LMFDB - Embedded newform 177.10.a.a.1.17

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			1.17
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)

$f(q)$	$=$	$q+27.0996 q^{2} +81.0000 q^{3} +222.388 q^{4} -1517.97 q^{5} +2195.07 q^{6} +2210.22 q^{7} -7848.37 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+27.0996 q^{2} +81.0000 q^{3} +222.388 q^{4} -1517.97 q^{5} +2195.07 q^{6} +2210.22 q^{7} -7848.37 q^{8} +6561.00 q^{9} -41136.3 q^{10} +20491.3 q^{11} +18013.4 q^{12} +146616. q^{13} +59896.0 q^{14} -122955. q^{15} -326550. q^{16} +10640.9 q^{17} +177800. q^{18} -363427. q^{19} -337578. q^{20} +179028. q^{21} +555306. q^{22} +1.47841e6 q^{23} -635718. q^{24} +351104. q^{25} +3.97324e6 q^{26} +531441. q^{27} +491526. q^{28} -7.12759e6 q^{29} -3.33204e6 q^{30} -8.92102e6 q^{31} -4.83102e6 q^{32} +1.65979e6 q^{33} +288365. q^{34} -3.35504e6 q^{35} +1.45909e6 q^{36} -3.34760e6 q^{37} -9.84874e6 q^{38} +1.18759e7 q^{39} +1.19136e7 q^{40} +1.53989e7 q^{41} +4.85158e6 q^{42} -2.67443e7 q^{43} +4.55702e6 q^{44} -9.95939e6 q^{45} +4.00644e7 q^{46} -5.05532e7 q^{47} -2.64506e7 q^{48} -3.54685e7 q^{49} +9.51477e6 q^{50} +861916. q^{51} +3.26057e7 q^{52} -5.26983e7 q^{53} +1.44018e7 q^{54} -3.11051e7 q^{55} -1.73466e7 q^{56} -2.94376e7 q^{57} -1.93155e8 q^{58} +1.21174e7 q^{59} -2.73438e7 q^{60} +3.72572e7 q^{61} -2.41756e8 q^{62} +1.45012e7 q^{63} +3.62751e7 q^{64} -2.22559e8 q^{65} +4.49798e7 q^{66} -1.12028e8 q^{67} +2.36642e6 q^{68} +1.19751e8 q^{69} -9.09203e7 q^{70} -2.42362e8 q^{71} -5.14931e7 q^{72} -1.68777e7 q^{73} -9.07187e7 q^{74} +2.84394e7 q^{75} -8.08219e7 q^{76} +4.52902e7 q^{77} +3.21832e8 q^{78} +5.59348e8 q^{79} +4.95693e8 q^{80} +4.30467e7 q^{81} +4.17303e8 q^{82} -7.22195e8 q^{83} +3.98136e7 q^{84} -1.61526e7 q^{85} -7.24760e8 q^{86} -5.77335e8 q^{87} -1.60823e8 q^{88} +5.52358e8 q^{89} -2.69896e8 q^{90} +3.24054e8 q^{91} +3.28781e8 q^{92} -7.22602e8 q^{93} -1.36997e9 q^{94} +5.51671e8 q^{95} -3.91312e8 q^{96} +3.40681e8 q^{97} -9.61183e8 q^{98} +1.34443e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	27.0996	1.19764	0.598822	−	0.800882i	$-0.295636\pi$
$2$	27.0996	1.19764	0.598822	+	0.800882i	$0.295636\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	222.388	0.434352
$5$	−1517.97	−1.08617	−0.543085	−	0.839678i	$-0.682744\pi$
$5$	−1517.97	−1.08617	−0.543085	+	0.839678i	$0.682744\pi$
$6$	2195.07	0.691460
$7$	2210.22	0.347932	0.173966	−	0.984752i	$-0.444342\pi$
$7$	2210.22	0.347932	0.173966	+	0.984752i	$0.444342\pi$
$8$	−7848.37	−0.677445
$9$	6561.00	0.333333
$10$	−41136.3	−1.30085
$11$	20491.3	0.421990	0.210995	−	0.977487i	$-0.432330\pi$
$11$	20491.3	0.421990	0.210995	+	0.977487i	$0.432330\pi$
$12$	18013.4	0.250773
$13$	146616.	1.42376	0.711880	−	0.702301i	$-0.247844\pi$
$13$	146616.	1.42376	0.711880	+	0.702301i	$0.247844\pi$
$14$	59896.0	0.416698
$15$	−122955.	−0.627101
$16$	−326550.	−1.24569
$17$	10640.9	0.0309001	0.0154500	−	0.999881i	$-0.495082\pi$
$17$	10640.9	0.0309001	0.0154500	+	0.999881i	$0.495082\pi$
$18$	177800.	0.399215
$19$	−363427.	−0.639774	−0.319887	−	0.947456i	$-0.603645\pi$
$19$	−363427.	−0.639774	−0.319887	+	0.947456i	$0.603645\pi$
$20$	−337578.	−0.471780
$21$	179028.	0.200878
$22$	555306.	0.505394
$23$	1.47841e6	1.10159	0.550796	−	0.834640i	$-0.314324\pi$
$23$	1.47841e6	1.10159	0.550796	+	0.834640i	$0.314324\pi$
$24$	−635718.	−0.391123
$25$	351104.	0.179765
$26$	3.97324e6	1.70516
$27$	531441.	0.192450
$28$	491526.	0.151125
$29$	−7.12759e6	−1.87134	−0.935668	−	0.352882i	$-0.885202\pi$
$29$	−7.12759e6	−1.87134	−0.935668	+	0.352882i	$0.885202\pi$
$30$	−3.33204e6	−0.751043
$31$	−8.92102e6	−1.73495	−0.867474	−	0.497482i	$-0.834258\pi$
$31$	−8.92102e6	−1.73495	−0.867474	+	0.497482i	$0.834258\pi$
$32$	−4.83102e6	−0.814448
$33$	1.65979e6	0.243636
$34$	288365.	0.0370073
$35$	−3.35504e6	−0.377913
$36$	1.45909e6	0.144784
$37$	−3.34760e6	−0.293647	−0.146824	−	0.989163i	$-0.546905\pi$
$37$	−3.34760e6	−0.293647	−0.146824	+	0.989163i	$0.546905\pi$
$38$	−9.84874e6	−0.766222
$39$	1.18759e7	0.822008
$40$	1.19136e7	0.735821
$41$	1.53989e7	0.851061	0.425531	−	0.904944i	$-0.360087\pi$
$41$	1.53989e7	0.851061	0.425531	+	0.904944i	$0.360087\pi$
$42$	4.85158e6	0.240581
$43$	−2.67443e7	−1.19295	−0.596477	−	0.802630i	$-0.703433\pi$
$43$	−2.67443e7	−1.19295	−0.596477	+	0.802630i	$0.703433\pi$
$44$	4.55702e6	0.183292
$45$	−9.95939e6	−0.362057
$46$	4.00644e7	1.31931
$47$	−5.05532e7	−1.51115	−0.755576	−	0.655061i	$-0.772643\pi$
$47$	−5.05532e7	−1.51115	−0.755576	+	0.655061i	$0.772643\pi$
$48$	−2.64506e7	−0.719200
$49$	−3.54685e7	−0.878944
$50$	9.51477e6	0.215295
$51$	861916.	0.0178402
$52$	3.26057e7	0.618413
$53$	−5.26983e7	−0.917393	−0.458696	−	0.888593i	$-0.651683\pi$
$53$	−5.26983e7	−0.917393	−0.458696	+	0.888593i	$0.651683\pi$
$54$	1.44018e7	0.230487
$55$	−3.11051e7	−0.458353
$56$	−1.73466e7	−0.235705
$57$	−2.94376e7	−0.369374
$58$	−1.93155e8	−2.24119
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	−2.73438e7	−0.272382
$61$	3.72572e7	0.344529	0.172265	−	0.985051i	$-0.444892\pi$
$61$	3.72572e7	0.344529	0.172265	+	0.985051i	$0.444892\pi$
$62$	−2.41756e8	−2.07785
$63$	1.45012e7	0.115977
$64$	3.62751e7	0.270271
$65$	−2.22559e8	−1.54645
$66$	4.49798e7	0.291789
$67$	−1.12028e8	−0.679186	−0.339593	−	0.940573i	$-0.610289\pi$
$67$	−1.12028e8	−0.679186	−0.339593	+	0.940573i	$0.610289\pi$
$68$	2.36642e6	0.0134215
$69$	1.19751e8	0.636004
$70$	−9.09203e7	−0.452605
$71$	−2.42362e8	−1.13188	−0.565942	−	0.824445i	$-0.691487\pi$
$71$	−2.42362e8	−1.13188	−0.565942	+	0.824445i	$0.691487\pi$
$72$	−5.14931e7	−0.225815
$73$	−1.68777e7	−0.0695603	−0.0347801	−	0.999395i	$-0.511073\pi$
$73$	−1.68777e7	−0.0695603	−0.0347801	+	0.999395i	$0.511073\pi$
$74$	−9.07187e7	−0.351685
$75$	2.84394e7	0.103787
$76$	−8.08219e7	−0.277887
$77$	4.52902e7	0.146824
$78$	3.21832e8	0.984474
$79$	5.59348e8	1.61570	0.807850	−	0.589389i	$-0.200631\pi$
$79$	5.59348e8	1.61570	0.807850	+	0.589389i	$0.200631\pi$
