LMFDB - Embedded newform 177.10.a.c.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$91.1613430010$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+17.2254 q^{2} -81.0000 q^{3} -215.286 q^{4} +27.4764 q^{5} -1395.26 q^{6} +8666.20 q^{7} -12527.8 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+17.2254 q^{2} -81.0000 q^{3} -215.286 q^{4} +27.4764 q^{5} -1395.26 q^{6} +8666.20 q^{7} -12527.8 q^{8} +6561.00 q^{9} +473.292 q^{10} +42328.6 q^{11} +17438.1 q^{12} -200715. q^{13} +149279. q^{14} -2225.59 q^{15} -105570. q^{16} +154813. q^{17} +113016. q^{18} -72431.9 q^{19} -5915.28 q^{20} -701962. q^{21} +729126. q^{22} +1.79253e6 q^{23} +1.01475e6 q^{24} -1.95237e6 q^{25} -3.45739e6 q^{26} -531441. q^{27} -1.86571e6 q^{28} +2.62285e6 q^{29} -38336.6 q^{30} -6.56272e6 q^{31} +4.59574e6 q^{32} -3.42861e6 q^{33} +2.66671e6 q^{34} +238116. q^{35} -1.41249e6 q^{36} +2.16272e6 q^{37} -1.24767e6 q^{38} +1.62579e7 q^{39} -344218. q^{40} -1.12147e7 q^{41} -1.20916e7 q^{42} -3.59092e7 q^{43} -9.11273e6 q^{44} +180273. q^{45} +3.08771e7 q^{46} +2.37517e7 q^{47} +8.55115e6 q^{48} +3.47495e7 q^{49} -3.36303e7 q^{50} -1.25398e7 q^{51} +4.32110e7 q^{52} +8.03425e6 q^{53} -9.15428e6 q^{54} +1.16304e6 q^{55} -1.08568e8 q^{56} +5.86699e6 q^{57} +4.51796e7 q^{58} +1.21174e7 q^{59} +479137. q^{60} +1.76705e8 q^{61} -1.13045e8 q^{62} +5.68590e7 q^{63} +1.33215e8 q^{64} -5.51492e6 q^{65} -5.90592e7 q^{66} +1.31033e8 q^{67} -3.33289e7 q^{68} -1.45195e8 q^{69} +4.10164e6 q^{70} +3.10987e8 q^{71} -8.21948e7 q^{72} +2.50223e8 q^{73} +3.72537e7 q^{74} +1.58142e8 q^{75} +1.55936e7 q^{76} +3.66828e8 q^{77} +2.80049e8 q^{78} +3.50930e8 q^{79} -2.90068e6 q^{80} +4.30467e7 q^{81} -1.93178e8 q^{82} +3.42539e8 q^{83} +1.51122e8 q^{84} +4.25369e6 q^{85} -6.18550e8 q^{86} -2.12451e8 q^{87} -5.30283e8 q^{88} +8.59131e8 q^{89} +3.10527e6 q^{90} -1.73943e9 q^{91} -3.85907e8 q^{92} +5.31580e8 q^{93} +4.09133e8 q^{94} -1.99017e6 q^{95} -3.72255e8 q^{96} +1.29447e9 q^{97} +5.98573e8 q^{98} +2.77718e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	17.2254	0.761262	0.380631	−	0.924727i	$-0.375707\pi$
$2$	17.2254	0.761262	0.380631	+	0.924727i	$0.375707\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	−215.286	−0.420480
$5$	27.4764	0.0196605	0.00983025	−	0.999952i	$-0.496871\pi$
$5$	27.4764	0.0196605	0.00983025	+	0.999952i	$0.496871\pi$
$6$	−1395.26	−0.439515
$7$	8666.20	1.36423	0.682115	−	0.731245i	$-0.261060\pi$
$7$	8666.20	1.36423	0.682115	+	0.731245i	$0.261060\pi$
$8$	−12527.8	−1.08136
$9$	6561.00	0.333333
$10$	473.292	0.0149668
$11$	42328.6	0.871699	0.435849	−	0.900020i	$-0.356448\pi$
$11$	42328.6	0.871699	0.435849	+	0.900020i	$0.356448\pi$
$12$	17438.1	0.242764
$13$	−200715.	−1.94910	−0.974550	−	0.224169i	$-0.928033\pi$
$13$	−200715.	−1.94910	−0.974550	+	0.224169i	$0.928033\pi$
$14$	149279.	1.03854
$15$	−2225.59	−0.0113510
$16$	−105570.	−0.402717
$17$	154813.	0.449558	0.224779	−	0.974410i	$-0.427834\pi$
$17$	154813.	0.449558	0.224779	+	0.974410i	$0.427834\pi$
$18$	113016.	0.253754
$19$	−72431.9	−0.127508	−0.0637542	−	0.997966i	$-0.520307\pi$
$19$	−72431.9	−0.127508	−0.0637542	+	0.997966i	$0.520307\pi$
$20$	−5915.28	−0.00826685
$21$	−701962.	−0.787639
$22$	729126.	0.663591
$23$	1.79253e6	1.33565	0.667824	−	0.744319i	$-0.267226\pi$
$23$	1.79253e6	1.33565	0.667824	+	0.744319i	$0.267226\pi$
$24$	1.01475e6	0.624322
$25$	−1.95237e6	−0.999613
$26$	−3.45739e6	−1.48378
$27$	−531441.	−0.192450
$28$	−1.86571e6	−0.573631
$29$	2.62285e6	0.688624	0.344312	−	0.938855i	$-0.388112\pi$
$29$	2.62285e6	0.688624	0.344312	+	0.938855i	$0.388112\pi$
$30$	−38336.6	−0.00864109
$31$	−6.56272e6	−1.27631	−0.638155	−	0.769908i	$-0.720302\pi$
$31$	−6.56272e6	−1.27631	−0.638155	+	0.769908i	$0.720302\pi$
$32$	4.59574e6	0.774785
$33$	−3.42861e6	−0.503275
$34$	2.66671e6	0.342232
$35$	238116.	0.0268215
$36$	−1.41249e6	−0.140160
$37$	2.16272e6	0.189711	0.0948554	−	0.995491i	$-0.469761\pi$
$37$	2.16272e6	0.189711	0.0948554	+	0.995491i	$0.469761\pi$
$38$	−1.24767e6	−0.0970673
$39$	1.62579e7	1.12531
$40$	−344218.	−0.0212600
$41$	−1.12147e7	−0.619813	−0.309906	−	0.950767i	$-0.600298\pi$
$41$	−1.12147e7	−0.619813	−0.309906	+	0.950767i	$0.600298\pi$
$42$	−1.20916e7	−0.599600
$43$	−3.59092e7	−1.60176	−0.800880	−	0.598825i	$-0.795635\pi$
$43$	−3.59092e7	−1.60176	−0.800880	+	0.598825i	$0.795635\pi$
$44$	−9.11273e6	−0.366532
$45$	180273.	0.00655350
$46$	3.08771e7	1.01678
$47$	2.37517e7	0.709994	0.354997	−	0.934868i	$-0.384482\pi$
$47$	2.37517e7	0.709994	0.354997	+	0.934868i	$0.384482\pi$
$48$	8.55115e6	0.232509
$49$	3.47495e7	0.861124
$50$	−3.36303e7	−0.760968
$51$	−1.25398e7	−0.259553
$52$	4.32110e7	0.819558
$53$	8.03425e6	0.139863	0.0699317	−	0.997552i	$-0.477722\pi$
$53$	8.03425e6	0.139863	0.0699317	+	0.997552i	$0.477722\pi$
$54$	−9.15428e6	−0.146505
$55$	1.16304e6	0.0171380
$56$	−1.08568e8	−1.47522
$57$	5.86699e6	0.0736170
$58$	4.51796e7	0.524224
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	479137.	0.00477287
$61$	1.76705e8	1.63405	0.817023	−	0.576605i	$-0.195623\pi$
$61$	1.76705e8	1.63405	0.817023	+	0.576605i	$0.195623\pi$
$62$	−1.13045e8	−0.971606
$63$	5.68590e7	0.454743
$64$	1.33215e8	0.992531
$65$	−5.51492e6	−0.0383203
$66$	−5.90592e7	−0.383125
$67$	1.31033e8	0.794406	0.397203	−	0.917731i	$-0.369981\pi$
$67$	1.31033e8	0.794406	0.397203	+	0.917731i	$0.369981\pi$
$68$	−3.33289e7	−0.189030
$69$	−1.45195e8	−0.771137
$70$	4.10164e6	0.0204182
$71$	3.10987e8	1.45238	0.726189	−	0.687495i	$-0.241290\pi$
$71$	3.10987e8	1.45238	0.726189	+	0.687495i	$0.241290\pi$
$72$	−8.21948e7	−0.360453
$73$	2.50223e8	1.03128	0.515638	−	0.856807i	$-0.327555\pi$
$73$	2.50223e8	1.03128	0.515638	+	0.856807i	$0.327555\pi$
$74$	3.72537e7	0.144420
$75$	1.58142e8	0.577127
$76$	1.55936e7	0.0536147
$77$	3.66828e8	1.18920
$78$	2.80049e8	0.856659
$79$	3.50930e8	1.01368	0.506838	−	0.862041i	$-0.330814\pi$
$79$	3.50930e8	1.01368	0.506838	+	0.862041i	$0.330814\pi$
$80$	−2.90068e6	−0.00791762
