LMFDB - Embedded newform 48.9.l.a.43.10

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			43.10
Character	$\chi$	$=$	48.43
Dual form			48.9.l.a.19.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.57765 - 12.8167i) q^{2} +(33.0681 + 33.0681i) q^{3} +(-72.5372 + 245.508i) q^{4} +(541.894 + 541.894i) q^{5} +(107.110 - 740.540i) q^{6} +1146.54 q^{7} +(3841.35 - 1421.70i) q^{8} +2187.00i q^{9} +O(q^{10})$	\(q+(-9.57765 - 12.8167i) q^{2} +(33.0681 + 33.0681i) q^{3} +(-72.5372 + 245.508i) q^{4} +(541.894 + 541.894i) q^{5} +(107.110 - 740.540i) q^{6} +1146.54 q^{7} +(3841.35 - 1421.70i) q^{8} +2187.00i q^{9} +(1755.24 - 12135.4i) q^{10} +(-8232.05 + 8232.05i) q^{11} +(-10517.2 + 5719.83i) q^{12} +(-8056.73 + 8056.73i) q^{13} +(-10981.2 - 14694.9i) q^{14} +35838.8i q^{15} +(-55012.7 - 35617.0i) q^{16} -84789.9 q^{17} +(28030.2 - 20946.3i) q^{18} +(33335.9 + 33335.9i) q^{19} +(-172347. + 93732.0i) q^{20} +(37913.9 + 37913.9i) q^{21} +(184352. + 26664.3i) q^{22} +91767.7 q^{23} +(174039. + 80013.2i) q^{24} +196673. i q^{25} +(180425. + 26096.4i) q^{26} +(-72320.0 + 72320.0i) q^{27} +(-83166.9 + 281485. i) q^{28} +(33668.6 - 33668.6i) q^{29} +(459337. - 343252. i) q^{30} +1.21183e6i q^{31} +(70399.0 + 1.04621e6i) q^{32} -544437. q^{33} +(812088. + 1.08673e6i) q^{34} +(621304. + 621304. i) q^{35} +(-536927. - 158639. i) q^{36} +(1.95637e6 + 1.95637e6i) q^{37} +(107978. - 746537. i) q^{38} -532842. q^{39} +(2.85202e6 + 1.31119e6i) q^{40} +697274. i q^{41} +(122806. - 849059. i) q^{42} +(-3.81964e6 + 3.81964e6i) q^{43} +(-1.42391e6 - 2.61817e6i) q^{44} +(-1.18512e6 + 1.18512e6i) q^{45} +(-878919. - 1.17616e6i) q^{46} -8.51922e6i q^{47} +(-641380. - 2.99695e6i) q^{48} -4.45024e6 q^{49} +(2.52071e6 - 1.88367e6i) q^{50} +(-2.80384e6 - 2.80384e6i) q^{51} +(-1.39358e6 - 2.56241e6i) q^{52} +(1.54585e6 + 1.54585e6i) q^{53} +(1.61956e6 + 234250. i) q^{54} -8.92180e6 q^{55} +(4.40427e6 - 1.63004e6i) q^{56} +2.20471e6i q^{57} +(-753988. - 109055. i) q^{58} +(-4.42591e6 + 4.42591e6i) q^{59} +(-8.79873e6 - 2.59965e6i) q^{60} +(-348448. + 348448. i) q^{61} +(1.55317e7 - 1.16065e7i) q^{62} +2.50749e6i q^{63} +(1.27347e7 - 1.09225e7i) q^{64} -8.73179e6 q^{65} +(5.21442e6 + 6.97790e6i) q^{66} +(1.95270e7 + 1.95270e7i) q^{67} +(6.15042e6 - 2.08166e7i) q^{68} +(3.03458e6 + 3.03458e6i) q^{69} +(2.01245e6 - 1.39137e7i) q^{70} -1.94639e7 q^{71} +(3.10926e6 + 8.40103e6i) q^{72} -2.88804e7i q^{73} +(6.33683e6 - 4.38116e7i) q^{74} +(-6.50362e6 + 6.50362e6i) q^{75} +(-1.06023e7 + 5.76615e6i) q^{76} +(-9.43838e6 + 9.43838e6i) q^{77} +(5.10337e6 + 6.82929e6i) q^{78} +7.21197e7i q^{79} +(-1.05104e7 - 4.91117e7i) q^{80} -4.78297e6 q^{81} +(8.93678e6 - 6.67825e6i) q^{82} +(3.45654e7 + 3.45654e7i) q^{83} +(-1.20584e7 + 6.55802e6i) q^{84} +(-4.59471e7 - 4.59471e7i) q^{85} +(8.55385e7 + 1.23721e7i) q^{86} +2.22672e6 q^{87} +(-1.99187e7 + 4.33257e7i) q^{88} -7.91558e7i q^{89} +(2.65401e7 + 3.83871e6i) q^{90} +(-9.23737e6 + 9.23737e6i) q^{91} +(-6.65657e6 + 2.25297e7i) q^{92} +(-4.00730e7 + 4.00730e7i) q^{93} +(-1.09189e8 + 8.15941e7i) q^{94} +3.61290e7i q^{95} +(-3.22682e7 + 3.69242e7i) q^{96} +5.29193e7 q^{97} +(4.26229e7 + 5.70376e7i) q^{98} +(-1.80035e7 - 1.80035e7i) 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 $

$2$	−9.57765	−	12.8167i	−0.598603	−	0.801046i
$2$	−9.57765	−	12.8167i	−0.598603	−	0.801046i
$3$	33.0681	+	33.0681i	0.408248	+	0.408248i
$3$	33.0681	+	33.0681i	0.408248	+	0.408248i
$4$	−72.5372	+	245.508i	−0.283349	+	0.959017i
$5$	541.894	+	541.894i	0.867031	+	0.867031i	0.992143	−	0.125112i	$-0.0399290\pi$
$5$	541.894	+	541.894i	0.867031	+	0.867031i	−0.125112	+	0.992143i	$0.539929\pi$
$6$	107.110	−	740.540i	0.0826468	−	0.571404i
$7$	1146.54			0.477526			0.238763	−	0.971078i	$-0.423258\pi$
$7$	1146.54			0.477526			0.238763	+	0.971078i	$0.423258\pi$
$8$	3841.35	−	1421.70i	0.937830	−	0.347095i
$9$			2187.00i			0.333333i
$10$	1755.24	−	12135.4i	0.175524	−	1.21354i
$11$	−8232.05	+	8232.05i	−0.562260	+	0.562260i	−0.929949	−	0.367689i	$-0.880149\pi$
$11$	−8232.05	+	8232.05i	−0.562260	+	0.562260i	0.367689	+	0.929949i	$0.380149\pi$
$12$	−10517.2	+	5719.83i	−0.507194	+	0.275840i
$13$	−8056.73	+	8056.73i	−0.282088	+	0.282088i	−0.833941	−	0.551853i	$-0.813921\pi$
$13$	−8056.73	+	8056.73i	−0.282088	+	0.282088i	0.551853	+	0.833941i	$0.313921\pi$
$14$	−10981.2	−	14694.9i	−0.285849	−	0.382521i
$15$			35838.8i			0.707927i
$16$	−55012.7	−	35617.0i	−0.839427	−	0.543472i
$17$	−84789.9			−1.01519			−0.507596	−	0.861595i	$-0.669466\pi$
$17$	−84789.9			−1.01519			−0.507596	+	0.861595i	$0.669466\pi$
$18$	28030.2	−	20946.3i	0.267015	−	0.199534i
$19$	33335.9	+	33335.9i	0.255798	+	0.255798i	0.823343	−	0.567544i	$-0.192106\pi$
$19$	33335.9	+	33335.9i	0.255798	+	0.255798i	−0.567544	+	0.823343i	$0.692106\pi$
$20$	−172347.	+	93732.0i	−1.07717	+	0.585825i
$21$	37913.9	+	37913.9i	0.194949	+	0.194949i
$22$	184352.	+	26664.3i	0.786966	+	0.113825i
$23$	91767.7			0.327928			0.163964	−	0.986466i	$-0.447572\pi$
$23$	91767.7			0.327928			0.163964	+	0.986466i	$0.447572\pi$
$24$	174039.	+	80013.2i	0.524569	+	0.241166i
$25$			196673.i			0.503484i
$26$	180425.	+	26096.4i	0.394825	+	0.0571067i
$27$	−72320.0	+	72320.0i	−0.136083	+	0.136083i
$28$	−83166.9	+	281485.i	−0.135306	+	0.457956i
$29$	33668.6	−	33668.6i	0.0476029	−	0.0476029i	−0.682905	−	0.730508i	$-0.739284\pi$
$29$	33668.6	−	33668.6i	0.0476029	−	0.0476029i	0.730508	+	0.682905i	$0.239284\pi$
$30$	459337.	−	343252.i	0.567082	−	0.423768i
$31$			1.21183e6i			1.31219i	0.754679	+	0.656094i	$0.227792\pi$
$31$			1.21183e6i			1.31219i	−0.754679	+	0.656094i	$0.772208\pi$
$32$	70399.0	+	1.04621e6i	0.0671377	+	0.997744i
$33$	−544437.			−0.459083
$34$	812088.	+	1.08673e6i	0.607697	+	0.813216i
$35$	621304.	+	621304.i	0.414030	+	0.414030i
$36$	−536927.	−	158639.i	−0.319672	−	0.0944495i
$37$	1.95637e6	+	1.95637e6i	1.04386	+	1.04386i	0.998993	+	0.0448694i	$0.0142872\pi$
$37$	1.95637e6	+	1.95637e6i	1.04386	+	1.04386i	0.0448694	+	0.998993i	$0.485713\pi$
$38$	107978.	−	746537.i	0.0517845	−	0.358028i
$39$	−532842.			−0.230324
$40$	2.85202e6	+	1.31119e6i	1.11407	+	0.512185i
$41$			697274.i			0.246756i	0.992360	+	0.123378i	$0.0393728\pi$
$41$			697274.i			0.246756i	−0.992360	+	0.123378i	$0.960627\pi$
$42$	122806.	−	849059.i	0.0394661	−	0.272861i
$43$	−3.81964e6	+	3.81964e6i	−1.11725	+	1.11725i	−0.125102	+	0.992144i	$0.539926\pi$
$43$	−3.81964e6	+	3.81964e6i	−1.11725	+	1.11725i	−0.992144	+	0.125102i	$0.960074\pi$
$44$	−1.42391e6	−	2.61817e6i	−0.379901	−	0.698532i
$45$	−1.18512e6	+	1.18512e6i	−0.289010	+	0.289010i
$46$	−878919.	−	1.17616e6i	−0.196299	−	0.262685i
$47$		−	8.51922e6i		−	1.74586i	−0.487849	−	0.872928i	$-0.662218\pi$
$47$		−	8.51922e6i		−	1.74586i	0.487849	−	0.872928i	$-0.337782\pi$
$48$	−641380.	−	2.99695e6i	−0.120823	−	0.564566i
$49$	−4.45024e6			−0.771968
$50$	2.52071e6	−	1.88367e6i	0.403314	−	0.301387i
$51$	−2.80384e6	−	2.80384e6i	−0.414451	−	0.414451i
$52$	−1.39358e6	−	2.56241e6i	−0.190598	−	0.350457i
$53$	1.54585e6	+	1.54585e6i	0.195913	+	0.195913i	0.798245	−	0.602332i	$-0.205762\pi$
$53$	1.54585e6	+	1.54585e6i	0.195913	+	0.195913i	−0.602332	+	0.798245i	$0.705762\pi$
$54$	1.61956e6	+	234250.i	0.190468	+	0.0275489i
$55$	−8.92180e6			−0.974993
$56$	4.40427e6	−	1.63004e6i	0.447839	−	0.165747i
$57$			2.20471e6i			0.208858i
$58$	−753988.	−	109055.i	−0.0666273	−	0.00963685i
$59$	−4.42591e6	+	4.42591e6i	−0.365253	+	0.365253i	−0.865743	−	0.500489i	$-0.833153\pi$
$59$	−4.42591e6	+	4.42591e6i	−0.365253	+	0.365253i	0.500489	+	0.865743i	$0.333153\pi$
$60$	−8.79873e6	−	2.59965e6i	−0.678914	−	0.200590i
$61$	−348448.	+	348448.i	−0.0251662	+	0.0251662i	−0.719578	−	0.694412i	$-0.755665\pi$
$61$	−348448.	+	348448.i	−0.0251662	+	0.0251662i	0.694412	+	0.719578i	$0.255665\pi$
$62$	1.55317e7	−	1.16065e7i	1.05112	−	0.785480i
$63$			2.50749e6i			0.159175i
$64$	1.27347e7	−	1.09225e7i	0.759049	−	0.651033i
$65$	−8.73179e6			−0.489159
$66$	5.21442e6	+	6.97790e6i	0.274809	+	0.367747i
$67$	1.95270e7	+	1.95270e7i	0.969027	+	0.969027i	0.999535	−	0.0305074i	$-0.00971231\pi$
$67$	1.95270e7	+	1.95270e7i	0.969027	+	0.969027i	−0.0305074	+	0.999535i	$0.509712\pi$
$68$	6.15042e6	−	2.08166e7i	0.287653	−	0.973587i
$69$	3.03458e6	+	3.03458e6i	0.133876	+	0.133876i
$70$	2.01245e6	−	1.39137e7i	0.0838173	−	0.579497i
$71$	−1.94639e7			−0.765945			−0.382972	−	0.923760i	$-0.625100\pi$
$71$	−1.94639e7			−0.765945			−0.382972	+	0.923760i	$0.625100\pi$
$72$	3.10926e6	+	8.40103e6i	0.115698	+	0.312610i
$73$		−	2.88804e7i		−	1.01698i	−0.861069	−	0.508489i	$-0.830204\pi$
$73$		−	2.88804e7i		−	1.01698i	0.861069	−	0.508489i	$-0.169796\pi$
$74$	6.33683e6	−	4.38116e7i	0.211322	−	1.46104i
$75$	−6.50362e6	+	6.50362e6i	−0.205546	+	0.205546i
$76$	−1.06023e7	+	5.76615e6i	−0.317795	+	0.172835i
$77$	−9.43838e6	+	9.43838e6i	−0.268494	+	0.268494i
$78$	5.10337e6	+	6.82929e6i	0.137873	+	0.184500i
$79$			7.21197e7i			1.85159i	0.378023	+	0.925796i	$0.376604\pi$
$79$			7.21197e7i			1.85159i	−0.378023	+	0.925796i	$0.623396\pi$
$80$	−1.05104e7	−	4.91117e7i	−0.256602	−	1.19902i
$81$	−4.78297e6			−0.111111
$82$	8.93678e6	−	6.67825e6i	0.197663	−	0.147709i
