LMFDB - Embedded newform 16.6.e.a.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,6,Mod(5,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("16.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	16.e (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:	$2.56614111701$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{16} - 30 x^{15} - 42 x^{14} - 344 x^{13} + 2904 x^{12} + 5344 x^{11} + 16576 x^{10} + \cdots + 68719476736 $ x^18 - 5x^16 - 30x^15 - 42x^14 - 344x^13 + 2904x^12 + 5344x^11 + 16576x^10 - 297472x^9 + 265216x^8 + 1368064x^7 + 11894784x^6 - 22544384x^5 - 44040192x^4 - 503316480x^3 - 1342177280*x^2 + 68719476736
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{36} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.2
Root			$-3.75808 - 1.36997i$ of defining polynomial
Character	$\chi$	$=$	16.13
Dual form			16.6.e.a.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.12805 + 2.38811i) q^{2} +(-4.57839 - 4.57839i) q^{3} +(20.5939 - 24.4927i) q^{4} +(48.5981 - 48.5981i) q^{5} +(34.4119 + 12.5445i) q^{6} -106.338i q^{7} +(-47.1150 + 174.780i) q^{8} -201.077i q^{9} +O(q^{10})$	\(q+(-5.12805 + 2.38811i) q^{2} +(-4.57839 - 4.57839i) q^{3} +(20.5939 - 24.4927i) q^{4} +(48.5981 - 48.5981i) q^{5} +(34.4119 + 12.5445i) q^{6} -106.338i q^{7} +(-47.1150 + 174.780i) q^{8} -201.077i q^{9} +(-133.156 + 365.272i) q^{10} +(-184.984 + 184.984i) q^{11} +(-206.424 + 17.8505i) q^{12} +(3.64729 + 3.64729i) q^{13} +(253.947 + 545.308i) q^{14} -445.003 q^{15} +(-175.786 - 1008.80i) q^{16} +2064.90 q^{17} +(480.193 + 1031.13i) q^{18} +(-1259.62 - 1259.62i) q^{19} +(-189.478 - 2191.12i) q^{20} +(-486.857 + 486.857i) q^{21} +(506.846 - 1390.37i) q^{22} +3861.52i q^{23} +(1015.92 - 584.502i) q^{24} -1598.56i q^{25} +(-27.4136 - 9.99337i) q^{26} +(-2033.16 + 2033.16i) q^{27} +(-2604.51 - 2189.91i) q^{28} +(1959.96 + 1959.96i) q^{29} +(2282.00 - 1062.72i) q^{30} +2760.10 q^{31} +(3310.57 + 4753.38i) q^{32} +1693.86 q^{33} +(-10588.9 + 4931.21i) q^{34} +(-5167.83 - 5167.83i) q^{35} +(-4924.91 - 4140.94i) q^{36} +(-6432.63 + 6432.63i) q^{37} +(9467.48 + 3451.28i) q^{38} -33.3975i q^{39} +(6204.30 + 10783.7i) q^{40} -11296.7i q^{41} +(1333.96 - 3659.30i) q^{42} +(12927.8 - 12927.8i) q^{43} +(721.228 + 8340.31i) q^{44} +(-9771.95 - 9771.95i) q^{45} +(-9221.73 - 19802.1i) q^{46} +25827.2 q^{47} +(-3813.86 + 5423.49i) q^{48} +5499.20 q^{49} +(3817.54 + 8197.49i) q^{50} +(-9453.92 - 9453.92i) q^{51} +(164.444 - 14.2203i) q^{52} +(-21801.8 + 21801.8i) q^{53} +(5570.73 - 15281.5i) q^{54} +17979.8i q^{55} +(18585.8 + 5010.13i) q^{56} +11534.0i q^{57} +(-14731.4 - 5370.17i) q^{58} +(-14102.8 + 14102.8i) q^{59} +(-9164.32 + 10899.3i) q^{60} +(6211.40 + 6211.40i) q^{61} +(-14154.0 + 6591.43i) q^{62} -21382.1 q^{63} +(-28328.3 - 16469.6i) q^{64} +354.503 q^{65} +(-8686.21 + 4045.13i) q^{66} +(28659.0 + 28659.0i) q^{67} +(42524.2 - 50575.0i) q^{68} +(17679.5 - 17679.5i) q^{69} +(38842.3 + 14159.6i) q^{70} -29423.1i q^{71} +(35144.3 + 9473.74i) q^{72} -2857.88i q^{73} +(17625.0 - 48348.7i) q^{74} +(-7318.83 + 7318.83i) q^{75} +(-56791.8 + 4911.07i) q^{76} +(19670.9 + 19670.9i) q^{77} +(79.7568 + 171.264i) q^{78} -23387.3 q^{79} +(-57568.6 - 40482.9i) q^{80} -30244.5 q^{81} +(26977.7 + 57930.0i) q^{82} +(-24575.3 - 24575.3i) q^{83} +(1898.19 + 21950.7i) q^{84} +(100350. - 100350. i) q^{85} +(-35421.5 + 97167.7i) q^{86} -17946.9i q^{87} +(-23616.1 - 41047.2i) q^{88} +19340.2i q^{89} +(73447.6 + 26774.6i) q^{90} +(387.846 - 387.846i) q^{91} +(94579.1 + 79523.5i) q^{92} +(-12636.8 - 12636.8i) q^{93} +(-132443. + 61678.1i) q^{94} -122430. q^{95} +(6605.75 - 36919.9i) q^{96} +44218.7 q^{97} +(-28200.2 + 13132.7i) q^{98} +(37196.0 + 37196.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8}+O(q^{10}) $ 18 * q - 2 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^5 + 112 * q^6 + 244 * q^8	\( 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8} - 436 q^{10} - 606 q^{11} + 4 q^{12} - 2 q^{13} - 100 q^{14} + 1796 q^{15} - 872 q^{16} - 4 q^{17} - 3138 q^{18} - 2362 q^{19} + 2972 q^{20} + 484 q^{21} + 4420 q^{22} + 8368 q^{24} + 7368 q^{26} + 4216 q^{27} - 7336 q^{28} + 4070 q^{29} - 30444 q^{30} - 11536 q^{31} - 23992 q^{32} - 4 q^{33} - 1740 q^{34} + 8636 q^{35} + 6892 q^{36} - 10650 q^{37} + 53248 q^{38} + 75272 q^{40} + 33400 q^{42} - 15382 q^{43} - 40124 q^{44} + 5762 q^{45} - 92532 q^{46} + 44176 q^{47} - 147992 q^{48} - 14410 q^{49} - 85050 q^{50} - 2748 q^{51} + 91572 q^{52} + 24726 q^{53} + 208672 q^{54} + 191128 q^{56} + 106776 q^{58} - 29734 q^{59} - 154368 q^{60} - 48082 q^{61} - 273872 q^{62} - 12156 q^{63} - 283776 q^{64} + 27684 q^{65} - 153356 q^{66} - 75210 q^{67} + 133712 q^{68} + 22804 q^{69} + 412160 q^{70} + 470244 q^{72} + 147148 q^{74} + 154726 q^{75} - 87468 q^{76} + 41060 q^{77} - 631780 q^{78} - 52864 q^{79} - 554456 q^{80} - 13126 q^{81} - 93216 q^{82} + 227838 q^{83} + 190888 q^{84} - 138652 q^{85} + 470468 q^{86} + 590328 q^{88} + 280152 q^{90} - 231164 q^{91} - 221896 q^{92} + 180688 q^{93} - 460912 q^{94} - 250380 q^{95} - 597328 q^{96} - 4 q^{97} - 444646 q^{98} - 296770 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^5 + 112 * q^6 + 244 * q^8 - 436 * q^10 - 606 * q^11 + 4 * q^12 - 2 * q^13 - 100 * q^14 + 1796 * q^15 - 872 * q^16 - 4 * q^17 - 3138 * q^18 - 2362 * q^19 + 2972 * q^20 + 484 * q^21 + 4420 * q^22 + 8368 * q^24 + 7368 * q^26 + 4216 * q^27 - 7336 * q^28 + 4070 * q^29 - 30444 * q^30 - 11536 * q^31 - 23992 * q^32 - 4 * q^33 - 1740 * q^34 + 8636 * q^35 + 6892 * q^36 - 10650 * q^37 + 53248 * q^38 + 75272 * q^40 + 33400 * q^42 - 15382 * q^43 - 40124 * q^44 + 5762 * q^45 - 92532 * q^46 + 44176 * q^47 - 147992 * q^48 - 14410 * q^49 - 85050 * q^50 - 2748 * q^51 + 91572 * q^52 + 24726 * q^53 + 208672 * q^54 + 191128 * q^56 + 106776 * q^58 - 29734 * q^59 - 154368 * q^60 - 48082 * q^61 - 273872 * q^62 - 12156 * q^63 - 283776 * q^64 + 27684 * q^65 - 153356 * q^66 - 75210 * q^67 + 133712 * q^68 + 22804 * q^69 + 412160 * q^70 + 470244 * q^72 + 147148 * q^74 + 154726 * q^75 - 87468 * q^76 + 41060 * q^77 - 631780 * q^78 - 52864 * q^79 - 554456 * q^80 - 13126 * q^81 - 93216 * q^82 + 227838 * q^83 + 190888 * q^84 - 138652 * q^85 + 470468 * q^86 + 590328 * q^88 + 280152 * q^90 - 231164 * q^91 - 221896 * q^92 + 180688 * q^93 - 460912 * q^94 - 250380 * q^95 - 597328 * q^96 - 4 * q^97 - 444646 * q^98 - 296770 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−5.12805	+	2.38811i	−0.906520	+	0.422162i
$2$	−5.12805	+	2.38811i	−0.906520	+	0.422162i
$3$	−4.57839	−	4.57839i	−0.293704	−	0.293704i	0.544838	−	0.838542i	$-0.316591\pi$
$3$	−4.57839	−	4.57839i	−0.293704	−	0.293704i	−0.838542	+	0.544838i	$0.816591\pi$
$4$	20.5939	−	24.4927i	0.643558	−	0.765397i
$5$	48.5981	−	48.5981i	0.869350	−	0.869350i	−0.123050	−	0.992400i	$-0.539268\pi$
$5$	48.5981	−	48.5981i	0.869350	−	0.869350i	0.992400	+	0.123050i	$0.0392677\pi$
$6$	34.4119	+	12.5445i	0.390239	+	0.142258i
$7$		−	106.338i		−	0.820246i	−0.912030	−	0.410123i	$-0.865486\pi$
$7$		−	106.338i		−	0.820246i	0.912030	−	0.410123i	$-0.134514\pi$
$8$	−47.1150	+	174.780i	−0.260276	+	0.965534i
$9$		−	201.077i		−	0.827476i
$10$	−133.156	+	365.272i	−0.421077	+	1.15509i
$11$	−184.984	+	184.984i	−0.460949	+	0.460949i	−0.898967	−	0.438017i	$-0.855681\pi$
$11$	−184.984	+	184.984i	−0.460949	+	0.460949i	0.438017	+	0.898967i	$0.355681\pi$
$12$	−206.424	+	17.8505i	−0.413816	+	0.0357847i
$13$	3.64729	+	3.64729i	0.00598566	+	0.00598566i	0.710093	−	0.704108i	$-0.248653\pi$
$13$	3.64729	+	3.64729i	0.00598566	+	0.00598566i	−0.704108	+	0.710093i	$0.748653\pi$
$14$	253.947	+	545.308i	0.346277	+	0.743569i
$15$	−445.003			−0.510663
$16$	−175.786	−	1008.80i	−0.171666	−	0.985155i
$17$	2064.90			1.73291			0.866456	−	0.499253i	$-0.166392\pi$
$17$	2064.90			1.73291			0.866456	+	0.499253i	$0.166392\pi$
$18$	480.193	+	1031.13i	0.349329	+	0.750124i
$19$	−1259.62	−	1259.62i	−0.800487	−	0.800487i	0.182685	−	0.983172i	$-0.441521\pi$
$19$	−1259.62	−	1259.62i	−0.800487	−	0.800487i	−0.983172	+	0.182685i	$0.941521\pi$
$20$	−189.478	−	2191.12i	−0.105921	−	1.22488i
$21$	−486.857	+	486.857i	−0.240909	+	0.240909i
$22$	506.846	−	1390.37i	0.223264	−	0.612455i
$23$			3861.52i			1.52208i	0.648703	+	0.761042i	$0.275312\pi$
$23$			3861.52i			1.52208i	−0.648703	+	0.761042i	$0.724688\pi$
$24$	1015.92	−	584.502i	0.360025	−	0.207137i
$25$		−	1598.56i		−	0.511539i
$26$	−27.4136	−	9.99337i	−0.00795304	−	0.00289920i
$27$	−2033.16	+	2033.16i	−0.536737	+	0.536737i
$28$	−2604.51	−	2189.91i	−0.627814	−	0.527876i
$29$	1959.96	+	1959.96i	0.432764	+	0.432764i	0.889568	−	0.456803i	$-0.151006\pi$
$29$	1959.96	+	1959.96i	0.432764	+	0.432764i	−0.456803	+	0.889568i	$0.651006\pi$
$30$	2282.00	−	1062.72i	0.462926	−	0.215583i
$31$	2760.10			0.515847			0.257924	−	0.966165i	$-0.416962\pi$
$31$	2760.10			0.515847			0.257924	+	0.966165i	$0.416962\pi$
$32$	3310.57	+	4753.38i	0.571514	+	0.820592i
$33$	1693.86			0.270765
$34$	−10588.9	+	4931.21i	−1.57092	+	0.731571i
$35$	−5167.83	−	5167.83i	−0.713080	−	0.713080i
$36$	−4924.91	−	4140.94i	−0.633348	−	0.532529i
$37$	−6432.63	+	6432.63i	−0.772475	+	0.772475i	−0.978539	−	0.206063i	$-0.933935\pi$
$37$	−6432.63	+	6432.63i	−0.772475	+	0.772475i	0.206063	+	0.978539i	$0.433935\pi$
$38$	9467.48	+	3451.28i	1.06359	+	0.387722i
$39$		−	33.3975i		−	0.00351602i
$40$	6204.30	+	10783.7i	0.613116	+	1.06566i
$41$		−	11296.7i		−	1.04952i	−0.851250	−	0.524761i	$-0.824155\pi$
$41$		−	11296.7i		−	1.04952i	0.851250	−	0.524761i	$-0.175845\pi$
$42$	1333.96	−	3659.30i	0.116686	−	0.320092i
$43$	12927.8	−	12927.8i	1.06624	−	1.06624i	0.0685944	−	0.997645i	$-0.478149\pi$
