LMFDB - Embedded newform 124.3.b.a.63.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,3,Mod(63,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, 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("124.63");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	124.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:	$3.37875527807$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			63.4
Character	$\chi$	$=$	124.63
Dual form			124.3.b.a.63.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.96086 + 0.393756i) q^{2} -3.47301i q^{3} +(3.68991 - 1.54420i) q^{4} +6.23763 q^{5} +(1.36752 + 6.81006i) q^{6} +1.04310i q^{7} +(-6.62735 + 4.48088i) q^{8} -3.06177 q^{9} +O(q^{10})$	\(q+(-1.96086 + 0.393756i) q^{2} -3.47301i q^{3} +(3.68991 - 1.54420i) q^{4} +6.23763 q^{5} +(1.36752 + 6.81006i) q^{6} +1.04310i q^{7} +(-6.62735 + 4.48088i) q^{8} -3.06177 q^{9} +(-12.2311 + 2.45611i) q^{10} -7.36340i q^{11} +(-5.36301 - 12.8151i) q^{12} +7.78405 q^{13} +(-0.410728 - 2.04537i) q^{14} -21.6633i q^{15} +(11.2309 - 11.3959i) q^{16} -4.56659 q^{17} +(6.00369 - 1.20559i) q^{18} -29.2140i q^{19} +(23.0163 - 9.63215i) q^{20} +3.62270 q^{21} +(2.89938 + 14.4386i) q^{22} +23.7927i q^{23} +(15.5621 + 23.0168i) q^{24} +13.9081 q^{25} +(-15.2634 + 3.06502i) q^{26} -20.6235i q^{27} +(1.61076 + 3.84896i) q^{28} -19.7741 q^{29} +(8.53008 + 42.4787i) q^{30} -5.56776i q^{31} +(-17.5350 + 26.7680i) q^{32} -25.5731 q^{33} +(8.95443 - 1.79812i) q^{34} +6.50649i q^{35} +(-11.2977 + 4.72798i) q^{36} +28.8792 q^{37} +(11.5032 + 57.2845i) q^{38} -27.0341i q^{39} +(-41.3390 + 27.9501i) q^{40} -57.2436 q^{41} +(-7.10359 + 1.42646i) q^{42} +32.7502i q^{43} +(-11.3705 - 27.1703i) q^{44} -19.0982 q^{45} +(-9.36853 - 46.6541i) q^{46} +83.6361i q^{47} +(-39.5781 - 39.0050i) q^{48} +47.9119 q^{49} +(-27.2717 + 5.47639i) q^{50} +15.8598i q^{51} +(28.7225 - 12.0201i) q^{52} +80.4078 q^{53} +(8.12064 + 40.4397i) q^{54} -45.9302i q^{55} +(-4.67401 - 6.91300i) q^{56} -101.461 q^{57} +(38.7742 - 7.78619i) q^{58} +85.6446i q^{59} +(-33.4525 - 79.9358i) q^{60} -0.194335 q^{61} +(2.19234 + 10.9176i) q^{62} -3.19374i q^{63} +(23.8435 - 59.3927i) q^{64} +48.5540 q^{65} +(50.1452 - 10.0696i) q^{66} +31.5692i q^{67} +(-16.8503 + 7.05173i) q^{68} +82.6322 q^{69} +(-2.56197 - 12.7583i) q^{70} +9.47727i q^{71} +(20.2914 - 13.7194i) q^{72} +10.2065 q^{73} +(-56.6279 + 11.3714i) q^{74} -48.3028i q^{75} +(-45.1123 - 107.797i) q^{76} +7.68077 q^{77} +(10.6448 + 53.0099i) q^{78} -96.7687i q^{79} +(70.0542 - 71.0835i) q^{80} -99.1815 q^{81} +(112.246 - 22.5400i) q^{82} +42.8225i q^{83} +(13.3674 - 5.59417i) q^{84} -28.4847 q^{85} +(-12.8956 - 64.2185i) q^{86} +68.6757i q^{87} +(32.9945 + 48.7998i) q^{88} +152.257 q^{89} +(37.4488 - 7.52004i) q^{90} +8.11956i q^{91} +(36.7407 + 87.7930i) q^{92} -19.3369 q^{93} +(-32.9323 - 163.998i) q^{94} -182.227i q^{95} +(92.9654 + 60.8990i) q^{96} -69.2650 q^{97} +(-93.9484 + 18.8656i) q^{98} +22.5450i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 2 q^{2} - 6 q^{4} - 4 q^{5} + 13 q^{8} - 82 q^{9}+O(q^{10}) $ 30 * q - 2 * q^2 - 6 * q^4 - 4 * q^5 + 13 * q^8 - 82 * q^9	$ 30 q - 2 q^{2} - 6 q^{4} - 4 q^{5} + 13 q^{8} - 82 q^{9} + q^{10} - 14 q^{12} + 12 q^{13} + 29 q^{14} + 50 q^{16} - 4 q^{17} - 34 q^{18} - 63 q^{20} - 16 q^{21} - 24 q^{22} - 20 q^{24} + 90 q^{25} + 38 q^{26} + 3 q^{28} - 4 q^{29} - 6 q^{30} + 118 q^{32} + 80 q^{33} + 4 q^{34} - 2 q^{36} + 76 q^{37} + 37 q^{38} - 180 q^{40} - 4 q^{41} - 38 q^{42} + 184 q^{44} - 20 q^{45} - 54 q^{46} - 172 q^{48} - 258 q^{49} - 31 q^{50} - 88 q^{52} - 132 q^{53} - 84 q^{54} - 28 q^{56} + 176 q^{57} + 164 q^{58} + 108 q^{60} - 100 q^{61} + 381 q^{64} - 104 q^{65} + 60 q^{66} + 214 q^{68} + 112 q^{69} + 45 q^{70} - 167 q^{72} - 132 q^{73} + 398 q^{74} - 317 q^{76} + 176 q^{77} - 188 q^{78} - 203 q^{80} + 158 q^{81} - 81 q^{82} + 176 q^{84} + 248 q^{85} - 78 q^{86} + 98 q^{88} - 20 q^{89} - 567 q^{90} - 260 q^{92} - 244 q^{94} - 90 q^{96} + 300 q^{97} - 371 q^{98}+O(q^{100}) $ 30 * q - 2 * q^2 - 6 * q^4 - 4 * q^5 + 13 * q^8 - 82 * q^9 + q^10 - 14 * q^12 + 12 * q^13 + 29 * q^14 + 50 * q^16 - 4 * q^17 - 34 * q^18 - 63 * q^20 - 16 * q^21 - 24 * q^22 - 20 * q^24 + 90 * q^25 + 38 * q^26 + 3 * q^28 - 4 * q^29 - 6 * q^30 + 118 * q^32 + 80 * q^33 + 4 * q^34 - 2 * q^36 + 76 * q^37 + 37 * q^38 - 180 * q^40 - 4 * q^41 - 38 * q^42 + 184 * q^44 - 20 * q^45 - 54 * q^46 - 172 * q^48 - 258 * q^49 - 31 * q^50 - 88 * q^52 - 132 * q^53 - 84 * q^54 - 28 * q^56 + 176 * q^57 + 164 * q^58 + 108 * q^60 - 100 * q^61 + 381 * q^64 - 104 * q^65 + 60 * q^66 + 214 * q^68 + 112 * q^69 + 45 * q^70 - 167 * q^72 - 132 * q^73 + 398 * q^74 - 317 * q^76 + 176 * q^77 - 188 * q^78 - 203 * q^80 + 158 * q^81 - 81 * q^82 + 176 * q^84 + 248 * q^85 - 78 * q^86 + 98 * q^88 - 20 * q^89 - 567 * q^90 - 260 * q^92 - 244 * q^94 - 90 * q^96 + 300 * q^97 - 371 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$-1$	$1$

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 $

$2$	−1.96086	+	0.393756i	−0.980428	+	0.196878i
$2$	−1.96086	+	0.393756i	−0.980428	+	0.196878i
$3$		−	3.47301i		−	1.15767i	−0.815445	−	0.578834i	$-0.803508\pi$
$3$		−	3.47301i		−	1.15767i	0.815445	−	0.578834i	$-0.196492\pi$
$4$	3.68991	−	1.54420i	0.922478	−	0.386050i
$5$	6.23763			1.24753			0.623763	−	0.781613i	$-0.285603\pi$
$5$	6.23763			1.24753			0.623763	+	0.781613i	$0.285603\pi$
$6$	1.36752	+	6.81006i	0.227920	+	1.13501i
$7$			1.04310i			0.149015i	0.997220	+	0.0745073i	$0.0237384\pi$
$7$			1.04310i			0.149015i	−0.997220	+	0.0745073i	$0.976262\pi$
$8$	−6.62735	+	4.48088i	−0.828418	+	0.560110i
$9$	−3.06177			−0.340197
$10$	−12.2311	+	2.45611i	−1.22311	+	0.245611i
$11$		−	7.36340i		−	0.669400i	−0.942325	−	0.334700i	$-0.891365\pi$
$11$		−	7.36340i		−	0.669400i	0.942325	−	0.334700i	$-0.108635\pi$
$12$	−5.36301	−	12.8151i	−0.446918	−	1.06792i
$13$	7.78405			0.598773			0.299387	−	0.954132i	$-0.403218\pi$
$13$	7.78405			0.598773			0.299387	+	0.954132i	$0.403218\pi$
$14$	−0.410728	−	2.04537i	−0.0293377	−	0.146098i
$15$		−	21.6633i		−	1.44422i
$16$	11.2309	−	11.3959i	0.701931	−	0.712245i
$17$	−4.56659			−0.268623			−0.134312	−	0.990939i	$-0.542882\pi$
$17$	−4.56659			−0.268623			−0.134312	+	0.990939i	$0.542882\pi$
$18$	6.00369	−	1.20559i	0.333538	−	0.0669773i
$19$		−	29.2140i		−	1.53758i	−0.639500	−	0.768791i	$-0.720859\pi$
$19$		−	29.2140i		−	1.53758i	0.639500	−	0.768791i	$-0.279141\pi$
$20$	23.0163	−	9.63215i	1.15082	−	0.481607i
$21$	3.62270			0.172510
$22$	2.89938	+	14.4386i	0.131790	+	0.656298i
$23$			23.7927i			1.03447i	0.855845	+	0.517233i	$0.173038\pi$
$23$			23.7927i			1.03447i	−0.855845	+	0.517233i	$0.826962\pi$
$24$	15.5621	+	23.0168i	0.648421	+	0.959034i
$25$	13.9081			0.556323
$26$	−15.2634	+	3.06502i	−0.587054	+	0.117885i
$27$		−	20.6235i		−	0.763834i
$28$	1.61076	+	3.84896i	0.0575270	+	0.137463i
$29$	−19.7741			−0.681867			−0.340933	−	0.940087i	$-0.610743\pi$
$29$	−19.7741			−0.681867			−0.340933	+	0.940087i	$0.610743\pi$
$30$	8.53008	+	42.4787i	0.284336	+	1.41596i
$31$		−	5.56776i		−	0.179605i
$31$		−	5.56776i		−	0.179605i
$32$	−17.5350	+	26.7680i	−0.547968	+	0.836500i
$33$	−25.5731			−0.774943
$34$	8.95443	−	1.79812i	0.263366	−	0.0528860i
$35$			6.50649i			0.185900i
$36$	−11.2977	+	4.72798i	−0.313824	+	0.131333i
$37$	28.8792			0.780519			0.390259	−	0.920705i	$-0.372385\pi$
$37$	28.8792			0.780519			0.390259	+	0.920705i	$0.372385\pi$
$38$	11.5032	+	57.2845i	0.302716	+	1.50749i
$39$		−	27.0341i		−	0.693181i
$40$	−41.3390	+	27.9501i	−1.03347	+	0.698752i
$41$	−57.2436			−1.39619			−0.698093	−	0.716007i	$-0.745968\pi$
$41$	−57.2436			−1.39619			−0.698093	+	0.716007i	$0.745968\pi$
$42$	−7.10359	+	1.42646i	−0.169133	+	0.0339634i
$43$			32.7502i			0.761633i	0.924651	+	0.380817i	$0.124357\pi$
$43$			32.7502i			0.761633i	−0.924651	+	0.380817i	$0.875643\pi$
$44$	−11.3705	−	27.1703i	−0.258422	−	0.617506i
$45$	−19.0982			−0.424404
$46$	−9.36853	−	46.6541i	−0.203664	−	1.01422i
$47$			83.6361i			1.77949i	0.456456	+	0.889746i	$0.349119\pi$
$47$			83.6361i			1.77949i	−0.456456	+	0.889746i	$0.650881\pi$
