LMFDB - Embedded newform 177.10.a.a.1.6

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			1.6
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)

$f(q)$	$=$	$q-26.8579 q^{2} +81.0000 q^{3} +209.348 q^{4} -2742.53 q^{5} -2175.49 q^{6} -8878.91 q^{7} +8128.61 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-26.8579 q^{2} +81.0000 q^{3} +209.348 q^{4} -2742.53 q^{5} -2175.49 q^{6} -8878.91 q^{7} +8128.61 q^{8} +6561.00 q^{9} +73658.6 q^{10} -61766.0 q^{11} +16957.2 q^{12} -93410.5 q^{13} +238469. q^{14} -222145. q^{15} -325504. q^{16} +540545. q^{17} -176215. q^{18} +591646. q^{19} -574143. q^{20} -719191. q^{21} +1.65891e6 q^{22} +571277. q^{23} +658417. q^{24} +5.56834e6 q^{25} +2.50881e6 q^{26} +531441. q^{27} -1.85878e6 q^{28} -1.20821e6 q^{29} +5.96635e6 q^{30} -3.72946e6 q^{31} +4.58050e6 q^{32} -5.00304e6 q^{33} -1.45179e7 q^{34} +2.43506e7 q^{35} +1.37353e6 q^{36} +1.40983e7 q^{37} -1.58904e7 q^{38} -7.56625e6 q^{39} -2.22929e7 q^{40} -7.71359e6 q^{41} +1.93160e7 q^{42} +3.91142e6 q^{43} -1.29306e7 q^{44} -1.79937e7 q^{45} -1.53433e7 q^{46} -5.70269e7 q^{47} -2.63658e7 q^{48} +3.84813e7 q^{49} -1.49554e8 q^{50} +4.37842e7 q^{51} -1.95553e7 q^{52} +4.11217e7 q^{53} -1.42734e7 q^{54} +1.69395e8 q^{55} -7.21731e7 q^{56} +4.79233e7 q^{57} +3.24500e7 q^{58} +1.21174e7 q^{59} -4.65055e7 q^{60} +5.31961e7 q^{61} +1.00165e8 q^{62} -5.82545e7 q^{63} +4.36350e7 q^{64} +2.56181e8 q^{65} +1.34371e8 q^{66} +2.25785e8 q^{67} +1.13162e8 q^{68} +4.62735e7 q^{69} -6.54008e8 q^{70} -2.29743e8 q^{71} +5.33318e7 q^{72} +1.11661e8 q^{73} -3.78651e8 q^{74} +4.51035e8 q^{75} +1.23860e8 q^{76} +5.48414e8 q^{77} +2.03214e8 q^{78} +7.39558e7 q^{79} +8.92703e8 q^{80} +4.30467e7 q^{81} +2.07171e8 q^{82} +1.07859e8 q^{83} -1.50561e8 q^{84} -1.48246e9 q^{85} -1.05053e8 q^{86} -9.78651e7 q^{87} -5.02071e8 q^{88} -6.13295e8 q^{89} +4.83274e8 q^{90} +8.29383e8 q^{91} +1.19596e8 q^{92} -3.02086e8 q^{93} +1.53162e9 q^{94} -1.62261e9 q^{95} +3.71021e8 q^{96} +6.55776e8 q^{97} -1.03353e9 q^{98} -4.05247e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−26.8579	−1.18696	−0.593482	−	0.804847i	$-0.702247\pi$
$2$	−26.8579	−1.18696	−0.593482	+	0.804847i	$0.702247\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	209.348	0.408883
$5$	−2742.53	−1.96239	−0.981197	−	0.193011i	$-0.938175\pi$
$5$	−2742.53	−1.96239	−0.981197	+	0.193011i	$0.938175\pi$
$6$	−2175.49	−0.685294
$7$	−8878.91	−1.39771	−0.698857	−	0.715262i	$-0.746308\pi$
$7$	−8878.91	−1.39771	−0.698857	+	0.715262i	$0.746308\pi$
$8$	8128.61	0.701635
$9$	6561.00	0.333333
$10$	73658.6	2.32929
$11$	−61766.0	−1.27199	−0.635993	−	0.771695i	$-0.719409\pi$
$11$	−61766.0	−1.27199	−0.635993	+	0.771695i	$0.719409\pi$
$12$	16957.2	0.236069
$13$	−93410.5	−0.907090	−0.453545	−	0.891233i	$-0.649841\pi$
$13$	−93410.5	−0.907090	−0.453545	+	0.891233i	$0.649841\pi$
$14$	238469.	1.65904
$15$	−222145.	−1.13299
$16$	−325504.	−1.24170
$17$	540545.	1.56968	0.784841	−	0.619697i	$-0.212744\pi$
$17$	540545.	1.56968	0.784841	+	0.619697i	$0.212744\pi$
$18$	−176215.	−0.395655
$19$	591646.	1.04153	0.520764	−	0.853701i	$-0.325647\pi$
$19$	591646.	1.04153	0.520764	+	0.853701i	$0.325647\pi$
$20$	−574143.	−0.802389
$21$	−719191.	−0.806970
$22$	1.65891e6	1.50980
$23$	571277.	0.425669	0.212834	−	0.977088i	$-0.431731\pi$
$23$	571277.	0.425669	0.212834	+	0.977088i	$0.431731\pi$
$24$	658417.	0.405089
$25$	5.56834e6	2.85099
$26$	2.50881e6	1.07668
$27$	531441.	0.192450
$28$	−1.85878e6	−0.571501
$29$	−1.20821e6	−0.317213	−0.158607	−	0.987342i	$-0.550700\pi$
$29$	−1.20821e6	−0.317213	−0.158607	+	0.987342i	$0.550700\pi$
$30$	5.96635e6	1.34482
$31$	−3.72946e6	−0.725301	−0.362650	−	0.931925i	$-0.618128\pi$
$31$	−3.72946e6	−0.725301	−0.362650	+	0.931925i	$0.618128\pi$
$32$	4.58050e6	0.772215
$33$	−5.00304e6	−0.734381
$34$	−1.45179e7	−1.86316
$35$	2.43506e7	2.74286
$36$	1.37353e6	0.136294
$37$	1.40983e7	1.23668	0.618342	−	0.785910i	$-0.287805\pi$
$37$	1.40983e7	1.23668	0.618342	+	0.785910i	$0.287805\pi$
$38$	−1.58904e7	−1.23626
$39$	−7.56625e6	−0.523709
$40$	−2.22929e7	−1.37688
$41$	−7.71359e6	−0.426314	−0.213157	−	0.977018i	$-0.568375\pi$
$41$	−7.71359e6	−0.426314	−0.213157	+	0.977018i	$0.568375\pi$
$42$	1.93160e7	0.957845
$43$	3.91142e6	0.174472	0.0872362	−	0.996188i	$-0.472197\pi$
$43$	3.91142e6	0.174472	0.0872362	+	0.996188i	$0.472197\pi$
$44$	−1.29306e7	−0.520093
$45$	−1.79937e7	−0.654131
$46$	−1.53433e7	−0.505253
$47$	−5.70269e7	−1.70467	−0.852333	−	0.523000i	$-0.824813\pi$
$47$	−5.70269e7	−1.70467	−0.852333	+	0.523000i	$0.824813\pi$
$48$	−2.63658e7	−0.716894
$49$	3.84813e7	0.953604
$50$	−1.49554e8	−3.38402
$51$	4.37842e7	0.906257
$52$	−1.95553e7	−0.370894
$53$	4.11217e7	0.715863	0.357932	−	0.933748i	$-0.383482\pi$
$53$	4.11217e7	0.715863	0.357932	+	0.933748i	$0.383482\pi$
$54$	−1.42734e7	−0.228431
$55$	1.69395e8	2.49614
$56$	−7.21731e7	−0.980685
$57$	4.79233e7	0.601326
$58$	3.24500e7	0.376521
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	−4.65055e7	−0.463259
$61$	5.31961e7	0.491921	0.245961	−	0.969280i	$-0.420897\pi$
$61$	5.31961e7	0.491921	0.245961	+	0.969280i	$0.420897\pi$
$62$	1.00165e8	0.860906
$63$	−5.82545e7	−0.465905
$64$	4.36350e7	0.325106
$65$	2.56181e8	1.78007
$66$	1.34371e8	0.871684
$67$	2.25785e8	1.36886	0.684430	−	0.729079i	$-0.260051\pi$
$67$	2.25785e8	1.36886	0.684430	+	0.729079i	$0.260051\pi$
$68$	1.13162e8	0.641816
$69$	4.62735e7	0.245760
$70$	−6.54008e8	−3.25568
$71$	−2.29743e8	−1.07295	−0.536476	−	0.843916i	$-0.680245\pi$
$71$	−2.29743e8	−1.07295	−0.536476	+	0.843916i	$0.680245\pi$
$72$	5.33318e7	0.233878
$73$	1.11661e8	0.460201	0.230100	−	0.973167i	$-0.426095\pi$
$73$	1.11661e8	0.460201	0.230100	+	0.973167i	$0.426095\pi$
$74$	−3.78651e8	−1.46790
$75$	4.51035e8	1.64602
$76$	1.23860e8	0.425863
$77$	5.48414e8	1.77787
$78$	2.03214e8	0.621623
$79$	7.39558e7	0.213624	0.106812	−	0.994279i	$-0.465936\pi$
$79$	7.39558e7	0.213624	0.106812	+	0.994279i	$0.465936\pi$
