LMFDB - Embedded newform 261.3.s.a.10.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("261.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.11173489980$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{28})$
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			10.3
Character	$\chi$	$=$	261.10
Dual form			261.3.s.a.235.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29187 - 0.811733i) q^{2} +(-0.725528 + 1.50658i) q^{4} +(-3.36294 - 0.767569i) q^{5} +(-0.255710 + 0.123143i) q^{7} +(0.968958 + 8.59974i) q^{8} +O(q^{10})$	\(q+(1.29187 - 0.811733i) q^{2} +(-0.725528 + 1.50658i) q^{4} +(-3.36294 - 0.767569i) q^{5} +(-0.255710 + 0.123143i) q^{7} +(0.968958 + 8.59974i) q^{8} +(-4.96753 + 1.73821i) q^{10} +(-1.62739 + 14.4435i) q^{11} +(-4.30976 + 3.43692i) q^{13} +(-0.230383 + 0.366653i) q^{14} +(4.06213 + 5.09375i) q^{16} +(-5.25353 - 5.25353i) q^{17} +(9.56906 + 27.3468i) q^{19} +(3.59631 - 4.50963i) q^{20} +(9.62189 + 19.9801i) q^{22} +(6.05686 + 26.5368i) q^{23} +(-11.8040 - 5.68451i) q^{25} +(-2.77777 + 7.93841i) q^{26} -0.474590i q^{28} +(-2.32625 - 28.9065i) q^{29} +(-12.9513 + 8.13783i) q^{31} +(-23.2916 - 8.15007i) q^{32} +(-11.0513 - 2.52239i) q^{34} +(0.954457 - 0.217849i) q^{35} +(3.05571 + 27.1202i) q^{37} +(34.5602 + 27.5609i) q^{38} +(3.34235 - 29.6642i) q^{40} +(45.8791 - 45.8791i) q^{41} +(35.9543 - 57.2209i) q^{43} +(-20.5795 - 12.9310i) q^{44} +(29.3655 + 29.3655i) q^{46} +(-17.2732 - 1.94622i) q^{47} +(-30.5008 + 38.2468i) q^{49} +(-19.8635 + 2.23808i) q^{50} +(-2.05112 - 8.98655i) q^{52} +(-1.31097 + 5.74372i) q^{53} +(16.5592 - 47.3235i) q^{55} +(-1.30677 - 2.07972i) q^{56} +(-26.4696 - 35.4551i) q^{58} +43.1476 q^{59} +(104.863 + 36.6931i) q^{61} +(-10.1256 + 21.0260i) q^{62} +(-62.1125 + 14.1768i) q^{64} +(17.1315 - 8.25011i) q^{65} +(-67.4283 - 53.7723i) q^{67} +(11.7264 - 4.10325i) q^{68} +(1.05620 - 1.05620i) q^{70} +(-45.1943 + 36.0413i) q^{71} +(-42.0399 - 26.4154i) q^{73} +(25.9619 + 32.5552i) q^{74} +(-48.1426 - 5.42437i) q^{76} +(-1.36248 - 3.89374i) q^{77} +(96.9173 - 10.9200i) q^{79} +(-9.75090 - 20.2479i) q^{80} +(22.0280 - 96.5112i) q^{82} +(0.956785 + 0.460763i) q^{83} +(13.6349 + 21.6998i) q^{85} -103.107i q^{86} -125.787 q^{88} +(-73.6381 + 46.2699i) q^{89} +(0.678813 - 1.40957i) q^{91} +(-44.3742 - 10.1281i) q^{92} +(-23.8944 + 11.5070i) q^{94} +(-11.1896 - 99.3106i) q^{95} +(54.6355 - 19.1178i) q^{97} +(-8.35675 + 74.1682i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) $ 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8	$ 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8} - 20 q^{10} + 8 q^{11} - 14 q^{13} - 26 q^{14} + 18 q^{16} + 26 q^{17} + 2 q^{19} - 46 q^{20} + 154 q^{22} - 56 q^{23} - 34 q^{25} - 110 q^{26} + 170 q^{29} - 88 q^{31} + 132 q^{32} - 224 q^{34} + 210 q^{35} - 56 q^{37} + 294 q^{38} - 492 q^{40} + 34 q^{41} + 176 q^{43} - 126 q^{44} + 744 q^{46} - 208 q^{47} + 506 q^{49} - 732 q^{50} + 690 q^{52} + 14 q^{53} + 284 q^{55} - 332 q^{56} - 508 q^{58} + 44 q^{59} - 30 q^{61} + 504 q^{62} - 896 q^{64} + 554 q^{65} - 574 q^{67} + 796 q^{68} - 1066 q^{70} - 224 q^{71} - 22 q^{73} - 820 q^{74} + 514 q^{76} - 436 q^{77} + 564 q^{79} - 1162 q^{80} - 18 q^{82} + 126 q^{83} + 38 q^{85} - 384 q^{88} + 160 q^{89} - 434 q^{91} + 1022 q^{92} - 2 q^{94} + 642 q^{95} + 604 q^{97} + 102 q^{98}+O(q^{100}) $ 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8 - 20 * q^10 + 8 * q^11 - 14 * q^13 - 26 * q^14 + 18 * q^16 + 26 * q^17 + 2 * q^19 - 46 * q^20 + 154 * q^22 - 56 * q^23 - 34 * q^25 - 110 * q^26 + 170 * q^29 - 88 * q^31 + 132 * q^32 - 224 * q^34 + 210 * q^35 - 56 * q^37 + 294 * q^38 - 492 * q^40 + 34 * q^41 + 176 * q^43 - 126 * q^44 + 744 * q^46 - 208 * q^47 + 506 * q^49 - 732 * q^50 + 690 * q^52 + 14 * q^53 + 284 * q^55 - 332 * q^56 - 508 * q^58 + 44 * q^59 - 30 * q^61 + 504 * q^62 - 896 * q^64 + 554 * q^65 - 574 * q^67 + 796 * q^68 - 1066 * q^70 - 224 * q^71 - 22 * q^73 - 820 * q^74 + 514 * q^76 - 436 * q^77 + 564 * q^79 - 1162 * q^80 - 18 * q^82 + 126 * q^83 + 38 * q^85 - 384 * q^88 + 160 * q^89 - 434 * q^91 + 1022 * q^92 - 2 * q^94 + 642 * q^95 + 604 * q^97 + 102 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.29187	−	0.811733i	0.645933	−	0.405867i	−0.168843	−	0.985643i	$-0.554003\pi$
$2$	1.29187	−	0.811733i	0.645933	−	0.405867i	0.814776	+	0.579776i	$0.196860\pi$
$3$		0			0
$3$		0			0
$4$	−0.725528	+	1.50658i	−0.181382	+	0.376644i
$5$	−3.36294	−	0.767569i	−0.672588	−	0.153514i	−0.127431	−	0.991847i	$-0.540673\pi$
$5$	−3.36294	−	0.767569i	−0.672588	−	0.153514i	−0.545158	+	0.838334i	$0.683530\pi$
$6$		0			0
$7$	−0.255710	+	0.123143i	−0.0365299	+	0.0175919i	−0.452060	−	0.891988i	$-0.649311\pi$
$7$	−0.255710	+	0.123143i	−0.0365299	+	0.0175919i	0.415530	+	0.909580i	$0.363596\pi$
$8$	0.968958	+	8.59974i	0.121120	+	1.07497i
$9$		0			0
$10$	−4.96753	+	1.73821i	−0.496753	+	0.173821i
$11$	−1.62739	+	14.4435i	−0.147945	+	1.31305i	0.671978	+	0.740571i	$0.265445\pi$
$11$	−1.62739	+	14.4435i	−0.147945	+	1.31305i	−0.819923	+	0.572474i	$0.805984\pi$
$12$		0			0
$13$	−4.30976	+	3.43692i	−0.331520	+	0.264378i	−0.775076	−	0.631869i	$-0.782288\pi$
$13$	−4.30976	+	3.43692i	−0.331520	+	0.264378i	0.443556	+	0.896247i	$0.353717\pi$
$14$	−0.230383	+	0.366653i	−0.0164559	+	0.0261895i
$15$		0			0
$16$	4.06213	+	5.09375i	0.253883	+	0.318359i
$17$	−5.25353	−	5.25353i	−0.309031	−	0.309031i	0.535503	−	0.844534i	$-0.320122\pi$
$17$	−5.25353	−	5.25353i	−0.309031	−	0.309031i	−0.844534	+	0.535503i	$0.820122\pi$
$18$		0			0
$19$	9.56906	+	27.3468i	0.503635	+	1.43930i	0.862568	+	0.505942i	$0.168855\pi$
$19$	9.56906	+	27.3468i	0.503635	+	1.43930i	−0.358933	+	0.933363i	$0.616859\pi$
$20$	3.59631	−	4.50963i	0.179816	−	0.225482i
$21$		0			0
$22$	9.62189	+	19.9801i	0.437359	+	0.908185i
$23$	6.05686	+	26.5368i	0.263342	+	1.15378i	0.917600	+	0.397505i	$0.130124\pi$
$23$	6.05686	+	26.5368i	0.263342	+	1.15378i	−0.654258	+	0.756271i	$0.727019\pi$
$24$		0			0
$25$	−11.8040	−	5.68451i	−0.472160	−	0.227380i
$26$	−2.77777	+	7.93841i	−0.106837	+	0.305323i
$27$		0			0
$28$		−	0.474590i		−	0.0169496i
$29$	−2.32625	−	28.9065i	−0.0802155	−	0.996778i
$29$	−2.32625	−	28.9065i	−0.0802155	−	0.996778i
$30$		0			0
$31$	−12.9513	+	8.13783i	−0.417783	+	0.262511i	−0.724479	−	0.689297i	$-0.757920\pi$
$31$	−12.9513	+	8.13783i	−0.417783	+	0.262511i	0.306695	+	0.951808i	$0.400777\pi$
$32$	−23.2916	−	8.15007i	−0.727862	−	0.254690i
$33$		0			0
$34$	−11.0513	−	2.52239i	−0.325039	−	0.0741880i
$35$	0.954457	−	0.217849i	0.0272702	−	0.00622425i
$36$		0			0
$37$	3.05571	+	27.1202i	0.0825867	+	0.732977i	0.964955	+	0.262417i	$0.0845196\pi$
$37$	3.05571	+	27.1202i	0.0825867	+	0.732977i	−0.882368	+	0.470560i	$0.844052\pi$
$38$	34.5602	+	27.5609i	0.909480	+	0.725286i
$39$		0			0
$40$	3.34235	−	29.6642i	0.0835587	−	0.741604i
$41$	45.8791	−	45.8791i	1.11900	−	1.11900i	0.127114	−	0.991888i	$-0.459429\pi$
$41$	45.8791	−	45.8791i	1.11900	−	1.11900i	0.991888	−	0.127114i	$-0.0405713\pi$
$42$		0			0
$43$	35.9543	−	57.2209i	0.836146	−	1.33072i	−0.105605	−	0.994408i	$-0.533678\pi$
$43$	35.9543	−	57.2209i	0.836146	−	1.33072i	0.941751	−	0.336311i	$-0.109179\pi$
$44$	−20.5795	−	12.9310i	−0.467716	−	0.293885i
$45$		0			0
$46$	29.3655	+	29.3655i	0.638380	+	0.638380i
$47$	−17.2732	−	1.94622i	−0.367514	−	0.0414089i	−0.0737238	−	0.997279i	$-0.523488\pi$
$47$	−17.2732	−	1.94622i	−0.367514	−	0.0414089i	−0.293791	+	0.955870i	$0.594917\pi$
$48$		0			0
$49$	−30.5008	+	38.2468i	−0.622465	+	0.780546i
$50$	−19.8635	+	2.23808i	−0.397270	+	0.0447616i
$51$		0			0
$52$	−2.05112	−	8.98655i	−0.0394447	−	0.172818i
$53$	−1.31097	+	5.74372i	−0.0247352	+	0.108372i	−0.985789	−	0.167991i	$-0.946272\pi$
$53$	−1.31097	+	5.74372i	−0.0247352	+	0.108372i	0.961053	+	0.276363i	$0.0891292\pi$
$54$		0			0
$55$	16.5592	−	47.3235i	0.301077	−	0.860427i
$56$	−1.30677	−	2.07972i	−0.0233352	−	0.0371378i
$57$		0			0
$58$	−26.4696	−	35.4551i	−0.456372	−	0.611295i
