LMFDB - Embedded newform 177.10.a.d.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,10,Mod(1,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	177.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:	$91.1613430010$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+37.7126 q^{2} +81.0000 q^{3} +910.242 q^{4} -2684.70 q^{5} +3054.72 q^{6} +8718.73 q^{7} +15018.8 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+37.7126 q^{2} +81.0000 q^{3} +910.242 q^{4} -2684.70 q^{5} +3054.72 q^{6} +8718.73 q^{7} +15018.8 q^{8} +6561.00 q^{9} -101247. q^{10} -29647.1 q^{11} +73729.6 q^{12} -62958.6 q^{13} +328806. q^{14} -217461. q^{15} +100353. q^{16} +515394. q^{17} +247433. q^{18} +165208. q^{19} -2.44373e6 q^{20} +706217. q^{21} -1.11807e6 q^{22} +2.59310e6 q^{23} +1.21652e6 q^{24} +5.25451e6 q^{25} -2.37434e6 q^{26} +531441. q^{27} +7.93616e6 q^{28} +5.90158e6 q^{29} -8.20103e6 q^{30} +6.31829e6 q^{31} -3.90503e6 q^{32} -2.40141e6 q^{33} +1.94369e7 q^{34} -2.34072e7 q^{35} +5.97210e6 q^{36} -1.29343e7 q^{37} +6.23042e6 q^{38} -5.09965e6 q^{39} -4.03209e7 q^{40} +406055. q^{41} +2.66333e7 q^{42} -8.02029e6 q^{43} -2.69860e7 q^{44} -1.76143e7 q^{45} +9.77926e7 q^{46} +1.31877e7 q^{47} +8.12859e6 q^{48} +3.56627e7 q^{49} +1.98161e8 q^{50} +4.17469e7 q^{51} -5.73076e7 q^{52} -5.16715e7 q^{53} +2.00420e7 q^{54} +7.95936e7 q^{55} +1.30945e8 q^{56} +1.33818e7 q^{57} +2.22564e8 q^{58} -1.21174e7 q^{59} -1.97942e8 q^{60} +1.69831e7 q^{61} +2.38279e8 q^{62} +5.72036e7 q^{63} -1.98650e8 q^{64} +1.69025e8 q^{65} -9.05635e7 q^{66} +2.43696e8 q^{67} +4.69133e8 q^{68} +2.10041e8 q^{69} -8.82748e8 q^{70} +3.15773e8 q^{71} +9.85381e7 q^{72} -3.21356e8 q^{73} -4.87786e8 q^{74} +4.25615e8 q^{75} +1.50379e8 q^{76} -2.58485e8 q^{77} -1.92321e8 q^{78} -5.46294e8 q^{79} -2.69418e8 q^{80} +4.30467e7 q^{81} +1.53134e7 q^{82} +2.03715e8 q^{83} +6.42829e8 q^{84} -1.38368e9 q^{85} -3.02466e8 q^{86} +4.78028e8 q^{87} -4.45262e8 q^{88} +2.89913e8 q^{89} -6.64283e8 q^{90} -5.48920e8 q^{91} +2.36035e9 q^{92} +5.11781e8 q^{93} +4.97344e8 q^{94} -4.43534e8 q^{95} -3.16308e8 q^{96} +7.57382e8 q^{97} +1.34493e9 q^{98} -1.94514e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9}+O(q^{10}) $ 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9} + 45337 q^{10} + 111769 q^{11} + 483894 q^{12} + 189121 q^{13} + 251053 q^{14} + 468666 q^{15} + 2311074 q^{16} + 1113841 q^{17} + 301806 q^{18} + 476068 q^{19} - 42495 q^{20} + 618921 q^{21} - 2252022 q^{22} + 7103062 q^{23} + 4972995 q^{24} + 10628442 q^{25} + 6871048 q^{26} + 11691702 q^{27} + 8112650 q^{28} + 15279316 q^{29} + 3672297 q^{30} + 17610338 q^{31} + 32378276 q^{32} + 9053289 q^{33} + 29339436 q^{34} + 7134904 q^{35} + 39195414 q^{36} + 21961411 q^{37} + 65195131 q^{38} + 15318801 q^{39} + 75185084 q^{40} + 52781575 q^{41} + 20335293 q^{42} + 76191313 q^{43} + 61127768 q^{44} + 37961946 q^{45} + 290208769 q^{46} + 160572396 q^{47} + 187196994 q^{48} + 156292703 q^{49} + 169504821 q^{50} + 90221121 q^{51} + 65465920 q^{52} - 8762038 q^{53} + 24446286 q^{54} + 147125140 q^{55} + 9671794 q^{56} + 38561508 q^{57} - 37665424 q^{58} - 266581942 q^{59} - 3442095 q^{60} + 120750754 q^{61} - 152465186 q^{62} + 50132601 q^{63} - 40658803 q^{64} + 331055798 q^{65} - 182413782 q^{66} + 41371828 q^{67} + 145606631 q^{68} + 575348022 q^{69} - 920887614 q^{70} + 261018751 q^{71} + 402812595 q^{72} + 178388 q^{73} - 303908734 q^{74} + 860903802 q^{75} - 94541144 q^{76} + 299640561 q^{77} + 556554888 q^{78} - 905381353 q^{79} + 939128289 q^{80} + 947027862 q^{81} - 551739753 q^{82} + 1173257869 q^{83} + 657124650 q^{84} - 1546633210 q^{85} + 1384869460 q^{86} + 1237624596 q^{87} + 189740713 q^{88} + 898004974 q^{89} + 297456057 q^{90} + 591272339 q^{91} + 4328210270 q^{92} + 1426437378 q^{93} + 122568068 q^{94} + 2487967134 q^{95} + 2622640356 q^{96} + 3175709684 q^{97} + 5095778404 q^{98} + 733316409 q^{99}+O(q^{100}) \) 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9 + 45337 * q^10 + 111769 * q^11 + 483894 * q^12 + 189121 * q^13 + 251053 * q^14 + 468666 * q^15 + 2311074 * q^16 + 1113841 * q^17 + 301806 * q^18 + 476068 * q^19 - 42495 * q^20 + 618921 * q^21 - 2252022 * q^22 + 7103062 * q^23 + 4972995 * q^24 + 10628442 * q^25 + 6871048 * q^26 + 11691702 * q^27 + 8112650 * q^28 + 15279316 * q^29 + 3672297 * q^30 + 17610338 * q^31 + 32378276 * q^32 + 9053289 * q^33 + 29339436 * q^34 + 7134904 * q^35 + 39195414 * q^36 + 21961411 * q^37 + 65195131 * q^38 + 15318801 * q^39 + 75185084 * q^40 + 52781575 * q^41 + 20335293 * q^42 + 76191313 * q^43 + 61127768 * q^44 + 37961946 * q^45 + 290208769 * q^46 + 160572396 * q^47 + 187196994 * q^48 + 156292703 * q^49 + 169504821 * q^50 + 90221121 * q^51 + 65465920 * q^52 - 8762038 * q^53 + 24446286 * q^54 + 147125140 * q^55 + 9671794 * q^56 + 38561508 * q^57 - 37665424 * q^58 - 266581942 * q^59 - 3442095 * q^60 + 120750754 * q^61 - 152465186 * q^62 + 50132601 * q^63 - 40658803 * q^64 + 331055798 * q^65 - 182413782 * q^66 + 41371828 * q^67 + 145606631 * q^68 + 575348022 * q^69 - 920887614 * q^70 + 261018751 * q^71 + 402812595 * q^72 + 178388 * q^73 - 303908734 * q^74 + 860903802 * q^75 - 94541144 * q^76 + 299640561 * q^77 + 556554888 * q^78 - 905381353 * q^79 + 939128289 * q^80 + 947027862 * q^81 - 551739753 * q^82 + 1173257869 * q^83 + 657124650 * q^84 - 1546633210 * q^85 + 1384869460 * q^86 + 1237624596 * q^87 + 189740713 * q^88 + 898004974 * q^89 + 297456057 * q^90 + 591272339 * q^91 + 4328210270 * q^92 + 1426437378 * q^93 + 122568068 * q^94 + 2487967134 * q^95 + 2622640356 * q^96 + 3175709684 * q^97 + 5095778404 * q^98 + 733316409 * 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 $

$2$	37.7126	1.66668	0.833339	−	0.552762i	$-0.186426\pi$
$2$	37.7126	1.66668	0.833339	+	0.552762i	$0.186426\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	910.242	1.77782
$5$	−2684.70	−1.92102	−0.960509	−	0.278249i	$-0.910246\pi$
$5$	−2684.70	−1.92102	−0.960509	+	0.278249i	$0.910246\pi$
$6$	3054.72	0.962257
$7$	8718.73	1.37250	0.686250	−	0.727366i	$-0.259256\pi$
$7$	8718.73	1.37250	0.686250	+	0.727366i	$0.259256\pi$
$8$	15018.8	1.29637
$9$	6561.00	0.333333
$10$	−101247.	−3.20172
$11$	−29647.1	−0.610540	−0.305270	−	0.952266i	$-0.598747\pi$
$11$	−29647.1	−0.610540	−0.305270	+	0.952266i	$0.598747\pi$
$12$	73729.6	1.02642
$13$	−62958.6	−0.611379	−0.305689	−	0.952131i	$-0.598887\pi$
$13$	−62958.6	−0.611379	−0.305689	+	0.952131i	$0.598887\pi$
$14$	328806.	2.28752
$15$	−217461.	−1.10910
$16$	100353.	0.382816
$17$	515394.	1.49665	0.748323	−	0.663334i	$-0.230859\pi$
$17$	515394.	1.49665	0.748323	+	0.663334i	$0.230859\pi$
$18$	247433.	0.555559
$19$	165208.	0.290830	0.145415	−	0.989371i	$-0.453548\pi$
$19$	165208.	0.290830	0.145415	+	0.989371i	$0.453548\pi$
