LMFDB - Embedded newform 169.3.d.d.99.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,3,Mod(70,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("169.70");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	169.d (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.60491646769$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 25 $ x^4 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			99.2
Root			$1.58114 + 1.58114i$ of defining polynomial
Character	$\chi$	$=$	169.99
Dual form			169.3.d.d.70.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.58114 + 2.58114i) q^{2} +2.16228 q^{3} +9.32456i q^{4} +(-0.418861 - 0.418861i) q^{5} +(5.58114 + 5.58114i) q^{6} +(1.41886 - 1.41886i) q^{7} +(-13.7434 + 13.7434i) q^{8} -4.32456 q^{9} +O(q^{10})$	\(q+(2.58114 + 2.58114i) q^{2} +2.16228 q^{3} +9.32456i q^{4} +(-0.418861 - 0.418861i) q^{5} +(5.58114 + 5.58114i) q^{6} +(1.41886 - 1.41886i) q^{7} +(-13.7434 + 13.7434i) q^{8} -4.32456 q^{9} -2.16228i q^{10} +(7.32456 - 7.32456i) q^{11} +20.1623i q^{12} +7.32456 q^{14} +(-0.905694 - 0.905694i) q^{15} -33.6491 q^{16} -15.9737i q^{17} +(-11.1623 - 11.1623i) q^{18} +(3.16228 + 3.16228i) q^{19} +(3.90569 - 3.90569i) q^{20} +(3.06797 - 3.06797i) q^{21} +37.8114 q^{22} +27.4868i q^{23} +(-29.7171 + 29.7171i) q^{24} -24.6491i q^{25} -28.8114 q^{27} +(13.2302 + 13.2302i) q^{28} +25.8114 q^{29} -4.67544i q^{30} +(-19.4868 - 19.4868i) q^{31} +(-31.8794 - 31.8794i) q^{32} +(15.8377 - 15.8377i) q^{33} +(41.2302 - 41.2302i) q^{34} -1.18861 q^{35} -40.3246i q^{36} +(4.23025 - 4.23025i) q^{37} +16.3246i q^{38} +11.5132 q^{40} +(-11.1623 - 11.1623i) q^{41} +15.8377 q^{42} -11.5132i q^{43} +(68.2982 + 68.2982i) q^{44} +(1.81139 + 1.81139i) q^{45} +(-70.9473 + 70.9473i) q^{46} +(-35.3662 + 35.3662i) q^{47} -72.7587 q^{48} +44.9737i q^{49} +(63.6228 - 63.6228i) q^{50} -34.5395i q^{51} -4.18861 q^{53} +(-74.3662 - 74.3662i) q^{54} -6.13594 q^{55} +39.0000i q^{56} +(6.83772 + 6.83772i) q^{57} +(66.6228 + 66.6228i) q^{58} +(30.2719 - 30.2719i) q^{59} +(8.44520 - 8.44520i) q^{60} -67.6754 q^{61} -100.596i q^{62} +(-6.13594 + 6.13594i) q^{63} -29.9737i q^{64} +81.7587 q^{66} +(81.0833 + 81.0833i) q^{67} +148.947 q^{68} +59.4342i q^{69} +(-3.06797 - 3.06797i) q^{70} +(-50.4452 - 50.4452i) q^{71} +(59.4342 - 59.4342i) q^{72} +(31.6228 - 31.6228i) q^{73} +21.8377 q^{74} -53.2982i q^{75} +(-29.4868 + 29.4868i) q^{76} -20.7851i q^{77} +50.7851 q^{79} +(14.0943 + 14.0943i) q^{80} -23.3772 q^{81} -57.6228i q^{82} +(-18.6228 - 18.6228i) q^{83} +(28.6075 + 28.6075i) q^{84} +(-6.69075 + 6.69075i) q^{85} +(29.7171 - 29.7171i) q^{86} +55.8114 q^{87} +201.329i q^{88} +(-91.1096 + 91.1096i) q^{89} +9.35089i q^{90} -256.302 q^{92} +(-42.1359 - 42.1359i) q^{93} -182.570 q^{94} -2.64911i q^{95} +(-68.9320 - 68.9320i) q^{96} +(-87.3552 - 87.3552i) q^{97} +(-116.083 + 116.083i) q^{98} +(-31.6754 + 31.6754i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} - 8 q^{5} + 16 q^{6} + 12 q^{7} - 36 q^{8} + 8 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 - 8 * q^5 + 16 * q^6 + 12 * q^7 - 36 * q^8 + 8 * q^9	$ 4 q + 4 q^{2} - 4 q^{3} - 8 q^{5} + 16 q^{6} + 12 q^{7} - 36 q^{8} + 8 q^{9} + 4 q^{11} + 4 q^{14} + 28 q^{15} - 84 q^{16} - 32 q^{18} - 16 q^{20} - 32 q^{21} + 88 q^{22} - 24 q^{24} - 52 q^{27} - 4 q^{28} + 40 q^{29} - 40 q^{31} - 20 q^{32} + 76 q^{33} + 108 q^{34} - 68 q^{35} - 40 q^{37} + 84 q^{40} - 32 q^{41} + 76 q^{42} + 172 q^{44} - 56 q^{45} - 132 q^{46} + 4 q^{47} - 76 q^{48} + 128 q^{50} - 80 q^{53} - 152 q^{54} + 64 q^{55} + 40 q^{57} + 140 q^{58} - 56 q^{59} + 116 q^{60} - 296 q^{61} + 64 q^{63} + 112 q^{66} + 84 q^{67} + 444 q^{68} + 32 q^{70} - 284 q^{71} + 48 q^{72} + 100 q^{74} - 80 q^{76} + 64 q^{79} + 88 q^{80} - 220 q^{81} + 52 q^{83} + 184 q^{84} + 144 q^{85} + 24 q^{86} + 160 q^{87} - 200 q^{89} - 456 q^{92} - 80 q^{93} - 452 q^{94} - 320 q^{96} + 68 q^{97} - 224 q^{98} - 152 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^3 - 8 * q^5 + 16 * q^6 + 12 * q^7 - 36 * q^8 + 8 * q^9 + 4 * q^11 + 4 * q^14 + 28 * q^15 - 84 * q^16 - 32 * q^18 - 16 * q^20 - 32 * q^21 + 88 * q^22 - 24 * q^24 - 52 * q^27 - 4 * q^28 + 40 * q^29 - 40 * q^31 - 20 * q^32 + 76 * q^33 + 108 * q^34 - 68 * q^35 - 40 * q^37 + 84 * q^40 - 32 * q^41 + 76 * q^42 + 172 * q^44 - 56 * q^45 - 132 * q^46 + 4 * q^47 - 76 * q^48 + 128 * q^50 - 80 * q^53 - 152 * q^54 + 64 * q^55 + 40 * q^57 + 140 * q^58 - 56 * q^59 + 116 * q^60 - 296 * q^61 + 64 * q^63 + 112 * q^66 + 84 * q^67 + 444 * q^68 + 32 * q^70 - 284 * q^71 + 48 * q^72 + 100 * q^74 - 80 * q^76 + 64 * q^79 + 88 * q^80 - 220 * q^81 + 52 * q^83 + 184 * q^84 + 144 * q^85 + 24 * q^86 + 160 * q^87 - 200 * q^89 - 456 * q^92 - 80 * q^93 - 452 * q^94 - 320 * q^96 + 68 * q^97 - 224 * q^98 - 152 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	2.58114	+	2.58114i	1.29057	+	1.29057i	0.934435	+	0.356135i	$0.115906\pi$
$2$	2.58114	+	2.58114i	1.29057	+	1.29057i	0.356135	+	0.934435i	$0.384094\pi$
$3$	2.16228			0.720759			0.360380	−	0.932806i	$-0.382647\pi$
$3$	2.16228			0.720759			0.360380	+	0.932806i	$0.382647\pi$
$4$			9.32456i			2.33114i
$5$	−0.418861	−	0.418861i	−0.0837722	−	0.0837722i	0.663979	−	0.747751i	$-0.268866\pi$
$5$	−0.418861	−	0.418861i	−0.0837722	−	0.0837722i	−0.747751	+	0.663979i	$0.768866\pi$
$6$	5.58114	+	5.58114i	0.930190	+	0.930190i
$7$	1.41886	−	1.41886i	0.202694	−	0.202694i	−0.598459	−	0.801153i	$-0.704220\pi$
$7$	1.41886	−	1.41886i	0.202694	−	0.202694i	0.801153	+	0.598459i	$0.204220\pi$
$8$	−13.7434	+	13.7434i	−1.71793	+	1.71793i
$9$	−4.32456			−0.480506
$10$		−	2.16228i		−	0.216228i
$11$	7.32456	−	7.32456i	0.665869	−	0.665869i	−0.290888	−	0.956757i	$-0.593951\pi$
$11$	7.32456	−	7.32456i	0.665869	−	0.665869i	0.956757	+	0.290888i	$0.0939508\pi$
$12$			20.1623i			1.68019i
$13$		0			0
$13$		0			0
$14$	7.32456			0.523183
$15$	−0.905694	−	0.905694i	−0.0603796	−	0.0603796i
$16$	−33.6491			−2.10307
$17$		−	15.9737i		−	0.939627i	−0.882766	−	0.469814i	$-0.844321\pi$
$17$		−	15.9737i		−	0.939627i	0.882766	−	0.469814i	$-0.155679\pi$
$18$	−11.1623	−	11.1623i	−0.620127	−	0.620127i
$19$	3.16228	+	3.16228i	0.166436	+	0.166436i	0.785411	−	0.618975i	$-0.212452\pi$
$19$	3.16228	+	3.16228i	0.166436	+	0.166436i	−0.618975	+	0.785411i	$0.712452\pi$
$20$	3.90569	−	3.90569i	0.195285	−	0.195285i
$21$	3.06797	−	3.06797i	0.146094	−	0.146094i
$22$	37.8114			1.71870
$23$			27.4868i			1.19508i	0.801839	+	0.597540i	$0.203855\pi$
$23$			27.4868i			1.19508i	−0.801839	+	0.597540i	$0.796145\pi$
$24$	−29.7171	+	29.7171i	−1.23821	+	1.23821i
$25$		−	24.6491i		−	0.985964i
$26$		0			0
$27$	−28.8114			−1.06709
$28$	13.2302	+	13.2302i	0.472509	+	0.472509i
$29$	25.8114			0.890048			0.445024	−	0.895519i	$-0.353195\pi$
$29$	25.8114			0.890048			0.445024	+	0.895519i	$0.353195\pi$
$30$		−	4.67544i		−	0.155848i
$31$	−19.4868	−	19.4868i	−0.628608	−	0.628608i	0.319110	−	0.947718i	$-0.396616\pi$
$31$	−19.4868	−	19.4868i	−0.628608	−	0.628608i	−0.947718	+	0.319110i	$0.896616\pi$
$32$	−31.8794	−	31.8794i	−0.996230	−	0.996230i
$33$	15.8377	−	15.8377i	0.479931	−	0.479931i
$34$	41.2302	−	41.2302i	1.21265	−	1.21265i
$35$	−1.18861			−0.0339603
$36$		−	40.3246i		−	1.12013i
$37$	4.23025	−	4.23025i	0.114331	−	0.114331i	−0.647627	−	0.761958i	$-0.724238\pi$
$37$	4.23025	−	4.23025i	0.114331	−	0.114331i	0.761958	+	0.647627i	$0.224238\pi$
$38$			16.3246i			0.429594i
$39$		0			0
$40$	11.5132			0.287829
$41$	−11.1623	−	11.1623i	−0.272251	−	0.272251i	0.557755	−	0.830006i	$-0.311663\pi$
$41$	−11.1623	−	11.1623i	−0.272251	−	0.272251i	−0.830006	+	0.557755i	$0.811663\pi$
$42$	15.8377			0.377089
$43$		−	11.5132i		−	0.267748i	−0.990998	−	0.133874i	$-0.957258\pi$
$43$		−	11.5132i		−	0.267748i	0.990998	−	0.133874i	$-0.0427418\pi$
$44$	68.2982	+	68.2982i	1.55223	+	1.55223i
$45$	1.81139	+	1.81139i	0.0402531	+	0.0402531i
$46$	−70.9473	+	70.9473i	−1.54233	+	1.54233i
$47$	−35.3662	+	35.3662i	−0.752472	+	0.752472i	−0.974940	−	0.222468i	$-0.928589\pi$
$47$	−35.3662	+	35.3662i	−0.752472	+	0.752472i	0.222468	+	0.974940i	$0.428589\pi$
$48$	−72.7587			−1.51581
$49$			44.9737i			0.917830i
$50$	63.6228	−	63.6228i	1.27246	−	1.27246i
