LMFDB - Embedded newform 48.9.l.a.43.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,9,Mod(19,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("48.19");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	48.l (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:	$19.5541732829$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.19
Character	$\chi$	$=$	48.43
Dual form			48.9.l.a.19.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.42993 + 15.6280i) q^{2} +(33.0681 + 33.0681i) q^{3} +(-232.471 + 107.206i) q^{4} +(-488.559 - 488.559i) q^{5} +(-403.369 + 630.211i) q^{6} -90.0632 q^{7} +(-2472.78 - 3265.36i) q^{8} +2187.00i q^{9} +O(q^{10})$	\(q+(3.42993 + 15.6280i) q^{2} +(33.0681 + 33.0681i) q^{3} +(-232.471 + 107.206i) q^{4} +(-488.559 - 488.559i) q^{5} +(-403.369 + 630.211i) q^{6} -90.0632 q^{7} +(-2472.78 - 3265.36i) q^{8} +2187.00i q^{9} +(5959.49 - 9310.93i) q^{10} +(5123.51 - 5123.51i) q^{11} +(-11232.5 - 4142.28i) q^{12} +(23449.5 - 23449.5i) q^{13} +(-308.910 - 1407.51i) q^{14} -32311.4i q^{15} +(42549.7 - 49844.6i) q^{16} +29351.3 q^{17} +(-34178.5 + 7501.25i) q^{18} +(-30921.9 - 30921.9i) q^{19} +(165952. + 61199.4i) q^{20} +(-2978.22 - 2978.22i) q^{21} +(97643.6 + 62497.1i) q^{22} -312697. q^{23} +(26209.2 - 189749. i) q^{24} +86753.9i q^{25} +(446899. + 286039. i) q^{26} +(-72320.0 + 72320.0i) q^{27} +(20937.1 - 9655.32i) q^{28} +(820677. - 820677. i) q^{29} +(504964. - 110826. i) q^{30} -353851. i q^{31} +(924916. + 494005. i) q^{32} +338849. q^{33} +(100673. + 458703. i) q^{34} +(44001.1 + 44001.1i) q^{35} +(-234460. - 508415. i) q^{36} +(1.50543e6 + 1.50543e6i) q^{37} +(377189. - 589308. i) q^{38} +1.55086e6 q^{39} +(-387222. + 2.80342e6i) q^{40} -1.63963e6i q^{41} +(36328.6 - 56758.8i) q^{42} +(-804316. + 804316. i) q^{43} +(-641797. + 1.74034e6i) q^{44} +(1.06848e6 - 1.06848e6i) q^{45} +(-1.07253e6 - 4.88685e6i) q^{46} -8.02812e6i q^{47} +(3.05531e6 - 241229. i) q^{48} -5.75669e6 q^{49} +(-1.35579e6 + 297560. i) q^{50} +(970591. + 970591. i) q^{51} +(-2.93740e6 + 7.96525e6i) q^{52} +(-9.84980e6 - 9.84980e6i) q^{53} +(-1.37827e6 - 882167. i) q^{54} -5.00627e6 q^{55} +(222706. + 294089. i) q^{56} -2.04506e6i q^{57} +(1.56404e7 + 1.00107e7i) q^{58} +(-6.21314e6 + 6.21314e6i) q^{59} +(3.46398e6 + 7.51147e6i) q^{60} +(5.08251e6 - 5.08251e6i) q^{61} +(5.53000e6 - 1.21368e6i) q^{62} -196968. i q^{63} +(-4.54794e6 + 1.61490e7i) q^{64} -2.29129e7 q^{65} +(1.16223e6 + 5.29555e6i) q^{66} +(-1.21895e7 - 1.21895e7i) q^{67} +(-6.82332e6 + 3.14663e6i) q^{68} +(-1.03403e7 - 1.03403e7i) q^{69} +(-536731. + 838572. i) q^{70} +1.42417e6 q^{71} +(7.14134e6 - 5.40797e6i) q^{72} +5.27643e6i q^{73} +(-1.83634e7 + 2.86904e7i) q^{74} +(-2.86879e6 + 2.86879e6i) q^{75} +(1.05035e7 + 3.87344e6i) q^{76} +(-461439. + 461439. i) q^{77} +(5.31933e6 + 2.42369e7i) q^{78} +2.02443e6i q^{79} +(-4.51401e7 + 3.56399e6i) q^{80} -4.78297e6 q^{81} +(2.56243e7 - 5.62383e6i) q^{82} +(1.30516e7 + 1.30516e7i) q^{83} +(1.01163e6 + 373067. i) q^{84} +(-1.43398e7 - 1.43398e7i) q^{85} +(-1.53286e7 - 9.81114e6i) q^{86} +5.42765e7 q^{87} +(-2.93994e7 - 4.06079e6i) q^{88} -6.83767e7i q^{89} +(2.03630e7 + 1.30334e7i) q^{90} +(-2.11193e6 + 2.11193e6i) q^{91} +(7.26931e7 - 3.35230e7i) q^{92} +(1.17012e7 - 1.17012e7i) q^{93} +(1.25464e8 - 2.75359e7i) q^{94} +3.02143e7i q^{95} +(1.42494e7 + 4.69211e7i) q^{96} +4.03711e7 q^{97} +(-1.97450e7 - 8.99658e7i) q^{98} +(1.12051e7 + 1.12051e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 372 q^{4} + 17460 q^{8}+O(q^{10}) $ 64 * q - 372 * q^4 + 17460 * q^8	\( 64 q - 372 q^{4} + 17460 q^{8} - 13784 q^{10} + 39552 q^{11} - 22680 q^{12} + 116772 q^{14} - 161824 q^{16} - 26244 q^{18} - 167552 q^{19} + 690000 q^{20} - 1252768 q^{22} + 1691136 q^{23} - 74844 q^{24} - 1682100 q^{26} + 678600 q^{28} - 2132352 q^{29} - 2054808 q^{30} + 1407840 q^{32} - 3704544 q^{34} - 2415744 q^{35} - 1041012 q^{36} - 4720512 q^{37} + 2413320 q^{38} - 3544848 q^{40} + 9436500 q^{42} - 7244672 q^{43} - 3982056 q^{44} + 11165992 q^{46} - 9467280 q^{48} + 52706752 q^{49} + 17072676 q^{50} + 13862016 q^{51} - 22890864 q^{52} - 5358720 q^{53} - 4960116 q^{54} - 46326784 q^{55} - 9637152 q^{56} + 25732944 q^{58} + 44938752 q^{59} + 40927032 q^{60} + 24476032 q^{61} - 17024868 q^{62} - 116303448 q^{64} + 29941632 q^{65} - 56828952 q^{66} - 44244736 q^{67} - 12614400 q^{68} - 8636544 q^{69} - 60922560 q^{70} + 159664128 q^{71} - 18502020 q^{72} + 140654028 q^{74} + 12918528 q^{75} + 204842760 q^{76} - 94964352 q^{77} + 14001660 q^{78} + 38076648 q^{80} - 306110016 q^{81} - 260917000 q^{82} + 209328000 q^{83} - 127862712 q^{84} + 106960000 q^{85} - 123451824 q^{86} + 104240736 q^{88} + 53520264 q^{90} - 45401472 q^{91} + 351567216 q^{92} + 208488216 q^{94} + 49597920 q^{96} - 681890712 q^{98} + 86500224 q^{99}+O(q^{100}) \) 64 * q - 372 * q^4 + 17460 * q^8 - 13784 * q^10 + 39552 * q^11 - 22680 * q^12 + 116772 * q^14 - 161824 * q^16 - 26244 * q^18 - 167552 * q^19 + 690000 * q^20 - 1252768 * q^22 + 1691136 * q^23 - 74844 * q^24 - 1682100 * q^26 + 678600 * q^28 - 2132352 * q^29 - 2054808 * q^30 + 1407840 * q^32 - 3704544 * q^34 - 2415744 * q^35 - 1041012 * q^36 - 4720512 * q^37 + 2413320 * q^38 - 3544848 * q^40 + 9436500 * q^42 - 7244672 * q^43 - 3982056 * q^44 + 11165992 * q^46 - 9467280 * q^48 + 52706752 * q^49 + 17072676 * q^50 + 13862016 * q^51 - 22890864 * q^52 - 5358720 * q^53 - 4960116 * q^54 - 46326784 * q^55 - 9637152 * q^56 + 25732944 * q^58 + 44938752 * q^59 + 40927032 * q^60 + 24476032 * q^61 - 17024868 * q^62 - 116303448 * q^64 + 29941632 * q^65 - 56828952 * q^66 - 44244736 * q^67 - 12614400 * q^68 - 8636544 * q^69 - 60922560 * q^70 + 159664128 * q^71 - 18502020 * q^72 + 140654028 * q^74 + 12918528 * q^75 + 204842760 * q^76 - 94964352 * q^77 + 14001660 * q^78 + 38076648 * q^80 - 306110016 * q^81 - 260917000 * q^82 + 209328000 * q^83 - 127862712 * q^84 + 106960000 * q^85 - 123451824 * q^86 + 104240736 * q^88 + 53520264 * q^90 - 45401472 * q^91 + 351567216 * q^92 + 208488216 * q^94 + 49597920 * q^96 - 681890712 * q^98 + 86500224 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	3.42993	+	15.6280i	0.214370	+	0.976752i
$2$	3.42993	+	15.6280i	0.214370	+	0.976752i
$3$	33.0681	+	33.0681i	0.408248	+	0.408248i
$3$	33.0681	+	33.0681i	0.408248	+	0.408248i
$4$	−232.471	+	107.206i	−0.908091	+	0.418774i
$5$	−488.559	−	488.559i	−0.781694	−	0.781694i	0.198423	−	0.980117i	$-0.436418\pi$
$5$	−488.559	−	488.559i	−0.781694	−	0.781694i	−0.980117	+	0.198423i	$0.936418\pi$
$6$	−403.369	+	630.211i	−0.311241	+	0.486274i
$7$	−90.0632			−0.0375107			−0.0187553	−	0.999824i	$-0.505970\pi$
$7$	−90.0632			−0.0375107			−0.0187553	+	0.999824i	$0.505970\pi$
$8$	−2472.78	−	3265.36i	−0.603706	−	0.797207i
$9$			2187.00i			0.333333i
$10$	5959.49	−	9310.93i	0.595949	−	0.931093i
$11$	5123.51	−	5123.51i	0.349942	−	0.349942i	−0.510146	−	0.860088i	$-0.670409\pi$
$11$	5123.51	−	5123.51i	0.349942	−	0.349942i	0.860088	+	0.510146i	$0.170409\pi$
$12$	−11232.5	−	4142.28i	−0.541690	−	0.199763i
$13$	23449.5	−	23449.5i	0.821031	−	0.821031i	−0.165225	−	0.986256i	$-0.552835\pi$
$13$	23449.5	−	23449.5i	0.821031	−	0.821031i	0.986256	+	0.165225i	$0.0528350\pi$
$14$	−308.910	−	1407.51i	−0.00804118	−	0.0366387i
$15$		−	32311.4i		−	0.638250i
$16$	42549.7	−	49844.6i	0.649257	−	0.760569i
$17$	29351.3			0.351424			0.175712	−	0.984442i	$-0.443777\pi$
$17$	29351.3			0.351424			0.175712	+	0.984442i	$0.443777\pi$
$18$	−34178.5	+	7501.25i	−0.325584	+	0.0714568i
$19$	−30921.9	−	30921.9i	−0.237275	−	0.237275i	0.578446	−	0.815721i	$-0.303659\pi$
$19$	−30921.9	−	30921.9i	−0.237275	−	0.237275i	−0.815721	+	0.578446i	$0.803659\pi$
$20$	165952.	+	61199.4i	1.03720	+	0.382496i
$21$	−2978.22	−	2978.22i	−0.0153137	−	0.0153137i
$22$	97643.6	+	62497.1i	0.416824	+	0.266790i
$23$	−312697.			−1.11741			−0.558705	−	0.829366i	$-0.688702\pi$
$23$	−312697.			−1.11741			−0.558705	+	0.829366i	$0.688702\pi$
$24$	26209.2	−	189749.i	0.0789965	−	0.571920i
$25$			86753.9i			0.222090i
$26$	446899.	+	286039.i	0.977949	+	0.625939i
$27$	−72320.0	+	72320.0i	−0.136083	+	0.136083i
$28$	20937.1	−	9655.32i	0.0340631	−	0.0157085i
$29$	820677.	−	820677.i	1.16033	−	1.16033i	0.175924	−	0.984404i	$-0.443709\pi$
$29$	820677.	−	820677.i	1.16033	−	1.16033i	0.984404	−	0.175924i	$-0.0562911\pi$
$30$	504964.	−	110826.i	0.623412	−	0.136822i
$31$		−	353851.i		−	0.383154i	−0.981478	−	0.191577i	$-0.938640\pi$
$31$		−	353851.i		−	0.383154i	0.981478	−	0.191577i	$-0.0613602\pi$
$32$	924916.	+	494005.i	0.882069	+	0.471120i
$33$	338849.			0.285727
$34$	100673.	+	458703.i	0.0753349	+	0.343254i
$35$	44001.1	+	44001.1i	0.0293219	+	0.0293219i
$36$	−234460.	−	508415.i	−0.139591	−	0.302697i
$37$	1.50543e6	+	1.50543e6i	0.803256	+	0.803256i	0.983603	−	0.180347i	$-0.0577222\pi$
$37$	1.50543e6	+	1.50543e6i	0.803256	+	0.803256i	−0.180347	+	0.983603i	$0.557722\pi$
$38$	377189.	−	589308.i	0.180894	−	0.282623i
$39$	1.55086e6			0.670369
$40$	−387222.	+	2.80342e6i	−0.151259	+	1.09508i
$41$		−	1.63963e6i		−	0.580245i	−0.956989	−	0.290123i	$-0.906304\pi$
$41$		−	1.63963e6i		−	0.580245i	0.956989	−	0.290123i	$-0.0936961\pi$
$42$	36328.6	−	56758.8i	0.0116749	−	0.0182405i
$43$	−804316.	+	804316.i	−0.235263	+	0.235263i	−0.814885	−	0.579622i	$-0.803200\pi$
$43$	−804316.	+	804316.i	−0.235263	+	0.235263i	0.579622	+	0.814885i	$0.303200\pi$
$44$	−641797.	+	1.74034e6i	−0.171233	+	0.464326i
$45$	1.06848e6	−	1.06848e6i	0.260565	−	0.260565i
$46$	−1.07253e6	−	4.88685e6i	−0.239540	−	1.09143i
$47$		−	8.02812e6i		−	1.64521i	−0.568610	−	0.822607i	$-0.692519\pi$
$47$		−	8.02812e6i		−	1.64521i	0.568610	−	0.822607i	$-0.307481\pi$
$48$	3.05531e6	−	241229.i	0.575559	−	0.0454427i
$49$	−5.75669e6			−0.998593
$50$	−1.35579e6	+	297560.i	−0.216927	+	0.0476095i
$51$	970591.	+	970591.i	0.143468	+	0.143468i
$52$	−2.93740e6	+	7.96525e6i	−0.401744	+	1.08940i
