LMFDB - Embedded newform 169.5.d.d.99.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,5,Mod(70,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("169.70");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	169.d (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$17.4695237612$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 152 x^{14} + 9190 x^{12} + 285720 x^{10} + 4862025 x^{8} + 43573680 x^{6} + 169417008 x^{4} + \cdots + 3779136 $ x^16 + 152x^14 + 9190x^12 + 285720x^10 + 4862025x^8 + 43573680x^6 + 169417008x^4 + 100636992*x^2 + 3779136
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{2}\cdot 13^{2} $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			99.5
Root			$3.68702i$ of defining polynomial
Character	$\chi$	$=$	169.99
Dual form			169.5.d.d.70.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.47633 + 1.47633i) q^{2} +16.4234 q^{3} -11.6409i q^{4} +(17.2508 + 17.2508i) q^{5} +(24.2464 + 24.2464i) q^{6} +(-8.05998 + 8.05998i) q^{7} +(40.8071 - 40.8071i) q^{8} +188.729 q^{9} +O(q^{10})$	\(q+(1.47633 + 1.47633i) q^{2} +16.4234 q^{3} -11.6409i q^{4} +(17.2508 + 17.2508i) q^{5} +(24.2464 + 24.2464i) q^{6} +(-8.05998 + 8.05998i) q^{7} +(40.8071 - 40.8071i) q^{8} +188.729 q^{9} +50.9358i q^{10} +(-74.4314 + 74.4314i) q^{11} -191.183i q^{12} -23.7984 q^{14} +(283.318 + 283.318i) q^{15} -65.7650 q^{16} -75.8836i q^{17} +(278.626 + 278.626i) q^{18} +(229.726 + 229.726i) q^{19} +(200.815 - 200.815i) q^{20} +(-132.372 + 132.372i) q^{21} -219.771 q^{22} -201.875i q^{23} +(670.192 - 670.192i) q^{24} -29.8174i q^{25} +1769.27 q^{27} +(93.8254 + 93.8254i) q^{28} -864.370 q^{29} +836.540i q^{30} +(-767.381 - 767.381i) q^{31} +(-750.004 - 750.004i) q^{32} +(-1222.42 + 1222.42i) q^{33} +(112.029 - 112.029i) q^{34} -278.083 q^{35} -2196.97i q^{36} +(553.621 - 553.621i) q^{37} +678.302i q^{38} +1407.91 q^{40} +(842.885 + 842.885i) q^{41} -390.850 q^{42} -367.287i q^{43} +(866.449 + 866.449i) q^{44} +(3255.73 + 3255.73i) q^{45} +(298.035 - 298.035i) q^{46} +(-308.850 + 308.850i) q^{47} -1080.09 q^{48} +2271.07i q^{49} +(44.0203 - 44.0203i) q^{50} -1246.27i q^{51} -2120.08 q^{53} +(2612.03 + 2612.03i) q^{54} -2568.01 q^{55} +657.808i q^{56} +(3772.88 + 3772.88i) q^{57} +(-1276.09 - 1276.09i) q^{58} +(-4011.92 + 4011.92i) q^{59} +(3298.07 - 3298.07i) q^{60} +5703.55 q^{61} -2265.81i q^{62} +(-1521.15 + 1521.15i) q^{63} -1162.27i q^{64} -3609.38 q^{66} +(-1436.21 - 1436.21i) q^{67} -883.354 q^{68} -3315.49i q^{69} +(-410.542 - 410.542i) q^{70} +(-1105.86 - 1105.86i) q^{71} +(7701.46 - 7701.46i) q^{72} +(-1577.77 + 1577.77i) q^{73} +1634.65 q^{74} -489.703i q^{75} +(2674.21 - 2674.21i) q^{76} -1199.83i q^{77} +4448.61 q^{79} +(-1134.50 - 1134.50i) q^{80} +13770.5 q^{81} +2488.75i q^{82} +(-4026.77 - 4026.77i) q^{83} +(1540.93 + 1540.93i) q^{84} +(1309.06 - 1309.06i) q^{85} +(542.237 - 542.237i) q^{86} -14195.9 q^{87} +6074.66i q^{88} +(-7784.52 + 7784.52i) q^{89} +9613.05i q^{90} -2350.01 q^{92} +(-12603.0 - 12603.0i) q^{93} -911.928 q^{94} +7925.92i q^{95} +(-12317.6 - 12317.6i) q^{96} +(-12148.8 - 12148.8i) q^{97} +(-3352.85 + 3352.85i) q^{98} +(-14047.3 + 14047.3i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} + 4 q^{3} + 8 q^{5} - 128 q^{6} + 56 q^{7} + 90 q^{8} + 328 q^{9}+O(q^{10}) $ 16 * q + 2 * q^2 + 4 * q^3 + 8 * q^5 - 128 * q^6 + 56 * q^7 + 90 * q^8 + 328 * q^9	$ 16 q + 2 q^{2} + 4 q^{3} + 8 q^{5} - 128 q^{6} + 56 q^{7} + 90 q^{8} + 328 q^{9} + 500 q^{11} + 808 q^{14} + 844 q^{15} - 460 q^{16} + 2434 q^{18} + 1712 q^{19} + 838 q^{20} - 1076 q^{21} + 3048 q^{22} + 5772 q^{24} + 3352 q^{27} + 2980 q^{28} - 1628 q^{29} + 4060 q^{31} + 3662 q^{32} - 860 q^{33} - 2502 q^{34} + 9784 q^{35} + 10468 q^{37} + 18816 q^{40} + 3440 q^{41} + 2408 q^{42} + 10736 q^{44} - 1004 q^{45} + 11436 q^{46} + 1484 q^{47} + 6004 q^{48} + 21616 q^{50} + 7204 q^{53} + 6760 q^{54} - 13872 q^{55} + 12736 q^{57} + 7974 q^{58} - 4840 q^{59} - 6472 q^{60} + 324 q^{61} - 13988 q^{63} - 23872 q^{66} + 2216 q^{67} + 12888 q^{68} - 34524 q^{70} - 1240 q^{71} - 6606 q^{72} - 15448 q^{73} + 5764 q^{74} - 39688 q^{76} - 17064 q^{79} - 37630 q^{80} - 4256 q^{81} + 12788 q^{83} - 7736 q^{84} - 22884 q^{85} + 67260 q^{86} - 58684 q^{87} - 37624 q^{89} - 49884 q^{92} - 2492 q^{93} + 61212 q^{94} - 94664 q^{96} - 57056 q^{97} + 27950 q^{98} - 21632 q^{99}+O(q^{100}) $ 16 * q + 2 * q^2 + 4 * q^3 + 8 * q^5 - 128 * q^6 + 56 * q^7 + 90 * q^8 + 328 * q^9 + 500 * q^11 + 808 * q^14 + 844 * q^15 - 460 * q^16 + 2434 * q^18 + 1712 * q^19 + 838 * q^20 - 1076 * q^21 + 3048 * q^22 + 5772 * q^24 + 3352 * q^27 + 2980 * q^28 - 1628 * q^29 + 4060 * q^31 + 3662 * q^32 - 860 * q^33 - 2502 * q^34 + 9784 * q^35 + 10468 * q^37 + 18816 * q^40 + 3440 * q^41 + 2408 * q^42 + 10736 * q^44 - 1004 * q^45 + 11436 * q^46 + 1484 * q^47 + 6004 * q^48 + 21616 * q^50 + 7204 * q^53 + 6760 * q^54 - 13872 * q^55 + 12736 * q^57 + 7974 * q^58 - 4840 * q^59 - 6472 * q^60 + 324 * q^61 - 13988 * q^63 - 23872 * q^66 + 2216 * q^67 + 12888 * q^68 - 34524 * q^70 - 1240 * q^71 - 6606 * q^72 - 15448 * q^73 + 5764 * q^74 - 39688 * q^76 - 17064 * q^79 - 37630 * q^80 - 4256 * q^81 + 12788 * q^83 - 7736 * q^84 - 22884 * q^85 + 67260 * q^86 - 58684 * q^87 - 37624 * q^89 - 49884 * q^92 - 2492 * q^93 + 61212 * q^94 - 94664 * q^96 - 57056 * q^97 + 27950 * q^98 - 21632 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	1.47633	+	1.47633i	0.369082	+	0.369082i	0.867143	−	0.498060i	$-0.165954\pi$
$2$	1.47633	+	1.47633i	0.369082	+	0.369082i	−0.498060	+	0.867143i	$0.665954\pi$
$3$	16.4234			1.82482			0.912412	−	0.409273i	$-0.134218\pi$
$3$	16.4234			1.82482			0.912412	+	0.409273i	$0.134218\pi$
$4$		−	11.6409i		−	0.727556i
$5$	17.2508	+	17.2508i	0.690033	+	0.690033i	0.962239	−	0.272206i	$-0.0877531\pi$
$5$	17.2508	+	17.2508i	0.690033	+	0.690033i	−0.272206	+	0.962239i	$0.587753\pi$
$6$	24.2464	+	24.2464i	0.673510	+	0.673510i
$7$	−8.05998	+	8.05998i	−0.164489	+	0.164489i	−0.784552	−	0.620063i	$-0.787107\pi$
$7$	−8.05998	+	8.05998i	−0.164489	+	0.164489i	0.620063	+	0.784552i	$0.287107\pi$
$8$	40.8071	−	40.8071i	0.637611	−	0.637611i
$9$	188.729			2.32998
$10$			50.9358i			0.509358i
$11$	−74.4314	+	74.4314i	−0.615136	+	0.615136i	−0.944280	−	0.329144i	$-0.893240\pi$
$11$	−74.4314	+	74.4314i	−0.615136	+	0.615136i	0.329144	+	0.944280i	$0.393240\pi$
$12$		−	191.183i		−	1.32766i
$13$		0			0
$13$		0			0
$14$	−23.7984			−0.121420
$15$	283.318	+	283.318i	1.25919	+	1.25919i
$16$	−65.7650			−0.256895
$17$		−	75.8836i		−	0.262573i	−0.991344	−	0.131287i	$-0.958089\pi$
$17$		−	75.8836i		−	0.262573i	0.991344	−	0.131287i	$-0.0419108\pi$
$18$	278.626	+	278.626i	0.859956	+	0.859956i
$19$	229.726	+	229.726i	0.636359	+	0.636359i	0.949655	−	0.313296i	$-0.101433\pi$
$19$	229.726	+	229.726i	0.636359	+	0.636359i	−0.313296	+	0.949655i	$0.601433\pi$
$20$	200.815	−	200.815i	0.502038	−	0.502038i
$21$	−132.372	+	132.372i	−0.300164	+	0.300164i
$22$	−219.771			−0.454072
$23$		−	201.875i		−	0.381617i	−0.981627	−	0.190809i	$-0.938889\pi$
$23$		−	201.875i		−	0.381617i	0.981627	−	0.190809i	$-0.0611110\pi$
$24$	670.192	−	670.192i	1.16353	−	1.16353i
$25$		−	29.8174i		−	0.0477078i
$26$		0			0
$27$	1769.27			2.42698
$28$	93.8254	+	93.8254i	0.119675	+	0.119675i
$29$	−864.370			−1.02779			−0.513894	−	0.857854i	$-0.671798\pi$
$29$	−864.370			−1.02779			−0.513894	+	0.857854i	$0.671798\pi$
$30$			836.540i			0.929489i
$31$	−767.381	−	767.381i	−0.798523	−	0.798523i	0.184339	−	0.982863i	$-0.440986\pi$
$31$	−767.381	−	767.381i	−0.798523	−	0.798523i	−0.982863	+	0.184339i	$0.940986\pi$
$32$	−750.004	−	750.004i	−0.732426	−	0.732426i
$33$	−1222.42	+	1222.42i	−1.12251	+	1.12251i
$34$	112.029	−	112.029i	0.0969111	−	0.0969111i
$35$	−278.083			−0.227006
$36$		−	2196.97i		−	1.69519i
$37$	553.621	−	553.621i	0.404398	−	0.404398i	−0.475382	−	0.879780i	$-0.657690\pi$
$37$	553.621	−	553.621i	0.404398	−	0.404398i	0.879780	+	0.475382i	$0.157690\pi$
$38$			678.302i			0.469738i
$39$		0			0
$40$	1407.91			0.879945
$41$	842.885	+	842.885i	0.501419	+	0.501419i	0.911879	−	0.410460i	$-0.134632\pi$
$41$	842.885	+	842.885i	0.501419	+	0.501419i	−0.410460	+	0.911879i	$0.634632\pi$
