LMFDB - Embedded newform 177.10.a.c.1.19

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			1.19
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)

$f(q)$	$=$	$q+34.5007 q^{2} -81.0000 q^{3} +678.300 q^{4} -2125.49 q^{5} -2794.56 q^{6} -11083.2 q^{7} +5737.48 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+34.5007 q^{2} -81.0000 q^{3} +678.300 q^{4} -2125.49 q^{5} -2794.56 q^{6} -11083.2 q^{7} +5737.48 q^{8} +6561.00 q^{9} -73331.0 q^{10} -12849.6 q^{11} -54942.3 q^{12} -98344.5 q^{13} -382379. q^{14} +172165. q^{15} -149342. q^{16} -55245.8 q^{17} +226359. q^{18} +134898. q^{19} -1.44172e6 q^{20} +897739. q^{21} -443321. q^{22} +1.76768e6 q^{23} -464736. q^{24} +2.56459e6 q^{25} -3.39296e6 q^{26} -531441. q^{27} -7.51774e6 q^{28} -1.27561e6 q^{29} +5.93981e6 q^{30} +655974. q^{31} -8.09001e6 q^{32} +1.04082e6 q^{33} -1.90602e6 q^{34} +2.35573e7 q^{35} +4.45033e6 q^{36} -1.12387e7 q^{37} +4.65407e6 q^{38} +7.96591e6 q^{39} -1.21950e7 q^{40} +9.02546e6 q^{41} +3.09727e7 q^{42} -3.12935e7 q^{43} -8.71589e6 q^{44} -1.39454e7 q^{45} +6.09862e7 q^{46} +4.08477e7 q^{47} +1.20967e7 q^{48} +8.24838e7 q^{49} +8.84803e7 q^{50} +4.47491e6 q^{51} -6.67071e7 q^{52} +5.63144e7 q^{53} -1.83351e7 q^{54} +2.73117e7 q^{55} -6.35897e7 q^{56} -1.09267e7 q^{57} -4.40095e7 q^{58} +1.21174e7 q^{59} +1.16780e8 q^{60} -5.05723e7 q^{61} +2.26316e7 q^{62} -7.27169e7 q^{63} -2.02648e8 q^{64} +2.09031e8 q^{65} +3.59090e7 q^{66} -2.08793e8 q^{67} -3.74732e7 q^{68} -1.43182e8 q^{69} +8.12743e8 q^{70} -2.83381e8 q^{71} +3.76436e7 q^{72} +3.02362e8 q^{73} -3.87743e8 q^{74} -2.07732e8 q^{75} +9.15013e7 q^{76} +1.42415e8 q^{77} +2.74830e8 q^{78} -6.85379e6 q^{79} +3.17426e8 q^{80} +4.30467e7 q^{81} +3.11385e8 q^{82} -7.30628e7 q^{83} +6.08937e8 q^{84} +1.17425e8 q^{85} -1.07965e9 q^{86} +1.03324e8 q^{87} -7.37244e7 q^{88} -9.42405e8 q^{89} -4.81125e8 q^{90} +1.08997e9 q^{91} +1.19902e9 q^{92} -5.31339e7 q^{93} +1.40928e9 q^{94} -2.86724e8 q^{95} +6.55291e8 q^{96} +5.45381e8 q^{97} +2.84575e9 q^{98} -8.43063e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	34.5007	1.52473	0.762366	−	0.647147i	$-0.224038\pi$
$2$	34.5007	1.52473	0.762366	+	0.647147i	$0.224038\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	678.300	1.32481
$5$	−2125.49	−1.52088	−0.760439	−	0.649409i	$-0.775016\pi$
$5$	−2125.49	−1.52088	−0.760439	+	0.649409i	$0.775016\pi$
$6$	−2794.56	−0.880304
$7$	−11083.2	−1.74471	−0.872357	−	0.488870i	$-0.837409\pi$
$7$	−11083.2	−1.74471	−0.872357	+	0.488870i	$0.837409\pi$
$8$	5737.48	0.495241
$9$	6561.00	0.333333
$10$	−73331.0	−2.31893
$11$	−12849.6	−0.264620	−0.132310	−	0.991208i	$-0.542239\pi$
$11$	−12849.6	−0.264620	−0.132310	+	0.991208i	$0.542239\pi$
$12$	−54942.3	−0.764877
$13$	−98344.5	−0.955004	−0.477502	−	0.878631i	$-0.658458\pi$
$13$	−98344.5	−0.955004	−0.477502	+	0.878631i	$0.658458\pi$
$14$	−382379.	−2.66022
$15$	172165.	0.878080
$16$	−149342.	−0.569696
$17$	−55245.8	−0.160428	−0.0802138	−	0.996778i	$-0.525560\pi$
$17$	−55245.8	−0.160428	−0.0802138	+	0.996778i	$0.525560\pi$
$18$	226359.	0.508244
$19$	134898.	0.237473	0.118736	−	0.992926i	$-0.462116\pi$
$19$	134898.	0.237473	0.118736	+	0.992926i	$0.462116\pi$
$20$	−1.44172e6	−2.01487
$21$	897739.	1.00731
$22$	−443321.	−0.403474
$23$	1.76768e6	1.31713	0.658564	−	0.752524i	$-0.271164\pi$
$23$	1.76768e6	1.31713	0.658564	+	0.752524i	$0.271164\pi$
$24$	−464736.	−0.285927
$25$	2.56459e6	1.31307
$26$	−3.39296e6	−1.45612
$27$	−531441.	−0.192450
$28$	−7.51774e6	−2.31141
$29$	−1.27561e6	−0.334909	−0.167455	−	0.985880i	$-0.553555\pi$
$29$	−1.27561e6	−0.334909	−0.167455	+	0.985880i	$0.553555\pi$
$30$	5.93981e6	1.33884
$31$	655974.	0.127573	0.0637866	−	0.997964i	$-0.479682\pi$
$31$	655974.	0.127573	0.0637866	+	0.997964i	$0.479682\pi$
$32$	−8.09001e6	−1.36387
$33$	1.04082e6	0.152778
$34$	−1.90602e6	−0.244609
$35$	2.35573e7	2.65350
$36$	4.45033e6	0.441602
$37$	−1.12387e7	−0.985843	−0.492922	−	0.870074i	$-0.664071\pi$
$37$	−1.12387e7	−0.985843	−0.492922	+	0.870074i	$0.664071\pi$
$38$	4.65407e6	0.362082
$39$	7.96591e6	0.551372
$40$	−1.21950e7	−0.753201
$41$	9.02546e6	0.498818	0.249409	−	0.968398i	$-0.419764\pi$
$41$	9.02546e6	0.498818	0.249409	+	0.968398i	$0.419764\pi$
$42$	3.09727e7	1.53588
$43$	−3.12935e7	−1.39587	−0.697936	−	0.716160i	$-0.745898\pi$
$43$	−3.12935e7	−1.39587	−0.697936	+	0.716160i	$0.745898\pi$
$44$	−8.71589e6	−0.350570
$45$	−1.39454e7	−0.506960
$46$	6.09862e7	2.00827
$47$	4.08477e7	1.22103	0.610517	−	0.792003i	$-0.290962\pi$
$47$	4.08477e7	1.22103	0.610517	+	0.792003i	$0.290962\pi$
$48$	1.20967e7	0.328914
$49$	8.24838e7	2.04403
$50$	8.84803e7	2.00208
$51$	4.47491e6	0.0926229
$52$	−6.67071e7	−1.26519
$53$	5.63144e7	0.980344	0.490172	−	0.871626i	$-0.336934\pi$
$53$	5.63144e7	0.980344	0.490172	+	0.871626i	$0.336934\pi$
$54$	−1.83351e7	−0.293435
$55$	2.73117e7	0.402455
$56$	−6.35897e7	−0.864053
$57$	−1.09267e7	−0.137105
$58$	−4.40095e7	−0.510647
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	1.16780e8	1.16328
$61$	−5.05723e7	−0.467658	−0.233829	−	0.972278i	$-0.575126\pi$
$61$	−5.05723e7	−0.467658	−0.233829	+	0.972278i	$0.575126\pi$
$62$	2.26316e7	0.194515
$63$	−7.27169e7	−0.581571
$64$	−2.02648e8	−1.50985
$65$	2.09031e8	1.45244
$66$	3.59090e7	0.232946
$67$	−2.08793e8	−1.26584	−0.632920	−	0.774217i	$-0.718144\pi$
$67$	−2.08793e8	−1.26584	−0.632920	+	0.774217i	$0.718144\pi$
$68$	−3.74732e7	−0.212535
$69$	−1.43182e8	−0.760445
$70$	8.12743e8	4.04587
$71$	−2.83381e8	−1.32345	−0.661727	−	0.749745i	$-0.730176\pi$
$71$	−2.83381e8	−1.32345	−0.661727	+	0.749745i	$0.730176\pi$
$72$	3.76436e7	0.165080
$73$	3.02362e8	1.24616	0.623081	−	0.782158i	$-0.285881\pi$
$73$	3.02362e8	1.24616	0.623081	+	0.782158i	$0.285881\pi$
$74$	−3.87743e8	−1.50315
$75$	−2.07732e8	−0.758102
$76$	9.15013e7	0.314605
$77$	1.42415e8	0.461686
$78$	2.74830e8	0.840694
$79$	−6.85379e6	−0.0197974	−0.00989872	−	0.999951i	$-0.503151\pi$
$79$	−6.85379e6	−0.0197974	−0.00989872	+	0.999951i	$0.503151\pi$
$80$	3.17426e8	0.866439
$81$	4.30467e7	0.111111
$82$	3.11385e8	0.760563
$83$	−7.30628e7	−0.168984	−0.0844919	−	0.996424i	$-0.526927\pi$
$83$	−7.30628e7	−0.168984	−0.0844919	+	0.996424i	$0.526927\pi$
$84$	6.08937e8	1.33449
$85$	1.17425e8	0.243991
$86$	−1.07965e9	−2.12833
$87$	1.03324e8	0.193360
$88$	−7.37244e7	−0.131051
$89$	−9.42405e8	−1.59215	−0.796073	−	0.605201i	$-0.793093\pi$
