LMFDB - Embedded newform 124.3.b.a.63.9

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			63.9
Character	$\chi$	$=$	124.63
Dual form			124.3.b.a.63.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23553 - 1.57273i) q^{2} +0.706826i q^{3} +(-0.946952 + 3.88629i) q^{4} -0.787341 q^{5} +(1.11164 - 0.873301i) q^{6} -0.940771i q^{7} +(7.28207 - 3.31232i) q^{8} +8.50040 q^{9} +O(q^{10})$	\(q+(-1.23553 - 1.57273i) q^{2} +0.706826i q^{3} +(-0.946952 + 3.88629i) q^{4} -0.787341 q^{5} +(1.11164 - 0.873301i) q^{6} -0.940771i q^{7} +(7.28207 - 3.31232i) q^{8} +8.50040 q^{9} +(0.972780 + 1.23827i) q^{10} +14.5438i q^{11} +(-2.74693 - 0.669330i) q^{12} +23.3174 q^{13} +(-1.47958 + 1.16235i) q^{14} -0.556513i q^{15} +(-14.2066 - 7.36027i) q^{16} +11.2680 q^{17} +(-10.5025 - 13.3688i) q^{18} -33.1335i q^{19} +(0.745574 - 3.05984i) q^{20} +0.664961 q^{21} +(22.8734 - 17.9692i) q^{22} +35.3610i q^{23} +(2.34123 + 5.14715i) q^{24} -24.3801 q^{25} +(-28.8093 - 36.6720i) q^{26} +12.3697i q^{27} +(3.65611 + 0.890865i) q^{28} +35.6479 q^{29} +(-0.875243 + 0.687586i) q^{30} +5.56776i q^{31} +(5.97687 + 31.4369i) q^{32} -10.2799 q^{33} +(-13.9219 - 17.7215i) q^{34} +0.740707i q^{35} +(-8.04947 + 33.0350i) q^{36} -11.9106 q^{37} +(-52.1100 + 40.9373i) q^{38} +16.4813i q^{39} +(-5.73347 + 2.60792i) q^{40} -45.5044 q^{41} +(-0.821576 - 1.04580i) q^{42} +16.0744i q^{43} +(-56.5215 - 13.7723i) q^{44} -6.69271 q^{45} +(55.6132 - 43.6894i) q^{46} +12.8690i q^{47} +(5.20242 - 10.0416i) q^{48} +48.1150 q^{49} +(30.1222 + 38.3433i) q^{50} +7.96449i q^{51} +(-22.0805 + 90.6183i) q^{52} -82.8998 q^{53} +(19.4542 - 15.2831i) q^{54} -11.4509i q^{55} +(-3.11613 - 6.85076i) q^{56} +23.4196 q^{57} +(-44.0439 - 56.0644i) q^{58} -77.3460i q^{59} +(2.16277 + 0.526991i) q^{60} -7.91627 q^{61} +(8.75658 - 6.87912i) q^{62} -7.99693i q^{63} +(42.0571 - 48.2411i) q^{64} -18.3587 q^{65} +(12.7011 + 16.1675i) q^{66} -59.9086i q^{67} +(-10.6702 + 43.7906i) q^{68} -24.9940 q^{69} +(1.16493 - 0.915163i) q^{70} +63.2942i q^{71} +(61.9005 - 28.1560i) q^{72} +46.6763 q^{73} +(14.7158 + 18.7321i) q^{74} -17.2325i q^{75} +(128.767 + 31.3758i) q^{76} +13.6824 q^{77} +(25.9207 - 20.3631i) q^{78} -119.890i q^{79} +(11.1854 + 5.79504i) q^{80} +67.7603 q^{81} +(56.2219 + 71.5661i) q^{82} -91.7383i q^{83} +(-0.629686 + 2.58423i) q^{84} -8.87173 q^{85} +(25.2807 - 19.8604i) q^{86} +25.1968i q^{87} +(48.1737 + 105.909i) q^{88} -94.4442 q^{89} +(8.26902 + 10.5258i) q^{90} -21.9363i q^{91} +(-137.423 - 33.4851i) q^{92} -3.93544 q^{93} +(20.2394 - 15.9000i) q^{94} +26.0874i q^{95} +(-22.2204 + 4.22461i) q^{96} -60.3061 q^{97} +(-59.4473 - 75.6718i) q^{98} +123.628i 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 $

$2$	−1.23553	−	1.57273i	−0.617763	−	0.786364i
$2$	−1.23553	−	1.57273i	−0.617763	−	0.786364i
$3$			0.706826i			0.235609i	0.993037	+	0.117804i	$0.0375855\pi$
$3$			0.706826i			0.235609i	−0.993037	+	0.117804i	$0.962414\pi$
$4$	−0.946952	+	3.88629i	−0.236738	+	0.971574i
$5$	−0.787341			−0.157468			−0.0787341	−	0.996896i	$-0.525088\pi$
$5$	−0.787341			−0.157468			−0.0787341	+	0.996896i	$0.525088\pi$
$6$	1.11164	−	0.873301i	0.185274	−	0.145550i
$7$		−	0.940771i		−	0.134396i	−0.997740	−	0.0671979i	$-0.978594\pi$
$7$		−	0.940771i		−	0.134396i	0.997740	−	0.0671979i	$-0.0214059\pi$
$8$	7.28207	−	3.31232i	0.910259	−	0.414040i
$9$	8.50040			0.944489
$10$	0.972780	+	1.23827i	0.0972780	+	0.123827i
$11$			14.5438i			1.32216i	0.750314	+	0.661082i	$0.229902\pi$
$11$			14.5438i			1.32216i	−0.750314	+	0.661082i	$0.770098\pi$
$12$	−2.74693	−	0.669330i	−0.228911	−	0.0557775i
$13$	23.3174			1.79365			0.896823	−	0.442389i	$-0.145869\pi$
$13$	23.3174			1.79365			0.896823	+	0.442389i	$0.145869\pi$
$14$	−1.47958	+	1.16235i	−0.105684	+	0.0830248i
$15$		−	0.556513i		−	0.0371008i
$16$	−14.2066	−	7.36027i	−0.887910	−	0.460017i
$17$	11.2680			0.662821			0.331411	−	0.943487i	$-0.392475\pi$
$17$	11.2680			0.662821			0.331411	+	0.943487i	$0.392475\pi$
$18$	−10.5025	−	13.3688i	−0.583470	−	0.742712i
$19$		−	33.1335i		−	1.74387i	−0.489623	−	0.871934i	$-0.662866\pi$
$19$		−	33.1335i		−	1.74387i	0.489623	−	0.871934i	$-0.337134\pi$
$20$	0.745574	−	3.05984i	0.0372787	−	0.152992i
$21$	0.664961			0.0316648
$22$	22.8734	−	17.9692i	1.03970	−	0.816783i
$23$			35.3610i			1.53743i	0.639590	+	0.768717i	$0.279104\pi$
$23$			35.3610i			1.53743i	−0.639590	+	0.768717i	$0.720896\pi$
$24$	2.34123	+	5.14715i	0.0975513	+	0.214465i
$25$	−24.3801			−0.975204
$26$	−28.8093	−	36.6720i	−1.10805	−	1.41046i
$27$			12.3697i			0.458138i
$28$	3.65611	+	0.890865i	0.130575	+	0.0318166i
$29$	35.6479			1.22924			0.614618	−	0.788825i	$-0.289310\pi$
$29$	35.6479			1.22924			0.614618	+	0.788825i	$0.289310\pi$
$30$	−0.875243	+	0.687586i	−0.0291748	+	0.0229195i
$31$			5.56776i			0.179605i
$31$			5.56776i			0.179605i
$32$	5.97687	+	31.4369i	0.186777	+	0.982402i
$33$	−10.2799			−0.311513
$34$	−13.9219	−	17.7215i	−0.409467	−	0.521219i
$35$			0.740707i			0.0211631i
$36$	−8.04947	+	33.0350i	−0.223596	+	0.917640i
$37$	−11.9106			−0.321907			−0.160953	−	0.986962i	$-0.551457\pi$
$37$	−11.9106			−0.321907			−0.160953	+	0.986962i	$0.551457\pi$
$38$	−52.1100	+	40.9373i	−1.37132	+	1.07730i
$39$			16.4813i			0.422599i
$40$	−5.73347	+	2.60792i	−0.143337	+	0.0651981i
$41$	−45.5044			−1.10986			−0.554932	−	0.831896i	$-0.687256\pi$
$41$	−45.5044			−1.10986			−0.554932	+	0.831896i	$0.687256\pi$
$42$	−0.821576	−	1.04580i	−0.0195613	−	0.0249001i
$43$			16.0744i			0.373824i	0.982377	+	0.186912i	$0.0598479\pi$
$43$			16.0744i			0.373824i	−0.982377	+	0.186912i	$0.940152\pi$
$44$	−56.5215	−	13.7723i	−1.28458	−	0.313006i
$45$	−6.69271			−0.148727
$46$	55.6132	−	43.6894i	1.20898	−	0.949769i
$47$			12.8690i			0.273808i	0.990584	+	0.136904i	$0.0437152\pi$
$47$			12.8690i			0.273808i	−0.990584	+	0.136904i	$0.956285\pi$
$48$	5.20242	−	10.0416i	0.108384	−	0.209199i
$49$	48.1150			0.981938
$50$	30.1222	+	38.3433i	0.602445	+	0.766866i
$51$			7.96449i			0.156166i
$52$	−22.0805	+	90.6183i	−0.424624	+	1.74266i
$53$	−82.8998			−1.56415			−0.782073	−	0.623186i	$-0.785838\pi$
$53$	−82.8998			−1.56415			−0.782073	+	0.623186i	$0.785838\pi$
$54$	19.4542	−	15.2831i	0.360263	−	0.283021i
$55$		−	11.4509i		−	0.208199i
$56$	−3.11613	−	6.85076i	−0.0556452	−	0.122335i
$57$	23.4196			0.410870
$58$	−44.0439	−	56.0644i	−0.759377	−	0.966628i
$59$		−	77.3460i		−	1.31095i	−0.755217	−	0.655474i	$-0.772469\pi$
$59$		−	77.3460i		−	1.31095i	0.755217	−	0.655474i	$-0.227531\pi$
$60$	2.16277	+	0.526991i	0.0360462	+	0.00878318i
$61$	−7.91627			−0.129775			−0.0648875	−	0.997893i	$-0.520669\pi$
$61$	−7.91627			−0.129775			−0.0648875	+	0.997893i	$0.520669\pi$
$62$	8.75658	−	6.87912i	0.141235	−	0.110953i
$63$		−	7.99693i		−	0.126935i
$64$	42.0571	−	48.2411i	0.657142	−	0.753767i
$65$	−18.3587			−0.282442
$66$	12.7011	+	16.1675i	0.192441	+	0.244963i
$67$		−	59.9086i		−	0.894158i	−0.894495	−	0.447079i	$-0.852464\pi$
$67$		−	59.9086i		−	0.894158i	0.894495	−	0.447079i	$-0.147536\pi$
$68$	−10.6702	+	43.7906i	−0.156915	+	0.643980i
$69$	−24.9940			−0.362232
$70$	1.16493	−	0.915163i	0.0166419	−	0.0130738i
$71$			63.2942i			0.891468i	0.895166	+	0.445734i	$0.147057\pi$
$71$			63.2942i			0.891468i	−0.895166	+	0.445734i	$0.852943\pi$
$72$	61.9005	−	28.1560i	0.859729	−	0.391056i
$73$	46.6763			0.639401			0.319701	−	0.947519i	$-0.396418\pi$
$73$	46.6763			0.639401			0.319701	+	0.947519i	$0.396418\pi$
$74$	14.7158	+	18.7321i	0.198862	+	0.253136i
$75$		−	17.2325i		−	0.229766i
$76$	128.767	+	31.3758i	1.69430	+	0.412840i
$77$	13.6824			0.177693
$78$	25.9207	−	20.3631i	0.332316	−	0.261066i
