LMFDB - Embedded newform 177.10.a.c.1.21

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:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.21
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)

$f(q)$	$=$	$q+39.3800 q^{2} -81.0000 q^{3} +1038.78 q^{4} +1743.34 q^{5} -3189.78 q^{6} +7501.70 q^{7} +20744.7 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+39.3800 q^{2} -81.0000 q^{3} +1038.78 q^{4} +1743.34 q^{5} -3189.78 q^{6} +7501.70 q^{7} +20744.7 q^{8} +6561.00 q^{9} +68652.8 q^{10} +2270.91 q^{11} -84141.5 q^{12} +89344.0 q^{13} +295417. q^{14} -141211. q^{15} +285070. q^{16} +535733. q^{17} +258372. q^{18} -1.00775e6 q^{19} +1.81096e6 q^{20} -607638. q^{21} +89428.4 q^{22} +1.67622e6 q^{23} -1.68032e6 q^{24} +1.08612e6 q^{25} +3.51837e6 q^{26} -531441. q^{27} +7.79264e6 q^{28} -1.20684e6 q^{29} -5.56088e6 q^{30} -8.78723e6 q^{31} +604756. q^{32} -183944. q^{33} +2.10972e7 q^{34} +1.30780e7 q^{35} +6.81546e6 q^{36} -1.85246e7 q^{37} -3.96852e7 q^{38} -7.23687e6 q^{39} +3.61652e7 q^{40} +3.35981e7 q^{41} -2.39288e7 q^{42} +2.69018e7 q^{43} +2.35898e6 q^{44} +1.14381e7 q^{45} +6.60095e7 q^{46} +1.61476e7 q^{47} -2.30907e7 q^{48} +1.59219e7 q^{49} +4.27713e7 q^{50} -4.33944e7 q^{51} +9.28091e7 q^{52} -3.89263e7 q^{53} -2.09281e7 q^{54} +3.95897e6 q^{55} +1.55621e8 q^{56} +8.16277e7 q^{57} -4.75252e7 q^{58} +1.21174e7 q^{59} -1.46687e8 q^{60} -1.72610e8 q^{61} -3.46041e8 q^{62} +4.92187e7 q^{63} -1.22141e8 q^{64} +1.55757e8 q^{65} -7.24370e6 q^{66} -8.66480e7 q^{67} +5.56510e8 q^{68} -1.35774e8 q^{69} +5.15013e8 q^{70} +2.50974e8 q^{71} +1.36106e8 q^{72} -4.77024e7 q^{73} -7.29497e8 q^{74} -8.79755e7 q^{75} -1.04683e9 q^{76} +1.70357e7 q^{77} -2.84988e8 q^{78} +5.50574e8 q^{79} +4.96975e8 q^{80} +4.30467e7 q^{81} +1.32309e9 q^{82} +6.47393e8 q^{83} -6.31204e8 q^{84} +9.33965e8 q^{85} +1.05939e9 q^{86} +9.77537e7 q^{87} +4.71094e7 q^{88} -7.22551e8 q^{89} +4.50431e8 q^{90} +6.70232e8 q^{91} +1.74123e9 q^{92} +7.11766e8 q^{93} +6.35890e8 q^{94} -1.75685e9 q^{95} -4.89852e7 q^{96} +5.53582e8 q^{97} +6.27004e8 q^{98} +1.48994e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9}+O(q^{10}) $ 22 * q + 36 * q^2 - 1782 * q^3 + 5718 * q^4 + 808 * q^5 - 2916 * q^6 + 21249 * q^7 + 9435 * q^8 + 144342 * q^9	\( 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9} + 68441 q^{10} - 68033 q^{11} - 463158 q^{12} + 283817 q^{13} + 80285 q^{14} - 65448 q^{15} + 1067674 q^{16} + 436893 q^{17} + 236196 q^{18} + 1207580 q^{19} + 4209677 q^{20} - 1721169 q^{21} + 5460442 q^{22} + 2421966 q^{23} - 764235 q^{24} + 7441842 q^{25} - 2736526 q^{26} - 11691702 q^{27} + 4095246 q^{28} - 2320594 q^{29} - 5543721 q^{30} - 3178024 q^{31} - 20786874 q^{32} + 5510673 q^{33} - 13809336 q^{34} - 2630800 q^{35} + 37515798 q^{36} + 3981807 q^{37} - 24156377 q^{38} - 22989177 q^{39} - 29544450 q^{40} - 885225 q^{41} - 6503085 q^{42} + 12360835 q^{43} - 117711882 q^{44} + 5301288 q^{45} + 161066949 q^{46} + 75901252 q^{47} - 86481594 q^{48} + 170907951 q^{49} - 61318927 q^{50} - 35388333 q^{51} - 100762 q^{52} - 34790192 q^{53} - 19131876 q^{54} + 151773316 q^{55} - 417630344 q^{56} - 97813980 q^{57} - 432929294 q^{58} + 266581942 q^{59} - 340983837 q^{60} - 290555332 q^{61} + 158267098 q^{62} + 139414689 q^{63} - 131794443 q^{64} - 650690086 q^{65} - 442295802 q^{66} + 86645184 q^{67} + 62738541 q^{68} - 196179246 q^{69} + 429714610 q^{70} - 36567631 q^{71} + 61903035 q^{72} + 907807228 q^{73} - 171827242 q^{74} - 602789202 q^{75} + 1744504396 q^{76} - 310688725 q^{77} + 221658606 q^{78} + 2508604687 q^{79} + 3509441927 q^{80} + 947027862 q^{81} + 1759214793 q^{82} + 2185672083 q^{83} - 331714926 q^{84} + 2868860198 q^{85} + 2397001564 q^{86} + 187968114 q^{87} + 7683735877 q^{88} + 1320145942 q^{89} + 449041401 q^{90} + 3894639897 q^{91} + 3505964640 q^{92} + 257419944 q^{93} + 5406355552 q^{94} + 3093659122 q^{95} + 1683736794 q^{96} + 3904552980 q^{97} + 6137683116 q^{98} - 446364513 q^{99}+O(q^{100}) \) 22 * q + 36 * q^2 - 1782 * q^3 + 5718 * q^4 + 808 * q^5 - 2916 * q^6 + 21249 * q^7 + 9435 * q^8 + 144342 * q^9 + 68441 * q^10 - 68033 * q^11 - 463158 * q^12 + 283817 * q^13 + 80285 * q^14 - 65448 * q^15 + 1067674 * q^16 + 436893 * q^17 + 236196 * q^18 + 1207580 * q^19 + 4209677 * q^20 - 1721169 * q^21 + 5460442 * q^22 + 2421966 * q^23 - 764235 * q^24 + 7441842 * q^25 - 2736526 * q^26 - 11691702 * q^27 + 4095246 * q^28 - 2320594 * q^29 - 5543721 * q^30 - 3178024 * q^31 - 20786874 * q^32 + 5510673 * q^33 - 13809336 * q^34 - 2630800 * q^35 + 37515798 * q^36 + 3981807 * q^37 - 24156377 * q^38 - 22989177 * q^39 - 29544450 * q^40 - 885225 * q^41 - 6503085 * q^42 + 12360835 * q^43 - 117711882 * q^44 + 5301288 * q^45 + 161066949 * q^46 + 75901252 * q^47 - 86481594 * q^48 + 170907951 * q^49 - 61318927 * q^50 - 35388333 * q^51 - 100762 * q^52 - 34790192 * q^53 - 19131876 * q^54 + 151773316 * q^55 - 417630344 * q^56 - 97813980 * q^57 - 432929294 * q^58 + 266581942 * q^59 - 340983837 * q^60 - 290555332 * q^61 + 158267098 * q^62 + 139414689 * q^63 - 131794443 * q^64 - 650690086 * q^65 - 442295802 * q^66 + 86645184 * q^67 + 62738541 * q^68 - 196179246 * q^69 + 429714610 * q^70 - 36567631 * q^71 + 61903035 * q^72 + 907807228 * q^73 - 171827242 * q^74 - 602789202 * q^75 + 1744504396 * q^76 - 310688725 * q^77 + 221658606 * q^78 + 2508604687 * q^79 + 3509441927 * q^80 + 947027862 * q^81 + 1759214793 * q^82 + 2185672083 * q^83 - 331714926 * q^84 + 2868860198 * q^85 + 2397001564 * q^86 + 187968114 * q^87 + 7683735877 * q^88 + 1320145942 * q^89 + 449041401 * q^90 + 3894639897 * q^91 + 3505964640 * q^92 + 257419944 * q^93 + 5406355552 * q^94 + 3093659122 * q^95 + 1683736794 * q^96 + 3904552980 * q^97 + 6137683116 * q^98 - 446364513 * 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 $

$2$	39.3800	1.74037	0.870183	−	0.492729i	$-0.164000\pi$
$2$	39.3800	1.74037	0.870183	+	0.492729i	$0.164000\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	1038.78	2.02887
$5$	1743.34	1.24743	0.623717	−	0.781650i	$-0.285622\pi$
$5$	1743.34	1.24743	0.623717	+	0.781650i	$0.285622\pi$
$6$	−3189.78	−1.00480
$7$	7501.70	1.18091	0.590457	−	0.807069i	$-0.298947\pi$
$7$	7501.70	1.18091	0.590457	+	0.807069i	$0.298947\pi$
$8$	20744.7	1.79062
$9$	6561.00	0.333333
$10$	68652.8	2.17099
$11$	2270.91	0.0467663	0.0233831	−	0.999727i	$-0.492556\pi$
$11$	2270.91	0.0467663	0.0233831	+	0.999727i	$0.492556\pi$
$12$	−84141.5	−1.17137
$13$	89344.0	0.867602	0.433801	−	0.901009i	$-0.357172\pi$
$13$	89344.0	0.867602	0.433801	+	0.901009i	$0.357172\pi$
$14$	295417.	2.05522
$15$	−141211.	−0.720206
$16$	285070.	1.08746
$17$	535733.	1.55571	0.777854	−	0.628445i	$-0.216308\pi$
$17$	535733.	1.55571	0.777854	+	0.628445i	$0.216308\pi$
$18$	258372.	0.580122
$19$	−1.00775e6	−1.77403	−0.887016	−	0.461738i	$-0.847226\pi$
