LMFDB - Embedded newform 547.8.a.a.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,8,Mod(1,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("547.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	547.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:	$170.874608940$
Analytic rank:	$1$
Dimension:	$156$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-19.3499 q^{2} +9.03641 q^{3} +246.418 q^{4} +20.2179 q^{5} -174.853 q^{6} +193.981 q^{7} -2291.37 q^{8} -2105.34 q^{9} +O(q^{10})$	\(q-19.3499 q^{2} +9.03641 q^{3} +246.418 q^{4} +20.2179 q^{5} -174.853 q^{6} +193.981 q^{7} -2291.37 q^{8} -2105.34 q^{9} -391.214 q^{10} +8270.50 q^{11} +2226.73 q^{12} +5611.50 q^{13} -3753.51 q^{14} +182.697 q^{15} +12796.3 q^{16} -26538.2 q^{17} +40738.1 q^{18} +12364.6 q^{19} +4982.05 q^{20} +1752.89 q^{21} -160033. q^{22} +1613.29 q^{23} -20705.8 q^{24} -77716.2 q^{25} -108582. q^{26} -38787.4 q^{27} +47800.3 q^{28} +42724.1 q^{29} -3535.17 q^{30} +313505. q^{31} +45689.3 q^{32} +74735.6 q^{33} +513512. q^{34} +3921.88 q^{35} -518794. q^{36} -191274. q^{37} -239253. q^{38} +50707.9 q^{39} -46326.7 q^{40} -190354. q^{41} -33918.2 q^{42} +269344. q^{43} +2.03800e6 q^{44} -42565.6 q^{45} -31217.0 q^{46} +169727. q^{47} +115632. q^{48} -785914. q^{49} +1.50380e6 q^{50} -239810. q^{51} +1.38277e6 q^{52} -1.21285e6 q^{53} +750531. q^{54} +167212. q^{55} -444482. q^{56} +111731. q^{57} -826706. q^{58} -1.32229e6 q^{59} +45019.8 q^{60} -2.44515e6 q^{61} -6.06629e6 q^{62} -408396. q^{63} -2.52200e6 q^{64} +113453. q^{65} -1.44613e6 q^{66} -2.20336e6 q^{67} -6.53949e6 q^{68} +14578.4 q^{69} -75888.0 q^{70} +1.91922e6 q^{71} +4.82412e6 q^{72} +989859. q^{73} +3.70114e6 q^{74} -702276. q^{75} +3.04685e6 q^{76} +1.60432e6 q^{77} -981191. q^{78} -145494. q^{79} +258713. q^{80} +4.25389e6 q^{81} +3.68333e6 q^{82} -8.23993e6 q^{83} +431944. q^{84} -536547. q^{85} -5.21177e6 q^{86} +386072. q^{87} -1.89508e7 q^{88} +593545. q^{89} +823639. q^{90} +1.08852e6 q^{91} +397544. q^{92} +2.83296e6 q^{93} -3.28419e6 q^{94} +249985. q^{95} +412867. q^{96} +1.11865e7 q^{97} +1.52073e7 q^{98} -1.74122e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 56 q^{2} - 284 q^{3} + 9690 q^{4} - 3751 q^{5} - 2322 q^{6} - 2559 q^{7} - 10752 q^{8} + 102594 q^{9}+O(q^{10}) $ 156 * q - 56 * q^2 - 284 * q^3 + 9690 * q^4 - 3751 * q^5 - 2322 * q^6 - 2559 * q^7 - 10752 * q^8 + 102594 * q^9	\( 156 q - 56 q^{2} - 284 q^{3} + 9690 q^{4} - 3751 q^{5} - 2322 q^{6} - 2559 q^{7} - 10752 q^{8} + 102594 q^{9} - 10570 q^{10} - 20090 q^{11} - 58311 q^{12} - 63021 q^{13} - 45057 q^{14} - 36391 q^{15} + 574338 q^{16} - 232394 q^{17} - 92277 q^{18} - 43100 q^{19} - 485568 q^{20} - 231868 q^{21} - 225008 q^{22} - 401950 q^{23} - 503569 q^{24} + 2076291 q^{25} - 530768 q^{26} - 959873 q^{27} - 617816 q^{28} - 1275618 q^{29} - 778474 q^{30} - 485945 q^{31} - 1903692 q^{32} - 1050846 q^{33} - 466263 q^{34} - 1826209 q^{35} + 5276156 q^{36} - 2129902 q^{37} - 2480555 q^{38} - 974653 q^{39} - 937648 q^{40} - 2309325 q^{41} - 2803500 q^{42} - 1756918 q^{43} - 3314520 q^{44} - 7492064 q^{45} - 1323786 q^{46} - 6203828 q^{47} - 7957494 q^{48} + 15095175 q^{49} - 5758152 q^{50} - 1556293 q^{51} - 7587898 q^{52} - 13775068 q^{53} - 6848423 q^{54} - 4045669 q^{55} - 8326655 q^{56} - 9421556 q^{57} - 4938892 q^{58} - 7755758 q^{59} - 5358502 q^{60} - 11693582 q^{61} - 14895366 q^{62} - 9477805 q^{63} + 31311690 q^{64} - 15629670 q^{65} - 5969892 q^{66} - 9560716 q^{67} - 34045735 q^{68} - 17825946 q^{69} - 4291177 q^{70} - 13661197 q^{71} - 21516953 q^{72} - 17125972 q^{73} - 19749599 q^{74} - 21752079 q^{75} - 15479244 q^{76} - 55632329 q^{77} - 12746879 q^{78} - 9534338 q^{79} - 61267539 q^{80} + 58468208 q^{81} - 29265046 q^{82} - 38447793 q^{83} - 33520873 q^{84} - 22365109 q^{85} - 21208733 q^{86} - 27018273 q^{87} - 40855385 q^{88} - 62436196 q^{89} - 19477679 q^{90} - 20640165 q^{91} - 78867734 q^{92} - 77801528 q^{93} + 2996793 q^{94} - 30557422 q^{95} - 82397286 q^{96} - 56264748 q^{97} - 72954494 q^{98} - 43444577 q^{99}+O(q^{100}) \) 156 * q - 56 * q^2 - 284 * q^3 + 9690 * q^4 - 3751 * q^5 - 2322 * q^6 - 2559 * q^7 - 10752 * q^8 + 102594 * q^9 - 10570 * q^10 - 20090 * q^11 - 58311 * q^12 - 63021 * q^13 - 45057 * q^14 - 36391 * q^15 + 574338 * q^16 - 232394 * q^17 - 92277 * q^18 - 43100 * q^19 - 485568 * q^20 - 231868 * q^21 - 225008 * q^22 - 401950 * q^23 - 503569 * q^24 + 2076291 * q^25 - 530768 * q^26 - 959873 * q^27 - 617816 * q^28 - 1275618 * q^29 - 778474 * q^30 - 485945 * q^31 - 1903692 * q^32 - 1050846 * q^33 - 466263 * q^34 - 1826209 * q^35 + 5276156 * q^36 - 2129902 * q^37 - 2480555 * q^38 - 974653 * q^39 - 937648 * q^40 - 2309325 * q^41 - 2803500 * q^42 - 1756918 * q^43 - 3314520 * q^44 - 7492064 * q^45 - 1323786 * q^46 - 6203828 * q^47 - 7957494 * q^48 + 15095175 * q^49 - 5758152 * q^50 - 1556293 * q^51 - 7587898 * q^52 - 13775068 * q^53 - 6848423 * q^54 - 4045669 * q^55 - 8326655 * q^56 - 9421556 * q^57 - 4938892 * q^58 - 7755758 * q^59 - 5358502 * q^60 - 11693582 * q^61 - 14895366 * q^62 - 9477805 * q^63 + 31311690 * q^64 - 15629670 * q^65 - 5969892 * q^66 - 9560716 * q^67 - 34045735 * q^68 - 17825946 * q^69 - 4291177 * q^70 - 13661197 * q^71 - 21516953 * q^72 - 17125972 * q^73 - 19749599 * q^74 - 21752079 * q^75 - 15479244 * q^76 - 55632329 * q^77 - 12746879 * q^78 - 9534338 * q^79 - 61267539 * q^80 + 58468208 * q^81 - 29265046 * q^82 - 38447793 * q^83 - 33520873 * q^84 - 22365109 * q^85 - 21208733 * q^86 - 27018273 * q^87 - 40855385 * q^88 - 62436196 * q^89 - 19477679 * q^90 - 20640165 * q^91 - 78867734 * q^92 - 77801528 * q^93 + 2996793 * q^94 - 30557422 * q^95 - 82397286 * q^96 - 56264748 * q^97 - 72954494 * q^98 - 43444577 * 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 $

$2$	−19.3499	−1.71030	−0.855152	−	0.518377i	$-0.826536\pi$
$2$	−19.3499	−1.71030	−0.855152	+	0.518377i	$0.826536\pi$
$3$	9.03641	0.193229	0.0966144	−	0.995322i	$-0.469199\pi$
$3$	9.03641	0.193229	0.0966144	+	0.995322i	$0.469199\pi$
$4$	246.418	1.92514
$5$	20.2179	0.0723337	0.0361669	−	0.999346i	$-0.488485\pi$
$5$	20.2179	0.0723337	0.0361669	+	0.999346i	$0.488485\pi$
$6$	−174.853	−0.330480
$7$	193.981	0.213755	0.106877	−	0.994272i	$-0.465915\pi$
$7$	193.981	0.213755	0.106877	+	0.994272i	$0.465915\pi$
$8$	−2291.37	−1.58227
$9$	−2105.34	−0.962663
$10$	−391.214	−0.123713
$11$	8270.50	1.87352	0.936758	−	0.349979i	$-0.113811\pi$
$11$	8270.50	1.87352	0.936758	+	0.349979i	$0.113811\pi$
$12$	2226.73	0.371992
$13$	5611.50	0.708398	0.354199	−	0.935170i	$-0.384754\pi$
$13$	5611.50	0.708398	0.354199	+	0.935170i	$0.384754\pi$
$14$	−3753.51	−0.365586
$15$	182.697	0.0139769
$16$	12796.3	0.781022
$17$	−26538.2	−1.31009	−0.655044	−	0.755590i	$-0.727350\pi$
