LMFDB - Embedded newform 83.16.a.a.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [83,16,Mod(1,83)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(83, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("83.1");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 83 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	83.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:	$118.435609233$
Analytic rank:	$1$
Dimension:	$48$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	83.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-157.812 q^{2} +2699.23 q^{3} -7863.32 q^{4} +170610. q^{5} -425971. q^{6} -2.85216e6 q^{7} +6.41212e6 q^{8} -7.06308e6 q^{9} +O(q^{10})$	\(q-157.812 q^{2} +2699.23 q^{3} -7863.32 q^{4} +170610. q^{5} -425971. q^{6} -2.85216e6 q^{7} +6.41212e6 q^{8} -7.06308e6 q^{9} -2.69244e7 q^{10} +8.82287e7 q^{11} -2.12249e7 q^{12} -4.00613e8 q^{13} +4.50105e8 q^{14} +4.60516e8 q^{15} -7.54245e8 q^{16} +2.05636e9 q^{17} +1.11464e9 q^{18} +2.89148e9 q^{19} -1.34156e9 q^{20} -7.69862e9 q^{21} -1.39236e10 q^{22} +3.59355e9 q^{23} +1.73078e10 q^{24} -1.40969e9 q^{25} +6.32216e10 q^{26} -5.77958e10 q^{27} +2.24274e10 q^{28} +9.32477e10 q^{29} -7.26751e10 q^{30} -8.06682e9 q^{31} -9.10832e10 q^{32} +2.38149e11 q^{33} -3.24518e11 q^{34} -4.86607e11 q^{35} +5.55392e10 q^{36} -2.61215e11 q^{37} -4.56310e11 q^{38} -1.08135e12 q^{39} +1.09397e12 q^{40} +8.52234e11 q^{41} +1.21494e12 q^{42} -2.66552e11 q^{43} -6.93771e11 q^{44} -1.20503e12 q^{45} -5.67106e11 q^{46} -4.32032e12 q^{47} -2.03588e12 q^{48} +3.38723e12 q^{49} +2.22467e11 q^{50} +5.55058e12 q^{51} +3.15015e12 q^{52} -7.23066e12 q^{53} +9.12088e12 q^{54} +1.50527e13 q^{55} -1.82884e13 q^{56} +7.80475e12 q^{57} -1.47156e13 q^{58} +3.00946e13 q^{59} -3.62119e12 q^{60} -7.17690e12 q^{61} +1.27304e12 q^{62} +2.01450e13 q^{63} +3.90891e13 q^{64} -6.83487e13 q^{65} -3.75829e13 q^{66} +6.42677e13 q^{67} -1.61698e13 q^{68} +9.69981e12 q^{69} +7.67925e13 q^{70} +1.81087e13 q^{71} -4.52893e13 q^{72} -5.09547e13 q^{73} +4.12229e13 q^{74} -3.80508e12 q^{75} -2.27366e13 q^{76} -2.51642e14 q^{77} +1.70649e14 q^{78} -1.19406e14 q^{79} -1.28682e14 q^{80} -5.46567e13 q^{81} -1.34493e14 q^{82} +2.71361e13 q^{83} +6.05367e13 q^{84} +3.50836e14 q^{85} +4.20652e13 q^{86} +2.51697e14 q^{87} +5.65733e14 q^{88} +3.84406e14 q^{89} +1.90169e14 q^{90} +1.14261e15 q^{91} -2.82572e13 q^{92} -2.17742e13 q^{93} +6.81798e14 q^{94} +4.93316e14 q^{95} -2.45854e14 q^{96} +9.79195e14 q^{97} -5.34546e14 q^{98} -6.23166e14 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 473 q^{2} - 5843 q^{3} + 680037 q^{4} - 442447 q^{5} + 296553 q^{6} - 7927854 q^{7} - 8537601 q^{8} + 201265585 q^{9}+O(q^{10}) $ 48 * q - 473 * q^2 - 5843 * q^3 + 680037 * q^4 - 442447 * q^5 + 296553 * q^6 - 7927854 * q^7 - 8537601 * q^8 + 201265585 * q^9	\( 48 q - 473 q^{2} - 5843 q^{3} + 680037 q^{4} - 442447 q^{5} + 296553 q^{6} - 7927854 q^{7} - 8537601 q^{8} + 201265585 q^{9} - 93241115 q^{10} - 45721275 q^{11} - 377854265 q^{12} - 745704099 q^{13} - 392421804 q^{14} - 1168377736 q^{15} + 8467920373 q^{16} - 2629486634 q^{17} - 7709183072 q^{18} - 5531098141 q^{19} - 18039154937 q^{20} - 847906109 q^{21} - 47911647107 q^{22} - 83924132873 q^{23} - 124449608127 q^{24} + 162107115775 q^{25} + 184146522913 q^{26} + 36372522745 q^{27} - 71841297868 q^{28} - 19181424465 q^{29} + 629437825372 q^{30} - 332963100244 q^{31} - 393743335061 q^{32} - 1482425278799 q^{33} - 1468922151850 q^{34} - 1159028725940 q^{35} - 461783529368 q^{36} - 3528614578273 q^{37} - 5029367527151 q^{38} - 4034986327034 q^{39} - 6971822086105 q^{40} - 4885450015231 q^{41} - 11511941818333 q^{42} - 2898728824729 q^{43} - 9293985416421 q^{44} - 6134907413849 q^{45} - 4884690151683 q^{46} - 213168900002 q^{47} - 11019361285633 q^{48} + 21878291008144 q^{49} + 18113403515282 q^{50} - 4114564648607 q^{51} + 989572768731 q^{52} - 25240879960039 q^{53} + 54416977542501 q^{54} + 10061754537534 q^{55} + 83758891995194 q^{56} + 2144964161830 q^{57} - 8449723551503 q^{58} - 16396353463329 q^{59} + 116252836147112 q^{60} - 26017465263825 q^{61} + 94212604839642 q^{62} + 5126445923855 q^{63} + 186326365661717 q^{64} + 92174682613046 q^{65} + 224566743891485 q^{66} - 127182509349881 q^{67} + 240579433865274 q^{68} + 122547131930146 q^{69} - 112950590057616 q^{70} + 8411915072406 q^{71} + 236831710917612 q^{72} - 230118245135128 q^{73} + 453976256379465 q^{74} - 260184225186765 q^{75} + 185545158559463 q^{76} - 487981581579147 q^{77} + 110466382430294 q^{78} - 293686576998568 q^{79} - 539484042180045 q^{80} + 730816042132624 q^{81} - 499426942251343 q^{82} + 13\!\cdots\!96 q^{83}+ \cdots - 19\!\cdots\!36 q^{99}+O(q^{100}) \) 48 * q - 473 * q^2 - 5843 * q^3 + 680037 * q^4 - 442447 * q^5 + 296553 * q^6 - 7927854 * q^7 - 8537601 * q^8 + 201265585 * q^9 - 93241115 * q^10 - 45721275 * q^11 - 377854265 * q^12 - 745704099 * q^13 - 392421804 * q^14 - 1168377736 * q^15 + 8467920373 * q^16 - 2629486634 * q^17 - 7709183072 * q^18 - 5531098141 * q^19 - 18039154937 * q^20 - 847906109 * q^21 - 47911647107 * q^22 - 83924132873 * q^23 - 124449608127 * q^24 + 162107115775 * q^25 + 184146522913 * q^26 + 36372522745 * q^27 - 71841297868 * q^28 - 19181424465 * q^29 + 629437825372 * q^30 - 332963100244 * q^31 - 393743335061 * q^32 - 1482425278799 * q^33 - 1468922151850 * q^34 - 1159028725940 * q^35 - 461783529368 * q^36 - 3528614578273 * q^37 - 5029367527151 * q^38 - 4034986327034 * q^39 - 6971822086105 * q^40 - 4885450015231 * q^41 - 11511941818333 * q^42 - 2898728824729 * q^43 - 9293985416421 * q^44 - 6134907413849 * q^45 - 4884690151683 * q^46 - 213168900002 * q^47 - 11019361285633 * q^48 + 21878291008144 * q^49 + 18113403515282 * q^50 - 4114564648607 * q^51 + 989572768731 * q^52 - 25240879960039 * q^53 + 54416977542501 * q^54 + 10061754537534 * q^55 + 83758891995194 * q^56 + 2144964161830 * q^57 - 8449723551503 * q^58 - 16396353463329 * q^59 + 116252836147112 * q^60 - 26017465263825 * q^61 + 94212604839642 * q^62 + 5126445923855 * q^63 + 186326365661717 * q^64 + 92174682613046 * q^65 + 224566743891485 * q^66 - 127182509349881 * q^67 + 240579433865274 * q^68 + 122547131930146 * q^69 - 112950590057616 * q^70 + 8411915072406 * q^71 + 236831710917612 * q^72 - 230118245135128 * q^73 + 453976256379465 * q^74 - 260184225186765 * q^75 + 185545158559463 * q^76 - 487981581579147 * q^77 + 110466382430294 * q^78 - 293686576998568 * q^79 - 539484042180045 * q^80 + 730816042132624 * q^81 - 499426942251343 * q^82 + 1302530447502096 * q^83 + 344572152969097 * q^84 - 987337964139519 * q^85 - 473158023061951 * q^86 - 331651268603165 * q^87 - 1261768867285811 * q^88 - 1529884970459758 * q^89 - 5249887977052001 * q^90 - 2821941165368823 * q^91 - 5393454125194245 * q^92 - 6369849411750419 * q^93 - 3702275724839446 * q^94 - 3484233647056932 * q^95 - 7346403487127915 * q^96 - 4526640473660276 * q^97 - 6918835080801735 * q^98 - 1971920884322036 * 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 $

$2$	−157.812	−0.871797	−0.435899	−	0.899996i	$-0.643569\pi$
$2$	−157.812	−0.871797	−0.435899	+	0.899996i	$0.643569\pi$