$51$		−	34.5395i		−	0.677245i
$52$		0			0
$53$	−4.18861			−0.0790304			−0.0395152	−	0.999219i	$-0.512581\pi$
$53$	−4.18861			−0.0790304			−0.0395152	+	0.999219i	$0.512581\pi$
$54$	−74.3662	−	74.3662i	−1.37715	−	1.37715i
$55$	−6.13594			−0.111563
$56$			39.0000i			0.696429i
$57$	6.83772	+	6.83772i	0.119960	+	0.119960i
$58$	66.6228	+	66.6228i	1.14867	+	1.14867i
$59$	30.2719	−	30.2719i	0.513083	−	0.513083i	−0.402387	−	0.915470i	$-0.631819\pi$
$59$	30.2719	−	30.2719i	0.513083	−	0.513083i	0.915470	+	0.402387i	$0.131819\pi$
$60$	8.44520	−	8.44520i	0.140753	−	0.140753i
$61$	−67.6754			−1.10943			−0.554717	−	0.832039i	$-0.687173\pi$
$61$	−67.6754			−1.10943			−0.554717	+	0.832039i	$0.687173\pi$
$62$		−	100.596i		−	1.62252i
$63$	−6.13594	+	6.13594i	−0.0973959	+	0.0973959i
$64$		−	29.9737i		−	0.468339i
$65$		0			0
$66$	81.7587			1.23877
$67$	81.0833	+	81.0833i	1.21020	+	1.21020i	0.970961	+	0.239237i	$0.0768973\pi$
$67$	81.0833	+	81.0833i	1.21020	+	1.21020i	0.239237	+	0.970961i	$0.423103\pi$
$68$	148.947			2.19040
$69$			59.4342i			0.861365i
$70$	−3.06797	−	3.06797i	−0.0438282	−	0.0438282i
$71$	−50.4452	−	50.4452i	−0.710496	−	0.710496i	0.256143	−	0.966639i	$-0.417548\pi$
$71$	−50.4452	−	50.4452i	−0.710496	−	0.710496i	−0.966639	+	0.256143i	$0.917548\pi$
$72$	59.4342	−	59.4342i	0.825475	−	0.825475i
$73$	31.6228	−	31.6228i	0.433189	−	0.433189i	−0.456523	−	0.889712i	$-0.650905\pi$
$73$	31.6228	−	31.6228i	0.433189	−	0.433189i	0.889712	+	0.456523i	$0.150905\pi$
$74$	21.8377			0.295104
$75$		−	53.2982i		−	0.710643i
$76$	−29.4868	+	29.4868i	−0.387985	+	0.387985i
$77$		−	20.7851i		−	0.269936i
$78$		0			0
$79$	50.7851			0.642849			0.321424	−	0.946935i	$-0.395838\pi$
$79$	50.7851			0.642849			0.321424	+	0.946935i	$0.395838\pi$
$80$	14.0943	+	14.0943i	0.176179	+	0.176179i
$81$	−23.3772			−0.288608
$82$		−	57.6228i		−	0.702717i
$83$	−18.6228	−	18.6228i	−0.224371	−	0.224371i	0.585965	−	0.810336i	$-0.300715\pi$
$83$	−18.6228	−	18.6228i	−0.224371	−	0.224371i	−0.810336	+	0.585965i	$0.800715\pi$
$84$	28.6075	+	28.6075i	0.340565	+	0.340565i
$85$	−6.69075	+	6.69075i	−0.0787147	+	0.0787147i
$86$	29.7171	−	29.7171i	0.345547	−	0.345547i
$87$	55.8114			0.641510
$88$			201.329i			2.28783i
$89$	−91.1096	+	91.1096i	−1.02370	+	1.02370i	−0.0239913	+	0.999712i	$0.507637\pi$
$89$	−91.1096	+	91.1096i	−1.02370	+	1.02370i	−0.999712	+	0.0239913i	$0.992363\pi$
$90$			9.35089i			0.103899i
$91$		0			0
$92$	−256.302			−2.78590
$93$	−42.1359	−	42.1359i	−0.453075	−	0.453075i
$94$	−182.570			−1.94224
$95$		−	2.64911i		−	0.0278854i
$96$	−68.9320	−	68.9320i	−0.718042	−	0.718042i
$97$	−87.3552	−	87.3552i	−0.900569	−	0.900569i	0.0949165	−	0.995485i	$-0.469742\pi$
$97$	−87.3552	−	87.3552i	−0.900569	−	0.900569i	−0.995485	+	0.0949165i	$0.969742\pi$
$98$	−116.083	+	116.083i	−1.18452	+	1.18452i
$99$	−31.6754	+	31.6754i	−0.319954	+	0.319954i
$100$	229.842			2.29842
$101$		−	8.92100i		−	0.0883267i	−0.999024	−	0.0441634i	$-0.985938\pi$
$101$		−	8.92100i		−	0.0883267i	0.999024	−	0.0441634i	$-0.0140622\pi$
$102$	89.1512	−	89.1512i	0.874032	−	0.874032i
$103$			59.4342i			0.577031i	0.957475	+	0.288515i	$0.0931616\pi$
$103$			59.4342i			0.577031i	−0.957475	+	0.288515i	$0.906838\pi$
$104$		0			0
$105$	−2.57011			−0.0244772
$106$	−10.8114	−	10.8114i	−0.101994	−	0.101994i
$107$	−143.570			−1.34178			−0.670888	−	0.741558i	$-0.734087\pi$
$107$	−143.570			−1.34178			−0.670888	+	0.741558i	$0.734087\pi$
$108$		−	268.653i		−	2.48753i
$109$	84.7740	+	84.7740i	0.777743	+	0.777743i	0.979447	−	0.201703i	$-0.0646477\pi$
$109$	84.7740	+	84.7740i	0.777743	+	0.777743i	−0.201703	+	0.979447i	$0.564648\pi$
$110$	−15.8377	−	15.8377i	−0.143979	−	0.143979i
$111$	9.14697	−	9.14697i	0.0824052	−	0.0824052i
$112$	−47.7434	+	47.7434i	−0.426281	+	0.426281i
$113$	−108.544			−0.960564			−0.480282	−	0.877114i	$-0.659466\pi$
$113$	−108.544			−0.960564			−0.480282	+	0.877114i	$0.659466\pi$
$114$			35.2982i			0.309634i
$115$	11.5132	−	11.5132i	0.100114	−	0.100114i
$116$			240.680i			2.07483i
$117$		0			0
$118$	156.272			1.32434
$119$	−22.6644	−	22.6644i	−0.190457	−	0.190457i
$120$	24.8947			0.207456
$121$			13.7018i			0.113238i
$122$	−174.680	−	174.680i	−1.43180	−	1.43180i
$123$	−24.1359	−	24.1359i	−0.196227	−	0.196227i
$124$	181.706	−	181.706i	1.46537	−	1.46537i
$125$	−20.7961	+	20.7961i	−0.166369	+	0.166369i
$126$	−31.6754			−0.251392
$127$		−	94.8377i		−	0.746754i	−0.927680	−	0.373377i	$-0.878200\pi$
$127$		−	94.8377i		−	0.746754i	0.927680	−	0.373377i	$-0.121800\pi$
$128$	−50.1512	+	50.1512i	−0.391807	+	0.391807i
$129$		−	24.8947i		−	0.192982i
$130$		0			0
$131$	−112.268			−0.857005			−0.428502	−	0.903541i	$-0.640959\pi$
$131$	−112.268			−0.857005			−0.428502	+	0.903541i	$0.640959\pi$
$132$	147.680	+	147.680i	1.11879	+	1.11879i
$133$	8.97367			0.0674712
$134$			418.574i			3.12369i
$135$	12.0680	+	12.0680i	0.0893924	+	0.0893924i
$136$	219.533	+	219.533i	1.61421	+	1.61421i
$137$	−86.7281	+	86.7281i	−0.633052	+	0.633052i	−0.948832	−	0.315780i	$-0.897734\pi$
$137$	−86.7281	+	86.7281i	−0.633052	+	0.633052i	0.315780	+	0.948832i	$0.397734\pi$
$138$	−153.408	+	153.408i	−1.11165	+	1.11165i
$139$	78.5395			0.565032			0.282516	−	0.959263i	$-0.408831\pi$
$139$	78.5395			0.565032			0.282516	+	0.959263i	$0.408831\pi$
$140$		−	11.0833i		−	0.0791663i
$141$	−76.4715	+	76.4715i	−0.542351	+	0.542351i
$142$		−	260.412i		−	1.83389i
$143$		0			0
$144$	145.517			1.01054
$145$	−10.8114	−	10.8114i	−0.0745613	−	0.0745613i
$146$	163.246			1.11812
$147$			97.2456i			0.661534i
$148$	39.4452	+	39.4452i	0.266522	+	0.266522i
$149$	128.219	+	128.219i	0.860532	+	0.860532i	0.991400	−	0.130868i	$-0.0417764\pi$
$149$	128.219	+	128.219i	0.860532	+	0.860532i	−0.130868	+	0.991400i	$0.541776\pi$
$150$	137.570	−	137.570i	0.917134	−	0.917134i
$151$	−29.1776	+	29.1776i	−0.193229	+	0.193229i	−0.797090	−	0.603861i	$-0.793628\pi$
$151$	−29.1776	+	29.1776i	−0.193229	+	0.193229i	0.603861	+	0.797090i	$0.293628\pi$
$152$	−86.9210			−0.571849
$153$			69.0790i			0.451497i
$154$	53.6491	−	53.6491i	0.348371	−	0.348371i
$155$			16.3246i			0.105320i
$156$		0			0
$157$	232.544			1.48117			0.740585	−	0.671962i	$-0.234548\pi$
$157$	232.544			1.48117			0.740585	+	0.671962i	$0.234548\pi$
$158$	131.083	+	131.083i	0.829641	+	0.829641i
$159$	−9.05694			−0.0569619
$160$			26.7061i			0.166913i
$161$	39.0000	+	39.0000i	0.242236	+	0.242236i
$162$	−60.3399	−	60.3399i	−0.372468	−	0.372468i
$163$	−11.4605	+	11.4605i	−0.0703098	+	0.0703098i	−0.741387	−	0.671077i	$-0.765832\pi$
$163$	−11.4605	+	11.4605i	−0.0703098	+	0.0703098i	0.671077	+	0.741387i	$0.265832\pi$
$164$	104.083	−	104.083i	0.634654	−	0.634654i
$165$	−13.2676			−0.0804098
$166$		−	96.1359i		−	0.579132i
$167$	206.785	−	206.785i	1.23823	−	1.23823i	0.277512	−	0.960722i	$-0.410490\pi$
$167$	206.785	−	206.785i	1.23823	−	1.23823i	0.960722	−	0.277512i	$-0.0895097\pi$
$168$			84.3288i			0.501957i
$169$		0			0
$170$	−34.5395			−0.203174
$171$	−13.6754	−	13.6754i	−0.0799734	−	0.0799734i
$172$	107.355			0.624158
$173$		−	91.3815i		−	0.528217i	−0.964493	−	0.264108i	$-0.914922\pi$
$173$		−	91.3815i		−	0.528217i	0.964493	−	0.264108i	$-0.0850777\pi$
$174$	144.057	+	144.057i	0.827913	+	0.827913i
$175$	−34.9737	−	34.9737i	−0.199850	−	0.199850i
$176$	−246.465	+	246.465i	−1.40037	+	1.40037i
$177$	65.4562	−	65.4562i	0.369809	−	0.369809i
$178$	−470.333			−2.64232
$179$		−	71.6712i		−	0.400398i	−0.979755	−	0.200199i	$-0.935841\pi$
$179$		−	71.6712i		−	0.400398i	0.979755	−	0.200199i	$-0.0641588\pi$
$180$	−16.8904	+	16.8904i	−0.0938355	+	0.0938355i
$181$			274.144i			1.51461i	0.653061	+	0.757305i	$0.273484\pi$
$181$			274.144i			1.51461i	−0.653061	+	0.757305i	$0.726516\pi$
$182$		0			0
$183$	−146.333			−0.799634
$184$	−377.763	−	377.763i	−2.05306	−	2.05306i
$185$	−3.54377			−0.0191555
$186$		−	217.517i		−	1.16945i
$187$	−117.000	−	117.000i	−0.625668	−	0.625668i
$188$	−329.774	−	329.774i	−1.75412	−	1.75412i
$189$	−40.8794	+	40.8794i	−0.216293	+	0.216293i
$190$	6.83772	−	6.83772i	0.0359880	−	0.0359880i
$191$	179.706			0.940869			0.470435	−	0.882435i	$-0.344097\pi$
$191$	179.706			0.940869			0.470435	+	0.882435i	$0.344097\pi$
$192$		−	64.8114i		−	0.337559i
