LMFDB - Embedded newform 547.8.a.a.1.2

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			1.2
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)

$f(q)$	$=$	$q-22.0518 q^{2} -47.8990 q^{3} +358.283 q^{4} -388.461 q^{5} +1056.26 q^{6} -154.038 q^{7} -5078.15 q^{8} +107.313 q^{9} +O(q^{10})$	\(q-22.0518 q^{2} -47.8990 q^{3} +358.283 q^{4} -388.461 q^{5} +1056.26 q^{6} -154.038 q^{7} -5078.15 q^{8} +107.313 q^{9} +8566.26 q^{10} -3074.88 q^{11} -17161.4 q^{12} +2349.51 q^{13} +3396.82 q^{14} +18606.9 q^{15} +66122.3 q^{16} -33185.7 q^{17} -2366.45 q^{18} -19918.8 q^{19} -139179. q^{20} +7378.27 q^{21} +67806.6 q^{22} -86348.8 q^{23} +243238. q^{24} +72776.6 q^{25} -51811.1 q^{26} +99614.9 q^{27} -55189.2 q^{28} +178730. q^{29} -410315. q^{30} -130686. q^{31} -808113. q^{32} +147283. q^{33} +731806. q^{34} +59837.7 q^{35} +38448.4 q^{36} +290304. q^{37} +439246. q^{38} -112539. q^{39} +1.97266e6 q^{40} -485672. q^{41} -162704. q^{42} +569307. q^{43} -1.10167e6 q^{44} -41686.9 q^{45} +1.90415e6 q^{46} -1.27130e6 q^{47} -3.16719e6 q^{48} -799815. q^{49} -1.60486e6 q^{50} +1.58956e6 q^{51} +841790. q^{52} -1.71044e6 q^{53} -2.19669e6 q^{54} +1.19447e6 q^{55} +782229. q^{56} +954091. q^{57} -3.94133e6 q^{58} -177514. q^{59} +6.66652e6 q^{60} -1.07255e6 q^{61} +2.88186e6 q^{62} -16530.3 q^{63} +9.35671e6 q^{64} -912694. q^{65} -3.24787e6 q^{66} -1.28926e6 q^{67} -1.18899e7 q^{68} +4.13602e6 q^{69} -1.31953e6 q^{70} +1.75740e6 q^{71} -544952. q^{72} -5.35559e6 q^{73} -6.40173e6 q^{74} -3.48593e6 q^{75} -7.13656e6 q^{76} +473648. q^{77} +2.48170e6 q^{78} -513927. q^{79} -2.56859e7 q^{80} -5.00615e6 q^{81} +1.07099e7 q^{82} +7.74813e6 q^{83} +2.64351e6 q^{84} +1.28913e7 q^{85} -1.25542e7 q^{86} -8.56101e6 q^{87} +1.56147e7 q^{88} +1.13327e7 q^{89} +919272. q^{90} -361915. q^{91} -3.09373e7 q^{92} +6.25973e6 q^{93} +2.80344e7 q^{94} +7.73767e6 q^{95} +3.87078e7 q^{96} +1.19300e7 q^{97} +1.76374e7 q^{98} -329974. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−22.0518	−1.94912	−0.974562	−	0.224119i	$-0.928050\pi$
$2$	−22.0518	−1.94912	−0.974562	+	0.224119i	$0.928050\pi$
$3$	−47.8990	−1.02424	−0.512120	−	0.858914i	$-0.671140\pi$
$3$	−47.8990	−1.02424	−0.512120	+	0.858914i	$0.671140\pi$
$4$	358.283	2.79908
$5$	−388.461	−1.38980	−0.694899	−	0.719107i	$-0.744551\pi$
$5$	−388.461	−1.38980	−0.694899	+	0.719107i	$0.744551\pi$
$6$	1056.26	1.99637
$7$	−154.038	−0.169740	−0.0848702	−	0.996392i	$-0.527048\pi$
$7$	−154.038	−0.169740	−0.0848702	+	0.996392i	$0.527048\pi$
$8$	−5078.15	−3.50664
$9$	107.313	0.0490686
$10$	8566.26	2.70889
$11$	−3074.88	−0.696551	−0.348276	−	0.937392i	$-0.613233\pi$
$11$	−3074.88	−0.696551	−0.348276	+	0.937392i	$0.613233\pi$
$12$	−17161.4	−2.86693
$13$	2349.51	0.296604	0.148302	−	0.988942i	$-0.452619\pi$
$13$	2349.51	0.296604	0.148302	+	0.988942i	$0.452619\pi$
$14$	3396.82	0.330845
$15$	18606.9	1.42349
$16$	66122.3	4.03578
$17$	−33185.7	−1.63825	−0.819125	−	0.573615i	$-0.805540\pi$
$17$	−33185.7	−1.63825	−0.819125	+	0.573615i	$0.805540\pi$
$18$	−2366.45	−0.0956408
$19$	−19918.8	−0.666232	−0.333116	−	0.942886i	$-0.608100\pi$
$19$	−19918.8	−0.666232	−0.333116	+	0.942886i	$0.608100\pi$
$20$	−139179.	−3.89016
$21$	7378.27	0.173855
$22$	67806.6	1.35766
$23$	−86348.8	−1.47982	−0.739910	−	0.672706i	$-0.765132\pi$
$23$	−86348.8	−1.47982	−0.739910	+	0.672706i	$0.765132\pi$
$24$	243238.	3.59164
$25$	72776.6	0.931541
$26$	−51811.1	−0.578117
$27$	99614.9	0.973982
$28$	−55189.2	−0.475117
$29$	178730.	1.36084	0.680418	−	0.732825i	$-0.261798\pi$
$29$	178730.	1.36084	0.680418	+	0.732825i	$0.261798\pi$
$30$	−410315.	−2.77455
$31$	−130686.	−0.787886	−0.393943	−	0.919135i	$-0.628889\pi$
$31$	−130686.	−0.787886	−0.393943	+	0.919135i	$0.628889\pi$
$32$	−808113.	−4.35960
$33$	147283.	0.713436
$34$	731806.	3.19315
$35$	59837.7	0.235905
$36$	38448.4	0.137347
$37$	290304.	0.942208	0.471104	−	0.882078i	$-0.343856\pi$
$37$	290304.	0.942208	0.471104	+	0.882078i	$0.343856\pi$
$38$	439246.	1.29857
$39$	−112539.	−0.303793
$40$	1.97266e6	4.87352
$41$	−485672.	−1.10052	−0.550262	−	0.834992i	$-0.685472\pi$
$41$	−485672.	−1.10052	−0.550262	+	0.834992i	$0.685472\pi$
$42$	−162704.	−0.338865
$43$	569307.	1.09196	0.545980	−	0.837798i	$-0.316157\pi$
$43$	569307.	1.09196	0.545980	+	0.837798i	$0.316157\pi$
$44$	−1.10167e6	−1.94971
$45$	−41686.9	−0.0681955
$46$	1.90415e6	2.88435
$47$	−1.27130e6	−1.78609	−0.893046	−	0.449965i	$-0.851437\pi$
$47$	−1.27130e6	−1.78609	−0.893046	+	0.449965i	$0.851437\pi$
$48$	−3.16719e6	−4.13361
$49$	−799815.	−0.971188
$50$	−1.60486e6	−1.81569
$51$	1.58956e6	1.67796
$52$	841790.	0.830218
$53$	−1.71044e6	−1.57813	−0.789064	−	0.614311i	$-0.789434\pi$
$53$	−1.71044e6	−1.57813	−0.789064	+	0.614311i	$0.789434\pi$
$54$	−2.19669e6	−1.89841
$55$	1.19447e6	0.968066
$56$	782229.	0.595217
$57$	954091.	0.682382
$58$	−3.94133e6	−2.65244
$59$	−177514.	−0.112525	−0.0562626	−	0.998416i	$-0.517918\pi$
$59$	−177514.	−0.112525	−0.0562626	+	0.998416i	$0.517918\pi$
$60$	6.66652e6	3.98446
$61$	−1.07255e6	−0.605011	−0.302505	−	0.953148i	$-0.597823\pi$
$61$	−1.07255e6	−0.605011	−0.302505	+	0.953148i	$0.597823\pi$
$62$	2.88186e6	1.53569
$63$	−16530.3	−0.00832892
$64$	9.35671e6	4.46163
$65$	−912694.	−0.412219
$66$	−3.24787e6	−1.39058
$67$	−1.28926e6	−0.523695	−0.261848	−	0.965109i	$-0.584332\pi$
$67$	−1.28926e6	−0.523695	−0.261848	+	0.965109i	$0.584332\pi$
$68$	−1.18899e7	−4.58560
$69$	4.13602e6	1.51569
$70$	−1.31953e6	−0.459808
$71$	1.75740e6	0.582727	0.291364	−	0.956612i	$-0.405891\pi$
$71$	1.75740e6	0.582727	0.291364	+	0.956612i	$0.405891\pi$
$72$	−544952.	−0.172066
$73$	−5.35559e6	−1.61130	−0.805651	−	0.592390i	$-0.798184\pi$
$73$	−5.35559e6	−1.61130	−0.805651	+	0.592390i	$0.798184\pi$
$74$	−6.40173e6	−1.83648
$75$	−3.48593e6	−0.954122
$76$	−7.13656e6	−1.86484
$77$	473648.	0.118233