$80$	4.95693e8	1.35303
$81$	4.30467e7	0.111111
$82$	4.17303e8	1.01927
$83$	−7.22195e8	−1.67033	−0.835167	−	0.549997i	$-0.814629\pi$
$83$	−7.22195e8	−1.67033	−0.835167	+	0.549997i	$0.814629\pi$
$84$	3.98136e7	0.0872519
$85$	−1.61526e7	−0.0335627
$86$	−7.24760e8	−1.42873
$87$	−5.77335e8	−1.08042
$88$	−1.60823e8	−0.285875
$89$	5.52358e8	0.933181	0.466590	−	0.884474i	$-0.345482\pi$
$89$	5.52358e8	0.933181	0.466590	+	0.884474i	$0.345482\pi$
$90$	−2.69896e8	−0.433615
$91$	3.24054e8	0.495371
$92$	3.28781e8	0.478478
$93$	−7.22602e8	−1.00167
$94$	−1.36997e9	−1.80982
$95$	5.51671e8	0.694903
$96$	−3.91312e8	−0.470222
$97$	3.40681e8	0.390728	0.195364	−	0.980731i	$-0.437411\pi$
$97$	3.40681e8	0.390728	0.195364	+	0.980731i	$0.437411\pi$
$98$	−9.61183e8	−1.05266
$99$	1.34443e8	0.140663
$100$	7.80813e7	0.0780813
$101$	−1.32540e7	−0.0126736	−0.00633680	−	0.999980i	$-0.502017\pi$
$101$	−1.32540e7	−0.0126736	−0.00633680	+	0.999980i	$0.502017\pi$
$102$	2.33576e7	0.0213662
$103$	1.81417e9	1.58822	0.794111	−	0.607773i	$-0.207937\pi$
$103$	1.81417e9	1.58822	0.794111	+	0.607773i	$0.207937\pi$
$104$	−1.15070e9	−0.964520
$105$	−2.71758e8	−0.218188
$106$	−1.42810e9	−1.09871
$107$	8.38202e8	0.618190	0.309095	−	0.951031i	$-0.399974\pi$
$107$	8.38202e8	0.618190	0.309095	+	0.951031i	$0.399974\pi$
$108$	1.18186e8	0.0835910
$109$	2.20518e9	1.49632	0.748159	−	0.663519i	$-0.230938\pi$
$109$	2.20518e9	1.49632	0.748159	+	0.663519i	$0.230938\pi$
$110$	−8.42937e8	−0.548944
$111$	−2.71156e8	−0.169537
$112$	−7.21747e8	−0.433415
$113$	−1.14724e9	−0.661915	−0.330958	−	0.943646i	$-0.607372\pi$
$113$	−1.14724e9	−0.661915	−0.330958	+	0.943646i	$0.607372\pi$
$114$	−7.97748e8	−0.442378
$115$	−2.24418e9	−1.19652
$116$	−1.58509e9	−0.812818
$117$	9.61949e8	0.474587
$118$	3.28376e8	0.155920
$119$	2.35188e7	0.0107511
$120$	9.64999e8	0.424826
$121$	−1.93805e9	−0.821924
$122$	1.00966e9	0.412623
$123$	1.24731e9	0.491361
$124$	−1.98393e9	−0.753578
$125$	2.43182e9	0.890914
$126$	3.92978e8	0.138899
$127$	−1.27289e9	−0.434183	−0.217091	−	0.976151i	$-0.569657\pi$
$127$	−1.27289e9	−0.434183	−0.217091	+	0.976151i	$0.569657\pi$
$128$	3.45652e9	1.13814
$129$	−2.16629e9	−0.688752
$130$	−6.03125e9	−1.85209
$131$	−1.54326e9	−0.457845	−0.228923	−	0.973445i	$-0.573520\pi$
$131$	−1.54326e9	−0.457845	−0.228923	+	0.973445i	$0.573520\pi$
$132$	3.69119e8	0.105824
$133$	−8.03254e8	−0.222598
$134$	−3.03590e9	−0.813423
$135$	−8.06711e8	−0.209034
$136$	−8.35140e7	−0.0209331
$137$	−7.41578e8	−0.179851	−0.0899257	−	0.995948i	$-0.528663\pi$
$137$	−7.41578e8	−0.179851	−0.0899257	+	0.995948i	$0.528663\pi$
$138$	3.24522e9	0.761707
$139$	−3.30588e7	−0.00751140	−0.00375570	−	0.999993i	$-0.501195\pi$
$139$	−3.30588e7	−0.00751140	−0.00375570	+	0.999993i	$0.501195\pi$
$140$	−7.46121e8	−0.164147
$141$	−4.09481e9	−0.872464
$142$	−6.56791e9	−1.35559
$143$	3.00436e9	0.600813
$144$	−2.14250e9	−0.415230
$145$	1.08195e10	2.03259
$146$	−4.57380e8	−0.0833085
$147$	−2.87295e9	−0.507458
$148$	−7.44467e8	−0.127546
$149$	2.41685e9	0.401708	0.200854	−	0.979621i	$-0.435628\pi$
$149$	2.41685e9	0.401708	0.200854	+	0.979621i	$0.435628\pi$
$150$	7.70696e8	0.124300
$151$	−1.13268e10	−1.77301	−0.886506	−	0.462718i	$-0.846874\pi$
$151$	−1.13268e10	−1.77301	−0.886506	+	0.462718i	$0.846874\pi$
$152$	2.85231e9	0.433412
$153$	6.98152e7	0.0103000
$154$	1.22735e9	0.175843
$155$	1.35418e10	1.88445
$156$	2.64106e9	0.357041
$157$	1.27072e10	1.66917	0.834587	−	0.550876i	$-0.185706\pi$
$157$	1.27072e10	1.66917	0.834587	+	0.550876i	$0.185706\pi$
$158$	1.51581e10	1.93503
$159$	−4.26856e9	−0.529657
$160$	7.33333e9	0.884629
$161$	3.26762e9	0.383279
$162$	1.16655e9	0.133072
$163$	−1.61227e9	−0.178893	−0.0894464	−	0.995992i	$-0.528510\pi$
$163$	−1.61227e9	−0.178893	−0.0894464	+	0.995992i	$0.528510\pi$
$164$	3.42452e9	0.369660
$165$	−2.51952e9	−0.264630
$166$	−1.95712e10	−2.00047
$167$	−1.92747e10	−1.91763	−0.958814	−	0.284035i	$-0.908327\pi$
$167$	−1.92747e10	−1.91763	−0.958814	+	0.284035i	$0.908327\pi$
$168$	−1.40507e9	−0.136084
$169$	1.08918e10	1.02709
$170$	−4.37729e8	−0.0401962
$171$	−2.38445e9	−0.213258
$172$	−5.94762e9	−0.518161
$173$	−1.21602e10	−1.03213	−0.516063	−	0.856550i	$-0.672603\pi$
$173$	−1.21602e10	−1.03213	−0.516063	+	0.856550i	$0.672603\pi$
$174$	−1.56455e10	−1.29395
$175$	7.76016e8	0.0625460
$176$	−6.69144e9	−0.525669
$177$	9.81506e8	0.0751646
$178$	1.49687e10	1.11762
$179$	−1.73653e10	−1.26428	−0.632141	−	0.774853i	$-0.717824\pi$
$179$	−1.73653e10	−1.26428	−0.632141	+	0.774853i	$0.717824\pi$
$180$	−2.21485e9	−0.157260
$181$	−6.72148e9	−0.465491	−0.232746	−	0.972538i	$-0.574771\pi$
$181$	−6.72148e9	−0.465491	−0.232746	+	0.972538i	$0.574771\pi$
$182$	8.78173e9	0.593279
$183$	3.01783e9	0.198914
$184$	−1.16031e10	−0.746268
$185$	5.08156e9	0.318951
$186$	−1.95822e10	−1.19965
$187$	2.18047e8	0.0130395
$188$	−1.12424e10	−0.656372
$189$	1.17460e9	0.0669595
$190$	1.49501e10	0.832247
$191$	1.29637e10	0.704820	0.352410	−	0.935846i	$-0.385362\pi$
$191$	1.29637e10	0.704820	0.352410	+	0.935846i	$0.385362\pi$
$192$	2.93829e9	0.156041
$193$	−2.92326e9	−0.151656	−0.0758280	−	0.997121i	$-0.524160\pi$
$193$	−2.92326e9	−0.151656	−0.0758280	+	0.997121i	$0.524160\pi$
$194$	9.23231e9	0.467953
$195$	−1.80273e10	−0.892841
$196$	−7.88778e9	−0.381771
$197$	−1.57311e10	−0.744151	−0.372076	−	0.928202i	$-0.621354\pi$
$197$	−1.57311e10	−0.744151	−0.372076	+	0.928202i	$0.621354\pi$
$198$	3.64336e9	0.168465
$199$	−1.47294e10	−0.665803	−0.332902	−	0.942962i	$-0.608028\pi$
$199$	−1.47294e10	−0.665803	−0.332902	+	0.942962i	$0.608028\pi$
$200$	−2.75559e9	−0.121781
$201$	−9.07424e9	−0.392128
$202$	−3.59177e8	−0.0151785
$203$	−1.57535e10	−0.651097
$204$	1.91680e8	0.00774891
$205$	−2.33750e10	−0.924397
$206$	4.91634e10	1.90213
$207$	9.69987e9	0.367197
$208$	−4.78776e10	−1.77356
$209$	−7.44710e9	−0.269978
$210$	−7.36454e9	−0.261312
$211$	−2.45527e10	−0.852762	−0.426381	−	0.904544i	$-0.640212\pi$
$211$	−2.45527e10	−0.852762	−0.426381	+	0.904544i	$0.640212\pi$