$89$	−9.42405e8	−1.59215	−0.796073	+	0.605201i	$0.793093\pi$
$90$	−4.81125e8	−0.772977
$91$	1.08997e9	1.66621
$92$	1.19902e9	1.74494
$93$	−5.31339e7	−0.0736544
$94$	1.40928e9	1.86175
$95$	−2.86724e8	−0.361167
$96$	6.55291e8	0.787433
$97$	5.45381e8	0.625499	0.312750	−	0.949836i	$-0.398750\pi$
$97$	5.45381e8	0.625499	0.312750	+	0.949836i	$0.398750\pi$
$98$	2.84575e9	3.11659
$99$	−8.43063e7	−0.0882067
$100$	1.73956e9	1.73956
$101$	−2.91991e8	−0.279205	−0.139603	−	0.990208i	$-0.544583\pi$
$101$	−2.91991e8	−0.279205	−0.139603	+	0.990208i	$0.544583\pi$
$102$	1.54388e8	0.141225
$103$	8.14008e8	0.712625	0.356313	−	0.934367i	$-0.384034\pi$
$103$	8.14008e8	0.712625	0.356313	+	0.934367i	$0.384034\pi$
$104$	−5.64250e8	−0.472957
$105$	−1.90814e9	−1.53200
$106$	1.94289e9	1.49476
$107$	−3.35348e8	−0.247325	−0.123663	−	0.992324i	$-0.539464\pi$
$107$	−3.35348e8	−0.247325	−0.123663	+	0.992324i	$0.539464\pi$
$108$	−3.60477e8	−0.254959
$109$	1.00621e9	0.682761	0.341381	−	0.939925i	$-0.389105\pi$
$109$	1.00621e9	0.682761	0.341381	+	0.939925i	$0.389105\pi$
$110$	9.42275e8	0.613636
$111$	9.10334e8	0.569177
$112$	1.65519e9	0.993957
$113$	−3.73099e8	−0.215264	−0.107632	−	0.994191i	$-0.534327\pi$
$113$	−3.73099e8	−0.215264	−0.107632	+	0.994191i	$0.534327\pi$
$114$	−3.76980e8	−0.209048
$115$	−3.75719e9	−2.00319
$116$	−8.65247e8	−0.443690
$117$	−6.45238e8	−0.318335
$118$	4.18058e8	0.198503
$119$	6.12300e8	0.279900
$120$	9.87793e8	0.434861
$121$	−2.19284e9	−0.929976
$122$	−1.74478e9	−0.713053
$123$	−7.31062e8	−0.287993
$124$	4.44947e8	0.169010
$125$	−1.29967e9	−0.476144
$126$	−2.50879e9	−0.886740
$127$	−2.03108e9	−0.692803	−0.346401	−	0.938086i	$-0.612596\pi$
$127$	−2.03108e9	−0.692803	−0.346401	+	0.938086i	$0.612596\pi$
$128$	−2.84942e9	−0.938234
$129$	2.53477e9	0.805907
$130$	7.21171e9	2.21459
$131$	3.15608e9	0.936326	0.468163	−	0.883642i	$-0.344916\pi$
$131$	3.15608e9	0.936326	0.468163	+	0.883642i	$0.344916\pi$
$132$	7.05987e8	0.202402
$133$	−1.49510e9	−0.414322
$134$	−7.20350e9	−1.93007
$135$	1.12957e9	0.292693
$136$	−3.16972e8	−0.0794503
$137$	5.88365e9	1.42693	0.713467	−	0.700688i	$-0.247124\pi$
$137$	5.88365e9	1.42693	0.713467	+	0.700688i	$0.247124\pi$
$138$	−4.93988e9	−1.15947
$139$	−6.07512e9	−1.38035	−0.690174	−	0.723643i	$-0.742466\pi$
$139$	−6.07512e9	−1.38035	−0.690174	+	0.723643i	$0.742466\pi$
$140$	1.59789e10	3.51537
$141$	−3.30867e9	−0.704964
$142$	−9.77686e9	−2.01791
$143$	1.26369e9	0.252713
$144$	−9.79836e8	−0.189899
$145$	2.71130e9	0.509357
$146$	1.04317e10	1.90006
$147$	−6.68119e9	−1.18012
$148$	−7.62320e9	−1.30605
$149$	−1.45458e9	−0.241768	−0.120884	−	0.992667i	$-0.538573\pi$
$149$	−1.45458e9	−0.241768	−0.120884	+	0.992667i	$0.538573\pi$
$150$	−7.16691e9	−1.15590
$151$	4.99891e9	0.782491	0.391245	−	0.920286i	$-0.372044\pi$
$151$	4.99891e9	0.782491	0.391245	+	0.920286i	$0.372044\pi$
$152$	7.73974e8	0.117606
$153$	−3.62468e8	−0.0534759
$154$	4.91341e9	0.703947
$155$	−1.39427e9	−0.194023
$156$	5.40328e9	0.730460
$157$	−9.43502e8	−0.123935	−0.0619675	−	0.998078i	$-0.519738\pi$
$157$	−9.43502e8	−0.123935	−0.0619675	+	0.998078i	$0.519738\pi$
$158$	−2.36461e8	−0.0301858
$159$	−4.56147e9	−0.566002
$160$	1.71953e10	2.07429
$161$	−1.95915e10	−2.29801
$162$	1.48514e9	0.169415
$163$	−5.47947e9	−0.607987	−0.303994	−	0.952674i	$-0.598320\pi$
$163$	−5.47947e9	−0.607987	−0.303994	+	0.952674i	$0.598320\pi$
$164$	6.12197e9	0.660837
$165$	−2.21225e9	−0.232357
$166$	−2.52072e9	−0.257655
$167$	1.84188e10	1.83247	0.916236	−	0.400639i	$-0.131212\pi$
$167$	1.84188e10	1.83247	0.916236	+	0.400639i	$0.131212\pi$
$168$	5.15076e9	0.498861
$169$	−9.32855e8	−0.0879678
$170$	4.05123e9	0.372021
$171$	8.85065e8	0.0791576
$172$	−2.12264e10	−1.84926
$173$	−4.05329e9	−0.344033	−0.172017	−	0.985094i	$-0.555028\pi$
$173$	−4.05329e9	−0.344033	−0.172017	+	0.985094i	$0.555028\pi$
$174$	3.56477e9	0.294822
$175$	−2.84239e10	−2.29093
$176$	1.91899e9	0.150753
$177$	−9.81506e8	−0.0751646
$178$	−3.25137e10	−2.42759
$179$	−1.52337e10	−1.10909	−0.554545	−	0.832154i	$-0.687108\pi$
$179$	−1.52337e10	−1.10909	−0.554545	+	0.832154i	$0.687108\pi$
$180$	−9.45914e9	−0.671623
$181$	2.36616e10	1.63866	0.819332	−	0.573320i	$-0.194345\pi$
$181$	2.36616e10	1.63866	0.819332	+	0.573320i	$0.194345\pi$
$182$	3.76048e10	2.54052
$183$	4.09636e9	0.270003
$184$	1.01420e10	0.652296
$185$	2.38877e10	1.49935
$186$	−1.83316e9	−0.112303
$187$	7.09887e8	0.0424524
$188$	2.77070e10	1.61763
$189$	5.89007e9	0.335770
$190$	−9.89220e9	−0.550683
$191$	1.67134e10	0.908686	0.454343	−	0.890827i	$-0.349874\pi$
$191$	1.67134e10	0.908686	0.454343	+	0.890827i	$0.349874\pi$
$192$	1.64145e10	0.871710
$193$	2.66584e10	1.38301	0.691507	−	0.722370i	$-0.256947\pi$
$193$	2.66584e10	1.38301	0.691507	+	0.722370i	$0.256947\pi$
$194$	1.88160e10	0.953718
$195$	−1.69315e10	−0.838569
$196$	5.59488e10	2.70794
$197$	1.97136e9	0.0932539	0.0466269	−	0.998912i	$-0.485153\pi$
$197$	1.97136e9	0.0932539	0.0466269	+	0.998912i	$0.485153\pi$
$198$	−2.90863e9	−0.134491
$199$	4.05270e10	1.83191	0.915957	−	0.401276i	$-0.131433\pi$
$199$	4.05270e10	1.83191	0.915957	+	0.401276i	$0.131433\pi$
$200$	1.47143e10	0.650287
$201$	1.69122e10	0.730833
$202$	−1.00739e10	−0.425713
$203$	1.41379e10	0.584321
$204$	3.03533e9	0.122707
$205$	−1.91836e10	−0.758642
$206$	2.80839e10	1.08656
$207$	1.15977e10	0.439043
$208$	1.46870e10	0.544062
$209$	−1.73338e9	−0.0628401
$210$	−6.58322e10	−2.33588
$211$	−1.95680e10	−0.679634	−0.339817	−	0.940492i	$-0.610365\pi$
$211$	−1.95680e10	−0.679634	−0.339817	+	0.940492i	$0.610365\pi$
$212$	3.81981e10	1.29876
$213$	2.29539e10	0.764096
$214$	−1.15697e10	−0.377104
$215$	6.65140e10	2.12295
$216$	−3.04913e9	−0.0953091
$217$	−7.27030e9	−0.222579
$218$	3.47149e10	1.04103
$219$	−2.44913e10	−0.719472
$220$	1.85256e10	0.533174
$221$	5.43312e9	0.153209
$222$	3.14072e10	0.867842
$223$	−4.91878e10	−1.33194	−0.665971	−	0.745977i	$-0.731983\pi$
$223$	−4.91878e10	−1.33194	−0.665971	+	0.745977i	$0.731983\pi$
$224$	8.96633e10	2.37957
$225$	1.68263e10	0.437691
$226$	−1.28722e10	−0.328219
$227$	−4.48168e10	−1.12027	−0.560137	−	0.828400i	$-0.689252\pi$
$227$	−4.48168e10	−1.12027	−0.560137	+	0.828400i	$0.689252\pi$
$228$	−7.41160e9	−0.181637
$229$	−4.38357e10	−1.05334	−0.526670	−	0.850070i	$-0.676560\pi$
$229$	−4.38357e10	−1.05334	−0.526670	+	0.850070i	$0.676560\pi$
$230$	−1.29626e11	−3.05433
$231$	−1.15356e10	−0.266555
$232$	−7.31880e9	−0.165861