$59$	43.1476			0.731315			0.365658	−	0.930749i	$-0.380844\pi$
$59$	43.1476			0.731315			0.365658	+	0.930749i	$0.380844\pi$
$60$		0			0
$61$	104.863	+	36.6931i	1.71906	+	0.601526i	0.996008	−	0.0892649i	$-0.0284518\pi$
$61$	104.863	+	36.6931i	1.71906	+	0.601526i	0.723055	+	0.690791i	$0.242737\pi$
$62$	−10.1256	+	21.0260i	−0.163316	+	0.339129i
$63$		0			0
$64$	−62.1125	+	14.1768i	−0.970507	+	0.221512i
$65$	17.1315	−	8.25011i	0.263562	−	0.126925i
$66$		0			0
$67$	−67.4283	−	53.7723i	−1.00639	−	0.802571i	−0.0260070	−	0.999662i	$-0.508279\pi$
$67$	−67.4283	−	53.7723i	−1.00639	−	0.802571i	−0.980385	+	0.197091i	$0.936851\pi$
$68$	11.7264	−	4.10325i	0.172447	−	0.0603419i
$69$		0			0
$70$	1.05620	−	1.05620i	0.0150885	−	0.0150885i
$71$	−45.1943	+	36.0413i	−0.636540	+	0.507623i	−0.887760	−	0.460306i	$-0.847740\pi$
$71$	−45.1943	+	36.0413i	−0.636540	+	0.507623i	0.251220	+	0.967930i	$0.419168\pi$
$72$		0			0
$73$	−42.0399	−	26.4154i	−0.575889	−	0.361855i	0.212379	−	0.977187i	$-0.431879\pi$
$73$	−42.0399	−	26.4154i	−0.575889	−	0.361855i	−0.788268	+	0.615332i	$0.789022\pi$
$74$	25.9619	+	32.5552i	0.350836	+	0.439935i
$75$		0			0
$76$	−48.1426	−	5.42437i	−0.633456	−	0.0713733i
$77$	−1.36248	−	3.89374i	−0.0176945	−	0.0505681i
$78$		0			0
$79$	96.9173	−	10.9200i	1.22680	−	0.138227i	0.525314	−	0.850909i	$-0.323948\pi$
$79$	96.9173	−	10.9200i	1.22680	−	0.138227i	0.701488	+	0.712681i	$0.252519\pi$
$80$	−9.75090	−	20.2479i	−0.121886	−	0.253099i
$81$		0			0
$82$	22.0280	−	96.5112i	0.268635	−	1.17697i
$83$	0.956785	+	0.460763i	0.0115275	+	0.00555137i	0.439639	−	0.898175i	$-0.355107\pi$
$83$	0.956785	+	0.460763i	0.0115275	+	0.00555137i	−0.428111	+	0.903726i	$0.640821\pi$
$84$		0			0
$85$	13.6349	+	21.6998i	0.160410	+	0.255291i
$86$		−	103.107i		−	1.19892i
$87$		0			0
$88$	−125.787			−1.42940
$89$	−73.6381	+	46.2699i	−0.827394	+	0.519886i	−0.877904	−	0.478837i	$-0.841058\pi$
$89$	−73.6381	+	46.2699i	−0.827394	+	0.519886i	0.0505095	+	0.998724i	$0.483915\pi$
$90$		0			0
$91$	0.678813	−	1.40957i	0.00745949	−	0.0154898i
$92$	−44.3742	−	10.1281i	−0.482328	−	0.110088i
$93$		0			0
$94$	−23.8944	+	11.5070i	−0.254196	+	0.122414i
$95$	−11.1896	−	99.3106i	−0.117785	−	1.04537i
$96$		0			0
$97$	54.6355	−	19.1178i	0.563252	−	0.197091i	−0.0336088	−	0.999435i	$-0.510700\pi$
$97$	54.6355	−	19.1178i	0.563252	−	0.197091i	0.596861	+	0.802345i	$0.296414\pi$
$98$	−8.35675	+	74.1682i	−0.0852729	+	0.756818i
$99$		0			0
$100$	17.1283	−	13.6594i	0.171283	−	0.136594i
$101$	43.1797	−	68.7201i	0.427522	−	0.680397i	−0.561614	−	0.827399i	$-0.689819\pi$
$101$	43.1797	−	68.7201i	0.427522	−	0.680397i	0.989136	+	0.147002i	$0.0469623\pi$
$102$		0			0
$103$	117.601	+	147.466i	1.14175	+	1.43171i	0.885217	+	0.465179i	$0.154010\pi$
$103$	117.601	+	147.466i	1.14175	+	1.43171i	0.256537	+	0.966534i	$0.417419\pi$
$104$	−33.7326	−	33.7326i	−0.324352	−	0.324352i
$105$		0			0
$106$	2.96878	+	8.48427i	0.0280073	+	0.0800403i
$107$	−17.2592	+	21.6423i	−0.161300	+	0.202264i	−0.855913	−	0.517119i	$-0.827004\pi$
$107$	−17.2592	+	21.6423i	−0.161300	+	0.202264i	0.694613	+	0.719384i	$0.255576\pi$
$108$		0			0
$109$	−40.5822	−	84.2699i	−0.372314	−	0.773118i	0.627672	−	0.778478i	$-0.284008\pi$
$109$	−40.5822	−	84.2699i	−0.372314	−	0.773118i	−0.999986	+	0.00536026i	$0.998294\pi$
$110$	−17.0218	−	74.5773i	−0.154743	−	0.677975i
$111$		0			0
$112$	−1.66599	−	0.802297i	−0.0148749	−	0.00716336i
$113$	−49.3986	+	141.173i	−0.437156	+	1.24932i	0.489035	+	0.872264i	$0.337349\pi$
$113$	−49.3986	+	141.173i	−0.437156	+	1.24932i	−0.926191	+	0.377055i	$0.876937\pi$
$114$		0			0
$115$		−	93.8909i		−	0.816443i
$116$	45.2377	+	17.4679i	0.389980	+	0.150585i
$117$		0			0
$118$	55.7409	−	35.0243i	0.472381	−	0.296816i
$119$	1.99031	+	0.696441i	0.0167253	+	0.00585245i
$120$		0			0
$121$	−88.0000	−	20.0854i	−0.727272	−	0.165995i
$122$	165.254	−	37.7181i	1.35454	−	0.309165i
$123$		0			0
$124$	−2.86373	−	25.4163i	−0.0230946	−	0.204970i
$125$	102.755	+	81.9441i	0.822037	+	0.655553i
$126$		0			0
$127$	−10.7711	+	95.5964i	−0.0848120	+	0.752727i	0.877276	+	0.479987i	$0.159359\pi$
$127$	−10.7711	+	95.5964i	−0.0848120	+	0.752727i	−0.962088	+	0.272740i	$0.912070\pi$
$128$	1.06196	−	1.06196i	0.00829659	−	0.00829659i
$129$		0			0
$130$	15.4348	−	24.5643i	0.118729	−	0.188956i
$131$	86.3851	+	54.2793i	0.659428	+	0.414346i	0.819752	−	0.572718i	$-0.194111\pi$
$131$	86.3851	+	54.2793i	0.659428	+	0.414346i	−0.160324	+	0.987064i	$0.551254\pi$
$132$		0			0
$133$	−5.81447	−	5.81447i	−0.0437178	−	0.0437178i
$134$	−130.757	−	14.7328i	−0.975798	−	0.109946i
$135$		0			0
$136$	40.0885	−	50.2694i	0.294769	−	0.369628i
$137$	43.6939	−	4.92312i	0.318933	−	0.0359351i	0.0489532	−	0.998801i	$-0.484411\pi$
$137$	43.6939	−	4.92312i	0.318933	−	0.0359351i	0.269980	+	0.962866i	$0.412983\pi$
$138$		0			0
$139$	13.4998	+	59.1466i	0.0971211	+	0.425515i	0.999990	−	0.00439991i	$-0.00140054\pi$
$139$	13.4998	+	59.1466i	0.0971211	+	0.425515i	−0.902869	+	0.429915i	$0.858543\pi$
$140$	−0.364281	+	1.59602i	−0.00260200	+	0.0114001i
$141$		0			0
$142$	−29.1291	+	83.2462i	−0.205135	+	0.586241i
$143$	−42.6274	−	67.8412i	−0.298094	−	0.474414i
$144$		0			0
$145$	−14.3647	+	98.9966i	−0.0990672	+	0.682735i
$146$	−75.7522			−0.518851
$147$		0			0
$148$	−43.0756	−	15.0728i	−0.291051	−	0.101843i
$149$	42.6095	−	88.4796i	0.285970	−	0.593823i	−0.707655	−	0.706558i	$-0.750247\pi$
$149$	42.6095	−	88.4796i	0.285970	−	0.593823i	0.993625	+	0.112735i	$0.0359612\pi$
$150$		0			0
$151$	2.28538	−	0.521624i	0.0151350	−	0.00345446i	−0.214947	−	0.976626i	$-0.568958\pi$
$151$	2.28538	−	0.521624i	0.0151350	−	0.00345446i	0.230082	+	0.973171i	$0.426101\pi$
$152$	−225.903	+	108.789i	−1.48621	+	0.715719i
$153$		0			0
$154$	−4.92082	−	3.92422i	−0.0319534	−	0.0254820i
$155$	49.8008	−	17.4260i	0.321295	−	0.112426i
$156$		0			0
$157$	55.3939	−	55.3939i	0.352828	−	0.352828i	−0.508333	−	0.861161i	$-0.669738\pi$
$157$	55.3939	−	55.3939i	0.352828	−	0.352828i	0.861161	+	0.508333i	$0.169738\pi$
$158$	116.340	−	92.7781i	0.736330	−	0.587203i
$159$		0			0
$160$	72.0724	+	45.2861i	0.450453	+	0.283038i
$161$	−4.81663	−	6.03986i	−0.0299170	−	0.0375147i
$162$		0			0
$163$	−59.0143	−	6.64931i	−0.362051	−	0.0407933i	−0.0709343	−	0.997481i	$-0.522598\pi$
$163$	−59.0143	−	6.64931i	−0.362051	−	0.0407933i	−0.291116	+	0.956688i	$0.594027\pi$
$164$	35.8337	+	102.407i	0.218498	+	0.624432i
$165$		0			0
$166$	1.61005	−	0.181410i	0.00969913	−	0.00109283i
$167$	−35.2685	−	73.2358i	−0.211189	−	0.438538i	0.768285	−	0.640107i	$-0.221110\pi$
$167$	−35.2685	−	73.2358i	−0.211189	−	0.438538i	−0.979474	+	0.201569i	$0.935396\pi$
$168$		0			0
$169$	−30.8444	+	135.138i	−0.182511	+	0.799635i
$170$	35.2288	+	16.9653i	0.207228	+	0.0997959i
$171$		0			0
$172$	60.1218	+	95.6833i	0.349545	+	0.556298i
$173$			34.1362i			0.197319i	0.995121	+	0.0986597i	$0.0314555\pi$
$173$			34.1362i			0.197319i	−0.995121	+	0.0986597i	$0.968544\pi$
$174$		0			0
$175$	3.71841			0.0212481
$176$	−80.1822	+	50.3818i	−0.455581	+	0.286260i
$177$		0			0
$178$	−57.5717	+	119.549i	−0.323437	+	0.671623i
$179$	71.0369	+	16.2137i	0.396854	+	0.0905793i	0.416290	−	0.909232i	$-0.363330\pi$
$179$	71.0369	+	16.2137i	0.396854	+	0.0905793i	−0.0194363	+	0.999811i	$0.506187\pi$
$180$		0			0
$181$	113.506	−	54.6618i	0.627107	−	0.301999i	−0.0932070	−	0.995647i	$-0.529712\pi$
$181$	113.506	−	54.6618i	0.627107	−	0.301999i	0.720314	+	0.693648i	$0.243998\pi$
$182$	−0.267259	−	2.37199i	−0.00146846	−	0.0130329i
$183$		0			0
$184$	−222.341	+	77.8005i	−1.20838	+	0.422829i
$185$	10.5404	−	93.5489i	0.0569753	−	0.505670i
$186$		0			0
$187$	84.4289	−	67.3298i	0.451491	−	0.360052i
$188$	15.4643	−	24.6113i	0.0822570	−	0.130911i
$189$		0			0
$190$	−95.0691	−	119.213i	−0.500364	−	0.627437i
$191$	107.857	+	107.857i	0.564698	+	0.564698i	0.930638	−	0.365940i	$-0.119253\pi$
$191$	107.857	+	107.857i	0.564698	+	0.564698i	−0.365940	+	0.930638i	$0.619253\pi$
$192$		0			0
$193$	66.7211	+	190.678i	0.345705	+	0.987969i	0.977151	+	0.212548i	$0.0681763\pi$
