LMFDB - Embedded newform 177.10.a.c.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+26.7529 q^{2} -81.0000 q^{3} +203.719 q^{4} -302.298 q^{5} -2166.99 q^{6} -5739.31 q^{7} -8247.43 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+26.7529 q^{2} -81.0000 q^{3} +203.719 q^{4} -302.298 q^{5} -2166.99 q^{6} -5739.31 q^{7} -8247.43 q^{8} +6561.00 q^{9} -8087.35 q^{10} +8930.69 q^{11} -16501.2 q^{12} -34150.1 q^{13} -153543. q^{14} +24486.1 q^{15} -324947. q^{16} +25141.2 q^{17} +175526. q^{18} +41188.0 q^{19} -61583.7 q^{20} +464884. q^{21} +238922. q^{22} -1.88606e6 q^{23} +668042. q^{24} -1.86174e6 q^{25} -913614. q^{26} -531441. q^{27} -1.16920e6 q^{28} +4.48207e6 q^{29} +655075. q^{30} -2.37511e6 q^{31} -4.47059e6 q^{32} -723386. q^{33} +672599. q^{34} +1.73498e6 q^{35} +1.33660e6 q^{36} +1.10711e7 q^{37} +1.10190e6 q^{38} +2.76616e6 q^{39} +2.49318e6 q^{40} +2.38530e7 q^{41} +1.24370e7 q^{42} +3.14335e7 q^{43} +1.81935e6 q^{44} -1.98338e6 q^{45} -5.04577e7 q^{46} +2.63227e7 q^{47} +2.63207e7 q^{48} -7.41390e6 q^{49} -4.98070e7 q^{50} -2.03643e6 q^{51} -6.95700e6 q^{52} -2.61342e7 q^{53} -1.42176e7 q^{54} -2.69973e6 q^{55} +4.73346e7 q^{56} -3.33623e6 q^{57} +1.19909e8 q^{58} +1.21174e7 q^{59} +4.98828e6 q^{60} -1.33430e7 q^{61} -6.35411e7 q^{62} -3.76556e7 q^{63} +4.67714e7 q^{64} +1.03235e7 q^{65} -1.93527e7 q^{66} +1.72934e8 q^{67} +5.12172e6 q^{68} +1.52771e8 q^{69} +4.64158e7 q^{70} +1.07910e8 q^{71} -5.41114e7 q^{72} -4.60374e8 q^{73} +2.96185e8 q^{74} +1.50801e8 q^{75} +8.39076e6 q^{76} -5.12560e7 q^{77} +7.40027e7 q^{78} +2.14806e8 q^{79} +9.82306e7 q^{80} +4.30467e7 q^{81} +6.38138e8 q^{82} +3.37429e8 q^{83} +9.47056e7 q^{84} -7.60012e6 q^{85} +8.40938e8 q^{86} -3.63048e8 q^{87} -7.36553e7 q^{88} +1.74288e8 q^{89} -5.30611e7 q^{90} +1.95998e8 q^{91} -3.84226e8 q^{92} +1.92384e8 q^{93} +7.04210e8 q^{94} -1.24510e7 q^{95} +3.62118e8 q^{96} +8.52762e8 q^{97} -1.98344e8 q^{98} +5.85943e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	26.7529	1.18232	0.591162	−	0.806553i	$-0.298670\pi$
$2$	26.7529	1.18232	0.591162	+	0.806553i	$0.298670\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	203.719	0.397888
$5$	−302.298	−0.216307	−0.108153	−	0.994134i	$-0.534494\pi$
$5$	−302.298	−0.216307	−0.108153	+	0.994134i	$0.534494\pi$
$6$	−2166.99	−0.682615
$7$	−5739.31	−0.903480	−0.451740	−	0.892150i	$-0.649197\pi$
$7$	−5739.31	−0.903480	−0.451740	+	0.892150i	$0.649197\pi$
$8$	−8247.43	−0.711891
$9$	6561.00	0.333333
$10$	−8087.35	−0.255744
$11$	8930.69	0.183915	0.0919577	−	0.995763i	$-0.470688\pi$
$11$	8930.69	0.183915	0.0919577	+	0.995763i	$0.470688\pi$
$12$	−16501.2	−0.229721
$13$	−34150.1	−0.331624	−0.165812	−	0.986157i	$-0.553025\pi$
$13$	−34150.1	−0.331624	−0.165812	+	0.986157i	$0.553025\pi$
$14$	−153543.	−1.06821
$15$	24486.1	0.124885
$16$	−324947.	−1.23957
$17$	25141.2	0.0730071	0.0365036	−	0.999334i	$-0.488378\pi$
$17$	25141.2	0.0730071	0.0365036	+	0.999334i	$0.488378\pi$
$18$	175526.	0.394108
$19$	41188.0	0.0725069	0.0362535	−	0.999343i	$-0.488458\pi$
$19$	41188.0	0.0725069	0.0362535	+	0.999343i	$0.488458\pi$
$20$	−61583.7	−0.0860658
$21$	464884.	0.521625
$22$	238922.	0.217447
$23$	−1.88606e6	−1.40534	−0.702670	−	0.711516i	$-0.748009\pi$
$23$	−1.88606e6	−1.40534	−0.702670	+	0.711516i	$0.748009\pi$
$24$	668042.	0.411011
$25$	−1.86174e6	−0.953211
$26$	−913614.	−0.392087
$27$	−531441.	−0.192450
$28$	−1.16920e6	−0.359484
$29$	4.48207e6	1.17676	0.588380	−	0.808584i	$-0.299766\pi$
$29$	4.48207e6	1.17676	0.588380	+	0.808584i	$0.299766\pi$
$30$	655075.	0.147654
$31$	−2.37511e6	−0.461909	−0.230954	−	0.972965i	$-0.574185\pi$
$31$	−2.37511e6	−0.461909	−0.230954	+	0.972965i	$0.574185\pi$
$32$	−4.47059e6	−0.753685
$33$	−723386.	−0.106184
$34$	672599.	0.0863180
$35$	1.73498e6	0.195429
$36$	1.33660e6	0.132629
$37$	1.10711e7	0.971147	0.485573	−	0.874196i	$-0.338611\pi$
$37$	1.10711e7	0.971147	0.485573	+	0.874196i	$0.338611\pi$
$38$	1.10190e6	0.0857266
$39$	2.76616e6	0.191463
$40$	2.49318e6	0.153987
$41$	2.38530e7	1.31831	0.659153	−	0.752009i	$-0.270915\pi$
$41$	2.38530e7	1.31831	0.659153	+	0.752009i	$0.270915\pi$
$42$	1.24370e7	0.616729
$43$	3.14335e7	1.40212	0.701060	−	0.713103i	$-0.252711\pi$
$43$	3.14335e7	1.40212	0.701060	+	0.713103i	$0.252711\pi$
$44$	1.81935e6	0.0731777
$45$	−1.98338e6	−0.0721022
$46$	−5.04577e7	−1.66157
$47$	2.63227e7	0.786848	0.393424	−	0.919357i	$-0.371291\pi$
$47$	2.63227e7	0.786848	0.393424	+	0.919357i	$0.371291\pi$
$48$	2.63207e7	0.715668
$49$	−7.41390e6	−0.183723
$50$	−4.98070e7	−1.12700
$51$	−2.03643e6	−0.0421507
$52$	−6.95700e6	−0.131949
$53$	−2.61342e7	−0.454955	−0.227478	−	0.973783i	$-0.573048\pi$
$53$	−2.61342e7	−0.454955	−0.227478	+	0.973783i	$0.573048\pi$
$54$	−1.42176e7	−0.227538
$55$	−2.69973e6	−0.0397821
$56$	4.73346e7	0.643180
$57$	−3.33623e6	−0.0418619
$58$	1.19909e8	1.39131
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	4.98828e6	0.0496901
$61$	−1.33430e7	−0.123387	−0.0616935	−	0.998095i	$-0.519650\pi$
$61$	−1.33430e7	−0.123387	−0.0616935	+	0.998095i	$0.519650\pi$
$62$	−6.35411e7	−0.546125
$63$	−3.76556e7	−0.301160
$64$	4.67714e7	0.348474
$65$	1.03235e7	0.0717326
$66$	−1.93527e7	−0.125543
$67$	1.72934e8	1.04844	0.524222	−	0.851582i	$-0.324356\pi$
$67$	1.72934e8	1.04844	0.524222	+	0.851582i	$0.324356\pi$
$68$	5.12172e6	0.0290486
$69$	1.52771e8	0.811373
$70$	4.64158e7	0.231060
$71$	1.07910e8	0.503965	0.251982	−	0.967732i	$-0.418918\pi$
$71$	1.07910e8	0.503965	0.251982	+	0.967732i	$0.418918\pi$
$72$	−5.41114e7	−0.237297
$73$	−4.60374e8	−1.89740	−0.948699	−	0.316182i	$-0.897599\pi$
$73$	−4.60374e8	−1.89740	−0.948699	+	0.316182i	$0.897599\pi$
$74$	2.96185e8	1.14821
$75$	1.50801e8	0.550337
$76$	8.39076e6	0.0288496
$77$	−5.12560e7	−0.166164
$78$	7.40027e7	0.226372
$79$	2.14806e8	0.620474	0.310237	−	0.950659i	$-0.399592\pi$
$79$	2.14806e8	0.620474	0.310237	+	0.950659i	$0.399592\pi$
$80$	9.82306e7	0.268128
$81$	4.30467e7	0.111111
$82$	6.38138e8	1.55866
