LMFDB - Embedded newform 49.16.c.b.30.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,16,Mod(18,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("49.18");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	49.c (of order $3$, degree $2$, not 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:	$69.9198174990$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			30.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	49.30
Dual form			49.16.c.b.18.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-108.000 + 187.061i) q^{2} +(-1674.00 - 2899.45i) q^{3} +(-6944.00 - 12027.4i) q^{4} +(26055.0 - 45128.6i) q^{5} +723168. q^{6} -4.07808e6 q^{8} +(1.56990e6 - 2.71915e6i) q^{9} +O(q^{10})$	\(q+(-108.000 + 187.061i) q^{2} +(-1674.00 - 2899.45i) q^{3} +(-6944.00 - 12027.4i) q^{4} +(26055.0 - 45128.6i) q^{5} +723168. q^{6} -4.07808e6 q^{8} +(1.56990e6 - 2.71915e6i) q^{9} +(5.62788e6 + 9.74777e6i) q^{10} +(-1.02934e7 - 1.78287e7i) q^{11} +(-2.32485e7 + 4.02676e7i) q^{12} +1.90073e8 q^{13} -1.74464e8 q^{15} +(6.67974e8 - 1.15696e9i) q^{16} +(8.23264e8 + 1.42594e9i) q^{17} +(3.39099e8 + 5.87336e8i) q^{18} +(7.81629e8 - 1.35382e9i) q^{19} -7.23704e8 q^{20} +4.44676e9 q^{22} +(-4.72556e9 + 8.18491e9i) q^{23} +(6.82671e9 + 1.18242e10i) q^{24} +(1.39011e10 + 2.40773e10i) q^{25} +(-2.05279e10 + 3.55554e10i) q^{26} -5.85522e10 q^{27} -3.69026e10 q^{29} +(1.88421e10 - 3.26355e10i) q^{30} +(3.57942e10 + 6.19974e10i) q^{31} +(7.74670e10 + 1.34177e11i) q^{32} +(-3.44624e10 + 5.96906e10i) q^{33} -3.55650e11 q^{34} -4.36056e10 q^{36} +(5.16826e11 - 8.95169e11i) q^{37} +(1.68832e11 + 2.92425e11i) q^{38} +(-3.18183e11 - 5.51109e11i) q^{39} +(-1.06254e11 + 1.84038e11i) q^{40} -1.64197e12 q^{41} -4.92403e11 q^{43} +(-1.42955e11 + 2.47605e11i) q^{44} +(-8.18076e10 - 1.41695e11i) q^{45} +(-1.02072e12 - 1.76794e12i) q^{46} +(-1.70534e12 + 2.95374e12i) q^{47} -4.47275e12 q^{48} -6.00526e12 q^{50} +(2.75629e12 - 4.77403e12i) q^{51} +(-1.31987e12 - 2.28608e12i) q^{52} +(-3.39858e12 - 5.88651e12i) q^{53} +(6.32364e12 - 1.09529e13i) q^{54} -1.07278e12 q^{55} -5.23379e12 q^{57} +(3.98548e12 - 6.90305e12i) q^{58} +(4.92943e12 + 8.53802e12i) q^{59} +(1.21148e12 + 2.09834e12i) q^{60} +(2.46592e12 - 4.27110e12i) q^{61} -1.54631e13 q^{62} +1.03106e13 q^{64} +(4.95236e12 - 8.57774e12i) q^{65} +(-7.44388e12 - 1.28932e13i) q^{66} +(1.44189e13 + 2.49743e13i) q^{67} +(1.14335e13 - 1.98034e13i) q^{68} +3.16423e13 q^{69} +1.25050e14 q^{71} +(-6.40218e12 + 1.10889e13i) q^{72} +(-4.10857e13 - 7.11626e13i) q^{73} +(1.11634e14 + 1.93356e14i) q^{74} +(4.65408e13 - 8.06110e13i) q^{75} -2.17105e13 q^{76} +1.37455e14 q^{78} +(1.27065e13 - 2.20084e13i) q^{79} +(-3.48081e13 - 6.02894e13i) q^{80} +(7.54900e13 + 1.30753e14i) q^{81} +(1.77333e14 - 3.07150e14i) q^{82} +2.81737e14 q^{83} +8.58006e13 q^{85} +(5.31795e13 - 9.21097e13i) q^{86} +(6.17749e13 + 1.06997e14i) q^{87} +(4.19774e13 + 7.27070e13i) q^{88} +(3.57809e14 - 6.19744e14i) q^{89} +3.53409e13 q^{90} +1.31257e14 q^{92} +(1.19839e14 - 2.07567e14i) q^{93} +(-3.68354e14 - 6.38008e14i) q^{94} +(-4.07307e13 - 7.05476e13i) q^{95} +(2.59360e14 - 4.49224e14i) q^{96} -6.12786e14 q^{97} -6.46387e13 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 216 q^{2} - 3348 q^{3} - 13888 q^{4} + 52110 q^{5} + 1446336 q^{6} - 8156160 q^{8} + 3139803 q^{9}+O(q^{10}) $ 2 * q - 216 * q^2 - 3348 * q^3 - 13888 * q^4 + 52110 * q^5 + 1446336 * q^6 - 8156160 * q^8 + 3139803 * q^9	\( 2 q - 216 q^{2} - 3348 q^{3} - 13888 q^{4} + 52110 q^{5} + 1446336 q^{6} - 8156160 q^{8} + 3139803 q^{9} + 11255760 q^{10} - 20586852 q^{11} - 46497024 q^{12} + 380146676 q^{13} - 348928560 q^{15} + 1335947264 q^{16} + 1646527986 q^{17} + 678197448 q^{18} + 1563257180 q^{19} - 1447407360 q^{20} + 8893520064 q^{22} - 9451116072 q^{23} + 13653411840 q^{24} + 27802126025 q^{25} - 41055841008 q^{26} - 117104402160 q^{27} - 73805136660 q^{29} + 37684284480 q^{30} + 71588483552 q^{31} + 154934083584 q^{32} - 68924780496 q^{33} - 711300089952 q^{34} - 87211168128 q^{36} + 1033652081554 q^{37} + 337663550880 q^{38} - 636365535624 q^{39} - 212508748800 q^{40} - 3283948036404 q^{41} - 984806218616 q^{43} - 285910200576 q^{44} - 163615134330 q^{45} - 2041441071552 q^{46} - 3410684952624 q^{47} - 8945502879744 q^{48} - 12010518442800 q^{50} + 5512575697128 q^{51} - 2639738518144 q^{52} - 6797151655902 q^{53} + 12647275433280 q^{54} - 2145561715440 q^{55} - 10467570077280 q^{57} + 7970954759280 q^{58} + 9858856815540 q^{59} + 2422959920640 q^{60} + 4931842626902 q^{61} - 30926224894464 q^{62} + 20621115785216 q^{64} + 9904721643180 q^{65} - 14887752587136 q^{66} + 28837826625364 q^{67} + 22866980669568 q^{68} + 63284673218112 q^{69} + 250100229829104 q^{71} - 12804367818240 q^{72} - 82171455513478 q^{73} + 223268849615664 q^{74} + 93081517931700 q^{75} - 43421031431680 q^{76} + 274909911389568 q^{78} + 25413078694480 q^{79} - 69616211927040 q^{80} + 150980027970519 q^{81} + 354666387931632 q^{82} + 563473461780936 q^{83} + 171601146700920 q^{85} + 106359071610528 q^{86} + 123549798768840 q^{87} + 83954829404160 q^{88} + 715618564776810 q^{89} + 70681738030560 q^{90} + 262514200015872 q^{92} + 239678242932096 q^{93} - 736707949766784 q^{94} - 81461331649800 q^{95} + 518719311839232 q^{96} - 12\!\cdots\!52 q^{97}+ \cdots - 129277319340312 q^{99}+O(q^{100}) \) 2 * q - 216 * q^2 - 3348 * q^3 - 13888 * q^4 + 52110 * q^5 + 1446336 * q^6 - 8156160 * q^8 + 3139803 * q^9 + 11255760 * q^10 - 20586852 * q^11 - 46497024 * q^12 + 380146676 * q^13 - 348928560 * q^15 + 1335947264 * q^16 + 1646527986 * q^17 + 678197448 * q^18 + 1563257180 * q^19 - 1447407360 * q^20 + 8893520064 * q^22 - 9451116072 * q^23 + 13653411840 * q^24 + 27802126025 * q^25 - 41055841008 * q^26 - 117104402160 * q^27 - 73805136660 * q^29 + 37684284480 * q^30 + 71588483552 * q^31 + 154934083584 * q^32 - 68924780496 * q^33 - 711300089952 * q^34 - 87211168128 * q^36 + 1033652081554 * q^37 + 337663550880 * q^38 - 636365535624 * q^39 - 212508748800 * q^40 - 3283948036404 * q^41 - 984806218616 * q^43 - 285910200576 * q^44 - 163615134330 * q^45 - 2041441071552 * q^46 - 3410684952624 * q^47 - 8945502879744 * q^48 - 12010518442800 * q^50 + 5512575697128 * q^51 - 2639738518144 * q^52 - 6797151655902 * q^53 + 12647275433280 * q^54 - 2145561715440 * q^55 - 10467570077280 * q^57 + 7970954759280 * q^58 + 9858856815540 * q^59 + 2422959920640 * q^60 + 4931842626902 * q^61 - 30926224894464 * q^62 + 20621115785216 * q^64 + 9904721643180 * q^65 - 14887752587136 * q^66 + 28837826625364 * q^67 + 22866980669568 * q^68 + 63284673218112 * q^69 + 250100229829104 * q^71 - 12804367818240 * q^72 - 82171455513478 * q^73 + 223268849615664 * q^74 + 93081517931700 * q^75 - 43421031431680 * q^76 + 274909911389568 * q^78 + 25413078694480 * q^79 - 69616211927040 * q^80 + 150980027970519 * q^81 + 354666387931632 * q^82 + 563473461780936 * q^83 + 171601146700920 * q^85 + 106359071610528 * q^86 + 123549798768840 * q^87 + 83954829404160 * q^88 + 715618564776810 * q^89 + 70681738030560 * q^90 + 262514200015872 * q^92 + 239678242932096 * q^93 - 736707949766784 * q^94 - 81461331649800 * q^95 + 518719311839232 * q^96 - 1225572272163652 * q^97 - 129277319340312 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

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

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 $

$2$	−108.000	+	187.061i	−0.596621	+	1.03338i	0.396695	+	0.917951i	$0.370157\pi$
$2$	−108.000	+	187.061i	−0.596621	+	1.03338i	−0.993316	+	0.115428i	$0.963176\pi$
$3$	−1674.00	−	2899.45i	−0.441922	−	0.765432i	0.555910	−	0.831243i	$-0.312370\pi$
$3$	−1674.00	−	2899.45i	−0.441922	−	0.765432i	−0.997832	+	0.0658106i	$0.979037\pi$
$4$	−6944.00	−	12027.4i	−0.211914	−	0.367046i
$5$	26055.0	−	45128.6i	0.149148	−	0.258331i	−0.781765	−	0.623573i	$-0.785680\pi$
$5$	26055.0	−	45128.6i	0.149148	−	0.258331i	0.930913	+	0.365242i	$0.119014\pi$
$6$	723168.			1.05464
$7$		0			0
$7$		0			0
$8$	−4.07808e6			−0.687513
$9$	1.56990e6	−	2.71915e6i	0.109409	−	0.189502i
$10$	5.62788e6	+	9.74777e6i	0.177969	+	0.308252i
$11$	−1.02934e7	−	1.78287e7i	−0.159263	−	0.275852i	0.775340	−	0.631544i	$-0.217578\pi$
$11$	−1.02934e7	−	1.78287e7i	−0.159263	−	0.275852i	−0.934603	+	0.355692i	$0.884245\pi$
$12$	−2.32485e7	+	4.02676e7i	−0.187299	+	0.324412i
$13$	1.90073e8			0.840129			0.420065	−	0.907494i	$-0.362007\pi$
$13$	1.90073e8			0.840129			0.420065	+	0.907494i	$0.362007\pi$
$14$		0			0
$15$	−1.74464e8			−0.263647
$16$	6.67974e8	−	1.15696e9i	0.622099	−	1.07751i
$17$	8.23264e8	+	1.42594e9i	0.486600	+	0.842816i	0.999881	−	0.0154043i	$-0.00490355\pi$
$17$	8.23264e8	+	1.42594e9i	0.486600	+	0.842816i	−0.513281	+	0.858220i	$0.671570\pi$
$18$	3.39099e8	+	5.87336e8i	0.130552	+	0.226122i
$19$	7.81629e8	−	1.35382e9i	0.200608	−	0.347463i	−0.748116	−	0.663567i	$-0.769042\pi$
$19$	7.81629e8	−	1.35382e9i	0.200608	−	0.347463i	0.948725	+	0.316104i	$0.102375\pi$
$20$	−7.23704e8			−0.126426
$21$		0			0
$22$	4.44676e9			0.380079
$23$	−4.72556e9	+	8.18491e9i	−0.289397	+	0.501251i	−0.973666	−	0.227979i	$-0.926788\pi$
$23$	−4.72556e9	+	8.18491e9i	−0.289397	+	0.501251i	0.684269	+	0.729230i	$0.260122\pi$
$24$	6.82671e9	+	1.18242e10i	0.303827	+	0.526244i
$25$	1.39011e10	+	2.40773e10i	0.455510	+	0.788967i
$26$	−2.05279e10	+	3.55554e10i	−0.501239	+	0.868171i
$27$	−5.85522e10			−1.07725
$28$		0			0
$29$	−3.69026e10			−0.397257			−0.198629	−	0.980075i	$-0.563649\pi$
$29$	−3.69026e10			−0.397257			−0.198629	+	0.980075i	$0.563649\pi$
