LMFDB - Embedded newform 14.11.d.a.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,11,Mod(3,14)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(14, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("14.3");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	14.d (of order $6$, 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:	$8.89500153743$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 7168 x^{10} - 191104 x^{9} + 39872585 x^{8} - 837614684 x^{7} + 83400850488 x^{6} + \cdots + 16\!\cdots\!56 $ x^12 + 7168x^10 - 191104x^9 + 39872585x^8 - 837614684x^7 + 83400850488x^6 - 1089499860800x^5 + 117569881085905x^4 - 972128975671236x^3 + 70590565447335180x^2 + 627290085157877232x + 16876036055394640656
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{24}\cdot 3^{4}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			3.1
Root			$18.8254 + 32.6066i$ of defining polynomial
Character	$\chi$	$=$	14.3
Dual form			14.11.d.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11.3137 - 19.5959i) q^{2} +(-304.740 - 175.942i) q^{3} +(-256.000 + 443.405i) q^{4} +(-3227.42 + 1863.35i) q^{5} +7962.22i q^{6} +(4145.11 - 16287.8i) q^{7} +11585.2 q^{8} +(32386.5 + 56095.1i) q^{9} +O(q^{10})$	\(q+(-11.3137 - 19.5959i) q^{2} +(-304.740 - 175.942i) q^{3} +(-256.000 + 443.405i) q^{4} +(-3227.42 + 1863.35i) q^{5} +7962.22i q^{6} +(4145.11 - 16287.8i) q^{7} +11585.2 q^{8} +(32386.5 + 56095.1i) q^{9} +(73028.2 + 42162.9i) q^{10} +(62430.6 - 108133. i) q^{11} +(156027. - 90082.2i) q^{12} +353762. i q^{13} +(-366071. + 103048. i) q^{14} +1.31137e6 q^{15} +(-131072. - 227023. i) q^{16} +(1.67588e6 + 967569. i) q^{17} +(732824. - 1.26929e6i) q^{18} +(-2.53946e6 + 1.46616e6i) q^{19} -1.90807e6i q^{20} +(-4.12889e6 + 4.23426e6i) q^{21} -2.82529e6 q^{22} +(-2.94410e6 - 5.09934e6i) q^{23} +(-3.53049e6 - 2.03833e6i) q^{24} +(2.06135e6 - 3.57037e6i) q^{25} +(6.93230e6 - 4.00236e6i) q^{26} -2.01421e6i q^{27} +(6.16096e6 + 6.00765e6i) q^{28} -2.02170e7 q^{29} +(-1.48364e7 - 2.56974e7i) q^{30} +(4.61441e7 + 2.66413e7i) q^{31} +(-2.96582e6 + 5.13695e6i) q^{32} +(-3.80502e7 + 2.19683e7i) q^{33} -4.37872e7i q^{34} +(1.69719e7 + 6.02915e7i) q^{35} -3.31638e7 q^{36} +(2.79458e7 + 4.84035e7i) q^{37} +(5.74614e7 + 3.31753e7i) q^{38} +(6.22416e7 - 1.07806e8i) q^{39} +(-3.73904e7 + 2.15874e7i) q^{40} -8.80023e7i q^{41} +(1.29687e8 + 3.30043e7i) q^{42} +2.63848e8 q^{43} +(3.19645e7 + 5.53641e7i) q^{44} +(-2.09050e8 - 1.20695e8i) q^{45} +(-6.66175e7 + 1.15385e8i) q^{46} +(-2.26047e8 + 1.30508e8i) q^{47} +9.22442e7i q^{48} +(-2.48111e8 - 1.35030e8i) q^{49} -9.32862e7 q^{50} +(-3.40472e8 - 5.89714e8i) q^{51} +(-1.56860e8 - 9.05632e7i) q^{52} +(-1.02485e8 + 1.77509e8i) q^{53} +(-3.94702e7 + 2.27882e7i) q^{54} +4.65321e8i q^{55} +(4.80221e7 - 1.88698e8i) q^{56} +1.03183e9 q^{57} +(2.28730e8 + 3.96171e8i) q^{58} +(-3.01275e8 - 1.73941e8i) q^{59} +(-3.35710e8 + 5.81466e8i) q^{60} +(2.29803e8 - 1.32677e8i) q^{61} -1.20565e9i q^{62} +(1.04791e9 - 2.94986e8i) q^{63} +1.34218e8 q^{64} +(-6.59184e8 - 1.14174e9i) q^{65} +(8.60979e8 + 4.97086e8i) q^{66} +(-8.34938e8 + 1.44615e9i) q^{67} +(-8.58050e8 + 4.95396e8i) q^{68} +2.07196e9i q^{69} +(9.89451e8 - 1.01470e9i) q^{70} +1.04860e9 q^{71} +(3.75206e8 + 6.49875e8i) q^{72} +(2.09399e9 + 1.20896e9i) q^{73} +(6.32341e8 - 1.09525e9i) q^{74} +(-1.25635e9 + 7.25357e8i) q^{75} -1.50134e9i q^{76} +(-1.50247e9 - 1.46508e9i) q^{77} -2.81673e9 q^{78} +(-1.34296e8 - 2.32607e8i) q^{79} +(8.46049e8 + 4.88467e8i) q^{80} +(1.55801e9 - 2.69855e9i) q^{81} +(-1.72448e9 + 9.95632e8i) q^{82} +2.25464e9i q^{83} +(-8.20494e8 - 2.91474e9i) q^{84} -7.21169e9 q^{85} +(-2.98510e9 - 5.17035e9i) q^{86} +(6.16094e9 + 3.55702e9i) q^{87} +(7.23274e8 - 1.25275e9i) q^{88} +(-6.78021e9 + 3.91456e9i) q^{89} +5.46204e9i q^{90} +(5.76202e9 + 1.46638e9i) q^{91} +3.01476e9 q^{92} +(-9.37464e9 - 1.62374e10i) q^{93} +(5.11485e9 + 2.95306e9i) q^{94} +(5.46393e9 - 9.46381e9i) q^{95} +(1.80761e9 - 1.04362e9i) q^{96} +1.20222e10i q^{97} +(1.61028e8 + 6.38966e9i) q^{98} +8.08765e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 486 q^{3} - 3072 q^{4} - 6666 q^{5} + 30576 q^{7} - 45528 q^{9}+O(q^{10}) $ 12 * q + 486 * q^3 - 3072 * q^4 - 6666 * q^5 + 30576 * q^7 - 45528 * q^9	\( 12 q + 486 q^{3} - 3072 q^{4} - 6666 q^{5} + 30576 q^{7} - 45528 q^{9} + 130944 q^{10} - 111210 q^{11} - 248832 q^{12} - 38976 q^{14} + 1065684 q^{15} - 1572864 q^{16} + 1439502 q^{17} + 715392 q^{18} - 452814 q^{19} - 2940462 q^{21} - 1922688 q^{22} + 853074 q^{23} - 9338880 q^{24} + 16905804 q^{25} - 8671872 q^{26} + 4064256 q^{28} + 60157248 q^{29} - 37409472 q^{30} + 87231186 q^{31} - 303597198 q^{33} + 153795138 q^{35} + 46620672 q^{36} - 7666506 q^{37} - 21703872 q^{38} - 71628084 q^{39} - 67043328 q^{40} + 129553536 q^{42} + 1066803336 q^{43} - 56939520 q^{44} - 948611736 q^{45} - 168245184 q^{46} - 985909398 q^{47} + 456183924 q^{49} + 1764094464 q^{50} - 319431390 q^{51} - 538871808 q^{52} - 600022554 q^{53} - 402417216 q^{54} - 243597312 q^{56} + 3357095652 q^{57} - 294598272 q^{58} - 2101762050 q^{59} - 272815104 q^{60} - 2201391150 q^{61} + 2691345552 q^{63} + 1610612736 q^{64} + 1536128076 q^{65} + 728780544 q^{66} - 1590058326 q^{67} - 737025024 q^{68} - 3745457856 q^{70} - 7739561160 q^{71} + 366280704 q^{72} + 2008593834 q^{73} + 1042308096 q^{74} + 12301086492 q^{75} + 464655282 q^{77} - 8450806272 q^{78} + 2310562242 q^{79} + 1747451904 q^{80} + 7562341422 q^{81} + 9636272256 q^{82} - 7405267968 q^{84} - 39581743596 q^{85} - 4924086912 q^{86} + 24592790952 q^{87} + 492208128 q^{88} + 2541648690 q^{89} - 4866473640 q^{91} - 873547776 q^{92} - 7836264270 q^{93} + 28852652352 q^{94} + 29024266590 q^{95} + 4781506560 q^{96} - 11553118080 q^{98} - 13213951200 q^{99}+O(q^{100}) \) 12 * q + 486 * q^3 - 3072 * q^4 - 6666 * q^5 + 30576 * q^7 - 45528 * q^9 + 130944 * q^10 - 111210 * q^11 - 248832 * q^12 - 38976 * q^14 + 1065684 * q^15 - 1572864 * q^16 + 1439502 * q^17 + 715392 * q^18 - 452814 * q^19 - 2940462 * q^21 - 1922688 * q^22 + 853074 * q^23 - 9338880 * q^24 + 16905804 * q^25 - 8671872 * q^26 + 4064256 * q^28 + 60157248 * q^29 - 37409472 * q^30 + 87231186 * q^31 - 303597198 * q^33 + 153795138 * q^35 + 46620672 * q^36 - 7666506 * q^37 - 21703872 * q^38 - 71628084 * q^39 - 67043328 * q^40 + 129553536 * q^42 + 1066803336 * q^43 - 56939520 * q^44 - 948611736 * q^45 - 168245184 * q^46 - 985909398 * q^47 + 456183924 * q^49 + 1764094464 * q^50 - 319431390 * q^51 - 538871808 * q^52 - 600022554 * q^53 - 402417216 * q^54 - 243597312 * q^56 + 3357095652 * q^57 - 294598272 * q^58 - 2101762050 * q^59 - 272815104 * q^60 - 2201391150 * q^61 + 2691345552 * q^63 + 1610612736 * q^64 + 1536128076 * q^65 + 728780544 * q^66 - 1590058326 * q^67 - 737025024 * q^68 - 3745457856 * q^70 - 7739561160 * q^71 + 366280704 * q^72 + 2008593834 * q^73 + 1042308096 * q^74 + 12301086492 * q^75 + 464655282 * q^77 - 8450806272 * q^78 + 2310562242 * q^79 + 1747451904 * q^80 + 7562341422 * q^81 + 9636272256 * q^82 - 7405267968 * q^84 - 39581743596 * q^85 - 4924086912 * q^86 + 24592790952 * q^87 + 492208128 * q^88 + 2541648690 * q^89 - 4866473640 * q^91 - 873547776 * q^92 - 7836264270 * q^93 + 28852652352 * q^94 + 29024266590 * q^95 + 4781506560 * q^96 - 11553118080 * q^98 - 13213951200 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−11.3137	−	19.5959i	−0.353553	−	0.612372i
$2$	−11.3137	−	19.5959i	−0.353553	−	0.612372i
$3$	−304.740	−	175.942i	−1.25407	−	0.724040i	−0.282159	−	0.959368i	$-0.591050\pi$
$3$	−304.740	−	175.942i	−1.25407	−	0.724040i	−0.971916	+	0.235327i	$0.924384\pi$
$4$	−256.000	+	443.405i	−0.250000	+	0.433013i
$5$	−3227.42	+	1863.35i	−1.03277	+	0.596273i	−0.917778	−	0.397093i	$-0.870019\pi$
$5$	−3227.42	+	1863.35i	−1.03277	+	0.596273i	−0.114997	+	0.993366i	$0.536686\pi$
$6$			7962.22i			1.02395i
$7$	4145.11	−	16287.8i	0.246630	−	0.969110i
$7$	4145.11	−	16287.8i	0.246630	−	0.969110i
$8$	11585.2			0.353553
$9$	32386.5	+	56095.1i	0.548469	+	0.949976i
$10$	73028.2	+	42162.9i	0.730282	+	0.421629i
$11$	62430.6	−	108133.i	0.387645	−	0.671421i	−0.604487	−	0.796615i	$-0.706622\pi$
$11$	62430.6	−	108133.i	0.387645	−	0.671421i	0.992132	+	0.125194i	$0.0399552\pi$
$12$	156027.	−	90082.2i	0.627037	−	0.362020i
$13$			353762.i			0.952785i	0.879233	+	0.476392i	$0.158056\pi$
$13$			353762.i			0.952785i	−0.879233	+	0.476392i	$0.841944\pi$
$14$	−366071.	+	103048.i	−0.680653	+	0.191603i
$15$	1.31137e6			1.72690
$16$	−131072.	−	227023.i	−0.125000	−	0.216506i
$17$	1.67588e6	+	967569.i	1.18032	+	0.681456i	0.956088	−	0.293081i	$-0.0946806\pi$
$17$	1.67588e6	+	967569.i	1.18032	+	0.681456i	0.224228	+	0.974537i	$0.428014\pi$
$18$	732824.	−	1.26929e6i	0.387826	−	0.671734i
$19$	−2.53946e6	+	1.46616e6i	−1.02559	+	0.592124i	−0.915718	−	0.401822i	$-0.868377\pi$
$19$	−2.53946e6	+	1.46616e6i	−1.02559	+	0.592124i	−0.109870	+	0.993946i	$0.535044\pi$
$20$		−	1.90807e6i		−	0.596273i
$21$	−4.12889e6	+	4.23426e6i	−1.01097	+	1.03677i
$22$	−2.82529e6			−0.548213
$23$	−2.94410e6	−	5.09934e6i	−0.457419	−	0.792272i	0.541405	−	0.840762i	$-0.317893\pi$
$23$	−2.94410e6	−	5.09934e6i	−0.457419	−	0.792272i	−0.998824	+	0.0484895i	$0.984559\pi$
$24$	−3.53049e6	−	2.03833e6i	−0.443382	−	0.255987i
$25$	2.06135e6	−	3.57037e6i	0.211083	−	0.365606i
$26$	6.93230e6	−	4.00236e6i	0.583459	−	0.336860i
$27$		−	2.01421e6i		−	0.140374i
$28$	6.16096e6	+	6.00765e6i	0.357979	+	0.349071i
$29$	−2.02170e7			−0.985660			−0.492830	−	0.870126i	$-0.664038\pi$
$29$	−2.02170e7			−0.985660			−0.492830	+	0.870126i	$0.664038\pi$
$30$	−1.48364e7	−	2.56974e7i	−0.610552	−	1.05751i
$31$	4.61441e7	+	2.66413e7i	1.61179	+	0.930566i	0.988956	+	0.148211i	$0.0473514\pi$
$31$	4.61441e7	+	2.66413e7i	1.61179	+	0.930566i	0.622832	+	0.782355i	$0.285982\pi$
$32$	−2.96582e6	+	5.13695e6i	−0.0883883	+	0.153093i
$33$	−3.80502e7	+	2.19683e7i	−0.972272	+	0.561342i
$34$		−	4.37872e7i		−	0.963724i
$35$	1.69719e7	+	6.02915e7i	0.323140	+	1.14793i
$36$	−3.31638e7			−0.548469
$37$	2.79458e7	+	4.84035e7i	0.403003	+	0.698021i	0.994087	−	0.108589i	$-0.0346332\pi$
$37$	2.79458e7	+	4.84035e7i	0.403003	+	0.698021i	−0.591084	+	0.806610i	$0.701300\pi$