$79$		−	119.890i		−	1.51760i	−0.651327	−	0.758798i	$-0.725787\pi$
$79$		−	119.890i		−	1.51760i	0.651327	−	0.758798i	$-0.274213\pi$
$80$	11.1854	+	5.79504i	0.139818	+	0.0724380i
$81$	67.7603			0.836547
$82$	56.2219	+	71.5661i	0.685633	+	0.872758i
$83$		−	91.7383i		−	1.10528i	−0.833420	−	0.552640i	$-0.813620\pi$
$83$		−	91.7383i		−	1.10528i	0.833420	−	0.552640i	$-0.186380\pi$
$84$	−0.629686	+	2.58423i	−0.00749626	+	0.0307647i
$85$	−8.87173			−0.104373
$86$	25.2807	−	19.8604i	0.293962	−	0.230934i
$87$			25.1968i			0.289619i
$88$	48.1737	+	105.909i	0.547428	+	1.20351i
$89$	−94.4442			−1.06117			−0.530585	−	0.847631i	$-0.678028\pi$
$89$	−94.4442			−1.06117			−0.530585	+	0.847631i	$0.678028\pi$
$90$	8.26902	+	10.5258i	0.0918780	+	0.116954i
$91$		−	21.9363i		−	0.241059i
$92$	−137.423	−	33.4851i	−1.49373	−	0.363969i
$93$	−3.93544			−0.0423165
$94$	20.2394	−	15.9000i	0.215313	−	0.169149i
$95$			26.0874i			0.274604i
$96$	−22.2204	+	4.22461i	−0.231462	+	0.0440063i
$97$	−60.3061			−0.621712			−0.310856	−	0.950457i	$-0.600616\pi$
$97$	−60.3061			−0.621712			−0.310856	+	0.950457i	$0.600616\pi$
$98$	−59.4473	−	75.6718i	−0.606605	−	0.772161i
$99$			123.628i			1.24877i
$100$	23.0868	−	94.7482i	0.230868	−	0.947482i
$101$	122.922			1.21705			0.608524	−	0.793535i	$-0.291762\pi$
$101$	122.922			1.21705			0.608524	+	0.793535i	$0.291762\pi$
$102$	12.5260	−	9.84033i	0.122804	−	0.0964738i
$103$			27.0558i			0.262677i	0.991338	+	0.131339i	$0.0419275\pi$
$103$			27.0558i			0.262677i	−0.991338	+	0.131339i	$0.958072\pi$
$104$	169.799	−	77.2347i	1.63268	−	0.742641i
$105$	−0.523551			−0.00498620
$106$	102.425	+	130.379i	0.966272	+	1.22999i
$107$			21.0989i			0.197186i	0.995128	+	0.0985930i	$0.0314342\pi$
$107$			21.0989i			0.197186i	−0.995128	+	0.0985930i	$0.968566\pi$
$108$	−48.0724	−	11.7135i	−0.445115	−	0.108459i
$109$	−167.438			−1.53613			−0.768063	−	0.640374i	$-0.778779\pi$
$109$	−167.438			−1.53613			−0.768063	+	0.640374i	$0.778779\pi$
$110$	−18.0092	+	14.1479i	−0.163720	+	0.128617i
$111$		−	8.41869i		−	0.0758440i
$112$	−6.92432	+	13.3651i	−0.0618243	+	0.119331i
$113$	−74.7950			−0.661903			−0.330951	−	0.943648i	$-0.607370\pi$
$113$	−74.7950			−0.661903			−0.330951	+	0.943648i	$0.607370\pi$
$114$	−28.9355	−	36.8327i	−0.253820	−	0.323094i
$115$		−	27.8411i		−	0.242097i
$116$	−33.7568	+	138.538i	−0.291007	+	1.19429i
$117$	198.207			1.69408
$118$	−121.644	+	95.5630i	−1.03088	+	0.809856i
$119$		−	10.6006i		−	0.0890804i
$120$	−1.84335	−	4.05256i	−0.0153612	−	0.0337714i
$121$	−90.5220			−0.748116
$122$	9.78076	+	12.4501i	0.0801702	+	0.102050i
$123$		−	32.1637i		−	0.261493i
$124$	−21.6380	−	5.27240i	−0.174500	−	0.0425194i
$125$	38.8790			0.311032
$126$	−12.5770	+	9.88041i	−0.0998174	+	0.0784159i
$127$			43.1831i			0.340024i	0.985442	+	0.170012i	$0.0543807\pi$
$127$			43.1831i			0.340024i	−0.985442	+	0.170012i	$0.945619\pi$
$128$	−127.833	−	6.54131i	−0.998693	−	0.0511040i
$129$	−11.3618			−0.0880761
$130$	22.6827	+	28.8733i	0.174482	+	0.222103i
$131$		−	65.8343i		−	0.502552i	−0.967915	−	0.251276i	$-0.919150\pi$
$131$		−	65.8343i		−	0.502552i	0.967915	−	0.251276i	$-0.0808502\pi$
$132$	9.73459	−	39.9508i	0.0737469	−	0.302658i
$133$	−31.1710			−0.234369
$134$	−94.2199	+	74.0186i	−0.703134	+	0.552377i
$135$		−	9.73919i		−	0.0721422i
$136$	82.0541	−	37.3231i	0.603339	−	0.274434i
$137$	−41.8646			−0.305581			−0.152791	−	0.988259i	$-0.548826\pi$
$137$	−41.8646			−0.305581			−0.152791	+	0.988259i	$0.548826\pi$
$138$	30.8808	+	39.3088i	0.223774	+	0.284847i
$139$		−	49.7791i		−	0.358123i	−0.983838	−	0.179062i	$-0.942694\pi$
$139$		−	49.7791i		−	0.358123i	0.983838	−	0.179062i	$-0.0573061\pi$
$140$	−2.87861	−	0.701414i	−0.0205615	−	0.00501010i
$141$	−9.09613			−0.0645115
$142$	99.5446	−	78.2016i	0.701019	−	0.550716i
$143$			339.124i			2.37149i
$144$	−120.761	−	62.5652i	−0.838621	−	0.434480i
$145$	−28.0670			−0.193566
$146$	−57.6698	−	73.4092i	−0.394999	−	0.502803i
$147$			34.0089i			0.231353i
$148$	11.2787	−	46.2879i	0.0762076	−	0.312756i
$149$	20.6841			0.138819			0.0694097	−	0.997588i	$-0.477888\pi$
$149$	20.6841			0.138819			0.0694097	+	0.997588i	$0.477888\pi$
$150$	−27.1020	+	21.2912i	−0.180680	+	0.141941i
$151$		−	2.51227i		−	0.0166376i	−0.999965	−	0.00831879i	$-0.997352\pi$
$151$		−	2.51227i		−	0.0166376i	0.999965	−	0.00831879i	$-0.00264798\pi$
$152$	−109.749	−	241.281i	−0.722031	−	1.58737i
$153$	95.7822			0.626027
$154$	−16.9049	−	21.5187i	−0.109772	−	0.139732i
$155$		−	4.38373i		−	0.0282821i
$156$	−64.0513	−	15.6070i	−0.410586	−	0.100045i
$157$	86.0336			0.547985			0.273992	−	0.961732i	$-0.411656\pi$
$157$	86.0336			0.547985			0.273992	+	0.961732i	$0.411656\pi$
$158$	−188.554	+	148.127i	−1.19338	+	0.937514i
$159$		−	58.5957i		−	0.368526i
$160$	−4.70584	−	24.7515i	−0.0294115	−	0.154697i
$161$	33.2666			0.206625
$162$	−83.7196	−	106.569i	−0.516788	−	0.657831i
$163$		−	11.8758i		−	0.0728578i	−0.999336	−	0.0364289i	$-0.988402\pi$
$163$		−	11.8758i		−	0.0728578i	0.999336	−	0.0364289i	$-0.0115982\pi$
$164$	43.0905	−	176.844i	0.262747	−	1.07831i
$165$	8.09381			0.0490534
$166$	−144.279	+	113.345i	−0.869153	+	0.682801i
$167$			173.179i			1.03700i	0.855078	+	0.518499i	$0.173509\pi$
$167$			173.179i			1.03700i	−0.855078	+	0.518499i	$0.826491\pi$
$168$	4.84229	−	2.20256i	0.0288232	−	0.0131105i
$169$	374.702			2.21717
$170$	10.9612	+	13.9528i	0.0644779	+	0.0820754i
$171$		−	281.648i		−	1.64706i
$172$	−62.4699	−	15.2217i	−0.363197	−	0.0884983i
$173$	−232.223			−1.34233			−0.671165	−	0.741308i	$-0.734206\pi$
$173$	−232.223			−1.34233			−0.671165	+	0.741308i	$0.734206\pi$
$174$	39.6278	−	31.1313i	0.227746	−	0.178916i
$175$			22.9361i			0.131063i
$176$	107.046	−	206.617i	0.608217	−	1.17396i
$177$	54.6701			0.308871
$178$	116.688	+	148.535i	0.655552	+	0.834467i
$179$		−	238.109i		−	1.33022i	−0.746746	−	0.665110i	$-0.768385\pi$
$179$		−	238.109i		−	1.33022i	0.746746	−	0.665110i	$-0.231615\pi$
$180$	6.33767	−	26.0098i	0.0352093	−	0.144499i
$181$	−129.201			−0.713820			−0.356910	−	0.934139i	$-0.616170\pi$
$181$	−129.201			−0.713820			−0.356910	+	0.934139i	$0.616170\pi$
$182$	−34.4999	+	27.1029i	−0.189560	+	0.148917i
$183$		−	5.59542i		−	0.0305761i
$184$	117.127	+	257.501i	0.636559	+	1.39946i
$185$	9.37767			0.0506901
$186$	4.86234	+	6.18938i	0.0261416	+	0.0332762i
$187$			163.879i			0.876358i
$188$	−50.0126	−	12.1863i	−0.266025	−	0.0648208i
$189$	11.6371			0.0615718
$190$	41.0283	−	32.2316i	0.215939	−	0.169640i
$191$			265.835i			1.39181i	0.718135	+	0.695904i	$0.244996\pi$
$191$			265.835i			1.39181i	−0.718135	+	0.695904i	$0.755004\pi$
$192$	34.0980	+	29.7270i	0.177594	+	0.154828i
$193$	−195.504			−1.01297			−0.506487	−	0.862248i	$-0.669056\pi$
$193$	−195.504			−1.01297			−0.506487	+	0.862248i	$0.669056\pi$
$194$	74.5097	+	94.8451i	0.384071	+	0.488892i
$195$		−	12.9764i		−	0.0665458i
$196$	−45.5625	+	186.989i	−0.232462	+	0.954025i
$197$	110.541			0.561124			0.280562	−	0.959836i	$-0.409479\pi$
$197$	110.541			0.561124			0.280562	+	0.959836i	$0.409479\pi$
$198$	194.433	−	152.746i	0.981987	−	0.771443i
$199$			248.117i			1.24682i	0.781896	+	0.623409i	$0.214253\pi$
$199$			248.117i			1.24682i	−0.781896	+	0.623409i	$0.785747\pi$
$200$	−177.538	+	80.7546i	−0.887688	+	0.403773i
$201$	42.3449			0.210671
$202$	−151.873	−	193.323i	−0.751847	−	0.957043i
$203$		−	33.5365i		−	0.165204i
$204$	−30.9523	−	7.54198i	−0.151727	−	0.0369705i
$205$	35.8275			0.174768
$206$	42.5514	−	33.4281i	0.206560	−	0.162272i
$207$			300.582i			1.45209i
$208$	−331.260	−	171.622i	−1.59260	−	0.825107i
$209$	481.887			2.30568
$210$	0.646861	+	0.823403i	0.00308029	+	0.00392097i