$17$	−26538.2	−1.31009	−0.655044	+	0.755590i	$0.727350\pi$
$18$	40738.1	1.64645
$19$	12364.6	0.413563	0.206781	−	0.978387i	$-0.433701\pi$
$19$	12364.6	0.413563	0.206781	+	0.978387i	$0.433701\pi$
$20$	4982.05	0.139252
$21$	1752.89	0.0413035
$22$	−160033.	−3.20428
$23$	1613.29	0.0276481	0.0138241	−	0.999904i	$-0.495600\pi$
$23$	1613.29	0.0276481	0.0138241	+	0.999904i	$0.495600\pi$
$24$	−20705.8	−0.305740
$25$	−77716.2	−0.994768
$26$	−108582.	−1.21158
$27$	−38787.4	−0.379243
$28$	47800.3	0.411508
$29$	42724.1	0.325297	0.162648	−	0.986684i	$-0.447996\pi$
$29$	42724.1	0.325297	0.162648	+	0.986684i	$0.447996\pi$
$30$	−3535.17	−0.0239048
$31$	313505.	1.89007	0.945037	−	0.326962i	$-0.106025\pi$
$31$	313505.	1.89007	0.945037	+	0.326962i	$0.106025\pi$
$32$	45689.3	0.246484
$33$	74735.6	0.362017
$34$	513512.	2.24065
$35$	3921.88	0.0154617
$36$	−518794.	−1.85326
$37$	−191274.	−0.620799	−0.310399	−	0.950606i	$-0.600463\pi$
$37$	−191274.	−0.620799	−0.310399	+	0.950606i	$0.600463\pi$
$38$	−239253.	−0.707318
$39$	50707.9	0.136883
$40$	−46326.7	−0.114451
$41$	−190354.	−0.431339	−0.215670	−	0.976466i	$-0.569193\pi$
$41$	−190354.	−0.431339	−0.215670	+	0.976466i	$0.569193\pi$
$42$	−33918.2	−0.0706416
$43$	269344.	0.516616	0.258308	−	0.966063i	$-0.416835\pi$
$43$	269344.	0.516616	0.258308	+	0.966063i	$0.416835\pi$
$44$	2.03800e6	3.60678
$45$	−42565.6	−0.0696330
$46$	−31217.0	−0.0472867
$47$	169727.	0.238456	0.119228	−	0.992867i	$-0.461958\pi$
$47$	169727.	0.238456	0.119228	+	0.992867i	$0.461958\pi$
$48$	115632.	0.150916
$49$	−785914.	−0.954309
$50$	1.50380e6	1.70136
$51$	−239810.	−0.253147
$52$	1.38277e6	1.36377
$53$	−1.21285e6	−1.11902	−0.559512	−	0.828822i	$-0.689012\pi$
$53$	−1.21285e6	−1.11902	−0.559512	+	0.828822i	$0.689012\pi$
$54$	750531.	0.648620
$55$	167212.	0.135518
$56$	−444482.	−0.338218
$57$	111731.	0.0799122
$58$	−826706.	−0.556356
$59$	−1.32229e6	−0.838192	−0.419096	−	0.907942i	$-0.637653\pi$
$59$	−1.32229e6	−0.838192	−0.419096	+	0.907942i	$0.637653\pi$
$60$	45019.8	0.0269076
$61$	−2.44515e6	−1.37927	−0.689637	−	0.724155i	$-0.742230\pi$
$61$	−2.44515e6	−1.37927	−0.689637	+	0.724155i	$0.742230\pi$
$62$	−6.06629e6	−3.23260
$63$	−408396.	−0.205774
$64$	−2.52200e6	−1.20259
$65$	113453.	0.0512411
$66$	−1.44613e6	−0.619159
$67$	−2.20336e6	−0.895001	−0.447501	−	0.894284i	$-0.647686\pi$
$67$	−2.20336e6	−0.895001	−0.447501	+	0.894284i	$0.647686\pi$
$68$	−6.53949e6	−2.52210
$69$	14578.4	0.00534242
$70$	−75888.0	−0.0264442
$71$	1.91922e6	0.636387	0.318194	−	0.948026i	$-0.396924\pi$
$71$	1.91922e6	0.636387	0.318194	+	0.948026i	$0.396924\pi$
$72$	4.82412e6	1.52319
$73$	989859.	0.297813	0.148906	−	0.988851i	$-0.452425\pi$
$73$	989859.	0.297813	0.148906	+	0.988851i	$0.452425\pi$
$74$	3.70114e6	1.06175
$75$	−702276.	−0.192218
$76$	3.04685e6	0.796166
$77$	1.60432e6	0.400473
$78$	−981191.	−0.234111
$79$	−145494.	−0.0332009	−0.0166005	−	0.999862i	$-0.505284\pi$
$79$	−145494.	−0.0332009	−0.0166005	+	0.999862i	$0.505284\pi$
$80$	258713.	0.0564942
$81$	4.25389e6	0.889382
$82$	3.68333e6	0.737721
$83$	−8.23993e6	−1.58179	−0.790897	−	0.611949i	$-0.790386\pi$
$83$	−8.23993e6	−1.58179	−0.790897	+	0.611949i	$0.790386\pi$
$84$	431944.	0.0795151
$85$	−536547.	−0.0947636
$86$	−5.21177e6	−0.883570
$87$	386072.	0.0628567
$88$	−1.89508e7	−2.96441
$89$	593545.	0.0892460	0.0446230	−	0.999004i	$-0.485791\pi$
$89$	593545.	0.0892460	0.0446230	+	0.999004i	$0.485791\pi$
$90$	823639.	0.119094
$91$	1.08852e6	0.151423
$92$	397544.	0.0532265
$93$	2.83296e6	0.365217
$94$	−3.28419e6	−0.407832
$95$	249985.	0.0299145
$96$	412867.	0.0476279
$97$	1.11865e7	1.24449	0.622246	−	0.782822i	$-0.286220\pi$
$97$	1.11865e7	1.24449	0.622246	+	0.782822i	$0.286220\pi$
$98$	1.52073e7	1.63216
$99$	−1.74122e7	−1.80356
$100$	−1.91507e7	−1.91507
$101$	1.55753e7	1.50422	0.752109	−	0.659039i	$-0.229037\pi$
$101$	1.55753e7	1.50422	0.752109	+	0.659039i	$0.229037\pi$
$102$	4.64030e6	0.432958
$103$	−1.74220e6	−0.157097	−0.0785486	−	0.996910i	$-0.525029\pi$
$103$	−1.74220e6	−0.157097	−0.0785486	+	0.996910i	$0.525029\pi$
$104$	−1.28580e7	−1.12088
$105$	35439.7	0.00298764
$106$	2.34684e7	1.91387
$107$	−2.45663e7	−1.93863	−0.969317	−	0.245815i	$-0.920945\pi$
$107$	−2.45663e7	−1.93863	−0.969317	+	0.245815i	$0.920945\pi$
$108$	−9.55790e6	−0.730095
$109$	−6.60807e6	−0.488744	−0.244372	−	0.969682i	$-0.578582\pi$
$109$	−6.60807e6	−0.488744	−0.244372	+	0.969682i	$0.578582\pi$
$110$	−3.23553e6	−0.231777
$111$	−1.72843e6	−0.119956
$112$	2.48223e6	0.166947
$113$	1.58582e7	1.03390	0.516951	−	0.856015i	$-0.327067\pi$
$113$	1.58582e7	1.03390	0.516951	+	0.856015i	$0.327067\pi$
$114$	−2.16199e6	−0.136674
$115$	32617.4	0.00199989
$116$	1.05280e7	0.626242
$117$	−1.18141e7	−0.681949
$118$	2.55861e7	1.43356
$119$	−5.14791e6	−0.280038
$120$	−418627.	−0.0221153
$121$	4.89139e7	2.51006
$122$	4.73133e7	2.35898
$123$	−1.72012e6	−0.0833471
$124$	7.72533e7	3.63866
$125$	−3.15078e6	−0.144289
$126$	7.90242e6	0.351936
$127$	9.19436e6	0.398298	0.199149	−	0.979969i	$-0.436182\pi$
$127$	9.19436e6	0.398298	0.199149	+	0.979969i	$0.436182\pi$
$128$	4.29522e7	1.81030
$129$	2.43390e6	0.0998250
$130$	−2.19530e6	−0.0876378
$131$	−2.68070e6	−0.104183	−0.0520917	−	0.998642i	$-0.516589\pi$
$131$	−2.68070e6	−0.104183	−0.0520917	+	0.998642i	$0.516589\pi$
$132$	1.84162e7	0.696933
$133$	2.39849e6	0.0884010
$134$	4.26347e7	1.53072
$135$	−784199.	−0.0274320
$136$	6.08089e7	2.07291
$137$	−3.32534e7	−1.10488	−0.552439	−	0.833553i	$-0.686303\pi$
$137$	−3.32534e7	−1.10488	−0.552439	+	0.833553i	$0.686303\pi$
$138$	−282090.	−0.00913715
$139$	5.59156e6	0.176596	0.0882981	−	0.996094i	$-0.471857\pi$
$139$	5.59156e6	0.176596	0.0882981	+	0.996094i	$0.471857\pi$
$140$	966422.	0.0297659
$141$	1.53372e6	0.0460765
$142$	−3.71368e7	−1.08842
$143$	4.64099e7	1.32719
$144$	−2.69405e7	−0.751861
$145$	863791.	0.0235299
$146$	−1.91536e7	−0.509350
$147$	−7.10185e6	−0.184400
$148$	−4.71334e7	−1.19512
$149$	3.40225e7	0.842586	0.421293	−	0.906925i	$-0.361576\pi$
$149$	3.40225e7	0.842586	0.421293	+	0.906925i	$0.361576\pi$
$150$	1.35890e7	0.328751
$151$	−1.86320e7	−0.440393	−0.220196	−	0.975456i	$-0.570670\pi$
$151$	−1.86320e7	−0.440393	−0.220196	+	0.975456i	$0.570670\pi$
$152$	−2.83318e7	−0.654367
$153$	5.58721e7	1.26117
$154$	−3.10434e7	−0.684930
$155$	6.33842e6	0.136716
$156$	1.24953e7	0.263519
$157$	−1.51994e7	−0.313457	−0.156728	−	0.987642i	$-0.550095\pi$
$157$	−1.51994e7	−0.313457	−0.156728	+	0.987642i	$0.550095\pi$
$158$	2.81529e6	0.0567837
$159$	−1.09598e7	−0.216228
$160$	923741.	0.0178291
$161$	312948.	0.00590992
$162$	−8.23122e7	−1.52111
$163$	5.59408e7	1.01175	0.505874	−	0.862608i	$-0.331170\pi$
$163$	5.59408e7	1.01175	0.505874	+	0.862608i	$0.331170\pi$
$164$	−4.69067e7	−0.830388
$165$	1.51100e6	0.0261860
$166$	1.59442e8	2.70535