$20$	−2.44373e6	−3.41522
$21$	706217.	0.792413
$22$	−1.11807e6	−1.01757
$23$	2.59310e6	1.93216	0.966081	−	0.258237i	$-0.0831417\pi$
$23$	2.59310e6	1.93216	0.966081	+	0.258237i	$0.0831417\pi$
$24$	1.21652e6	0.748460
$25$	5.25451e6	2.69031
$26$	−2.37434e6	−1.01897
$27$	531441.	0.192450
$28$	7.93616e6	2.44005
$29$	5.90158e6	1.54945	0.774724	−	0.632299i	$-0.217889\pi$
$29$	5.90158e6	1.54945	0.774724	+	0.632299i	$0.217889\pi$
$30$	−8.20103e6	−1.84851
$31$	6.31829e6	1.22877	0.614387	−	0.789005i	$-0.289403\pi$
$31$	6.31829e6	1.22877	0.614387	+	0.789005i	$0.289403\pi$
$32$	−3.90503e6	−0.658339
$33$	−2.40141e6	−0.352496
$34$	1.94369e7	2.49443
$35$	−2.34072e7	−2.63660
$36$	5.97210e6	0.592606
$37$	−1.29343e7	−1.13458	−0.567289	−	0.823519i	$-0.692008\pi$
$37$	−1.29343e7	−1.13458	−0.567289	+	0.823519i	$0.692008\pi$
$38$	6.23042e6	0.484720
$39$	−5.09965e6	−0.352980
$40$	−4.03209e7	−2.49035
$41$	406055.	0.0224418	0.0112209	−	0.999937i	$-0.496428\pi$
$41$	406055.	0.0224418	0.0112209	+	0.999937i	$0.496428\pi$
$42$	2.66333e7	1.32070
$43$	−8.02029e6	−0.357752	−0.178876	−	0.983872i	$-0.557246\pi$
$43$	−8.02029e6	−0.357752	−0.178876	+	0.983872i	$0.557246\pi$
$44$	−2.69860e7	−1.08543
$45$	−1.76143e7	−0.640339
$46$	9.77926e7	3.22029
$47$	1.31877e7	0.394212	0.197106	−	0.980382i	$-0.436846\pi$
$47$	1.31877e7	0.394212	0.197106	+	0.980382i	$0.436846\pi$
$48$	8.12859e6	0.221019
$49$	3.56627e7	0.883755
$50$	1.98161e8	4.48388
$51$	4.17469e7	0.864089
$52$	−5.73076e7	−1.08692
$53$	−5.16715e7	−0.899517	−0.449759	−	0.893150i	$-0.648490\pi$
$53$	−5.16715e7	−0.899517	−0.449759	+	0.893150i	$0.648490\pi$
$54$	2.00420e7	0.320752
$55$	7.95936e7	1.17286
$56$	1.30945e8	1.77927
$57$	1.33818e7	0.167911
$58$	2.22564e8	2.58243
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	−1.97942e8	−1.97178
$61$	1.69831e7	0.157048	0.0785242	−	0.996912i	$-0.474979\pi$
$61$	1.69831e7	0.157048	0.0785242	+	0.996912i	$0.474979\pi$
$62$	2.38279e8	2.04797
$63$	5.72036e7	0.457500
$64$	−1.98650e8	−1.48006
$65$	1.69025e8	1.17447
$66$	−9.05635e7	−0.587497
$67$	2.43696e8	1.47745	0.738724	−	0.674008i	$-0.235429\pi$
$67$	2.43696e8	1.47745	0.738724	+	0.674008i	$0.235429\pi$
$68$	4.69133e8	2.66076
$69$	2.10041e8	1.11553
$70$	−8.82748e8	−4.39436
$71$	3.15773e8	1.47473	0.737364	−	0.675495i	$-0.236070\pi$
$71$	3.15773e8	1.47473	0.737364	+	0.675495i	$0.236070\pi$
$72$	9.85381e7	0.432124
$73$	−3.21356e8	−1.32444	−0.662221	−	0.749308i	$-0.730386\pi$
$73$	−3.21356e8	−1.32444	−0.662221	+	0.749308i	$0.730386\pi$
$74$	−4.87786e8	−1.89098
$75$	4.25615e8	1.55325
$76$	1.50379e8	0.517042
$77$	−2.58485e8	−0.837967
$78$	−1.92321e8	−0.588304
$79$	−5.46294e8	−1.57799	−0.788995	−	0.614400i	$-0.789398\pi$
$79$	−5.46294e8	−1.57799	−0.788995	+	0.614400i	$0.789398\pi$
$80$	−2.69418e8	−0.735397
$81$	4.30467e7	0.111111
$82$	1.53134e7	0.0374033
$83$	2.03715e8	0.471163	0.235581	−	0.971855i	$-0.424301\pi$
$83$	2.03715e8	0.471163	0.235581	+	0.971855i	$0.424301\pi$
$84$	6.42829e8	1.40877
$85$	−1.38368e9	−2.87508
$86$	−3.02466e8	−0.596258
$87$	4.78028e8	0.894575
$88$	−4.45262e8	−0.791487
$89$	2.89913e8	0.489793	0.244897	−	0.969549i	$-0.421246\pi$
$89$	2.89913e8	0.489793	0.244897	+	0.969549i	$0.421246\pi$
$90$	−6.64283e8	−1.06724
$91$	−5.48920e8	−0.839117
$92$	2.36035e9	3.43503
$93$	5.11781e8	0.709433
$94$	4.97344e8	0.657025
$95$	−4.43534e8	−0.558689
$96$	−3.16308e8	−0.380092
$97$	7.57382e8	0.868645	0.434322	−	0.900758i	$-0.356988\pi$
$97$	7.57382e8	0.868645	0.434322	+	0.900758i	$0.356988\pi$
$98$	1.34493e9	1.47294
$99$	−1.94514e8	−0.203513
$100$	4.78288e9	4.78288
$101$	1.04159e9	0.995976	0.497988	−	0.867184i	$-0.334072\pi$
$101$	1.04159e9	0.995976	0.497988	+	0.867184i	$0.334072\pi$
$102$	1.57439e9	1.44016
$103$	1.02405e9	0.896509	0.448255	−	0.893906i	$-0.352046\pi$
$103$	1.02405e9	0.896509	0.448255	+	0.893906i	$0.352046\pi$
$104$	−9.45561e8	−0.792573
$105$	−1.89598e9	−1.52224
$106$	−1.94867e9	−1.49921
$107$	1.59574e9	1.17689	0.588444	−	0.808538i	$-0.299741\pi$
$107$	1.59574e9	1.17689	0.588444	+	0.808538i	$0.299741\pi$
$108$	4.83740e8	0.342141
$109$	1.72861e8	0.117295	0.0586473	−	0.998279i	$-0.481321\pi$
$109$	1.72861e8	0.117295	0.0586473	+	0.998279i	$0.481321\pi$
$110$	3.00168e9	1.95478
$111$	−1.04768e9	−0.655049
$112$	8.74951e8	0.525415
$113$	−2.58205e9	−1.48974	−0.744872	−	0.667207i	$-0.767490\pi$
$113$	−2.58205e9	−1.48974	−0.744872	+	0.667207i	$0.767490\pi$
$114$	5.04664e8	0.279853
$115$	−6.96170e9	−3.71172
$116$	5.37187e9	2.75464
$117$	−4.13072e8	−0.203793
$118$	−4.56978e8	−0.216983
$119$	4.49358e9	2.05415
$120$	−3.26600e9	−1.43781
$121$	−1.47900e9	−0.627240
$122$	6.40479e8	0.261749
$123$	3.28905e7	0.0129568
$124$	5.75117e9	2.18453
$125$	−8.86324e9	−3.24711
$126$	2.15730e9	0.762505
$127$	−1.44051e9	−0.491361	−0.245681	−	0.969351i	$-0.579011\pi$
$127$	−1.44051e9	−0.491361	−0.245681	+	0.969351i	$0.579011\pi$
$128$	−5.49223e9	−1.80844
$129$	−6.49644e8	−0.206548
$130$	6.37439e9	1.95746
$131$	−9.89228e8	−0.293478	−0.146739	−	0.989175i	$-0.546878\pi$
$131$	−9.89228e8	−0.293478	−0.146739	+	0.989175i	$0.546878\pi$
$132$	−2.18587e9	−0.626673
$133$	1.44040e9	0.399164
$134$	9.19042e9	2.46243
$135$	−1.42676e9	−0.369700
$136$	7.74058e9	1.94021
$137$	4.29261e9	1.04107	0.520534	−	0.853841i	$-0.325733\pi$
$137$	4.29261e9	1.04107	0.520534	+	0.853841i	$0.325733\pi$
$138$	7.92120e9	1.85924
$139$	1.77464e9	0.403222	0.201611	−	0.979466i	$-0.435382\pi$
$139$	1.77464e9	0.403222	0.201611	+	0.979466i	$0.435382\pi$
$140$	−2.13062e10	−4.68739
$141$	1.06821e9	0.227598
$142$	1.19086e10	2.45790
$143$	1.86654e9	0.373271
$144$	6.58416e8	0.127605
$145$	−1.58440e10	−2.97652
$146$	−1.21192e10	−2.20742
$147$	2.88868e9	0.510236
$148$	−1.17733e10	−2.01707
$149$	−2.93967e9	−0.488609	−0.244304	−	0.969699i	$-0.578560\pi$
$149$	−2.93967e9	−0.488609	−0.244304	+	0.969699i	$0.578560\pi$
$150$	1.60511e10	2.58877
$151$	−1.11610e10	−1.74706	−0.873532	−	0.486767i	$-0.838176\pi$
$151$	−1.11610e10	−1.74706	−0.873532	+	0.486767i	$0.838176\pi$
$152$	2.48122e9	0.377023
$153$	3.38150e9	0.498882
$154$	−9.74814e9	−1.39662
$155$	−1.69627e10	−2.36050
$156$	−4.64192e9	−0.627533
$157$	1.33277e10	1.75068	0.875338	−	0.483511i	$-0.160639\pi$
$157$	1.33277e10	1.75068	0.875338	+	0.483511i	$0.160639\pi$
$158$	−2.06022e10	−2.63000
$159$	−4.18539e9	−0.519337
$160$	1.04839e10	1.26468
$161$	2.26085e10	2.65189
$162$	1.62340e9	0.185186
$163$	1.67599e8	0.0185964	0.00929819	−	0.999957i	$-0.497040\pi$
$163$	1.67599e8	0.0185964	0.00929819	+	0.999957i	$0.497040\pi$
$164$	3.69609e8	0.0398974
$165$	6.44708e9	0.677151
$166$	7.68262e9	0.785277
$167$	1.54656e10	1.53866	0.769330	−	0.638851i	$-0.220590\pi$
$167$	1.54656e10	1.53866	0.769330	+	0.638851i	$0.220590\pi$
$168$	1.06065e10	1.02726
$169$	−6.64071e9	−0.626216
$170$	−5.21822e10	−4.79184
$171$	1.08393e9	0.0969433
$172$	−7.30041e9	−0.636018