$78$	2.48170e6	0.592131
$79$	−513927.	−0.117275	−0.0586377	−	0.998279i	$-0.518676\pi$
$79$	−513927.	−0.117275	−0.0586377	+	0.998279i	$0.518676\pi$
$80$	−2.56859e7	−5.60893
$81$	−5.00615e6	−1.04666
$82$	1.07099e7	2.14506
$83$	7.74813e6	1.48739	0.743693	−	0.668521i	$-0.233072\pi$
$83$	7.74813e6	1.48739	0.743693	+	0.668521i	$0.233072\pi$
$84$	2.64351e6	0.486634
$85$	1.28913e7	2.27684
$86$	−1.25542e7	−2.12836
$87$	−8.56101e6	−1.39382
$88$	1.56147e7	2.44255
$89$	1.13327e7	1.70400	0.852000	−	0.523541i	$-0.175389\pi$
$89$	1.13327e7	1.70400	0.852000	+	0.523541i	$0.175389\pi$
$90$	919272.	0.132922
$91$	−361915.	−0.0503456
$92$	−3.09373e7	−4.14214
$93$	6.25973e6	0.806984
$94$	2.80344e7	3.48132
$95$	7.73767e6	0.925929
$96$	3.87078e7	4.46528
$97$	1.19300e7	1.32721	0.663604	−	0.748084i	$-0.269026\pi$
$97$	1.19300e7	1.32721	0.663604	+	0.748084i	$0.269026\pi$
$98$	1.76374e7	1.89297
$99$	−329974.	−0.0341788
$100$	2.60746e7	2.60746
$101$	1.43876e7	1.38952	0.694758	−	0.719244i	$-0.255512\pi$
$101$	1.43876e7	1.38952	0.694758	+	0.719244i	$0.255512\pi$
$102$	−3.50527e7	−3.27056
$103$	−9.37928e6	−0.845745	−0.422872	−	0.906189i	$-0.638978\pi$
$103$	−9.37928e6	−0.845745	−0.422872	+	0.906189i	$0.638978\pi$
$104$	−1.19312e7	−1.04008
$105$	−2.86617e6	−0.241623
$106$	3.77183e7	3.07597
$107$	4.59407e6	0.362539	0.181269	−	0.983433i	$-0.441979\pi$
$107$	4.59407e6	0.362539	0.181269	+	0.983433i	$0.441979\pi$
$108$	3.56903e7	2.72626
$109$	1.42012e7	1.05035	0.525174	−	0.850995i	$-0.324000\pi$
$109$	1.42012e7	1.05035	0.525174	+	0.850995i	$0.324000\pi$
$110$	−2.63402e7	−1.88688
$111$	−1.39053e7	−0.965048
$112$	−1.01853e7	−0.685035
$113$	−2.73983e7	−1.78628	−0.893138	−	0.449783i	$-0.851501\pi$
$113$	−2.73983e7	−1.78628	−0.893138	+	0.449783i	$0.851501\pi$
$114$	−2.10394e7	−1.33005
$115$	3.35431e7	2.05665
$116$	6.40360e7	3.80909
$117$	252134.	0.0145539
$118$	3.91450e6	0.219326
$119$	5.11187e6	0.278077
$120$	−9.44885e7	−4.99165
$121$	−1.00323e7	−0.514816
$122$	2.36517e7	1.17924
$123$	2.32632e7	1.12720
$124$	−4.68225e7	−2.20536
$125$	2.07763e6	0.0951443
$126$	364523.	0.0162341
$127$	8.08624e6	0.350295	0.175147	−	0.984542i	$-0.443960\pi$
$127$	8.08624e6	0.350295	0.175147	+	0.984542i	$0.443960\pi$
$128$	−1.02894e8	−4.33666
$129$	−2.72692e7	−1.11843
$130$	2.01266e7	0.803466
$131$	2.05083e7	0.797040	0.398520	−	0.917160i	$-0.369524\pi$
$131$	2.05083e7	0.797040	0.398520	+	0.917160i	$0.369524\pi$
$132$	5.27691e7	1.99697
$133$	3.06826e6	0.113086
$134$	2.84305e7	1.02075
$135$	−3.86965e7	−1.35364
$136$	1.68522e8	5.74474
$137$	1.89454e7	0.629481	0.314741	−	0.949178i	$-0.398082\pi$
$137$	1.89454e7	0.629481	0.314741	+	0.949178i	$0.398082\pi$
$138$	−9.12067e7	−2.95427
$139$	−3.87665e7	−1.22435	−0.612174	−	0.790723i	$-0.709705\pi$
$139$	−3.87665e7	−1.22435	−0.612174	+	0.790723i	$0.709705\pi$
$140$	2.14388e7	0.660317
$141$	6.08938e7	1.82939
$142$	−3.87538e7	−1.13581
$143$	−7.22446e6	−0.206600
$144$	7.09578e6	0.198030
$145$	−6.94297e7	−1.89129
$146$	1.18100e8	3.14063
$147$	3.83103e7	0.994730
$148$	1.04011e8	2.63732
$149$	3.92737e7	0.972634	0.486317	−	0.873782i	$-0.338340\pi$
$149$	3.92737e7	0.972634	0.486317	+	0.873782i	$0.338340\pi$
$150$	7.68710e7	1.85970
$151$	2.99655e7	0.708275	0.354138	−	0.935193i	$-0.384774\pi$
$151$	2.99655e7	0.708275	0.354138	+	0.935193i	$0.384774\pi$
$152$	1.01151e8	2.33623
$153$	−3.56126e6	−0.0803867
$154$	−1.04448e7	−0.230450
$155$	5.07664e7	1.09500
$156$	−4.03209e7	−0.850343
$157$	5.27013e7	1.08686	0.543429	−	0.839455i	$-0.317126\pi$
$157$	5.27013e7	1.08686	0.543429	+	0.839455i	$0.317126\pi$
$158$	1.13330e7	0.228584
$159$	8.19283e7	1.61638
$160$	3.13920e8	6.05897
$161$	1.33010e7	0.251185
$162$	1.10395e8	2.04007
$163$	1.00714e8	1.82152	0.910760	−	0.412936i	$-0.135497\pi$
$163$	1.00714e8	1.82152	0.910760	+	0.412936i	$0.135497\pi$
$164$	−1.74008e8	−3.08046
$165$	−5.72138e7	−0.991533
$166$	−1.70860e8	−2.89910
$167$	−2.20334e7	−0.366078	−0.183039	−	0.983106i	$-0.558593\pi$
$167$	−2.20334e7	−0.366078	−0.183039	+	0.983106i	$0.558593\pi$
$168$	−3.74680e7	−0.609646
$169$	−5.72283e7	−0.912026
$170$	−2.84278e8	−4.43784
$171$	−2.13755e6	−0.0326911
$172$	2.03973e8	3.05649
$173$	−1.33122e7	−0.195474	−0.0977368	−	0.995212i	$-0.531160\pi$
$173$	−1.33122e7	−0.195474	−0.0977368	+	0.995212i	$0.531160\pi$
$174$	1.88786e8	2.71673
$175$	−1.12104e7	−0.158120
$176$	−2.03318e8	−2.81113
$177$	8.50273e6	0.115253
$178$	−2.49907e8	−3.32131
$179$	1.36594e8	1.78011	0.890056	−	0.455851i	$-0.150665\pi$
$179$	1.36594e8	1.78011	0.890056	+	0.455851i	$0.150665\pi$
$180$	−1.49357e7	−0.190885
$181$	7.86489e7	0.985866	0.492933	−	0.870067i	$-0.335925\pi$
$181$	7.86489e7	0.985866	0.492933	+	0.870067i	$0.335925\pi$
$182$	7.98088e6	0.0981298
$183$	5.13741e7	0.619677
$184$	4.38492e8	5.18919
$185$	−1.12772e8	−1.30948
$186$	−1.38038e8	−1.57291
$187$	1.02042e8	1.14113
$188$	−4.55483e8	−4.99942
$189$	−1.53445e7	−0.165324
$190$	−1.70630e8	−1.80475
$191$	1.65108e8	1.71456	0.857279	−	0.514852i	$-0.172153\pi$
$191$	1.65108e8	1.71456	0.857279	+	0.514852i	$0.172153\pi$
$192$	−4.48177e8	−4.56978
$193$	−7.57671e7	−0.758630	−0.379315	−	0.925268i	$-0.623840\pi$
$193$	−7.57671e7	−0.758630	−0.379315	+	0.925268i	$0.623840\pi$
$194$	−2.63078e8	−2.58689
$195$	4.37171e7	0.422212
$196$	−2.86560e8	−2.71844
$197$	−5.37593e6	−0.0500982	−0.0250491	−	0.999686i	$-0.507974\pi$
$197$	−5.37593e6	−0.0500982	−0.0250491	+	0.999686i	$0.507974\pi$
$198$	7.27653e6	0.0666187
$199$	6.11940e6	0.0550456	0.0275228	−	0.999621i	$-0.491238\pi$
$199$	6.11940e6	0.0550456	0.0275228	+	0.999621i	$0.491238\pi$
$200$	−3.69571e8	−3.26657
$201$	6.17543e7	0.536390
$202$	−3.17273e8	−2.70834
$203$	−2.75313e7	−0.230989
$204$	5.69513e8	4.69675
$205$	1.88664e8	1.52951
$206$	2.06830e8	1.64846
$207$	−9.26635e6	−0.0726127
$208$	1.55355e8	1.19703
$209$	6.12479e7	0.464065
$210$	6.32042e7	0.470954
