LMFDB - Embedded newform 136.4.c.b.69.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,4,Mod(69,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("136.69");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	136.c (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:	$8.02425976078$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			69.10
Character	$\chi$	$=$	136.69
Dual form			136.4.c.b.69.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20282 + 2.55993i) q^{2} -8.56686i q^{3} +(-5.10645 - 6.15826i) q^{4} -20.6960i q^{5} +(21.9305 + 10.3044i) q^{6} -8.05854 q^{7} +(21.9068 - 5.66486i) q^{8} -46.3911 q^{9} +O(q^{10})$	\(q+(-1.20282 + 2.55993i) q^{2} -8.56686i q^{3} +(-5.10645 - 6.15826i) q^{4} -20.6960i q^{5} +(21.9305 + 10.3044i) q^{6} -8.05854 q^{7} +(21.9068 - 5.66486i) q^{8} -46.3911 q^{9} +(52.9801 + 24.8935i) q^{10} +5.25206i q^{11} +(-52.7570 + 43.7463i) q^{12} +39.0312i q^{13} +(9.69297 - 20.6293i) q^{14} -177.299 q^{15} +(-11.8483 + 62.8937i) q^{16} +17.0000 q^{17} +(55.8002 - 118.758i) q^{18} +4.13334i q^{19} +(-127.451 + 105.683i) q^{20} +69.0364i q^{21} +(-13.4449 - 6.31729i) q^{22} +165.019 q^{23} +(-48.5301 - 187.673i) q^{24} -303.322 q^{25} +(-99.9169 - 46.9475i) q^{26} +166.121i q^{27} +(41.1505 + 49.6266i) q^{28} -210.630i q^{29} +(213.259 - 453.873i) q^{30} +207.818 q^{31} +(-146.752 - 105.981i) q^{32} +44.9937 q^{33} +(-20.4479 + 43.5188i) q^{34} +166.779i q^{35} +(236.894 + 285.689i) q^{36} -199.271i q^{37} +(-10.5810 - 4.97166i) q^{38} +334.375 q^{39} +(-117.240 - 453.383i) q^{40} -330.295 q^{41} +(-176.728 - 83.0383i) q^{42} -142.199i q^{43} +(32.3436 - 26.8194i) q^{44} +960.109i q^{45} +(-198.488 + 422.437i) q^{46} -433.772 q^{47} +(538.802 + 101.503i) q^{48} -278.060 q^{49} +(364.842 - 776.483i) q^{50} -145.637i q^{51} +(240.364 - 199.311i) q^{52} +412.498i q^{53} +(-425.258 - 199.814i) q^{54} +108.696 q^{55} +(-176.537 + 45.6505i) q^{56} +35.4097 q^{57} +(539.198 + 253.350i) q^{58} +694.642i q^{59} +(905.370 + 1091.86i) q^{60} -638.897i q^{61} +(-249.968 + 531.999i) q^{62} +373.845 q^{63} +(447.819 - 248.198i) q^{64} +807.787 q^{65} +(-54.1193 + 115.181i) q^{66} -40.6728i q^{67} +(-86.8096 - 104.690i) q^{68} -1413.70i q^{69} +(-426.942 - 200.605i) q^{70} +627.885 q^{71} +(-1016.28 + 262.799i) q^{72} -344.074 q^{73} +(510.119 + 239.687i) q^{74} +2598.52i q^{75} +(25.4542 - 21.1067i) q^{76} -42.3240i q^{77} +(-402.192 + 855.975i) q^{78} -615.792 q^{79} +(1301.64 + 245.213i) q^{80} +170.577 q^{81} +(397.286 - 845.532i) q^{82} -421.512i q^{83} +(425.144 - 352.531i) q^{84} -351.831i q^{85} +(364.020 + 171.040i) q^{86} -1804.44 q^{87} +(29.7522 + 115.056i) q^{88} +1213.65 q^{89} +(-2457.81 - 1154.84i) q^{90} -314.534i q^{91} +(-842.662 - 1016.23i) q^{92} -1780.35i q^{93} +(521.749 - 1110.42i) q^{94} +85.5433 q^{95} +(-907.922 + 1257.20i) q^{96} -1821.02 q^{97} +(334.456 - 711.813i) q^{98} -243.649i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} + 5 q^{4} + 40 q^{6} + 84 q^{7} + 13 q^{8} - 216 q^{9}+O(q^{10}) $ 24 * q + q^2 + 5 * q^4 + 40 * q^6 + 84 * q^7 + 13 * q^8 - 216 * q^9	$ 24 q + q^{2} + 5 q^{4} + 40 q^{6} + 84 q^{7} + 13 q^{8} - 216 q^{9} - 16 q^{10} - 18 q^{12} + 26 q^{14} - 180 q^{15} - 103 q^{16} + 408 q^{17} - 5 q^{18} - 24 q^{20} + 172 q^{22} + 624 q^{23} - 310 q^{24} - 600 q^{25} - 180 q^{26} - 132 q^{28} - 80 q^{30} - 744 q^{31} - 39 q^{32} - 280 q^{33} + 17 q^{34} + 791 q^{36} - 162 q^{38} + 1236 q^{39} - 1396 q^{40} + 1132 q^{42} + 886 q^{44} - 1246 q^{46} - 956 q^{47} - 2226 q^{48} + 1688 q^{49} + 2505 q^{50} + 2544 q^{52} - 3264 q^{54} + 1684 q^{55} - 1100 q^{56} - 168 q^{57} + 2800 q^{58} + 2520 q^{60} - 1946 q^{62} - 2520 q^{63} - 2143 q^{64} - 72 q^{65} + 3660 q^{66} + 85 q^{68} - 5084 q^{70} + 1532 q^{71} - 2277 q^{72} + 216 q^{73} + 2188 q^{74} + 2094 q^{76} - 4748 q^{78} - 3176 q^{79} + 116 q^{80} + 2040 q^{81} + 3198 q^{82} + 5916 q^{84} - 2066 q^{86} - 236 q^{87} - 3598 q^{88} - 424 q^{89} + 2180 q^{90} + 1940 q^{92} - 2156 q^{94} - 1248 q^{95} - 4674 q^{96} - 1304 q^{97} + 3705 q^{98}+O(q^{100}) $ 24 * q + q^2 + 5 * q^4 + 40 * q^6 + 84 * q^7 + 13 * q^8 - 216 * q^9 - 16 * q^10 - 18 * q^12 + 26 * q^14 - 180 * q^15 - 103 * q^16 + 408 * q^17 - 5 * q^18 - 24 * q^20 + 172 * q^22 + 624 * q^23 - 310 * q^24 - 600 * q^25 - 180 * q^26 - 132 * q^28 - 80 * q^30 - 744 * q^31 - 39 * q^32 - 280 * q^33 + 17 * q^34 + 791 * q^36 - 162 * q^38 + 1236 * q^39 - 1396 * q^40 + 1132 * q^42 + 886 * q^44 - 1246 * q^46 - 956 * q^47 - 2226 * q^48 + 1688 * q^49 + 2505 * q^50 + 2544 * q^52 - 3264 * q^54 + 1684 * q^55 - 1100 * q^56 - 168 * q^57 + 2800 * q^58 + 2520 * q^60 - 1946 * q^62 - 2520 * q^63 - 2143 * q^64 - 72 * q^65 + 3660 * q^66 + 85 * q^68 - 5084 * q^70 + 1532 * q^71 - 2277 * q^72 + 216 * q^73 + 2188 * q^74 + 2094 * q^76 - 4748 * q^78 - 3176 * q^79 + 116 * q^80 + 2040 * q^81 + 3198 * q^82 + 5916 * q^84 - 2066 * q^86 - 236 * q^87 - 3598 * q^88 - 424 * q^89 + 2180 * q^90 + 1940 * q^92 - 2156 * q^94 - 1248 * q^95 - 4674 * q^96 - 1304 * q^97 + 3705 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	−1.20282	+	2.55993i	−0.425261	+	0.905071i
$2$	−1.20282	+	2.55993i	−0.425261	+	0.905071i
$3$		−	8.56686i		−	1.64869i	−0.566085	−	0.824347i	$-0.691543\pi$
$3$		−	8.56686i		−	1.64869i	0.566085	−	0.824347i	$-0.308457\pi$
$4$	−5.10645	−	6.15826i	−0.638306	−	0.769783i
$5$		−	20.6960i		−	1.85110i	−0.378623	−	0.925551i	$-0.623602\pi$
$5$		−	20.6960i		−	1.85110i	0.378623	−	0.925551i	$-0.376398\pi$
$6$	21.9305	+	10.3044i	1.49218	+	0.701125i
$7$	−8.05854			−0.435120			−0.217560	−	0.976047i	$-0.569810\pi$
$7$	−8.05854			−0.435120			−0.217560	+	0.976047i	$0.569810\pi$
$8$	21.9068	−	5.66486i	0.968154	−	0.250354i
$9$	−46.3911			−1.71819
$10$	52.9801	+	24.8935i	1.67538	+	0.787201i
$11$			5.25206i			0.143960i	0.997406	+	0.0719799i	$0.0229317\pi$
$11$			5.25206i			0.143960i	−0.997406	+	0.0719799i	$0.977068\pi$
$12$	−52.7570	+	43.7463i	−1.26914	+	1.05237i
$13$			39.0312i			0.832715i	0.909201	+	0.416358i	$0.136694\pi$
$13$			39.0312i			0.832715i	−0.909201	+	0.416358i	$0.863306\pi$
$14$	9.69297	−	20.6293i	0.185040	−	0.393815i
$15$	−177.299			−3.05190
$16$	−11.8483	+	62.8937i	−0.185130	+	0.982714i
$17$	17.0000			0.242536
$17$	17.0000			0.242536
$18$	55.8002	−	118.758i	0.730679	−	1.55508i
$19$			4.13334i			0.0499080i	0.999689	+	0.0249540i	$0.00794393\pi$
$19$			4.13334i			0.0499080i	−0.999689	+	0.0249540i	$0.992056\pi$
$20$	−127.451	+	105.683i	−1.42495	+	1.18157i
$21$			69.0364i			0.717380i
$22$	−13.4449	−	6.31729i	−0.130294	−	0.0612204i
$23$	165.019			1.49604			0.748019	−	0.663678i	$-0.231005\pi$
$23$	165.019			1.49604			0.748019	+	0.663678i	$0.231005\pi$
$24$	−48.5301	−	187.673i	−0.412757	−	1.59619i
$25$	−303.322			−2.42658
$26$	−99.9169	−	46.9475i	−0.753666	−	0.354121i
$27$			166.121i			1.18408i
$28$	41.1505	+	49.6266i	0.277740	+	0.334948i
$29$		−	210.630i		−	1.34873i	−0.738400	−	0.674363i	$-0.764418\pi$
$29$		−	210.630i		−	1.34873i	0.738400	−	0.674363i	$-0.235582\pi$
$30$	213.259	−	453.873i	1.29785	−	2.76219i
$31$	207.818			1.20404			0.602020	−	0.798481i	$-0.294363\pi$
$31$	207.818			1.20404			0.602020	+	0.798481i	$0.294363\pi$
$32$	−146.752	−	105.981i	−0.810697	−	0.585466i
$33$	44.9937			0.237345
$34$	−20.4479	+	43.5188i	−0.103141	+	0.219512i
$35$			166.779i			0.805452i
$36$	236.894	+	285.689i	1.09673	+	1.32263i
$37$		−	199.271i		−	0.885403i	−0.896669	−	0.442702i	$-0.854020\pi$
$37$		−	199.271i		−	0.885403i	0.896669	−	0.442702i	$-0.145980\pi$
$38$	−10.5810	−	4.97166i	−0.0451703	−	0.0212239i
$39$	334.375			1.37289
$40$	−117.240	−	453.383i	−0.463431	−	1.79215i
$41$	−330.295			−1.25813			−0.629067	−	0.777351i	$-0.716563\pi$
$41$	−330.295			−1.25813			−0.629067	+	0.777351i	$0.716563\pi$
$42$	−176.728	−	83.0383i	−0.649279	−	0.305074i
$43$		−	142.199i		−	0.504306i	−0.967687	−	0.252153i	$-0.918861\pi$
$43$		−	142.199i		−	0.504306i	0.967687	−	0.252153i	$-0.0811387\pi$
$44$	32.3436	−	26.8194i	0.110818	−	0.0918904i
$45$			960.109i			3.18055i
$46$	−198.488	+	422.437i	−0.636206	+	1.35402i
$47$	−433.772			−1.34622			−0.673108	−	0.739544i	$-0.735041\pi$
