LMFDB - Embedded newform 507.2.q.b.16.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(16,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("507.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.q (of order $39$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$16$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			16.14
Character	$\chi$	$=$	507.16
Dual form			507.2.q.b.412.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.08178 + 0.168058i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(2.33145 + 0.378897i) q^{4} +(-3.16521 - 2.80413i) q^{5} +(-1.66968 - 1.25468i) q^{6} +(1.01537 - 1.05711i) q^{7} +(0.734161 + 0.180955i) q^{8} +(0.428693 + 0.903450i) q^{9} +(-6.11801 - 6.36952i) q^{10} +(-0.519908 + 1.09568i) q^{11} +(-1.76801 - 1.56632i) q^{12} +(-3.43723 - 1.08878i) q^{13} +(2.29143 - 2.03003i) q^{14} +(1.17649 + 4.06173i) q^{15} +(-2.98301 - 0.995875i) q^{16} +(4.82875 - 5.02726i) q^{17} +(0.740610 + 1.95283i) q^{18} +(1.79041 - 3.10107i) q^{19} +(-6.31706 - 7.73699i) q^{20} +(-1.42317 + 0.350780i) q^{21} +(-1.26647 + 2.19359i) q^{22} +(-2.81335 - 4.87286i) q^{23} +(-0.523792 - 0.545325i) q^{24} +(1.55272 + 12.7878i) q^{25} +(-6.97257 - 2.84425i) q^{26} +(0.120537 - 0.992709i) q^{27} +(2.76782 - 2.07988i) q^{28} +(4.41714 + 0.356589i) q^{29} +(1.76659 + 8.65332i) q^{30} +(-1.10143 + 9.07108i) q^{31} +(-7.43385 - 3.16727i) q^{32} +(1.02503 - 0.648187i) q^{33} +(10.8973 - 9.65413i) q^{34} +(-6.17815 + 0.498752i) q^{35} +(0.657160 + 2.26878i) q^{36} +(4.75529 - 2.02604i) q^{37} +(4.24839 - 6.15485i) q^{38} +(2.32320 + 2.75731i) q^{39} +(-1.81636 - 2.63145i) q^{40} +(6.71701 + 4.24758i) q^{41} +(-3.02168 + 0.491070i) q^{42} +(-0.0577265 - 0.0245950i) q^{43} +(-1.62729 + 2.35754i) q^{44} +(1.17649 - 4.06173i) q^{45} +(-5.03784 - 10.6170i) q^{46} +(3.45521 - 9.11065i) q^{47} +(1.98895 + 2.43602i) q^{48} +(0.195352 + 4.84760i) q^{49} +(1.08332 + 26.8823i) q^{50} +(-6.76812 + 1.66819i) q^{51} +(-7.60120 - 3.84079i) q^{52} +(-1.88835 - 0.465437i) q^{53} +(0.417763 - 2.04634i) q^{54} +(4.71806 - 2.01018i) q^{55} +(0.936735 - 0.592355i) q^{56} +(-3.17065 + 1.66409i) q^{57} +(9.13558 + 1.48468i) q^{58} +(8.63269 - 2.88202i) q^{59} +(1.20396 + 9.91548i) q^{60} +(1.17043 - 4.04079i) q^{61} +(-3.81740 + 18.6989i) q^{62} +(1.39033 + 0.464160i) q^{63} +(-9.37406 - 4.91989i) q^{64} +(7.82649 + 13.0847i) q^{65} +(2.24281 - 1.17712i) q^{66} +(0.970272 - 0.157684i) q^{67} +(13.1628 - 9.89121i) q^{68} +(-0.226564 + 5.62213i) q^{69} -12.9453 q^{70} +(-0.209870 + 5.20786i) q^{71} +(0.151246 + 0.740852i) q^{72} +(2.98331 + 4.32208i) q^{73} +(10.2400 - 3.41860i) q^{74} +(5.52231 - 11.6380i) q^{75} +(5.34923 - 6.55162i) q^{76} +(0.630360 + 1.66212i) q^{77} +(4.37299 + 6.13053i) q^{78} +(-2.05439 + 5.41697i) q^{79} +(6.64929 + 11.5169i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(13.2695 + 9.97136i) q^{82} +(-11.9731 - 6.28398i) q^{83} +(-3.45096 + 0.278590i) q^{84} +(-29.3812 + 2.37189i) q^{85} +(-0.116040 - 0.0609027i) q^{86} +(-3.54274 - 2.66220i) q^{87} +(-0.579965 + 0.710328i) q^{88} +(-8.42108 - 14.5857i) q^{89} +(3.13180 - 8.25789i) q^{90} +(-4.64102 + 2.52803i) q^{91} +(-4.71286 - 12.4268i) q^{92} +(5.77910 - 7.07811i) q^{93} +(8.72410 - 18.3857i) q^{94} +(-14.3628 + 4.79502i) q^{95} +(4.59022 + 6.65008i) q^{96} +(-2.07636 - 10.1707i) q^{97} +(-0.408002 + 10.1245i) q^{98} -1.21277 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19}+ \cdots - 18 q^{99}+O(q^{100}) $ 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{39}\right)$

Coefficient data

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

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

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

$2$	2.08178	+	0.168058i	1.47204	+	0.118835i	0.790282	−	0.612744i	$-0.209934\pi$
$2$	2.08178	+	0.168058i	1.47204	+	0.118835i	0.681757	+	0.731579i	$0.261216\pi$
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$4$	2.33145	+	0.378897i	1.16572	+	0.189449i
$5$	−3.16521	−	2.80413i	−1.41553	−	1.25405i	−0.923571	−	0.383427i	$-0.874744\pi$
$5$	−3.16521	−	2.80413i	−1.41553	−	1.25405i	−0.491955	−	0.870620i	$-0.663718\pi$
$6$	−1.66968	−	1.25468i	−0.681642	−	0.512221i
$7$	1.01537	−	1.05711i	0.383774	−	0.399551i	−0.501094	−	0.865393i	$-0.667069\pi$
$7$	1.01537	−	1.05711i	0.383774	−	0.399551i	0.884868	+	0.465842i	$0.154248\pi$
$8$	0.734161	+	0.180955i	0.259565	+	0.0639771i
$9$	0.428693	+	0.903450i	0.142898	+	0.301150i
$10$	−6.11801	−	6.36952i	−1.93468	−	2.01422i
$11$	−0.519908	+	1.09568i	−0.156758	+	0.330361i	−0.966601	−	0.256286i	$-0.917501\pi$
$11$	−0.519908	+	1.09568i	−0.156758	+	0.330361i	0.809843	+	0.586647i	$0.199552\pi$
$12$	−1.76801	−	1.56632i	−0.510381	−	0.452158i
$13$	−3.43723	−	1.08878i	−0.953316	−	0.301973i
$13$	−3.43723	−	1.08878i	−0.953316	−	0.301973i
$14$	2.29143	−	2.03003i	0.612411	−	0.542548i
$15$	1.17649	+	4.06173i	0.303769	+	1.04873i
$16$	−2.98301	−	0.995875i	−0.745752	−	0.248969i
$17$	4.82875	−	5.02726i	1.17114	−	1.21929i	0.200260	−	0.979743i	$-0.435821\pi$
$17$	4.82875	−	5.02726i	1.17114	−	1.21929i	0.970884	−	0.239548i	$-0.0769993\pi$
$18$	0.740610	+	1.95283i	0.174563	+	0.460286i
$19$	1.79041	−	3.10107i	0.410747	−	0.711435i	−0.584224	−	0.811592i	$-0.698601\pi$
$19$	1.79041	−	3.10107i	0.410747	−	0.711435i	0.994972	+	0.100157i	$0.0319346\pi$
$20$	−6.31706	−	7.73699i	−1.41254	−	1.73004i
$21$	−1.42317	+	0.350780i	−0.310561	+	0.0765465i
$22$	−1.26647	+	2.19359i	−0.270012	+	0.467675i
$23$	−2.81335	−	4.87286i	−0.586623	−	1.01606i	−0.994671	−	0.103101i	$-0.967124\pi$
$23$	−2.81335	−	4.87286i	−0.586623	−	1.01606i	0.408047	−	0.912961i	$-0.366210\pi$
$24$	−0.523792	−	0.545325i	−0.106919	−	0.111314i
$25$	1.55272	+	12.7878i	0.310545	+	2.55757i
$26$	−6.97257	−	2.84425i	−1.36743	−	0.557804i
$27$	0.120537	−	0.992709i	0.0231973	−	0.191047i
$28$	2.76782	−	2.07988i	0.523069	−	0.393061i
$29$	4.41714	+	0.356589i	0.820243	+	0.0662169i	0.483461	−	0.875366i	$-0.339379\pi$
$29$	4.41714	+	0.356589i	0.820243	+	0.0662169i	0.336782	+	0.941583i	$0.390661\pi$
$30$	1.76659	+	8.65332i	0.322534	+	1.57987i
$31$	−1.10143	+	9.07108i	−0.197822	+	1.62921i	0.468439	+	0.883496i	$0.344817\pi$
$31$	−1.10143	+	9.07108i	−0.197822	+	1.62921i	−0.666261	+	0.745719i	$0.732106\pi$
$32$	−7.43385	−	3.16727i	−1.31413	−	0.559899i
$33$	1.02503	−	0.648187i	0.178434	−	0.112835i
$34$	10.8973	−	9.65413i	1.86886	−	1.65567i
$35$	−6.17815	+	0.498752i	−1.04430	+	0.0843044i
$36$	0.657160	+	2.26878i	0.109527	+	0.378130i
$37$	4.75529	−	2.02604i	0.781765	−	0.333079i	0.0360554	−	0.999350i	$-0.488521\pi$
$37$	4.75529	−	2.02604i	0.781765	−	0.333079i	0.745710	+	0.666271i	$0.232110\pi$
$38$	4.24839	−	6.15485i	0.689179	−	0.998448i
$39$	2.32320	+	2.75731i	0.372009	+	0.441523i
$40$	−1.81636	−	2.63145i	−0.287191	−	0.416068i
$41$	6.71701	+	4.24758i	1.04902	+	0.663360i	0.943607	−	0.331068i	$-0.107409\pi$
$41$	6.71701	+	4.24758i	1.04902	+	0.663360i	0.105413	+	0.994428i	$0.466383\pi$
$42$	−3.02168	+	0.491070i	−0.466255	+	0.0757738i
$43$	−0.0577265	−	0.0245950i	−0.00880321	−	0.00375070i	0.387561	−	0.921844i	$-0.373318\pi$
$43$	−0.0577265	−	0.0245950i	−0.00880321	−	0.00375070i	−0.396364	+	0.918094i	$0.629728\pi$
$44$	−1.62729	+	2.35754i	−0.245323	+	0.355412i
$45$	1.17649	−	4.06173i	0.175381	−	0.605486i
$46$	−5.03784	−	10.6170i	−0.742788	−	1.56539i
$47$	3.45521	−	9.11065i	0.503995	−	1.32892i	−0.405836	−	0.913946i	$-0.633020\pi$