$81$	4.30467e7	0.111111
$82$	−1.93178e8	−0.471840
$83$	3.42539e8	0.792243	0.396121	−	0.918198i	$-0.370356\pi$
$83$	3.42539e8	0.792243	0.396121	+	0.918198i	$0.370356\pi$
$84$	1.51122e8	0.331186
$85$	4.25369e6	0.00883854
$86$	−6.18550e8	−1.21936
$87$	−2.12451e8	−0.397578
$88$	−5.30283e8	−0.942618
$89$	8.59131e8	1.45146	0.725729	−	0.687981i	$-0.241503\pi$
$89$	8.59131e8	1.45146	0.725729	+	0.687981i	$0.241503\pi$
$90$	3.10527e6	0.00498893
$91$	−1.73943e9	−2.65902
$92$	−3.85907e8	−0.561613
$93$	5.31580e8	0.736878
$94$	4.09133e8	0.540491
$95$	−1.99017e6	−0.00250688
$96$	−3.72255e8	−0.447322
$97$	1.29447e9	1.48463	0.742317	−	0.670049i	$-0.233727\pi$
$97$	1.29447e9	1.48463	0.742317	+	0.670049i	$0.233727\pi$
$98$	5.98573e8	0.655541
$99$	2.77718e8	0.290566
$100$	4.20317e8	0.420317
$101$	7.34234e8	0.702082	0.351041	−	0.936360i	$-0.385828\pi$
$101$	7.34234e8	0.702082	0.351041	+	0.936360i	$0.385828\pi$
$102$	−2.16003e8	−0.197588
$103$	−1.48780e9	−1.30250	−0.651249	−	0.758864i	$-0.725755\pi$
$103$	−1.48780e9	−1.30250	−0.651249	+	0.758864i	$0.725755\pi$
$104$	2.51451e9	2.10767
$105$	−1.92874e7	−0.0154854
$106$	1.38393e8	0.106473
$107$	1.83548e9	1.35370	0.676851	−	0.736120i	$-0.263344\pi$
$107$	1.83548e9	1.35370	0.676851	+	0.736120i	$0.263344\pi$
$108$	1.14412e8	0.0809214
$109$	9.99882e8	0.678468	0.339234	−	0.940702i	$-0.389832\pi$
$109$	9.99882e8	0.678468	0.339234	+	0.940702i	$0.389832\pi$
$110$	2.00338e7	0.0130465
$111$	−1.75180e8	−0.109530
$112$	−9.14889e8	−0.549398
$113$	1.86271e8	0.107471	0.0537355	−	0.998555i	$-0.482887\pi$
$113$	1.86271e8	0.107471	0.0537355	+	0.998555i	$0.482887\pi$
$114$	1.01061e8	0.0560419
$115$	4.92524e7	0.0262595
$116$	−5.64662e8	−0.289553
$117$	−1.31689e9	−0.649700
$118$	2.08726e8	0.0991079
$119$	1.34164e9	0.613301
$120$	2.78817e7	0.0122745
$121$	−5.66241e8	−0.240141
$122$	3.04381e9	1.24394
$123$	9.08391e8	0.357849
$124$	1.41286e9	0.536662
$125$	−1.07309e8	−0.0393134
$126$	9.79418e8	0.346179
$127$	−3.39236e9	−1.15714	−0.578569	−	0.815634i	$-0.696389\pi$
$127$	−3.39236e9	−1.15714	−0.578569	+	0.815634i	$0.696389\pi$
$128$	−5.83357e7	−0.0192083
$129$	2.90864e9	0.924777
$130$	−9.49967e7	−0.0291718
$131$	−3.75251e9	−1.11327	−0.556636	−	0.830756i	$-0.687908\pi$
$131$	−3.75251e9	−1.11327	−0.556636	+	0.830756i	$0.687908\pi$
$132$	7.38131e8	0.211617
$133$	−6.27710e8	−0.173951
$134$	2.25709e9	0.604752
$135$	−1.46021e7	−0.00378367
$136$	−1.93946e9	−0.486133
$137$	−2.12368e9	−0.515045	−0.257523	−	0.966272i	$-0.582906\pi$
$137$	−2.12368e9	−0.515045	−0.257523	+	0.966272i	$0.582906\pi$
$138$	−2.50105e9	−0.587037
$139$	2.46199e9	0.559398	0.279699	−	0.960088i	$-0.409765\pi$
$139$	2.46199e9	0.559398	0.279699	+	0.960088i	$0.409765\pi$
$140$	−5.12630e7	−0.0112779
$141$	−1.92389e9	−0.409915
$142$	5.35687e9	1.10564
$143$	−8.49597e9	−1.69903
$144$	−6.92643e8	−0.134239
$145$	7.20665e7	0.0135387
$146$	4.31019e9	0.785071
$147$	−2.81471e9	−0.497170
$148$	−4.65602e8	−0.0797696
$149$	−8.87541e9	−1.47520	−0.737598	−	0.675240i	$-0.764040\pi$
$149$	−8.87541e9	−1.47520	−0.737598	+	0.675240i	$0.764040\pi$
$150$	2.72406e9	0.439345
$151$	−3.09187e8	−0.0483977	−0.0241989	−	0.999707i	$-0.507703\pi$
$151$	−3.09187e8	−0.0483977	−0.0241989	+	0.999707i	$0.507703\pi$
$152$	9.07412e8	0.137882
$153$	1.01572e9	0.149853
$154$	6.31876e9	0.905291
$155$	−1.80320e8	−0.0250929
$156$	−3.50009e9	−0.473172
$157$	−3.14639e9	−0.413299	−0.206649	−	0.978415i	$-0.566256\pi$
$157$	−3.14639e9	−0.413299	−0.206649	+	0.978415i	$0.566256\pi$
$158$	6.04491e9	0.771673
$159$	−6.50774e8	−0.0807502
$160$	1.26275e8	0.0152327
$161$	1.55345e10	1.82213
$162$	7.41497e8	0.0845847
$163$	−1.13192e10	−1.25595	−0.627976	−	0.778233i	$-0.716116\pi$
$163$	−1.13192e10	−1.25595	−0.627976	+	0.778233i	$0.716116\pi$
$164$	2.41437e9	0.260619
$165$	−9.42059e7	−0.00989465
$166$	5.90037e9	0.603104
$167$	1.94041e10	1.93050	0.965248	−	0.261336i	$-0.0841630\pi$
$167$	1.94041e10	1.93050	0.965248	+	0.261336i	$0.0841630\pi$
$168$	8.79403e9	0.851719
$169$	2.96819e10	2.79899
$170$	7.32715e7	0.00672845
$171$	−4.75226e8	−0.0425028
$172$	7.73073e9	0.673508
$173$	1.25396e10	1.06433	0.532165	−	0.846641i	$-0.321379\pi$
$173$	1.25396e10	1.06433	0.532165	+	0.846641i	$0.321379\pi$
$174$	−3.65955e9	−0.302661
$175$	−1.69196e10	−1.36370
$176$	−4.46862e9	−0.351048
$177$	−9.81506e8	−0.0751646
$178$	1.47989e10	1.10494
$179$	3.11531e8	0.0226810	0.0113405	−	0.999936i	$-0.496390\pi$
$179$	3.11531e8	0.0226810	0.0113405	+	0.999936i	$0.496390\pi$
$180$	−3.88101e7	−0.00275562
$181$	1.03952e10	0.719913	0.359956	−	0.932969i	$-0.382792\pi$
$181$	1.03952e10	0.719913	0.359956	+	0.932969i	$0.382792\pi$
$182$	−2.99625e10	−2.02421
$183$	−1.43131e10	−0.943417
$184$	−2.24565e10	−1.44431
$185$	5.94237e7	0.00372981
$186$	9.15668e9	0.560957
$187$	6.55299e9	0.391879
$188$	−5.11340e9	−0.298538
$189$	−4.60558e9	−0.262546
$190$	−3.42814e7	−0.00190839
$191$	−3.78429e9	−0.205747	−0.102874	−	0.994694i	$-0.532804\pi$
$191$	−3.78429e9	−0.205747	−0.102874	+	0.994694i	$0.532804\pi$
$192$	−1.07904e10	−0.573038
$193$	9.41435e9	0.488408	0.244204	−	0.969724i	$-0.421473\pi$
$193$	9.41435e9	0.488408	0.244204	+	0.969724i	$0.421473\pi$
$194$	2.22978e10	1.13020
$195$	4.46708e8	0.0221242
$196$	−7.48106e9	−0.362085
$197$	7.75555e9	0.366872	0.183436	−	0.983032i	$-0.441278\pi$
$197$	7.75555e9	0.366872	0.183436	+	0.983032i	$0.441278\pi$
$198$	4.78380e9	0.221197
$199$	2.33479e10	1.05538	0.527690	−	0.849437i	$-0.323058\pi$
$199$	2.33479e10	1.05538	0.527690	+	0.849437i	$0.323058\pi$
$200$	2.44589e10	1.08094
$201$	−1.06136e10	−0.458651
$202$	1.26475e10	0.534469
$203$	2.27302e10	0.939442
$204$	2.69964e9	0.109137
$205$	−3.08140e8	−0.0121858
$206$	−2.56280e10	−0.991543
$207$	1.17608e10	0.445216
$208$	2.11894e10	0.784935
$209$	−3.06594e9	−0.111149
$210$	−3.32233e8	−0.0117884
$211$	−1.25430e10	−0.435643	−0.217822	−	0.975989i	$-0.569895\pi$
$211$	−1.25430e10	−0.435643	−0.217822	+	0.975989i	$0.569895\pi$
$212$	−1.72966e9	−0.0588097
$213$	−2.51899e10	−0.838531