$30$	1.88421e10	−	3.26355e10i	0.157297	−	0.272447i
$31$	3.57942e10	+	6.19974e10i	0.233669	+	0.404726i	0.958885	−	0.283795i	$-0.0915936\pi$
$31$	3.57942e10	+	6.19974e10i	0.233669	+	0.404726i	−0.725216	+	0.688521i	$0.758260\pi$
$32$	7.74670e10	+	1.34177e11i	0.398559	+	0.690324i
$33$	−3.44624e10	+	5.96906e10i	−0.140764	+	0.243810i
$34$	−3.55650e11			−1.16126
$35$		0			0
$36$	−4.36056e10			−0.0927413
$37$	5.16826e11	−	8.95169e11i	0.895017	−	1.55022i	0.0612342	−	0.998123i	$-0.480496\pi$
$37$	5.16826e11	−	8.95169e11i	0.895017	−	1.55022i	0.833783	−	0.552092i	$-0.186170\pi$
$38$	1.68832e11	+	2.92425e11i	0.239374	+	0.414608i
$39$	−3.18183e11	−	5.51109e11i	−0.371272	−	0.643062i
$40$	−1.06254e11	+	1.84038e11i	−0.102541	+	0.177606i
$41$	−1.64197e12			−1.31670			−0.658351	−	0.752711i	$-0.728746\pi$
$41$	−1.64197e12			−1.31670			−0.658351	+	0.752711i	$0.728746\pi$
$42$		0			0
$43$	−4.92403e11			−0.276253			−0.138127	−	0.990415i	$-0.544108\pi$
$43$	−4.92403e11			−0.276253			−0.138127	+	0.990415i	$0.544108\pi$
$44$	−1.42955e11	+	2.47605e11i	−0.0675001	+	0.116914i
$45$	−8.18076e10	−	1.41695e11i	−0.0326362	−	0.0565276i
$46$	−1.02072e12	−	1.76794e12i	−0.345321	−	0.598114i
$47$	−1.70534e12	+	2.95374e12i	−0.490996	+	0.850429i	−0.999946	−	0.0103663i	$-0.996700\pi$
$47$	−1.70534e12	+	2.95374e12i	−0.490996	+	0.850429i	0.508951	+	0.860796i	$0.330034\pi$
$48$	−4.47275e12			−1.09968
$49$		0			0
$50$	−6.00526e12			−1.08707
$51$	2.75629e12	−	4.77403e12i	0.430079	−	0.744919i
$52$	−1.31987e12	−	2.28608e12i	−0.178035	−	0.308366i
$53$	−3.39858e12	−	5.88651e12i	−0.397400	−	0.688317i	0.596004	−	0.802981i	$-0.296754\pi$
$53$	−3.39858e12	−	5.88651e12i	−0.397400	−	0.688317i	−0.993404	+	0.114664i	$0.963421\pi$
$54$	6.32364e12	−	1.09529e13i	0.642708	−	1.11320i
$55$	−1.07278e12			−0.0950147
$56$		0			0
$57$	−5.23379e12			−0.354613
$58$	3.98548e12	−	6.90305e12i	0.237012	−	0.410517i
$59$	4.92943e12	+	8.53802e12i	0.257873	+	0.446650i	0.965672	−	0.259764i	$-0.0836449\pi$
$59$	4.92943e12	+	8.53802e12i	0.257873	+	0.446650i	−0.707799	+	0.706414i	$0.750312\pi$
$60$	1.21148e12	+	2.09834e12i	0.0558704	+	0.0967704i
$61$	2.46592e12	−	4.27110e12i	0.100463	−	0.174007i	−0.811413	−	0.584474i	$-0.801301\pi$
$61$	2.46592e12	−	4.27110e12i	0.100463	−	0.174007i	0.911875	+	0.410467i	$0.134634\pi$
$62$	−1.54631e13			−0.557647
$63$		0			0
$64$	1.03106e13			0.293044
$65$	4.95236e12	−	8.57774e12i	0.125303	−	0.217031i
$66$	−7.44388e12	−	1.28932e13i	−0.167965	−	0.290924i
$67$	1.44189e13	+	2.49743e13i	0.290651	+	0.503422i	0.973964	−	0.226704i	$-0.0727949\pi$
$67$	1.44189e13	+	2.49743e13i	0.290651	+	0.503422i	−0.683313	+	0.730126i	$0.739462\pi$
$68$	1.14335e13	−	1.98034e13i	0.206235	−	0.357209i
$69$	3.16423e13			0.511564
$70$		0			0
$71$	1.25050e14			1.63172			0.815862	−	0.578247i	$-0.196263\pi$
$71$	1.25050e14			1.63172			0.815862	+	0.578247i	$0.196263\pi$
$72$	−6.40218e12	+	1.10889e13i	−0.0752202	+	0.130285i
$73$	−4.10857e13	−	7.11626e13i	−0.435281	−	0.753928i	0.562038	−	0.827112i	$-0.310018\pi$
$73$	−4.10857e13	−	7.11626e13i	−0.435281	−	0.753928i	−0.997319	+	0.0731831i	$0.976684\pi$
$74$	1.11634e14	+	1.93356e14i	1.06797	+	1.84978i
$75$	4.65408e13	−	8.06110e13i	0.402600	−	0.697324i
$76$	−2.17105e13			−0.170047
$77$		0			0
$78$	1.37455e14			0.886035
$79$	1.27065e13	−	2.20084e13i	0.0744430	−	0.128939i	−0.826401	−	0.563082i	$-0.809615\pi$
$79$	1.27065e13	−	2.20084e13i	0.0744430	−	0.128939i	0.900844	+	0.434143i	$0.142949\pi$
$80$	−3.48081e13	−	6.02894e13i	−0.185569	−	0.321415i
$81$	7.54900e13	+	1.30753e14i	0.366650	+	0.635057i
$82$	1.77333e14	−	3.07150e14i	0.785572	−	1.36065i
$83$	2.81737e14			1.13961			0.569807	−	0.821779i	$-0.307018\pi$
$83$	2.81737e14			1.13961			0.569807	+	0.821779i	$0.307018\pi$
$84$		0			0
$85$	8.58006e13			0.290301
$86$	5.31795e13	−	9.21097e13i	0.164819	−	0.285474i
$87$	6.17749e13	+	1.06997e14i	0.175557	+	0.304073i
$88$	4.19774e13	+	7.27070e13i	0.109495	+	0.189651i
$89$	3.57809e14	−	6.19744e14i	0.857485	−	1.48521i	−0.0168353	−	0.999858i	$-0.505359\pi$
$89$	3.57809e14	−	6.19744e14i	0.857485	−	1.48521i	0.874320	−	0.485349i	$-0.161308\pi$
$90$	3.53409e13			0.0778858
$91$		0			0
$92$	1.31257e14			0.245309
$93$	1.19839e14	−	2.07567e14i	0.206527	−	0.357715i
$94$	−3.68354e14	−	6.38008e14i	−0.585877	−	1.01477i
$95$	−4.07307e13	−	7.05476e13i	−0.0598404	−	0.103647i
$96$	2.59360e14	−	4.49224e14i	0.352264	−	0.610139i
$97$	−6.12786e14			−0.770054			−0.385027	−	0.922905i	$-0.625808\pi$
$97$	−6.12786e14			−0.770054			−0.385027	+	0.922905i	$0.625808\pi$
$98$		0			0
$99$	−6.46387e13			−0.0696993
$100$	1.93058e14	−	3.34386e14i	0.193058	−	0.334386i
$101$	−4.08821e14	−	7.08098e14i	−0.379422	−	0.657178i	0.611556	−	0.791201i	$-0.290544\pi$
$101$	−4.08821e14	−	7.08098e14i	−0.379422	−	0.657178i	−0.990978	+	0.134023i	$0.957211\pi$
$102$	5.95358e14	+	1.03119e15i	0.513189	+	0.888869i
$103$	3.70557e14	−	6.41824e14i	0.296877	−	0.514206i	−0.678543	−	0.734561i	$-0.737388\pi$
$103$	3.70557e14	−	6.41824e14i	0.296877	−	0.514206i	0.975420	+	0.220355i	$0.0707216\pi$
$104$	−7.75134e14			−0.577600
$105$		0			0
$106$	1.46818e15			0.948389
$107$	1.25715e15	−	2.17745e15i	0.756849	−	1.31090i	−0.187601	−	0.982245i	$-0.560071\pi$
$107$	1.25715e15	−	2.17745e15i	0.756849	−	1.31090i	0.944450	−	0.328655i	$-0.106595\pi$
$108$	4.06586e14	+	7.04228e14i	0.228284	+	0.395399i
$109$	−6.34177e14	−	1.09843e15i	−0.332286	−	0.575536i	0.650674	−	0.759357i	$-0.274487\pi$
$109$	−6.34177e14	−	1.09843e15i	−0.332286	−	0.575536i	−0.982960	+	0.183821i	$0.941153\pi$
$110$	1.15860e14	−	2.00676e14i	0.0566878	−	0.0981862i
$111$	−3.46067e15			−1.58211
$112$		0			0
$113$	−2.05416e15			−0.821385			−0.410692	−	0.911774i	$-0.634713\pi$
$113$	−2.05416e15			−0.821385			−0.410692	+	0.911774i	$0.634713\pi$
$114$	5.65249e14	−	9.79040e14i	0.211570	−	0.366449i
$115$	2.46249e14	+	4.26515e14i	0.0863258	+	0.149521i
$116$	2.56251e14	+	4.43841e14i	0.0841844	+	0.145812i
$117$	2.98396e14	−	5.16838e14i	0.0919178	−	0.159206i
$118$	−2.12951e15			−0.615411
$119$		0			0
$120$	7.11479e14			0.181260
$121$	1.87671e15	−	3.25057e15i	0.449271	−	0.778160i
$122$	5.32639e14	+	9.22558e14i	0.119877	+	0.207632i
$123$	2.74866e15	+	4.76083e15i	0.581880	+	1.00785i
$124$	4.97110e14	−	8.61021e14i	0.0990353	−	0.171534i
$125$	3.03904e15			0.570048
$126$		0			0
$127$	2.99068e15			0.498014			0.249007	−	0.968502i	$-0.419896\pi$
$127$	2.99068e15			0.498014			0.249007	+	0.968502i	$0.419896\pi$
$128$	−3.65198e15	+	6.32542e15i	−0.573395	+	0.993149i
$129$	8.24283e14	+	1.42770e15i	0.122082	+	0.211453i
$130$	1.06971e15	+	1.85279e15i	0.149517	+	0.258971i
$131$	−8.13113e14	+	1.40835e15i	−0.107304	+	0.185856i	−0.914677	−	0.404185i	$-0.867555\pi$
$131$	−8.13113e14	+	1.40835e15i	−0.107304	+	0.185856i	0.807373	+	0.590041i	$0.200889\pi$
$132$	9.57227e14			0.119319
$133$		0			0
$134$	−6.22897e15			−0.693634
$135$	−1.52558e15	+	2.64238e15i	−0.160669	+	0.278286i
$136$	−3.35734e15	−	5.81508e15i	−0.334544	−	0.579447i
$137$	−5.29610e15	−	9.17312e15i	−0.499519	−	0.865192i	0.500481	−	0.865748i	$-0.333157\pi$
$137$	−5.29610e15	−	9.17312e15i	−0.499519	−	0.865192i	−1.00000		0.000555358i	$0.999823\pi$
$138$	−3.41737e15	+	5.91906e15i	−0.305210	+	0.528640i
$139$	1.86709e16			1.57963			0.789813	−	0.613347i	$-0.210177\pi$
$139$	1.86709e16			1.57963			0.789813	+	0.613347i	$0.210177\pi$
$140$		0			0
$141$	1.14190e16			0.867928
$142$	−1.35054e16	+	2.33921e16i	−0.973521	+	1.68619i
$143$	−1.95651e15	−	3.38877e15i	−0.133801	−	0.231751i
$144$	−2.09731e15	−	3.63264e15i	−0.136127	−	0.235778i
$145$	−9.61496e14	+	1.66536e15i	−0.0592499	+	0.102624i
$146$	1.77490e16			1.03879
$147$		0			0
$148$	−1.43554e16			−0.758667
$149$	6.27798e15	−	1.08738e16i	0.315444	−	0.546366i	−0.664087	−	0.747655i	$-0.731180\pi$
$149$	6.27798e15	−	1.08738e16i	0.315444	−	0.546366i	0.979532	+	0.201289i	$0.0645131\pi$
$150$	1.00528e16	+	1.74120e16i	0.480400	+	0.832077i
$151$	−1.43794e16	−	2.49058e16i	−0.653753	−	1.13233i	−0.982205	−	0.187812i	$-0.939860\pi$
$151$	−1.43794e16	−	2.49058e16i	−0.653753	−	1.13233i	0.328452	−	0.944521i	$-0.393473\pi$
$152$	−3.18754e15	+	5.52099e15i	−0.137921	+	0.238886i
$153$	5.16977e15			0.212954
$154$		0			0
$155$	3.73048e15			0.139404
$156$	−4.41892e15	+	7.65380e15i	−0.157355	+	0.272548i
$157$	−7.26382e15	−	1.25813e16i	−0.246557	−	0.427050i	0.716011	−	0.698089i	$-0.245966\pi$
$157$	−7.26382e15	−	1.25813e16i	−0.246557	−	0.427050i	−0.962568	+	0.271039i	$0.912633\pi$
$158$	2.74461e15	+	4.75381e15i	0.0888286	+	0.153856i
$159$	−1.13784e16	+	1.97080e16i	−0.351240	+	0.608366i
$160$	8.07362e15			0.237776
$161$		0			0
$162$	−3.26117e16			−0.875005
$163$	−8.38707e15	+	1.45268e16i	−0.214884	+	0.372189i	−0.953237	−	0.302225i	$-0.902271\pi$
$163$	−8.38707e15	+	1.45268e16i	−0.214884	+	0.372189i	0.738353	+	0.674414i	$0.235604\pi$
$164$	1.14019e16	+	1.97486e16i	0.279028	+	0.483290i
$165$	1.79584e15	+	3.11048e15i	0.0419891	+	0.0727273i
$166$	−3.04276e16	+	5.27021e16i	−0.679918	+	1.17765i
$167$	−6.41999e16			−1.37139			−0.685695	−	0.727889i	$-0.740502\pi$
$167$	−6.41999e16			−1.37139			−0.685695	+	0.727889i	$0.740502\pi$
$168$		0			0
$169$	−1.50580e16			−0.294183
$170$	−9.26646e15	+	1.60500e16i	−0.173200	+	0.299991i
$171$	−2.45416e15	−	4.25073e15i	−0.0438967	−	0.0760313i
$172$	3.41925e15	+	5.92231e15i	0.0585419	+	0.101398i
$173$	−3.79930e16	+	6.58058e16i	−0.622814	+	1.07874i	0.366146	+	0.930558i	$0.380677\pi$
$173$	−3.79930e16	+	6.58058e16i	−0.622814	+	1.07874i	−0.988959	+	0.148187i	$0.952656\pi$
$174$	−2.66868e16			−0.418964
$175$		0			0
