LMFDB - Embedded newform 177.10.a.d.1.5

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			1.5
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)

$f(q)$	$=$	$q-28.6453 q^{2} +81.0000 q^{3} +308.554 q^{4} +1354.22 q^{5} -2320.27 q^{6} +4084.12 q^{7} +5827.78 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-28.6453 q^{2} +81.0000 q^{3} +308.554 q^{4} +1354.22 q^{5} -2320.27 q^{6} +4084.12 q^{7} +5827.78 q^{8} +6561.00 q^{9} -38792.0 q^{10} -47231.4 q^{11} +24992.9 q^{12} -33052.0 q^{13} -116991. q^{14} +109692. q^{15} -324918. q^{16} +443216. q^{17} -187942. q^{18} +725628. q^{19} +417849. q^{20} +330814. q^{21} +1.35296e6 q^{22} -125298. q^{23} +472050. q^{24} -119222. q^{25} +946784. q^{26} +531441. q^{27} +1.26017e6 q^{28} -4.03480e6 q^{29} -3.14215e6 q^{30} +8.12353e6 q^{31} +6.32356e6 q^{32} -3.82574e6 q^{33} -1.26961e7 q^{34} +5.53079e6 q^{35} +2.02442e6 q^{36} +1.61698e7 q^{37} -2.07858e7 q^{38} -2.67721e6 q^{39} +7.89208e6 q^{40} +2.56190e7 q^{41} -9.47627e6 q^{42} -5.08260e6 q^{43} -1.45734e7 q^{44} +8.88501e6 q^{45} +3.58920e6 q^{46} +3.17136e6 q^{47} -2.63184e7 q^{48} -2.36736e7 q^{49} +3.41516e6 q^{50} +3.59005e7 q^{51} -1.01983e7 q^{52} +2.86075e6 q^{53} -1.52233e7 q^{54} -6.39615e7 q^{55} +2.38014e7 q^{56} +5.87759e7 q^{57} +1.15578e8 q^{58} -1.21174e7 q^{59} +3.38457e7 q^{60} -1.34012e8 q^{61} -2.32701e8 q^{62} +2.67959e7 q^{63} -1.47822e7 q^{64} -4.47595e7 q^{65} +1.09590e8 q^{66} -2.02434e8 q^{67} +1.36756e8 q^{68} -1.01491e7 q^{69} -1.58431e8 q^{70} -2.73218e8 q^{71} +3.82361e7 q^{72} -4.58780e7 q^{73} -4.63189e8 q^{74} -9.65702e6 q^{75} +2.23895e8 q^{76} -1.92899e8 q^{77} +7.66895e7 q^{78} +1.56459e7 q^{79} -4.40009e8 q^{80} +4.30467e7 q^{81} -7.33865e8 q^{82} +4.78761e8 q^{83} +1.02074e8 q^{84} +6.00210e8 q^{85} +1.45593e8 q^{86} -3.26819e8 q^{87} -2.75254e8 q^{88} +5.24028e8 q^{89} -2.54514e8 q^{90} -1.34988e8 q^{91} -3.86612e7 q^{92} +6.58006e8 q^{93} -9.08446e7 q^{94} +9.82657e8 q^{95} +5.12208e8 q^{96} +5.11682e8 q^{97} +6.78136e8 q^{98} -3.09885e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9}+O(q^{10}) $ 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9} + 45337 q^{10} + 111769 q^{11} + 483894 q^{12} + 189121 q^{13} + 251053 q^{14} + 468666 q^{15} + 2311074 q^{16} + 1113841 q^{17} + 301806 q^{18} + 476068 q^{19} - 42495 q^{20} + 618921 q^{21} - 2252022 q^{22} + 7103062 q^{23} + 4972995 q^{24} + 10628442 q^{25} + 6871048 q^{26} + 11691702 q^{27} + 8112650 q^{28} + 15279316 q^{29} + 3672297 q^{30} + 17610338 q^{31} + 32378276 q^{32} + 9053289 q^{33} + 29339436 q^{34} + 7134904 q^{35} + 39195414 q^{36} + 21961411 q^{37} + 65195131 q^{38} + 15318801 q^{39} + 75185084 q^{40} + 52781575 q^{41} + 20335293 q^{42} + 76191313 q^{43} + 61127768 q^{44} + 37961946 q^{45} + 290208769 q^{46} + 160572396 q^{47} + 187196994 q^{48} + 156292703 q^{49} + 169504821 q^{50} + 90221121 q^{51} + 65465920 q^{52} - 8762038 q^{53} + 24446286 q^{54} + 147125140 q^{55} + 9671794 q^{56} + 38561508 q^{57} - 37665424 q^{58} - 266581942 q^{59} - 3442095 q^{60} + 120750754 q^{61} - 152465186 q^{62} + 50132601 q^{63} - 40658803 q^{64} + 331055798 q^{65} - 182413782 q^{66} + 41371828 q^{67} + 145606631 q^{68} + 575348022 q^{69} - 920887614 q^{70} + 261018751 q^{71} + 402812595 q^{72} + 178388 q^{73} - 303908734 q^{74} + 860903802 q^{75} - 94541144 q^{76} + 299640561 q^{77} + 556554888 q^{78} - 905381353 q^{79} + 939128289 q^{80} + 947027862 q^{81} - 551739753 q^{82} + 1173257869 q^{83} + 657124650 q^{84} - 1546633210 q^{85} + 1384869460 q^{86} + 1237624596 q^{87} + 189740713 q^{88} + 898004974 q^{89} + 297456057 q^{90} + 591272339 q^{91} + 4328210270 q^{92} + 1426437378 q^{93} + 122568068 q^{94} + 2487967134 q^{95} + 2622640356 q^{96} + 3175709684 q^{97} + 5095778404 q^{98} + 733316409 q^{99}+O(q^{100}) \) 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9 + 45337 * q^10 + 111769 * q^11 + 483894 * q^12 + 189121 * q^13 + 251053 * q^14 + 468666 * q^15 + 2311074 * q^16 + 1113841 * q^17 + 301806 * q^18 + 476068 * q^19 - 42495 * q^20 + 618921 * q^21 - 2252022 * q^22 + 7103062 * q^23 + 4972995 * q^24 + 10628442 * q^25 + 6871048 * q^26 + 11691702 * q^27 + 8112650 * q^28 + 15279316 * q^29 + 3672297 * q^30 + 17610338 * q^31 + 32378276 * q^32 + 9053289 * q^33 + 29339436 * q^34 + 7134904 * q^35 + 39195414 * q^36 + 21961411 * q^37 + 65195131 * q^38 + 15318801 * q^39 + 75185084 * q^40 + 52781575 * q^41 + 20335293 * q^42 + 76191313 * q^43 + 61127768 * q^44 + 37961946 * q^45 + 290208769 * q^46 + 160572396 * q^47 + 187196994 * q^48 + 156292703 * q^49 + 169504821 * q^50 + 90221121 * q^51 + 65465920 * q^52 - 8762038 * q^53 + 24446286 * q^54 + 147125140 * q^55 + 9671794 * q^56 + 38561508 * q^57 - 37665424 * q^58 - 266581942 * q^59 - 3442095 * q^60 + 120750754 * q^61 - 152465186 * q^62 + 50132601 * q^63 - 40658803 * q^64 + 331055798 * q^65 - 182413782 * q^66 + 41371828 * q^67 + 145606631 * q^68 + 575348022 * q^69 - 920887614 * q^70 + 261018751 * q^71 + 402812595 * q^72 + 178388 * q^73 - 303908734 * q^74 + 860903802 * q^75 - 94541144 * q^76 + 299640561 * q^77 + 556554888 * q^78 - 905381353 * q^79 + 939128289 * q^80 + 947027862 * q^81 - 551739753 * q^82 + 1173257869 * q^83 + 657124650 * q^84 - 1546633210 * q^85 + 1384869460 * q^86 + 1237624596 * q^87 + 189740713 * q^88 + 898004974 * q^89 + 297456057 * q^90 + 591272339 * q^91 + 4328210270 * q^92 + 1426437378 * q^93 + 122568068 * q^94 + 2487967134 * q^95 + 2622640356 * q^96 + 3175709684 * q^97 + 5095778404 * q^98 + 733316409 * 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 $

$2$	−28.6453	−1.26596	−0.632978	−	0.774170i	$-0.718168\pi$
$2$	−28.6453	−1.26596	−0.632978	+	0.774170i	$0.718168\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	308.554	0.602644
$5$	1354.22	0.968999	0.484499	−	0.874792i	$-0.339002\pi$
$5$	1354.22	0.968999	0.484499	+	0.874792i	$0.339002\pi$
$6$	−2320.27	−0.730900
$7$	4084.12	0.642921	0.321460	−	0.946923i	$-0.395826\pi$
$7$	4084.12	0.642921	0.321460	+	0.946923i	$0.395826\pi$
$8$	5827.78	0.503035
$9$	6561.00	0.333333
$10$	−38792.0	−1.22671
$11$	−47231.4	−0.972666	−0.486333	−	0.873774i	$-0.661666\pi$
$11$	−47231.4	−0.972666	−0.486333	+	0.873774i	$0.661666\pi$
$12$	24992.9	0.347937
$13$	−33052.0	−0.320961	−0.160481	−	0.987039i	$-0.551304\pi$
$13$	−33052.0	−0.320961	−0.160481	+	0.987039i	$0.551304\pi$
$14$	−116991.	−0.813909
$15$	109692.	0.559452
$16$	−324918.	−1.23946
$17$	443216.	1.28705	0.643524	−	0.765426i	$-0.277471\pi$
$17$	443216.	1.28705	0.643524	+	0.765426i	$0.277471\pi$
$18$	−187942.	−0.421985
$19$	725628.	1.27739	0.638694	−	0.769461i	$-0.279475\pi$
$19$	725628.	1.27739	0.638694	+	0.769461i	$0.279475\pi$
$20$	417849.	0.583961
$21$	330814.	0.371191
$22$	1.35296e6	1.23135
$23$	−125298.	−0.0933618	−0.0466809	−	0.998910i	$-0.514864\pi$