$19$	−1.00775e6	−1.77403	−0.887016	+	0.461738i	$0.847226\pi$
$20$	1.81096e6	2.53089
$21$	−607638.	−0.681801
$22$	89428.4	0.0813905
$23$	1.67622e6	1.24898	0.624490	−	0.781033i	$-0.285307\pi$
$23$	1.67622e6	1.24898	0.624490	+	0.781033i	$0.285307\pi$
$24$	−1.68032e6	−1.03381
$25$	1.08612e6	0.556092
$26$	3.51837e6	1.50994
$27$	−531441.	−0.192450
$28$	7.79264e6	2.39593
$29$	−1.20684e6	−0.316853	−0.158426	−	0.987371i	$-0.550642\pi$
$29$	−1.20684e6	−0.316853	−0.158426	+	0.987371i	$0.550642\pi$
$30$	−5.56088e6	−1.25342
$31$	−8.78723e6	−1.70893	−0.854465	−	0.519508i	$-0.826115\pi$
$31$	−8.78723e6	−1.70893	−0.854465	+	0.519508i	$0.826115\pi$
$32$	604756.	0.101954
$33$	−183944.	−0.0270005
$34$	2.10972e7	2.70750
$35$	1.30780e7	1.47311
$36$	6.81546e6	0.676291
$37$	−1.85246e7	−1.62495	−0.812476	−	0.582995i	$-0.801881\pi$
$37$	−1.85246e7	−1.62495	−0.812476	+	0.582995i	$0.801881\pi$
$38$	−3.96852e7	−3.08747
$39$	−7.23687e6	−0.500910
$40$	3.61652e7	2.23368
$41$	3.35981e7	1.85689	0.928447	−	0.371465i	$-0.121144\pi$
$41$	3.35981e7	1.85689	0.928447	+	0.371465i	$0.121144\pi$
$42$	−2.39288e7	−1.18658
$43$	2.69018e7	1.19998	0.599989	−	0.800008i	$-0.295171\pi$
$43$	2.69018e7	1.19998	0.599989	+	0.800008i	$0.295171\pi$
$44$	2.35898e6	0.0948829
$45$	1.14381e7	0.415811
$46$	6.60095e7	2.17368
$47$	1.61476e7	0.482688	0.241344	−	0.970440i	$-0.422412\pi$
$47$	1.61476e7	0.482688	0.241344	+	0.970440i	$0.422412\pi$
$48$	−2.30907e7	−0.627843
$49$	1.59219e7	0.394559
$50$	4.27713e7	0.967803
$51$	−4.33944e7	−0.898188
$52$	9.28091e7	1.76026
$53$	−3.89263e7	−0.677645	−0.338822	−	0.940850i	$-0.610029\pi$
$53$	−3.89263e7	−0.677645	−0.338822	+	0.940850i	$0.610029\pi$
$54$	−2.09281e7	−0.334934
$55$	3.95897e6	0.0583379
$56$	1.55621e8	2.11457
$57$	8.16277e7	1.02424
$58$	−4.75252e7	−0.551439
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	−1.46687e8	−1.46121
$61$	−1.72610e8	−1.59618	−0.798090	−	0.602539i	$-0.794156\pi$
$61$	−1.72610e8	−1.59618	−0.798090	+	0.602539i	$0.794156\pi$
$62$	−3.46041e8	−2.97416
$63$	4.92187e7	0.393638
$64$	−1.22141e8	−0.910019
$65$	1.55757e8	1.08228
$66$	−7.24370e6	−0.0469908
$67$	−8.66480e7	−0.525318	−0.262659	−	0.964889i	$-0.584599\pi$
$67$	−8.66480e7	−0.525318	−0.262659	+	0.964889i	$0.584599\pi$
$68$	5.56510e8	3.15634
$69$	−1.35774e8	−0.721099
$70$	5.15013e8	2.56376
$71$	2.50974e8	1.17211	0.586053	−	0.810273i	$-0.300681\pi$
$71$	2.50974e8	1.17211	0.586053	+	0.810273i	$0.300681\pi$
$72$	1.36106e8	0.596873
$73$	−4.77024e7	−0.196602	−0.0983009	−	0.995157i	$-0.531341\pi$
$73$	−4.77024e7	−0.196602	−0.0983009	+	0.995157i	$0.531341\pi$
$74$	−7.29497e8	−2.82801
$75$	−8.79755e7	−0.321060
$76$	−1.04683e9	−3.59929
$77$	1.70357e7	0.0552270
$78$	−2.84988e8	−0.871767
$79$	5.50574e8	1.59035	0.795177	−	0.606377i	$-0.207378\pi$
$79$	5.50574e8	1.59035	0.795177	+	0.606377i	$0.207378\pi$
$80$	4.96975e8	1.35653
$81$	4.30467e7	0.111111
$82$	1.32309e9	3.23168
$83$	6.47393e8	1.49733	0.748664	−	0.662950i	$-0.230696\pi$
$83$	6.47393e8	1.49733	0.748664	+	0.662950i	$0.230696\pi$
$84$	−6.31204e8	−1.38329
$85$	9.33965e8	1.94064
$86$	1.05939e9	2.08840
$87$	9.77537e7	0.182935
$88$	4.71094e7	0.0837405
$89$	−7.22551e8	−1.22071	−0.610356	−	0.792127i	$-0.708974\pi$
$89$	−7.22551e8	−1.22071	−0.610356	+	0.792127i	$0.708974\pi$
$90$	4.50431e8	0.723664
$91$	6.70232e8	1.02456
$92$	1.74123e9	2.53402
$93$	7.11766e8	0.986652
$94$	6.35890e8	0.840054
$95$	−1.75685e9	−2.21299
$96$	−4.89852e7	−0.0588633
$97$	5.53582e8	0.634905	0.317453	−	0.948274i	$-0.397173\pi$
$97$	5.53582e8	0.634905	0.317453	+	0.948274i	$0.397173\pi$
$98$	6.27004e8	0.686678
$99$	1.48994e7	0.0155888
$100$	1.12824e9	1.12824
$101$	−2.19968e8	−0.210336	−0.105168	−	0.994454i	$-0.533538\pi$
$101$	−2.19968e8	−0.210336	−0.105168	+	0.994454i	$0.533538\pi$
$102$	−1.70887e9	−1.56318
$103$	4.06127e8	0.355545	0.177773	−	0.984072i	$-0.443111\pi$
$103$	4.06127e8	0.355545	0.177773	+	0.984072i	$0.443111\pi$
$104$	1.85342e9	1.55354
$105$	−1.05932e9	−0.850502
$106$	−1.53292e9	−1.17935
$107$	5.52324e8	0.407349	0.203674	−	0.979039i	$-0.434712\pi$
$107$	5.52324e8	0.407349	0.203674	+	0.979039i	$0.434712\pi$
$108$	−5.52052e8	−0.390457
$109$	8.28657e8	0.562284	0.281142	−	0.959666i	$-0.409287\pi$
$109$	8.28657e8	0.562284	0.281142	+	0.959666i	$0.409287\pi$
$110$	1.55904e8	0.101529
$111$	1.50049e9	0.938166
$112$	2.13851e9	1.28419
$113$	1.33856e9	0.772300	0.386150	−	0.922436i	$-0.373805\pi$
$113$	1.33856e9	0.772300	0.386150	+	0.922436i	$0.373805\pi$
$114$	3.21450e9	1.78255
$115$	2.92222e9	1.55802
$116$	−1.25364e9	−0.642854
$117$	5.86186e8	0.289201
$118$	4.77182e8	0.226576
$119$	4.01891e9	1.83716
$120$	−2.92938e9	−1.28961
$121$	−2.35279e9	−0.997813
$122$	−6.79738e9	−2.77794
$123$	−2.72144e9	−1.07208
$124$	−9.12803e9	−3.46721
$125$	−1.51149e9	−0.553746
$126$	1.93823e9	0.685075
$127$	2.60470e9	0.888468	0.444234	−	0.895911i	$-0.353476\pi$
$127$	2.60470e9	0.888468	0.444234	+	0.895911i	$0.353476\pi$
$128$	−5.11953e9	−1.68572
$129$	−2.17905e9	−0.692808
$130$	6.13372e9	1.88356
$131$	3.98900e9	1.18343	0.591715	−	0.806147i	$-0.298451\pi$
$131$	3.98900e9	1.18343	0.591715	+	0.806147i	$0.298451\pi$
$132$	−1.91078e8	−0.0547807
$133$	−7.55984e9	−2.09498
$134$	−3.41220e9	−0.914245
$135$	−9.26483e8	−0.240069
$136$	1.11136e10	2.78568
$137$	−6.79151e9	−1.64712	−0.823558	−	0.567232i	$-0.808014\pi$
$137$	−6.79151e9	−1.64712	−0.823558	+	0.567232i	$0.808014\pi$
$138$	−5.34677e9	−1.25498
$139$	−6.78574e9	−1.54181	−0.770904	−	0.636951i	$-0.780195\pi$
$139$	−6.78574e9	−1.54181	−0.770904	+	0.636951i	$0.780195\pi$
$140$	1.35852e10	2.98876
$141$	−1.30795e9	−0.278680
$142$	9.88336e9	2.03989
$143$	2.02892e8	0.0405745
$144$	1.87035e9	0.362485
$145$	−2.10393e9	−0.395253
$146$	−1.87852e9	−0.342159
$147$	−1.28967e9	−0.227799
$148$	−1.92430e10	−3.29682
$149$	−1.19337e9	−0.198351	−0.0991757	−	0.995070i	$-0.531621\pi$
$149$	−1.19337e9	−0.198351	−0.0991757	+	0.995070i	$0.531621\pi$
$150$	−3.46447e9	−0.558761
$151$	5.71467e9	0.894530	0.447265	−	0.894401i	$-0.352398\pi$
$151$	5.71467e9	0.894530	0.447265	+	0.894401i	$0.352398\pi$
$152$	−2.09055e10	−3.17661
$153$	3.51494e9	0.518569
$154$	6.70865e8	0.0961152
$155$	−1.53191e10	−2.13178
$156$	−7.51754e9	−1.01628
$157$	−9.74545e9	−1.28013	−0.640064	−	0.768322i	$-0.721092\pi$
$157$	−9.74545e9	−1.28013	−0.640064	+	0.768322i	$0.721092\pi$
$158$	2.16816e10	2.76780
$159$	3.15303e9	0.391238
$160$	1.05430e9	0.127181
$161$	1.25745e10	1.47494
$162$	1.69518e9	0.193374
$163$	−1.28528e10	−1.42611	−0.713054	−	0.701109i	$-0.752688\pi$
$163$	−1.28528e10	−1.42611	−0.713054	+	0.701109i	$0.752688\pi$
$164$	3.49011e10	3.76740
$165$	−3.20677e8	−0.0336814
$166$	2.54943e10	2.60590
$167$	1.17443e10	1.16843	0.584216	−	0.811598i	$-0.301402\pi$
$167$	1.17443e10	1.16843	0.584216	+	0.811598i	$0.301402\pi$
$168$	−1.26053e10	−1.22085
$169$	−2.62214e9	−0.247267
$170$	3.67796e10	3.37743