$167$	2.02297e7	0.336110	0.168055	−	0.985778i	$-0.446251\pi$
$167$	2.02297e7	0.336110	0.168055	+	0.985778i	$0.446251\pi$
$168$	−4.01652e6	−0.0653533
$169$	−3.12595e7	−0.498172
$170$	1.03821e7	0.162075
$171$	−2.60317e7	−0.398121
$172$	6.63711e7	0.994557
$173$	−8.75790e7	−1.28599	−0.642996	−	0.765869i	$-0.722309\pi$
$173$	−8.75790e7	−1.28599	−0.642996	+	0.765869i	$0.722309\pi$
$174$	−7.47045e6	−0.107504
$175$	−1.50755e7	−0.212636
$176$	1.05831e8	1.46326
$177$	−1.19487e7	−0.161963
$178$	−1.14850e7	−0.152638
$179$	2.09262e6	0.0272713	0.0136356	−	0.999907i	$-0.495660\pi$
$179$	2.09262e6	0.0272713	0.0136356	+	0.999907i	$0.495660\pi$
$180$	−1.04889e7	−0.134053
$181$	7.13448e7	0.894308	0.447154	−	0.894457i	$-0.352438\pi$
$181$	7.13448e7	0.894308	0.447154	+	0.894457i	$0.352438\pi$
$182$	−2.10628e7	−0.258980
$183$	−2.20954e7	−0.266515
$184$	−3.69665e6	−0.0437468
$185$	−3.86716e6	−0.0449047
$186$	−5.48175e7	−0.624632
$187$	−2.19484e8	−2.45447
$188$	4.18237e7	0.459060
$189$	−7.52401e6	−0.0810649
$190$	−4.83719e6	−0.0511629
$191$	1.80230e8	1.87159	0.935793	−	0.352551i	$-0.114686\pi$
$191$	1.80230e8	1.87159	0.935793	+	0.352551i	$0.114686\pi$
$192$	−2.27899e7	−0.232374
$193$	−1.51475e7	−0.151667	−0.0758334	−	0.997121i	$-0.524162\pi$
$193$	−1.51475e7	−0.151667	−0.0758334	+	0.997121i	$0.524162\pi$
$194$	−2.16457e8	−2.12846
$195$	1.02521e6	0.00990125
$196$	−1.93663e8	−1.83718
$197$	1.06372e8	0.991276	0.495638	−	0.868529i	$-0.334934\pi$
$197$	1.06372e8	0.991276	0.495638	+	0.868529i	$0.334934\pi$
$198$	3.36925e8	3.08464
$199$	−9.18811e7	−0.826496	−0.413248	−	0.910619i	$-0.635606\pi$
$199$	−9.18811e7	−0.826496	−0.413248	+	0.910619i	$0.635606\pi$
$200$	1.78077e8	1.57399
$201$	−1.99105e7	−0.172940
$202$	−3.01379e8	−2.57267
$203$	8.28765e6	0.0695337
$204$	−5.90936e7	−0.487343
$205$	−3.84856e6	−0.0312004
$206$	3.37114e7	0.268684
$207$	−3.39654e6	−0.0266158
$208$	7.18063e7	0.553275
$209$	1.02261e8	0.774816
$210$	−685755.	−0.00510977
$211$	−1.54110e7	−0.112938	−0.0564692	−	0.998404i	$-0.517984\pi$
$211$	−1.54110e7	−0.112938	−0.0564692	+	0.998404i	$0.517984\pi$
$212$	−2.98867e8	−2.15428
$213$	1.73429e7	0.122968
$214$	4.75354e8	3.31565
$215$	5.44556e6	0.0373687
$216$	8.88763e7	0.600064
$217$	6.08140e7	0.404012
$218$	1.27865e8	0.835901
$219$	8.94477e6	0.0575460
$220$	4.12040e7	0.260892
$221$	−1.48919e8	−0.928065
$222$	3.34450e7	0.205161
$223$	1.05287e8	0.635781	0.317891	−	0.948127i	$-0.397026\pi$
$223$	1.05287e8	0.635781	0.317891	+	0.948127i	$0.397026\pi$
$224$	8.86284e6	0.0526872
$225$	1.63619e8	0.957626
$226$	−3.06855e8	−1.76829
$227$	−2.45819e8	−1.39484	−0.697420	−	0.716663i	$-0.745669\pi$
$227$	−2.45819e8	−1.39484	−0.697420	+	0.716663i	$0.745669\pi$
$228$	2.75326e7	0.153842
$229$	3.55480e7	0.195610	0.0978051	−	0.995206i	$-0.468818\pi$
$229$	3.55480e7	0.195610	0.0978051	+	0.995206i	$0.468818\pi$
$230$	−631143.	−0.00342042
$231$	1.44973e7	0.0773828
$232$	−9.78967e7	−0.514707
$233$	1.92831e7	0.0998692	0.0499346	−	0.998752i	$-0.484099\pi$
$233$	1.92831e7	0.0998692	0.0499346	+	0.998752i	$0.484099\pi$
$234$	2.28602e8	1.16634
$235$	3.43152e6	0.0172484
$236$	−3.25835e8	−1.61364
$237$	−1.31474e6	−0.00641538
$238$	9.96114e7	0.478950
$239$	2.02811e8	0.960945	0.480472	−	0.877010i	$-0.340465\pi$
$239$	2.02811e8	0.960945	0.480472	+	0.877010i	$0.340465\pi$
$240$	2.33784e6	0.0109163
$241$	4.06852e8	1.87231	0.936153	−	0.351593i	$-0.114360\pi$
$241$	4.06852e8	1.87231	0.936153	+	0.351593i	$0.114360\pi$
$242$	−9.46479e8	−4.29296
$243$	1.23268e8	0.551097
$244$	−6.02528e8	−2.65529
$245$	−1.58895e7	−0.0690287
$246$	3.32841e7	0.142549
$247$	6.93838e7	0.292967
$248$	−7.18357e8	−2.99061
$249$	−7.44594e7	−0.305648
$250$	6.09672e7	0.246778
$251$	−4.17434e8	−1.66621	−0.833105	−	0.553115i	$-0.813439\pi$
$251$	−4.17434e8	−1.66621	−0.833105	+	0.553115i	$0.813439\pi$
$252$	−1.00636e8	−0.396143
$253$	1.33427e7	0.0517992
$254$	−1.77910e8	−0.681211
$255$	−4.84846e6	−0.0183110
$256$	−5.08304e8	−1.89358
$257$	2.50627e8	0.921005	0.460503	−	0.887658i	$-0.347669\pi$
$257$	2.50627e8	0.921005	0.460503	+	0.887658i	$0.347669\pi$
$258$	−4.70957e7	−0.170731
$259$	−3.71036e7	−0.132699
$260$	2.79568e7	0.0986462
$261$	−8.99489e7	−0.313151
$262$	5.18713e7	0.178185
$263$	−1.89235e8	−0.641442	−0.320721	−	0.947174i	$-0.603925\pi$
$263$	−1.89235e8	−0.641442	−0.320721	+	0.947174i	$0.603925\pi$
$264$	−1.71247e8	−0.572808
$265$	−2.45212e7	−0.0809432
$266$	−4.64105e7	−0.151192
$267$	5.36352e6	0.0172449
$268$	−5.42947e8	−1.72300
$269$	−5.15850e8	−1.61581	−0.807905	−	0.589313i	$-0.799399\pi$
$269$	−5.15850e8	−1.61581	−0.807905	+	0.589313i	$0.799399\pi$
$270$	1.51742e7	0.0469171
$271$	4.03726e8	1.23224	0.616119	−	0.787653i	$-0.288704\pi$
$271$	4.03726e8	1.23224	0.616119	+	0.787653i	$0.288704\pi$
$272$	−3.39590e8	−1.02321
$273$	9.83635e6	0.0292594
$274$	6.43449e8	1.88968
$275$	−6.42752e8	−1.86371
$276$	3.59237e6	0.0102849
$277$	1.12148e8	0.317038	0.158519	−	0.987356i	$-0.449328\pi$
$277$	1.12148e8	0.317038	0.158519	+	0.987356i	$0.449328\pi$
$278$	−1.08196e8	−0.302033
$279$	−6.60036e8	−1.81950
$280$	−8.98649e6	−0.0244645
$281$	−4.37031e8	−1.17501	−0.587503	−	0.809222i	$-0.699889\pi$
$281$	−4.37031e8	−1.17501	−0.587503	+	0.809222i	$0.699889\pi$
$282$	−2.96773e7	−0.0788048
$283$	−1.35469e8	−0.355293	−0.177646	−	0.984094i	$-0.556848\pi$
$283$	−1.35469e8	−0.355293	−0.177646	+	0.984094i	$0.556848\pi$
$284$	4.72931e8	1.22513
$285$	2.25897e6	0.00578034
$286$	−8.98026e8	−2.26991
$287$	−3.69251e7	−0.0922008
$288$	−9.61916e7	−0.237281
$289$	2.93939e8	0.716333
$290$	−1.67142e7	−0.0402433
$291$	1.01086e8	0.240472
$292$	2.43919e8	0.573331
$293$	−2.57802e8	−0.598755	−0.299378	−	0.954135i	$-0.596779\pi$
$293$	−2.57802e8	−0.598755	−0.299378	+	0.954135i	$0.596779\pi$
$294$	1.37420e8	0.315380
$295$	−2.67338e7	−0.0606295
$296$	4.38280e8	0.982270
$297$	−3.20791e8	−0.710517
$298$	−6.58331e8	−1.44108
$299$	9.05300e6	0.0195859
$300$	−1.73053e8	−0.370046
$301$	5.22475e7	0.110429
$302$	3.60527e8	0.753205
$303$	1.40745e8	0.290658
$304$	1.58220e8	0.323001
$305$	−4.94357e7	−0.0997680
$306$	−1.08112e9	−2.15699
$307$	−8.87361e8	−1.75031	−0.875157	−	0.483839i	$-0.839242\pi$
$307$	−8.87361e8	−1.75031	−0.875157	+	0.483839i	$0.839242\pi$
$308$	3.95333e8	0.770966
$309$	−1.57433e7	−0.0303557
$310$	−1.22648e8	−0.233826
$311$	−5.84444e8	−1.10175	−0.550873	−	0.834589i	$-0.685705\pi$
$311$	−5.84444e8	−1.10175	−0.550873	+	0.834589i	$0.685705\pi$
$312$	−1.16191e8	−0.216586
$313$	−4.14447e8	−0.763948	−0.381974	−	0.924173i	$-0.624756\pi$
$313$	−4.14447e8	−0.763948	−0.381974	+	0.924173i	$0.624756\pi$
$314$	2.94106e8	0.536106
$315$	−8.25691e6	−0.0148844
$316$	−3.58523e7	−0.0639164
$317$	−7.32187e8	−1.29097	−0.645483	−	0.763775i	$-0.723344\pi$
$317$	−7.32187e8	−1.29097	−0.645483	+	0.763775i	$0.723344\pi$
$318$	2.12070e8	0.369815
