LMFDB - Embedded newform 17.12.a.a.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,12,Mod(1,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("17.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	17.a (trivial)

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:	yes
Analytic conductor:	$13.0618340695$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 8440x^{4} - 21100x^{3} + 19034528x^{2} + 24205632x - 12354600960 $ x^6 - 3x^5 - 8440x^4 - 21100x^3 + 19034528x^2 + 24205632*x - 12354600960
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$78.1598$ of defining polynomial
Character	$\chi$	$=$	17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+76.1598 q^{2} -475.782 q^{3} +3752.32 q^{4} -7399.94 q^{5} -36235.5 q^{6} -16117.6 q^{7} +129800. q^{8} +49221.7 q^{9} +O(q^{10})$	\(q+76.1598 q^{2} -475.782 q^{3} +3752.32 q^{4} -7399.94 q^{5} -36235.5 q^{6} -16117.6 q^{7} +129800. q^{8} +49221.7 q^{9} -563578. q^{10} -768734. q^{11} -1.78528e6 q^{12} -283251. q^{13} -1.22751e6 q^{14} +3.52076e6 q^{15} +2.20082e6 q^{16} +1.41986e6 q^{17} +3.74872e6 q^{18} +1.38302e7 q^{19} -2.77669e7 q^{20} +7.66847e6 q^{21} -5.85466e7 q^{22} -2.22729e7 q^{23} -6.17567e7 q^{24} +5.93099e6 q^{25} -2.15723e7 q^{26} +6.08646e7 q^{27} -6.04784e7 q^{28} +1.69049e8 q^{29} +2.68140e8 q^{30} -1.63646e8 q^{31} -9.82167e7 q^{32} +3.65750e8 q^{33} +1.08136e8 q^{34} +1.19269e8 q^{35} +1.84695e8 q^{36} -8.00852e8 q^{37} +1.05331e9 q^{38} +1.34766e8 q^{39} -9.60515e8 q^{40} +1.34460e9 q^{41} +5.84029e8 q^{42} +5.27578e8 q^{43} -2.88453e9 q^{44} -3.64238e8 q^{45} -1.69630e9 q^{46} -4.34821e7 q^{47} -1.04711e9 q^{48} -1.71755e9 q^{49} +4.51703e8 q^{50} -6.75543e8 q^{51} -1.06285e9 q^{52} -7.98307e8 q^{53} +4.63543e9 q^{54} +5.68858e9 q^{55} -2.09207e9 q^{56} -6.58017e9 q^{57} +1.28748e10 q^{58} -7.30594e9 q^{59} +1.32110e10 q^{60} -7.72470e9 q^{61} -1.24633e10 q^{62} -7.93337e8 q^{63} -1.19875e10 q^{64} +2.09604e9 q^{65} +2.78554e10 q^{66} -3.43304e9 q^{67} +5.32775e9 q^{68} +1.05970e10 q^{69} +9.08353e9 q^{70} -1.76368e10 q^{71} +6.38900e9 q^{72} -1.27283e9 q^{73} -6.09927e10 q^{74} -2.82186e9 q^{75} +5.18953e10 q^{76} +1.23902e10 q^{77} +1.02637e10 q^{78} -1.03457e10 q^{79} -1.62860e10 q^{80} -3.76778e10 q^{81} +1.02404e11 q^{82} +2.61604e10 q^{83} +2.87745e10 q^{84} -1.05069e10 q^{85} +4.01802e10 q^{86} -8.04307e10 q^{87} -9.97819e10 q^{88} -2.52900e10 q^{89} -2.77403e10 q^{90} +4.56532e9 q^{91} -8.35748e10 q^{92} +7.78601e10 q^{93} -3.31159e9 q^{94} -1.02343e11 q^{95} +4.67298e10 q^{96} -7.42689e9 q^{97} -1.30808e11 q^{98} -3.78384e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 9 q^{2} - 476 q^{3} + 4613 q^{4} - 12884 q^{5} + 552 q^{6} - 23436 q^{7} + 74805 q^{8} + 296398 q^{9}+O(q^{10}) $ 6 * q - 9 * q^2 - 476 * q^3 + 4613 * q^4 - 12884 * q^5 + 552 * q^6 - 23436 * q^7 + 74805 * q^8 + 296398 * q^9	\( 6 q - 9 q^{2} - 476 q^{3} + 4613 q^{4} - 12884 q^{5} + 552 q^{6} - 23436 q^{7} + 74805 q^{8} + 296398 q^{9} - 676038 q^{10} - 962060 q^{11} - 2352344 q^{12} - 435268 q^{13} - 7990948 q^{14} - 9450288 q^{15} - 12496671 q^{16} + 8519142 q^{17} - 20195421 q^{18} - 26398480 q^{19} - 47202914 q^{20} - 56428792 q^{21} - 51774200 q^{22} - 99172772 q^{23} - 110557128 q^{24} + 66085866 q^{25} + 74451914 q^{26} + 105183712 q^{27} + 102848900 q^{28} + 165683964 q^{29} + 401475744 q^{30} - 199133468 q^{31} + 465766501 q^{32} + 518429376 q^{33} - 12778713 q^{34} + 804442912 q^{35} + 627274777 q^{36} - 785778644 q^{37} + 2174484940 q^{38} + 627357728 q^{39} + 657666206 q^{40} + 166444428 q^{41} + 652753248 q^{42} - 1110947880 q^{43} - 997577064 q^{44} - 1706447988 q^{45} - 1891667412 q^{46} - 5828211928 q^{47} - 2359114472 q^{48} - 1968801674 q^{49} - 126509183 q^{50} - 675851932 q^{51} - 6633403554 q^{52} - 9889898636 q^{53} - 1961072736 q^{54} - 10730153984 q^{55} + 5703448884 q^{56} - 13522850128 q^{57} + 14316796258 q^{58} + 204095112 q^{59} + 22313648592 q^{60} - 15864546948 q^{61} - 1838602020 q^{62} + 504344540 q^{63} + 6177095465 q^{64} + 12794774792 q^{65} + 56255165136 q^{66} + 17196640232 q^{67} + 6549800341 q^{68} + 2949266904 q^{69} + 52391765944 q^{70} + 8751653884 q^{71} + 38682669705 q^{72} - 13704156916 q^{73} - 9383651494 q^{74} - 15917467268 q^{75} + 59548672452 q^{76} - 12012382872 q^{77} + 35038956192 q^{78} - 89923384436 q^{79} + 25877503334 q^{80} - 152313828506 q^{81} + 57834669670 q^{82} - 26042106648 q^{83} + 3397466240 q^{84} - 18293437588 q^{85} + 29108045060 q^{86} - 195382431072 q^{87} - 228837945880 q^{88} + 53269579420 q^{89} - 10044062046 q^{90} - 226028668544 q^{91} - 9212077436 q^{92} - 62709484936 q^{93} + 83948222448 q^{94} - 170219637424 q^{95} + 116885663928 q^{96} - 106272517044 q^{97} + 132039821039 q^{98} - 10550584980 q^{99}+O(q^{100}) \) 6 * q - 9 * q^2 - 476 * q^3 + 4613 * q^4 - 12884 * q^5 + 552 * q^6 - 23436 * q^7 + 74805 * q^8 + 296398 * q^9 - 676038 * q^10 - 962060 * q^11 - 2352344 * q^12 - 435268 * q^13 - 7990948 * q^14 - 9450288 * q^15 - 12496671 * q^16 + 8519142 * q^17 - 20195421 * q^18 - 26398480 * q^19 - 47202914 * q^20 - 56428792 * q^21 - 51774200 * q^22 - 99172772 * q^23 - 110557128 * q^24 + 66085866 * q^25 + 74451914 * q^26 + 105183712 * q^27 + 102848900 * q^28 + 165683964 * q^29 + 401475744 * q^30 - 199133468 * q^31 + 465766501 * q^32 + 518429376 * q^33 - 12778713 * q^34 + 804442912 * q^35 + 627274777 * q^36 - 785778644 * q^37 + 2174484940 * q^38 + 627357728 * q^39 + 657666206 * q^40 + 166444428 * q^41 + 652753248 * q^42 - 1110947880 * q^43 - 997577064 * q^44 - 1706447988 * q^45 - 1891667412 * q^46 - 5828211928 * q^47 - 2359114472 * q^48 - 1968801674 * q^49 - 126509183 * q^50 - 675851932 * q^51 - 6633403554 * q^52 - 9889898636 * q^53 - 1961072736 * q^54 - 10730153984 * q^55 + 5703448884 * q^56 - 13522850128 * q^57 + 14316796258 * q^58 + 204095112 * q^59 + 22313648592 * q^60 - 15864546948 * q^61 - 1838602020 * q^62 + 504344540 * q^63 + 6177095465 * q^64 + 12794774792 * q^65 + 56255165136 * q^66 + 17196640232 * q^67 + 6549800341 * q^68 + 2949266904 * q^69 + 52391765944 * q^70 + 8751653884 * q^71 + 38682669705 * q^72 - 13704156916 * q^73 - 9383651494 * q^74 - 15917467268 * q^75 + 59548672452 * q^76 - 12012382872 * q^77 + 35038956192 * q^78 - 89923384436 * q^79 + 25877503334 * q^80 - 152313828506 * q^81 + 57834669670 * q^82 - 26042106648 * q^83 + 3397466240 * q^84 - 18293437588 * q^85 + 29108045060 * q^86 - 195382431072 * q^87 - 228837945880 * q^88 + 53269579420 * q^89 - 10044062046 * q^90 - 226028668544 * q^91 - 9212077436 * q^92 - 62709484936 * q^93 + 83948222448 * q^94 - 170219637424 * q^95 + 116885663928 * q^96 - 106272517044 * q^97 + 132039821039 * q^98 - 10550584980 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	76.1598	1.68291	0.841455	−	0.540327i	$-0.181700\pi$
$2$	76.1598	1.68291	0.841455	+	0.540327i	$0.181700\pi$
$3$	−475.782	−1.13042	−0.565212	−	0.824946i	$-0.691206\pi$
$3$	−475.782	−1.13042	−0.565212	+	0.824946i	$0.691206\pi$
$4$	3752.32	1.83219
$5$	−7399.94	−1.05899	−0.529497	−	0.848312i	$-0.677619\pi$