$83$	3.45654e7	+	3.45654e7i	0.728331	+	0.728331i	0.970287	−	0.241956i	$-0.0777891\pi$
$83$	3.45654e7	+	3.45654e7i	0.728331	+	0.728331i	−0.241956	+	0.970287i	$0.577789\pi$
$84$	−1.20584e7	+	6.55802e6i	−0.242198	+	0.131721i
$85$	−4.59471e7	−	4.59471e7i	−0.880203	−	0.880203i
$86$	8.55385e7	+	1.23721e7i	1.56375	+	0.226178i
$87$	2.22672e6			0.0388676
$88$	−1.99187e7	+	4.33257e7i	−0.332146	+	0.722462i
$89$		−	7.91558e7i		−	1.26160i	−0.775945	−	0.630801i	$-0.782726\pi$
$89$		−	7.91558e7i		−	1.26160i	0.775945	−	0.630801i	$-0.217274\pi$
$90$	2.65401e7	+	3.83871e6i	0.404513	+	0.0585080i
$91$	−9.23737e6	+	9.23737e6i	−0.134705	+	0.134705i
$92$	−6.65657e6	+	2.25297e7i	−0.0929179	+	0.314488i
$93$	−4.00730e7	+	4.00730e7i	−0.535698	+	0.535698i
$94$	−1.09189e8	+	8.15941e7i	−1.39851	+	1.04507i
$95$			3.61290e7i			0.443570i
$96$	−3.22682e7	+	3.69242e7i	−0.379918	+	0.434736i
$97$	5.29193e7			0.597761			0.298880	−	0.954291i	$-0.403387\pi$
$97$	5.29193e7			0.597761			0.298880	+	0.954291i	$0.403387\pi$
$98$	4.26229e7	+	5.70376e7i	0.462103	+	0.618382i
$99$	−1.80035e7	−	1.80035e7i	−0.187420	−	0.187420i
$100$	−4.82850e7	−	1.42661e7i	−0.482850	−	0.142661i
$101$	−5.47294e7	−	5.47294e7i	−0.525939	−	0.525939i	0.393420	−	0.919359i	$-0.371292\pi$
$101$	−5.47294e7	−	5.47294e7i	−0.525939	−	0.525939i	−0.919359	+	0.393420i	$0.871292\pi$
$102$	−9.08187e6	+	6.27903e7i	−0.0839025	+	0.580085i
$103$	−4.13371e7			−0.367275			−0.183638	−	0.982994i	$-0.558787\pi$
$103$	−4.13371e7			−0.367275			−0.183638	+	0.982994i	$0.558787\pi$
$104$	−1.94944e7	+	4.24030e7i	−0.166639	+	0.362463i
$105$			4.10907e7i			0.338054i
$106$	5.00713e6	−	3.46183e7i	0.0396612	−	0.274210i
$107$	6.24636e7	−	6.24636e7i	0.476531	−	0.476531i	−0.427489	−	0.904021i	$-0.640602\pi$
$107$	6.24636e7	−	6.24636e7i	0.476531	−	0.476531i	0.904021	+	0.427489i	$0.140602\pi$
$108$	−1.25093e7	−	2.30010e7i	−0.0919468	−	0.169065i
$109$	1.35991e8	−	1.35991e8i	0.963396	−	0.963396i	−0.0359570	−	0.999353i	$-0.511448\pi$
$109$	1.35991e8	−	1.35991e8i	0.963396	−	0.963396i	0.999353	+	0.0359570i	$0.0114479\pi$
$110$	8.54498e7	+	1.14348e8i	0.583634	+	0.781014i
$111$			1.29387e8i			0.852310i
$112$	−6.30743e7	−	4.08363e7i	−0.400849	−	0.259522i
$113$	3.22431e8			1.97753			0.988766	−	0.149470i	$-0.0477567\pi$
$113$	3.22431e8			1.97753			0.988766	+	0.149470i	$0.0477567\pi$
$114$	2.82572e7	−	2.11159e7i	0.167305	−	0.125023i
$115$	4.97284e7	+	4.97284e7i	0.284323	+	0.284323i
$116$	5.82370e6	+	1.07082e7i	0.0321638	+	0.0591402i
$117$	−1.76201e7	−	1.76201e7i	−0.0940295	−	0.0940295i
$118$	9.91155e7	+	1.43359e7i	0.511227	+	0.0739428i
$119$	−9.72151e7			−0.484781
$120$	5.09522e7	+	1.37670e8i	0.245718	+	0.663915i
$121$			7.88257e7i			0.367728i
$122$	7.80327e6	+	1.12865e6i	0.0352239	+	0.00509472i
$123$	−2.30575e7	+	2.30575e7i	−0.100738	+	0.100738i
$124$	−2.97515e8	−	8.79030e7i	−1.25841	−	0.371806i
$125$	1.05101e8	−	1.05101e8i	0.430495	−	0.430495i
$126$	3.21378e7	−	2.40158e7i	0.127507	−	0.0952829i
$127$			1.24415e8i			0.478255i	0.970988	+	0.239127i	$0.0768614\pi$
$127$			1.24415e8i			0.478255i	−0.970988	+	0.239127i	$0.923139\pi$
$128$	−2.61960e8	−	5.86056e7i	−0.975877	−	0.218323i
$129$	−2.52617e8			−0.912228
$130$	8.36300e7	+	1.11913e8i	0.292812	+	0.391838i
$131$	9.90526e7	+	9.90526e7i	0.336342	+	0.336342i	0.854989	−	0.518647i	$-0.173564\pi$
$131$	9.90526e7	+	9.90526e7i	0.336342	+	0.336342i	−0.518647	+	0.854989i	$0.673564\pi$
$132$	3.94919e7	−	1.33664e8i	0.130081	−	0.440269i
$133$	3.82210e7	+	3.82210e7i	0.122150	+	0.122150i
$134$	6.32495e7	−	4.37295e8i	0.196172	−	1.35630i
$135$	−7.83795e7			−0.235976
$136$	−3.25708e8	+	1.20546e8i	−0.952078	+	0.352369i
$137$		−	6.31526e8i		−	1.79271i	−0.443342	−	0.896353i	$-0.646207\pi$
$137$		−	6.31526e8i		−	1.79271i	0.443342	−	0.896353i	$-0.353793\pi$
$138$	9.82926e6	−	6.79576e7i	0.0271022	−	0.187379i
$139$	3.24801e8	−	3.24801e8i	0.870079	−	0.870079i	−0.122402	−	0.992481i	$-0.539060\pi$
$139$	3.24801e8	−	3.24801e8i	0.870079	−	0.870079i	0.992481	+	0.122402i	$0.0390597\pi$
$140$	−1.97603e8	+	1.07468e8i	−0.514377	+	0.279747i
$141$	2.81714e8	−	2.81714e8i	0.712743	−	0.712743i
$142$	1.86419e8	+	2.49464e8i	0.458497	+	0.613557i
$143$		−	1.32647e8i		−	0.317214i
$144$	7.78944e7	−	1.20313e8i	0.181157	−	0.279809i
$145$	3.64897e7			0.0825463
$146$	−3.70152e8	+	2.76606e8i	−0.814646	+	0.608766i
$147$	−1.47161e8	−	1.47161e8i	−0.315155	−	0.315155i
$148$	−6.22214e8	+	3.38395e8i	−1.29686	+	0.705305i
$149$	−5.98598e8	−	5.98598e8i	−1.21448	−	1.21448i	−0.969538	−	0.244943i	$-0.921231\pi$
$149$	−5.98598e8	−	5.98598e8i	−1.21448	−	1.21448i	−0.244943	−	0.969538i	$-0.578769\pi$
$150$	1.45644e8	+	2.10657e7i	0.287693	+	0.0416114i
$151$	5.67326e8			1.09125			0.545626	−	0.838029i	$-0.316292\pi$
$151$	5.67326e8			1.09125			0.545626	+	0.838029i	$0.316292\pi$
$152$	1.75449e8	+	8.06611e7i	0.328682	+	0.151109i
$153$		−	1.85435e8i		−	0.338398i
$154$	2.11367e8	+	3.05717e7i	0.375797	+	0.0543546i
$155$	−6.56685e8	+	6.56685e8i	−1.13771	+	1.13771i
$156$	3.86509e7	−	1.30817e8i	0.0652621	−	0.220885i
$157$	7.24025e8	−	7.24025e8i	1.19167	−	1.19167i	0.215068	−	0.976599i	$-0.431003\pi$
$157$	7.24025e8	−	7.24025e8i	1.19167	−	1.19167i	0.976599	−	0.215068i	$-0.0689972\pi$
$158$	9.24339e8	−	6.90737e8i	1.48321	−	1.10837i
$159$			1.02237e8i			0.159962i
$160$	−5.28786e8	+	6.05084e8i	−0.806864	+	0.923285i
$161$	1.05215e8			0.156594
$162$	4.58096e7	+	6.13020e7i	0.0665115	+	0.0890051i
$163$	2.76845e8	+	2.76845e8i	0.392181	+	0.392181i	0.875464	−	0.483283i	$-0.160556\pi$
$163$	2.76845e8	+	2.76845e8i	0.392181	+	0.392181i	−0.483283	+	0.875464i	$0.660556\pi$
$164$	−1.71187e8	−	5.05783e7i	−0.236643	−	0.0699180i
$165$	−2.95027e8	−	2.95027e8i	−0.398039	−	0.398039i
$166$	1.11960e8	−	7.74070e8i	0.147445	−	1.01941i
$167$	−1.00358e9			−1.29029			−0.645145	−	0.764060i	$-0.723203\pi$
$167$	−1.00358e9			−1.29029			−0.645145	+	0.764060i	$0.723203\pi$
$168$	1.99543e8	+	9.17384e7i	0.250495	+	0.115163i
$169$			6.85909e8i			0.840852i
$170$	−1.48827e8	+	1.02896e9i	−0.178191	+	1.23198i
$171$	−7.29056e7	+	7.29056e7i	−0.0852661	+	0.0852661i
$172$	−6.60688e8	−	1.21482e9i	−0.754888	−	1.38803i
$173$	−7.21163e8	+	7.21163e8i	−0.805098	+	0.805098i	−0.983887	−	0.178789i	$-0.942782\pi$
$173$	−7.21163e8	+	7.21163e8i	−0.805098	+	0.805098i	0.178789	+	0.983887i	$0.442782\pi$
$174$	−2.13267e7	−	2.85392e7i	−0.0232663	−	0.0311347i
$175$			2.25494e8i			0.240427i
$176$	7.46068e8	−	1.59666e8i	0.777549	−	0.166404i
$177$	−2.92713e8			−0.298228
$178$	−1.01452e9	+	7.58126e8i	−1.01060	+	0.755199i
$179$	7.67047e8	+	7.67047e8i	0.747154	+	0.747154i	0.973944	−	0.226790i	$-0.0728231\pi$
$179$	7.67047e8	+	7.67047e8i	0.747154	+	0.747154i	−0.226790	+	0.973944i	$0.572823\pi$
$180$	−2.04992e8	−	3.76923e8i	−0.195275	−	0.359056i
$181$	5.91768e7	+	5.91768e7i	0.0551362	+	0.0551362i	0.734137	−	0.679001i	$-0.237587\pi$
$181$	5.91768e7	+	5.91768e7i	0.0551362	+	0.0551362i	−0.679001	+	0.734137i	$0.737587\pi$
$182$	2.06865e8	+	2.99206e7i	0.188539	+	0.0272700i
$183$	−2.30450e7			−0.0205481
$184$	3.52512e8	−	1.30466e8i	0.307541	−	0.113822i
$185$			2.12029e9i			1.81012i
$186$	8.97411e8	+	1.29800e8i	0.749790	+	0.108448i
$187$	6.97994e8	−	6.97994e8i	0.570802	−	0.570802i
$188$	2.09154e9	+	6.17961e8i	1.67431	+	0.494686i
$189$	−8.29178e7	+	8.29178e7i	−0.0649831	+	0.0649831i
$190$	4.63056e8	−	3.46031e8i	0.355320	−	0.265522i
$191$			1.84876e9i			1.38914i	0.719423	+	0.694572i	$0.244406\pi$
$191$			1.84876e9i			1.38914i	−0.719423	+	0.694572i	$0.755594\pi$
$192$	7.82301e8	+	5.99266e7i	0.575664	+	0.0440976i
$193$	1.08701e9			0.783437			0.391718	−	0.920085i	$-0.371881\pi$
$193$	1.08701e9			0.783437			0.391718	+	0.920085i	$0.371881\pi$
$194$	−5.06843e8	−	6.78253e8i	−0.357821	−	0.478834i
$195$	−2.88744e8	−	2.88744e8i	−0.199698	−	0.199698i
$196$	3.22808e8	−	1.09257e9i	0.218736	−	0.740331i
$197$	−3.33420e8	−	3.33420e8i	−0.221374	−	0.221374i	0.587703	−	0.809077i	$-0.300032\pi$
$197$	−3.33420e8	−	3.33420e8i	−0.221374	−	0.221374i	−0.809077	+	0.587703i	$0.800032\pi$
$198$	−5.83148e7	+	4.03177e8i	−0.0379418	+	0.262322i
$199$	3.08400e7			0.0196654			0.00983270	−	0.999952i	$-0.496870\pi$
$199$	3.08400e7			0.0196654			0.00983270	+	0.999952i	$0.496870\pi$
$200$	2.79611e8	+	7.55492e8i	0.174757	+	0.472182i
$201$			1.29144e9i			0.791207i
$202$	−1.77273e8	+	1.22563e9i	−0.106472	+	0.736130i
$203$	3.86025e7	−	3.86025e7i	0.0227316	−	0.0227316i
$204$	8.91749e8	−	4.84984e8i	0.514899	−	0.280031i
$205$	−3.77849e8	+	3.77849e8i	−0.213945	+	0.213945i
$206$	3.95913e8	+	5.29807e8i	0.219852	+	0.294204i
$207$			2.00696e8i			0.109309i
$208$	7.30179e8	−	1.56266e8i	0.390100	−	0.0834855i
$209$	−5.48845e8			−0.287650
$210$	5.26648e8	−	3.93552e8i	0.270797	−	0.202360i
$211$	−7.35629e8	−	7.35629e8i	−0.371132	−	0.371132i	0.496757	−	0.867890i	$-0.334524\pi$
$211$	−7.35629e8	−	7.35629e8i	−0.371132	−	0.371132i	−0.867890	+	0.496757i	$0.834524\pi$
$212$	−4.91650e8	+	2.67387e8i	−0.243396	+	0.132372i
$213$	−6.43636e8	−	6.43636e8i	−0.312696	−	0.312696i
$214$	−1.39883e9	−	2.02325e8i	−0.666977	−	0.0964703i
$215$	−4.13968e9			−1.93737
$216$	−1.74989e8	+	3.80624e8i	−0.0803888	+	0.174856i
$217$			1.38942e9i			0.626604i
$218$	−3.04544e9	−	4.40487e8i	−1.34842	−	0.195032i