$42$	−390.850			−0.221571
$43$		−	367.287i		−	0.198641i	−0.995055	−	0.0993205i	$-0.968333\pi$
$43$		−	367.287i		−	0.198641i	0.995055	−	0.0993205i	$-0.0316669\pi$
$44$	866.449	+	866.449i	0.447546	+	0.447546i
$45$	3255.73	+	3255.73i	1.60777	+	1.60777i
$46$	298.035	−	298.035i	0.140848	−	0.140848i
$47$	−308.850	+	308.850i	−0.139814	+	0.139814i	−0.773550	−	0.633736i	$-0.781521\pi$
$47$	−308.850	+	308.850i	−0.139814	+	0.139814i	0.633736	+	0.773550i	$0.281521\pi$
$48$	−1080.09			−0.468788
$49$			2271.07i			0.945887i
$50$	44.0203	−	44.0203i	0.0176081	−	0.0176081i
$51$		−	1246.27i		−	0.479150i
$52$		0			0
$53$	−2120.08			−0.754746			−0.377373	−	0.926061i	$-0.623173\pi$
$53$	−2120.08			−0.754746			−0.377373	+	0.926061i	$0.623173\pi$
$54$	2612.03	+	2612.03i	0.895757	+	0.895757i
$55$	−2568.01			−0.848928
$56$			657.808i			0.209760i
$57$	3772.88	+	3772.88i	1.16124	+	1.16124i
$58$	−1276.09	−	1276.09i	−0.379338	−	0.379338i
$59$	−4011.92	+	4011.92i	−1.15252	+	1.15252i	−0.166475	+	0.986046i	$0.553239\pi$
$59$	−4011.92	+	4011.92i	−1.15252	+	1.15252i	−0.986046	+	0.166475i	$0.946761\pi$
$60$	3298.07	−	3298.07i	0.916131	−	0.916131i
$61$	5703.55			1.53280			0.766400	−	0.642364i	$-0.222046\pi$
$61$	5703.55			1.53280			0.766400	+	0.642364i	$0.222046\pi$
$62$		−	2265.81i		−	0.589442i
$63$	−1521.15	+	1521.15i	−0.383257	+	0.383257i
$64$		−	1162.27i		−	0.283756i
$65$		0			0
$66$	−3609.38			−0.828601
$67$	−1436.21	−	1436.21i	−0.319941	−	0.319941i	0.528804	−	0.848744i	$-0.322641\pi$
$67$	−1436.21	−	1436.21i	−0.319941	−	0.319941i	−0.848744	+	0.528804i	$0.822641\pi$
$68$	−883.354			−0.191037
$69$		−	3315.49i		−	0.696384i
$70$	−410.542	−	410.542i	−0.0837840	−	0.0837840i
$71$	−1105.86	−	1105.86i	−0.219373	−	0.219373i	0.588861	−	0.808234i	$-0.299577\pi$
$71$	−1105.86	−	1105.86i	−0.219373	−	0.219373i	−0.808234	+	0.588861i	$0.799577\pi$
$72$	7701.46	−	7701.46i	1.48562	−	1.48562i
$73$	−1577.77	+	1577.77i	−0.296072	+	0.296072i	−0.839473	−	0.543401i	$-0.817136\pi$
$73$	−1577.77	+	1577.77i	−0.296072	+	0.296072i	0.543401	+	0.839473i	$0.317136\pi$
$74$	1634.65			0.298512
$75$		−	489.703i		−	0.0870583i
$76$	2674.21	−	2674.21i	0.462987	−	0.462987i
$77$		−	1199.83i		−	0.202367i
$78$		0			0
$79$	4448.61			0.712804			0.356402	−	0.934333i	$-0.384003\pi$
$79$	4448.61			0.712804			0.356402	+	0.934333i	$0.384003\pi$
$80$	−1134.50	−	1134.50i	−0.177266	−	0.177266i
$81$	13770.5			2.09884
$82$			2488.75i			0.370130i
$83$	−4026.77	−	4026.77i	−0.584521	−	0.584521i	0.351621	−	0.936142i	$-0.385631\pi$
$83$	−4026.77	−	4026.77i	−0.584521	−	0.584521i	−0.936142	+	0.351621i	$0.885631\pi$
$84$	1540.93	+	1540.93i	0.218386	+	0.218386i
$85$	1309.06	−	1309.06i	0.181184	−	0.181184i
$86$	542.237	−	542.237i	0.0733149	−	0.0733149i
$87$	−14195.9			−1.87553
$88$			6074.66i			0.784434i
$89$	−7784.52	+	7784.52i	−0.982770	+	0.982770i	−0.999854	−	0.0170842i	$-0.994562\pi$
$89$	−7784.52	+	7784.52i	−0.982770	+	0.982770i	0.0170842	+	0.999854i	$0.494562\pi$
$90$			9613.05i			1.18680i
$91$		0			0
$92$	−2350.01			−0.277648
$93$	−12603.0	−	12603.0i	−1.45716	−	1.45716i
$94$	−911.928			−0.103206
$95$			7925.92i			0.878218i
$96$	−12317.6	−	12317.6i	−1.33655	−	1.33655i
$97$	−12148.8	−	12148.8i	−1.29119	−	1.29119i	−0.934052	−	0.357138i	$-0.883753\pi$
$97$	−12148.8	−	12148.8i	−1.29119	−	1.29119i	−0.357138	−	0.934052i	$-0.616247\pi$
$98$	−3352.85	+	3352.85i	−0.349110	+	0.349110i
$99$	−14047.3	+	14047.3i	−1.43326	+	1.43326i
$100$	−347.101			−0.0347101
$101$			6113.20i			0.599275i	0.954053	+	0.299637i	$0.0968657\pi$
$101$			6113.20i			0.599275i	−0.954053	+	0.299637i	$0.903134\pi$
$102$	1839.90	−	1839.90i	0.176846	−	0.176846i
$103$		−	5625.33i		−	0.530242i	−0.964215	−	0.265121i	$-0.914588\pi$
$103$		−	5625.33i		−	0.530242i	0.964215	−	0.265121i	$-0.0854119\pi$
$104$		0			0
$105$	−4567.07			−0.414246
$106$	−3129.94	−	3129.94i	−0.278563	−	0.278563i
$107$	−9733.41			−0.850154			−0.425077	−	0.905157i	$-0.639753\pi$
$107$	−9733.41			−0.850154			−0.425077	+	0.905157i	$0.639753\pi$
$108$		−	20595.9i		−	1.76577i
$109$	−6384.24	−	6384.24i	−0.537349	−	0.537349i	0.385401	−	0.922749i	$-0.374063\pi$
$109$	−6384.24	−	6384.24i	−0.537349	−	0.537349i	−0.922749	+	0.385401i	$0.874063\pi$
$110$	−3791.23	−	3791.23i	−0.313325	−	0.313325i
$111$	9092.34	−	9092.34i	0.737955	−	0.737955i
$112$	530.065	−	530.065i	0.0422564	−	0.0422564i
$113$	5877.72			0.460312			0.230156	−	0.973154i	$-0.426076\pi$
$113$	5877.72			0.460312			0.230156	+	0.973154i	$0.426076\pi$
$114$			11140.0i			0.857189i
$115$	3482.52	−	3482.52i	0.263329	−	0.263329i
$116$			10062.0i			0.747774i
$117$		0			0
$118$	−11845.8			−0.850750
$119$	611.620	+	611.620i	0.0431905	+	0.0431905i
$120$	23122.7			1.60575
$121$			3560.93i			0.243216i
$122$	8420.31	+	8420.31i	0.565729	+	0.565729i
$123$	13843.0	+	13843.0i	0.915001	+	0.915001i
$124$	−8933.01	+	8933.01i	−0.580971	+	0.580971i
$125$	11296.1	−	11296.1i	0.722953	−	0.722953i
$126$	−4491.43			−0.282907
$127$		−	15572.8i		−	0.965515i	−0.875754	−	0.482758i	$-0.839635\pi$
$127$		−	15572.8i		−	0.965515i	0.875754	−	0.482758i	$-0.160365\pi$
$128$	−10284.2	+	10284.2i	−0.627696	+	0.627696i
$129$		−	6032.11i		−	0.362485i
$130$		0			0
$131$	−6751.71			−0.393433			−0.196717	−	0.980460i	$-0.563028\pi$
$131$	−6751.71			−0.393433			−0.196717	+	0.980460i	$0.563028\pi$
$132$	14230.1	+	14230.1i	0.816693	+	0.816693i
$133$	−3703.17			−0.209349
$134$		−	4240.65i		−	0.236169i
$135$	30521.4	+	30521.4i	1.67470	+	1.67470i
$136$	−3096.59	−	3096.59i	−0.167419	−	0.167419i
$137$	9522.56	−	9522.56i	0.507356	−	0.507356i	−0.406358	−	0.913714i	$-0.633201\pi$
$137$	9522.56	−	9522.56i	0.507356	−	0.507356i	0.913714	+	0.406358i	$0.133201\pi$
$138$	4894.75	−	4894.75i	0.257023	−	0.257023i
$139$	20909.6			1.08222			0.541110	−	0.840952i	$-0.318004\pi$
$139$	20909.6			1.08222			0.541110	+	0.840952i	$0.318004\pi$
$140$			3237.13i			0.165160i
$141$	−5072.37	+	5072.37i	−0.255136	+	0.255136i
$142$		−	3265.23i		−	0.161934i
$143$		0			0
$144$	−12411.7			−0.598560
$145$	−14911.1	−	14911.1i	−0.709208	−	0.709208i
$146$	−4658.61			−0.218550
$147$			37298.8i			1.72608i
$148$	−6444.64	−	6444.64i	−0.294222	−	0.294222i
$149$	−1931.45	−	1931.45i	−0.0869985	−	0.0869985i	0.662268	−	0.749267i	$-0.269594\pi$
$149$	−1931.45	−	1931.45i	−0.0869985	−	0.0869985i	−0.749267	+	0.662268i	$0.769594\pi$
$150$	722.963	−	722.963i	0.0321317	−	0.0321317i
$151$	22287.7	−	22287.7i	0.977490	−	0.977490i	−0.0222623	−	0.999752i	$-0.507087\pi$
$151$	22287.7	−	22287.7i	0.977490	−	0.977490i	0.999752	+	0.0222623i	$0.00708691\pi$
$152$	18748.9			0.811499
$153$		−	14321.4i		−	0.611791i
$154$	1771.35	−	1771.35i	0.0746899	−	0.0746899i
$155$		−	26475.9i		−	1.10202i
$156$		0			0
$157$	17116.8			0.694421			0.347210	−	0.937787i	$-0.387129\pi$
$157$	17116.8			0.694421			0.347210	+	0.937787i	$0.387129\pi$
$158$	6567.62	+	6567.62i	0.263083	+	0.263083i
$159$	−34819.0			−1.37728
$160$		−	25876.4i		−	1.01080i
$161$	1627.11	+	1627.11i	0.0627719	+	0.0627719i
$162$	20329.8	+	20329.8i	0.774644	+	0.774644i
$163$	−28988.2	+	28988.2i	−1.09105	+	1.09105i	−0.0956360	+	0.995416i	$0.530488\pi$
$163$	−28988.2	+	28988.2i	−1.09105	+	1.09105i	−0.995416	+	0.0956360i	$0.969512\pi$
$164$	9811.94	−	9811.94i	0.364810	−	0.364810i
$165$	−42175.5			−1.54915
$166$		−	11889.7i		−	0.431473i
$167$	5183.65	−	5183.65i	0.185867	−	0.185867i	−0.608040	−	0.793907i	$-0.708044\pi$
$167$	5183.65	−	5183.65i	0.185867	−	0.185867i	0.793907	+	0.608040i	$0.208044\pi$
$168$			10803.5i			0.382776i
$169$		0			0
$170$	3865.19			0.133744
$171$	43355.8	+	43355.8i	1.48271	+	1.48271i
$172$	−4275.56			−0.144523
$173$			10632.9i			0.355270i	0.984096	+	0.177635i	$0.0568446\pi$
$173$			10632.9i			0.355270i	−0.984096	+	0.177635i	$0.943155\pi$
$174$	−20957.8	−	20957.8i	−0.692226	−	0.692226i
$175$	240.327	+	240.327i	0.00784742	+	0.00784742i
$176$	4894.99	−	4894.99i	0.158025	−	0.158025i
$177$	−65889.5	+	65889.5i	−2.10315	+	2.10315i
$178$	−22985.0			−0.725446
$179$			5015.04i			0.156520i	0.996933	+	0.0782598i	$0.0249364\pi$
$179$			5015.04i			0.156520i	−0.996933	+	0.0782598i	$0.975064\pi$
$180$	37899.6	−	37899.6i	1.16974	−	1.16974i
$181$			60491.1i			1.84643i	0.384278	+	0.923217i	$0.374450\pi$
