LMFDB - Embedded newform 261.3.s.a.37.4

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			37.4
Character	$\chi$	$=$	261.37
Dual form			261.3.s.a.127.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.32673 + 0.814157i) q^{2} +(1.62348 + 1.29468i) q^{4} +(3.83207 + 7.95737i) q^{5} +(2.23777 + 2.80607i) q^{7} +(-2.52264 - 4.01476i) q^{8} +O(q^{10})$	\(q+(2.32673 + 0.814157i) q^{2} +(1.62348 + 1.29468i) q^{4} +(3.83207 + 7.95737i) q^{5} +(2.23777 + 2.80607i) q^{7} +(-2.52264 - 4.01476i) q^{8} +(2.43763 + 21.6345i) q^{10} +(-4.04453 + 6.43684i) q^{11} +(-7.19807 + 1.64291i) q^{13} +(2.92209 + 8.35085i) q^{14} +(-4.44912 - 19.4929i) q^{16} +(-1.60706 - 1.60706i) q^{17} +(33.1033 - 3.72985i) q^{19} +(-4.08097 + 17.8799i) q^{20} +(-14.6511 + 11.6839i) q^{22} +(20.4388 + 9.84282i) q^{23} +(-33.0478 + 41.4406i) q^{25} +(-18.0855 - 2.03775i) q^{26} +7.45278i q^{28} +(-14.4627 - 25.1362i) q^{29} +(5.30982 + 1.85799i) q^{31} +(3.39483 - 30.1300i) q^{32} +(-2.43079 - 5.04759i) q^{34} +(-13.7537 + 28.5598i) q^{35} +(8.64092 + 13.7519i) q^{37} +(80.0590 + 18.2729i) q^{38} +(22.2800 - 35.4584i) q^{40} +(42.1095 - 42.1095i) q^{41} +(1.74483 + 4.98643i) q^{43} +(-14.8999 + 5.21368i) q^{44} +(39.5419 + 39.5419i) q^{46} +(-60.4551 - 37.9864i) q^{47} +(8.03709 - 35.2128i) q^{49} +(-110.632 + 69.5148i) q^{50} +(-13.8130 - 6.65197i) q^{52} +(78.2991 - 37.7068i) q^{53} +(-66.7192 - 7.51745i) q^{55} +(5.62062 - 16.0628i) q^{56} +(-13.1859 - 70.2600i) q^{58} -67.9548 q^{59} +(5.72557 - 50.8159i) q^{61} +(10.8418 + 8.64605i) q^{62} +(-2.27117 + 4.71614i) q^{64} +(-40.6568 - 50.9820i) q^{65} +(-29.4645 - 6.72508i) q^{67} +(-0.528398 - 4.68966i) q^{68} +(-55.2532 + 55.2532i) q^{70} +(-17.3364 + 3.95693i) q^{71} +(29.8255 - 10.4364i) q^{73} +(8.90881 + 39.0321i) q^{74} +(58.5714 + 36.8029i) q^{76} +(-27.1129 + 3.05489i) q^{77} +(-38.0418 + 23.9032i) q^{79} +(138.063 - 110.101i) q^{80} +(132.261 - 63.6936i) q^{82} +(-3.87179 + 4.85507i) q^{83} +(6.62962 - 18.9464i) q^{85} +13.0226i q^{86} +36.0453 q^{88} +(19.6772 + 6.88537i) q^{89} +(-20.7177 - 16.5218i) q^{91} +(20.4387 + 42.4413i) q^{92} +(-109.735 - 137.604i) q^{94} +(156.534 + 249.122i) q^{95} +(5.86295 + 52.0352i) q^{97} +(47.3689 - 75.3871i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{3}{28}\right)$	$1$

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 $

$2$	2.32673	+	0.814157i	1.16336	+	0.407078i	0.841789	−	0.539806i	$-0.181502\pi$
$2$	2.32673	+	0.814157i	1.16336	+	0.407078i	0.321574	+	0.946885i	$0.395788\pi$
$3$		0			0
$3$		0			0
$4$	1.62348	+	1.29468i	0.405869	+	0.323670i
$5$	3.83207	+	7.95737i	0.766414	+	1.59147i	0.805755	+	0.592248i	$0.201760\pi$
$5$	3.83207	+	7.95737i	0.766414	+	1.59147i	−0.0393418	+	0.999226i	$0.512526\pi$
$6$		0			0
$7$	2.23777	+	2.80607i	0.319681	+	0.400867i	0.915543	−	0.402219i	$-0.131761\pi$
$7$	2.23777	+	2.80607i	0.319681	+	0.400867i	−0.595862	+	0.803087i	$0.703190\pi$
$8$	−2.52264	−	4.01476i	−0.315330	−	0.501845i
$9$		0			0
$10$	2.43763	+	21.6345i	0.243763	+	2.16345i
$11$	−4.04453	+	6.43684i	−0.367685	+	0.585167i	−0.978409	−	0.206676i	$-0.933735\pi$
$11$	−4.04453	+	6.43684i	−0.367685	+	0.585167i	0.610725	+	0.791843i	$0.290878\pi$
$12$		0			0
$13$	−7.19807	+	1.64291i	−0.553698	+	0.126378i	−0.490210	−	0.871605i	$-0.663080\pi$
$13$	−7.19807	+	1.64291i	−0.553698	+	0.126378i	−0.0634884	+	0.997983i	$0.520223\pi$
$14$	2.92209	+	8.35085i	0.208721	+	0.596489i
$15$		0			0
$16$	−4.44912	−	19.4929i	−0.278070	−	1.21830i
$17$	−1.60706	−	1.60706i	−0.0945331	−	0.0945331i	0.658259	−	0.752792i	$-0.271293\pi$
$17$	−1.60706	−	1.60706i	−0.0945331	−	0.0945331i	−0.752792	+	0.658259i	$0.771293\pi$
$18$		0			0
$19$	33.1033	−	3.72985i	1.74228	−	0.196308i	0.817270	−	0.576254i	$-0.195486\pi$
$19$	33.1033	−	3.72985i	1.74228	−	0.196308i	0.925008	+	0.379947i	$0.124058\pi$
$20$	−4.08097	+	17.8799i	−0.204049	+	0.893996i
$21$		0			0
$22$	−14.6511	+	11.6839i	−0.665960	+	0.531085i
$23$	20.4388	+	9.84282i	0.888644	+	0.427948i	0.821774	−	0.569813i	$-0.192984\pi$
$23$	20.4388	+	9.84282i	0.888644	+	0.427948i	0.0668700	+	0.997762i	$0.478699\pi$
$24$		0			0
$25$	−33.0478	+	41.4406i	−1.32191	+	1.65762i
$26$	−18.0855	−	2.03775i	−0.695597	−	0.0783750i
$27$		0			0
$28$			7.45278i			0.266171i
$29$	−14.4627	−	25.1362i	−0.498714	−	0.866766i
$29$	−14.4627	−	25.1362i	−0.498714	−	0.866766i
$30$		0			0
$31$	5.30982	+	1.85799i	0.171284	+	0.0599350i	0.414559	−	0.910022i	$-0.363936\pi$
$31$	5.30982	+	1.85799i	0.171284	+	0.0599350i	−0.243275	+	0.969957i	$0.578222\pi$
$32$	3.39483	−	30.1300i	0.106089	−	0.941562i
$33$		0			0
$34$	−2.43079	−	5.04759i	−0.0714939	−	0.148459i
$35$	−13.7537	+	28.5598i	−0.392962	+	0.815994i
$36$		0			0
$37$	8.64092	+	13.7519i	0.233538	+	0.371674i	0.942848	−	0.333223i	$-0.108136\pi$
$37$	8.64092	+	13.7519i	0.233538	+	0.371674i	−0.709310	+	0.704897i	$0.750993\pi$
$38$	80.0590	+	18.2729i	2.10682	+	0.480867i
$39$		0			0
$40$	22.2800	−	35.4584i	0.557000	−	0.886461i
$41$	42.1095	−	42.1095i	1.02706	−	1.02706i	0.0274377	−	0.999624i	$-0.491265\pi$
$41$	42.1095	−	42.1095i	1.02706	−	1.02706i	0.999624	−	0.0274377i	$-0.00873478\pi$
$42$		0			0
$43$	1.74483	+	4.98643i	0.0405774	+	0.115964i	0.962389	−	0.271674i	$-0.0875771\pi$
$43$	1.74483	+	4.98643i	0.0405774	+	0.115964i	−0.921812	+	0.387637i	$0.873291\pi$
$44$	−14.8999	+	5.21368i	−0.338633	+	0.118493i
$45$		0			0
$46$	39.5419	+	39.5419i	0.859607	+	0.859607i
$47$	−60.4551	−	37.9864i	−1.28628	−	0.808222i	−0.297086	−	0.954851i	$-0.596015\pi$
$47$	−60.4551	−	37.9864i	−1.28628	−	0.808222i	−0.989192	+	0.146629i	$0.953158\pi$
$48$		0			0
$49$	8.03709	−	35.2128i	0.164022	−	0.718629i
$50$	−110.632	+	69.5148i	−2.21264	+	1.39030i
$51$		0			0
$52$	−13.8130	−	6.65197i	−0.265634	−	0.127923i
$53$	78.2991	−	37.7068i	1.47734	−	0.711450i	0.490246	−	0.871584i	$-0.336907\pi$
$53$	78.2991	−	37.7068i	1.47734	−	0.711450i	0.987095	+	0.160134i	$0.0511928\pi$
$54$		0			0
$55$	−66.7192	−	7.51745i	−1.21308	−	0.136681i
$56$	5.62062	−	16.0628i	0.100368	−	0.286836i
$57$		0			0
$58$	−13.1859	−	70.2600i	−0.227344	−	1.21138i
$59$	−67.9548			−1.15178			−0.575888	−	0.817528i	$-0.695344\pi$
$59$	−67.9548			−1.15178			−0.575888	+	0.817528i	$0.695344\pi$
$60$		0			0
$61$	5.72557	−	50.8159i	0.0938619	−	0.833047i	−0.855273	−	0.518178i	$-0.826611\pi$
$61$	5.72557	−	50.8159i	0.0938619	−	0.833047i	0.949135	−	0.314870i	$-0.101961\pi$
$62$	10.8418	+	8.64605i	0.174868	+	0.139452i
$63$		0			0
$64$	−2.27117	+	4.71614i	−0.0354871	+	0.0736897i
$65$	−40.6568	−	50.9820i	−0.625489	−	0.784338i
$66$		0			0
$67$	−29.4645	−	6.72508i	−0.439769	−	0.100374i	−0.00309676	−	0.999995i	$-0.500986\pi$
$67$	−29.4645	−	6.72508i	−0.439769	−	0.100374i	−0.436672	+	0.899621i	$0.643843\pi$
$68$	−0.528398	−	4.68966i	−0.00777056	−	0.0689656i
$69$		0			0
$70$	−55.2532	+	55.2532i	−0.789331	+	0.789331i
$71$	−17.3364	+	3.95693i	−0.244175	+	0.0557314i	−0.342857	−	0.939388i	$-0.611395\pi$
$71$	−17.3364	+	3.95693i	−0.244175	+	0.0557314i	0.0986817	+	0.995119i	$0.468537\pi$
$72$		0			0
$73$	29.8255	−	10.4364i	0.408569	−	0.142965i	−0.118166	−	0.992994i	$-0.537702\pi$
$73$	29.8255	−	10.4364i	0.408569	−	0.142965i	0.526735	+	0.850029i	$0.323416\pi$
$74$	8.90881	+	39.0321i	0.120389	+	0.527460i
$75$		0			0
$76$	58.5714	+	36.8029i	0.770677	+	0.484248i
$77$	−27.1129	+	3.05489i	−0.352116	+	0.0396739i
$78$		0			0
$79$	−38.0418	+	23.9032i	−0.481541	+	0.302572i	−0.750840	−	0.660484i	$-0.770351\pi$
$79$	−38.0418	+	23.9032i	−0.481541	+	0.302572i	0.269299	+	0.963057i	$0.413208\pi$