$193$	1.13594	−	1.13594i	0.00588572	−	0.00588572i	−0.704158	−	0.710044i	$-0.748675\pi$
$193$	1.13594	−	1.13594i	0.00588572	−	0.00588572i	0.710044	+	0.704158i	$0.248675\pi$
$194$		−	450.952i		−	2.32449i
$195$		0			0
$196$	−419.359			−2.13959
$197$	−141.906	−	141.906i	−0.720333	−	0.720333i	0.248340	−	0.968673i	$-0.420115\pi$
$197$	−141.906	−	141.906i	−0.720333	−	0.720333i	−0.968673	+	0.248340i	$0.920115\pi$
$198$	−163.517			−0.825846
$199$		−	259.759i		−	1.30532i	−0.757651	−	0.652660i	$-0.773653\pi$
$199$		−	259.759i		−	1.30532i	0.757651	−	0.652660i	$-0.226347\pi$
$200$	338.763	+	338.763i	1.69381	+	1.69381i
$201$	175.325	+	175.325i	0.872261	+	0.872261i
$202$	23.0263	−	23.0263i	0.113992	−	0.113992i
$203$	36.6228	−	36.6228i	0.180408	−	0.180408i
$204$	322.065			1.57875
$205$			9.35089i			0.0456141i
$206$	−153.408	+	153.408i	−0.744698	+	0.744698i
$207$		−	118.868i		−	0.574243i
$208$		0			0
$209$	46.3246			0.221649
$210$	−6.63381	−	6.63381i	−0.0315896	−	0.0315896i
$211$	325.574			1.54301			0.771503	−	0.636225i	$-0.219505\pi$
$211$	325.574			1.54301			0.771503	+	0.636225i	$0.219505\pi$
$212$		−	39.0569i		−	0.184231i
$213$	−109.077	−	109.077i	−0.512096	−	0.512096i
$214$	−370.574	−	370.574i	−1.73166	−	1.73166i
$215$	−4.82242	+	4.82242i	−0.0224299	+	0.0224299i
$216$	395.967	−	395.967i	1.83318	−	1.83318i
$217$	−55.2982			−0.254831
$218$			437.627i			2.00746i
$219$	68.3772	−	68.3772i	0.312225	−	0.312225i
$220$		−	57.2149i		−	0.260068i
$221$		0			0
$222$	47.2192			0.212699
$223$	243.774	+	243.774i	1.09316	+	1.09316i	0.995190	+	0.0979674i	$0.0312341\pi$
$223$	243.774	+	243.774i	1.09316	+	1.09316i	0.0979674	+	0.995190i	$0.468766\pi$
$224$	−90.4648			−0.403861
$225$			106.596i			0.473762i
$226$	−280.167	−	280.167i	−1.23968	−	1.23968i
$227$	100.732	+	100.732i	0.443755	+	0.443755i	0.893272	−	0.449517i	$-0.148404\pi$
$227$	100.732	+	100.732i	0.443755	+	0.443755i	−0.449517	+	0.893272i	$0.648404\pi$
$228$	−63.7587	+	63.7587i	−0.279644	+	0.279644i
$229$	240.366	−	240.366i	1.04963	−	1.04963i	0.0509319	−	0.998702i	$-0.483781\pi$
$229$	240.366	−	240.366i	1.04963	−	1.04963i	0.998702	−	0.0509319i	$-0.0162191\pi$
$230$	59.4342			0.258409
$231$		−	44.9431i		−	0.194559i
$232$	−354.737	+	354.737i	−1.52904	+	1.52904i
$233$		−	10.7893i		−	0.0463061i	−0.999732	−	0.0231531i	$-0.992629\pi$
$233$		−	10.7893i		−	0.0463061i	0.999732	−	0.0231531i	$-0.00737051\pi$
$234$		0			0
$235$	29.6271			0.126073
$236$	282.272	+	282.272i	1.19607	+	1.19607i
$237$	109.811			0.463339
$238$		−	117.000i		−	0.491597i
$239$	98.0153	+	98.0153i	0.410106	+	0.410106i	0.881775	−	0.471670i	$-0.156348\pi$
$239$	98.0153	+	98.0153i	0.410106	+	0.410106i	−0.471670	+	0.881775i	$0.656348\pi$
$240$	30.4758	+	30.4758i	0.126983	+	0.126983i
$241$	196.197	−	196.197i	0.814096	−	0.814096i	−0.171149	−	0.985245i	$-0.554748\pi$
$241$	196.197	−	196.197i	0.814096	−	0.814096i	0.985245	+	0.171149i	$0.0547480\pi$
$242$	−35.3662	+	35.3662i	−0.146141	+	0.146141i
$243$	208.754			0.859072
$244$		−	631.043i		−	2.58624i
$245$	18.8377	−	18.8377i	0.0768887	−	0.0768887i
$246$		−	124.596i		−	0.506490i
$247$		0			0
$248$	535.631			2.15980
$249$	−40.2676	−	40.2676i	−0.161717	−	0.161717i
$250$	−107.355			−0.429421
$251$		−	95.8420i		−	0.381841i	−0.981606	−	0.190920i	$-0.938853\pi$
$251$		−	95.8420i		−	0.381841i	0.981606	−	0.190920i	$-0.0611472\pi$
$252$	−57.2149	−	57.2149i	−0.227043	−	0.227043i
$253$	201.329	+	201.329i	0.795766	+	0.795766i
$254$	244.789	−	244.789i	0.963738	−	0.963738i
$255$	−14.4673	+	14.4673i	−0.0567343	+	0.0567343i
$256$	−378.789			−1.47965
$257$			450.579i			1.75322i	0.481198	+	0.876612i	$0.340202\pi$
$257$			450.579i			1.75322i	−0.481198	+	0.876612i	$0.659798\pi$
$258$	64.2566	−	64.2566i	0.249057	−	0.249057i
$259$		−	12.0043i		−	0.0463485i
$260$		0			0
$261$	−111.623			−0.427673
$262$	−289.778	−	289.778i	−1.10602	−	1.10602i
$263$	166.982			0.634913			0.317457	−	0.948273i	$-0.397171\pi$
$263$	166.982			0.634913			0.317457	+	0.948273i	$0.397171\pi$
$264$			435.329i			1.64897i
$265$	1.75445	+	1.75445i	0.00662055	+	0.00662055i
$266$	23.1623	+	23.1623i	0.0870762	+	0.0870762i
$267$	−197.004	+	197.004i	−0.737844	+	0.737844i
$268$	−756.065	+	756.065i	−2.82114	+	2.82114i
$269$	170.061			0.632198			0.316099	−	0.948726i	$-0.397627\pi$
$269$	170.061			0.632198			0.316099	+	0.948726i	$0.397627\pi$
$270$			62.2982i			0.230734i
$271$	217.072	−	217.072i	0.801005	−	0.801005i	−0.182248	−	0.983253i	$-0.558337\pi$
$271$	217.072	−	217.072i	0.801005	−	0.801005i	0.983253	+	0.182248i	$0.0583374\pi$
$272$			537.500i			1.97610i
$273$		0			0
$274$	−447.715			−1.63399
$275$	−180.544	−	180.544i	−0.656523	−	0.656523i
$276$	−554.197			−2.00796
$277$			187.947i			0.678510i	0.940694	+	0.339255i	$0.110175\pi$
$277$			187.947i			0.678510i	−0.940694	+	0.339255i	$0.889825\pi$
$278$	202.721	+	202.721i	0.729214	+	0.729214i
$279$	84.2719	+	84.2719i	0.302050	+	0.302050i
$280$	16.3356	−	16.3356i	0.0583414	−	0.0583414i
$281$	−286.846	+	286.846i	−1.02081	+	1.02081i	−0.0210263	+	0.999779i	$0.506693\pi$
$281$	−286.846	+	286.846i	−1.02081	+	1.02081i	−0.999779	+	0.0210263i	$0.993307\pi$
$282$	−394.767			−1.39988
$283$		−	399.201i		−	1.41061i	−0.708906	−	0.705303i	$-0.750811\pi$
$283$		−	399.201i		−	1.41061i	0.708906	−	0.705303i	$-0.249189\pi$
$284$	470.379	−	470.379i	1.65626	−	1.65626i
$285$		−	5.72811i		−	0.0200986i
$286$		0			0
$287$	−31.6754			−0.110367
$288$	137.864	+	137.864i	0.478695	+	0.478695i
$289$	33.8420			0.117100
$290$		−	55.8114i		−	0.192453i
$291$	−188.886	−	188.886i	−0.649093	−	0.649093i
$292$	294.868	+	294.868i	1.00982	+	1.00982i
$293$	−136.156	+	136.156i	−0.464695	+	0.464695i	−0.900191	−	0.435496i	$-0.856573\pi$
$293$	−136.156	+	136.156i	−0.464695	+	0.464695i	0.435496	+	0.900191i	$0.356573\pi$
$294$	−251.004	+	251.004i	−0.853756	+	0.853756i
$295$	−25.3594			−0.0859642
$296$			116.276i			0.392825i
$297$	−211.031	+	211.031i	−0.710541	+	0.710541i
$298$			661.903i			2.22115i
$299$		0			0
$300$	496.982			1.65661
$301$	−16.3356	−	16.3356i	−0.0542710	−	0.0542710i
$302$	−150.623			−0.498751
$303$		−	19.2897i		−	0.0636623i
$304$	−106.408	−	106.408i	−0.350026	−	0.350026i
$305$	28.3466	+	28.3466i	0.0929397	+	0.0929397i
$306$	−178.302	+	178.302i	−0.582688	+	0.582688i
$307$	235.684	−	235.684i	0.767700	−	0.767700i	−0.210001	−	0.977701i	$-0.567347\pi$
$307$	235.684	−	235.684i	0.767700	−	0.767700i	0.977701	+	0.210001i	$0.0673467\pi$
$308$	193.811			0.629258
$309$			128.513i			0.415900i
$310$	−42.1359	+	42.1359i	−0.135922	+	0.135922i
$311$		−	113.684i		−	0.365543i	−0.983155	−	0.182772i	$-0.941493\pi$
$311$		−	113.684i		−	0.365543i	0.983155	−	0.182772i	$-0.0585069\pi$
$312$		0			0
$313$	223.483			0.714002			0.357001	−	0.934104i	$-0.383799\pi$
$313$	223.483			0.714002			0.357001	+	0.934104i	$0.383799\pi$
$314$	600.228	+	600.228i	1.91155	+	1.91155i
$315$	5.14022			0.0163181
$316$			473.548i			1.49857i
$317$	125.140	+	125.140i	0.394764	+	0.394764i	0.876382	−	0.481617i	$-0.159951\pi$
$317$	125.140	+	125.140i	0.394764	+	0.394764i	−0.481617	+	0.876382i	$0.659951\pi$
$318$	−23.3772	−	23.3772i	−0.0735133	−	0.0735133i
$319$	189.057	−	189.057i	0.592655	−	0.592655i
$320$	−12.5548	+	12.5548i	−0.0392338	+	0.0392338i
$321$	−310.438			−0.967098
$322$			201.329i			0.625245i
$323$	50.5132	−	50.5132i	0.156388	−	0.156388i
$324$		−	217.982i		−	0.672785i
$325$		0			0
$326$	−59.1623			−0.181479
$327$	183.305	+	183.305i	0.560566	+	0.560566i
$328$	306.816			0.935414
$329$			100.359i			0.305044i
$330$	−34.2456	−	34.2456i	−0.103774	−	0.103774i
$331$	−309.982	−	309.982i	−0.936502	−	0.936502i	0.0615988	−	0.998101i	$-0.480380\pi$
$331$	−309.982	−	309.982i	−0.936502	−	0.936502i	−0.998101	+	0.0615988i	$0.980380\pi$
$332$	173.649	−	173.649i	0.523039	−	0.523039i
$333$	−18.2939	+	18.2939i	−0.0549368	+	0.0549368i
$334$	1067.48			3.19605
$335$		−	67.9253i		−	0.202762i
$336$	−103.235	+	103.235i	−0.307246	+	0.307246i
$337$			5.32456i			0.0157999i	0.999969	+	0.00789993i	$0.00251465\pi$
$337$			5.32456i			0.0157999i	−0.999969	+	0.00789993i	$0.997485\pi$
$338$		0			0
$339$	−234.702			−0.692336
$340$	−62.3883	−	62.3883i	−0.183495	−	0.183495i
$341$	−285.465			−0.837140
