$312$			36.6795i			0.117562i
$313$	151.473			0.483938			0.241969	−	0.970284i	$-0.422207\pi$
$313$	151.473			0.483938			0.241969	+	0.970284i	$0.422207\pi$
$314$		−	322.236i		−	1.02623i
$315$	−26.5706	−	26.5706i	−0.0843512	−	0.0843512i
$316$	−277.096			−0.876887
$317$	−406.287	−	406.287i	−1.28166	−	1.28166i	−0.939722	−	0.341939i	$-0.888916\pi$
$317$	−406.287	−	406.287i	−1.28166	−	1.28166i	−0.341939	−	0.939722i	$-0.611084\pi$
$318$			39.6526i			0.124694i
$319$	−299.296	−	299.296i	−0.938233	−	0.938233i
$320$		−	33.0726i		−	0.103352i
$321$	229.065			0.713597
$322$	40.0162			0.124274
$323$	−47.4126			−0.146788
$324$			9.30830i			0.0287293i
$325$		−	53.5289i		−	0.164704i
$326$	−72.3638			−0.221975
$327$	210.433			0.643526
$328$	−140.479	+	140.479i	−0.428290	+	0.428290i
$329$	50.7868	−	50.7868i	0.154367	−	0.154367i
$330$	−216.220			−0.655211
$331$	−23.3131			−0.0704322			−0.0352161	−	0.999380i	$-0.511212\pi$
$331$	−23.3131			−0.0704322			−0.0352161	+	0.999380i	$0.511212\pi$
$332$	−63.1774	−	63.1774i	−0.190293	−	0.190293i
$333$		−	374.457i		−	1.12449i
$334$		−	237.627i		−	0.711459i
$335$	193.478			0.577547
$336$	−13.0750			−0.0389136
$337$	−213.864	+	213.864i	−0.634610	+	0.634610i	−0.949221	−	0.314611i	$-0.898126\pi$
$337$	−213.864	+	213.864i	−0.634610	+	0.634610i	0.314611	+	0.949221i	$0.398126\pi$
$338$	−123.197	−	123.197i	−0.364489	−	0.364489i
$339$	246.679			0.727665
$340$	137.834	−	137.834i	0.405395	−	0.405395i
$341$	93.3615	+	93.3615i	0.273787	+	0.273787i
$342$			15.1543i			0.0443108i
$343$	114.701	+	114.701i	0.334406	+	0.334406i
$344$	−17.0710	−	17.0710i	−0.0496249	−	0.0496249i
$345$	−92.9114	−	92.9114i	−0.269308	−	0.269308i
$346$	−135.664	−	135.664i	−0.392093	−	0.392093i
$347$	394.336			1.13642			0.568208	−	0.822885i	$-0.307637\pi$
$347$	394.336			1.13642			0.568208	+	0.822885i	$0.307637\pi$
$348$			84.0446i			0.241507i
$349$	152.225			0.436176			0.218088	−	0.975929i	$-0.430018\pi$
$349$	152.225			0.436176			0.218088	+	0.975929i	$0.430018\pi$
$350$	19.0812			0.0545178
$351$	131.389	+	131.389i	0.374327	+	0.374327i
$352$	77.2021	−	77.2021i	0.219324	−	0.219324i
$353$		−	293.430i		−	0.831246i	−0.909537	−	0.415623i	$-0.863564\pi$
$353$		−	293.430i		−	0.831246i	0.909537	−	0.415623i	$-0.136436\pi$
$354$	−199.323	−	199.323i	−0.563058	−	0.563058i
$355$	−227.839	+	227.839i	−0.641800	+	0.641800i
$356$	180.461			0.506912
$357$	−54.4916	−	54.4916i	−0.152637	−	0.152637i
$358$		−	431.102i		−	1.20419i
$359$	−393.911	+	393.911i	−1.09725	+	1.09725i	−0.102514	+	0.994732i	$0.532688\pi$
$359$	−393.911	+	393.911i	−1.09725	+	1.09725i	−0.994732	+	0.102514i	$0.967312\pi$
$360$	−44.0554	−	44.0554i	−0.122376	−	0.122376i
$361$			356.956i			0.988797i
$362$	35.9234			0.0992359
$363$	−340.779	−	340.779i	−0.938786	−	0.938786i
$364$	−16.3271	+	16.3271i	−0.0448546	+	0.0448546i
$365$		−	579.569i		−	1.58786i
$366$		−	25.9412i		−	0.0708777i
$367$	−46.3660	+	46.3660i	−0.126338	+	0.126338i	−0.767448	−	0.641111i	$-0.778474\pi$
$367$	−46.3660	+	46.3660i	−0.126338	+	0.126338i	0.641111	+	0.767448i	$0.278474\pi$
$368$	66.3488			0.180296
$369$			374.259i			1.01425i
$370$	−290.529	−	290.529i	−0.785215	−	0.785215i
$371$	−17.6505	+	17.6505i	−0.0475755	+	0.0475755i
$372$		−	26.2166i		−	0.0704747i
$373$	−373.447	−	373.447i	−1.00120	−	1.00120i	−0.999999	−	0.00119810i	$-0.999619\pi$
$373$	−373.447	−	373.447i	−1.00120	−	1.00120i	−0.00119810	−	0.999999i	$-0.500381\pi$
$374$	643.499			1.72059
$375$	−184.339	−	184.339i	−0.491569	−	0.491569i
$376$	84.2070	−	84.2070i	0.223955	−	0.223955i
$377$	104.949	+	104.949i	0.278379	+	0.278379i
$378$	−46.8356	+	46.8356i	−0.123904	+	0.123904i
$379$	437.082	−	437.082i	1.15325	−	1.15325i	0.167353	−	0.985897i	$-0.446478\pi$
$379$	437.082	−	437.082i	1.15325	−	1.15325i	0.985897	−	0.167353i	$-0.0535218\pi$
$380$	11.7577	+	11.7577i	0.0309414	+	0.0309414i
$381$	−122.540	+	122.540i	−0.321627	+	0.321627i
$382$	0.142693	−	0.142693i	0.000373543	−	0.000373543i
$383$	208.459	+	208.459i	0.544280	+	0.544280i	0.924781	−	0.380501i	$-0.124248\pi$
$383$	208.459	+	208.459i	0.544280	+	0.544280i	−0.380501	+	0.924781i	$0.624248\pi$
$384$	−21.6789			−0.0564555
$385$	−96.2456	−	96.2456i	−0.249989	−	0.249989i
$386$	284.206			0.736286
$387$	−45.4798			−0.117519
$388$	141.932			0.365805
$389$	−204.658			−0.526112			−0.263056	−	0.964781i	$-0.584730\pi$
$389$	−204.658			−0.526112			−0.263056	+	0.964781i	$0.584730\pi$
$390$	75.8179			0.194405
$391$	276.517	+	276.517i	0.707205	+	0.707205i
$392$	92.1800	+	92.1800i	0.235153	+	0.235153i
$393$	−174.675	−	174.675i	−0.444466	−	0.444466i
$394$	−194.113			−0.492674
$395$			572.769i			1.45005i
$396$		−	205.679i		−	0.519391i
$397$	408.960	−	408.960i	1.03013	−	1.03013i	0.0305950	−	0.999532i	$-0.490260\pi$
$397$	408.960	−	408.960i	1.03013	−	1.03013i	0.999532	−	0.0305950i	$-0.00974021\pi$
$398$	271.148	−	271.148i	0.681277	−	0.681277i
$399$	4.64832	−	4.64832i	0.0116499	−	0.0116499i
$400$	31.6376			0.0790939
$401$	146.930	+	146.930i	0.366409	+	0.366409i	0.866166	−	0.499757i	$-0.166577\pi$
$401$	146.930	+	146.930i	0.366409	+	0.366409i	−0.499757	+	0.866166i	$0.666577\pi$
$402$		−	126.824i		−	0.315482i
$403$	−32.7374	−	32.7374i	−0.0812342	−	0.0812342i
$404$	−234.831	+	234.831i	−0.581265	+	0.581265i
$405$	19.2406			0.0475077