$181$			60491.1i			1.84643i	−0.384278	+	0.923217i	$0.625550\pi$
$182$		0			0
$183$	93671.7			2.79709
$184$	−8237.95	−	8237.95i	−0.243323	−	0.243323i
$185$	19100.8			0.558096
$186$		−	37212.4i		−	1.07563i
$187$	5648.12	+	5648.12i	0.161518	+	0.161518i
$188$	3595.29	+	3595.29i	0.101723	+	0.101723i
$189$	−14260.3	+	14260.3i	−0.399213	+	0.399213i
$190$	−11701.3	+	11701.3i	−0.324135	+	0.324135i
$191$	30751.2			0.842937			0.421469	−	0.906843i	$-0.361515\pi$
$191$	30751.2			0.842937			0.421469	+	0.906843i	$0.361515\pi$
$192$		−	19088.4i		−	0.517805i
$193$	21969.7	−	21969.7i	0.589805	−	0.589805i	−0.347773	−	0.937579i	$-0.613062\pi$
$193$	21969.7	−	21969.7i	0.589805	−	0.589805i	0.937579	+	0.347773i	$0.113062\pi$
$194$		−	35871.3i		−	0.953111i
$195$		0			0
$196$	26437.3			0.688186
$197$	−5500.99	−	5500.99i	−0.141745	−	0.141745i	0.632673	−	0.774419i	$-0.281958\pi$
$197$	−5500.99	−	5500.99i	−0.141745	−	0.141745i	−0.774419	+	0.632673i	$0.781958\pi$
$198$	−41477.0			−1.05798
$199$			44411.0i			1.12146i	0.827998	+	0.560731i	$0.189480\pi$
$199$			44411.0i			1.12146i	−0.827998	+	0.560731i	$0.810520\pi$
$200$	−1216.76	−	1216.76i	−0.0304190	−	0.0304190i
$201$	−23587.5	−	23587.5i	−0.583835	−	0.583835i
$202$	−9025.10	+	9025.10i	−0.221182	+	0.221182i
$203$	6966.80	−	6966.80i	0.169060	−	0.169060i
$204$	−14507.7			−0.348608
$205$			29080.9i			0.691991i
$206$	8304.85	−	8304.85i	0.195703	−	0.195703i
$207$		−	38099.7i		−	0.889162i
$208$		0			0
$209$	−34197.6			−0.782895
$210$	−6742.50	−	6742.50i	−0.152891	−	0.152891i
$211$	−14466.7			−0.324940			−0.162470	−	0.986713i	$-0.551946\pi$
$211$	−14466.7			−0.324940			−0.162470	+	0.986713i	$0.551946\pi$
$212$			24679.7i			0.549120i
$213$	−18162.0	−	18162.0i	−0.400318	−	0.400318i
$214$	−14369.7	−	14369.7i	−0.313777	−	0.313777i
$215$	6336.01	−	6336.01i	0.137069	−	0.137069i
$216$	72198.8	−	72198.8i	1.54747	−	1.54747i
$217$	12370.1			0.262697
$218$		−	18850.5i		−	0.396652i
$219$	−25912.3	+	25912.3i	−0.540279	+	0.540279i
$220$			29893.9i			0.617643i
$221$		0			0
$222$	26846.6			0.544732
$223$	26828.1	+	26828.1i	0.539486	+	0.539486i	0.923378	−	0.383892i	$-0.125417\pi$
$223$	26828.1	+	26828.1i	0.539486	+	0.539486i	−0.383892	+	0.923378i	$0.625417\pi$
$224$	12090.0			0.240952
$225$		−	5627.39i		−	0.111158i
$226$	8677.45	+	8677.45i	0.169893	+	0.169893i
$227$	69811.8	+	69811.8i	1.35481	+	1.35481i	0.880195	+	0.474612i	$0.157412\pi$
$227$	69811.8	+	69811.8i	1.35481	+	1.35481i	0.474612	+	0.880195i	$0.342588\pi$
$228$	43919.7	−	43919.7i	0.844870	−	0.844870i
$229$	−22254.1	+	22254.1i	−0.424364	+	0.424364i	−0.886703	−	0.462339i	$-0.847010\pi$
$229$	−22254.1	+	22254.1i	−0.424364	+	0.424364i	0.462339	+	0.886703i	$0.347010\pi$
$230$	10282.7			0.194380
$231$		−	19705.3i		−	0.369283i
$232$	−35272.4	+	35272.4i	−0.655328	+	0.655328i
$233$		−	89857.7i		−	1.65517i	−0.561338	−	0.827586i	$-0.689713\pi$
$233$		−	89857.7i		−	1.65517i	0.561338	−	0.827586i	$-0.310287\pi$
$234$		0			0
$235$	−10655.8			−0.192953
$236$	46702.4	+	46702.4i	0.838524	+	0.838524i
$237$	73061.4			1.30074
$238$			1805.91i			0.0318817i
$239$	71939.7	+	71939.7i	1.25943	+	1.25943i	0.951367	+	0.308061i	$0.0996800\pi$
$239$	71939.7	+	71939.7i	1.25943	+	1.25943i	0.308061	+	0.951367i	$0.400320\pi$
$240$	−18632.4	−	18632.4i	−0.323479	−	0.323479i
$241$	34491.7	−	34491.7i	0.593855	−	0.593855i	−0.344815	−	0.938671i	$-0.612058\pi$
$241$	34491.7	−	34491.7i	0.593855	−	0.593855i	0.938671	+	0.344815i	$0.112058\pi$
$242$	−5257.10	+	5257.10i	−0.0897668	+	0.0897668i
$243$	82847.2			1.40302
$244$		−	66394.4i		−	1.11520i
$245$	−39177.9	+	39177.9i	−0.652693	+	0.652693i
$246$			40873.8i			0.675421i
$247$		0			0
$248$	−62629.2			−1.01829
$249$	−66133.3	−	66133.3i	−1.06665	−	1.06665i
$250$	33353.7			0.533659
$251$		−	118898.i		−	1.88725i	−0.331022	−	0.943623i	$-0.607394\pi$
$251$		−	118898.i		−	1.88725i	0.331022	−	0.943623i	$-0.392606\pi$
$252$	17707.5	+	17707.5i	0.278841	+	0.278841i
$253$	15025.9	+	15025.9i	0.234746	+	0.234746i
$254$	22990.6	−	22990.6i	0.356355	−	0.356355i
$255$	21499.2	−	21499.2i	0.330629	−	0.330629i
$256$	−48961.9			−0.747100
$257$			116656.i			1.76620i	0.469184	+	0.883100i	$0.344548\pi$
$257$			116656.i			1.76620i	−0.469184	+	0.883100i	$0.655452\pi$
$258$	8905.39	−	8905.39i	0.133787	−	0.133787i
$259$			8924.34i			0.133038i
$260$		0			0
$261$	−163131.			−2.39473
$262$	−9967.74	−	9967.74i	−0.145209	−	0.145209i
$263$	−59797.4			−0.864511			−0.432256	−	0.901751i	$-0.642282\pi$
$263$	−59797.4			−0.864511			−0.432256	+	0.901751i	$0.642282\pi$
$264$			99766.6i			1.43145i
$265$	−36573.2	−	36573.2i	−0.520800	−	0.520800i
$266$	−5467.09	−	5467.09i	−0.0772669	−	0.0772669i
$267$	−127848.	+	127848.i	−1.79338	+	1.79338i
$268$	−16718.8	+	16718.8i	−0.232775	+	0.232775i
$269$	28117.0			0.388566			0.194283	−	0.980946i	$-0.437762\pi$
$269$	28117.0			0.388566			0.194283	+	0.980946i	$0.437762\pi$
$270$			90119.3i			1.23620i
$271$	60260.0	−	60260.0i	0.820522	−	0.820522i	−0.165661	−	0.986183i	$-0.552976\pi$
$271$	60260.0	−	60260.0i	0.820522	−	0.820522i	0.986183	+	0.165661i	$0.0529757\pi$
$272$			4990.49i			0.0674536i
$273$		0			0
$274$	28116.9			0.374512
$275$	2219.35	+	2219.35i	0.0293468	+	0.0293468i
$276$	−38595.2			−0.506659
$277$		−	50385.3i		−	0.656666i	−0.944562	−	0.328333i	$-0.893513\pi$
$277$		−	50385.3i		−	0.656666i	0.944562	−	0.328333i	$-0.106487\pi$
$278$	30869.4	+	30869.4i	0.399428	+	0.399428i
$279$	−144827.	−	144827.i	−1.86055	−	1.86055i
$280$	−11347.7	+	11347.7i	−0.144742	+	0.144742i
$281$	26228.7	−	26228.7i	0.332173	−	0.332173i	−0.521238	−	0.853411i	$-0.674530\pi$
$281$	26228.7	−	26228.7i	0.332173	−	0.332173i	0.853411	+	0.521238i	$0.174530\pi$
$282$	−14977.0			−0.188333
$283$			32916.3i			0.410996i	0.978658	+	0.205498i	$0.0658814\pi$
$283$			32916.3i			0.410996i	−0.978658	+	0.205498i	$0.934119\pi$
$284$	−12873.2	+	12873.2i	−0.159607	+	0.159607i
$285$			130171.i			1.60259i
$286$		0			0
$287$	−13587.3			−0.164956
$288$	−141547.	−	141547.i	−1.70654	−	1.70654i
$289$	77762.7			0.931055
$290$		−	44027.4i		−	0.523512i
$291$	−199525.	−	199525.i	−2.35619	−	2.35619i
$292$	18366.6	+	18366.6i	0.215409	+	0.215409i
$293$	63695.3	−	63695.3i	0.741946	−	0.741946i	−0.231006	−	0.972952i	$-0.574202\pi$
$293$	63695.3	−	63695.3i	0.741946	−	0.741946i	0.972952	+	0.231006i	$0.0742018\pi$
$294$	−55065.3	+	55065.3i	−0.637064	+	0.637064i
$295$	−138418.			−1.59056
$296$		−	45183.3i		−	0.515697i
$297$	−131689.	+	131689.i	−1.49293	+	1.49293i
$298$		−	5702.92i		−	0.0642192i
$299$		0			0
$300$	−5700.59			−0.0633398
$301$	2960.33	+	2960.33i	0.0326743	+	0.0326743i
$302$	65808.1			0.721549
$303$			100400.i			1.09357i
$304$	−15107.9	−	15107.9i	−0.163477	−	0.163477i
$305$	98390.9	+	98390.9i	1.05768	+	1.05768i
$306$	21143.1	−	21143.1i	0.225801	−	0.225801i
$307$	−102971.	+	102971.i	−1.09254	+	1.09254i	−0.0972877	+	0.995256i	$0.531017\pi$
$307$	−102971.	+	102971.i	−1.09254	+	1.09254i	−0.995256	+	0.0972877i	$0.968983\pi$
$308$	−13967.1			−0.147233
$309$		−	92387.2i		−	0.967598i
$310$	39087.2	−	39087.2i	0.406735	−	0.406735i
$311$			123419.i			1.27603i	0.770023	+	0.638016i	$0.220244\pi$
$311$			123419.i			1.27603i	−0.770023	+	0.638016i	$0.779756\pi$
$312$		0			0
$313$	32784.5			0.334642			0.167321	−	0.985902i	$-0.446488\pi$
$313$	32784.5			0.334642			0.167321	+	0.985902i	$0.446488\pi$
$314$	25270.0	+	25270.0i	0.256298	+	0.256298i
$315$	−52482.1			−0.528921
$316$		−	51785.8i		−	0.518605i
$317$	80351.9	+	80351.9i	0.799609	+	0.799609i	0.983034	−	0.183425i	$-0.0587184\pi$
$317$	80351.9	+	80351.9i	0.799609	+	0.799609i	−0.183425	+	0.983034i	$0.558718\pi$
$318$	−51404.3	−	51404.3i	−0.508329	−	0.508329i
$319$	64336.3	−	64336.3i	0.632229	−	0.632229i
$320$	20050.1	−	20050.1i	0.195801	−	0.195801i
$321$	−159856.			−1.55138
$322$			4804.31i			0.0463360i
$323$	17432.4	−	17432.4i	0.167091	−	0.167091i
$324$		−	160301.i		−	1.52702i
$325$		0			0
$326$	−85592.2			−0.805376
$327$	−104851.	−	104851.i	−0.980567	−	0.980567i
$328$	68791.3			0.639420
$329$		−	4978.64i		−	0.0459959i
$330$	−62264.9	−	62264.9i	−0.571762	−	0.571762i
$331$	−65042.2	−	65042.2i	−0.593662	−	0.593662i	0.344956	−	0.938619i	$-0.387894\pi$
