LMFDB - Embedded newform 177.10.a.a.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$91.1613430010$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+6.97380 q^{2} +81.0000 q^{3} -463.366 q^{4} +1656.32 q^{5} +564.878 q^{6} +2037.84 q^{7} -6802.01 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+6.97380 q^{2} +81.0000 q^{3} -463.366 q^{4} +1656.32 q^{5} +564.878 q^{6} +2037.84 q^{7} -6802.01 q^{8} +6561.00 q^{9} +11550.8 q^{10} +9319.57 q^{11} -37532.7 q^{12} -111282. q^{13} +14211.5 q^{14} +134162. q^{15} +189808. q^{16} -499680. q^{17} +45755.1 q^{18} +572598. q^{19} -767480. q^{20} +165065. q^{21} +64992.8 q^{22} -1.77436e6 q^{23} -550963. q^{24} +790255. q^{25} -776059. q^{26} +531441. q^{27} -944267. q^{28} -1.11174e6 q^{29} +935616. q^{30} -2.68419e6 q^{31} +4.80631e6 q^{32} +754885. q^{33} -3.48467e6 q^{34} +3.37531e6 q^{35} -3.04014e6 q^{36} +6.12013e6 q^{37} +3.99319e6 q^{38} -9.01385e6 q^{39} -1.12663e7 q^{40} +7.80122e6 q^{41} +1.15113e6 q^{42} -8.86375e6 q^{43} -4.31837e6 q^{44} +1.08671e7 q^{45} -1.23741e7 q^{46} +8.20162e6 q^{47} +1.53744e7 q^{48} -3.62008e7 q^{49} +5.51108e6 q^{50} -4.04741e7 q^{51} +5.15644e7 q^{52} -2.44307e7 q^{53} +3.70616e6 q^{54} +1.54361e7 q^{55} -1.38614e7 q^{56} +4.63805e7 q^{57} -7.75306e6 q^{58} +1.21174e7 q^{59} -6.21659e7 q^{60} +9.11754e7 q^{61} -1.87190e7 q^{62} +1.33703e7 q^{63} -6.36632e7 q^{64} -1.84318e8 q^{65} +5.26442e6 q^{66} -2.68575e7 q^{67} +2.31535e8 q^{68} -1.43724e8 q^{69} +2.35387e7 q^{70} -3.59390e8 q^{71} -4.46280e7 q^{72} -1.80655e8 q^{73} +4.26806e7 q^{74} +6.40107e7 q^{75} -2.65323e8 q^{76} +1.89918e7 q^{77} -6.28608e7 q^{78} -4.32646e8 q^{79} +3.14381e8 q^{80} +4.30467e7 q^{81} +5.44042e7 q^{82} -4.86509e8 q^{83} -7.64856e7 q^{84} -8.27627e8 q^{85} -6.18140e7 q^{86} -9.00510e7 q^{87} -6.33918e7 q^{88} +3.77036e8 q^{89} +7.57849e7 q^{90} -2.26775e8 q^{91} +8.22180e8 q^{92} -2.17419e8 q^{93} +5.71965e7 q^{94} +9.48404e8 q^{95} +3.89311e8 q^{96} -2.52026e8 q^{97} -2.52457e8 q^{98} +6.11457e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9}+O(q^{10}) $ 21 * q - 66 * q^2 + 1701 * q^3 + 5206 * q^4 - 2964 * q^5 - 5346 * q^6 - 30775 * q^7 - 24621 * q^8 + 137781 * q^9	\( 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9} - 54663 q^{10} - 151769 q^{11} + 421686 q^{12} - 153611 q^{13} - 286771 q^{14} - 240084 q^{15} + 805530 q^{16} - 723621 q^{17} - 433026 q^{18} - 549388 q^{19} - 527311 q^{20} - 2492775 q^{21} + 2973158 q^{22} + 169962 q^{23} - 1994301 q^{24} + 8035779 q^{25} - 2337392 q^{26} + 11160261 q^{27} - 22659054 q^{28} - 16845442 q^{29} - 4427703 q^{30} - 19307976 q^{31} - 44923568 q^{32} - 12293289 q^{33} - 35547496 q^{34} - 34882596 q^{35} + 34156566 q^{36} - 41561129 q^{37} - 52335371 q^{38} - 12442491 q^{39} - 125735038 q^{40} - 68169291 q^{41} - 23228451 q^{42} - 25719587 q^{43} - 126277032 q^{44} - 19446804 q^{45} - 292814271 q^{46} - 174095332 q^{47} + 65247930 q^{48} + 7479350 q^{49} - 227877439 q^{50} - 58613301 q^{51} - 232397708 q^{52} - 228390500 q^{53} - 35075106 q^{54} - 29426208 q^{55} + 326778474 q^{56} - 44500428 q^{57} + 480343762 q^{58} + 254464581 q^{59} - 42712191 q^{60} - 183928964 q^{61} - 21753862 q^{62} - 201914775 q^{63} + 310571245 q^{64} + 5308466 q^{65} + 240825798 q^{66} - 82724114 q^{67} - 138336205 q^{68} + 13766922 q^{69} + 1030274876 q^{70} - 404721965 q^{71} - 161538381 q^{72} + 154162574 q^{73} + 36352054 q^{74} + 650898099 q^{75} + 1068940636 q^{76} - 448535481 q^{77} - 189328752 q^{78} + 272529635 q^{79} - 345587859 q^{80} + 903981141 q^{81} - 38412637 q^{82} + 432518643 q^{83} - 1835383374 q^{84} - 126211490 q^{85} - 3699273072 q^{86} - 1364480802 q^{87} + 170111045 q^{88} - 1255621070 q^{89} - 358643943 q^{90} + 1448885849 q^{91} + 1568933320 q^{92} - 1563946056 q^{93} - 1908445164 q^{94} - 2896546490 q^{95} - 3638809008 q^{96} + 1007235486 q^{97} - 9506868248 q^{98} - 995756409 q^{99}+O(q^{100}) \) 21 * q - 66 * q^2 + 1701 * q^3 + 5206 * q^4 - 2964 * q^5 - 5346 * q^6 - 30775 * q^7 - 24621 * q^8 + 137781 * q^9 - 54663 * q^10 - 151769 * q^11 + 421686 * q^12 - 153611 * q^13 - 286771 * q^14 - 240084 * q^15 + 805530 * q^16 - 723621 * q^17 - 433026 * q^18 - 549388 * q^19 - 527311 * q^20 - 2492775 * q^21 + 2973158 * q^22 + 169962 * q^23 - 1994301 * q^24 + 8035779 * q^25 - 2337392 * q^26 + 11160261 * q^27 - 22659054 * q^28 - 16845442 * q^29 - 4427703 * q^30 - 19307976 * q^31 - 44923568 * q^32 - 12293289 * q^33 - 35547496 * q^34 - 34882596 * q^35 + 34156566 * q^36 - 41561129 * q^37 - 52335371 * q^38 - 12442491 * q^39 - 125735038 * q^40 - 68169291 * q^41 - 23228451 * q^42 - 25719587 * q^43 - 126277032 * q^44 - 19446804 * q^45 - 292814271 * q^46 - 174095332 * q^47 + 65247930 * q^48 + 7479350 * q^49 - 227877439 * q^50 - 58613301 * q^51 - 232397708 * q^52 - 228390500 * q^53 - 35075106 * q^54 - 29426208 * q^55 + 326778474 * q^56 - 44500428 * q^57 + 480343762 * q^58 + 254464581 * q^59 - 42712191 * q^60 - 183928964 * q^61 - 21753862 * q^62 - 201914775 * q^63 + 310571245 * q^64 + 5308466 * q^65 + 240825798 * q^66 - 82724114 * q^67 - 138336205 * q^68 + 13766922 * q^69 + 1030274876 * q^70 - 404721965 * q^71 - 161538381 * q^72 + 154162574 * q^73 + 36352054 * q^74 + 650898099 * q^75 + 1068940636 * q^76 - 448535481 * q^77 - 189328752 * q^78 + 272529635 * q^79 - 345587859 * q^80 + 903981141 * q^81 - 38412637 * q^82 + 432518643 * q^83 - 1835383374 * q^84 - 126211490 * q^85 - 3699273072 * q^86 - 1364480802 * q^87 + 170111045 * q^88 - 1255621070 * q^89 - 358643943 * q^90 + 1448885849 * q^91 + 1568933320 * q^92 - 1563946056 * q^93 - 1908445164 * q^94 - 2896546490 * q^95 - 3638809008 * q^96 + 1007235486 * q^97 - 9506868248 * q^98 - 995756409 * 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 $

$2$	6.97380	0.308201	0.154101	−	0.988055i	$-0.450752\pi$
$2$	6.97380	0.308201	0.154101	+	0.988055i	$0.450752\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	−463.366	−0.905012
$5$	1656.32	1.18516	0.592581	−	0.805511i	$-0.298109\pi$
$5$	1656.32	1.18516	0.592581	+	0.805511i	$0.298109\pi$
$6$	564.878	0.177940
$7$	2037.84	0.320796	0.160398	−	0.987052i	$-0.448722\pi$
$7$	2037.84	0.320796	0.160398	+	0.987052i	$0.448722\pi$
$8$	−6802.01	−0.587127
$9$	6561.00	0.333333
$10$	11550.8	0.365269
$11$	9319.57	0.191924	0.0959618	−	0.995385i	$-0.469407\pi$
$11$	9319.57	0.191924	0.0959618	+	0.995385i	$0.469407\pi$
$12$	−37532.7	−0.522509
$13$	−111282.	−1.08064	−0.540319	−	0.841460i	$-0.681696\pi$
$13$	−111282.	−1.08064	−0.540319	+	0.841460i	$0.681696\pi$
$14$	14211.5	0.0988699
$15$	134162.	0.684254
$16$	189808.	0.724058
$17$	−499680.	−1.45101	−0.725507	−	0.688215i	$-0.758395\pi$
$17$	−499680.	−1.45101	−0.725507	+	0.688215i	$0.758395\pi$
$18$	45755.1	0.102734
$19$	572598.	1.00800	0.503998	−	0.863705i	$-0.331862\pi$
$19$	572598.	1.00800	0.503998	+	0.863705i	$0.331862\pi$
$20$	−767480.	−1.07259