$53$	−9.84980e6	−	9.84980e6i	−1.24831	−	1.24831i	−0.956464	−	0.291851i	$-0.905729\pi$
$53$	−9.84980e6	−	9.84980e6i	−1.24831	−	1.24831i	−0.291851	−	0.956464i	$-0.594271\pi$
$54$	−1.37827e6	−	882167.i	−0.162091	−	0.103747i
$55$	−5.00627e6			−0.547095
$56$	222706.	+	294089.i	0.0226454	+	0.0299038i
$57$		−	2.04506e6i		−	0.193734i
$58$	1.56404e7	+	1.00107e7i	1.38209	+	0.884613i
$59$	−6.21314e6	+	6.21314e6i	−0.512747	+	0.512747i	−0.915367	−	0.402620i	$-0.868100\pi$
$59$	−6.21314e6	+	6.21314e6i	−0.512747	+	0.512747i	0.402620	+	0.915367i	$0.368100\pi$
$60$	3.46398e6	+	7.51147e6i	0.267282	+	0.579589i
$61$	5.08251e6	−	5.08251e6i	0.367079	−	0.367079i	−0.499332	−	0.866411i	$-0.666421\pi$
$61$	5.08251e6	−	5.08251e6i	0.367079	−	0.367079i	0.866411	+	0.499332i	$0.166421\pi$
$62$	5.53000e6	−	1.21368e6i	0.374247	−	0.0821370i
$63$		−	196968.i		−	0.0125036i
$64$	−4.54794e6	+	1.61490e7i	−0.271078	+	0.962557i
$65$	−2.29129e7			−1.28359
$66$	1.16223e6	+	5.29555e6i	0.0612514	+	0.279084i
$67$	−1.21895e7	−	1.21895e7i	−0.604906	−	0.604906i	0.336704	−	0.941611i	$-0.390688\pi$
$67$	−1.21895e7	−	1.21895e7i	−0.604906	−	0.604906i	−0.941611	+	0.336704i	$0.890688\pi$
$68$	−6.82332e6	+	3.14663e6i	−0.319125	+	0.147167i
$69$	−1.03403e7	−	1.03403e7i	−0.456181	−	0.456181i
$70$	−536731.	+	838572.i	−0.0223545	+	0.0349259i
$71$	1.42417e6			0.0560440			0.0280220	−	0.999607i	$-0.491079\pi$
$71$	1.42417e6			0.0560440			0.0280220	+	0.999607i	$0.491079\pi$
$72$	7.14134e6	−	5.40797e6i	0.265736	−	0.201235i
$73$			5.27643e6i			0.185801i	0.995675	+	0.0929007i	$0.0296139\pi$
$73$			5.27643e6i			0.185801i	−0.995675	+	0.0929007i	$0.970386\pi$
$74$	−1.83634e7	+	2.86904e7i	−0.612388	+	0.956776i
$75$	−2.86879e6	+	2.86879e6i	−0.0906679	+	0.0906679i
$76$	1.05035e7	+	3.87344e6i	0.314831	+	0.116103i
$77$	−461439.	+	461439.i	−0.0131266	+	0.0131266i
$78$	5.31933e6	+	2.42369e7i	0.143707	+	0.654785i
$79$			2.02443e6i			0.0519750i	0.999662	+	0.0259875i	$0.00827301\pi$
$79$			2.02443e6i			0.0519750i	−0.999662	+	0.0259875i	$0.991727\pi$
$80$	−4.51401e7	+	3.56399e6i	−1.10205	+	0.0870115i
$81$	−4.78297e6			−0.111111
$82$	2.56243e7	−	5.62383e6i	0.566756	−	0.124387i
$83$	1.30516e7	+	1.30516e7i	0.275012	+	0.275012i	0.831114	−	0.556102i	$-0.187704\pi$
$83$	1.30516e7	+	1.30516e7i	0.275012	+	0.275012i	−0.556102	+	0.831114i	$0.687704\pi$
$84$	1.01163e6	+	373067.i	0.0203192	+	0.00749324i
$85$	−1.43398e7	−	1.43398e7i	−0.274706	−	0.274706i
$86$	−1.53286e7	−	9.81114e6i	−0.280227	−	0.179360i
$87$	5.42765e7			0.947403
$88$	−2.93994e7	−	4.06079e6i	−0.490239	−	0.0677143i
$89$		−	6.83767e7i		−	1.08980i	−0.838500	−	0.544902i	$-0.816567\pi$
$89$		−	6.83767e7i		−	1.08980i	0.838500	−	0.544902i	$-0.183433\pi$
$90$	2.03630e7	+	1.30334e7i	0.310364	+	0.198650i
$91$	−2.11193e6	+	2.11193e6i	−0.0307974	+	0.0307974i
$92$	7.26931e7	−	3.35230e7i	1.01471	−	0.467942i
$93$	1.17012e7	−	1.17012e7i	0.156422	−	0.156422i
$94$	1.25464e8	−	2.75359e7i	1.60697	−	0.352685i
$95$			3.02143e7i			0.370952i
$96$	1.42494e7	+	4.69211e7i	0.167769	+	0.552437i
$97$	4.03711e7			0.456020			0.228010	−	0.973659i	$-0.426778\pi$
$97$	4.03711e7			0.456020			0.228010	+	0.973659i	$0.426778\pi$
$98$	−1.97450e7	−	8.99658e7i	−0.214069	−	0.975378i
$99$	1.12051e7	+	1.12051e7i	0.116647	+	0.116647i
$100$	−9.30055e6	−	2.01678e7i	−0.0930055	−	0.201678i
$101$	−1.14801e8	−	1.14801e8i	−1.10321	−	1.10321i	−0.994021	−	0.109190i	$-0.965174\pi$
$101$	−1.14801e8	−	1.14801e8i	−1.10321	−	1.10321i	−0.109190	−	0.994021i	$-0.534826\pi$
$102$	−1.18394e7	+	1.84975e7i	−0.109378	+	0.170888i
$103$	2.16102e8			1.92004			0.960018	−	0.279938i	$-0.0903139\pi$
$103$	2.16102e8			1.92004			0.960018	+	0.279938i	$0.0903139\pi$
$104$	−1.34556e8	−	1.85856e7i	−1.15019	−	0.158870i
$105$			2.91007e6i			0.0239412i
$106$	1.20149e8	−	1.87717e8i	0.951693	−	1.48690i
$107$	1.96589e6	−	1.96589e6i	0.0149976	−	0.0149976i	−0.699568	−	0.714566i	$-0.746624\pi$
$107$	1.96589e6	−	1.96589e6i	0.0149976	−	0.0149976i	0.714566	+	0.699568i	$0.246624\pi$
$108$	9.05917e6	−	2.45654e7i	0.0665876	−	0.180563i
$109$	−8.24500e6	+	8.24500e6i	−0.0584097	+	0.0584097i	−0.735708	−	0.677299i	$-0.763151\pi$
$109$	−8.24500e6	+	8.24500e6i	−0.0584097	+	0.0584097i	0.677299	+	0.735708i	$0.263151\pi$
$110$	−1.71711e7	−	7.82381e7i	−0.117281	−	0.534377i
$111$			9.95635e7i			0.655856i
$112$	−3.83216e6	+	4.48917e6i	−0.0243541	+	0.0285295i
$113$	−4.65915e7			−0.285755			−0.142877	−	0.989740i	$-0.545635\pi$
$113$	−4.65915e7			−0.285755			−0.142877	+	0.989740i	$0.545635\pi$
$114$	3.19602e7	−	7.01439e6i	0.189230	−	0.0415308i
$115$	1.52771e8	+	1.52771e8i	0.873473	+	0.873473i
$116$	−1.02802e8	+	2.78765e8i	−0.567768	+	1.53960i
$117$	5.12840e7	+	5.12840e7i	0.273677	+	0.273677i
$118$	−1.18410e8	−	7.57886e7i	−0.610745	−	0.390909i
$119$	−2.64347e6			−0.0131821
$120$	−1.05508e8	+	7.98990e7i	−0.508818	+	0.385315i
$121$			1.61858e8i			0.755081i
$122$	9.68623e7	+	6.19970e7i	0.437236	+	0.279854i
$123$	5.42196e7	−	5.42196e7i	0.236884	−	0.236884i
$124$	3.79350e7	+	8.22602e7i	0.160455	+	0.347939i
$125$	−1.48459e8	+	1.48459e8i	−0.608087	+	0.608087i
$126$	3.07823e6	−	675586.i	0.0122129	−	0.00268039i
$127$			3.99221e8i			1.53461i	0.641282	+	0.767306i	$0.278403\pi$
$127$			3.99221e8i			1.53461i	−0.641282	+	0.767306i	$0.721597\pi$
$128$	−2.67977e8	−	1.56854e7i	−0.998291	−	0.0584326i
$129$	−5.31944e7			−0.192091
$130$	−7.85895e7	−	3.58083e8i	−0.275164	−	1.25375i
$131$	2.27810e8	+	2.27810e8i	0.773549	+	0.773549i	0.978725	−	0.205176i	$-0.0657766\pi$
$131$	2.27810e8	+	2.27810e8i	0.773549	+	0.773549i	−0.205176	+	0.978725i	$0.565777\pi$
$132$	−7.87727e7	+	3.63267e7i	−0.259466	+	0.119655i
$133$	2.78492e6	+	2.78492e6i	0.00890034	+	0.00890034i
$134$	1.48689e8	−	2.32308e8i	0.461170	−	0.720518i
$135$	7.06651e7			0.212750
$136$	−7.25792e7	−	9.58425e7i	−0.212157	−	0.280158i
$137$		−	6.43715e8i		−	1.82731i	−0.406495	−	0.913653i	$-0.633249\pi$
$137$		−	6.43715e8i		−	1.82731i	0.406495	−	0.913653i	$-0.366751\pi$
$138$	1.26132e8	−	1.97065e8i	0.347784	−	0.543368i
$139$	−5.05320e8	+	5.05320e8i	−1.35365	+	1.35365i	−0.472115	+	0.881537i	$0.656509\pi$
$139$	−5.05320e8	+	5.05320e8i	−1.35365	+	1.35365i	−0.881537	+	0.472115i	$0.843491\pi$
$140$	−1.49462e7	−	5.51181e6i	−0.0389061	−	0.0143477i
$141$	2.65475e8	−	2.65475e8i	0.671656	−	0.671656i
$142$	4.88481e6	+	2.22570e7i	0.0120142	+	0.0547411i
$143$		−	2.40287e8i		−	0.574627i
$144$	1.09010e8	+	9.30563e7i	0.253523	+	0.216419i
$145$	−8.01898e8			−1.81404
$146$	−8.24603e7	+	1.80978e7i	−0.181482	+	0.0398303i
$147$	−1.90363e8	−	1.90363e8i	−0.407674	−	0.407674i
$148$	−5.11361e8	−	1.88578e8i	−1.06581	−	0.393047i
$149$	4.77788e8	+	4.77788e8i	0.969372	+	0.969372i	0.999545	−	0.0301726i	$-0.00960569\pi$
$149$	4.77788e8	+	4.77788e8i	0.969372	+	0.969372i	−0.0301726	+	0.999545i	$0.509606\pi$
$150$	−5.46733e7	−	3.49938e7i	−0.107997	−	0.0691236i
$151$	1.37633e7			0.0264736			0.0132368	−	0.999912i	$-0.495786\pi$
$151$	1.37633e7			0.0264736			0.0132368	+	0.999912i	$0.495786\pi$
$152$	−2.45081e7	+	1.77434e8i	−0.0459130	+	0.332401i
$153$			6.41912e7i			0.117141i
$154$	−8.79409e6	−	5.62869e6i	−0.0156354	−	0.0100075i
$155$	−1.72877e8	+	1.72877e8i	−0.299509	+	0.299509i
$156$	−3.60530e8	+	1.66261e8i	−0.608756	+	0.280733i
$157$	−6.65632e7	+	6.65632e7i	−0.109556	+	0.109556i	−0.759760	−	0.650204i	$-0.774683\pi$
$157$	−6.65632e7	+	6.65632e7i	−0.109556	+	0.109556i	0.650204	+	0.759760i	$0.274683\pi$
$158$	−3.16379e7	+	6.94364e6i	−0.0507667	+	0.0111419i
$159$		−	6.51429e8i		−	1.01924i
$160$	−2.10525e8	−	6.93226e8i	−0.321236	−	1.05778i
$161$	2.81625e7			0.0419148
$162$	−1.64052e7	−	7.47484e7i	−0.0238189	−	0.108528i
$163$	5.80605e8	+	5.80605e8i	0.822489	+	0.822489i	0.986464	−	0.163975i	$-0.0524317\pi$
$163$	5.80605e8	+	5.80605e8i	0.822489	+	0.822489i	−0.163975	+	0.986464i	$0.552432\pi$
$164$	1.75779e8	+	3.81168e8i	0.242991	+	0.526915i
$165$	−1.65548e8	−	1.65548e8i	−0.223351	−	0.223351i
$166$	−1.59205e8	+	2.48737e8i	−0.209664	+	0.327573i
$167$	1.28131e8			0.164735			0.0823677	−	0.996602i	$-0.473752\pi$
$167$	1.28131e8			0.164735			0.0823677	+	0.996602i	$0.473752\pi$
$168$	−2.36048e6	+	1.70894e7i	−0.00296321	+	0.0214531i
$169$		−	2.84024e8i		−	0.348184i
$170$	1.74919e8	−	2.73288e8i	0.209431	−	0.327208i
$171$	6.76262e7	−	6.76262e7i	0.0790916	−	0.0790916i
$172$	1.00753e8	−	2.73208e8i	0.115118	−	0.312162i
$173$	3.45331e8	−	3.45331e8i	0.385524	−	0.385524i	−0.487564	−	0.873087i	$-0.662114\pi$
$173$	3.45331e8	−	3.45331e8i	0.385524	−	0.385524i	0.873087	+	0.487564i	$0.162114\pi$
$174$	1.86164e8	+	8.48235e8i	0.203095	+	0.925379i
$175$		−	7.81333e6i		−	0.00833075i
$176$	−3.73755e7	−	4.73383e8i	−0.0389526	−	0.493358i
$177$	−4.10914e8			−0.418656
$178$	1.06859e9	−	2.34527e8i	1.06447	−	0.233622i
$179$	1.21816e9	+	1.21816e9i	1.18657	+	1.18657i	0.978009	+	0.208561i	$0.0668781\pi$
$179$	1.21816e9	+	1.21816e9i	1.18657	+	1.18657i	0.208561	+	0.978009i	$0.433122\pi$
$180$	−1.33843e8	+	3.62938e8i	−0.127499	+	0.345734i
$181$	6.42192e8	+	6.42192e8i	0.598344	+	0.598344i	0.939872	−	0.341528i	$-0.110944\pi$
$181$	6.42192e8	+	6.42192e8i	0.598344	+	0.598344i	−0.341528	+	0.939872i	$0.610944\pi$
$182$	−4.02492e7	−	2.57616e7i	−0.0366835	−	0.0234794i
$183$	3.36138e8			0.299718
$184$	7.73232e8	+	1.02107e9i	0.674587	+	0.890808i
$185$		−	1.47098e9i		−	1.25580i
$186$	2.23001e8	+	1.42732e8i	0.186318	+	0.119253i
$187$	1.50381e8	−	1.50381e8i	0.122978	−	0.122978i
$188$	8.60663e8	+	1.86631e9i	0.688973	+	1.49400i
$189$	6.51336e6	−	6.51336e6i	0.00510456	−	0.00510456i
$190$	−4.72190e8	+	1.03633e8i	−0.362329	+	0.0795212i
$191$		−	1.52894e9i		−	1.14883i	−0.818564	−	0.574416i	$-0.805229\pi$
$191$		−	1.52894e9i		−	1.14883i	0.818564	−	0.574416i	$-0.194771\pi$
$192$	−6.84410e8	+	3.83626e8i	−0.503630	+	0.282295i
$193$	−2.13278e9			−1.53716			−0.768578	−	0.639756i	$-0.779035\pi$
$193$	−2.13278e9			−1.53716			−0.768578	+	0.639756i	$0.779035\pi$