$171$	−6.61185e9	−0.591344
$172$	2.79452e10	2.43461
$173$	−6.82218e9	−0.579049	−0.289525	−	0.957171i	$-0.593497\pi$
$173$	−6.82218e9	−0.579049	−0.289525	+	0.957171i	$0.593497\pi$
$174$	3.84954e9	0.318374
$175$	8.14772e9	0.656697
$176$	6.47369e8	0.0508563
$177$	−9.81506e8	−0.0751646
$178$	−2.84540e10	−2.12449
$179$	−8.20417e9	−0.597305	−0.298652	−	0.954362i	$-0.596537\pi$
$179$	−8.20417e9	−0.597305	−0.298652	+	0.954362i	$0.596537\pi$
$180$	1.18817e10	0.843629
$181$	−1.62996e10	−1.12882	−0.564410	−	0.825495i	$-0.690896\pi$
$181$	−1.62996e10	−1.12882	−0.564410	+	0.825495i	$0.690896\pi$
$182$	2.63937e10	1.78312
$183$	1.39814e10	0.921554
$184$	3.47727e10	2.23644
$185$	−3.22947e10	−2.02702
$186$	2.80293e10	1.71713
$187$	1.21660e9	0.0727547
$188$	1.67738e10	0.979313
$189$	−3.98671e9	−0.227267
$190$	−6.91848e10	−3.85141
$191$	2.05160e10	1.11543	0.557715	−	0.830032i	$-0.311678\pi$
$191$	2.05160e10	1.11543	0.557715	+	0.830032i	$0.311678\pi$
$192$	9.89339e9	0.525399
$193$	1.04684e10	0.543089	0.271545	−	0.962426i	$-0.412466\pi$
$193$	1.04684e10	0.543089	0.271545	+	0.962426i	$0.412466\pi$
$194$	2.18000e10	1.10497
$195$	−1.26163e10	−0.624852
$196$	1.65394e10	0.800511
$197$	−1.65346e10	−0.782160	−0.391080	−	0.920357i	$-0.627898\pi$
$197$	−1.65346e10	−0.782160	−0.391080	+	0.920357i	$0.627898\pi$
$198$	5.86740e8	0.0271302
$199$	−3.36893e10	−1.52284	−0.761419	−	0.648260i	$-0.775497\pi$
$199$	−3.36893e10	−1.52284	−0.761419	+	0.648260i	$0.775497\pi$
$200$	2.25312e10	0.995748
$201$	7.01849e9	0.303292
$202$	−8.66233e9	−0.366061
$203$	−9.05332e9	−0.374176
$204$	−4.50773e10	−1.82231
$205$	5.85729e10	2.31635
$206$	1.59933e10	0.618779
$207$	1.09977e10	0.416327
$208$	2.54693e10	0.943479
$209$	−2.28851e9	−0.0829649
$210$	−4.17160e10	−1.48019
$211$	−5.02369e10	−1.74482	−0.872412	−	0.488772i	$-0.837445\pi$
$211$	−5.02369e10	−1.74482	−0.872412	+	0.488772i	$0.837445\pi$
$212$	−4.04360e10	−1.37486
$213$	−2.03289e10	−0.676715
$214$	2.17505e10	0.708936
$215$	4.68991e10	1.49689
$216$	−1.10246e10	−0.344605
$217$	−6.59192e10	−2.01810
$218$	3.26325e10	0.978580
$219$	3.86390e9	0.113508
$220$	4.11252e9	0.118360
$221$	4.78645e10	1.34974
$222$	5.90893e10	1.63275
$223$	2.59222e10	0.701941	0.350971	−	0.936386i	$-0.385852\pi$
$223$	2.59222e10	0.701941	0.350971	+	0.936386i	$0.385852\pi$
$224$	4.53669e9	0.120399
$225$	7.12601e9	0.185364
$226$	5.27126e10	1.34408
$227$	−5.41518e10	−1.35362	−0.676810	−	0.736158i	$-0.736638\pi$
$227$	−5.41518e10	−1.35362	−0.676810	+	0.736158i	$0.736638\pi$
$228$	8.47935e10	2.07805
$229$	2.75149e10	0.661162	0.330581	−	0.943778i	$-0.392755\pi$
$229$	2.75149e10	0.661162	0.330581	+	0.943778i	$0.392755\pi$
$230$	1.15077e11	2.71152
$231$	−1.37989e9	−0.0318853
$232$	−2.50355e10	−0.567362
$233$	6.03358e7	0.00134114	0.000670569	−	1.00000i	$-0.499787\pi$
$233$	6.03358e7	0.00134114	0.000670569		1.00000i	$0.499787\pi$
$234$	2.30840e10	0.503315
$235$	2.81507e10	0.602121
$236$	1.25873e10	0.264137
$237$	−4.45965e10	−0.918191
$238$	1.58264e11	3.19733
$239$	1.36306e10	0.270225	0.135112	−	0.990830i	$-0.456860\pi$
$239$	1.36306e10	0.270225	0.135112	+	0.990830i	$0.456860\pi$
$240$	−4.02550e10	−0.783193
$241$	−1.59097e9	−0.0303799	−0.0151899	−	0.999885i	$-0.504835\pi$
$241$	−1.59097e9	−0.0303799	−0.0151899	+	0.999885i	$0.504835\pi$
$242$	−9.26529e10	−1.73656
$243$	−3.48678e9	−0.0641500
$244$	−1.79304e11	−3.23845
$245$	2.77573e10	0.492187
$246$	−1.07170e11	−1.86581
$247$	−9.00364e10	−1.53915
$248$	−1.82289e11	−3.06004
$249$	−5.24389e10	−0.864483
$250$	−5.95225e10	−0.963721
$251$	7.14635e10	1.13646	0.568228	−	0.822871i	$-0.307629\pi$
$251$	7.14635e10	1.13646	0.568228	+	0.822871i	$0.307629\pi$
$252$	5.11275e10	0.798642
$253$	3.80654e9	0.0584101
$254$	1.02573e11	1.54626
$255$	−7.56512e10	−1.12043
$256$	−1.39071e11	−2.02375
$257$	2.53990e10	0.363177	0.181589	−	0.983375i	$-0.441876\pi$
$257$	2.53990e10	0.363177	0.181589	+	0.983375i	$0.441876\pi$
$258$	−8.58109e10	−1.20574
$259$	−1.38966e11	−1.91893
$260$	1.61798e11	2.19580
$261$	−7.91805e9	−0.105618
$262$	1.57087e11	2.05960
$263$	−1.51096e10	−0.194739	−0.0973694	−	0.995248i	$-0.531043\pi$
$263$	−1.51096e10	−0.194739	−0.0973694	+	0.995248i	$0.531043\pi$
$264$	−3.81586e9	−0.0483476
$265$	−6.78619e10	−0.845317
$266$	−2.97706e11	−3.64603
$267$	5.85266e10	0.704779
$268$	−9.00086e10	−1.06580
$269$	4.60288e10	0.535975	0.267988	−	0.963422i	$-0.413641\pi$
$269$	4.60288e10	0.535975	0.267988	+	0.963422i	$0.413641\pi$
$270$	−3.64849e10	−0.417808
$271$	−9.95910e10	−1.12165	−0.560826	−	0.827933i	$-0.689516\pi$
$271$	−9.95910e10	−1.12165	−0.560826	+	0.827933i	$0.689516\pi$
$272$	1.52721e11	1.69176
$273$	−5.42888e10	−0.591532
$274$	−2.67450e11	−2.86658
$275$	2.46647e9	0.0260063
$276$	−1.41039e11	−1.46302
$277$	3.73937e10	0.381627	0.190813	−	0.981626i	$-0.438887\pi$
$277$	3.73937e10	0.381627	0.190813	+	0.981626i	$0.438887\pi$
$278$	−2.67222e11	−2.68331
$279$	−5.76530e10	−0.569644
$280$	2.71300e11	2.63778
$281$	−7.85734e10	−0.751791	−0.375896	−	0.926662i	$-0.622665\pi$
$281$	−7.85734e10	−0.751791	−0.375896	+	0.926662i	$0.622665\pi$
$282$	−5.15071e10	−0.485005
$283$	−1.79764e11	−1.66596	−0.832979	−	0.553305i	$-0.813367\pi$
$283$	−1.79764e11	−1.66596	−0.832979	+	0.553305i	$0.813367\pi$
$284$	2.60708e11	2.37805
$285$	1.42305e11	1.27767
$286$	7.98990e9	0.0706145
$287$	2.52043e11	2.19283
$288$	3.96780e9	0.0339847
$289$	1.68422e11	1.42023
$290$	−8.28527e10	−0.687884
$291$	−4.48401e10	−0.366563
$292$	−4.95525e10	−0.398880
$293$	9.10407e10	0.721658	0.360829	−	0.932632i	$-0.382494\pi$
$293$	9.10407e10	0.721658	0.360829	+	0.932632i	$0.382494\pi$
$294$	−5.07873e10	−0.396454
$295$	2.11247e10	0.162402
$296$	−3.84287e11	−2.90967
$297$	−1.20685e9	−0.00900018
$298$	−4.69947e10	−0.345204
$299$	1.49760e11	1.08362
$300$	−9.13875e10	−0.651390
$301$	2.01809e11	1.41707
$302$	2.25044e11	1.55681
$303$	1.78174e10	0.121437
$304$	−2.87279e11	−1.92918
$305$	−3.00918e11	−1.99113
$306$	1.38418e11	0.902500
$307$	9.89919e10	0.636029	0.318015	−	0.948086i	$-0.396984\pi$
$307$	9.89919e10	0.636029	0.318015	+	0.948086i	$0.396984\pi$
$308$	1.76964e10	0.112049
$309$	−3.28963e10	−0.205274
$310$	−6.03268e11	−3.71007
$311$	−8.96213e10	−0.543237	−0.271619	−	0.962405i	$-0.587559\pi$
$311$	−8.96213e10	−0.543237	−0.271619	+	0.962405i	$0.587559\pi$
$312$	−1.50127e11	−0.896939
$313$	6.72330e10	0.395943	0.197972	−	0.980208i	$-0.436565\pi$
$313$	6.72330e10	0.395943	0.197972	+	0.980208i	$0.436565\pi$
$314$	−3.83776e11	−2.22789
$315$	8.58050e10	0.491038
$316$	5.71927e11	3.22663
$317$	−1.43031e11	−0.795544	−0.397772	−	0.917484i	$-0.630217\pi$
$317$	−1.43031e11	−0.795544	−0.397772	+	0.917484i	$0.630217\pi$
$318$	1.24166e11	0.680898
$319$	−2.74062e9	−0.0148180
$320$	−2.12933e11	−1.13519
$321$	−4.47382e10	−0.235183
$322$	4.95183e11	2.56693
$323$	−5.39885e11	−2.75988
$324$	4.47162e10	0.225430
$325$	9.70381e10	0.482466