$331$	−65042.2	−	65042.2i	−0.593662	−	0.593662i	−0.938619	+	0.344956i	$0.887894\pi$
$332$	−46875.2	+	46875.2i	−0.425272	+	0.425272i
$333$	104484.	−	104484.i	0.942240	−	0.942240i
$334$	15305.5			0.137200
$335$		−	49551.8i		−	0.441540i
$336$	8705.47	−	8705.47i	0.0771105	−	0.0771105i
$337$		−	65948.7i		−	0.580693i	−0.956922	−	0.290347i	$-0.906229\pi$
$337$		−	65948.7i		−	0.580693i	0.956922	−	0.290347i	$-0.0937706\pi$
$338$		0			0
$339$	96532.3			0.839988
$340$	−15238.6	−	15238.6i	−0.131822	−	0.131822i
$341$	114235.			0.982401
$342$			128015.i			1.09448i
$343$	−37656.8	−	37656.8i	−0.320078	−	0.320078i
$344$	−14987.9	−	14987.9i	−0.126656	−	0.126656i
$345$	57194.9	−	57194.9i	0.480528	−	0.480528i
$346$	−15697.6	+	15697.6i	−0.131124	+	0.131124i
$347$	181615.			1.50832			0.754158	−	0.656693i	$-0.228045\pi$
$347$	181615.			1.50832			0.754158	+	0.656693i	$0.228045\pi$
$348$			165253.i			1.36456i
$349$	49531.5	−	49531.5i	0.406659	−	0.406659i	−0.473913	−	0.880572i	$-0.657159\pi$
$349$	49531.5	−	49531.5i	0.406659	−	0.406659i	0.880572	+	0.473913i	$0.157159\pi$
$350$			709.605i			0.00579269i
$351$		0			0
$352$	111648.			0.901083
$353$	114596.	+	114596.i	0.919641	+	0.919641i	0.997003	−	0.0773622i	$-0.0246498\pi$
$353$	114596.	+	114596.i	0.919641	+	0.919641i	−0.0773622	+	0.997003i	$0.524650\pi$
$354$	−194549.			−1.55247
$355$		−	38154.1i		−	0.302750i
$356$	90618.8	+	90618.8i	0.715020	+	0.715020i
$357$	10044.9	+	10044.9i	0.0788150	+	0.0788150i
$358$	−7403.85	+	7403.85i	−0.0577686	+	0.0577686i
$359$	122825.	−	122825.i	0.953014	−	0.953014i	−0.0459305	−	0.998945i	$-0.514625\pi$
$359$	122825.	−	122825.i	0.953014	−	0.953014i	0.998945	+	0.0459305i	$0.0146253\pi$
$360$	265713.			2.05026
$361$		−	24773.2i		−	0.190094i
$362$	−89304.7	+	89304.7i	−0.681487	+	0.681487i
$363$			58482.6i			0.443826i
$364$		0			0
$365$	−54435.6			−0.408599
$366$	138290.	+	138290.i	1.03236	+	1.03236i
$367$	−63673.4			−0.472744			−0.236372	−	0.971663i	$-0.575958\pi$
$367$	−63673.4			−0.472744			−0.236372	+	0.971663i	$0.575958\pi$
$368$			13276.3i			0.0980354i
$369$	159076.	+	159076.i	1.16830	+	1.16830i
$370$	28199.1	+	28199.1i	0.205983	+	0.205983i
$371$	17087.8	−	17087.8i	0.124148	−	0.124148i
$372$	−146711.	+	146711.i	−1.06017	+	1.06017i
$373$	−31655.4			−0.227526			−0.113763	−	0.993508i	$-0.536290\pi$
$373$	−31655.4			−0.227526			−0.113763	+	0.993508i	$0.536290\pi$
$374$			16677.0i			0.119227i
$375$	185521.	−	185521.i	1.31926	−	1.31926i
$376$			25206.5i			0.178294i
$377$		0			0
$378$	−42105.8			−0.294685
$379$	−5335.60	−	5335.60i	−0.0371454	−	0.0371454i	0.688290	−	0.725436i	$-0.258362\pi$
$379$	−5335.60	−	5335.60i	−0.0371454	−	0.0371454i	−0.725436	+	0.688290i	$0.758362\pi$
$380$	92264.9			0.638953
$381$		−	255758.i		−	1.76190i
$382$	45398.9	+	45398.9i	0.311113	+	0.311113i
$383$	78654.7	+	78654.7i	0.536201	+	0.536201i	0.922411	−	0.386210i	$-0.126216\pi$
$383$	78654.7	+	78654.7i	0.536201	+	0.536201i	−0.386210	+	0.922411i	$0.626216\pi$
$384$	−168901.	+	168901.i	−1.14544	+	1.14544i
$385$	20698.1	−	20698.1i	0.139640	−	0.139640i
$386$	64868.9			0.435373
$387$		−	69317.6i		−	0.462830i
$388$	−141423.	+	141423.i	−0.939413	+	0.939413i
$389$		−	246139.i		−	1.62660i	−0.581843	−	0.813301i	$-0.697668\pi$
$389$		−	246139.i		−	1.62660i	0.581843	−	0.813301i	$-0.302332\pi$
$390$		0			0
$391$	−15319.0			−0.100202
$392$	92675.9	+	92675.9i	0.603107	+	0.603107i
$393$	−110886.			−0.717946
$394$		−	16242.6i		−	0.104631i
$395$	76742.3	+	76742.3i	0.491859	+	0.491859i
$396$	163524.	+	163524.i	1.04277	+	1.04277i
$397$	123204.	−	123204.i	0.781707	−	0.781707i	−0.198412	−	0.980119i	$-0.563578\pi$
$397$	123204.	−	123204.i	0.781707	−	0.781707i	0.980119	+	0.198412i	$0.0635784\pi$
$398$	−65565.2	+	65565.2i	−0.413912	+	0.413912i
$399$	−60818.7			−0.382024
$400$			1960.94i			0.0122559i
$401$	55153.2	−	55153.2i	0.342991	−	0.342991i	−0.514500	−	0.857490i	$-0.672022\pi$
$401$	55153.2	−	55153.2i	0.342991	−	0.342991i	0.857490	+	0.514500i	$0.172022\pi$
$402$		−	69646.0i		−	0.430967i
$403$		0			0
$404$	71163.2			0.436006
$405$	237552.	+	237552.i	1.44827	+	1.44827i
$406$	20570.6			0.124794
$407$			82413.5i			0.497519i
$408$	−50856.6	−	50856.6i	−0.305511	−	0.305511i
$409$	121854.	+	121854.i	0.728439	+	0.728439i	0.970309	−	0.241869i	$-0.0777606\pi$
$409$	121854.	+	121854.i	0.728439	+	0.728439i	−0.241869	+	0.970309i	$0.577761\pi$
$410$	−42933.0	+	42933.0i	−0.255402	+	0.255402i
$411$	156393.	−	156393.i	0.925835	−	0.925835i
$412$	−65484.0			−0.385781
$413$		−	64672.0i		−	0.379155i
$414$	56247.7	−	56247.7i	0.328174	−	0.328174i
$415$		−	138930.i		−	0.806678i
$416$		0			0
$417$	343406.			1.97486
$418$	−50487.0	−	50487.0i	−0.288953	−	0.288953i
$419$	5570.03			0.0317270			0.0158635	−	0.999874i	$-0.494950\pi$
$419$	5570.03			0.0317270			0.0158635	+	0.999874i	$0.494950\pi$
$420$			53164.8i			0.301388i
$421$	−145168.	−	145168.i	−0.819042	−	0.819042i	0.166927	−	0.985969i	$-0.446616\pi$
$421$	−145168.	−	145168.i	−0.819042	−	0.819042i	−0.985969	+	0.166927i	$0.946616\pi$
$422$	−21357.6	−	21357.6i	−0.119930	−	0.119930i
$423$	−58288.8	+	58288.8i	−0.325765	+	0.325765i
$424$	−86514.3	+	86514.3i	−0.481234	+	0.481234i
$425$	−2262.65			−0.0125268
$426$		−	53626.3i		−	0.295501i
$427$	−45970.4	+	45970.4i	−0.252129	+	0.252129i
$428$			113306.i			0.618535i
$429$		0			0
$430$	18708.1			0.101179
$431$	−135160.	−	135160.i	−0.727599	−	0.727599i	0.242542	−	0.970141i	$-0.422019\pi$
$431$	−135160.	−	135160.i	−0.727599	−	0.727599i	−0.970141	+	0.242542i	$0.922019\pi$
$432$	−116356.			−0.623479
$433$			270116.i			1.44071i	0.693608	+	0.720353i	$0.256020\pi$
$433$			270116.i			1.44071i	−0.693608	+	0.720353i	$0.743980\pi$
$434$	18262.4	+	18262.4i	0.0969569	+	0.0969569i
$435$	−244891.	−	244891.i	−1.29418	−	1.29418i
$436$	−74318.3	+	74318.3i	−0.390952	+	0.390952i
$437$	46376.0	−	46376.0i	0.242846	−	0.242846i
$438$	−76510.3			−0.398815
$439$		−	44497.0i		−	0.230888i	−0.993314	−	0.115444i	$-0.963171\pi$
$439$		−	44497.0i		−	0.230888i	0.993314	−	0.115444i	$-0.0368291\pi$
$440$	−104793.	+	104793.i	−0.541286	+	0.541286i
$441$			428617.i			2.20390i
$442$		0			0
$443$	−150334.			−0.766035			−0.383018	−	0.923741i	$-0.625115\pi$
$443$	−150334.			−0.766035			−0.383018	+	0.923741i	$0.625115\pi$
$444$	−105843.	−	105843.i	−0.536904	−	0.536904i
$445$	−268579.			−1.35629
$446$			79214.2i			0.398229i
$447$	−31721.1	−	31721.1i	−0.158757	−	0.158757i
$448$	9367.84	+	9367.84i	0.0466749	+	0.0466749i
$449$	−181654.	+	181654.i	−0.901056	+	0.901056i	−0.995528	−	0.0944715i	$-0.969884\pi$
$449$	−181654.	+	181654.i	−0.901056	+	0.901056i	0.0944715	+	0.995528i	$0.469884\pi$
$450$	8307.88	−	8307.88i	0.0410266	−	0.0410266i
$451$	−125474.			−0.616881
$452$		−	68422.0i		−	0.334903i
$453$	366041.	−	366041.i	1.78375	−	1.78375i
$454$			206131.i			1.00007i
$455$		0			0
$456$	307920.			1.48084
$457$	−6744.61	−	6744.61i	−0.0322942	−	0.0322942i	0.690775	−	0.723070i	$-0.257269\pi$
$457$	−6744.61	−	6744.61i	−0.0322942	−	0.0322942i	−0.723070	+	0.690775i	$0.757269\pi$
$458$	−65708.7			−0.313251
$459$		−	134259.i		−	0.637261i
$460$	−40539.7	−	40539.7i	−0.191586	−	0.191586i
$461$	−34959.9	−	34959.9i	−0.164501	−	0.164501i	0.620056	−	0.784557i	$-0.287110\pi$
$461$	−34959.9	−	34959.9i	−0.164501	−	0.164501i	−0.784557	+	0.620056i	$0.787110\pi$
$462$	29091.6	−	29091.6i	0.136296	−	0.136296i
$463$	117898.	−	117898.i	0.549978	−	0.549978i	−0.376456	−	0.926434i	$-0.622857\pi$
$463$	117898.	−	117898.i	0.549978	−	0.549978i	0.926434	+	0.376456i	$0.122857\pi$
$464$	56845.3			0.264033
$465$		−	434825.i		−	2.01098i
$466$	132660.	−	132660.i	0.610895	−	0.610895i
$467$		−	62768.3i		−	0.287811i	−0.989591	−	0.143905i	$-0.954034\pi$
$467$		−	62768.3i		−	0.287811i	0.989591	−	0.143905i	$-0.0459661\pi$
$468$		0			0
$469$	23151.7			0.105254
$470$	−15731.5	−	15731.5i	−0.0712156	−	0.0712156i
$471$	281116.			1.26720
$472$			327430.i			1.46972i
$473$	27337.7	+	27337.7i	0.122191	+	0.122191i
$474$	107863.	+	107863.i	0.480081	+	0.480081i
$475$	6849.82	−	6849.82i	0.0303593	−	0.0303593i
$476$	7119.81	−	7119.81i	0.0314235	−	0.0314235i
$477$	−400120.			−1.75855
$478$			212414.i			0.929665i
$479$	−208783.	+	208783.i	−0.909963	+	0.909963i	−0.996269	−	0.0863057i	$-0.972494\pi$