$176$	−2.75029e16			−0.396309
$177$	1.65037e16	−	2.85853e16i	0.227920	−	0.394769i
$178$	7.72868e16	+	1.33865e17i	1.02319	+	1.77221i
$179$	−4.66874e16	−	8.08650e16i	−0.592655	−	1.02651i	−0.993873	−	0.110527i	$-0.964746\pi$
$179$	−4.66874e16	−	8.08650e16i	−0.592655	−	1.02651i	0.401218	−	0.915983i	$-0.368587\pi$
$180$	−1.13614e15	+	1.96786e15i	−0.0138321	+	0.0239580i
$181$	−7.43177e16			−0.867966			−0.433983	−	0.900921i	$-0.642892\pi$
$181$	−7.43177e16			−0.867966			−0.433983	+	0.900921i	$0.642892\pi$
$182$		0			0
$183$	−1.65118e16			−0.177587
$184$	1.92712e16	−	3.33787e16i	0.198964	−	0.344616i
$185$	−2.69318e16	−	4.66473e16i	−0.266979	−	0.462422i
$186$	2.58853e16	+	4.48346e16i	0.246437	+	0.426841i
$187$	1.69484e16	−	2.93555e16i	0.154995	−	0.268459i
$188$	4.73676e16			0.416196
$189$		0			0
$190$	1.75956e16			0.142808
$191$	4.93112e16	−	8.54095e16i	0.384765	−	0.666432i	−0.606972	−	0.794723i	$-0.707616\pi$
$191$	4.93112e16	−	8.54095e16i	0.384765	−	0.666432i	0.991737	+	0.128291i	$0.0409492\pi$
$192$	−1.72599e16	−	2.98950e16i	−0.129503	−	0.224305i
$193$	4.45589e15	+	7.71782e15i	0.0321554	+	0.0556949i	0.881655	−	0.471894i	$-0.156430\pi$
$193$	4.45589e15	+	7.71782e15i	0.0321554	+	0.0556949i	−0.849500	+	0.527589i	$0.823096\pi$
$194$	6.61809e16	−	1.14629e17i	0.459430	−	0.795757i
$195$	−3.31610e16			−0.221497
$196$		0			0
$197$	3.54176e16			0.219140			0.109570	−	0.993979i	$-0.465053\pi$
$197$	3.54176e16			0.219140			0.109570	+	0.993979i	$0.465053\pi$
$198$	6.98098e15	−	1.20914e16i	0.0415841	−	0.0720258i
$199$	−1.43230e17	−	2.48082e17i	−0.821556	−	1.42298i	−0.904523	−	0.426425i	$-0.859773\pi$
$199$	−1.43230e17	−	2.48082e17i	−0.821556	−	1.42298i	0.0829664	−	0.996552i	$-0.473561\pi$
$200$	−5.66896e16	−	9.81893e16i	−0.313169	−	0.542425i
$201$	4.82745e16	−	8.36139e16i	0.256890	−	0.444947i
$202$	1.76611e17			0.905485
$203$		0			0
$204$	−7.65587e16			−0.364559
$205$	−4.27816e16	+	7.41000e16i	−0.196383	+	0.340145i
$206$	8.00404e16	+	1.38634e17i	0.354246	+	0.613572i
$207$	1.48373e16	+	2.56990e16i	0.0633254	+	0.109683i
$208$	1.26964e17	−	2.19908e17i	0.522643	−	0.905245i
$209$	−3.21825e16			−0.127798
$210$		0			0
$211$	3.75834e17			1.38956			0.694780	−	0.719222i	$-0.255502\pi$
$211$	3.75834e17			1.38956			0.694780	+	0.719222i	$0.255502\pi$
$212$	−4.71994e16	+	8.17518e16i	−0.168429	+	0.291728i
$213$	−2.09334e17	−	3.62577e17i	−0.721095	−	1.24897i
$214$	2.71545e17	+	4.70329e17i	0.903104	+	1.56422i
$215$	−1.28296e16	+	2.22215e16i	−0.0412025	+	0.0713648i
$216$	2.38781e17			0.740621
$217$		0			0
$218$	2.73964e17			0.792995
$219$	−1.37555e17	+	2.38252e17i	−0.384721	+	0.666356i
$220$	7.44939e15	+	1.29027e16i	0.0201350	+	0.0348748i
$221$	1.56481e17	+	2.71032e17i	0.408807	+	0.708074i
$222$	3.73752e17	−	6.47358e17i	0.943922	−	1.63492i
$223$	2.53078e16			0.0617970			0.0308985	−	0.999523i	$-0.490163\pi$
$223$	2.53078e16			0.0617970			0.0308985	+	0.999523i	$0.490163\pi$
$224$		0			0
$225$	8.72932e16			0.199348
$226$	2.21850e17	−	3.84255e17i	0.490056	−	0.848801i
$227$	1.51846e17	+	2.63005e17i	0.324496	+	0.562044i	0.981410	−	0.191922i	$-0.0614720\pi$
$227$	1.51846e17	+	2.63005e17i	0.324496	+	0.562044i	−0.656914	+	0.753965i	$0.728139\pi$
$228$	3.63434e16	+	6.29486e16i	0.0751474	+	0.130159i
$229$	5.39958e16	−	9.35235e16i	0.108042	−	0.187135i	−0.806935	−	0.590641i	$-0.798875\pi$
$229$	5.39958e16	−	9.35235e16i	0.108042	−	0.187135i	0.914977	+	0.403506i	$0.132208\pi$
$230$	−1.06379e17			−0.206015
$231$		0			0
$232$	1.50492e17			0.273119
$233$	3.95253e17	−	6.84598e17i	0.694554	−	1.20300i	−0.275777	−	0.961222i	$-0.588935\pi$
$233$	3.95253e17	−	6.84598e17i	0.694554	−	1.20300i	0.970331	−	0.241781i	$-0.0777315\pi$
$234$	6.44536e16	+	1.11637e17i	0.109680	+	0.189972i
$235$	8.88654e16	+	1.53919e17i	0.146462	+	0.253679i
$236$	6.84599e16	−	1.18576e17i	0.109294	−	0.189303i
$237$	−8.50830e16			−0.131592
$238$		0			0
$239$	3.52956e17			0.512551			0.256275	−	0.966604i	$-0.417505\pi$
$239$	3.52956e17			0.512551			0.256275	+	0.966604i	$0.417505\pi$
$240$	−1.16538e17	+	2.01849e17i	−0.164014	+	0.284081i
$241$	3.42845e16	+	5.93825e16i	0.0467703	+	0.0810085i	0.888463	−	0.458949i	$-0.151774\pi$
$241$	3.42845e16	+	5.93825e16i	0.0467703	+	0.0810085i	−0.841693	+	0.539957i	$0.818440\pi$
$242$	4.05370e17	+	7.02122e17i	0.536089	+	0.928533i
$243$	−1.67339e17	+	2.89840e17i	−0.214561	+	0.371631i
$244$	−6.84934e16			−0.0851580
$245$		0			0
$246$	−1.18742e18			−1.38865
$247$	1.48567e17	−	2.57325e17i	0.168537	−	0.291914i
$248$	−1.45972e17	−	2.52831e17i	−0.160650	−	0.278254i
$249$	−4.71627e17	−	8.16882e17i	−0.503621	−	0.872297i
$250$	−3.28216e17	+	5.68487e17i	−0.340103	+	0.589075i
$251$	−1.58806e18			−1.59703			−0.798515	−	0.601975i	$-0.794381\pi$
$251$	−1.58806e18			−1.59703			−0.798515	+	0.601975i	$0.794381\pi$
$252$		0			0
$253$	1.94569e17			0.184361
$254$	−3.22993e17	+	5.59440e17i	−0.297126	+	0.514637i
$255$	−1.43630e17	−	2.48775e17i	−0.128290	−	0.222206i
$256$	−6.19900e17	−	1.07370e18i	−0.537677	−	0.931284i
$257$	−4.14281e17	+	7.17556e17i	−0.348977	+	0.604446i	−0.986068	−	0.166343i	$-0.946804\pi$
$257$	−4.14281e17	+	7.17556e17i	−0.348977	+	0.604446i	0.637091	+	0.770788i	$0.280137\pi$
$258$	−3.56090e17			−0.291348
$259$		0			0
$260$	−1.37557e17			−0.106214
$261$	−5.79334e16	+	1.00344e17i	−0.0434635	+	0.0752811i
$262$	−1.75632e17	−	3.04204e17i	−0.128040	−	0.221772i
$263$	−7.02227e17	−	1.21629e18i	−0.497519	−	0.861728i	0.502477	−	0.864591i	$-0.332422\pi$
$263$	−7.02227e17	−	1.21629e18i	−0.497519	−	0.861728i	−0.999996	+	0.00286244i	$0.999089\pi$
$264$	1.40540e17	−	2.43423e17i	0.0967769	−	0.167622i
$265$	−3.54200e17			−0.237085
$266$		0			0
$267$	−2.39589e18			−1.51577
$268$	2.00250e17	−	3.46843e17i	0.123186	−	0.213364i
$269$	7.17910e17	+	1.24346e18i	0.429465	+	0.743856i	0.996826	−	0.0796139i	$-0.0253687\pi$
$269$	7.17910e17	+	1.24346e18i	0.429465	+	0.743856i	−0.567361	+	0.823469i	$0.692035\pi$
$270$	−3.29525e17	−	5.70754e17i	−0.191717	−	0.332063i
$271$	2.54580e17	−	4.40945e17i	0.144064	−	0.249526i	−0.784960	−	0.619547i	$-0.787316\pi$
$271$	2.54580e17	−	4.40945e17i	0.144064	−	0.249526i	0.929023	+	0.370021i	$0.120650\pi$
$272$	2.19967e18			1.21085
$273$		0			0
$274$	2.28792e18			1.19209
$275$	2.86179e17	−	4.95677e17i	0.145092	−	0.251306i
$276$	−2.19724e17	−	3.80574e17i	−0.108408	−	0.187768i
$277$	−2.84473e17	−	4.92722e17i	−0.136598	−	0.236594i	0.789609	−	0.613610i	$-0.210283\pi$
$277$	−2.84473e17	−	4.92722e17i	−0.136598	−	0.236594i	−0.926207	+	0.377016i	$0.876950\pi$
$278$	−2.01646e18	+	3.49261e18i	−0.942439	+	1.63235i
$279$	2.24774e17			0.102262
$280$		0			0
$281$	−4.06184e18			−1.75156			−0.875780	−	0.482710i	$-0.839652\pi$
$281$	−4.06184e18			−1.75156			−0.875780	+	0.482710i	$0.839652\pi$
$282$	−1.23325e18	+	2.13605e18i	−0.517824	+	0.896898i
$283$	1.39253e18	+	2.41193e18i	0.569385	+	0.986204i	0.996627	+	0.0820667i	$0.0261520\pi$
$283$	1.39253e18	+	2.41193e18i	0.569385	+	0.986204i	−0.427242	+	0.904137i	$0.640515\pi$
$284$	−8.68348e17	−	1.50402e18i	−0.345785	−	0.598917i
$285$	−1.36366e17	+	2.36193e17i	−0.0528896	+	0.0916075i
$286$	8.45211e17			0.319315
$287$		0			0
$288$	4.86463e17			0.174424
$289$	7.56843e16	−	1.31089e17i	0.0264406	−	0.0457965i
$290$	−2.07683e17	−	3.59718e17i	−0.0706995	−	0.122455i
$291$	1.02580e18	+	1.77674e18i	0.340304	+	0.589424i
$292$	−5.70599e17	+	9.88306e17i	−0.184484	+	0.319536i
$293$	3.63803e18			1.14646			0.573230	−	0.819395i	$-0.305690\pi$
$293$	3.63803e18			1.14646			0.573230	+	0.819395i	$0.305690\pi$
$294$		0			0
$295$	5.13745e17			0.153845
$296$	−2.10766e18	+	3.65057e18i	−0.615336	+	1.06579i
$297$	6.02703e17	+	1.04391e18i	0.171565	+	0.297160i
$298$	1.35604e18	+	2.34874e18i	0.376402	+	0.651947i
$299$	−8.98203e17	+	1.55573e18i	−0.243131	+	0.421115i
$300$	−1.29272e18			−0.341267
$301$		0			0
$302$	6.21190e18			1.56017
$303$	−1.36873e18	+	2.37071e18i	−0.335350	+	0.580844i
$304$	−1.04421e18	−	1.80863e18i	−0.249596	−	0.432313i
$305$	−1.28499e17	−	2.22567e17i	−0.0299676	−	0.0519053i
$306$	−5.58336e17	+	9.67066e17i	−0.127053	+	0.220062i
$307$	9.75296e17			0.216570			0.108285	−	0.994120i	$-0.465464\pi$
$307$	9.75296e17			0.216570			0.108285	+	0.994120i	$0.465464\pi$
$308$		0			0
$309$	−2.48125e18			−0.524786
$310$	−4.02891e17	+	6.97828e17i	−0.0831716	+	0.144058i
$311$	1.68346e17	+	2.91584e17i	0.0339234	+	0.0587571i	0.882489	−	0.470334i	$-0.155866\pi$
$311$	1.68346e17	+	2.91584e17i	0.0339234	+	0.0587571i	−0.848565	+	0.529091i	$0.822533\pi$
$312$	1.29757e18	+	2.24747e18i	0.255254	+	0.442113i
$313$	1.82776e18	−	3.16577e18i	0.351023	−	0.607990i	−0.635406	−	0.772178i	$-0.719167\pi$
$313$	1.82776e18	−	3.16577e18i	0.351023	−	0.607990i	0.986429	+	0.164189i	$0.0525005\pi$
$314$	3.13797e18			0.588405
$315$		0			0
$316$	−3.52937e17			−0.0631021
$317$	3.98690e17	−	6.90551e17i	0.0696131	−	0.120573i	−0.829118	−	0.559074i	$-0.811157\pi$
$317$	3.98690e17	−	6.90551e17i	0.0696131	−	0.120573i	0.898731	+	0.438500i	$0.144490\pi$
$318$	−2.45774e18	−	4.25693e18i	−0.419115	−	0.725928i
$319$	3.79854e17	+	6.57926e17i	0.0632683	+	0.109584i
$320$	2.68642e17	−	4.65301e17i	0.0437067	−	0.0757023i
$321$	−8.41788e18			−1.33787
$322$		0			0
$323$	2.57395e18			0.390464
$324$	1.04841e18	−	1.81589e18i	0.155397	−	0.269155i
$325$	2.64222e18	+	4.57646e18i	0.382687	+	0.662834i
$326$	−1.81161e18	−	3.13780e18i	−0.256408	−	0.444112i
$327$	−2.12322e18	+	3.67753e18i	−0.293689	+	0.508684i
$328$	6.69610e18			0.905249
$329$		0			0
$330$	−7.75801e17			−0.100206
$331$	5.07926e18	−	8.79753e18i	0.641343	−	1.11084i	−0.343791	−	0.939046i	$-0.611711\pi$