$80$	138.063	−	110.101i	1.72578	−	1.37627i
$81$		0			0
$82$	132.261	−	63.6936i	1.61294	−	0.776751i
$83$	−3.87179	+	4.85507i	−0.0466480	+	0.0584948i	−0.804608	−	0.593806i	$-0.797625\pi$
$83$	−3.87179	+	4.85507i	−0.0466480	+	0.0584948i	0.757960	+	0.652301i	$0.226196\pi$
$84$		0			0
$85$	6.62962	−	18.9464i	0.0779955	−	0.222898i
$86$			13.0226i			0.151426i
$87$		0			0
$88$	36.0453			0.409605
$89$	19.6772	+	6.88537i	0.221093	+	0.0773637i	0.438552	−	0.898706i	$-0.355491\pi$
$89$	19.6772	+	6.88537i	0.221093	+	0.0773637i	−0.217460	+	0.976069i	$0.569777\pi$
$90$		0			0
$91$	−20.7177	−	16.5218i	−0.227667	−	0.181559i
$92$	20.4387	+	42.4413i	0.222159	+	0.461319i
$93$		0			0
$94$	−109.735	−	137.604i	−1.16740	−	1.46387i
$95$	156.534	+	249.122i	1.64772	+	2.62234i
$96$		0			0
$97$	5.86295	+	52.0352i	0.0604428	+	0.536445i	0.987050	+	0.160414i	$0.0512829\pi$
$97$	5.86295	+	52.0352i	0.0604428	+	0.536445i	−0.926607	+	0.376031i	$0.877289\pi$
$98$	47.3689	−	75.3871i	0.483356	−	0.769256i
$99$		0			0
$100$	−107.305	+	24.4916i	−1.07305	+	0.244916i
$101$	13.5414	+	38.6991i	0.134073	+	0.383159i	0.991273	−	0.131825i	$-0.0420836\pi$
$101$	13.5414	+	38.6991i	0.134073	+	0.383159i	−0.857200	+	0.514984i	$0.827798\pi$
$102$		0			0
$103$	−18.1203	−	79.3902i	−0.175925	−	0.770779i	−0.983485	−	0.180992i	$-0.942069\pi$
$103$	−18.1203	−	79.3902i	−0.175925	−	0.770779i	0.807559	−	0.589786i	$-0.200788\pi$
$104$	24.7541	+	24.7541i	0.238020	+	0.238020i
$105$		0			0
$106$	212.880	−	23.9858i	2.00830	−	0.226281i
$107$	−3.47716	+	15.2344i	−0.0324968	+	0.142378i	−0.988574	−	0.150738i	$-0.951835\pi$
$107$	−3.47716	+	15.2344i	−0.0324968	+	0.142378i	0.956077	+	0.293116i	$0.0946921\pi$
$108$		0			0
$109$	−24.8134	+	19.7880i	−0.227646	+	0.181542i	−0.730670	−	0.682731i	$-0.760792\pi$
$109$	−24.8134	+	19.7880i	−0.227646	+	0.181542i	0.503024	+	0.864272i	$0.332221\pi$
$110$	−149.117	−	71.8109i	−1.35561	−	0.652827i
$111$		0			0
$112$	44.7422	−	56.1050i	0.399484	−	0.500937i
$113$	−80.1964	−	9.03596i	−0.709703	−	0.0799643i	−0.250269	−	0.968176i	$-0.580519\pi$
$113$	−80.1964	−	9.03596i	−0.709703	−	0.0799643i	−0.459434	+	0.888212i	$0.651948\pi$
$114$		0			0
$115$			200.358i			1.74224i
$116$	9.06348	−	59.5327i	0.0781335	−	0.513213i
$117$		0			0
$118$	−158.112	−	55.3259i	−1.33993	−	0.468863i
$119$	0.913300	−	8.10576i	0.00767479	−	0.0681156i
$120$		0			0
$121$	27.4253	+	56.9493i	0.226655	+	0.470655i
$122$	54.6939	−	113.573i	0.448311	−	0.930927i
$123$		0			0
$124$	6.21487	+	9.89091i	0.0501199	+	0.0797654i
$125$	−241.135	−	55.0375i	−1.92908	−	0.440300i
$126$		0			0
$127$	−47.5028	+	75.6003i	−0.374038	+	0.595278i	−0.979706	−	0.200439i	$-0.935763\pi$
$127$	−47.5028	+	75.6003i	−0.374038	+	0.595278i	0.605668	+	0.795717i	$0.292906\pi$
$128$	−94.8838	+	94.8838i	−0.741279	+	0.741279i
$129$		0			0
$130$	−53.0899	−	151.722i	−0.408384	−	1.16709i
$131$	122.442	−	42.8444i	0.934674	−	0.327057i	0.180383	−	0.983596i	$-0.442266\pi$
$131$	122.442	−	42.8444i	0.934674	−	0.327057i	0.754291	+	0.656540i	$0.227981\pi$
$132$		0			0
$133$	84.5437	+	84.5437i	0.635667	+	0.635667i
$134$	−63.0805	−	39.6361i	−0.470750	−	0.295792i
$135$		0			0
$136$	−2.39793	+	10.5060i	−0.0176318	+	0.0772501i
$137$	104.753	−	65.8204i	0.764618	−	0.480441i	−0.0924040	−	0.995722i	$-0.529455\pi$
$137$	104.753	−	65.8204i	0.764618	−	0.480441i	0.857022	+	0.515281i	$0.172312\pi$
$138$		0			0
$139$	40.2937	+	19.4044i	0.289883	+	0.139600i	0.573174	−	0.819434i	$-0.305712\pi$
$139$	40.2937	+	19.4044i	0.289883	+	0.139600i	−0.283291	+	0.959034i	$0.591426\pi$
$140$	−59.3046	+	28.5596i	−0.423604	+	0.203997i
$141$		0			0
$142$	−43.5587	−	4.90789i	−0.306751	−	0.0345626i
$143$	18.5377	−	52.9776i	0.129634	−	0.370473i
$144$		0			0
$145$	144.596	−	211.409i	0.997215	−	1.45799i
$146$	77.8928			0.533512
$147$		0			0
$148$	−3.77603	+	33.5132i	−0.0255137	+	0.226440i
$149$	92.6321	+	73.8716i	0.621692	+	0.495783i	0.882938	−	0.469489i	$-0.155562\pi$
$149$	92.6321	+	73.8716i	0.621692	+	0.495783i	−0.261246	+	0.965272i	$0.584133\pi$
$150$		0			0
$151$	−79.3234	+	164.717i	−0.525320	+	1.09084i	0.454461	+	0.890767i	$0.349832\pi$
$151$	−79.3234	+	164.717i	−0.525320	+	1.09084i	−0.979781	+	0.200072i	$0.935882\pi$
$152$	−98.4822	−	123.493i	−0.647909	−	0.812453i
$153$		0			0
$154$	−65.5715	−	14.9663i	−0.425789	−	0.0971836i
$155$	5.56290	+	49.3721i	0.0358897	+	0.318530i
$156$		0			0
$157$	−78.3608	+	78.3608i	−0.499113	+	0.499113i	−0.911162	−	0.412049i	$-0.864813\pi$
$157$	−78.3608	+	78.3608i	−0.499113	+	0.499113i	0.412049	+	0.911162i	$0.364813\pi$
$158$	−107.974	+	24.6443i	−0.683378	+	0.155977i
$159$		0			0
$160$	252.765	−	88.4462i	1.57978	−	0.552789i
$161$	18.1177	+	79.3787i	0.112532	+	0.493035i
$162$		0			0
$163$	−12.8408	−	8.06844i	−0.0787782	−	0.0494996i	0.492067	−	0.870557i	$-0.336242\pi$
$163$	−12.8408	−	8.06844i	−0.0787782	−	0.0494996i	−0.570845	+	0.821058i	$0.693384\pi$
$164$	122.882	−	13.8455i	0.749282	−	0.0844238i
$165$		0			0
$166$	−12.9614	+	8.14417i	−0.0780806	+	0.0490613i
$167$	−205.173	+	163.620i	−1.22858	+	0.979760i	−0.228600	+	0.973521i	$0.573415\pi$
$167$	−205.173	+	163.620i	−1.22858	+	0.979760i	−0.999981	+	0.00623948i	$0.998014\pi$
$168$		0			0
$169$	−103.151	+	49.6747i	−0.610359	+	0.293933i
$170$	30.8506	−	38.6854i	0.181474	−	0.227561i
$171$		0			0
$172$	−3.62315	+	10.3544i	−0.0210648	+	0.0601998i
$173$			61.9144i			0.357887i	0.983859	+	0.178943i	$0.0572679\pi$
$173$			61.9144i			0.357887i	−0.983859	+	0.178943i	$0.942732\pi$
$174$		0			0
$175$	−190.238			−1.08708
$176$	143.467	+	50.2012i	0.815153	+	0.285234i
$177$		0			0
$178$	40.1778	+	32.0407i	0.225718	+	0.180004i
$179$	−139.692	−	290.074i	−0.780403	−	1.62052i	−0.784182	−	0.620531i	$-0.786917\pi$
$179$	−139.692	−	290.074i	−0.780403	−	1.62052i	0.00377939	−	0.999993i	$-0.498797\pi$
$180$		0			0
$181$	−185.369	−	232.445i	−1.02414	−	1.28423i	−0.958108	−	0.286408i	$-0.907539\pi$
$181$	−185.369	−	232.445i	−1.02414	−	1.28423i	−0.0660276	−	0.997818i	$-0.521033\pi$
$182$	−34.7531	−	55.3093i	−0.190951	−	0.303897i
$183$		0			0
$184$	−12.0433	−	106.887i	−0.0654525	−	0.580907i
$185$	−76.3167	+	121.457i	−0.412523	+	0.656526i
$186$		0			0
$187$	16.8442	−	3.84458i	0.0900760	−	0.0205593i
$188$	−48.9672	−	139.940i	−0.260464	−	0.744362i
$189$		0			0
$190$	161.387	+	707.082i	0.849405	+	3.72149i
$191$	191.734	+	191.734i	1.00384	+	1.00384i	0.999993	+	0.00384775i	$0.00122478\pi$
$191$	191.734	+	191.734i	1.00384	+	1.00384i	0.00384775	+	0.999993i	$0.498775\pi$
$192$		0			0
$193$	134.893	−	15.1987i	0.698925	−	0.0787500i	0.244650	−	0.969611i	$-0.421327\pi$
$193$	134.893	−	15.1987i	0.698925	−	0.0787500i	0.454275	+	0.890861i	$0.349898\pi$
$194$	−28.7233	+	125.845i	−0.148058	+	0.648685i
$195$		0			0
$196$	58.6374	−	46.7617i	0.299170	−	0.238580i
$197$	102.900	+	49.5541i	0.522336	+	0.251544i	0.676423	−	0.736514i	$-0.263529\pi$
$197$	102.900	+	49.5541i	0.522336	+	0.251544i	−0.154087	+	0.988057i	$0.549244\pi$
$198$		0			0
$199$	−50.0688	+	62.7843i	−0.251602	+	0.315499i	−0.891553	−	0.452917i	$-0.850383\pi$
$199$	−50.0688	+	62.7843i	−0.251602	+	0.315499i	0.639951	+	0.768416i	$0.278955\pi$
$200$	249.742	+	28.1391i	1.24871	+	0.140696i
$201$		0			0
$202$			101.067i			0.500332i
$203$	38.1698	−	96.8324i	0.188029	−	0.477007i
$204$		0			0
$205$	496.447	+	173.714i	2.42170	+	0.847388i
$206$	22.4751	−	199.472i	0.109102	−	0.968311i
$207$		0			0
$208$	64.0501	+	133.001i	0.307933	+	0.639430i
$209$	−109.879	+	228.166i	−0.525737	+	1.09170i
$210$		0			0
$211$	−34.1531	−	54.3543i	−0.161863	−	0.257604i	0.755939	−	0.654642i	$-0.227181\pi$