$80$	8.92703e8	2.43670
$81$	4.30467e7	0.111111
$82$	2.07171e8	0.506019
$83$	1.07859e8	0.249463	0.124732	−	0.992191i	$-0.460193\pi$
$83$	1.07859e8	0.249463	0.124732	+	0.992191i	$0.460193\pi$
$84$	−1.50561e8	−0.329956
$85$	−1.48246e9	−3.08033
$86$	−1.05053e8	−0.207092
$87$	−9.78651e7	−0.183143
$88$	−5.02071e8	−0.892470
$89$	−6.13295e8	−1.03613	−0.518065	−	0.855341i	$-0.673347\pi$
$89$	−6.13295e8	−1.03613	−0.518065	+	0.855341i	$0.673347\pi$
$90$	4.83274e8	0.776430
$91$	8.29383e8	1.26785
$92$	1.19596e8	0.174049
$93$	−3.02086e8	−0.418753
$94$	1.53162e9	2.02338
$95$	−1.62261e9	−2.04389
$96$	3.71021e8	0.445839
$97$	6.55776e8	0.752112	0.376056	−	0.926597i	$-0.377280\pi$
$97$	6.55776e8	0.752112	0.376056	+	0.926597i	$0.377280\pi$
$98$	−1.03353e9	−1.13189
$99$	−4.05247e8	−0.423995
$100$	1.16572e9	1.16572
$101$	4.54527e7	0.0434624	0.0217312	−	0.999764i	$-0.493082\pi$
$101$	4.54527e7	0.0434624	0.0217312	+	0.999764i	$0.493082\pi$
$102$	−1.17595e9	−1.07569
$103$	−1.48991e9	−1.30435	−0.652174	−	0.758070i	$-0.726143\pi$
$103$	−1.48991e9	−1.30435	−0.652174	+	0.758070i	$0.726143\pi$
$104$	−7.59297e8	−0.636446
$105$	1.97240e9	1.58359
$106$	−1.10444e9	−0.849704
$107$	−8.57527e7	−0.0632442	−0.0316221	−	0.999500i	$-0.510067\pi$
$107$	−8.57527e7	−0.0632442	−0.0316221	+	0.999500i	$0.510067\pi$
$108$	1.11256e8	0.0786895
$109$	2.78093e9	1.88700	0.943499	−	0.331375i	$-0.107513\pi$
$109$	2.78093e9	1.88700	0.943499	+	0.331375i	$0.107513\pi$
$110$	−4.54960e9	−2.96282
$111$	1.14196e9	0.713999
$112$	2.89012e9	1.73554
$113$	1.75843e9	1.01455	0.507274	−	0.861785i	$-0.330653\pi$
$113$	1.75843e9	1.01455	0.507274	+	0.861785i	$0.330653\pi$
$114$	−1.28712e9	−0.713753
$115$	−1.56674e9	−0.835330
$116$	−2.52936e8	−0.129703
$117$	−6.12866e8	−0.302363
$118$	−3.25447e8	−0.154530
$119$	−4.79945e9	−2.19397
$120$	−1.80573e9	−0.794944
$121$	1.45709e9	0.617948
$122$	−1.42874e9	−0.583892
$123$	−6.24801e8	−0.246132
$124$	−7.80754e8	−0.296563
$125$	−9.91482e9	−3.63237
$126$	1.56459e9	0.553012
$127$	3.48699e9	1.18942	0.594709	−	0.803941i	$-0.297267\pi$
$127$	3.48699e9	1.18942	0.594709	+	0.803941i	$0.297267\pi$
$128$	−3.51716e9	−1.15810
$129$	3.16825e8	0.100732
$130$	−6.88049e9	−2.11288
$131$	−5.58769e9	−1.65772	−0.828860	−	0.559456i	$-0.811010\pi$
$131$	−5.58769e9	−1.65772	−0.828860	+	0.559456i	$0.811010\pi$
$132$	−1.04738e9	−0.300276
$133$	−5.25317e9	−1.45576
$134$	−6.06412e9	−1.62479
$135$	−1.45749e9	−0.377663
$136$	4.39388e9	1.10134
$137$	7.07450e9	1.71575	0.857873	−	0.513861i	$-0.171785\pi$
$137$	7.07450e9	1.71575	0.857873	+	0.513861i	$0.171785\pi$
$138$	−1.24281e9	−0.291708
$139$	−7.81032e9	−1.77461	−0.887304	−	0.461186i	$-0.847424\pi$
$139$	−7.81032e9	−1.77461	−0.887304	+	0.461186i	$0.847424\pi$
$140$	5.09776e9	1.12151
$141$	−4.61918e9	−0.984189
$142$	6.17043e9	1.27355
$143$	5.76959e9	1.15381
$144$	−2.13563e9	−0.413899
$145$	3.31355e9	0.622498
$146$	−2.99897e9	−0.546242
$147$	3.11699e9	0.550563
$148$	2.95145e9	0.505658
$149$	3.65520e9	0.607537	0.303768	−	0.952746i	$-0.401755\pi$
$149$	3.65520e9	0.607537	0.303768	+	0.952746i	$0.401755\pi$
$150$	−1.21139e10	−1.95376
$151$	5.30736e9	0.830774	0.415387	−	0.909645i	$-0.363646\pi$
$151$	5.30736e9	0.830774	0.415387	+	0.909645i	$0.363646\pi$
$152$	4.80926e9	0.730772
$153$	3.54652e9	0.523228
$154$	−1.47293e10	−2.11027
$155$	1.02281e10	1.42333
$156$	−1.58398e9	−0.214135
$157$	−7.06139e9	−0.927560	−0.463780	−	0.885950i	$-0.653507\pi$
$157$	−7.06139e9	−0.927560	−0.463780	+	0.885950i	$0.653507\pi$
$158$	−1.98630e9	−0.253564
$159$	3.33086e9	0.413304
$160$	−1.25622e10	−1.51539
$161$	−5.07232e9	−0.594963
$162$	−1.15615e9	−0.131885
$163$	−7.27115e9	−0.806787	−0.403393	−	0.915027i	$-0.632169\pi$
$163$	−7.27115e9	−0.806787	−0.403393	+	0.915027i	$0.632169\pi$
$164$	−1.61482e9	−0.174312
$165$	1.37210e10	1.44115
$166$	−2.89688e9	−0.296104
$167$	−8.95764e9	−0.891189	−0.445594	−	0.895235i	$-0.647008\pi$
$167$	−8.95764e9	−0.891189	−0.445594	+	0.895235i	$0.647008\pi$
$168$	−5.84602e9	−0.566198
$169$	−1.87898e9	−0.177187
$170$	3.98158e10	3.65625
$171$	3.88179e9	0.347176
$172$	8.18848e8	0.0713387
$173$	−7.27592e9	−0.617562	−0.308781	−	0.951133i	$-0.599921\pi$
$173$	−7.27592e9	−0.617562	−0.308781	+	0.951133i	$0.599921\pi$
$174$	2.62845e9	0.217384
$175$	−4.94407e10	−3.98486
$176$	2.01050e10	1.57942
$177$	9.81506e8	0.0751646
$178$	1.64718e10	1.22985
$179$	−2.08457e10	−1.51767	−0.758836	−	0.651281i	$-0.774232\pi$
$179$	−2.08457e10	−1.51767	−0.758836	+	0.651281i	$0.774232\pi$
$180$	−3.76695e9	−0.267463
$181$	1.27240e10	0.881192	0.440596	−	0.897706i	$-0.354767\pi$
$181$	1.27240e10	0.881192	0.440596	+	0.897706i	$0.354767\pi$
$182$	−2.22755e10	−1.50489
$183$	4.30888e9	0.284011
$184$	4.64369e9	0.298664
$185$	−3.86649e10	−2.42686
$186$	8.11340e9	0.497044
$187$	−3.33873e10	−1.99661
$188$	−1.19385e10	−0.697008
$189$	−4.71861e9	−0.268990
$190$	4.35798e10	2.42602
$191$	2.88968e10	1.57108	0.785541	−	0.618809i	$-0.212385\pi$
$191$	2.88968e10	1.57108	0.785541	+	0.618809i	$0.212385\pi$
$192$	3.53444e9	0.187700
$193$	1.58940e10	0.824564	0.412282	−	0.911056i	$-0.364732\pi$
$193$	1.58940e10	0.824564	0.412282	+	0.911056i	$0.364732\pi$
$194$	−1.76128e10	−0.892729
$195$	2.07507e10	1.02772
$196$	8.05599e9	0.389912
$197$	−1.71196e10	−0.809835	−0.404917	−	0.914353i	$-0.632700\pi$
$197$	−1.71196e10	−0.809835	−0.404917	+	0.914353i	$0.632700\pi$
$198$	1.08841e10	0.503267
$199$	−3.69899e10	−1.67203	−0.836015	−	0.548707i	$-0.815120\pi$
$199$	−3.69899e10	−1.67203	−0.836015	+	0.548707i	$0.815120\pi$
$200$	4.52628e10	2.00035
$201$	1.82886e10	0.790312
$202$	−1.22077e9	−0.0515883
$203$	1.07276e10	0.443374
$204$	9.16612e9	0.370553
$205$	2.11547e10	0.836595
$206$	4.00160e10	1.54821
$207$	3.74815e9	0.141890
$208$	3.04054e10	1.12633
$209$	−3.65436e10	−1.32481
$210$	−5.29746e10	−1.87967
$211$	2.82074e10	0.979697	0.489848	−	0.871808i	$-0.337052\pi$
$211$	2.82074e10	0.979697	0.489848	+	0.871808i	$0.337052\pi$