$3$	2699.23	0.712574	0.356287	−	0.934377i	$-0.384042\pi$
$3$	2699.23	0.712574	0.356287	+	0.934377i	$0.384042\pi$
$4$	−7863.32	−0.239969
$5$	170610.	0.976631	0.488315	−	0.872667i	$-0.337612\pi$
$5$	170610.	0.976631	0.488315	+	0.872667i	$0.337612\pi$
$6$	−425971.	−0.621220
$7$	−2.85216e6	−1.30899	−0.654497	−	0.756064i	$-0.727120\pi$
$7$	−2.85216e6	−1.30899	−0.654497	+	0.756064i	$0.727120\pi$
$8$	6.41212e6	1.08100
$9$	−7.06308e6	−0.492238
$10$	−2.69244e7	−0.851424
$11$	8.82287e7	1.36510	0.682551	−	0.730838i	$-0.260871\pi$
$11$	8.82287e7	1.36510	0.682551	+	0.730838i	$0.260871\pi$
$12$	−2.12249e7	−0.170996
$13$	−4.00613e8	−1.77072	−0.885360	−	0.464907i	$-0.846088\pi$
$13$	−4.00613e8	−1.77072	−0.885360	+	0.464907i	$0.846088\pi$
$14$	4.50105e8	1.14118
$15$	4.60516e8	0.695922
$16$	−7.54245e8	−0.702445
$17$	2.05636e9	1.21543	0.607717	−	0.794153i	$-0.292085\pi$
$17$	2.05636e9	1.21543	0.607717	+	0.794153i	$0.292085\pi$
$18$	1.11464e9	0.429132
$19$	2.89148e9	0.742109	0.371054	−	0.928611i	$-0.378996\pi$
$19$	2.89148e9	0.742109	0.371054	+	0.928611i	$0.378996\pi$
$20$	−1.34156e9	−0.234362
$21$	−7.69862e9	−0.932756
$22$	−1.39236e10	−1.19009
$23$	3.59355e9	0.220072	0.110036	−	0.993928i	$-0.464903\pi$
$23$	3.59355e9	0.220072	0.110036	+	0.993928i	$0.464903\pi$
$24$	1.73078e10	0.770294
$25$	−1.40969e9	−0.0461928
$26$	6.32216e10	1.54371
$27$	−5.77958e10	−1.06333
$28$	2.24274e10	0.314119
$29$	9.32477e10	1.00381	0.501907	−	0.864922i	$-0.332632\pi$
$29$	9.32477e10	1.00381	0.501907	+	0.864922i	$0.332632\pi$
$30$	−7.26751e10	−0.606703
$31$	−8.06682e9	−0.0526611	−0.0263305	−	0.999653i	$-0.508382\pi$
$31$	−8.06682e9	−0.0526611	−0.0263305	+	0.999653i	$0.508382\pi$
$32$	−9.10832e10	−0.468612
$33$	2.38149e11	0.972736
$34$	−3.24518e11	−1.05961
$35$	−4.86607e11	−1.27840
$36$	5.55392e10	0.118122
$37$	−2.61215e11	−0.452361	−0.226180	−	0.974085i	$-0.572624\pi$
$37$	−2.61215e11	−0.452361	−0.226180	+	0.974085i	$0.572624\pi$
$38$	−4.56310e11	−0.646969
$39$	−1.08135e12	−1.26177
$40$	1.09397e12	1.05574
$41$	8.52234e11	0.683408	0.341704	−	0.939808i	$-0.388996\pi$
$41$	8.52234e11	0.683408	0.341704	+	0.939808i	$0.388996\pi$
$42$	1.21494e12	0.813174
$43$	−2.66552e11	−0.149544	−0.0747720	−	0.997201i	$-0.523823\pi$
$43$	−2.66552e11	−0.149544	−0.0747720	+	0.997201i	$0.523823\pi$
$44$	−6.93771e11	−0.327583
$45$	−1.20503e12	−0.480735
$46$	−5.67106e11	−0.191858
$47$	−4.32032e12	−1.24389	−0.621944	−	0.783061i	$-0.713657\pi$
$47$	−4.32032e12	−1.24389	−0.621944	+	0.783061i	$0.713657\pi$
$48$	−2.03588e12	−0.500544
$49$	3.38723e12	0.713467
$50$	2.22467e11	0.0402708
$51$	5.55058e12	0.866088
$52$	3.15015e12	0.424919
$53$	−7.23066e12	−0.845491	−0.422746	−	0.906248i	$-0.638934\pi$
$53$	−7.23066e12	−0.845491	−0.422746	+	0.906248i	$0.638934\pi$
$54$	9.12088e12	0.927009
$55$	1.50527e13	1.33320
$56$	−1.82884e13	−1.41503
$57$	7.80475e12	0.528808
$58$	−1.47156e13	−0.875122
$59$	3.00946e13	1.57434	0.787171	−	0.616735i	$-0.211545\pi$
$59$	3.00946e13	1.57434	0.787171	+	0.616735i	$0.211545\pi$
$60$	−3.62119e12	−0.167000
$61$	−7.17690e12	−0.292391	−0.146195	−	0.989256i	$-0.546703\pi$
$61$	−7.17690e12	−0.292391	−0.146195	+	0.989256i	$0.546703\pi$
$62$	1.27304e12	0.0459098
$63$	2.01450e13	0.644337
$64$	3.90891e13	1.11098
$65$	−6.83487e13	−1.72934
$66$	−3.75829e13	−0.848029
$67$	6.42677e13	1.29548	0.647742	−	0.761860i	$-0.275713\pi$
$67$	6.42677e13	1.29548	0.647742	+	0.761860i	$0.275713\pi$
$68$	−1.61698e13	−0.291667
$69$	9.69981e12	0.156818
$70$	7.67925e13	1.11451
$71$	1.81087e13	0.236292	0.118146	−	0.992996i	$-0.462305\pi$
$71$	1.81087e13	0.236292	0.118146	+	0.992996i	$0.462305\pi$
$72$	−4.52893e13	−0.532110
$73$	−5.09547e13	−0.539838	−0.269919	−	0.962883i	$-0.586997\pi$
$73$	−5.09547e13	−0.539838	−0.269919	+	0.962883i	$0.586997\pi$
$74$	4.12229e13	0.394367
$75$	−3.80508e12	−0.0329158
$76$	−2.27366e13	−0.178084
$77$	−2.51642e14	−1.78691
$78$	1.70649e14	1.10001
$79$	−1.19406e14	−0.699556	−0.349778	−	0.936833i	$-0.613743\pi$
$79$	−1.19406e14	−0.699556	−0.349778	+	0.936833i	$0.613743\pi$
$80$	−1.28682e14	−0.686029
$81$	−5.46567e13	−0.265464
$82$	−1.34493e14	−0.595793
$83$	2.71361e13	0.109764
$83$	2.71361e13	0.109764
$84$	6.05367e13	0.223833
$85$	3.50836e14	1.18703
$86$	4.20652e13	0.130372
$87$	2.51697e14	0.715292
$88$	5.65733e14	1.47568
$89$	3.84406e14	0.921224	0.460612	−	0.887602i	$-0.347630\pi$
$89$	3.84406e14	0.921224	0.460612	+	0.887602i	$0.347630\pi$
$90$	1.90169e14	0.419103
$91$	1.14261e15	2.31786
$92$	−2.82572e13	−0.0528106
$93$	−2.17742e13	−0.0375249
$94$	6.81798e14	1.08442
$95$	4.93316e14	0.724766
$96$	−2.45854e14	−0.333921
$97$	9.79195e14	1.23050	0.615250	−	0.788332i	$-0.289055\pi$
$97$	9.79195e14	1.23050	0.615250	+	0.788332i	$0.289055\pi$
$98$	−5.34546e14	−0.621998
$99$	−6.23166e14	−0.671954
$100$	1.10849e13	0.0110849
$101$	1.66476e15	1.54505	0.772525	−	0.634984i	$-0.218993\pi$
$101$	1.66476e15	1.54505	0.772525	+	0.634984i	$0.218993\pi$
$102$	−8.75949e14	−0.755053
$103$	−1.03840e15	−0.831925	−0.415962	−	0.909382i	$-0.636555\pi$
$103$	−1.03840e15	−0.831925	−0.415962	+	0.909382i	$0.636555\pi$
$104$	−2.56878e15	−1.91415
$105$	−1.31346e15	−0.910958
$106$	1.14109e15	0.737097
$107$	−3.08276e15	−1.85593	−0.927965	−	0.372668i	$-0.878443\pi$
$107$	−3.08276e15	−1.85593	−0.927965	+	0.372668i	$0.878443\pi$
$108$	4.54467e14	0.255167
$109$	−1.33594e15	−0.699984	−0.349992	−	0.936753i	$-0.613816\pi$
$109$	−1.33594e15	−0.699984	−0.349992	+	0.936753i	$0.613816\pi$
$110$	−2.37550e15	−1.16228
$111$	−7.05079e14	−0.322341
$112$	2.15122e15	0.919497
$113$	−2.62503e15	−1.04965	−0.524827	−	0.851209i	$-0.675870\pi$
$113$	−2.62503e15	−1.04965	−0.524827	+	0.851209i	$0.675870\pi$
$114$	−1.23169e15	−0.461013
$115$	6.13096e14	0.214929
$116$	−7.33236e14	−0.240885
$117$	2.82956e15	0.871615
$118$	−4.74930e15	−1.37251
$119$	−5.86505e15	−1.59100
$120$	2.95288e15	0.752293
$121$	3.60706e15	0.863501
$122$	1.13260e15	0.254905
$123$	2.30037e15	0.486979
$124$	6.34320e13	0.0126370
$125$	−5.44712e15	−1.02174
$126$	−3.17912e15	−0.561731
$127$	5.61481e14	0.0934990	0.0467495	−	0.998907i	$-0.485114\pi$
$127$	5.61481e14	0.0934990	0.0467495	+	0.998907i	$0.485114\pi$
$128$	−3.18413e15	−0.499937
$129$	−7.19485e14	−0.106561
$130$	1.07863e16	1.50763
$131$	−1.50562e16	−1.98692	−0.993460	−	0.114184i	$-0.963575\pi$
$131$	−1.50562e16	−1.98692	−0.993460	+	0.114184i	$0.963575\pi$
$132$	−1.87265e15	−0.233427
$133$	−8.24694e15	−0.971417
$134$	−1.01422e16	−1.12940
$135$	−9.86056e15	−1.03848
$136$	1.31856e16	1.31389
$137$	−1.69710e16	−1.60068	−0.800340	−	0.599547i	$-0.795347\pi$
$137$	−1.69710e16	−1.60068	−0.800340	+	0.599547i	$0.795347\pi$
$138$	−1.53075e15	−0.136713
$139$	−1.11003e16	−0.939122	−0.469561	−	0.882900i	$-0.655588\pi$
$139$	−1.11003e16	−0.939122	−0.469561	+	0.882900i	$0.655588\pi$
$140$	3.82635e15	0.306778
$141$	−1.16615e16	−0.886363
$142$	−2.85777e15	−0.205999
$143$	−3.53456e16	−2.41721
$144$	5.32729e15	0.345770
$145$	1.59090e16	0.980355
$146$	8.04128e15	0.470629
$147$	9.14290e15	0.508398
$148$	2.05402e15	0.108553
$149$	1.68858e16	0.848445	0.424222	−	0.905558i	$-0.360547\pi$
$149$	1.68858e16	0.848445	0.424222	+	0.905558i	$0.360547\pi$
$150$	6.00488e14	0.0286959
$151$	−2.60907e16	−1.18620	−0.593102	−	0.805127i	$-0.702097\pi$