$211$	−34.1531	−	54.3543i	−0.161863	−	0.257604i	−0.917802	+	0.397039i	$0.870038\pi$
$212$	175.935	+	40.1560i	0.829883	+	0.189415i
$213$		0			0
$214$	−20.4936	+	32.6154i	−0.0957645	+	0.152408i
$215$	−32.9926	+	32.9926i	−0.153454	+	0.153454i
$216$		0			0
$217$	6.66849	+	19.0575i	0.0307304	+	0.0878224i
$218$	−73.8446	+	25.8393i	−0.338736	+	0.118529i
$219$		0			0
$220$	−98.5845	−	98.5845i	−0.448111	−	0.448111i
$221$	14.2080	+	8.92749i	0.0642897	+	0.0403959i
$222$		0			0
$223$	−47.0630	+	206.196i	−0.211045	+	0.924648i	0.752814	+	0.658234i	$0.228696\pi$
$223$	−47.0630	+	206.196i	−0.211045	+	0.924648i	−0.963859	+	0.266414i	$0.914161\pi$
$224$	92.1437	−	57.8977i	0.411356	−	0.258472i
$225$		0			0
$226$	−179.238	−	86.3166i	−0.793090	−	0.381932i
$227$	−276.625	+	133.216i	−1.21861	+	0.586853i	−0.928925	−	0.370268i	$-0.879266\pi$
$227$	−276.625	+	133.216i	−1.21861	+	0.586853i	−0.289688	+	0.957121i	$0.593552\pi$
$228$		0			0
$229$	85.7684	+	9.66378i	0.374535	+	0.0421999i	0.297226	−	0.954807i	$-0.403939\pi$
$229$	85.7684	+	9.66378i	0.374535	+	0.0421999i	0.0773089	+	0.997007i	$0.475367\pi$
$230$	−163.122	+	466.177i	−0.709228	+	2.02686i
$231$		0			0
$232$	−64.4317	+	121.474i	−0.277723	+	0.523595i
$233$	141.899			0.609008			0.304504	−	0.952511i	$-0.401509\pi$
$233$	141.899			0.609008			0.304504	+	0.952511i	$0.401509\pi$
$234$		0			0
$235$	70.6042	−	626.630i	0.300444	−	2.66651i
$236$	−110.323	−	87.9797i	−0.467471	−	0.372796i
$237$		0			0
$238$	8.72436	−	18.1163i	0.0366570	−	0.0761190i
$239$	−86.5736	−	108.560i	−0.362233	−	0.454225i	0.567002	−	0.823717i	$-0.308103\pi$
$239$	−86.5736	−	108.560i	−0.362233	−	0.454225i	−0.929234	+	0.369491i	$0.879532\pi$
$240$		0			0
$241$	−178.803	−	40.8106i	−0.741922	−	0.169339i	−0.165178	−	0.986264i	$-0.552820\pi$
$241$	−178.803	−	40.8106i	−0.741922	−	0.169339i	−0.576744	+	0.816925i	$0.695677\pi$
$242$	17.4456	+	154.834i	0.0720892	+	0.639809i
$243$		0			0
$244$	75.0857	−	75.0857i	0.307728	−	0.307728i
$245$	311.000	−	70.9837i	1.26939	−	0.289730i
$246$		0			0
$247$	−232.152	+	81.2336i	−0.939887	+	0.328881i
$248$	−5.93540	−	26.0047i	−0.0239331	−	0.104858i
$249$		0			0
$250$	−516.246	−	324.379i	−2.06498	−	1.29752i
$251$	253.427	−	28.5543i	1.00967	−	0.113762i	0.408394	−	0.912806i	$-0.366089\pi$
$251$	253.427	−	28.5543i	1.00967	−	0.113762i	0.601273	+	0.799043i	$0.294660\pi$
$252$		0			0
$253$	−146.022	+	91.7517i	−0.577162	+	0.362655i
$254$	−172.077	+	137.227i	−0.677467	+	0.540262i
$255$		0			0
$256$	−279.154	+	134.434i	−1.09045	+	0.525131i
$257$	9.57230	−	12.0033i	0.0372463	−	0.0467054i	−0.762859	−	0.646564i	$-0.776205\pi$
$257$	9.57230	−	12.0033i	0.0372463	−	0.0467054i	0.800106	+	0.599859i	$0.204777\pi$
$258$		0			0
$259$	−19.2526	+	55.0206i	−0.0743342	+	0.212435i
$260$		−	135.406i		−	0.520791i
$261$		0			0
$262$	319.772			1.22050
$263$	−210.667	−	73.7155i	−0.801014	−	0.280287i	−0.101435	−	0.994842i	$-0.532343\pi$
$263$	−210.667	−	73.7155i	−0.801014	−	0.280287i	−0.699579	+	0.714555i	$0.746629\pi$
$264$		0			0
$265$	600.095	+	478.560i	2.26451	+	1.80589i
$266$	127.878	+	265.542i	0.480745	+	0.998277i
$267$		0			0
$268$	−39.1281	−	49.0651i	−0.146000	−	0.183079i
$269$	−206.896	−	329.273i	−0.769129	−	1.22406i	−0.969680	−	0.244379i	$-0.921416\pi$
$269$	−206.896	−	329.273i	−0.769129	−	1.22406i	0.200551	−	0.979683i	$-0.435727\pi$
$270$		0			0
$271$	43.4468	+	385.601i	0.160320	+	1.42288i	0.773929	+	0.633273i	$0.218289\pi$
$271$	43.4468	+	385.601i	0.160320	+	1.42288i	−0.613608	+	0.789611i	$0.710283\pi$
$272$	−24.1762	+	38.4762i	−0.0888831	+	0.141457i
$273$		0			0
$274$	297.319	−	67.8611i	1.08511	−	0.247668i
$275$	−133.084	−	380.331i	−0.483940	−	1.38302i
$276$		0			0
$277$	−73.9544	−	324.015i	−0.266983	−	1.16973i	−0.913503	−	0.406833i	$-0.866633\pi$
$277$	−73.9544	−	324.015i	−0.266983	−	1.16973i	0.646519	−	0.762897i	$-0.276224\pi$
$278$	77.9542	+	77.9542i	0.280411	+	0.280411i
$279$		0			0
$280$	149.356	−	16.8284i	0.533415	−	0.0601015i
$281$	0.644237	−	2.82259i	0.00229266	−	0.0100448i	−0.973769	−	0.227540i	$-0.926932\pi$
$281$	0.644237	−	2.82259i	0.00229266	−	0.0100448i	0.976061	+	0.217496i	$0.0697888\pi$
$282$		0			0
$283$	275.054	−	219.348i	0.971921	−	0.775081i	−0.00245718	−	0.999997i	$-0.500782\pi$
$283$	275.054	−	219.348i	0.971921	−	0.775081i	0.974378	+	0.224916i	$0.0722107\pi$
$284$	−33.2683	−	16.0212i	−0.117142	−	0.0564125i
$285$		0			0
$286$	86.2642	−	108.172i	0.301623	−	0.378223i
$287$	212.393	+	23.9310i	0.740047	+	0.0833833i
$288$		0			0
$289$		−	283.835i		−	0.982127i
$290$	508.556	−	374.167i	1.75364	−	1.29023i
$291$		0			0
$292$	61.9329	+	21.6713i	0.212099	+	0.0742167i
$293$	10.4159	−	92.4441i	0.0355493	−	0.315509i	−0.963336	−	0.268299i	$-0.913538\pi$
$293$	10.4159	−	92.4441i	0.0355493	−	0.315509i	0.998885	−	0.0472098i	$-0.0150329\pi$
$294$		0			0
$295$	−260.407	−	540.742i	−0.882737	−	1.83302i
$296$	33.4128	−	69.3824i	0.112881	−	0.234400i
$297$		0			0
$298$	155.386	+	247.296i	0.521431	+	0.829853i
$299$	−163.291	−	37.2701i	−0.546124	−	0.124649i
$300$		0			0
$301$	−10.0878	+	16.0546i	−0.0335142	+	0.0533375i
$302$	−318.669	+	318.669i	−1.05520	+	1.05520i
$303$		0			0
$304$	−219.986	−	628.683i	−0.723637	−	2.06804i
$305$	426.302	−	149.169i	1.39771	−	0.489080i
$306$		0			0
$307$	−32.6117	−	32.6117i	−0.106227	−	0.106227i	0.651996	−	0.758223i	$-0.273932\pi$
$307$	−32.6117	−	32.6117i	−0.106227	−	0.106227i	−0.758223	+	0.651996i	$0.773932\pi$
$308$	−47.9724	−	30.1430i	−0.155754	−	0.0978670i
$309$		0			0
$310$	−27.2533	+	119.404i	−0.0879138	+	0.385176i
$311$	−55.7972	+	35.0597i	−0.179412	+	0.112732i	−0.618744	−	0.785593i	$-0.712358\pi$
$311$	−55.7972	+	35.0597i	−0.179412	+	0.112732i	0.439332	+	0.898325i	$0.355215\pi$
$312$		0			0
$313$	−145.236	−	69.9418i	−0.464012	−	0.223456i	0.187246	−	0.982313i	$-0.440044\pi$
$313$	−145.236	−	69.9418i	−0.464012	−	0.223456i	−0.651257	+	0.758857i	$0.725758\pi$
$314$	−246.122	+	118.526i	−0.783828	+	0.377472i
$315$		0			0
$316$	−92.7070	−	10.4456i	−0.293377	−	0.0330556i
$317$	−92.7815	+	265.154i	−0.292686	+	0.836449i	0.699827	+	0.714312i	$0.253260\pi$
$317$	−92.7815	+	265.154i	−0.292686	+	0.836449i	−0.992513	+	0.122137i	$0.961025\pi$
$318$		0			0
$319$	220.293	+	8.57016i	0.690573	+	0.0268657i
$320$	−46.2314			−0.144473
$321$		0			0
$322$	−22.4718	+	199.443i	−0.0697883	+	0.619388i
$323$	−59.1931	−	47.2050i	−0.183261	−	0.146145i
$324$		0			0
$325$	169.797	−	352.587i	0.522452	−	1.08488i
$326$	−23.3082	−	29.2275i	−0.0714974	−	0.0896549i
$327$		0			0
$328$	−275.287	−	62.8324i	−0.839289	−	0.191562i
$329$	−28.6917	−	254.646i	−0.0872088	−	0.774000i
$330$		0			0
$331$	−35.3548	+	35.3548i	−0.106812	+	0.106812i	−0.758493	−	0.651681i	$-0.774064\pi$
$331$	−35.3548	+	35.3548i	−0.106812	+	0.106812i	0.651681	+	0.758493i	$0.274064\pi$
$332$	−12.5715	+	2.86937i	−0.0378660	+	0.00864268i
$333$		0			0
$334$	−610.593	+	213.656i	−1.82812	+	0.639688i
$335$	−59.3960	−	260.231i	−0.177301	−	0.776808i
$336$		0			0
$337$	−233.227	−	146.546i	−0.692069	−	0.434856i	0.139541	−	0.990216i	$-0.455437\pi$
$337$	−233.227	−	146.546i	−0.692069	−	0.434856i	−0.831610	+	0.555361i	$0.812580\pi$
$338$	−280.446	+	31.5987i	−0.829723	+	0.0934873i
$339$		0			0
$340$	35.2925	−	22.1758i	0.103802	−	0.0652228i
$341$	−33.4353	+	26.6637i	−0.0980506	+	0.0781928i
$342$		0			0
$343$	275.244	−	132.551i	0.802462	−	0.386445i
$344$	15.6178	−	19.5841i	0.0454005	−	0.0569304i
$345$		0			0
$346$	−50.4080	+	144.058i	−0.145688	+	0.416352i