$194$	1.38470e8	+	6.30922e8i	0.0977572	+	0.445419i
$195$	−7.57686e8	−	7.57686e8i	−0.524023	−	0.524023i
$196$	1.33826e9	−	6.17152e8i	0.906813	−	0.418184i
$197$	−2.21148e8	−	2.21148e8i	−0.146831	−	0.146831i	0.629870	−	0.776701i	$-0.283108\pi$
$197$	−2.21148e8	−	2.21148e8i	−0.146831	−	0.146831i	−0.776701	+	0.629870i	$0.783108\pi$
$198$	−1.36681e8	+	2.13547e8i	−0.0889299	+	0.138941i
$199$	4.00665e8			0.255487			0.127744	−	0.991807i	$-0.459227\pi$
$199$	4.00665e8			0.255487			0.127744	+	0.991807i	$0.459227\pi$
$200$	2.83283e8	−	2.14523e8i	0.177052	−	0.134077i
$201$		−	8.06170e8i		−	0.493904i
$202$	1.40035e9	−	2.18786e9i	0.841068	−	1.31406i
$203$	−7.39128e7	+	7.39128e7i	−0.0435247	+	0.0435247i
$204$	−3.29688e8	−	1.21581e8i	−0.190363	−	0.0702014i
$205$	−8.01058e8	+	8.01058e8i	−0.453574	+	0.453574i
$206$	7.41213e8	+	3.37725e9i	0.411599	+	1.87540i
$207$		−	6.83869e8i		−	0.372470i
$208$	−1.71062e8	−	2.16660e9i	−0.0913902	−	1.15751i
$209$	−3.16857e8			−0.166065
$210$	−4.54787e7	+	9.98132e6i	−0.0233846	+	0.00513229i
$211$	−2.13776e9	−	2.13776e9i	−1.07852	−	1.07852i	−0.996642	−	0.0818789i	$-0.973908\pi$
$211$	−2.13776e9	−	2.13776e9i	−1.07852	−	1.07852i	−0.0818789	−	0.996642i	$-0.526092\pi$
$212$	3.34575e9	+	1.23384e9i	1.65634	+	0.610822i
$213$	4.70947e7	+	4.70947e7i	0.0228799	+	0.0228799i
$214$	3.74658e7	+	2.39801e7i	0.0178640	+	0.0114339i
$215$	7.85911e8			0.367807
$216$	4.14982e8	+	5.73194e7i	0.190640	+	0.0263322i
$217$			3.18690e7i			0.0143724i
$218$	−1.57133e8	−	1.00573e8i	−0.0695731	−	0.0445305i
$219$	−1.74482e8	+	1.74482e8i	−0.0758531	+	0.0758531i
$220$	1.16381e9	−	5.36702e8i	0.496812	−	0.229109i
$221$	6.88272e8	−	6.88272e8i	0.288530	−	0.288530i
$222$	−1.55598e9	+	3.41495e8i	−0.640608	+	0.140596i
$223$		−	2.57978e9i		−	1.04319i	−0.853194	−	0.521594i	$-0.825338\pi$
$223$		−	2.57978e9i		−	1.04319i	0.853194	−	0.521594i	$-0.174662\pi$
$224$	−8.33009e7	−	4.44917e7i	−0.0330870	−	0.0176720i
$225$	−1.89731e8			−0.0740300
$226$	−1.59806e8	−	7.28134e8i	−0.0612573	−	0.279112i
$227$	−2.13882e9	−	2.13882e9i	−0.805509	−	0.805509i	0.178441	−	0.983951i	$-0.442895\pi$
$227$	−2.13882e9	−	2.13882e9i	−0.805509	−	0.805509i	−0.983951	+	0.178441i	$0.942895\pi$
$228$	2.19242e8	+	4.75417e8i	0.0811307	+	0.175928i
$229$	3.05430e9	+	3.05430e9i	1.11063	+	1.11063i	0.993065	+	0.117567i	$0.0375096\pi$
$229$	3.05430e9	+	3.05430e9i	1.11063	+	1.11063i	0.117567	+	0.993065i	$0.462490\pi$
$230$	−1.86352e9	+	2.91150e9i	−0.665920	+	1.04041i
$231$	−3.05178e7			−0.0107178
$232$	−4.70916e9	−	6.50453e8i	−1.62552	−	0.224525i
$233$		−	1.67275e9i		−	0.567554i	−0.958890	−	0.283777i	$-0.908412\pi$
$233$		−	1.67275e9i		−	0.567554i	0.958890	−	0.283777i	$-0.0915876\pi$
$234$	−6.25568e8	+	9.77368e8i	−0.208646	+	0.325983i
$235$	−3.92221e9	+	3.92221e9i	−1.28605	+	1.28605i
$236$	7.78291e8	−	2.11046e9i	0.250896	−	0.680346i
$237$	−6.69441e7	+	6.69441e7i	−0.0212187	+	0.0212187i
$238$	−9.06690e6	−	4.13122e7i	−0.00282586	−	0.0128757i
$239$			2.74879e8i			0.0842461i	0.999112	+	0.0421230i	$0.0134121\pi$
$239$			2.74879e8i			0.0842461i	−0.999112	+	0.0421230i	$0.986588\pi$
$240$	−1.61055e9	−	1.37484e9i	−0.485433	−	0.414389i
$241$	5.08903e9			1.50857			0.754287	−	0.656544i	$-0.227983\pi$
$241$	5.08903e9			1.50857			0.754287	+	0.656544i	$0.227983\pi$
$242$	−2.52953e9	+	5.55162e8i	−0.737527	+	0.161867i
$243$	−1.58164e8	−	1.58164e8i	−0.0453609	−	0.0453609i
$244$	−6.36662e8	+	1.72641e9i	−0.179618	+	0.487063i
$245$	2.81248e9	+	2.81248e9i	0.780594	+	0.780594i
$246$	1.03332e9	+	6.61377e8i	0.282158	+	0.180596i
$247$	−1.45020e9			−0.389620
$248$	−1.15545e9	+	8.74996e8i	−0.305453	+	0.231313i
$249$			8.63184e8i			0.224546i
$250$	−2.82932e9	−	1.81092e9i	−0.724307	−	0.463595i
$251$	−4.29947e9	+	4.29947e9i	−1.08323	+	1.08323i	−0.0870215	+	0.996206i	$0.527735\pi$
$251$	−4.29947e9	+	4.29947e9i	−1.08323	+	1.08323i	−0.996206	+	0.0870215i	$0.972265\pi$
$252$	2.11162e7	+	4.57894e7i	0.00523616	+	0.0113544i
$253$	−1.60211e9	+	1.60211e9i	−0.391029	+	0.391029i
$254$	−6.23904e9	+	1.36930e9i	−1.49894	+	0.328975i
$255$		−	9.48381e8i		−	0.224296i
$256$	−6.74009e8	−	4.24175e9i	−0.156930	−	0.987610i
$257$	−3.17468e9			−0.727725			−0.363863	−	0.931453i	$-0.618542\pi$
$257$	−3.17468e9			−0.727725			−0.363863	+	0.931453i	$0.618542\pi$
$258$	−1.82453e8	−	8.31325e8i	−0.0411787	−	0.187626i
$259$	−1.35584e8	−	1.35584e8i	−0.0301307	−	0.0301307i
$260$	5.32658e9	−	2.45640e9i	1.16562	−	0.537533i
$261$	1.79482e9	+	1.79482e9i	0.386776	+	0.386776i
$262$	−2.77885e9	+	4.34160e9i	−0.589740	+	0.921392i
$263$	6.67510e8			0.139519			0.0697597	−	0.997564i	$-0.477777\pi$
$263$	6.67510e8			0.139519			0.0697597	+	0.997564i	$0.477777\pi$
$264$	−8.37900e8	−	1.10647e9i	−0.172495	−	0.227783i
$265$			9.62441e9i			1.95160i
$266$	−3.39708e7	+	5.30750e7i	−0.00678546	+	0.0106014i
$267$	2.26109e9	−	2.26109e9i	0.444910	−	0.444910i
$268$	4.14051e9	+	1.52693e9i	0.802629	+	0.295991i
$269$	5.06867e9	−	5.06867e9i	0.968021	−	0.968021i	−0.0314835	−	0.999504i	$-0.510023\pi$
$269$	5.06867e9	−	5.06867e9i	0.968021	−	0.968021i	0.999504	+	0.0314835i	$0.0100232\pi$
$270$	2.42376e8	+	1.10436e9i	0.0456073	+	0.207804i
$271$		−	8.47734e9i		−	1.57175i	−0.618388	−	0.785873i	$-0.712214\pi$
$271$		−	8.47734e9i		−	1.57175i	0.618388	−	0.785873i	$-0.287786\pi$
$272$	1.24889e9	−	1.46300e9i	0.228164	−	0.267282i
$273$	−1.39675e8			−0.0251460
$274$	1.00600e10	−	2.20790e9i	1.78483	−	0.391720i
$275$	4.44484e8	+	4.44484e8i	0.0777187	+	0.0777187i
$276$	3.51237e9	+	1.29528e9i	0.605290	+	0.223217i
$277$	5.98147e9	+	5.98147e9i	1.01599	+	1.01599i	0.999870	+	0.0161193i	$0.00513115\pi$
$277$	5.98147e9	+	5.98147e9i	1.01599	+	1.01599i	0.0161193	+	0.999870i	$0.494869\pi$
$278$	−9.63037e9	−	6.16395e9i	−1.61237	−	1.03200i
$279$	7.73872e8			0.127718
$280$	3.48745e7	−	2.52485e8i	0.00567382	−	0.0410774i
$281$		−	1.31226e9i		−	0.210472i	−0.994447	−	0.105236i	$-0.966440\pi$
$281$		−	1.31226e9i		−	0.210472i	0.994447	−	0.105236i	$-0.0335598\pi$
$282$	5.05941e9	+	3.23829e9i	0.800025	+	0.512059i
$283$	−2.91829e9	+	2.91829e9i	−0.454970	+	0.454970i	−0.897000	−	0.442030i	$-0.854259\pi$
$283$	−2.91829e9	+	2.91829e9i	−0.454970	+	0.454970i	0.442030	+	0.897000i	$0.354259\pi$
$284$	−3.31079e8	+	1.52680e8i	−0.0508930	+	0.0234697i
$285$	−9.99130e8	+	9.99130e8i	−0.151441	+	0.151441i
$286$	3.75521e9	−	8.24167e8i	0.561268	−	0.123183i
$287$			1.47671e8i			0.0217654i
$288$	−1.08039e9	+	2.02279e9i	−0.157040	+	0.294023i
$289$	−6.11426e9			−0.876501
$290$	−2.75045e9	−	1.25321e10i	−0.388877	−	1.77187i
$291$	1.33500e9	+	1.33500e9i	0.186169	+	0.186169i
$292$	−5.65665e8	−	1.22662e9i	−0.0778087	−	0.168724i
$293$	5.30384e8	+	5.30384e8i	0.0719648	+	0.0719648i	0.742173	−	0.670208i	$-0.233795\pi$
$293$	5.30384e8	+	5.30384e8i	0.0719648	+	0.0719648i	−0.670208	+	0.742173i	$0.733795\pi$
$294$	2.32207e9	−	3.62793e9i	0.310803	−	0.485590i
$295$	6.07097e9			0.801623
$296$	1.19318e9	−	8.63837e9i	0.155431	−	1.12529i
$297$			7.41064e8i			0.0952422i
$298$	−5.82812e9	+	9.10567e9i	−0.739032	+	1.15464i
$299$	−7.33259e9	+	7.33259e9i	−0.917429	+	0.917429i
$300$	3.59359e8	−	9.74462e8i	0.0443653	−	0.120304i
$301$	7.24393e7	−	7.24393e7i	0.00882486	−	0.00882486i
$302$	4.72069e7	+	2.15093e8i	0.00567516	+	0.0258582i
$303$		−	7.59247e9i		−	0.900768i
$304$	−2.85701e9	+	2.25572e8i	−0.334516	+	0.0264114i
$305$	−4.96621e9			−0.573886
$306$	−1.00318e9	+	2.20171e8i	−0.114418	+	0.0251116i
$307$	7.30082e9	+	7.30082e9i	0.821898	+	0.821898i	0.986380	−	0.164482i	$-0.0525953\pi$
$307$	7.30082e9	+	7.30082e9i	0.821898	+	0.821898i	−0.164482	+	0.986380i	$0.552595\pi$
$308$	5.78023e7	−	1.56740e8i	0.00642306	−	0.0174172i
$309$	7.14608e9	+	7.14608e9i	0.783851	+	0.783851i
$310$	−3.29468e9	−	2.10877e9i	−0.356752	−	0.228341i
$311$	1.31284e10			1.40336			0.701681	−	0.712491i	$-0.252433\pi$
$311$	1.31284e10			1.40336			0.701681	+	0.712491i	$0.252433\pi$
$312$	−3.83493e9	−	5.06411e9i	−0.404706	−	0.534423i
$313$		−	1.32662e10i		−	1.38219i	−0.722764	−	0.691095i	$-0.757128\pi$
$313$		−	1.32662e10i		−	1.38219i	0.722764	−	0.691095i	$-0.242872\pi$
$314$	−1.26856e9	−	8.11946e8i	−0.130495	−	0.0835235i
$315$	−9.62305e7	+	9.62305e7i	−0.00977396	+	0.00977396i
$316$	−2.17031e8	−	4.70622e8i	−0.0217657	−	0.0471980i
$317$	5.71864e9	−	5.71864e9i	0.566312	−	0.566312i	−0.364781	−	0.931093i	$-0.618856\pi$
$317$	5.71864e9	−	5.71864e9i	0.566312	−	0.566312i	0.931093	+	0.364781i	$0.118856\pi$
$318$	1.01806e10	−	2.23435e9i	0.995550	−	0.218496i
$319$		−	8.40949e9i		−	0.812095i
$320$	1.01117e10	−	5.66781e9i	0.964325	−	0.540525i
$321$	1.30016e8			0.0122455
$322$	9.65953e7	+	4.40125e8i	0.00898530	+	0.0409404i
$323$	−9.07597e8	−	9.07597e8i	−0.0833840	−	0.0833840i
$324$	1.11190e9	−	5.12763e8i	0.100899	−	0.0465304i
$325$	2.03433e9	+	2.03433e9i	0.182343	+	0.182343i
$326$	−7.08228e9	+	1.10651e10i	−0.627051	+	0.979686i
$327$	−5.45293e8			−0.0476913
$328$	−5.35400e9	+	4.05446e9i	−0.462576	+	0.350298i
$329$			7.23038e8i			0.0617131i
$330$	2.01937e9	−	3.15500e9i	0.170279	−	0.266038i
$331$	6.57264e9	−	6.57264e9i	0.547555	−	0.547555i	−0.378178	−	0.925733i	$-0.623449\pi$
$331$	6.57264e9	−	6.57264e9i	0.547555	−	0.547555i	0.925733	+	0.378178i	$0.123449\pi$
$332$	−4.43333e9	−	1.63491e9i	−0.364904	−	0.134568i
$333$	−3.29238e9	+	3.29238e9i	−0.267752	+	0.267752i
$334$	4.39479e8	+	2.00243e9i	0.0353144	+	0.160906i
$335$			1.19106e10i			0.945703i
$336$	−2.75171e8	+	2.17258e7i	−0.0215896	+	0.00170459i
$337$	1.26133e9			0.0977936			0.0488968	−	0.998804i	$-0.484429\pi$
$337$	1.26133e9			0.0977936			0.0488968	+	0.998804i	$0.484429\pi$
$338$	4.43874e9	−	9.74182e8i	0.340089	−	0.0746403i
$339$	−1.54069e9	−	1.54069e9i	−0.116659	−	0.116659i
$340$	4.87091e9	+	1.79628e9i	0.364497	+	0.134418i
$341$	−1.81296e9	−	1.81296e9i	−0.134082	−	0.134082i
$342$	1.28882e9	+	8.24912e8i	0.0942078	+	0.0602980i
$343$	1.03766e9			0.0749686
$344$	4.61528e9	+	6.37486e8i	0.329583	+	0.0455236i
$345$			1.01037e10i			0.713188i