$151$	−2.60907e16	−1.18620	−0.593102	+	0.805127i	$0.702097\pi$
$152$	1.85405e16	0.802221
$153$	−1.45242e16	−0.598283
$154$	3.97122e16	1.55782
$155$	−1.37628e15	−0.0514304
$156$	8.50297e15	0.302786
$157$	−4.08753e16	−1.38744	−0.693720	−	0.720245i	$-0.744029\pi$
$157$	−4.08753e16	−1.38744	−0.693720	+	0.720245i	$0.744029\pi$
$158$	1.88437e16	0.609871
$159$	−1.95172e16	−0.602475
$160$	−1.55397e16	−0.457661
$161$	−1.02494e16	−0.288073
$162$	8.62549e15	0.231431
$163$	−5.04820e16	−1.29339	−0.646695	−	0.762748i	$-0.723850\pi$
$163$	−5.04820e16	−1.29339	−0.646695	+	0.762748i	$0.723850\pi$
$164$	−6.70139e15	−0.163997
$165$	4.06307e16	0.950004
$166$	−4.28240e15	−0.0956922
$167$	−3.69593e15	−0.0789496	−0.0394748	−	0.999221i	$-0.512568\pi$
$167$	−3.69593e15	−0.0789496	−0.0394748	+	0.999221i	$0.512568\pi$
$168$	−4.93644e16	−1.00831
$169$	1.09305e17	2.13545
$170$	−5.53662e16	−1.03485
$171$	−2.04227e16	−0.365294
$172$	2.09599e15	0.0358860
$173$	−3.91294e16	−0.641441	−0.320721	−	0.947174i	$-0.603925\pi$
$173$	−3.91294e16	−0.641441	−0.320721	+	0.947174i	$0.603925\pi$
$174$	−3.97208e16	−0.623589
$175$	4.02066e15	0.0604661
$176$	−6.65460e16	−0.958909
$177$	8.12323e16	1.12184
$178$	−6.06640e16	−0.803121
$179$	9.80903e16	1.24517	0.622585	−	0.782552i	$-0.286083\pi$
$179$	9.80903e16	1.24517	0.622585	+	0.782552i	$0.286083\pi$
$180$	9.47556e15	0.115362
$181$	−3.43233e16	−0.400866	−0.200433	−	0.979707i	$-0.564235\pi$
$181$	−3.43233e16	−0.400866	−0.200433	+	0.979707i	$0.564235\pi$
$182$	−1.80318e17	−2.02071
$183$	−1.93721e16	−0.208350
$184$	2.30422e16	0.237898
$185$	−4.45660e16	−0.441789
$186$	3.43623e15	0.0327141
$187$	1.81430e17	1.65919
$188$	3.39720e16	0.298495
$189$	1.64843e17	1.39189
$190$	−7.78512e16	−0.631849
$191$	5.02868e16	0.392377	0.196189	−	0.980566i	$-0.437144\pi$
$191$	5.02868e16	0.392377	0.196189	+	0.980566i	$0.437144\pi$
$192$	1.05510e17	0.791656
$193$	−1.50024e17	−1.08263	−0.541315	−	0.840820i	$-0.682073\pi$
$193$	−1.50024e17	−1.08263	−0.541315	+	0.840820i	$0.682073\pi$
$194$	−1.54529e17	−1.07275
$195$	−1.84489e17	−1.23228
$196$	−2.66349e16	−0.171210
$197$	−1.44904e17	−0.896567	−0.448283	−	0.893892i	$-0.647964\pi$
$197$	−1.44904e17	−0.896567	−0.448283	+	0.893892i	$0.647964\pi$
$198$	9.83432e16	0.585808
$199$	−2.39762e17	−1.37525	−0.687625	−	0.726066i	$-0.741347\pi$
$199$	−2.39762e17	−1.37525	−0.687625	+	0.726066i	$0.741347\pi$
$200$	−9.03911e15	−0.0499345
$201$	1.73473e17	0.923129
$202$	−2.62720e17	−1.34697
$203$	−2.65957e17	−1.31399
$204$	−4.36460e16	−0.207835
$205$	1.45400e17	0.667437
$206$	1.63872e17	0.725270
$207$	−2.53815e16	−0.108328
$208$	3.02160e17	1.24383
$209$	2.55111e17	1.01305
$210$	2.07281e17	0.794171
$211$	1.99916e17	0.739143	0.369572	−	0.929202i	$-0.379504\pi$
$211$	1.99916e17	0.739143	0.369572	+	0.929202i	$0.379504\pi$
$212$	5.68570e16	0.202892
$213$	4.88794e16	0.168376
$214$	4.86497e17	1.61799
$215$	−4.54766e16	−0.146049
$216$	−3.70594e17	−1.14946
$217$	2.30078e16	0.0689331
$218$	2.10827e17	0.610244
$219$	−1.37538e17	−0.384674
$220$	−1.18364e17	−0.319927
$221$	−8.23803e17	−2.15219
$222$	1.11270e17	0.281016
$223$	1.46102e17	0.356754	0.178377	−	0.983962i	$-0.442915\pi$
$223$	1.46102e17	0.356754	0.178377	+	0.983962i	$0.442915\pi$
$224$	2.59784e17	0.613411
$225$	9.95676e15	0.0227378
$226$	4.14262e17	0.915085
$227$	−2.43257e17	−0.519841	−0.259921	−	0.965630i	$-0.583696\pi$
$227$	−2.43257e17	−0.519841	−0.259921	+	0.965630i	$0.583696\pi$
$228$	−6.13713e16	−0.126898
$229$	1.31385e17	0.262893	0.131446	−	0.991323i	$-0.458038\pi$
$229$	1.31385e17	0.262893	0.131446	+	0.991323i	$0.458038\pi$
$230$	−9.67541e16	−0.187375
$231$	−6.79239e17	−1.27331
$232$	5.97915e17	1.08512
$233$	2.09033e16	0.0367321	0.0183661	−	0.999831i	$-0.494154\pi$
$233$	2.09033e16	0.0367321	0.0183661	+	0.999831i	$0.494154\pi$
$234$	−4.46539e17	−0.759872
$235$	−7.37090e17	−1.21482
$236$	−2.36644e17	−0.377794
$237$	−3.22304e17	−0.498486
$238$	9.25576e17	1.38703
$239$	1.23675e17	0.179596	0.0897981	−	0.995960i	$-0.471378\pi$
$239$	1.23675e17	0.179596	0.0897981	+	0.995960i	$0.471378\pi$
$240$	−3.47342e17	−0.488847
$241$	7.36896e17	1.00526	0.502630	−	0.864502i	$-0.332366\pi$
$241$	7.36896e17	1.00526	0.502630	+	0.864502i	$0.332366\pi$
$242$	−5.69237e17	−0.752798
$243$	6.81776e17	0.874167
$244$	5.64343e16	0.0701648
$245$	5.77896e17	0.696793
$246$	−3.63027e17	−0.424547
$247$	−1.15836e18	−1.31407
$248$	−5.17254e16	−0.0569267
$249$	7.32464e16	0.0782152
$250$	8.59622e17	0.890754
$251$	−1.58985e18	−1.59884	−0.799419	−	0.600774i	$-0.794859\pi$
$251$	−1.58985e18	−1.59884	−0.799419	+	0.600774i	$0.794859\pi$
$252$	−1.58406e17	−0.154621
$253$	3.17054e17	0.300420
$254$	−8.86085e16	−0.0815122
$255$	9.46986e17	0.845848
$256$	−7.78379e17	−0.675136
$257$	1.06518e18	0.897271	0.448636	−	0.893715i	$-0.351910\pi$
$257$	1.06518e18	0.897271	0.448636	+	0.893715i	$0.351910\pi$
$258$	1.13544e17	0.0928998
$259$	7.45025e17	0.592138
$260$	5.37448e17	0.414988
$261$	−6.58615e17	−0.494115
$262$	2.37605e18	1.73219
$263$	7.86754e17	0.557405	0.278702	−	0.960378i	$-0.410096\pi$
$263$	7.86754e17	0.557405	0.278702	+	0.960378i	$0.410096\pi$
$264$	1.52704e18	1.05153
$265$	−1.23363e18	−0.825733
$266$	1.30147e18	0.846878
$267$	1.03760e18	0.656441
$268$	−5.05358e17	−0.310877
$269$	6.58179e16	0.0393733	0.0196867	−	0.999806i	$-0.493733\pi$
$269$	6.58179e16	0.0393733	0.0196867	+	0.999806i	$0.493733\pi$
$270$	1.55612e18	0.905345
$271$	−1.90397e18	−1.07743	−0.538717	−	0.842486i	$-0.681091\pi$
$271$	−1.90397e18	−1.07743	−0.538717	+	0.842486i	$0.681091\pi$
$272$	−1.55100e18	−0.853776
$273$	3.08416e18	1.65165
$274$	2.67824e18	1.39547
$275$	−1.24375e17	−0.0630578
$276$	−7.62727e16	−0.0376314
$277$	−9.72903e17	−0.467166	−0.233583	−	0.972337i	$-0.575045\pi$
$277$	−9.72903e17	−0.467166	−0.233583	+	0.972337i	$0.575045\pi$
$278$	1.75176e18	0.818724
$279$	5.69766e16	0.0259218
$280$	−3.12018e18	−1.38196
$281$	3.13534e18	1.35203	0.676017	−	0.736886i	$-0.263704\pi$
$281$	3.13534e18	1.35203	0.676017	+	0.736886i	$0.263704\pi$
$282$	1.84033e18	0.772729
$283$	−2.49493e18	−1.02014	−0.510070	−	0.860133i	$-0.670381\pi$
$283$	−2.49493e18	−1.02014	−0.510070	+	0.860133i	$0.670381\pi$
$284$	−1.42394e17	−0.0567028
$285$	1.33157e18	0.516450
$286$	5.57796e18	2.10732
$287$	−2.43070e18	−0.894577
$288$	6.43328e17	0.230669
$289$	1.36618e18	0.477281
$290$	−2.51064e18	−0.854671
$291$	2.64307e18	0.876822
$292$	4.00673e17	0.129545
$293$	−4.45469e18	−1.40382	−0.701908	−	0.712267i	$-0.747668\pi$
$293$	−4.45469e18	−1.40382	−0.701908	+	0.712267i	$0.747668\pi$
$294$	−1.44286e18	−0.443220
$295$	5.13446e18	1.53755
$296$	−1.67494e18	−0.489003
$297$	−5.09925e18	−1.45155
$298$	−2.66478e18	−0.739672
$299$	−1.43962e18	−0.389686
$300$	2.99206e16	0.00789879
$301$	7.60248e17	0.195752
$302$	4.11744e18	1.03413
$303$	4.49358e18	1.10096
$304$	−2.18088e18	−0.521291
$305$	−1.22445e18	−0.285558
$306$	2.29210e18	0.521581
$307$	−2.74229e18	−0.608942	−0.304471	−	0.952522i	$-0.598480\pi$
$307$	−2.74229e18	−0.608942	−0.304471	+	0.952522i	$0.598480\pi$
$308$	1.97874e18	0.428804
$309$	−2.80287e18	−0.592808
$310$	2.17194e17	0.0448369
$311$	−6.45332e18	−1.30041	−0.650205	−	0.759759i	$-0.725317\pi$