$219$	9.55020e8	−	9.55020e8i	0.415179	−	0.415179i
$220$	6.47162e8	−	2.19038e9i	0.276263	−	0.935035i
$221$	6.83129e8	−	6.83129e8i	0.286374	−	0.286374i
$222$	1.65831e9	−	1.23922e9i	0.682739	−	0.510195i
$223$			2.42086e9i			0.978928i	0.872024	+	0.489464i	$0.162807\pi$
$223$			2.42086e9i			0.978928i	−0.872024	+	0.489464i	$0.837193\pi$
$224$	8.07153e7	+	1.19952e9i	0.0320600	+	0.476449i
$225$	−4.30125e8			−0.167828
$226$	−3.08814e9	−	4.13252e9i	−1.18376	−	1.58409i
$227$	−1.28881e9	−	1.28881e9i	−0.485382	−	0.485382i	0.421463	−	0.906846i	$-0.361517\pi$
$227$	−1.28881e9	−	1.28881e9i	−0.485382	−	0.485382i	−0.906846	+	0.421463i	$0.861517\pi$
$228$	−5.41275e8	−	1.59924e8i	−0.200299	−	0.0591797i
$229$	−1.96027e9	−	1.96027e9i	−0.712809	−	0.712809i	0.254313	−	0.967122i	$-0.418151\pi$
$229$	−1.96027e9	−	1.96027e9i	−0.712809	−	0.712809i	−0.967122	+	0.254313i	$0.918151\pi$
$230$	1.61074e8	−	1.11364e9i	0.0575592	−	0.397953i
$231$	−6.24219e8			−0.219224
$232$	8.14662e7	−	1.77200e8i	0.0281207	−	0.0611662i
$233$			2.49134e9i			0.845297i	0.906294	+	0.422649i	$0.138900\pi$
$233$			2.49134e9i			0.845297i	−0.906294	+	0.422649i	$0.861100\pi$
$234$	−5.70728e7	+	3.94591e8i	−0.0190356	+	0.131608i
$235$	4.61651e9	−	4.61651e9i	1.51371	−	1.51371i
$236$	−7.65554e8	−	1.40764e9i	−0.246790	−	0.453778i
$237$	−2.38486e9	+	2.38486e9i	−0.755910	+	0.755910i
$238$	9.31092e8	+	1.24598e9i	0.290192	+	0.388332i
$239$		−	1.35733e9i		−	0.416002i	−0.978129	−	0.208001i	$-0.933304\pi$
$239$		−	1.35733e9i		−	0.416002i	0.978129	−	0.208001i	$-0.0666957\pi$
$240$	1.27647e9	−	1.97159e9i	0.384739	−	0.594254i
$241$	2.65917e9			0.788276			0.394138	−	0.919051i	$-0.371043\pi$
$241$	2.65917e9			0.788276			0.394138	+	0.919051i	$0.371043\pi$
$242$	1.01029e9	−	7.54965e8i	0.294567	−	0.220123i
$243$	−1.58164e8	−	1.58164e8i	−0.0453609	−	0.0453609i
$244$	−6.02714e7	−	1.10822e8i	−0.0170040	−	0.0312657i
$245$	−2.41156e9	−	2.41156e9i	−0.669320	−	0.669320i
$246$	5.16359e8	+	7.46852e7i	0.140998	+	0.0203936i
$247$	−5.37157e8			−0.144316
$248$	1.72287e9	+	4.65508e9i	0.455454	+	1.23061i
$249$			2.28602e9i			0.594680i
$250$	−2.35368e9	−	3.40431e8i	−0.602541	−	0.0871504i
$251$	4.31028e9	−	4.31028e9i	1.08595	−	1.08595i	0.0900102	−	0.995941i	$-0.471310\pi$
$251$	4.31028e9	−	4.31028e9i	1.08595	−	1.08595i	0.995941	−	0.0900102i	$-0.0286900\pi$
$252$	−6.15609e8	−	1.81886e8i	−0.152652	−	0.0451021i
$253$	−7.55436e8	+	7.55436e8i	−0.184381	+	0.184381i
$254$	1.59460e9	−	1.19161e9i	0.383104	−	0.286285i
$255$		−	3.03877e9i		−	0.718683i
$256$	1.75783e9	+	3.91877e9i	0.409276	+	0.912411i
$257$	7.17766e9			1.64532			0.822660	−	0.568533i	$-0.192489\pi$
$257$	7.17766e9			1.64532			0.822660	+	0.568533i	$0.192489\pi$
$258$	2.41947e9	+	3.23772e9i	0.546062	+	0.730736i
$259$	2.24305e9	+	2.24305e9i	0.498472	+	0.498472i
$260$	6.33380e8	−	2.14373e9i	0.138602	−	0.469111i
$261$	7.36333e7	+	7.36333e7i	0.0158676	+	0.0158676i
$262$	3.20840e8	−	2.21822e9i	0.0680899	−	0.470760i
$263$	−3.26231e9			−0.681871			−0.340936	−	0.940087i	$-0.610744\pi$
$263$	−3.26231e9			−0.681871			−0.340936	+	0.940087i	$0.610744\pi$
$264$	−2.09137e9	+	7.74027e8i	−0.430542	+	0.159346i
$265$			1.67537e9i			0.339725i
$266$	1.23801e8	−	8.55935e8i	0.0247285	−	0.170968i
$267$	2.61753e9	−	2.61753e9i	0.515047	−	0.515047i
$268$	−6.21047e9	+	3.37760e9i	−1.20389	+	0.654741i
$269$	2.23705e9	−	2.23705e9i	0.427235	−	0.427235i	−0.460450	−	0.887686i	$-0.652312\pi$
$269$	2.23705e9	−	2.23705e9i	0.427235	−	0.427235i	0.887686	+	0.460450i	$0.152312\pi$
$270$	7.50692e8	+	1.00457e9i	0.141256	+	0.189027i
$271$		−	6.05098e9i		−	1.12189i	−0.827855	−	0.560943i	$-0.810439\pi$
$271$		−	6.05098e9i		−	1.12189i	0.827855	−	0.560943i	$-0.189561\pi$
$272$	4.66452e9	+	3.01996e9i	0.852180	+	0.551729i
$273$	−6.10925e8			−0.109986
$274$	−8.09410e9	+	6.04853e9i	−1.43604	+	1.07312i
$275$	−1.61902e9	−	1.61902e9i	−0.283089	−	0.283089i
$276$	−9.65136e8	+	5.24895e8i	−0.166323	+	0.0904558i
$277$	1.61216e9	+	1.61216e9i	0.273835	+	0.273835i	0.830642	−	0.556807i	$-0.187974\pi$
$277$	1.61216e9	+	1.61216e9i	0.273835	+	0.273835i	−0.556807	+	0.830642i	$0.687974\pi$
$278$	−7.27372e9	−	1.05206e9i	−1.21780	−	0.176141i
$279$	−2.65028e9			−0.437396
$280$	3.26996e9	+	1.50334e9i	0.531998	+	0.244582i
$281$			1.27847e9i			0.205053i	0.994730	+	0.102527i	$0.0326927\pi$
$281$			1.27847e9i			0.205053i	−0.994730	+	0.102527i	$0.967307\pi$
$282$	−6.30882e9	−	9.12496e8i	−0.997589	−	0.144289i
$283$	3.08632e9	−	3.08632e9i	0.481166	−	0.481166i	−0.424338	−	0.905504i	$-0.639493\pi$
$283$	3.08632e9	−	3.08632e9i	0.481166	−	0.481166i	0.905504	+	0.424338i	$0.139493\pi$
$284$	1.41186e9	−	4.77856e9i	0.217029	−	0.734554i
$285$	−1.19472e9	+	1.19472e9i	−0.181087	+	0.181087i
$286$	−1.70010e9	+	1.27044e9i	−0.254103	+	0.189885i
$287$			7.99453e8i			0.117833i
$288$	−2.28806e9	+	1.53963e8i	−0.332581	+	0.0223792i
$289$	2.13569e8			0.0306158
$290$	−3.49485e8	−	4.67678e8i	−0.0494125	−	0.0661234i
$291$	1.74994e9	+	1.74994e9i	0.244035	+	0.244035i
$292$	7.09037e9	+	2.09490e9i	0.975299	+	0.288159i
$293$	3.43184e9	+	3.43184e9i	0.465647	+	0.465647i	0.900501	−	0.434854i	$-0.143200\pi$
$293$	3.43184e9	+	3.43184e9i	0.465647	+	0.465647i	−0.434854	+	0.900501i	$0.643200\pi$
$294$	−4.76667e8	+	3.29558e9i	−0.0638008	+	0.441106i
$295$	−4.79675e9			−0.633372
$296$	1.02965e10	+	4.73372e9i	1.34129	+	0.616645i
$297$		−	1.19068e9i		−	0.153028i
$298$	−1.93891e9	+	1.34052e10i	−0.245863	+	1.69985i
$299$	−7.39347e8	+	7.39347e8i	−0.0925047	+	0.0925047i
$300$	−1.12494e9	−	2.06845e9i	−0.138881	−	0.255364i
$301$	−4.37938e9	+	4.37938e9i	−0.533515	+	0.533515i
$302$	−5.43365e9	−	7.27126e9i	−0.653226	−	0.874142i
$303$		−	3.61960e9i		−	0.429427i
$304$	−6.46573e8	−	3.02122e9i	−0.0757048	−	0.353743i
$305$	−3.77643e8			−0.0436398
$306$	−2.37668e9	+	1.77604e9i	−0.271072	+	0.202566i
$307$	4.57550e9	+	4.57550e9i	0.515093	+	0.515093i	0.916082	−	0.400990i	$-0.131334\pi$
$307$	4.57550e9	+	4.57550e9i	0.515093	+	0.515093i	−0.400990	+	0.916082i	$0.631334\pi$
$308$	−1.63257e9	−	3.00183e9i	−0.181413	−	0.333568i
$309$	−1.36694e9	−	1.36694e9i	−0.149939	−	0.149939i
$310$	1.47061e10	+	2.12706e9i	1.59239	+	0.230320i
$311$	9.76560e8			0.104390			0.0521948	−	0.998637i	$-0.483378\pi$
$311$	9.76560e8			0.104390			0.0521948	+	0.998637i	$0.483378\pi$
$312$	−2.04683e9	+	7.57543e8i	−0.216005	+	0.0799445i
$313$			1.71530e10i			1.78716i	0.448905	+	0.893580i	$0.351814\pi$
$313$			1.71530e10i			1.78716i	−0.448905	+	0.893580i	$0.648186\pi$
$314$	−1.62141e10	−	2.34518e9i	−1.66792	−	0.241244i
$315$	−1.35879e9	+	1.35879e9i	−0.138010	+	0.138010i
$316$	−1.77060e10	−	5.23136e9i	−1.77571	−	0.524646i
$317$	1.38587e10	−	1.38587e10i	1.37241	−	1.37241i	0.515563	−	0.856852i	$-0.327583\pi$
$317$	1.38587e10	−	1.38587e10i	1.37241	−	1.37241i	0.856852	−	0.515563i	$-0.172417\pi$
$318$	1.31034e9	−	9.79187e8i	0.128137	−	0.0957540i
$319$			5.54323e8i			0.0535304i
$320$	1.28197e10	+	9.82030e8i	1.22258	+	0.0936537i
$321$	4.13110e9			0.389086
$322$	−1.00772e9	−	1.34852e9i	−0.0937378	−	0.125439i
$323$	−2.82655e9	−	2.82655e9i	−0.259685	−	0.259685i
$324$	3.46943e8	−	1.17426e9i	0.0314832	−	0.106557i
$325$	−1.58454e9	−	1.58454e9i	−0.142027	−	0.142027i
$326$	8.96724e8	−	6.19977e9i	0.0793941	−	0.548915i
$327$	8.99395e9			0.786610
$328$	9.91317e8	+	2.67847e9i	0.0856480	+	0.231415i
$329$		−	9.76763e9i		−	0.833692i
$330$	−9.55616e8	+	6.60695e9i	−0.0805801	+	0.557115i
$331$	5.99907e9	−	5.99907e9i	0.499772	−	0.499772i	−0.411595	−	0.911367i	$-0.635028\pi$
$331$	5.99907e9	−	5.99907e9i	0.499772	−	0.499772i	0.911367	+	0.411595i	$0.135028\pi$
$332$	−1.09934e10	+	5.97881e9i	−0.904853	+	0.492110i
$333$	−4.27857e9	+	4.27857e9i	−0.347954	+	0.347954i
$334$	9.61197e9	+	1.28627e10i	0.772372	+	1.03358i
$335$			2.11631e10i			1.68035i
$336$	−7.35368e8	−	3.43613e9i	−0.0576962	−	0.269595i
$337$	−1.87578e10			−1.45433			−0.727164	−	0.686464i	$-0.759162\pi$
$337$	−1.87578e10			−1.45433			−0.727164	+	0.686464i	$0.759162\pi$
$338$	8.79111e9	−	6.56940e9i	0.673561	−	0.503337i
$339$	1.06622e10	+	1.06622e10i	0.807324	+	0.807324i
$340$	1.46133e10	−	7.94753e9i	1.09353	−	0.594725i
$341$	−9.97587e9	−	9.97587e9i	−0.737791	−	0.737791i
$342$	1.63268e9	+	2.36147e8i	0.119343	+	0.0172615i
$343$	−1.17120e10			−0.846162
$344$	−9.24219e9	+	2.01030e10i	−0.659996	+	1.43558i
$345$			3.28885e9i			0.232149i
$346$	1.61500e10	+	2.33590e9i	1.12685	+	0.162986i
$347$	−1.94718e9	+	1.94718e9i	−0.134304	+	0.134304i	−0.771063	−	0.636759i	$-0.780275\pi$
$347$	−1.94718e9	+	1.94718e9i	−0.134304	+	0.134304i	0.636759	+	0.771063i	$0.280275\pi$
$348$	−1.61520e8	+	5.46677e8i	−0.0110131	+	0.0372747i
$349$	−3.40450e8	+	3.40450e8i	−0.0229484	+	0.0229484i	−0.718488	−	0.695539i	$-0.755165\pi$
$349$	−3.40450e8	+	3.40450e8i	−0.0229484	+	0.0229484i	0.695539	+	0.718488i	$0.255165\pi$
$350$	2.89010e9	−	2.15970e9i	0.192593	−	0.143920i
$351$		−	1.16532e9i		−	0.0767748i
$352$	−9.19198e9	−	8.03292e9i	−0.598740	−	0.523242i
$353$	1.00275e10			0.645792			0.322896	−	0.946434i	$-0.395344\pi$
$353$	1.00275e10			0.645792			0.322896	+	0.946434i	$0.395344\pi$
$354$	2.80350e9	+	3.75162e9i	0.178520	+	0.238894i
$355$	−1.05474e10	−	1.05474e10i	−0.664097	−	0.664097i