$47$	3.45521	−	9.11065i	0.503995	−	1.32892i	0.909831	−	0.414979i	$-0.136211\pi$
$48$	1.98895	+	2.43602i	0.287080	+	0.351609i
$49$	0.195352	+	4.84760i	0.0279074	+	0.692515i
$50$	1.08332	+	26.8823i	0.153205	+	3.80174i
$51$	−6.76812	+	1.66819i	−0.947726	+	0.233593i
$52$	−7.60120	−	3.84079i	−1.05410	−	0.532622i
$53$	−1.88835	−	0.465437i	−0.259385	−	0.0639327i	0.107478	−	0.994207i	$-0.465722\pi$
$53$	−1.88835	−	0.465437i	−0.259385	−	0.0639327i	−0.366864	+	0.930275i	$0.619568\pi$
$54$	0.417763	−	2.04634i	0.0568504	−	0.278472i
$55$	4.71806	−	2.01018i	0.636183	−	0.271052i
$56$	0.936735	−	0.592355i	0.125176	−	0.0791568i
$57$	−3.17065	+	1.66409i	−0.419963	+	0.220414i
$58$	9.13558	+	1.48468i	1.19956	+	0.194948i
$59$	8.63269	−	2.88202i	1.12388	−	0.375206i	0.306825	−	0.951766i	$-0.400733\pi$
$59$	8.63269	−	2.88202i	1.12388	−	0.375206i	0.817055	+	0.576559i	$0.195605\pi$
$60$	1.20396	+	9.91548i	0.155430	+	1.28008i
$61$	1.17043	−	4.04079i	0.149858	−	0.517370i	−0.850099	−	0.526623i	$-0.823458\pi$
$61$	1.17043	−	4.04079i	0.149858	−	0.517370i	0.999957	+	0.00925259i	$0.00294523\pi$
$62$	−3.81740	+	18.6989i	−0.484810	+	2.37476i
$63$	1.39033	+	0.464160i	0.175165	+	0.0584787i
$64$	−9.37406	−	4.91989i	−1.17176	−	0.614986i
$65$	7.82649	+	13.0847i	0.970756	+	1.62295i
$66$	2.24281	−	1.17712i	0.276070	−	0.144893i
$67$	0.970272	−	0.157684i	0.118538	−	0.0192642i	−0.100853	−	0.994901i	$-0.532157\pi$
$67$	0.970272	−	0.157684i	0.118538	−	0.0192642i	0.219391	+	0.975637i	$0.429593\pi$
$68$	13.1628	−	9.89121i	1.59623	−	1.19949i
$69$	−0.226564	+	5.62213i	−0.0272751	+	0.676825i
$70$	−12.9453			−1.54726
$71$	−0.209870	+	5.20786i	−0.0249070	+	0.618060i	0.937746	+	0.347322i	$0.112909\pi$
$71$	−0.209870	+	5.20786i	−0.0249070	+	0.618060i	−0.962653	+	0.270738i	$0.912732\pi$
$72$	0.151246	+	0.740852i	0.0178245	+	0.0873103i
$73$	2.98331	+	4.32208i	0.349171	+	0.505861i	0.957738	−	0.287641i	$-0.0928710\pi$
$73$	2.98331	+	4.32208i	0.349171	+	0.505861i	−0.608568	+	0.793502i	$0.708256\pi$
$74$	10.2400	−	3.41860i	1.19037	−	0.397404i
$75$	5.52231	−	11.6380i	0.637661	−	1.34384i
$76$	5.34923	−	6.55162i	0.613599	−	0.751522i
$77$	0.630360	+	1.66212i	0.0718362	+	0.189417i
$78$	4.37299	+	6.13053i	0.495144	+	0.694146i
$79$	−2.05439	+	5.41697i	−0.231136	+	0.609457i	−0.999534	−	0.0305158i	$-0.990285\pi$
$79$	−2.05439	+	5.41697i	−0.231136	+	0.609457i	0.768398	+	0.639972i	$0.221054\pi$
$80$	6.64929	+	11.5169i	0.743414	+	1.28763i
$81$	−0.632445	+	0.774605i	−0.0702717	+	0.0860672i
$82$	13.2695	+	9.97136i	1.46537	+	1.10115i
$83$	−11.9731	−	6.28398i	−1.31422	−	0.689756i	−0.345620	−	0.938375i	$-0.612331\pi$
$83$	−11.9731	−	6.28398i	−1.31422	−	0.689756i	−0.968602	+	0.248618i	$0.920024\pi$
$84$	−3.45096	+	0.278590i	−0.376531	+	0.0303967i
$85$	−29.3812	+	2.37189i	−3.18683	+	0.257268i
$86$	−0.116040	−	0.0609027i	−0.0125130	−	0.00656730i
$87$	−3.54274	−	2.66220i	−0.379822	−	0.285418i
$88$	−0.579965	+	0.710328i	−0.0618244	+	0.0757212i
$89$	−8.42108	−	14.5857i	−0.892632	−	1.54608i	−0.836708	−	0.547650i	$-0.815523\pi$
$89$	−8.42108	−	14.5857i	−0.892632	−	1.54608i	−0.0559249	−	0.998435i	$-0.517811\pi$
$90$	3.13180	−	8.25789i	0.330121	−	0.870458i
$91$	−4.64102	+	2.52803i	−0.486512	+	0.265009i
$92$	−4.71286	−	12.4268i	−0.491350	−	1.29558i
$93$	5.77910	−	7.07811i	0.599265	−	0.733966i
$94$	8.72410	−	18.3857i	0.899823	−	1.89634i
$95$	−14.3628	+	4.79502i	−1.47360	+	0.491959i
$96$	4.59022	+	6.65008i	0.468487	+	0.678721i
$97$	−2.07636	−	10.1707i	−0.210822	−	1.03268i	−0.938108	−	0.346342i	$-0.887424\pi$
$97$	−2.07636	−	10.1707i	−0.210822	−	1.03268i	0.727286	−	0.686335i	$-0.240781\pi$
$98$	−0.408002	+	10.1245i	−0.0412144	+	1.02272i
$99$	−1.21277			−0.121888
$100$	−1.22518	+	30.4025i	−0.122518	+	3.04025i
$101$	5.98932	−	4.50068i	0.595960	−	0.447835i	−0.259472	−	0.965751i	$-0.583548\pi$
$101$	5.98932	−	4.50068i	0.595960	−	0.447835i	0.855431	+	0.517916i	$0.173292\pi$
$102$	−14.3701	+	2.33536i	−1.42285	+	0.231235i
$103$	2.86021	−	1.50115i	0.281824	−	0.147913i	−0.317889	−	0.948128i	$-0.602974\pi$
$103$	2.86021	−	1.50115i	0.281824	−	0.147913i	0.599713	+	0.800215i	$0.295281\pi$
$104$	−2.32646	−	1.42132i	−0.228128	−	0.139372i
$105$	5.48828	+	2.88047i	0.535601	+	0.281105i
$106$	−3.85291	−	1.28629i	−0.374228	−	0.124936i
$107$	−1.63787	+	8.02280i	−0.158339	+	0.775594i	0.820610	+	0.571488i	$0.193634\pi$
$107$	−1.63787	+	8.02280i	−0.158339	+	0.775594i	−0.978949	+	0.204105i	$0.934571\pi$
$108$	0.657160	−	2.26878i	0.0632353	−	0.218313i
$109$	−1.59843	−	13.1642i	−0.153102	−	1.26091i	−0.843363	−	0.537345i	$-0.819427\pi$
$109$	−1.59843	−	13.1642i	−0.153102	−	1.26091i	0.690261	−	0.723560i	$-0.257496\pi$
$110$	10.1598	−	3.39183i	0.968696	−	0.323398i
$111$	−5.10198	−	0.829152i	−0.484258	−	0.0786996i
$112$	−4.08161	+	2.14219i	−0.385676	+	0.202418i
$113$	−8.48958	+	5.36849i	−0.798633	+	0.505025i	−0.870370	−	0.492399i	$-0.836120\pi$
$113$	−8.48958	+	5.36849i	−0.798633	+	0.505025i	0.0717371	+	0.997424i	$0.477146\pi$
$114$	−6.88025	+	2.93140i	−0.644394	+	0.274551i
$115$	−4.75931	+	23.3126i	−0.443808	+	2.17392i
$116$	10.1632	+	2.50501i	0.943633	+	0.232585i
$117$	−0.489857	−	3.57212i	−0.0452873	−	0.330243i
$118$	18.4557	−	4.54892i	1.69898	−	0.418762i
$119$	−0.411411	−	10.2091i	−0.0377140	−	0.935864i
$120$	0.128748	+	3.19485i	0.0117530	+	0.291649i
$121$	6.02668	+	7.38135i	0.547880	+	0.671032i
$122$	3.11566	−	8.21532i	0.282079	−	0.743780i
$123$	−3.40696	−	7.18002i	−0.307195	−	0.647401i
$124$	−6.00494	+	20.7314i	−0.539259	+	1.86174i
$125$	18.9333	−	27.4296i	1.69344	−	2.45337i
$126$	2.81635	+	1.19993i	0.250900	+	0.106899i
$127$	14.9779	−	2.43415i	1.32908	−	0.215996i	0.545929	−	0.837832i	$-0.316177\pi$
$127$	14.9779	−	2.43415i	1.32908	−	0.215996i	0.783148	+	0.621836i	$0.213613\pi$
$128$	−5.02885	−	3.18005i	−0.444491	−	0.281079i
$129$	0.0356447	+	0.0516403i	0.00313834	+	0.00454667i
$130$	14.0940	+	28.5547i	1.23613	+	2.50441i
$131$	−2.48411	+	3.59885i	−0.217038	+	0.314433i	−0.916346	−	0.400387i	$-0.868876\pi$
$131$	−2.48411	+	3.59885i	−0.217038	+	0.314433i	0.699309	+	0.714820i	$0.253491\pi$
$132$	2.63539	−	1.12284i	0.229381	−	0.0977303i
$133$	−1.46026	−	5.04140i	−0.126620	−	0.437144i
$134$	2.04639	−	0.165202i	0.176781	−	0.0142712i
$135$	−3.16521	+	2.80413i	−0.272418	+	0.241341i
$136$	4.45479	−	2.81704i	0.381995	−	0.241559i
$137$	−0.179384	−	0.0764282i	−0.0153258	−	0.00652970i	0.384290	−	0.923212i	$-0.374446\pi$
$137$	−0.179384	−	0.0764282i	−0.0153258	−	0.00652970i	−0.399616	+	0.916683i	$0.630856\pi$
$138$	−1.41650	+	11.6659i	−0.120581	+	0.993071i
$139$	1.01744	+	4.98374i	0.0862980	+	0.422716i	0.999871	+	0.0160415i	$0.00510639\pi$
$139$	1.01744	+	4.98374i	0.0862980	+	0.422716i	−0.913573	+	0.406674i	$0.866688\pi$
$140$	−14.5930	−	1.17807i	−1.23334	−	0.0995651i
$141$	−7.78964	+	5.85354i	−0.656006	+	0.492957i
$142$	−1.31213	+	10.8063i	−0.110111	+	0.906848i
$143$	2.98000	−	3.20005i	0.249200	−	0.267601i
$144$	−0.379070	−	3.12192i	−0.0315892	−	0.260160i
$145$	−12.9813	−	13.5149i	−1.07804	−	1.12236i
$146$	5.48423	+	9.49897i	0.453878	+	0.786141i
$147$	2.42577	−	4.20155i	0.200074	−	0.346538i
$148$	11.8544	−	2.92184i	0.974425	−	0.240174i
$149$	−9.33674	−	11.4354i	−0.764896	−	0.936827i	0.234481	−	0.972121i	$-0.424661\pi$
$149$	−9.33674	−	11.4354i	−0.764896	−	0.936827i	−0.999377	+	0.0352932i	$0.988763\pi$
$150$	13.4521	−	23.2997i	1.09836	−	1.90241i
$151$	1.47893	+	3.89962i	0.120354	+	0.317346i	0.981631	−	0.190788i	$-0.0611045\pi$