$406$	−37.4107	+	37.4107i	−0.0921445	+	0.0921445i
$407$		−	1356.38i		−	3.33262i
$408$	−90.3496	−	90.3496i	−0.221445	−	0.221445i
$409$	−460.109	−	460.109i	−1.12496	−	1.12496i	−0.990985	−	0.133976i	$-0.957226\pi$
$409$	−460.109	−	460.109i	−1.12496	−	1.12496i	−0.133976	−	0.990985i	$-0.542774\pi$
$410$	290.376	+	290.376i	0.708234	+	0.708234i
$411$	−168.575			−0.410158
$412$	−237.217			−0.575770
$413$		−	177.448i		−	0.429657i
$414$	88.3818	−	88.3818i	0.213483	−	0.213483i
$415$	−130.590	+	130.590i	−0.314675	+	0.314675i
$416$	−27.0711	+	27.0711i	−0.0650747	+	0.0650747i
$417$			316.270i			0.758442i
$418$			54.8927i			0.131322i
$419$			211.254i			0.504185i	0.967703	+	0.252093i	$0.0811188\pi$
$419$			211.254i			0.504185i	−0.967703	+	0.252093i	$0.918881\pi$
$420$			27.0265i			0.0643487i
$421$		−	322.049i		−	0.764963i	−0.923963	−	0.382482i	$-0.875070\pi$
$421$		−	322.049i		−	0.764963i	0.923963	−	0.382482i	$-0.124930\pi$
$422$	−37.2983	+	37.2983i	−0.0883845	+	0.0883845i
$423$		−	224.341i		−	0.530356i
$424$	−29.2654	+	29.2654i	−0.0690222	+	0.0690222i
$425$	131.854	+	131.854i	0.310244	+	0.310244i
$426$	149.347	+	149.347i	0.350580	+	0.350580i
$427$	11.5472	−	11.5472i	0.0270426	−	0.0270426i
$428$	169.060	+	169.060i	0.395000	+	0.395000i
$429$	176.983	+	176.983i	0.412548	+	0.412548i
$430$	−35.2864	+	35.2864i	−0.0820613	+	0.0820613i
$431$	477.829	+	477.829i	1.10865	+	1.10865i	0.993328	+	0.115325i	$0.0367909\pi$
$431$	477.829	+	477.829i	1.10865	+	1.10865i	0.115325	+	0.993328i	$0.463209\pi$
$432$	−77.6556	+	77.6556i	−0.179758	+	0.179758i
$433$		−	289.332i		−	0.668204i	−0.942537	−	0.334102i	$-0.891567\pi$
$433$		−	289.332i		−	0.668204i	0.942537	−	0.334102i	$-0.108433\pi$
$434$	11.6698	−	11.6698i	0.0268888	−	0.0268888i
$435$	173.723			0.399364
$436$	155.309	+	155.309i	0.356213	+	0.356213i
$437$	−23.5878	+	23.5878i	−0.0539767	+	0.0539767i
$438$	−379.904			−0.867360
$439$			381.467i			0.868946i	0.900685	+	0.434473i	$0.143065\pi$
$439$			381.467i			0.868946i	−0.900685	+	0.434473i	$0.856935\pi$
$440$	−159.580	−	159.580i	−0.362681	−	0.362681i
$441$	245.582			0.556876
$442$	−225.644			−0.510507
$443$	94.1250	+	94.1250i	0.212472	+	0.212472i	0.805317	−	0.592845i	$-0.201995\pi$
$443$	94.1250	+	94.1250i	0.212472	+	0.212472i	−0.592845	+	0.805317i	$0.701995\pi$
$444$	−190.440	+	190.440i	−0.428920	+	0.428920i
$445$		−	373.019i		−	0.838245i
$446$	451.058			1.01134
$447$	−152.243	+	152.243i	−0.340589	+	0.340589i
$448$	−9.64990	−	9.64990i	−0.0215400	−	0.0215400i
$449$	−386.968			−0.861844			−0.430922	−	0.902389i	$-0.641812\pi$
$449$	−386.968			−0.861844			−0.430922	+	0.902389i	$0.641812\pi$
$450$	42.1438	−	42.1438i	0.0936528	−	0.0936528i
$451$			1355.66i			3.00590i
$452$	182.060	+	182.060i	0.402787	+	0.402787i
$453$	290.917	−	290.917i	0.642201	−	0.642201i
$454$	−2.79089			−0.00614733
$455$	33.7487	+	33.7487i	0.0741730	+	0.0741730i
$456$	7.70713	−	7.70713i	0.0169016	−	0.0169016i
$457$			260.561i			0.570156i	0.958504	+	0.285078i	$0.0920195\pi$
$457$			260.561i			0.570156i	−0.958504	+	0.285078i	$0.907981\pi$
$458$			508.791i			1.11090i
$459$	−647.279			−1.41019
$460$		−	137.145i		−	0.298142i
$461$	−140.515	+	140.515i	−0.304806	+	0.304806i	−0.842891	−	0.538085i	$-0.819148\pi$
$461$	−140.515	+	140.515i	−0.304806	+	0.304806i	0.538085	+	0.842891i	$0.319148\pi$
$462$	−63.0884	+	63.0884i	−0.136555	+	0.136555i
$463$	13.7465	−	13.7465i	0.0296900	−	0.0296900i	−0.692106	−	0.721796i	$-0.743317\pi$
$463$	13.7465	−	13.7465i	0.0296900	−	0.0296900i	0.721796	+	0.692106i	$0.243317\pi$
$464$	−62.0286	+	62.0286i	−0.133682	+	0.133682i
$465$	−54.1907			−0.116539
$466$	−189.112	+	189.112i	−0.405819	+	0.405819i
$467$	379.509	+	379.509i	0.812654	+	0.812654i	0.985031	−	0.172377i	$-0.0551448\pi$
$467$	379.509	+	379.509i	0.812654	+	0.812654i	−0.172377	+	0.985031i	$0.555145\pi$
$468$			72.1216i			0.154106i
$469$	56.4529	−	56.4529i	0.120369	−	0.120369i
$470$	−174.059	−	174.059i	−0.370339	−	0.370339i
$471$			436.608i			0.926981i
$472$		−	294.218i		−	0.623343i
$473$	−164.739			−0.348286
$474$	375.446			0.792081
$475$	−11.2476	+	11.2476i	−0.0236791	+	0.0236791i
$476$		−	80.4344i		−	0.168980i
$477$			77.9677i			0.163454i
$478$	−183.675	−	183.675i	−0.384258	−	0.384258i
$479$	−106.505	−	106.505i	−0.222348	−	0.222348i	0.587139	−	0.809486i	$-0.300254\pi$
$479$	−106.505	−	106.505i	−0.222348	−	0.222348i	−0.809486	+	0.587139i	$0.800254\pi$
$480$			44.8112i			0.0933566i
$481$			475.616i			0.988807i
$482$	640.054			1.32791
$483$	−54.2192			−0.112255
$484$		−	503.021i		−	1.03930i
$485$		−	293.380i		−	0.604907i
$486$			336.838i			0.693082i
$487$	734.709			1.50864			0.754322	−	0.656505i	$-0.227966\pi$
$487$	734.709			1.50864			0.754322	+	0.656505i	$0.227966\pi$
$488$	19.1458	−	19.1458i	0.0392332	−	0.0392332i
$489$	98.0480			0.200507
$490$	190.540	−	190.540i	0.388856	−	0.388856i
$491$			93.2662i			0.189952i	0.995480	+	0.0949758i	$0.0302774\pi$
$491$			93.2662i			0.189952i	−0.995480	+	0.0949758i	$0.969723\pi$
$492$	190.340	−	190.340i	0.386869	−	0.386869i
$493$	−517.025			−1.04873
$494$		−	19.2482i		−	0.0389640i
$495$	−425.146			−0.858881
$496$	19.3490	−	19.3490i	0.0390101	−	0.0390101i
$497$			132.957i			0.267520i
$498$	85.6011	+	85.6011i	0.171890	+	0.171890i