$47$	−433.772			−1.34622			−0.673108	+	0.739544i	$0.735041\pi$
$48$	538.802	+	101.503i	1.62019	+	0.305223i
$49$	−278.060			−0.810670
$50$	364.842	−	776.483i	1.03193	−	2.19623i
$51$		−	145.637i		−	0.399867i
$52$	240.364	−	199.311i	0.641010	−	0.531527i
$53$			412.498i			1.06907i	0.845145	+	0.534537i	$0.179514\pi$
$53$			412.498i			1.06907i	−0.845145	+	0.534537i	$0.820486\pi$
$54$	−425.258	−	199.814i	−1.07167	−	0.503541i
$55$	108.696			0.266484
$56$	−176.537	+	45.6505i	−0.421264	+	0.108934i
$57$	35.4097			0.0822830
$58$	539.198	+	253.350i	1.22069	+	0.573561i
$59$			694.642i			1.53279i	0.642369	+	0.766396i	$0.277952\pi$
$59$			694.642i			1.53279i	−0.642369	+	0.766396i	$0.722048\pi$
$60$	905.370	+	1091.86i	1.94805	+	2.34930i
$61$		−	638.897i		−	1.34102i	−0.741900	−	0.670511i	$-0.766075\pi$
$61$		−	638.897i		−	1.34102i	0.741900	−	0.670511i	$-0.233925\pi$
$62$	−249.968	+	531.999i	−0.512031	+	1.08974i
$63$	373.845			0.747619
$64$	447.819	−	248.198i	0.874646	−	0.484762i
$65$	807.787			1.54144
$66$	−54.1193	+	115.181i	−0.100934	+	0.214814i
$67$		−	40.6728i		−	0.0741639i	−0.999312	−	0.0370819i	$-0.988194\pi$
$67$		−	40.6728i		−	0.0741639i	0.999312	−	0.0370819i	$-0.0118063\pi$
$68$	−86.8096	−	104.690i	−0.154812	−	0.186700i
$69$		−	1413.70i		−	2.46651i
$70$	−426.942	−	200.605i	−0.728991	−	0.342527i
$71$	627.885			1.04953			0.524763	−	0.851249i	$-0.324154\pi$
$71$	627.885			1.04953			0.524763	+	0.851249i	$0.324154\pi$
$72$	−1016.28	+	262.799i	−1.66347	+	0.430156i
$73$	−344.074			−0.551655			−0.275827	−	0.961207i	$-0.588952\pi$
$73$	−344.074			−0.551655			−0.275827	+	0.961207i	$0.588952\pi$
$74$	510.119	+	239.687i	0.801353	+	0.376527i
$75$			2598.52i			4.00069i
$76$	25.4542	−	21.1067i	0.0384183	−	0.0318566i
$77$		−	42.3240i		−	0.0626398i
$78$	−402.192	+	855.975i	−0.583837	+	1.24256i
$79$	−615.792			−0.876987			−0.438493	−	0.898734i	$-0.644488\pi$
$79$	−615.792			−0.876987			−0.438493	+	0.898734i	$0.644488\pi$
$80$	1301.64	+	245.213i	1.81910	+	0.342695i
$81$	170.577			0.233987
$82$	397.286	−	845.532i	0.535035	−	1.13870i
$83$		−	421.512i		−	0.557433i	−0.960373	−	0.278716i	$-0.910091\pi$
$83$		−	421.512i		−	0.557433i	0.960373	−	0.278716i	$-0.0899090\pi$
$84$	425.144	−	352.531i	0.552226	−	0.457908i
$85$		−	351.831i		−	0.448958i
$86$	364.020	+	171.040i	0.456433	+	0.214462i
$87$	−1804.44			−2.22364
$88$	29.7522	+	115.056i	0.0360409	+	0.139375i
$89$	1213.65			1.44547			0.722735	−	0.691126i	$-0.242885\pi$
$89$	1213.65			1.44547			0.722735	+	0.691126i	$0.242885\pi$
$90$	−2457.81	−	1154.84i	−2.87862	−	1.35256i
$91$		−	314.534i		−	0.362331i
$92$	−842.662	−	1016.23i	−0.954930	−	1.15162i
$93$		−	1780.35i		−	1.98509i
$94$	521.749	−	1110.42i	0.572493	−	1.21842i
$95$	85.5433			0.0923848
$96$	−907.922	+	1257.20i	−0.965254	+	1.33659i
$97$	−1821.02			−1.90615			−0.953074	−	0.302737i	$-0.902100\pi$
$97$	−1821.02			−1.90615			−0.953074	+	0.302737i	$0.902100\pi$
$98$	334.456	−	711.813i	0.344746	−	0.733714i
$99$		−	243.649i		−	0.247350i
$100$	1548.90	+	1867.94i	1.54890	+	1.86794i
$101$		−	773.610i		−	0.762149i	−0.924544	−	0.381074i	$-0.875554\pi$
$101$		−	773.610i		−	0.762149i	0.924544	−	0.381074i	$-0.124446\pi$
$102$	372.819	+	175.175i	0.361908	+	0.170048i
$103$	941.936			0.901085			0.450542	−	0.892755i	$-0.351231\pi$
$103$	941.936			0.901085			0.450542	+	0.892755i	$0.351231\pi$
$104$	221.106	+	855.049i	0.208473	+	0.806197i
$105$	1428.77			1.32794
$106$	−1055.96	−	496.160i	−0.967587	−	0.454635i
$107$		−	563.716i		−	0.509313i	−0.967032	−	0.254657i	$-0.918038\pi$
$107$		−	563.716i		−	0.509313i	0.967032	−	0.254657i	$-0.0819624\pi$
$108$	1023.02	−	848.290i	0.911481	−	0.755803i
$109$		−	1098.80i		−	0.965558i	−0.875742	−	0.482779i	$-0.839627\pi$
$109$		−	1098.80i		−	0.965558i	0.875742	−	0.482779i	$-0.160373\pi$
$110$	−130.742	+	278.255i	−0.113325	+	0.241187i
$111$	−1707.13			−1.45976
$112$	95.4803	−	506.831i	0.0805539	−	0.427599i
$113$	622.868			0.518535			0.259268	−	0.965806i	$-0.416519\pi$
$113$	622.868			0.518535			0.259268	+	0.965806i	$0.416519\pi$
$114$	−42.5915	+	90.6463i	−0.0349918	+	0.0744720i
$115$		−	3415.23i		−	2.76932i
$116$	−1297.12	+	1075.57i	−1.03823	+	0.860900i
$117$		−	1810.70i		−	1.43076i
$118$	−1778.23	−	835.529i	−1.38728	−	0.651836i
$119$	−136.995			−0.105532
$120$	−3884.07	+	1004.38i	−2.95471	+	0.764055i
$121$	1303.42			0.979276
$122$	1635.53	+	768.477i	1.21372	+	0.570284i
$123$			2829.60i			2.07428i
$124$	−1061.21	−	1279.80i	−0.768547	−	0.926849i
$125$			3690.55i			2.64074i
$126$	−449.668	+	957.015i	−0.317933	+	0.676648i
$127$	431.637			0.301587			0.150794	−	0.988565i	$-0.451817\pi$
$127$	431.637			0.301587			0.150794	+	0.988565i	$0.451817\pi$
$128$	96.7245	+	1444.92i	0.0667916	+	0.997767i
$129$	−1218.20			−0.831447
$130$	−971.622	+	2067.88i	−0.655515	+	1.39511i
$131$			1832.51i			1.22219i	0.791557	+	0.611096i	$0.209271\pi$
$131$			1832.51i			1.22219i	−0.791557	+	0.611096i	$0.790729\pi$
$132$	−229.758	−	277.083i	−0.151499	−	0.182704i
$133$		−	33.3087i		−	0.0217160i
$134$	104.119	+	48.9221i	0.0671235	+	0.0315390i
$135$	3438.04			2.19184
$136$	372.416	−	96.3026i	0.234812	−	0.0607197i
$137$	54.5018			0.0339884			0.0169942	−	0.999856i	$-0.494590\pi$
$137$	54.5018			0.0339884			0.0169942	+	0.999856i	$0.494590\pi$
$138$	3618.96	+	1700.42i	2.23236	+	1.04891i
$139$		−	590.938i		−	0.360595i	−0.983612	−	0.180298i	$-0.942294\pi$
$139$		−	590.938i		−	0.360595i	0.983612	−	0.180298i	$-0.0577061\pi$
$140$	1027.07	−	851.649i	0.620023	−	0.514125i
$141$			3716.06i			2.21950i
$142$	−755.233	+	1607.34i	−0.446322	+	0.949895i
$143$	−204.994			−0.119877
$144$	549.658	−	2917.71i	0.318089	−	1.68849i
$145$	−4359.19			−2.49663
$146$	413.859	−	880.803i	0.234597	−	0.499286i
$147$			2382.10i			1.33655i
$148$	−1227.16	+	1017.57i	−0.681568	+	0.565158i
$149$		−	1526.38i		−	0.839234i	−0.907701	−	0.419617i	$-0.862164\pi$
$149$		−	1526.38i		−	0.839234i	0.907701	−	0.419617i	$-0.137836\pi$
$150$	−6652.02	−	3125.55i	−3.62090	−	1.70134i
$151$	3439.31			1.85356			0.926779	−	0.375607i	$-0.122566\pi$
$151$	3439.31			1.85356			0.926779	+	0.375607i	$0.122566\pi$
$152$	23.4148	+	90.5483i	0.0124947	+	0.0483187i
$153$	−788.649			−0.416722
$154$	108.346	+	50.9081i	0.0566934	+	0.0266383i
$155$		−	4301.00i		−	2.22880i
$156$	−1707.47	−	2059.17i	−0.876326	−	1.05683i
$157$			543.393i			0.276226i	0.990416	+	0.138113i	$0.0441037\pi$
$157$			543.393i			0.276226i	−0.990416	+	0.138113i	$0.955896\pi$
$158$	740.686	−	1576.38i	0.372948	−	0.793735i
$159$	3533.81			1.76257
$160$	−2193.37	+	3037.17i	−1.08376	+	1.50068i
$161$	−1329.81			−0.650956
$162$	−205.173	+	436.664i	−0.0995057	+	0.211775i
$163$		−	2602.40i		−	1.25053i	−0.780414	−	0.625263i	$-0.784992\pi$
$163$		−	2602.40i		−	1.25053i	0.780414	−	0.625263i	$-0.215008\pi$
$164$	1686.64	+	2034.05i	0.803075	+	0.968489i
$165$		−	931.188i		−	0.439351i
$166$	1079.04	+	507.003i	0.504516	+	0.237054i
$167$	1019.95			0.472613			0.236306	−	0.971679i	$-0.424063\pi$
$167$	1019.95			0.472613			0.236306	+	0.971679i	$0.424063\pi$
$168$	391.082	+	1512.37i	0.179599	+	0.694534i
$169$	673.568			0.306585
$170$	900.662	+	423.189i	0.406339	+	0.190924i
$171$		−	191.750i		−	0.0857515i
$172$	−875.700	+	726.133i	−0.388206	+	0.321902i
$173$		−	753.537i		−	0.331158i	−0.986197	−	0.165579i	$-0.947051\pi$
$173$		−	753.537i		−	0.331158i	0.986197	−	0.165579i	$-0.0529493\pi$
$174$	2170.42	−	4619.24i	0.945625	−	2.01255i
$175$	2444.34			1.05585
$176$	−330.322	−	62.2282i	−0.141471	−	0.0266513i
$177$	5950.90			2.52710
$178$	−1459.80	+	3106.86i	−0.614702	+	1.30825i
$179$			1421.13i			0.593408i	0.954970	+	0.296704i	$0.0958874\pi$
$179$			1421.13i			0.593408i	−0.954970	+	0.296704i	$0.904113\pi$
$180$	5912.60	−	4902.75i	2.44833	−	2.03016i
$181$			438.282i			0.179985i	0.995942	+	0.0899924i	$0.0286843\pi$
$181$			438.282i			0.179985i	−0.995942	+	0.0899924i	$0.971316\pi$
$182$	805.184	+	378.328i	0.327935	+	0.154085i
$183$	−5473.34			−2.21093
$184$	3615.05	−	934.810i	1.44840	−	0.374539i
$185$	−4124.10			−1.63897
$186$	4557.57	+	2141.44i	1.79665	+	0.844183i
$187$			89.2851i			0.0349154i
$188$	2215.03	+	2671.28i	0.859298	+	1.03629i
$189$		−	1338.69i		−	0.515215i