$83$	3.37429e8	0.780425	0.390212	−	0.920725i	$-0.372402\pi$
$83$	3.37429e8	0.780425	0.390212	+	0.920725i	$0.372402\pi$
$84$	9.47056e7	0.207548
$85$	−7.60012e6	−0.0157919
$86$	8.40938e8	1.65776
$87$	−3.63048e8	−0.679403
$88$	−7.36553e7	−0.130928
$89$	1.74288e8	0.294450	0.147225	−	0.989103i	$-0.452966\pi$
$89$	1.74288e8	0.294450	0.147225	+	0.989103i	$0.452966\pi$
$90$	−5.30611e7	−0.0852481
$91$	1.95998e8	0.299616
$92$	−3.84226e8	−0.559167
$93$	1.92384e8	0.266683
$94$	7.04210e8	0.930308
$95$	−1.24510e7	−0.0156837
$96$	3.62118e8	0.435140
$97$	8.52762e8	0.978037	0.489018	−	0.872274i	$-0.337355\pi$
$97$	8.52762e8	0.978037	0.489018	+	0.872274i	$0.337355\pi$
$98$	−1.98344e8	−0.217220
$99$	5.85943e7	0.0613051
$100$	−3.79271e8	−0.379271
$101$	6.13488e7	0.0586624	0.0293312	−	0.999570i	$-0.490662\pi$
$101$	6.13488e7	0.0586624	0.0293312	+	0.999570i	$0.490662\pi$
$102$	−5.44806e7	−0.0498357
$103$	1.83989e9	1.61073	0.805366	−	0.592777i	$-0.201969\pi$
$103$	1.83989e9	1.61073	0.805366	+	0.592777i	$0.201969\pi$
$104$	2.81650e8	0.236081
$105$	−1.40533e8	−0.112831
$106$	−6.99167e8	−0.537904
$107$	2.11452e8	0.155950	0.0779748	−	0.996955i	$-0.475155\pi$
$107$	2.11452e8	0.155950	0.0779748	+	0.996955i	$0.475155\pi$
$108$	−1.08264e8	−0.0765735
$109$	1.71147e8	0.116132	0.0580658	−	0.998313i	$-0.481507\pi$
$109$	1.71147e8	0.116132	0.0580658	+	0.998313i	$0.481507\pi$
$110$	−7.22256e7	−0.0470353
$111$	−8.96763e8	−0.560692
$112$	1.86497e9	1.11993
$113$	3.33129e8	0.192202	0.0961012	−	0.995372i	$-0.469363\pi$
$113$	3.33129e8	0.192202	0.0961012	+	0.995372i	$0.469363\pi$
$114$	−8.92538e7	−0.0494943
$115$	5.70153e8	0.303984
$116$	9.13082e8	0.468219
$117$	−2.24059e8	−0.110541
$118$	3.24175e8	0.153925
$119$	−1.44293e8	−0.0659605
$120$	−2.01947e8	−0.0889043
$121$	−2.27819e9	−0.966175
$122$	−3.56965e8	−0.145883
$123$	−1.93209e9	−0.761124
$124$	−4.83854e8	−0.183788
$125$	1.15323e9	0.422493
$126$	−1.00740e9	−0.356069
$127$	−5.28337e8	−0.180216	−0.0901082	−	0.995932i	$-0.528721\pi$
$127$	−5.28337e8	−0.180216	−0.0901082	+	0.995932i	$0.528721\pi$
$128$	3.54021e9	1.16569
$129$	−2.54612e9	−0.809514
$130$	2.76183e8	0.0848111
$131$	1.10426e8	0.0327605	0.0163803	−	0.999866i	$-0.494786\pi$
$131$	1.10426e8	0.0327605	0.0163803	+	0.999866i	$0.494786\pi$
$132$	−1.47367e8	−0.0422492
$133$	−2.36391e8	−0.0655086
$134$	4.62650e9	1.23960
$135$	1.60653e8	0.0416282
$136$	−2.07350e8	−0.0519731
$137$	−8.18316e8	−0.198462	−0.0992312	−	0.995064i	$-0.531638\pi$
$137$	−8.18316e8	−0.198462	−0.0992312	+	0.995064i	$0.531638\pi$
$138$	4.08708e9	0.959305
$139$	−7.12323e8	−0.161849	−0.0809245	−	0.996720i	$-0.525787\pi$
$139$	−7.12323e8	−0.161849	−0.0809245	+	0.996720i	$0.525787\pi$
$140$	3.53448e8	0.0777587
$141$	−2.13214e9	−0.454287
$142$	2.88691e9	0.595849
$143$	−3.04984e8	−0.0609909
$144$	−2.13197e9	−0.413191
$145$	−1.35492e9	−0.254541
$146$	−1.23164e10	−2.24334
$147$	6.00526e8	0.106073
$148$	2.25540e9	0.386407
$149$	2.50956e9	0.417119	0.208559	−	0.978010i	$-0.433123\pi$
$149$	2.50956e9	0.417119	0.208559	+	0.978010i	$0.433123\pi$
$150$	4.03437e9	0.650676
$151$	−1.14855e10	−1.79785	−0.898925	−	0.438103i	$-0.855651\pi$
$151$	−1.14855e10	−1.79785	−0.898925	+	0.438103i	$0.855651\pi$
$152$	−3.39695e8	−0.0516170
$153$	1.64951e8	0.0243357
$154$	−1.37125e9	−0.196459
$155$	7.17990e8	0.0999139
$156$	5.63517e8	0.0761810
$157$	6.11357e9	0.803057	0.401529	−	0.915846i	$-0.368479\pi$
$157$	6.11357e9	0.803057	0.401529	+	0.915846i	$0.368479\pi$
$158$	5.74668e9	0.733601
$159$	2.11687e9	0.262668
$160$	1.35145e9	0.163027
$161$	1.08247e10	1.26970
$162$	1.15163e9	0.131369
$163$	−3.77542e9	−0.418910	−0.209455	−	0.977818i	$-0.567169\pi$
$163$	−3.77542e9	−0.418910	−0.209455	+	0.977818i	$0.567169\pi$
$164$	4.85930e9	0.524538
$165$	2.18678e8	0.0229682
$166$	9.02721e9	0.922714
$167$	−1.45074e10	−1.44333	−0.721664	−	0.692244i	$-0.756622\pi$
$167$	−1.45074e10	−1.44333	−0.721664	+	0.692244i	$0.756622\pi$
$168$	−3.83410e9	−0.371340
$169$	−9.43827e9	−0.890025
$170$	−2.03325e8	−0.0186712
$171$	2.70234e8	0.0241690
$172$	6.40359e9	0.557886
$173$	8.68202e9	0.736908	0.368454	−	0.929646i	$-0.379887\pi$
$173$	8.68202e9	0.736908	0.368454	+	0.929646i	$0.379887\pi$
$174$	−9.71259e9	−0.803274
$175$	1.06851e10	0.861208
$176$	−2.90200e9	−0.227977
$177$	−9.81506e8	−0.0751646
$178$	4.66271e9	0.348135
$179$	1.56613e10	1.14022	0.570112	−	0.821567i	$-0.306900\pi$
$179$	1.56613e10	1.14022	0.570112	+	0.821567i	$0.306900\pi$
$180$	−4.04050e8	−0.0286886
$181$	−1.27073e10	−0.880037	−0.440019	−	0.897989i	$-0.645028\pi$
$181$	−1.27073e10	−0.880037	−0.440019	+	0.897989i	$0.645028\pi$
$182$	5.24352e9	0.354243
$183$	1.08078e9	0.0712376
$184$	1.55552e10	1.00045
$185$	−3.34678e9	−0.210065
$186$	5.14683e9	0.315305
$187$	2.24528e8	0.0134271
$188$	5.36243e9	0.313077
$189$	3.05011e9	0.173875
$190$	−3.33102e8	−0.0185432
$191$	3.61646e10	1.96623	0.983114	−	0.182994i	$-0.0585789\pi$
$191$	3.61646e10	1.96623	0.983114	+	0.182994i	$0.0585789\pi$
$192$	−3.78849e9	−0.201192
$193$	−4.94541e9	−0.256563	−0.128281	−	0.991738i	$-0.540946\pi$
$193$	−4.94541e9	−0.256563	−0.128281	+	0.991738i	$0.540946\pi$
$194$	2.28139e10	1.15636
$195$	−8.36203e8	−0.0414148
$196$	−1.51035e9	−0.0731013
$197$	3.44918e10	1.63161	0.815807	−	0.578324i	$-0.196293\pi$
$197$	3.44918e10	1.63161	0.815807	+	0.578324i	$0.196293\pi$
$198$	1.56757e9	0.0724825
$199$	−1.72131e10	−0.778075	−0.389037	−	0.921222i	$-0.627192\pi$
$199$	−1.72131e10	−0.778075	−0.389037	+	0.921222i	$0.627192\pi$
$200$	1.53546e10	0.678583
$201$	−1.40077e10	−0.605319
$202$	1.64126e9	0.0693579
$203$	−2.57240e10	−1.06318
$204$	−4.14859e8	−0.0167712
$205$	−7.21071e9	−0.285158
$206$	4.92223e10	1.90441
$207$	−1.23745e10	−0.468446
$208$	1.10970e10	0.411073
$209$	3.67837e8	0.0133351
$210$	−3.75968e9	−0.133403
$211$	2.21547e10	0.769477	0.384738	−	0.923026i	$-0.374292\pi$
$211$	2.21547e10	0.769477	0.384738	+	0.923026i	$0.374292\pi$
$212$	−5.32403e9	−0.181021
$213$	−8.74073e9	−0.290964
$214$	5.65695e9	0.184383