$5$	−7399.94	−1.05899	−0.529497	+	0.848312i	$0.677619\pi$
$6$	−36235.5	−1.90240
$7$	−16117.6	−0.362461	−0.181231	−	0.983441i	$-0.558008\pi$
$7$	−16117.6	−0.362461	−0.181231	+	0.983441i	$0.558008\pi$
$8$	129800.	1.40049
$9$	49221.7	0.277858
$10$	−563578.	−1.78219
$11$	−768734.	−1.43918	−0.719592	−	0.694397i	$-0.755671\pi$
$11$	−768734.	−1.43918	−0.719592	+	0.694397i	$0.755671\pi$
$12$	−1.78528e6	−2.07115
$13$	−283251.	−0.211584	−0.105792	−	0.994388i	$-0.533738\pi$
$13$	−283251.	−0.211584	−0.105792	+	0.994388i	$0.533738\pi$
$14$	−1.22751e6	−0.609989
$15$	3.52076e6	1.19711
$16$	2.20082e6	0.524717
$17$	1.41986e6	0.242536
$17$	1.41986e6	0.242536
$18$	3.74872e6	0.467610
$19$	1.38302e7	1.28140	0.640699	−	0.767792i	$-0.278645\pi$
$19$	1.38302e7	1.28140	0.640699	+	0.767792i	$0.278645\pi$
$20$	−2.77669e7	−1.94027
$21$	7.66847e6	0.409735
$22$	−5.85466e7	−2.42202
$23$	−2.22729e7	−0.721561	−0.360780	−	0.932651i	$-0.617490\pi$
$23$	−2.22729e7	−0.721561	−0.360780	+	0.932651i	$0.617490\pi$
$24$	−6.17567e7	−1.58315
$25$	5.93099e6	0.121467
$26$	−2.15723e7	−0.356076
$27$	6.08646e7	0.816326
$28$	−6.04784e7	−0.664096
$29$	1.69049e8	1.53047	0.765235	−	0.643751i	$-0.222623\pi$
$29$	1.69049e8	1.53047	0.765235	+	0.643751i	$0.222623\pi$
$30$	2.68140e8	2.01463
$31$	−1.63646e8	−1.02664	−0.513319	−	0.858198i	$-0.671584\pi$
$31$	−1.63646e8	−1.02664	−0.513319	+	0.858198i	$0.671584\pi$
$32$	−9.82167e7	−0.517440
$33$	3.65750e8	1.62689
$34$	1.08136e8	0.408166
$35$	1.19269e8	0.383844
$36$	1.84695e8	0.509088
$37$	−8.00852e8	−1.89864	−0.949320	−	0.314311i	$-0.898226\pi$
$37$	−8.00852e8	−1.89864	−0.949320	+	0.314311i	$0.898226\pi$
$38$	1.05331e9	2.15648
$39$	1.34766e8	0.239179
$40$	−9.60515e8	−1.48311
$41$	1.34460e9	1.81251	0.906257	−	0.422726i	$-0.138927\pi$
$41$	1.34460e9	1.81251	0.906257	+	0.422726i	$0.138927\pi$
$42$	5.84029e8	0.689546
$43$	5.27578e8	0.547281	0.273640	−	0.961832i	$-0.411772\pi$
$43$	5.27578e8	0.547281	0.273640	+	0.961832i	$0.411772\pi$
$44$	−2.88453e9	−2.63685
$45$	−3.64238e8	−0.294250
$46$	−1.69630e9	−1.21432
$47$	−4.34821e7	−0.0276549	−0.0138275	−	0.999904i	$-0.504402\pi$
$47$	−4.34821e7	−0.0276549	−0.0138275	+	0.999904i	$0.504402\pi$
$48$	−1.04711e9	−0.593153
$49$	−1.71755e9	−0.868622
$50$	4.51703e8	0.204417
$51$	−6.75543e8	−0.274168
$52$	−1.06285e9	−0.387661
$53$	−7.98307e8	−0.262212	−0.131106	−	0.991368i	$-0.541853\pi$
$53$	−7.98307e8	−0.262212	−0.131106	+	0.991368i	$0.541853\pi$
$54$	4.63543e9	1.37380
$55$	5.68858e9	1.52409
$56$	−2.09207e9	−0.507624
$57$	−6.58017e9	−1.44852
$58$	1.28748e10	2.57564
$59$	−7.30594e9	−1.33042	−0.665212	−	0.746655i	$-0.731659\pi$
$59$	−7.30594e9	−1.33042	−0.665212	+	0.746655i	$0.731659\pi$
$60$	1.32110e10	2.19333
$61$	−7.72470e9	−1.17103	−0.585514	−	0.810662i	$-0.699107\pi$
$61$	−7.72470e9	−1.17103	−0.585514	+	0.810662i	$0.699107\pi$
$62$	−1.24633e10	−1.72774
$63$	−7.93337e8	−0.100713
$64$	−1.19875e10	−1.39552
$65$	2.09604e9	0.224066
$66$	2.78554e10	2.73791
$67$	−3.43304e9	−0.310647	−0.155324	−	0.987864i	$-0.549642\pi$
$67$	−3.43304e9	−0.310647	−0.155324	+	0.987864i	$0.549642\pi$
$68$	5.32775e9	0.444370
$69$	1.05970e10	0.815670
$70$	9.08353e9	0.645975
$71$	−1.76368e10	−1.16011	−0.580054	−	0.814578i	$-0.696969\pi$
$71$	−1.76368e10	−1.16011	−0.580054	+	0.814578i	$0.696969\pi$
$72$	6.38900e9	0.389138
$73$	−1.27283e9	−0.0718613	−0.0359307	−	0.999354i	$-0.511440\pi$
$73$	−1.27283e9	−0.0718613	−0.0359307	+	0.999354i	$0.511440\pi$
$74$	−6.09927e10	−3.19524
$75$	−2.82186e9	−0.137309
$76$	5.18953e10	2.34776
$77$	1.23902e10	0.521648
$78$	1.02637e10	0.402517
$79$	−1.03457e10	−0.378279	−0.189140	−	0.981950i	$-0.560570\pi$
$79$	−1.03457e10	−0.378279	−0.189140	+	0.981950i	$0.560570\pi$
$80$	−1.62860e10	−0.555672
$81$	−3.76778e10	−1.20065
$82$	1.02404e11	3.05030
$83$	2.61604e10	0.728979	0.364490	−	0.931207i	$-0.381243\pi$
$83$	2.61604e10	0.728979	0.364490	+	0.931207i	$0.381243\pi$
$84$	2.87745e10	0.750710
$85$	−1.05069e10	−0.256844
$86$	4.01802e10	0.921024
$87$	−8.04307e10	−1.73008
$88$	−9.97819e10	−2.01557
$89$	−2.52900e10	−0.480069	−0.240034	−	0.970764i	$-0.577159\pi$
$89$	−2.52900e10	−0.480069	−0.240034	+	0.970764i	$0.577159\pi$
$90$	−2.77403e10	−0.495196
$91$	4.56532e9	0.0766909
$92$	−8.35748e10	−1.32203
$93$	7.78601e10	1.16054
$94$	−3.31159e9	−0.0465407
$95$	−1.02343e11	−1.35699
$96$	4.67298e10	0.584927
$97$	−7.42689e9	−0.0878137	−0.0439068	−	0.999036i	$-0.513980\pi$
$97$	−7.42689e9	−0.0878137	−0.0439068	+	0.999036i	$0.513980\pi$
$98$	−1.30808e11	−1.46181
$99$	−3.78384e10	−0.399889
$100$	2.22549e10	0.222549
$101$	1.35463e11	1.28249	0.641245	−	0.767336i	$-0.278418\pi$
$101$	1.35463e11	1.28249	0.641245	+	0.767336i	$0.278418\pi$
$102$	−5.14492e10	−0.461400
$103$	−9.51262e9	−0.0808528	−0.0404264	−	0.999183i	$-0.512872\pi$
$103$	−9.51262e9	−0.0808528	−0.0404264	+	0.999183i	$0.512872\pi$
$104$	−3.67660e10	−0.296321
$105$	−5.67462e10	−0.433906
$106$	−6.07989e10	−0.441279
$107$	−5.06496e10	−0.349113	−0.174556	−	0.984647i	$-0.555849\pi$
$107$	−5.06496e10	−0.349113	−0.174556	+	0.984647i	$0.555849\pi$
$108$	2.28383e11	1.49566
$109$	2.62842e11	1.63625	0.818125	−	0.575040i	$-0.195014\pi$
$109$	2.62842e11	1.63625	0.818125	+	0.575040i	$0.195014\pi$
$110$	4.33241e11	2.56490
$111$	3.81031e11	2.14627
$112$	−3.54720e10	−0.190190
$113$	8.92005e10	0.455445	0.227723	−	0.973726i	$-0.426872\pi$
$113$	8.92005e10	0.455445	0.227723	+	0.973726i	$0.426872\pi$
$114$	−5.01144e11	−2.43773
$115$	1.64818e11	0.764128
$116$	6.34327e11	2.80410
$117$	−1.39421e10	−0.0587903
$118$	−5.56419e11	−2.23898
$119$	−2.28847e10	−0.0879097
$120$	4.56996e11	1.67655
$121$	3.05640e11	1.07125
$122$	−5.88311e11	−1.97074
$123$	−6.39736e11	−2.04891
$124$	−6.14053e11	−1.88099
$125$	3.17436e11	0.930361
$126$	−6.04204e10	−0.169490
$127$	−6.19553e11	−1.66402	−0.832010	−	0.554761i	$-0.812810\pi$
$127$	−6.19553e11	−1.66402	−0.832010	+	0.554761i	$0.812810\pi$
$128$	−7.11814e11	−1.83110
$129$	−2.51012e11	−0.618659
$130$	1.59634e11	0.377082
$131$	−4.89145e11	−1.10776	−0.553879	−	0.832597i	$-0.686853\pi$
$131$	−4.89145e11	−1.10776	−0.553879	+	0.832597i	$0.686853\pi$
$132$	1.37241e12	2.98076
$133$	−2.22910e11	−0.464457
$134$	−2.61460e11	−0.522791
$135$	−4.50394e11	−0.864484
$136$	1.84298e11	0.339669
$137$	1.01540e12	1.79752	0.898759	−	0.438442i	$-0.144470\pi$
$137$	1.01540e12	1.79752	0.898759	+	0.438442i	$0.144470\pi$
$138$	8.07068e11	1.37270
$139$	1.06408e12	1.73938	0.869689	−	0.493599i	$-0.164319\pi$
$139$	1.06408e12	1.73938	0.869689	+	0.493599i	$0.164319\pi$
$140$	4.47536e11	0.703273
$141$	2.06880e10	0.0312618
$142$	−1.34321e12	−1.95236
$143$	2.17744e11	0.304508
$144$	1.08328e11	0.145797
$145$	−1.25096e12	−1.62076
$146$	−9.69386e10	−0.120936
$147$	8.17179e11	0.981911
$148$	−3.00505e12	−3.47866
$149$	−4.67984e11	−0.522043	−0.261022	−	0.965333i	$-0.584059\pi$
$149$	−4.67984e11	−0.522043	−0.261022	+	0.965333i	$0.584059\pi$
$150$	−2.14912e11	−0.231078
$151$	4.00323e9	0.00414990	0.00207495	−	0.999998i	$-0.499340\pi$
$151$	4.00323e9	0.00414990	0.00207495	+	0.999998i	$0.499340\pi$
$152$	1.79517e12	1.79459
$153$	6.98878e10	0.0673905
$154$	9.43632e11	0.877887