$48$	−39.5781	−	39.0050i	−0.824543	−	0.812604i
$49$	47.9119			0.977795
$50$	−27.2717	+	5.47639i	−0.545434	+	0.109528i
$51$			15.8598i			0.310977i
$52$	28.7225	−	12.0201i	0.552355	−	0.231156i
$53$	80.4078			1.51713			0.758564	−	0.651599i	$-0.225901\pi$
$53$	80.4078			1.51713			0.758564	+	0.651599i	$0.225901\pi$
$54$	8.12064	+	40.4397i	0.150382	+	0.748884i
$55$		−	45.9302i		−	0.835094i
$56$	−4.67401	−	6.91300i	−0.0834645	−	0.123446i
$57$	−101.461			−1.78001
$58$	38.7742	−	7.78619i	0.668521	−	0.134245i
$59$			85.6446i			1.45160i	0.687904	+	0.725802i	$0.258531\pi$
$59$			85.6446i			1.45160i	−0.687904	+	0.725802i	$0.741469\pi$
$60$	−33.4525	−	79.9358i	−0.557542	−	1.33226i
$61$	−0.194335			−0.00318583			−0.00159291	−	0.999999i	$-0.500507\pi$
$61$	−0.194335			−0.00318583			−0.00159291	+	0.999999i	$0.500507\pi$
$62$	2.19234	+	10.9176i	0.0353604	+	0.176090i
$63$		−	3.19374i		−	0.0506943i
$64$	23.8435	−	59.3927i	0.372554	−	0.928010i
$65$	48.5540			0.746985
$66$	50.1452	−	10.0696i	0.759776	−	0.152569i
$67$			31.5692i			0.471182i	0.971852	+	0.235591i	$0.0757026\pi$
$67$			31.5692i			0.471182i	−0.971852	+	0.235591i	$0.924297\pi$
$68$	−16.8503	+	7.05173i	−0.247799	+	0.103702i
$69$	82.6322			1.19757
$70$	−2.56197	−	12.7583i	−0.0365996	−	0.182261i
$71$			9.47727i			0.133483i	0.997770	+	0.0667414i	$0.0212602\pi$
$71$			9.47727i			0.133483i	−0.997770	+	0.0667414i	$0.978740\pi$
$72$	20.2914	−	13.7194i	0.281825	−	0.190547i
$73$	10.2065			0.139815			0.0699076	−	0.997553i	$-0.477730\pi$
$73$	10.2065			0.139815			0.0699076	+	0.997553i	$0.477730\pi$
$74$	−56.6279	+	11.3714i	−0.765242	+	0.153667i
$75$		−	48.3028i		−	0.644037i
$76$	−45.1123	−	107.797i	−0.593583	−	1.41838i
$77$	7.68077			0.0997503
$78$	10.6448	+	53.0099i	0.136472	+	0.679614i
$79$		−	96.7687i		−	1.22492i	−0.790502	−	0.612460i	$-0.790180\pi$
$79$		−	96.7687i		−	1.22492i	0.790502	−	0.612460i	$-0.209820\pi$
$80$	70.0542	−	71.0835i	0.875678	−	0.888544i
$81$	−99.1815			−1.22446
$82$	112.246	−	22.5400i	1.36886	−	0.274878i
$83$			42.8225i			0.515934i	0.966154	+	0.257967i	$0.0830526\pi$
$83$			42.8225i			0.515934i	−0.966154	+	0.257967i	$0.916947\pi$
$84$	13.3674	−	5.59417i	0.159136	−	0.0665973i
$85$	−28.4847			−0.335114
$86$	−12.8956	−	64.2185i	−0.149949	−	0.746727i
$87$			68.6757i			0.789376i
$88$	32.9945	+	48.7998i	0.374937	+	0.554543i
$89$	152.257			1.71076			0.855379	−	0.518002i	$-0.173324\pi$
$89$	152.257			1.71076			0.855379	+	0.518002i	$0.173324\pi$
$90$	37.4488	−	7.52004i	0.416098	−	0.0835560i
$91$			8.11956i			0.0892259i
$92$	36.7407	+	87.7930i	0.399355	+	0.954271i
$93$	−19.3369			−0.207923
$94$	−32.9323	−	163.998i	−0.350343	−	1.74466i
$95$		−	182.227i		−	1.91817i
$96$	92.9654	+	60.8990i	0.968389	+	0.634365i
$97$	−69.2650			−0.714072			−0.357036	−	0.934091i	$-0.616213\pi$
$97$	−69.2650			−0.714072			−0.357036	+	0.934091i	$0.616213\pi$
$98$	−93.9484	+	18.8656i	−0.958657	+	0.192506i
$99$			22.5450i			0.227727i
$100$	51.3195	−	21.4768i	0.513195	−	0.214768i
$101$	−191.369			−1.89474			−0.947371	−	0.320138i	$-0.896271\pi$
$101$	−191.369			−1.89474			−0.947371	+	0.320138i	$0.896271\pi$
$102$	−6.24490	−	31.0988i	−0.0612245	−	0.304890i
$103$			153.346i			1.48880i	0.667735	+	0.744399i	$0.267264\pi$
$103$			153.346i			1.48880i	−0.667735	+	0.744399i	$0.732736\pi$
$104$	−51.5876	+	34.8794i	−0.496035	+	0.335379i
$105$	22.5971			0.215210
$106$	−157.668	+	31.6611i	−1.48743	+	0.298689i
$107$		−	46.4120i		−	0.433757i	−0.976199	−	0.216879i	$-0.930412\pi$
$107$		−	46.4120i		−	0.433757i	0.976199	−	0.216879i	$-0.0695876\pi$
$108$	−31.8468	−	76.0989i	−0.294878	−	0.704620i
$109$	7.85635			0.0720766			0.0360383	−	0.999350i	$-0.488526\pi$
$109$	7.85635			0.0720766			0.0360383	+	0.999350i	$0.488526\pi$
$110$	18.0853	+	90.0624i	0.164412	+	0.818749i
$111$		−	100.298i		−	0.903582i
$112$	11.8871	+	11.7150i	0.106135	+	0.104598i
$113$	−142.676			−1.26262			−0.631310	−	0.775531i	$-0.717482\pi$
$113$	−142.676			−1.26262			−0.631310	+	0.775531i	$0.717482\pi$
$114$	198.950	−	39.9507i	1.74517	−	0.350445i
$115$			148.410i			1.29052i
$116$	−72.9648	+	30.5352i	−0.629007	+	0.263235i
$117$	−23.8330			−0.203701
$118$	−33.7231	−	167.937i	−0.285789	−	1.42319i
$119$		−	4.76342i		−	0.0400288i
$120$	97.0708	+	143.570i	0.808923	+	1.19642i
$121$	66.7804			0.551904
$122$	0.381064	−	0.0765208i	0.00312347	−	0.000627220i
$123$			198.807i			1.61632i
$124$	−8.59774	−	20.5446i	−0.0693366	−	0.165682i
$125$	−69.1874			−0.553499
$126$	1.25756	+	6.26246i	0.00998060	+	0.0497021i
$127$		−	49.7915i		−	0.392059i	−0.980598	−	0.196030i	$-0.937195\pi$
$127$		−	49.7915i		−	0.392059i	0.980598	−	0.196030i	$-0.0628049\pi$
$128$	−23.3674	+	125.849i	−0.182558	+	0.983195i
$129$	113.742			0.881719
$130$	−95.2075	+	19.1185i	−0.732365	+	0.147065i
$131$			142.982i			1.09146i	0.837960	+	0.545731i	$0.183748\pi$
$131$			142.982i			1.09146i	−0.837960	+	0.545731i	$0.816252\pi$
$132$	−94.3625	+	39.4900i	−0.714868	+	0.299166i
$133$	30.4732			0.229122
$134$	−12.4306	−	61.9027i	−0.0927655	−	0.461960i
$135$		−	128.642i		−	0.952903i
$136$	30.2644	−	20.4623i	0.222532	−	0.150458i
$137$	15.0552			0.109892			0.0549461	−	0.998489i	$-0.482501\pi$
$137$	15.0552			0.109892			0.0549461	+	0.998489i	$0.482501\pi$
$138$	−162.030	+	32.5369i	−1.17413	+	0.235775i
$139$			162.042i			1.16577i	0.812554	+	0.582886i	$0.198077\pi$
$139$			162.042i			1.16577i	−0.812554	+	0.582886i	$0.801923\pi$
$140$	10.0473	+	24.0084i	0.0717665	+	0.171488i
$141$	290.469			2.06006
$142$	−3.73174	−	18.5836i	−0.0262798	−	0.130870i
$143$		−	57.3170i		−	0.400818i
$144$	−34.3864	+	34.8917i	−0.238795	+	0.242303i
$145$	−123.344			−0.850647
$146$	−20.0135	+	4.01888i	−0.137079	+	0.0275265i
$147$		−	166.398i		−	1.13196i
$148$	106.562	−	44.5952i	0.720011	−	0.301319i
$149$	275.547			1.84931			0.924654	−	0.380808i	$-0.124354\pi$
$149$	275.547			1.84931			0.924654	+	0.380808i	$0.124354\pi$
$150$	19.0195	+	94.7148i	0.126797	+	0.631432i
$151$			50.2267i			0.332627i	0.986073	+	0.166313i	$0.0531864\pi$
$151$			50.2267i			0.332627i	−0.986073	+	0.166313i	$0.946814\pi$
$152$	130.905	+	193.612i	0.861214	+	1.27376i
$153$	13.9819			0.0913847
$154$	−15.0609	+	3.02435i	−0.0977980	+	0.0196387i
$155$		−	34.7297i		−	0.224062i
$156$	−41.7460	−	99.7533i	−0.267602	−	0.639444i
$157$	−9.47710			−0.0603637			−0.0301819	−	0.999544i	$-0.509609\pi$
$157$	−9.47710			−0.0603637			−0.0301819	+	0.999544i	$0.509609\pi$
$158$	38.1033	+	189.749i	0.241160	+	1.20095i
$159$		−	279.257i		−	1.75633i
$160$	−109.377	+	166.969i	−0.683604	+	1.04356i
$161$	−24.8182			−0.154150
$162$	194.481	−	39.0533i	1.20050	−	0.241070i
$163$			120.250i			0.737728i	0.929483	+	0.368864i	$0.120253\pi$
$163$			120.250i			0.737728i	−0.929483	+	0.368864i	$0.879747\pi$
$164$	−211.224	+	88.3955i	−1.28795	+	0.538997i
$165$	−159.516			−0.966762
$166$	−16.8616	−	83.9688i	−0.101576	−	0.505836i
$167$		−	325.605i		−	1.94973i	−0.222792	−	0.974866i	$-0.571517\pi$
$167$		−	325.605i		−	1.94973i	0.222792	−	0.974866i	$-0.428483\pi$
$168$	−24.0089	+	16.2329i	−0.142910	+	0.0966243i
$169$	−108.409			−0.641471
$170$	55.8545	−	11.2160i	0.328556	−	0.0659767i
$171$			89.4467i			0.523080i
$172$	50.5729	+	120.845i	0.294028	+	0.702590i
$173$	−200.945			−1.16153			−0.580765	−	0.814072i	$-0.697246\pi$
$173$	−200.945			−1.16153			−0.580765	+	0.814072i	$0.697246\pi$
$174$	−27.0415	−	134.663i	−0.155411	−	0.773926i
$175$			14.5075i			0.0829002i
$176$	−83.9126	−	82.6976i	−0.476776	−	0.469872i
$177$	297.444			1.68048
$178$	−298.555	+	59.9524i	−1.67728	+	0.336811i
$179$		−	334.658i		−	1.86960i	−0.355181	−	0.934798i	$-0.615581\pi$
$179$		−	334.658i		−	1.86960i	0.355181	−	0.934798i	$-0.384419\pi$
$180$	−70.4707	+	29.4914i	−0.391504	+	0.163841i
$181$	−18.7083			−0.103361			−0.0516804	−	0.998664i	$-0.516458\pi$
$181$	−18.7083			−0.103361			−0.0516804	+	0.998664i	$0.516458\pi$
$182$	−3.19713	−	15.9213i	−0.0175666	−	0.0874796i
$183$			0.674928i			0.00368813i
$184$	−106.612	−	157.682i	−0.579414	−	0.856970i
$185$	180.138			0.973718
$186$	37.9168	−	7.61402i	0.203854	−	0.0409356i
$187$			33.6256i			0.179816i
$188$	129.151	+	308.610i	0.686972	+	1.64154i
$189$	21.5124			0.113822
