LMFDB - Embedded newform 261.3.s.a.235.1

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			235.1
Character	$\chi$	$=$	261.235
Dual form			261.3.s.a.10.1

$q$-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 $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{5}{28}\right)$	$1$

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	−0.0919649	−	0.995762i	$-0.529315\pi$
$2$	−2.05804	−	1.29315i	−1.02902	−	0.646575i	−0.937053	+	0.349188i	$0.886458\pi$
$3$		0			0
$3$		0			0
$4$	0.827740	+	1.71882i	0.206935	+	0.429705i
$5$	−5.87720	+	1.34143i	−1.17544	+	0.268286i	−0.765262	−	0.643719i	$-0.777390\pi$
$5$	−5.87720	+	1.34143i	−1.17544	+	0.268286i	−0.410177	+	0.912006i	$0.634533\pi$
$6$		0			0
$7$	−9.36468	−	4.50979i	−1.33781	−	0.644256i	−0.378237	−	0.925709i	$-0.623470\pi$
$7$	−9.36468	−	4.50979i	−1.33781	−	0.644256i	−0.959575	+	0.281452i	$0.909184\pi$
$8$	−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	−0.956571	−	0.291499i	$-0.905846\pi$
$11$	−0.977326	−	8.67401i	−0.0888478	−	0.788546i	0.867723	−	0.497048i	$-0.165583\pi$
$12$		0			0
$13$	8.98997	+	7.16926i	0.691536	+	0.551482i	0.904970	−	0.425476i	$-0.139893\pi$
$13$	8.98997	+	7.16926i	0.691536	+	0.551482i	−0.213433	+	0.976958i	$0.568465\pi$
$14$	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	−0.358554	−	0.933509i	$-0.616730\pi$
$17$	9.77422	−	9.77422i	0.574954	−	0.574954i	0.933509	+	0.358554i	$0.116730\pi$
$18$		0			0
$19$	−4.49203	+	12.8375i	−0.236423	+	0.675658i	0.763144	+	0.646228i	$0.223655\pi$
$19$	−4.49203	+	12.8375i	−0.236423	+	0.675658i	−0.999567	+	0.0294292i	$0.990631\pi$
$20$	−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	0.616853	+	0.787078i	$0.288407\pi$
$23$	−6.44949	+	28.2571i	−0.280413	+	1.22857i	−0.897266	+	0.441490i	$0.854450\pi$
$24$		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	0.944628	−	0.328144i	$-0.106423\pi$
$31$	32.8240	+	20.6247i	1.05884	+	0.665313i	0.114212	+	0.993456i	$0.463566\pi$
$32$	−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	−0.508768	−	0.860904i	$-0.669899\pi$
$37$	6.61609	−	58.7194i	0.178813	−	1.58701i	0.687581	−	0.726107i	$-0.258672\pi$
$38$	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	0.260594	−	0.965448i	$-0.416081\pi$
$41$	−28.8990	−	28.8990i	−0.704854	−	0.704854i	−0.965448	+	0.260594i	$0.916081\pi$
$42$		0			0
$43$	23.3701	+	37.1932i	0.543490	+	0.864959i	0.999689	−	0.0249182i	$-0.00793254\pi$
$43$	23.3701	+	37.1932i	0.543490	+	0.864959i	−0.456200	+	0.889877i	$0.650790\pi$
$44$	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	0.0656518	−	0.997843i	$-0.479087\pi$
$47$	16.5298	−	1.86246i	0.351698	−	0.0396269i	0.286047	+	0.958216i	$0.407659\pi$
$48$		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	0.937975	+	0.346702i	$0.112698\pi$
$53$	12.8958	+	56.5002i	0.243317	+	1.06604i	−0.694659	+	0.719340i	$0.744445\pi$
$54$		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	−0.281462	−	0.959572i	$-0.590819\pi$
$61$	5.90275	−	2.06546i	0.0967664	−	0.0338600i	0.378228	+	0.925712i	$0.376534\pi$
$62$	−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	−0.934037	−	0.357176i	$-0.883740\pi$
$67$	−53.1751	+	42.4058i	−0.793659	+	0.632922i	0.140378	+	0.990098i	$0.455168\pi$
$68$	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	0.780504	−	0.625151i	$-0.214963\pi$
$71$	24.4740	+	19.5174i	0.344704	+	0.274893i	−0.435799	+	0.900044i	$0.643534\pi$
$72$		0			0
$73$	−43.4053	+	27.2734i	−0.594593	+	0.373608i	−0.795456	−	0.606012i	$-0.792768\pi$
$73$	−43.4053	+	27.2734i	−0.594593	+	0.373608i	0.200862	+	0.979619i	$0.435626\pi$
$74$	−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	0.342855	−	0.939388i	$-0.388606\pi$
$79$	36.9784	+	4.16647i	0.468081	+	0.0527401i	0.125226	+	0.992128i	$0.460034\pi$