$214$	3.16169e10	1.03052
$215$	−9.86655e8	−0.0314914
$216$	6.65778e9	0.208107
$217$	−5.68738e10	−1.74118
$218$	1.72234e10	0.516492
$219$	−2.02681e10	−0.595407
$220$	−2.50385e8	−0.00720620
$221$	−3.10732e10	−0.876234
$222$	−3.01755e9	−0.0833807
$223$	−4.79430e10	−1.29823	−0.649117	−	0.760688i	$-0.724862\pi$
$223$	−4.79430e10	−1.29823	−0.649117	+	0.760688i	$0.724862\pi$
$224$	3.98277e10	1.05698
$225$	−1.28095e10	−0.333204
$226$	3.20859e9	0.0818137
$227$	4.75115e10	1.18763	0.593816	−	0.804601i	$-0.297621\pi$
$227$	4.75115e10	1.18763	0.593816	+	0.804601i	$0.297621\pi$
$228$	−1.26308e9	−0.0309545
$229$	2.54035e10	0.610427	0.305214	−	0.952284i	$-0.401272\pi$
$229$	2.54035e10	0.610427	0.305214	+	0.952284i	$0.401272\pi$
$230$	8.48392e8	0.0199904
$231$	−2.97131e10	−0.686584
$232$	−3.28585e10	−0.744649
$233$	4.20530e10	0.934750	0.467375	−	0.884059i	$-0.345200\pi$
$233$	4.20530e10	0.934750	0.467375	+	0.884059i	$0.345200\pi$
$234$	−2.26839e10	−0.494592
$235$	6.52611e8	0.0139588
$236$	−2.60869e9	−0.0547418
$237$	−2.84254e10	−0.585246
$238$	2.31102e10	0.466883
$239$	−8.98700e10	−1.78166	−0.890829	−	0.454339i	$-0.849876\pi$
$239$	−8.98700e10	−1.78166	−0.890829	+	0.454339i	$0.849876\pi$
$240$	2.34955e8	0.00457124
$241$	2.72838e10	0.520989	0.260495	−	0.965475i	$-0.416114\pi$
$241$	2.72838e10	0.520989	0.260495	+	0.965475i	$0.416114\pi$
$242$	−9.75372e9	−0.182811
$243$	−3.48678e9	−0.0641500
$244$	−3.80420e10	−0.687083
$245$	9.54790e8	0.0169301
$246$	1.56474e10	0.272417
$247$	1.45382e10	0.248527
$248$	8.22163e10	1.38015
$249$	−2.77456e10	−0.457402
$250$	−1.84844e9	−0.0299278
$251$	−2.84422e10	−0.452305	−0.226153	−	0.974092i	$-0.572615\pi$
$251$	−2.84422e10	−0.452305	−0.226153	+	0.974092i	$0.572615\pi$
$252$	−1.22409e10	−0.191210
$253$	7.58754e10	1.16428
$254$	−5.84347e10	−0.880885
$255$	−3.44549e8	−0.00510294
$256$	−6.92111e10	−1.00715
$257$	1.08804e11	1.55578	0.777889	−	0.628402i	$-0.216291\pi$
$257$	1.08804e11	1.55578	0.777889	+	0.628402i	$0.216291\pi$
$258$	5.01025e10	0.703997
$259$	1.87425e10	0.258809
$260$	1.18728e9	0.0161129
$261$	1.72085e10	0.229541
$262$	−6.46385e10	−0.847492
$263$	−5.93819e10	−0.765338	−0.382669	−	0.923886i	$-0.624995\pi$
$263$	−5.93819e10	−0.765338	−0.382669	+	0.923886i	$0.624995\pi$
$264$	4.29529e10	0.544221
$265$	2.20752e8	0.00274979
$266$	−1.08126e10	−0.132422
$267$	−6.95896e10	−0.838000
$268$	−2.82094e10	−0.334032
$269$	−4.76655e10	−0.555033	−0.277516	−	0.960721i	$-0.589511\pi$
$269$	−4.76655e10	−0.555033	−0.277516	+	0.960721i	$0.589511\pi$
$270$	−2.51527e8	−0.00288036
$271$	−9.88434e9	−0.111323	−0.0556616	−	0.998450i	$-0.517727\pi$
$271$	−9.88434e9	−0.111323	−0.0556616	+	0.998450i	$0.517727\pi$
$272$	−1.63435e10	−0.181045
$273$	1.40894e11	1.53519
$274$	−3.65811e10	−0.392085
$275$	−8.26410e10	−0.871362
$276$	3.12585e10	0.324248
$277$	−1.03401e11	−1.05527	−0.527637	−	0.849470i	$-0.676922\pi$
$277$	−1.03401e11	−1.05527	−0.527637	+	0.849470i	$0.676922\pi$
$278$	4.24088e10	0.425848
$279$	−4.30580e10	−0.425436
$280$	−2.98307e9	−0.0290036
$281$	−1.73580e11	−1.66082	−0.830408	−	0.557155i	$-0.811893\pi$
$281$	−1.73580e11	−1.66082	−0.830408	+	0.557155i	$0.811893\pi$
$282$	−3.31397e10	−0.312053
$283$	1.94147e11	1.79925	0.899624	−	0.436665i	$-0.143840\pi$
$283$	1.94147e11	1.79925	0.899624	+	0.436665i	$0.143840\pi$
$284$	−6.69510e10	−0.610696
$285$	1.61204e8	0.00144735
$286$	−1.46346e11	−1.29341
$287$	−9.71889e10	−0.845568
$288$	3.01527e10	0.258262
$289$	−9.46210e10	−0.797897
$290$	1.24137e9	0.0103065
$291$	−1.04852e11	−0.857154
$292$	−5.38695e10	−0.433631
$293$	9.53710e10	0.755983	0.377992	−	0.925809i	$-0.376615\pi$
$293$	9.53710e10	0.755983	0.377992	+	0.925809i	$0.376615\pi$
$294$	−4.84844e10	−0.378477
$295$	3.32941e8	0.00255958
$296$	−2.70941e10	−0.205145
$297$	−2.24951e10	−0.167758
$298$	−1.52882e11	−1.12301
$299$	−3.59788e11	−2.60331
$300$	−3.40457e10	−0.242670
$301$	−3.11196e11	−2.18517
$302$	−5.32587e9	−0.0368433
$303$	−5.94729e10	−0.405347
$304$	7.64662e9	0.0513498
$305$	4.85521e9	0.0321262
$306$	1.74963e10	0.114077
$307$	−4.48666e10	−0.288270	−0.144135	−	0.989558i	$-0.546040\pi$
$307$	−4.48666e10	−0.288270	−0.144135	+	0.989558i	$0.546040\pi$
$308$	−7.89728e10	−0.500034
$309$	1.20512e11	0.751998
$310$	−3.10608e9	−0.0191023
$311$	1.91873e11	1.16303	0.581516	−	0.813535i	$-0.302460\pi$
$311$	1.91873e11	1.16303	0.581516	+	0.813535i	$0.302460\pi$
$312$	−2.03675e11	−1.21687
$313$	2.55978e11	1.50748	0.753742	−	0.657170i	$-0.228247\pi$
$313$	2.55978e11	1.50748	0.753742	+	0.657170i	$0.228247\pi$
$314$	−5.41978e10	−0.314629
$315$	1.56228e9	0.00894049
$316$	−7.55503e10	−0.426230
$317$	−1.27243e11	−0.707731	−0.353866	−	0.935296i	$-0.615133\pi$
$317$	−1.27243e11	−0.707731	−0.353866	+	0.935296i	$0.615133\pi$
$318$	−1.12098e10	−0.0614720
$319$	1.11021e11	0.600273
$320$	3.66028e9	0.0195137
$321$	−1.48674e11	−0.781561
$322$	2.67587e11	1.38712
$323$	−1.12134e10	−0.0573225
$324$	−9.26734e9	−0.0467200
$325$	3.91870e11	1.94835
$326$	−1.94978e11	−0.956109
$327$	−8.09904e10	−0.391714
$328$	1.40495e11	0.670239
$329$	2.05837e11	0.968595
$330$	−1.62273e9	−0.00753242
$331$	1.12243e11	0.513963	0.256981	−	0.966416i	$-0.417272\pi$
$331$	1.12243e11	0.513963	0.256981	+	0.966416i	$0.417272\pi$
$332$	−7.37437e10	−0.333122
$333$	1.41896e10	0.0632369
$334$	3.34243e11	1.46961
$335$	3.60030e9	0.0156184
$336$	7.41060e10	0.317195
$337$	2.62199e11	1.10738	0.553690	−	0.832723i	$-0.313219\pi$
$337$	2.62199e11	1.10738	0.553690	+	0.832723i	$0.313219\pi$
$338$	5.11283e11	2.13077
$339$	−1.50879e10	−0.0620485
$340$	−9.15759e8	−0.00371643
$341$	−2.77790e11	−1.11256
$342$	−8.18595e9	−0.0323558
$343$	−4.85666e10	−0.189459
$344$	4.49862e11	1.73208
$345$	−3.98944e9	−0.0151609
$346$	2.16000e11	0.810234
$347$	1.93522e11	0.716552	0.358276	−	0.933616i	$-0.383365\pi$
$347$	1.93522e11	0.716552	0.358276	+	0.933616i	$0.383365\pi$
$348$	4.57376e10	0.167173
$349$	2.92833e11	1.05659	0.528295	−	0.849061i	$-0.322832\pi$
$349$	2.92833e11	1.05659	0.528295	+	0.849061i	$0.322832\pi$