$499$	−53.3635	−	53.3635i	−0.106941	−	0.106941i	0.651612	−	0.758553i	$-0.274093\pi$
$499$	−53.3635	−	53.3635i	−0.106941	−	0.106941i	−0.758553	+	0.651612i	$0.774093\pi$
$500$		−	272.100i		−	0.544200i
$501$			321.969i			0.642652i
$502$		−	562.631i		−	1.12078i
$503$	−305.574	−	305.574i	−0.607504	−	0.607504i	0.334789	−	0.942293i	$-0.391335\pi$
$503$	−305.574	−	305.574i	−0.607504	−	0.607504i	−0.942293	+	0.334789i	$0.891335\pi$
$504$	−25.7089			−0.0510097
$505$	485.405	+	485.405i	0.961198	+	0.961198i
$506$	320.142	−	320.142i	0.632691	−	0.632691i
$507$	166.924	+	166.924i	0.329239	+	0.329239i
$508$	−180.880			−0.356063
$509$	578.603	+	578.603i	1.13674	+	1.13674i	0.989030	+	0.147714i	$0.0471915\pi$
$509$	578.603	+	578.603i	1.13674	+	1.13674i	0.147714	+	0.989030i	$0.452808\pi$
$510$	−186.756	+	186.756i	−0.366189	+	0.366189i
$511$	−169.106	−	169.106i	−0.330932	−	0.330932i
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$		−	55.2151i		−	0.107632i
$514$			374.808i			0.729198i
$515$			490.337i			0.952111i
$516$	23.1300	+	23.1300i	0.0448256	+	0.0448256i
$517$		−	812.619i		−	1.57180i
$518$	−169.541			−0.327299
$519$	183.816	+	183.816i	0.354173	+	0.354173i
$520$	55.9570	+	55.9570i	0.107610	+	0.107610i
$521$	−394.206	+	394.206i	−0.756634	+	0.756634i	−0.975708	−	0.219075i	$-0.929696\pi$
$521$	−394.206	+	394.206i	−0.756634	+	0.756634i	0.219075	+	0.975708i	$0.429696\pi$
$522$			165.254i			0.316579i
$523$	−250.522	+	250.522i	−0.479010	+	0.479010i	−0.904815	−	0.425805i	$-0.859991\pi$
$523$	−250.522	+	250.522i	−0.479010	+	0.479010i	0.425805	+	0.904815i	$0.359991\pi$
$524$		−	257.836i		−	0.492053i
$525$	−25.8538			−0.0492453
$526$	169.518	+	169.518i	0.322278	+	0.322278i
$527$	161.279			0.306032
$528$	−104.604	+	104.604i	−0.198113	+	0.198113i
$529$	−253.865			−0.479896
$530$	60.4927	+	60.4927i	0.114137	+	0.114137i
$531$	−391.922	−	391.922i	−0.738082	−	0.738082i
$532$	6.86133			0.0128972
$533$		−	475.365i		−	0.891867i
$534$	−244.512			−0.457887
$535$	349.453	−	349.453i	0.653184	−	0.653184i
$536$	93.6016	−	93.6016i	0.174630	−	0.174630i
$537$			584.113i			1.08773i
$538$	−359.283	−	125.052i	−0.667811	−	0.232439i
$539$	889.561			1.65039
$540$	160.517	+	160.517i	0.297254	+	0.297254i
$541$	197.420	+	197.420i	0.364917	+	0.364917i	0.865619	−	0.500702i	$-0.166925\pi$
$541$	197.420	+	197.420i	0.364917	+	0.364917i	−0.500702	+	0.865619i	$0.666925\pi$
$542$			537.296i			0.991321i
$543$	−48.6738			−0.0896386
$544$		−	133.364i		−	0.245155i
$545$	321.029	−	321.029i	0.589045	−	0.589045i
$546$	22.1221	−	22.1221i	0.0405166	−	0.0405166i
$547$		−	207.786i		−	0.379865i	−0.981797	−	0.189933i	$-0.939173\pi$
$547$		−	207.786i		−	0.379865i	0.981797	−	0.189933i	$-0.0608270\pi$
$548$	−124.416	−	124.416i	−0.227036	−	0.227036i
$549$		−	51.0074i		−	0.0929097i
$550$	152.655	−	152.655i	0.277555	−	0.277555i
$551$		−	44.1039i		−	0.0800434i
$552$	−89.8981			−0.162859
$553$	167.122	+	167.122i	0.302210	+	0.302210i
$554$	420.822			0.759606
$555$	393.648	+	393.648i	0.709275	+	0.709275i
$556$	−233.421	+	233.421i	−0.419823	+	0.419823i
$557$	−184.731	+	184.731i	−0.331653	+	0.331653i	−0.853214	−	0.521561i	$-0.825350\pi$
$557$	−184.731	+	184.731i	−0.331653	+	0.331653i	0.521561	+	0.853214i	$0.325350\pi$
$558$		−	51.5488i		−	0.0923814i
$559$	57.7662			0.103338
$560$	−19.9467	+	19.9467i	−0.0356192	+	0.0356192i
$561$	−871.898			−1.55419
$562$	−465.466			−0.828232
$563$	−45.2885			−0.0804413			−0.0402207	−	0.999191i	$-0.512806\pi$
$563$	−45.2885			−0.0804413			−0.0402207	+	0.999191i	$0.512806\pi$
$564$	−114.095	+	114.095i	−0.202296	+	0.202296i
$565$	376.325	−	376.325i	0.666061	−	0.666061i
$566$	−125.573	−	125.573i	−0.221860	−	0.221860i
$567$	5.61401	−	5.61401i	0.00990125	−	0.00990125i
$568$			220.449i			0.388115i
$569$	170.994	−	170.994i	0.300517	−	0.300517i	−0.540699	−	0.841216i	$-0.681840\pi$
$569$	170.994	−	170.994i	0.300517	−	0.300517i	0.841216	+	0.540699i	$0.181840\pi$
$570$	−15.9309	−	15.9309i	−0.0279490	−	0.0279490i
$571$	604.531	−	604.531i	1.05872	−	1.05872i	0.0605590	−	0.998165i	$-0.480712\pi$
$571$	604.531	−	604.531i	1.05872	−	1.05872i	0.998165	−	0.0605590i	$-0.0192883\pi$
$572$			261.243i			0.456718i
$573$	−0.193340	+	0.193340i	−0.000337416	+	0.000337416i
$574$	169.451			0.295211
$575$	131.195			0.228165
$576$	−42.6266			−0.0740044
$577$	431.928	−	431.928i	0.748575	−	0.748575i	−0.225636	−	0.974212i	$-0.572446\pi$
$577$	431.928	−	431.928i	0.748575	−	0.748575i	0.974212	+	0.225636i	$0.0724462\pi$
$578$	266.812	−	266.812i	0.461612	−	0.461612i
$579$	−385.080			−0.665078
$580$	128.216	+	128.216i	0.221061	+	0.221061i
$581$			76.2070i			0.131165i
$582$	−192.309			−0.330427
$583$			282.419i			0.484423i
$584$	−280.386	−	280.386i	−0.480113	−	0.480113i
$585$	149.078			0.254835
$586$	217.883	+	217.883i	0.371814	+	0.371814i
$587$		−	165.837i		−	0.282515i	−0.989973	−	0.141258i	$-0.954885\pi$
$587$		−	165.837i		−	0.282515i	0.989973	−	0.141258i	$-0.0451146\pi$
$588$	−124.898	−	124.898i	−0.212411	−	0.212411i
$589$			13.7576i			0.0233576i
$590$	−608.160			−1.03078
$591$	263.010			0.445026
$592$	−281.107			−0.474843
$593$			420.098i			0.708428i	0.935164	+	0.354214i	$0.115252\pi$
$593$			420.098i			0.708428i	−0.935164	+	0.354214i	$0.884748\pi$
$594$			749.397i			1.26161i
