LMFDB - Embedded newform 177.10.a.a.1.20

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			1.20
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)

$f(q)$	$=$	$q+37.7088 q^{2} +81.0000 q^{3} +909.951 q^{4} -1229.57 q^{5} +3054.41 q^{6} -1968.46 q^{7} +15006.2 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+37.7088 q^{2} +81.0000 q^{3} +909.951 q^{4} -1229.57 q^{5} +3054.41 q^{6} -1968.46 q^{7} +15006.2 q^{8} +6561.00 q^{9} -46365.5 q^{10} -54823.4 q^{11} +73706.0 q^{12} +34302.8 q^{13} -74228.3 q^{14} -99595.0 q^{15} +99972.0 q^{16} -122669. q^{17} +247407. q^{18} +838314. q^{19} -1.11885e6 q^{20} -159446. q^{21} -2.06732e6 q^{22} -2.32811e6 q^{23} +1.21551e6 q^{24} -441287. q^{25} +1.29352e6 q^{26} +531441. q^{27} -1.79121e6 q^{28} -6.13023e6 q^{29} -3.75561e6 q^{30} +3.50327e6 q^{31} -3.91338e6 q^{32} -4.44070e6 q^{33} -4.62569e6 q^{34} +2.42036e6 q^{35} +5.97019e6 q^{36} -9.25273e6 q^{37} +3.16118e7 q^{38} +2.77852e6 q^{39} -1.84512e7 q^{40} -1.75636e7 q^{41} -6.01249e6 q^{42} +2.04392e7 q^{43} -4.98866e7 q^{44} -8.06720e6 q^{45} -8.77902e7 q^{46} +1.13961e7 q^{47} +8.09773e6 q^{48} -3.64788e7 q^{49} -1.66404e7 q^{50} -9.93618e6 q^{51} +3.12138e7 q^{52} -5.64902e7 q^{53} +2.00400e7 q^{54} +6.74091e7 q^{55} -2.95392e7 q^{56} +6.79034e7 q^{57} -2.31163e8 q^{58} +1.21174e7 q^{59} -9.06266e7 q^{60} -1.93157e8 q^{61} +1.32104e8 q^{62} -1.29151e7 q^{63} -1.98754e8 q^{64} -4.21776e7 q^{65} -1.67453e8 q^{66} +2.97914e8 q^{67} -1.11623e8 q^{68} -1.88577e8 q^{69} +9.12688e7 q^{70} -3.55939e8 q^{71} +9.84560e7 q^{72} +4.51678e8 q^{73} -3.48909e8 q^{74} -3.57443e7 q^{75} +7.62824e8 q^{76} +1.07918e8 q^{77} +1.04775e8 q^{78} +3.03934e8 q^{79} -1.22922e8 q^{80} +4.30467e7 q^{81} -6.62302e8 q^{82} +6.28705e8 q^{83} -1.45088e8 q^{84} +1.50830e8 q^{85} +7.70735e8 q^{86} -4.96548e8 q^{87} -8.22693e8 q^{88} -8.08718e8 q^{89} -3.04204e8 q^{90} -6.75237e7 q^{91} -2.11847e9 q^{92} +2.83765e8 q^{93} +4.29732e8 q^{94} -1.03076e9 q^{95} -3.16984e8 q^{96} +5.73218e8 q^{97} -1.37557e9 q^{98} -3.59696e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	37.7088	1.66651	0.833254	−	0.552891i	$-0.186475\pi$
$2$	37.7088	1.66651	0.833254	+	0.552891i	$0.186475\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	909.951	1.77725
$5$	−1229.57	−0.879807	−0.439904	−	0.898045i	$-0.644987\pi$
$5$	−1229.57	−0.879807	−0.439904	+	0.898045i	$0.644987\pi$
$6$	3054.41	0.962159
$7$	−1968.46	−0.309875	−0.154937	−	0.987924i	$-0.549518\pi$
$7$	−1968.46	−0.309875	−0.154937	+	0.987924i	$0.549518\pi$
$8$	15006.2	1.29529
$9$	6561.00	0.333333
$10$	−46365.5	−1.46621
$11$	−54823.4	−1.12901	−0.564507	−	0.825429i	$-0.690934\pi$
$11$	−54823.4	−1.12901	−0.564507	+	0.825429i	$0.690934\pi$
$12$	73706.0	1.02609
$13$	34302.8	0.333107	0.166554	−	0.986032i	$-0.446736\pi$
$13$	34302.8	0.333107	0.166554	+	0.986032i	$0.446736\pi$
$14$	−74228.3	−0.516409
$15$	−99595.0	−0.507957
$16$	99972.0	0.381363
$17$	−122669.	−0.356217	−0.178108	−	0.984011i	$-0.556998\pi$
$17$	−122669.	−0.356217	−0.178108	+	0.984011i	$0.556998\pi$
$18$	247407.	0.555503
$19$	838314.	1.47576	0.737879	−	0.674933i	$-0.235827\pi$
$19$	838314.	1.47576	0.737879	+	0.674933i	$0.235827\pi$
$20$	−1.11885e6	−1.56364
$21$	−159446.	−0.178906
$22$	−2.06732e6	−1.88151
$23$	−2.32811e6	−1.73472	−0.867358	−	0.497684i	$-0.834184\pi$
$23$	−2.32811e6	−1.73472	−0.867358	+	0.497684i	$0.834184\pi$
$24$	1.21551e6	0.747836
$25$	−441287.	−0.225939
$26$	1.29352e6	0.555126
$27$	531441.	0.192450
$28$	−1.79121e6	−0.550724
$29$	−6.13023e6	−1.60948	−0.804740	−	0.593628i	$-0.797695\pi$
$29$	−6.13023e6	−1.60948	−0.804740	+	0.593628i	$0.797695\pi$
$30$	−3.75561e6	−0.846514
$31$	3.50327e6	0.681312	0.340656	−	0.940188i	$-0.389351\pi$
$31$	3.50327e6	0.681312	0.340656	+	0.940188i	$0.389351\pi$
$32$	−3.91338e6	−0.659746
$33$	−4.44070e6	−0.651836
$34$	−4.62569e6	−0.593638
$35$	2.42036e6	0.272630
$36$	5.97019e6	0.592416
$37$	−9.25273e6	−0.811638	−0.405819	−	0.913953i	$-0.633014\pi$
$37$	−9.25273e6	−0.811638	−0.405819	+	0.913953i	$0.633014\pi$
$38$	3.16118e7	2.45936
$39$	2.77852e6	0.192320
$40$	−1.84512e7	−1.13961
$41$	−1.75636e7	−0.970703	−0.485352	−	0.874319i	$-0.661308\pi$
$41$	−1.75636e7	−0.970703	−0.485352	+	0.874319i	$0.661308\pi$
$42$	−6.01249e6	−0.298149
$43$	2.04392e7	0.911706	0.455853	−	0.890055i	$-0.349334\pi$
$43$	2.04392e7	0.911706	0.455853	+	0.890055i	$0.349334\pi$
$44$	−4.98866e7	−2.00654
$45$	−8.06720e6	−0.293269
$46$	−8.77902e7	−2.89092
$47$	1.13961e7	0.340655	0.170328	−	0.985387i	$-0.445517\pi$
$47$	1.13961e7	0.340655	0.170328	+	0.985387i	$0.445517\pi$
$48$	8.09773e6	0.220180
$49$	−3.64788e7	−0.903978
$50$	−1.66404e7	−0.376529
$51$	−9.93618e6	−0.205662
$52$	3.12138e7	0.592014
$53$	−5.64902e7	−0.983403	−0.491701	−	0.870764i	$-0.663625\pi$
$53$	−5.64902e7	−0.983403	−0.491701	+	0.870764i	$0.663625\pi$
$54$	2.00400e7	0.320720
$55$	6.74091e7	0.993314
$56$	−2.95392e7	−0.401378
$57$	6.79034e7	0.852030
$58$	−2.31163e8	−2.68221
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	−9.06266e7	−0.902766
$61$	−1.93157e8	−1.78618	−0.893090	−	0.449878i	$-0.851468\pi$
$61$	−1.93157e8	−1.78618	−0.893090	+	0.449878i	$0.851468\pi$
$62$	1.32104e8	1.13541
$63$	−1.29151e7	−0.103292
$64$	−1.98754e8	−1.48083
$65$	−4.21776e7	−0.293070
$66$	−1.67453e8	−1.08629
$67$	2.97914e8	1.80615	0.903075	−	0.429482i	$-0.141304\pi$
$67$	2.97914e8	1.80615	0.903075	+	0.429482i	$0.141304\pi$
$68$	−1.11623e8	−0.633086
$69$	−1.88577e8	−1.00154
$70$	9.12688e7	0.454340
$71$	−3.55939e8	−1.66231	−0.831157	−	0.556037i	$-0.812321\pi$
$71$	−3.55939e8	−1.66231	−0.831157	+	0.556037i	$0.812321\pi$
$72$	9.84560e7	0.431763
$73$	4.51678e8	1.86156	0.930778	−	0.365586i	$-0.119131\pi$
$73$	4.51678e8	1.86156	0.930778	+	0.365586i	$0.119131\pi$
$74$	−3.48909e8	−1.35260
$75$	−3.57443e7	−0.130446
$76$	7.62824e8	2.62279
$77$	1.07918e8	0.349853
$78$	1.04775e8	0.320502
$79$	3.03934e8	0.877926	0.438963	−	0.898505i	$-0.355346\pi$