$155$	1.21097e12	1.08720
$156$	5.05683e11	0.438221
$157$	5.60352e11	0.468828	0.234414	−	0.972137i	$-0.424683\pi$
$157$	5.60352e11	0.468828	0.234414	+	0.972137i	$0.424683\pi$
$158$	−7.87929e11	−0.636610
$159$	3.79820e11	0.296411
$160$	7.26798e11	0.547966
$161$	3.58985e11	0.261538
$162$	−2.86953e12	−2.02059
$163$	−6.39408e11	−0.435257	−0.217629	−	0.976032i	$-0.569832\pi$
$163$	−6.39408e11	−0.435257	−0.217629	+	0.976032i	$0.569832\pi$
$164$	5.04536e12	3.32086
$165$	−2.70653e12	−1.72286
$166$	1.99237e12	1.22681
$167$	−8.88645e10	−0.0529405	−0.0264702	−	0.999650i	$-0.508427\pi$
$167$	−8.88645e10	−0.0529405	−0.0264702	+	0.999650i	$0.508427\pi$
$168$	9.95370e11	0.573830
$169$	−1.71193e12	−0.955232
$170$	−8.00200e11	−0.432245
$171$	6.80747e11	0.356047
$172$	1.97964e12	1.00272
$173$	−4.51720e11	−0.221624	−0.110812	−	0.993841i	$-0.535345\pi$
$173$	−4.51720e11	−0.221624	−0.110812	+	0.993841i	$0.535345\pi$
$174$	−6.12559e12	−2.91157
$175$	−9.55933e10	−0.0440269
$176$	−1.69185e12	−0.755165
$177$	3.47604e12	1.50394
$178$	−1.92608e12	−0.807913
$179$	2.73087e12	1.11073	0.555366	−	0.831606i	$-0.312578\pi$
$179$	2.73087e12	1.11073	0.555366	+	0.831606i	$0.312578\pi$
$180$	−1.36674e12	−0.539120
$181$	−7.72678e11	−0.295642	−0.147821	−	0.989014i	$-0.547226\pi$
$181$	−7.72678e11	−0.295642	−0.147821	+	0.989014i	$0.547226\pi$
$182$	3.47694e11	0.129064
$183$	3.67527e12	1.32376
$184$	−2.89102e12	−1.01054
$185$	5.92625e12	2.01065
$186$	5.92981e12	1.95308
$187$	−1.09149e12	−0.349053
$188$	−1.63158e11	−0.0506689
$189$	−9.80991e11	−0.295887
$190$	−7.79440e12	−2.28369
$191$	−5.54018e12	−1.57703	−0.788516	−	0.615014i	$-0.789150\pi$
$191$	−5.54018e12	−1.57703	−0.788516	+	0.615014i	$0.789150\pi$
$192$	5.70342e12	1.57753
$193$	−2.70102e12	−0.726044	−0.363022	−	0.931781i	$-0.618255\pi$
$193$	−2.70102e12	−0.726044	−0.363022	+	0.931781i	$0.618255\pi$
$194$	−5.65630e11	−0.147783
$195$	−9.97257e11	−0.253289
$196$	−6.44479e12	−1.59148
$197$	4.43950e12	1.06603	0.533016	−	0.846105i	$-0.321059\pi$
$197$	4.43950e12	1.06603	0.533016	+	0.846105i	$0.321059\pi$
$198$	−2.88177e12	−0.672977
$199$	3.06245e10	0.00695628	0.00347814	−	0.999994i	$-0.498893\pi$
$199$	3.06245e10	0.00695628	0.00347814	+	0.999994i	$0.498893\pi$
$200$	7.69844e11	0.170113
$201$	1.63338e12	0.351163
$202$	1.03169e13	2.15831
$203$	−2.72467e12	−0.554736
$204$	−2.53485e12	−0.502327
$205$	−9.94995e12	−1.91944
$206$	−7.24479e11	−0.136068
$207$	−1.09631e12	−0.200492
$208$	−6.23385e11	−0.111022
$209$	−1.06318e13	−1.84417
$210$	−4.32178e12	−0.730225
$211$	−4.89518e11	−0.0805778	−0.0402889	−	0.999188i	$-0.512828\pi$
$211$	−4.89518e11	−0.0805778	−0.0402889	+	0.999188i	$0.512828\pi$
$212$	−2.99550e12	−0.480421
$213$	8.39127e12	1.31141
$214$	−3.85747e12	−0.587525
$215$	−3.90405e12	−0.579567
$216$	7.90024e12	1.14326
$217$	2.63759e12	0.372116
$218$	2.00180e13	2.75366
$219$	6.05591e11	0.0812337
$220$	2.13454e13	2.79241
$221$	−4.02175e11	−0.0513166
$222$	2.90192e13	3.61198
$223$	−1.35603e13	−1.64662	−0.823310	−	0.567592i	$-0.807875\pi$
$223$	−1.35603e13	−1.64662	−0.823310	+	0.567592i	$0.807875\pi$
$224$	1.58302e12	0.187552
$225$	2.91933e11	0.0337505
$226$	6.79350e12	0.766473
$227$	−7.12110e12	−0.784160	−0.392080	−	0.919931i	$-0.628244\pi$
$227$	−7.12110e12	−0.784160	−0.392080	+	0.919931i	$0.628244\pi$
$228$	−2.46909e13	−2.65396
$229$	4.45926e12	0.467916	0.233958	−	0.972247i	$-0.424832\pi$
$229$	4.45926e12	0.467916	0.233958	+	0.972247i	$0.424832\pi$
$230$	1.25525e13	1.28596
$231$	−5.89501e12	−0.589684
$232$	2.19427e13	2.14341
$233$	−1.23638e13	−1.17949	−0.589746	−	0.807589i	$-0.700772\pi$
$233$	−1.23638e13	−1.17949	−0.589746	+	0.807589i	$0.700772\pi$
$234$	−1.06183e12	−0.0989387
$235$	3.21765e11	0.0292864
$236$	−2.74142e13	−2.43758
$237$	4.92232e12	0.427616
$238$	−1.74289e12	−0.147944
$239$	−1.49142e13	−1.23712	−0.618560	−	0.785738i	$-0.712284\pi$
$239$	−1.49142e13	−1.23712	−0.618560	+	0.785738i	$0.712284\pi$
$240$	7.74858e12	0.628145
$241$	2.35950e13	1.86950	0.934751	−	0.355305i	$-0.115623\pi$
$241$	2.35950e13	1.86950	0.934751	+	0.355305i	$0.115623\pi$
$242$	2.32775e13	1.80282
$243$	7.14443e12	0.540920
$244$	−2.89855e13	−2.14554
$245$	1.27098e13	0.919865
$246$	−4.87222e13	−3.44813
$247$	−3.91742e12	−0.271123
$248$	−2.12414e13	−1.43780
$249$	−1.24467e13	−0.824056
$250$	2.41759e13	1.56571
$251$	−1.53328e12	−0.0971439	−0.0485720	−	0.998820i	$-0.515467\pi$
$251$	−1.53328e12	−0.0971439	−0.0485720	+	0.998820i	$0.515467\pi$
$252$	−2.97685e12	−0.184524
$253$	1.71219e13	1.03846
$254$	−4.71851e13	−2.80039
$255$	4.99898e12	0.290342
$256$	−2.96613e13	−1.68605
$257$	1.92655e13	1.07189	0.535943	−	0.844254i	$-0.319956\pi$
$257$	1.92655e13	1.07189	0.535943	+	0.844254i	$0.319956\pi$
$258$	−1.91170e13	−1.04115
$259$	1.29078e13	0.688183
$260$	7.86499e12	0.410530
$261$	8.32090e12	0.425253
$262$	−3.72532e13	−1.86426
$263$	1.22053e13	0.598127	0.299064	−	0.954233i	$-0.403326\pi$
$263$	1.22053e13	0.598127	0.299064	+	0.954233i	$0.403326\pi$
$264$	4.74745e13	2.27844
$265$	5.90743e12	0.277681
$266$	−1.69768e13	−0.781639
$267$	1.20325e13	0.542681
$268$	−1.28819e13	−0.569163
$269$	1.22809e13	0.531608	0.265804	−	0.964027i	$-0.414363\pi$
$269$	1.22809e13	0.531608	0.265804	+	0.964027i	$0.414363\pi$
$270$	−3.43019e13	−1.45485
$271$	−2.60433e13	−1.08234	−0.541172	−	0.840912i	$-0.682019\pi$
$271$	−2.60433e13	−1.08234	−0.541172	+	0.840912i	$0.682019\pi$
$272$	3.12486e12	0.127263
$273$	−2.17210e12	−0.0866932
$274$	7.73326e13	3.02506
$275$	−4.55935e12	−0.174813
$276$	3.97634e13	1.49446
$277$	9.77448e12	0.360126	0.180063	−	0.983655i	$-0.442370\pi$
$277$	9.77448e12	0.360126	0.180063	+	0.983655i	$0.442370\pi$
$278$	8.10404e13	2.92722
$279$	−8.05496e12	−0.285260
$280$	1.54812e13	0.537570
$281$	2.78423e13	0.948025	0.474013	−	0.880518i	$-0.342805\pi$
$281$	2.78423e13	0.948025	0.474013	+	0.880518i	$0.342805\pi$
$282$	1.57559e12	0.0526107
$283$	−2.97423e13	−0.973979	−0.486990	−	0.873408i	$-0.661905\pi$
$283$	−2.97423e13	−0.973979	−0.486990	+	0.873408i	$0.661905\pi$
$284$	−6.61788e13	−2.12553
$285$	4.86929e13	1.53398
$286$	1.65834e13	0.512459
$287$	−2.16717e13	−0.656966
$288$	−4.83439e12	−0.143775
$289$	2.01599e12	0.0588235
$290$	−9.52725e13	−2.72759
$291$	3.53358e12	0.0992667
$292$	−4.77606e12	−0.131663
$293$	7.27084e12	0.196704	0.0983519	−	0.995152i	$-0.468643\pi$
$293$	7.27084e12	0.196704	0.0983519	+	0.995152i	$0.468643\pi$
$294$	6.22362e13	1.65247
$295$	5.40635e13	1.40891
$296$	−1.03951e14	−2.65903
$297$	−4.67887e13	−1.17484
$298$	−3.56416e13	−0.878551
$299$	6.30880e12	0.152671
$300$	−1.05885e13	−0.251575
$301$	−8.50330e12	−0.198368
$302$	3.04886e11	0.00698391
$303$	−6.44510e13	−1.44976
$304$	3.04379e13	0.672372
$305$	5.71623e13	1.24011
$306$	5.32264e12	0.113412
$307$	−8.69319e13	−1.81936	−0.909679	−	0.415313i	$-0.863672\pi$
$307$	−8.69319e13	−1.81936	−0.909679	+	0.415313i	$0.863672\pi$
$308$	4.64918e13	0.955756
$309$	4.52593e12	0.0913980
$310$	9.22275e13	1.82966
$311$	8.64207e13	1.68436	0.842181	−	0.539195i	$-0.181271\pi$
$311$	8.64207e13	1.68436	0.842181	+	0.539195i	$0.181271\pi$
$312$	1.74926e13	0.334969