$190$	71.7528	+	357.320i	0.377647	+	1.88063i
$191$		−	6.71131i		−	0.0351378i	−0.999846	−	0.0175689i	$-0.994407\pi$
$191$		−	6.71131i		−	0.0351378i	0.999846	−	0.0175689i	$-0.00559264\pi$
$192$	−206.271	−	82.8085i	−1.07433	−	0.431294i
$193$	−98.0742			−0.508156			−0.254078	−	0.967184i	$-0.581772\pi$
$193$	−98.0742			−0.508156			−0.254078	+	0.967184i	$0.581772\pi$
$194$	135.819	−	27.2735i	0.700096	−	0.140585i
$195$		−	168.628i		−	0.864761i
$196$	176.791	−	73.9856i	0.901994	−	0.377477i
$197$	−49.6007			−0.251780			−0.125890	−	0.992044i	$-0.540179\pi$
$197$	−49.6007			−0.251780			−0.125890	+	0.992044i	$0.540179\pi$
$198$	−8.87725	−	44.2075i	−0.0448346	−	0.223270i
$199$			131.350i			0.660052i	0.943972	+	0.330026i	$0.107058\pi$
$199$			131.350i			0.660052i	−0.943972	+	0.330026i	$0.892942\pi$
$200$	−92.1736	+	62.3204i	−0.460868	+	0.311602i
$201$	109.640			0.545473
$202$	375.247	−	75.3527i	1.85766	−	0.373033i
$203$		−	20.6265i		−	0.101608i
$204$	24.4907	+	58.5213i	0.120052	+	0.286869i
$205$	−357.065			−1.74178
$206$	−60.3810	−	300.690i	−0.293112	−	1.45966i
$207$		−	72.8478i		−	0.351922i
$208$	87.4219	−	88.7064i	0.420298	−	0.426473i
$209$	−215.115			−1.02926
$210$	−44.3096	+	8.89774i	−0.210998	+	0.0423702i
$211$			152.412i			0.722333i	0.932501	+	0.361166i	$0.117621\pi$
$211$			152.412i			0.722333i	−0.932501	+	0.361166i	$0.882379\pi$
$212$	296.698	−	124.166i	1.39952	−	0.585687i
$213$	32.9146			0.154529
$214$	18.2750	+	91.0073i	0.0853973	+	0.425268i
$215$			204.284i			0.950158i
$216$	92.4114	+	136.679i	0.427831	+	0.632774i
$217$	5.80775			0.0267638
$218$	−15.4052	+	3.09349i	−0.0706659	+	0.0141903i
$219$		−	35.4472i		−	0.161860i
$220$	−70.9253	−	169.478i	−0.322388	−	0.770356i
$221$	−35.5466			−0.160844
$222$	39.4928	+	196.669i	0.177896	+	0.885897i
$223$		−	422.776i		−	1.89586i	−0.318482	−	0.947929i	$-0.603173\pi$
$223$		−	422.776i		−	1.89586i	0.318482	−	0.947929i	$-0.396827\pi$
$224$	−27.9217	−	18.2908i	−0.124651	−	0.0816552i
$225$	−42.5833			−0.189259
$226$	279.767	−	56.1796i	1.23791	−	0.248582i
$227$			135.163i			0.595432i	0.954654	+	0.297716i	$0.0962248\pi$
$227$			135.163i			0.595432i	−0.954654	+	0.297716i	$0.903775\pi$
$228$	−374.381	+	156.675i	−1.64202	+	0.687172i
$229$	−120.646			−0.526838			−0.263419	−	0.964681i	$-0.584850\pi$
$229$	−120.646			−0.526838			−0.263419	+	0.964681i	$0.584850\pi$
$230$	−58.4374	−	291.011i	−0.254076	−	1.26526i
$231$		−	26.6754i		−	0.115478i
$232$	131.050	−	88.6055i	0.564871	−	0.381920i
$233$	211.082			0.905931			0.452966	−	0.891528i	$-0.350366\pi$
$233$	211.082			0.905931			0.452966	+	0.891528i	$0.350366\pi$
$234$	46.7330	−	9.38438i	0.199714	−	0.0401042i
$235$			521.691i			2.21996i
$236$	132.252	+	316.021i	0.560391	+	1.33907i
$237$	−336.078			−1.41805
$238$	1.87563	+	9.34039i	0.00788079	+	0.0392453i
$239$			58.9808i			0.246782i	0.992358	+	0.123391i	$0.0393769\pi$
$239$			58.9808i			0.246782i	−0.992358	+	0.123391i	$0.960623\pi$
$240$	−246.874	−	243.299i	−1.02864	−	1.01374i
$241$	377.957			1.56829			0.784144	−	0.620579i	$-0.213103\pi$
$241$	377.957			1.56829			0.784144	+	0.620579i	$0.213103\pi$
$242$	−130.947	+	26.2952i	−0.541102	+	0.108658i
$243$			158.846i			0.653689i
$244$	−0.717081	+	0.300093i	−0.00293886	+	0.00122989i
$245$	298.857			1.21982
$246$	−78.2817	−	389.833i	−0.318218	−	1.58469i
$247$		−	227.404i		−	0.920662i
$248$	24.9485	+	36.8995i	0.100599	+	0.148788i
$249$	148.723			0.597280
$250$	135.667	−	27.2430i	0.542666	−	0.108972i
$251$		−	305.072i		−	1.21543i	−0.794157	−	0.607713i	$-0.792087\pi$
$251$		−	305.072i		−	1.21543i	0.794157	−	0.607713i	$-0.207913\pi$
$252$	−4.93177	−	11.7846i	−0.0195705	−	0.0467643i
$253$	175.195			0.692471
$254$	19.6057	+	97.6340i	0.0771879	+	0.384386i
$255$			98.9276i			0.387952i
$256$	−3.73378	−	255.973i	−0.0145851	−	0.999894i
$257$	−239.163			−0.930597			−0.465298	−	0.885154i	$-0.654053\pi$
$257$	−239.163			−0.930597			−0.465298	+	0.885154i	$0.654053\pi$
$258$	−223.031	+	44.7865i	−0.864462	+	0.173591i
$259$			30.1240i			0.116309i
$260$	179.160	−	74.9771i	0.689078	−	0.288373i
$261$	60.5439			0.231969
$262$	−56.2999	−	280.366i	−0.214885	−	1.07010i
$263$			310.660i			1.18122i	0.806958	+	0.590609i	$0.201112\pi$
$263$			310.660i			1.18122i	−0.806958	+	0.590609i	$0.798888\pi$
$264$	169.482	−	114.590i	0.641977	−	0.434053i
$265$	501.554			1.89266
$266$	−59.7536	+	11.9990i	−0.224638	+	0.0451091i
$267$		−	528.791i		−	1.98049i
$268$	48.7492	+	116.488i	0.181900	+	0.434655i
$269$	−124.916			−0.464374			−0.232187	−	0.972671i	$-0.574588\pi$
$269$	−124.916			−0.464374			−0.232187	+	0.972671i	$0.574588\pi$
$270$	50.6536	+	252.248i	0.187606	+	0.934253i
$271$		−	182.930i		−	0.675019i	−0.941322	−	0.337510i	$-0.890415\pi$
$271$		−	182.930i		−	0.675019i	0.941322	−	0.337510i	$-0.109585\pi$
$272$	−51.2869	+	52.0405i	−0.188555	+	0.191325i
$273$	28.1993			0.103294
$274$	−29.5211	+	5.92809i	−0.107741	+	0.0216354i
$275$		−	102.411i		−	0.372402i
$276$	304.905	−	127.601i	1.10473	−	0.462321i
$277$	−31.8323			−0.114918			−0.0574590	−	0.998348i	$-0.518300\pi$
$277$	−31.8323			−0.114918			−0.0574590	+	0.998348i	$0.518300\pi$
$278$	−63.8052	−	317.742i	−0.229515	−	1.14296i
$279$			17.0472i			0.0611011i
$280$	−29.1548	−	43.1208i	−0.104124	−	0.154003i
$281$	125.723			0.447414			0.223707	−	0.974656i	$-0.428184\pi$
$281$	125.723			0.447414			0.223707	+	0.974656i	$0.428184\pi$
$282$	−569.567	+	114.374i	−2.01974	+	0.405581i
$283$			79.5201i			0.280990i	0.990081	+	0.140495i	$0.0448693\pi$
$283$			79.5201i			0.280990i	−0.990081	+	0.140495i	$0.955131\pi$
$284$	14.6348	+	34.9703i	0.0515310	+	0.123135i
$285$	−632.874			−2.22061
$286$	22.5689	+	112.390i	0.0789124	+	0.392974i
$287$		−	59.7109i		−	0.208052i
$288$	53.6880	−	81.9574i	0.186417	−	0.284574i
$289$	−268.146			−0.927842
$290$	241.860	−	48.5674i	0.833998	−	0.167474i
$291$			240.558i			0.826659i
$292$	37.6611	−	15.7609i	0.128976	−	0.0539756i
$293$	84.5185			0.288459			0.144230	−	0.989544i	$-0.453930\pi$
$293$	84.5185			0.288459			0.144230	+	0.989544i	$0.453930\pi$
$294$	65.5204	+	326.283i	0.222859	+	1.10981i
$295$			534.220i			1.81091i
$296$	−191.392	+	129.404i	−0.646596	+	0.437176i
$297$	−151.859			−0.511310
$298$	−540.308	+	108.498i	−1.81311	+	0.364088i
$299$			185.204i			0.619410i
$300$	−74.5891	−	178.233i	−0.248630	−	0.594110i
$301$	−34.1618			−0.113494
$302$	−19.7771	−	98.4873i	−0.0654870	−	0.326117i
$303$			664.625i			2.19348i
$304$	−332.921	−	328.100i	−1.09513	−	1.07928i
$305$	−1.21219			−0.00397440
$306$	−27.4164	+	5.50544i	−0.0895961	+	0.0179916i
$307$			105.755i			0.344480i	0.985055	+	0.172240i	$0.0551004\pi$
$307$			105.755i			0.344480i	−0.985055	+	0.172240i	$0.944900\pi$
$308$	28.3414	−	11.8606i	0.0920175	−	0.0385086i
$309$	532.572			1.72353
$310$	13.6750	+	68.0999i	0.0441130	+	0.219677i
$311$		−	3.48363i		−	0.0112014i	−0.999984	−	0.00560069i	$-0.998217\pi$
$311$		−	3.48363i		−	0.0112014i	0.999984	−	0.00560069i	$-0.00178276\pi$
$312$	121.136	+	179.164i	0.388257	+	0.574244i
$313$	−343.348			−1.09696			−0.548479	−	0.836164i	$-0.684793\pi$
$313$	−343.348			−1.09696			−0.548479	+	0.836164i	$0.684793\pi$
$314$	18.5832	−	3.73167i	0.0591823	−	0.0118843i
$315$		−	19.9214i		−	0.0632425i
$316$	−149.430	−	357.068i	−0.472880	−	1.12996i
$317$	243.076			0.766802			0.383401	−	0.923582i	$-0.374753\pi$
$317$	243.076			0.766802			0.383401	+	0.923582i	$0.374753\pi$
$318$	109.959	+	547.582i	0.345783	+	1.72196i
$319$			145.605i			0.456441i
$320$	148.727	−	370.470i	0.464771	−	1.15772i
$321$	−161.189			−0.502147
$322$	48.6649	−	9.77233i	0.151133	−	0.0303489i
$323$			133.409i			0.413030i
$324$	−365.971	+	153.156i	−1.12954	+	0.472704i
$325$	108.261			0.333111
$326$	−47.3491	−	235.792i	−0.145243	−	0.723289i
$327$		−	27.2852i		−	0.0834409i
$328$	379.373	−	256.502i	1.15663	−	0.782017i
$329$	−87.2410			−0.265170
$330$	312.787	−	62.8103i	0.947840	−	0.190334i
$331$			439.523i			1.32786i	0.747793	+	0.663932i	$0.231114\pi$
$331$			439.523i			1.32786i	−0.747793	+	0.663932i	$0.768886\pi$
$332$	66.1265	+	158.011i	0.199176	+	0.475938i
$333$	−88.4214			−0.265530
$334$	128.209	+	638.465i	0.383860	+	1.91157i
$335$			196.917i			0.587813i