$342$		−	70.5964i		−	0.206422i
$343$	133.336	+	133.336i	0.388733	+	0.388733i
$344$	158.230	+	158.230i	0.459972	+	0.459972i
$345$	24.8947	−	24.8947i	0.0721584	−	0.0721584i
$346$	235.868	−	235.868i	0.681700	−	0.681700i
$347$	−47.2413			−0.136142			−0.0680710	−	0.997680i	$-0.521684\pi$
$347$	−47.2413			−0.136142			−0.0680710	+	0.997680i	$0.521684\pi$
$348$			520.416i			1.49545i
$349$	−223.581	+	223.581i	−0.640634	+	0.640634i	−0.950711	−	0.310078i	$-0.899645\pi$
$349$	−223.581	+	223.581i	−0.640634	+	0.640634i	0.310078	+	0.950711i	$0.399645\pi$
$350$		−	180.544i		−	0.515839i
$351$		0			0
$352$	−467.004			−1.32672
$353$	−110.320	−	110.320i	−0.312522	−	0.312522i	0.533364	−	0.845886i	$-0.320928\pi$
$353$	−110.320	−	110.320i	−0.312522	−	0.312522i	−0.845886	+	0.533364i	$0.820928\pi$
$354$	337.903			0.954529
$355$			42.2591i			0.119040i
$356$	−849.557	−	849.557i	−2.38639	−	2.38639i
$357$	−49.0068	−	49.0068i	−0.137274	−	0.137274i
$358$	184.993	−	184.993i	0.516741	−	0.516741i
$359$	−63.2149	+	63.2149i	−0.176086	+	0.176086i	−0.789647	−	0.613561i	$-0.789736\pi$
$359$	−63.2149	+	63.2149i	−0.176086	+	0.176086i	0.613561	+	0.789647i	$0.289736\pi$
$360$	−49.7893			−0.138304
$361$		−	341.000i		−	0.944598i
$362$	−707.605	+	707.605i	−1.95471	+	1.95471i
$363$			29.6271i			0.0816172i
$364$		0			0
$365$	−26.4911			−0.0725784
$366$	−377.706	−	377.706i	−1.03198	−	1.03198i
$367$	−318.416			−0.867620			−0.433810	−	0.901004i	$-0.642831\pi$
$367$	−318.416			−0.867620			−0.433810	+	0.901004i	$0.642831\pi$
$368$		−	924.907i		−	2.51334i
$369$	48.2719	+	48.2719i	0.130818	+	0.130818i
$370$	−9.14697	−	9.14697i	−0.0247216	−	0.0247216i
$371$	−5.94306	+	5.94306i	−0.0160190	+	0.0160190i
$372$	392.899	−	392.899i	1.05618	−	1.05618i
$373$	8.87688			0.0237986			0.0118993	−	0.999929i	$-0.496212\pi$
$373$	8.87688			0.0237986			0.0118993	+	0.999929i	$0.496212\pi$
$374$		−	603.986i		−	1.61494i
$375$	−44.9669	+	44.9669i	−0.119912	+	0.119912i
$376$		−	972.105i		−	2.58538i
$377$		0			0
$378$	−211.031			−0.558282
$379$	144.698	+	144.698i	0.381788	+	0.381788i	0.871746	−	0.489958i	$-0.162988\pi$
$379$	144.698	+	144.698i	0.381788	+	0.381788i	−0.489958	+	0.871746i	$0.662988\pi$
$380$	24.7018			0.0650047
$381$		−	205.065i		−	0.538230i
$382$	463.846	+	463.846i	1.21426	+	1.21426i
$383$	−357.261	−	357.261i	−0.932796	−	0.932796i	0.0650838	−	0.997880i	$-0.479269\pi$
$383$	−357.261	−	357.261i	−0.932796	−	0.932796i	−0.997880	+	0.0650838i	$0.979269\pi$
$384$	−108.441	+	108.441i	−0.282398	+	0.282398i
$385$	−8.70605	+	8.70605i	−0.0226131	+	0.0226131i
$386$	5.86406			0.0151919
$387$			49.7893i			0.128655i
$388$	814.548	−	814.548i	2.09935	−	2.09935i
$389$			438.342i			1.12684i	0.826170	+	0.563421i	$0.190515\pi$
$389$			438.342i			1.12684i	−0.826170	+	0.563421i	$0.809485\pi$
$390$		0			0
$391$	439.065			1.12293
$392$	−618.092	−	618.092i	−1.57676	−	1.57676i
$393$	−242.754			−0.617694
$394$		−	732.557i		−	1.85928i
$395$	−21.2719	−	21.2719i	−0.0538529	−	0.0538529i
$396$	−295.359	−	295.359i	−0.745857	−	0.745857i
$397$	−250.061	+	250.061i	−0.629877	+	0.629877i	−0.948037	−	0.318160i	$-0.896935\pi$
$397$	−250.061	+	250.061i	−0.629877	+	0.629877i	0.318160	+	0.948037i	$0.396935\pi$
$398$	670.473	−	670.473i	1.68461	−	1.68461i
$399$	19.4036			0.0486305
$400$			829.421i			2.07355i
$401$	−93.7018	+	93.7018i	−0.233670	+	0.233670i	−0.814223	−	0.580553i	$-0.802837\pi$
$401$	−93.7018	+	93.7018i	−0.233670	+	0.233670i	0.580553	+	0.814223i	$0.302837\pi$
$402$			905.074i			2.25143i
$403$		0			0
$404$	83.1843			0.205902
$405$	9.79181	+	9.79181i	0.0241773	+	0.0241773i
$406$	189.057			0.465657
$407$		−	61.9694i		−	0.152259i
$408$	474.691	+	474.691i	1.16346	+	1.16346i
$409$	−370.140	−	370.140i	−0.904988	−	0.904988i	0.0908741	−	0.995862i	$-0.471034\pi$
$409$	−370.140	−	370.140i	−0.904988	−	0.904988i	−0.995862	+	0.0908741i	$0.971034\pi$
$410$	−24.1359	+	24.1359i	−0.0588682	+	0.0588682i
$411$	−187.530	+	187.530i	−0.456278	+	0.456278i
$412$	−554.197			−1.34514
$413$		−	85.9032i		−	0.207998i
$414$	306.816	−	306.816i	0.741101	−	0.741101i
$415$			15.6007i			0.0375921i
$416$		0			0
$417$	169.824			0.407252
$418$	119.570	+	119.570i	0.286053	+	0.286053i
$419$	−658.767			−1.57224			−0.786118	−	0.618076i	$-0.787912\pi$
$419$	−658.767			−1.57224			−0.786118	+	0.618076i	$0.787912\pi$
$420$		−	23.9651i		−	0.0570598i
$421$	80.3135	+	80.3135i	0.190768	+	0.190768i	0.796028	−	0.605260i	$-0.206931\pi$
$421$	80.3135	+	80.3135i	0.190768	+	0.190768i	−0.605260	+	0.796028i	$0.706931\pi$
$422$	840.353	+	840.353i	1.99136	+	1.99136i
$423$	152.943	−	152.943i	0.361568	−	0.361568i
$424$	57.5658	−	57.5658i	0.135768	−	0.135768i
$425$	−393.737			−0.926439
$426$		−	563.083i		−	1.32179i
$427$	−96.0221	+	96.0221i	−0.224876	+	0.224876i
$428$		−	1338.73i		−	3.12787i
$429$		0			0
$430$	−24.8947			−0.0578946
$431$	−296.037	−	296.037i	−0.686862	−	0.686862i	0.274675	−	0.961537i	$-0.411430\pi$
$431$	−296.037	−	296.037i	−0.686862	−	0.686862i	−0.961537	+	0.274675i	$0.911430\pi$
$432$	969.478			2.24416
$433$			156.140i			0.360601i	0.983612	+	0.180300i	$0.0577070\pi$
$433$			156.140i			0.360601i	−0.983612	+	0.180300i	$0.942293\pi$
$434$	−142.732	−	142.732i	−0.328876	−	0.328876i
$435$	−23.3772	−	23.3772i	−0.0537407	−	0.0537407i
$436$	−790.480	+	790.480i	−1.81303	+	1.81303i
$437$	−86.9210	+	86.9210i	−0.198904	+	0.198904i
$438$	352.982			0.805895
$439$			448.710i			1.02212i	0.859545	+	0.511060i	$0.170747\pi$
$439$			448.710i			1.02212i	−0.859545	+	0.511060i	$0.829253\pi$
$440$	84.3288	−	84.3288i	0.191656	−	0.191656i
$441$		−	194.491i		−	0.441023i
$442$		0			0
$443$	−577.372			−1.30332			−0.651662	−	0.758510i	$-0.725928\pi$
$443$	−577.372			−1.30332			−0.651662	+	0.758510i	$0.725928\pi$
$444$	85.2915	+	85.2915i	0.192098	+	0.192098i
$445$	76.3246			0.171516
$446$			1258.43i			2.82159i
$447$	277.246	+	277.246i	0.620236	+	0.620236i
$448$	−42.5285	−	42.5285i	−0.0949296	−	0.0949296i
$449$	107.127	−	107.127i	0.238591	−	0.238591i	−0.577675	−	0.816267i	$-0.696040\pi$
$449$	107.127	−	107.127i	0.238591	−	0.238591i	0.816267	+	0.577675i	$0.196040\pi$
$450$	−275.140	+	275.140i	−0.611423	+	0.611423i
$451$	−163.517			−0.362566
$452$		−	1012.12i		−	2.23921i
$453$	−63.0900	+	63.0900i	−0.139272	+	0.139272i
$454$			520.009i			1.14539i
$455$		0			0
$456$	−187.947			−0.412165
$457$	356.092	+	356.092i	0.779194	+	0.779194i	0.979694	−	0.200499i	$-0.0642565\pi$
$457$	356.092	+	356.092i	0.779194	+	0.779194i	−0.200499	+	0.979694i	$0.564256\pi$
$458$	1240.84			2.70925
$459$			460.223i			1.00267i
$460$	107.355	+	107.355i	0.233381	+	0.233381i
$461$	−33.7477	−	33.7477i	−0.0732054	−	0.0732054i	0.669556	−	0.742761i	$-0.266484\pi$
$461$	−33.7477	−	33.7477i	−0.0732054	−	0.0732054i	−0.742761	+	0.669556i	$0.766484\pi$
$462$	116.004	−	116.004i	0.251092	−	0.251092i
$463$	−336.355	+	336.355i	−0.726469	+	0.726469i	−0.969915	−	0.243446i	$-0.921722\pi$
$463$	−336.355	+	336.355i	−0.726469	+	0.726469i	0.243446	+	0.969915i	$0.421722\pi$
$464$	−868.530			−1.87183
$465$			35.2982i			0.0759102i
$466$	27.8488	−	27.8488i	0.0597613	−	0.0597613i
$467$		−	308.263i		−	0.660093i	−0.943965	−	0.330046i	$-0.892936\pi$
$467$		−	308.263i		−	0.660093i	0.943965	−	0.330046i	$-0.107064\pi$
$468$		0			0
$469$	230.092			0.490601
$470$	76.4715	+	76.4715i	0.162705	+	0.162705i
$471$	502.824			1.06757
$472$			832.078i			1.76288i
$473$	−84.3288	−	84.3288i	−0.178285	−	0.178285i
$474$	283.438	+	283.438i	0.597971	+	0.597971i
$475$	77.9473	−	77.9473i	0.164100	−	0.164100i
$476$	211.336	−	211.336i	0.443982	−	0.443982i
$477$	18.1139			0.0379746
$478$			505.982i			1.05854i
$479$	−76.6424	+	76.6424i	−0.160005	+	0.160005i	−0.782569	−	0.622564i	$-0.786091\pi$
$479$	−76.6424	+	76.6424i	−0.160005	+	0.160005i	0.622564	+	0.782569i	$0.286091\pi$
$480$			57.7459i			0.120304i
$481$		0			0
$482$	1012.82			2.10130
$483$	84.3288	+	84.3288i	0.174594	+	0.174594i
$484$	−127.763			−0.263973
$485$			73.1794i			0.150885i
$486$	538.824	+	538.824i	1.10869	+	1.10869i
$487$	69.0655	+	69.0655i	0.141818	+	0.141818i	0.774452	−	0.632633i	$-0.218026\pi$
$487$	69.0655	+	69.0655i	0.141818	+	0.141818i	−0.632633	+	0.774452i	$0.718026\pi$
$488$	930.092	−	930.092i	1.90593	−	1.90593i