$319$	3.53349e8	0.609448
$320$	−5.09896e7	−0.0869874
$321$	−2.21991e8	−0.374600
$322$	−6.05551e6	−0.0101078
$323$	−3.28134e8	−0.541804
$324$	1.04823e9	1.71218
$325$	−4.36105e8	−0.704692
$326$	−1.08245e9	−1.73040
$327$	−5.97132e7	−0.0944394
$328$	4.36172e8	0.682495
$329$	3.29237e7	0.0509710
$330$	−2.92376e7	−0.0447861
$331$	−3.13189e8	−0.474688	−0.237344	−	0.971426i	$-0.576277\pi$
$331$	−3.13189e8	−0.474688	−0.237344	+	0.971426i	$0.576277\pi$
$332$	−2.03046e9	−3.04517
$333$	4.02698e8	0.597620
$334$	−3.91442e8	−0.574851
$335$	−4.45473e7	−0.0647388
$336$	2.24305e7	0.0322590
$337$	5.63239e8	0.801656	0.400828	−	0.916153i	$-0.368723\pi$
$337$	5.63239e8	0.801656	0.400828	+	0.916153i	$0.368723\pi$
$338$	6.04868e8	0.852025
$339$	1.43301e8	0.199780
$340$	−1.32215e8	−0.182433
$341$	2.59284e9	3.54108
$342$	5.03709e8	0.680908
$343$	−3.12204e8	−0.417743
$344$	−6.17167e8	−0.817425
$345$	294744.	0.000386437 0
$346$	1.69464e9	2.19944
$347$	−6.47509e8	−0.831941	−0.415970	−	0.909378i	$-0.636558\pi$
$347$	−6.47509e8	−0.831941	−0.415970	+	0.909378i	$0.636558\pi$
$348$	9.51351e7	0.121008
$349$	−1.14216e8	−0.143826	−0.0719129	−	0.997411i	$-0.522910\pi$
$349$	−1.14216e8	−0.143826	−0.0719129	+	0.997411i	$0.522910\pi$
$350$	2.91708e8	0.363673
$351$	−2.17656e8	−0.268655
$352$	3.77873e8	0.461792
$353$	−1.15059e9	−1.39223	−0.696113	−	0.717932i	$-0.745089\pi$
$353$	−1.15059e9	−1.39223	−0.696113	+	0.717932i	$0.745089\pi$
$354$	2.31206e8	0.277006
$355$	3.88027e7	0.0460323
$356$	1.46260e8	0.171811
$357$	−4.65186e7	−0.0541113
$358$	−4.04920e7	−0.0466421
$359$	−1.01313e9	−1.15567	−0.577836	−	0.816153i	$-0.696103\pi$
$359$	−1.01313e9	−1.15567	−0.577836	+	0.816153i	$0.696103\pi$
$360$	9.75335e7	0.110178
$361$	−7.40989e8	−0.828966
$362$	−1.38051e9	−1.52954
$363$	4.42007e8	0.485015
$364$	2.68232e8	0.291511
$365$	2.00129e7	0.0215419
$366$	4.27542e8	0.455822
$367$	−9.30316e8	−0.982425	−0.491212	−	0.871040i	$-0.663446\pi$
$367$	−9.30316e8	−0.982425	−0.491212	+	0.871040i	$0.663446\pi$
$368$	2.06441e7	0.0215938
$369$	4.00761e8	0.415234
$370$	7.48291e7	0.0768006
$371$	−2.35269e8	−0.239197
$372$	6.98093e8	0.703093
$373$	2.78811e8	0.278182	0.139091	−	0.990280i	$-0.455582\pi$
$373$	2.78811e8	0.278182	0.139091	+	0.990280i	$0.455582\pi$
$374$	4.24700e9	4.19789
$375$	−2.84718e7	−0.0278808
$376$	−3.88907e8	−0.377301
$377$	2.39746e8	0.230440
$378$	1.45589e8	0.138646
$379$	−2.98335e8	−0.281493	−0.140746	−	0.990046i	$-0.544950\pi$
$379$	−2.98335e8	−0.281493	−0.140746	+	0.990046i	$0.544950\pi$
$380$	6.16009e7	0.0575896
$381$	8.30840e7	0.0769626
$382$	−3.48742e9	−3.20098
$383$	1.57744e9	1.43468	0.717342	−	0.696722i	$-0.245359\pi$
$383$	1.57744e9	1.43468	0.717342	+	0.696722i	$0.245359\pi$
$384$	3.88134e8	0.349802
$385$	3.24359e7	0.0289677
$386$	2.93102e8	0.259396
$387$	−5.67061e8	−0.497327
$388$	2.75655e9	2.39582
$389$	7.05421e8	0.607610	0.303805	−	0.952734i	$-0.401743\pi$
$389$	7.05421e8	0.607610	0.303805	+	0.952734i	$0.401743\pi$
$390$	−1.98376e7	−0.0169341
$391$	−4.28140e7	−0.0362215
$392$	1.80082e9	1.50997
$393$	−2.42239e7	−0.0201312
$394$	−2.05828e9	−1.69538
$395$	−2.94158e6	−0.00240155
$396$	−4.29068e9	−3.47211
$397$	9.89393e8	0.793601	0.396800	−	0.917905i	$-0.370121\pi$
$397$	9.89393e8	0.793601	0.396800	+	0.917905i	$0.370121\pi$
$398$	1.77789e9	1.41356
$399$	2.16737e7	0.0170816
$400$	−9.94478e8	−0.776936
$401$	−8.08078e8	−0.625818	−0.312909	−	0.949783i	$-0.601303\pi$
$401$	−8.08078e8	−0.625818	−0.312909	+	0.949783i	$0.601303\pi$
$402$	3.85265e8	0.295780
$403$	1.75924e9	1.33893
$404$	3.83802e9	2.89583
$405$	8.60046e7	0.0643323
$406$	−1.60365e8	−0.118924
$407$	−1.58193e9	−1.16308
$408$	5.49495e8	0.400546
$409$	−1.15339e9	−0.833577	−0.416788	−	0.909004i	$-0.636844\pi$
$409$	−1.15339e9	−0.833577	−0.416788	+	0.909004i	$0.636844\pi$
$410$	7.44692e7	0.0533621
$411$	−3.00492e8	−0.213494
$412$	−4.29310e8	−0.302434
$413$	−2.56498e8	−0.179167
$414$	6.57226e7	0.0455212
$415$	−1.66594e8	−0.114417
$416$	2.56386e8	0.174609
$417$	5.05277e7	0.0341235
$418$	−1.97874e9	−1.32517
$419$	1.45498e8	0.0966290	0.0483145	−	0.998832i	$-0.484615\pi$
$419$	1.45498e8	0.0966290	0.0483145	+	0.998832i	$0.484615\pi$
$420$	8.73299e6	0.00575162
$421$	−6.76271e8	−0.441706	−0.220853	−	0.975307i	$-0.570884\pi$
$421$	−6.76271e8	−0.441706	−0.220853	+	0.975307i	$0.570884\pi$
$422$	2.98201e8	0.193159
$423$	−3.57333e8	−0.229552
$424$	2.77908e9	1.77060
$425$	2.06245e9	1.30323
$426$	−3.35583e8	−0.210313
$427$	−4.74312e8	−0.294826
$428$	−6.05356e9	−3.73214
$429$	4.19379e8	0.256452
$430$	−1.05371e8	−0.0639119
$431$	−1.93485e9	−1.16407	−0.582033	−	0.813165i	$-0.697743\pi$
$431$	−1.93485e9	−1.16407	−0.582033	+	0.813165i	$0.697743\pi$
$432$	−4.96334e8	−0.296197
$433$	1.58634e9	0.939048	0.469524	−	0.882920i	$-0.344425\pi$
$433$	1.58634e9	0.939048	0.469524	+	0.882920i	$0.344425\pi$
$434$	−1.17674e9	−0.690984
$435$	7.80557e6	0.00454666
$436$	−1.62835e9	−0.940901
$437$	1.99477e7	0.0114342
$438$	−1.73080e8	−0.0984211
$439$	1.54305e8	0.0870469	0.0435234	−	0.999052i	$-0.486142\pi$
$439$	1.54305e8	0.0870469	0.0435234	+	0.999052i	$0.486142\pi$
$440$	−3.83145e8	−0.214426
$441$	1.65462e9	0.918678
$442$	2.88157e9	1.58727
$443$	−8.70562e8	−0.475759	−0.237879	−	0.971295i	$-0.576452\pi$
$443$	−8.70562e8	−0.475759	−0.237879	+	0.971295i	$0.576452\pi$
$444$	−4.25917e8	−0.230932
$445$	1.20002e7	0.00645550
$446$	−2.03729e9	−1.08738
$447$	3.07441e8	0.162812
$448$	−4.89220e8	−0.257058
$449$	−6.42999e8	−0.335234	−0.167617	−	0.985852i	$-0.553607\pi$
$449$	−6.42999e8	−0.335234	−0.167617	+	0.985852i	$0.553607\pi$
$450$	−3.16601e9	−1.63783
$451$	−1.57432e9	−0.808121
$452$	3.90775e9	1.99041
$453$	−1.68366e8	−0.0850965
$454$	4.75656e9	2.38560
$455$	2.20077e7	0.0109530
$456$	−2.56018e8	−0.126443
$457$	−1.12380e9	−0.550783	−0.275391	−	0.961332i	$-0.588807\pi$
$457$	−1.12380e9	−0.550783	−0.275391	+	0.961332i	$0.588807\pi$
$458$	−6.87850e8	−0.334553
$459$	1.02935e9	0.496842
$460$	8.03751e6	0.00385007
$461$	−2.85488e9	−1.35717	−0.678586	−	0.734521i	$-0.737407\pi$
$461$	−2.85488e9	−1.35717	−0.678586	+	0.734521i	$0.737407\pi$
$462$	−2.80521e8	−0.132348
$463$	2.41160e9	1.12920	0.564601	−	0.825364i	$-0.309030\pi$
$463$	2.41160e9	1.12920	0.564601	+	0.825364i	$0.309030\pi$
$464$	5.46709e8	0.254064
$465$	5.72765e7	0.0264175
$466$	−3.73126e8	−0.170807
$467$	−6.41861e8	−0.291630	−0.145815	−	0.989312i	$-0.546580\pi$
$467$	−6.41861e8	−0.291630	−0.145815	+	0.989312i	$0.546580\pi$
$468$	−2.91121e9	−1.31285
$469$	−4.27410e8	−0.191311
$470$	−6.63994e7	−0.0295000
$471$	−1.37348e8	−0.0605688
$472$	3.02985e9	1.32625
$473$	2.22761e9	0.967887
$474$	2.54401e7	0.0109722
$475$	−9.60927e8	−0.411399
$476$	−1.26854e9	−0.539112
$477$	2.55346e9	1.07724
$478$	−3.92436e9	−1.64351
$479$	−3.17936e8	−0.132180	−0.0660899	−	0.997814i	$-0.521052\pi$