$215$	−9.50228e9	−0.303288
$216$	4.38302e9	0.137004
$217$	1.36315e10	0.417325
$218$	4.57869e9	0.137305
$219$	3.72903e10	1.09546
$220$	−5.49985e8	−0.0158288
$221$	−8.58573e8	−0.0242109
$222$	−2.39910e10	−0.662919
$223$	−4.46986e9	−0.121038	−0.0605190	−	0.998167i	$-0.519276\pi$
$223$	−4.46986e9	−0.121038	−0.0605190	+	0.998167i	$0.519276\pi$
$224$	2.56581e10	0.680939
$225$	−1.22149e10	−0.317737
$226$	8.91216e9	0.227245
$227$	1.10694e8	0.00276698	0.00138349	−	0.999999i	$-0.499560\pi$
$227$	1.10694e8	0.00276698	0.00138349	+	0.999999i	$0.499560\pi$
$228$	−6.79651e8	−0.0166563
$229$	−6.91253e10	−1.66103	−0.830515	−	0.556997i	$-0.811954\pi$
$229$	−6.91253e10	−1.66103	−0.830515	+	0.556997i	$0.811954\pi$
$230$	1.52533e10	0.359408
$231$	4.15174e9	0.0959348
$232$	−3.69656e10	−0.837725
$233$	−6.67113e9	−0.148285	−0.0741426	−	0.997248i	$-0.523622\pi$
$233$	−6.67113e9	−0.148285	−0.0741426	+	0.997248i	$0.523622\pi$
$234$	−5.99422e9	−0.130696
$235$	−7.95730e9	−0.170200
$236$	2.46853e9	0.0518006
$237$	−1.73993e10	−0.358231
$238$	−3.86026e9	−0.0779866
$239$	1.60016e10	0.317229	0.158615	−	0.987341i	$-0.449297\pi$
$239$	1.60016e10	0.317229	0.158615	+	0.987341i	$0.449297\pi$
$240$	−7.95668e9	−0.154804
$241$	−3.22187e9	−0.0615220	−0.0307610	−	0.999527i	$-0.509793\pi$
$241$	−3.22187e9	−0.0615220	−0.0307610	+	0.999527i	$0.509793\pi$
$242$	−6.09482e10	−1.14233
$243$	−3.48678e9	−0.0641500
$244$	−2.71822e9	−0.0490942
$245$	2.24121e9	0.0397406
$246$	−5.16892e10	−0.899894
$247$	−1.40657e9	−0.0240451
$248$	1.95885e10	0.328829
$249$	−2.73317e10	−0.450578
$250$	3.08521e10	0.499523
$251$	−5.76479e10	−0.916752	−0.458376	−	0.888758i	$-0.651569\pi$
$251$	−5.76479e10	−0.916752	−0.458376	+	0.888758i	$0.651569\pi$
$252$	−7.67115e9	−0.119828
$253$	−1.68439e10	−0.258464
$254$	−1.41345e10	−0.213074
$255$	6.15609e8	0.00911747
$256$	7.07641e10	1.02975
$257$	−1.30863e10	−0.187120	−0.0935598	−	0.995614i	$-0.529825\pi$
$257$	−1.30863e10	−0.187120	−0.0935598	+	0.995614i	$0.529825\pi$
$258$	−6.81160e10	−0.957107
$259$	−6.35408e10	−0.877412
$260$	2.10309e9	0.0285415
$261$	2.94069e10	0.392253
$262$	2.95422e9	0.0387335
$263$	−1.22943e11	−1.58454	−0.792270	−	0.610170i	$-0.791101\pi$
$263$	−1.22943e11	−1.58454	−0.792270	+	0.610170i	$0.791101\pi$
$264$	5.96608e9	0.0755912
$265$	7.90032e9	0.0984098
$266$	−6.32414e9	−0.0774523
$267$	−1.41173e10	−0.170001
$268$	3.52300e10	0.417163
$269$	2.20233e10	0.256447	0.128224	−	0.991745i	$-0.459072\pi$
$269$	2.20233e10	0.256447	0.128224	+	0.991745i	$0.459072\pi$
$270$	4.29795e9	0.0492180
$271$	−1.58720e10	−0.178760	−0.0893798	−	0.995998i	$-0.528488\pi$
$271$	−1.58720e10	−0.178760	−0.0893798	+	0.995998i	$0.528488\pi$
$272$	−8.16954e9	−0.0904977
$273$	−1.58758e10	−0.172983
$274$	−2.18923e10	−0.234647
$275$	−1.66266e10	−0.175310
$276$	3.11223e10	0.322835
$277$	1.26897e10	0.129506	0.0647532	−	0.997901i	$-0.479374\pi$
$277$	1.26897e10	0.129506	0.0647532	+	0.997901i	$0.479374\pi$
$278$	−1.90567e10	−0.191358
$279$	−1.55831e10	−0.153970
$280$	−1.43091e10	−0.139124
$281$	−1.28463e11	−1.22913	−0.614567	−	0.788865i	$-0.710669\pi$
$281$	−1.28463e11	−1.22913	−0.614567	+	0.788865i	$0.710669\pi$
$282$	−5.70410e10	−0.537114
$283$	8.79744e10	0.815300	0.407650	−	0.913138i	$-0.366348\pi$
$283$	8.79744e10	0.815300	0.407650	+	0.913138i	$0.366348\pi$
$284$	2.19833e10	0.200521
$285$	1.00853e9	0.00905500
$286$	−8.15921e9	−0.0721109
$287$	−1.36900e11	−1.19106
$288$	−2.93315e10	−0.251228
$289$	−1.17956e11	−0.994670
$290$	−3.62481e10	−0.300950
$291$	−6.90737e10	−0.564670
$292$	−9.37868e10	−0.754951
$293$	−9.48080e10	−0.751520	−0.375760	−	0.926717i	$-0.622618\pi$
$293$	−9.48080e10	−0.751520	−0.375760	+	0.926717i	$0.622618\pi$
$294$	1.60658e10	0.125412
$295$	−3.66305e9	−0.0281607
$296$	−9.13085e10	−0.691351
$297$	−4.74614e9	−0.0353945
$298$	6.71381e10	0.493169
$299$	6.44092e10	0.466045
$300$	3.07210e10	0.218972
$301$	−1.80407e11	−1.26679
$302$	−3.07270e11	−2.12564
$303$	−4.96925e9	−0.0338688
$304$	−1.33839e10	−0.0898776
$305$	4.03356e9	0.0266894
$306$	4.41293e9	0.0287727
$307$	2.65087e11	1.70320	0.851601	−	0.524191i	$-0.175632\pi$
$307$	2.65087e11	1.70320	0.851601	+	0.524191i	$0.175632\pi$
$308$	−1.04418e10	−0.0661146
$309$	−1.49031e11	−0.929957
$310$	1.92083e10	0.118130
$311$	2.17731e11	1.31977	0.659885	−	0.751367i	$-0.270605\pi$
$311$	2.17731e11	1.31977	0.659885	+	0.751367i	$0.270605\pi$
$312$	−2.28137e10	−0.136301
$313$	−2.32312e11	−1.36811	−0.684056	−	0.729430i	$-0.739786\pi$
$313$	−2.32312e11	−1.36811	−0.684056	+	0.729430i	$0.739786\pi$
$314$	1.63556e11	0.949473
$315$	1.13832e10	0.0651429
$316$	4.37599e10	0.246879
$317$	2.47206e11	1.37497	0.687483	−	0.726200i	$-0.258715\pi$
$317$	2.47206e11	1.37497	0.687483	+	0.726200i	$0.258715\pi$
$318$	5.66325e10	0.310559
$319$	4.00280e10	0.216424
$320$	−1.41389e10	−0.0753773
$321$	−1.71276e10	−0.0900375
$322$	2.89593e11	1.50119
$323$	1.03551e9	0.00529352
$324$	8.76942e9	0.0442098
$325$	6.35786e10	0.316108
$326$	−1.01003e11	−0.495287
$327$	−1.38629e10	−0.0670487
$328$	−1.96726e11	−0.938490
$329$	−1.51074e11	−0.710901
$330$	5.85027e9	0.0271559
$331$	1.18106e11	0.540810	0.270405	−	0.962747i	$-0.412842\pi$
$331$	1.18106e11	0.540810	0.270405	+	0.962747i	$0.412842\pi$
$332$	6.87405e10	0.310521
$333$	7.26378e10	0.323716
$334$	−3.88115e11	−1.70648
$335$	−5.22777e10	−0.226785
$336$	−1.51063e11	−0.646592
$337$	2.37871e11	1.00463	0.502315	−	0.864685i	$-0.332482\pi$
$337$	2.37871e11	1.00463	0.502315	+	0.864685i	$0.332482\pi$
$338$	−2.52501e11	−1.05230
$339$	−2.69834e10	−0.110968
$340$	−1.54828e9	−0.00628342
$341$	−2.12114e10	−0.0849521
$342$	7.22956e9	0.0285755
$343$	2.74153e11	1.06947
$344$	−2.59246e11	−0.998156
$345$	−4.61824e10	−0.175505
$346$	2.32269e11	0.871263
$347$	2.95829e11	1.09536	0.547682	−	0.836687i	$-0.315510\pi$
$347$	2.95829e11	1.09536	0.547682	+	0.836687i	$0.315510\pi$
$348$	−7.39596e10	−0.270326
$349$	2.93184e11	1.05785	0.528926	−	0.848668i	$-0.322595\pi$
$349$	2.93184e11	1.05785	0.528926	+	0.848668i	$0.322595\pi$