$489$	−24.7808	+	24.7808i	−0.0506764	+	0.0506764i
$490$	97.2456			0.198460
$491$		−	685.302i		−	1.39573i	−0.716230	−	0.697864i	$-0.754134\pi$
$491$		−	685.302i		−	1.39573i	0.716230	−	0.697864i	$-0.245866\pi$
$492$	225.057	−	225.057i	0.457433	−	0.457433i
$493$		−	412.302i		−	0.836313i
$494$		0			0
$495$	26.5352			0.0536065
$496$	655.715	+	655.715i	1.32201	+	1.32201i
$497$	−143.149			−0.288027
$498$		−	207.873i		−	0.417415i
$499$	−349.329	−	349.329i	−0.700058	−	0.700058i	0.264365	−	0.964423i	$-0.414838\pi$
$499$	−349.329	−	349.329i	−0.700058	−	0.700058i	−0.964423	+	0.264365i	$0.914838\pi$
$500$	−193.914	−	193.914i	−0.387828	−	0.387828i
$501$	447.127	−	447.127i	0.892468	−	0.892468i
$502$	247.381	−	247.381i	0.492792	−	0.492792i
$503$	42.2719			0.0840395			0.0420198	−	0.999117i	$-0.486621\pi$
$503$	42.2719			0.0840395			0.0420198	+	0.999117i	$0.486621\pi$
$504$		−	168.658i		−	0.334638i
$505$	−3.73666	+	3.73666i	−0.00739933	+	0.00739933i
$506$			1039.32i			2.05398i
$507$		0			0
$508$	884.320			1.74079
$509$	−184.280	−	184.280i	−0.362044	−	0.362044i	0.502521	−	0.864565i	$-0.332406\pi$
$509$	−184.280	−	184.280i	−0.362044	−	0.362044i	−0.864565	+	0.502521i	$0.832406\pi$
$510$	−74.6840			−0.146439
$511$		−	89.7367i		−	0.175610i
$512$	−777.103	−	777.103i	−1.51778	−	1.51778i
$513$	−91.1096	−	91.1096i	−0.177602	−	0.177602i
$514$	−1163.01	+	1163.01i	−2.26266	+	2.26266i
$515$	24.8947	−	24.8947i	0.0483392	−	0.0483392i
$516$	232.132			0.449868
$517$			518.083i			1.00210i
$518$	30.9847	−	30.9847i	0.0598160	−	0.0598160i
$519$		−	197.592i		−	0.380717i
$520$		0			0
$521$	−757.122			−1.45321			−0.726605	−	0.687055i	$-0.758903\pi$
$521$	−757.122			−1.45321			−0.726605	+	0.687055i	$0.758903\pi$
$522$	−288.114	−	288.114i	−0.551942	−	0.551942i
$523$	−221.851			−0.424188			−0.212094	−	0.977249i	$-0.568028\pi$
$523$	−221.851			−0.424188			−0.212094	+	0.977249i	$0.568028\pi$
$524$		−	1046.85i		−	1.99780i
$525$	−75.6228	−	75.6228i	−0.144043	−	0.144043i
$526$	431.004	+	431.004i	0.819400	+	0.819400i
$527$	−311.276	+	311.276i	−0.590657	+	0.590657i
$528$	−532.925	+	532.925i	−1.00933	+	1.00933i
$529$	−226.526			−0.428215
$530$			9.05694i			0.0170886i
$531$	−130.912	+	130.912i	−0.246539	+	0.246539i
$532$			83.6754i			0.157285i
$533$		0			0
$534$	−1016.99			−1.90448
$535$	60.1359	+	60.1359i	0.112404	+	0.112404i
$536$	−2228.72			−4.15806
$537$		−	154.973i		−	0.288590i
$538$	438.952	+	438.952i	0.815895	+	0.815895i
$539$	329.412	+	329.412i	0.611154	+	0.611154i
$540$	−112.528	+	112.528i	−0.208386	+	0.208386i
$541$	243.379	−	243.379i	0.449869	−	0.449869i	−0.445442	−	0.895311i	$-0.646953\pi$
$541$	243.379	−	243.379i	0.449869	−	0.449869i	0.895311	+	0.445442i	$0.146953\pi$
$542$	1120.59			2.06750
$543$			592.777i			1.09167i
$544$	−509.230	+	509.230i	−0.936085	+	0.936085i
$545$		−	71.0171i		−	0.130307i
$546$		0			0
$547$	−317.777			−0.580944			−0.290472	−	0.956883i	$-0.593812\pi$
$547$	−317.777			−0.580944			−0.290472	+	0.956883i	$0.593812\pi$
$548$	−808.701	−	808.701i	−1.47573	−	1.47573i
$549$	292.666			0.533090
$550$		−	932.017i		−	1.69458i
$551$	81.6228	+	81.6228i	0.148136	+	0.148136i
$552$	−816.828	−	816.828i	−1.47976	−	1.47976i
$553$	72.0569	−	72.0569i	0.130302	−	0.130302i
$554$	−485.118	+	485.118i	−0.875665	+	0.875665i
$555$	−7.66262			−0.0138065
$556$			732.346i			1.31717i
$557$	479.423	−	479.423i	0.860724	−	0.860724i	−0.130698	−	0.991422i	$-0.541722\pi$
$557$	479.423	−	479.423i	0.860724	−	0.860724i	0.991422	+	0.130698i	$0.0417220\pi$
$558$			435.035i			0.779632i
$559$		0			0
$560$	39.9957			0.0714209
$561$	−252.986	−	252.986i	−0.450956	−	0.450956i
$562$	−1480.78			−2.63484
$563$		−	461.671i		−	0.820020i	−0.912081	−	0.410010i	$-0.865525\pi$
$563$		−	461.671i		−	0.820020i	0.912081	−	0.410010i	$-0.134475\pi$
$564$	−713.063	−	713.063i	−1.26430	−	1.26430i
$565$	45.4648	+	45.4648i	0.0804686	+	0.0804686i
$566$	1030.39	−	1030.39i	1.82048	−	1.82048i
$567$	−33.1690	+	33.1690i	−0.0584992	+	0.0584992i
$568$	1386.58			2.44116
$569$			523.394i			0.919849i	0.887958	+	0.459925i	$0.152124\pi$
$569$			523.394i			0.919849i	−0.887958	+	0.459925i	$0.847876\pi$
$570$	14.7851	−	14.7851i	0.0259387	−	0.0259387i
$571$			115.715i			0.202654i	0.994853	+	0.101327i	$0.0323088\pi$
$571$			115.715i			0.202654i	−0.994853	+	0.101327i	$0.967691\pi$
$572$		0			0
$573$	388.574			0.678140
$574$	−81.7587	−	81.7587i	−0.142437	−	0.142437i
$575$	677.526			1.17831
$576$			129.623i			0.225040i
$577$	−130.158	−	130.158i	−0.225577	−	0.225577i	0.585265	−	0.810842i	$-0.300990\pi$
$577$	−130.158	−	130.158i	−0.225577	−	0.225577i	−0.810842	+	0.585265i	$0.800990\pi$
$578$	87.3509	+	87.3509i	0.151126	+	0.151126i
$579$	2.45623	−	2.45623i	0.00424219	−	0.00424219i
$580$	100.811	−	100.811i	0.173813	−	0.173813i
$581$	−52.8463			−0.0909574
$582$		−	975.083i		−	1.67540i
$583$	−30.6797	+	30.6797i	−0.0526239	+	0.0526239i
$584$			869.210i			1.48837i
$585$		0			0
$586$	−702.873			−1.19944
$587$	347.311	+	347.311i	0.591671	+	0.591671i	0.938083	−	0.346411i	$-0.112600\pi$
$587$	347.311	+	347.311i	0.591671	+	0.591671i	−0.346411	+	0.938083i	$0.612600\pi$
$588$	−906.772			−1.54213
$589$		−	123.246i		−	0.209245i
$590$	−65.4562	−	65.4562i	−0.110943	−	0.110943i
$591$	−306.840	−	306.840i	−0.519187	−	0.519187i
$592$	−142.344	+	142.344i	−0.240446	+	0.240446i
$593$	240.285	−	240.285i	0.405202	−	0.405202i	−0.474860	−	0.880062i	$-0.657501\pi$
$593$	240.285	−	240.285i	0.405202	−	0.405202i	0.880062	+	0.474860i	$0.157501\pi$
$594$	−1089.40			−1.83400
$595$			18.9865i			0.0319101i
$596$	−1195.59	+	1195.59i	−2.00602	+	2.00602i
$597$		−	561.670i		−	0.940822i
$598$		0			0
$599$	1044.77			1.74419			0.872096	−	0.489334i	$-0.162760\pi$
$599$	1044.77			1.74419			0.872096	+	0.489334i	$0.162760\pi$
$600$	732.500	+	732.500i	1.22083	+	1.22083i
$601$	933.298			1.55291			0.776454	−	0.630174i	$-0.217016\pi$
$601$	933.298			1.55291			0.776454	+	0.630174i	$0.217016\pi$
$602$		−	84.3288i		−	0.140081i
$603$	−350.649	−	350.649i	−0.581508	−	0.581508i
$604$	−272.068	−	272.068i	−0.450444	−	0.450444i
$605$	5.73914	−	5.73914i	0.00948619	−	0.00948619i
$606$	49.7893	−	49.7893i	0.0821606	−	0.0821606i
$607$	579.912			0.955374			0.477687	−	0.878530i	$-0.341475\pi$
$607$	579.912			0.955374			0.477687	+	0.878530i	$0.341475\pi$
$608$		−	201.623i		−	0.331616i
$609$	79.1886	−	79.1886i	0.130031	−	0.130031i
$610$			146.333i			0.239890i
$611$		0			0
$612$	−644.131			−1.05250
$613$	288.460	+	288.460i	0.470572	+	0.470572i	0.902100	−	0.431528i	$-0.142025\pi$
$613$	288.460	+	288.460i	0.470572	+	0.470572i	−0.431528	+	0.902100i	$0.642025\pi$
$614$	1216.67			1.98154
$615$			20.2192i			0.0328768i
$616$	285.658	+	285.658i	0.463730	+	0.463730i
$617$	−95.4121	−	95.4121i	−0.154639	−	0.154639i	0.625547	−	0.780186i	$-0.284876\pi$
$617$	−95.4121	−	95.4121i	−0.154639	−	0.154639i	−0.780186	+	0.625547i	$0.784876\pi$
$618$	−331.710	+	331.710i	−0.536748	+	0.536748i
$619$	544.952	−	544.952i	0.880374	−	0.880374i	−0.113198	−	0.993572i	$-0.536110\pi$
$619$	544.952	−	544.952i	0.880374	−	0.880374i	0.993572	+	0.113198i	$0.0361095\pi$
$620$	−152.219			−0.245515
$621$		−	791.934i		−	1.27526i
$622$	293.434	−	293.434i	0.471759	−	0.471759i
$623$			258.544i			0.414998i
$624$		0			0
$625$	−598.806			−0.958090
$626$	576.840	+	576.840i	0.921469	+	0.921469i
$627$	100.167			0.159755
$628$			2168.37i			3.45281i
$629$	−67.5726	−	67.5726i	−0.107429	−	0.107429i
$630$	13.2676	+	13.2676i	0.0210597	+	0.0210597i
$631$	642.537	−	642.537i	1.01828	−	1.01828i	0.0184540	−	0.999830i	$-0.494126\pi$
$631$	642.537	−	642.537i	1.01828	−	1.01828i	0.999830	−	0.0184540i	$-0.00587442\pi$
$632$	−697.960	+	697.960i	−1.10437	+	1.10437i
$633$	703.982			1.11214
$634$			646.009i			1.01894i
$635$	−39.7238	+	39.7238i	−0.0625572	+	0.0625572i
$636$		−	84.4520i		−	0.132786i
$637$		0			0
$638$	975.964			1.52972
$639$	218.153	+	218.153i	0.341398	+	0.341398i
$640$	42.0128			0.0656450
$641$		−	487.290i		−	0.760202i	−0.924945	−	0.380101i	$-0.875889\pi$
$641$		−	487.290i		−	0.760202i	0.924945	−	0.380101i	$-0.124111\pi$
$642$	−801.285	−	801.285i	−1.24811	−	1.24811i
$643$	797.688	+	797.688i	1.24057	+	1.24057i	0.959764	+	0.280809i	$0.0906028\pi$