$313$	−6.33787e13	−1.19248	−0.596238	−	0.802808i	$-0.703339\pi$
$313$	−6.33787e13	−1.19248	−0.596238	+	0.802808i	$0.703339\pi$
$314$	4.26763e13	0.788995
$315$	5.87064e12	0.106654
$316$	−3.88205e13	−0.693077
$317$	8.75797e13	1.53666	0.768329	−	0.640055i	$-0.221088\pi$
$317$	8.75797e13	1.53666	0.768329	+	0.640055i	$0.221088\pi$
$318$	2.89270e13	0.498833
$319$	−1.29954e14	−2.20263
$320$	8.87064e13	1.47785
$321$	2.40982e13	0.394645
$322$	2.73402e13	0.440144
$323$	1.96369e13	0.310785
$324$	−1.41379e14	−2.19982
$325$	−1.67995e12	−0.0257004
$326$	−4.86972e13	−0.732499
$327$	−1.25056e14	−1.84966
$328$	1.74529e14	2.53841
$329$	7.00827e11	0.0100238
$330$	−2.06129e14	−2.89942
$331$	4.31249e13	0.596588	0.298294	−	0.954474i	$-0.403582\pi$
$331$	4.31249e13	0.596588	0.298294	+	0.954474i	$0.403582\pi$
$332$	9.81622e13	1.33563
$333$	−3.94193e13	−0.527552
$334$	−6.76790e12	−0.0890940
$335$	2.54043e13	0.328973
$336$	1.68770e13	0.214995
$337$	−7.57883e13	−0.949813	−0.474906	−	0.880036i	$-0.657518\pi$
$337$	−7.57883e13	−0.949813	−0.474906	+	0.880036i	$0.657518\pi$
$338$	−1.30380e14	−1.60757
$339$	−4.24400e13	−0.514846
$340$	−3.94250e13	−0.470585
$341$	1.25801e14	1.47752
$342$	5.18456e13	0.599195
$343$	5.95526e13	0.677303
$344$	6.84798e13	0.766463
$345$	−7.84174e13	−0.863789
$346$	−3.44029e13	−0.372973
$347$	−4.92183e13	−0.525188	−0.262594	−	0.964906i	$-0.584578\pi$
$347$	−4.92183e13	−0.525188	−0.262594	+	0.964906i	$0.584578\pi$
$348$	−3.01801e14	−3.16983
$349$	−5.55652e12	−0.0574464	−0.0287232	−	0.999587i	$-0.509144\pi$
$349$	−5.55652e12	−0.0574464	−0.0287232	+	0.999587i	$0.509144\pi$
$350$	−7.28037e12	−0.0740933
$351$	−1.72399e13	−0.172721
$352$	7.55025e13	0.744692
$353$	−1.17001e14	−1.13613	−0.568066	−	0.822983i	$-0.692308\pi$
$353$	−1.17001e14	−1.13613	−0.568066	+	0.822983i	$0.692308\pi$
$354$	2.64734e14	2.53100
$355$	1.30511e14	1.22855
$356$	−9.48960e13	−0.879575
$357$	1.08881e13	0.0993753
$358$	2.07983e14	1.86926
$359$	4.43308e13	0.392361	0.196181	−	0.980568i	$-0.437146\pi$
$359$	4.43308e13	0.392361	0.196181	+	0.980568i	$0.437146\pi$
$360$	−4.72782e13	−0.412095
$361$	7.47845e13	0.641981
$362$	−5.88470e13	−0.497539
$363$	−1.45418e14	−1.21097
$364$	1.71305e13	0.140512
$365$	9.41888e12	0.0761006
$366$	2.79908e14	2.22777
$367$	−1.42957e14	−1.12084	−0.560420	−	0.828209i	$-0.689360\pi$
$367$	−1.42957e14	−1.12084	−0.560420	+	0.828209i	$0.689360\pi$
$368$	−4.90187e13	−0.378616
$369$	6.61835e13	0.503622
$370$	4.51342e14	3.38374
$371$	1.28668e13	0.0950417
$372$	2.92156e14	2.12632
$373$	1.83233e14	1.31403	0.657016	−	0.753876i	$-0.271818\pi$
$373$	1.83233e14	1.31403	0.657016	+	0.753876i	$0.271818\pi$
$374$	−8.31278e13	−0.587425
$375$	−1.51031e14	−1.05170
$376$	−5.64399e12	−0.0387305
$377$	−4.78833e13	−0.323822
$378$	−7.47121e13	−0.497950
$379$	−6.95045e13	−0.456560	−0.228280	−	0.973596i	$-0.573310\pi$
$379$	−6.95045e13	−0.456560	−0.228280	+	0.973596i	$0.573310\pi$
$380$	−3.84022e14	−2.48626
$381$	2.94773e14	1.88105
$382$	−4.21939e14	−2.65400
$383$	5.53414e13	0.343128	0.171564	−	0.985173i	$-0.445118\pi$
$383$	5.53414e13	0.343128	0.171564	+	0.985173i	$0.445118\pi$
$384$	3.38669e14	2.06992
$385$	−9.16864e13	−0.552422
$386$	−2.05709e14	−1.22187
$387$	2.59683e13	0.152066
$388$	−2.78680e13	−0.160891
$389$	−1.47052e14	−0.837046	−0.418523	−	0.908206i	$-0.637452\pi$
$389$	−1.47052e14	−0.837046	−0.418523	+	0.908206i	$0.637452\pi$
$390$	−7.59509e13	−0.426263
$391$	−3.16243e13	−0.175004
$392$	−2.22938e14	−1.21650
$393$	2.32726e14	1.25224
$394$	3.38112e14	1.79404
$395$	7.65578e13	0.400595
$396$	−1.41982e14	−0.732671
$397$	−3.15799e14	−1.60718	−0.803588	−	0.595187i	$-0.797078\pi$
$397$	−3.15799e14	−1.60718	−0.803588	+	0.595187i	$0.797078\pi$
$398$	2.33235e12	0.0117068
$399$	1.06057e14	0.525033
$400$	1.30531e13	0.0637356
$401$	−3.27022e14	−1.57501	−0.787503	−	0.616311i	$-0.788627\pi$
$401$	−3.27022e14	−1.57501	−0.787503	+	0.616311i	$0.788627\pi$
$402$	1.24398e14	0.590976
$403$	4.63529e13	0.217220
$404$	5.08301e14	2.34976
$405$	2.78813e14	1.27148
$406$	−2.07510e14	−0.933570
$407$	6.15642e14	2.73249
$408$	−8.76857e13	−0.383970
$409$	1.01721e14	0.439475	0.219737	−	0.975559i	$-0.429480\pi$
$409$	1.01721e14	0.439475	0.219737	+	0.975559i	$0.429480\pi$
$410$	−7.57786e14	−3.23025
$411$	−4.83109e14	−2.03196
$412$	−3.56943e13	−0.148137
$413$	1.17754e14	0.482227
$414$	−8.34947e13	−0.337409
$415$	−1.93586e14	−0.771984
$416$	2.78199e13	0.109482
$417$	−5.06272e14	−1.96624
$418$	−8.09712e14	−3.10357
$419$	1.00005e14	0.378308	0.189154	−	0.981947i	$-0.439426\pi$
$419$	1.00005e14	0.378308	0.189154	+	0.981947i	$0.439426\pi$
$420$	−2.12930e14	−0.794997
$421$	−8.46893e13	−0.312088	−0.156044	−	0.987750i	$-0.549874\pi$
$421$	−8.46893e13	−0.312088	−0.156044	+	0.987750i	$0.549874\pi$
$422$	−3.72816e13	−0.135605
$423$	−2.14026e12	−0.00768414
$424$	−1.03621e14	−0.367226
$425$	8.42115e12	0.0294600
$426$	6.39077e14	2.20699
$427$	1.24504e14	0.424452
$428$	−1.90053e14	−0.639639
$429$	−1.03599e14	−0.344223
$430$	−2.97331e14	−0.975358
$431$	2.95783e14	0.957963	0.478981	−	0.877825i	$-0.341006\pi$
$431$	2.95783e14	0.957963	0.478981	+	0.877825i	$0.341006\pi$
$432$	1.33952e14	0.428341
$433$	2.49989e14	0.789292	0.394646	−	0.918833i	$-0.370867\pi$
$433$	2.49989e14	0.789292	0.394646	+	0.918833i	$0.370867\pi$
$434$	2.00878e14	0.626238
$435$	5.95182e14	1.83214
$436$	9.86268e14	2.99791
$437$	−3.08038e14	−0.924607
$438$	4.61217e13	0.136709
$439$	1.65198e14	0.483561	0.241780	−	0.970331i	$-0.422269\pi$
$439$	1.65198e14	0.483561	0.241780	+	0.970331i	$0.422269\pi$
$440$	7.38380e14	2.13447
$441$	−8.45408e13	−0.241354
$442$	−3.06296e13	−0.0863612
$443$	−1.91709e14	−0.533852	−0.266926	−	0.963717i	$-0.586008\pi$
$443$	−1.91709e14	−0.533852	−0.266926	+	0.963717i	$0.586008\pi$
$444$	1.42975e15	3.93236
$445$	1.87144e14	0.508390
$446$	−1.03275e15	−2.77111
$447$	2.22658e14	0.590130
$448$	1.93209e14	0.505823
$449$	6.04457e14	1.56318	0.781592	−	0.623790i	$-0.214408\pi$
$449$	6.04457e14	1.56318	0.781592	+	0.623790i	$0.214408\pi$
$450$	2.22336e13	0.0567990
$451$	−1.03364e15	−2.60854
$452$	3.34709e14	0.834460
$453$	−1.90467e12	−0.00469115
$454$	−5.42341e14	−1.31967
$455$	−3.37831e13	−0.0812151
$456$	−8.54108e14	−2.02865
$457$	2.52943e14	0.593586	0.296793	−	0.954942i	$-0.404083\pi$
$457$	2.52943e14	0.593586	0.296793	+	0.954942i	$0.404083\pi$
$458$	3.39616e14	0.787460
$459$	8.64190e13	0.197988
$460$	6.18449e14	1.40002
$461$	4.85126e14	1.08517	0.542587	−	0.839999i	$-0.317445\pi$
$461$	4.85126e14	1.08517	0.542587	+	0.839999i	$0.317445\pi$
$462$	−4.48963e14	−0.992384
$463$	−4.08320e14	−0.891878	−0.445939	−	0.895063i	$-0.647130\pi$
$463$	−4.08320e14	−0.891878	−0.445939	+	0.895063i	$0.647130\pi$
$464$	3.72048e14	0.803064
$465$	−5.76160e14	−1.22900
$466$	−9.41625e14	−1.98498
$467$	−3.96079e14	−0.825161	−0.412581	−	0.910921i	$-0.635373\pi$
$467$	−3.96079e14	−0.825161	−0.412581	+	0.910921i	$0.635373\pi$
$468$	−5.23151e13	−0.107715
$469$	5.53324e13	0.112598
$470$	2.45055e13	0.0492863
$471$	−2.66606e14	−0.529974
$472$	−9.48313e14	−1.86325
$473$	−4.05567e14	−0.787638
$474$	3.74883e14	0.719639
$475$	8.20268e13	0.155647