$38$	5.74614e7	+	3.31753e7i	0.725200	+	0.418695i
$39$	6.22416e7	−	1.07806e8i	0.689855	−	1.19486i
$40$	−3.73904e7	+	2.15874e7i	−0.365141	+	0.210814i
$41$		−	8.80023e7i		−	0.759582i	−0.925072	−	0.379791i	$-0.875996\pi$
$41$		−	8.80023e7i		−	0.759582i	0.925072	−	0.379791i	$-0.124004\pi$
$42$	1.29687e8	+	3.30043e7i	0.992318	+	0.252536i
$43$	2.63848e8			1.79478			0.897392	−	0.441234i	$-0.145459\pi$
$43$	2.63848e8			1.79478			0.897392	+	0.441234i	$0.145459\pi$
$44$	3.19645e7	+	5.53641e7i	0.193823	+	0.335711i
$45$	−2.09050e8	−	1.20695e8i	−1.13289	−	0.654074i
$46$	−6.66175e7	+	1.15385e8i	−0.323444	+	0.560221i
$47$	−2.26047e8	+	1.30508e8i	−0.985618	+	0.569047i	−0.903962	−	0.427613i	$-0.859354\pi$
$47$	−2.26047e8	+	1.30508e8i	−0.985618	+	0.569047i	−0.0816567	+	0.996661i	$0.526021\pi$
$48$			9.22442e7i			0.362020i
$49$	−2.48111e8	−	1.35030e8i	−0.878347	−	0.478023i
$50$	−9.32862e7			−0.298516
$51$	−3.40472e8	−	5.89714e8i	−0.986803	−	1.70919i
$52$	−1.56860e8	−	9.05632e7i	−0.412568	−	0.238196i
$53$	−1.02485e8	+	1.77509e8i	−0.245065	+	0.424465i	−0.962150	−	0.272521i	$-0.912143\pi$
$53$	−1.02485e8	+	1.77509e8i	−0.245065	+	0.424465i	0.717085	+	0.696986i	$0.245476\pi$
$54$	−3.94702e7	+	2.27882e7i	−0.0859609	+	0.0496296i
$55$			4.65321e8i			0.924569i
$56$	4.80221e7	−	1.88698e8i	0.0871969	−	0.342632i
$57$	1.03183e9			1.71489
$58$	2.28730e8	+	3.96171e8i	0.348484	+	0.603591i
$59$	−3.01275e8	−	1.73941e8i	−0.421408	−	0.243300i	0.274272	−	0.961652i	$-0.411563\pi$
$59$	−3.01275e8	−	1.73941e8i	−0.421408	−	0.243300i	−0.695679	+	0.718352i	$0.744897\pi$
$60$	−3.35710e8	+	5.81466e8i	−0.431726	+	0.747771i
$61$	2.29803e8	−	1.32677e8i	0.272086	−	0.157089i	−0.357749	−	0.933818i	$-0.616456\pi$
$61$	2.29803e8	−	1.32677e8i	0.272086	−	0.157089i	0.629835	+	0.776729i	$0.283122\pi$
$62$		−	1.20565e9i		−	1.31602i
$63$	1.04791e9	−	2.94986e8i	1.05590	−	0.297234i
$64$	1.34218e8			0.125000
$65$	−6.59184e8	−	1.14174e9i	−0.568120	−	0.984012i
$66$	8.60979e8	+	4.97086e8i	0.687500	+	0.396928i
$67$	−8.34938e8	+	1.44615e9i	−0.618415	+	1.07113i	0.371360	+	0.928489i	$0.378892\pi$
$67$	−8.34938e8	+	1.44615e9i	−0.618415	+	1.07113i	−0.989775	+	0.142637i	$0.954442\pi$
$68$	−8.58050e8	+	4.95396e8i	−0.590158	+	0.340728i
$69$			2.07196e9i			1.32476i
$70$	9.89451e8	−	1.01470e9i	0.588714	−	0.603737i
$71$	1.04860e9			0.581190			0.290595	−	0.956846i	$-0.406147\pi$
$71$	1.04860e9			0.581190			0.290595	+	0.956846i	$0.406147\pi$
$72$	3.75206e8	+	6.49875e8i	0.193913	+	0.335867i
$73$	2.09399e9	+	1.20896e9i	1.01009	+	0.583175i	0.911218	−	0.411925i	$-0.135143\pi$
$73$	2.09399e9	+	1.20896e9i	1.01009	+	0.583175i	0.0988713	+	0.995100i	$0.468477\pi$
$74$	6.32341e8	−	1.09525e9i	0.284966	−	0.493575i
$75$	−1.25635e9	+	7.25357e8i	−0.529427	+	0.305665i
$76$		−	1.50134e9i		−	0.592124i
$77$	−1.50247e9	−	1.46508e9i	−0.555076	−	0.541263i
$78$	−2.81673e9			−0.975602
$79$	−1.34296e8	−	2.32607e8i	−0.0436442	−	0.0755940i	0.843378	−	0.537321i	$-0.180563\pi$
$79$	−1.34296e8	−	2.32607e8i	−0.0436442	−	0.0755940i	−0.887022	+	0.461727i	$0.847230\pi$
$80$	8.46049e8	+	4.88467e8i	0.258194	+	0.149068i
$81$	1.55801e9	−	2.69855e9i	0.446833	−	0.773937i
$82$	−1.72448e9	+	9.95632e8i	−0.465147	+	0.268553i
$83$			2.25464e9i			0.572383i	0.958172	+	0.286191i	$0.0923893\pi$
$83$			2.25464e9i			0.572383i	−0.958172	+	0.286191i	$0.907611\pi$
$84$	−8.20494e8	−	2.91474e9i	−0.196191	−	0.696953i
$85$	−7.21169e9			−1.62533
$86$	−2.98510e9	−	5.17035e9i	−0.634552	−	1.09908i
$87$	6.16094e9	+	3.55702e9i	1.23609	+	0.713658i
$88$	7.23274e8	−	1.25275e9i	0.137053	−	0.237383i
$89$	−6.78021e9	+	3.91456e9i	−1.21421	+	0.701024i	−0.963673	−	0.267084i	$-0.913940\pi$
$89$	−6.78021e9	+	3.91456e9i	−1.21421	+	0.701024i	−0.250536	+	0.968107i	$0.580607\pi$
$90$			5.46204e9i			0.925001i
$91$	5.76202e9	+	1.46638e9i	0.923353	+	0.234985i
$92$	3.01476e9			0.457419
$93$	−9.37464e9	−	1.62374e10i	−1.34754	−	2.33400i
$94$	5.11485e9	+	2.95306e9i	0.696937	+	0.402377i
$95$	5.46393e9	−	9.46381e9i	0.706134	−	1.22306i
$96$	1.80761e9	−	1.04362e9i	0.221691	−	0.127993i
$97$			1.20222e10i			1.39999i	0.714149	+	0.699993i	$0.246814\pi$
$97$			1.20222e10i			1.39999i	−0.714149	+	0.699993i	$0.753186\pi$
$98$	1.61028e8	+	6.38966e9i	0.0178144	+	0.706882i
$99$	8.08765e9			0.850445
$100$	1.05541e9	+	1.82803e9i	0.105541	+	0.182803i
$101$	1.65056e7	+	9.52954e6i	0.00157046	+	0.000906703i	0.500785	−	0.865572i	$-0.333045\pi$
$101$	1.65056e7	+	9.52954e6i	0.00157046	+	0.000906703i	−0.499215	+	0.866478i	$0.666378\pi$
$102$	−7.70400e9	+	1.33437e10i	−0.697775	+	1.20858i
$103$	−4.65315e9	+	2.68650e9i	−0.401385	+	0.231740i	−0.687081	−	0.726581i	$-0.741108\pi$
$103$	−4.65315e9	+	2.68650e9i	−0.401385	+	0.231740i	0.285697	+	0.958320i	$0.407775\pi$
$104$			4.09842e9i			0.336860i
$105$	5.43576e9	−	2.13593e10i	0.425906	−	1.67356i
$106$	4.63794e9			0.346574
$107$	7.54918e9	+	1.30756e10i	0.538246	+	0.932269i	0.998999	+	0.0447407i	$0.0142462\pi$
$107$	7.54918e9	+	1.30756e10i	0.538246	+	0.932269i	−0.460753	+	0.887529i	$0.652421\pi$
$108$	8.93110e8	+	5.15637e8i	0.0607836	+	0.0350934i
$109$	−7.20002e9	+	1.24708e10i	−0.467952	+	0.810517i	−0.999329	−	0.0366184i	$-0.988341\pi$
$109$	−7.20002e9	+	1.24708e10i	−0.467952	+	0.810517i	0.531377	+	0.847135i	$0.321675\pi$
$110$	9.11840e9	−	5.26451e9i	0.566181	−	0.326885i
$111$		−	1.96673e10i		−	1.16716i
$112$	−4.24103e9	+	1.19384e9i	−0.240647	+	0.0677417i
$113$	−1.17781e9			−0.0639268			−0.0319634	−	0.999489i	$-0.510176\pi$
$113$	−1.17781e9			−0.0639268			−0.0319634	+	0.999489i	$0.510176\pi$
$114$	−1.16739e10	−	2.02197e10i	−0.606304	−	1.05015i
$115$	1.90037e10	+	1.09718e10i	0.944821	+	0.545493i
$116$	5.17556e9	−	8.96433e9i	0.246415	−	0.426803i
$117$	−1.98443e10	+	1.14571e10i	−0.905123	+	0.522573i
$118$			7.87167e9i			0.344078i
$119$	2.27063e10	−	2.32857e10i	0.951506	−	0.975788i
$120$	1.51925e10			0.610552
$121$	5.17354e9	+	8.96084e9i	0.199462	+	0.345479i
$122$	−5.19985e9	−	3.00214e9i	−0.192394	−	0.111079i
$123$	−1.54833e10	+	2.68178e10i	−0.549968	+	0.952572i
$124$	−2.36258e10	+	1.36404e10i	−0.805894	+	0.465283i
$125$		−	2.10295e10i		−	0.689094i
$126$	−1.76363e10	−	1.71974e10i	−0.555335	−	0.541516i
$127$	−1.56755e10			−0.474462			−0.237231	−	0.971453i	$-0.576240\pi$
$127$	−1.56755e10			−0.474462			−0.237231	+	0.971453i	$0.576240\pi$
$128$	−1.51850e9	−	2.63012e9i	−0.0441942	−	0.0765466i
$129$	−8.04052e10	−	4.64220e10i	−2.25079	−	1.29950i
$130$	−1.49156e10	+	2.58346e10i	−0.401721	+	0.695802i
$131$	−2.85531e10	+	1.64852e10i	−0.740112	+	0.427304i	−0.822110	−	0.569329i	$-0.807203\pi$
$131$	−2.85531e10	+	1.64852e10i	−0.740112	+	0.427304i	0.0819981	+	0.996632i	$0.473870\pi$
$132$		−	2.24956e10i		−	0.561342i
$133$	1.33542e10	+	4.74396e10i	0.320892	+	1.13994i
$134$	3.77850e10			0.874571
$135$	3.75318e9	+	6.50070e9i	0.0837010	+	0.144974i
$136$	1.94155e10	+	1.12095e10i	0.417305	+	0.240931i
$137$	1.26064e10	−	2.18349e10i	0.261209	−	0.452427i	−0.705355	−	0.708855i	$-0.749212\pi$
$137$	1.26064e10	−	2.18349e10i	0.261209	−	0.452427i	0.966563	+	0.256428i	$0.0825456\pi$
$138$	4.06020e10	−	2.34416e10i	0.811245	−	0.468373i
$139$			3.77615e10i			0.727738i	0.931450	+	0.363869i	$0.118544\pi$
$139$			3.77615e10i			0.727738i	−0.931450	+	0.363869i	$0.881456\pi$
$140$	−3.10784e10	−	7.90918e9i	−0.577854	−	0.147059i
$141$	9.18473e10			1.64805
$142$	−1.18635e10	−	2.05483e10i	−0.205482	−	0.355905i
$143$	3.82534e10	+	2.20856e10i	0.639720	+	0.369342i
$144$	8.48994e9	−	1.47050e10i	0.137117	−	0.237494i
$145$	6.52489e10	−	3.76714e10i	1.01797	−	0.587722i
$146$		−	5.47115e10i		−	0.824734i
$147$	5.18521e10	+	8.48021e10i	0.755405	+	1.23544i
$148$	−2.86165e10			−0.403003
$149$	−3.22645e9	−	5.58837e9i	−0.0439333	−	0.0760946i	0.843223	−	0.537565i	$-0.180656\pi$
$149$	−3.22645e9	−	5.58837e9i	−0.0439333	−	0.0760946i	−0.887156	+	0.461470i	$0.847322\pi$
$150$	2.84281e10	+	1.64130e10i	0.374361	+	0.216138i
$151$	4.80584e10	−	8.32396e10i	0.612188	−	1.06034i	−0.378683	−	0.925526i	$-0.623623\pi$
$151$	4.80584e10	−	8.32396e10i	0.612188	−	1.06034i	0.990871	−	0.134814i	$-0.0430436\pi$
$152$	−2.94202e10	+	1.69858e10i	−0.362600	+	0.209347i
$153$			1.25345e11i			1.49503i
$154$	−1.17111e10	+	4.60178e10i	−0.135206	+	0.531279i
$155$	−1.98569e11			−2.21949
$156$	3.18677e10	+	5.51965e10i	0.344927	+	0.597432i
$157$	−4.65154e10	−	2.68557e10i	−0.487639	−	0.281539i	0.235955	−	0.971764i	$-0.424178\pi$
$157$	−4.65154e10	−	2.68557e10i	−0.487639	−	0.281539i	−0.723595	+	0.690225i	$0.757511\pi$
$158$	−3.03876e9	+	5.26329e9i	−0.0308611	+	0.0534530i
$159$	6.24626e10	−	3.60628e10i	0.614659	−	0.354873i
$160$		−	2.21055e10i		−	0.210814i
$161$	−9.52608e10	+	2.68157e10i	−0.880612	+	0.247891i
$162$	−7.05075e10			−0.631917
$163$	5.58524e9	+	9.67391e9i	0.0485404	+	0.0840745i	0.889275	−	0.457373i	$-0.151210\pi$
$163$	5.58524e9	+	9.67391e9i	0.0485404	+	0.0840745i	−0.840734	+	0.541448i	$0.817876\pi$
$164$	3.90206e10	+	2.25286e10i	0.328909	+	0.189895i
$165$	8.18695e10	−	1.41802e11i	0.669425	−	1.15948i
$166$	4.41817e10	−	2.55083e10i	0.350511	−	0.202368i
$167$		−	1.57530e11i		−	1.21278i	−0.795168	−	0.606390i	$-0.792617\pi$
$167$		−	1.57530e11i		−	1.21278i	0.795168	−	0.606390i	$-0.207383\pi$
$168$	−4.78342e10	+	4.90549e10i	−0.357431	+	0.366552i
$169$	1.27107e10			0.0922012
$170$	8.15910e10	+	1.41320e11i	0.574642	+	0.995310i
$171$	−1.64488e11	−	9.49675e10i	−1.12501	−	0.649523i
$172$	−6.75452e10	+	1.16992e11i	−0.448696	+	0.777164i
$173$	−8.75350e10	+	5.05383e10i	−0.564873	+	0.326130i	−0.755099	−	0.655611i	$-0.772411\pi$
$173$	−8.75350e10	+	5.05383e10i	−0.564873	+	0.326130i	0.190226	+	0.981740i	$0.439078\pi$
$174$		−	1.60972e11i		−	1.00926i
$175$	−4.96090e10	−	4.83746e10i	−0.302253	−	0.294732i
$176$	−3.27316e10			−0.193823
$177$	6.12070e10	+	1.06014e11i	0.352318	+	0.610232i
$178$	1.53419e11	+	8.85764e10i	0.858575	+	0.495699i
$179$	1.06248e11	−	1.84028e11i	0.578173	−	1.00142i	−0.417516	−	0.908669i	$-0.637099\pi$
$179$	1.06248e11	−	1.84028e11i	0.578173	−	1.00142i	0.995689	−	0.0927550i	$-0.0295673\pi$
$180$	1.07034e11	−	6.17959e10i	0.566445	−	0.327037i
$181$			7.36013e10i			0.378872i	0.981893	+	0.189436i	$0.0606660\pi$
$181$			7.36013e10i			0.378872i	−0.981893	+	0.189436i	$0.939334\pi$