$79$	3.03934e8	0.877926	0.438963	+	0.898505i	$0.355346\pi$
$80$	−1.22922e8	−0.335526
$81$	4.30467e7	0.111111
$82$	−6.62302e8	−1.61768
$83$	6.28705e8	1.45411	0.727053	−	0.686582i	$-0.240890\pi$
$83$	6.28705e8	1.45411	0.727053	+	0.686582i	$0.240890\pi$
$84$	−1.45088e8	−0.317961
$85$	1.50830e8	0.313402
$86$	7.70735e8	1.51937
$87$	−4.96548e8	−0.929233
$88$	−8.22693e8	−1.46240
$89$	−8.08718e8	−1.36629	−0.683144	−	0.730284i	$-0.739388\pi$
$89$	−8.08718e8	−1.36629	−0.683144	+	0.730284i	$0.739388\pi$
$90$	−3.04204e8	−0.488735
$91$	−6.75237e7	−0.103222
$92$	−2.11847e9	−3.08302
$93$	2.83765e8	0.393356
$94$	4.29732e8	0.567704
$95$	−1.03076e9	−1.29838
$96$	−3.16984e8	−0.380905
$97$	5.73218e8	0.657427	0.328713	−	0.944430i	$-0.393385\pi$
$97$	5.73218e8	0.657427	0.328713	+	0.944430i	$0.393385\pi$
$98$	−1.37557e9	−1.50649
$99$	−3.59696e8	−0.376338
$100$	−4.01550e8	−0.401550
$101$	−9.04619e8	−0.865007	−0.432503	−	0.901632i	$-0.642370\pi$
$101$	−9.04619e8	−0.865007	−0.432503	+	0.901632i	$0.642370\pi$
$102$	−3.74681e8	−0.342737
$103$	9.29642e8	0.813857	0.406929	−	0.913460i	$-0.366600\pi$
$103$	9.29642e8	0.813857	0.406929	+	0.913460i	$0.366600\pi$
$104$	5.14756e8	0.431471
$105$	1.96049e8	0.157403
$106$	−2.13017e9	−1.63885
$107$	−5.27465e8	−0.389015	−0.194508	−	0.980901i	$-0.562311\pi$
$107$	−5.27465e8	−0.389015	−0.194508	+	0.980901i	$0.562311\pi$
$108$	4.83585e8	0.342032
$109$	6.39618e7	0.0434012	0.0217006	−	0.999765i	$-0.493092\pi$
$109$	6.39618e7	0.0434012	0.0217006	+	0.999765i	$0.493092\pi$
$110$	2.54191e9	1.65537
$111$	−7.49471e8	−0.468599
$112$	−1.96791e8	−0.118175
$113$	2.05416e9	1.18517	0.592587	−	0.805506i	$-0.298107\pi$
$113$	2.05416e9	1.18517	0.592587	+	0.805506i	$0.298107\pi$
$114$	2.56055e9	1.41991
$115$	2.86257e9	1.52622
$116$	−5.57821e9	−2.86044
$117$	2.25060e8	0.111036
$118$	4.56931e8	0.216961
$119$	2.41469e8	0.110383
$120$	−1.49455e9	−0.657952
$121$	6.47659e8	0.274671
$122$	−7.28370e9	−2.97668
$123$	−1.42265e9	−0.560436
$124$	3.18781e9	1.21086
$125$	2.94409e9	1.07859
$126$	−4.87012e8	−0.172136
$127$	2.40390e9	0.819974	0.409987	−	0.912091i	$-0.365533\pi$
$127$	2.40390e9	0.819974	0.409987	+	0.912091i	$0.365533\pi$
$128$	−5.49113e9	−1.80808
$129$	1.65557e9	0.526374
$130$	−1.59046e9	−0.488404
$131$	2.24064e9	0.664740	0.332370	−	0.943149i	$-0.392152\pi$
$131$	2.24064e9	0.664740	0.332370	+	0.943149i	$0.392152\pi$
$132$	−4.04082e9	−1.15847
$133$	−1.65019e9	−0.457300
$134$	1.12340e10	3.00996
$135$	−6.53443e8	−0.169319
$136$	−1.84080e9	−0.461404
$137$	2.68246e9	0.650566	0.325283	−	0.945617i	$-0.394540\pi$
$137$	2.68246e9	0.650566	0.325283	+	0.945617i	$0.394540\pi$
$138$	−7.11101e9	−1.66907
$139$	2.86442e9	0.650833	0.325417	−	0.945571i	$-0.394495\pi$
$139$	2.86442e9	0.650833	0.325417	+	0.945571i	$0.394495\pi$
$140$	2.20241e9	0.484531
$141$	9.23082e8	0.196677
$142$	−1.34220e10	−2.77026
$143$	−1.88060e9	−0.376083
$144$	6.55916e8	0.127121
$145$	7.53753e9	1.41603
$146$	1.70322e10	3.10230
$147$	−2.95478e9	−0.521912
$148$	−8.41954e9	−1.44248
$149$	−4.90150e9	−0.814687	−0.407344	−	0.913275i	$-0.633545\pi$
$149$	−4.90150e9	−0.814687	−0.407344	+	0.913275i	$0.633545\pi$
$150$	−1.34787e9	−0.217389
$151$	−1.12831e10	−1.76617	−0.883084	−	0.469216i	$-0.844537\pi$
$151$	−1.12831e10	−1.76617	−0.883084	+	0.469216i	$0.844537\pi$
$152$	1.25799e10	1.91154
$153$	−8.04831e8	−0.118739
$154$	4.06945e9	0.583032
$155$	−4.30751e9	−0.599424
$156$	2.52832e9	0.341800
$157$	−9.88726e9	−1.29876	−0.649378	−	0.760466i	$-0.724971\pi$
$157$	−9.88726e9	−1.29876	−0.649378	+	0.760466i	$0.724971\pi$
$158$	1.14610e10	1.46307
$159$	−4.57570e9	−0.567768
$160$	4.81176e9	0.580449
$161$	4.58280e9	0.537545
$162$	1.62324e9	0.185168
$163$	3.26956e9	0.362781	0.181390	−	0.983411i	$-0.441940\pi$
$163$	3.26956e9	0.362781	0.181390	+	0.983411i	$0.441940\pi$
$164$	−1.59820e10	−1.72518
$165$	5.46014e9	0.573490
$166$	2.37077e10	2.42328
$167$	1.42782e10	1.42052	0.710261	−	0.703938i	$-0.248577\pi$
$167$	1.42782e10	1.42052	0.710261	+	0.703938i	$0.248577\pi$
$168$	−2.39268e9	−0.231735
$169$	−9.42782e9	−0.889040
$170$	5.68761e9	0.522287
$171$	5.50018e9	0.491920
$172$	1.85986e10	1.62033
$173$	1.09311e10	0.927808	0.463904	−	0.885886i	$-0.346448\pi$
$173$	1.09311e10	0.927808	0.463904	+	0.885886i	$0.346448\pi$
$174$	−1.87242e10	−1.54857
$175$	8.68658e8	0.0700128
$176$	−5.48080e9	−0.430564
$177$	9.81506e8	0.0751646
$178$	−3.04958e10	−2.27693
$179$	−1.02017e9	−0.0742738	−0.0371369	−	0.999310i	$-0.511824\pi$
$179$	−1.02017e9	−0.0742738	−0.0371369	+	0.999310i	$0.511824\pi$
$180$	−7.34075e9	−0.521212
$181$	9.70649e9	0.672216	0.336108	−	0.941823i	$-0.390889\pi$
$181$	9.70649e9	0.672216	0.336108	+	0.941823i	$0.390889\pi$
$182$	−2.54624e9	−0.172019
$183$	−1.56457e10	−1.03125
$184$	−3.49362e10	−2.24696
$185$	1.13769e10	0.714085
$186$	1.07004e10	0.655531
$187$	6.72513e9	0.402174
$188$	1.03699e10	0.605429
$189$	−1.04612e9	−0.0596354
$190$	−3.88688e10	−2.16377
$191$	−3.09671e10	−1.68365	−0.841823	−	0.539753i	$-0.818518\pi$
$191$	−3.09671e10	−1.68365	−0.841823	+	0.539753i	$0.818518\pi$
$192$	−1.60991e10	−0.854960
$193$	−3.31776e10	−1.72122	−0.860611	−	0.509263i	$-0.829918\pi$
$193$	−3.31776e10	−1.72122	−0.860611	+	0.509263i	$0.829918\pi$
$194$	2.16154e10	1.09561
$195$	−3.41638e9	−0.169204
$196$	−3.31939e10	−1.60659
$197$	−1.47501e10	−0.697745	−0.348872	−	0.937170i	$-0.613435\pi$
$197$	−1.47501e10	−0.697745	−0.348872	+	0.937170i	$0.613435\pi$
$198$	−1.35637e10	−0.627170
$199$	−4.72288e8	−0.0213485	−0.0106743	−	0.999943i	$-0.503398\pi$
$199$	−4.72288e8	−0.0213485	−0.0106743	+	0.999943i	$0.503398\pi$
$200$	−6.62206e9	−0.292657
$201$	2.41310e10	1.04278
$202$	−3.41121e10	−1.44154
$203$	1.20671e10	0.498737
$204$	−9.04144e9	−0.365512
$205$	2.15957e10	0.854032
$206$	3.50557e10	1.35630
$207$	−1.52747e10	−0.578239
$208$	3.42931e9	0.127035
$209$	−4.59592e10	−1.66615
$210$	7.39277e9	0.262313
$211$	−4.37403e10	−1.51918	−0.759592	−	0.650400i	$-0.774601\pi$
$211$	−4.37403e10	−1.51918	−0.759592	+	0.650400i	$0.774601\pi$