$233$	−9.01688e9	−0.200426	−0.100213	−	0.994966i	$-0.531952\pi$
$233$	−9.01688e9	−0.200426	−0.100213	+	0.994966i	$0.531952\pi$
$234$	−2.22612e10	−0.485375
$235$	−8.68215e10	−1.85704
$236$	8.21921e9	0.172475
$237$	5.55157e8	0.0114301
$238$	2.11248e10	0.426773
$239$	−4.04272e10	−0.801463	−0.400731	−	0.916196i	$-0.631244\pi$
$239$	−4.04272e10	−0.801463	−0.400731	+	0.916196i	$0.631244\pi$
$240$	−2.57115e10	−0.500239
$241$	−3.52928e9	−0.0673921	−0.0336960	−	0.999432i	$-0.510728\pi$
$241$	−3.52928e9	−0.0673921	−0.0336960	+	0.999432i	$0.510728\pi$
$242$	−7.56544e10	−1.41796
$243$	−3.48678e9	−0.0641500
$244$	−3.43032e10	−0.619556
$245$	−1.75319e11	−3.10871
$246$	−2.52222e10	−0.439111
$247$	−1.32665e10	−0.226787
$248$	3.76364e9	0.0631794
$249$	5.91809e9	0.0975629
$250$	−4.48396e10	−0.725992
$251$	1.08446e11	1.72458	0.862290	−	0.506414i	$-0.169029\pi$
$251$	1.08446e11	1.72458	0.862290	+	0.506414i	$0.169029\pi$
$252$	−4.93239e10	−0.770469
$253$	−2.27140e10	−0.348539
$254$	−7.00736e10	−1.05634
$255$	−9.51139e9	−0.140868
$256$	5.44879e9	0.0792904
$257$	−1.07464e11	−1.53661	−0.768307	−	0.640082i	$-0.778900\pi$
$257$	−1.07464e11	−1.53661	−0.768307	+	0.640082i	$0.778900\pi$
$258$	8.74514e10	1.22879
$259$	1.24561e11	1.72001
$260$	1.41785e11	1.92421
$261$	−8.36928e9	−0.111636
$262$	1.08887e11	1.42765
$263$	2.40331e9	0.0309748	0.0154874	−	0.999880i	$-0.495070\pi$
$263$	2.40331e9	0.0309748	0.0154874	+	0.999880i	$0.495070\pi$
$264$	5.97168e9	0.0756621
$265$	−1.19696e11	−1.49098
$266$	−5.15821e10	−0.631730
$267$	7.63348e10	0.919225
$268$	−1.41624e11	−1.67699
$269$	−1.62916e11	−1.89705	−0.948526	−	0.316699i	$-0.897426\pi$
$269$	−1.62916e11	−1.89705	−0.948526	+	0.316699i	$0.897426\pi$
$270$	3.89711e10	0.446279
$271$	5.27406e10	0.593996	0.296998	−	0.954878i	$-0.404015\pi$
$271$	5.27406e10	0.593996	0.296998	+	0.954878i	$0.404015\pi$
$272$	8.25054e9	0.0913950
$273$	−8.82878e10	−0.961986
$274$	2.02990e11	2.17569
$275$	−3.29540e10	−0.347465
$276$	−9.71204e10	−1.00744
$277$	−1.30739e11	−1.33427	−0.667137	−	0.744935i	$-0.732480\pi$
$277$	−1.30739e11	−1.33427	−0.667137	+	0.744935i	$0.732480\pi$
$278$	−2.09596e11	−2.10466
$279$	4.30385e9	0.0425244
$280$	1.35159e11	1.31412
$281$	−3.34613e10	−0.320158	−0.160079	−	0.987104i	$-0.551175\pi$
$281$	−3.34613e10	−0.320158	−0.160079	+	0.987104i	$0.551175\pi$
$282$	−1.14151e11	−1.07488
$283$	1.28327e11	1.18926	0.594631	−	0.803998i	$-0.297298\pi$
$283$	1.28327e11	1.18926	0.594631	+	0.803998i	$0.297298\pi$
$284$	−1.92218e11	−1.75332
$285$	2.32247e10	0.208520
$286$	4.35982e10	0.385320
$287$	−1.00031e11	−0.870294
$288$	−5.30786e10	−0.454625
$289$	−1.15536e11	−0.974263
$290$	9.35419e10	0.776632
$291$	−4.41758e10	−0.361132
$292$	2.05092e11	1.65092
$293$	1.99282e11	1.57966	0.789832	−	0.613324i	$-0.210168\pi$
$293$	1.99282e11	1.57966	0.789832	+	0.613324i	$0.210168\pi$
$294$	−2.30506e11	−1.79936
$295$	−2.57554e10	−0.198002
$296$	−6.44818e10	−0.488230
$297$	6.82881e9	0.0509262
$298$	−5.01840e10	−0.368631
$299$	−1.73842e11	−1.25786
$300$	−1.40905e11	−1.00434
$301$	3.46832e11	2.43540
$302$	1.72466e11	1.19309
$303$	2.36513e10	0.161199
$304$	−2.01460e10	−0.135287
$305$	1.07491e11	0.711251
$306$	−1.25054e10	−0.0815363
$307$	1.03383e11	0.664244	0.332122	−	0.943236i	$-0.392235\pi$
$307$	1.03383e11	0.664244	0.332122	+	0.943236i	$0.392235\pi$
$308$	9.66000e10	0.611644
$309$	−6.59347e10	−0.411434
$310$	−4.81033e10	−0.295833
$311$	2.01487e11	1.22131	0.610654	−	0.791898i	$-0.290907\pi$
$311$	2.01487e11	1.22131	0.610654	+	0.791898i	$0.290907\pi$
$312$	4.57042e10	0.273062
$313$	−1.69614e11	−0.998879	−0.499439	−	0.866349i	$-0.666461\pi$
$313$	−1.69614e11	−0.998879	−0.499439	+	0.866349i	$0.666461\pi$
$314$	−3.25515e10	−0.188968
$315$	1.54559e11	0.884499
$316$	−4.64893e9	−0.0262277
$317$	1.25759e11	0.699474	0.349737	−	0.936848i	$-0.386271\pi$
$317$	1.25759e11	0.699474	0.349737	+	0.936848i	$0.386271\pi$
$318$	−1.57374e11	−0.863001
$319$	1.63911e10	0.0886237
$320$	4.30727e11	2.29629
$321$	2.71632e10	0.142793
$322$	−6.75923e11	−3.50385
$323$	−7.45254e9	−0.0380972
$324$	2.91986e10	0.147201
$325$	−2.52214e11	−1.25399
$326$	−1.89046e11	−0.927017
$327$	−8.15029e10	−0.394192
$328$	5.17834e10	0.247035
$329$	−4.52724e11	−2.13035
$330$	−7.63243e10	−0.354283
$331$	−4.16265e11	−1.90609	−0.953046	−	0.302827i	$-0.902070\pi$
$331$	−4.16265e11	−1.90609	−0.953046	+	0.302827i	$0.902070\pi$
$332$	−4.95585e10	−0.223871
$333$	−7.37370e10	−0.328614
$334$	6.35462e11	2.79403
$335$	4.43787e11	1.92519
$336$	−1.34071e11	−0.573861
$337$	3.94584e11	1.66650	0.833248	−	0.552899i	$-0.186479\pi$
$337$	3.94584e11	1.66650	0.833248	+	0.552899i	$0.186479\pi$
$338$	−3.21842e10	−0.134127
$339$	3.02210e10	0.124282
$340$	7.96491e10	0.323240
$341$	−8.42901e9	−0.0337584
$342$	3.05354e10	0.120694
$343$	−4.66937e11	−1.82152
$344$	−1.79546e11	−0.691293
$345$	3.04332e11	1.15654
$346$	−1.39842e11	−0.524558
$347$	−2.58895e11	−0.958609	−0.479305	−	0.877649i	$-0.659111\pi$
$347$	−2.58895e11	−0.958609	−0.479305	+	0.877649i	$0.659111\pi$
$348$	7.00850e10	0.256164
$349$	3.25345e11	1.17390	0.586949	−	0.809624i	$-0.300329\pi$
$349$	3.25345e11	1.17390	0.586949	+	0.809624i	$0.300329\pi$
$350$	−9.80646e11	−3.49306
$351$	5.22643e10	0.183791
$352$	1.03953e11	0.360908
$353$	5.23092e11	1.79305	0.896524	−	0.442996i	$-0.146084\pi$
$353$	5.23092e11	1.79305	0.896524	+	0.442996i	$0.146084\pi$
$354$	−3.38627e10	−0.114606
$355$	6.02325e11	2.01281
$356$	−6.39234e11	−2.10928
$357$	−4.95963e10	−0.161600
$358$	−5.25574e11	−1.69106
$359$	1.44888e11	0.460369	0.230184	−	0.973147i	$-0.426067\pi$
$359$	1.44888e11	0.460369	0.230184	+	0.973147i	$0.426067\pi$
$360$	−8.00112e10	−0.251067
$361$	−3.04490e11	−0.943607
$362$	8.16341e11	2.49852
$363$	1.77620e11	0.536922
$364$	7.39329e11	2.20740
$365$	−6.42668e11	−1.89526
$366$	1.41327e11	0.411681
$367$	5.33904e11	1.53626	0.768131	−	0.640292i	$-0.221187\pi$
$367$	5.33904e11	1.53626	0.768131	+	0.640292i	$0.221187\pi$
$368$	−2.63990e11	−0.750363
$369$	5.92161e10	0.166273
$370$	8.24145e11	2.28610
$371$	−6.24144e11	−1.71042
$372$	−3.60407e10	−0.0975777
$373$	4.21409e11	1.12724	0.563618	−	0.826036i	$-0.309409\pi$
$373$	4.21409e11	1.12724	0.563618	+	0.826036i	$0.309409\pi$
$374$	2.44916e10	0.0647284
$375$	1.05273e11	0.274902
$376$	2.34363e11	0.604705
$377$	1.25449e11	0.319840
$378$	2.03212e11	0.511959
$379$	−2.78603e11	−0.693600	−0.346800	−	0.937939i	$-0.612732\pi$