$23$	−125298.	−0.0933618	−0.0466809	+	0.998910i	$0.514864\pi$
$24$	472050.	0.290427
$25$	−119222.	−0.0610419
$26$	946784.	0.406323
$27$	531441.	0.192450
$28$	1.26017e6	0.387452
$29$	−4.03480e6	−1.05933	−0.529664	−	0.848207i	$-0.677682\pi$
$29$	−4.03480e6	−1.05933	−0.529664	+	0.848207i	$0.677682\pi$
$30$	−3.14215e6	−0.708241
$31$	8.12353e6	1.57985	0.789927	−	0.613201i	$-0.210118\pi$
$31$	8.12353e6	1.57985	0.789927	+	0.613201i	$0.210118\pi$
$32$	6.32356e6	1.06607
$33$	−3.82574e6	−0.561569
$34$	−1.26961e7	−1.62935
$35$	5.53079e6	0.622989
$36$	2.02442e6	0.200881
$37$	1.61698e7	1.41839	0.709197	−	0.705011i	$-0.249058\pi$
$37$	1.61698e7	1.41839	0.709197	+	0.705011i	$0.249058\pi$
$38$	−2.07858e7	−1.61712
$39$	−2.67721e6	−0.185307
$40$	7.89208e6	0.487440
$41$	2.56190e7	1.41591	0.707954	−	0.706258i	$-0.249618\pi$
$41$	2.56190e7	1.41591	0.707954	+	0.706258i	$0.249618\pi$
$42$	−9.47627e6	−0.469911
$43$	−5.08260e6	−0.226714	−0.113357	−	0.993554i	$-0.536160\pi$
$43$	−5.08260e6	−0.226714	−0.113357	+	0.993554i	$0.536160\pi$
$44$	−1.45734e7	−0.586171
$45$	8.88501e6	0.323000
$46$	3.58920e6	0.118192
$47$	3.17136e6	0.0947993	0.0473996	−	0.998876i	$-0.484907\pi$
$47$	3.17136e6	0.0947993	0.0473996	+	0.998876i	$0.484907\pi$
$48$	−2.63184e7	−0.715605
$49$	−2.36736e7	−0.586653
$50$	3.41516e6	0.0772763
$51$	3.59005e7	0.743078
$52$	−1.01983e7	−0.193425
$53$	2.86075e6	0.0498011	0.0249005	−	0.999690i	$-0.492073\pi$
$53$	2.86075e6	0.0498011	0.0249005	+	0.999690i	$0.492073\pi$
$54$	−1.52233e7	−0.243633
$55$	−6.39615e7	−0.942512
$56$	2.38014e7	0.323412
$57$	5.87759e7	0.737500
$58$	1.15578e8	1.34106
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	3.38457e7	0.337150
$61$	−1.34012e8	−1.23926	−0.619628	−	0.784896i	$-0.712716\pi$
$61$	−1.34012e8	−1.23926	−0.619628	+	0.784896i	$0.712716\pi$
$62$	−2.32701e8	−2.00003
$63$	2.67959e7	0.214307
$64$	−1.47822e7	−0.110136
$65$	−4.47595e7	−0.311011
$66$	1.09590e8	0.710921
$67$	−2.02434e8	−1.22729	−0.613645	−	0.789582i	$-0.710297\pi$
$67$	−2.02434e8	−1.22729	−0.613645	+	0.789582i	$0.710297\pi$
$68$	1.36756e8	0.775632
$69$	−1.01491e7	−0.0539025
$70$	−1.58431e8	−0.788677
$71$	−2.73218e8	−1.27599	−0.637994	−	0.770041i	$-0.720235\pi$
$71$	−2.73218e8	−1.27599	−0.637994	+	0.770041i	$0.720235\pi$
$72$	3.82361e7	0.167678
$73$	−4.58780e7	−0.189083	−0.0945413	−	0.995521i	$-0.530138\pi$
$73$	−4.58780e7	−0.189083	−0.0945413	+	0.995521i	$0.530138\pi$
$74$	−4.63189e8	−1.79562
$75$	−9.65702e6	−0.0352426
$76$	2.23895e8	0.769810
$77$	−1.92899e8	−0.625347
$78$	7.66895e7	0.234590
$79$	1.56459e7	0.0451939	0.0225969	−	0.999745i	$-0.492807\pi$
$79$	1.56459e7	0.0451939	0.0225969	+	0.999745i	$0.492807\pi$
$80$	−4.40009e8	−1.20104
$81$	4.30467e7	0.111111
$82$	−7.33865e8	−1.79248
$83$	4.78761e8	1.10730	0.553652	−	0.832748i	$-0.313234\pi$
$83$	4.78761e8	1.10730	0.553652	+	0.832748i	$0.313234\pi$
$84$	1.02074e8	0.223696
$85$	6.00210e8	1.24715
$86$	1.45593e8	0.287009
$87$	−3.26819e8	−0.611604
$88$	−2.75254e8	−0.489285
$89$	5.24028e8	0.885318	0.442659	−	0.896690i	$-0.354035\pi$
$89$	5.24028e8	0.885318	0.442659	+	0.896690i	$0.354035\pi$
$90$	−2.54514e8	−0.408903
$91$	−1.34988e8	−0.206353
$92$	−3.86612e7	−0.0562640
$93$	6.58006e8	0.912129
$94$	−9.08446e7	−0.120012
$95$	9.82657e8	1.23779
$96$	5.12208e8	0.615497
$97$	5.11682e8	0.586850	0.293425	−	0.955982i	$-0.405205\pi$
$97$	5.11682e8	0.586850	0.293425	+	0.955982i	$0.405205\pi$
$98$	6.78136e8	0.742676
$99$	−3.09885e8	−0.324222
$100$	−3.67865e7	−0.0367865
$101$	1.06176e9	1.01526	0.507632	−	0.861574i	$-0.330521\pi$
$101$	1.06176e9	1.01526	0.507632	+	0.861574i	$0.330521\pi$
$102$	−1.02838e9	−0.940704
$103$	2.00504e9	1.75532	0.877659	−	0.479286i	$-0.159104\pi$
$103$	2.00504e9	1.75532	0.877659	+	0.479286i	$0.159104\pi$
$104$	−1.92620e8	−0.161455
$105$	4.47994e8	0.359683
$106$	−8.19472e7	−0.0630460
$107$	−2.24978e9	−1.65926	−0.829628	−	0.558316i	$-0.811448\pi$
$107$	−2.24978e9	−1.65926	−0.829628	+	0.558316i	$0.811448\pi$
$108$	1.63978e8	0.115979
$109$	−6.76835e8	−0.459265	−0.229633	−	0.973277i	$-0.573752\pi$
$109$	−6.76835e8	−0.459265	−0.229633	+	0.973277i	$0.573752\pi$
$110$	1.83220e9	1.19318
$111$	1.30975e9	0.818910
$112$	−1.32701e9	−0.796877
$113$	2.76684e9	1.59636	0.798180	−	0.602419i	$-0.205796\pi$
$113$	2.76684e9	1.59636	0.798180	+	0.602419i	$0.205796\pi$
$114$	−1.68365e9	−0.933643
$115$	−1.69681e8	−0.0904675
$116$	−1.24495e9	−0.638398
$117$	−2.16854e8	−0.106987
$118$	3.47106e8	0.164813
$119$	1.81015e9	0.827471
$120$	6.39258e8	0.281424
$121$	−1.27143e8	−0.0539212
$122$	3.83883e9	1.56884
$123$	2.07514e9	0.817475
$124$	2.50654e9	0.952090
$125$	−2.80641e9	−1.02815
$126$	−7.67578e8	−0.271303
$127$	−4.06332e9	−1.38600	−0.693001	−	0.720937i	$-0.743712\pi$
$127$	−4.06332e9	−1.38600	−0.693001	+	0.720937i	$0.743712\pi$
$128$	−2.81422e9	−0.926645
$129$	−4.11690e8	−0.130893
$130$	1.28215e9	0.393726
$131$	3.39487e9	1.00717	0.503585	−	0.863946i	$-0.332014\pi$
$131$	3.39487e9	1.00717	0.503585	+	0.863946i	$0.332014\pi$
$132$	−1.18045e9	−0.338426
$133$	2.96355e9	0.821259
$134$	5.79879e9	1.55369
$135$	7.19686e8	0.186484
$136$	2.58296e9	0.647431
$137$	−4.94042e8	−0.119818	−0.0599089	−	0.998204i	$-0.519081\pi$
$137$	−4.94042e8	−0.119818	−0.0599089	+	0.998204i	$0.519081\pi$
$138$	2.90725e8	0.0682381
$139$	6.29148e9	1.42951	0.714753	−	0.699377i	$-0.246539\pi$
$139$	6.29148e9	1.42951	0.714753	+	0.699377i	$0.246539\pi$
$140$	1.70654e9	0.375441
$141$	2.56880e8	0.0547324
$142$	7.82641e9	1.61534
$143$	1.56109e9	0.312188
$144$	−2.13179e9	−0.413155
$145$	−5.46399e9	−1.02649
$146$	1.31419e9	0.239370
$147$	−1.91756e9	−0.338704
$148$	4.98925e9	0.854787
$149$	8.26886e9	1.37438	0.687191	−	0.726477i	$-0.258844\pi$
$149$	8.26886e9	1.37438	0.687191	+	0.726477i	$0.258844\pi$
$150$	2.76628e8	0.0446155
$151$	3.56053e9	0.557337	0.278669	−	0.960387i	$-0.410107\pi$
$151$	3.56053e9	0.557337	0.278669	+	0.960387i	$0.410107\pi$
$152$	4.22880e9	0.642571
$153$	2.90794e9	0.429016
$154$	5.52564e9	0.791662
$155$	1.10010e10	1.53088
$156$	−8.26063e8	−0.111674
$157$	2.52887e8	0.0332183	0.0166091	−	0.999862i	$-0.494713\pi$
$157$	2.52887e8	0.0332183	0.0166091	+	0.999862i	$0.494713\pi$
$158$	−4.48182e8	−0.0572134
$159$	2.31721e8	0.0287527
$160$	8.56347e9	1.03302
$161$	−5.11733e8	−0.0600243
$162$	−1.23309e9	−0.140662
$163$	−6.06403e9	−0.672848	−0.336424	−	0.941711i	$-0.609218\pi$
$163$	−6.06403e9	−0.672848	−0.336424	+	0.941711i	$0.609218\pi$
$164$	7.90484e9	0.853289
$165$	−5.18088e9	−0.544159
$166$	−1.37143e10	−1.40180
$167$	1.12715e10	1.12139	0.560697	−	0.828021i	$-0.310533\pi$
$167$	1.12715e10	1.12139	0.560697	+	0.828021i	$0.310533\pi$
$168$	1.92791e9	0.186722
$169$	−9.51207e9	−0.896984
$170$	−1.71932e10	−1.57883
$171$	4.76084e9	0.425796
$172$	−1.56825e9	−0.136628
$173$	3.53662e8	0.0300179	0.0150090	−	0.999887i	$-0.495222\pi$