$21$	165065.	0.185212
$22$	64992.8	0.0591512
$23$	−1.77436e6	−1.32211	−0.661055	−	0.750338i	$-0.729891\pi$
$23$	−1.77436e6	−1.32211	−0.661055	+	0.750338i	$0.729891\pi$
$24$	−550963.	−0.338978
$25$	790255.	0.404611
$26$	−776059.	−0.333054
$27$	531441.	0.192450
$28$	−944267.	−0.290324
$29$	−1.11174e6	−0.291886	−0.145943	−	0.989293i	$-0.546622\pi$
$29$	−1.11174e6	−0.291886	−0.145943	+	0.989293i	$0.546622\pi$
$30$	935616.	0.210888
$31$	−2.68419e6	−0.522018	−0.261009	−	0.965336i	$-0.584055\pi$
$31$	−2.68419e6	−0.522018	−0.261009	+	0.965336i	$0.584055\pi$
$32$	4.80631e6	0.810283
$33$	754885.	0.110807
$34$	−3.48467e6	−0.447205
$35$	3.37531e6	0.380196
$36$	−3.04014e6	−0.301671
$37$	6.12013e6	0.536850	0.268425	−	0.963301i	$-0.413497\pi$
$37$	6.12013e6	0.536850	0.268425	+	0.963301i	$0.413497\pi$
$38$	3.99319e6	0.310666
$39$	−9.01385e6	−0.623907
$40$	−1.12663e7	−0.695841
$41$	7.80122e6	0.431157	0.215578	−	0.976487i	$-0.430836\pi$
$41$	7.80122e6	0.431157	0.215578	+	0.976487i	$0.430836\pi$
$42$	1.15113e6	0.0570825
$43$	−8.86375e6	−0.395375	−0.197688	−	0.980265i	$-0.563343\pi$
$43$	−8.86375e6	−0.395375	−0.197688	+	0.980265i	$0.563343\pi$
$44$	−4.31837e6	−0.173693
$45$	1.08671e7	0.395054
$46$	−1.23741e7	−0.407476
$47$	8.20162e6	0.245166	0.122583	−	0.992458i	$-0.460882\pi$
$47$	8.20162e6	0.245166	0.122583	+	0.992458i	$0.460882\pi$
$48$	1.53744e7	0.418035
$49$	−3.62008e7	−0.897090
$50$	5.51108e6	0.124702
$51$	−4.04741e7	−0.837744
$52$	5.15644e7	0.977990
$53$	−2.44307e7	−0.425300	−0.212650	−	0.977128i	$-0.568209\pi$
$53$	−2.44307e7	−0.425300	−0.212650	+	0.977128i	$0.568209\pi$
$54$	3.70616e6	0.0593134
$55$	1.54361e7	0.227461
$56$	−1.38614e7	−0.188348
$57$	4.63805e7	0.581967
$58$	−7.75306e6	−0.0899595
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	−6.21659e7	−0.619258
$61$	9.11754e7	0.843128	0.421564	−	0.906799i	$-0.361481\pi$
$61$	9.11754e7	0.843128	0.421564	+	0.906799i	$0.361481\pi$
$62$	−1.87190e7	−0.160887
$63$	1.33703e7	0.106932
$64$	−6.36632e7	−0.474328
$65$	−1.84318e8	−1.28073
$66$	5.26442e6	0.0341509
$67$	−2.68575e7	−0.162828	−0.0814139	−	0.996680i	$-0.525944\pi$
$67$	−2.68575e7	−0.162828	−0.0814139	+	0.996680i	$0.525944\pi$
$68$	2.31535e8	1.31319
$69$	−1.43724e8	−0.763320
$70$	2.35387e7	0.117177
$71$	−3.59390e8	−1.67843	−0.839215	−	0.543800i	$-0.816985\pi$
$71$	−3.59390e8	−1.67843	−0.839215	+	0.543800i	$0.816985\pi$
$72$	−4.46280e7	−0.195709
$73$	−1.80655e8	−0.744557	−0.372278	−	0.928121i	$-0.621423\pi$
$73$	−1.80655e8	−0.744557	−0.372278	+	0.928121i	$0.621423\pi$
$74$	4.26806e7	0.165458
$75$	6.40107e7	0.233602
$76$	−2.65323e8	−0.912249
$77$	1.89918e7	0.0615684
$78$	−6.28608e7	−0.192289
$79$	−4.32646e8	−1.24971	−0.624857	−	0.780739i	$-0.714843\pi$
$79$	−4.32646e8	−1.24971	−0.624857	+	0.780739i	$0.714843\pi$
$80$	3.14381e8	0.858127
$81$	4.30467e7	0.111111
$82$	5.44042e7	0.132883
$83$	−4.86509e8	−1.12523	−0.562613	−	0.826720i	$-0.690204\pi$
$83$	−4.86509e8	−1.12523	−0.562613	+	0.826720i	$0.690204\pi$
$84$	−7.64856e7	−0.167619
$85$	−8.27627e8	−1.71969
$86$	−6.18140e7	−0.121855
$87$	−9.00510e7	−0.168520
$88$	−6.33918e7	−0.112684
$89$	3.77036e8	0.636983	0.318492	−	0.947926i	$-0.396824\pi$
$89$	3.77036e8	0.636983	0.318492	+	0.947926i	$0.396824\pi$
$90$	7.57849e7	0.121756
$91$	−2.26775e8	−0.346665
$92$	8.22180e8	1.19653
$93$	−2.17419e8	−0.301387
$94$	5.71965e7	0.0755604
$95$	9.48404e8	1.19464
$96$	3.89311e8	0.467817
$97$	−2.52026e8	−0.289050	−0.144525	−	0.989501i	$-0.546165\pi$
$97$	−2.52026e8	−0.289050	−0.144525	+	0.989501i	$0.546165\pi$
$98$	−2.52457e8	−0.276484
$99$	6.11457e7	0.0639746
$100$	−3.66177e8	−0.366177
$101$	6.97073e8	0.666549	0.333274	−	0.942830i	$-0.391846\pi$
$101$	6.97073e8	0.666549	0.333274	+	0.942830i	$0.391846\pi$
$102$	−2.82258e8	−0.258194
$103$	7.01753e8	0.614351	0.307176	−	0.951653i	$-0.400616\pi$
$103$	7.01753e8	0.614351	0.307176	+	0.951653i	$0.400616\pi$
$104$	7.56942e8	0.634472
$105$	2.73400e8	0.219506
$106$	−1.70375e8	−0.131078
$107$	1.87738e9	1.38460	0.692301	−	0.721609i	$-0.256597\pi$
$107$	1.87738e9	1.38460	0.692301	+	0.721609i	$0.256597\pi$
$108$	−2.46252e8	−0.174170
$109$	−2.21590e9	−1.50359	−0.751796	−	0.659396i	$-0.770812\pi$
$109$	−2.21590e9	−1.50359	−0.751796	+	0.659396i	$0.770812\pi$
$110$	1.07649e8	0.0701037
$111$	4.95731e8	0.309951
$112$	3.86798e8	0.232275
$113$	−1.76119e9	−1.01614	−0.508069	−	0.861316i	$-0.669640\pi$
$113$	−1.76119e9	−1.01614	−0.508069	+	0.861316i	$0.669640\pi$
$114$	3.23448e8	0.179363
$115$	−2.93891e9	−1.56692
$116$	5.15143e8	0.264160
$117$	−7.30122e8	−0.360213
$118$	8.45041e7	0.0401244
$119$	−1.01827e9	−0.465480
$120$	−9.12568e8	−0.401744
$121$	−2.27109e9	−0.963165
$122$	6.35840e8	0.259853
$123$	6.31899e8	0.248928
$124$	1.24376e9	0.472432
$125$	−1.92608e9	−0.705633
$126$	9.32417e7	0.0329566
$127$	−5.83227e8	−0.198940	−0.0994698	−	0.995041i	$-0.531715\pi$
$127$	−5.83227e8	−0.198940	−0.0994698	+	0.995041i	$0.531715\pi$
$128$	−2.90481e9	−0.956472
$129$	−7.17964e8	−0.228270
$130$	−1.28540e9	−0.394723
$131$	1.83968e9	0.545785	0.272892	−	0.962045i	$-0.412020\pi$
$131$	1.83968e9	0.545785	0.272892	+	0.962045i	$0.412020\pi$
$132$	−3.49788e8	−0.100282
$133$	1.16687e9	0.323361
$134$	−1.87299e8	−0.0501838
$135$	8.80234e8	0.228085
$136$	3.39883e9	0.851930
$137$	−5.44710e9	−1.32106	−0.660530	−	0.750799i	$-0.729668\pi$
$137$	−5.44710e9	−1.32106	−0.660530	+	0.750799i	$0.729668\pi$
$138$	−1.00230e9	−0.235256
$139$	3.96648e9	0.901236	0.450618	−	0.892717i	$-0.351204\pi$
$139$	3.96648e9	0.901236	0.450618	+	0.892717i	$0.351204\pi$
$140$	−1.56400e9	−0.344082
$141$	6.64332e8	0.141546
$142$	−2.50631e9	−0.517294
$143$	−1.03710e9	−0.207400
$144$	1.24533e9	0.241353
$145$	−1.84139e9	−0.345932
$146$	−1.25985e9	−0.229473
$147$	−2.93227e9	−0.517935
$148$	−2.83586e9	−0.485856
$149$	−6.55473e9	−1.08947	−0.544736	−	0.838607i	$-0.683370\pi$
$149$	−6.55473e9	−1.08947	−0.544736	+	0.838607i	$0.683370\pi$
$150$	4.46398e8	0.0719965
$151$	−5.30903e9	−0.831033	−0.415517	−	0.909586i	$-0.636399\pi$
$151$	−5.30903e9	−0.831033	−0.415517	+	0.909586i	$0.636399\pi$
$152$	−3.89482e9	−0.591822
$153$	−3.27840e9	−0.483671
$154$	1.32445e8	0.0189755
$155$	−4.44586e9	−0.618676
$156$	4.17671e9	0.564643
$157$	−1.25372e10	−1.64684	−0.823418	−	0.567435i	$-0.807936\pi$
$157$	−1.25372e10	−1.64684	−0.823418	+	0.567435i	$0.807936\pi$
$158$	−3.01719e9	−0.385164
$159$	−1.97889e9	−0.245547
$160$	7.96076e9	0.960317
$161$	−3.61587e9	−0.424128
$162$	3.00199e8	0.0342446
$163$	−7.70421e9	−0.854838	−0.427419	−	0.904054i	$-0.640577\pi$
$163$	−7.70421e9	−0.854838	−0.427419	+	0.904054i	$0.640577\pi$
$164$	−3.61482e9	−0.390202
$165$	1.25033e9	0.131325
$166$	−3.39282e9	−0.346796
$167$	4.66653e9	0.464270	0.232135	−	0.972684i	$-0.425429\pi$
$167$	4.66653e9	0.464270	0.232135	+	0.972684i	$0.425429\pi$
$168$	−1.12278e9	−0.108743
$169$	1.77921e9	0.167779
$170$	−5.77171e9	−0.530010
$171$	3.75682e9	0.335999