$182$	−3.64547e10	−	1.29502e11i	−0.182556	−	0.648516i
$183$	−9.33737e10			−0.454956
$184$	−3.41081e10	−	5.90770e10i	−0.161722	−	0.280111i
$185$	−1.80386e11	−	1.04146e11i	−0.832422	−	0.480599i
$186$	−2.12124e11	+	3.67410e11i	−0.952851	+	1.65039i
$187$	2.09252e11	−	1.20812e11i	0.915087	−	0.528326i
$188$		−	1.33640e11i		−	0.569047i
$189$	−3.28071e10	−	8.34912e9i	−0.136037	−	0.0346204i
$190$	−2.47269e11			−0.998625
$191$	2.16782e11	+	3.75478e11i	0.852818	+	1.47712i	0.878654	+	0.477458i	$0.158442\pi$
$191$	2.16782e11	+	3.75478e11i	0.852818	+	1.47712i	−0.0258361	+	0.999666i	$0.508225\pi$
$192$	−4.09015e10	−	2.36145e10i	−0.156759	−	0.0905050i
$193$	−9.55820e10	+	1.65553e11i	−0.356935	+	0.618230i	−0.987447	−	0.157950i	$-0.949512\pi$
$193$	−9.55820e10	+	1.65553e11i	−0.356935	+	0.618230i	0.630512	+	0.776180i	$0.282845\pi$
$194$	2.35585e11	−	1.36015e11i	0.857313	−	0.494970i
$195$			4.63912e11i			1.64537i
$196$	1.23389e11	−	7.54462e10i	0.426577	−	0.260830i
$197$	4.53461e11			1.52830			0.764150	−	0.645039i	$-0.223159\pi$
$197$	4.53461e11			1.52830			0.764150	+	0.645039i	$0.223159\pi$
$198$	−9.15013e10	−	1.58485e11i	−0.300678	−	0.520789i
$199$	−2.64623e11	−	1.52780e11i	−0.847936	−	0.489556i	0.0120180	−	0.999928i	$-0.496174\pi$
$199$	−2.64623e11	−	1.52780e11i	−0.847936	−	0.489556i	−0.859954	+	0.510372i	$0.829508\pi$
$200$	2.38813e10	−	4.13636e10i	0.0746290	−	0.129261i
$201$	5.08878e11	−	2.93801e11i	1.55108	−	0.895515i
$202$		−	4.31258e8i		−	0.00128227i
$203$	−8.38018e10	+	3.29291e11i	−0.243093	+	0.955213i
$204$	3.48643e11			0.986803
$205$	1.63979e11	+	2.84020e11i	0.452918	+	0.784477i
$206$	1.05289e11	+	6.07885e10i	0.283822	+	0.163865i
$207$	1.90699e11	−	3.30300e11i	0.501760	−	0.869073i
$208$	8.03123e10	−	4.63683e10i	0.206284	−	0.119098i
$209$			3.66132e11i			0.918135i
$210$	−4.80054e11	+	1.35134e11i	−1.17542	+	0.330879i
$211$	−3.31445e11			−0.792499			−0.396249	−	0.918143i	$-0.629688\pi$
$211$	−3.31445e11			−0.792499			−0.396249	+	0.918143i	$0.629688\pi$
$212$	−5.24723e10	−	9.08847e10i	−0.122532	−	0.212232i
$213$	−3.19550e11	−	1.84492e11i	−0.728855	−	0.420805i
$214$	1.70818e11	−	2.95866e11i	0.380597	−	0.659214i
$215$	−8.51550e11	+	4.91643e11i	−1.85361	+	1.07018i
$216$		−	2.33351e10i		−	0.0496296i
$217$	6.25202e11	−	6.41156e11i	1.29934	−	1.33249i
$218$	3.25836e11			0.661784
$219$	−4.25415e11	−	7.36840e11i	−0.844485	−	1.46269i
$220$	−2.06326e11	−	1.19122e11i	−0.400350	−	0.231142i
$221$	−3.42290e11	+	5.92863e11i	−0.649280	+	1.12459i
$222$	−3.85400e11	+	2.22511e11i	−0.714737	+	0.412654i
$223$		−	8.19970e11i		−	1.48687i	−0.668807	−	0.743436i	$-0.733195\pi$
$223$		−	8.19970e11i		−	1.48687i	0.668807	−	0.743436i	$-0.266805\pi$
$224$	7.13761e10	+	6.96000e10i	0.126565	+	0.123415i
$225$	2.67041e11			0.463089
$226$	1.33254e10	+	2.30803e10i	0.0226015	+	0.0391470i
$227$	2.63498e11	+	1.52131e11i	0.437168	+	0.252399i	0.702395	−	0.711787i	$-0.252114\pi$
$227$	2.63498e11	+	1.52131e11i	0.437168	+	0.252399i	−0.265228	+	0.964186i	$0.585447\pi$
$228$	−2.64149e11	+	4.57520e11i	−0.428721	+	0.742567i
$229$	−3.39756e11	+	1.96158e11i	−0.539498	+	0.311479i	−0.744875	−	0.667204i	$-0.767491\pi$
$229$	−3.39756e11	+	1.96158e11i	−0.539498	+	0.311479i	0.205378	+	0.978683i	$0.434158\pi$
$230$		−	4.96527e11i		−	0.771443i
$231$	2.00094e11	+	7.10817e11i	0.304210	+	1.08068i
$232$	−2.34219e11			−0.348484
$233$	2.80594e11	+	4.86004e11i	0.408601	+	0.707718i	0.994733	−	0.102498i	$-0.0326835\pi$
$233$	2.80594e11	+	4.86004e11i	0.408601	+	0.707718i	−0.586132	+	0.810215i	$0.699350\pi$
$234$	4.49026e11	+	2.59245e11i	0.640018	+	0.369515i
$235$	4.86365e11	−	8.42409e11i	0.678615	−	1.17540i
$236$	1.54253e11	−	8.90578e10i	0.210704	−	0.121650i
$237$			9.45129e10i			0.126401i
$238$	−7.13198e11	−	1.81503e11i	−0.933954	−	0.237683i
$239$	−1.15203e12			−1.47731			−0.738657	−	0.674082i	$-0.764539\pi$
$239$	−1.15203e12			−1.47731			−0.738657	+	0.674082i	$0.764539\pi$
$240$	−1.71883e11	−	2.97711e11i	−0.215863	−	0.373885i
$241$	2.86668e11	+	1.65508e11i	0.352609	+	0.203579i	0.665834	−	0.746100i	$-0.268076\pi$
$241$	2.86668e11	+	1.65508e11i	0.352609	+	0.203579i	−0.313225	+	0.949679i	$0.601409\pi$
$242$	1.17064e11	−	2.02761e11i	0.141041	−	0.244291i
$243$	−1.05258e12	+	6.07706e11i	−1.24229	+	0.717237i
$244$			1.35861e11i			0.157089i
$245$	1.05237e12	−	2.65211e10i	1.19217	−	0.0300443i
$246$	7.00693e11			0.777772
$247$	−5.18671e11	−	8.98364e11i	−0.564166	−	0.977165i
$248$	5.34591e11	+	3.08646e11i	0.569853	+	0.329005i
$249$	3.96685e11	−	6.87079e11i	0.414428	−	0.717811i
$250$	−4.12092e11	+	2.37921e11i	−0.421982	+	0.243632i
$251$		−	7.94487e11i		−	0.797477i	−0.917065	−	0.398739i	$-0.869448\pi$
$251$		−	7.94487e11i		−	0.797477i	0.917065	−	0.398739i	$-0.130552\pi$
$252$	−1.37468e11	+	5.40166e11i	−0.135269	+	0.531526i
$253$	−7.35209e11			−0.709265
$254$	1.77348e11	+	3.07175e11i	0.167748	+	0.290548i
$255$	2.19769e12	+	1.26884e12i	2.03829	+	1.17681i
$256$	−3.43597e10	+	5.95128e10i	−0.0312500	+	0.0541266i
$257$	5.42224e11	−	3.13053e11i	0.483630	−	0.279224i	−0.238298	−	0.971192i	$-0.576590\pi$
$257$	5.42224e11	−	3.13053e11i	0.483630	−	0.279224i	0.721928	+	0.691968i	$0.243256\pi$
$258$			2.10082e12i			1.83776i
$259$	9.04227e11	−	2.54538e11i	0.775852	−	0.218401i
$260$	6.75004e11			0.568120
$261$	−6.54759e11	−	1.13408e12i	−0.540604	−	0.936354i
$262$	6.46084e11	+	3.73017e11i	0.523338	+	0.302149i
$263$	−7.71635e11	+	1.33651e12i	−0.613244	+	1.06217i	0.377446	+	0.926031i	$0.376802\pi$
$263$	−7.71635e11	+	1.33651e12i	−0.613244	+	1.06217i	−0.990690	+	0.136137i	$0.956531\pi$
$264$	−4.40821e11	+	2.54508e11i	−0.343750	+	0.198464i
$265$		−	7.63862e11i		−	0.584502i
$266$	7.78538e11	−	7.98405e11i	0.584617	−	0.599536i
$267$	2.75494e12			2.03028
$268$	−4.27488e11	−	7.40431e11i	−0.309208	−	0.535563i
$269$	−1.55680e12	−	8.98817e11i	−1.10528	−	0.638131i	−0.167674	−	0.985842i	$-0.553626\pi$
$269$	−1.55680e12	−	8.98817e11i	−1.10528	−	0.638131i	−0.937602	+	0.347711i	$0.886959\pi$
$270$	8.49248e10	−	1.47094e11i	0.0591855	−	0.102512i
$271$	7.20142e11	−	4.15774e11i	0.492687	−	0.284453i	−0.233001	−	0.972476i	$-0.574855\pi$
$271$	7.20142e11	−	4.15774e11i	0.492687	−	0.284453i	0.725689	+	0.688023i	$0.241521\pi$
$272$		−	5.07285e11i		−	0.340728i
$273$	−1.49792e12	−	1.46065e12i	−0.987815	−	0.963234i
$274$	−5.70500e11			−0.369405
$275$	−2.57383e11	−	4.45801e11i	−0.163650	−	0.283451i
$276$	−9.18719e11	−	5.30423e11i	−0.573637	−	0.331190i
$277$	−1.48759e12	+	2.57658e12i	−0.912188	+	1.57996i	−0.101222	+	0.994864i	$0.532275\pi$
$277$	−1.48759e12	+	2.57658e12i	−0.912188	+	1.57996i	−0.810966	+	0.585093i	$0.801058\pi$
$278$	7.39971e11	−	4.27223e11i	0.445647	−	0.257294i
$279$			3.45128e12i			2.04155i
$280$	1.96624e11	+	6.98491e11i	0.114247	+	0.405855i
$281$	−7.02074e11			−0.400730			−0.200365	−	0.979721i	$-0.564213\pi$
$281$	−7.02074e11			−0.400730			−0.200365	+	0.979721i	$0.564213\pi$
$282$	−1.03913e12	−	1.79983e12i	−0.582674	−	1.00922i
$283$	1.02458e11	+	5.91544e10i	0.0564437	+	0.0325878i	0.527956	−	0.849272i	$-0.322958\pi$
$283$	1.02458e11	+	5.91544e10i	0.0564437	+	0.0325878i	−0.471513	+	0.881859i	$0.656292\pi$
$284$	−2.68441e11	+	4.64954e11i	−0.145297	+	0.251663i
$285$	−3.33016e12	+	1.92267e12i	−1.77109	+	1.02254i
$286$		−	9.99481e11i		−	0.522329i
$287$	−1.43337e12	−	3.64779e11i	−0.736118	−	0.187336i
$288$	−3.84211e11			−0.193913
$289$	8.64384e11	+	1.49716e12i	0.428763	+	0.742640i
$290$	−1.47641e12	−	8.52408e11i	−0.719810	−	0.415583i
$291$	2.11520e12	−	3.66364e12i	1.01365	−	1.75569i
$292$	−1.07212e12	+	6.18989e11i	−0.505044	+	0.291588i
$293$			1.24473e12i			0.576419i	0.957567	+	0.288210i	$0.0930600\pi$
$293$			1.24473e12i			0.576419i	−0.957567	+	0.288210i	$0.906940\pi$
$294$	1.07514e12	−	1.97552e12i	0.489471	−	0.899382i
$295$	1.29645e12			0.580293
$296$	3.23759e11	+	5.60767e11i	0.142483	+	0.246788i
$297$	−2.17802e11	−	1.25748e11i	−0.0942498	−	0.0544152i
$298$	−7.30062e10	+	1.26450e11i	−0.0310655	+	0.0538070i
$299$	1.80395e12	−	1.04151e12i	0.754865	−	0.435822i
$300$		−	7.42765e11i		−	0.305665i
$301$	1.09368e12	−	4.29752e12i	0.442648	−	1.73934i
$302$	−2.17487e12			−0.865764
$303$	−3.35329e9	−	5.80807e9i	−0.00131298	−	0.00227415i
$304$	6.65704e11	+	3.84344e11i	0.256397	+	0.148031i
$305$	−4.94448e11	+	8.56409e11i	−0.187336	+	0.324476i
$306$	2.45625e12	−	1.41812e12i	0.915514	−	0.528572i
$307$			3.15405e12i			1.15658i	0.815831	+	0.578291i	$0.196280\pi$
$307$			3.15405e12i			1.15658i	−0.815831	+	0.578291i	$0.803720\pi$
$308$	1.03426e12	−	2.91142e11i	0.373143	−	0.105039i
$309$	1.89067e12			0.671155
$310$	2.24655e12	+	3.89114e12i	0.784707	+	1.35915i
$311$	2.22193e12	+	1.28283e12i	0.763711	+	0.440929i	0.830627	−	0.556830i	$-0.187982\pi$
$311$	2.22193e12	+	1.28283e12i	0.763711	+	0.440929i	−0.0669156	+	0.997759i	$0.521316\pi$
$312$	7.21083e11	−	1.24895e12i	0.243900	−	0.422448i
$313$	−4.30776e11	+	2.48708e11i	−0.143394	+	0.0827883i	−0.569980	−	0.821658i	$-0.693049\pi$
$313$	−4.30776e11	+	2.48708e11i	−0.143394	+	0.0827883i	0.426587	+	0.904447i	$0.359716\pi$
$314$			1.21535e12i			0.398156i
$315$	−2.83240e12	+	2.90468e12i	−0.913274	+	0.936580i
$316$	1.37519e11			0.0436442
$317$	−2.17249e11	−	3.76286e11i	−0.0678674	−	0.117550i	0.830095	−	0.557622i	$-0.188286\pi$
$317$	−2.17249e11	−	3.76286e11i	−0.0678674	−	0.117550i	−0.897962	+	0.440072i	$0.854953\pi$
$318$	−1.41337e12	−	8.16007e11i	−0.434629	−	0.250933i
$319$	−1.26216e12	+	2.18613e12i	−0.382086	+	0.661793i
$320$	−4.33177e11	+	2.50095e11i	−0.129097	+	0.0745341i
$321$		−	5.31286e12i		−	1.55885i
$322$	1.60323e12	+	1.56334e12i	0.463145	+	0.451620i
$323$	−5.67443e12			−1.61402
$324$	7.97701e11	+	1.38166e12i	0.223416	+	0.386968i
$325$	1.26306e12	+	7.29229e11i	0.348344	+	0.201116i
$326$	1.26379e11	−	2.18896e11i	0.0343233	−	0.0594496i
$327$	4.38827e12	−	2.53357e12i	1.17369	−	0.677633i
$328$		−	1.01953e12i		−	0.268553i
$329$	1.18870e12	+	4.22278e12i	0.308386	+	1.09552i
$330$	−3.70499e12			−0.946711
$331$	4.68669e11	+	8.11759e11i	0.117958	+	0.204309i	0.918958	−	0.394355i	$-0.129032\pi$
$331$	4.68669e11	+	8.11759e11i	0.117958	+	0.204309i	−0.801000	+	0.598664i	$0.795699\pi$
$332$	−9.99718e11	−	5.77187e11i	−0.247849	−	0.143096i
$333$	−1.81014e12	+	3.13525e12i	−0.442069	+	0.765686i