$80$	−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	−0.772597	−	0.634896i	$-0.781043\pi$
$83$	−62.9075	+	30.2947i	−0.757922	+	0.364996i	0.0146754	+	0.999892i	$0.495329\pi$
$84$		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	0.391941	−	0.919990i	$-0.371804\pi$
$89$	−23.7527	−	14.9248i	−0.266885	−	0.167695i	−0.658826	+	0.752296i	$0.728947\pi$
$90$		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	0.149693	−	0.988732i	$-0.452171\pi$
$97$	−33.9244	−	11.8707i	−0.349736	−	0.122378i	−0.499430	+	0.866354i	$0.666457\pi$
$98$	−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	0.969591	−	0.244730i	$-0.0786994\pi$
$101$	33.1691	+	52.7883i	0.328407	+	0.522657i	−0.641184	+	0.767387i	$0.721557\pi$
$102$		0			0
$103$	−73.2496	+	91.8521i	−0.711161	+	0.891768i	−0.997802	−	0.0662704i	$-0.978890\pi$
$103$	−73.2496	+	91.8521i	−0.711161	+	0.891768i	0.286641	+	0.958038i	$0.407461\pi$
$104$	−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	0.940033	−	0.341083i	$-0.110794\pi$
$107$	42.6207	+	53.4447i	0.398324	+	0.499483i	−0.541709	+	0.840566i	$0.682222\pi$
$108$		0			0
$109$	5.04985	−	10.4861i	0.0463289	−	0.0962029i	−0.876519	−	0.481366i	$-0.840141\pi$
$109$	5.04985	−	10.4861i	0.0463289	−	0.0962029i	0.922848	+	0.385163i	$0.125855\pi$
$110$	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	0.989460	−	0.144807i	$-0.0462560\pi$
$113$	14.1909	+	40.5554i	0.125584	+	0.358897i	−0.863876	+	0.503704i	$0.831970\pi$
$114$		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	0.905710	+	0.423897i	$0.139338\pi$
$127$	14.8633	+	131.916i	0.117034	+	1.03871i	−0.788676	+	0.614809i	$0.789233\pi$
$128$	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	−0.762127	−	0.647427i	$-0.775845\pi$
$131$	−66.7432	+	41.9375i	−0.509490	+	0.320134i	0.252637	+	0.967561i	$0.418702\pi$
$132$		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	0.677179	−	0.735819i	$-0.263202\pi$
$137$	160.789	+	18.1166i	1.17364	+	0.132238i	0.496465	+	0.868057i	$0.334631\pi$
$138$		0			0
$139$	24.4796	−	107.252i	0.176112	−	0.771599i	−0.807289	−	0.590156i	$-0.799066\pi$
$139$	24.4796	−	107.252i	0.176112	−	0.771599i	0.983401	−	0.181443i	$-0.0580767\pi$
$140$	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	−0.998448	−	0.0556878i	$-0.982265\pi$
$149$	−62.5002	−	129.783i	−0.419464	−	0.871027i	0.578984	−	0.815339i	$-0.303449\pi$
$150$		0			0
$151$	279.422	+	63.7763i	1.85048	+	0.422359i	0.995372	−	0.0960946i	$-0.0306351\pi$
$151$	279.422	+	63.7763i	1.85048	+	0.422359i	0.855105	+	0.518454i	$0.173492\pi$
$152$	−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	0.984824	+	0.173555i	$0.0555255\pi$
$157$	181.866	+	181.866i	1.15838	+	1.15838i	0.173555	+	0.984824i	$0.444474\pi$
$158$	−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	0.0724098	−	0.997375i	$-0.476931\pi$
$163$	59.4854	−	6.70239i	0.364941	−	0.0411190i	0.292531	+	0.956256i	$0.405502\pi$
$164$	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	0.512693	+	0.858572i	$0.328648\pi$
$167$	−79.8635	+	165.838i	−0.478225	+	0.993044i	−0.990917	+	0.134472i	$0.957066\pi$
$168$		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	$-0.977545\pi$
$173$		−	24.3883i		−	0.140973i	0.997513	−	0.0704864i	$-0.0224551\pi$
$174$		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	0.0959623	−	0.995385i	$-0.469407\pi$
$179$	109.960	−	25.0977i	0.614303	−	0.140211i	0.518340	+	0.855174i	$0.326550\pi$
$180$		0			0
$181$	−181.835	−	87.5671i	−1.00461	−	0.483796i	−0.142111	−	0.989851i	$-0.545389\pi$
$181$	−181.835	−	87.5671i	−1.00461	−	0.483796i	−0.862501	+	0.506055i	$0.831103\pi$
$182$	−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	−0.682658	−	0.730738i	$-0.739176\pi$