$173$	−1.88972e10	−1.60395	−0.801973	−	0.597360i	$-0.796216\pi$
$173$	−1.88972e10	−1.60395	−0.801973	+	0.597360i	$0.796216\pi$
$174$	1.80277e10	1.49097
$175$	4.58127e10	3.69245
$176$	−2.97517e9	−0.233725
$177$	−9.81506e8	−0.0751646
$178$	1.09334e10	0.816328
$179$	7.91689e9	0.576389	0.288195	−	0.957572i	$-0.406945\pi$
$179$	7.91689e9	0.576389	0.288195	+	0.957572i	$0.406945\pi$
$180$	−1.60333e10	−1.13841
$181$	−9.67084e9	−0.669747	−0.334873	−	0.942263i	$-0.608694\pi$
$181$	−9.67084e9	−0.669747	−0.334873	+	0.942263i	$0.608694\pi$
$182$	−2.07012e10	−1.39854
$183$	1.37563e9	0.0906719
$184$	3.89451e10	2.50480
$185$	3.47247e10	2.17955
$186$	1.93006e10	1.18240
$187$	−1.52799e10	−0.913763
$188$	1.20040e10	0.700837
$189$	4.63349e9	0.264138
$190$	−1.67268e10	−0.931156
$191$	−8.34529e9	−0.453723	−0.226862	−	0.973927i	$-0.572847\pi$
$191$	−8.34529e9	−0.453723	−0.226862	+	0.973927i	$0.572847\pi$
$192$	−1.60906e10	−0.854511
$193$	−1.47147e10	−0.763383	−0.381691	−	0.924290i	$-0.624658\pi$
$193$	−1.47147e10	−0.763383	−0.381691	+	0.924290i	$0.624658\pi$
$194$	2.85629e10	1.44775
$195$	1.36911e10	0.678080
$196$	3.24617e10	1.57115
$197$	−1.93698e10	−0.916279	−0.458140	−	0.888880i	$-0.651484\pi$
$197$	−1.93698e10	−0.916279	−0.458140	+	0.888880i	$0.651484\pi$
$198$	−7.33565e9	−0.339192
$199$	−2.78962e10	−1.26098	−0.630488	−	0.776199i	$-0.717145\pi$
$199$	−2.78962e10	−1.26098	−0.630488	+	0.776199i	$0.717145\pi$
$200$	7.89162e10	3.48764
$201$	1.97394e10	0.853005
$202$	3.92809e10	1.65997
$203$	5.14543e10	2.12662
$204$	3.79998e10	1.53619
$205$	−1.09014e9	−0.0431111
$206$	3.86197e10	1.49419
$207$	1.70133e10	0.644054
$208$	−6.31809e9	−0.234046
$209$	−4.89792e9	−0.177563
$210$	−7.15026e10	−2.53708
$211$	−1.95764e10	−0.679927	−0.339964	−	0.940439i	$-0.610415\pi$
$211$	−1.95764e10	−0.679927	−0.339964	+	0.940439i	$0.610415\pi$
$212$	−4.70336e10	−1.59918
$213$	2.55776e10	0.851435
$214$	6.01796e10	1.96149
$215$	2.15321e10	0.687248
$216$	7.98159e9	0.249487
$217$	5.50875e10	1.68649
$218$	6.51904e9	0.195492
$219$	−2.60298e10	−0.764667
$220$	7.24494e10	2.08513
$221$	−3.24485e10	−0.915017
$222$	−3.95107e10	−1.09176
$223$	2.64641e9	0.0716614	0.0358307	−	0.999358i	$-0.488592\pi$
$223$	2.64641e9	0.0716614	0.0358307	+	0.999358i	$0.488592\pi$
$224$	−3.40469e10	−0.903570
$225$	3.44748e10	0.896770
$226$	−9.73759e10	−2.48292
$227$	−1.39185e10	−0.347918	−0.173959	−	0.984753i	$-0.555656\pi$
$227$	−1.39185e10	−0.347918	−0.173959	+	0.984753i	$0.555656\pi$
$228$	1.21807e10	0.298515
$229$	2.39412e10	0.575290	0.287645	−	0.957737i	$-0.407128\pi$
$229$	2.39412e10	0.575290	0.287645	+	0.957737i	$0.407128\pi$
$230$	−2.62544e11	−6.18624
$231$	−2.09373e10	−0.483800
$232$	8.86344e10	2.00866
$233$	−1.94275e10	−0.431832	−0.215916	−	0.976412i	$-0.569274\pi$
$233$	−1.94275e10	−0.431832	−0.215916	+	0.976412i	$0.569274\pi$
$234$	−1.55780e10	−0.339657
$235$	−3.54052e10	−0.757288
$236$	−1.10297e10	−0.231452
$237$	−4.42498e10	−0.911053
$238$	1.69465e11	3.42360
$239$	−3.65784e10	−0.725160	−0.362580	−	0.931953i	$-0.618104\pi$
$239$	−3.65784e10	−0.725160	−0.362580	+	0.931953i	$0.618104\pi$
$240$	−2.18229e10	−0.424582
$241$	2.75986e10	0.527000	0.263500	−	0.964659i	$-0.415123\pi$
$241$	2.75986e10	0.527000	0.263500	+	0.964659i	$0.415123\pi$
$242$	−5.57770e10	−1.04541
$243$	3.48678e9	0.0641500
$244$	1.54588e10	0.279203
$245$	−9.57438e10	−1.69771
$246$	1.24039e9	0.0215948
$247$	−1.04013e10	−0.177807
$248$	9.48929e10	1.59295
$249$	1.65009e10	0.272026
$250$	−3.34256e11	−5.41189
$251$	−7.68115e10	−1.22150	−0.610751	−	0.791823i	$-0.709132\pi$
$251$	−7.68115e10	−1.22150	−0.610751	+	0.791823i	$0.709132\pi$
$252$	5.20691e10	0.813351
$253$	−7.68777e10	−1.17966
$254$	−5.43256e10	−0.818941
$255$	−1.12078e11	−1.65993
$256$	−1.05418e11	−1.53403
$257$	2.41025e10	0.344638	0.172319	−	0.985041i	$-0.444874\pi$
$257$	2.41025e10	0.344638	0.172319	+	0.985041i	$0.444874\pi$
$258$	−2.44998e10	−0.344250
$259$	−1.12771e11	−1.55721
$260$	1.53854e11	2.08799
$261$	3.87203e10	0.516483
$262$	−3.73064e10	−0.489134
$263$	9.54317e10	1.22996	0.614981	−	0.788542i	$-0.289164\pi$
$263$	9.54317e10	1.22996	0.614981	+	0.788542i	$0.289164\pi$
$264$	−3.60662e10	−0.456965
$265$	1.38723e11	1.72799
$266$	5.43213e10	0.665278
$267$	2.34830e10	0.282782
$268$	2.21823e11	2.62663
$269$	8.71165e10	1.01441	0.507207	−	0.861824i	$-0.330678\pi$
$269$	8.71165e10	1.01441	0.507207	+	0.861824i	$0.330678\pi$
$270$	−5.38069e10	−0.616171
$271$	−1.29398e11	−1.45735	−0.728677	−	0.684858i	$-0.759864\pi$
$271$	−1.29398e11	−1.45735	−0.728677	+	0.684858i	$0.759864\pi$
$272$	5.17213e10	0.572941
$273$	−4.44625e10	−0.484464
$274$	1.61886e11	1.73513
$275$	−1.55781e11	−1.64254
$276$	1.91188e11	1.98322
$277$	−1.54712e11	−1.57894	−0.789470	−	0.613789i	$-0.789645\pi$
$277$	−1.54712e11	−1.57894	−0.789470	+	0.613789i	$0.789645\pi$
$278$	6.69264e10	0.672042
$279$	4.14543e10	0.409591
$280$	−3.51547e11	−3.41801
$281$	1.50279e11	1.43787	0.718934	−	0.695078i	$-0.244630\pi$
$281$	1.50279e11	1.43787	0.718934	+	0.695078i	$0.244630\pi$
$282$	4.02849e10	0.379333
$283$	4.34423e10	0.402601	0.201300	−	0.979530i	$-0.435483\pi$
$283$	4.34423e10	0.402601	0.201300	+	0.979530i	$0.435483\pi$
$284$	2.87430e11	2.62180
$285$	−3.59262e10	−0.322560
$286$	7.03921e10	0.622123
$287$	3.54029e9	0.0308014
$288$	−2.56209e10	−0.219446
$289$	1.47043e11	1.23995
$290$	−5.97519e11	−4.96090
$291$	6.13479e10	0.501512
$292$	−2.92512e11	−2.35462
$293$	5.89544e10	0.467317	0.233659	−	0.972319i	$-0.424930\pi$
$293$	5.89544e10	0.467317	0.233659	+	0.972319i	$0.424930\pi$
$294$	1.08940e11	0.850400
$295$	3.25315e10	0.250095
$296$	−1.94257e11	−1.47083
$297$	−1.57557e10	−0.117499
$298$	−1.10863e11	−0.814353
$299$	−1.63258e11	−1.18128
$300$	3.87413e11	2.76140
$301$	−6.99268e10	−0.491015
$302$	−4.20912e11	−2.91179
$303$	8.43684e10	0.575027
$304$	1.65791e10	0.111334
$305$	−4.55947e10	−0.301693
$306$	1.27525e11	0.831476
$307$	7.67544e10	0.493152	0.246576	−	0.969123i	$-0.420694\pi$
$307$	7.67544e10	0.493152	0.246576	+	0.969123i	$0.420694\pi$
$308$	−2.35284e11	−1.48975
$309$	8.29483e10	0.517600
$310$	−6.39709e11	−3.93419
$311$	6.02515e10	0.365213	0.182607	−	0.983186i	$-0.441547\pi$
$311$	6.02515e10	0.365213	0.182607	+	0.983186i	$0.441547\pi$
$312$	−7.65904e10	−0.457593
$313$	−1.71527e11	−1.01015	−0.505073	−	0.863077i	$-0.668534\pi$
$313$	−1.71527e11	−1.01015	−0.505073	+	0.863077i	$0.668534\pi$
$314$	5.02622e11	2.91782
$315$	−1.53575e11	−0.878865
$316$	−4.97260e11	−2.80538
$317$	2.11191e11	1.17465	0.587324	−	0.809352i	$-0.300181\pi$
$317$	2.11191e11	1.17465	0.587324	+	0.809352i	$0.300181\pi$
$318$	−1.57842e11	−0.865567
$319$	−1.74964e11	−0.946001
$320$	5.33316e11	2.84321
$321$	1.29255e11	0.679477
$322$	8.52627e11	4.41985
$323$	8.51470e10	0.435269
$324$	3.91829e10	0.197535
$325$	−3.30817e11	−1.64480