$311$	−6.45332e18	−1.30041	−0.650205	+	0.759759i	$0.725317\pi$
$312$	−6.93371e18	−1.36398
$313$	−9.52968e18	−1.83019	−0.915094	−	0.403239i	$-0.867884\pi$
$313$	−9.52968e18	−1.83019	−0.915094	+	0.403239i	$0.867884\pi$
$314$	6.45062e18	1.20957
$315$	3.43694e18	0.629279
$316$	9.38927e17	0.167872
$317$	−3.89195e18	−0.679553	−0.339776	−	0.940506i	$-0.610351\pi$
$317$	−3.89195e18	−0.679553	−0.339776	+	0.940506i	$0.610351\pi$
$318$	3.08005e18	0.525236
$319$	8.22712e18	1.37031
$320$	6.66901e18	1.08502
$321$	−8.32107e18	−1.32249
$322$	1.61747e18	0.251141
$323$	5.94591e18	0.901985
$324$	4.29783e17	0.0637033
$325$	5.64741e17	0.0817945
$326$	7.96668e18	1.12757
$327$	−3.60600e18	−0.498790
$328$	5.46462e18	0.738765
$329$	1.23222e19	1.62824
$330$	−6.41203e18	−0.828211
$331$	5.71521e18	0.721643	0.360821	−	0.932635i	$-0.382496\pi$
$331$	5.71521e18	0.721643	0.360821	+	0.932635i	$0.382496\pi$
$332$	−2.13379e17	−0.0263401
$333$	1.84498e18	0.222669
$334$	5.83263e17	0.0688281
$335$	1.09647e19	1.26521
$336$	5.80664e18	0.655210
$337$	−6.86429e17	−0.0757481	−0.0378740	−	0.999283i	$-0.512059\pi$
$337$	−6.86429e17	−0.0757481	−0.0378740	+	0.999283i	$0.512059\pi$
$338$	−1.72496e19	−1.86168
$339$	−7.08555e18	−0.747956
$340$	−2.75873e18	−0.284851
$341$	−7.11725e17	−0.0718877
$342$	3.22295e18	0.318462
$343$	3.87988e18	0.375070
$344$	−1.70916e18	−0.161657
$345$	1.65489e18	0.153153
$346$	6.17509e18	0.559207
$347$	−2.02412e19	−1.79376	−0.896882	−	0.442271i	$-0.854173\pi$
$347$	−2.02412e19	−1.79376	−0.896882	+	0.442271i	$0.854173\pi$
$348$	−1.97917e18	−0.171648
$349$	−8.07340e18	−0.685276	−0.342638	−	0.939467i	$-0.611320\pi$
$349$	−8.07340e18	−0.685276	−0.342638	+	0.939467i	$0.611320\pi$
$350$	−6.34509e17	−0.0527142
$351$	2.31537e19	1.88286
$352$	−8.03616e18	−0.639703
$353$	−2.36921e19	−1.84627	−0.923133	−	0.384482i	$-0.874380\pi$
$353$	−2.36921e19	−1.84627	−0.923133	+	0.384482i	$0.874380\pi$
$354$	−1.28194e19	−0.978013
$355$	3.08953e18	0.230770
$356$	−3.02271e18	−0.221066
$357$	−1.58311e19	−1.13370
$358$	−1.54798e19	−1.08554
$359$	−4.23117e18	−0.290571	−0.145285	−	0.989390i	$-0.546410\pi$
$359$	−4.23117e18	−0.290571	−0.145285	+	0.989390i	$0.546410\pi$
$360$	−7.72682e18	−0.519675
$361$	−6.82049e18	−0.449274
$362$	5.41663e18	0.349474
$363$	9.73627e18	0.615308
$364$	−8.98471e18	−0.556216
$365$	−8.69340e18	−0.527222
$366$	3.05715e18	0.181639
$367$	1.32911e19	0.773687	0.386843	−	0.922145i	$-0.373565\pi$
$367$	1.32911e19	0.773687	0.386843	+	0.922145i	$0.373565\pi$
$368$	−2.71041e18	−0.154588
$369$	−6.01939e18	−0.336399
$370$	7.03305e18	0.385151
$371$	2.06230e19	1.10674
$372$	1.71217e17	0.00900484
$373$	−1.65517e19	−0.853150	−0.426575	−	0.904452i	$-0.640280\pi$
$373$	−1.65517e19	−0.853150	−0.426575	+	0.904452i	$0.640280\pi$
$374$	−2.86318e19	−1.44648
$375$	−1.47030e19	−0.728068
$376$	−2.77024e19	−1.34465
$377$	−3.73562e19	−1.77747
$378$	−2.60142e19	−1.21345
$379$	7.90359e17	0.0361435	0.0180718	−	0.999837i	$-0.494247\pi$
$379$	7.90359e17	0.0361435	0.0180718	+	0.999837i	$0.494247\pi$
$380$	−3.87910e18	−0.173922
$381$	1.51557e18	0.0666250
$382$	−7.93587e18	−0.342073
$383$	3.32591e19	1.40579	0.702893	−	0.711296i	$-0.251891\pi$
$383$	3.32591e19	1.40579	0.702893	+	0.711296i	$0.251891\pi$
$384$	−8.59468e18	−0.356242
$385$	−4.29327e19	−1.74515
$386$	2.36756e19	0.943834
$387$	1.88268e18	0.0736112
$388$	−7.69973e18	−0.295282
$389$	3.15545e19	1.18697	0.593484	−	0.804846i	$-0.297752\pi$
$389$	3.15545e19	1.18697	0.593484	+	0.804846i	$0.297752\pi$
$390$	2.91146e19	1.07430
$391$	7.38962e18	0.267483
$392$	2.17193e19	0.771259
$393$	−4.06401e19	−1.41583
$394$	2.28676e19	0.781624
$395$	−2.03719e19	−0.683208
$396$	4.90015e18	0.161249
$397$	1.26209e19	0.407533	0.203766	−	0.979020i	$-0.434682\pi$
$397$	1.26209e19	0.407533	0.203766	+	0.979020i	$0.434682\pi$
$398$	3.78373e19	1.19894
$399$	−2.22604e19	−0.692206
$400$	1.06325e18	0.0324479
$401$	4.44097e19	1.33013	0.665066	−	0.746785i	$-0.268403\pi$
$401$	4.44097e19	1.33013	0.665066	+	0.746785i	$0.268403\pi$
$402$	−2.73762e19	−0.804781
$403$	3.23167e18	0.0932480
$404$	−1.30906e19	−0.370765
$405$	−9.32500e18	−0.259260
$406$	4.19712e19	1.14553
$407$	−2.30467e19	−0.617518
$408$	3.55909e19	0.936242
$409$	1.85362e19	0.478736	0.239368	−	0.970929i	$-0.423060\pi$
$409$	1.85362e19	0.478736	0.239368	+	0.970929i	$0.423060\pi$
$410$	−2.29459e19	−0.581870
$411$	−4.58087e19	−1.14060
$412$	8.16524e18	0.199637
$413$	−8.58346e19	−2.06080
$414$	4.00551e18	0.0944398
$415$	4.62969e18	0.107199
$416$	3.64891e19	0.829781
$417$	−2.99621e19	−0.669194
$418$	−4.02597e19	−0.883177
$419$	−9.81436e18	−0.211474	−0.105737	−	0.994394i	$-0.533720\pi$
$419$	−9.81436e18	−0.211474	−0.105737	+	0.994394i	$0.533720\pi$
$420$	1.03282e19	0.218602
$421$	1.42601e19	0.296487	0.148244	−	0.988951i	$-0.452638\pi$
$421$	1.42601e19	0.296487	0.148244	+	0.988951i	$0.452638\pi$
$422$	−3.15491e19	−0.644383
$423$	3.05147e19	0.612289
$424$	−4.63639e19	−0.913978
$425$	−2.89883e18	−0.0561443
$426$	−7.71377e18	−0.146789
$427$	2.04696e19	0.382738
$428$	2.42407e19	0.445366
$429$	−9.54057e19	−1.72244
$430$	7.17676e18	0.127325
$431$	5.45748e19	0.951508	0.475754	−	0.879578i	$-0.342175\pi$
$431$	5.45748e19	0.951508	0.475754	+	0.879578i	$0.342175\pi$
$432$	4.35922e19	0.746931
$433$	1.11979e20	1.88572	0.942861	−	0.333188i	$-0.108124\pi$
$433$	1.11979e20	1.88572	0.942861	+	0.333188i	$0.108124\pi$
$434$	−3.63091e18	−0.0600956
$435$	4.29421e19	0.698576
$436$	1.05049e19	0.167975
$437$	1.03907e19	0.163317
$438$	2.17052e19	0.335358
$439$	−7.46694e19	−1.13412	−0.567060	−	0.823676i	$-0.691919\pi$
$439$	−7.46694e19	−1.13412	−0.567060	+	0.823676i	$0.691919\pi$
$440$	9.65199e19	1.44119
$441$	−2.39242e19	−0.351195
$442$	1.30006e20	1.87628
$443$	−4.03892e19	−0.573109	−0.286555	−	0.958064i	$-0.592510\pi$
$443$	−4.03892e19	−0.573109	−0.286555	+	0.958064i	$0.592510\pi$
$444$	5.54426e18	0.0773519
$445$	6.55837e19	0.899696
$446$	−2.30566e19	−0.311017
$447$	4.55785e19	0.604580
$448$	−1.11488e20	−1.45427
$449$	1.33981e20	1.71868	0.859342	−	0.511401i	$-0.170873\pi$
$449$	1.33981e20	1.71868	0.859342	+	0.511401i	$0.170873\pi$
$450$	−1.57130e18	−0.0198228
$451$	7.51915e19	0.932921
$452$	2.06414e19	0.251885
$453$	−7.04249e19	−0.845258
$454$	3.83889e19	0.453196
$455$	1.94941e20	2.26369
$456$	5.00450e19	0.571642
$457$	1.29635e20	1.45664	0.728320	−	0.685237i	$-0.240301\pi$
$457$	1.29635e20	1.45664	0.728320	+	0.685237i	$0.240301\pi$
$458$	−2.07341e19	−0.229189
$459$	−1.18849e20	−1.29241
$460$	−4.82097e18	−0.0515764
$461$	−4.44166e19	−0.467507	−0.233753	−	0.972296i	$-0.575101\pi$
$461$	−4.44166e19	−0.467507	−0.233753	+	0.972296i	$0.575101\pi$
$462$	1.07192e20	1.11006
$463$	−1.02547e20	−1.04488	−0.522438	−	0.852677i	$-0.674978\pi$
$463$	−1.02547e20	−1.04488	−0.522438	+	0.852677i	$0.674978\pi$
$464$	−7.03316e19	−0.705124
$465$	−3.71490e18	−0.0366480
$466$	−3.29880e18	−0.0320230
$467$	1.33602e20	1.27625	0.638124	−	0.769933i	$-0.279711\pi$
$467$	1.33602e20	1.27625	0.638124	+	0.769933i	$0.279711\pi$
$468$	−2.22497e19	−0.209161
$469$	−1.83302e20	−1.69578
$470$	1.16322e20	1.05908
$471$	−1.10332e20	−0.988653
$472$	1.92970e20	1.70187
$473$	−2.35176e19	−0.204143
$474$	5.08635e19	0.434579
$475$	−4.07609e18	−0.0342801