$211$	−1.51916e8	−1.11331	−0.556653	−	0.830745i	$-0.687915\pi$
$211$	−1.51916e8	−1.11331	−0.556653	+	0.830745i	$0.687915\pi$
$212$	−6.12821e8	−4.41731
$213$	−8.41775e7	−0.596853
$214$	−1.01308e8	−0.706633
$215$	−2.21153e8	−1.51760
$216$	−5.05859e8	−3.41540
$217$	2.01306e7	0.133736
$218$	−3.13163e8	−2.04726
$219$	2.56527e8	1.65036
$220$	4.27957e8	2.70970
$221$	−7.79703e7	−0.485911
$222$	3.06636e8	1.88100
$223$	2.65009e8	1.60027	0.800137	−	0.599817i	$-0.204760\pi$
$223$	2.65009e8	1.60027	0.800137	+	0.599817i	$0.204760\pi$
$224$	1.24480e8	0.740001
$225$	7.80989e6	0.0457094
$226$	6.04182e8	3.48167
$227$	−3.19216e8	−1.81132	−0.905659	−	0.424007i	$-0.860623\pi$
$227$	−3.19216e8	−1.81132	−0.905659	+	0.424007i	$0.860623\pi$
$228$	3.41834e8	1.91004
$229$	9.71816e7	0.534761	0.267380	−	0.963591i	$-0.413842\pi$
$229$	9.71816e7	0.534761	0.267380	+	0.963591i	$0.413842\pi$
$230$	−7.39686e8	−4.00867
$231$	−2.26873e7	−0.121099
$232$	−9.07620e8	−4.77195
$233$	9.39020e7	0.486328	0.243164	−	0.969985i	$-0.421815\pi$
$233$	9.39020e7	0.486328	0.243164	+	0.969985i	$0.421815\pi$
$234$	−5.56000e6	−0.0283674
$235$	4.93848e8	2.48231
$236$	−6.36001e7	−0.314967
$237$	2.46166e7	0.120118
$238$	−1.12726e8	−0.542007
$239$	8.66047e7	0.410345	0.205172	−	0.978726i	$-0.434225\pi$
$239$	8.66047e7	0.410345	0.205172	+	0.978726i	$0.434225\pi$
$240$	1.23033e9	5.74489
$241$	−1.83689e8	−0.845324	−0.422662	−	0.906287i	$-0.638904\pi$
$241$	−1.83689e8	−0.845324	−0.422662	+	0.906287i	$0.638904\pi$
$242$	2.21231e8	1.00344
$243$	2.19316e7	0.0980501
$244$	−3.84276e8	−1.69348
$245$	3.10697e8	1.34976
$246$	−5.12996e8	−2.19705
$247$	−4.67995e7	−0.197607
$248$	6.63643e8	2.76283
$249$	−3.71128e8	−1.52344
$250$	−4.58155e7	−0.185448
$251$	2.18897e8	0.873737	0.436869	−	0.899525i	$-0.356087\pi$
$251$	2.18897e8	0.873737	0.436869	+	0.899525i	$0.356087\pi$
$252$	−5.92252e6	−0.0233133
$253$	2.65512e8	1.03077
$254$	−1.78316e8	−0.682768
$255$	−6.17483e8	−2.33203
$256$	1.07134e9	3.99105
$257$	−1.45669e7	−0.0535306	−0.0267653	−	0.999642i	$-0.508521\pi$
$257$	−1.45669e7	−0.0535306	−0.0267653	+	0.999642i	$0.508521\pi$
$258$	6.01336e8	2.17996
$259$	−4.47179e7	−0.159931
$260$	−3.27002e8	−1.15384
$261$	1.91801e7	0.0667743
$262$	−4.52245e8	−1.55353
$263$	−1.50626e8	−0.510570	−0.255285	−	0.966866i	$-0.582169\pi$
$263$	−1.50626e8	−0.510570	−0.255285	+	0.966866i	$0.582169\pi$
$264$	−7.47927e8	−2.50176
$265$	6.64438e8	2.19328
$266$	−6.76606e7	−0.220420
$267$	−5.42827e8	−1.74531
$268$	−4.61920e8	−1.46587
$269$	−3.52819e8	−1.10514	−0.552571	−	0.833466i	$-0.686353\pi$
$269$	−3.52819e8	−1.10514	−0.552571	+	0.833466i	$0.686353\pi$
$270$	8.53327e8	2.63841
$271$	−2.72603e8	−0.832029	−0.416014	−	0.909358i	$-0.636573\pi$
$271$	−2.72603e8	−0.832029	−0.416014	+	0.909358i	$0.636573\pi$
$272$	−2.19432e9	−6.61162
$273$	1.73353e7	0.0515660
$274$	−4.17782e8	−1.22694
$275$	−2.23779e8	−0.648866
$276$	1.48186e9	4.24255
$277$	1.10693e8	0.312924	0.156462	−	0.987684i	$-0.449991\pi$
$277$	1.10693e8	0.312924	0.156462	+	0.987684i	$0.449991\pi$
$278$	8.54872e8	2.38640
$279$	−1.40243e7	−0.0386605
$280$	−3.03865e8	−0.827232
$281$	3.18037e8	0.855076	0.427538	−	0.903997i	$-0.359381\pi$
$281$	3.18037e8	0.855076	0.427538	+	0.903997i	$0.359381\pi$
$282$	−1.34282e9	−3.56570
$283$	−1.65031e8	−0.432825	−0.216412	−	0.976302i	$-0.569436\pi$
$283$	−1.65031e8	−0.432825	−0.216412	+	0.976302i	$0.569436\pi$
$284$	6.29644e8	1.63110
$285$	−3.70627e8	−0.948374
$286$	1.59313e8	0.402688
$287$	7.48120e7	0.186803
$288$	−8.67211e7	−0.213920
$289$	6.90954e8	1.68386
$290$	1.53105e9	3.68635
$291$	−5.71434e8	−1.35938
$292$	−1.91881e9	−4.51017
$293$	−4.31258e8	−1.00161	−0.500807	−	0.865559i	$-0.666963\pi$
$293$	−4.31258e8	−1.00161	−0.500807	+	0.865559i	$0.666963\pi$
$294$	−8.44813e8	−1.93885
$295$	6.89571e7	0.156387
$296$	−1.47421e9	−3.30398
$297$	−3.06303e8	−0.678429
$298$	−8.66056e8	−1.89578
$299$	−2.02878e8	−0.438920
$300$	−1.24895e9	−2.67067
$301$	−8.76949e7	−0.185350
$302$	−6.60793e8	−1.38052
$303$	−6.89151e8	−1.42320
$304$	−1.31708e9	−2.68877
$305$	4.16643e8	0.840843
$306$	7.85323e7	0.156684
$307$	1.01458e8	0.200126	0.100063	−	0.994981i	$-0.468096\pi$
$307$	1.01458e8	0.200126	0.100063	+	0.994981i	$0.468096\pi$
$308$	1.69700e8	0.330944
$309$	4.49258e8	0.866246
$310$	−1.11949e9	−2.13430
$311$	3.13754e8	0.591463	0.295732	−	0.955271i	$-0.404437\pi$
$311$	3.13754e8	0.591463	0.295732	+	0.955271i	$0.404437\pi$
$312$	5.71492e8	1.06529
$313$	5.62409e7	0.103668	0.0518342	−	0.998656i	$-0.483493\pi$
$313$	5.62409e7	0.103668	0.0518342	+	0.998656i	$0.483493\pi$
$314$	−1.16216e9	−2.11842
$315$	6.42137e6	0.0115755
$316$	−1.84131e8	−0.328263
$317$	3.90736e8	0.688931	0.344466	−	0.938799i	$-0.388060\pi$
$317$	3.90736e8	0.688931	0.344466	+	0.938799i	$0.388060\pi$
$318$	−1.80667e9	−3.15053
$319$	−5.49574e8	−0.947892
$320$	−3.63471e9	−6.20076
$321$	−2.20051e8	−0.371327
$322$	−2.93311e8	−0.489591
$323$	6.61020e8	1.09146
$324$	−1.79362e9	−2.92969
$325$	1.70990e8	0.276298
$326$	−2.22093e9	−3.55037
$327$	−6.80225e8	−1.07581
$328$	2.46631e9	3.85914
$329$	1.95828e8	0.303172
$330$	1.26167e9	1.93262
$331$	−6.73979e8	−1.02152	−0.510762	−	0.859722i	$-0.670637\pi$
$331$	−6.73979e8	−1.02152	−0.510762	+	0.859722i	$0.670637\pi$
$332$	2.77602e9	4.16332
$333$	3.11534e7	0.0462329
$334$	4.85876e8	0.713531
$335$	5.00827e8	0.727831
$336$	4.87868e8	0.701641
$337$	−2.82978e8	−0.402761	−0.201381	−	0.979513i	$-0.564543\pi$
$337$	−2.82978e8	−0.402761	−0.201381	+	0.979513i	$0.564543\pi$
$338$	1.26199e9	1.77765
$339$	1.31235e9	1.82958
$340$	4.61875e9	6.37306
$341$	4.01843e8	0.548803
$342$	4.71368e7	0.0637190
$343$	2.50059e8	0.334590
$344$	−2.89102e9	−3.82910
$345$	−1.60668e9	−2.10651
$346$	2.93558e8	0.381002
$347$	4.66237e6	0.00599037	0.00299519	−	0.999996i	$-0.499047\pi$
$347$	4.66237e6	0.00599037	0.00299519	+	0.999996i	$0.499047\pi$