$43$	12927.8	−	12927.8i	1.06624	−	1.06624i	0.997645	−	0.0685944i	$-0.0218514\pi$
$44$	721.228	+	8340.31i	0.0561618	+	0.649457i
$45$	−9771.95	−	9771.95i	−0.719366	−	0.719366i
$46$	−9221.73	−	19802.1i	−0.642566	−	1.37980i
$47$	25827.2			1.70542			0.852711	−	0.522382i	$-0.174957\pi$
$47$	25827.2			1.70542			0.852711	+	0.522382i	$0.174957\pi$
$48$	−3813.86	+	5423.49i	−0.238925	+	0.339763i
$49$	5499.20			0.327197
$50$	3817.54	+	8197.49i	0.215952	+	0.463720i
$51$	−9453.92	−	9453.92i	−0.508963	−	0.508963i
$52$	164.444	−	14.2203i	0.00843353	−	0.000729290i
$53$	−21801.8	+	21801.8i	−1.06611	+	1.06611i	−0.0684597	+	0.997654i	$0.521808\pi$
$53$	−21801.8	+	21801.8i	−1.06611	+	1.06611i	−0.997654	+	0.0684597i	$0.978192\pi$
$54$	5570.73	−	15281.5i	0.259973	−	0.713153i
$55$			17979.8i			0.801452i
$56$	18585.8	+	5010.13i	0.791975	+	0.213491i
$57$			11534.0i			0.470212i
$58$	−14731.4	−	5370.17i	−0.575007	−	0.209613i
$59$	−14102.8	+	14102.8i	−0.527444	+	0.527444i	−0.919809	−	0.392366i	$-0.871657\pi$
$59$	−14102.8	+	14102.8i	−0.527444	+	0.527444i	0.392366	+	0.919809i	$0.371657\pi$
$60$	−9164.32	+	10899.3i	−0.328641	+	0.390860i
$61$	6211.40	+	6211.40i	0.213730	+	0.213730i	0.805850	−	0.592120i	$-0.201709\pi$
$61$	6211.40	+	6211.40i	0.213730	+	0.213730i	−0.592120	+	0.805850i	$0.701709\pi$
$62$	−14154.0	+	6591.43i	−0.467626	+	0.217771i
$63$	−21382.1			−0.678734
$64$	−28328.3	−	16469.6i	−0.864512	−	0.502611i
$65$	354.503			0.0104073
$66$	−8686.21	+	4045.13i	−0.245454	+	0.114307i
$67$	28659.0	+	28659.0i	0.779963	+	0.779963i	0.979824	−	0.199861i	$-0.0640491\pi$
$67$	28659.0	+	28659.0i	0.779963	+	0.779963i	−0.199861	+	0.979824i	$0.564049\pi$
$68$	42524.2	−	50575.0i	1.11523	−	1.32637i
$69$	17679.5	−	17679.5i	0.447042	−	0.447042i
$70$	38842.3	+	14159.6i	0.947458	+	0.345386i
$71$		−	29423.1i		−	0.692696i	−0.938106	−	0.346348i	$-0.887422\pi$
$71$		−	29423.1i		−	0.692696i	0.938106	−	0.346348i	$-0.112578\pi$
$72$	35144.3	+	9473.74i	0.798956	+	0.215372i
$73$		−	2857.88i		−	0.0627678i	−0.999507	−	0.0313839i	$-0.990009\pi$
$73$		−	2857.88i		−	0.0627678i	0.999507	−	0.0313839i	$-0.00999144\pi$
$74$	17625.0	−	48348.7i	0.374154	−	1.02637i
$75$	−7318.83	+	7318.83i	−0.150241	+	0.150241i
$76$	−56791.8	+	4911.07i	−1.12785	+	0.0975309i
$77$	19670.9	+	19670.9i	0.378092	+	0.378092i
$78$	79.7568	+	171.264i	0.00148433	+	0.00318735i
$79$	−23387.3			−0.421612			−0.210806	−	0.977528i	$-0.567609\pi$
$79$	−23387.3			−0.421612			−0.210806	+	0.977528i	$0.567609\pi$
$80$	−57568.6	−	40482.9i	−1.00568	−	0.707206i
$81$	−30244.5			−0.512193
$82$	26977.7	+	57930.0i	0.443069	+	0.951413i
$83$	−24575.3	−	24575.3i	−0.391564	−	0.391564i	0.483681	−	0.875245i	$-0.339300\pi$
$83$	−24575.3	−	24575.3i	−0.391564	−	0.391564i	−0.875245	+	0.483681i	$0.839300\pi$
$84$	1898.19	+	21950.7i	0.0293523	+	0.339430i
$85$	100350.	−	100350.i	1.50651	−	1.50651i
$86$	−35421.5	+	97167.7i	−0.516441	+	1.41669i
$87$		−	17946.9i		−	0.254209i
$88$	−23616.1	−	41047.2i	−0.325088	−	0.565036i
$89$			19340.2i			0.258813i	0.991592	+	0.129407i	$0.0413073\pi$
$89$			19340.2i			0.258813i	−0.991592	+	0.129407i	$0.958693\pi$
$90$	73447.6	+	26774.6i	0.955809	+	0.348431i
$91$	387.846	−	387.846i	0.00490971	−	0.00490971i
$92$	94579.1	+	79523.5i	1.16500	+	0.979549i
$93$	−12636.8	−	12636.8i	−0.151506	−	0.151506i
$94$	−132443.	+	61678.1i	−1.54600	+	0.719965i
$95$	−122430.			−1.39181
$96$	6605.75	−	36919.9i	0.0731550	−	0.408867i
$97$	44218.7			0.477174			0.238587	−	0.971121i	$-0.423316\pi$
$97$	44218.7			0.477174			0.238587	+	0.971121i	$0.423316\pi$
$98$	−28200.2	+	13132.7i	−0.296611	+	0.138130i
$99$	37196.0	+	37196.0i	0.381424	+	0.381424i
$100$	−39153.0	−	32920.5i	−0.391530	−	0.329205i
$101$	−10119.1	+	10119.1i	−0.0987050	+	0.0987050i	−0.754735	−	0.656030i	$-0.772234\pi$
$101$	−10119.1	+	10119.1i	−0.0987050	+	0.0987050i	0.656030	+	0.754735i	$0.272234\pi$
$102$	71057.2	+	25903.2i	0.676251	+	0.246520i
$103$			5350.67i			0.0496953i	0.999691	+	0.0248476i	$0.00791006\pi$
$103$			5350.67i			0.0496953i	−0.999691	+	0.0248476i	$0.992090\pi$
$104$	−809.317	+	465.633i	−0.00733729	+	0.00422143i
$105$			47320.7i			0.418869i
$106$	59735.8	−	163866.i	0.516381	−	1.41653i
$107$	12337.4	−	12337.4i	0.104175	−	0.104175i	−0.653098	−	0.757273i	$-0.726531\pi$
$107$	12337.4	−	12337.4i	0.104175	−	0.104175i	0.757273	+	0.653098i	$0.226531\pi$
$108$	7927.00	+	91668.1i	0.0653957	+	0.756238i
$109$	−25846.6	−	25846.6i	−0.208371	−	0.208371i	0.595204	−	0.803575i	$-0.297071\pi$
$109$	−25846.6	−	25846.6i	−0.208371	−	0.208371i	−0.803575	+	0.595204i	$0.797071\pi$
$110$	−42937.7	−	92201.3i	−0.338343	−	0.726533i
$111$	58902.2			0.453758
$112$	−107274.	+	18692.8i	−0.808069	+	0.140809i
$113$	−159991.			−1.17869			−0.589344	−	0.807882i	$-0.700614\pi$
$113$	−159991.			−1.17869			−0.589344	+	0.807882i	$0.700614\pi$
$114$	−27544.5	−	59147.1i	−0.198506	−	0.426257i
$115$	187663.	+	187663.i	1.32322	+	1.32322i
$116$	88367.8	−	7641.61i	0.609746	−	0.0527278i
$117$	733.385	−	733.385i	0.00495299	−	0.00495299i
$118$	38640.9	−	105999.i	0.255472	−	0.700805i
$119$		−	219578.i		−	1.42141i
$120$	20966.3	−	77777.7i	0.132913	−	0.493063i
$121$			92612.6i			0.575052i
$122$	−46685.9	−	17018.9i	−0.283979	−	0.103522i
$123$	−51720.6	+	51720.6i	−0.308249	+	0.308249i
$124$	56841.2	−	67602.4i	0.331978	−	0.394828i
$125$	74182.2	+	74182.2i	0.424644	+	0.424644i
$126$	109649.	−	51062.9i	0.615286	−	0.286536i
$127$	139544.			0.767717			0.383858	−	0.923392i	$-0.374595\pi$
$127$	139544.			0.767717			0.383858	+	0.923392i	$0.374595\pi$
$128$	184600.	+	16805.6i	0.995882	+	0.0906628i
$129$	−118377.			−0.626317
$130$	−1817.91	+	846.593i	−0.00943440	+	0.00439356i
$131$	−144551.	−	144551.i	−0.735942	−	0.735942i	0.235848	−	0.971790i	$-0.424213\pi$
$131$	−144551.	−	144551.i	−0.735942	−	0.735942i	−0.971790	+	0.235848i	$0.924213\pi$
$132$	34883.1	−	41487.2i	0.174253	−	0.207243i
$133$	−133945.	+	133945.i	−0.656596	+	0.656596i
$134$	−215406.	−	78524.0i	−1.03632	−	0.377781i
$135$			197615.i			0.933224i
$136$	−97287.9	+	360904.i	−0.451036	+	1.67319i
$137$			34191.5i			0.155638i	0.996967	+	0.0778192i	$0.0247957\pi$
$137$			34191.5i			0.155638i	−0.996967	+	0.0778192i	$0.975204\pi$
$138$	−48440.9	+	132882.i	−0.216528	+	0.593977i
$139$	133333.	−	133333.i	0.585331	−	0.585331i	−0.351032	−	0.936363i	$-0.614169\pi$
$139$	133333.	−	133333.i	0.585331	−	0.585331i	0.936363	+	0.351032i	$0.114169\pi$
$140$	−233000.	+	20148.7i	−1.00470	+	0.0868814i
$141$	−118247.	−	118247.i	−0.500889	−	0.500889i
$142$	70265.7	+	150883.i	0.292430	+	0.627943i
$143$	−1349.38			−0.00551817
$144$	−202846.	+	35346.5i	−0.815192	+	0.142050i
$145$	190501.			0.752448
$146$	6824.93	+	14655.4i	0.0264982	+	0.0569002i
$147$	−25177.5	−	25177.5i	−0.0960991	−	0.0960991i
$148$	25080.0	+	290025.i	0.0941180	+	1.08838i
$149$	−83201.8	+	83201.8i	−0.307020	+	0.307020i	−0.843753	−	0.536732i	$-0.819658\pi$
$149$	−83201.8	+	83201.8i	−0.307020	+	0.307020i	0.536732	+	0.843753i	$0.319658\pi$
$150$	20053.2	−	55009.5i	0.0727704	−	0.199622i
$151$			136797.i			0.488242i	0.969745	+	0.244121i	$0.0784995\pi$
$151$			136797.i			0.488242i	−0.969745	+	0.244121i	$0.921501\pi$
$152$	279503.	−	160809.i	0.981245	−	0.564550i
$153$		−	415203.i		−	1.43394i
$154$	−147850.	−	53897.1i	−0.502364	−	0.183132i
$155$	134136.	−	134136.i	0.448452	−	0.448452i
$156$	−817.994	−	687.782i	−0.00269116	−	0.00226277i
$157$	−129460.	−	129460.i	−0.419165	−	0.419165i	0.465751	−	0.884916i	$-0.345784\pi$
$157$	−129460.	−	129460.i	−0.419165	−	0.419165i	−0.884916	+	0.465751i	$0.845784\pi$
$158$	119932.	−	55851.6i	0.382200	−	0.177989i
$159$	199635.			0.626243
$160$	391893.	+	70117.9i	1.21023	+	0.216536i
$161$	410627.			1.24848
$162$	155095.	−	72227.1i	0.464313	−	0.216228i
$163$	−463046.	−	463046.i	−1.36507	−	1.36507i	−0.867321	−	0.497749i	$-0.834160\pi$
$163$	−463046.	−	463046.i	−1.36507	−	1.36507i	−0.497749	−	0.867321i	$-0.665840\pi$
$164$	−276687.	−	232642.i	−0.803301	−	0.675428i
$165$	82318.5	−	82318.5i	0.235390	−	0.235390i
$166$	184712.	+	67334.8i	0.520264	+	0.189657i
$167$			211138.i			0.585836i	0.956138	+	0.292918i	$0.0946263\pi$
$167$			211138.i			0.585836i	−0.956138	+	0.292918i	$0.905374\pi$
$168$	−62154.8	−	108031.i	−0.169903	−	0.295309i
$169$		−	371266.i		−	0.999928i
$170$	−274954.	+	754249.i	−0.729689	+	2.00167i
$171$	−253279.	+	253279.i	−0.662384	+	0.662384i
$172$	−50403.9	−	582872.i	−0.129910	−	1.50228i
$173$	354951.	+	354951.i	0.901682	+	0.901682i	0.995582	−	0.0939001i	$-0.0299334\pi$
$173$	354951.	+	354951.i	0.901682	+	0.901682i	−0.0939001	+	0.995582i	$0.529933\pi$
$174$	42859.2	+	92032.7i	0.107318	+	0.230446i
$175$	−169988.			−0.419587
$176$	219130.	+	154094.i	0.533236	+	0.374977i
$177$	129136.			0.309825
$178$	−46186.6	−	99177.8i	−0.109261	−	0.234620i
$179$	56209.7	+	56209.7i	0.131123	+	0.131123i	0.769622	−	0.638499i	$-0.220445\pi$
$179$	56209.7	+	56209.7i	0.131123	+	0.131123i	−0.638499	+	0.769622i	$0.720445\pi$
$180$	−440584.	+	38099.5i	−1.01355	+	0.0876472i
$181$	−157838.	+	157838.i	−0.358109	+	0.358109i	−0.863116	−	0.505006i	$-0.831490\pi$
$181$	−157838.	+	157838.i	−0.358109	+	0.358109i	0.505006	+	0.863116i	$0.331490\pi$
$182$	−1062.68	+	2915.12i	−0.00237806	+	0.00652345i
$183$		−	56876.4i		−	0.125547i
$184$	−674917.	−	181936.i	−1.46962	−	0.396162i
$185$			625228.i			1.34310i
$186$	94980.5	+	34624.2i	0.201304	+	0.0733833i
$187$	−381974.	+	381974.i	−0.798785	+	0.798785i
$188$	531881.	−	632577.i	1.09754	−	1.30533i
$189$	216202.	+	216202.i	0.440256	+	0.440256i
$190$	627828.	−	292376.i	1.26170	−	0.587568i
$191$	−234025.			−0.464171			−0.232086	−	0.972695i	$-0.574555\pi$
$191$	−234025.			−0.464171			−0.232086	+	0.972695i	$0.574555\pi$