$212$	8.60875e9	0.292704
$213$	−1.86092e10	−0.619469
$214$	2.30314e9	0.0750686
$215$	−1.07272e10	−0.342383
$216$	4.31987e9	0.135030
$217$	3.31135e10	1.01376
$218$	−7.46901e10	−2.23980
$219$	9.04452e9	0.265697
$220$	3.54625e10	1.02063
$221$	−5.04926e10	−1.42384
$222$	−3.06707e10	−0.847491
$223$	−2.75802e10	−0.746837	−0.373419	−	0.927663i	$-0.621815\pi$
$223$	−2.75802e10	−0.746837	−0.373419	+	0.927663i	$0.621815\pi$
$224$	−4.06699e10	−1.07934
$225$	3.65338e10	0.950329
$226$	−4.72278e10	−1.20423
$227$	−2.76405e10	−0.690922	−0.345461	−	0.938433i	$-0.612277\pi$
$227$	−2.76405e10	−0.690922	−0.345461	+	0.938433i	$0.612277\pi$
$228$	1.00327e10	0.245872
$229$	3.15202e10	0.757407	0.378704	−	0.925518i	$-0.376370\pi$
$229$	3.15202e10	0.757407	0.378704	+	0.925518i	$0.376370\pi$
$230$	4.20795e10	0.991506
$231$	4.44216e10	1.02645
$232$	−9.82107e9	−0.222568
$233$	3.03425e10	0.674450	0.337225	−	0.941424i	$-0.390512\pi$
$233$	3.03425e10	0.674450	0.337225	+	0.941424i	$0.390512\pi$
$234$	1.64603e10	0.358894
$235$	1.56398e11	3.34522
$236$	2.53674e9	0.0532320
$237$	5.99042e9	0.123336
$238$	1.28903e11	2.60416
$239$	−3.01660e10	−0.598036	−0.299018	−	0.954247i	$-0.596659\pi$
$239$	−3.01660e10	−0.598036	−0.299018	+	0.954247i	$0.596659\pi$
$240$	7.23089e10	1.40683
$241$	2.56192e10	0.489203	0.244601	−	0.969624i	$-0.421343\pi$
$241$	2.56192e10	0.489203	0.244601	+	0.969624i	$0.421343\pi$
$242$	−3.91344e10	−0.733482
$243$	3.48678e9	0.0641500
$244$	1.11365e10	0.201138
$245$	−1.05536e11	−1.87135
$246$	1.67809e10	0.292150
$247$	−5.52660e10	−0.944760
$248$	−3.03153e10	−0.508896
$249$	8.73661e9	0.144028
$250$	2.66291e11	4.31149
$251$	1.93681e10	0.308003	0.154002	−	0.988071i	$-0.450784\pi$
$251$	1.93681e10	0.308003	0.154002	+	0.988071i	$0.450784\pi$
$252$	−1.21955e10	−0.190500
$253$	−3.52855e10	−0.541445
$254$	−9.36534e10	−1.41180
$255$	−1.20079e11	−1.77843
$256$	7.21226e10	1.04952
$257$	1.20699e11	1.72585	0.862926	−	0.505330i	$-0.168629\pi$
$257$	1.20699e11	1.72585	0.862926	+	0.505330i	$0.168629\pi$
$258$	−8.50927e9	−0.119565
$259$	−1.25177e11	−1.72853
$260$	5.36309e10	0.727839
$261$	−7.92707e9	−0.105738
$262$	1.50074e11	1.96765
$263$	1.68684e10	0.217407	0.108703	−	0.994074i	$-0.465330\pi$
$263$	1.68684e10	0.217407	0.108703	+	0.994074i	$0.465330\pi$
$264$	−4.06678e10	−0.515268
$265$	−1.12778e11	−1.40481
$266$	1.41089e11	1.72793
$267$	−4.96769e10	−0.598210
$268$	4.72677e10	0.559703
$269$	1.17255e11	1.36535	0.682676	−	0.730721i	$-0.260816\pi$
$269$	1.17255e11	1.36535	0.682676	+	0.730721i	$0.260816\pi$
$270$	3.91452e10	0.448272
$271$	−3.54818e9	−0.0399617	−0.0199808	−	0.999800i	$-0.506361\pi$
$271$	−3.54818e9	−0.0399617	−0.0199808	+	0.999800i	$0.506361\pi$
$272$	−1.75949e11	−1.94907
$273$	6.71800e10	0.731995
$274$	−1.90006e11	−2.03653
$275$	−3.43934e11	−3.62642
$276$	9.68726e9	0.100487
$277$	8.36832e10	0.854042	0.427021	−	0.904242i	$-0.359563\pi$
$277$	8.36832e10	0.854042	0.427021	+	0.904242i	$0.359563\pi$
$278$	2.09769e11	2.10639
$279$	−2.44690e10	−0.241767
$280$	1.97937e11	1.92449
$281$	−3.07370e10	−0.294092	−0.147046	−	0.989130i	$-0.546977\pi$
$281$	−3.07370e10	−0.294092	−0.147046	+	0.989130i	$0.546977\pi$
$282$	1.24061e11	1.16820
$283$	−1.78139e11	−1.65090	−0.825449	−	0.564477i	$-0.809078\pi$
$283$	−1.78139e11	−1.65090	−0.825449	+	0.564477i	$0.809078\pi$
$284$	−4.80963e10	−0.438711
$285$	−1.31431e11	−1.18004
$286$	−1.54959e11	−1.36953
$287$	6.84883e10	0.595865
$288$	3.00527e10	0.257405
$289$	1.73601e11	1.46390
$290$	−8.89951e10	−0.738882
$291$	5.31178e10	0.434232
$292$	2.33759e10	0.188168
$293$	−1.81919e11	−1.44203	−0.721014	−	0.692921i	$-0.756324\pi$
$293$	−1.81919e11	−1.44203	−0.721014	+	0.692921i	$0.756324\pi$
$294$	−8.37159e10	−0.653499
$295$	−3.32322e10	−0.255482
$296$	1.14599e11	0.867700
$297$	−3.28250e10	−0.244794
$298$	−9.81710e10	−0.721124
$299$	−5.33633e10	−0.386120
$300$	9.44233e10	0.673028
$301$	−3.47291e10	−0.243862
$302$	−1.42545e11	−0.986098
$303$	3.68167e9	0.0250930
$304$	−1.92583e11	−1.29326
$305$	−1.45892e11	−0.965343
$306$	−9.52521e10	−0.621052
$307$	2.35783e11	1.51492	0.757460	−	0.652882i	$-0.226440\pi$
$307$	2.35783e11	1.51492	0.757460	+	0.652882i	$0.226440\pi$
$308$	1.14809e11	0.726941
$309$	−1.20683e11	−0.753065
$310$	−2.74707e11	−1.68944
$311$	8.77054e10	0.531624	0.265812	−	0.964025i	$-0.414360\pi$
$311$	8.77054e10	0.531624	0.265812	+	0.964025i	$0.414360\pi$
$312$	−6.15031e10	−0.367452
$313$	1.15319e11	0.679126	0.339563	−	0.940583i	$-0.389721\pi$
$313$	1.15319e11	0.679126	0.339563	+	0.940583i	$0.389721\pi$
$314$	1.89654e11	1.10098
$315$	1.59765e11	0.914288
$316$	1.54825e10	0.0873472
$317$	−2.91934e11	−1.62374	−0.811872	−	0.583835i	$-0.801551\pi$
$317$	−2.91934e11	−1.62374	−0.811872	+	0.583835i	$0.801551\pi$
$318$	−8.94600e10	−0.490577
$319$	7.46263e10	0.403491
$320$	−1.19670e11	−0.637986
$321$	−6.94597e9	−0.0365141
$322$	1.36232e11	0.706200
$323$	3.19812e11	1.63487
$324$	9.01174e9	0.0454314
$325$	−5.20141e11	−2.58610
$326$	1.95288e11	0.957627
$327$	2.25256e11	1.08946
$328$	−6.27008e10	−0.299117
$329$	5.06336e11	2.38263
$330$	−3.68517e11	−1.71059
$331$	3.45536e11	1.58222	0.791110	−	0.611674i	$-0.209504\pi$
$331$	3.45536e11	1.58222	0.791110	+	0.611674i	$0.209504\pi$
$332$	2.25801e10	0.102001
$333$	9.24988e10	0.412228
$334$	2.40584e11	1.05781
$335$	−6.19223e11	−2.68624
$336$	2.34099e11	1.00201
$337$	2.55218e11	1.07789	0.538947	−	0.842340i	$-0.318822\pi$
$337$	2.55218e11	1.07789	0.538947	+	0.842340i	$0.318822\pi$
$338$	5.04655e10	0.210315
$339$	1.42433e11	0.585749
$340$	−3.10350e11	−1.25950
$341$	2.30354e11	0.922572
$342$	−1.04257e11	−0.412085
$343$	1.66236e10	0.0648488
$344$	3.17944e10	0.122416
$345$	−1.26906e11	−0.482278
$346$	1.95416e11	0.733024
$347$	2.89107e11	1.07047	0.535237	−	0.844702i	$-0.320222\pi$
$347$	2.89107e11	1.07047	0.535237	+	0.844702i	$0.320222\pi$
$348$	−2.04878e10	−0.0748841
$349$	5.91146e10	0.213295	0.106647	−	0.994297i	$-0.465988\pi$