$173$	3.53662e8	0.0300179	0.0150090	+	0.999887i	$0.495222\pi$
$174$	9.36182e9	0.774263
$175$	−4.86919e8	−0.0392451
$176$	1.53463e10	1.20558
$177$	−9.81506e8	−0.0751646
$178$	−1.50109e10	−1.12077
$179$	2.67931e10	1.95067	0.975337	−	0.220723i	$-0.0708417\pi$
$179$	2.67931e10	1.95067	0.975337	+	0.220723i	$0.0708417\pi$
$180$	2.74151e9	0.194654
$181$	8.45963e9	0.585865	0.292933	−	0.956133i	$-0.405369\pi$
$181$	8.45963e9	0.585865	0.292933	+	0.956133i	$0.405369\pi$
$182$	3.86678e9	0.261233
$183$	−1.08550e10	−0.715484
$184$	−7.30210e8	−0.0469643
$185$	2.18974e10	1.37442
$186$	−1.88488e10	−1.15472
$187$	−2.09337e10	−1.25187
$188$	9.78535e8	0.0571302
$189$	2.17047e9	0.123730
$190$	−2.81485e10	−1.56698
$191$	2.08046e10	1.13112	0.565562	−	0.824706i	$-0.308659\pi$
$191$	2.08046e10	1.13112	0.565562	+	0.824706i	$0.308659\pi$
$192$	−1.19736e9	−0.0635869
$193$	−3.43043e10	−1.77967	−0.889837	−	0.456278i	$-0.849182\pi$
$193$	−3.43043e10	−1.77967	−0.889837	+	0.456278i	$0.849182\pi$
$194$	−1.46573e10	−0.742927
$195$	−3.62552e9	−0.179562
$196$	−7.30457e9	−0.353543
$197$	1.76011e10	0.832612	0.416306	−	0.909225i	$-0.363325\pi$
$197$	1.76011e10	0.832612	0.416306	+	0.909225i	$0.363325\pi$
$198$	8.87676e9	0.410451
$199$	2.10369e10	0.950919	0.475459	−	0.879738i	$-0.342282\pi$
$199$	2.10369e10	0.950919	0.475459	+	0.879738i	$0.342282\pi$
$200$	−6.94802e8	−0.0307062
$201$	−1.63972e10	−0.708576
$202$	−3.04144e10	−1.28528
$203$	−1.64786e10	−0.681064
$204$	1.10772e10	0.447812
$205$	3.46937e10	1.37201
$206$	−5.74350e10	−2.22215
$207$	−8.22081e8	−0.0311206
$208$	1.07392e10	0.397820
$209$	−3.42724e10	−1.24247
$210$	−1.28329e10	−0.455343
$211$	−2.39137e10	−0.830569	−0.415285	−	0.909692i	$-0.636318\pi$
$211$	−2.39137e10	−0.830569	−0.415285	+	0.909692i	$0.636318\pi$
$212$	8.82696e8	0.0300123
$213$	−2.21306e10	−0.736692
$214$	6.44457e10	2.10055
$215$	−6.88294e9	−0.219685
$216$	3.09712e9	0.0968091
$217$	3.31775e10	1.01572
$218$	1.93882e10	0.581410
$219$	−3.71612e9	−0.109167
$220$	−1.97356e10	−0.567999
$221$	−1.46492e10	−0.413093
$222$	−3.75183e10	−1.03670
$223$	−2.05884e10	−0.557506	−0.278753	−	0.960363i	$-0.589921\pi$
$223$	−2.05884e10	−0.557506	−0.278753	+	0.960363i	$0.589921\pi$
$224$	2.58262e10	0.685400
$225$	−7.82219e8	−0.0203473
$226$	−7.92569e10	−2.02092
$227$	−3.29798e10	−0.824388	−0.412194	−	0.911096i	$-0.635237\pi$
$227$	−3.29798e10	−0.824388	−0.412194	+	0.911096i	$0.635237\pi$
$228$	1.81355e10	0.444450
$229$	−1.94734e10	−0.467931	−0.233965	−	0.972245i	$-0.575170\pi$
$229$	−1.94734e10	−0.467931	−0.233965	+	0.972245i	$0.575170\pi$
$230$	4.86056e9	0.114528
$231$	−1.56248e10	−0.361044
$232$	−2.35139e10	−0.532879
$233$	6.07481e10	1.35030	0.675152	−	0.737679i	$-0.264078\pi$
$233$	6.07481e10	1.35030	0.675152	+	0.737679i	$0.264078\pi$
$234$	6.21185e9	0.135441
$235$	4.29471e9	0.0918604
$236$	−3.73886e9	−0.0784576
$237$	1.26732e9	0.0260927
$238$	−5.18522e10	−1.04754
$239$	−3.35535e10	−0.665193	−0.332596	−	0.943069i	$-0.607925\pi$
$239$	−3.35535e10	−0.665193	−0.332596	+	0.943069i	$0.607925\pi$
$240$	−3.56408e10	−0.693420
$241$	3.23723e10	0.618154	0.309077	−	0.951037i	$-0.399980\pi$
$241$	3.23723e10	0.618154	0.309077	+	0.951037i	$0.399980\pi$
$242$	3.64206e9	0.0682619
$243$	3.48678e9	0.0641500
$244$	−4.13500e10	−0.746830
$245$	−3.20591e10	−0.568466
$246$	−5.94430e10	−1.03489
$247$	−2.39834e10	−0.409992
$248$	4.73421e10	0.794722
$249$	3.87796e10	0.639303
$250$	8.03904e10	1.30159
$251$	5.38436e10	0.856253	0.428127	−	0.903719i	$-0.359174\pi$
$251$	5.38436e10	0.856253	0.428127	+	0.903719i	$0.359174\pi$
$252$	8.26798e9	0.129151
$253$	5.91800e9	0.0908098
$254$	1.16395e11	1.75462
$255$	4.86170e10	0.720041
$256$	8.81827e10	1.28323
$257$	6.94605e10	0.993205	0.496602	−	0.867978i	$-0.334581\pi$
$257$	6.94605e10	0.993205	0.496602	+	0.867978i	$0.334581\pi$
$258$	1.17930e10	0.165705
$259$	6.60394e10	0.911915
$260$	−1.38107e10	−0.187429
$261$	−2.64723e10	−0.353109
$262$	−9.72471e10	−1.27503
$263$	2.38776e10	0.307744	0.153872	−	0.988091i	$-0.450826\pi$
$263$	2.38776e10	0.307744	0.153872	+	0.988091i	$0.450826\pi$
$264$	−2.22956e10	−0.282489
$265$	3.87408e9	0.0482572
$266$	−8.48919e10	−1.03968
$267$	4.24462e10	0.511139
$268$	−6.24618e10	−0.739619
$269$	−2.93724e10	−0.342022	−0.171011	−	0.985269i	$-0.554703\pi$
$269$	−2.93724e10	−0.342022	−0.171011	+	0.985269i	$0.554703\pi$
$270$	−2.06156e10	−0.236080
$271$	−6.30264e10	−0.709841	−0.354920	−	0.934897i	$-0.615492\pi$
$271$	−6.30264e10	−0.709841	−0.354920	+	0.934897i	$0.615492\pi$
$272$	−1.44009e11	−1.59525
$273$	−1.09341e10	−0.119138
$274$	1.41520e10	0.151684
$275$	5.63104e9	0.0593734
$276$	−3.13156e9	−0.0324840
$277$	−1.38561e11	−1.41411	−0.707055	−	0.707158i	$-0.749977\pi$
$277$	−1.38561e11	−1.41411	−0.707055	+	0.707158i	$0.749977\pi$
$278$	−1.80221e11	−1.80969
$279$	5.32984e10	0.526618
$280$	3.22322e10	0.313385
$281$	9.40553e10	0.899922	0.449961	−	0.893048i	$-0.351438\pi$
$281$	9.40553e10	0.899922	0.449961	+	0.893048i	$0.351438\pi$
$282$	−7.35841e9	−0.0692888
$283$	2.32349e10	0.215328	0.107664	−	0.994187i	$-0.465663\pi$
$283$	2.32349e10	0.215328	0.107664	+	0.994187i	$0.465663\pi$
$284$	−8.43024e10	−0.768967
$285$	7.95952e10	0.714636
$286$	−4.47179e10	−0.395216
$287$	1.04631e11	0.910317
$288$	4.14889e10	0.355357
$289$	7.78523e10	0.656495
$290$	1.56518e11	1.29949
$291$	4.14463e10	0.338818
$292$	−1.41558e10	−0.113950
$293$	−6.03723e10	−0.478557	−0.239278	−	0.970951i	$-0.576911\pi$
$293$	−6.03723e10	−0.478557	−0.239278	+	0.970951i	$0.576911\pi$
$294$	5.49290e10	0.428784
$295$	−1.64095e10	−0.126153
$296$	9.42340e10	0.713502
$297$	−2.51007e10	−0.187190
$298$	−2.36864e11	−1.73991
$299$	4.14135e9	0.0299655
$300$	−2.97971e9	−0.0212387
$301$	−2.07579e10	−0.145759
$302$	−1.01992e11	−0.705564
$303$	8.60024e10	0.586163
$304$	−2.35770e11	−1.58328
$305$	−1.81482e11	−1.20084
$306$	−8.32988e10	−0.543116
$307$	−1.34298e11	−0.862870	−0.431435	−	0.902144i	$-0.641993\pi$
$307$	−1.34298e11	−0.862870	−0.431435	+	0.902144i	$0.641993\pi$
$308$	−5.95196e10	−0.376862
$309$	1.62408e11	1.01343
$310$	−3.15127e11	−1.93802
$311$	3.18179e11	1.92864	0.964318	−	0.264747i	$-0.0852883\pi$
$311$	3.18179e11	1.92864	0.964318	+	0.264747i	$0.0852883\pi$
$312$	−1.56022e10	−0.0932159
$313$	−7.68389e10	−0.452513	−0.226257	−	0.974068i	$-0.572649\pi$
$313$	−7.68389e10	−0.452513	−0.226257	+	0.974068i	$0.572649\pi$
$314$	−7.24401e9	−0.0420529
$315$	3.62875e10	0.207663
$316$	4.82761e9	0.0272358
$317$	1.69384e11	0.942121	0.471060	−	0.882101i	$-0.343871\pi$
$317$	1.69384e11	0.942121	0.471060	+	0.882101i	$0.343871\pi$
$318$	−6.63772e9	−0.0363996
$319$	1.90569e11	1.03037
$320$	−2.00183e10	−0.106721
$321$	−1.82232e11	−0.957972
$322$	1.46587e10	0.0759881
$323$	3.21610e11	1.64406
$324$	1.32822e10	0.0669605
$325$	3.94054e9	0.0195921
$326$	1.73706e11	0.851796
$327$	−5.48236e10	−0.265157
$328$	1.49302e11	0.712251