$212$	−5.14033e10	−1.74775
$213$	−2.88311e10	−0.959738
$214$	−1.98900e10	−0.648297
$215$	−2.51313e10	−0.802126
$216$	7.97493e9	0.249279
$217$	−6.89606e9	−0.211121
$218$	2.41192e9	0.0723284
$219$	3.65859e10	1.07477
$220$	6.13390e10	1.76537
$221$	−4.20788e9	−0.118658
$222$	−2.82616e10	−0.780925
$223$	−5.12163e9	−0.138687	−0.0693436	−	0.997593i	$-0.522090\pi$
$223$	−5.12163e9	−0.138687	−0.0693436	+	0.997593i	$0.522090\pi$
$224$	7.70334e9	0.204439
$225$	−2.89529e9	−0.0753130
$226$	7.74600e10	1.97510
$227$	2.08665e10	0.521594	0.260797	−	0.965394i	$-0.416015\pi$
$227$	2.08665e10	0.521594	0.260797	+	0.965394i	$0.416015\pi$
$228$	6.17888e10	1.51427
$229$	6.41955e7	0.00154257	0.000771285	−	1.00000i	$-0.499754\pi$
$229$	6.41955e7	0.00154257	0.000771285		1.00000i	$0.499754\pi$
$230$	1.07944e11	2.54345
$231$	8.74135e9	0.201988
$232$	−9.19917e10	−2.08474
$233$	3.05598e10	0.679279	0.339640	−	0.940556i	$-0.389695\pi$
$233$	3.05598e10	0.679279	0.339640	+	0.940556i	$0.389695\pi$
$234$	8.48675e9	0.185042
$235$	−1.40123e10	−0.299711
$236$	1.10262e10	0.231378
$237$	2.46187e10	0.506871
$238$	9.10551e9	0.183953
$239$	7.82466e10	1.55123	0.775613	−	0.631209i	$-0.217441\pi$
$239$	7.82466e10	1.55123	0.775613	+	0.631209i	$0.217441\pi$
$240$	−9.95671e9	−0.193716
$241$	2.17115e10	0.414584	0.207292	−	0.978279i	$-0.433535\pi$
$241$	2.17115e10	0.414584	0.207292	+	0.978279i	$0.433535\pi$
$242$	2.44224e10	0.457741
$243$	3.48678e9	0.0641500
$244$	−1.75763e11	−3.17449
$245$	4.48531e10	0.795326
$246$	−5.36465e10	−0.933971
$247$	2.87565e10	0.491586
$248$	5.25710e10	0.882497
$249$	5.09251e10	0.839528
$250$	1.11018e11	1.79748
$251$	−1.21004e11	−1.92428	−0.962141	−	0.272551i	$-0.912133\pi$
$251$	−1.21004e11	−1.92428	−0.962141	+	0.272551i	$0.912133\pi$
$252$	−1.17521e10	−0.183575
$253$	1.27635e11	1.95852
$254$	9.06482e10	1.36649
$255$	1.22172e10	0.180943
$256$	−1.05302e11	−1.53234
$257$	7.96267e10	1.13857	0.569285	−	0.822140i	$-0.307220\pi$
$257$	7.96267e10	1.13857	0.569285	+	0.822140i	$0.307220\pi$
$258$	6.24296e10	0.877206
$259$	1.82137e10	0.251506
$260$	−3.83795e10	−0.520858
$261$	−4.02204e10	−0.536493
$262$	8.44919e10	1.10779
$263$	7.06283e10	0.910286	0.455143	−	0.890418i	$-0.349588\pi$
$263$	7.06283e10	0.910286	0.455143	+	0.890418i	$0.349588\pi$
$264$	−6.66382e10	−0.844317
$265$	6.94585e10	0.865205
$266$	−6.22266e10	−0.762094
$267$	−6.55061e10	−0.788826
$268$	2.71087e11	3.20998
$269$	−4.68471e10	−0.545503	−0.272752	−	0.962084i	$-0.587934\pi$
$269$	−4.68471e10	−0.545503	−0.272752	+	0.962084i	$0.587934\pi$
$270$	−2.46405e10	−0.282171
$271$	−1.82719e10	−0.205789	−0.102894	−	0.994692i	$-0.532810\pi$
$271$	−1.82719e10	−0.205789	−0.102894	+	0.994692i	$0.532810\pi$
$272$	−1.22635e10	−0.135848
$273$	−5.46942e9	−0.0595950
$274$	1.01152e11	1.08417
$275$	2.41929e10	0.255088
$276$	−1.71596e11	−1.77998
$277$	−1.08957e10	−0.111198	−0.0555988	−	0.998453i	$-0.517707\pi$
$277$	−1.08957e10	−0.111198	−0.0555988	+	0.998453i	$0.517707\pi$
$278$	1.08014e11	1.08462
$279$	2.29850e10	0.227104
$280$	3.63205e10	0.353135
$281$	1.25313e11	1.19899	0.599497	−	0.800377i	$-0.295367\pi$
$281$	1.25313e11	1.19899	0.599497	+	0.800377i	$0.295367\pi$
$282$	3.48083e10	0.327764
$283$	4.91058e10	0.455087	0.227543	−	0.973768i	$-0.426931\pi$
$283$	4.91058e10	0.455087	0.227543	+	0.973768i	$0.426931\pi$
$284$	−3.23887e11	−2.95435
$285$	−8.34919e10	−0.749622
$286$	−7.09149e10	−0.626744
$287$	3.45733e10	0.300796
$288$	−2.56757e10	−0.219915
$289$	−1.03540e11	−0.873110
$290$	2.84231e11	2.35983
$291$	4.64307e10	0.379565
$292$	4.11005e11	3.30845
$293$	1.93751e11	1.53581	0.767907	−	0.640561i	$-0.221298\pi$
$293$	1.93751e11	1.53581	0.767907	+	0.640561i	$0.221298\pi$
$294$	−1.11421e11	−0.869770
$295$	−1.48991e10	−0.114541
$296$	−1.38849e11	−1.05131
$297$	−2.91354e10	−0.217279
$298$	−1.84830e11	−1.35768
$299$	−7.98607e10	−0.577847
$300$	−3.25255e10	−0.231835
$301$	−4.02337e10	−0.282515
$302$	−4.25471e11	−2.94333
$303$	−7.32741e10	−0.499412
$304$	8.38079e10	0.562799
$305$	2.37499e11	1.57149
$306$	−3.03492e10	−0.197879
$307$	1.59101e11	1.02224	0.511118	−	0.859511i	$-0.329232\pi$
$307$	1.59101e11	1.02224	0.511118	+	0.859511i	$0.329232\pi$
$308$	9.82000e10	0.621775
$309$	7.53010e10	0.469881
$310$	−1.62431e11	−0.998944
$311$	1.03591e11	0.627913	0.313957	−	0.949437i	$-0.398345\pi$
$311$	1.03591e11	0.627913	0.313957	+	0.949437i	$0.398345\pi$
$312$	4.16952e10	0.249110
$313$	−4.45093e10	−0.262120	−0.131060	−	0.991374i	$-0.541838\pi$
$313$	−4.45093e10	−0.262120	−0.131060	+	0.991374i	$0.541838\pi$
$314$	−3.72836e11	−2.16439
$315$	1.58800e10	0.0908767
$316$	2.76565e11	1.56029
$317$	−9.15058e10	−0.508958	−0.254479	−	0.967078i	$-0.581904\pi$
$317$	−9.15058e10	−0.508958	−0.254479	+	0.967078i	$0.581904\pi$
$318$	−1.72544e11	−0.946190
$319$	3.36080e11	1.81712
$320$	2.44382e11	1.30285
$321$	−4.27247e10	−0.224598
$322$	1.72812e11	0.895822
$323$	−1.02835e11	−0.525690
$324$	3.91704e10	0.197472
$325$	−1.51374e10	−0.0752620
$326$	1.23291e11	0.604577
$327$	5.18091e9	0.0250577
$328$	−2.63564e11	−1.25734
$329$	−2.24328e10	−0.105560
$330$	2.05895e11	0.955726
$331$	1.49265e11	0.683492	0.341746	−	0.939792i	$-0.388982\pi$
$331$	1.49265e11	0.683492	0.341746	+	0.939792i	$0.388982\pi$
$332$	5.72091e11	2.58431
$333$	−6.07072e10	−0.270546
$334$	5.38412e11	2.36731
$335$	−3.66305e11	−1.58906
$336$	−1.59401e10	−0.0682282
$337$	−1.51793e11	−0.641085	−0.320543	−	0.947234i	$-0.603865\pi$
$337$	−1.51793e11	−0.641085	−0.320543	+	0.947234i	$0.603865\pi$
$338$	−3.55511e11	−1.48159
$339$	1.66387e11	0.684261
$340$	1.37248e11	0.556993
$341$	−1.92061e11	−0.769211
$342$	2.07405e11	0.819788
$343$	1.51242e11	0.589994
$344$	3.06715e11	1.18092
$345$	2.31868e11	0.881161
$346$	4.12200e11	1.54620
$347$	−2.24014e11	−0.829453	−0.414726	−	0.909946i	$-0.636123\pi$
$347$	−2.24014e11	−0.829453	−0.414726	+	0.909946i	$0.636123\pi$
$348$	−4.51835e11	−1.65148
$349$	−5.50922e11	−1.98781	−0.993906	−	0.110228i	$-0.964842\pi$