$347$		−	506.789i		−	1.46049i	−0.683186	−	0.730244i	$-0.739406\pi$
$347$		−	506.789i		−	1.46049i	0.683186	−	0.730244i	$-0.260594\pi$
$348$		0			0
$349$	−308.138			−0.882917			−0.441459	−	0.897282i	$-0.645539\pi$
$349$	−308.138			−0.882917			−0.441459	+	0.897282i	$0.645539\pi$
$350$	−442.633	−	154.884i	−1.26466	−	0.442525i
$351$		0			0
$352$	180.211	+	143.714i	0.511964	+	0.408277i
$353$	−48.7910	−	101.316i	−0.138218	−	0.287013i	0.820358	−	0.571851i	$-0.193774\pi$
$353$	−48.7910	−	101.316i	−0.138218	−	0.287013i	−0.958576	+	0.284838i	$0.908060\pi$
$354$		0			0
$355$	−97.9212	−	122.789i	−0.275834	−	0.345885i
$356$	23.0312	+	36.6540i	0.0646945	+	0.102961i
$357$		0			0
$358$	−88.8599	−	788.653i	−0.248212	−	2.20294i
$359$	38.4941	−	61.2630i	0.107226	−	0.170649i	−0.788801	−	0.614648i	$-0.789298\pi$
$359$	38.4941	−	61.2630i	0.107226	−	0.170649i	0.896027	+	0.443999i	$0.146441\pi$
$360$		0			0
$361$	729.968	−	166.610i	2.02207	−	0.461525i
$362$	−242.055	−	691.754i	−0.668661	−	1.91092i
$363$		0			0
$364$	−12.2443	−	53.6457i	−0.0336381	−	0.147378i
$365$	197.340	+	197.340i	0.540657	+	0.540657i
$366$		0			0
$367$	39.4991	−	4.45048i	0.107627	−	0.0121267i	−0.0579866	−	0.998317i	$-0.518468\pi$
$367$	39.4991	−	4.45048i	0.107627	−	0.0121267i	0.165614	+	0.986191i	$0.447040\pi$
$368$	100.930	−	442.203i	0.274266	−	1.20164i
$369$		0			0
$370$	−276.453	+	220.464i	−0.747171	+	0.595849i
$371$	281.023	+	135.334i	0.757475	+	0.364781i
$372$		0			0
$373$	−312.636	+	392.033i	−0.838165	+	1.05103i	0.159793	+	0.987151i	$0.448917\pi$
$373$	−312.636	+	392.033i	−0.838165	+	1.05103i	−0.997958	+	0.0638753i	$0.979654\pi$
$374$	42.3220	+	4.76854i	0.113160	+	0.0127501i
$375$		0			0
$376$			338.539i			0.900369i
$377$	145.400	+	157.171i	0.385677	+	0.416900i
$378$		0			0
$379$	−296.798	−	103.854i	−0.783109	−	0.274022i	−0.0910346	−	0.995848i	$-0.529017\pi$
$379$	−296.798	−	103.854i	−0.783109	−	0.274022i	−0.692075	+	0.721826i	$0.743303\pi$
$380$	−68.4044	+	607.106i	−0.180012	+	1.59765i
$381$		0			0
$382$	290.010	+	602.212i	0.759189	+	1.57647i
$383$	−184.851	+	383.847i	−0.482639	+	1.00221i	0.507438	+	0.861688i	$0.330593\pi$
$383$	−184.851	+	383.847i	−0.482639	+	1.00221i	−0.990077	+	0.140522i	$0.955122\pi$
$384$		0			0
$385$	−128.208	−	204.041i	−0.333007	−	0.529977i
$386$	326.232	+	74.4604i	0.845161	+	0.192903i
$387$		0			0
$388$	−57.8505	+	92.0686i	−0.149099	+	0.237290i
$389$	−11.1950	+	11.1950i	−0.0287790	+	0.0287790i	−0.721350	−	0.692571i	$-0.756478\pi$
$389$	−11.1950	+	11.1950i	−0.0287790	+	0.0287790i	0.692571	+	0.721350i	$0.256478\pi$
$390$		0			0
$391$	−17.0284	−	48.6645i	−0.0435510	−	0.124462i
$392$	−161.646	+	56.5623i	−0.412362	+	0.144292i
$393$		0			0
$394$	199.076	+	199.076i	0.505268	+	0.505268i
$395$	−335.985	−	211.114i	−0.850596	−	0.534465i
$396$		0			0
$397$	56.3270	−	246.785i	0.141882	−	0.621624i	−0.853116	−	0.521722i	$-0.825290\pi$
$397$	56.3270	−	246.785i	0.141882	−	0.621624i	0.994997	−	0.0999023i	$-0.0318530\pi$
$398$	−167.613	+	105.318i	−0.421137	+	0.264618i
$399$		0			0
$400$	954.829	+	459.821i	2.38707	+	1.14955i
$401$	400.299	−	192.774i	0.998253	−	0.480733i	0.137908	−	0.990445i	$-0.455962\pi$
$401$	400.299	−	192.774i	0.998253	−	0.480733i	0.860345	+	0.509712i	$0.170248\pi$
$402$		0			0
$403$	−41.2730	−	4.65035i	−0.102414	−	0.0115393i
$404$	−28.1188	+	80.3589i	−0.0696010	+	0.198908i
$405$		0			0
$406$	167.648	−	194.226i	0.412925	−	0.478390i
$407$	−123.467			−0.303360
$408$		0			0
$409$	−60.3508	+	535.628i	−0.147557	+	1.30960i	0.673683	+	0.739021i	$0.264711\pi$
$409$	−60.3508	+	535.628i	−0.147557	+	1.30960i	−0.821240	+	0.570583i	$0.806717\pi$
$410$	1013.67	+	808.372i	2.47236	+	1.97164i
$411$		0			0
$412$	73.3670	−	152.348i	0.178075	−	0.369777i
$413$	−152.067	−	190.686i	−0.368201	−	0.461709i
$414$		0			0
$415$	−53.4705	−	12.2043i	−0.128845	−	0.0294080i
$416$	25.0647	+	222.455i	0.0602516	+	0.534748i
$417$		0			0
$418$	−441.421	+	441.421i	−1.05603	+	1.05603i
$419$	428.228	−	97.7402i	1.02202	−	0.233270i	0.321508	−	0.946907i	$-0.395810\pi$
$419$	428.228	−	97.7402i	1.02202	−	0.233270i	0.700516	+	0.713637i	$0.252953\pi$
$420$		0			0
$421$	736.985	−	257.882i	1.75056	−	0.612547i	0.751664	−	0.659546i	$-0.229251\pi$
$421$	736.985	−	257.882i	1.75056	−	0.612547i	0.998895	+	0.0469987i	$0.0149657\pi$
$422$	−35.2120	−	154.274i	−0.0834407	−	0.365577i
$423$		0			0
$424$	−348.905	−	219.231i	−0.822888	−	0.517055i
$425$	119.707	−	13.4878i	0.281664	−	0.0317360i
$426$		0			0
$427$	155.405	−	97.6477i	0.363947	−	0.228683i
$428$	−25.3688	+	20.2309i	−0.0592729	+	0.0472685i
$429$		0			0
$430$	−103.626	+	49.9036i	−0.240990	+	0.116055i
$431$	−476.007	+	596.893i	−1.10442	+	1.38490i	−0.189209	+	0.981937i	$0.560592\pi$
$431$	−476.007	+	596.893i	−1.10442	+	1.38490i	−0.915215	+	0.402967i	$0.867979\pi$
$432$		0			0
$433$	−91.9842	+	262.876i	−0.212435	+	0.607104i	−0.999958	−	0.00918154i	$-0.997077\pi$
$433$	−91.9842	+	262.876i	−0.212435	+	0.607104i	0.787523	+	0.616285i	$0.211363\pi$
$434$			49.7707i			0.114679i
$435$		0			0
$436$	−65.9032			−0.151154
$437$	713.304	+	249.596i	1.63228	+	0.571158i
$438$		0			0
$439$	−116.941	−	93.2577i	−0.266382	−	0.212432i	0.481185	−	0.876619i	$-0.340207\pi$
$439$	−116.941	−	93.2577i	−0.266382	−	0.212432i	−0.747567	+	0.664187i	$0.768778\pi$
$440$	138.128	+	286.826i	0.313927	+	0.651876i
$441$		0			0
$442$	25.7898	+	32.3394i	0.0583479	+	0.0731660i
$443$	391.882	+	623.676i	0.884609	+	1.40785i	0.912872	+	0.408246i	$0.133859\pi$
$443$	391.882	+	623.676i	0.884609	+	1.40785i	−0.0282635	+	0.999601i	$0.508998\pi$
$444$		0			0
$445$	20.6151	+	182.964i	0.0463261	+	0.411156i
$446$	−277.379	+	441.446i	−0.621926	+	0.989790i
$447$		0			0
$448$	−18.3162	+	4.18055i	−0.0408843	+	0.00933158i
$449$	24.4486	+	69.8700i	0.0544511	+	0.155612i	0.967897	−	0.251349i	$-0.0808741\pi$
$449$	24.4486	+	69.8700i	0.0544511	+	0.155612i	−0.913445	+	0.406961i	$0.866588\pi$
$450$		0			0
$451$	100.739	+	441.365i	0.223367	+	0.978637i
$452$	−118.498	−	118.498i	−0.262165	−	0.262165i
$453$		0			0
$454$	−752.089	+	84.7401i	−1.65658	+	0.186652i
$455$	52.0787	−	228.172i	0.114459	−	0.501476i
$456$		0			0
$457$	617.662	−	492.569i	1.35156	−	1.07783i	0.362237	−	0.932086i	$-0.382013\pi$
$457$	617.662	−	492.569i	1.35156	−	1.07783i	0.989322	−	0.145746i	$-0.0465582\pi$
$458$	191.692	+	92.3139i	0.418541	+	0.201559i
$459$		0			0
$460$	−259.399	+	325.276i	−0.563911	+	0.707122i
$461$	−444.021	−	50.0291i	−0.963169	−	0.108523i	−0.383647	−	0.923480i	$-0.625332\pi$
$461$	−444.021	−	50.0291i	−0.963169	−	0.108523i	−0.579522	+	0.814957i	$0.696761\pi$
$462$		0			0
$463$		−	515.055i		−	1.11243i	−0.831039	−	0.556215i	$-0.812253\pi$
$463$		−	515.055i		−	1.11243i	0.831039	−	0.556215i	$-0.187747\pi$
$464$	−425.630	+	393.754i	−0.917307	+	0.848607i
$465$		0			0
$466$	330.160	+	115.528i	0.708498	+	0.247914i
$467$	−62.2491	+	552.476i	−0.133296	+	1.18303i	0.731834	+	0.681483i	$0.238665\pi$
$467$	−62.2491	+	552.476i	−0.133296	+	1.18303i	−0.865129	+	0.501549i	$0.832764\pi$
$468$		0			0
$469$	−47.0636	−	97.7286i	−0.100349	−	0.208376i
$470$	674.452	−	1400.51i	1.43500	−	2.97982i
$471$		0			0
$472$	171.426	+	272.822i	0.363190	+	0.578013i
$473$	−39.1539	−	8.93661i	−0.0827777	−	0.0188935i
$474$		0			0
$475$	−939.423	+	1495.08i	−1.97773	+	3.14754i
$476$	11.9771	−	11.9771i	0.0251619	−	0.0251619i
$477$		0			0
$478$	−113.048	−	323.074i	−0.236503	−	0.675886i
$479$	−47.7444	+	16.7065i	−0.0996752	+	0.0348779i	−0.379656	−	0.925128i	$-0.623958\pi$
$479$	−47.7444	+	16.7065i	−0.0996752	+	0.0348779i	0.279981	+	0.960006i	$0.409672\pi$