$346$	6.58131e9	+	4.21239e9i	0.459206	+	0.293916i
$347$	−7.56366e9	+	7.56366e9i	−0.521692	+	0.521692i	−0.918082	−	0.396390i	$-0.870263\pi$
$347$	−7.56366e9	+	7.56366e9i	−0.521692	+	0.521692i	0.396390	+	0.918082i	$0.370263\pi$
$348$	−1.26177e10	+	5.81877e9i	−0.860328	+	0.396748i
$349$	−3.94045e9	+	3.94045e9i	−0.265610	+	0.265610i	−0.827328	−	0.561719i	$-0.810140\pi$
$349$	−3.94045e9	+	3.94045e9i	−0.265610	+	0.265610i	0.561719	+	0.827328i	$0.310140\pi$
$350$	1.22107e8	−	2.67992e7i	0.00813708	−	0.00178587i
$351$			3.39173e9i			0.223456i
$352$	7.26985e9	−	2.20778e9i	0.473538	−	0.143808i
$353$	−1.98302e10			−1.27711			−0.638556	−	0.769576i	$-0.720468\pi$
$353$	−1.98302e10			−1.27711			−0.638556	+	0.769576i	$0.720468\pi$
$354$	−1.40940e9	−	6.42178e9i	−0.0897475	−	0.408924i
$355$	−6.95792e8	−	6.95792e8i	−0.0438092	−	0.0438092i
$356$	7.33040e9	+	1.58956e10i	0.456381	+	0.989640i
$357$	−8.74145e7	−	8.74145e7i	−0.00538159	−	0.00538159i
$358$	−1.48593e10	+	2.32157e10i	−0.904620	+	1.41335i
$359$	−1.93670e10			−1.16596			−0.582981	−	0.812486i	$-0.698114\pi$
$359$	−1.93670e10			−1.16596			−0.582981	+	0.812486i	$0.698114\pi$
$360$	−6.13107e9	−	8.46855e8i	−0.365028	−	0.0504196i
$361$		−	1.50712e10i		−	0.887401i
$362$	−7.83353e9	+	1.22389e10i	−0.456166	+	0.712701i
$363$	−5.35235e9	+	5.35235e9i	−0.308260	+	0.308260i
$364$	2.64552e8	−	7.17376e8i	0.0150697	−	0.0408640i
$365$	2.57785e9	−	2.57785e9i	0.145240	−	0.145240i
$366$	1.15293e9	+	5.25318e9i	0.0642508	+	0.292751i
$367$		−	1.30098e10i		−	0.717146i	−0.933502	−	0.358573i	$-0.883264\pi$
$367$		−	1.30098e10i		−	0.717146i	0.933502	−	0.358573i	$-0.116736\pi$
$368$	−1.33052e10	+	1.55863e10i	−0.725487	+	0.849868i
$369$	3.58588e9			0.193415
$370$	2.29886e10	−	5.04536e9i	1.22661	−	0.269206i
$371$	8.87104e8	+	8.87104e8i	0.0468251	+	0.0468251i
$372$	−1.46575e9	+	3.97463e9i	−0.0765400	+	0.207551i
$373$	−1.63106e10	−	1.63106e10i	−0.842627	−	0.842627i	0.146572	−	0.989200i	$-0.453176\pi$
$373$	−1.63106e10	−	1.63106e10i	−0.842627	−	0.842627i	−0.989200	+	0.146572i	$0.953176\pi$
$374$	2.86596e9	+	1.83437e9i	0.146482	+	0.0937563i
$375$	−9.81850e9			−0.496501
$376$	−2.62147e10	+	1.98518e10i	−1.31158	+	0.993226i
$377$		−	3.84889e10i		−	1.90533i
$378$	1.24131e8	+	7.94508e7i	0.00608016	+	0.00389162i
$379$	1.65804e10	−	1.65804e10i	0.803595	−	0.803595i	−0.180061	−	0.983655i	$-0.557629\pi$
$379$	1.65804e10	−	1.65804e10i	0.803595	−	0.803595i	0.983655	+	0.180061i	$0.0576295\pi$
$380$	−3.23916e9	−	7.02396e9i	−0.155345	−	0.336858i
$381$	−1.32015e10	+	1.32015e10i	−0.626502	+	0.626502i
$382$	2.38943e10	−	5.24415e9i	1.12212	−	0.246276i
$383$			3.20903e10i			1.49135i	0.666311	+	0.745674i	$0.267872\pi$
$383$			3.20903e10i			1.49135i	−0.666311	+	0.745674i	$0.732128\pi$
$384$	−8.34280e9	−	9.38017e9i	−0.383696	−	0.431406i
$385$	4.50880e8			0.0205219
$386$	−7.31529e9	−	3.33312e10i	−0.329521	−	1.50142i
$387$	−1.75904e9	−	1.75904e9i	−0.0784209	−	0.0784209i
$388$	−9.38513e9	+	4.32803e9i	−0.414108	+	0.190969i
$389$	−2.48954e10	−	2.48954e10i	−1.08723	−	1.08723i	−0.995813	−	0.0914164i	$-0.970861\pi$
$389$	−2.48954e10	−	2.48954e10i	−1.08723	−	1.08723i	−0.0914164	−	0.995813i	$-0.529139\pi$
$390$	9.24233e9	−	1.44399e10i	0.399506	−	0.624176i
$391$	−9.17806e9			−0.392685
$392$	1.42350e10	+	1.87977e10i	0.602856	+	0.796085i
$393$			1.50665e10i			0.631600i
$394$	2.69759e9	−	4.21463e9i	0.111941	−	0.174894i
$395$	9.89052e8	−	9.89052e8i	0.0406285	−	0.0406285i
$396$	−3.80612e9	−	1.40361e9i	−0.154775	−	0.0570776i
$397$	3.40229e9	−	3.40229e9i	0.136965	−	0.136965i	−0.635300	−	0.772265i	$-0.719124\pi$
$397$	3.40229e9	−	3.40229e9i	0.136965	−	0.136965i	0.772265	+	0.635300i	$0.219124\pi$
$398$	1.37425e9	+	6.26161e9i	0.0547689	+	0.249548i
$399$			1.84184e8i			0.00726710i
$400$	4.32422e9	+	3.69136e9i	0.168915	+	0.144194i
$401$	1.99989e10			0.773444			0.386722	−	0.922196i	$-0.373607\pi$
$401$	1.99989e10			0.773444			0.386722	+	0.922196i	$0.373607\pi$
$402$	1.25989e10	−	2.76511e9i	0.482422	−	0.105878i
$403$	−8.29762e9	−	8.29762e9i	−0.314582	−	0.314582i
$404$	3.89951e10	+	1.43805e10i	1.46381	+	0.539820i
$405$	2.33676e9	+	2.33676e9i	0.0868549	+	0.0868549i
$406$	−1.40863e9	−	9.01597e8i	−0.0518432	−	0.0331824i
$407$	1.54262e10			0.562186
$408$	7.69272e8	−	5.56939e9i	0.0277613	−	0.200986i
$409$		−	2.14424e10i		−	0.766268i	−0.923693	−	0.383134i	$-0.874845\pi$
$409$		−	2.14424e10i		−	0.766268i	0.923693	−	0.383134i	$-0.125155\pi$
$410$	−1.52665e10	−	9.77139e9i	−0.540263	−	0.345797i
$411$	2.12864e10	−	2.12864e10i	0.745995	−	0.745995i
$412$	−5.02374e10	+	2.31674e10i	−1.74357	+	0.804060i
$413$	5.59575e8	−	5.59575e8i	0.0192335	−	0.0192335i
$414$	1.06875e10	−	2.34562e9i	0.363811	−	0.0798466i
$415$		−	1.27529e10i		−	0.429950i
$416$	3.32730e10	−	1.01046e10i	1.11101	−	0.337402i
$417$	−3.34199e10			−1.10525
$418$	−1.08680e9	−	4.95185e9i	−0.0355994	−	0.162204i
$419$	3.65932e10	+	3.65932e10i	1.18725	+	1.18725i	0.977823	+	0.209432i	$0.0671613\pi$
$419$	3.65932e10	+	3.65932e10i	1.18725	+	1.18725i	0.209432	+	0.977823i	$0.432839\pi$
$420$	−3.11977e8	−	6.76507e8i	−0.0100259	−	0.0217408i
$421$	−2.44831e10	−	2.44831e10i	−0.779358	−	0.779358i	0.200363	−	0.979722i	$-0.435788\pi$
$421$	−2.44831e10	−	2.44831e10i	−0.779358	−	0.779358i	−0.979722	+	0.200363i	$0.935788\pi$
$422$	2.60766e10	−	4.07413e10i	0.822245	−	1.28465i
$423$	1.75575e10			0.548405
$424$	−7.80676e9	+	5.65195e10i	−0.241550	+	1.74878i
$425$			2.54634e9i			0.0780477i
$426$	−5.74466e8	+	8.97529e8i	−0.0174432	+	0.0272527i
$427$	−4.57747e8	+	4.57747e8i	−0.0137694	+	0.0137694i
$428$	−2.46257e8	+	6.67767e8i	−0.00733861	+	0.0198998i
$429$	7.94584e9	−	7.94584e9i	0.234591	−	0.234591i
$430$	2.69562e9	+	1.22823e10i	0.0788469	+	0.359256i
$431$			5.13249e10i			1.48737i	0.668529	+	0.743686i	$0.266924\pi$
$431$			5.13249e10i			1.48737i	−0.668529	+	0.743686i	$0.733076\pi$
$432$	5.27568e8	+	6.68196e9i	0.0151476	+	0.191853i
$433$	2.75359e10			0.783334			0.391667	−	0.920107i	$-0.371898\pi$
$433$	2.75359e10			0.783334			0.391667	+	0.920107i	$0.371898\pi$
$434$	−4.98049e8	+	1.09308e8i	−0.0140383	+	0.00308101i
$435$	−2.65173e10	−	2.65173e10i	−0.740579	−	0.740579i
$436$	1.03281e9	−	2.80064e9i	0.0285808	−	0.0775017i
$437$	9.66919e9	+	9.66919e9i	0.265133	+	0.265133i
$438$	−3.32526e9	−	2.12835e9i	−0.0903503	−	0.0578290i
$439$	1.40065e10			0.377114			0.188557	−	0.982062i	$-0.439619\pi$
$439$	1.40065e10			0.377114			0.188557	+	0.982062i	$0.439619\pi$
$440$	1.23794e10	+	1.63473e10i	0.330285	+	0.436148i
$441$		−	1.25899e10i		−	0.332864i
$442$	1.31171e10	+	8.39561e9i	0.343674	+	0.219970i
$443$	6.55378e9	−	6.55378e9i	0.170168	−	0.170168i	−0.616885	−	0.787053i	$-0.711606\pi$
$443$	6.55378e9	−	6.55378e9i	0.170168	−	0.170168i	0.787053	+	0.616885i	$0.211606\pi$
$444$	−1.06738e10	−	2.31456e10i	−0.274655	−	0.595576i
$445$	−3.34060e10	+	3.34060e10i	−0.851893	+	0.851893i
$446$	4.03168e10	−	8.84844e9i	1.01894	−	0.223629i
$447$			3.15991e10i			0.791489i
$448$	4.09602e8	−	1.45443e9i	0.0101683	−	0.0361062i
$449$	1.82943e10			0.450121			0.225061	−	0.974345i	$-0.427742\pi$
$449$	1.82943e10			0.450121			0.225061	+	0.974345i	$0.427742\pi$
$450$	−6.50763e8	−	2.96512e9i	−0.0158698	−	0.0723090i
$451$	−8.40068e9	−	8.40068e9i	−0.203052	−	0.203052i
$452$	1.08312e10	−	4.99489e9i	0.259491	−	0.119666i
$453$	4.55125e8	+	4.55125e8i	0.0108078	+	0.0108078i
$454$	2.60895e10	−	4.07615e10i	0.614106	−	0.959460i
$455$	2.06361e9			0.0481483
$456$	−6.67785e9	+	5.05697e9i	−0.154446	+	0.116958i
$457$			6.62170e10i			1.51812i	0.651023	+	0.759058i	$0.274340\pi$
$457$			6.62170e10i			1.51812i	−0.651023	+	0.759058i	$0.725660\pi$
$458$	−3.72567e10	+	5.82088e10i	−0.846726	+	1.32290i
$459$	−2.12268e9	+	2.12268e9i	−0.0478227	+	0.0478227i
$460$	−5.18928e10	−	1.91369e10i	−1.15898	−	0.427405i
$461$	3.04951e10	−	3.04951e10i	0.675191	−	0.675191i	−0.283717	−	0.958908i	$-0.591568\pi$
$461$	3.04951e10	−	3.04951e10i	0.675191	−	0.675191i	0.958908	+	0.283717i	$0.0915677\pi$
$462$	−1.04674e8	−	4.76934e8i	−0.00229758	−	0.0104686i
$463$		−	2.74356e10i		−	0.597022i	−0.954406	−	0.298511i	$-0.903510\pi$
$463$		−	2.74356e10i		−	0.597022i	0.954406	−	0.298511i	$-0.0964899\pi$
$464$	−5.98677e9	−	7.58260e10i	−0.129158	−	1.63586i
$465$	−1.14334e10			−0.244548
$466$	2.61418e10	−	5.73741e9i	0.554360	−	0.121667i
$467$	6.69462e10	+	6.69462e10i	1.40753	+	1.40753i	0.772418	+	0.635114i	$0.219047\pi$
$467$	6.69462e10	+	6.69462e10i	1.40753	+	1.40753i	0.635114	+	0.772418i	$0.280953\pi$
$468$	−1.74200e10	−	6.42410e9i	−0.363132	−	0.133915i
$469$	1.09783e9	+	1.09783e9i	0.0226905	+	0.0226905i
$470$	−7.47493e10	−	4.78435e10i	−1.53185	−	0.980464i
$471$	−4.40224e9			−0.0894520
$472$	3.56519e10	+	4.92442e9i	0.718314	+	0.0992172i
$473$			8.24184e9i			0.164657i
$474$	−1.27582e9	−	8.16591e8i	−0.0252741	−	0.0161768i
$475$	2.68260e9	−	2.68260e9i	0.0526964	−	0.0526964i
$476$	6.14530e8	−	2.83396e8i	0.0119706	−	0.00552034i
$477$	2.15415e10	−	2.15415e10i	0.416105	−	0.416105i
$478$	−4.29582e9	+	9.42814e8i	−0.0822875	+	0.0180599i
$479$			4.72519e10i			0.897589i	0.893635	+	0.448794i	$0.148146\pi$
$479$			4.72519e10i			0.897589i	−0.893635	+	0.448794i	$0.851854\pi$
$480$	1.59620e10	−	2.98854e10i	0.300693	−	0.562981i
$481$	7.06031e10			1.31900
$482$	1.74550e10	+	7.95316e10i	0.323394	+	1.47350i
$483$	9.31281e8	+	9.31281e8i	0.0171117	+	0.0171117i
$484$	−1.73522e10	−	3.76274e10i	−0.316208	−	0.685682i
$485$	−1.97237e10	−	1.97237e10i	−0.356468	−	0.356468i
$486$	1.92930e9	−	3.01428e9i	0.0345824	−	0.0540304i
$487$	−2.96060e10			−0.526337			−0.263168	−	0.964750i	$-0.584767\pi$
$487$	−2.96060e10			−0.526337			−0.263168	+	0.964750i	$0.584767\pi$
$488$	−2.91642e10	−	4.02830e9i	−0.514245	−	0.0710301i
$489$			3.83990e10i			0.671560i
$490$	−3.43069e10	+	5.36001e10i	−0.595111	+	0.929783i
$491$	3.92296e10	−	3.92296e10i	0.674975	−	0.674975i	−0.283884	−	0.958859i	$-0.591623\pi$