$151$	1.47893	+	3.89962i	0.120354	+	0.317346i	−0.861278	+	0.508135i	$0.830335\pi$
$152$	1.87560	−	1.95271i	0.152131	−	0.158385i
$153$	6.61194	+	2.20739i	0.534543	+	0.178457i
$154$	1.03294	+	3.56611i	0.0832363	+	0.287365i
$155$	28.9228	−	25.6234i	2.32314	−	2.05812i
$156$	4.37168	+	7.30878i	0.350015	+	0.585171i
$157$	−6.90739	−	6.11941i	−0.551270	−	0.488382i	0.340889	−	0.940103i	$-0.389272\pi$
$157$	−6.90739	−	6.11941i	−0.551270	−	0.488382i	−0.892159	+	0.451721i	$0.850810\pi$
$158$	−5.18714	+	10.9317i	−0.412667	+	0.869676i
$159$	1.34726	+	1.40264i	0.106844	+	0.111237i
$160$	14.6483	+	30.8706i	1.15805	+	2.44053i
$161$	−8.00775	−	1.97373i	−0.631099	−	0.155552i
$162$	−1.44679	+	1.50627i	−0.113670	+	0.118343i
$163$	0.126235	+	0.0948597i	0.00988751	+	0.00742998i	0.605675	−	0.795712i	$-0.292903\pi$
$163$	0.126235	+	0.0948597i	0.00988751	+	0.00742998i	−0.595787	+	0.803142i	$0.703160\pi$
$164$	14.0510	+	12.4481i	1.09720	+	0.972031i
$165$	−5.06203	−	0.822659i	−0.394078	−	0.0640439i
$166$	−23.8693	−	15.0940i	−1.85262	−	1.17152i
$167$	−19.6204	−	1.58392i	−1.51827	−	0.122567i	−0.706989	−	0.707225i	$-0.749947\pi$
$167$	−19.6204	−	1.58392i	−1.51827	−	0.122567i	−0.811280	+	0.584657i	$0.801229\pi$
$168$	−1.10831			−0.0855082
$169$	10.6291	+	7.48477i	0.817624	+	0.575752i
$170$	−61.5636			−4.72172
$171$	3.56920	+	0.288136i	0.272943	+	0.0220343i
$172$	−0.125268	−	0.0792144i	−0.00955156	−	0.00604004i
$173$	7.17703	+	1.16638i	0.545660	+	0.0886783i	0.426991	−	0.904256i	$-0.359573\pi$
$173$	7.17703	+	1.16638i	0.545660	+	0.0886783i	0.118668	+	0.992934i	$0.462138\pi$
$174$	−6.92779	−	6.13749i	−0.525195	−	0.465282i
$175$	15.0948	+	11.3430i	1.14106	+	0.857448i
$176$	2.64205	−	2.75067i	0.199152	−	0.207339i
$177$	−8.83660	−	2.17803i	−0.664200	−	0.163711i
$178$	−15.0795	−	31.7795i	−1.13026	−	2.38197i
$179$	10.9971	+	11.4492i	0.821959	+	0.855750i	0.991545	−	0.129765i	$-0.0414224\pi$
$179$	10.9971	+	11.4492i	0.821959	+	0.855750i	−0.169586	+	0.985515i	$0.554243\pi$
$180$	4.28191	−	9.02394i	0.319155	−	0.672605i
$181$	4.77807	+	4.23300i	0.355151	+	0.314636i	0.821767	−	0.569824i	$-0.192988\pi$
$181$	4.77807	+	4.23300i	0.355151	+	0.314636i	−0.466616	+	0.884460i	$0.654527\pi$
$182$	−10.0864	+	4.48282i	−0.747656	+	0.332289i
$183$	−3.14890	+	2.78968i	−0.232773	+	0.206219i
$184$	−1.18368	−	4.08655i	−0.0872624	−	0.301265i
$185$	−20.7328	−	6.92163i	−1.52431	−	0.508888i
$186$	13.2203	−	13.7638i	0.969362	−	1.00921i
$187$	2.99778	+	7.90449i	0.219219	+	0.578034i
$188$	11.5077	−	19.9319i	0.839282	−	1.45368i
$189$	−0.927015	−	1.13539i	−0.0674304	−	0.0825873i
$190$	−30.7061	+	7.56837i	−2.22765	+	0.549067i
$191$	7.00663	−	12.1358i	0.506982	−	0.878118i	−0.492985	−	0.870038i	$-0.664094\pi$
$191$	7.00663	−	12.1358i	0.506982	−	0.878118i	0.999967	−	0.00808090i	$-0.00257226\pi$
$192$	5.29335	+	9.16836i	0.382015	+	0.661669i
$193$	0.357522	+	0.372220i	0.0257350	+	0.0267930i	0.733946	−	0.679208i	$-0.237677\pi$
$193$	0.357522	+	0.372220i	0.0257350	+	0.0267930i	−0.708211	+	0.706001i	$0.750497\pi$
$194$	−2.61325	−	21.5220i	−0.187620	−	1.54519i
$195$	0.378445	−	15.2420i	0.0271010	−	1.09150i
$196$	−1.38129	+	11.3760i	−0.0986637	+	0.812569i
$197$	11.2021	−	8.41785i	0.798118	−	0.599747i	−0.121486	−	0.992593i	$-0.538766\pi$
$197$	11.2021	−	8.41785i	0.798118	−	0.599747i	0.919604	+	0.392846i	$0.128509\pi$
$198$	−2.52473	−	0.203817i	−0.179424	−	0.0144846i
$199$	3.29067	+	16.1187i	0.233269	+	1.14263i	0.912618	+	0.408812i	$0.134057\pi$
$199$	3.29067	+	16.1187i	0.233269	+	1.14263i	−0.679349	+	0.733815i	$0.737738\pi$
$200$	−1.17407	+	9.66930i	−0.0830190	+	0.683723i
$201$	−0.904341	−	0.385304i	−0.0637873	−	0.0271772i
$202$	13.2248	−	8.36286i	0.930494	−	0.588409i
$203$	4.86199	−	4.30735i	0.341245	−	0.302317i
$204$	−16.4116	+	1.32488i	−1.14904	+	0.0927602i
$205$	−9.34998	−	32.2799i	−0.653031	−	2.25452i
$206$	6.20659	−	2.64438i	0.432434	−	0.184243i
$207$	3.19633	−	4.63068i	0.222160	−	0.321854i
$208$	9.16900	+	6.67089i	0.635756	+	0.462543i
$209$	2.46694	+	3.57399i	0.170642	+	0.247218i
$210$	10.9413	+	6.91884i	0.755020	+	0.477446i
$211$	−19.3413	+	3.14327i	−1.33151	+	0.216392i	−0.784185	−	0.620527i	$-0.786919\pi$
$211$	−19.3413	+	3.14327i	−1.33151	+	0.216392i	−0.547327	+	0.836919i	$0.684355\pi$
$212$	−4.22625	−	1.80064i	−0.290260	−	0.123668i
$213$	2.96081	−	4.28947i	0.202871	−	0.293909i
$214$	−4.75797	+	16.4264i	−0.325248	+	1.12289i
$215$	0.113749	+	0.239721i	0.00775763	+	0.0163489i
$216$	0.268129	−	0.706997i	0.0182438	−	0.0481050i
$217$	8.47080	+	10.3748i	0.575035	+	0.704290i
$218$	−1.11521	−	27.6736i	−0.0755315	−	1.87429i
$219$	−0.211465	−	5.24746i	−0.0142895	−	0.354590i
$220$	11.7616	−	2.89897i	0.792965	−	0.195448i
$221$	−22.0711	+	12.0224i	−1.48466	+	0.808716i
$222$	−10.4818	−	2.58354i	−0.703494	−	0.173396i
$223$	−2.13768	+	10.4710i	−0.143150	+	0.701193i	0.843342	+	0.537378i	$0.180585\pi$
$223$	−2.13768	+	10.4710i	−0.143150	+	0.701193i	−0.986491	+	0.163815i	$0.947620\pi$
$224$	−10.8963	+	4.64246i	−0.728037	+	0.310188i
$225$	−10.8875	+	6.88485i	−0.725835	+	0.458990i
$226$	−18.5756	+	9.74924i	−1.23563	+	0.648510i
$227$	16.5703	+	2.69293i	1.09981	+	0.178736i	0.683115	−	0.730311i	$-0.260625\pi$
$227$	16.5703	+	2.69293i	1.09981	+	0.178736i	0.416693	+	0.909047i	$0.363189\pi$
$228$	−8.02273	+	2.67838i	−0.531318	+	0.177380i
$229$	−2.82098	−	23.2329i	−0.186416	−	1.53527i	−0.722656	−	0.691208i	$-0.757079\pi$
$229$	−2.82098	−	23.2329i	−0.186416	−	1.53527i	0.536240	−	0.844065i	$-0.319844\pi$
$230$	−13.8257	+	47.7319i	−0.911640	+	3.14735i
$231$	0.355574	−	1.74172i	0.0233950	−	0.114597i
$232$	3.17837	+	1.06110i	0.208670	+	0.0696644i
$233$	16.9947	+	8.91949i	1.11336	+	0.584335i	0.918073	−	0.396412i	$-0.129745\pi$
$233$	16.9947	+	8.91949i	1.11336	+	0.584335i	0.195284	+	0.980747i	$0.437437\pi$
$234$	−0.419448	−	7.51868i	−0.0274202	−	0.491511i
$235$	−36.4840	+	19.1483i	−2.37995	+	1.24910i
$236$	21.2187	−	3.44837i	1.38122	−	0.224470i
$237$	4.63153	−	3.48037i	0.300850	−	0.226074i
$238$	0.859253	−	21.3221i	0.0556971	−	1.38211i
$239$	11.6734			0.755088			0.377544	−	0.925992i	$-0.376769\pi$
$239$	11.6734			0.755088			0.377544	+	0.925992i	$0.376769\pi$
$240$	0.535480	−	13.2878i	0.0345651	−	0.857724i
$241$	2.14827	+	10.5229i	0.138383	+	0.677843i	0.988496	+	0.151244i	$0.0483278\pi$
$241$	2.14827	+	10.5229i	0.138383	+	0.677843i	−0.850114	+	0.526599i	$0.823467\pi$
$242$	11.3057	+	16.3792i	0.726759	+	1.05289i
$243$	0.948536	−	0.316668i	0.0608486	−	0.0203143i
$244$	4.25984	−	8.97743i	0.272708	−	0.574721i
$245$	12.9750	−	15.8915i	0.828942	−	1.01527i
$246$	−5.88587	−	15.5198i	−0.375269	−	0.989504i
$247$	−9.53042	+	8.70975i	−0.606406	+	0.554188i
$248$	−2.45008	+	6.46033i	−0.155580	+	0.410231i
$249$	6.76099	+	11.7104i	0.428461	+	0.742115i
$250$	44.0246	−	53.9203i	2.78436	−	3.41022i
$251$	2.82371	+	2.12188i	0.178231	+	0.133932i	0.686114	−	0.727494i	$-0.259315\pi$
$251$	2.82371	+	2.12188i	0.178231	+	0.133932i	−0.507883	+	0.861426i	$0.669572\pi$
$252$	3.06562	+	1.60896i	0.193116	+	0.101355i
$253$	6.80179	−	0.549097i	0.427625	−	0.0345214i
$254$	31.5898	−	2.55019i	1.98212	−	0.160013i
$255$	26.1004	+	13.6985i	1.63447	+	0.857835i
$256$	6.99243	+	5.25447i	0.437027	+	0.328404i
$257$	−8.73122	+	10.6938i	−0.544639	+	0.667061i	−0.971440	−	0.237284i	$-0.923743\pi$
$257$	−8.73122	+	10.6938i	−0.544639	+	0.667061i	0.426802	+	0.904345i	$0.359640\pi$
$258$	0.0655258	+	0.113494i	0.00407946	+	0.00706582i