$191$	9.18326	−	9.18326i	0.0480799	−	0.0480799i	0.730738	+	0.682658i	$0.239176\pi$
$192$		0			0
$193$	−38.7349	+	110.698i	−0.200699	+	0.573564i	−0.999611	−	0.0278831i	$-0.991123\pi$
$193$	−38.7349	+	110.698i	−0.200699	+	0.573564i	0.798912	+	0.601447i	$0.205409\pi$
$194$	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	−0.746228	−	0.665690i	$-0.768137\pi$
$197$	42.3417	−	185.511i	0.214932	−	0.941681i	0.961160	−	0.275990i	$-0.0890057\pi$
$198$		0			0
$199$	134.765	−	64.8992i	0.677209	−	0.326127i	−0.0634720	−	0.997984i	$-0.520217\pi$
$199$	134.765	−	64.8992i	0.677209	−	0.326127i	0.740681	+	0.671857i	$0.234503\pi$
$200$	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	0.970071	+	0.242821i	$0.0780727\pi$
$211$	−6.26902	+	55.6391i	−0.0297110	+	0.263692i	−0.999782	+	0.0208716i	$0.993356\pi$
$212$	−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	0.933391	−	0.358860i	$-0.116835\pi$
$223$	83.8099	+	105.094i	0.375829	+	0.471275i	−0.557562	+	0.830135i	$0.688263\pi$
$224$	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	0.987542	+	0.157357i	$0.0502973\pi$
$227$	37.6983	+	165.167i	0.166072	+	0.727609i	−0.821470	+	0.570252i	$0.806846\pi$
$228$		0			0
$229$	51.6406	+	147.580i	0.225505	+	0.644456i	0.999930	+	0.0117911i	$0.00375331\pi$
$229$	51.6406	+	147.580i	0.225505	+	0.644456i	−0.774426	+	0.632665i	$0.781961\pi$
$230$	−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	0.850693	−	0.525662i	$-0.176182\pi$
$239$	231.857	+	111.656i	0.970113	+	0.467182i	0.119420	+	0.992844i	$0.461897\pi$
$240$		0			0
$241$	−18.6581	+	14.8793i	−0.0774196	+	0.0617400i	−0.661435	−	0.750003i	$-0.730052\pi$
$241$	−18.6581	+	14.8793i	−0.0774196	+	0.0617400i	0.584015	+	0.811743i	$0.301481\pi$
$242$	−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	−0.998880	−	0.0473132i	$-0.984934\pi$
$251$	−47.2947	+	135.160i	−0.188425	+	0.538487i	0.810455	+	0.585801i	$0.199220\pi$
$252$		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	−0.580854	−	0.814008i	$-0.697281\pi$
$257$	−78.7944	+	37.9454i	−0.306593	+	0.147647i	0.274261	+	0.961655i	$0.411567\pi$
$258$		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	0.680077	−	0.733140i	$-0.261946\pi$
$263$	82.7439	+	51.9914i	0.314615	+	0.197686i	−0.365462	+	0.930826i	$0.619089\pi$
$264$		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	−0.986905	−	0.161303i	$-0.948430\pi$
$269$	2.99923	−	26.6189i	0.0111496	−	0.0989551i	0.998054	+	0.0623480i	$0.0198589\pi$
$270$		0			0
$271$	−164.750	−	57.6486i	−0.607935	−	0.212725i	0.00871663	−	0.999962i	$-0.497225\pi$
$271$	−164.750	−	57.6486i	−0.607935	−	0.212725i	−0.616651	+	0.787237i	$0.711511\pi$
$272$	−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	0.00180677	−	0.999998i	$-0.499425\pi$
$277$	270.444	−	339.126i	0.976331	−	1.22428i	0.974524	−	0.224282i	$-0.0720037\pi$
$278$	−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	−0.994202	−	0.107526i	$-0.965707\pi$
$281$	−246.662	−	309.305i	−0.877802	−	1.10073i	0.116400	−	0.993202i	$-0.462864\pi$
$282$		0			0
$283$	70.0980	−	145.560i	0.247696	−	0.514346i	−0.739637	−	0.673006i	$-0.765003\pi$
$283$	70.0980	−	145.560i	0.247696	−	0.514346i	0.987333	+	0.158660i	$0.0507172\pi$
$284$	−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	0.705191	−	0.709018i	$-0.250861\pi$
$293$	497.689	−	174.149i	1.69860	−	0.594365i	0.993406	+	0.114653i	$0.0365756\pi$
$294$		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	−0.991016	−	0.133742i	$-0.957301\pi$
$307$	−263.183	+	263.183i	−0.857275	+	0.857275i	0.133742	+	0.991016i	$0.457301\pi$
$308$	−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	0.559711	−	0.828688i	$-0.310912\pi$
$311$	286.428	+	32.2726i	0.920989	+	0.103771i	0.361278	+	0.932458i	$0.382341\pi$
$312$		0			0