$326$	−5.06142e11	−2.48195
$327$	−6.71212e10	−0.324635
$328$	6.96983e11	3.32499
$329$	1.21134e11	0.570013
$330$	−1.26283e10	−0.0586179
$331$	6.35802e9	0.0291136	0.0145568	−	0.999894i	$-0.495366\pi$
$331$	6.35802e9	0.0291136	0.0145568	+	0.999894i	$0.495366\pi$
$332$	6.72502e11	3.03789
$333$	−1.21540e11	−0.541650
$334$	4.62491e11	2.03350
$335$	−1.51057e11	−0.655299
$336$	−1.73219e11	−0.741429
$337$	1.67848e11	0.708894	0.354447	−	0.935076i	$-0.384669\pi$
$337$	1.67848e11	0.708894	0.354447	+	0.935076i	$0.384669\pi$
$338$	−1.03260e11	−0.430335
$339$	−1.08424e11	−0.445887
$340$	9.70188e11	3.93732
$341$	−1.99550e10	−0.0799203
$342$	−2.60374e11	−1.02916
$343$	−1.83279e11	−0.714974
$344$	5.58071e11	2.14870
$345$	−2.36700e11	−0.899523
$346$	−2.68657e11	−1.00776
$347$	−4.20659e11	−1.55757	−0.778784	−	0.627292i	$-0.784163\pi$
$347$	−4.20659e11	−1.55757	−0.778784	+	0.627292i	$0.784163\pi$
$348$	1.01545e11	0.371152
$349$	−6.82254e10	−0.246168	−0.123084	−	0.992396i	$-0.539278\pi$
$349$	−6.82254e10	−0.246168	−0.123084	+	0.992396i	$0.539278\pi$
$350$	3.20857e11	1.14289
$351$	−4.74811e10	−0.166970
$352$	1.37335e9	0.00476802
$353$	4.21122e10	0.144352	0.0721759	−	0.997392i	$-0.477006\pi$
$353$	4.21122e10	0.144352	0.0721759	+	0.997392i	$0.477006\pi$
$354$	−3.86517e10	−0.130814
$355$	4.37534e11	1.46212
$356$	−7.50574e11	−2.47667
$357$	−3.25531e11	−1.06068
$358$	−3.23080e11	−1.03953
$359$	1.81066e11	0.575323	0.287661	−	0.957732i	$-0.407122\pi$
$359$	1.81066e11	0.575323	0.287661	+	0.957732i	$0.407122\pi$
$360$	2.37280e11	0.744559
$361$	6.92872e11	2.14719
$362$	−6.41880e11	−1.96456
$363$	1.90576e11	0.576088
$364$	6.96226e11	2.07871
$365$	−8.31617e10	−0.245248
$366$	5.50588e11	1.60384
$367$	−1.33152e11	−0.383132	−0.191566	−	0.981480i	$-0.561357\pi$
$367$	−1.33152e11	−0.383132	−0.191566	+	0.981480i	$0.561357\pi$
$368$	4.77840e11	1.35821
$369$	2.20437e11	0.618965
$370$	−1.27176e12	−3.52776
$371$	−2.92014e11	−0.800241
$372$	7.39371e11	2.00179
$373$	−7.05351e11	−1.88676	−0.943378	−	0.331720i	$-0.892371\pi$
$373$	−7.05351e11	−1.88676	−0.943378	+	0.331720i	$0.892371\pi$
$374$	4.79097e10	0.126620
$375$	1.22431e11	0.319706
$376$	3.34977e11	0.864309
$377$	−1.07824e11	−0.274902
$378$	−1.56997e11	−0.395528
$379$	5.67740e11	1.41342	0.706712	−	0.707501i	$-0.250177\pi$
$379$	5.67740e11	1.41342	0.706712	+	0.707501i	$0.250177\pi$
$380$	−1.82499e12	−4.48987
$381$	−2.10981e11	−0.512957
$382$	8.07920e11	1.94126
$383$	−5.63760e10	−0.133875	−0.0669375	−	0.997757i	$-0.521323\pi$
$383$	−5.63760e10	−0.133875	−0.0669375	+	0.997757i	$0.521323\pi$
$384$	4.14682e11	0.973251
$385$	2.96990e10	0.0688920
$386$	4.12244e11	0.945174
$387$	1.76503e11	0.399993
$388$	5.75052e11	1.28814
$389$	−1.48276e11	−0.328320	−0.164160	−	0.986434i	$-0.552491\pi$
$389$	−1.48276e11	−0.328320	−0.164160	+	0.986434i	$0.552491\pi$
$390$	−4.96831e11	−1.08747
$391$	8.98005e11	1.94305
$392$	3.30295e11	0.706505
$393$	−3.23109e11	−0.683254
$394$	−6.51132e11	−1.36125
$395$	9.59839e11	1.98386
$396$	1.54773e10	0.0316276
$397$	3.07929e11	0.622148	0.311074	−	0.950386i	$-0.399311\pi$
$397$	3.07929e11	0.622148	0.311074	+	0.950386i	$0.399311\pi$
$398$	−1.32669e12	−2.65029
$399$	6.12347e11	1.20954
$400$	3.09619e11	0.604725
$401$	−9.43673e10	−0.182252	−0.0911260	−	0.995839i	$-0.529047\pi$
$401$	−9.43673e10	−0.182252	−0.0911260	+	0.995839i	$0.529047\pi$
$402$	2.76388e11	0.527840
$403$	−7.85087e11	−1.48267
$404$	−2.28499e11	−0.426745
$405$	7.50452e10	0.138604
$406$	−3.56520e11	−0.651203
$407$	−4.20676e10	−0.0759929
$408$	−9.00204e11	−1.60831
$409$	5.71877e11	1.01053	0.505264	−	0.862965i	$-0.331395\pi$
$409$	5.71877e11	1.01053	0.505264	+	0.862965i	$0.331395\pi$
$410$	2.30660e12	4.03130
$411$	5.50113e11	0.950963
$412$	4.21878e11	0.721356
$413$	9.09008e10	0.153742
$414$	4.33088e11	0.724561
$415$	1.12863e12	1.86782
$416$	5.40313e10	0.0884556
$417$	5.49645e11	0.890163
$418$	−9.01215e10	−0.144389
$419$	1.01134e12	1.60300	0.801501	−	0.597993i	$-0.204035\pi$
$419$	1.01134e12	1.60300	0.801501	+	0.597993i	$0.204035\pi$
$420$	−1.10040e12	−1.72556
$421$	−2.17158e11	−0.336903	−0.168452	−	0.985710i	$-0.553877\pi$
$421$	−2.17158e11	−0.336903	−0.168452	+	0.985710i	$0.553877\pi$
$422$	−1.97833e12	−3.03663
$423$	1.05944e11	0.160896
$424$	−8.07516e11	−1.21340
$425$	5.81868e11	0.865116
$426$	−8.00552e11	−1.17773
$427$	−1.29487e12	−1.88495
$428$	5.73745e11	0.826460
$429$	−1.64343e10	−0.0234257
$430$	1.84688e12	2.60514
$431$	1.00752e12	1.40639	0.703197	−	0.710995i	$-0.251755\pi$
$431$	1.00752e12	1.40639	0.703197	+	0.710995i	$0.251755\pi$
$432$	−1.51498e11	−0.209281
$433$	1.62524e10	0.0222189	0.0111094	−	0.999938i	$-0.496464\pi$
$433$	1.62524e10	0.0222189	0.0111094	+	0.999938i	$0.496464\pi$
$434$	−2.59590e12	−3.51223
$435$	1.70418e11	0.228199
$436$	8.60796e11	1.14080
$437$	−1.68921e12	−2.21573
$438$	1.52160e11	0.197546
$439$	8.32564e11	1.06986	0.534930	−	0.844896i	$-0.320338\pi$
$439$	8.32564e11	1.06986	0.534930	+	0.844896i	$0.320338\pi$
$440$	8.21278e10	0.104461
$441$	1.04464e11	0.131520
$442$	1.88490e12	2.34903
$443$	−4.77881e11	−0.589525	−0.294763	−	0.955570i	$-0.595241\pi$
$443$	−4.77881e11	−0.589525	−0.294763	+	0.955570i	$0.595241\pi$
$444$	1.55868e12	1.90342
$445$	−1.25965e12	−1.52276
$446$	1.02082e12	1.22163
$447$	9.66626e10	0.114518
$448$	−9.16262e11	−1.07465
$449$	9.47960e11	1.10073	0.550366	−	0.834924i	$-0.314488\pi$
$449$	9.47960e11	1.10073	0.550366	+	0.834924i	$0.314488\pi$
$450$	2.80622e11	0.322601
$451$	7.62982e10	0.0868400
$452$	1.39048e12	1.56690
$453$	−4.62888e11	−0.516457
$454$	−2.13250e12	−2.35579
$455$	1.16844e12	1.27808
$456$	1.69335e12	1.83402
$457$	−1.53995e12	−1.65152	−0.825761	−	0.564020i	$-0.809254\pi$
$457$	−1.53995e12	−1.65152	−0.825761	+	0.564020i	$0.809254\pi$
$458$	1.08354e12	1.15066
$459$	−2.84710e11	−0.299396
$460$	3.03556e12	3.16103
$461$	3.05448e11	0.314980	0.157490	−	0.987521i	$-0.449660\pi$
$461$	3.05448e11	0.314980	0.157490	+	0.987521i	$0.449660\pi$
$462$	−5.43401e10	−0.0554921
$463$	−6.19374e11	−0.626381	−0.313190	−	0.949690i	$-0.601398\pi$
$463$	−6.19374e11	−0.626381	−0.313190	+	0.949690i	$0.601398\pi$
$464$	−3.44033e11	−0.344563
$465$	1.24085e12	1.23078
$466$	2.37602e9	0.00233407
$467$	8.79002e11	0.855192	0.427596	−	0.903970i	$-0.359361\pi$
$467$	8.79002e11	0.855192	0.427596	+	0.903970i	$0.359361\pi$
$468$	6.08921e11	0.586752
$469$	−6.50008e11	−0.620356
$470$	1.10857e12	1.04791
$471$	7.89381e11	0.739082
$472$	2.51371e11	0.233119
$473$	6.10916e10	0.0561185
$474$	−1.75621e12	−1.59799
$475$	−1.09453e12	−0.986525
$476$	4.17477e12	3.72736
$477$	−2.55396e11	−0.225882
$478$	5.36774e11	0.470290
$479$	−8.42089e11	−0.730883	−0.365442	−	0.930834i	$-0.619082\pi$
$479$	−8.42089e11	−0.730883	−0.365442	+	0.930834i	$0.619082\pi$
$480$	−8.53980e10	−0.0734280
$481$	−1.65506e12	−1.40981
$482$	−6.26525e10	−0.0528721