$476$	−8.58706e13	−0.161067
$477$	−3.92941e13	−0.0728578
$478$	−1.13586e15	−2.08196
$479$	4.61502e14	0.836235	0.418117	−	0.908393i	$-0.362690\pi$
$479$	4.61502e14	0.836235	0.418117	+	0.908393i	$0.362690\pi$
$480$	−3.45797e14	−0.619434
$481$	2.26842e14	0.401721
$482$	1.79699e15	3.14620
$483$	−1.70799e14	−0.295648
$484$	1.14686e15	1.96273
$485$	5.49585e13	0.0929941
$486$	5.44119e14	0.910320
$487$	−2.88323e14	−0.476946	−0.238473	−	0.971149i	$-0.576647\pi$
$487$	−2.88323e14	−0.476946	−0.238473	+	0.971149i	$0.576647\pi$
$488$	−1.00267e15	−1.64002
$489$	3.04219e14	0.492025
$490$	9.67973e14	1.54805
$491$	5.19531e14	0.821606	0.410803	−	0.911724i	$-0.365248\pi$
$491$	5.19531e14	0.821606	0.410803	+	0.911724i	$0.365248\pi$
$492$	−2.40049e15	−3.75398
$493$	2.40026e14	0.371193
$494$	−2.98350e14	−0.456276
$495$	2.80002e14	0.423480
$496$	−3.60157e14	−0.538695
$497$	2.84263e14	0.420494
$498$	−9.47936e14	−1.38681
$499$	9.36393e14	1.35489	0.677446	−	0.735572i	$-0.263087\pi$
$499$	9.36393e14	1.35489	0.677446	+	0.735572i	$0.263087\pi$
$500$	1.19112e15	1.70459
$501$	4.22802e13	0.0598452
$502$	−1.16774e14	−0.163484
$503$	−6.40511e14	−0.886957	−0.443479	−	0.896285i	$-0.646256\pi$
$503$	−6.40511e14	−0.886957	−0.443479	+	0.896285i	$0.646256\pi$
$504$	−1.02975e14	−0.141047
$505$	−1.00242e15	−1.35815
$506$	1.30400e15	1.74763
$507$	8.14506e14	1.07982
$508$	−2.32476e15	−3.04879
$509$	−6.55872e13	−0.0850886	−0.0425443	−	0.999095i	$-0.513546\pi$
$509$	−6.55872e13	−0.0850886	−0.0425443	+	0.999095i	$0.513546\pi$
$510$	3.80721e14	0.488620
$511$	2.05150e13	0.0260469
$512$	−8.01205e14	−1.00637
$513$	8.41770e14	1.04604
$514$	1.46726e15	1.80389
$515$	7.03928e13	0.0856226
$516$	−9.41877e14	−1.13350
$517$	3.34262e13	0.0398005
$518$	9.83057e14	1.15815
$519$	2.14921e14	0.250529
$520$	2.72066e14	0.313802
$521$	−7.87980e14	−0.899307	−0.449653	−	0.893203i	$-0.648453\pi$
$521$	−7.87980e14	−0.899307	−0.449653	+	0.893203i	$0.648453\pi$
$522$	6.33718e14	0.715663
$523$	−4.94333e14	−0.552408	−0.276204	−	0.961099i	$-0.589077\pi$
$523$	−4.94333e14	−0.552408	−0.276204	+	0.961099i	$0.589077\pi$
$524$	−1.83543e15	−2.02962
$525$	4.54816e13	0.0497691
$526$	9.29557e14	1.00659
$527$	−2.32355e14	−0.248996
$528$	8.04951e14	0.853656
$529$	−4.56729e14	−0.479350
$530$	4.49908e14	0.467312
$531$	−3.59611e14	−0.369669
$532$	−8.36429e14	−0.850971
$533$	−3.80858e14	−0.383499
$534$	9.16395e14	0.913284
$535$	3.74804e14	0.369708
$536$	−4.45610e14	−0.435059
$537$	−1.29930e15	−1.25560
$538$	9.35309e14	0.894649
$539$	1.32034e15	1.25011
$540$	−1.69002e15	−1.58390
$541$	1.00297e15	0.930473	0.465237	−	0.885186i	$-0.345969\pi$
$541$	1.00297e15	0.930473	0.465237	+	0.885186i	$0.345969\pi$
$542$	−1.98345e15	−1.82149
$543$	3.67626e14	0.334201
$544$	−1.39454e14	−0.125498
$545$	−1.94502e15	−1.73278
$546$	−1.65427e14	−0.145897
$547$	−9.73116e14	−0.849639	−0.424819	−	0.905278i	$-0.639662\pi$
$547$	−9.73116e14	−0.849639	−0.424819	+	0.905278i	$0.639662\pi$
$548$	3.81010e15	3.29339
$549$	−3.80223e14	−0.325380
$550$	−3.47239e14	−0.294194
$551$	2.33799e15	1.96114
$552$	1.37550e15	1.14234
$553$	1.66749e14	0.137111
$554$	7.44423e14	0.606060
$555$	−2.81961e15	−2.27288
$556$	3.99278e15	3.18686
$557$	−2.45322e14	−0.193880	−0.0969400	−	0.995290i	$-0.530905\pi$
$557$	−2.45322e14	−0.193880	−0.0969400	+	0.995290i	$0.530905\pi$
$558$	−6.13464e14	−0.480066
$559$	−1.49437e14	−0.115796
$560$	2.62491e14	0.201410
$561$	5.19313e14	0.394578
$562$	2.12046e15	1.59544
$563$	8.57890e14	0.639198	0.319599	−	0.947553i	$-0.396452\pi$
$563$	8.57890e14	0.639198	0.319599	+	0.947553i	$0.396452\pi$
$564$	7.76279e13	0.0572773
$565$	−6.60079e14	−0.482313
$566$	−2.26517e15	−1.63912
$567$	6.07275e14	0.435190
$568$	−2.28926e15	−1.62472
$569$	−2.51501e15	−1.76776	−0.883879	−	0.467716i	$-0.845077\pi$
$569$	−2.51501e15	−1.76776	−0.883879	+	0.467716i	$0.845077\pi$
$570$	3.70844e15	2.58154
$571$	3.78708e14	0.261099	0.130550	−	0.991442i	$-0.458326\pi$
$571$	3.78708e14	0.261099	0.130550	+	0.991442i	$0.458326\pi$
$572$	8.17045e14	0.557915
$573$	2.63592e15	1.78271
$574$	−1.65051e15	−1.10561
$575$	−1.32100e14	−0.0876455
$576$	−5.90043e14	−0.387757
$577$	5.67733e14	0.369553	0.184777	−	0.982781i	$-0.440844\pi$
$577$	5.67733e14	0.369553	0.184777	+	0.982781i	$0.440844\pi$
$578$	1.53538e14	0.0989947
$579$	1.28510e15	0.820737
$580$	−4.69398e15	−2.96953
$581$	−4.21643e14	−0.264227
$582$	2.69117e14	0.167057
$583$	6.13686e14	0.377371
$584$	−1.65214e14	−0.100641
$585$	1.03171e14	0.0622585
$586$	5.53746e14	0.331035
$587$	1.16912e15	0.692386	0.346193	−	0.938163i	$-0.387474\pi$
$587$	1.16912e15	0.692386	0.346193	+	0.938163i	$0.387474\pi$
$588$	3.06632e15	1.79904
$589$	−2.26327e15	−1.31553
$590$	4.11747e15	2.37107
$591$	−2.11224e15	−1.20507
$592$	−1.76253e15	−0.996250
$593$	−2.50538e15	−1.40305	−0.701523	−	0.712647i	$-0.747496\pi$
$593$	−2.50538e15	−1.40305	−0.701523	+	0.712647i	$0.747496\pi$
$594$	−3.56341e15	−1.97716
$595$	1.69345e14	0.0930958
$596$	−1.75602e15	−0.956480
$597$	−1.45706e13	−0.00786354
$598$	4.80477e14	0.256931
$599$	−3.54639e15	−1.87906	−0.939528	−	0.342473i	$-0.888735\pi$
$599$	−3.54639e15	−1.87906	−0.939528	+	0.342473i	$0.888735\pi$
$600$	−3.66278e14	−0.192300
$601$	−1.19051e15	−0.619334	−0.309667	−	0.950845i	$-0.600218\pi$
$601$	−1.19051e15	−0.619334	−0.309667	+	0.950845i	$0.600218\pi$
$602$	−6.47609e14	−0.333835
$603$	−1.68980e14	−0.0863159
$604$	1.50214e13	0.00760339
$605$	−2.26172e15	−1.13445
$606$	−4.90858e15	−2.43981
$607$	−1.12608e15	−0.554666	−0.277333	−	0.960774i	$-0.589451\pi$
$607$	−1.12608e15	−0.554666	−0.277333	+	0.960774i	$0.589451\pi$
$608$	−1.35836e15	−0.663047
$609$	1.29635e15	0.627086
$610$	4.35347e15	2.08699
$611$	1.23163e13	0.00585133
$612$	2.62241e14	0.123472
$613$	−2.83429e15	−1.32255	−0.661274	−	0.750144i	$-0.729984\pi$
$613$	−2.83429e15	−1.32255	−0.661274	+	0.750144i	$0.729984\pi$
$614$	−6.62071e15	−3.06181
$615$	4.73401e15	2.16978
$616$	1.60825e15	0.730564
$617$	2.46296e15	1.10889	0.554446	−	0.832220i	$-0.312930\pi$
$617$	2.46296e15	1.10889	0.554446	+	0.832220i	$0.312930\pi$
$618$	3.44694e14	0.153815
$619$	2.62277e15	1.16001	0.580004	−	0.814614i	$-0.303051\pi$
$619$	2.62277e15	1.16001	0.580004	+	0.814614i	$0.303051\pi$
$620$	4.54396e15	1.99196
$621$	−1.35563e15	−0.589029
$622$	6.58178e15	2.83463
$623$	4.07614e14	0.174006
$624$	2.96595e14	0.125502
$625$	−2.63861e15	−1.10671
$626$	−4.82691e15	−2.00683
$627$	5.05840e15	2.08469
$628$	2.10262e15	0.858979
$629$	−1.13709e15	−0.460488
$630$	4.47107e14	0.179489
$631$	7.69350e14	0.306170	0.153085	−	0.988213i	$-0.451079\pi$
$631$	7.69350e14	0.306170	0.153085	+	0.988213i	$0.451079\pi$
$632$	−1.34288e15	−0.529777
$633$	2.32904e14	0.0910871
$634$	6.67005e15	2.58606
$635$	4.58466e15	1.76218
$636$	1.42521e15	0.543080
$637$	4.86497e14	0.183786
$638$	−9.89727e15	−3.70682
$639$	−8.68113e14	−0.322345
$640$	5.26738e15	1.93912
$641$	2.08321e15	0.760352	0.380176	−	0.924914i	$-0.375863\pi$
$641$	2.08321e15	0.760352	0.380176	+	0.924914i	$0.375863\pi$
$642$	1.83531e15	0.664152
$643$	2.70044e15	0.968891	0.484446	−	0.874821i	$-0.339021\pi$
