LMFDB - Embedded newform 261.3.s.a.10.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,3,Mod(10,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([0, 23]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("261.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	261.s (of order $28$, degree $12$, 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:	$7.11173489980$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{28})$
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			10.1
Character	$\chi$	$=$	261.10
Dual form			261.3.s.a.235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.05804 + 1.29315i) q^{2} +(0.827740 - 1.71882i) q^{4} +(-5.87720 - 1.34143i) q^{5} +(-9.36468 + 4.50979i) q^{7} +(-0.569384 - 5.05343i) q^{8} +O(q^{10})$	\(q+(-2.05804 + 1.29315i) q^{2} +(0.827740 - 1.71882i) q^{4} +(-5.87720 - 1.34143i) q^{5} +(-9.36468 + 4.50979i) q^{7} +(-0.569384 - 5.05343i) q^{8} +(13.8301 - 4.83938i) q^{10} +(-0.977326 + 8.67401i) q^{11} +(8.98997 - 7.16926i) q^{13} +(13.4410 - 21.3913i) q^{14} +(12.4645 + 15.6300i) q^{16} +(9.77422 + 9.77422i) q^{17} +(-4.49203 - 12.8375i) q^{19} +(-7.17047 + 8.99148i) q^{20} +(-9.20542 - 19.1153i) q^{22} +(-6.44949 - 28.2571i) q^{23} +(10.2178 + 4.92062i) q^{25} +(-9.23075 + 26.3800i) q^{26} +19.8291i q^{28} +(28.9618 - 1.48885i) q^{29} +(32.8240 - 20.6247i) q^{31} +(-26.6642 - 9.33019i) q^{32} +(-32.7552 - 7.47617i) q^{34} +(61.0877 - 13.9429i) q^{35} +(6.61609 + 58.7194i) q^{37} +(25.8456 + 20.6112i) q^{38} +(-3.43244 + 30.4638i) q^{40} +(-28.8990 + 28.8990i) q^{41} +(23.3701 - 37.1932i) q^{43} +(14.1001 + 8.85967i) q^{44} +(49.8139 + 49.8139i) q^{46} +(16.5298 + 1.86246i) q^{47} +(36.8081 - 46.1559i) q^{49} +(-27.3916 + 3.08629i) q^{50} +(-4.88131 - 21.3864i) q^{52} +(12.8958 - 56.5002i) q^{53} +(17.3795 - 49.6678i) q^{55} +(28.1220 + 44.7559i) q^{56} +(-57.6790 + 40.5160i) q^{58} +34.0756 q^{59} +(5.90275 + 2.06546i) q^{61} +(-40.8822 + 84.8927i) q^{62} +(-11.0199 + 2.51523i) q^{64} +(-62.4529 + 30.0757i) q^{65} +(-53.1751 - 42.4058i) q^{67} +(24.8906 - 8.70961i) q^{68} +(-107.690 + 107.690i) q^{70} +(24.4740 - 19.5174i) q^{71} +(-43.4053 - 27.2734i) q^{73} +(-89.5491 - 112.291i) q^{74} +(-25.7836 - 2.90511i) q^{76} +(-29.9657 - 85.6369i) q^{77} +(36.9784 - 4.16647i) q^{79} +(-52.2897 - 108.581i) q^{80} +(22.1045 - 96.8459i) q^{82} +(-62.9075 - 30.2947i) q^{83} +(-44.3336 - 70.5565i) q^{85} +106.766i q^{86} +44.3899 q^{88} +(-23.7527 + 14.9248i) q^{89} +(-51.8564 + 107.681i) q^{91} +(-53.9073 - 12.3040i) q^{92} +(-36.4274 + 17.5425i) q^{94} +(9.17994 + 81.4742i) q^{95} +(-33.9244 + 11.8707i) q^{97} +(-16.0659 + 142.589i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) $ 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8	$ 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8} - 20 q^{10} + 8 q^{11} - 14 q^{13} - 26 q^{14} + 18 q^{16} + 26 q^{17} + 2 q^{19} - 46 q^{20} + 154 q^{22} - 56 q^{23} - 34 q^{25} - 110 q^{26} + 170 q^{29} - 88 q^{31} + 132 q^{32} - 224 q^{34} + 210 q^{35} - 56 q^{37} + 294 q^{38} - 492 q^{40} + 34 q^{41} + 176 q^{43} - 126 q^{44} + 744 q^{46} - 208 q^{47} + 506 q^{49} - 732 q^{50} + 690 q^{52} + 14 q^{53} + 284 q^{55} - 332 q^{56} - 508 q^{58} + 44 q^{59} - 30 q^{61} + 504 q^{62} - 896 q^{64} + 554 q^{65} - 574 q^{67} + 796 q^{68} - 1066 q^{70} - 224 q^{71} - 22 q^{73} - 820 q^{74} + 514 q^{76} - 436 q^{77} + 564 q^{79} - 1162 q^{80} - 18 q^{82} + 126 q^{83} + 38 q^{85} - 384 q^{88} + 160 q^{89} - 434 q^{91} + 1022 q^{92} - 2 q^{94} + 642 q^{95} + 604 q^{97} + 102 q^{98}+O(q^{100}) $ 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8 - 20 * q^10 + 8 * q^11 - 14 * q^13 - 26 * q^14 + 18 * q^16 + 26 * q^17 + 2 * q^19 - 46 * q^20 + 154 * q^22 - 56 * q^23 - 34 * q^25 - 110 * q^26 + 170 * q^29 - 88 * q^31 + 132 * q^32 - 224 * q^34 + 210 * q^35 - 56 * q^37 + 294 * q^38 - 492 * q^40 + 34 * q^41 + 176 * q^43 - 126 * q^44 + 744 * q^46 - 208 * q^47 + 506 * q^49 - 732 * q^50 + 690 * q^52 + 14 * q^53 + 284 * q^55 - 332 * q^56 - 508 * q^58 + 44 * q^59 - 30 * q^61 + 504 * q^62 - 896 * q^64 + 554 * q^65 - 574 * q^67 + 796 * q^68 - 1066 * q^70 - 224 * q^71 - 22 * q^73 - 820 * q^74 + 514 * q^76 - 436 * q^77 + 564 * q^79 - 1162 * q^80 - 18 * q^82 + 126 * q^83 + 38 * q^85 - 384 * q^88 + 160 * q^89 - 434 * q^91 + 1022 * q^92 - 2 * q^94 + 642 * q^95 + 604 * q^97 + 102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{23}{28}\right)$	$1$

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 $

$2$	−2.05804	+	1.29315i	−1.02902	+	0.646575i	−0.937053	−	0.349188i	$-0.886458\pi$
$2$	−2.05804	+	1.29315i	−1.02902	+	0.646575i	−0.0919649	+	0.995762i	$0.529315\pi$
$3$		0			0
$3$		0			0
$4$	0.827740	−	1.71882i	0.206935	−	0.429705i
$5$	−5.87720	−	1.34143i	−1.17544	−	0.268286i	−0.410177	−	0.912006i	$-0.634533\pi$
$5$	−5.87720	−	1.34143i	−1.17544	−	0.268286i	−0.765262	+	0.643719i	$0.777390\pi$
$6$		0			0
$7$	−9.36468	+	4.50979i	−1.33781	+	0.644256i	−0.959575	−	0.281452i	$-0.909184\pi$
$7$	−9.36468	+	4.50979i	−1.33781	+	0.644256i	−0.378237	+	0.925709i	$0.623470\pi$
$8$	−0.569384	−	5.05343i	−0.0711730	−	0.631678i
$9$		0			0
$10$	13.8301	−	4.83938i	1.38301	−	0.483938i
$11$	−0.977326	+	8.67401i	−0.0888478	+	0.788546i	0.867723	+	0.497048i	$0.165583\pi$
$11$	−0.977326	+	8.67401i	−0.0888478	+	0.788546i	−0.956571	+	0.291499i	$0.905846\pi$
$12$		0			0
$13$	8.98997	−	7.16926i	0.691536	−	0.551482i	−0.213433	−	0.976958i	$-0.568465\pi$
$13$	8.98997	−	7.16926i	0.691536	−	0.551482i	0.904970	+	0.425476i	$0.139893\pi$
$14$	13.4410	−	21.3913i	0.960073	−	1.52795i
$15$		0			0
$16$	12.4645	+	15.6300i	0.779031	+	0.976873i
$17$	9.77422	+	9.77422i	0.574954	+	0.574954i	0.933509	−	0.358554i	$-0.116730\pi$
$17$	9.77422	+	9.77422i	0.574954	+	0.574954i	−0.358554	+	0.933509i	$0.616730\pi$
$18$		0			0
$19$	−4.49203	−	12.8375i	−0.236423	−	0.675658i	−0.999567	−	0.0294292i	$-0.990631\pi$
$19$	−4.49203	−	12.8375i	−0.236423	−	0.675658i	0.763144	−	0.646228i	$-0.223655\pi$
$20$	−7.17047	+	8.99148i	−0.358523	+	0.449574i
$21$		0			0
$22$	−9.20542	−	19.1153i	−0.418428	−	0.868875i
$23$	−6.44949	−	28.2571i	−0.280413	−	1.22857i	−0.897266	−	0.441490i	$-0.854450\pi$
$23$	−6.44949	−	28.2571i	−0.280413	−	1.22857i	0.616853	−	0.787078i	$-0.288407\pi$
$24$		0			0
$25$	10.2178	+	4.92062i	0.408711	+	0.196825i
$26$	−9.23075	+	26.3800i	−0.355029	+	1.01461i
$27$		0			0
$28$			19.8291i			0.708184i
$29$	28.9618	−	1.48885i	0.998681	−	0.0513395i
$29$	28.9618	−	1.48885i	0.998681	−	0.0513395i
$30$		0			0
$31$	32.8240	−	20.6247i	1.05884	−	0.665313i	0.114212	−	0.993456i	$-0.463566\pi$
$31$	32.8240	−	20.6247i	1.05884	−	0.665313i	0.944628	+	0.328144i	$0.106423\pi$
$32$	−26.6642	−	9.33019i	−0.833255	−	0.291568i
$33$		0			0
$34$	−32.7552	−	7.47617i	−0.963389	−	0.219887i
$35$	61.0877	−	13.9429i	1.74536	−	0.398367i
$36$		0			0
$37$	6.61609	+	58.7194i	0.178813	+	1.58701i	0.687581	+	0.726107i	$0.258672\pi$
$37$	6.61609	+	58.7194i	0.178813	+	1.58701i	−0.508768	+	0.860904i	$0.669899\pi$
$38$	25.8456	+	20.6112i	0.680146	+	0.542399i
$39$		0			0
$40$	−3.43244	+	30.4638i	−0.0858110	+	0.761594i
$41$	−28.8990	+	28.8990i	−0.704854	+	0.704854i	−0.965448	−	0.260594i	$-0.916081\pi$
$41$	−28.8990	+	28.8990i	−0.704854	+	0.704854i	0.260594	+	0.965448i	$0.416081\pi$
$42$		0			0
$43$	23.3701	−	37.1932i	0.543490	−	0.864959i	−0.456200	−	0.889877i	$-0.650790\pi$
$43$	23.3701	−	37.1932i	0.543490	−	0.864959i	0.999689	+	0.0249182i	$0.00793254\pi$
$44$	14.1001	+	8.85967i	0.320457	+	0.201356i
$45$		0			0
$46$	49.8139	+	49.8139i	1.08291	+	1.08291i
$47$	16.5298	+	1.86246i	0.351698	+	0.0396269i	0.286047	−	0.958216i	$-0.407659\pi$
$47$	16.5298	+	1.86246i	0.351698	+	0.0396269i	0.0656518	+	0.997843i	$0.479087\pi$
$48$		0			0
$49$	36.8081	−	46.1559i	0.751185	−	0.941956i
$50$	−27.3916	+	3.08629i	−0.547832	+	0.0617259i
$51$		0			0
$52$	−4.88131	−	21.3864i	−0.0938714	−	0.411278i
$53$	12.8958	−	56.5002i	0.243317	−	1.06604i	−0.694659	−	0.719340i	$-0.744445\pi$