$259$	2.68663	−	7.08406i	0.166939	−	0.440182i
$260$	13.2893	+	33.4717i	0.824168	+	2.07583i
$261$	1.57144	+	4.14354i	0.0972695	+	0.256479i
$262$	−5.77618	+	7.07453i	−0.356853	+	0.437066i
$263$	−8.70089	+	18.3367i	−0.536520	+	1.13069i	0.436443	+	0.899732i	$0.356238\pi$
$263$	−8.70089	+	18.3367i	−0.536520	+	1.13069i	−0.972963	+	0.230960i	$0.925813\pi$
$264$	0.869826	−	0.290391i	0.0535341	−	0.0178723i
$265$	4.67189	+	6.76840i	0.286992	+	0.415780i
$266$	−2.19268	−	10.7405i	−0.134442	−	0.658540i
$267$	−0.678165	+	16.8285i	−0.0415030	+	1.02989i
$268$	2.32189			0.141832
$269$	−0.783734	+	19.4482i	−0.0477851	+	1.18578i	0.780385	+	0.625299i	$0.215023\pi$
$269$	−0.783734	+	19.4482i	−0.0477851	+	1.18578i	−0.828171	+	0.560476i	$0.810618\pi$
$270$	−7.06053	+	5.30564i	−0.429690	+	0.322891i
$271$	6.08503	−	0.988913i	0.369639	−	0.0600722i	0.0272454	−	0.999629i	$-0.491326\pi$
$271$	6.08503	−	0.988913i	0.369639	−	0.0600722i	0.342394	+	0.939557i	$0.388762\pi$
$272$	−19.4107	+	10.1875i	−1.17695	+	0.617710i
$273$	5.27369	+	0.343807i	0.319178	+	0.0208082i
$274$	−0.360592	−	0.189253i	−0.0217842	−	0.0114332i
$275$	−14.8187	−	4.94720i	−0.893599	−	0.298327i
$276$	−2.65843	+	13.0219i	−0.160019	+	0.783825i
$277$	1.34628	−	4.64791i	0.0808903	−	0.279266i	−0.909869	−	0.414895i	$-0.863818\pi$
$277$	1.34628	−	4.64791i	0.0808903	−	0.279266i	0.990760	+	0.135629i	$0.0433055\pi$
$278$	1.28052	+	10.5460i	0.0768005	+	0.632509i
$279$	−8.66745	+	2.89362i	−0.518907	+	0.173236i
$280$	−4.62601	−	0.751800i	−0.276457	−	0.0449286i
$281$	16.4602	−	8.63897i	0.981932	−	0.515358i	0.104224	−	0.994554i	$-0.466764\pi$
$281$	16.4602	−	8.63897i	0.981932	−	0.515358i	0.877708	+	0.479196i	$0.159072\pi$
$282$	−17.2000	+	10.8766i	−1.02425	+	0.647695i
$283$	17.6561	−	7.52255i	1.04955	−	0.447169i	0.202829	−	0.979214i	$-0.434986\pi$
$283$	17.6561	−	7.52255i	1.04955	−	0.447169i	0.846716	+	0.532045i	$0.178576\pi$
$284$	−2.46255	+	12.0624i	−0.146125	+	0.715769i
$285$	14.7021	+	3.62374i	0.870878	+	0.214652i
$286$	6.74149	−	6.16097i	0.398632	−	0.364306i
$287$	11.3104	−	2.78777i	0.667633	−	0.164557i
$288$	−0.325367	−	8.07389i	−0.0191724	−	0.475759i
$289$	−1.27201	−	31.5646i	−0.0748242	−	1.85674i
$290$	−24.7528	−	30.3167i	−1.45354	−	1.78026i
$291$	−3.68096	+	9.70590i	−0.215782	+	0.568970i
$292$	5.31782	+	11.2071i	0.311202	+	0.655845i
$293$	−0.617789	+	2.13286i	−0.0360916	+	0.124603i	−0.976541	−	0.215330i	$-0.930917\pi$
$293$	−0.617789	+	2.13286i	−0.0360916	+	0.124603i	0.940450	+	0.339933i	$0.110404\pi$
$294$	5.75601	−	8.33903i	0.335698	−	0.486342i
$295$	−35.4059	−	15.0850i	−2.06141	−	0.878285i
$296$	3.85777	−	0.626949i	0.224229	−	0.0364407i
$297$	1.02503	+	0.648187i	0.0594780	+	0.0376116i
$298$	−17.5152	−	25.3751i	−1.01463	−	1.46994i
$299$	4.36465	+	19.8123i	0.252414	+	1.14577i
$300$	17.2846	−	25.0411i	0.997927	−	1.44575i
$301$	−0.0846134	+	0.0360504i	−0.00487704	+	0.00207791i
$302$	2.42344	+	8.36667i	0.139453	+	0.481448i
$303$	−7.46758	+	0.602845i	−0.429001	+	0.0346325i
$304$	−8.42907	+	7.46751i	−0.483441	+	0.428291i
$305$	−15.0356	+	9.50792i	−0.860935	+	0.544422i
$306$	13.3936	+	5.70648i	0.765661	+	0.326218i
$307$	−2.69380	+	22.1855i	−0.153743	+	1.26619i	0.687760	+	0.725938i	$0.258594\pi$
$307$	−2.69380	+	22.1855i	−0.153743	+	1.26619i	−0.841503	+	0.540252i	$0.818329\pi$
$308$	0.839879	+	4.11400i	0.0478565	+	0.234417i
$309$	−3.21973	−	0.259924i	−0.183164	−	0.0147865i
$310$	64.5170	−	48.4814i	3.66432	−	2.75356i
$311$	−0.000496143		0.00408610i	−2.81337e−5		0.000231702i	−0.992723	−	0.120421i	$-0.961576\pi$
$311$	−0.000496143		0.00408610i	−2.81337e−5		0.000231702i	0.992695	+	0.120653i	$0.0384987\pi$
$312$	1.20665	+	2.44470i	0.0683134	+	0.138404i
$313$	−0.474965	−	3.91169i	−0.0268466	−	0.221102i	0.973111	−	0.230338i	$-0.0739831\pi$
$313$	−0.474965	−	3.91169i	−0.0268466	−	0.221102i	−0.999957	+	0.00923597i	$0.997060\pi$
$314$	−13.3512	−	13.9001i	−0.753453	−	0.784428i
$315$	−3.09912	−	5.36784i	−0.174616	−	0.302444i
$316$	−6.84217	+	11.8510i	−0.384902	+	0.666670i
$317$	−21.9025	+	5.39848i	−1.23017	+	0.303209i	−0.800254	−	0.599662i	$-0.795302\pi$
$317$	−21.9025	+	5.39848i	−1.23017	+	0.303209i	−0.429913	+	0.902870i	$0.641456\pi$
$318$	2.56896	+	3.14641i	0.144060	+	0.176442i
$319$	−2.68721	+	4.65439i	−0.150455	+	0.260596i
$320$	15.8749	+	41.8586i	0.887433	+	2.33997i
$321$	5.67222	−	5.90541i	0.316593	−	0.329608i
$322$	−16.3386	−	5.45464i	−0.910517	−	0.303975i
$323$	−6.94449	−	23.9752i	−0.386402	−	1.33401i
$324$	−1.76801	+	1.56632i	−0.0982228	+	0.0870178i
$325$	8.58606	−	45.6453i	0.476269	−	2.53195i
$326$	0.246852	+	0.218692i	0.0136719	+	0.0121122i
$327$	−5.68486	+	11.9806i	−0.314373	+	0.662528i
$328$	4.16275	+	4.33388i	0.229849	+	0.239298i
$329$	−6.12266	−	12.9032i	−0.337553	−	0.711378i
$330$	−10.3998	−	2.56331i	−0.572488	−	0.141106i
$331$	−6.43435	+	6.69886i	−0.353664	+	0.368203i	−0.874141	−	0.485673i	$-0.838575\pi$
$331$	−6.43435	+	6.69886i	−0.353664	+	0.368203i	0.520477	+	0.853876i	$0.325754\pi$
$332$	−25.5338	−	19.1874i	−1.40135	−	1.05304i
$333$	3.86899	+	3.42762i	0.212019	+	0.187833i
$334$	−40.5790	−	6.59473i	−2.22039	−	0.360848i
$335$	−3.51329	−	2.22167i	−0.191951	−	0.121383i
$336$	4.59466	+	0.370920i	0.250659	+	0.0202353i
$337$	16.6988			0.909644			0.454822	−	0.890582i	$-0.349703\pi$
$337$	16.6988			0.909644			0.454822	+	0.890582i	$0.349703\pi$
$338$	20.8696	+	17.3679i	1.13515	+	0.944691i
$339$	10.0446			0.545547
$340$	−69.3994	−	5.60250i	−3.76371	−	0.303838i
$341$	−9.36638	−	5.92294i	−0.507218	−	0.320745i
$342$	7.38185	+	1.19967i	0.399165	+	0.0648706i
$343$	13.0028	+	11.5195i	0.702085	+	0.621993i
$344$	−0.0379300	−	0.0285026i	−0.00204505	−	0.00153675i
$345$	16.4823	−	17.1599i	0.887379	−	0.923860i
$346$	14.7450	+	3.63431i	0.792694	+	0.195381i
$347$	−4.45728	−	9.39351i	−0.239279	−	0.504270i	0.747915	−	0.663795i	$-0.231055\pi$
$347$	−4.45728	−	9.39351i	−0.239279	−	0.504270i	−0.987194	+	0.159525i	$0.949004\pi$
$348$	−7.25103	−	7.54912i	−0.388696	−	0.404675i
$349$	10.9096	−	22.9915i	0.583978	−	1.23071i	−0.369497	−	0.929232i	$-0.620470\pi$
$349$	10.9096	−	22.9915i	0.583978	−	1.23071i	0.953474	−	0.301475i	$-0.0974788\pi$
$350$	29.5176	+	26.1503i	1.57778	+	1.39779i
$351$	−1.49515	+	3.28093i	−0.0798054	+	0.175123i
$352$	7.33523	−	6.49845i	0.390969	−	0.346368i
$353$	−4.61223	−	15.9233i	−0.245484	−	0.847511i	−0.984732	−	0.174077i	$-0.944306\pi$
$353$	−4.61223	−	15.9233i	−0.245484	−	0.847511i	0.739248	−	0.673434i	$-0.235181\pi$
$354$	−18.0298	−	6.01923i	−0.958273	−	0.319919i
$355$	15.2678	−	15.8955i	0.810333	−	0.843646i
$356$	−14.1068	−	37.1966i	−0.747660	−	1.97142i
$357$	−5.10868	+	8.84849i	−0.270380	+	0.468312i
$358$	20.9693	+	25.6827i	1.10826	+	1.35737i
$359$	−7.83439	+	1.93100i	−0.413483	+	0.101914i	−0.440569	−	0.897719i	$-0.645223\pi$
$359$	−7.83439	+	1.93100i	−0.413483	+	0.101914i	0.0270860	+	0.999633i	$0.491377\pi$
$360$	1.59872	−	2.76907i	0.0842601	−	0.145943i
$361$	3.08890	+	5.35013i	0.162574	+	0.281586i
$362$	9.23548	+	9.61515i	0.485406	+	0.505361i
$363$	−1.14862	−	9.45970i	−0.0602867	−	0.496505i
$364$	−11.7782	+	4.13549i	−0.617344	+	0.216759i
$365$	2.67686	−	22.0459i	0.140113	−	1.15394i
$366$	−7.02413	+	5.27829i	−0.367157	+	0.275901i
$367$	−5.91890	−	0.477823i	−0.308964	−	0.0249422i	−0.0749878	−	0.997184i	$-0.523892\pi$
$367$	−5.91890	−	0.477823i	−0.308964	−	0.0249422i	−0.233976	+	0.972242i	$0.575174\pi$
$368$	3.53948	+	17.3375i	0.184508	+	0.903781i
$369$	−0.957945	+	7.88939i	−0.0498686	+	0.410705i