$193$	66.7211	+	190.678i	0.345705	+	0.987969i	−0.631445	+	0.775420i	$0.717538\pi$
$194$	55.0632	−	69.0470i	0.283831	−	0.355913i
$195$		0			0
$196$	−35.4925	−	73.7008i	−0.181084	−	0.376025i
$197$	76.3058	+	334.317i	0.387339	+	1.69704i	0.673769	+	0.738942i	$0.264674\pi$
$197$	76.3058	+	334.317i	0.387339	+	1.69704i	−0.286431	+	0.958101i	$0.592469\pi$
$198$		0			0
$199$	267.208	+	128.681i	1.34275	+	0.646636i	0.960722	−	0.277513i	$-0.0895101\pi$
$199$	267.208	+	128.681i	1.34275	+	0.646636i	0.382032	+	0.924149i	$0.375224\pi$
$200$	37.4477	−	107.020i	0.187239	−	0.535098i
$201$		0			0
$202$		−	123.828i		−	0.613008i
$203$	4.15449	+	7.10522i	0.0204655	+	0.0350011i
$204$		0			0
$205$	−189.504	+	119.073i	−0.924410	+	0.580845i
$206$	271.628	+	95.0466i	1.31858	+	0.461391i
$207$		0			0
$208$	−35.0136	−	7.99162i	−0.168335	−	0.0384213i
$209$	−410.556	+	93.7067i	−1.96438	+	0.448357i
$210$		0			0
$211$	−23.1896	−	205.814i	−0.109903	−	0.975420i	−0.920748	−	0.390158i	$-0.872420\pi$
$211$	−23.1896	−	205.814i	−0.109903	−	0.975420i	0.810845	−	0.585262i	$-0.199008\pi$
$212$	−7.70221	−	6.14231i	−0.0363312	−	0.0289731i
$213$		0			0
$214$	−4.72874	+	41.9688i	−0.0220969	+	0.196116i
$215$	−164.833	+	164.833i	−0.766666	+	0.766666i
$216$		0			0
$217$	2.30965	−	3.67579i	0.0106435	−	0.0169391i
$218$	−120.831	−	75.9234i	−0.554273	−	0.348272i
$219$		0			0
$220$	59.2822	+	59.2822i	0.269465	+	0.269465i
$221$	40.6974	+	4.58549i	0.184151	+	0.0207488i
$222$		0			0
$223$	−17.9820	+	22.5487i	−0.0806367	+	0.101115i	−0.820513	−	0.571627i	$-0.806312\pi$
$223$	−17.9820	+	22.5487i	−0.0806367	+	0.101115i	0.739877	+	0.672742i	$0.234884\pi$
$224$	6.95951	−	0.784148i	0.0310692	−	0.00350066i
$225$		0			0
$226$	50.7785	+	222.475i	0.224684	+	0.984403i
$227$	34.9328	−	153.050i	0.153889	−	0.674231i	−0.837844	−	0.545910i	$-0.816184\pi$
$227$	34.9328	−	153.050i	0.153889	−	0.674231i	0.991733	−	0.128321i	$-0.0409588\pi$
$228$		0			0
$229$	−104.546	+	298.776i	−0.456534	+	1.30470i	0.453902	+	0.891051i	$0.350031\pi$
$229$	−104.546	+	298.776i	−0.456534	+	1.30470i	−0.910437	+	0.413648i	$0.864254\pi$
$230$	−76.2143	−	121.294i	−0.331367	−	0.527367i
$231$		0			0
$232$	246.335	−	48.0144i	1.06179	−	0.206959i
$233$	−421.117			−1.80737			−0.903684	−	0.428200i	$-0.859148\pi$
$233$	−421.117			−1.80737			−0.903684	+	0.428200i	$0.859148\pi$
$234$		0			0
$235$	56.5948	+	19.8034i	0.240829	+	0.0842697i
$236$	−31.3048	+	65.0051i	−0.132648	+	0.275445i
$237$		0			0
$238$	3.13654	−	0.715895i	0.0131788	−	0.00300796i
$239$	187.354	−	90.2247i	0.783906	−	0.377509i	0.00127824	−	0.999999i	$-0.499593\pi$
$239$	187.354	−	90.2247i	0.783906	−	0.377509i	0.782628	+	0.622490i	$0.213879\pi$
$240$		0			0
$241$	10.8085	+	8.61948i	0.0448485	+	0.0357655i	0.645658	−	0.763627i	$-0.276583\pi$
$241$	10.8085	+	8.61948i	0.0448485	+	0.0357655i	−0.600809	+	0.799393i	$0.705155\pi$
$242$	−129.988	+	45.4848i	−0.537141	+	0.187954i
$243$		0			0
$244$	−131.362	+	131.362i	−0.538368	+	0.538368i
$245$	131.929	−	105.210i	0.538487	−	0.429429i
$246$		0			0
$247$	−135.229	−	84.9700i	−0.547486	−	0.344008i
$248$	−82.5325	−	103.493i	−0.332792	−	0.417309i
$249$		0			0
$250$	199.262	+	22.4514i	0.797048	+	0.0898057i
$251$	20.8320	+	59.5343i	0.0829959	+	0.237189i	0.977901	−	0.209067i	$-0.0670428\pi$
$251$	20.8320	+	59.5343i	0.0829959	+	0.237189i	−0.894905	+	0.446256i	$0.852757\pi$
$252$		0			0
$253$	−393.142	+	44.2964i	−1.55392	+	0.175085i
$254$	63.6839	+	132.241i	0.250724	+	0.520634i
$255$		0			0
$256$	57.2170	−	250.684i	0.223504	−	0.979234i
$257$	387.505	+	186.613i	1.50780	+	0.726120i	0.991478	−	0.130273i	$-0.0415854\pi$
$257$	387.505	+	186.613i	1.50780	+	0.726120i	0.516325	+	0.856393i	$0.327300\pi$
$258$		0			0
$259$	−4.12104	−	6.55859i	−0.0159113	−	0.0253228i
$260$			31.7956i			0.122291i
$261$		0			0
$262$	155.658			0.594116
$263$	−10.7365	+	6.74620i	−0.0408232	+	0.0256509i	−0.552289	−	0.833653i	$-0.686246\pi$
$263$	−10.7365	+	6.74620i	−0.0408232	+	0.0256509i	0.511466	+	0.859304i	$0.329103\pi$
$264$		0			0
$265$	8.81741	−	18.3095i	0.0332733	−	0.0690926i
$266$	−12.2313	−	2.79172i	−0.0459824	−	0.0104952i
$267$		0			0
$268$	129.933	−	62.5725i	0.484825	−	0.233479i
$269$	28.0878	+	249.286i	0.104416	+	0.926714i	0.931278	+	0.364310i	$0.118695\pi$
$269$	28.0878	+	249.286i	0.104416	+	0.926714i	−0.826862	+	0.562404i	$0.809876\pi$
$270$		0			0
$271$	214.664	−	75.1142i	0.792119	−	0.277174i	0.0962629	−	0.995356i	$-0.469311\pi$
$271$	214.664	−	75.1142i	0.792119	−	0.277174i	0.695856	+	0.718182i	$0.255025\pi$
$272$	5.41964	−	48.1007i	0.0199252	−	0.176841i
$273$		0			0
$274$	52.4503	−	41.8278i	0.191425	−	0.152656i
$275$	101.314	−	161.240i	0.368415	−	0.586328i
$276$		0			0
$277$	−266.485	−	334.162i	−0.962040	−	1.20636i	−0.978448	−	0.206495i	$-0.933794\pi$
$277$	−266.485	−	334.162i	−0.962040	−	1.20636i	0.0164075	−	0.999865i	$-0.494777\pi$
$278$	65.4513	+	65.4513i	0.235436	+	0.235436i
$279$		0			0
$280$	2.79827	+	7.99700i	0.00999383	+	0.0285607i
$281$	259.886	−	325.887i	0.924862	−	1.15974i	−0.0619844	−	0.998077i	$-0.519743\pi$
$281$	259.886	−	325.887i	0.924862	−	1.15974i	0.986846	−	0.161663i	$-0.0516857\pi$
$282$		0			0
$283$	−202.446	−	420.383i	−0.715356	−	1.48545i	−0.867681	−	0.497121i	$-0.834390\pi$
$283$	−202.446	−	420.383i	−0.715356	−	1.48545i	0.152325	−	0.988330i	$-0.451324\pi$
$284$	−21.5091	−	94.2376i	−0.0757363	−	0.331823i
$285$		0			0
$286$	−110.138	−	53.0396i	−0.385097	−	0.185453i
$287$	−6.08202	+	17.3814i	−0.0211917	+	0.0605624i
$288$		0			0
$289$		−	233.801i		−	0.809000i
$290$	61.8015	+	139.551i	0.213109	+	0.481209i
$291$		0			0
$292$	70.2980	−	44.1712i	0.240747	−	0.151271i
$293$	−285.468	−	99.8897i	−0.974295	−	0.340921i	−0.204256	−	0.978917i	$-0.565478\pi$
$293$	−285.468	−	99.8897i	−0.974295	−	0.340921i	−0.770039	+	0.637997i	$0.779763\pi$
$294$		0			0
$295$	−145.103	−	33.1188i	−0.491874	−	0.112267i
$296$	−230.265	+	52.5566i	−0.777924	+	0.177556i
$297$		0			0
$298$	−16.7760	−	148.891i	−0.0562954	−	0.499635i
$299$	−117.309	−	93.5504i	−0.392336	−	0.312878i
$300$		0			0
$301$	−2.14749	+	19.0595i	−0.00713451	+	0.0633205i
$302$	2.52899	−	2.52899i	0.00837414	−	0.00837414i
$303$		0			0
$304$	−100.427	+	159.829i	−0.330352	+	0.525752i
$305$	−324.483	−	203.886i	−1.06388	−	0.668479i
$306$		0			0
$307$	−271.866	−	271.866i	−0.885558	−	0.885558i	0.108534	−	0.994093i	$-0.465384\pi$
$307$	−271.866	−	271.866i	−0.885558	−	0.885558i	−0.994093	+	0.108534i	$0.965384\pi$
$308$	6.85474	+	0.772343i	0.0222556	+	0.00250761i
$309$		0			0
$310$	50.1906	−	62.9370i	0.161905	−	0.203023i
$311$	124.784	−	14.0597i	0.401233	−	0.0452081i	0.0909576	−	0.995855i	$-0.471007\pi$
$311$	124.784	−	14.0597i	0.401233	−	0.0452081i	0.310276	+	0.950647i	$0.399579\pi$
$312$		0			0
$313$	13.5770	+	59.4846i	0.0433769	+	0.190047i	0.991975	−	0.126438i	$-0.0403545\pi$
$313$	13.5770	+	59.4846i	0.0433769	+	0.190047i	−0.948598	+	0.316485i	$0.897497\pi$
$314$	26.5964	−	116.527i	0.0847020	−	0.371104i
$315$		0			0
$316$	−53.8645	+	153.936i	−0.170457	+	0.487139i
$317$	−239.824	−	381.678i	−0.756543	−	1.20403i	−0.973686	−	0.227892i	$-0.926817\pi$
$317$	−239.824	−	381.678i	−0.756543	−	1.20403i	0.217143	−	0.976140i	$-0.430326\pi$
$318$		0			0
$319$	421.297	+	13.4431i	1.32068	+	0.0421413i
$320$	219.762			0.686757
$321$		0			0
$322$	−11.1252	−	3.89288i	−0.0345503	−	0.0120897i
$323$	93.3958	−	193.938i	0.289151	−	0.600429i
$324$		0			0
$325$	70.4096	−	16.0705i	0.216645	−	0.0494478i
$326$	−81.6360	+	39.3138i	−0.250417	+	0.120594i
$327$		0			0
$328$	439.003	+	350.093i	1.33842	+	1.06736i
$329$	4.65658	−	1.62941i	0.0141537	−	0.00495261i
$330$		0			0
$331$	295.773	−	295.773i	0.893575	−	0.893575i	−0.101283	−	0.994858i	$-0.532295\pi$
$331$	295.773	−	295.773i	0.893575	−	0.893575i	0.994858	+	0.101283i	$0.0322946\pi$
$332$	−1.38835	+	1.10717i	−0.00418178	+	0.00333486i
$333$		0			0
$334$	−105.010	−	65.9822i	−0.314402	−	0.197552i
$335$	185.483	+	232.589i	0.553682	+	0.694295i
$336$		0			0
$337$	−90.2891	−	10.1731i	−0.267920	−	0.0301873i	−0.0230176	−	0.999735i	$-0.507327\pi$