$212$	−1.17195e10	−0.398471
$213$	−1.96313e10	−0.653494
$214$	2.27149e10	0.740371
$215$	4.05970e10	1.29575
$216$	−4.17094e9	−0.130374
$217$	−1.97174e10	−0.603644
$218$	5.97594e10	1.79206
$219$	−1.36710e9	−0.0401606
$220$	−6.91741e9	−0.199086
$221$	1.56013e9	0.0439943
$222$	−7.34821e9	−0.203046
$223$	−6.08234e10	−1.64702	−0.823510	−	0.567301i	$-0.807987\pi$
$223$	−6.08234e10	−1.64702	−0.823510	+	0.567301i	$0.807987\pi$
$224$	−1.06776e10	−0.283372
$225$	2.30359e9	0.0599217
$226$	−3.10898e10	−0.792739
$227$	5.45777e10	1.36427	0.682133	−	0.731228i	$-0.261053\pi$
$227$	5.45777e10	1.36427	0.682133	+	0.731228i	$0.261053\pi$
$228$	−6.54658e9	−0.160438
$229$	2.14644e9	0.0515774	0.0257887	−	0.999667i	$-0.491790\pi$
$229$	2.14644e9	0.0515774	0.0257887	+	0.999667i	$0.491790\pi$
$230$	−6.08165e10	−1.43300
$231$	3.66851e9	0.0847687
$232$	5.59399e10	1.26773
$233$	5.86692e10	1.30409	0.652047	−	0.758179i	$-0.273911\pi$
$233$	5.86692e10	1.30409	0.652047	+	0.758179i	$0.273911\pi$
$234$	2.60684e10	0.568386
$235$	7.67382e10	1.64137
$236$	2.69476e9	0.0565478
$237$	4.53072e10	0.932824
$238$	6.37350e8	0.0128760
$239$	1.00854e9	0.0199941	0.00999707	−	0.999950i	$-0.496818\pi$
$239$	1.00854e9	0.0199941	0.00999707	+	0.999950i	$0.496818\pi$
$240$	4.01511e10	0.781173
$241$	1.96232e9	0.0374707	0.0187354	−	0.999824i	$-0.494036\pi$
$241$	1.96232e9	0.0374707	0.0187354	+	0.999824i	$0.494036\pi$
$242$	−5.25205e10	−0.984373
$243$	3.48678e9	0.0641500
$244$	8.28556e9	0.149647
$245$	5.38401e10	0.954682
$246$	3.38015e10	0.588475
$247$	−5.32844e10	−0.910885
$248$	7.00154e10	1.17533
$249$	−5.84978e10	−0.964368
$250$	6.59013e10	1.06700
$251$	1.01815e11	1.61912	0.809560	−	0.587037i	$-0.199706\pi$
$251$	1.01815e11	1.61912	0.809560	+	0.587037i	$0.199706\pi$
$252$	3.22490e9	0.0503749
$253$	3.02946e10	0.464861
$254$	−3.44947e10	−0.519996
$255$	−1.30836e9	−0.0193775
$256$	7.50975e10	1.09281
$257$	−1.38531e11	−1.98084	−0.990420	−	0.138089i	$-0.955904\pi$
$257$	−1.38531e11	−1.98084	−0.990420	+	0.138089i	$0.955904\pi$
$258$	−5.87056e10	−0.824880
$259$	−7.39893e9	−0.102169
$260$	−4.94944e10	−0.671701
$261$	−4.67641e10	−0.623779
$262$	−4.18218e10	−0.548336
$263$	6.09592e10	0.785667	0.392833	−	0.919610i	$-0.371495\pi$
$263$	6.09592e10	0.785667	0.392833	+	0.919610i	$0.371495\pi$
$264$	−1.30267e10	−0.165050
$265$	7.99944e10	0.996444
$266$	−2.17679e10	−0.266593
$267$	4.47410e10	0.538772
$268$	−2.49136e10	−0.295005
$269$	−1.27333e10	−0.148270	−0.0741352	−	0.997248i	$-0.523620\pi$
$269$	−1.27333e10	−0.148270	−0.0741352	+	0.997248i	$0.523620\pi$
$270$	−2.18615e10	−0.250348
$271$	6.61671e10	0.745213	0.372607	−	0.927989i	$-0.378464\pi$
$271$	6.61671e10	0.745213	0.372607	+	0.927989i	$0.378464\pi$
$272$	−3.47480e9	−0.0384919
$273$	2.62484e10	0.286003
$274$	−2.00965e10	−0.215398
$275$	7.19457e9	0.0758591
$276$	2.66313e10	0.276249
$277$	1.43076e11	1.46018	0.730092	−	0.683349i	$-0.239477\pi$
$277$	1.43076e11	1.46018	0.730092	+	0.683349i	$0.239477\pi$
$278$	−8.95881e8	−0.00899599
$279$	−5.85308e10	−0.578316
$280$	2.63316e10	0.256015
$281$	−2.20811e10	−0.211272	−0.105636	−	0.994405i	$-0.533688\pi$
$281$	−2.20811e10	−0.211272	−0.105636	+	0.994405i	$0.533688\pi$
$282$	−1.10968e11	−1.04490
$283$	2.05484e11	1.90431	0.952156	−	0.305611i	$-0.0988608\pi$
$283$	2.05484e11	1.90431	0.952156	+	0.305611i	$0.0988608\pi$
$284$	−5.38984e10	−0.491636
$285$	4.46854e10	0.401203
$286$	8.14168e10	0.719560
$287$	3.40348e10	0.296111
$288$	−3.16963e10	−0.271483
$289$	−1.18475e11	−0.999045
$290$	2.93203e11	2.43432
$291$	2.75951e10	0.225587
$292$	−3.75341e9	−0.0302136
$293$	−1.49334e11	−1.18374	−0.591869	−	0.806034i	$-0.701610\pi$
$293$	−1.49334e11	−1.18374	−0.591869	+	0.806034i	$0.701610\pi$
$294$	−7.78558e10	−0.607755
$295$	−1.83938e10	−0.141407
$296$	2.62732e10	0.198930
$297$	1.08899e10	0.0812120
$298$	6.54955e10	0.481103
$299$	2.16759e11	1.56840
$300$	6.32459e9	0.0450803
$301$	−5.91108e10	−0.415066
$302$	−3.06952e11	−2.12344
$303$	−1.07357e9	−0.00731711
$304$	1.18677e11	0.796960
$305$	−5.65553e10	−0.374217
$306$	1.89196e9	0.0123358
$307$	8.55676e10	0.549777	0.274889	−	0.961476i	$-0.411359\pi$
$307$	8.55676e10	0.549777	0.274889	+	0.961476i	$0.411359\pi$
$308$	1.00720e10	0.0637731
$309$	1.46948e11	0.916961
$310$	3.66978e11	2.25690
$311$	−5.01393e10	−0.303918	−0.151959	−	0.988387i	$-0.548558\pi$
$311$	−5.01393e10	−0.303918	−0.151959	+	0.988387i	$0.548558\pi$
$312$	−9.32065e10	−0.556866
$313$	3.25435e11	1.91652	0.958262	−	0.285892i	$-0.0922897\pi$
$313$	3.25435e11	1.91652	0.958262	+	0.285892i	$0.0922897\pi$
$314$	3.44360e11	1.99908
$315$	−2.20124e10	−0.125971
$316$	1.24392e11	0.701782
$317$	−1.76459e11	−0.981472	−0.490736	−	0.871308i	$-0.663272\pi$
$317$	−1.76459e11	−0.981472	−0.490736	+	0.871308i	$0.663272\pi$
$318$	−1.15676e11	−0.634341
$319$	−1.46054e11	−0.789685
$320$	−5.50645e10	−0.293560
$321$	6.78944e10	0.356912
$322$	8.85511e10	0.459031
$323$	−3.86721e9	−0.0197691
$324$	9.57308e9	0.0482613
$325$	5.14775e10	0.255943
$326$	−4.36918e10	−0.214250
$327$	1.78619e11	0.863900
$328$	−1.20856e11	−0.576548
$329$	−1.11734e11	−0.525778
$330$	−6.82779e10	−0.316933
$331$	2.19730e11	1.00615	0.503075	−	0.864243i	$-0.332202\pi$
$331$	2.19730e11	1.00615	0.503075	+	0.864243i	$0.332202\pi$
$332$	−1.60608e11	−0.725512
$333$	−2.19636e10	−0.0978825
$334$	−5.22337e11	−2.29664
$335$	1.70054e11	0.737711
$336$	−5.84615e10	−0.250232
$337$	4.62471e11	1.95321	0.976607	−	0.215030i	$-0.0689850\pi$
$337$	4.62471e11	1.95321	0.976607	+	0.215030i	$0.0689850\pi$
$338$	2.95164e11	1.23009
$339$	−9.29266e10	−0.382157
$340$	−3.59215e9	−0.0145780
$341$	−1.82803e11	−0.732131
$342$	−6.46176e10	−0.255407
$343$	−1.67583e11	−0.653744
$344$	2.09899e11	0.808161
$345$	−1.81779e11	−0.690809
$346$	−3.29536e11	−1.23612
$347$	5.15153e11	1.90745	0.953727	−	0.300674i	$-0.0972117\pi$
$347$	5.15153e11	1.90745	0.953727	+	0.300674i	$0.0972117\pi$
$348$	−1.28392e11	−0.469281
$349$	3.01493e10	0.108783	0.0543917	−	0.998520i	$-0.482678\pi$