$379$	−2.78603e11	−0.693600	−0.346800	+	0.937939i	$0.612732\pi$
$380$	−1.94485e11	−0.478476
$381$	1.64517e11	0.399990
$382$	5.76624e11	1.38550
$383$	−7.13578e11	−1.69452	−0.847260	−	0.531178i	$-0.821749\pi$
$383$	−7.13578e11	−1.69452	−0.847260	+	0.531178i	$0.821749\pi$
$384$	2.30803e11	0.541690
$385$	−3.02702e11	−0.702169
$386$	9.19735e11	2.10872
$387$	−2.05316e11	−0.465291
$388$	3.69932e11	0.828665
$389$	−4.13305e10	−0.0915160	−0.0457580	−	0.998953i	$-0.514570\pi$
$389$	−4.13305e10	−0.0915160	−0.0457580	+	0.998953i	$0.514570\pi$
$390$	−5.84148e11	−1.27859
$391$	−9.76569e10	−0.211304
$392$	4.73249e11	1.01228
$393$	−2.55642e11	−0.540588
$394$	6.80132e10	0.142187
$395$	1.45677e10	0.0301095
$396$	−5.71850e10	−0.116857
$397$	−8.80592e10	−0.177917	−0.0889585	−	0.996035i	$-0.528354\pi$
$397$	−8.80592e10	−0.177917	−0.0889585	+	0.996035i	$0.528354\pi$
$398$	1.39821e12	2.79318
$399$	1.21103e11	0.239209
$400$	−3.83003e11	−0.748052
$401$	3.55570e11	0.686714	0.343357	−	0.939205i	$-0.388436\pi$
$401$	3.55570e11	0.686714	0.343357	+	0.939205i	$0.388436\pi$
$402$	5.83484e11	1.11432
$403$	−6.45115e10	−0.121833
$404$	−1.98058e11	−0.369893
$405$	−9.14955e10	−0.168987
$406$	4.87766e11	0.890932
$407$	1.44413e11	0.260874
$408$	2.56747e10	0.0458706
$409$	−6.47031e11	−1.14333	−0.571663	−	0.820488i	$-0.693702\pi$
$409$	−6.47031e11	−1.14333	−0.571663	+	0.820488i	$0.693702\pi$
$410$	−6.61847e11	−1.15672
$411$	−4.76575e11	−0.823841
$412$	5.52142e11	0.944090
$413$	−1.34299e11	−0.227142
$414$	4.00131e11	0.669422
$415$	1.55295e11	0.257004
$416$	7.95609e11	1.30251
$417$	4.92085e11	0.796944
$418$	−5.98030e10	−0.0958142
$419$	6.62242e11	1.04967	0.524836	−	0.851203i	$-0.324127\pi$
$419$	6.62242e11	1.04967	0.524836	+	0.851203i	$0.324127\pi$
$420$	−1.29429e12	−2.02960
$421$	−7.29715e11	−1.13210	−0.566049	−	0.824372i	$-0.691529\pi$
$421$	−7.29715e11	−1.13210	−0.566049	+	0.824372i	$0.691529\pi$
$422$	−6.75110e11	−1.03626
$423$	2.68002e11	0.407011
$424$	3.23103e11	0.485506
$425$	−1.41683e11	−0.210653
$426$	7.91926e11	1.16504
$427$	5.60503e11	0.815929
$428$	−2.27466e11	−0.327658
$429$	−1.02359e11	−0.145904
$430$	2.29478e12	3.23693
$431$	1.04484e10	0.0145849	0.00729243	−	0.999973i	$-0.497679\pi$
$431$	1.04484e10	0.0145849	0.00729243	+	0.999973i	$0.497679\pi$
$432$	7.93667e10	0.109638
$433$	9.48860e11	1.29720	0.648599	−	0.761130i	$-0.275355\pi$
$433$	9.48860e11	1.29720	0.648599	+	0.761130i	$0.275355\pi$
$434$	−2.50830e11	−0.339372
$435$	−2.19615e11	−0.294077
$436$	6.82512e11	0.904526
$437$	2.38456e11	0.312782
$438$	−8.44968e11	−1.09700
$439$	1.41652e12	1.82025	0.910125	−	0.414335i	$-0.135986\pi$
$439$	1.41652e12	1.82025	0.910125	+	0.414335i	$0.135986\pi$
$440$	1.56701e11	0.199312
$441$	5.41176e11	0.681342
$442$	1.87447e11	0.233602
$443$	4.09272e11	0.504889	0.252444	−	0.967611i	$-0.418766\pi$
$443$	4.09272e11	0.504889	0.252444	+	0.967611i	$0.418766\pi$
$444$	6.17480e11	0.754048
$445$	2.00308e12	2.42146
$446$	−1.69702e12	−2.03085
$447$	1.17821e11	0.139585
$448$	2.24599e12	2.63425
$449$	−3.44730e11	−0.400287	−0.200143	−	0.979767i	$-0.564141\pi$
$449$	−3.44730e11	−0.400287	−0.200143	+	0.979767i	$0.564141\pi$
$450$	5.80520e11	0.667361
$451$	−1.15974e11	−0.131997
$452$	−2.53073e11	−0.285182
$453$	−4.04912e11	−0.451771
$454$	−1.54621e12	−1.70812
$455$	−2.31673e12	−2.53410
$456$	−6.26919e10	−0.0679000
$457$	9.96315e11	1.06850	0.534249	−	0.845327i	$-0.320594\pi$
$457$	9.96315e11	1.06850	0.534249	+	0.845327i	$0.320594\pi$
$458$	−1.51236e12	−1.60606
$459$	2.93599e10	0.0308743
$460$	−2.54850e12	−2.65384
$461$	−5.63457e11	−0.581041	−0.290520	−	0.956869i	$-0.593828\pi$
$461$	−5.63457e11	−0.581041	−0.290520	+	0.956869i	$0.593828\pi$
$462$	−3.97987e11	−0.406424
$463$	−1.07447e12	−1.08663	−0.543315	−	0.839529i	$-0.682831\pi$
$463$	−1.07447e12	−1.08663	−0.543315	+	0.839529i	$0.682831\pi$
$464$	1.90503e11	0.190797
$465$	1.12936e11	0.112019
$466$	−3.11089e11	−0.305596
$467$	−1.72279e11	−0.167612	−0.0838062	−	0.996482i	$-0.526708\pi$
$467$	−1.72279e11	−0.167612	−0.0838062	+	0.996482i	$0.526708\pi$
$468$	−4.37665e11	−0.421731
$469$	2.31409e12	2.20853
$470$	−2.99541e12	−2.83149
$471$	7.64236e10	0.0715539
$472$	6.95231e10	0.0644749
$473$	4.02109e11	0.369376
$474$	1.91533e10	0.0174278
$475$	3.45958e11	0.311819
$476$	4.15324e11	0.370813
$477$	3.69479e11	0.326781
$478$	−1.39477e12	−1.22202
$479$	1.17803e12	1.02246	0.511232	−	0.859443i	$-0.329189\pi$
$479$	1.17803e12	1.02246	0.511232	+	0.859443i	$0.329189\pi$
$480$	−1.39282e12	−1.19759
$481$	1.10526e12	0.941484
$482$	−1.21763e11	−0.102755
$483$	1.58692e12	1.32676
$484$	−1.48740e12	−1.23204
$485$	−1.15920e12	−0.951309
$486$	−1.20297e11	−0.0978116
$487$	1.41964e12	1.14366	0.571830	−	0.820372i	$-0.306234\pi$
$487$	1.41964e12	1.14366	0.571830	+	0.820372i	$0.306234\pi$
$488$	−2.90158e11	−0.231603
$489$	4.43837e11	0.351022
$490$	−6.04862e12	−4.73995
$491$	−3.65591e11	−0.283876	−0.141938	−	0.989876i	$-0.545333\pi$
$491$	−3.65591e11	−0.283876	−0.141938	+	0.989876i	$0.545333\pi$
$492$	−4.95880e11	−0.381534
$493$	7.04722e10	0.0537287
$494$	−4.57703e11	−0.345790
$495$	1.79192e11	0.134152
$496$	−9.79648e10	−0.0726779
$497$	3.14077e12	2.30905
$498$	2.04178e11	0.148757
$499$	2.55102e12	1.84188	0.920941	−	0.389703i	$-0.127422\pi$
$499$	2.55102e12	1.84188	0.920941	+	0.389703i	$0.127422\pi$
$500$	−8.81568e11	−0.630799
$501$	−1.49192e12	−1.05798
$502$	3.74148e12	2.62952
$503$	−1.67849e12	−1.16913	−0.584566	−	0.811346i	$-0.698735\pi$
$503$	−1.67849e12	−1.16913	−0.584566	+	0.811346i	$0.698735\pi$
$504$	−4.17212e11	−0.288018
$505$	6.20625e11	0.424637
$506$	−7.83649e11	−0.531428
$507$	7.55612e10	0.0507883
$508$	−1.37768e12	−0.917829
$509$	−1.57010e12	−1.03681	−0.518403	−	0.855137i	$-0.673473\pi$
$509$	−1.57010e12	−1.03681	−0.518403	+	0.855137i	$0.673473\pi$
$510$	−3.28150e11	−0.214786
$511$	−3.35114e12	−2.17419
$512$	1.64689e12	1.05913
$513$	−7.16903e10	−0.0457017
$514$	−3.70759e12	−2.34292
$515$	−1.73017e12	−1.08382
$516$	1.71934e12	1.06767
$517$	−5.24877e11	−0.323110
$518$	4.29743e12	2.62256
$519$	3.28317e11	0.198628
$520$	1.19931e12	0.719310
$521$	1.78780e12	1.06304	0.531519	−	0.847046i	$-0.321621\pi$
$521$	1.78780e12	1.06304	0.531519	+	0.847046i	$0.321621\pi$
$522$	−2.88746e11	−0.170216
$523$	−1.34218e11	−0.0784431	−0.0392215	−	0.999231i	$-0.512488\pi$
$523$	−1.34218e11	−0.0784431	−0.0392215	+	0.999231i	$0.512488\pi$
$524$	2.14077e12	1.24045