$349$	−5.50922e11	−1.98781	−0.993906	+	0.110228i	$0.964842\pi$
$350$	3.27560e10	0.116677
$351$	1.82299e10	0.0641065
$352$	2.14545e11	0.744862
$353$	4.45986e11	1.52875	0.764373	−	0.644774i	$-0.223049\pi$
$353$	4.45986e11	1.52875	0.764373	+	0.644774i	$0.223049\pi$
$354$	3.70114e10	0.125262
$355$	4.37652e11	1.46252
$356$	−7.35894e11	−2.42823
$357$	1.95590e10	0.0637294
$358$	−3.84695e10	−0.123778
$359$	2.89771e11	0.920723	0.460362	−	0.887731i	$-0.347720\pi$
$359$	2.89771e11	0.920723	0.460362	+	0.887731i	$0.347720\pi$
$360$	−1.21058e11	−0.379869
$361$	3.80082e11	1.17786
$362$	3.66020e11	1.12025
$363$	5.24604e10	0.158581
$364$	−6.14433e10	−0.183450
$365$	−5.55369e11	−1.63781
$366$	−5.89979e11	−1.71859
$367$	−6.50943e11	−1.87303	−0.936517	−	0.350623i	$-0.885970\pi$
$367$	−6.50943e11	−1.87303	−0.936517	+	0.350623i	$0.885970\pi$
$368$	−2.32746e11	−0.661556
$369$	−1.15235e11	−0.323568
$370$	4.29008e11	1.19003
$371$	1.11199e11	0.304732
$372$	2.58212e11	0.699091
$373$	−1.12418e11	−0.300708	−0.150354	−	0.988632i	$-0.548041\pi$
$373$	−1.12418e11	−0.300708	−0.150354	+	0.988632i	$0.548041\pi$
$374$	2.53596e11	0.670225
$375$	2.38472e11	0.622724
$376$	1.71012e11	0.441247
$377$	−2.10284e11	−0.536129
$378$	−3.94480e10	−0.0993829
$379$	3.08628e11	0.768349	0.384174	−	0.923261i	$-0.374486\pi$
$379$	3.08628e11	0.768349	0.384174	+	0.923261i	$0.374486\pi$
$380$	−9.37945e11	−2.30755
$381$	1.94716e11	0.473412
$382$	−1.16773e12	−2.80581
$383$	−2.45330e10	−0.0582582	−0.0291291	−	0.999576i	$-0.509273\pi$
$383$	−2.45330e10	−0.0582582	−0.0291291	+	0.999576i	$0.509273\pi$
$384$	−4.44781e11	−1.04389
$385$	−1.32692e11	−0.307803
$386$	−1.25109e12	−2.86843
$387$	1.34101e11	0.303902
$388$	5.21601e11	1.16841
$389$	−6.10513e11	−1.35183	−0.675914	−	0.736980i	$-0.736251\pi$
$389$	−6.10513e11	−1.35183	−0.675914	+	0.736980i	$0.736251\pi$
$390$	−1.28828e11	−0.281980
$391$	2.85587e11	0.617935
$392$	−5.47409e11	−1.17091
$393$	1.81492e11	0.383788
$394$	−5.56208e11	−1.16280
$395$	−3.73708e11	−0.772406
$396$	−3.27306e11	−0.668846
$397$	−4.47627e11	−0.904396	−0.452198	−	0.891917i	$-0.649360\pi$
$397$	−4.47627e11	−0.904396	−0.452198	+	0.891917i	$0.649360\pi$
$398$	−1.78094e10	−0.0355775
$399$	−1.33665e11	−0.264022
$400$	−4.41164e10	−0.0861648
$401$	−5.80109e11	−1.12037	−0.560183	−	0.828369i	$-0.689269\pi$
$401$	−5.80109e11	−1.12037	−0.560183	+	0.828369i	$0.689269\pi$
$402$	9.09951e11	1.73780
$403$	1.20172e11	0.226950
$404$	−8.23159e11	−1.53733
$405$	−5.29289e10	−0.0977564
$406$	4.55036e11	0.831149
$407$	5.07267e11	0.916350
$408$	−1.49105e11	−0.266392
$409$	3.49105e11	0.616880	0.308440	−	0.951244i	$-0.400193\pi$
$409$	3.49105e11	0.616880	0.308440	+	0.951244i	$0.400193\pi$
$410$	8.14346e11	1.42325
$411$	2.17280e11	0.375604
$412$	8.45929e11	1.44643
$413$	−2.38526e10	−0.0403422
$414$	−5.75992e11	−0.963639
$415$	−7.73036e11	−1.27933
$416$	−1.34240e11	−0.219766
$417$	2.32018e11	0.375759
$418$	−1.73307e12	−2.77665
$419$	−1.19183e11	−0.188908	−0.0944541	−	0.995529i	$-0.530111\pi$
$419$	−1.19183e11	−0.188908	−0.0944541	+	0.995529i	$0.530111\pi$
$420$	1.78395e11	0.279744
$421$	−2.91158e11	−0.451709	−0.225855	−	0.974161i	$-0.572517\pi$
$421$	−2.91158e11	−0.451709	−0.225855	+	0.974161i	$0.572517\pi$
$422$	−1.64939e12	−2.53173
$423$	7.47697e10	0.113552
$424$	−8.47705e11	−1.27379
$425$	5.41322e10	0.0804833
$426$	−1.08718e12	−1.59941
$427$	3.80222e11	0.553492
$428$	−4.79967e11	−0.691376
$429$	−1.52328e11	−0.217131
$430$	−9.47672e11	−1.33675
$431$	−3.30127e11	−0.460822	−0.230411	−	0.973093i	$-0.574007\pi$
$431$	−3.30127e11	−0.460822	−0.230411	+	0.973093i	$0.574007\pi$
$432$	5.31292e10	0.0733933
$433$	−6.15872e11	−0.841966	−0.420983	−	0.907069i	$-0.638315\pi$
$433$	−6.15872e11	−0.841966	−0.420983	+	0.907069i	$0.638315\pi$
$434$	−2.60042e11	−0.351836
$435$	6.10540e11	0.817546
$436$	5.82021e10	0.0771347
$437$	−1.95169e12	−2.56002
$438$	1.37961e12	1.79111
$439$	1.71665e11	0.220593	0.110297	−	0.993899i	$-0.464820\pi$
$439$	1.71665e11	0.220593	0.110297	+	0.993899i	$0.464820\pi$
$440$	1.01156e12	1.28663
$441$	−2.39337e11	−0.301326
$442$	−1.58674e11	−0.197745
$443$	1.14879e12	1.41717	0.708587	−	0.705623i	$-0.249333\pi$
$443$	1.14879e12	1.41717	0.708587	+	0.705623i	$0.249333\pi$
$444$	−6.81982e11	−0.832817
$445$	9.94374e11	1.20207
$446$	−1.93130e11	−0.231123
$447$	−3.97022e11	−0.470360
$448$	3.91240e11	0.458873
$449$	4.41175e11	0.512274	0.256137	−	0.966641i	$-0.417550\pi$
$449$	4.41175e11	0.512274	0.256137	+	0.966641i	$0.417550\pi$
$450$	−1.09178e11	−0.125510
$451$	9.62897e11	1.09594
$452$	1.86919e12	2.10635
$453$	−9.13930e11	−1.01970
$454$	7.86850e11	0.869241
$455$	8.30250e10	0.0908150
$456$	1.01897e12	1.10363
$457$	−1.18772e12	−1.27377	−0.636885	−	0.770959i	$-0.719777\pi$
$457$	−1.18772e12	−1.27377	−0.636885	+	0.770959i	$0.719777\pi$
$458$	2.42073e9	0.00257071
$459$	−6.51913e10	−0.0685540
$460$	2.60480e12	2.71246
$461$	3.70002e11	0.381549	0.190774	−	0.981634i	$-0.438900\pi$
$461$	3.70002e11	0.381549	0.190774	+	0.981634i	$0.438900\pi$
$462$	3.29625e11	0.336614
$463$	1.60791e12	1.62610	0.813049	−	0.582196i	$-0.197806\pi$
$463$	1.60791e12	1.62610	0.813049	+	0.582196i	$0.197806\pi$
$464$	−6.12851e11	−0.613796
$465$	−3.48908e11	−0.346077
$466$	1.15237e12	1.13202
$467$	−1.16153e12	−1.13007	−0.565035	−	0.825067i	$-0.691137\pi$
$467$	−1.16153e12	−1.13007	−0.565035	+	0.825067i	$0.691137\pi$
$468$	2.04794e11	0.197338
$469$	−5.86432e11	−0.559680
$470$	−5.28385e11	−0.499471
$471$	−8.00868e11	−0.749837
$472$	1.81836e11	0.168632
$473$	−1.12054e12	−1.02933
$474$	9.28340e11	0.844704
$475$	−3.69937e11	−0.333432
$476$	2.19725e11	0.196177
$477$	−3.70632e11	−0.327801
$478$	2.95058e12	2.58513
$479$	−1.05602e12	−0.916560	−0.458280	−	0.888808i	$-0.651534\pi$
$479$	−1.05602e12	−0.916560	−0.458280	+	0.888808i	$0.651534\pi$
$480$	3.89753e11	0.335123
$481$	−3.17394e11	−0.270362
$482$	8.18713e11	0.690907
$483$	3.71207e11	0.310352
$484$	5.89338e11	0.488158
$485$	−7.04811e11	−0.578409