$192$	54294.1	+	205102.i	0.106292	+	0.401530i
$193$	−162458.			−0.313940			−0.156970	−	0.987603i	$-0.550173\pi$
$193$	−162458.			−0.313940			−0.156970	+	0.987603i	$0.550173\pi$
$194$	−226756.	+	105599.i	−0.432568	+	0.201445i
$195$	−1623.05	−	1623.05i	−0.00305666	−	0.00305666i
$196$	113250.	−	134690.i	0.210570	−	0.250436i
$197$	−28244.9	+	28244.9i	−0.0518530	+	0.0518530i	−0.732558	−	0.680705i	$-0.761674\pi$
$197$	−28244.9	+	28244.9i	−0.0518530	+	0.0518530i	0.680705	+	0.732558i	$0.261674\pi$
$198$	−279571.	−	101915.i	−0.506792	−	0.184746i
$199$			792440.i			1.41851i	0.704950	+	0.709257i	$0.250970\pi$
$199$			792440.i			1.41851i	−0.704950	+	0.709257i	$0.749030\pi$
$200$	279397.	+	75316.2i	0.493908	+	0.133141i
$201$		−	262424.i		−	0.458156i
$202$	27725.8	−	76056.9i	0.0478085	−	0.131148i
$203$	208418.	−	208418.i	0.354973	−	0.354973i
$204$	−426245.	+	36859.5i	−0.717106	+	0.0620118i
$205$	−548998.	−	548998.i	−0.912402	−	0.912402i
$206$	−12778.0	−	27438.5i	−0.0209795	−	0.0450498i
$207$	776461.			1.25949
$208$	3038.24	−	4320.53i	0.00486927	−	0.00692434i
$209$	466018.			0.737968
$210$	−113007.	−	242663.i	−0.176831	−	0.379713i
$211$	264651.	+	264651.i	0.409229	+	0.409229i	0.881470	−	0.472240i	$-0.156555\pi$
$211$	264651.	+	264651.i	0.409229	+	0.409229i	−0.472240	+	0.881470i	$0.656555\pi$
$212$	85002.4	+	982970.i	0.129895	+	1.50211i
$213$	−134711.	+	134711.i	−0.203448	+	0.203448i
$214$	−33803.7	+	92729.7i	−0.0504579	+	0.138415i
$215$		−	1.25654e6i		−	1.85387i
$216$	−259564.	−	451148.i	−0.378538	−	0.657938i
$217$		−	293504.i		−	0.423121i
$218$	194268.	+	70818.3i	0.276859	+	0.100926i
$219$	−13084.5	+	13084.5i	−0.0184351	+	0.0184351i
$220$	440374.	+	370273.i	0.613430	+	0.515781i
$221$	7531.29	+	7531.29i	0.0103726	+	0.0103726i
$222$	−302054.	+	140665.i	−0.411341	+	0.191559i
$223$	−1.22374e6			−1.64788			−0.823942	−	0.566674i	$-0.808230\pi$
$223$	−1.22374e6			−1.64788			−0.823942	+	0.566674i	$0.808230\pi$
$224$	505465.	−	352039.i	0.673087	−	0.468782i
$225$	−321433.			−0.423286
$226$	820442.	−	382076.i	1.06851	−	0.497598i
$227$	−134620.	−	134620.i	−0.173398	−	0.173398i	0.615072	−	0.788471i	$-0.289127\pi$
$227$	−134620.	−	134620.i	−0.173398	−	0.173398i	−0.788471	+	0.615072i	$0.789127\pi$
$228$	282500.	+	237530.i	0.359899	+	0.302609i
$229$	316394.	−	316394.i	0.398694	−	0.398694i	−0.479078	−	0.877772i	$-0.659029\pi$
$229$	316394.	−	316394.i	0.398694	−	0.398694i	0.877772	+	0.479078i	$0.159029\pi$
$230$	−1.41050e6	−	514185.i	−1.75814	−	0.640914i
$231$		−	180122.i		−	0.222094i
$232$	−434906.	+	250219.i	−0.530487	+	0.305211i
$233$			561597.i			0.677697i	0.940841	+	0.338848i	$0.110037\pi$
$233$			561597.i			0.677697i	−0.940841	+	0.338848i	$0.889963\pi$
$234$	−2009.43	+	5512.24i	−0.00239902	+	0.00658095i
$235$	1.25515e6	−	1.25515e6i	1.48261	−	1.48261i
$236$	54985.0	+	635848.i	0.0642635	+	0.743145i
$237$	107076.	+	107076.i	0.123829	+	0.123829i
$238$	524376.	+	1.12601e6i	0.600067	+	1.28854i
$239$	1.42167e6			1.60992			0.804962	−	0.593327i	$-0.202186\pi$
$239$	1.42167e6			1.60992			0.804962	+	0.593327i	$0.202186\pi$
$240$	78225.4	+	448918.i	0.0876637	+	0.503082i
$241$	−1.07355e6			−1.19063			−0.595317	−	0.803491i	$-0.702973\pi$
$241$	−1.07355e6			−1.19063			−0.595317	+	0.803491i	$0.702973\pi$
$242$	−221169.	−	474922.i	−0.242765	−	0.521296i
$243$	632528.	+	632528.i	0.687170	+	0.687170i
$244$	280051.	−	24217.4i	0.301136	−	0.0260407i
$245$	267251.	−	267251.i	0.284449	−	0.284449i
$246$	141712.	−	388741.i	0.149303	−	0.409565i
$247$		−	9188.38i		−	0.00958289i
$248$	−130042.	+	482412.i	−0.134263	+	0.498068i
$249$			225030.i			0.230008i
$250$	−557566.	−	203255.i	−0.564217	−	0.205680i
$251$	−812499.	+	812499.i	−0.814027	+	0.814027i	−0.985235	−	0.171208i	$-0.945233\pi$
$251$	−812499.	+	812499.i	−0.814027	+	0.814027i	0.171208	+	0.985235i	$0.445233\pi$
$252$	−440340.	+	523706.i	−0.436804	+	0.519501i
$253$	−714320.	−	714320.i	−0.701603	−	0.701603i
$254$	−715588.	+	333246.i	−0.695951	+	0.324101i
$255$	−918886.			−0.884934
$256$	−986774.	+	354666.i	−0.941061	+	0.338236i
$257$	−1.97617e6			−1.86635			−0.933174	−	0.359426i	$-0.882973\pi$
$257$	−1.97617e6			−1.86635			−0.933174	+	0.359426i	$0.882973\pi$
$258$	607045.	−	282698.i	0.567769	−	0.264407i
$259$	684034.	+	684034.i	0.633619	+	0.633619i
$260$	7300.59	−	8682.75i	0.00669768	−	0.00796570i
$261$	394102.	−	394102.i	0.358102	−	0.358102i
$262$	1.08647e6	+	396062.i	0.977833	+	0.356459i
$263$		−	723548.i		−	0.645027i	−0.946565	−	0.322514i	$-0.895472\pi$
$263$		−	723548.i		−	0.645027i	0.946565	−	0.322514i	$-0.104528\pi$
$264$	−79806.3	+	296054.i	−0.0704738	+	0.261433i
$265$			2.11906e6i			1.85365i
$266$	367002.	−	1.00675e6i	0.318027	−	0.872408i
$267$	88547.2	−	88547.2i	0.0760145	−	0.0760145i
$268$	1.29214e6	−	111738.i	1.09893	−	0.0950303i
$269$	1.31496e6	+	1.31496e6i	1.10798	+	1.10798i	0.993416	+	0.114563i	$0.0365467\pi$
$269$	1.31496e6	+	1.31496e6i	1.10798	+	1.10798i	0.114563	+	0.993416i	$0.463453\pi$
$270$	−471927.	−	1.01338e6i	−0.393972	−	0.845987i
$271$	−324667.			−0.268543			−0.134272	−	0.990945i	$-0.542869\pi$
$271$	−324667.			−0.268543			−0.134272	+	0.990945i	$0.542869\pi$
$272$	−362981.	−	2.08307e6i	−0.297483	−	1.70719i
$273$	−3551.42			−0.00288400
$274$	−81653.1	−	175336.i	−0.0657046	−	0.141089i
$275$	295708.	+	295708.i	0.235793	+	0.235793i
$276$	−68930.1	−	797110.i	−0.0544673	−	0.629862i
$277$	576423.	−	576423.i	0.451379	−	0.451379i	−0.444433	−	0.895812i	$-0.646595\pi$
$277$	576423.	−	576423.i	0.451379	−	0.451379i	0.895812	+	0.444433i	$0.146595\pi$
$278$	−365326.	+	1.00216e6i	−0.283510	+	0.777719i
$279$		−	554992.i		−	0.426851i
$280$	1.14672e6	−	659753.i	0.874101	−	0.502906i
$281$		−	1.64048e6i		−	1.23938i	−0.784847	−	0.619690i	$-0.787258\pi$
$281$		−	1.64048e6i		−	1.23938i	0.784847	−	0.619690i	$-0.212742\pi$
$282$	888763.	+	323989.i	0.665523	+	0.242610i
$283$	−733673.	+	733673.i	−0.544548	+	0.544548i	−0.924859	−	0.380311i	$-0.875817\pi$
$283$	−733673.	+	733673.i	−0.544548	+	0.544548i	0.380311	+	0.924859i	$0.375817\pi$
$284$	−720652.	−	605935.i	−0.530188	−	0.445790i
$285$	560532.	+	560532.i	0.408779	+	0.408779i
$286$	6919.71	−	3222.48i	0.00500233	−	0.00232956i
$287$	−1.20127e6			−0.860866
$288$	955793.	−	665677.i	0.679020	−	0.472915i
$289$	2.84395e6			2.00299
$290$	−976897.	+	454936.i	−0.682109	+	0.317655i
$291$	−202451.	−	202451.i	−0.140148	−	0.140148i
$292$	−69997.2	−	58854.7i	−0.0480423	−	0.0403947i
$293$	−316230.	+	316230.i	−0.215196	+	0.215196i	−0.806470	−	0.591275i	$-0.798625\pi$
$293$	−316230.	+	316230.i	−0.215196	+	0.215196i	0.591275	+	0.806470i	$0.298625\pi$
$294$	189238.	+	68984.9i	0.127685	+	0.0465464i
$295$			1.37074e6i			0.917066i
$296$	−821224.	−	1.42737e6i	−0.544794	−	0.946908i
$297$		−	752204.i		−	0.494817i
$298$	227968.	−	625358.i	0.148708	−	0.407932i
$299$	−14084.1	+	14084.1i	−0.00911067	+	0.00911067i
$300$	28535.1	+	329981.i	0.0183053	+	0.211683i
$301$	−1.37472e6	−	1.37472e6i	−0.874578	−	0.874578i
$302$	−326687.	−	701504.i	−0.206117	−	0.442602i
$303$	92658.5			0.0579801
$304$	−1.04928e6	+	1.49212e6i	−0.651187	+	0.926021i
$305$	603725.			0.371612
$306$	991551.	+	2.12918e6i	0.605357	+	1.29990i
$307$	−96146.0	−	96146.0i	−0.0582217	−	0.0582217i	0.677396	−	0.735618i	$-0.263108\pi$
$307$	−96146.0	−	96146.0i	−0.0582217	−	0.0582217i	−0.735618	+	0.677396i	$0.763108\pi$
$308$	886893.	−	76694.1i	0.532714	−	0.0460665i
$309$	24497.5	−	24497.5i	0.0145957	−	0.0145957i
$310$	−367525.	+	1.00819e6i	−0.217211	+	0.595850i
$311$			810338.i			0.475078i	0.971378	+	0.237539i	$0.0763408\pi$
$311$			810338.i			0.475078i	−0.971378	+	0.237539i	$0.923659\pi$
$312$	5837.22	+	1573.52i	0.00339484	+	0.000915138i
$313$			1.82461e6i			1.05271i	0.850265	+	0.526355i	$0.176442\pi$
$313$			1.82461e6i			1.05271i	−0.850265	+	0.526355i	$0.823558\pi$
$314$	973039.	+	354712.i	0.556937	+	0.203026i
$315$	−1.03913e6	+	1.03913e6i	−0.590057	+	0.590057i
$316$	−481635.	+	572820.i	−0.271332	+	0.322701i
$317$	−726996.	−	726996.i	−0.406334	−	0.406334i	0.474124	−	0.880458i	$-0.342765\pi$
$317$	−726996.	−	726996.i	−0.406334	−	0.406334i	−0.880458	+	0.474124i	$0.842765\pi$
$318$	−1.02374e6	+	476750.i	−0.567702	+	0.264376i
$319$	−725123.			−0.398965
$320$	−2.17710e6	+	576314.i	−1.18851	+	0.314619i
$321$	−112971.			−0.0611932
$322$	−2.10571e6	+	980622.i	−1.13177	+	0.527062i
$323$	−2.60098e6	−	2.60098e6i	−1.38717	−	1.38717i
$324$	−622850.	+	740769.i	−0.329626	+	0.392031i
$325$	5830.41	−	5830.41i	0.00306190	−	0.00306190i
$326$	3.48033e6	+	1.26872e6i	1.81374	+	0.661183i
$327$			236672.i			0.122399i
$328$	1.97444e6	+	532244.i	1.01335	+	0.273166i
$329$		−	2.74641e6i		−	1.39887i
$330$	−225548.	+	618719.i	−0.114013	+	0.312758i
$331$	2.52917e6	−	2.52917e6i	1.26884	−	1.26884i	0.322159	−	0.946685i	$-0.395591\pi$
$331$	2.52917e6	−	2.52917e6i	1.26884	−	1.26884i	0.946685	−	0.322159i	$-0.104409\pi$
$332$	−1.10801e6	+	95815.6i	−0.551696	+	0.0477080i
$333$	1.29345e6	+	1.29345e6i	0.639205	+	0.639205i
$334$	−504222.	−	1.08273e6i	−0.247318	−	0.531072i
$335$	2.78555e6			1.35612
$336$	576724.	+	405558.i	0.278689	+	0.195977i
$337$	1.70272e6			0.816712			0.408356	−	0.912823i	$-0.366102\pi$
$337$	1.70272e6			0.816712			0.408356	+	0.912823i	$0.366102\pi$
$338$	886625.	+	1.90387e6i	0.422132	+	0.906455i
$339$	732501.	+	732501.i	0.346186	+	0.346186i
$340$	−391252.	−	4.52445e6i	−0.183552	−	2.12260i
$341$	−510576.	+	510576.i	−0.237779	+	0.237779i
$342$	693971.	−	1.90369e6i	0.320831	−	0.880098i
$343$		−	2.37200e6i		−	1.08863i
$344$	1.65044e6	+	2.86863e6i	0.751973	+	1.30701i
$345$		−	1.71839e6i		−	0.777272i
$346$	−2.66787e6	−	972545.i	−1.19805	−	0.436737i
$347$	−2.13008e6	+	2.13008e6i	−0.949670	+	0.949670i	−0.998793	−	0.0491224i	$-0.984358\pi$