$326$	6.32062e9	0.0309942
$327$	1.40017e10	0.0677200
$328$	6.09845e9	0.0290929
$329$	1.14980e11	0.541056
$330$	2.43136e11	1.12859
$331$	−2.30634e10	−0.105608	−0.0528041	−	0.998605i	$-0.516816\pi$
$331$	−2.30634e10	−0.105608	−0.0528041	+	0.998605i	$0.516816\pi$
$332$	1.85430e11	0.837641
$333$	−8.48618e10	−0.378193
$334$	5.83249e11	2.56445
$335$	−6.54252e11	−2.83820
$336$	7.08710e10	0.303349
$337$	4.02987e11	1.70199	0.850994	−	0.525175i	$-0.176000\pi$
$337$	4.02987e11	1.70199	0.850994	+	0.525175i	$0.176000\pi$
$338$	−2.50439e11	−1.04370
$339$	−2.09146e11	−0.860104
$340$	−1.25948e12	−5.11137
$341$	−1.87319e11	−0.750216
$342$	4.08778e10	0.161573
$343$	−4.08987e10	−0.159546
$344$	−1.20455e11	−0.463779
$345$	−5.63898e11	−2.14296
$346$	−7.12663e11	−2.67326
$347$	−3.14698e11	−1.16523	−0.582615	−	0.812748i	$-0.697971\pi$
$347$	−3.14698e11	−1.16523	−0.582615	+	0.812748i	$0.697971\pi$
$348$	4.35121e11	1.59039
$349$	1.07454e11	0.387711	0.193856	−	0.981030i	$-0.437901\pi$
$349$	1.07454e11	0.387711	0.193856	+	0.981030i	$0.437901\pi$
$350$	1.72772e12	6.15412
$351$	−3.34588e10	−0.117660
$352$	1.15773e11	0.401943
$353$	1.24803e11	0.427800	0.213900	−	0.976856i	$-0.431383\pi$
$353$	1.24803e11	0.427800	0.213900	+	0.976856i	$0.431383\pi$
$354$	−3.70152e10	−0.125275
$355$	−8.47757e11	−2.83298
$356$	2.63891e11	0.870763
$357$	3.63980e11	1.18596
$358$	2.98567e11	0.960656
$359$	2.55234e11	0.810988	0.405494	−	0.914098i	$-0.367100\pi$
$359$	2.55234e11	0.810988	0.405494	+	0.914098i	$0.367100\pi$
$360$	−2.64546e11	−0.830117
$361$	−2.95394e11	−0.915418
$362$	−3.64713e11	−1.11625
$363$	−1.19799e11	−0.362137
$364$	−4.99650e11	−1.49180
$365$	8.62745e11	2.54428
$366$	5.18788e10	0.151121
$367$	−4.01666e11	−1.15576	−0.577880	−	0.816122i	$-0.696120\pi$
$367$	−4.01666e11	−1.15576	−0.577880	+	0.816122i	$0.696120\pi$
$368$	2.60225e11	0.739664
$369$	2.66413e9	0.00748060
$370$	1.30956e12	3.63260
$371$	−4.50510e11	−1.23459
$372$	4.65845e11	1.26124
$373$	−2.60275e11	−0.696214	−0.348107	−	0.937455i	$-0.613175\pi$
$373$	−2.60275e11	−0.696214	−0.348107	+	0.937455i	$0.613175\pi$
$374$	−5.76246e11	−1.52295
$375$	−7.17923e11	−1.87472
$376$	1.98063e11	0.511045
$377$	−3.71555e11	−0.947300
$378$	1.74741e11	0.440233
$379$	1.10582e11	0.275301	0.137651	−	0.990481i	$-0.456045\pi$
$379$	1.10582e11	0.275301	0.137651	+	0.990481i	$0.456045\pi$
$380$	−4.03723e11	−0.993248
$381$	−1.16682e11	−0.283687
$382$	−3.14723e11	−0.756211
$383$	−1.02360e11	−0.243072	−0.121536	−	0.992587i	$-0.538782\pi$
$383$	−1.02360e11	−0.243072	−0.121536	+	0.992587i	$0.538782\pi$
$384$	−4.44870e11	−1.04410
$385$	6.93955e11	1.60975
$386$	−5.54928e11	−1.27231
$387$	−5.26211e10	−0.119251
$388$	6.89401e11	1.54429
$389$	4.50698e11	0.997958	0.498979	−	0.866614i	$-0.333708\pi$
$389$	4.50698e11	0.997958	0.498979	+	0.866614i	$0.333708\pi$
$390$	5.16325e11	1.13014
$391$	1.33647e12	2.89176
$392$	5.35610e11	1.14567
$393$	−8.01275e10	−0.169440
$394$	−7.30487e11	−1.52714
$395$	1.46664e12	3.03135
$396$	−1.77055e11	−0.361810
$397$	−2.59155e10	−0.0523604	−0.0261802	−	0.999657i	$-0.508334\pi$
$397$	−2.59155e10	−0.0523604	−0.0261802	+	0.999657i	$0.508334\pi$
$398$	−1.05204e12	−2.10164
$399$	1.16673e11	0.230457
$400$	5.27306e11	1.02989
$401$	5.09445e10	0.0983893	0.0491947	−	0.998789i	$-0.484335\pi$
$401$	5.09445e10	0.0983893	0.0491947	+	0.998789i	$0.484335\pi$
$402$	7.44424e11	1.42168
$403$	−3.97791e11	−0.751246
$404$	9.48095e11	1.77066
$405$	−1.15568e11	−0.213446
$406$	1.94048e12	3.54439
$407$	3.83463e11	0.692706
$408$	6.26987e11	1.12018
$409$	3.18061e11	0.562025	0.281013	−	0.959704i	$-0.409330\pi$
$409$	3.18061e11	0.562025	0.281013	+	0.959704i	$0.409330\pi$
$410$	−4.11120e10	−0.0718524
$411$	3.47702e11	0.601061
$412$	9.32136e11	1.59383
$413$	−1.05648e11	−0.178684
$414$	6.41617e11	1.07343
$415$	−5.46914e11	−0.905112
$416$	2.45855e11	0.402494
$417$	1.43746e11	0.232800
$418$	−1.84714e11	−0.295941
$419$	3.49468e11	0.553916	0.276958	−	0.960882i	$-0.410674\pi$
$419$	3.49468e11	0.553916	0.276958	+	0.960882i	$0.410674\pi$
$420$	−1.72581e12	−2.70626
$421$	4.66258e11	0.723364	0.361682	−	0.932302i	$-0.382203\pi$
$421$	4.66258e11	0.723364	0.361682	+	0.932302i	$0.382203\pi$
$422$	−7.38278e11	−1.13322
$423$	8.65247e10	0.131404
$424$	−7.76042e11	−1.16611
$425$	2.70814e12	4.02644
$426$	9.64599e11	1.41907
$427$	1.48071e11	0.215549
$428$	1.45251e12	2.09229
$429$	1.51190e11	0.215508
$430$	8.12032e11	1.14542
$431$	2.23331e11	0.311746	0.155873	−	0.987777i	$-0.450181\pi$
$431$	2.23331e11	0.311746	0.155873	+	0.987777i	$0.450181\pi$
$432$	5.33317e10	0.0736730
$433$	2.87584e11	0.393160	0.196580	−	0.980488i	$-0.437016\pi$
$433$	2.87584e11	0.393160	0.196580	+	0.980488i	$0.437016\pi$
$434$	2.07749e12	2.81084
$435$	−1.28336e12	−1.71849
$436$	1.57345e11	0.208528
$437$	4.28400e11	0.561931
$438$	−9.81653e11	−1.27445
$439$	3.84850e9	0.00494539	0.00247270	−	0.999997i	$-0.499213\pi$
$439$	3.84850e9	0.00494539	0.00247270	+	0.999997i	$0.499213\pi$
$440$	1.19540e12	1.52046
$441$	2.33983e11	0.294585
$442$	−1.22372e12	−1.52504
$443$	−4.55745e11	−0.562218	−0.281109	−	0.959676i	$-0.590702\pi$
$443$	−4.55745e11	−0.562218	−0.281109	+	0.959676i	$0.590702\pi$
$444$	−9.53640e11	−1.16456
$445$	−7.78331e11	−0.940901
$446$	9.98031e10	0.119437
$447$	−2.38114e11	−0.282098
$448$	−1.73197e12	−2.03138
$449$	−2.12096e11	−0.246277	−0.123139	−	0.992389i	$-0.539296\pi$
$449$	−2.12096e11	−0.246277	−0.123139	+	0.992389i	$0.539296\pi$
$450$	1.30014e12	1.49463
$451$	−1.20383e10	−0.0137016
$452$	−2.35029e12	−2.64849
$453$	−9.04045e11	−1.00867
$454$	−5.24904e11	−0.579867
$455$	1.47369e12	1.61196
$456$	2.00978e11	0.217675
$457$	4.71276e11	0.505420	0.252710	−	0.967542i	$-0.418678\pi$
$457$	4.71276e11	0.505420	0.252710	+	0.967542i	$0.418678\pi$
$458$	9.02887e11	0.958823
$459$	2.73901e11	0.288030
$460$	−6.33684e12	−6.59876
$461$	4.29257e11	0.442653	0.221326	−	0.975200i	$-0.428961\pi$
$461$	4.29257e11	0.442653	0.221326	+	0.975200i	$0.428961\pi$
$462$	−7.89599e11	−0.806339
$463$	−1.66714e12	−1.68600	−0.843001	−	0.537912i	$-0.819213\pi$
$463$	−1.66714e12	−1.68600	−0.843001	+	0.537912i	$0.819213\pi$
$464$	5.92241e11	0.593154
$465$	−1.37398e12	−1.36283
$466$	−7.32662e11	−0.719725
$467$	−1.03665e12	−1.00857	−0.504286	−	0.863537i	$-0.668244\pi$
$467$	−1.03665e12	−1.00857	−0.504286	+	0.863537i	$0.668244\pi$
$468$	−3.75995e11	−0.362306
$469$	2.12472e12	2.02780
$470$	−1.33522e12	−1.26216
$471$	1.07954e12	1.01075
$472$	−1.81988e11	−0.168773
$473$	2.37778e11	0.218422
$474$	−1.66878e12	−1.51843
$475$	8.68086e11	0.782422
$476$	4.09025e12	3.65190
$477$	−3.39017e11	−0.299839
$478$	−1.37947e12	−1.20861
$479$	8.90476e10	0.0772881	0.0386440	−	0.999253i	$-0.487696\pi$
$479$	8.90476e10	0.0772881	0.0386440	+	0.999253i	$0.487696\pi$
$480$	8.49192e11	0.730164
$481$	8.14325e11	0.693657
$482$	1.04082e12	0.878340