$643$	797.688	+	797.688i	1.24057	+	1.24057i	0.280809	+	0.959764i	$0.409397\pi$
$644$	−363.658	+	363.658i	−0.564686	+	0.564686i
$645$	−10.4274	+	10.4274i	−0.0161665	+	0.0161665i
$646$	260.763			0.403658
$647$			989.526i			1.52941i	0.644383	+	0.764703i	$0.277114\pi$
$647$			989.526i			1.52941i	−0.644383	+	0.764703i	$0.722886\pi$
$648$	321.283	−	321.283i	0.495807	−	0.495807i
$649$		−	443.456i		−	0.683292i
$650$		0			0
$651$	−119.570			−0.183671
$652$	−106.864	−	106.864i	−0.163902	−	0.163902i
$653$	−86.3075			−0.132171			−0.0660853	−	0.997814i	$-0.521051\pi$
$653$	−86.3075			−0.132171			−0.0660853	+	0.997814i	$0.521051\pi$
$654$			946.271i			1.44690i
$655$	47.0245	+	47.0245i	0.0717932	+	0.0717932i
$656$	375.601	+	375.601i	0.572562	+	0.572562i
$657$	−136.754	+	136.754i	−0.208150	+	0.208150i
$658$	−259.042	+	259.042i	−0.393680	+	0.393680i
$659$	−1184.99			−1.79817			−0.899083	−	0.437779i	$-0.855765\pi$
$659$	−1184.99			−1.79817			−0.899083	+	0.437779i	$0.855765\pi$
$660$		−	123.715i		−	0.187446i
$661$	194.408	−	194.408i	0.294112	−	0.294112i	−0.544590	−	0.838702i	$-0.683315\pi$
$661$	194.408	−	194.408i	0.294112	−	0.294112i	0.838702	+	0.544590i	$0.183315\pi$
$662$		−	1600.21i		−	2.41724i
$663$		0			0
$664$	511.881			0.770905
$665$	−3.75872	−	3.75872i	−0.00565221	−	0.00565221i
$666$	−94.4384			−0.141799
$667$			709.473i			1.06368i
$668$	1928.18	+	1928.18i	2.88650	+	2.88650i
$669$	527.107	+	527.107i	0.787903	+	0.787903i
$670$	175.325	−	175.325i	0.261678	−	0.261678i
$671$	−495.693	+	495.693i	−0.738737	+	0.738737i
$672$	−195.610			−0.291086
$673$		−	615.500i		−	0.914561i	−0.889322	−	0.457281i	$-0.848824\pi$
$673$		−	615.500i		−	0.914561i	0.889322	−	0.457281i	$-0.151176\pi$
$674$	−13.7434	+	13.7434i	−0.0203908	+	0.0203908i
$675$			710.175i			1.05211i
$676$		0			0
$677$	−412.031			−0.608612			−0.304306	−	0.952574i	$-0.598425\pi$
$677$	−412.031			−0.608612			−0.304306	+	0.952574i	$0.598425\pi$
$678$	−605.798	−	605.798i	−0.893507	−	0.893507i
$679$	−247.890			−0.365081
$680$		−	183.907i		−	0.270452i
$681$	217.811	+	217.811i	0.319841	+	0.319841i
$682$	−736.824	−	736.824i	−1.08039	−	1.08039i
$683$	−129.044	+	129.044i	−0.188937	+	0.188937i	−0.795237	−	0.606299i	$-0.792653\pi$
$683$	−129.044	+	129.044i	−0.188937	+	0.188937i	0.606299	+	0.795237i	$0.292653\pi$
$684$	127.517	−	127.517i	0.186429	−	0.186429i
$685$	72.6541			0.106064
$686$			688.315i			1.00338i
$687$	519.738	−	519.738i	0.756533	−	0.756533i
$688$			387.408i			0.563093i
$689$		0			0
$690$	128.513			0.186251
$691$	−727.105	−	727.105i	−1.05225	−	1.05225i	−0.998558	−	0.0536923i	$-0.982901\pi$
$691$	−727.105	−	727.105i	−1.05225	−	1.05225i	−0.0536923	−	0.998558i	$-0.517099\pi$
$692$	852.092			1.23135
$693$			89.8861i			0.129706i
$694$	−121.936	−	121.936i	−0.175701	−	0.175701i
$695$	−32.8971	−	32.8971i	−0.0473340	−	0.0473340i
$696$	−767.039	+	767.039i	−1.10207	+	1.10207i
$697$	−178.302	+	178.302i	−0.255814	+	0.255814i
$698$	−1154.19			−1.65356
$699$		−	23.3295i		−	0.0333756i
$700$	326.114	−	326.114i	0.465877	−	0.465877i
$701$			635.934i			0.907181i	0.891210	+	0.453590i	$0.149857\pi$
$701$			635.934i			0.907181i	−0.891210	+	0.453590i	$0.850143\pi$
$702$		0			0
$703$	26.7544			0.0380575
$704$	−219.544	−	219.544i	−0.311852	−	0.311852i
$705$	64.0619			0.0908680
$706$		−	569.504i		−	0.806663i
$707$	−12.6577	−	12.6577i	−0.0179033	−	0.0179033i
$708$	610.350	+	610.350i	0.862077	+	0.862077i
$709$	−695.315	+	695.315i	−0.980699	+	0.980699i	−0.999817	−	0.0191186i	$-0.993914\pi$
$709$	−695.315	+	695.315i	−0.980699	+	0.980699i	0.0191186	+	0.999817i	$0.493914\pi$
$710$	−109.077	+	109.077i	−0.153629	+	0.153629i
$711$	−219.623			−0.308893
$712$		−	2504.31i		−	3.51730i
$713$	535.631	−	535.631i	0.751236	−	0.751236i
$714$		−	252.986i		−	0.354323i
$715$		0			0
$716$	668.302			0.933382
$717$	211.936	+	211.936i	0.295588	+	0.295588i
$718$	−326.333			−0.454503
$719$		−	859.565i		−	1.19550i	−0.801682	−	0.597750i	$-0.796061\pi$
$719$		−	859.565i		−	1.19550i	0.801682	−	0.597750i	$-0.203939\pi$
$720$	−60.9516	−	60.9516i	−0.0846550	−	0.0846550i
$721$	84.3288	+	84.3288i	0.116961	+	0.116961i
$722$	880.168	−	880.168i	1.21907	−	1.21907i
$723$	424.233	−	424.233i	0.586767	−	0.586767i
$724$	−2556.28			−3.53077
$725$		−	636.228i		−	0.877556i
$726$	−76.4715	+	76.4715i	−0.105333	+	0.105333i
$727$			437.337i			0.601564i	0.953693	+	0.300782i	$0.0972477\pi$
$727$			437.337i			0.601564i	−0.953693	+	0.300782i	$0.902752\pi$
$728$		0			0
$729$	661.780			0.907792
$730$	−68.3772	−	68.3772i	−0.0936674	−	0.0936674i
$731$	−183.907			−0.251583
$732$		−	1364.49i		−	1.86406i
$733$	−39.5591	−	39.5591i	−0.0539687	−	0.0539687i	0.679607	−	0.733576i	$-0.262150\pi$
$733$	−39.5591	−	39.5591i	−0.0539687	−	0.0539687i	−0.733576	+	0.679607i	$0.762150\pi$
$734$	−821.877	−	821.877i	−1.11972	−	1.11972i
$735$	40.7324	−	40.7324i	0.0554182	−	0.0554182i
$736$	876.263	−	876.263i	1.19057	−	1.19057i
$737$	1187.80			1.61167
$738$			249.193i			0.337660i
$739$	−919.732	+	919.732i	−1.24456	+	1.24456i	−0.286475	+	0.958088i	$0.592483\pi$
$739$	−919.732	+	919.732i	−1.24456	+	1.24456i	−0.958088	+	0.286475i	$0.907517\pi$
$740$		−	33.0441i		−	0.0446542i
$741$		0			0
$742$	−30.6797			−0.0413473
$743$	−730.642	−	730.642i	−0.983368	−	0.983368i	0.0164960	−	0.999864i	$-0.494749\pi$
$743$	−730.642	−	730.642i	−0.983368	−	0.983368i	−0.999864	+	0.0164960i	$0.994749\pi$
$744$	1158.18			1.55670
$745$		−	107.412i		−	0.144177i
$746$	22.9125	+	22.9125i	0.0307137	+	0.0307137i
$747$	80.5352	+	80.5352i	0.107812	+	0.107812i
$748$	1090.97	−	1090.97i	1.45852	−	1.45852i
$749$	−203.706	+	203.706i	−0.271971	+	0.271971i
$750$	−232.132			−0.309509
$751$			199.764i			0.265997i	0.991116	+	0.132998i	$0.0424605\pi$
$751$			199.764i			0.265997i	−0.991116	+	0.132998i	$0.957539\pi$
$752$	1190.04	−	1190.04i	1.58250	−	1.58250i
$753$		−	207.237i		−	0.275215i
$754$		0			0
$755$	24.4427			0.0323745
$756$	−381.182	−	381.182i	−0.504209	−	0.504209i
$757$	124.549			0.164529			0.0822647	−	0.996611i	$-0.473785\pi$
$757$	124.549			0.164529			0.0822647	+	0.996611i	$0.473785\pi$
$758$			746.969i			0.985447i
$759$	435.329	+	435.329i	0.573556	+	0.573556i
$760$	36.4078	+	36.4078i	0.0479050	+	0.0479050i
$761$	−161.412	+	161.412i	−0.212105	+	0.212105i	−0.805161	−	0.593056i	$-0.797921\pi$
$761$	−161.412	+	161.412i	−0.212105	+	0.212105i	0.593056	+	0.805161i	$0.297921\pi$
$762$	529.302	−	529.302i	0.694623	−	0.694623i
$763$	240.565			0.315289
$764$			1675.68i			2.19330i
$765$	28.9345	−	28.9345i	0.0378229	−	0.0378229i
$766$		−	1844.28i		−	2.40768i
$767$		0			0
$768$	−819.048			−1.06647
$769$	−137.947	−	137.947i	−0.179385	−	0.179385i	0.611703	−	0.791088i	$-0.290485\pi$
$769$	−137.947	−	137.947i	−0.179385	−	0.179385i	−0.791088	+	0.611703i	$0.790485\pi$
$770$	−44.9431			−0.0583676
$771$			974.276i			1.26365i
$772$	10.5922	+	10.5922i	0.0137204	+	0.0137204i
$773$	−550.813	−	550.813i	−0.712566	−	0.712566i	0.254506	−	0.967071i	$-0.418087\pi$
$773$	−550.813	−	550.813i	−0.712566	−	0.712566i	−0.967071	+	0.254506i	$0.918087\pi$
$774$	−128.513	+	128.513i	−0.166038	+	0.166038i
$775$	−480.333	+	480.333i	−0.619785	+	0.619785i
$776$	2401.12			3.09422
$777$		−	25.9566i		−	0.0334061i
$778$	−1131.42	+	1131.42i	−1.45427	+	1.45427i
$779$		−	70.5964i		−	0.0906244i
$780$		0			0
$781$	−738.977			−0.946194
$782$	1133.29	+	1133.29i	1.44922	+	1.44922i
$783$	−743.662			−0.949760
$784$		−	1513.32i		−	1.93026i
$785$	−97.4036	−	97.4036i	−0.124081	−	0.124081i
$786$	−626.581	−	626.581i	−0.797177	−	0.797177i
$787$	−729.434	+	729.434i	−0.926854	+	0.926854i	−0.997501	−	0.0706473i	$-0.977494\pi$
$787$	−729.434	+	729.434i	−0.926854	+	0.926854i	0.0706473	+	0.997501i	$0.477494\pi$
$788$	1323.21	−	1323.21i	1.67920	−	1.67920i
$789$	361.062			0.457620
$790$		−	109.811i		−	0.139002i
$791$	−154.009	+	154.009i	−0.194701	+	0.194701i
$792$		−	870.658i		−	1.09932i
$793$		0			0
$794$	−1290.89			−1.62580
$795$	3.79360	+	3.79360i	0.00477183	+	0.00477183i
$796$	2422.13			3.04288
$797$			444.974i			0.558311i	0.960246	+	0.279155i	$0.0900545\pi$
$797$			444.974i			0.558311i	−0.960246	+	0.279155i	$0.909946\pi$
$798$	50.0833	+	50.0833i	0.0627610	+	0.0627610i