$334$	−3.08695e12	+	1.78225e12i	−0.742673	+	0.428782i
$335$		−	6.22313e12i		−	1.47498i
$336$	1.50246e12	+	3.82362e11i	0.350837	+	0.0892851i
$337$	4.96489e12			1.14225			0.571124	−	0.820864i	$-0.306508\pi$
$337$	4.96489e12			1.14225			0.571124	+	0.820864i	$0.306508\pi$
$338$	−1.43805e11	−	2.49078e11i	−0.0325981	−	0.0564615i
$339$	3.58926e11	+	2.07226e11i	0.0801690	+	0.0462856i
$340$	1.84619e12	−	3.19770e12i	0.406333	−	0.703790i
$341$	5.76161e12	−	3.32647e12i	1.24960	−	0.721459i
$342$			4.29774e12i			0.918564i
$343$	−3.22779e12	+	3.48148e12i	−0.679884	+	0.733320i
$344$	3.05675e12			0.634552
$345$	−3.86080e12	−	6.68710e12i	−0.789917	−	1.36818i
$346$	1.98069e12	+	1.14355e12i	0.399426	+	0.230609i
$347$	2.99228e12	−	5.18278e12i	0.594777	−	1.03018i	−0.398801	−	0.917038i	$-0.630574\pi$
$347$	2.99228e12	−	5.18278e12i	0.594777	−	1.03018i	0.993578	−	0.113147i	$-0.0360931\pi$
$348$	−3.15440e12	+	1.82119e12i	−0.618046	+	0.356829i
$349$			1.16507e12i			0.225022i	0.993650	+	0.112511i	$0.0358894\pi$
$349$			1.16507e12i			0.225022i	−0.993650	+	0.112511i	$0.964111\pi$
$350$	−3.86682e11	+	1.51943e12i	−0.0736230	+	0.289295i
$351$	7.12551e11			0.133746
$352$	3.70316e11	+	6.41407e11i	0.0685266	+	0.118692i
$353$	−2.31406e12	−	1.33602e12i	−0.422183	−	0.243748i	0.273828	−	0.961779i	$-0.411710\pi$
$353$	−2.31406e12	−	1.33602e12i	−0.422183	−	0.243748i	−0.696011	+	0.718031i	$0.745044\pi$
$354$	1.38496e12	−	2.39881e12i	0.249126	−	0.431500i
$355$	−3.38427e12	+	1.95391e12i	−0.600238	+	0.346548i
$356$		−	4.00851e12i		−	0.701024i
$357$	−1.10165e13	+	3.10111e12i	−1.89977	+	0.534782i
$358$	−4.80826e12			−0.817660
$359$	4.82715e11	+	8.36086e11i	0.0809503	+	0.140210i	0.903658	−	0.428254i	$-0.140871\pi$
$359$	4.82715e11	+	8.36086e11i	0.0809503	+	0.140210i	−0.822708	+	0.568464i	$0.807538\pi$
$360$	−2.42189e12	−	1.39828e12i	−0.400537	−	0.231250i
$361$	1.23370e12	−	2.13682e12i	0.201221	−	0.348524i
$362$	1.44229e12	−	8.32704e11i	0.232011	−	0.133952i
$363$		−	3.64097e12i		−	0.577675i
$364$	−2.12528e12	+	2.17951e12i	−0.332590	+	0.341077i
$365$	−9.01090e12			−1.39093
$366$	1.05640e12	+	1.82974e12i	0.160851	+	0.278602i
$367$	−5.14728e12	−	2.97179e12i	−0.773121	−	0.446362i	0.0608656	−	0.998146i	$-0.480614\pi$
$367$	−5.14728e12	−	2.97179e12i	−0.773121	−	0.446362i	−0.833987	+	0.551784i	$0.813947\pi$
$368$	−7.71779e11	+	1.33676e12i	−0.114355	+	0.198068i
$369$	4.93650e12	−	2.85009e12i	0.721584	−	0.416607i
$370$			4.71310e12i			0.679670i
$371$	2.46643e12	+	2.40505e12i	0.350912	+	0.342180i
$372$	9.59964e12			1.34754
$373$	3.73512e12	+	6.46943e12i	0.517322	+	0.896028i	0.999798	+	0.0201185i	$0.00640436\pi$
$373$	3.73512e12	+	6.46943e12i	0.517322	+	0.896028i	−0.482476	+	0.875909i	$0.660262\pi$
$374$	−4.73484e12	−	2.73366e12i	−0.647064	−	0.373583i
$375$	−3.69997e12	+	6.40853e12i	−0.498932	+	0.864176i
$376$	−2.61880e12	+	1.51197e12i	−0.348469	+	0.201189i
$377$		−	7.15202e12i		−	0.939122i
$378$	2.07561e11	+	7.37344e11i	0.0268959	+	0.0955457i
$379$	−1.92794e11			−0.0246545			−0.0123273	−	0.999924i	$-0.503924\pi$
$379$	−1.92794e11			−0.0246545			−0.0123273	+	0.999924i	$0.503924\pi$
$380$	2.79753e12	+	4.84547e12i	0.353067	+	0.611530i
$381$	4.77694e12	+	2.75797e12i	0.595011	+	0.343530i
$382$	4.90522e12	−	8.49609e12i	0.603034	−	1.04448i
$383$	4.64774e12	−	2.68338e12i	0.563960	−	0.325602i	−0.190773	−	0.981634i	$-0.561100\pi$
$383$	4.64774e12	−	2.68338e12i	0.563960	−	0.325602i	0.754733	+	0.656032i	$0.227766\pi$
$384$			1.06867e12i			0.127993i
$385$	7.57907e12	+	1.92881e12i	0.896009	+	0.228027i
$386$	4.32555e12			0.504783
$387$	8.54514e12	+	1.48006e13i	0.984383	+	1.70500i
$388$	−5.33069e12	−	3.07767e12i	−0.606212	−	0.349997i
$389$	−3.84473e12	+	6.65927e12i	−0.431637	+	0.747617i	−0.997014	−	0.0772155i	$-0.975397\pi$
$389$	−3.84473e12	+	6.65927e12i	−0.431637	+	0.747617i	0.565378	+	0.824832i	$0.308730\pi$
$390$	9.09078e12	−	5.24857e12i	1.00758	−	0.581725i
$391$		−	1.13945e13i		−	1.24684i
$392$	−2.87443e12	−	1.56435e12i	−0.310543	−	0.169007i
$393$	1.16017e13			1.23754
$394$	−5.13032e12	−	8.88598e12i	−0.540336	−	0.935889i
$395$	8.66858e11	+	5.00480e11i	0.0901493	+	0.0520477i
$396$	−2.07044e12	+	3.58610e12i	−0.212611	+	0.368254i
$397$	−5.51580e12	+	3.18455e12i	−0.559314	+	0.322920i	−0.752870	−	0.658169i	$-0.771331\pi$
$397$	−5.51580e12	+	3.18455e12i	−0.559314	+	0.322920i	0.193556	+	0.981089i	$0.437998\pi$
$398$			6.91405e12i			0.692337i
$399$	4.27706e12	−	1.68063e13i	0.422942	−	1.66191i
$400$	−1.08074e12			−0.105541
$401$	5.92788e12	+	1.02674e13i	0.571712	+	0.990234i	0.996390	+	0.0848899i	$0.0270539\pi$
$401$	5.92788e12	+	1.02674e13i	0.571712	+	0.990234i	−0.424678	+	0.905344i	$0.639613\pi$
$402$	−1.15146e13	−	6.64796e12i	−1.09678	−	0.633225i
$403$	−9.42470e12	+	1.63241e13i	−0.886629	+	1.53569i
$404$	−8.45089e9	+	4.87912e9i	−0.000785228	+	0.000453351i
$405$			1.16125e13i			1.06574i
$406$	7.40088e12	−	2.08333e12i	0.670893	−	0.188855i
$407$	6.97870e12			0.624888
$408$	−3.94445e12	−	6.83198e12i	−0.348887	−	0.604291i
$409$	4.58382e12	+	2.64647e12i	0.400507	+	0.231233i	0.686703	−	0.726938i	$-0.259057\pi$
$409$	4.58382e12	+	2.64647e12i	0.400507	+	0.231233i	−0.286195	+	0.958171i	$0.592391\pi$
$410$	3.71043e12	−	6.42665e12i	0.320261	−	0.554709i
$411$	−7.68334e12	+	4.43598e12i	−0.655150	+	0.378251i
$412$		−	2.75097e12i		−	0.231740i
$413$	−4.08194e12	+	4.18610e12i	−0.339716	+	0.348385i
$414$	−8.63004e12			−0.709596
$415$	−4.20119e12	−	7.27667e12i	−0.341296	−	0.591142i
$416$	−1.81726e12	−	1.04920e12i	−0.145865	−	0.0842151i
$417$	6.64383e12	−	1.15074e13i	0.526912	−	0.912638i
$418$	7.17470e12	−	4.14232e12i	0.562241	−	0.324610i
$419$		−	6.87658e12i		−	0.532479i	−0.963907	−	0.266239i	$-0.914219\pi$
$419$		−	6.87658e12i		−	0.532479i	0.963907	−	0.266239i	$-0.0857812\pi$
$420$	8.07927e12	+	7.87823e12i	0.618195	+	0.602812i
$421$	−1.87185e13			−1.41534			−0.707668	−	0.706545i	$-0.750253\pi$
$421$	−1.87185e13			−1.41534			−0.707668	+	0.706545i	$0.750253\pi$
$422$	3.74987e12	+	6.49496e12i	0.280191	+	0.485304i
$423$	−1.46417e13	−	8.45341e12i	−1.08116	−	0.624209i
$424$	−1.18731e12	+	2.05649e12i	−0.0866435	+	0.150071i
$425$	6.90916e12	−	3.98901e12i	0.498288	−	0.287687i
$426$			8.34918e12i			0.595108i
$427$	−1.20846e12	−	4.29296e12i	−0.0851320	−	0.302425i
$428$	−7.73036e12			−0.538246
$429$	−7.77156e12	−	1.34607e13i	−0.534838	−	0.926366i
$430$	1.92684e13	+	1.11246e13i	1.31070	+	0.756732i
$431$	−2.87925e12	+	4.98700e12i	−0.193594	+	0.335315i	−0.946439	−	0.322883i	$-0.895348\pi$
$431$	−2.87925e12	+	4.98700e12i	−0.193594	+	0.335315i	0.752845	+	0.658198i	$0.228681\pi$
$432$	−4.57272e11	+	2.64006e11i	−0.0303918	+	0.0175467i
$433$			1.31856e13i			0.866284i	0.901326	+	0.433142i	$0.142595\pi$
$433$			1.31856e13i			0.866284i	−0.901326	+	0.433142i	$0.857405\pi$
$434$	−1.96374e13	−	4.99755e12i	−1.27537	−	0.324570i
$435$	−2.65119e13			−1.70214
$436$	−3.68641e12	−	6.38505e12i	−0.233976	−	0.405258i
$437$	1.49529e13	+	8.63303e12i	0.938246	+	0.541697i
$438$	−9.62603e12	+	1.66728e13i	−0.597141	+	1.03428i
$439$	1.11065e13	−	6.41233e12i	0.681168	−	0.393272i	−0.119127	−	0.992879i	$-0.538010\pi$
$439$	1.11065e13	−	6.41233e12i	0.681168	−	0.393272i	0.800295	+	0.599607i	$0.204676\pi$
$440$			5.39086e12i			0.326885i
$441$	−4.60958e11	−	1.82910e13i	−0.0276356	−	1.09659i
$442$	1.54903e13			0.918221
$443$	−1.48813e12	−	2.57751e12i	−0.0872211	−	0.151071i	0.819114	−	0.573630i	$-0.194465\pi$
$443$	−1.48813e12	−	2.57751e12i	−0.0872211	−	0.151071i	−0.906335	+	0.422559i	$0.861132\pi$
$444$	8.72060e12	+	5.03484e12i	0.505395	+	0.291790i
$445$	1.45884e13	−	2.52679e13i	0.836003	−	1.44800i
$446$	−1.60681e13	+	9.27690e12i	−0.910519	+	0.525689i
$447$			2.27067e12i			0.127238i
$448$	5.56347e11	−	2.18612e12i	0.0308288	−	0.121139i
$449$	2.45035e13			1.34276			0.671378	−	0.741115i	$-0.265703\pi$
$449$	2.45035e13			1.34276			0.671378	+	0.741115i	$0.265703\pi$
$450$	−3.02122e12	−	5.23290e12i	−0.163727	−	0.283583i
$451$	−9.51595e12	−	5.49404e12i	−0.509999	−	0.294448i
$452$	3.01519e11	−	5.22247e11i	0.0159817	−	0.0276811i
$453$	−2.92906e13	+	1.69110e13i	−1.53546	+	0.886497i
$454$		−	6.88464e12i		−	0.356946i
$455$	−2.13289e13	+	6.00403e12i	−1.09373	+	0.307883i
$456$	1.19540e13			0.606304
$457$	−1.74564e13	−	3.02354e13i	−0.875739	−	1.51682i	−0.855974	−	0.517019i	$-0.827042\pi$
$457$	−1.74564e13	−	3.02354e13i	−0.875739	−	1.51682i	−0.0197647	−	0.999805i	$-0.506292\pi$
$458$	7.68780e12	+	4.43855e12i	0.381482	+	0.220249i
$459$	1.94889e12	−	3.37557e12i	0.0956584	−	0.165685i
$460$	−9.72991e12	+	5.61757e12i	−0.472411	+	0.272746i
$461$			1.91543e13i			0.919945i	0.887933	+	0.459973i	$0.152141\pi$
$461$			1.91543e13i			0.919945i	−0.887933	+	0.459973i	$0.847859\pi$
$462$	1.16653e13	−	1.19630e13i	0.554225	−	0.568369i
$463$	2.16907e13			1.01945			0.509727	−	0.860336i	$-0.329746\pi$
$463$	2.16907e13			1.01945			0.509727	+	0.860336i	$0.329746\pi$
$464$	2.64989e12	+	4.58974e12i	0.123208	+	0.213402i
$465$	6.05119e13	+	3.49365e13i	2.78340	+	1.60700i
$466$	6.34913e12	−	1.09970e13i	0.288924	−	0.500432i
$467$	9.70919e12	−	5.60560e12i	0.437118	−	0.252370i	−0.265256	−	0.964178i	$-0.585457\pi$
$467$	9.70919e12	−	5.60560e12i	0.437118	−	0.252370i	0.702374	+	0.711808i	$0.252123\pi$
$468$		−	1.17321e13i		−	0.522573i
$469$	2.00938e13	+	1.95938e13i	0.885519	+	0.863484i
$470$	−2.20104e13			−0.959706
$471$	9.45008e12	+	1.63680e13i	0.407691	+	0.706141i
$472$	−3.49034e12	−	2.01515e12i	−0.148990	−	0.0860195i
$473$	1.64722e13	−	2.85307e13i	0.695739	−	1.20506i
$474$	1.85207e12	−	1.06929e12i	0.0774043	−	0.0446894i
$475$			1.20891e13i			0.499948i
$476$	4.51220e12	+	1.60292e13i	0.184652	+	0.655961i
$477$	−1.32765e13			−0.537641
$478$	1.30337e13	+	2.25750e13i	0.522309	+	0.904666i
$479$	−1.04240e13	−	6.01830e12i	−0.413387	−	0.238669i	0.278857	−	0.960333i	$-0.410044\pi$
$479$	−1.04240e13	−	6.01830e12i	−0.413387	−	0.238669i	−0.692244	+	0.721664i	$0.743378\pi$
$480$	−3.88928e12	+	6.73643e12i	−0.152638	+	0.264377i
$481$	−1.71234e13	+	9.88617e12i	−0.665064	+	0.383975i
$482$		−	7.49002e12i		−	0.287904i
$483$	3.37478e13	+	8.58852e12i	1.28384	+	0.326725i
$484$	−5.29771e12			−0.199462
$485$	−2.24015e13	−	3.88006e13i	−0.834774	−	1.44587i