$331$	5.07926e18	−	8.79753e18i	0.641343	−	1.11084i	0.985133	−	0.171792i	$-0.0549556\pi$
$332$	−1.95638e18	−	3.38855e18i	−0.241500	−	0.418291i
$333$	−1.62273e18	−	2.81065e18i	−0.195846	−	0.339215i
$334$	6.93359e18	−	1.20093e19i	0.818201	−	1.41716i
$335$	1.50274e18			0.173399
$336$		0			0
$337$	−4.81465e18			−0.531301			−0.265651	−	0.964069i	$-0.585587\pi$
$337$	−4.81465e18			−0.531301			−0.265651	+	0.964069i	$0.585587\pi$
$338$	1.62627e18	−	2.81678e18i	0.175516	−	0.304002i
$339$	3.43867e18	+	5.95595e18i	0.362988	+	0.628714i
$340$	−5.95799e17	−	1.03195e18i	−0.0615188	−	0.106554i
$341$	7.36891e17	−	1.27633e18i	0.0744295	−	0.128916i
$342$	1.06020e18			0.104759
$343$		0			0
$344$	2.00806e18			0.189928
$345$	8.24441e17	−	1.42797e18i	0.0762986	−	0.132153i
$346$	−8.20649e18	−	1.42141e19i	−0.743168	−	1.28720i
$347$	−2.25138e18	−	3.89950e18i	−0.199516	−	0.345571i	0.748856	−	0.662733i	$-0.230604\pi$
$347$	−2.25138e18	−	3.89950e18i	−0.199516	−	0.345571i	−0.948371	+	0.317162i	$0.897270\pi$
$348$	8.57930e17	−	1.48598e18i	0.0744059	−	0.128875i
$349$	−2.24323e19			−1.90407			−0.952036	−	0.305986i	$-0.901014\pi$
$349$	−2.24323e19			−1.90407			−0.952036	+	0.305986i	$0.901014\pi$
$350$		0			0
$351$	−1.11292e19			−0.905026
$352$	1.59480e18	−	2.76228e18i	0.126951	−	0.219886i
$353$	4.01255e18	+	6.94994e18i	0.312687	+	0.541590i	0.978943	−	0.204133i	$-0.0654375\pi$
$353$	4.01255e18	+	6.94994e18i	0.312687	+	0.541590i	−0.666256	+	0.745723i	$0.732104\pi$
$354$	3.56480e18	+	6.17442e18i	0.271964	+	0.471055i
$355$	3.25818e18	−	5.64333e18i	0.243367	−	0.421525i
$356$	−9.93851e18			−0.726853
$357$		0			0
$358$	2.01690e19			1.41436
$359$	−8.07536e17	+	1.39869e18i	−0.0554567	+	0.0960538i	−0.892421	−	0.451204i	$-0.850995\pi$
$359$	−8.07536e17	+	1.39869e18i	−0.0554567	+	0.0960538i	0.836964	+	0.547257i	$0.184328\pi$
$360$	3.33618e17	+	5.77843e17i	0.0224378	+	0.0388634i
$361$	6.36868e18	+	1.10309e19i	0.419513	+	0.726617i
$362$	8.02631e18	−	1.39020e19i	0.517847	−	0.896938i
$363$	−1.25665e19			−0.794171
$364$		0			0
$365$	−4.28195e18			−0.259684
$366$	1.78328e18	−	3.08872e18i	0.105952	−	0.183515i
$367$	−4.98900e18	−	8.64120e18i	−0.290414	−	0.503012i	0.683494	−	0.729957i	$-0.260460\pi$
$367$	−4.98900e18	−	8.64120e18i	−0.290414	−	0.503012i	−0.973908	+	0.226944i	$0.927126\pi$
$368$	6.31310e18	+	1.09346e19i	0.360067	+	0.623655i
$369$	−2.57774e18	+	4.46477e18i	−0.144059	+	0.249518i
$370$	1.16345e19			0.637142
$371$		0			0
$372$	−3.32865e18			−0.175064
$373$	1.18433e19	−	2.05132e19i	0.610459	−	1.05735i	−0.380704	−	0.924697i	$-0.624318\pi$
$373$	1.18433e19	−	2.05132e19i	0.610459	−	1.05735i	0.991163	−	0.132649i	$-0.0423482\pi$
$374$	3.66086e18	+	6.34079e18i	0.184946	+	0.320336i
$375$	−5.08735e18	−	8.81155e18i	−0.251917	−	0.436333i
$376$	6.95452e18	−	1.20456e19i	0.337566	−	0.584681i
$377$	−7.01419e18			−0.333747
$378$		0			0
$379$	1.86851e19			0.854480			0.427240	−	0.904138i	$-0.359486\pi$
$379$	1.86851e19			0.854480			0.427240	+	0.904138i	$0.359486\pi$
$380$	−5.65667e17	+	9.79765e17i	−0.0253620	+	0.0439283i
$381$	−5.00639e18	−	8.67132e18i	−0.220084	−	0.381196i
$382$	1.06512e19	+	1.84485e19i	0.459118	+	0.795215i
$383$	−1.51260e19	+	2.61991e19i	−0.639343	+	1.10738i	0.346234	+	0.938148i	$0.387460\pi$
$383$	−1.51260e19	+	2.61991e19i	−0.639343	+	1.10738i	−0.985577	+	0.169227i	$0.945873\pi$
$384$	2.44537e19			1.01358
$385$		0			0
$386$	−1.92494e18			−0.0767385
$387$	−7.73024e17	+	1.33892e18i	−0.0302246	+	0.0523506i
$388$	4.25519e18	+	7.37020e18i	0.163185	+	0.282645i
$389$	5.03572e17	+	8.72212e17i	0.0189426	+	0.0328095i	0.875341	−	0.483506i	$-0.160637\pi$
$389$	5.03572e17	+	8.72212e17i	0.0189426	+	0.0328095i	−0.856399	+	0.516315i	$0.827303\pi$
$390$	3.58139e18	−	6.20315e18i	0.132150	−	0.228890i
$391$	−1.55615e19			−0.563283
$392$		0			0
$393$	5.44461e18			0.189680
$394$	−3.82510e18	+	6.62526e18i	−0.130744	+	0.226455i
$395$	−6.62138e17	−	1.14686e18i	−0.0222060	−	0.0384619i
$396$	4.48851e17	+	7.77432e17i	0.0147703	+	0.0255828i
$397$	1.78162e19	−	3.08586e19i	0.575290	−	0.996431i	−0.420721	−	0.907190i	$-0.638223\pi$
$397$	1.78162e19	−	3.08586e19i	0.575290	−	0.996431i	0.996010	−	0.0892405i	$-0.0284440\pi$
$398$	6.18756e19			1.96063
$399$		0			0
$400$	3.71422e19			1.13349
$401$	−1.97164e19	+	3.41497e19i	−0.590532	+	1.02283i	0.403628	+	0.914923i	$0.367749\pi$
$401$	−1.97164e19	+	3.41497e19i	−0.590532	+	1.02283i	−0.994161	+	0.107909i	$0.965584\pi$
$402$	1.04273e19	+	1.80606e19i	0.306532	+	0.530930i
$403$	6.80353e18	+	1.17841e19i	0.196312	+	0.340022i
$404$	−5.67770e18	+	9.83407e18i	−0.160810	+	0.278531i
$405$	7.86757e18			0.218740
$406$		0			0
$407$	−2.12796e19			−0.570172
$408$	−1.12404e19	+	1.94689e19i	−0.295685	+	0.512141i
$409$	−2.63912e19	−	4.57108e19i	−0.681607	−	1.18058i	−0.974490	−	0.224429i	$-0.927948\pi$
$409$	−2.63912e19	−	4.57108e19i	−0.681607	−	1.18058i	0.292884	−	0.956148i	$-0.405385\pi$
$410$	−9.24083e18	−	1.60056e19i	−0.234332	−	0.405875i
$411$	−1.77313e19	+	3.07116e19i	−0.441497	+	0.764696i
$412$	−1.02926e19			−0.251649
$413$		0			0
$414$	−6.40972e18			−0.151125
$415$	7.34065e18	−	1.27144e19i	0.169971	−	0.294398i
$416$	1.47244e19	+	2.55034e19i	0.334841	+	0.579961i
$417$	−3.12551e19	−	5.41354e19i	−0.698073	−	1.20910i
$418$	3.47571e18	−	6.02011e18i	0.0762469	−	0.132063i
$419$	−8.62630e18			−0.185874			−0.0929372	−	0.995672i	$-0.529626\pi$
$419$	−8.62630e18			−0.185874			−0.0929372	+	0.995672i	$0.529626\pi$
$420$		0			0
$421$	−4.29249e19			−0.892469			−0.446235	−	0.894916i	$-0.647235\pi$
$421$	−4.29249e19			−0.892469			−0.446235	+	0.894916i	$0.647235\pi$
$422$	−4.05901e19	+	7.03040e19i	−0.829041	+	1.43594i
$423$	5.35444e18	+	9.27416e18i	0.107439	+	0.186090i
$424$	1.38597e19	+	2.40056e19i	0.273218	+	0.473227i
$425$	−2.28885e19	+	3.96440e19i	−0.443302	+	0.767822i
$426$	9.04322e19			1.72088
$427$		0			0
$428$	−3.49186e19			−0.641547
$429$	−6.55038e18	+	1.13456e19i	−0.118260	+	0.204832i
$430$	−2.77119e18	−	4.79983e18i	−0.0491646	−	0.0851555i
$431$	−2.52382e19	−	4.37138e19i	−0.440026	−	0.762148i	0.557665	−	0.830066i	$-0.311698\pi$
$431$	−2.52382e19	−	4.37138e19i	−0.440026	−	0.762148i	−0.997691	+	0.0679185i	$0.978364\pi$
$432$	−3.91113e19	+	6.77428e19i	−0.670154	+	1.16074i
$433$	−5.05734e19			−0.851653			−0.425827	−	0.904805i	$-0.640017\pi$
$433$	−5.05734e19			−0.851653			−0.425827	+	0.904805i	$0.640017\pi$
$434$		0			0
$435$	6.43818e18			0.104735
$436$	−8.80745e18	+	1.52550e19i	−0.140832	+	0.243928i
$437$	7.38726e18	+	1.27951e19i	0.116111	+	0.201110i
$438$	−2.97119e19	−	5.14625e19i	−0.459065	−	0.795124i
$439$	1.23973e19	−	2.14728e19i	0.188297	−	0.326140i	−0.756386	−	0.654126i	$-0.773037\pi$
$439$	1.23973e19	−	2.14728e19i	0.188297	−	0.326140i	0.944683	+	0.327986i	$0.106370\pi$
$440$	4.37489e18			0.0653238
$441$		0			0
$442$	−6.75996e19			−0.975612
$443$	6.53271e19	−	1.13150e20i	0.926970	−	1.60556i	0.138608	−	0.990347i	$-0.455737\pi$
$443$	6.53271e19	−	1.13150e20i	0.926970	−	1.60556i	0.788362	−	0.615212i	$-0.210930\pi$
$444$	2.40309e19	+	4.16227e19i	0.335272	+	0.580708i
$445$	−1.86454e19	−	3.22949e19i	−0.255784	−	0.443030i
$446$	−2.73324e18	+	4.73411e18i	−0.0368694	+	0.0638597i
$447$	−4.20373e19			−0.557608
$448$		0			0
$449$	−7.78280e19			−0.998363			−0.499181	−	0.866498i	$-0.666366\pi$
$449$	−7.78280e19			−0.998363			−0.499181	+	0.866498i	$0.666366\pi$
$450$	−9.42767e18	+	1.63292e19i	−0.118935	+	0.206002i
$451$	1.69015e19	+	2.92743e19i	0.209702	+	0.363214i
$452$	1.42641e19	+	2.47062e19i	0.174063	+	0.301486i
$453$	−4.81422e19	+	8.33848e19i	−0.577816	+	1.00081i
$454$	−6.55975e19			−0.774405
$455$		0			0
$456$	2.13438e19			0.243801
$457$	5.92254e19	−	1.02581e20i	0.665482	−	1.15265i	−0.313672	−	0.949531i	$-0.601559\pi$
$457$	5.92254e19	−	1.02581e20i	0.665482	−	1.15265i	0.979154	−	0.203118i	$-0.0651075\pi$
$458$	1.16631e19	+	2.02011e19i	0.128921	+	0.223297i
$459$	−4.82039e19	−	8.34916e19i	−0.524188	−	0.907921i
$460$	3.41990e18	−	5.92345e18i	0.0365873	−	0.0633710i
$461$	−1.38643e20			−1.45929			−0.729644	−	0.683827i	$-0.760314\pi$
$461$	−1.38643e20			−1.45929			−0.729644	+	0.683827i	$0.760314\pi$
$462$		0			0
$463$	1.75645e20			1.78969			0.894846	−	0.446375i	$-0.147285\pi$
$463$	1.75645e20			1.78969			0.894846	+	0.446375i	$0.147285\pi$
$464$	−2.46499e19	+	4.26950e19i	−0.247133	+	0.428047i
$465$	−6.24482e18	−	1.08163e19i	−0.0616059	−	0.106705i
$466$	8.53747e19	+	1.47873e20i	0.828771	+	1.43547i
$467$	−6.83155e19	+	1.18326e20i	−0.652593	+	1.13032i	0.329898	+	0.944017i	$0.392986\pi$
$467$	−6.83155e19	+	1.18326e20i	−0.652593	+	1.13032i	−0.982491	+	0.186308i	$0.940348\pi$
$468$	−8.28826e18			−0.0779147
$469$		0			0
$470$	−3.83899e19			−0.349528
$471$	−2.43193e19	+	4.21222e19i	−0.217918	+	0.377446i
$472$	−2.01026e19	−	3.48187e19i	−0.177291	−	0.307077i
$473$	5.06851e18	+	8.77893e18i	0.0439969	+	0.0762049i
$474$	9.18896e18	−	1.59158e19i	0.0785107	−	0.135985i
$475$	4.34619e19			0.365516
$476$		0			0
$477$	−2.13417e19			−0.173917
$478$	−3.81193e19	+	6.60246e19i	−0.305799	+	0.529659i
$479$	3.20529e19	+	5.55173e19i	0.253134	+	0.438442i	0.964387	−	0.264495i	$-0.0852052\pi$
$479$	3.20529e19	+	5.55173e19i	0.253134	+	0.438442i	−0.711253	+	0.702936i	$0.751872\pi$
$480$	−1.35152e19	−	2.34091e19i	−0.105079	−	0.182001i
$481$	9.82349e19	−	1.70148e20i	0.751930	−	1.30238i
$482$	−1.48109e19			−0.111617
$483$		0			0
$484$	−5.21276e19			−0.380827
$485$	−1.59661e19	+	2.76542e19i	−0.114852	+	0.198929i
$486$	−3.61453e19	−	6.26055e19i	−0.256024	−	0.443446i
$487$	1.20672e19	+	2.09009e19i	0.0841662	+	0.145780i	0.905036	−	0.425336i	$-0.139844\pi$