$53$	12.8958	−	56.5002i	0.243317	−	1.06604i	0.937975	−	0.346702i	$-0.112698\pi$
$54$		0			0
$55$	17.3795	−	49.6678i	0.315991	−	0.903052i
$56$	28.1220	+	44.7559i	0.502179	+	0.799213i
$57$		0			0
$58$	−57.6790	+	40.5160i	−0.994466	+	0.698551i
$59$	34.0756			0.577552			0.288776	−	0.957397i	$-0.406752\pi$
$59$	34.0756			0.577552			0.288776	+	0.957397i	$0.406752\pi$
$60$		0			0
$61$	5.90275	+	2.06546i	0.0967664	+	0.0338600i	0.378228	−	0.925712i	$-0.376534\pi$
$61$	5.90275	+	2.06546i	0.0967664	+	0.0338600i	−0.281462	+	0.959572i	$0.590819\pi$
$62$	−40.8822	+	84.8927i	−0.659390	+	1.36924i
$63$		0			0
$64$	−11.0199	+	2.51523i	−0.172186	+	0.0393004i
$65$	−62.4529	+	30.0757i	−0.960814	+	0.462704i
$66$		0			0
$67$	−53.1751	−	42.4058i	−0.793659	−	0.632922i	0.140378	−	0.990098i	$-0.455168\pi$
$67$	−53.1751	−	42.4058i	−0.793659	−	0.632922i	−0.934037	+	0.357176i	$0.883740\pi$
$68$	24.8906	−	8.70961i	0.366039	−	0.128083i
$69$		0			0
$70$	−107.690	+	107.690i	−1.53843	+	1.53843i
$71$	24.4740	−	19.5174i	0.344704	−	0.274893i	−0.435799	−	0.900044i	$-0.643534\pi$
$71$	24.4740	−	19.5174i	0.344704	−	0.274893i	0.780504	+	0.625151i	$0.214963\pi$
$72$		0			0
$73$	−43.4053	−	27.2734i	−0.594593	−	0.373608i	0.200862	−	0.979619i	$-0.435626\pi$
$73$	−43.4053	−	27.2734i	−0.594593	−	0.373608i	−0.795456	+	0.606012i	$0.792768\pi$
$74$	−89.5491	−	112.291i	−1.21012	−	1.51745i
$75$		0			0
$76$	−25.7836	−	2.90511i	−0.339258	−	0.0382252i
$77$	−29.9657	−	85.6369i	−0.389164	−	1.11217i
$78$		0			0
$79$	36.9784	−	4.16647i	0.468081	−	0.0527401i	0.125226	−	0.992128i	$-0.460034\pi$
$79$	36.9784	−	4.16647i	0.468081	−	0.0527401i	0.342855	+	0.939388i	$0.388606\pi$
$80$	−52.2897	−	108.581i	−0.653621	−	1.35726i
$81$		0			0
$82$	22.1045	−	96.8459i	0.269566	−	1.18105i
$83$	−62.9075	−	30.2947i	−0.757922	−	0.364996i	0.0146754	−	0.999892i	$-0.495329\pi$
$83$	−62.9075	−	30.2947i	−0.757922	−	0.364996i	−0.772597	+	0.634896i	$0.781043\pi$
$84$		0			0
$85$	−44.3336	−	70.5565i	−0.521571	−	0.830076i
$86$			106.766i			1.24147i
$87$		0			0
$88$	44.3899			0.504431
$89$	−23.7527	+	14.9248i	−0.266885	+	0.167695i	−0.658826	−	0.752296i	$-0.728947\pi$
$89$	−23.7527	+	14.9248i	−0.266885	+	0.167695i	0.391941	+	0.919990i	$0.371804\pi$
$90$		0			0
$91$	−51.8564	+	107.681i	−0.569850	+	1.18331i
$92$	−53.9073	−	12.3040i	−0.585949	−	0.133739i
$93$		0			0
$94$	−36.4274	+	17.5425i	−0.387526	+	0.186623i
$95$	9.17994	+	81.4742i	0.0966310	+	0.857623i
$96$		0			0
$97$	−33.9244	+	11.8707i	−0.349736	+	0.122378i	−0.499430	−	0.866354i	$-0.666457\pi$
$97$	−33.9244	+	11.8707i	−0.349736	+	0.122378i	0.149693	+	0.988732i	$0.452171\pi$
$98$	−16.0659	+	142.589i	−0.163938	+	1.45499i
$99$		0			0
$100$	16.9153	−	13.4895i	0.169153	−	0.134895i
$101$	33.1691	−	52.7883i	0.328407	−	0.522657i	−0.641184	−	0.767387i	$-0.721557\pi$
$101$	33.1691	−	52.7883i	0.328407	−	0.522657i	0.969591	+	0.244730i	$0.0786994\pi$
$102$		0			0
$103$	−73.2496	−	91.8521i	−0.711161	−	0.891768i	0.286641	−	0.958038i	$-0.407461\pi$
$103$	−73.2496	−	91.8521i	−0.711161	−	0.891768i	−0.997802	+	0.0662704i	$0.978890\pi$
$104$	−41.3481	−	41.3481i	−0.397578	−	0.397578i
$105$		0			0
$106$	46.5232	+	132.956i	0.438898	+	1.25430i
$107$	42.6207	−	53.4447i	0.398324	−	0.499483i	−0.541709	−	0.840566i	$-0.682222\pi$
$107$	42.6207	−	53.4447i	0.398324	−	0.499483i	0.940033	+	0.341083i	$0.110794\pi$
$108$		0			0
$109$	5.04985	+	10.4861i	0.0463289	+	0.0962029i	0.922848	−	0.385163i	$-0.125855\pi$
$109$	5.04985	+	10.4861i	0.0463289	+	0.0962029i	−0.876519	+	0.481366i	$0.840141\pi$
$110$	28.4603	+	124.693i	0.258730	+	1.13357i
$111$		0			0
$112$	−187.214	−	90.1575i	−1.67155	−	0.804978i
$113$	14.1909	−	40.5554i	0.125584	−	0.358897i	−0.863876	−	0.503704i	$-0.831970\pi$
$113$	14.1909	−	40.5554i	0.125584	−	0.358897i	0.989460	+	0.144807i	$0.0462560\pi$
$114$		0			0
$115$			174.724i			1.51934i
$116$	21.4137	−	51.0124i	0.184601	−	0.439762i
$117$		0			0
$118$	−70.1287	+	44.0648i	−0.594311	+	0.373431i
$119$	−135.612	−	47.4528i	−1.13960	−	0.398763i
$120$		0			0
$121$	43.6830	+	9.97036i	0.361016	+	0.0823996i
$122$	−14.8190	+	3.38234i	−0.121467	+	0.0277241i
$123$		0			0
$124$	−8.28039	−	73.4905i	−0.0667773	−	0.592665i
$125$	64.3775	+	51.3393i	0.515020	+	0.410715i
$126$		0			0
$127$	14.8633	−	131.916i	0.117034	−	1.03871i	−0.788676	−	0.614809i	$-0.789233\pi$
$127$	14.8633	−	131.916i	0.117034	−	1.03871i	0.905710	−	0.423897i	$-0.139338\pi$
$128$	99.3283	−	99.3283i	0.776002	−	0.776002i
$129$		0			0
$130$	89.6379	−	142.658i	0.689522	−	1.09737i
$131$	−66.7432	−	41.9375i	−0.509490	−	0.320134i	0.252637	−	0.967561i	$-0.418702\pi$
$131$	−66.7432	−	41.9375i	−0.509490	−	0.320134i	−0.762127	+	0.647427i	$0.775845\pi$
$132$		0			0
$133$	99.9609	+	99.9609i	0.751586	+	0.751586i
$134$	164.273	+	18.5092i	1.22592	+	0.138128i
$135$		0			0
$136$	43.8280	−	54.9586i	0.322265	−	0.404107i
$137$	160.789	−	18.1166i	1.17364	−	0.132238i	0.496465	−	0.868057i	$-0.334631\pi$
$137$	160.789	−	18.1166i	1.17364	−	0.132238i	0.677179	+	0.735819i	$0.263202\pi$
$138$		0			0
$139$	24.4796	+	107.252i	0.176112	+	0.771599i	0.983401	+	0.181443i	$0.0580767\pi$
$139$	24.4796	+	107.252i	0.176112	+	0.771599i	−0.807289	+	0.590156i	$0.799066\pi$
$140$	26.5994	−	116.540i	0.189996	−	0.832427i
$141$		0			0
$142$	−25.1295	+	71.8160i	−0.176968	+	0.505747i
$143$	53.4001	+	84.9858i	0.373428	+	0.594306i
$144$		0			0
$145$	−172.211	−	30.1000i	−1.18766	−	0.207586i
$146$	124.598			0.853412
$147$		0			0
$148$	106.404	+	37.2325i	0.718949	+	0.251571i
$149$	−62.5002	+	129.783i	−0.419464	+	0.871027i	0.578984	+	0.815339i	$0.303449\pi$
$149$	−62.5002	+	129.783i	−0.419464	+	0.871027i	−0.998448	+	0.0556878i	$0.982265\pi$
$150$		0			0
$151$	279.422	−	63.7763i	1.85048	−	0.422359i	0.855105	−	0.518454i	$-0.173492\pi$
$151$	279.422	−	63.7763i	1.85048	−	0.422359i	0.995372	+	0.0960946i	$0.0306351\pi$
$152$	−62.3156	+	30.0096i	−0.409971	+	0.197432i
$153$		0			0
$154$	172.412	+	137.494i	1.11956	+	0.892817i
$155$	−220.580	+	77.1842i	−1.42310	+	0.497963i
$156$		0			0
$157$	181.866	−	181.866i	1.15838	−	1.15838i	0.173555	−	0.984824i	$-0.444474\pi$
$157$	181.866	−	181.866i	1.15838	−	1.15838i	0.984824	−	0.173555i	$-0.0555255\pi$
$158$	−70.7150	+	56.3934i	−0.447564	+	0.356920i
$159$		0			0
$160$	144.195	+	90.6035i	0.901216	+	0.566272i
$161$	187.831	+	235.533i	1.16665	+	1.46294i
$162$		0			0
$163$	59.4854	+	6.70239i	0.364941	+	0.0411190i	0.292531	−	0.956256i	$-0.405502\pi$
$163$	59.4854	+	6.70239i	0.364941	+	0.0411190i	0.0724098	+	0.997375i	$0.476931\pi$
$164$	25.7513	+	73.5931i	0.157020	+	0.448738i
$165$		0			0
$166$	168.641	−	19.0013i	1.01591	−	0.114466i
$167$	−79.8635	−	165.838i	−0.478225	−	0.993044i	−0.990917	−	0.134472i	$-0.957066\pi$
$167$	−79.8635	−	165.838i	−0.478225	−	0.993044i	0.512693	−	0.858572i	$-0.328648\pi$
$168$		0			0
$169$	−8.18478	+	35.8598i	−0.0484306	+	0.212188i
$170$	182.480	+	87.8778i	1.07341	+	0.516928i
$171$		0			0
$172$	−44.5842	−	70.9553i	−0.259210	−	0.412531i
$173$			24.3883i			0.140973i	0.997513	+	0.0704864i	$0.0224551\pi$
$173$			24.3883i			0.140973i	−0.997513	+	0.0704864i	$0.977545\pi$
$174$		0			0
$175$	−117.877			−0.673584
$176$	−147.756	+	92.8415i	−0.839525	+	0.527509i
$177$		0			0
$178$	29.5840	−	61.4317i	0.166202	−	0.345122i
$179$	109.960	+	25.0977i	0.614303	+	0.140211i	0.518340	−	0.855174i	$-0.326550\pi$
$179$	109.960	+	25.0977i	0.614303	+	0.140211i	0.0959623	+	0.995385i	$0.469407\pi$
$180$		0			0
$181$	−181.835	+	87.5671i	−1.00461	+	0.483796i	−0.862501	−	0.506055i	$-0.831103\pi$
$181$	−181.835	+	87.5671i	−1.00461	+	0.483796i	−0.142111	+	0.989851i	$0.545389\pi$
$182$	−32.5252	−	288.669i	−0.178710	−	1.58609i
$183$		0			0
$184$	−139.123	+	48.6812i	−0.756102	+	0.264572i
$185$	39.8840	−	353.980i	0.215589	−	1.91341i
$186$		0			0
$187$	−94.3343	+	75.2291i	−0.504462	+	0.402295i
$188$	16.8836	−	26.8702i	0.0898066	−	0.142926i
$189$		0			0
$190$	−124.251	−	155.806i	−0.653953	−	0.820031i
$191$	9.18326	+	9.18326i	0.0480799	+	0.0480799i	0.730738	−	0.682658i	$-0.239176\pi$