$211$		−	324.736i		−	1.53903i	−0.638628	−	0.769515i	$-0.720498\pi$
$211$		−	324.736i		−	1.53903i	0.638628	−	0.769515i	$-0.279502\pi$
$212$	78.5021	−	322.173i	0.370293	−	1.51968i
$213$	−44.7380			−0.210037
$214$	33.1828	−	26.0682i	0.155060	−	0.121814i
$215$		−	12.6560i		−	0.0588653i
$216$	40.9725	+	90.0772i	0.189687	+	0.417024i
$217$	5.23799			0.0241382
$218$	206.874	+	263.334i	0.948962	+	1.20795i
$219$			32.9920i			0.150648i
$220$	44.5017	+	10.8435i	0.202280	+	0.0492885i
$221$	262.740			1.18887
$222$	−13.2403	+	10.4015i	−0.0596410	+	0.0468536i
$223$			206.822i			0.927451i	0.885979	+	0.463725i	$0.153488\pi$
$223$			206.822i			0.927451i	−0.885979	+	0.463725i	$0.846512\pi$
$224$	29.5749	−	5.62287i	0.132031	−	0.0251021i
$225$	−207.240			−0.921069
$226$	92.4112	+	117.632i	0.408899	+	0.520497i
$227$			238.914i			1.05248i	0.850335	+	0.526242i	$0.176399\pi$
$227$			238.914i			1.05248i	−0.850335	+	0.526242i	$0.823601\pi$
$228$	−22.1772	+	91.0155i	−0.0972686	+	0.399191i
$229$	5.37304			0.0234631			0.0117315	−	0.999931i	$-0.496266\pi$
$229$	5.37304			0.0234631			0.0117315	+	0.999931i	$0.496266\pi$
$230$	−43.7865	+	34.3984i	−0.190376	+	0.149558i
$231$			9.67105i			0.0418660i
$232$	259.590	−	118.077i	1.11892	−	0.508953i
$233$	110.815			0.475602			0.237801	−	0.971314i	$-0.423573\pi$
$233$	110.815			0.475602			0.237801	+	0.971314i	$0.423573\pi$
$234$	−244.890	−	311.726i	−1.04654	−	1.33216i
$235$		−	10.1323i		−	0.0431161i
$236$	300.589	+	73.2429i	1.27368	+	0.310351i
$237$	84.7413			0.357558
$238$	−16.6718	+	13.0973i	−0.0700497	+	0.0550306i
$239$		−	370.759i		−	1.55129i	−0.631167	−	0.775647i	$-0.717424\pi$
$239$		−	370.759i		−	1.55129i	0.631167	−	0.775647i	$-0.282576\pi$
$240$	−4.09608	+	7.90613i	−0.0170670	+	0.0329422i
$241$	−279.478			−1.15966			−0.579830	−	0.814737i	$-0.696881\pi$
$241$	−279.478			−1.15966			−0.579830	+	0.814737i	$0.696881\pi$
$242$	111.842	+	142.367i	0.462158	+	0.588292i
$243$			159.222i			0.655236i
$244$	7.49633	−	30.7650i	0.0307227	−	0.126086i
$245$	−37.8829			−0.154624
$246$	−50.5848	+	39.7391i	−0.205629	+	0.161541i
$247$		−	772.588i		−	3.12788i
$248$	18.4422	+	40.5449i	0.0743637	+	0.163487i
$249$	64.8430			0.260413
$250$	−48.0360	−	61.1461i	−0.192144	−	0.244584i
$251$		−	138.890i		−	0.553346i	−0.960964	−	0.276673i	$-0.910768\pi$
$251$		−	138.890i		−	0.553346i	0.960964	−	0.276673i	$-0.0892319\pi$
$252$	31.0784	+	7.57270i	0.123327	+	0.0300504i
$253$	−514.283			−2.03274
$254$	67.9153	−	53.3538i	0.267383	−	0.210054i
$255$		−	6.27076i		−	0.0245912i
$256$	147.653	+	209.128i	0.576769	+	0.816907i
$257$	−139.333			−0.542150			−0.271075	−	0.962558i	$-0.587379\pi$
$257$	−139.333			−0.542150			−0.271075	+	0.962558i	$0.587379\pi$
$258$	14.0378	+	17.8690i	0.0544101	+	0.0692599i
$259$			11.2051i			0.0432629i
$260$	17.3848	−	71.3475i	0.0668648	−	0.274413i
$261$	303.021			1.16100
$262$	−103.540	+	81.3400i	−0.395189	+	0.310458i
$263$		−	245.402i		−	0.933087i	−0.884498	−	0.466544i	$-0.845499\pi$
$263$		−	245.402i		−	0.933087i	0.884498	−	0.466544i	$-0.154501\pi$
$264$	−74.8591	+	34.0504i	−0.283557	+	0.128979i
$265$	65.2704			0.246303
$266$	38.5126	+	49.0236i	0.144784	+	0.184299i
$267$		−	66.7556i		−	0.250021i
$268$	232.822	+	56.7305i	0.868740	+	0.211681i
$269$	89.2799			0.331895			0.165948	−	0.986135i	$-0.446932\pi$
$269$	89.2799			0.331895			0.165948	+	0.986135i	$0.446932\pi$
$270$	−15.3171	+	12.0330i	−0.0567300	+	0.0445668i
$271$			116.449i			0.429701i	0.976647	+	0.214850i	$0.0689264\pi$
$271$			116.449i			0.429701i	−0.976647	+	0.214850i	$0.931074\pi$
$272$	−160.079	−	82.9352i	−0.588526	−	0.304909i
$273$	15.5052			0.0567955
$274$	51.7248	+	65.8417i	0.188777	+	0.240298i
$275$		−	354.579i		−	1.28938i
$276$	23.6681	−	97.1342i	0.0857541	−	0.351935i
$277$	−197.610			−0.713393			−0.356696	−	0.934220i	$-0.616097\pi$
$277$	−197.610			−0.713393			−0.356696	+	0.934220i	$0.616097\pi$
$278$	−78.2891	+	61.5034i	−0.281615	+	0.221235i
$279$			47.3282i			0.169635i
$280$	2.45346	+	5.39388i	0.00876235	+	0.0192639i
$281$	−206.139			−0.733591			−0.366796	−	0.930302i	$-0.619545\pi$
$281$	−206.139			−0.733591			−0.366796	+	0.930302i	$0.619545\pi$
$282$	11.2385	+	14.3057i	0.0398528	+	0.0507296i
$283$			191.708i			0.677412i	0.940892	+	0.338706i	$0.109989\pi$
$283$			191.708i			0.677412i	−0.940892	+	0.338706i	$0.890011\pi$
$284$	−245.980	−	59.9366i	−0.866127	−	0.211044i
$285$	−18.4392			−0.0646990
$286$	533.350	−	418.996i	1.86486	−	1.46502i
$287$			42.8092i			0.149161i
$288$	50.8058	+	267.226i	0.176409	+	0.927868i
$289$	−162.033			−0.560668
$290$	34.6775	+	44.1418i	0.119578	+	0.152213i
$291$		−	42.6259i		−	0.146481i
$292$	−44.2002	+	181.398i	−0.151371	+	0.621226i
$293$	−27.2109			−0.0928698			−0.0464349	−	0.998921i	$-0.514786\pi$
$293$	−27.2109			−0.0928698			−0.0464349	+	0.998921i	$0.514786\pi$
$294$	53.4867	−	42.0188i	0.181928	−	0.142921i
$295$			60.8976i			0.206433i
$296$	−86.7335	+	39.4516i	−0.293019	+	0.133282i
$297$	−179.903			−0.605733
$298$	−25.5557	−	32.5305i	−0.0857575	−	0.109163i
$299$			824.526i			2.75761i
$300$	66.9705	+	16.3183i	0.223235	+	0.0543944i
$301$	15.1223			0.0502403
$302$	−3.95113	+	3.10398i	−0.0130832	+	0.0102781i
$303$			86.8843i			0.286747i
$304$	−243.871	+	470.713i	−0.802209	+	1.54840i
$305$	6.23280			0.0204354
$306$	−118.341	−	150.639i	−0.386736	−	0.492286i
$307$		−	492.719i		−	1.60495i	−0.596687	−	0.802474i	$-0.703517\pi$
$307$		−	492.719i		−	1.60495i	0.596687	−	0.802474i	$-0.296483\pi$
$308$	−12.9566	+	53.1737i	−0.0420667	+	0.172642i
$309$	−19.1237			−0.0618890
$310$	−6.89442	+	5.41621i	−0.0222400	+	0.0174716i
$311$		−	335.416i		−	1.07851i	−0.842143	−	0.539254i	$-0.818706\pi$
$311$		−	335.416i		−	1.07851i	0.842143	−	0.539254i	$-0.181294\pi$
$312$	54.5915	+	120.018i	0.174973	+	0.384674i
$313$	−216.314			−0.691100			−0.345550	−	0.938400i	$-0.612308\pi$
$313$	−216.314			−0.691100			−0.345550	+	0.938400i	$0.612308\pi$
$314$	−106.297	−	135.307i	−0.338525	−	0.430916i
$315$			6.29631i			0.0199883i
$316$	465.928	+	113.530i	1.47446	+	0.359272i
$317$	−149.637			−0.472041			−0.236021	−	0.971748i	$-0.575843\pi$
$317$	−149.637			−0.472041			−0.236021	+	0.971748i	$0.575843\pi$
$318$	−92.1551	+	72.3965i	−0.289796	+	0.227662i
$319$			518.455i			1.62525i
$320$	−33.1133	+	37.9822i	−0.103479	+	0.118694i
$321$	−14.9132			−0.0464587
$322$	−41.1017	−	52.3193i	−0.127645	−	0.162482i
$323$		−	373.347i		−	1.15587i
$324$	−64.1658	+	263.337i	−0.198043	+	0.812767i
$325$	−568.481			−1.74917
$326$	−18.6775	+	14.6729i	−0.0572928	+	0.0450089i
$327$		−	118.349i		−	0.361924i
$328$	−331.366	+	150.725i	−1.01026	+	0.459528i
$329$	12.1068			0.0367987
$330$	−10.0001	−	12.7294i	−0.0303034	−	0.0385738i
$331$		−	586.812i		−	1.77285i	−0.462876	−	0.886423i	$-0.653183\pi$
$331$		−	586.812i		−	1.77285i	0.462876	−	0.886423i	$-0.346817\pi$
$332$	356.522	+	86.8717i	1.07386	+	0.261662i
$333$	−101.244			−0.304037
$334$	272.363	−	213.967i	0.815458	−	0.640618i
$335$			47.1685i			0.140801i
$336$	−9.44681	−	4.89429i	−0.0281155	−	0.0145663i
$337$	281.712			0.835940			0.417970	−	0.908461i	$-0.362742\pi$
$337$	281.712			0.835940			0.417970	+	0.908461i	$0.362742\pi$
$338$	−462.954	−	589.304i	−1.36969	−	1.74350i
$339$		−	52.8670i		−	0.155950i
$340$	8.40110	−	34.4781i	0.0247091	−	0.101406i
$341$	−80.9764			−0.237468
$342$	−442.956	+	347.983i	−1.29519	+	1.01750i
$343$		−	91.3629i		−	0.266364i
$344$	53.2436	+	117.055i	0.154778	+	0.340276i
$345$	19.6788			0.0570401
$346$	286.918	+	365.224i	0.829242	+	1.05556i
$347$			648.661i			1.86934i	0.355516	+	0.934670i	$0.384305\pi$
$347$			648.661i			1.86934i	−0.355516	+	0.934670i	$0.615695\pi$