$487$	1.20672e19	+	2.09009e19i	0.0841662	+	0.145780i	−0.820869	+	0.571116i	$0.806511\pi$
$488$	−1.00562e19	+	1.74179e19i	−0.0690695	+	0.119632i
$489$	5.61598e19			0.379847
$490$		0			0
$491$	−2.80908e19			−0.184269			−0.0921346	−	0.995747i	$-0.529369\pi$
$491$	−2.80908e19			−0.184269			−0.0921346	+	0.995747i	$0.529369\pi$
$492$	3.81735e19	−	6.61184e19i	0.246617	−	0.427153i
$493$	−3.03806e19	−	5.26207e19i	−0.193305	−	0.334815i
$494$	3.20904e19	+	5.55822e19i	0.201105	+	0.348324i
$495$	−1.68416e18	+	2.91705e18i	−0.0103955	+	0.0180055i
$496$	9.56384e19			0.581460
$497$		0			0
$498$	2.03743e20			1.20188
$499$	8.59968e19	−	1.48951e20i	0.499722	−	0.865543i	−0.500278	−	0.865865i	$-0.666769\pi$
$499$	8.59968e19	−	1.48951e20i	0.499722	−	0.865543i	1.00000		0.000321324i	$0.000102281\pi$
$500$	−2.11031e19	−	3.65516e19i	−0.120801	−	0.209234i
$501$	1.07471e20	+	1.86145e20i	0.606048	+	1.04971i
$502$	1.71510e20	−	2.97064e20i	0.952822	−	1.65034i
$503$	1.83497e20			1.00431			0.502155	−	0.864778i	$-0.332541\pi$
$503$	1.83497e20			1.00431			0.502155	+	0.864778i	$0.332541\pi$
$504$		0			0
$505$	−4.26073e19			−0.226359
$506$	−2.10134e19	+	3.63963e19i	−0.109994	+	0.190515i
$507$	2.52071e19	+	4.36600e19i	0.130006	+	0.225177i
$508$	−2.07673e19	−	3.59699e19i	−0.105536	−	0.182794i
$509$	1.33602e20	−	2.31405e20i	0.669004	−	1.15875i	−0.309179	−	0.951004i	$-0.600054\pi$
$509$	1.33602e20	−	2.31405e20i	0.669004	−	1.15875i	0.978183	−	0.207746i	$-0.0666126\pi$
$510$	6.20482e19			0.306163
$511$		0			0
$512$	2.84604e19			0.136369
$513$	−4.57661e19	+	7.92692e19i	−0.216104	+	0.374304i
$514$	−8.94847e19	−	1.54992e20i	−0.416414	−	0.721250i
$515$	−1.93097e19	−	3.34454e19i	−0.0885569	−	0.153385i
$516$	1.14476e19	−	1.98279e19i	0.0517420	−	0.0896198i
$517$	7.02153e19			0.312790
$518$		0			0
$519$	2.54401e20			1.10094
$520$	−2.01961e19	+	3.49807e19i	−0.0861476	+	0.149212i
$521$	−1.00734e20	−	1.74476e20i	−0.423538	−	0.733589i	0.572745	−	0.819734i	$-0.305879\pi$
$521$	−1.00734e20	−	1.74476e20i	−0.423538	−	0.733589i	−0.996283	+	0.0861445i	$0.972545\pi$
$522$	−1.25136e19	−	2.16742e19i	−0.0518626	−	0.0898286i
$523$	1.79494e20	−	3.10893e20i	0.733311	−	1.27013i	−0.222150	−	0.975013i	$-0.571307\pi$
$523$	1.79494e20	−	3.10893e20i	0.733311	−	1.27013i	0.955461	−	0.295119i	$-0.0953593\pi$
$524$	2.25850e19			0.0909570
$525$		0			0
$526$	3.03362e20			1.18732
$527$	−5.89362e19	+	1.02081e20i	−0.227406	+	0.393879i
$528$	4.60399e19	+	7.97435e19i	0.175138	+	0.303348i
$529$	8.86558e19	+	1.53556e20i	0.332499	+	0.575904i
$530$	3.82536e19	−	6.62571e19i	0.141450	−	0.244998i
$531$	3.09549e19			0.112855
$532$		0			0
$533$	−3.12095e20			−1.10620
$534$	2.58756e20	−	4.48179e20i	0.904339	−	1.56636i
$535$	−6.55101e19	−	1.13467e20i	−0.225764	−	0.391035i
$536$	−5.88015e19	−	1.01847e20i	−0.199826	−	0.346109i
$537$	−1.56310e20	+	2.70736e20i	−0.523816	+	0.907275i
$538$	−3.10137e20			−1.02491
$539$		0			0
$540$	4.23744e19			0.136192
$541$	−1.01164e20	+	1.75221e20i	−0.320662	+	0.555402i	−0.980625	−	0.195896i	$-0.937239\pi$
$541$	−1.01164e20	+	1.75221e20i	−0.320662	+	0.555402i	0.659963	+	0.751298i	$0.270572\pi$
$542$	5.49893e19	+	9.52442e19i	0.171903	+	0.297745i
$543$	1.24408e20	+	2.15481e20i	0.383574	+	0.664369i
$544$	−1.27552e20	+	2.20926e20i	−0.387877	+	0.671823i
$545$	−6.60939e19			−0.198238
$546$		0			0
$547$	7.40963e19			0.216218			0.108109	−	0.994139i	$-0.465520\pi$
$547$	7.40963e19			0.216218			0.108109	+	0.994139i	$0.465520\pi$
$548$	−7.35522e19	+	1.27396e20i	−0.211710	+	0.366693i
$549$	−7.74251e18	−	1.34104e19i	−0.0219831	−	0.0380759i
$550$	6.18147e19	+	1.07066e20i	0.173130	+	0.299869i
$551$	−2.88441e19	+	4.99595e19i	−0.0796930	+	0.138032i
$552$	−1.29040e20			−0.351707
$553$		0			0
$554$	1.22892e20			0.325988
$555$	−9.01677e19	+	1.56175e20i	−0.235968	+	0.408709i
$556$	−1.29651e20	−	2.24562e20i	−0.334745	−	0.579796i
$557$	−1.04813e18	−	1.81541e18i	−0.00266994	−	0.00462446i	0.864687	−	0.502310i	$-0.167517\pi$
$557$	−1.04813e18	−	1.81541e18i	−0.00266994	−	0.00462446i	−0.867357	+	0.497686i	$0.834183\pi$
$558$	−2.42756e19	+	4.20465e19i	−0.0610117	+	0.105675i
$559$	−9.35927e19			−0.232088
$560$		0			0
$561$	−1.13487e20			−0.273983
$562$	4.38678e20	−	7.59813e20i	1.04502	−	1.81002i
$563$	3.43676e20	+	5.95265e20i	0.807861	+	1.39926i	0.914342	+	0.404942i	$0.132708\pi$
$563$	3.43676e20	+	5.95265e20i	0.807861	+	1.39926i	−0.106481	+	0.994315i	$0.533958\pi$
$564$	−7.92934e19	−	1.37340e20i	−0.183926	−	0.318569i
$565$	−5.35212e19	+	9.27015e19i	−0.122507	+	0.212189i
$566$	−6.01573e20			−1.35883
$567$		0			0
$568$	−5.09964e20			−1.12183
$569$	4.52609e19	−	7.83942e19i	0.0982610	−	0.170193i	−0.812704	−	0.582677i	$-0.802005\pi$
$569$	4.52609e19	−	7.83942e19i	0.0982610	−	0.170193i	0.910965	+	0.412484i	$0.135339\pi$
$570$	−2.94551e19	−	5.10178e19i	−0.0631102	−	0.109310i
$571$	−1.02887e20	−	1.78205e20i	−0.217565	−	0.376834i	0.736498	−	0.676440i	$-0.236478\pi$
$571$	−1.02887e20	−	1.78205e20i	−0.217565	−	0.376834i	−0.954063	+	0.299606i	$0.903145\pi$
$572$	−2.71720e19	+	4.70632e19i	−0.0567088	+	0.0982226i
$573$	−3.30188e20			−0.680145
$574$		0			0
$575$	−2.62761e20			−0.527293
$576$	1.61866e19	−	2.80359e19i	0.0320617	−	0.0555324i
$577$	2.85389e20	+	4.94309e20i	0.557980	+	0.966450i	0.997665	+	0.0682981i	$0.0217569\pi$
$577$	2.85389e20	+	4.94309e20i	0.557980	+	0.966450i	−0.439685	+	0.898152i	$0.644910\pi$
$578$	1.63478e19	+	2.83152e19i	0.0315501	+	0.0546464i
$579$	1.49183e19	−	2.58393e19i	0.0284204	−	0.0492256i
$580$	2.67065e19			0.0502236
$581$		0			0
$582$	−4.43147e20			−0.812130
$583$	−6.99660e19	+	1.21185e20i	−0.126582	+	0.219247i
$584$	1.67551e20	+	2.90207e20i	0.299261	+	0.518336i
$585$	−1.55494e19	−	2.69324e19i	−0.0274186	−	0.0474905i
$586$	−3.92907e20	+	6.80535e20i	−0.684002	+	1.18473i
$587$	9.30363e20			1.59907			0.799534	−	0.600621i	$-0.205080\pi$
$587$	9.30363e20			1.59907			0.799534	+	0.600621i	$0.205080\pi$
$588$		0			0
$589$	1.11911e20			0.187503
$590$	−5.54845e19	+	9.61019e19i	−0.0917870	+	0.158980i
$591$	−5.92890e19	−	1.02692e20i	−0.0968430	−	0.167737i
$592$	−6.90452e20	−	1.19590e21i	−1.11358	−	1.92877i
$593$	1.77112e20	−	3.06768e20i	0.282058	−	0.488539i	−0.689833	−	0.723968i	$-0.742316\pi$
$593$	1.77112e20	−	3.06768e20i	0.282058	−	0.488539i	0.971892	+	0.235429i	$0.0756495\pi$
$594$	−2.60368e20			−0.409438
$595$		0			0
$596$	−1.74377e20			−0.267388
$597$	−4.79536e20	+	8.30580e20i	−0.726128	+	1.25769i
$598$	−1.94012e20	−	3.36038e20i	−0.290114	−	0.502493i
$599$	1.65023e20	+	2.85828e20i	0.243693	+	0.422088i	0.961763	−	0.273882i	$-0.0883079\pi$
$599$	1.65023e20	+	2.85828e20i	0.243693	+	0.422088i	−0.718071	+	0.695970i	$0.754975\pi$
$600$	−1.89797e20	+	3.28738e20i	−0.276793	+	0.479419i
$601$	3.35884e20			0.483761			0.241880	−	0.970306i	$-0.422236\pi$
$601$	3.35884e20			0.483761			0.241880	+	0.970306i	$0.422236\pi$
$602$		0			0
$603$	9.05451e19			0.127199
$604$	−1.99701e20	+	3.45892e20i	−0.277079	+	0.479915i
$605$	−9.77956e19	−	1.69387e20i	−0.134015	−	0.232121i
$606$	−2.95646e20	−	5.12074e20i	−0.400154	−	0.693088i
$607$	−6.67188e20	+	1.15560e21i	−0.891934	+	1.54488i	−0.0543812	+	0.998520i	$0.517319\pi$
$607$	−6.67188e20	+	1.15560e21i	−0.891934	+	1.54488i	−0.837553	+	0.546356i	$0.816015\pi$
$608$	2.42202e20			0.319816
$609$		0			0
$610$	5.55116e19			0.0715172
$611$	−3.24140e20	+	5.61427e20i	−0.412500	+	0.714471i
$612$	−3.58989e19	−	6.21787e19i	−0.0451279	−	0.0781639i
$613$	−2.84422e18	−	4.92633e18i	−0.00353191	−	0.00611744i	0.864254	−	0.503056i	$-0.167791\pi$
$613$	−2.84422e18	−	4.92633e18i	−0.00353191	−	0.00611744i	−0.867786	+	0.496938i	$0.834458\pi$
$614$	−1.05332e20	+	1.82440e20i	−0.129210	+	0.223799i
$615$	2.86466e20			0.347144
$616$		0			0
$617$	3.98915e20			0.471783			0.235891	−	0.971779i	$-0.424199\pi$
$617$	3.98915e20			0.471783			0.235891	+	0.971779i	$0.424199\pi$
$618$	2.67975e20	−	4.64147e20i	0.313098	−	0.542303i
$619$	−2.70008e20	−	4.67668e20i	−0.311672	−	0.539831i	0.667053	−	0.745010i	$-0.267556\pi$
$619$	−2.70008e20	−	4.67668e20i	−0.311672	−	0.539831i	−0.978724	+	0.205179i	$0.934222\pi$
$620$	−2.59044e19	−	4.48678e19i	−0.0295418	−	0.0511678i
$621$	2.76692e20	−	4.79244e20i	0.311752	−	0.539970i
$622$	−7.27254e19			−0.0809577
$623$		0			0
$624$	−8.50151e20			−0.923871
$625$	−3.45045e20	+	5.97635e20i	−0.370489	+	0.641705i
$626$	3.94795e20	+	6.83805e20i	0.418856	+	0.725479i
$627$	5.38736e19	+	9.33118e19i	0.0564767	+	0.0978205i
$628$	−1.00880e20	+	1.74729e20i	−0.104498	+	0.180996i
$629$	1.70194e21			1.74206
$630$		0			0
$631$	9.59111e20			0.958625			0.479312	−	0.877644i	$-0.340886\pi$
$631$	9.59111e20			0.958625			0.479312	+	0.877644i	$0.340886\pi$
$632$	−5.18183e19	+	8.97519e19i	−0.0511805	+	0.0886473i
$633$	−6.29146e20	−	1.08971e21i	−0.614078	−	1.06361i
$634$	8.61170e19	+	1.49159e20i	0.0830653	+	0.143873i
$635$	7.79221e19	−	1.34965e20i	0.0742775	−	0.128652i
$636$	3.16047e20			0.297731
$637$		0			0
$638$	−1.64097e20			−0.150989
$639$	1.96316e20	−	3.40030e20i	0.178525	−	0.309215i
$640$	1.90305e20	+	3.29617e20i	0.171041	+	0.296251i
$641$	4.62963e20	+	8.01875e20i	0.411255	+	0.712314i	0.995027	−	0.0996033i	$-0.0317574\pi$
$641$	4.62963e20	+	8.01875e20i	0.411255	+	0.712314i	−0.583773	+	0.811917i	$0.698424\pi$
$642$	9.09131e20	−	1.57466e21i	0.798204	−	1.38253i
$643$	7.65928e20			0.664669			0.332335	−	0.943162i	$-0.392164\pi$
$643$	7.65928e20			0.664669			0.332335	+	0.943162i	$0.392164\pi$
$644$		0			0
$645$	8.59068e19			0.0728332
$646$	−2.77986e20	+	4.81486e20i	−0.232959	+	0.403497i