$350$	−2.91447e11	−1.03814
$351$	1.06668e11	0.375105
$352$	1.94531e11	0.675379
$353$	−2.02190e11	−0.693065	−0.346532	−	0.938038i	$-0.612641\pi$
$353$	−2.02190e11	−0.693065	−0.346532	+	0.938038i	$0.612641\pi$
$354$	−1.69068e10	−0.0572200
$355$	8.54480e9	0.0285545
$356$	−1.84959e11	−0.610309
$357$	−1.08673e11	−0.354089
$358$	5.36625e9	0.0172662
$359$	−4.49596e11	−1.42856	−0.714279	−	0.699861i	$-0.753245\pi$
$359$	−4.49596e11	−1.42856	−0.714279	+	0.699861i	$0.753245\pi$
$360$	−2.25842e9	−0.00708668
$361$	−3.17441e11	−0.983742
$362$	1.79062e11	0.548042
$363$	4.58655e10	0.138646
$364$	3.74475e11	1.11807
$365$	6.87523e9	0.0202754
$366$	−2.46549e11	−0.718188
$367$	2.94702e11	0.847979	0.423990	−	0.905667i	$-0.360629\pi$
$367$	2.94702e11	0.847979	0.423990	+	0.905667i	$0.360629\pi$
$368$	−1.89237e11	−0.537888
$369$	−7.35797e10	−0.206604
$370$	1.02360e9	0.00283936
$371$	6.96265e10	0.190806
$372$	−1.14442e11	−0.309842
$373$	−2.80024e11	−0.749040	−0.374520	−	0.927219i	$-0.622193\pi$
$373$	−2.80024e11	−0.749040	−0.374520	+	0.927219i	$0.622193\pi$
$374$	1.12878e11	0.298323
$375$	8.69202e9	0.0226976
$376$	−2.97556e11	−0.767757
$377$	−5.26445e11	−1.34220
$378$	−7.93329e10	−0.199867
$379$	−6.78144e10	−0.168829	−0.0844143	−	0.996431i	$-0.526902\pi$
$379$	−6.78144e10	−0.168829	−0.0844143	+	0.996431i	$0.526902\pi$
$380$	4.28455e8	0.00105409
$381$	2.74781e11	0.668074
$382$	−6.51858e10	−0.156627
$383$	7.06249e11	1.67712	0.838559	−	0.544811i	$-0.183399\pi$
$383$	7.06249e11	1.67712	0.838559	+	0.544811i	$0.183399\pi$
$384$	4.72519e9	0.0110899
$385$	1.00791e10	0.0233802
$386$	1.62166e11	0.371806
$387$	−2.35600e11	−0.533920
$388$	−2.78681e11	−0.624259
$389$	1.18632e11	0.262681	0.131340	−	0.991337i	$-0.458072\pi$
$389$	1.18632e11	0.262681	0.131340	+	0.991337i	$0.458072\pi$
$390$	7.69473e9	0.0168423
$391$	2.77507e11	0.600452
$392$	−4.35334e11	−0.931183
$393$	3.03954e11	0.642748
$394$	1.33592e11	0.279286
$395$	9.64230e9	0.0199294
$396$	−5.97886e10	−0.122177
$397$	−7.04778e11	−1.42395	−0.711976	−	0.702204i	$-0.752199\pi$
$397$	−7.04778e11	−1.42395	−0.711976	+	0.702204i	$0.752199\pi$
$398$	4.02177e11	0.803421
$399$	5.08445e10	0.100431
$400$	2.06111e11	0.402561
$401$	6.83839e11	1.32070	0.660350	−	0.750958i	$-0.270408\pi$
$401$	6.83839e11	1.32070	0.660350	+	0.750958i	$0.270408\pi$
$402$	−1.82824e11	−0.349153
$403$	1.31723e12	2.48766
$404$	−1.58070e11	−0.295212
$405$	1.18277e9	0.00218450
$406$	3.91536e11	0.715162
$407$	9.15447e10	0.165371
$408$	1.57096e11	0.280669
$409$	−3.58211e11	−0.632971	−0.316485	−	0.948597i	$-0.602503\pi$
$409$	−3.58211e11	−0.632971	−0.316485	+	0.948597i	$0.602503\pi$
$410$	−5.30783e9	−0.00927662
$411$	1.72018e11	0.297362
$412$	3.20302e11	0.547674
$413$	1.05012e11	0.177608
$414$	2.02585e11	0.338926
$415$	9.41173e9	0.0155759
$416$	−9.22434e11	−1.51013
$417$	−1.99422e11	−0.322968
$418$	−5.28120e10	−0.0846135
$419$	2.98661e11	0.473385	0.236693	−	0.971585i	$-0.423937\pi$
$419$	2.98661e11	0.473385	0.236693	+	0.971585i	$0.423937\pi$
$420$	4.15230e9	0.00651129
$421$	1.19703e12	1.85710	0.928549	−	0.371209i	$-0.121057\pi$
$421$	1.19703e12	1.85710	0.928549	+	0.371209i	$0.121057\pi$
$422$	−2.16058e11	−0.331639
$423$	1.55835e11	0.236665
$424$	−1.00651e11	−0.151242
$425$	−3.02251e11	−0.449384
$426$	−4.33907e11	−0.638342
$427$	1.53136e12	2.22921
$428$	−3.95153e11	−0.569205
$429$	6.88173e11	0.980935
$430$	−1.69955e10	−0.0239732
$431$	4.88311e11	0.681630	0.340815	−	0.940130i	$-0.389297\pi$
$431$	4.88311e11	0.681630	0.340815	+	0.940130i	$0.389297\pi$
$432$	5.61041e10	0.0775029
$433$	3.36258e11	0.459703	0.229851	−	0.973226i	$-0.426176\pi$
$433$	3.36258e11	0.459703	0.229851	+	0.973226i	$0.426176\pi$
$434$	−9.79674e11	−1.32549
$435$	−5.83738e9	−0.00781658
$436$	−2.15260e11	−0.285282
$437$	−1.29837e11	−0.170306
$438$	−3.49126e11	−0.453261
$439$	1.51937e11	0.195243	0.0976213	−	0.995224i	$-0.468877\pi$
$439$	1.51937e11	0.195243	0.0976213	+	0.995224i	$0.468877\pi$
$440$	−1.45703e10	−0.0185324
$441$	2.27991e11	0.287041
$442$	−5.35247e11	−0.667044
$443$	−1.98945e11	−0.245423	−0.122712	−	0.992442i	$-0.539159\pi$
$443$	−1.98945e11	−0.245423	−0.122712	+	0.992442i	$0.539159\pi$
$444$	3.77138e10	0.0460550
$445$	2.36058e10	0.0285364
$446$	−8.25837e11	−0.988297
$447$	7.18908e11	0.851705
$448$	1.15447e12	1.35404
$449$	5.76477e11	0.669382	0.334691	−	0.942328i	$-0.391368\pi$
$449$	5.76477e11	0.669382	0.334691	+	0.942328i	$0.391368\pi$
$450$	−2.20649e11	−0.253656
$451$	−4.74702e11	−0.540290
$452$	−4.01014e10	−0.0451894
$453$	2.50441e10	0.0279424
$454$	8.18404e11	0.904100
$455$	−4.77934e10	−0.0522777
$456$	−7.35003e10	−0.0796063
$457$	−8.72269e10	−0.0935465	−0.0467732	−	0.998906i	$-0.514894\pi$
$457$	−8.72269e10	−0.0935465	−0.0467732	+	0.998906i	$0.514894\pi$
$458$	4.37585e11	0.464695
$459$	−8.22737e10	−0.0865175
$460$	−1.06033e10	−0.0110416
$461$	5.48921e11	0.566052	0.283026	−	0.959112i	$-0.408662\pi$
$461$	5.48921e11	0.566052	0.283026	+	0.959112i	$0.408662\pi$
$462$	−5.11819e11	−0.522670
$463$	1.79739e12	1.81773	0.908863	−	0.417095i	$-0.136952\pi$
$463$	1.79739e12	1.81773	0.908863	+	0.417095i	$0.136952\pi$
$464$	−2.76894e11	−0.277321
$465$	1.46059e10	0.0144874
$466$	7.24380e11	0.711590
$467$	−1.58907e12	−1.54603	−0.773013	−	0.634391i	$-0.781251\pi$
$467$	−1.58907e12	−1.54603	−0.773013	+	0.634391i	$0.781251\pi$
$468$	2.83508e11	0.273186
$469$	1.13555e12	1.08375
$470$	1.12415e10	0.0106263
$471$	2.54858e11	0.238618
$472$	−1.51804e11	−0.140781
$473$	−1.51998e12	−1.39625
$474$	−4.89638e11	−0.445526
$475$	1.41414e11	0.127459
$476$	−2.88835e11	−0.257881
$477$	5.27127e10	0.0466211
$478$	−1.54805e12	−1.35631
$479$	4.96331e11	0.430786	0.215393	−	0.976527i	$-0.430897\pi$
$479$	4.96331e11	0.430786	0.215393	+	0.976527i	$0.430897\pi$
$480$	−1.02282e10	−0.00879458
$481$	−4.34089e11	−0.369765
$482$	4.69975e11	0.396609
$483$	−1.25829e12	−1.05201
$484$	1.21904e11	0.100975
$485$	3.55674e10	0.0291887
$486$	−6.00612e10	−0.0488350