$349$	5.91146e10	0.213295	0.106647	+	0.994297i	$0.465988\pi$
$350$	1.32787e12	4.72989
$351$	−4.96422e10	−0.174570
$352$	−2.82919e11	−0.982247
$353$	−2.63011e11	−0.901547	−0.450774	−	0.892638i	$-0.648852\pi$
$353$	−2.63011e11	−0.901547	−0.450774	+	0.892638i	$0.648852\pi$
$354$	−2.63612e10	−0.0892176
$355$	6.30077e11	2.10555
$356$	−1.28392e11	−0.423655
$357$	−3.88755e11	−1.26669
$358$	5.59873e11	1.80142
$359$	−3.28022e11	−1.04226	−0.521132	−	0.853476i	$-0.674490\pi$
$359$	−3.28022e11	−1.04226	−0.521132	+	0.853476i	$0.674490\pi$
$360$	−1.46264e11	−0.458961
$361$	2.73576e10	0.0847804
$362$	−3.41740e11	−1.04594
$363$	1.18024e11	0.356772
$364$	1.73630e11	0.518403
$365$	−3.06233e11	−0.903095
$366$	−1.15728e11	−0.337110
$367$	2.02654e11	0.583121	0.291560	−	0.956552i	$-0.405826\pi$
$367$	2.02654e11	0.583121	0.291560	+	0.956552i	$0.405826\pi$
$368$	−1.85953e11	−0.528552
$369$	−5.06089e10	−0.142105
$370$	1.03846e12	2.88059
$371$	−3.65116e11	−1.00057
$372$	−6.32411e10	−0.171221
$373$	6.72717e11	1.79946	0.899731	−	0.436446i	$-0.143763\pi$
$373$	6.72717e11	1.79946	0.899731	+	0.436446i	$0.143763\pi$
$374$	8.96714e11	2.36991
$375$	−8.03100e11	−2.09715
$376$	−4.63549e11	−1.19605
$377$	1.12860e11	0.287741
$378$	1.26732e11	0.319282
$379$	5.61509e11	1.39791	0.698956	−	0.715164i	$-0.253648\pi$
$379$	5.61509e11	1.39791	0.698956	+	0.715164i	$0.253648\pi$
$380$	−3.39689e11	−0.835710
$381$	2.82446e11	0.686711
$382$	−7.76107e11	−1.86482
$383$	2.38068e11	0.565335	0.282668	−	0.959218i	$-0.408781\pi$
$383$	2.38068e11	0.565335	0.282668	+	0.959218i	$0.408781\pi$
$384$	−2.84890e11	−0.668632
$385$	−1.50404e12	−3.48888
$386$	−4.26879e11	−0.978727
$387$	2.56628e10	0.0581575
$388$	1.37285e11	0.307526
$389$	5.45633e10	0.120817	0.0604084	−	0.998174i	$-0.480760\pi$
$389$	5.45633e10	0.120817	0.0604084	+	0.998174i	$0.480760\pi$
$390$	−5.57319e11	−1.21987
$391$	3.08801e11	0.668165
$392$	3.12800e11	0.669082
$393$	−4.52603e11	−0.957085
$394$	4.59798e11	0.961245
$395$	−2.02826e11	−0.419215
$396$	−8.48375e10	−0.173364
$397$	−2.81399e11	−0.568546	−0.284273	−	0.958743i	$-0.591752\pi$
$397$	−2.81399e11	−0.568546	−0.284273	+	0.958743i	$0.591752\pi$
$398$	9.93471e11	1.98464
$399$	−4.25507e11	−0.840482
$400$	−1.81251e12	−3.54006
$401$	−5.46924e11	−1.05628	−0.528138	−	0.849159i	$-0.677110\pi$
$401$	−5.46924e11	−1.05628	−0.528138	+	0.849159i	$0.677110\pi$
$402$	−4.91194e11	−0.938071
$403$	3.48370e11	0.657913
$404$	9.51544e9	0.0177710
$405$	−1.18057e11	−0.218044
$406$	−2.88121e11	−0.526268
$407$	−8.70794e11	−1.57304
$408$	3.55904e11	0.635861
$409$	−4.16938e11	−0.736745	−0.368372	−	0.929678i	$-0.620085\pi$
$409$	−4.16938e11	−0.736745	−0.368372	+	0.929678i	$0.620085\pi$
$410$	−5.68172e11	−0.993008
$411$	5.73035e11	0.990587
$412$	−3.11910e11	−0.533325
$413$	−1.07589e11	−0.181967
$414$	−1.00668e11	−0.168418
$415$	−2.95807e11	−0.489545
$416$	−4.27867e11	−0.700469
$417$	−6.32636e11	−1.02457
$418$	9.81486e11	1.57250
$419$	−2.29898e10	−0.0364395	−0.0182197	−	0.999834i	$-0.505800\pi$
$419$	−2.29898e10	−0.0364395	−0.0182197	+	0.999834i	$0.505800\pi$
$420$	4.12918e11	0.647504
$421$	−1.12164e12	−1.74013	−0.870066	−	0.492935i	$-0.835924\pi$
$421$	−1.12164e12	−1.74013	−0.870066	+	0.492935i	$0.835924\pi$
$422$	−7.57591e11	−1.16286
$423$	−3.74153e11	−0.568222
$424$	3.34262e11	0.502275
$425$	3.00994e12	4.47515
$426$	4.99805e11	0.735287
$427$	−4.72323e11	−0.687565
$428$	−1.79522e10	−0.0258595
$429$	4.67337e11	0.666150
$430$	2.88110e11	0.406397
$431$	3.60756e11	0.503577	0.251789	−	0.967782i	$-0.418981\pi$
$431$	3.60756e11	0.503577	0.251789	+	0.967782i	$0.418981\pi$
$432$	−1.72986e11	−0.238965
$433$	−6.41294e11	−0.876721	−0.438361	−	0.898799i	$-0.644441\pi$
$433$	−6.41294e11	−0.876721	−0.438361	+	0.898799i	$0.644441\pi$
$434$	−8.89360e11	−1.20330
$435$	2.68398e11	0.359399
$436$	5.82183e11	0.771561
$437$	3.37994e11	0.443346
$438$	−2.42917e11	−0.315373
$439$	6.52702e11	0.838735	0.419368	−	0.907816i	$-0.362252\pi$
$439$	6.52702e11	0.838735	0.419368	+	0.907816i	$0.362252\pi$
$440$	1.37694e12	1.75138
$441$	2.52476e11	0.317868
$442$	1.35613e12	1.69005
$443$	1.30215e11	0.160636	0.0803182	−	0.996769i	$-0.474406\pi$
$443$	1.30215e11	0.160636	0.0803182	+	0.996769i	$0.474406\pi$
$444$	2.39067e11	0.291942
$445$	1.68198e12	2.03329
$446$	7.40748e11	0.886469
$447$	2.96071e11	0.350761
$448$	−3.87431e11	−0.454406
$449$	−8.31004e11	−0.964927	−0.482463	−	0.875916i	$-0.660258\pi$
$449$	−8.31004e11	−0.964927	−0.482463	+	0.875916i	$0.660258\pi$
$450$	−9.81223e11	−1.12801
$451$	4.76438e11	0.542265
$452$	3.68124e11	0.414831
$453$	4.29897e11	0.479647
$454$	7.42366e11	0.820099
$455$	−2.27461e12	−2.48803
$456$	3.89550e11	0.421912
$457$	−6.65343e11	−0.713547	−0.356773	−	0.934191i	$-0.616123\pi$
$457$	−6.65343e11	−0.713547	−0.356773	+	0.934191i	$0.616123\pi$
$458$	−8.46567e11	−0.899015
$459$	2.87268e11	0.302086
$460$	−3.27995e11	−0.341552
$461$	−1.11231e12	−1.14702	−0.573512	−	0.819197i	$-0.694419\pi$
$461$	−1.11231e12	−1.14702	−0.573512	+	0.819197i	$0.694419\pi$
$462$	−1.19307e12	−1.21836
$463$	−9.99926e11	−1.01124	−0.505619	−	0.862757i	$-0.668736\pi$
$463$	−9.99926e11	−1.01124	−0.505619	+	0.862757i	$0.668736\pi$
$464$	3.93277e11	0.393883
$465$	8.28480e11	0.821757
$466$	−8.14937e11	−0.800548
$467$	−1.02910e12	−1.00123	−0.500614	−	0.865671i	$-0.666892\pi$
$467$	−1.02910e12	−1.00123	−0.500614	+	0.865671i	$0.666892\pi$
$468$	−1.28302e11	−0.123631
$469$	−2.00473e12	−1.91327
$470$	−4.20052e12	−3.97066
$471$	−5.71973e11	−0.535527
$472$	9.84972e10	0.0913451
$473$	−2.41593e11	−0.221926
$474$	−1.60890e11	−0.146395
$475$	3.29448e12	2.96938
$476$	−1.00475e12	−0.897075
$477$	2.69800e11	0.238621
$478$	8.10196e11	0.709847
$479$	7.17132e10	0.0622429	0.0311214	−	0.999516i	$-0.490092\pi$
$479$	7.17132e10	0.0622429	0.0311214	+	0.999516i	$0.490092\pi$
$480$	−1.01753e12	−0.874911
$481$	−1.31693e12	−1.12178
$482$	−6.88078e11	−0.580666
$483$	−4.10858e11	−0.343502
$484$	3.05039e11	0.252668
$485$	−1.79848e12	−1.47594