$190$	−102.893	+	218.985i	−0.0392877	+	0.0836148i
$191$	1343.47			0.508955			0.254477	−	0.967079i	$-0.418097\pi$
$191$	1343.47			0.508955			0.254477	+	0.967079i	$0.418097\pi$
$192$	−2126.28	−	3836.40i	−0.799225	−	1.44202i
$193$	−3143.62			−1.17245			−0.586226	−	0.810148i	$-0.699387\pi$
$193$	−3143.62			−1.17245			−0.586226	+	0.810148i	$0.699387\pi$
$194$	2190.36	−	4661.67i	0.810610	−	1.72520i
$195$		−	6920.20i		−	2.54136i
$196$	1419.90	+	1712.37i	0.517456	+	0.624040i
$197$			1470.98i			0.531995i	0.963974	+	0.265997i	$0.0857013\pi$
$197$			1470.98i			0.531995i	−0.963974	+	0.265997i	$0.914299\pi$
$198$	623.724	+	293.066i	0.223869	+	0.105188i
$199$	−1671.06			−0.595268			−0.297634	−	0.954680i	$-0.596198\pi$
$199$	−1671.06			−0.595268			−0.297634	+	0.954680i	$0.596198\pi$
$200$	−6644.83	+	1718.28i	−2.34930	+	0.607504i
$201$	−348.439			−0.122273
$202$	1980.38	+	930.513i	0.689799	+	0.324112i
$203$			1697.37i			0.586858i
$204$	−896.868	+	743.686i	−0.307811	+	0.255238i
$205$			6835.78i			2.32893i
$206$	−1132.98	+	2411.29i	−0.383196	+	0.815546i
$207$	−7655.42			−2.57048
$208$	−2454.81	−	462.454i	−0.818321	−	0.154161i
$209$	−21.7085			−0.00718474
$210$	−1718.56	+	3657.56i	−0.564722	+	1.20188i
$211$			644.447i			0.210263i	0.994458	+	0.105132i	$0.0335264\pi$
$211$			644.447i			0.210263i	−0.994458	+	0.105132i	$0.966474\pi$
$212$	2540.27	−	2106.40i	0.822954	−	0.682396i
$213$		−	5379.01i		−	1.73035i
$214$	1443.07	+	678.049i	0.460964	+	0.216591i
$215$	−2942.95			−0.933523
$216$	941.054	+	3639.19i	0.296438	+	1.14637i
$217$	−1674.71			−0.523902
$218$	2812.84	+	1321.66i	0.873899	+	0.410614i
$219$			2947.63i			0.909509i
$220$	−555.053	−	669.381i	−0.170098	−	0.205135i
$221$			663.530i			0.201963i
$222$	2053.36	−	4370.12i	0.620778	−	1.32118i
$223$	−2250.73			−0.675874			−0.337937	−	0.941169i	$-0.609729\pi$
$223$	−2250.73			−0.675874			−0.337937	+	0.941169i	$0.609729\pi$
$224$	1182.61	+	854.049i	0.352751	+	0.254748i
$225$	14071.5			4.16932
$226$	−749.198	+	1594.50i	−0.220513	+	0.469311i
$227$		−	5544.75i		−	1.62122i	−0.585583	−	0.810612i	$-0.699135\pi$
$227$		−	5544.75i		−	1.62122i	0.585583	−	0.810612i	$-0.300865\pi$
$228$	−180.818	−	218.062i	−0.0525218	−	0.0633400i
$229$		−	2760.05i		−	0.796460i	−0.917286	−	0.398230i	$-0.869625\pi$
$229$		−	2760.05i		−	0.796460i	0.917286	−	0.398230i	$-0.130375\pi$
$230$	8742.73	+	4107.90i	2.50643	+	1.17768i
$231$	−362.584			−0.103274
$232$	−1193.19	−	4614.24i	−0.337659	−	1.30578i
$233$	630.553			0.177291			0.0886457	−	0.996063i	$-0.471746\pi$
$233$	630.553			0.177291			0.0886457	+	0.996063i	$0.471746\pi$
$234$	4635.26	+	2177.95i	1.29494	+	0.608448i
$235$			8977.32i			2.49198i
$236$	4277.79	−	3547.16i	1.17992	−	0.978390i
$237$			5275.40i			1.44588i
$238$	164.780	−	350.698i	0.0448787	−	0.0955141i
$239$	−13.5558			−0.00366882			−0.00183441	−	0.999998i	$-0.500584\pi$
$239$	−13.5558			−0.00366882			−0.00183441	+	0.999998i	$0.500584\pi$
$240$	2100.70	−	11151.0i	0.564999	−	2.99914i
$241$	−222.260			−0.0594066			−0.0297033	−	0.999559i	$-0.509456\pi$
$241$	−222.260			−0.0594066			−0.0297033	+	0.999559i	$0.509456\pi$
$242$	−1567.77	+	3336.65i	−0.416448	+	0.886314i
$243$			3023.96i			0.798302i
$244$	−3934.49	+	3262.49i	−1.03230	+	0.855983i
$245$			5754.72i			1.50063i
$246$	−7243.56	−	3403.49i	−1.87737	−	0.882109i
$247$	−161.329			−0.0415592
$248$	4552.64	−	1177.26i	1.16570	−	0.301436i
$249$	−3611.03			−0.919036
$250$	−9447.54	−	4439.07i	−2.39006	−	1.12301i
$251$		−	147.843i		−	0.0371783i	−0.999827	−	0.0185891i	$-0.994083\pi$
$251$		−	147.843i		−	0.0371783i	0.999827	−	0.0185891i	$-0.00591745\pi$
$252$	−1909.02	−	2302.23i	−0.477210	−	0.575504i
$253$			866.691i			0.215369i
$254$	−519.182	+	1104.96i	−0.128253	+	0.272958i
$255$	−3014.09			−0.740194
$256$	−3815.23	−	1490.37i	−0.931454	−	0.363860i
$257$	6549.04			1.58956			0.794782	−	0.606895i	$-0.207585\pi$
$257$	6549.04			1.58956			0.794782	+	0.606895i	$0.207585\pi$
$258$	1465.28	−	3118.51i	0.353582	−	0.752518i
$259$			1605.83i			0.385257i
$260$	−4124.92	−	4974.56i	−0.983911	−	1.18657i
$261$			9771.38i			2.31737i
$262$	−4691.09	−	2204.18i	−1.10617	−	0.519750i
$263$	−6384.10			−1.49681			−0.748404	−	0.663243i	$-0.769179\pi$
$263$	−6384.10			−1.49681			−0.748404	+	0.663243i	$0.769179\pi$
$264$	985.670	−	254.883i	0.229787	−	0.0594204i
$265$	8537.03			1.97896
$266$	85.2677	+	40.0643i	0.0196545	+	0.00923496i
$267$		−	10397.2i		−	2.38314i
$268$	−250.474	+	207.694i	−0.0570900	+	0.0473392i
$269$			3003.62i			0.680794i	0.940282	+	0.340397i	$0.110562\pi$
$269$			3003.62i			0.680794i	−0.940282	+	0.340397i	$0.889438\pi$
$270$	−4135.34	+	8801.12i	−0.932106	+	1.98377i
$271$	2933.44			0.657541			0.328770	−	0.944410i	$-0.393366\pi$
$271$	2933.44			0.657541			0.328770	+	0.944410i	$0.393366\pi$
$272$	−201.422	+	1069.19i	−0.0449007	+	0.238343i
$273$	−2694.57			−0.597373
$274$	−65.5558	+	139.521i	−0.0144539	+	0.0307619i
$275$		−	1593.07i		−	0.349330i
$276$	−8705.91	+	7218.97i	−1.89867	+	1.57439i
$277$		−	2200.81i		−	0.477378i	−0.971096	−	0.238689i	$-0.923282\pi$
$277$		−	2200.81i		−	0.477378i	0.971096	−	0.238689i	$-0.0767176\pi$
$278$	1512.76	+	710.792i	0.326364	+	0.153347i
$279$	−9640.92			−2.06877
$280$	944.781	+	3653.60i	0.201648	+	0.779802i
$281$	−241.674			−0.0513062			−0.0256531	−	0.999671i	$-0.508167\pi$
$281$	−241.674			−0.0513062			−0.0256531	+	0.999671i	$0.508167\pi$
$282$	−9512.85	−	4469.76i	−2.00880	−	0.943865i
$283$		−	5902.22i		−	1.23975i	−0.784699	−	0.619877i	$-0.787183\pi$
$283$		−	5902.22i		−	1.23975i	0.784699	−	0.619877i	$-0.212817\pi$
$284$	−3206.27	−	3866.68i	−0.669918	−	0.807906i
$285$		−	732.838i		−	0.152314i
$286$	246.571	−	524.770i	0.0509792	−	0.108498i
$287$	2661.70			0.547439
$288$	6807.98	+	4916.56i	1.39293	+	1.00594i
$289$	289.000			0.0588235
$290$	5243.32	−	11159.2i	1.06172	−	2.25963i
$291$			15600.4i			3.14265i
$292$	1757.00	+	2118.90i	0.352125	+	0.424654i
$293$		−	5782.55i		−	1.15297i	−0.817107	−	0.576485i	$-0.804424\pi$
$293$		−	5782.55i		−	1.15297i	0.817107	−	0.576485i	$-0.195576\pi$
$294$	−6098.01	−	2865.24i	−1.20967	−	0.568381i
$295$	14376.3			2.83735
$296$	−1128.84	−	4365.39i	−0.221664	−	0.857207i
$297$	−872.479			−0.170459
$298$	3907.42	+	1835.96i	0.759566	+	0.356893i
$299$			6440.89i			1.24577i
$300$	16002.4	−	13269.2i	3.07966	−	2.55366i
$301$			1145.92i			0.219434i
$302$	−4136.87	+	8804.39i	−0.788246	+	1.67760i
$303$	−6627.41			−1.25655
$304$	−259.961	−	48.9732i	−0.0490453	−	0.00923949i
$305$	−13222.6			−2.48237
$306$	948.603	−	2018.88i	0.177216	−	0.377163i
$307$		−	416.404i		−	0.0774119i	−0.999251	−	0.0387060i	$-0.987676\pi$
$307$		−	416.404i		−	0.0774119i	0.999251	−	0.0387060i	$-0.0123236\pi$
$308$	−260.642	+	216.125i	−0.0482190	+	0.0399834i
$309$		−	8069.44i		−	1.48561i
$310$	11010.2	+	5173.32i	2.01722	+	0.947823i
$311$	7291.97			1.32955			0.664774	−	0.747044i	$-0.268528\pi$
$311$	7291.97			1.32955			0.664774	+	0.747044i	$0.268528\pi$
$312$	7325.09	−	1894.19i	1.32917	−	0.343709i
$313$	−228.725			−0.0413046			−0.0206523	−	0.999787i	$-0.506574\pi$
$313$	−228.725			−0.0413046			−0.0206523	+	0.999787i	$0.506574\pi$
$314$	−1391.05	−	653.604i	−0.250004	−	0.117468i
$315$		−	7737.07i		−	1.38392i
$316$	3144.51	+	3792.20i	0.559786	+	0.675089i
$317$		−	415.114i		−	0.0735494i	−0.999324	−	0.0367747i	$-0.988292\pi$
$317$		−	415.114i		−	0.0735494i	0.999324	−	0.0367747i	$-0.0117084\pi$
$318$	−4250.54	+	9046.30i	−0.749554	+	1.59526i
$319$	1106.24			0.194162
$320$	−5136.70	−	9268.03i	−0.897345	−	1.61906i
$321$	−4829.28			−0.839701
$322$	1599.53	−	3404.22i	0.276826	−	0.589161i
$323$			70.2667i			0.0121045i
$324$	−871.042	−	1050.46i	−0.149356	−	0.180119i
$325$		−	11839.0i		−	2.02065i
$326$	6661.95	+	3130.22i	1.13181	+	0.531800i
$327$	−9413.26			−1.59191
$328$	−7235.73	+	1871.08i	−1.21807	+	0.314979i
$329$	3495.57			0.585766
$330$	2383.77	+	1120.05i	0.397643	+	0.186839i
$331$		−	4064.52i		−	0.674944i	−0.941336	−	0.337472i	$-0.890428\pi$
$331$		−	4064.52i		−	0.674944i	0.941336	−	0.337472i	$-0.109572\pi$
$332$	−2595.78	+	2152.43i	−0.429102	+	0.355813i
$333$			9244.40i			1.52129i
$334$	−1226.82	+	2611.00i	−0.200984	+	0.427748i
$335$	−841.763			−0.137285