$337$	−90.2891	−	10.1731i	−0.267920	−	0.0301873i	−0.244902	+	0.969548i	$0.578756\pi$
$338$	69.8493	+	199.618i	0.206655	+	0.590586i
$339$		0			0
$340$	−42.5848	+	4.79815i	−0.125249	+	0.0141122i
$341$	−96.4620	−	200.305i	−0.282880	−	0.587406i
$342$		0			0
$343$	6.18411	−	27.0944i	0.0180295	−	0.0789923i
$344$	526.923	+	253.753i	1.53175	+	0.737654i
$345$		0			0
$346$	27.7095	+	44.0994i	0.0800853	+	0.127455i
$347$		−	392.579i		−	1.13135i	−0.824628	−	0.565676i	$-0.808615\pi$
$347$		−	392.579i		−	1.13135i	0.824628	−	0.565676i	$-0.191385\pi$
$348$		0			0
$349$	−487.106			−1.39572			−0.697860	−	0.716234i	$-0.745864\pi$
$349$	−487.106			−1.39572			−0.697860	+	0.716234i	$0.745864\pi$
$350$	4.80368	−	3.01836i	0.0137248	−	0.00862387i
$351$		0			0
$352$	155.620	−	323.148i	0.442103	−	0.918035i
$353$	−98.6003	−	22.5049i	−0.279321	−	0.0637532i	0.0805655	−	0.996749i	$-0.474327\pi$
$353$	−98.6003	−	22.5049i	−0.279321	−	0.0637532i	−0.359886	+	0.932996i	$0.617185\pi$
$354$		0			0
$355$	179.650	−	86.5149i	0.506056	−	0.243704i
$356$	−16.2825	−	144.511i	−0.0457374	−	0.405931i
$357$		0			0
$358$	104.931	−	36.7170i	0.293104	−	0.102562i
$359$	−3.96158	+	35.1600i	−0.0110350	+	0.0979386i	−0.998022	−	0.0628592i	$-0.979978\pi$
$359$	−3.96158	+	35.1600i	−0.0110350	+	0.0979386i	0.986987	+	0.160798i	$0.0514067\pi$
$360$		0			0
$361$	−374.039	+	298.286i	−1.03612	+	0.826277i
$362$	102.264	−	162.753i	0.282498	−	0.449593i
$363$		0			0
$364$	1.63113	+	2.04537i	0.00448111	+	0.00561914i
$365$	121.102	+	121.102i	0.331787	+	0.331787i
$366$		0			0
$367$	−76.1146	−	217.523i	−0.207397	−	0.592706i	0.792455	−	0.609930i	$-0.208803\pi$
$367$	−76.1146	−	217.523i	−0.207397	−	0.592706i	−0.999852	+	0.0172247i	$0.994517\pi$
$368$	−110.568	+	138.648i	−0.300457	+	0.376761i
$369$		0			0
$370$	−62.3199	−	129.409i	−0.168432	−	0.349753i
$371$	−0.372074	−	1.63016i	−0.00100289	−	0.00439397i
$372$		0			0
$373$	402.935	+	194.043i	1.08026	+	0.520224i	0.887398	−	0.461003i	$-0.152510\pi$
$373$	402.935	+	194.043i	1.08026	+	0.520224i	0.192857	+	0.981227i	$0.438225\pi$
$374$	54.4170	−	155.515i	0.145500	−	0.415815i
$375$		0			0
$376$		−	150.431i		−	0.400082i
$377$	109.375	+	116.585i	0.290119	+	0.309244i
$378$		0			0
$379$	−215.124	+	135.171i	−0.567609	+	0.356653i	−0.785061	−	0.619419i	$-0.787368\pi$
$379$	−215.124	+	135.171i	−0.567609	+	0.356653i	0.217452	+	0.976071i	$0.430226\pi$
$380$	157.737	+	55.1946i	0.415098	+	0.145249i
$381$		0			0
$382$	226.888	+	51.7858i	0.593949	+	0.135565i
$383$	215.485	−	49.1830i	0.562624	−	0.128415i	0.0682557	−	0.997668i	$-0.478257\pi$
$383$	215.485	−	49.1830i	0.562624	−	0.128415i	0.494368	+	0.869253i	$0.335399\pi$
$384$		0			0
$385$	1.59322	+	14.1402i	0.00413824	+	0.0367279i
$386$	240.974	+	192.171i	0.624286	+	0.497851i
$387$		0			0
$388$	−10.8372	+	96.1830i	−0.0279310	+	0.247894i
$389$	−408.712	+	408.712i	−1.05067	+	1.05067i	−0.0520279	+	0.998646i	$0.516568\pi$
$389$	−408.712	+	408.712i	−1.05067	+	1.05067i	−0.998646	+	0.0520279i	$0.983432\pi$
$390$		0			0
$391$	107.592	−	171.232i	0.275172	−	0.437933i
$392$	−358.466	−	225.239i	−0.914455	−	0.574590i
$393$		0			0
$394$	369.953	+	369.953i	0.938968	+	0.938968i
$395$	−334.309	−	37.6676i	−0.846352	−	0.0953610i
$396$		0			0
$397$	−173.996	+	218.184i	−0.438277	+	0.549582i	−0.951088	−	0.308919i	$-0.900033\pi$
$397$	−173.996	+	218.184i	−0.438277	+	0.549582i	0.512811	+	0.858501i	$0.328604\pi$
$398$	449.651	−	50.6635i	1.12978	−	0.127295i
$399$		0			0
$400$	−18.9939	−	83.2179i	−0.0474849	−	0.208045i
$401$	71.9206	−	315.105i	0.179353	−	0.785797i	−0.802576	−	0.596549i	$-0.796538\pi$
$401$	71.9206	−	315.105i	0.179353	−	0.785797i	0.981929	−	0.189248i	$-0.0606049\pi$
$402$		0			0
$403$	27.8478	−	79.5846i	0.0691014	−	0.197480i
$404$	72.2040	+	114.912i	0.178723	+	0.284435i
$405$		0			0
$406$	11.1346	+	5.80665i	0.0274251	+	0.0143021i
$407$	−396.683			−0.974650
$408$		0			0
$409$	138.542	+	48.4780i	0.338734	+	0.118528i	0.494285	−	0.869300i	$-0.335430\pi$
$409$	138.542	+	48.4780i	0.338734	+	0.118528i	−0.155552	+	0.987828i	$0.549715\pi$
$410$	−148.158	+	307.653i	−0.361361	+	0.750374i
$411$		0			0
$412$	−307.492	+	70.1830i	−0.746340	+	0.170347i
$413$	−11.0333	+	5.31334i	−0.0267149	+	0.0128652i
$414$		0			0
$415$	−2.86394	−	2.28392i	−0.00690107	−	0.00550342i
$416$	128.392	−	44.9264i	0.308635	−	0.107996i
$417$		0			0
$418$	−454.318	+	454.318i	−1.08689	+	1.08689i
$419$	−554.089	+	441.871i	−1.32241	+	1.05459i	−0.328485	+	0.944509i	$0.606538\pi$
$419$	−554.089	+	441.871i	−1.32241	+	1.05459i	−0.993923	+	0.110076i	$0.964891\pi$
$420$		0			0
$421$	−408.042	−	256.390i	−0.969220	−	0.609001i	−0.0483331	−	0.998831i	$-0.515391\pi$
$421$	−408.042	−	256.390i	−0.969220	−	0.609001i	−0.920887	+	0.389830i	$0.872534\pi$
$422$	−197.024	−	247.060i	−0.466880	−	0.585449i
$423$		0			0
$424$	−50.6648	−	5.70855i	−0.119492	−	0.0134636i
$425$	32.1490	+	91.8764i	0.0756446	+	0.216180i
$426$		0			0
$427$	−31.3329	+	3.53037i	−0.0733792	+	0.00826786i
$428$	−20.0837	−	41.7043i	−0.0469246	−	0.0974400i
$429$		0			0
$430$	−79.1418	+	346.743i	−0.184051	+	0.806379i
$431$	−158.220	−	76.1946i	−0.367099	−	0.176786i	0.241235	−	0.970467i	$-0.422448\pi$
$431$	−158.220	−	76.1946i	−0.367099	−	0.176786i	−0.608334	+	0.793681i	$0.708162\pi$
$432$		0			0
$433$	2.79964	+	4.45560i	0.00646568	+	0.0102901i	0.849941	−	0.526877i	$-0.176637\pi$
$433$	2.79964	+	4.45560i	0.00646568	+	0.0102901i	−0.843476	+	0.537167i	$0.819494\pi$
$434$		−	6.62344i		−	0.0152614i
$435$		0			0
$436$	156.402			0.358721
$437$	−667.739	+	419.568i	−1.52801	+	0.960110i
$438$		0			0
$439$	−232.675	+	483.154i	−0.530010	+	1.10058i	0.448386	+	0.893840i	$0.351999\pi$
$439$	−232.675	+	483.154i	−0.530010	+	1.10058i	−0.978396	+	0.206738i	$0.933715\pi$
$440$	423.015	+	96.5504i	0.961398	+	0.219433i
$441$		0			0
$442$	56.2977	−	27.1116i	0.127370	−	0.0613384i
$443$	−49.1601	−	436.308i	−0.110971	−	0.984894i	−0.918596	−	0.395198i	$-0.870676\pi$
$443$	−49.1601	−	436.308i	−0.110971	−	0.984894i	0.807625	−	0.589696i	$-0.200753\pi$
$444$		0			0
$445$	283.156	−	99.0805i	0.636305	−	0.222653i
$446$	−4.92679	+	43.7265i	−0.0110466	+	0.0980414i
$447$		0			0
$448$	14.1370	−	11.2739i	0.0315558	−	0.0251649i
$449$	−27.2504	+	43.3687i	−0.0606912	+	0.0965896i	−0.875691	−	0.482871i	$-0.839594\pi$
$449$	−27.2504	+	43.3687i	−0.0606912	+	0.0965896i	0.815000	+	0.579461i	$0.196737\pi$
$450$		0			0
$451$	587.991	+	737.318i	1.30375	+	1.63485i
$452$	−176.848	−	176.848i	−0.391256	−	0.391256i
$453$		0			0
$454$	−79.1076	−	226.077i	−0.174246	−	0.497966i
$455$	−3.36475	+	4.21927i	−0.00739506	+	0.00927311i
$456$		0			0
$457$	141.198	+	293.202i	0.308968	+	0.641579i	0.996410	−	0.0846606i	$-0.0269806\pi$
$457$	141.198	+	293.202i	0.308968	+	0.641579i	−0.687442	+	0.726240i	$0.741266\pi$
$458$	107.467	+	470.843i	0.234644	+	1.02804i
$459$		0			0
$460$	141.454	+	68.1205i	0.307508	+	0.148088i
$461$	3.04533	−	8.70305i	0.00660592	−	0.0188786i	−0.940533	−	0.339702i	$-0.889674\pi$
$461$	3.04533	−	8.70305i	0.00660592	−	0.0188786i	0.947139	+	0.320823i	$0.103960\pi$
$462$		0			0
$463$			107.108i			0.231334i	0.993288	+	0.115667i	$0.0369005\pi$
$463$			107.108i			0.231334i	−0.993288	+	0.115667i	$0.963099\pi$
$464$	137.793	−	129.271i	0.296968	−	0.278602i
$465$		0			0
$466$	−544.026	+	341.834i	−1.16744	+	0.733550i
$467$	666.211	+	233.117i	1.42658	+	0.499180i	0.929595	−	0.368582i	$-0.120157\pi$
$467$	666.211	+	233.117i	1.42658	+	0.499180i	0.496980	+	0.867762i	$0.334442\pi$
$468$		0			0
$469$	23.8638	+	5.44675i	0.0508822	+	0.0116135i
$470$	89.1880	−	20.3566i	0.189762	−	0.0433119i
$471$		0			0
$472$	41.8082	+	371.058i	0.0885768	+	0.786140i
$473$	767.959	+	612.427i	1.62359	+	1.29477i
$474$		0			0
$475$	42.4999	−	377.197i	0.0894735	−	0.794099i
$476$	−2.49327	+	2.49327i	−0.00523796	+	0.00523796i
$477$		0			0
$478$	168.797	−	268.639i	0.353132	−	0.562007i
$479$	268.422	+	168.661i	0.560380	+	0.352110i	0.782249	−	0.622966i	$-0.214073\pi$