$486$	−9.36478e10	−0.0761438
$487$	−1.95850e12	−1.57777	−0.788884	−	0.614542i	$-0.789341\pi$
$487$	−1.95850e12	−1.57777	−0.788884	+	0.614542i	$0.789341\pi$
$488$	4.32410e11	0.345149
$489$	−5.88963e11	−0.465799
$490$	2.83448e12	2.22122
$491$	−9.39570e11	−0.729563	−0.364781	−	0.931093i	$-0.618856\pi$
$491$	−9.39570e11	−0.729563	−0.364781	+	0.931093i	$0.618856\pi$
$492$	−1.30801e11	−0.100639
$493$	−6.53092e11	−0.497924
$494$	1.48433e12	1.12140
$495$	1.11140e12	0.832046
$496$	1.21395e12	0.900604
$497$	2.03987e12	1.49968
$498$	−2.34647e11	−0.170956
$499$	1.84042e12	1.32881	0.664406	−	0.747372i	$-0.268684\pi$
$499$	1.84042e12	1.32881	0.664406	+	0.747372i	$0.268684\pi$
$500$	−2.07565e12	−1.48521
$501$	−7.25569e11	−0.514528
$502$	−5.20187e11	−0.365589
$503$	1.93179e12	1.34556	0.672781	−	0.739842i	$-0.265100\pi$
$503$	1.93179e12	1.34556	0.672781	+	0.739842i	$0.265100\pi$
$504$	−4.73528e11	−0.326895
$505$	−1.24655e11	−0.0852904
$506$	9.47696e11	0.642675
$507$	−1.52197e11	−0.102299
$508$	7.29995e11	0.486332
$509$	1.57321e12	1.03886	0.519430	−	0.854513i	$-0.326144\pi$
$509$	1.57321e12	1.03886	0.519430	+	0.854513i	$0.326144\pi$
$510$	3.22508e12	2.11093
$511$	−9.91425e11	−0.643229
$512$	−1.36275e11	−0.0876395
$513$	3.14425e11	0.200442
$514$	−3.24172e12	−2.04852
$515$	4.08613e12	2.55964
$516$	6.63267e10	0.0411874
$517$	3.52232e12	2.16831
$518$	3.36200e12	2.05170
$519$	−5.89350e11	−0.356550
$520$	2.08239e12	1.24896
$521$	−1.47553e12	−0.877362	−0.438681	−	0.898643i	$-0.644554\pi$
$521$	−1.47553e12	−0.877362	−0.438681	+	0.898643i	$0.644554\pi$
$522$	2.12905e11	0.125507
$523$	1.84774e11	0.107990	0.0539951	−	0.998541i	$-0.482804\pi$
$523$	1.84774e11	0.107990	0.0539951	+	0.998541i	$0.482804\pi$
$524$	−1.16977e12	−0.677813
$525$	−4.00470e12	−2.30066
$526$	−4.53050e11	−0.258054
$527$	−2.01594e12	−1.13849
$528$	1.62851e12	0.911880
$529$	−1.47479e12	−0.818806
$530$	3.02897e12	1.66745
$531$	7.95020e10	0.0433963
$532$	−1.09974e12	−0.595234
$533$	7.20530e11	0.386705
$534$	1.33422e12	0.710053
$535$	2.35179e11	0.124110
$536$	1.83532e12	0.960440
$537$	−1.68850e12	−0.876229
$538$	−3.14922e12	−1.62062
$539$	−2.37684e12	−1.21297
$540$	−3.05123e11	−0.154420
$541$	−6.52891e11	−0.327682	−0.163841	−	0.986487i	$-0.552388\pi$
$541$	−6.52891e11	−0.327682	−0.163841	+	0.986487i	$0.552388\pi$
$542$	9.52967e10	0.0474330
$543$	1.03064e12	0.508756
$544$	2.47597e12	1.21213
$545$	−7.62679e12	−3.70303
$546$	−1.80432e12	−0.868852
$547$	3.32658e12	1.58875	0.794375	−	0.607428i	$-0.207799\pi$
$547$	3.32658e12	1.58875	0.794375	+	0.607428i	$0.207799\pi$
$548$	1.48103e12	0.701539
$549$	3.49020e11	0.163974
$550$	9.23734e12	4.30442
$551$	−7.14833e11	−0.330387
$552$	3.76139e11	0.172434
$553$	−6.56647e11	−0.298585
$554$	−2.24756e12	−1.01372
$555$	−3.13186e12	−1.40115
$556$	−1.63507e12	−0.725606
$557$	1.94559e12	0.856453	0.428226	−	0.903672i	$-0.359139\pi$
$557$	1.94559e12	0.856453	0.428226	+	0.903672i	$0.359139\pi$
$558$	6.57186e11	0.286969
$559$	−3.65368e11	−0.158262
$560$	−7.92622e12	−3.40581
$561$	−2.70437e12	−1.15275
$562$	8.25533e11	0.349077
$563$	2.30080e12	0.965144	0.482572	−	0.875856i	$-0.339703\pi$
$563$	2.30080e12	0.965144	0.482572	+	0.875856i	$0.339703\pi$
$564$	−9.67015e11	−0.402418
$565$	−4.82255e12	−1.99094
$566$	4.78444e12	1.95956
$567$	−3.82208e11	−0.155302
$568$	−1.86749e12	−0.752820
$569$	9.87978e11	0.395132	0.197566	−	0.980290i	$-0.436696\pi$
$569$	9.87978e11	0.395132	0.197566	+	0.980290i	$0.436696\pi$
$570$	3.52997e12	1.40066
$571$	−8.55231e11	−0.336683	−0.168341	−	0.985729i	$-0.553841\pi$
$571$	−8.55231e11	−0.336683	−0.168341	+	0.985729i	$0.553841\pi$
$572$	1.20785e12	0.471771
$573$	2.34064e12	0.907065
$574$	−1.83945e12	−0.707270
$575$	3.18106e12	1.21358
$576$	2.86289e11	0.108369
$577$	−1.50266e12	−0.564378	−0.282189	−	0.959359i	$-0.591061\pi$
$577$	−1.50266e12	−0.564378	−0.282189	+	0.959359i	$0.591061\pi$
$578$	−4.66257e12	−1.73760
$579$	1.28741e12	0.476062
$580$	6.93685e11	0.254528
$581$	−9.57673e11	−0.348678
$582$	−1.42663e12	−0.515418
$583$	−2.53993e12	−0.910568
$584$	9.07646e11	0.322893
$585$	1.68080e12	0.593356
$586$	4.88596e12	1.71163
$587$	5.14820e12	1.78972	0.894858	−	0.446351i	$-0.147277\pi$
$587$	5.14820e12	1.78972	0.894858	+	0.446351i	$0.147277\pi$
$588$	6.52535e11	0.225116
$589$	−2.20652e12	−0.755421
$590$	8.92548e11	0.303248
$591$	−1.38669e12	−0.467558
$592$	−4.58904e12	−1.53559
$593$	2.46084e11	0.0817218	0.0408609	−	0.999165i	$-0.486990\pi$
$593$	2.46084e11	0.0817218	0.0408609	+	0.999165i	$0.486990\pi$
$594$	8.81611e11	0.290561
$595$	1.31626e13	4.30543
$596$	7.65208e11	0.248411
$597$	−2.99618e12	−0.965347
$598$	1.43323e12	0.458310
$599$	4.30285e12	1.36564	0.682819	−	0.730588i	$-0.260754\pi$
$599$	4.30285e12	1.36564	0.682819	+	0.730588i	$0.260754\pi$
$600$	3.66629e12	1.15490
$601$	−8.32379e11	−0.260247	−0.130124	−	0.991498i	$-0.541537\pi$
$601$	−8.32379e11	−0.260247	−0.130124	+	0.991498i	$0.541537\pi$
$602$	9.32753e11	0.289456
$603$	1.48138e12	0.456287
$604$	1.11109e12	0.339689
$605$	−3.99611e12	−1.21266
$606$	−9.88821e10	−0.0297845
$607$	−4.24000e12	−1.26770	−0.633850	−	0.773456i	$-0.718526\pi$
$607$	−4.24000e12	−1.26770	−0.633850	+	0.773456i	$0.718526\pi$
$608$	2.71004e12	0.804284
$609$	8.68935e11	0.255982
$610$	3.91835e12	1.14583
$611$	5.32691e12	1.54629
$612$	7.42456e11	0.213939
$613$	−2.49618e11	−0.0714008	−0.0357004	−	0.999363i	$-0.511366\pi$
$613$	−2.49618e11	−0.0714008	−0.0357004	+	0.999363i	$0.511366\pi$
$614$	−6.33264e12	−1.79815
$615$	1.71353e12	0.483008
$616$	4.45784e12	1.24742
$617$	−6.24706e12	−1.73537	−0.867686	−	0.497113i	$-0.834394\pi$
$617$	−6.24706e12	−1.73537	−0.867686	+	0.497113i	$0.834394\pi$
$618$	3.24129e12	0.893861
$619$	−2.45716e12	−0.672707	−0.336354	−	0.941736i	$-0.609194\pi$
$619$	−2.45716e12	−0.672707	−0.336354	+	0.941736i	$0.609194\pi$
$620$	2.14124e12	0.581973
$621$	3.03600e11	0.0819200
$622$	−2.35558e12	−0.631018
$623$	5.44538e12	1.44821