$486$	1.31482e11	0.106907
$487$	−3.50079e11	−0.282023	−0.141012	−	0.990008i	$-0.545036\pi$
$487$	−3.50079e11	−0.282023	−0.141012	+	0.990008i	$0.545036\pi$
$488$	−2.89855e12	−2.31362
$489$	2.64834e11	0.209452
$490$	1.69136e12	1.32542
$491$	−1.76362e12	−1.36942	−0.684711	−	0.728814i	$-0.740072\pi$
$491$	−1.76362e12	−1.36942	−0.684711	+	0.728814i	$0.740072\pi$
$492$	−1.29454e12	−0.996034
$493$	7.51988e11	0.573324
$494$	1.08437e12	0.819232
$495$	4.42271e11	0.331105
$496$	3.50229e11	0.259827
$497$	7.00653e11	0.515109
$498$	1.92032e12	1.39908
$499$	−1.33296e12	−0.962418	−0.481209	−	0.876606i	$-0.659802\pi$
$499$	−1.33296e12	−0.962418	−0.481209	+	0.876606i	$0.659802\pi$
$500$	2.67898e12	1.91692
$501$	1.15653e12	0.820139
$502$	−4.56292e12	−3.20683
$503$	−1.31118e12	−0.913285	−0.456643	−	0.889650i	$-0.650948\pi$
$503$	−1.31118e12	−0.913285	−0.456643	+	0.889650i	$0.650948\pi$
$504$	−1.93807e11	−0.133793
$505$	1.11229e12	0.761039
$506$	4.81296e12	3.26388
$507$	−7.63653e11	−0.513287
$508$	2.18743e12	1.45730
$509$	1.55199e12	1.02485	0.512424	−	0.858732i	$-0.328748\pi$
$509$	1.55199e12	1.02485	0.512424	+	0.858732i	$0.328748\pi$
$510$	4.60696e11	0.301543
$511$	−8.89111e11	−0.576849
$512$	−1.15933e12	−0.745578
$513$	4.45514e11	0.284010
$514$	3.00263e12	1.89744
$515$	−1.14306e12	−0.716038
$516$	1.50649e12	0.935497
$517$	−6.24772e11	−0.384604
$518$	6.86815e11	0.419137
$519$	8.85422e11	0.535670
$520$	−6.32927e11	−0.379611
$521$	−1.16071e12	−0.690167	−0.345083	−	0.938572i	$-0.612149\pi$
$521$	−1.16071e12	−0.690167	−0.345083	+	0.938572i	$0.612149\pi$
$522$	−1.51666e12	−0.894070
$523$	−1.29386e12	−0.756188	−0.378094	−	0.925767i	$-0.623420\pi$
$523$	−1.29386e12	−0.756188	−0.378094	+	0.925767i	$0.623420\pi$
$524$	2.03888e12	1.18141
$525$	7.03613e10	0.0404219
$526$	2.66331e12	1.51700
$527$	−4.29743e11	−0.242695
$528$	−4.43945e11	−0.248586
$529$	3.61895e12	2.00924
$530$	2.61920e12	1.44187
$531$	7.95020e10	0.0433963
$532$	−1.50159e12	−0.812736
$533$	−6.02481e11	−0.323348
$534$	−2.47016e12	−1.31459
$535$	6.48554e11	0.342258
$536$	4.47057e12	2.33949
$537$	−8.26341e10	−0.0428820
$538$	−1.76655e12	−0.909085
$539$	1.99989e12	1.02060
$540$	−5.94601e11	−0.300922
$541$	−1.05100e12	−0.527492	−0.263746	−	0.964592i	$-0.584958\pi$
$541$	−1.05100e12	−0.527492	−0.263746	+	0.964592i	$0.584958\pi$
$542$	−6.89011e11	−0.342949
$543$	7.86226e11	0.388104
$544$	4.80050e11	0.235013
$545$	−7.86454e10	−0.0381847
$546$	−2.06245e11	−0.0993155
$547$	−9.08834e11	−0.434052	−0.217026	−	0.976166i	$-0.569636\pi$
$547$	−9.08834e11	−0.434052	−0.217026	+	0.976166i	$0.569636\pi$
$548$	2.44091e12	1.15622
$549$	−1.26730e12	−0.595393
$550$	9.12284e11	0.425107
$551$	−5.13905e12	−2.37520
$552$	−2.82983e12	−1.29728
$553$	−5.98284e11	−0.272047
$554$	−4.10863e11	−0.185312
$555$	9.21526e11	0.412277
$556$	2.60648e12	1.15669
$557$	−2.33074e12	−1.02599	−0.512997	−	0.858390i	$-0.671465\pi$
$557$	−2.33074e12	−1.02599	−0.512997	+	0.858390i	$0.671465\pi$
$558$	8.66735e11	0.378471
$559$	7.01120e11	0.303696
$560$	2.41968e11	0.103971
$561$	5.44736e11	0.232195
$562$	4.72539e12	1.99813
$563$	−3.08395e11	−0.129366	−0.0646829	−	0.997906i	$-0.520604\pi$
$563$	−3.08395e11	−0.129366	−0.0646829	+	0.997906i	$0.520604\pi$
$564$	8.39960e11	0.349544
$565$	−2.52574e12	−1.04273
$566$	1.85172e12	0.758405
$567$	−8.47359e10	−0.0344305
$568$	−5.34131e12	−2.15318
$569$	−2.54066e12	−1.01611	−0.508056	−	0.861324i	$-0.669636\pi$
$569$	−2.54066e12	−1.01611	−0.508056	+	0.861324i	$0.669636\pi$
$570$	−3.14838e12	−1.24925
$571$	−3.83142e12	−1.50833	−0.754167	−	0.656683i	$-0.771959\pi$
$571$	−3.83142e12	−1.50833	−0.754167	+	0.656683i	$0.771959\pi$
$572$	−1.71125e12	−0.668392
$573$	−2.50834e12	−0.972054
$574$	1.30372e12	0.501280
$575$	1.02737e12	0.391940
$576$	−1.30403e12	−0.493612
$577$	−3.89311e12	−1.46219	−0.731097	−	0.682273i	$-0.760991\pi$
$577$	−3.89311e12	−1.46219	−0.731097	+	0.682273i	$0.760991\pi$
$578$	−3.90437e12	−1.45504
$579$	−2.68738e12	−0.993748
$580$	6.85878e12	2.51664
$581$	−1.23758e12	−0.450590
$582$	1.75084e12	0.632549
$583$	3.09698e12	1.11027
$584$	6.77799e12	2.41125
$585$	−2.76727e11	−0.0976901
$586$	7.30609e12	2.55945
$587$	−1.18968e12	−0.413578	−0.206789	−	0.978386i	$-0.566301\pi$
$587$	−1.18968e12	−0.413578	−0.206789	+	0.978386i	$0.566301\pi$
$588$	−2.68870e12	−0.927567
$589$	2.93684e12	1.00545
$590$	−5.61827e11	−0.190884
$591$	−1.19476e12	−0.402843
$592$	−9.25014e11	−0.309528
$593$	3.51766e12	1.16817	0.584087	−	0.811691i	$-0.301453\pi$
$593$	3.51766e12	1.16817	0.584087	+	0.811691i	$0.301453\pi$
$594$	−1.09866e12	−0.362097
$595$	−2.96903e11	−0.0971154
$596$	−4.46013e12	−1.44790
$597$	−3.82553e10	−0.0123256
$598$	−3.01145e12	−0.962986
$599$	4.65537e12	1.47752	0.738760	−	0.673968i	$-0.235412\pi$
$599$	4.65537e12	1.47752	0.738760	+	0.673968i	$0.235412\pi$
$600$	−5.36387e11	−0.168965
$601$	−3.04398e12	−0.951713	−0.475857	−	0.879523i	$-0.657862\pi$
$601$	−3.04398e12	−0.951713	−0.475857	+	0.879523i	$0.657862\pi$
$602$	−1.51716e12	−0.470813
$603$	1.95461e12	0.602050
$604$	−1.02671e13	−3.13892
$605$	−7.96341e11	−0.241657
$606$	−2.76308e12	−0.832274
$607$	1.65582e12	0.495066	0.247533	−	0.968879i	$-0.420380\pi$
$607$	1.65582e12	0.495066	0.247533	+	0.968879i	$0.420380\pi$
$608$	−3.28064e12	−0.973626
$609$	9.77437e11	0.287946
$610$	8.95580e12	2.61891
$611$	3.90917e11	0.113475
$612$	−7.32357e11	−0.211029
$613$	9.71802e11	0.277975	0.138988	−	0.990294i	$-0.455615\pi$
$613$	9.71802e11	0.277975	0.138988	+	0.990294i	$0.455615\pi$
$614$	5.99951e12	1.70356
$615$	1.74925e12	0.493076
$616$	1.61944e12	0.453161
$617$	−6.68130e12	−1.85600	−0.927999	−	0.372583i	$-0.878472\pi$
$617$	−6.68130e12	−1.85600	−0.927999	+	0.372583i	$0.878472\pi$
$618$	2.83951e12	0.783060
$619$	−4.90937e12	−1.34406	−0.672028	−	0.740525i	$-0.734577\pi$
$619$	−4.90937e12	−1.34406	−0.672028	+	0.740525i	$0.734577\pi$
$620$	−3.91963e12	−1.06532
$621$	−1.23725e12	−0.333846
$622$	3.90628e12	1.04642
$623$	1.59193e12	0.423378