$336$	−4341.95	−	817.966i	−0.704979	−	0.132809i
$337$	117.457			0.0189861			0.00949303	−	0.999955i	$-0.496978\pi$
$337$	117.457			0.0189861			0.00949303	+	0.999955i	$0.496978\pi$
$338$	−810.181	+	1724.28i	−0.130379	+	0.277481i
$339$		−	5336.02i		−	0.854906i
$340$	−2166.67	+	1796.61i	−0.345600	+	0.286573i
$341$			1091.47i			0.173333i
$342$	490.866	+	230.641i	0.0776112	+	0.0364668i
$343$	5004.84			0.787859
$344$	−805.539	−	3115.13i	−0.126255	−	0.488247i
$345$	−29257.8			−4.56576
$346$	1929.00	+	906.369i	0.299722	+	0.140829i
$347$		−	6292.18i		−	0.973435i	−0.873559	−	0.486718i	$-0.838194\pi$
$347$		−	6292.18i		−	0.973435i	0.873559	−	0.486718i	$-0.161806\pi$
$348$	9214.28	+	11112.2i	1.41936	+	1.71172i
$349$			147.615i			0.0226409i	0.999936	+	0.0113204i	$0.00360349\pi$
$349$			147.615i			0.0226409i	−0.999936	+	0.0113204i	$0.996397\pi$
$350$	−2940.09	+	6257.32i	−0.449013	+	0.955622i
$351$	−6483.90			−0.985998
$352$	556.617	−	770.750i	0.0842835	−	0.116708i
$353$	458.797			0.0691764			0.0345882	−	0.999402i	$-0.488988\pi$
$353$	458.797			0.0691764			0.0345882	+	0.999402i	$0.488988\pi$
$354$	−7157.86	+	15233.9i	−1.07468	+	2.28721i
$355$		−	12994.7i		−	1.94278i
$356$	−6197.45	−	7473.98i	−0.922652	−	1.11270i
$357$			1173.62i			0.173990i
$358$	−3637.98	−	1709.36i	−0.537076	−	0.252353i
$359$	5691.99			0.836801			0.418400	−	0.908263i	$-0.362591\pi$
$359$	5691.99			0.836801			0.418400	+	0.908263i	$0.362591\pi$
$360$	5438.88	+	21032.9i	0.796262	+	3.07926i
$361$	6841.92			0.997509
$362$	−1121.97	−	527.174i	−0.162899	−	0.0765405i
$363$		−	11166.2i		−	1.61453i
$364$	−1936.98	+	1606.15i	−0.278916	+	0.231278i
$365$			7120.93i			1.02117i
$366$	6583.44	−	14011.3i	0.940224	−	2.00105i
$367$	−7237.82			−1.02946			−0.514729	−	0.857353i	$-0.672107\pi$
$367$	−7237.82			−1.02946			−0.514729	+	0.857353i	$0.672107\pi$
$368$	−1955.20	+	10378.7i	−0.276962	+	1.47018i
$369$	15322.8			2.16171
$370$	4960.55	−	10557.4i	0.696991	−	1.48339i
$371$		−	3324.13i		−	0.465176i
$372$	−10963.9	+	9091.27i	−1.52809	+	1.26710i
$373$			3883.46i			0.539083i	0.962989	+	0.269542i	$0.0868722\pi$
$373$			3883.46i			0.539083i	−0.962989	+	0.269542i	$0.913128\pi$
$374$	−228.563	−	107.394i	−0.0316009	−	0.0148481i
$375$	31616.5			4.35378
$376$	−9502.57	+	2457.26i	−1.30334	+	0.337030i
$377$	8221.14			1.12310
$378$	3426.96	+	1610.21i	0.466306	+	0.219101i
$379$			548.095i			0.0742844i	0.999310	+	0.0371422i	$0.0118254\pi$
$379$			548.095i			0.0742844i	−0.999310	+	0.0371422i	$0.988175\pi$
$380$	−436.823	−	526.798i	−0.0589698	−	0.0711162i
$381$		−	3697.78i		−	0.497225i
$382$	−1615.96	+	3439.20i	−0.216439	+	0.460640i
$383$	−1947.62			−0.259840			−0.129920	−	0.991524i	$-0.541472\pi$
$383$	−1947.62			−0.259840			−0.129920	+	0.991524i	$0.541472\pi$
$384$	12378.4	−	828.626i	1.64501	−	0.110119i
$385$	−875.935			−0.115953
$386$	3781.21	−	8047.45i	0.498598	−	1.06115i
$387$			6596.78i			0.866494i
$388$	9298.94	+	11214.3i	1.21671	+	1.46732i
$389$			4709.09i			0.613780i	0.951745	+	0.306890i	$0.0992884\pi$
$389$			4709.09i			0.613780i	−0.951745	+	0.306890i	$0.900712\pi$
$390$	17715.2	+	8323.75i	2.30011	+	1.08074i
$391$	2805.33			0.362842
$392$	−6091.41	+	1575.17i	−0.784854	+	0.202954i
$393$	15698.9			2.01502
$394$	−3765.60	−	1769.32i	−0.481493	−	0.226237i
$395$			12744.4i			1.62339i
$396$	−1500.46	+	1244.18i	−0.190406	+	0.157885i
$397$		−	10430.6i		−	1.31863i	−0.751868	−	0.659313i	$-0.770847\pi$
$397$		−	10430.6i		−	1.31863i	0.751868	−	0.659313i	$-0.229153\pi$
$398$	2009.98	−	4277.79i	0.253144	−	0.538760i
$399$	−285.351			−0.0358030
$400$	3593.87	−	19077.1i	0.449233	−	2.38463i
$401$	−3594.45			−0.447626			−0.223813	−	0.974632i	$-0.571850\pi$
$401$	−3594.45			−0.447626			−0.223813	+	0.974632i	$0.571850\pi$
$402$	419.109	−	891.977i	0.0519981	−	0.110666i
$403$			8111.39i			1.00262i
$404$	−4764.09	+	3950.40i	−0.586689	+	0.486484i
$405$		−	3530.25i		−	0.433135i
$406$	−4345.15	−	2041.63i	−0.531148	−	0.249568i
$407$	1046.58			0.127462
$408$	−825.012	−	3190.44i	−0.100108	−	0.387133i
$409$	367.898			0.0444778			0.0222389	−	0.999753i	$-0.492921\pi$
$409$	367.898			0.0444778			0.0222389	+	0.999753i	$0.492921\pi$
$410$	−17499.1	−	8222.21i	−2.10785	−	0.990405i
$411$		−	466.910i		−	0.0560364i
$412$	−4809.95	−	5800.69i	−0.575168	−	0.693639i
$413$		−	5597.80i		−	0.666949i
$414$	9208.09	−	19597.3i	1.09312	−	2.32646i
$415$	−8723.59			−1.03187
$416$	4136.55	−	5727.90i	0.487526	−	0.675080i
$417$	−5062.49			−0.594511
$418$	26.1115	−	55.5723i	0.00305539	−	0.00650270i
$419$		−	1808.11i		−	0.210816i	−0.994429	−	0.105408i	$-0.966385\pi$
$419$		−	1808.11i		−	0.210816i	0.994429	−	0.105408i	$-0.0336149\pi$
$420$	−7295.96	−	8798.76i	−0.847635	−	1.02223i
$421$			7265.16i			0.841050i	0.907281	+	0.420525i	$0.138154\pi$
$421$			7265.16i			0.841050i	−0.907281	+	0.420525i	$0.861846\pi$
$422$	−1649.74	−	775.153i	−0.190303	−	0.0894168i
$423$	20123.2			2.31305
$424$	2336.74	+	9036.52i	0.267647	+	1.03503i
$425$	−5156.48			−0.588532
$426$	13769.9	+	6469.98i	1.56608	+	0.735848i
$427$			5148.57i			0.583506i
$428$	−3471.51	+	2878.59i	−0.392060	+	0.325098i
$429$			1756.16i			0.197641i
$430$	3539.84	−	7533.73i	0.396991	−	0.844904i
$431$	14869.3			1.66178			0.830892	−	0.556434i	$-0.187831\pi$
$431$	14869.3			1.66178			0.830892	+	0.556434i	$0.187831\pi$
$432$	−10448.0	−	1968.26i	−1.16361	−	0.219208i
$433$	−972.466			−0.107930			−0.0539650	−	0.998543i	$-0.517186\pi$
$433$	−972.466			−0.107930			−0.0539650	+	0.998543i	$0.517186\pi$
$434$	2014.38	−	4287.14i	0.222795	−	0.474169i
$435$			37344.6i			4.11618i
$436$	−6766.69	+	5610.96i	−0.743270	+	0.616322i
$437$			682.080i			0.0746643i
$438$	−7545.72	−	3545.47i	−0.823170	−	0.386779i
$439$	8576.61			0.932436			0.466218	−	0.884670i	$-0.345616\pi$
$439$	8576.61			0.932436			0.466218	+	0.884670i	$0.345616\pi$
$440$	2381.20	−	615.750i	0.257998	−	0.0667153i
$441$	12899.5			1.39289
$442$	−1698.59	−	798.107i	−0.182791	−	0.0858870i
$443$		−	13103.7i		−	1.40536i	−0.711505	−	0.702681i	$-0.751986\pi$
$443$		−	13103.7i		−	1.40536i	0.711505	−	0.702681i	$-0.248014\pi$
$444$	8717.35	+	10512.9i	0.931773	+	1.12370i
$445$		−	25117.7i		−	2.67571i
$446$	2707.22	−	5761.70i	0.287423	−	0.611714i
$447$	−13076.3			−1.38364
$448$	−3608.76	+	2000.12i	−0.380576	+	0.210930i
$449$	13740.9			1.44426			0.722128	−	0.691759i	$-0.243164\pi$
$449$	13740.9			1.44426			0.722128	+	0.691759i	$0.243164\pi$
$450$	−16925.4	+	36021.9i	−1.77305	+	3.77353i
$451$		−	1734.73i		−	0.181121i
$452$	−3180.64	−	3835.78i	−0.330984	−	0.399159i
$453$		−	29464.1i		−	3.05595i
$454$	14194.2	+	6669.33i	1.46732	+	0.689443i
$455$	−6509.58			−0.670712
$456$	775.715	−	200.591i	0.0796627	−	0.0205999i
$457$	16793.1			1.71892			0.859461	−	0.511201i	$-0.170799\pi$
$457$	16793.1			1.71892			0.859461	+	0.511201i	$0.170799\pi$
$458$	7065.53	+	3319.84i	0.720852	+	0.338703i
$459$			2824.06i			0.287181i
$460$	−21031.9	+	17439.7i	−2.13177	+	1.76767i
$461$			12378.9i			1.25063i	0.780371	+	0.625317i	$0.215030\pi$
$461$			12378.9i			1.25063i	−0.780371	+	0.625317i	$0.784970\pi$
$462$	436.123	−	928.187i	0.0439183	−	0.0934701i
$463$	−6756.12			−0.678150			−0.339075	−	0.940759i	$-0.610114\pi$
$463$	−6756.12			−0.678150			−0.339075	+	0.940759i	$0.610114\pi$
$464$	13247.3	+	2495.62i	1.32541	+	0.249690i
$465$	−36846.0			−3.67461
$466$	−758.441	+	1614.17i	−0.0753951	+	0.160461i
$467$			11878.5i			1.17703i	0.808487	+	0.588514i	$0.200287\pi$
$467$			11878.5i			1.17703i	−0.808487	+	0.588514i	$0.799713\pi$
$468$	−11150.8	+	9246.25i	−1.10138	+	0.913265i
$469$			327.764i			0.0322702i
$470$	−22981.3	−	10798.1i	−2.25542	−	1.05974i
$471$	4655.17			0.455412
$472$	3935.05	+	15217.4i	0.383740	+	1.48398i
$473$	746.839			0.0725998
$474$	−13504.6	−	6345.36i	−1.30863	−	0.614877i
$475$		−	1253.73i		−	0.121106i
$476$	699.559	+	843.652i	0.0673618	+	0.0812368i
$477$		−	19136.2i		−	1.83687i
$478$	16.3051	−	34.7017i	0.00156021	−	0.00332054i
$479$	−11912.4			−1.13631			−0.568153	−	0.822923i	$-0.692342\pi$
$479$	−11912.4			−1.13631			−0.568153	+	0.822923i	$0.692342\pi$
$480$	26019.0	+	18790.3i	2.47417	+	1.78678i
$481$	7777.77			0.737289
$482$	267.338	−	568.968i	0.0252633	−	0.0537672i