$356$	1.94334e10	+	5.74174e9i	1.20990	+	0.357473i
$357$	−3.21472e9	−	3.21472e9i	−0.197911	−	0.197911i
$358$	2.48453e9	−	1.71776e10i	0.151256	−	1.04575i
$359$	3.62599e9			0.218297			0.109149	−	0.994025i	$-0.465188\pi$
$359$	3.62599e9			0.218297			0.109149	+	0.994025i	$0.465188\pi$
$360$	−2.86758e9	+	6.23736e9i	−0.170728	+	0.371356i
$361$		−	1.47610e10i		−	0.869134i
$362$	1.91678e8	−	1.32523e9i	0.0111619	−	0.0771713i
$363$	−2.60662e9	+	2.60662e9i	−0.150124	+	0.150124i
$364$	−1.59780e9	−	2.93790e9i	−0.0910157	−	0.167352i
$365$	1.56501e10	−	1.56501e10i	0.881751	−	0.881751i
$366$	2.20717e8	+	2.95362e8i	0.0123002	+	0.0164600i
$367$			2.72017e9i			0.149945i	0.997186	+	0.0749726i	$0.0238869\pi$
$367$			2.72017e9i			0.149945i	−0.997186	+	0.0749726i	$0.976113\pi$
$368$	−5.04839e9	−	3.26849e9i	−0.275272	−	0.178220i
$369$	−1.52494e9			−0.0822521
$370$	2.71751e10	−	2.03074e10i	1.44999	−	1.08354i
$371$	1.77238e9	+	1.77238e9i	0.0935537	+	0.0935537i
$372$	−6.93148e9	−	1.27450e10i	−0.361955	−	0.665533i
$373$	−2.13430e10	−	2.13430e10i	−1.10261	−	1.10261i	−0.994095	−	0.108513i	$-0.965391\pi$
$373$	−2.13430e10	−	2.13430e10i	−1.10261	−	1.10261i	−0.108513	−	0.994095i	$-0.534609\pi$
$374$	−1.56312e10	−	2.26086e9i	−0.798922	−	0.115555i
$375$	6.95100e9			0.351497
$376$	−1.21118e10	−	3.27253e10i	−0.605979	−	1.63732i
$377$			5.42518e8i			0.0268565i
$378$	1.85689e9	+	2.68578e8i	0.0909536	+	0.0131554i
$379$	−5.30361e9	+	5.30361e9i	−0.257048	+	0.257048i	−0.823853	−	0.566804i	$-0.808180\pi$
$379$	−5.30361e9	+	5.30361e9i	−0.257048	+	0.257048i	0.566804	+	0.823853i	$0.308180\pi$
$380$	−8.86998e9	−	2.62070e9i	−0.425391	−	0.125685i
$381$	−4.11418e9	+	4.11418e9i	−0.195247	+	0.195247i
$382$	2.36951e10	−	1.77068e10i	1.11277	−	0.831546i
$383$			2.41969e10i			1.12452i	0.826962	+	0.562258i	$0.190067\pi$
$383$			2.41969e10i			1.12452i	−0.826962	+	0.562258i	$0.809933\pi$
$384$	−6.72454e9	−	1.06005e10i	−0.309270	−	0.487530i
$385$	−1.02292e10			−0.465585
$386$	−1.04110e10	−	1.39319e10i	−0.468968	−	0.627569i
$387$	−8.35356e9	−	8.35356e9i	−0.372415	−	0.372415i
$388$	−3.83862e9	+	1.29921e10i	−0.169375	+	0.573263i
$389$	4.06745e9	+	4.06745e9i	0.177633	+	0.177633i	0.790323	−	0.612690i	$-0.209913\pi$
$389$	4.06745e9	+	4.06745e9i	0.177633	+	0.177633i	−0.612690	+	0.790323i	$0.709913\pi$
$390$	−9.35264e8	+	6.46624e9i	−0.0404274	+	0.279507i
$391$	−7.78097e9			−0.332910
$392$	−1.70950e10	+	6.32693e9i	−0.723975	+	0.267947i
$393$			6.55097e9i			0.274622i
$394$	−1.07998e9	+	7.46674e9i	−0.0448156	+	0.309846i
$395$	−3.90812e10	+	3.90812e10i	−1.60539	+	1.60539i
$396$	5.72593e9	−	3.11408e9i	0.232844	−	0.126634i
$397$	−1.97487e10	+	1.97487e10i	−0.795016	+	0.795016i	−0.982305	−	0.187289i	$-0.940030\pi$
$397$	−1.97487e10	+	1.97487e10i	−0.795016	+	0.795016i	0.187289	+	0.982305i	$0.440030\pi$
$398$	−2.95375e8	−	3.95268e8i	−0.0117718	−	0.0157529i
$399$			2.52779e9i			0.0997354i
$400$	7.00491e9	−	1.08195e10i	0.273629	−	0.422638i
$401$	3.55263e10			1.37396			0.686978	−	0.726679i	$-0.258937\pi$
$401$	3.55263e10			1.37396			0.686978	+	0.726679i	$0.258937\pi$
$402$	1.65521e10	−	1.23690e10i	0.633793	−	0.473619i
$403$	−9.76341e9	−	9.76341e9i	−0.370153	−	0.370153i
$404$	1.74064e10	−	9.46661e9i	0.653408	−	0.355360i
$405$	−2.59186e9	−	2.59186e9i	−0.0963367	−	0.0963367i
$406$	−8.64478e8	−	1.25037e8i	−0.0318163	−	0.00460185i
$407$	−3.22098e10			−1.17384
$408$	−1.47568e10	−	6.78431e9i	−0.532538	−	0.244830i
$409$			1.68457e10i			0.601998i	0.953624	+	0.300999i	$0.0973201\pi$
$409$			1.68457e10i			0.601998i	−0.953624	+	0.300999i	$0.902680\pi$
$410$	8.46169e9	+	1.22388e9i	0.299448	+	0.0433116i
$411$	2.08834e10	−	2.08834e10i	0.731869	−	0.731869i
$412$	2.99848e9	−	1.01486e10i	0.104067	−	0.352223i
$413$	−5.07448e9	+	5.07448e9i	−0.174418	+	0.174418i
$414$	2.57227e9	−	1.92219e9i	0.0875617	−	0.0654329i
$415$			3.74615e10i			1.26297i
$416$	−8.99622e9	−	7.86185e9i	−0.300391	−	0.262513i
$417$	2.14811e10			0.710416
$418$	5.25665e9	+	7.03440e9i	0.172188	+	0.230421i
$419$	1.25905e10	+	1.25905e10i	0.408495	+	0.408495i	0.881214	−	0.472718i	$-0.156727\pi$
$419$	1.25905e10	+	1.25905e10i	0.408495	+	0.408495i	−0.472718	+	0.881214i	$0.656727\pi$
$420$	−1.00881e10	−	2.98060e9i	−0.324200	−	0.0957871i
$421$	2.54004e10	+	2.54004e10i	0.808558	+	0.808558i	0.984416	−	0.175857i	$-0.0562697\pi$
$421$	2.54004e10	+	2.54004e10i	0.808558	+	0.808558i	−0.175857	+	0.984416i	$0.556270\pi$
$422$	−2.38276e9	+	1.64740e10i	−0.0751330	+	0.519455i
$423$	1.86315e10			0.581952
$424$	8.13589e9	+	3.74041e9i	0.251734	+	0.115733i
$425$		−	1.66759e10i		−	0.511133i
$426$	−2.08479e9	+	1.44138e10i	−0.0633029	+	0.437664i
$427$	−3.99510e8	+	3.99510e8i	−0.0120175	+	0.0120175i
$428$	1.08044e10	+	1.98663e10i	0.321977	+	0.592026i
$429$	4.38638e9	−	4.38638e9i	0.129502	−	0.129502i
$430$	3.96484e10	+	5.30572e10i	1.15972	+	1.55192i
$431$		−	1.93468e10i		−	0.560662i	−0.959903	−	0.280331i	$-0.909556\pi$
$431$		−	1.93468e10i		−	0.560662i	0.959903	−	0.280331i	$-0.0904442\pi$
$432$	6.55434e9	−	1.40270e9i	0.188189	−	0.0402744i
$433$	−4.72416e10			−1.34392			−0.671959	−	0.740588i	$-0.734547\pi$
$433$	−4.72416e10			−1.34392			−0.671959	+	0.740588i	$0.734547\pi$
$434$	1.78078e10	−	1.33073e10i	0.501939	−	0.375087i
$435$	1.20664e9	+	1.20664e9i	0.0336994	+	0.0336994i
$436$	2.35226e10	+	4.32514e10i	0.650937	+	1.19689i
$437$	3.05916e9	+	3.05916e9i	0.0838834	+	0.0838834i
$438$	−2.13871e10	−	3.09339e9i	−0.581105	−	0.0840500i
$439$	5.30947e10			1.42953			0.714764	−	0.699365i	$-0.246534\pi$
$439$	5.30947e10			1.42953			0.714764	+	0.699365i	$0.246534\pi$
$440$	−3.42717e10	+	1.26841e10i	−0.914377	+	0.338416i
$441$		−	9.73269e9i		−	0.257323i
$442$	−1.52983e10	−	2.21271e9i	−0.400823	−	0.0579743i
$443$	−4.24048e10	+	4.24048e10i	−1.10103	+	1.10103i	−0.106745	+	0.994286i	$0.534043\pi$
$443$	−4.24048e10	+	4.24048e10i	−1.10103	+	1.10103i	−0.994286	+	0.106745i	$0.965957\pi$
$444$	−3.17655e10	−	9.38535e9i	−0.817380	−	0.241501i
$445$	4.28940e10	−	4.28940e10i	1.09385	−	1.09385i
$446$	3.10275e10	−	2.31862e10i	0.784166	−	0.585989i
$447$		−	3.95890e10i		−	0.991619i
$448$	1.46009e10	−	1.25231e10i	0.362466	−	0.310885i
$449$	1.20946e10			0.297581			0.148791	−	0.988869i	$-0.452462\pi$
$449$	1.20946e10			0.297581			0.148791	+	0.988869i	$0.452462\pi$
$450$	4.11958e9	+	5.51279e9i	0.100462	+	0.134438i
$451$	−5.73999e9	−	5.73999e9i	−0.138741	−	0.138741i
$452$	−2.33883e10	+	7.91596e10i	−0.560331	+	1.89649i
$453$	1.87604e10	+	1.87604e10i	0.445501	+	0.445501i
$454$	−4.17455e9	+	2.88620e10i	−0.0982621	+	0.679365i
$455$	−1.00114e10			−0.233586
$456$	3.13444e9	+	8.46907e9i	0.0724938	+	0.195874i
$457$		−	8.02343e10i		−	1.83948i	−0.392527	−	0.919740i	$-0.628399\pi$
$457$		−	8.02343e10i		−	1.83948i	0.392527	−	0.919740i	$-0.371601\pi$
$458$	−6.34946e9	+	4.38989e10i	−0.144303	+	0.997682i
$459$	6.13200e9	−	6.13200e9i	0.138150	−	0.138150i
$460$	−1.58159e10	+	8.60157e9i	−0.353234	+	0.192108i
$461$	−1.17603e10	+	1.17603e10i	−0.260384	+	0.260384i	−0.825210	−	0.564826i	$-0.808943\pi$
$461$	−1.17603e10	+	1.17603e10i	−0.260384	+	0.260384i	0.564826	+	0.825210i	$0.308943\pi$
$462$	5.97855e9	+	8.00044e9i	0.131228	+	0.175609i
$463$			1.50064e10i			0.326553i	0.986580	+	0.163277i	$0.0522063\pi$
$463$			1.50064e10i			0.326553i	−0.986580	+	0.163277i	$0.947794\pi$
$464$	−3.05138e9	+	6.53027e8i	−0.0658300	+	0.0140883i
$465$	−4.34307e10			−0.928934
$466$	3.19309e10	−	2.38612e10i	0.677122	−	0.505998i
$467$	4.46307e10	+	4.46307e10i	0.938353	+	0.938353i	0.998207	−	0.0598542i	$-0.0190636\pi$
$467$	4.46307e10	+	4.46307e10i	0.938353	+	0.938353i	−0.0598542	+	0.998207i	$0.519064\pi$
$468$	5.60398e9	−	3.04776e9i	0.116819	−	0.0635328i
$469$	2.23885e10	+	2.23885e10i	0.462736	+	0.462736i
$470$	−1.03384e11	−	1.49533e10i	−2.11866	−	0.306439i
$471$	4.78843e10			0.972992
$472$	−1.07091e10	+	2.32938e10i	−0.215768	+	0.469323i
$473$		−	6.28870e10i		−	1.25637i
$474$	5.34075e10	+	7.72476e9i	1.05801	+	0.153028i
$475$	−6.55628e9	+	6.55628e9i	−0.128790	+	0.128790i
$476$	7.05171e9	−	2.38671e10i	0.137362	−	0.464913i
$477$	−3.38077e9	+	3.38077e9i	−0.0653044	+	0.0653044i
$478$	−1.73966e10	+	1.30001e10i	−0.333237	+	0.249020i
$479$		−	6.81118e10i		−	1.29384i	−0.762558	−	0.646920i	$-0.776057\pi$
$479$		−	6.81118e10i		−	1.29384i	0.762558	−	0.646920i	$-0.223943\pi$
$480$	−3.74949e10	+	2.52302e9i	−0.706330	+	0.0475286i
$481$	−3.15238e10			−0.588923
$482$	−2.54686e10	−	3.40819e10i	−0.471864	−	0.631445i
$483$	3.47927e9	+	3.47927e9i	0.0639293	+	0.0639293i
$484$	−1.93524e10	−	5.71780e9i	−0.352657	−	0.104195i
$485$	2.86767e10	+	2.86767e10i	0.518277	+	0.518277i
$486$	−5.12305e8	+	3.54198e9i	−0.00918298	+	0.0634894i
$487$	1.39157e10			0.247394			0.123697	−	0.992320i	$-0.460525\pi$
$487$	1.39157e10			0.247394			0.123697	+	0.992320i	$0.460525\pi$
$488$	−8.43121e8	+	1.83390e9i	−0.0148666	+	0.0323367i
$489$			1.83095e10i			0.320214i
$490$	−7.81124e9	+	5.40054e10i	−0.135499	+	0.936813i
$491$	−1.58686e10	+	1.58686e10i	−0.273031	+	0.273031i	−0.830319	−	0.557288i	$-0.811842\pi$
$491$	−1.58686e10	+	1.58686e10i	−0.273031	+	0.273031i	0.557288	+	0.830319i	$0.311842\pi$
$492$	−3.98829e9	−	7.33335e9i	−0.0680654	−	0.125153i
$493$	−2.85476e9	+	2.85476e9i	−0.0483261	+	0.0483261i