$329$	1.29522e10	0.0609484
$330$	1.48408e11	0.688882
$331$	2.71014e11	1.24098	0.620491	−	0.784214i	$-0.286933\pi$
$331$	2.71014e11	1.24098	0.620491	+	0.784214i	$0.286933\pi$
$332$	1.47723e11	0.667311
$333$	1.06090e11	0.472798
$334$	−3.22876e11	−1.41964
$335$	−2.74140e11	−1.18924
$336$	−1.07487e11	−0.460077
$337$	2.83802e11	1.19862	0.599310	−	0.800517i	$-0.295442\pi$
$337$	2.83802e11	1.19862	0.599310	+	0.800517i	$0.295442\pi$
$338$	2.72476e11	1.13554
$339$	2.24114e11	0.921659
$340$	1.85197e11	0.751587
$341$	−3.83685e11	−1.53667
$342$	−1.36376e11	−0.539039
$343$	−2.61495e11	−1.02009
$344$	−2.96203e10	−0.114045
$345$	−1.37441e10	−0.0522314
$346$	−1.01308e10	−0.0380014
$347$	−4.25894e10	−0.157695	−0.0788477	−	0.996887i	$-0.525124\pi$
$347$	−4.25894e10	−0.157695	−0.0788477	+	0.996887i	$0.525124\pi$
$348$	−1.00841e11	−0.368579
$349$	4.18211e11	1.50897	0.754485	−	0.656317i	$-0.227887\pi$
$349$	4.18211e11	1.50897	0.754485	+	0.656317i	$0.227887\pi$
$350$	1.39479e10	0.0496826
$351$	−1.75652e10	−0.0617690
$352$	−2.98670e11	−1.03693
$353$	−3.98462e11	−1.36584	−0.682921	−	0.730492i	$-0.739291\pi$
$353$	−3.98462e11	−1.36584	−0.682921	+	0.730492i	$0.739291\pi$
$354$	2.81156e10	0.0951551
$355$	−3.69996e11	−1.23643
$356$	1.61691e11	0.533532
$357$	1.46622e11	0.477740
$358$	−7.67497e11	−2.46947
$359$	2.30556e11	0.732573	0.366287	−	0.930502i	$-0.380629\pi$
$359$	2.30556e11	0.732573	0.366287	+	0.930502i	$0.380629\pi$
$360$	5.17799e10	0.162480
$361$	2.03848e11	0.631719
$362$	−2.42329e11	−0.741679
$363$	−1.02986e10	−0.0311314
$364$	−4.16512e10	−0.124357
$365$	−6.21288e10	−0.183221
$366$	3.10945e11	0.905772
$367$	2.13955e11	0.615639	0.307819	−	0.951445i	$-0.400401\pi$
$367$	2.13955e11	0.615639	0.307819	+	0.951445i	$0.400401\pi$
$368$	4.07116e10	0.115719
$369$	1.68086e11	0.471969
$370$	−6.27258e11	−1.73996
$371$	1.16837e10	0.0320182
$372$	2.03030e11	0.549689
$373$	5.62850e11	1.50558	0.752789	−	0.658262i	$-0.228708\pi$
$373$	5.62850e11	1.50558	0.752789	+	0.658262i	$0.228708\pi$
$374$	5.99652e11	1.58481
$375$	−2.27319e11	−0.593602
$376$	1.84820e10	0.0476874
$377$	1.33358e11	0.340003
$378$	−6.21738e10	−0.156637
$379$	−6.38760e11	−1.59023	−0.795117	−	0.606456i	$-0.792591\pi$
$379$	−6.38760e11	−1.59023	−0.795117	+	0.606456i	$0.792591\pi$
$380$	3.03203e11	0.745945
$381$	−3.29129e11	−0.800209
$382$	−5.95955e11	−1.43195
$383$	−3.26247e11	−0.774734	−0.387367	−	0.921926i	$-0.626615\pi$
$383$	−3.26247e11	−0.774734	−0.387367	+	0.921926i	$0.626615\pi$
$384$	−2.27952e11	−0.534999
$385$	−2.61227e11	−0.605960
$386$	9.82657e11	2.25299
$387$	−3.33469e10	−0.0755712
$388$	1.57881e11	0.353662
$389$	−5.60425e11	−1.24092	−0.620460	−	0.784238i	$-0.713054\pi$
$389$	−5.60425e11	−1.24092	−0.620460	+	0.784238i	$0.713054\pi$
$390$	1.03854e11	0.227318
$391$	−5.55341e10	−0.120161
$392$	−1.37964e11	−0.295107
$393$	2.74985e11	0.581489
$394$	−5.04190e11	−1.05405
$395$	2.11880e10	0.0437928
$396$	−9.56162e10	−0.195390
$397$	6.45371e11	1.30392	0.651962	−	0.758252i	$-0.273946\pi$
$397$	6.45371e11	1.30392	0.651962	+	0.758252i	$0.273946\pi$
$398$	−6.02609e11	−1.20382
$399$	2.40048e11	0.474154
$400$	3.87375e10	0.0756592
$401$	−1.70193e11	−0.328693	−0.164347	−	0.986403i	$-0.552552\pi$
$401$	−1.70193e11	−0.328693	−0.164347	+	0.986403i	$0.552552\pi$
$402$	4.69702e11	0.897026
$403$	−2.68499e11	−0.507072
$404$	3.27609e11	0.611843
$405$	5.82946e10	0.107667
$406$	4.72035e11	0.862197
$407$	−7.63722e11	−1.37962
$408$	2.09220e11	0.373794
$409$	−1.19142e11	−0.210529	−0.105264	−	0.994444i	$-0.533569\pi$
$409$	−1.19142e11	−0.210529	−0.105264	+	0.994444i	$0.533569\pi$
$410$	−9.93812e11	−1.73691
$411$	−4.00174e10	−0.0691768
$412$	6.18663e11	1.05783
$413$	−4.94888e10	−0.0837012
$414$	2.35488e10	0.0393973
$415$	6.48346e11	1.07298
$416$	−2.09006e11	−0.342168
$417$	5.09610e11	0.825326
$418$	9.81744e11	1.57291
$419$	−5.36922e10	−0.0851036	−0.0425518	−	0.999094i	$-0.513549\pi$
$419$	−5.36922e10	−0.0851036	−0.0425518	+	0.999094i	$0.513549\pi$
$420$	1.38230e11	0.216761
$421$	−7.34555e10	−0.113961	−0.0569803	−	0.998375i	$-0.518147\pi$
$421$	−7.34555e10	−0.113961	−0.0569803	+	0.998375i	$0.518147\pi$
$422$	6.85015e11	1.05146
$423$	2.08073e10	0.0315998
$424$	1.66718e10	0.0250517
$425$	−5.28413e10	−0.0785639
$426$	6.33939e11	0.932619
$427$	−5.47323e11	−0.796743
$428$	−6.94179e11	−0.999941
$429$	1.26448e11	0.180242
$430$	1.97164e11	0.278112
$431$	6.88580e11	0.961184	0.480592	−	0.876944i	$-0.340422\pi$
$431$	6.88580e11	0.961184	0.480592	+	0.876944i	$0.340422\pi$
$432$	−1.72675e11	−0.238535
$433$	5.38627e10	0.0736364	0.0368182	−	0.999322i	$-0.488278\pi$
$433$	5.38627e10	0.0736364	0.0368182	+	0.999322i	$0.488278\pi$
$434$	−9.50379e11	−1.28586
$435$	−4.42583e11	−0.592643
$436$	−2.08840e11	−0.276774
$437$	−9.09198e10	−0.119259
$438$	1.06449e11	0.138201
$439$	1.10606e12	1.42130	0.710652	−	0.703544i	$-0.248400\pi$
$439$	1.10606e12	1.42130	0.710652	+	0.703544i	$0.248400\pi$
$440$	−3.72754e11	−0.474116
$441$	−1.55322e11	−0.195551
$442$	4.19630e11	0.522957
$443$	−2.16781e11	−0.267427	−0.133714	−	0.991020i	$-0.542690\pi$
$443$	−2.16781e11	−0.267427	−0.133714	+	0.991020i	$0.542690\pi$
$444$	4.04129e11	0.493511
$445$	7.09647e11	0.857872
$446$	5.89760e11	0.705778
$447$	6.69778e11	0.793500
$448$	−6.03722e10	−0.0708086
$449$	2.71054e11	0.314736	0.157368	−	0.987540i	$-0.449699\pi$
$449$	2.71054e11	0.314736	0.157368	+	0.987540i	$0.449699\pi$
$450$	2.24069e10	0.0257588
$451$	−1.21002e12	−1.37721
$452$	8.53719e11	0.962037
$453$	2.88403e11	0.321779
$454$	9.44717e11	1.04364
$455$	−1.82803e11	−0.199955
$456$	3.42533e11	0.370988
$457$	8.41235e11	0.902182	0.451091	−	0.892478i	$-0.351035\pi$
$457$	8.41235e11	0.902182	0.451091	+	0.892478i	$0.351035\pi$
$458$	5.57821e11	0.592379
$459$	2.35543e11	0.247693
$460$	−5.23557e10	−0.0545197
$461$	−2.27551e11	−0.234652	−0.117326	−	0.993093i	$-0.537432\pi$
$461$	−2.27551e11	−0.234652	−0.117326	+	0.993093i	$0.537432\pi$
$462$	4.47577e11	0.457066
$463$	8.72284e11	0.882152	0.441076	−	0.897470i	$-0.354597\pi$
$463$	8.72284e11	0.882152	0.441076	+	0.897470i	$0.354597\pi$
$464$	1.31098e12	1.31300
$465$	8.91082e11	0.883852
$466$	−1.74015e12	−1.70942
$467$	1.10977e12	1.07971	0.539854	−	0.841758i	$-0.318479\pi$
$467$	1.10977e12	1.07971	0.539854	+	0.841758i	$0.318479\pi$
$468$	−6.69111e10	−0.0644751
$469$	−8.26766e11	−0.789050
$470$	−1.23023e11	−0.116291
$471$	2.04838e10	0.0191786
$472$	−7.06173e10	−0.0654896
$473$	2.40058e11	0.220517
$474$	−3.63028e10	−0.0330322
$475$	−8.65111e10	−0.0779742
$476$	5.58528e11	0.498670
$477$	1.87694e10	0.0166004
$478$	9.61151e11	0.842105
$479$	1.61589e12	1.40249	0.701247	−	0.712918i	$-0.252627\pi$
$479$	1.61589e12	1.40249	0.701247	+	0.712918i	$0.252627\pi$
$480$	6.93641e11	0.596416
$481$	−5.34444e11	−0.455249
$482$	−9.27314e11	−0.782555
$483$	−4.14504e10	−0.0346550