$483$			11392.3i			1.07323i
$484$	−6655.83	−	8026.77i	−0.625078	−	0.753829i
$485$			37687.7i			3.52848i
$486$	−7741.13	−	3637.28i	−0.722520	−	0.339487i
$487$	−9422.28			−0.876724			−0.438362	−	0.898799i	$-0.644441\pi$
$487$	−9422.28			−0.876724			−0.438362	+	0.898799i	$0.644441\pi$
$488$	−3619.26	−	13996.2i	−0.335730	−	1.29832i
$489$	−22294.4			−2.06173
$490$	−14731.6	−	6921.88i	−1.35818	−	0.638161i
$491$		−	7843.75i		−	0.720944i	−0.932770	−	0.360472i	$-0.882616\pi$
$491$		−	7843.75i		−	0.720944i	0.932770	−	0.360472i	$-0.117384\pi$
$492$	17425.4	−	14449.2i	1.59674	−	1.32402i
$493$		−	3580.71i		−	0.327114i
$494$	194.050	−	412.990i	0.0176735	−	0.0376140i
$495$	−5042.55			−0.457870
$496$	−2462.30	+	13070.5i	−0.222904	+	1.18323i
$497$	−5059.84			−0.456670
$498$	4343.42	−	9243.98i	0.390830	−	0.831793i
$499$			16829.7i			1.50982i	0.655829	+	0.754909i	$0.272319\pi$
$499$			16829.7i			1.50982i	−0.655829	+	0.754909i	$0.727681\pi$
$500$	22727.4	−	18845.6i	2.03280	−	1.68560i
$501$		−	8737.80i		−	0.779193i
$502$	378.467	+	177.828i	0.0336490	+	0.0158105i
$503$	2021.33			0.179178			0.0895891	−	0.995979i	$-0.471445\pi$
$503$	2021.33			0.179178			0.0895891	+	0.995979i	$0.471445\pi$
$504$	8189.75	−	2117.78i	0.723811	−	0.187169i
$505$	−16010.6			−1.41082
$506$	−2218.67	−	1042.47i	−0.194924	−	0.0915881i
$507$		−	5770.36i		−	0.505465i
$508$	−2204.13	−	2658.13i	−0.192505	−	0.232157i
$509$			15155.0i			1.31971i	0.751392	+	0.659856i	$0.229383\pi$
$509$			15155.0i			1.31971i	−0.751392	+	0.659856i	$0.770617\pi$
$510$	3625.41	−	7715.85i	0.314776	−	0.669928i
$511$	2772.73			0.240036
$512$	8404.28	−	7974.07i	0.725430	−	0.688296i
$513$	−686.635			−0.0590949
$514$	−7877.31	+	16765.1i	−0.675979	+	1.43867i
$515$		−	19494.3i		−	1.66800i
$516$	6220.68	+	7502.00i	0.530718	+	0.640033i
$517$		−	2278.20i		−	0.193801i
$518$	−4110.81	−	1931.53i	−0.348685	−	0.163835i
$519$	−6455.45			−0.545978
$520$	17696.1	−	4576.00i	1.49235	−	0.385906i
$521$	−3326.50			−0.279724			−0.139862	−	0.990171i	$-0.544666\pi$
$521$	−3326.50			−0.279724			−0.139862	+	0.990171i	$0.544666\pi$
$522$	−25014.0	−	11753.2i	−2.09738	−	0.985486i
$523$		−	16126.0i		−	1.34826i	−0.738611	−	0.674131i	$-0.764518\pi$
$523$		−	16126.0i		−	1.34826i	0.738611	−	0.674131i	$-0.235482\pi$
$524$	11285.1	−	9357.62i	0.940822	−	0.780132i
$525$		−	20940.3i		−	1.74078i
$526$	7678.92	−	16342.8i	0.636534	−	1.35472i
$527$	3532.91			0.292023
$528$	−533.101	+	2829.82i	−0.0439398	+	0.233243i
$529$	15064.3			1.23813
$530$	−10268.5	+	21854.2i	−0.841576	+	1.79110i
$531$		−	32225.2i		−	2.63363i
$532$	−205.123	+	170.089i	−0.0167166	+	0.0138615i
$533$		−	12891.8i		−	1.04767i
$534$	26616.0	+	12505.9i	2.15691	+	1.01345i
$535$	−11666.6			−0.942791
$536$	−230.406	−	891.013i	−0.0185672	−	0.0718021i
$537$	12174.6			0.978348
$538$	−7689.04	−	3612.81i	−0.616167	−	0.289515i
$539$		−	1460.39i		−	0.116704i
$540$	−17556.2	−	21172.3i	−1.39907	−	1.68724i
$541$		−	8047.04i		−	0.639500i	−0.947502	−	0.319750i	$-0.896401\pi$
$541$		−	8047.04i		−	0.639500i	0.947502	−	0.319750i	$-0.103599\pi$
$542$	−3528.39	+	7509.38i	−0.279626	+	0.595121i
$543$	3754.70			0.296740
$544$	−2494.78	−	1801.67i	−0.196623	−	0.141996i
$545$	−22740.7			−1.78735
$546$	3241.08	−	6897.90i	0.254039	−	0.540665i
$547$			21777.6i			1.70227i	0.524944	+	0.851137i	$0.324086\pi$
$547$			21777.6i			1.70227i	−0.524944	+	0.851137i	$0.675914\pi$
$548$	−278.311	−	335.636i	−0.0216950	−	0.0261636i
$549$			29639.1i			2.30413i
$550$	4078.14	+	1916.17i	0.316168	+	0.148556i
$551$	870.606			0.0673122
$552$	−8008.39	−	30969.6i	−0.617500	−	2.38796i
$553$	4962.38			0.381595
$554$	5633.91	+	2647.17i	0.432061	+	0.203010i
$555$			35330.6i			2.70216i
$556$	−3639.15	+	3017.60i	−0.277580	+	0.230170i
$557$			7384.24i			0.561724i	0.959748	+	0.280862i	$0.0906203\pi$
$557$			7384.24i			0.561724i	−0.959748	+	0.280862i	$0.909380\pi$
$558$	11596.3	−	24680.1i	0.879767	−	1.87238i
$559$	5550.20			0.419944
$560$	−10489.4	−	1976.06i	−0.791529	−	0.149114i
$561$	764.893			0.0575647
$562$	290.690	−	618.666i	0.0218185	−	0.0464357i
$563$		−	14417.9i		−	1.07929i	−0.841891	−	0.539647i	$-0.818558\pi$
$563$		−	14417.9i		−	1.07929i	0.841891	−	0.539647i	$-0.181442\pi$
$564$	22884.5	−	18975.9i	1.70853	−	1.41672i
$565$		−	12890.8i		−	0.959862i
$566$	15109.2	+	7099.30i	1.12206	+	0.527219i
$567$	−1374.60			−0.101813
$568$	13755.0	−	3556.88i	1.01610	−	0.262753i
$569$	17082.5			1.25858			0.629292	−	0.777169i	$-0.283345\pi$
$569$	17082.5			1.25858			0.629292	+	0.777169i	$0.283345\pi$
$570$	1876.01	+	881.472i	0.137855	+	0.0647733i
$571$			543.480i			0.0398317i	0.999802	+	0.0199159i	$0.00633984\pi$
$571$			543.480i			0.0398317i	−0.999802	+	0.0199159i	$0.993660\pi$
$572$	1046.79	+	1262.41i	0.0765185	+	0.0922796i
$573$		−	11509.4i		−	0.839111i
$574$	−3201.54	+	6813.75i	−0.232805	+	0.495471i
$575$	−50054.0			−3.63025
$576$	−20774.8	+	11514.2i	−1.50281	+	0.832914i
$577$	−19194.3			−1.38487			−0.692433	−	0.721482i	$-0.743461\pi$
$577$	−19194.3			−1.38487			−0.692433	+	0.721482i	$0.743461\pi$
$578$	−347.615	+	739.819i	−0.0250154	+	0.0532395i
$579$			26931.0i			1.93301i
$580$	22260.0	+	26845.0i	1.59361	+	1.92186i
$581$			3396.77i			0.242550i
$582$	−39935.9	−	18764.5i	−2.84432	−	1.33645i
$583$	−2166.46			−0.153904
$584$	−7537.56	+	1949.13i	−0.534087	+	0.138109i
$585$	−37474.2			−2.64849
$586$	14802.9	+	6955.37i	1.04352	+	0.490313i
$587$			26909.8i			1.89214i	0.323959	+	0.946071i	$0.394986\pi$
$587$			26909.8i			1.89214i	−0.323959	+	0.946071i	$0.605014\pi$
$588$	14669.6	−	12164.1i	1.02885	−	0.853126i
$589$			858.983i			0.0600913i
$590$	−17292.1	+	36802.2i	−1.20662	+	2.56801i
$591$	12601.7			0.877096
$592$	12532.9	+	2361.03i	0.870098	+	0.163915i
$593$	−2821.37			−0.195379			−0.0976895	−	0.995217i	$-0.531145\pi$
$593$	−2821.37			−0.195379			−0.0976895	+	0.995217i	$0.531145\pi$
$594$	1049.44	−	2233.48i	0.0724896	−	0.154278i
$595$			2835.25i			0.195351i
$596$	−9399.84	+	7794.38i	−0.646028	+	0.535688i
$597$			14315.7i			0.981415i
$598$	−16488.2	−	7747.23i	−1.12751	−	0.529779i
$599$	1551.65			0.105841			0.0529203	−	0.998599i	$-0.483147\pi$
$599$	1551.65			0.105841			0.0529203	+	0.998599i	$0.483147\pi$
$600$	14720.3	+	56925.4i	1.00159	+	3.87328i
$601$	23011.4			1.56182			0.780912	−	0.624641i	$-0.214755\pi$
$601$	23011.4			1.56182			0.780912	+	0.624641i	$0.214755\pi$
$602$	−2933.47	−	1378.33i	−0.198603	−	0.0933167i
$603$			1886.86i			0.127428i
$604$	−17562.7	−	21180.2i	−1.18314	−	1.42684i
$605$		−	26975.4i		−	1.81274i
$606$	7971.58	−	16965.7i	0.534362	−	1.13727i
$607$	−3339.61			−0.223312			−0.111656	−	0.993747i	$-0.535615\pi$
$607$	−3339.61			−0.223312			−0.111656	+	0.993747i	$0.535615\pi$
$608$	438.054	−	606.575i	0.0292194	−	0.0404603i
$609$	14541.2			0.967549
$610$	15904.4	−	33848.8i	1.05565	−	2.24672i
$611$		−	16930.6i		−	1.12101i
$612$	4027.20	+	4856.71i	0.265996	+	0.320786i
$613$			25245.2i			1.66337i	0.555249	+	0.831684i	$0.312623\pi$
$613$			25245.2i			1.66337i	−0.555249	+	0.831684i	$0.687377\pi$
$614$	1065.96	+	500.859i	0.0700633	+	0.0329203i
$615$	58561.2			3.83970
$616$	−239.759	−	927.184i	−0.0156821	−	0.0606450i
$617$	−23301.2			−1.52037			−0.760186	−	0.649706i	$-0.774892\pi$
$617$	−23301.2			−1.52037			−0.760186	+	0.649706i	$0.774892\pi$
$618$	20657.2	+	9706.08i	1.34458	+	0.631773i
$619$			19894.1i			1.29178i	0.763429	+	0.645891i	$0.223514\pi$
$619$			19894.1i			1.29178i	−0.763429	+	0.645891i	$0.776486\pi$
$620$	−26486.7	+	21962.8i	−1.71569	+	1.42266i
$621$			27413.2i			1.77142i
$622$	−8770.93	+	18666.9i	−0.565405	+	1.20334i
$623$	−9780.26			−0.628953
$624$	−3961.78	+	21030.1i	−0.254164	+	1.34916i
$625$	38464.2			2.46171
$626$	275.115	−	585.520i	0.0175652	−	0.0373835i
$627$			185.974i			0.0118454i
$628$	3346.35	−	2774.81i	0.212634	−	0.176317i
$629$		−	3387.60i		−	0.214742i
$630$	19806.3	+	9306.30i	1.25255	+	0.588527i
$631$	−6189.26			−0.390477			−0.195238	−	0.980756i	$-0.562548\pi$
$631$	−6189.26			−0.390477			−0.195238	+	0.980756i	$0.562548\pi$
$632$	−13490.0	+	3488.37i	−0.849059	+	0.219557i
$633$	5520.89			0.346660
$634$	1062.66	+	499.308i	0.0665674	+	0.0312777i
$635$		−	8933.14i		−	0.558269i