$348$	−97.9223	−	23.8602i	−0.281386	−	0.0685637i
$349$	317.602			0.910033			0.455017	−	0.890483i	$-0.349633\pi$
$349$	317.602			0.910033			0.455017	+	0.890483i	$0.349633\pi$
$350$	36.0722	−	28.3381i	0.103064	−	0.0809661i
$351$			288.430i			0.821738i
$352$	−457.211	+	86.9264i	−1.29890	+	0.246950i
$353$	−6.19333			−0.0175449			−0.00877243	−	0.999962i	$-0.502792\pi$
$353$	−6.19333			−0.0175449			−0.00877243	+	0.999962i	$0.502792\pi$
$354$	−67.5463	−	85.9813i	−0.190809	−	0.242885i
$355$		−	49.8341i		−	0.140378i
$356$	89.4341	−	367.038i	0.251219	−	1.03101i
$357$	7.49276			0.0209881
$358$	−374.481	+	294.190i	−1.04604	+	0.821760i
$359$			235.514i			0.656028i	0.944673	+	0.328014i	$0.106379\pi$
$359$			235.514i			0.656028i	−0.944673	+	0.328014i	$0.893621\pi$
$360$	−48.7368	+	22.1684i	−0.135380	+	0.0615789i
$361$	−736.829			−2.04108
$362$	159.632	+	203.199i	0.440972	+	0.561323i
$363$		−	63.9833i		−	0.176262i
$364$	85.2511	+	20.7727i	0.234206	+	0.0570677i
$365$	−36.7502			−0.100685
$366$	−8.80008	+	6.91329i	−0.0240439	+	0.0188888i
$367$			20.1210i			0.0548257i	0.999624	+	0.0274129i	$0.00872688\pi$
$367$			20.1210i			0.0548257i	−0.999624	+	0.0274129i	$0.991273\pi$
$368$	260.266	−	502.358i	0.707245	−	1.36510i
$369$	−386.806			−1.04825
$370$	−11.5863	−	14.7485i	−0.0313145	−	0.0398609i
$371$			77.9897i			0.210215i
$372$	3.72667	−	15.2943i	0.0100179	−	0.0411136i
$373$	432.222			1.15877			0.579386	−	0.815054i	$-0.303293\pi$
$373$	432.222			1.15877			0.579386	+	0.815054i	$0.303293\pi$
$374$	257.737	−	202.477i	0.689137	−	0.541382i
$375$			27.4806i			0.0732817i
$376$	42.6262	+	93.7128i	0.113367	+	0.249236i
$377$	831.216			2.20482
$378$	−14.3779	−	18.3020i	−0.0380368	−	0.0484179i
$379$		−	274.935i		−	0.725422i	−0.931902	−	0.362711i	$-0.881851\pi$
$379$		−	274.935i		−	0.725422i	0.931902	−	0.362711i	$-0.118149\pi$
$380$	−101.383	−	24.7035i	−0.266798	−	0.0650091i
$381$	−30.5229			−0.0801126
$382$	418.087	−	328.446i	1.09447	−	0.859807i
$383$		−	163.266i		−	0.426282i	−0.977021	−	0.213141i	$-0.931631\pi$
$383$		−	163.266i		−	0.426282i	0.977021	−	0.213141i	$-0.0683694\pi$
$384$	4.62356	−	90.3555i	0.0120405	−	0.235301i
$385$	−10.7727			−0.0279810
$386$	241.550	+	307.475i	0.625778	+	0.796566i
$387$			136.639i			0.353072i
$388$	57.1069	−	234.367i	0.147183	−	0.604039i
$389$	−156.447			−0.402177			−0.201088	−	0.979573i	$-0.564448\pi$
$389$	−156.447			−0.402177			−0.201088	+	0.979573i	$0.564448\pi$
$390$	−20.4084	+	16.0327i	−0.0523293	+	0.0411095i
$391$			398.446i			1.01904i
$392$	350.376	−	159.372i	0.893817	−	0.406561i
$393$	46.5334			0.118406
$394$	−136.577	−	173.852i	−0.346641	−	0.441248i
$395$			94.3943i			0.238973i
$396$	−480.455	−	117.070i	−1.21327	−	0.295631i
$397$	746.159			1.87949			0.939746	−	0.341872i	$-0.111061\pi$
$397$	746.159			1.87949			0.939746	+	0.341872i	$0.111061\pi$
$398$	390.221	−	306.555i	0.980454	−	0.770238i
$399$		−	22.0325i		−	0.0552193i
$400$	346.357	+	179.444i	0.865893	+	0.448610i
$401$	362.317			0.903533			0.451767	−	0.892136i	$-0.350794\pi$
$401$	362.317			0.903533			0.451767	+	0.892136i	$0.350794\pi$
$402$	−52.3182	−	66.5971i	−0.130145	−	0.165664i
$403$			129.826i			0.322149i
$404$	−116.401	+	477.711i	−0.288122	+	1.18245i
$405$	−53.3505			−0.131730
$406$	−52.7438	+	41.4352i	−0.129911	+	0.102057i
$407$		−	173.225i		−	0.425613i
$408$	26.3809	+	57.9979i	0.0646591	+	0.142152i
$409$	296.428			0.724762			0.362381	−	0.932030i	$-0.381964\pi$
$409$	296.428			0.724762			0.362381	+	0.932030i	$0.381964\pi$
$410$	−44.2658	−	56.3469i	−0.107965	−	0.137432i
$411$		−	29.5910i		−	0.0719976i
$412$	−105.147	−	25.6205i	−0.255210	−	0.0621857i
$413$	−72.7648			−0.176186
$414$	472.734	−	371.377i	1.14187	−	0.897046i
$415$			72.2293i			0.174046i
$416$	139.365	+	733.026i	0.335013	+	1.76208i
$417$	35.1852			0.0843769
$418$	−595.384	−	757.877i	−1.42436	−	1.81310i
$419$		−	470.224i		−	1.12225i	−0.827730	−	0.561126i	$-0.810368\pi$
$419$		−	470.224i		−	1.12225i	0.827730	−	0.561126i	$-0.189632\pi$
$420$	0.495777	−	2.03467i	0.00118042	−	0.00484446i
$421$	252.672			0.600171			0.300086	−	0.953912i	$-0.402985\pi$
$421$	252.672			0.600171			0.300086	+	0.953912i	$0.402985\pi$
$422$	−510.721	+	401.219i	−1.21024	+	0.950756i
$423$			109.391i			0.258609i
$424$	−603.682	+	274.590i	−1.42378	+	0.647619i
$425$	−274.714			−0.646386
$426$	55.2749	+	70.3607i	0.129753	+	0.165166i
$427$			7.44740i			0.0174412i
$428$	−81.9965	−	19.9796i	−0.191581	−	0.0466814i
$429$	−239.701			−0.558744
$430$	−19.9045	+	15.6369i	−0.0462896	+	0.0363648i
$431$		−	64.5006i		−	0.149653i	−0.997197	−	0.0748267i	$-0.976160\pi$
$431$		−	64.5006i		−	0.149653i	0.997197	−	0.0748267i	$-0.0238403\pi$
$432$	91.0445	−	175.731i	0.210751	−	0.406786i
$433$	696.600			1.60878			0.804388	−	0.594104i	$-0.202493\pi$
$433$	696.600			1.60878			0.804388	+	0.594104i	$0.202493\pi$
$434$	−6.47167	−	8.23794i	−0.0149117	−	0.0189814i
$435$		−	19.8385i		−	0.0456057i
$436$	158.555	−	650.712i	0.363659	−	1.49246i
$437$	1171.63			2.68108
$438$	51.8875	−	40.7625i	0.118465	−	0.0930650i
$439$			123.565i			0.281468i	0.990047	+	0.140734i	$0.0449463\pi$
$439$			123.565i			0.281468i	−0.990047	+	0.140734i	$0.955054\pi$
$440$	−37.9291	−	83.3864i	−0.0862025	−	0.189515i
$441$	408.996			0.927429
$442$	−324.622	−	413.218i	−0.734438	−	0.934883i
$443$			210.668i			0.475548i	0.971321	+	0.237774i	$0.0764177\pi$
$443$			210.668i			0.475548i	−0.971321	+	0.237774i	$0.923582\pi$
$444$	32.7175	+	7.97209i	0.0736880	+	0.0179552i
$445$	74.3598			0.167101
$446$	325.274	−	255.533i	0.729314	−	0.572945i
$447$			14.6200i			0.0327070i
$448$	−45.3838	−	39.5661i	−0.101303	−	0.0883171i
$449$	74.9713			0.166974			0.0834869	−	0.996509i	$-0.473394\pi$
$449$	74.9713			0.166974			0.0834869	+	0.996509i	$0.473394\pi$
$450$	256.051	+	325.933i	0.569002	+	0.724296i
$451$		−	661.807i		−	1.46742i
$452$	70.8273	−	290.675i	0.156697	−	0.643087i
$453$	1.77574			0.00391995
$454$	375.746	−	295.184i	0.827635	−	0.650185i
$455$			17.2714i			0.0379591i
$456$	170.543	−	77.5732i	0.373998	−	0.170117i
$457$	−120.814			−0.264362			−0.132181	−	0.991226i	$-0.542198\pi$
$457$	−120.814			−0.264362			−0.132181	+	0.991226i	$0.542198\pi$
$458$	−6.63853	−	8.45034i	−0.0144946	−	0.0184505i
$459$			139.382i			0.303664i
$460$	108.199	+	26.3642i	0.235215	+	0.0573135i
$461$	−446.034			−0.967535			−0.483767	−	0.875197i	$-0.660732\pi$
$461$	−446.034			−0.967535			−0.483767	+	0.875197i	$0.660732\pi$
$462$	15.2099	−	11.9488i	0.0329220	−	0.0258633i
$463$		−	270.723i		−	0.584715i	−0.956309	−	0.292357i	$-0.905560\pi$
$463$		−	270.723i		−	0.584715i	0.956309	−	0.292357i	$-0.0944397\pi$
$464$	−506.434	−	262.378i	−1.09145	−	0.565469i
$465$	3.09853			0.00666351
$466$	−136.915	−	174.282i	−0.293809	−	0.373997i
$467$			680.054i			1.45622i	0.685461	+	0.728109i	$0.259601\pi$
$467$			680.054i			1.45622i	−0.685461	+	0.728109i	$0.740399\pi$
$468$	−187.693	+	770.292i	−0.401053	+	1.64592i
$469$	−56.3602			−0.120171
$470$	−15.9353	+	12.5187i	−0.0339049	+	0.0266355i
$471$			60.8107i			0.129110i
$472$	−256.195	−	563.239i	−0.542785	−	1.19330i
$473$	−233.783			−0.494256
$474$	−104.700	−	133.275i	−0.220886	−	0.281171i
$475$			807.798i			1.70063i
$476$	41.1969	+	10.0382i	0.0865482	+	0.0210887i
$477$	−704.681			−1.47732
$478$	−583.103	+	458.082i	−1.21988	+	0.958331i
$479$		−	647.390i		−	1.35154i	−0.737111	−	0.675772i	$-0.763810\pi$
$479$		−	647.390i		−	1.35154i	0.737111	−	0.675772i	$-0.236190\pi$
$480$	17.4950	−	3.32621i	0.0364480	−	0.00692960i
$481$	−277.723			−0.577387
$482$	345.303	+	439.544i	0.716395	+	0.911916i
$483$			23.5137i			0.0486825i