$480$		0			0
$481$	−84.7912	−	84.7912i	−0.176281	−	0.176281i
$482$	−382.800	−	240.529i	−0.794190	−	0.499023i
$483$		0			0
$484$	−29.2067	+	127.963i	−0.0603444	+	0.264386i
$485$	−391.596	+	246.056i	−0.807414	+	0.507332i
$486$		0			0
$487$	565.353	+	272.260i	1.16089	+	0.559055i	0.912288	−	0.409550i	$-0.134314\pi$
$487$	565.353	+	272.260i	1.16089	+	0.559055i	0.248603	+	0.968606i	$0.420029\pi$
$488$	−218.457	+	105.203i	−0.447658	+	0.215581i
$489$		0			0
$490$	781.404	+	88.0431i	1.59470	+	0.179680i
$491$	213.075	−	608.934i	0.433962	−	1.24019i	−0.494634	−	0.869101i	$-0.664698\pi$
$491$	213.075	−	608.934i	0.433962	−	1.24019i	0.928596	−	0.371091i	$-0.121016\pi$
$492$		0			0
$493$	−17.1530	+	63.6380i	−0.0347931	+	0.129083i
$494$	−606.291			−1.22731
$495$		0			0
$496$	12.5934	−	111.770i	0.0253900	−	0.225342i
$497$	−49.8983	−	39.7926i	−0.100399	−	0.0800655i
$498$		0			0
$499$	59.2142	−	122.960i	0.118666	−	0.246412i	−0.833172	−	0.553014i	$-0.813478\pi$
$499$	59.2142	−	122.960i	0.118666	−	0.246412i	0.951838	+	0.306602i	$0.0991920\pi$
$500$	−320.221	−	401.545i	−0.640443	−	0.803090i
$501$		0			0
$502$	612.902	+	139.891i	1.22092	+	0.278667i
$503$	−0.982486	−	8.71980i	−0.00195325	−	0.0173356i	0.992698	−	0.120628i	$-0.0384908\pi$
$503$	−0.982486	−	8.71980i	−0.00195325	−	0.0173356i	−0.994651	+	0.103292i	$0.967062\pi$
$504$		0			0
$505$	−256.052	+	256.052i	−0.507033	+	0.507033i
$506$	−414.454	+	94.5963i	−0.819078	+	0.186949i
$507$		0			0
$508$	−174.998	+	61.2345i	−0.344484	+	0.120540i
$509$	29.4818	+	129.168i	0.0579210	+	0.253768i	0.995596	−	0.0937442i	$-0.0298836\pi$
$509$	29.4818	+	129.168i	0.0579210	+	0.253768i	−0.937675	+	0.347512i	$0.887026\pi$
$510$		0			0
$511$	96.0279	+	60.3383i	0.187922	+	0.118079i
$512$	−225.597	+	25.4186i	−0.440619	+	0.0496458i
$513$		0			0
$514$	32.0447	−	20.1350i	0.0623437	−	0.0391732i
$515$	562.299	−	448.419i	1.09184	−	0.870716i
$516$		0			0
$517$	489.025	−	235.502i	0.945889	−	0.455516i
$518$	−89.5908	+	112.343i	−0.172955	+	0.216879i
$519$		0			0
$520$	−102.118	+	291.837i	−0.196381	+	0.561224i
$521$		−	754.287i		−	1.44777i	−0.689921	−	0.723884i	$-0.742355\pi$
$521$		−	754.287i		−	1.44777i	0.689921	−	0.723884i	$-0.257645\pi$
$522$		0			0
$523$	−645.744			−1.23469			−0.617346	−	0.786692i	$-0.711792\pi$
$523$	−645.744			−1.23469			−0.617346	+	0.786692i	$0.711792\pi$
$524$	254.252	+	88.9667i	0.485214	+	0.169784i
$525$		0			0
$526$	−430.148	−	343.031i	−0.817771	−	0.652151i
$527$	−5.54731	−	11.5191i	−0.0105262	−	0.0218579i
$528$		0			0
$529$	−8.96189	−	11.2379i	−0.0169412	−	0.0212436i
$530$	1006.63	+	1602.05i	1.89931	+	3.02273i
$531$		0			0
$532$	27.7977	+	246.712i	0.0522514	+	0.463744i
$533$	−233.925	+	372.290i	−0.438884	+	0.698480i
$534$		0			0
$535$	−134.551	+	30.7103i	−0.251496	+	0.0574024i
$536$	47.3288	+	135.258i	0.0883000	+	0.252347i
$537$		0			0
$538$	−213.310	−	934.573i	−0.396487	−	1.73712i
$539$	194.153	+	194.153i	0.360209	+	0.360209i
$540$		0			0
$541$	447.985	−	50.4757i	0.828068	−	0.0933008i	0.312251	−	0.950000i	$-0.398917\pi$
$541$	447.985	−	50.4757i	0.828068	−	0.0933008i	0.515817	+	0.856699i	$0.327488\pi$
$542$	−212.851	+	932.561i	−0.392714	+	1.72059i
$543$		0			0
$544$	−53.8764	+	42.9650i	−0.0990376	+	0.0789798i
$545$	−252.547	−	121.620i	−0.463390	−	0.223157i
$546$		0			0
$547$	−506.301	+	634.881i	−0.925596	+	1.16066i	0.0611077	+	0.998131i	$0.480537\pi$
$547$	−506.301	+	634.881i	−0.925596	+	1.16066i	−0.986704	+	0.162530i	$0.948035\pi$
$548$	255.280	+	28.7631i	0.465839	+	0.0524875i
$549$		0			0
$550$		−	993.277i		−	1.80596i
$551$	−572.518	−	778.148i	−1.03905	−	1.41225i
$552$		0			0
$553$	−152.203	−	53.2580i	−0.275231	−	0.0963075i
$554$	91.7276	−	814.105i	0.165573	−	1.46950i
$555$		0			0
$556$	40.2934	+	83.6702i	0.0724702	+	0.150486i
$557$	293.291	−	609.025i	0.526554	−	1.09340i	−0.452868	−	0.891578i	$-0.649599\pi$
$557$	293.291	−	609.025i	0.526554	−	1.09340i	0.979422	−	0.201824i	$-0.0646867\pi$
$558$		0			0
$559$	−20.7517	−	33.0261i	−0.0371229	−	0.0590807i
$560$	617.903	+	141.032i	1.10340	+	0.251844i
$561$		0			0
$562$	3.79699	−	6.04288i	0.00675622	−	0.0107525i
$563$	−429.885	+	429.885i	−0.763562	+	0.763562i	−0.976964	−	0.213403i	$-0.931545\pi$
$563$	−429.885	+	429.885i	−0.763562	+	0.763562i	0.213403	+	0.976964i	$0.431545\pi$
$564$		0			0
$565$	−235.416	−	672.779i	−0.416665	−	1.19076i
$566$	818.558	−	286.426i	1.44622	−	0.506053i
$567$		0			0
$568$	59.6197	+	59.6197i	0.104964	+	0.104964i
$569$	−630.677	−	396.281i	−1.10840	−	0.696451i	−0.151958	−	0.988387i	$-0.548558\pi$
$569$	−630.677	−	396.281i	−1.10840	−	0.696451i	−0.956438	+	0.291936i	$0.905701\pi$
$570$		0			0
$571$	30.9764	−	135.717i	0.0542495	−	0.237682i	−0.940533	−	0.339703i	$-0.889674\pi$
$571$	30.9764	−	135.717i	0.0542495	−	0.237682i	0.994782	+	0.102020i	$0.0325307\pi$
$572$	98.6846	−	62.0076i	0.172526	−	0.108405i
$573$		0			0
$574$	474.698	+	228.602i	0.827000	+	0.398262i
$575$	−1083.35	+	521.714i	−1.88409	+	0.907328i
$576$		0			0
$577$	−751.398	−	84.6622i	−1.30225	−	0.146728i	−0.566545	−	0.824031i	$-0.691720\pi$
$577$	−751.398	−	84.6622i	−1.30225	−	0.146728i	−0.735705	+	0.677302i	$0.763149\pi$
$578$	231.086	−	660.406i	0.399803	−	1.14257i
$579$		0			0
$580$	508.456	−	156.012i	0.876648	−	0.268986i
$581$	−22.2878			−0.0383611
$582$		0			0
$583$	−73.9703	+	656.505i	−0.126879	+	1.12608i
$584$	−117.139	−	93.4151i	−0.200580	−	0.159957i
$585$		0			0
$586$	99.4990	−	206.612i	0.169794	−	0.352580i
$587$	481.461	+	603.732i	0.820205	+	1.02850i	0.999004	+	0.0446193i	$0.0142075\pi$
$587$	481.461	+	603.732i	0.820205	+	1.02850i	−0.178799	+	0.983886i	$0.557221\pi$
$588$		0			0
$589$	182.702	+	41.7006i	0.310191	+	0.0707990i
$590$	−165.648	−	1470.17i	−0.280760	−	2.49181i
$591$		0			0
$592$	229.620	−	229.620i	0.387872	−	0.387872i
$593$	636.417	−	145.258i	1.07322	−	0.244954i	0.350826	−	0.936441i	$-0.385901\pi$
$593$	636.417	−	145.258i	1.07322	−	0.244954i	0.722390	+	0.691486i	$0.243044\pi$
$594$		0			0
$595$	68.0004	−	23.7944i	0.114286	−	0.0399905i
$596$	54.7460	+	239.858i	0.0918557	+	0.402446i
$597$		0			0
$598$	−349.590	−	219.662i	−0.584598	−	0.367327i
$599$	106.941	−	12.0494i	0.178533	−	0.0201158i	−0.0222453	−	0.999753i	$-0.507081\pi$
$599$	106.941	−	12.0494i	0.178533	−	0.0201158i	0.200778	+	0.979637i	$0.435653\pi$
$600$		0			0
$601$	561.034	−	352.521i	0.933500	−	0.586557i	0.0228515	−	0.999739i	$-0.492726\pi$
$601$	561.034	−	352.521i	0.933500	−	0.586557i	0.910649	+	0.413182i	$0.135583\pi$
$602$	−36.5424	+	29.1416i	−0.0607017	+	0.0484080i
$603$		0			0
$604$	−342.035	+	164.715i	−0.566283	+	0.272708i
$605$	−348.071	+	436.467i	−0.575323	+	0.721433i
$606$		0			0
$607$	−170.406	+	486.993i	−0.280735	+	0.802294i	0.714031	+	0.700114i	$0.246868\pi$
$607$	−170.406	+	486.993i	−0.280735	+	0.802294i	−0.994766	+	0.102180i	$0.967418\pi$
$608$		−	1010.06i		−	1.66129i
$609$		0			0
$610$	1113.33			1.82514
$611$	497.568	+	174.107i	0.814351	+	0.284954i
$612$		0			0
$613$	437.145	+	348.611i	0.713124	+	0.568697i	0.911436	−	0.411442i	$-0.134975\pi$
$613$	437.145	+	348.611i	0.713124	+	0.568697i	−0.198313	+	0.980139i	$0.563546\pi$
$614$	−49.3275	−	102.430i	−0.0803380	−	0.166824i
$615$		0			0
$616$	80.6609	+	101.146i	0.130943	+	0.164197i
$617$	−365.703	−	582.013i	−0.592711	−	0.943295i	−0.999556	−	0.0297975i	$-0.990514\pi$
$617$	−365.703	−	582.013i	−0.592711	−	0.943295i	0.406844	−	0.913497i	$-0.366629\pi$
$618$		0			0
$619$	−113.508	−	1007.42i	−0.183374	−	1.62749i	−0.662024	−	0.749483i	$-0.730302\pi$