$636$	−18045.2	−	21762.1i	−1.12506	−	1.35680i
$637$		−	10853.0i		−	0.675058i
$638$	−1330.61	+	2831.90i	−0.0825696	+	0.175731i
$639$	−29128.3			−1.80328
$640$	29904.0	−	2001.81i	1.84697	−	0.123638i
$641$	15120.0			0.931676			0.465838	−	0.884870i	$-0.345753\pi$
$641$	15120.0			0.931676			0.465838	+	0.884870i	$0.345753\pi$
$642$	5808.75	−	12362.6i	0.357092	−	0.759989i
$643$			5421.77i			0.332525i	0.986081	+	0.166263i	$0.0531700\pi$
$643$			5421.77i			0.332525i	−0.986081	+	0.166263i	$0.946830\pi$
$644$	6790.62	+	8189.33i	0.415509	+	0.501095i
$645$			25211.8i			1.53909i
$646$	−179.878	−	84.5182i	−0.0109554	−	0.00514756i
$647$	−14138.0			−0.859077			−0.429538	−	0.903049i	$-0.641324\pi$
$647$	−14138.0			−0.859077			−0.429538	+	0.903049i	$0.641324\pi$
$648$	3736.80	−	966.294i	0.226536	−	0.0585797i
$649$	−3648.30			−0.220660
$650$	30307.0	+	14240.2i	1.82883	+	0.859303i
$651$			14347.0i			0.863754i
$652$	−16026.3	+	13289.0i	−0.962633	+	0.798218i
$653$			4624.70i			0.277150i	0.990352	+	0.138575i	$0.0442521\pi$
$653$			4624.70i			0.277150i	−0.990352	+	0.138575i	$0.955748\pi$
$654$	11322.5	−	24097.3i	0.676977	−	1.44079i
$655$	37925.5			2.26240
$656$	3913.45	−	20773.5i	0.232919	−	1.23639i
$657$	15962.0			0.947847
$658$	−4204.54	+	8948.40i	−0.249103	+	0.530159i
$659$			1757.29i			0.103876i	0.998650	+	0.0519381i	$0.0165399\pi$
$659$			1757.29i			0.103876i	−0.998650	+	0.0519381i	$0.983460\pi$
$660$	−5734.50	+	4755.06i	−0.338204	+	0.280440i
$661$		−	6124.52i		−	0.360388i	−0.983631	−	0.180194i	$-0.942327\pi$
$661$		−	6124.52i		−	0.360388i	0.983631	−	0.180194i	$-0.0576725\pi$
$662$	10404.9	+	4888.89i	0.610872	+	0.287027i
$663$	5684.37			0.332975
$664$	−2387.81	−	9233.99i	−0.139556	−	0.539681i
$665$	−689.354			−0.0401985
$666$	−23665.0	−	11119.3i	−1.37688	−	0.646946i
$667$		−	34758.0i		−	2.01774i
$668$	−5208.34	−	6281.13i	−0.301672	−	0.363809i
$669$			19281.7i			1.11431i
$670$	1012.49	−	2154.85i	0.0583819	−	0.124253i
$671$	3355.53			0.193053
$672$	7316.52	−	10131.2i	0.420001	−	0.581578i
$673$	−23827.6			−1.36477			−0.682383	−	0.730995i	$-0.739056\pi$
$673$	−23827.6			−1.36477			−0.682383	+	0.730995i	$0.739056\pi$
$674$	−141.280	+	300.682i	−0.00807403	+	0.0171837i
$675$		−	50388.3i		−	2.87325i
$676$	−3439.54	−	4148.01i	−0.195695	−	0.236004i
$677$		−	16611.9i		−	0.943053i	−0.881852	−	0.471527i	$-0.843703\pi$
$677$		−	16611.9i		−	0.943053i	0.881852	−	0.471527i	$-0.156297\pi$
$678$	13659.8	+	6418.27i	0.773750	+	0.363558i
$679$	14674.7			0.829404
$680$	−1993.07	−	7707.51i	−0.112398	−	0.434661i
$681$	−47501.1			−2.67290
$682$	−2794.10	−	1312.85i	−0.156879	−	0.0737119i
$683$			17726.7i			0.993111i	0.868005	+	0.496556i	$0.165402\pi$
$683$			17726.7i			0.993111i	−0.868005	+	0.496556i	$0.834598\pi$
$684$	−1180.85	+	979.163i	−0.0660100	+	0.0547357i
$685$		−	1127.97i		−	0.0629159i
$686$	−6019.91	+	12812.0i	−0.335046	+	0.713068i
$687$	−23645.0			−1.31312
$688$	8943.43	+	1684.82i	0.495589	+	0.0933624i
$689$	−16100.3			−0.890234
$690$	35191.8	−	74897.8i	1.94164	−	4.13233i
$691$		−	11716.9i		−	0.645055i	−0.946560	−	0.322527i	$-0.895468\pi$
$691$		−	11716.9i		−	0.645055i	0.946560	−	0.322527i	$-0.104532\pi$
$692$	−4640.48	+	3847.90i	−0.254920	+	0.211380i
$693$			1963.46i			0.107627i
$694$	16107.5	+	7568.36i	0.881028	+	0.413964i
$695$	−12230.0			−0.667499
$696$	−39529.6	+	10221.9i	−2.15282	+	0.556696i
$697$	−5615.02			−0.305142
$698$	−377.885	−	177.555i	−0.0204916	−	0.00962829i
$699$		−	5401.86i		−	0.292299i
$700$	−12481.9	−	15052.9i	−0.673958	−	0.812778i
$701$		−	14664.7i		−	0.790123i	−0.918655	−	0.395062i	$-0.870723\pi$
$701$		−	14664.7i		−	0.790123i	0.918655	−	0.395062i	$-0.129277\pi$
$702$	7798.97	−	16598.3i	0.419306	−	0.892398i
$703$	823.653			0.0441887
$704$	1303.55	+	2351.97i	0.0697863	+	0.125914i
$705$	76907.5			4.10852
$706$	−551.850	+	1174.49i	−0.0294180	+	0.0626096i
$707$			6234.16i			0.331626i
$708$	−30388.0	−	36647.2i	−1.61307	−	1.94532i
$709$		−	14265.9i		−	0.755668i	−0.925873	−	0.377834i	$-0.876669\pi$
$709$		−	14265.9i		−	0.755668i	0.925873	−	0.377834i	$-0.123331\pi$
$710$	33265.4	+	15630.3i	1.75835	+	0.826188i
$711$	28567.3			1.50683
$712$	26587.3	−	6875.17i	1.39944	−	0.361879i
$713$	34294.0			1.80129
$714$	−3004.38	−	1411.65i	−0.157473	−	0.0739912i
$715$			4242.55i			0.221905i
$716$	8751.67	−	7256.91i	0.456795	−	0.378776i
$717$			116.130i			0.00604876i
$718$	−6846.43	+	14571.1i	−0.355859	+	0.757364i
$719$	−11096.8			−0.575578			−0.287789	−	0.957694i	$-0.592920\pi$
$719$	−11096.8			−0.575578			−0.287789	+	0.957694i	$0.592920\pi$
$720$	−60384.8	−	11375.7i	−3.12557	−	0.588815i
$721$	−7590.63			−0.392080
$722$	−8229.59	+	17514.8i	−0.424202	+	0.902816i
$723$			1904.07i			0.0979433i
$724$	2699.05	−	2238.06i	0.138549	−	0.114885i
$725$			63888.9i			3.27279i
$726$	28584.6	+	13430.9i	1.46126	+	0.686595i
$727$	7441.77			0.379642			0.189821	−	0.981819i	$-0.439209\pi$
$727$	7441.77			0.379642			0.189821	+	0.981819i	$0.439209\pi$
$728$	−1781.79	−	6890.45i	−0.0907110	−	0.350793i
$729$	30511.5			1.55014
$730$	−18229.1	−	8565.20i	−0.924230	−	0.434263i
$731$		−	2417.39i		−	0.122312i
$732$	27949.3	+	33706.2i	1.41125	+	1.70194i
$733$		−	33515.8i		−	1.68886i	−0.535665	−	0.844431i	$-0.679939\pi$
$733$		−	33515.8i		−	1.68886i	0.535665	−	0.844431i	$-0.320061\pi$
$734$	8705.79	−	18528.3i	0.437788	−	0.931732i
$735$	49299.9			2.47409
$736$	−24216.9	−	17488.8i	−1.21283	−	0.875879i
$737$	213.616			0.0106766
$738$	−18430.5	+	39225.2i	−0.919292	+	1.95650i
$739$		−	12955.1i		−	0.644872i	−0.946591	−	0.322436i	$-0.895498\pi$
$739$		−	12955.1i		−	0.644872i	0.946591	−	0.322436i	$-0.104502\pi$
$740$	21059.5	+	25397.3i	1.04617	+	1.26165i
$741$			1382.08i			0.0685183i
$742$	8509.52	+	3998.33i	0.421017	+	0.197821i
$743$	12309.9			0.607813			0.303907	−	0.952702i	$-0.401709\pi$
$743$	12309.9			0.607813			0.303907	+	0.952702i	$0.401709\pi$
$744$	−10085.4	−	39001.8i	−0.496976	−	1.92188i
$745$	−31589.9			−1.55351
$746$	−9941.38	−	4671.11i	−0.487909	−	0.229251i
$747$			19554.4i			0.957776i
$748$	549.841	−	455.930i	0.0268772	−	0.0222867i
$749$			4542.73i			0.221612i
$750$	−38028.9	+	80935.8i	−1.85149	+	3.94048i
$751$	12807.5			0.622305			0.311153	−	0.950360i	$-0.399285\pi$
$751$	12807.5			0.622305			0.311153	+	0.950360i	$0.399285\pi$
$752$	5139.48	−	27281.5i	0.249225	−	1.32294i
$753$	−1266.55			−0.0612956
$754$	−9888.55	+	21045.5i	−0.477613	+	1.01649i
$755$		−	71179.9i		−	3.43113i
$756$	−8244.03	+	6835.97i	−0.396604	+	0.328865i
$757$		−	5388.72i		−	0.258727i	−0.991597	−	0.129363i	$-0.958707\pi$
$757$		−	5388.72i		−	0.258727i	0.991597	−	0.129363i	$-0.0412934\pi$
$758$	−1403.08	−	659.260i	−0.0672326	−	0.0315902i
$759$	7424.82			0.355078
$760$	1873.98	−	484.591i	0.0894428	−	0.0231289i
$761$	−13989.0			−0.666359			−0.333180	−	0.942863i	$-0.608122\pi$
$761$	−13989.0			−0.666359			−0.333180	+	0.942863i	$0.608122\pi$
$762$	9466.03	+	4447.76i	0.450024	+	0.211450i
$763$			8854.71i			0.420134i
$764$	−6860.38	−	8273.46i	−0.324869	−	0.391785i
$765$			16321.8i			0.771396i
$766$	2342.64	−	4985.77i	0.110500	−	0.235174i
$767$	−27112.7			−1.27638
$768$	−12767.8	+	32684.6i	−0.599894	+	1.53568i
$769$	−35283.3			−1.65455			−0.827275	−	0.561798i	$-0.810110\pi$
$769$	−35283.3			−1.65455			−0.827275	+	0.561798i	$0.810110\pi$
$770$	1053.59	−	2242.33i	0.0493101	−	0.104945i
$771$		−	56104.7i		−	2.62070i
$772$	16052.8	+	19359.3i	0.748383	+	0.902532i
$773$			850.590i			0.0395778i	0.999804	+	0.0197889i	$0.00629941\pi$
$773$			850.590i			0.0395778i	−0.999804	+	0.0197889i	$0.993701\pi$
$774$	−16887.3	−	7934.74i	−0.784239	−	0.368486i
$775$	−63035.9			−2.92170
$776$	−39892.7	+	10315.8i	−1.84545	+	0.477212i
$777$	13756.9			0.635170
$778$	−12054.9	−	5664.19i	−0.555515	−	0.261017i
$779$		−	1365.22i		−	0.0627910i
$780$	−42616.4	+	35337.7i	−1.95630	+	1.62217i
$781$			3297.69i			0.151089i
$782$	−3374.30	+	7181.43i	−0.154303	+	0.328398i
$783$	34990.1			1.59699
$784$	3294.55	−	17488.2i	0.150080	−	0.796657i
$785$	11246.0			0.511322
$786$	−18882.9	+	40187.9i	−0.856909	+	1.82373i
$787$			28860.8i			1.30721i	0.756834	+	0.653607i	$0.226745\pi$
$787$			28860.8i			1.30721i	−0.756834	+	0.653607i	$0.773255\pi$