$479$	268.422	+	168.661i	0.560380	+	0.352110i	−0.221868	+	0.975077i	$0.571216\pi$
$480$		0			0
$481$	−106.379	−	106.379i	−0.221162	−	0.221162i
$482$	20.9598	+	2.36160i	0.0434851	+	0.00489959i
$483$		0			0
$484$	94.1067	−	118.006i	0.194435	−	0.243814i
$485$	−198.410	+	22.3555i	−0.409093	+	0.0460937i
$486$		0			0
$487$	−60.5532	−	265.301i	−0.124339	−	0.544765i	−0.998274	−	0.0587228i	$-0.981297\pi$
$487$	−60.5532	−	265.301i	−0.124339	−	0.544765i	0.873935	−	0.486042i	$-0.161560\pi$
$488$	−213.943	+	937.347i	−0.438409	+	1.92079i
$489$		0			0
$490$	85.0325	−	243.009i	0.173536	−	0.495936i
$491$	21.2173	+	33.7671i	0.0432123	+	0.0687720i	0.867632	−	0.497207i	$-0.165641\pi$
$491$	21.2173	+	33.7671i	0.0432123	+	0.0687720i	−0.824420	+	0.565979i	$0.808498\pi$
$492$		0			0
$493$	−139.640	+	164.082i	−0.283246	+	0.332824i
$494$	−243.671			−0.493260
$495$		0			0
$496$	−94.0619	−	32.9137i	−0.189641	−	0.0663582i
$497$	7.11838	−	14.7815i	0.0143227	−	0.0297414i
$498$		0			0
$499$	−733.757	+	167.475i	−1.47046	+	0.335622i	−0.881362	−	0.472442i	$-0.843372\pi$
$499$	−733.757	+	167.475i	−1.47046	+	0.335622i	−0.589094	+	0.808064i	$0.700515\pi$
$500$	−198.006	+	95.3549i	−0.396013	+	0.190710i
$501$		0			0
$502$	75.2381	+	60.0004i	0.149877	+	0.119523i
$503$	475.580	−	166.413i	0.945487	−	0.330840i	0.186875	−	0.982384i	$-0.440164\pi$
$503$	475.580	−	166.413i	0.945487	−	0.330840i	0.758611	+	0.651544i	$0.225878\pi$
$504$		0			0
$505$	−197.958	+	197.958i	−0.391997	+	0.391997i
$506$	−471.929	+	376.351i	−0.932667	+	0.743777i
$507$		0			0
$508$	−136.208	−	85.5854i	−0.268127	−	0.168475i
$509$	156.669	+	196.457i	0.307798	+	0.385967i	0.911539	−	0.411214i	$-0.134895\pi$
$509$	156.669	+	196.457i	0.307798	+	0.385967i	−0.603741	+	0.797181i	$0.706324\pi$
$510$		0			0
$511$	14.0029	+	1.57775i	0.0274029	+	0.00308757i
$512$	−127.588	−	364.624i	−0.249195	−	0.712157i
$513$		0			0
$514$	652.085	−	73.4723i	1.26865	−	0.142942i
$515$	−282.293	−	586.188i	−0.548142	−	1.13823i
$516$		0			0
$517$	56.2205	−	246.318i	0.108744	−	0.476437i
$518$	−10.6477	−	5.12764i	−0.0205553	−	0.00989892i
$519$		0			0
$520$	87.5486	+	139.333i	0.168363	+	0.267948i
$521$		−	240.735i		−	0.462063i	−0.972946	−	0.231031i	$-0.925790\pi$
$521$		−	240.735i		−	0.462063i	0.972946	−	0.231031i	$-0.0742100\pi$
$522$		0			0
$523$	−250.645			−0.479245			−0.239623	−	0.970866i	$-0.577024\pi$
$523$	−250.645			−0.479245			−0.239623	+	0.970866i	$0.577024\pi$
$524$	−144.451	+	90.7644i	−0.275669	+	0.173215i
$525$		0			0
$526$	−8.39402	+	17.4304i	−0.0159582	+	0.0331376i
$527$	110.792	+	25.2876i	0.210232	+	0.0479841i
$528$		0			0
$529$	−190.906	+	91.9355i	−0.360881	+	0.173791i
$530$	−3.47155	−	30.8109i	−0.00655009	−	0.0581337i
$531$		0			0
$532$	12.9785	−	4.54138i	0.0243957	−	0.00853642i
$533$	−40.0451	+	355.410i	−0.0751315	+	0.666811i
$534$		0			0
$535$	74.6535	−	59.5342i	0.139539	−	0.111279i
$536$	397.092	−	631.969i	0.740844	−	1.17905i
$537$		0			0
$538$	238.639	+	299.244i	0.443568	+	0.556216i
$539$	−502.780	−	502.780i	−0.932802	−	0.932802i
$540$		0			0
$541$	288.943	+	825.753i	0.534091	+	1.52635i	0.822458	+	0.568826i	$0.192602\pi$
$541$	288.943	+	825.753i	0.534091	+	1.52635i	−0.288367	+	0.957520i	$0.593112\pi$
$542$	216.345	−	271.287i	0.399160	−	0.500530i
$543$		0			0
$544$	79.5463	+	165.180i	0.146225	+	0.303639i
$545$	71.7927	+	314.544i	0.131730	+	0.577145i
$546$		0			0
$547$	885.756	+	426.558i	1.61930	+	0.779813i	0.999986	−	0.00533110i	$-0.00169695\pi$
$547$	885.756	+	426.558i	1.61930	+	0.779813i	0.619313	+	0.785144i	$0.287411\pi$
$548$	−24.2841	+	69.3999i	−0.0443140	+	0.126642i
$549$		0			0
$550$		−	290.541i		−	0.528256i
$551$	768.241	−	340.224i	1.39427	−	0.617466i
$552$		0			0
$553$	−23.4380	+	14.7271i	−0.0423833	+	0.0266312i
$554$	−615.513	−	215.377i	−1.11103	−	0.388768i
$555$		0			0
$556$	−98.9034	−	22.5741i	−0.177884	−	0.0406008i
$557$	697.102	−	159.109i	1.25153	−	0.285653i	0.455130	−	0.890425i	$-0.349593\pi$
$557$	697.102	−	159.109i	1.25153	−	0.285653i	0.796399	+	0.604771i	$0.206736\pi$
$558$		0			0
$559$	41.7093	+	370.180i	0.0746141	+	0.662219i
$560$	4.98680	+	3.97684i	0.00890499	+	0.00710150i
$561$		0			0
$562$	71.2048	−	631.960i	0.126699	−	1.12448i
$563$	−509.988	+	509.988i	−0.905840	+	0.905840i	−0.995933	−	0.0900931i	$-0.971284\pi$
$563$	−509.988	+	509.988i	−0.905840	+	0.905840i	0.0900931	+	0.995933i	$0.471284\pi$
$564$		0			0
$565$	274.485	−	436.840i	0.485814	−	0.773168i
$566$	−602.771	−	378.746i	−1.06497	−	0.669163i
$567$		0			0
$568$	−353.737	−	353.737i	−0.622776	−	0.622776i
$569$	−19.5814	−	2.20630i	−0.0344137	−	0.00387750i	0.0947408	−	0.995502i	$-0.469798\pi$
$569$	−19.5814	−	2.20630i	−0.0344137	−	0.00387750i	−0.129155	+	0.991624i	$0.541226\pi$
$570$		0			0
$571$	153.514	−	192.500i	0.268851	−	0.337128i	−0.629019	−	0.777390i	$-0.716543\pi$
$571$	153.514	−	192.500i	0.268851	−	0.337128i	0.897869	+	0.440262i	$0.145115\pi$
$572$	133.135	−	15.0007i	0.232754	−	0.0262251i
$573$		0			0
$574$	6.25192	+	27.3914i	0.0108918	+	0.0477203i
$575$	79.3537	−	347.671i	0.138007	−	0.604646i
$576$		0			0
$577$	305.351	−	872.644i	0.529205	−	1.51238i	−0.300279	−	0.953852i	$-0.597080\pi$
$577$	305.351	−	872.644i	0.529205	−	1.51238i	0.829484	−	0.558530i	$-0.188635\pi$
$578$	−189.784	−	302.039i	−0.328346	−	0.522559i
$579$		0			0
$580$	−138.724	−	93.4664i	−0.239179	−	0.161149i
$581$	−0.301399			−0.000518759
$582$		0			0
$583$	−80.8260	−	28.2822i	−0.138638	−	0.0485116i
$584$	186.431	−	387.128i	0.319231	−	0.662890i
$585$		0			0
$586$	−449.871	+	102.680i	−0.767697	+	0.175222i
$587$	507.435	−	244.368i	0.864456	−	0.416300i	0.0515328	−	0.998671i	$-0.483589\pi$
$587$	507.435	−	244.368i	0.864456	−	0.416300i	0.812923	+	0.582371i	$0.197875\pi$
$588$		0			0
$589$	−346.475	−	276.305i	−0.588243	−	0.469108i
$590$	−214.337	+	74.9998i	−0.363283	+	0.127118i
$591$		0			0
$592$	−125.731	+	125.731i	−0.212383	+	0.212383i
$593$	−40.7023	+	32.4590i	−0.0686380	+	0.0547370i	−0.657208	−	0.753709i	$-0.728263\pi$
$593$	−40.7023	+	32.4590i	−0.0686380	+	0.0547370i	0.588570	+	0.808446i	$0.299691\pi$
$594$		0			0
$595$	−6.15874	−	3.86979i	−0.0103508	−	0.00650386i
$596$	102.387	+	128.389i	0.171790	+	0.215418i
$597$		0			0
$598$	−227.485	−	25.6314i	−0.380409	−	0.0428618i
$599$	211.707	+	605.024i	0.353434	+	1.01006i	0.974127	+	0.226002i	$0.0725657\pi$
$599$	211.707	+	605.024i	0.353434	+	1.01006i	−0.620693	+	0.784054i	$0.713149\pi$
$600$		0			0
$601$	333.408	−	37.5661i	0.554756	−	0.0625060i	0.169864	−	0.985468i	$-0.445667\pi$
$601$	333.408	−	37.5661i	0.554756	−	0.0625060i	0.384892	+	0.922962i	$0.374239\pi$
$602$	12.6969	+	26.3655i	0.0210913	+	0.0437964i
$603$		0			0
$604$	−0.872245	+	3.82156i	−0.00144411	+	0.00632708i
$605$	280.522	+	135.092i	0.463672	+	0.223293i
$606$		0			0
$607$	−54.8088	−	87.2277i	−0.0902945	−	0.143703i	0.798523	−	0.601965i	$-0.205615\pi$
$607$	−54.8088	−	87.2277i	−0.0902945	−	0.143703i	−0.888817	+	0.458262i	$0.848472\pi$
$608$		−	714.938i		−	1.17589i
$609$		0			0
$610$	−584.690			−0.958508
$611$	81.1322	−	50.9787i	0.132786	−	0.0834349i
$612$		0			0
$613$	356.350	−	739.969i	0.581322	−	1.20713i	−0.378261	−	0.925699i	$-0.623478\pi$
$613$	356.350	−	739.969i	0.581322	−	1.20713i	0.959582	−	0.281428i	$-0.0908080\pi$
$614$	−571.898	−	130.532i	−0.931430	−	0.212593i
$615$		0			0
$616$	32.1650	−	15.4899i	0.0522159	−	0.0251459i
$617$	−12.5149	−	111.073i	−0.0202835	−	0.180021i	0.979486	−	0.201515i	$-0.0645863\pi$
$617$	−12.5149	−	111.073i	−0.0202835	−	0.180021i	−0.999769	+	0.0214938i	$0.993158\pi$
$618$		0			0
$619$	−86.4870	+	30.2631i	−0.139721	+	0.0488903i	−0.399233	−	0.916849i	$-0.630724\pi$
$619$	−86.4870	+	30.2631i	−0.139721	+	0.0488903i	0.259513	+	0.965740i	$0.416438\pi$
$620$	−9.87823	+	87.6717i	−0.0159326	+	0.141406i
$621$		0			0
$622$	149.791	−	119.454i	0.240821	−	0.192049i
$623$	13.1321	−	20.8997i	0.0210789	−	0.0335468i
$624$		0			0
$625$	−78.4444	−	98.3662i	−0.125511	−	0.157386i
$626$	65.8253	+	65.8253i	0.105152	+	0.105152i
$627$		0			0
$628$	43.2653	+	123.645i	0.0688937	+	0.196887i