$487$	−3.90751e10	−0.0314789	−0.0157394	−	0.999876i	$-0.505010\pi$
$487$	−3.90751e10	−0.0314789	−0.0157394	+	0.999876i	$0.505010\pi$
$488$	−2.21372e12	−1.76699
$489$	9.16859e11	0.725124
$490$	1.64466e10	0.0128883
$491$	8.90650e11	0.691576	0.345788	−	0.938313i	$-0.387612\pi$
$491$	8.90650e11	0.691576	0.345788	+	0.938313i	$0.387612\pi$
$492$	−1.95564e11	−0.150468
$493$	4.06050e11	0.309577
$494$	2.50426e11	0.189194
$495$	7.63068e9	0.00571268
$496$	6.92824e11	0.513991
$497$	2.69508e12	1.98138
$498$	−4.77930e11	−0.348203
$499$	−1.41461e12	−1.02137	−0.510687	−	0.859767i	$-0.670609\pi$
$499$	−1.41461e12	−1.02137	−0.510687	+	0.859767i	$0.670609\pi$
$500$	2.31021e10	0.0165305
$501$	−1.57173e12	−1.11457
$502$	−4.89928e11	−0.344323
$503$	−1.87741e12	−1.30768	−0.653842	−	0.756631i	$-0.726844\pi$
$503$	−1.87741e12	−1.30768	−0.653842	+	0.756631i	$0.726844\pi$
$504$	−7.12317e11	−0.491740
$505$	2.01741e10	0.0138033
$506$	1.30698e12	0.886324
$507$	−2.40424e12	−1.61600
$508$	7.30326e11	0.486553
$509$	−2.71545e12	−1.79313	−0.896564	−	0.442914i	$-0.853945\pi$
$509$	−2.71545e12	−1.79313	−0.896564	+	0.442914i	$0.853945\pi$
$510$	−5.93499e9	−0.00388467
$511$	2.16848e12	1.40690
$512$	−1.16232e12	−0.747500
$513$	3.84933e10	0.0245390
$514$	1.87420e12	1.18435
$515$	−4.08794e10	−0.0256078
$516$	−6.26189e11	−0.388850
$517$	1.00538e12	0.618900
$518$	3.22848e11	0.197022
$519$	−1.01571e12	−0.614491
$520$	6.90897e10	0.0414380
$521$	8.14744e11	0.484453	0.242226	−	0.970220i	$-0.422122\pi$
$521$	8.14744e11	0.484453	0.242226	+	0.970220i	$0.422122\pi$
$522$	2.96424e11	0.174741
$523$	−1.99159e12	−1.16397	−0.581987	−	0.813198i	$-0.697724\pi$
$523$	−1.99159e12	−1.16397	−0.581987	+	0.813198i	$0.697724\pi$
$524$	8.07862e11	0.468109
$525$	1.37049e12	0.787334
$526$	−1.02288e12	−0.582623
$527$	−1.01599e12	−0.573775
$528$	3.61958e11	0.202677
$529$	1.41202e12	0.783956
$530$	3.80255e9	0.00209331
$531$	7.95020e10	0.0433963
$532$	1.35137e11	0.0731428
$533$	2.25096e12	1.20808
$534$	−1.19871e12	−0.637937
$535$	5.04324e10	0.0266145
$536$	−1.64155e12	−0.859037
$537$	−2.52340e10	−0.0130949
$538$	−8.21056e11	−0.422525
$539$	1.47089e12	0.750641
$540$	3.14362e9	0.00159096
$541$	−2.12747e12	−1.06776	−0.533882	−	0.845559i	$-0.679267\pi$
$541$	−2.12747e12	−1.06776	−0.533882	+	0.845559i	$0.679267\pi$
$542$	−1.70262e11	−0.0847462
$543$	−8.42013e11	−0.415642
$544$	7.11479e11	0.348311
$545$	2.74731e10	0.0133390
$546$	2.42696e12	1.16868
$547$	−2.87537e12	−1.37325	−0.686627	−	0.727010i	$-0.740910\pi$
$547$	−2.87537e12	−1.37325	−0.686627	+	0.727010i	$0.740910\pi$
$548$	4.57197e11	0.216566
$549$	1.15936e12	0.544682
$550$	−1.42352e12	−0.663335
$551$	−1.89978e11	−0.0878054
$552$	1.81897e12	0.833875
$553$	3.04123e12	1.38289
$554$	−1.78112e12	−0.803341
$555$	−4.81332e9	−0.00215341
$556$	−5.30032e11	−0.235215
$557$	−2.82464e12	−1.24341	−0.621706	−	0.783251i	$-0.713560\pi$
$557$	−2.82464e12	−1.24341	−0.621706	+	0.783251i	$0.713560\pi$
$558$	−7.41691e11	−0.323869
$559$	7.20750e12	3.12199
$560$	−2.51379e10	−0.0108015
$561$	−5.30792e11	−0.226252
$562$	−2.98999e12	−1.26432
$563$	4.36111e11	0.182940	0.0914702	−	0.995808i	$-0.470843\pi$
$563$	4.36111e11	0.182940	0.0914702	+	0.995808i	$0.470843\pi$
$564$	4.14186e11	0.172361
$565$	5.11805e9	0.00211294
$566$	3.34426e12	1.36970
$567$	3.73052e11	0.151581
$568$	−3.89598e12	−1.57054
$569$	1.82046e12	0.728074	0.364037	−	0.931385i	$-0.381398\pi$
$569$	1.82046e12	0.728074	0.364037	+	0.931385i	$0.381398\pi$
$570$	2.77680e9	0.00110181
$571$	−1.82132e12	−0.717009	−0.358505	−	0.933528i	$-0.616713\pi$
$571$	−1.82132e12	−0.717009	−0.358505	+	0.933528i	$0.616713\pi$
$572$	1.82906e12	0.714407
$573$	3.06527e11	0.118788
$574$	−1.67412e12	−0.643699
$575$	−3.49969e12	−1.33513
$576$	8.74025e11	0.330844
$577$	−1.30800e12	−0.491266	−0.245633	−	0.969363i	$-0.578996\pi$
$577$	−1.30800e12	−0.491266	−0.245633	+	0.969363i	$0.578996\pi$
$578$	−1.62988e12	−0.607409
$579$	−7.62562e11	−0.281982
$580$	−1.55149e10	−0.00569275
$581$	2.96851e12	1.08080
$582$	−1.80612e12	−0.652519
$583$	3.40078e11	0.121919
$584$	−3.13474e12	−1.11518
$585$	−3.61834e10	−0.0127734
$586$	1.64280e12	0.575501
$587$	−3.56619e12	−1.23975	−0.619873	−	0.784702i	$-0.712816\pi$
$587$	−3.56619e12	−1.23975	−0.619873	+	0.784702i	$0.712816\pi$
$588$	6.05966e11	0.209050
$589$	4.75350e11	0.162740
$590$	5.73505e9	0.00194851
$591$	−6.28199e11	−0.211814
$592$	−2.28318e11	−0.0763997
$593$	−1.29385e12	−0.429673	−0.214837	−	0.976650i	$-0.568922\pi$
$593$	−1.29385e12	−0.429673	−0.214837	+	0.976650i	$0.568922\pi$
$594$	−3.87488e11	−0.127708
$595$	3.68633e10	0.0120578
$596$	1.91075e12	0.620291
$597$	−1.89118e12	−0.609324
$598$	−6.19749e12	−1.98180
$599$	5.93442e12	1.88347	0.941733	−	0.336361i	$-0.109196\pi$
$599$	5.93442e12	1.88347	0.941733	+	0.336361i	$0.109196\pi$
$600$	−1.98117e12	−0.624081
$601$	−2.75644e12	−0.861812	−0.430906	−	0.902397i	$-0.641806\pi$
$601$	−2.75644e12	−0.861812	−0.430906	+	0.902397i	$0.641806\pi$
$602$	−5.36048e12	−1.66349
$603$	8.59705e11	0.264802
$604$	6.65635e10	0.0203503
$605$	−1.55583e10	−0.00472130
$606$	−1.02444e12	−0.308576
$607$	−1.28829e12	−0.385180	−0.192590	−	0.981279i	$-0.561689\pi$
$607$	−1.28829e12	−0.385180	−0.192590	+	0.981279i	$0.561689\pi$
$608$	−3.32879e11	−0.0987916
$609$	−1.84114e12	−0.542387
$610$	8.36330e10	0.0244564
$611$	−4.76732e12	−1.38385
$612$	−2.18671e11	−0.0630101
$613$	−4.32866e12	−1.23817	−0.619086	−	0.785323i	$-0.712497\pi$
$613$	−4.32866e12	−1.23817	−0.619086	+	0.785323i	$0.712497\pi$
$614$	−7.72844e11	−0.219449
$615$	2.49593e10	0.00703550
$616$	−4.59554e12	−1.28595
$617$	1.32521e12	0.368131	0.184066	−	0.982914i	$-0.441074\pi$
$617$	1.32521e12	0.368131	0.184066	+	0.982914i	$0.441074\pi$
$618$	2.07586e12	0.572467
$619$	3.57099e12	0.977645	0.488823	−	0.872383i	$-0.337427\pi$
$619$	3.57099e12	0.977645	0.488823	+	0.872383i	$0.337427\pi$
$620$	3.88203e10	0.0105511
$621$	−9.52626e11	−0.257046
$622$	3.30509e12	0.885372
$623$	7.44540e12	1.98012
$624$	−1.71634e12	−0.453183
$625$	3.81027e12	0.998841