$313$	41.7918	−	183.102i	0.133520	−	0.584990i	−0.863257	−	0.504765i	$-0.831579\pi$
$313$	41.7918	−	183.102i	0.133520	−	0.584990i	0.996777	−	0.0802250i	$-0.0255639\pi$
$314$	−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	−0.0797787	+	0.996813i	$0.525421\pi$
$317$	−299.014	+	475.878i	−0.943261	+	1.50119i	−0.863482	+	0.504379i	$0.831721\pi$
$318$		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	0.0865265	−	0.996250i	$-0.472423\pi$
$331$	−301.118	−	301.118i	−0.909723	−	0.909723i	−0.996250	+	0.0865265i	$0.972423\pi$
$332$	−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	0.430316	−	0.902678i	$-0.358402\pi$
$337$	354.089	−	39.8962i	1.05071	−	0.118386i	0.620392	+	0.784292i	$0.286973\pi$
$338$	−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	$-0.996314\pi$
$347$		−	8.03629i		−	0.0231593i	0.999933	−	0.0115797i	$-0.00368600\pi$
$348$		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	0.496505	−	0.868034i	$-0.334617\pi$
$353$	466.124	−	106.390i	1.32047	−	0.301388i	0.823961	+	0.566646i	$0.191759\pi$
$354$		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	−0.999964	−	0.00851817i	$-0.997289\pi$
$359$	−9.68103	−	85.9215i	−0.0269666	−	0.239336i	0.972997	−	0.230817i	$-0.0741400\pi$
$360$		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	0.436442	+	0.899732i	$0.356238\pi$
$367$	−170.932	+	488.497i	−0.465756	+	1.33105i	−0.902198	+	0.431322i	$0.858047\pi$
$368$	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	−0.622194	−	0.782863i	$-0.713759\pi$
$373$	−148.476	+	71.5023i	−0.398059	+	0.191695i	0.224135	+	0.974558i	$0.428044\pi$
$374$	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	−0.0831508	−	0.996537i	$-0.526498\pi$
$379$	−385.472	−	242.208i	−1.01708	−	0.639072i	−0.933927	+	0.357465i	$0.883641\pi$
$380$	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	−0.159645	−	0.987174i	$-0.551035\pi$
$383$	−280.279	−	63.9719i	−0.731799	−	0.167028i	−0.572154	+	0.820146i	$0.693892\pi$
$384$		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	0.780528	−	0.625121i	$-0.214950\pi$
$389$	60.4535	+	60.4535i	0.155408	+	0.155408i	−0.625121	+	0.780528i	$0.714950\pi$
$390$		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	0.235894	−	0.971779i	$-0.424198\pi$
$397$	−303.313	−	380.342i	−0.764012	−	0.958040i	−0.999906	+	0.0137384i	$0.995627\pi$
$398$	−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	0.859980	+	0.510328i	$0.170476\pi$
$401$	122.942	+	538.643i	0.306588	+	1.34325i	−0.553392	+	0.832921i	$0.686667\pi$
$402$		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	−0.156537	−	0.987672i	$-0.550033\pi$
$409$	137.784	−	48.2128i	0.336881	−	0.117880i	0.493418	+	0.869792i	$0.335747\pi$
$410$	−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	0.784890	−	0.619635i	$-0.212720\pi$
$419$	148.931	+	118.769i	0.355444	+	0.283457i	−0.429445	+	0.903093i	$0.641291\pi$
$420$		0			0
$421$	−357.054	+	224.352i	−0.848108	+	0.532902i	−0.884556	−	0.466434i	$-0.845539\pi$
$421$	−357.054	+	224.352i	−0.848108	+	0.532902i	0.0364479	+	0.999336i	$0.488396\pi$
$422$	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	−0.320050	−	0.947401i	$-0.603700\pi$
$431$	95.2983	−	45.8932i	0.221110	−	0.106481i	0.541160	+	0.840920i	$0.317985\pi$
$432$		0			0
$433$	−408.562	+	650.223i	−0.943562	+	1.50167i	−0.0803883	+	0.996764i	$0.525616\pi$
$433$	−408.562	+	650.223i	−0.943562	+	1.50167i	−0.863174	+	0.504907i	$0.831527\pi$
$434$			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	0.981047	+	0.193769i	$0.0620711\pi$
$439$	228.661	+	474.820i	0.520869	+	1.08160i	−0.460179	+	0.887826i	$0.652215\pi$
$440$	−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	0.926667	+	0.375883i	$0.122661\pi$
$443$	−26.7609	+	237.510i	−0.0604084	+	0.536139i	−0.987075	+	0.160256i	$0.948768\pi$