$624$	2.77775e11	0.0733435
$625$	−2.75807e12	−0.723012
$626$	−1.67839e12	−0.436826
$627$	−3.72270e12	−0.961953
$628$	−8.99692e12	−2.30821
$629$	1.13502e12	0.289119
$630$	5.98814e11	0.151447
$631$	5.31433e12	1.33449	0.667246	−	0.744837i	$-0.267473\pi$
$631$	5.31433e12	1.33449	0.667246	+	0.744837i	$0.267473\pi$
$632$	4.56091e12	1.13717
$633$	−3.54296e12	−0.877101
$634$	−3.45057e12	−0.848183
$635$	−2.95576e12	−0.721419
$636$	−4.16367e12	−1.00906
$637$	−1.25132e12	−0.301122
$638$	1.26732e13	3.02825
$639$	−2.33532e12	−0.554105
$640$	6.75172e12	1.59076
$641$	−1.72255e11	−0.0403005	−0.0201503	−	0.999797i	$-0.506414\pi$
$641$	−1.72255e11	−0.0403005	−0.0201503	+	0.999797i	$0.506414\pi$
$642$	−1.61109e12	−0.374294
$643$	−7.19928e12	−1.66089	−0.830443	−	0.557104i	$-0.811913\pi$
$643$	−7.19928e12	−1.66089	−0.830443	+	0.557104i	$0.811913\pi$
$644$	4.17012e12	0.955350
$645$	−2.03564e12	−0.463108
$646$	−3.87778e12	−0.876067
$647$	−3.07938e11	−0.0690866	−0.0345433	−	0.999403i	$-0.510998\pi$
$647$	−3.07938e11	−0.0690866	−0.0345433	+	0.999403i	$0.510998\pi$
$648$	6.45970e11	0.143921
$649$	−6.64315e11	−0.146985
$650$	−5.70812e11	−0.125425
$651$	−5.58581e11	−0.121891
$652$	2.97514e12	0.644752
$653$	−1.58359e12	−0.340827	−0.170413	−	0.985373i	$-0.554510\pi$
$653$	−1.58359e12	−0.340827	−0.170413	+	0.985373i	$0.554510\pi$
$654$	1.95366e11	0.0417588
$655$	−2.75502e12	−0.584843
$656$	−1.75587e12	−0.370190
$657$	2.96346e12	0.620518
$658$	−8.45912e11	−0.175917
$659$	2.99583e12	0.618776	0.309388	−	0.950936i	$-0.399876\pi$
$659$	2.99583e12	0.618776	0.309388	+	0.950936i	$0.399876\pi$
$660$	4.96846e12	1.01923
$661$	8.52932e10	0.0173783	0.00868916	−	0.999962i	$-0.497234\pi$
$661$	8.52932e10	0.0173783	0.00868916	+	0.999962i	$0.497234\pi$
$662$	5.62861e12	1.13904
$663$	−3.40839e11	−0.0685075
$664$	9.43451e12	1.88349
$665$	2.02902e12	0.402336
$666$	−2.28919e12	−0.450867
$667$	1.42718e13	2.79199
$668$	1.29924e13	2.52462
$669$	−4.14852e11	−0.0800711
$670$	−1.38129e13	−2.64819
$671$	1.05895e13	2.01662
$672$	6.23970e11	0.118033
$673$	5.60383e12	1.05297	0.526487	−	0.850183i	$-0.323509\pi$
$673$	5.60383e12	1.05297	0.526487	+	0.850183i	$0.323509\pi$
$674$	−5.72391e12	−1.06837
$675$	−2.34518e11	−0.0434820
$676$	−8.57885e12	−1.58004
$677$	5.42123e10	0.00991856	0.00495928	−	0.999988i	$-0.498421\pi$
$677$	5.42123e10	0.00991856	0.00495928	+	0.999988i	$0.498421\pi$
$678$	6.27426e12	1.14033
$679$	−1.12836e12	−0.203720
$680$	2.26339e12	0.405947
$681$	1.69019e12	0.301143
$682$	−7.24240e12	−1.28190
$683$	3.94513e12	0.693694	0.346847	−	0.937922i	$-0.387252\pi$
$683$	3.94513e12	0.693694	0.346847	+	0.937922i	$0.387252\pi$
$684$	5.00489e12	0.874263
$685$	−3.29827e12	−0.572373
$686$	5.70314e12	0.983230
$687$	5.19984e9	0.000890604 0
$688$	2.04334e12	0.347691
$689$	−1.93777e12	−0.327579
$690$	8.74347e12	1.46846
$691$	−6.44422e12	−1.07527	−0.537637	−	0.843176i	$-0.680683\pi$
$691$	−6.44422e12	−1.07527	−0.537637	+	0.843176i	$0.680683\pi$
$692$	9.94680e12	1.64894
$693$	7.08049e11	0.116618
$694$	−8.44728e12	−1.38229
$695$	−3.52200e12	−0.572608
$696$	−7.45132e12	−1.20363
$697$	2.15451e12	0.345781
$698$	−2.07746e13	−3.31271
$699$	2.47534e12	0.392182
$700$	7.90436e11	0.124430
$701$	−3.63823e12	−0.569062	−0.284531	−	0.958667i	$-0.591838\pi$
$701$	−3.63823e12	−0.569062	−0.284531	+	0.958667i	$0.591838\pi$
$702$	6.87427e11	0.106834
$703$	−7.75669e12	−1.19778
$704$	1.08964e13	1.67188
$705$	−1.13499e12	−0.173038
$706$	1.68176e13	2.54767
$707$	1.78071e12	0.268044
$708$	8.93123e11	0.133586
$709$	−3.78886e12	−0.563119	−0.281560	−	0.959544i	$-0.590852\pi$
$709$	−3.78886e12	−0.563119	−0.281560	+	0.959544i	$0.590852\pi$
$710$	1.65033e13	2.43730
$711$	1.99411e12	0.292642
$712$	−1.21358e13	−1.76974
$713$	−8.15601e12	−1.18188
$714$	7.37546e11	0.106206
$715$	2.31232e12	0.330880
$716$	−9.28309e11	−0.132003
$717$	6.33798e12	0.895601
$718$	1.09269e13	1.53439
$719$	4.05107e11	0.0565314	0.0282657	−	0.999600i	$-0.491002\pi$
$719$	4.05107e11	0.0565314	0.0282657	+	0.999600i	$0.491002\pi$
$720$	−8.06493e11	−0.111842
$721$	−1.82997e12	−0.252194
$722$	1.43324e13	1.96292
$723$	1.75863e12	0.239360
$724$	8.83243e12	1.19469
$725$	2.70519e12	0.363644
$726$	1.97822e12	0.264277
$727$	−6.44546e12	−0.855755	−0.427877	−	0.903837i	$-0.640738\pi$
$727$	−6.44546e12	−0.855755	−0.427877	+	0.903837i	$0.640738\pi$
$728$	−1.01328e12	−0.133702
$729$	2.82430e11	0.0370370
$730$	−2.09423e13	−2.72942
$731$	−2.50725e12	−0.324765
$732$	−1.42368e13	−1.83279
$733$	−6.47343e12	−0.828260	−0.414130	−	0.910218i	$-0.635914\pi$
$733$	−6.47343e12	−0.828260	−0.414130	+	0.910218i	$0.635914\pi$
$734$	−2.45462e13	−3.12142
$735$	3.63310e12	0.459182
$736$	9.11078e12	1.14447
$737$	−1.63327e13	−2.03917
$738$	−4.34536e12	−0.539228
$739$	8.07204e12	0.995597	0.497799	−	0.867293i	$-0.334142\pi$
$739$	8.07204e12	0.995597	0.497799	+	0.867293i	$0.334142\pi$
$740$	1.03524e13	1.26911
$741$	2.32927e12	0.283817
$742$	4.19317e12	0.507838
$743$	−2.00695e12	−0.241594	−0.120797	−	0.992677i	$-0.538545\pi$
$743$	−2.00695e12	−0.241594	−0.120797	+	0.992677i	$0.538545\pi$
$744$	4.25825e12	0.509510
$745$	6.02673e12	0.716768
$746$	−4.23913e12	−0.501132
$747$	4.12494e12	0.484702
$748$	6.11954e12	0.714762
$749$	1.03830e12	0.120546
$750$	8.99247e12	1.03777
$751$	−1.30296e13	−1.49469	−0.747345	−	0.664436i	$-0.768672\pi$
$751$	−1.30296e13	−1.49469	−0.747345	+	0.664436i	$0.768672\pi$
$752$	1.13929e12	0.129913
$753$	−9.80135e12	−1.11099
$754$	−7.92954e12	−0.893464
$755$	1.38733e13	1.55389
$756$	−9.51920e11	−0.105987
$757$	−1.01558e13	−1.12405	−0.562024	−	0.827121i	$-0.689977\pi$
$757$	−1.01558e13	−1.12405	−0.562024	+	0.827121i	$0.689977\pi$
$758$	1.16380e13	1.28046
$759$	1.03384e13	1.13075
$760$	−1.54679e13	−1.68178
$761$	4.34966e11	0.0470137	0.0235069	−	0.999724i	$-0.492517\pi$
$761$	4.34966e11	0.0470137	0.0235069	+	0.999724i	$0.492517\pi$
$762$	7.34250e12	0.788945
$763$	−1.25906e11	−0.0134489
$764$	−2.81786e13	−2.99226
$765$	9.89594e11	0.104467