$350$	2.85858e11	1.01823
$351$	1.81487e10	0.0638212
$352$	−3.99254e10	−0.138614
$353$	−1.49690e10	−0.0513104	−0.0256552	−	0.999671i	$-0.508167\pi$
$353$	−1.49690e10	−0.0513104	−0.0256552	+	0.999671i	$0.508167\pi$
$354$	−2.62582e10	−0.0888688
$355$	−3.26210e10	−0.109011
$356$	3.55057e10	0.117158
$357$	1.16877e10	0.0380823
$358$	4.18986e11	1.34811
$359$	−4.00848e11	−1.27366	−0.636832	−	0.771002i	$-0.719756\pi$
$359$	−4.00848e11	−1.27366	−0.636832	+	0.771002i	$0.719756\pi$
$360$	1.63577e10	0.0513289
$361$	−3.20991e11	−0.994743
$362$	−3.39958e11	−1.04049
$363$	1.84533e11	0.557821
$364$	3.99284e10	0.119214
$365$	1.39170e11	0.410420
$366$	2.89141e10	0.0842258
$367$	−1.86564e11	−0.536823	−0.268412	−	0.963304i	$-0.586499\pi$
$367$	−1.86564e11	−0.536823	−0.268412	+	0.963304i	$0.586499\pi$
$368$	6.12870e11	1.74202
$369$	1.56500e11	0.439435
$370$	−8.95362e10	−0.248365
$371$	1.49993e11	0.411043
$372$	3.91922e10	0.106110
$373$	1.70506e11	0.456091	0.228045	−	0.973651i	$-0.426767\pi$
$373$	1.70506e11	0.456091	0.228045	+	0.973651i	$0.426767\pi$
$374$	6.00678e9	0.0158752
$375$	−9.34113e10	−0.243926
$376$	−2.17095e11	−0.560150
$377$	−1.53063e11	−0.390242
$378$	8.15992e10	0.205576
$379$	6.72931e11	1.67531	0.837653	−	0.546202i	$-0.183927\pi$
$379$	6.72931e11	1.67531	0.837653	+	0.546202i	$0.183927\pi$
$380$	−2.53651e9	−0.00624036
$381$	4.27953e10	0.104048
$382$	9.67509e11	2.32472
$383$	−3.81727e11	−0.906480	−0.453240	−	0.891389i	$-0.649732\pi$
$383$	−3.81727e11	−0.906480	−0.453240	+	0.891389i	$0.649732\pi$
$384$	−2.86757e11	−0.673014
$385$	1.54946e10	0.0359424
$386$	−1.32304e11	−0.303340
$387$	2.06235e11	0.467373
$388$	1.73723e11	0.389149
$389$	−2.35278e11	−0.520964	−0.260482	−	0.965479i	$-0.583881\pi$
$389$	−2.35278e11	−0.520964	−0.260482	+	0.965479i	$0.583881\pi$
$390$	−2.23709e10	−0.0489657
$391$	−4.74178e10	−0.102600
$392$	6.11456e10	0.130791
$393$	−8.94452e9	−0.0189143
$394$	9.22756e11	1.92910
$395$	−6.49352e10	−0.134213
$396$	1.19367e10	0.0243926
$397$	1.06947e11	0.216079	0.108040	−	0.994147i	$-0.465543\pi$
$397$	1.06947e11	0.216079	0.108040	+	0.994147i	$0.465543\pi$
$398$	−4.60502e11	−0.919936
$399$	1.91476e10	0.0378214
$400$	6.04967e11	1.18158
$401$	−4.34250e11	−0.838667	−0.419334	−	0.907832i	$-0.637736\pi$
$401$	−4.34250e11	−0.838667	−0.419334	+	0.907832i	$0.637736\pi$
$402$	−3.74747e11	−0.715683
$403$	8.11102e10	0.153180
$404$	1.24979e10	0.0233411
$405$	−1.30129e10	−0.0240341
$406$	−6.88193e11	−1.25702
$407$	9.88730e10	0.178609
$408$	1.67953e10	0.0300067
$409$	9.37763e11	1.65706	0.828530	−	0.559945i	$-0.189178\pi$
$409$	9.37763e11	1.65706	0.828530	+	0.559945i	$0.189178\pi$
$410$	−1.92908e11	−0.337149
$411$	6.62836e10	0.114582
$412$	3.74819e11	0.640891
$413$	−6.95453e10	−0.117623
$414$	−3.31053e11	−0.553855
$415$	−1.02004e11	−0.168811
$416$	1.52671e11	0.249940
$417$	5.76981e10	0.0934436
$418$	9.84072e9	0.0157664
$419$	4.16830e11	0.660687	0.330344	−	0.943861i	$-0.392835\pi$
$419$	4.16830e11	0.660687	0.330344	+	0.943861i	$0.392835\pi$
$420$	−2.86293e10	−0.0448940
$421$	5.26815e11	0.817314	0.408657	−	0.912688i	$-0.365997\pi$
$421$	5.26815e11	0.817314	0.408657	+	0.912688i	$0.365997\pi$
$422$	5.92704e11	0.909770
$423$	1.72703e11	0.262283
$424$	2.15540e11	0.323878
$425$	−4.68063e10	−0.0695912
$426$	−2.33840e11	−0.344013
$427$	7.65797e10	0.111478
$428$	4.30766e10	0.0620504
$429$	2.47037e10	0.0352131
$430$	−2.54214e11	−0.358584
$431$	−8.48282e11	−1.18411	−0.592056	−	0.805897i	$-0.701684\pi$
$431$	−8.48282e11	−1.18411	−0.592056	+	0.805897i	$0.701684\pi$
$432$	1.72690e11	0.238556
$433$	5.30333e11	0.725025	0.362513	−	0.931979i	$-0.381919\pi$
$433$	5.30333e11	0.725025	0.362513	+	0.931979i	$0.381919\pi$
$434$	3.64682e11	0.493413
$435$	1.09749e11	0.146959
$436$	3.48659e10	0.0462074
$437$	−7.76832e10	−0.101897
$438$	9.97625e11	1.29519
$439$	8.03608e11	1.03265	0.516326	−	0.856392i	$-0.327299\pi$
$439$	8.03608e11	1.03265	0.516326	+	0.856392i	$0.327299\pi$
$440$	2.22658e10	0.0283205
$441$	−4.86426e10	−0.0612411
$442$	−2.29693e10	−0.0286252
$443$	1.27320e12	1.57065	0.785323	−	0.619086i	$-0.212497\pi$
$443$	1.27320e12	1.57065	0.785323	+	0.619086i	$0.212497\pi$
$444$	−1.82687e11	−0.223092
$445$	−5.26868e10	−0.0636915
$446$	−1.19582e11	−0.143106
$447$	−2.03275e11	−0.240824
$448$	−2.68436e11	−0.314840
$449$	−7.80521e11	−0.906308	−0.453154	−	0.891432i	$-0.649701\pi$
$449$	−7.80521e11	−0.906308	−0.453154	+	0.891432i	$0.649701\pi$
$450$	−3.26784e11	−0.375668
$451$	2.13024e11	0.242457
$452$	6.78645e10	0.0764750
$453$	9.30325e11	1.03799
$454$	2.96138e9	0.00327147
$455$	−5.92497e10	−0.0648090
$456$	2.75153e10	0.0298011
$457$	1.61465e12	1.73164	0.865818	−	0.500359i	$-0.166799\pi$
$457$	1.61465e12	1.73164	0.865818	+	0.500359i	$0.166799\pi$
$458$	−1.84930e12	−1.96387
$459$	−1.33610e10	−0.0140502
$460$	1.16151e11	0.120952
$461$	6.00901e11	0.619654	0.309827	−	0.950793i	$-0.399729\pi$
$461$	6.00901e11	0.619654	0.309827	+	0.950793i	$0.399729\pi$
$462$	1.11071e11	0.113426
$463$	1.50181e12	1.51880	0.759400	−	0.650623i	$-0.225492\pi$
$463$	1.50181e12	1.51880	0.759400	+	0.650623i	$0.225492\pi$
$464$	−1.45643e12	−1.45868
$465$	−5.81572e10	−0.0576853
$466$	−1.78472e11	−0.175321
$467$	−4.12507e11	−0.401333	−0.200667	−	0.979660i	$-0.564311\pi$
$467$	−4.12507e11	−0.401333	−0.200667	+	0.979660i	$0.564311\pi$
$468$	−4.56449e10	−0.0439831
$469$	−9.92525e11	−0.947248
$470$	−2.12881e11	−0.201232
$471$	−4.95199e11	−0.463645
$472$	−9.99371e10	−0.0926803
$473$	2.80723e11	0.257871
$474$	−4.65481e11	−0.423545
$475$	−7.66814e10	−0.0691144
$476$	−2.93952e10	−0.0262449
$477$	−1.71467e11	−0.151652
$478$	4.28090e11	0.375067
$479$	−1.35808e11	−0.117873	−0.0589365	−	0.998262i	$-0.518771\pi$
$479$	−1.35808e11	−0.117873	−0.0589365	+	0.998262i	$0.518771\pi$
$480$	−1.09467e11	−0.0941237
$481$	−3.78080e11	−0.322056
$482$	−8.61943e10	−0.0727389
$483$	−8.76802e11	−0.733060
$484$	−4.64110e11	−0.384429
$485$	−2.57788e11	−0.211556
$486$	−9.32817e10	−0.0758461