$479$	−3.17936e8	−0.132180	−0.0660899	+	0.997814i	$0.521052\pi$
$480$	8.34730e6	0.00344510
$481$	−1.07334e9	−0.439773
$482$	−7.87254e9	−3.20221
$483$	2.82793e6	0.00114197
$484$	1.20533e10	4.83221
$485$	2.26167e8	0.0900187
$486$	−2.38522e9	−0.942543
$487$	2.53964e9	0.996372	0.498186	−	0.867070i	$-0.334000\pi$
$487$	2.53964e9	0.996372	0.498186	+	0.867070i	$0.334000\pi$
$488$	5.60274e9	2.18238
$489$	5.05504e8	0.195499
$490$	3.07460e8	0.118060
$491$	−1.70423e9	−0.649745	−0.324873	−	0.945758i	$-0.605321\pi$
$491$	−1.70423e9	−0.649745	−0.324873	+	0.945758i	$0.605321\pi$
$492$	−4.23868e8	−0.160455
$493$	−1.13382e9	−0.426168
$494$	−1.34257e9	−0.501063
$495$	−3.52039e8	−0.130458
$496$	4.01170e9	1.47619
$497$	3.72293e8	0.136031
$498$	1.44078e9	0.522751
$499$	4.14624e9	1.49384	0.746918	−	0.664916i	$-0.231533\pi$
$499$	4.14624e9	1.49384	0.746918	+	0.664916i	$0.231533\pi$
$500$	−7.76408e8	−0.277776
$501$	1.82804e8	0.0649462
$502$	8.07729e9	2.84972
$503$	5.59095e8	0.195884	0.0979418	−	0.995192i	$-0.468774\pi$
$503$	5.59095e8	0.195884	0.0979418	+	0.995192i	$0.468774\pi$
$504$	9.35787e8	0.325589
$505$	3.14899e8	0.108806
$506$	−2.58180e8	−0.0885924
$507$	−2.82474e8	−0.0962611
$508$	2.26565e9	0.766779
$509$	−1.16229e9	−0.390663	−0.195331	−	0.980737i	$-0.562578\pi$
$509$	−1.16229e9	−0.390663	−0.195331	+	0.980737i	$0.562578\pi$
$510$	9.38171e7	0.0313175
$511$	1.92014e8	0.0636589
$512$	4.33774e9	1.42830
$513$	−4.79589e8	−0.156841
$514$	−4.84961e9	−1.57520
$515$	−3.52237e7	−0.0113634
$516$	5.99757e8	0.192177
$517$	1.40372e9	0.446750
$518$	7.17949e8	0.226955
$519$	−7.91400e8	−0.248491
$520$	−2.59962e8	−0.0810772
$521$	1.65228e9	0.511861	0.255931	−	0.966695i	$-0.417618\pi$
$521$	1.65228e9	0.511861	0.255931	+	0.966695i	$0.417618\pi$
$522$	1.74050e9	0.535583
$523$	1.44913e9	0.442946	0.221473	−	0.975167i	$-0.428914\pi$
$523$	1.44913e9	0.442946	0.221473	+	0.975167i	$0.428914\pi$
$524$	−6.60573e8	−0.200568
$525$	−1.36228e8	−0.0410874
$526$	3.66168e9	1.09706
$527$	−8.31988e9	−2.47617
$528$	9.56337e8	0.282743
$529$	−3.40222e9	−0.999236
$530$	4.74482e8	0.138438
$531$	2.78387e9	0.806896
$532$	5.91030e8	0.170184
$533$	−1.06817e9	−0.305560
$534$	−1.03783e8	−0.0294940
$535$	−4.96678e8	−0.140229
$536$	5.04871e9	1.41613
$537$	1.89098e7	0.00526959
$538$	9.98163e9	2.76353
$539$	−6.49990e9	−1.78791
$540$	−1.93241e8	−0.0528105
$541$	7.69090e8	0.208827	0.104413	−	0.994534i	$-0.466703\pi$
$541$	7.69090e8	0.208827	0.104413	+	0.994534i	$0.466703\pi$
$542$	−7.81205e9	−2.10750
$543$	6.44701e8	0.172806
$544$	−1.21251e9	−0.322916
$545$	−1.33601e8	−0.0353527
$546$	−1.90332e8	−0.0500424
$547$	1.63667e8	0.0427569
$547$	1.63667e8	0.0427569
$548$	−8.19423e9	−2.12704
$549$	5.14787e9	1.32778
$550$	1.24372e10	3.18751
$551$	5.28265e8	0.134531
$552$	−3.34045e7	−0.00845314
$553$	−2.82231e7	−0.00709686
$554$	−2.17004e9	−0.542231
$555$	−3.49453e7	−0.00867687
$556$	1.37786e9	0.339972
$557$	−3.68508e9	−0.903554	−0.451777	−	0.892131i	$-0.649210\pi$
$557$	−3.68508e9	−0.903554	−0.451777	+	0.892131i	$0.649210\pi$
$558$	1.27716e10	3.11191
$559$	1.51142e9	0.365970
$560$	5.01854e7	0.0120759
$561$	−1.98335e9	−0.474274
$562$	8.45649e9	2.00962
$563$	−3.94906e9	−0.932640	−0.466320	−	0.884616i	$-0.654421\pi$
$563$	−3.94906e9	−0.932640	−0.466320	+	0.884616i	$0.654421\pi$
$564$	3.77936e8	0.0887037
$565$	3.20620e8	0.0747860
$566$	2.62130e9	0.607659
$567$	8.25173e8	0.190110
$568$	−4.39766e9	−1.00694
$569$	−3.81272e9	−0.867644	−0.433822	−	0.900999i	$-0.642835\pi$
$569$	−3.81272e9	−0.867644	−0.433822	+	0.900999i	$0.642835\pi$
$570$	−4.37108e7	−0.00988614
$571$	−4.98156e9	−1.11980	−0.559898	−	0.828562i	$-0.689160\pi$
$571$	−4.98156e9	−1.11980	−0.559898	+	0.828562i	$0.689160\pi$
$572$	1.14362e10	2.55503
$573$	1.62863e9	0.361644
$574$	7.14496e8	0.157691
$575$	−1.25379e8	−0.0275035
$576$	5.30968e9	1.15768
$577$	3.34133e9	0.724109	0.362054	−	0.932157i	$-0.382075\pi$
$577$	3.34133e9	0.724109	0.362054	+	0.932157i	$0.382075\pi$
$578$	−5.68769e9	−1.22515
$579$	−1.36879e8	−0.0293064
$580$	2.12853e8	0.0452984
$581$	−1.59839e9	−0.338116
$582$	−1.95599e9	−0.411280
$583$	−1.00308e10	−2.09651
$584$	−2.26813e9	−0.471220
$585$	−2.38857e8	−0.0493279
$586$	4.98843e9	1.02405
$587$	−5.47510e9	−1.11727	−0.558635	−	0.829413i	$-0.688675\pi$
$587$	−5.47510e9	−1.11727	−0.558635	+	0.829413i	$0.688675\pi$
$588$	−1.75002e9	−0.354995
$589$	3.87636e9	0.781664
$590$	5.17297e8	0.103695
$591$	9.61219e8	0.191543
$592$	−2.44760e9	−0.484857
$593$	−6.63437e9	−1.30650	−0.653248	−	0.757144i	$-0.726594\pi$
$593$	−6.63437e9	−1.30650	−0.653248	+	0.757144i	$0.726594\pi$
$594$	6.20727e9	1.21520
$595$	−1.04080e8	−0.0202562
$596$	8.38375e9	1.62209
$597$	−8.30276e8	−0.159703
$598$	−1.75175e8	−0.0334978
$599$	−6.85291e9	−1.30281	−0.651405	−	0.758730i	$-0.725820\pi$
$599$	−6.85291e9	−1.30281	−0.651405	+	0.758730i	$0.725820\pi$
$600$	1.60917e9	0.304140
$601$	−2.20618e9	−0.414554	−0.207277	−	0.978282i	$-0.566460\pi$
$601$	−2.20618e9	−0.414554	−0.207277	+	0.978282i	$0.566460\pi$
$602$	−1.01098e9	−0.188867
$603$	4.63883e9	0.861584
$604$	−4.59126e9	−0.847817
$605$	9.88937e8	0.181562
$606$	−2.72339e9	−0.497113
$607$	6.51774e9	1.18287	0.591434	−	0.806353i	$-0.298562\pi$
$607$	6.51774e9	1.18287	0.591434	+	0.806353i	$0.298562\pi$
$608$	5.64928e8	0.101937
$609$	7.48906e7	0.0134359
$610$	9.56575e8	0.170634
$611$	9.52422e8	0.168922
$612$	1.37679e10	2.42794
$613$	−1.03438e9	−0.181372	−0.0906859	−	0.995880i	$-0.528906\pi$
$613$	−1.03438e9	−0.181372	−0.0906859	+	0.995880i	$0.528906\pi$
$614$	1.71703e10	2.99357
$615$	−3.47772e7	−0.00602881
$616$	−3.67609e9	−0.633656
$617$	−6.58037e9	−1.12785	−0.563926	−	0.825825i	$-0.690710\pi$
$617$	−6.58037e9	−1.12785	−0.563926	+	0.825825i	$0.690710\pi$
$618$	3.04630e8	0.0519175
$619$	−9.30192e9	−1.57636	−0.788180	−	0.615445i	$-0.788976\pi$
$619$	−9.30192e9	−1.57636	−0.788180	+	0.615445i	$0.788976\pi$
$620$	1.56190e9	0.263198
$621$	−6.25754e7	−0.0104854
$622$	1.13089e10	1.88432
$623$	1.15136e8	0.0190768
$624$	6.48871e8	0.106909
$625$	6.00788e9	0.984331
$626$	8.01950e9	1.30658
$627$	9.24073e8	0.149717
$628$	−3.74540e9	−0.603448
$629$	5.07608e9	0.813301
$630$	1.59770e8	0.0254568
$631$	1.24958e10	1.97998	0.989992	−	0.141122i	$-0.0450710\pi$
$631$	1.24958e10	1.97998	0.989992	+	0.141122i	$0.0450710\pi$
$632$	3.33381e8	0.0525328
$633$	−1.39260e8	−0.0218229
$634$	1.41677e10	2.20794
$635$	1.85890e8	0.0288104
$636$	−2.70068e9	−0.416269
$637$	−4.41016e9	−0.676031
$638$	−6.83727e9	−1.04234
$639$	−4.04063e9	−0.612626
$640$	8.68404e8	0.130946
$641$	6.63748e9	0.995405	0.497703	−	0.867348i	$-0.334177\pi$
$641$	6.63748e9	0.995405	0.497703	+	0.867348i	$0.334177\pi$
$642$	4.29550e9	0.640679
$643$	−1.08266e10	−1.60602	−0.803011	−	0.595964i	$-0.796770\pi$
$643$	−1.08266e10	−1.60602	−0.803011	+	0.595964i	$0.796770\pi$
$644$	7.71160e7	0.0113774