$766$	−9.25111e11	−0.0970877
$767$	4.15659e11	0.0433669
$768$	−8.52942e12	−0.884696
$769$	7.77469e12	0.801705	0.400852	−	0.916143i	$-0.368714\pi$
$769$	7.77469e12	0.801705	0.400852	+	0.916143i	$0.368714\pi$
$770$	−5.00367e12	−0.512956
$771$	6.44976e12	0.657354
$772$	−3.01900e13	−3.05904
$773$	1.37897e13	1.38914	0.694571	−	0.719424i	$-0.255594\pi$
$773$	1.37897e13	1.38914	0.694571	+	0.719424i	$0.255594\pi$
$774$	5.05680e12	0.506455
$775$	−1.54595e12	−0.153935
$776$	8.60185e12	0.851558
$777$	1.47531e12	0.145207
$778$	−2.30217e13	−2.25283
$779$	−1.47238e13	−1.43252
$780$	−3.10874e12	−0.300718
$781$	1.95138e13	1.87678
$782$	1.07691e13	1.02979
$783$	−3.25785e12	−0.309744
$784$	−3.64685e12	−0.344743
$785$	1.21571e13	1.14266
$786$	6.84384e12	0.639586
$787$	1.68157e13	1.56253	0.781265	−	0.624200i	$-0.214575\pi$
$787$	1.68157e13	1.56253	0.781265	+	0.624200i	$0.214575\pi$
$788$	−1.34219e13	−1.24007
$789$	5.72089e12	0.525554
$790$	−1.40921e13	−1.28722
$791$	−4.04355e12	−0.367256
$792$	−5.39769e12	−0.487467
$793$	−6.62581e12	−0.594990
$794$	−1.68795e13	−1.50718
$795$	5.62614e12	0.499526
$796$	−4.29759e11	−0.0379416
$797$	4.29486e12	0.377040	0.188520	−	0.982069i	$-0.439631\pi$
$797$	4.29486e12	0.377040	0.188520	+	0.982069i	$0.439631\pi$
$798$	−5.04036e12	−0.439995
$799$	−1.39794e12	−0.121347
$800$	1.72692e12	0.149062
$801$	−5.30600e12	−0.455429
$802$	−2.18752e13	−1.86710
$803$	−2.47625e13	−2.10172
$804$	2.19580e13	1.85328
$805$	−5.63487e12	−0.472936
$806$	4.53154e12	0.378214
$807$	−3.79461e12	−0.314946
$808$	−1.35749e13	−1.12043
$809$	−1.42375e13	−1.16860	−0.584300	−	0.811538i	$-0.698631\pi$
$809$	−1.42375e13	−1.16860	−0.584300	+	0.811538i	$0.698631\pi$
$810$	−1.99588e12	−0.162912
$811$	−6.09093e12	−0.494413	−0.247206	−	0.968963i	$-0.579513\pi$
$811$	−6.09093e12	−0.494413	−0.247206	+	0.968963i	$0.579513\pi$
$812$	1.09805e13	0.886379
$813$	−1.48002e12	−0.118812
$814$	1.91284e13	1.52710
$815$	−4.02014e12	−0.319177
$816$	−9.93340e11	−0.0784318
$817$	1.71344e13	1.34546
$818$	1.31643e13	1.02804
$819$	−4.43023e11	−0.0344072
$820$	1.96510e13	1.51783
$821$	1.97006e13	1.51334	0.756668	−	0.653799i	$-0.226826\pi$
$821$	1.97006e13	1.51334	0.756668	+	0.653799i	$0.226826\pi$
$822$	8.19334e12	0.625948
$823$	1.67540e13	1.27297	0.636486	−	0.771289i	$-0.280387\pi$
$823$	1.67540e13	1.27297	0.636486	+	0.771289i	$0.280387\pi$
$824$	1.39504e13	1.05418
$825$	1.95962e12	0.147275
$826$	−8.99451e11	−0.0672307
$827$	−7.37166e12	−0.548013	−0.274006	−	0.961728i	$-0.588349\pi$
$827$	−7.37166e12	−0.548013	−0.274006	+	0.961728i	$0.588349\pi$
$828$	−1.38993e13	−1.02767
$829$	1.37833e13	1.01358	0.506790	−	0.862070i	$-0.330832\pi$
$829$	1.37833e13	1.01358	0.506790	+	0.862070i	$0.330832\pi$
$830$	−2.91502e13	−2.13202
$831$	−8.82551e11	−0.0642000
$832$	−6.81782e12	−0.493277
$833$	4.47481e12	0.322012
$834$	8.74911e12	0.626205
$835$	−1.75560e13	−1.24979
$836$	−4.18206e13	−2.96116
$837$	1.86178e12	0.131119
$838$	−4.49424e12	−0.314817
$839$	−1.73944e13	−1.21194	−0.605969	−	0.795488i	$-0.707214\pi$
$839$	−1.73944e13	−1.21194	−0.605969	+	0.795488i	$0.707214\pi$
$840$	2.94196e12	0.203883
$841$	2.30725e13	1.59042
$842$	−1.09792e13	−0.752777
$843$	1.01503e13	0.692240
$844$	−3.98015e13	−2.69997
$845$	1.15921e13	0.782183
$846$	2.81947e12	0.189235
$847$	−1.27489e12	−0.0851135
$848$	−5.64743e12	−0.375033
$849$	3.97757e12	0.262744
$850$	2.04126e12	0.134126
$851$	2.15414e13	1.40796
$852$	−2.62349e13	−1.70569
$853$	2.90733e13	1.88029	0.940143	−	0.340781i	$-0.110691\pi$
$853$	2.90733e13	1.88029	0.940143	+	0.340781i	$0.110691\pi$
$854$	1.43377e13	0.922399
$855$	−6.76284e12	−0.432794
$856$	−7.91527e12	−0.503887
$857$	−1.80812e13	−1.14502	−0.572509	−	0.819898i	$-0.694030\pi$
$857$	−1.80812e13	−1.14502	−0.572509	+	0.819898i	$0.694030\pi$
$858$	−5.74411e12	−0.361851
$859$	2.42753e13	1.52123	0.760615	−	0.649203i	$-0.224897\pi$
$859$	2.42753e13	1.52123	0.760615	+	0.649203i	$0.224897\pi$
$860$	−2.28683e13	−1.42558
$861$	2.80044e12	0.173665
$862$	−1.24487e13	−0.767963
$863$	−1.03192e13	−0.633280	−0.316640	−	0.948546i	$-0.602555\pi$
$863$	−1.03192e13	−0.633280	−0.316640	+	0.948546i	$0.602555\pi$
$864$	−2.07973e12	−0.126968
$865$	−1.34406e13	−0.816292
$866$	−2.32238e13	−1.40314
$867$	−8.38676e12	−0.504090
$868$	−6.27508e12	−0.375215
$869$	−1.66627e13	−0.991190
$870$	2.30227e13	1.36245
$871$	1.02193e13	0.601642
$872$	9.59827e11	0.0562171
$873$	3.76089e12	0.219142
$874$	−7.35957e13	−4.26630
$875$	−5.79534e12	−0.334228
$876$	3.32914e13	1.91013
$877$	2.00090e13	1.14216	0.571081	−	0.820894i	$-0.306524\pi$
$877$	2.00090e13	1.14216	0.571081	+	0.820894i	$0.306524\pi$
$878$	6.47329e12	0.367620
$879$	1.56938e13	0.886703
$880$	6.73902e12	0.378813
$881$	7.75286e12	0.433581	0.216791	−	0.976218i	$-0.430441\pi$
$881$	7.75286e12	0.433581	0.216791	+	0.976218i	$0.430441\pi$
$882$	−9.02511e12	−0.502162
$883$	−1.02439e13	−0.567078	−0.283539	−	0.958961i	$-0.591508\pi$
$883$	−1.02439e13	−0.567078	−0.283539	+	0.958961i	$0.591508\pi$
$884$	−3.82897e12	−0.210885
$885$	−1.20683e12	−0.0661304
$886$	4.33194e13	2.36173
$887$	−1.04930e13	−0.569170	−0.284585	−	0.958651i	$-0.591856\pi$
$887$	−1.04930e13	−0.569170	−0.284585	+	0.958651i	$0.591856\pi$
$888$	−1.12468e13	−0.606972
$889$	−4.73199e12	−0.254089
$890$	3.74966e13	2.00326
$891$	−2.35997e12	−0.125446
$892$	−4.66043e12	−0.246482
$893$	9.55349e12	0.502725
$894$	−1.49712e13	−0.783858
$895$	1.25437e12	0.0653467
$896$	1.08091e13	0.560277
$897$	−6.46871e12	−0.333620
$898$	1.66361e13	0.853708
$899$	−2.14759e13	−1.09656
$900$	−2.63457e12	−0.133850
$901$	6.92959e12	0.350305
$902$	3.63097e13	1.82639
$903$	−3.25893e12	−0.163110
$904$	3.08253e13	1.53514
$905$	−1.19348e13	−0.591420
$906$	−3.44632e13	−1.69933
$907$	3.40016e13	1.66827	0.834135	−	0.551560i	$-0.185967\pi$
$907$	3.40016e13	1.66827	0.834135	+	0.551560i	$0.185967\pi$
$908$	1.89875e13	0.927003
$909$	−5.93520e12	−0.288336
$910$	3.13077e12	0.151344