$349$	3.01493e10	0.108783	0.0543917	+	0.998520i	$0.482678\pi$
$350$	2.10297e10	0.0749078
$351$	7.79179e10	0.274003
$352$	−9.89938e10	−0.343689
$353$	−1.03856e11	−0.355997	−0.177999	−	0.984031i	$-0.556962\pi$
$353$	−1.03856e11	−0.355997	−0.177999	+	0.984031i	$0.556962\pi$
$354$	2.65984e10	0.0900205
$355$	3.67898e11	1.22942
$356$	1.22838e11	0.405329
$357$	1.90502e9	0.00620716
$358$	−4.70593e11	−1.51416
$359$	−1.87883e11	−0.596982	−0.298491	−	0.954412i	$-0.596483\pi$
$359$	−1.87883e11	−0.596982	−0.298491	+	0.954412i	$0.596483\pi$
$360$	7.81650e10	0.245274
$361$	−1.90608e11	−0.590689
$362$	−1.82149e11	−0.557493
$363$	−1.56982e11	−0.474538
$364$	7.20657e10	0.215165
$365$	2.56199e10	0.0755543
$366$	8.17821e10	0.238228
$367$	−4.28989e9	−0.0123438	−0.00617190	−	0.999981i	$-0.501965\pi$
$367$	−4.28989e9	−0.0123438	−0.00617190	+	0.999981i	$0.501965\pi$
$368$	−4.82776e11	−1.37224
$369$	1.01032e11	0.283687
$370$	1.37708e11	0.381990
$371$	−1.16475e11	−0.319190
$372$	−1.60698e11	−0.435079
$373$	1.70398e11	0.455800	0.227900	−	0.973685i	$-0.426814\pi$
$373$	1.70398e11	0.455800	0.227900	+	0.973685i	$0.426814\pi$
$374$	5.90897e9	0.0156167
$375$	1.96977e11	0.514370
$376$	3.96760e11	1.02372
$377$	−1.04502e12	−2.66433
$378$	3.18312e10	0.0801936
$379$	9.02573e10	0.224702	0.112351	−	0.993669i	$-0.464162\pi$
$379$	9.02573e10	0.224702	0.112351	+	0.993669i	$0.464162\pi$
$380$	1.22685e11	0.301832
$381$	−1.03104e11	−0.250676
$382$	3.51310e11	0.844123
$383$	3.19534e11	0.758792	0.379396	−	0.925234i	$-0.376132\pi$
$383$	3.19534e11	0.758792	0.379396	+	0.925234i	$0.376132\pi$
$384$	2.79978e11	0.657104
$385$	−6.87491e10	−0.159476
$386$	−7.92192e10	−0.181630
$387$	−1.75469e11	−0.397651
$388$	7.57633e10	0.169713
$389$	−2.31291e11	−0.512136	−0.256068	−	0.966659i	$-0.582427\pi$
$389$	−2.31291e11	−0.512136	−0.256068	+	0.966659i	$0.582427\pi$
$390$	−4.88532e11	−1.06931
$391$	1.57317e10	0.0340393
$392$	2.78370e11	0.595436
$393$	−1.25004e11	−0.264337
$394$	−4.26307e11	−0.891229
$395$	−8.49073e11	−1.75492
$396$	2.98986e10	0.0610974
$397$	5.25050e11	1.06082	0.530412	−	0.847740i	$-0.322037\pi$
$397$	5.25050e11	1.06082	0.530412	+	0.847740i	$0.322037\pi$
$398$	−3.99160e11	−0.797395
$399$	−6.50636e10	−0.128517
$400$	−1.14653e11	−0.223932
$401$	−4.99786e11	−0.965238	−0.482619	−	0.875830i	$-0.660314\pi$
$401$	−4.99786e11	−0.965238	−0.482619	+	0.875830i	$0.660314\pi$
$402$	−2.45908e11	−0.469630
$403$	−1.30797e12	−2.47015
$404$	−2.94753e9	−0.00550480
$405$	−6.53436e10	−0.120686
$406$	−4.26914e11	−0.779783
$407$	−6.85967e10	−0.123916
$408$	−6.76463e9	−0.0120857
$409$	−4.76147e10	−0.0841368	−0.0420684	−	0.999115i	$-0.513395\pi$
$409$	−4.76147e10	−0.0841368	−0.0420684	+	0.999115i	$0.513395\pi$
$410$	−6.33452e11	−1.10710
$411$	−6.00678e10	−0.103837
$412$	4.03451e11	0.689847
$413$	2.67820e10	0.0452968
$414$	2.62863e11	0.439772
$415$	1.09627e12	1.81427
$416$	−7.08305e11	−1.15958
$417$	−2.67777e9	−0.00433671
$418$	−2.01813e11	−0.323338
$419$	−1.07510e12	−1.70406	−0.852029	−	0.523495i	$-0.824628\pi$
$419$	−1.07510e12	−1.70406	−0.852029	+	0.523495i	$0.824628\pi$
$420$	−6.04358e10	−0.0947704
$421$	−8.47296e11	−1.31452	−0.657258	−	0.753666i	$-0.728284\pi$
$421$	−8.47296e11	−1.31452	−0.657258	+	0.753666i	$0.728284\pi$
$422$	−6.65368e11	−1.02131
$423$	−3.31680e11	−0.503718
$424$	4.13596e11	0.621483
$425$	3.73607e9	0.00555476
$426$	−5.32001e11	−0.782653
$427$	8.23466e10	0.119873
$428$	1.86406e11	0.268512
$429$	2.43353e11	0.346879
$430$	1.10016e12	1.55185
$431$	−7.52112e11	−1.04987	−0.524934	−	0.851143i	$-0.675910\pi$
$431$	−7.52112e11	−1.04987	−0.524934	+	0.851143i	$0.675910\pi$
$432$	−1.73542e11	−0.239733
$433$	−4.65766e11	−0.636755	−0.318377	−	0.947964i	$-0.603138\pi$
$433$	−4.65766e11	−0.636755	−0.318377	+	0.947964i	$0.603138\pi$
$434$	−5.34333e11	−0.722950
$435$	8.76376e11	1.17352
$436$	4.90405e11	0.649929
$437$	−5.37296e11	−0.704770
$438$	−3.70478e10	−0.0480982
$439$	4.37413e11	0.562085	0.281042	−	0.959695i	$-0.409320\pi$
$439$	4.37413e11	0.562085	0.281042	+	0.959695i	$0.409320\pi$
$440$	2.44125e11	0.310509
$441$	−2.32709e11	−0.292981
$442$	4.22790e10	0.0526896
$443$	−1.51523e12	−1.86922	−0.934611	−	0.355671i	$-0.884252\pi$
$443$	−1.51523e12	−1.86922	−0.934611	+	0.355671i	$0.884252\pi$
$444$	−6.03018e10	−0.0736389
$445$	−8.38462e11	−1.01359
$446$	−1.64829e12	−1.97254
$447$	1.95764e11	0.231926
$448$	8.01760e10	0.0940358
$449$	7.17098e11	0.832664	0.416332	−	0.909213i	$-0.363315\pi$
$449$	7.17098e11	0.832664	0.416332	+	0.909213i	$0.363315\pi$
$450$	6.24264e10	0.0717649
$451$	3.15542e11	0.359140
$452$	−2.55133e11	−0.287504
$453$	−9.17472e11	−1.02365
$454$	1.47903e12	1.63391
$455$	−4.91904e11	−0.538057
$456$	2.31037e11	0.250230
$457$	4.12562e10	0.0442452	0.0221226	−	0.999755i	$-0.492958\pi$
$457$	4.12562e10	0.0442452	0.0221226	+	0.999755i	$0.492958\pi$
$458$	5.81678e10	0.0617714
$459$	5.65503e9	0.00594673
$460$	−4.99080e11	−0.519709
$461$	1.07089e12	1.10431	0.552154	−	0.833742i	$-0.313806\pi$
$461$	1.07089e12	1.10431	0.552154	+	0.833742i	$0.313806\pi$
$462$	9.94151e10	0.101523
$463$	−3.76411e11	−0.380669	−0.190334	−	0.981719i	$-0.560957\pi$
$463$	−3.76411e11	−0.380669	−0.190334	+	0.981719i	$0.560957\pi$
$464$	2.32752e12	2.33110
$465$	1.09689e12	1.08799
$466$	1.58991e12	1.56184
$467$	−7.84332e11	−0.763087	−0.381543	−	0.924351i	$-0.624607\pi$
$467$	−7.84332e11	−0.763087	−0.381543	+	0.924351i	$0.624607\pi$
$468$	2.13926e11	0.206138
$469$	−2.47605e11	−0.236310
$470$	2.07957e12	1.96578
$471$	1.02928e12	0.963699
$472$	−9.51015e10	−0.0881959
$473$	−5.48025e11	−0.503414
$474$	1.22781e12	1.11719
$475$	−1.27601e11	−0.115009
$476$	5.23030e9	0.00466977
$477$	−3.45754e11	−0.305798
$478$	2.73310e10	0.0239459
$479$	1.69258e12	1.46906	0.734529	−	0.678577i	$-0.237403\pi$
$479$	1.69258e12	1.46906	0.734529	+	0.678577i	$0.237403\pi$
$480$	5.94000e11	0.510741
$481$	−4.90813e11	−0.418084
$482$	5.31779e10	0.0448766
$483$	2.64677e11	0.221286
$484$	−4.31000e11	−0.357004
$485$	−5.17143e11	−0.424397