$619$	−113.508	−	1007.42i	−0.183374	−	1.62749i	0.478650	−	0.878006i	$-0.341126\pi$
$620$	−54.8898	+	87.3567i	−0.0885320	+	0.140898i
$621$		0			0
$622$	−158.369	+	36.1467i	−0.254612	+	0.0581136i
$623$	24.7123	+	70.6236i	0.0396665	+	0.113360i
$624$		0			0
$625$	−191.227	−	837.819i	−0.305963	−	1.34051i
$626$	−280.980	−	280.980i	−0.448850	−	0.448850i
$627$		0			0
$628$	−228.669	+	25.7648i	−0.364123	+	0.0410268i
$629$	8.21373	−	35.9867i	0.0130584	−	0.0572126i
$630$		0			0
$631$	−402.770	+	321.198i	−0.638304	+	0.509030i	−0.888328	−	0.459209i	$-0.848133\pi$
$631$	−402.770	+	321.198i	−0.638304	+	0.509030i	0.250025	+	0.968240i	$0.419561\pi$
$632$	191.931	+	92.4293i	0.303689	+	0.146249i
$633$		0			0
$634$	−431.754	+	541.403i	−0.681001	+	0.853948i
$635$	−783.614	−	88.2921i	−1.23404	−	0.139043i
$636$		0			0
$637$			266.669i			0.418632i
$638$	505.583	+	199.293i	0.792450	+	0.312372i
$639$		0			0
$640$	−1118.63	−	391.424i	−1.74785	−	0.611600i
$641$	−44.9011	+	398.508i	−0.0700485	+	0.621698i	0.908817	+	0.417194i	$0.136987\pi$
$641$	−44.9011	+	398.508i	−0.0700485	+	0.621698i	−0.978866	+	0.204504i	$0.934442\pi$
$642$		0			0
$643$	−470.130	−	976.234i	−0.731150	−	1.51825i	−0.850833	−	0.525437i	$-0.823902\pi$
$643$	−470.130	−	976.234i	−0.731150	−	1.51825i	0.119683	−	0.992812i	$-0.461812\pi$
$644$	−73.3564	+	152.326i	−0.113907	+	0.236531i
$645$		0			0
$646$	−99.2940	−	158.026i	−0.153706	−	0.244622i
$647$	625.852	+	142.847i	0.967313	+	0.220783i	0.676865	−	0.736108i	$-0.263338\pi$
$647$	625.852	+	142.847i	0.967313	+	0.220783i	0.290449	+	0.956891i	$0.406195\pi$
$648$		0			0
$649$	274.845	−	437.414i	0.423491	−	0.673981i
$650$	682.132	−	682.132i	1.04943	−	1.04943i
$651$		0			0
$652$	−10.4008	−	29.7237i	−0.0159521	−	0.0455885i
$653$	459.623	−	160.829i	0.703863	−	0.246292i	0.0454690	−	0.998966i	$-0.485522\pi$
$653$	459.623	−	160.829i	0.703863	−	0.246292i	0.658394	+	0.752673i	$0.271236\pi$
$654$		0			0
$655$	810.136	+	810.136i	1.23685	+	1.23685i
$656$	−1008.18	−	633.484i	−1.53687	−	0.965677i
$657$		0			0
$658$	140.564	−	615.851i	0.213623	−	0.935943i
$659$	−782.367	+	491.594i	−1.18720	+	0.745969i	−0.972997	−	0.230820i	$-0.925859\pi$
$659$	−782.367	+	491.594i	−1.18720	+	0.745969i	−0.214206	+	0.976788i	$0.568716\pi$
$660$		0			0
$661$	−504.495	−	242.952i	−0.763229	−	0.367552i	0.0114268	−	0.999935i	$-0.496363\pi$
$661$	−504.495	−	242.952i	−0.763229	−	0.367552i	−0.774656	+	0.632383i	$0.782077\pi$
$662$	−111.045	+	53.4767i	−0.167742	+	0.0807805i
$663$		0			0
$664$	29.2591	+	3.29671i	0.0440649	+	0.00496492i
$665$	−348.768	+	996.722i	−0.524463	+	1.49883i
$666$		0			0
$667$	−48.1895	−	656.109i	−0.0722482	−	0.983671i
$668$	−544.929			−0.815762
$669$		0			0
$670$	73.6705	−	653.844i	0.109956	−	0.975886i
$671$	303.936	+	242.381i	0.452960	+	0.361224i
$672$		0			0
$673$	−326.415	+	677.808i	−0.485015	+	1.00714i	0.504594	+	0.863357i	$0.331642\pi$
$673$	−326.415	+	677.808i	−0.485015	+	1.00714i	−0.989609	+	0.143787i	$0.954072\pi$
$674$	−423.344	−	530.857i	−0.628107	−	0.787621i
$675$		0			0
$676$	−231.776	−	52.9013i	−0.342863	−	0.0782563i
$677$	−34.5918	−	307.011i	−0.0510957	−	0.453487i	−0.993045	−	0.117733i	$-0.962437\pi$
$677$	−34.5918	−	307.011i	−0.0510957	−	0.453487i	0.941950	−	0.335754i	$-0.108991\pi$
$678$		0			0
$679$	−132.894	+	132.894i	−0.195721	+	0.195721i
$680$	−92.7893	+	21.1785i	−0.136455	+	0.0311449i
$681$		0			0
$682$	−99.5032	+	34.8177i	−0.145899	+	0.0510523i
$683$	39.2932	+	172.155i	0.0575304	+	0.252057i	0.995513	−	0.0946254i	$-0.0301653\pi$
$683$	39.2932	+	172.155i	0.0575304	+	0.252057i	−0.937983	+	0.346682i	$0.887308\pi$
$684$		0			0
$685$	925.177	+	581.327i	1.35062	+	0.848653i
$686$	748.335	−	84.3171i	1.09087	−	0.122911i
$687$		0			0
$688$	89.4368	−	56.1969i	0.129995	−	0.0816815i
$689$	−501.653	+	400.055i	−0.728089	+	0.580632i
$690$		0			0
$691$	−1218.08	+	586.597i	−1.76278	+	0.848910i	−0.791430	+	0.611260i	$0.790663\pi$
$691$	−1218.08	+	586.597i	−1.76278	+	0.848910i	−0.971351	+	0.237651i	$0.923623\pi$
$692$	−80.1593	+	100.517i	−0.115837	+	0.145255i
$693$		0			0
$694$	412.606	−	1179.16i	0.594533	−	1.69908i
$695$			394.991i			0.568333i
$696$		0			0
$697$	−135.345			−0.194182
$698$	−716.953	−	250.873i	−1.02715	−	0.359417i
$699$		0			0
$700$	−308.848	−	246.298i	−0.441211	−	0.351854i
$701$	358.817	+	745.091i	0.511865	+	1.06290i	0.983467	+	0.181087i	$0.0579615\pi$
$701$	358.817	+	745.091i	0.511865	+	1.06290i	−0.471602	+	0.881811i	$0.656324\pi$
$702$		0			0
$703$	337.335	+	423.005i	0.479851	+	0.601714i
$704$	−21.1712	−	33.6938i	−0.0300727	−	0.0478605i
$705$		0			0
$706$	−31.0366	−	275.457i	−0.0439611	−	0.390166i
$707$	−78.2899	+	124.598i	−0.110735	+	0.176234i
$708$		0			0
$709$	−149.080	+	34.0265i	−0.210268	+	0.0479923i	−0.326357	−	0.945246i	$-0.605821\pi$
$709$	−149.080	+	34.0265i	−0.210268	+	0.0479923i	0.116089	+	0.993239i	$0.462964\pi$
$710$	−127.866	−	365.420i	−0.180093	−	0.514676i
$711$		0			0
$712$	−21.9955	−	96.3688i	−0.0308926	−	0.135349i
$713$	90.2386	+	90.2386i	0.126562	+	0.126562i
$714$		0			0
$715$	492.600	−	55.5027i	0.688952	−	0.0776262i
$716$	148.766	−	651.785i	0.207773	−	0.910314i
$717$		0			0
$718$	139.443	−	111.202i	0.194210	−	0.154877i
$719$	−188.055	−	90.5627i	−0.261551	−	0.125957i	0.298513	−	0.954406i	$-0.403509\pi$
$719$	−188.055	−	90.5627i	−0.261551	−	0.125957i	−0.560064	+	0.828449i	$0.689224\pi$
$720$		0			0
$721$	182.226	−	228.504i	0.252740	−	0.316926i
$722$	1834.08	+	206.651i	2.54028	+	0.286221i
$723$		0			0
$724$		−	617.362i		−	0.852710i
$725$	1519.62	+	231.353i	2.09603	+	0.319107i
$726$		0			0
$727$	1244.50	+	435.470i	1.71183	+	0.598996i	0.995147	−	0.0984004i	$-0.0313726\pi$
$727$	1244.50	+	435.470i	1.71183	+	0.598996i	0.716686	+	0.697396i	$0.245658\pi$
$728$	−14.0678	+	124.855i	−0.0193239	+	0.171505i
$729$		0			0
$730$	298.490	+	619.822i	0.408891	+	0.849071i
$731$	5.20946	−	10.8176i	0.00712648	−	0.0147983i
$732$		0			0
$733$	63.1015	+	100.425i	0.0860866	+	0.137006i	0.886992	−	0.461785i	$-0.152791\pi$
$733$	63.1015	+	100.425i	0.0860866	+	0.137006i	−0.800905	+	0.598791i	$0.795648\pi$
$734$	95.5271	+	21.8034i	0.130146	+	0.0297050i
$735$		0			0
$736$	365.950	−	582.406i	0.497215	−	0.791313i
$737$	162.458	−	162.458i	0.220432	−	0.220432i
$738$		0			0
$739$	235.151	+	672.023i	0.318202	+	0.909369i	0.986251	+	0.165252i	$0.0528437\pi$
$739$	235.151	+	672.023i	0.318202	+	0.909369i	−0.668050	+	0.744117i	$0.732871\pi$
$740$	−281.147	+	98.3776i	−0.379928	+	0.132943i
$741$		0			0
$742$	543.681	+	543.681i	0.732724	+	0.732724i
$743$	1147.96	+	721.309i	1.54503	+	0.970806i	0.990326	+	0.138757i	$0.0443107\pi$
$743$	1147.96	+	721.309i	1.54503	+	0.970806i	0.554702	+	0.832049i	$0.312832\pi$
$744$		0			0
$745$	−232.852	+	1020.19i	−0.312552	+	1.36938i
$746$	−1046.59	+	657.618i	−1.40294	+	0.881526i
$747$		0			0
$748$	32.3237	+	15.5663i	0.0432135	+	0.0208105i
$749$	−50.5299	+	24.3339i	−0.0674632	+	0.0324885i
$750$		0			0
$751$	601.896	+	67.8174i	0.801460	+	0.0903028i	0.503187	−	0.864178i	$-0.332161\pi$
$751$	601.896	+	67.8174i	0.801460	+	0.0903028i	0.298273	+	0.954481i	$0.403589\pi$
$752$	−471.492	+	1347.45i	−0.626984	+	1.79182i
$753$		0			0
$754$	210.345	+	484.074i	0.278972	+	0.642007i
$755$	−1614.68			−2.13866
$756$		0			0
$757$	−84.2696	+	747.913i	−0.111320	+	0.987997i	0.806563	+	0.591148i	$0.201325\pi$
$757$	−84.2696	+	747.913i	−0.111320	+	0.987997i	−0.917884	+	0.396849i	$0.870104\pi$
$758$	−606.015	−	483.281i	−0.799492	−	0.637574i
$759$		0			0
$760$	605.287	−	1256.89i	0.796431	−	1.65381i