$494$	5.14470e9	+	6.88459e9i	0.0863877	+	0.115603i
$495$		−	1.95120e10i		−	0.324998i
$496$	4.31618e10	−	6.66662e10i	0.713137	−	1.10149i
$497$	−2.23162e10			−0.365759
$498$	2.92993e10	−	2.18947e10i	0.476366	−	0.355977i
$499$	2.74149e9	+	2.74149e9i	0.0442166	+	0.0442166i	0.728869	−	0.684653i	$-0.240046\pi$
$499$	2.74149e9	+	2.74149e9i	0.0442166	+	0.0442166i	−0.684653	+	0.728869i	$0.740046\pi$
$500$	1.81795e10	+	3.34270e10i	0.290872	+	0.534832i
$501$	−3.31866e10	−	3.31866e10i	−0.526759	−	0.526759i
$502$	−9.65260e10	−	1.39613e10i	−1.51995	−	0.219843i
$503$	6.69740e10			1.04625			0.523123	−	0.852257i	$-0.324767\pi$
$503$	6.69740e10			1.04625			0.523123	+	0.852257i	$0.324767\pi$
$504$	3.56490e9	+	9.63213e9i	0.0552491	+	0.149280i
$505$		−	5.93151e10i		−	0.912010i
$506$	1.69175e10	+	2.44692e9i	0.258068	+	0.0373265i
$507$	−2.26817e10	+	2.26817e10i	−0.343276	+	0.343276i
$508$	−3.05450e10	−	9.02475e9i	−0.458655	−	0.135513i
$509$	1.18240e10	−	1.18240e10i	0.176154	−	0.176154i	−0.613523	−	0.789677i	$-0.710248\pi$
$509$	1.18240e10	−	1.18240e10i	0.176154	−	0.176154i	0.789677	+	0.613523i	$0.210248\pi$
$510$	−3.89471e10	+	2.91043e10i	−0.575698	+	0.430206i
$511$		−	3.31125e10i		−	0.485634i
$512$	3.33900e10	−	6.00622e10i	0.485889	−	0.874021i
$513$	−4.82170e9			−0.0696195
$514$	−6.87452e10	−	9.19942e10i	−0.984894	−	1.31798i
$515$	−2.24004e10	−	2.24004e10i	−0.318439	−	0.318439i
$516$	1.83241e10	−	6.20195e10i	0.258478	−	0.874842i
$517$	7.01306e10	+	7.01306e10i	0.981625	+	0.981625i
$518$	7.26543e9	−	5.02318e10i	0.100912	−	0.697686i
$519$	−4.76950e10			−0.657360
$520$	−3.35419e10	+	1.24140e10i	−0.458748	+	0.169785i
$521$		−	8.05938e10i		−	1.09383i	−0.837188	−	0.546916i	$-0.815802\pi$
$521$		−	8.05938e10i		−	1.09383i	0.837188	−	0.546916i	$-0.184198\pi$
$522$	2.38504e8	−	1.64897e9i	0.00321228	−	0.0222091i
$523$	1.62775e10	−	1.62775e10i	0.217561	−	0.217561i	−0.589909	−	0.807470i	$-0.700836\pi$
$523$	1.62775e10	−	1.62775e10i	0.217561	−	0.217561i	0.807470	+	0.589909i	$0.200836\pi$
$524$	−3.15033e10	+	1.71332e10i	−0.417859	+	0.227256i
$525$	−7.45666e9	+	7.45666e9i	−0.0981539	+	0.0981539i
$526$	3.12453e10	+	4.18122e10i	0.408170	+	0.546210i
$527$		−	1.02751e11i		−	1.33212i
$528$	2.99509e10	+	1.93912e10i	0.385367	+	0.249499i
$529$	−6.98897e10			−0.892463
$530$	2.14728e10	−	1.60461e10i	0.272136	−	0.203361i
$531$	−9.67946e9	−	9.67946e9i	−0.121751	−	0.121751i
$532$	−1.21560e10	+	6.61112e9i	−0.151756	+	0.0825332i
$533$	−5.61775e9	−	5.61775e9i	−0.0696071	−	0.0696071i
$534$	−5.86180e10	−	8.47840e9i	−0.720885	−	0.104267i
$535$	6.76973e10			0.826335
$536$	1.02772e11	+	4.72484e10i	1.24513	+	0.572438i
$537$			5.07296e10i			0.610049i
$538$	−5.00974e10	−	7.24600e9i	−0.597979	−	0.0864906i
$539$	3.66346e10	−	3.66346e10i	0.434047	−	0.434047i
$540$	5.68543e9	−	1.92428e10i	0.0668634	−	0.226305i
$541$	−1.04971e10	+	1.04971e10i	−0.122540	+	0.122540i	−0.765717	−	0.643177i	$-0.777616\pi$
$541$	−1.04971e10	+	1.04971e10i	−0.122540	+	0.122540i	0.643177	+	0.765717i	$0.277616\pi$
$542$	−7.75538e10	+	5.79542e10i	−0.898681	+	0.671564i
$543$			3.91373e9i			0.0450185i
$544$	−5.96912e9	−	8.87080e10i	−0.0681577	−	1.01290i
$545$	1.47386e11			1.67059
$546$	5.85122e9	+	7.83006e9i	0.0658379	+	0.0881038i
$547$	−7.64183e10	−	7.64183e10i	−0.853588	−	0.853588i	0.136985	−	0.990573i	$-0.456259\pi$
$547$	−7.64183e10	−	7.64183e10i	−0.853588	−	0.853588i	−0.990573	+	0.136985i	$0.956259\pi$
$548$	1.55045e11	+	4.58091e10i	1.71923	+	0.507960i
$549$	−7.62055e8	−	7.62055e8i	−0.00838875	−	0.00838875i
$550$	−5.24415e9	+	3.62571e10i	−0.0573092	+	0.396225i
$551$	2.24475e9			0.0243535
$552$	1.59712e10	+	7.34262e9i	0.172021	+	0.0790851i
$553$			8.26882e10i			0.884185i
$554$	5.22192e9	−	3.61033e10i	0.0554359	−	0.383273i
$555$	−7.01139e10	+	7.01139e10i	−0.738979	+	0.738979i
$556$	5.61812e10	+	1.03302e11i	0.587885	+	1.08096i
$557$	−1.08581e11	+	1.08581e11i	−1.12807	+	1.12807i	−0.137575	+	0.990491i	$0.543931\pi$
$557$	−1.08581e11	+	1.08581e11i	−1.12807	+	1.12807i	−0.990491	+	0.137575i	$0.956069\pi$
$558$	2.53834e10	+	3.39679e10i	0.261827	+	0.350374i
$559$		−	6.15477e10i		−	0.630325i
$560$	−1.20506e10	−	5.63086e10i	−0.122534	−	0.572562i
$561$	4.61627e10			0.466058
$562$	1.63859e10	−	1.22448e10i	0.164257	−	0.122746i
$563$	−7.84449e10	−	7.84449e10i	−0.780784	−	0.780784i	0.199179	−	0.979963i	$-0.436172\pi$
$563$	−7.84449e10	−	7.84449e10i	−0.780784	−	0.780784i	−0.979963	+	0.199179i	$0.936172\pi$
$564$	4.87285e10	+	8.95980e10i	0.481578	+	0.885487i
$565$	1.74724e11	+	1.74724e11i	1.71458	+	1.71458i
$566$	−6.91162e10	−	9.99684e9i	−0.673463	−	0.0974085i
$567$	−5.48387e9			−0.0530585
$568$	−7.47678e10	+	2.76719e10i	−0.718326	+	0.265856i
$569$			4.25376e10i			0.405811i	0.979198	+	0.202906i	$0.0650385\pi$
$569$			4.25376e10i			0.405811i	−0.979198	+	0.202906i	$0.934962\pi$
$570$	2.67550e10	+	3.86979e9i	0.253458	+	0.0366597i
$571$	1.28517e11	−	1.28517e11i	1.20897	−	1.20897i	0.237611	−	0.971360i	$-0.423636\pi$
$571$	1.28517e11	−	1.28517e11i	1.20897	−	1.20897i	0.971360	−	0.237611i	$-0.0763644\pi$
$572$	3.25659e10	+	9.62183e9i	0.304214	+	0.0898821i
$573$	−6.11350e10	+	6.11350e10i	−0.567116	+	0.567116i
$574$	1.02464e10	−	7.65688e9i	0.0943893	−	0.0705350i
$575$			1.80483e10i			0.165106i
$576$	2.38876e10	+	2.78509e10i	0.217011	+	0.253016i
$577$	−1.18483e11			−1.06893			−0.534467	−	0.845189i	$-0.679488\pi$
$577$	−1.18483e11			−1.06893			−0.534467	+	0.845189i	$0.679488\pi$
$578$	−2.04549e9	−	2.73725e9i	−0.0183267	−	0.0245247i
$579$	3.59453e10	+	3.59453e10i	0.319837	+	0.319837i
$580$	−2.64686e9	+	8.95852e9i	−0.0233894	+	0.0791633i
$581$	3.96306e10	+	3.96306e10i	0.347797	+	0.347797i
$582$	5.66821e9	−	3.91889e10i	0.0494030	−	0.341563i
$583$	−2.54510e10			−0.220308
$584$	−4.10593e10	−	1.10940e11i	−0.352988	−	0.953752i
$585$		−	1.90964e10i		−	0.163053i
$586$	1.11160e10	−	7.68539e10i	0.0942667	−	0.651742i
$587$	−9.09257e10	+	9.09257e10i	−0.765833	+	0.765833i	−0.977370	−	0.211537i	$-0.932153\pi$
$587$	−9.09257e10	+	9.09257e10i	−0.765833	+	0.765833i	0.211537	+	0.977370i	$0.432153\pi$
$588$	4.68040e10	−	2.54546e10i	0.391537	−	0.212940i
$589$	−4.03975e10	+	4.03975e10i	−0.335655	+	0.335655i
$590$	4.59416e10	+	6.14786e10i	0.379138	+	0.507360i
$591$		−	2.20512e10i		−	0.180751i
$592$	−3.79451e10	−	1.77305e11i	−0.308936	−	1.44356i
$593$	−9.05473e10			−0.732245			−0.366123	−	0.930567i	$-0.619315\pi$
$593$	−9.05473e10			−0.732245			−0.366123	+	0.930567i	$0.619315\pi$
$594$	−1.52607e10	+	1.14039e10i	−0.122582	+	0.0916029i
$595$	−5.26803e10	−	5.26803e10i	−0.420320	−	0.420320i
$596$	1.90382e11	−	1.03540e11i	1.50883	−	0.820586i
$597$	1.01982e9	+	1.01982e9i	0.00802836	+	0.00802836i
$598$	1.65572e10	+	2.39481e9i	0.129474	+	0.0187269i
$599$	−3.75917e9			−0.0292001			−0.0146001	−	0.999893i	$-0.504648\pi$
$599$	−3.75917e9			−0.0292001			−0.0146001	+	0.999893i	$0.504648\pi$
$600$	−1.57365e10	+	3.42289e10i	−0.121423	+	0.264112i
$601$			9.23563e10i			0.707895i	0.935265	+	0.353947i	$0.115161\pi$
$601$			9.23563e10i			0.707895i	−0.935265	+	0.353947i	$0.884839\pi$
$602$	9.80734e10	+	1.41852e10i	0.746733	+	0.108006i
$603$	−4.27055e10	+	4.27055e10i	−0.323009	+	0.323009i
$604$	−4.11522e10	+	1.39283e11i	−0.309204	+	1.04653i
$605$	−4.27152e10	+	4.27152e10i	−0.318831	+	0.318831i
$606$	−4.63914e10	+	3.46672e10i	−0.343991	+	0.257057i
$607$			2.15380e11i			1.58654i	0.608872	+	0.793268i	$0.291622\pi$
$607$			2.15380e11i			1.58654i	−0.608872	+	0.793268i	$0.708378\pi$
$608$	−3.25295e10	+	3.72232e10i	−0.238047	+	0.272395i
$609$	2.55302e9			0.0185603
$610$	3.61694e9	+	4.84016e9i	0.0261229	+	0.0349575i
$611$	6.86370e10	+	6.86370e10i	0.492486	+	0.492486i
$612$	4.55260e10	+	1.34510e10i	0.324529	+	0.0958844i
$613$	−3.33976e10	−	3.33976e10i	−0.236523	−	0.236523i	0.578886	−	0.815409i	$-0.303488\pi$
$613$	−3.33976e10	−	3.33976e10i	−0.236523	−	0.236523i	−0.815409	+	0.578886i	$0.803488\pi$
$614$	1.48204e10	−	1.02466e11i	0.104277	−	0.720949i
$615$	−2.49895e10			−0.174686
$616$	−2.28376e10	+	4.96747e10i	−0.158609	+	0.344995i
$617$			2.06755e11i			1.42664i	0.700838	+	0.713321i	$0.252810\pi$
$617$			2.06755e11i			1.42664i	−0.700838	+	0.713321i	$0.747190\pi$
$618$	−4.42763e9	+	3.06118e10i	−0.0303541	+	0.209863i
$619$	4.20826e10	−	4.20826e10i	0.286642	−	0.286642i	−0.549109	−	0.835751i	$-0.685033\pi$
$619$	4.20826e10	−	4.20826e10i	0.286642	−	0.286642i	0.835751	+	0.549109i	$0.185033\pi$
$620$	−1.13588e11	−	2.08856e11i	−0.768713	−	1.41345i
$621$	−6.63663e9	+	6.63663e9i	−0.0446253	+	0.0446253i
$622$	−9.35315e9	−	1.25163e10i	−0.0624880	−	0.0836209i
$623$		−	9.07553e10i		−	0.602448i
$624$	2.93131e10	+	1.89782e10i	0.193340	+	0.125175i
$625$	1.90733e11			1.24999
$626$	2.19846e11	−	1.64286e11i	1.43160	−	1.06980i
$627$	−1.81493e10	−	1.81493e10i	−0.117433	−	0.117433i
$628$	1.25235e11	+	2.30273e11i	0.805172	+	1.48049i
$629$	−1.65880e11	−	1.65880e11i	−1.05972	−	1.05972i
$630$	3.04293e10	+	4.40124e9i	0.193166	+	0.0279391i
$631$	−2.89174e10			−0.182407			−0.0912037	−	0.995832i	$-0.529071\pi$
$631$	−2.89174e10			−0.182407			−0.0912037	+	0.995832i	$0.529071\pi$
$632$	1.02533e11	+	2.77037e11i	0.642679	+	1.73648i
$633$		−	4.86517e10i		−	0.303028i