$483$	−1.01853e12	−0.851556
$484$	−2.44404e12	−2.02444
$485$	9.65082e11	0.792003
$486$	−1.37310e11	−0.111645
$487$	−2.58993e10	−0.0208645	−0.0104322	−	0.999946i	$-0.503321\pi$
$487$	−2.58993e10	−0.0208645	−0.0104322	+	0.999946i	$0.503321\pi$
$488$	−3.58075e12	−2.85815
$489$	1.04107e12	0.823364
$490$	1.09308e12	0.856585
$491$	−2.18119e12	−1.69366	−0.846831	−	0.531862i	$-0.821493\pi$
$491$	−2.18119e12	−1.69366	−0.846831	+	0.531862i	$0.821493\pi$
$492$	−2.82699e12	−2.17511
$493$	−6.46542e11	−0.492930
$494$	−3.54563e12	−2.67869
$495$	2.59748e10	0.0194460
$496$	−2.50498e12	−1.85839
$497$	1.88273e12	1.38416
$498$	−2.06504e12	−1.50452
$499$	2.53375e12	1.82941	0.914706	−	0.404120i	$-0.132422\pi$
$499$	2.53375e12	1.82941	0.914706	+	0.404120i	$0.132422\pi$
$500$	−1.57011e12	−1.12348
$501$	−9.51289e11	−0.674594
$502$	2.81423e12	1.97785
$503$	2.94003e11	0.204784	0.102392	−	0.994744i	$-0.467350\pi$
$503$	2.94003e11	0.204784	0.102392	+	0.994744i	$0.467350\pi$
$504$	1.02103e12	0.704856
$505$	−3.83479e11	−0.262380
$506$	1.49902e11	0.101655
$507$	2.12393e11	0.142760
$508$	2.70572e12	1.80259
$509$	−2.16095e12	−1.42697	−0.713484	−	0.700671i	$-0.752884\pi$
$509$	−2.16095e12	−1.42697	−0.713484	+	0.700671i	$0.752884\pi$
$510$	−2.97914e12	−1.94996
$511$	−3.57849e11	−0.232170
$512$	−2.85542e12	−1.83635
$513$	5.35560e11	0.341413
$514$	1.00021e12	0.632061
$515$	7.08019e11	0.443519
$516$	−2.26356e12	−1.40562
$517$	3.66696e10	0.0225735
$518$	−5.47247e12	−3.33964
$519$	5.52596e11	0.334314
$520$	3.23114e12	1.93794
$521$	−1.35198e12	−0.803895	−0.401947	−	0.915663i	$-0.631667\pi$
$521$	−1.35198e12	−0.803895	−0.401947	+	0.915663i	$0.631667\pi$
$522$	−3.11813e11	−0.183813
$523$	1.67778e12	0.980564	0.490282	−	0.871564i	$-0.336894\pi$
$523$	1.67778e12	0.980564	0.490282	+	0.871564i	$0.336894\pi$
$524$	4.14370e12	2.40103
$525$	−6.59965e11	−0.379144
$526$	−5.95017e11	−0.338917
$527$	−4.70761e12	−2.65860
$528$	−5.24369e10	−0.0293619
$529$	1.00856e12	0.559950
$530$	−2.67240e12	−1.47116
$531$	7.95020e10	0.0433963
$532$	−7.85303e12	−4.25045
$533$	3.00179e12	1.61104
$534$	2.30478e12	1.22657
$535$	9.62889e11	0.508141
$536$	−1.79749e12	−0.940643
$537$	6.64538e11	0.344854
$538$	1.81261e12	0.932793
$539$	3.61572e10	0.0184521
$540$	−9.62416e11	−0.487069
$541$	−1.65085e12	−0.828554	−0.414277	−	0.910151i	$-0.635966\pi$
$541$	−1.65085e12	−0.828554	−0.414277	+	0.910151i	$0.635966\pi$
$542$	−3.92189e12	−1.95209
$543$	1.32027e12	0.651725
$544$	3.23987e11	0.158611
$545$	1.44463e12	0.701412
$546$	−2.13789e12	−1.02948
$547$	1.13550e12	0.542308	0.271154	−	0.962536i	$-0.412595\pi$
$547$	1.13550e12	0.542308	0.271154	+	0.962536i	$0.412595\pi$
$548$	−7.05491e12	−3.34179
$549$	−1.13249e12	−0.532060
$550$	9.71297e10	0.0452606
$551$	1.21619e12	0.562107
$552$	−2.81659e12	−1.29121
$553$	4.13024e12	1.87807
$554$	1.47256e12	0.664170
$555$	2.61587e12	1.17030
$556$	−7.04891e12	−3.12813
$557$	3.20421e12	1.41050	0.705249	−	0.708960i	$-0.250835\pi$
$557$	3.20421e12	1.41050	0.705249	+	0.708960i	$0.250835\pi$
$558$	−2.27038e12	−0.991388
$559$	2.40352e12	1.04110
$560$	3.72816e12	1.60195
$561$	−9.85447e10	−0.0420049
$562$	−3.09422e12	−1.30839
$563$	1.10960e12	0.465458	0.232729	−	0.972542i	$-0.425235\pi$
$563$	1.10960e12	0.465458	0.232729	+	0.972542i	$0.425235\pi$
$564$	−1.35868e12	−0.565407
$565$	2.33357e12	0.963393
$566$	−7.07911e12	−2.89938
$567$	3.22924e11	0.131213
$568$	5.20639e12	2.09879
$569$	1.72304e12	0.689113	0.344556	−	0.938766i	$-0.388029\pi$
$569$	1.72304e12	0.689113	0.344556	+	0.938766i	$0.388029\pi$
$570$	5.60397e12	2.22361
$571$	−8.12516e11	−0.319867	−0.159934	−	0.987128i	$-0.551128\pi$
$571$	−8.12516e11	−0.319867	−0.159934	+	0.987128i	$0.551128\pi$
$572$	2.10761e11	0.0823206
$573$	−1.66180e12	−0.643994
$574$	9.92544e12	3.81633
$575$	1.82057e12	0.694547
$576$	−8.01365e11	−0.303340
$577$	−3.01480e12	−1.13232	−0.566158	−	0.824297i	$-0.691571\pi$
$577$	−3.01480e12	−1.13232	−0.566158	+	0.824297i	$0.691571\pi$
$578$	6.63245e12	2.47172
$579$	−8.47938e11	−0.313553
$580$	−2.18553e12	−0.801918
$581$	4.85655e12	1.76822
$582$	−1.76580e12	−0.637953
$583$	−8.83982e10	−0.0316909
$584$	−9.89574e11	−0.352039
$585$	1.02192e12	0.360759
$586$	3.58518e12	1.25595
$587$	−8.98823e11	−0.312466	−0.156233	−	0.987720i	$-0.549935\pi$
$587$	−8.98823e11	−0.312466	−0.156233	+	0.987720i	$0.549935\pi$
$588$	−1.33969e12	−0.462175
$589$	8.85533e12	3.03170
$590$	8.31891e11	0.282639
$591$	1.33930e12	0.451580
$592$	−5.28080e12	−1.76706
$593$	−8.83432e11	−0.293378	−0.146689	−	0.989183i	$-0.546862\pi$
$593$	−8.83432e11	−0.293378	−0.146689	+	0.989183i	$0.546862\pi$
$594$	−4.75259e10	−0.0156636
$595$	7.00633e12	2.29173
$596$	−1.23965e12	−0.402430
$597$	2.72884e12	0.879211
$598$	5.89755e12	1.88589
$599$	2.25918e12	0.717020	0.358510	−	0.933526i	$-0.383285\pi$
$599$	2.25918e12	0.717020	0.358510	+	0.933526i	$0.383285\pi$
$600$	−1.82503e12	−0.574895
$601$	4.59803e11	0.143760	0.0718798	−	0.997413i	$-0.477100\pi$
$601$	4.59803e11	0.143760	0.0718798	+	0.997413i	$0.477100\pi$
$602$	7.94725e12	2.46622
$603$	−5.68498e11	−0.175106
$604$	5.93631e12	1.81489
$605$	−4.10172e12	−1.24471
$606$	7.01649e11	0.211346
$607$	−4.92340e11	−0.147203	−0.0736014	−	0.997288i	$-0.523449\pi$
$607$	−4.92340e11	−0.147203	−0.0736014	+	0.997288i	$0.523449\pi$
$608$	−6.09442e11	−0.180870
$609$	7.33319e11	0.216031
$610$	−1.18502e13	−3.46529
$611$	1.44269e12	0.418781
$612$	3.65126e12	1.05211
$613$	−3.40664e12	−0.974436	−0.487218	−	0.873280i	$-0.661988\pi$
$613$	−3.40664e12	−0.974436	−0.487218	+	0.873280i	$0.661988\pi$
$614$	3.89830e12	1.10692
$615$	−4.74441e12	−1.33735
$616$	3.53401e11	0.0988904
$617$	−1.32603e12	−0.368359	−0.184179	−	0.982893i	$-0.558963\pi$
$617$	−1.32603e12	−0.368359	−0.184179	+	0.982893i	$0.558963\pi$
$618$	−1.29546e12	−0.357252
$619$	2.11335e12	0.578581	0.289290	−	0.957241i	$-0.406581\pi$
$619$	2.11335e12	0.578581	0.289290	+	0.957241i	$0.406581\pi$
$620$	−1.59133e13	−4.32511
$621$	−8.90811e11	−0.240366
$622$	−3.52929e12	−0.945432
$623$	−5.42036e12	−1.44156
$624$	−2.06301e12	−0.544718
$625$	−4.75637e12	−1.24685
$626$	2.64764e12	0.689086
$627$	1.85369e11	0.0478998
$628$	−1.01234e13	−2.59722
$629$	−9.92422e12	−2.52795
$630$	3.37900e12	0.854585
$631$	5.04435e12	1.26670	0.633349	−	0.773866i	$-0.281680\pi$
$631$	5.04435e12	1.26670	0.633349	+	0.773866i	$0.281680\pi$
$632$	1.14215e13	2.84772
$633$	4.06919e12	1.00737
$634$	−5.63257e12	−1.38454
$635$	4.54089e12	1.10830
$636$	3.27532e12	0.793774
$637$	1.42253e12	0.342321
$638$	−1.07925e11	−0.0257888
$639$	1.64664e12	0.390702
$640$	−8.92509e12	−2.10282
$641$	4.31997e12	1.01069	0.505347	−	0.862916i	$-0.331365\pi$
$641$	4.31997e12	1.01069	0.505347	+	0.862916i	$0.331365\pi$
$642$	−1.76179e12	−0.409305
$643$	−1.37519e12	−0.317258	−0.158629	−	0.987338i	$-0.550707\pi$
$643$	−1.37519e12	−0.317258	−0.158629	+	0.987338i	$0.550707\pi$