$483$	1.83129e12	1.53107
$484$	−1.34625e12	−1.11512
$485$	−2.03335e12	−1.66868
$486$	1.31496e11	0.106917
$487$	1.54005e12	1.24067	0.620334	−	0.784338i	$-0.286997\pi$
$487$	1.54005e12	1.24067	0.620334	+	0.784338i	$0.286997\pi$
$488$	2.55066e11	0.203593
$489$	1.35756e10	0.0107366
$490$	−3.61075e12	−2.82954
$491$	−1.44485e12	−1.12191	−0.560953	−	0.827848i	$-0.689565\pi$
$491$	−1.44485e12	−1.12191	−0.560953	+	0.827848i	$0.689565\pi$
$492$	2.99383e10	0.0230348
$493$	3.04164e12	2.31898
$494$	−3.92259e11	−0.296347
$495$	5.22213e11	0.390953
$496$	6.34059e11	0.470395
$497$	2.75314e12	2.02406
$498$	6.22292e11	0.453380
$499$	2.36049e12	1.70431	0.852157	−	0.523286i	$-0.175294\pi$
$499$	2.36049e12	1.70431	0.852157	+	0.523286i	$0.175294\pi$
$500$	−8.06770e12	−5.77277
$501$	1.25271e12	0.888346
$502$	−2.89676e12	−2.03585
$503$	1.34281e12	0.935315	0.467658	−	0.883910i	$-0.345098\pi$
$503$	1.34281e12	0.935315	0.467658	+	0.883910i	$0.345098\pi$
$504$	8.59128e11	0.593089
$505$	−2.79635e12	−1.91329
$506$	−2.89926e12	−1.96612
$507$	−5.37897e11	−0.361546
$508$	−1.31122e12	−0.873550
$509$	−1.80032e11	−0.118883	−0.0594414	−	0.998232i	$-0.518932\pi$
$509$	−1.80032e11	−0.118883	−0.0594414	+	0.998232i	$0.518932\pi$
$510$	−4.22676e12	−2.76657
$511$	−2.80181e12	−1.81780
$512$	−1.16356e12	−0.748295
$513$	8.77982e10	0.0559702
$514$	9.08970e11	0.574401
$515$	−2.74928e12	−1.72221
$516$	−5.91333e11	−0.367205
$517$	−3.90977e11	−0.240682
$518$	−4.25288e12	−2.59537
$519$	−1.53067e12	−0.926039
$520$	2.53855e12	1.52255
$521$	−1.65240e11	−0.0982529	−0.0491265	−	0.998793i	$-0.515644\pi$
$521$	−1.65240e11	−0.0982529	−0.0491265	+	0.998793i	$0.515644\pi$
$522$	1.46024e12	0.860811
$523$	−2.42593e12	−1.41782	−0.708908	−	0.705301i	$-0.750812\pi$
$523$	−2.42593e12	−1.41782	−0.708908	+	0.705301i	$0.750812\pi$
$524$	−9.00437e11	−0.521750
$525$	3.71083e12	2.13184
$526$	3.59898e12	2.04995
$527$	3.25641e12	1.83904
$528$	−2.40989e11	−0.134941
$529$	4.92301e12	2.73325
$530$	5.23160e12	2.88000
$531$	−7.95020e10	−0.0433963
$532$	1.31111e12	0.709640
$533$	−2.55647e10	−0.0137204
$534$	8.85604e11	0.471307
$535$	−4.28409e12	−2.26082
$536$	3.66001e12	1.91532
$537$	6.41268e11	0.332779
$538$	3.28539e12	1.69070
$539$	−1.05729e12	−0.539568
$540$	−1.29870e12	−0.657259
$541$	4.55520e11	0.228623	0.114311	−	0.993445i	$-0.463534\pi$
$541$	4.55520e11	0.228623	0.114311	+	0.993445i	$0.463534\pi$
$542$	−4.87993e12	−2.42894
$543$	−7.83338e11	−0.386678
$544$	−2.01263e12	−0.985301
$545$	−4.64081e11	−0.225325
$546$	−1.67680e12	−0.807446
$547$	−9.68091e11	−0.462352	−0.231176	−	0.972912i	$-0.574257\pi$
$547$	−9.68091e11	−0.462352	−0.231176	+	0.972912i	$0.574257\pi$
$548$	3.90732e12	1.85083
$549$	1.11426e11	0.0523495
$550$	−5.87490e12	−2.73759
$551$	9.74986e11	0.450626
$552$	3.15456e12	1.44615
$553$	−4.76299e12	−2.16579
$554$	−5.83461e12	−2.63159
$555$	2.81270e12	1.25836
$556$	1.61535e12	0.716855
$557$	1.60833e12	0.707991	0.353996	−	0.935247i	$-0.384823\pi$
$557$	1.60833e12	0.707991	0.353996	+	0.935247i	$0.384823\pi$
$558$	1.56335e12	0.682657
$559$	5.04947e11	0.218722
$560$	−2.34898e12	−1.00933
$561$	−1.23767e12	−0.527561
$562$	5.66740e12	2.39646
$563$	2.03919e12	0.855403	0.427702	−	0.903920i	$-0.359323\pi$
$563$	2.03919e12	0.855403	0.427702	+	0.903920i	$0.359323\pi$
$564$	9.72327e11	0.404628
$565$	6.93204e12	2.86183
$566$	1.63833e12	0.671006
$567$	3.75313e11	0.152500
$568$	4.74252e12	1.91180
$569$	−3.82797e12	−1.53096	−0.765479	−	0.643461i	$-0.777498\pi$
$569$	−3.82797e12	−1.53096	−0.765479	+	0.643461i	$0.777498\pi$
$570$	−1.35487e12	−0.537603
$571$	−3.15952e12	−1.24382	−0.621912	−	0.783087i	$-0.713644\pi$
$571$	−3.15952e12	−1.24382	−0.621912	+	0.783087i	$0.713644\pi$
$572$	1.69900e12	0.663608
$573$	−6.75968e11	−0.261957
$574$	1.33514e11	0.0513360
$575$	1.36255e13	5.19812
$576$	−1.30334e12	−0.493352
$577$	3.80747e11	0.143003	0.0715015	−	0.997440i	$-0.477221\pi$
$577$	3.80747e11	0.143003	0.0715015	+	0.997440i	$0.477221\pi$
$578$	5.54538e12	2.06660
$579$	−1.19189e12	−0.440739
$580$	−1.44219e13	−5.29170
$581$	1.77613e12	0.646671
$582$	2.31359e12	0.835860
$583$	1.53191e12	0.549192
$584$	−4.82637e12	−1.71697
$585$	1.10898e12	0.391490
$586$	2.22332e12	0.778867
$587$	−1.87272e12	−0.651031	−0.325515	−	0.945537i	$-0.605538\pi$
$587$	−1.87272e12	−0.651031	−0.325515	+	0.945537i	$0.605538\pi$
$588$	2.62940e12	0.907107
$589$	1.04383e12	0.357364
$590$	1.22685e12	0.416828
$591$	−1.56896e12	−0.529014
$592$	−1.29799e12	−0.434335
$593$	−2.65121e12	−0.880436	−0.440218	−	0.897891i	$-0.645099\pi$
$593$	−2.65121e12	−0.880436	−0.440218	+	0.897891i	$0.645099\pi$
$594$	−5.94187e11	−0.195832
$595$	−1.20639e13	−3.94605
$596$	−2.67582e12	−0.868657
$597$	−2.25959e12	−0.728024
$598$	−6.15689e12	−1.96882
$599$	1.09816e12	0.348533	0.174267	−	0.984698i	$-0.444245\pi$
$599$	1.09816e12	0.348533	0.174267	+	0.984698i	$0.444245\pi$
$600$	6.39222e12	2.01359
$601$	3.22983e12	1.00982	0.504911	−	0.863171i	$-0.331525\pi$
$601$	3.22983e12	1.00982	0.504911	+	0.863171i	$0.331525\pi$
$602$	−2.63712e12	−0.818363
$603$	1.59889e12	0.492482
$604$	−1.01593e13	−3.10596
$605$	3.97068e12	1.20494
$606$	3.18176e12	0.958385
$607$	5.65303e12	1.69018	0.845089	−	0.534626i	$-0.179548\pi$
$607$	5.65303e12	1.69018	0.845089	+	0.534626i	$0.179548\pi$
$608$	−6.45141e11	−0.191465
$609$	4.16780e12	1.22780
$610$	−1.71950e12	−0.502825
$611$	−8.30282e11	−0.241013
$612$	3.07798e12	0.886921
$613$	6.24408e12	1.78606	0.893031	−	0.449996i	$-0.148574\pi$
$613$	6.24408e12	1.78606	0.893031	+	0.449996i	$0.148574\pi$
$614$	2.89461e12	0.821926
$615$	−8.83012e10	−0.0248902
$616$	−3.88212e12	−1.08632
$617$	−2.50075e12	−0.694683	−0.347341	−	0.937739i	$-0.612916\pi$
$617$	−2.50075e12	−0.694683	−0.347341	+	0.937739i	$0.612916\pi$
$618$	3.12820e12	0.862672
$619$	−4.57288e12	−1.25194	−0.625968	−	0.779849i	$-0.715296\pi$
$619$	−4.57288e12	−1.25194	−0.625968	+	0.779849i	$0.715296\pi$
$620$	−1.54402e13	−4.19653
$621$	1.37808e12	0.371845
$622$	2.27224e12	0.608693
$623$	2.52767e12	0.672241
$624$	−5.11765e11	−0.135126
$625$	1.35325e13	3.54745
$626$	−6.46875e12	−1.68359
$627$	−3.96732e11	−0.102516
$628$	1.21314e13	3.11238
$629$	−6.66625e12	−1.69806
$630$	−5.79171e12	−1.46479
$631$	−7.23797e12	−1.81754	−0.908771	−	0.417295i	$-0.862978\pi$
$631$	−7.23797e12	−1.81754	−0.908771	+	0.417295i	$0.862978\pi$
$632$	−8.20466e12	−2.04566
$633$	−1.58569e12	−0.392556
$634$	7.96455e12	1.95776
$635$	3.86735e12	0.943913
$636$	−3.80972e12	−0.923286
$637$	−2.24528e12	−0.540309
$638$	−6.59837e12	−1.57668
$639$	2.07179e12	0.491576
$640$	1.47450e13	3.47404
$641$	−5.23968e12	−1.22587	−0.612934	−	0.790134i	$-0.710011\pi$
$641$	−5.23968e12	−1.22587	−0.612934	+	0.790134i	$0.710011\pi$
$642$	4.87454e12	1.13247
$643$	3.47830e11	0.0802450	0.0401225	−	0.999195i	$-0.487225\pi$