$595$	−166.261			−0.279430
$596$	−224.725			−0.377055
$597$	−367.388	+	367.388i	−0.615390	+	0.615390i
$598$	−112.258	+	112.258i	−0.187723	+	0.187723i
$599$	52.4767			0.0876071			0.0438036	−	0.999040i	$-0.486052\pi$
$599$	52.4767			0.0876071			0.0438036	+	0.999040i	$0.486052\pi$
$600$	−42.8668			−0.0714446
$601$	404.839	+	404.839i	0.673608	+	0.673608i	0.958546	−	0.284938i	$-0.0919729\pi$
$601$	404.839	+	404.839i	0.673608	+	0.673608i	−0.284938	+	0.958546i	$0.591973\pi$
$602$			20.5916i			0.0342054i
$603$		−	249.370i		−	0.413548i
$604$	429.419			0.710959
$605$	−1039.76			−1.71862
$606$	318.180	−	318.180i	0.525050	−	0.525050i
$607$	19.7360	+	19.7360i	0.0325140	+	0.0325140i	0.723177	−	0.690663i	$-0.242681\pi$
$607$	19.7360	+	19.7360i	0.0325140	+	0.0325140i	−0.690663	+	0.723177i	$0.742681\pi$
$608$	11.3764			0.0187112
$609$	50.6889	−	50.6889i	0.0832330	−	0.0832330i
$610$	−39.5751	−	39.5751i	−0.0648772	−	0.0648772i
$611$			284.947i			0.466361i
$612$	−177.652	−	177.652i	−0.290280	−	0.290280i
$613$	−515.187	−	515.187i	−0.840435	−	0.840435i	0.148480	−	0.988915i	$-0.452562\pi$
$613$	−515.187	−	515.187i	−0.840435	−	0.840435i	−0.988915	+	0.148480i	$0.952562\pi$
$614$	347.530	+	347.530i	0.566010	+	0.566010i
$615$	−393.440	−	393.440i	−0.639740	−	0.639740i
$616$	−93.1241			−0.151176
$617$			1001.26i			1.62278i	0.584504	+	0.811391i	$0.301289\pi$
$617$			1001.26i			1.62278i	−0.584504	+	0.811391i	$0.698711\pi$
$618$	321.413			0.520086
$619$	506.265			0.817875			0.408937	−	0.912562i	$-0.365899\pi$
$619$	506.265			0.817875			0.408937	+	0.912562i	$0.365899\pi$
$620$	−39.9951	−	39.9951i	−0.0645083	−	0.0645083i
$621$	−322.022	+	322.022i	−0.518554	+	0.518554i
$622$			143.271i			0.230339i
$623$	−108.839	−	108.839i	−0.174702	−	0.174702i
$624$	36.6795	−	36.6795i	0.0587812	−	0.0587812i
$625$	−364.707			−0.583531
$626$	−151.473	−	151.473i	−0.241969	−	0.241969i
$627$		−	74.3758i		−	0.118622i
$628$	−322.236	+	322.236i	−0.513115	+	0.513115i
$629$	−1171.55	−	1171.55i	−1.86256	−	1.86256i
$630$			53.1413i			0.0843512i
$631$	1228.46			1.94685			0.973426	−	0.229003i	$-0.0735466\pi$
$631$	1228.46			1.94685			0.973426	+	0.229003i	$0.0735466\pi$
$632$	277.096	+	277.096i	0.438443	+	0.438443i
$633$	50.5366	−	50.5366i	0.0798366	−	0.0798366i
$634$			812.573i			1.28166i
$635$			373.886i			0.588796i
$636$	39.6526	−	39.6526i	0.0623469	−	0.0623469i
$637$	−311.926			−0.489680
$638$			598.593i			0.938233i
$639$	293.656	+	293.656i	0.459556	+	0.459556i
$640$	−33.0726	+	33.0726i	−0.0516760	+	0.0516760i
$641$		−	806.884i		−	1.25879i	−0.777086	−	0.629394i	$-0.783303\pi$
$641$		−	806.884i		−	1.25879i	0.777086	−	0.629394i	$-0.216697\pi$
$642$	−229.065	−	229.065i	−0.356799	−	0.356799i
$643$	−164.483			−0.255806			−0.127903	−	0.991787i	$-0.540825\pi$
$643$	−164.483			−0.255806			−0.127903	+	0.991787i	$0.540825\pi$
$644$	−40.0162	−	40.0162i	−0.0621370	−	0.0621370i
$645$	47.8106	−	47.8106i	0.0741250	−	0.0741250i
$646$	47.4126	+	47.4126i	0.0733942	+	0.0733942i
$647$	297.797	−	297.797i	0.460274	−	0.460274i	−0.438471	−	0.898745i	$-0.644480\pi$
$647$	297.797	−	297.797i	0.460274	−	0.460274i	0.898745	+	0.438471i	$0.144480\pi$
$648$	9.30830	−	9.30830i	0.0143647	−	0.0143647i
$649$	−1419.64	−	1419.64i	−2.18743	−	2.18743i
$650$	−53.5289	+	53.5289i	−0.0823522	+	0.0823522i
$651$	−15.8117	+	15.8117i	−0.0242884	+	0.0242884i
$652$	72.3638	+	72.3638i	0.110987	+	0.110987i
$653$	203.101			0.311027			0.155514	−	0.987834i	$-0.450297\pi$
$653$	203.101			0.311027			0.155514	+	0.987834i	$0.450297\pi$
$654$	−210.433	−	210.433i	−0.321763	−	0.321763i
$655$	−532.957			−0.813675
$656$	280.958			0.428290
$657$	−746.993			−1.13698
$658$	−101.574			−0.154367
$659$	1116.98			1.69496			0.847478	−	0.530831i	$-0.178120\pi$
$659$	1116.98			1.69496			0.847478	+	0.530831i	$0.178120\pi$
$660$	216.220	+	216.220i	0.327606	+	0.327606i
$661$	256.482	+	256.482i	0.388021	+	0.388021i	0.873981	−	0.485960i	$-0.161530\pi$
$661$	256.482	+	256.482i	0.388021	+	0.388021i	−0.485960	+	0.873981i	$0.661530\pi$
$662$	23.3131	+	23.3131i	0.0352161	+	0.0352161i
$663$	305.733			0.461135
$664$			126.355i			0.190293i
$665$		−	14.1826i		−	0.0213273i
$666$	−374.457	+	374.457i	−0.562247	+	0.562247i
$667$	−257.220	+	257.220i	−0.385638	+	0.385638i
$668$	−237.627	+	237.627i	−0.355730	+	0.355730i
$669$	−611.154			−0.913533
$670$	−193.478	−	193.478i	−0.288773	−	0.288773i
$671$		−	184.762i		−	0.275353i
$672$	13.0750	+	13.0750i	0.0194568	+	0.0194568i
$673$	419.313	−	419.313i	0.623051	−	0.623051i	−0.323260	−	0.946310i	$-0.604779\pi$
$673$	419.313	−	419.313i	0.623051	−	0.623051i	0.946310	+	0.323260i	$0.104779\pi$
$674$	427.727			0.634610
$675$	−153.552	+	153.552i	−0.227485	+	0.227485i
$676$			246.395i			0.364489i
$677$	−167.928	−	167.928i	−0.248047	−	0.248047i	0.572122	−	0.820169i	$-0.306120\pi$
$677$	−167.928	−	167.928i	−0.248047	−	0.248047i	−0.820169	+	0.572122i	$0.806120\pi$
$678$	−246.679	−	246.679i	−0.363833	−	0.363833i
$679$	−85.6021	−	85.6021i	−0.126071	−	0.126071i
$680$	−275.669			−0.405395
$681$	3.78146			0.00555281
$682$		−	186.723i		−	0.273787i
$683$	−130.637	+	130.637i	−0.191270	+	0.191270i	−0.796245	−	0.604975i	$-0.793183\pi$
$683$	−130.637	+	130.637i	−0.191270	+	0.191270i	0.604975	+	0.796245i	$0.293183\pi$