$629$	126.423	−	158.530i	0.200991	−	0.252035i
$630$		0			0
$631$	106.650	+	221.460i	0.169017	+	0.350967i	0.968222	−	0.250091i	$-0.0804605\pi$
$631$	106.650	+	221.460i	0.169017	+	0.350967i	−0.799206	+	0.601058i	$0.794746\pi$
$632$	187.818	+	822.883i	0.297180	+	1.30203i
$633$		0			0
$634$	−619.641	−	298.404i	−0.977352	−	0.470668i
$635$	109.600	−	313.217i	0.172598	−	0.493256i
$636$		0			0
$637$		−	269.663i		−	0.423333i
$638$	555.172	−	324.614i	0.870175	−	0.508800i
$639$		0			0
$640$	−4.38645	+	2.75619i	−0.00685383	+	0.00430655i
$641$	−916.494	−	320.695i	−1.42979	−	0.500305i	−0.499237	−	0.866466i	$-0.666386\pi$
$641$	−916.494	−	320.695i	−1.42979	−	0.500305i	−0.930551	+	0.366161i	$0.880672\pi$
$642$		0			0
$643$	48.0847	+	10.9750i	0.0747817	+	0.0170684i	0.259748	−	0.965676i	$-0.416360\pi$
$643$	48.0847	+	10.9750i	0.0747817	+	0.0170684i	−0.184966	+	0.982745i	$0.559218\pi$
$644$	12.5941	−	2.87452i	0.0195561	−	0.00446355i
$645$		0			0
$646$	−36.7714	−	326.355i	−0.0569216	−	0.505193i
$647$	71.4194	+	56.9551i	0.110386	+	0.0880295i	0.677127	−	0.735866i	$-0.263225\pi$
$647$	71.4194	+	56.9551i	0.110386	+	0.0880295i	−0.566742	+	0.823896i	$0.691796\pi$
$648$		0			0
$649$	−70.2180	+	623.202i	−0.108194	+	0.960250i
$650$	77.9148	−	77.9148i	0.119869	−	0.119869i
$651$		0			0
$652$	52.8342	−	84.0852i	0.0810341	−	0.128965i
$653$	−207.926	−	130.649i	−0.318416	−	0.200074i	0.363334	−	0.931659i	$-0.381638\pi$
$653$	−207.926	−	130.649i	−0.318416	−	0.200074i	−0.681751	+	0.731585i	$0.738781\pi$
$654$		0			0
$655$	−248.845	−	248.845i	−0.379916	−	0.379916i
$656$	420.063	+	47.3298i	0.640340	+	0.0721490i
$657$		0			0
$658$	4.69303	−	5.88488i	0.00713227	−	0.00894359i
$659$	259.653	−	29.2559i	0.394011	−	0.0443943i	0.0872632	−	0.996185i	$-0.472188\pi$
$659$	259.653	−	29.2559i	0.394011	−	0.0443943i	0.306747	+	0.951791i	$0.400759\pi$
$660$		0			0
$661$	217.845	+	954.443i	0.329569	+	1.44394i	0.819953	+	0.572431i	$0.194000\pi$
$661$	217.845	+	954.443i	0.329569	+	1.44394i	−0.490383	+	0.871507i	$0.663143\pi$
$662$	142.010	−	622.188i	0.214517	−	0.939862i
$663$		0			0
$664$	−3.03536	+	8.67457i	−0.00457133	+	0.0130641i
$665$	15.0907	+	24.0167i	0.0226928	+	0.0361154i
$666$		0			0
$667$	752.999	−	236.814i	1.12893	−	0.355044i
$668$	135.924			0.203478
$669$		0			0
$670$	428.420	+	149.911i	0.639432	+	0.223747i
$671$	−700.629	+	1454.87i	−1.04416	+	2.16821i
$672$		0			0
$673$	593.737	−	135.517i	0.882225	−	0.201362i	0.242671	−	0.970109i	$-0.421976\pi$
$673$	593.737	−	135.517i	0.882225	−	0.201362i	0.639554	+	0.768747i	$0.279119\pi$
$674$	−124.899	+	60.1483i	−0.185310	+	0.0892408i
$675$		0			0
$676$	−181.217	−	144.516i	−0.268073	−	0.213781i
$677$	−559.076	+	195.629i	−0.825814	+	0.288965i	−0.709907	−	0.704295i	$-0.751263\pi$
$677$	−559.076	+	195.629i	−0.825814	+	0.288965i	−0.115907	+	0.993260i	$0.536977\pi$
$678$		0			0
$679$	−11.6166	+	11.6166i	−0.0171084	+	0.0171084i
$680$	−173.401	+	138.282i	−0.255001	+	0.203357i
$681$		0			0
$682$	−287.210	−	180.466i	−0.421130	−	0.264613i
$683$	−217.747	−	273.046i	−0.318809	−	0.399774i	0.596443	−	0.802656i	$-0.296580\pi$
$683$	−217.747	−	273.046i	−0.318809	−	0.399774i	−0.915252	+	0.402881i	$0.868009\pi$
$684$		0			0
$685$	−150.719	−	16.9819i	−0.220027	−	0.0247911i
$686$	−14.0043	−	40.0221i	−0.0204145	−	0.0583413i
$687$		0			0
$688$	437.520	−	49.2967i	0.635930	−	0.0716521i
$689$	−14.0907	−	29.2597i	−0.0204510	−	0.0424670i
$690$		0			0
$691$	181.564	−	795.482i	0.262755	−	1.15120i	−0.655494	−	0.755200i	$-0.727540\pi$
$691$	181.564	−	795.482i	0.262755	−	1.15120i	0.918249	−	0.396004i	$-0.129603\pi$
$692$	−51.4288	−	24.7668i	−0.0743191	−	0.0357902i
$693$		0			0
$694$	−318.669	−	507.159i	−0.459178	−	0.730777i
$695$		−	209.269i		−	0.301106i
$696$		0			0
$697$	−482.054			−0.691613
$698$	−629.276	+	395.400i	−0.901541	+	0.566476i
$699$		0			0
$700$	−2.69781	+	5.60206i	−0.00385402	+	0.00800295i
$701$	924.382	+	210.984i	1.31866	+	0.300976i	0.823249	−	0.567681i	$-0.192159\pi$
$701$	924.382	+	210.984i	1.31866	+	0.300976i	0.495414	+	0.868657i	$0.335016\pi$
$702$		0			0
$703$	−712.409	+	343.078i	−1.01338	+	0.488020i
$704$	−103.681	−	920.193i	−0.147274	−	1.30709i
$705$		0			0
$706$	−145.646	+	50.9638i	−0.206298	+	0.0721867i
$707$	−2.57905	+	22.8897i	−0.00364788	+	0.0323758i
$708$		0			0
$709$	−268.833	+	214.387i	−0.379172	+	0.302380i	−0.794467	−	0.607307i	$-0.792250\pi$
$709$	−268.833	+	214.387i	−0.379172	+	0.302380i	0.415295	+	0.909687i	$0.363678\pi$
$710$	161.857	−	257.593i	0.227967	−	0.362808i
$711$		0			0
$712$	−469.261	−	588.435i	−0.659075	−	0.826454i
$713$	−294.397	−	294.397i	−0.412898	−	0.412898i
$714$		0			0
$715$	91.2808	+	260.865i	0.127665	+	0.364847i
$716$	−75.9664	+	95.2589i	−0.106098	+	0.133043i
$717$		0			0
$718$	23.4227	+	48.6377i	0.0326221	+	0.0677405i
$719$	258.798	+	1133.87i	0.359942	+	1.57701i	0.753334	+	0.657639i	$0.228445\pi$
$719$	258.798	+	1133.87i	0.359942	+	1.57701i	−0.393391	+	0.919371i	$0.628698\pi$
$720$		0			0
$721$	−48.2311	−	23.2269i	−0.0668947	−	0.0322148i
$722$	−241.079	+	688.965i	−0.333905	+	0.954246i
$723$		0			0
$724$			210.665i			0.290973i
$725$	−136.861	+	354.437i	−0.188773	+	0.488878i
$726$		0			0
$727$	606.627	−	381.169i	0.834425	−	0.524304i	−0.0457500	−	0.998953i	$-0.514568\pi$
$727$	606.627	−	381.169i	0.834425	−	0.524304i	0.880175	+	0.474649i	$0.157425\pi$
$728$	12.7797	+	4.47180i	0.0175545	+	0.00614259i
$729$		0			0
$730$	254.750	+	58.1451i	0.348973	+	0.0796508i
$731$	−489.499	+	111.725i	−0.669629	+	0.152838i
$732$		0			0
$733$	−5.44223	−	48.3011i	−0.00742460	−	0.0658951i	0.989454	−	0.144850i	$-0.0462701\pi$
$733$	−5.44223	−	48.3011i	−0.00742460	−	0.0658951i	−0.996878	+	0.0789554i	$0.974842\pi$
$734$	−274.900	−	219.226i	−0.374524	−	0.298673i
$735$		0			0
$736$	75.2034	−	667.449i	0.102179	−	0.906860i
$737$	886.392	−	886.392i	1.20270	−	1.20270i
$738$		0			0
$739$	266.443	−	424.041i	0.360545	−	0.573804i	−0.616364	−	0.787462i	$-0.711395\pi$
$739$	266.443	−	424.041i	0.360545	−	0.573804i	0.976909	+	0.213658i	$0.0685378\pi$
$740$	133.291	+	83.7524i	0.180123	+	0.113179i
$741$		0			0
$742$	−1.80393	−	1.80393i	−0.00243117	−	0.00243117i
$743$	353.124	+	39.7875i	0.475267	+	0.0535498i	0.346350	−	0.938106i	$-0.387421\pi$
$743$	353.124	+	39.7875i	0.475267	+	0.0535498i	0.128918	+	0.991655i	$0.458850\pi$
$744$		0			0
$745$	−211.208	+	264.846i	−0.283500	+	0.355498i
$746$	678.050	−	76.3979i	0.908914	−	0.102410i
$747$		0			0
$748$	40.1818	+	176.048i	0.0537190	+	0.235358i
$749$	1.74823	−	7.65949i	0.00233408	−	0.0102263i
$750$		0			0
$751$	−225.087	+	643.260i	−0.299716	+	0.856539i	0.691273	+	0.722594i	$0.257050\pi$
$751$	−225.087	+	643.260i	−0.299716	+	0.856539i	−0.990989	+	0.133945i	$0.957235\pi$
$752$	−60.2523	−	95.8910i	−0.0801228	−	0.127515i
$753$		0			0
$754$	235.934	+	61.8290i	0.312909	+	0.0820013i
$755$	−8.08599			−0.0107099
$756$		0			0
$757$	−546.623	−	191.272i	−0.722091	−	0.252671i	−0.0558840	−	0.998437i	$-0.517798\pi$
$757$	−546.623	−	191.272i	−0.722091	−	0.252671i	−0.666207	+	0.745767i	$0.732083\pi$
$758$	−168.188	+	349.246i	−0.221884	+	0.460747i
$759$		0			0
$760$	843.203	−	192.456i	1.10948	−	0.253231i
$761$	−918.062	+	442.116i	−1.20639	+	0.580966i	−0.925490	−	0.378771i	$-0.876347\pi$
$761$	−918.062	+	442.116i	−1.20639	+	0.580966i	−0.280899	+	0.959737i	$0.590633\pi$
$762$		0			0
$763$	20.7545	+	16.5512i	0.0272012	+	0.0216922i
$764$	−240.749	+	84.2416i	−0.315116	+	0.110264i
$765$		0			0
$766$	238.454	−	238.454i	0.311298	−	0.311298i
$767$	−185.956	+	148.295i	−0.242446	+	0.193344i
$768$		0			0
$769$	165.357	+	103.901i	0.215028	+	0.135111i	0.635240	−	0.772315i	$-0.280901\pi$
$769$	165.357	+	103.901i	0.215028	+	0.135111i	−0.420211	+	0.907426i	$0.638044\pi$
$770$	13.5363	+	16.9740i	0.0175796	+	0.0220442i
$771$		0			0
$772$	−335.679	−	37.8219i	−0.434817	−	0.0489921i
$773$	−269.245	−	769.458i	−0.348312	−	0.995418i	−0.976154	−	0.217078i	$-0.930347\pi$
$773$	−269.245	−	769.458i	−0.348312	−	0.995418i	0.627842	−	0.778341i	$-0.283938\pi$
$774$		0			0