$370$	−41.9978	−	17.8936i	−2.18336	−	0.930244i
$371$	−2.40940	+	1.52361i	−0.125090	+	0.0791019i
$372$	16.1556	−	14.3126i	0.837627	−	0.742073i
$373$	7.22602	−	0.583345i	0.374149	−	0.0302045i	0.108038	−	0.994147i	$-0.465543\pi$
$373$	7.22602	−	0.583345i	0.374149	−	0.0302045i	0.266111	+	0.963942i	$0.414261\pi$
$374$	4.91229	+	16.9592i	0.254008	+	0.876939i
$375$	−30.6624	+	13.0640i	−1.58340	+	0.674623i
$376$	4.18530	−	6.06345i	0.215840	−	0.312699i
$377$	−14.7945	−	6.03498i	−0.761956	−	0.310817i
$378$	−1.73903	−	2.51942i	−0.0894459	−	0.129585i
$379$	10.3495	+	6.54465i	0.531620	+	0.336176i	0.773156	−	0.634216i	$-0.218677\pi$
$379$	10.3495	+	6.54465i	0.531620	+	0.336176i	−0.241536	+	0.970392i	$0.577651\pi$
$380$	−35.3031	+	5.73731i	−1.81101	+	0.294318i
$381$	−13.9602	−	5.94787i	−0.715201	−	0.304719i
$382$	16.6258	−	24.0866i	0.850648	−	1.23238i
$383$	−5.66828	+	19.5692i	−0.289636	+	0.999939i	0.675320	+	0.737525i	$0.264006\pi$
$383$	−5.66828	+	19.5692i	−0.289636	+	0.999939i	−0.964956	+	0.262414i	$0.915482\pi$
$384$	2.55070	+	5.37549i	0.130165	+	0.274317i
$385$	2.66559	−	7.02859i	0.135851	−	0.358210i
$386$	0.681726	+	0.834963i	0.0346990	+	0.0424985i
$387$	−0.00252659	−	0.0626967i	−0.000128434	−	0.00318705i
$388$	−0.987283	−	24.4992i	−0.0501217	−	1.24376i
$389$	−30.9430	+	7.62677i	−1.56887	+	0.386693i	−0.925466	−	0.378831i	$-0.876326\pi$
$389$	−30.9430	+	7.62677i	−1.56887	+	0.386693i	−0.643408	+	0.765523i	$0.722480\pi$
$390$	3.34939	−	31.6669i	0.169603	−	1.60352i
$391$	−38.0821	−	9.38640i	−1.92590	−	0.474691i
$392$	−0.733776	+	3.59427i	−0.0370613	+	0.181538i
$393$	4.02301	−	1.71404i	0.202934	−	0.0864620i
$394$	24.7350	−	15.6415i	1.24613	−	0.788006i
$395$	21.6925	−	11.3851i	1.09147	−	0.572846i
$396$	−2.82752	−	0.459517i	−0.142088	−	0.0230916i
$397$	−29.7427	+	9.92958i	−1.49274	+	0.498351i	−0.941795	−	0.336187i	$-0.890863\pi$
$397$	−29.7427	+	9.92958i	−1.49274	+	0.498351i	−0.550949	+	0.834539i	$0.685734\pi$
$398$	4.14154	+	34.1086i	0.207597	+	1.70971i
$399$	−1.46026	+	5.04140i	−0.0731043	+	0.252385i
$400$	8.10328	−	39.6925i	0.405164	−	1.98463i
$401$	3.64955	+	1.21840i	0.182250	+	0.0608439i	0.406328	−	0.913727i	$-0.366809\pi$
$401$	3.64955	+	1.21840i	0.182250	+	0.0608439i	−0.224078	+	0.974571i	$0.571937\pi$
$402$	−1.81788	−	0.954098i	−0.0906677	−	0.0475861i
$403$	13.6623	−	29.9802i	0.680567	−	1.49342i
$404$	15.6691	−	8.22378i	0.779567	−	0.409148i
$405$	4.17392	−	0.678328i	0.207404	−	0.0337064i
$406$	10.8455	−	8.14984i	0.538251	−	0.404470i
$407$	−0.252416	+	6.26364i	−0.0125118	+	0.310477i
$408$	−5.27076			−0.260941
$409$	−0.695899	+	17.2686i	−0.0344100	+	0.853876i	0.886179	+	0.463343i	$0.153350\pi$
$409$	−0.695899	+	17.2686i	−0.0344100	+	0.853876i	−0.920589	+	0.390533i	$0.872291\pi$
$410$	−14.0397	−	68.7708i	−0.693370	−	3.39635i
$411$	0.110765	+	0.160471i	0.00546363	+	0.00791544i
$412$	7.23721	−	2.41613i	0.356552	−	0.119034i
$413$	5.71876	−	12.0520i	0.281402	−	0.593042i
$414$	7.43226	−	9.10287i	0.365276	−	0.447382i
$415$	20.2764	+	53.4644i	0.995328	+	2.62446i
$416$	22.1034	+	18.9804i	1.08371	+	0.930593i
$417$	1.80371	−	4.75600i	0.0883281	−	0.232902i
$418$	4.53499	+	7.85483i	0.221814	+	0.384192i
$419$	−15.9483	+	19.5331i	−0.779123	+	0.954253i	−0.999777	−	0.0210993i	$-0.993283\pi$
$419$	−15.9483	+	19.5331i	−0.779123	+	0.954253i	0.220654	+	0.975352i	$0.429181\pi$
$420$	11.7042	+	8.79516i	0.571108	+	0.429160i
$421$	−26.9424	−	14.1405i	−1.31309	−	0.689165i	−0.344729	−	0.938702i	$-0.612029\pi$
$421$	−26.9424	−	14.1405i	−1.31309	−	0.689165i	−0.968365	+	0.249538i	$0.919721\pi$
$422$	−40.7926	+	3.29312i	−1.98575	+	0.160307i
$423$	9.71224	−	0.784053i	0.472225	−	0.0381220i
$424$	−1.30213	−	0.683412i	−0.0632372	−	0.0331894i
$425$	71.7855	+	53.9433i	3.48211	+	2.61663i
$426$	6.88462	−	8.43212i	0.333561	−	0.408538i
$427$	−3.08315	−	5.34017i	−0.149204	−	0.258429i
$428$	−6.85842	+	18.0842i	−0.331514	+	0.874132i
$429$	−4.22898	+	1.11194i	−0.204177	+	0.0536850i
$430$	0.196513	+	0.518163i	0.00947671	+	0.0249880i
$431$	17.0349	−	20.8639i	0.820540	−	1.00498i	−0.179236	−	0.983806i	$-0.557362\pi$
$431$	17.0349	−	20.8639i	0.820540	−	1.00498i	0.999776	−	0.0211732i	$-0.00674016\pi$
$432$	−1.34818	+	2.84122i	−0.0648641	+	0.136698i
$433$	20.6120	−	6.88129i	0.990548	−	0.330693i	0.225202	−	0.974312i	$-0.427696\pi$
$433$	20.6120	−	6.88129i	0.990548	−	0.330693i	0.765346	+	0.643619i	$0.222568\pi$
$434$	15.8907	+	23.0217i	0.762779	+	1.10508i
$435$	3.74837	+	18.3608i	0.179721	+	0.880331i
$436$	1.26124	−	31.2974i	0.0604025	−	1.49887i
$437$	−20.1481			−0.963816
$438$	0.441656	−	10.9596i	0.0211031	−	0.523669i
$439$	−12.3041	+	9.24596i	−0.587245	+	0.441286i	−0.852378	−	0.522926i	$-0.824840\pi$
$439$	−12.3041	+	9.24596i	−0.587245	+	0.441286i	0.265133	+	0.964212i	$0.414584\pi$
$440$	3.82757	−	0.622040i	0.182472	−	0.0296546i
$441$	−4.29582	+	2.25462i	−0.204563	+	0.107363i
$442$	−47.9676	+	21.3188i	−2.28159	+	1.01403i
$443$	21.0627	+	11.0545i	1.00072	+	0.525217i	0.883770	−	0.467921i	$-0.154997\pi$
$443$	21.0627	+	11.0545i	1.00072	+	0.525217i	0.116948	+	0.993138i	$0.462689\pi$
$444$	−11.5808	−	3.86625i	−0.549602	−	0.183484i
$445$	−14.2459	+	69.7808i	−0.675318	+	3.30793i
$446$	−6.20992	+	21.4391i	−0.294048	+	1.01517i
$447$	1.77947	+	14.6553i	0.0841662	+	0.693171i
$448$	−14.7190	+	4.91393i	−0.695408	+	0.232161i
$449$	11.8895	+	1.93223i	0.561099	+	0.0911874i	0.434345	−	0.900747i	$-0.356980\pi$
$449$	11.8895	+	1.93223i	0.561099	+	0.0911874i	0.126754	+	0.991934i	$0.459544\pi$
$450$	−23.8225	+	12.5030i	−1.12300	+	0.589397i
$451$	−8.14622	+	5.15135i	−0.383590	+	0.242568i
$452$	−21.8271	+	9.29967i	−1.02666	+	0.437420i
$453$	0.834235	−	4.08635i	0.0391958	−	0.191994i
$454$	34.0430	+	8.39086i	1.59772	+	0.393802i
$455$	21.7788	+	5.01232i	1.02100	+	0.234981i
$456$	−2.62889	+	0.647964i	−0.123109	+	0.0303437i
$457$	−1.27060	−	31.5297i	−0.0594364	−	1.47490i	−0.703919	−	0.710280i	$-0.748568\pi$
$457$	−1.27060	−	31.5297i	−0.0594364	−	1.47490i	0.644483	−	0.764619i	$-0.277073\pi$
$458$	−1.96818	−	48.8398i	−0.0919668	−	2.28213i
$459$	−4.40857	−	5.39952i	−0.205774	−	0.252028i
$460$	−19.9292	+	52.5490i	−0.929204	+	2.45011i
$461$	8.06586	+	16.9984i	0.375664	+	0.791696i	0.999945	+	0.0104958i	$0.00334097\pi$
$461$	8.06586	+	16.9984i	0.375664	+	0.791696i	−0.624280	+	0.781200i	$0.714608\pi$
$462$	1.03294	−	3.56611i	0.0480565	−	0.165910i
$463$	8.16704	−	11.8320i	0.379555	−	0.549880i	−0.585923	−	0.810367i	$-0.699268\pi$
$463$	8.16704	−	11.8320i	0.379555	−	0.549880i	0.965477	+	0.260487i	$0.0838832\pi$
$464$	−12.8213	−	5.46263i	−0.595212	−	0.253596i
$465$	−38.1401	+	6.19837i	−1.76870	+	0.287442i
$466$	33.8801	+	21.4245i	1.56946	+	0.992469i
$467$	−7.96654	−	11.5415i	−0.368648	−	0.534078i	0.594131	−	0.804368i	$-0.297496\pi$
$467$	−7.96654	−	11.5415i	−0.368648	−	0.534078i	−0.962779	+	0.270290i	$0.912881\pi$
$468$	0.211390	−	8.51382i	0.00977150	−	0.393552i
$469$	0.818495	−	1.18579i	0.0377946	−	0.0547549i
$470$	−79.1695	+	33.7310i	−3.65182	+	1.55589i
$471$	2.56744	+	8.86383i	0.118301	+	0.408424i
$472$	6.85930	−	0.553740i	0.315725	−	0.0254880i
$473$	0.0569607	−	0.0504628i	0.00261906	−	0.00232028i
$474$	10.2267	−	6.46698i	0.469729	−	0.297038i
$475$	42.4360	+	18.0803i	1.94710	+	0.829580i
$476$	2.90901	−	23.9578i	0.133334	−	1.09810i
$477$	−0.389023	−	1.90556i	−0.0178122	−	0.0872497i
$478$	24.3014	+	1.96181i	1.11152	+	0.0897311i
$479$	−8.18102	+	6.14764i	−0.373801	+	0.280893i	−0.770995	−	0.636842i	$-0.780240\pi$