$476$	4.61188e19	0.381791
$477$	5.10707e19	0.416183
$478$	−1.95174e19	−0.156571
$479$	−2.06274e20	−1.62903	−0.814515	−	0.580143i	$-0.802997\pi$
$479$	−2.06274e20	−1.62903	−0.814515	+	0.580143i	$0.802997\pi$
$480$	−4.19453e19	−0.326117
$481$	1.04646e20	0.801004
$482$	−1.16291e20	−0.876383
$483$	−2.76654e19	−0.205273
$484$	−2.83634e19	−0.207214
$485$	1.67061e20	1.20174
$486$	−1.07593e20	−0.762097
$487$	−3.42834e19	−0.239120	−0.119560	−	0.992827i	$-0.538148\pi$
$487$	−3.42834e19	−0.239120	−0.119560	+	0.992827i	$0.538148\pi$
$488$	−4.60191e19	−0.316075
$489$	−1.36263e20	−0.921637
$490$	−9.11990e19	−0.607463
$491$	−1.54863e20	−1.01587	−0.507935	−	0.861396i	$-0.669591\pi$
$491$	−1.54863e20	−1.01587	−0.507935	+	0.861396i	$0.669591\pi$
$492$	−1.80886e19	−0.116860
$493$	1.91750e20	1.22007
$494$	1.82804e20	1.14560
$495$	−1.06319e20	−0.656251
$496$	6.08436e18	0.0369915
$497$	−5.16487e19	−0.309305
$498$	−1.15592e19	−0.0681878
$499$	1.65842e20	0.963699	0.481850	−	0.876254i	$-0.339965\pi$
$499$	1.65842e20	0.963699	0.481850	+	0.876254i	$0.339965\pi$
$500$	4.28325e19	0.245187
$501$	−9.97616e18	−0.0562575
$502$	2.50898e20	1.39386
$503$	2.78182e20	1.52254	0.761272	−	0.648433i	$-0.224575\pi$
$503$	2.78182e20	1.52254	0.761272	+	0.648433i	$0.224575\pi$
$504$	1.29172e20	0.696529
$505$	2.84026e20	1.50894
$506$	−5.00350e19	−0.261906
$507$	2.95038e20	1.52166
$508$	−4.41510e18	−0.0224369
$509$	−1.42767e20	−0.714900	−0.357450	−	0.933932i	$-0.616354\pi$
$509$	−1.42767e20	−0.714900	−0.357450	+	0.933932i	$0.616354\pi$
$510$	−1.49446e20	−0.737408
$511$	1.45331e20	0.706644
$512$	2.27175e20	1.08852
$513$	−1.67115e20	−0.789107
$514$	−1.68098e20	−0.782239
$515$	−1.77161e20	−0.812483
$516$	5.65754e18	0.0255714
$517$	−3.81176e20	−1.69803
$518$	−1.17574e20	−0.516224
$519$	−1.05619e20	−0.457075
$520$	−4.38260e20	−1.86942
$521$	−1.19078e20	−0.500666	−0.250333	−	0.968160i	$-0.580540\pi$
$521$	−1.19078e20	−0.500666	−0.250333	+	0.968160i	$0.580540\pi$
$522$	1.03937e20	0.430768
$523$	1.27835e20	0.522261	0.261130	−	0.965304i	$-0.415905\pi$
$523$	1.27835e20	0.522261	0.261130	+	0.965304i	$0.415905\pi$
$524$	1.18392e20	0.476800
$525$	1.08527e19	0.0430866
$526$	−1.24159e20	−0.485944
$527$	−1.65883e19	−0.0640061
$528$	−1.79623e20	−0.683294
$529$	−2.53722e20	−0.951568
$530$	1.94681e20	0.719871
$531$	−2.12561e20	−0.774951
$532$	6.48483e19	0.233110
$533$	−3.41416e20	−1.21012
$534$	−1.63746e20	−0.572283
$535$	−5.25951e20	−1.81256
$536$	4.12092e20	1.40042
$537$	2.64768e20	0.887276
$538$	−1.03869e19	−0.0343255
$539$	2.98851e20	0.973954
$540$	7.75368e19	0.249204
$541$	−2.48542e20	−0.787809	−0.393905	−	0.919151i	$-0.628876\pi$
$541$	−2.48542e20	−0.787809	−0.393905	+	0.919151i	$0.628876\pi$
$542$	3.00470e20	0.939305
$543$	−9.26464e19	−0.285647
$544$	−1.87300e20	−0.569568
$545$	−2.27925e20	−0.683625
$546$	−4.86719e20	−1.43990
$547$	2.56672e20	0.748986	0.374493	−	0.927230i	$-0.377817\pi$
$547$	2.56672e20	0.748986	0.374493	+	0.927230i	$0.377817\pi$
$548$	1.33449e20	0.384114
$549$	5.06910e19	0.143926
$550$	1.96279e19	0.0549737
$551$	2.69623e20	0.744939
$552$	6.21963e19	0.169520
$553$	3.40564e20	0.915716
$554$	1.53536e20	0.407274
$555$	−1.20294e20	−0.314808
$556$	8.72849e19	0.225361
$557$	4.27032e19	0.108779	0.0543896	−	0.998520i	$-0.482679\pi$
$557$	4.27032e19	0.108779	0.0543896	+	0.998520i	$0.482679\pi$
$558$	−8.99159e18	−0.0225985
$559$	1.06784e20	0.264800
$560$	3.67021e20	0.898009
$561$	4.89720e20	1.18230
$562$	−4.94795e20	−1.17870
$563$	7.88211e20	1.85280	0.926402	−	0.376536i	$-0.122885\pi$
$563$	7.88211e20	1.85280	0.926402	+	0.376536i	$0.122885\pi$
$564$	9.16982e19	0.212700
$565$	−4.47857e20	−1.02512
$566$	3.93730e20	0.889356
$567$	1.55889e20	0.347491
$568$	1.16115e20	0.255432
$569$	−4.76216e20	−1.03386	−0.516931	−	0.856027i	$-0.672925\pi$
$569$	−4.76216e20	−1.03386	−0.516931	+	0.856027i	$0.672925\pi$
$570$	−2.10138e20	−0.450240
$571$	−6.11755e20	−1.29362	−0.646810	−	0.762651i	$-0.723897\pi$
$571$	−6.11755e20	−1.29362	−0.646810	+	0.762651i	$0.723897\pi$
$572$	2.77933e20	0.580057
$573$	1.35735e20	0.279598
$574$	3.83595e20	0.779890
$575$	−5.06580e18	−0.0101657
$576$	−2.76089e20	−0.546866
$577$	6.41621e20	1.25447	0.627234	−	0.778831i	$-0.284187\pi$
$577$	6.41621e20	1.25447	0.627234	+	0.778831i	$0.284187\pi$
$578$	−2.15600e20	−0.416093
$579$	−4.04948e20	−0.771454
$580$	−1.25098e20	−0.235255
$581$	−7.73962e19	−0.143681
$582$	−4.17109e20	−0.764411
$583$	−6.37952e20	−1.15418
$584$	−3.26728e20	−0.583565
$585$	4.82752e20	0.851246
$586$	7.03004e20	1.22384
$587$	−2.11915e19	−0.0364229	−0.0182115	−	0.999834i	$-0.505797\pi$
$587$	−2.11915e19	−0.0364229	−0.0182115	+	0.999834i	$0.505797\pi$
$588$	−7.18935e19	−0.122000
$589$	−2.33250e19	−0.0390802
$590$	−8.10280e20	−1.34043
$591$	−3.91128e20	−0.638870
$592$	1.97020e20	0.317759
$593$	2.18834e20	0.348502	0.174251	−	0.984701i	$-0.444250\pi$
$593$	2.18834e20	0.348502	0.174251	+	0.984701i	$0.444250\pi$
$594$	8.04724e20	1.26546
$595$	−1.00064e21	−1.55382
$596$	−1.32778e20	−0.203601
$597$	−6.47171e20	−0.979968
$598$	2.27190e20	0.339727
$599$	−8.31650e20	−1.22812	−0.614058	−	0.789261i	$-0.710464\pi$
$599$	−8.31650e20	−1.22812	−0.614058	+	0.789261i	$0.710464\pi$
$600$	−2.43986e19	−0.0355821
$601$	4.23472e20	0.609910	0.304955	−	0.952367i	$-0.401359\pi$
$601$	4.23472e20	0.609910	0.304955	+	0.952367i	$0.401359\pi$
$602$	−1.19976e20	−0.170656
$603$	−4.53928e20	−0.637686
$604$	2.05160e20	0.284653
$605$	6.15401e20	0.843321
$606$	−7.09141e20	−0.959816
$607$	9.89054e20	1.32222	0.661111	−	0.750288i	$-0.270085\pi$
$607$	9.89054e20	1.32222	0.661111	+	0.750288i	$0.270085\pi$
$608$	−2.63365e20	−0.347761
$609$	−7.17878e20	−0.936313
$610$	1.93234e20	0.248948
$611$	1.73077e21	2.20258
$612$	1.14208e20	0.143570
$613$	−1.28885e21	−1.60048	−0.800238	−	0.599683i	$-0.795294\pi$
$613$	−1.28885e21	−1.60048	−0.800238	+	0.599683i	$0.795294\pi$
$614$	4.32767e20	0.530874
$615$	3.92468e20	0.475598
$616$	−1.61356e21	−1.93165
$617$	6.20383e20	0.733705	0.366852	−	0.930279i	$-0.380435\pi$
$617$	6.20383e20	0.733705	0.366852	+	0.930279i	$0.380435\pi$
$618$	4.42327e20	0.516809
$619$	−2.97699e20	−0.343635	−0.171818	−	0.985129i	$-0.554964\pi$
$619$	−2.97699e20	−0.343635	−0.171818	+	0.985129i	$0.554964\pi$
$620$	1.08222e19	0.0123417
$621$	−2.07692e20	−0.234009
$622$	1.01841e21	1.13369
$623$	−1.09639e21	−1.20588
$624$	8.15599e20	0.886324
$625$	−8.86315e20	−0.951673
$626$	1.50390e21	1.59555
$627$	6.88603e20	0.721876
$628$	3.21416e20	0.332943
$629$	−5.37151e20	−0.549815
$630$	−5.42391e20	−0.548604
$631$	1.23950e19	0.0123888	0.00619438	−	0.999981i	$-0.498028\pi$
$631$	1.23950e19	0.0123888	0.00619438	+	0.999981i	$0.498028\pi$
$632$	−7.65645e20	−0.756222
$633$	5.39618e20	0.526694
$634$	6.14198e20	0.592432
$635$	9.57945e19	0.0913140
$636$	1.53470e20	0.144576
$637$	−1.35697e21	−1.26335
$638$	−1.29834e21	−1.19463
$639$	−1.27903e20	−0.116312
$640$	−5.43245e20	−0.488254
$641$	−1.60029e21	−1.42155	−0.710777	−	0.703418i	$-0.751656\pi$
$641$	−1.60029e21	−1.42155	−0.710777	+	0.703418i	$0.751656\pi$
$642$	1.31317e21	1.15294
$643$	−9.07785e20	−0.787773	−0.393886	−	0.919159i	$-0.628870\pi$
$643$	−9.07785e20	−0.787773	−0.393886	+	0.919159i	$0.628870\pi$