$348$	−3.06726e9	−3.90143
$349$	7.53972e8	0.949438	0.474719	−	0.880138i	$-0.342550\pi$
$349$	7.53972e8	0.949438	0.474719	+	0.880138i	$0.342550\pi$
$350$	2.47209e8	0.308196
$351$	2.34047e8	0.288887
$352$	2.48485e9	3.03669
$353$	2.36732e8	0.286448	0.143224	−	0.989690i	$-0.454253\pi$
$353$	2.36732e8	0.286448	0.143224	+	0.989690i	$0.454253\pi$
$354$	−1.87501e8	−0.224642
$355$	−6.82679e8	−0.809873
$356$	4.06032e9	4.76964
$357$	−2.44853e8	−0.284818
$358$	−3.01216e9	−3.46966
$359$	6.61232e8	0.754264	0.377132	−	0.926160i	$-0.376910\pi$
$359$	6.61232e8	0.754264	0.377132	+	0.926160i	$0.376910\pi$
$360$	2.11692e8	0.239137
$361$	−4.97113e8	−0.556134
$362$	−1.73435e9	−1.92157
$363$	4.80538e8	0.527296
$364$	−1.29668e8	−0.140921
$365$	2.08043e9	2.23939
$366$	−1.13289e9	−1.20783
$367$	6.67183e6	0.00704554	0.00352277	−	0.999994i	$-0.498879\pi$
$367$	6.67183e6	0.00704554	0.00352277	+	0.999994i	$0.498879\pi$
$368$	−5.70958e9	−5.97223
$369$	−5.21189e7	−0.0540012
$370$	2.48682e9	2.55234
$371$	2.63473e8	0.267872
$372$	2.24275e9	2.25882
$373$	−1.45577e8	−0.145248	−0.0726241	−	0.997359i	$-0.523137\pi$
$373$	−1.45577e8	−0.145248	−0.0726241	+	0.997359i	$0.523137\pi$
$374$	−2.25021e9	−2.22419
$375$	−9.95163e7	−0.0974507
$376$	6.45583e9	6.26318
$377$	4.19930e8	0.403629
$378$	3.38374e8	0.322237
$379$	−3.62754e8	−0.342275	−0.171137	−	0.985247i	$-0.554744\pi$
$379$	−3.62754e8	−0.342275	−0.171137	+	0.985247i	$0.554744\pi$
$380$	2.77227e9	2.59175
$381$	−3.87323e8	−0.358786
$382$	−3.64094e9	−3.34189
$383$	−1.49969e9	−1.36397	−0.681985	−	0.731366i	$-0.738883\pi$
$383$	−1.49969e9	−1.36397	−0.681985	+	0.731366i	$0.738883\pi$
$384$	4.92852e9	4.44178
$385$	−1.83994e8	−0.164320
$386$	1.67080e9	1.47866
$387$	6.10941e7	0.0535810
$388$	4.27431e9	3.71496
$389$	−6.30355e7	−0.0542952	−0.0271476	−	0.999631i	$-0.508642\pi$
$389$	−6.30355e7	−0.0542952	−0.0271476	+	0.999631i	$0.508642\pi$
$390$	−9.64042e8	−0.822943
$391$	2.86555e9	2.42431
$392$	4.06158e9	3.40560
$393$	−9.82327e8	−0.816361
$394$	1.18549e8	0.0976476
$395$	1.99640e8	0.162989
$396$	−1.18224e8	−0.0956693
$397$	−1.54742e9	−1.24120	−0.620599	−	0.784128i	$-0.713111\pi$
$397$	−1.54742e9	−1.24120	−0.620599	+	0.784128i	$0.713111\pi$
$398$	−1.34944e8	−0.107291
$399$	−1.46966e8	−0.115828
$400$	4.81216e9	3.75950
$401$	1.90874e9	1.47823	0.739116	−	0.673579i	$-0.235244\pi$
$401$	1.90874e9	1.47823	0.739116	+	0.673579i	$0.235244\pi$
$402$	−1.36179e9	−1.04549
$403$	−3.07049e8	−0.233690
$404$	5.15483e9	3.88937
$405$	1.94469e9	1.45465
$406$	6.07115e8	0.450225
$407$	−8.92649e8	−0.656297
$408$	−8.07204e9	−5.88400
$409$	2.10722e9	1.52293	0.761464	−	0.648207i	$-0.224481\pi$
$409$	2.10722e9	1.52293	0.761464	+	0.648207i	$0.224481\pi$
$410$	−4.16039e9	−2.98120
$411$	−9.07468e8	−0.644740
$412$	−3.36043e9	−2.36731
$413$	2.73439e7	0.0191001
$414$	2.04340e8	0.141531
$415$	−3.00984e9	−2.06717
$416$	−1.89867e9	−1.29307
$417$	1.85688e9	1.25403
$418$	−1.35063e9	−0.904520
$419$	6.47934e8	0.430310	0.215155	−	0.976580i	$-0.430974\pi$
$419$	6.47934e8	0.430310	0.215155	+	0.976580i	$0.430974\pi$
$420$	−1.02690e9	−0.676324
$421$	1.26059e9	0.823354	0.411677	−	0.911330i	$-0.364943\pi$
$421$	1.26059e9	0.823354	0.411677	+	0.911330i	$0.364943\pi$
$422$	3.35002e9	2.16997
$423$	−1.36427e8	−0.0876411
$424$	8.68587e9	5.53392
$425$	−2.41515e9	−1.52610
$426$	1.85627e9	1.16334
$427$	1.65214e8	0.102695
$428$	1.64598e9	1.01478
$429$	3.46044e8	0.211608
$430$	4.87683e9	2.95800
$431$	−2.24387e9	−1.34998	−0.674989	−	0.737827i	$-0.735852\pi$
$431$	−2.24387e9	−1.34998	−0.674989	+	0.737827i	$0.735852\pi$
$432$	6.58676e9	3.93078
$433$	5.29984e8	0.313730	0.156865	−	0.987620i	$-0.449861\pi$
$433$	5.29984e8	0.313730	0.156865	+	0.987620i	$0.449861\pi$
$434$	−4.43917e8	−0.260668
$435$	3.32561e9	1.93713
$436$	5.08806e9	2.94001
$437$	1.71996e9	0.985904
$438$	−5.65689e9	−3.21676
$439$	−1.48500e9	−0.837725	−0.418863	−	0.908050i	$-0.637571\pi$
$439$	−1.48500e9	−0.837725	−0.418863	+	0.908050i	$0.637571\pi$
$440$	−6.06569e9	−3.39466
$441$	−8.58306e7	−0.0476549
$442$	1.71939e9	0.947100
$443$	−1.17305e9	−0.641067	−0.320533	−	0.947237i	$-0.603862\pi$
$443$	−1.17305e9	−0.641067	−0.320533	+	0.947237i	$0.603862\pi$
$444$	−4.98202e9	−2.70125
$445$	−4.40232e9	−2.36822
$446$	−5.84394e9	−3.11913
$447$	−1.88117e9	−0.996211
$448$	−1.44129e9	−0.757318
$449$	1.56784e8	0.0817409	0.0408704	−	0.999164i	$-0.486987\pi$
$449$	1.56784e8	0.0817409	0.0408704	+	0.999164i	$0.486987\pi$
$450$	−1.72222e8	−0.0890933
$451$	1.49338e9	0.766571
$452$	−9.81632e9	−4.99993
$453$	−1.43532e9	−0.725444
$454$	7.03930e9	3.53048
$455$	1.40590e8	0.0699702
$456$	−4.84502e9	−2.39287
$457$	2.93693e9	1.43942	0.719710	−	0.694275i	$-0.244275\pi$
$457$	2.93693e9	1.43942	0.719710	+	0.694275i	$0.244275\pi$
$458$	−2.14303e9	−1.04232
$459$	−3.30579e9	−1.59563
$460$	1.20179e10	5.75674
$461$	−3.77602e9	−1.79507	−0.897533	−	0.440947i	$-0.854643\pi$
$461$	−3.77602e9	−1.79507	−0.897533	+	0.440947i	$0.854643\pi$
$462$	5.00295e8	0.236037
$463$	−3.22089e9	−1.50814	−0.754072	−	0.656792i	$-0.771913\pi$
$463$	−3.22089e9	−1.50814	−0.754072	+	0.656792i	$0.771913\pi$
$464$	1.18181e10	5.49204
$465$	−2.43166e9	−1.12155
$466$	−2.07071e9	−0.947913
$467$	2.52540e8	0.114742	0.0573708	−	0.998353i	$-0.481728\pi$
$467$	2.52540e8	0.114742	0.0573708	+	0.998353i	$0.481728\pi$
$468$	9.03351e7	0.0407377
$469$	1.98595e8	0.0888922
$470$	−1.08903e10	−4.83833
$471$	−2.52434e9	−1.11320
$472$	9.01441e8	0.394585
$473$	−1.75055e9	−0.760606
$474$	−5.42841e8	−0.234125
$475$	−1.44962e9	−0.620623
$476$	1.83149e9	0.778361
$477$	−1.83552e8	−0.0774365
$478$	−1.90979e9	−0.799812
$479$	2.21846e9	0.922313	0.461156	−	0.887319i	$-0.347435\pi$
$479$	2.21846e9	0.922313	0.461156	+	0.887319i	$0.347435\pi$
$480$	−1.50365e10	−6.20585
$481$	6.82073e8	0.279462
$482$	4.05067e9	1.64764
$483$	−6.37104e8	−0.257274
$484$	−3.59440e9	−1.44101