$336$	40.6862	−	41.2840i	0.121090	−	0.122869i
$337$	−428.538			−1.27163			−0.635813	−	0.771843i	$-0.719335\pi$
$337$	−428.538			−1.27163			−0.635813	+	0.771843i	$0.719335\pi$
$338$	212.574	−	42.6866i	0.628916	−	0.126292i
$339$			495.514i			1.46169i
$340$	−105.106	+	43.9861i	−0.309136	+	0.129371i
$341$	−40.9977			−0.120228
$342$	−35.2202	−	175.392i	−0.102983	−	0.512842i
$343$			101.089i			0.294720i
$344$	−146.750	−	217.047i	−0.426598	−	0.630951i
$345$	515.429			1.49400
$346$	394.023	−	79.1232i	1.13880	−	0.228680i
$347$		−	122.364i		−	0.352635i	−0.984333	−	0.176317i	$-0.943582\pi$
$347$		−	122.364i		−	0.352635i	0.984333	−	0.176317i	$-0.0564185\pi$
$348$	106.049	+	253.407i	0.304738	+	0.728182i
$349$	332.730			0.953381			0.476690	−	0.879071i	$-0.341836\pi$
$349$	332.730			0.953381			0.476690	+	0.879071i	$0.341836\pi$
$350$	−5.71243	−	28.4472i	−0.0163212	−	0.0812777i
$351$		−	160.534i		−	0.457363i
$352$	197.103	+	129.117i	0.559952	+	0.366809i
$353$	−650.476			−1.84271			−0.921354	−	0.388724i	$-0.872916\pi$
$353$	−650.476			−1.84271			−0.921354	+	0.388724i	$0.872916\pi$
$354$	−583.245	+	117.121i	−1.64759	+	0.330849i
$355$			59.1158i			0.166523i
$356$	561.817	−	235.116i	1.57814	−	0.660438i
$357$	−16.5434			−0.0463400
$358$	131.774	+	656.215i	0.368082	+	1.83300i
$359$		−	286.018i		−	0.796707i	−0.917232	−	0.398354i	$-0.869582\pi$
$359$		−	286.018i		−	0.796707i	0.917232	−	0.398354i	$-0.130418\pi$
$360$	126.570	−	85.5767i	0.351584	−	0.237713i
$361$	−492.460			−1.36416
$362$	36.6843	−	7.36651i	0.101338	−	0.0203495i
$363$		−	231.929i		−	0.638922i
$364$	12.5382	+	29.9605i	0.0344456	+	0.0823090i
$365$	63.6644			0.174423
$366$	−0.265757	−	1.32344i	−0.000726113	−	0.00361595i
$367$		−	459.888i		−	1.25310i	−0.779381	−	0.626551i	$-0.784466\pi$
$367$		−	459.888i		−	1.25310i	0.779381	−	0.626551i	$-0.215534\pi$
$368$	271.140	+	267.213i	0.736792	+	0.726123i
$369$	175.267			0.474978
$370$	−353.224	+	70.9304i	−0.954660	+	0.191704i
$371$			83.8735i			0.226074i
$372$	−71.3514	+	29.8600i	−0.191805	+	0.0802688i
$373$	−158.470			−0.424853			−0.212427	−	0.977177i	$-0.568137\pi$
$373$	−158.470			−0.424853			−0.212427	+	0.977177i	$0.568137\pi$
$374$	−13.2403	−	65.9350i	−0.0354019	−	0.176297i
$375$			240.288i			0.640769i
$376$	−374.763	−	554.286i	−0.996711	−	1.47416i
$377$	−153.923			−0.408284
$378$	−42.1828	+	8.47065i	−0.111595	+	0.0224091i
$379$		−	691.531i		−	1.82462i	−0.409500	−	0.912310i	$-0.634297\pi$
$379$		−	691.531i		−	1.82462i	0.409500	−	0.912310i	$-0.365703\pi$
$380$	−281.394	−	672.400i	−0.740510	−	1.76947i
$381$	−172.926			−0.453875
$382$	2.64262	+	13.1599i	0.00691786	+	0.0344501i
$383$		−	411.736i		−	1.07503i	−0.843254	−	0.537515i	$-0.819363\pi$
$383$		−	411.736i		−	1.07503i	0.843254	−	0.537515i	$-0.180637\pi$
$384$	437.074	+	81.1550i	1.13821	+	0.211341i
$385$	47.9099			0.124441
$386$	192.309	−	38.6173i	0.498211	−	0.100045i
$387$		−	100.274i		−	0.259105i
$388$	−255.582	+	106.959i	−0.658716	+	0.275667i
$389$	379.644			0.975950			0.487975	−	0.872858i	$-0.337736\pi$
$389$	379.644			0.975950			0.487975	+	0.872858i	$0.337736\pi$
$390$	66.3985	+	330.656i	0.170253	+	0.847836i
$391$		−	108.652i		−	0.277881i
$392$	−317.529	+	214.688i	−0.810023	+	0.547672i
$393$	496.576			1.26355
$394$	97.2598	−	19.5306i	0.246852	−	0.0495700i
$395$		−	603.607i		−	1.52812i
$396$	34.8140	+	83.1891i	0.0879141	+	0.210074i
$397$	−119.247			−0.300369			−0.150185	−	0.988658i	$-0.547987\pi$
$397$	−119.247			−0.300369			−0.150185	+	0.988658i	$0.547987\pi$
$398$	−51.7200	−	257.559i	−0.129950	−	0.647133i
$399$		−	105.834i		−	0.265247i
$400$	156.200	−	158.495i	0.390500	−	0.396238i
$401$	335.174			0.835844			0.417922	−	0.908483i	$-0.362758\pi$
$401$	335.174			0.835844			0.417922	+	0.908483i	$0.362758\pi$
$402$	−214.988	+	43.1715i	−0.534797	+	0.107392i
$403$		−	43.3398i		−	0.107543i
$404$	−706.135	+	295.512i	−1.74786	+	0.731465i
$405$	−618.658			−1.52755
$406$	8.12180	+	40.4455i	0.0200044	+	0.0996195i
$407$		−	212.649i		−	0.522479i
$408$	−71.0658	−	105.108i	−0.174181	−	0.257619i
$409$	−763.262			−1.86617			−0.933083	−	0.359662i	$-0.882892\pi$
$409$	−763.262			−1.86617			−0.933083	+	0.359662i	$0.882892\pi$
$410$	700.152	−	140.596i	1.70769	−	0.342918i
$411$		−	52.2869i		−	0.127219i
$412$	236.797	+	565.834i	0.574750	+	1.37338i
$413$	−89.3361			−0.216310
$414$	28.6843	+	142.844i	0.0692857	+	0.345034i
$415$			267.111i			0.643641i
$416$	−136.493	+	208.363i	−0.328108	+	0.500873i
$417$	562.774			1.34958
$418$	421.809	−	84.7027i	1.00911	−	0.202638i
$419$		−	576.967i		−	1.37701i	−0.725231	−	0.688505i	$-0.758267\pi$
$419$		−	576.967i		−	1.37701i	0.725231	−	0.688505i	$-0.241733\pi$
$420$	83.3812	−	34.8944i	0.198527	−	0.0830819i
$421$	307.985			0.731555			0.365778	−	0.930702i	$-0.380803\pi$
$421$	307.985			0.731555			0.365778	+	0.930702i	$0.380803\pi$
$422$	−60.0133	−	298.858i	−0.142212	−	0.708195i
$423$		−	256.075i		−	0.605377i
$424$	−532.890	+	360.297i	−1.25682	+	0.849758i
$425$	−63.5125			−0.149441
$426$	−64.5408	+	12.9603i	−0.151504	+	0.0304233i
$427$		−	0.202712i		−	0.000474735i
$428$	−71.6694	−	171.256i	−0.167452	−	0.400131i
$429$	−199.062			−0.464015
$430$	−80.4381	−	400.571i	−0.187065	−	0.931561i
$431$			359.778i			0.834752i	0.908734	+	0.417376i	$0.137050\pi$
$431$			359.778i			0.834752i	−0.908734	+	0.417376i	$0.862950\pi$
$432$	−235.024	−	231.621i	−0.544036	−	0.536159i
$433$	771.968			1.78284			0.891418	−	0.453182i	$-0.149711\pi$
$433$	771.968			1.78284			0.891418	+	0.453182i	$0.149711\pi$
$434$	−11.3882	+	2.28684i	−0.0262400	+	0.00526921i
$435$			428.374i			0.984768i
$436$	28.9893	−	12.1318i	0.0664891	−	0.0278252i
$437$	695.081			1.59057
$438$	13.9576	+	69.5069i	0.0318666	+	0.158692i
$439$		−	753.517i		−	1.71644i	−0.513282	−	0.858220i	$-0.671570\pi$
$439$		−	753.517i		−	1.71644i	0.513282	−	0.858220i	$-0.328430\pi$
$440$	205.807	+	304.395i	0.467744	+	0.691807i
$441$	−146.695			−0.332642
$442$	69.7017	−	13.9967i	0.157696	−	0.0316667i
$443$		−	440.608i		−	0.994600i	−0.867579	−	0.497300i	$-0.834325\pi$
$443$		−	440.608i		−	0.994600i	0.867579	−	0.497300i	$-0.165675\pi$
$444$	−154.879	−	370.089i	−0.348828	−	0.833535i
$445$	949.726			2.13422
$446$	166.471	+	829.003i	0.373253	+	1.85875i
$447$		−	956.976i		−	2.14089i
$448$	61.9526	+	24.8712i	0.138287	+	0.0555160i
$449$	−471.911			−1.05103			−0.525514	−	0.850785i	$-0.676127\pi$
$449$	−471.911			−1.05103			−0.525514	+	0.850785i	$0.676127\pi$
$450$	83.4997	−	16.7674i	0.185555	−	0.0372610i
$451$			421.507i			0.934606i
$452$	−526.462	+	220.320i	−1.16474	+	0.487434i
$453$	174.438			0.385072
$454$	−53.2213	−	265.035i	−0.117228	−	0.583778i
$455$			50.6468i			0.111312i
$456$	672.414	−	454.632i	1.47459	−	0.997001i
$457$	561.121			1.22784			0.613918	−	0.789370i	$-0.289593\pi$
$457$	561.121			1.22784			0.613918	+	0.789370i	$0.289593\pi$
$458$	236.569	−	47.5051i	0.516527	−	0.103723i
$459$			94.1792i			0.205183i
$460$	229.175	+	547.620i	0.498206	+	1.19048i
$461$	394.506			0.855761			0.427880	−	0.903835i	$-0.359260\pi$
$461$	394.506			0.855761			0.427880	+	0.903835i	$0.359260\pi$
$462$	10.5036	+	52.3066i	0.0227351	+	0.113218i
$463$		−	13.8034i		−	0.0298129i	−0.999889	−	0.0149064i	$-0.995255\pi$
$463$		−	13.8034i		−	0.0298129i	0.999889	−	0.0149064i	$-0.00474504\pi$
$464$	−222.081	+	225.344i	−0.478624	+	0.485656i
$465$	−120.616			−0.259390
$466$	−413.901	+	83.1149i	−0.888200	+	0.178358i
$467$			191.969i			0.411070i	0.978650	+	0.205535i	$0.0658934\pi$
$467$			191.969i			0.411070i	−0.978650	+	0.205535i	$0.934107\pi$
$468$	−87.9416	+	36.8028i	−0.187909	+	0.0786386i
$469$	−32.9299			−0.0702131
$470$	−205.419	−	1022.96i	−0.437062	−	2.17651i
$471$			32.9140i			0.0698812i
$472$	−383.763	−	567.597i	−0.813057	−	1.20254i
$473$	241.153			0.509837
$474$	659.001	−	132.333i	1.39030	−	0.279183i
$475$		−	406.311i		−	0.855391i
$476$	−7.35567	−	17.5766i	−0.0154531	−	0.0369257i
$477$	−246.190			−0.516122
$478$	−23.2241	−	115.653i	−0.0485859	−	0.241952i
$479$			385.857i			0.805546i	0.915300	+	0.402773i	$0.131954\pi$
$479$			385.857i			0.805546i	−0.915300	+	0.402773i	$0.868046\pi$
$480$	579.884	+	379.866i	1.20809	+	0.791387i