$799$	564.928	+	564.928i	0.707043	+	0.707043i
$800$	−785.798	+	785.798i	−0.982247	+	0.982247i
$801$	394.009	−	394.009i	0.491896	−	0.491896i
$802$	−483.715			−0.603135
$803$		−	463.246i		−	0.576894i
$804$	−1634.82	+	1634.82i	−2.03336	+	2.03336i
$805$		−	32.6712i		−	0.0405853i
$806$		0			0
$807$	367.720			0.455662
$808$	122.605	+	122.605i	0.151739	+	0.151739i
$809$	−1090.36			−1.34779			−0.673893	−	0.738829i	$-0.735379\pi$
$809$	−1090.36			−1.34779			−0.673893	+	0.738829i	$0.735379\pi$
$810$			50.5480i			0.0624050i
$811$	−445.614	−	445.614i	−0.549463	−	0.549463i	0.376823	−	0.926285i	$-0.377017\pi$
$811$	−445.614	−	445.614i	−0.549463	−	0.549463i	−0.926285	+	0.376823i	$0.877017\pi$
$812$	341.491	+	341.491i	0.420556	+	0.420556i
$813$	469.370	−	469.370i	0.577331	−	0.577331i
$814$	159.952	−	159.952i	0.196501	−	0.196501i
$815$	9.60072			0.0117800
$816$			1162.22i			1.42429i
$817$	36.4078	−	36.4078i	0.0445628	−	0.0445628i
$818$		−	1910.77i		−	2.33590i
$819$		0			0
$820$	−87.1929			−0.106333
$821$	242.186	+	242.186i	0.294989	+	0.294989i	0.839047	−	0.544058i	$-0.183113\pi$
$821$	242.186	+	242.186i	0.294989	+	0.294989i	−0.544058	+	0.839047i	$0.683113\pi$
$822$	−968.083			−1.17772
$823$			99.5787i			0.120995i	0.998168	+	0.0604974i	$0.0192687\pi$
$823$			99.5787i			0.120995i	−0.998168	+	0.0604974i	$0.980731\pi$
$824$	−816.828	−	816.828i	−0.991297	−	0.991297i
$825$	−390.386	−	390.386i	−0.473195	−	0.473195i
$826$	221.728	−	221.728i	0.268436	−	0.268436i
$827$	899.548	−	899.548i	1.08772	−	1.08772i	0.0919618	−	0.995763i	$-0.470686\pi$
$827$	899.548	−	899.548i	1.08772	−	1.08772i	0.995763	−	0.0919618i	$-0.0293138\pi$
$828$	1108.39			1.33864
$829$		−	32.1103i		−	0.0387338i	−0.999812	−	0.0193669i	$-0.993835\pi$
$829$		−	32.1103i		−	0.0387338i	0.999812	−	0.0193669i	$-0.00616506\pi$
$830$	−40.2676	+	40.2676i	−0.0485152	+	0.0485152i
$831$			406.394i			0.489042i
$832$		0			0
$833$	718.394			0.862418
$834$	438.340	+	438.340i	0.525587	+	0.525587i
$835$	−173.228			−0.207459
$836$			431.956i			0.516694i
$837$	561.443	+	561.443i	0.670780	+	0.670780i
$838$	−1700.37	−	1700.37i	−2.02908	−	2.02908i
$839$	−408.794	+	408.794i	−0.487239	+	0.487239i	−0.907434	−	0.420195i	$-0.861962\pi$
$839$	−408.794	+	408.794i	−0.487239	+	0.487239i	0.420195	+	0.907434i	$0.361962\pi$
$840$	35.3221	−	35.3221i	0.0420501	−	0.0420501i
$841$	−174.772			−0.207815
$842$			414.601i			0.492400i
$843$	−620.241	+	620.241i	−0.735755	+	0.735755i
$844$			3035.84i			3.59696i
$845$		0			0
$846$	789.535			0.933256
$847$	19.4409	+	19.4409i	0.0229527	+	0.0229527i
$848$	140.943			0.166206
$849$		−	863.184i		−	1.01671i
$850$	−1016.29	−	1016.29i	−1.19563	−	1.19563i
$851$	116.276	+	116.276i	0.136635	+	0.136635i
$852$	1017.09	−	1017.09i	1.19377	−	1.19377i
$853$	−529.546	+	529.546i	−0.620804	+	0.620804i	−0.945737	−	0.324933i	$-0.894658\pi$
$853$	−529.546	+	529.546i	−0.620804	+	0.620804i	0.324933	+	0.945737i	$0.394658\pi$
$854$	−495.693			−0.580436
$855$			11.4562i			0.0133991i
$856$	1973.14	−	1973.14i	2.30507	−	2.30507i
$857$			1586.76i			1.85153i	0.378097	+	0.925766i	$0.376579\pi$
$857$			1586.76i			1.85153i	−0.378097	+	0.925766i	$0.623421\pi$
$858$		0			0
$859$	145.062			0.168873			0.0844365	−	0.996429i	$-0.473091\pi$
$859$	145.062			0.168873			0.0844365	+	0.996429i	$0.473091\pi$
$860$	−44.9669	−	44.9669i	−0.0522871	−	0.0522871i
$861$	−68.4911			−0.0795483
$862$		−	1528.23i		−	1.77289i
$863$	1005.80	+	1005.80i	1.16547	+	1.16547i	0.983258	+	0.182216i	$0.0583271\pi$
$863$	1005.80	+	1005.80i	1.16547	+	1.16547i	0.182216	+	0.983258i	$0.441673\pi$
$864$	918.489	+	918.489i	1.06307	+	1.06307i
$865$	−38.2762	+	38.2762i	−0.0442499	+	0.0442499i
$866$	−403.020	+	403.020i	−0.465381	+	0.465381i
$867$	73.1758			0.0844011
$868$		−	515.631i		−	0.594045i
$869$	371.978	−	371.978i	0.428053	−	0.428053i
$870$		−	120.680i		−	0.138712i
$871$		0			0
$872$	−2330.17			−2.67221
$873$	377.772	+	377.772i	0.432729	+	0.432729i
$874$	−448.710			−0.513399
$875$			59.0135i			0.0674440i
$876$	637.587	+	637.587i	0.727839	+	0.727839i
$877$	−689.532	−	689.532i	−0.786240	−	0.786240i	0.194636	−	0.980876i	$-0.437647\pi$
$877$	−689.532	−	689.532i	−0.786240	−	0.786240i	−0.980876	+	0.194636i	$0.937647\pi$
$878$	−1158.18	+	1158.18i	−1.31912	+	1.31912i
$879$	−294.406	+	294.406i	−0.334933	+	0.334933i
$880$	206.469			0.234624
$881$		−	1607.31i		−	1.82442i	−0.409722	−	0.912210i	$-0.634374\pi$
$881$		−	1607.31i		−	1.82442i	0.409722	−	0.912210i	$-0.365626\pi$
$882$	502.009	−	502.009i	0.569171	−	0.569171i
$883$		−	153.969i		−	0.174370i	−0.996192	−	0.0871850i	$-0.972213\pi$
$883$		−	153.969i		−	0.174370i	0.996192	−	0.0871850i	$-0.0277871\pi$
$884$		0			0
$885$	−54.8341			−0.0619595
$886$	−1490.28	−	1490.28i	−1.68203	−	1.68203i
$887$	125.273			0.141232			0.0706159	−	0.997504i	$-0.477504\pi$
$887$	125.273			0.141232			0.0706159	+	0.997504i	$0.477504\pi$
$888$			251.421i			0.283132i
$889$	−134.562	−	134.562i	−0.151363	−	0.151363i
$890$	197.004	+	197.004i	0.221353	+	0.221353i
$891$	−171.228	+	171.228i	−0.192175	+	0.192175i
$892$	−2273.08	+	2273.08i	−2.54830	+	2.54830i
$893$	−223.675			−0.250476
$894$			1431.22i			1.60092i
$895$	−30.0203	+	30.0203i	−0.0335422	+	0.0335422i
$896$			142.315i			0.158834i
$897$		0			0
$898$	553.021			0.615837
$899$	−502.982	−	502.982i	−0.559491	−	0.559491i
$900$	−993.964			−1.10440
$901$			66.9075i			0.0742591i
$902$	−422.061	−	422.061i	−0.467917	−	0.467917i
$903$	−35.3221	−	35.3221i	−0.0391164	−	0.0391164i
$904$	1491.76	−	1491.76i	1.65018	−	1.65018i
$905$	114.828	−	114.828i	0.126882	−	0.126882i
$906$	−325.688			−0.359479
$907$		−	354.574i		−	0.390930i	−0.980711	−	0.195465i	$-0.937378\pi$
$907$		−	354.574i		−	0.390930i	0.980711	−	0.195465i	$-0.0626216\pi$
$908$	−939.285	+	939.285i	−1.03445	+	1.03445i
$909$			38.5793i			0.0424415i
$910$		0			0
$911$	1040.31			1.14194			0.570972	−	0.820970i	$-0.306566\pi$
$911$	1040.31			1.14194			0.570972	+	0.820970i	$0.306566\pi$
$912$	−230.083	−	230.083i	−0.252284	−	0.252284i
$913$	−272.807			−0.298803
$914$			1838.24i			2.01121i
$915$	61.2933	+	61.2933i	0.0669872	+	0.0669872i
$916$	2241.31	+	2241.31i	2.44684	+	2.44684i
$917$	−159.292	+	159.292i	−0.173710	+	0.173710i
$918$	−1187.90	+	1187.90i	−1.29401	+	1.29401i
$919$	−416.201			−0.452884			−0.226442	−	0.974025i	$-0.572709\pi$
$919$	−416.201			−0.452884			−0.226442	+	0.974025i	$0.572709\pi$
$920$			316.460i			0.343979i
$921$	509.614	−	509.614i	0.553327	−	0.553327i
$922$		−	174.215i		−	0.188953i
$923$		0			0
$924$	419.074			0.453543
$925$	−104.272	−	104.272i	−0.112726	−	0.112726i
$926$	−1736.36			−1.87512
$927$		−	257.026i		−	0.277267i
$928$	−822.851	−	822.851i	−0.886692	−	0.886692i
$929$	428.403	+	428.403i	0.461144	+	0.461144i	0.899030	−	0.437886i	$-0.144273\pi$
$929$	428.403	+	428.403i	0.461144	+	0.461144i	−0.437886	+	0.899030i	$0.644273\pi$
$930$	−91.1096	+	91.1096i	−0.0979673	+	0.0979673i
$931$	−142.219	+	142.219i	−0.152760	+	0.152760i
$932$	100.606			0.107946
$933$		−	245.816i		−	0.263469i
$934$	795.670	−	795.670i	0.851896	−	0.851896i
$935$			98.0135i			0.104827i
$936$		0			0
$937$	−990.702			−1.05731			−0.528656	−	0.848836i	$-0.677304\pi$
$937$	−990.702			−1.05731			−0.528656	+	0.848836i	$0.677304\pi$
$938$	593.899	+	593.899i	0.633155	+	0.633155i
$939$	483.231			0.514623
$940$			276.259i			0.293893i
$941$	−974.392	−	974.392i	−1.03549	−	1.03549i	−0.999347	−	0.0361387i	$-0.988494\pi$
$941$	−974.392	−	974.392i	−1.03549	−	1.03549i	−0.0361387	−	0.999347i	$-0.511506\pi$
$942$	1297.86	+	1297.86i	1.37777	+	1.37777i
$943$	306.816	−	306.816i	0.325361	−	0.325361i
$944$	−1018.62	+	1018.62i	−1.07905	+	1.07905i
$945$	34.2456			0.0362387
$946$		−	435.329i		−	0.460178i
$947$	−897.569	+	897.569i	−0.947803	+	0.947803i	−0.998704	−	0.0509007i	$-0.983791\pi$
$947$	−897.569	+	897.569i	−0.947803	+	0.947803i	0.0509007	+	0.998704i	$0.483791\pi$
$948$			1023.94i			1.08011i
$949$		0			0
$950$	402.386			0.423564
$951$	270.588	+	270.588i	0.284530	+	0.284530i
$952$	622.973			0.654383
$953$			1111.71i			1.16654i	0.812279	+	0.583269i	$0.198227\pi$
$953$			1111.71i			1.16654i	−0.812279	+	0.583269i	$0.801773\pi$
$954$	46.7544	+	46.7544i	0.0490089	+	0.0490089i