$172$	4.10716e9	0.357819
$173$	−6.30084e9	−0.534800	−0.267400	−	0.963586i	$-0.586164\pi$
$173$	−6.30084e9	−0.534800	−0.267400	+	0.963586i	$0.586164\pi$
$174$	−6.27998e8	−0.0519382
$175$	1.61041e9	0.129798
$176$	1.76892e9	0.138964
$177$	9.81506e8	0.0751646
$178$	2.62938e9	0.196319
$179$	5.49833e9	0.400306	0.200153	−	0.979765i	$-0.435856\pi$
$179$	5.49833e9	0.400306	0.200153	+	0.979765i	$0.435856\pi$
$180$	−5.03544e9	−0.357529
$181$	−3.74888e9	−0.259626	−0.129813	−	0.991539i	$-0.541438\pi$
$181$	−3.74888e9	−0.259626	−0.129813	+	0.991539i	$0.541438\pi$
$182$	−1.58149e9	−0.106843
$183$	7.38521e9	0.486780
$184$	1.20692e10	0.776247
$185$	1.01369e10	0.636255
$186$	−1.51624e9	−0.0928879
$187$	−4.65680e9	−0.278484
$188$	−3.80035e9	−0.221878
$189$	1.08299e9	0.0617373
$190$	6.61398e9	0.368190
$191$	2.90555e10	1.57972	0.789858	−	0.613290i	$-0.210154\pi$
$191$	2.90555e10	1.57972	0.789858	+	0.613290i	$0.210154\pi$
$192$	−5.15672e9	−0.273853
$193$	−2.66990e9	−0.138512	−0.0692560	−	0.997599i	$-0.522063\pi$
$193$	−2.66990e9	−0.138512	−0.0692560	+	0.997599i	$0.522063\pi$
$194$	−1.75758e9	−0.0890855
$195$	−1.49298e10	−0.739431
$196$	1.67742e10	0.811877
$197$	−2.62776e10	−1.24305	−0.621524	−	0.783395i	$-0.713486\pi$
$197$	−2.62776e10	−1.24305	−0.621524	+	0.783395i	$0.713486\pi$
$198$	4.26418e8	0.0197171
$199$	2.52453e10	1.14115	0.570573	−	0.821247i	$-0.306721\pi$
$199$	2.52453e10	1.14115	0.570573	+	0.821247i	$0.306721\pi$
$200$	−5.37532e9	−0.237558
$201$	−2.17546e9	−0.0940087
$202$	4.86125e9	0.205431
$203$	−2.26555e9	−0.0936358
$204$	1.87543e10	0.758168
$205$	1.29213e10	0.510991
$206$	4.89388e9	0.189344
$207$	−1.16416e10	−0.440703
$208$	−2.11222e10	−0.782445
$209$	5.33637e9	0.193458
$210$	1.90664e9	0.0676521
$211$	2.64313e10	0.918010	0.459005	−	0.888434i	$-0.348206\pi$
$211$	2.64313e10	0.918010	0.459005	+	0.888434i	$0.348206\pi$
$212$	1.13204e10	0.384901
$213$	−2.91106e10	−0.969042
$214$	1.30925e10	0.426736
$215$	−1.46812e10	−0.468584
$216$	−3.61487e9	−0.112993
$217$	−5.46995e9	−0.167461
$218$	−1.54532e10	−0.463409
$219$	−1.46331e10	−0.429870
$220$	−7.15258e9	−0.205855
$221$	5.56054e10	1.56802
$222$	3.45713e9	0.0955272
$223$	5.29799e9	0.143463	0.0717314	−	0.997424i	$-0.477148\pi$
$223$	5.29799e9	0.143463	0.0717314	+	0.997424i	$0.477148\pi$
$224$	9.79450e9	0.259936
$225$	5.18486e9	0.134870
$226$	−1.22822e10	−0.313175
$227$	−2.60396e10	−0.650905	−0.325453	−	0.945558i	$-0.605517\pi$
$227$	−2.60396e10	−0.650905	−0.325453	+	0.945558i	$0.605517\pi$
$228$	−2.14911e10	−0.526687
$229$	5.92649e10	1.42409	0.712046	−	0.702133i	$-0.247769\pi$
$229$	5.92649e10	1.42409	0.712046	+	0.702133i	$0.247769\pi$
$230$	−2.04954e10	−0.482926
$231$	1.53834e9	0.0355465
$232$	7.56207e9	0.171374
$233$	4.95948e10	1.10239	0.551194	−	0.834377i	$-0.314172\pi$
$233$	4.95948e10	1.10239	0.551194	+	0.834377i	$0.314172\pi$
$234$	−5.09173e9	−0.111018
$235$	1.35845e10	0.290561
$236$	−5.61477e9	−0.117823
$237$	−3.50443e10	−0.721523
$238$	−7.10120e9	−0.143462
$239$	3.78267e10	0.749909	0.374954	−	0.927043i	$-0.377658\pi$
$239$	3.78267e10	0.749909	0.374954	+	0.927043i	$0.377658\pi$
$240$	2.54649e10	0.495440
$241$	3.74529e9	0.0715170	0.0357585	−	0.999360i	$-0.488615\pi$
$241$	3.74529e9	0.0715170	0.0357585	+	0.999360i	$0.488615\pi$
$242$	−1.58382e10	−0.296849
$243$	3.48678e9	0.0641500
$244$	−4.22476e10	−0.763041
$245$	−5.99599e10	−1.06320
$246$	4.40674e9	0.0767201
$247$	−6.37200e10	−1.08928
$248$	1.82579e10	0.306491
$249$	−3.94073e10	−0.649649
$250$	−1.34321e10	−0.217477
$251$	−6.27144e10	−0.997323	−0.498661	−	0.866797i	$-0.666175\pi$
$251$	−6.27144e10	−0.997323	−0.498661	+	0.866797i	$0.666175\pi$
$252$	−6.19533e9	−0.0967748
$253$	−1.65363e10	−0.253744
$254$	−4.06731e9	−0.0613134
$255$	−6.70378e10	−0.992862
$256$	1.23380e10	0.179542
$257$	5.88644e10	0.841693	0.420846	−	0.907132i	$-0.361733\pi$
$257$	5.88644e10	0.841693	0.420846	+	0.907132i	$0.361733\pi$
$258$	−5.00694e9	−0.0703531
$259$	1.24719e10	0.172220
$260$	8.54068e10	1.15908
$261$	−7.29413e9	−0.0972952
$262$	1.28296e10	0.168212
$263$	−2.79857e10	−0.360691	−0.180345	−	0.983603i	$-0.557722\pi$
$263$	−2.79857e10	−0.360691	−0.180345	+	0.983603i	$0.557722\pi$
$264$	−5.13473e9	−0.0650579
$265$	−4.04650e10	−0.504049
$266$	8.13749e9	0.0996605
$267$	3.05399e10	0.367762
$268$	1.24448e10	0.147361
$269$	9.17632e10	1.06852	0.534261	−	0.845320i	$-0.320590\pi$
$269$	9.17632e10	1.06852	0.534261	+	0.845320i	$0.320590\pi$
$270$	6.13858e9	0.0702960
$271$	6.91684e9	0.0779015	0.0389508	−	0.999241i	$-0.487598\pi$
$271$	6.91684e9	0.0779015	0.0389508	+	0.999241i	$0.487598\pi$
$272$	−9.48430e10	−1.05062
$273$	−1.83688e10	−0.200147
$274$	−3.79870e10	−0.407153
$275$	7.36483e9	0.0776543
$276$	6.65966e10	0.690814
$277$	1.69250e11	1.72731	0.863654	−	0.504085i	$-0.168170\pi$
$277$	1.69250e11	1.72731	0.863654	+	0.504085i	$0.168170\pi$
$278$	2.76614e10	0.277762
$279$	−1.76109e10	−0.174006
$280$	−2.29589e10	−0.223223
$281$	1.14212e11	1.09278	0.546389	−	0.837532i	$-0.316002\pi$
$281$	1.14212e11	1.09278	0.546389	+	0.837532i	$0.316002\pi$
$282$	4.63292e9	0.0436248
$283$	9.35537e10	0.867006	0.433503	−	0.901152i	$-0.357277\pi$
$283$	9.35537e10	0.867006	0.433503	+	0.901152i	$0.357277\pi$
$284$	1.66529e11	1.51900
$285$	7.68207e10	0.689726
$286$	−7.23254e9	−0.0639210
$287$	1.58977e10	0.138313
$288$	3.15342e10	0.270094
$289$	1.31092e11	1.10544
$290$	−1.28415e10	−0.106617
$291$	−2.04141e10	−0.166883
$292$	8.37095e10	0.673833
$293$	7.64105e10	0.605688	0.302844	−	0.953040i	$-0.402064\pi$
$293$	7.64105e10	0.605688	0.302844	+	0.953040i	$0.402064\pi$
$294$	−2.04490e10	−0.159628
$295$	2.00702e10	0.154295
$296$	−4.16292e10	−0.315199
$297$	4.95280e9	0.0369357
$298$	−4.57114e10	−0.335777
$299$	1.97455e11	1.42872
$300$	−2.96604e10	−0.211413
$301$	−1.80629e10	−0.126835
$302$	−3.70241e10	−0.256126
$303$	5.64629e10	0.384832
$304$	1.08684e11	0.729848
$305$	1.51015e11	0.999244
$306$	−2.28629e10	−0.149068
$307$	−4.60264e10	−0.295722	−0.147861	−	0.989008i	$-0.547239\pi$
$307$	−4.60264e10	−0.295722	−0.147861	+	0.989008i	$0.547239\pi$
$308$	−8.80016e9	−0.0557201
$309$	5.68420e10	0.354696
$310$	−3.10045e10	−0.190677
$311$	−9.44043e10	−0.572229	−0.286115	−	0.958195i	$-0.592364\pi$
$311$	−9.44043e10	−0.572229	−0.286115	+	0.958195i	$0.592364\pi$
$312$	6.13123e10	0.366313
$313$	2.92689e11	1.72368	0.861842	−	0.507178i	$-0.169311\pi$
$313$	2.92689e11	1.72368	0.861842	+	0.507178i	$0.169311\pi$
$314$	−8.74316e10	−0.507557
$315$	2.21454e10	0.126732
$316$	2.00473e11	1.13101
$317$	−2.16676e11	−1.20516	−0.602581	−	0.798058i	$-0.705861\pi$
$317$	−2.16676e11	−1.20516	−0.602581	+	0.798058i	$0.705861\pi$
$318$	−1.38004e10	−0.0756779
$319$	−1.03609e10	−0.0560197
$320$	−1.05446e11	−0.562156
$321$	1.52068e11	0.799400
$322$	−2.52164e10	−0.130717
$323$	−2.86116e11	−1.46262
$324$	−1.99464e10	−0.100557
$325$	−8.79413e10	−0.437238
$326$	−5.37276e10	−0.263462
$327$	−1.79488e11	−0.868099