$643$	3.47830e11	0.0802450	0.0401225	+	0.999195i	$0.487225\pi$
$644$	2.05792e13	4.71458
$645$	1.74410e12	0.396783
$646$	3.21112e12	0.725454
$647$	−6.78788e11	−0.152288	−0.0761439	−	0.997097i	$-0.524261\pi$
$647$	−6.78788e11	−0.152288	−0.0761439	+	0.997097i	$0.524261\pi$
$648$	6.46509e11	0.144041
$649$	3.59244e11	0.0794856
$650$	−1.24760e13	−2.74135
$651$	4.46209e12	0.973696
$652$	1.52556e11	0.0330610
$653$	−4.84386e12	−1.04252	−0.521258	−	0.853399i	$-0.674537\pi$
$653$	−4.84386e12	−1.04252	−0.521258	+	0.853399i	$0.674537\pi$
$654$	5.28042e11	0.112868
$655$	2.65578e12	0.563777
$656$	4.07489e10	0.00859109
$657$	−2.10841e12	−0.441481
$658$	4.33621e12	0.901766
$659$	−7.06815e12	−1.45989	−0.729947	−	0.683504i	$-0.760455\pi$
$659$	−7.06815e12	−1.45989	−0.729947	+	0.683504i	$0.760455\pi$
$660$	5.86840e12	1.20385
$661$	2.76923e12	0.564225	0.282112	−	0.959381i	$-0.408965\pi$
$661$	2.76923e12	0.564225	0.282112	+	0.959381i	$0.408965\pi$
$662$	−8.69781e11	−0.176015
$663$	−2.62833e12	−0.528286
$664$	3.05954e12	0.610802
$665$	−3.86705e12	−0.766801
$666$	−3.20036e12	−0.630326
$667$	1.53034e13	2.99379
$668$	1.40775e13	2.73546
$669$	2.14359e11	0.0413737
$670$	−2.46736e13	−4.73037
$671$	−5.03500e11	−0.0958844
$672$	−2.75780e12	−0.521676
$673$	−5.79571e12	−1.08903	−0.544513	−	0.838752i	$-0.683286\pi$
$673$	−5.79571e12	−1.08903	−0.544513	+	0.838752i	$0.683286\pi$
$674$	1.51977e13	2.83667
$675$	2.79246e12	0.517750
$676$	−6.04465e12	−1.11330
$677$	−4.41498e12	−0.807755	−0.403878	−	0.914813i	$-0.632338\pi$
$677$	−4.41498e12	−0.807755	−0.403878	+	0.914813i	$0.632338\pi$
$678$	−7.88745e12	−1.43352
$679$	6.60341e12	1.19221
$680$	−2.07812e13	−3.72717
$681$	−1.12740e12	−0.200871
$682$	−7.06428e12	−1.25037
$683$	−2.14581e12	−0.377310	−0.188655	−	0.982043i	$-0.560413\pi$
$683$	−2.14581e12	−0.377310	−0.188655	+	0.982043i	$0.560413\pi$
$684$	9.86637e11	0.172347
$685$	−1.15244e13	−1.99991
$686$	−1.54240e12	−0.265912
$687$	1.93924e12	0.332144
$688$	−8.04861e11	−0.136953
$689$	3.25317e12	0.549946
$690$	−2.12661e13	−3.57163
$691$	−1.21012e12	−0.201920	−0.100960	−	0.994890i	$-0.532191\pi$
$691$	−1.21012e12	−0.201920	−0.100960	+	0.994890i	$0.532191\pi$
$692$	−1.72010e13	−2.85152
$693$	−1.69592e12	−0.279322
$694$	−1.18681e13	−1.94207
$695$	−4.76439e12	−0.774597
$696$	7.17939e12	1.15970
$697$	2.09278e11	0.0335874
$698$	4.05237e12	0.646190
$699$	−1.57363e12	−0.249318
$700$	4.17006e13	6.56450
$701$	4.58684e12	0.717435	0.358717	−	0.933446i	$-0.383214\pi$
$701$	4.58684e12	0.717435	0.358717	+	0.933446i	$0.383214\pi$
$702$	−1.26182e12	−0.196101
$703$	−2.13684e12	−0.329969
$704$	5.88938e12	0.903634
$705$	−2.86782e12	−0.437221
$706$	4.70667e12	0.713005
$707$	9.08131e12	1.36698
$708$	−8.93409e11	−0.133629
$709$	−1.21012e13	−1.79854	−0.899271	−	0.437393i	$-0.855902\pi$
$709$	−1.21012e13	−1.79854	−0.899271	+	0.437393i	$0.855902\pi$
$710$	−3.19711e13	−4.72167
$711$	−3.58423e12	−0.525997
$712$	4.35414e12	0.634954
$713$	1.63839e13	2.37419
$714$	1.37266e13	1.97662
$715$	−5.01110e12	−0.717061
$716$	7.20629e12	1.02472
$717$	−2.96285e12	−0.418671
$718$	9.62556e12	1.35166
$719$	3.23141e12	0.450933	0.225467	−	0.974251i	$-0.427609\pi$
$719$	3.23141e12	0.450933	0.225467	+	0.974251i	$0.427609\pi$
$720$	−1.76765e12	−0.245132
$721$	8.92844e12	1.23046
$722$	−1.11401e13	−1.52571
$723$	2.23549e12	0.304264
$724$	−8.80281e12	−1.19069
$725$	3.10099e13	4.16850
$726$	−4.51793e12	−0.603567
$727$	1.39712e13	1.85494	0.927468	−	0.373902i	$-0.121980\pi$
$727$	1.39712e13	1.85494	0.927468	+	0.373902i	$0.121980\pi$
$728$	−8.24409e12	−1.08781
$729$	2.82430e11	0.0370370
$730$	3.25364e13	4.24049
$731$	−4.13361e12	−0.535428
$732$	1.25216e12	0.161198
$733$	−6.76655e12	−0.865764	−0.432882	−	0.901451i	$-0.642503\pi$
$733$	−6.76655e12	−0.865764	−0.432882	+	0.901451i	$0.642503\pi$
$734$	−1.51479e13	−1.92628
$735$	−7.75525e12	−0.980173
$736$	−1.01261e13	−1.27202
$737$	−7.22487e12	−0.902041
$738$	1.00471e11	0.0124678
$739$	1.34500e13	1.65891	0.829456	−	0.558572i	$-0.188650\pi$
$739$	1.34500e13	1.65891	0.829456	+	0.558572i	$0.188650\pi$
$740$	3.16079e13	3.87483
$741$	−8.42502e11	−0.102657
$742$	−1.69899e13	−2.05766
$743$	−1.48305e13	−1.78528	−0.892641	−	0.450769i	$-0.851150\pi$
$743$	−1.48305e13	−1.78528	−0.892641	+	0.450769i	$0.851150\pi$
$744$	7.68632e12	0.919688
$745$	7.89216e12	0.938626
$746$	−9.81565e12	−1.16036
$747$	1.33657e12	0.157054
$748$	−1.39084e13	−1.62450
$749$	1.39128e13	1.61528
$750$	−2.70747e13	−3.12456
$751$	−2.98445e12	−0.342362	−0.171181	−	0.985240i	$-0.554758\pi$
$751$	−2.98445e12	−0.342362	−0.171181	+	0.985240i	$0.554758\pi$
$752$	1.32343e12	0.150911
$753$	−6.22173e12	−0.705235
$754$	−1.40123e13	−1.57884
$755$	2.99641e13	3.35614
$756$	4.21760e12	0.469588
$757$	7.48619e12	0.828570	0.414285	−	0.910147i	$-0.364032\pi$
$757$	7.48619e12	0.828570	0.414285	+	0.910147i	$0.364032\pi$
$758$	4.17034e12	0.458838
$759$	−6.22710e12	−0.681079
$760$	−6.66133e12	−0.724269
$761$	−6.74085e12	−0.728590	−0.364295	−	0.931284i	$-0.618690\pi$
$761$	−6.74085e12	−0.728590	−0.364295	+	0.931284i	$0.618690\pi$
$762$	−4.40037e12	−0.472816
$763$	1.50713e12	0.160987
$764$	−7.59624e12	−0.806637
$765$	−9.07832e12	−0.958361
$766$	−3.86026e12	−0.405123
$767$	7.62893e11	0.0795947
$768$	−8.53883e12	−0.885672
$769$	−1.61315e13	−1.66343	−0.831716	−	0.555202i	$-0.812641\pi$
$769$	−1.61315e13	−1.66343	−0.831716	+	0.555202i	$0.812641\pi$
$770$	2.61709e13	2.68293
$771$	1.95231e12	0.198977
$772$	−1.33939e13	−1.35715
$773$	−5.10799e12	−0.514568	−0.257284	−	0.966336i	$-0.582828\pi$
$773$	−5.10799e12	−0.514568	−0.257284	+	0.966336i	$0.582828\pi$
$774$	−1.98448e12	−0.198753
$775$	3.31995e13	3.30578
$776$	1.13749e13	1.12609
$777$	−9.13442e12	−0.899055
$778$	1.69970e13	1.66328
$779$	6.70835e10	0.00652675
$780$	1.24622e13	1.20550
$781$	−9.36173e12	−0.900382
$782$	5.04017e13	4.81964
$783$	3.13634e12	0.298192
$784$	3.57886e12	0.338316
$785$	−3.57809e13	−3.36308
$786$	−3.02182e12	−0.282401
$787$	3.10210e12	0.288250	0.144125	−	0.989559i	$-0.453963\pi$
$787$	3.10210e12	0.288250	0.144125	+	0.989559i	$0.453963\pi$
$788$	−1.76312e13	−1.62898
$789$	7.72997e12	0.710119
$790$	5.53107e13	5.05228
$791$	−2.25122e13	−2.04467
$792$	−2.92136e12	−0.263829
$793$	−1.06924e12	−0.0960160
$794$	−9.77343e11	−0.0872679
$795$	1.12365e13	0.997655
$796$	−2.53923e13	−2.24178
$797$	−6.73763e12	−0.591486	−0.295743	−	0.955268i	$-0.595567\pi$
$797$	−6.73763e12	−0.591486	−0.295743	+	0.955268i	$0.595567\pi$
$798$	4.40003e12	0.384098
$799$	6.79688e12	0.589996
$800$	−2.05190e13	−1.77114
$801$	1.90212e12	0.163264
$802$	1.92125e12	0.163983
$803$	9.52725e12	0.808626
$804$	1.79676e13	1.51649
$805$	−6.06972e13	−5.09433
$806$	−1.50017e13	−1.25209
$807$	7.05644e12	0.585672
$808$	1.56433e13	1.29115
$809$	−3.96895e12	−0.325767	−0.162884	−	0.986645i	$-0.552080\pi$