$634$	−3.10357e11	−	4.48895e10i	−1.92090	−	0.277835i
$635$	−6.74200e10	+	6.74200e10i	−0.414662	+	0.414662i
$636$	−2.50999e10	−	7.41596e9i	−0.153407	−	0.0453251i
$637$	3.58544e10	−	3.58544e10i	0.217763	−	0.217763i
$638$	7.10461e9	−	5.30912e9i	0.0428803	−	0.0320435i
$639$		−	4.25676e10i		−	0.255315i
$640$	−1.10196e11	−	1.73713e11i	−0.656822	−	1.03541i
$641$	−1.65875e11			−0.982536			−0.491268	−	0.871008i	$-0.663467\pi$
$641$	−1.65875e11			−0.982536			−0.491268	+	0.871008i	$0.663467\pi$
$642$	−3.95663e10	−	5.29472e10i	−0.232908	−	0.311676i
$643$	5.17052e10	+	5.17052e10i	0.302475	+	0.302475i	0.841982	−	0.539506i	$-0.181389\pi$
$643$	5.17052e10	+	5.17052e10i	0.302475	+	0.302475i	−0.539506	+	0.841982i	$0.681389\pi$
$644$	−7.63203e9	+	2.58313e10i	−0.0443707	+	0.150177i
$645$	−1.36892e11	−	1.36892e11i	−0.790929	−	0.790929i
$646$	−9.15542e9	+	6.32988e10i	−0.0525712	+	0.363467i
$647$	6.39094e10			0.364710			0.182355	−	0.983233i	$-0.441628\pi$
$647$	6.39094e10			0.364710			0.182355	+	0.983233i	$0.441628\pi$
$648$	−1.83731e10	+	6.79996e9i	−0.104203	+	0.0385662i
$649$		−	7.28686e10i		−	0.410735i
$650$	−5.13247e9	+	3.54849e10i	−0.0287523	+	0.198788i
$651$	−4.59454e10	+	4.59454e10i	−0.255810	+	0.255810i
$652$	−8.80493e10	+	4.78862e10i	−0.487232	+	0.264984i
$653$	5.89690e10	−	5.89690e10i	0.324318	−	0.324318i	−0.526103	−	0.850421i	$-0.676347\pi$
$653$	5.89690e10	−	5.89690e10i	0.324318	−	0.324318i	0.850421	+	0.526103i	$0.176347\pi$
$654$	−8.61409e10	−	1.15273e11i	−0.470867	−	0.630110i
$655$			1.07352e11i			0.583237i
$656$	2.48348e10	−	3.83589e10i	0.134105	−	0.207134i
$657$	6.31614e10			0.338993
$658$	−1.25189e11	+	9.35510e10i	−0.667826	+	0.499051i
$659$	−8.92526e10	−	8.92526e10i	−0.473238	−	0.473238i	0.429723	−	0.902961i	$-0.358611\pi$
$659$	−8.92526e10	−	8.92526e10i	−0.473238	−	0.473238i	−0.902961	+	0.429723i	$0.858611\pi$
$660$	9.38320e10	−	5.10311e10i	0.494510	−	0.268943i
$661$	1.45108e11	+	1.45108e11i	0.760127	+	0.760127i	0.976345	−	0.216218i	$-0.0693721\pi$
$661$	1.45108e11	+	1.45108e11i	0.760127	+	0.760127i	−0.216218	+	0.976345i	$0.569372\pi$
$662$	−1.34345e11	−	1.94315e10i	−0.699505	−	0.101175i
$663$	4.51796e10			0.233823
$664$	1.81919e11	+	8.36360e10i	0.935851	+	0.430250i
$665$			4.14234e10i			0.211816i
$666$	9.58160e10	+	1.38586e10i	0.487014	+	0.0704407i
$667$	3.08969e9	−	3.08969e9i	0.0156103	−	0.0156103i
$668$	7.27972e10	−	2.46388e11i	0.365602	−	1.23741i
$669$	−8.00533e10	+	8.00533e10i	−0.399646	+	0.399646i
$670$	2.71242e11	−	2.02693e11i	1.34604	−	1.00586i
$671$		−	5.73688e9i		−	0.0282999i
$672$	−3.69969e10	+	4.23351e10i	−0.181421	+	0.207598i
$673$	−2.06470e11			−1.00646			−0.503230	−	0.864153i	$-0.667855\pi$
$673$	−2.06470e11			−1.00646			−0.503230	+	0.864153i	$0.667855\pi$
$674$	1.79656e11	+	2.40414e11i	0.870565	+	1.16498i
$675$	−1.42234e10	−	1.42234e10i	−0.0685155	−	0.0685155i
$676$	−1.68396e11	−	4.97539e10i	−0.806392	−	0.238254i
$677$	1.76862e8	+	1.76862e8i	0.000841937	+	0.000841937i	0.707528	−	0.706686i	$-0.249810\pi$
$677$	1.76862e8	+	1.76862e8i	0.000841937	+	0.000841937i	−0.706686	+	0.707528i	$0.749810\pi$
$678$	3.45357e10	−	2.38773e11i	0.163437	−	1.12997i
$679$	6.06742e10			0.285447
$680$	−2.41822e11	−	1.11176e11i	−1.13099	−	0.519966i
$681$		−	8.52368e10i		−	0.396313i
$682$	−3.23126e10	+	2.23403e11i	−0.149360	+	1.03265i
$683$	4.47509e10	−	4.47509e10i	0.205645	−	0.205645i	−0.596768	−	0.802414i	$-0.703549\pi$
$683$	4.47509e10	−	4.47509e10i	0.205645	−	0.205645i	0.802414	+	0.596768i	$0.203549\pi$
$684$	−1.26106e10	−	2.31873e10i	−0.0576116	−	0.105932i
$685$	3.42220e11	−	3.42220e11i	1.55433	−	1.55433i
$686$	1.12173e11	+	1.50109e11i	0.506515	+	0.677814i
$687$		−	1.29645e11i		−	0.582006i
$688$	3.46173e11	−	7.40847e10i	1.54504	−	0.330655i
$689$	−2.49090e10			−0.110530
$690$	4.21523e10	−	3.14994e10i	0.185962	−	0.138965i
$691$	1.50288e11	+	1.50288e11i	0.659194	+	0.659194i	0.955189	−	0.295996i	$-0.0956514\pi$
$691$	1.50288e11	+	1.50288e11i	0.659194	+	0.659194i	−0.295996	+	0.955189i	$0.595651\pi$
$692$	−1.24740e11	−	2.29363e11i	−0.543979	−	1.00023i
$693$	−2.06417e10	−	2.06417e10i	−0.0894980	−	0.0894980i
$694$	4.36059e10	+	6.30708e9i	0.187978	+	0.0271888i
$695$	3.52016e11			1.50877
$696$	8.55360e9	−	3.16573e9i	0.0364512	−	0.0134908i
$697$		−	5.91218e10i		−	0.250505i
$698$	7.62418e9	+	1.10275e9i	0.0321197	+	0.00464573i
$699$	−8.23839e10	+	8.23839e10i	−0.345091	+	0.345091i
$700$	−5.53607e10	−	1.63567e10i	−0.230573	−	0.0681246i
$701$	−8.09465e9	+	8.09465e9i	−0.0335217	+	0.0335217i	−0.723669	−	0.690147i	$-0.757546\pi$
$701$	−8.09465e9	+	8.09465e9i	−0.0335217	+	0.0335217i	0.690147	+	0.723669i	$0.257546\pi$
$702$	−1.49357e10	+	1.11611e10i	−0.0615001	+	0.0459576i
$703$			1.30434e11i			0.534036i
$704$	−1.49183e10	+	1.94748e11i	−0.0607334	+	0.792833i
$705$	3.05319e11			1.23594
$706$	−9.60396e10	−	1.28519e11i	−0.386573	−	0.517309i
$707$	−6.27495e10	−	6.27495e10i	−0.251150	−	0.251150i
$708$	2.12326e10	−	7.18634e10i	0.0845025	−	0.286006i
$709$	−1.72783e10	−	1.72783e10i	−0.0683778	−	0.0683778i	0.672091	−	0.740469i	$-0.265396\pi$
$709$	−1.72783e10	−	1.72783e10i	−0.0683778	−	0.0683778i	−0.740469	+	0.672091i	$0.765396\pi$
$710$	−3.41639e10	+	2.36202e11i	−0.134442	+	0.929503i
$711$	−1.57726e11			−0.617198
$712$	−1.12536e11	−	3.04065e11i	−0.437896	−	1.18317i
$713$			1.11207e11i			0.430303i
$714$	−1.04127e10	+	7.19917e10i	−0.0400656	+	0.277006i
$715$	7.18805e10	−	7.18805e10i	0.275034	−	0.275034i
$716$	−2.43956e11	+	1.32677e11i	−0.928238	+	0.504828i
$717$	4.48845e10	−	4.48845e10i	0.169832	−	0.169832i
$718$	−3.47284e10	−	4.64733e10i	−0.130674	−	0.174866i
$719$		−	2.02092e10i		−	0.0756196i	−0.999285	−	0.0378098i	$-0.987962\pi$
$719$		−	2.02092e10i		−	0.0756196i	0.999285	−	0.0378098i	$-0.0120381\pi$
$720$	1.07407e11	−	2.29863e10i	0.399672	−	0.0855340i
$721$	−4.73947e10			−0.175384
$722$	−1.89188e11	+	1.41376e11i	−0.696216	+	0.520267i
$723$	8.79338e10	+	8.79338e10i	0.321812	+	0.321812i
$724$	−1.88209e10	+	1.02359e10i	−0.0684993	+	0.0372538i
$725$	6.62172e9	+	6.62172e9i	0.0239673	+	0.0239673i
$726$	5.83736e10	+	8.44304e9i	0.210121	+	0.0303915i
$727$	−3.81423e11			−1.36543			−0.682714	−	0.730686i	$-0.739200\pi$
$727$	−3.81423e11			−1.36543			−0.682714	+	0.730686i	$0.739200\pi$
$728$	−2.23512e10	+	4.86168e10i	−0.0795747	+	0.173085i
$729$		−	1.04604e10i		−	0.0370370i
$730$	−3.50474e11	−	5.06920e10i	−1.23414	−	0.178504i
$731$	3.23867e11	−	3.23867e11i	1.13422	−	1.13422i
$732$	1.67162e9	−	5.65774e9i	0.00582229	−	0.0197060i
$733$	2.22792e11	−	2.22792e11i	0.771762	−	0.771762i	−0.206652	−	0.978414i	$-0.566257\pi$
$733$	2.22792e11	−	2.22792e11i	0.771762	−	0.771762i	0.978414	+	0.206652i	$0.0662569\pi$
$734$	3.48637e10	−	2.60529e10i	0.120113	−	0.0897576i
$735$		−	1.59492e11i		−	0.546498i
$736$	6.46035e9	+	9.60083e10i	0.0220163	+	0.327188i
$737$	−3.21494e11			−1.08969
$738$	1.46053e10	+	1.95447e10i	0.0492364	+	0.0658877i
$739$	−3.26765e11	−	3.26765e11i	−1.09561	−	1.09561i	−0.994917	−	0.100697i	$-0.967893\pi$
$739$	−3.26765e11	−	3.26765e11i	−1.09561	−	1.09561i	−0.100697	−	0.994917i	$-0.532107\pi$
$740$	−5.20548e11	−	1.53800e11i	−1.73594	−	0.512895i
$741$	−1.77628e10	−	1.77628e10i	−0.0589166	−	0.0589166i
$742$	5.74088e9	−	3.96913e10i	0.0189393	−	0.130942i
$743$	−3.64185e11			−1.19500			−0.597498	−	0.801870i	$-0.703839\pi$
$743$	−3.64185e11			−1.19500			−0.597498	+	0.801870i	$0.703839\pi$
$744$	−9.69626e10	+	2.10906e11i	−0.316455	+	0.688332i
$745$		−	6.48754e11i		−	2.10598i
$746$	−6.91319e10	+	4.77964e11i	−0.223215	+	1.54326i
$747$	−7.55944e10	+	7.55944e10i	−0.242777	+	0.242777i
$748$	1.20733e11	+	2.21994e11i	0.385673	+	0.709145i
$749$	7.16170e10	−	7.16170e10i	0.227556	−	0.227556i
$750$	−6.65742e10	−	8.90891e10i	−0.210407	−	0.281565i
$751$			4.39737e11i			1.38240i	0.722664	+	0.691200i	$0.242918\pi$
$751$			4.39737e11i			1.38240i	−0.722664	+	0.691200i	$0.757082\pi$
$752$	−3.03429e11	+	4.68665e11i	−0.948824	+	1.46552i
$753$	2.85065e11			0.886675
$754$	6.95331e9	−	5.19605e9i	0.0215133	−	0.0160764i
$755$	3.07430e11	+	3.07430e11i	0.946148	+	0.946148i
$756$	−1.43424e10	−	2.63716e10i	−0.0439070	−	0.0807328i
$757$	−3.06305e11	−	3.06305e11i	−0.932762	−	0.932762i	0.0651153	−	0.997878i	$-0.479258\pi$
$757$	−3.06305e11	−	3.06305e11i	−0.932762	−	0.932762i	−0.997878	+	0.0651153i	$0.979258\pi$
$758$	1.18771e11	+	1.71788e10i	0.359778	+	0.0520376i
$759$	−4.99617e10			−0.150546
$760$	5.13648e10	+	1.38784e11i	0.153961	+	0.415993i
$761$			1.55420e11i			0.463415i	0.972786	+	0.231707i	$0.0744312\pi$
$761$			1.55420e11i			0.463415i	−0.972786	+	0.231707i	$0.925569\pi$
$762$	9.21346e10	+	1.33262e10i	0.273277	+	0.0395263i
$763$	1.55920e11	−	1.55920e11i	0.460047	−	0.460047i
$764$	−4.53886e11	−	1.34104e11i	−1.33221	−	0.393612i
$765$	1.00486e11	−	1.00486e11i	0.293401	−	0.293401i
$766$	3.10126e11	−	2.31750e11i	0.900788	−	0.673138i
$767$		−	7.13167e10i		−	0.206068i
$768$	−7.14584e10	+	1.87714e11i	−0.205404	+	0.539576i
$769$	1.15505e11			0.330291			0.165145	−	0.986269i	$-0.447191\pi$
$769$	1.15505e11			0.330291			0.165145	+	0.986269i	$0.447191\pi$
$770$	9.79717e10	+	1.31105e11i	0.278701	+	0.372955i
$771$	2.37352e11	+	2.37352e11i	0.671699	+	0.671699i