$644$	8.05940e19	0.0691287
$645$	−1.22752e20	−0.104071
$646$	−9.38337e20	−0.786348
$647$	1.52292e21	1.26152	0.630762	−	0.775976i	$-0.282742\pi$
$647$	1.52292e21	1.26152	0.630762	+	0.775976i	$0.282742\pi$
$648$	−3.50465e20	−0.286967
$649$	2.65521e21	2.14914
$650$	−8.91230e19	−0.0713082
$651$	6.21034e19	0.0491199
$652$	3.96956e20	0.310374
$653$	−2.74506e20	−0.212179	−0.106089	−	0.994357i	$-0.533833\pi$
$653$	−2.74506e20	−0.212179	−0.106089	+	0.994357i	$0.533833\pi$
$654$	5.69071e20	0.434844
$655$	−2.56874e21	−1.94049
$656$	−6.42793e20	−0.480056
$657$	3.59897e20	0.265728
$658$	−1.94459e21	−1.41950
$659$	−8.40586e19	−0.0606654	−0.0303327	−	0.999540i	$-0.509657\pi$
$659$	−8.40586e19	−0.0606654	−0.0303327	+	0.999540i	$0.509657\pi$
$660$	−3.19493e20	−0.227972
$661$	1.33139e21	0.939281	0.469641	−	0.882858i	$-0.344384\pi$
$661$	1.33139e21	0.939281	0.469641	+	0.882858i	$0.344384\pi$
$662$	−9.01930e20	−0.629126
$663$	−2.22363e21	−1.53360
$664$	1.74000e20	0.118655
$665$	−1.40701e21	−0.948715
$666$	−2.91160e20	−0.194122
$667$	3.35090e20	0.220911
$668$	2.90623e19	0.0189455
$669$	3.94362e20	0.254214
$670$	−1.73037e21	−1.10301
$671$	−6.33209e20	−0.399143
$672$	7.01215e20	0.437101
$673$	2.05646e21	1.26767	0.633837	−	0.773466i	$-0.281479\pi$
$673$	2.05646e21	1.26767	0.633837	+	0.773466i	$0.281479\pi$
$674$	1.08327e20	0.0660370
$675$	8.14743e19	0.0491182
$676$	−8.59498e20	−0.512442
$677$	9.82072e20	0.579067	0.289533	−	0.957168i	$-0.406500\pi$
$677$	9.82072e20	0.579067	0.289533	+	0.957168i	$0.406500\pi$
$678$	1.11819e21	0.652066
$679$	−2.79282e21	−1.61072
$680$	2.24960e21	1.28318
$681$	−6.56605e20	−0.370426
$682$	1.12319e20	0.0626715
$683$	1.17147e20	0.0646509	0.0323255	−	0.999477i	$-0.489709\pi$
$683$	1.17147e20	0.0646509	0.0323255	+	0.999477i	$0.489709\pi$
$684$	1.60590e20	0.0876594
$685$	−2.89544e21	−1.56327
$686$	−6.12293e20	−0.326985
$687$	3.54637e20	0.187331
$688$	2.01046e20	0.105046
$689$	2.89670e21	1.49713
$690$	−2.61161e20	−0.133518
$691$	7.80177e20	0.394555	0.197278	−	0.980348i	$-0.436790\pi$
$691$	7.80177e20	0.394555	0.197278	+	0.980348i	$0.436790\pi$
$692$	3.07687e20	0.153926
$693$	1.77737e21	0.879585
$694$	3.19431e21	1.56380
$695$	−1.89382e21	−0.917176
$696$	1.61391e21	0.773232
$697$	1.75250e21	0.830637
$698$	1.27408e21	0.597422
$699$	5.64229e19	0.0261744
$700$	−3.16157e19	−0.0145100
$701$	−1.50122e21	−0.681648	−0.340824	−	0.940127i	$-0.610706\pi$
$701$	−1.50122e21	−0.681648	−0.340824	+	0.940127i	$0.610706\pi$
$702$	−3.65394e21	−1.64147
$703$	−7.55297e20	−0.335701
$704$	3.44878e21	1.51660
$705$	−1.98958e21	−0.865649
$706$	3.73891e21	1.60957
$707$	−4.74817e21	−2.02246
$708$	−6.38755e20	−0.269206
$709$	−3.48294e21	−1.45244	−0.726221	−	0.687461i	$-0.758725\pi$
$709$	−3.48294e21	−1.45244	−0.726221	+	0.687461i	$0.758725\pi$
$710$	−4.87565e20	−0.201185
$711$	8.43373e20	0.344348
$712$	2.46486e21	0.995845
$713$	−2.89885e19	−0.0115892
$714$	2.49834e21	0.988360
$715$	−6.03032e21	−2.36072
$716$	−7.71316e20	−0.298803
$717$	3.33826e20	0.127976
$718$	6.67730e20	0.253319
$719$	3.72828e21	1.39972	0.699861	−	0.714279i	$-0.253245\pi$
$719$	3.72828e21	1.39972	0.699861	+	0.714279i	$0.253245\pi$
$720$	9.08890e20	0.337690
$721$	2.96167e21	1.08898
$722$	1.07636e21	0.391676
$723$	1.98905e21	0.716323
$724$	2.69895e20	0.0961957
$725$	−1.31451e20	−0.0463689
$726$	−1.53650e21	−0.536424
$727$	3.85885e21	1.33337	0.666684	−	0.745341i	$-0.267713\pi$
$727$	3.85885e21	1.33337	0.666684	+	0.745341i	$0.267713\pi$
$728$	7.32655e21	2.50561
$729$	2.62453e21	0.888373
$730$	1.37192e21	0.459631
$731$	−5.48127e20	−0.181761
$732$	1.52329e20	0.0499977
$733$	−9.48275e20	−0.308074	−0.154037	−	0.988065i	$-0.549227\pi$
$733$	−9.48275e20	−0.308074	−0.154037	+	0.988065i	$0.549227\pi$
$734$	−2.09750e21	−0.674498
$735$	1.55987e21	0.496517
$736$	−3.27312e20	−0.103128
$737$	5.67026e21	1.76847
$738$	9.49933e20	0.293272
$739$	−2.01265e21	−0.615086	−0.307543	−	0.951534i	$-0.599507\pi$
$739$	−2.01265e21	−0.615086	−0.307543	+	0.951534i	$0.599507\pi$
$740$	3.50436e20	0.106016
$741$	−3.12668e21	−0.936370
$742$	−3.25456e21	−0.964856
$743$	2.15678e21	0.632979	0.316490	−	0.948596i	$-0.397496\pi$
$743$	2.15678e21	0.632979	0.316490	+	0.948596i	$0.397496\pi$
$744$	−1.39619e20	−0.0405645
$745$	2.88089e21	0.828617
$746$	2.61205e21	0.743774
$747$	−1.91664e20	−0.0540301
$748$	−1.42664e21	−0.398155
$749$	8.79251e21	2.42940
$750$	2.32032e21	0.634728
$751$	3.35901e21	0.909728	0.454864	−	0.890561i	$-0.349688\pi$
$751$	3.35901e21	0.909728	0.454864	+	0.890561i	$0.349688\pi$
$752$	3.25858e21	0.873764
$753$	−4.29138e21	−1.13929
$754$	5.89526e21	1.54959
$755$	−4.45135e21	−1.15848
$756$	−1.29621e21	−0.334012
$757$	4.34013e20	0.110735	0.0553674	−	0.998466i	$-0.482367\pi$
$757$	4.34013e20	0.110735	0.0553674	+	0.998466i	$0.482367\pi$
$758$	−1.24728e20	−0.0315098
$759$	8.55801e20	0.214072
$760$	3.16320e21	0.783474
$761$	−3.68509e21	−0.903780	−0.451890	−	0.892074i	$-0.649250\pi$
$761$	−3.68509e21	−0.903780	−0.451890	+	0.892074i	$0.649250\pi$
$762$	−2.39175e20	−0.0580835
$763$	3.81030e21	0.916275
$764$	−3.95421e20	−0.0941585
$765$	−2.47798e21	−0.584301
$766$	−5.24868e21	−1.22556
$767$	−1.20563e22	−2.78772
$768$	−2.10102e21	−0.481085
$769$	7.98353e20	0.181029	0.0905144	−	0.995895i	$-0.471149\pi$
$769$	7.98353e20	0.181029	0.0905144	+	0.995895i	$0.471149\pi$
$770$	6.77531e21	1.52142
$771$	2.87516e21	0.639373
$772$	1.17968e21	0.259798
$773$	−8.75684e21	−1.90986	−0.954930	−	0.296832i	$-0.904070\pi$
$773$	−8.75684e21	−1.90986	−0.954930	+	0.296832i	$0.904070\pi$
$774$	−2.97110e20	−0.0641741
$775$	1.13717e19	0.00243256
$776$	6.27872e21	1.33017
$777$	2.01099e21	0.421942
$778$	−4.97968e21	−1.03480
$779$	2.46421e21	0.507163
$780$	1.45069e21	0.295710
$781$	1.59770e21	0.322562
$782$	−1.16617e21	−0.233191
$783$	−5.38932e21	−1.06739
$784$	−2.55480e21	−0.501171
$785$	−6.97375e21	−1.35502
$786$	6.41350e21	1.23431
$787$	5.91376e20	0.112734	0.0563668	−	0.998410i	$-0.482048\pi$
$787$	5.91376e20	0.112734	0.0563668	+	0.998410i	$0.482048\pi$
$788$	1.13942e21	0.215149
$789$	2.12363e21	0.397192
$790$	3.21493e21	0.595619
$791$	7.48699e21	1.37399
$792$	−3.99581e21	−0.726384
$793$	2.87516e21	0.517742
$794$	−1.99174e21	−0.355286
$795$	−3.32984e21	−0.588396
$796$	1.88532e21	0.330018
$797$	−8.87507e21	−1.53898	−0.769492	−	0.638656i	$-0.779491\pi$
$797$	−8.87507e21	−1.53898	−0.769492	+	0.638656i	$0.779491\pi$
$798$	3.51296e21	0.603464
$799$	−8.88411e21	−1.51187
$800$	1.28399e20	0.0216465
$801$	−2.71509e21	−0.453461
$802$	−7.00838e21	−1.15961
$803$	−4.49567e21	−0.736933
$804$	−1.36408e21	−0.221523
$805$	−1.74865e21	−0.281341
$806$	−5.09997e20	−0.0812933
$807$	1.77657e20	0.0280564
$808$	1.06747e22	1.67020
$809$	−3.90755e21	−0.605746	−0.302873	−	0.953031i	$-0.597946\pi$
$809$	−3.90755e21	−0.605746	−0.302873	+	0.953031i	$0.597946\pi$
$810$	1.47160e21	0.226022
$811$	5.69280e21	0.866303	0.433152	−	0.901321i	$-0.357401\pi$
$811$	5.69280e21	0.866303	0.433152	+	0.901321i	$0.357401\pi$
$812$	2.09130e21	0.315317
$813$	−5.13926e21	−0.767753
$814$	3.63704e21	0.538351
$815$	−8.61276e21	−1.26316
$816$	−4.18649e21	−0.608379
$817$	−7.70730e20	−0.110978
$818$	−2.92524e21	−0.417360
$819$	−8.07034e21	−1.14094
$820$	−1.14333e21	−0.160164