$191$	9.18326	+	9.18326i	0.0480799	+	0.0480799i	−0.682658	+	0.730738i	$0.739176\pi$
$192$		0			0
$193$	−38.7349	−	110.698i	−0.200699	−	0.573564i	0.798912	−	0.601447i	$-0.205409\pi$
$193$	−38.7349	−	110.698i	−0.200699	−	0.573564i	−0.999611	+	0.0278831i	$0.991123\pi$
$194$	54.4671	−	68.2996i	0.280758	−	0.352060i
$195$		0			0
$196$	−48.8661	−	101.471i	−0.249317	−	0.517712i
$197$	42.3417	+	185.511i	0.214932	+	0.941681i	0.961160	+	0.275990i	$0.0890057\pi$
$197$	42.3417	+	185.511i	0.214932	+	0.941681i	−0.746228	+	0.665690i	$0.768137\pi$
$198$		0			0
$199$	134.765	+	64.8992i	0.677209	+	0.326127i	0.740681	−	0.671857i	$-0.234503\pi$
$199$	134.765	+	64.8992i	0.677209	+	0.326127i	−0.0634720	+	0.997984i	$0.520217\pi$
$200$	19.0481	−	54.4364i	0.0952407	−	0.272182i
$201$		0			0
$202$			151.533i			0.750163i
$203$	−264.503	+	144.554i	−1.30297	+	0.712089i
$204$		0			0
$205$	208.611	−	131.079i	1.01762	−	0.639410i
$206$	269.529	+	94.3122i	1.30839	+	0.457826i
$207$		0			0
$208$	224.111	+	51.1518i	1.07746	+	0.245922i
$209$	115.743	−	26.4175i	0.553793	−	0.126400i
$210$		0			0
$211$	−6.26902	−	55.6391i	−0.0297110	−	0.263692i	−0.999782	−	0.0208716i	$-0.993356\pi$
$211$	−6.26902	−	55.6391i	−0.0297110	−	0.263692i	0.970071	−	0.242821i	$-0.0780727\pi$
$212$	−86.4393	−	68.9330i	−0.407732	−	0.325156i
$213$		0			0
$214$	−18.6030	+	165.106i	−0.0869298	+	0.771523i
$215$	−187.243	+	187.243i	−0.870896	+	0.870896i
$216$		0			0
$217$	−214.373	+	341.173i	−0.987896	+	1.57223i
$218$	−23.9529	−	15.0506i	−0.109876	−	0.0690394i
$219$		0			0
$220$	−70.9843	−	70.9843i	−0.322656	−	0.322656i
$221$	157.944	+	17.7960i	0.714679	+	0.0805250i
$222$		0			0
$223$	83.8099	−	105.094i	0.375829	−	0.471275i	−0.557562	−	0.830135i	$-0.688263\pi$
$223$	83.8099	−	105.094i	0.375829	−	0.471275i	0.933391	+	0.358860i	$0.116835\pi$
$224$	291.779	−	32.8756i	1.30258	−	0.146766i
$225$		0			0
$226$	23.2387	+	101.815i	0.102826	+	0.450511i
$227$	37.6983	−	165.167i	0.166072	−	0.727609i	−0.821470	−	0.570252i	$-0.806846\pi$
$227$	37.6983	−	165.167i	0.166072	−	0.727609i	0.987542	−	0.157357i	$-0.0502973\pi$
$228$		0			0
$229$	51.6406	−	147.580i	0.225505	−	0.644456i	−0.774426	−	0.632665i	$-0.781961\pi$
$229$	51.6406	−	147.580i	0.225505	−	0.644456i	0.999930	−	0.0117911i	$-0.00375331\pi$
$230$	−225.944	−	359.588i	−0.982366	−	1.56343i
$231$		0			0
$232$	−24.0141	−	145.508i	−0.103509	−	0.627191i
$233$	−296.039			−1.27055			−0.635276	−	0.772285i	$-0.719114\pi$
$233$	−296.039			−1.27055			−0.635276	+	0.772285i	$0.719114\pi$
$234$		0			0
$235$	−94.6506	−	33.1197i	−0.402769	−	0.140935i
$236$	28.2057	−	58.5698i	0.119516	−	0.248177i
$237$		0			0
$238$	340.458	−	77.7074i	1.43050	−	0.326502i
$239$	231.857	−	111.656i	0.970113	−	0.467182i	0.119420	−	0.992844i	$-0.461897\pi$
$239$	231.857	−	111.656i	0.970113	−	0.467182i	0.850693	+	0.525662i	$0.176182\pi$
$240$		0			0
$241$	−18.6581	−	14.8793i	−0.0774196	−	0.0617400i	0.584015	−	0.811743i	$-0.301481\pi$
$241$	−18.6581	−	14.8793i	−0.0774196	−	0.0617400i	−0.661435	+	0.750003i	$0.730052\pi$
$242$	−102.794	+	35.9693i	−0.424770	+	0.148633i
$243$		0			0
$244$	8.43610	−	8.43610i	0.0345742	−	0.0345742i
$245$	−278.243	+	221.892i	−1.13569	+	0.905680i
$246$		0			0
$247$	−132.419	−	83.2042i	−0.536108	−	0.336859i
$248$	−122.915	−	154.130i	−0.495625	−	0.621493i
$249$		0			0
$250$	−198.881	−	22.4085i	−0.795522	−	0.0896338i
$251$	−47.2947	−	135.160i	−0.188425	−	0.538487i	0.810455	−	0.585801i	$-0.199220\pi$
$251$	−47.2947	−	135.160i	−0.188425	−	0.538487i	−0.998880	+	0.0473132i	$0.984934\pi$
$252$		0			0
$253$	251.405	−	28.3266i	0.993697	−	0.111963i
$254$	139.997	+	290.708i	0.551171	+	1.14452i
$255$		0			0
$256$	−65.9139	+	288.788i	−0.257476	+	1.12808i
$257$	−78.7944	−	37.9454i	−0.306593	−	0.147647i	0.274261	−	0.961655i	$-0.411567\pi$
$257$	−78.7944	−	37.9454i	−0.306593	−	0.147647i	−0.580854	+	0.814008i	$0.697281\pi$
$258$		0			0
$259$	−326.770	−	520.051i	−1.26166	−	2.00792i
$260$			132.240i			0.508616i
$261$		0			0
$262$	191.591			0.731265
$263$	82.7439	−	51.9914i	0.314615	−	0.197686i	−0.365462	−	0.930826i	$-0.619089\pi$
$263$	82.7439	−	51.9914i	0.314615	−	0.197686i	0.680077	+	0.733140i	$0.261946\pi$
$264$		0			0
$265$	−151.582	+	314.764i	−0.572009	+	1.18779i
$266$	−334.988	−	76.4587i	−1.25935	−	0.287439i
$267$		0			0
$268$	−116.903	+	56.2975i	−0.436205	+	0.210065i
$269$	2.99923	+	26.6189i	0.0111496	+	0.0989551i	0.998054	−	0.0623480i	$-0.0198589\pi$
$269$	2.99923	+	26.6189i	0.0111496	+	0.0989551i	−0.986905	+	0.161303i	$0.948430\pi$
$270$		0			0
$271$	−164.750	+	57.6486i	−0.607935	+	0.212725i	−0.616651	−	0.787237i	$-0.711511\pi$
$271$	−164.750	+	57.6486i	−0.607935	+	0.212725i	0.00871663	+	0.999962i	$0.497225\pi$
$272$	−30.9402	+	274.602i	−0.113751	+	1.00956i
$273$		0			0
$274$	−307.482	+	245.209i	−1.12220	+	0.894924i
$275$	−52.6676	+	83.8200i	−0.191518	+	0.304800i
$276$		0			0
$277$	270.444	+	339.126i	0.976331	+	1.22428i	0.974524	+	0.224282i	$0.0720037\pi$
$277$	270.444	+	339.126i	0.976331	+	1.22428i	0.00180677	+	0.999998i	$0.499425\pi$
$278$	−189.073	−	189.073i	−0.680119	−	0.680119i
$279$		0			0
$280$	−105.242	−	300.763i	−0.375863	−	1.07415i
$281$	−246.662	+	309.305i	−0.877802	+	1.10073i	0.116400	+	0.993202i	$0.462864\pi$
$281$	−246.662	+	309.305i	−0.877802	+	1.10073i	−0.994202	+	0.107526i	$0.965707\pi$
$282$		0			0
$283$	70.0980	+	145.560i	0.247696	+	0.514346i	0.987333	−	0.158660i	$-0.0507172\pi$
$283$	70.0980	+	145.560i	0.247696	+	0.514346i	−0.739637	+	0.673006i	$0.765003\pi$
$284$	−13.2887	−	58.2217i	−0.0467913	−	0.205006i
$285$		0			0
$286$	−219.799	−	105.849i	−0.768527	−	0.370103i
$287$	140.302	−	400.959i	0.488855	−	1.39707i
$288$		0			0
$289$		−	97.9291i		−	0.338855i
$290$	393.340	−	160.748i	1.35635	−	0.554303i
$291$		0			0
$292$	−82.8063	+	52.0307i	−0.283583	+	0.178187i
$293$	497.689	+	174.149i	1.69860	+	0.594365i	0.993406	−	0.114653i	$-0.0365756\pi$
$293$	497.689	+	174.149i	1.69860	+	0.594365i	0.705191	+	0.709018i	$0.250861\pi$
$294$		0			0
$295$	−200.269	−	45.7100i	−0.678877	−	0.154949i
$296$	292.967	−	66.8678i	0.989754	−	0.225905i
$297$		0			0
$298$	−39.2012	−	347.920i	−0.131548	−	1.16752i
$299$	−260.563	−	207.792i	−0.871449	−	0.694957i
$300$		0			0
$301$	−51.1194	+	453.697i	−0.169832	+	1.50730i
$302$	−492.588	+	492.588i	−1.63109	+	1.63109i
$303$		0			0
$304$	144.659	−	230.223i	0.475851	−	0.757313i
$305$	−31.9209	−	20.0573i	−0.104659	−	0.0657615i
$306$		0			0
$307$	−263.183	−	263.183i	−0.857275	−	0.857275i	0.133742	−	0.991016i	$-0.457301\pi$
$307$	−263.183	−	263.183i	−0.857275	−	0.857275i	−0.991016	+	0.133742i	$0.957301\pi$
$308$	−171.998	−	19.3795i	−0.558436	−	0.0629206i
$309$		0			0
$310$	354.150	−	444.091i	1.14242	−	1.43255i
$311$	286.428	−	32.2726i	0.920989	−	0.103771i	0.361278	−	0.932458i	$-0.382341\pi$
$311$	286.428	−	32.2726i	0.920989	−	0.103771i	0.559711	+	0.828688i	$0.310912\pi$
$312$		0			0
$313$	41.7918	+	183.102i	0.133520	+	0.584990i	0.996777	+	0.0802250i	$0.0255639\pi$
$313$	41.7918	+	183.102i	0.133520	+	0.584990i	−0.863257	+	0.504765i	$0.831579\pi$
$314$	−139.106	+	609.465i	−0.443014	+	1.94097i
$315$		0			0
$316$	23.4471	−	67.0080i	0.0741997	−	0.212051i
$317$	−299.014	−	475.878i	−0.943261	−	1.50119i	−0.863482	−	0.504379i	$-0.831721\pi$
$317$	−299.014	−	475.878i	−0.943261	−	1.50119i	−0.0797787	−	0.996813i	$-0.525421\pi$
$318$		0			0
$319$	−15.3908	+	252.670i	−0.0482471	+	0.792068i
$320$	68.1403			0.212938
$321$		0			0
$322$	−691.142	−	241.841i	−2.14640	−	0.751059i
$323$	81.5704	−	169.383i	0.252540	−	0.524405i
$324$		0			0
$325$	127.135	−	29.0176i	0.391183	−	0.0892851i
$326$	−131.090	+	63.1297i	−0.402117	+	0.193649i
$327$		0			0
$328$	162.494	+	129.584i	0.495407	+	0.395074i
$329$	−163.196	+	57.1047i	−0.496036	+	0.173571i
$330$		0			0
$331$	−301.118	+	301.118i	−0.909723	+	0.909723i	−0.996250	−	0.0865265i	$-0.972423\pi$
$331$	−301.118	+	301.118i	−0.909723	+	0.909723i	0.0865265	+	0.996250i	$0.472423\pi$
$332$	−104.142	+	83.0506i	−0.313681	+	0.250152i