$684$	15.1543	−	15.1543i	0.0221554	−	0.0221554i
$685$	−257.172	+	257.172i	−0.375434	+	0.375434i
$686$		−	229.402i		−	0.334406i
$687$		−	689.377i		−	1.00346i
$688$			34.1419i			0.0496249i
$689$		−	99.0307i		−	0.143731i
$690$			185.823i			0.269308i
$691$	−440.968	+	440.968i	−0.638160	+	0.638160i	−0.950101	−	0.311942i	$-0.899021\pi$
$691$	−440.968	+	440.968i	−0.638160	+	0.638160i	0.311942	+	0.950101i	$0.399021\pi$
$692$			271.328i			0.392093i
$693$	−124.049	+	124.049i	−0.179003	+	0.179003i
$694$	−394.336	−	394.336i	−0.568208	−	0.568208i
$695$	482.491	+	482.491i	0.694232	+	0.694232i
$696$	84.0446	−	84.0446i	0.120754	−	0.120754i
$697$	1170.93	+	1170.93i	1.67996	+	1.67996i
$698$	−152.225	−	152.225i	−0.218088	−	0.218088i
$699$	256.233	−	256.233i	0.366571	−	0.366571i
$700$	−19.0812	−	19.0812i	−0.0272589	−	0.0272589i
$701$	−199.862	+	199.862i	−0.285110	+	0.285110i	−0.835143	−	0.550033i	$-0.814615\pi$
$701$	−199.862	+	199.862i	−0.285110	+	0.285110i	0.550033	+	0.835143i	$0.314615\pi$
$702$		−	262.777i		−	0.374327i
$703$	99.9370	−	99.9370i	0.142158	−	0.142158i
$704$	−154.404			−0.219324
$705$	235.838	+	235.838i	0.334522	+	0.334522i
$706$	−293.430	+	293.430i	−0.415623	+	0.415623i
$707$	283.262			0.400654
$708$			398.645i			0.563058i
$709$	50.4814	+	50.4814i	0.0712009	+	0.0712009i	0.741810	−	0.670610i	$-0.233967\pi$
$709$	50.4814	+	50.4814i	0.0712009	+	0.0712009i	−0.670610	+	0.741810i	$0.733967\pi$
$710$	455.678			0.641800
$711$	738.228			1.03830
$712$	−180.461	−	180.461i	−0.253456	−	0.253456i
$713$	80.2364	−	80.2364i	0.112534	−	0.112534i
$714$			108.983i			0.152637i
$715$	539.999			0.755244
$716$	−431.102	+	431.102i	−0.602097	+	0.602097i
$717$	248.868	+	248.868i	0.347096	+	0.347096i
$718$	787.822			1.09725
$719$	27.8704	−	27.8704i	0.0387627	−	0.0387627i	−0.687460	−	0.726222i	$-0.741274\pi$
$719$	27.8704	−	27.8704i	0.0387627	−	0.0387627i	0.726222	+	0.687460i	$0.241274\pi$
$720$			88.1108i			0.122376i
$721$	143.070	+	143.070i	0.198433	+	0.198433i
$722$	356.956	−	356.956i	0.494398	−	0.494398i
$723$	−867.230			−1.19949
$724$	−35.9234	−	35.9234i	−0.0496180	−	0.0496180i
$725$	−122.652	+	122.652i	−0.169176	+	0.169176i
$726$			681.559i			0.938786i
$727$			520.753i			0.716305i	0.933663	+	0.358152i	$0.116593\pi$
$727$			520.753i			0.716305i	−0.933663	+	0.358152i	$0.883407\pi$
$728$	32.6542			0.0448546
$729$		−	498.280i		−	0.683512i
$730$	−579.569	+	579.569i	−0.793930	+	0.793930i
$731$	−142.291	+	142.291i	−0.194652	+	0.194652i
$732$	−25.9412	+	25.9412i	−0.0354388	+	0.0354388i
$733$	200.793	−	200.793i	0.273934	−	0.273934i	−0.556748	−	0.830681i	$-0.687951\pi$
$733$	200.793	−	200.793i	0.273934	−	0.273934i	0.830681	+	0.556748i	$0.187951\pi$
$734$	92.7319			0.126338
$735$	−258.168	+	258.168i	−0.351249	+	0.351249i
$736$	−66.3488	−	66.3488i	−0.0901478	−	0.0901478i
$737$		−	903.280i		−	1.22562i
$738$	374.259	−	374.259i	0.507126	−	0.507126i
$739$	632.167	+	632.167i	0.855436	+	0.855436i	0.990796	−	0.135360i	$-0.0432193\pi$
$739$	632.167	+	632.167i	0.855436	+	0.855436i	−0.135360	+	0.990796i	$0.543219\pi$
$740$			581.059i			0.785215i
$741$			26.0800i			0.0351957i
$742$	35.3010			0.0475755
$743$	−57.7485			−0.0777234			−0.0388617	−	0.999245i	$-0.512373\pi$
$743$	−57.7485			−0.0777234			−0.0388617	+	0.999245i	$0.512373\pi$
$744$	−26.2166	+	26.2166i	−0.0352373	+	0.0352373i
$745$			464.515i			0.623510i
$746$			746.893i			1.00120i
$747$	168.315	+	168.315i	0.225321	+	0.225321i
$748$	−643.499	−	643.499i	−0.860293	−	0.860293i
$749$		−	203.926i		−	0.272265i
$750$			368.677i			0.491569i
$751$	−248.434			−0.330805			−0.165402	−	0.986226i	$-0.552892\pi$
$751$	−248.434			−0.330805			−0.165402	+	0.986226i	$0.552892\pi$
$752$	−168.414			−0.223955
$753$			762.326i			1.01239i
$754$		−	209.898i		−	0.278379i
$755$		−	887.627i		−	1.17566i
$756$	93.6711			0.123904
$757$	842.600	−	842.600i	1.11308	−	1.11308i	0.120345	−	0.992732i	$-0.461600\pi$
$757$	842.600	−	842.600i	1.11308	−	1.11308i	0.992732	−	0.120345i	$-0.0384001\pi$
$758$	−874.163			−1.15325
$759$	−433.770	+	433.770i	−0.571502	+	0.571502i
$760$		−	23.5155i		−	0.0309414i
$761$	547.919	−	547.919i	0.719998	−	0.719998i	−0.248606	−	0.968605i	$-0.579973\pi$
$761$	547.919	−	547.919i	0.719998	−	0.719998i	0.968605	+	0.248606i	$0.0799725\pi$
$762$	245.080			0.321627
$763$		−	187.339i		−	0.245530i
$764$	−0.285386			−0.000373543
$765$	−367.213	+	367.213i	−0.480017	+	0.480017i
$766$		−	416.919i		−	0.544280i
$767$	497.799	+	497.799i	0.649021	+	0.649021i
$768$	21.6789	+	21.6789i	0.0282277	+	0.0282277i
$769$		−	786.986i		−	1.02339i	−0.859167	−	0.511695i	$-0.829018\pi$
$769$		−	786.986i		−	1.02339i	0.859167	−	0.511695i	$-0.170982\pi$
$770$			192.491i			0.249989i
$771$		−	507.839i		−	0.658676i
$772$	−284.206	−	284.206i	−0.368143	−	0.368143i
$773$	918.105			1.18772			0.593859	−	0.804569i	$-0.297604\pi$
$773$	918.105			1.18772			0.593859	+	0.804569i	$0.297604\pi$
$774$	45.4798	+	45.4798i	0.0587594	+	0.0587594i
$775$	38.2597	−	38.2597i	0.0493674	−	0.0493674i
$776$	−141.932	−	141.932i	−0.182903	−	0.182903i
$777$	229.716			0.295645
$778$	204.658	+	204.658i	0.263056	+	0.263056i
$779$	−99.8843	+	99.8843i	−0.128221	+	0.128221i
$780$	−75.8179	−	75.8179i	−0.0972024	−	0.0972024i
$781$	1063.70	+	1063.70i	1.36197	+	1.36197i