$647$	6.80377e20	+	1.17845e21i	0.563596	+	0.976176i	0.997179	+	0.0750627i	$0.0239157\pi$
$647$	6.80377e20	+	1.17845e21i	0.563596	+	0.976176i	−0.433583	+	0.901114i	$0.642751\pi$
$648$	−3.07854e20	−	5.33219e20i	−0.252077	−	0.436610i
$649$	1.01481e20	−	1.75771e20i	0.0821394	−	0.142270i
$650$	−1.14144e21			−0.913278
$651$		0			0
$652$	2.32959e20			0.182147
$653$	1.35904e20	−	2.35393e20i	0.105047	−	0.181947i	−0.808710	−	0.588207i	$-0.799834\pi$
$653$	1.35904e20	−	2.35393e20i	0.105047	−	0.181947i	0.913757	+	0.406260i	$0.133167\pi$
$654$	−4.58616e20	−	7.94347e20i	−0.350442	−	0.606984i
$655$	4.23713e19	+	7.33893e19i	0.0320083	+	0.0554400i
$656$	−1.09680e21	+	1.89971e21i	−0.819119	+	1.41876i
$657$	−2.58002e20			−0.190495
$658$		0			0
$659$	6.74316e20			0.486657			0.243329	−	0.969944i	$-0.421761\pi$
$659$	6.74316e20			0.486657			0.243329	+	0.969944i	$0.421761\pi$
$660$	2.49406e19	−	4.31983e19i	0.0177962	−	0.0308239i
$661$	6.33634e20	+	1.09749e21i	0.447021	+	0.774263i	0.998191	−	0.0601303i	$-0.0191516\pi$
$661$	6.33634e20	+	1.09749e21i	0.447021	+	0.774263i	−0.551170	+	0.834393i	$0.685818\pi$
$662$	1.09712e21	+	1.90027e21i	0.765278	+	1.32550i
$663$	5.23897e20	−	9.07416e20i	0.361322	−	0.625828i
$664$	−1.14894e21			−0.783499
$665$		0			0
$666$	7.01020e20			0.467384
$667$	1.74385e20	−	3.02044e20i	0.114965	−	0.199125i
$668$	4.45804e20	+	7.72156e20i	0.290617	+	0.503363i
$669$	−4.23652e19	−	7.33787e19i	−0.0273095	−	0.0473014i
$670$	−1.62296e20	+	2.81105e20i	−0.103454	+	0.179187i
$671$	−1.01531e20			−0.0640000
$672$		0			0
$673$	−1.13945e21			−0.702394			−0.351197	−	0.936302i	$-0.614225\pi$
$673$	−1.13945e21			−0.702394			−0.351197	+	0.936302i	$0.614225\pi$
$674$	5.19983e20	−	9.00636e20i	0.316986	−	0.549035i
$675$	−8.13938e20	−	1.40978e21i	−0.490696	−	0.849911i
$676$	1.04563e20	+	1.81108e20i	0.0623415	+	0.107979i
$677$	8.72156e20	−	1.51062e21i	0.514256	−	0.890717i	−0.485607	−	0.874177i	$-0.661402\pi$
$677$	8.72156e20	−	1.51062e21i	0.514256	−	0.890717i	0.999863	−	0.0165401i	$-0.00526512\pi$
$678$	−1.48550e21			−0.866266
$679$		0			0
$680$	−3.49902e20			−0.199586
$681$	5.08380e20	−	8.80541e20i	0.286804	−	0.496759i
$682$	1.59168e20	+	2.75688e20i	0.0888125	+	0.153828i
$683$	7.18695e20	+	1.24482e21i	0.396634	+	0.686990i	0.993308	−	0.115494i	$-0.0368450\pi$
$683$	7.18695e20	+	1.24482e21i	0.396634	+	0.686990i	−0.596675	+	0.802483i	$0.703512\pi$
$684$	−3.40834e19	+	5.90341e19i	−0.0186047	+	0.0322242i
$685$	−5.51960e20			−0.298008
$686$		0			0
$687$	−3.61556e20			−0.190985
$688$	−3.28912e20	+	5.69693e20i	−0.171857	+	0.297665i
$689$	−6.45979e20	−	1.11887e21i	−0.333867	−	0.578275i
$690$	1.78079e20	+	3.08442e20i	0.0910427	+	0.157691i
$691$	−8.87738e20	+	1.53761e21i	−0.448951	+	0.777607i	−0.998318	−	0.0579748i	$-0.981536\pi$
$691$	−8.87738e20	+	1.53761e21i	−0.448951	+	0.777607i	0.549367	+	0.835581i	$0.314869\pi$
$692$	1.05529e21			0.527932
$693$		0			0
$694$	9.72594e20			0.476141
$695$	4.86471e20	−	8.42592e20i	0.235597	−	0.408067i
$696$	−2.51923e20	−	4.36343e20i	−0.120698	−	0.209054i
$697$	−1.35178e21	−	2.34135e21i	−0.640707	−	1.10974i
$698$	2.42269e21	−	4.19622e21i	1.13601	−	1.96763i
$699$	−2.64661e21			−1.22776
$700$		0			0
$701$	1.43100e21			0.649764			0.324882	−	0.945755i	$-0.394675\pi$
$701$	1.43100e21			0.649764			0.324882	+	0.945755i	$0.394675\pi$
$702$	1.20195e21	−	2.08185e21i	0.539958	−	0.935234i
$703$	−8.07932e20	−	1.39938e21i	−0.359095	−	0.621972i
$704$	−1.06131e20	−	1.83824e20i	−0.0466710	−	0.0808366i
$705$	2.97521e20	−	5.15322e20i	0.129449	−	0.224213i
$706$	−1.73342e21			−0.746223
$707$		0			0
$708$	−4.58408e20			−0.193198
$709$	1.20920e21	−	2.09440e21i	0.504257	−	0.873399i	−0.495731	−	0.868476i	$-0.665100\pi$
$709$	1.20920e21	−	2.09440e21i	0.504257	−	0.873399i	0.999988	−	0.00492257i	$-0.00156691\pi$
$710$	7.03767e20	+	1.21896e21i	0.290396	+	0.502981i
$711$	−3.98960e19	−	6.91020e19i	−0.0162895	−	0.0282142i
$712$	−1.45917e21	+	2.52737e21i	−0.589532	+	1.02110i
$713$	−6.76591e20			−0.270492
$714$		0			0
$715$	−2.03907e20			−0.0798246
$716$	−6.48395e20	+	1.12305e21i	−0.251184	+	0.435064i
$717$	−5.90849e20	−	1.02338e21i	−0.226508	−	0.392323i
$718$	−1.74428e20	−	3.02118e20i	−0.0661733	−	0.114615i
$719$	2.37222e21	−	4.10880e21i	0.890611	−	1.54258i	0.0514670	−	0.998675i	$-0.483610\pi$
$719$	2.37222e21	−	4.10880e21i	0.890611	−	1.54258i	0.839144	−	0.543909i	$-0.183056\pi$
$720$	−2.18581e20			−0.0812118
$721$		0			0
$722$	−2.75127e21			−1.00116
$723$	1.14784e20	−	1.98813e20i	0.0413377	−	0.0715989i
$724$	5.16062e20	+	8.93845e20i	0.183934	+	0.318583i
$725$	−5.12985e20	−	8.88516e20i	−0.180955	−	0.313423i
$726$	1.35718e21	−	2.35070e21i	0.473819	−	0.820679i
$727$	3.59265e21			1.24138			0.620692	−	0.784054i	$-0.286852\pi$
$727$	3.59265e21			1.24138			0.620692	+	0.784054i	$0.286852\pi$
$728$		0			0
$729$	3.28690e21			1.11258
$730$	4.62451e20	−	8.00989e20i	0.154933	−	0.268352i
$731$	−4.05378e20	−	7.02135e20i	−0.134425	−	0.232831i
$732$	1.14658e20	+	1.98593e20i	0.0376332	+	0.0651826i
$733$	−1.38412e21	+	2.39736e21i	−0.449669	+	0.778850i	−0.998364	−	0.0571725i	$-0.981791\pi$
$733$	−1.38412e21	+	2.39736e21i	−0.449669	+	0.778850i	0.548695	+	0.836023i	$0.315125\pi$
$734$	2.15525e21			0.693069
$735$		0			0
$736$	−1.46430e21			−0.461367
$737$	2.96840e20	−	5.14142e20i	0.0925798	−	0.160353i
$738$	−5.56791e20	−	9.64391e20i	−0.171898	−	0.297735i
$739$	−1.77912e21	−	3.08153e21i	−0.543716	−	0.941744i	−0.998687	−	0.0512372i	$-0.983684\pi$
$739$	−1.77912e21	−	3.08153e21i	−0.543716	−	0.941744i	0.454971	−	0.890507i	$-0.349650\pi$
$740$	−3.74029e20	+	6.47837e20i	−0.113153	+	0.195987i
$741$	−9.94803e20			−0.297921
$742$		0			0
$743$	−1.94092e21			−0.569628			−0.284814	−	0.958583i	$-0.591932\pi$
$743$	−1.94092e21			−0.569628			−0.284814	+	0.958583i	$0.591932\pi$
$744$	−4.88714e20	+	8.46477e20i	−0.141990	+	0.245934i
$745$	−3.27145e20	−	5.66633e20i	−0.0940955	−	0.162978i
$746$	2.55815e21	+	4.43085e21i	0.728425	+	1.26167i
$747$	4.42299e20	−	7.66084e20i	0.124684	−	0.215959i
$748$	−4.70759e20			−0.131382
$749$		0			0
$750$	2.19774e21			0.601196
$751$	−2.37782e21	+	4.11851e21i	−0.643992	+	1.11543i	0.340542	+	0.940229i	$0.389390\pi$
$751$	−2.37782e21	+	4.11851e21i	−0.643992	+	1.11543i	−0.984533	+	0.175197i	$0.943944\pi$
$752$	2.27825e21	+	3.94604e21i	0.610896	+	1.05810i
$753$	2.65841e21	+	4.60450e21i	0.705763	+	1.22242i
$754$	7.57533e20	−	1.31209e21i	0.199121	−	0.344887i
$755$	−1.49862e21			−0.390022
$756$		0			0
$757$	3.62137e21			0.923960			0.461980	−	0.886890i	$-0.347139\pi$
$757$	3.62137e21			0.923960			0.461980	+	0.886890i	$0.347139\pi$
$758$	−2.01799e21	+	3.49527e21i	−0.509801	+	0.883001i
$759$	−3.25708e20	−	5.64143e20i	−0.0814733	−	0.141116i
$760$	1.66103e20	+	2.87699e20i	0.0411410	+	0.0712584i
$761$	−1.93181e21	+	3.34599e21i	−0.473782	+	0.820614i	−0.999549	−	0.0300139i	$-0.990445\pi$
$761$	−1.93181e21	+	3.34599e21i	−0.473782	+	0.820614i	0.525768	+	0.850628i	$0.323778\pi$
$762$	2.16276e21			0.525226
$763$		0			0
$764$	−1.36967e21			−0.326148
$765$	1.34698e20	−	2.33305e20i	0.0317616	−	0.0550126i
$766$	−3.26722e21	−	5.65900e21i	−0.762892	−	1.32137i
$767$	9.36953e20	+	1.62285e21i	0.216647	+	0.375243i
$768$	−2.07542e21	+	3.59474e21i	−0.475223	+	0.823111i
$769$	5.39327e21			1.22294			0.611469	−	0.791268i	$-0.290579\pi$
$769$	5.39327e21			1.22294			0.611469	+	0.791268i	$0.290579\pi$
$770$		0			0
$771$	2.77403e21			0.616883
$772$	6.18834e19	−	1.07185e20i	0.0136284	−	0.0236050i
$773$	3.28518e21	+	5.69011e21i	0.716496	+	1.24101i	0.962380	+	0.271708i	$0.0875884\pi$
$773$	3.28518e21	+	5.69011e21i	0.716496	+	1.24101i	−0.245884	+	0.969299i	$0.579078\pi$
$774$	−1.66973e20	−	2.89206e20i	−0.0360653	−	0.0624670i
$775$	−9.95156e20	+	1.72366e21i	−0.212877	+	0.368713i
$776$	2.49899e21			0.529422
$777$		0			0
$778$	−2.17543e20			−0.0452062
$779$	−1.28341e21	+	2.22294e21i	−0.264141	+	0.457506i
$780$	2.30270e20	+	3.98839e20i	0.0469384	+	0.0812996i
$781$	−1.28719e21	−	2.22949e21i	−0.259873	−	0.450113i
$782$	1.68064e21	−	2.91096e21i	0.336067	−	0.582084i
$783$	2.16073e21			0.427944
$784$		0			0
$785$	−7.57035e20			−0.147094
$786$	−5.88018e20	+	1.01848e21i	−0.113167	+	0.196012i
$787$	−1.86037e20	−	3.22225e20i	−0.0354641	−	0.0614255i	0.847749	−	0.530398i	$-0.177958\pi$
$787$	−1.86037e20	−	3.22225e20i	−0.0354641	−	0.0614255i	−0.883213	+	0.468973i	$0.844624\pi$
$788$	−2.45940e20	−	4.25980e20i	−0.0464389	−	0.0804345i
$789$	−2.35106e21	+	4.07215e21i	−0.439730	+	0.761634i
$790$	2.86044e20			0.0529943
$791$		0			0
$792$	2.63602e20			0.0479192
$793$	4.68706e20	−	8.11822e20i	0.0844018	−	0.146188i
$794$	3.84830e21	+	6.66545e21i	0.686460	+	1.18898i
$795$	5.92930e20	+	1.02699e21i	0.104773	+	0.181472i
$796$	−1.98919e21	+	3.44537e21i	−0.348199	+	0.603098i
$797$	−2.61511e21			−0.453474			−0.226737	−	0.973956i	$-0.572806\pi$
$797$	−2.61511e21			−0.453474			−0.226737	+	0.973956i	$0.572806\pi$
$798$		0			0
$799$	−5.61579e21			−0.955674
$800$	−2.15375e21	+	3.73040e21i	−0.363095	+	0.628899i
$801$	−1.12345e21	−	1.94587e21i	−0.187633	−	0.324991i
$802$	−4.25873e21	−	7.37634e21i	−0.704649	−	1.22049i
$803$	−8.45826e20	+	1.46501e21i	−0.138648	+	0.240146i
$804$	−1.34087e21			−0.217755
$805$		0			0
$806$	−2.93913e21			−0.468495
$807$	2.40356e21	−	4.16309e21i	0.379581	−	0.657453i
$808$	1.66720e21	+	2.88768e21i	0.260858	+	0.451819i
$809$	−2.67450e21	−	4.63236e21i	−0.414599	−	0.718106i	0.580787	−	0.814055i	$-0.302745\pi$
$809$	−2.67450e21	−	4.63236e21i	−0.414599	−	0.718106i	−0.995386	+	0.0959490i	$0.969411\pi$
$810$	−8.49697e20	+	1.47172e21i	−0.130505	+	0.226041i