$809$	−3.96895e12	−0.325767	−0.162884	+	0.986645i	$0.552080\pi$
$810$	−4.35836e12	−0.355747
$811$	4.77001e12	0.387191	0.193596	−	0.981081i	$-0.437985\pi$
$811$	4.77001e12	0.387191	0.193596	+	0.981081i	$0.437985\pi$
$812$	4.68359e13	3.78074
$813$	−1.04812e13	−0.841404
$814$	1.44614e13	1.15452
$815$	−4.49955e11	−0.0357240
$816$	4.18943e12	0.330787
$817$	−1.32501e12	−0.104045
$818$	1.19949e13	0.936715
$819$	−3.60146e12	−0.279706
$820$	−9.92290e11	−0.0766437
$821$	3.01276e12	0.231430	0.115715	−	0.993282i	$-0.463084\pi$
$821$	3.01276e12	0.231430	0.115715	+	0.993282i	$0.463084\pi$
$822$	1.31127e13	1.00178
$823$	−9.94134e12	−0.755346	−0.377673	−	0.925939i	$-0.623276\pi$
$823$	−9.94134e12	−0.755346	−0.377673	+	0.925939i	$0.623276\pi$
$824$	1.53800e13	1.16221
$825$	−1.26182e13	−0.948322
$826$	−3.98427e12	−0.297809
$827$	−1.66093e13	−1.23475	−0.617373	−	0.786671i	$-0.711803\pi$
$827$	−1.66093e13	−1.23475	−0.617373	+	0.786671i	$0.711803\pi$
$828$	1.54862e13	1.14501
$829$	−8.34298e12	−0.613516	−0.306758	−	0.951788i	$-0.599244\pi$
$829$	−8.34298e12	−0.613516	−0.306758	+	0.951788i	$0.599244\pi$
$830$	−2.06255e13	−1.50853
$831$	−1.25317e13	−0.911602
$832$	1.25067e13	0.904875
$833$	1.83803e13	1.32267
$834$	5.42104e12	0.388003
$835$	−4.15206e13	−2.95579
$836$	−4.45830e12	−0.315675
$837$	3.35780e12	0.236478
$838$	1.31793e13	0.923200
$839$	2.62298e13	1.82754	0.913770	−	0.406233i	$-0.133158\pi$
$839$	2.62298e13	1.82754	0.913770	+	0.406233i	$0.133158\pi$
$840$	−2.84753e13	−1.97339
$841$	2.03215e13	1.40079
$842$	1.75838e13	1.20561
$843$	1.21726e13	0.830153
$844$	−1.78193e13	−1.20879
$845$	1.78283e13	1.20297
$846$	3.26307e12	0.219008
$847$	−1.28950e13	−0.860887
$848$	−5.18539e12	−0.344350
$849$	3.51883e12	0.232442
$850$	1.02131e14	6.71078
$851$	−3.35399e13	−2.19219
$852$	2.32818e13	1.51370
$853$	−1.91183e13	−1.23646	−0.618229	−	0.785998i	$-0.712150\pi$
$853$	−1.91183e13	−1.23646	−0.618229	+	0.785998i	$0.712150\pi$
$854$	5.58416e12	0.359251
$855$	−2.91003e12	−0.186230
$856$	2.39660e13	1.52568
$857$	2.55437e13	1.61760	0.808799	−	0.588086i	$-0.200118\pi$
$857$	2.55437e13	1.61760	0.808799	+	0.588086i	$0.200118\pi$
$858$	5.70176e12	0.359183
$859$	−1.63534e13	−1.02480	−0.512398	−	0.858748i	$-0.671243\pi$
$859$	−1.63534e13	−1.02480	−0.512398	+	0.858748i	$0.671243\pi$
$860$	1.95994e13	1.22180
$861$	2.86763e11	0.0177832
$862$	8.42238e12	0.519580
$863$	4.89259e12	0.300255	0.150127	−	0.988667i	$-0.452032\pi$
$863$	4.89259e12	0.300255	0.150127	+	0.988667i	$0.452032\pi$
$864$	−2.07529e12	−0.126697
$865$	5.07334e13	3.08121
$866$	1.08455e13	0.655271
$867$	1.19105e13	0.715885
$868$	5.01430e13	2.99827
$869$	1.61960e13	0.963427
$870$	−4.83990e13	−2.86418
$871$	−1.53428e13	−0.903280
$872$	2.59616e12	0.152057
$873$	4.96918e12	0.289548
$874$	1.61561e13	0.936558
$875$	−7.72762e13	−4.45666
$876$	−2.36934e13	−1.35944
$877$	−1.26114e13	−0.719887	−0.359943	−	0.932974i	$-0.617204\pi$
$877$	−1.26114e13	−0.719887	−0.359943	+	0.932974i	$0.617204\pi$
$878$	1.45137e11	0.00824238
$879$	4.77530e12	0.269806
$880$	7.98745e12	0.448990
$881$	3.04432e13	1.70255	0.851273	−	0.524722i	$-0.175831\pi$
$881$	3.04432e13	1.70255	0.851273	+	0.524722i	$0.175831\pi$
$882$	8.82411e12	0.490978
$883$	−8.12469e12	−0.449763	−0.224881	−	0.974386i	$-0.572199\pi$
$883$	−8.12469e12	−0.449763	−0.224881	+	0.974386i	$0.572199\pi$
$884$	−2.95360e13	−1.62673
$885$	2.63505e12	0.144393
$886$	−1.71873e13	−0.937037
$887$	1.35980e13	0.737596	0.368798	−	0.929510i	$-0.379769\pi$
$887$	1.35980e13	0.737596	0.368798	+	0.929510i	$0.379769\pi$
$888$	−1.57348e13	−0.849187
$889$	−1.25595e13	−0.674393
$890$	−2.93529e13	−1.56818
$891$	−1.27621e12	−0.0678378
$892$	2.40888e12	0.127401
$893$	2.17872e12	0.114649
$894$	−8.97989e12	−0.470167
$895$	−2.12545e13	−1.10725
$896$	−4.78853e13	−2.48208
$897$	−1.32239e13	−0.682014
$898$	−7.99871e12	−0.410465
$899$	3.72879e13	1.90392
$900$	3.13805e13	1.59429
$901$	−2.66312e13	−1.34626
$902$	−4.53998e11	−0.0228362
$903$	−5.66407e12	−0.283487
$904$	−3.87792e13	−1.93126
$905$	2.59633e13	1.28660
$906$	−3.40939e13	−1.68112
$907$	−1.34500e13	−0.659917	−0.329959	−	0.943995i	$-0.607035\pi$
$907$	−1.34500e13	−0.659917	−0.329959	+	0.943995i	$0.607035\pi$
$908$	−1.26692e13	−0.618534
$909$	6.83384e12	0.331992
$910$	5.55766e13	2.68662
$911$	−1.49411e13	−0.718702	−0.359351	−	0.933202i	$-0.617002\pi$
$911$	−1.49411e13	−0.718702	−0.359351	+	0.933202i	$0.617002\pi$
$912$	1.34291e12	0.0642790
$913$	−6.03954e12	−0.287664
$914$	1.77730e13	0.842372
$915$	−3.69317e12	−0.174182
$916$	2.17923e13	1.02276
$917$	−8.62482e12	−0.402799
$918$	1.03295e13	0.480053
$919$	1.87777e13	0.868405	0.434203	−	0.900815i	$-0.357030\pi$
$919$	1.87777e13	0.868405	0.434203	+	0.900815i	$0.357030\pi$
$920$	−1.04556e14	−4.81176
$921$	6.21711e12	0.284721
$922$	1.61884e13	0.737760
$923$	−1.98806e13	−0.901618
$924$	−1.90580e13	−0.860108
$925$	−6.79633e13	−3.05237
$926$	−6.28723e13	−2.81002
$927$	6.71881e12	0.298836
$928$	−2.30458e13	−1.02006
$929$	−1.45957e13	−0.642918	−0.321459	−	0.946923i	$-0.604173\pi$
$929$	−1.45957e13	−0.642918	−0.321459	+	0.946923i	$0.604173\pi$
$930$	−5.18165e13	−2.27140
$931$	5.89175e12	0.257022
$932$	−1.76837e13	−0.767719
$933$	4.88038e12	0.210856
$934$	−3.90948e13	−1.68096
$935$	4.10220e13	1.75535
$936$	−6.20383e12	−0.264191
$937$	−2.50294e13	−1.06077	−0.530386	−	0.847757i	$-0.677953\pi$
$937$	−2.50294e13	−1.06077	−0.530386	+	0.847757i	$0.677953\pi$
$938$	8.01288e13	3.37968
$939$	−1.38937e13	−0.583208
$940$	−3.22273e13	−1.34632
$941$	3.34102e13	1.38907	0.694537	−	0.719457i	$-0.255609\pi$
$941$	3.34102e13	1.38907	0.694537	+	0.719457i	$0.255609\pi$
$942$	4.07124e13	1.68460
$943$	1.05294e12	0.0433612
$944$	−1.21601e12	−0.0498384
$945$	−1.24396e13	−0.507413
$946$	8.96723e12	0.364039
$947$	−3.09383e13	−1.25003	−0.625016	−	0.780612i	$-0.714908\pi$
$947$	−3.09383e13	−1.25003	−0.625016	+	0.780612i	$0.714908\pi$
$948$	−4.02780e13	−1.61969
$949$	2.02321e13	0.809736
$950$	3.27378e13	1.30405
$951$	1.71064e13	0.678183
$952$	6.74880e13	2.66294
$953$	8.22593e12	0.323048	0.161524	−	0.986869i	$-0.448359\pi$
$953$	8.22593e12	0.323048	0.161524	+	0.986869i	$0.448359\pi$
$954$	−1.27852e13	−0.499735
$955$	2.24046e13	0.871611
$956$	−3.32952e13	−1.28920
$957$	−1.41721e13	−0.546174
$958$	3.35822e12	0.128814
$959$	3.74261e13	1.42887
$960$	4.31986e13	1.64153
$961$	1.34812e13	0.509885
$962$	3.07103e13	1.15610
$963$	1.04697e13	0.392296
$964$	2.51214e13	0.936910
$965$	3.95045e13	1.46647
$966$	6.90628e13	2.55180
$967$	4.11299e13	1.51265	0.756326	−	0.654195i	$-0.226993\pi$
$967$	4.11299e13	1.51265	0.756326	+	0.654195i	$0.226993\pi$
$968$	−2.22128e13	−0.813136
$969$	6.89691e12	0.251303
$970$	−7.66828e13	−2.78116
$971$	8.74724e12	0.315780	0.157890	−	0.987457i	$-0.449531\pi$
$971$	8.74724e12	0.315780	0.157890	+	0.987457i	$0.449531\pi$
$972$	3.17382e12	0.114047