$333$		0			0
$334$	378.816	+	238.026i	1.13418	+	0.712652i
$335$	255.636	+	320.558i	0.763093	+	0.956889i
$336$		0			0
$337$	354.089	+	39.8962i	1.05071	+	0.118386i	0.620392	−	0.784292i	$-0.286973\pi$
$337$	354.089	+	39.8962i	1.05071	+	0.118386i	0.430316	+	0.902678i	$0.358402\pi$
$338$	−29.5276	−	84.3850i	−0.0873597	−	0.249660i
$339$		0			0
$340$	−157.971	+	17.7990i	−0.464619	+	0.0523500i
$341$	146.819	+	304.873i	0.430554	+	0.894056i
$342$		0			0
$343$	−23.2111	+	101.695i	−0.0676709	+	0.296485i
$344$	−201.260	−	96.9216i	−0.585058	−	0.281749i
$345$		0			0
$346$	−31.5377	−	50.1920i	−0.0911495	−	0.145064i
$347$			8.03629i			0.0231593i	0.999933	+	0.0115797i	$0.00368600\pi$
$347$			8.03629i			0.0231593i	−0.999933	+	0.0115797i	$0.996314\pi$
$348$		0			0
$349$	635.847			1.82191			0.910956	−	0.412504i	$-0.135346\pi$
$349$	635.847			1.82191			0.910956	+	0.412504i	$0.135346\pi$
$350$	242.595	−	152.433i	0.693129	−	0.435522i
$351$		0			0
$352$	106.990	−	222.167i	0.303948	−	0.631155i
$353$	466.124	+	106.390i	1.32047	+	0.301388i	0.823961	−	0.566646i	$-0.191759\pi$
$353$	466.124	+	106.390i	1.32047	+	0.301388i	0.496505	+	0.868034i	$0.334617\pi$
$354$		0			0
$355$	−170.020	+	81.8772i	−0.478929	+	0.230640i
$356$	5.99201	+	53.1806i	0.0168315	+	0.149384i
$357$		0			0
$358$	−258.757	+	90.5430i	−0.722785	+	0.252913i
$359$	−9.68103	+	85.9215i	−0.0269666	+	0.239336i	0.972997	+	0.230817i	$0.0741400\pi$
$359$	−9.68103	+	85.9215i	−0.0269666	+	0.239336i	−0.999964	+	0.00851817i	$0.997289\pi$
$360$		0			0
$361$	137.618	−	109.747i	0.381214	−	0.304008i
$362$	260.985	−	415.356i	0.720954	−	1.14739i
$363$		0			0
$364$	142.160	+	178.263i	0.390550	+	0.489735i
$365$	218.516	+	218.516i	0.598674	+	0.598674i
$366$		0			0
$367$	−170.932	−	488.497i	−0.465756	−	1.33105i	−0.902198	−	0.431322i	$-0.858047\pi$
$367$	−170.932	−	488.497i	−0.465756	−	1.33105i	0.436442	−	0.899732i	$-0.356238\pi$
$368$	361.268	−	453.015i	0.981706	−	1.23102i
$369$		0			0
$370$	375.667	+	780.080i	1.01532	+	2.10833i
$371$	134.039	+	587.264i	0.361291	+	1.58292i
$372$		0			0
$373$	−148.476	−	71.5023i	−0.398059	−	0.191695i	0.224135	−	0.974558i	$-0.428044\pi$
$373$	−148.476	−	71.5023i	−0.398059	−	0.191695i	−0.622194	+	0.782863i	$0.713759\pi$
$374$	96.8609	−	276.813i	0.258986	−	0.740141i
$375$		0			0
$376$		−	84.5927i		−	0.224981i
$377$	249.691	−	221.019i	0.662312	−	0.586258i
$378$		0			0
$379$	−385.472	+	242.208i	−1.01708	+	0.639072i	−0.933927	−	0.357465i	$-0.883641\pi$
$379$	−385.472	+	242.208i	−1.01708	+	0.639072i	−0.0831508	+	0.996537i	$0.526498\pi$
$380$	147.638	+	51.6608i	0.388521	+	0.135950i
$381$		0			0
$382$	−30.7748	−	7.02415i	−0.0805623	−	0.0183878i
$383$	−280.279	+	63.9719i	−0.731799	+	0.167028i	−0.572154	−	0.820146i	$-0.693892\pi$
$383$	−280.279	+	63.9719i	−0.731799	+	0.167028i	−0.159645	+	0.987174i	$0.551035\pi$
$384$		0			0
$385$	61.2379	+	543.502i	0.159060	+	1.41169i
$386$	222.867	+	177.730i	0.577375	+	0.460441i
$387$		0			0
$388$	−7.67706	+	68.1358i	−0.0197862	+	0.175608i
$389$	60.4535	−	60.4535i	0.155408	−	0.155408i	−0.625121	−	0.780528i	$-0.714950\pi$
$389$	60.4535	−	60.4535i	0.155408	−	0.155408i	0.780528	+	0.625121i	$0.214950\pi$
$390$		0			0
$391$	213.152	−	339.230i	0.545146	−	0.867595i
$392$	−254.203	−	159.726i	−0.648477	−	0.407465i
$393$		0			0
$394$	−327.034	−	327.034i	−0.830036	−	0.830036i
$395$	−222.918	−	25.1169i	−0.564350	−	0.0635870i
$396$		0			0
$397$	−303.313	+	380.342i	−0.764012	+	0.958040i	−0.999906	−	0.0137384i	$-0.995627\pi$
$397$	−303.313	+	380.342i	−0.764012	+	0.958040i	0.235894	+	0.971779i	$0.424198\pi$
$398$	−361.275	+	40.7059i	−0.907725	+	0.102276i
$399$		0			0
$400$	50.4501	+	221.036i	0.126125	+	0.552591i
$401$	122.942	−	538.643i	0.306588	−	1.34325i	−0.553392	−	0.832921i	$-0.686667\pi$
$401$	122.942	−	538.643i	0.306588	−	1.34325i	0.859980	−	0.510328i	$-0.170476\pi$
$402$		0			0
$403$	147.223	−	420.740i	0.365318	−	1.04402i
$404$	−63.2782	−	100.707i	−0.156629	−	0.249274i
$405$		0			0
$406$	357.427	−	639.540i	0.880362	−	1.57522i
$407$	−515.799			−1.26732
$408$		0			0
$409$	137.784	+	48.2128i	0.336881	+	0.117880i	0.493418	−	0.869792i	$-0.335747\pi$
$409$	137.784	+	48.2128i	0.336881	+	0.117880i	−0.156537	+	0.987672i	$0.550033\pi$
$410$	−259.824	+	539.531i	−0.633718	+	1.31593i
$411$		0			0
$412$	−218.509	+	49.8732i	−0.530361	+	0.121051i
$413$	−319.107	+	153.674i	−0.772656	+	0.372092i
$414$		0			0
$415$	329.082	+	262.434i	0.792968	+	0.632371i
$416$	−306.601	+	107.284i	−0.737021	+	0.257895i
$417$		0			0
$418$	−204.041	+	204.041i	−0.488136	+	0.488136i
$419$	148.931	−	118.769i	0.355444	−	0.283457i	−0.429445	−	0.903093i	$-0.641291\pi$
$419$	148.931	−	118.769i	0.355444	−	0.283457i	0.784890	+	0.619635i	$0.212720\pi$
$420$		0			0
$421$	−357.054	−	224.352i	−0.848108	−	0.532902i	0.0364479	−	0.999336i	$-0.488396\pi$
$421$	−357.054	−	224.352i	−0.848108	−	0.532902i	−0.884556	+	0.466434i	$0.845539\pi$
$422$	84.8515	+	106.400i	0.201070	+	0.252134i
$423$		0			0
$424$	−292.862	−	32.9976i	−0.690713	−	0.0778246i
$425$	51.7755	+	147.966i	0.121825	+	0.348155i
$426$		0			0
$427$	−64.5922	+	7.27779i	−0.151270	+	0.0170440i
$428$	−56.5829	−	117.496i	−0.132203	−	0.274522i
$429$		0			0
$430$	143.219	−	627.485i	0.333068	−	1.45927i
$431$	95.2983	+	45.8932i	0.221110	+	0.106481i	0.541160	−	0.840920i	$-0.317985\pi$
$431$	95.2983	+	45.8932i	0.221110	+	0.106481i	−0.320050	+	0.947401i	$0.603700\pi$
$432$		0			0
$433$	−408.562	−	650.223i	−0.943562	−	1.50167i	−0.863174	−	0.504907i	$-0.831527\pi$
$433$	−408.562	−	650.223i	−0.943562	−	1.50167i	−0.0803883	−	0.996764i	$-0.525616\pi$
$434$		−	979.364i		−	2.25660i
$435$		0			0
$436$	22.2037			0.0509260
$437$	−333.779	+	209.727i	−0.763796	+	0.479925i
$438$		0			0
$439$	228.661	−	474.820i	0.520869	−	1.08160i	−0.460179	−	0.887826i	$-0.652215\pi$
$439$	228.661	−	474.820i	0.520869	−	1.08160i	0.981047	−	0.193769i	$-0.0620711\pi$
$440$	−260.888	−	59.5461i	−0.592928	−	0.135332i
$441$		0			0
$442$	−348.067	+	167.620i	−0.787483	+	0.379232i
$443$	−26.7609	−	237.510i	−0.0604084	−	0.536139i	−0.987075	−	0.160256i	$-0.948768\pi$
$443$	−26.7609	−	237.510i	−0.0604084	−	0.536139i	0.926667	−	0.375883i	$-0.122661\pi$
$444$		0			0
$445$	159.620	−	55.8535i	0.358697	−	0.125514i
$446$	−36.5811	+	324.666i	−0.0820204	+	0.727952i
$447$		0			0
$448$	91.8550	−	73.2519i	0.205034	−	0.163509i
$449$	−162.359	+	258.393i	−0.361601	+	0.575485i	−0.977133	−	0.212627i	$-0.931798\pi$
$449$	−162.359	+	258.393i	−0.361601	+	0.575485i	0.615532	+	0.788112i	$0.288941\pi$
$450$		0			0
$451$	−222.427	−	278.914i	−0.493185	−	0.618435i
$452$	−57.9610	−	57.9610i	−0.128232	−	0.128232i
$453$		0			0
$454$	136.001	+	388.670i	0.299563	+	0.856100i
$455$	449.216	−	563.299i	0.987289	−	1.23802i
$456$		0			0
$457$	181.449	+	376.783i	0.397045	+	0.824472i	0.999651	+	0.0264327i	$0.00841477\pi$
$457$	181.449	+	376.783i	0.397045	+	0.824472i	−0.602606	+	0.798039i	$0.705871\pi$
$458$	84.5653	+	370.505i	0.184640	+	0.808963i
$459$		0			0
$460$	300.319	+	144.626i	0.652867	+	0.314404i
$461$	196.436	−	561.383i	0.426109	−	1.21775i	−0.508185	−	0.861248i	$-0.669683\pi$
$461$	196.436	−	561.383i	0.426109	−	1.21775i	0.934294	−	0.356502i	$-0.116031\pi$
$462$		0			0
$463$			903.693i			1.95182i	0.218171	+	0.975910i	$0.429991\pi$
$463$			903.693i			1.95182i	−0.218171	+	0.975910i	$0.570009\pi$
$464$	384.264	+	434.114i	0.828155	+	0.935590i
$465$		0			0
$466$	609.258	−	382.822i	1.30742	−	0.821507i
$467$	−674.139	−	235.892i	−1.44355	−	0.505121i	−0.508945	−	0.860799i	$-0.669964\pi$
$467$	−674.139	−	235.892i	−1.44355	−	0.505121i	−0.934609	+	0.355678i	$0.884250\pi$
$468$		0			0
$469$	689.210	+	157.308i	1.46953	+	0.335411i
$470$	237.623	−	54.2359i	0.505581	−	0.115396i
$471$		0			0
$472$	−19.4021	−	172.198i	−0.0411061	−	0.364827i
$473$	299.774	+	239.062i	0.633773	+	0.505417i
$474$		0			0
$475$	17.2698	−	153.274i	0.0363576	−	0.322682i
$476$	−193.814	+	193.814i	−0.407173	+	0.407173i
$477$		0			0
$478$	−332.781	+	529.619i	−0.696196	+	1.10799i