$645$	4.92084e7	0.00722071
$646$	6.34935e9	0.926649
$647$	5.83102e9	0.846407	0.423204	−	0.906035i	$-0.360906\pi$
$647$	5.83102e9	0.846407	0.423204	+	0.906035i	$0.360906\pi$
$648$	−9.74723e9	−1.40724
$649$	−1.09360e10	−1.57037
$650$	8.43858e9	1.20524
$651$	5.49541e8	0.0780668
$652$	1.37848e10	1.94776
$653$	−3.75176e8	−0.0527277	−0.0263639	−	0.999652i	$-0.508393\pi$
$653$	−3.75176e8	−0.0527277	−0.0263639	+	0.999652i	$0.508393\pi$
$654$	1.15544e9	0.161520
$655$	−5.41981e7	−0.00753598
$656$	−2.43582e9	−0.336885
$657$	−2.08399e9	−0.286693
$658$	−6.37070e8	−0.0871760
$659$	−7.80877e9	−1.06288	−0.531439	−	0.847096i	$-0.678349\pi$
$659$	−7.80877e9	−1.06288	−0.531439	+	0.847096i	$0.678349\pi$
$660$	3.72336e8	0.0504117
$661$	−3.30941e9	−0.445703	−0.222851	−	0.974852i	$-0.571536\pi$
$661$	−3.30941e9	−0.445703	−0.222851	+	0.974852i	$0.571536\pi$
$662$	6.06016e9	0.811861
$663$	−1.34570e9	−0.179329
$664$	1.88807e10	2.50282
$665$	4.84924e7	0.00639437
$666$	−7.79216e9	−1.02211
$667$	6.89265e7	0.00899385
$668$	4.98496e9	0.647059
$669$	9.51416e8	0.122851
$670$	8.61984e8	0.110723
$671$	−2.02226e10	−2.58409
$672$	8.00883e7	0.0101807
$673$	−1.27559e10	−1.61308	−0.806541	−	0.591178i	$-0.798663\pi$
$673$	−1.27559e10	−1.61308	−0.806541	+	0.591178i	$0.798663\pi$
$674$	−1.08986e10	−1.37108
$675$	3.01441e9	0.377259
$676$	−7.70291e9	−0.959050
$677$	1.83549e9	0.227349	0.113674	−	0.993518i	$-0.463738\pi$
$677$	1.83549e9	0.227349	0.113674	+	0.993518i	$0.463738\pi$
$678$	−2.77286e9	−0.341684
$679$	2.16996e9	0.266016
$680$	1.22943e9	0.149942
$681$	−2.22132e9	−0.269523
$682$	−5.01712e10	−6.05633
$683$	−2.66994e9	−0.320648	−0.160324	−	0.987064i	$-0.551254\pi$
$683$	−2.66994e9	−0.320648	−0.160324	+	0.987064i	$0.551254\pi$
$684$	−6.41466e9	−0.766439
$685$	−6.72314e8	−0.0799199
$686$	6.04111e9	0.714467
$687$	3.21227e8	0.0377975
$688$	3.44660e9	0.403488
$689$	−6.80588e9	−0.792715
$690$	−5.70326e6	−0.000660924 0
$691$	−1.67932e9	−0.193624	−0.0968122	−	0.995303i	$-0.530865\pi$
$691$	−1.67932e9	−0.193624	−0.0968122	+	0.995303i	$0.530865\pi$
$692$	−2.15810e10	−2.47572
$693$	−3.37764e9	−0.385520
$694$	1.25292e10	1.42287
$695$	1.13050e8	0.0127739
$696$	−8.84635e8	−0.0994562
$697$	5.05166e9	0.565093
$698$	2.21006e9	0.245986
$699$	1.74250e8	0.0192976
$700$	−3.71486e9	−0.409355
$701$	1.74343e10	1.91157	0.955786	−	0.294064i	$-0.0950079\pi$
$701$	1.74343e10	1.91157	0.955786	+	0.294064i	$0.0950079\pi$
$702$	4.21161e9	0.459482
$703$	−2.36502e9	−0.256739
$704$	−2.08582e10	−2.25306
$705$	3.10086e7	0.00333288
$706$	2.22638e10	2.38113
$707$	3.02130e9	0.321534
$708$	−2.94438e9	−0.311801
$709$	−1.80009e10	−1.89685	−0.948426	−	0.316998i	$-0.897325\pi$
$709$	−1.80009e10	−1.89685	−0.948426	+	0.316998i	$0.897325\pi$
$710$	−7.50827e8	−0.0787292
$711$	3.06315e8	0.0319613
$712$	−1.36003e9	−0.141211
$713$	5.05776e8	0.0522571
$714$	9.00130e8	0.0925468
$715$	9.38310e8	0.0960009
$716$	5.15659e8	0.0525010
$717$	1.83268e9	0.185682
$718$	1.96040e10	1.97655
$719$	7.50801e9	0.753310	0.376655	−	0.926354i	$-0.377074\pi$
$719$	7.50801e9	0.753310	0.376655	+	0.926354i	$0.377074\pi$
$720$	−5.44681e8	−0.0543849
$721$	−3.37954e8	−0.0335803
$722$	1.43381e10	1.41778
$723$	3.67648e9	0.361783
$724$	1.75806e10	1.72167
$725$	−3.32035e9	−0.323595
$726$	−8.55277e9	−0.829524
$727$	1.26968e10	1.22553	0.612765	−	0.790265i	$-0.290057\pi$
$727$	1.26968e10	1.22553	0.612765	+	0.790265i	$0.290057\pi$
$728$	−2.49421e9	−0.239593
$729$	−8.18935e9	−0.782894
$730$	−3.87246e8	−0.0368432
$731$	−7.14791e9	−0.676812
$732$	−5.44469e9	−0.513079
$733$	1.54553e10	1.44948	0.724741	−	0.689022i	$-0.241959\pi$
$733$	1.54553e10	1.44948	0.724741	+	0.689022i	$0.241959\pi$
$734$	1.80015e10	1.68025
$735$	−1.43584e8	−0.0133383
$736$	7.37102e7	0.00681484
$737$	−1.82229e10	−1.67680
$738$	−7.75468e9	−0.710177
$739$	−4.25742e9	−0.388053	−0.194027	−	0.980996i	$-0.562155\pi$
$739$	−4.25742e9	−0.388053	−0.194027	+	0.980996i	$0.562155\pi$
$740$	−9.52938e8	−0.0864477
$741$	6.26981e8	0.0566096
$742$	4.55242e9	0.409099
$743$	−5.28541e9	−0.472735	−0.236368	−	0.971664i	$-0.575957\pi$
$743$	−5.28541e9	−0.472735	−0.236368	+	0.971664i	$0.575957\pi$
$744$	−6.49137e9	−0.577871
$745$	6.87863e8	0.0609474
$746$	−5.39497e9	−0.475776
$747$	1.73479e10	1.52273
$748$	−5.40849e10	−4.72520
$749$	−4.76538e9	−0.414392
$750$	5.50925e8	0.0476846
$751$	3.12416e9	0.269150	0.134575	−	0.990903i	$-0.457033\pi$
$751$	3.12416e9	0.269150	0.134575	+	0.990903i	$0.457033\pi$
$752$	2.17187e9	0.186239
$753$	−3.77210e9	−0.321960
$754$	−4.63906e9	−0.394122
$755$	−3.76700e8	−0.0318552
$756$	−1.85405e9	−0.156061
$757$	2.10722e10	1.76552	0.882762	−	0.469820i	$-0.155681\pi$
$757$	2.10722e10	1.76552	0.882762	+	0.469820i	$0.155681\pi$
$758$	5.77275e9	0.481438
$759$	1.20570e8	0.0100091
$760$	−5.72809e8	−0.0473328
$761$	−5.27137e9	−0.433588	−0.216794	−	0.976217i	$-0.569560\pi$
$761$	−5.27137e9	−0.433588	−0.216794	+	0.976217i	$0.569560\pi$
$762$	−1.60767e9	−0.131629
$763$	−1.28184e9	−0.104471
$764$	4.44118e10	3.60306
$765$	1.12962e9	0.0912254
$766$	−3.05232e10	−2.45374
$767$	−7.42001e9	−0.593774
$768$	−4.59325e9	−0.365894
$769$	9.38484e9	0.744191	0.372096	−	0.928194i	$-0.378639\pi$
$769$	9.38484e9	0.744191	0.372096	+	0.928194i	$0.378639\pi$
$770$	−6.27631e8	−0.0495435
$771$	2.26477e9	0.177965
$772$	−3.73261e9	−0.291980
$773$	−7.22957e9	−0.562969	−0.281484	−	0.959566i	$-0.590827\pi$
$773$	−7.22957e9	−0.562969	−0.281484	+	0.959566i	$0.590827\pi$
$774$	1.09726e10	0.850579
$775$	−2.43645e10	−1.88019
$776$	−2.56324e10	−1.96912
$777$	−3.35283e8	−0.0256412
$778$	−1.36498e10	−1.03920
$779$	−2.35365e9	−0.178386
$780$	2.52629e8	0.0190613
$781$	1.58729e10	1.19228
$782$	8.28445e8	0.0619498
$783$	−1.65716e9	−0.123366
$784$	−1.00568e10	−0.745336
$785$	−3.07300e8	−0.0226735
$786$	4.68730e8	0.0344305
$787$	−2.24491e10	−1.64168	−0.820840	−	0.571159i	$-0.806494\pi$
$787$	−2.24491e10	−1.64168	−0.820840	+	0.571159i	$0.806494\pi$
$788$	2.62119e10	1.90834
$789$	−1.71001e9	−0.123945
$790$	5.69193e7	0.00410738
$791$	3.07619e9	0.221002
$792$	3.98979e10	2.85372
$793$	−1.37209e10	−0.977075
$794$	−1.91446e10	−1.35730
$795$	−2.21583e8	−0.0156406
$796$	−2.26412e10	−1.59112
$797$	3.25570e9	0.227793	0.113897	−	0.993493i	$-0.463667\pi$
$797$	3.25570e9	0.227793	0.113897	+	0.993493i	$0.463667\pi$
$798$	−4.19384e8	−0.0292147
$799$	−4.50425e9	−0.312398
$800$	−3.55080e9	−0.245195
$801$	−1.24962e9	−0.0859138
$802$	1.56362e10	1.07034
$803$	8.18662e9	0.557957
$804$	−4.90629e9	−0.332933
$805$	6.32715e6	0.000427487 0
$806$	−3.40410e10	−2.28997
$807$	−4.66143e9	−0.312221
$808$	−3.56887e10	−2.38008
$809$	−1.82472e10	−1.21165	−0.605824	−	0.795599i	$-0.707156\pi$
$809$	−1.82472e10	−1.21165	−0.605824	+	0.795599i	$0.707156\pi$
$810$	−1.66418e9	−0.110028
$811$	1.98406e10	1.30611	0.653057	−	0.757308i	$-0.273486\pi$