$525$	2.30234e12	1.32267
$526$	8.29160e10	0.0472283
$527$	−3.62398e10	−0.0204662
$528$	−1.55438e11	−0.0870373
$529$	1.32354e12	0.734828
$530$	−4.12960e12	−2.27335
$531$	7.95020e10	0.0433963
$532$	−1.01413e12	−0.548896
$533$	−8.87605e11	−0.476373
$534$	2.63361e12	1.40157
$535$	7.12779e11	0.376152
$536$	−1.19794e12	−0.626896
$537$	1.23393e12	0.640333
$538$	−5.62073e12	−2.89249
$539$	−1.05988e12	−0.540890
$540$	7.66190e11	0.387762
$541$	1.55224e12	0.779060	0.389530	−	0.921014i	$-0.372637\pi$
$541$	1.55224e12	0.779060	0.389530	+	0.921014i	$0.372637\pi$
$542$	1.81959e12	0.905684
$543$	−1.91659e12	−0.946083
$544$	4.46939e11	0.218803
$545$	−2.13869e12	−1.03840
$546$	−3.04599e12	−1.46677
$547$	1.87430e12	0.895153	0.447576	−	0.894246i	$-0.352287\pi$
$547$	1.87430e12	0.895153	0.447576	+	0.894246i	$0.352287\pi$
$548$	3.99088e12	1.89041
$549$	−3.31805e11	−0.155886
$550$	−1.13694e12	−0.529791
$551$	−1.72077e11	−0.0795319
$552$	−8.21504e11	−0.376603
$553$	7.59619e10	0.0345408
$554$	−4.51058e12	−2.03441
$555$	−1.93491e12	−0.865649
$556$	−4.12076e12	−1.82869
$557$	3.54150e12	1.55897	0.779486	−	0.626419i	$-0.215480\pi$
$557$	3.54150e12	1.55897	0.779486	+	0.626419i	$0.215480\pi$
$558$	1.48486e11	0.0648382
$559$	3.07754e12	1.33306
$560$	−3.51810e12	−1.51169
$561$	−5.75008e10	−0.0245099
$562$	−1.15444e12	−0.488156
$563$	−3.12012e12	−1.30883	−0.654416	−	0.756135i	$-0.727085\pi$
$563$	−3.12012e12	−1.30883	−0.654416	+	0.756135i	$0.727085\pi$
$564$	−2.24427e12	−0.933940
$565$	7.93018e11	0.327390
$566$	4.42736e12	1.81331
$567$	−4.77096e11	−0.193857
$568$	−1.62590e12	−0.655428
$569$	1.25747e12	0.502914	0.251457	−	0.967868i	$-0.419090\pi$
$569$	1.25747e12	0.502914	0.251457	+	0.967868i	$0.419090\pi$
$570$	8.01268e11	0.317937
$571$	3.04709e12	1.19956	0.599782	−	0.800163i	$-0.295254\pi$
$571$	3.04709e12	1.19956	0.599782	+	0.800163i	$0.295254\pi$
$572$	8.57160e11	0.334796
$573$	−1.35378e12	−0.524630
$574$	−3.45114e12	−1.32697
$575$	4.53338e12	1.72948
$576$	−1.32957e12	−0.503282
$577$	4.93378e12	1.85305	0.926527	−	0.376227i	$-0.122779\pi$
$577$	4.93378e12	1.85305	0.926527	+	0.376227i	$0.122779\pi$
$578$	−3.98607e12	−1.48549
$579$	−2.15933e12	−0.798483
$580$	1.83908e12	0.674798
$581$	8.09770e11	0.294828
$582$	−1.52410e12	−0.550630
$583$	−7.23618e11	−0.259419
$584$	1.73480e12	0.617150
$585$	1.37145e12	0.484148
$586$	6.87539e12	2.40856
$587$	−1.04516e12	−0.363338	−0.181669	−	0.983360i	$-0.558150\pi$
$587$	−1.04516e12	−0.363338	−0.181669	+	0.983360i	$0.558150\pi$
$588$	−4.53185e12	−1.56343
$589$	8.84895e10	0.0302951
$590$	−8.88579e11	−0.301899
$591$	−1.59680e11	−0.0538401
$592$	1.67841e12	0.561631
$593$	2.78359e12	0.924397	0.462198	−	0.886777i	$-0.347061\pi$
$593$	2.78359e12	0.924397	0.462198	+	0.886777i	$0.347061\pi$
$594$	2.35599e11	0.0776487
$595$	−1.30144e12	−0.425694
$596$	−9.86641e11	−0.320296
$597$	−3.28268e12	−1.05766
$598$	−5.99766e12	−1.91790
$599$	−1.00164e12	−0.317901	−0.158950	−	0.987287i	$-0.550811\pi$
$599$	−1.00164e12	−0.317901	−0.158950	+	0.987287i	$0.550811\pi$
$600$	−1.19186e12	−0.375443
$601$	−5.94601e12	−1.85905	−0.929524	−	0.368761i	$-0.879782\pi$
$601$	−5.94601e12	−1.85905	−0.929524	+	0.368761i	$0.879782\pi$
$602$	1.19659e13	3.71332
$603$	−1.36989e12	−0.421947
$604$	3.39076e12	1.03665
$605$	4.66086e12	1.41438
$606$	8.15987e11	0.245786
$607$	−1.71818e12	−0.513713	−0.256856	−	0.966450i	$-0.582687\pi$
$607$	−1.71818e12	−0.513713	−0.256856	+	0.966450i	$0.582687\pi$
$608$	−1.09133e12	−0.323883
$609$	−1.14517e12	−0.337358
$610$	3.70852e12	1.08447
$611$	−4.01715e12	−1.16609
$612$	−2.45862e11	−0.0708451
$613$	4.34986e12	1.24424	0.622119	−	0.782923i	$-0.286272\pi$
$613$	4.34986e12	1.24424	0.622119	+	0.782923i	$0.286272\pi$
$614$	3.56680e12	1.01279
$615$	1.55387e12	0.438002
$616$	8.17102e11	0.228646
$617$	4.75580e12	1.32111	0.660557	−	0.750776i	$-0.270320\pi$
$617$	4.75580e12	1.32111	0.660557	+	0.750776i	$0.270320\pi$
$618$	−2.27479e12	−0.627327
$619$	2.98381e12	0.816891	0.408445	−	0.912783i	$-0.366071\pi$
$619$	2.98381e12	0.816891	0.408445	+	0.912783i	$0.366071\pi$
$620$	−9.45733e11	−0.257043
$621$	−9.39417e11	−0.253482
$622$	6.95144e12	1.86217
$623$	1.04449e13	2.77784
$624$	−1.18965e12	−0.314114
$625$	−2.24653e12	−0.588914
$626$	−5.85181e12	−1.52302
$627$	1.40404e11	0.0362807
$628$	−6.39977e11	−0.164190
$629$	6.20890e11	0.158156
$630$	5.33241e12	1.34862
$631$	3.14683e12	0.790206	0.395103	−	0.918637i	$-0.370709\pi$
$631$	3.14683e12	0.790206	0.395103	+	0.918637i	$0.370709\pi$
$632$	−3.93235e10	−0.00980450
$633$	1.58501e12	0.392387
$634$	4.33877e12	1.06651
$635$	4.31704e12	1.05367
$636$	−3.09405e12	−0.749842
$637$	−8.11183e12	−1.95205
$638$	5.65505e11	0.135127
$639$	−1.85927e12	−0.441151
$640$	6.05642e12	1.42694
$641$	−6.90121e12	−1.61460	−0.807299	−	0.590143i	$-0.799071\pi$
$641$	−6.90121e12	−1.61460	−0.807299	+	0.590143i	$0.799071\pi$
$642$	9.37149e11	0.217721
$643$	2.39255e12	0.551965	0.275983	−	0.961163i	$-0.410997\pi$
$643$	2.39255e12	0.551965	0.275983	+	0.961163i	$0.410997\pi$
$644$	−1.32890e13	−3.04442
$645$	−5.38764e12	−1.22569
$646$	−2.57118e11	−0.0580880
$647$	−5.61890e12	−1.26061	−0.630307	−	0.776346i	$-0.717071\pi$
$647$	−5.61890e12	−1.26061	−0.630307	+	0.776346i	$0.717071\pi$
$648$	2.46980e11	0.0550268
$649$	−1.55703e11	−0.0344506
$650$	−8.70156e12	−1.91200
$651$	5.88894e11	0.128506
$652$	−3.71673e12	−0.805465
$653$	4.52224e12	0.973295	0.486647	−	0.873599i	$-0.338220\pi$
$653$	4.52224e12	0.973295	0.486647	+	0.873599i	$0.338220\pi$
$654$	−2.81191e12	−0.601038
$655$	−6.70822e12	−1.42404
$656$	−1.34788e12	−0.284175
$657$	1.98380e12	0.415387
$658$	−1.56193e13	−3.24822
$659$	1.98801e12	0.410613	0.205307	−	0.978698i	$-0.434181\pi$
$659$	1.98801e12	0.410613	0.205307	+	0.978698i	$0.434181\pi$
$660$	−1.50057e12	−0.307828
$661$	3.75691e12	0.765463	0.382731	−	0.923860i	$-0.374983\pi$
$661$	3.75691e12	0.765463	0.382731	+	0.923860i	$0.374983\pi$
$662$	−1.43614e13	−2.90628
$663$	−4.40083e11	−0.0884552
$664$	−4.19197e11	−0.0836877
$665$	3.17782e12	0.630133
$666$	−2.54398e12	−0.501049
$667$	−2.25487e12	−0.441119
$668$	1.24935e13	2.42767
$669$	3.98421e12	0.768998
$670$	1.53110e13	2.93540
$671$	6.49834e11	0.123752
$672$	−7.26273e12	−1.37385
$673$	−4.50273e12	−0.846074	−0.423037	−	0.906112i	$-0.639036\pi$
$673$	−4.50273e12	−0.846074	−0.423037	+	0.906112i	$0.639036\pi$
$674$	1.36134e13	2.54096
$675$	−1.36293e12	−0.252701