$811$	−8.46492e21			−1.28815			−0.644075	−	0.764962i	$-0.722758\pi$
$811$	−8.46492e21			−1.28815			−0.644075	+	0.764962i	$0.722758\pi$
$812$		0			0
$813$	−1.70467e21			−0.254660
$814$	2.29820e21	−	3.98060e21i	0.340177	−	0.589204i
$815$	4.37050e20	+	7.56993e20i	0.0640987	+	0.111022i
$816$	−3.68226e21	−	6.37785e21i	−0.535103	−	0.926826i
$817$	−3.84876e20	+	6.66625e20i	−0.0554186	+	0.0959879i
$818$	1.14010e22			1.62664
$819$		0			0
$820$	1.18830e21			0.166465
$821$	−3.99699e21	+	6.92298e21i	−0.554829	+	0.960992i	0.443088	+	0.896478i	$0.353883\pi$
$821$	−3.99699e21	+	6.92298e21i	−0.554829	+	0.960992i	−0.997917	+	0.0645136i	$0.979450\pi$
$822$	−3.82997e21	−	6.63370e21i	−0.526813	−	0.912468i
$823$	−9.84203e20	−	1.70469e21i	−0.134148	−	0.232352i	0.791123	−	0.611657i	$-0.209497\pi$
$823$	−9.84203e20	−	1.70469e21i	−0.134148	−	0.232352i	−0.925272	+	0.379305i	$0.876163\pi$
$824$	−1.51116e21	+	2.61741e21i	−0.204107	+	0.353523i
$825$	−1.91626e21			−0.256477
$826$		0			0
$827$	−1.43539e22			−1.88659			−0.943296	−	0.331954i	$-0.892292\pi$
$827$	−1.43539e22			−1.88659			−0.943296	+	0.331954i	$0.892292\pi$
$828$	2.06061e20	−	3.56908e20i	0.0268391	−	0.0464867i
$829$	−4.41664e21	−	7.64984e21i	−0.570076	−	0.987400i	−0.996558	−	0.0829041i	$-0.973580\pi$
$829$	−4.41664e21	−	7.64984e21i	−0.570076	−	0.987400i	0.426482	−	0.904496i	$-0.359753\pi$
$830$	1.58558e21	+	2.74631e21i	0.202816	+	0.351288i
$831$	−9.52416e20	+	1.64963e21i	−0.120731	+	0.209112i
$832$	1.95976e21			0.246195
$833$		0			0
$834$	1.35022e22			1.66594
$835$	−1.67273e21	+	2.89725e21i	−0.204539	+	0.354273i
$836$	2.23476e20	+	3.87071e20i	0.0270821	+	0.0469076i
$837$	−2.09583e21	−	3.63009e21i	−0.251719	−	0.435990i
$838$	9.31640e20	−	1.61365e21i	0.110897	−	0.192079i
$839$	−1.26696e22			−1.49469			−0.747343	−	0.664439i	$-0.768671\pi$
$839$	−1.26696e22			−1.49469			−0.747343	+	0.664439i	$0.768671\pi$
$840$		0			0
$841$	−7.26739e21			−0.842187
$842$	4.63588e21	−	8.02959e21i	0.532466	−	0.922258i
$843$	6.79951e21	+	1.17771e22i	0.774054	+	1.34070i
$844$	−2.60979e21	−	4.52029e21i	−0.294467	−	0.510033i
$845$	−3.92337e20	+	6.79547e20i	−0.0438767	+	0.0759966i
$846$	−2.31312e21			−0.256401
$847$		0			0
$848$	−9.08064e21			−0.988889
$849$	4.66219e21	−	8.07515e21i	0.503248	−	0.871651i
$850$	−4.94391e21	−	8.56311e21i	−0.528967	−	0.916198i
$851$	4.88458e21	+	8.46035e21i	0.518031	+	0.897256i
$852$	−2.90723e21	+	5.03547e21i	−0.305620	+	0.529350i
$853$	−6.00532e21			−0.625776			−0.312888	−	0.949790i	$-0.601296\pi$
$853$	−6.00532e21			−0.625776			−0.312888	+	0.949790i	$0.601296\pi$
$854$		0			0
$855$	−2.55773e20			−0.0261883
$856$	−5.12676e21	+	8.87981e21i	−0.520343	+	0.901261i
$857$	7.37947e21	+	1.27816e22i	0.742453	+	1.28597i	0.951375	+	0.308035i	$0.0996713\pi$
$857$	7.37947e21	+	1.27816e22i	0.742453	+	1.28597i	−0.208922	+	0.977932i	$0.566995\pi$
$858$	−1.41488e21	−	2.45065e21i	−0.141113	−	0.244414i
$859$	4.82478e20	−	8.35677e20i	0.0477012	−	0.0826208i	−0.841189	−	0.540741i	$-0.818144\pi$
$859$	4.82478e20	−	8.35677e20i	0.0477012	−	0.0826208i	0.888890	+	0.458120i	$0.151477\pi$
$860$	3.56354e20			0.0349255
$861$		0			0
$862$	1.09029e22			1.05012
$863$	−1.72195e21	+	2.98251e21i	−0.164415	+	0.284775i	−0.936447	−	0.350808i	$-0.885907\pi$
$863$	−1.72195e21	+	2.98251e21i	−0.164415	+	0.284775i	0.772033	+	0.635583i	$0.219240\pi$
$864$	−4.53587e21	−	7.85635e21i	−0.429346	−	0.743649i
$865$	1.97982e21	+	3.42914e21i	0.185782	+	0.321784i
$866$	5.46193e21	−	9.46033e21i	0.508115	−	0.880080i
$867$	−5.06782e20			−0.0467389
$868$		0			0
$869$	−5.23175e20			−0.0474241
$870$	−6.95323e20	+	1.20434e21i	−0.0624874	+	0.108231i
$871$	2.74065e21	+	4.74695e21i	0.244184	+	0.422939i
$872$	2.58622e21	+	4.47947e21i	0.228451	+	0.395688i
$873$	−9.62014e20	+	1.66626e21i	−0.0842509	+	0.145927i
$874$	−3.19130e21			−0.277097
$875$		0			0
$876$	3.82073e21			0.326111
$877$	5.49251e21	−	9.51331e21i	0.464808	−	0.805072i	−0.534384	−	0.845242i	$-0.679457\pi$
$877$	5.49251e21	−	9.51331e21i	0.464808	−	0.805072i	0.999193	+	0.0401697i	$0.0127898\pi$
$878$	2.67782e21	+	4.63812e21i	0.224684	+	0.389164i
$879$	−6.09006e21	−	1.05483e22i	−0.506646	−	0.877537i
$880$	−7.16589e20	+	1.24117e21i	−0.0591085	+	0.102379i
$881$	7.98462e21			0.653033			0.326516	−	0.945192i	$-0.394125\pi$
$881$	7.98462e21			0.653033			0.326516	+	0.945192i	$0.394125\pi$
$882$		0			0
$883$	5.45236e21			0.438409			0.219204	−	0.975679i	$-0.429654\pi$
$883$	5.45236e21			0.438409			0.219204	+	0.975679i	$0.429654\pi$
$884$	2.17320e21	−	3.76410e21i	0.173264	−	0.300102i
$885$	−8.60009e20	−	1.48958e21i	−0.0679874	−	0.117758i
$886$	1.41107e22	+	2.44404e22i	1.10610	+	1.91582i
$887$	8.35636e21	−	1.44736e22i	0.649517	−	1.12500i	−0.333722	−	0.942672i	$-0.608305\pi$
$887$	8.35636e21	−	1.44736e22i	0.649517	−	1.12500i	0.983238	−	0.182324i	$-0.0583620\pi$
$888$	1.41129e22			1.08772
$889$		0			0
$890$	8.05483e21			0.610424
$891$	1.55410e21	−	2.69178e21i	0.116788	−	0.202282i
$892$	−1.75737e20	−	3.04386e20i	−0.0130957	−	0.0226824i
$893$	2.66589e21	+	4.61745e21i	0.196995	+	0.341206i
$894$	4.54003e21	−	7.86357e21i	0.332681	−	0.576220i
$895$	−4.86576e21			−0.353572
$896$		0			0
$897$	6.01436e21			0.429780
$898$	8.40542e21	−	1.45586e22i	0.595644	−	1.03169i
$899$	−1.32090e21	−	2.28786e21i	−0.0928265	−	0.160780i
$900$	−6.06164e20	−	1.04991e21i	−0.0422446	−	0.0731698i
$901$	5.59585e21	−	9.69230e21i	0.386750	−	0.669870i
$902$	−7.30146e21			−0.500450
$903$		0			0
$904$	8.37704e21			0.564712
$905$	−1.93635e21	+	3.35385e21i	−0.129455	+	0.224223i
$906$	−1.03987e22	−	1.80111e22i	−0.689475	−	1.19421i
$907$	7.66922e21	+	1.32835e22i	0.504309	+	0.873488i	0.999988	+	0.00498245i	$0.00158597\pi$
$907$	7.66922e21	+	1.32835e22i	0.504309	+	0.873488i	−0.495679	+	0.868506i	$0.665081\pi$
$908$	2.10884e21	−	3.65261e21i	0.137531	−	0.238210i
$909$	−2.56723e21			−0.166049
$910$		0			0
$911$	−1.49134e22			−0.948829			−0.474415	−	0.880302i	$-0.657340\pi$
$911$	−1.49134e22			−0.948829			−0.474415	+	0.880302i	$0.657340\pi$
$912$	−3.49603e21	+	6.05530e21i	−0.220604	+	0.382098i
$913$	−2.90004e21	−	5.02301e21i	−0.181498	−	0.314364i
$914$	1.27927e22	+	2.21576e22i	0.794082	+	1.37539i
$915$	−4.30215e20	+	7.45155e20i	−0.0264867	+	0.0458763i
$916$	−1.49979e21			−0.0915827
$917$		0			0
$918$	2.08241e22			1.25097
$919$	2.93334e21	−	5.08069e21i	0.174782	−	0.302731i	−0.765304	−	0.643669i	$-0.777411\pi$
$919$	2.93334e21	−	5.08069e21i	0.174782	−	0.302731i	0.940086	+	0.340938i	$0.110745\pi$
$920$	−1.00422e21	−	1.73936e21i	−0.0593501	−	0.102797i
$921$	−1.63265e21	−	2.82783e21i	−0.0957072	−	0.165770i
$922$	1.49734e22	−	2.59348e22i	0.870643	−	1.50800i
$923$	2.37687e22			1.37086
$924$		0			0
$925$	2.87377e22			1.63076
$926$	−1.89697e22	+	3.28564e22i	−1.06777	+	1.84943i
$927$	−1.16348e21	−	2.01520e21i	−0.0649621	−	0.112518i
$928$	−2.85873e21	−	4.95147e21i	−0.158330	−	0.274236i
$929$	−8.39732e21	+	1.45446e22i	−0.461342	+	0.799067i	−0.999028	−	0.0440775i	$-0.985965\pi$
$929$	−8.39732e21	+	1.45446e22i	−0.461342	+	0.799067i	0.537686	+	0.843145i	$0.319298\pi$
$930$	2.69776e21			0.147022
$931$		0			0
$932$	−1.09786e22			−0.588743
$933$	5.63622e20	−	9.76222e20i	0.0299830	−	0.0519321i
$934$	−1.47561e22	−	2.55584e22i	−0.778702	−	1.34875i
$935$	−8.83182e20	−	1.52972e21i	−0.0462342	−	0.0800799i
$936$	−1.21688e21	+	2.10771e21i	−0.0631947	+	0.109456i
$937$	−5.04466e21			−0.259887			−0.129944	−	0.991521i	$-0.541480\pi$
$937$	−5.04466e21			−0.259887			−0.129944	+	0.991521i	$0.541480\pi$
$938$		0			0
$939$	−1.22387e22			−0.620500
$940$	1.23416e21	−	2.13763e21i	0.0620745	−	0.107516i
$941$	8.27127e21	+	1.43263e22i	0.412715	+	0.714843i	0.995186	−	0.0980084i	$-0.0312472\pi$
$941$	8.27127e21	+	1.43263e22i	0.412715	+	0.714843i	−0.582471	+	0.812852i	$0.697914\pi$
$942$	−5.25296e21	−	9.09840e21i	−0.260029	−	0.450384i
$943$	7.75924e21	−	1.34394e22i	0.381050	−	0.659998i
$944$	1.31709e22			0.641691
$945$		0			0
$946$	−2.18960e21			−0.104998
$947$	4.90792e21	−	8.50076e21i	0.233492	−	0.404420i	−0.725341	−	0.688389i	$-0.758318\pi$
$947$	4.90792e21	−	8.50076e21i	0.233492	−	0.404420i	0.958833	+	0.283969i	$0.0916514\pi$
$948$	5.90816e20	+	1.02332e21i	0.0278862	+	0.0483004i
$949$	−7.80930e21	−	1.35261e22i	−0.365692	−	0.633397i
$950$	−4.69388e21	+	8.13004e21i	−0.218075	+	0.377716i
$951$	−2.66963e21			−0.123054
$952$		0			0
$953$	−5.97914e21			−0.271295			−0.135648	−	0.990757i	$-0.543311\pi$
$953$	−5.97914e21			−0.271295			−0.135648	+	0.990757i	$0.543311\pi$
$954$	2.30491e21	−	3.99221e21i	0.103762	−	0.179722i
$955$	−2.56961e21	−	4.45069e21i	−0.114773	−	0.198793i
$956$	−2.45093e21	−	4.24514e21i	−0.108617	−	0.188130i
$957$	1.27175e21	−	2.20274e21i	0.0559194	−	0.0968552i
$958$	−1.38469e22			−0.604101
$959$		0			0
$960$	−1.79882e21			−0.0772600
$961$	9.17018e21	−	1.58832e22i	0.390798	−	0.676882i
$962$	2.12187e22	+	3.67519e22i	0.897235	+	1.55406i
$963$	−3.94721e21	−	6.83676e21i	−0.165612	−	0.286849i
$964$	4.76143e20	−	8.24704e20i	0.0198226	−	0.0343337i
$965$	4.64393e20			0.0191836
$966$		0			0
$967$	−1.44757e22			−0.588764			−0.294382	−	0.955688i	$-0.595114\pi$
$967$	−1.44757e22			−0.588764			−0.294382	+	0.955688i	$0.595114\pi$
$968$	−7.65339e21	+	1.32561e22i	−0.308879	+	0.534995i
$969$	−4.30879e21	−	7.46304e21i	−0.172555	−	0.298873i
$970$	−3.44869e21	−	5.97330e21i	−0.137046	−	0.237370i
$971$	8.89606e20	−	1.54084e21i	0.0350795	−	0.0607595i	−0.847953	−	0.530072i	$-0.822165\pi$
$971$	8.89606e20	−	1.54084e21i	0.0350795	−	0.0607595i	0.883032	+	0.469313i	$0.155498\pi$
$972$	4.64802e21			0.181874
$973$		0			0
$974$	−5.21301e21			−0.200861