$347$	−2.13008e6	+	2.13008e6i	−0.949670	+	0.949670i	0.0491224	+	0.998793i	$0.484358\pi$
$348$	−439568.	−	369596.i	−0.194571	−	0.163598i
$349$	409768.	+	409768.i	0.180084	+	0.180084i	0.791392	−	0.611309i	$-0.209357\pi$
$349$	409768.	+	409768.i	0.180084	+	0.180084i	−0.611309	+	0.791392i	$0.709357\pi$
$350$	871706.	−	405950.i	0.380364	−	0.177134i
$351$	−14831.0			−0.00642545
$352$	−1.49170e6	−	266897.i	−0.641690	−	0.114812i
$353$	−908761.			−0.388162			−0.194081	−	0.980986i	$-0.562172\pi$
$353$	−908761.			−0.388162			−0.194081	+	0.980986i	$0.562172\pi$
$354$	−662219.	+	308392.i	−0.280862	+	0.130796i
$355$	−1.42991e6	−	1.42991e6i	−0.602196	−	0.602196i
$356$	473695.	+	398290.i	0.198095	+	0.166561i
$357$	−1.00531e6	+	1.00531e6i	−0.417475	+	0.417475i
$358$	−422482.	−	154011.i	−0.174221	−	0.0635105i
$359$			2.57742e6i			1.05548i	0.849406	+	0.527740i	$0.176960\pi$
$359$			2.57742e6i			1.05548i	−0.849406	+	0.527740i	$0.823040\pi$
$360$	2.16835e6	−	1.24754e6i	0.881807	−	0.507339i
$361$			697168.i			0.281559i
$362$	432468.	−	1.18634e6i	0.173453	−	0.475814i
$363$	424017.	−	424017.i	0.168895	−	0.168895i
$364$	−1512.16	−	17486.7i	−0.000598197	−	0.00691756i
$365$	−138888.	−	138888.i	−0.0545671	−	0.0545671i
$366$	135827.	+	291665.i	0.0530010	+	0.113810i
$367$	1.72383e6			0.668080			0.334040	−	0.942559i	$-0.391588\pi$
$367$	1.72383e6			0.668080			0.334040	+	0.942559i	$0.391588\pi$
$368$	3.89549e6	−	678802.i	1.49949	−	0.261291i
$369$	−2.27150e6			−0.868454
$370$	−1.49311e6	−	3.20620e6i	−0.567007	−	1.21755i
$371$	2.31837e6	+	2.31837e6i	0.874475	+	0.874475i
$372$	−569751.	+	49269.3i	−0.213466	+	0.0184594i
$373$	−2.31946e6	+	2.31946e6i	−0.863206	+	0.863206i	−0.991709	−	0.128503i	$-0.958983\pi$
$373$	−2.31946e6	+	2.31946e6i	−0.863206	+	0.863206i	0.128503	+	0.991709i	$0.458983\pi$
$374$	1.04659e6	−	2.87098e6i	0.386898	−	1.06133i
$375$		−	679270.i		−	0.249439i
$376$	−1.21685e6	+	4.51408e6i	−0.443881	+	1.64664i
$377$			14297.1i			0.00518076i
$378$	−1.62501e6	−	592381.i	−0.584960	−	0.213241i
$379$	2.71615e6	−	2.71615e6i	0.971304	−	0.971304i	−0.0282951	−	0.999600i	$-0.509008\pi$
$379$	2.71615e6	−	2.71615e6i	0.971304	−	0.971304i	0.999600	+	0.0282951i	$0.00900782\pi$
$380$	−2.52131e6	+	2.99864e6i	−0.895708	+	1.06529i
$381$	−638886.	−	638886.i	−0.225481	−	0.225481i
$382$	1.20009e6	−	558877.i	0.420781	−	0.195956i
$383$	1.85005e6			0.644447			0.322224	−	0.946664i	$-0.395570\pi$
$383$	1.85005e6			0.644447			0.322224	+	0.946664i	$0.395570\pi$
$384$	−768230.	−	922115.i	−0.265866	−	0.319122i
$385$	1.91194e6			0.657388
$386$	833092.	−	387967.i	0.284593	−	0.132534i
$387$	−2.59949e6	−	2.59949e6i	−0.882287	−	0.882287i
$388$	910634.	−	1.08304e6i	0.307089	−	0.365228i
$389$	−1.47439e6	+	1.47439e6i	−0.494013	+	0.494013i	−0.909568	−	0.415555i	$-0.863587\pi$
$389$	−1.47439e6	+	1.47439e6i	−0.494013	+	0.494013i	0.415555	+	0.909568i	$0.363587\pi$
$390$	12199.1	+	4447.07i	0.00406132	+	0.00148052i
$391$			7.97365e6i			2.63764i
$392$	−259095.	+	961153.i	−0.0851617	+	0.315920i
$393$			1.32362e6i			0.432298i
$394$	77389.3	−	212293.i	0.0251154	−	0.0688962i
$395$	−1.13658e6	+	1.13658e6i	−0.366529	+	0.366529i
$396$	1.67704e6	−	145022.i	0.537410	−	0.0464726i
$397$	−1.78362e6	−	1.78362e6i	−0.567969	−	0.567969i	0.363590	−	0.931559i	$-0.381551\pi$
$397$	−1.78362e6	−	1.78362e6i	−0.567969	−	0.567969i	−0.931559	+	0.363590i	$0.881551\pi$
$398$	−1.89244e6	−	4.06368e6i	−0.598843	−	1.28591i
$399$	1.22651e6			0.385690
$400$	−1.61262e6	+	281005.i	−0.503945	+	0.0878140i
$401$	−284391.			−0.0883192			−0.0441596	−	0.999024i	$-0.514061\pi$
$401$	−284391.			−0.0883192			−0.0441596	+	0.999024i	$0.514061\pi$
$402$	626698.	+	1.34573e6i	0.193416	+	0.415328i
$403$	10066.9	+	10066.9i	0.00308769	+	0.00308769i
$404$	39453.0	+	456236.i	0.0120262	+	0.139071i
$405$	−1.46982e6	+	1.46982e6i	−0.445275	+	0.445275i
$406$	−571054.	+	1.56651e6i	−0.171934	+	0.471647i
$407$		−	2.37987e6i		−	0.712144i
$408$	2.09778e6	−	1.20694e6i	0.623892	−	0.358950i
$409$			2.21457e6i			0.654608i	0.944919	+	0.327304i	$0.106140\pi$
$409$			2.21457e6i			0.654608i	−0.944919	+	0.327304i	$0.893860\pi$
$410$	4.12636e6	+	1.50422e6i	1.21229	+	0.441929i
$411$	156542.	−	156542.i	0.0457116	−	0.0457116i
$412$	131052.	+	110191.i	0.0380366	+	0.0319818i
$413$	1.49967e6	+	1.49967e6i	0.432633	+	0.432633i
$414$	−3.98173e6	+	1.85428e6i	−1.14175	+	0.531708i
$415$	−2.38862e6			−0.680812
$416$	−5262.35	+	29411.5i	−0.00149089	+	0.00833268i
$417$	−1.22090e6			−0.343828
$418$	−2.38977e6	+	1.11290e6i	−0.668983	+	0.311542i
$419$	1.20162e6	+	1.20162e6i	0.334374	+	0.334374i	0.854245	−	0.519871i	$-0.174020\pi$
$419$	1.20162e6	+	1.20162e6i	0.334374	+	0.334374i	−0.519871	+	0.854245i	$0.674020\pi$
$420$	1.15901e6	+	974516.i	0.320601	+	0.269566i
$421$	2.42933e6	−	2.42933e6i	0.668007	−	0.668007i	−0.289247	−	0.957254i	$-0.593405\pi$
$421$	2.42933e6	−	2.42933e6i	0.668007	−	0.668007i	0.957254	+	0.289247i	$0.0934050\pi$
$422$	−1.98916e6	−	725127.i	−0.543736	−	0.198213i
$423$		−	5.19324e6i		−	1.41120i
$424$	−2.78334e6	−	4.83773e6i	−0.751885	−	1.30685i
$425$		−	3.30086e6i		−	0.886452i
$426$	369099.	−	1.01251e6i	0.0985415	−	0.270317i
$427$	660509.	−	660509.i	0.175311	−	0.175311i
$428$	−48101.7	−	556250.i	−0.0126926	−	0.146778i
$429$	6178.00	+	6178.00i	0.00162071	+	0.00162071i
$430$	3.00075e6	+	6.44359e6i	0.782634	+	1.68057i
$431$	−1.37294e6			−0.356006			−0.178003	−	0.984030i	$-0.556964\pi$
$431$	−1.37294e6			−0.356006			−0.178003	+	0.984030i	$0.556964\pi$
$432$	2.40845e6	+	1.69364e6i	0.620909	+	0.436629i
$433$	3.17249e6			0.813167			0.406584	−	0.913614i	$-0.366720\pi$
$433$	3.17249e6			0.813167			0.406584	+	0.913614i	$0.366720\pi$
$434$	700920.	+	1.50510e6i	0.178626	+	0.383568i
$435$	−872186.	−	872186.i	−0.220997	−	0.220997i
$436$	−1.16534e6	+	100772.i	−0.293586	+	0.0253878i
$437$	4.86403e6	−	4.86403e6i	1.21841	−	1.21841i
$438$	35850.7	−	98345.1i	0.00892920	−	0.0244944i
$439$		−	6.08336e6i		−	1.50655i	−0.657708	−	0.753273i	$-0.728474\pi$
$439$		−	6.08336e6i		−	1.50655i	0.657708	−	0.753273i	$-0.271526\pi$
$440$	−3.14251e6	−	847118.i	−0.773830	−	0.208599i
$441$		−	1.10576e6i		−	0.270748i
$442$	−56606.4	−	20635.3i	−0.0137819	−	0.00502406i
$443$	−6441.25	+	6441.25i	−0.00155941	+	0.00155941i	−0.707886	−	0.706327i	$-0.750351\pi$
$443$	−6441.25	+	6441.25i	−0.00155941	+	0.00155941i	0.706327	+	0.707886i	$0.250351\pi$
$444$	1.21302e6	−	1.44268e6i	0.292019	−	0.347305i
$445$	939900.	+	939900.i	0.224999	+	0.224999i
$446$	6.27540e6	−	2.92243e6i	1.49384	−	0.695675i
$447$	761860.			0.180346
$448$	−1.75134e6	+	3.01238e6i	−0.412265	+	0.709112i
$449$	−2.31061e6			−0.540892			−0.270446	−	0.962735i	$-0.587171\pi$
$449$	−2.31061e6			−0.540892			−0.270446	+	0.962735i	$0.587171\pi$
$450$	1.64832e6	−	767617.i	0.383717	−	0.178695i
$451$	2.08971e6	+	2.08971e6i	0.483776	+	0.483776i
$452$	−3.29483e6	+	3.91861e6i	−0.758555	+	0.902165i
$453$	626312.	−	626312.i	0.143399	−	0.143399i
$454$	1.01182e6	+	368851.i	0.230391	+	0.0839868i
$455$		−	37697.2i		−	0.00853652i
$456$	−2.01592e6	−	543426.i	−0.454006	−	0.122385i
$457$		−	186457.i		−	0.0417627i	−0.999782	−	0.0208814i	$-0.993353\pi$
$457$		−	186457.i		−	0.0417627i	0.999782	−	0.0208814i	$-0.00664723\pi$
$458$	−866902.	+	2.37807e6i	−0.193111	+	0.529738i
$459$	−4.19826e6	+	4.19826e6i	−0.930118	+	0.930118i
$460$	8.46106e6	−	731671.i	1.86436	−	0.161221i
$461$	−3.57050e6	−	3.57050e6i	−0.782487	−	0.782487i	0.197763	−	0.980250i	$-0.436632\pi$
$461$	−3.57050e6	−	3.57050e6i	−0.782487	−	0.782487i	−0.980250	+	0.197763i	$0.936632\pi$
$462$	430151.	+	923675.i	0.0937597	+	0.201333i
$463$	−6.84013e6			−1.48290			−0.741450	−	0.671008i	$-0.765862\pi$
$463$	−6.84013e6			−1.48290			−0.741450	+	0.671008i	$0.765862\pi$
$464$	1.63267e6	−	2.32174e6i	0.352049	−	0.500631i
$465$	−1.22825e6			−0.263424
$466$	−1.34116e6	−	2.87990e6i	−0.286098	−	0.614346i
$467$	5.90183e6	+	5.90183e6i	1.25226	+	1.25226i	0.954704	+	0.297556i	$0.0961715\pi$
$467$	5.90183e6	+	5.90183e6i	1.25226	+	1.25226i	0.297556	+	0.954704i	$0.403829\pi$
$468$	−2859.37	−	33065.8i	−0.000603470	−	0.00697854i
$469$	3.04754e6	−	3.04754e6i	0.639761	−	0.639761i
$470$	−3.43904e6	+	9.43393e6i	−0.718113	+	1.96992i
$471$			1.18543e6i			0.246221i
$472$	−1.80044e6	−	3.12935e6i	−0.371984	−	0.646546i
$473$			4.78289e6i			0.982964i
$474$	−804804.	−	293383.i	−0.164530	−	0.0599776i
$475$	−2.01357e6	+	2.01357e6i	−0.409480	+	0.409480i
$476$	−5.37805e6	−	4.52195e6i	−1.08795	−	0.914762i
$477$	4.38384e6	+	4.38384e6i	0.882183	+	0.882183i
$478$	−7.29042e6	+	3.39511e6i	−1.45943	+	0.679649i
$479$	−6.99964e6			−1.39392			−0.696958	−	0.717111i	$-0.745464\pi$
$479$	−6.99964e6			−1.39392			−0.696958	+	0.717111i	$0.745464\pi$
$480$	−1.47321e6	−	2.11526e6i	−0.291851	−	0.419046i
$481$	−46923.4			−0.00924755
$482$	5.50520e6	−	2.56375e6i	1.07933	−	0.502641i
$483$	−1.88001e6	−	1.88001e6i	−0.366684	−	0.366684i
$484$	2.26834e6	+	1.90725e6i	0.440143	+	0.370079i
$485$	2.14895e6	−	2.14895e6i	0.414831	−	0.414831i
$486$	−4.75418e6	−	1.73309e6i	−0.913031	−	0.332836i
$487$			2.66337e6i			0.508873i	0.967090	+	0.254436i	$0.0818899\pi$
$487$			2.66337e6i			0.508873i	−0.967090	+	0.254436i	$0.918110\pi$
$488$	−1.37828e6	+	792980.i	−0.261992	+	0.150735i
$489$			4.24001e6i			0.801853i
$490$	−732253.	+	2.00870e6i	−0.137775	+	0.377942i
$491$	1.43092e6	−	1.43092e6i	0.267862	−	0.267862i	−0.560376	−	0.828238i	$-0.689343\pi$
$491$	1.43092e6	−	1.43092e6i	0.267862	−	0.267862i	0.828238	+	0.560376i	$0.189343\pi$
$492$	201652.	+	2.33191e6i	0.0375569	+	0.434309i
$493$	4.04712e6	+	4.04712e6i	0.749943	+	0.749943i
$494$	21942.9	+	47118.5i	0.00404553	+	0.00868708i
$495$	3.61532e6			0.663183