$761$	315.470	+	395.587i	0.414547	+	0.519825i	0.944638	−	0.328116i	$-0.106414\pi$
$761$	315.470	+	395.587i	0.414547	+	0.519825i	−0.530091	+	0.847941i	$0.677842\pi$
$762$		0			0
$763$	−111.053	−	25.3472i	−0.145548	−	0.0332204i
$764$	63.0415	+	559.509i	0.0825150	+	0.732341i
$765$		0			0
$766$	−742.608	+	742.608i	−0.969463	+	0.969463i
$767$	489.144	−	111.644i	0.637736	−	0.145559i
$768$		0			0
$769$	−331.756	+	116.087i	−0.431413	+	0.150958i	−0.537245	−	0.843426i	$-0.680535\pi$
$769$	−331.756	+	116.087i	−0.431413	+	0.150958i	0.105832	+	0.994384i	$0.466249\pi$
$770$	−132.182	−	579.129i	−0.171665	−	0.752115i
$771$		0			0
$772$	238.673	+	149.968i	0.309161	+	0.194259i
$773$	440.543	−	49.6373i	0.569914	−	0.0642139i	0.177695	−	0.984086i	$-0.443136\pi$
$773$	440.543	−	49.6373i	0.569914	−	0.0642139i	0.392219	+	0.919872i	$0.371707\pi$
$774$		0			0
$775$	−252.474	+	158.640i	−0.325772	+	0.204696i
$776$	194.119	−	154.804i	0.250153	−	0.199490i
$777$		0			0
$778$	−35.1623	+	16.9332i	−0.0451957	+	0.0217651i
$779$	1236.90	−	1551.03i	1.58781	−	1.99105i
$780$		0			0
$781$	44.6477	−	127.596i	0.0571673	−	0.163375i
$782$		−	127.093i		−	0.162523i
$783$		0			0
$784$	−722.156			−0.921117
$785$	−923.830	−	323.262i	−1.17685	−	0.411799i
$786$		0			0
$787$	−201.707	−	160.856i	−0.256298	−	0.204391i	0.486908	−	0.873453i	$-0.338125\pi$
$787$	−201.707	−	160.856i	−0.256298	−	0.204391i	−0.743206	+	0.669062i	$0.766696\pi$
$788$	102.899	+	213.673i	0.130583	+	0.271158i
$789$		0			0
$790$	−609.867	−	764.748i	−0.771983	−	0.968036i
$791$	−154.105	−	245.257i	−0.194823	−	0.310059i
$792$		0			0
$793$	42.2730	+	375.183i	0.0533077	+	0.473119i
$794$	331.979	−	528.342i	0.418110	−	0.665418i
$795$		0			0
$796$	−162.571	+	37.1058i	−0.204235	+	0.0466153i
$797$	−410.768	−	1173.91i	−0.515393	−	1.47291i	−0.848079	−	0.529870i	$-0.822241\pi$
$797$	−410.768	−	1173.91i	−0.515393	−	1.47291i	0.332686	−	0.943038i	$-0.392045\pi$
$798$		0			0
$799$	36.1085	+	158.202i	0.0451921	+	0.197999i
$800$	1136.41	+	1136.41i	1.42052	+	1.42052i
$801$		0			0
$802$	1088.34	−	122.626i	1.35703	−	0.152900i
$803$	−53.4529	+	234.193i	−0.0665665	+	0.291647i
$804$		0			0
$805$	−562.217	+	448.353i	−0.698407	+	0.556961i
$806$	−92.2448	−	44.4227i	−0.114448	−	0.0551151i
$807$		0			0
$808$	121.208	−	151.990i	0.150009	−	0.188106i
$809$	578.014	+	65.1265i	0.714480	+	0.0805025i	0.461719	−	0.887026i	$-0.347233\pi$
$809$	578.014	+	65.1265i	0.714480	+	0.0805025i	0.252761	+	0.967529i	$0.418661\pi$
$810$		0			0
$811$		−	316.853i		−	0.390694i	−0.980734	−	0.195347i	$-0.937417\pi$
$811$		−	316.853i		−	0.390694i	0.980734	−	0.195347i	$-0.0625833\pi$
$812$	187.335	−	107.787i	0.230708	−	0.132743i
$813$		0			0
$814$	−287.275	−	100.522i	−0.352918	−	0.123491i
$815$	14.9966	−	133.098i	0.0184007	−	0.163311i
$816$		0			0
$817$	76.3582	+	158.559i	0.0934617	+	0.194075i
$818$	−576.505	+	1197.12i	−0.704774	+	1.46348i
$819$		0			0
$820$	581.067	+	924.762i	0.708618	+	1.12776i
$821$	809.855	+	184.844i	0.986425	+	0.225145i	0.685158	−	0.728395i	$-0.259733\pi$
$821$	809.855	+	184.844i	0.986425	+	0.225145i	0.301267	+	0.953540i	$0.402590\pi$
$822$		0			0
$823$	158.294	−	251.923i	0.192337	−	0.306103i	−0.736608	−	0.676320i	$-0.763574\pi$
$823$	158.294	−	251.923i	0.192337	−	0.306103i	0.928945	+	0.370217i	$0.120717\pi$
$824$	−273.022	+	273.022i	−0.331337	+	0.331337i
$825$		0			0
$826$	−198.570	−	567.480i	−0.240399	−	0.687022i
$827$	−893.953	+	312.808i	−1.08096	+	0.378244i	−0.811251	−	0.584699i	$-0.801213\pi$
$827$	−893.953	+	312.808i	−1.08096	+	0.378244i	−0.269708	+	0.962942i	$0.586927\pi$
$828$		0			0
$829$	−1036.72	−	1036.72i	−1.25057	−	1.25057i	−0.955465	−	0.295104i	$-0.904646\pi$
$829$	−1036.72	−	1036.72i	−1.25057	−	1.25057i	−0.295104	−	0.955465i	$-0.595354\pi$
$830$	−114.475	−	71.9295i	−0.137922	−	0.0866620i
$831$		0			0
$832$	8.59987	−	37.6785i	0.0103364	−	0.0452866i
$833$	−69.5053	+	43.6731i	−0.0834397	+	0.0524286i
$834$		0			0
$835$	−2088.22	−	1005.63i	−2.50086	−	1.20435i
$836$	−473.788	+	228.164i	−0.566732	+	0.272924i
$837$		0			0
$838$	1075.94	+	121.230i	1.28394	+	0.144666i
$839$	−12.6413	+	36.1268i	−0.0150671	+	0.0430593i	−0.951171	−	0.308663i	$-0.900118\pi$
$839$	−12.6413	+	36.1268i	−0.0150671	+	0.0430593i	0.936104	+	0.351723i	$0.114404\pi$
$840$		0			0
$841$	−422.660	+	727.076i	−0.502568	+	0.864538i
$842$	1924.72			2.28589
$843$		0			0
$844$	14.9247	−	132.460i	0.0176833	−	0.156944i
$845$	−790.561	−	630.451i	−0.935575	−	0.746096i
$846$		0			0
$847$	−98.4321	+	204.396i	−0.116213	+	0.241318i
$848$	−1083.38	−	1358.51i	−1.27757	−	1.60202i
$849$		0			0
$850$	289.508	+	66.0782i	0.340597	+	0.0777391i
$851$	41.2523	+	366.124i	0.0484751	+	0.430228i
$852$		0			0
$853$	381.669	−	381.669i	0.447443	−	0.447443i	−0.447060	−	0.894504i	$-0.647529\pi$
$853$	381.669	−	381.669i	0.447443	−	0.447443i	0.894504	+	0.447060i	$0.147529\pi$
$854$	441.086	−	100.675i	0.516495	−	0.117887i
$855$		0			0
$856$	69.9342	−	24.4710i	0.0816988	−	0.0285876i
$857$	209.189	+	916.515i	0.244094	+	1.06945i	0.937250	+	0.348658i	$0.113363\pi$
$857$	209.189	+	916.515i	0.244094	+	1.06945i	−0.693156	+	0.720788i	$0.743780\pi$
$858$		0			0
$859$	−1335.81	−	839.347i	−1.55508	−	0.977121i	−0.988174	−	0.153338i	$-0.950998\pi$
$859$	−1335.81	−	839.347i	−1.55508	−	0.977121i	−0.566905	−	0.823783i	$-0.691859\pi$
$860$	−96.2776	+	10.8479i	−0.111951	+	0.0126138i
$861$		0			0
$862$	−1593.50	+	1001.26i	−1.84861	+	1.16156i
$863$	−465.366	+	371.117i	−0.539243	+	0.430032i	−0.854863	−	0.518854i	$-0.826359\pi$
$863$	−465.366	+	371.117i	−0.539243	+	0.430032i	0.315620	+	0.948886i	$0.397787\pi$
$864$		0			0
$865$	−492.676	+	237.260i	−0.569567	+	0.274289i
$866$	−428.044	+	536.751i	−0.494277	+	0.619804i
$867$		0			0
$868$	−13.8472	+	39.5729i	−0.0159530	+	0.0455909i
$869$		−	341.546i		−	0.393033i
$870$		0			0
$871$	223.136			0.256184
$872$	142.040	+	49.7018i	0.162889	+	0.0569975i
$873$		0			0
$874$	1456.45	+	1161.48i	1.66642	+	1.32893i
$875$	−385.165	−	799.803i	−0.440188	−	0.914060i
$876$		0			0
$877$	146.391	+	183.569i	0.166923	+	0.209315i	0.858256	−	0.513221i	$-0.171548\pi$
$877$	146.391	+	183.569i	0.166923	+	0.209315i	−0.691334	+	0.722536i	$0.742976\pi$
$878$	−196.164	−	312.194i	−0.223422	−	0.355574i
$879$		0			0
$880$	150.305	+	1333.99i	0.170801	+	1.51590i
$881$	−342.549	+	545.164i	−0.388818	+	0.618801i	−0.982580	−	0.185840i	$-0.940499\pi$
$881$	−342.549	+	545.164i	−0.388818	+	0.618801i	0.593762	+	0.804641i	$0.297642\pi$
$882$		0			0
$883$	1021.02	−	233.042i	1.15631	−	0.263921i	0.398985	−	0.916957i	$-0.369362\pi$
$883$	1021.02	−	233.042i	1.15631	−	0.263921i	0.757326	+	0.653037i	$0.226505\pi$
$884$	11.5082	+	32.8884i	0.0130183	+	0.0372041i
$885$		0			0
$886$	404.031	+	1770.18i	0.456017	+	1.99794i
$887$	−613.993	−	613.993i	−0.692213	−	0.692213i	0.270506	−	0.962718i	$-0.412809\pi$
$887$	−613.993	−	613.993i	−0.692213	−	0.692213i	−0.962718	+	0.270506i	$0.912809\pi$
$888$		0			0
$889$	−318.440	+	35.8796i	−0.358200	+	0.0403595i
$890$	−100.996	+	442.492i	−0.113479	+	0.497182i
$891$		0			0
$892$	−343.364	+	273.824i	−0.384938	+	0.306977i
$893$	−2142.95	−	1031.99i	−2.39971	−	1.15564i
$894$		0			0
$895$	1772.91	−	2223.16i	1.98091	−	2.48398i
$896$	−478.578	−	53.9228i	−0.534127	−	0.0601817i
$897$		0			0
$898$			182.473i			0.203200i
$899$	−30.0916	−	160.340i	−0.0334723	−	0.178354i
$900$		0			0
$901$	−186.429	−	65.2342i	−0.206913	−	0.0724020i
$902$	−124.949	+	1108.95i	−0.138524	+	1.22944i
$903$		0			0
$904$	166.030	+	344.764i	0.183661	+	0.381376i
$905$	1139.30	−	2365.79i	1.25890	−	2.61413i
$906$		0			0