$485$	−4.63433e9	−1.84455
$486$	−4.83631e8	−0.191112
$487$	−3.20389e9	−1.25698	−0.628488	−	0.777820i	$-0.716326\pi$
$487$	−3.20389e9	−1.25698	−0.628488	+	0.777820i	$0.716326\pi$
$488$	5.44657e9	2.12155
$489$	−4.82411e9	−1.86567
$490$	−6.85143e9	−2.63084
$491$	2.21397e9	0.844086	0.422043	−	0.906576i	$-0.361313\pi$
$491$	2.21397e9	0.844086	0.422043	+	0.906576i	$0.361313\pi$
$492$	8.33480e9	3.15513
$493$	−5.93130e9	−2.22939
$494$	1.03201e9	0.385160
$495$	1.28182e8	0.0475017
$496$	−8.64126e9	−3.17974
$497$	−2.70706e8	−0.0989123
$498$	8.18404e9	2.96937
$499$	2.11989e8	0.0763767	0.0381884	−	0.999271i	$-0.487841\pi$
$499$	2.11989e8	0.0763767	0.0381884	+	0.999271i	$0.487841\pi$
$500$	7.44378e8	0.266317
$501$	1.05538e9	0.374952
$502$	−4.82707e9	−1.70302
$503$	4.82266e8	0.168966	0.0844829	−	0.996425i	$-0.473076\pi$
$503$	4.82266e8	0.168966	0.0844829	+	0.996425i	$0.473076\pi$
$504$	8.39434e7	0.0292065
$505$	−5.58901e9	−1.93115
$506$	−5.85502e9	−2.00910
$507$	2.74118e9	0.934134
$508$	2.89716e9	0.980504
$509$	−1.23692e9	−0.415748	−0.207874	−	0.978156i	$-0.566654\pi$
$509$	−1.23692e9	−0.415748	−0.207874	+	0.978156i	$0.566654\pi$
$510$	1.36166e10	4.54541
$511$	8.24964e8	0.273503
$512$	−1.04546e10	−3.44240
$513$	−1.98421e9	−0.648899
$514$	3.21227e8	0.104338
$515$	3.64348e9	1.17541
$516$	−9.77009e9	−3.13058
$517$	3.90908e9	1.24411
$518$	9.86110e8	0.311725
$519$	6.37641e8	0.200212
$520$	4.63480e9	1.44550
$521$	1.40069e8	0.0433921	0.0216961	−	0.999765i	$-0.493093\pi$
$521$	1.40069e8	0.0433921	0.0216961	+	0.999765i	$0.493093\pi$
$522$	−4.22956e8	−0.130151
$523$	4.62951e9	1.41507	0.707537	−	0.706677i	$-0.249806\pi$
$523$	4.62951e9	1.41507	0.707537	+	0.706677i	$0.249806\pi$
$524$	7.34777e9	2.23098
$525$	5.36966e8	0.161953
$526$	3.32158e9	0.995164
$527$	4.33691e9	1.29075
$528$	9.73871e9	2.87927
$529$	4.05129e9	1.18987
$530$	−1.46521e10	−4.27497
$531$	−1.90495e7	−0.00552146
$532$	1.09930e9	0.316538
$533$	−1.14109e9	−0.326419
$534$	1.19703e10	3.40182
$535$	−1.78462e9	−0.503856
$536$	6.54706e9	1.83641
$537$	−6.54274e9	−1.82326
$538$	7.78029e9	2.15406
$539$	2.45933e9	0.676482
$540$	−1.38643e10	−3.78895
$541$	1.87633e9	0.509469	0.254735	−	0.967011i	$-0.418012\pi$
$541$	1.87633e9	0.509469	0.254735	+	0.967011i	$0.418012\pi$
$542$	6.01140e9	1.62173
$543$	−3.76720e9	−1.00976
$544$	2.68178e10	7.14212
$545$	−5.51662e9	−1.45977
$546$	−3.82276e8	−0.100508
$547$	1.63667e8	0.0427569
$547$	1.63667e8	0.0427569
$548$	6.78783e9	1.76197
$549$	−1.15099e8	−0.0296871
$550$	4.93474e9	1.26472
$551$	−3.56010e9	−0.906633
$552$	−2.10033e10	−5.31498
$553$	7.91644e7	0.0199064
$554$	−2.44097e9	−0.609928
$555$	5.40165e9	1.34122
$556$	−1.38894e10	−3.42705
$557$	6.93650e9	1.70078	0.850388	−	0.526156i	$-0.176367\pi$
$557$	6.93650e9	1.70078	0.850388	+	0.526156i	$0.176367\pi$
$558$	3.09262e8	0.0753540
$559$	1.33759e9	0.323879
$560$	3.95661e9	0.952061
$561$	−4.88771e9	−1.16879
$562$	−7.01328e9	−1.66665
$563$	−7.51271e9	−1.77426	−0.887130	−	0.461519i	$-0.847305\pi$
$563$	−7.51271e9	−1.77426	−0.887130	+	0.461519i	$0.847305\pi$
$564$	2.18172e10	5.12061
$565$	1.06431e10	2.48256
$566$	3.63923e9	0.843629
$567$	7.71137e8	0.177661
$568$	−8.92432e9	−2.04341
$569$	−6.19328e8	−0.140938	−0.0704689	−	0.997514i	$-0.522450\pi$
$569$	−6.19328e8	−0.140938	−0.0704689	+	0.997514i	$0.522450\pi$
$570$	8.17299e9	1.84850
$571$	2.20975e9	0.496726	0.248363	−	0.968667i	$-0.420107\pi$
$571$	2.20975e9	0.496726	0.248363	+	0.968667i	$0.420107\pi$
$572$	−2.58840e9	−0.578289
$573$	−7.90852e9	−1.75612
$574$	−1.64974e9	−0.364103
$575$	−6.28417e9	−1.37851
$576$	1.00410e9	0.218926
$577$	−4.96906e9	−1.07686	−0.538429	−	0.842671i	$-0.680982\pi$
$577$	−4.96906e9	−1.07686	−0.538429	+	0.842671i	$0.680982\pi$
$578$	−1.52368e10	−3.28206
$579$	3.62917e9	0.777019
$580$	−2.48755e10	−5.29387
$581$	−1.19351e9	−0.252469
$582$	1.26012e10	2.64960
$583$	5.25939e9	1.09925
$584$	2.71965e10	5.65025
$585$	−9.79440e7	−0.0202270
$586$	9.51002e9	1.95227
$587$	−6.96571e8	−0.142145	−0.0710726	−	0.997471i	$-0.522642\pi$
$587$	−6.96571e8	−0.142145	−0.0710726	+	0.997471i	$0.522642\pi$
$588$	1.37259e10	2.78433
$589$	2.60311e9	0.524915
$590$	−1.52063e9	−0.304818
$591$	2.57502e8	0.0513126
$592$	1.91956e10	3.80255
$593$	−5.90599e9	−1.16306	−0.581529	−	0.813526i	$-0.697545\pi$
$593$	−5.90599e9	−1.16306	−0.581529	+	0.813526i	$0.697545\pi$
$594$	6.75455e9	1.32234
$595$	−1.98576e9	−0.386471
$596$	1.40711e10	2.72248
$597$	−2.93113e8	−0.0563800
$598$	4.47382e9	0.855509
$599$	−1.00967e10	−1.91949	−0.959746	−	0.280868i	$-0.909378\pi$
$599$	−1.00967e10	−1.91949	−0.959746	+	0.280868i	$0.909378\pi$
$600$	1.77021e10	3.34576
$601$	6.48672e9	1.21889	0.609445	−	0.792828i	$-0.291392\pi$
$601$	6.48672e9	1.21889	0.609445	+	0.792828i	$0.291392\pi$
$602$	1.93383e9	0.361269
$603$	−1.38355e8	−0.0256970
$604$	1.07361e10	1.98252
$605$	3.89716e9	0.715491
$606$	1.51970e10	2.77399
$607$	−9.01878e8	−0.163677	−0.0818384	−	0.996646i	$-0.526079\pi$
$607$	−9.01878e8	−0.163677	−0.0818384	+	0.996646i	$0.526079\pi$
$608$	1.60966e10	2.90451
$609$	1.31872e9	0.236588
$610$	−9.18775e9	−1.63891
$611$	−2.98693e9	−0.529761
$612$	−1.27594e9	−0.225009
$613$	−1.60514e9	−0.281451	−0.140725	−	0.990049i	$-0.544943\pi$
$613$	−1.60514e9	−0.281451	−0.140725	+	0.990049i	$0.544943\pi$
$614$	−2.23734e9	−0.390069
$615$	−9.03683e9	−1.56658
$616$	−2.40526e9	−0.414599
$617$	5.15108e9	0.882877	0.441439	−	0.897291i	$-0.354468\pi$
$617$	5.15108e9	0.882877	0.441439	+	0.897291i	$0.354468\pi$
$618$	−9.90696e9	−1.68842
$619$	−2.90533e9	−0.492355	−0.246177	−	0.969225i	$-0.579175\pi$
$619$	−2.90533e9	−0.492355	−0.246177	+	0.969225i	$0.579175\pi$
$620$	1.81887e10	3.06500
$621$	−8.60162e9	−1.44132
$622$	−6.91884e9	−1.15283
$623$	−1.74567e9	−0.289238
$624$	−7.44136e9	−1.22604
$625$	−6.49275e9	−1.06377
$626$	−1.24021e9	−0.202063
$627$	−2.93371e9	−0.475314