$486$	2.38171e13	+	1.37508e13i	0.878432	+	0.507163i
$487$	−6.60665e12	+	1.14431e13i	−0.241178	+	0.417732i	−0.961050	−	0.276375i	$-0.910867\pi$
$487$	−6.60665e12	+	1.14431e13i	−0.241178	+	0.417732i	0.719872	+	0.694106i	$0.244200\pi$
$488$	2.66233e12	−	1.53709e12i	0.0961971	−	0.0555394i
$489$		−	3.93071e12i		−	0.140581i
$490$	−1.24259e13	−	2.03221e13i	−0.439893	−	0.719428i
$491$	2.30249e12			0.0806844			0.0403422	−	0.999186i	$-0.487155\pi$
$491$	2.30249e12			0.0806844			0.0403422	+	0.999186i	$0.487155\pi$
$492$	−7.92744e12	−	1.37307e13i	−0.274984	−	0.476286i
$493$	−3.38813e13	−	1.95614e13i	−1.16339	−	0.671684i
$494$	−1.17362e13	+	2.03277e13i	−0.398926	+	0.690960i
$495$	−2.61023e13	+	1.50701e13i	−0.878319	+	0.507097i
$496$		−	1.39677e13i		−	0.465283i
$497$	4.34656e12	−	1.70794e13i	0.143339	−	0.563237i
$498$	−1.79519e13			−0.586090
$499$	−2.00988e13	−	3.48122e13i	−0.649632	−	1.12520i	−0.983211	−	0.182474i	$-0.941589\pi$
$499$	−2.00988e13	−	3.48122e13i	−0.649632	−	1.12520i	0.333578	−	0.942722i	$-0.391744\pi$
$500$	9.32458e12	+	5.38355e12i	0.298387	+	0.172274i
$501$	−2.77162e13	+	4.80058e13i	−0.878101	+	1.52092i
$502$	−1.55687e13	+	8.98859e12i	−0.488353	+	0.281951i
$503$			3.47129e13i			1.07808i	0.842280	+	0.539041i	$0.181213\pi$
$503$			3.47129e13i			1.07808i	−0.842280	+	0.539041i	$0.818787\pi$
$504$	1.21403e13	−	3.41748e12i	0.373317	−	0.105088i
$505$	−7.10276e10			−0.00216257
$506$	8.31794e12	+	1.44071e13i	0.250763	+	0.434334i
$507$	−3.87347e12	−	2.23635e12i	−0.115627	−	0.0667574i
$508$	4.01292e12	−	6.95058e12i	0.118616	−	0.205448i
$509$	−1.23800e13	+	7.14762e12i	−0.362354	+	0.209205i	−0.670113	−	0.742259i	$-0.733754\pi$
$509$	−1.23800e13	+	7.14762e12i	−0.362354	+	0.209205i	0.307759	+	0.951464i	$0.400421\pi$
$510$		−	5.74211e13i		−	1.66426i
$511$	2.83712e13	−	2.90952e13i	0.814279	−	0.835059i
$512$	1.55494e12			0.0441942
$513$	2.95314e12	+	5.11499e12i	0.0831185	+	0.143965i
$514$	−1.22691e13	−	7.08358e12i	−0.341978	−	0.197441i
$515$	1.00118e13	−	1.73409e13i	0.276360	−	0.478670i
$516$	4.11675e13	−	2.37680e13i	1.12540	−	0.649748i
$517$			3.25908e13i			0.882353i
$518$	−1.52181e13	−	1.48394e13i	−0.408048	−	0.397894i
$519$	3.55672e13			0.944525
$520$	−7.63680e12	−	1.32273e13i	−0.200861	−	0.347901i
$521$	−5.44150e13	−	3.14165e13i	−1.41752	−	0.818406i	−0.421441	−	0.906856i	$-0.638475\pi$
$521$	−5.44150e13	−	3.14165e13i	−1.41752	−	0.818406i	−0.996081	+	0.0884495i	$0.971809\pi$
$522$	−1.48155e13	+	2.56612e13i	−0.382265	+	0.662102i
$523$	2.98496e13	−	1.72337e13i	0.762834	−	0.440422i	−0.0674785	−	0.997721i	$-0.521495\pi$
$523$	2.98496e13	−	1.72337e13i	0.762834	−	0.440422i	0.830312	+	0.557298i	$0.188162\pi$
$524$		−	1.68808e13i		−	0.427304i
$525$	6.60675e12	+	2.34700e13i	0.165650	+	0.588459i
$526$	3.49202e13			0.867257
$527$	5.15547e13	+	8.92953e13i	1.26828	+	2.19672i
$528$	9.97464e12	+	5.75886e12i	0.243068	+	0.140335i
$529$	3.37776e12	−	5.85046e12i	0.0815363	−	0.141225i
$530$	−1.49686e13	+	8.64212e12i	−0.357933	+	0.206653i
$531$		−	2.25334e13i		−	0.533770i
$532$	−2.44536e13	−	6.22324e12i	−0.573833	−	0.146035i
$533$	3.11319e13			0.723718
$534$	−3.11686e13	−	5.39855e13i	−0.717812	−	1.24329i
$535$	−4.87288e13	−	2.81336e13i	−1.11177	−	0.641883i
$536$	−9.67295e12	+	1.67540e13i	−0.218643	+	0.378700i
$537$	−6.47564e13	+	3.73871e13i	−1.45014	+	0.837241i
$538$			4.06758e13i			0.902454i
$539$	−3.00909e13	+	1.83990e13i	−0.661442	+	0.404438i
$540$	−3.84326e12			−0.0837010
$541$	−1.02819e12	−	1.78088e12i	−0.0221865	−	0.0384281i	0.854719	−	0.519091i	$-0.173729\pi$
$541$	−1.02819e12	−	1.78088e12i	−0.0221865	−	0.0384281i	−0.876905	+	0.480663i	$0.840396\pi$
$542$	−1.62949e13	−	9.40789e12i	−0.348383	−	0.201139i
$543$	1.29496e13	−	2.24293e13i	0.274319	−	0.475134i
$544$	−9.94072e12	+	5.73927e12i	−0.208652	+	0.120465i
$545$		−	5.36647e13i		−	1.11611i
$546$	−1.16757e13	+	4.58784e13i	−0.240613	+	0.945465i
$547$	5.01089e13			1.02324			0.511620	−	0.859212i	$-0.329045\pi$
$547$	5.01089e13			1.02324			0.511620	+	0.859212i	$0.329045\pi$
$548$	6.45447e12	+	1.11795e13i	0.130604	+	0.226213i
$549$	1.48851e13	+	8.59389e12i	0.298462	+	0.172317i
$550$	−5.82392e12	+	1.00873e13i	−0.115718	+	0.200430i
$551$	5.13403e13	−	2.96413e13i	1.01088	−	0.583633i
$552$			2.40042e13i			0.468373i
$553$	−4.34533e12	+	1.22320e12i	−0.0840228	+	0.0236523i
$554$	6.73207e13			1.29003
$555$	3.66472e13	+	6.34748e13i	0.695946	+	1.20541i
$556$	−1.67436e13	−	9.66695e12i	−0.315120	−	0.181935i
$557$	−1.21070e12	+	2.09700e12i	−0.0225819	+	0.0391130i	−0.877096	−	0.480316i	$-0.840522\pi$
$557$	−1.21070e12	+	2.09700e12i	−0.0225819	+	0.0391130i	0.854514	+	0.519429i	$0.173855\pi$
$558$	6.76310e13	−	3.90468e13i	1.25019	−	0.721796i
$559$			9.33396e13i			1.71004i
$560$	1.14630e13	−	1.17556e13i	0.208142	−	0.213453i
$561$	−8.50235e13			−1.53012
$562$	7.94306e12	+	1.37578e13i	0.141679	+	0.245396i
$563$	3.35694e13	+	1.93813e13i	0.593475	+	0.342643i	0.766470	−	0.642280i	$-0.222011\pi$
$563$	3.35694e13	+	1.93813e13i	0.593475	+	0.342643i	−0.172996	+	0.984923i	$0.555345\pi$
$564$	−2.35129e13	+	4.07256e13i	−0.412013	+	0.713627i
$565$	3.80129e12	−	2.19468e12i	0.0660220	−	0.0381178i
$566$		−	2.67702e12i		−	0.0460861i
$567$	−3.74954e13	−	3.65624e13i	−0.639827	−	0.623906i
$568$	1.21483e13			0.205482
$569$	−2.09865e13	−	3.63498e13i	−0.351868	−	0.609453i	0.634709	−	0.772751i	$-0.281120\pi$
$569$	−2.09865e13	−	3.63498e13i	−0.351868	−	0.609453i	−0.986577	+	0.163298i	$0.947787\pi$
$570$	7.53529e13	+	4.35050e13i	1.25235	+	0.723045i
$571$	4.34451e13	−	7.52491e13i	0.715748	−	1.23971i	−0.246922	−	0.969035i	$-0.579419\pi$
$571$	4.34451e13	−	7.52491e13i	0.715748	−	1.23971i	0.962670	−	0.270677i	$-0.0872476\pi$
$572$	−1.95857e13	+	1.13078e13i	−0.319860	+	0.184671i
$573$		−	1.52564e14i		−	2.46990i
$574$	9.06850e12	+	3.22151e13i	0.145538	+	0.517012i
$575$	−2.42754e13			−0.386213
$576$	4.34685e12	+	7.52896e12i	0.0685586	+	0.118747i
$577$	6.44420e13	+	3.72056e13i	1.00760	+	0.581741i	0.910489	−	0.413533i	$-0.135705\pi$
$577$	6.44420e13	+	3.72056e13i	1.00760	+	0.581741i	0.0971150	+	0.995273i	$0.469039\pi$
$578$	1.95588e13	−	3.38768e13i	0.303181	−	0.525126i
$579$	5.82553e13	−	3.36337e13i	0.895247	−	0.516871i
$580$			3.85756e13i			0.587722i
$581$	3.67232e13	+	9.34573e12i	0.554702	+	0.141167i
$582$	−9.57231e13			−1.43351
$583$	1.27964e13	+	2.21640e13i	0.189996	+	0.329083i
$584$	2.42593e13	+	1.40061e13i	0.357120	+	0.206184i
$585$	4.26974e13	−	7.39540e13i	0.623192	−	1.07940i
$586$	2.43917e13	−	1.40826e13i	0.352983	−	0.203795i
$587$		−	3.95333e13i		−	0.567248i	−0.958936	−	0.283624i	$-0.908463\pi$
$587$		−	3.95333e13i		−	0.567248i	0.958936	−	0.283624i	$-0.0915368\pi$
$588$	−5.08758e13	+	1.28214e12i	−0.723811	+	0.0182410i
$589$	−1.56241e14			−2.20404
$590$	−1.46677e13	−	2.54052e13i	−0.205164	−	0.355355i
$591$	−1.38188e14	−	7.97827e13i	−1.91660	−	1.10655i
$592$	7.32582e12	−	1.26887e13i	0.100751	−	0.174505i
$593$	4.89463e13	−	2.82592e13i	0.667493	−	0.385377i	−0.127633	−	0.991821i	$-0.540738\pi$
$593$	4.89463e13	−	2.82592e13i	0.667493	−	0.385377i	0.795126	+	0.606444i	$0.207405\pi$
$594$			5.69072e12i			0.0769546i
$595$	−2.98933e13	+	1.17463e14i	−0.400856	+	1.57513i
$596$	3.30388e12			0.0439333
$597$	5.37609e13	+	9.31167e13i	0.708917	+	1.22788i
$598$	−4.08188e13	−	2.35667e13i	−0.533770	−	0.308172i
$599$	−6.65661e13	+	1.15296e14i	−0.863215	+	1.49513i	0.00559444	+	0.999984i	$0.498219\pi$
$599$	−6.65661e13	+	1.15296e14i	−0.863215	+	1.49513i	−0.868809	+	0.495147i	$0.835114\pi$
$600$	−1.45552e13	+	8.40343e12i	−0.187181	+	0.108069i
$601$			1.04422e14i			1.33174i	0.746066	+	0.665872i	$0.231940\pi$
$601$			1.04422e14i			1.33174i	−0.746066	+	0.665872i	$0.768060\pi$
$602$	−9.65874e13	+	2.71892e13i	−1.22162	+	0.343885i
$603$	−1.08163e14			−1.35673
$604$	2.46059e13	+	4.26187e13i	0.306094	+	0.530170i
$605$	−3.33944e13	−	1.92803e13i	−0.412000	−	0.237868i
$606$	−7.58762e10	+	1.31422e11i	−0.000928416	+	0.00160806i
$607$	−1.94634e13	+	1.12372e13i	−0.236198	+	0.136369i	−0.613428	−	0.789751i	$-0.710210\pi$
$607$	−1.94634e13	+	1.12372e13i	−0.236198	+	0.136369i	0.377230	+	0.926119i	$0.376877\pi$
$608$		−	1.73934e13i		−	0.209347i
$609$	8.34739e13	−	8.56041e13i	0.996470	−	1.02190i
$610$	2.23762e13			0.264933
$611$	−4.61688e13	−	7.99668e13i	−0.542179	−	0.939082i
$612$	−5.55785e13	−	3.20883e13i	−0.647366	−	0.373757i
$613$	1.91975e12	−	3.32511e12i	0.0221791	−	0.0384153i	−0.854723	−	0.519085i	$-0.826273\pi$
$613$	1.91975e12	−	3.32511e12i	0.0221791	−	0.0384153i	0.876902	+	0.480669i	$0.159606\pi$
$614$	6.18065e13	−	3.56840e13i	0.708259	−	0.408914i
$615$		−	1.15403e14i		−	1.31172i
$616$	−1.74065e13	−	1.69733e13i	−0.196249	−	0.191366i
$617$	−5.26203e12			−0.0588474			−0.0294237	−	0.999567i	$-0.509367\pi$
$617$	−5.26203e12			−0.0588474			−0.0294237	+	0.999567i	$0.509367\pi$
$618$	−2.13905e13	−	3.70494e13i	−0.237289	−	0.410997i
$619$	4.63233e13	+	2.67448e13i	0.509737	+	0.294297i	0.732726	−	0.680524i	$-0.238248\pi$
$619$	4.63233e13	+	2.67448e13i	0.509737	+	0.294297i	−0.222989	+	0.974821i	$0.571581\pi$
$620$	5.08336e13	−	8.80464e13i	0.554871	−	0.961065i
$621$	−1.02711e13	+	5.93004e12i	−0.111214	+	0.0642095i
$622$		−	5.80544e13i		−	0.623567i
$623$	3.56549e13	+	1.26661e14i	0.379909	+	1.34960i
$624$	−3.26325e13			−0.344927
$625$	5.93158e13	+	1.02738e14i	0.621971	+	1.07729i
$626$	9.74734e12	+	5.62763e12i	0.101395	+	0.0585402i
$627$	6.44180e13	−	1.11575e14i	0.664767	−	1.15141i
$628$	2.38159e13	−	1.37501e13i	0.243820	−	0.140769i
$629$			1.08158e14i			1.09851i
$630$	8.89647e13	+	2.26407e13i	0.896427	+	0.228133i
$631$	−7.88490e13			−0.788224			−0.394112	−	0.919062i	$-0.628948\pi$
$631$	−7.88490e13			−0.788224			−0.394112	+	0.919062i	$0.628948\pi$
$632$	−1.55585e12	−	2.69481e12i	−0.0154306	−	0.0267265i
$633$	1.01004e14	+	5.83150e13i	0.993853	+	0.573801i
$634$	−4.91578e12	+	8.51439e12i	−0.0479895	+	0.0831203i
$635$	5.05913e13	−	2.92089e13i	0.490013	−	0.282909i
$636$			3.69283e13i			0.354873i
$637$	4.77684e13	−	8.77724e13i	0.455453	−	0.836876i
$638$	5.71189e13			0.540352
$639$	3.39605e13	+	5.88213e13i	0.318764	+	0.552116i
$640$	9.80168e12	+	5.65900e12i	0.0912853	+	0.0527036i
$641$	−7.62218e13	+	1.32020e14i	−0.704351	+	1.21997i	0.262575	+	0.964912i	$0.415428\pi$