$955$	−75.2719	−	75.2719i	−0.0788187	−	0.0788187i
$956$	−913.949	+	913.949i	−0.956014	+	0.956014i
$957$	408.794	−	408.794i	0.427162	−	0.427162i
$958$	−395.649			−0.412995
$959$			246.110i			0.256632i
$960$	−27.1470	+	27.1470i	−0.0282781	+	0.0282781i
$961$		−	201.527i		−	0.209705i
$962$		0			0
$963$	620.877			0.644732
$964$	1829.45	+	1829.45i	1.89777	+	1.89777i
$965$	−0.951605			−0.000986120
$966$			435.329i			0.450651i
$967$	1333.92	+	1333.92i	1.37944	+	1.37944i	0.845561	+	0.533879i	$0.179266\pi$
$967$	1333.92	+	1333.92i	1.37944	+	1.37944i	0.533879	+	0.845561i	$0.320734\pi$
$968$	−188.309	−	188.309i	−0.194534	−	0.194534i
$969$	109.223	−	109.223i	0.112718	−	0.112718i
$970$	−188.886	+	188.886i	−0.194728	+	0.194728i
$971$	−556.110			−0.572718			−0.286359	−	0.958122i	$-0.592445\pi$
$971$	−556.110			−0.572718			−0.286359	+	0.958122i	$0.592445\pi$
$972$			1946.54i			2.00262i
$973$	111.437	−	111.437i	0.114529	−	0.114529i
$974$			356.535i			0.366053i
$975$		0			0
$976$	2277.22			2.33322
$977$	1103.56	+	1103.56i	1.12954	+	1.12954i	0.990252	+	0.139288i	$0.0444815\pi$
$977$	1103.56	+	1103.56i	1.12954	+	1.12954i	0.139288	+	0.990252i	$0.455518\pi$
$978$	−127.925			−0.130803
$979$			1334.67i			1.36330i
$980$	175.653	+	175.653i	0.179238	+	0.179238i
$981$	−366.610	−	366.610i	−0.373710	−	0.373710i
$982$	1768.86	−	1768.86i	1.80128	−	1.80128i
$983$	901.475	−	901.475i	0.917065	−	0.917065i	−0.0797497	−	0.996815i	$-0.525412\pi$
$983$	901.475	−	901.475i	0.917065	−	0.917065i	0.996815	+	0.0797497i	$0.0254121\pi$
$984$	663.421			0.674208
$985$			118.878i			0.120688i
$986$	1064.21	−	1064.21i	1.07932	−	1.07932i
$987$			217.005i			0.219863i
$988$		0			0
$989$	316.460			0.319980
$990$	68.4911	+	68.4911i	0.0691829	+	0.0691829i
$991$	765.341			0.772292			0.386146	−	0.922438i	$-0.373806\pi$
$991$	765.341			0.772292			0.386146	+	0.922438i	$0.373806\pi$
$992$			1242.46i			1.25248i
$993$	−670.268	−	670.268i	−0.674993	−	0.674993i
$994$	−369.489	−	369.489i	−0.371719	−	0.371719i
$995$	−108.803	+	108.803i	−0.109350	+	0.109350i
$996$	375.478	−	375.478i	0.376986	−	0.376986i
$997$	1075.40			1.07863			0.539317	−	0.842103i	$-0.318682\pi$
$997$	1075.40			1.07863			0.539317	+	0.842103i	$0.318682\pi$
$998$		−	1803.33i		−	1.80695i
$999$	−121.879	+	121.879i	−0.122001	+	0.122001i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.3.d.d.99.2		4
13.2	odd	12		169.3.f.d.19.2		8
13.3	even	3		169.3.f.d.150.1		8
13.4	even	6		169.3.f.f.89.1		8
13.5	odd	4	inner	169.3.d.d.70.2		4
13.6	odd	12		169.3.f.d.80.1		8
13.7	odd	12		169.3.f.f.80.2		8
13.8	odd	4		13.3.d.a.5.1	✓	4
13.9	even	3		169.3.f.d.89.2		8
13.10	even	6		169.3.f.f.150.2		8
13.11	odd	12		169.3.f.f.19.1		8
13.12	even	2		13.3.d.a.8.1	yes	4
39.8	even	4		117.3.j.a.109.2		4
39.38	odd	2		117.3.j.a.73.2		4
52.47	even	4		208.3.t.c.161.1		4
52.51	odd	2		208.3.t.c.177.1		4
65.8	even	4		325.3.g.b.174.2		4
65.12	odd	4		325.3.g.b.99.2		4
65.34	odd	4		325.3.j.a.226.2		4
65.38	odd	4		325.3.g.a.99.1		4
65.47	even	4		325.3.g.a.174.1		4
65.64	even	2		325.3.j.a.151.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.3.d.a.5.1	✓	4	13.8	odd	4
13.3.d.a.8.1	yes	4	13.12	even	2
117.3.j.a.73.2		4	39.38	odd	2
117.3.j.a.109.2		4	39.8	even	4
169.3.d.d.70.2		4	13.5	odd	4	inner
169.3.d.d.99.2		4	1.1	even	1	trivial
169.3.f.d.19.2		8	13.2	odd	12
169.3.f.d.80.1		8	13.6	odd	12
169.3.f.d.89.2		8	13.9	even	3
169.3.f.d.150.1		8	13.3	even	3
169.3.f.f.19.1		8	13.11	odd	12
169.3.f.f.80.2		8	13.7	odd	12
169.3.f.f.89.1		8	13.4	even	6
169.3.f.f.150.2		8	13.10	even	6
208.3.t.c.161.1		4	52.47	even	4
208.3.t.c.177.1		4	52.51	odd	2
325.3.g.a.99.1		4	65.38	odd	4
325.3.g.a.174.1		4	65.47	even	4
325.3.g.b.99.2		4	65.12	odd	4
325.3.g.b.174.2		4	65.8	even	4
325.3.j.a.151.2		4	65.64	even	2
325.3.j.a.226.2		4	65.34	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	169.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.58114 + 2.58114i) q^{2} +2.16228 q^{3} +9.32456i q^{4} +(-0.418861 - 0.418861i) q^{5} +(5.58114 + 5.58114i) q^{6} +(1.41886 - 1.41886i) q^{7} +(-13.7434 + 13.7434i) q^{8} -4.32456 q^{9} +O(q^{10})\)	\(q+(2.58114 + 2.58114i) q^{2} +2.16228 q^{3} +9.32456i q^{4} +(-0.418861 - 0.418861i) q^{5} +(5.58114 + 5.58114i) q^{6} +(1.41886 - 1.41886i) q^{7} +(-13.7434 + 13.7434i) q^{8} -4.32456 q^{9} -2.16228i q^{10} +(7.32456 - 7.32456i) q^{11} +20.1623i q^{12} +7.32456 q^{14} +(-0.905694 - 0.905694i) q^{15} -33.6491 q^{16} -15.9737i q^{17} +(-11.1623 - 11.1623i) q^{18} +(3.16228 + 3.16228i) q^{19} +(3.90569 - 3.90569i) q^{20} +(3.06797 - 3.06797i) q^{21} +37.8114 q^{22} +27.4868i q^{23} +(-29.7171 + 29.7171i) q^{24} -24.6491i q^{25} -28.8114 q^{27} +(13.2302 + 13.2302i) q^{28} +25.8114 q^{29} -4.67544i q^{30} +(-19.4868 - 19.4868i) q^{31} +(-31.8794 - 31.8794i) q^{32} +(15.8377 - 15.8377i) q^{33} +(41.2302 - 41.2302i) q^{34} -1.18861 q^{35} -40.3246i q^{36} +(4.23025 - 4.23025i) q^{37} +16.3246i q^{38} +11.5132 q^{40} +(-11.1623 - 11.1623i) q^{41} +15.8377 q^{42} -11.5132i q^{43} +(68.2982 + 68.2982i) q^{44} +(1.81139 + 1.81139i) q^{45} +(-70.9473 + 70.9473i) q^{46} +(-35.3662 + 35.3662i) q^{47} -72.7587 q^{48} +44.9737i q^{49} +(63.6228 - 63.6228i) q^{50} -34.5395i q^{51} -4.18861 q^{53} +(-74.3662 - 74.3662i) q^{54} -6.13594 q^{55} +39.0000i q^{56} +(6.83772 + 6.83772i) q^{57} +(66.6228 + 66.6228i) q^{58} +(30.2719 - 30.2719i) q^{59} +(8.44520 - 8.44520i) q^{60} -67.6754 q^{61} -100.596i q^{62} +(-6.13594 + 6.13594i) q^{63} -29.9737i q^{64} +81.7587 q^{66} +(81.0833 + 81.0833i) q^{67} +148.947 q^{68} +59.4342i q^{69} +(-3.06797 - 3.06797i) q^{70} +(-50.4452 - 50.4452i) q^{71} +(59.4342 - 59.4342i) q^{72} +(31.6228 - 31.6228i) q^{73} +21.8377 q^{74} -53.2982i q^{75} +(-29.4868 + 29.4868i) q^{76} -20.7851i q^{77} +50.7851 q^{79} +(14.0943 + 14.0943i) q^{80} -23.3772 q^{81} -57.6228i q^{82} +(-18.6228 - 18.6228i) q^{83} +(28.6075 + 28.6075i) q^{84} +(-6.69075 + 6.69075i) q^{85} +(29.7171 - 29.7171i) q^{86} +55.8114 q^{87} +201.329i q^{88} +(-91.1096 + 91.1096i) q^{89} +9.35089i q^{90} -256.302 q^{92} +(-42.1359 - 42.1359i) q^{93} -182.570 q^{94} -2.64911i q^{95} +(-68.9320 - 68.9320i) q^{96} +(-87.3552 - 87.3552i) q^{97} +(-116.083 + 116.083i) q^{98} +(-31.6754 + 31.6754i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} - 8 q^{5} + 16 q^{6} + 12 q^{7} - 36 q^{8} + 8 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 - 8 * q^5 + 16 * q^6 + 12 * q^7 - 36 * q^8 + 8 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} - 8 q^{5} + 16 q^{6} + 12 q^{7} - 36 q^{8} + 8 q^{9} + 4 q^{11} + 4 q^{14} + 28 q^{15} - 84 q^{16} - 32 q^{18} - 16 q^{20} - 32 q^{21} + 88 q^{22} - 24 q^{24} - 52 q^{27} - 4 q^{28} + 40 q^{29} - 40 q^{31} - 20 q^{32} + 76 q^{33} + 108 q^{34} - 68 q^{35} - 40 q^{37} + 84 q^{40} - 32 q^{41} + 76 q^{42} + 172 q^{44} - 56 q^{45} - 132 q^{46} + 4 q^{47} - 76 q^{48} + 128 q^{50} - 80 q^{53} - 152 q^{54} + 64 q^{55} + 40 q^{57} + 140 q^{58} - 56 q^{59} + 116 q^{60} - 296 q^{61} + 64 q^{63} + 112 q^{66} + 84 q^{67} + 444 q^{68} + 32 q^{70} - 284 q^{71} + 48 q^{72} + 100 q^{74} - 80 q^{76} + 64 q^{79} + 88 q^{80} - 220 q^{81} + 52 q^{83} + 184 q^{84} + 144 q^{85} + 24 q^{86} + 160 q^{87} - 200 q^{89} - 456 q^{92} - 80 q^{93} - 452 q^{94} - 320 q^{96} + 68 q^{97} - 224 q^{98} - 152 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 - 8 * q^5 + 16 * q^6 + 12 * q^7 - 36 * q^8 + 8 * q^9 + 4 * q^11 + 4 * q^14 + 28 * q^15 - 84 * q^16 - 32 * q^18 - 16 * q^20 - 32 * q^21 + 88 * q^22 - 24 * q^24 - 52 * q^27 - 4 * q^28 + 40 * q^29 - 40 * q^31 - 20 * q^32 + 76 * q^33 + 108 * q^34 - 68 * q^35 - 40 * q^37 + 84 * q^40 - 32 * q^41 + 76 * q^42 + 172 * q^44 - 56 * q^45 - 132 * q^46 + 4 * q^47 - 76 * q^48 + 128 * q^50 - 80 * q^53 - 152 * q^54 + 64 * q^55 + 40 * q^57 + 140 * q^58 - 56 * q^59 + 116 * q^60 - 296 * q^61 + 64 * q^63 + 112 * q^66 + 84 * q^67 + 444 * q^68 + 32 * q^70 - 284 * q^71 + 48 * q^72 + 100 * q^74 - 80 * q^76 + 64 * q^79 + 88 * q^80 - 220 * q^81 + 52 * q^83 + 184 * q^84 + 144 * q^85 + 24 * q^86 + 160 * q^87 - 200 * q^89 - 456 * q^92 - 80 * q^93 - 452 * q^94 - 320 * q^96 + 68 * q^97 - 224 * q^98 - 152 * q^99

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