$484$	85.7200	−	351.795i	0.177107	−	0.726849i
$485$	47.4814			0.0978999
$486$	250.413	−	196.723i	0.515254	−	0.404780i
$487$		−	280.397i		−	0.575764i	−0.957666	−	0.287882i	$-0.907049\pi$
$487$		−	280.397i		−	0.575764i	0.957666	−	0.287882i	$-0.0929511\pi$
$488$	−57.6469	+	26.2212i	−0.118129	+	0.0537320i
$489$	8.39414			0.0171659
$490$	46.8053	+	59.5795i	0.0955209	+	0.121591i
$491$			398.839i			0.812300i	0.913806	+	0.406150i	$0.133129\pi$
$491$			398.839i			0.812300i	−0.913806	+	0.406150i	$0.866871\pi$
$492$	124.998	+	30.4575i	0.254060	+	0.0619054i
$493$	401.679			0.814764
$494$	−1215.07	+	954.552i	−2.45966	+	1.93229i
$495$		−	97.3374i		−	0.196641i
$496$	40.9802	−	79.0988i	0.0826214	−	0.159473i
$497$	59.5453			0.119810
$498$	−80.1152	−	101.980i	−0.160874	−	0.204780i
$499$			500.902i			1.00381i	0.864922	+	0.501906i	$0.167368\pi$
$499$			500.902i			1.00381i	−0.864922	+	0.501906i	$0.832632\pi$
$500$	−36.8165	+	151.095i	−0.0736330	+	0.302190i
$501$	−122.407			−0.244325
$502$	−218.436	+	171.602i	−0.435132	+	0.341837i
$503$			91.7632i			0.182432i	0.995831	+	0.0912159i	$0.0290753\pi$
$503$			91.7632i			0.182432i	−0.995831	+	0.0912159i	$0.970925\pi$
$504$	−26.4884	−	58.2342i	−0.0525563	−	0.115544i
$505$	−96.7814			−0.191646
$506$	635.409	+	808.827i	1.25575	+	1.59847i
$507$			264.849i			0.522384i
$508$	−167.822	−	40.8923i	−0.330359	−	0.0804967i
$509$	445.179			0.874615			0.437307	−	0.899312i	$-0.355932\pi$
$509$	445.179			0.874615			0.437307	+	0.899312i	$0.355932\pi$
$510$	−9.86221	+	7.74769i	−0.0193377	+	0.0151916i
$511$		−	43.9117i		−	0.0859329i
$512$	146.473	−	490.601i	0.286080	−	0.958206i
$513$	409.852			0.798933
$514$	172.149	+	219.132i	0.334920	+	0.426328i
$515$		−	21.3021i		−	0.0413633i
$516$	10.7591	−	44.1553i	0.0208509	−	0.0855724i
$517$	−187.164			−0.362019
$518$	17.6226	−	13.8442i	0.0340204	−	0.0267262i
$519$		−	164.141i		−	0.316265i
$520$	−133.690	+	60.8100i	−0.257096	+	0.116942i
$521$	224.863			0.431599			0.215799	−	0.976438i	$-0.430764\pi$
$521$	224.863			0.431599			0.215799	+	0.976438i	$0.430764\pi$
$522$	−374.390	−	476.570i	−0.717223	−	0.912969i
$523$			933.663i			1.78521i	0.450843	+	0.892603i	$0.351123\pi$
$523$			933.663i			1.78521i	−0.450843	+	0.892603i	$0.648877\pi$
$524$	255.852	+	62.3419i	0.488266	+	0.118973i
$525$	−16.2118			−0.0308796
$526$	−385.951	+	303.200i	−0.733747	+	0.576427i
$527$			62.7374i			0.119046i
$528$	146.042	+	75.6630i	0.276596	+	0.143301i
$529$	−721.398			−1.36370
$530$	−80.6432	−	102.653i	−0.152157	−	0.193684i
$531$		−	657.472i		−	1.23818i
$532$	29.5175	−	121.140i	0.0554840	−	0.227706i
$533$	−1061.05			−1.99070
$534$	−104.988	+	82.4783i	−0.196608	+	0.154454i
$535$		−	16.6120i		−	0.0310505i
$536$	−198.436	−	436.258i	−0.370217	−	0.813915i
$537$	168.302			0.313411
$538$	−110.308	−	140.413i	−0.205033	−	0.260991i
$539$			699.774i			1.29828i
$540$	37.8494	+	9.22255i	0.0700914	+	0.0170788i
$541$	−188.226			−0.347923			−0.173962	−	0.984752i	$-0.555657\pi$
$541$	−188.226			−0.347923			−0.173962	+	0.984752i	$0.555657\pi$
$542$	183.142	−	143.876i	0.337901	−	0.265453i
$543$		−	91.3229i		−	0.168182i
$544$	67.3472	+	354.230i	0.123800	+	0.651157i
$545$	131.831			0.241891
$546$	−19.1570	−	24.3854i	−0.0350861	−	0.0446619i
$547$			711.529i			1.30078i	0.759599	+	0.650392i	$0.225395\pi$
$547$			711.529i			1.30078i	−0.759599	+	0.650392i	$0.774605\pi$
$548$	39.6438	−	162.698i	0.0723427	−	0.296895i
$549$	−67.2915			−0.122571
$550$	−557.657	+	438.092i	−1.01392	+	0.796530i
$551$		−	1181.14i		−	2.14363i
$552$	−182.008	+	82.7882i	−0.329725	+	0.149979i
$553$	−112.789			−0.203958
$554$	244.152	+	310.787i	0.440707	+	0.560987i
$555$			6.62837i			0.0119430i
$556$	193.456	+	47.1384i	0.347943	+	0.0847814i
$557$	507.393			0.910938			0.455469	−	0.890252i	$-0.349472\pi$
$557$	507.393			0.910938			0.455469	+	0.890252i	$0.349472\pi$
$558$	74.4344	−	58.4752i	0.133395	−	0.104794i
$559$			374.814i			0.670508i
$560$	5.45180	−	10.5229i	0.00973536	−	0.0187909i
$561$	−115.834			−0.206477
$562$	254.690	+	324.201i	0.453185	+	0.576870i
$563$		−	47.4849i		−	0.0843426i	−0.999110	−	0.0421713i	$-0.986572\pi$
$563$		−	47.4849i		−	0.0843426i	0.999110	−	0.0421713i	$-0.0134275\pi$
$564$	8.61359	−	35.3502i	0.0152723	−	0.0626777i
$565$	58.8892			0.104229
$566$	301.504	−	236.860i	0.532693	−	0.418480i
$567$		−	63.7469i		−	0.112428i
$568$	209.651	+	460.913i	0.369103	+	0.811466i
$569$	−611.407			−1.07453			−0.537265	−	0.843414i	$-0.680542\pi$
$569$	−611.407			−1.07453			−0.537265	+	0.843414i	$0.680542\pi$
$570$	22.7821	+	28.9999i	0.0399686	+	0.0508770i
$571$		−	282.614i		−	0.494947i	−0.968895	−	0.247473i	$-0.920400\pi$
$571$		−	282.614i		−	0.494947i	0.968895	−	0.247473i	$-0.0796002\pi$
$572$	−1317.93	−	321.134i	−2.30408	−	0.561423i
$573$	−187.899			−0.327922
$574$	67.3273	−	52.8919i	0.117295	−	0.0921462i
$575$		−	862.104i		−	1.49931i
$576$	357.502	−	410.068i	0.620663	−	0.711924i
$577$	−514.538			−0.891747			−0.445874	−	0.895096i	$-0.647107\pi$
$577$	−514.538			−0.891747			−0.445874	+	0.895096i	$0.647107\pi$
$578$	200.196	+	254.834i	0.346360	+	0.440889i
$579$		−	138.187i		−	0.238665i
$580$	26.5781	−	109.077i	0.0458243	−	0.188063i
$581$	−86.3047			−0.148545
$582$	−67.0389	+	52.6654i	−0.115187	+	0.0904903i
$583$		−	1205.68i		−	2.06806i
$584$	339.900	−	154.607i	0.582021	−	0.264738i
$585$	−156.057			−0.266764
$586$	33.6197	+	42.7953i	0.0573715	+	0.0730295i
$587$		−	66.5101i		−	0.113305i	−0.998394	−	0.0566526i	$-0.981957\pi$
$587$		−	66.5101i		−	0.113305i	0.998394	−	0.0566526i	$-0.0180427\pi$
$588$	−132.169	−	32.2048i	−0.224776	−	0.0547700i
$589$	184.480			0.313208
$590$	95.7755	−	75.2406i	0.162331	−	0.127526i
$591$			78.1335i			0.132206i
$592$	169.208	+	87.6649i	0.285824	+	0.148083i
$593$	−484.536			−0.817093			−0.408546	−	0.912738i	$-0.633964\pi$
$593$	−484.536			−0.817093			−0.408546	+	0.912738i	$0.633964\pi$
$594$	222.275	+	282.938i	0.374200	+	0.476327i
$595$			8.34626i			0.0140273i
$596$	−19.5868	+	80.3844i	−0.0328638	+	0.134873i
$597$	−175.375			−0.293761
$598$	1296.76	−	1018.72i	2.16849	−	1.70355i
$599$		−	10.2756i		−	0.0171546i	−0.999963	−	0.00857731i	$-0.997270\pi$
$599$		−	10.2756i		−	0.0171546i	0.999963	−	0.00857731i	$-0.00273028\pi$
$600$	−57.0794	−	125.488i	−0.0951324	−	0.209147i
$601$	−653.797			−1.08785			−0.543925	−	0.839134i	$-0.683062\pi$
$601$	−653.797			−1.08785			−0.543925	+	0.839134i	$0.683062\pi$
$602$	−18.6840	−	23.7833i	−0.0310366	−	0.0395072i
$603$		−	509.247i		−	0.844522i
$604$	9.76344	+	2.37900i	0.0161646	+	0.00393875i
$605$	71.2717			0.117804
$606$	136.645	−	107.348i	0.225488	−	0.177142i
$607$			608.301i			1.00214i	0.865406	+	0.501072i	$0.167061\pi$
$607$			608.301i			1.00214i	−0.865406	+	0.501072i	$0.832939\pi$
$608$	1041.61	−	198.035i	1.71318	−	0.325715i
$609$	23.7044			0.0389235
$610$	−7.70079	−	9.80251i	−0.0126242	−	0.0160697i
$611$			300.071i			0.491115i
$612$	−90.7011	+	372.238i	−0.148204	+	0.608232i
$613$	−223.600			−0.364763			−0.182382	−	0.983228i	$-0.558381\pi$
$613$	−223.600			−0.364763			−0.182382	+	0.983228i	$0.558381\pi$
$614$	−774.913	+	608.767i	−1.26207	+	0.991477i
$615$			25.3238i			0.0411769i
$616$	99.6360	−	45.3204i	0.161747	−	0.0735721i
$617$	−344.233			−0.557913			−0.278957	−	0.960304i	$-0.589989\pi$
$617$	−344.233			−0.557913			−0.278957	+	0.960304i	$0.589989\pi$
$618$	23.6278	+	30.0764i	0.0382328	+	0.0486673i
$619$		−	1101.58i		−	1.77962i	−0.456334	−	0.889809i	$-0.650838\pi$
$619$		−	1101.58i		−	1.77962i	0.456334	−	0.889809i	$-0.349162\pi$
$620$	17.0365	+	4.15118i	0.0274782	+	0.00669545i
$621$	−437.405			−0.704357
$622$	−527.518	+	414.415i	−0.848100	+	0.666262i
$623$			88.8504i			0.142617i