$644$	1.30622e13	2.99246
$645$	−3.79882e12	−0.864232
$646$	−2.12606e13	−4.80319
$647$	6.94667e12	1.55850	0.779251	−	0.626712i	$-0.215600\pi$
$647$	6.94667e12	1.55850	0.779251	+	0.626712i	$0.215600\pi$
$648$	8.92993e11	0.198958
$649$	2.75174e10	0.00608845
$650$	3.82136e12	0.839668
$651$	5.33945e12	1.16515
$652$	−1.33512e13	−2.89339
$653$	−2.81331e12	−0.605492	−0.302746	−	0.953071i	$-0.597903\pi$
$653$	−2.81331e12	−0.605492	−0.302746	+	0.953071i	$0.597903\pi$
$654$	−2.64323e12	−0.564983
$655$	6.95419e12	1.47625
$656$	9.57781e12	2.01929
$657$	−3.12976e11	−0.0655340
$658$	4.77026e12	0.992032
$659$	6.81146e12	1.40688	0.703438	−	0.710757i	$-0.251647\pi$
$659$	6.81146e12	1.40688	0.703438	+	0.710757i	$0.251647\pi$
$660$	−3.33114e11	−0.0683353
$661$	7.26008e11	0.147923	0.0739613	−	0.997261i	$-0.476436\pi$
$661$	7.26008e11	0.147923	0.0739613	+	0.997261i	$0.476436\pi$
$662$	2.50379e11	0.0506683
$663$	−3.87703e12	−0.779270
$664$	1.34300e13	2.68114
$665$	−1.31794e13	−2.61335
$666$	−4.78623e12	−0.942670
$667$	−2.02292e12	−0.395742
$668$	1.21998e13	2.37060
$669$	−2.09970e12	−0.405266
$670$	−5.94863e12	−1.14046
$671$	−3.91982e11	−0.0746474
$672$	−3.67472e11	−0.0695125
$673$	−4.85759e12	−0.912752	−0.456376	−	0.889787i	$-0.650853\pi$
$673$	−4.85759e12	−0.912752	−0.456376	+	0.889787i	$0.650853\pi$
$674$	6.60985e12	1.23373
$675$	−5.77207e11	−0.107020
$676$	−2.72384e12	−0.501673
$677$	4.52063e12	0.827084	0.413542	−	0.910485i	$-0.364292\pi$
$677$	4.52063e12	0.827084	0.413542	+	0.910485i	$0.364292\pi$
$678$	−4.26972e12	−0.776007
$679$	4.15280e12	0.749769
$680$	1.93749e13	3.47495
$681$	4.38630e12	0.781513
$682$	−7.85828e11	−0.139091
$683$	−8.60311e12	−1.51273	−0.756367	−	0.654148i	$-0.773027\pi$
$683$	−8.60311e12	−1.51273	−0.756367	+	0.654148i	$0.773027\pi$
$684$	−6.86828e12	−1.19976
$685$	−1.18399e13	−2.05467
$686$	−7.21754e12	−1.24432
$687$	−2.22870e12	−0.381722
$688$	7.66890e12	1.30492
$689$	−3.47784e12	−0.587926
$690$	−9.32124e12	−1.56550
$691$	−9.71725e12	−1.62141	−0.810704	−	0.585456i	$-0.800915\pi$
$691$	−9.71725e12	−1.62141	−0.810704	+	0.585456i	$0.800915\pi$
$692$	−7.08677e12	−1.17482
$693$	1.11771e11	0.0184090
$694$	−1.65655e13	−2.71074
$695$	−1.18299e13	−1.92330
$696$	2.02787e12	0.327566
$697$	1.79996e13	2.88878
$698$	−2.68672e12	−0.428423
$699$	−4.88720e9	−0.000774306 0
$700$	8.46372e12	1.33236
$701$	−8.03820e12	−1.25727	−0.628634	−	0.777702i	$-0.716385\pi$
$701$	−8.03820e12	−1.25727	−0.628634	+	0.777702i	$0.716385\pi$
$702$	−1.86980e12	−0.290589
$703$	1.86681e13	2.88272
$704$	−2.77370e11	−0.0425582
$705$	−2.28021e12	−0.347635
$706$	1.65838e12	0.251225
$707$	−1.65013e12	−0.248389
$708$	−1.01957e12	−0.152500
$709$	3.61988e12	0.538005	0.269002	−	0.963140i	$-0.413306\pi$
$709$	3.61988e12	0.538005	0.269002	+	0.963140i	$0.413306\pi$
$710$	1.72301e13	2.54463
$711$	3.61232e12	0.530118
$712$	−1.49891e13	−2.18583
$713$	−1.47293e13	−2.13442
$714$	−1.28194e13	−1.84598
$715$	3.53711e11	0.0506140
$716$	−8.52236e12	−1.21186
$717$	−1.10408e12	−0.156014
$718$	7.13037e12	1.00127
$719$	4.49742e12	0.627601	0.313800	−	0.949489i	$-0.398398\pi$
$719$	4.49742e12	0.627601	0.313800	+	0.949489i	$0.398398\pi$
$720$	3.26065e12	0.452177
$721$	3.04665e12	0.419869
$722$	2.72853e13	3.73690
$723$	1.28869e11	0.0175398
$724$	−1.69318e13	−2.29023
$725$	−1.31076e12	−0.176199
$726$	7.50488e12	1.00260
$727$	1.11441e13	1.47959	0.739796	−	0.672831i	$-0.234922\pi$
$727$	1.11441e13	1.47959	0.739796	+	0.672831i	$0.234922\pi$
$728$	1.39038e13	1.83460
$729$	2.82430e11	0.0370370
$730$	−3.27491e12	−0.426821
$731$	1.44122e13	1.86682
$732$	1.45237e13	1.86972
$733$	−9.40397e11	−0.120322	−0.0601608	−	0.998189i	$-0.519161\pi$
$733$	−9.40397e11	−0.120322	−0.0601608	+	0.998189i	$0.519161\pi$
$734$	−5.24351e12	−0.666791
$735$	−2.24834e12	−0.284164
$736$	1.01370e12	0.127339
$737$	−1.96770e11	−0.0245672
$738$	8.68081e12	1.07723
$739$	8.78778e11	0.108388	0.0541938	−	0.998530i	$-0.482741\pi$
$739$	8.78778e11	0.108388	0.0541938	+	0.998530i	$0.482741\pi$
$740$	−3.35472e13	−4.11257
$741$	7.29295e12	0.888631
$742$	−1.14995e13	−1.39271
$743$	−4.29266e12	−0.516745	−0.258373	−	0.966045i	$-0.583186\pi$
$743$	−4.29266e12	−0.516745	−0.258373	+	0.966045i	$0.583186\pi$
$744$	1.47654e13	1.76672
$745$	−2.08044e12	−0.247430
$746$	−2.77767e13	−3.28365
$747$	4.24755e12	0.499109
$748$	1.26379e12	0.147610
$749$	4.14337e12	0.481044
$750$	4.82133e12	0.556405
$751$	−9.75240e12	−1.11875	−0.559374	−	0.828916i	$-0.688958\pi$
$751$	−9.75240e12	−1.11875	−0.559374	+	0.828916i	$0.688958\pi$
$752$	4.60318e12	0.524902
$753$	−5.78854e12	−0.656133
$754$	−4.24609e12	−0.478430
$755$	9.96263e12	1.11587
$756$	−4.14133e12	−0.461096
$757$	1.28330e13	1.42036	0.710179	−	0.704022i	$-0.248614\pi$
$757$	1.28330e13	1.42036	0.710179	+	0.704022i	$0.248614\pi$
$758$	2.23576e13	2.45988
$759$	−3.08330e11	−0.0337231
$760$	−3.64454e13	−3.96262
$761$	−8.34452e12	−0.901925	−0.450963	−	0.892543i	$-0.648919\pi$
$761$	−8.34452e12	−0.901925	−0.450963	+	0.892543i	$0.648919\pi$
$762$	−8.30843e12	−0.892733
$763$	6.21634e12	0.664009
$764$	2.13117e13	2.26307
$765$	6.12775e12	0.646881
$766$	−2.22008e12	−0.232991
$767$	1.08261e12	0.112952
$768$	1.12648e13	1.16841
$769$	3.46187e12	0.356979	0.178490	−	0.983942i	$-0.442879\pi$
$769$	3.46187e12	0.356979	0.178490	+	0.983942i	$0.442879\pi$
$770$	1.16955e12	0.119897
$771$	−2.05732e12	−0.209680
$772$	1.08744e13	1.10186
$773$	4.16579e12	0.419653	0.209826	−	0.977739i	$-0.432710\pi$
$773$	4.16579e12	0.419653	0.209826	+	0.977739i	$0.432710\pi$
$774$	6.95068e12	0.696134
$775$	−9.54396e12	−0.950322
$776$	1.14839e13	1.13687
$777$	1.12562e13	1.10789
$778$	−5.83910e12	−0.571396
$779$	−3.38585e13	−3.29419
$780$	−1.31056e13	−1.26775
$781$	5.69940e11	0.0548150
$782$	3.53634e13	3.38161
$783$	6.41362e11	0.0609783
$784$	4.53886e12	0.429066
$785$	−1.69896e13	−1.59688
$786$	−1.27240e13	−1.18911
$787$	−1.34968e13	−1.25414	−0.627068	−	0.778964i	$-0.715745\pi$
$787$	−1.34968e13	−1.25414	−0.627068	+	0.778964i	$0.715745\pi$
$788$	−1.71759e13	−1.58690
$789$	1.22388e12	0.112433
$790$	3.77984e13	3.45265
$791$	1.00415e13	0.912020
$792$	3.09085e11	0.0279135
$793$	−1.54217e13	−1.38485
$794$	1.21263e13	1.08277
$795$	5.49682e12	0.488044
$796$	−3.49959e13	−3.08965
$797$	1.09669e13	0.962767	0.481384	−	0.876510i	$-0.340134\pi$
$797$	1.09669e13	0.962767	0.481384	+	0.876510i	$0.340134\pi$
$798$	2.41142e13	2.10504
$799$	8.65077e12	0.750921
$800$	6.56835e11	0.0566959
$801$	−4.74065e12	−0.406904
$802$	−3.71619e12	−0.317185
$803$	−1.08328e11	−0.00919434
$804$	7.29069e12	0.615342
$805$	2.19216e13	1.83989
$806$	−3.09167e13	−2.58039
$807$	−3.72833e12	−0.309445
$808$	−4.56317e12	−0.376631
$809$	−6.45211e12	−0.529582	−0.264791	−	0.964306i	$-0.585303\pi$
$809$	−6.45211e12	−0.529582	−0.264791	+	0.964306i	$0.585303\pi$
$810$	2.95528e12	0.241221
$811$	−1.29661e13	−1.05248	−0.526242	−	0.850335i	$-0.676399\pi$