$487$	4.64384e11	0.374108	0.187054	−	0.982350i	$-0.440106\pi$
$487$	4.64384e11	0.374108	0.187054	+	0.982350i	$0.440106\pi$
$488$	1.10046e11	0.0878382
$489$	3.05809e11	0.241858
$490$	5.99588e10	0.0469862
$491$	−2.27566e12	−1.76702	−0.883510	−	0.468412i	$-0.844826\pi$
$491$	−2.27566e12	−1.76702	−0.883510	+	0.468412i	$0.844826\pi$
$492$	−3.93604e11	−0.302842
$493$	1.12685e11	0.0859119
$494$	−3.76299e10	−0.0284290
$495$	−1.77129e10	−0.0132607
$496$	7.71784e11	0.572569
$497$	−6.19330e11	−0.455322
$498$	−7.31204e11	−0.532729
$499$	−9.59453e11	−0.692742	−0.346371	−	0.938098i	$-0.612586\pi$
$499$	−9.59453e11	−0.692742	−0.346371	+	0.938098i	$0.612586\pi$
$500$	2.34933e11	0.168105
$501$	1.17510e12	0.833306
$502$	−1.54225e12	−1.08390
$503$	1.59860e12	1.11348	0.556742	−	0.830685i	$-0.312051\pi$
$503$	1.59860e12	1.11348	0.556742	+	0.830685i	$0.312051\pi$
$504$	3.10562e11	0.214393
$505$	−1.85456e10	−0.0126891
$506$	−4.50622e11	−0.305587
$507$	7.64500e11	0.513856
$508$	−1.07632e11	−0.0717059
$509$	1.17983e12	0.779096	0.389548	−	0.921006i	$-0.372631\pi$
$509$	1.17983e12	0.779096	0.389548	+	0.921006i	$0.372631\pi$
$510$	1.64693e10	0.0107798
$511$	2.64223e12	1.71426
$512$	8.05557e10	0.0518062
$513$	−2.18890e10	−0.0139540
$514$	−3.50098e11	−0.221236
$515$	−5.56193e11	−0.348412
$516$	−5.18691e11	−0.322096
$517$	2.35080e11	0.144713
$518$	−1.69990e12	−1.03738
$519$	−7.03243e11	−0.425454
$520$	−8.51422e10	−0.0510658
$521$	−7.90131e11	−0.469818	−0.234909	−	0.972017i	$-0.575479\pi$
$521$	−7.90131e11	−0.469818	−0.234909	+	0.972017i	$0.575479\pi$
$522$	7.86720e11	0.463770
$523$	−1.02714e12	−0.600303	−0.300152	−	0.953891i	$-0.597037\pi$
$523$	−1.02714e12	−0.600303	−0.300152	+	0.953891i	$0.597037\pi$
$524$	2.24959e10	0.0130350
$525$	−8.65494e11	−0.497219
$526$	−3.28909e12	−1.87344
$527$	−5.97130e10	−0.0337226
$528$	2.35062e11	0.131622
$529$	1.75609e12	0.974979
$530$	2.11357e11	0.116352
$531$	7.95020e10	0.0433963
$532$	−4.81572e10	−0.0260651
$533$	−8.14582e11	−0.437182
$534$	−3.77679e11	−0.200996
$535$	−6.39214e10	−0.0337329
$536$	−1.42626e12	−0.746377
$537$	−1.26857e12	−0.658309
$538$	5.89188e11	0.303203
$539$	−6.62113e10	−0.0337896
$540$	3.27281e10	0.0165634
$541$	2.60129e12	1.30557	0.652786	−	0.757542i	$-0.273600\pi$
$541$	2.60129e12	1.30557	0.652786	+	0.757542i	$0.273600\pi$
$542$	−4.24622e11	−0.211352
$543$	1.02929e12	0.508090
$544$	−1.12396e11	−0.0550244
$545$	−5.17374e10	−0.0251201
$546$	−4.24725e11	−0.204522
$547$	1.91631e12	0.915215	0.457608	−	0.889154i	$-0.348706\pi$
$547$	1.91631e12	0.915215	0.457608	+	0.889154i	$0.348706\pi$
$548$	−1.66706e11	−0.0789658
$549$	−8.75435e10	−0.0411290
$550$	−4.44811e11	−0.207273
$551$	1.84608e11	0.0853232
$552$	−1.25997e12	−0.577609
$553$	−1.23284e12	−0.560586
$554$	3.39485e11	0.153118
$555$	2.71089e11	0.121281
$556$	−1.45113e11	−0.0643978
$557$	3.32274e12	1.46267	0.731337	−	0.682016i	$-0.238897\pi$
$557$	3.32274e12	1.46267	0.731337	+	0.682016i	$0.238897\pi$
$558$	−4.16893e11	−0.182042
$559$	−1.07346e12	−0.464977
$560$	−5.63776e11	−0.242248
$561$	−1.81868e10	−0.00775216
$562$	−3.43676e12	−1.45323
$563$	1.35624e12	0.568918	0.284459	−	0.958688i	$-0.408186\pi$
$563$	1.35624e12	0.568918	0.284459	+	0.958688i	$0.408186\pi$
$564$	−4.34357e11	−0.180755
$565$	−1.00704e11	−0.0415747
$566$	2.35357e12	0.963948
$567$	−2.47059e11	−0.100387
$568$	−8.89982e11	−0.358768
$569$	−1.80406e12	−0.721516	−0.360758	−	0.932659i	$-0.617482\pi$
$569$	−1.80406e12	−0.721516	−0.360758	+	0.932659i	$0.617482\pi$
$570$	2.69812e10	0.0107059
$571$	−3.82279e12	−1.50493	−0.752467	−	0.658629i	$-0.771136\pi$
$571$	−3.82279e12	−1.50493	−0.752467	+	0.658629i	$0.771136\pi$
$572$	−6.21309e10	−0.0242675
$573$	−2.92934e12	−1.13520
$574$	−3.66247e12	−1.40822
$575$	3.51136e12	1.33959
$576$	3.06867e11	0.116158
$577$	3.15806e12	1.18612	0.593060	−	0.805158i	$-0.297920\pi$
$577$	3.15806e12	1.18612	0.593060	+	0.805158i	$0.297920\pi$
$578$	−3.15566e12	−1.17602
$579$	4.00578e11	0.148127
$580$	−2.76022e11	−0.101279
$581$	−1.93661e12	−0.705098
$582$	−1.84792e12	−0.667622
$583$	−2.33397e11	−0.0836733
$584$	3.79690e12	1.35074
$585$	6.77324e10	0.0239109
$586$	−2.53639e12	−0.888540
$587$	2.31843e12	0.805977	0.402988	−	0.915205i	$-0.367972\pi$
$587$	2.31843e12	0.805977	0.402988	+	0.915205i	$0.367972\pi$
$588$	1.22338e11	0.0422051
$589$	−9.78260e10	−0.0334916
$590$	−9.79973e10	−0.0332951
$591$	−2.79383e12	−0.942013
$592$	−3.59753e12	−1.20381
$593$	3.39023e12	1.12586	0.562928	−	0.826506i	$-0.309675\pi$
$593$	3.39023e12	1.12586	0.562928	+	0.826506i	$0.309675\pi$
$594$	−1.26973e11	−0.0418478
$595$	4.36194e10	0.0142677
$596$	5.11244e11	0.165966
$597$	1.39426e12	0.449222
$598$	1.72313e12	0.551016
$599$	1.25426e12	0.398076	0.199038	−	0.979992i	$-0.436218\pi$
$599$	1.25426e12	0.398076	0.199038	+	0.979992i	$0.436218\pi$
$600$	−1.24372e12	−0.391780
$601$	5.55160e12	1.73573	0.867867	−	0.496797i	$-0.165491\pi$
$601$	5.55160e12	1.73573	0.867867	+	0.496797i	$0.165491\pi$
$602$	−4.82641e12	−1.49775
$603$	1.13462e12	0.349481
$604$	−2.33981e12	−0.715342
$605$	6.88692e11	0.208990
$606$	−1.32942e11	−0.0400438
$607$	6.35706e12	1.90067	0.950337	−	0.311223i	$-0.100739\pi$
$607$	6.35706e12	1.90067	0.950337	+	0.311223i	$0.100739\pi$
$608$	−1.84135e11	−0.0546473
$609$	2.08365e12	0.613827
$610$	1.07910e11	0.0315555
$611$	−8.98923e11	−0.260938
$612$	3.36036e10	0.00968288
$613$	−1.99633e12	−0.571032	−0.285516	−	0.958374i	$-0.592165\pi$
$613$	−1.99633e12	−0.571032	−0.285516	+	0.958374i	$0.592165\pi$
$614$	7.09185e12	2.01373
$615$	5.84068e11	0.164636
$616$	4.22730e11	0.118291
$617$	6.38934e9	0.00177489	0.000887447	−	1.00000i	$-0.499718\pi$
$617$	6.38934e9	0.00177489	0.000887447		1.00000i	$0.499718\pi$
$618$	−3.98701e12	−1.09951
$619$	−2.99662e12	−0.820398	−0.410199	−	0.911996i	$-0.634541\pi$
$619$	−2.99662e12	−0.820398	−0.410199	+	0.911996i	$0.634541\pi$
$620$	1.46268e11	0.0397545
$621$	1.00233e12	0.270458
$622$	5.82493e12	1.56039
$623$	−1.00029e12	−0.266030
$624$	−8.98853e11	−0.237333