$496$	−485188.	−	2.78439e6i	−0.0885536	−	0.508189i
$497$	−3.12880e6			−0.568181
$498$	−537397.	−	1.15397e6i	−0.0971006	−	0.208507i
$499$	−2.44704e6	−	2.44704e6i	−0.439937	−	0.439937i	0.452054	−	0.891991i	$-0.350692\pi$
$499$	−2.44704e6	−	2.44704e6i	−0.439937	−	0.439937i	−0.891991	+	0.452054i	$0.850692\pi$
$500$	3.34462e6	−	289226.i	0.598304	−	0.0517384i
$501$	966674.	−	966674.i	0.172062	−	0.172062i
$502$	2.22620e6	−	6.10688e6i	0.394280	−	1.08158i
$503$			3.84992e6i			0.678472i	0.940701	+	0.339236i	$0.110168\pi$
$503$			3.84992e6i			0.678472i	−0.940701	+	0.339236i	$0.889832\pi$
$504$	1.00742e6	−	3.73717e6i	0.176658	−	0.655340i
$505$			983540.i			0.171618i
$506$	5.36895e6	+	1.95720e6i	0.932208	+	0.339827i
$507$	−1.69980e6	+	1.69980e6i	−0.293683	+	0.293683i
$508$	2.87374e6	−	3.41781e6i	0.494070	−	0.587609i
$509$	−3.89074e6	−	3.89074e6i	−0.665638	−	0.665638i	0.291065	−	0.956703i	$-0.405990\pi$
$509$	−3.89074e6	−	3.89074e6i	−0.665638	−	0.665638i	−0.956703	+	0.291065i	$0.905990\pi$
$510$	4.71209e6	−	2.19440e6i	0.802211	−	0.373586i
$511$	−303901.			−0.0514850
$512$	4.21325e6	−	4.17527e6i	0.710301	−	0.703898i
$513$	5.12199e6			0.859302
$514$	1.01339e7	−	4.71932e6i	1.69188	−	0.787902i
$515$	260033.	+	260033.i	0.0432026	+	0.0432026i
$516$	−2.43785e6	+	2.89938e6i	−0.403071	+	0.479381i
$517$	−4.77762e6	+	4.77762e6i	−0.786113	+	0.786113i
$518$	−5.14131e6	−	1.87421e6i	−0.841879	−	0.306899i
$519$		−	3.25021e6i		−	0.529655i
$520$	−16702.4	+	61960.2i	−0.00270877	+	0.0100486i
$521$		−	1.24942e6i		−	0.201658i	−0.994904	−	0.100829i	$-0.967850\pi$
$521$		−	1.24942e6i		−	0.201658i	0.994904	−	0.100829i	$-0.0321495\pi$
$522$	−1.07982e6	+	2.96213e6i	−0.173450	+	0.475804i
$523$	7.84375e6	−	7.84375e6i	1.25392	−	1.25392i	0.299972	−	0.953948i	$-0.403023\pi$
$523$	7.84375e6	−	7.84375e6i	1.25392	−	1.25392i	0.953948	−	0.299972i	$-0.0969772\pi$
$524$	−6.51732e6	+	563585.i	−1.03691	+	0.0896667i
$525$	778270.	+	778270.i	0.123234	+	0.123234i
$526$	1.72791e6	+	3.71039e6i	0.272306	+	0.584730i
$527$	5.69934e6			0.893918
$528$	−297758.	−	1.70876e6i	−0.0464813	−	0.266746i
$529$	−8.47497e6			−1.31674
$530$	−5.06054e6	−	1.08666e7i	−0.782542	−	1.68037i
$531$	2.83575e6	+	2.83575e6i	0.436447	+	0.436447i
$532$	522234.	+	6.03913e6i	0.0799993	+	0.925114i
$533$	41202.3	−	41202.3i	0.00628208	−	0.00628208i
$534$	−242614.	+	665535.i	−0.0368182	+	0.100999i
$535$		−	1.19915e6i		−	0.181129i
$536$	−6.35930e6	+	3.65876e6i	−0.956087	+	0.550075i
$537$		−	514700.i		−	0.0770227i
$538$	−9.88344e6	−	3.60291e6i	−1.47215	−	0.536658i
$539$	−1.01727e6	+	1.01727e6i	−0.150821	+	0.150821i
$540$	4.84013e6	+	4.06966e6i	0.714287	+	0.600584i
$541$	−7.29337e6	−	7.29337e6i	−1.07136	−	1.07136i	−0.997250	−	0.0741091i	$-0.976389\pi$
$541$	−7.29337e6	−	7.29337e6i	−1.07136	−	1.07136i	−0.0741091	−	0.997250i	$-0.523611\pi$
$542$	1.66491e6	−	775340.i	0.243440	−	0.113369i
$543$	1.44529e6			0.210356
$544$	6.83599e6	+	9.81525e6i	0.990385	+	1.42201i
$545$	−2.51220e6			−0.362295
$546$	18211.9	−	8481.19i	0.00261441	−	0.00121752i
$547$	3.29684e6	+	3.29684e6i	0.471117	+	0.471117i	0.902276	−	0.431159i	$-0.141895\pi$
$547$	3.29684e6	+	3.29684e6i	0.471117	+	0.471117i	−0.431159	+	0.902276i	$0.641895\pi$
$548$	837442.	+	704134.i	0.119125	+	0.100162i
$549$	1.24897e6	−	1.24897e6i	0.176856	−	0.176856i
$550$	−2.22259e6	−	810223.i	−0.313295	−	0.114208i
$551$		−	4.93759e6i		−	0.692845i
$552$	2.25706e6	+	3.92301e6i	0.315280	+	0.547988i
$553$			2.48697e6i			0.345825i
$554$	−1.57936e6	+	4.33249e6i	−0.218629	+	0.599740i
$555$	2.86254e6	−	2.86254e6i	0.394474	−	0.394474i
$556$	−519848.	−	6.01154e6i	−0.0713165	−	0.824706i
$557$	4.14420e6	+	4.14420e6i	0.565982	+	0.565982i	0.931000	−	0.365019i	$-0.118937\pi$
$557$	4.14420e6	+	4.14420e6i	0.565982	+	0.565982i	−0.365019	+	0.931000i	$0.618937\pi$
$558$	1.32538e6	+	2.84603e6i	0.180200	+	0.386949i
$559$	94303.1			0.0127643
$560$	−4.30487e6	+	6.12174e6i	−0.580083	+	0.824907i
$561$	3.49765e6			0.469212
$562$	3.91764e6	+	8.41246e6i	0.523220	+	1.12352i
$563$	−4.06016e6	−	4.06016e6i	−0.539849	−	0.539849i	0.383635	−	0.923485i	$-0.374672\pi$
$563$	−4.06016e6	−	4.06016e6i	−0.539849	−	0.539849i	−0.923485	+	0.383635i	$0.874672\pi$
$564$	−5.33134e6	+	461028.i	−0.705731	+	0.0610281i
$565$	−7.77526e6	+	7.77526e6i	−1.02469	+	1.02469i
$566$	2.01022e6	−	5.51440e6i	0.263756	−	0.723532i
$567$			3.21614e6i			0.420124i
$568$	5.14258e6	+	1.38627e6i	0.668822	+	0.180292i
$569$		−	1.21386e7i		−	1.57177i	−0.618373	−	0.785885i	$-0.712208\pi$
$569$		−	1.21386e7i		−	1.57177i	0.618373	−	0.785885i	$-0.287792\pi$
$570$	−4.21305e6	−	1.53583e6i	−0.543138	−	0.197995i
$571$	−2.02470e6	+	2.02470e6i	−0.259879	+	0.259879i	−0.825005	−	0.565126i	$-0.808828\pi$
$571$	−2.02470e6	+	2.02470e6i	−0.259879	+	0.259879i	0.565126	+	0.825005i	$0.308828\pi$
$572$	−27789.0	+	33050.1i	−0.00355126	+	0.00422359i
$573$	1.07146e6	+	1.07146e6i	0.136329	+	0.136329i
$574$	6.16017e6	−	2.86876e6i	0.780392	−	0.363425i
$575$	6.17286e6			0.778605
$576$	−3.31165e6	+	5.69617e6i	−0.415899	+	0.715363i
$577$	731916.			0.0915212			0.0457606	−	0.998952i	$-0.485429\pi$
$577$	731916.			0.0915212			0.0457606	+	0.998952i	$0.485429\pi$
$578$	−1.45840e7	+	6.79168e6i	−1.81575	+	0.845586i
$579$	743795.	+	743795.i	0.0922055	+	0.0922055i
$580$	3.92314e6	−	4.66588e6i	0.484244	−	0.575921i
$581$	−2.61329e6	+	2.61329e6i	−0.321179	+	0.321179i
$582$	1.52165e6	+	554703.i	0.186212	+	0.0678817i
$583$		−	8.06600e6i		−	0.982848i
$584$	499501.	+	134649.i	0.0606044	+	0.0163370i
$585$		−	71282.3i		−	0.00861177i
$586$	866451.	−	2.37683e6i	0.104232	−	0.285927i
$587$	−3.98122e6	+	3.98122e6i	−0.476893	+	0.476893i	−0.904136	−	0.427244i	$-0.859485\pi$
$587$	−3.98122e6	+	3.98122e6i	−0.476893	+	0.476893i	0.427244	+	0.904136i	$0.359485\pi$
$588$	−1.13517e6	+	98163.7i	−0.135399	+	0.0117087i
$589$	−3.47667e6	−	3.47667e6i	−0.412929	−	0.412929i
$590$	−3.27348e6	−	7.02924e6i	−0.387151	−	0.831339i
$591$	258632.			0.0304588
$592$	7.62000e6	+	5.35846e6i	0.893616	+	0.628400i
$593$	3.74221e6			0.437010			0.218505	−	0.975836i	$-0.429882\pi$
$593$	3.74221e6			0.437010			0.218505	+	0.975836i	$0.429882\pi$
$594$	1.79635e6	+	3.85734e6i	0.208893	+	0.448562i
$595$	−1.06711e7	−	1.06711e7i	−1.23571	−	1.23571i
$596$	324392.	+	3.75128e6i	0.0374072	+	0.432578i
$597$	3.62810e6	−	3.62810e6i	0.416623	−	0.416623i
$598$	38589.6	−	105858.i	0.00441283	−	0.0121052i
$599$			9.02706e6i			1.02797i	0.857800	+	0.513984i	$0.171831\pi$
$599$			9.02706e6i			1.02797i	−0.857800	+	0.513984i	$0.828169\pi$
$600$	−934360.	−	1.62401e6i	−0.105959	−	0.184167i
$601$			3.36352e6i			0.379846i	0.981799	+	0.189923i	$0.0608238\pi$
$601$			3.36352e6i			0.379846i	−0.981799	+	0.189923i	$0.939176\pi$
$602$	1.03326e7	+	3.76666e6i	1.16204	+	0.423609i
$603$	5.76266e6	−	5.76266e6i	0.645401	−	0.645401i
$604$	3.35054e6	+	2.81719e6i	0.373699	+	0.314212i
$605$	4.50080e6	+	4.50080e6i	0.499921	+	0.499921i
$606$	−475158.	+	221279.i	−0.0525601	+	0.0244770i
$607$	8.35767e6			0.920690			0.460345	−	0.887740i	$-0.347726\pi$
$607$	8.35767e6			0.920690			0.460345	+	0.887740i	$0.347726\pi$
$608$	1.81739e6	−	1.01575e7i	0.199383	−	1.11436i
$609$	−1.90844e6			−0.208514
$610$	−3.09593e6	+	1.44176e6i	−0.336874	+	0.156881i
$611$	94199.2	+	94199.2i	0.0102081	+	0.0102081i
$612$	−1.01695e7	−	8.55063e6i	−1.09754	−	0.922826i
$613$	609703.	−	609703.i	0.0655341	−	0.0655341i	−0.673580	−	0.739114i	$-0.735244\pi$
$613$	609703.	−	609703.i	0.0655341	−	0.0655341i	0.739114	+	0.673580i	$0.235244\pi$
$614$	722649.	+	263434.i	0.0773582	+	0.0282002i
$615$			5.02705e6i			0.535952i
$616$	−4.36488e6	+	2.51129e6i	−0.463469	+	0.266652i
$617$		−	4.89131e6i		−	0.517264i	−0.965976	−	0.258632i	$-0.916728\pi$
$617$		−	4.89131e6i		−	0.517264i	0.965976	−	0.258632i	$-0.0832717\pi$
$618$	−67121.6	+	184127.i	−0.00706954	+	0.0193930i
$619$	−7.55777e6	+	7.55777e6i	−0.792807	+	0.792807i	−0.981950	−	0.189143i	$-0.939429\pi$
$619$	−7.55777e6	+	7.55777e6i	−0.792807	+	0.792807i	0.189143	+	0.981950i	$0.439429\pi$
$620$	−522977.	−	6.04773e6i	−0.0546391	−	0.631848i
$621$	−7.85107e6	−	7.85107e6i	−0.816958	−	0.816958i
$622$	−1.93518e6	−	4.15546e6i	−0.200560	−	0.430668i
$623$	2.05660e6			0.212291
$624$	−33691.3	+	5870.82i	−0.00346383	+	0.000603583i
$625$	1.22057e7			1.24987
$626$	−4.35736e6	−	9.35668e6i	−0.444414	−	0.954302i
$627$	−2.13361e6	−	2.13361e6i	−0.216744	−	0.216744i
$628$	−5.83689e6	+	504745.i	−0.590585	+	0.0510709i
$629$	−1.32827e7	+	1.32827e7i	−1.33863	+	1.33863i
$630$	2.84716e6	−	7.81028e6i	0.285799	−	0.783998i
$631$			1.92664e7i			1.92631i	0.268947	+	0.963155i	$0.413324\pi$
$631$			1.92664e7i			1.92631i	−0.268947	+	0.963155i	$0.586676\pi$
$632$	1.10190e6	−	4.08765e6i	0.109736	−	0.407081i
$633$		−	2.42335e6i		−	0.240384i
$634$	5.46422e6	+	1.99193e6i	0.539889	+	0.196811i
$635$	6.78157e6	−	6.78157e6i	0.667415	−	0.667415i
$636$	4.11125e6	−	4.88960e6i	0.403024	−	0.479325i
$637$	20057.2	+	20057.2i	0.00195849	+	0.00195849i
$638$	3.71847e6	−	1.73167e6i	0.361670	−	0.168428i
$639$	−5.91630e6			−0.573190
$640$	9.78796e6	−	8.15452e6i	0.944587	−	0.786952i
$641$	1.91377e7			1.83969			0.919843	−	0.392287i	$-0.128316\pi$
$641$	1.91377e7			1.83969			0.919843	+	0.392287i	$0.128316\pi$
$642$	579319.	−	269786.i	0.0554728	−	0.0258334i
$643$	2.89342e6	+	2.89342e6i	0.275984	+	0.275984i	0.831503	−	0.555520i	$-0.187481\pi$
$643$	2.89342e6	+	2.89342e6i	0.275984	+	0.275984i	−0.555520	+	0.831503i	$0.687481\pi$
$644$	8.45638e6	−	1.00574e7i	0.803470	−	0.955585i
$645$	−5.75292e6	+	5.75292e6i	−0.544489	+	0.544489i
$646$	1.95494e7	+	7.12654e6i	1.84311	+	0.671889i
$647$		−	410001.i		−	0.0385056i	−0.999815	−	0.0192528i	$-0.993871\pi$