$491$	3.92296e10	−	3.92296e10i	0.674975	−	0.674975i	0.958859	+	0.283884i	$0.0916231\pi$
$492$	−6.79183e9	+	1.84172e10i	−0.115911	+	0.314313i
$493$	2.40879e10	−	2.40879e10i	0.407767	−	0.407767i
$494$	−4.97409e9	−	2.26638e10i	−0.0835230	−	0.380562i
$495$		−	1.09487e10i		−	0.182365i
$496$	−1.76376e10	−	1.50563e10i	−0.291415	−	0.248766i
$497$	−1.28265e8			−0.00210225
$498$	−1.34899e10	+	2.96066e9i	−0.219326	+	0.0481361i
$499$	2.06290e10	+	2.06290e10i	0.332717	+	0.332717i	0.853618	−	0.520900i	$-0.174404\pi$
$499$	2.06290e10	+	2.06290e10i	0.332717	+	0.332717i	−0.520900	+	0.853618i	$0.674404\pi$
$500$	1.85967e10	−	5.04281e10i	0.297547	−	0.806849i
$501$	4.23704e9	+	4.23704e9i	0.0672530	+	0.0672530i
$502$	−8.19391e10	−	5.24454e10i	−1.29026	−	0.825834i
$503$	−6.31542e10			−0.986575			−0.493287	−	0.869866i	$-0.664205\pi$
$503$	−6.31542e10			−0.986575			−0.493287	+	0.869866i	$0.664205\pi$
$504$	−6.43172e8	+	4.87059e8i	−0.00996793	+	0.00754848i
$505$			1.12174e11i			1.72475i
$506$	−3.05329e10	−	1.95427e10i	−0.465764	−	0.298114i
$507$	9.39215e9	−	9.39215e9i	0.142145	−	0.142145i
$508$	−4.27989e10	−	9.28074e10i	−0.642655	−	1.39357i
$509$	−3.81011e10	+	3.81011e10i	−0.567632	+	0.567632i	−0.931464	−	0.363832i	$-0.881468\pi$
$509$	−3.81011e10	+	3.81011e10i	−0.567632	+	0.567632i	0.363832	+	0.931464i	$0.381468\pi$
$510$	1.48213e10	−	3.25288e9i	0.219082	−	0.0480825i
$511$		−	4.75212e8i		−	0.00696954i
$512$	6.39785e10	−	2.50823e10i	0.931009	−	0.364996i
$513$	4.47254e9			0.0645780
$514$	−1.08889e10	−	4.96140e10i	−0.156003	−	0.710808i
$515$	−1.05578e11	−	1.05578e11i	−1.50088	−	1.50088i
$516$	1.23662e10	−	5.70277e9i	0.174436	−	0.0804427i
$517$	−4.11321e10	−	4.11321e10i	−0.575730	−	0.575730i
$518$	1.65387e9	−	2.58395e9i	0.0229711	−	0.0358893i
$519$	2.28389e10			0.314779
$520$	5.66585e10	+	7.48188e10i	0.774911	+	1.02329i
$521$		−	2.93538e10i		−	0.398394i	−0.979959	−	0.199197i	$-0.936167\pi$
$521$		−	2.93538e10i		−	0.398394i	0.979959	−	0.199197i	$-0.0638334\pi$
$522$	−2.18934e10	+	3.42056e10i	−0.294871	+	0.460697i
$523$	−4.31877e10	+	4.31877e10i	−0.577236	+	0.577236i	−0.934141	−	0.356905i	$-0.883832\pi$
$523$	−4.31877e10	+	4.31877e10i	−0.577236	+	0.577236i	0.356905	+	0.934141i	$0.383832\pi$
$524$	−7.73819e10	−	2.85367e10i	−1.02639	−	0.378511i
$525$	2.58372e8	−	2.58372e8i	0.00340102	−	0.00340102i
$526$	2.28951e9	+	1.04319e10i	0.0299088	+	0.136276i
$527$		−	1.03860e10i		−	0.134650i
$528$	1.44179e10	−	1.68898e10i	0.185510	−	0.217315i
$529$	1.94686e10			0.248607
$530$	−1.50411e11	+	3.30110e10i	−1.90623	+	0.418365i
$531$	−1.35881e10	−	1.35881e10i	−0.170916	−	0.170916i
$532$	−9.45975e8	−	3.48854e8i	−0.0118095	−	0.00435509i
$533$	−3.84486e10	−	3.84486e10i	−0.476399	−	0.476399i
$534$	4.30918e10	+	2.75810e10i	0.529943	+	0.339192i
$535$	−1.92090e9			−0.0234471
$536$	−9.66120e9	+	6.99453e10i	−0.117050	+	0.847421i
$537$			8.05648e10i			0.968831i
$538$	9.65985e10	+	6.18282e10i	1.15303	+	0.738002i
$539$	−2.94944e10	+	2.94944e10i	−0.349450	+	0.349450i
$540$	−1.64276e10	+	7.57572e9i	−0.193196	+	0.0890941i
$541$	−9.13417e10	+	9.13417e10i	−1.06630	+	1.06630i	−0.0686618	+	0.997640i	$0.521873\pi$
$541$	−9.13417e10	+	9.13417e10i	−1.06630	+	1.06630i	−0.997640	+	0.0686618i	$0.978127\pi$
$542$	1.32484e11	−	2.90766e10i	1.53521	−	0.336936i
$543$			4.24722e10i			0.488546i
$544$	2.71475e10	+	1.44997e10i	0.309980	+	0.165563i
$545$	8.05633e9			0.0913169
$546$	−4.79076e8	−	2.18285e9i	−0.00539056	−	0.0245614i
$547$	3.39984e10	+	3.39984e10i	0.379760	+	0.379760i	0.871015	−	0.491256i	$-0.163462\pi$
$547$	3.39984e10	+	3.39984e10i	0.379760	+	0.379760i	−0.491256	+	0.871015i	$0.663462\pi$
$548$	6.90101e10	+	1.49645e11i	0.765228	+	1.65936i
$549$	1.11155e10	+	1.11155e10i	0.122360	+	0.122360i
$550$	−5.42187e9	+	8.47097e9i	−0.0592514	+	0.0925725i
$551$	−5.07538e10			−0.550633
$552$	−8.19553e9	+	5.93341e10i	−0.0882716	+	0.639070i
$553$		−	1.82327e8i		−	0.00194962i
$554$	−7.29627e10	+	1.13995e11i	−0.774572	+	1.21017i
$555$	4.86426e10	−	4.86426e10i	0.512678	−	0.512678i
$556$	6.32990e10	−	1.71646e11i	0.662365	−	1.79611i
$557$	7.43649e9	−	7.43649e9i	0.0772587	−	0.0772587i	−0.667421	−	0.744680i	$-0.732602\pi$
$557$	7.43649e9	−	7.43649e9i	0.0772587	−	0.0772587i	0.744680	+	0.667421i	$0.232602\pi$
$558$	2.65433e9	+	1.20941e10i	0.0273790	+	0.124749i
$559$			3.77216e10i			0.386316i
$560$	4.06546e9	−	3.20984e8i	0.0413387	−	0.00326386i
$561$	9.94566e9			0.100411
$562$	2.05081e10	−	4.50096e9i	0.205579	−	0.0451190i
$563$	−6.89582e10	−	6.89582e10i	−0.686360	−	0.686360i	0.275065	−	0.961426i	$-0.411301\pi$
$563$	−6.89582e10	−	6.89582e10i	−0.686360	−	0.686360i	−0.961426	+	0.275065i	$0.911301\pi$
$564$	−3.32548e10	+	9.01758e10i	−0.328653	+	0.891196i
$565$	2.27627e10	+	2.27627e10i	0.223373	+	0.223373i
$566$	−5.56167e10	−	3.55977e10i	−0.541926	−	0.346861i
$567$	4.30769e8			0.00416785
$568$	−3.52166e9	−	4.65044e9i	−0.0338341	−	0.0446787i
$569$			7.08275e10i			0.675698i	0.941200	+	0.337849i	$0.109699\pi$
$569$			7.08275e10i			0.675698i	−0.941200	+	0.337849i	$0.890301\pi$
$570$	−1.90414e10	−	1.21875e10i	−0.180384	−	0.115456i
$571$	1.20077e11	−	1.20077e11i	1.12957	−	1.12957i	0.139324	−	0.990247i	$-0.455507\pi$
$571$	1.20077e11	−	1.20077e11i	1.12957	−	1.12957i	0.990247	−	0.139324i	$-0.0444931\pi$
$572$	2.57602e10	+	5.58598e10i	0.240639	+	0.521813i
$573$	5.05591e10	−	5.05591e10i	0.469009	−	0.469009i
$574$	−2.30780e9	+	5.06500e8i	−0.0212594	+	0.00466586i
$575$		−	2.71277e10i		−	0.248166i
$576$	−3.53179e10	−	9.94634e9i	−0.320852	−	0.0903594i
$577$	1.60024e11			1.44372			0.721859	−	0.692040i	$-0.243288\pi$
$577$	1.60024e11			1.44372			0.721859	+	0.692040i	$0.243288\pi$
$578$	−2.09715e10	−	9.55539e10i	−0.187896	−	0.856125i
$579$	−7.05272e10	−	7.05272e10i	−0.627541	−	0.627541i
$580$	1.86418e11	−	8.59683e10i	1.64731	−	0.759673i
$581$	−1.17547e9	−	1.17547e9i	−0.0103159	−	0.0103159i
$582$	−1.62844e10	+	2.54423e10i	−0.141932	+	0.221751i
$583$	−1.00931e11			−0.873676
$584$	1.72294e10	−	1.30474e10i	0.148122	−	0.112169i
$585$		−	5.01105e10i		−	0.427863i
$586$	−6.46969e9	+	1.01080e10i	−0.0548647	+	0.0857189i
$587$	8.62771e10	−	8.62771e10i	0.726680	−	0.726680i	−0.243277	−	0.969957i	$-0.578222\pi$
$587$	8.62771e10	−	8.62771e10i	0.726680	−	0.726680i	0.969957	+	0.243277i	$0.0782224\pi$
$588$	6.46619e10	+	2.38458e10i	0.540928	+	0.199482i
$589$	−1.09417e10	+	1.09417e10i	−0.0909129	+	0.0909129i
$590$	2.08230e10	+	9.48773e10i	0.171844	+	0.782987i
$591$		−	1.46259e10i		−	0.119887i
$592$	1.39093e11	−	1.09820e10i	1.13245	−	0.0894116i
$593$	1.62089e11			1.31079			0.655397	−	0.755285i	$-0.272501\pi$
$593$	1.62089e11			1.31079			0.655397	+	0.755285i	$0.272501\pi$
$594$	−1.15814e10	+	2.54179e9i	−0.0930281	+	0.0204171i
$595$	1.29149e9	+	1.29149e9i	0.0103044	+	0.0103044i
$596$	−1.62294e11	−	5.98502e10i	−1.28623	−	0.474330i
$597$	1.32492e10	+	1.32492e10i	0.104302	+	0.104302i
$598$	−1.39744e11	−	8.94437e10i	−1.09277	−	0.699431i
$599$	4.49719e9			0.0349329			0.0174664	−	0.999847i	$-0.494440\pi$
$599$	4.49719e9			0.0349329			0.0174664	+	0.999847i	$0.494440\pi$
$600$	1.64615e10	+	2.27375e9i	0.127018	+	0.0175443i
$601$		−	1.18550e11i		−	0.908665i	−0.890832	−	0.454332i	$-0.849878\pi$
$601$		−	1.18550e11i		−	0.908665i	0.890832	−	0.454332i	$-0.150122\pi$
$602$	1.38055e9	+	8.83622e8i	0.0105115	+	0.00672792i
$603$	2.66585e10	−	2.66585e10i	0.201635	−	0.201635i
$604$	−3.19956e9	+	1.47550e9i	−0.0240404	+	0.0110865i
$605$	7.90772e10	−	7.90772e10i	0.590242	−	0.590242i
$606$	1.18655e11	−	2.60416e10i	0.879827	−	0.193098i
$607$			4.46186e9i			0.0328671i	0.999865	+	0.0164335i	$0.00523119\pi$
$607$			4.46186e9i			0.0328671i	−0.999865	+	0.0164335i	$0.994769\pi$
$608$	−1.33246e10	−	4.38757e10i	−0.0975078	−	0.321078i
$609$	−4.88831e9			−0.0355378
$610$	−1.70337e10	−	7.76121e10i	−0.123024	−	0.560545i
$611$	−1.88255e11	−	1.88255e11i	−1.35077	−	1.35077i
$612$	−6.88169e9	−	1.49226e10i	−0.0490557	−	0.106375i
$613$	−4.56490e10	−	4.56490e10i	−0.323288	−	0.323288i	0.526739	−	0.850027i	$-0.323414\pi$
$613$	−4.56490e10	−	4.56490e10i	−0.323288	−	0.323288i	−0.850027	+	0.526739i	$0.823414\pi$
$614$	−8.90562e10	+	1.39139e11i	−0.626600	+	0.978981i
$615$	−5.29789e10			−0.370342
$616$	2.64780e9	+	3.65728e8i	0.0183892	+	0.00254001i
$617$			7.79351e10i			0.537765i	0.963173	+	0.268883i	$0.0866544\pi$
$617$			7.79351e10i			0.537765i	−0.963173	+	0.268883i	$0.913346\pi$
$618$	−8.71687e10	+	1.36190e11i	−0.597594	+	0.933663i
$619$	−1.35607e11	+	1.35607e11i	−0.923675	+	0.923675i	−0.997287	−	0.0736116i	$-0.976547\pi$
$619$	−1.35607e11	+	1.35607e11i	−0.923675	+	0.923675i	0.0736116	+	0.997287i	$0.476547\pi$
$620$	2.16555e10	−	5.87224e10i	0.146555	−	0.397408i
$621$	2.26143e10	−	2.26143e10i	0.152060	−	0.152060i
$622$	4.50294e10	+	2.05171e11i	0.300839	+	1.37074i
$623$			6.15822e9i			0.0408793i
$624$	6.59886e10	−	7.73020e10i	0.435242	−	0.509862i
$625$	1.78950e11			1.17277
$626$	2.07324e11	−	4.55020e10i	1.35006	−	0.296301i
$627$	−1.04779e10	−	1.04779e10i	−0.0677958	−	0.0677958i
$628$	8.33806e9	−	2.26100e10i	0.0536076	−	0.145366i
$629$	4.41863e10	+	4.41863e10i	0.282283	+	0.282283i
$630$	−1.83396e9	−	1.17383e9i	−0.0116420	−	0.00745149i
$631$	−9.79341e10			−0.617755			−0.308878	−	0.951102i	$-0.599953\pi$
$631$	−9.79341e10			−0.617755			−0.308878	+	0.951102i	$0.599953\pi$
$632$	6.61049e9	−	5.00597e9i	0.0414348	−	0.0313776i
$633$		−	1.41383e11i		−	0.880609i
$634$	1.08986e11	+	6.97566e10i	0.674547	+	0.431746i
$635$	1.95043e11	−	1.95043e11i	1.19960	−	1.19960i
$636$	6.98371e10	+	1.51438e11i	0.426833	+	0.925566i
$637$	−1.34991e11	+	1.34991e11i	−0.819876	+	0.819876i
$638$	1.31424e11	−	2.88439e10i	0.793216	−	0.174089i
$639$			3.11466e9i			0.0186813i
$640$	1.23259e11	+	1.38586e11i	0.734682	+	0.826034i
$641$	−2.26424e11			−1.34119			−0.670594	−	0.741824i	$-0.733961\pi$
$641$	−2.26424e11			−1.34119			−0.670594	+	0.741824i	$0.733961\pi$
$642$	4.45946e8	+	2.03190e9i	0.00262508	+	0.0119609i