$481$	224.797			0.467354
$482$	−741.120	+	148.823i	−1.53759	+	0.308762i
$483$			86.1938i			0.178455i
$484$	246.414	−	103.122i	0.509119	−	0.213062i
$485$	−432.050			−0.890824
$486$	−62.5468	−	311.475i	−0.128697	−	0.640895i
$487$			319.465i			0.655986i	0.944680	+	0.327993i	$0.106372\pi$
$487$			319.465i			0.655986i	−0.944680	+	0.327993i	$0.893628\pi$
$488$	1.28793	−	0.870793i	0.00263920	−	0.00178441i
$489$	417.628			0.854044
$490$	−586.016	+	117.677i	−1.19595	+	0.240157i
$491$		−	460.023i		−	0.936911i	−0.883487	−	0.468455i	$-0.844811\pi$
$491$		−	460.023i		−	0.936911i	0.883487	−	0.468455i	$-0.155189\pi$
$492$	306.998	+	733.582i	0.623980	+	1.49102i
$493$	90.3004			0.183165
$494$	89.5416	+	445.906i	0.181258	+	0.902643i
$495$			140.628i			0.284096i
$496$	−63.4498	−	62.5310i	−0.127923	−	0.126071i
$497$	−9.88577			−0.0198909
$498$	−291.624	+	58.5606i	−0.585590	+	0.117591i
$499$		−	9.88810i		−	0.0198158i	−0.999951	−	0.00990792i	$-0.996846\pi$
$499$		−	9.88810i		−	0.0198158i	0.999951	−	0.00990792i	$-0.00315384\pi$
$500$	−255.295	+	106.839i	−0.510591	+	0.213678i
$501$	−1130.83			−2.25714
$502$	120.124	+	598.202i	0.239291	+	1.19164i
$503$			533.698i			1.06103i	0.847675	+	0.530515i	$0.178002\pi$
$503$			533.698i			1.06103i	−0.847675	+	0.530515i	$0.821998\pi$
$504$	14.3108	+	21.1660i	0.0283944	+	0.0419961i
$505$	−1193.69			−2.36374
$506$	−343.532	+	68.9842i	−0.678917	+	0.136332i
$507$			376.504i			0.742611i
$508$	−76.8880	−	183.726i	−0.151354	−	0.361666i
$509$	−211.426			−0.415375			−0.207688	−	0.978195i	$-0.566594\pi$
$509$	−211.426			−0.415375			−0.207688	+	0.978195i	$0.566594\pi$
$510$	−38.9534	−	193.983i	−0.0763792	−	0.380359i
$511$			10.6464i			0.0208345i
$512$	108.112	+	500.456i	0.211157	+	0.977452i
$513$	−602.496			−1.17446
$514$	468.965	−	94.1721i	0.912383	−	0.183214i
$515$			956.517i			1.85731i
$516$	419.697	−	175.640i	0.813366	−	0.340387i
$517$	615.846			1.19119
$518$	−11.8615	−	59.0687i	−0.0228986	−	0.114032i
$519$			697.882i			1.34467i
$520$	−321.785	+	217.565i	−0.618816	+	0.418394i
$521$	108.087			0.207461			0.103730	−	0.994605i	$-0.466922\pi$
$521$	108.087			0.207461			0.103730	+	0.994605i	$0.466922\pi$
$522$	−118.718	+	23.8395i	−0.227429	+	0.0456696i
$523$		−	64.4901i		−	0.123308i	−0.998098	−	0.0616540i	$-0.980362\pi$
$523$		−	64.4901i		−	0.123308i	0.998098	−	0.0616540i	$-0.0196375\pi$
$524$	220.792	+	527.590i	0.421359	+	1.00685i
$525$	50.3848			0.0959710
$526$	−122.324	−	609.160i	−0.232556	−	1.15810i
$527$			25.4257i			0.0482461i
$528$	−287.209	+	291.429i	−0.543957	+	0.551949i
$529$	−37.0924			−0.0701180
$530$	−983.475	+	197.490i	−1.85561	+	0.372623i
$531$		−	262.224i		−	0.493831i
$532$	112.444	−	47.0567i	0.211360	−	0.0884525i
$533$	−445.587			−0.835998
$534$	208.215	+	1036.88i	0.389915	+	1.94173i
$535$		−	289.501i		−	0.541124i
$536$	−141.458	−	209.220i	−0.263914	−	0.390336i
$537$	−1162.27			−2.16437
$538$	244.943	−	49.1867i	0.455285	−	0.0914250i
$539$		−	352.795i		−	0.654535i
$540$	−198.649	−	474.677i	−0.367868	−	0.879032i
$541$	626.989			1.15894			0.579472	−	0.814992i	$-0.303259\pi$
$541$	626.989			1.15894			0.579472	+	0.814992i	$0.303259\pi$
$542$	72.0299	+	358.700i	0.132897	+	0.661808i
$543$			64.9740i			0.119658i
$544$	80.0750	−	122.238i	0.147197	−	0.224703i
$545$	49.0051			0.0899175
$546$	−55.2947	+	11.1036i	−0.101272	+	0.0203363i
$547$		−	224.306i		−	0.410066i	−0.978755	−	0.205033i	$-0.934270\pi$
$547$		−	224.306i		−	0.410066i	0.978755	−	0.205033i	$-0.0657302\pi$
$548$	55.5525	−	23.2483i	0.101373	−	0.0424238i
$549$	0.595010			0.00108381
$550$	40.3248	+	200.812i	0.0733179	+	0.365114i
$551$			577.683i			1.04843i
$552$	−547.632	+	370.265i	−0.992087	+	0.670769i
$553$	100.940			0.182531
$554$	62.4185	−	12.5342i	0.112669	−	0.0226248i
$555$		−	625.620i		−	1.12724i
$556$	250.226	+	597.922i	0.450046	+	1.07540i
$557$	848.114			1.52265			0.761323	−	0.648373i	$-0.224550\pi$
$557$	848.114			1.52265			0.761323	+	0.648373i	$0.224550\pi$
$558$	−6.71245	−	33.4271i	−0.0120295	−	0.0599052i
$559$			254.929i			0.456046i
$560$	74.1474	+	73.0737i	0.132406	+	0.130489i
$561$	116.782			0.208168
$562$	−246.526	+	49.5044i	−0.438658	+	0.0880861i
$563$		−	479.921i		−	0.852435i	−0.904621	−	0.426217i	$-0.859846\pi$
$563$		−	479.921i		−	0.852435i	0.904621	−	0.426217i	$-0.140154\pi$
$564$	1071.80	−	448.542i	1.90036	−	0.795286i
$565$	−889.960			−1.57515
$566$	−31.3115	−	155.927i	−0.0553207	−	0.275490i
$567$		−	103.456i		−	0.182463i
$568$	−42.4665	−	62.8092i	−0.0747650	−	0.110580i
$569$	−411.847			−0.723808			−0.361904	−	0.932215i	$-0.617873\pi$
$569$	−411.847			−0.723808			−0.361904	+	0.932215i	$0.617873\pi$
$570$	1240.97	−	249.198i	2.17715	−	0.437190i
$571$			601.628i			1.05364i	0.849977	+	0.526820i	$0.176616\pi$
$571$			601.628i			1.05364i	−0.849977	+	0.526820i	$0.823384\pi$
$572$	−88.5089	−	211.495i	−0.154736	−	0.369746i
$573$	−23.3084			−0.0406779
$574$	23.5116	+	117.085i	0.0409609	+	0.203980i
$575$			330.910i			0.575496i
$576$	−73.0032	+	181.847i	−0.126742	+	0.315706i
$577$	235.147			0.407533			0.203767	−	0.979019i	$-0.434682\pi$
$577$	235.147			0.407533			0.203767	+	0.979019i	$0.434682\pi$
$578$	525.796	−	105.584i	0.909682	−	0.182672i
$579$			340.612i			0.588277i
$580$	−455.128	+	190.467i	−0.784703	+	0.328392i
$581$	−44.6683			−0.0768817
$582$	−94.7212	−	471.699i	−0.162751	−	0.810480i
$583$		−	592.074i		−	1.01556i
$584$	−67.6420	+	45.7341i	−0.115825	+	0.0783118i
$585$	−148.661			−0.254122
$586$	−165.729	+	33.2797i	−0.282813	+	0.0567913i
$587$		−	700.107i		−	1.19269i	−0.802729	−	0.596343i	$-0.796620\pi$
$587$		−	700.107i		−	1.19269i	0.802729	−	0.596343i	$-0.203380\pi$
$588$	−256.952	−	613.996i	−0.436994	−	1.04421i
$589$	−162.657			−0.276158
$590$	−210.352	−	1047.53i	−0.356529	−	1.77547i
$591$			172.263i			0.291478i
$592$	324.339	−	329.105i	0.547870	−	0.555920i
$593$	356.883			0.601826			0.300913	−	0.953652i	$-0.402709\pi$
$593$	356.883			0.601826			0.300913	+	0.953652i	$0.402709\pi$
$594$	297.774	−	59.7955i	0.501303	−	0.100666i
$595$		−	29.7125i		−	0.0499370i
$596$	1016.74	−	425.499i	1.70595	−	0.713925i
$597$	456.180			0.764121
$598$	−72.9251	−	363.157i	−0.121948	−	0.607287i
$599$		−	72.0345i		−	0.120258i	−0.998191	−	0.0601290i	$-0.980849\pi$
$599$		−	72.0345i		−	0.120258i	0.998191	−	0.0601290i	$-0.0191512\pi$
$600$	216.439	+	320.119i	0.360732	+	0.533532i
$601$	−475.009			−0.790364			−0.395182	−	0.918603i	$-0.629318\pi$
$601$	−475.009			−0.790364			−0.395182	+	0.918603i	$0.629318\pi$
$602$	66.9864	−	13.4514i	0.111273	−	0.0223446i
$603$		−	96.6577i		−	0.160295i
$604$	77.5600	+	185.332i	0.128411	+	0.306841i
$605$	416.552			0.688515
$606$	−261.700	−	1303.23i	−0.431849	−	2.15055i
$607$		−	712.080i		−	1.17311i	−0.809908	−	0.586557i	$-0.800483\pi$
$607$		−	712.080i		−	1.17311i	0.809908	−	0.586557i	$-0.199517\pi$
$608$	782.001	+	512.267i	1.28619	+	0.842545i
$609$	−71.6358			−0.117629
$610$	2.37694	−	0.477309i	0.00389662	−	0.000782473i
$611$			651.028i			1.06551i
$612$	51.5918	−	21.5908i	0.0843004	−	0.0352790i
$613$	263.588			0.429996			0.214998	−	0.976614i	$-0.431025\pi$
$613$	263.588			0.429996			0.214998	+	0.976614i	$0.431025\pi$
$614$	−41.6418	−	207.371i	−0.0678205	−	0.337737i
$615$			1240.09i			2.01640i
$616$	−50.9032	+	34.4166i	−0.0826350	+	0.0558711i
$617$	213.720			0.346386			0.173193	−	0.984888i	$-0.444592\pi$
$617$	213.720			0.346386			0.173193	+	0.984888i	$0.444592\pi$
$618$	−1044.30	+	209.704i	−1.68980	+	0.339326i
$619$		−	254.897i		−	0.411788i	−0.978574	−	0.205894i	$-0.933990\pi$
$619$		−	254.897i		−	0.411788i	0.978574	−	0.205894i	$-0.0660102\pi$
$620$	−53.6295	−	128.149i	−0.0864992	−	0.206693i
$621$	490.689			0.790159
$622$	1.37170	+	6.83089i	0.00220531	+	0.0109821i
$623$			158.820i			0.254928i
$624$	−308.078	−	303.617i	−0.493714	−	0.486565i
$625$	−779.267			−1.24683
$626$	673.256	−	135.195i	1.07549	−	0.215967i
$627$			747.094i			1.19154i
$628$	−34.9697	+	14.6345i	−0.0556842	+	0.0233034i
$629$	−131.880			−0.209665
$630$	7.84417	+	39.0629i	0.0124511	+	0.0620047i
$631$			780.044i			1.23620i	0.786098	+	0.618102i	$0.212098\pi$
$631$			780.044i			1.23620i	−0.786098	+	0.618102i	$0.787902\pi$