$628$	1.88820e10	3.04221
$629$	−9.63395e9	−1.54357
$630$	−1.41603e8	−0.0225621
$631$	2.10049e9	0.332826	0.166413	−	0.986056i	$-0.446781\pi$
$631$	2.10049e9	0.332826	0.166413	+	0.986056i	$0.446781\pi$
$632$	2.60980e9	0.411242
$633$	7.27661e9	1.14029
$634$	−8.61644e9	−1.34281
$635$	−3.14119e9	−0.486839
$636$	2.93535e10	4.52439
$637$	−1.87918e9	−0.288058
$638$	1.21191e10	1.84756
$639$	1.88592e8	0.0285936
$640$	3.99702e10	6.02708
$641$	−7.23821e9	−1.08550	−0.542748	−	0.839896i	$-0.682616\pi$
$641$	−7.23821e9	−1.08550	−0.542748	+	0.839896i	$0.682616\pi$
$642$	4.85253e9	0.723762
$643$	2.05973e9	0.305543	0.152771	−	0.988262i	$-0.451180\pi$
$643$	2.05973e9	0.305543	0.152771	+	0.988262i	$0.451180\pi$
$644$	4.76552e9	0.703088
$645$	1.05930e10	1.55439
$646$	−1.45767e10	−2.12738
$647$	−8.56591e9	−1.24339	−0.621697	−	0.783258i	$-0.713556\pi$
$647$	−8.56591e9	−1.24339	−0.621697	+	0.783258i	$0.713556\pi$
$648$	2.54220e10	3.67026
$649$	5.45833e8	0.0783796
$650$	−3.77063e9	−0.538540
$651$	−9.64237e8	−0.136978
$652$	3.60841e10	5.09859
$653$	−1.23740e10	−1.73906	−0.869528	−	0.493883i	$-0.835577\pi$
$653$	−1.23740e10	−1.73906	−0.869528	+	0.493883i	$0.835577\pi$
$654$	1.50002e10	2.09689
$655$	−7.96667e9	−1.10773
$656$	−3.21137e10	−4.44147
$657$	−5.74725e8	−0.0790644
$658$	−4.31836e9	−0.590920
$659$	−1.66225e9	−0.226255	−0.113127	−	0.993580i	$-0.536087\pi$
$659$	−1.66225e9	−0.226255	−0.113127	+	0.993580i	$0.536087\pi$
$660$	−2.04987e10	−2.77538
$661$	−8.20471e9	−1.10499	−0.552495	−	0.833517i	$-0.686324\pi$
$661$	−8.20471e9	−1.10499	−0.552495	+	0.833517i	$0.686324\pi$
$662$	1.48625e10	1.99108
$663$	3.73470e9	0.497689
$664$	−3.93462e10	−5.21572
$665$	−1.19190e9	−0.157167
$666$	−6.86990e8	−0.0901136
$667$	−1.54332e10	−2.01379
$668$	−7.89418e9	−1.02468
$669$	−1.26937e10	−1.63907
$670$	−1.10441e10	−1.41863
$671$	3.29796e9	0.421421
$672$	−5.96247e9	−0.757939
$673$	−6.51092e9	−0.823359	−0.411680	−	0.911329i	$-0.635058\pi$
$673$	−6.51092e9	−0.823359	−0.411680	+	0.911329i	$0.635058\pi$
$674$	6.24017e9	0.785031
$675$	7.24964e9	0.907305
$676$	−2.05039e10	−2.55284
$677$	9.79611e9	1.21337	0.606685	−	0.794942i	$-0.292499\pi$
$677$	9.79611e9	1.21337	0.606685	+	0.794942i	$0.292499\pi$
$678$	−2.89397e10	−3.56607
$679$	−1.83767e9	−0.225281
$680$	−6.54642e10	−7.98404
$681$	1.52901e10	1.85523
$682$	−8.86137e9	−1.06968
$683$	1.07702e10	1.29345	0.646726	−	0.762722i	$-0.276138\pi$
$683$	1.07702e10	1.29345	0.646726	+	0.762722i	$0.276138\pi$
$684$	−7.65847e8	−0.0915051
$685$	−7.35956e9	−0.874853
$686$	−5.51426e9	−0.652157
$687$	−4.65490e9	−0.547724
$688$	3.76438e10	4.40691
$689$	−4.01870e9	−0.468078
$690$	3.54302e10	4.10584
$691$	1.19361e10	1.37622	0.688112	−	0.725605i	$-0.258440\pi$
$691$	1.19361e10	1.37622	0.688112	+	0.725605i	$0.258440\pi$
$692$	−4.76953e9	−0.547147
$693$	5.08286e7	0.00580152
$694$	−1.02814e8	−0.0116760
$695$	1.50593e10	1.70160
$696$	4.34741e10	4.88763
$697$	1.61174e10	1.80293
$698$	−1.66265e10	−1.85057
$699$	−4.49781e9	−0.498117
$700$	−4.01648e9	−0.442591
$701$	1.71994e10	1.88582	0.942911	−	0.333046i	$-0.108076\pi$
$701$	1.71994e10	1.88582	0.942911	+	0.333046i	$0.108076\pi$
$702$	−5.16115e9	−0.563076
$703$	−5.78251e9	−0.627730
$704$	−2.87707e10	−3.10775
$705$	−2.36548e10	−2.54248
$706$	−5.22037e9	−0.558322
$707$	−2.21624e9	−0.235857
$708$	3.04638e9	0.322602
$709$	1.31221e10	1.38274	0.691371	−	0.722500i	$-0.257007\pi$
$709$	1.31221e10	1.38274	0.691371	+	0.722500i	$0.257007\pi$
$710$	1.50543e10	1.57854
$711$	−5.51511e7	−0.00575454
$712$	−5.75493e10	−5.97531
$713$	1.12846e10	1.16593
$714$	5.39946e9	0.555145
$715$	2.80642e9	0.287132
$716$	4.89394e10	4.98268
$717$	−4.14828e9	−0.420292
$718$	−1.45814e10	−1.47015
$719$	5.76003e9	0.577928	0.288964	−	0.957340i	$-0.406689\pi$
$719$	5.76003e9	0.577928	0.288964	+	0.957340i	$0.406689\pi$
$720$	−2.75643e9	−0.275222
$721$	1.44477e9	0.143557
$722$	1.09622e10	1.08397
$723$	8.79851e9	0.865815
$724$	2.81785e10	2.75952
$725$	1.30074e10	1.26767
$726$	−1.05967e10	−1.02776
$727$	1.25866e10	1.21490	0.607448	−	0.794360i	$-0.292193\pi$
$727$	1.25866e10	1.21490	0.607448	+	0.794360i	$0.292193\pi$
$728$	1.83786e9	0.176544
$729$	9.89794e9	0.946234
$730$	−4.58774e10	−4.36484
$731$	−1.88929e10	−1.78890
$732$	1.84064e10	1.73453
$733$	−9.04751e9	−0.848526	−0.424263	−	0.905539i	$-0.639467\pi$
$733$	−9.04751e9	−0.848526	−0.424263	+	0.905539i	$0.639467\pi$
$734$	−1.47126e8	−0.0137326
$735$	−1.48821e10	−1.38248
$736$	6.97796e10	6.45143
$737$	3.96432e9	0.364781
$738$	1.14932e9	0.105255
$739$	1.22937e10	1.12054	0.560269	−	0.828311i	$-0.310698\pi$
$739$	1.22937e10	1.12054	0.560269	+	0.828311i	$0.310698\pi$
$740$	−4.04041e10	−3.66534
$741$	2.24165e9	0.202397
$742$	−5.81005e9	−0.522115
$743$	2.06443e10	1.84646	0.923229	−	0.384251i	$-0.125540\pi$
$743$	2.06443e10	1.84646	0.923229	+	0.384251i	$0.125540\pi$
$744$	−3.17878e10	−2.82980
$745$	−1.52563e10	−1.35177
$746$	3.21023e9	0.283107
$747$	8.31476e8	0.0729840
$748$	3.65599e10	3.19410
$749$	−7.07662e8	−0.0615374
$750$	2.19452e9	0.189943
$751$	−1.39530e9	−0.120206	−0.0601031	−	0.998192i	$-0.519143\pi$
$751$	−1.39530e9	−0.120206	−0.0601031	+	0.998192i	$0.519143\pi$
$752$	−8.40609e10	−7.20828
$753$	−1.04849e10	−0.894917
$754$	−9.26021e9	−0.786722
$755$	−1.16404e10	−0.984360
$756$	−5.49766e9	−0.462756
$757$	−1.04010e10	−0.871445	−0.435722	−	0.900081i	$-0.643507\pi$
$757$	−1.04010e10	−0.871445	−0.435722	+	0.900081i	$0.643507\pi$
$758$	7.99938e9	0.667136
$759$	−1.27177e10	−1.05576
$760$	−3.92931e10	−3.24690
$761$	−1.80327e10	−1.48325	−0.741626	−	0.670814i	$-0.765945\pi$
$761$	−1.80327e10	−1.48325	−0.741626	+	0.670814i	$0.765945\pi$
$762$	8.54117e9	0.699319
$763$	−2.18753e9	−0.178287
$764$	5.91554e10	4.79919
$765$	1.38341e9	0.111721
$766$	3.30708e10	2.65854
$767$	−4.17071e8	−0.0333754
$768$	−5.13161e10	−4.08780