$641$	−7.62218e13	+	1.32020e14i	−0.704351	+	1.21997i	−0.966925	+	0.255059i	$0.917905\pi$
$642$	−1.04110e14	+	6.01082e13i	−0.954595	+	0.551136i
$643$		−	3.79024e13i		−	0.344836i	−0.985024	−	0.172418i	$-0.944842\pi$
$643$		−	3.79024e13i		−	0.344836i	0.985024	−	0.172418i	$-0.0551579\pi$
$644$	1.24965e13	−	4.91039e13i	0.112813	−	0.443289i
$645$	3.46002e14			3.09942
$646$	6.41989e13	+	1.11196e14i	0.570643	+	0.988383i
$647$	−5.24193e12	−	3.02643e12i	−0.0462349	−	0.0266937i	0.476704	−	0.879064i	$-0.341831\pi$
$647$	−5.24193e12	−	3.02643e12i	−0.0462349	−	0.0266937i	−0.522939	+	0.852370i	$0.675165\pi$
$648$	1.80499e13	−	3.12634e13i	0.157979	−	0.273628i
$649$	−3.76175e13	+	2.17185e13i	−0.326713	+	0.188628i
$650$		−	3.30012e13i		−	0.284421i
$651$	−3.03330e14	+	8.53869e13i	−2.59424	+	0.730275i
$652$	−5.71928e12			−0.0485404
$653$	−1.03099e14	−	1.78573e14i	−0.868338	−	1.50401i	−0.863694	−	0.504017i	$-0.831855\pi$
$653$	−1.03099e14	−	1.78573e14i	−0.868338	−	1.50401i	−0.00464465	−	0.999989i	$-0.501478\pi$
$654$	−9.92953e13	−	5.73282e13i	−0.829927	−	0.479159i
$655$	6.14353e13	−	1.06409e14i	0.509579	−	0.882617i
$656$	−1.99786e13	+	1.15346e13i	−0.164454	+	0.0949477i
$657$			1.56617e14i			1.27941i
$658$	6.93006e13	−	7.10691e13i	0.561833	−	0.576171i
$659$	−2.38586e13			−0.191963			−0.0959814	−	0.995383i	$-0.530599\pi$
$659$	−2.38586e13			−0.191963			−0.0959814	+	0.995383i	$0.530599\pi$
$660$	4.19172e13	+	7.26027e13i	0.334713	+	0.579739i
$661$	−7.59935e13	−	4.38749e13i	−0.602240	−	0.347703i	0.167683	−	0.985841i	$-0.446372\pi$
$661$	−7.59935e13	−	4.38749e13i	−0.602240	−	0.347703i	−0.769922	+	0.638138i	$0.779705\pi$
$662$	1.06048e13	−	1.83680e13i	0.0834087	−	0.144468i
$663$	2.08619e14	−	1.20446e14i	1.62849	−	0.940210i
$664$			2.61205e13i			0.202368i
$665$	−1.31496e14	−	1.28224e14i	−1.01113	−	0.985965i
$666$	8.19174e13			0.625180
$667$	5.95210e13	+	1.03093e14i	0.450859	+	0.780911i
$668$	6.98498e13	+	4.03278e13i	0.525149	+	0.303195i
$669$	−1.44267e14	+	2.49878e14i	−1.07656	+	1.86465i
$670$	−1.21948e14	+	7.04067e13i	−0.903235	+	0.521483i
$671$		−	3.31324e13i		−	0.243580i
$672$	−9.50562e12	−	3.37680e13i	−0.0693640	−	0.246410i
$673$	1.89893e14			1.37541			0.687707	−	0.725989i	$-0.258618\pi$
$673$	1.89893e14			1.37541			0.687707	+	0.725989i	$0.258618\pi$
$674$	−5.61713e13	−	9.72916e13i	−0.403845	−	0.699481i
$675$	−7.19147e12	−	4.15200e12i	−0.0513214	−	0.0296304i
$676$	−3.25394e12	+	5.63600e12i	−0.0230503	+	0.0399243i
$677$	−2.98291e12	+	1.72219e12i	−0.0209748	+	0.0121098i	−0.510451	−	0.859907i	$-0.670521\pi$
$677$	−2.98291e12	+	1.72219e12i	−0.0209748	+	0.0121098i	0.489476	+	0.872017i	$0.337188\pi$
$678$		−	9.37798e12i		−	0.0654577i
$679$	1.95815e14	+	4.98332e13i	1.35674	+	0.345279i
$680$	−8.35492e13			−0.574642
$681$	−5.35323e13	−	9.27206e13i	−0.365494	−	0.633054i
$682$	−1.30370e14	−	7.52694e13i	−0.883603	−	0.510149i
$683$	−1.16220e14	+	2.01299e14i	−0.781948	+	1.35437i	0.148857	+	0.988859i	$0.452440\pi$
$683$	−1.16220e14	+	2.01299e14i	−0.781948	+	1.35437i	−0.930805	+	0.365515i	$0.880893\pi$
$684$	8.42181e13	−	4.86233e13i	0.562503	−	0.324761i
$685$			9.39605e13i			0.623007i
$686$	1.04741e14	+	2.38630e13i	0.689440	+	0.157074i
$687$	1.38050e14			0.902094
$688$	−3.45831e13	−	5.98997e13i	−0.224348	−	0.388582i
$689$	−6.27960e13	−	3.62553e13i	−0.404423	−	0.233494i
$690$	−8.73599e13	+	1.51312e14i	−0.558556	+	0.967447i
$691$	−1.59678e14	+	9.21899e13i	−1.01357	+	0.585185i	−0.912235	−	0.409668i	$-0.865645\pi$
$691$	−1.59678e14	+	9.21899e13i	−1.01357	+	0.585185i	−0.101335	+	0.994852i	$0.532311\pi$
$692$		−	5.17513e13i		−	0.326130i
$693$	3.35242e13	−	1.31730e14i	0.209745	−	0.824175i
$694$	−1.35415e14			−0.841142
$695$	−7.03630e13	−	1.21872e14i	−0.433931	−	0.751590i
$696$	7.13759e13	+	4.12089e13i	0.437024	+	0.252316i
$697$	8.51483e13	−	1.47481e14i	0.517621	−	0.896546i
$698$	2.28306e13	−	1.31813e13i	0.137797	−	0.0795574i
$699$		−	1.97473e14i		−	1.18337i
$700$	3.41494e13	−	9.61300e12i	0.203186	−	0.0571964i
$701$	−2.53830e12			−0.0149952			−0.00749761	−	0.999972i	$-0.502387\pi$
$701$	−2.53830e12			−0.0149952			−0.00749761	+	0.999972i	$0.502387\pi$
$702$	−8.06159e12	−	1.39631e13i	−0.0472863	−	0.0819023i
$703$	−1.41934e14	−	8.19458e13i	−0.826629	−	0.477255i
$704$	8.37930e12	−	1.45134e13i	0.0484557	−	0.0839276i
$705$	−2.96430e14	+	1.71144e14i	−1.70207	+	0.982689i
$706$			6.04615e13i			0.344711i
$707$	2.23633e11	−	2.29340e11i	0.00126602	−	0.00129832i
$708$	−6.26760e13			−0.352318
$709$	−1.69619e14	−	2.93788e14i	−0.946765	−	1.63985i	−0.752178	−	0.658960i	$-0.770997\pi$
$709$	−1.69619e14	−	2.93788e14i	−0.946765	−	1.63985i	−0.194587	−	0.980885i	$-0.562337\pi$
$710$	7.65773e13	+	4.42120e13i	0.424432	+	0.245046i
$711$	8.69874e12	−	1.50667e13i	0.0478750	−	0.0829219i
$712$	−7.85504e13	+	4.53511e13i	−0.429288	+	0.247849i
$713$		−	3.13739e14i		−	1.70263i
$714$	1.85406e14	+	1.80793e14i	0.999156	+	0.974293i
$715$	−1.64613e14			−0.880916
$716$	5.43992e13	+	9.42222e13i	0.289086	+	0.500712i
$717$	3.51068e14	+	2.02689e14i	1.85266	+	1.06963i
$718$	1.09226e13	−	1.89185e13i	0.0572405	−	0.0991434i
$719$	−1.34933e14	+	7.79036e13i	−0.702220	+	0.405427i	−0.808174	−	0.588944i	$-0.799544\pi$
$719$	−1.34933e14	+	7.79036e13i	−0.702220	+	0.405427i	0.105953	+	0.994371i	$0.466211\pi$
$720$			6.32790e13i			0.327037i
$721$	2.44694e13	+	8.69255e13i	0.125588	+	0.446140i
$722$	−5.58307e13			−0.284569
$723$	−5.82394e13	−	1.00874e14i	−0.294799	−	0.510606i
$724$	−3.26352e13	−	1.88419e13i	−0.164057	−	0.0947181i
$725$	−4.16745e13	+	7.21823e13i	−0.208056	+	0.360363i
$726$	−7.13481e13	+	4.11929e13i	−0.353752	+	0.204239i
$727$		−	2.39410e14i		−	1.17888i	−0.807812	−	0.589440i	$-0.799348\pi$
$727$		−	2.39410e14i		−	1.17888i	0.807812	−	0.589440i	$-0.200652\pi$
$728$	6.67544e13	+	1.69884e13i	0.326455	+	0.0830799i
$729$	2.43686e14			1.18357
$730$	1.01947e14	+	1.76577e14i	0.491767	+	0.851765i
$731$	4.42178e14	+	2.55292e14i	2.11841	+	1.22307i
$732$	2.39037e13	−	4.14024e13i	0.113739	−	0.197002i
$733$	2.48309e14	−	1.43361e14i	1.17347	−	0.677504i	0.218976	−	0.975730i	$-0.429728\pi$
$733$	2.48309e14	−	1.43361e14i	1.17347	−	0.677504i	0.954495	+	0.298227i	$0.0963952\pi$
$734$			1.34488e14i			0.631251i
$735$	−3.25365e14	−	1.77073e14i	−1.51682	−	0.825499i
$736$	3.49267e13			0.161722
$737$	1.04251e14	+	1.80569e14i	0.479451	+	0.830434i
$738$	−1.11700e14	−	6.44901e13i	−0.510237	−	0.294586i
$739$	1.71579e14	−	2.97183e14i	0.778470	−	1.34835i	−0.154354	−	0.988016i	$-0.549330\pi$
$739$	1.71579e14	−	2.97183e14i	0.778470	−	1.34835i	0.932824	−	0.360334i	$-0.117337\pi$
$740$	9.23575e13	−	5.33226e13i	0.416211	−	0.240300i
$741$			3.65024e14i			1.63392i
$742$	1.92248e13	−	7.55420e13i	0.0854755	−	0.335868i
$743$	−1.82367e14			−0.805382			−0.402691	−	0.915336i	$-0.631925\pi$
$743$	−1.82367e14			−0.805382			−0.402691	+	0.915336i	$0.631925\pi$
$744$	−1.08607e14	−	1.88114e14i	−0.476426	−	0.825193i
$745$	2.08262e13	+	1.20240e13i	0.0907463	+	0.0523924i
$746$	8.45162e13	−	1.46386e14i	0.365802	−	0.633587i
$747$	−1.26474e14	+	7.30199e13i	−0.543750	+	0.313934i
$748$			1.23711e14i			0.528326i
$749$	2.44265e14	−	6.87600e13i	1.03622	−	0.291694i
$750$	1.67441e14			0.705596
$751$	5.58913e12	+	9.68066e12i	0.0233962	+	0.0405234i	0.877486	−	0.479601i	$-0.159219\pi$
$751$	5.58913e12	+	9.68066e12i	0.0233962	+	0.0405234i	−0.854090	+	0.520125i	$0.825885\pi$
$752$	5.92568e13	+	3.42119e13i	0.246405	+	0.142262i
$753$	−1.39783e14	+	2.42112e14i	−0.577406	+	1.00010i
$754$	−1.40150e14	+	8.09159e13i	−0.575092	+	0.332030i
$755$			3.58199e14i			1.46012i
$756$	1.21006e13	−	1.24094e13i	0.0490004	−	0.0502508i
$757$	3.01594e13			0.121323			0.0606614	−	0.998158i	$-0.480679\pi$
$757$	3.01594e13			0.121323			0.0606614	+	0.998158i	$0.480679\pi$
$758$	2.18121e12	+	3.77797e12i	0.00871669	+	0.0150978i
$759$	2.24048e14	+	1.29354e14i	0.889471	+	0.513536i
$760$	6.33010e13	−	1.09640e14i	0.249656	−	0.432417i
$761$	−3.79343e14	+	2.19014e14i	−1.48631	+	0.858120i	−0.999878	−	0.0156001i	$-0.995034\pi$
$761$	−3.79343e14	+	2.19014e14i	−1.48631	+	0.858120i	−0.486429	+	0.873720i	$0.661701\pi$
$762$		−	1.24811e14i		−	0.485825i
$763$	1.73277e14	+	1.68966e14i	0.670069	+	0.653395i
$764$	−2.21985e14			−0.852818
$765$	−2.33562e14	−	4.04541e14i	−0.891445	−	1.54403i
$766$	−1.05166e14	−	6.07179e13i	−0.398780	−	0.230236i
$767$	6.15338e13	−	1.06580e14i	0.231812	−	0.401511i
$768$	2.09416e13	−	1.20906e13i	0.0783797	−	0.0452525i
$769$			1.06046e14i			0.394333i	0.980370	+	0.197167i	$0.0631740\pi$
$769$			1.06046e14i			0.394333i	−0.980370	+	0.197167i	$0.936826\pi$
$770$	−4.79506e13	−	1.70341e14i	−0.177150	−	0.629311i
$771$	−2.20316e14			−0.808677
$772$	−4.89380e13	−	8.47631e13i	−0.178468	−	0.309115i
$773$	4.12393e14	+	2.38095e14i	1.49422	+	0.862687i	0.999978	−	0.00663852i	$-0.00211312\pi$
$773$	4.12393e14	+	2.38095e14i	1.49422	+	0.862687i	0.494240	+	0.869326i	$0.335446\pi$
$774$	1.93354e14	−	3.34900e14i	0.696064	−	1.20562i
$775$	1.90239e14	−	1.09834e14i	0.680441	−	0.392853i
$776$			1.39280e14i			0.494970i
$777$	−3.20338e14	−	8.15233e13i	−1.13111	−	0.287857i
$778$	1.73993e14			0.610426
$779$	1.29025e14	+	2.23478e14i	0.449766	+	0.779018i
$780$	−2.05701e14	−	1.18761e14i	−0.712465	−	0.411342i
$781$	6.54647e13	−	1.13388e14i	0.225295	−	0.390223i
$782$	−2.23286e14	+	1.28914e14i	−0.763532	+	0.440825i
$783$			4.07213e13i			0.138361i
$784$	1.86555e12	+	7.40257e13i	0.00629835	+	0.249921i
$785$	2.00167e14			0.671496
$786$	−1.31258e14	−	2.27346e14i	−0.437537	−	0.757836i
$787$	−4.21202e14	−	2.43181e14i	−1.39514	−	0.805482i	−0.401258	−	0.915965i	$-0.631427\pi$
$787$	−4.21202e14	−	2.43181e14i	−1.39514	−	0.805482i	−0.993878	+	0.110483i	$0.964760\pi$
$788$	−1.16086e14	+	2.01067e14i	−0.382075	+	0.661773i
$789$	4.70296e14	−	2.71526e14i	1.53811	−	0.888026i
$790$		−	2.26492e13i		−	0.0736066i
$791$	−4.88215e12	+	1.91840e13i	−0.0157663	+	0.0619521i
$792$	9.36973e13			0.300678
$793$	4.69361e13	+	8.12957e13i	0.149672	+	0.259240i
$794$	1.24808e14	+	7.20581e13i	0.395495	+	0.228339i
$795$	−1.34395e14	+	2.32780e14i	−0.423203	+	0.733009i
$796$	1.35487e14	−	7.82236e13i	0.423968	−	0.244778i
$797$		−	3.41848e14i		−	1.06302i	−0.847052	−	0.531510i	$-0.821625\pi$