$647$		−	410001.i		−	0.0385056i	0.999815	−	0.0192528i	$-0.00612874\pi$
$648$	1.42497e6	−	5.28614e6i	0.133312	−	0.494540i
$649$		−	5.21760e6i		−	0.486250i
$650$	−15975.0	+	43822.3i	−0.00148305	+	0.00406829i
$651$	−1.34378e6	+	1.34378e6i	−0.124272	+	0.124272i
$652$	−2.08771e7	+	1.80535e6i	−1.92332	+	0.166319i
$653$	1.05317e7	+	1.05317e7i	0.966533	+	0.966533i	0.999458	−	0.0329247i	$-0.0104822\pi$
$653$	1.05317e7	+	1.05317e7i	0.966533	+	0.966533i	−0.0329247	+	0.999458i	$0.510482\pi$
$654$	−565199.	−	1.21367e6i	−0.0516722	−	0.110957i
$655$	−1.40498e7			−1.27958
$656$	−1.13961e7	+	1.98580e6i	−1.03394	+	0.180168i
$657$	−574653.			−0.0519388
$658$	6.55874e6	+	1.40837e7i	0.590548	+	1.26810i
$659$	−1.25500e7	−	1.25500e7i	−1.12572	−	1.12572i	−0.990865	−	0.134857i	$-0.956942\pi$
$659$	−1.25500e7	−	1.25500e7i	−1.12572	−	1.12572i	−0.134857	−	0.990865i	$-0.543058\pi$
$660$	−320948.	−	3.71146e6i	−0.0286798	−	0.331654i
$661$	1.00506e7	−	1.00506e7i	0.894723	−	0.894723i	−0.100240	−	0.994963i	$-0.531961\pi$
$661$	1.00506e7	−	1.00506e7i	0.894723	−	0.894723i	0.994963	+	0.100240i	$0.0319611\pi$
$662$	−6.92979e6	+	1.90097e7i	−0.614575	+	1.68589i
$663$		−	68962.4i		−	0.00609296i
$664$	5.45314e6	−	3.13741e6i	0.479983	−	0.276154i
$665$			1.30190e7i			1.14162i
$666$	−9.72180e6	−	3.54399e6i	−0.849300	−	0.309604i
$667$	−7.56841e6	+	7.56841e6i	−0.658704	+	0.658704i
$668$	5.17135e6	+	4.34815e6i	0.448397	+	0.377019i
$669$	5.60276e6	+	5.60276e6i	0.483990	+	0.483990i
$670$	−1.42844e7	+	6.65220e6i	−1.22935	+	0.572503i
$671$	−2.29802e6			−0.197037
$672$	−3.92599e6	−	702443.i	−0.335371	−	0.0600051i
$673$	−1.57084e7			−1.33689			−0.668445	−	0.743762i	$-0.733040\pi$
$673$	−1.57084e7			−1.33689			−0.668445	+	0.743762i	$0.733040\pi$
$674$	−8.73165e6	+	4.06629e6i	−0.740366	+	0.344785i
$675$	3.25012e6	+	3.25012e6i	0.274562	+	0.274562i
$676$	−9.09332e6	−	7.64581e6i	−0.765343	−	0.643512i
$677$	7.76320e6	−	7.76320e6i	0.650982	−	0.650982i	−0.302247	−	0.953230i	$-0.597737\pi$
$677$	7.76320e6	−	7.76320e6i	0.650982	−	0.650982i	0.953230	+	0.302247i	$0.0977368\pi$
$678$	−5.50560e6	−	2.00701e6i	−0.459971	−	0.167678i
$679$		−	4.70213e6i		−	0.391400i
$680$	1.28113e7	+	2.22673e7i	1.06248	+	1.84669i
$681$			1.23268e6i			0.101855i
$682$	1.39895e6	−	3.83757e6i	0.115170	−	0.315933i
$683$	−7.86345e6	+	7.86345e6i	−0.645002	+	0.645002i	−0.951781	−	0.306779i	$-0.900749\pi$
$683$	−7.86345e6	+	7.86345e6i	−0.645002	+	0.645002i	0.306779	+	0.951781i	$0.400749\pi$
$684$	987502.	+	1.14195e7i	0.0807045	+	0.933269i
$685$	1.66164e6	+	1.66164e6i	0.135304	+	0.135304i
$686$	5.66460e6	+	1.21637e7i	0.459578	+	0.986863i
$687$	−2.89715e6			−0.234196
$688$	−1.53141e7	−	1.07690e7i	−1.23345	−	0.867373i
$689$	−159035.			−0.0127628
$690$	4.10369e6	+	8.81197e6i	0.328135	+	0.704612i
$691$	5.68810e6	+	5.68810e6i	0.453181	+	0.453181i	0.896409	−	0.443228i	$-0.146167\pi$
$691$	5.68810e6	+	5.68810e6i	0.453181	+	0.453181i	−0.443228	+	0.896409i	$0.646167\pi$
$692$	1.60035e7	−	1.38391e6i	1.27043	−	0.109860i
$693$	3.95536e6	−	3.95536e6i	0.312862	−	0.312862i
$694$	5.83630e6	−	1.60101e7i	0.459980	−	1.26181i
$695$		−	1.29595e7i		−	1.01772i
$696$	3.13677e6	+	845569.i	0.245448	+	0.0661646i
$697$		−	2.33265e7i		−	1.81873i
$698$	−3.07988e6	−	1.12274e6i	−0.239274	−	0.0872250i
$699$	2.57121e6	−	2.57121e6i	0.199042	−	0.199042i
$700$	−3.50070e6	+	4.16346e6i	−0.270029	+	0.321151i
$701$	−1.00320e7	−	1.00320e7i	−0.771070	−	0.771070i	0.207224	−	0.978294i	$-0.433557\pi$
$701$	−1.00320e7	−	1.00320e7i	−0.771070	−	0.771070i	−0.978294	+	0.207224i	$0.933557\pi$
$702$	76054.3	−	35418.1i	0.00582480	−	0.00271258i
$703$	1.62053e7			1.23671
$704$	8.28691e6	−	2.19369e6i	0.630175	−	0.166818i
$705$	−1.14932e7			−0.870896
$706$	4.66017e6	−	2.17022e6i	0.351876	−	0.163867i
$707$	1.07605e6	+	1.07605e6i	0.0809623	+	0.0809623i
$708$	2.65942e6	−	3.16290e6i	0.199390	−	0.237139i
$709$	9.85700e6	−	9.85700e6i	0.736426	−	0.736426i	−0.235458	−	0.971884i	$-0.575659\pi$
$709$	9.85700e6	−	9.85700e6i	0.736426	−	0.736426i	0.971884	+	0.235458i	$0.0756591\pi$
$710$	1.07474e7	+	3.91787e6i	0.800127	+	0.291678i
$711$			4.70265e6i			0.348874i
$712$	−3.38029e6	−	911216.i	−0.249893	−	0.0673630i
$713$			1.06582e7i			0.785162i
$714$	2.75450e6	−	7.55609e6i	0.202207	−	0.554692i
$715$	−65577.5	+	65577.5i	−0.00479722	+	0.00479722i
$716$	2.53430e6	−	219154.i	0.184746	−	0.0159760i
$717$	−6.50898e6	−	6.50898e6i	−0.472841	−	0.472841i
$718$	−6.15517e6	−	1.32172e7i	−0.445584	−	0.956813i
$719$	1.06685e6			0.0769630			0.0384815	−	0.999259i	$-0.487748\pi$
$719$	1.06685e6			0.0769630			0.0384815	+	0.999259i	$0.487748\pi$
$720$	−8.14016e6	+	1.15757e7i	−0.585196	+	0.832178i
$721$	568980.			0.0407623
$722$	−1.66491e6	−	3.57511e6i	−0.118864	−	0.255239i
$723$	4.91511e6	+	4.91511e6i	0.349694	+	0.349694i
$724$	615390.	+	7.11638e6i	0.0436319	+	0.504560i
$725$	3.13311e6	−	3.13311e6i	0.221376	−	0.221376i
$726$	−1.16178e6	+	3.18698e6i	−0.0818056	+	0.224408i
$727$		−	1.74630e7i		−	1.22541i	−0.790310	−	0.612707i	$-0.790081\pi$
$727$		−	1.74630e7i		−	1.22541i	0.790310	−	0.612707i	$-0.209919\pi$
$728$	49514.5	+	86061.3i	0.00346261	+	0.00601838i
$729$			1.55748e6i			0.108544i
$730$	1.04390e6	+	380544.i	0.0725024	+	0.0264300i
$731$	2.66947e7	−	2.66947e7i	1.84770	−	1.84770i
$732$	−1.39306e6	−	1.17130e6i	−0.0960930	−	0.0807964i
$733$	9.04898e6	+	9.04898e6i	0.622070	+	0.622070i	0.946060	−	0.323990i	$-0.105024\pi$
$733$	9.04898e6	+	9.04898e6i	0.622070	+	0.622070i	−0.323990	+	0.946060i	$0.605024\pi$
$734$	−8.83988e6	+	4.11669e6i	−0.605628	+	0.282038i
$735$	−2.44716e6			−0.167088
$736$	−1.83552e7	+	1.27838e7i	−1.24901	+	0.869893i
$737$	−1.06029e7			−0.719047
$738$	1.16484e7	−	5.42459e6i	0.787271	−	0.366629i
$739$	6.08082e6	+	6.08082e6i	0.409592	+	0.409592i	0.881596	−	0.472005i	$-0.156469\pi$
$739$	6.08082e6	+	6.08082e6i	0.409592	+	0.409592i	−0.472005	+	0.881596i	$0.656469\pi$
$740$	1.53135e7	+	1.28759e7i	1.02801	+	0.864364i
$741$	−42068.0	+	42068.0i	−0.00281453	+	0.00281453i
$742$	−1.74252e7	−	6.35219e6i	−1.16190	−	0.423559i
$743$		−	1.29381e7i		−	0.859804i	−0.902875	−	0.429902i	$-0.858548\pi$
$743$		−	1.29381e7i		−	0.859804i	0.902875	−	0.429902i	$-0.141452\pi$
$744$	2.80405e6	−	1.61328e6i	0.185718	−	0.106851i
$745$			8.08690e6i			0.533816i
$746$	6.35518e6	−	1.74334e7i	0.418101	−	1.14693i
$747$	−4.94151e6	+	4.94151e6i	−0.324010	+	0.324010i
$748$	1.48926e6	+	1.72219e7i	0.0973235	+	1.12545i
$749$	−1.31193e6	−	1.31193e6i	−0.0854490	−	0.0854490i
$750$	1.62217e6	+	3.48333e6i	0.105304	+	0.226122i
$751$	−1.81776e7			−1.17608			−0.588040	−	0.808832i	$-0.700100\pi$
$751$	−1.81776e7			−1.17608			−0.588040	+	0.808832i	$0.700100\pi$
$752$	−4.54006e6	−	2.60544e7i	−0.292764	−	1.68011i
$753$	7.43988e6			0.478166
$754$	−34143.0	−	73316.1i	−0.00218712	−	0.00469647i
$755$	6.64810e6	+	6.64810e6i	0.424453	+	0.424453i
$756$	9.74781e6	−	842942.i	0.620301	−	0.0536406i
$757$	−1.53256e7	+	1.53256e7i	−0.972027	+	0.972027i	−0.999619	−	0.0275926i	$-0.991216\pi$
$757$	−1.53256e7	+	1.53256e7i	−0.972027	+	0.972027i	0.0275926	+	0.999619i	$0.491216\pi$
$758$	−7.44209e6	+	2.04150e7i	−0.470459	+	1.29056i
$759$			6.54087e6i			0.412127i
$760$	5.76830e6	−	2.13984e7i	0.362254	−	1.34384i
$761$			3.17565e7i			1.98779i	0.110327	+	0.993895i	$0.464810\pi$
$761$			3.17565e7i			1.98779i	−0.110327	+	0.993895i	$0.535190\pi$
$762$	4.80197e6	+	1.75051e6i	0.299593	+	0.109214i
$763$	−2.74848e6	+	2.74848e6i	−0.170916	+	0.170916i
$764$	−4.81947e6	+	5.73190e6i	−0.298721	+	0.355276i
$765$	−2.01781e7	−	2.01781e7i	−1.24660	−	1.24660i
$766$	−9.48717e6	+	4.41813e6i	−0.584204	+	0.272061i
$767$	−102874.			−0.00631420
$768$	6.14164e6	+	2.89404e6i	0.375735	+	0.177052i
$769$	−6.64122e6			−0.404979			−0.202489	−	0.979284i	$-0.564903\pi$
$769$	−6.64122e6			−0.404979			−0.202489	+	0.979284i	$0.564903\pi$
$770$	−9.80451e6	+	4.56592e6i	−0.595935	+	0.277524i
$771$	9.04770e6	+	9.04770e6i	0.548153	+	0.548153i
$772$	−3.34563e6	+	3.97903e6i	−0.202039	+	0.240289i
$773$	−9.67679e6	+	9.67679e6i	−0.582482	+	0.582482i	−0.935585	−	0.353102i	$-0.885127\pi$
$773$	−9.67679e6	+	9.67679e6i	−0.582482	+	0.582482i	0.353102	+	0.935585i	$0.385127\pi$
$774$	1.95382e7	+	7.12244e6i	1.17228	+	0.427343i
$775$		−	4.41219e6i		−	0.263876i
$776$	−2.08337e6	+	7.72856e6i	−0.124197	+	0.460728i
$777$		−	6.26355e6i		−	0.372193i
$778$	4.03974e6	−	1.10818e7i	0.239279	−	0.656387i
$779$	−1.42295e7	+	1.42295e7i	−0.840129	+	0.840129i
$780$	−73177.9	+	6328.07i	−0.00430669	+	0.000372421i
$781$	5.44281e6	+	5.44281e6i	0.319298	+	0.319298i
$782$	−1.90420e7	−	4.08893e7i	−1.11351	−	2.39107i
$783$	−7.96980e6			−0.464561
$784$	−966685.	−	5.54759e6i	−0.0561688	−	0.322340i
$785$	−1.25830e7			−0.728802
$786$	−3.16096e6	−	6.78761e6i	−0.182500	−	0.391887i
$787$	5.77308e6	+	5.77308e6i	0.332254	+	0.332254i	0.853442	−	0.521188i	$-0.174511\pi$
$787$	5.77308e6	+	5.77308e6i	0.332254	+	0.332254i	−0.521188	+	0.853442i	$0.674511\pi$
$788$	110123.	+	1.27346e6i	0.00631774	+	0.0730585i
$789$	−3.31269e6	+	3.31269e6i	−0.189447	+	0.189447i
$790$	3.11417e6	−	8.54273e6i	0.177531	−	0.487000i
$791$			1.70131e7i			0.966814i
$792$	−8.25363e6	+	4.74864e6i	−0.467554	+	0.269003i
$793$			45309.6i			0.00255863i
$794$	1.34059e7	+	4.88700e6i	0.754651	+	0.275100i
$795$	9.70187e6	−	9.70187e6i	0.544425	−	0.544425i
$796$	1.94090e7	+	1.63194e7i	1.08573	+	0.912896i
$797$	1.39476e7	+	1.39476e7i	0.777773	+	0.777773i	0.979452	−	0.201678i	$-0.0646396\pi$
$797$	1.39476e7	+	1.39476e7i	0.777773	+	0.777773i	−0.201678	+	0.979452i	$0.564640\pi$
$798$	−6.28959e6	+	2.92903e6i	−0.349635	+	0.162824i
$799$	5.33305e7			2.95535
$800$	7.59855e6	−	5.29213e6i	0.419765	−	0.292352i
$801$	3.88887e6			0.214162
$802$	1.45837e6	−	679157.i	0.0800631	−	0.0372850i