$782$		−	553.034i		−	0.707205i
$783$		−	602.109i		−	0.768977i
$784$		−	184.360i		−	0.235153i
$785$	666.075	+	666.075i	0.848503	+	0.848503i
$786$			349.350i			0.444466i
$787$	904.951			1.14987			0.574937	−	0.818198i	$-0.305026\pi$
$787$	904.951			1.14987			0.574937	+	0.818198i	$0.305026\pi$
$788$	194.113	+	194.113i	0.246337	+	0.246337i
$789$	−229.685	−	229.685i	−0.291110	−	0.291110i
$790$	572.769	−	572.769i	0.725024	−	0.725024i
$791$		−	219.607i		−	0.277633i
$792$	−205.679	+	205.679i	−0.259695	+	0.259695i
$793$			64.7871i			0.0816987i
$794$	−817.921			−1.03013
$795$	−81.9635	−	81.9635i	−0.103099	−	0.103099i
$796$	−542.297			−0.681277
$797$	−839.661	+	839.661i	−1.05353	+	1.05353i	−0.0550428	+	0.998484i	$0.517530\pi$
$797$	−839.661	+	839.661i	−1.05353	+	1.05353i	−0.998484	+	0.0550428i	$0.982470\pi$
$798$	−9.29663			−0.0116499
$799$	−701.887	−	701.887i	−0.878456	−	0.878456i
$800$	−31.6376	−	31.6376i	−0.0395470	−	0.0395470i
$801$	−480.776			−0.600219
$802$		−	293.860i		−	0.366409i
$803$	−2705.80			−3.36961
$804$	−126.824	+	126.824i	−0.157741	+	0.157741i
$805$	−82.7151	+	82.7151i	−0.102752	+	0.102752i
$806$			65.4748i			0.0812342i
$807$	486.803	+	169.437i	0.603226	+	0.209959i
$808$	469.662			0.581265
$809$	−265.986	−	265.986i	−0.328783	−	0.328783i	0.523340	−	0.852124i	$-0.324686\pi$
$809$	−265.986	−	265.986i	−0.328783	−	0.328783i	−0.852124	+	0.523340i	$0.824686\pi$
$810$	−19.2406	−	19.2406i	−0.0237538	−	0.0237538i
$811$			656.818i			0.809887i	0.914342	+	0.404943i	$0.132709\pi$
$811$			656.818i			0.809887i	−0.914342	+	0.404943i	$0.867291\pi$
$812$	74.8213			0.0921445
$813$		−	727.999i		−	0.895448i
$814$	−1356.38	+	1356.38i	−1.66631	+	1.66631i
$815$	149.579	−	149.579i	0.183532	−	0.183532i
$816$			180.699i			0.221445i
$817$	−12.1379	−	12.1379i	−0.0148567	−	0.0148567i
$818$			920.218i			1.12496i
$819$	43.4979	−	43.4979i	0.0531110	−	0.0531110i
$820$		−	580.752i		−	0.708234i
$821$	40.4097			0.0492202			0.0246101	−	0.999697i	$-0.492166\pi$
$821$	40.4097			0.0492202			0.0246101	+	0.999697i	$0.492166\pi$
$822$	168.575	+	168.575i	0.205079	+	0.205079i
$823$	1024.68			1.24506			0.622529	−	0.782597i	$-0.286105\pi$
$823$	1024.68			1.24506			0.622529	+	0.782597i	$0.286105\pi$
$824$	237.217	+	237.217i	0.287885	+	0.287885i
$825$	−206.838	+	206.838i	−0.250712	+	0.250712i
$826$	−177.448	+	177.448i	−0.214829	+	0.214829i
$827$		−	1592.90i		−	1.92611i	−0.269299	−	0.963057i	$-0.586792\pi$
$827$		−	1592.90i		−	1.92611i	0.269299	−	0.963057i	$-0.413208\pi$
$828$	−176.764			−0.213483
$829$	81.5564	−	81.5564i	0.0983792	−	0.0983792i	−0.656204	−	0.754583i	$-0.727839\pi$
$829$	81.5564	−	81.5564i	0.0983792	−	0.0983792i	0.754583	+	0.656204i	$0.227839\pi$
$830$	261.180			0.314675
$831$	−570.185			−0.686143
$832$	54.1421			0.0650747
$833$	768.344	−	768.344i	0.922381	−	0.922381i
$834$	316.270	−	316.270i	0.379221	−	0.379221i
$835$	491.185	+	491.185i	0.588246	+	0.588246i
$836$	54.8927	−	54.8927i	0.0656611	−	0.0656611i
$837$			187.820i			0.224396i
$838$	211.254	−	211.254i	0.252093	−	0.252093i
$839$	−309.574	−	309.574i	−0.368979	−	0.368979i	0.498125	−	0.867105i	$-0.334022\pi$
$839$	−309.574	−	309.574i	−0.368979	−	0.368979i	−0.867105	+	0.498125i	$0.834022\pi$
$840$	27.0265	−	27.0265i	0.0321744	−	0.0321744i
$841$			360.056i			0.428128i
$842$	−322.049	+	322.049i	−0.382482	+	0.382482i
$843$	630.675			0.748132
$844$	74.5965			0.0883845
$845$	509.307			0.602731
$846$	−224.341	+	224.341i	−0.265178	+	0.265178i
$847$	−303.381	+	303.381i	−0.358183	+	0.358183i
$848$	58.5308			0.0690222
$849$	170.143	+	170.143i	0.200404	+	0.200404i
$850$		−	263.707i		−	0.310244i
$851$	−1165.69			−1.36979
$852$		−	298.694i		−	0.350580i
$853$	602.946	+	602.946i	0.706853	+	0.706853i	0.965872	−	0.259019i	$-0.0833993\pi$
$853$	602.946	+	602.946i	0.706853	+	0.706853i	−0.259019	+	0.965872i	$0.583399\pi$
$854$	−23.0944			−0.0270426
$855$	−31.3245	−	31.3245i	−0.0366368	−	0.0366368i
$856$		−	338.120i		−	0.395000i
$857$	−1071.10	−	1071.10i	−1.24983	−	1.24983i	−0.955795	−	0.294035i	$-0.905002\pi$
$857$	−1071.10	−	1071.10i	−1.24983	−	1.24983i	−0.294035	−	0.955795i	$-0.594998\pi$
$858$		−	353.966i		−	0.412548i
$859$	−1305.37			−1.51964			−0.759819	−	0.650135i	$-0.774712\pi$
$859$	−1305.37			−1.51964			−0.759819	+	0.650135i	$0.774712\pi$
$860$	70.5727			0.0820613
$861$	−229.595			−0.266661
$862$		−	955.659i		−	1.10865i
$863$		−	992.682i		−	1.15027i	−0.818059	−	0.575134i	$-0.804950\pi$
$863$		−	992.682i		−	1.15027i	0.818059	−	0.575134i	$-0.195050\pi$
$864$	155.311			0.179758
$865$	560.846			0.648377
$866$	−289.332	+	289.332i	−0.334102	+	0.334102i
$867$	−361.512	+	361.512i	−0.416969	+	0.416969i
$868$	−23.3395			−0.0268888
$869$	2674.05			3.07716
$870$	−173.723	−	173.723i	−0.199682	−	0.199682i
$871$			316.737i			0.363647i
$872$		−	310.618i		−	0.356213i
$873$	−378.131			−0.433139
$874$	47.1757			0.0539767
$875$	−164.109	+	164.109i	−0.187553	+	0.187553i
$876$	379.904	+	379.904i	0.433680	+	0.433680i
$877$	1229.53			1.40197			0.700986	−	0.713175i	$-0.252744\pi$
$877$	1229.53			1.40197			0.700986	+	0.713175i	$0.252744\pi$
$878$	381.467	−	381.467i	0.434473	−	0.434473i
$879$	−295.217	−	295.217i	−0.335855	−	0.335855i
$880$			319.160i			0.362681i
$881$	−598.057	−	598.057i	−0.678839	−	0.678839i	0.280898	−	0.959738i	$-0.409368\pi$