$769$	−5.95924e9	−0.472551	−0.236276	−	0.971686i	$-0.575927\pi$
$769$	−5.95924e9	−0.472551	−0.236276	+	0.971686i	$0.575927\pi$
$770$	4.05739e9	0.320280
$771$	6.97741e8	0.0548282
$772$	−2.71460e10	−2.12347
$773$	1.36784e10	1.06514	0.532572	−	0.846385i	$-0.321225\pi$
$773$	1.36784e10	1.06514	0.532572	+	0.846385i	$0.321225\pi$
$774$	−1.34723e9	−0.104436
$775$	−9.51089e9	−0.733948
$776$	−6.05823e10	−4.65403
$777$	2.14194e9	0.163808
$778$	1.39005e9	0.105828
$779$	9.67400e9	0.733205
$780$	1.56631e10	1.18181
$781$	−5.40377e9	−0.405899
$782$	−6.31905e10	−4.72529
$783$	1.78042e10	1.32543
$784$	−5.28856e10	−3.91950
$785$	−2.04724e10	−1.51051
$786$	2.16621e10	1.59119
$787$	1.19416e10	0.873277	0.436638	−	0.899637i	$-0.356169\pi$
$787$	1.19416e10	0.873277	0.436638	+	0.899637i	$0.356169\pi$
$788$	−1.92610e9	−0.140229
$789$	7.21484e9	0.522946
$790$	−4.40243e9	−0.317686
$791$	4.22038e9	0.303203
$792$	1.67566e9	0.119853
$793$	−2.51997e9	−0.179448
$794$	3.41234e10	2.41925
$795$	−3.18259e10	−2.24645
$796$	2.19247e9	0.154077
$797$	1.48998e10	1.04250	0.521250	−	0.853404i	$-0.325466\pi$
$797$	1.48998e10	1.04250	0.521250	+	0.853404i	$0.325466\pi$
$798$	3.24087e9	0.225763
$799$	4.21889e10	2.92607
$800$	−5.88117e10	−4.06115
$801$	1.21615e9	0.0836130
$802$	−4.20913e10	−2.88126
$803$	1.64678e10	1.12235
$804$	2.21255e10	1.50140
$805$	−5.16691e9	−0.349097
$806$	6.77098e9	0.455490
$807$	1.68997e10	1.13193
$808$	−7.30624e10	−4.87253
$809$	−1.46424e10	−0.972280	−0.486140	−	0.873881i	$-0.661596\pi$
$809$	−1.46424e10	−0.972280	−0.486140	+	0.873881i	$0.661596\pi$
$810$	−4.28840e10	−2.83529
$811$	−1.47785e10	−0.972875	−0.486438	−	0.873715i	$-0.661704\pi$
$811$	−1.47785e10	−0.972875	−0.486438	+	0.873715i	$0.661704\pi$
$812$	−9.86399e9	−0.646556
$813$	1.30574e10	0.852198
$814$	1.96845e10	1.27920
$815$	−3.91235e10	−2.53155
$816$	1.05105e11	6.77189
$817$	−1.13399e10	−0.727499
$818$	−4.64681e10	−2.96837
$819$	−3.88382e7	−0.00247039
$820$	6.75952e10	4.28122
$821$	1.87949e9	0.118533	0.0592666	−	0.998242i	$-0.481124\pi$
$821$	1.87949e9	0.118533	0.0592666	+	0.998242i	$0.481124\pi$
$822$	2.00113e10	1.25668
$823$	−7.77621e8	−0.0486260	−0.0243130	−	0.999704i	$-0.507740\pi$
$823$	−7.77621e8	−0.0486260	−0.0243130	+	0.999704i	$0.507740\pi$
$824$	4.76294e10	2.96572
$825$	1.07188e10	0.664595
$826$	−6.02982e8	−0.0372284
$827$	8.45893e9	0.520051	0.260026	−	0.965602i	$-0.416269\pi$
$827$	8.45893e9	0.520051	0.260026	+	0.965602i	$0.416269\pi$
$828$	−3.31997e9	−0.203249
$829$	6.47280e7	0.00394595	0.00197298	−	0.999998i	$-0.499372\pi$
$829$	6.47280e7	0.00394595	0.00197298	+	0.999998i	$0.499372\pi$
$830$	6.63725e10	4.02916
$831$	−5.30206e9	−0.320510
$832$	2.19837e10	1.32333
$833$	2.65425e10	1.59105
$834$	−4.09475e10	−2.44425
$835$	8.55910e9	0.508775
$836$	2.19440e10	1.29896
$837$	−1.30183e10	−0.767387
$838$	−1.42881e10	−0.838728
$839$	−9.24080e9	−0.540185	−0.270093	−	0.962834i	$-0.587054\pi$
$839$	−9.24080e9	−0.540185	−0.270093	+	0.962834i	$0.587054\pi$
$840$	1.45548e10	0.847285
$841$	1.46947e10	0.851873
$842$	−2.77983e10	−1.60482
$843$	−1.52336e10	−0.875804
$844$	−5.44288e10	−3.11624
$845$	2.22309e10	1.26753
$846$	3.00846e9	0.170823
$847$	1.54536e9	0.0873851
$848$	−1.13098e11	−6.36898
$849$	7.90480e9	0.443317
$850$	5.32583e10	2.97455
$851$	−2.50674e10	−1.39430
$852$	−3.01593e10	−1.67064
$853$	−2.37438e10	−1.30987	−0.654936	−	0.755684i	$-0.727304\pi$
$853$	−2.37438e10	−1.30987	−0.654936	+	0.755684i	$0.727304\pi$
$854$	−3.64326e9	−0.200165
$855$	8.30353e8	0.0454341
$856$	−2.33294e10	−1.27129
$857$	−3.15336e10	−1.71136	−0.855680	−	0.517506i	$-0.826861\pi$
$857$	−3.15336e10	−1.71136	−0.855680	+	0.517506i	$0.826861\pi$
$858$	−7.63091e9	−0.412450
$859$	−1.29713e10	−0.698246	−0.349123	−	0.937077i	$-0.613521\pi$
$859$	−1.29713e10	−0.698246	−0.349123	+	0.937077i	$0.613521\pi$
$860$	−7.92354e10	−4.24790
$861$	−3.58342e9	−0.191331
$862$	4.94814e10	2.63128
$863$	2.19073e10	1.16025	0.580124	−	0.814528i	$-0.303004\pi$
$863$	2.19073e10	1.16025	0.580124	+	0.814528i	$0.303004\pi$
$864$	−8.05001e10	−4.24618
$865$	5.17126e9	0.271669
$866$	−1.16871e10	−0.611498
$867$	−3.30960e10	−1.72468
$868$	7.21245e9	0.374338
$869$	1.58026e9	0.0816883
$870$	−7.33358e10	−3.77571
$871$	−3.02914e9	−0.155330
$872$	−7.21160e10	−3.68319
$873$	1.28024e9	0.0651243
$874$	−3.79283e10	−1.92165
$875$	−3.20034e8	−0.0161498
$876$	9.19092e10	4.61950
$877$	1.71215e10	0.857121	0.428560	−	0.903513i	$-0.359021\pi$
$877$	1.71215e10	0.857121	0.428560	+	0.903513i	$0.359021\pi$
$878$	3.27470e10	1.63283
$879$	2.06568e10	1.02589
$880$	7.89809e10	3.90691
$881$	−1.78532e10	−0.879630	−0.439815	−	0.898088i	$-0.644956\pi$
$881$	−1.78532e10	−0.879630	−0.439815	+	0.898088i	$0.644956\pi$
$882$	1.89272e9	0.0928852
$883$	−3.13106e10	−1.53049	−0.765243	−	0.643741i	$-0.777381\pi$
$883$	−3.13106e10	−1.53049	−0.765243	+	0.643741i	$0.777381\pi$
$884$	−2.79354e10	−1.36010
$885$	−3.30297e9	−0.160178
$886$	2.58679e10	1.24952
$887$	−1.25277e10	−0.602753	−0.301377	−	0.953505i	$-0.597446\pi$
$887$	−1.25277e10	−0.602753	−0.301377	+	0.953505i	$0.597446\pi$
$888$	7.06130e10	3.38407
$889$	−1.24559e9	−0.0594592
$890$	9.70792e10	4.61595
$891$	1.53933e10	0.729053
$892$	9.49483e10	4.47930
$893$	2.53227e10	1.18995
$894$	4.14832e10	1.94174
$895$	−5.30616e10	−2.47400
$896$	1.58496e10	0.736105
$897$	9.71763e9	0.449559
$898$	−3.45737e9	−0.159323
$899$	−2.33576e10	−1.07218
$900$	2.79815e9	0.127945
$901$	5.67622e10	2.58537
$902$	−3.29318e10	−1.49414
$903$	4.20050e9	0.189843
$904$	1.39133e11	6.26382
$905$	−3.05520e10	−1.37015
$906$	3.16513e10	1.41398
$907$	−2.44523e10	−1.08817	−0.544083	−	0.839031i	$-0.683122\pi$
$907$	−2.44523e10	−1.08817	−0.544083	+	0.839031i	$0.683122\pi$
$908$	−1.14370e11	−5.07003
$909$	1.54398e9	0.0681816
$910$	−3.10026e9	−0.136381
$911$	−1.39105e10	−0.609576	−0.304788	−	0.952420i	$-0.598586\pi$