$328$	−5.30640e10	−0.253144
$329$	1.67136e10	0.0786482
$330$	8.71953e9	0.0404744
$331$	2.21936e11	1.01625	0.508125	−	0.861283i	$-0.330339\pi$
$331$	2.21936e11	1.01625	0.508125	+	0.861283i	$0.330339\pi$
$332$	2.25432e11	1.01834
$333$	4.01542e10	0.178950
$334$	3.25435e10	0.143089
$335$	−4.44844e10	−0.192977
$336$	3.13306e10	0.134104
$337$	3.86863e11	1.63389	0.816944	−	0.576717i	$-0.195667\pi$
$337$	3.86863e11	1.63389	0.816944	+	0.576717i	$0.195667\pi$
$338$	1.24079e10	0.0517097
$339$	−1.42656e11	−0.586667
$340$	3.83494e11	1.55634
$341$	−2.50155e10	−0.100188
$342$	2.61993e10	0.103555
$343$	−1.56006e11	−0.608579
$344$	6.02913e10	0.232136
$345$	−2.38051e11	−0.904659
$346$	−4.39408e10	−0.164826
$347$	1.98018e11	0.733198	0.366599	−	0.930379i	$-0.380522\pi$
$347$	1.98018e11	0.733198	0.366599	+	0.930379i	$0.380522\pi$
$348$	4.17266e10	0.152513
$349$	−4.76713e11	−1.72006	−0.860029	−	0.510246i	$-0.829554\pi$
$349$	−4.76713e11	−1.72006	−0.860029	+	0.510246i	$0.829554\pi$
$350$	1.12307e10	0.0400038
$351$	−5.91399e10	−0.207969
$352$	4.47927e10	0.155513
$353$	−2.76454e11	−0.947625	−0.473813	−	0.880626i	$-0.657123\pi$
$353$	−2.76454e11	−0.947625	−0.473813	+	0.880626i	$0.657123\pi$
$354$	6.84483e9	0.0231658
$355$	−5.95263e11	−1.98921
$356$	−1.74706e11	−0.576477
$357$	−8.24798e10	−0.268745
$358$	3.83443e10	0.123375
$359$	−4.47701e11	−1.42254	−0.711268	−	0.702920i	$-0.751879\pi$
$359$	−4.47701e11	−1.42254	−0.711268	+	0.702920i	$0.751879\pi$
$360$	−7.39180e10	−0.231947
$361$	5.18134e9	0.0160568
$362$	−2.61439e10	−0.0800170
$363$	−1.83959e11	−0.556084
$364$	1.05080e11	0.313736
$365$	−2.99222e11	−0.882421
$366$	5.15030e10	0.150026
$367$	3.36782e11	0.969063	0.484531	−	0.874774i	$-0.338990\pi$
$367$	3.36782e11	0.969063	0.484531	+	0.874774i	$0.338990\pi$
$368$	−3.36788e11	−0.957285
$369$	5.11838e10	0.143719
$370$	7.06925e10	0.196095
$371$	−4.97860e10	−0.136435
$372$	1.00745e11	0.272759
$373$	−4.94266e11	−1.32212	−0.661061	−	0.750333i	$-0.729893\pi$
$373$	−4.94266e11	−1.32212	−0.661061	+	0.750333i	$0.729893\pi$
$374$	−3.24756e10	−0.0858292
$375$	−1.56012e11	−0.407398
$376$	−5.57875e10	−0.143943
$377$	1.23717e11	0.315423
$378$	7.55258e9	0.0190275
$379$	4.73473e11	1.17874	0.589371	−	0.807862i	$-0.299375\pi$
$379$	4.73473e11	1.17874	0.589371	+	0.807862i	$0.299375\pi$
$380$	−4.39458e11	−1.08116
$381$	−4.72414e10	−0.114858
$382$	2.02628e11	0.486871
$383$	2.96289e11	0.703593	0.351796	−	0.936077i	$-0.385571\pi$
$383$	2.96289e11	0.703593	0.351796	+	0.936077i	$0.385571\pi$
$384$	−2.35289e11	−0.552219
$385$	3.14564e10	0.0729686
$386$	−1.86194e10	−0.0426896
$387$	−5.81551e10	−0.131792
$388$	1.16780e11	0.261593
$389$	−4.72137e11	−1.04543	−0.522715	−	0.852507i	$-0.675081\pi$
$389$	−4.72137e11	−1.04543	−0.522715	+	0.852507i	$0.675081\pi$
$390$	−1.04117e11	−0.227894
$391$	8.86614e11	1.91840
$392$	2.46238e11	0.526706
$393$	1.49014e11	0.315109
$394$	−1.83255e11	−0.383109
$395$	−7.16598e11	−1.48111
$396$	−2.83328e10	−0.0578977
$397$	5.41550e10	0.109416	0.0547080	−	0.998502i	$-0.482577\pi$
$397$	5.41550e10	0.109416	0.0547080	+	0.998502i	$0.482577\pi$
$398$	1.76056e11	0.351703
$399$	9.45161e10	0.186693
$400$	1.49996e11	0.292962
$401$	2.07074e11	0.399923	0.199962	−	0.979804i	$-0.435918\pi$
$401$	2.07074e11	0.399923	0.199962	+	0.979804i	$0.435918\pi$
$402$	−1.51712e10	−0.0289736
$403$	2.98702e11	0.564112
$404$	−3.23000e11	−0.603235
$405$	7.12989e10	0.131685
$406$	−1.57995e10	−0.0288587
$407$	5.70370e10	0.103034
$408$	2.75305e11	0.491862
$409$	−2.67467e11	−0.472624	−0.236312	−	0.971677i	$-0.575939\pi$
$409$	−2.67467e11	−0.472624	−0.236312	+	0.971677i	$0.575939\pi$
$410$	9.01105e10	0.157488
$411$	−4.41215e11	−0.762715
$412$	−3.25168e11	−0.555995
$413$	2.46933e10	0.0417641
$414$	−8.11862e10	−0.135825
$415$	−8.05813e11	−1.33358
$416$	−5.34856e11	−0.875623
$417$	3.21285e11	0.520329
$418$	3.72148e10	0.0596241
$419$	−1.06460e10	−0.0168742	−0.00843708	−	0.999964i	$-0.502686\pi$
$419$	−1.06460e10	−0.0168742	−0.00843708	+	0.999964i	$0.502686\pi$
$420$	−1.26684e11	−0.198656
$421$	−8.05067e11	−1.24900	−0.624500	−	0.781025i	$-0.714697\pi$
$421$	−8.05067e11	−1.24900	−0.624500	+	0.781025i	$0.714697\pi$
$422$	1.84327e11	0.282932
$423$	5.38109e10	0.0817219
$424$	1.66178e11	0.249705
$425$	−3.94874e11	−0.587096
$426$	−2.03011e11	−0.298660
$427$	1.85801e11	0.270472
$428$	−8.69913e11	−1.25308
$429$	−8.40052e10	−0.119742
$430$	−1.02384e11	−0.144418
$431$	3.73994e10	0.0522056	0.0261028	−	0.999659i	$-0.491690\pi$
$431$	3.73994e10	0.0522056	0.0261028	+	0.999659i	$0.491690\pi$
$432$	1.00872e11	0.139345
$433$	−6.09034e11	−0.832619	−0.416309	−	0.909223i	$-0.636677\pi$
$433$	−6.09034e11	−0.832619	−0.416309	+	0.909223i	$0.636677\pi$
$434$	−3.81463e10	−0.0516118
$435$	−1.49153e11	−0.199724
$436$	1.02677e12	1.36077
$437$	−1.01600e12	−1.33268
$438$	−1.02048e11	−0.132487
$439$	1.17139e12	1.50525	0.752626	−	0.658448i	$-0.228787\pi$
$439$	1.17139e12	1.50525	0.752626	+	0.658448i	$0.228787\pi$
$440$	−1.04997e11	−0.133548
$441$	−2.37513e11	−0.299030
$442$	3.87781e11	0.483266
$443$	1.76734e11	0.218023	0.109012	−	0.994040i	$-0.465231\pi$
$443$	1.76734e11	0.218023	0.109012	+	0.994040i	$0.465231\pi$
$444$	−2.29705e11	−0.280509
$445$	6.24491e11	0.754929
$446$	3.69471e10	0.0442154
$447$	−5.30933e11	−0.629007
$448$	−1.29736e11	−0.152163
$449$	−2.81182e11	−0.326497	−0.163249	−	0.986585i	$-0.552197\pi$
$449$	−2.81182e11	−0.326497	−0.163249	+	0.986585i	$0.552197\pi$
$450$	3.61582e10	0.0415672
$451$	7.27040e10	0.0827492
$452$	8.16074e11	0.919617
$453$	−4.30031e11	−0.479797
$454$	−1.81595e11	−0.200610
$455$	−3.75611e11	−0.410854
$456$	−3.15480e11	−0.341689
$457$	8.82306e11	0.946229	0.473115	−	0.881001i	$-0.343130\pi$
$457$	8.82306e11	0.946229	0.473115	+	0.881001i	$0.343130\pi$
$458$	4.13302e11	0.438907
$459$	−2.65550e11	−0.279248
$460$	1.36179e12	1.41808
$461$	1.12815e12	1.16336	0.581679	−	0.813419i	$-0.302396\pi$
$461$	1.12815e12	1.16336	0.581679	+	0.813419i	$0.302396\pi$
$462$	1.07280e10	0.0109555
$463$	−4.66156e11	−0.471429	−0.235715	−	0.971822i	$-0.575743\pi$
$463$	−4.66156e11	−0.471429	−0.235715	+	0.971822i	$0.575743\pi$
$464$	−2.11017e11	−0.211342
$465$	−3.60115e11	−0.357193
$466$	3.45864e11	0.339757
$467$	−1.11435e12	−1.08416	−0.542081	−	0.840326i	$-0.682363\pi$
$467$	−1.11435e12	−1.08416	−0.542081	+	0.840326i	$0.682363\pi$
$468$	3.38314e11	0.325997
$469$	−5.47313e10	−0.0522346
$470$	9.47354e10	0.0895513
$471$	−1.01551e12	−0.950801
$472$	−8.24224e10	−0.0764375
$473$	−8.26063e10	−0.0758819
$474$	−2.44392e11	−0.222374
$475$	4.52499e11	0.407846
$476$	4.71831e11	0.421265
$477$	−1.60290e11	−0.141767
$478$	2.63796e11	0.231123
$479$	−1.46666e11	−0.127298	−0.0636488	−	0.997972i	$-0.520274\pi$
$479$	−1.46666e11	−0.127298	−0.0636488	+	0.997972i	$0.520274\pi$
$480$	6.44822e11	0.554440
$481$	−6.81061e11	−0.580141
$482$	2.61189e10	0.0220416
$483$	−2.92886e11	−0.244870
$484$	1.05235e12	0.871676