$479$	−9.59607	−	6.02961i	−0.0200336	−	0.0125879i	0.521978	−	0.852959i	$-0.325194\pi$
$479$	−9.59607	−	6.02961i	−0.0200336	−	0.0125879i	−0.542012	+	0.840371i	$0.682337\pi$
$480$		0			0
$481$	480.453	+	480.453i	0.998863	+	0.998863i
$482$	57.6403	+	6.49450i	0.119586	+	0.0134741i
$483$		0			0
$484$	53.2954	−	66.8303i	0.110114	−	0.138079i
$485$	215.304	−	24.2589i	0.443926	−	0.0500185i
$486$		0			0
$487$	−178.718	−	783.016i	−0.366978	−	1.60784i	−0.735033	−	0.678031i	$-0.762833\pi$
$487$	−178.718	−	783.016i	−0.366978	−	1.60784i	0.368055	−	0.929804i	$-0.380024\pi$
$488$	7.07672	−	31.0051i	0.0145015	−	0.0635351i
$489$		0			0
$490$	285.695	−	816.471i	0.583052	−	1.66627i
$491$	−197.816	−	314.823i	−0.402885	−	0.641187i	0.582242	−	0.813015i	$-0.302176\pi$
$491$	−197.816	−	314.823i	−0.402885	−	0.641187i	−0.985127	+	0.171828i	$0.945033\pi$
$492$		0			0
$493$	297.631	+	268.526i	0.603714	+	0.544678i
$494$	380.118			0.769469
$495$		0			0
$496$	731.498	+	255.962i	1.47479	+	0.516053i
$497$	−141.172	+	293.147i	−0.284048	+	0.589833i
$498$		0			0
$499$	468.476	−	106.927i	0.938830	−	0.214282i	0.274386	−	0.961620i	$-0.411526\pi$
$499$	468.476	−	106.927i	0.938830	−	0.214282i	0.664444	+	0.747338i	$0.268668\pi$
$500$	141.531	−	68.1577i	0.283062	−	0.136315i
$501$		0			0
$502$	272.117	+	217.006i	0.542065	+	0.432282i
$503$	344.807	−	120.653i	0.685501	−	0.239867i	0.0350167	−	0.999387i	$-0.488852\pi$
$503$	344.807	−	120.653i	0.685501	−	0.239867i	0.650485	+	0.759519i	$0.274566\pi$
$504$		0			0
$505$	−265.753	+	265.753i	−0.526244	+	0.526244i
$506$	−480.771	+	383.402i	−0.950140	+	0.757711i
$507$		0			0
$508$	−214.436	−	134.739i	−0.422119	−	0.265235i
$509$	−525.388	−	658.816i	−1.03220	−	1.29433i	−0.954773	−	0.297335i	$-0.903902\pi$
$509$	−525.388	−	658.816i	−1.03220	−	1.29433i	−0.0774230	−	0.996998i	$-0.524669\pi$
$510$		0			0
$511$	529.474	+	59.6574i	1.03615	+	0.116746i
$512$	−52.2135	−	149.217i	−0.101979	−	0.291440i
$513$		0			0
$514$	211.231	−	23.8000i	0.410955	−	0.0463035i
$515$	307.289	+	638.092i	0.596677	+	1.23901i
$516$		0			0
$517$	−32.3101	+	141.560i	−0.0624953	+	0.273810i
$518$	1345.01	+	647.722i	2.59654	+	1.25043i
$519$		0			0
$520$	187.545	+	298.476i	0.360664	+	0.573993i
$521$		−	150.865i		−	0.289569i	−0.989463	−	0.144784i	$-0.953751\pi$
$521$		−	150.865i		−	0.289569i	0.989463	−	0.144784i	$-0.0462489\pi$
$522$		0			0
$523$	−792.504			−1.51530			−0.757652	−	0.652659i	$-0.773653\pi$
$523$	−792.504			−1.51530			−0.757652	+	0.652659i	$0.773653\pi$
$524$	−127.329	+	80.0062i	−0.242994	+	0.152684i
$525$		0			0
$526$	−103.057	+	214.000i	−0.195926	+	0.406845i
$527$	522.420	+	119.239i	0.991309	+	0.226260i
$528$		0			0
$529$	−280.254	+	134.963i	−0.529781	+	0.255129i
$530$	−95.0750	−	843.814i	−0.179387	−	1.59210i
$531$		0			0
$532$	254.557	−	89.0732i	0.478490	−	0.167431i
$533$	−52.6167	+	466.986i	−0.0987180	+	0.876146i
$534$		0			0
$535$	−322.183	+	256.932i	−0.602210	+	0.480247i
$536$	−184.017	+	292.862i	−0.343316	+	0.546384i
$537$		0			0
$538$	−40.5948	−	50.9042i	−0.0754550	−	0.0946176i
$539$	364.383	+	364.383i	0.676035	+	0.676035i
$540$		0			0
$541$	−71.8125	−	205.228i	−0.132740	−	0.379350i	0.858259	−	0.513217i	$-0.171546\pi$
$541$	−71.8125	−	205.228i	−0.132740	−	0.379350i	−0.990999	+	0.133867i	$0.957261\pi$
$542$	264.514	−	331.690i	0.488033	−	0.611973i
$543$		0			0
$544$	−169.426	−	351.817i	−0.311445	−	0.646722i
$545$	−15.6125	−	68.4030i	−0.0286469	−	0.125510i
$546$		0			0
$547$	−396.400	−	190.896i	−0.724680	−	0.348987i	0.0349094	−	0.999390i	$-0.488886\pi$
$547$	−396.400	−	190.896i	−0.724680	−	0.348987i	−0.759589	+	0.650403i	$0.774600\pi$
$548$	101.952	−	291.363i	0.186045	−	0.531685i
$549$		0			0
$550$		−	240.611i		−	0.437475i
$551$	−149.210	−	365.108i	−0.270799	−	0.662629i
$552$		0			0
$553$	−327.501	+	205.783i	−0.592227	+	0.372121i
$554$	−995.123	−	348.209i	−1.79625	−	0.628535i
$555$		0			0
$556$	204.610	+	46.7009i	0.368004	+	0.0839945i
$557$	−593.083	+	135.367i	−1.06478	+	0.243029i	−0.718803	−	0.695214i	$-0.755310\pi$
$557$	−593.083	+	135.367i	−1.06478	+	0.243029i	−0.345977	+	0.938243i	$0.612453\pi$
$558$		0			0
$559$	−56.5520	−	501.912i	−0.101166	−	0.897876i
$560$	979.353	+	781.008i	1.74884	+	1.39466i
$561$		0			0
$562$	107.663	−	955.532i	0.191570	−	1.70023i
$563$	−498.815	+	498.815i	−0.885995	+	0.885995i	−0.994136	−	0.108141i	$-0.965510\pi$
$563$	−498.815	+	498.815i	−0.885995	+	0.885995i	0.108141	+	0.994136i	$0.465510\pi$
$564$		0			0
$565$	−137.805	+	219.316i	−0.243903	+	0.388170i
$566$	−332.495	−	208.920i	−0.587447	−	0.369117i
$567$		0			0
$568$	−112.565	−	112.565i	−0.198177	−	0.198177i
$569$	315.227	+	35.5176i	0.554002	+	0.0624210i	0.384527	−	0.923114i	$-0.374364\pi$
$569$	315.227	+	35.5176i	0.554002	+	0.0624210i	0.169474	+	0.985535i	$0.445793\pi$
$570$		0			0
$571$	−321.408	+	403.033i	−0.562886	+	0.705836i	−0.979088	−	0.203436i	$-0.934789\pi$
$571$	−321.408	+	403.033i	−0.562886	+	0.705836i	0.416203	+	0.909272i	$0.363361\pi$
$572$	190.277	−	21.4390i	0.332652	−	0.0374808i
$573$		0			0
$574$	229.754	+	1006.62i	0.400268	+	1.75369i
$575$	73.1428	−	320.460i	0.127205	−	0.557321i
$576$		0			0
$577$	325.366	−	929.842i	0.563892	−	1.61151i	−0.209657	−	0.977775i	$-0.567235\pi$
$577$	325.366	−	929.842i	0.563892	−	1.61151i	0.773549	−	0.633736i	$-0.218480\pi$
$578$	126.637	+	201.542i	0.219095	+	0.348688i
$579$		0			0
$580$	−194.282	+	271.085i	−0.334970	+	0.467388i
$581$	725.732			1.24911
$582$		0			0
$583$	477.480	+	167.077i	0.819005	+	0.286582i
$584$	−113.110	+	234.875i	−0.193681	+	0.402182i
$585$		0			0
$586$	−1249.46	+	285.181i	−2.13219	+	0.486658i
$587$	−758.249	+	365.153i	−1.29174	+	0.622067i	−0.948379	−	0.317138i	$-0.897278\pi$
$587$	−758.249	+	365.153i	−1.29174	+	0.622067i	−0.343356	+	0.939205i	$0.611564\pi$
$588$		0			0
$589$	−412.216	−	328.731i	−0.699858	−	0.558118i
$590$	471.270	−	164.905i	0.798763	−	0.279499i
$591$		0			0
$592$	−835.317	+	835.317i	−1.41101	+	1.41101i
$593$	27.0486	−	21.5706i	0.0456132	−	0.0363753i	−0.600418	−	0.799686i	$-0.704999\pi$
$593$	27.0486	−	21.5706i	0.0456132	−	0.0363753i	0.646031	+	0.763311i	$0.276428\pi$
$594$		0			0
$595$	733.365	+	460.804i	1.23255	+	0.774460i
$596$	171.340	+	214.853i	0.287483	+	0.360492i
$597$		0			0
$598$	804.955	+	90.6966i	1.34608	+	0.151667i
$599$	−3.54858	−	10.1412i	−0.00592417	−	0.0169303i	0.940883	−	0.338731i	$-0.109998\pi$
$599$	−3.54858	−	10.1412i	−0.00592417	−	0.0169303i	−0.946807	+	0.321801i	$0.895712\pi$
$600$		0			0
$601$	368.282	−	41.4954i	0.612783	−	0.0690440i	0.199882	−	0.979820i	$-0.435944\pi$
$601$	368.282	−	41.4954i	0.612783	−	0.0690440i	0.412901	+	0.910776i	$0.364516\pi$
$602$	−481.493	−	999.830i	−0.799822	−	1.66085i
$603$		0			0
$604$	121.669	−	533.067i	0.201439	−	0.882560i
$605$	−243.359	−	117.195i	−0.402246	−	0.193712i
$606$		0			0
$607$	−219.680	−	349.619i	−0.361912	−	0.575979i	0.615288	−	0.788302i	$-0.289040\pi$
$607$	−219.680	−	349.619i	−0.361912	−	0.575979i	−0.977199	+	0.212324i	$0.931897\pi$
$608$			384.212i			0.631928i
$609$		0			0
$610$	91.6314			0.150215
$611$	161.955	−	101.763i	0.265066	−	0.166552i
$612$		0			0
$613$	−443.542	+	921.025i	−0.723560	+	1.50249i	0.135591	+	0.990765i	$0.456707\pi$
$613$	−443.542	+	921.025i	−0.723560	+	1.50249i	−0.859151	+	0.511722i	$0.829008\pi$
$614$	881.976	+	201.305i	1.43644	+	0.327859i
$615$		0			0
$616$	−415.698	+	200.190i	−0.674834	+	0.324983i
$617$	−12.9759	−	115.164i	−0.0210306	−	0.186652i	0.978805	−	0.204795i	$-0.0656529\pi$
$617$	−12.9759	−	115.164i	−0.0210306	−	0.186652i	−0.999835	+	0.0181438i	$0.994224\pi$
$618$		0			0
$619$	36.6784	−	12.8343i	0.0592543	−	0.0207340i	−0.300489	−	0.953785i	$-0.597150\pi$
$619$	36.6784	−	12.8343i	0.0592543	−	0.0207340i	0.359743	+	0.933051i	$0.382864\pi$
$620$	−49.9170	+	443.025i	−0.0805113	+	0.714557i
$621$		0			0
$622$	−547.745	+	436.812i	−0.880619	+	0.702270i
$623$	155.129	−	246.886i	0.249003	−	0.396286i
$624$		0			0
$625$	−486.264	−	609.755i	−0.778022	−	0.975609i
$626$	−322.787	−	322.787i	−0.515635	−	0.515635i