$486$	9.44904e10	0.0768289
$487$	1.93469e12	1.55858	0.779292	−	0.626661i	$-0.215579\pi$
$487$	1.93469e12	1.55858	0.779292	+	0.626661i	$0.215579\pi$
$488$	−2.92408e11	−0.233400
$489$	−1.30594e11	−0.103284
$490$	1.45905e12	1.14337
$491$	1.30146e12	1.01056	0.505282	−	0.862954i	$-0.331388\pi$
$491$	1.30146e12	1.01056	0.505282	+	0.862954i	$0.331388\pi$
$492$	2.77386e11	0.213423
$493$	−7.58442e10	−0.0578244
$494$	−1.44398e12	−1.09092
$495$	−2.04081e11	−0.152784
$496$	2.91316e12	2.16121
$497$	−5.35673e11	−0.393818
$498$	−1.58527e12	−1.15497
$499$	2.28177e12	1.64748	0.823738	−	0.566971i	$-0.191885\pi$
$499$	2.28177e12	1.64748	0.823738	+	0.566971i	$0.191885\pi$
$500$	5.40807e11	0.386970
$501$	−1.56125e12	−1.10714
$502$	2.75914e12	1.93913
$503$	−9.08924e11	−0.633099	−0.316550	−	0.948576i	$-0.602524\pi$
$503$	−9.08924e11	−0.633099	−0.316550	+	0.948576i	$0.602524\pi$
$504$	−1.13811e11	−0.0785682
$505$	2.01191e10	0.0137657
$506$	8.20971e11	0.556738
$507$	8.82237e11	0.592993
$508$	−2.83075e11	−0.188588
$509$	−1.79179e12	−1.18320	−0.591600	−	0.806232i	$-0.701503\pi$
$509$	−1.79179e12	−1.18320	−0.591600	+	0.806232i	$0.701503\pi$
$510$	−3.54561e10	−0.0232073
$511$	−3.73035e10	−0.0242022
$512$	2.65372e11	0.170663
$513$	−1.93140e11	−0.123125
$514$	−3.75415e12	−2.37234
$515$	−2.75386e12	−1.72508
$516$	−4.81757e11	−0.299161
$517$	−1.03590e12	−0.637691
$518$	−2.00508e11	−0.122362
$519$	−9.84975e11	−0.595899
$520$	1.74672e12	1.04763
$521$	2.11097e11	0.125520	0.0627600	−	0.998029i	$-0.480010\pi$
$521$	2.11097e11	0.125520	0.0627600	+	0.998029i	$0.480010\pi$
$522$	−1.26729e12	−0.747065
$523$	−1.05833e12	−0.618532	−0.309266	−	0.950976i	$-0.600083\pi$
$523$	−1.05833e12	−0.618532	−0.309266	+	0.950976i	$0.600083\pi$
$524$	−3.43203e11	−0.198866
$525$	6.28573e10	0.0361109
$526$	1.65197e12	0.940949
$527$	−9.49280e10	−0.0536101
$528$	−5.42006e11	−0.303495
$529$	3.84553e11	0.213504
$530$	2.16782e12	1.19339
$531$	7.95020e10	0.0433963
$532$	−1.78634e11	−0.0966857
$533$	2.25772e12	1.21171
$534$	1.21246e12	0.645257
$535$	−1.27236e12	−0.671459
$536$	8.79234e11	0.460111
$537$	−1.40659e12	−0.729934
$538$	−3.45066e11	−0.177575
$539$	−7.26796e11	−0.370905
$540$	−1.79403e11	−0.0907941
$541$	−4.87448e10	−0.0244647	−0.0122324	−	0.999925i	$-0.503894\pi$
$541$	−4.87448e10	−0.0244647	−0.0122324	+	0.999925i	$0.503894\pi$
$542$	1.79310e12	0.892500
$543$	−5.44440e11	−0.268751
$544$	−5.14065e10	−0.0251665
$545$	−3.34739e12	−1.62526
$546$	7.11320e11	0.342530
$547$	−1.10428e12	−0.527395	−0.263698	−	0.964605i	$-0.584942\pi$
$547$	−1.10428e12	−0.527395	−0.263698	+	0.964605i	$0.584942\pi$
$548$	−1.64918e11	−0.0781188
$549$	2.44445e11	0.114843
$550$	1.94970e11	0.0908522
$551$	2.59036e12	1.19723
$552$	−9.39853e11	−0.430858
$553$	1.23628e12	0.562153
$554$	3.87730e12	1.74878
$555$	4.11606e11	0.184146
$556$	−7.35189e9	−0.00326259
$557$	−2.95668e12	−1.30154	−0.650768	−	0.759277i	$-0.725553\pi$
$557$	−2.95668e12	−1.30154	−0.650768	+	0.759277i	$0.725553\pi$
$558$	−1.58616e12	−0.692617
$559$	−3.92115e12	−1.69848
$560$	1.09559e12	0.470762
$561$	1.76618e10	0.00752838
$562$	−5.98388e11	−0.253029
$563$	3.12555e12	1.31111	0.655554	−	0.755148i	$-0.272435\pi$
$563$	3.12555e12	1.31111	0.655554	+	0.755148i	$0.272435\pi$
$564$	−9.10637e11	−0.378956
$565$	1.74148e12	0.718952
$566$	5.56852e12	2.28069
$567$	9.51426e10	0.0386591
$568$	1.90215e12	0.766790
$569$	−4.28087e12	−1.71209	−0.856046	−	0.516900i	$-0.827086\pi$
$569$	−4.28087e12	−1.71209	−0.856046	+	0.516900i	$0.827086\pi$
$570$	1.21096e12	0.480498
$571$	−2.27517e12	−0.895678	−0.447839	−	0.894114i	$-0.647806\pi$
$571$	−2.27517e12	−0.895678	−0.447839	+	0.894114i	$0.647806\pi$
$572$	6.68133e11	0.260964
$573$	1.05006e12	0.406928
$574$	9.22330e11	0.354636
$575$	5.19077e11	0.198028
$576$	2.38001e11	0.0900903
$577$	4.94509e12	1.85730	0.928651	−	0.370954i	$-0.120969\pi$
$577$	4.94509e12	1.85730	0.928651	+	0.370954i	$0.120969\pi$
$578$	−3.21062e12	−1.19650
$579$	−2.36784e11	−0.0875586
$580$	2.40612e12	0.882858
$581$	−1.59621e12	−0.581162
$582$	7.47817e11	0.270173
$583$	−1.07986e12	−0.387131
$584$	1.32463e11	0.0471233
$585$	−1.46021e12	−0.515482
$586$	−4.04690e12	−1.41770
$587$	3.65831e12	1.27177	0.635886	−	0.771783i	$-0.280635\pi$
$587$	3.65831e12	1.27177	0.635886	+	0.771783i	$0.280635\pi$
$588$	−6.38910e11	−0.220415
$589$	3.24214e12	1.10998
$590$	−4.98464e11	−0.169356
$591$	−1.27422e12	−0.429636
$592$	1.09316e12	0.365794
$593$	−1.48698e12	−0.493810	−0.246905	−	0.969040i	$-0.579414\pi$
$593$	−1.48698e12	−0.493810	−0.246905	+	0.969040i	$0.579414\pi$
$594$	2.95112e11	0.0972631
$595$	−3.57008e10	−0.0116775
$596$	5.37478e11	0.174483
$597$	−1.19308e12	−0.384402
$598$	5.87409e12	1.87839
$599$	−7.33466e11	−0.232787	−0.116394	−	0.993203i	$-0.537133\pi$
$599$	−7.33466e11	−0.232787	−0.116394	+	0.993203i	$0.537133\pi$
$600$	−2.23203e11	−0.0703103
$601$	−5.59924e12	−1.75063	−0.875315	−	0.483553i	$-0.839346\pi$
$601$	−5.59924e12	−1.75063	−0.875315	+	0.483553i	$0.839346\pi$
$602$	−1.60188e12	−0.497102
$603$	−7.35013e11	−0.226395
$604$	−2.51895e12	−0.770110
$605$	2.94191e12	0.892750
$606$	−2.90934e10	−0.00876329
$607$	3.51612e12	1.05127	0.525635	−	0.850710i	$-0.323828\pi$
$607$	3.51612e12	1.05127	0.525635	+	0.850710i	$0.323828\pi$
$608$	1.75572e12	0.521063
$609$	−1.27604e12	−0.375911
$610$	−1.53263e12	−0.448179
$611$	−7.41192e12	−2.15152
$612$	1.55261e10	0.00447384
$613$	−9.62938e10	−0.0275439	−0.0137720	−	0.999905i	$-0.504384\pi$
$613$	−9.62938e10	−0.0275439	−0.0137720	+	0.999905i	$0.504384\pi$
$614$	2.31885e12	0.658437
$615$	−1.89337e12	−0.533701
$616$	−3.55454e11	−0.0994650
$617$	3.01324e12	0.837048	0.418524	−	0.908206i	$-0.362548\pi$
$617$	3.01324e12	0.837048	0.418524	+	0.908206i	$0.362548\pi$
$618$	3.98223e12	1.09819
$619$	−2.35963e12	−0.646006	−0.323003	−	0.946398i	$-0.604692\pi$
$619$	−2.35963e12	−0.646006	−0.323003	+	0.946398i	$0.604692\pi$
$620$	3.01154e12	0.818514
$621$	7.85689e11	0.212001
$622$	−1.35875e12	−0.363985
$623$	1.22083e12	0.324683