$484$	−3.92306e10	−0.0324953
$485$	6.92928e11	0.568657
$486$	−9.98800e10	−0.0812111
$487$	3.44921e11	0.277868	0.138934	−	0.990302i	$-0.455632\pi$
$487$	3.44921e11	0.277868	0.138934	+	0.990302i	$0.455632\pi$
$488$	−7.80995e11	−0.623389
$489$	−4.91187e11	−0.388469
$490$	9.18343e11	0.719652
$491$	−1.29529e12	−1.00578	−0.502889	−	0.864351i	$-0.667729\pi$
$491$	−1.29529e12	−1.00578	−0.502889	+	0.864351i	$0.667729\pi$
$492$	6.40292e11	0.492647
$493$	−1.78829e12	−1.36341
$494$	6.87013e11	0.519031
$495$	−4.19652e11	−0.314171
$496$	−2.63948e12	−1.95817
$497$	−1.11585e12	−0.820359
$498$	−1.11085e12	−0.809329
$499$	2.12865e12	1.53692	0.768460	−	0.639898i	$-0.221023\pi$
$499$	2.12865e12	1.53692	0.768460	+	0.639898i	$0.221023\pi$
$500$	−8.65928e11	−0.619607
$501$	9.12993e11	0.647437
$502$	−1.54237e12	−1.08398
$503$	3.00207e11	0.209105	0.104552	−	0.994519i	$-0.466659\pi$
$503$	3.00207e11	0.209105	0.104552	+	0.994519i	$0.466659\pi$
$504$	1.56161e11	0.107804
$505$	1.43785e12	0.983790
$506$	−1.69523e11	−0.114961
$507$	−7.70477e11	−0.517874
$508$	−1.25375e12	−0.835266
$509$	−1.25461e12	−0.828476	−0.414238	−	0.910169i	$-0.635952\pi$
$509$	−1.25461e12	−0.828476	−0.414238	+	0.910169i	$0.635952\pi$
$510$	−1.39265e12	−0.911541
$511$	−1.87371e11	−0.121565
$512$	−1.08514e12	−0.697864
$513$	3.85628e11	0.245833
$514$	−1.98972e12	−1.25735
$515$	2.71526e12	1.70090
$516$	−1.27029e11	−0.0788820
$517$	−1.49788e11	−0.0922080
$518$	−1.89172e12	−1.15444
$519$	2.86466e10	0.0173309
$520$	−2.60849e11	−0.156449
$521$	9.46973e11	0.563077	0.281538	−	0.959550i	$-0.409155\pi$
$521$	9.46973e11	0.563077	0.281538	+	0.959550i	$0.409155\pi$
$522$	7.58307e11	0.447021
$523$	8.86122e11	0.517888	0.258944	−	0.965892i	$-0.416626\pi$
$523$	8.86122e11	0.517888	0.258944	+	0.965892i	$0.416626\pi$
$524$	1.04750e12	0.606965
$525$	−3.94404e10	−0.0226582
$526$	−6.83980e11	−0.389590
$527$	3.60047e12	2.03335
$528$	1.24305e12	0.696044
$529$	−1.78545e12	−0.991284
$530$	−1.10974e11	−0.0610915
$531$	−7.95020e10	−0.0433963
$532$	9.14415e11	0.494927
$533$	−8.46759e11	−0.454451
$534$	−1.21589e12	−0.647079
$535$	−3.04669e12	−1.60782
$536$	−1.17974e12	−0.617370
$537$	2.17024e12	1.12622
$538$	8.41381e11	0.432985
$539$	1.11813e12	0.570617
$540$	2.22062e11	0.112383
$541$	1.98760e11	0.0997566	0.0498783	−	0.998755i	$-0.484117\pi$
$541$	1.98760e11	0.0997566	0.0498783	+	0.998755i	$0.484117\pi$
$542$	1.80541e12	0.898627
$543$	6.85230e11	0.338249
$544$	2.80270e12	1.37209
$545$	−9.16581e11	−0.445027
$546$	3.13209e11	0.150823
$547$	−3.79463e12	−1.81228	−0.906141	−	0.422975i	$-0.860986\pi$
$547$	−3.79463e12	−1.81228	−0.906141	+	0.422975i	$0.860986\pi$
$548$	−1.52438e11	−0.0722075
$549$	−8.79255e11	−0.413085
$550$	−1.61303e11	−0.0751641
$551$	−2.92776e12	−1.35317
$552$	−5.91470e10	−0.0271148
$553$	6.38999e10	0.0290561
$554$	3.96913e12	1.79020
$555$	1.77369e12	0.793522
$556$	1.94126e12	0.861484
$557$	−3.70966e12	−1.63300	−0.816499	−	0.577347i	$-0.804088\pi$
$557$	−3.70966e12	−1.63300	−0.816499	+	0.577347i	$0.804088\pi$
$558$	−1.52675e12	−0.666675
$559$	1.67990e11	0.0727662
$560$	−1.79705e12	−0.772173
$561$	−1.69563e12	−0.722767
$562$	−2.69424e12	−1.13926
$563$	2.84950e12	1.19531	0.597656	−	0.801753i	$-0.296099\pi$
$563$	2.84950e12	1.19531	0.597656	+	0.801753i	$0.296099\pi$
$564$	7.92613e10	0.0329842
$565$	3.74690e12	1.54687
$566$	−6.65570e11	−0.272596
$567$	1.75808e11	0.0714357
$568$	−1.59225e12	−0.641866
$569$	−2.26268e12	−0.904934	−0.452467	−	0.891781i	$-0.649456\pi$
$569$	−2.26268e12	−0.904934	−0.452467	+	0.891781i	$0.649456\pi$
$570$	−2.28003e12	−0.904698
$571$	−2.06202e12	−0.811763	−0.405882	−	0.913926i	$-0.633035\pi$
$571$	−2.06202e12	−0.811763	−0.405882	+	0.913926i	$0.633035\pi$
$572$	4.81681e11	0.188138
$573$	1.68518e12	0.653054
$574$	−2.99719e12	−1.15242
$575$	1.49383e10	0.00569898
$576$	−9.69859e10	−0.0367119
$577$	−4.03734e12	−1.51636	−0.758182	−	0.652043i	$-0.773912\pi$
$577$	−4.03734e12	−1.51636	−0.758182	+	0.652043i	$0.773912\pi$
$578$	−2.23010e12	−0.831093
$579$	−2.77865e12	−1.02750
$580$	−1.68593e12	−0.618607
$581$	1.95532e12	0.711909
$582$	−1.18724e12	−0.428929
$583$	−1.35117e11	−0.0484398
$584$	−2.67367e11	−0.0951152
$585$	−2.93667e11	−0.103670
$586$	1.72938e12	0.605832
$587$	9.45156e11	0.328573	0.164287	−	0.986413i	$-0.447468\pi$
$587$	9.45156e11	0.328573	0.164287	+	0.986413i	$0.447468\pi$
$588$	−5.91670e11	−0.204118
$589$	5.89466e12	2.01809
$590$	4.70056e11	0.159704
$591$	1.42569e12	0.480709
$592$	−5.25386e12	−1.75805
$593$	−1.49025e12	−0.494894	−0.247447	−	0.968901i	$-0.579592\pi$
$593$	−1.49025e12	−0.494894	−0.247447	+	0.968901i	$0.579592\pi$
$594$	7.19017e11	0.236974
$595$	2.45133e12	0.801818
$596$	2.55139e12	0.828263
$597$	1.70399e12	0.549013
$598$	−1.18630e11	−0.0379350
$599$	−3.03885e12	−0.964468	−0.482234	−	0.876042i	$-0.660175\pi$
$599$	−3.03885e12	−0.964468	−0.482234	+	0.876042i	$0.660175\pi$
$600$	−5.62790e10	−0.0177282
$601$	−1.25441e12	−0.392196	−0.196098	−	0.980584i	$-0.562827\pi$
$601$	−1.25441e12	−0.392196	−0.196098	+	0.980584i	$0.562827\pi$
$602$	5.94618e11	0.184524
$603$	−1.32817e12	−0.409097
$604$	1.09861e12	0.335876
$605$	−1.72180e11	−0.0522496
$606$	−2.46356e12	−0.742057
$607$	−4.35236e12	−1.30130	−0.650648	−	0.759380i	$-0.725503\pi$
$607$	−4.35236e12	−1.30130	−0.650648	+	0.759380i	$0.725503\pi$
$608$	4.58855e12	1.36179
$609$	−1.33477e12	−0.393213
$610$	5.19860e12	1.52021
$611$	−1.04820e11	−0.0304269
$612$	8.97255e11	0.258544
$613$	−1.38782e12	−0.396974	−0.198487	−	0.980104i	$-0.563603\pi$
$613$	−1.38782e12	−0.396974	−0.198487	+	0.980104i	$0.563603\pi$
$614$	3.84700e12	1.09236
$615$	2.81019e12	0.792132
$616$	−1.12417e12	−0.314571
$617$	5.72130e12	1.58932	0.794660	−	0.607055i	$-0.207649\pi$
$617$	5.72130e12	1.58932	0.794660	+	0.607055i	$0.207649\pi$
$618$	−4.65224e12	−1.28296
$619$	−3.70038e12	−1.01307	−0.506534	−	0.862220i	$-0.669073\pi$
$619$	−3.70038e12	−1.01307	−0.506534	+	0.862220i	$0.669073\pi$
$620$	3.39440e12	0.922573
$621$	−6.65886e10	−0.0179675
$622$	−9.11435e12	−2.44157
$623$	2.14019e12	0.569189
$624$	8.69874e11	0.229681
$625$	−3.56763e12	−0.935232
$626$	2.20107e12	0.572862
$627$	−2.77607e12	−0.717341
$628$	7.80291e10	0.0200188
$629$	7.16671e12	1.82554
$630$	−1.03947e12	−0.262892
$631$	−2.31097e12	−0.580313	−0.290156	−	0.956979i	$-0.593707\pi$
$631$	−2.31097e12	−0.580313	−0.290156	+	0.956979i	$0.593707\pi$
$632$	9.11810e10	0.0227341
$633$	−1.93701e12	−0.479529
$634$	−4.85207e12	−1.19268
$635$	−5.50261e12	−1.34303
$636$	7.14984e10	0.0173276
$637$	7.82458e11	0.188293
$638$	−5.45891e12	−1.30441
$639$	−1.79258e12	−0.425329
$640$	−3.81106e12	−0.897918
$641$	4.10989e12	0.961544	0.480772	−	0.876846i	$-0.340357\pi$
$641$	4.10989e12	0.961544	0.480772	+	0.876846i	$0.340357\pi$
$642$	5.22010e12	1.21275
$643$	4.69775e12	1.08378	0.541889	−	0.840450i	$-0.317709\pi$