$775$	199.137	−	22.4373i	0.256951	−	0.0289514i
$776$	217.348	+	451.327i	0.280087	+	0.581607i
$777$		0			0
$778$	−196.236	+	859.766i	−0.252231	+	1.10510i
$779$	1693.66	+	815.626i	2.17415	+	1.04702i
$780$		0			0
$781$	−447.013	−	711.417i	−0.572360	−	0.910906i
$782$		−	308.545i		−	0.394559i
$783$		0			0
$784$	−318.718			−0.406527
$785$	−228.805	+	143.768i	−0.291472	+	0.183144i
$786$		0			0
$787$	354.355	−	735.826i	0.450261	−	0.934976i	−0.545064	−	0.838394i	$-0.683495\pi$
$787$	354.355	−	735.826i	0.450261	−	0.934976i	0.995325	−	0.0965819i	$-0.0307910\pi$
$788$	−559.036	−	127.596i	−0.709437	−	0.161924i
$789$		0			0
$790$	−462.459	+	222.708i	−0.585391	+	0.281909i
$791$	−4.75282	−	42.1824i	−0.00600862	−	0.0533280i
$792$		0			0
$793$	−578.044	+	202.266i	−0.728934	+	0.255065i
$794$	−47.6722	+	423.103i	−0.0600406	+	0.532875i
$795$		0			0
$796$	−387.734	+	309.208i	−0.487103	+	0.388452i
$797$	398.246	−	633.804i	0.499681	−	0.795238i	−0.497716	−	0.867340i	$-0.665828\pi$
$797$	398.246	−	633.804i	0.499681	−	0.795238i	0.997397	+	0.0721022i	$0.0229708\pi$
$798$		0			0
$799$	80.5206	+	100.970i	0.100777	+	0.126370i
$800$	228.605	+	228.605i	0.285756	+	0.285756i
$801$		0			0
$802$	−162.869	−	465.453i	−0.203079	−	0.580366i
$803$	449.947	−	564.215i	0.560332	−	0.702634i
$804$		0			0
$805$	11.5620	+	24.0088i	0.0143628	+	0.0298246i
$806$	−28.6258	−	125.418i	−0.0355158	−	0.155605i
$807$		0			0
$808$	632.815	+	304.748i	0.783187	+	0.377163i
$809$	332.410	−	949.974i	0.410890	−	1.17426i	−0.533605	−	0.845734i	$-0.679163\pi$
$809$	332.410	−	949.974i	0.410890	−	1.17426i	0.944496	−	0.328524i	$-0.106551\pi$
$810$		0			0
$811$			477.481i			0.588755i	0.955689	+	0.294378i	$0.0951124\pi$
$811$			477.481i			0.588755i	−0.955689	+	0.294378i	$0.904888\pi$
$812$	−13.7188	+	1.10401i	−0.0168950	+	0.00135962i
$813$		0			0
$814$	−512.461	+	322.000i	−0.629559	+	0.395578i
$815$	193.358	+	67.6588i	0.237249	+	0.0830169i
$816$		0			0
$817$	1908.86	+	435.684i	2.33642	+	0.533273i
$818$	218.329	−	49.8322i	0.266906	−	0.0609195i
$819$		0			0
$820$	−41.9023	−	371.893i	−0.0511003	−	0.453528i
$821$	287.826	+	229.534i	0.350580	+	0.279578i	0.782907	−	0.622139i	$-0.213736\pi$
$821$	287.826	+	229.534i	0.350580	+	0.279578i	−0.432327	+	0.901717i	$0.642307\pi$
$822$		0			0
$823$	−133.488	+	1184.74i	−0.162196	+	1.43953i	0.604030	+	0.796962i	$0.293561\pi$
$823$	−133.488	+	1184.74i	−0.162196	+	1.43953i	−0.766226	+	0.642571i	$0.777868\pi$
$824$	−1154.22	+	1154.22i	−1.40076	+	1.40076i
$825$		0			0
$826$	−9.94048	+	15.8202i	−0.0120345	+	0.0191528i
$827$	−1156.66	−	726.779i	−1.39862	−	0.878814i	−0.399347	−	0.916800i	$-0.630763\pi$
$827$	−1156.66	−	726.779i	−1.39862	−	0.878814i	−0.999278	+	0.0379859i	$0.987906\pi$
$828$		0			0
$829$	1047.04	+	1047.04i	1.26302	+	1.26302i	0.949622	+	0.313398i	$0.101467\pi$
$829$	1047.04	+	1047.04i	1.26302	+	1.26302i	0.313398	+	0.949622i	$0.398533\pi$
$830$	−5.55376	−	0.625759i	−0.00669128	−	0.000753927i
$831$		0			0
$832$	218.965	−	274.574i	0.263179	−	0.330017i
$833$	361.167	−	40.6938i	0.433574	−	0.0488521i
$834$		0			0
$835$	62.3924	+	273.359i	0.0747214	+	0.327376i
$836$	156.694	−	686.520i	0.187433	−	0.821197i
$837$		0			0
$838$	−357.127	+	1020.61i	−0.426166	+	1.21791i
$839$	−613.856	−	976.947i	−0.731652	−	1.16442i	−0.980622	−	0.195907i	$-0.937235\pi$
$839$	−613.856	−	976.947i	−0.731652	−	1.16442i	0.248970	−	0.968511i	$-0.419908\pi$
$840$		0			0
$841$	−830.177	+	134.488i	−0.987131	+	0.159914i
$842$	−735.255			−0.873224
$843$		0			0
$844$	326.898	+	114.387i	0.387320	+	0.135529i
$845$	207.456	−	430.787i	0.245510	−	0.509807i
$846$		0			0
$847$	24.9758	−	5.70057i	0.0294874	−	0.00673031i
$848$	−34.5824	+	16.6540i	−0.0407811	+	0.0196392i
$849$		0			0
$850$	116.111	+	92.5957i	0.136602	+	0.108936i
$851$	−701.175	+	245.352i	−0.823943	+	0.288310i
$852$		0			0
$853$	−338.738	+	338.738i	−0.397114	+	0.397114i	−0.877214	−	0.480100i	$-0.840600\pi$
$853$	−338.738	+	338.738i	−0.397114	+	0.397114i	0.480100	+	0.877214i	$0.340600\pi$
$854$	−37.6122	+	29.9948i	−0.0440424	+	0.0351227i
$855$		0			0
$856$	−202.842	−	127.454i	−0.236964	−	0.148895i
$857$	455.913	+	571.697i	0.531987	+	0.667091i	0.973106	−	0.230358i	$-0.0739898\pi$
$857$	455.913	+	571.697i	0.531987	+	0.667091i	−0.441119	+	0.897449i	$0.645418\pi$
$858$		0			0
$859$	152.501	+	17.1827i	0.177533	+	0.0200031i	0.200283	−	0.979738i	$-0.435814\pi$
$859$	152.501	+	17.1827i	0.177533	+	0.0200031i	−0.0227505	+	0.999741i	$0.507242\pi$
$860$	−128.742	−	367.925i	−0.149701	−	0.427820i
$861$		0			0
$862$	−266.248	+	29.9990i	−0.308873	+	0.0348016i
$863$	−163.086	−	338.651i	−0.188975	−	0.392411i	0.784858	−	0.619676i	$-0.212736\pi$
$863$	−163.086	−	338.651i	−0.188975	−	0.392411i	−0.973833	+	0.227265i	$0.927022\pi$
$864$		0			0
$865$	26.2019	−	114.798i	0.0302913	−	0.132715i
$866$	7.23351	+	3.48348i	0.00835279	+	0.00402249i
$867$		0			0
$868$	3.86213	+	6.14655i	0.00444946	+	0.00708128i
$869$			1417.60i			1.63130i
$870$		0			0
$871$	475.410			0.545821
$872$	685.377	−	430.651i	0.785982	−	0.493865i
$873$		0			0
$874$	−522.052	+	1084.05i	−0.597313	+	1.24033i
$875$	−36.3662	−	8.30035i	−0.0415614	−	0.00948612i
$876$		0			0
$877$	−57.8702	+	27.8688i	−0.0659866	+	0.0317775i	−0.466586	−	0.884476i	$-0.654516\pi$
$877$	−57.8702	+	27.8688i	−0.0659866	+	0.0317775i	0.400599	+	0.916253i	$0.368802\pi$
$878$	91.6075	+	813.039i	0.104337	+	0.926013i
$879$		0			0
$880$	308.320	−	107.886i	0.350363	−	0.122597i
$881$	−45.7401	+	405.955i	−0.0519184	+	0.460789i	0.940675	+	0.339308i	$0.110193\pi$
$881$	−45.7401	+	405.955i	−0.0519184	+	0.460789i	−0.992594	+	0.121481i	$0.961236\pi$
$882$		0			0
$883$	215.197	−	171.614i	0.243711	−	0.194353i	−0.494015	−	0.869454i	$-0.664471\pi$
$883$	215.197	−	171.614i	0.243711	−	0.194353i	0.737726	+	0.675100i	$0.235900\pi$
$884$	−36.4355	+	57.9867i	−0.0412166	+	0.0655959i
$885$		0			0
$886$	−417.674	−	523.747i	−0.471415	−	0.591136i
$887$	519.628	+	519.628i	0.585826	+	0.585826i	0.936498	−	0.350672i	$-0.114047\pi$
$887$	519.628	+	519.628i	0.585826	+	0.585826i	−0.350672	+	0.936498i	$0.614047\pi$
$888$		0			0
$889$	−9.01777	−	25.7713i	−0.0101437	−	0.0289891i
$890$	285.372	−	357.846i	0.320643	−	0.402074i
$891$		0			0
$892$	−20.9249	−	43.4509i	−0.0234584	−	0.0487118i
$893$	−112.065	−	490.990i	−0.125493	−	0.549820i
$894$		0			0
$895$	−226.448	−	109.051i	−0.253014	−	0.121845i
$896$	−0.140781	+	0.402328i	−0.000157121	+	0.000449027i
$897$		0			0
$898$			78.1466i			0.0870229i
$899$	265.365	+	355.446i	0.295178	+	0.395380i
$900$		0			0
$901$	37.0620	−	23.2876i	0.0411343	−	0.0258464i
$902$	1358.11	+	475.223i	1.50567	+	0.526855i
$903$		0			0
$904$	−1261.92	−	288.024i	−1.39593	−	0.318611i
$905$	−423.672	+	96.7004i	−0.468146	+	0.106851i
$906$		0			0
$907$	−71.1673	−	631.627i	−0.0784645	−	0.696391i	−0.969944	−	0.243330i	$-0.921760\pi$
$907$	−71.1673	−	631.627i	−0.0784645	−	0.696391i	0.891479	−	0.453062i	$-0.149668\pi$
$908$	205.237	+	163.671i	0.226032	+	0.180255i
$909$		0			0
$910$	−0.921891	+	8.18201i	−0.00101307	+	0.00899122i
$911$	−1005.04	+	1005.04i	−1.10323	+	1.10323i	−0.109207	+	0.994019i	$0.534831\pi$
$911$	−1005.04	+	1005.04i	−1.10323	+	1.10323i	−0.994019	+	0.109207i	$0.965169\pi$
$912$		0			0
$913$	−8.21210	+	13.0695i	−0.00899463	+	0.0143149i
$914$	420.411	+	264.162i	0.459968	+	0.289017i
$915$		0			0
$916$	−374.278	−	374.278i	−0.408600	−	0.408600i
$917$	−28.7736	−	3.24201i	−0.0313780	−	0.00353545i
$918$		0			0
$919$	390.750	−	489.985i	0.425190	−	0.533172i	−0.522383	−	0.852711i	$-0.674957\pi$
$919$	390.750	−	489.985i	0.425190	−	0.533172i	0.947573	+	0.319539i	$0.103528\pi$
$920$	807.438	−	90.9764i	0.877650	−	0.0988874i
$921$		0			0
$922$	−3.13040	−	13.7152i	−0.00339523	−	0.0148755i
$923$	70.9057	−	310.658i	0.0768209	−	0.336574i
$924$		0			0
$925$	118.095	−	337.497i	0.127671	−	0.364861i
$926$	86.9427	+	138.369i	0.0938906	+	0.149426i
$927$		0			0
$928$	−181.408	+	692.238i	−0.195483	+	0.745946i
$929$	−314.415			−0.338445			−0.169222	−	0.985578i	$-0.554126\pi$