$624$	−3.87808e12	−1.02397
$625$	−4.37717e12	−1.14745
$626$	8.81915e12	2.29531
$627$	−6.03215e11	−0.155872
$628$	2.82593e12	0.725009
$629$	−3.56216e10	−0.00907373
$630$	−5.96528e11	−0.150868
$631$	1.16636e12	0.292887	0.146444	−	0.989219i	$-0.453217\pi$
$631$	1.16636e12	0.292887	0.146444	+	0.989219i	$0.453217\pi$
$632$	−4.38997e12	−1.09455
$633$	−1.98877e12	−0.492342
$634$	−4.78198e12	−1.17545
$635$	1.93220e12	0.471596
$636$	−9.49278e11	−0.230057
$637$	−5.20026e12	−1.25141
$638$	−3.95799e12	−0.945762
$639$	−1.59014e12	−0.377295
$640$	−5.24689e12	−1.23621
$641$	3.45037e12	0.807245	0.403622	−	0.914926i	$-0.367751\pi$
$641$	3.45037e12	0.807245	0.403622	+	0.914926i	$0.367751\pi$
$642$	1.83991e12	0.427454
$643$	2.83775e12	0.654674	0.327337	−	0.944908i	$-0.393849\pi$
$643$	2.83775e12	0.654674	0.327337	+	0.944908i	$0.393849\pi$
$644$	7.26679e11	0.166478
$645$	3.28836e12	0.748102
$646$	−1.04800e11	−0.0236763
$647$	8.39979e12	1.88451	0.942256	−	0.334892i	$-0.108700\pi$
$647$	8.39979e12	1.88451	0.942256	+	0.334892i	$0.108700\pi$
$648$	−3.37846e11	−0.0752717
$649$	2.48300e11	0.0549384
$650$	1.39502e12	0.306528
$651$	−1.59711e12	−0.348514
$652$	−3.58549e11	−0.0777024
$653$	−1.28646e12	−0.276877	−0.138439	−	0.990371i	$-0.544208\pi$
$653$	−1.28646e12	−0.276877	−0.138439	+	0.990371i	$0.544208\pi$
$654$	4.84051e12	1.03464
$655$	2.34262e12	0.497298
$656$	−5.02850e12	−1.06016
$657$	−1.10735e11	−0.0231868
$658$	−3.02794e12	−0.629695
$659$	−1.00991e12	−0.208592	−0.104296	−	0.994546i	$-0.533259\pi$
$659$	−1.00991e12	−0.208592	−0.104296	+	0.994546i	$0.533259\pi$
$660$	−5.60310e11	−0.114943
$661$	−2.30424e12	−0.469484	−0.234742	−	0.972058i	$-0.575425\pi$
$661$	−2.30424e12	−0.469484	−0.234742	+	0.972058i	$0.575425\pi$
$662$	5.95458e12	1.20501
$663$	1.26371e11	0.0254001
$664$	5.66805e12	1.13156
$665$	1.21931e12	0.241779
$666$	−5.95205e11	−0.117228
$667$	−1.05375e13	−2.06145
$668$	−4.28647e12	−0.832925
$669$	−4.92670e12	−0.950908
$670$	4.60841e12	0.883515
$671$	7.63448e11	0.145388
$672$	−8.64886e11	−0.163605
$673$	6.41400e12	1.20521	0.602603	−	0.798041i	$-0.294130\pi$
$673$	6.41400e12	1.20521	0.602603	+	0.798041i	$0.294130\pi$
$674$	1.25328e13	2.33926
$675$	1.86591e11	0.0345958
$676$	2.42221e12	0.446120
$677$	−4.42017e12	−0.808704	−0.404352	−	0.914603i	$-0.632503\pi$
$677$	−4.42017e12	−0.808704	−0.404352	+	0.914603i	$0.632503\pi$
$678$	−2.51827e12	−0.457688
$679$	7.52979e11	0.135947
$680$	1.26772e11	0.0227369
$681$	4.42079e12	0.787659
$682$	−4.95389e12	−0.876833
$683$	1.21590e12	0.213799	0.106900	−	0.994270i	$-0.465908\pi$
$683$	1.21590e12	0.213799	0.106900	+	0.994270i	$0.465908\pi$
$684$	−5.30273e11	−0.0926290
$685$	1.12569e12	0.195349
$686$	−4.54144e12	−0.782953
$687$	1.73862e11	0.0297783
$688$	8.73336e12	1.48605
$689$	−7.72643e12	−1.30615
$690$	−4.92614e12	−0.827343
$691$	−6.17385e12	−1.03016	−0.515080	−	0.857142i	$-0.672238\pi$
$691$	−6.17385e12	−1.03016	−0.515080	+	0.857142i	$0.672238\pi$
$692$	−2.70428e12	−0.448306
$693$	2.97149e11	0.0489412
$694$	1.39605e13	2.28445
$695$	5.01823e10	0.00815866
$696$	4.53113e12	0.731923
$697$	1.63858e11	0.0262979
$698$	8.17034e11	0.130284
$699$	4.75221e12	0.752918
$700$	1.72577e11	0.0271670
$701$	1.04454e13	1.63378	0.816890	−	0.576794i	$-0.195696\pi$
$701$	1.04454e13	1.63378	0.816890	+	0.576794i	$0.195696\pi$
$702$	2.11154e12	0.328158
$703$	1.21661e12	0.187868
$704$	7.43325e11	0.114052
$705$	6.21579e12	0.947645
$706$	−2.81446e12	−0.426358
$707$	−2.92942e10	−0.00440955
$708$	2.18275e11	0.0326479
$709$	−1.00404e13	−1.49226	−0.746131	−	0.665800i	$-0.768091\pi$
$709$	−1.00404e13	−1.49226	−0.746131	+	0.665800i	$0.768091\pi$
$710$	9.96989e12	1.47241
$711$	3.66989e12	0.538566
$712$	−4.33511e12	−0.632179
$713$	−1.31889e13	−1.91121
$714$	5.16253e10	0.00743397
$715$	−4.56052e12	−0.652585
$716$	−3.86184e12	−0.549143
$717$	8.16918e10	0.0115436
$718$	−5.09154e12	−0.714972
$719$	2.36265e12	0.329701	0.164850	−	0.986319i	$-0.447286\pi$
$719$	2.36265e12	0.329701	0.164850	+	0.986319i	$0.447286\pi$
$720$	3.25224e12	0.451010
$721$	4.00972e12	0.552593
$722$	−5.16540e12	−0.707436
$723$	1.58948e11	0.0216337
$724$	−1.49478e12	−0.202187
$725$	−2.50252e12	−0.336401
$726$	−4.25416e12	−0.568328
$727$	1.99053e12	0.264279	0.132140	−	0.991231i	$-0.457815\pi$
$727$	1.99053e12	0.264279	0.132140	+	0.991231i	$0.457815\pi$
$728$	−2.54329e12	−0.335587
$729$	2.82430e11	0.0370370
$730$	6.94288e11	0.0904872
$731$	−2.84585e11	−0.0368624
$732$	6.71130e11	0.0863987
$733$	−9.77749e11	−0.125101	−0.0625503	−	0.998042i	$-0.519923\pi$
$733$	−9.77749e11	−0.125101	−0.0625503	+	0.998042i	$0.519923\pi$
$734$	−1.16254e11	−0.0147835
$735$	4.36105e12	0.551186
$736$	−7.14224e12	−0.897189
$737$	−2.29559e12	−0.286610
$738$	2.73792e12	0.339756
$739$	−2.84759e12	−0.351219	−0.175609	−	0.984460i	$-0.556190\pi$
$739$	−2.84759e12	−0.351219	−0.175609	+	0.984460i	$0.556190\pi$
$740$	1.13008e12	0.138537
$741$	−4.31603e12	−0.525900
$742$	−3.15642e12	−0.382276
$743$	−6.47321e12	−0.779238	−0.389619	−	0.920976i	$-0.627393\pi$
$743$	−6.47321e12	−0.779238	−0.389619	+	0.920976i	$0.627393\pi$
$744$	5.67125e12	0.678579
$745$	−3.66870e12	−0.436323
$746$	4.61771e12	0.545886
$747$	−4.73832e12	−0.556778
$748$	4.84910e10	0.00566374
$749$	1.85261e12	0.215088
$750$	5.33800e12	0.616032
$751$	8.14699e12	0.934582	0.467291	−	0.884103i	$-0.345230\pi$
$751$	8.14699e12	0.934582	0.467291	+	0.884103i	$0.345230\pi$
$752$	1.65082e13	1.88243
$753$	8.24700e12	0.934799
$754$	−2.83196e13	−3.19092
$755$	1.71937e13	1.92579
$756$	2.61217e11	0.0290840
$757$	4.96495e12	0.549520	0.274760	−	0.961513i	$-0.411402\pi$
$757$	4.96495e12	0.549520	0.274760	+	0.961513i	$0.411402\pi$
$758$	2.44594e12	0.269113
$759$	2.45386e12	0.268387
$760$	−4.32972e12	−0.470759
$761$	−3.30511e12	−0.357236	−0.178618	−	0.983919i	$-0.557163\pi$
$761$	−3.30511e12	−0.357236	−0.178618	+	0.983919i	$0.557163\pi$
$762$	−2.79407e12	−0.300220
$763$	4.87392e12	0.520617
$764$	2.88297e12	0.306140
$765$	−1.05977e11	−0.0111876