$625$	3.28760e12	0.861823
$626$	−6.21502e12	−1.61755
$627$	−2.97948e10	−0.00769905
$628$	1.24545e12	0.319527
$629$	2.78342e11	0.0709006
$630$	3.04534e11	0.0770200
$631$	1.38378e12	0.347484	0.173742	−	0.984791i	$-0.444414\pi$
$631$	1.38378e12	0.347484	0.173742	+	0.984791i	$0.444414\pi$
$632$	−1.77159e12	−0.441710
$633$	−1.79453e12	−0.444258
$634$	6.61348e12	1.62565
$635$	1.59715e11	0.0389820
$636$	4.31246e11	0.104513
$637$	2.53185e11	0.0609272
$638$	1.07087e12	0.255883
$639$	7.07999e11	0.167988
$640$	−1.07020e12	−0.252147
$641$	−7.20380e12	−1.68539	−0.842695	−	0.538391i	$-0.819032\pi$
$641$	−7.20380e12	−1.68539	−0.842695	+	0.538391i	$0.819032\pi$
$642$	−4.58213e11	−0.106453
$643$	−7.58171e10	−0.0174911	−0.00874556	−	0.999962i	$-0.502784\pi$
$643$	−7.58171e10	−0.0174911	−0.00874556	+	0.999962i	$0.502784\pi$
$644$	2.20519e12	0.505197
$645$	7.69685e11	0.175103
$646$	2.77030e10	0.00625865
$647$	4.30805e11	0.0966522	0.0483261	−	0.998832i	$-0.484611\pi$
$647$	4.30805e11	0.0966522	0.0483261	+	0.998832i	$0.484611\pi$
$648$	−3.55025e11	−0.0790990
$649$	1.08216e11	0.0239437
$650$	1.70091e12	0.373742
$651$	−1.10415e12	−0.240943
$652$	−7.69122e11	−0.166679
$653$	−4.31846e12	−0.929436	−0.464718	−	0.885459i	$-0.653844\pi$
$653$	−4.31846e12	−0.929436	−0.464718	+	0.885459i	$0.653844\pi$
$654$	−3.70874e11	−0.0792732
$655$	−3.33816e10	−0.00708632
$656$	−7.75096e12	−1.63414
$657$	−3.02052e12	−0.632466
$658$	−4.04168e12	−0.840515
$659$	5.42048e12	1.11958	0.559788	−	0.828636i	$-0.310883\pi$
$659$	5.42048e12	1.11958	0.559788	+	0.828636i	$0.310883\pi$
$660$	4.45488e10	0.00913878
$661$	4.32120e12	0.880437	0.440219	−	0.897891i	$-0.354901\pi$
$661$	4.32120e12	0.880437	0.440219	+	0.897891i	$0.354901\pi$
$662$	3.15967e12	0.639413
$663$	6.95444e10	0.0139782
$664$	−2.78292e12	−0.555577
$665$	7.14604e10	0.0141699
$666$	1.94327e12	0.382736
$667$	−8.45348e12	−1.65375
$668$	−2.95542e12	−0.574282
$669$	3.62058e11	0.0698813
$670$	−1.39858e12	−0.268133
$671$	−1.19162e11	−0.0226928
$672$	−2.07831e12	−0.393140
$673$	−7.53010e12	−1.41492	−0.707462	−	0.706751i	$-0.750160\pi$
$673$	−7.53010e12	−1.41492	−0.707462	+	0.706751i	$0.750160\pi$
$674$	6.36373e12	1.18780
$675$	9.89406e11	0.183446
$676$	−1.92275e12	−0.354130
$677$	4.96788e12	0.908912	0.454456	−	0.890769i	$-0.349834\pi$
$677$	4.96788e12	0.908912	0.454456	+	0.890769i	$0.349834\pi$
$678$	−7.21885e11	−0.131200
$679$	−4.89427e12	−0.883637
$680$	6.26814e10	0.0112421
$681$	−8.96618e9	−0.00159752
$682$	−5.67466e11	−0.100441
$683$	7.07573e11	0.124417	0.0622083	−	0.998063i	$-0.480186\pi$
$683$	7.07573e11	0.124417	0.0622083	+	0.998063i	$0.480186\pi$
$684$	5.50518e10	0.00961654
$685$	2.47375e11	0.0429287
$686$	7.33438e12	1.26446
$687$	5.59915e12	0.958996
$688$	−1.02142e13	−1.73803
$689$	8.92486e11	0.150874
$690$	−1.23551e12	−0.207504
$691$	2.18601e12	0.364754	0.182377	−	0.983229i	$-0.441621\pi$
$691$	2.18601e12	0.364754	0.182377	+	0.983229i	$0.441621\pi$
$692$	1.76869e12	0.293207
$693$	−3.36291e11	−0.0553880
$694$	7.91429e12	1.29507
$695$	2.15334e11	0.0350090
$696$	2.99421e12	0.483661
$697$	5.99693e11	0.0962457
$698$	7.84352e12	1.25072
$699$	5.40362e11	0.0856125
$700$	2.17676e12	0.342664
$701$	4.70760e12	0.736324	0.368162	−	0.929762i	$-0.379987\pi$
$701$	4.70760e12	0.736324	0.368162	+	0.929762i	$0.379987\pi$
$702$	4.85532e11	0.0754572
$703$	4.55998e11	0.0704148
$704$	4.17701e11	0.0640898
$705$	6.44542e11	0.0982652
$706$	−4.00463e11	−0.0606655
$707$	−3.52100e11	−0.0530004
$708$	−1.99951e11	−0.0299071
$709$	−1.54756e12	−0.230006	−0.115003	−	0.993365i	$-0.536688\pi$
$709$	−1.54756e12	−0.230006	−0.115003	+	0.993365i	$0.536688\pi$
$710$	−8.72707e11	−0.128886
$711$	1.40934e12	0.206825
$712$	−1.43743e12	−0.209617
$713$	4.47961e12	0.649138
$714$	3.12681e11	0.0450256
$715$	9.21959e10	0.0131927
$716$	3.19051e12	0.453681
$717$	−1.29613e12	−0.183152
$718$	−1.07239e13	−1.50588
$719$	2.98027e12	0.415887	0.207944	−	0.978141i	$-0.433323\pi$
$719$	2.98027e12	0.415887	0.207944	+	0.978141i	$0.433323\pi$
$720$	6.44491e11	0.0893760
$721$	−1.05597e13	−1.45527
$722$	−8.58745e12	−1.17611
$723$	2.60971e11	0.0355198
$724$	−2.58872e12	−0.350156
$725$	−8.34446e12	−1.12170
$726$	4.93681e12	0.659525
$727$	1.01794e12	0.135150	0.0675751	−	0.997714i	$-0.478474\pi$
$727$	1.01794e12	0.135150	0.0675751	+	0.997714i	$0.478474\pi$
$728$	−1.61648e12	−0.213294
$729$	2.82430e11	0.0370370
$730$	3.72321e12	0.485249
$731$	7.90275e11	0.102365
$732$	2.20176e11	0.0283446
$733$	−3.38521e12	−0.433130	−0.216565	−	0.976268i	$-0.569485\pi$
$733$	−3.38521e12	−0.433130	−0.216565	+	0.976268i	$0.569485\pi$
$734$	−4.99114e12	−0.634699
$735$	−1.81538e11	−0.0229442
$736$	8.43181e12	1.05918
$737$	1.54442e12	0.192825
$738$	4.18682e12	0.519554
$739$	−4.84788e12	−0.597932	−0.298966	−	0.954264i	$-0.596642\pi$
$739$	−4.84788e12	−0.597932	−0.298966	+	0.954264i	$0.596642\pi$
$740$	−6.81802e11	−0.0835825
$741$	1.13932e11	0.0138824
$742$	4.01274e12	0.485986
$743$	6.68869e12	0.805177	0.402589	−	0.915381i	$-0.368111\pi$
$743$	6.68869e12	0.805177	0.402589	+	0.915381i	$0.368111\pi$
$744$	−1.58667e12	−0.189849
$745$	−7.58635e11	−0.0902256
$746$	4.56155e12	0.539247
$747$	2.21387e12	0.260142
$748$	4.57405e10	0.00534249
$749$	−1.21359e12	−0.140897
$750$	−2.49902e12	−0.288400
$751$	−5.48484e12	−0.629193	−0.314597	−	0.949225i	$-0.601869\pi$
$751$	−5.48484e12	−0.629193	−0.314597	+	0.949225i	$0.601869\pi$
$752$	−8.55348e12	−0.975355
$753$	4.66948e12	0.529287
$754$	−4.09489e12	−0.461393
$755$	3.47204e12	0.388887
$756$	6.21363e11	0.0691827
$757$	1.19762e12	0.132553	0.0662763	−	0.997801i	$-0.478888\pi$
$757$	1.19762e12	0.132553	0.0662763	+	0.997801i	$0.478888\pi$
$758$	1.80029e13	1.98075
$759$	1.36435e12	0.149224
$760$	1.02689e11	0.0111651
$761$	4.53518e12	0.490189	0.245094	−	0.969499i	$-0.421181\pi$
$761$	4.53518e12	0.490189	0.245094	+	0.969499i	$0.421181\pi$
$762$	1.14490e12	0.123018
$763$	−9.82268e11	−0.104923
$764$	7.36741e12	0.782338
$765$	−4.98644e10	−0.00526398