$643$	4.69775e12	1.08378	0.541889	+	0.840450i	$0.317709\pi$
$644$	−1.57897e11	−0.0361733
$645$	−5.57518e11	−0.126835
$646$	−9.21261e12	−2.08131
$647$	5.84716e11	0.131183	0.0655913	−	0.997847i	$-0.479107\pi$
$647$	5.84716e11	0.131183	0.0655913	+	0.997847i	$0.479107\pi$
$648$	2.50867e11	0.0558928
$649$	5.72320e11	0.126630
$650$	−1.12878e11	−0.0248027
$651$	2.68737e12	0.586427
$652$	−1.87108e12	−0.405488
$653$	−4.93511e12	−1.06215	−0.531077	−	0.847324i	$-0.678212\pi$
$653$	−4.93511e12	−1.06215	−0.531077	+	0.847324i	$0.678212\pi$
$654$	1.57044e12	0.335677
$655$	4.59739e12	0.975945
$656$	−8.32408e12	−1.75497
$657$	−3.01006e11	−0.0630276
$658$	−3.71020e11	−0.0771580
$659$	−6.38476e12	−1.31874	−0.659372	−	0.751817i	$-0.729178\pi$
$659$	−6.38476e12	−1.31874	−0.659372	+	0.751817i	$0.729178\pi$
$660$	−1.59858e12	−0.327934
$661$	−6.05954e12	−1.23462	−0.617310	−	0.786720i	$-0.711777\pi$
$661$	−6.05954e12	−1.23462	−0.617310	+	0.786720i	$0.711777\pi$
$662$	−7.76327e12	−1.57103
$663$	−1.18658e12	−0.238499
$664$	2.79011e12	0.557013
$665$	4.01329e12	0.795799
$666$	−3.03898e12	−0.598541
$667$	5.05552e11	0.0989008
$668$	3.47787e12	0.675802
$669$	−1.66766e12	−0.321876
$670$	7.85281e12	1.50553
$671$	6.32959e12	1.20538
$672$	2.09192e12	0.395716
$673$	−3.64991e12	−0.685827	−0.342913	−	0.939367i	$-0.611414\pi$
$673$	−3.64991e12	−0.685827	−0.342913	+	0.939367i	$0.611414\pi$
$674$	−8.12961e12	−1.51740
$675$	−6.33597e10	−0.0117475
$676$	−2.93498e12	−0.540562
$677$	−3.48204e12	−0.637067	−0.318534	−	0.947912i	$-0.603190\pi$
$677$	−3.48204e12	−0.637067	−0.318534	+	0.947912i	$0.603190\pi$
$678$	−6.41981e12	−1.16678
$679$	2.08977e12	0.377298
$680$	3.49789e12	0.627359
$681$	−2.67136e12	−0.475961
$682$	1.09908e13	1.94536
$683$	−7.32087e12	−1.28727	−0.643635	−	0.765332i	$-0.722575\pi$
$683$	−7.32087e12	−1.28727	−0.643635	+	0.765332i	$0.722575\pi$
$684$	1.46898e12	0.256603
$685$	−6.69040e11	−0.116103
$686$	7.49060e12	1.29139
$687$	−1.57734e12	−0.270160
$688$	1.65143e12	0.281003
$689$	−9.45535e10	−0.0159842
$690$	3.93705e11	0.0661227
$691$	6.66621e12	1.11232	0.556158	−	0.831077i	$-0.312275\pi$
$691$	6.66621e12	1.11232	0.556158	+	0.831077i	$0.312275\pi$
$692$	1.09124e11	0.0180901
$693$	−1.26561e12	−0.208449
$694$	1.21999e12	0.199635
$695$	8.52002e12	1.38519
$696$	−1.90463e12	−0.307658
$697$	1.13548e13	1.82234
$698$	−1.19798e13	−1.91029
$699$	4.92060e12	0.779598
$700$	−1.50241e11	−0.0236508
$701$	−7.34214e12	−1.14840	−0.574198	−	0.818717i	$-0.694686\pi$
$701$	−7.34214e12	−1.14840	−0.574198	+	0.818717i	$0.694686\pi$
$702$	5.03160e11	0.0781968
$703$	1.17333e13	1.81184
$704$	6.98183e11	0.107125
$705$	3.47871e11	0.0530356
$706$	1.14141e13	1.72910
$707$	4.33635e12	0.652735
$708$	−3.02847e11	−0.0452975
$709$	−1.07027e13	−1.59068	−0.795342	−	0.606161i	$-0.792709\pi$
$709$	−1.07027e13	−1.59068	−0.795342	+	0.606161i	$0.792709\pi$
$710$	1.05987e13	1.56527
$711$	1.02653e11	0.0150646
$712$	3.05392e12	0.445346
$713$	−1.01786e12	−0.147498
$714$	−4.20003e12	−0.604798
$715$	2.11406e12	0.302510
$716$	8.26712e12	1.17556
$717$	−2.71784e12	−0.384049
$718$	−6.60434e12	−0.927405
$719$	2.17776e12	0.303900	0.151950	−	0.988388i	$-0.451445\pi$
$719$	2.17776e12	0.303900	0.151950	+	0.988388i	$0.451445\pi$
$720$	−2.88690e12	−0.400346
$721$	8.18883e12	1.12853
$722$	−5.83929e12	−0.799729
$723$	2.62215e12	0.356891
$724$	2.61025e12	0.353068
$725$	4.81038e11	0.0646634
$726$	2.95007e11	0.0394110
$727$	1.12664e13	1.49583	0.747915	−	0.663795i	$-0.231055\pi$
$727$	1.12664e13	1.49583	0.747915	+	0.663795i	$0.231055\pi$
$728$	−7.86682e11	−0.103803
$729$	2.82430e11	0.0370370
$730$	1.77970e12	0.231949
$731$	−2.25269e12	−0.291791
$732$	−3.34935e12	−0.431182
$733$	1.14706e13	1.46764	0.733818	−	0.679346i	$-0.237737\pi$
$733$	1.14706e13	1.46764	0.733818	+	0.679346i	$0.237737\pi$
$734$	−6.12882e12	−0.779371
$735$	−2.59679e12	−0.328204
$736$	−7.92330e11	−0.0995304
$737$	9.56124e12	1.19374
$738$	−4.81489e12	−0.597492
$739$	5.18921e12	0.640032	0.320016	−	0.947412i	$-0.396312\pi$
$739$	5.18921e12	0.640032	0.320016	+	0.947412i	$0.396312\pi$
$740$	6.75653e12	0.828287
$741$	−1.94266e12	−0.236709
$742$	−3.34682e11	−0.0405336
$743$	−1.22170e13	−1.47067	−0.735335	−	0.677704i	$-0.762975\pi$
$743$	−1.22170e13	−1.47067	−0.735335	+	0.677704i	$0.762975\pi$
$744$	3.83471e12	0.458833
$745$	1.11978e13	1.33177
$746$	−1.61230e13	−1.90599
$747$	3.14115e12	0.369102
$748$	−6.45917e12	−0.754431
$749$	−9.18839e12	−1.06677
$750$	6.51162e12	0.751473
$751$	−1.48708e13	−1.70591	−0.852953	−	0.521987i	$-0.825191\pi$
$751$	−1.48708e13	−1.70591	−0.852953	+	0.521987i	$0.825191\pi$
$752$	−1.03043e12	−0.117500
$753$	4.36133e12	0.494358
$754$	−3.82008e12	−0.430429
$755$	4.82172e12	0.540059
$756$	6.69707e11	0.0745653
$757$	1.16388e13	1.28818	0.644088	−	0.764951i	$-0.277237\pi$
$757$	1.16388e13	1.28818	0.644088	+	0.764951i	$0.277237\pi$
$758$	1.82975e13	2.01317
$759$	4.79358e11	0.0524291
$760$	5.72671e12	0.622650
$761$	1.49171e13	1.61233	0.806163	−	0.591694i	$-0.201541\pi$
$761$	1.49171e13	1.61233	0.806163	+	0.591694i	$0.201541\pi$
$762$	9.42799e12	1.01303
$763$	−2.76428e12	−0.295271
$764$	6.41935e12	0.681665
$765$	3.93798e12	0.415716
$766$	9.34545e12	0.980779
$767$	4.00503e11	0.0417856
$768$	7.14280e12	0.740872
$769$	3.29875e12	0.340158	0.170079	−	0.985430i	$-0.445598\pi$
$769$	3.29875e12	0.340158	0.170079	+	0.985430i	$0.445598\pi$
$770$	7.48292e12	0.767119
$771$	5.62630e12	0.573427
$772$	−1.05847e13	−1.07251
$773$	−1.33569e13	−1.34554	−0.672770	−	0.739851i	$-0.734896\pi$
$773$	−1.33569e13	−1.34554	−0.672770	+	0.739851i	$0.734896\pi$
$774$	9.55233e11	0.0956698
$775$	−9.68507e11	−0.0964373
$776$	2.98197e12	0.295206
$777$	5.34919e12	0.526494
$778$	1.60535e13	1.57095
$779$	1.85899e13	1.80866
$780$	−1.11867e12	−0.108212
$781$	1.29045e13	1.24111
$782$	1.59079e12	0.152119
$783$	−2.14426e12	−0.203868
$784$	7.69197e12	0.727135
$785$	3.42463e11	0.0321885
$786$	−7.87702e12	−0.736140
$787$	−1.80700e13	−1.67908	−0.839542	−	0.543294i	$-0.817177\pi$
$787$	−1.80700e13	−1.67908	−0.839542	+	0.543294i	$0.817177\pi$
$788$	5.43090e12	0.501769
$789$	1.93408e12	0.177676
$790$	−6.06936e11	−0.0554397
$791$	1.13001e13	1.02633
$792$	−1.80594e12	−0.163095
$793$	4.42938e12	0.397753
$794$	−1.84869e13	−1.65071
$795$	3.13800e11	0.0278613
$796$	6.49102e12	0.573066
$797$	−1.44535e13	−1.26885	−0.634423	−	0.772986i	$-0.718762\pi$
$797$	−1.44535e13	−1.26885	−0.634423	+	0.772986i	$0.718762\pi$
$798$	−6.87624e12	−0.600258
$799$	1.40560e12	0.122011
$800$	−7.53910e11	−0.0650751
$801$	3.43815e12	0.295106
$802$	4.87522e12	0.416111
$803$	2.16688e12	0.183914
$804$	−5.05941e12	−0.427019
$805$	−6.92997e11	−0.0581634
$806$	7.69123e12	0.641930
$807$	−2.37916e12	−0.197466
$808$	6.18769e12	0.510714
$809$	2.01256e13	1.65188	0.825942	−	0.563755i	$-0.190644\pi$
$809$	2.01256e13	1.65188	0.825942	+	0.563755i	$0.190644\pi$