$766$	8.65925e12	0.908763
$767$	1.77660e12	0.185358
$768$	6.08290e12	0.630935
$769$	−5.13105e12	−0.529100	−0.264550	−	0.964372i	$-0.585223\pi$
$769$	−5.13105e12	−0.529100	−0.264550	+	0.964372i	$0.585223\pi$
$770$	−1.86307e12	−0.190995
$771$	−1.12210e13	−1.14364
$772$	−6.50098e11	−0.0658720
$773$	−4.46041e12	−0.449332	−0.224666	−	0.974436i	$-0.572129\pi$
$773$	−4.46041e12	−0.449332	−0.224666	+	0.974436i	$0.572129\pi$
$774$	−4.75515e12	−0.476244
$775$	−3.13220e12	−0.311883
$776$	−2.67379e12	−0.264697
$777$	−5.99314e11	−0.0589874
$778$	−6.26789e12	−0.613357
$779$	−5.59637e12	−0.544487
$780$	−4.00905e12	−0.387807
$781$	−4.96631e12	−0.477644
$782$	4.26323e11	0.0407669
$783$	−3.78789e12	−0.360139
$784$	1.15823e13	1.09489
$785$	−1.92891e13	−1.81301
$786$	−3.38756e12	−0.316582
$787$	1.49260e13	1.38694	0.693469	−	0.720486i	$-0.256081\pi$
$787$	1.49260e13	1.38694	0.693469	+	0.720486i	$0.256081\pi$
$788$	−3.49841e12	−0.323223
$789$	4.93769e12	0.453605
$790$	−2.30095e13	−2.10177
$791$	−2.53566e12	−0.230301
$792$	−1.05516e12	−0.0952917
$793$	5.46251e12	0.490527
$794$	1.42287e13	1.27049
$795$	6.47954e12	0.575297
$796$	−3.27564e12	−0.289193
$797$	1.20121e12	0.105452	0.0527260	−	0.998609i	$-0.483209\pi$
$797$	1.20121e12	0.105452	0.0527260	+	0.998609i	$0.483209\pi$
$798$	−1.76320e12	−0.153917
$799$	−5.37933e11	−0.0466948
$800$	−1.69619e12	−0.146409
$801$	3.62402e12	0.311060
$802$	−1.35440e13	−1.15601
$803$	−3.45847e11	−0.0293537
$804$	−2.01800e12	−0.170321
$805$	−4.96014e12	−0.416306
$806$	−3.54453e13	−2.95836
$807$	−1.03139e12	−0.0856039
$808$	1.04022e11	0.00858567
$809$	1.01524e13	0.833298	0.416649	−	0.909067i	$-0.363204\pi$
$809$	1.01524e13	0.833298	0.416649	+	0.909067i	$0.363204\pi$
$810$	−1.77078e12	−0.144538
$811$	−6.37555e12	−0.517516	−0.258758	−	0.965942i	$-0.583313\pi$
$811$	−6.37555e12	−0.517516	−0.258758	+	0.965942i	$0.583313\pi$
$812$	−3.50340e12	−0.282805
$813$	5.35954e12	0.430249
$814$	−1.85894e12	−0.148408
$815$	2.44737e12	0.194308
$816$	−2.81459e11	−0.0222233
$817$	9.71962e12	0.763220
$818$	−1.29034e12	−0.100766
$819$	2.12612e12	0.165124
$820$	−5.19832e12	−0.401514
$821$	7.50250e12	0.576317	0.288159	−	0.957583i	$-0.406957\pi$
$821$	7.50250e12	0.576317	0.288159	+	0.957583i	$0.406957\pi$
$822$	−1.62781e12	−0.124360
$823$	−7.71506e12	−0.586192	−0.293096	−	0.956083i	$-0.594686\pi$
$823$	−7.71506e12	−0.586192	−0.293096	+	0.956083i	$0.594686\pi$
$824$	−1.42383e13	−1.07593
$825$	5.82760e11	0.0437973
$826$	7.25782e11	0.0542495
$827$	−1.52511e13	−1.13377	−0.566886	−	0.823796i	$-0.691852\pi$
$827$	−1.52511e13	−1.13377	−0.566886	+	0.823796i	$0.691852\pi$
$828$	2.15714e12	0.159493
$829$	−1.77884e13	−1.30810	−0.654050	−	0.756451i	$-0.726931\pi$
$829$	−1.77884e13	−1.30810	−0.654050	+	0.756451i	$0.726931\pi$
$830$	2.97085e13	2.17285
$831$	1.15891e13	0.843038
$832$	5.31852e12	0.384801
$833$	−3.77419e11	−0.0271594
$834$	−7.25664e10	−0.00519384
$835$	2.92584e13	2.08287
$836$	−1.65615e12	−0.117266
$837$	−4.74099e12	−0.333891
$838$	−2.91347e13	−2.04086
$839$	−2.77513e13	−1.93355	−0.966773	−	0.255637i	$-0.917715\pi$
$839$	−2.77513e13	−1.93355	−0.966773	+	0.255637i	$0.917715\pi$
$840$	2.13286e12	0.147811
$841$	3.62954e13	2.50190
$842$	−2.29614e13	−1.57432
$843$	−1.78857e12	−0.121978
$844$	−5.46022e12	−0.370399
$845$	−1.65334e13	−1.11560
$846$	−8.98838e12	−0.603274
$847$	−4.28352e12	−0.285974
$848$	1.72086e13	1.14279
$849$	1.66442e13	1.09946
$850$	1.01246e11	0.00665263
$851$	−4.94914e12	−0.323480
$852$	−4.36577e12	−0.283846
$853$	6.16511e11	0.0398722	0.0199361	−	0.999801i	$-0.493654\pi$
$853$	6.16511e11	0.0398722	0.0199361	+	0.999801i	$0.493654\pi$
$854$	2.23156e12	0.143565
$855$	3.61952e12	0.231634
$856$	−6.57852e12	−0.418790
$857$	1.39335e13	0.882364	0.441182	−	0.897418i	$-0.354559\pi$
$857$	1.39335e13	0.882364	0.441182	+	0.897418i	$0.354559\pi$
$858$	6.59476e12	0.415438
$859$	−2.84121e13	−1.78047	−0.890233	−	0.455505i	$-0.849459\pi$
$859$	−2.84121e13	−1.78047	−0.890233	+	0.455505i	$0.849459\pi$
$860$	9.02829e12	0.562811
$861$	2.75682e12	0.170960
$862$	−2.03819e13	−1.25737
$863$	−9.12009e12	−0.559694	−0.279847	−	0.960045i	$-0.590284\pi$
$863$	−9.12009e12	−0.559694	−0.279847	+	0.960045i	$0.590284\pi$
$864$	−2.56740e12	−0.156741
$865$	1.84588e13	1.12106
$866$	−1.26221e13	−0.762606
$867$	−9.59645e12	−0.576799
$868$	−4.38491e12	−0.262194
$869$	1.14618e13	0.681809
$870$	2.37494e13	1.40545
$871$	−1.64251e13	−0.966997
$872$	−1.73070e13	−1.01367
$873$	2.23521e12	0.130243
$874$	−1.45605e13	−0.844063
$875$	5.37485e12	0.309977
$876$	−3.04026e11	−0.0174438
$877$	1.02362e13	0.584309	0.292154	−	0.956371i	$-0.405628\pi$
$877$	1.02362e13	0.584309	0.292154	+	0.956371i	$0.405628\pi$
$878$	1.18537e13	0.673177
$879$	−1.20961e13	−0.683432
$880$	1.01574e13	0.570966
$881$	1.16506e13	0.651563	0.325781	−	0.945445i	$-0.394373\pi$
$881$	1.16506e13	0.651563	0.325781	+	0.945445i	$0.394373\pi$
$882$	−6.30632e12	−0.350887
$883$	2.88623e13	1.59774	0.798872	−	0.601501i	$-0.205430\pi$
$883$	2.88623e13	1.59774	0.798872	+	0.601501i	$0.205430\pi$
$884$	3.46955e11	0.0191090
$885$	−1.48990e12	−0.0816415
$886$	−4.10620e13	−2.23866
$887$	−2.34243e13	−1.27061	−0.635303	−	0.772263i	$-0.719125\pi$
$887$	−2.34243e13	−1.27061	−0.635303	+	0.772263i	$0.719125\pi$
$888$	2.12813e12	0.114852
$889$	−2.81335e12	−0.151066
$890$	−2.27220e13	−1.21392
$891$	8.82083e11	0.0468878
$892$	−1.35264e13	−0.715386
$893$	1.83724e13	0.966796
$894$	5.30514e12	0.277765
$895$	2.63600e13	1.37323
$896$	7.63967e12	0.395994
$897$	1.75575e13	0.905518
$898$	1.94331e13	0.997235
$899$	6.35853e13	3.24667
$900$	5.12291e11	0.0260271
$901$	−5.60759e11	−0.0283475
$902$	8.55107e12	0.430121
$903$	−4.78797e12	−0.239639
$904$	9.00398e12	0.448411
$905$	1.02030e13	0.505603
$906$	−2.48631e13	−1.22597
$907$	−3.23704e13	−1.58824	−0.794118	−	0.607763i	$-0.792067\pi$
$907$	−3.23704e13	−1.58824	−0.794118	+	0.607763i	$0.792067\pi$
$908$	1.21374e13	0.592571
$909$	−8.69593e10	−0.00422453
$910$	−1.33304e13	−0.644401