$803$	528663.	+	528663.i	0.0289327	+	0.0289327i
$804$	−6.42748e6	−	5.40433e6i	−0.350672	−	0.294850i
$805$	1.99557e7	−	1.99557e7i	1.08537	−	1.08537i
$806$	−75664.5	−	27582.7i	−0.00410255	−	0.00149555i
$807$		−	1.20408e7i		−	0.650835i
$808$	−1.29186e6	−	2.24538e6i	−0.0696124	−	0.120994i
$809$			1.01170e7i			0.543478i	0.962371	+	0.271739i	$0.0875988\pi$
$809$			1.01170e7i			0.543478i	−0.962371	+	0.271739i	$0.912401\pi$
$810$	4.02723e6	−	1.10474e7i	0.215672	−	0.591629i
$811$	−1.17874e6	+	1.17874e6i	−0.0629311	+	0.0629311i	−0.737872	−	0.674941i	$-0.764169\pi$
$811$	−1.17874e6	+	1.17874e6i	−0.0629311	+	0.0629311i	0.674941	+	0.737872i	$0.264169\pi$
$812$	−812594.	−	9.39686e6i	−0.0432497	−	0.500141i
$813$	1.48645e6	+	1.48645e6i	0.0788722	+	0.0788722i
$814$	5.68340e6	+	1.22041e7i	0.300640	+	0.645573i
$815$	−4.50063e7			−2.37345
$816$	−7.87523e6	+	1.11990e7i	−0.414036	+	0.588780i
$817$	−3.25682e7			−1.70702
$818$	−5.28864e6	−	1.13564e7i	−0.276351	−	0.593415i
$819$	−77986.8	−	77986.8i	−0.00406267	−	0.00406267i
$820$	−2.47524e7	+	2.14047e6i	−1.28553	+	0.111167i
$821$	1.58156e7	−	1.58156e7i	0.818893	−	0.818893i	−0.167055	−	0.985948i	$-0.553426\pi$
$821$	1.58156e7	−	1.58156e7i	0.818893	−	0.818893i	0.985948	+	0.167055i	$0.0534258\pi$
$822$	−428916.	+	1.17660e6i	−0.0221408	+	0.0607362i
$823$			4.45762e6i			0.229405i	0.993400	+	0.114703i	$0.0365916\pi$
$823$			4.45762e6i			0.229405i	−0.993400	+	0.114703i	$0.963408\pi$
$824$	−935192.	−	252097.i	−0.0479825	−	0.0129345i
$825$		−	2.70774e6i		−	0.138507i
$826$	−1.12717e7	−	4.10900e6i	−0.574832	−	0.209549i
$827$	2.20433e6	−	2.20433e6i	0.112076	−	0.112076i	−0.648845	−	0.760921i	$-0.724748\pi$
$827$	2.20433e6	−	2.20433e6i	0.112076	−	0.112076i	0.760921	+	0.648845i	$0.224748\pi$
$828$	1.59903e7	−	1.90176e7i	0.810553	−	0.964008i
$829$	6.74803e6	+	6.74803e6i	0.341028	+	0.341028i	0.856754	−	0.515726i	$-0.172478\pi$
$829$	6.74803e6	+	6.74803e6i	0.341028	+	0.341028i	−0.515726	+	0.856754i	$0.672478\pi$
$830$	1.22490e7	−	5.70430e6i	0.617170	−	0.287413i
$831$	−5.27818e6			−0.265144
$832$	−43252.4	−	163391.i	−0.00216622	−	0.00818314i
$833$	1.13553e7			0.567004
$834$	6.26086e6	−	2.91565e6i	0.311687	−	0.145151i
$835$	1.02609e7	+	1.02609e7i	0.509296	+	0.509296i
$836$	9.59712e6	−	1.14141e7i	0.474925	−	0.564839i
$837$	−5.61172e6	+	5.61172e6i	−0.276874	+	0.276874i
$838$	−9.03158e6	−	3.29237e6i	−0.444277	−	0.161957i
$839$		−	2.39429e7i		−	1.17428i	−0.809485	−	0.587140i	$-0.800254\pi$
$839$		−	2.39429e7i		−	1.17428i	0.809485	−	0.587140i	$-0.199746\pi$
$840$	−8.27073e6	−	2.22952e6i	−0.404432	−	0.109022i
$841$		−	1.28283e7i		−	0.625430i
$842$	−6.65622e6	+	1.82592e7i	−0.323555	+	0.887569i
$843$	−7.51075e6	+	7.51075e6i	−0.364011	+	0.364011i
$844$	1.19322e7	−	1.03184e6i	0.576586	−	0.0498603i
$845$	−1.80429e7	−	1.80429e7i	−0.869288	−	0.869288i
$846$	1.24020e7	+	2.66312e7i	0.595754	+	1.27928i
$847$	9.84825e6			0.471683
$848$	2.58261e7	+	1.81612e7i	1.23330	+	0.867271i
$849$	6.71808e6			0.319872
$850$	7.88283e6	+	1.69270e7i	0.374227	+	0.803587i
$851$	−2.48397e7	−	2.48397e7i	−1.17577	−	1.17577i
$852$	525218.	+	6.07364e6i	0.0247880	+	0.286649i
$853$	1.00182e7	−	1.00182e7i	0.471430	−	0.471430i	−0.430947	−	0.902377i	$-0.641821\pi$
$853$	1.00182e7	−	1.00182e7i	0.471430	−	0.471430i	0.902377	+	0.430947i	$0.141821\pi$
$854$	−1.80976e6	+	4.96449e6i	−0.0849132	+	0.232932i
$855$			2.46178e7i			1.15169i
$856$	1.57505e6	+	2.73761e6i	0.0734702	+	0.127699i
$857$		−	1.85006e7i		−	0.860465i	−0.902718	−	0.430232i	$-0.858432\pi$
$857$		−	1.85006e7i		−	0.860465i	0.902718	−	0.430232i	$-0.141568\pi$
$858$	−46434.9	−	16927.4i	−0.00215341	−	0.000785003i
$859$	−5.56880e6	+	5.56880e6i	−0.257501	+	0.257501i	−0.824037	−	0.566536i	$-0.808283\pi$
$859$	−5.56880e6	+	5.56880e6i	−0.257501	+	0.257501i	0.566536	+	0.824037i	$0.308283\pi$
$860$	−3.07760e7	−	2.58769e7i	−1.41895	−	1.19307i
$861$	5.49988e6	+	5.49988e6i	0.252840	+	0.252840i
$862$	7.04050e6	−	3.27873e6i	0.322727	−	0.150292i
$863$	−1.36785e7			−0.625191			−0.312596	−	0.949886i	$-0.601198\pi$
$863$	−1.36785e7			−0.625191			−0.312596	+	0.949886i	$0.601198\pi$
$864$	−1.63953e7	−	2.93346e6i	−0.747195	−	0.133689i
$865$	3.44999e7			1.56775
$866$	−1.62687e7	+	7.57625e6i	−0.737153	+	0.343289i
$867$	−1.30207e7	−	1.30207e7i	−0.588285	−	0.588285i
$868$	−7.18871e6	−	6.04438e6i	−0.323856	−	0.272303i
$869$	4.32629e6	−	4.32629e6i	0.194342	−	0.194342i
$870$	6.55549e6	+	2.38974e6i	0.293635	+	0.107042i
$871$			209055.i			0.00933719i
$872$	5.73525e6	−	3.29972e6i	0.255424	−	0.146955i
$873$		−	8.89135e6i		−	0.394850i
$874$	−1.33272e7	+	3.65588e7i	−0.590145	+	1.61888i
$875$	7.88840e6	−	7.88840e6i	0.348312	−	0.348312i
$876$	51014.6	+	589934.i	0.00224613	+	0.0259743i
$877$	3.17332e7	+	3.17332e7i	1.39321	+	1.39321i	0.818029	+	0.575176i	$0.195067\pi$
$877$	3.17332e7	+	3.17332e7i	1.39321	+	1.39321i	0.575176	+	0.818029i	$0.304933\pi$
$878$	1.45277e7	+	3.11958e7i	0.636007	+	1.36571i
$879$	2.89565e6			0.126408
$880$	1.81380e7	−	3.16060e6i	0.789555	−	0.137582i
$881$	1.66529e7			0.722853			0.361427	−	0.932401i	$-0.382290\pi$
$881$	1.66529e7			0.722853			0.361427	+	0.932401i	$0.382290\pi$
$882$	2.64068e6	+	5.67040e6i	0.114300	+	0.245438i
$883$	−1.77861e7	−	1.77861e7i	−0.767678	−	0.767678i	0.210019	−	0.977697i	$-0.432647\pi$
$883$	−1.77861e7	−	1.77861e7i	−0.767678	−	0.767678i	−0.977697	+	0.210019i	$0.932647\pi$
$884$	339560.	−	29363.5i	0.0146146	−	0.00126380i
$885$	6.27579e6	−	6.27579e6i	0.269346	−	0.269346i
$886$	17648.7	−	48413.5i	0.000755314	−	0.00207196i
$887$			1.26187e6i			0.0538523i	0.999637	+	0.0269261i	$0.00857189\pi$
$887$			1.26187e6i			0.0538523i	−0.999637	+	0.0269261i	$0.991428\pi$
$888$	−2.77518e6	+	1.02950e7i	−0.118102	+	0.438119i
$889$		−	1.48388e7i		−	0.629716i
$890$	−7.06444e6	−	2.57527e6i	−0.298953	−	0.108980i
$891$	5.59475e6	−	5.59475e6i	0.236095	−	0.236095i
$892$	−2.52015e7	+	2.99727e7i	−1.06051	+	1.26129i
$893$	−3.25323e7	−	3.25323e7i	−1.36517	−	1.36517i
$894$	−3.90686e6	+	1.81941e6i	−0.163487	+	0.0761353i
$895$	5.46338e6			0.227984
$896$	1.78708e6	−	1.96301e7i	0.0743658	−	0.816867i
$897$	128965.			0.00535168
$898$	1.18489e7	−	5.51799e6i	0.490329	−	0.228344i
$899$	5.40968e6	+	5.40968e6i	0.223240	+	0.223240i
$900$	−6.61954e6	+	7.87276e6i	−0.272409	+	0.323982i
$901$	−4.50186e7	+	4.50186e7i	−1.84748	+	1.84748i
$902$	−1.57066e7	−	5.72568e6i	−0.642785	−	0.234321i
$903$			1.25880e7i			0.513734i
$904$	7.53798e6	−	2.79633e7i	0.306785	−	1.13806i
$905$			1.53413e7i			0.622645i
$906$	−1.71606e6	+	4.70746e6i	−0.0694563	+	0.190531i
$907$	−1.77739e7	+	1.77739e7i	−0.717406	+	0.717406i	−0.968073	−	0.250668i	$-0.919350\pi$
$907$	−1.77739e7	+	1.77739e7i	−0.717406	+	0.717406i	0.250668	+	0.968073i	$0.419350\pi$
$908$	−6.06955e6	+	524864.i	−0.244310	+	0.0211267i
$909$	2.03472e6	+	2.03472e6i	0.0816760	+	0.0816760i
$910$	90025.1	+	193313.i	0.00360380	+	0.00773852i
$911$	−1.64034e6			−0.0654843			−0.0327422	−	0.999464i	$-0.510424\pi$
$911$	−1.64034e6			−0.0654843			−0.0327422	+	0.999464i	$0.510424\pi$
$912$	1.16355e7	−	2.02753e6i	0.463232	−	0.0807196i
$913$	9.09207e6			0.360982
$914$	445281.	+	956163.i	0.0176307	+	0.0378588i
$915$	−2.76409e6	−	2.76409e6i	−0.109144	−	0.109144i
$916$	−1.23358e6	−	1.42651e7i	−0.0485767	−	0.561742i
$917$	−1.53713e7	+	1.53713e7i	−0.603653	+	0.603653i
$918$	1.15030e7	−	3.15548e7i	0.450510	−	1.23583i
$919$			1.33815e7i			0.522657i	0.965250	+	0.261328i	$0.0841606\pi$
$919$			1.33815e7i			0.522657i	−0.965250	+	0.261328i	$0.915839\pi$
$920$	−4.16415e7	+	2.39580e7i	−1.62202	+	0.933213i
$921$			880388.i			0.0341999i
$922$	2.68365e7	+	9.78297e6i	1.03968	+	0.379004i
$923$	107315.	−	107315.i	0.00414625	−	0.00414625i
$924$	−4.41168e6	−	3.70940e6i	−0.169990	−	0.142930i
$925$	1.02829e7	+	1.02829e7i	0.395151	+	0.395151i
$926$	3.50765e7	−	1.63350e7i	1.34428	−	0.626024i
$927$	1.07589e6			0.0411216
$928$	−2.82785e6	+	1.58050e7i	−0.107792	+	0.602454i
$929$	1.74486e7			0.663318			0.331659	−	0.943399i	$-0.392392\pi$
$929$	1.74486e7			0.663318			0.331659	+	0.943399i	$0.392392\pi$
$930$	6.29854e6	−	2.93320e6i	0.238799	−	0.111208i
$931$	−6.92689e6	−	6.92689e6i	−0.261917	−	0.261917i
$932$	1.37550e7	+	1.15655e7i	0.518707	+	0.436137i
$933$	3.71004e6	−	3.71004e6i	0.139532	−	0.139532i
$934$	−4.43591e7	−	1.61707e7i	−1.66386	−	0.606542i
$935$			3.71265e7i			1.38885i
$936$	93627.9	+	162735.i	0.00349314	+	0.00607143i
$937$		−	3.22416e7i		−	1.19969i	−0.800117	−	0.599843i	$-0.795230\pi$
$937$		−	3.22416e7i		−	1.19969i	0.800117	−	0.599843i	$-0.204770\pi$
$938$	−8.35009e6	+	2.29058e7i	−0.309873	+	0.850040i
$939$	8.35376e6	−	8.35376e6i	0.309185	−	0.309185i
$940$	−4.89367e6	−	5.65905e7i	−0.180640	−	2.08893i
$941$	−1.84117e7	−	1.84117e7i	−0.677828	−	0.677828i	0.281680	−	0.959508i	$-0.409108\pi$
$941$	−1.84117e7	−	1.84117e7i	−0.677828	−	0.677828i	−0.959508	+	0.281680i	$0.909108\pi$
$942$	−2.83095e6	−	6.07896e6i	−0.103945	−	0.223204i
$943$	4.36224e7			1.59746
$944$	1.67060e7	+	1.17478e7i	0.610158	+	0.429070i
$945$	2.10140e7			0.765473
$946$	−1.14221e7	−	2.45269e7i	−0.414970	−	0.891077i
$947$	−7.17798e6	−	7.17798e6i	−0.260092	−	0.260092i	0.564999	−	0.825091i	$-0.308876\pi$
$947$	−7.17798e6	−	7.17798e6i	−0.260092	−	0.260092i	−0.825091	+	0.564999i	$0.808876\pi$
$948$	4.82771e6	−	417476.i	0.174470	−	0.0150873i
$949$	10423.5	−	10423.5i	0.000375707	−	0.000375707i
$950$	5.51707e6	−	1.51343e7i	0.198335	−	0.544069i
$951$			6.65694e6i			0.238684i
$952$	3.83778e7	+	1.03454e7i	1.37242	+	0.369960i
$953$			3.08295e6i			0.109960i	0.998487	+	0.0549799i	$0.0175095\pi$
$953$			3.08295e6i			0.109960i	−0.998487	+	0.0549799i	$0.982491\pi$
$954$	−3.29497e7	−	1.20115e7i	−1.17214	−	0.427293i