$797$		−	3.41848e14i		−	1.06302i	0.847052	−	0.531510i	$-0.178375\pi$
$798$	−3.77725e14	+	1.06329e14i	−1.16724	+	0.328576i
$799$	−5.05103e14			−1.55112
$800$	1.22272e13	+	2.11782e13i	0.0373145	+	0.0646306i
$801$	−4.39175e14	−	2.53558e14i	−1.33191	−	0.768979i
$802$	1.34133e14	−	2.32324e14i	0.404261	−	0.700201i
$803$	2.61458e14	−	1.50953e14i	0.783112	−	0.452130i
$804$			3.00852e14i			0.895515i
$805$	2.57479e14	−	2.64050e14i	0.761664	−	0.781100i
$806$	4.26513e14			1.25388
$807$	3.16279e14	+	5.47811e14i	0.924065	+	1.60053i
$808$	1.91222e11	+	1.10402e11i	0.000555240	+	0.000320568i
$809$	−2.89752e14	+	5.01865e14i	−0.836149	+	1.44825i	0.0569423	+	0.998377i	$0.481865\pi$
$809$	−2.89752e14	+	5.01865e14i	−0.836149	+	1.44825i	−0.893091	+	0.449875i	$0.851468\pi$
$810$	2.27557e14	−	1.31380e14i	0.652628	−	0.376795i
$811$		−	4.12673e14i		−	1.17626i	−0.808768	−	0.588128i	$-0.799865\pi$
$811$		−	4.12673e14i		−	1.17626i	0.808768	−	0.588128i	$-0.200135\pi$
$812$	−1.24556e14	−	1.21457e14i	−0.352846	−	0.344066i
$813$	−2.92608e14			−0.823822
$814$	−7.89550e13	−	1.36754e14i	−0.220931	−	0.382664i
$815$	−3.60518e13	−	2.08145e13i	−0.100263	−	0.0578867i
$816$	−8.92526e13	+	1.54590e14i	−0.246701	+	0.427298i
$817$	−6.70032e14	+	3.86843e14i	−1.84071	+	1.06273i
$818$		−	1.19765e14i		−	0.327013i
$819$	1.04355e14	+	3.70712e14i	0.283200	+	1.00605i
$820$	−1.67915e14			−0.452918
$821$	−3.30677e14	−	5.72750e14i	−0.886520	−	1.53550i	−0.843962	−	0.536403i	$-0.819783\pi$
$821$	−3.30677e14	−	5.72750e14i	−0.886520	−	1.53550i	−0.0425575	−	0.999094i	$-0.513551\pi$
$822$	1.73854e14	+	1.00375e14i	0.463261	+	0.267464i
$823$	−2.42074e14	+	4.19284e14i	−0.641134	+	1.11048i	0.344046	+	0.938953i	$0.388202\pi$
$823$	−2.42074e14	+	4.19284e14i	−0.641134	+	1.11048i	−0.985180	+	0.171524i	$0.945131\pi$
$824$	−5.39078e13	+	3.11237e13i	−0.141911	+	0.0819323i
$825$			1.81138e14i			0.473958i
$826$	1.28212e14	+	3.26290e13i	0.333449	+	0.0848600i
$827$	1.39654e14			0.361014			0.180507	−	0.983574i	$-0.442226\pi$
$827$	1.39654e14			0.361014			0.180507	+	0.983574i	$0.442226\pi$
$828$	9.76377e13	+	1.69113e14i	0.250880	+	0.434537i
$829$	−3.35282e14	−	1.93575e14i	−0.856324	−	0.494399i	0.00645578	−	0.999979i	$-0.497945\pi$
$829$	−3.35282e14	−	1.93575e14i	−0.856324	−	0.494399i	−0.862779	+	0.505580i	$0.831278\pi$
$830$	−9.50620e13	+	1.64652e14i	−0.241333	+	0.418001i
$831$	9.06657e14	−	5.23459e14i	2.28790	−	1.32092i
$832$			4.74812e13i			0.119098i
$833$	−2.85154e14	−	4.66358e14i	−0.710975	−	1.16277i
$834$	−3.00665e14			−0.745166
$835$	2.93535e14	+	5.08417e14i	0.723148	+	1.25253i
$836$	−1.62345e14	−	9.37299e13i	−0.397564	−	0.229534i
$837$	5.36612e13	−	9.29438e13i	0.130627	−	0.226252i
$838$	−1.34753e14	+	7.77996e13i	−0.326075	+	0.188260i
$839$		−	2.04031e14i		−	0.490778i	−0.969425	−	0.245389i	$-0.921084\pi$
$839$		−	2.04031e14i		−	0.490778i	0.969425	−	0.245389i	$-0.0789157\pi$
$840$	6.29746e13	−	2.47453e14i	0.150581	−	0.591692i
$841$	−1.19792e13			−0.0284738
$842$	2.11775e14	+	3.66806e14i	0.500397	+	0.866713i
$843$	2.13950e14	+	1.23524e14i	0.502545	+	0.290144i
$844$	8.48498e13	−	1.46964e14i	0.198125	−	0.343162i
$845$	−4.10229e13	+	2.36846e13i	−0.0952231	+	0.0549771i
$846$			3.82558e14i			0.882765i
$847$	1.67397e14	−	4.71221e13i	0.384000	−	0.108095i
$848$	5.37316e13			0.122532
$849$	−2.08154e13	−	3.60534e13i	−0.0471897	−	0.0817350i
$850$	−1.56336e14	−	9.02609e13i	−0.352343	−	0.203425i
$851$	1.64551e14	−	2.85010e14i	0.368682	−	0.638576i
$852$	1.63610e14	−	9.44602e13i	0.364428	−	0.210402i
$853$			3.93692e14i			0.871790i	0.899998	+	0.435895i	$0.143568\pi$
$853$			3.93692e14i			0.871790i	−0.899998	+	0.435895i	$0.856432\pi$
$854$	−7.04523e13	+	7.22501e13i	−0.155098	+	0.159056i
$855$	7.07832e14			1.54917
$856$	8.74590e13	+	1.51483e14i	0.190299	+	0.329607i
$857$	3.05786e14	+	1.76546e14i	0.661476	+	0.381903i	0.792839	−	0.609431i	$-0.208602\pi$
$857$	3.05786e14	+	1.76546e14i	0.661476	+	0.381903i	−0.131363	+	0.991334i	$0.541935\pi$
$858$	−1.75850e14	+	3.04582e14i	−0.378187	+	0.655040i
$859$	7.37596e14	−	4.25851e14i	1.57708	−	0.910526i	0.581812	−	0.813323i	$-0.302344\pi$
$859$	7.37596e14	−	4.25851e14i	1.57708	−	0.910526i	0.995265	−	0.0972023i	$-0.0309894\pi$
$860$		−	5.03442e14i		−	1.07018i
$861$	3.72624e14	+	3.63352e14i	0.787508	+	0.767912i
$862$	1.30300e14			0.273784
$863$	2.88794e14	+	5.00205e14i	0.603300	+	1.04495i	0.992318	+	0.123716i	$0.0394813\pi$
$863$	2.88794e14	+	5.00205e14i	0.603300	+	1.04495i	−0.389017	+	0.921230i	$0.627185\pi$
$864$	1.03469e13	+	5.97378e12i	0.0214902	+	0.0124074i
$865$	1.88342e14	−	3.26217e14i	0.388925	−	0.673637i
$866$	2.58384e14	−	1.49178e14i	0.530489	−	0.306278i
$867$		−	6.08325e14i		−	1.24177i
$868$	1.24240e14	+	4.41354e14i	0.252153	+	0.895753i
$869$	−3.35367e13			−0.0676739
$870$	2.99948e14	+	5.19526e14i	0.601797	+	1.04234i
$871$	−5.11595e14	−	2.95369e14i	−1.02055	−	0.589216i
$872$	−8.34140e13	+	1.44477e14i	−0.165446	+	0.286561i
$873$	−6.74385e14	+	3.89356e14i	−1.32995	+	0.767849i
$874$		−	3.90686e14i		−	0.766075i
$875$	−3.42525e14	−	8.71696e13i	−0.667808	−	0.169951i
$876$	4.35625e14			0.844485
$877$	3.62810e14	+	6.28406e14i	0.699329	+	1.21127i	0.968699	+	0.248237i	$0.0798512\pi$
$877$	3.62810e14	+	6.28406e14i	0.699329	+	1.21127i	−0.269370	+	0.963037i	$0.586815\pi$
$878$	−2.51311e14	−	1.45095e14i	−0.481658	−	0.278086i
$879$	2.19001e14	−	3.79320e14i	0.417351	−	0.722873i
$880$	1.05639e14	−	6.09906e13i	0.200175	−	0.115571i
$881$		−	6.29593e14i		−	1.18626i	−0.805106	−	0.593131i	$-0.797892\pi$
$881$		−	6.29593e14i		−	1.18626i	0.805106	−	0.593131i	$-0.202108\pi$
$882$	−3.53213e14	+	2.15972e14i	−0.661751	+	0.404626i
$883$	−1.82768e14			−0.340485			−0.170242	−	0.985402i	$-0.554455\pi$
$883$	−1.82768e14			−0.340485			−0.170242	+	0.985402i	$0.554455\pi$
$884$	−1.75252e14	−	3.03546e14i	−0.324640	−	0.562293i
$885$	−3.95082e14	−	2.28100e14i	−0.727730	−	0.420155i
$886$	−3.36725e13	+	5.83224e13i	−0.0616746	+	0.106824i
$887$	−7.93881e14	+	4.58348e14i	−1.44590	+	0.834789i	−0.998233	−	0.0594128i	$-0.981077\pi$
$887$	−7.93881e14	+	4.58348e14i	−1.44590	+	0.834789i	−0.447664	+	0.894202i	$0.647744\pi$
$888$		−	2.27851e14i		−	0.412654i
$889$	−6.49766e13	+	2.55319e14i	−0.117017	+	0.459806i
$890$	−6.60196e14			−1.18229
$891$	−1.94535e14	−	3.36945e14i	−0.346425	−	0.600026i
$892$	3.63579e14	+	2.09912e14i	0.643834	+	0.371718i
$893$	3.82691e14	−	6.62840e14i	0.673892	−	1.16722i
$894$	4.44958e13	−	2.56897e13i	0.0779169	−	0.0449853i
$895$			7.91914e14i			1.37899i
$896$	−4.91333e13	+	1.38309e13i	−0.0850816	+	0.0239503i
$897$	−7.32983e14			−1.26221
$898$	−2.77226e14	−	4.80169e14i	−0.474736	−	0.822266i
$899$	−9.32897e14	−	5.38608e14i	−1.58868	−	0.917222i
$900$	−6.83624e13	+	1.18407e14i	−0.115772	+	0.200523i
$901$	−3.43505e14	+	1.98323e14i	−0.578507	+	0.334001i
$902$			2.48632e14i			0.416413i
$903$	−1.08940e15	+	1.11720e15i	−1.81447	+	1.86077i
$904$	−1.36452e13			−0.0226015
$905$	−1.37145e14	−	2.37543e14i	−0.225911	−	0.391290i
$906$	6.62772e14	+	3.82651e14i	1.08573	+	0.626848i
$907$	3.34972e14	−	5.80189e14i	0.545723	−	0.945220i	−0.452838	−	0.891593i	$-0.649588\pi$
$907$	3.34972e14	−	5.80189e14i	0.545723	−	0.945220i	0.998561	−	0.0536272i	$-0.0170783\pi$
$908$	−1.34911e14	+	7.78909e13i	−0.218584	+	0.126199i
$909$			1.23451e12i			0.00198919i
$910$	3.58963e14	+	3.50031e14i	0.575232	+	0.560918i
$911$	7.75029e14			1.23517			0.617584	−	0.786505i	$-0.288111\pi$
$911$	7.75029e14			1.23517			0.617584	+	0.786505i	$0.288111\pi$
$912$	−1.35244e14	−	2.34250e14i	−0.214361	−	0.371284i
$913$	2.43801e14	+	1.40759e14i	0.384310	+	0.221881i
$914$	−3.94994e14	+	6.84150e14i	−0.619241	+	1.07256i
$915$	3.01356e14	−	1.73988e14i	0.469867	−	0.271278i
$916$		−	2.00866e14i		−	0.311479i
$917$	1.50152e14	+	5.33401e14i	0.231570	+	0.822636i
$918$	−8.81965e13			−0.135281
$919$	−1.68532e14	−	2.91905e14i	−0.257101	−	0.445312i	0.708363	−	0.705848i	$-0.249434\pi$
$919$	−1.68532e14	−	2.91905e14i	−0.257101	−	0.445312i	−0.965464	+	0.260536i	$0.916101\pi$
$920$	2.20163e14	+	1.27111e14i	0.334045	+	0.192861i
$921$	5.54929e14	−	9.61165e14i	0.837412	−	1.45044i
$922$	3.75346e14	−	2.16706e14i	0.563349	−	0.325250i
$923$			3.70955e14i			0.553749i
$924$	−3.66404e14	−	9.32466e13i	−0.544002	−	0.138444i
$925$	2.30425e14			0.340268
$926$	−2.45402e14	−	4.25049e14i	−0.360432	−	0.624286i
$927$	−3.01399e14	−	1.74013e14i	−0.440294	−	0.254204i
$928$	5.99601e13	−	1.03854e14i	0.0871209	−	0.150898i
$929$	9.17505e14	−	5.29721e14i	1.32596	−	0.765542i	0.341286	−	0.939960i	$-0.389138\pi$
$929$	9.17505e14	−	5.29721e14i	1.32596	−	0.765542i	0.984672	+	0.174418i	$0.0558042\pi$
$930$		−	1.58105e15i		−	2.27264i
$931$	8.28043e14	−	2.08678e13i	1.18387	−	0.0298352i
$932$	−2.87329e14			−0.408601
$933$	−4.51408e14	−	7.81862e14i	−0.638500	−	1.10591i
$934$	−2.19694e14	−	1.26840e14i	−0.309089	−	0.178453i
$935$	−4.50231e14	+	7.79822e14i	−0.630053	+	1.09128i
$936$	−2.29901e14	+	1.32734e14i	−0.320009	+	0.184757i
$937$			1.23782e15i			1.71380i	0.515485	+	0.856898i	$0.327612\pi$
$937$			1.23782e15i			1.71380i	−0.515485	+	0.856898i	$0.672388\pi$
$938$	1.56623e14	−	6.15435e14i	0.215695	−	0.847555i
$939$	1.75033e14			0.239768
$940$	2.49019e14	+	4.31314e14i	0.339307	+	0.587698i
$941$	8.66549e14	+	5.00302e14i	1.17448	+	0.678085i	0.954731	−	0.297472i	$-0.0961434\pi$
$941$	8.66549e14	+	5.00302e14i	1.17448	+	0.678085i	0.219747	+	0.975557i	$0.429477\pi$
$942$	2.13831e14	−	3.70366e14i	0.288281	−	0.499317i
$943$	−4.48753e14	+	2.59088e14i	−0.601796	+	0.347447i
$944$			9.11952e13i			0.121650i
$945$	1.21440e14	−	3.41850e13i	0.161139	−	0.0453604i
$946$	−7.45448e14			−0.983924
$947$	3.18915e14	+	5.52377e14i	0.418721	+	0.725247i	0.995811	−	0.0914340i	$-0.0291451\pi$
$947$	3.18915e14	+	5.52377e14i	0.418721	+	0.725247i	−0.577090	+	0.816681i	$0.695812\pi$
$948$	−4.19075e13	−	2.41953e13i	−0.0547331	−	0.0316002i
$949$	−4.27686e14	+	7.40774e14i	−0.555640	+	0.962397i
$950$	2.36896e14	−	1.36772e14i	0.306154	−	0.176758i
$951$			1.52893e14i			0.196555i
$952$	2.63058e14	−	2.69771e14i	0.336408	−	0.344993i
$953$	−5.71713e14			−0.727300			−0.363650	−	0.931536i	$-0.618470\pi$
$953$	−5.71713e14			−0.727300			−0.363650	+	0.931536i	$0.618470\pi$
$954$	1.50207e14	+	2.60166e14i	0.190085	+	0.329237i