$788$	9058.68	−	7511.48i	0.409520	−	0.339576i
$789$			54691.7i			2.46778i
$790$	−32624.7	−	15329.2i	−1.46928	−	0.690365i
$791$	−5019.41			−0.225625
$792$	−1380.24	−	5337.58i	−0.0619251	−	0.239473i
$793$	24936.9			1.11669
$794$	26701.5	+	12546.1i	1.19345	+	0.560760i
$795$		−	73135.6i		−	3.26271i
$796$	8533.19	+	10290.8i	0.379963	+	0.458227i
$797$		−	16858.1i		−	0.749238i	−0.927179	−	0.374619i	$-0.877773\pi$
$797$		−	16858.1i		−	0.749238i	0.927179	−	0.374619i	$-0.122227\pi$
$798$	343.225	−	730.477i	0.0152256	−	0.0324043i
$799$	−7374.12			−0.326505
$800$	44513.1	+	32146.3i	1.96722	+	1.42068i
$801$	−56302.7			−2.48359
$802$	4323.47	−	9201.52i	0.190358	−	0.405133i
$803$		−	1807.10i		−	0.0794160i
$804$	1779.28	+	2145.78i	0.0780479	+	0.0941240i
$805$			27521.7i			1.20499i
$806$	−20764.6	−	9756.54i	−0.907445	−	0.426376i
$807$	25731.6			1.12242
$808$	−4382.39	−	16947.3i	−0.190807	−	0.737878i
$809$	20750.9			0.901807			0.450903	−	0.892573i	$-0.351102\pi$
$809$	20750.9			0.901807			0.450903	+	0.892573i	$0.351102\pi$
$810$	9037.18	+	4246.25i	0.392017	+	0.184195i
$811$			30953.6i			1.34023i	0.742257	+	0.670116i	$0.233756\pi$
$811$			30953.6i			1.34023i	−0.742257	+	0.670116i	$0.766244\pi$
$812$	10452.9	−	8667.54i	0.451753	−	0.374595i
$813$		−	25130.3i		−	1.08408i
$814$	−1258.85	+	2679.18i	−0.0542048	+	0.115362i
$815$	−53859.1			−2.31485
$816$	9159.63	+	1725.55i	0.392955	+	0.0740275i
$817$	587.757			0.0251689
$818$	−442.515	+	941.793i	−0.0189147	+	0.0402555i
$819$			14591.6i			0.622554i
$820$	42096.5	−	34906.6i	1.79277	−	1.48657i
$821$		−	43022.3i		−	1.82885i	−0.404752	−	0.914427i	$-0.632642\pi$
$821$		−	43022.3i		−	1.82885i	0.404752	−	0.914427i	$-0.367358\pi$
$822$	1195.25	+	561.608i	0.0507169	+	0.0238301i
$823$	16576.9			0.702109			0.351055	−	0.936355i	$-0.385823\pi$
$823$	16576.9			0.702109			0.351055	+	0.936355i	$0.385823\pi$
$824$	20634.8	−	5335.94i	0.872389	−	0.225590i
$825$	−13647.6			−0.575938
$826$	14330.0	+	6733.14i	0.603636	+	0.283627i
$827$			24170.6i			1.01632i	0.861263	+	0.508159i	$0.169674\pi$
$827$			24170.6i			1.01632i	−0.861263	+	0.508159i	$0.830326\pi$
$828$	39092.0	+	47144.1i	1.64075	+	1.97871i
$829$			1458.19i			0.0610918i	0.999533	+	0.0305459i	$0.00972457\pi$
$829$			1458.19i			0.0610918i	−0.999533	+	0.0305459i	$0.990275\pi$
$830$	10492.9	−	22331.7i	0.438812	−	0.933911i
$831$	−18854.0			−0.787050
$832$	9687.47	+	17478.9i	0.403669	+	0.728331i
$833$	−4727.02			−0.196616
$834$	6089.26	−	12959.6i	0.252822	−	0.538074i
$835$		−	21108.9i		−	0.874854i
$836$	110.854	+	133.687i	0.00458607	+	0.00553069i
$837$			34523.0i			1.42568i
$838$	4628.63	+	2174.83i	0.190804	+	0.0896519i
$839$	−41349.0			−1.70146			−0.850730	−	0.525603i	$-0.823840\pi$
$839$	−41349.0			−1.70146			−0.850730	+	0.525603i	$0.823840\pi$
$840$	31299.9	−	8093.81i	1.28565	−	0.332456i
$841$	−19976.1			−0.819062
$842$	−18598.3	−	8738.68i	−0.761210	−	0.357666i
$843$			2070.38i			0.0845881i
$844$	3968.67	−	3290.84i	0.161857	−	0.134212i
$845$		−	13940.1i		−	0.567521i
$846$	−24204.5	+	51513.8i	−0.983652	+	2.09348i
$847$	−10503.6			−0.426103
$848$	−25943.5	−	4887.41i	−1.05059	−	0.197918i
$849$	−50563.5			−2.04397
$850$	6202.32	−	13200.2i	0.250280	−	0.532663i
$851$		−	32883.5i		−	1.32460i
$852$	−33125.3	+	27467.6i	−1.33199	+	1.10449i
$853$			28531.1i			1.14524i	0.819823	+	0.572618i	$0.194072\pi$
$853$			28531.1i			1.14524i	−0.819823	+	0.572618i	$0.805928\pi$
$854$	−13180.0	−	6192.80i	−0.528114	−	0.248142i
$855$	−3968.45			−0.158735
$856$	−3193.37	−	12349.2i	−0.127509	−	0.493094i
$857$	32741.4			1.30505			0.652523	−	0.757769i	$-0.273711\pi$
$857$	32741.4			1.30505			0.652523	+	0.757769i	$0.273711\pi$
$858$	−4495.63	−	2112.34i	−0.178879	−	0.0840491i
$859$			20090.8i			0.798008i	0.916949	+	0.399004i	$0.130644\pi$
$859$			20090.8i			0.798008i	−0.916949	+	0.399004i	$0.869356\pi$
$860$	15028.0	+	18123.4i	0.595873	+	0.718610i
$861$		−	22802.4i		−	0.902560i
$862$	−17885.1	+	38064.3i	−0.706692	+	1.50403i
$863$	36960.9			1.45790			0.728948	−	0.684569i	$-0.240010\pi$
$863$	36960.9			1.45790			0.728948	+	0.684569i	$0.240010\pi$
$864$	17605.6	−	24378.6i	0.693236	−	0.959927i
$865$	−15595.2			−0.613007
$866$	1169.70	−	2489.44i	0.0458984	−	0.0976843i
$867$		−	2475.82i		−	0.0969820i
$868$	8551.83	+	10313.3i	0.334410	+	0.403291i
$869$		−	3234.18i		−	0.126251i
$870$	−95599.5	−	44918.8i	−3.72543	−	1.75045i
$871$	1587.51			0.0617574
$872$	−6224.54	−	24071.2i	−0.241731	−	0.934809i
$873$	84479.1			3.27513
$874$	−1746.07	−	820.419i	−0.0675765	−	0.0317518i
$875$		−	29740.5i		−	1.14904i
$876$	18152.3	−	15051.9i	0.700124	−	0.580545i
$877$			5.94030i			0.000228723i	1.00000		0.000114361i	$3.64023e-5\pi$
$877$			5.94030i			0.000228723i	−1.00000		0.000114361i	$0.999964\pi$
$878$	−10316.1	+	21955.5i	−0.396529	+	0.843921i
$879$	−49538.3			−1.90090
$880$	−1287.87	+	6836.32i	−0.0493343	+	0.261878i
$881$	4903.14			0.187504			0.0937520	−	0.995596i	$-0.470114\pi$
$881$	4903.14			0.187504			0.0937520	+	0.995596i	$0.470114\pi$
$882$	−15515.8	+	33021.8i	−0.592340	+	1.26066i
$883$			20565.9i			0.783803i	0.920007	+	0.391902i	$0.128183\pi$
$883$			20565.9i			0.783803i	−0.920007	+	0.391902i	$0.871817\pi$
$884$	4086.19	−	3388.28i	0.155468	−	0.128914i
$885$		−	123160.i		−	4.67793i
$886$	33544.5	+	15761.4i	1.27195	+	0.597645i
$887$	17073.3			0.646297			0.323148	−	0.946348i	$-0.395259\pi$
$887$	17073.3			0.646297			0.323148	+	0.946348i	$0.395259\pi$
$888$	−37397.7	+	9670.63i	−1.41327	+	0.365456i
$889$	−3478.36			−0.131227
$890$	64299.4	+	30212.0i	2.42171	+	1.13788i
$891$			895.880i			0.0336848i
$892$	11493.2	+	13860.6i	0.431415	+	0.520276i
$893$		−	1792.93i		−	0.0671870i
$894$	15728.4	−	33474.3i	0.588408	−	1.25229i
$895$	29411.6			1.09846
$896$	−779.458	−	11644.0i	−0.0290624	−	0.434149i
$897$	55178.2			2.05390
$898$	−16527.8	+	35175.6i	−0.614186	+	1.30715i
$899$		−	43772.8i		−	1.62392i
$900$	−71855.3	−	86655.8i	−2.66131	−	3.20947i
$901$			7012.46i			0.259288i
$902$	4440.79	+	2086.57i	0.163927	+	0.0770235i
$903$	9816.92			0.361779
$904$	13645.1	−	3528.46i	0.502022	−	0.129817i
$905$	9070.66			0.333170
$906$	75426.0	+	35440.0i	2.76585	+	1.29958i
$907$			3032.99i			0.111035i	0.998458	+	0.0555175i	$0.0176809\pi$
$907$			3032.99i			0.111035i	−0.998458	+	0.0555175i	$0.982319\pi$
$908$	−34146.0	+	28314.0i	−1.24799	+	1.03484i
$909$			35888.6i			1.30952i
$910$	7829.85	−	16664.1i	0.285228	−	0.607042i
$911$	15016.9			0.546137			0.273068	−	0.961995i	$-0.411961\pi$
$911$	15016.9			0.546137			0.273068	+	0.961995i	$0.411961\pi$
$912$	−419.546	+	2227.05i	−0.0152331	+	0.0808607i
$913$	2213.81			0.0802479
$914$	−20199.1	+	42989.1i	−0.730991	+	1.55575i
$915$			113276.i			4.09266i
$916$	−16997.1	+	14094.1i	−0.613101	+	0.508385i
$917$		−	14767.3i		−	0.531800i
$918$	−7229.39	−	3396.84i	−0.259919	−	0.122127i
$919$	−10110.9			−0.362923			−0.181462	−	0.983398i	$-0.558083\pi$
$919$	−10110.9			−0.362923			−0.181462	+	0.983398i	$0.558083\pi$
$920$	−19346.8	−	74816.8i	−0.693310	−	2.68113i
$921$	−3567.28			−0.127629
$922$	−31689.0	−	14889.6i	−1.13191	−	0.531846i
$923$			24507.1i			0.873956i
$924$	1851.51	+	2232.88i	0.0659203	+	0.0794984i
$925$			60443.3i			2.14850i
$926$	8126.39	−	17295.2i	0.288391	−	0.613774i
$927$	−43697.5			−1.54824
$928$	−22322.7	+	30910.4i	−0.789633	+	1.09341i
$929$	46605.2			1.64593			0.822965	−	0.568093i	$-0.192318\pi$
$929$	46605.2			1.64593			0.822965	+	0.568093i	$0.192318\pi$
$930$	44319.1	−	94323.2i	1.56267	−	3.32578i
$931$		−	1149.32i		−	0.0404590i
$932$	−3219.89	−	3883.11i	−0.113166	−	0.136476i
$933$		−	62469.3i		−	2.19202i
$934$	−30408.1	−	14287.7i	−1.06529	−	0.500544i
$935$	1847.84			0.0646319
$936$	−10257.4	−	39666.7i	−0.358197	−	1.38520i
$937$	−10445.2			−0.364174			−0.182087	−	0.983282i	$-0.558285\pi$
$937$	−10445.2			−0.364174			−0.182087	+	0.983282i	$0.558285\pi$
$938$	−839.051	−	394.241i	−0.0292068	−	0.0137233i
$939$			1959.46i			0.0680985i
$940$	55284.7	−	45842.2i	1.91828	−	1.59065i
$941$			19779.0i			0.685205i	0.939480	+	0.342602i	$0.111308\pi$
$941$			19779.0i			0.685205i	−0.939480	+	0.342602i	$0.888692\pi$
$942$	−5599.33	+	11916.9i	−0.193669	+	0.412180i