$479$	−8.18102	+	6.14764i	−0.373801	+	0.280893i	0.397194	+	0.917735i	$0.369984\pi$
$480$	4.11870	−	33.9205i	0.187992	−	1.54825i
$481$	−18.5510	+	1.78651i	−0.845851	+	0.0814577i
$482$	2.70376	+	22.2675i	0.123153	+	1.01425i
$483$	5.71318	+	5.94805i	0.259959	+	0.270646i
$484$	11.2541	+	19.4927i	0.511552	+	0.886034i
$485$	−21.9478	+	38.0148i	−0.996600	+	1.72616i
$486$	2.02786	−	0.499823i	0.0919856	−	0.0226724i
$487$	9.38423	+	11.4936i	0.425240	+	0.520824i	0.942139	−	0.335222i	$-0.108811\pi$
$487$	9.38423	+	11.4936i	0.425240	+	0.520824i	−0.516899	+	0.856046i	$0.672914\pi$
$488$	1.59048	−	2.75480i	0.0719978	−	0.124704i
$489$	−0.0559936	−	0.147643i	−0.00253212	−	0.00667664i
$490$	29.6818	−	30.9020i	1.34088	−	1.39601i
$491$	40.3183	+	13.4602i	1.81954	+	0.607451i	0.999376	+	0.0353203i	$0.0112451\pi$
$491$	40.3183	+	13.4602i	1.81954	+	0.607451i	0.820162	+	0.572131i	$0.193883\pi$
$492$	−5.22267	−	18.0307i	−0.235456	−	0.812889i
$493$	23.1220	−	20.4843i	1.04136	−	0.922565i
$494$	−21.3040	+	16.5301i	−0.958510	+	0.743724i
$495$	3.83869	+	3.40078i	0.172536	+	0.152854i
$496$	12.3192	−	25.9622i	0.553150	−	1.16574i
$497$	5.29220	+	5.50977i	0.237388	+	0.247147i
$498$	12.1068	+	25.5146i	0.542521	+	1.14334i
$499$	20.4050	+	5.02937i	0.913451	+	0.225146i	0.667911	−	0.744241i	$-0.267189\pi$
$499$	20.4050	+	5.02937i	0.913451	+	0.225146i	0.245540	+	0.969386i	$0.421035\pi$
$500$	54.5349	−	56.7769i	2.43888	−	2.53914i
$501$	15.7364	+	11.8251i	0.703050	+	0.528308i
$502$	5.52174	+	4.89183i	0.246447	+	0.218333i
$503$	16.1929	+	2.63160i	0.722005	+	0.117337i	0.510300	−	0.859996i	$-0.329534\pi$
$503$	16.1929	+	2.63160i	0.722005	+	0.117337i	0.211705	+	0.977334i	$0.432098\pi$
$504$	0.936735	+	0.592355i	0.0417255	+	0.0263856i
$505$	−31.5780	−	2.54924i	−1.40520	−	0.113440i
$506$	14.2521			0.633582
$507$	−4.98327	−	12.0070i	−0.221315	−	0.533248i
$508$	35.8426			1.59026
$509$	15.7065	+	1.26796i	0.696180	+	0.0562015i	0.423491	−	0.905901i	$-0.360805\pi$
$509$	15.7065	+	1.26796i	0.696180	+	0.0562015i	0.272690	+	0.962102i	$0.412087\pi$
$510$	52.0330	+	32.9037i	2.30406	+	1.45700i
$511$	7.59809	+	1.23481i	0.336120	+	0.0546248i
$512$	22.5808	+	20.0049i	0.997941	+	0.884099i
$513$	−2.86265	−	2.15114i	−0.126389	−	0.0949753i
$514$	−19.9736	+	20.7948i	−0.881000	+	0.917218i
$515$	−13.2626	−	3.26894i	−0.584420	−	0.144046i
$516$	0.0635375	+	0.133902i	0.00279708	+	0.00589473i
$517$	8.18598	+	8.52251i	0.360019	+	0.374820i
$518$	6.78350	−	14.2959i	0.298050	−	0.628127i
$519$	−5.44257	−	4.82169i	−0.238902	−	0.211649i
$520$	3.37817	+	11.0225i	0.148143	+	0.483369i
$521$	−11.0477	+	9.78740i	−0.484008	+	0.428794i	−0.869512	−	0.493912i	$-0.835566\pi$
$521$	−11.0477	+	9.78740i	−0.484008	+	0.428794i	0.385503	+	0.922706i	$0.374028\pi$
$522$	2.57502	+	8.89001i	0.112706	+	0.389105i
$523$	6.31374	+	2.10784i	0.276081	+	0.0921693i	0.451337	−	0.892354i	$-0.350947\pi$
$523$	6.31374	+	2.10784i	0.276081	+	0.0921693i	−0.175256	+	0.984523i	$0.556075\pi$
$524$	−7.15517	+	7.44932i	−0.312575	+	0.325425i
$525$	−6.69551	−	17.6546i	−0.292216	−	0.770510i
$526$	−21.1950	+	36.7107i	−0.924144	+	1.60066i
$527$	40.2842	+	49.3392i	1.75481	+	2.14925i
$528$	−3.70317	+	0.912750i	−0.161160	+	0.0397223i
$529$	−4.32985	+	7.49951i	−0.188254	+	0.326066i
$530$	8.58835	+	14.8755i	0.373054	+	0.646149i
$531$	6.30453	+	6.56371i	0.273593	+	0.284841i
$532$	−1.49435	−	12.3070i	−0.0647881	−	0.533578i
$533$	−18.4632	−	21.9132i	−0.799731	−	0.949168i
$534$	−4.23996	+	34.9192i	−0.183481	+	1.51110i
$535$	27.6812	−	20.8011i	1.19676	−	0.899309i
$536$	0.740870	+	0.0598092i	0.0320007	+	0.00258336i
$537$	−3.17543	−	15.5543i	−0.137030	−	0.671216i
$538$	−4.89998	+	40.3550i	−0.211253	+	1.73983i
$539$	−5.41300	−	2.30626i	−0.233154	−	0.0993377i
$540$	−8.44202	+	5.33841i	−0.363287	+	0.229728i
$541$	−8.64865	+	7.66204i	−0.371835	+	0.329417i	−0.828259	−	0.560345i	$-0.810668\pi$
$541$	−8.64865	+	7.66204i	−0.371835	+	0.329417i	0.456424	+	0.889762i	$0.349130\pi$
$542$	12.8339	−	1.03606i	0.551262	−	0.0445024i
$543$	−1.77598	−	6.13140i	−0.0762147	−	0.263124i
$544$	−51.8189	+	22.0780i	−2.22172	+	0.946585i
$545$	−31.8549	+	46.1498i	−1.36452	+	1.97684i
$546$	10.9209	+	1.60202i	0.467370	+	0.0685600i
$547$	17.0680	+	24.7272i	0.729774	+	1.05726i	0.995643	+	0.0932512i	$0.0297260\pi$
$547$	17.0680	+	24.7272i	0.729774	+	1.05726i	−0.265868	+	0.964009i	$0.585659\pi$
$548$	−0.389265	−	0.246157i	−0.0166286	−	0.0105153i
$549$	4.15241	−	0.674832i	0.177220	−	0.0288011i
$550$	−30.0177	−	12.7894i	−1.27996	−	0.545340i
$551$	9.01429	−	13.0594i	0.384022	−	0.556351i
$552$	−1.18368	+	4.08655i	−0.0503810	+	0.173935i
$553$	3.64038	+	7.67194i	0.154805	+	0.326244i
$554$	3.58378	−	9.44965i	0.152260	−	0.401477i
$555$	13.8238	+	16.9311i	0.586787	+	0.718684i
$556$	0.483779	+	12.0049i	0.0205168	+	0.509119i
$557$	0.188366	+	4.67425i	0.00798132	+	0.198054i	0.998260	+	0.0589594i	$0.0187783\pi$
$557$	0.188366	+	4.67425i	0.00798132	+	0.198054i	−0.990279	+	0.139095i	$0.955581\pi$
$558$	−18.5300	+	4.56723i	−0.784437	+	0.193346i
$559$	0.171641	+	0.147390i	0.00725964	+	0.00623394i
$560$	18.9262	+	4.66488i	0.799776	+	0.197127i
$561$	1.69099	−	8.28301i	0.0713936	−	0.349709i
$562$	35.7183	−	15.2181i	1.50668	−	0.641938i
$563$	−15.1419	+	9.57515i	−0.638155	+	0.403545i	−0.813993	−	0.580874i	$-0.802711\pi$
$563$	−15.1419	+	9.57515i	−0.638155	+	0.403545i	0.175838	+	0.984419i	$0.443736\pi$
$564$	−20.3791	+	10.6958i	−0.858113	+	0.450372i
$565$	41.9253	+	6.81352i	1.76381	+	0.286647i
$566$	38.0202	−	12.6930i	1.59811	−	0.533528i
$567$	0.176678	+	1.45508i	0.00741979	+	0.0611075i
$568$	−1.09646	+	3.78544i	−0.0460066	+	0.158833i
$569$	−1.02893	+	5.04001i	−0.0431348	+	0.211288i	−0.995646	−	0.0932154i	$-0.970285\pi$
$569$	−1.02893	+	5.04001i	−0.0431348	+	0.211288i	0.952511	+	0.304504i	$0.0984906\pi$
$570$	29.9975	+	10.0146i	1.25646	+	0.419467i
$571$	−12.9346	−	6.78861i	−0.541297	−	0.284094i	0.171834	−	0.985126i	$-0.445031\pi$
$571$	−12.9346	−	6.78861i	−0.541297	−	0.284094i	−0.713130	+	0.701032i	$0.752723\pi$
$572$	8.16021	−	6.33164i	0.341195	−	0.264739i
$573$	−12.4081	+	6.51229i	−0.518357	+	0.272055i
$574$	24.0143	−	3.90270i	1.00234	−	0.162895i
$575$	57.9449	−	43.5428i	2.41647	−	1.81586i
$576$	0.426284	−	10.5781i	0.0177618	−	0.440755i
$577$	16.3870			0.682200			0.341100	−	0.940027i	$-0.389201\pi$
$577$	16.3870			0.682200			0.341100	+	0.940027i	$0.389201\pi$
$578$	2.65666	−	65.9243i	0.110502	−	2.74209i
$579$	−0.103235	−	0.505680i	−0.00429031	−	0.0210153i
$580$	−25.1444	−	36.4280i	−1.04407	−	1.51259i
$581$	−18.8000	+	6.27637i	−0.779956	+	0.260388i
$582$	−9.29410	+	19.5869i	−0.385253	+	0.811903i
$583$	1.49174	−	1.82705i	0.0617816	−	0.0756687i
$584$	1.40813	+	3.71295i	0.0582690	+	0.153643i
$585$	−8.46620	+	12.6801i	−0.350034	+	0.524260i
$586$	−1.64454	+	4.33630i	−0.0679354	+	0.179131i
$587$	−14.8909	−	25.7919i	−0.614615	−	1.06454i	−0.990452	−	0.137859i	$-0.955978\pi$
$587$	−14.8909	−	25.7919i	−0.614615	−	1.06454i	0.375837	−	0.926686i	$-0.377355\pi$
$588$	7.24752	−	8.87660i	0.298883	−	0.366065i
$589$	26.1581	+	19.6565i	1.07783	+	0.809933i
$590$	−71.1720	−	37.3539i	−2.93010	−	1.53784i
$591$	−13.9670	+	1.12753i	−0.574525	+	0.0463804i
$592$	−16.2028	+	1.30802i	−0.665929	+	0.0537594i
$593$	−21.9839	−	11.5380i	−0.902770	−	0.473810i	−0.0515807	−	0.998669i	$-0.516426\pi$
$593$	−21.9839	−	11.5380i	−0.902770	−	0.473810i	−0.851190	+	0.524858i	$0.824118\pi$