$811$	−1.29661e13	−1.05248	−0.526242	+	0.850335i	$0.676399\pi$
$812$	−9.40444e12	−0.759156
$813$	8.06687e12	0.647586
$814$	−1.65662e12	−0.132256
$815$	−2.24068e13	−1.77898
$816$	−1.23704e13	−0.976741
$817$	−2.71103e13	−2.12880
$818$	2.25205e13	1.75869
$819$	4.39739e12	0.341521
$820$	6.08446e13	4.69959
$821$	1.93127e13	1.48354	0.741770	−	0.670654i	$-0.233986\pi$
$821$	1.93127e13	1.48354	0.741770	+	0.670654i	$0.233986\pi$
$822$	2.16634e13	1.65502
$823$	1.00624e12	0.0764540	0.0382270	−	0.999269i	$-0.487829\pi$
$823$	1.00624e12	0.0764540	0.0382270	+	0.999269i	$0.487829\pi$
$824$	8.42500e12	0.636646
$825$	−1.99784e11	−0.0150148
$826$	3.57967e12	0.267567
$827$	−8.17815e12	−0.607967	−0.303984	−	0.952677i	$-0.598317\pi$
$827$	−8.17815e12	−0.607967	−0.303984	+	0.952677i	$0.598317\pi$
$828$	1.14242e13	0.844674
$829$	4.96724e12	0.365275	0.182637	−	0.983180i	$-0.441537\pi$
$829$	4.96724e12	0.365275	0.182637	+	0.983180i	$0.441537\pi$
$830$	4.44454e13	3.25069
$831$	−3.02889e12	−0.220332
$832$	−1.09125e13	−0.789534
$833$	8.52988e12	0.613819
$834$	2.16450e13	1.54921
$835$	2.04743e13	1.45754
$836$	−2.37727e12	−0.168325
$837$	4.66989e12	0.328884
$838$	3.98266e13	2.78981
$839$	8.69981e12	0.606151	0.303075	−	0.952967i	$-0.401987\pi$
$839$	8.69981e12	0.606151	0.303075	+	0.952967i	$0.401987\pi$
$840$	−2.19753e13	−1.52292
$841$	−1.30507e13	−0.899604
$842$	−8.55166e12	−0.586335
$843$	6.36445e12	0.434047
$844$	−5.21852e13	−3.54003
$845$	−4.57129e12	−0.308449
$846$	4.17208e12	0.280018
$847$	−1.76499e13	−1.17833
$848$	−1.10967e13	−0.736909
$849$	1.45609e13	0.961841
$850$	2.29140e13	1.50562
$851$	−3.10512e13	−2.02953
$852$	−2.11173e13	−1.37297
$853$	−5.23690e12	−0.338691	−0.169345	−	0.985557i	$-0.554165\pi$
$853$	−5.23690e12	−0.338691	−0.169345	+	0.985557i	$0.554165\pi$
$854$	−5.09919e13	−3.28051
$855$	−1.15267e13	−0.737663
$856$	1.14578e13	0.729406
$857$	1.51278e13	0.957994	0.478997	−	0.877817i	$-0.341000\pi$
$857$	1.51278e13	0.957994	0.478997	+	0.877817i	$0.341000\pi$
$858$	−6.47182e11	−0.0407693
$859$	2.58752e13	1.62149	0.810745	−	0.585400i	$-0.199062\pi$
$859$	2.58752e13	1.62149	0.810745	+	0.585400i	$0.199062\pi$
$860$	4.87180e13	3.03701
$861$	−2.04155e13	−1.26603
$862$	3.96762e13	2.44764
$863$	−1.12008e13	−0.687383	−0.343691	−	0.939083i	$-0.611677\pi$
$863$	−1.12008e13	−0.687383	−0.343691	+	0.939083i	$0.611677\pi$
$864$	−3.21392e11	−0.0196211
$865$	−1.18934e13	−0.722326
$866$	6.40019e11	0.0386690
$867$	−1.36422e13	−0.819969
$868$	−6.84758e13	−4.09447
$869$	1.25030e12	0.0743750
$870$	6.71106e12	0.397150
$871$	−7.74149e12	−0.455767
$872$	1.71903e13	1.00684
$873$	3.63205e12	0.211635
$874$	−6.65210e13	−3.85618
$875$	−1.13388e13	−0.653927
$876$	4.01375e12	0.230294
$877$	1.55673e13	0.888619	0.444309	−	0.895873i	$-0.353449\pi$
$877$	1.55673e13	0.888619	0.444309	+	0.895873i	$0.353449\pi$
$878$	3.27864e13	1.86195
$879$	−7.37430e12	−0.416650
$880$	1.12858e12	0.0634399
$881$	8.62829e12	0.482540	0.241270	−	0.970458i	$-0.422436\pi$
$881$	8.62829e12	0.482540	0.241270	+	0.970458i	$0.422436\pi$
$882$	4.11377e12	0.228893
$883$	5.03429e12	0.278686	0.139343	−	0.990244i	$-0.455501\pi$
$883$	5.03429e12	0.278686	0.139343	+	0.990244i	$0.455501\pi$
$884$	4.97209e13	2.73844
$885$	−1.71110e12	−0.0937629
$886$	−1.88189e13	−1.02599
$887$	−1.57373e13	−0.853637	−0.426818	−	0.904337i	$-0.640366\pi$
$887$	−1.57373e13	−0.853637	−0.426818	+	0.904337i	$0.640366\pi$
$888$	3.11273e13	1.67990
$889$	1.95397e13	1.04920
$890$	−4.96051e13	−2.65016
$891$	9.77552e10	0.00519625
$892$	2.69276e13	1.42415
$893$	−1.62727e13	−0.856304
$894$	3.80657e12	0.199304
$895$	−1.43027e13	−0.745098
$896$	−3.84052e13	−1.99069
$897$	−1.21306e13	−0.625627
$898$	3.73307e13	1.91568
$899$	1.06047e13	0.541479
$900$	7.40238e12	0.376080
$901$	−2.08541e13	−1.05422
$902$	3.00462e12	0.151133
$903$	−1.63466e13	−0.818147
$904$	2.77681e13	1.38289
$905$	−2.84159e13	−1.40813
$906$	−1.82285e13	−0.898825
$907$	1.81842e13	0.892196	0.446098	−	0.894984i	$-0.352813\pi$
$907$	1.81842e13	0.892196	0.446098	+	0.894984i	$0.352813\pi$
$908$	−5.62520e13	−2.74632
$909$	−1.44321e12	−0.0701119
$910$	4.60133e13	2.22432
$911$	−3.08914e13	−1.48595	−0.742976	−	0.669318i	$-0.766587\pi$
$911$	−3.08914e13	−1.48595	−0.742976	+	0.669318i	$0.766587\pi$
$912$	2.32696e13	1.11381
$913$	1.47017e12	0.0700245
$914$	−6.06433e13	−2.87425
$915$	2.43744e13	1.14958
$916$	2.85820e13	1.34141
$917$	2.99243e13	1.39753
$918$	−1.12119e13	−0.521059
$919$	6.59161e12	0.304840	0.152420	−	0.988316i	$-0.451293\pi$
$919$	6.59161e12	0.304840	0.152420	+	0.988316i	$0.451293\pi$
$920$	6.06207e13	2.78982
$921$	−8.01835e12	−0.367212
$922$	1.20285e13	0.548180
$923$	2.24231e13	1.01692
$924$	−1.43341e12	−0.0646913
$925$	−2.01198e13	−0.903622
$926$	−2.43909e13	−1.09013
$927$	2.66460e12	0.118515
$928$	−7.29841e11	−0.0323044
$929$	3.51352e13	1.54765	0.773823	−	0.633402i	$-0.218342\pi$
$929$	3.51352e13	1.54765	0.773823	+	0.633402i	$0.218342\pi$
$930$	4.88647e13	2.14201
$931$	−1.60453e13	−0.699961
$932$	6.26758e10	0.00272100
$933$	7.25932e12	0.313638
$934$	3.46151e13	1.48835
$935$	2.12095e12	0.0907567
$936$	1.21603e13	0.517848
$937$	−2.69874e13	−1.14376	−0.571878	−	0.820339i	$-0.693785\pi$
$937$	−2.69874e13	−1.14376	−0.571878	+	0.820339i	$0.693785\pi$
$938$	−2.55973e13	−1.07965
$939$	−5.44587e12	−0.228598
$940$	2.92425e13	1.22163
$941$	−3.82324e13	−1.58957	−0.794783	−	0.606894i	$-0.792415\pi$
$941$	−3.82324e13	−1.58957	−0.794783	+	0.606894i	$0.792415\pi$
$942$	3.10858e13	1.28627
$943$	5.63177e13	2.31922
$944$	3.45430e12	0.141575
$945$	−6.95020e12	−0.283501
$946$	2.40579e12	0.0976668
$947$	1.43528e13	0.579912	0.289956	−	0.957040i	$-0.406359\pi$
$947$	1.43528e13	0.579912	0.289956	+	0.957040i	$0.406359\pi$
$948$	−4.63261e13	−1.86289
$949$	−4.26193e12	−0.170572
$950$	−4.31027e13	−1.71691
$951$	1.15855e13	0.459308
$952$	8.33711e13	3.28965
$953$	−1.35149e13	−0.530756	−0.265378	−	0.964144i	$-0.585497\pi$
$953$	−1.35149e13	−0.530756	−0.265378	+	0.964144i	$0.585497\pi$
$954$	−1.00575e13	−0.393117
$955$	3.57664e13	1.39143
$956$	1.41593e13	0.548252
$957$	2.21990e11	0.00855519
$958$	−3.31614e13	−1.27200
$959$	−5.09479e13	−1.94510
$960$	1.72476e13	0.655401
$961$	5.07758e13	1.92044
$962$	−6.51762e13	−2.45359
$963$	3.62380e12	0.135783
$964$	−1.65268e12	−0.0616369
$965$	1.82500e13	0.677468
$966$	−4.01098e13	−1.48202
$967$	−1.21267e13	−0.445989	−0.222995	−	0.974820i	$-0.571583\pi$
$967$	−1.21267e13	−0.445989	−0.222995	+	0.974820i	$0.571583\pi$
$968$	−4.88080e13	−1.78670
$969$	4.37307e13	1.59342
$970$	3.80049e13	1.37837
$971$	1.30060e13	0.469522	0.234761	−	0.972053i	$-0.424569\pi$
$971$	1.30060e13	0.469522	0.234761	+	0.972053i	$0.424569\pi$
$972$	−3.62201e12	−0.130152
$973$	−5.09046e13	−1.82074
$974$	−1.01991e12	−0.0363118
$975$	−7.86008e12	−0.278552
$976$	−4.92059e13	−1.73577