$821$	1.08209e22	1.50207	0.751033	−	0.660265i	$-0.229556\pi$
$821$	1.08209e22	1.50207	0.751033	+	0.660265i	$0.229556\pi$
$822$	7.22917e21	0.994374
$823$	−8.12058e21	−1.10685	−0.553424	−	0.832899i	$-0.686679\pi$
$823$	−8.12058e21	−1.10685	−0.553424	+	0.832899i	$0.686679\pi$
$824$	−6.65832e21	−0.899312
$825$	−3.35717e20	−0.0449334
$826$	1.35457e22	1.79660
$827$	1.23977e22	1.62948	0.814741	−	0.579826i	$-0.196879\pi$
$827$	1.23977e22	1.62948	0.814741	+	0.579826i	$0.196879\pi$
$828$	1.99583e20	0.0259954
$829$	1.11379e21	0.143762	0.0718812	−	0.997413i	$-0.477100\pi$
$829$	1.11379e21	0.143762	0.0718812	+	0.997413i	$0.477100\pi$
$830$	−7.30622e20	−0.0934559
$831$	−2.62609e21	−0.332891
$832$	−1.56596e22	−1.96723
$833$	6.96535e21	0.867172
$834$	4.72839e21	0.583402
$835$	−6.30564e20	−0.0771046
$836$	−2.00602e21	−0.243102
$837$	4.66228e20	0.0559961
$838$	1.54882e21	0.184362
$839$	1.27216e22	1.50082	0.750409	−	0.660974i	$-0.229857\pi$
$839$	1.27216e22	1.50082	0.750409	+	0.660974i	$0.229857\pi$
$840$	−8.42208e21	−0.984747
$841$	6.59366e19	0.00764111
$842$	−2.25041e21	−0.258477
$843$	8.46301e21	0.963425
$844$	−1.57200e21	−0.177372
$845$	1.86485e22	2.08554
$846$	−4.81559e21	−0.533792
$847$	−1.02879e22	−1.13032
$848$	5.45369e21	0.593911
$849$	−6.73438e21	−0.726926
$850$	4.57471e20	0.0489465
$851$	−9.38688e20	−0.0995519
$852$	−3.84354e20	−0.0404050
$853$	1.15472e22	1.20326	0.601632	−	0.798774i	$-0.294517\pi$
$853$	1.15472e22	1.20326	0.601632	+	0.798774i	$0.294517\pi$
$854$	−3.23036e21	−0.333670
$855$	−3.48433e21	−0.356757
$856$	−1.97670e22	−2.00626
$857$	1.38975e20	0.0139823	0.00699117	−	0.999976i	$-0.497775\pi$
$857$	1.38975e20	0.0139823	0.00699117	+	0.999976i	$0.497775\pi$
$858$	1.50562e22	1.50162
$859$	−6.98046e21	−0.690137	−0.345069	−	0.938577i	$-0.612144\pi$
$859$	−6.98046e21	−0.690137	−0.345069	+	0.938577i	$0.612144\pi$
$860$	3.57597e20	0.0350474
$861$	−6.56102e21	−0.637453
$862$	−8.61256e21	−0.829522
$863$	9.38588e21	0.896177	0.448089	−	0.893989i	$-0.352105\pi$
$863$	9.38588e21	0.896177	0.448089	+	0.893989i	$0.352105\pi$
$864$	5.26423e21	0.498290
$865$	−6.67587e21	−0.626451
$866$	−1.76717e22	−1.64397
$867$	3.68763e21	0.340098
$868$	−1.80918e20	−0.0165418
$869$	−1.05350e22	−0.954965
$870$	−6.77678e21	−0.609016
$871$	−2.57465e22	−2.29394
$872$	−8.56620e21	−0.756684
$873$	−6.91613e21	−0.605698
$874$	−1.63977e21	−0.142380
$875$	1.55360e22	1.33746
$876$	1.08151e21	0.0923101
$877$	5.39503e20	0.0456559	0.0228279	−	0.999739i	$-0.492733\pi$
$877$	5.39503e20	0.0456559	0.0228279	+	0.999739i	$0.492733\pi$
$878$	1.17837e22	0.988723
$879$	−1.20242e22	−1.00032
$880$	−1.13534e22	−0.936499
$881$	8.51459e21	0.696377	0.348188	−	0.937425i	$-0.386797\pi$
$881$	8.51459e21	0.696377	0.348188	+	0.937425i	$0.386797\pi$
$882$	3.77554e21	0.306171
$883$	1.42198e22	1.14337	0.571687	−	0.820472i	$-0.306289\pi$
$883$	1.42198e22	1.14337	0.571687	+	0.820472i	$0.306289\pi$
$884$	6.47783e21	0.516461
$885$	1.38591e22	1.09562
$886$	6.37391e21	0.499635
$887$	1.23600e22	0.960704	0.480352	−	0.877076i	$-0.340509\pi$
$887$	1.23600e22	0.960704	0.480352	+	0.877076i	$0.340509\pi$
$888$	−4.52105e21	−0.348451
$889$	−1.60143e21	−0.122390
$890$	−1.03499e22	−0.784352
$891$	−4.82229e21	−0.362385
$892$	−1.14884e21	−0.0856100
$893$	−1.24921e22	−0.923101
$894$	−7.19284e21	−0.527071
$895$	1.67352e22	1.21607
$896$	9.08162e21	0.654415
$897$	−3.88587e21	−0.277680
$898$	−2.11439e22	−1.49834
$899$	−7.52212e20	−0.0528619
$900$	−7.82932e19	−0.00545639
$901$	−1.48688e22	−1.02764
$902$	−1.18661e22	−0.813318
$903$	2.05208e21	0.139488
$904$	−1.68320e22	−1.13468
$905$	−5.85591e21	−0.391498
$906$	1.11139e22	0.736894
$907$	−1.69475e22	−1.11442	−0.557212	−	0.830370i	$-0.688129\pi$
$907$	−1.69475e22	−1.11442	−0.557212	+	0.830370i	$0.688129\pi$
$908$	1.91280e21	0.124746
$909$	−1.17584e22	−0.760532
$910$	−3.07641e22	−1.97348
$911$	−1.10351e22	−0.702083	−0.351041	−	0.936360i	$-0.614172\pi$
$911$	−1.10351e22	−0.702083	−0.351041	+	0.936360i	$0.614172\pi$
$912$	−5.88670e21	−0.371458
$913$	2.39418e21	0.149839
$914$	−2.04581e22	−1.26990
$915$	−3.30508e21	−0.203481
$916$	−1.03312e21	−0.0630863
$917$	4.29426e22	2.60087
$918$	1.87558e22	1.12672
$919$	−2.66487e22	−1.58785	−0.793924	−	0.608016i	$-0.791965\pi$
$919$	−2.66487e22	−1.58785	−0.793924	+	0.608016i	$0.791965\pi$
$920$	3.93125e21	0.232339
$921$	−7.40207e21	−0.433916
$922$	7.00948e21	0.407571
$923$	−7.25456e21	−0.418407
$924$	5.34107e21	0.305555
$925$	3.68233e20	0.0208958
$926$	1.61831e22	0.910921
$927$	7.33427e21	0.409505
$928$	−8.49330e21	−0.470399
$929$	−1.40482e21	−0.0771798	−0.0385899	−	0.999255i	$-0.512287\pi$
$929$	−1.40482e21	−0.0771798	−0.0385899	+	0.999255i	$0.512287\pi$
$930$	5.86257e20	0.0319496
$931$	9.79409e21	0.529470
$932$	−1.64370e20	−0.00881459
$933$	−1.74190e22	−0.926639
$934$	−2.10840e22	−1.11263
$935$	3.09538e22	1.62042
$936$	1.81435e22	0.942218
$937$	2.14268e21	0.110385	0.0551925	−	0.998476i	$-0.482423\pi$
$937$	2.14268e21	0.110385	0.0551925	+	0.998476i	$0.482423\pi$
$938$	2.89272e22	1.47838
$939$	−2.57228e22	−1.30415
$940$	5.79598e21	0.291520
$941$	2.72168e22	1.35804	0.679022	−	0.734117i	$-0.262404\pi$
$941$	2.72168e22	1.35804	0.679022	+	0.734117i	$0.262404\pi$
$942$	1.74117e22	0.861905
$943$	3.06254e21	0.150399
$944$	−2.26987e22	−1.10589
$945$	2.81239e22	1.35937
$946$	3.71136e21	0.177971
$947$	−1.55881e22	−0.741597	−0.370799	−	0.928713i	$-0.620916\pi$
$947$	−1.55881e22	−0.741597	−0.370799	+	0.928713i	$0.620916\pi$
$948$	2.53438e21	0.119621
$949$	2.04131e22	0.955901
$950$	6.43257e20	0.0298853
$951$	−1.05053e22	−0.484232
$952$	−3.76074e22	−1.71987
$953$	−2.02888e22	−0.920576	−0.460288	−	0.887770i	$-0.652254\pi$
$953$	−2.02888e22	−0.920576	−0.460288	+	0.887770i	$0.652254\pi$
$954$	−8.05958e21	−0.362827
$955$	8.57944e21	0.383207
$956$	−9.72494e20	−0.0430976
$957$	2.22069e22	0.976445
$958$	3.25526e22	1.42018
$959$	4.84040e22	2.09528
$960$	1.80012e22	0.773155
$961$	−2.34002e22	−0.997227
$962$	−1.65144e22	−0.698313
$963$	2.17738e22	0.913559
$964$	−5.79445e21	−0.241232
$965$	−2.55956e22	−1.05733
$966$	4.36593e21	0.178957
$967$	1.17451e22	0.477705	0.238853	−	0.971056i	$-0.423229\pi$
$967$	1.17451e22	0.477705	0.238853	+	0.971056i	$0.423229\pi$
$968$	2.31289e22	0.933446
$969$	1.60494e22	0.642731
$970$	−2.63642e22	−1.04768
$971$	−2.20415e22	−0.869153	−0.434576	−	0.900635i	$-0.643102\pi$
$971$	−2.20415e22	−0.869153	−0.434576	+	0.900635i	$0.643102\pi$
$972$	−5.36102e21	−0.209774
$973$	3.16597e22	1.22931
$974$	5.41034e21	0.208464
$975$	1.52436e21	0.0582847
$976$	5.41314e21	0.205388
$977$	2.46112e22	0.926667	0.463334	−	0.886184i	$-0.346653\pi$
$977$	2.46112e22	0.926667	0.463334	+	0.886184i	$0.346653\pi$
$978$	2.15039e22	0.803481
$979$	3.39157e22	1.25756
$980$	−4.54418e21	−0.167209
$981$	9.43584e21	0.344558
$982$	2.44393e22	0.885632
$983$	−4.92044e22	−1.76951	−0.884754	−	0.466059i	$-0.845673\pi$
$983$	−4.92044e22	−1.76951	−0.884754	+	0.466059i	$0.845673\pi$
$984$	1.47503e22	0.526425
$985$	−2.47221e22	−0.875614
$986$	−3.02606e22	−1.06365
$987$	3.32605e22	1.16024
$988$	9.10858e21	0.315336
$989$	−9.57868e20	−0.0329104
$990$	1.67784e22	0.572118
$991$	−1.29143e22	−0.437037	−0.218518	−	0.975833i	$-0.570122\pi$