$907$	758.621	+	1207.34i	0.836407	+	1.33113i	0.941617	+	0.336685i	$0.109306\pi$
$907$	758.621	+	1207.34i	0.836407	+	1.33113i	−0.105210	+	0.994450i	$0.533552\pi$
$908$	−621.566	−	141.868i	−0.684545	−	0.156243i
$909$		0			0
$910$	306.940	−	488.493i	0.337297	−	0.536805i
$911$	−256.863	+	256.863i	−0.281957	+	0.281957i	−0.833889	−	0.551932i	$-0.813891\pi$
$911$	−256.863	+	256.863i	−0.281957	+	0.281957i	0.551932	+	0.833889i	$0.313891\pi$
$912$		0			0
$913$	−15.5917	−	44.5585i	−0.0170774	−	0.0488045i
$914$	1838.16	−	643.200i	2.01112	−	0.703720i
$915$		0			0
$916$	126.732	+	126.732i	0.138353	+	0.138353i
$917$	394.222	+	247.706i	0.429904	+	0.270126i
$918$		0			0
$919$	101.413	−	444.317i	0.110351	−	0.483479i	−0.889307	−	0.457311i	$-0.848812\pi$
$919$	101.413	−	444.317i	0.110351	−	0.483479i	0.999658	−	0.0261677i	$-0.00833038\pi$
$920$	804.388	−	505.430i	0.874335	−	0.549381i
$921$		0			0
$922$	−992.384	−	477.907i	−1.07634	−	0.518337i
$923$	118.288	−	56.9645i	0.128156	−	0.0617167i
$924$		0			0
$925$	−855.451	−	96.3862i	−0.924812	−	0.104201i
$926$	419.335	−	1198.39i	0.452846	−	1.29416i
$927$		0			0
$928$	−806.452	+	350.428i	−0.869022	+	0.377616i
$929$	−358.064			−0.385429			−0.192715	−	0.981255i	$-0.561729\pi$
$929$	−358.064			−0.385429			−0.192715	+	0.981255i	$0.561729\pi$
$930$		0			0
$931$	134.716	−	1195.64i	0.144700	−	1.28425i
$932$	230.370	+	183.714i	0.247178	+	0.197118i
$933$		0			0
$934$	−594.639	+	1234.78i	−0.636658	+	1.32203i
$935$	95.1409	+	119.303i	0.101755	+	0.127597i
$936$		0			0
$937$	1623.44	+	370.539i	1.73259	+	0.395452i	0.968373	−	0.249507i	$-0.0802685\pi$
$937$	1623.44	+	370.539i	1.73259	+	0.395452i	0.764217	+	0.644959i	$0.223126\pi$
$938$	−29.9377	−	265.705i	−0.0319166	−	0.283267i
$939$		0			0
$940$	925.910	−	925.910i	0.985011	−	0.985011i
$941$	−1055.19	+	240.841i	−1.12135	+	0.255941i	−0.742717	−	0.669605i	$-0.766463\pi$
$941$	−1055.19	+	240.841i	−1.12135	+	0.255941i	−0.378634	+	0.925546i	$0.623606\pi$
$942$		0			0
$943$	1275.14	−	446.192i	1.35222	−	0.473163i
$944$	302.339	+	1324.63i	0.320274	+	1.40321i
$945$		0			0
$946$	−83.8245	−	52.6704i	−0.0886094	−	0.0556770i
$947$	425.484	−	47.9406i	0.449297	−	0.0506236i	0.115583	−	0.993298i	$-0.463126\pi$
$947$	425.484	−	47.9406i	0.449297	−	0.0506236i	0.333714	+	0.942674i	$0.391698\pi$
$948$		0			0
$949$	−197.540	+	124.123i	−0.208156	+	0.130793i
$950$	−3403.01	+	2713.81i	−3.58212	+	2.85664i
$951$		0			0
$952$	−34.8466	+	16.7812i	−0.0366036	+	0.0176274i
$953$	385.015	−	482.793i	0.404003	−	0.506604i	−0.537660	−	0.843162i	$-0.680691\pi$
$953$	385.015	−	482.793i	0.404003	−	0.506604i	0.941663	+	0.336558i	$0.109263\pi$
$954$		0			0
$955$	−790.959	+	2260.43i	−0.828229	+	2.36694i
$956$		−	288.330i		−	0.301600i
$957$		0			0
$958$	−124.690			−0.130156
$959$	419.109	+	146.652i	0.437027	+	0.152922i
$960$		0			0
$961$	−726.598	−	579.443i	−0.756085	−	0.602958i
$962$	−128.253	−	266.319i	−0.133319	−	0.276839i
$963$		0			0
$964$	−237.446	−	297.748i	−0.246313	−	0.308867i
$965$	637.860	+	1015.15i	0.660994	+	1.05197i
$966$		0			0
$967$	68.8333	+	610.913i	0.0711823	+	0.631761i	0.977761	+	0.209723i	$0.0672563\pi$
$967$	68.8333	+	610.913i	0.0711823	+	0.631761i	−0.906578	+	0.422037i	$0.861315\pi$
$968$	159.453	−	253.769i	0.164725	−	0.262158i
$969$		0			0
$970$	−1111.46	+	253.684i	−1.14584	+	0.261530i
$971$	−15.0755	−	43.0834i	−0.0155258	−	0.0443701i	0.935860	−	0.352373i	$-0.114625\pi$
$971$	−15.0755	−	43.0834i	−0.0155258	−	0.0443701i	−0.951385	+	0.308003i	$0.900339\pi$
$972$		0			0
$973$	35.7177	+	156.490i	0.0367089	+	0.160832i
$974$	1093.76	+	1093.76i	1.12296	+	1.12296i
$975$		0			0
$976$	−1016.02	+	114.478i	−1.04100	+	0.117293i
$977$	−57.8695	+	253.543i	−0.0592318	+	0.259512i	−0.995870	−	0.0907855i	$-0.971062\pi$
$977$	−57.8695	+	253.543i	−0.0592318	+	0.259512i	0.936639	+	0.350297i	$0.113919\pi$
$978$		0			0
$979$	−123.905	+	98.8111i	−0.126563	+	0.100931i
$980$	596.803	+	287.405i	0.608983	+	0.293271i
$981$		0			0
$982$	991.536	−	1243.35i	1.00971	−	1.26614i
$983$	1059.25	+	119.349i	1.07757	+	0.121413i	0.632863	−	0.774263i	$-0.281879\pi$
$983$	1059.25	+	119.349i	1.07757	+	0.121413i	0.444706	+	0.895676i	$0.353308\pi$
$984$		0			0
$985$			1008.71i			1.02407i
$986$	−91.7216	+	134.103i	−0.0930239	+	0.136007i
$987$		0			0
$988$	−482.065	−	168.682i	−0.487920	−	0.170731i
$989$	−13.4183	+	119.091i	−0.0135676	+	0.120415i
$990$		0			0
$991$	−491.742	−	1021.11i	−0.496207	−	1.03039i	−0.987239	−	0.159244i	$-0.949094\pi$
$991$	−491.742	−	1021.11i	−0.496207	−	1.03039i	0.491032	−	0.871142i	$-0.336620\pi$
$992$	74.0070	−	153.677i	0.0746038	−	0.154916i
$993$		0			0
$994$	−83.7023	−	133.211i	−0.0842076	−	0.134016i
$995$	−691.465	−	157.822i	−0.694940	−	0.158615i
$996$		0			0
$997$	717.538	−	1141.96i	0.719697	−	1.14539i	−0.263819	−	0.964572i	$-0.584982\pi$
$997$	717.538	−	1141.96i	0.719697	−	1.14539i	0.983516	−	0.180820i	$-0.0578750\pi$
$998$	237.884	−	237.884i	0.238360	−	0.238360i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.3.s.a.37.4		48
3.2	odd	2		29.3.f.a.8.1	✓	48
29.11	odd	28	inner	261.3.s.a.127.4		48
87.11	even	28		29.3.f.a.11.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.3.f.a.8.1	✓	48	3.2	odd	2
29.3.f.a.11.1	yes	48	87.11	even	28
261.3.s.a.37.4		48	1.1	even	1	trivial
261.3.s.a.127.4		48	29.11	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)

\(f(q)\)	\(=\)	\(q+(2.32673 + 0.814157i) q^{2} +(1.62348 + 1.29468i) q^{4} +(3.83207 + 7.95737i) q^{5} +(2.23777 + 2.80607i) q^{7} +(-2.52264 - 4.01476i) q^{8} +O(q^{10})\)	\(q+(2.32673 + 0.814157i) q^{2} +(1.62348 + 1.29468i) q^{4} +(3.83207 + 7.95737i) q^{5} +(2.23777 + 2.80607i) q^{7} +(-2.52264 - 4.01476i) q^{8} +(2.43763 + 21.6345i) q^{10} +(-4.04453 + 6.43684i) q^{11} +(-7.19807 + 1.64291i) q^{13} +(2.92209 + 8.35085i) q^{14} +(-4.44912 - 19.4929i) q^{16} +(-1.60706 - 1.60706i) q^{17} +(33.1033 - 3.72985i) q^{19} +(-4.08097 + 17.8799i) q^{20} +(-14.6511 + 11.6839i) q^{22} +(20.4388 + 9.84282i) q^{23} +(-33.0478 + 41.4406i) q^{25} +(-18.0855 - 2.03775i) q^{26} +7.45278i q^{28} +(-14.4627 - 25.1362i) q^{29} +(5.30982 + 1.85799i) q^{31} +(3.39483 - 30.1300i) q^{32} +(-2.43079 - 5.04759i) q^{34} +(-13.7537 + 28.5598i) q^{35} +(8.64092 + 13.7519i) q^{37} +(80.0590 + 18.2729i) q^{38} +(22.2800 - 35.4584i) q^{40} +(42.1095 - 42.1095i) q^{41} +(1.74483 + 4.98643i) q^{43} +(-14.8999 + 5.21368i) q^{44} +(39.5419 + 39.5419i) q^{46} +(-60.4551 - 37.9864i) q^{47} +(8.03709 - 35.2128i) q^{49} +(-110.632 + 69.5148i) q^{50} +(-13.8130 - 6.65197i) q^{52} +(78.2991 - 37.7068i) q^{53} +(-66.7192 - 7.51745i) q^{55} +(5.62062 - 16.0628i) q^{56} +(-13.1859 - 70.2600i) q^{58} -67.9548 q^{59} +(5.72557 - 50.8159i) q^{61} +(10.8418 + 8.64605i) q^{62} +(-2.27117 + 4.71614i) q^{64} +(-40.6568 - 50.9820i) q^{65} +(-29.4645 - 6.72508i) q^{67} +(-0.528398 - 4.68966i) q^{68} +(-55.2532 + 55.2532i) q^{70} +(-17.3364 + 3.95693i) q^{71} +(29.8255 - 10.4364i) q^{73} +(8.90881 + 39.0321i) q^{74} +(58.5714 + 36.8029i) q^{76} +(-27.1129 + 3.05489i) q^{77} +(-38.0418 + 23.9032i) q^{79} +(138.063 - 110.101i) q^{80} +(132.261 - 63.6936i) q^{82} +(-3.87179 + 4.85507i) q^{83} +(6.62962 - 18.9464i) q^{85} +13.0226i q^{86} +36.0453 q^{88} +(19.6772 + 6.88537i) q^{89} +(-20.7177 - 16.5218i) q^{91} +(20.4387 + 42.4413i) q^{92} +(-109.735 - 137.604i) q^{94} +(156.534 + 249.122i) q^{95} +(5.86295 + 52.0352i) q^{97} +(47.3689 - 75.3871i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) \) 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