$676$	−6.32756e11	−0.116540
$677$	−4.77303e12	−0.873262	−0.436631	−	0.899641i	$-0.643829\pi$
$677$	−4.77303e12	−0.873262	−0.436631	+	0.899641i	$0.643829\pi$
$678$	1.04265e12	0.189497
$679$	−6.04456e12	−1.09132
$680$	6.73721e11	0.120834
$681$	3.63016e12	0.646791
$682$	−2.90807e11	−0.0514725
$683$	6.92003e12	1.21679	0.608394	−	0.793635i	$-0.291814\pi$
$683$	6.92003e12	1.21679	0.608394	+	0.793635i	$0.291814\pi$
$684$	6.00340e11	0.104868
$685$	−1.25056e13	−2.17019
$686$	−1.61097e13	−2.77734
$687$	3.55069e12	0.608146
$688$	4.67344e12	0.795223
$689$	−5.53822e12	−0.936232
$690$	1.04997e13	1.76342
$691$	−3.26738e12	−0.545190	−0.272595	−	0.962129i	$-0.587882\pi$
$691$	−3.26738e12	−0.545190	−0.272595	+	0.962129i	$0.587882\pi$
$692$	−2.74935e12	−0.455777
$693$	9.34383e11	0.153895
$694$	−8.93208e12	−1.46162
$695$	1.29126e13	2.09934
$696$	5.92822e11	0.0957598
$697$	−4.98619e11	−0.0800242
$698$	1.12247e13	1.78988
$699$	7.30368e11	0.115716
$700$	−1.92799e13	−3.03504
$701$	−8.23416e12	−1.28792	−0.643959	−	0.765060i	$-0.722709\pi$
$701$	−8.23416e12	−1.28792	−0.643959	+	0.765060i	$0.722709\pi$
$702$	1.80316e12	0.280231
$703$	−1.51607e12	−0.234111
$704$	2.60395e12	0.399535
$705$	7.03254e12	1.07216
$706$	1.80470e13	2.73391
$707$	3.23620e12	0.487133
$708$	−6.65756e11	−0.0995785
$709$	7.57359e12	1.12563	0.562813	−	0.826584i	$-0.309719\pi$
$709$	7.57359e12	1.12563	0.562813	+	0.826584i	$0.309719\pi$
$710$	2.07807e13	3.06900
$711$	−4.49677e10	−0.00659914
$712$	−5.40703e12	−0.788495
$713$	1.15955e12	0.168030
$714$	−1.71111e12	−0.246397
$715$	−2.68596e12	−0.384346
$716$	−1.03330e13	−1.46933
$717$	3.27461e12	0.462725
$718$	4.99872e12	0.701939
$719$	8.97769e12	1.25281	0.626404	−	0.779499i	$-0.284526\pi$
$719$	8.97769e12	1.25281	0.626404	+	0.779499i	$0.284526\pi$
$720$	2.08263e12	0.288813
$721$	−9.02182e12	−1.24333
$722$	−1.05051e13	−1.43875
$723$	2.85871e11	0.0389088
$724$	1.60496e13	2.17091
$725$	−3.27142e12	−0.439760
$726$	6.12801e12	0.818662
$727$	−9.56364e11	−0.126975	−0.0634875	−	0.997983i	$-0.520222\pi$
$727$	−9.56364e11	−0.126975	−0.0634875	+	0.997983i	$0.520222\pi$
$728$	6.25370e12	0.825174
$729$	2.82430e11	0.0370370
$730$	−2.21725e13	−2.88976
$731$	1.72883e12	0.223936
$732$	2.77856e12	0.357701
$733$	8.77585e12	1.12285	0.561424	−	0.827528i	$-0.310254\pi$
$733$	8.77585e12	1.12285	0.561424	+	0.827528i	$0.310254\pi$
$734$	1.84201e13	2.34239
$735$	1.42008e13	1.79482
$736$	−1.43006e13	−1.79640
$737$	2.68290e12	0.334967
$738$	2.04300e12	0.253521
$739$	−9.96504e12	−1.22908	−0.614538	−	0.788887i	$-0.710658\pi$
$739$	−9.96504e12	−1.22908	−0.614538	+	0.788887i	$0.710658\pi$
$740$	1.62031e13	1.98634
$741$	1.07458e12	0.130936
$742$	−2.15334e13	−2.60793
$743$	−3.30829e12	−0.398249	−0.199124	−	0.979974i	$-0.563810\pi$
$743$	−3.30829e12	−0.398249	−0.199124	+	0.979974i	$0.563810\pi$
$744$	−3.04855e11	−0.0364766
$745$	3.09170e12	0.367700
$746$	1.45389e13	1.71873
$747$	−4.79365e11	−0.0563279
$748$	4.81516e11	0.0562411
$749$	3.71673e12	0.431512
$750$	3.63201e12	0.419152
$751$	6.43513e12	0.738206	0.369103	−	0.929389i	$-0.379665\pi$
$751$	6.43513e12	0.738206	0.369103	+	0.929389i	$0.379665\pi$
$752$	−6.10030e12	−0.695618
$753$	−8.78416e12	−0.995687
$754$	4.32809e12	0.487670
$755$	−1.06251e13	−1.19007
$756$	3.99524e12	0.444830
$757$	−7.76173e12	−0.859068	−0.429534	−	0.903051i	$-0.641322\pi$
$757$	−7.76173e12	−0.859068	−0.429534	+	0.903051i	$0.641322\pi$
$758$	−9.61200e12	−1.05755
$759$	1.83983e12	0.201229
$760$	−1.64508e12	−0.178865
$761$	−9.64688e12	−1.04269	−0.521346	−	0.853345i	$-0.674570\pi$
$761$	−9.64688e12	−1.04269	−0.521346	+	0.853345i	$0.674570\pi$
$762$	5.67596e12	0.609877
$763$	−1.11520e13	−1.19122
$764$	1.13367e13	1.20383
$765$	7.70422e11	0.0813303
$766$	−2.46190e13	−2.58369
$767$	−1.19168e12	−0.124331
$768$	−4.41352e11	−0.0457783
$769$	−3.19835e12	−0.329805	−0.164903	−	0.986310i	$-0.552731\pi$
$769$	−3.19835e12	−0.329805	−0.164903	+	0.986310i	$0.552731\pi$
$770$	−1.04434e13	−1.07062
$771$	8.70460e12	0.887164
$772$	1.80824e13	1.83222
$773$	−4.99654e12	−0.503341	−0.251670	−	0.967813i	$-0.580980\pi$
$773$	−4.99654e12	−0.503341	−0.251670	+	0.967813i	$0.580980\pi$
$774$	−7.08356e12	−0.709443
$775$	1.68231e12	0.167513
$776$	3.12911e12	0.309773
$777$	−1.00894e13	−0.993050
$778$	−1.42593e12	−0.139537
$779$	1.21752e12	0.118456
$780$	−1.14846e13	−1.11094
$781$	3.64134e12	0.350212
$782$	−3.36923e12	−0.322182
$783$	6.77912e11	0.0644533
$784$	−1.23183e13	−1.16447
$785$	2.00541e12	0.188490
$786$	−8.81985e12	−0.824252
$787$	−2.48095e12	−0.230532	−0.115266	−	0.993335i	$-0.536772\pi$
$787$	−2.48095e12	−0.230532	−0.115266	+	0.993335i	$0.536772\pi$
$788$	1.33717e12	0.123543
$789$	−1.94668e11	−0.0178833
$790$	5.02596e11	0.0459089
$791$	4.13513e12	0.375573
$792$	−4.83706e11	−0.0436835
$793$	4.97351e12	0.446615
$794$	−3.03811e12	−0.271275
$795$	9.69537e12	0.860820
$796$	2.74895e13	2.42693
$797$	4.01929e12	0.352847	0.176424	−	0.984314i	$-0.443547\pi$
$797$	4.01929e12	0.352847	0.176424	+	0.984314i	$0.443547\pi$
$798$	4.17815e12	0.364729
$799$	−2.25667e12	−0.195887
$800$	−2.07476e13	−1.79087
$801$	−6.18312e12	−0.530715
$802$	1.22674e13	1.04705
$803$	−3.88523e12	−0.329759
$804$	1.14716e13	0.968212
$805$	4.16417e13	3.49500
$806$	−2.22569e12	−0.185762
$807$	1.31962e13	1.09526
$808$	−1.67529e12	−0.138274
$809$	−1.76189e13	−1.44614	−0.723068	−	0.690776i	$-0.757269\pi$
$809$	−1.76189e13	−1.44614	−0.723068	+	0.690776i	$0.757269\pi$
$810$	−3.15666e12	−0.257659
$811$	1.43610e13	1.16571	0.582856	−	0.812576i	$-0.301935\pi$
$811$	1.43610e13	1.16571	0.582856	+	0.812576i	$0.301935\pi$
$812$	9.58971e12	0.774111
$813$	−4.27199e12	−0.342944
$814$	4.98234e12	0.397762
$815$	1.16466e13	0.924675
$816$	−6.68294e11	−0.0527669
$817$	−4.22142e12	−0.331482
$818$	−2.23230e13	−1.74327
$819$	7.15131e12	0.555403
$820$	−1.30122e13	−1.00505
$821$	−1.27547e13	−0.979772	−0.489886	−	0.871787i	$-0.662962\pi$
$821$	−1.27547e13	−0.979772	−0.489886	+	0.871787i	$0.662962\pi$
$822$	−1.64422e13	−1.25614
$823$	−1.55652e13	−1.18265	−0.591326	−	0.806433i	$-0.701395\pi$
$823$	−1.55652e13	−1.18265	−0.591326	+	0.806433i	$0.701395\pi$
$824$	4.67036e12	0.352921
$825$	2.66928e12	0.200609
$826$	−4.63342e12	−0.346331
$827$	2.98542e12	0.221937	0.110969	−	0.993824i	$-0.464605\pi$
$827$	2.98542e12	0.221937	0.110969	+	0.993824i	$0.464605\pi$
$828$	7.86675e12	0.581646
$829$	1.23183e13	0.905848	0.452924	−	0.891549i	$-0.350381\pi$