$881$	−598.057	−	598.057i	−0.678839	−	0.678839i	−0.959738	+	0.280898i	$0.909368\pi$
$882$	−245.582	−	245.582i	−0.278438	−	0.278438i
$883$	−425.379	−	425.379i	−0.481743	−	0.481743i	0.423945	−	0.905688i	$-0.360645\pi$
$883$	−425.379	−	425.379i	−0.481743	−	0.481743i	−0.905688	+	0.423945i	$0.860645\pi$
$884$	225.644	+	225.644i	0.255254	+	0.255254i
$885$	824.015			0.931091
$886$		−	188.250i		−	0.212472i
$887$	−481.156			−0.542453			−0.271226	−	0.962516i	$-0.587429\pi$
$887$	−481.156			−0.542453			−0.271226	+	0.962516i	$0.587429\pi$
$888$	380.881			0.428920
$889$	109.092	+	109.092i	0.122713	+	0.122713i
$890$	−373.019	+	373.019i	−0.419123	+	0.419123i
$891$		−	89.8275i		−	0.100817i
$892$	−451.058	−	451.058i	−0.505671	−	0.505671i
$893$	59.8733	−	59.8733i	0.0670474	−	0.0670474i
$894$	304.487			0.340589
$895$	891.104	+	891.104i	0.995647	+	0.995647i
$896$			19.2998i			0.0215400i
$897$	152.102	−	152.102i	0.169568	−	0.169568i
$898$	386.968	+	386.968i	0.430922	+	0.430922i
$899$			150.024i			0.166879i
$900$	−84.2876			−0.0936528
$901$	243.935	+	243.935i	0.270738	+	0.270738i
$902$	1355.66	−	1355.66i	1.50295	−	1.50295i
$903$		−	27.9003i		−	0.0308973i
$904$		−	364.119i		−	0.402787i
$905$	−74.2551	+	74.2551i	−0.0820498	+	0.0820498i
$906$	−581.834			−0.642201
$907$		−	1536.20i		−	1.69371i	−0.531821	−	0.846857i	$-0.678492\pi$
$907$		−	1536.20i		−	1.69371i	0.531821	−	0.846857i	$-0.321508\pi$
$908$	2.79089	+	2.79089i	0.00307367	+	0.00307367i
$909$	625.628	−	625.628i	0.688259	−	0.688259i
$910$		−	67.4974i		−	0.0741730i
$911$	87.5534	+	87.5534i	0.0961070	+	0.0961070i	0.753526	−	0.657419i	$-0.228352\pi$
$911$	87.5534	+	87.5534i	0.0961070	+	0.0961070i	−0.657419	+	0.753526i	$0.728352\pi$
$912$	−15.4143			−0.0169016
$913$	609.679	+	609.679i	0.667775	+	0.667775i
$914$	260.561	−	260.561i	0.285078	−	0.285078i
$915$	53.6215	+	53.6215i	0.0586028	+	0.0586028i
$916$	508.791	−	508.791i	0.555448	−	0.555448i
$917$	−155.506	+	155.506i	−0.169581	+	0.169581i
$918$	647.279	+	647.279i	0.705097	+	0.705097i
$919$	6.03185	−	6.03185i	0.00656349	−	0.00656349i	−0.703817	−	0.710381i	$-0.748523\pi$
$919$	6.03185	−	6.03185i	0.00656349	−	0.00656349i	0.710381	+	0.703817i	$0.248523\pi$
$920$	−137.145	+	137.145i	−0.149071	+	0.149071i
$921$	−470.879	−	470.879i	−0.511270	−	0.511270i
$922$	281.031			0.304806
$923$	−372.988	−	372.988i	−0.404104	−	0.404104i
$924$	126.177			0.136555
$925$	−555.846			−0.600915
$926$	−27.4930			−0.0296900
$927$	631.984			0.681752
$928$	124.057			0.133682
$929$	536.793	+	536.793i	0.577818	+	0.577818i	0.934302	−	0.356484i	$-0.116024\pi$
$929$	536.793	+	536.793i	0.577818	+	0.577818i	−0.356484	+	0.934302i	$0.616024\pi$
$930$	54.1907	+	54.1907i	0.0582696	+	0.0582696i
$931$	65.5423	+	65.5423i	0.0703999	+	0.0703999i
$932$	378.223			0.405819
$933$		−	194.122i		−	0.208062i
$934$		−	759.019i		−	0.812654i
$935$	−1330.14	+	1330.14i	−1.42261	+	1.42261i
$936$	72.1216	−	72.1216i	0.0770530	−	0.0770530i
$937$	−97.2104	+	97.2104i	−0.103746	+	0.103746i	−0.757075	−	0.653328i	$-0.773372\pi$
$937$	−97.2104	+	97.2104i	−0.103746	+	0.103746i	0.653328	+	0.757075i	$0.273372\pi$
$938$	−112.906			−0.120369
$939$	205.235	+	205.235i	0.218568	+	0.218568i
$940$			348.118i			0.370339i
$941$	−217.936	−	217.936i	−0.231600	−	0.231600i	0.581760	−	0.813360i	$-0.302364\pi$
$941$	−217.936	−	217.936i	−0.231600	−	0.231600i	−0.813360	+	0.581760i	$0.802364\pi$
$942$	436.608	−	436.608i	0.463491	−	0.463491i
$943$	1165.08			1.23550
$944$	−294.218	+	294.218i	−0.311671	+	0.311671i
$945$		−	193.622i		−	0.204891i
$946$	164.739	+	164.739i	0.174143	+	0.174143i
$947$	519.946	+	519.946i	0.549045	+	0.549045i	0.926165	−	0.377119i	$-0.123085\pi$
$947$	519.946	+	519.946i	0.549045	+	0.549045i	−0.377119	+	0.926165i	$0.623085\pi$
$948$	−375.446	−	375.446i	−0.396041	−	0.396041i
$949$	948.793			0.999782
$950$	22.4951			0.0236791
$951$		−	1100.98i		−	1.15771i
$952$	−80.4344	+	80.4344i	−0.0844899	+	0.0844899i
$953$	558.260	−	558.260i	0.585792	−	0.585792i	−0.350697	−	0.936489i	$-0.614055\pi$
$953$	558.260	−	558.260i	0.585792	−	0.585792i	0.936489	+	0.350697i	$0.114055\pi$
$954$	77.9677	−	77.9677i	0.0817271	−	0.0817271i
$955$			0.589905i			0.000617702i
$956$			367.351i			0.384258i
$957$		−	811.053i		−	0.847495i
$958$			213.009i			0.222348i
$959$			150.075i			0.156491i
$960$	44.8112	−	44.8112i	0.0466783	−	0.0466783i
$961$			914.202i			0.951303i
$962$	475.616	−	475.616i	0.494404	−	0.494404i
$963$	−450.403	−	450.403i	−0.467708	−	0.467708i
$964$	−640.054	−	640.054i	−0.663957	−	0.663957i
$965$	−587.466	+	587.466i	−0.608773	+	0.608773i
$966$	54.2192	+	54.2192i	0.0561276	+	0.0561276i
$967$	−1080.62	−	1080.62i	−1.11749	−	1.11749i	−0.992108	−	0.125385i	$-0.959984\pi$
$967$	−1080.62	−	1080.62i	−1.11749	−	1.11749i	−0.125385	−	0.992108i	$-0.540016\pi$
$968$	−503.021	+	503.021i	−0.519650	+	0.519650i
$969$	−64.2409	−	64.2409i	−0.0662961	−	0.0662961i
$970$	−293.380	+	293.380i	−0.302453	+	0.302453i
$971$			1129.10i			1.16282i	0.813611	+	0.581410i	$0.197499\pi$
$971$			1129.10i			1.16282i	−0.813611	+	0.581410i	$0.802501\pi$
$972$	336.838	−	336.838i	0.346541	−	0.346541i
$973$	281.562			0.289375
$974$	−734.709	−	734.709i	−0.754322	−	0.754322i
$975$	72.5281	−	72.5281i	0.0743878	−	0.0743878i