$643$	1.19516e11	+	1.19516e11i	0.699171	+	0.699171i	0.964232	−	0.265061i	$-0.0853921\pi$
$643$	1.19516e11	+	1.19516e11i	0.699171	+	0.699171i	−0.265061	+	0.964232i	$0.585392\pi$
$644$	−6.54697e9	+	3.01919e9i	−0.0380625	+	0.0175528i
$645$	2.59886e10	+	2.59886e10i	0.150156	+	0.150156i
$646$	1.10710e10	−	1.72969e10i	0.0635705	−	0.0993206i
$647$	−1.63287e11			−0.931824			−0.465912	−	0.884831i	$-0.654274\pi$
$647$	−1.63287e11			−0.931824			−0.465912	+	0.884831i	$0.654274\pi$
$648$	1.18272e10	+	1.56181e10i	0.0670784	+	0.0885786i
$649$			6.36662e10i			0.358864i
$650$	−2.48150e10	+	3.87703e10i	−0.139015	+	0.217193i
$651$	−1.05385e9	+	1.05385e9i	−0.00586750	+	0.00586750i
$652$	−1.97218e11	−	7.27296e10i	−1.09133	−	0.402458i
$653$	−2.35840e8	+	2.35840e8i	−0.00129707	+	0.00129707i	−0.707755	−	0.706458i	$-0.750292\pi$
$653$	−2.35840e8	+	2.35840e8i	−0.00129707	+	0.00129707i	0.706458	+	0.707755i	$0.250292\pi$
$654$	−1.87032e9	−	8.52187e9i	−0.0102236	−	0.0465826i
$655$		−	2.22597e11i		−	1.20936i
$656$	−8.17270e10	−	6.97660e10i	−0.441317	−	0.376729i
$657$	−1.15396e10			−0.0619338
$658$	−1.12997e10	+	2.47997e9i	−0.0602785	+	0.0132295i
$659$	3.95446e10	+	3.95446e10i	0.209674	+	0.209674i	0.804129	−	0.594455i	$-0.202632\pi$
$659$	3.95446e10	+	3.95446e10i	0.209674	+	0.209674i	−0.594455	+	0.804129i	$0.702632\pi$
$660$	5.62328e10	+	2.07374e10i	0.296356	+	0.109289i
$661$	−1.65713e11	−	1.65713e11i	−0.868063	−	0.868063i	0.124195	−	0.992258i	$-0.460365\pi$
$661$	−1.65713e11	−	1.65713e11i	−0.868063	−	0.868063i	−0.992258	+	0.124195i	$0.960365\pi$
$662$	1.25261e11	+	8.01738e10i	0.652206	+	0.417446i
$663$	4.55197e10			0.235584
$664$	1.03445e10	−	7.48919e10i	0.0532151	−	0.385268i
$665$		−	2.72120e9i		−	0.0139147i
$666$	−6.27460e10	−	4.01608e10i	−0.318925	−	0.204129i
$667$	−2.56624e11	+	2.56624e11i	−1.29656	+	1.29656i
$668$	−2.97867e10	+	1.37364e10i	−0.149595	+	0.0689869i
$669$	8.53083e10	−	8.53083e10i	0.425880	−	0.425880i
$670$	−1.86140e11	+	4.08525e10i	−0.923718	+	0.202731i
$671$		−	5.20806e10i		−	0.256913i
$672$	−1.28335e9	−	4.22586e9i	−0.00629314	−	0.0207223i
$673$	−6.86891e10			−0.334833			−0.167416	−	0.985886i	$-0.553542\pi$
$673$	−6.86891e10			−0.334833			−0.167416	+	0.985886i	$0.553542\pi$
$674$	4.32628e9	+	1.97122e10i	0.0209641	+	0.0955201i
$675$	−6.27404e9	−	6.27404e9i	−0.0302226	−	0.0302226i
$676$	3.04491e10	+	6.60275e10i	0.145810	+	0.316182i
$677$	1.93104e11	+	1.93104e11i	0.919254	+	0.919254i	0.996975	−	0.0777208i	$-0.0247643\pi$
$677$	1.93104e11	+	1.93104e11i	0.919254	+	0.919254i	−0.0777208	+	0.996975i	$0.524764\pi$
$678$	1.87936e10	−	2.93625e10i	0.0889386	−	0.138955i
$679$	−3.63595e9			−0.0171056
$680$	−1.13655e10	+	8.22838e10i	−0.0531559	+	0.384839i
$681$		−	1.41453e11i		−	0.657695i
$682$	2.21147e10	−	3.45513e10i	0.102222	−	0.159708i
$683$	−7.46953e10	+	7.46953e10i	−0.343250	+	0.343250i	−0.857588	−	0.514338i	$-0.828038\pi$
$683$	−7.46953e10	+	7.46953e10i	−0.343250	+	0.343250i	0.514338	+	0.857588i	$0.328038\pi$
$684$	−8.47120e9	+	2.29711e10i	−0.0387009	+	0.104944i
$685$	−3.14492e11	+	3.14492e11i	−1.42839	+	1.42839i
$686$	3.55910e9	+	1.62166e10i	0.0160710	+	0.0732258i
$687$			2.02000e11i			0.906827i
$688$	5.86742e9	+	7.43143e10i	0.0261874	+	0.331679i
$689$	−4.61945e11			−2.04981
$690$	−1.57901e11	+	3.46549e10i	−0.696608	+	0.152886i
$691$	2.55829e11	+	2.55829e11i	1.12211	+	1.12211i	0.991423	+	0.130692i	$0.0417198\pi$
$691$	2.55829e11	+	2.55829e11i	1.12211	+	1.12211i	0.130692	+	0.991423i	$0.458280\pi$
$692$	−4.32579e10	+	1.17301e11i	−0.188643	+	0.511538i
$693$	−1.00917e9	−	1.00917e9i	−0.00437553	−	0.00437553i
$694$	−1.44148e11	−	9.22624e10i	−0.621399	−	0.397728i
$695$	4.93757e11			2.11628
$696$	−1.34214e11	−	1.77232e11i	−0.571953	−	0.755277i
$697$		−	4.81254e10i		−	0.203912i
$698$	−7.50970e10	−	4.80661e10i	−0.316374	−	0.202496i
$699$	5.53147e10	−	5.53147e10i	0.231703	−	0.231703i
$700$	8.37637e8	+	1.81638e9i	0.00348870	+	0.00756508i
$701$	1.94718e11	−	1.94718e11i	0.806368	−	0.806368i	−0.177715	−	0.984082i	$-0.556870\pi$
$701$	1.94718e11	−	1.94718e11i	0.806368	−	0.806368i	0.984082	+	0.177715i	$0.0568704\pi$
$702$	−5.30061e10	+	1.16334e10i	−0.218262	+	0.0479024i
$703$		−	9.31015e10i		−	0.381185i
$704$	5.94383e10	+	1.06041e11i	0.241978	+	0.431701i
$705$	−2.59400e11			−1.05006
$706$	−6.80162e10	−	3.09907e11i	−0.273775	−	1.24742i
$707$	1.03393e10	+	1.03393e10i	0.0413822	+	0.0413822i
$708$	9.55256e10	−	4.40525e10i	0.380178	−	0.175322i
$709$	1.70266e11	+	1.70266e11i	0.673819	+	0.673819i	0.958594	−	0.284775i	$-0.0919189\pi$
$709$	1.70266e11	+	1.70266e11i	0.673819	+	0.673819i	−0.284775	+	0.958594i	$0.591919\pi$
$710$	8.48734e9	−	1.32604e10i	0.0333994	−	0.0521822i
$711$	−4.42743e9			−0.0173250
$712$	−2.23275e11	+	1.69081e11i	−0.868799	+	0.657921i
$713$			1.10648e11i			0.428141i
$714$	1.06629e9	−	1.66594e9i	0.00410283	−	0.00641013i
$715$	−1.17394e11	+	1.17394e11i	−0.449182	+	0.449182i
$716$	−4.13783e11	−	1.52594e11i	−1.57442	−	0.580609i
$717$	−9.08972e9	+	9.08972e9i	−0.0343933	+	0.0343933i
$718$	−6.64273e10	−	3.02668e11i	−0.249948	−	1.13886i
$719$			8.01152e10i			0.299778i	0.988703	+	0.149889i	$0.0478916\pi$
$719$			8.01152e10i			0.299778i	−0.988703	+	0.149889i	$0.952108\pi$
$720$	−7.79445e9	−	9.87213e10i	−0.0290038	−	0.367351i
$721$	−1.94628e10			−0.0720219
$722$	2.35534e11	−	5.16932e10i	0.866771	−	0.190233i
$723$	1.68285e11	+	1.68285e11i	0.615873	+	0.615873i
$724$	−2.18138e11	−	8.04443e10i	−0.793921	−	0.292780i
$725$	7.11970e10	+	7.11970e10i	0.257697	+	0.257697i
$726$	−1.02005e11	−	6.52885e10i	−0.367176	−	0.235012i
$727$	6.97955e10			0.249856			0.124928	−	0.992166i	$-0.460130\pi$
$727$	6.97955e10			0.249856			0.124928	+	0.992166i	$0.460130\pi$
$728$	1.21186e10	+	1.67388e9i	0.0431445	+	0.00595934i
$729$		−	1.04604e10i		−	0.0370370i
$730$	4.91285e10	+	3.14448e10i	0.172998	+	0.110728i
$731$	−2.36077e10	+	2.36077e10i	−0.0826769	+	0.0826769i
$732$	−7.81424e10	+	3.60360e10i	−0.272171	+	0.125514i
$733$	2.60055e11	−	2.60055e11i	0.900842	−	0.900842i	−0.0946668	−	0.995509i	$-0.530179\pi$
$733$	2.60055e11	−	2.60055e11i	0.900842	−	0.900842i	0.995509	+	0.0946668i	$0.0301786\pi$
$734$	2.03318e11	−	4.46228e10i	0.700474	−	0.153735i
$735$			1.86007e11i			0.637352i
$736$	−2.89219e11	−	1.54474e11i	−0.985633	−	0.526435i
$737$	−1.24906e11			−0.423365
$738$	1.22993e10	+	5.60403e10i	0.0414625	+	0.188919i
$739$	3.65239e11	+	3.65239e11i	1.22461	+	1.22461i	0.965974	+	0.258640i	$0.0832744\pi$
$739$	3.65239e11	+	3.65239e11i	1.22461	+	1.22461i	0.258640	+	0.965974i	$0.416726\pi$
$740$	1.57698e11	+	3.41961e11i	0.525896	+	1.14038i
$741$	−4.79555e10	−	4.79555e10i	−0.159062	−	0.159062i
$742$	−1.08210e10	+	1.69064e10i	−0.0356986	+	0.0557745i
$743$	4.17057e11			1.36848			0.684242	−	0.729255i	$-0.260133\pi$
$743$	4.17057e11			1.36848			0.684242	+	0.729255i	$0.260133\pi$
$744$	−6.71431e10	−	9.27414e9i	−0.219134	−	0.0302679i
$745$		−	4.66855e11i		−	1.51550i
$746$	1.98959e11	−	3.10848e11i	0.642404	−	1.00367i
$747$	−2.85439e10	+	2.85439e10i	−0.0916707	+	0.0916707i
$748$	−1.88375e10	+	5.10811e10i	−0.0601753	+	0.163175i
$749$	−1.77054e8	+	1.77054e8i	−0.000562572	+	0.000562572i
$750$	−3.36767e10	−	1.53444e11i	−0.106435	−	0.484959i
$751$		−	4.31889e11i		−	1.35773i	−0.734265	−	0.678863i	$-0.762473\pi$
$751$		−	4.31889e11i		−	1.35773i	0.734265	−	0.678863i	$-0.237527\pi$
$752$	−4.00159e11	−	3.41594e11i	−1.25130	−	1.06817i
$753$	−2.84351e11			−0.884452
$754$	6.01506e11	−	1.32014e11i	1.86104	−	0.408446i
$755$	−6.72415e9	−	6.72415e9i	−0.0206943	−	0.0206943i
$756$	−8.15898e8	+	2.21244e9i	−0.00249775	+	0.00677306i
$757$	−2.10357e11	−	2.10357e11i	−0.640581	−	0.640581i	0.310118	−	0.950698i	$-0.399632\pi$
$757$	−2.10357e11	−	2.10357e11i	−0.640581	−	0.640581i	−0.950698	+	0.310118i	$0.899632\pi$
$758$	3.15988e11	+	2.02249e11i	0.957180	+	0.612646i
$759$	−1.05957e11			−0.319274
$760$	9.86606e10	−	7.47133e10i	0.295726	−	0.223946i
$761$			4.01538e11i			1.19726i	0.801026	+	0.598630i	$0.204288\pi$
$761$			4.01538e11i			1.19726i	−0.801026	+	0.598630i	$0.795712\pi$
$762$	−2.51593e11	−	1.61033e11i	−0.746241	−	0.477634i
$763$	7.42571e8	−	7.42571e8i	0.00219099	−	0.00219099i
$764$	1.63911e11	+	3.55434e11i	0.481101	+	1.04324i
$765$	3.13612e10	−	3.13612e10i	0.0915686	−	0.0915686i
$766$	−5.01509e11	+	1.10067e11i	−1.45668	+	0.319701i
$767$			2.91390e11i			0.841963i
$768$	1.17979e11	−	1.62555e11i	0.339124	−	0.467256i
$769$	4.37717e11			1.25166			0.625832	−	0.779958i	$-0.284760\pi$
$769$	4.37717e11			1.25166			0.625832	+	0.779958i	$0.284760\pi$
$770$	1.54649e9	+	7.04637e9i	0.00439929	+	0.0200448i
$771$	−1.04981e11	−	1.04981e11i	−0.297093	−	0.297093i
$772$	4.95811e11	−	2.28647e11i	1.39588	−	0.643720i
$773$	2.51017e11	+	2.51017e11i	0.703048	+	0.703048i	0.965064	−	0.262015i	$-0.0843872\pi$
$773$	2.51017e11	+	2.51017e11i	0.703048	+	0.703048i	−0.262015	+	0.965064i	$0.584387\pi$
$774$	2.14570e10	−	3.35237e10i	0.0597867	−	0.0934089i
$775$	3.06980e10			0.0850948
$776$	−9.98289e10	−	1.31826e11i	−0.275302	−	0.363542i
$777$		−	8.96700e9i		−	0.0246016i
$778$	3.03677e11	−	4.74456e11i	0.828884	−	1.29502i
$779$	−5.07006e10	+	5.07006e10i	−0.137678	+	0.137678i
$780$	2.57369e11	+	9.49116e10i	0.695308	+	0.256413i
$781$	7.29675e9	−	7.29675e9i	0.0196122	−	0.0196122i
$782$	−3.14801e10	−	1.43435e11i	−0.0841800	−	0.383556i
$783$			1.18703e11i			0.315801i
$784$	−2.44946e11	+	2.86940e11i	−0.648344	+	0.759499i
$785$	6.50401e10			0.171278
$786$	−2.35460e11	+	5.16770e10i	−0.616917	+	0.135396i
$787$	−1.05296e11	−	1.05296e11i	−0.274481	−	0.274481i	0.556420	−	0.830901i	$-0.312175\pi$
$787$	−1.05296e11	−	1.05296e11i	−0.274481	−	0.274481i	−0.830901	+	0.556420i	$0.812175\pi$
$788$	7.51190e10	+	2.77022e10i	0.194825	+	0.0718470i
$789$	2.20733e10	+	2.20733e10i	0.0569586	+	0.0569586i
$790$	1.88493e10	+	1.20646e10i	0.0483935	+	0.0309744i
$791$	4.19618e9			0.0107189
$792$	8.88095e9	−	6.42965e10i	0.0225714	−	0.163413i