$772$	−7.88486e10	+	2.66870e11i	−0.221986	+	0.751329i
$773$	−3.66903e11	−	3.66903e11i	−1.02762	−	1.02762i	−0.999608	−	0.0280140i	$-0.991082\pi$
$773$	−3.66903e11	−	3.66903e11i	−1.02762	−	1.02762i	−0.0280140	−	0.999608i	$-0.508918\pi$
$774$	−2.70579e10	+	1.87073e11i	−0.0753927	+	0.521251i
$775$	−2.38335e11			−0.660665
$776$	2.03282e11	−	7.52356e10i	0.560598	−	0.207480i
$777$			1.48347e11i			0.407001i
$778$	1.31748e10	−	9.10880e10i	0.0359605	−	0.248624i
$779$	−2.32443e10	+	2.32443e10i	−0.0631198	+	0.0631198i
$780$	9.18337e10	−	4.99443e10i	0.248098	−	0.134930i
$781$	1.60228e11	−	1.60228e11i	0.430660	−	0.430660i
$782$	7.45234e10	+	9.97266e10i	0.199281	+	0.266676i
$783$			4.86983e9i			0.0129559i
$784$	2.44820e11	+	1.58504e11i	0.648011	+	0.419543i
$785$	7.84690e11			2.06642
$786$	8.39620e10	−	6.27429e10i	0.219985	−	0.164390i
$787$	4.43800e11	+	4.43800e11i	1.15688	+	1.15688i	0.985143	+	0.171737i	$0.0549381\pi$
$787$	4.43800e11	+	4.43800e11i	1.15688	+	1.15688i	0.171737	+	0.985143i	$0.445062\pi$
$788$	1.06043e11	−	5.76721e10i	0.275028	−	0.149576i
$789$	−1.07878e11	−	1.07878e11i	−0.278373	−	0.278373i
$790$	8.75200e11	+	1.26587e11i	2.24698	+	0.324999i
$791$	3.69681e11			0.944324
$792$	−9.47533e10	−	4.35621e10i	−0.240821	−	0.110715i
$793$		−	5.61470e9i		−	0.0141982i
$794$	4.42259e11	+	6.39675e10i	1.11274	+	0.160945i
$795$	−5.54014e10	+	5.54014e10i	−0.138692	+	0.138692i
$796$	−2.23705e9	+	7.57149e9i	−0.00557216	+	0.0188594i
$797$	−4.95142e11	+	4.95142e11i	−1.22715	+	1.22715i	−0.262107	+	0.965039i	$0.584417\pi$
$797$	−4.95142e11	+	4.95142e11i	−1.22715	+	1.22715i	−0.965039	+	0.262107i	$0.915583\pi$
$798$	3.23980e10	−	2.42103e10i	0.0798927	−	0.0597020i
$799$			7.22344e11i			1.77238i
$800$	−2.05762e11	+	1.38456e10i	−0.502348	+	0.0338028i
$801$	1.73114e11			0.420534
$802$	−3.40259e11	−	4.55331e11i	−0.822454	−	1.10060i
$803$	2.37745e11	+	2.37745e11i	0.571806	+	0.571806i
$804$	−3.17060e11	−	9.36775e10i	−0.758781	−	0.224187i
$805$	5.70156e10	+	5.70156e10i	0.135772	+	0.135772i
$806$	−3.16245e10	+	2.18646e11i	−0.0749347	+	0.518084i
$807$	1.47950e11			0.348836
$808$	−2.88044e11	−	1.32426e11i	−0.675792	−	0.310690i
$809$			6.32437e11i			1.47647i	0.674546	+	0.738233i	$0.264339\pi$
$809$			6.32437e11i			1.47647i	−0.674546	+	0.738233i	$0.735661\pi$
$810$	−8.39525e9	+	5.80432e10i	−0.0195027	+	0.134838i
$811$	9.03786e10	−	9.03786e10i	0.208921	−	0.208921i	−0.594888	−	0.803809i	$-0.702804\pi$
$811$	9.03786e10	−	9.03786e10i	0.208921	−	0.208921i	0.803809	+	0.594888i	$0.202804\pi$
$812$	6.67711e9	+	1.22773e10i	0.0153591	+	0.0282410i
$813$	2.00094e11	−	2.00094e11i	0.458008	−	0.458008i
$814$	3.08494e11	+	4.12824e11i	0.702667	+	0.940303i
$815$			3.00041e11i			0.680065i
$816$	5.43825e10	+	2.54111e11i	0.122659	+	0.573143i
$817$	−2.54662e11			−0.571579
$818$	2.15907e11	−	1.61342e11i	0.482228	−	0.360358i
$819$	−2.02021e10	−	2.02021e10i	−0.0449016	−	0.0449016i
$820$	−6.53569e10	−	1.20173e11i	−0.144556	−	0.265798i
$821$	−1.74216e11	−	1.74216e11i	−0.383457	−	0.383457i	0.488889	−	0.872346i	$-0.337402\pi$
$821$	−1.74216e11	−	1.74216e11i	−0.383457	−	0.383457i	−0.872346	+	0.488889i	$0.837402\pi$
$822$	−4.67670e11	−	6.76429e10i	−1.02436	−	0.148161i
$823$	−8.42614e11			−1.83666			−0.918331	−	0.395814i	$-0.870463\pi$
$823$	−8.42614e11			−1.83666			−0.918331	+	0.395814i	$0.870463\pi$
$824$	−1.58790e11	+	5.87691e10i	−0.344442	+	0.127480i
$825$		−	1.07076e11i		−	0.231141i
$826$	1.13640e11	+	1.64367e10i	0.244124	+	0.0353097i
$827$	1.62152e11	−	1.62152e11i	0.346657	−	0.346657i	−0.512206	−	0.858863i	$-0.671172\pi$
$827$	1.62152e11	−	1.62152e11i	0.346657	−	0.346657i	0.858863	+	0.512206i	$0.171172\pi$
$828$	−4.92725e10	−	1.45579e10i	−0.104829	−	0.0309726i
$829$	−2.43372e11	+	2.43372e11i	−0.515290	+	0.515290i	−0.916143	−	0.400853i	$-0.868714\pi$
$829$	−2.43372e11	+	2.43372e11i	−0.515290	+	0.515290i	0.400853	+	0.916143i	$0.368714\pi$
$830$	4.80134e11	−	3.58793e11i	1.01170	−	0.756018i
$831$			1.06622e11i			0.223585i
$832$	−1.46005e10	+	1.90600e11i	−0.0304702	+	0.397768i
$833$	3.77336e11			0.783697
$834$	−2.05739e11	−	2.75318e11i	−0.425257	−	0.569076i
$835$	−5.43836e11	−	5.43836e11i	−1.11872	−	1.11872i
$836$	3.98117e10	−	1.34746e11i	0.0815053	−	0.275862i
$837$	−8.76397e10	−	8.76397e10i	−0.178566	−	0.178566i
$838$	4.07817e10	−	2.81957e11i	0.0826969	−	0.571750i
$839$	−3.41228e11			−0.688648			−0.344324	−	0.938851i	$-0.611892\pi$
$839$	−3.41228e11			−0.688648			−0.344324	+	0.938851i	$0.611892\pi$
$840$	5.84188e10	+	1.57844e11i	0.117337	+	0.317037i
$841$			4.97979e11i			0.995468i
$842$	8.22738e10	−	5.68825e11i	0.163687	−	1.13170i
$843$	−4.22767e10	+	4.22767e10i	−0.0837127	+	0.0837127i
$844$	2.33963e11	−	1.27243e11i	0.461082	−	0.250762i
$845$	−3.71690e11	+	3.71690e11i	−0.729045	+	0.729045i
$846$	−1.78446e11	−	2.38795e11i	−0.348358	−	0.466170i
$847$			9.03769e10i			0.175600i
$848$	−2.99828e10	−	1.40100e11i	−0.0579815	−	0.270928i
$849$	2.04117e11			0.392870
$850$	−2.13731e11	+	1.59716e11i	−0.409441	+	0.305966i
$851$	1.79531e11	+	1.79531e11i	0.342312	+	0.342312i
$852$	2.04706e11	−	1.11330e11i	0.388482	−	0.211279i
$853$	4.81584e11	+	4.81584e11i	0.909653	+	0.909653i	0.996244	−	0.0865914i	$-0.0275975\pi$
$853$	4.81584e11	+	4.81584e11i	0.909653	+	0.909653i	−0.0865914	+	0.996244i	$0.527597\pi$
$854$	8.94677e9	+	1.29404e9i	0.0168203	+	0.00243286i
$855$	−7.90142e10			−0.147857
$856$	1.51140e11	−	3.28749e11i	0.281504	−	0.612307i
$857$		−	4.17379e11i		−	0.773762i	−0.922130	−	0.386881i	$-0.873552\pi$
$857$		−	4.17379e11i		−	0.773762i	0.922130	−	0.386881i	$-0.126448\pi$
$858$	−9.82302e10	−	1.42078e10i	−0.181257	−	0.0262167i
$859$	3.19928e11	−	3.19928e11i	0.587597	−	0.587597i	−0.349383	−	0.936980i	$-0.613609\pi$
$859$	3.19928e11	−	3.19928e11i	0.587597	−	0.587597i	0.936980	+	0.349383i	$0.113609\pi$
$860$	3.00281e11	−	1.01633e12i	0.548952	−	1.85797i
$861$	−2.64364e10	+	2.64364e10i	−0.0481050	+	0.0481050i
$862$	−2.47963e11	+	1.85297e11i	−0.449116	+	0.335614i
$863$		−	3.37009e11i		−	0.607573i	−0.952740	−	0.303787i	$-0.901749\pi$
$863$		−	3.37009e11i		−	0.607573i	0.952740	−	0.303787i	$-0.0982510\pi$
$864$	−8.07531e10	−	7.05706e10i	−0.144912	−	0.126639i
$865$	−7.81588e11			−1.39609
$866$	4.52463e11	+	6.05482e11i	0.804473	+	1.07654i
$867$	7.06231e9	+	7.06231e9i	0.0124989	+	0.0124989i
$868$	−3.41113e11	−	1.00784e11i	−0.600924	−	0.177547i
$869$	−5.93693e11	−	5.93693e11i	−1.04108	−	1.04108i
$870$	3.90842e9	−	2.70220e10i	0.00682219	−	0.0471673i
$871$	−3.14647e11			−0.546703
$872$	3.29051e11	−	7.15729e11i	0.569111	−	1.23789i
$873$			1.15735e11i			0.199254i
$874$	9.90886e9	−	6.85079e10i	0.0169816	−	0.117407i
$875$	1.20503e11	−	1.20503e11i	0.205573	−	0.205573i
$876$	1.65191e11	+	3.03740e11i	0.280524	+	0.515805i
$877$	1.14536e11	−	1.14536e11i	0.193617	−	0.193617i	−0.603640	−	0.797257i	$-0.706284\pi$
$877$	1.14536e11	−	1.14536e11i	0.193617	−	0.193617i	0.797257	+	0.603640i	$0.206284\pi$
$878$	−5.08522e11	−	6.80500e11i	−0.855720	−	1.14512i
$879$			2.26969e11i			0.380199i
$880$	4.90812e11	+	3.17767e11i	0.818436	+	0.529882i
$881$	5.78314e11			0.959976			0.479988	−	0.877275i	$-0.340641\pi$
$881$	5.78314e11			0.959976			0.479988	+	0.877275i	$0.340641\pi$
$882$	−1.24741e11	+	9.32163e10i	−0.206127	+	0.154034i
$883$	−7.77087e11	−	7.77087e11i	−1.27828	−	1.27828i	−0.941629	−	0.336653i	$-0.890705\pi$
$883$	−7.77087e11	−	7.77087e11i	−1.27828	−	1.27828i	−0.336653	−	0.941629i	$-0.609295\pi$
$884$	1.18162e11	+	2.17266e11i	0.193494	+	0.355781i
$885$	−1.58619e11	−	1.58619e11i	−0.258573	−	0.258573i
$886$	9.49628e11	+	1.37352e11i	1.54106	+	0.222896i
$887$	−3.37503e11			−0.545235			−0.272617	−	0.962123i	$-0.587889\pi$
$887$	−3.37503e11			−0.545235			−0.272617	+	0.962123i	$0.587889\pi$
$888$	1.83949e11	+	4.97020e11i	0.295833	+	0.799322i
$889$			1.42647e11i			0.228379i
$890$	−9.60585e11	−	1.38937e11i	−1.53100	−	0.221441i
$891$	3.93736e10	−	3.93736e10i	0.0624733	−	0.0624733i
$892$	−5.94342e11	−	1.75603e11i	−0.938808	−	0.277378i
$893$	2.83996e11	−	2.83996e11i	0.446587	−	0.446587i
$894$	−5.07402e11	+	3.79170e11i	−0.794332	+	0.593586i
$895$			8.31317e11i			1.29561i
$896$	−3.00348e11	−	6.71938e10i	−0.466007	−	0.104255i
$897$	−4.88976e10			−0.0755298
$898$	−1.15838e11	−	1.55013e11i	−0.178133	−	0.238376i
$899$	4.08008e10	+	4.08008e10i	0.0624639	+	0.0624639i
$900$	3.12001e10	−	1.05599e11i	0.0475538	−	0.160950i
$901$	−1.31072e11	−	1.31072e11i	−0.198890	−	0.198890i
$902$	−1.85923e10	+	1.28544e11i	−0.0280871	+	0.194189i
$903$	−2.89635e11			−0.435613
$904$	1.23857e12	−	4.58402e11i	1.85459	−	0.686393i
$905$			6.41351e10i			0.0956096i
$906$	6.07664e10	−	4.20127e11i	0.0901885	−	0.623546i
$907$	5.31088e11	−	5.31088e11i	0.784761	−	0.784761i	−0.195869	−	0.980630i	$-0.562753\pi$
$907$	5.31088e11	−	5.31088e11i	0.784761	−	0.784761i	0.980630	+	0.195869i	$0.0627528\pi$
$908$	4.09899e11	−	2.22926e11i	0.603022	−	0.327958i
$909$	1.19693e11	−	1.19693e11i	0.175313	−	0.175313i
$910$	9.58852e10	+	1.28313e11i	0.139825	+	0.187113i
$911$		−	1.32798e12i		−	1.92804i	−0.265825	−	0.964021i	$-0.585644\pi$
$911$		−	1.32798e12i		−	1.92804i	0.265825	−	0.964021i	$-0.414356\pi$
$912$	7.85251e10	−	1.21287e11i	0.113509	−	0.175321i
$913$	−5.69087e11			−0.819022