$643$	2.70044e15	0.968891	0.484446	+	0.874821i	$0.339021\pi$
$644$	1.34703e15	0.479186
$645$	1.85748e15	0.655156
$646$	1.49554e15	0.523023
$647$	−5.38071e15	−1.86581	−0.932903	−	0.360129i	$-0.882733\pi$
$647$	−5.38071e15	−1.86581	−0.932903	+	0.360129i	$0.882733\pi$
$648$	−4.89059e15	−1.68151
$649$	5.61632e15	1.91472
$650$	−1.27945e14	−0.0432514
$651$	−1.25492e15	−0.420649
$652$	−2.39926e15	−0.797472
$653$	−1.88263e15	−0.620500	−0.310250	−	0.950655i	$-0.600413\pi$
$653$	−1.88263e15	−0.620500	−0.310250	+	0.950655i	$0.600413\pi$
$654$	−9.52422e15	−3.11281
$655$	3.61964e15	1.17311
$656$	2.95923e15	0.951058
$657$	−6.26510e13	−0.0199672
$658$	5.33749e13	0.0168692
$659$	4.70441e15	1.47447	0.737234	−	0.675637i	$-0.236131\pi$
$659$	4.70441e15	1.47447	0.737234	+	0.675637i	$0.236131\pi$
$660$	−1.01557e16	−3.15660
$661$	−3.93259e15	−1.21219	−0.606095	−	0.795392i	$-0.707265\pi$
$661$	−3.93259e15	−1.21219	−0.606095	+	0.795392i	$0.707265\pi$
$662$	3.28438e15	1.00400
$663$	1.91348e14	0.0580095
$664$	3.39563e15	1.02093
$665$	1.64952e15	0.491857
$666$	−3.00217e15	−0.887823
$667$	−3.76521e15	−1.10433
$668$	−3.33448e14	−0.0969967
$669$	6.45176e15	1.86138
$670$	1.93479e15	0.553633
$671$	5.93824e15	1.68533
$672$	−7.53172e14	−0.212013
$673$	2.31304e15	0.645804	0.322902	−	0.946432i	$-0.395342\pi$
$673$	2.31304e15	0.645804	0.322902	+	0.946432i	$0.395342\pi$
$674$	−5.77202e15	−1.59845
$675$	3.60987e14	0.0991564
$676$	−6.42370e15	−1.75016
$677$	1.98129e15	0.535441	0.267720	−	0.963497i	$-0.413730\pi$
$677$	1.98129e15	0.535441	0.267720	+	0.963497i	$0.413730\pi$
$678$	−3.23222e15	−0.866439
$679$	1.19704e14	0.0318290
$680$	−1.36379e15	−0.359708
$681$	3.38809e15	0.886433
$682$	9.58095e15	2.48653
$683$	−5.09094e15	−1.31064	−0.655322	−	0.755350i	$-0.727467\pi$
$683$	−5.09094e15	−1.31064	−0.655322	+	0.755350i	$0.727467\pi$
$684$	2.55438e15	0.652344
$685$	−7.51389e15	−1.90356
$686$	4.53551e15	1.13984
$687$	−2.12164e15	−0.528943
$688$	1.16111e15	0.287168
$689$	2.26121e14	0.0554798
$690$	−5.97225e15	−1.45368
$691$	2.99169e15	0.722416	0.361208	−	0.932485i	$-0.382364\pi$
$691$	2.99169e15	0.722416	0.361208	+	0.932485i	$0.382364\pi$
$692$	−1.69500e15	−0.406056
$693$	6.09865e14	0.144944
$694$	−3.74846e15	−0.883844
$695$	−7.87415e15	−1.84199
$696$	−1.04399e16	−2.42296
$697$	1.90914e15	0.439599
$698$	−4.23183e14	−0.0966772
$699$	5.88248e15	1.33333
$700$	−3.58696e14	−0.0806655
$701$	−2.53424e15	−0.565456	−0.282728	−	0.959200i	$-0.591239\pi$
$701$	−2.53424e15	−0.565456	−0.282728	+	0.959200i	$0.591239\pi$
$702$	−1.31299e15	−0.290675
$703$	−1.10759e16	−2.43291
$704$	9.21516e15	2.00841
$705$	−1.53090e14	−0.0331060
$706$	−8.91078e15	−1.91201
$707$	−2.18334e15	−0.464853
$708$	1.30432e16	2.75550
$709$	−3.27687e15	−0.686918	−0.343459	−	0.939168i	$-0.611599\pi$
$709$	−3.27687e15	−0.686918	−0.343459	+	0.939168i	$0.611599\pi$
$710$	9.93970e15	2.06753
$711$	−5.09235e14	−0.105108
$712$	−3.28265e15	−0.672333
$713$	3.64487e15	0.740782
$714$	8.29238e14	0.167240
$715$	−1.61129e15	−0.322472
$716$	1.02471e16	2.03507
$717$	7.09592e15	1.39847
$718$	3.37622e15	0.660308
$719$	−7.21415e15	−1.40016	−0.700078	−	0.714066i	$-0.746851\pi$
$719$	−7.21415e15	−1.40016	−0.700078	+	0.714066i	$0.746851\pi$
$720$	−8.01624e14	−0.154398
$721$	1.53321e14	0.0293060
$722$	5.69558e15	1.08040
$723$	−1.12261e16	−2.11333
$724$	−2.89933e15	−0.541671
$725$	1.00263e15	0.185901
$726$	−1.10750e16	−2.03795
$727$	3.76313e15	0.687242	0.343621	−	0.939108i	$-0.388346\pi$
$727$	3.76313e15	0.687242	0.343621	+	0.939108i	$0.388346\pi$
$728$	5.92580e14	0.107405
$729$	3.27531e15	0.589184
$730$	7.17340e14	0.128071
$731$	7.49085e14	0.132735
$732$	1.37908e16	2.42537
$733$	−5.06786e15	−0.884612	−0.442306	−	0.896864i	$-0.645840\pi$
$733$	−5.06786e15	−0.884612	−0.442306	+	0.896864i	$0.645840\pi$
$734$	−1.08876e16	−1.88627
$735$	−6.04708e15	−1.03984
$736$	2.18757e15	0.373365
$737$	2.63910e15	0.447079
$738$	5.04052e15	0.847550
$739$	−8.19208e15	−1.36726	−0.683628	−	0.729831i	$-0.739599\pi$
$739$	−8.19208e15	−1.36726	−0.683628	+	0.729831i	$0.739599\pi$
$740$	2.22372e16	3.68388
$741$	1.86384e15	0.306484
$742$	9.79933e14	0.159947
$743$	−7.44595e14	−0.120637	−0.0603187	−	0.998179i	$-0.519212\pi$
$743$	−7.44595e14	−0.120637	−0.0603187	+	0.998179i	$0.519212\pi$
$744$	1.01063e16	1.62532
$745$	3.46305e15	0.552840
$746$	1.39550e16	2.21140
$747$	1.28766e15	0.202553
$748$	−4.09562e15	−0.639530
$749$	8.16351e14	0.126540
$750$	−1.15025e16	−1.76992
$751$	2.59088e15	0.395756	0.197878	−	0.980227i	$-0.436595\pi$
$751$	2.59088e15	0.395756	0.197878	+	0.980227i	$0.436595\pi$
$752$	−9.56964e13	−0.0145110
$753$	7.29507e14	0.109814
$754$	−3.64679e15	−0.544964
$755$	−2.96237e13	−0.00439472
$756$	−3.68099e15	−0.542119
$757$	−4.20187e15	−0.614349	−0.307175	−	0.951653i	$-0.599384\pi$
$757$	−4.20187e15	−0.614349	−0.307175	+	0.951653i	$0.599384\pi$
$758$	−5.29345e15	−0.768349
$759$	−8.14630e15	−1.17390
$760$	−1.32841e16	−1.90046
$761$	2.80738e15	0.398737	0.199368	−	0.979925i	$-0.436111\pi$
$761$	2.80738e15	0.398737	0.199368	+	0.979925i	$0.436111\pi$
$762$	2.24498e16	3.16563
$763$	−4.23639e15	−0.593077
$764$	−2.07885e16	−2.88941
$765$	−5.17166e14	−0.0713661
$766$	4.21479e15	0.577454
$767$	2.06941e15	0.281496
$768$	1.41123e16	1.90595
$769$	−6.34582e15	−0.850928	−0.425464	−	0.904975i	$-0.639889\pi$
$769$	−6.34582e15	−0.850928	−0.425464	+	0.904975i	$0.639889\pi$
$770$	−6.98282e15	−0.929676
$771$	−9.16619e15	−1.21169
$772$	−1.01351e16	−1.33025
$773$	9.41216e15	1.22660	0.613298	−	0.789851i	$-0.289842\pi$
$773$	9.41216e15	1.22660	0.613298	+	0.789851i	$0.289842\pi$
$774$	1.97774e15	0.255914
$775$	−9.70585e14	−0.124702
$776$	−9.64012e14	−0.122982
$777$	−6.14131e15	−0.777939
$778$	−1.11995e16	−1.40867
$779$	1.85961e16	2.32255
$780$	−3.74202e15	−0.464073
$781$	1.35580e16	1.66961
$782$	−2.40850e15	−0.294516
$783$	1.02891e16	1.24936
$784$	−3.78003e15	−0.455781
$785$	−4.14657e15	−0.496485
$786$	1.77244e16	2.10740
$787$	1.80992e15	0.213697	0.106848	−	0.994275i	$-0.465924\pi$
$787$	1.80992e15	0.213697	0.106848	+	0.994275i	$0.465924\pi$
$788$	1.66584e16	1.95317
$789$	−5.80709e15	−0.676137
$790$	5.83063e15	0.674165
$791$	−1.43770e15	−0.165081
$792$	−4.91144e15	−0.560041
$793$	2.18802e15	0.247771
$794$	−2.40512e16	−2.70473
$795$	−2.81065e15	−0.313897
$796$	1.14913e14	0.0127452
$797$	−5.10476e15	−0.562283	−0.281141	−	0.959666i	$-0.590713\pi$
$797$	−5.10476e15	−0.562283	−0.281141	+	0.959666i	$0.590713\pi$
$798$	8.07725e15	0.883584
$799$	−6.17383e13	−0.00670730
$800$	−5.82522e14	−0.0628517
$801$	−1.24482e15	−0.133391
$802$	−2.49059e16	−2.65059
$803$	9.78469e14	0.103422
$804$	6.12896e15	0.643396
$805$	−2.65647e15	−0.276967
$806$	3.53023e15	0.365561
$807$	−5.84302e15	−0.600943
$808$	1.75832e16	1.79612
$809$	−6.79240e15	−0.689139	−0.344569	−	0.938761i	$-0.611975\pi$
$809$	−6.79240e15	−0.689139	−0.344569	+	0.938761i	$0.611975\pi$
$810$	2.12344e16	2.13979
$811$	1.91624e16	1.91795	0.958973	−	0.283499i	$-0.0914953\pi$
$811$	1.91624e16	1.91795	0.958973	+	0.283499i	$0.0914953\pi$
$812$	−1.02238e16	−1.01638
$813$	1.23910e16	1.22351
$814$	4.68872e16	4.59854