$485$	−4.17435e11	−0.342571
$486$	2.43161e10	0.0197711
$487$	−3.30530e11	−0.266276	−0.133138	−	0.991098i	$-0.542505\pi$
$487$	−3.30530e11	−0.266276	−0.133138	+	0.991098i	$0.542505\pi$
$488$	−6.20176e11	−0.495024
$489$	−6.24041e11	−0.493541
$490$	−4.18149e11	−0.327679
$491$	−1.27609e12	−0.990866	−0.495433	−	0.868646i	$-0.664991\pi$
$491$	−1.27609e12	−0.990866	−0.495433	+	0.868646i	$0.664991\pi$
$492$	−2.92801e11	−0.225283
$493$	5.55514e11	0.423530
$494$	−4.44370e11	−0.335717
$495$	1.01276e11	0.0758203
$496$	−5.09479e11	−0.377971
$497$	−7.32379e11	−0.538434
$498$	−2.74818e11	−0.200223
$499$	1.53938e11	0.111146	0.0555730	−	0.998455i	$-0.482301\pi$
$499$	1.53938e11	0.111146	0.0555730	+	0.998455i	$0.482301\pi$
$500$	8.92480e11	0.638607
$501$	3.77989e11	0.268046
$502$	−4.37358e11	−0.307376
$503$	−1.40720e12	−0.980165	−0.490082	−	0.871676i	$-0.663033\pi$
$503$	−1.40720e12	−0.980165	−0.490082	+	0.871676i	$0.663033\pi$
$504$	−9.09448e10	−0.0627828
$505$	1.15457e12	0.789969
$506$	−1.15321e11	−0.0782043
$507$	1.44116e11	0.0968672
$508$	2.70248e11	0.180043
$509$	2.46798e12	1.62971	0.814856	−	0.579663i	$-0.196816\pi$
$509$	2.46798e12	1.62971	0.814856	+	0.579663i	$0.196816\pi$
$510$	−4.67508e11	−0.306002
$511$	−3.68147e11	−0.238851
$512$	1.57330e12	1.01181
$513$	3.04302e11	0.193989
$514$	4.10509e11	0.259411
$515$	1.16232e12	0.728106
$516$	3.32680e11	0.206587
$517$	7.64356e10	0.0470531
$518$	8.69763e10	0.0530783
$519$	−5.10368e11	−0.308767
$520$	1.25373e12	0.751953
$521$	1.13556e12	0.675211	0.337606	−	0.941288i	$-0.390383\pi$
$521$	1.13556e12	0.675211	0.337606	+	0.941288i	$0.390383\pi$
$522$	−5.08678e10	−0.0299865
$523$	−1.50720e12	−0.880874	−0.440437	−	0.897783i	$-0.645177\pi$
$523$	−1.50720e12	−0.880874	−0.440437	+	0.897783i	$0.645177\pi$
$524$	−8.52445e11	−0.493942
$525$	1.30444e11	0.0749387
$526$	−1.95167e11	−0.111165
$527$	1.34123e12	0.757455
$528$	1.43283e11	0.0802309
$529$	1.34722e12	0.747975
$530$	−2.82195e11	−0.155349
$531$	7.95020e10	0.0433963
$532$	−5.40686e11	−0.292646
$533$	−8.68136e11	−0.465924
$534$	2.12979e11	0.113345
$535$	3.10953e12	1.64098
$536$	1.82685e11	0.0956007
$537$	4.45365e11	0.231117
$538$	6.39938e11	0.329320
$539$	−3.37376e11	−0.172173
$540$	−4.07870e11	−0.206419
$541$	1.81202e12	0.909441	0.454720	−	0.890634i	$-0.349739\pi$
$541$	1.81202e12	0.909441	0.454720	+	0.890634i	$0.349739\pi$
$542$	4.82367e10	0.0240094
$543$	−3.03659e11	−0.149895
$544$	−2.40162e12	−1.17573
$545$	−3.67022e12	−1.78200
$546$	−1.28100e11	−0.0616856
$547$	−1.11829e12	−0.534088	−0.267044	−	0.963684i	$-0.586047\pi$
$547$	−1.11829e12	−0.534088	−0.267044	+	0.963684i	$0.586047\pi$
$548$	2.52400e12	1.19558
$549$	5.98202e11	0.281043
$550$	5.13609e10	0.0239332
$551$	−6.36581e11	−0.294220
$552$	9.77609e11	0.448166
$553$	−8.81664e11	−0.400903
$554$	1.18032e12	0.532359
$555$	8.21086e11	0.367342
$556$	−1.83793e12	−0.815629
$557$	1.83564e12	0.808052	0.404026	−	0.914748i	$-0.367611\pi$
$557$	1.83564e12	0.808052	0.404026	+	0.914748i	$0.367611\pi$
$558$	−1.22815e11	−0.0536288
$559$	9.86377e11	0.427258
$560$	6.40659e11	0.275284
$561$	−3.77201e11	−0.160783
$562$	7.96489e11	0.336795
$563$	−1.13767e12	−0.477230	−0.238615	−	0.971114i	$-0.576693\pi$
$563$	−1.13767e12	−0.477230	−0.238615	+	0.971114i	$0.576693\pi$
$564$	−3.07829e11	−0.128101
$565$	−2.91708e12	−1.20429
$566$	6.52425e11	0.267212
$567$	8.77224e10	0.0356440
$568$	2.44457e12	0.985452
$569$	−2.07358e12	−0.829308	−0.414654	−	0.909979i	$-0.636097\pi$
$569$	−2.07358e12	−0.829308	−0.414654	+	0.909979i	$0.636097\pi$
$570$	5.35732e11	0.212574
$571$	1.61959e12	0.637591	0.318796	−	0.947824i	$-0.396722\pi$
$571$	1.61959e12	0.637591	0.318796	+	0.947824i	$0.396722\pi$
$572$	4.80557e11	0.187700
$573$	2.35350e12	0.912049
$574$	1.10867e11	0.0426284
$575$	−1.40220e12	−0.534940
$576$	−4.17694e11	−0.158109
$577$	2.97523e12	1.11745	0.558727	−	0.829351i	$-0.311290\pi$
$577$	2.97523e12	1.11745	0.558727	+	0.829351i	$0.311290\pi$
$578$	9.14210e11	0.340699
$579$	−2.16262e11	−0.0799700
$580$	8.53239e11	0.313072
$581$	−9.91429e11	−0.360968
$582$	−1.42364e11	−0.0514336
$583$	−2.27684e11	−0.0816251
$584$	1.22882e12	0.437150
$585$	−1.20931e12	−0.426911
$586$	5.32872e11	0.186674
$587$	−6.58615e10	−0.0228960	−0.0114480	−	0.999934i	$-0.503644\pi$
$587$	−6.58615e10	−0.0228960	−0.0114480	+	0.999934i	$0.503644\pi$
$588$	1.35871e12	0.468737
$589$	−1.53696e12	−0.526192
$590$	1.39965e11	0.0475539
$591$	−2.12849e12	−0.717675
$592$	1.16165e12	0.388711
$593$	2.01058e12	0.667692	0.333846	−	0.942628i	$-0.391654\pi$
$593$	2.01058e12	0.667692	0.333846	+	0.942628i	$0.391654\pi$
$594$	3.45398e10	0.0113836
$595$	−1.68657e12	−0.551669
$596$	3.03724e12	0.985986
$597$	2.04487e12	0.658841
$598$	1.37701e12	0.440334
$599$	2.89415e12	0.918544	0.459272	−	0.888296i	$-0.348110\pi$
$599$	2.89415e12	0.918544	0.459272	+	0.888296i	$0.348110\pi$
$600$	−4.35401e11	−0.137154
$601$	2.23107e12	0.697553	0.348777	−	0.937206i	$-0.386597\pi$
$601$	2.23107e12	0.697553	0.348777	+	0.937206i	$0.386597\pi$
$602$	−1.25967e11	−0.0390907
$603$	−1.76212e11	−0.0542759
$604$	2.46002e12	0.752095
$605$	−3.76165e12	−1.14151
$606$	3.93761e11	0.118606
$607$	−4.90097e12	−1.46532	−0.732660	−	0.680595i	$-0.761721\pi$
$607$	−4.90097e12	−1.46532	−0.732660	+	0.680595i	$0.761721\pi$
$608$	2.75209e12	0.816763
$609$	−1.83510e11	−0.0540606
$610$	1.05315e12	0.307968
$611$	−9.12694e11	−0.264935
$612$	1.51910e12	0.437728
$613$	5.95404e11	0.170310	0.0851548	−	0.996368i	$-0.472862\pi$
$613$	5.95404e11	0.170310	0.0851548	+	0.996368i	$0.472862\pi$
$614$	−3.20979e11	−0.0911421
$615$	1.04662e12	0.295021
$616$	−1.29182e11	−0.0361485
$617$	−6.95953e12	−1.93329	−0.966645	−	0.256122i	$-0.917555\pi$
$617$	−6.95953e12	−1.93329	−0.966645	+	0.256122i	$0.917555\pi$
$618$	3.96405e11	0.109318
$619$	3.61258e12	0.989031	0.494515	−	0.869169i	$-0.335346\pi$
$619$	3.61258e12	0.989031	0.494515	+	0.869169i	$0.335346\pi$
$620$	2.06006e12	0.559909
$621$	−9.42970e11	−0.254440
$622$	−6.58357e11	−0.176362
$623$	7.68340e11	0.204342
$624$	−1.71090e12	−0.451745
$625$	−4.73366e12	−1.24090
$626$	2.04116e12	0.531242
$627$	4.32246e11	0.111693
$628$	5.80929e12	1.49041
$629$	−3.05811e12	−0.778977
$630$	1.54438e11	0.0390590
$631$	−6.30561e12	−1.58342	−0.791709	−	0.610899i	$-0.790808\pi$
$631$	−6.30561e12	−1.58342	−0.791709	+	0.610899i	$0.790808\pi$
$632$	2.94286e12	0.733741
$633$	2.14094e12	0.530014
$634$	−1.51106e12	−0.371432
$635$	−9.66008e11	−0.235776
$636$	9.16950e11	0.222223
$637$	4.02850e12	0.969429
$638$	−7.22551e10	−0.0172654
$639$	−2.35796e12	−0.559476
$640$	−4.81127e12	−1.13357
$641$	−1.20099e12	−0.280982	−0.140491	−	0.990082i	$-0.544868\pi$
$641$	−1.20099e12	−0.280982	−0.140491	+	0.990082i	$0.544868\pi$
$642$	1.06049e12	0.246376
$643$	−6.88682e12	−1.58880	−0.794400	−	0.607394i	$-0.792215\pi$
$643$	−6.88682e12	−1.58880	−0.794400	+	0.607394i	$0.792215\pi$
$644$	1.67547e12	0.383841