$444$		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	0.615532	−	0.788112i	$-0.288941\pi$
$449$	−162.359	−	258.393i	−0.361601	−	0.575485i	−0.977133	+	0.212627i	$0.931798\pi$
$450$		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	−0.602606	−	0.798039i	$-0.705871\pi$
$457$	181.449	−	376.783i	0.397045	−	0.824472i	0.999651	−	0.0264327i	$-0.00841477\pi$
$458$	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	0.934294	+	0.356502i	$0.116031\pi$
$461$	196.436	+	561.383i	0.426109	+	1.21775i	−0.508185	+	0.861248i	$0.669683\pi$
$462$		0			0
$463$		−	903.693i		−	1.95182i	−0.218171	−	0.975910i	$-0.570009\pi$
$463$		−	903.693i		−	1.95182i	0.218171	−	0.975910i	$-0.429991\pi$
$464$	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	−0.934609	−	0.355678i	$-0.884250\pi$
$467$	−674.139	+	235.892i	−1.44355	+	0.505121i	−0.508945	+	0.860799i	$0.669964\pi$
$468$		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	−0.542012	−	0.840371i	$-0.682337\pi$
$479$	−9.59607	+	6.02961i	−0.0200336	+	0.0125879i	0.521978	+	0.852959i	$0.325194\pi$
$480$		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	0.368055	+	0.929804i	$0.380024\pi$
$487$	−178.718	+	783.016i	−0.366978	+	1.60784i	−0.735033	+	0.678031i	$0.762833\pi$
$488$	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	−0.985127	−	0.171828i	$-0.945033\pi$
$491$	−197.816	+	314.823i	−0.402885	+	0.641187i	0.582242	+	0.813015i	$0.302176\pi$
$492$		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	0.664444	−	0.747338i	$-0.268668\pi$
$499$	468.476	+	106.927i	0.938830	+	0.214282i	0.274386	+	0.961620i	$0.411526\pi$
$500$	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	0.650485	−	0.759519i	$-0.274566\pi$
$503$	344.807	+	120.653i	0.685501	+	0.239867i	0.0350167	+	0.999387i	$0.488852\pi$
$504$		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	−0.0774230	+	0.996998i	$0.524669\pi$
$509$	−525.388	+	658.816i	−1.03220	+	1.29433i	−0.954773	+	0.297335i	$0.903902\pi$
$510$		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	$0.0462489\pi$
$521$			150.865i			0.289569i	−0.989463	+	0.144784i	$0.953751\pi$
$522$		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	−0.990999	−	0.133867i	$-0.957261\pi$
$541$	−71.8125	+	205.228i	−0.132740	+	0.379350i	0.858259	+	0.513217i	$0.171546\pi$
$542$	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	−0.759589	−	0.650403i	$-0.774600\pi$
$547$	−396.400	+	190.896i	−0.724680	+	0.348987i	0.0349094	+	0.999390i	$0.488886\pi$
$548$	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	−0.345977	−	0.938243i	$-0.612453\pi$
$557$	−593.083	−	135.367i	−1.06478	−	0.243029i	−0.718803	+	0.695214i	$0.755310\pi$
$558$		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	0.108141	−	0.994136i	$-0.465510\pi$
$563$	−498.815	−	498.815i	−0.885995	−	0.885995i	−0.994136	+	0.108141i	$0.965510\pi$
$564$		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	0.169474	−	0.985535i	$-0.445793\pi$
$569$	315.227	−	35.5176i	0.554002	−	0.0624210i	0.384527	+	0.923114i	$0.374364\pi$
$570$		0			0
$571$	−321.408	−	403.033i	−0.562886	−	0.705836i	0.416203	−	0.909272i	$-0.363361\pi$
$571$	−321.408	−	403.033i	−0.562886	−	0.705836i	−0.979088	+	0.203436i	$0.934789\pi$
$572$	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	0.773549	+	0.633736i	$0.218480\pi$
$577$	325.366	+	929.842i	0.563892	+	1.61151i	−0.209657	+	0.977775i	$0.567235\pi$
$578$	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	−0.343356	−	0.939205i	$-0.611564\pi$
$587$	−758.249	−	365.153i	−1.29174	−	0.622067i	−0.948379	+	0.317138i	$0.897278\pi$
$588$		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	0.646031	−	0.763311i	$-0.276428\pi$