$793$		−	2.38364e11i		−	0.602766i
$794$	6.48407e10	+	4.15015e10i	0.163142	+	0.104420i
$795$	−3.18261e11	+	3.18261e11i	−0.796737	+	0.796737i
$796$	−9.31431e10	+	4.29537e10i	−0.232006	+	0.106991i
$797$	−2.21289e11	+	2.21289e11i	−0.548437	+	0.548437i	−0.925988	−	0.377552i	$-0.876766\pi$
$797$	−2.21289e11	+	2.21289e11i	−0.548437	+	0.548437i	0.377552	+	0.925988i	$0.376766\pi$
$798$	−2.87844e9	+	6.31739e8i	−0.00709816	+	0.00155785i
$799$		−	2.35636e11i		−	0.578168i
$800$	−4.28569e10	+	8.02401e10i	−0.104631	+	0.195899i
$801$	1.49540e11			0.363268
$802$	6.85948e10	+	3.12544e11i	0.165804	+	0.755464i
$803$	2.70338e10	+	2.70338e10i	0.0650198	+	0.0650198i
$804$	8.64263e10	+	1.87411e11i	0.206834	+	0.448510i
$805$	−1.37590e10	−	1.37590e10i	−0.0327646	−	0.0327646i
$806$	1.01215e11	−	1.58136e11i	0.239831	−	0.374705i
$807$	3.35223e11			0.790386
$808$	−9.09887e10	+	6.58742e11i	−0.213473	+	1.54550i
$809$		−	2.71322e11i		−	0.633418i	−0.948523	−	0.316709i	$-0.897422\pi$
$809$		−	2.71322e11i		−	0.633418i	0.948523	−	0.316709i	$-0.102578\pi$
$810$	−2.85041e10	+	4.45339e10i	−0.0662166	+	0.103455i
$811$	−5.19492e11	+	5.19492e11i	−1.20087	+	1.20087i	−0.226966	+	0.973903i	$0.572881\pi$
$811$	−5.19492e11	+	5.19492e11i	−1.20087	+	1.20087i	−0.973903	+	0.226966i	$0.927119\pi$
$812$	9.25870e9	−	2.51065e10i	0.0212974	−	0.0577513i
$813$	2.80329e11	−	2.80329e11i	0.641662	−	0.641662i
$814$	5.29106e10	+	2.41081e11i	0.120516	+	0.549117i
$815$		−	5.67319e11i		−	1.28587i
$816$	8.96771e10	−	7.08038e9i	0.202265	−	0.0159697i
$817$	4.97420e10			0.111644
$818$	3.35103e11	−	7.35460e10i	0.748455	−	0.164265i
$819$	−4.61880e9	−	4.61880e9i	−0.0102658	−	0.0102658i
$820$	1.00345e11	−	2.72101e11i	0.221942	−	0.601831i
$821$	2.34066e11	+	2.34066e11i	0.515188	+	0.515188i	0.916111	−	0.400924i	$-0.131311\pi$
$821$	2.34066e11	+	2.34066e11i	0.515188	+	0.515188i	−0.400924	+	0.916111i	$0.631311\pi$
$822$	4.05676e11	+	2.59654e11i	0.888571	+	0.568733i
$823$	7.06265e11			1.53946			0.769730	−	0.638370i	$-0.220391\pi$
$823$	7.06265e11			1.53946			0.769730	+	0.638370i	$0.220391\pi$
$824$	−5.34372e11	−	7.05650e11i	−1.15914	−	1.53067i
$825$			2.93965e10i			0.0634571i
$826$	1.06644e10	+	6.82576e9i	0.0229095	+	0.0146633i
$827$	−2.43638e10	+	2.43638e10i	−0.0520861	+	0.0520861i	−0.732670	−	0.680584i	$-0.761726\pi$
$827$	−2.43638e10	+	2.43638e10i	−0.0520861	+	0.0520861i	0.680584	+	0.732670i	$0.261726\pi$
$828$	7.33149e10	+	1.58980e11i	0.155981	+	0.338237i
$829$	4.10887e10	−	4.10887e10i	0.0869971	−	0.0869971i	−0.662269	−	0.749266i	$-0.730406\pi$
$829$	4.10887e10	−	4.10887e10i	0.0869971	−	0.0869971i	0.749266	+	0.662269i	$0.230406\pi$
$830$	1.99304e11	−	4.37417e10i	0.419955	−	0.0921686i
$831$			3.95592e11i			0.829552i
$832$	2.72039e11	+	4.85333e11i	0.567726	+	1.01285i
$833$	−1.68966e11			−0.350929
$834$	−1.14628e11	−	5.22288e11i	−0.236933	−	1.07956i
$835$	−6.25993e10	−	6.25993e10i	−0.128773	−	0.128773i
$836$	7.36601e10	−	3.39690e10i	0.150802	−	0.0695436i
$837$	2.55905e10	+	2.55905e10i	0.0521407	+	0.0521407i
$838$	−4.46368e11	+	6.97391e11i	−0.905142	+	1.41417i
$839$	1.80976e11			0.365237			0.182618	−	0.983184i	$-0.441543\pi$
$839$	1.80976e11			0.365237			0.182618	+	0.983184i	$0.441543\pi$
$840$	9.50242e9	−	7.19596e9i	0.0190861	−	0.0144534i
$841$		−	8.46777e11i		−	1.69272i
$842$	2.98647e11	−	4.66597e11i	0.594169	−	0.928312i
$843$	4.33940e10	−	4.33940e10i	0.0859250	−	0.0859250i
$844$	7.26148e11	+	2.67787e11i	1.43105	+	0.527739i
$845$	−1.38762e11	+	1.38762e11i	−0.272173	+	0.272173i
$846$	6.02209e10	+	2.74389e11i	0.117562	+	0.535656i
$847$		−	1.45775e10i		−	0.0283236i
$848$	−9.10066e11	+	7.18534e10i	−1.75991	+	0.138952i
$849$	−1.93005e11			−0.371482
$850$	−3.97943e10	+	8.73375e9i	−0.0762333	+	0.0167311i
$851$	−4.70744e11	−	4.70744e11i	−0.897567	−	0.897567i
$852$	−1.59970e10	−	5.89932e9i	−0.0303585	−	0.0111955i
$853$	−4.07840e11	−	4.07840e11i	−0.770360	−	0.770360i	0.207809	−	0.978169i	$-0.433367\pi$
$853$	−4.07840e11	−	4.07840e11i	−0.770360	−	0.770360i	−0.978169	+	0.207809i	$0.933367\pi$
$854$	−8.72373e9	−	5.58365e9i	−0.0164010	−	0.0104975i
$855$	−6.60787e10			−0.123651
$856$	−1.12805e10	−	1.55812e9i	−0.0210104	−	0.00290206i
$857$			4.20387e11i			0.779338i	0.920955	+	0.389669i	$0.127411\pi$
$857$			4.20387e11i			0.779338i	−0.920955	+	0.389669i	$0.872589\pi$
$858$	1.51431e11	+	9.69242e10i	0.279426	+	0.178848i
$859$	1.48157e11	−	1.48157e11i	0.272113	−	0.272113i	−0.557838	−	0.829950i	$-0.688369\pi$
$859$	1.48157e11	−	1.48157e11i	0.272113	−	0.272113i	0.829950	+	0.557838i	$0.188369\pi$
$860$	−1.82702e11	+	8.42544e10i	−0.334002	+	0.154028i
$861$	−4.88319e9	+	4.88319e9i	−0.00888569	+	0.00888569i
$862$	−8.02108e11	+	1.76041e11i	−1.45279	+	0.318848i
$863$			2.01243e11i			0.362808i	0.983409	+	0.181404i	$0.0580642\pi$
$863$			2.01243e11i			0.362808i	−0.983409	+	0.181404i	$0.941936\pi$
$864$	−1.02616e11	+	3.11635e10i	−0.184146	+	0.0559230i
$865$	−3.37429e11			−0.602723
$866$	9.44460e10	+	4.30332e11i	0.167924	+	0.765124i
$867$	−2.02187e11	−	2.02187e11i	−0.357830	−	0.357830i
$868$	−3.41654e9	−	7.40861e9i	−0.00601878	−	0.0130514i
$869$	1.03722e10	+	1.03722e10i	0.0181882	+	0.0181882i
$870$	3.23460e11	−	5.05365e11i	0.564604	−	0.882121i
$871$	−5.71677e11			−0.993294
$872$	4.73110e10	+	6.53483e9i	0.0818269	+	0.0113023i
$873$			8.82917e10i			0.152007i
$874$	−1.17946e11	+	1.84275e11i	−0.202133	+	0.315806i
$875$	1.33707e10	−	1.33707e10i	0.0228098	−	0.0228098i
$876$	2.18565e10	−	5.92674e10i	0.0371162	−	0.100647i
$877$	−2.74279e10	+	2.74279e10i	−0.0463653	+	0.0463653i	−0.729909	−	0.683544i	$-0.760438\pi$
$877$	−2.74279e10	+	2.74279e10i	−0.0463653	+	0.0463653i	0.683544	+	0.729909i	$0.260438\pi$
$878$	4.80414e10	+	2.18895e11i	0.0808420	+	0.368347i
$879$			3.50776e10i			0.0587590i
$880$	−2.13015e11	+	2.49536e11i	−0.355206	+	0.416104i
$881$	−8.40964e11			−1.39596			−0.697981	−	0.716116i	$-0.745918\pi$
$881$	−8.40964e11			−1.39596			−0.697981	+	0.716116i	$0.745918\pi$
$882$	1.96755e11	−	4.31824e10i	0.325126	−	0.0713563i
$883$	4.12539e11	+	4.12539e11i	0.678612	+	0.678612i	0.959686	−	0.281074i	$-0.0906906\pi$
$883$	4.12539e11	+	4.12539e11i	0.678612	+	0.678612i	−0.281074	+	0.959686i	$0.590691\pi$
$884$	−8.62164e10	+	2.33790e11i	−0.141183	+	0.382840i
$885$	2.00755e11	+	2.00755e11i	0.327261	+	0.327261i
$886$	1.24902e11	+	7.99437e10i	0.202690	+	0.129733i
$887$	−8.97425e11			−1.44979			−0.724893	−	0.688862i	$-0.758111\pi$
$887$	−8.97425e11			−1.44979			−0.724893	+	0.688862i	$0.758111\pi$
$888$	3.25111e11	−	2.46199e11i	0.522853	−	0.395944i
$889$		−	3.59551e10i		−	0.0575643i
$890$	−6.36651e11	−	4.07491e11i	−1.01471	−	0.649468i
$891$	−2.45056e10	+	2.45056e10i	−0.0388825	+	0.0388825i
$892$	2.76568e11	+	5.99724e11i	0.436860	+	0.947309i
$893$	−2.48245e11	+	2.48245e11i	−0.390368	+	0.390368i
$894$	−4.93832e11	+	1.08383e11i	−0.773089	+	0.169672i
$895$		−	1.19029e12i		−	1.85507i
$896$	2.41348e10	+	1.41268e9i	0.0374466	+	0.00219185i
$897$	−4.84950e11			−0.749078
$898$	6.27480e10	+	2.85903e11i	0.0964927	+	0.439657i
$899$	−2.90398e11	−	2.90398e11i	−0.444585	−	0.444585i
$900$	4.41070e10	−	2.03403e10i	0.0672260	−	0.0310018i
$901$	−2.89104e11	−	2.89104e11i	−0.438687	−	0.438687i
$902$	1.02472e11	−	1.60100e11i	0.154804	−	0.241860i
$903$	4.79086e9			0.00720547
$904$	1.15211e11	+	1.52138e11i	0.172512	+	0.227806i
$905$		−	6.27497e11i		−	0.935443i
$906$	−5.55166e9	+	8.67375e9i	−0.00823968	+	0.0128734i
$907$	1.31811e11	−	1.31811e11i	0.194770	−	0.194770i	−0.602984	−	0.797753i	$-0.706022\pi$
$907$	1.31811e11	−	1.31811e11i	0.194770	−	0.194770i	0.797753	+	0.602984i	$0.206022\pi$
$908$	7.26508e11	+	2.67919e11i	1.06880	+	0.394149i
$909$	2.51069e11	−	2.51069e11i	0.367737	−	0.367737i
$910$	7.07802e9	+	3.22501e10i	0.0103216	+	0.0470290i
$911$		−	1.25641e12i		−	1.82413i	−0.410043	−	0.912066i	$-0.634486\pi$
$911$		−	1.25641e12i		−	1.82413i	0.410043	−	0.912066i	$-0.365514\pi$
$912$	−1.01935e11	−	8.70166e10i	−0.147348	−	0.125783i
$913$	1.33740e11			0.192477
$914$	−1.03484e12	+	2.27120e11i	−1.48282	+	0.325439i
$915$	−1.64223e11	−	1.64223e11i	−0.234288	−	0.234288i
$916$	−1.03748e12	−	3.82598e11i	−1.47366	−	0.543451i
$917$	−2.05173e10	−	2.05173e10i	−0.0290164	−	0.0290164i
$918$	−4.04540e10	−	2.58927e10i	−0.0569627	−	0.0364592i
$919$	8.02552e11			1.12515			0.562576	−	0.826746i	$-0.309810\pi$
$919$	8.02552e11			1.12515			0.562576	+	0.826746i	$0.309810\pi$
$920$	1.21083e11	−	8.76621e11i	0.169018	−	1.22366i
$921$			4.82848e11i			0.671077i
$922$	5.81175e11	+	3.71983e11i	0.804235	+	0.514753i
$923$	3.33961e10	−	3.33961e10i	0.0460139	−	0.0460139i
$924$	7.09452e9	−	3.27170e9i	0.00973274	−	0.00448834i
$925$	−1.30602e11	+	1.30602e11i	−0.178395	+	0.178395i
$926$	4.28764e11	−	9.41020e10i	0.583142	−	0.127984i
$927$			4.72615e11i			0.640012i
$928$	1.16448e12	−	3.53639e11i	1.57014	−	0.476835i
$929$	4.13334e11			0.554930			0.277465	−	0.960736i	$-0.410506\pi$
$929$	4.13334e11			0.554930			0.277465	+	0.960736i	$0.410506\pi$
$930$	−3.92158e10	−	1.78682e11i	−0.0524239	−	0.238863i
$931$	1.78008e11	+	1.78008e11i	0.236941	+	0.236941i
$932$	1.79329e11	+	3.88866e11i	0.237677	+	0.515391i
$933$	4.34131e11	+	4.34131e11i	0.572920	+	0.572920i
$934$	−8.16617e11	+	1.27586e12i	−1.07308	+	1.67654i
$935$	−1.46940e11			−0.192262
$936$	4.06467e10	−	2.94275e11i	0.0529568	−	0.383398i
$937$			7.32903e11i			0.950798i	0.879770	+	0.475399i	$0.157696\pi$
$937$			7.32903e11i			0.950798i	−0.879770	+	0.475399i	$0.842304\pi$
$938$	−1.33914e10	+	2.09224e10i	−0.0172988	+	0.0270271i
$939$	4.38687e11	−	4.38687e11i	0.564277	−	0.564277i
$940$	4.91316e11	−	1.33228e12i	0.629288	−	1.70642i
$941$	1.30100e11	−	1.30100e11i	0.165927	−	0.165927i	−0.619259	−	0.785187i	$-0.712567\pi$
$941$	1.30100e11	−	1.30100e11i	0.165927	−	0.165927i	0.785187	+	0.619259i	$0.212567\pi$
$942$	−1.50994e10	−	6.87984e10i	−0.0191759	−	0.0873725i
$943$			5.12709e11i			0.648372i
$944$	4.53243e10	+	5.74060e11i	0.0570747	+	0.722885i