$977$	−1.46992e12	−0.0516140	−0.0258070	−	0.999667i	$-0.508216\pi$
$977$	−1.46992e12	−0.0516140	−0.0258070	+	0.999667i	$0.508216\pi$
$978$	4.09975e13	1.43295
$979$	−1.64085e12	−0.0570882
$980$	2.88338e13	0.998585
$981$	5.43682e12	0.187428
$982$	−8.58953e13	−2.94759
$983$	−1.45935e13	−0.498503	−0.249251	−	0.968439i	$-0.580185\pi$
$983$	−1.45935e13	−0.498503	−0.249251	+	0.968439i	$0.580185\pi$
$984$	−5.64556e13	−1.91968
$985$	−2.88255e13	−0.975693
$986$	−2.54608e13	−0.857879
$987$	−9.81186e12	−0.329097
$988$	−9.35284e13	−3.12275
$989$	4.50933e13	1.49875
$990$	1.02289e12	0.0338431
$991$	−4.38424e13	−1.44399	−0.721993	−	0.691901i	$-0.756774\pi$
$991$	−4.38424e13	−1.44399	−0.721993	+	0.691901i	$0.756774\pi$
$992$	−5.31413e12	−0.174233
$993$	−5.15000e11	−0.0168088
$994$	7.41420e13	2.40894
$995$	−5.87320e13	−1.89964
$996$	−5.44726e13	−1.75393
$997$	−6.97073e12	−0.223434	−0.111717	−	0.993740i	$-0.535635\pi$
$997$	−6.97073e12	−0.223434	−0.111717	+	0.993740i	$0.535635\pi$
$998$	9.97791e13	3.18385
$999$	9.84471e12	0.312722

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.c.1.21	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.c.1.21	✓	22	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)

\(f(q)\)	\(=\)	\(q+39.3800 q^{2} -81.0000 q^{3} +1038.78 q^{4} +1743.34 q^{5} -3189.78 q^{6} +7501.70 q^{7} +20744.7 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+39.3800 q^{2} -81.0000 q^{3} +1038.78 q^{4} +1743.34 q^{5} -3189.78 q^{6} +7501.70 q^{7} +20744.7 q^{8} +6561.00 q^{9} +68652.8 q^{10} +2270.91 q^{11} -84141.5 q^{12} +89344.0 q^{13} +295417. q^{14} -141211. q^{15} +285070. q^{16} +535733. q^{17} +258372. q^{18} -1.00775e6 q^{19} +1.81096e6 q^{20} -607638. q^{21} +89428.4 q^{22} +1.67622e6 q^{23} -1.68032e6 q^{24} +1.08612e6 q^{25} +3.51837e6 q^{26} -531441. q^{27} +7.79264e6 q^{28} -1.20684e6 q^{29} -5.56088e6 q^{30} -8.78723e6 q^{31} +604756. q^{32} -183944. q^{33} +2.10972e7 q^{34} +1.30780e7 q^{35} +6.81546e6 q^{36} -1.85246e7 q^{37} -3.96852e7 q^{38} -7.23687e6 q^{39} +3.61652e7 q^{40} +3.35981e7 q^{41} -2.39288e7 q^{42} +2.69018e7 q^{43} +2.35898e6 q^{44} +1.14381e7 q^{45} +6.60095e7 q^{46} +1.61476e7 q^{47} -2.30907e7 q^{48} +1.59219e7 q^{49} +4.27713e7 q^{50} -4.33944e7 q^{51} +9.28091e7 q^{52} -3.89263e7 q^{53} -2.09281e7 q^{54} +3.95897e6 q^{55} +1.55621e8 q^{56} +8.16277e7 q^{57} -4.75252e7 q^{58} +1.21174e7 q^{59} -1.46687e8 q^{60} -1.72610e8 q^{61} -3.46041e8 q^{62} +4.92187e7 q^{63} -1.22141e8 q^{64} +1.55757e8 q^{65} -7.24370e6 q^{66} -8.66480e7 q^{67} +5.56510e8 q^{68} -1.35774e8 q^{69} +5.15013e8 q^{70} +2.50974e8 q^{71} +1.36106e8 q^{72} -4.77024e7 q^{73} -7.29497e8 q^{74} -8.79755e7 q^{75} -1.04683e9 q^{76} +1.70357e7 q^{77} -2.84988e8 q^{78} +5.50574e8 q^{79} +4.96975e8 q^{80} +4.30467e7 q^{81} +1.32309e9 q^{82} +6.47393e8 q^{83} -6.31204e8 q^{84} +9.33965e8 q^{85} +1.05939e9 q^{86} +9.77537e7 q^{87} +4.71094e7 q^{88} -7.22551e8 q^{89} +4.50431e8 q^{90} +6.70232e8 q^{91} +1.74123e9 q^{92} +7.11766e8 q^{93} +6.35890e8 q^{94} -1.75685e9 q^{95} -4.89852e7 q^{96} +5.53582e8 q^{97} +6.27004e8 q^{98} +1.48994e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9}+O(q^{10}) \) 22 * q + 36 * q^2 - 1782 * q^3 + 5718 * q^4 + 808 * q^5 - 2916 * q^6 + 21249 * q^7 + 9435 * q^8 + 144342 * q^9	\( 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9} + 68441 q^{10} - 68033 q^{11} - 463158 q^{12} + 283817 q^{13} + 80285 q^{14} - 65448 q^{15} + 1067674 q^{16} + 436893 q^{17} + 236196 q^{18} + 1207580 q^{19} + 4209677 q^{20} - 1721169 q^{21} + 5460442 q^{22} + 2421966 q^{23} - 764235 q^{24} + 7441842 q^{25} - 2736526 q^{26} - 11691702 q^{27} + 4095246 q^{28} - 2320594 q^{29} - 5543721 q^{30} - 3178024 q^{31} - 20786874 q^{32} + 5510673 q^{33} - 13809336 q^{34} - 2630800 q^{35} + 37515798 q^{36} + 3981807 q^{37} - 24156377 q^{38} - 22989177 q^{39} - 29544450 q^{40} - 885225 q^{41} - 6503085 q^{42} + 12360835 q^{43} - 117711882 q^{44} + 5301288 q^{45} + 161066949 q^{46} + 75901252 q^{47} - 86481594 q^{48} + 170907951 q^{49} - 61318927 q^{50} - 35388333 q^{51} - 100762 q^{52} - 34790192 q^{53} - 19131876 q^{54} + 151773316 q^{55} - 417630344 q^{56} - 97813980 q^{57} - 432929294 q^{58} + 266581942 q^{59} - 340983837 q^{60} - 290555332 q^{61} + 158267098 q^{62} + 139414689 q^{63} - 131794443 q^{64} - 650690086 q^{65} - 442295802 q^{66} + 86645184 q^{67} + 62738541 q^{68} - 196179246 q^{69} + 429714610 q^{70} - 36567631 q^{71} + 61903035 q^{72} + 907807228 q^{73} - 171827242 q^{74} - 602789202 q^{75} + 1744504396 q^{76} - 310688725 q^{77} + 221658606 q^{78} + 2508604687 q^{79} + 3509441927 q^{80} + 947027862 q^{81} + 1759214793 q^{82} + 2185672083 q^{83} - 331714926 q^{84} + 2868860198 q^{85} + 2397001564 q^{86} + 187968114 q^{87} + 7683735877 q^{88} + 1320145942 q^{89} + 449041401 q^{90} + 3894639897 q^{91} + 3505964640 q^{92} + 257419944 q^{93} + 5406355552 q^{94} + 3093659122 q^{95} + 1683736794 q^{96} + 3904552980 q^{97} + 6137683116 q^{98} - 446364513 q^{99}+O(q^{100}) \) 22 * q + 36 * q^2 - 1782 * q^3 + 5718 * q^4 + 808 * q^5 - 2916 * q^6 + 21249 * q^7 + 9435 * q^8 + 144342 * q^9 + 68441 * q^10 - 68033 * q^11 - 463158 * q^12 + 283817 * q^13 + 80285 * q^14 - 65448 * q^15 + 1067674 * q^16 + 436893 * q^17 + 236196 * q^18 + 1207580 * q^19 + 4209677 * q^20 - 1721169 * q^21 + 5460442 * q^22 + 2421966 * q^23 - 764235 * q^24 + 7441842 * q^25 - 2736526 * q^26 - 11691702 * q^27 + 4095246 * q^28 - 2320594 * q^29 - 5543721 * q^30 - 3178024 * q^31 - 20786874 * q^32 + 5510673 * q^33 - 13809336 * q^34 - 2630800 * q^35 + 37515798 * q^36 + 3981807 * q^37 - 24156377 * q^38 - 22989177 * q^39 - 29544450 * q^40 - 885225 * q^41 - 6503085 * q^42 + 12360835 * q^43 - 117711882 * q^44 + 5301288 * q^45 + 161066949 * q^46 + 75901252 * q^47 - 86481594 * q^48 + 170907951 * q^49 - 61318927 * q^50 - 35388333 * q^51 - 100762 * q^52 - 34790192 * q^53 - 19131876 * q^54 + 151773316 * q^55 - 417630344 * q^56 - 97813980 * q^57 - 432929294 * q^58 + 266581942 * q^59 - 340983837 * q^60 - 290555332 * q^61 + 158267098 * q^62 + 139414689 * q^63 - 131794443 * q^64 - 650690086 * q^65 - 442295802 * q^66 + 86645184 * q^67 + 62738541 * q^68 - 196179246 * q^69 + 429714610 * q^70 - 36567631 * q^71 + 61903035 * q^72 + 907807228 * q^73 - 171827242 * q^74 - 602789202 * q^75 + 1744504396 * q^76 - 310688725 * q^77 + 221658606 * q^78 + 2508604687 * q^79 + 3509441927 * q^80 + 947027862 * q^81 + 1759214793 * q^82 + 2185672083 * q^83 - 331714926 * q^84 + 2868860198 * q^85 + 2397001564 * q^86 + 187968114 * q^87 + 7683735877 * q^88 + 1320145942 * q^89 + 449041401 * q^90 + 3894639897 * q^91 + 3505964640 * q^92 + 257419944 * q^93 + 5406355552 * q^94 + 3093659122 * q^95 + 1683736794 * q^96 + 3904552980 * q^97 + 6137683116 * q^98 - 446364513 * q^99

Introduction

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