$626$	4.40932e12	1.14759
$627$	2.48341e11	0.0641719
$628$	6.77373e11	0.173784
$629$	3.34816e11	0.0852860
$630$	2.69109e10	0.00680605
$631$	4.33954e12	1.08971	0.544856	−	0.838530i	$-0.316584\pi$
$631$	4.33954e12	1.08971	0.544856	+	0.838530i	$0.316584\pi$
$632$	−4.39638e12	−1.09615
$633$	1.01598e12	0.251519
$634$	−2.19182e12	−0.538769
$635$	−9.32098e10	−0.0227499
$636$	1.40102e11	0.0339538
$637$	−6.97473e12	−1.67842
$638$	1.91239e12	0.456965
$639$	2.04039e12	0.484126
$640$	−1.60285e9	−0.000377645 0
$641$	−3.93432e11	−0.0920467	−0.0460233	−	0.998940i	$-0.514655\pi$
$641$	−3.93432e11	−0.0920467	−0.0460233	+	0.998940i	$0.514655\pi$
$642$	−2.56097e12	−0.594972
$643$	2.11944e12	0.488958	0.244479	−	0.969655i	$-0.421383\pi$
$643$	2.11944e12	0.488958	0.244479	+	0.969655i	$0.421383\pi$
$644$	−3.34435e12	−0.766170
$645$	7.99190e10	0.0181816
$646$	−1.93155e11	−0.0436374
$647$	3.53345e12	0.792739	0.396370	−	0.918091i	$-0.370270\pi$
$647$	3.53345e12	0.792739	0.396370	+	0.918091i	$0.370270\pi$
$648$	−5.39280e11	−0.120151
$649$	5.12910e11	0.113486
$650$	6.75011e12	1.48320
$651$	4.60678e12	1.00527
$652$	2.43687e12	0.528103
$653$	−4.17496e12	−0.898551	−0.449275	−	0.893393i	$-0.648318\pi$
$653$	−4.17496e12	−0.898551	−0.449275	+	0.893393i	$0.648318\pi$
$654$	−1.39509e12	−0.298197
$655$	−1.03106e11	−0.0218875
$656$	1.18393e12	0.249609
$657$	1.64171e12	0.343758
$658$	3.54563e12	0.737355
$659$	7.07218e11	0.146073	0.0730363	−	0.997329i	$-0.476731\pi$
$659$	7.07218e11	0.146073	0.0730363	+	0.997329i	$0.476731\pi$
$660$	2.02812e10	0.00416050
$661$	−4.72588e12	−0.962889	−0.481444	−	0.876477i	$-0.659888\pi$
$661$	−4.72588e12	−0.962889	−0.481444	+	0.876477i	$0.659888\pi$
$662$	1.93342e12	0.391260
$663$	2.51693e12	0.505894
$664$	−4.29125e12	−0.856698
$665$	−1.72472e10	−0.00341996
$666$	2.44421e11	0.0481399
$667$	4.70155e12	0.919760
$668$	−4.17742e12	−0.811735
$669$	3.88338e12	0.749536
$670$	6.20167e10	0.0118897
$671$	7.47966e12	1.42440
$672$	−3.22604e12	−0.610250
$673$	3.81623e11	0.0717078	0.0358539	−	0.999357i	$-0.488585\pi$
$673$	3.81623e11	0.0717078	0.0358539	+	0.999357i	$0.488585\pi$
$674$	4.51648e12	0.843007
$675$	1.03757e12	0.192376
$676$	−6.39009e12	−1.17692
$677$	6.27405e12	1.14789	0.573943	−	0.818895i	$-0.305413\pi$
$677$	6.27405e12	1.14789	0.573943	+	0.818895i	$0.305413\pi$
$678$	−2.59896e11	−0.0472351
$679$	1.12181e13	2.02538
$680$	−5.32893e10	−0.00955763
$681$	−3.84843e12	−0.685680
$682$	−4.78505e12	−0.846948
$683$	4.49896e11	0.0791078	0.0395539	−	0.999217i	$-0.487406\pi$
$683$	4.49896e11	0.0791078	0.0395539	+	0.999217i	$0.487406\pi$
$684$	1.02309e11	0.0178716
$685$	−5.83509e10	−0.0101261
$686$	−8.36580e11	−0.144228
$687$	−2.05768e12	−0.352430
$688$	3.79092e12	0.645056
$689$	−1.61259e12	−0.272608
$690$	−6.87197e10	−0.0115415
$691$	−4.47844e12	−0.747266	−0.373633	−	0.927577i	$-0.621888\pi$
$691$	−4.47844e12	−0.747266	−0.373633	+	0.927577i	$0.621888\pi$
$692$	−2.69960e12	−0.447529
$693$	2.40676e12	0.396399
$694$	3.33349e12	0.545484
$695$	6.76467e10	0.0109980
$696$	2.66154e12	0.429923
$697$	−1.73618e12	−0.278642
$698$	5.04417e12	0.804342
$699$	−3.40630e12	−0.539678
$700$	3.64256e12	0.573410
$701$	−8.09287e12	−1.26582	−0.632909	−	0.774226i	$-0.718139\pi$
$701$	−8.09287e12	−1.26582	−0.632909	+	0.774226i	$0.718139\pi$
$702$	1.83740e12	0.285553
$703$	−1.56650e11	−0.0241897
$704$	5.63881e12	0.865188
$705$	−5.28615e10	−0.00805914
$706$	−3.48281e12	−0.527604
$707$	6.36302e12	0.957802
$708$	2.11304e11	0.0316052
$709$	−4.40528e12	−0.654735	−0.327368	−	0.944897i	$-0.606162\pi$
$709$	−4.40528e12	−0.654735	−0.327368	+	0.944897i	$0.606162\pi$
$710$	1.47188e11	0.0217375
$711$	2.30245e12	0.337892
$712$	−1.07630e13	−1.56955
$713$	−1.17639e13	−1.70470
$714$	−1.87193e12	−0.269555
$715$	−2.33439e11	−0.0334038
$716$	−6.70682e10	−0.00953691
$717$	7.27947e12	1.02864
$718$	−7.74447e12	−1.08751
$719$	−8.91334e12	−1.24383	−0.621914	−	0.783085i	$-0.713645\pi$
$719$	−8.91334e12	−1.24383	−0.621914	+	0.783085i	$0.713645\pi$
$720$	−1.90313e10	−0.00263921
$721$	−1.28936e13	−1.77691
$722$	−5.46805e12	−0.748885
$723$	−2.20999e12	−0.300793
$724$	−2.23794e12	−0.302709
$725$	−5.12077e12	−0.688358
$726$	7.90052e11	0.105546
$727$	1.39275e13	1.84913	0.924565	−	0.381023i	$-0.124428\pi$
$727$	1.39275e13	1.84913	0.924565	+	0.381023i	$0.124428\pi$
$728$	2.17913e13	2.87535
$729$	2.82430e11	0.0370370
$730$	1.18429e11	0.0154349
$731$	−5.55919e12	−0.720084
$732$	3.08140e12	0.396688
$733$	1.08129e12	0.138349	0.0691744	−	0.997605i	$-0.477964\pi$
$733$	1.08129e12	0.138349	0.0691744	+	0.997605i	$0.477964\pi$
$734$	5.07635e12	0.645535
$735$	−7.73380e10	−0.00977462
$736$	8.23803e12	1.03484
$737$	5.54642e12	0.692483
$738$	−1.26744e12	−0.157280
$739$	−3.69678e11	−0.0455956	−0.0227978	−	0.999740i	$-0.507257\pi$
$739$	−3.69678e11	−0.0455956	−0.0227978	+	0.999740i	$0.507257\pi$
$740$	−1.27931e10	−0.00156831
$741$	−1.17759e12	−0.143487
$742$	1.19934e12	0.145253
$743$	1.56143e12	0.187963	0.0939816	−	0.995574i	$-0.470041\pi$
$743$	1.56143e12	0.187963	0.0939816	+	0.995574i	$0.470041\pi$
$744$	−6.65952e12	−0.796828
$745$	−2.43864e11	−0.0290031
$746$	−4.82352e12	−0.570216
$747$	2.24740e12	0.264081
$748$	−1.41077e12	−0.164777
$749$	1.59067e13	1.84676
$750$	1.49724e11	0.0172788
$751$	−1.21763e12	−0.139680	−0.0698402	−	0.997558i	$-0.522249\pi$
$751$	−1.21763e12	−0.139680	−0.0698402	+	0.997558i	$0.522249\pi$
$752$	−2.50746e12	−0.285926
$753$	2.30382e12	0.261139
$754$	−9.06822e12	−1.02176
$755$	−8.49534e9	−0.000951524 0
$756$	9.91515e11	0.110395
$757$	−1.39602e12	−0.154511	−0.0772556	−	0.997011i	$-0.524616\pi$
$757$	−1.39602e12	−0.154511	−0.0772556	+	0.997011i	$0.524616\pi$
$758$	−1.16813e12	−0.128523
$759$	−6.14590e12	−0.672199
$760$	2.49324e10	0.00271083
$761$	2.93526e11	0.0317260	0.0158630	−	0.999874i	$-0.494950\pi$
$761$	2.93526e11	0.0317260	0.0158630	+	0.999874i	$0.494950\pi$
$762$	4.73321e12	0.508579
$763$	8.66518e12	0.925587
$764$	8.14703e11	0.0865125
$765$	2.79085e10	0.00294618