$829$	1.23183e13	0.905848	0.452924	+	0.891549i	$0.350381\pi$
$830$	5.35777e12	0.391862
$831$	1.05898e13	0.770344
$832$	1.99293e13	1.44191
$833$	−4.55688e12	−0.327918
$834$	1.69773e13	1.21513
$835$	−3.91490e13	−2.78697
$836$	−1.17576e12	−0.0832508
$837$	−3.48612e11	−0.0245515
$838$	2.28478e13	1.60047
$839$	−1.86372e13	−1.29853	−0.649264	−	0.760563i	$-0.724923\pi$
$839$	−1.86372e13	−1.29853	−0.649264	+	0.760563i	$0.724923\pi$
$840$	−1.09479e13	−0.758708
$841$	−1.28800e13	−0.887836
$842$	−2.51757e13	−1.72614
$843$	2.71037e12	0.184844
$844$	−1.32730e13	−0.900383
$845$	1.98278e12	0.133788
$846$	9.24626e12	0.620583
$847$	2.43036e13	1.62254
$848$	−8.41014e12	−0.558498
$849$	−1.03945e13	−0.686621
$850$	−4.88817e12	−0.321189
$851$	−1.98664e13	−1.29848
$852$	1.55696e13	1.01228
$853$	2.02588e13	1.31022	0.655110	−	0.755534i	$-0.272622\pi$
$853$	2.02588e13	1.31022	0.655110	+	0.755534i	$0.272622\pi$
$854$	1.93378e13	1.24407
$855$	−1.88120e12	−0.120389
$856$	−1.92405e12	−0.122486
$857$	−1.79742e13	−1.13825	−0.569124	−	0.822252i	$-0.692718\pi$
$857$	−1.79742e13	−1.13825	−0.569124	+	0.822252i	$0.692718\pi$
$858$	−3.53145e12	−0.222464
$859$	8.13333e11	0.0509682	0.0254841	−	0.999675i	$-0.491887\pi$
$859$	8.13333e11	0.0509682	0.0254841	+	0.999675i	$0.491887\pi$
$860$	4.51165e13	2.81250
$861$	8.10251e12	0.502465
$862$	3.60478e11	0.0222380
$863$	2.73063e13	1.67577	0.837885	−	0.545848i	$-0.183792\pi$
$863$	2.73063e13	1.67577	0.837885	+	0.545848i	$0.183792\pi$
$864$	4.29937e12	0.262478
$865$	8.61525e12	0.523233
$866$	3.27363e13	1.97788
$867$	9.35840e12	0.562491
$868$	−4.93144e12	−0.294873
$869$	8.80685e10	0.00523880
$870$	−7.57689e12	−0.448389
$871$	2.05336e13	1.20888
$872$	5.77311e12	0.338131
$873$	3.57824e12	0.208500
$874$	8.22691e12	0.476909
$875$	1.44045e13	0.830735
$876$	−1.66125e13	−0.953160
$877$	2.50307e13	1.42881	0.714405	−	0.699732i	$-0.246697\pi$
$877$	2.50307e13	1.42881	0.714405	+	0.699732i	$0.246697\pi$
$878$	4.88708e13	2.77539
$879$	−1.61419e13	−0.912019
$880$	−4.07880e12	−0.229277
$881$	−3.22785e13	−1.80518	−0.902591	−	0.430499i	$-0.858338\pi$
$881$	−3.22785e13	−1.80518	−0.902591	+	0.430499i	$0.858338\pi$
$882$	1.86710e13	1.03886
$883$	8.95417e12	0.495681	0.247840	−	0.968801i	$-0.420279\pi$
$883$	8.95417e12	0.495681	0.247840	+	0.968801i	$0.420279\pi$
$884$	3.68529e12	0.202972
$885$	2.08618e12	0.114316
$886$	1.41202e13	0.769819
$887$	−1.32363e13	−0.717978	−0.358989	−	0.933342i	$-0.616879\pi$
$887$	−1.32363e13	−0.717978	−0.358989	+	0.933342i	$0.616879\pi$
$888$	5.22302e12	0.281880
$889$	2.25108e13	1.20874
$890$	6.91076e13	3.69208
$891$	−5.53133e11	−0.0294022
$892$	−3.33641e13	−1.76456
$893$	5.51027e12	0.289962
$894$	4.06491e12	0.212829
$895$	3.23791e13	1.68679
$896$	3.15807e13	1.63695
$897$	1.40812e13	0.726227
$898$	−1.18934e13	−0.610329
$899$	−8.36768e11	−0.0427254
$900$	1.14133e13	0.579855
$901$	−3.11114e12	−0.157274
$902$	−4.00118e12	−0.201260
$903$	−2.80934e13	−1.40608
$904$	−2.14065e12	−0.106607
$905$	−5.02925e13	−2.49221
$906$	−1.39698e13	−0.688830
$907$	3.19713e13	1.56866	0.784328	−	0.620347i	$-0.213008\pi$
$907$	3.19713e13	1.56866	0.784328	+	0.620347i	$0.213008\pi$
$908$	−3.03992e13	−1.48415
$909$	−1.91575e12	−0.0930684
$910$	−7.99288e13	−3.86382
$911$	8.00387e12	0.385006	0.192503	−	0.981296i	$-0.438340\pi$
$911$	8.00387e12	0.385006	0.192503	+	0.981296i	$0.438340\pi$
$912$	1.63182e12	0.0781082
$913$	9.38829e11	0.0447165
$914$	3.43736e13	1.62917
$915$	−8.70677e12	−0.410641
$916$	−2.97338e13	−1.39547
$917$	−3.49795e13	−1.63362
$918$	1.01294e12	0.0470750
$919$	−1.03567e13	−0.478965	−0.239482	−	0.970901i	$-0.576978\pi$
$919$	−1.03567e13	−0.478965	−0.239482	+	0.970901i	$0.576978\pi$
$920$	−2.15568e13	−0.992063
$921$	−8.37405e12	−0.383501
$922$	−1.94397e13	−0.885931
$923$	2.78690e13	1.26390
$924$	−7.82460e12	−0.353133
$925$	−2.88227e13	−1.29448
$926$	−3.70701e13	−1.65682
$927$	5.34071e12	0.237542
$928$	1.03197e13	0.456774
$929$	−3.17313e13	−1.39771	−0.698856	−	0.715263i	$-0.746307\pi$
$929$	−3.17313e13	−1.39771	−0.698856	+	0.715263i	$0.746307\pi$
$930$	3.89636e12	0.170799
$931$	1.11269e13	0.485400
$932$	−6.11616e12	−0.265526
$933$	−1.63204e13	−0.705122
$934$	−5.94375e12	−0.255564
$935$	−1.50886e12	−0.0645649
$936$	−3.70204e12	−0.157652
$937$	−1.29178e13	−0.547469	−0.273735	−	0.961805i	$-0.588259\pi$
$937$	−1.29178e13	−0.547469	−0.273735	+	0.961805i	$0.588259\pi$
$938$	7.98379e13	3.36741
$939$	1.37388e13	0.576703
$940$	−5.88911e13	−2.46022
$941$	−3.12085e13	−1.29754	−0.648769	−	0.760986i	$-0.724716\pi$
$941$	−3.12085e13	−1.29754	−0.648769	+	0.760986i	$0.724716\pi$
$942$	2.63667e12	0.109101
$943$	1.59541e13	0.657008
$944$	−1.80964e12	−0.0741681
$945$	−1.25193e13	−0.510666
$946$	1.38730e13	0.563199
$947$	2.66359e13	1.07620	0.538099	−	0.842882i	$-0.319143\pi$
$947$	2.66359e13	1.07620	0.538099	+	0.842882i	$0.319143\pi$
$948$	3.76563e11	0.0151426
$949$	−2.97356e13	−1.19009
$950$	1.19358e13	0.475440
$951$	−1.01865e13	−0.403842
$952$	3.51306e12	0.138618
$953$	−3.20298e13	−1.25787	−0.628936	−	0.777457i	$-0.716509\pi$
$953$	−3.20298e13	−1.25787	−0.628936	+	0.777457i	$0.716509\pi$
$954$	1.27473e13	0.498254
$955$	−3.55242e13	−1.38200
$956$	−2.74218e13	−1.06178
$957$	−1.32768e12	−0.0511669
$958$	4.06430e13	1.55898
$959$	−6.52097e13	−2.48959
$960$	−3.48889e13	−1.32576
$961$	−2.60093e13	−0.983725
$962$	3.81324e13	1.43551
$963$	−2.20022e12	−0.0824417
$964$	−2.39391e12	−0.0892814
$965$	−5.66623e13	−2.10340
$966$	5.47497e13	2.02295
$967$	3.00424e12	0.110488	0.0552440	−	0.998473i	$-0.482406\pi$
$967$	3.00424e12	0.110488	0.0552440	+	0.998473i	$0.482406\pi$
$968$	−1.25814e13	−0.460562
$969$	6.03656e11	0.0219954
$970$	−3.99933e13	−1.45049
$971$	−1.27149e13	−0.459016	−0.229508	−	0.973307i	$-0.573712\pi$
$971$	−1.27149e13	−0.459016	−0.229508	+	0.973307i	$0.573712\pi$
$972$	−2.36509e12	−0.0849863
$973$	6.73318e13	2.40831
$974$	4.89785e13	1.74377
$975$	2.04293e13	0.723991
$976$	7.55259e12	0.266423
$977$	1.84870e13	0.649143	0.324571	−	0.945861i	$-0.394780\pi$
$977$	1.84870e13	0.649143	0.324571	+	0.945861i	$0.394780\pi$
$978$	1.53127e13	0.535214
$979$	1.21095e13	0.421314
$980$	−1.18919e14	−4.11844
$981$	6.60174e12	0.227587
$982$	−1.26131e13	−0.432834
$983$	3.61480e13	1.23479	0.617395	−	0.786654i	$-0.288188\pi$
$983$	3.61480e13	1.23479	0.617395	+	0.786654i	$0.288188\pi$
$984$	−4.19446e12	−0.142626
$985$	−4.19010e12	−0.141828