$766$	−1.02123e13	−1.07175
$767$	−4.13809e11	−0.0431738
$768$	−5.73189e12	−0.594528
$769$	3.02965e12	0.312409	0.156205	−	0.987725i	$-0.450074\pi$
$769$	3.02965e12	0.312409	0.156205	+	0.987725i	$0.450074\pi$
$770$	4.14525e11	0.0424955
$771$	1.05999e12	0.108034
$772$	−1.00747e12	−0.102083
$773$	6.30421e11	0.0635072	0.0317536	−	0.999496i	$-0.489891\pi$
$773$	6.30421e11	0.0635072	0.0317536	+	0.999496i	$0.489891\pi$
$774$	5.51740e12	0.552586
$775$	4.42184e12	0.440296
$776$	−7.03309e12	−0.696256
$777$	5.14680e12	0.506574
$778$	−6.29436e12	−0.615947
$779$	9.82458e11	0.0955863
$780$	−1.70350e11	−0.0164785
$781$	9.63713e11	0.0926868
$782$	−1.26857e12	−0.121306
$783$	−2.38196e12	−0.226468
$784$	2.40912e12	0.227739
$785$	−1.84812e12	−0.173707
$786$	−2.39292e11	−0.0223628
$787$	7.21786e12	0.670691	0.335345	−	0.942095i	$-0.391147\pi$
$787$	7.21786e12	0.670691	0.335345	+	0.942095i	$0.391147\pi$
$788$	7.02662e12	0.649200
$789$	9.95839e12	0.914835
$790$	−1.73721e12	−0.158683
$791$	−1.91193e12	−0.173651
$792$	−4.83252e11	−0.0436426
$793$	4.55665e11	0.0409182
$794$	2.86115e12	0.255475
$795$	−6.39926e11	−0.0568169
$796$	−3.50664e12	−0.309586
$797$	−1.09692e13	−0.962968	−0.481484	−	0.876455i	$-0.659902\pi$
$797$	−1.09692e13	−0.962968	−0.481484	+	0.876455i	$0.659902\pi$
$798$	5.12255e11	0.0447171
$799$	6.61784e11	0.0574455
$800$	8.32308e12	0.718421
$801$	1.14350e12	0.0981501
$802$	−1.16174e13	−0.991576
$803$	−4.11146e12	−0.348961
$804$	−2.85363e12	−0.240849
$805$	−3.27229e12	−0.274644
$806$	2.16993e12	0.181108
$807$	−1.78389e12	−0.148060
$808$	−5.05970e11	−0.0417613
$809$	−9.11493e12	−0.748144	−0.374072	−	0.927400i	$-0.622039\pi$
$809$	−9.11493e12	−0.748144	−0.374072	+	0.927400i	$0.622039\pi$
$810$	−3.48134e11	−0.0284160
$811$	−1.70270e11	−0.0138211	−0.00691056	−	0.999976i	$-0.502200\pi$
$811$	−1.70270e11	−0.0138211	−0.00691056	+	0.999976i	$0.502200\pi$
$812$	−5.24046e12	−0.423026
$813$	1.28563e12	0.103207
$814$	2.64514e12	0.211173
$815$	1.14130e12	0.0906130
$816$	6.61733e11	0.0522489
$817$	1.29468e12	0.101663
$818$	2.50879e13	1.95918
$819$	1.28594e12	0.0998721
$820$	−1.46896e12	−0.113461
$821$	−9.42511e11	−0.0724006	−0.0362003	−	0.999345i	$-0.511525\pi$
$821$	−9.42511e11	−0.0724006	−0.0362003	+	0.999345i	$0.511525\pi$
$822$	1.77328e12	0.135473
$823$	2.08266e13	1.58241	0.791203	−	0.611553i	$-0.209455\pi$
$823$	2.08266e13	1.58241	0.791203	+	0.611553i	$0.209455\pi$
$824$	−1.51743e13	−1.14667
$825$	1.34676e12	0.101215
$826$	−1.86054e12	−0.139069
$827$	−1.79987e13	−1.33803	−0.669014	−	0.743250i	$-0.733283\pi$
$827$	−1.79987e13	−1.33803	−0.669014	+	0.743250i	$0.733283\pi$
$828$	−2.52091e12	−0.186389
$829$	−1.31848e13	−0.969571	−0.484786	−	0.874633i	$-0.661102\pi$
$829$	−1.31848e13	−0.969571	−0.484786	+	0.874633i	$0.661102\pi$
$830$	−2.72891e12	−0.199589
$831$	−1.02786e12	−0.0747705
$832$	−1.59725e12	−0.115563
$833$	−1.86394e11	−0.0134131
$834$	1.54359e12	0.110481
$835$	4.38555e12	0.312201
$836$	7.49353e10	0.00530589
$837$	1.26223e12	0.0888943
$838$	1.11514e13	0.781146
$839$	6.35148e12	0.442533	0.221267	−	0.975213i	$-0.428981\pi$
$839$	6.35148e12	0.442533	0.221267	+	0.975213i	$0.428981\pi$
$840$	1.15904e12	0.0803233
$841$	5.58184e12	0.384765
$842$	1.40938e13	0.966329
$843$	1.04055e13	0.709641
$844$	4.51333e12	0.306165
$845$	2.85317e12	0.192518
$846$	4.62032e12	0.310103
$847$	1.30752e13	0.872920
$848$	8.49224e12	0.563950
$849$	−7.12592e12	−0.470713
$850$	−1.25221e12	−0.0822793
$851$	−2.08809e13	−1.36479
$852$	−1.78065e12	−0.115771
$853$	9.92635e12	0.641976	0.320988	−	0.947083i	$-0.395985\pi$
$853$	9.92635e12	0.641976	0.320988	+	0.947083i	$0.395985\pi$
$854$	2.04873e12	0.131803
$855$	−8.16912e10	−0.00522791
$856$	−1.74393e12	−0.111019
$857$	−3.48897e12	−0.220945	−0.110472	−	0.993879i	$-0.535236\pi$
$857$	−3.48897e12	−0.220945	−0.110472	+	0.993879i	$0.535236\pi$
$858$	6.60896e11	0.0416332
$859$	3.68799e12	0.231111	0.115555	−	0.993301i	$-0.463135\pi$
$859$	3.68799e12	0.231111	0.115555	+	0.993301i	$0.463135\pi$
$860$	−1.93579e12	−0.120674
$861$	1.10889e13	0.687661
$862$	−2.26940e13	−1.40000
$863$	1.46271e12	0.0897655	0.0448827	−	0.998992i	$-0.485709\pi$
$863$	1.46271e12	0.0897655	0.0448827	+	0.998992i	$0.485709\pi$
$864$	2.37585e12	0.145047
$865$	−2.62455e12	−0.159398
$866$	1.41880e13	0.857214
$867$	9.55442e12	0.574273
$868$	2.77699e12	0.166049
$869$	1.91836e12	0.114115
$870$	2.93609e12	0.173753
$871$	−5.90572e12	−0.347689
$872$	−1.41152e12	−0.0826731
$873$	5.59497e12	0.326012
$874$	−2.07825e12	−0.120475
$875$	−6.61872e12	−0.381714
$876$	7.59673e12	0.435871
$877$	−4.67161e12	−0.266667	−0.133333	−	0.991071i	$-0.542568\pi$
$877$	−4.67161e12	−0.266667	−0.133333	+	0.991071i	$0.542568\pi$
$878$	2.14989e13	1.22093
$879$	7.67945e12	0.433891
$880$	8.77268e11	0.0493129
$881$	−1.19601e13	−0.668874	−0.334437	−	0.942418i	$-0.608546\pi$
$881$	−1.19601e13	−0.668874	−0.334437	+	0.942418i	$0.608546\pi$
$882$	−1.30133e12	−0.0724068
$883$	3.43104e13	1.89934	0.949670	−	0.313252i	$-0.101418\pi$
$883$	3.43104e13	1.89934	0.949670	+	0.313252i	$0.101418\pi$
$884$	−1.74907e11	−0.00963324
$885$	2.96707e11	0.0162586
$886$	3.40617e13	1.85701
$887$	−7.13921e12	−0.387252	−0.193626	−	0.981075i	$-0.562025\pi$
$887$	−7.13921e12	−0.387252	−0.193626	+	0.981075i	$0.562025\pi$
$888$	7.39599e12	0.399152
$889$	3.03229e12	0.162822
$890$	−1.40953e12	−0.0753040
$891$	3.84437e11	0.0204350
$892$	−9.10593e11	−0.0481595
$893$	1.08418e12	0.0570519
$894$	−5.43819e12	−0.284731
$895$	−4.73439e12	−0.246638
$896$	−2.03184e13	−1.05318
$897$	−5.21715e12	−0.269071
$898$	−2.08812e13	−1.07155
$899$	−1.06454e13	−0.543556
$900$	−2.48840e12	−0.126424
$901$	−6.57045e11	−0.0332150
$902$	5.69901e12	0.286662
$903$	1.46129e13	0.731380
$904$	−2.74745e12	−0.136827
$905$	3.84140e12	0.190358
$906$	2.48889e13	1.22724
$907$	1.56876e13	0.769706	0.384853	−	0.922978i	$-0.374252\pi$
$907$	1.56876e13	0.769706	0.384853	+	0.922978i	$0.374252\pi$
$908$	2.25503e10	0.00110095
$909$	4.02510e11	0.0195541
$910$	−1.58510e12	−0.0766251