$911$	−1.39105e10	−0.609576	−0.304788	+	0.952420i	$0.598586\pi$
$912$	6.30866e10	2.75395
$913$	−2.38245e10	−1.03604
$914$	−6.47647e10	−2.80561
$915$	−1.99568e10	−0.861226
$916$	3.48185e10	1.49684
$917$	−3.15906e9	−0.135290
$918$	7.28987e10	3.11007
$919$	−2.50574e10	−1.06496	−0.532479	−	0.846443i	$-0.678739\pi$
$919$	−2.50574e10	−1.06496	−0.532479	+	0.846443i	$0.678739\pi$
$920$	−1.70337e11	−7.21193
$921$	−4.85974e9	−0.204977
$922$	8.32680e10	3.49881
$923$	4.12902e9	0.172839
$924$	−8.12845e9	−0.338966
$925$	2.11273e10	0.877706
$926$	7.10265e10	2.93956
$927$	−1.00652e9	−0.0414995
$928$	−1.44434e11	−5.93270
$929$	4.33126e10	1.77239	0.886194	−	0.463314i	$-0.153340\pi$
$929$	4.33126e10	1.77239	0.886194	+	0.463314i	$0.153340\pi$
$930$	5.36225e10	2.18603
$931$	1.59314e10	0.647037
$932$	3.36435e10	1.36127
$933$	−1.50285e10	−0.605801
$934$	−5.56896e9	−0.223646
$935$	−3.96393e10	−1.58593
$936$	−1.28037e9	−0.0510353
$937$	2.95740e10	1.17441	0.587207	−	0.809437i	$-0.300227\pi$
$937$	2.95740e10	1.17441	0.587207	+	0.809437i	$0.300227\pi$
$938$	−4.37939e9	−0.173262
$939$	−2.69388e9	−0.106181
$940$	1.76937e11	6.94819
$941$	−1.14295e10	−0.447162	−0.223581	−	0.974685i	$-0.571775\pi$
$941$	−1.14295e10	−0.447162	−0.223581	+	0.974685i	$0.571775\pi$
$942$	5.56663e10	2.16977
$943$	4.19372e10	1.62858
$944$	−1.17376e10	−0.454127
$945$	5.96073e9	0.229767
$946$	3.86027e10	1.48252
$947$	8.02715e9	0.307140	0.153570	−	0.988138i	$-0.450923\pi$
$947$	8.02715e9	0.307140	0.153570	+	0.988138i	$0.450923\pi$
$948$	8.81970e9	0.336221
$949$	−1.25830e10	−0.477918
$950$	3.19668e10	1.20967
$951$	−1.87159e10	−0.705631
$952$	−2.59588e10	−0.975115
$953$	−3.61768e10	−1.35396	−0.676979	−	0.736003i	$-0.736711\pi$
$953$	−3.61768e10	−1.35396	−0.676979	+	0.736003i	$0.736711\pi$
$954$	4.04767e9	0.150933
$955$	−6.41381e10	−2.38289
$956$	3.10290e10	1.14859
$957$	2.63240e10	0.970869
$958$	−4.89212e10	−1.79770
$959$	−2.91832e9	−0.106848
$960$	1.74099e11	6.35107
$961$	−1.04338e10	−0.379236
$962$	−1.50410e10	−0.544707
$963$	4.93004e8	0.0177893
$964$	−6.58125e10	−2.36613
$965$	2.94325e10	1.05434
$966$	1.40493e10	0.501459
$967$	3.82330e10	1.35971	0.679854	−	0.733347i	$-0.262043\pi$
$967$	3.82330e10	1.35971	0.679854	+	0.733347i	$0.262043\pi$
$968$	5.09456e10	1.80527
$969$	−3.16622e10	−1.11791
$970$	1.02195e11	3.59526
$971$	−7.03461e9	−0.246589	−0.123294	−	0.992370i	$-0.539346\pi$
$971$	−7.03461e9	−0.246589	−0.123294	+	0.992370i	$0.539346\pi$
$972$	7.85770e9	0.274450
$973$	5.97152e9	0.207821
$974$	7.06517e10	2.45000
$975$	−8.19024e9	−0.282996
$976$	−7.09194e10	−2.44169
$977$	1.84829e10	0.634074	0.317037	−	0.948413i	$-0.397312\pi$
$977$	1.84829e10	0.634074	0.317037	+	0.948413i	$0.397312\pi$
$978$	1.06380e11	3.63643
$979$	−3.48468e10	−1.18692
$980$	1.11317e11	3.77808
$981$	1.52398e9	0.0515392
$982$	−4.88221e10	−1.64523
$983$	9.86662e8	0.0331307	0.0165654	−	0.999863i	$-0.494727\pi$
$983$	9.86662e8	0.0331307	0.0165654	+	0.999863i	$0.494727\pi$
$984$	−1.18134e11	−3.95268
$985$	2.08834e9	0.0696264
$986$	1.30796e11	4.34535
$987$	−9.37996e9	−0.310521
$988$	−1.67675e10	−0.553118
$989$	−4.91589e10	−1.61590
$990$	−2.82665e9	−0.0925867
$991$	−3.27861e9	−0.107012	−0.0535060	−	0.998568i	$-0.517040\pi$
$991$	−3.27861e9	−0.107012	−0.0535060	+	0.998568i	$0.517040\pi$
$992$	1.05609e11	3.43487
$993$	3.22829e10	1.04629
$994$	5.96955e9	0.192792
$995$	−2.37714e9	−0.0765023
$996$	−1.32969e11	−4.26424
$997$	−6.10306e10	−1.95036	−0.975180	−	0.221414i	$-0.928933\pi$
$997$	−6.10306e10	−1.95036	−0.975180	+	0.221414i	$0.928933\pi$
$998$	−4.67474e9	−0.148868
$999$	2.89186e10	0.917695

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.8.a.a.1.2	✓	156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.8.a.a.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-22.0518 q^{2} -47.8990 q^{3} +358.283 q^{4} -388.461 q^{5} +1056.26 q^{6} -154.038 q^{7} -5078.15 q^{8} +107.313 q^{9} +O(q^{10})\)	\(q-22.0518 q^{2} -47.8990 q^{3} +358.283 q^{4} -388.461 q^{5} +1056.26 q^{6} -154.038 q^{7} -5078.15 q^{8} +107.313 q^{9} +8566.26 q^{10} -3074.88 q^{11} -17161.4 q^{12} +2349.51 q^{13} +3396.82 q^{14} +18606.9 q^{15} +66122.3 q^{16} -33185.7 q^{17} -2366.45 q^{18} -19918.8 q^{19} -139179. q^{20} +7378.27 q^{21} +67806.6 q^{22} -86348.8 q^{23} +243238. q^{24} +72776.6 q^{25} -51811.1 q^{26} +99614.9 q^{27} -55189.2 q^{28} +178730. q^{29} -410315. q^{30} -130686. q^{31} -808113. q^{32} +147283. q^{33} +731806. q^{34} +59837.7 q^{35} +38448.4 q^{36} +290304. q^{37} +439246. q^{38} -112539. q^{39} +1.97266e6 q^{40} -485672. q^{41} -162704. q^{42} +569307. q^{43} -1.10167e6 q^{44} -41686.9 q^{45} +1.90415e6 q^{46} -1.27130e6 q^{47} -3.16719e6 q^{48} -799815. q^{49} -1.60486e6 q^{50} +1.58956e6 q^{51} +841790. q^{52} -1.71044e6 q^{53} -2.19669e6 q^{54} +1.19447e6 q^{55} +782229. q^{56} +954091. q^{57} -3.94133e6 q^{58} -177514. q^{59} +6.66652e6 q^{60} -1.07255e6 q^{61} +2.88186e6 q^{62} -16530.3 q^{63} +9.35671e6 q^{64} -912694. q^{65} -3.24787e6 q^{66} -1.28926e6 q^{67} -1.18899e7 q^{68} +4.13602e6 q^{69} -1.31953e6 q^{70} +1.75740e6 q^{71} -544952. q^{72} -5.35559e6 q^{73} -6.40173e6 q^{74} -3.48593e6 q^{75} -7.13656e6 q^{76} +473648. q^{77} +2.48170e6 q^{78} -513927. q^{79} -2.56859e7 q^{80} -5.00615e6 q^{81} +1.07099e7 q^{82} +7.74813e6 q^{83} +2.64351e6 q^{84} +1.28913e7 q^{85} -1.25542e7 q^{86} -8.56101e6 q^{87} +1.56147e7 q^{88} +1.13327e7 q^{89} +919272. q^{90} -361915. q^{91} -3.09373e7 q^{92} +6.25973e6 q^{93} +2.80344e7 q^{94} +7.73767e6 q^{95} +3.87078e7 q^{96} +1.19300e7 q^{97} +1.76374e7 q^{98} -329974. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 56 q^{2} - 284 q^{3} + 9690 q^{4} - 3751 q^{5} - 2322 q^{6} - 2559 q^{7} - 10752 q^{8} + 102594 q^{9}+O(q^{10}) \) 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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