$627$		0			0
$628$	−162.057	−	463.132i	−0.258052	−	0.737471i
$629$	−509.269	+	638.604i	−0.809649	+	1.01527i
$630$		0			0
$631$	116.281	+	241.460i	0.184280	+	0.382662i	0.972559	−	0.232656i	$-0.0747417\pi$
$631$	116.281	+	241.460i	0.184280	+	0.382662i	−0.788279	+	0.615318i	$0.789027\pi$
$632$	−42.1099	−	184.495i	−0.0666295	−	0.291923i
$633$		0			0
$634$	1230.76	+	592.704i	1.94127	+	0.934864i
$635$	−264.310	+	755.356i	−0.416237	+	1.18954i
$636$		0			0
$637$		−	678.827i		−	1.06566i
$638$	−295.065	−	539.906i	−0.462484	−	0.846247i
$639$		0			0
$640$	−717.014	+	450.530i	−1.12033	+	0.703952i
$641$	937.367	+	327.999i	1.46235	+	0.511699i	0.940043	−	0.341057i	$-0.110785\pi$
$641$	937.367	+	327.999i	1.46235	+	0.511699i	0.522309	+	0.852756i	$0.325071\pi$
$642$		0			0
$643$	311.987	+	71.2090i	0.485206	+	0.110745i	0.458124	−	0.888888i	$-0.348522\pi$
$643$	311.987	+	71.2090i	0.485206	+	0.110745i	0.0270814	+	0.999633i	$0.491379\pi$
$644$	560.314	−	127.888i	0.870052	−	0.198584i
$645$		0			0
$646$	51.1623	+	454.078i	0.0791987	+	0.702908i
$647$	288.416	+	230.004i	0.445774	+	0.355493i	0.820504	−	0.571641i	$-0.193693\pi$
$647$	288.416	+	230.004i	0.445774	+	0.355493i	−0.374730	+	0.927134i	$0.622264\pi$
$648$		0			0
$649$	−33.3029	+	295.572i	−0.0513142	+	0.455427i
$650$	−224.123	+	224.123i	−0.344805	+	0.344805i
$651$		0			0
$652$	60.7586	−	96.6968i	0.0931881	−	0.148308i
$653$	257.346	+	161.701i	0.394098	+	0.247628i	0.714474	−	0.699662i	$-0.246666\pi$
$653$	257.346	+	161.701i	0.394098	+	0.247628i	−0.320375	+	0.947291i	$0.603809\pi$
$654$		0			0
$655$	336.007	+	336.007i	0.512987	+	0.512987i
$656$	−811.902	−	91.4794i	−1.23766	−	0.139450i
$657$		0			0
$658$	262.018	−	328.560i	0.398204	−	0.499332i
$659$	331.819	−	37.3870i	0.503518	−	0.0567329i	0.143448	−	0.989658i	$-0.454181\pi$
$659$	331.819	−	37.3870i	0.503518	−	0.0567329i	0.360071	+	0.932925i	$0.382753\pi$
$660$		0			0
$661$	−231.074	−	1012.40i	−0.349583	−	1.53162i	−0.778131	−	0.628103i	$-0.783832\pi$
$661$	−231.074	−	1012.40i	−0.349583	−	1.53162i	0.428548	−	0.903519i	$-0.359025\pi$
$662$	230.321	−	1009.10i	0.347917	−	1.52433i
$663$		0			0
$664$	−117.273	+	335.148i	−0.176616	+	0.504741i
$665$	−453.399	−	721.581i	−0.681803	−	1.08508i
$666$		0			0
$667$	−228.859	−	808.772i	−0.343117	−	1.21255i
$668$	−351.152			−0.525677
$669$		0			0
$670$	−940.638	−	329.143i	−1.40394	−	0.491259i
$671$	−23.6847	+	49.1819i	−0.0352977	+	0.0732964i
$672$		0			0
$673$	145.913	−	33.3038i	0.216810	−	0.0494856i	−0.112736	−	0.993625i	$-0.535961\pi$
$673$	145.913	−	33.3038i	0.216810	−	0.0494856i	0.329546	+	0.944139i	$0.393104\pi$
$674$	−780.319	+	375.782i	−1.15774	+	0.557540i
$675$		0			0
$676$	54.8617	+	43.7508i	0.0811564	+	0.0647201i
$677$	−458.596	+	160.470i	−0.677395	+	0.237031i	−0.646980	−	0.762507i	$-0.723968\pi$
$677$	−458.596	+	160.470i	−0.677395	+	0.237031i	−0.0304143	+	0.999537i	$0.509683\pi$
$678$		0			0
$679$	264.157	−	264.157i	0.389039	−	0.389039i
$680$	−331.309	+	264.210i	−0.487219	+	0.388544i
$681$		0			0
$682$	−696.405	−	437.580i	−1.02112	−	0.641613i
$683$	−431.703	−	541.338i	−0.632069	−	0.792589i	0.357918	−	0.933753i	$-0.383487\pi$
$683$	−431.703	−	541.338i	−0.632069	−	0.792589i	−0.989986	+	0.141164i	$0.954915\pi$
$684$		0			0
$685$	−969.292	−	109.213i	−1.41502	−	0.159435i
$686$	−83.7369	−	239.306i	−0.122065	−	0.348843i
$687$		0			0
$688$	872.626	−	98.3213i	1.26835	−	0.142909i
$689$	−289.132	−	600.389i	−0.419640	−	0.871391i
$690$		0			0
$691$	126.440	−	553.969i	0.182981	−	0.801691i	−0.797221	−	0.603688i	$-0.793697\pi$
$691$	126.440	−	553.969i	0.182981	−	0.801691i	0.980201	−	0.198003i	$-0.0634456\pi$
$692$	41.9191	+	20.1872i	0.0605767	+	0.0291722i
$693$		0			0
$694$	−10.3921	−	16.5390i	−0.0149742	−	0.0238314i
$695$		−	663.180i		−	0.954216i
$696$		0			0
$697$	−564.931			−0.810518
$698$	−1308.60	+	822.245i	−1.87478	+	1.17800i
$699$		0			0
$700$	−97.5716	+	202.610i	−0.139388	+	0.289442i
$701$	−669.767	−	152.870i	−0.955445	−	0.218074i	−0.283747	−	0.958899i	$-0.591578\pi$
$701$	−669.767	−	152.870i	−0.955445	−	0.218074i	−0.671698	+	0.740825i	$0.734435\pi$
$702$		0			0
$703$	724.090	−	348.704i	1.03000	−	0.496022i
$704$	−11.0470	−	98.0452i	−0.0156918	−	0.139269i
$705$		0			0
$706$	−1096.88	+	383.814i	−1.55365	+	0.543646i
$707$	−72.5537	+	643.932i	−0.102622	+	0.910795i
$708$		0			0
$709$	361.110	−	287.976i	0.509324	−	0.406172i	−0.334826	−	0.942280i	$-0.608677\pi$
$709$	361.110	−	287.976i	0.509324	−	0.406172i	0.844149	+	0.536108i	$0.180106\pi$
$710$	244.027	−	388.367i	0.343700	−	0.546996i
$711$		0			0
$712$	88.9460	+	111.535i	0.124924	+	0.156650i
$713$	−794.492	−	794.492i	−1.11429	−	1.11429i
$714$		0			0
$715$	−199.840	−	571.111i	−0.279497	−	0.798757i
$716$	134.157	−	168.227i	0.187370	−	0.234954i
$717$		0			0
$718$	−91.1854	−	189.349i	−0.126999	−	0.263717i
$719$	115.701	+	506.920i	0.160920	+	0.705035i	0.989424	+	0.145052i	$0.0463350\pi$
$719$	115.701	+	506.920i	0.160920	+	0.705035i	−0.828504	+	0.559983i	$0.810808\pi$
$720$		0			0
$721$	1100.19	+	529.825i	1.52593	+	0.734848i
$722$	−141.304	+	403.824i	−0.195712	+	0.559313i
$723$		0			0
$724$			385.024i			0.531801i
$725$	303.250	+	127.297i	0.418276	+	0.175582i
$726$		0			0
$727$	−1047.82	+	658.389i	−1.44129	+	0.905624i	−0.441327	+	0.897346i	$0.645492\pi$
$727$	−1047.82	+	658.389i	−1.44129	+	0.905624i	−0.999966	+	0.00827820i	$0.997365\pi$
$728$	573.683	+	200.740i	0.788026	+	0.275742i
$729$		0			0
$730$	−732.288	−	167.140i	−1.00313	−	0.228959i
$731$	591.959	−	135.111i	0.809794	−	0.184830i
$732$		0			0
$733$	11.3513	+	100.746i	0.0154861	+	0.137443i	0.999076	−	0.0429750i	$-0.0136836\pi$
$733$	11.3513	+	100.746i	0.0154861	+	0.137443i	−0.983590	+	0.180418i	$0.942255\pi$
$734$	983.484	+	784.303i	1.33990	+	1.06853i
$735$		0			0
$736$	−91.6736	+	813.626i	−0.124557	+	1.10547i
$737$	419.797	−	419.797i	0.569603	−	0.569603i
$738$		0			0
$739$	−408.803	+	650.606i	−0.553184	+	0.880387i	−0.999898	−	0.0142895i	$-0.995451\pi$
$739$	−408.803	+	650.606i	−0.553184	+	0.880387i	0.446714	+	0.894677i	$0.352594\pi$
$740$	−575.415	−	361.557i	−0.777588	−	0.488591i
$741$		0			0
$742$	−1035.28	−	1035.28i	−1.39525	−	1.39525i
$743$	576.403	+	64.9450i	0.775778	+	0.0874091i	0.490971	−	0.871176i	$-0.336642\pi$
$743$	576.403	+	64.9450i	0.775778	+	0.0874091i	0.284807	+	0.958585i	$0.408071\pi$
$744$		0			0
$745$	541.421	−	678.920i	0.726739	−	0.911302i
$746$	398.032	−	44.8475i	0.533555	−	0.0601172i
$747$		0			0
$748$	51.2210	+	224.414i	0.0684773	+	0.300019i
$749$	−158.105	+	692.703i	−0.211088	+	0.924837i
$750$		0			0
$751$	−322.426	+	921.441i	−0.429329	+	1.22695i	0.502666	+	0.864481i	$0.332353\pi$
$751$	−322.426	+	921.441i	−0.429329	+	1.22695i	−0.931995	+	0.362471i	$0.881933\pi$
$752$	176.926	+	281.575i	0.235273	+	0.374435i
$753$		0			0
$754$	−228.063	+	777.754i	−0.302471	+	1.03150i
$755$	−1727.77			−2.28844
$756$		0			0
$757$	804.590	+	281.538i	1.06287	+	0.371913i	0.804388	−	0.594104i	$-0.202493\pi$
$757$	804.590	+	281.538i	1.06287	+	0.371913i	0.258478	+	0.966017i	$0.416779\pi$
$758$	480.104	−	996.947i	0.633383	−	1.31523i
$759$		0			0
$760$	406.497	−	92.7803i	0.534865	−	0.122079i
$761$	−327.551	+	157.740i	−0.430422	+	0.207280i	−0.636535	−	0.771248i	$-0.719633\pi$
$761$	−327.551	+	157.740i	−0.430422	+	0.207280i	0.206113	+	0.978528i	$0.433919\pi$
$762$		0			0
$763$	−94.5805	−	75.4254i	−0.123959	−	0.0988538i
$764$	23.3857	−	8.18302i	0.0306096	−	0.0107108i
$765$		0			0
$766$	494.099	−	494.099i	0.645038	−	0.645038i
$767$	306.338	−	244.297i	0.399398	−	0.318509i
$768$		0			0
$769$	−350.812	−	220.430i	−0.456192	−	0.286644i	0.284268	−	0.958745i	$-0.408249\pi$
$769$	−350.812	−	220.430i	−0.456192	−	0.286644i	−0.740460	+	0.672100i	$0.765392\pi$
$770$	−828.859	−	1039.36i	−1.07644	−	1.34981i
$771$		0			0
$772$	−222.332	−	25.0508i	−0.287995	−	0.0324493i
$773$	229.136	+	654.833i	0.296424	+	0.847132i	0.991721	+	0.128409i	$0.0409871\pi$
$773$	229.136	+	654.833i	0.296424	+	0.847132i	−0.695297	+	0.718722i	$0.744727\pi$