$624$	2.46284e12	0.650288
$625$	1.63160e13	4.27714
$626$	−3.09722e12	−0.806098
$627$	−2.96003e12	−0.764879
$628$	−1.47829e12	−0.379263
$629$	7.62076e12	1.94120
$630$	−4.29094e12	−1.08523
$631$	−3.57158e12	−0.896867	−0.448434	−	0.893816i	$-0.648018\pi$
$631$	−3.57158e12	−0.896867	−0.448434	+	0.893816i	$0.648018\pi$
$632$	6.01158e11	0.149886
$633$	2.28480e12	0.565628
$634$	7.84074e12	1.92733
$635$	−9.56318e12	−2.33411
$636$	6.97309e11	0.168993
$637$	−3.59456e12	−0.865005
$638$	−2.00431e12	−0.478929
$639$	−1.50735e12	−0.357651
$640$	9.64592e12	2.27266
$641$	−2.29585e12	−0.537133	−0.268567	−	0.963261i	$-0.586550\pi$
$641$	−2.29585e12	−0.537133	−0.268567	+	0.963261i	$0.586550\pi$
$642$	1.86554e11	0.0433409
$643$	3.40634e12	0.785848	0.392924	−	0.919571i	$-0.371464\pi$
$643$	3.40634e12	0.785848	0.392924	+	0.919571i	$0.371464\pi$
$644$	−1.06188e12	−0.243270
$645$	−8.68902e11	−0.197675
$646$	−8.58947e12	−1.94053
$647$	5.01929e12	1.12609	0.563045	−	0.826426i	$-0.309630\pi$
$647$	5.01929e12	1.12609	0.563045	+	0.826426i	$0.309630\pi$
$648$	3.49910e11	0.0779594
$649$	−7.48441e11	−0.165598
$650$	1.39699e13	3.06961
$651$	2.68219e12	0.585296
$652$	−1.52220e12	−0.329881
$653$	−3.46316e12	−0.745354	−0.372677	−	0.927961i	$-0.621560\pi$
$653$	−3.46316e12	−0.745354	−0.372677	+	0.927961i	$0.621560\pi$
$654$	−6.04990e12	−1.29315
$655$	1.53244e13	3.25310
$656$	2.51080e12	0.529353
$657$	7.32606e11	0.153400
$658$	−1.35991e13	−2.82810
$659$	1.58198e12	0.326751	0.163376	−	0.986564i	$-0.447762\pi$
$659$	1.58198e12	0.326751	0.163376	+	0.986564i	$0.447762\pi$
$660$	2.87246e12	0.589259
$661$	2.53721e12	0.516951	0.258476	−	0.966018i	$-0.416780\pi$
$661$	2.53721e12	0.516951	0.258476	+	0.966018i	$0.416780\pi$
$662$	−9.28037e12	−1.87804
$663$	−4.08990e12	−0.822057
$664$	8.76746e11	0.175032
$665$	1.44070e13	2.85677
$666$	−2.48433e12	−0.489299
$667$	−6.90223e11	−0.135028
$668$	−1.87526e12	−0.364392
$669$	−2.23400e12	−0.431187
$670$	1.66310e13	3.18847
$671$	−3.28571e12	−0.625717
$672$	−3.29426e12	−0.623155
$673$	−4.06419e12	−0.763672	−0.381836	−	0.924230i	$-0.624708\pi$
$673$	−4.06419e12	−0.763672	−0.381836	+	0.924230i	$0.624708\pi$
$674$	−6.85461e12	−1.27942
$675$	2.95924e12	0.548673
$676$	−3.93361e11	−0.0724487
$677$	5.16546e11	0.0945061	0.0472531	−	0.998883i	$-0.484953\pi$
$677$	5.16546e11	0.0945061	0.0472531	+	0.998883i	$0.484953\pi$
$678$	−3.82545e12	−0.695263
$679$	−5.82257e12	−1.05124
$680$	−1.20503e13	−2.16127
$681$	−2.23888e12	−0.398904
$682$	−6.18682e12	−1.09506
$683$	−6.87660e12	−1.20915	−0.604576	−	0.796548i	$-0.706657\pi$
$683$	−6.87660e12	−1.20915	−0.604576	+	0.796548i	$0.706657\pi$
$684$	8.12645e11	0.141954
$685$	−1.94020e13	−3.36697
$686$	−4.46476e11	−0.0769731
$687$	2.55314e12	0.437289
$688$	−1.27318e12	−0.216642
$689$	−3.84120e12	−0.649353
$690$	3.40844e12	0.572446
$691$	−3.00307e12	−0.501089	−0.250544	−	0.968105i	$-0.580610\pi$
$691$	−3.00307e12	−0.501089	−0.250544	+	0.968105i	$0.580610\pi$
$692$	−1.52320e12	−0.252510
$693$	3.59815e12	0.592624
$694$	−7.76481e12	−1.27061
$695$	2.14200e13	3.48248
$696$	−7.95506e11	−0.128500
$697$	−4.16955e12	−0.669177
$698$	−1.58769e12	−0.253173
$699$	2.45774e12	0.389394
$700$	−1.03503e13	−1.62934
$701$	2.97144e12	0.464768	0.232384	−	0.972624i	$-0.425347\pi$
$701$	2.97144e12	0.464768	0.232384	+	0.972624i	$0.425347\pi$
$702$	1.33329e12	0.207208
$703$	8.34120e12	1.28804
$704$	−2.69516e12	−0.413531
$705$	1.26682e13	1.93137
$706$	7.06394e12	1.07010
$707$	−4.03571e11	−0.0607480
$708$	2.05476e11	0.0307335
$709$	7.47955e12	1.11165	0.555824	−	0.831300i	$-0.312403\pi$
$709$	7.47955e12	1.11165	0.555824	+	0.831300i	$0.312403\pi$
$710$	−1.69226e13	−2.49922
$711$	4.85224e11	0.0712081
$712$	−4.98523e12	−0.726985
$713$	−2.13056e12	−0.308738
$714$	1.04412e13	1.50351
$715$	−1.58233e13	−2.26422
$716$	−4.36401e12	−0.620550
$717$	−2.44345e12	−0.345276
$718$	8.80999e12	1.23713
$719$	−8.56748e12	−1.19556	−0.597782	−	0.801659i	$-0.703951\pi$
$719$	−8.56748e12	−1.19556	−0.597782	+	0.801659i	$0.703951\pi$
$720$	5.85702e12	0.812233
$721$	1.32288e13	1.82310
$722$	−7.34768e11	−0.100631
$723$	2.07516e12	0.282441
$724$	2.66374e12	0.360304
$725$	−6.72772e12	−0.904372
$726$	−3.16989e12	−0.423476
$727$	−8.91360e12	−1.18345	−0.591723	−	0.806142i	$-0.701552\pi$
$727$	−8.91360e12	−1.18345	−0.591723	+	0.806142i	$0.701552\pi$
$728$	6.74173e12	0.889570
$729$	2.82430e11	0.0370370
$730$	8.22477e12	1.07194
$731$	2.11430e12	0.273866
$732$	9.02056e11	0.116127
$733$	−1.54952e12	−0.198258	−0.0991290	−	0.995075i	$-0.531606\pi$
$733$	−1.54952e12	−0.198258	−0.0991290	+	0.995075i	$0.531606\pi$
$734$	−5.44287e12	−0.692143
$735$	−8.54843e12	−1.08042
$736$	2.61674e12	0.328708
$737$	−1.39459e13	−1.74117
$738$	1.35925e12	0.168673
$739$	−1.32347e13	−1.63236	−0.816178	−	0.577800i	$-0.803911\pi$
$739$	−1.32347e13	−1.63236	−0.816178	+	0.577800i	$0.803911\pi$
$740$	−8.09442e12	−0.992300
$741$	−4.47654e12	−0.545457
$742$	9.80626e12	1.18764
$743$	−3.83362e12	−0.461487	−0.230743	−	0.973015i	$-0.574116\pi$
$743$	−3.83362e12	−0.461487	−0.230743	+	0.973015i	$0.574116\pi$
$744$	−2.45554e12	−0.293811
$745$	−1.00245e13	−1.19223
$746$	−1.80678e13	−2.13590
$747$	7.07665e11	0.0831544
$748$	−6.98956e12	−0.816381
$749$	7.61390e11	0.0883973
$750$	2.15696e13	2.48924
$751$	−7.32602e12	−0.840404	−0.420202	−	0.907431i	$-0.638041\pi$
$751$	−7.32602e12	−0.840404	−0.420202	+	0.907431i	$0.638041\pi$
$752$	1.85624e13	2.11668
$753$	1.56882e12	0.177826
$754$	−3.03117e12	−0.341538
$755$	−1.45556e13	−1.63030
$756$	−9.87832e11	−0.109985
$757$	7.43989e11	0.0823446	0.0411723	−	0.999152i	$-0.486891\pi$
$757$	7.43989e11	0.0823446	0.0411723	+	0.999152i	$0.486891\pi$
$758$	−1.50810e13	−1.65927
$759$	−2.85813e12	−0.312603
$760$	−1.31895e13	−1.43406
$761$	1.54943e13	1.67472	0.837359	−	0.546653i	$-0.184098\pi$
$761$	1.54943e13	1.67472	0.837359	+	0.546653i	$0.184098\pi$
$762$	−7.58592e12	−0.815100
$763$	−2.46916e13	−2.63748
$764$	6.04948e12	0.642388