$815$	4.73158e15	0.460935
$816$	−1.48675e15	−0.143861
$817$	7.29652e15	0.701284
$818$	7.74707e15	0.739596
$819$	2.24713e14	0.0213092
$820$	−3.73354e16	−3.51677
$821$	−2.80606e15	−0.262549	−0.131274	−	0.991346i	$-0.541907\pi$
$821$	−2.80606e15	−0.262549	−0.131274	+	0.991346i	$0.541907\pi$
$822$	−3.67935e16	−3.41960
$823$	−1.15894e16	−1.06995	−0.534975	−	0.844868i	$-0.679679\pi$
$823$	−1.15894e16	−1.06995	−0.534975	+	0.844868i	$0.679679\pi$
$824$	−1.23474e15	−0.113234
$825$	2.16926e15	0.197612
$826$	8.96814e15	0.811544
$827$	−1.62300e16	−1.45894	−0.729471	−	0.684012i	$-0.760234\pi$
$827$	−1.62300e16	−1.45894	−0.729471	+	0.684012i	$0.760234\pi$
$828$	−4.11370e15	−0.367338
$829$	−8.24213e15	−0.731122	−0.365561	−	0.930787i	$-0.619123\pi$
$829$	−8.24213e15	−0.731122	−0.365561	+	0.930787i	$0.619123\pi$
$830$	−1.47434e16	−1.29918
$831$	−4.65053e15	−0.407096
$832$	3.39545e15	0.295270
$833$	−2.43867e15	−0.210672
$834$	−3.85576e16	−3.30900
$835$	6.57592e14	0.0560636
$836$	−3.98937e16	−3.37886
$837$	−9.96027e15	−0.838072
$838$	7.61637e15	0.636658
$839$	8.39768e15	0.697378	0.348689	−	0.937238i	$-0.386627\pi$
$839$	8.39768e15	0.697378	0.348689	+	0.937238i	$0.386627\pi$
$840$	−7.36568e15	−0.607682
$841$	1.63772e16	1.34234
$842$	−6.44992e15	−0.525216
$843$	−1.32469e16	−1.07167
$844$	−1.83683e15	−0.147633
$845$	1.26682e16	1.01158
$846$	−1.63002e14	−0.0129317
$847$	−4.92619e15	−0.388286
$848$	−1.75693e15	−0.137587
$849$	1.41509e16	1.10101
$850$	6.41353e14	0.0495785
$851$	1.78373e16	1.36998
$852$	3.14867e16	2.40275
$853$	−5.18492e15	−0.393118	−0.196559	−	0.980492i	$-0.562977\pi$
$853$	−5.18492e15	−0.393118	−0.196559	+	0.980492i	$0.562977\pi$
$854$	9.48217e15	0.714315
$855$	−5.03749e15	−0.377051
$856$	−6.57434e15	−0.488930
$857$	−2.03069e15	−0.150054	−0.0750271	−	0.997181i	$-0.523904\pi$
$857$	−2.03069e15	−0.150054	−0.0750271	+	0.997181i	$0.523904\pi$
$858$	−7.89007e15	−0.579296
$859$	1.48577e16	1.08390	0.541951	−	0.840410i	$-0.317686\pi$
$859$	1.48577e16	1.08390	0.541951	+	0.840410i	$0.317686\pi$
$860$	−1.46492e16	−1.06187
$861$	1.03110e16	0.742650
$862$	2.25268e16	1.61216
$863$	2.63376e16	1.87291	0.936455	−	0.350788i	$-0.114086\pi$
$863$	2.63376e16	1.87291	0.936455	+	0.350788i	$0.114086\pi$
$864$	−5.97792e15	−0.422400
$865$	3.34270e15	0.234698
$866$	1.90391e16	1.32831
$867$	−9.59174e14	−0.0664955
$868$	9.89707e15	0.681786
$869$	7.95312e15	0.544413
$870$	4.53290e16	3.08333
$871$	9.72411e14	0.0657279
$872$	3.41170e16	2.29156
$873$	−3.65564e14	−0.0243997
$874$	−2.34601e16	−1.55603
$875$	−5.11631e15	−0.337220
$876$	2.27237e15	0.148835
$877$	−1.10052e16	−0.716307	−0.358154	−	0.933663i	$-0.616594\pi$
$877$	−1.10052e16	−0.716307	−0.358154	+	0.933663i	$0.616594\pi$
$878$	1.25815e16	0.813789
$879$	−3.45934e15	−0.222359
$880$	1.25196e16	0.799715
$881$	−1.32358e16	−0.840203	−0.420101	−	0.907477i	$-0.638005\pi$
$881$	−1.32358e16	−0.840203	−0.420101	+	0.907477i	$0.638005\pi$
$882$	−6.43861e15	−0.406176
$883$	−2.16884e16	−1.35970	−0.679852	−	0.733349i	$-0.737956\pi$
$883$	−2.16884e16	−1.35970	−0.679852	+	0.733349i	$0.737956\pi$
$884$	−1.50909e15	−0.0940215
$885$	−2.57225e16	−1.59266
$886$	−1.46005e16	−0.898426
$887$	−1.32659e16	−0.811253	−0.405626	−	0.914039i	$-0.632947\pi$
$887$	−1.32659e16	−0.811253	−0.405626	+	0.914039i	$0.632947\pi$
$888$	4.94579e16	3.00583
$889$	9.98572e15	0.603142
$890$	1.42529e16	0.855574
$891$	2.89642e16	1.72796
$892$	−5.08826e16	−3.01691
$893$	−6.01366e14	−0.0354369
$894$	1.69576e16	0.993135
$895$	−2.02083e16	−1.17626
$896$	1.14727e16	0.663702
$897$	−3.00162e15	−0.172582
$898$	4.60353e16	2.63070
$899$	−2.76643e16	−1.57124
$900$	1.09543e15	0.0618371
$901$	−1.13348e15	−0.0635958
$902$	−7.87217e16	−4.38994
$903$	4.04572e15	0.224240
$904$	1.15783e16	0.637848
$905$	5.71777e15	0.313083
$906$	−1.45059e14	−0.00789478
$907$	6.11248e15	0.330657	0.165328	−	0.986239i	$-0.447132\pi$
$907$	6.11248e15	0.330657	0.165328	+	0.986239i	$0.447132\pi$
$908$	−2.67206e16	−1.43673
$909$	6.66774e15	0.356350
$910$	−2.57291e15	−0.136678
$911$	2.87241e16	1.51669	0.758344	−	0.651855i	$-0.226009\pi$
$911$	2.87241e16	1.51669	0.758344	+	0.651855i	$0.226009\pi$
$912$	−1.44818e16	−0.760065
$913$	−2.01104e16	−1.04914
$914$	1.92641e16	0.998952
$915$	−2.71968e16	−1.40185
$916$	1.67326e16	0.857308
$917$	7.88384e15	0.401519
$918$	6.58165e15	0.333196
$919$	−6.93398e15	−0.348937	−0.174469	−	0.984663i	$-0.555821\pi$
$919$	−6.93398e15	−0.348937	−0.174469	+	0.984663i	$0.555821\pi$
$920$	2.13934e16	1.07016
$921$	4.13606e16	2.05664
$922$	3.69471e16	1.82625
$923$	4.99563e15	0.245460
$924$	−2.21200e16	−1.08041
$925$	−4.74984e15	−0.230621
$926$	−3.10976e16	−1.50095
$927$	−4.68227e14	−0.0224656
$928$	−1.66035e16	−0.791927
$929$	1.14374e16	0.542299	0.271150	−	0.962537i	$-0.412596\pi$
$929$	1.14374e16	0.542299	0.271150	+	0.962537i	$0.412596\pi$
$930$	−4.38802e16	−2.06830
$931$	−2.37541e16	−1.11305
$932$	−4.63929e16	−2.16105
$933$	−4.11174e16	−1.90404
$934$	−3.01653e16	−1.38867
$935$	8.07698e15	0.369645
$936$	−1.80969e15	−0.0823353
$937$	−2.31740e15	−0.104817	−0.0524087	−	0.998626i	$-0.516690\pi$
$937$	−2.31740e15	−0.104817	−0.0524087	+	0.998626i	$0.516690\pi$
$938$	4.21411e15	0.189492
$939$	3.01545e16	1.34800
$940$	1.20736e15	0.0536580
$941$	1.17574e16	0.519481	0.259741	−	0.965678i	$-0.416363\pi$
$941$	1.17574e16	0.519481	0.259741	+	0.965678i	$0.416363\pi$
$942$	−2.03046e16	−0.891898
$943$	−2.99481e16	−1.30784
$944$	−1.60791e16	−0.698097
$945$	7.25928e15	0.313342
$946$	−3.08879e16	−1.32552
$947$	5.32679e15	0.227269	0.113635	−	0.993523i	$-0.463751\pi$
$947$	5.32679e15	0.227269	0.113635	+	0.993523i	$0.463751\pi$
$948$	1.84701e16	0.783471
$949$	3.60530e14	0.0152047
$950$	6.24714e15	0.261940
$951$	−4.16688e16	−1.73708
$952$	−2.97044e15	−0.123117
$953$	2.82021e16	1.16217	0.581086	−	0.813842i	$-0.302628\pi$
$953$	2.82021e16	1.16217	0.581086	+	0.813842i	$0.302628\pi$
$954$	−2.99263e15	−0.122613
$955$	4.09970e16	1.67007
$956$	−5.59628e16	−2.26663
$957$	6.18298e16	2.48990
$958$	3.51479e16	1.40731
$959$	−1.63658e16	−0.651531
$960$	−4.22049e16	−1.67060
$961$	1.37169e15	0.0539854
$962$	1.72762e16	0.676061
$963$	−2.49306e15	−0.0970038
$964$	8.85358e16	3.42527
$965$	1.99874e16	0.768875
$966$	−1.30080e16	−0.497550
$967$	2.88415e16	1.09691	0.548456	−	0.836179i	$-0.315216\pi$
$967$	2.88415e16	1.09691	0.548456	+	0.836179i	$0.315216\pi$
$968$	3.96722e16	1.50028
$969$	−9.34290e15	−0.351318
$970$	4.18563e15	0.156501
$971$	3.07278e16	1.14242	0.571210	−	0.820804i	$-0.306474\pi$
$971$	3.07278e16	1.14242	0.571210	+	0.820804i	$0.306474\pi$
$972$	2.68082e16	0.991066
$973$	−1.71505e16	−0.630457
$974$	−2.19586e16	−0.802658
$975$	7.99293e14	0.0290523
$976$	−1.70007e16	−0.614459
$977$	−2.16981e16	−0.779835	−0.389917	−	0.920850i	$-0.627496\pi$
$977$	−2.16981e16	−0.779835	−0.389917	+	0.920850i	$0.627496\pi$
$978$	2.31693e16	0.828034
$979$	1.94413e16	0.690907
$980$	4.76910e16	1.68536
$981$	1.29376e16	0.454645
$982$	3.95674e16	1.38269
$983$	1.15928e16	0.402849	0.201425	−	0.979504i	$-0.435443\pi$
$983$	1.15928e16	0.402849	0.201425	+	0.979504i	$0.435443\pi$
$984$	−8.30380e16	−2.86948