$811$	1.98406e10	1.30611	0.653057	+	0.757308i	$0.273486\pi$
$812$	2.04223e9	0.133862
$813$	3.64824e9	0.238104
$814$	3.06102e10	1.98921
$815$	1.13101e9	0.0731835
$816$	−3.06868e9	−0.197713
$817$	3.33032e9	0.213653
$818$	2.23180e10	1.42567
$819$	−2.29172e9	−0.145770
$820$	−9.48354e8	−0.0600651
$821$	−1.85588e10	−1.17044	−0.585220	−	0.810874i	$-0.698992\pi$
$821$	−1.85588e10	−1.17044	−0.585220	+	0.810874i	$0.698992\pi$
$822$	5.81447e9	0.365140
$823$	3.23706e9	0.202419	0.101209	−	0.994865i	$-0.467729\pi$
$823$	3.23706e9	0.202419	0.101209	+	0.994865i	$0.467729\pi$
$824$	3.99203e9	0.248570
$825$	−5.80817e9	−0.360123
$826$	4.96321e9	0.306431
$827$	−1.67976e10	−1.03271	−0.516354	−	0.856375i	$-0.672711\pi$
$827$	−1.67976e10	−1.03271	−0.516354	+	0.856375i	$0.672711\pi$
$828$	−8.36967e8	−0.0512392
$829$	1.45439e9	0.0886628	0.0443314	−	0.999017i	$-0.485884\pi$
$829$	1.45439e9	0.0886628	0.0443314	+	0.999017i	$0.485884\pi$
$830$	3.22357e9	0.195688
$831$	1.01341e9	0.0612608
$832$	−1.41522e10	−0.851909
$833$	2.08568e10	1.25023
$834$	−9.77704e8	−0.0583615
$835$	4.09002e8	0.0243121
$836$	2.51990e10	1.49163
$837$	−1.21601e10	−0.716797
$838$	−2.81536e9	−0.165265
$839$	−1.35705e10	−0.793282	−0.396641	−	0.917974i	$-0.629824\pi$
$839$	−1.35705e10	−0.793282	−0.396641	+	0.917974i	$0.629824\pi$
$840$	−8.12056e7	−0.00472725
$841$	−1.54245e10	−0.894182
$842$	1.30858e10	0.755452
$843$	−3.94919e9	−0.227045
$844$	−3.79754e9	−0.217422
$845$	−6.32002e8	−0.0360346
$846$	6.91435e9	0.392604
$847$	9.48837e9	0.536537
$848$	−1.55199e10	−0.873983
$849$	−1.22415e9	−0.0686528
$850$	−3.99082e10	−2.22893
$851$	−3.08582e8	−0.0171639
$852$	4.27360e9	0.236731
$853$	9.80912e9	0.541138	0.270569	−	0.962701i	$-0.412788\pi$
$853$	9.80912e9	0.541138	0.270569	+	0.962701i	$0.412788\pi$
$854$	9.17787e9	0.504243
$855$	−5.26305e8	−0.0287976
$856$	5.62904e10	3.06744
$857$	1.15854e10	0.628752	0.314376	−	0.949299i	$-0.398205\pi$
$857$	1.15854e10	0.628752	0.314376	+	0.949299i	$0.398205\pi$
$858$	−8.11494e9	−0.438611
$859$	−1.04699e10	−0.563597	−0.281798	−	0.959474i	$-0.590931\pi$
$859$	−1.04699e10	−0.563597	−0.281798	+	0.959474i	$0.590931\pi$
$860$	1.34188e9	0.0719400
$861$	−3.33670e8	−0.0178158
$862$	3.74392e10	1.99091
$863$	1.15944e10	0.614062	0.307031	−	0.951700i	$-0.400664\pi$
$863$	1.15944e10	0.614062	0.307031	+	0.951700i	$0.400664\pi$
$864$	−1.77217e9	−0.0934774
$865$	−1.77066e9	−0.0930206
$866$	−3.06954e10	−1.60606
$867$	2.65616e9	0.138416
$868$	1.49857e10	0.777780
$869$	−1.20331e9	−0.0622025
$870$	−1.51037e8	−0.00777616
$871$	−1.23642e10	−0.634017
$872$	1.51415e10	0.773325
$873$	−2.35514e10	−1.19803
$874$	−3.85985e8	−0.0195560
$875$	−6.11191e8	−0.0308424
$876$	2.20415e9	0.110784
$877$	−1.22047e10	−0.610983	−0.305492	−	0.952195i	$-0.598821\pi$
$877$	−1.22047e10	−0.610983	−0.305492	+	0.952195i	$0.598821\pi$
$878$	−2.98578e9	−0.148877
$879$	−2.32960e9	−0.115697
$880$	2.13969e9	0.105843
$881$	−1.81705e9	−0.0895264	−0.0447632	−	0.998998i	$-0.514253\pi$
$881$	−1.81705e9	−0.0895264	−0.0447632	+	0.998998i	$0.514253\pi$
$882$	−3.20167e10	−1.57122
$883$	−1.90131e10	−0.929372	−0.464686	−	0.885476i	$-0.653833\pi$
$883$	−1.90131e10	−0.929372	−0.464686	+	0.885476i	$0.653833\pi$
$884$	−3.66964e10	−1.78665
$885$	−2.41578e8	−0.0117154
$886$	1.68453e10	0.813692
$887$	−1.82697e10	−0.879022	−0.439511	−	0.898237i	$-0.644848\pi$
$887$	−1.82697e10	−0.879022	−0.439511	+	0.898237i	$0.644848\pi$
$888$	3.96048e9	0.189803
$889$	1.78353e9	0.0851381
$890$	−2.32203e8	−0.0110409
$891$	3.51818e10	1.66627
$892$	2.59446e10	1.22397
$893$	2.09860e9	0.0986164
$894$	−5.94895e9	−0.278458
$895$	4.23084e7	0.00197263
$896$	8.33191e9	0.386961
$897$	8.18067e7	0.00378456
$898$	1.24420e10	0.573352
$899$	1.33942e10	0.614835
$900$	4.03187e10	1.84356
$901$	3.21868e10	1.46602
$902$	3.04630e10	1.38213
$903$	4.72130e8	0.0213381
$904$	−3.63370e10	−1.63591
$905$	1.44244e9	0.0646886
$906$	3.25787e9	0.145541
$907$	−2.06884e9	−0.0920666	−0.0460333	−	0.998940i	$-0.514658\pi$
$907$	−2.06884e9	−0.0920666	−0.0460333	+	0.998940i	$0.514658\pi$
$908$	−6.05741e10	−2.68526
$909$	−3.27913e10	−1.44805
$910$	−4.25846e8	−0.0187330
$911$	2.80648e10	1.22984	0.614919	−	0.788590i	$-0.289189\pi$
$911$	2.80648e10	1.22984	0.614919	+	0.788590i	$0.289189\pi$
$912$	1.42974e9	0.0624132
$913$	−6.81483e10	−2.96352
$914$	2.17453e10	0.942006
$915$	−4.46721e8	−0.0192780
$916$	8.75967e9	0.376577
$917$	−5.20005e8	−0.0222697
$918$	−1.99178e10	−0.849750
$919$	3.15348e10	1.34025	0.670125	−	0.742248i	$-0.266240\pi$
$919$	3.15348e10	1.34025	0.670125	+	0.742248i	$0.266240\pi$
$920$	−7.47385e7	−0.00316437
$921$	−8.01856e9	−0.338211
$922$	5.52416e10	2.32117
$923$	1.07697e10	0.450816
$924$	3.57239e9	0.148973
$925$	1.48651e10	0.617550
$926$	−4.66641e10	−1.93128
$927$	3.66794e9	0.151232
$928$	1.95203e9	0.0801806
$929$	3.94676e10	1.61505	0.807524	−	0.589835i	$-0.200807\pi$
$929$	3.94676e10	1.61505	0.807524	+	0.589835i	$0.200807\pi$
$930$	−1.10829e9	−0.0451819
$931$	−9.71749e9	−0.394666
$932$	4.75171e9	0.192262
$933$	−5.28128e9	−0.212889
$934$	1.24199e10	0.498776
$935$	−4.43751e9	−0.177541
$936$	2.70706e10	1.07903
$937$	−6.54259e9	−0.259813	−0.129907	−	0.991526i	$-0.541468\pi$
$937$	−6.54259e9	−0.259813	−0.129907	+	0.991526i	$0.541468\pi$
$938$	8.27032e9	0.327199
$939$	−3.74512e9	−0.147617
$940$	8.45587e8	0.0332055
$941$	1.99968e10	0.782341	0.391170	−	0.920318i	$-0.372070\pi$
$941$	1.99968e10	0.782341	0.391170	+	0.920318i	$0.372070\pi$
$942$	2.65767e9	0.103591
$943$	−3.07097e8	−0.0119257
$944$	−1.69203e10	−0.654646
$945$	−1.52120e8	−0.00586373
$946$	−4.31039e10	−1.65538
$947$	−2.16731e10	−0.829269	−0.414635	−	0.909988i	$-0.636091\pi$
$947$	−2.16731e10	−0.829269	−0.414635	+	0.909988i	$0.636091\pi$
$948$	−3.23976e8	−0.0123505
$949$	5.55460e9	0.210970
$950$	1.85938e10	0.703617
$951$	−6.61635e9	−0.249452
$952$	1.17958e10	0.443095
$953$	−6.49407e9	−0.243048	−0.121524	−	0.992589i	$-0.538778\pi$
$953$	−6.49407e9	−0.243048	−0.121524	+	0.992589i	$0.538778\pi$
$954$	−4.94090e10	−1.84241
$955$	3.64386e9	0.135379
$956$	4.99762e10	1.84995
$957$	3.19301e9	0.117763
$958$	6.15202e9	0.226068
$959$	−6.45052e9	−0.236173
$960$	−4.60763e8	−0.0168085
$961$	7.07730e10	2.57238
$962$	2.07689e10	0.752145
$963$	5.17204e10	1.86625
$964$	1.00256e11	3.60445
$965$	−3.06250e8	−0.0109706
$966$	−5.47201e7	−0.00195311
$967$	−3.36028e9	−0.119504	−0.0597520	−	0.998213i	$-0.519031\pi$
$967$	−3.36028e9	−0.119504	−0.0597520	+	0.998213i	$0.519031\pi$
$968$	−1.12080e11	−3.97159
$969$	−2.96515e9	−0.104692
$970$	−4.37630e9	−0.153959
$971$	2.52180e10	0.883983	0.441992	−	0.897019i	$-0.354272\pi$
$971$	2.52180e10	0.883983	0.441992	+	0.897019i	$0.354272\pi$
$972$	3.03754e10	1.06094
$973$	1.08466e9	0.0377483
$974$	−4.91418e10	−1.70410
$975$	−3.94082e9	−0.136167
$976$	−3.12887e10	−1.07724