$765$	−9.72642e12	−1.02678
$766$	−6.39400e12	−0.671032
$767$	−1.13189e12	−0.118093
$768$	5.84193e12	0.605942
$769$	1.38198e13	1.42506	0.712532	−	0.701639i	$-0.247548\pi$
$769$	1.38198e13	1.42506	0.712532	+	0.701639i	$0.247548\pi$
$770$	4.03954e13	4.14118
$771$	9.77659e12	0.996421
$772$	3.32737e12	0.337150
$773$	−1.14859e13	−1.15706	−0.578531	−	0.815660i	$-0.696374\pi$
$773$	−1.14859e13	−1.15706	−0.578531	+	0.815660i	$0.696374\pi$
$774$	−6.89251e11	−0.0690308
$775$	−2.07669e13	−2.06782
$776$	5.33054e12	0.527708
$777$	−1.01394e13	−0.997967
$778$	−1.46546e12	−0.143405
$779$	−4.56372e12	−0.444018
$780$	4.34411e12	0.420218
$781$	1.41903e13	1.36478
$782$	−8.29376e12	−0.793087
$783$	−6.42093e11	−0.0610478
$784$	−1.25258e13	−1.18409
$785$	1.93661e13	1.82024
$786$	1.21560e13	1.13603
$787$	−1.14994e13	−1.06853	−0.534265	−	0.845317i	$-0.679412\pi$
$787$	−1.14994e13	−1.06853	−0.534265	+	0.845317i	$0.679412\pi$
$788$	−3.58396e12	−0.331127
$789$	1.36634e12	0.125520
$790$	5.44748e12	0.497593
$791$	−1.56129e13	−1.41805
$792$	−3.29409e12	−0.297490
$793$	−4.96907e12	−0.446217
$794$	7.55779e12	0.674843
$795$	−9.13498e12	−0.811065
$796$	−7.74375e12	−0.683664
$797$	−3.89098e11	−0.0341583	−0.0170792	−	0.999854i	$-0.505437\pi$
$797$	−3.89098e11	−0.0341583	−0.0170792	+	0.999854i	$0.505437\pi$
$798$	1.14282e13	0.997622
$799$	−3.08256e13	−2.67578
$800$	2.55058e13	2.20158
$801$	−4.02383e12	−0.345377
$802$	1.46892e13	1.25376
$803$	−6.89683e12	−0.585369
$804$	3.82868e12	0.323145
$805$	1.39110e13	1.16755
$806$	−9.35651e12	−0.780919
$807$	9.49763e12	0.788287
$808$	3.69467e11	0.0304947
$809$	−1.48311e13	−1.21732	−0.608661	−	0.793430i	$-0.708293\pi$
$809$	−1.48311e13	−1.21732	−0.608661	+	0.793430i	$0.708293\pi$
$810$	3.17076e12	0.258810
$811$	−2.16295e13	−1.75571	−0.877855	−	0.478926i	$-0.841026\pi$
$811$	−2.16295e13	−1.75571	−0.877855	+	0.478926i	$0.841026\pi$
$812$	2.24580e12	0.181288
$813$	−2.87402e11	−0.0230719
$814$	2.33877e13	1.86715
$815$	1.99413e13	1.58323
$816$	−1.42519e13	−1.12530
$817$	2.31418e12	0.181718
$818$	1.11981e13	0.874489
$819$	5.44158e12	0.422618
$820$	4.42870e12	0.342069
$821$	4.44081e12	0.341129	0.170564	−	0.985347i	$-0.445441\pi$
$821$	4.44081e12	0.341129	0.170564	+	0.985347i	$0.445441\pi$
$822$	−1.53905e13	−1.17579
$823$	1.73705e13	1.31982	0.659908	−	0.751347i	$-0.270595\pi$
$823$	1.73705e13	1.31982	0.659908	+	0.751347i	$0.270595\pi$
$824$	−1.21109e13	−0.915176
$825$	−2.78586e13	−2.09371
$826$	2.88961e12	0.215988
$827$	−9.92279e12	−0.737665	−0.368832	−	0.929496i	$-0.620242\pi$
$827$	−9.92279e12	−0.737665	−0.368832	+	0.929496i	$0.620242\pi$
$828$	7.84668e11	0.0580162
$829$	4.10308e12	0.301728	0.150864	−	0.988555i	$-0.451795\pi$
$829$	4.10308e12	0.301728	0.150864	+	0.988555i	$0.451795\pi$
$830$	7.94477e12	0.581072
$831$	6.77834e12	0.493081
$832$	−4.07597e12	−0.294901
$833$	2.08009e13	1.49686
$834$	1.69913e13	1.21613
$835$	2.45666e13	1.74886
$836$	−7.65033e12	−0.541691
$837$	−1.98199e12	−0.139584
$838$	6.17458e11	0.0432523
$839$	9.17820e12	0.639483	0.319741	−	0.947505i	$-0.396404\pi$
$839$	9.17820e12	0.639483	0.319741	+	0.947505i	$0.396404\pi$
$840$	1.60329e13	1.11110
$841$	−1.30474e13	−0.899376
$842$	3.01248e13	2.06547
$843$	−2.48970e12	−0.169794
$844$	5.90516e12	0.400581
$845$	5.15316e12	0.347711
$846$	1.00490e13	0.674459
$847$	−1.29374e13	−0.863715
$848$	−1.33853e13	−0.888886
$849$	−1.44293e13	−0.953146
$850$	−8.08406e13	−5.31183
$851$	8.05403e12	0.526417
$852$	−3.89580e12	−0.253290
$853$	1.05675e13	0.683444	0.341722	−	0.939801i	$-0.388990\pi$
$853$	1.05675e13	0.683444	0.341722	+	0.939801i	$0.388990\pi$
$854$	1.26856e13	0.816114
$855$	−1.06459e13	−0.681296
$856$	−6.97050e11	−0.0443743
$857$	9.21033e12	0.583259	0.291629	−	0.956531i	$-0.405803\pi$
$857$	9.21033e12	0.583259	0.291629	+	0.956531i	$0.405803\pi$
$858$	−1.25517e13	−0.790696
$859$	−1.86736e12	−0.117020	−0.0585099	−	0.998287i	$-0.518635\pi$
$859$	−1.86736e12	−0.117020	−0.0585099	+	0.998287i	$0.518635\pi$
$860$	−2.24571e12	−0.139995
$861$	5.54755e12	0.344023
$862$	−9.68916e12	−0.597728
$863$	−2.25160e13	−1.38179	−0.690896	−	0.722954i	$-0.742784\pi$
$863$	−2.25160e13	−1.38179	−0.690896	+	0.722954i	$0.742784\pi$
$864$	2.43427e12	0.148613
$865$	1.99544e13	1.21190
$866$	1.72238e13	1.04064
$867$	1.40617e13	0.845185
$868$	6.93224e12	0.414510
$869$	−4.56795e12	−0.271727
$870$	−7.20860e12	−0.426594
$871$	−2.10907e13	−1.24168
$872$	2.26051e13	1.32398
$873$	4.30254e12	0.250704
$874$	−9.07782e12	−0.526236
$875$	8.80327e13	5.07701
$876$	1.89345e12	0.108639
$877$	−3.32866e13	−1.90008	−0.950039	−	0.312130i	$-0.898957\pi$
$877$	−3.32866e13	−1.90008	−0.950039	+	0.312130i	$0.898957\pi$
$878$	−1.75302e13	−0.995548
$879$	−1.47354e13	−0.832555
$880$	−5.51387e13	−3.09945
$881$	8.33047e12	0.465884	0.232942	−	0.972491i	$-0.425165\pi$
$881$	8.33047e12	0.465884	0.232942	+	0.972491i	$0.425165\pi$
$882$	−6.78098e12	−0.377298
$883$	−8.05324e12	−0.445808	−0.222904	−	0.974840i	$-0.571554\pi$
$883$	−8.05324e12	−0.445808	−0.222904	+	0.974840i	$0.571554\pi$
$884$	−1.05705e13	−0.582185
$885$	−2.69181e12	−0.147503
$886$	−3.49730e12	−0.190670
$887$	1.49443e13	0.810626	0.405313	−	0.914178i	$-0.367162\pi$
$887$	1.49443e13	0.810626	0.405313	+	0.914178i	$0.367162\pi$
$888$	9.28255e12	0.500967
$889$	−3.09607e13	−1.66247
$890$	−4.51744e13	−2.41345
$891$	−2.65882e12	−0.141332
$892$	−5.77386e12	−0.305369
$893$	−3.37397e13	−1.77546
$894$	−7.95185e12	−0.416341
$895$	5.71700e13	2.97827
$896$	3.12286e13	1.61870
$897$	−4.32243e12	−0.222927
$898$	2.23190e13	1.14533
$899$	4.50597e12	0.230075
$900$	7.64829e12	0.388573
$901$	2.22282e13	1.12368
$902$	−1.27961e13	−0.643649
$903$	−2.81306e12	−0.140794
$904$	1.42936e13	0.711842
$905$	−3.48960e13	−1.72924
$906$	−1.15461e13	−0.569324
$907$	−2.42002e13	−1.18737	−0.593686	−	0.804697i	$-0.702328\pi$
$907$	−2.42002e13	−1.18737	−0.593686	+	0.804697i	$0.702328\pi$
$908$	−5.78647e12	−0.282506
$909$	2.98215e11	0.0144875
$910$	6.10912e13	2.95320