$645$	−1.18917e12	−0.270537
$646$	−1.99532e12	−0.450781
$647$	−5.02747e12	−1.12793	−0.563963	−	0.825800i	$-0.690724\pi$
$647$	−5.02747e12	−1.12793	−0.563963	+	0.825800i	$0.690724\pi$
$648$	−2.92804e11	−0.0652364
$649$	1.12929e11	0.0249863
$650$	−6.13285e11	−0.134757
$651$	−4.43066e11	−0.0966838
$652$	3.56987e12	0.773639
$653$	7.99080e12	1.71981	0.859906	−	0.510453i	$-0.170522\pi$
$653$	7.99080e12	1.71981	0.859906	+	0.510453i	$0.170522\pi$
$654$	−1.25171e12	−0.267549
$655$	3.04709e12	0.646843
$656$	1.48073e12	0.312183
$657$	−1.18528e12	−0.248186
$658$	1.16557e11	0.0242395
$659$	1.08821e12	0.224765	0.112383	−	0.993665i	$-0.464152\pi$
$659$	1.08821e12	0.224765	0.112383	+	0.993665i	$0.464152\pi$
$660$	−5.79359e11	−0.118850
$661$	−7.12468e12	−1.45164	−0.725820	−	0.687885i	$-0.758539\pi$
$661$	−7.12468e12	−1.45164	−0.725820	+	0.687885i	$0.758539\pi$
$662$	1.54773e12	0.313210
$663$	4.50404e12	0.905298
$664$	3.30924e12	0.660651
$665$	1.93270e12	0.383236
$666$	2.80027e11	0.0551527
$667$	1.97263e12	0.385905
$668$	−2.16231e12	−0.420170
$669$	4.29137e11	0.0828283
$670$	−3.10226e11	−0.0594759
$671$	8.49716e11	0.161816
$672$	7.93354e11	0.150074
$673$	2.58329e12	0.485407	0.242703	−	0.970101i	$-0.421966\pi$
$673$	2.58329e12	0.485407	0.242703	+	0.970101i	$0.421966\pi$
$674$	2.69790e12	0.503567
$675$	4.19974e11	0.0778673
$676$	−8.24426e11	−0.151842
$677$	−3.72169e12	−0.680913	−0.340456	−	0.940260i	$-0.610582\pi$
$677$	−3.72169e12	−0.680913	−0.340456	+	0.940260i	$0.610582\pi$
$678$	−9.94856e11	−0.180812
$679$	−5.13589e11	−0.0927261
$680$	5.62953e12	1.00968
$681$	−2.10921e12	−0.375800
$682$	−1.74453e11	−0.0308779
$683$	−9.43594e12	−1.65917	−0.829587	−	0.558378i	$-0.811424\pi$
$683$	−9.43594e12	−1.65917	−0.829587	+	0.558378i	$0.811424\pi$
$684$	−1.74078e12	−0.304083
$685$	−9.02211e12	−1.56567
$686$	−1.08795e12	−0.187565
$687$	4.80046e12	0.822199
$688$	−1.68241e12	−0.286275
$689$	2.71870e12	0.459595
$690$	−1.66012e12	−0.278817
$691$	6.76124e12	1.12817	0.564085	−	0.825716i	$-0.309229\pi$
$691$	6.76124e12	1.12817	0.564085	+	0.825716i	$0.309229\pi$
$692$	2.91960e12	0.484000
$693$	1.24605e11	0.0205228
$694$	1.38094e12	0.225973
$695$	6.56974e12	1.06811
$696$	6.12528e11	0.0989428
$697$	−3.89811e12	−0.625615
$698$	−3.32450e12	−0.530124
$699$	4.01718e12	0.636464
$700$	−7.46212e11	−0.117468
$701$	−1.74524e12	−0.272976	−0.136488	−	0.990642i	$-0.543581\pi$
$701$	−1.74524e12	−0.272976	−0.136488	+	0.990642i	$0.543581\pi$
$702$	−4.12430e11	−0.0640963
$703$	3.50438e12	0.541143
$704$	−5.93314e11	−0.0910348
$705$	1.10034e12	0.167756
$706$	−1.92794e12	−0.292060
$707$	1.42052e12	0.213826
$708$	−4.54797e11	−0.0680249
$709$	9.43306e12	1.40199	0.700994	−	0.713167i	$-0.252740\pi$
$709$	9.43306e12	1.40199	0.700994	+	0.713167i	$0.252740\pi$
$710$	−4.15124e12	−0.613078
$711$	−2.83859e12	−0.416571
$712$	−2.56460e12	−0.373990
$713$	4.76272e12	0.690165
$714$	−5.75197e11	−0.0828276
$715$	−1.71777e12	−0.245803
$716$	−2.54774e12	−0.362282
$717$	3.06397e12	0.432960
$718$	−3.12218e12	−0.438428
$719$	9.24288e12	1.28981	0.644907	−	0.764261i	$-0.276896\pi$
$719$	9.24288e12	1.28981	0.644907	+	0.764261i	$0.276896\pi$
$720$	2.06265e12	0.286042
$721$	1.43006e12	0.197082
$722$	3.61336e10	0.00494873
$723$	3.03369e11	0.0412904
$724$	1.73710e12	0.234964
$725$	−8.78559e11	−0.118100
$726$	−1.28289e12	−0.171386
$727$	9.55964e12	1.26922	0.634610	−	0.772833i	$-0.281161\pi$
$727$	9.55964e12	1.26922	0.634610	+	0.772833i	$0.281161\pi$
$728$	1.54253e12	0.203536
$729$	2.82430e11	0.0370370
$730$	−2.08672e12	−0.271963
$731$	4.42904e12	0.573695
$732$	−3.42206e12	−0.440542
$733$	−7.41098e12	−0.948217	−0.474108	−	0.880466i	$-0.657230\pi$
$733$	−7.41098e12	−0.948217	−0.474108	+	0.880466i	$0.657230\pi$
$734$	2.34865e12	0.298666
$735$	−4.85676e12	−0.613837
$736$	−8.52814e12	−1.07128
$737$	−2.50300e11	−0.0312505
$738$	3.56946e11	0.0442944
$739$	6.76149e12	0.833955	0.416978	−	0.908917i	$-0.363089\pi$
$739$	6.76149e12	0.833955	0.416978	+	0.908917i	$0.363089\pi$
$740$	−4.69708e12	−0.575818
$741$	−5.16132e12	−0.628896
$742$	−3.47198e11	−0.0420493
$743$	−3.63997e12	−0.438176	−0.219088	−	0.975705i	$-0.570308\pi$
$743$	−3.63997e12	−0.438176	−0.219088	+	0.975705i	$0.570308\pi$
$744$	1.47889e12	0.176953
$745$	−1.08567e13	−1.29120
$746$	−3.44692e12	−0.407480
$747$	−3.19199e12	−0.375075
$748$	2.15780e12	0.252031
$749$	3.82580e12	0.444175
$750$	−1.08800e12	−0.125561
$751$	−9.87646e12	−1.13298	−0.566489	−	0.824069i	$-0.691699\pi$
$751$	−9.87646e12	−1.13298	−0.566489	+	0.824069i	$0.691699\pi$
$752$	1.55673e12	0.177514
$753$	−5.07987e12	−0.575804
$754$	8.62777e11	0.0972137
$755$	−8.79342e12	−0.984910
$756$	−5.01822e11	−0.0558730
$757$	9.86774e11	0.109216	0.0546080	−	0.998508i	$-0.482609\pi$
$757$	9.86774e11	0.109216	0.0546080	+	0.998508i	$0.482609\pi$
$758$	3.30191e12	0.363290
$759$	−1.33944e12	−0.146499
$760$	−6.45105e12	−0.701406
$761$	9.66515e12	1.04467	0.522333	−	0.852741i	$-0.325062\pi$
$761$	9.66515e12	1.04467	0.522333	+	0.852741i	$0.325062\pi$
$762$	−3.29452e11	−0.0353993
$763$	−4.51564e12	−0.482347
$764$	−1.34634e13	−1.42966
$765$	−5.43006e12	−0.573229
$766$	2.06626e12	0.216848
$767$	−1.34845e12	−0.140687
$768$	9.99381e11	0.103659
$769$	9.61157e11	0.0991119	0.0495560	−	0.998771i	$-0.484219\pi$
$769$	9.61157e11	0.0991119	0.0495560	+	0.998771i	$0.484219\pi$
$770$	2.19371e11	0.0224890
$771$	4.76802e12	0.485952
$772$	1.23714e12	0.125355
$773$	1.38282e12	0.139302	0.0696512	−	0.997571i	$-0.477811\pi$
$773$	1.38282e12	0.139302	0.0696512	+	0.997571i	$0.477811\pi$
$774$	−4.05562e11	−0.0406184
$775$	−2.12119e12	−0.211214
$776$	1.71428e12	0.169709
$777$	1.01022e12	0.0994310
$778$	−3.29259e12	−0.322203
$779$	4.46697e12	0.434604
$780$	6.91795e12	0.669194
$781$	−3.34936e12	−0.322130
$782$	6.18307e12	0.591254
$783$	−5.90825e11	−0.0561734
$784$	−6.87119e12	−0.649545
$785$	−2.07655e13	−1.95177
$786$	1.03919e12	0.0971170
$787$	8.16174e12	0.758396	0.379198	−	0.925315i	$-0.376200\pi$
$787$	8.16174e12	0.758396	0.379198	+	0.925315i	$0.376200\pi$
$788$	1.21762e13	1.12497
$789$	−2.26684e12	−0.208245
$790$	−4.99741e12	−0.456481
$791$	−3.58902e12	−0.325973
$792$	−4.15913e11	−0.0375612
$793$	−1.01462e13	−0.911117
$794$	3.77666e11	0.0337222
$795$	−3.27766e12	−0.291013
$796$	−1.16978e13	−1.03275
$797$	7.82220e12	0.686699	0.343350	−	0.939208i	$-0.388438\pi$
$797$	7.82220e12	0.686699	0.343350	+	0.939208i	$0.388438\pi$
$798$	6.59136e11	0.0575390
$799$	−4.09819e12	−0.355739
$800$	3.79821e12	0.327849
$801$	2.47373e12	0.212328
$802$	1.44410e12	0.123257
$803$	−1.68363e12	−0.142898
$804$	1.00803e12	0.0850790
$805$	−5.98903e12	−0.502661
$806$	2.08309e12	0.173860
$807$	7.43282e12	0.616911
$808$	−4.74150e12	−0.391349
$809$	−1.50184e13	−1.23270	−0.616349	−	0.787473i	$-0.711389\pi$
$809$	−1.50184e13	−1.23270	−0.616349	+	0.787473i	$0.711389\pi$
$810$	4.97225e11	0.0405854
$811$	−5.72708e12	−0.464878	−0.232439	−	0.972611i	$-0.574671\pi$