$929$	−314.415			−0.338445			−0.169222	+	0.985578i	$0.554126\pi$
$930$		0			0
$931$	−1337.79	−	468.113i	−1.43694	−	0.502807i
$932$	305.532	−	634.444i	0.327824	−	0.680734i
$933$		0			0
$934$	1049.88	−	239.629i	1.12407	−	0.256562i
$935$	−335.610	+	161.621i	−0.358941	+	0.172857i
$936$		0			0
$937$	1133.62	+	904.034i	1.20984	+	0.964818i	0.999917	−	0.0128995i	$-0.00410614\pi$
$937$	1133.62	+	904.034i	1.20984	+	0.964818i	0.209926	+	0.977717i	$0.432678\pi$
$938$	35.2501	−	12.3345i	0.0375800	−	0.0131498i
$939$		0			0
$940$	−70.8965	+	70.8965i	−0.0754218	+	0.0754218i
$941$	774.360	−	617.532i	0.822912	−	0.656250i	−0.118708	−	0.992929i	$-0.537875\pi$
$941$	774.360	−	617.532i	0.822912	−	0.656250i	0.941620	+	0.336679i	$0.109304\pi$
$942$		0			0
$943$	1495.37	+	939.603i	1.58576	+	0.996397i
$944$	175.271	+	219.783i	0.185669	+	0.232821i
$945$		0			0
$946$	1489.23	+	167.796i	1.57424	+	0.177374i
$947$	223.766	+	639.488i	0.236290	+	0.675278i	0.999573	+	0.0292137i	$0.00930034\pi$
$947$	223.766	+	639.488i	0.236290	+	0.675278i	−0.763283	+	0.646064i	$0.776414\pi$
$948$		0			0
$949$	271.969	−	30.6436i	0.286585	−	0.0322904i
$950$	−251.279	−	521.787i	−0.264504	−	0.549249i
$951$		0			0
$952$	−4.06068	+	17.7910i	−0.00426542	+	0.0186880i
$953$	−109.037	−	52.5095i	−0.114415	−	0.0550992i	0.375801	−	0.926700i	$-0.377368\pi$
$953$	−109.037	−	52.5095i	−0.114415	−	0.0550992i	−0.490216	+	0.871601i	$0.663082\pi$
$954$		0			0
$955$	−279.930	−	445.506i	−0.293120	−	0.466498i
$956$			347.723i			0.363727i
$957$		0			0
$958$	483.673			0.504878
$959$	−10.5667	+	6.63949i	−0.0110184	+	0.00692335i
$960$		0			0
$961$	−315.451	+	655.040i	−0.328253	+	0.681624i
$962$	−223.779	−	51.0761i	−0.232618	−	0.0530936i
$963$		0			0
$964$	−20.8277	+	10.0301i	−0.0216055	+	0.0104047i
$965$	−78.0206	−	692.452i	−0.0808504	−	0.717567i
$966$		0			0
$967$	−929.620	+	325.288i	−0.961345	+	0.336389i	−0.764917	−	0.644129i	$-0.777220\pi$
$967$	−929.620	+	325.288i	−0.961345	+	0.336389i	−0.196428	+	0.980518i	$0.562934\pi$
$968$	87.4611	−	776.239i	0.0903524	−	0.801900i
$969$		0			0
$970$	−238.173	+	189.936i	−0.245539	+	0.195811i
$971$	−13.1141	+	20.8709i	−0.0135058	+	0.0214943i	−0.853409	−	0.521242i	$-0.825469\pi$
$971$	−13.1141	+	20.8709i	−0.0135058	+	0.0214943i	0.839903	+	0.542736i	$0.182612\pi$
$972$		0			0
$973$	−10.7356	−	13.4620i	−0.0110335	−	0.0138355i
$974$	−293.580	−	293.580i	−0.301417	−	0.301417i
$975$		0			0
$976$	239.061	+	683.197i	0.244939	+	0.699997i
$977$	−778.385	+	976.064i	−0.796709	+	0.999042i	0.203093	+	0.979159i	$0.434901\pi$
$977$	−778.385	+	976.064i	−0.796709	+	0.999042i	−0.999802	+	0.0198824i	$0.993671\pi$
$978$		0			0
$979$	−548.461	−	1138.89i	−0.560226	−	1.16332i
$980$	62.7885	+	275.094i	0.0640699	+	0.280709i
$981$		0			0
$982$	54.8197	+	26.3998i	0.0558245	+	0.0268837i
$983$	470.193	−	1343.73i	0.478324	−	1.36697i	−0.411809	−	0.911270i	$-0.635103\pi$
$983$	470.193	−	1343.73i	0.478324	−	1.36697i	0.890133	−	0.455701i	$-0.150611\pi$
$984$		0			0
$985$		−	1182.86i		−	1.20087i
$986$	−47.2055	+	325.323i	−0.0478757	+	0.329942i
$987$		0			0
$988$	226.126	−	142.084i	0.228873	−	0.143810i
$989$	1736.23	+	607.534i	1.75554	+	0.614291i
$990$		0			0
$991$	−598.205	−	136.536i	−0.603638	−	0.137776i	−0.0902298	−	0.995921i	$-0.528760\pi$
$991$	−598.205	−	136.536i	−0.603638	−	0.137776i	−0.513408	+	0.858145i	$0.671617\pi$
$992$	367.980	−	83.9890i	0.370947	−	0.0846663i
$993$		0			0
$994$	−2.80262	−	24.8739i	−0.00281953	−	0.0250241i
$995$	−799.834	−	637.846i	−0.803853	−	0.641051i
$996$		0			0
$997$	−157.753	+	1400.10i	−0.158228	+	1.40431i	0.624053	+	0.781382i	$0.285485\pi$
$997$	−157.753	+	1400.10i	−0.158228	+	1.40431i	−0.782280	+	0.622927i	$0.785943\pi$
$998$	−811.971	+	811.971i	−0.813598	+	0.813598i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.3.s.a.10.3		48
3.2	odd	2		29.3.f.a.10.2	yes	48
29.3	odd	28	inner	261.3.s.a.235.3		48
87.32	even	28		29.3.f.a.3.2	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.3.f.a.3.2	✓	48	87.32	even	28
29.3.f.a.10.2	yes	48	3.2	odd	2
261.3.s.a.10.3		48	1.1	even	1	trivial
261.3.s.a.235.3		48	29.3	odd	28	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.29187 - 0.811733i) q^{2} +(-0.725528 + 1.50658i) q^{4} +(-3.36294 - 0.767569i) q^{5} +(-0.255710 + 0.123143i) q^{7} +(0.968958 + 8.59974i) q^{8} +O(q^{10})\)	\(q+(1.29187 - 0.811733i) q^{2} +(-0.725528 + 1.50658i) q^{4} +(-3.36294 - 0.767569i) q^{5} +(-0.255710 + 0.123143i) q^{7} +(0.968958 + 8.59974i) q^{8} +(-4.96753 + 1.73821i) q^{10} +(-1.62739 + 14.4435i) q^{11} +(-4.30976 + 3.43692i) q^{13} +(-0.230383 + 0.366653i) q^{14} +(4.06213 + 5.09375i) q^{16} +(-5.25353 - 5.25353i) q^{17} +(9.56906 + 27.3468i) q^{19} +(3.59631 - 4.50963i) q^{20} +(9.62189 + 19.9801i) q^{22} +(6.05686 + 26.5368i) q^{23} +(-11.8040 - 5.68451i) q^{25} +(-2.77777 + 7.93841i) q^{26} -0.474590i q^{28} +(-2.32625 - 28.9065i) q^{29} +(-12.9513 + 8.13783i) q^{31} +(-23.2916 - 8.15007i) q^{32} +(-11.0513 - 2.52239i) q^{34} +(0.954457 - 0.217849i) q^{35} +(3.05571 + 27.1202i) q^{37} +(34.5602 + 27.5609i) q^{38} +(3.34235 - 29.6642i) q^{40} +(45.8791 - 45.8791i) q^{41} +(35.9543 - 57.2209i) q^{43} +(-20.5795 - 12.9310i) q^{44} +(29.3655 + 29.3655i) q^{46} +(-17.2732 - 1.94622i) q^{47} +(-30.5008 + 38.2468i) q^{49} +(-19.8635 + 2.23808i) q^{50} +(-2.05112 - 8.98655i) q^{52} +(-1.31097 + 5.74372i) q^{53} +(16.5592 - 47.3235i) q^{55} +(-1.30677 - 2.07972i) q^{56} +(-26.4696 - 35.4551i) q^{58} +43.1476 q^{59} +(104.863 + 36.6931i) q^{61} +(-10.1256 + 21.0260i) q^{62} +(-62.1125 + 14.1768i) q^{64} +(17.1315 - 8.25011i) q^{65} +(-67.4283 - 53.7723i) q^{67} +(11.7264 - 4.10325i) q^{68} +(1.05620 - 1.05620i) q^{70} +(-45.1943 + 36.0413i) q^{71} +(-42.0399 - 26.4154i) q^{73} +(25.9619 + 32.5552i) q^{74} +(-48.1426 - 5.42437i) q^{76} +(-1.36248 - 3.89374i) q^{77} +(96.9173 - 10.9200i) q^{79} +(-9.75090 - 20.2479i) q^{80} +(22.0280 - 96.5112i) q^{82} +(0.956785 + 0.460763i) q^{83} +(13.6349 + 21.6998i) q^{85} -103.107i q^{86} -125.787 q^{88} +(-73.6381 + 46.2699i) q^{89} +(0.678813 - 1.40957i) q^{91} +(-44.3742 - 10.1281i) q^{92} +(-23.8944 + 11.5070i) q^{94} +(-11.1896 - 99.3106i) q^{95} +(54.6355 - 19.1178i) q^{97} +(-8.35675 + 74.1682i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) \) 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8	\( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8} - 20 q^{10} + 8 q^{11} - 14 q^{13} - 26 q^{14} + 18 q^{16} + 26 q^{17} + 2 q^{19} - 46 q^{20} + 154 q^{22} - 56 q^{23} - 34 q^{25} - 110 q^{26} + 170 q^{29} - 88 q^{31} + 132 q^{32} - 224 q^{34} + 210 q^{35} - 56 q^{37} + 294 q^{38} - 492 q^{40} + 34 q^{41} + 176 q^{43} - 126 q^{44} + 744 q^{46} - 208 q^{47} + 506 q^{49} - 732 q^{50} + 690 q^{52} + 14 q^{53} + 284 q^{55} - 332 q^{56} - 508 q^{58} + 44 q^{59} - 30 q^{61} + 504 q^{62} - 896 q^{64} + 554 q^{65} - 574 q^{67} + 796 q^{68} - 1066 q^{70} - 224 q^{71} - 22 q^{73} - 820 q^{74} + 514 q^{76} - 436 q^{77} + 564 q^{79} - 1162 q^{80} - 18 q^{82} + 126 q^{83} + 38 q^{85} - 384 q^{88} + 160 q^{89} - 434 q^{91} + 1022 q^{92} - 2 q^{94} + 642 q^{95} + 604 q^{97} + 102 q^{98}+O(q^{100}) \) 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8 - 20 * q^10 + 8 * q^11 - 14 * q^13 - 26 * q^14 + 18 * q^16 + 26 * q^17 + 2 * q^19 - 46 * q^20 + 154 * q^22 - 56 * q^23 - 34 * q^25 - 110 * q^26 + 170 * q^29 - 88 * q^31 + 132 * q^32 - 224 * q^34 + 210 * q^35 - 56 * q^37 + 294 * q^38 - 492 * q^40 + 34 * q^41 + 176 * q^43 - 126 * q^44 + 744 * q^46 - 208 * q^47 + 506 * q^49 - 732 * q^50 + 690 * q^52 + 14 * q^53 + 284 * q^55 - 332 * q^56 - 508 * q^58 + 44 * q^59 - 30 * q^61 + 504 * q^62 - 896 * q^64 + 554 * q^65 - 574 * q^67 + 796 * q^68 - 1066 * q^70 - 224 * q^71 - 22 * q^73 - 820 * q^74 + 514 * q^76 - 436 * q^77 + 564 * q^79 - 1162 * q^80 - 18 * q^82 + 126 * q^83 + 38 * q^85 - 384 * q^88 + 160 * q^89 - 434 * q^91 + 1022 * q^92 - 2 * q^94 + 642 * q^95 + 604 * q^97 + 102 * q^98

Introduction

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