$955$	−1.13732e7	+	1.13732e7i	−0.403527	+	0.403527i
$956$	2.92777e7	−	3.48207e7i	1.03608	−	1.23223i
$957$	3.31989e6	+	3.31989e6i	0.117178	+	0.117178i
$958$	3.58945e7	−	1.67159e7i	1.26361	−	0.588459i
$959$	3.63586e6			0.127662
$960$	1.26062e7	+	7.32900e6i	0.441474	+	0.256665i
$961$	−2.10110e7			−0.733902
$962$	240626.	−	112058.i	0.00838309	−	0.00390397i
$963$	−2.48076e6	−	2.48076e6i	−0.0862023	−	0.0862023i
$964$	−2.21085e7	+	2.62941e7i	−0.766242	+	0.911308i
$965$	−7.89514e6	+	7.89514e6i	−0.272924	+	0.272924i
$966$	1.41305e7	+	5.15111e6i	0.487207	+	0.177606i
$967$		−	3.51323e7i		−	1.20820i	−0.796907	−	0.604102i	$-0.793532\pi$
$967$		−	3.51323e7i		−	1.20820i	0.796907	−	0.604102i	$-0.206468\pi$
$968$	−1.61869e7	−	4.36345e6i	−0.555232	−	0.149672i
$969$			2.38166e7i			0.814837i
$970$	−5.88799e6	+	1.61518e7i	−0.200927	+	0.551179i
$971$	2.90507e7	−	2.90507e7i	0.988800	−	0.988800i	−0.0111382	−	0.999938i	$-0.503545\pi$
$971$	2.90507e7	−	2.90507e7i	0.988800	−	0.988800i	0.999938	+	0.0111382i	$0.00354547\pi$
$972$	2.85185e7	−	2.46614e6i	0.968192	−	0.0837244i
$973$	−1.41784e7	−	1.41784e7i	−0.480115	−	0.480115i
$974$	−6.36042e6	−	1.36579e7i	−0.214827	−	0.461303i
$975$	−53387.8			−0.00179858
$976$	5.17417e6	−	7.35793e6i	0.173867	−	0.247247i
$977$	650099.			0.0217893			0.0108947	−	0.999941i	$-0.496532\pi$
$977$	650099.			0.0217893			0.0108947	+	0.999941i	$0.496532\pi$
$978$	−1.01256e7	−	2.17430e7i	−0.338512	−	0.726896i
$979$	−3.57764e6	−	3.57764e6i	−0.119300	−	0.119300i
$980$	−1.04198e6	−	1.20494e7i	−0.0346571	−	0.400776i
$981$	−5.19715e6	+	5.19715e6i	−0.172422	+	0.172422i
$982$	−3.92064e6	+	1.07550e7i	−0.129741	+	0.355904i
$983$			1.51329e7i			0.499502i	0.968310	+	0.249751i	$0.0803488\pi$
$983$			1.51329e7i			0.499502i	−0.968310	+	0.249751i	$0.919651\pi$
$984$	−6.60293e6	−	1.14766e7i	−0.217395	−	0.377854i
$985$			2.74529e6i			0.0901568i
$986$	−3.04188e7	−	1.10889e7i	−0.996436	−	0.363241i
$987$	−1.25741e7	+	1.25741e7i	−0.410852	+	0.410852i
$988$	−225048.	−	189224.i	−0.00733472	−	0.00616714i
$989$	4.99210e7	+	4.99210e7i	1.62290	+	1.62290i
$990$	−1.85395e7	+	8.63377e6i	−0.601189	+	0.279971i
$991$	−2.88015e7			−0.931605			−0.465802	−	0.884889i	$-0.654234\pi$
$991$	−2.88015e7			−0.931605			−0.465802	+	0.884889i	$0.654234\pi$
$992$	9.13750e6	+	1.31198e7i	0.294814	+	0.423300i
$993$	−2.31591e7			−0.745329
$994$	1.60446e7	−	7.47192e6i	0.515068	−	0.239865i
$995$	3.85111e7	+	3.85111e7i	1.23319	+	1.23319i
$996$	5.51160e6	+	4.63424e6i	0.176047	+	0.148023i
$997$	8.86804e6	−	8.86804e6i	0.282547	−	0.282547i	−0.551577	−	0.834124i	$-0.685974\pi$
$997$	8.86804e6	−	8.86804e6i	0.282547	−	0.282547i	0.834124	+	0.551577i	$0.185974\pi$
$998$	1.83924e7	+	6.70476e6i	0.584537	+	0.213087i
$999$		−	2.61571e7i		−	0.829232i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.6.e.a.13.2	yes	18
3.2	odd	2		144.6.k.a.109.8		18
4.3	odd	2		64.6.e.a.17.6		18
8.3	odd	2		128.6.e.a.33.4		18
8.5	even	2		128.6.e.b.33.6		18
12.11	even	2		576.6.k.a.145.2		18
16.3	odd	4		128.6.e.a.97.4		18
16.5	even	4	inner	16.6.e.a.5.2	✓	18
16.11	odd	4		64.6.e.a.49.6		18
16.13	even	4		128.6.e.b.97.6		18
32.5	even	8		1024.6.a.k.1.12		18
32.11	odd	8		1024.6.a.l.1.12		18
32.21	even	8		1024.6.a.k.1.7		18
32.27	odd	8		1024.6.a.l.1.7		18
48.5	odd	4		144.6.k.a.37.8		18
48.11	even	4		576.6.k.a.433.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.6.e.a.5.2	✓	18	16.5	even	4	inner
16.6.e.a.13.2	yes	18	1.1	even	1	trivial
64.6.e.a.17.6		18	4.3	odd	2
64.6.e.a.49.6		18	16.11	odd	4
128.6.e.a.33.4		18	8.3	odd	2
128.6.e.a.97.4		18	16.3	odd	4
128.6.e.b.33.6		18	8.5	even	2
128.6.e.b.97.6		18	16.13	even	4
144.6.k.a.37.8		18	48.5	odd	4
144.6.k.a.109.8		18	3.2	odd	2
576.6.k.a.145.2		18	12.11	even	2
576.6.k.a.433.2		18	48.11	even	4
1024.6.a.k.1.7		18	32.21	even	8
1024.6.a.k.1.12		18	32.5	even	8
1024.6.a.l.1.7		18	32.27	odd	8
1024.6.a.l.1.12		18	32.11	odd	8

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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	16.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.12805 + 2.38811i) q^{2} +(-4.57839 - 4.57839i) q^{3} +(20.5939 - 24.4927i) q^{4} +(48.5981 - 48.5981i) q^{5} +(34.4119 + 12.5445i) q^{6} -106.338i q^{7} +(-47.1150 + 174.780i) q^{8} -201.077i q^{9} +O(q^{10})\)	\(q+(-5.12805 + 2.38811i) q^{2} +(-4.57839 - 4.57839i) q^{3} +(20.5939 - 24.4927i) q^{4} +(48.5981 - 48.5981i) q^{5} +(34.4119 + 12.5445i) q^{6} -106.338i q^{7} +(-47.1150 + 174.780i) q^{8} -201.077i q^{9} +(-133.156 + 365.272i) q^{10} +(-184.984 + 184.984i) q^{11} +(-206.424 + 17.8505i) q^{12} +(3.64729 + 3.64729i) q^{13} +(253.947 + 545.308i) q^{14} -445.003 q^{15} +(-175.786 - 1008.80i) q^{16} +2064.90 q^{17} +(480.193 + 1031.13i) q^{18} +(-1259.62 - 1259.62i) q^{19} +(-189.478 - 2191.12i) q^{20} +(-486.857 + 486.857i) q^{21} +(506.846 - 1390.37i) q^{22} +3861.52i q^{23} +(1015.92 - 584.502i) q^{24} -1598.56i q^{25} +(-27.4136 - 9.99337i) q^{26} +(-2033.16 + 2033.16i) q^{27} +(-2604.51 - 2189.91i) q^{28} +(1959.96 + 1959.96i) q^{29} +(2282.00 - 1062.72i) q^{30} +2760.10 q^{31} +(3310.57 + 4753.38i) q^{32} +1693.86 q^{33} +(-10588.9 + 4931.21i) q^{34} +(-5167.83 - 5167.83i) q^{35} +(-4924.91 - 4140.94i) q^{36} +(-6432.63 + 6432.63i) q^{37} +(9467.48 + 3451.28i) q^{38} -33.3975i q^{39} +(6204.30 + 10783.7i) q^{40} -11296.7i q^{41} +(1333.96 - 3659.30i) q^{42} +(12927.8 - 12927.8i) q^{43} +(721.228 + 8340.31i) q^{44} +(-9771.95 - 9771.95i) q^{45} +(-9221.73 - 19802.1i) q^{46} +25827.2 q^{47} +(-3813.86 + 5423.49i) q^{48} +5499.20 q^{49} +(3817.54 + 8197.49i) q^{50} +(-9453.92 - 9453.92i) q^{51} +(164.444 - 14.2203i) q^{52} +(-21801.8 + 21801.8i) q^{53} +(5570.73 - 15281.5i) q^{54} +17979.8i q^{55} +(18585.8 + 5010.13i) q^{56} +11534.0i q^{57} +(-14731.4 - 5370.17i) q^{58} +(-14102.8 + 14102.8i) q^{59} +(-9164.32 + 10899.3i) q^{60} +(6211.40 + 6211.40i) q^{61} +(-14154.0 + 6591.43i) q^{62} -21382.1 q^{63} +(-28328.3 - 16469.6i) q^{64} +354.503 q^{65} +(-8686.21 + 4045.13i) q^{66} +(28659.0 + 28659.0i) q^{67} +(42524.2 - 50575.0i) q^{68} +(17679.5 - 17679.5i) q^{69} +(38842.3 + 14159.6i) q^{70} -29423.1i q^{71} +(35144.3 + 9473.74i) q^{72} -2857.88i q^{73} +(17625.0 - 48348.7i) q^{74} +(-7318.83 + 7318.83i) q^{75} +(-56791.8 + 4911.07i) q^{76} +(19670.9 + 19670.9i) q^{77} +(79.7568 + 171.264i) q^{78} -23387.3 q^{79} +(-57568.6 - 40482.9i) q^{80} -30244.5 q^{81} +(26977.7 + 57930.0i) q^{82} +(-24575.3 - 24575.3i) q^{83} +(1898.19 + 21950.7i) q^{84} +(100350. - 100350. i) q^{85} +(-35421.5 + 97167.7i) q^{86} -17946.9i q^{87} +(-23616.1 - 41047.2i) q^{88} +19340.2i q^{89} +(73447.6 + 26774.6i) q^{90} +(387.846 - 387.846i) q^{91} +(94579.1 + 79523.5i) q^{92} +(-12636.8 - 12636.8i) q^{93} +(-132443. + 61678.1i) q^{94} -122430. q^{95} +(6605.75 - 36919.9i) q^{96} +44218.7 q^{97} +(-28200.2 + 13132.7i) q^{98} +(37196.0 + 37196.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8}+O(q^{10}) \) 18 * q - 2 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^5 + 112 * q^6 + 244 * q^8	\( 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8} - 436 q^{10} - 606 q^{11} + 4 q^{12} - 2 q^{13} - 100 q^{14} + 1796 q^{15} - 872 q^{16} - 4 q^{17} - 3138 q^{18} - 2362 q^{19} + 2972 q^{20} + 484 q^{21} + 4420 q^{22} + 8368 q^{24} + 7368 q^{26} + 4216 q^{27} - 7336 q^{28} + 4070 q^{29} - 30444 q^{30} - 11536 q^{31} - 23992 q^{32} - 4 q^{33} - 1740 q^{34} + 8636 q^{35} + 6892 q^{36} - 10650 q^{37} + 53248 q^{38} + 75272 q^{40} + 33400 q^{42} - 15382 q^{43} - 40124 q^{44} + 5762 q^{45} - 92532 q^{46} + 44176 q^{47} - 147992 q^{48} - 14410 q^{49} - 85050 q^{50} - 2748 q^{51} + 91572 q^{52} + 24726 q^{53} + 208672 q^{54} + 191128 q^{56} + 106776 q^{58} - 29734 q^{59} - 154368 q^{60} - 48082 q^{61} - 273872 q^{62} - 12156 q^{63} - 283776 q^{64} + 27684 q^{65} - 153356 q^{66} - 75210 q^{67} + 133712 q^{68} + 22804 q^{69} + 412160 q^{70} + 470244 q^{72} + 147148 q^{74} + 154726 q^{75} - 87468 q^{76} + 41060 q^{77} - 631780 q^{78} - 52864 q^{79} - 554456 q^{80} - 13126 q^{81} - 93216 q^{82} + 227838 q^{83} + 190888 q^{84} - 138652 q^{85} + 470468 q^{86} + 590328 q^{88} + 280152 q^{90} - 231164 q^{91} - 221896 q^{92} + 180688 q^{93} - 460912 q^{94} - 250380 q^{95} - 597328 q^{96} - 4 q^{97} - 444646 q^{98} - 296770 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^5 + 112 * q^6 + 244 * q^8 - 436 * q^10 - 606 * q^11 + 4 * q^12 - 2 * q^13 - 100 * q^14 + 1796 * q^15 - 872 * q^16 - 4 * q^17 - 3138 * q^18 - 2362 * q^19 + 2972 * q^20 + 484 * q^21 + 4420 * q^22 + 8368 * q^24 + 7368 * q^26 + 4216 * q^27 - 7336 * q^28 + 4070 * q^29 - 30444 * q^30 - 11536 * q^31 - 23992 * q^32 - 4 * q^33 - 1740 * q^34 + 8636 * q^35 + 6892 * q^36 - 10650 * q^37 + 53248 * q^38 + 75272 * q^40 + 33400 * q^42 - 15382 * q^43 - 40124 * q^44 + 5762 * q^45 - 92532 * q^46 + 44176 * q^47 - 147992 * q^48 - 14410 * q^49 - 85050 * q^50 - 2748 * q^51 + 91572 * q^52 + 24726 * q^53 + 208672 * q^54 + 191128 * q^56 + 106776 * q^58 - 29734 * q^59 - 154368 * q^60 - 48082 * q^61 - 273872 * q^62 - 12156 * q^63 - 283776 * q^64 + 27684 * q^65 - 153356 * q^66 - 75210 * q^67 + 133712 * q^68 + 22804 * q^69 + 412160 * q^70 + 470244 * q^72 + 147148 * q^74 + 154726 * q^75 - 87468 * q^76 + 41060 * q^77 - 631780 * q^78 - 52864 * q^79 - 554456 * q^80 - 13126 * q^81 - 93216 * q^82 + 227838 * q^83 + 190888 * q^84 - 138652 * q^85 + 470468 * q^86 + 590328 * q^88 + 280152 * q^90 - 231164 * q^91 - 221896 * q^92 + 180688 * q^93 - 460912 * q^94 - 250380 * q^95 - 597328 * q^96 - 4 * q^97 - 444646 * q^98 - 296770 * q^99

Introduction

L-functions

Modular forms

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