$945$	−6.36432e9			−0.00798040
$946$	−1.28804e11	+	2.82689e10i	−0.160829	+	0.0352975i
$947$	4.03947e11	+	4.03947e11i	0.502255	+	0.502255i	0.912138	−	0.409883i	$-0.134431\pi$
$947$	4.03947e11	+	4.03947e11i	0.502255	+	0.502255i	−0.409883	+	0.912138i	$0.634431\pi$
$948$	8.38576e9	−	2.27394e10i	0.0103827	−	0.0281543i
$949$	1.23729e11	+	1.23729e11i	0.152549	+	0.152549i
$950$	5.11248e10	+	3.27226e10i	0.0627679	+	0.0401748i
$951$	3.78209e11			0.462392
$952$	6.53671e9	+	8.63188e9i	0.00795814	+	0.0105089i
$953$			5.94277e10i			0.0720473i	0.999351	+	0.0360236i	$0.0114692\pi$
$953$			5.94277e10i			0.0720473i	−0.999351	+	0.0360236i	$0.988531\pi$
$954$	4.10537e11	+	2.62766e11i	0.495632	+	0.317231i
$955$	−7.46976e11	+	7.46976e11i	−0.898035	+	0.898035i
$956$	−2.94687e10	−	6.39014e10i	−0.0352800	−	0.0765031i
$957$	2.78086e11	−	2.78086e11i	0.331537	−	0.331537i
$958$	−7.38455e11	+	1.62071e11i	−0.876722	+	0.192416i
$959$			5.79750e10i			0.0685435i
$960$	5.21798e11	+	1.46950e11i	0.614352	+	0.173016i
$961$	7.27680e11			0.853193
$962$	2.42163e11	+	1.10339e12i	0.282754	+	1.28833i
$963$	4.29939e9	+	4.29939e9i	0.00499922	+	0.00499922i
$964$	−1.18305e12	+	5.45575e11i	−1.36992	+	0.631751i
$965$	1.04199e12	+	1.04199e12i	1.20158	+	1.20158i
$966$	−1.13599e10	+	1.77483e10i	−0.0130456	+	0.0203821i
$967$	−9.25697e11			−1.05868			−0.529338	−	0.848411i	$-0.677560\pi$
$967$	−9.25697e11			−1.05868			−0.529338	+	0.848411i	$0.677560\pi$
$968$	5.28526e11	−	4.00240e11i	0.601956	−	0.455847i
$969$		−	6.00250e10i		−	0.0680828i
$970$	2.40591e11	−	3.75893e11i	0.271765	−	0.424597i
$971$	−2.08652e9	+	2.08652e9i	−0.00234718	+	0.00234718i	−0.708279	−	0.705932i	$-0.750528\pi$
$971$	−2.08652e9	+	2.08652e9i	−0.00234718	+	0.00234718i	0.705932	+	0.708279i	$0.250528\pi$
$972$	5.37246e10	+	1.98124e10i	0.0601878	+	0.0221959i
$973$	4.55107e10	−	4.55107e10i	0.0507764	−	0.0507764i
$974$	−1.01546e11	−	4.62683e11i	−0.112831	−	0.514101i
$975$			1.34543e11i			0.148882i
$976$	−3.70765e10	−	4.69595e11i	−0.0408601	−	0.517517i
$977$	−4.13901e11			−0.454275			−0.227137	−	0.973863i	$-0.572937\pi$
$977$	−4.13901e11			−0.454275			−0.227137	+	0.973863i	$0.572937\pi$
$978$	−6.00101e11	+	1.31706e11i	−0.655948	+	0.143963i
$979$	−3.50329e11	−	3.50329e11i	−0.381368	−	0.381368i
$980$	−9.55335e11	−	3.52306e11i	−1.03574	−	0.381958i
$981$	−1.80318e10	−	1.80318e10i	−0.0194699	−	0.0194699i
$982$	7.47635e11	+	4.78526e11i	0.803978	+	0.514588i
$983$	−1.23122e12			−1.31863			−0.659315	−	0.751867i	$-0.729154\pi$
$983$	−1.23122e12			−1.31863			−0.659315	+	0.751867i	$0.729154\pi$
$984$	−3.11120e11	−	4.29734e10i	−0.331854	−	0.0458374i
$985$			2.16088e11i			0.229554i
$986$	4.59067e11	+	2.93827e11i	0.485700	+	0.310874i
$987$	−2.39095e10	+	2.39095e10i	−0.0251943	+	0.0251943i
$988$	3.37131e11	−	1.55471e11i	0.353810	−	0.163163i
$989$	2.51508e11	−	2.51508e11i	0.262885	−	0.262885i
$990$	1.71107e11	−	3.75532e10i	0.178126	−	0.0390937i
$991$		−	1.64300e12i		−	1.70350i	−0.523949	−	0.851750i	$-0.675542\pi$
$991$		−	1.64300e12i		−	1.70350i	0.523949	−	0.851750i	$-0.324458\pi$
$992$	1.74804e11	−	3.27283e11i	0.180512	−	0.337969i
$993$	4.34690e11			0.447077
$994$	−4.39941e8	−	2.00454e9i	−0.000450660	−	0.00205338i
$995$	−1.95748e11	−	1.95748e11i	−0.199713	−	0.199713i
$996$	−9.25385e10	−	2.00665e11i	−0.0940341	−	0.203908i
$997$	9.87695e11	+	9.87695e11i	0.999637	+	0.999637i	1.00000		0.000363043i	$-0.000115560\pi$
$997$	9.87695e11	+	9.87695e11i	0.999637	+	0.999637i	−0.000363043		1.00000i	$0.500116\pi$
$998$	−2.51635e11	+	3.93146e11i	−0.253658	+	0.396307i
$999$	−2.17745e11			−0.218619

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.9.l.a.43.19	yes	64
4.3	odd	2		192.9.l.a.79.4		64
16.3	odd	4	inner	48.9.l.a.19.19	✓	64
16.13	even	4		192.9.l.a.175.4		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.9.l.a.19.19	✓	64	16.3	odd	4	inner
48.9.l.a.43.19	yes	64	1.1	even	1	trivial
192.9.l.a.79.4		64	4.3	odd	2
192.9.l.a.175.4		64	16.13	even	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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	48.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.42993 + 15.6280i) q^{2} +(33.0681 + 33.0681i) q^{3} +(-232.471 + 107.206i) q^{4} +(-488.559 - 488.559i) q^{5} +(-403.369 + 630.211i) q^{6} -90.0632 q^{7} +(-2472.78 - 3265.36i) q^{8} +2187.00i q^{9} +O(q^{10})\)	\(q+(3.42993 + 15.6280i) q^{2} +(33.0681 + 33.0681i) q^{3} +(-232.471 + 107.206i) q^{4} +(-488.559 - 488.559i) q^{5} +(-403.369 + 630.211i) q^{6} -90.0632 q^{7} +(-2472.78 - 3265.36i) q^{8} +2187.00i q^{9} +(5959.49 - 9310.93i) q^{10} +(5123.51 - 5123.51i) q^{11} +(-11232.5 - 4142.28i) q^{12} +(23449.5 - 23449.5i) q^{13} +(-308.910 - 1407.51i) q^{14} -32311.4i q^{15} +(42549.7 - 49844.6i) q^{16} +29351.3 q^{17} +(-34178.5 + 7501.25i) q^{18} +(-30921.9 - 30921.9i) q^{19} +(165952. + 61199.4i) q^{20} +(-2978.22 - 2978.22i) q^{21} +(97643.6 + 62497.1i) q^{22} -312697. q^{23} +(26209.2 - 189749. i) q^{24} +86753.9i q^{25} +(446899. + 286039. i) q^{26} +(-72320.0 + 72320.0i) q^{27} +(20937.1 - 9655.32i) q^{28} +(820677. - 820677. i) q^{29} +(504964. - 110826. i) q^{30} -353851. i q^{31} +(924916. + 494005. i) q^{32} +338849. q^{33} +(100673. + 458703. i) q^{34} +(44001.1 + 44001.1i) q^{35} +(-234460. - 508415. i) q^{36} +(1.50543e6 + 1.50543e6i) q^{37} +(377189. - 589308. i) q^{38} +1.55086e6 q^{39} +(-387222. + 2.80342e6i) q^{40} -1.63963e6i q^{41} +(36328.6 - 56758.8i) q^{42} +(-804316. + 804316. i) q^{43} +(-641797. + 1.74034e6i) q^{44} +(1.06848e6 - 1.06848e6i) q^{45} +(-1.07253e6 - 4.88685e6i) q^{46} -8.02812e6i q^{47} +(3.05531e6 - 241229. i) q^{48} -5.75669e6 q^{49} +(-1.35579e6 + 297560. i) q^{50} +(970591. + 970591. i) q^{51} +(-2.93740e6 + 7.96525e6i) q^{52} +(-9.84980e6 - 9.84980e6i) q^{53} +(-1.37827e6 - 882167. i) q^{54} -5.00627e6 q^{55} +(222706. + 294089. i) q^{56} -2.04506e6i q^{57} +(1.56404e7 + 1.00107e7i) q^{58} +(-6.21314e6 + 6.21314e6i) q^{59} +(3.46398e6 + 7.51147e6i) q^{60} +(5.08251e6 - 5.08251e6i) q^{61} +(5.53000e6 - 1.21368e6i) q^{62} -196968. i q^{63} +(-4.54794e6 + 1.61490e7i) q^{64} -2.29129e7 q^{65} +(1.16223e6 + 5.29555e6i) q^{66} +(-1.21895e7 - 1.21895e7i) q^{67} +(-6.82332e6 + 3.14663e6i) q^{68} +(-1.03403e7 - 1.03403e7i) q^{69} +(-536731. + 838572. i) q^{70} +1.42417e6 q^{71} +(7.14134e6 - 5.40797e6i) q^{72} +5.27643e6i q^{73} +(-1.83634e7 + 2.86904e7i) q^{74} +(-2.86879e6 + 2.86879e6i) q^{75} +(1.05035e7 + 3.87344e6i) q^{76} +(-461439. + 461439. i) q^{77} +(5.31933e6 + 2.42369e7i) q^{78} +2.02443e6i q^{79} +(-4.51401e7 + 3.56399e6i) q^{80} -4.78297e6 q^{81} +(2.56243e7 - 5.62383e6i) q^{82} +(1.30516e7 + 1.30516e7i) q^{83} +(1.01163e6 + 373067. i) q^{84} +(-1.43398e7 - 1.43398e7i) q^{85} +(-1.53286e7 - 9.81114e6i) q^{86} +5.42765e7 q^{87} +(-2.93994e7 - 4.06079e6i) q^{88} -6.83767e7i q^{89} +(2.03630e7 + 1.30334e7i) q^{90} +(-2.11193e6 + 2.11193e6i) q^{91} +(7.26931e7 - 3.35230e7i) q^{92} +(1.17012e7 - 1.17012e7i) q^{93} +(1.25464e8 - 2.75359e7i) q^{94} +3.02143e7i q^{95} +(1.42494e7 + 4.69211e7i) q^{96} +4.03711e7 q^{97} +(-1.97450e7 - 8.99658e7i) q^{98} +(1.12051e7 + 1.12051e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 372 q^{4} + 17460 q^{8}+O(q^{10}) \) 64 * q - 372 * q^4 + 17460 * q^8	\( 64 q - 372 q^{4} + 17460 q^{8} - 13784 q^{10} + 39552 q^{11} - 22680 q^{12} + 116772 q^{14} - 161824 q^{16} - 26244 q^{18} - 167552 q^{19} + 690000 q^{20} - 1252768 q^{22} + 1691136 q^{23} - 74844 q^{24} - 1682100 q^{26} + 678600 q^{28} - 2132352 q^{29} - 2054808 q^{30} + 1407840 q^{32} - 3704544 q^{34} - 2415744 q^{35} - 1041012 q^{36} - 4720512 q^{37} + 2413320 q^{38} - 3544848 q^{40} + 9436500 q^{42} - 7244672 q^{43} - 3982056 q^{44} + 11165992 q^{46} - 9467280 q^{48} + 52706752 q^{49} + 17072676 q^{50} + 13862016 q^{51} - 22890864 q^{52} - 5358720 q^{53} - 4960116 q^{54} - 46326784 q^{55} - 9637152 q^{56} + 25732944 q^{58} + 44938752 q^{59} + 40927032 q^{60} + 24476032 q^{61} - 17024868 q^{62} - 116303448 q^{64} + 29941632 q^{65} - 56828952 q^{66} - 44244736 q^{67} - 12614400 q^{68} - 8636544 q^{69} - 60922560 q^{70} + 159664128 q^{71} - 18502020 q^{72} + 140654028 q^{74} + 12918528 q^{75} + 204842760 q^{76} - 94964352 q^{77} + 14001660 q^{78} + 38076648 q^{80} - 306110016 q^{81} - 260917000 q^{82} + 209328000 q^{83} - 127862712 q^{84} + 106960000 q^{85} - 123451824 q^{86} + 104240736 q^{88} + 53520264 q^{90} - 45401472 q^{91} + 351567216 q^{92} + 208488216 q^{94} + 49597920 q^{96} - 681890712 q^{98} + 86500224 q^{99}+O(q^{100}) \) 64 * q - 372 * q^4 + 17460 * q^8 - 13784 * q^10 + 39552 * q^11 - 22680 * q^12 + 116772 * q^14 - 161824 * q^16 - 26244 * q^18 - 167552 * q^19 + 690000 * q^20 - 1252768 * q^22 + 1691136 * q^23 - 74844 * q^24 - 1682100 * q^26 + 678600 * q^28 - 2132352 * q^29 - 2054808 * q^30 + 1407840 * q^32 - 3704544 * q^34 - 2415744 * q^35 - 1041012 * q^36 - 4720512 * q^37 + 2413320 * q^38 - 3544848 * q^40 + 9436500 * q^42 - 7244672 * q^43 - 3982056 * q^44 + 11165992 * q^46 - 9467280 * q^48 + 52706752 * q^49 + 17072676 * q^50 + 13862016 * q^51 - 22890864 * q^52 - 5358720 * q^53 - 4960116 * q^54 - 46326784 * q^55 - 9637152 * q^56 + 25732944 * q^58 + 44938752 * q^59 + 40927032 * q^60 + 24476032 * q^61 - 17024868 * q^62 - 116303448 * q^64 + 29941632 * q^65 - 56828952 * q^66 - 44244736 * q^67 - 12614400 * q^68 - 8636544 * q^69 - 60922560 * q^70 + 159664128 * q^71 - 18502020 * q^72 + 140654028 * q^74 + 12918528 * q^75 + 204842760 * q^76 - 94964352 * q^77 + 14001660 * q^78 + 38076648 * q^80 - 306110016 * q^81 - 260917000 * q^82 + 209328000 * q^83 - 127862712 * q^84 + 106960000 * q^85 - 123451824 * q^86 + 104240736 * q^88 + 53520264 * q^90 - 45401472 * q^91 + 351567216 * q^92 + 208488216 * q^94 + 49597920 * q^96 - 681890712 * q^98 + 86500224 * q^99

Introduction

L-functions

Modular forms

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