$977$	9.80736e8	0.0336451	0.0168225	−	0.999858i	$-0.494645\pi$
$977$	9.80736e8	0.0336451	0.0168225	+	0.999858i	$0.494645\pi$
$978$	−9.78145e9	−0.334362
$979$	4.90891e9	0.167204
$980$	−3.91546e9	−0.132890
$981$	1.39123e10	0.470496
$982$	3.29767e10	1.11126
$983$	−3.97823e10	−1.33583	−0.667917	−	0.744236i	$-0.732814\pi$
$983$	−3.97823e10	−1.33583	−0.667917	+	0.744236i	$0.732814\pi$
$984$	3.94143e9	0.131878
$985$	2.15061e9	0.0717027
$986$	2.19393e10	0.728876
$987$	2.97512e8	0.00984907
$988$	1.70974e10	0.564002
$989$	4.34531e8	0.0142835
$990$	6.81190e9	0.223124
$991$	3.00606e10	0.981159	0.490580	−	0.871396i	$-0.336785\pi$
$991$	3.00606e10	0.981159	0.490580	+	0.871396i	$0.336785\pi$
$992$	1.43238e10	0.465874
$993$	−2.83010e9	−0.0917233
$994$	−7.20382e9	−0.232654
$995$	−1.85764e9	−0.0597835
$996$	−1.83481e10	−0.588415
$997$	−2.91914e10	−0.932872	−0.466436	−	0.884555i	$-0.654462\pi$
$997$	−2.91914e10	−0.932872	−0.466436	+	0.884555i	$0.654462\pi$
$998$	−8.02293e10	−2.55491
$999$	7.41903e9	0.235433

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.8.a.a.1.17	✓	156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.8.a.a.1.17	✓	156	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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	547.a (trivial)

\(f(q)\)	\(=\)	\(q-19.3499 q^{2} +9.03641 q^{3} +246.418 q^{4} +20.2179 q^{5} -174.853 q^{6} +193.981 q^{7} -2291.37 q^{8} -2105.34 q^{9} +O(q^{10})\)	\(q-19.3499 q^{2} +9.03641 q^{3} +246.418 q^{4} +20.2179 q^{5} -174.853 q^{6} +193.981 q^{7} -2291.37 q^{8} -2105.34 q^{9} -391.214 q^{10} +8270.50 q^{11} +2226.73 q^{12} +5611.50 q^{13} -3753.51 q^{14} +182.697 q^{15} +12796.3 q^{16} -26538.2 q^{17} +40738.1 q^{18} +12364.6 q^{19} +4982.05 q^{20} +1752.89 q^{21} -160033. q^{22} +1613.29 q^{23} -20705.8 q^{24} -77716.2 q^{25} -108582. q^{26} -38787.4 q^{27} +47800.3 q^{28} +42724.1 q^{29} -3535.17 q^{30} +313505. q^{31} +45689.3 q^{32} +74735.6 q^{33} +513512. q^{34} +3921.88 q^{35} -518794. q^{36} -191274. q^{37} -239253. q^{38} +50707.9 q^{39} -46326.7 q^{40} -190354. q^{41} -33918.2 q^{42} +269344. q^{43} +2.03800e6 q^{44} -42565.6 q^{45} -31217.0 q^{46} +169727. q^{47} +115632. q^{48} -785914. q^{49} +1.50380e6 q^{50} -239810. q^{51} +1.38277e6 q^{52} -1.21285e6 q^{53} +750531. q^{54} +167212. q^{55} -444482. q^{56} +111731. q^{57} -826706. q^{58} -1.32229e6 q^{59} +45019.8 q^{60} -2.44515e6 q^{61} -6.06629e6 q^{62} -408396. q^{63} -2.52200e6 q^{64} +113453. q^{65} -1.44613e6 q^{66} -2.20336e6 q^{67} -6.53949e6 q^{68} +14578.4 q^{69} -75888.0 q^{70} +1.91922e6 q^{71} +4.82412e6 q^{72} +989859. q^{73} +3.70114e6 q^{74} -702276. q^{75} +3.04685e6 q^{76} +1.60432e6 q^{77} -981191. q^{78} -145494. q^{79} +258713. q^{80} +4.25389e6 q^{81} +3.68333e6 q^{82} -8.23993e6 q^{83} +431944. q^{84} -536547. q^{85} -5.21177e6 q^{86} +386072. q^{87} -1.89508e7 q^{88} +593545. q^{89} +823639. q^{90} +1.08852e6 q^{91} +397544. q^{92} +2.83296e6 q^{93} -3.28419e6 q^{94} +249985. q^{95} +412867. q^{96} +1.11865e7 q^{97} +1.52073e7 q^{98} -1.74122e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 56 q^{2} - 284 q^{3} + 9690 q^{4} - 3751 q^{5} - 2322 q^{6} - 2559 q^{7} - 10752 q^{8} + 102594 q^{9}+O(q^{10}) \) 156 * q - 56 * q^2 - 284 * q^3 + 9690 * q^4 - 3751 * q^5 - 2322 * q^6 - 2559 * q^7 - 10752 * q^8 + 102594 * q^9	\( 156 q - 56 q^{2} - 284 q^{3} + 9690 q^{4} - 3751 q^{5} - 2322 q^{6} - 2559 q^{7} - 10752 q^{8} + 102594 q^{9} - 10570 q^{10} - 20090 q^{11} - 58311 q^{12} - 63021 q^{13} - 45057 q^{14} - 36391 q^{15} + 574338 q^{16} - 232394 q^{17} - 92277 q^{18} - 43100 q^{19} - 485568 q^{20} - 231868 q^{21} - 225008 q^{22} - 401950 q^{23} - 503569 q^{24} + 2076291 q^{25} - 530768 q^{26} - 959873 q^{27} - 617816 q^{28} - 1275618 q^{29} - 778474 q^{30} - 485945 q^{31} - 1903692 q^{32} - 1050846 q^{33} - 466263 q^{34} - 1826209 q^{35} + 5276156 q^{36} - 2129902 q^{37} - 2480555 q^{38} - 974653 q^{39} - 937648 q^{40} - 2309325 q^{41} - 2803500 q^{42} - 1756918 q^{43} - 3314520 q^{44} - 7492064 q^{45} - 1323786 q^{46} - 6203828 q^{47} - 7957494 q^{48} + 15095175 q^{49} - 5758152 q^{50} - 1556293 q^{51} - 7587898 q^{52} - 13775068 q^{53} - 6848423 q^{54} - 4045669 q^{55} - 8326655 q^{56} - 9421556 q^{57} - 4938892 q^{58} - 7755758 q^{59} - 5358502 q^{60} - 11693582 q^{61} - 14895366 q^{62} - 9477805 q^{63} + 31311690 q^{64} - 15629670 q^{65} - 5969892 q^{66} - 9560716 q^{67} - 34045735 q^{68} - 17825946 q^{69} - 4291177 q^{70} - 13661197 q^{71} - 21516953 q^{72} - 17125972 q^{73} - 19749599 q^{74} - 21752079 q^{75} - 15479244 q^{76} - 55632329 q^{77} - 12746879 q^{78} - 9534338 q^{79} - 61267539 q^{80} + 58468208 q^{81} - 29265046 q^{82} - 38447793 q^{83} - 33520873 q^{84} - 22365109 q^{85} - 21208733 q^{86} - 27018273 q^{87} - 40855385 q^{88} - 62436196 q^{89} - 19477679 q^{90} - 20640165 q^{91} - 78867734 q^{92} - 77801528 q^{93} + 2996793 q^{94} - 30557422 q^{95} - 82397286 q^{96} - 56264748 q^{97} - 72954494 q^{98} - 43444577 q^{99}+O(q^{100}) \) 156 * q - 56 * q^2 - 284 * q^3 + 9690 * q^4 - 3751 * q^5 - 2322 * q^6 - 2559 * q^7 - 10752 * q^8 + 102594 * q^9 - 10570 * q^10 - 20090 * q^11 - 58311 * q^12 - 63021 * q^13 - 45057 * q^14 - 36391 * q^15 + 574338 * q^16 - 232394 * q^17 - 92277 * q^18 - 43100 * q^19 - 485568 * q^20 - 231868 * q^21 - 225008 * q^22 - 401950 * q^23 - 503569 * q^24 + 2076291 * q^25 - 530768 * q^26 - 959873 * q^27 - 617816 * q^28 - 1275618 * q^29 - 778474 * q^30 - 485945 * q^31 - 1903692 * q^32 - 1050846 * q^33 - 466263 * q^34 - 1826209 * q^35 + 5276156 * q^36 - 2129902 * q^37 - 2480555 * q^38 - 974653 * q^39 - 937648 * q^40 - 2309325 * q^41 - 2803500 * q^42 - 1756918 * q^43 - 3314520 * q^44 - 7492064 * q^45 - 1323786 * q^46 - 6203828 * q^47 - 7957494 * q^48 + 15095175 * q^49 - 5758152 * q^50 - 1556293 * q^51 - 7587898 * q^52 - 13775068 * q^53 - 6848423 * q^54 - 4045669 * q^55 - 8326655 * q^56 - 9421556 * q^57 - 4938892 * q^58 - 7755758 * q^59 - 5358502 * q^60 - 11693582 * q^61 - 14895366 * q^62 - 9477805 * q^63 + 31311690 * q^64 - 15629670 * q^65 - 5969892 * q^66 - 9560716 * q^67 - 34045735 * q^68 - 17825946 * q^69 - 4291177 * q^70 - 13661197 * q^71 - 21516953 * q^72 - 17125972 * q^73 - 19749599 * q^74 - 21752079 * q^75 - 15479244 * q^76 - 55632329 * q^77 - 12746879 * q^78 - 9534338 * q^79 - 61267539 * q^80 + 58468208 * q^81 - 29265046 * q^82 - 38447793 * q^83 - 33520873 * q^84 - 22365109 * q^85 - 21208733 * q^86 - 27018273 * q^87 - 40855385 * q^88 - 62436196 * q^89 - 19477679 * q^90 - 20640165 * q^91 - 78867734 * q^92 - 77801528 * q^93 + 2996793 * q^94 - 30557422 * q^95 - 82397286 * q^96 - 56264748 * q^97 - 72954494 * q^98 - 43444577 * q^99

Introduction

L-functions

Modular forms

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