$624$	121.307	−	234.143i	0.194402	−	0.375230i
$625$	578.891			0.926226
$626$	267.262	+	340.204i	0.426936	+	0.543457i
$627$			340.610i			0.543238i
$628$	−81.4696	+	334.352i	−0.129729	+	0.532407i
$629$	−134.208			−0.213367
$630$	9.90238	−	7.77925i	0.0157181	−	0.0123480i
$631$		−	714.061i		−	1.13163i	−0.824531	−	0.565817i	$-0.808561\pi$
$631$		−	714.061i		−	1.13163i	0.824531	−	0.565817i	$-0.191439\pi$
$632$	−397.114	−	873.048i	−0.628345	−	1.38140i
$633$	229.531			0.362609
$634$	184.880	+	235.338i	0.291610	+	0.371196i
$635$		−	33.9998i		−	0.0535430i
$636$	227.720	+	55.4873i	0.358050	+	0.0872442i
$637$	1121.92			1.76125
$638$	815.390	−	640.565i	1.27804	−	1.00402i
$639$			538.026i			0.841981i
$640$	100.648	+	5.15024i	0.157262	+	0.00804725i
$641$	−92.5153			−0.144330			−0.0721648	−	0.997393i	$-0.522991\pi$
$641$	−92.5153			−0.144330			−0.0721648	+	0.997393i	$0.522991\pi$
$642$	18.4257	+	23.4545i	0.0287005	+	0.0365335i
$643$		−	168.579i		−	0.262176i	−0.991371	−	0.131088i	$-0.958153\pi$
$643$		−	168.579i		−	0.262176i	0.991371	−	0.131088i	$-0.0418471\pi$
$644$	−31.5018	+	129.284i	−0.0489159	+	0.200751i
$645$	8.94562			0.0138692
$646$	−587.174	+	461.280i	−0.908938	+	0.714056i
$647$		−	176.006i		−	0.272033i	−0.990707	−	0.136017i	$-0.956570\pi$
$647$		−	176.006i		−	0.272033i	0.990707	−	0.136017i	$-0.0434301\pi$
$648$	493.436	−	224.444i	0.761475	−	0.346364i
$649$	1124.90			1.73329
$650$	702.373	+	894.066i	1.08057	+	1.37549i
$651$			3.70235i			0.00568717i
$652$	46.1529	+	11.2458i	0.0707867	+	0.0172482i
$653$	327.010			0.500781			0.250391	−	0.968145i	$-0.419441\pi$
$653$	327.010			0.500781			0.250391	+	0.968145i	$0.419441\pi$
$654$	−186.131	+	146.224i	−0.284604	+	0.223583i
$655$			51.8341i			0.0791360i
$656$	646.462	+	334.925i	0.985460	+	0.510556i
$657$	396.767			0.603907
$658$	−14.9582	−	19.0407i	−0.0227329	−	0.0289372i
$659$		−	432.074i		−	0.655651i	−0.944738	−	0.327826i	$-0.893684\pi$
$659$		−	432.074i		−	0.655651i	0.944738	−	0.327826i	$-0.106316\pi$
$660$	−7.66444	+	31.4549i	−0.0116128	+	0.0476590i
$661$	227.659			0.344416			0.172208	−	0.985061i	$-0.444910\pi$
$661$	227.659			0.344416			0.172208	+	0.985061i	$0.444910\pi$
$662$	−922.896	+	725.021i	−1.39410	+	1.09520i
$663$			185.711i			0.280107i
$664$	−303.866	−	668.045i	−0.457630	−	1.00609i
$665$	24.5422			0.0369056
$666$	125.090	+	159.230i	0.187823	+	0.239084i
$667$			1260.54i			1.88987i
$668$	−673.023	−	163.992i	−1.00752	−	0.245497i
$669$	−146.187			−0.218515
$670$	74.1832	−	58.2778i	0.110721	−	0.0869819i
$671$		−	115.133i		−	0.171584i
$672$	3.97439	+	20.9043i	0.00591427	+	0.0311076i
$673$	920.889			1.36833			0.684167	−	0.729325i	$-0.260166\pi$
$673$	920.889			1.36833			0.684167	+	0.729325i	$0.260166\pi$
$674$	−348.062	−	443.056i	−0.516413	−	0.657353i
$675$		−	301.575i		−	0.446778i
$676$	−354.824	+	1456.20i	−0.524888	+	2.15414i
$677$	−35.6256			−0.0526227			−0.0263114	−	0.999654i	$-0.508376\pi$
$677$	−35.6256			−0.0526227			−0.0263114	+	0.999654i	$0.508376\pi$
$678$	−83.1455	+	65.3186i	−0.122633	+	0.0963401i
$679$			56.7342i			0.0835555i
$680$	−64.6045	+	29.3860i	−0.0950067	+	0.0432147i
$681$	−168.870			−0.247974
$682$	100.048	+	127.354i	0.146699	+	0.186736i
$683$		−	753.528i		−	1.10326i	−0.834088	−	0.551631i	$-0.814006\pi$
$683$		−	753.528i		−	1.10326i	0.834088	−	0.551631i	$-0.185994\pi$
$684$	1094.57	+	266.707i	1.60024	+	0.389923i
$685$	32.9617			0.0481193
$686$	−143.689	+	112.881i	−0.209459	+	0.164550i
$687$			3.79780i			0.00552810i
$688$	118.312	−	228.362i	0.171965	−	0.331922i
$689$	−1933.01			−2.80553
$690$	−24.3137	−	30.9494i	−0.0352372	−	0.0448543i
$691$			830.253i			1.20152i	0.799428	+	0.600762i	$0.205136\pi$
$691$			830.253i			1.20152i	−0.799428	+	0.600762i	$0.794864\pi$
$692$	219.904	−	902.488i	0.317781	−	1.30417i
$693$	116.306			0.167829
$694$	1020.17	−	801.438i	1.46998	−	1.15481i
$695$			39.1931i			0.0563930i
$696$	83.4599	+	183.485i	0.119914	+	0.263628i
$697$	−512.742			−0.735642
$698$	−392.405	−	499.501i	−0.562185	−	0.715618i
$699$			78.3271i			0.112056i
$700$	−89.1364	−	21.7194i	−0.127338	−	0.0310277i
$701$	−1258.01			−1.79460			−0.897300	−	0.441422i	$-0.854474\pi$
$701$	−1258.01			−1.79460			−0.897300	+	0.441422i	$0.854474\pi$
$702$	453.622	−	356.363i	0.646186	−	0.507639i
$703$			394.638i			0.561363i
$704$	701.608	+	611.670i	0.996603	+	0.868849i
$705$	7.16175			0.0101585
$706$	7.65203	+	9.74044i	0.0108386	+	0.0137967i
$707$		−	115.641i		−	0.163566i
$708$	−51.7700	+	212.464i	−0.0731214	+	0.300091i
$709$	23.0170			0.0324640			0.0162320	−	0.999868i	$-0.494833\pi$
$709$	23.0170			0.0324640			0.0162320	+	0.999868i	$0.494833\pi$
$710$	−78.3756	+	61.5713i	−0.110388	+	0.0867202i
$711$		−	1019.11i		−	1.43335i
$712$	−687.749	+	312.829i	−0.965940	+	0.439367i
$713$	−196.882			−0.276131
$714$	−9.25749	−	11.7841i	−0.0129657	−	0.0165043i
$715$		−	267.006i		−	0.373435i
$716$	925.362	+	225.478i	1.29241	+	0.314913i
$717$	262.062			0.365498
$718$	370.400	−	290.984i	0.515877	−	0.405270i
$719$			969.900i			1.34896i	0.738295	+	0.674478i	$0.235631\pi$
$719$			969.900i			1.34896i	−0.738295	+	0.674478i	$0.764369\pi$
$720$	95.0804	+	49.2601i	0.132056	+	0.0684168i
$721$	25.4533			0.0353027
$722$	910.372	+	1158.83i	1.26090	+	1.60503i
$723$		−	197.542i		−	0.273226i
$724$	122.348	−	502.115i	0.168988	−	0.693529i
$725$	−869.098			−1.19876
$726$	−100.628	+	79.0530i	−0.138606	+	0.108888i
$727$		−	29.8525i		−	0.0410626i	−0.999789	−	0.0205313i	$-0.993464\pi$
$727$		−	29.8525i		−	0.0410626i	0.999789	−	0.0205313i	$-0.00653578\pi$
$728$	−72.6601	−	159.742i	−0.0998079	−	0.219426i
$729$	497.301			0.682168
$730$	45.4058	+	57.7980i	0.0621997	+	0.0791754i
$731$			181.126i			0.247778i
$732$	21.7455	+	5.29860i	0.0297069	+	0.00723852i
$733$	836.844			1.14167			0.570835	−	0.821065i	$-0.306620\pi$
$733$	836.844			1.14167			0.570835	+	0.821065i	$0.306620\pi$
$734$	31.6450	−	24.8601i	0.0431130	−	0.0338693i
$735$		−	26.7766i		−	0.0364307i
$736$	−1111.64	+	211.348i	−1.51038	+	0.287158i
$737$	871.298			1.18222
$738$	477.908	+	608.340i	0.647572	+	0.824310i
$739$			292.453i			0.395741i	0.980228	+	0.197871i	$0.0634026\pi$
$739$			292.453i			0.395741i	−0.980228	+	0.197871i	$0.936597\pi$
$740$	−8.88020	+	36.4444i	−0.0120003	+	0.0492491i
$741$	546.085			0.736956
$742$	122.657	−	96.3583i	0.165305	−	0.129863i
$743$		−	659.281i		−	0.887323i	−0.896194	−	0.443662i	$-0.853679\pi$
$743$		−	659.281i		−	0.887323i	0.896194	−	0.443662i	$-0.146321\pi$
$744$	−28.6581	+	13.0354i	−0.0385190	+	0.0175207i
$745$	−16.2854			−0.0218596
$746$	−534.021	−	679.767i	−0.715846	−	0.911216i
$747$		−	779.812i		−	1.04392i
$748$	−636.882	−	155.185i	−0.851446	−	0.207467i
$749$	19.8492			0.0265010
$750$	43.2196	−	33.9530i	0.0576261	−	0.0452707i
$751$			1183.45i			1.57583i	0.615783	+	0.787915i	$0.288840\pi$
$751$			1183.45i			1.57583i	−0.615783	+	0.787915i	$0.711160\pi$
$752$	94.7191	−	182.824i	0.125956	−	0.243117i
$753$	98.1709			0.130373
$754$	−1026.99	−	1307.28i	−1.36205	−	1.73379i
$755$			1.97802i			0.00261989i
$756$	−11.0198	+	45.2251i	−0.0145764	+	0.0598216i
$757$	219.268			0.289655			0.144827	−	0.989457i	$-0.453737\pi$
$757$	219.268			0.289655			0.144827	+	0.989457i	$0.453737\pi$
$758$	−432.398	+	339.689i	−0.570446	+	0.448139i
$759$		−	363.508i		−	0.478930i
$760$	86.4096	+	189.970i	0.113697	+	0.249961i
$761$	663.955			0.872476			0.436238	−	0.899831i	$-0.356311\pi$
$761$	663.955			0.872476			0.436238	+	0.899831i	$0.356311\pi$
$762$	37.7118	+	48.0043i	0.0494906	+	0.0629977i
$763$			157.521i			0.206449i
$764$	−1033.11	−	251.733i	−1.35224	−	0.329494i
$765$	−75.4132			−0.0985794