$911$	4.74352e12	0.228175	0.114087	−	0.993471i	$-0.463606\pi$
$911$	4.74352e12	0.228175	0.114087	+	0.993471i	$0.463606\pi$
$912$	9.61286e12	0.460125
$913$	−1.47987e13	−0.704864
$914$	1.11803e12	0.0529900
$915$	−4.58098e12	−0.216054
$916$	4.77343e11	0.0224028
$917$	−3.41095e12	−0.159299
$918$	1.53249e11	0.00712206
$919$	−1.19100e13	−0.550800	−0.275400	−	0.961330i	$-0.588810\pi$
$919$	−1.19100e13	−0.550800	−0.275400	+	0.961330i	$0.588810\pi$
$920$	1.76132e13	0.810574
$921$	6.93098e12	0.317414
$922$	2.90206e13	1.32257
$923$	−3.55342e13	−1.61153
$924$	8.15832e11	0.0368194
$925$	−1.17536e12	−0.0527876
$926$	−1.02006e13	−0.455906
$927$	1.19028e13	0.529407
$928$	3.44335e13	1.52411
$929$	−1.64263e13	−0.723551	−0.361776	−	0.932265i	$-0.617829\pi$
$929$	−1.64263e13	−0.723551	−0.361776	+	0.932265i	$0.617829\pi$
$930$	2.97252e13	1.30302
$931$	1.28902e13	0.562325
$932$	1.30473e13	0.566435
$933$	−4.06128e12	−0.175467
$934$	−2.12551e13	−0.913907
$935$	−3.30988e11	−0.0141631
$936$	−7.54973e12	−0.321507
$937$	−3.25084e13	−1.37774	−0.688869	−	0.724885i	$-0.741893\pi$
$937$	−3.25084e13	−1.37774	−0.688869	+	0.724885i	$0.741893\pi$
$938$	−6.71001e12	−0.283015
$939$	2.63602e13	1.10651
$940$	1.70657e13	0.712931
$941$	−1.89705e13	−0.788724	−0.394362	−	0.918955i	$-0.629034\pi$
$941$	−1.89705e13	−0.788724	−0.394362	+	0.918955i	$0.629034\pi$
$942$	2.78932e13	1.15417
$943$	2.27659e13	0.937522
$944$	−3.95693e12	−0.162175
$945$	−1.78301e12	−0.0727294
$946$	−1.48513e13	−0.602911
$947$	−6.79131e12	−0.274396	−0.137198	−	0.990544i	$-0.543810\pi$
$947$	−6.79131e12	−0.274396	−0.137198	+	0.990544i	$0.543810\pi$
$948$	1.00758e13	0.405174
$949$	−2.47455e12	−0.0990372
$950$	−3.45793e12	−0.137740
$951$	−1.42932e13	−0.566653
$952$	−1.84584e11	−0.00728330
$953$	−4.84372e12	−0.190222	−0.0951110	−	0.995467i	$-0.530321\pi$
$953$	−4.84372e12	−0.190222	−0.0951110	+	0.995467i	$0.530321\pi$
$954$	−9.36978e12	−0.366237
$955$	−1.96785e13	−0.765554
$956$	2.24287e11	0.00868449
$957$	−1.18303e13	−0.455925
$958$	4.58682e13	1.75941
$959$	−1.63905e12	−0.0625760
$960$	−4.46023e12	−0.169487
$961$	5.31449e13	2.01005
$962$	−1.33008e13	−0.500715
$963$	5.49944e12	0.206063
$964$	4.36396e11	0.0162755
$965$	4.43742e12	0.164724
$966$	7.17264e12	0.265022
$967$	3.10571e13	1.14220	0.571100	−	0.820880i	$-0.306517\pi$
$967$	3.10571e13	1.14220	0.571100	+	0.820880i	$0.306517\pi$
$968$	1.52106e13	0.556809
$969$	−3.13244e11	−0.0114137
$970$	−1.40144e13	−0.508277
$971$	−2.31521e13	−0.835802	−0.417901	−	0.908493i	$-0.637234\pi$
$971$	−2.31521e13	−0.835802	−0.417901	+	0.908493i	$0.637234\pi$
$972$	7.75419e11	0.0278637
$973$	−7.30673e10	−0.00261346
$974$	5.24292e13	1.86663
$975$	4.16968e12	0.147768
$976$	−1.21664e13	−0.429177
$977$	−3.02951e13	−1.06377	−0.531884	−	0.846817i	$-0.678516\pi$
$977$	−3.02951e13	−1.06377	−0.531884	+	0.846817i	$0.678516\pi$
$978$	−3.53904e12	−0.123697
$979$	1.13185e13	0.393793
$980$	1.19734e13	0.414668
$981$	1.44682e13	0.498773
$982$	3.52690e13	1.21030
$983$	−3.84935e13	−1.31491	−0.657456	−	0.753493i	$-0.728367\pi$
$983$	−3.84935e13	−1.31491	−0.657456	+	0.753493i	$0.728367\pi$
$984$	−9.78932e12	−0.332870
$985$	2.38793e13	0.808275
$986$	−2.05535e12	−0.0692531
$987$	−9.05042e12	−0.303558
$988$	−1.18498e13	−0.395644
$989$	−3.95391e13	−1.31415
$990$	−5.53051e12	−0.182981
$991$	2.74204e13	0.903112	0.451556	−	0.892243i	$-0.350869\pi$
$991$	2.74204e13	0.903112	0.451556	+	0.892243i	$0.350869\pi$
$992$	4.30976e13	1.41303
$993$	1.77981e13	0.580901
$994$	−1.45165e13	−0.471654
$995$	2.23587e13	0.723175
$996$	−1.30092e13	−0.418875
$997$	−1.87482e13	−0.600942	−0.300471	−	0.953791i	$-0.597144\pi$
$997$	−1.87482e13	−0.600942	−0.300471	+	0.953791i	$0.597144\pi$
$998$	6.18350e13	1.97309
$999$	−1.77905e12	−0.0565125

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.a.1.17	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.a.1.17	✓	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)

\(f(q)\)	\(=\)	\(q+27.0996 q^{2} +81.0000 q^{3} +222.388 q^{4} -1517.97 q^{5} +2195.07 q^{6} +2210.22 q^{7} -7848.37 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+27.0996 q^{2} +81.0000 q^{3} +222.388 q^{4} -1517.97 q^{5} +2195.07 q^{6} +2210.22 q^{7} -7848.37 q^{8} +6561.00 q^{9} -41136.3 q^{10} +20491.3 q^{11} +18013.4 q^{12} +146616. q^{13} +59896.0 q^{14} -122955. q^{15} -326550. q^{16} +10640.9 q^{17} +177800. q^{18} -363427. q^{19} -337578. q^{20} +179028. q^{21} +555306. q^{22} +1.47841e6 q^{23} -635718. q^{24} +351104. q^{25} +3.97324e6 q^{26} +531441. q^{27} +491526. q^{28} -7.12759e6 q^{29} -3.33204e6 q^{30} -8.92102e6 q^{31} -4.83102e6 q^{32} +1.65979e6 q^{33} +288365. q^{34} -3.35504e6 q^{35} +1.45909e6 q^{36} -3.34760e6 q^{37} -9.84874e6 q^{38} +1.18759e7 q^{39} +1.19136e7 q^{40} +1.53989e7 q^{41} +4.85158e6 q^{42} -2.67443e7 q^{43} +4.55702e6 q^{44} -9.95939e6 q^{45} +4.00644e7 q^{46} -5.05532e7 q^{47} -2.64506e7 q^{48} -3.54685e7 q^{49} +9.51477e6 q^{50} +861916. q^{51} +3.26057e7 q^{52} -5.26983e7 q^{53} +1.44018e7 q^{54} -3.11051e7 q^{55} -1.73466e7 q^{56} -2.94376e7 q^{57} -1.93155e8 q^{58} +1.21174e7 q^{59} -2.73438e7 q^{60} +3.72572e7 q^{61} -2.41756e8 q^{62} +1.45012e7 q^{63} +3.62751e7 q^{64} -2.22559e8 q^{65} +4.49798e7 q^{66} -1.12028e8 q^{67} +2.36642e6 q^{68} +1.19751e8 q^{69} -9.09203e7 q^{70} -2.42362e8 q^{71} -5.14931e7 q^{72} -1.68777e7 q^{73} -9.07187e7 q^{74} +2.84394e7 q^{75} -8.08219e7 q^{76} +4.52902e7 q^{77} +3.21832e8 q^{78} +5.59348e8 q^{79} +4.95693e8 q^{80} +4.30467e7 q^{81} +4.17303e8 q^{82} -7.22195e8 q^{83} +3.98136e7 q^{84} -1.61526e7 q^{85} -7.24760e8 q^{86} -5.77335e8 q^{87} -1.60823e8 q^{88} +5.52358e8 q^{89} -2.69896e8 q^{90} +3.24054e8 q^{91} +3.28781e8 q^{92} -7.22602e8 q^{93} -1.36997e9 q^{94} +5.51671e8 q^{95} -3.91312e8 q^{96} +3.40681e8 q^{97} -9.61183e8 q^{98} +1.34443e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9}+O(q^{10}) \) 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

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