$632$	433.609	+	641.320i	0.686089	+	1.01475i
$633$	529.329			0.836222
$634$	−476.638	+	95.7128i	−0.751794	+	0.150967i
$635$		−	310.581i		−	0.489104i
$636$	−431.228	−	1030.43i	−0.678031	−	1.62018i
$637$	372.949			0.585477
$638$	−57.3328	−	285.510i	−0.0898634	−	0.447508i
$639$		−	29.0172i		−	0.0454104i
$640$	−145.757	+	785.000i	−0.227745	+	1.22656i
$641$	−233.940			−0.364961			−0.182481	−	0.983209i	$-0.558413\pi$
$641$	−233.940			−0.364961			−0.182481	+	0.983209i	$0.558413\pi$
$642$	316.069	−	63.4693i	0.492319	−	0.0988618i
$643$			703.844i			1.09462i	0.836928	+	0.547312i	$0.184349\pi$
$643$			703.844i			1.09462i	−0.836928	+	0.547312i	$0.815651\pi$
$644$	−91.5770	+	38.3243i	−0.142200	+	0.0595097i
$645$	709.479			1.09997
$646$	−52.5305	−	261.595i	−0.0813166	−	0.404946i
$647$			686.881i			1.06164i	0.847485	+	0.530820i	$0.178116\pi$
$647$			686.881i			1.06164i	−0.847485	+	0.530820i	$0.821884\pi$
$648$	657.310	−	444.420i	1.01437	−	0.685834i
$649$	630.635			0.971703
$650$	−212.284	+	42.6285i	−0.326591	+	0.0655823i
$651$		−	20.1703i		−	0.0309836i
$652$	185.689	+	443.711i	0.284800	+	0.680538i
$653$	−237.000			−0.362940			−0.181470	−	0.983397i	$-0.558085\pi$
$653$	−237.000			−0.362940			−0.181470	+	0.983397i	$0.558085\pi$
$654$	10.7437	+	53.5023i	0.0164277	+	0.0818078i
$655$			891.867i			1.36163i
$656$	−642.897	+	652.343i	−0.980026	+	0.994426i
$657$	−31.2500			−0.0475646
$658$	171.067	−	34.3517i	0.259980	−	0.0522062i
$659$			235.447i			0.357280i	0.983915	+	0.178640i	$0.0571697\pi$
$659$			235.447i			0.357280i	−0.983915	+	0.178640i	$0.942830\pi$
$660$	−588.599	+	246.324i	−0.891817	+	0.373218i
$661$	123.985			0.187571			0.0937856	−	0.995592i	$-0.470103\pi$
$661$	123.985			0.187571			0.0937856	+	0.995592i	$0.470103\pi$
$662$	−173.065	−	861.841i	−0.261427	−	1.30188i
$663$			123.453i			0.186204i
$664$	−191.882	−	283.800i	−0.288980	−	0.427409i
$665$	190.081			0.285836
$666$	173.382	−	34.8165i	0.260333	−	0.0522770i
$667$		−	470.480i		−	0.705368i
$668$	−502.799	−	1201.45i	−0.752694	−	1.79859i
$669$	−1468.30			−2.19478
$670$	−77.5374	−	386.126i	−0.115727	−	0.576308i
$671$			1.43097i			0.00213259i
$672$	−63.5239	+	96.9724i	−0.0945296	+	0.144304i
$673$	−219.287			−0.325835			−0.162917	−	0.986640i	$-0.552090\pi$
$673$	−219.287			−0.325835			−0.162917	+	0.986640i	$0.552090\pi$
$674$	840.301	−	168.739i	1.24674	−	0.250355i
$675$		−	286.833i		−	0.424938i
$676$	−400.018	+	167.404i	−0.591743	+	0.247640i
$677$	−775.698			−1.14579			−0.572893	−	0.819630i	$-0.694179\pi$
$677$	−775.698			−1.14579			−0.572893	+	0.819630i	$0.694179\pi$
$678$	−195.112	−	971.632i	−0.287776	−	1.43309i
$679$		−	72.2505i		−	0.106407i
$680$	188.778	−	127.637i	0.277615	−	0.187701i
$681$	469.422			0.689313
$682$	80.3905	−	16.1431i	0.117875	−	0.0236702i
$683$		−	1169.98i		−	1.71301i	−0.516140	−	0.856504i	$-0.672632\pi$
$683$		−	1169.98i		−	1.71301i	0.516140	−	0.856504i	$-0.327368\pi$
$684$	138.123	+	330.050i	0.201935	+	0.482530i
$685$	93.9090			0.137093
$686$	−39.8045	−	198.221i	−0.0580240	−	0.288952i
$687$			419.004i			0.609904i
$688$	373.219	+	367.815i	0.542469	+	0.534614i
$689$	625.898			0.908415
$690$	−1010.68	+	202.954i	−1.46476	+	0.294136i
$691$		−	525.248i		−	0.760127i	−0.924960	−	0.380064i	$-0.875902\pi$
$691$		−	525.248i		−	0.760127i	0.924960	−	0.380064i	$-0.124098\pi$
$692$	−741.468	+	310.298i	−1.07149	+	0.448408i
$693$	−23.5168			−0.0339347
$694$	48.1817	+	239.939i	0.0694261	+	0.345733i
$695$			1010.76i			1.45433i
$696$	−307.727	−	455.138i	−0.442137	−	0.653934i
$697$	261.408			0.375048
$698$	−652.435	+	131.014i	−0.934721	+	0.187700i
$699$		−	733.089i		−	1.04877i
$700$	22.4025	+	53.5315i	0.0320036	+	0.0764736i
$701$	−686.722			−0.979633			−0.489816	−	0.871826i	$-0.662936\pi$
$701$	−686.722			−0.979633			−0.489816	+	0.871826i	$0.662936\pi$
$702$	63.2114	+	314.785i	0.0900448	+	0.448411i
$703$		−	843.678i		−	1.20011i
$704$	−437.332	−	175.569i	−0.621210	−	0.249388i
$705$	1811.84			2.56998
$706$	1275.49	−	256.129i	1.80664	−	0.362789i
$707$		−	199.617i		−	0.282344i
$708$	1097.54	−	459.313i	1.55020	−	0.648747i
$709$	−765.783			−1.08009			−0.540045	−	0.841636i	$-0.681593\pi$
$709$	−765.783			−1.08009			−0.540045	+	0.841636i	$0.681593\pi$
$710$	−23.2772	−	115.917i	−0.0327848	−	0.163264i
$711$			296.283i			0.416714i
$712$	−1009.06	+	682.247i	−1.41722	+	0.958212i
$713$	132.472			0.185795
$714$	32.4392	−	6.51407i	0.0454331	−	0.00912334i
$715$		−	357.523i		−	0.500032i
$716$	−516.778	−	1234.86i	−0.721757	−	1.72466i
$717$	204.841			0.285691
$718$	112.621	+	560.840i	0.156854	+	0.781114i
$719$			706.909i			0.983183i	0.870826	+	0.491591i	$0.163585\pi$
$719$			706.909i			0.983183i	−0.870826	+	0.491591i	$0.836415\pi$
$720$	−214.490	+	217.641i	−0.297903	+	0.302280i
$721$	−159.956			−0.221853
$722$	965.644	−	193.909i	1.33746	−	0.268573i
$723$		−	1312.65i		−	1.81556i
$724$	−69.0320	+	28.8893i	−0.0953480	+	0.0399024i
$725$	−275.020			−0.379338
$726$	91.3234	+	454.779i	0.125790	+	0.626417i
$727$			6.07910i			0.00836190i	0.999991	+	0.00418095i	$0.00133084\pi$
$727$			6.07910i			0.00836190i	−0.999991	+	0.00418095i	$0.998669\pi$
$728$	−36.3828	−	53.8111i	−0.0499763	−	0.0739164i
$729$	−340.959			−0.467708
$730$	−124.837	+	25.0683i	−0.171009	+	0.0343401i
$731$		−	149.557i		−	0.204592i
$732$	1.04222	+	2.49043i	0.00142380	+	0.00340222i
$733$	−855.753			−1.16747			−0.583733	−	0.811945i	$-0.698409\pi$
$733$	−855.753			−1.16747			−0.583733	+	0.811945i	$0.698409\pi$
$734$	181.084	+	901.775i	0.246708	+	1.22858i
$735$		−	1037.93i		−	1.41215i
$736$	−636.883	−	417.204i	−0.865330	−	0.566853i
$737$	232.457			0.315409
$738$	−343.673	+	69.0124i	−0.465681	+	0.0935127i
$739$		−	305.103i		−	0.412859i	−0.978461	−	0.206430i	$-0.933816\pi$
$739$		−	305.103i		−	0.412859i	0.978461	−	0.206430i	$-0.0661845\pi$
$740$	664.693	−	278.169i	0.898233	−	0.375904i
$741$	−789.774			−1.06582
$742$	−33.0257	−	164.464i	−0.0445091	−	0.221649i
$743$			652.078i			0.877628i	0.898578	+	0.438814i	$0.144601\pi$
$743$			652.078i			0.877628i	−0.898578	+	0.438814i	$0.855399\pi$
$744$	128.152	−	86.6462i	0.172248	−	0.116460i
$745$	1718.76			2.30706
$746$	310.737	−	62.3986i	0.416538	−	0.0836443i
$747$		−	131.113i		−	0.175519i
$748$	51.9247	+	124.076i	0.0694180	+	0.165876i
$749$	48.4125			0.0646362
$750$	−94.6150	−	471.171i	−0.126153	−	0.628228i
$751$		−	1126.07i		−	1.49942i	−0.661766	−	0.749710i	$-0.730193\pi$
$751$		−	1126.07i		−	1.49942i	0.661766	−	0.749710i	$-0.269807\pi$
$752$	953.110	+	939.309i	1.26743	+	1.24908i
$753$	−1059.52			−1.40706
$754$	301.821	−	60.6081i	0.400293	−	0.0803821i
$755$			313.296i			0.414961i
$756$	79.3790	−	33.2195i	0.104999	−	0.0439411i
$757$	127.654			0.168631			0.0843154	−	0.996439i	$-0.473130\pi$
$757$	127.654			0.168631			0.0843154	+	0.996439i	$0.473130\pi$
$758$	272.295	+	1355.99i	0.359228	+	1.78891i
$759$		−	608.453i		−	0.801651i
$760$	816.535	+	1207.68i	1.07439	+	1.58905i
$761$	−515.043			−0.676797			−0.338399	−	0.941003i	$-0.609885\pi$
$761$	−515.043			−0.676797			−0.338399	+	0.941003i	$0.609885\pi$
$762$	339.083	−	68.0908i	0.444991	−	0.0893580i
$763$			8.19498i			0.0107405i
$764$	−10.3636	−	24.7642i	−0.0135649	−	0.0324138i
$765$	87.2137			0.114005
$766$	162.124	+	807.355i	0.211650	+	1.05399i
$767$			666.662i			0.869181i
$768$	−888.995	+	12.9675i	−1.15755	+	0.0168847i
$769$	595.349			0.774185			0.387093	−	0.922041i	$-0.373479\pi$
$769$	595.349			0.774185			0.387093	+	0.922041i	$0.373479\pi$
$770$	−93.9443	+	18.8648i	−0.122006	+	0.0244998i
$771$			830.616i			1.07732i
$772$	−361.885	+	151.446i	−0.468763	+	0.196174i
$773$	910.504			1.17788			0.588942	−	0.808176i	$-0.299545\pi$
$773$	910.504			1.17788			0.588942	+	0.808176i	$0.299545\pi$
$774$	39.4834	+	196.622i	0.0510121	+	0.254034i
$775$		−	77.4368i		−	0.0999185i
$776$	459.043	−	310.368i	0.591551	−	0.399959i
$777$	104.621			0.134647
$778$	−744.428	+	149.487i	−0.956848	+	0.192143i
$779$			1672.32i			2.14675i
$780$	−260.396	−	622.224i	−0.333841	−	0.797723i
$781$	69.7849			0.0893533
$782$	42.7822	+	213.050i	0.0547087	+	0.272443i
$783$			407.812i			0.520833i
$784$	538.094	−	546.000i	0.686345	−	0.696429i
$785$	−59.1147			−0.0753053