$593$	27.0486	+	21.5706i	0.0456132	+	0.0363753i	−0.600418	+	0.799686i	$0.704999\pi$
$594$		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	−0.946807	−	0.321801i	$-0.895712\pi$
$599$	−3.54858	+	10.1412i	−0.00592417	+	0.0169303i	0.940883	+	0.338731i	$0.109998\pi$
$600$		0			0
$601$	368.282	+	41.4954i	0.612783	+	0.0690440i	0.412901	−	0.910776i	$-0.364516\pi$
$601$	368.282	+	41.4954i	0.612783	+	0.0690440i	0.199882	+	0.979820i	$0.435944\pi$
$602$	−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	−0.977199	−	0.212324i	$-0.931897\pi$
$607$	−219.680	+	349.619i	−0.361912	+	0.575979i	0.615288	+	0.788302i	$0.289040\pi$
$608$		−	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	−0.859151	−	0.511722i	$-0.829008\pi$
$613$	−443.542	−	921.025i	−0.723560	−	1.50249i	0.135591	−	0.990765i	$-0.456707\pi$
$614$	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	−0.999835	−	0.0181438i	$-0.994224\pi$
$617$	−12.9759	+	115.164i	−0.0210306	+	0.186652i	0.978805	+	0.204795i	$0.0656529\pi$
$618$		0			0
$619$	36.6784	+	12.8343i	0.0592543	+	0.0207340i	0.359743	−	0.933051i	$-0.382864\pi$
$619$	36.6784	+	12.8343i	0.0592543	+	0.0207340i	−0.300489	+	0.953785i	$0.597150\pi$
$620$	−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	−0.788279	−	0.615318i	$-0.789027\pi$
$631$	116.281	−	241.460i	0.184280	−	0.382662i	0.972559	+	0.232656i	$0.0747417\pi$
$632$	−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	0.522309	−	0.852756i	$-0.325071\pi$
$641$	937.367	−	327.999i	1.46235	−	0.511699i	0.940043	+	0.341057i	$0.110785\pi$
$642$		0			0
$643$	311.987	−	71.2090i	0.485206	−	0.110745i	0.0270814	−	0.999633i	$-0.491379\pi$
$643$	311.987	−	71.2090i	0.485206	−	0.110745i	0.458124	+	0.888888i	$0.348522\pi$
$644$	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	−0.374730	−	0.927134i	$-0.622264\pi$
$647$	288.416	−	230.004i	0.445774	−	0.355493i	0.820504	+	0.571641i	$0.193693\pi$
$648$		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	−0.320375	−	0.947291i	$-0.603809\pi$
$653$	257.346	−	161.701i	0.394098	−	0.247628i	0.714474	+	0.699662i	$0.246666\pi$
$654$		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	0.360071	−	0.932925i	$-0.382753\pi$
$659$	331.819	+	37.3870i	0.503518	+	0.0567329i	0.143448	+	0.989658i	$0.454181\pi$
$660$		0			0
$661$	−231.074	+	1012.40i	−0.349583	+	1.53162i	0.428548	+	0.903519i	$0.359025\pi$
$661$	−231.074	+	1012.40i	−0.349583	+	1.53162i	−0.778131	+	0.628103i	$0.783832\pi$
$662$	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	0.329546	−	0.944139i	$-0.393104\pi$
$673$	145.913	+	33.3038i	0.216810	+	0.0494856i	−0.112736	+	0.993625i	$0.535961\pi$
$674$	−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	−0.0304143	−	0.999537i	$-0.509683\pi$
$677$	−458.596	−	160.470i	−0.677395	−	0.237031i	−0.646980	+	0.762507i	$0.723968\pi$
$678$		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	−0.989986	−	0.141164i	$-0.954915\pi$
$683$	−431.703	+	541.338i	−0.632069	+	0.792589i	0.357918	+	0.933753i	$0.383487\pi$
$684$		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	0.980201	+	0.198003i	$0.0634456\pi$
$691$	126.440	+	553.969i	0.182981	+	0.801691i	−0.797221	+	0.603688i	$0.793697\pi$
$692$	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	−0.671698	−	0.740825i	$-0.734435\pi$
$701$	−669.767	+	152.870i	−0.955445	+	0.218074i	−0.283747	+	0.958899i	$0.591578\pi$
$702$		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	0.844149	−	0.536108i	$-0.180106\pi$
$709$	361.110	+	287.976i	0.509324	+	0.406172i	−0.334826	+	0.942280i	$0.608677\pi$
$710$	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	−0.828504	−	0.559983i	$-0.810808\pi$
$719$	115.701	−	506.920i	0.160920	−	0.705035i	0.989424	−	0.145052i	$-0.0463350\pi$