$774$		0			0
$775$	436.874	−	49.2239i	0.563709	−	0.0635147i
$776$	79.3036	+	164.676i	0.102195	+	0.212211i
$777$		0			0
$778$	−46.2401	+	202.591i	−0.0594345	+	0.260400i
$779$	500.806	+	241.176i	0.642883	+	0.309596i
$780$		0			0
$781$	145.375	+	231.363i	0.186139	+	0.296239i
$782$			973.785i			1.24525i
$783$		0			0
$784$	1180.21			1.50537
$785$	−1312.82	+	824.899i	−1.67238	+	1.05083i
$786$		0			0
$787$	−266.444	+	553.276i	−0.338556	+	0.703019i	−0.998848	−	0.0479904i	$-0.984718\pi$
$787$	−266.444	+	553.276i	−0.338556	+	0.703019i	0.660292	+	0.751009i	$0.270433\pi$
$788$	353.908	+	80.7772i	0.449122	+	0.102509i
$789$		0			0
$790$	491.254	−	236.575i	0.621840	−	0.299463i
$791$	50.0028	+	443.787i	0.0632146	+	0.561045i
$792$		0			0
$793$	67.8734	−	23.7499i	0.0855907	−	0.0299495i
$794$	132.389	−	1174.99i	0.166737	−	1.47983i
$795$		0			0
$796$	223.100	−	177.916i	0.280276	−	0.223513i
$797$	750.466	−	1194.36i	0.941614	−	1.49857i	0.0764542	−	0.997073i	$-0.475640\pi$
$797$	750.466	−	1194.36i	0.941614	−	1.49857i	0.865160	−	0.501497i	$-0.167217\pi$
$798$		0			0
$799$	143.362	+	179.770i	0.179427	+	0.224994i
$800$	−226.538	−	226.538i	−0.283172	−	0.283172i
$801$		0			0
$802$	443.527	+	1267.53i	0.553027	+	1.58046i
$803$	278.991	−	349.843i	0.347435	−	0.435670i
$804$		0			0
$805$	−787.969	−	1636.23i	−0.978843	−	2.03259i
$806$	241.089	+	1056.28i	0.299117	+	1.31052i
$807$		0			0
$808$	−285.648	−	137.561i	−0.353525	−	0.170248i
$809$	25.5805	−	73.1050i	0.0316200	−	0.0903646i	−0.926991	−	0.375083i	$-0.877614\pi$
$809$	25.5805	−	73.1050i	0.0316200	−	0.0903646i	0.958611	+	0.284718i	$0.0919000\pi$
$810$		0			0
$811$		−	342.716i		−	0.422584i	−0.977423	−	0.211292i	$-0.932233\pi$
$811$		−	342.716i		−	0.422584i	0.977423	−	0.211292i	$-0.0677672\pi$
$812$	29.5225	+	574.287i	0.0363578	+	0.707250i
$813$		0			0
$814$	1061.53	−	667.005i	1.30409	−	0.819416i
$815$	−340.616	−	119.187i	−0.417934	−	0.146241i
$816$		0			0
$817$	−582.447	−	132.940i	−0.712910	−	0.162717i
$818$	−345.911	+	78.9520i	−0.422874	+	0.0965183i
$819$		0			0
$820$	−52.6255	−	467.064i	−0.0641775	−	0.569591i
$821$	−583.761	−	465.534i	−0.711036	−	0.567033i	0.199782	−	0.979840i	$-0.435977\pi$
$821$	−583.761	−	465.534i	−0.711036	−	0.567033i	−0.910818	+	0.412808i	$0.864548\pi$
$822$		0			0
$823$	50.1031	−	444.677i	0.0608786	−	0.540312i	−0.925845	−	0.377903i	$-0.876645\pi$
$823$	50.1031	−	444.677i	0.0608786	−	0.540312i	0.986724	−	0.162409i	$-0.0519263\pi$
$824$	−422.461	+	422.461i	−0.512695	+	0.512695i
$825$		0			0
$826$	458.010	−	728.919i	0.554492	−	0.882469i
$827$	450.290	+	282.936i	0.544486	+	0.342123i	0.776025	−	0.630702i	$-0.217233\pi$
$827$	450.290	+	282.936i	0.544486	+	0.342123i	−0.231539	+	0.972826i	$0.574376\pi$
$828$		0			0
$829$	626.306	+	626.306i	0.755496	+	0.755496i	0.975499	−	0.220004i	$-0.0706069\pi$
$829$	626.306	+	626.306i	0.755496	+	0.755496i	−0.220004	+	0.975499i	$0.570607\pi$
$830$	−1016.63	−	114.546i	−1.22485	−	0.138008i
$831$		0			0
$832$	−81.0366	+	101.617i	−0.0973997	+	0.122135i
$833$	810.908	−	91.3674i	0.973479	−	0.109685i
$834$		0			0
$835$	246.913	+	1081.80i	0.295704	+	1.29556i
$836$	50.3979	−	220.808i	0.0602846	−	0.264124i
$837$		0			0
$838$	−152.920	+	437.020i	−0.182482	+	0.521504i
$839$	−617.246	−	982.342i	−0.735693	−	1.17085i	−0.979582	−	0.201046i	$-0.935566\pi$
$839$	−617.246	−	982.342i	−0.735693	−	1.17085i	0.243889	−	0.969803i	$-0.421577\pi$
$840$		0			0
$841$	836.567	−	86.2392i	0.994729	−	0.102544i
$842$	1024.95			1.21728
$843$		0			0
$844$	−100.823	−	35.2794i	−0.119458	−	0.0418002i
$845$	96.2070	−	199.776i	0.113854	−	0.236421i
$846$		0			0
$847$	−454.042	+	103.632i	−0.536059	+	0.122352i
$848$	1043.84	−	502.685i	1.23094	−	0.592789i
$849$		0			0
$850$	−297.898	−	237.566i	−0.350468	−	0.279489i
$851$	1616.57	−	565.662i	1.89961	−	0.664702i
$852$		0			0
$853$	−735.868	+	735.868i	−0.862682	+	0.862682i	−0.991649	−	0.128967i	$-0.958834\pi$
$853$	−735.868	+	735.868i	−0.862682	+	0.862682i	0.128967	+	0.991649i	$0.458834\pi$
$854$	123.522	−	98.5053i	0.144639	−	0.115346i
$855$		0			0
$856$	−294.346	−	184.950i	−0.343862	−	0.216063i
$857$	900.939	+	1129.74i	1.05127	+	1.31825i	0.946127	+	0.323795i	$0.104959\pi$
$857$	900.939	+	1129.74i	1.05127	+	1.31825i	0.105143	+	0.994457i	$0.466470\pi$
$858$		0			0
$859$	513.758	+	57.8866i	0.598088	+	0.0673883i	0.405818	−	0.913954i	$-0.366987\pi$
$859$	513.758	+	57.8866i	0.598088	+	0.0673883i	0.192270	+	0.981342i	$0.438415\pi$
$860$	166.848	+	476.825i	0.194009	+	0.554447i
$861$		0			0
$862$	−255.474	+	28.7850i	−0.296374	+	0.0333933i
$863$	−306.543	−	636.543i	−0.355206	−	0.737594i	0.644427	−	0.764666i	$-0.277096\pi$
$863$	−306.543	−	636.543i	−0.355206	−	0.737594i	−0.999633	+	0.0270721i	$0.991382\pi$
$864$		0			0
$865$	32.7152	−	143.335i	0.0378211	−	0.165705i
$866$	1681.67	+	809.851i	1.94188	+	0.935162i
$867$		0			0
$868$	408.970	+	650.872i	0.471164	+	0.749853i
$869$			324.823i			0.373790i
$870$		0			0
$871$	−782.061			−0.897889
$872$	50.1155	−	31.4897i	0.0574719	−	0.0361120i
$873$		0			0
$874$	415.720	−	863.252i	0.475652	−	0.987702i
$875$	−834.405	−	190.447i	−0.953605	−	0.217654i
$876$		0			0
$877$	1111.88	−	535.454i	1.26782	−	0.610552i	0.325591	−	0.945511i	$-0.394437\pi$
$877$	1111.88	−	535.454i	1.26782	−	0.610552i	0.942233	+	0.334959i	$0.108722\pi$
$878$	143.420	+	1272.89i	0.163349	+	1.44976i
$879$		0			0
$880$	992.934	−	347.443i	1.12833	−	0.394821i
$881$	117.244	−	1040.57i	0.133080	−	1.18112i	−0.732648	−	0.680607i	$-0.761716\pi$
$881$	117.244	−	1040.57i	0.133080	−	1.18112i	0.865729	−	0.500514i	$-0.166855\pi$
$882$		0			0
$883$	1077.75	−	859.480i	1.22056	−	0.973364i	0.220561	−	0.975373i	$-0.429211\pi$
$883$	1077.75	−	859.480i	1.22056	−	0.973364i	0.999998	+	0.00200940i	$0.000639611\pi$
$884$	161.325	−	256.747i	0.182494	−	0.290438i
$885$		0			0
$886$	362.210	+	454.197i	0.408815	+	0.512638i
$887$	763.056	+	763.056i	0.860266	+	0.860266i	0.991369	−	0.131103i	$-0.0418517\pi$
$887$	763.056	+	763.056i	0.860266	+	0.860266i	−0.131103	+	0.991369i	$0.541852\pi$
$888$		0			0
$889$	455.722	+	1302.38i	0.512623	+	1.46499i
$890$	−256.277	+	321.361i	−0.287952	+	0.361080i
$891$		0			0
$892$	−111.265	−	231.045i	−0.124737	−	0.259019i
$893$	−50.3432	−	220.568i	−0.0563753	−	0.246996i
$894$		0			0
$895$	−612.591	−	295.008i	−0.684459	−	0.329618i
$896$	−482.228	+	1378.13i	−0.538201	+	1.53809i
$897$		0			0
$898$		−	741.736i		−	0.825986i
$899$	919.934	−	646.197i	1.02329	−	0.718796i
$900$		0			0
$901$	678.292	−	426.199i	0.752821	−	0.473029i
$902$	818.439	+	286.384i	0.907361	+	0.317499i
$903$		0			0
$904$	−213.024	−	48.6213i	−0.235646	−	0.0537846i
$905$	1186.14	−	270.730i	1.31066	−	0.299149i
$906$		0			0
$907$	19.3797	+	171.999i	0.0213668	+	0.189635i	0.999862	−	0.0166359i	$-0.00529562\pi$
$907$	19.3797	+	171.999i	0.0213668	+	0.189635i	−0.978495	+	0.206271i	$0.933867\pi$
$908$	−252.688	−	201.512i	−0.278291	−	0.221930i
$909$		0			0
$910$	−196.073	+	1740.19i	−0.215465	+	1.91230i
$911$	−462.418	+	462.418i	−0.507594	+	0.507594i	−0.913787	−	0.406193i	$-0.866856\pi$
$911$	−462.418	+	462.418i	−0.507594	+	0.507594i	0.406193	+	0.913787i	$0.366856\pi$
$912$		0			0
$913$	324.257	−	516.053i	0.355156	−	0.565227i
$914$	−860.667	−	540.793i	−0.941648	−	0.591677i
$915$		0			0
$916$	−210.919	−	210.919i	−0.230261	−	0.230261i
$917$	814.159	+	91.7337i	0.887850	+	0.100037i
$918$		0			0
$919$	50.4859	−	63.3073i	0.0549356	−	0.0688871i	−0.753605	−	0.657328i	$-0.771687\pi$
$919$	50.4859	−	63.3073i	0.0549356	−	0.0688871i	0.808540	+	0.588441i	$0.200258\pi$
$920$	882.954	−	99.4851i	0.959733	−	0.108136i
$921$		0			0
$922$	321.679	+	1409.37i	0.348893	+	1.52860i
$923$	80.0955	−	350.921i	0.0867774	−	0.380196i
$924$		0			0
$925$	−221.334	+	632.536i	−0.239280	+	0.683823i
$926$	−1168.61	−	1859.83i	−1.26200	−	2.00846i
$927$		0			0
$928$	−786.132	−	230.520i	−0.847125	−	0.248405i
$929$	101.318			0.109061			0.0545307	−	0.998512i	$-0.482634\pi$
$929$	101.318			0.109061			0.0545307	+	0.998512i	$0.482634\pi$