$766$	1.21654e13	1.27673
$767$	−2.43213e12	−0.253751
$768$	5.60610e12	0.581480
$769$	7.49150e12	0.772503	0.386251	−	0.922394i	$-0.373770\pi$
$769$	7.49150e12	0.772503	0.386251	+	0.922394i	$0.373770\pi$
$770$	1.73617e11	0.0177985
$771$	−8.81316e12	−0.898229
$772$	−2.02677e12	−0.205366
$773$	−1.21725e12	−0.122623	−0.0613117	−	0.998119i	$-0.519528\pi$
$773$	−1.21725e12	−0.122623	−0.0613117	+	0.998119i	$0.519528\pi$
$774$	−4.05831e12	−0.406453
$775$	1.28129e13	1.27582
$776$	−1.62169e13	−1.60542
$777$	−1.51815e12	−0.149424
$778$	2.04348e12	0.199969
$779$	8.12303e11	0.0790314
$780$	−9.61699e10	−0.00930280
$781$	1.31636e13	1.26604
$782$	4.78016e12	0.457101
$783$	−1.39389e12	−0.132526
$784$	−3.66849e12	−0.346789
$785$	−8.64514e10	−0.00812566
$786$	5.23572e12	0.489300
$787$	−5.80375e12	−0.539290	−0.269645	−	0.962960i	$-0.586906\pi$
$787$	−5.80375e12	−0.539290	−0.269645	+	0.962960i	$0.586906\pi$
$788$	−1.66966e12	−0.154262
$789$	4.80993e12	0.441868
$790$	1.66092e11	0.0151715
$791$	1.61426e12	0.146615
$792$	−3.47919e12	−0.314206
$793$	−3.54673e13	−3.18492
$794$	−1.21401e13	−1.08400
$795$	−1.78809e10	−0.00158759
$796$	−5.02647e12	−0.443766
$797$	−1.83092e13	−1.60734	−0.803669	−	0.595076i	$-0.797122\pi$
$797$	−1.83092e13	−1.60734	−0.803669	+	0.595076i	$0.797122\pi$
$798$	8.75817e11	0.0764540
$799$	3.67706e12	0.319183
$800$	−8.97259e12	−0.774485
$801$	5.63676e12	0.483819
$802$	1.17794e13	1.00540
$803$	1.05916e13	0.898961
$804$	2.28496e12	0.192853
$805$	4.26831e11	0.0358240
$806$	2.26899e13	1.89376
$807$	3.86090e12	0.320448
$808$	−9.19832e12	−0.759202
$809$	2.07773e12	0.170538	0.0852688	−	0.996358i	$-0.472825\pi$
$809$	2.07773e12	0.170538	0.0852688	+	0.996358i	$0.472825\pi$
$810$	2.03737e10	0.00166298
$811$	1.77755e13	1.44287	0.721437	−	0.692481i	$-0.243482\pi$
$811$	1.77755e13	1.44287	0.721437	+	0.692481i	$0.243482\pi$
$812$	−4.89348e12	−0.395017
$813$	8.00632e11	0.0642725
$814$	1.57689e12	0.125890
$815$	−3.11012e11	−0.0246927
$816$	1.32383e12	0.104526
$817$	2.60097e12	0.204238
$818$	−6.17032e12	−0.481857
$819$	−1.14124e13	−0.886341
$820$	6.63381e10	0.00512390
$821$	−3.14471e12	−0.241566	−0.120783	−	0.992679i	$-0.538541\pi$
$821$	−3.14471e12	−0.241566	−0.120783	+	0.992679i	$0.538541\pi$
$822$	2.96307e12	0.226370
$823$	−1.07039e13	−0.813286	−0.406643	−	0.913587i	$-0.633301\pi$
$823$	−1.07039e13	−0.813286	−0.406643	+	0.913587i	$0.633301\pi$
$824$	1.86388e13	1.40847
$825$	6.69392e12	0.503081
$826$	1.80886e12	0.135206
$827$	1.96147e13	1.45817	0.729083	−	0.684425i	$-0.239947\pi$
$827$	1.96147e13	1.45817	0.729083	+	0.684425i	$0.239947\pi$
$828$	−2.53194e12	−0.187204
$829$	2.11168e13	1.55286	0.776431	−	0.630202i	$-0.217028\pi$
$829$	2.11168e13	1.55286	0.776431	+	0.630202i	$0.217028\pi$
$830$	1.62121e11	0.0118573
$831$	8.37548e12	0.609263
$832$	−2.67383e13	−1.93454
$833$	5.37965e12	0.387125
$834$	−3.43512e12	−0.245864
$835$	5.33154e11	0.0379545
$836$	6.60053e11	0.0467359
$837$	3.48770e12	0.245626
$838$	5.14455e12	0.360370
$839$	2.06022e13	1.43544	0.717718	−	0.696334i	$-0.245187\pi$
$839$	2.06022e13	1.43544	0.717718	+	0.696334i	$0.245187\pi$
$840$	2.41628e11	0.0167452
$841$	−7.62780e12	−0.525796
$842$	2.06193e13	1.41374
$843$	1.40600e13	0.958873
$844$	2.70033e12	0.183179
$845$	8.15552e11	0.0550296
$846$	2.68432e12	0.180164
$847$	−4.90716e12	−0.327608
$848$	−8.48174e11	−0.0563253
$849$	−1.57259e13	−1.03880
$850$	−5.20640e12	−0.342099
$851$	3.87674e12	0.253387
$852$	5.42303e12	0.352585
$853$	1.13087e13	0.731375	0.365688	−	0.930738i	$-0.380834\pi$
$853$	1.13087e13	0.731375	0.365688	+	0.930738i	$0.380834\pi$
$854$	2.63783e13	1.69702
$855$	−1.30575e10	−0.000835627 0
$856$	−2.29945e13	−1.46384
$857$	−1.77296e13	−1.12276	−0.561378	−	0.827560i	$-0.689729\pi$
$857$	−1.77296e13	−1.12276	−0.561378	+	0.827560i	$0.689729\pi$
$858$	1.18541e13	0.746748
$859$	−2.03010e13	−1.27218	−0.636089	−	0.771616i	$-0.719449\pi$
$859$	−2.03010e13	−1.27218	−0.636089	+	0.771616i	$0.719449\pi$
$860$	2.12413e11	0.0132415
$861$	7.87230e12	0.488189
$862$	8.41135e12	0.518899
$863$	6.31451e12	0.387517	0.193759	−	0.981049i	$-0.437932\pi$
$863$	6.31451e12	0.387517	0.193759	+	0.981049i	$0.437932\pi$
$864$	−2.44237e12	−0.149107
$865$	3.44543e11	0.0209253
$866$	5.79218e12	0.349954
$867$	7.66430e12	0.460666
$868$	1.22441e13	0.732131
$869$	1.48544e13	0.883620
$870$	−1.00551e11	−0.00595046
$871$	−2.63002e13	−1.54838
$872$	−1.25263e13	−0.733667
$873$	8.49303e12	0.494878
$874$	−2.23649e12	−0.129648
$875$	−9.29961e11	−0.0536326
$876$	4.36343e12	0.250357
$877$	8.63725e12	0.493035	0.246517	−	0.969138i	$-0.420714\pi$
$877$	8.63725e12	0.493035	0.246517	+	0.969138i	$0.420714\pi$
$878$	2.61718e12	0.148631
$879$	−7.72505e12	−0.436467
$880$	−1.22781e11	−0.00690178
$881$	−5.05552e12	−0.282731	−0.141366	−	0.989957i	$-0.545149\pi$
$881$	−5.05552e12	−0.282731	−0.141366	+	0.989957i	$0.545149\pi$
$882$	3.92724e12	0.218514
$883$	−1.22521e13	−0.678244	−0.339122	−	0.940742i	$-0.610130\pi$
$883$	−1.22521e13	−0.678244	−0.339122	+	0.940742i	$0.610130\pi$
$884$	6.68961e12	0.368439
$885$	−2.69683e10	−0.00147777
$886$	−3.42690e12	−0.186832
$887$	−1.96690e13	−1.06691	−0.533454	−	0.845829i	$-0.679106\pi$
$887$	−1.96690e13	−1.06691	−0.533454	+	0.845829i	$0.679106\pi$
$888$	2.19462e12	0.118441
$889$	−2.93989e13	−1.57860
$890$	4.06620e11	0.0217237
$891$	1.82211e12	0.0968554
$892$	1.03214e13	0.545882
$893$	−1.72038e12	−0.0905302
$894$	1.23835e13	0.648371
$895$	8.55975e9	0.000445920 0
$896$	−5.05549e11	−0.0262046
$897$	2.91428e13	1.50302
$898$	9.93005e12	0.509575
$899$	−1.72130e13	−0.878898
$900$	2.75770e12	0.140106
$901$	1.24380e12	0.0628767
$902$	−8.17694e12	−0.411302
$903$	2.52069e13	1.26161
$904$	−2.33356e12	−0.116215
$905$	2.85623e11	0.0141539
$906$	4.31395e11	0.0212715
$907$	−8.46134e11	−0.0415151	−0.0207576	−	0.999785i	$-0.506608\pi$
$907$	−8.46134e11	−0.0415151	−0.0207576	+	0.999785i	$0.506608\pi$
$908$	−1.02285e13	−0.499376
$909$	4.81731e12	0.234027
$910$	−8.23260e11	−0.0397971