$594$	2.02494	+	1.52164i	0.0830843	+	0.0624338i
$595$	−27.3254	+	33.4675i	−1.12023	+	1.37204i
$596$	−17.4353	−	30.1988i	−0.714177	−	1.23699i
$597$	5.83368	−	15.3822i	0.238757	−	0.629549i
$598$	5.75662	+	41.9782i	0.235406	+	1.71662i
$599$	−7.43824	−	19.6130i	−0.303918	−	0.801367i	−0.996772	−	0.0802884i	$-0.974416\pi$
$599$	−7.43824	−	19.6130i	−0.303918	−	0.801367i	0.692853	−	0.721079i	$-0.256353\pi$
$600$	6.16022	−	7.54490i	0.251490	−	0.308019i
$601$	13.4174	−	28.2765i	0.547305	−	1.15342i	−0.421781	−	0.906698i	$-0.638595\pi$
$601$	13.4174	−	28.2765i	0.547305	−	1.15342i	0.969086	−	0.246723i	$-0.0793539\pi$
$602$	−0.182205	+	0.0608289i	−0.00742612	+	0.00247920i
$603$	0.558408	+	0.808994i	0.0227401	+	0.0329448i
$604$	1.97049	+	9.65212i	0.0801783	+	0.392739i
$605$	1.62255	−	40.2632i	0.0659661	−	1.63693i
$606$	−15.6471			−0.635622
$607$	−0.585324	+	14.5247i	−0.0237576	+	0.589538i	0.942841	+	0.333243i	$0.108143\pi$
$607$	−0.585324	+	14.5247i	−0.0237576	+	0.589538i	−0.966599	+	0.256295i	$0.917498\pi$
$608$	−23.1315	+	17.3822i	−0.938107	+	0.704942i
$609$	−6.41144	+	1.04196i	−0.259805	+	0.0422223i
$610$	−32.8986	+	17.2665i	−1.33203	+	0.699101i
$611$	−21.7959	+	27.5534i	−0.881766	+	1.11469i
$612$	14.5790	+	7.65166i	0.589322	+	0.309300i
$613$	−23.9828	−	8.00663i	−0.968656	−	0.323385i	−0.212052	−	0.977258i	$-0.568015\pi$
$613$	−23.9828	−	8.00663i	−0.968656	−	0.323385i	−0.756604	+	0.653874i	$0.773143\pi$
$614$	−9.33634	+	45.7324i	−0.376784	+	1.84561i
$615$	−9.34998	+	32.2799i	−0.377028	+	1.30165i
$616$	0.162017	+	1.33433i	0.00652787	+	0.0537618i
$617$	6.79284	−	2.26778i	0.273469	−	0.0912975i	−0.176626	−	0.984278i	$-0.556518\pi$
$617$	6.79284	−	2.26778i	0.273469	−	0.0912975i	0.450095	+	0.892981i	$0.351390\pi$
$618$	−6.65908	−	1.08221i	−0.267867	−	0.0435327i
$619$	−31.0963	+	16.3206i	−1.24986	+	0.655979i	−0.954159	−	0.299300i	$-0.903247\pi$
$619$	−31.0963	+	16.3206i	−1.24986	+	0.655979i	−0.295705	+	0.955279i	$0.595555\pi$
$620$	77.1407	−	48.7808i	3.09804	−	1.95908i
$621$	−5.17644	+	2.20548i	−0.207724	+	0.0885027i
$622$	−0.00171956	+	0.00842297i	−6.89482e−5	+	0.000337730i
$623$	−23.9693	−	5.90789i	−0.960309	−	0.236695i
$624$	−4.18419	−	10.5387i	−0.167502	−	0.421885i
$625$	−74.3069	+	18.3150i	−2.97227	+	0.732600i
$626$	−0.331379	−	8.22309i	−0.0132446	−	0.328661i
$627$	−0.174864	−	4.33919i	−0.00698338	−	0.173291i
$628$	−13.7856	−	16.8843i	−0.550105	−	0.673757i
$629$	12.7767	−	33.6894i	0.509440	−	1.34328i
$630$	−5.54957	−	11.6955i	−0.221100	−	0.465959i
$631$	8.61196	−	29.7319i	0.342837	−	1.18361i	−0.585128	−	0.810941i	$-0.698956\pi$
$631$	8.61196	−	29.7319i	0.342837	−	1.18361i	0.927964	−	0.372669i	$-0.121557\pi$
$632$	−2.48847	+	3.60518i	−0.0989862	+	0.143406i
$633$	18.0271	+	7.68062i	0.716512	+	0.305277i
$634$	−46.5034	+	7.55753i	−1.84688	+	0.300148i
$635$	−54.2340	−	34.2955i	−2.15221	−	1.36098i
$636$	2.60960	+	3.78066i	0.103478	+	0.149913i
$637$	4.60650	−	16.8750i	0.182516	−	0.668613i
$638$	−6.37639	+	9.23780i	−0.252444	+	0.365728i
$639$	−4.79502	+	2.04297i	−0.189688	+	0.0808185i
$640$	7.00008	+	24.1671i	0.276703	+	0.955288i
$641$	30.8758	−	2.49256i	1.21952	−	0.0984500i	0.546108	−	0.837715i	$-0.316109\pi$
$641$	30.8758	−	2.49256i	1.21952	−	0.0984500i	0.673415	+	0.739265i	$0.264827\pi$
$642$	12.8008	−	11.3405i	0.505205	−	0.447573i
$643$	−25.4960	+	16.1227i	−1.00546	+	0.635816i	−0.932369	−	0.361509i	$-0.882262\pi$
$643$	−25.4960	+	16.1227i	−1.00546	+	0.635816i	−0.0730941	+	0.997325i	$0.523287\pi$
$644$	−17.9218	−	7.63577i	−0.706219	−	0.300892i
$645$	0.0319832	−	0.263405i	0.00125934	−	0.0103716i
$646$	−10.4276	−	51.0780i	−0.410270	−	2.00964i
$647$	−10.2054	−	0.823868i	−0.401217	−	0.0323896i	−0.121788	−	0.992556i	$-0.538863\pi$
$647$	−10.2054	−	0.823868i	−0.401217	−	0.0323896i	−0.279429	+	0.960166i	$0.590145\pi$
$648$	−0.604485	+	0.454241i	−0.0237464	+	0.0178443i
$649$	−1.33043	+	10.9571i	−0.0522239	+	0.430102i
$650$	25.5453	−	93.5803i	1.00197	−	3.67052i
$651$	−1.61443	−	13.2961i	−0.0632747	−	0.521114i
$652$	0.258369	+	0.268991i	0.0101185	+	0.0105345i
$653$	15.2071	+	26.3395i	0.595101	+	1.03075i	0.993533	+	0.113548i	$0.0362214\pi$
$653$	15.2071	+	26.3395i	0.595101	+	1.03075i	−0.398431	+	0.917198i	$0.630445\pi$
$654$	−13.8480	+	23.9855i	−0.541501	+	0.937908i
$655$	17.9544	−	4.42536i	0.701536	−	0.172913i
$656$	−15.8068	−	19.3599i	−0.617153	−	0.755875i
$657$	−2.62586	+	4.54812i	−0.102444	+	0.177439i
$658$	−10.5775	−	27.8906i	−0.412354	−	1.08729i
$659$	−15.3952	+	16.0281i	−0.599710	+	0.624365i	−0.949990	−	0.312281i	$-0.898907\pi$
$659$	−15.3952	+	16.0281i	−0.599710	+	0.624365i	0.350280	+	0.936645i	$0.386087\pi$
$660$	−11.4902	−	3.83598i	−0.447254	−	0.149315i
$661$	−6.53531	−	22.5625i	−0.254194	−	0.877579i	−0.981532	−	0.191300i	$-0.938730\pi$
$661$	−6.53531	−	22.5625i	−0.254194	−	0.877579i	0.727338	−	0.686280i	$-0.240757\pi$
$662$	−14.5207	+	12.8642i	−0.564362	+	0.499981i
$663$	25.0799	+	1.63503i	0.974022	+	0.0634993i
$664$	−7.65309	−	6.78005i	−0.296997	−	0.263117i
$665$	−9.51472	+	20.0519i	−0.368965	+	0.777578i
$666$	7.47833	+	7.78576i	0.289779	+	0.301692i
$667$	−10.6894	−	22.5273i	−0.413893	−	0.872262i
$668$	−45.1437	−	11.1269i	−1.74666	−	0.430514i
$669$	7.40316	−	7.70751i	0.286223	−	0.297989i
$670$	−6.94051	−	5.21545i	−0.268135	−	0.201490i
$671$	3.81891	+	3.38326i	0.147427	+	0.130609i
$672$	11.6906	+	1.89992i	0.450977	+	0.0732908i
$673$	31.0169	+	19.6139i	1.19562	+	0.756061i	0.975626	−	0.219441i	$-0.0704233\pi$
$673$	31.0169	+	19.6139i	1.19562	+	0.756061i	0.219990	+	0.975502i	$0.429398\pi$
$674$	34.7633	+	2.80638i	1.33903	+	0.108098i
$675$	12.8817			0.495819
$676$	21.9453	+	21.4777i	0.844050	+	0.826066i
$677$	−1.69242			−0.0650449			−0.0325225	−	0.999471i	$-0.510354\pi$
$677$	−1.69242			−0.0650449			−0.0325225	+	0.999471i	$0.510354\pi$
$678$	20.9106	+	1.68808i	0.803066	+	0.0648302i
$679$	−12.8598	−	8.13206i	−0.493515	−	0.312080i
$680$	−21.9997	−	3.57530i	−0.843651	−	0.137107i
$681$	−12.5658	−	11.1323i	−0.481521	−	0.426590i
$682$	−18.5033	−	13.9043i	−0.708528	−	0.532425i
$683$	−29.0412	+	30.2351i	−1.11123	+	1.15691i	−0.124894	+	0.992170i	$0.539859\pi$
$683$	−29.0412	+	30.2351i	−1.11123	+	1.15691i	−0.986336	+	0.164744i	$0.947320\pi$
$684$	8.21223	+	2.02413i	0.314003	+	0.0773947i
$685$	0.353472	+	0.744927i	0.0135055	+	0.0284622i
$686$	25.1330	+	26.1662i	0.959581	+	0.999030i
$687$	−10.0329	+	21.1439i	−0.382780	+	0.806691i
$688$	0.147705	+	0.130855i	0.00563121	+	0.00498882i
$689$	5.98395	+	3.65582i	0.227970	+	0.139275i
$690$	37.1964	−	32.9531i	1.41604	−	1.25450i
$691$	−2.14745	−	7.41384i	−0.0816927	−	0.282036i	0.909264	−	0.416221i	$-0.136646\pi$
$691$	−2.14745	−	7.41384i	−0.0816927	−	0.282036i	−0.990956	+	0.134185i	$0.957158\pi$
$692$	16.2910	+	5.43872i	0.619289	+	0.206749i
$693$	−1.23142	+	1.28204i	−0.0467776	+	0.0487006i
$694$	−7.70039	−	20.3043i	−0.292303	−	0.770739i
$695$	10.7547	−	18.6276i	0.407948	−	0.706587i
$696$	−2.11921	−	2.59556i	−0.0803284	−	0.0983844i
$697$	53.7885	−	13.2577i	2.03738	−	0.502170i
$698$	26.5753	−	46.0297i	1.00589	−	1.74225i
$699$	−9.59656	−	16.6217i	−0.362975	−	0.628691i
$700$	30.8948	+	32.1649i	1.16772	+	1.21572i
$701$	1.74646	+	14.3834i	0.0659629	+	0.543253i	0.987806	+	0.155690i	$0.0497600\pi$
$701$	1.74646	+	14.3834i	0.0659629	+	0.543253i	−0.921843	+	0.387563i	$0.873317\pi$
$702$	−3.66396	+	6.57889i	−0.138287	+	0.248304i
$703$	2.23100	−	18.3739i	0.0841438	−	0.692987i
$704$	10.2643	−	7.71310i	0.386849	−	0.290699i