$720$		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	−0.999966	−	0.00827820i	$-0.997365\pi$
$727$	−1047.82	−	658.389i	−1.44129	−	0.905624i	−0.441327	−	0.897346i	$-0.645492\pi$
$728$	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	−0.983590	−	0.180418i	$-0.942255\pi$
$733$	11.3513	−	100.746i	0.0154861	−	0.137443i	0.999076	+	0.0429750i	$0.0136836\pi$
$734$	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	0.446714	−	0.894677i	$-0.352594\pi$
$739$	−408.803	−	650.606i	−0.553184	−	0.880387i	−0.999898	+	0.0142895i	$0.995451\pi$
$740$	−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	0.284807	−	0.958585i	$-0.408071\pi$
$743$	576.403	−	64.9450i	0.775778	−	0.0874091i	0.490971	+	0.871176i	$0.336642\pi$
$744$		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	−0.931995	−	0.362471i	$-0.881933\pi$
$751$	−322.426	−	921.441i	−0.429329	−	1.22695i	0.502666	−	0.864481i	$-0.332353\pi$
$752$	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	0.258478	−	0.966017i	$-0.416779\pi$
$757$	804.590	−	281.538i	1.06287	−	0.371913i	0.804388	+	0.594104i	$0.202493\pi$
$758$	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	0.206113	−	0.978528i	$-0.433919\pi$
$761$	−327.551	−	157.740i	−0.430422	−	0.207280i	−0.636535	+	0.771248i	$0.719633\pi$
$762$		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	−0.740460	−	0.672100i	$-0.765392\pi$
$769$	−350.812	+	220.430i	−0.456192	+	0.286644i	0.284268	+	0.958745i	$0.408249\pi$
$770$	−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	−0.695297	−	0.718722i	$-0.744727\pi$
$773$	229.136	−	654.833i	0.296424	−	0.847132i	0.991721	−	0.128409i	$-0.0409871\pi$
$774$		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	0.660292	−	0.751009i	$-0.270433\pi$
$787$	−266.444	−	553.276i	−0.338556	−	0.703019i	−0.998848	+	0.0479904i	$0.984718\pi$
$788$	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	0.865160	+	0.501497i	$0.167217\pi$
$797$	750.466	+	1194.36i	0.941614	+	1.49857i	0.0764542	+	0.997073i	$0.475640\pi$
$798$		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	0.958611	−	0.284718i	$-0.0919000\pi$
$809$	25.5805	+	73.1050i	0.0316200	+	0.0903646i	−0.926991	+	0.375083i	$0.877614\pi$
$810$		0			0
$811$			342.716i			0.422584i	0.977423	+	0.211292i	$0.0677672\pi$
$811$			342.716i			0.422584i	−0.977423	+	0.211292i	$0.932233\pi$
$812$	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	−0.910818	−	0.412808i	$-0.864548\pi$
$821$	−583.761	+	465.534i	−0.711036	+	0.567033i	0.199782	+	0.979840i	$0.435977\pi$
$822$		0			0
$823$	50.1031	+	444.677i	0.0608786	+	0.540312i	0.986724	+	0.162409i	$0.0519263\pi$
$823$	50.1031	+	444.677i	0.0608786	+	0.540312i	−0.925845	+	0.377903i	$0.876645\pi$
$824$	−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	−0.231539	−	0.972826i	$-0.574376\pi$
$827$	450.290	−	282.936i	0.544486	−	0.342123i	0.776025	+	0.630702i	$0.217233\pi$
$828$		0			0
$829$	626.306	−	626.306i	0.755496	−	0.755496i	−0.220004	−	0.975499i	$-0.570607\pi$
$829$	626.306	−	626.306i	0.755496	−	0.755496i	0.975499	+	0.220004i	$0.0706069\pi$
$830$	−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	0.243889	+	0.969803i	$0.421577\pi$
$839$	−617.246	+	982.342i	−0.735693	+	1.17085i	−0.979582	+	0.201046i	$0.935566\pi$
$840$		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	0.128967	−	0.991649i	$-0.458834\pi$
$853$	−735.868	−	735.868i	−0.862682	−	0.862682i	−0.991649	+	0.128967i	$0.958834\pi$
$854$	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	0.105143	−	0.994457i	$-0.466470\pi$
$857$	900.939	−	1129.74i	1.05127	−	1.31825i	0.946127	−	0.323795i	$-0.104959\pi$
$858$		0			0
$859$	513.758	−	57.8866i	0.598088	−	0.0673883i	0.192270	−	0.981342i	$-0.438415\pi$
$859$	513.758	−	57.8866i	0.598088	−	0.0673883i	0.405818	+	0.913954i	$0.366987\pi$