$911$	1.05487e13	0.507419	0.253710	−	0.967280i	$-0.418349\pi$
$911$	1.05487e13	0.507419	0.253710	+	0.967280i	$0.418349\pi$
$912$	6.78844e12	0.324932
$913$	−3.44678e13	−1.64170
$914$	−4.47874e13	−2.12275
$915$	1.92374e13	0.907303
$916$	5.84148e10	0.00274153
$917$	−4.41062e12	−0.205986
$918$	−2.45828e12	−0.114246
$919$	1.63341e13	0.755397	0.377698	−	0.925929i	$-0.376716\pi$
$919$	1.63341e13	0.755397	0.377698	+	0.925929i	$0.376716\pi$
$920$	4.29564e13	1.97689
$921$	1.28872e13	0.590188
$922$	1.39523e13	0.635854
$923$	−1.22097e13	−0.553729
$924$	7.95420e12	0.358982
$925$	4.08311e12	0.183381
$926$	6.06322e13	2.70990
$927$	6.09938e12	0.271286
$928$	2.39899e13	1.06185
$929$	−2.40994e13	−1.06154	−0.530770	−	0.847516i	$-0.678097\pi$
$929$	−2.40994e13	−1.06154	−0.530770	+	0.847516i	$0.678097\pi$
$930$	−1.31569e13	−0.576741
$931$	−3.05806e13	−1.33405
$932$	2.78079e13	1.20725
$933$	8.39086e12	0.362526
$934$	−4.37999e13	−1.88327
$935$	−8.26901e12	−0.353835
$936$	3.37731e12	0.143824
$937$	−1.28907e13	−0.546322	−0.273161	−	0.961968i	$-0.588069\pi$
$937$	−1.28907e13	−0.546322	−0.273161	+	0.961968i	$0.588069\pi$
$938$	−2.21136e13	−0.932712
$939$	−3.60525e12	−0.151335
$940$	−1.27505e13	−0.532661
$941$	5.56232e12	0.231261	0.115630	−	0.993292i	$-0.463111\pi$
$941$	5.56232e12	0.231261	0.115630	+	0.993292i	$0.463111\pi$
$942$	−3.01997e13	−1.24961
$943$	4.08900e13	1.68390
$944$	1.21140e12	0.0496492
$945$	1.28628e12	0.0524677
$946$	−4.22544e13	−1.71538
$947$	2.78874e13	1.12677	0.563383	−	0.826196i	$-0.309500\pi$
$947$	2.78874e13	1.12677	0.563383	+	0.826196i	$0.309500\pi$
$948$	2.24018e13	0.900835
$949$	1.54938e13	0.620098
$950$	−1.39499e13	−0.555666
$951$	−7.41197e12	−0.293847
$952$	3.62355e12	0.142977
$953$	−1.74771e13	−0.686359	−0.343179	−	0.939270i	$-0.611504\pi$
$953$	−1.74771e13	−0.686359	−0.343179	+	0.939270i	$0.611504\pi$
$954$	−1.39761e13	−0.546283
$955$	3.80762e13	1.48128
$956$	7.12006e13	2.75691
$957$	2.72225e13	1.04912
$958$	−3.98211e13	−1.52745
$959$	−5.28033e12	−0.201594
$960$	1.97949e13	0.752200
$961$	−1.41667e13	−0.535813
$962$	−1.19686e13	−0.450561
$963$	−3.46070e12	−0.129672
$964$	1.97564e13	0.736819
$965$	4.07941e13	1.51434
$966$	1.39978e13	0.517203
$967$	−1.21293e13	−0.446086	−0.223043	−	0.974809i	$-0.571599\pi$
$967$	−1.21293e13	−0.446086	−0.223043	+	0.974809i	$0.571599\pi$
$968$	9.71893e12	0.355778
$969$	−8.32964e12	−0.303507
$970$	−2.65776e13	−0.963923
$971$	−2.65153e13	−0.957216	−0.478608	−	0.878029i	$-0.658858\pi$
$971$	−2.65153e13	−0.957216	−0.478608	+	0.878029i	$0.658858\pi$
$972$	3.17280e12	0.114011
$973$	−5.63850e12	−0.201677
$974$	−1.32010e13	−0.469994
$975$	−1.22613e12	−0.0434525
$976$	−1.93102e13	−0.681183
$977$	−4.50088e13	−1.58042	−0.790209	−	0.612837i	$-0.790028\pi$
$977$	−4.50088e13	−1.58042	−0.790209	+	0.612837i	$0.790028\pi$
$978$	9.98656e12	0.349053
$979$	4.43367e13	1.54256
$980$	4.08141e13	1.41349
$981$	4.19654e11	0.0144671
$982$	−6.65038e13	−2.28215
$983$	−1.71512e13	−0.585875	−0.292937	−	0.956132i	$-0.594633\pi$
$983$	−1.71512e13	−0.585875	−0.292937	+	0.956132i	$0.594633\pi$
$984$	−2.13487e13	−0.725927
$985$	1.81362e13	0.613881
$986$	2.83565e13	0.955448
$987$	−1.81705e12	−0.0609453
$988$	2.61670e13	0.873670
$989$	−4.75846e13	−1.58155
$990$	1.66775e13	0.551789
$991$	7.04586e12	0.232061	0.116031	−	0.993246i	$-0.462983\pi$
$991$	7.04586e12	0.232061	0.116031	+	0.993246i	$0.462983\pi$
$992$	−1.37096e13	−0.449493
$993$	1.20905e13	0.394614
$994$	2.64208e13	0.858434
$995$	5.80710e11	0.0187826
$996$	4.63394e13	1.49205
$997$	−1.13340e13	−0.363292	−0.181646	−	0.983364i	$-0.558142\pi$
$997$	−1.13340e13	−0.363292	−0.181646	+	0.983364i	$0.558142\pi$
$998$	−5.02642e13	−1.60388
$999$	−4.91728e12	−0.156200

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.a.1.20	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.a.1.20	✓	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)

\(f(q)\)	\(=\)	\(q+37.7088 q^{2} +81.0000 q^{3} +909.951 q^{4} -1229.57 q^{5} +3054.41 q^{6} -1968.46 q^{7} +15006.2 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+37.7088 q^{2} +81.0000 q^{3} +909.951 q^{4} -1229.57 q^{5} +3054.41 q^{6} -1968.46 q^{7} +15006.2 q^{8} +6561.00 q^{9} -46365.5 q^{10} -54823.4 q^{11} +73706.0 q^{12} +34302.8 q^{13} -74228.3 q^{14} -99595.0 q^{15} +99972.0 q^{16} -122669. q^{17} +247407. q^{18} +838314. q^{19} -1.11885e6 q^{20} -159446. q^{21} -2.06732e6 q^{22} -2.32811e6 q^{23} +1.21551e6 q^{24} -441287. q^{25} +1.29352e6 q^{26} +531441. q^{27} -1.79121e6 q^{28} -6.13023e6 q^{29} -3.75561e6 q^{30} +3.50327e6 q^{31} -3.91338e6 q^{32} -4.44070e6 q^{33} -4.62569e6 q^{34} +2.42036e6 q^{35} +5.97019e6 q^{36} -9.25273e6 q^{37} +3.16118e7 q^{38} +2.77852e6 q^{39} -1.84512e7 q^{40} -1.75636e7 q^{41} -6.01249e6 q^{42} +2.04392e7 q^{43} -4.98866e7 q^{44} -8.06720e6 q^{45} -8.77902e7 q^{46} +1.13961e7 q^{47} +8.09773e6 q^{48} -3.64788e7 q^{49} -1.66404e7 q^{50} -9.93618e6 q^{51} +3.12138e7 q^{52} -5.64902e7 q^{53} +2.00400e7 q^{54} +6.74091e7 q^{55} -2.95392e7 q^{56} +6.79034e7 q^{57} -2.31163e8 q^{58} +1.21174e7 q^{59} -9.06266e7 q^{60} -1.93157e8 q^{61} +1.32104e8 q^{62} -1.29151e7 q^{63} -1.98754e8 q^{64} -4.21776e7 q^{65} -1.67453e8 q^{66} +2.97914e8 q^{67} -1.11623e8 q^{68} -1.88577e8 q^{69} +9.12688e7 q^{70} -3.55939e8 q^{71} +9.84560e7 q^{72} +4.51678e8 q^{73} -3.48909e8 q^{74} -3.57443e7 q^{75} +7.62824e8 q^{76} +1.07918e8 q^{77} +1.04775e8 q^{78} +3.03934e8 q^{79} -1.22922e8 q^{80} +4.30467e7 q^{81} -6.62302e8 q^{82} +6.28705e8 q^{83} -1.45088e8 q^{84} +1.50830e8 q^{85} +7.70735e8 q^{86} -4.96548e8 q^{87} -8.22693e8 q^{88} -8.08718e8 q^{89} -3.04204e8 q^{90} -6.75237e7 q^{91} -2.11847e9 q^{92} +2.83765e8 q^{93} +4.29732e8 q^{94} -1.03076e9 q^{95} -3.16984e8 q^{96} +5.73218e8 q^{97} -1.37557e9 q^{98} -3.59696e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9}+O(q^{10}) \) 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

L-functions

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