$786$	−973.714	+	195.530i	−1.23882	+	0.248766i
$787$		−	928.469i		−	1.17976i	−0.807492	−	0.589879i	$-0.799175\pi$
$787$		−	928.469i		−	1.17976i	0.807492	−	0.589879i	$-0.200825\pi$
$788$	−183.022	+	76.5933i	−0.232262	+	0.0971997i
$789$	1078.93			1.36746
$790$	237.674	+	1183.59i	0.300853	+	1.49821i
$791$		−	148.826i		−	0.188149i
$792$	−101.021	−	149.414i	−0.127552	−	0.188654i
$793$	−1.51272			−0.00190759
$794$	233.825	−	46.9541i	0.294491	−	0.0591362i
$795$		−	1741.90i		−	2.19107i
$796$	202.831	+	484.671i	0.254813	+	0.608883i
$797$	181.052			0.227167			0.113584	−	0.993528i	$-0.463767\pi$
$797$	181.052			0.227167			0.113584	+	0.993528i	$0.463767\pi$
$798$	41.6727	+	207.525i	0.0522214	+	0.260056i
$799$		−	381.932i		−	0.478013i
$800$	−243.877	+	372.291i	−0.304847	+	0.465364i
$801$	−466.177			−0.581994
$802$	−657.227	+	131.977i	−0.819485	+	0.164559i
$803$		−	75.1545i		−	0.0935922i
$804$	404.562	−	169.306i	0.503187	−	0.210580i
$805$	−154.807			−0.192307
$806$	17.0653	+	84.9830i	0.0211728	+	0.105438i
$807$			433.836i			0.537591i
$808$	1268.27	−	857.501i	1.56964	−	1.06126i
$809$	−343.411			−0.424489			−0.212244	−	0.977217i	$-0.568077\pi$
$809$	−343.411			−0.424489			−0.212244	+	0.977217i	$0.568077\pi$
$810$	1213.10	−	243.600i	1.49765	−	0.300741i
$811$			1324.63i			1.63333i	0.577109	+	0.816667i	$0.304181\pi$
$811$			1324.63i			1.63333i	−0.577109	+	0.816667i	$0.695819\pi$
$812$	−31.8513	−	76.1098i	−0.0392258	−	0.0937313i
$813$	−635.318			−0.781449
$814$	83.7319	+	416.974i	0.102865	+	0.512253i
$815$			750.073i			0.920335i
$816$	180.737	+	178.120i	0.221491	+	0.218284i
$817$	956.767			1.17107
$818$	1496.65	−	300.539i	1.82964	−	0.367407i
$819$		−	24.8602i		−	0.0303544i
$820$	−1317.54	+	551.379i	−1.60675	+	0.672413i
$821$	−1353.78			−1.64894			−0.824468	−	0.565909i	$-0.808525\pi$
$821$	−1353.78			−1.64894			−0.824468	+	0.565909i	$0.808525\pi$
$822$	20.5883	+	102.527i	0.0250466	+	0.124729i
$823$			741.603i			0.901097i	0.892752	+	0.450548i	$0.148771\pi$
$823$			741.603i			0.901097i	−0.892752	+	0.450548i	$0.851229\pi$
$824$	−687.125	−	1016.28i	−0.833890	−	1.23335i
$825$	−355.673			−0.431118
$826$	175.175	−	35.1766i	0.212076	−	0.0425867i
$827$		−	710.733i		−	0.859411i	−0.902969	−	0.429705i	$-0.858617\pi$
$827$		−	710.733i		−	0.859411i	0.902969	−	0.429705i	$-0.141383\pi$
$828$	−112.491	−	268.802i	−0.135859	−	0.324640i
$829$	−488.962			−0.589821			−0.294911	−	0.955525i	$-0.595290\pi$
$829$	−488.962			−0.589821			−0.294911	+	0.955525i	$0.595290\pi$
$830$	−105.177	−	523.766i	−0.126719	−	0.631044i
$831$			110.554i			0.133037i
$832$	185.599	−	462.315i	0.223075	−	0.555668i
$833$	−218.794			−0.262658
$834$	−1103.52	+	221.596i	−1.32316	+	0.265703i
$835$		−	2031.01i		−	2.43234i
$836$	−793.754	+	332.180i	−0.949466	+	0.397344i
$837$	−114.827			−0.137189
$838$	227.185	+	1131.35i	0.271103	+	1.35006i
$839$		−	251.785i		−	0.300102i	−0.988678	−	0.150051i	$-0.952056\pi$
$839$		−	251.785i		−	0.300102i	0.988678	−	0.150051i	$-0.0479437\pi$
$840$	−149.759	+	101.255i	−0.178284	+	0.120541i
$841$	−449.983			−0.535057
$842$	−603.914	+	121.271i	−0.717237	+	0.144027i
$843$		−	436.638i		−	0.517958i
$844$	235.355	+	562.388i	0.278856	+	0.666336i
$845$	−676.213			−0.800252
$846$	100.831	+	502.125i	0.119186	+	0.593529i
$847$			69.6588i			0.0822418i
$848$	903.051	−	916.320i	1.06492	−	1.08057i
$849$	276.174			0.325293
$850$	124.539	−	25.0084i	0.146516	−	0.0294217i
$851$			687.114i			0.807419i
$852$	121.452	−	50.8267i	0.142549	−	0.0596558i
$853$	−959.658			−1.12504			−0.562519	−	0.826784i	$-0.690168\pi$
$853$	−959.658			−1.12504			−0.562519	+	0.826784i	$0.690168\pi$
$854$	0.0798190	+	0.397489i	9.34649e−5	+	0.000465443i
$855$			557.936i			0.652556i
$856$	207.967	+	307.589i	0.242952	+	0.359332i
$857$	−800.055			−0.933553			−0.466776	−	0.884375i	$-0.654585\pi$
$857$	−800.055			−0.933553			−0.466776	+	0.884375i	$0.654585\pi$
$858$	390.333	−	78.3821i	0.454933	−	0.0913544i
$859$		−	1530.84i		−	1.78212i	−0.453882	−	0.891062i	$-0.649961\pi$
$859$		−	1530.84i		−	1.78212i	0.453882	−	0.891062i	$-0.350039\pi$
$860$	315.455	+	753.790i	0.366808	+	0.876500i
$861$	−207.376			−0.240855
$862$	−141.665	−	705.473i	−0.164344	−	0.818414i
$863$		−	732.251i		−	0.848494i	−0.905546	−	0.424247i	$-0.860539\pi$
$863$		−	732.251i		−	0.848494i	0.905546	−	0.424247i	$-0.139461\pi$
$864$	552.050	+	361.632i	0.638947	+	0.418556i
$865$	−1253.42			−1.44904
$866$	−1513.72	+	303.967i	−1.74794	+	0.351002i
$867$			931.273i			1.07413i
$868$	21.4301	−	8.96832i	0.0246890	−	0.0103322i
$869$	−712.546			−0.819961
$870$	−168.675	−	839.979i	−0.193879	−	0.965494i
$871$			245.736i			0.282131i
$872$	−52.0668	+	35.2034i	−0.0597096	+	0.0403708i
$873$	212.074			0.242925
$874$	−1362.95	+	273.693i	−1.55944	+	0.313149i
$875$		−	72.1695i		−	0.0824795i
$876$	−54.7376	−	130.797i	−0.0624858	−	0.149312i
$877$	1415.78			1.61434			0.807171	−	0.590317i	$-0.200997\pi$
$877$	1415.78			1.61434			0.807171	+	0.590317i	$0.200997\pi$
$878$	296.702	+	1477.54i	0.337930	+	1.68285i
$879$		−	293.533i		−	0.333940i
$880$	−523.416	−	515.837i	−0.594791	−	0.586178i
$881$	1635.13			1.85599			0.927997	−	0.372588i	$-0.121530\pi$
$881$	1635.13			1.85599			0.927997	+	0.372588i	$0.121530\pi$
$882$	287.648	−	57.7622i	0.326132	−	0.0654900i
$883$			993.877i			1.12557i	0.826604	+	0.562784i	$0.190270\pi$
$883$			993.877i			1.12557i	−0.826604	+	0.562784i	$0.809730\pi$
$884$	−131.164	+	54.8910i	−0.148375	+	0.0620939i
$885$	1855.35			2.09644
$886$	173.492	+	863.969i	0.195815	+	0.975134i
$887$		−	537.557i		−	0.606039i	−0.952984	−	0.303020i	$-0.902005\pi$
$887$		−	537.557i		−	0.606039i	0.952984	−	0.303020i	$-0.0979948\pi$
$888$	449.421	+	664.707i	0.506105	+	0.748544i
$889$	51.9377			0.0584226
$890$	−1862.28	+	373.961i	−2.09245	+	0.420181i
$891$			730.313i			0.819655i
$892$	−652.851	−	1560.01i	−0.731895	−	1.74889i
$893$	2443.35			2.73611
$894$	376.815	+	1876.49i	0.421494	+	2.09899i
$895$		−	2087.47i		−	2.33237i
$896$	−131.273	−	24.3746i	−0.146510	−	0.0272037i
$897$	643.213			0.717071
$898$	925.350	−	185.818i	1.03046	−	0.206924i
$899$			110.098i			0.122467i
$900$	−157.129	+	65.7571i	−0.174587	+	0.0730634i
$901$	−367.189			−0.407535
$902$	−165.971	−	826.515i	−0.184004	−	0.916314i
$903$			118.644i			0.131389i
$904$	945.563	−	639.314i	1.04598	−	0.707205i
$905$	−116.695			−0.128945
$906$	−342.047	+	68.6859i	−0.377535	+	0.0758122i
$907$			595.362i			0.656408i	0.944607	+	0.328204i	$0.106443\pi$
$907$			595.362i			0.656408i	−0.944607	+	0.328204i	$0.893557\pi$
$908$	208.719	+	498.740i	0.229866	+	0.549273i
$909$	585.928			0.644585
$910$	−19.9425	−	99.3112i	−0.0219148	−	0.109133i
$911$			1286.85i			1.41257i	0.707930	+	0.706283i	$0.249629\pi$
$911$			1286.85i			1.41257i	−0.707930	+	0.706283i	$0.750371\pi$
$912$	−1139.49	+	1156.24i	−1.24944	+	1.26780i
$913$	315.319			0.345366
$914$	−1100.28	+	220.945i	−1.20380	+	0.241734i
$915$			4.20995i			0.00460104i
$916$	−445.173	+	186.301i	−0.485997	+	0.203386i
$917$	−149.144			−0.162644
$918$	−37.0836	−	184.672i	−0.0403961	−	0.201167i
$919$			335.954i			0.365565i	0.983153	+	0.182783i	$0.0585105\pi$
$919$			335.954i			0.365565i	−0.983153	+	0.182783i	$0.941490\pi$
$920$	−665.008	−	983.565i	−0.722834	−	1.06909i
$921$	367.289			0.398793
$922$	−773.569	+	155.339i	−0.839012	+	0.168481i
$923$			73.7716i			0.0799259i
$924$	−41.1921	−	98.4298i	−0.0445802	−	0.106526i
$925$	401.654			0.434220
$926$	5.43516	+	27.0664i	0.00586950	+	0.0292294i
$927$		−	469.511i		−	0.506484i
$928$	346.739	−	529.314i	0.373641	−	0.570381i
$929$	−450.323			−0.484740			−0.242370	−	0.970184i	$-0.577925\pi$
$929$	−450.323			−0.484740			−0.242370	+	0.970184i	$0.577925\pi$
$930$	236.511	−	47.4935i	0.254313	−	0.0510682i
$931$		−	1399.70i		−	1.50344i
$932$	778.874	−	325.953i	0.835702	−	0.349735i
$933$	−12.0987			−0.0129675
$934$	−75.5892	−	376.424i	−0.0809306	−	0.403024i
$935$			209.744i			0.224325i
$936$	157.949	−	106.793i	0.168749	−	0.114095i
$937$	−1235.98			−1.31908			−0.659542	−	0.751667i	$-0.729250\pi$
$937$	−1235.98			−1.31908			−0.659542	+	0.751667i	$0.729250\pi$
$938$	64.5709	−	12.9664i	0.0688389	−	0.0138234i