$986$	2.43134e12	0.0819218
$987$	3.66706e13	1.22996
$988$	−8.99865e12	−0.300449
$989$	−5.53168e13	−1.83854
$990$	6.18227e12	0.204545
$991$	3.82897e10	0.00126110	0.000630552	−	1.00000i	$-0.499799\pi$
$991$	3.82897e10	0.00126110	0.000630552		1.00000i	$0.499799\pi$
$992$	−5.30684e12	−0.173994
$993$	3.37174e13	1.10048
$994$	1.08359e14	3.52068
$995$	−8.61398e13	−2.78612
$996$	4.01424e12	0.129252
$997$	−7.31678e12	−0.234526	−0.117263	−	0.993101i	$-0.537412\pi$
$997$	−7.31678e12	−0.234526	−0.117263	+	0.993101i	$0.537412\pi$
$998$	8.80121e13	2.80837
$999$	5.97270e12	0.189726

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.c.1.19	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.c.1.19	✓	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)

\(f(q)\)	\(=\)	\(q+34.5007 q^{2} -81.0000 q^{3} +678.300 q^{4} -2125.49 q^{5} -2794.56 q^{6} -11083.2 q^{7} +5737.48 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+34.5007 q^{2} -81.0000 q^{3} +678.300 q^{4} -2125.49 q^{5} -2794.56 q^{6} -11083.2 q^{7} +5737.48 q^{8} +6561.00 q^{9} -73331.0 q^{10} -12849.6 q^{11} -54942.3 q^{12} -98344.5 q^{13} -382379. q^{14} +172165. q^{15} -149342. q^{16} -55245.8 q^{17} +226359. q^{18} +134898. q^{19} -1.44172e6 q^{20} +897739. q^{21} -443321. q^{22} +1.76768e6 q^{23} -464736. q^{24} +2.56459e6 q^{25} -3.39296e6 q^{26} -531441. q^{27} -7.51774e6 q^{28} -1.27561e6 q^{29} +5.93981e6 q^{30} +655974. q^{31} -8.09001e6 q^{32} +1.04082e6 q^{33} -1.90602e6 q^{34} +2.35573e7 q^{35} +4.45033e6 q^{36} -1.12387e7 q^{37} +4.65407e6 q^{38} +7.96591e6 q^{39} -1.21950e7 q^{40} +9.02546e6 q^{41} +3.09727e7 q^{42} -3.12935e7 q^{43} -8.71589e6 q^{44} -1.39454e7 q^{45} +6.09862e7 q^{46} +4.08477e7 q^{47} +1.20967e7 q^{48} +8.24838e7 q^{49} +8.84803e7 q^{50} +4.47491e6 q^{51} -6.67071e7 q^{52} +5.63144e7 q^{53} -1.83351e7 q^{54} +2.73117e7 q^{55} -6.35897e7 q^{56} -1.09267e7 q^{57} -4.40095e7 q^{58} +1.21174e7 q^{59} +1.16780e8 q^{60} -5.05723e7 q^{61} +2.26316e7 q^{62} -7.27169e7 q^{63} -2.02648e8 q^{64} +2.09031e8 q^{65} +3.59090e7 q^{66} -2.08793e8 q^{67} -3.74732e7 q^{68} -1.43182e8 q^{69} +8.12743e8 q^{70} -2.83381e8 q^{71} +3.76436e7 q^{72} +3.02362e8 q^{73} -3.87743e8 q^{74} -2.07732e8 q^{75} +9.15013e7 q^{76} +1.42415e8 q^{77} +2.74830e8 q^{78} -6.85379e6 q^{79} +3.17426e8 q^{80} +4.30467e7 q^{81} +3.11385e8 q^{82} -7.30628e7 q^{83} +6.08937e8 q^{84} +1.17425e8 q^{85} -1.07965e9 q^{86} +1.03324e8 q^{87} -7.37244e7 q^{88} -9.42405e8 q^{89} -4.81125e8 q^{90} +1.08997e9 q^{91} +1.19902e9 q^{92} -5.31339e7 q^{93} +1.40928e9 q^{94} -2.86724e8 q^{95} +6.55291e8 q^{96} +5.45381e8 q^{97} +2.84575e9 q^{98} -8.43063e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9}+O(q^{10}) \) 22 * q + 36 * q^2 - 1782 * q^3 + 5718 * q^4 + 808 * q^5 - 2916 * q^6 + 21249 * q^7 + 9435 * q^8 + 144342 * q^9	\( 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9} + 68441 q^{10} - 68033 q^{11} - 463158 q^{12} + 283817 q^{13} + 80285 q^{14} - 65448 q^{15} + 1067674 q^{16} + 436893 q^{17} + 236196 q^{18} + 1207580 q^{19} + 4209677 q^{20} - 1721169 q^{21} + 5460442 q^{22} + 2421966 q^{23} - 764235 q^{24} + 7441842 q^{25} - 2736526 q^{26} - 11691702 q^{27} + 4095246 q^{28} - 2320594 q^{29} - 5543721 q^{30} - 3178024 q^{31} - 20786874 q^{32} + 5510673 q^{33} - 13809336 q^{34} - 2630800 q^{35} + 37515798 q^{36} + 3981807 q^{37} - 24156377 q^{38} - 22989177 q^{39} - 29544450 q^{40} - 885225 q^{41} - 6503085 q^{42} + 12360835 q^{43} - 117711882 q^{44} + 5301288 q^{45} + 161066949 q^{46} + 75901252 q^{47} - 86481594 q^{48} + 170907951 q^{49} - 61318927 q^{50} - 35388333 q^{51} - 100762 q^{52} - 34790192 q^{53} - 19131876 q^{54} + 151773316 q^{55} - 417630344 q^{56} - 97813980 q^{57} - 432929294 q^{58} + 266581942 q^{59} - 340983837 q^{60} - 290555332 q^{61} + 158267098 q^{62} + 139414689 q^{63} - 131794443 q^{64} - 650690086 q^{65} - 442295802 q^{66} + 86645184 q^{67} + 62738541 q^{68} - 196179246 q^{69} + 429714610 q^{70} - 36567631 q^{71} + 61903035 q^{72} + 907807228 q^{73} - 171827242 q^{74} - 602789202 q^{75} + 1744504396 q^{76} - 310688725 q^{77} + 221658606 q^{78} + 2508604687 q^{79} + 3509441927 q^{80} + 947027862 q^{81} + 1759214793 q^{82} + 2185672083 q^{83} - 331714926 q^{84} + 2868860198 q^{85} + 2397001564 q^{86} + 187968114 q^{87} + 7683735877 q^{88} + 1320145942 q^{89} + 449041401 q^{90} + 3894639897 q^{91} + 3505964640 q^{92} + 257419944 q^{93} + 5406355552 q^{94} + 3093659122 q^{95} + 1683736794 q^{96} + 3904552980 q^{97} + 6137683116 q^{98} - 446364513 q^{99}+O(q^{100}) \) 22 * q + 36 * q^2 - 1782 * q^3 + 5718 * q^4 + 808 * q^5 - 2916 * q^6 + 21249 * q^7 + 9435 * q^8 + 144342 * q^9 + 68441 * q^10 - 68033 * q^11 - 463158 * q^12 + 283817 * q^13 + 80285 * q^14 - 65448 * q^15 + 1067674 * q^16 + 436893 * q^17 + 236196 * q^18 + 1207580 * q^19 + 4209677 * q^20 - 1721169 * q^21 + 5460442 * q^22 + 2421966 * q^23 - 764235 * q^24 + 7441842 * q^25 - 2736526 * q^26 - 11691702 * q^27 + 4095246 * q^28 - 2320594 * q^29 - 5543721 * q^30 - 3178024 * q^31 - 20786874 * q^32 + 5510673 * q^33 - 13809336 * q^34 - 2630800 * q^35 + 37515798 * q^36 + 3981807 * q^37 - 24156377 * q^38 - 22989177 * q^39 - 29544450 * q^40 - 885225 * q^41 - 6503085 * q^42 + 12360835 * q^43 - 117711882 * q^44 + 5301288 * q^45 + 161066949 * q^46 + 75901252 * q^47 - 86481594 * q^48 + 170907951 * q^49 - 61318927 * q^50 - 35388333 * q^51 - 100762 * q^52 - 34790192 * q^53 - 19131876 * q^54 + 151773316 * q^55 - 417630344 * q^56 - 97813980 * q^57 - 432929294 * q^58 + 266581942 * q^59 - 340983837 * q^60 - 290555332 * q^61 + 158267098 * q^62 + 139414689 * q^63 - 131794443 * q^64 - 650690086 * q^65 - 442295802 * q^66 + 86645184 * q^67 + 62738541 * q^68 - 196179246 * q^69 + 429714610 * q^70 - 36567631 * q^71 + 61903035 * q^72 + 907807228 * q^73 - 171827242 * q^74 - 602789202 * q^75 + 1744504396 * q^76 - 310688725 * q^77 + 221658606 * q^78 + 2508604687 * q^79 + 3509441927 * q^80 + 947027862 * q^81 + 1759214793 * q^82 + 2185672083 * q^83 - 331714926 * q^84 + 2868860198 * q^85 + 2397001564 * q^86 + 187968114 * q^87 + 7683735877 * q^88 + 1320145942 * q^89 + 449041401 * q^90 + 3894639897 * q^91 + 3505964640 * q^92 + 257419944 * q^93 + 5406355552 * q^94 + 3093659122 * q^95 + 1683736794 * q^96 + 3904552980 * q^97 + 6137683116 * q^98 - 446364513 * q^99

Introduction

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