$860$	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	−0.999633	−	0.0270721i	$-0.991382\pi$
$863$	−306.543	+	636.543i	−0.355206	+	0.737594i	0.644427	+	0.764666i	$0.277096\pi$
$864$		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	0.942233	−	0.334959i	$-0.108722\pi$
$877$	1111.88	+	535.454i	1.26782	+	0.610552i	0.325591	+	0.945511i	$0.394437\pi$
$878$	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	0.865729	+	0.500514i	$0.166855\pi$
$881$	117.244	+	1040.57i	0.133080	+	1.18112i	−0.732648	+	0.680607i	$0.761716\pi$
$882$		0			0
$883$	1077.75	+	859.480i	1.22056	+	0.973364i	0.999998	−	0.00200940i	$-0.000639611\pi$
$883$	1077.75	+	859.480i	1.22056	+	0.973364i	0.220561	+	0.975373i	$0.429211\pi$
$884$	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	−0.131103	−	0.991369i	$-0.541852\pi$
$887$	763.056	−	763.056i	0.860266	−	0.860266i	0.991369	+	0.131103i	$0.0418517\pi$
$888$		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	−0.978495	−	0.206271i	$-0.933867\pi$
$907$	19.3797	−	171.999i	0.0213668	−	0.189635i	0.999862	+	0.0166359i	$0.00529562\pi$
$908$	−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	0.406193	−	0.913787i	$-0.366856\pi$
$911$	−462.418	−	462.418i	−0.507594	−	0.507594i	−0.913787	+	0.406193i	$0.866856\pi$
$912$		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	0.808540	−	0.588441i	$-0.200258\pi$
$919$	50.4859	+	63.3073i	0.0549356	+	0.0688871i	−0.753605	+	0.657328i	$0.771687\pi$
$920$	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	−0.393724	−	0.919229i	$-0.628813\pi$
$937$	388.710	−	309.986i	0.414846	−	0.330828i	0.808570	+	0.588400i	$0.200242\pi$
$938$	−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	0.929723	−	0.368260i	$-0.120046\pi$
$941$	731.701	+	583.512i	0.777578	+	0.620098i	−0.152144	+	0.988358i	$0.548618\pi$
$942$		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	−0.822027	−	0.569449i	$-0.807157\pi$
$947$	166.393	−	475.524i	0.175705	−	0.502137i	0.997732	+	0.0673119i	$0.0214423\pi$
$948$		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	0.318925	−	0.947780i	$-0.396678\pi$
$953$	1199.61	−	577.703i	1.25878	−	0.606195i	0.939851	+	0.341585i	$0.110964\pi$
$954$		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	0.999996	+	0.00274474i	$0.000873680\pi$
$967$	1724.68	+	603.491i	1.78354	+	0.624086i	0.783540	+	0.621342i	$0.213412\pi$
$968$	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	0.941885	−	0.335936i	$-0.109053\pi$
$971$	223.862	+	356.274i	0.230548	+	0.366915i	−0.711337	+	0.702851i	$0.751910\pi$
$972$		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	0.950162	−	0.311756i	$-0.100917\pi$
$977$	424.792	+	532.672i	0.434792	+	0.545212i	−0.515370	+	0.856968i	$0.672346\pi$
$978$		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	0.999979	−	0.00650528i	$-0.00207071\pi$
$983$	210.468	+	601.483i	0.214108	+	0.611885i	−0.785871	+	0.618391i	$0.787785\pi$
$984$		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	−0.744686	−	0.667415i	$-0.767401\pi$
$991$	−1115.91	+	254.699i	−1.12604	+	0.257012i	−0.381358	+	0.924427i	$0.624543\pi$
$992$	−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	0.995839	+	0.0911349i	$0.0290494\pi$
$997$	45.1114	+	400.375i	0.0452472	+	0.401580i	−0.950591	+	0.310445i	$0.899522\pi$
$998$	−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.235.1		48
3.2	odd	2		29.3.f.a.3.4	✓	48
29.10	odd	28	inner	261.3.s.a.10.1		48
87.68	even	28		29.3.f.a.10.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.3.f.a.3.4	✓	48	3.2	odd	2
29.3.f.a.10.4	yes	48	87.68	even	28
261.3.s.a.10.1		48	29.10	odd	28	inner
261.3.s.a.235.1		48	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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more