$973$	1.54726e13	0.553422
$974$	5.80795e13	2.06779
$975$	−2.67962e13	−0.949624
$976$	1.70431e12	0.0601207
$977$	1.00439e13	0.352676	0.176338	−	0.984330i	$-0.443575\pi$
$977$	1.00439e13	0.352676	0.176338	+	0.984330i	$0.443575\pi$
$978$	5.11970e11	0.0178945
$979$	−8.59507e12	−0.299039
$980$	−8.71501e13	−3.01822
$981$	1.13414e12	0.0390982
$982$	−5.44891e13	−1.86986
$983$	5.44392e12	0.185961	0.0929803	−	0.995668i	$-0.470361\pi$
$983$	5.44392e12	0.185961	0.0929803	+	0.995668i	$0.470361\pi$
$984$	4.93974e11	0.0167968
$985$	5.20023e13	1.76019
$986$	1.14708e14	3.86499
$987$	9.31341e12	0.312379
$988$	−9.46766e12	−0.316109
$989$	−2.07974e13	−0.691235
$990$	1.96940e13	0.651593
$991$	−5.35928e13	−1.76512	−0.882561	−	0.470197i	$-0.844183\pi$
$991$	−5.35928e13	−1.76512	−0.882561	+	0.470197i	$0.844183\pi$
$992$	−2.46731e13	−0.808950
$993$	−1.86814e12	−0.0609729
$994$	1.03828e14	3.37347
$995$	7.48931e13	2.42236
$996$	1.50198e13	0.483612
$997$	−3.42583e12	−0.109809	−0.0549044	−	0.998492i	$-0.517485\pi$
$997$	−3.42583e12	−0.109809	−0.0549044	+	0.998492i	$0.517485\pi$
$998$	8.90203e13	2.84054
$999$	−6.87381e12	−0.218350

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.d.1.19	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.d.1.19	✓	22	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+37.7126 q^{2} +81.0000 q^{3} +910.242 q^{4} -2684.70 q^{5} +3054.72 q^{6} +8718.73 q^{7} +15018.8 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+37.7126 q^{2} +81.0000 q^{3} +910.242 q^{4} -2684.70 q^{5} +3054.72 q^{6} +8718.73 q^{7} +15018.8 q^{8} +6561.00 q^{9} -101247. q^{10} -29647.1 q^{11} +73729.6 q^{12} -62958.6 q^{13} +328806. q^{14} -217461. q^{15} +100353. q^{16} +515394. q^{17} +247433. q^{18} +165208. q^{19} -2.44373e6 q^{20} +706217. q^{21} -1.11807e6 q^{22} +2.59310e6 q^{23} +1.21652e6 q^{24} +5.25451e6 q^{25} -2.37434e6 q^{26} +531441. q^{27} +7.93616e6 q^{28} +5.90158e6 q^{29} -8.20103e6 q^{30} +6.31829e6 q^{31} -3.90503e6 q^{32} -2.40141e6 q^{33} +1.94369e7 q^{34} -2.34072e7 q^{35} +5.97210e6 q^{36} -1.29343e7 q^{37} +6.23042e6 q^{38} -5.09965e6 q^{39} -4.03209e7 q^{40} +406055. q^{41} +2.66333e7 q^{42} -8.02029e6 q^{43} -2.69860e7 q^{44} -1.76143e7 q^{45} +9.77926e7 q^{46} +1.31877e7 q^{47} +8.12859e6 q^{48} +3.56627e7 q^{49} +1.98161e8 q^{50} +4.17469e7 q^{51} -5.73076e7 q^{52} -5.16715e7 q^{53} +2.00420e7 q^{54} +7.95936e7 q^{55} +1.30945e8 q^{56} +1.33818e7 q^{57} +2.22564e8 q^{58} -1.21174e7 q^{59} -1.97942e8 q^{60} +1.69831e7 q^{61} +2.38279e8 q^{62} +5.72036e7 q^{63} -1.98650e8 q^{64} +1.69025e8 q^{65} -9.05635e7 q^{66} +2.43696e8 q^{67} +4.69133e8 q^{68} +2.10041e8 q^{69} -8.82748e8 q^{70} +3.15773e8 q^{71} +9.85381e7 q^{72} -3.21356e8 q^{73} -4.87786e8 q^{74} +4.25615e8 q^{75} +1.50379e8 q^{76} -2.58485e8 q^{77} -1.92321e8 q^{78} -5.46294e8 q^{79} -2.69418e8 q^{80} +4.30467e7 q^{81} +1.53134e7 q^{82} +2.03715e8 q^{83} +6.42829e8 q^{84} -1.38368e9 q^{85} -3.02466e8 q^{86} +4.78028e8 q^{87} -4.45262e8 q^{88} +2.89913e8 q^{89} -6.64283e8 q^{90} -5.48920e8 q^{91} +2.36035e9 q^{92} +5.11781e8 q^{93} +4.97344e8 q^{94} -4.43534e8 q^{95} -3.16308e8 q^{96} +7.57382e8 q^{97} +1.34493e9 q^{98} -1.94514e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9}+O(q^{10}) \) 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9} + 45337 q^{10} + 111769 q^{11} + 483894 q^{12} + 189121 q^{13} + 251053 q^{14} + 468666 q^{15} + 2311074 q^{16} + 1113841 q^{17} + 301806 q^{18} + 476068 q^{19} - 42495 q^{20} + 618921 q^{21} - 2252022 q^{22} + 7103062 q^{23} + 4972995 q^{24} + 10628442 q^{25} + 6871048 q^{26} + 11691702 q^{27} + 8112650 q^{28} + 15279316 q^{29} + 3672297 q^{30} + 17610338 q^{31} + 32378276 q^{32} + 9053289 q^{33} + 29339436 q^{34} + 7134904 q^{35} + 39195414 q^{36} + 21961411 q^{37} + 65195131 q^{38} + 15318801 q^{39} + 75185084 q^{40} + 52781575 q^{41} + 20335293 q^{42} + 76191313 q^{43} + 61127768 q^{44} + 37961946 q^{45} + 290208769 q^{46} + 160572396 q^{47} + 187196994 q^{48} + 156292703 q^{49} + 169504821 q^{50} + 90221121 q^{51} + 65465920 q^{52} - 8762038 q^{53} + 24446286 q^{54} + 147125140 q^{55} + 9671794 q^{56} + 38561508 q^{57} - 37665424 q^{58} - 266581942 q^{59} - 3442095 q^{60} + 120750754 q^{61} - 152465186 q^{62} + 50132601 q^{63} - 40658803 q^{64} + 331055798 q^{65} - 182413782 q^{66} + 41371828 q^{67} + 145606631 q^{68} + 575348022 q^{69} - 920887614 q^{70} + 261018751 q^{71} + 402812595 q^{72} + 178388 q^{73} - 303908734 q^{74} + 860903802 q^{75} - 94541144 q^{76} + 299640561 q^{77} + 556554888 q^{78} - 905381353 q^{79} + 939128289 q^{80} + 947027862 q^{81} - 551739753 q^{82} + 1173257869 q^{83} + 657124650 q^{84} - 1546633210 q^{85} + 1384869460 q^{86} + 1237624596 q^{87} + 189740713 q^{88} + 898004974 q^{89} + 297456057 q^{90} + 591272339 q^{91} + 4328210270 q^{92} + 1426437378 q^{93} + 122568068 q^{94} + 2487967134 q^{95} + 2622640356 q^{96} + 3175709684 q^{97} + 5095778404 q^{98} + 733316409 q^{99}+O(q^{100}) \) 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9 + 45337 * q^10 + 111769 * q^11 + 483894 * q^12 + 189121 * q^13 + 251053 * q^14 + 468666 * q^15 + 2311074 * q^16 + 1113841 * q^17 + 301806 * q^18 + 476068 * q^19 - 42495 * q^20 + 618921 * q^21 - 2252022 * q^22 + 7103062 * q^23 + 4972995 * q^24 + 10628442 * q^25 + 6871048 * q^26 + 11691702 * q^27 + 8112650 * q^28 + 15279316 * q^29 + 3672297 * q^30 + 17610338 * q^31 + 32378276 * q^32 + 9053289 * q^33 + 29339436 * q^34 + 7134904 * q^35 + 39195414 * q^36 + 21961411 * q^37 + 65195131 * q^38 + 15318801 * q^39 + 75185084 * q^40 + 52781575 * q^41 + 20335293 * q^42 + 76191313 * q^43 + 61127768 * q^44 + 37961946 * q^45 + 290208769 * q^46 + 160572396 * q^47 + 187196994 * q^48 + 156292703 * q^49 + 169504821 * q^50 + 90221121 * q^51 + 65465920 * q^52 - 8762038 * q^53 + 24446286 * q^54 + 147125140 * q^55 + 9671794 * q^56 + 38561508 * q^57 - 37665424 * q^58 - 266581942 * q^59 - 3442095 * q^60 + 120750754 * q^61 - 152465186 * q^62 + 50132601 * q^63 - 40658803 * q^64 + 331055798 * q^65 - 182413782 * q^66 + 41371828 * q^67 + 145606631 * q^68 + 575348022 * q^69 - 920887614 * q^70 + 261018751 * q^71 + 402812595 * q^72 + 178388 * q^73 - 303908734 * q^74 + 860903802 * q^75 - 94541144 * q^76 + 299640561 * q^77 + 556554888 * q^78 - 905381353 * q^79 + 939128289 * q^80 + 947027862 * q^81 - 551739753 * q^82 + 1173257869 * q^83 + 657124650 * q^84 - 1546633210 * q^85 + 1384869460 * q^86 + 1237624596 * q^87 + 189740713 * q^88 + 898004974 * q^89 + 297456057 * q^90 + 591272339 * q^91 + 4328210270 * q^92 + 1426437378 * q^93 + 122568068 * q^94 + 2487967134 * q^95 + 2622640356 * q^96 + 3175709684 * q^97 + 5095778404 * q^98 + 733316409 * q^99

Introduction

L-functions

Modular forms

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