$991$	−1.29143e22	−0.437037	−0.218518	+	0.975833i	$0.570122\pi$
$992$	7.34752e20	0.0246776
$993$	1.54267e22	0.514224
$994$	8.15080e21	0.269651
$995$	−4.09058e22	−1.34311
$996$	−5.75960e20	−0.0187693
$997$	4.74704e22	1.53535	0.767677	−	0.640836i	$-0.221412\pi$
$997$	4.74704e22	1.53535	0.767677	+	0.640836i	$0.221412\pi$
$998$	−2.61720e22	−0.840150
$999$	1.50971e22	0.481009

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	83.16.a.a.1.18	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
83.16.a.a.1.18	✓	48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 83 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	83.a (trivial)

\(f(q)\)	\(=\)	\(q-157.812 q^{2} +2699.23 q^{3} -7863.32 q^{4} +170610. q^{5} -425971. q^{6} -2.85216e6 q^{7} +6.41212e6 q^{8} -7.06308e6 q^{9} +O(q^{10})\)	\(q-157.812 q^{2} +2699.23 q^{3} -7863.32 q^{4} +170610. q^{5} -425971. q^{6} -2.85216e6 q^{7} +6.41212e6 q^{8} -7.06308e6 q^{9} -2.69244e7 q^{10} +8.82287e7 q^{11} -2.12249e7 q^{12} -4.00613e8 q^{13} +4.50105e8 q^{14} +4.60516e8 q^{15} -7.54245e8 q^{16} +2.05636e9 q^{17} +1.11464e9 q^{18} +2.89148e9 q^{19} -1.34156e9 q^{20} -7.69862e9 q^{21} -1.39236e10 q^{22} +3.59355e9 q^{23} +1.73078e10 q^{24} -1.40969e9 q^{25} +6.32216e10 q^{26} -5.77958e10 q^{27} +2.24274e10 q^{28} +9.32477e10 q^{29} -7.26751e10 q^{30} -8.06682e9 q^{31} -9.10832e10 q^{32} +2.38149e11 q^{33} -3.24518e11 q^{34} -4.86607e11 q^{35} +5.55392e10 q^{36} -2.61215e11 q^{37} -4.56310e11 q^{38} -1.08135e12 q^{39} +1.09397e12 q^{40} +8.52234e11 q^{41} +1.21494e12 q^{42} -2.66552e11 q^{43} -6.93771e11 q^{44} -1.20503e12 q^{45} -5.67106e11 q^{46} -4.32032e12 q^{47} -2.03588e12 q^{48} +3.38723e12 q^{49} +2.22467e11 q^{50} +5.55058e12 q^{51} +3.15015e12 q^{52} -7.23066e12 q^{53} +9.12088e12 q^{54} +1.50527e13 q^{55} -1.82884e13 q^{56} +7.80475e12 q^{57} -1.47156e13 q^{58} +3.00946e13 q^{59} -3.62119e12 q^{60} -7.17690e12 q^{61} +1.27304e12 q^{62} +2.01450e13 q^{63} +3.90891e13 q^{64} -6.83487e13 q^{65} -3.75829e13 q^{66} +6.42677e13 q^{67} -1.61698e13 q^{68} +9.69981e12 q^{69} +7.67925e13 q^{70} +1.81087e13 q^{71} -4.52893e13 q^{72} -5.09547e13 q^{73} +4.12229e13 q^{74} -3.80508e12 q^{75} -2.27366e13 q^{76} -2.51642e14 q^{77} +1.70649e14 q^{78} -1.19406e14 q^{79} -1.28682e14 q^{80} -5.46567e13 q^{81} -1.34493e14 q^{82} +2.71361e13 q^{83} +6.05367e13 q^{84} +3.50836e14 q^{85} +4.20652e13 q^{86} +2.51697e14 q^{87} +5.65733e14 q^{88} +3.84406e14 q^{89} +1.90169e14 q^{90} +1.14261e15 q^{91} -2.82572e13 q^{92} -2.17742e13 q^{93} +6.81798e14 q^{94} +4.93316e14 q^{95} -2.45854e14 q^{96} +9.79195e14 q^{97} -5.34546e14 q^{98} -6.23166e14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 473 q^{2} - 5843 q^{3} + 680037 q^{4} - 442447 q^{5} + 296553 q^{6} - 7927854 q^{7} - 8537601 q^{8} + 201265585 q^{9}+O(q^{10}) \) 48 * q - 473 * q^2 - 5843 * q^3 + 680037 * q^4 - 442447 * q^5 + 296553 * q^6 - 7927854 * q^7 - 8537601 * q^8 + 201265585 * q^9	\( 48 q - 473 q^{2} - 5843 q^{3} + 680037 q^{4} - 442447 q^{5} + 296553 q^{6} - 7927854 q^{7} - 8537601 q^{8} + 201265585 q^{9} - 93241115 q^{10} - 45721275 q^{11} - 377854265 q^{12} - 745704099 q^{13} - 392421804 q^{14} - 1168377736 q^{15} + 8467920373 q^{16} - 2629486634 q^{17} - 7709183072 q^{18} - 5531098141 q^{19} - 18039154937 q^{20} - 847906109 q^{21} - 47911647107 q^{22} - 83924132873 q^{23} - 124449608127 q^{24} + 162107115775 q^{25} + 184146522913 q^{26} + 36372522745 q^{27} - 71841297868 q^{28} - 19181424465 q^{29} + 629437825372 q^{30} - 332963100244 q^{31} - 393743335061 q^{32} - 1482425278799 q^{33} - 1468922151850 q^{34} - 1159028725940 q^{35} - 461783529368 q^{36} - 3528614578273 q^{37} - 5029367527151 q^{38} - 4034986327034 q^{39} - 6971822086105 q^{40} - 4885450015231 q^{41} - 11511941818333 q^{42} - 2898728824729 q^{43} - 9293985416421 q^{44} - 6134907413849 q^{45} - 4884690151683 q^{46} - 213168900002 q^{47} - 11019361285633 q^{48} + 21878291008144 q^{49} + 18113403515282 q^{50} - 4114564648607 q^{51} + 989572768731 q^{52} - 25240879960039 q^{53} + 54416977542501 q^{54} + 10061754537534 q^{55} + 83758891995194 q^{56} + 2144964161830 q^{57} - 8449723551503 q^{58} - 16396353463329 q^{59} + 116252836147112 q^{60} - 26017465263825 q^{61} + 94212604839642 q^{62} + 5126445923855 q^{63} + 186326365661717 q^{64} + 92174682613046 q^{65} + 224566743891485 q^{66} - 127182509349881 q^{67} + 240579433865274 q^{68} + 122547131930146 q^{69} - 112950590057616 q^{70} + 8411915072406 q^{71} + 236831710917612 q^{72} - 230118245135128 q^{73} + 453976256379465 q^{74} - 260184225186765 q^{75} + 185545158559463 q^{76} - 487981581579147 q^{77} + 110466382430294 q^{78} - 293686576998568 q^{79} - 539484042180045 q^{80} + 730816042132624 q^{81} - 499426942251343 q^{82} + 13\!\cdots\!96 q^{83}+ \cdots - 19\!\cdots\!36 q^{99}+O(q^{100}) \) 48 * q - 473 * q^2 - 5843 * q^3 + 680037 * q^4 - 442447 * q^5 + 296553 * q^6 - 7927854 * q^7 - 8537601 * q^8 + 201265585 * q^9 - 93241115 * q^10 - 45721275 * q^11 - 377854265 * q^12 - 745704099 * q^13 - 392421804 * q^14 - 1168377736 * q^15 + 8467920373 * q^16 - 2629486634 * q^17 - 7709183072 * q^18 - 5531098141 * q^19 - 18039154937 * q^20 - 847906109 * q^21 - 47911647107 * q^22 - 83924132873 * q^23 - 124449608127 * q^24 + 162107115775 * q^25 + 184146522913 * q^26 + 36372522745 * q^27 - 71841297868 * q^28 - 19181424465 * q^29 + 629437825372 * q^30 - 332963100244 * q^31 - 393743335061 * q^32 - 1482425278799 * q^33 - 1468922151850 * q^34 - 1159028725940 * q^35 - 461783529368 * q^36 - 3528614578273 * q^37 - 5029367527151 * q^38 - 4034986327034 * q^39 - 6971822086105 * q^40 - 4885450015231 * q^41 - 11511941818333 * q^42 - 2898728824729 * q^43 - 9293985416421 * q^44 - 6134907413849 * q^45 - 4884690151683 * q^46 - 213168900002 * q^47 - 11019361285633 * q^48 + 21878291008144 * q^49 + 18113403515282 * q^50 - 4114564648607 * q^51 + 989572768731 * q^52 - 25240879960039 * q^53 + 54416977542501 * q^54 + 10061754537534 * q^55 + 83758891995194 * q^56 + 2144964161830 * q^57 - 8449723551503 * q^58 - 16396353463329 * q^59 + 116252836147112 * q^60 - 26017465263825 * q^61 + 94212604839642 * q^62 + 5126445923855 * q^63 + 186326365661717 * q^64 + 92174682613046 * q^65 + 224566743891485 * q^66 - 127182509349881 * q^67 + 240579433865274 * q^68 + 122547131930146 * q^69 - 112950590057616 * q^70 + 8411915072406 * q^71 + 236831710917612 * q^72 - 230118245135128 * q^73 + 453976256379465 * q^74 - 260184225186765 * q^75 + 185545158559463 * q^76 - 487981581579147 * q^77 + 110466382430294 * q^78 - 293686576998568 * q^79 - 539484042180045 * q^80 + 730816042132624 * q^81 - 499426942251343 * q^82 + 1302530447502096 * q^83 + 344572152969097 * q^84 - 987337964139519 * q^85 - 473158023061951 * q^86 - 331651268603165 * q^87 - 1261768867285811 * q^88 - 1529884970459758 * q^89 - 5249887977052001 * q^90 - 2821941165368823 * q^91 - 5393454125194245 * q^92 - 6369849411750419 * q^93 - 3702275724839446 * q^94 - 3484233647056932 * q^95 - 7346403487127915 * q^96 - 4526640473660276 * q^97 - 6918835080801735 * q^98 - 1971920884322036 * q^99

Introduction

L-functions

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