$976$	−38.2916			−0.0392332
$977$			1569.15i			1.60609i	0.595919	+	0.803045i	$0.296788\pi$
$977$			1569.15i			1.60609i	−0.595919	+	0.803045i	$0.703212\pi$
$978$	−98.0480	−	98.0480i	−0.100254	−	0.100254i
$979$	−1741.49			−1.77885
$980$	−381.079			−0.388856
$981$	−413.767	−	413.767i	−0.421781	−	0.421781i
$982$	93.2662	−	93.2662i	0.0949758	−	0.0949758i
$983$		−	481.288i		−	0.489611i	−0.969572	−	0.244806i	$-0.921276\pi$
$983$		−	481.288i		−	0.489611i	0.969572	−	0.244806i	$-0.0787242\pi$
$984$	−380.680			−0.386869
$985$	401.240	−	401.240i	0.407350	−	0.407350i
$986$	517.025	+	517.025i	0.524366	+	0.524366i
$987$	137.625			0.139438
$988$	−19.2482	+	19.2482i	−0.0194820	+	0.0194820i
$989$			141.580i			0.143154i
$990$	425.146	+	425.146i	0.429440	+	0.429440i
$991$	1126.22	−	1126.22i	1.13645	−	1.13645i	0.147364	−	0.989082i	$-0.452921\pi$
$991$	1126.22	−	1126.22i	1.13645	−	1.13645i	0.989082	−	0.147364i	$-0.0470790\pi$
$992$	−38.6980			−0.0390101
$993$	−31.5876	−	31.5876i	−0.0318103	−	0.0318103i
$994$	132.957	−	132.957i	0.133760	−	0.133760i
$995$			1120.95i			1.12658i
$996$		−	171.202i		−	0.171890i
$997$	−1588.31			−1.59309			−0.796547	−	0.604577i	$-0.793342\pi$
$997$	−1588.31			−1.59309			−0.796547	+	0.604577i	$0.793342\pi$
$998$			106.727i			0.106941i
$999$	1364.34	−	1364.34i	1.36571	−	1.36571i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	538.3.c.b.187.17	✓	46
269.82	odd	4	inner	538.3.c.b.351.17	yes	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.3.c.b.187.17	✓	46	1.1	even	1	trivial
538.3.c.b.351.17	yes	46	269.82	odd	4	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:	\( N \)	\(=\)	\( 538 = 2 \cdot 269 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	538.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(1.35493 + 1.35493i) q^{3} +2.00000i q^{4} +4.13408 q^{5} -2.70986i q^{6} +(1.20624 - 1.20624i) q^{7} +(2.00000 - 2.00000i) q^{8} -5.32832i q^{9} +(-4.13408 - 4.13408i) q^{10} -19.3005i q^{11} +(-2.70986 + 2.70986i) q^{12} +6.76777i q^{13} -2.41248 q^{14} +(5.60140 + 5.60140i) q^{15} -4.00000 q^{16} +(-16.6705 - 16.6705i) q^{17} +(-5.32832 + 5.32832i) q^{18} +(1.42205 - 1.42205i) q^{19} +8.26816i q^{20} +3.26874 q^{21} +(-19.3005 + 19.3005i) q^{22} -16.5872 q^{23} +5.41973 q^{24} -7.90939 q^{25} +(6.76777 - 6.76777i) q^{26} +(19.4139 - 19.4139i) q^{27} +(2.41248 + 2.41248i) q^{28} +(15.5072 - 15.5072i) q^{29} -11.2028i q^{30} +(-4.83725 + 4.83725i) q^{31} +(4.00000 + 4.00000i) q^{32} +(26.1509 - 26.1509i) q^{33} +33.3410i q^{34} +(4.98668 - 4.98668i) q^{35} +10.6566 q^{36} +70.2767 q^{37} -2.84410 q^{38} +(-9.16986 + 9.16986i) q^{39} +(8.26816 - 8.26816i) q^{40} -70.2396 q^{41} +(-3.26874 - 3.26874i) q^{42} -8.53548i q^{43} +38.6011 q^{44} -22.0277i q^{45} +(16.5872 + 16.5872i) q^{46} +42.1035 q^{47} +(-5.41973 - 5.41973i) q^{48} +46.0900i q^{49} +(7.90939 + 7.90939i) q^{50} -45.1748i q^{51} -13.5355 q^{52} -14.6327 q^{53} -38.8278 q^{54} -79.7899i q^{55} -4.82495i q^{56} +3.85356 q^{57} -31.0143 q^{58} +(73.5545 - 73.5545i) q^{59} +(-11.2028 + 11.2028i) q^{60} +9.57289 q^{61} +9.67450 q^{62} +(-6.42722 - 6.42722i) q^{63} -8.00000i q^{64} +27.9785i q^{65} -52.3018 q^{66} +46.8008 q^{67} +(33.3410 - 33.3410i) q^{68} +(-22.4745 - 22.4745i) q^{69} -9.97337 q^{70} +(-55.1124 + 55.1124i) q^{71} +(-10.6566 - 10.6566i) q^{72} -140.193i q^{73} +(-70.2767 - 70.2767i) q^{74} +(-10.7167 - 10.7167i) q^{75} +(2.84410 + 2.84410i) q^{76} +(-23.2810 - 23.2810i) q^{77} +18.3397 q^{78} +138.548i q^{79} -16.5363 q^{80} +4.65415 q^{81} +(70.2396 + 70.2396i) q^{82} +(-31.5887 + 31.5887i) q^{83} +6.53748i q^{84} +(-68.9172 - 68.9172i) q^{85} +(-8.53548 + 8.53548i) q^{86} +42.0223 q^{87} +(-38.6011 - 38.6011i) q^{88} -90.2303i q^{89} +(-22.0277 + 22.0277i) q^{90} +(8.16354 + 8.16354i) q^{91} -33.1744i q^{92} -13.1083 q^{93} +(-42.1035 - 42.1035i) q^{94} +(5.87887 - 5.87887i) q^{95} +10.8395i q^{96} -70.9662i q^{97} +(46.0900 - 46.0900i) q^{98} -102.839 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 46 q^{2} - 6 q^{3} - 32 q^{5} + 4 q^{7} + 92 q^{8} + 32 q^{10} + 12 q^{12} - 8 q^{14} - 10 q^{15} - 184 q^{16} - 50 q^{17} + 118 q^{18} + 10 q^{19} + 16 q^{21} + 8 q^{22} - 124 q^{23} - 24 q^{24}+ \cdots + 508 q^{99}+O(q^{100}) \) 46 * q - 46 * q^2 - 6 * q^3 - 32 * q^5 + 4 * q^7 + 92 * q^8 + 32 * q^10 + 12 * q^12 - 8 * q^14 - 10 * q^15 - 184 * q^16 - 50 * q^17 + 118 * q^18 + 10 * q^19 + 16 * q^21 + 8 * q^22 - 124 * q^23 - 24 * q^24 + 178 * q^25 + 4 * q^26 + 90 * q^27 + 8 * q^28 + 40 * q^29 + 40 * q^31 + 184 * q^32 - 64 * q^33 - 14 * q^35 - 236 * q^36 - 32 * q^37 - 20 * q^38 - 54 * q^39 - 64 * q^40 - 132 * q^41 - 16 * q^42 - 16 * q^44 + 124 * q^46 - 60 * q^47 + 24 * q^48 - 178 * q^50 - 8 * q^52 - 188 * q^53 - 180 * q^54 - 40 * q^57 - 80 * q^58 + 190 * q^59 + 20 * q^60 - 80 * q^62 - 266 * q^63 + 128 * q^66 - 164 * q^67 + 100 * q^68 + 170 * q^69 + 28 * q^70 - 92 * q^71 + 236 * q^72 + 32 * q^74 - 190 * q^75 + 20 * q^76 + 20 * q^77 + 108 * q^78 + 128 * q^80 - 298 * q^81 + 132 * q^82 + 190 * q^83 + 298 * q^85 + 228 * q^86 - 92 * q^87 + 16 * q^88 - 528 * q^90 + 2 * q^91 + 232 * q^93 + 60 * q^94 - 280 * q^95 - 226 * q^98 + 508 * q^99

Introduction

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