$911$	6.28371e12	0.302262	0.151131	−	0.988514i	$-0.451708\pi$
$911$	6.28371e12	0.302262	0.151131	+	0.988514i	$0.451708\pi$
$912$	−1.55992e13	−0.746666
$913$	−6.66204e12	−0.317314
$914$	1.78697e13	0.846954
$915$	−1.18172e13	−0.557341
$916$	6.59869e12	0.309691
$917$	4.96125e13	2.31702
$918$	−7.71542e12	−0.358565
$919$	−8.71865e12	−0.403208	−0.201604	−	0.979467i	$-0.564615\pi$
$919$	−8.71865e12	−0.403208	−0.201604	+	0.979467i	$0.564615\pi$
$920$	−1.27354e13	−0.586096
$921$	1.90984e13	0.874639
$922$	2.98744e13	1.36147
$923$	2.14604e13	0.973264
$924$	9.29956e12	0.419700
$925$	7.85040e13	3.52577
$926$	2.68559e13	1.20030
$927$	−9.77532e12	−0.434783
$928$	−5.53421e12	−0.244957
$929$	2.66041e13	1.17186	0.585932	−	0.810360i	$-0.300728\pi$
$929$	2.66041e13	1.17186	0.585932	+	0.810360i	$0.300728\pi$
$930$	−2.22512e13	−0.975396
$931$	2.27673e13	0.993205
$932$	6.35214e12	0.275771
$933$	7.10414e12	0.306933
$934$	2.76395e13	1.18842
$935$	9.15656e13	3.91814
$936$	−4.98175e12	−0.212149
$937$	−1.41793e13	−0.600933	−0.300466	−	0.953792i	$-0.597142\pi$
$937$	−1.41793e13	−0.600933	−0.300466	+	0.953792i	$0.597142\pi$
$938$	5.38428e13	2.27099
$939$	9.34082e12	0.392094
$940$	3.27415e13	1.36780
$941$	−1.47256e13	−0.612238	−0.306119	−	0.951993i	$-0.599031\pi$
$941$	−1.47256e13	−0.612238	−0.306119	+	0.951993i	$0.599031\pi$
$942$	1.53620e13	0.635651
$943$	−4.40660e12	−0.181468
$944$	−3.94424e12	−0.161655
$945$	1.29409e13	0.527864
$946$	6.48868e12	0.263419
$947$	−1.08853e13	−0.439812	−0.219906	−	0.975521i	$-0.570575\pi$
$947$	−1.08853e13	−0.439812	−0.219906	+	0.975521i	$0.570575\pi$
$948$	1.25408e12	0.0504299
$949$	−1.04303e13	−0.417444
$950$	−8.84830e13	−3.52455
$951$	−2.36466e13	−0.937469
$952$	−3.90128e13	−1.53936
$953$	2.18030e12	0.0856244	0.0428122	−	0.999083i	$-0.486368\pi$
$953$	2.18030e12	0.0856244	0.0428122	+	0.999083i	$0.486368\pi$
$954$	−7.24626e12	−0.283235
$955$	−7.92502e13	−3.08308
$956$	−6.31519e12	−0.244527
$957$	6.04473e12	0.232956
$958$	−1.92607e12	−0.0738800
$959$	−6.28138e13	−2.39812
$960$	−9.69329e12	−0.368342
$961$	−1.25308e13	−0.473939
$962$	3.53699e13	1.33152
$963$	−5.62623e11	−0.0210814
$964$	5.36333e12	0.200027
$965$	−4.35896e13	−1.61812
$966$	1.10348e13	0.407725
$967$	1.05073e13	0.386431	0.193215	−	0.981156i	$-0.438108\pi$
$967$	1.05073e13	0.386431	0.193215	+	0.981156i	$0.438108\pi$
$968$	1.18441e13	0.433574
$969$	2.59047e13	0.943892
$970$	4.83035e13	1.75189
$971$	−3.59410e13	−1.29749	−0.648745	−	0.761006i	$-0.724706\pi$
$971$	−3.59410e13	−1.29749	−0.648745	+	0.761006i	$0.724706\pi$
$972$	7.29951e11	0.0262298
$973$	6.93471e13	2.48039
$974$	5.26012e13	1.87275
$975$	−4.21314e13	−1.49309
$976$	−1.73155e13	−0.610817
$977$	2.61860e13	0.919484	0.459742	−	0.888053i	$-0.347942\pi$
$977$	2.61860e13	0.919484	0.459742	+	0.888053i	$0.347942\pi$
$978$	1.58183e13	0.552886
$979$	3.78807e13	1.31794
$980$	−2.20938e13	−0.765161
$981$	1.82457e13	0.628999
$982$	2.52349e13	0.865964
$983$	−7.35083e11	−0.0251099	−0.0125550	−	0.999921i	$-0.503996\pi$
$983$	−7.35083e11	−0.0251099	−0.0125550	+	0.999921i	$0.503996\pi$
$984$	−5.07876e12	−0.172695
$985$	4.69511e13	1.58921
$986$	1.75407e13	0.591018
$987$	4.10132e13	1.37561
$988$	−1.15698e13	−0.386296
$989$	2.23451e12	0.0742674
$990$	−2.98499e13	−0.987608
$991$	1.94771e13	0.641493	0.320747	−	0.947165i	$-0.396066\pi$
$991$	1.94771e13	0.641493	0.320747	+	0.947165i	$0.396066\pi$
$992$	−1.70828e13	−0.560088
$993$	2.79884e13	0.913495
$994$	−5.47866e13	−1.78006
$995$	1.01446e14	3.28118
$996$	1.82899e12	0.0588904
$997$	−5.96015e13	−1.91042	−0.955210	−	0.295930i	$-0.904371\pi$
$997$	−5.96015e13	−1.91042	−0.955210	+	0.295930i	$0.904371\pi$
$998$	−4.94298e13	−1.57725
$999$	7.49240e12	0.238000

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.a.1.6	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.a.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-26.8579 q^{2} +81.0000 q^{3} +209.348 q^{4} -2742.53 q^{5} -2175.49 q^{6} -8878.91 q^{7} +8128.61 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-26.8579 q^{2} +81.0000 q^{3} +209.348 q^{4} -2742.53 q^{5} -2175.49 q^{6} -8878.91 q^{7} +8128.61 q^{8} +6561.00 q^{9} +73658.6 q^{10} -61766.0 q^{11} +16957.2 q^{12} -93410.5 q^{13} +238469. q^{14} -222145. q^{15} -325504. q^{16} +540545. q^{17} -176215. q^{18} +591646. q^{19} -574143. q^{20} -719191. q^{21} +1.65891e6 q^{22} +571277. q^{23} +658417. q^{24} +5.56834e6 q^{25} +2.50881e6 q^{26} +531441. q^{27} -1.85878e6 q^{28} -1.20821e6 q^{29} +5.96635e6 q^{30} -3.72946e6 q^{31} +4.58050e6 q^{32} -5.00304e6 q^{33} -1.45179e7 q^{34} +2.43506e7 q^{35} +1.37353e6 q^{36} +1.40983e7 q^{37} -1.58904e7 q^{38} -7.56625e6 q^{39} -2.22929e7 q^{40} -7.71359e6 q^{41} +1.93160e7 q^{42} +3.91142e6 q^{43} -1.29306e7 q^{44} -1.79937e7 q^{45} -1.53433e7 q^{46} -5.70269e7 q^{47} -2.63658e7 q^{48} +3.84813e7 q^{49} -1.49554e8 q^{50} +4.37842e7 q^{51} -1.95553e7 q^{52} +4.11217e7 q^{53} -1.42734e7 q^{54} +1.69395e8 q^{55} -7.21731e7 q^{56} +4.79233e7 q^{57} +3.24500e7 q^{58} +1.21174e7 q^{59} -4.65055e7 q^{60} +5.31961e7 q^{61} +1.00165e8 q^{62} -5.82545e7 q^{63} +4.36350e7 q^{64} +2.56181e8 q^{65} +1.34371e8 q^{66} +2.25785e8 q^{67} +1.13162e8 q^{68} +4.62735e7 q^{69} -6.54008e8 q^{70} -2.29743e8 q^{71} +5.33318e7 q^{72} +1.11661e8 q^{73} -3.78651e8 q^{74} +4.51035e8 q^{75} +1.23860e8 q^{76} +5.48414e8 q^{77} +2.03214e8 q^{78} +7.39558e7 q^{79} +8.92703e8 q^{80} +4.30467e7 q^{81} +2.07171e8 q^{82} +1.07859e8 q^{83} -1.50561e8 q^{84} -1.48246e9 q^{85} -1.05053e8 q^{86} -9.78651e7 q^{87} -5.02071e8 q^{88} -6.13295e8 q^{89} +4.83274e8 q^{90} +8.29383e8 q^{91} +1.19596e8 q^{92} -3.02086e8 q^{93} +1.53162e9 q^{94} -1.62261e9 q^{95} +3.71021e8 q^{96} +6.55776e8 q^{97} -1.03353e9 q^{98} -4.05247e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9}+O(q^{10}) \) 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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