$766$	−256.773	+	201.720i	−0.335213	+	0.263341i
$767$		−	1803.51i		−	2.35138i
$768$	−147.817	+	104.365i	−0.192470	+	0.135892i
$769$	1252.83			1.62916			0.814581	−	0.580050i	$-0.196967\pi$
$769$	1252.83			1.62916			0.814581	+	0.580050i	$0.196967\pi$
$770$	13.3099	+	16.9425i	0.0172856	+	0.0220033i
$771$		−	98.4838i		−	0.127735i
$772$	185.133	−	759.786i	0.239809	−	0.984178i
$773$	−289.709			−0.374786			−0.187393	−	0.982285i	$-0.560004\pi$
$773$	−289.709			−0.374786			−0.187393	+	0.982285i	$0.560004\pi$
$774$	214.896	−	168.821i	0.277643	−	0.218115i
$775$		−	135.743i		−	0.175152i
$776$	−439.153	+	199.753i	−0.565919	+	0.257414i
$777$	−7.92005			−0.0101931
$778$	193.294	+	246.048i	0.248450	+	0.316257i
$779$			1507.72i			1.93546i
$780$	50.4302	+	12.2881i	0.0646541	+	0.0157539i
$781$	−920.538			−1.17867
$782$	626.648	−	492.290i	0.801340	−	0.629527i
$783$			440.954i			0.563160i
$784$	−683.548	−	354.139i	−0.871873	−	0.451708i
$785$	−67.7377			−0.0862901
$786$	−57.4932	−	73.1844i	−0.0731466	−	0.0931099i
$787$			355.537i			0.451762i	0.974155	+	0.225881i	$0.0725261\pi$
$787$			355.537i			0.451762i	−0.974155	+	0.225881i	$0.927474\pi$
$788$	−104.677	+	429.596i	−0.132839	+	0.545173i
$789$	173.456			0.219843
$790$	148.457	−	116.627i	0.187920	−	0.147629i
$791$			70.3650i			0.0889570i
$792$	409.495	+	900.268i	0.517040	+	1.13670i
$793$	−184.587			−0.232770
$794$	−921.898	−	1173.51i	−1.16108	−	1.47797i
$795$			46.1348i			0.0580312i
$796$	−964.255	−	234.955i	−1.21138	−	0.295169i
$797$	13.2166			0.0165829			0.00829144	−	0.999966i	$-0.497361\pi$
$797$	13.2166			0.0165829			0.00829144	+	0.999966i	$0.497361\pi$
$798$	−34.6511	+	27.2217i	−0.0434225	+	0.0341124i
$799$			145.007i			0.181486i
$800$	−145.717	−	766.434i	−0.182146	−	0.958042i
$801$	−802.813			−1.00226
$802$	−447.652	−	569.826i	−0.558169	−	0.710506i
$803$			678.851i			0.845393i
$804$	−40.0986	+	164.565i	−0.0498739	+	0.204683i
$805$	−26.1921			−0.0325368
$806$	204.181	−	160.403i	0.253326	−	0.199011i
$807$			63.1053i			0.0781974i
$808$	895.126	−	407.156i	1.10783	−	0.503906i
$809$	221.139			0.273348			0.136674	−	0.990616i	$-0.456359\pi$
$809$	221.139			0.273348			0.136674	+	0.990616i	$0.456359\pi$
$810$	65.9159	+	83.9058i	0.0813776	+	0.103587i
$811$			322.414i			0.397551i	0.980045	+	0.198775i	$0.0636964\pi$
$811$			322.414i			0.397551i	−0.980045	+	0.198775i	$0.936304\pi$
$812$	130.333	+	31.7574i	0.160508	+	0.0391101i
$813$	−82.3090			−0.101241
$814$	−272.435	+	214.024i	−0.334687	+	0.262928i
$815$			9.35032i			0.0114728i
$816$	58.6207	−	113.148i	0.0718391	−	0.138662i
$817$	532.602			0.651899
$818$	−366.244	−	466.200i	−0.447731	−	0.569927i
$819$		−	186.468i		−	0.227677i
$820$	−33.9269	+	139.236i	−0.0413743	+	0.169800i
$821$	−304.861			−0.371329			−0.185664	−	0.982613i	$-0.559444\pi$
$821$	−304.861			−0.371329			−0.185664	+	0.982613i	$0.559444\pi$
$822$	−46.5386	+	36.5604i	−0.0566163	+	0.0444774i
$823$			663.042i			0.805640i	0.915279	+	0.402820i	$0.131970\pi$
$823$			663.042i			0.805640i	−0.915279	+	0.402820i	$0.868030\pi$
$824$	89.6173	+	197.022i	0.108759	+	0.239104i
$825$	250.626			0.303789
$826$	89.9028	+	114.439i	0.108841	+	0.138546i
$827$			681.814i			0.824442i	0.911084	+	0.412221i	$0.135247\pi$
$827$			681.814i			0.824442i	−0.911084	+	0.412221i	$0.864753\pi$
$828$	−1168.15	−	284.637i	−1.41081	−	0.343764i
$829$	−68.9045			−0.0831177			−0.0415588	−	0.999136i	$-0.513232\pi$
$829$	−68.9045			−0.0831177			−0.0415588	+	0.999136i	$0.513232\pi$
$830$	113.597	−	89.2411i	0.136864	−	0.107519i
$831$		−	139.676i		−	0.168081i
$832$	980.662	−	1124.86i	1.17868	−	1.35199i
$833$	542.158			0.650849
$834$	−43.4722	−	55.3367i	−0.0521249	−	0.0663510i
$835$		−	136.351i		−	0.163294i
$836$	−456.324	+	1872.75i	−0.545842	+	2.24014i
$837$	−68.8717			−0.0822840
$838$	−739.534	+	580.973i	−0.882499	+	0.693286i
$839$			295.772i			0.352530i	0.984343	+	0.176265i	$0.0564015\pi$
$839$			295.772i			0.352530i	−0.984343	+	0.176265i	$0.943599\pi$
$840$	−3.81253	+	1.73417i	−0.00453873	+	0.00206448i
$841$	429.770			0.511023
$842$	−312.183	−	397.385i	−0.370763	−	0.471953i
$843$		−	145.704i		−	0.172840i
$844$	1262.02	+	307.509i	1.49528	+	0.364347i
$845$	−295.018			−0.349134
$846$	172.043	−	135.156i	0.203361	−	0.159759i
$847$			85.1604i			0.100544i
$848$	1177.72	+	610.164i	1.38882	+	0.719534i
$849$	−135.504			−0.159604
$850$	339.416	+	432.051i	0.399313	+	0.508295i
$851$		−	421.169i		−	0.494910i
$852$	42.3647	−	173.865i	0.0497238	−	0.204067i
$853$	551.895			0.647005			0.323503	−	0.946227i	$-0.395140\pi$
$853$	551.895			0.647005			0.323503	+	0.946227i	$0.395140\pi$
$854$	11.7127	−	9.20145i	0.0137151	−	0.0107745i
$855$			221.753i			0.259360i
$856$	69.8863	+	153.644i	0.0816428	+	0.179490i
$857$	−1071.30			−1.25006			−0.625032	−	0.780599i	$-0.714914\pi$
$857$	−1071.30			−1.25006			−0.625032	+	0.780599i	$0.714914\pi$
$858$	296.157	+	376.985i	0.345171	+	0.439377i
$859$			446.786i			0.520124i	0.965592	+	0.260062i	$0.0837429\pi$
$859$			446.786i			0.520124i	−0.965592	+	0.260062i	$0.916257\pi$
$860$	49.1851	+	11.9847i	0.0571920	+	0.0139357i
$861$	−30.2587			−0.0351436
$862$	−101.442	+	79.6921i	−0.117682	+	0.0924503i
$863$		−	159.686i		−	0.185036i	−0.995711	−	0.0925181i	$-0.970508\pi$
$863$		−	159.686i		−	0.185036i	0.995711	−	0.0925181i	$-0.0294916\pi$
$864$	−388.866	+	73.9323i	−0.450076	+	0.0855698i
$865$	182.839			0.211374
$866$	−860.668	−	1095.56i	−0.993843	−	1.26508i
$867$		−	114.529i		−	0.132098i
$868$	−4.96012	+	20.3564i	−0.00571443	+	0.0234520i
$869$	1743.66			2.00651
$870$	−31.2006	+	24.5110i	−0.0358627	+	0.0281735i
$871$		−	1396.91i		−	1.60380i
$872$	−1219.29	+	554.607i	−1.39827	+	0.636017i
$873$	−512.626			−0.587200
$874$	−1447.58	−	1842.66i	−1.65627	−	2.10831i
$875$		−	36.5762i		−	0.0418014i
$876$	−128.217	−	31.2418i	−0.146366	−	0.0356642i
$877$	−1625.00			−1.85291			−0.926454	−	0.376408i	$-0.877159\pi$
$877$	−1625.00			−1.85291			−0.926454	+	0.376408i	$0.877159\pi$
$878$	194.334	−	152.667i	0.221337	−	0.173881i
$879$		−	19.2333i		−	0.0218809i
$880$	−84.2818	+	162.678i	−0.0957748	+	0.184862i
$881$	−715.298			−0.811916			−0.405958	−	0.913892i	$-0.633062\pi$
$881$	−715.298			−0.811916			−0.405958	+	0.913892i	$0.633062\pi$
$882$	−505.325	−	643.240i	−0.572931	−	0.729297i
$883$			862.600i			0.976897i	0.872593	+	0.488448i	$0.162437\pi$
$883$			862.600i			0.976897i	−0.872593	+	0.488448i	$0.837563\pi$
$884$	−248.802	+	1021.08i	−0.281450	+	1.15507i
$885$	−43.0440			−0.0486373
$886$	331.323	−	260.285i	0.373954	−	0.293776i
$887$		−	1280.02i		−	1.44309i	−0.692369	−	0.721544i	$-0.743433\pi$
$887$		−	1280.02i		−	1.44309i	0.692369	−	0.721544i	$-0.256567\pi$
$888$	−27.8854	−	61.3055i	−0.0314024	−	0.0690377i
$889$	40.6254			0.0456979
$890$	−91.8734	−	116.948i	−0.103229	−	0.131402i
$891$			985.493i			1.10605i
$892$	−803.769	−	195.850i	−0.901087	−	0.219563i
$893$	426.394			0.477485
$894$	22.9934	−	18.0634i	0.0257196	−	0.0202052i
$895$			187.473i			0.209467i
$896$	−6.15387	+	120.261i	−0.00686816	+	0.134220i
$897$	−582.796			−0.649717
$898$	−92.6289	−	117.909i	−0.103150	−	0.131302i
$899$			198.479i			0.220777i
$900$	196.247	−	805.398i	0.218052	−	0.894886i
$901$	−934.112			−1.03675
$902$	−1040.84	+	817.680i	−1.15393	+	0.906519i
$903$			10.6889i			0.0118371i
$904$	−544.663	+	247.745i	−0.602503	+	0.274054i
$905$	101.726			0.112404
$906$	−2.19397	−	2.79276i	−0.00242160	−	0.00308251i
$907$			523.993i			0.577721i	0.957371	+	0.288860i	$0.0932764\pi$
$907$			523.993i			0.577721i	−0.957371	+	0.288860i	$0.906724\pi$
$908$	−928.489	−	226.240i	−1.02256	−	0.249163i
$909$	1044.88			1.14949
$910$	27.1632	−	21.3392i	0.0298497	−	0.0234497i