$479$	−208783.	+	208783.i	−0.909963	+	0.909963i	0.0863057	+	0.996269i	$0.472494\pi$
$480$		−	424979.i		−	1.84453i
$481$		0			0
$482$	101842.			0.438363
$483$	26722.7	+	26722.7i	0.114548	+	0.114548i
$484$	41452.4			0.176953
$485$		−	419154.i		−	1.78193i
$486$	122310.	+	122310.i	0.517831	+	0.517831i
$487$	−127702.	−	127702.i	−0.538442	−	0.538442i	0.384629	−	0.923071i	$-0.374329\pi$
$487$	−127702.	−	127702.i	−0.538442	−	0.538442i	−0.923071	+	0.384629i	$0.874329\pi$
$488$	232745.	−	232745.i	0.977329	−	0.977329i
$489$	−476085.	+	476085.i	−1.99098	+	1.99098i
$490$	−115679.			−0.481795
$491$			173629.i			0.720210i	0.932912	+	0.360105i	$0.117259\pi$
$491$			173629.i			0.720210i	−0.932912	+	0.360105i	$0.882741\pi$
$492$	161146.	−	161146.i	0.665715	−	0.665715i
$493$			65591.5i			0.269869i
$494$		0			0
$495$	−484657.			−1.97799
$496$	50466.8	+	50466.8i	0.205136	+	0.205136i
$497$	17826.4			0.0721692
$498$		−	195269.i		−	0.787362i
$499$	−100154.	−	100154.i	−0.402223	−	0.402223i	0.476793	−	0.879016i	$-0.341799\pi$
$499$	−100154.	−	100154.i	−0.402223	−	0.402223i	−0.879016	+	0.476793i	$0.841799\pi$
$500$	−131497.	−	131497.i	−0.525989	−	0.525989i
$501$	85133.2	−	85133.2i	0.339175	−	0.339175i
$502$	175533.	−	175533.i	0.696549	−	0.696549i
$503$	491436.			1.94237			0.971183	−	0.238336i	$-0.0766018\pi$
$503$	491436.			1.94237			0.971183	+	0.238336i	$0.0766018\pi$
$504$			124147.i			0.488738i
$505$	−105458.	+	105458.i	−0.413520	+	0.413520i
$506$			44366.3i			0.173282i
$507$		0			0
$508$	−181281.			−0.702467
$509$	200349.	+	200349.i	0.773307	+	0.773307i	0.978683	−	0.205376i	$-0.0658419\pi$
$509$	200349.	+	200349.i	0.773307	+	0.773307i	−0.205376	+	0.978683i	$0.565842\pi$
$510$	63479.7			0.244059
$511$		−	25433.5i		−	0.0974013i
$512$	92262.9	+	92262.9i	0.351955	+	0.351955i
$513$	406447.	+	406447.i	1.54443	+	1.54443i
$514$	−172222.	+	172222.i	−0.651874	+	0.651874i
$515$	97041.7	−	97041.7i	0.365884	−	0.365884i
$516$	−70219.2			−0.263728
$517$		−	45976.3i		−	0.172010i
$518$	−13175.3	+	13175.3i	−0.0491021	+	0.0491021i
$519$			174628.i			0.648305i
$520$		0			0
$521$	43309.3			0.159553			0.0797766	−	0.996813i	$-0.474579\pi$
$521$	43309.3			0.159553			0.0797766	+	0.996813i	$0.474579\pi$
$522$	−240836.	−	240836.i	−0.883852	−	0.883852i
$523$	−353134.			−1.29103			−0.645515	−	0.763747i	$-0.723357\pi$
$523$	−353134.			−1.29103			−0.645515	+	0.763747i	$0.723357\pi$
$524$			78596.0i			0.286245i
$525$	3947.00	+	3947.00i	0.0143202	+	0.0143202i
$526$	−88280.6	−	88280.6i	−0.319076	−	0.319076i
$527$	−58231.6	+	58231.6i	−0.209671	+	0.209671i
$528$	80392.4	−	80392.4i	0.288368	−	0.288368i
$529$	239087.			0.854368
$530$		−	107988.i		−	0.384436i
$531$	−757165.	+	757165.i	−2.68535	+	2.68535i
$532$			43108.2i			0.152313i
$533$		0			0
$534$	−377493.			−1.32381
$535$	−167910.	−	167910.i	−0.586635	−	0.586635i
$536$	−117215.			−0.407995
$537$			82364.1i			0.285621i
$538$	41510.0	+	41510.0i	0.143413	+	0.143413i
$539$	−169039.	−	169039.i	−0.581849	−	0.581849i
$540$	355297.	−	355297.i	1.21844	−	1.21844i
$541$	129117.	−	129117.i	0.441152	−	0.441152i	−0.451247	−	0.892399i	$-0.649021\pi$
$541$	129117.	−	129117.i	0.441152	−	0.441152i	0.892399	+	0.451247i	$0.149021\pi$
$542$	177927.			0.605681
$543$			993470.i			3.36942i
$544$	−56913.0	+	56913.0i	−0.192315	+	0.192315i
$545$		−	220267.i		−	0.741577i
$546$		0			0
$547$	−494292.			−1.65199			−0.825997	−	0.563674i	$-0.809387\pi$
$547$	−494292.			−1.65199			−0.825997	+	0.563674i	$0.809387\pi$
$548$	−110851.	−	110851.i	−0.369130	−	0.369130i
$549$	1.07642e6			3.57140
$550$			6552.98i			0.0216628i
$551$	−198568.	−	198568.i	−0.654042	−	0.654042i
$552$	−135295.	−	135295.i	−0.444022	−	0.444022i
$553$	−35855.7	+	35855.7i	−0.117249	+	0.117249i
$554$	74385.3	−	74385.3i	0.242364	−	0.242364i
$555$	313701.			1.01843
$556$		−	243406.i		−	0.787376i
$557$	323877.	−	323877.i	1.04393	−	1.04393i	0.0449372	−	0.998990i	$-0.485691\pi$
$557$	323877.	−	323877.i	1.04393	−	1.04393i	0.998990	−	0.0449372i	$-0.0143088\pi$
$558$		−	427624.i		−	1.37339i
$559$		0			0
$560$	18288.1			0.0583167
$561$	92761.5	+	92761.5i	0.294742	+	0.294742i
$562$	77444.5			0.245199
$563$			31173.0i			0.0983471i	0.998790	+	0.0491736i	$0.0156587\pi$
$563$			31173.0i			0.0983471i	−0.998790	+	0.0491736i	$0.984341\pi$
$564$	59046.9	+	59046.9i	0.185626	+	0.185626i
$565$	101396.	+	101396.i	0.317631	+	0.317631i
$566$	−48595.2	+	48595.2i	−0.151691	+	0.151691i
$567$	−110990.	+	110990.i	−0.345236	+	0.345236i
$568$	−90254.0			−0.279750
$569$			520171.i			1.60665i	0.595539	+	0.803326i	$0.296938\pi$
$569$			520171.i			1.60665i	−0.595539	+	0.803326i	$0.703062\pi$
$570$	−192175.	+	192175.i	−0.591489	+	0.591489i
$571$		−	167278.i		−	0.513057i	−0.966537	−	0.256528i	$-0.917421\pi$
$571$		−	167278.i		−	0.513057i	0.966537	−	0.256528i	$-0.0825787\pi$
$572$		0			0
$573$	505040.			1.53821
$574$	−20059.3	−	20059.3i	−0.0608823	−	0.0608823i
$575$	−6019.40			−0.0182061
$576$		−	219353.i		−	0.661147i
$577$	113625.	+	113625.i	0.341290	+	0.341290i	0.856852	−	0.515562i	$-0.172417\pi$
$577$	113625.	+	113625.i	0.341290	+	0.341290i	−0.515562	+	0.856852i	$0.672417\pi$
$578$	114803.	+	114803.i	0.343636	+	0.343636i
$579$	360817.	−	360817.i	1.07629	−	1.07629i
$580$	−173579.	+	173579.i	−0.515989	+	0.515989i
$581$	64911.3			0.192295
$582$		−	589129.i		−	1.73926i
$583$	157801.	−	157801.i	0.464271	−	0.464271i
$584$			128768.i			0.377557i
$585$		0			0
$586$	188071.			0.547678
$587$	−234582.	−	234582.i	−0.680800	−	0.680800i	0.279381	−	0.960180i	$-0.409871\pi$
$587$	−234582.	−	234582.i	−0.680800	−	0.680800i	−0.960180	+	0.279381i	$0.909871\pi$
$588$	434192.			1.25582
$589$		−	352574.i		−	1.01630i
$590$	−204351.	−	204351.i	−0.587046	−	0.587046i
$591$	−90345.1	−	90345.1i	−0.258660	−	0.258660i
$592$	−36408.9	+	36408.9i	−0.103888	+	0.103888i
$593$	−60427.5	+	60427.5i	−0.171840	+	0.171840i	−0.787788	−	0.615947i	$-0.788773\pi$
$593$	−60427.5	+	60427.5i	−0.171840	+	0.171840i	0.615947	+	0.787788i	$0.288773\pi$
$594$	−388834.			−1.10202
$595$			21101.9i			0.0596057i
$596$	−22483.9	+	22483.9i	−0.0632963	+	0.0632963i
$597$			729380.i			2.04647i
$598$		0			0
$599$	−292574.			−0.815421			−0.407710	−	0.913111i	$-0.633673\pi$
$599$	−292574.			−0.815421			−0.407710	+	0.913111i	$0.633673\pi$
$600$	−19983.4	−	19983.4i	−0.0555093	−	0.0555093i
$601$	12974.1			0.0359194			0.0179597	−	0.999839i	$-0.494283\pi$
$601$	12974.1			0.0359194			0.0179597	+	0.999839i	$0.494283\pi$
$602$			8740.84i			0.0241190i
$603$	−271055.	−	271055.i	−0.745456	−	0.745456i
$604$	−259449.	−	259449.i	−0.711179	−	0.711179i
$605$	−61428.9	+	61428.9i	−0.167827	+	0.167827i
$606$	−148223.	+	148223.i	−0.403618	+	0.403618i
$607$	−194088.			−0.526769			−0.263385	−	0.964691i	$-0.584839\pi$
$607$	−194088.			−0.526769			−0.263385	+	0.964691i	$0.584839\pi$
$608$		−	344590.i		−	0.932172i
$609$	114419.	−	114419.i	0.308505	−	0.308505i
$610$			290515.i			0.780744i
$611$		0			0
$612$	−166714.			−0.445112
$613$	−217264.	−	217264.i	−0.578184	−	0.578184i	0.356218	−	0.934403i	$-0.384066\pi$
$613$	−217264.	−	217264.i	−0.578184	−	0.578184i	−0.934403	+	0.356218i	$0.884066\pi$
$614$	−304039.			−0.806477
$615$			477608.i			1.26276i
$616$	−48961.6	−	48961.6i	−0.129031	−	0.129031i
$617$	−123675.	−	123675.i	−0.324872	−	0.324872i	0.525760	−	0.850633i	$-0.323781\pi$
$617$	−123675.	−	123675.i	−0.324872	−	0.324872i	−0.850633	+	0.525760i	$0.823781\pi$
$618$	136394.	−	136394.i	0.357123	−	0.357123i
$619$	−184299.	+	184299.i	−0.480997	+	0.480997i	−0.905450	−	0.424453i	$-0.860467\pi$
$619$	−184299.	+	184299.i	−0.480997	+	0.480997i	0.424453	+	0.905450i	$0.360467\pi$
$620$	−308204.			−0.801779
$621$		−	357173.i		−	0.926179i
$622$	−182207.	+	182207.i	−0.470961	+	0.470961i
$623$		−	125486.i		−	0.323310i
$624$		0			0
$625$	371100.			0.950016
$626$	48400.8	+	48400.8i	0.123510	+	0.123510i
$627$	−561642.			−1.42864
$628$		−	199255.i		−	0.505230i
$629$	−42010.7	−	42010.7i	−0.106184	−	0.106184i
$630$	−77480.9	−	77480.9i	−0.195215	−	0.195215i
$631$	−266824.	+	266824.i	−0.670141	+	0.670141i	−0.957748	−	0.287607i	$-0.907140\pi$
$631$	−266824.	+	266824.i	−0.670141	+	0.670141i	0.287607	+	0.957748i	$0.407140\pi$
$632$	181535.	−	181535.i	0.454492	−	0.454492i