$930$		0			0
$931$	−757.869	−	265.190i	−0.814037	−	0.284844i
$932$	−245.043	+	508.837i	−0.262922	+	0.545962i
$933$		0			0
$934$	1692.45	−	386.290i	1.81204	−	0.413586i
$935$	655.336	−	315.593i	0.700894	−	0.337533i
$936$		0			0
$937$	388.710	+	309.986i	0.414846	+	0.330828i	0.808570	−	0.588400i	$-0.200242\pi$
$937$	388.710	+	309.986i	0.414846	+	0.330828i	−0.393724	+	0.919229i	$0.628813\pi$
$938$	−1621.84	+	567.506i	−1.72904	+	0.605018i
$939$		0			0
$940$	−135.273	+	135.273i	−0.143907	+	0.143907i
$941$	731.701	−	583.512i	0.777578	−	0.620098i	−0.152144	−	0.988358i	$-0.548618\pi$
$941$	731.701	−	583.512i	0.777578	−	0.620098i	0.929723	+	0.368260i	$0.120046\pi$
$942$		0			0
$943$	1002.99	+	630.218i	1.06361	+	0.668311i
$944$	424.735	+	532.600i	0.449931	+	0.564195i
$945$		0			0
$946$	−926.090	−	104.345i	−0.978953	−	0.110302i
$947$	166.393	+	475.524i	0.175705	+	0.502137i	0.997732	−	0.0673119i	$-0.0214423\pi$
$947$	166.393	+	475.524i	0.175705	+	0.502137i	−0.822027	+	0.569449i	$0.807157\pi$
$948$		0			0
$949$	−585.742	+	65.9973i	−0.617221	+	0.0695441i
$950$	162.664	+	337.776i	0.171226	+	0.355554i
$951$		0			0
$952$	−162.584	+	712.325i	−0.170781	+	0.748241i
$953$	1199.61	+	577.703i	1.25878	+	0.606195i	0.939851	−	0.341585i	$-0.110964\pi$
$953$	1199.61	+	577.703i	1.25878	+	0.606195i	0.318925	+	0.947780i	$0.396678\pi$
$954$		0			0
$955$	−41.6531	−	66.2906i	−0.0436158	−	0.0694142i
$956$		−	490.943i		−	0.513539i
$957$		0			0
$958$	27.5463			0.0287539
$959$	−1424.04	+	894.782i	−1.48492	+	0.933037i
$960$		0			0
$961$	235.076	−	488.140i	0.244616	−	0.507950i
$962$	−1610.09	−	367.492i	−1.67369	−	0.382008i
$963$		0			0
$964$	−41.0190	+	19.7537i	−0.0425508	+	0.0204914i
$965$	79.1588	+	702.554i	0.0820298	+	0.728035i
$966$		0			0
$967$	1724.68	−	603.491i	1.78354	−	0.624086i	0.783540	−	0.621342i	$-0.213412\pi$
$967$	1724.68	−	603.491i	1.78354	−	0.624086i	0.999996	−	0.00274474i	$-0.000873680\pi$
$968$	25.5121	−	226.426i	0.0263554	−	0.233911i
$969$		0			0
$970$	−411.733	+	328.346i	−0.424467	+	0.338501i
$971$	223.862	−	356.274i	0.230548	−	0.366915i	−0.711337	−	0.702851i	$-0.751910\pi$
$971$	223.862	−	356.274i	0.230548	−	0.366915i	0.941885	+	0.335936i	$0.109053\pi$
$972$		0			0
$973$	−712.930	−	893.986i	−0.732713	−	0.918793i
$974$	1380.37	+	1380.37i	1.41721	+	1.41721i
$975$		0			0
$976$	41.2916	+	118.005i	0.0423070	+	0.120906i
$977$	424.792	−	532.672i	0.434792	−	0.545212i	−0.515370	−	0.856968i	$-0.672346\pi$
$977$	424.792	−	532.672i	0.434792	−	0.545212i	0.950162	+	0.311756i	$0.100917\pi$
$978$		0			0
$979$	−106.244	−	220.618i	−0.108523	−	0.225350i
$980$	151.079	+	661.918i	0.154162	+	0.675427i
$981$		0			0
$982$	814.226	+	392.111i	0.829151	+	0.399298i
$983$	210.468	−	601.483i	0.214108	−	0.611885i	−0.785871	−	0.618391i	$-0.787785\pi$
$983$	210.468	−	601.483i	0.214108	−	0.611885i	0.999979	+	0.00650528i	$0.00207071\pi$
$984$		0			0
$985$		−	1147.08i		−	1.16455i
$986$	−959.780	−	167.755i	−0.973408	−	0.170137i
$987$		0			0
$988$	−252.621	+	158.732i	−0.255689	+	0.160660i
$989$	−1201.70	−	420.492i	−1.21506	−	0.425169i
$990$		0			0
$991$	−1115.91	−	254.699i	−1.12604	−	0.257012i	−0.381358	−	0.924427i	$-0.624543\pi$
$991$	−1115.91	−	254.699i	−1.12604	−	0.257012i	−0.744686	+	0.667415i	$0.767401\pi$
$992$	−1067.66	+	243.686i	−1.07627	+	0.245651i
$993$		0			0
$994$	−88.5455	−	785.863i	−0.0890800	−	0.790607i
$995$	−704.980	−	562.203i	−0.708522	−	0.565028i
$996$		0			0
$997$	45.1114	−	400.375i	0.0452472	−	0.401580i	−0.950591	−	0.310445i	$-0.899522\pi$
$997$	45.1114	−	400.375i	0.0452472	−	0.401580i	0.995839	−	0.0911349i	$-0.0290494\pi$
$998$	−825.868	+	825.868i	−0.827523	+	0.827523i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.3.s.a.10.1		48
3.2	odd	2		29.3.f.a.10.4	yes	48
29.3	odd	28	inner	261.3.s.a.235.1		48
87.32	even	28		29.3.f.a.3.4	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.3.f.a.3.4	✓	48	87.32	even	28
29.3.f.a.10.4	yes	48	3.2	odd	2
261.3.s.a.10.1		48	1.1	even	1	trivial
261.3.s.a.235.1		48	29.3	odd	28	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	261.s (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.05804 + 1.29315i) q^{2} +(0.827740 - 1.71882i) q^{4} +(-5.87720 - 1.34143i) q^{5} +(-9.36468 + 4.50979i) q^{7} +(-0.569384 - 5.05343i) q^{8} +O(q^{10})\)	\(q+(-2.05804 + 1.29315i) q^{2} +(0.827740 - 1.71882i) q^{4} +(-5.87720 - 1.34143i) q^{5} +(-9.36468 + 4.50979i) q^{7} +(-0.569384 - 5.05343i) q^{8} +(13.8301 - 4.83938i) q^{10} +(-0.977326 + 8.67401i) q^{11} +(8.98997 - 7.16926i) q^{13} +(13.4410 - 21.3913i) q^{14} +(12.4645 + 15.6300i) q^{16} +(9.77422 + 9.77422i) q^{17} +(-4.49203 - 12.8375i) q^{19} +(-7.17047 + 8.99148i) q^{20} +(-9.20542 - 19.1153i) q^{22} +(-6.44949 - 28.2571i) q^{23} +(10.2178 + 4.92062i) q^{25} +(-9.23075 + 26.3800i) q^{26} +19.8291i q^{28} +(28.9618 - 1.48885i) q^{29} +(32.8240 - 20.6247i) q^{31} +(-26.6642 - 9.33019i) q^{32} +(-32.7552 - 7.47617i) q^{34} +(61.0877 - 13.9429i) q^{35} +(6.61609 + 58.7194i) q^{37} +(25.8456 + 20.6112i) q^{38} +(-3.43244 + 30.4638i) q^{40} +(-28.8990 + 28.8990i) q^{41} +(23.3701 - 37.1932i) q^{43} +(14.1001 + 8.85967i) q^{44} +(49.8139 + 49.8139i) q^{46} +(16.5298 + 1.86246i) q^{47} +(36.8081 - 46.1559i) q^{49} +(-27.3916 + 3.08629i) q^{50} +(-4.88131 - 21.3864i) q^{52} +(12.8958 - 56.5002i) q^{53} +(17.3795 - 49.6678i) q^{55} +(28.1220 + 44.7559i) q^{56} +(-57.6790 + 40.5160i) q^{58} +34.0756 q^{59} +(5.90275 + 2.06546i) q^{61} +(-40.8822 + 84.8927i) q^{62} +(-11.0199 + 2.51523i) q^{64} +(-62.4529 + 30.0757i) q^{65} +(-53.1751 - 42.4058i) q^{67} +(24.8906 - 8.70961i) q^{68} +(-107.690 + 107.690i) q^{70} +(24.4740 - 19.5174i) q^{71} +(-43.4053 - 27.2734i) q^{73} +(-89.5491 - 112.291i) q^{74} +(-25.7836 - 2.90511i) q^{76} +(-29.9657 - 85.6369i) q^{77} +(36.9784 - 4.16647i) q^{79} +(-52.2897 - 108.581i) q^{80} +(22.1045 - 96.8459i) q^{82} +(-62.9075 - 30.2947i) q^{83} +(-44.3336 - 70.5565i) q^{85} +106.766i q^{86} +44.3899 q^{88} +(-23.7527 + 14.9248i) q^{89} +(-51.8564 + 107.681i) q^{91} +(-53.9073 - 12.3040i) q^{92} +(-36.4274 + 17.5425i) q^{94} +(9.17994 + 81.4742i) q^{95} +(-33.9244 + 11.8707i) q^{97} +(-16.0659 + 142.589i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) \) 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8	\( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8} - 20 q^{10} + 8 q^{11} - 14 q^{13} - 26 q^{14} + 18 q^{16} + 26 q^{17} + 2 q^{19} - 46 q^{20} + 154 q^{22} - 56 q^{23} - 34 q^{25} - 110 q^{26} + 170 q^{29} - 88 q^{31} + 132 q^{32} - 224 q^{34} + 210 q^{35} - 56 q^{37} + 294 q^{38} - 492 q^{40} + 34 q^{41} + 176 q^{43} - 126 q^{44} + 744 q^{46} - 208 q^{47} + 506 q^{49} - 732 q^{50} + 690 q^{52} + 14 q^{53} + 284 q^{55} - 332 q^{56} - 508 q^{58} + 44 q^{59} - 30 q^{61} + 504 q^{62} - 896 q^{64} + 554 q^{65} - 574 q^{67} + 796 q^{68} - 1066 q^{70} - 224 q^{71} - 22 q^{73} - 820 q^{74} + 514 q^{76} - 436 q^{77} + 564 q^{79} - 1162 q^{80} - 18 q^{82} + 126 q^{83} + 38 q^{85} - 384 q^{88} + 160 q^{89} - 434 q^{91} + 1022 q^{92} - 2 q^{94} + 642 q^{95} + 604 q^{97} + 102 q^{98}+O(q^{100}) \) 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8 - 20 * q^10 + 8 * q^11 - 14 * q^13 - 26 * q^14 + 18 * q^16 + 26 * q^17 + 2 * q^19 - 46 * q^20 + 154 * q^22 - 56 * q^23 - 34 * q^25 - 110 * q^26 + 170 * q^29 - 88 * q^31 + 132 * q^32 - 224 * q^34 + 210 * q^35 - 56 * q^37 + 294 * q^38 - 492 * q^40 + 34 * q^41 + 176 * q^43 - 126 * q^44 + 744 * q^46 - 208 * q^47 + 506 * q^49 - 732 * q^50 + 690 * q^52 + 14 * q^53 + 284 * q^55 - 332 * q^56 - 508 * q^58 + 44 * q^59 - 30 * q^61 + 504 * q^62 - 896 * q^64 + 554 * q^65 - 574 * q^67 + 796 * q^68 - 1066 * q^70 - 224 * q^71 - 22 * q^73 - 820 * q^74 + 514 * q^76 - 436 * q^77 + 564 * q^79 - 1162 * q^80 - 18 * q^82 + 126 * q^83 + 38 * q^85 - 384 * q^88 + 160 * q^89 - 434 * q^91 + 1022 * q^92 - 2 * q^94 + 642 * q^95 + 604 * q^97 + 102 * q^98

Introduction

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