$911$			900.255i			0.988205i	0.869404	+	0.494102i	$0.164503\pi$
$911$			900.255i			0.988205i	−0.869404	+	0.494102i	$0.835497\pi$
$912$	−332.712	−	172.375i	−0.364816	−	0.189007i
$913$	1334.22			1.46136
$914$	149.268	+	190.007i	0.163313	+	0.207885i
$915$			4.40551i			0.00481476i
$916$	−5.08801	+	20.8812i	−0.00555460	+	0.0227961i
$917$	−61.9350			−0.0675409
$918$	219.210	−	172.210i	0.238790	−	0.187592i
$919$			1498.60i			1.63068i	0.578981	+	0.815341i	$0.303451\pi$
$919$			1498.60i			1.63068i	−0.578981	+	0.815341i	$0.696549\pi$
$920$	−92.2187	−	202.741i	−0.100238	−	0.220371i
$921$	348.266			0.378139
$922$	551.086	+	701.490i	0.597707	+	0.760835i
$923$			1475.86i			1.59898i
$924$	−37.5846	−	9.15802i	−0.0406759	−	0.00991128i
$925$	290.380			0.313925
$926$	−425.774	+	334.485i	−0.459799	+	0.361215i
$927$			229.985i			0.248096i
$928$	213.063	+	1120.66i	0.229594	+	1.20760i
$929$	−13.6633			−0.0147076			−0.00735379	−	0.999973i	$-0.502341\pi$
$929$	−13.6633			−0.0147076			−0.00735379	+	0.999973i	$0.502341\pi$
$930$	−3.82832	−	4.87315i	−0.00411647	−	0.00523995i
$931$		−	1594.22i		−	1.71237i
$932$	−104.937	+	430.661i	−0.112593	+	0.462083i
$933$	237.081			0.254106
$934$	1069.54	−	840.224i	1.14512	−	0.899598i
$935$		−	129.029i		−	0.137999i
$936$	1443.36	−	656.526i	1.54205	−	0.701416i
$937$	1312.98			1.40126			0.700628	−	0.713527i	$-0.252903\pi$
$937$	1312.98			1.40126			0.700628	+	0.713527i	$0.252903\pi$
$938$	69.6345	+	88.6393i	0.0742372	+	0.0944982i
$939$		−	152.897i		−	0.162829i
$940$	39.3770	+	9.59477i	0.0418904	+	0.0102072i
$941$	−220.470			−0.234294			−0.117147	−	0.993115i	$-0.537375\pi$
$941$	−220.470			−0.234294			−0.117147	+	0.993115i	$0.537375\pi$
$942$	95.6388	−	75.1332i	0.101527	−	0.0797593i
$943$		−	1609.08i		−	1.70634i
$944$	−569.287	+	1098.82i	−0.603058	+	1.16400i
$945$	−9.16235			−0.00969561
$946$	288.845	+	367.677i	0.305333	+	0.388665i
$947$		−	813.849i		−	0.859397i	−0.902972	−	0.429698i	$-0.858620\pi$
$947$		−	813.849i		−	0.859397i	0.902972	−	0.429698i	$-0.141380\pi$
$948$	−80.2460	+	329.330i	−0.0846476	+	0.347394i
$949$	1088.37			1.14686
$950$	1270.45	−	998.055i	1.33731	−	1.05058i
$951$		−	105.767i		−	0.111217i
$952$	−35.1125	−	77.1941i	−0.0368828	−	0.0810862i
$953$	−684.578			−0.718340			−0.359170	−	0.933272i	$-0.616940\pi$
$953$	−684.578			−0.718340			−0.359170	+	0.933272i	$0.616940\pi$
$954$	870.652	+	1108.27i	0.912633	+	1.16171i
$955$		−	209.303i		−	0.219165i
$956$	1440.88	+	351.091i	1.50720	+	0.367250i
$957$	−366.457			−0.382923
$958$	−1018.17	+	799.867i	−1.06281	+	0.834934i
$959$			39.3850i			0.0410689i
$960$	−26.8468	−	23.4053i	−0.0279654	−	0.0243805i
$961$	−31.0000			−0.0322581
$962$	343.134	+	436.783i	0.356688	+	0.454037i
$963$			179.349i			0.186240i
$964$	264.652	−	1086.13i	0.274536	−	1.12670i
$965$	153.928			0.159511
$966$	36.9806	−	29.0517i	0.0382822	−	0.0300743i
$967$		−	397.830i		−	0.411406i	−0.978614	−	0.205703i	$-0.934052\pi$
$967$		−	397.830i		−	0.411406i	0.978614	−	0.205703i	$-0.0659481\pi$
$968$	−659.188	+	299.838i	−0.680979	+	0.309750i
$969$	263.891			0.272334
$970$	−58.6645	−	74.6754i	−0.0604789	−	0.0769850i
$971$			711.961i			0.733224i	0.930374	+	0.366612i	$0.119482\pi$
$971$			711.961i			0.733224i	−0.930374	+	0.366612i	$0.880518\pi$
$972$	−618.785	−	150.776i	−0.636610	−	0.155119i
$973$	−46.8307			−0.0481303
$974$	−440.989	+	346.438i	−0.452761	+	0.355686i
$975$		−	401.817i		−	0.412120i
$976$	112.463	+	58.2659i	0.115229	+	0.0596986i
$977$	−544.066			−0.556874			−0.278437	−	0.960455i	$-0.589816\pi$
$977$	−544.066			−0.556874			−0.278437	+	0.960455i	$0.589816\pi$
$978$	−10.3712	−	13.2017i	−0.0106045	−	0.0134987i
$979$		−	1373.58i		−	1.40304i
$980$	35.8732	−	147.224i	0.0366054	−	0.150229i
$981$	−1423.29			−1.45085
$982$	627.266	−	492.776i	0.638764	−	0.501809i
$983$			613.146i			0.623750i	0.950123	+	0.311875i	$0.100957\pi$
$983$			613.146i			0.623750i	−0.950123	+	0.311875i	$0.899043\pi$
$984$	−106.536	−	234.218i	−0.108269	−	0.238027i
$985$	−87.0337			−0.0883591
$986$	−496.285	−	631.732i	−0.503331	−	0.640702i
$987$			8.55737i			0.00867008i
$988$	3002.50	+	731.603i	3.03897	+	0.740489i
$989$	−568.407			−0.574729
$990$	−153.085	+	120.263i	−0.154632	+	0.121478i
$991$			1167.30i			1.17790i	0.808170	+	0.588949i	$0.200458\pi$
$991$			1167.30i			1.17790i	−0.808170	+	0.588949i	$0.799542\pi$
$992$	−175.033	+	33.2778i	−0.176445	+	0.0335462i
$993$	414.774			0.417698
$994$	−73.5698	−	93.6487i	−0.0740139	−	0.0942140i
$995$		−	195.353i		−	0.196334i
$996$	−61.4032	+	251.999i	−0.0616498	+	0.253011i
$997$	583.247			0.585002			0.292501	−	0.956265i	$-0.405513\pi$
$997$	583.247			0.585002			0.292501	+	0.956265i	$0.405513\pi$
$998$	787.783	−	618.878i	0.789362	−	0.620118i
$999$		−	147.330i		−	0.147478i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.3.b.a.63.9	✓	30
4.3	odd	2	inner	124.3.b.a.63.10	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.3.b.a.63.9	✓	30	1.1	even	1	trivial
124.3.b.a.63.10	yes	30	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.23553 - 1.57273i) q^{2} +0.706826i q^{3} +(-0.946952 + 3.88629i) q^{4} -0.787341 q^{5} +(1.11164 - 0.873301i) q^{6} -0.940771i q^{7} +(7.28207 - 3.31232i) q^{8} +8.50040 q^{9} +O(q^{10})\)	\(q+(-1.23553 - 1.57273i) q^{2} +0.706826i q^{3} +(-0.946952 + 3.88629i) q^{4} -0.787341 q^{5} +(1.11164 - 0.873301i) q^{6} -0.940771i q^{7} +(7.28207 - 3.31232i) q^{8} +8.50040 q^{9} +(0.972780 + 1.23827i) q^{10} +14.5438i q^{11} +(-2.74693 - 0.669330i) q^{12} +23.3174 q^{13} +(-1.47958 + 1.16235i) q^{14} -0.556513i q^{15} +(-14.2066 - 7.36027i) q^{16} +11.2680 q^{17} +(-10.5025 - 13.3688i) q^{18} -33.1335i q^{19} +(0.745574 - 3.05984i) q^{20} +0.664961 q^{21} +(22.8734 - 17.9692i) q^{22} +35.3610i q^{23} +(2.34123 + 5.14715i) q^{24} -24.3801 q^{25} +(-28.8093 - 36.6720i) q^{26} +12.3697i q^{27} +(3.65611 + 0.890865i) q^{28} +35.6479 q^{29} +(-0.875243 + 0.687586i) q^{30} +5.56776i q^{31} +(5.97687 + 31.4369i) q^{32} -10.2799 q^{33} +(-13.9219 - 17.7215i) q^{34} +0.740707i q^{35} +(-8.04947 + 33.0350i) q^{36} -11.9106 q^{37} +(-52.1100 + 40.9373i) q^{38} +16.4813i q^{39} +(-5.73347 + 2.60792i) q^{40} -45.5044 q^{41} +(-0.821576 - 1.04580i) q^{42} +16.0744i q^{43} +(-56.5215 - 13.7723i) q^{44} -6.69271 q^{45} +(55.6132 - 43.6894i) q^{46} +12.8690i q^{47} +(5.20242 - 10.0416i) q^{48} +48.1150 q^{49} +(30.1222 + 38.3433i) q^{50} +7.96449i q^{51} +(-22.0805 + 90.6183i) q^{52} -82.8998 q^{53} +(19.4542 - 15.2831i) q^{54} -11.4509i q^{55} +(-3.11613 - 6.85076i) q^{56} +23.4196 q^{57} +(-44.0439 - 56.0644i) q^{58} -77.3460i q^{59} +(2.16277 + 0.526991i) q^{60} -7.91627 q^{61} +(8.75658 - 6.87912i) q^{62} -7.99693i q^{63} +(42.0571 - 48.2411i) q^{64} -18.3587 q^{65} +(12.7011 + 16.1675i) q^{66} -59.9086i q^{67} +(-10.6702 + 43.7906i) q^{68} -24.9940 q^{69} +(1.16493 - 0.915163i) q^{70} +63.2942i q^{71} +(61.9005 - 28.1560i) q^{72} +46.6763 q^{73} +(14.7158 + 18.7321i) q^{74} -17.2325i q^{75} +(128.767 + 31.3758i) q^{76} +13.6824 q^{77} +(25.9207 - 20.3631i) q^{78} -119.890i q^{79} +(11.1854 + 5.79504i) q^{80} +67.7603 q^{81} +(56.2219 + 71.5661i) q^{82} -91.7383i q^{83} +(-0.629686 + 2.58423i) q^{84} -8.87173 q^{85} +(25.2807 - 19.8604i) q^{86} +25.1968i q^{87} +(48.1737 + 105.909i) q^{88} -94.4442 q^{89} +(8.26902 + 10.5258i) q^{90} -21.9363i q^{91} +(-137.423 - 33.4851i) q^{92} -3.93544 q^{93} +(20.2394 - 15.9000i) q^{94} +26.0874i q^{95} +(-22.2204 + 4.22461i) q^{96} -60.3061 q^{97} +(-59.4473 - 75.6718i) q^{98} +123.628i 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

Introduction

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