$633$	−237592.			−0.592959
$634$			237252.i			0.590243i
$635$	268644.	−	268644.i	0.666238	−	0.666238i
$636$			405324.i			1.00205i
$637$		0			0
$638$	189963.			0.466689
$639$	−208708.	−	208708.i	−0.511136	−	0.511136i
$640$	−354821.			−0.866263
$641$			699022.i			1.70128i	0.525751	+	0.850638i	$0.323784\pi$
$641$			699022.i			1.70128i	−0.525751	+	0.850638i	$0.676216\pi$
$642$	−236000.	−	236000.i	−0.572588	−	0.572588i
$643$	−256844.	−	256844.i	−0.621224	−	0.621224i	0.324620	−	0.945844i	$-0.394763\pi$
$643$	−256844.	−	256844.i	−0.621224	−	0.621224i	−0.945844	+	0.324620i	$0.894763\pi$
$644$	18941.0	−	18941.0i	0.0456701	−	0.0456701i
$645$	104059.	−	104059.i	0.250127	−	0.250127i
$646$	51472.0			0.123341
$647$			323178.i			0.772029i	0.922493	+	0.386014i	$0.126148\pi$
$647$			323178.i			0.772029i	−0.922493	+	0.386014i	$0.873852\pi$
$648$	561933.	−	561933.i	1.33824	−	1.33824i
$649$		−	597227.i		−	1.41791i
$650$		0			0
$651$	203160.			0.479376
$652$	337448.	+	337448.i	0.793802	+	0.793802i
$653$	−449186.			−1.05341			−0.526707	−	0.850047i	$-0.676574\pi$
$653$	−449186.			−1.05341			−0.526707	+	0.850047i	$0.676574\pi$
$654$		−	309589.i		−	0.723820i
$655$	−116473.	−	116473.i	−0.271482	−	0.271482i
$656$	−55432.3	−	55432.3i	−0.128812	−	0.128812i
$657$	−297770.	+	297770.i	−0.689842	+	0.689842i
$658$	7350.12	−	7350.12i	0.0169763	−	0.0169763i
$659$	−711339.			−1.63797			−0.818984	−	0.573816i	$-0.805462\pi$
$659$	−711339.			−1.63797			−0.818984	+	0.573816i	$0.805462\pi$
$660$			490961.i			1.12709i
$661$	−280301.	+	280301.i	−0.641538	+	0.641538i	−0.950933	−	0.309396i	$-0.899873\pi$
$661$	−280301.	+	280301.i	−0.641538	+	0.641538i	0.309396	+	0.950933i	$0.399873\pi$
$662$		−	192048.i		−	0.438221i
$663$		0			0
$664$	−328641.			−0.745394
$665$	−63882.7	−	63882.7i	−0.144458	−	0.144458i
$666$	308506.			0.695528
$667$			174495.i			0.392222i
$668$	−60342.3	−	60342.3i	−0.135229	−	0.135229i
$669$	440609.	+	440609.i	0.984467	+	0.984467i
$670$	73154.7	−	73154.7i	0.162964	−	0.162964i
$671$	−424523.	+	424523.i	−0.942880	+	0.942880i
$672$	198560.			0.439696
$673$		−	406226.i		−	0.896887i	−0.893811	−	0.448444i	$-0.851978\pi$
$673$		−	406226.i		−	0.896887i	0.893811	−	0.448444i	$-0.148022\pi$
$674$	97362.1	−	97362.1i	0.214324	−	0.214324i
$675$		−	52755.0i		−	0.115786i
$676$		0			0
$677$	−273635.			−0.597027			−0.298514	−	0.954405i	$-0.596491\pi$
$677$	−273635.			−0.597027			−0.298514	+	0.954405i	$0.596491\pi$
$678$	142513.	+	142513.i	0.310025	+	0.310025i
$679$	195838.			0.424774
$680$		−	106837.i		−	0.231050i
$681$	1.14655e6	+	1.14655e6i	2.47228	+	2.47228i
$682$	168648.	+	168648.i	0.362587	+	0.362587i
$683$	36206.0	−	36206.0i	0.0776138	−	0.0776138i	−0.667234	−	0.744848i	$-0.732522\pi$
$683$	36206.0	−	36206.0i	0.0776138	−	0.0776138i	0.744848	+	0.667234i	$0.232522\pi$
$684$	504701.	−	504701.i	1.07875	−	1.07875i
$685$	328544.			0.700185
$686$		−	111188.i		−	0.236270i
$687$	−365488.	+	365488.i	−0.774390	+	0.774390i
$688$			24154.7i			0.0510298i
$689$		0			0
$690$	168877.			0.354709
$691$	182874.	+	182874.i	0.382998	+	0.382998i	0.872181	−	0.489183i	$-0.162705\pi$
$691$	182874.	+	182874.i	0.382998	+	0.382998i	−0.489183	+	0.872181i	$0.662705\pi$
$692$	123776.			0.258479
$693$		−	226442.i		−	0.471510i
$694$	268123.	+	268123.i	0.556693	+	0.556693i
$695$	360707.	+	360707.i	0.746767	+	0.746767i
$696$	−579293.	+	579293.i	−1.19586	+	1.19586i
$697$	63961.1	−	63961.1i	0.131659	−	0.131659i
$698$	146250.			0.300182
$699$		−	1.47577e6i		−	3.02040i
$700$	2797.63	−	2797.63i	0.00570944	−	0.00570944i
$701$			361445.i			0.735540i	0.929917	+	0.367770i	$0.119879\pi$
$701$			361445.i			0.735540i	−0.929917	+	0.367770i	$0.880121\pi$
$702$		0			0
$703$	254362.			0.514685
$704$	86509.1	+	86509.1i	0.174549	+	0.174549i
$705$	−175005.			−0.352105
$706$			338362.i			0.678846i
$707$	−49272.3	−	49272.3i	−0.0985743	−	0.0985743i
$708$	767013.	+	767013.i	1.53016	+	1.53016i
$709$	374612.	−	374612.i	0.745227	−	0.745227i	−0.228351	−	0.973579i	$-0.573333\pi$
$709$	374612.	−	374612.i	0.745227	−	0.745227i	0.973579	+	0.228351i	$0.0733335\pi$
$710$	56328.0	−	56328.0i	0.111740	−	0.111740i
$711$	839580.			1.66082
$712$			635327.i			1.25325i
$713$	−154915.	+	154915.i	−0.304730	+	0.304730i
$714$			29659.1i			0.0581784i
$715$		0			0
$716$	58379.6			0.113877
$717$	1.18150e6	+	1.18150e6i	2.29823	+	2.29823i
$718$	362662.			0.703481
$719$			57608.2i			0.111436i	0.998447	+	0.0557181i	$0.0177448\pi$
$719$			57608.2i			0.111436i	−0.998447	+	0.0557181i	$0.982255\pi$
$720$	−214113.	−	214113.i	−0.413027	−	0.413027i
$721$	45340.1	+	45340.1i	0.0872191	+	0.0872191i
$722$	36573.4	−	36573.4i	0.0701603	−	0.0701603i
$723$	566472.	−	566472.i	1.08368	−	1.08368i
$724$	704170.			1.34339
$725$			25773.2i			0.0490335i
$726$	−86339.5	+	86339.5i	−0.163809	+	0.163809i
$727$			1582.61i			0.00299437i	0.999999	+	0.00149718i	$0.000476569\pi$
$727$			1582.61i			0.00299437i	−0.999999	+	0.00149718i	$0.999523\pi$
$728$		0			0
$729$	245225.			0.461435
$730$	−80364.9	−	80364.9i	−0.150807	−	0.150807i
$731$	−27871.1			−0.0521578
$732$		−	1.09042e6i		−	2.03504i
$733$	364582.	+	364582.i	0.678559	+	0.678559i	0.959674	−	0.281115i	$-0.0907043\pi$
$733$	364582.	+	364582.i	0.678559	+	0.678559i	−0.281115	+	0.959674i	$0.590704\pi$
$734$	−94003.0	−	94003.0i	−0.174481	−	0.174481i
$735$	−643435.	+	643435.i	−1.19105	+	1.19105i
$736$	−151407.	+	151407.i	−0.279506	+	0.279506i
$737$	213799.			0.393614
$738$			469698.i			0.862395i
$739$	416067.	−	416067.i	0.761859	−	0.761859i	−0.214799	−	0.976658i	$-0.568910\pi$
$739$	416067.	−	416067.i	0.761859	−	0.761859i	0.976658	+	0.214799i	$0.0689097\pi$
$740$		−	222351.i		−	0.406046i
$741$		0			0
$742$	50454.5			0.0916414
$743$	−366616.	−	366616.i	−0.664101	−	0.664101i	0.292243	−	0.956344i	$-0.405598\pi$
$743$	−366616.	−	366616.i	−0.664101	−	0.664101i	−0.956344	+	0.292243i	$0.905598\pi$
$744$	−1.02858e6			−1.85821
$745$		−	66638.4i		−	0.120064i
$746$	−46733.8	−	46733.8i	−0.0839757	−	0.0839757i
$747$	−759966.	−	759966.i	−1.36192	−	1.36192i
$748$	65749.3	−	65749.3i	0.117513	−	0.117513i
$749$	78451.1	−	78451.1i	0.139841	−	0.139841i
$750$	547781.			0.973833
$751$		−	175249.i		−	0.310724i	−0.987858	−	0.155362i	$-0.950346\pi$
$751$		−	175249.i		−	0.310724i	0.987858	−	0.155362i	$-0.0496544\pi$
$752$	20311.5	−	20311.5i	0.0359175	−	0.0359175i
$753$		−	1.95272e6i		−	3.44389i
$754$		0			0
$755$	768964.			1.34900
$756$	166003.	+	166003.i	0.290450	+	0.290450i
$757$	433490.			0.756463			0.378232	−	0.925711i	$-0.376532\pi$
$757$	433490.			0.756463			0.378232	+	0.925711i	$0.376532\pi$
$758$		−	15754.2i		−	0.0274194i
$759$	246776.	+	246776.i	0.428371	+	0.428371i
$760$	323434.	+	323434.i	0.559961	+	0.559961i
$761$	1199.86	−	1199.86i	0.00207187	−	0.00207187i	−0.706070	−	0.708142i	$-0.749534\pi$
$761$	1199.86	−	1199.86i	0.00207187	−	0.00207187i	0.708142	+	0.706070i	$0.249534\pi$
$762$	377584.	−	377584.i	0.650284	−	0.650284i
$763$	102914.			0.176776
$764$		−	357972.i		−	0.613285i
$765$	247056.	−	247056.i	0.422156	−	0.422156i
$766$			232241.i			0.395804i
$767$		0			0
$768$	−804122.			−1.36333
$769$	284883.	+	284883.i	0.481741	+	0.481741i	0.905687	−	0.423946i	$-0.139355\pi$
$769$	284883.	+	284883.i	0.481741	+	0.481741i	−0.423946	+	0.905687i	$0.639355\pi$
$770$	61114.4			0.103077
$771$			1.91589e6i			3.22301i
$772$	−255747.	−	255747.i	−0.429117	−	0.429117i
$773$	63921.0	+	63921.0i	0.106976	+	0.106976i	0.758569	−	0.651593i	$-0.225899\pi$
$773$	63921.0	+	63921.0i	0.106976	+	0.106976i	−0.651593	+	0.758569i	$0.725899\pi$
$774$	102336.	−	102336.i	0.170823	−	0.170823i
$775$	−22881.3	+	22881.3i	−0.0380958	+	0.0380958i
$776$	−991514.			−1.64655
$777$			146568.i			0.242771i
$778$	363383.	−	363383.i	0.600350	−	0.600350i
$779$			387264.i			0.638165i
$780$		0			0
$781$	164622.			0.269889
$782$	−22615.9	−	22615.9i	−0.0369829	−	0.0369829i
$783$	−1.52930e6			−2.49443
$784$		−	149357.i		−	0.242993i
$785$	295279.	+	295279.i	0.479173	+	0.479173i
$786$	−163704.	−	163704.i	−0.264981	−	0.264981i
$787$	160602.	−	160602.i	0.259300	−	0.259300i	−0.565469	−	0.824769i	$-0.691305\pi$
$787$	160602.	−	160602.i	0.259300	−	0.259300i	0.824769	+	0.565469i	$0.191305\pi$