$911$	5.16410e12	0.248406	0.124203	−	0.992257i	$-0.460363\pi$
$911$	5.16410e12	0.248406	0.124203	+	0.992257i	$0.460363\pi$
$912$	1.08410e12	0.0518909
$913$	3.01347e12	0.143532
$914$	4.31967e13	2.04735
$915$	−3.26719e11	−0.0154092
$916$	−1.40821e13	−0.660903
$917$	−6.33770e11	−0.0295985
$918$	−3.57447e11	−0.0166119
$919$	1.96145e13	0.907106	0.453553	−	0.891229i	$-0.350156\pi$
$919$	1.96145e13	0.907106	0.453553	+	0.891229i	$0.350156\pi$
$920$	−4.70230e12	−0.216404
$921$	−2.14721e13	−0.983344
$922$	1.60759e13	0.732631
$923$	−3.68514e12	−0.167127
$924$	8.45786e11	0.0381713
$925$	−2.06116e13	−0.925708
$926$	4.01778e13	1.79571
$927$	1.20715e13	0.536911
$928$	−2.00375e13	−0.886906
$929$	−2.42990e13	−1.07033	−0.535164	−	0.844748i	$-0.679750\pi$
$929$	−2.42990e13	−1.07033	−0.535164	+	0.844748i	$0.679750\pi$
$930$	−1.55587e12	−0.0682027
$931$	−3.05364e11	−0.0133212
$932$	−1.35903e12	−0.0590009
$933$	−1.76362e13	−0.761969
$934$	−1.10358e13	−0.474506
$935$	−6.78743e10	−0.00290438
$936$	1.84791e12	0.0786935
$937$	−2.65518e12	−0.112529	−0.0562647	−	0.998416i	$-0.517919\pi$
$937$	−2.65518e12	−0.112529	−0.0562647	+	0.998416i	$0.517919\pi$
$938$	−2.65529e13	−1.11995
$939$	1.88173e13	0.789880
$940$	−1.62105e12	−0.0677207
$941$	−3.36624e13	−1.39956	−0.699781	−	0.714358i	$-0.746719\pi$
$941$	−3.36624e13	−1.39956	−0.699781	+	0.714358i	$0.746719\pi$
$942$	−1.32480e13	−0.548179
$943$	−4.49883e13	−1.85267
$944$	−3.93750e12	−0.161379
$945$	−9.22040e11	−0.0376103
$946$	7.51016e12	0.304887
$947$	−2.44759e13	−0.988927	−0.494463	−	0.869198i	$-0.664635\pi$
$947$	−2.44759e13	−0.988927	−0.494463	+	0.869198i	$0.664635\pi$
$948$	−3.54455e12	−0.142536
$949$	1.57218e13	0.629223
$950$	−2.05145e12	−0.0817156
$951$	−2.00237e13	−0.793837
$952$	1.19005e12	0.0469567
$953$	−4.04016e13	−1.58665	−0.793324	−	0.608800i	$-0.791651\pi$
$953$	−4.04016e13	−1.58665	−0.793324	+	0.608800i	$0.791651\pi$
$954$	−4.58724e12	−0.179301
$955$	−1.09325e13	−0.425308
$956$	3.25982e12	0.126222
$957$	−3.24227e12	−0.124953
$958$	−3.63325e12	−0.139364
$959$	4.69657e12	0.179307
$960$	1.14525e12	0.0435191
$961$	−2.07985e13	−0.786641
$962$	−1.01148e13	−0.380774
$963$	1.38733e12	0.0519832
$964$	−6.56354e11	−0.0244789
$965$	1.49498e12	0.0554963
$966$	−2.34570e13	−0.866713
$967$	−7.98913e12	−0.293819	−0.146910	−	0.989150i	$-0.546933\pi$
$967$	−7.98913e12	−0.293819	−0.146910	+	0.989150i	$0.546933\pi$
$968$	1.87892e13	0.687812
$969$	−8.38766e10	−0.00305622
$970$	−6.89658e12	−0.250127
$971$	1.75900e13	0.635009	0.317505	−	0.948257i	$-0.397155\pi$
$971$	1.75900e13	0.635009	0.317505	+	0.948257i	$0.397155\pi$
$972$	−7.10323e11	−0.0255245
$973$	4.08824e12	0.146227
$974$	1.24236e13	0.442317
$975$	−5.14987e12	−0.182505
$976$	4.33577e12	0.152947
$977$	−3.46357e13	−1.21618	−0.608091	−	0.793867i	$-0.708065\pi$
$977$	−3.46357e13	−1.21618	−0.608091	+	0.793867i	$0.708065\pi$
$978$	8.18127e12	0.285954
$979$	1.55651e12	0.0541539
$980$	4.56575e11	0.0158123
$981$	1.12290e12	0.0387106
$982$	−6.08807e13	−2.08919
$983$	3.17285e13	1.08382	0.541912	−	0.840435i	$-0.317700\pi$
$983$	3.17285e13	1.08382	0.541912	+	0.840435i	$0.317700\pi$
$984$	1.59348e13	0.541837
$985$	−1.04268e13	−0.352929
$986$	3.01464e12	0.101576
$987$	1.22370e13	0.410439
$988$	−2.86545e11	−0.00956724
$989$	−5.92856e13	−1.97045
$990$	−4.73872e11	−0.0156784
$991$	−4.34623e13	−1.43147	−0.715733	−	0.698374i	$-0.753907\pi$
$991$	−4.34623e13	−1.43147	−0.715733	+	0.698374i	$0.753907\pi$
$992$	1.06181e13	0.348133
$993$	−9.56656e12	−0.312237
$994$	−1.65689e13	−0.538338
$995$	5.20349e12	0.168303
$996$	−5.56798e12	−0.179280
$997$	−1.79904e13	−0.576650	−0.288325	−	0.957533i	$-0.593098\pi$
$997$	−1.79904e13	−0.576650	−0.288325	+	0.957533i	$0.593098\pi$
$998$	−2.56682e13	−0.819045
$999$	−5.88366e12	−0.186897

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.c.1.17	✓	22

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

\(f(q)\)	\(=\)	\(q+26.7529 q^{2} -81.0000 q^{3} +203.719 q^{4} -302.298 q^{5} -2166.99 q^{6} -5739.31 q^{7} -8247.43 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+26.7529 q^{2} -81.0000 q^{3} +203.719 q^{4} -302.298 q^{5} -2166.99 q^{6} -5739.31 q^{7} -8247.43 q^{8} +6561.00 q^{9} -8087.35 q^{10} +8930.69 q^{11} -16501.2 q^{12} -34150.1 q^{13} -153543. q^{14} +24486.1 q^{15} -324947. q^{16} +25141.2 q^{17} +175526. q^{18} +41188.0 q^{19} -61583.7 q^{20} +464884. q^{21} +238922. q^{22} -1.88606e6 q^{23} +668042. q^{24} -1.86174e6 q^{25} -913614. q^{26} -531441. q^{27} -1.16920e6 q^{28} +4.48207e6 q^{29} +655075. q^{30} -2.37511e6 q^{31} -4.47059e6 q^{32} -723386. q^{33} +672599. q^{34} +1.73498e6 q^{35} +1.33660e6 q^{36} +1.10711e7 q^{37} +1.10190e6 q^{38} +2.76616e6 q^{39} +2.49318e6 q^{40} +2.38530e7 q^{41} +1.24370e7 q^{42} +3.14335e7 q^{43} +1.81935e6 q^{44} -1.98338e6 q^{45} -5.04577e7 q^{46} +2.63227e7 q^{47} +2.63207e7 q^{48} -7.41390e6 q^{49} -4.98070e7 q^{50} -2.03643e6 q^{51} -6.95700e6 q^{52} -2.61342e7 q^{53} -1.42176e7 q^{54} -2.69973e6 q^{55} +4.73346e7 q^{56} -3.33623e6 q^{57} +1.19909e8 q^{58} +1.21174e7 q^{59} +4.98828e6 q^{60} -1.33430e7 q^{61} -6.35411e7 q^{62} -3.76556e7 q^{63} +4.67714e7 q^{64} +1.03235e7 q^{65} -1.93527e7 q^{66} +1.72934e8 q^{67} +5.12172e6 q^{68} +1.52771e8 q^{69} +4.64158e7 q^{70} +1.07910e8 q^{71} -5.41114e7 q^{72} -4.60374e8 q^{73} +2.96185e8 q^{74} +1.50801e8 q^{75} +8.39076e6 q^{76} -5.12560e7 q^{77} +7.40027e7 q^{78} +2.14806e8 q^{79} +9.82306e7 q^{80} +4.30467e7 q^{81} +6.38138e8 q^{82} +3.37429e8 q^{83} +9.47056e7 q^{84} -7.60012e6 q^{85} +8.40938e8 q^{86} -3.63048e8 q^{87} -7.36553e7 q^{88} +1.74288e8 q^{89} -5.30611e7 q^{90} +1.95998e8 q^{91} -3.84226e8 q^{92} +1.92384e8 q^{93} +7.04210e8 q^{94} -1.24510e7 q^{95} +3.62118e8 q^{96} +8.52762e8 q^{97} -1.98344e8 q^{98} +5.85943e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9}+O(q^{10}) \) 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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