$943$	−54505.1			−1.88222
$944$	−43688.6	−	8230.35i	−1.50630	−	0.283766i
$945$	−27705.5			−0.953716
$946$	−898.313	+	1911.85i	−0.0308739	+	0.0657080i
$947$			3223.67i			0.110618i	0.998469	+	0.0553091i	$0.0176144\pi$
$947$			3223.67i			0.110618i	−0.998469	+	0.0553091i	$0.982386\pi$
$948$	32487.3	−	26938.6i	1.11302	−	0.922916i
$949$		−	13429.6i		−	0.459371i
$950$	3209.47	+	1508.02i	0.109609	+	0.0515016i
$951$	−3556.23			−0.121260
$952$	−3001.13	+	776.059i	−0.102171	+	0.0264204i
$953$	41160.3			1.39907			0.699535	−	0.714599i	$-0.253391\pi$
$953$	41160.3			1.39907			0.699535	+	0.714599i	$0.253391\pi$
$954$	48987.4	+	23017.4i	1.66250	+	0.781150i
$955$		−	27804.5i		−	0.942127i
$956$	69.2218	+	83.4799i	0.00234183	+	0.00282420i
$957$		−	9477.04i		−	0.320114i
$958$	14328.4	−	30494.8i	0.483226	−	1.02844i
$959$	−439.205			−0.0147890
$960$	−79398.0	+	44005.4i	−2.66933	+	1.47945i
$961$	13397.4			0.449714
$962$	−9355.26	+	19910.5i	−0.313540	+	0.667299i
$963$			26151.4i			0.875097i
$964$	1134.96	+	1368.73i	0.0379196	+	0.0457302i
$965$			65060.3i			2.17033i
$966$	−29163.5	−	13702.9i	−0.971347	−	0.456402i
$967$	30521.2			1.01499			0.507495	−	0.861655i	$-0.330571\pi$
$967$	30521.2			1.01499			0.507495	+	0.861655i	$0.330571\pi$
$968$	28553.7	−	7383.67i	0.948090	−	0.245165i
$969$	601.965			0.0199566
$970$	−96477.8	−	45331.5i	−3.19352	−	1.50052i
$971$		−	16185.0i		−	0.534913i	−0.963570	−	0.267457i	$-0.913817\pi$
$971$		−	16185.0i		−	0.534913i	0.963570	−	0.267457i	$-0.0861832\pi$
$972$	18622.4	−	15441.7i	0.614519	−	0.509561i
$973$			4762.10i			0.156902i
$974$	11333.3	−	24120.4i	0.372836	−	0.793497i
$975$	−101423.			−3.33143
$976$	40182.6	+	7569.86i	1.31784	+	0.248264i
$977$	44428.8			1.45486			0.727432	−	0.686180i	$-0.240714\pi$
$977$	44428.8			1.45486			0.727432	+	0.686180i	$0.240714\pi$
$978$	26816.1	−	57072.0i	0.876775	−	1.86601i
$979$			6374.17i			0.208089i
$980$	35439.0	−	29386.2i	1.15516	−	0.957864i
$981$			50974.5i			1.65901i
$982$	20079.4	+	9434.62i	0.652506	+	0.306589i
$983$	45428.4			1.47400			0.736999	−	0.675894i	$-0.236242\pi$
$983$	45428.4			1.47400			0.736999	+	0.675894i	$0.236242\pi$
$984$	16029.3	+	61987.5i	0.519303	+	2.00822i
$985$	30443.3			0.984777
$986$	9166.37	+	4306.95i	0.296061	+	0.139109i
$987$		−	29946.0i		−	0.965748i
$988$	823.818	+	993.506i	0.0265275	+	0.0319915i
$989$		−	23465.6i		−	0.754461i
$990$	6065.28	−	12908.6i	0.194714	−	0.414405i
$991$	46670.2			1.49599			0.747997	−	0.663703i	$-0.231016\pi$
$991$	46670.2			1.49599			0.747997	+	0.663703i	$0.231016\pi$
$992$	−30497.7	−	22024.7i	−0.976112	−	0.704925i
$993$	−34820.2			−1.11278
$994$	6086.07	−	12952.8i	0.194204	−	0.413318i
$995$			34584.2i			1.10190i
$996$	18439.6	+	22237.7i	0.586626	+	0.707458i
$997$			12290.5i			0.390416i	0.980762	+	0.195208i	$0.0625382\pi$
$997$			12290.5i			0.390416i	−0.980762	+	0.195208i	$0.937462\pi$
$998$	−43082.7	−	20243.1i	−1.36649	−	0.642067i
$999$	33103.1			1.04838

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.4.c.b.69.10	yes	24
4.3	odd	2		544.4.c.a.273.22		24
8.3	odd	2		544.4.c.a.273.3		24
8.5	even	2	inner	136.4.c.b.69.9	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.4.c.b.69.9	✓	24	8.5	even	2	inner
136.4.c.b.69.10	yes	24	1.1	even	1	trivial
544.4.c.a.273.3		24	8.3	odd	2
544.4.c.a.273.22		24	4.3	odd	2

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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	136.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20282 + 2.55993i) q^{2} -8.56686i q^{3} +(-5.10645 - 6.15826i) q^{4} -20.6960i q^{5} +(21.9305 + 10.3044i) q^{6} -8.05854 q^{7} +(21.9068 - 5.66486i) q^{8} -46.3911 q^{9} +O(q^{10})\)	\(q+(-1.20282 + 2.55993i) q^{2} -8.56686i q^{3} +(-5.10645 - 6.15826i) q^{4} -20.6960i q^{5} +(21.9305 + 10.3044i) q^{6} -8.05854 q^{7} +(21.9068 - 5.66486i) q^{8} -46.3911 q^{9} +(52.9801 + 24.8935i) q^{10} +5.25206i q^{11} +(-52.7570 + 43.7463i) q^{12} +39.0312i q^{13} +(9.69297 - 20.6293i) q^{14} -177.299 q^{15} +(-11.8483 + 62.8937i) q^{16} +17.0000 q^{17} +(55.8002 - 118.758i) q^{18} +4.13334i q^{19} +(-127.451 + 105.683i) q^{20} +69.0364i q^{21} +(-13.4449 - 6.31729i) q^{22} +165.019 q^{23} +(-48.5301 - 187.673i) q^{24} -303.322 q^{25} +(-99.9169 - 46.9475i) q^{26} +166.121i q^{27} +(41.1505 + 49.6266i) q^{28} -210.630i q^{29} +(213.259 - 453.873i) q^{30} +207.818 q^{31} +(-146.752 - 105.981i) q^{32} +44.9937 q^{33} +(-20.4479 + 43.5188i) q^{34} +166.779i q^{35} +(236.894 + 285.689i) q^{36} -199.271i q^{37} +(-10.5810 - 4.97166i) q^{38} +334.375 q^{39} +(-117.240 - 453.383i) q^{40} -330.295 q^{41} +(-176.728 - 83.0383i) q^{42} -142.199i q^{43} +(32.3436 - 26.8194i) q^{44} +960.109i q^{45} +(-198.488 + 422.437i) q^{46} -433.772 q^{47} +(538.802 + 101.503i) q^{48} -278.060 q^{49} +(364.842 - 776.483i) q^{50} -145.637i q^{51} +(240.364 - 199.311i) q^{52} +412.498i q^{53} +(-425.258 - 199.814i) q^{54} +108.696 q^{55} +(-176.537 + 45.6505i) q^{56} +35.4097 q^{57} +(539.198 + 253.350i) q^{58} +694.642i q^{59} +(905.370 + 1091.86i) q^{60} -638.897i q^{61} +(-249.968 + 531.999i) q^{62} +373.845 q^{63} +(447.819 - 248.198i) q^{64} +807.787 q^{65} +(-54.1193 + 115.181i) q^{66} -40.6728i q^{67} +(-86.8096 - 104.690i) q^{68} -1413.70i q^{69} +(-426.942 - 200.605i) q^{70} +627.885 q^{71} +(-1016.28 + 262.799i) q^{72} -344.074 q^{73} +(510.119 + 239.687i) q^{74} +2598.52i q^{75} +(25.4542 - 21.1067i) q^{76} -42.3240i q^{77} +(-402.192 + 855.975i) q^{78} -615.792 q^{79} +(1301.64 + 245.213i) q^{80} +170.577 q^{81} +(397.286 - 845.532i) q^{82} -421.512i q^{83} +(425.144 - 352.531i) q^{84} -351.831i q^{85} +(364.020 + 171.040i) q^{86} -1804.44 q^{87} +(29.7522 + 115.056i) q^{88} +1213.65 q^{89} +(-2457.81 - 1154.84i) q^{90} -314.534i q^{91} +(-842.662 - 1016.23i) q^{92} -1780.35i q^{93} +(521.749 - 1110.42i) q^{94} +85.5433 q^{95} +(-907.922 + 1257.20i) q^{96} -1821.02 q^{97} +(334.456 - 711.813i) q^{98} -243.649i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} + 5 q^{4} + 40 q^{6} + 84 q^{7} + 13 q^{8} - 216 q^{9}+O(q^{10}) \) 24 * q + q^2 + 5 * q^4 + 40 * q^6 + 84 * q^7 + 13 * q^8 - 216 * q^9	\( 24 q + q^{2} + 5 q^{4} + 40 q^{6} + 84 q^{7} + 13 q^{8} - 216 q^{9} - 16 q^{10} - 18 q^{12} + 26 q^{14} - 180 q^{15} - 103 q^{16} + 408 q^{17} - 5 q^{18} - 24 q^{20} + 172 q^{22} + 624 q^{23} - 310 q^{24} - 600 q^{25} - 180 q^{26} - 132 q^{28} - 80 q^{30} - 744 q^{31} - 39 q^{32} - 280 q^{33} + 17 q^{34} + 791 q^{36} - 162 q^{38} + 1236 q^{39} - 1396 q^{40} + 1132 q^{42} + 886 q^{44} - 1246 q^{46} - 956 q^{47} - 2226 q^{48} + 1688 q^{49} + 2505 q^{50} + 2544 q^{52} - 3264 q^{54} + 1684 q^{55} - 1100 q^{56} - 168 q^{57} + 2800 q^{58} + 2520 q^{60} - 1946 q^{62} - 2520 q^{63} - 2143 q^{64} - 72 q^{65} + 3660 q^{66} + 85 q^{68} - 5084 q^{70} + 1532 q^{71} - 2277 q^{72} + 216 q^{73} + 2188 q^{74} + 2094 q^{76} - 4748 q^{78} - 3176 q^{79} + 116 q^{80} + 2040 q^{81} + 3198 q^{82} + 5916 q^{84} - 2066 q^{86} - 236 q^{87} - 3598 q^{88} - 424 q^{89} + 2180 q^{90} + 1940 q^{92} - 2156 q^{94} - 1248 q^{95} - 4674 q^{96} - 1304 q^{97} + 3705 q^{98}+O(q^{100}) \) 24 * q + q^2 + 5 * q^4 + 40 * q^6 + 84 * q^7 + 13 * q^8 - 216 * q^9 - 16 * q^10 - 18 * q^12 + 26 * q^14 - 180 * q^15 - 103 * q^16 + 408 * q^17 - 5 * q^18 - 24 * q^20 + 172 * q^22 + 624 * q^23 - 310 * q^24 - 600 * q^25 - 180 * q^26 - 132 * q^28 - 80 * q^30 - 744 * q^31 - 39 * q^32 - 280 * q^33 + 17 * q^34 + 791 * q^36 - 162 * q^38 + 1236 * q^39 - 1396 * q^40 + 1132 * q^42 + 886 * q^44 - 1246 * q^46 - 956 * q^47 - 2226 * q^48 + 1688 * q^49 + 2505 * q^50 + 2544 * q^52 - 3264 * q^54 + 1684 * q^55 - 1100 * q^56 - 168 * q^57 + 2800 * q^58 + 2520 * q^60 - 1946 * q^62 - 2520 * q^63 - 2143 * q^64 - 72 * q^65 + 3660 * q^66 + 85 * q^68 - 5084 * q^70 + 1532 * q^71 - 2277 * q^72 + 216 * q^73 + 2188 * q^74 + 2094 * q^76 - 4748 * q^78 - 3176 * q^79 + 116 * q^80 + 2040 * q^81 + 3198 * q^82 + 5916 * q^84 - 2066 * q^86 - 236 * q^87 - 3598 * q^88 - 424 * q^89 + 2180 * q^90 + 1940 * q^92 - 2156 * q^94 - 1248 * q^95 - 4674 * q^96 - 1304 * q^97 + 3705 * q^98

Introduction

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