$810$	−1.66987e12	−0.136301
$811$	−1.90075e13	−1.54288	−0.771439	−	0.636303i	$-0.780463\pi$
$811$	−1.90075e13	−1.54288	−0.771439	+	0.636303i	$0.780463\pi$
$812$	−5.08454e12	−0.410439
$813$	−5.10514e12	−0.409827
$814$	2.18771e13	1.74654
$815$	−8.21201e12	−0.651989
$816$	−1.16647e13	−0.921019
$817$	−3.68807e12	−0.289601
$818$	3.41287e12	0.266520
$819$	−8.85658e11	−0.0687842
$820$	1.07049e13	0.826836
$821$	−5.47269e12	−0.420394	−0.210197	−	0.977659i	$-0.567411\pi$
$821$	−5.47269e12	−0.420394	−0.210197	+	0.977659i	$0.567411\pi$
$822$	1.14631e12	0.0875748
$823$	−3.86167e12	−0.293411	−0.146705	−	0.989180i	$-0.546867\pi$
$823$	−3.86167e12	−0.293411	−0.146705	+	0.989180i	$0.546867\pi$
$824$	1.16849e13	0.882986
$825$	4.56114e11	0.0342792
$826$	1.41762e12	0.105962
$827$	−2.06193e13	−1.53285	−0.766425	−	0.642333i	$-0.777966\pi$
$827$	−2.06193e13	−1.53285	−0.766425	+	0.642333i	$0.777966\pi$
$828$	−2.53656e11	−0.0187547
$829$	−1.10675e13	−0.813870	−0.406935	−	0.913457i	$-0.633402\pi$
$829$	−1.10675e13	−0.813870	−0.406935	+	0.913457i	$0.633402\pi$
$830$	−1.85721e13	−1.35834
$831$	−1.12235e13	−0.816437
$832$	4.88580e11	0.0353493
$833$	−1.04925e13	−0.755051
$834$	−1.45979e13	−1.04483
$835$	1.52641e13	1.08663
$836$	−1.05749e13	−0.748768
$837$	4.31717e12	0.304043
$838$	1.53803e12	0.107737
$839$	−1.11383e13	−0.776052	−0.388026	−	0.921649i	$-0.626843\pi$
$839$	−1.11383e13	−0.776052	−0.388026	+	0.921649i	$0.626843\pi$
$840$	2.61081e12	0.180933
$841$	1.77244e12	0.122177
$842$	2.10416e12	0.144269
$843$	7.61848e12	0.519570
$844$	−7.37866e12	−0.500538
$845$	−1.28814e13	−0.869176
$846$	−5.96031e11	−0.0400039
$847$	−5.19269e11	−0.0346671
$848$	−9.29510e11	−0.0617267
$849$	1.88202e12	0.124320
$850$	1.51365e12	0.0994584
$851$	−2.02604e12	−0.132424
$852$	−6.82849e12	−0.443963
$853$	1.30570e12	0.0844447	0.0422224	−	0.999108i	$-0.486556\pi$
$853$	1.30570e12	0.0844447	0.0422224	+	0.999108i	$0.486556\pi$
$854$	1.56782e13	1.00864
$855$	6.44721e12	0.412596
$856$	−1.31112e13	−0.834664
$857$	4.94604e12	0.313216	0.156608	−	0.987661i	$-0.449944\pi$
$857$	4.94604e12	0.313216	0.156608	+	0.987661i	$0.449944\pi$
$858$	−3.62215e12	−0.228178
$859$	−1.36929e13	−0.858079	−0.429040	−	0.903286i	$-0.641148\pi$
$859$	−1.36929e13	−0.858079	−0.429040	+	0.903286i	$0.641148\pi$
$860$	−2.12376e12	−0.132392
$861$	8.47513e12	0.525572
$862$	−1.97246e13	−1.21682
$863$	5.25820e12	0.322692	0.161346	−	0.986898i	$-0.448416\pi$
$863$	5.25820e12	0.322692	0.161346	+	0.986898i	$0.448416\pi$
$864$	3.36060e12	0.205166
$865$	4.78935e11	0.0290873
$866$	−1.54291e12	−0.0932204
$867$	6.30604e12	0.379027
$868$	1.02370e13	0.612118
$869$	−7.38979e11	−0.0439585
$870$	1.26779e13	0.750260
$871$	6.69085e12	0.393912
$872$	−3.94445e12	−0.231026
$873$	3.35715e12	0.195617
$874$	2.60443e12	0.150977
$875$	−1.14617e13	−0.661018
$876$	−1.14662e12	−0.0657888
$877$	2.98371e13	1.70317	0.851585	−	0.524216i	$-0.175642\pi$
$877$	2.98371e13	1.70317	0.851585	+	0.524216i	$0.175642\pi$
$878$	−3.16833e13	−1.79931
$879$	−4.89016e12	−0.276295
$880$	2.07823e13	1.16821
$881$	−1.01896e13	−0.569858	−0.284929	−	0.958549i	$-0.591970\pi$
$881$	−1.01896e13	−0.569858	−0.284929	+	0.958549i	$0.591970\pi$
$882$	4.44925e12	0.247559
$883$	−1.30284e13	−0.721220	−0.360610	−	0.932717i	$-0.617431\pi$
$883$	−1.30284e13	−0.721220	−0.360610	+	0.932717i	$0.617431\pi$
$884$	−4.52005e12	−0.248948
$885$	−1.32917e12	−0.0728344
$886$	6.20977e12	0.338551
$887$	−1.76648e13	−0.958189	−0.479095	−	0.877763i	$-0.659035\pi$
$887$	−1.76648e13	−0.958189	−0.479095	+	0.877763i	$0.659035\pi$
$888$	7.63295e12	0.411940
$889$	−1.65951e13	−0.891089
$890$	−2.03281e13	−1.08603
$891$	−2.03316e12	−0.108074
$892$	−6.35262e12	−0.335978
$893$	2.30123e12	0.121095
$894$	−1.91860e13	−1.00454
$895$	3.62837e13	1.89020
$896$	−1.14936e13	−0.595759
$897$	3.35449e11	0.0173006
$898$	−7.76442e12	−0.398442
$899$	−3.27768e13	−1.67358
$900$	−2.41357e11	−0.0122622
$901$	1.26793e12	0.0640964
$902$	3.46614e13	1.74348
$903$	−1.68139e12	−0.0841539
$904$	1.61245e13	0.803025
$905$	1.14562e13	0.567702
$906$	−8.26138e12	−0.407358
$907$	1.51366e13	0.742670	0.371335	−	0.928499i	$-0.378900\pi$
$907$	1.51366e13	0.742670	0.371335	+	0.928499i	$0.378900\pi$
$908$	−1.01760e13	−0.496813
$909$	6.96619e12	0.338421
$910$	5.23646e12	0.253135
$911$	−1.57055e13	−0.755475	−0.377737	−	0.925913i	$-0.623298\pi$
$911$	−1.57055e13	−0.755475	−0.377737	+	0.925913i	$0.623298\pi$
$912$	−1.90973e13	−0.914105
$913$	−2.26125e13	−1.07704
$914$	−2.40974e13	−1.14212
$915$	−1.47000e13	−0.693303
$916$	−6.00858e12	−0.281996
$917$	1.38651e13	0.647530
$918$	−6.74720e12	−0.313568
$919$	−1.90392e13	−0.880499	−0.440249	−	0.897876i	$-0.645110\pi$
$919$	−1.90392e13	−0.880499	−0.440249	+	0.897876i	$0.645110\pi$
$920$	−9.88862e11	−0.0455083
$921$	−1.08781e13	−0.498178
$922$	6.51826e12	0.297059
$923$	9.03039e12	0.409542
$924$	−4.82109e12	−0.217581
$925$	−1.92780e12	−0.0865814
$926$	−2.49868e13	−1.11677
$927$	1.31551e13	0.585106
$928$	−2.55143e13	−1.12932
$929$	−6.52504e12	−0.287417	−0.143709	−	0.989620i	$-0.545903\pi$
$929$	−6.52504e12	−0.287417	−0.143709	+	0.989620i	$0.545903\pi$
$930$	−2.55253e13	−1.11892
$931$	−1.71782e13	−0.749383
$932$	1.87441e13	0.813752
$933$	2.57725e13	1.11350
$934$	−3.17897e13	−1.36686
$935$	−2.83488e13	−1.21306
$936$	−1.26378e12	−0.0538182
$937$	2.08263e13	0.882639	0.441320	−	0.897350i	$-0.354511\pi$
$937$	2.08263e13	0.882639	0.441320	+	0.897350i	$0.354511\pi$
$938$	2.36830e13	0.998903
$939$	−6.22395e12	−0.261259
$940$	1.32515e12	0.0553591
$941$	−3.04865e13	−1.26752	−0.633759	−	0.773531i	$-0.718489\pi$
$941$	−3.04865e13	−1.26752	−0.633759	+	0.773531i	$0.718489\pi$
$942$	−5.86765e11	−0.0242792
$943$	−3.21001e12	−0.132192
$944$	3.93715e12	0.161364
$945$	2.93929e12	0.119894
$946$	−6.87654e12	−0.279164
$947$	−2.68526e13	−1.08495	−0.542477	−	0.840070i	$-0.682514\pi$
$947$	−2.68526e13	−1.08495	−0.542477	+	0.840070i	$0.682514\pi$
$948$	3.91036e11	0.0157246
$949$	1.51636e12	0.0606882
$950$	2.47814e12	0.0987118
$951$	1.37201e13	0.543934
$952$	1.05491e13	0.416247
$953$	3.94794e13	1.55043	0.775215	−	0.631698i	$-0.217642\pi$
$953$	3.94794e13	1.55043	0.775215	+	0.631698i	$0.217642\pi$
$954$	−5.37655e11	−0.0210153
$955$	2.81740e13	1.09606
$956$	−1.03531e13	−0.400875
$957$	1.54361e13	0.594886
$958$	−4.62876e13	−1.77550
$959$	−2.01773e12	−0.0770333
$960$	−1.62148e12	−0.0616156
$961$	3.95520e13	1.49594
$962$	1.53093e13	0.576325
$963$	−1.47608e13	−0.553086
$964$	9.98859e12	0.372527
$965$	−4.64554e13	−1.72450
$966$	1.18736e12	0.0438717
$967$	−2.15101e13	−0.791084	−0.395542	−	0.918448i	$-0.629443\pi$
$967$	−2.15101e13	−0.791084	−0.395542	+	0.918448i	$0.629443\pi$
$968$	−7.40964e11	−0.0271243
$969$	2.60504e13	0.949199
$970$	−1.98492e13	−0.719895
$971$	3.93783e13	1.42158	0.710788	−	0.703407i	$-0.248339\pi$