$811$	−5.72708e12	−0.464878	−0.232439	+	0.972611i	$0.574671\pi$
$812$	1.04978e12	0.0847415
$813$	5.60264e11	0.0449765
$814$	3.97765e11	0.0317553
$815$	−1.27606e13	−1.01312
$816$	−7.68228e12	−0.606575
$817$	−5.07537e12	−0.398537
$818$	−1.86526e12	−0.145663
$819$	−1.48787e12	−0.115555
$820$	−5.98728e12	−0.462453
$821$	6.35671e12	0.488301	0.244151	−	0.969737i	$-0.421491\pi$
$821$	6.35671e12	0.488301	0.244151	+	0.969737i	$0.421491\pi$
$822$	−3.07695e12	−0.235070
$823$	−3.22525e12	−0.245055	−0.122528	−	0.992465i	$-0.539100\pi$
$823$	−3.22525e12	−0.245055	−0.122528	+	0.992465i	$0.539100\pi$
$824$	−4.77333e12	−0.360702
$825$	5.96551e11	0.0448338
$826$	1.72206e11	0.0128718
$827$	1.04678e12	0.0778184	0.0389092	−	0.999243i	$-0.487612\pi$
$827$	1.04678e12	0.0778184	0.0389092	+	0.999243i	$0.487612\pi$
$828$	5.39432e12	0.398842
$829$	3.56167e12	0.261914	0.130957	−	0.991388i	$-0.458195\pi$
$829$	3.56167e12	0.261914	0.130957	+	0.991388i	$0.458195\pi$
$830$	−5.61958e12	−0.411010
$831$	1.37093e13	0.997262
$832$	7.08458e12	0.512577
$833$	1.80888e13	1.30169
$834$	2.24058e12	0.160366
$835$	7.72925e12	0.550235
$836$	−2.47269e12	−0.175082
$837$	−1.42649e12	−0.100462
$838$	−7.42429e10	−0.00520064
$839$	−7.82346e12	−0.545092	−0.272546	−	0.962143i	$-0.587866\pi$
$839$	−7.82346e12	−0.545092	−0.272546	+	0.962143i	$0.587866\pi$
$840$	−1.85967e12	−0.128878
$841$	−1.32712e13	−0.914803
$842$	−5.61438e12	−0.384944
$843$	9.25114e12	0.630915
$844$	−1.22474e13	−0.830810
$845$	2.94694e12	0.198845
$846$	3.75266e11	0.0251868
$847$	−4.62813e12	−0.308980
$848$	−4.63714e12	−0.307942
$849$	7.57785e12	0.500566
$850$	−2.75378e12	−0.180944
$851$	−1.08593e13	−0.709775
$852$	1.34889e13	0.876994
$853$	1.80541e13	1.16763	0.583815	−	0.811886i	$-0.301559\pi$
$853$	1.80541e13	1.16763	0.583815	+	0.811886i	$0.301559\pi$
$854$	1.29574e12	0.0833600
$855$	6.22248e12	0.398213
$856$	−1.27699e13	−0.812937
$857$	5.49137e12	0.347750	0.173875	−	0.984768i	$-0.444371\pi$
$857$	5.49137e12	0.347750	0.173875	+	0.984768i	$0.444371\pi$
$858$	−5.85835e11	−0.0369048
$859$	2.01758e13	1.26433	0.632167	−	0.774832i	$-0.282166\pi$
$859$	2.01758e13	1.26433	0.632167	+	0.774832i	$0.282166\pi$
$860$	6.80275e12	0.424074
$861$	1.28771e12	0.0798553
$862$	2.60816e11	0.0160898
$863$	−2.20984e13	−1.35617	−0.678083	−	0.734985i	$-0.737189\pi$
$863$	−2.20984e13	−1.35617	−0.678083	+	0.734985i	$0.737189\pi$
$864$	2.55427e12	0.155939
$865$	−1.04362e13	−0.633825
$866$	−4.24729e12	−0.256614
$867$	1.06185e13	0.638228
$868$	2.53459e12	0.151554
$869$	−4.03207e12	−0.239850
$870$	−1.04016e12	−0.0615552
$871$	2.98876e12	0.175958
$872$	1.50725e13	0.882800
$873$	−1.65354e12	−0.0963499
$874$	−7.08537e12	−0.410734
$875$	−3.92505e12	−0.226365
$876$	6.78047e12	0.389037
$877$	−1.18555e13	−0.676739	−0.338369	−	0.941013i	$-0.609875\pi$
$877$	−1.18555e13	−0.676739	−0.338369	+	0.941013i	$0.609875\pi$
$878$	8.16901e12	0.463921
$879$	6.18925e12	0.349694
$880$	2.92990e12	0.164695
$881$	−1.15586e12	−0.0646419	−0.0323209	−	0.999478i	$-0.510290\pi$
$881$	−1.15586e12	−0.0646419	−0.0323209	+	0.999478i	$0.510290\pi$
$882$	−1.65637e12	−0.0921614
$883$	−3.02410e12	−0.167407	−0.0837035	−	0.996491i	$-0.526675\pi$
$883$	−3.02410e12	−0.167407	−0.0837035	+	0.996491i	$0.526675\pi$
$884$	−2.57657e13	−1.41908
$885$	1.62568e12	0.0890823
$886$	1.23251e12	0.0671951
$887$	2.27028e13	1.23147	0.615735	−	0.787953i	$-0.288859\pi$
$887$	2.27028e13	1.23147	0.615735	+	0.787953i	$0.288859\pi$
$888$	−3.37197e12	−0.181980
$889$	−1.18852e12	−0.0638191
$890$	4.35507e12	0.232670
$891$	4.01177e11	0.0213249
$892$	−2.45491e12	−0.129836
$893$	4.69624e12	0.247126
$894$	−3.70262e12	−0.193861
$895$	9.10697e12	0.474428
$896$	−5.91953e12	−0.306833
$897$	1.59939e13	0.824873
$898$	−1.96091e12	−0.100627
$899$	2.98412e12	0.152369
$900$	−2.40249e12	−0.122059
$901$	1.22075e13	0.617116
$902$	5.07023e11	0.0255034
$903$	−1.46310e12	−0.0732282
$904$	1.19796e13	0.596602
$905$	−6.20932e12	−0.307699
$906$	−2.99895e12	−0.147874
$907$	−2.05820e13	−1.00984	−0.504922	−	0.863165i	$-0.668479\pi$
$907$	−2.05820e13	−1.00984	−0.504922	+	0.863165i	$0.668479\pi$
$908$	1.20659e13	0.589077
$909$	4.57350e12	0.222183
$910$	−2.61944e12	−0.126626
$911$	−1.51079e13	−0.726726	−0.363363	−	0.931648i	$-0.618372\pi$
$911$	−1.51079e13	−0.726726	−0.363363	+	0.931648i	$0.618372\pi$
$912$	8.80337e12	0.421378
$913$	−4.53405e12	−0.215957
$914$	6.15303e12	0.291629
$915$	1.22322e13	0.576914
$916$	−2.74613e13	−1.28882
$917$	3.74898e12	0.175086
$918$	−1.85190e12	−0.0860646
$919$	1.63234e13	0.754905	0.377452	−	0.926029i	$-0.376800\pi$
$919$	1.63234e13	0.754905	0.377452	+	0.926029i	$0.376800\pi$
$920$	1.99905e13	0.919979
$921$	−3.72814e12	−0.170735
$922$	7.86751e12	0.358549
$923$	3.99937e13	1.81378
$924$	−7.12813e11	−0.0321700
$925$	4.83647e12	0.217215
$926$	−3.25088e12	−0.145295
$927$	4.60420e12	0.204784
$928$	−5.34337e12	−0.236510
$929$	6.53837e12	0.288004	0.144002	−	0.989577i	$-0.454003\pi$
$929$	6.53837e12	0.288004	0.144002	+	0.989577i	$0.454003\pi$
$930$	−2.51137e12	−0.110087
$931$	−2.07285e13	−0.904263
$932$	−2.29805e13	−0.997674
$933$	−7.64675e12	−0.330377
$934$	−7.77123e12	−0.334140
$935$	−7.71313e12	−0.330049
$936$	4.96630e12	0.211491
$937$	5.34424e12	0.226495	0.113247	−	0.993567i	$-0.463875\pi$
$937$	5.34424e12	0.226495	0.113247	+	0.993567i	$0.463875\pi$
$938$	−3.81685e11	−0.0160988
$939$	2.37078e13	0.995169
$940$	−6.29459e12	−0.262961
$941$	5.37071e12	0.223295	0.111647	−	0.993748i	$-0.464387\pi$
$941$	5.37071e12	0.223295	0.111647	+	0.993748i	$0.464387\pi$
$942$	−7.08196e12	−0.293038
$943$	−1.38422e13	−0.570037
$944$	2.29997e12	0.0942644
$945$	1.79378e12	0.0731687
$946$	−5.76080e11	−0.0233869
$947$	−9.73662e11	−0.0393399	−0.0196700	−	0.999807i	$-0.506262\pi$
$947$	−9.73662e11	−0.0393399	−0.0196700	+	0.999807i	$0.506262\pi$
$948$	1.62383e13	0.652986
$949$	2.01037e13	0.804596
$950$	3.15564e12	0.125699
$951$	−1.75508e13	−0.695800
$952$	6.92627e12	0.273296
$953$	−1.00939e13	−0.396405	−0.198203	−	0.980161i	$-0.563510\pi$
$953$	−1.00939e13	−0.396405	−0.198203	+	0.980161i	$0.563510\pi$
$954$	−1.11783e12	−0.0436927
$955$	4.81251e13	1.87222
$956$	−1.75276e13	−0.678676
$957$	−8.39236e11	−0.0323430
$958$	−1.02282e12	−0.0392333
$959$	−1.11003e13	−0.423791
$960$	−8.54116e12	−0.324561
$961$	−1.92348e13	−0.727498
$962$	−4.74959e12	−0.178800
$963$	1.23175e13	0.461534
$964$	−1.73544e12	−0.0647237
$965$	−4.42220e12	−0.164159
$966$	−2.04253e12	−0.0754694
$967$	−1.95926e13	−0.720565	−0.360282	−	0.932843i	$-0.617320\pi$
$967$	−1.95926e13	−0.720565	−0.360282	+	0.932843i	$0.617320\pi$
$968$	1.54480e13	0.565501
$969$	−2.31754e13	−0.844442
$970$	−2.91111e12	−0.105581
$971$	4.14092e13	1.49489	0.747447	−	0.664322i	$-0.231280\pi$
$971$	4.14092e13	1.49489	0.747447	+	0.664322i	$0.231280\pi$
$972$	−1.61566e12	−0.0580565
$973$	8.08306e12	0.289113
$974$	−2.30505e12	−0.0820665