$914$	−1.02834e12	+	7.68456e11i	−1.47351	+	1.10112i
$915$	−1.24880e10	−	1.24880e10i	−0.0178159	−	0.0178159i
$916$	6.23454e11	−	3.39069e11i	0.885569	−	0.481622i
$917$	1.13568e11	+	1.13568e11i	0.160612	+	0.160612i
$918$	−1.37322e11	−	1.98621e10i	−0.193362	−	0.0279675i
$919$	−1.34594e11			−0.188697			−0.0943483	−	0.995539i	$-0.530077\pi$
$919$	−1.34594e11			−0.188697			−0.0943483	+	0.995539i	$0.530077\pi$
$920$	2.61723e11	+	1.20325e11i	0.365334	+	0.167960i
$921$			3.02606e11i			0.420571i
$922$	2.63365e11	+	3.80926e10i	0.364447	+	0.0527129i
$923$	1.56816e11	−	1.56816e11i	0.216064	−	0.216064i
$924$	4.52791e10	−	1.53251e11i	0.0621169	−	0.210240i
$925$	−3.84765e11	+	3.84765e11i	−0.525568	+	0.525568i
$926$	1.92334e11	−	1.43726e11i	0.261584	−	0.195476i
$927$		−	9.04043e10i		−	0.122425i
$928$	3.75947e10	+	3.28542e10i	0.0506914	+	0.0442995i
$929$	−6.95168e11			−0.933312			−0.466656	−	0.884439i	$-0.654541\pi$
$929$	−6.95168e11			−0.933312			−0.466656	+	0.884439i	$0.654541\pi$
$930$	4.15964e11	+	5.56639e11i	0.556063	+	0.744118i
$931$	−1.48353e11	−	1.48353e11i	−0.197468	−	0.197468i
$932$	−6.11645e11	−	1.80715e11i	−0.810655	−	0.239514i
$933$	3.22930e10	+	3.22930e10i	0.0426169	+	0.0426169i
$934$	1.44562e11	−	9.99477e11i	0.189963	−	1.31336i
$935$	7.56478e11			0.989806
$936$	−9.27354e10	−	4.26344e10i	−0.120821	−	0.0555465i
$937$			1.32795e12i			1.72276i	0.507965	+	0.861378i	$0.330398\pi$
$937$			1.32795e12i			1.72276i	−0.507965	+	0.861378i	$0.669602\pi$
$938$	7.25181e10	−	5.01376e11i	0.0936775	−	0.647668i
$939$	−5.67218e11	+	5.67218e11i	−0.729605	+	0.729605i
$940$	7.98524e11	+	1.46826e12i	1.02277	+	1.88058i
$941$	1.45069e11	−	1.45069e11i	0.185019	−	0.185019i	−0.608520	−	0.793539i	$-0.708236\pi$
$941$	1.45069e11	−	1.45069e11i	0.185019	−	0.185019i	0.793539	+	0.608520i	$0.208236\pi$
$942$	−4.58619e11	−	6.13720e11i	−0.582436	−	0.779411i
$943$			6.39872e10i			0.0809182i
$944$	4.01119e11	−	8.58436e10i	0.505109	−	0.108099i
$945$	−8.98653e10			−0.112685
$946$	−8.06005e11	+	6.02309e11i	−1.00641	+	0.752064i
$947$	4.10774e11	+	4.10774e11i	0.510744	+	0.510744i	0.914754	−	0.404010i	$-0.132384\pi$
$947$	4.10774e11	+	4.10774e11i	0.510744	+	0.510744i	−0.404010	+	0.914754i	$0.632384\pi$
$948$	−4.12512e11	−	7.58495e11i	−0.510744	−	0.939116i
$949$	2.32681e11	+	2.32681e11i	0.286878	+	0.286878i
$950$	1.46824e11	+	2.12363e10i	0.180261	+	0.0260726i
$951$	9.16562e11			1.12057
$952$	−3.73437e11	+	1.38211e11i	−0.454642	+	0.168265i
$953$			6.77802e10i			0.0821735i	0.999156	+	0.0410867i	$0.0130820\pi$
$953$			6.77802e10i			0.0821735i	−0.999156	+	0.0410867i	$0.986918\pi$
$954$	7.57103e10	+	1.09506e10i	0.0914032	+	0.0132204i
$955$	−1.00183e12	+	1.00183e12i	−1.20443	+	1.20443i
$956$	3.33237e11	+	9.84573e10i	0.398953	+	0.117874i
$957$	−1.83304e10	+	1.83304e10i	−0.0218537	+	0.0218537i
$958$	−8.72971e11	+	6.52351e11i	−1.03642	+	0.774496i
$959$		−	7.24070e11i		−	0.856064i
$960$	3.91450e11	+	4.56398e11i	0.460884	+	0.537352i
$961$	−6.15648e11			−0.721837
$962$	3.01924e11	+	4.04032e11i	0.352531	+	0.471754i
$963$	1.36608e11	+	1.36608e11i	0.158844	+	0.158844i
$964$	−1.92889e11	+	6.52849e11i	−0.223357	+	0.755970i
$965$	5.89044e11	+	5.89044e11i	0.679264	+	0.679264i
$966$	1.12697e10	−	7.79162e10i	0.0129420	−	0.0894786i
$967$	1.14603e12			1.31066			0.655332	−	0.755341i	$-0.272529\pi$
$967$	1.14603e12			1.31066			0.655332	+	0.755341i	$0.272529\pi$
$968$	1.12067e11	+	3.02797e11i	0.127637	+	0.344866i
$969$		−	1.86937e11i		−	0.212032i
$970$	9.28861e10	−	6.42196e11i	0.104921	−	0.725406i
$971$	−1.47682e10	+	1.47682e10i	−0.0166131	+	0.0166131i	−0.715365	−	0.698751i	$-0.753739\pi$
$971$	−1.47682e10	+	1.47682e10i	−0.0166131	+	0.0166131i	0.698751	+	0.715365i	$0.253739\pi$
$972$	5.03033e10	−	2.73578e10i	0.0563548	−	0.0306489i
$973$	3.72398e11	−	3.72398e11i	0.415486	−	0.415486i
$974$	−1.33280e11	−	1.78354e11i	−0.148091	−	0.198174i
$975$		−	1.04796e11i		−	0.115965i
$976$	3.15797e10	−	6.75839e9i	0.0348024	−	0.00744807i
$977$	5.65253e11			0.620390			0.310195	−	0.950673i	$-0.399606\pi$
$977$	5.65253e11			0.620390			0.310195	+	0.950673i	$0.399606\pi$
$978$	2.34668e11	−	1.75362e11i	0.256506	−	0.191681i
$979$	6.51614e11	+	6.51614e11i	0.709348	+	0.709348i
$980$	7.66986e11	−	4.17130e11i	0.831540	−	0.452239i
$981$	2.97413e11	+	2.97413e11i	0.321132	+	0.321132i
$982$	3.55367e11	+	5.13997e10i	0.382148	+	0.0552732i
$983$	2.61906e11			0.280499			0.140250	−	0.990116i	$-0.455209\pi$
$983$	2.61906e11			0.280499			0.140250	+	0.990116i	$0.455209\pi$
$984$	−5.57911e10	+	1.21353e11i	−0.0595093	+	0.129441i
$985$		−	3.61357e11i		−	0.383877i
$986$	6.39306e10	+	9.24680e9i	0.0676396	+	0.00978326i
$987$	3.22997e11	−	3.22997e11i	0.340353	−	0.340353i
$988$	3.89638e10	−	1.31876e11i	0.0408916	−	0.138401i
$989$	−3.50520e11	+	3.50520e11i	−0.366376	+	0.366376i
$990$	−2.50080e11	+	1.86879e11i	−0.260338	+	0.194545i
$991$		−	3.41677e11i		−	0.354259i	−0.984188	−	0.177130i	$-0.943319\pi$
$991$		−	3.41677e11i		−	0.354259i	0.984188	−	0.177130i	$-0.0566812\pi$
$992$	−1.26783e12	+	8.53118e10i	−1.30923	+	0.0880973i
$993$	3.96756e11			0.408062
$994$	2.13737e11	+	2.86021e11i	0.218944	+	0.292990i
$995$	1.67120e10	+	1.67120e10i	0.0170505	+	0.0170505i
$996$	−5.61237e11	−	1.65822e11i	−0.570308	−	0.168502i
$997$	6.65850e11	+	6.65850e11i	0.673901	+	0.673901i	0.958613	−	0.284712i	$-0.0918981\pi$
$997$	6.65850e11	+	6.65850e11i	0.673901	+	0.673901i	−0.284712	+	0.958613i	$0.591898\pi$
$998$	8.87992e9	−	6.13941e10i	0.00895132	−	0.0618877i
$999$	−2.82969e11			−0.284103

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.9.l.a.43.10	yes	64
4.3	odd	2		192.9.l.a.79.14		64
16.3	odd	4	inner	48.9.l.a.19.10	✓	64
16.13	even	4		192.9.l.a.175.14		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.9.l.a.19.10	✓	64	16.3	odd	4	inner
48.9.l.a.43.10	yes	64	1.1	even	1	trivial
192.9.l.a.79.14		64	4.3	odd	2
192.9.l.a.175.14		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)

\(f(q)\)	\(=\)	\(q+(-9.57765 - 12.8167i) q^{2} +(33.0681 + 33.0681i) q^{3} +(-72.5372 + 245.508i) q^{4} +(541.894 + 541.894i) q^{5} +(107.110 - 740.540i) q^{6} +1146.54 q^{7} +(3841.35 - 1421.70i) q^{8} +2187.00i q^{9} +O(q^{10})\)	\(q+(-9.57765 - 12.8167i) q^{2} +(33.0681 + 33.0681i) q^{3} +(-72.5372 + 245.508i) q^{4} +(541.894 + 541.894i) q^{5} +(107.110 - 740.540i) q^{6} +1146.54 q^{7} +(3841.35 - 1421.70i) q^{8} +2187.00i q^{9} +(1755.24 - 12135.4i) q^{10} +(-8232.05 + 8232.05i) q^{11} +(-10517.2 + 5719.83i) q^{12} +(-8056.73 + 8056.73i) q^{13} +(-10981.2 - 14694.9i) q^{14} +35838.8i q^{15} +(-55012.7 - 35617.0i) q^{16} -84789.9 q^{17} +(28030.2 - 20946.3i) q^{18} +(33335.9 + 33335.9i) q^{19} +(-172347. + 93732.0i) q^{20} +(37913.9 + 37913.9i) q^{21} +(184352. + 26664.3i) q^{22} +91767.7 q^{23} +(174039. + 80013.2i) q^{24} +196673. i q^{25} +(180425. + 26096.4i) q^{26} +(-72320.0 + 72320.0i) q^{27} +(-83166.9 + 281485. i) q^{28} +(33668.6 - 33668.6i) q^{29} +(459337. - 343252. i) q^{30} +1.21183e6i q^{31} +(70399.0 + 1.04621e6i) q^{32} -544437. q^{33} +(812088. + 1.08673e6i) q^{34} +(621304. + 621304. i) q^{35} +(-536927. - 158639. i) q^{36} +(1.95637e6 + 1.95637e6i) q^{37} +(107978. - 746537. i) q^{38} -532842. q^{39} +(2.85202e6 + 1.31119e6i) q^{40} +697274. i q^{41} +(122806. - 849059. i) q^{42} +(-3.81964e6 + 3.81964e6i) q^{43} +(-1.42391e6 - 2.61817e6i) q^{44} +(-1.18512e6 + 1.18512e6i) q^{45} +(-878919. - 1.17616e6i) q^{46} -8.51922e6i q^{47} +(-641380. - 2.99695e6i) q^{48} -4.45024e6 q^{49} +(2.52071e6 - 1.88367e6i) q^{50} +(-2.80384e6 - 2.80384e6i) q^{51} +(-1.39358e6 - 2.56241e6i) q^{52} +(1.54585e6 + 1.54585e6i) q^{53} +(1.61956e6 + 234250. i) q^{54} -8.92180e6 q^{55} +(4.40427e6 - 1.63004e6i) q^{56} +2.20471e6i q^{57} +(-753988. - 109055. i) q^{58} +(-4.42591e6 + 4.42591e6i) q^{59} +(-8.79873e6 - 2.59965e6i) q^{60} +(-348448. + 348448. i) q^{61} +(1.55317e7 - 1.16065e7i) q^{62} +2.50749e6i q^{63} +(1.27347e7 - 1.09225e7i) q^{64} -8.73179e6 q^{65} +(5.21442e6 + 6.97790e6i) q^{66} +(1.95270e7 + 1.95270e7i) q^{67} +(6.15042e6 - 2.08166e7i) q^{68} +(3.03458e6 + 3.03458e6i) q^{69} +(2.01245e6 - 1.39137e7i) q^{70} -1.94639e7 q^{71} +(3.10926e6 + 8.40103e6i) q^{72} -2.88804e7i q^{73} +(6.33683e6 - 4.38116e7i) q^{74} +(-6.50362e6 + 6.50362e6i) q^{75} +(-1.06023e7 + 5.76615e6i) q^{76} +(-9.43838e6 + 9.43838e6i) q^{77} +(5.10337e6 + 6.82929e6i) q^{78} +7.21197e7i q^{79} +(-1.05104e7 - 4.91117e7i) q^{80} -4.78297e6 q^{81} +(8.93678e6 - 6.67825e6i) q^{82} +(3.45654e7 + 3.45654e7i) q^{83} +(-1.20584e7 + 6.55802e6i) q^{84} +(-4.59471e7 - 4.59471e7i) q^{85} +(8.55385e7 + 1.23721e7i) q^{86} +2.22672e6 q^{87} +(-1.99187e7 + 4.33257e7i) q^{88} -7.91558e7i q^{89} +(2.65401e7 + 3.83871e6i) q^{90} +(-9.23737e6 + 9.23737e6i) q^{91} +(-6.65657e6 + 2.25297e7i) q^{92} +(-4.00730e7 + 4.00730e7i) q^{93} +(-1.09189e8 + 8.15941e7i) q^{94} +3.61290e7i q^{95} +(-3.22682e7 + 3.69242e7i) q^{96} +5.29193e7 q^{97} +(4.26229e7 + 5.70376e7i) q^{98} +(-1.80035e7 - 1.80035e7i) 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

Varieties

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Database

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