$985$	−3.28521e16	−1.12892
$986$	1.82803e16	0.624685
$987$	−3.33441e14	−0.0113312
$988$	−1.46994e16	−0.496748
$989$	−1.17507e16	−0.394896
$990$	2.13249e16	0.712678
$991$	−1.06425e16	−0.353702	−0.176851	−	0.984238i	$-0.556591\pi$
$991$	−1.06425e16	−0.353702	−0.176851	+	0.984238i	$0.556591\pi$
$992$	1.60728e16	0.531224
$993$	−2.05181e16	−0.674397
$994$	2.16494e16	0.707653
$995$	−2.26619e14	−0.00736665
$996$	−4.67038e16	−1.50982
$997$	−9.12792e15	−0.293460	−0.146730	−	0.989177i	$-0.546875\pi$
$997$	−9.12792e15	−0.293460	−0.146730	+	0.989177i	$0.546875\pi$
$998$	7.13155e16	2.28016
$999$	−4.87435e16	−1.54991

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.12.a.a.1.6	✓	6
3.2	odd	2		153.12.a.a.1.1		6
4.3	odd	2		272.12.a.f.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.12.a.a.1.6	✓	6	1.1	even	1	trivial
153.12.a.a.1.1		6	3.2	odd	2
272.12.a.f.1.4		6	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	17.a (trivial)

\(f(q)\)	\(=\)	\(q+76.1598 q^{2} -475.782 q^{3} +3752.32 q^{4} -7399.94 q^{5} -36235.5 q^{6} -16117.6 q^{7} +129800. q^{8} +49221.7 q^{9} +O(q^{10})\)	\(q+76.1598 q^{2} -475.782 q^{3} +3752.32 q^{4} -7399.94 q^{5} -36235.5 q^{6} -16117.6 q^{7} +129800. q^{8} +49221.7 q^{9} -563578. q^{10} -768734. q^{11} -1.78528e6 q^{12} -283251. q^{13} -1.22751e6 q^{14} +3.52076e6 q^{15} +2.20082e6 q^{16} +1.41986e6 q^{17} +3.74872e6 q^{18} +1.38302e7 q^{19} -2.77669e7 q^{20} +7.66847e6 q^{21} -5.85466e7 q^{22} -2.22729e7 q^{23} -6.17567e7 q^{24} +5.93099e6 q^{25} -2.15723e7 q^{26} +6.08646e7 q^{27} -6.04784e7 q^{28} +1.69049e8 q^{29} +2.68140e8 q^{30} -1.63646e8 q^{31} -9.82167e7 q^{32} +3.65750e8 q^{33} +1.08136e8 q^{34} +1.19269e8 q^{35} +1.84695e8 q^{36} -8.00852e8 q^{37} +1.05331e9 q^{38} +1.34766e8 q^{39} -9.60515e8 q^{40} +1.34460e9 q^{41} +5.84029e8 q^{42} +5.27578e8 q^{43} -2.88453e9 q^{44} -3.64238e8 q^{45} -1.69630e9 q^{46} -4.34821e7 q^{47} -1.04711e9 q^{48} -1.71755e9 q^{49} +4.51703e8 q^{50} -6.75543e8 q^{51} -1.06285e9 q^{52} -7.98307e8 q^{53} +4.63543e9 q^{54} +5.68858e9 q^{55} -2.09207e9 q^{56} -6.58017e9 q^{57} +1.28748e10 q^{58} -7.30594e9 q^{59} +1.32110e10 q^{60} -7.72470e9 q^{61} -1.24633e10 q^{62} -7.93337e8 q^{63} -1.19875e10 q^{64} +2.09604e9 q^{65} +2.78554e10 q^{66} -3.43304e9 q^{67} +5.32775e9 q^{68} +1.05970e10 q^{69} +9.08353e9 q^{70} -1.76368e10 q^{71} +6.38900e9 q^{72} -1.27283e9 q^{73} -6.09927e10 q^{74} -2.82186e9 q^{75} +5.18953e10 q^{76} +1.23902e10 q^{77} +1.02637e10 q^{78} -1.03457e10 q^{79} -1.62860e10 q^{80} -3.76778e10 q^{81} +1.02404e11 q^{82} +2.61604e10 q^{83} +2.87745e10 q^{84} -1.05069e10 q^{85} +4.01802e10 q^{86} -8.04307e10 q^{87} -9.97819e10 q^{88} -2.52900e10 q^{89} -2.77403e10 q^{90} +4.56532e9 q^{91} -8.35748e10 q^{92} +7.78601e10 q^{93} -3.31159e9 q^{94} -1.02343e11 q^{95} +4.67298e10 q^{96} -7.42689e9 q^{97} -1.30808e11 q^{98} -3.78384e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 9 q^{2} - 476 q^{3} + 4613 q^{4} - 12884 q^{5} + 552 q^{6} - 23436 q^{7} + 74805 q^{8} + 296398 q^{9}+O(q^{10}) \) 6 * q - 9 * q^2 - 476 * q^3 + 4613 * q^4 - 12884 * q^5 + 552 * q^6 - 23436 * q^7 + 74805 * q^8 + 296398 * q^9	\( 6 q - 9 q^{2} - 476 q^{3} + 4613 q^{4} - 12884 q^{5} + 552 q^{6} - 23436 q^{7} + 74805 q^{8} + 296398 q^{9} - 676038 q^{10} - 962060 q^{11} - 2352344 q^{12} - 435268 q^{13} - 7990948 q^{14} - 9450288 q^{15} - 12496671 q^{16} + 8519142 q^{17} - 20195421 q^{18} - 26398480 q^{19} - 47202914 q^{20} - 56428792 q^{21} - 51774200 q^{22} - 99172772 q^{23} - 110557128 q^{24} + 66085866 q^{25} + 74451914 q^{26} + 105183712 q^{27} + 102848900 q^{28} + 165683964 q^{29} + 401475744 q^{30} - 199133468 q^{31} + 465766501 q^{32} + 518429376 q^{33} - 12778713 q^{34} + 804442912 q^{35} + 627274777 q^{36} - 785778644 q^{37} + 2174484940 q^{38} + 627357728 q^{39} + 657666206 q^{40} + 166444428 q^{41} + 652753248 q^{42} - 1110947880 q^{43} - 997577064 q^{44} - 1706447988 q^{45} - 1891667412 q^{46} - 5828211928 q^{47} - 2359114472 q^{48} - 1968801674 q^{49} - 126509183 q^{50} - 675851932 q^{51} - 6633403554 q^{52} - 9889898636 q^{53} - 1961072736 q^{54} - 10730153984 q^{55} + 5703448884 q^{56} - 13522850128 q^{57} + 14316796258 q^{58} + 204095112 q^{59} + 22313648592 q^{60} - 15864546948 q^{61} - 1838602020 q^{62} + 504344540 q^{63} + 6177095465 q^{64} + 12794774792 q^{65} + 56255165136 q^{66} + 17196640232 q^{67} + 6549800341 q^{68} + 2949266904 q^{69} + 52391765944 q^{70} + 8751653884 q^{71} + 38682669705 q^{72} - 13704156916 q^{73} - 9383651494 q^{74} - 15917467268 q^{75} + 59548672452 q^{76} - 12012382872 q^{77} + 35038956192 q^{78} - 89923384436 q^{79} + 25877503334 q^{80} - 152313828506 q^{81} + 57834669670 q^{82} - 26042106648 q^{83} + 3397466240 q^{84} - 18293437588 q^{85} + 29108045060 q^{86} - 195382431072 q^{87} - 228837945880 q^{88} + 53269579420 q^{89} - 10044062046 q^{90} - 226028668544 q^{91} - 9212077436 q^{92} - 62709484936 q^{93} + 83948222448 q^{94} - 170219637424 q^{95} + 116885663928 q^{96} - 106272517044 q^{97} + 132039821039 q^{98} - 10550584980 q^{99}+O(q^{100}) \) 6 * q - 9 * q^2 - 476 * q^3 + 4613 * q^4 - 12884 * q^5 + 552 * q^6 - 23436 * q^7 + 74805 * q^8 + 296398 * q^9 - 676038 * q^10 - 962060 * q^11 - 2352344 * q^12 - 435268 * q^13 - 7990948 * q^14 - 9450288 * q^15 - 12496671 * q^16 + 8519142 * q^17 - 20195421 * q^18 - 26398480 * q^19 - 47202914 * q^20 - 56428792 * q^21 - 51774200 * q^22 - 99172772 * q^23 - 110557128 * q^24 + 66085866 * q^25 + 74451914 * q^26 + 105183712 * q^27 + 102848900 * q^28 + 165683964 * q^29 + 401475744 * q^30 - 199133468 * q^31 + 465766501 * q^32 + 518429376 * q^33 - 12778713 * q^34 + 804442912 * q^35 + 627274777 * q^36 - 785778644 * q^37 + 2174484940 * q^38 + 627357728 * q^39 + 657666206 * q^40 + 166444428 * q^41 + 652753248 * q^42 - 1110947880 * q^43 - 997577064 * q^44 - 1706447988 * q^45 - 1891667412 * q^46 - 5828211928 * q^47 - 2359114472 * q^48 - 1968801674 * q^49 - 126509183 * q^50 - 675851932 * q^51 - 6633403554 * q^52 - 9889898636 * q^53 - 1961072736 * q^54 - 10730153984 * q^55 + 5703448884 * q^56 - 13522850128 * q^57 + 14316796258 * q^58 + 204095112 * q^59 + 22313648592 * q^60 - 15864546948 * q^61 - 1838602020 * q^62 + 504344540 * q^63 + 6177095465 * q^64 + 12794774792 * q^65 + 56255165136 * q^66 + 17196640232 * q^67 + 6549800341 * q^68 + 2949266904 * q^69 + 52391765944 * q^70 + 8751653884 * q^71 + 38682669705 * q^72 - 13704156916 * q^73 - 9383651494 * q^74 - 15917467268 * q^75 + 59548672452 * q^76 - 12012382872 * q^77 + 35038956192 * q^78 - 89923384436 * q^79 + 25877503334 * q^80 - 152313828506 * q^81 + 57834669670 * q^82 - 26042106648 * q^83 + 3397466240 * q^84 - 18293437588 * q^85 + 29108045060 * q^86 - 195382431072 * q^87 - 228837945880 * q^88 + 53269579420 * q^89 - 10044062046 * q^90 - 226028668544 * q^91 - 9212077436 * q^92 - 62709484936 * q^93 + 83948222448 * q^94 - 170219637424 * q^95 + 116885663928 * q^96 - 106272517044 * q^97 + 132039821039 * q^98 - 10550584980 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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