$975$	−7.12324e12	−0.252439
$976$	1.73058e13	0.610474
$977$	3.94375e13	1.38479	0.692395	−	0.721518i	$-0.256555\pi$
$977$	3.94375e13	1.38479	0.692395	+	0.721518i	$0.256555\pi$
$978$	−4.35194e12	−0.152110
$979$	3.51381e12	0.122252
$980$	2.77834e13	0.962206
$981$	−1.45385e13	−0.501197
$982$	−8.89920e12	−0.305386
$983$	1.49277e13	0.509922	0.254961	−	0.966951i	$-0.417937\pi$
$983$	1.49277e13	0.509922	0.254961	+	0.966951i	$0.417937\pi$
$984$	−4.29818e12	−0.146153
$985$	−4.35240e13	−1.47322
$986$	3.87405e12	0.130533
$987$	1.35380e12	0.0454076
$988$	2.95257e13	0.985811
$989$	1.57275e13	0.522730
$990$	7.06282e11	0.0233679
$991$	5.10772e13	1.68227	0.841136	−	0.540824i	$-0.181888\pi$
$991$	5.10772e13	1.68227	0.841136	+	0.540824i	$0.181888\pi$
$992$	−1.29010e13	−0.422982
$993$	1.79768e13	0.586733
$994$	−5.10747e12	−0.165946
$995$	4.18141e13	1.35244
$996$	1.82600e13	0.587940
$997$	−8.85595e12	−0.283862	−0.141931	−	0.989877i	$-0.545331\pi$
$997$	−8.85595e12	−0.283862	−0.141931	+	0.989877i	$0.545331\pi$
$998$	1.07353e12	0.0342553
$999$	3.25249e12	0.103317

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.a.1.14	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.a.1.14	✓	21	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+6.97380 q^{2} +81.0000 q^{3} -463.366 q^{4} +1656.32 q^{5} +564.878 q^{6} +2037.84 q^{7} -6802.01 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+6.97380 q^{2} +81.0000 q^{3} -463.366 q^{4} +1656.32 q^{5} +564.878 q^{6} +2037.84 q^{7} -6802.01 q^{8} +6561.00 q^{9} +11550.8 q^{10} +9319.57 q^{11} -37532.7 q^{12} -111282. q^{13} +14211.5 q^{14} +134162. q^{15} +189808. q^{16} -499680. q^{17} +45755.1 q^{18} +572598. q^{19} -767480. q^{20} +165065. q^{21} +64992.8 q^{22} -1.77436e6 q^{23} -550963. q^{24} +790255. q^{25} -776059. q^{26} +531441. q^{27} -944267. q^{28} -1.11174e6 q^{29} +935616. q^{30} -2.68419e6 q^{31} +4.80631e6 q^{32} +754885. q^{33} -3.48467e6 q^{34} +3.37531e6 q^{35} -3.04014e6 q^{36} +6.12013e6 q^{37} +3.99319e6 q^{38} -9.01385e6 q^{39} -1.12663e7 q^{40} +7.80122e6 q^{41} +1.15113e6 q^{42} -8.86375e6 q^{43} -4.31837e6 q^{44} +1.08671e7 q^{45} -1.23741e7 q^{46} +8.20162e6 q^{47} +1.53744e7 q^{48} -3.62008e7 q^{49} +5.51108e6 q^{50} -4.04741e7 q^{51} +5.15644e7 q^{52} -2.44307e7 q^{53} +3.70616e6 q^{54} +1.54361e7 q^{55} -1.38614e7 q^{56} +4.63805e7 q^{57} -7.75306e6 q^{58} +1.21174e7 q^{59} -6.21659e7 q^{60} +9.11754e7 q^{61} -1.87190e7 q^{62} +1.33703e7 q^{63} -6.36632e7 q^{64} -1.84318e8 q^{65} +5.26442e6 q^{66} -2.68575e7 q^{67} +2.31535e8 q^{68} -1.43724e8 q^{69} +2.35387e7 q^{70} -3.59390e8 q^{71} -4.46280e7 q^{72} -1.80655e8 q^{73} +4.26806e7 q^{74} +6.40107e7 q^{75} -2.65323e8 q^{76} +1.89918e7 q^{77} -6.28608e7 q^{78} -4.32646e8 q^{79} +3.14381e8 q^{80} +4.30467e7 q^{81} +5.44042e7 q^{82} -4.86509e8 q^{83} -7.64856e7 q^{84} -8.27627e8 q^{85} -6.18140e7 q^{86} -9.00510e7 q^{87} -6.33918e7 q^{88} +3.77036e8 q^{89} +7.57849e7 q^{90} -2.26775e8 q^{91} +8.22180e8 q^{92} -2.17419e8 q^{93} +5.71965e7 q^{94} +9.48404e8 q^{95} +3.89311e8 q^{96} -2.52026e8 q^{97} -2.52457e8 q^{98} +6.11457e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9}+O(q^{10}) \) 21 * q - 66 * q^2 + 1701 * q^3 + 5206 * q^4 - 2964 * q^5 - 5346 * q^6 - 30775 * q^7 - 24621 * q^8 + 137781 * q^9	\( 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9} - 54663 q^{10} - 151769 q^{11} + 421686 q^{12} - 153611 q^{13} - 286771 q^{14} - 240084 q^{15} + 805530 q^{16} - 723621 q^{17} - 433026 q^{18} - 549388 q^{19} - 527311 q^{20} - 2492775 q^{21} + 2973158 q^{22} + 169962 q^{23} - 1994301 q^{24} + 8035779 q^{25} - 2337392 q^{26} + 11160261 q^{27} - 22659054 q^{28} - 16845442 q^{29} - 4427703 q^{30} - 19307976 q^{31} - 44923568 q^{32} - 12293289 q^{33} - 35547496 q^{34} - 34882596 q^{35} + 34156566 q^{36} - 41561129 q^{37} - 52335371 q^{38} - 12442491 q^{39} - 125735038 q^{40} - 68169291 q^{41} - 23228451 q^{42} - 25719587 q^{43} - 126277032 q^{44} - 19446804 q^{45} - 292814271 q^{46} - 174095332 q^{47} + 65247930 q^{48} + 7479350 q^{49} - 227877439 q^{50} - 58613301 q^{51} - 232397708 q^{52} - 228390500 q^{53} - 35075106 q^{54} - 29426208 q^{55} + 326778474 q^{56} - 44500428 q^{57} + 480343762 q^{58} + 254464581 q^{59} - 42712191 q^{60} - 183928964 q^{61} - 21753862 q^{62} - 201914775 q^{63} + 310571245 q^{64} + 5308466 q^{65} + 240825798 q^{66} - 82724114 q^{67} - 138336205 q^{68} + 13766922 q^{69} + 1030274876 q^{70} - 404721965 q^{71} - 161538381 q^{72} + 154162574 q^{73} + 36352054 q^{74} + 650898099 q^{75} + 1068940636 q^{76} - 448535481 q^{77} - 189328752 q^{78} + 272529635 q^{79} - 345587859 q^{80} + 903981141 q^{81} - 38412637 q^{82} + 432518643 q^{83} - 1835383374 q^{84} - 126211490 q^{85} - 3699273072 q^{86} - 1364480802 q^{87} + 170111045 q^{88} - 1255621070 q^{89} - 358643943 q^{90} + 1448885849 q^{91} + 1568933320 q^{92} - 1563946056 q^{93} - 1908445164 q^{94} - 2896546490 q^{95} - 3638809008 q^{96} + 1007235486 q^{97} - 9506868248 q^{98} - 995756409 q^{99}+O(q^{100}) \) 21 * q - 66 * q^2 + 1701 * q^3 + 5206 * q^4 - 2964 * q^5 - 5346 * q^6 - 30775 * q^7 - 24621 * q^8 + 137781 * q^9 - 54663 * q^10 - 151769 * q^11 + 421686 * q^12 - 153611 * q^13 - 286771 * q^14 - 240084 * q^15 + 805530 * q^16 - 723621 * q^17 - 433026 * q^18 - 549388 * q^19 - 527311 * q^20 - 2492775 * q^21 + 2973158 * q^22 + 169962 * q^23 - 1994301 * q^24 + 8035779 * q^25 - 2337392 * q^26 + 11160261 * q^27 - 22659054 * q^28 - 16845442 * q^29 - 4427703 * q^30 - 19307976 * q^31 - 44923568 * q^32 - 12293289 * q^33 - 35547496 * q^34 - 34882596 * q^35 + 34156566 * q^36 - 41561129 * q^37 - 52335371 * q^38 - 12442491 * q^39 - 125735038 * q^40 - 68169291 * q^41 - 23228451 * q^42 - 25719587 * q^43 - 126277032 * q^44 - 19446804 * q^45 - 292814271 * q^46 - 174095332 * q^47 + 65247930 * q^48 + 7479350 * q^49 - 227877439 * q^50 - 58613301 * q^51 - 232397708 * q^52 - 228390500 * q^53 - 35075106 * q^54 - 29426208 * q^55 + 326778474 * q^56 - 44500428 * q^57 + 480343762 * q^58 + 254464581 * q^59 - 42712191 * q^60 - 183928964 * q^61 - 21753862 * q^62 - 201914775 * q^63 + 310571245 * q^64 + 5308466 * q^65 + 240825798 * q^66 - 82724114 * q^67 - 138336205 * q^68 + 13766922 * q^69 + 1030274876 * q^70 - 404721965 * q^71 - 161538381 * q^72 + 154162574 * q^73 + 36352054 * q^74 + 650898099 * q^75 + 1068940636 * q^76 - 448535481 * q^77 - 189328752 * q^78 + 272529635 * q^79 - 345587859 * q^80 + 903981141 * q^81 - 38412637 * q^82 + 432518643 * q^83 - 1835383374 * q^84 - 126211490 * q^85 - 3699273072 * q^86 - 1364480802 * q^87 + 170111045 * q^88 - 1255621070 * q^89 - 358643943 * q^90 + 1448885849 * q^91 + 1568933320 * q^92 - 1563946056 * q^93 - 1908445164 * q^94 - 2896546490 * q^95 - 3638809008 * q^96 + 1007235486 * q^97 - 9506868248 * q^98 - 995756409 * q^99

Introduction

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