$955$	−1.39929e15	−	8.07883e14i	−1.76154	−	1.01702i
$956$	2.94919e14	−	5.10814e14i	0.369328	−	0.639695i
$957$	7.69263e14	−	4.44134e14i	0.958330	−	0.553292i
$958$			2.72357e14i			0.337529i
$959$	−3.03388e14	−	2.95839e14i	−0.374029	−	0.364722i
$960$	1.76009e14			0.215863
$961$	1.00971e15	+	1.74886e15i	1.23191	+	2.13373i
$962$	3.87457e14	+	2.23699e14i	0.470271	+	0.271511i
$963$	−4.88983e14	+	8.46944e14i	−0.590422	+	1.02264i
$964$	−1.46774e14	+	8.47399e13i	−0.176305	+	0.101789i
$965$		−	7.12412e14i		−	0.851323i
$966$	−2.13513e14	−	7.58487e14i	−0.253827	−	0.901701i
$967$	4.33996e14			0.513279			0.256640	−	0.966507i	$-0.417385\pi$
$967$	4.33996e14			0.513279			0.256640	+	0.966507i	$0.417385\pi$
$968$	5.99367e13	+	1.03813e14i	0.0705206	+	0.122145i
$969$	1.72923e15	+	9.98370e14i	2.02411	+	1.16862i
$970$	−5.06889e14	+	8.77957e14i	−0.590275	+	1.02239i
$971$	−3.83104e14	+	2.21185e14i	−0.443834	+	0.256247i	−0.705222	−	0.708986i	$-0.749153\pi$
$971$	−3.83104e14	+	2.21185e14i	−0.443834	+	0.256247i	0.261389	+	0.965234i	$0.415820\pi$
$972$		−	6.22291e14i		−	0.717237i
$973$	6.15053e14	+	1.56526e14i	0.705258	+	0.179482i
$974$	2.98983e14			0.341077
$975$	−2.56604e14	−	4.44451e14i	−0.291233	−	0.504430i
$976$	−6.02415e13	−	3.47805e13i	−0.0680216	−	0.0392723i
$977$	7.24131e14	−	1.25423e15i	0.813475	−	1.40898i	−0.0969433	−	0.995290i	$-0.530907\pi$
$977$	7.24131e14	−	1.25423e15i	0.813475	−	1.40898i	0.910418	−	0.413690i	$-0.135760\pi$
$978$	−7.70258e13	+	4.44709e13i	−0.0860879	+	0.0497029i
$979$			9.77554e14i			1.08699i
$980$	−2.57647e14	+	4.73415e14i	−0.285032	+	0.523735i
$981$	−9.32735e14			−1.02663
$982$	−2.60497e13	−	4.51193e13i	−0.0285263	−	0.0494089i
$983$	5.52232e14	+	3.18832e14i	0.601664	+	0.347371i	0.769696	−	0.638410i	$-0.220408\pi$
$983$	5.52232e14	+	3.18832e14i	0.601664	+	0.347371i	−0.168032	+	0.985782i	$0.553741\pi$
$984$	−1.79377e14	+	3.10691e14i	−0.194443	+	0.336785i
$985$	−1.46351e15	+	8.44957e14i	−1.57839	+	0.911284i
$986$			8.85247e14i			0.949904i
$987$	3.80717e14	−	1.49599e15i	0.406459	−	1.59714i
$988$	5.31119e14			0.564166
$989$	−7.76797e14	−	1.34545e15i	−0.820968	−	1.42196i
$990$	5.90627e14	+	3.40998e14i	0.621065	+	0.358572i
$991$	5.43044e14	−	9.40579e14i	0.568155	−	0.984072i	−0.428594	−	0.903497i	$-0.640991\pi$
$991$	5.43044e14	−	9.40579e14i	0.568155	−	0.984072i	0.996749	−	0.0805753i	$-0.0256757\pi$
$992$	−2.73710e14	+	1.58027e14i	−0.284927	+	0.164502i
$993$		−	3.29834e14i		−	0.341625i
$994$	−3.83862e14	+	1.08057e14i	−0.395588	+	0.111357i
$995$	1.13874e15			1.16764
$996$	2.03103e14	+	3.51784e14i	0.207214	+	0.358905i
$997$	−4.09816e14	−	2.36607e14i	−0.416019	−	0.240189i	0.277354	−	0.960768i	$-0.410543\pi$
$997$	−4.09816e14	−	2.36607e14i	−0.416019	−	0.240189i	−0.693373	+	0.720579i	$0.743876\pi$
$998$	−4.54784e14	+	7.87709e14i	−0.459359	+	0.795634i
$999$	9.74948e13	−	5.62886e13i	0.0979837	−	0.0565709i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.11.d.a.3.1	✓	12
3.2	odd	2		126.11.n.b.73.6		12
4.3	odd	2		112.11.s.a.17.6		12
7.2	even	3		98.11.d.a.19.3		12
7.3	odd	6		98.11.b.c.97.7		12
7.4	even	3		98.11.b.c.97.12		12
7.5	odd	6	inner	14.11.d.a.5.1	yes	12
7.6	odd	2		98.11.d.a.31.3		12
21.5	even	6		126.11.n.b.19.6		12
28.19	even	6		112.11.s.a.33.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.11.d.a.3.1	✓	12	1.1	even	1	trivial
14.11.d.a.5.1	yes	12	7.5	odd	6	inner
98.11.b.c.97.7		12	7.3	odd	6
98.11.b.c.97.12		12	7.4	even	3
98.11.d.a.19.3		12	7.2	even	3
98.11.d.a.31.3		12	7.6	odd	2
112.11.s.a.17.6		12	4.3	odd	2
112.11.s.a.33.6		12	28.19	even	6
126.11.n.b.19.6		12	21.5	even	6
126.11.n.b.73.6		12	3.2	odd	2

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:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	14.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-11.3137 - 19.5959i) q^{2} +(-304.740 - 175.942i) q^{3} +(-256.000 + 443.405i) q^{4} +(-3227.42 + 1863.35i) q^{5} +7962.22i q^{6} +(4145.11 - 16287.8i) q^{7} +11585.2 q^{8} +(32386.5 + 56095.1i) q^{9} +O(q^{10})\)	\(q+(-11.3137 - 19.5959i) q^{2} +(-304.740 - 175.942i) q^{3} +(-256.000 + 443.405i) q^{4} +(-3227.42 + 1863.35i) q^{5} +7962.22i q^{6} +(4145.11 - 16287.8i) q^{7} +11585.2 q^{8} +(32386.5 + 56095.1i) q^{9} +(73028.2 + 42162.9i) q^{10} +(62430.6 - 108133. i) q^{11} +(156027. - 90082.2i) q^{12} +353762. i q^{13} +(-366071. + 103048. i) q^{14} +1.31137e6 q^{15} +(-131072. - 227023. i) q^{16} +(1.67588e6 + 967569. i) q^{17} +(732824. - 1.26929e6i) q^{18} +(-2.53946e6 + 1.46616e6i) q^{19} -1.90807e6i q^{20} +(-4.12889e6 + 4.23426e6i) q^{21} -2.82529e6 q^{22} +(-2.94410e6 - 5.09934e6i) q^{23} +(-3.53049e6 - 2.03833e6i) q^{24} +(2.06135e6 - 3.57037e6i) q^{25} +(6.93230e6 - 4.00236e6i) q^{26} -2.01421e6i q^{27} +(6.16096e6 + 6.00765e6i) q^{28} -2.02170e7 q^{29} +(-1.48364e7 - 2.56974e7i) q^{30} +(4.61441e7 + 2.66413e7i) q^{31} +(-2.96582e6 + 5.13695e6i) q^{32} +(-3.80502e7 + 2.19683e7i) q^{33} -4.37872e7i q^{34} +(1.69719e7 + 6.02915e7i) q^{35} -3.31638e7 q^{36} +(2.79458e7 + 4.84035e7i) q^{37} +(5.74614e7 + 3.31753e7i) q^{38} +(6.22416e7 - 1.07806e8i) q^{39} +(-3.73904e7 + 2.15874e7i) q^{40} -8.80023e7i q^{41} +(1.29687e8 + 3.30043e7i) q^{42} +2.63848e8 q^{43} +(3.19645e7 + 5.53641e7i) q^{44} +(-2.09050e8 - 1.20695e8i) q^{45} +(-6.66175e7 + 1.15385e8i) q^{46} +(-2.26047e8 + 1.30508e8i) q^{47} +9.22442e7i q^{48} +(-2.48111e8 - 1.35030e8i) q^{49} -9.32862e7 q^{50} +(-3.40472e8 - 5.89714e8i) q^{51} +(-1.56860e8 - 9.05632e7i) q^{52} +(-1.02485e8 + 1.77509e8i) q^{53} +(-3.94702e7 + 2.27882e7i) q^{54} +4.65321e8i q^{55} +(4.80221e7 - 1.88698e8i) q^{56} +1.03183e9 q^{57} +(2.28730e8 + 3.96171e8i) q^{58} +(-3.01275e8 - 1.73941e8i) q^{59} +(-3.35710e8 + 5.81466e8i) q^{60} +(2.29803e8 - 1.32677e8i) q^{61} -1.20565e9i q^{62} +(1.04791e9 - 2.94986e8i) q^{63} +1.34218e8 q^{64} +(-6.59184e8 - 1.14174e9i) q^{65} +(8.60979e8 + 4.97086e8i) q^{66} +(-8.34938e8 + 1.44615e9i) q^{67} +(-8.58050e8 + 4.95396e8i) q^{68} +2.07196e9i q^{69} +(9.89451e8 - 1.01470e9i) q^{70} +1.04860e9 q^{71} +(3.75206e8 + 6.49875e8i) q^{72} +(2.09399e9 + 1.20896e9i) q^{73} +(6.32341e8 - 1.09525e9i) q^{74} +(-1.25635e9 + 7.25357e8i) q^{75} -1.50134e9i q^{76} +(-1.50247e9 - 1.46508e9i) q^{77} -2.81673e9 q^{78} +(-1.34296e8 - 2.32607e8i) q^{79} +(8.46049e8 + 4.88467e8i) q^{80} +(1.55801e9 - 2.69855e9i) q^{81} +(-1.72448e9 + 9.95632e8i) q^{82} +2.25464e9i q^{83} +(-8.20494e8 - 2.91474e9i) q^{84} -7.21169e9 q^{85} +(-2.98510e9 - 5.17035e9i) q^{86} +(6.16094e9 + 3.55702e9i) q^{87} +(7.23274e8 - 1.25275e9i) q^{88} +(-6.78021e9 + 3.91456e9i) q^{89} +5.46204e9i q^{90} +(5.76202e9 + 1.46638e9i) q^{91} +3.01476e9 q^{92} +(-9.37464e9 - 1.62374e10i) q^{93} +(5.11485e9 + 2.95306e9i) q^{94} +(5.46393e9 - 9.46381e9i) q^{95} +(1.80761e9 - 1.04362e9i) q^{96} +1.20222e10i q^{97} +(1.61028e8 + 6.38966e9i) q^{98} +8.08765e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 486 q^{3} - 3072 q^{4} - 6666 q^{5} + 30576 q^{7} - 45528 q^{9}+O(q^{10}) \) 12 * q + 486 * q^3 - 3072 * q^4 - 6666 * q^5 + 30576 * q^7 - 45528 * q^9	\( 12 q + 486 q^{3} - 3072 q^{4} - 6666 q^{5} + 30576 q^{7} - 45528 q^{9} + 130944 q^{10} - 111210 q^{11} - 248832 q^{12} - 38976 q^{14} + 1065684 q^{15} - 1572864 q^{16} + 1439502 q^{17} + 715392 q^{18} - 452814 q^{19} - 2940462 q^{21} - 1922688 q^{22} + 853074 q^{23} - 9338880 q^{24} + 16905804 q^{25} - 8671872 q^{26} + 4064256 q^{28} + 60157248 q^{29} - 37409472 q^{30} + 87231186 q^{31} - 303597198 q^{33} + 153795138 q^{35} + 46620672 q^{36} - 7666506 q^{37} - 21703872 q^{38} - 71628084 q^{39} - 67043328 q^{40} + 129553536 q^{42} + 1066803336 q^{43} - 56939520 q^{44} - 948611736 q^{45} - 168245184 q^{46} - 985909398 q^{47} + 456183924 q^{49} + 1764094464 q^{50} - 319431390 q^{51} - 538871808 q^{52} - 600022554 q^{53} - 402417216 q^{54} - 243597312 q^{56} + 3357095652 q^{57} - 294598272 q^{58} - 2101762050 q^{59} - 272815104 q^{60} - 2201391150 q^{61} + 2691345552 q^{63} + 1610612736 q^{64} + 1536128076 q^{65} + 728780544 q^{66} - 1590058326 q^{67} - 737025024 q^{68} - 3745457856 q^{70} - 7739561160 q^{71} + 366280704 q^{72} + 2008593834 q^{73} + 1042308096 q^{74} + 12301086492 q^{75} + 464655282 q^{77} - 8450806272 q^{78} + 2310562242 q^{79} + 1747451904 q^{80} + 7562341422 q^{81} + 9636272256 q^{82} - 7405267968 q^{84} - 39581743596 q^{85} - 4924086912 q^{86} + 24592790952 q^{87} + 492208128 q^{88} + 2541648690 q^{89} - 4866473640 q^{91} - 873547776 q^{92} - 7836264270 q^{93} + 28852652352 q^{94} + 29024266590 q^{95} + 4781506560 q^{96} - 11553118080 q^{98} - 13213951200 q^{99}+O(q^{100}) \) 12 * q + 486 * q^3 - 3072 * q^4 - 6666 * q^5 + 30576 * q^7 - 45528 * q^9 + 130944 * q^10 - 111210 * q^11 - 248832 * q^12 - 38976 * q^14 + 1065684 * q^15 - 1572864 * q^16 + 1439502 * q^17 + 715392 * q^18 - 452814 * q^19 - 2940462 * q^21 - 1922688 * q^22 + 853074 * q^23 - 9338880 * q^24 + 16905804 * q^25 - 8671872 * q^26 + 4064256 * q^28 + 60157248 * q^29 - 37409472 * q^30 + 87231186 * q^31 - 303597198 * q^33 + 153795138 * q^35 + 46620672 * q^36 - 7666506 * q^37 - 21703872 * q^38 - 71628084 * q^39 - 67043328 * q^40 + 129553536 * q^42 + 1066803336 * q^43 - 56939520 * q^44 - 948611736 * q^45 - 168245184 * q^46 - 985909398 * q^47 + 456183924 * q^49 + 1764094464 * q^50 - 319431390 * q^51 - 538871808 * q^52 - 600022554 * q^53 - 402417216 * q^54 - 243597312 * q^56 + 3357095652 * q^57 - 294598272 * q^58 - 2101762050 * q^59 - 272815104 * q^60 - 2201391150 * q^61 + 2691345552 * q^63 + 1610612736 * q^64 + 1536128076 * q^65 + 728780544 * q^66 - 1590058326 * q^67 - 737025024 * q^68 - 3745457856 * q^70 - 7739561160 * q^71 + 366280704 * q^72 + 2008593834 * q^73 + 1042308096 * q^74 + 12301086492 * q^75 + 464655282 * q^77 - 8450806272 * q^78 + 2310562242 * q^79 + 1747451904 * q^80 + 7562341422 * q^81 + 9636272256 * q^82 - 7405267968 * q^84 - 39581743596 * q^85 - 4924086912 * q^86 + 24592790952 * q^87 + 492208128 * q^88 + 2541648690 * q^89 - 4866473640 * q^91 - 873547776 * q^92 - 7836264270 * q^93 + 28852652352 * q^94 + 29024266590 * q^95 + 4781506560 * q^96 - 11553118080 * q^98 - 13213951200 * q^99

Introduction

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