$788$	−64036.5	+	64036.5i	−0.103128	+	0.103128i
$789$	−982077.			−1.57758
$790$			226594.i			0.363073i
$791$	−47374.3	+	47374.3i	−0.0757164	+	0.0757164i
$792$			1.14646e6i			1.82772i
$793$		0			0
$794$	363780.			0.577028
$795$	−600657.	−	600657.i	−0.950368	−	0.950368i
$796$	516984.			0.815926
$797$		−	1.03077e6i		−	1.62272i	−0.584546	−	0.811361i	$-0.698727\pi$
$797$		−	1.03077e6i		−	1.62272i	0.584546	−	0.811361i	$-0.301273\pi$
$798$	−89788.4	−	89788.4i	−0.140998	−	0.140998i
$799$	23436.6	+	23436.6i	0.0367115	+	0.0367115i
$800$	−22363.2	+	22363.2i	−0.0349424	+	0.0349424i
$801$	−1.46916e6	+	1.46916e6i	−2.28984	+	2.28984i
$802$	162849.			0.253184
$803$		−	234871.i		−	0.364249i
$804$	−274580.	+	274580.i	−0.424773	+	0.424773i
$805$			56138.1i			0.0866295i
$806$		0			0
$807$	461777.			0.709064
$808$	249462.	+	249462.i	0.382104	+	0.382104i
$809$	559540.			0.854937			0.427468	−	0.904030i	$-0.359406\pi$
$809$	559540.			0.854937			0.427468	+	0.904030i	$0.359406\pi$
$810$			701410.i			1.06906i
$811$	−15617.4	−	15617.4i	−0.0237447	−	0.0237447i	0.695135	−	0.718879i	$-0.255345\pi$
$811$	−15617.4	−	15617.4i	−0.0237447	−	0.0237447i	−0.718879	+	0.695135i	$0.755345\pi$
$812$	−81099.8	−	81099.8i	−0.123001	−	0.123001i
$813$	989674.	−	989674.i	1.49731	−	1.49731i
$814$	−121670.	+	121670.i	−0.183626	+	0.183626i
$815$	−1.00014e6			−1.50573
$816$			81960.9i			0.123091i
$817$	84375.3	−	84375.3i	0.126407	−	0.126407i
$818$			359794.i			0.537708i
$819$		0			0
$820$	338528.			0.503463
$821$	−286644.	−	286644.i	−0.425263	−	0.425263i	0.461748	−	0.887011i	$-0.347222\pi$
$821$	−286644.	−	286644.i	−0.425263	−	0.425263i	−0.887011	+	0.461748i	$0.847222\pi$
$822$	461775.			0.683419
$823$		−	866161.i		−	1.27879i	−0.768879	−	0.639394i	$-0.779185\pi$
$823$		−	866161.i		−	1.27879i	0.768879	−	0.639394i	$-0.220815\pi$
$824$	−229553.	−	229553.i	−0.338088	−	0.338088i
$825$	36449.3	+	36449.3i	0.0535527	+	0.0535527i
$826$	95477.2	−	95477.2i	0.139939	−	0.139939i
$827$	−276075.	+	276075.i	−0.403661	+	0.403661i	−0.879521	−	0.475860i	$-0.842137\pi$
$827$	−276075.	+	276075.i	−0.403661	+	0.403661i	0.475860	+	0.879521i	$0.342137\pi$
$828$	−443515.			−0.646915
$829$		−	448687.i		−	0.652881i	−0.945218	−	0.326441i	$-0.894151\pi$
$829$		−	448687.i		−	0.652881i	0.945218	−	0.326441i	$-0.105849\pi$
$830$	205107.	−	205107.i	0.297731	−	0.297731i
$831$		−	827499.i		−	1.19830i
$832$		0			0
$833$	172337.			0.248364
$834$	506981.	+	506981.i	0.728886	+	0.728886i
$835$	178844.			0.256509
$836$			398091.i			0.569600i
$837$	−1.35771e6	−	1.35771e6i	−1.93800	−	1.93800i
$838$	8223.20	+	8223.20i	0.0117099	+	0.0117099i
$839$	−96430.6	+	96430.6i	−0.136991	+	0.136991i	−0.772277	−	0.635286i	$-0.780882\pi$
$839$	−96430.6	+	96430.6i	−0.136991	+	0.136991i	0.635286	+	0.772277i	$0.280882\pi$
$840$	−186369.	+	186369.i	−0.264128	+	0.264128i
$841$	39853.8			0.0563479
$842$		−	428631.i		−	0.604588i
$843$	430765.	−	430765.i	0.606158	−	0.606158i
$844$			168405.i			0.236412i
$845$		0			0
$846$	−172107.			−0.240468
$847$	−28701.0	−	28701.0i	−0.0400064	−	0.0400064i
$848$	139427.			0.193890
$849$			540597.i			0.749995i
$850$	−3340.42	−	3340.42i	−0.00462341	−	0.00462341i
$851$	−111762.	−	111762.i	−0.154325	−	0.154325i
$852$	−211422.	+	211422.i	−0.291254	+	0.291254i
$853$	933402.	−	933402.i	1.28283	−	1.28283i	0.343787	−	0.939048i	$-0.388290\pi$
$853$	933402.	−	933402.i	1.28283	−	1.28283i	0.939048	−	0.343787i	$-0.111710\pi$
$854$	−135735.			−0.186113
$855$			1.49585e6i			2.04623i
$856$	−397192.	+	397192.i	−0.542067	+	0.542067i
$857$			1.09474e6i			1.49055i	0.666755	+	0.745277i	$0.267683\pi$
$857$			1.09474e6i			1.49055i	−0.666755	+	0.745277i	$0.732317\pi$
$858$		0			0
$859$	639678.			0.866912			0.433456	−	0.901175i	$-0.357294\pi$
$859$	639678.			0.866912			0.433456	+	0.901175i	$0.357294\pi$
$860$	−73756.9	−	73756.9i	−0.0997254	−	0.0997254i
$861$	−223149.			−0.301016
$862$		−	399080.i		−	0.537088i
$863$	−831636.	−	831636.i	−1.11664	−	1.11664i	−0.992231	−	0.124405i	$-0.960298\pi$
$863$	−831636.	−	831636.i	−1.11664	−	1.11664i	−0.124405	−	0.992231i	$-0.539702\pi$
$864$	−1.32696e6	−	1.32696e6i	−1.77759	−	1.77759i
$865$	−183426.	+	183426.i	−0.245148	+	0.245148i
$866$	−398781.	+	398781.i	−0.531739	+	0.531739i
$867$	1.27713e6			1.69901
$868$		−	144000.i		−	0.191127i
$869$	−331116.	+	331116.i	−0.438471	+	0.438471i
$870$		−	723080.i		−	0.955318i
$871$		0			0
$872$	−521044.			−0.685239
$873$	−2.29283e6	−	2.29283e6i	−3.00845	−	3.00845i
$874$	136932.			0.179260
$875$			182093.i			0.237836i
$876$	301643.	+	301643.i	0.393084	+	0.393084i
$877$	541183.	+	541183.i	0.703631	+	0.703631i	0.965188	−	0.261557i	$-0.0842358\pi$
$877$	541183.	+	541183.i	0.703631	+	0.703631i	−0.261557	+	0.965188i	$0.584236\pi$
$878$	65692.2	−	65692.2i	0.0852168	−	0.0852168i
$879$	1.04609e6	−	1.04609e6i	1.35392	−	1.35392i
$880$	168885.			0.218085
$881$			70936.9i			0.0913946i	0.998955	+	0.0456973i	$0.0145510\pi$
$881$			70936.9i			0.0913946i	−0.998955	+	0.0456973i	$0.985449\pi$
$882$	−632779.	+	632779.i	−0.813420	+	0.813420i
$883$		−	230442.i		−	0.295557i	−0.989020	−	0.147778i	$-0.952788\pi$
$883$		−	230442.i		−	0.295557i	0.989020	−	0.147778i	$-0.0472123\pi$
$884$		0			0
$885$	−2.27330e6			−2.90248
$886$	−221942.	−	221942.i	−0.282730	−	0.282730i
$887$	501652.			0.637611			0.318805	−	0.947820i	$-0.396718\pi$
$887$	501652.			0.637611			0.318805	+	0.947820i	$0.396718\pi$
$888$		−	742064.i		−	0.941056i
$889$	125516.	+	125516.i	0.158817	+	0.158817i
$890$	−396511.	−	396511.i	−0.500582	−	0.500582i
$891$	−1.02496e6	+	1.02496e6i	−1.29107	+	1.29107i
$892$	312303.	−	312303.i	0.392506	−	0.392506i
$893$	−141901.			−0.177944
$894$		−	93661.5i		−	0.117189i
$895$	−86513.7	+	86513.7i	−0.108004	+	0.108004i
$896$		−	165780.i		−	0.206499i
$897$		0			0
$898$	−536362.			−0.665128
$899$	663301.	+	663301.i	0.820713	+	0.820713i
$900$	−65507.9			−0.0808740
$901$			160879.i			0.198176i
$902$	−185241.	−	185241.i	−0.227680	−	0.227680i
$903$	48618.7	+	48618.7i	0.0596249	+	0.0596249i
$904$	239853.	−	239853.i	0.293500	−	0.293500i
$905$	−1.04352e6	+	1.04352e6i	−1.27410	+	1.27410i
$906$	1.08079e6			1.31670
$907$			96792.8i			0.117660i	0.998268	+	0.0588299i	$0.0187370\pi$
$907$			96792.8i			0.117660i	−0.998268	+	0.0588299i	$0.981263\pi$
$908$	812673.	−	812673.i	0.985698	−	0.985698i
$909$			1.15374e6i			1.39630i
$910$		0			0
$911$	583928.			0.703595			0.351798	−	0.936076i	$-0.385571\pi$
$911$	583928.			0.703595			0.351798	+	0.936076i	$0.385571\pi$
$912$	−248124.	−	248124.i	−0.298317	−	0.298317i
$913$	599436.			0.719120
$914$		−	19914.5i		−	0.0238385i
$915$	1.61592e6	+	1.61592e6i	1.93009	+	1.93009i
$916$	259058.	+	259058.i	0.308749	+	0.308749i
$917$	54418.6	−	54418.6i	0.0647155	−	0.0647155i
$918$	198210.	−	198210.i	0.235202	−	0.235202i
$919$	791760.			0.937481			0.468741	−	0.883336i	$-0.344708\pi$
$919$	791760.			0.937481			0.468741	+	0.883336i	$0.344708\pi$
$920$		−	284223.i		−	0.335802i
$921$	−1.69114e6	+	1.69114e6i	−1.99370	+	1.99370i
$922$		−	103225.i		−	0.121429i
$923$		0			0
$924$	−229388.			−0.268674
$925$	−16507.5	−	16507.5i	−0.0192929	−	0.0192929i
$926$	348113.			0.405975
$927$		−	1.06166e6i		−	1.23545i
$928$	648281.	+	648281.i	0.752779	+	0.752779i
$929$	481776.	+	481776.i	0.558231	+	0.558231i	0.928803	−	0.370573i	$-0.120839\pi$
$929$	481776.	+	481776.i	0.558231	+	0.558231i	−0.370573	+	0.928803i	$0.620839\pi$
$930$	641945.	−	641945.i	0.742219	−	0.742219i
$931$	−521724.	+	521724.i	−0.601924	+	0.601924i
$932$	−1.04602e6			−1.20423
$933$			2.02696e6i			2.32853i
$934$	92666.7	−	92666.7i	0.106226	−	0.106226i
$935$			194870.i			0.222906i
$936$		0			0
$937$	−1.42104e6			−1.61856			−0.809278	−	0.587426i	$-0.800141\pi$
$937$	−1.42104e6			−1.61856			−0.809278	+	0.587426i	$0.800141\pi$
$938$	34179.5	+	34179.5i	0.0388473	+	0.0388473i
$939$	538434.			0.610663
$940$			124044.i			0.140384i
$941$	−549268.	−	549268.i	−0.620305	−	0.620305i	0.325305	−	0.945609i	$-0.394533\pi$
$941$	−549268.	−	549268.i	−0.620305	−	0.620305i	−0.945609	+	0.325305i	$0.894533\pi$
$942$	415020.	+	415020.i	0.467700	+	0.467700i
$943$	170158.	−	170158.i	0.191350	−	0.191350i
$944$	263844.	−	263844.i	0.296076	−	0.296076i
$945$	−492004.			−0.550941