$705$	41.0700	+	3.31551i	1.54679	+	0.124869i
$706$	−6.92560	−	33.9238i	−0.260648	−	1.27674i
$707$	1.32365	−	10.9012i	0.0497810	−	0.409983i
$708$	−19.7768	−	8.42613i	−0.743259	−	0.316673i
$709$	5.08754	−	3.21716i	0.191067	−	0.120823i	−0.435507	−	0.900185i	$-0.643431\pi$
$709$	5.08754	−	3.21716i	0.191067	−	0.120823i	0.626574	+	0.779362i	$0.284457\pi$
$710$	34.4556	−	30.5250i	1.29310	−	1.14558i
$711$	−5.77466	+	0.466179i	−0.216567	+	0.0174831i
$712$	−3.54308	−	12.2321i	−0.132782	−	0.458418i
$713$	47.3008	−	20.1530i	1.77143	−	0.754736i
$714$	−12.1222	+	17.5620i	−0.453661	+	0.657242i
$715$	−18.4057	+	1.77252i	−0.688334	+	0.0662884i
$716$	21.3010	+	30.8599i	0.796057	+	1.15329i
$717$	−9.86623	−	6.23903i	−0.368461	−	0.233001i
$718$	−16.6340	+	2.70328i	−0.620774	+	0.100886i
$719$	−18.0509	−	7.69077i	−0.673185	−	0.286817i	0.0281974	−	0.999602i	$-0.491023\pi$
$719$	−18.0509	−	7.69077i	−0.673185	−	0.286817i	−0.701383	+	0.712785i	$0.747434\pi$
$720$	−7.55446	+	10.9445i	−0.281538	+	0.407878i
$721$	1.31728	−	4.54778i	0.0490581	−	0.169368i
$722$	5.53126	+	11.6569i	0.205852	+	0.433824i
$723$	3.80845	−	10.0421i	0.141638	−	0.373469i
$724$	9.53596	+	11.6794i	0.354401	+	0.434062i
$725$	2.29861	+	57.0394i	0.0853682	+	2.11839i
$726$	−0.801379	−	19.8860i	−0.0297420	−	0.738039i
$727$	35.7558	−	8.81302i	1.32611	−	0.326857i	0.488232	−	0.872714i	$-0.337642\pi$
$727$	35.7558	−	8.81302i	1.32611	−	0.326857i	0.837878	+	0.545857i	$0.183796\pi$
$728$	−3.86472	+	1.01616i	−0.143236	+	0.0376615i
$729$	−0.970942	−	0.239316i	−0.0359608	−	0.00886354i
$730$	9.27762	−	45.4448i	0.343380	−	1.68199i
$731$	−0.402393	+	0.171443i	−0.0148830	+	0.00634107i
$732$	−8.39850	+	5.31089i	−0.310418	+	0.196296i
$733$	25.9288	−	13.6085i	0.957701	−	0.502640i	0.0879467	−	0.996125i	$-0.471969\pi$
$733$	25.9288	−	13.6085i	0.957701	−	0.502640i	0.869754	+	0.493485i	$0.164277\pi$
$734$	−12.2415	−	1.98944i	−0.451843	−	0.0734317i
$735$	−19.4598	+	6.49664i	−0.717786	+	0.239632i
$736$	5.48035	+	45.1347i	0.202008	+	1.66369i
$737$	−0.331679	+	1.14509i	−0.0122176	+	0.0421799i
$738$	−3.32011	+	16.2630i	−0.122215	+	0.598648i
$739$	26.1192	+	8.71987i	0.960810	+	0.320765i	0.753454	−	0.657500i	$-0.228386\pi$
$739$	26.1192	+	8.71987i	0.960810	+	0.320765i	0.207355	+	0.978266i	$0.433514\pi$
$740$	−45.7149	−	23.9930i	−1.68051	−	0.882002i
$741$	12.7101	−	2.26771i	0.466916	−	0.0833063i
$742$	−5.27188	+	2.76690i	−0.193537	+	0.101576i
$743$	36.5939	−	5.94709i	1.34250	−	0.218178i	0.553643	−	0.832754i	$-0.313237\pi$
$743$	36.5939	−	5.94709i	1.34250	−	0.218178i	0.788857	+	0.614577i	$0.210673\pi$
$744$	5.52361	−	4.15072i	0.202505	−	0.152173i
$745$	−2.51371	+	62.3771i	−0.0920952	+	2.28532i
$746$	15.1410			0.554352
$747$	0.544475	−	13.5110i	0.0199213	−	0.494342i
$748$	3.99418	+	19.5648i	0.146042	+	0.715359i
$749$	6.81796	+	9.87752i	0.249123	+	0.360917i
$750$	−66.0277	+	22.0433i	−2.41099	+	0.804907i
$751$	−6.84678	+	14.4293i	−0.249843	+	0.526532i	−0.989163	−	0.146822i	$-0.953096\pi$
$751$	−6.84678	+	14.4293i	−0.249843	+	0.526532i	0.739320	+	0.673354i	$0.235147\pi$
$752$	−19.3800	+	23.7362i	−0.706716	+	0.865570i
$753$	−1.25250	−	3.30257i	−0.0456436	−	0.120352i
$754$	−29.7846	−	15.0498i	−1.08469	−	0.548082i
$755$	6.25392	−	16.4902i	0.227603	−	0.600141i
$756$	−1.73109	−	2.99834i	−0.0629593	−	0.109049i
$757$	10.0549	−	12.3150i	0.365451	−	0.447597i	−0.558845	−	0.829272i	$-0.688755\pi$
$757$	10.0549	−	12.3150i	0.365451	−	0.447597i	0.924296	+	0.381675i	$0.124653\pi$
$758$	20.4455	+	15.3638i	0.742615	+	0.558039i
$759$	−6.04227	−	3.17123i	−0.219321	−	0.115108i
$760$	−11.4123	+	0.921298i	−0.413968	+	0.0334190i
$761$	29.1973	−	2.35705i	1.05840	−	0.0854431i	0.461012	−	0.887394i	$-0.347486\pi$
$761$	29.1973	−	2.35705i	1.05840	−	0.0854431i	0.597390	+	0.801951i	$0.296204\pi$
$762$	−28.0624	−	14.7283i	−1.01659	−	0.533549i
$763$	−15.5391	−	11.6769i	−0.562552	−	0.422731i
$764$	20.9338	−	25.6393i	0.757360	−	0.927597i
$765$	−14.7384	−	25.5276i	−0.532867	−	0.922953i
$766$	−15.0889	+	39.7861i	−0.545183	+	1.43753i
$767$	−32.8104	+	0.507057i	−1.18472	+	0.0183088i
$768$	−3.10160	−	8.17824i	−0.111919	−	0.295107i
$769$	−0.231307	+	0.283299i	−0.00834113	+	0.0102160i	−0.778759	−	0.627324i	$-0.784150\pi$

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(2.08178 + 0.168058i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(2.33145 + 0.378897i) q^{4} +(-3.16521 - 2.80413i) q^{5} +(-1.66968 - 1.25468i) q^{6} +(1.01537 - 1.05711i) q^{7} +(0.734161 + 0.180955i) q^{8} +(0.428693 + 0.903450i) q^{9} +(-6.11801 - 6.36952i) q^{10} +(-0.519908 + 1.09568i) q^{11} +(-1.76801 - 1.56632i) q^{12} +(-3.43723 - 1.08878i) q^{13} +(2.29143 - 2.03003i) q^{14} +(1.17649 + 4.06173i) q^{15} +(-2.98301 - 0.995875i) q^{16} +(4.82875 - 5.02726i) q^{17} +(0.740610 + 1.95283i) q^{18} +(1.79041 - 3.10107i) q^{19} +(-6.31706 - 7.73699i) q^{20} +(-1.42317 + 0.350780i) q^{21} +(-1.26647 + 2.19359i) q^{22} +(-2.81335 - 4.87286i) q^{23} +(-0.523792 - 0.545325i) q^{24} +(1.55272 + 12.7878i) q^{25} +(-6.97257 - 2.84425i) q^{26} +(0.120537 - 0.992709i) q^{27} +(2.76782 - 2.07988i) q^{28} +(4.41714 + 0.356589i) q^{29} +(1.76659 + 8.65332i) q^{30} +(-1.10143 + 9.07108i) q^{31} +(-7.43385 - 3.16727i) q^{32} +(1.02503 - 0.648187i) q^{33} +(10.8973 - 9.65413i) q^{34} +(-6.17815 + 0.498752i) q^{35} +(0.657160 + 2.26878i) q^{36} +(4.75529 - 2.02604i) q^{37} +(4.24839 - 6.15485i) q^{38} +(2.32320 + 2.75731i) q^{39} +(-1.81636 - 2.63145i) q^{40} +(6.71701 + 4.24758i) q^{41} +(-3.02168 + 0.491070i) q^{42} +(-0.0577265 - 0.0245950i) q^{43} +(-1.62729 + 2.35754i) q^{44} +(1.17649 - 4.06173i) q^{45} +(-5.03784 - 10.6170i) q^{46} +(3.45521 - 9.11065i) q^{47} +(1.98895 + 2.43602i) q^{48} +(0.195352 + 4.84760i) q^{49} +(1.08332 + 26.8823i) q^{50} +(-6.76812 + 1.66819i) q^{51} +(-7.60120 - 3.84079i) q^{52} +(-1.88835 - 0.465437i) q^{53} +(0.417763 - 2.04634i) q^{54} +(4.71806 - 2.01018i) q^{55} +(0.936735 - 0.592355i) q^{56} +(-3.17065 + 1.66409i) q^{57} +(9.13558 + 1.48468i) q^{58} +(8.63269 - 2.88202i) q^{59} +(1.20396 + 9.91548i) q^{60} +(1.17043 - 4.04079i) q^{61} +(-3.81740 + 18.6989i) q^{62} +(1.39033 + 0.464160i) q^{63} +(-9.37406 - 4.91989i) q^{64} +(7.82649 + 13.0847i) q^{65} +(2.24281 - 1.17712i) q^{66} +(0.970272 - 0.157684i) q^{67} +(13.1628 - 9.89121i) q^{68} +(-0.226564 + 5.62213i) q^{69} -12.9453 q^{70} +(-0.209870 + 5.20786i) q^{71} +(0.151246 + 0.740852i) q^{72} +(2.98331 + 4.32208i) q^{73} +(10.2400 - 3.41860i) q^{74} +(5.52231 - 11.6380i) q^{75} +(5.34923 - 6.55162i) q^{76} +(0.630360 + 1.66212i) q^{77} +(4.37299 + 6.13053i) q^{78} +(-2.05439 + 5.41697i) q^{79} +(6.64929 + 11.5169i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(13.2695 + 9.97136i) q^{82} +(-11.9731 - 6.28398i) q^{83} +(-3.45096 + 0.278590i) q^{84} +(-29.3812 + 2.37189i) q^{85} +(-0.116040 - 0.0609027i) q^{86} +(-3.54274 - 2.66220i) q^{87} +(-0.579965 + 0.710328i) q^{88} +(-8.42108 - 14.5857i) q^{89} +(3.13180 - 8.25789i) q^{90} +(-4.64102 + 2.52803i) q^{91} +(-4.71286 - 12.4268i) q^{92} +(5.77910 - 7.07811i) q^{93} +(8.72410 - 18.3857i) q^{94} +(-14.3628 + 4.79502i) q^{95} +(4.59022 + 6.65008i) q^{96} +(-2.07636 - 10.1707i) q^{97} +(-0.408002 + 10.1245i) q^{98} -1.21277 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19}+ \cdots - 18 q^{99}+O(q^{100}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

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