$939$			1192.45i			1.26991i
$940$	805.595	+	1925.00i	0.857016	+	2.04787i
$941$	−1649.00			−1.75239			−0.876194	−	0.481959i	$-0.839925\pi$
$941$	−1649.00			−1.75239			−0.876194	+	0.481959i	$0.839925\pi$
$942$	−12.9601	−	64.5397i	−0.0137581	−	0.0685135i
$943$		−	1361.98i		−	1.44431i
$944$	975.999	+	961.866i	1.03390	+	1.01893i
$945$	134.187			0.141996
$946$	−472.866	+	94.9555i	−0.499858	+	0.100376i
$947$			593.961i			0.627203i	0.949555	+	0.313602i	$0.101536\pi$
$947$			593.961i			0.627203i	−0.949555	+	0.313602i	$0.898464\pi$
$948$	−1240.10	+	518.971i	−1.30812	+	0.547438i
$949$	79.4479			0.0837175
$950$	159.988	+	796.717i	0.168408	+	0.838650i
$951$		−	844.205i		−	0.887703i
$952$	21.3443	+	31.5689i	0.0224205	+	0.0331606i
$953$	−619.338			−0.649882			−0.324941	−	0.945734i	$-0.605344\pi$
$953$	−619.338			−0.649882			−0.324941	+	0.945734i	$0.605344\pi$
$954$	482.743	−	96.9389i	0.506020	−	0.101613i
$955$		−	41.8627i		−	0.0438353i
$956$	91.0781	+	217.634i	0.0952700	+	0.227651i
$957$	505.686			0.528408
$958$	−151.934	−	756.609i	−0.158594	−	0.789780i
$959$			15.7041i			0.0163755i
$960$	−1286.64	−	516.529i	−1.34025	−	0.538051i
$961$	−31.0000			−0.0322581
$962$	−440.795	+	88.5153i	−0.458207	+	0.0920117i
$963$			142.103i			0.147563i
$964$	1394.63	−	583.641i	1.44671	−	0.605437i
$965$	−611.751			−0.633939
$966$	−33.9394	−	169.014i	−0.0351339	−	0.174962i
$967$			620.704i			0.641886i	0.947099	+	0.320943i	$0.104000\pi$
$967$			620.704i			0.641886i	−0.947099	+	0.320943i	$0.896000\pi$
$968$	−442.577	+	299.235i	−0.457208	+	0.309127i
$969$	463.329			0.478152
$970$	847.187	−	170.122i	0.873389	−	0.175384i
$971$			324.363i			0.334051i	0.985953	+	0.167025i	$0.0534161\pi$
$971$			324.363i			0.334051i	−0.985953	+	0.167025i	$0.946584\pi$
$972$	245.290	+	586.129i	0.252356	+	0.603013i
$973$	−169.027			−0.173717
$974$	−125.791	−	626.425i	−0.129149	−	0.643147i
$975$		−	375.991i		−	0.385632i
$976$	−2.18256	+	2.21463i	−0.00223623	+	0.00226909i
$977$	211.435			0.216413			0.108206	−	0.994128i	$-0.465489\pi$
$977$	211.435			0.216413			0.108206	+	0.994128i	$0.465489\pi$
$978$	−818.908	+	164.444i	−0.837329	+	0.168143i
$979$		−	1121.13i		−	1.14518i
$980$	1102.76	−	461.495i	1.12526	−	0.470913i
$981$	−24.0543			−0.0245202
$982$	181.137	+	902.039i	0.184457	+	0.918574i
$983$			338.949i			0.344811i	0.985026	+	0.172405i	$0.0551539\pi$
$983$			338.949i			0.344811i	−0.985026	+	0.172405i	$0.944846\pi$
$984$	−890.832	−	1317.57i	−0.905317	−	1.33899i
$985$	−309.391			−0.314102
$986$	−177.066	+	35.5564i	−0.179580	+	0.0360612i
$987$			302.989i			0.306979i
$988$	−351.156	−	839.099i	−0.355421	−	0.849291i
$989$	−779.216			−0.787883
$990$	−55.3730	−	275.750i	−0.0559323	−	0.278536i
$991$			1495.75i			1.50933i	0.656109	+	0.754666i	$0.272201\pi$
$991$			1495.75i			1.50933i	−0.656109	+	0.754666i	$0.727799\pi$
$992$	149.038	+	97.6305i	0.150240	+	0.0984179i
$993$	1526.47			1.53723
$994$	19.3846	−	3.89258i	0.0195016	−	0.00391608i
$995$			819.315i			0.823432i
$996$	548.774	−	229.658i	0.550978	−	0.230580i
$997$	1340.24			1.34427			0.672136	−	0.740428i	$-0.265377\pi$
$997$	1340.24			1.34427			0.672136	+	0.740428i	$0.265377\pi$
$998$	3.89350	+	19.3891i	0.00390131	+	0.0194280i
$999$		−	595.590i		−	0.596186i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.3.b.a.63.4	yes	30
4.3	odd	2	inner	124.3.b.a.63.3	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.3.b.a.63.3	✓	30	4.3	odd	2	inner
124.3.b.a.63.4	yes	30	1.1	even	1	trivial

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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:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	124.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.96086 + 0.393756i) q^{2} -3.47301i q^{3} +(3.68991 - 1.54420i) q^{4} +6.23763 q^{5} +(1.36752 + 6.81006i) q^{6} +1.04310i q^{7} +(-6.62735 + 4.48088i) q^{8} -3.06177 q^{9} +O(q^{10})\)	\(q+(-1.96086 + 0.393756i) q^{2} -3.47301i q^{3} +(3.68991 - 1.54420i) q^{4} +6.23763 q^{5} +(1.36752 + 6.81006i) q^{6} +1.04310i q^{7} +(-6.62735 + 4.48088i) q^{8} -3.06177 q^{9} +(-12.2311 + 2.45611i) q^{10} -7.36340i q^{11} +(-5.36301 - 12.8151i) q^{12} +7.78405 q^{13} +(-0.410728 - 2.04537i) q^{14} -21.6633i q^{15} +(11.2309 - 11.3959i) q^{16} -4.56659 q^{17} +(6.00369 - 1.20559i) q^{18} -29.2140i q^{19} +(23.0163 - 9.63215i) q^{20} +3.62270 q^{21} +(2.89938 + 14.4386i) q^{22} +23.7927i q^{23} +(15.5621 + 23.0168i) q^{24} +13.9081 q^{25} +(-15.2634 + 3.06502i) q^{26} -20.6235i q^{27} +(1.61076 + 3.84896i) q^{28} -19.7741 q^{29} +(8.53008 + 42.4787i) q^{30} -5.56776i q^{31} +(-17.5350 + 26.7680i) q^{32} -25.5731 q^{33} +(8.95443 - 1.79812i) q^{34} +6.50649i q^{35} +(-11.2977 + 4.72798i) q^{36} +28.8792 q^{37} +(11.5032 + 57.2845i) q^{38} -27.0341i q^{39} +(-41.3390 + 27.9501i) q^{40} -57.2436 q^{41} +(-7.10359 + 1.42646i) q^{42} +32.7502i q^{43} +(-11.3705 - 27.1703i) q^{44} -19.0982 q^{45} +(-9.36853 - 46.6541i) q^{46} +83.6361i q^{47} +(-39.5781 - 39.0050i) q^{48} +47.9119 q^{49} +(-27.2717 + 5.47639i) q^{50} +15.8598i q^{51} +(28.7225 - 12.0201i) q^{52} +80.4078 q^{53} +(8.12064 + 40.4397i) q^{54} -45.9302i q^{55} +(-4.67401 - 6.91300i) q^{56} -101.461 q^{57} +(38.7742 - 7.78619i) q^{58} +85.6446i q^{59} +(-33.4525 - 79.9358i) q^{60} -0.194335 q^{61} +(2.19234 + 10.9176i) q^{62} -3.19374i q^{63} +(23.8435 - 59.3927i) q^{64} +48.5540 q^{65} +(50.1452 - 10.0696i) q^{66} +31.5692i q^{67} +(-16.8503 + 7.05173i) q^{68} +82.6322 q^{69} +(-2.56197 - 12.7583i) q^{70} +9.47727i q^{71} +(20.2914 - 13.7194i) q^{72} +10.2065 q^{73} +(-56.6279 + 11.3714i) q^{74} -48.3028i q^{75} +(-45.1123 - 107.797i) q^{76} +7.68077 q^{77} +(10.6448 + 53.0099i) q^{78} -96.7687i q^{79} +(70.0542 - 71.0835i) q^{80} -99.1815 q^{81} +(112.246 - 22.5400i) q^{82} +42.8225i q^{83} +(13.3674 - 5.59417i) q^{84} -28.4847 q^{85} +(-12.8956 - 64.2185i) q^{86} +68.6757i q^{87} +(32.9945 + 48.7998i) q^{88} +152.257 q^{89} +(37.4488 - 7.52004i) q^{90} +8.11956i q^{91} +(36.7407 + 87.7930i) q^{92} -19.3369 q^{93} +(-32.9323 - 163.998i) q^{94} -182.227i q^{95} +(92.9654 + 60.8990i) q^{96} -69.2650 q^{97} +(-93.9484 + 18.8656i) q^{98} +22.5450i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 2 q^{2} - 6 q^{4} - 4 q^{5} + 13 q^{8} - 82 q^{9}+O(q^{10}) \) 30 * q - 2 * q^2 - 6 * q^4 - 4 * q^5 + 13 * q^8 - 82 * q^9	\( 30 q - 2 q^{2} - 6 q^{4} - 4 q^{5} + 13 q^{8} - 82 q^{9} + q^{10} - 14 q^{12} + 12 q^{13} + 29 q^{14} + 50 q^{16} - 4 q^{17} - 34 q^{18} - 63 q^{20} - 16 q^{21} - 24 q^{22} - 20 q^{24} + 90 q^{25} + 38 q^{26} + 3 q^{28} - 4 q^{29} - 6 q^{30} + 118 q^{32} + 80 q^{33} + 4 q^{34} - 2 q^{36} + 76 q^{37} + 37 q^{38} - 180 q^{40} - 4 q^{41} - 38 q^{42} + 184 q^{44} - 20 q^{45} - 54 q^{46} - 172 q^{48} - 258 q^{49} - 31 q^{50} - 88 q^{52} - 132 q^{53} - 84 q^{54} - 28 q^{56} + 176 q^{57} + 164 q^{58} + 108 q^{60} - 100 q^{61} + 381 q^{64} - 104 q^{65} + 60 q^{66} + 214 q^{68} + 112 q^{69} + 45 q^{70} - 167 q^{72} - 132 q^{73} + 398 q^{74} - 317 q^{76} + 176 q^{77} - 188 q^{78} - 203 q^{80} + 158 q^{81} - 81 q^{82} + 176 q^{84} + 248 q^{85} - 78 q^{86} + 98 q^{88} - 20 q^{89} - 567 q^{90} - 260 q^{92} - 244 q^{94} - 90 q^{96} + 300 q^{97} - 371 q^{98}+O(q^{100}) \) 30 * q - 2 * q^2 - 6 * q^4 - 4 * q^5 + 13 * q^8 - 82 * q^9 + q^10 - 14 * q^12 + 12 * q^13 + 29 * q^14 + 50 * q^16 - 4 * q^17 - 34 * q^18 - 63 * q^20 - 16 * q^21 - 24 * q^22 - 20 * q^24 + 90 * q^25 + 38 * q^26 + 3 * q^28 - 4 * q^29 - 6 * q^30 + 118 * q^32 + 80 * q^33 + 4 * q^34 - 2 * q^36 + 76 * q^37 + 37 * q^38 - 180 * q^40 - 4 * q^41 - 38 * q^42 + 184 * q^44 - 20 * q^45 - 54 * q^46 - 172 * q^48 - 258 * q^49 - 31 * q^50 - 88 * q^52 - 132 * q^53 - 84 * q^54 - 28 * q^56 + 176 * q^57 + 164 * q^58 + 108 * q^60 - 100 * q^61 + 381 * q^64 - 104 * q^65 + 60 * q^66 + 214 * q^68 + 112 * q^69 + 45 * q^70 - 167 * q^72 - 132 * q^73 + 398 * q^74 - 317 * q^76 + 176 * q^77 - 188 * q^78 - 203 * q^80 + 158 * q^81 - 81 * q^82 + 176 * q^84 + 248 * q^85 - 78 * q^86 + 98 * q^88 - 20 * q^89 - 567 * q^90 - 260 * q^92 - 244 * q^94 - 90 * q^96 + 300 * q^97 - 371 * q^98

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