$911$	3.21048e12	0.154432	0.0772159	−	0.997014i	$-0.475397\pi$
$911$	3.21048e12	0.154432	0.0772159	+	0.997014i	$0.475397\pi$
$912$	−6.19376e11	−0.0296468
$913$	1.44992e13	0.690597
$914$	−1.50252e12	−0.0712134
$915$	−3.93272e11	−0.0185481
$916$	−5.46901e12	−0.256672
$917$	−3.25200e13	−1.51876
$918$	−1.41720e12	−0.0658625
$919$	−1.14327e13	−0.528726	−0.264363	−	0.964423i	$-0.585162\pi$
$919$	−1.14327e13	−0.528726	−0.264363	+	0.964423i	$0.585162\pi$
$920$	−6.17023e11	−0.0283959
$921$	3.63419e12	0.166433
$922$	9.45539e12	0.430914
$923$	−6.24197e13	−2.83083
$924$	6.39680e12	0.288695
$925$	−4.22242e12	−0.189637
$926$	3.09608e13	1.38377
$927$	−9.76146e12	−0.434166
$928$	1.20539e13	0.533536
$929$	−3.21191e13	−1.41479	−0.707396	−	0.706818i	$-0.750130\pi$
$929$	−3.21191e13	−1.41479	−0.707396	+	0.706818i	$0.750130\pi$
$930$	2.51592e11	0.0110287
$931$	−2.51697e12	−0.109801
$932$	−9.05342e12	−0.393044
$933$	−1.55417e13	−0.671477
$934$	−2.73723e13	−1.17693
$935$	1.80053e11	0.00770455
$936$	1.64977e13	0.702558
$937$	3.84448e13	1.62933	0.814665	−	0.579931i	$-0.196921\pi$
$937$	3.84448e13	1.62933	0.814665	+	0.579931i	$0.196921\pi$
$938$	1.95604e13	0.825020
$939$	−2.07342e13	−0.870347
$940$	−1.40498e11	−0.00586941
$941$	3.06768e13	1.27543	0.637715	−	0.770273i	$-0.279880\pi$
$941$	3.06768e13	1.27543	0.637715	+	0.770273i	$0.279880\pi$
$942$	4.39002e12	0.181651
$943$	−2.01027e13	−0.827852
$944$	−1.27923e12	−0.0524293
$945$	−1.26545e11	−0.00516179
$946$	−2.61823e13	−1.06291
$947$	−2.27641e13	−0.919761	−0.459881	−	0.887981i	$-0.652108\pi$
$947$	−2.27641e13	−0.919761	−0.459881	+	0.887981i	$0.652108\pi$
$948$	6.11957e12	0.246084
$949$	−5.02235e13	−2.01006
$950$	2.43591e12	0.0970298
$951$	1.03067e13	0.408609
$952$	−1.68077e13	−0.663198
$953$	4.09179e13	1.60692	0.803462	−	0.595356i	$-0.202989\pi$
$953$	4.09179e13	1.60692	0.803462	+	0.595356i	$0.202989\pi$
$954$	9.07998e11	0.0354909
$955$	−1.03979e11	−0.00404509
$956$	1.93477e13	0.749151
$957$	−8.99274e12	−0.346568
$958$	8.54950e12	0.327941
$959$	−1.84042e13	−0.702641
$960$	−2.96482e11	−0.0112662
$961$	1.66296e13	0.628966
$962$	−7.47736e12	−0.281488
$963$	1.20426e13	0.451234
$964$	−5.87382e12	−0.219065
$965$	2.58672e11	0.00960234
$966$	−2.16746e13	−0.800854
$967$	4.36312e13	1.60464	0.802320	−	0.596894i	$-0.203599\pi$
$967$	4.36312e13	1.60464	0.802320	+	0.596894i	$0.203599\pi$
$968$	7.09374e12	0.259679
$969$	9.08283e11	0.0330951
$970$	6.12663e11	0.0222202
$971$	3.13294e13	1.13101	0.565503	−	0.824746i	$-0.308682\pi$
$971$	3.13294e13	1.13101	0.565503	+	0.824746i	$0.308682\pi$
$972$	7.50655e11	0.0269738
$973$	2.13361e13	0.763147
$974$	−6.73084e11	−0.0239637
$975$	−3.17414e13	−1.12488
$976$	−1.86547e13	−0.658058
$977$	−1.36750e13	−0.480178	−0.240089	−	0.970751i	$-0.577177\pi$
$977$	−1.36750e13	−0.480178	−0.240089	+	0.970751i	$0.577177\pi$
$978$	1.57933e13	0.552010
$979$	3.63658e13	1.26523
$980$	−2.05553e11	−0.00711878
$981$	6.56022e12	0.226156
$982$	1.53418e13	0.526471
$983$	−3.93740e13	−1.34499	−0.672494	−	0.740103i	$-0.734777\pi$
$983$	−3.93740e13	−1.34499	−0.672494	+	0.740103i	$0.734777\pi$
$984$	−1.13801e13	−0.386963
$985$	2.13095e11	0.00721289
$986$	6.99437e12	0.235669
$987$	−1.66728e13	−0.559218
$988$	−3.12986e12	−0.104500
$989$	−6.43684e13	−2.13939
$990$	1.31442e11	0.00434885
$991$	−2.46053e12	−0.0810397	−0.0405198	−	0.999179i	$-0.512901\pi$
$991$	−2.46053e12	−0.0810397	−0.0405198	+	0.999179i	$0.512901\pi$
$992$	−3.01606e13	−0.988865
$993$	−9.09165e12	−0.296737
$994$	4.64238e13	1.50835
$995$	6.41516e11	0.0207493
$996$	5.97324e12	0.192328
$997$	−4.74114e13	−1.51969	−0.759845	−	0.650104i	$-0.774725\pi$
$997$	−4.74114e13	−1.51969	−0.759845	+	0.650104i	$0.774725\pi$
$998$	−2.43672e13	−0.777533
$999$	−1.14936e12	−0.0365098

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.c.1.14	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.c.1.14	✓	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)

\(f(q)\)	\(=\)	\(q+17.2254 q^{2} -81.0000 q^{3} -215.286 q^{4} +27.4764 q^{5} -1395.26 q^{6} +8666.20 q^{7} -12527.8 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+17.2254 q^{2} -81.0000 q^{3} -215.286 q^{4} +27.4764 q^{5} -1395.26 q^{6} +8666.20 q^{7} -12527.8 q^{8} +6561.00 q^{9} +473.292 q^{10} +42328.6 q^{11} +17438.1 q^{12} -200715. q^{13} +149279. q^{14} -2225.59 q^{15} -105570. q^{16} +154813. q^{17} +113016. q^{18} -72431.9 q^{19} -5915.28 q^{20} -701962. q^{21} +729126. q^{22} +1.79253e6 q^{23} +1.01475e6 q^{24} -1.95237e6 q^{25} -3.45739e6 q^{26} -531441. q^{27} -1.86571e6 q^{28} +2.62285e6 q^{29} -38336.6 q^{30} -6.56272e6 q^{31} +4.59574e6 q^{32} -3.42861e6 q^{33} +2.66671e6 q^{34} +238116. q^{35} -1.41249e6 q^{36} +2.16272e6 q^{37} -1.24767e6 q^{38} +1.62579e7 q^{39} -344218. q^{40} -1.12147e7 q^{41} -1.20916e7 q^{42} -3.59092e7 q^{43} -9.11273e6 q^{44} +180273. q^{45} +3.08771e7 q^{46} +2.37517e7 q^{47} +8.55115e6 q^{48} +3.47495e7 q^{49} -3.36303e7 q^{50} -1.25398e7 q^{51} +4.32110e7 q^{52} +8.03425e6 q^{53} -9.15428e6 q^{54} +1.16304e6 q^{55} -1.08568e8 q^{56} +5.86699e6 q^{57} +4.51796e7 q^{58} +1.21174e7 q^{59} +479137. q^{60} +1.76705e8 q^{61} -1.13045e8 q^{62} +5.68590e7 q^{63} +1.33215e8 q^{64} -5.51492e6 q^{65} -5.90592e7 q^{66} +1.31033e8 q^{67} -3.33289e7 q^{68} -1.45195e8 q^{69} +4.10164e6 q^{70} +3.10987e8 q^{71} -8.21948e7 q^{72} +2.50223e8 q^{73} +3.72537e7 q^{74} +1.58142e8 q^{75} +1.55936e7 q^{76} +3.66828e8 q^{77} +2.80049e8 q^{78} +3.50930e8 q^{79} -2.90068e6 q^{80} +4.30467e7 q^{81} -1.93178e8 q^{82} +3.42539e8 q^{83} +1.51122e8 q^{84} +4.25369e6 q^{85} -6.18550e8 q^{86} -2.12451e8 q^{87} -5.30283e8 q^{88} +8.59131e8 q^{89} +3.10527e6 q^{90} -1.73943e9 q^{91} -3.85907e8 q^{92} +5.31580e8 q^{93} +4.09133e8 q^{94} -1.99017e6 q^{95} -3.72255e8 q^{96} +1.29447e9 q^{97} +5.98573e8 q^{98} +2.77718e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9}+O(q^{10}) \) 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

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