$971$	3.93783e13	1.42158	0.710788	+	0.703407i	$0.248339\pi$
$972$	1.07586e12	0.0386596
$973$	2.56952e13	0.919059
$974$	−9.88036e12	−0.351769
$975$	3.19184e11	0.0113115
$976$	4.35431e13	1.53601
$977$	1.28009e13	0.449486	0.224743	−	0.974418i	$-0.427846\pi$
$977$	1.28009e13	0.449486	0.224743	+	0.974418i	$0.427846\pi$
$978$	1.40702e13	0.491785
$979$	−2.47506e13	−0.861118
$980$	−9.89196e12	−0.342582
$981$	−4.44071e12	−0.153088
$982$	3.71041e13	1.27327
$983$	−1.49540e13	−0.510817	−0.255409	−	0.966833i	$-0.582210\pi$
$983$	−1.49540e13	−0.510817	−0.255409	+	0.966833i	$0.582210\pi$
$984$	1.20935e13	0.411218
$985$	2.38357e13	0.806800
$986$	5.12260e13	1.72601
$987$	1.04913e12	0.0351886
$988$	−7.40018e12	−0.247079
$989$	6.36840e11	0.0211664
$990$	1.20211e13	0.397726
$991$	−1.75648e13	−0.578510	−0.289255	−	0.957252i	$-0.593408\pi$
$991$	−1.75648e13	−0.578510	−0.289255	+	0.957252i	$0.593408\pi$
$992$	5.13696e13	1.68424
$993$	2.19521e13	0.716481
$994$	3.19640e13	1.03854
$995$	2.84886e13	0.921439
$996$	1.19656e13	0.385272
$997$	1.48830e13	0.477047	0.238523	−	0.971137i	$-0.423337\pi$
$997$	1.48830e13	0.477047	0.238523	+	0.971137i	$0.423337\pi$
$998$	−6.09758e13	−1.94567
$999$	8.59329e12	0.272970

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.d.1.5	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.d.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-28.6453 q^{2} +81.0000 q^{3} +308.554 q^{4} +1354.22 q^{5} -2320.27 q^{6} +4084.12 q^{7} +5827.78 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-28.6453 q^{2} +81.0000 q^{3} +308.554 q^{4} +1354.22 q^{5} -2320.27 q^{6} +4084.12 q^{7} +5827.78 q^{8} +6561.00 q^{9} -38792.0 q^{10} -47231.4 q^{11} +24992.9 q^{12} -33052.0 q^{13} -116991. q^{14} +109692. q^{15} -324918. q^{16} +443216. q^{17} -187942. q^{18} +725628. q^{19} +417849. q^{20} +330814. q^{21} +1.35296e6 q^{22} -125298. q^{23} +472050. q^{24} -119222. q^{25} +946784. q^{26} +531441. q^{27} +1.26017e6 q^{28} -4.03480e6 q^{29} -3.14215e6 q^{30} +8.12353e6 q^{31} +6.32356e6 q^{32} -3.82574e6 q^{33} -1.26961e7 q^{34} +5.53079e6 q^{35} +2.02442e6 q^{36} +1.61698e7 q^{37} -2.07858e7 q^{38} -2.67721e6 q^{39} +7.89208e6 q^{40} +2.56190e7 q^{41} -9.47627e6 q^{42} -5.08260e6 q^{43} -1.45734e7 q^{44} +8.88501e6 q^{45} +3.58920e6 q^{46} +3.17136e6 q^{47} -2.63184e7 q^{48} -2.36736e7 q^{49} +3.41516e6 q^{50} +3.59005e7 q^{51} -1.01983e7 q^{52} +2.86075e6 q^{53} -1.52233e7 q^{54} -6.39615e7 q^{55} +2.38014e7 q^{56} +5.87759e7 q^{57} +1.15578e8 q^{58} -1.21174e7 q^{59} +3.38457e7 q^{60} -1.34012e8 q^{61} -2.32701e8 q^{62} +2.67959e7 q^{63} -1.47822e7 q^{64} -4.47595e7 q^{65} +1.09590e8 q^{66} -2.02434e8 q^{67} +1.36756e8 q^{68} -1.01491e7 q^{69} -1.58431e8 q^{70} -2.73218e8 q^{71} +3.82361e7 q^{72} -4.58780e7 q^{73} -4.63189e8 q^{74} -9.65702e6 q^{75} +2.23895e8 q^{76} -1.92899e8 q^{77} +7.66895e7 q^{78} +1.56459e7 q^{79} -4.40009e8 q^{80} +4.30467e7 q^{81} -7.33865e8 q^{82} +4.78761e8 q^{83} +1.02074e8 q^{84} +6.00210e8 q^{85} +1.45593e8 q^{86} -3.26819e8 q^{87} -2.75254e8 q^{88} +5.24028e8 q^{89} -2.54514e8 q^{90} -1.34988e8 q^{91} -3.86612e7 q^{92} +6.58006e8 q^{93} -9.08446e7 q^{94} +9.82657e8 q^{95} +5.12208e8 q^{96} +5.11682e8 q^{97} +6.78136e8 q^{98} -3.09885e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9}+O(q^{10}) \) 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9} + 45337 q^{10} + 111769 q^{11} + 483894 q^{12} + 189121 q^{13} + 251053 q^{14} + 468666 q^{15} + 2311074 q^{16} + 1113841 q^{17} + 301806 q^{18} + 476068 q^{19} - 42495 q^{20} + 618921 q^{21} - 2252022 q^{22} + 7103062 q^{23} + 4972995 q^{24} + 10628442 q^{25} + 6871048 q^{26} + 11691702 q^{27} + 8112650 q^{28} + 15279316 q^{29} + 3672297 q^{30} + 17610338 q^{31} + 32378276 q^{32} + 9053289 q^{33} + 29339436 q^{34} + 7134904 q^{35} + 39195414 q^{36} + 21961411 q^{37} + 65195131 q^{38} + 15318801 q^{39} + 75185084 q^{40} + 52781575 q^{41} + 20335293 q^{42} + 76191313 q^{43} + 61127768 q^{44} + 37961946 q^{45} + 290208769 q^{46} + 160572396 q^{47} + 187196994 q^{48} + 156292703 q^{49} + 169504821 q^{50} + 90221121 q^{51} + 65465920 q^{52} - 8762038 q^{53} + 24446286 q^{54} + 147125140 q^{55} + 9671794 q^{56} + 38561508 q^{57} - 37665424 q^{58} - 266581942 q^{59} - 3442095 q^{60} + 120750754 q^{61} - 152465186 q^{62} + 50132601 q^{63} - 40658803 q^{64} + 331055798 q^{65} - 182413782 q^{66} + 41371828 q^{67} + 145606631 q^{68} + 575348022 q^{69} - 920887614 q^{70} + 261018751 q^{71} + 402812595 q^{72} + 178388 q^{73} - 303908734 q^{74} + 860903802 q^{75} - 94541144 q^{76} + 299640561 q^{77} + 556554888 q^{78} - 905381353 q^{79} + 939128289 q^{80} + 947027862 q^{81} - 551739753 q^{82} + 1173257869 q^{83} + 657124650 q^{84} - 1546633210 q^{85} + 1384869460 q^{86} + 1237624596 q^{87} + 189740713 q^{88} + 898004974 q^{89} + 297456057 q^{90} + 591272339 q^{91} + 4328210270 q^{92} + 1426437378 q^{93} + 122568068 q^{94} + 2487967134 q^{95} + 2622640356 q^{96} + 3175709684 q^{97} + 5095778404 q^{98} + 733316409 q^{99}+O(q^{100}) \) 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9 + 45337 * q^10 + 111769 * q^11 + 483894 * q^12 + 189121 * q^13 + 251053 * q^14 + 468666 * q^15 + 2311074 * q^16 + 1113841 * q^17 + 301806 * q^18 + 476068 * q^19 - 42495 * q^20 + 618921 * q^21 - 2252022 * q^22 + 7103062 * q^23 + 4972995 * q^24 + 10628442 * q^25 + 6871048 * q^26 + 11691702 * q^27 + 8112650 * q^28 + 15279316 * q^29 + 3672297 * q^30 + 17610338 * q^31 + 32378276 * q^32 + 9053289 * q^33 + 29339436 * q^34 + 7134904 * q^35 + 39195414 * q^36 + 21961411 * q^37 + 65195131 * q^38 + 15318801 * q^39 + 75185084 * q^40 + 52781575 * q^41 + 20335293 * q^42 + 76191313 * q^43 + 61127768 * q^44 + 37961946 * q^45 + 290208769 * q^46 + 160572396 * q^47 + 187196994 * q^48 + 156292703 * q^49 + 169504821 * q^50 + 90221121 * q^51 + 65465920 * q^52 - 8762038 * q^53 + 24446286 * q^54 + 147125140 * q^55 + 9671794 * q^56 + 38561508 * q^57 - 37665424 * q^58 - 266581942 * q^59 - 3442095 * q^60 + 120750754 * q^61 - 152465186 * q^62 + 50132601 * q^63 - 40658803 * q^64 + 331055798 * q^65 - 182413782 * q^66 + 41371828 * q^67 + 145606631 * q^68 + 575348022 * q^69 - 920887614 * q^70 + 261018751 * q^71 + 402812595 * q^72 + 178388 * q^73 - 303908734 * q^74 + 860903802 * q^75 - 94541144 * q^76 + 299640561 * q^77 + 556554888 * q^78 - 905381353 * q^79 + 939128289 * q^80 + 947027862 * q^81 - 551739753 * q^82 + 1173257869 * q^83 + 657124650 * q^84 - 1546633210 * q^85 + 1384869460 * q^86 + 1237624596 * q^87 + 189740713 * q^88 + 898004974 * q^89 + 297456057 * q^90 + 591272339 * q^91 + 4328210270 * q^92 + 1426437378 * q^93 + 122568068 * q^94 + 2487967134 * q^95 + 2622640356 * q^96 + 3175709684 * q^97 + 5095778404 * q^98 + 733316409 * q^99

Introduction

L-functions

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