$946$			80719.0i			0.0901973i
$947$	−585133.	+	585133.i	−0.652461	+	0.652461i	−0.953585	−	0.301124i	$-0.902638\pi$
$947$	−585133.	+	585133.i	−0.652461	+	0.652461i	0.301124	+	0.953585i	$0.402638\pi$
$948$		−	850501.i		−	0.946363i
$949$		0			0
$950$	20225.2			0.0224102
$951$	1.31965e6	+	1.31965e6i	1.45915	+	1.45915i
$952$	49916.9			0.0550774
$953$			810617.i			0.892545i	0.894897	+	0.446273i	$0.147249\pi$
$953$			810617.i			0.892545i	−0.894897	+	0.446273i	$0.852751\pi$
$954$	−590709.	−	590709.i	−0.649048	−	0.649048i
$955$	530484.	+	530484.i	0.581655	+	0.581655i
$956$	837444.	−	837444.i	0.916304	−	0.916304i
$957$	1.05662e6	−	1.05662e6i	1.15371	−	1.15371i
$958$	−616464.			−0.671703
$959$			153503.i			0.166909i
$960$	329290.	−	329290.i	0.357303	−	0.357303i
$961$			254226.i			0.275280i
$962$		0			0
$963$	−1.83697e6			−1.98084
$964$	−401515.	−	401515.i	−0.432063	−	0.432063i
$965$	757990.			0.813971
$966$			78903.1i			0.0845551i
$967$	1.08406e6	+	1.08406e6i	1.15931	+	1.15931i	0.984625	+	0.174682i	$0.0558897\pi$
$967$	1.08406e6	+	1.08406e6i	1.15931	+	1.15931i	0.174682	+	0.984625i	$0.444110\pi$
$968$	145311.	+	145311.i	0.155077	+	0.155077i
$969$	286300.	−	286300.i	0.304911	−	0.304911i
$970$	618809.	−	618809.i	0.657678	−	0.657678i
$971$	−363772.			−0.385825			−0.192913	−	0.981216i	$-0.561793\pi$
$971$	−363772.			−0.385825			−0.192913	+	0.981216i	$0.561793\pi$
$972$		−	964416.i		−	1.02078i
$973$	−168531.	+	168531.i	−0.178014	+	0.178014i
$974$		−	377059.i		−	0.397459i
$975$		0			0
$976$	−375094.			−0.393768
$977$	271667.	+	271667.i	0.284608	+	0.284608i	0.834944	−	0.550335i	$-0.185500\pi$
$977$	271667.	+	271667.i	0.284608	+	0.284608i	−0.550335	+	0.834944i	$0.685500\pi$
$978$	−1.40572e6			−1.46967
$979$		−	1.15883e6i		−	1.20907i
$980$	456066.	+	456066.i	0.474871	+	0.474871i
$981$	−1.20489e6	−	1.20489e6i	−1.25201	−	1.25201i
$982$	−256333.	+	256333.i	−0.265817	+	0.265817i
$983$	−200018.	+	200018.i	−0.206996	+	0.206996i	−0.802989	−	0.595993i	$-0.796758\pi$
$983$	−200018.	+	200018.i	−0.206996	+	0.206996i	0.595993	+	0.802989i	$0.296758\pi$
$984$	1.12979e6			1.16683
$985$		−	189793.i		−	0.195618i
$986$	−96834.6	+	96834.6i	−0.0996040	+	0.0996040i
$987$		−	81766.3i		−	0.0839344i
$988$		0			0
$989$	−74146.3			−0.0758048
$990$	−715513.	−	715513.i	−0.730041	−	0.730041i
$991$	−1.45767e6			−1.48426			−0.742131	−	0.670255i	$-0.766185\pi$
$991$	−1.45767e6			−1.48426			−0.742131	+	0.670255i	$0.766185\pi$
$992$			1.15108e6i			1.16972i
$993$	−1.06822e6	−	1.06822e6i	−1.08333	−	1.08333i
$994$	26317.7	+	26317.7i	0.0266364	+	0.0266364i
$995$	−766127.	+	766127.i	−0.773846	+	0.773846i
$996$	−769851.	+	769851.i	−0.776047	+	0.776047i
$997$	−763737.			−0.768341			−0.384170	−	0.923262i	$-0.625512\pi$
$997$	−763737.			−0.768341			−0.384170	+	0.923262i	$0.625512\pi$
$998$		−	295721.i		−	0.296907i
$999$	979505.	−	979505.i	0.981467	−	0.981467i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.5.d.d.99.5		16
13.2	odd	12		13.5.f.a.6.3	✓	16
13.5	odd	4	inner	169.5.d.d.70.5		16
13.8	odd	4		169.5.d.c.70.4		16
13.9	even	3		13.5.f.a.11.3	yes	16
13.12	even	2		169.5.d.c.99.4		16
39.2	even	12		117.5.bd.c.19.2		16
39.35	odd	6		117.5.bd.c.37.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.5.f.a.6.3	✓	16	13.2	odd	12
13.5.f.a.11.3	yes	16	13.9	even	3
117.5.bd.c.19.2		16	39.2	even	12
117.5.bd.c.37.2		16	39.35	odd	6
169.5.d.c.70.4		16	13.8	odd	4
169.5.d.c.99.4		16	13.12	even	2
169.5.d.d.70.5		16	13.5	odd	4	inner
169.5.d.d.99.5		16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	169.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.47633 + 1.47633i) q^{2} +16.4234 q^{3} -11.6409i q^{4} +(17.2508 + 17.2508i) q^{5} +(24.2464 + 24.2464i) q^{6} +(-8.05998 + 8.05998i) q^{7} +(40.8071 - 40.8071i) q^{8} +188.729 q^{9} +O(q^{10})\)	\(q+(1.47633 + 1.47633i) q^{2} +16.4234 q^{3} -11.6409i q^{4} +(17.2508 + 17.2508i) q^{5} +(24.2464 + 24.2464i) q^{6} +(-8.05998 + 8.05998i) q^{7} +(40.8071 - 40.8071i) q^{8} +188.729 q^{9} +50.9358i q^{10} +(-74.4314 + 74.4314i) q^{11} -191.183i q^{12} -23.7984 q^{14} +(283.318 + 283.318i) q^{15} -65.7650 q^{16} -75.8836i q^{17} +(278.626 + 278.626i) q^{18} +(229.726 + 229.726i) q^{19} +(200.815 - 200.815i) q^{20} +(-132.372 + 132.372i) q^{21} -219.771 q^{22} -201.875i q^{23} +(670.192 - 670.192i) q^{24} -29.8174i q^{25} +1769.27 q^{27} +(93.8254 + 93.8254i) q^{28} -864.370 q^{29} +836.540i q^{30} +(-767.381 - 767.381i) q^{31} +(-750.004 - 750.004i) q^{32} +(-1222.42 + 1222.42i) q^{33} +(112.029 - 112.029i) q^{34} -278.083 q^{35} -2196.97i q^{36} +(553.621 - 553.621i) q^{37} +678.302i q^{38} +1407.91 q^{40} +(842.885 + 842.885i) q^{41} -390.850 q^{42} -367.287i q^{43} +(866.449 + 866.449i) q^{44} +(3255.73 + 3255.73i) q^{45} +(298.035 - 298.035i) q^{46} +(-308.850 + 308.850i) q^{47} -1080.09 q^{48} +2271.07i q^{49} +(44.0203 - 44.0203i) q^{50} -1246.27i q^{51} -2120.08 q^{53} +(2612.03 + 2612.03i) q^{54} -2568.01 q^{55} +657.808i q^{56} +(3772.88 + 3772.88i) q^{57} +(-1276.09 - 1276.09i) q^{58} +(-4011.92 + 4011.92i) q^{59} +(3298.07 - 3298.07i) q^{60} +5703.55 q^{61} -2265.81i q^{62} +(-1521.15 + 1521.15i) q^{63} -1162.27i q^{64} -3609.38 q^{66} +(-1436.21 - 1436.21i) q^{67} -883.354 q^{68} -3315.49i q^{69} +(-410.542 - 410.542i) q^{70} +(-1105.86 - 1105.86i) q^{71} +(7701.46 - 7701.46i) q^{72} +(-1577.77 + 1577.77i) q^{73} +1634.65 q^{74} -489.703i q^{75} +(2674.21 - 2674.21i) q^{76} -1199.83i q^{77} +4448.61 q^{79} +(-1134.50 - 1134.50i) q^{80} +13770.5 q^{81} +2488.75i q^{82} +(-4026.77 - 4026.77i) q^{83} +(1540.93 + 1540.93i) q^{84} +(1309.06 - 1309.06i) q^{85} +(542.237 - 542.237i) q^{86} -14195.9 q^{87} +6074.66i q^{88} +(-7784.52 + 7784.52i) q^{89} +9613.05i q^{90} -2350.01 q^{92} +(-12603.0 - 12603.0i) q^{93} -911.928 q^{94} +7925.92i q^{95} +(-12317.6 - 12317.6i) q^{96} +(-12148.8 - 12148.8i) q^{97} +(-3352.85 + 3352.85i) q^{98} +(-14047.3 + 14047.3i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} + 4 q^{3} + 8 q^{5} - 128 q^{6} + 56 q^{7} + 90 q^{8} + 328 q^{9}+O(q^{10}) \) 16 * q + 2 * q^2 + 4 * q^3 + 8 * q^5 - 128 * q^6 + 56 * q^7 + 90 * q^8 + 328 * q^9	\( 16 q + 2 q^{2} + 4 q^{3} + 8 q^{5} - 128 q^{6} + 56 q^{7} + 90 q^{8} + 328 q^{9} + 500 q^{11} + 808 q^{14} + 844 q^{15} - 460 q^{16} + 2434 q^{18} + 1712 q^{19} + 838 q^{20} - 1076 q^{21} + 3048 q^{22} + 5772 q^{24} + 3352 q^{27} + 2980 q^{28} - 1628 q^{29} + 4060 q^{31} + 3662 q^{32} - 860 q^{33} - 2502 q^{34} + 9784 q^{35} + 10468 q^{37} + 18816 q^{40} + 3440 q^{41} + 2408 q^{42} + 10736 q^{44} - 1004 q^{45} + 11436 q^{46} + 1484 q^{47} + 6004 q^{48} + 21616 q^{50} + 7204 q^{53} + 6760 q^{54} - 13872 q^{55} + 12736 q^{57} + 7974 q^{58} - 4840 q^{59} - 6472 q^{60} + 324 q^{61} - 13988 q^{63} - 23872 q^{66} + 2216 q^{67} + 12888 q^{68} - 34524 q^{70} - 1240 q^{71} - 6606 q^{72} - 15448 q^{73} + 5764 q^{74} - 39688 q^{76} - 17064 q^{79} - 37630 q^{80} - 4256 q^{81} + 12788 q^{83} - 7736 q^{84} - 22884 q^{85} + 67260 q^{86} - 58684 q^{87} - 37624 q^{89} - 49884 q^{92} - 2492 q^{93} + 61212 q^{94} - 94664 q^{96} - 57056 q^{97} + 27950 q^{98} - 21632 q^{99}+O(q^{100}) \) 16 * q + 2 * q^2 + 4 * q^3 + 8 * q^5 - 128 * q^6 + 56 * q^7 + 90 * q^8 + 328 * q^9 + 500 * q^11 + 808 * q^14 + 844 * q^15 - 460 * q^16 + 2434 * q^18 + 1712 * q^19 + 838 * q^20 - 1076 * q^21 + 3048 * q^22 + 5772 * q^24 + 3352 * q^27 + 2980 * q^28 - 1628 * q^29 + 4060 * q^31 + 3662 * q^32 - 860 * q^33 - 2502 * q^34 + 9784 * q^35 + 10468 * q^37 + 18816 * q^40 + 3440 * q^41 + 2408 * q^42 + 10736 * q^44 - 1004 * q^45 + 11436 * q^46 + 1484 * q^47 + 6004 * q^48 + 21616 * q^50 + 7204 * q^53 + 6760 * q^54 - 13872 * q^55 + 12736 * q^57 + 7974 * q^58 - 4840 * q^59 - 6472 * q^60 + 324 * q^61 - 13988 * q^63 - 23872 * q^66 + 2216 * q^67 + 12888 * q^68 - 34524 * q^70 - 1240 * q^71 - 6606 * q^72 - 15448 * q^73 + 5764 * q^74 - 39688 * q^76 - 17064 * q^79 - 37630 * q^80 - 4256 * q^81 + 12788 * q^83 - 7736 * q^84 - 22884 * q^85 + 67260 * q^86 - 58684 * q^87 - 37624 * q^89 - 49884 * q^92 - 2492 * q^93 + 61212 * q^94 - 94664 * q^96 - 57056 * q^97 + 27950 * q^98 - 21632 * q^99

Introduction

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