$975$	8.84616e21	−	1.53220e22i	0.338236	−	0.585842i
$976$	−3.29434e21	−	5.70597e21i	−0.124996	−	0.216499i
$977$	−5.20438e21	−	9.01426e21i	−0.195957	−	0.339407i	0.751257	−	0.660010i	$-0.229448\pi$
$977$	−5.20438e21	−	9.01426e21i	−0.195957	−	0.339407i	−0.947214	+	0.320603i	$0.896115\pi$
$978$	−6.06526e21	+	1.05053e22i	−0.226625	+	0.392526i
$979$	−1.47323e22			−0.546262
$980$		0			0
$981$	−3.98238e21			−0.145420
$982$	3.03381e21	−	5.25471e21i	0.109939	−	0.190420i
$983$	1.63231e22	+	2.82724e22i	0.587017	+	1.01674i	0.994621	+	0.103584i	$0.0330310\pi$
$983$	1.63231e22	+	2.82724e22i	0.587017	+	1.01674i	−0.407604	+	0.913159i	$0.633636\pi$
$984$	−1.12093e22	−	1.94150e22i	−0.400050	−	0.692907i
$985$	9.22805e20	−	1.59834e21i	0.0326842	−	0.0566107i
$986$	1.31244e22			0.461320
$987$		0			0
$988$	−4.12659e21			−0.142861
$989$	2.32688e21	−	4.03027e21i	0.0799469	−	0.138472i
$990$	−3.63779e20	−	6.30083e20i	−0.0124043	−	0.0214849i
$991$	3.73664e21	+	6.47204e21i	0.126453	+	0.219023i	0.922300	−	0.386475i	$-0.126307\pi$
$991$	3.73664e21	+	6.47204e21i	0.126453	+	0.219023i	−0.795847	+	0.605498i	$0.792974\pi$
$992$	−5.54575e21	+	9.60552e21i	−0.186261	+	0.322614i
$993$	−3.40107e22			−1.13369
$994$		0			0
$995$	−1.49275e22			−0.490132
$996$	−6.54996e21	+	1.13449e22i	−0.213449	+	0.369704i
$997$	−1.55405e22	−	2.69169e22i	−0.502632	−	0.870585i	−0.999995	−	0.00304233i	$-0.999032\pi$
$997$	−1.55405e22	−	2.69169e22i	−0.502632	−	0.870585i	0.497363	−	0.867543i	$-0.334302\pi$
$998$	1.85753e22	+	3.21734e22i	0.596289	+	1.03280i
$999$	−3.02613e22	+	5.24141e22i	−0.964154	+	1.66996i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.16.c.b.30.1		2
7.2	even	3		49.16.a.a.1.1		1
7.3	odd	6		49.16.c.c.18.1		2
7.4	even	3	inner	49.16.c.b.18.1		2
7.5	odd	6		1.16.a.a.1.1	✓	1
7.6	odd	2		49.16.c.c.30.1		2
21.5	even	6		9.16.a.a.1.1		1
28.19	even	6		16.16.a.d.1.1		1
35.12	even	12		25.16.b.a.24.2		2
35.19	odd	6		25.16.a.a.1.1		1
35.33	even	12		25.16.b.a.24.1		2
56.5	odd	6		64.16.a.i.1.1		1
56.19	even	6		64.16.a.c.1.1		1
77.54	even	6		121.16.a.a.1.1		1
84.47	odd	6		144.16.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.16.a.a.1.1	✓	1	7.5	odd	6
9.16.a.a.1.1		1	21.5	even	6
16.16.a.d.1.1		1	28.19	even	6
25.16.a.a.1.1		1	35.19	odd	6
25.16.b.a.24.1		2	35.33	even	12
25.16.b.a.24.2		2	35.12	even	12
49.16.a.a.1.1		1	7.2	even	3
49.16.c.b.18.1		2	7.4	even	3	inner
49.16.c.b.30.1		2	1.1	even	1	trivial
49.16.c.c.18.1		2	7.3	odd	6
49.16.c.c.30.1		2	7.6	odd	2
64.16.a.c.1.1		1	56.19	even	6
64.16.a.i.1.1		1	56.5	odd	6
121.16.a.a.1.1		1	77.54	even	6
144.16.a.f.1.1		1	84.47	odd	6

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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	49.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-108.000 + 187.061i) q^{2} +(-1674.00 - 2899.45i) q^{3} +(-6944.00 - 12027.4i) q^{4} +(26055.0 - 45128.6i) q^{5} +723168. q^{6} -4.07808e6 q^{8} +(1.56990e6 - 2.71915e6i) q^{9} +O(q^{10})\)	\(q+(-108.000 + 187.061i) q^{2} +(-1674.00 - 2899.45i) q^{3} +(-6944.00 - 12027.4i) q^{4} +(26055.0 - 45128.6i) q^{5} +723168. q^{6} -4.07808e6 q^{8} +(1.56990e6 - 2.71915e6i) q^{9} +(5.62788e6 + 9.74777e6i) q^{10} +(-1.02934e7 - 1.78287e7i) q^{11} +(-2.32485e7 + 4.02676e7i) q^{12} +1.90073e8 q^{13} -1.74464e8 q^{15} +(6.67974e8 - 1.15696e9i) q^{16} +(8.23264e8 + 1.42594e9i) q^{17} +(3.39099e8 + 5.87336e8i) q^{18} +(7.81629e8 - 1.35382e9i) q^{19} -7.23704e8 q^{20} +4.44676e9 q^{22} +(-4.72556e9 + 8.18491e9i) q^{23} +(6.82671e9 + 1.18242e10i) q^{24} +(1.39011e10 + 2.40773e10i) q^{25} +(-2.05279e10 + 3.55554e10i) q^{26} -5.85522e10 q^{27} -3.69026e10 q^{29} +(1.88421e10 - 3.26355e10i) q^{30} +(3.57942e10 + 6.19974e10i) q^{31} +(7.74670e10 + 1.34177e11i) q^{32} +(-3.44624e10 + 5.96906e10i) q^{33} -3.55650e11 q^{34} -4.36056e10 q^{36} +(5.16826e11 - 8.95169e11i) q^{37} +(1.68832e11 + 2.92425e11i) q^{38} +(-3.18183e11 - 5.51109e11i) q^{39} +(-1.06254e11 + 1.84038e11i) q^{40} -1.64197e12 q^{41} -4.92403e11 q^{43} +(-1.42955e11 + 2.47605e11i) q^{44} +(-8.18076e10 - 1.41695e11i) q^{45} +(-1.02072e12 - 1.76794e12i) q^{46} +(-1.70534e12 + 2.95374e12i) q^{47} -4.47275e12 q^{48} -6.00526e12 q^{50} +(2.75629e12 - 4.77403e12i) q^{51} +(-1.31987e12 - 2.28608e12i) q^{52} +(-3.39858e12 - 5.88651e12i) q^{53} +(6.32364e12 - 1.09529e13i) q^{54} -1.07278e12 q^{55} -5.23379e12 q^{57} +(3.98548e12 - 6.90305e12i) q^{58} +(4.92943e12 + 8.53802e12i) q^{59} +(1.21148e12 + 2.09834e12i) q^{60} +(2.46592e12 - 4.27110e12i) q^{61} -1.54631e13 q^{62} +1.03106e13 q^{64} +(4.95236e12 - 8.57774e12i) q^{65} +(-7.44388e12 - 1.28932e13i) q^{66} +(1.44189e13 + 2.49743e13i) q^{67} +(1.14335e13 - 1.98034e13i) q^{68} +3.16423e13 q^{69} +1.25050e14 q^{71} +(-6.40218e12 + 1.10889e13i) q^{72} +(-4.10857e13 - 7.11626e13i) q^{73} +(1.11634e14 + 1.93356e14i) q^{74} +(4.65408e13 - 8.06110e13i) q^{75} -2.17105e13 q^{76} +1.37455e14 q^{78} +(1.27065e13 - 2.20084e13i) q^{79} +(-3.48081e13 - 6.02894e13i) q^{80} +(7.54900e13 + 1.30753e14i) q^{81} +(1.77333e14 - 3.07150e14i) q^{82} +2.81737e14 q^{83} +8.58006e13 q^{85} +(5.31795e13 - 9.21097e13i) q^{86} +(6.17749e13 + 1.06997e14i) q^{87} +(4.19774e13 + 7.27070e13i) q^{88} +(3.57809e14 - 6.19744e14i) q^{89} +3.53409e13 q^{90} +1.31257e14 q^{92} +(1.19839e14 - 2.07567e14i) q^{93} +(-3.68354e14 - 6.38008e14i) q^{94} +(-4.07307e13 - 7.05476e13i) q^{95} +(2.59360e14 - 4.49224e14i) q^{96} -6.12786e14 q^{97} -6.46387e13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 216 q^{2} - 3348 q^{3} - 13888 q^{4} + 52110 q^{5} + 1446336 q^{6} - 8156160 q^{8} + 3139803 q^{9}+O(q^{10}) \) 2 * q - 216 * q^2 - 3348 * q^3 - 13888 * q^4 + 52110 * q^5 + 1446336 * q^6 - 8156160 * q^8 + 3139803 * q^9	\( 2 q - 216 q^{2} - 3348 q^{3} - 13888 q^{4} + 52110 q^{5} + 1446336 q^{6} - 8156160 q^{8} + 3139803 q^{9} + 11255760 q^{10} - 20586852 q^{11} - 46497024 q^{12} + 380146676 q^{13} - 348928560 q^{15} + 1335947264 q^{16} + 1646527986 q^{17} + 678197448 q^{18} + 1563257180 q^{19} - 1447407360 q^{20} + 8893520064 q^{22} - 9451116072 q^{23} + 13653411840 q^{24} + 27802126025 q^{25} - 41055841008 q^{26} - 117104402160 q^{27} - 73805136660 q^{29} + 37684284480 q^{30} + 71588483552 q^{31} + 154934083584 q^{32} - 68924780496 q^{33} - 711300089952 q^{34} - 87211168128 q^{36} + 1033652081554 q^{37} + 337663550880 q^{38} - 636365535624 q^{39} - 212508748800 q^{40} - 3283948036404 q^{41} - 984806218616 q^{43} - 285910200576 q^{44} - 163615134330 q^{45} - 2041441071552 q^{46} - 3410684952624 q^{47} - 8945502879744 q^{48} - 12010518442800 q^{50} + 5512575697128 q^{51} - 2639738518144 q^{52} - 6797151655902 q^{53} + 12647275433280 q^{54} - 2145561715440 q^{55} - 10467570077280 q^{57} + 7970954759280 q^{58} + 9858856815540 q^{59} + 2422959920640 q^{60} + 4931842626902 q^{61} - 30926224894464 q^{62} + 20621115785216 q^{64} + 9904721643180 q^{65} - 14887752587136 q^{66} + 28837826625364 q^{67} + 22866980669568 q^{68} + 63284673218112 q^{69} + 250100229829104 q^{71} - 12804367818240 q^{72} - 82171455513478 q^{73} + 223268849615664 q^{74} + 93081517931700 q^{75} - 43421031431680 q^{76} + 274909911389568 q^{78} + 25413078694480 q^{79} - 69616211927040 q^{80} + 150980027970519 q^{81} + 354666387931632 q^{82} + 563473461780936 q^{83} + 171601146700920 q^{85} + 106359071610528 q^{86} + 123549798768840 q^{87} + 83954829404160 q^{88} + 715618564776810 q^{89} + 70681738030560 q^{90} + 262514200015872 q^{92} + 239678242932096 q^{93} - 736707949766784 q^{94} - 81461331649800 q^{95} + 518719311839232 q^{96} - 12\!\cdots\!52 q^{97}+ \cdots - 129277319340312 q^{99}+O(q^{100}) \) 2 * q - 216 * q^2 - 3348 * q^3 - 13888 * q^4 + 52110 * q^5 + 1446336 * q^6 - 8156160 * q^8 + 3139803 * q^9 + 11255760 * q^10 - 20586852 * q^11 - 46497024 * q^12 + 380146676 * q^13 - 348928560 * q^15 + 1335947264 * q^16 + 1646527986 * q^17 + 678197448 * q^18 + 1563257180 * q^19 - 1447407360 * q^20 + 8893520064 * q^22 - 9451116072 * q^23 + 13653411840 * q^24 + 27802126025 * q^25 - 41055841008 * q^26 - 117104402160 * q^27 - 73805136660 * q^29 + 37684284480 * q^30 + 71588483552 * q^31 + 154934083584 * q^32 - 68924780496 * q^33 - 711300089952 * q^34 - 87211168128 * q^36 + 1033652081554 * q^37 + 337663550880 * q^38 - 636365535624 * q^39 - 212508748800 * q^40 - 3283948036404 * q^41 - 984806218616 * q^43 - 285910200576 * q^44 - 163615134330 * q^45 - 2041441071552 * q^46 - 3410684952624 * q^47 - 8945502879744 * q^48 - 12010518442800 * q^50 + 5512575697128 * q^51 - 2639738518144 * q^52 - 6797151655902 * q^53 + 12647275433280 * q^54 - 2145561715440 * q^55 - 10467570077280 * q^57 + 7970954759280 * q^58 + 9858856815540 * q^59 + 2422959920640 * q^60 + 4931842626902 * q^61 - 30926224894464 * q^62 + 20621115785216 * q^64 + 9904721643180 * q^65 - 14887752587136 * q^66 + 28837826625364 * q^67 + 22866980669568 * q^68 + 63284673218112 * q^69 + 250100229829104 * q^71 - 12804367818240 * q^72 - 82171455513478 * q^73 + 223268849615664 * q^74 + 93081517931700 * q^75 - 43421031431680 * q^76 + 274909911389568 * q^78 + 25413078694480 * q^79 - 69616211927040 * q^80 + 150980027970519 * q^81 + 354666387931632 * q^82 + 563473461780936 * q^83 + 171601146700920 * q^85 + 106359071610528 * q^86 + 123549798768840 * q^87 + 83954829404160 * q^88 + 715618564776810 * q^89 + 70681738030560 * q^90 + 262514200015872 * q^92 + 239678242932096 * q^93 - 736707949766784 * q^94 - 81461331649800 * q^95 + 518719311839232 * q^96 - 1225572272163652 * q^97 - 129277319340312 * q^99

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