LMFDB - Embedded newform 38.10.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,10,Mod(1,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("38.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	38.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:	$19.5713617742$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4552x + 85948 $ x^3 - x^2 - 4552*x + 85948
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$55.2385$ of defining polynomial
Character	$\chi$	$=$	38.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-16.0000 q^{2} +165.716 q^{3} +256.000 q^{4} +936.105 q^{5} -2651.45 q^{6} -11191.8 q^{7} -4096.00 q^{8} +7778.66 q^{9} +O(q^{10})$	\(q-16.0000 q^{2} +165.716 q^{3} +256.000 q^{4} +936.105 q^{5} -2651.45 q^{6} -11191.8 q^{7} -4096.00 q^{8} +7778.66 q^{9} -14977.7 q^{10} -64045.2 q^{11} +42423.2 q^{12} +48918.1 q^{13} +179068. q^{14} +155127. q^{15} +65536.0 q^{16} -319167. q^{17} -124459. q^{18} -130321. q^{19} +239643. q^{20} -1.85465e6 q^{21} +1.02472e6 q^{22} +1.99602e6 q^{23} -678771. q^{24} -1.07683e6 q^{25} -782690. q^{26} -1.97273e6 q^{27} -2.86509e6 q^{28} -7.18134e6 q^{29} -2.48203e6 q^{30} -504237. q^{31} -1.04858e6 q^{32} -1.06133e7 q^{33} +5.10667e6 q^{34} -1.04767e7 q^{35} +1.99134e6 q^{36} +6.41963e6 q^{37} +2.08514e6 q^{38} +8.10650e6 q^{39} -3.83429e6 q^{40} -8.82437e6 q^{41} +2.96744e7 q^{42} +5.84267e6 q^{43} -1.63956e7 q^{44} +7.28164e6 q^{45} -3.19363e7 q^{46} +4.17667e7 q^{47} +1.08603e7 q^{48} +8.49017e7 q^{49} +1.72293e7 q^{50} -5.28909e7 q^{51} +1.25230e7 q^{52} -9.36845e7 q^{53} +3.15638e7 q^{54} -5.99530e7 q^{55} +4.58414e7 q^{56} -2.15962e7 q^{57} +1.14901e8 q^{58} +1.84166e7 q^{59} +3.97126e7 q^{60} -2.82616e7 q^{61} +8.06780e6 q^{62} -8.70569e7 q^{63} +1.67772e7 q^{64} +4.57925e7 q^{65} +1.69813e8 q^{66} -2.44114e8 q^{67} -8.17067e7 q^{68} +3.30771e8 q^{69} +1.67626e8 q^{70} +1.69035e8 q^{71} -3.18614e7 q^{72} -3.11236e8 q^{73} -1.02714e8 q^{74} -1.78448e8 q^{75} -3.33622e7 q^{76} +7.16778e8 q^{77} -1.29704e8 q^{78} +7.76696e6 q^{79} +6.13486e7 q^{80} -4.80020e8 q^{81} +1.41190e8 q^{82} +2.83143e8 q^{83} -4.74790e8 q^{84} -2.98774e8 q^{85} -9.34826e7 q^{86} -1.19006e9 q^{87} +2.62329e8 q^{88} +8.16355e8 q^{89} -1.16506e8 q^{90} -5.47480e8 q^{91} +5.10981e8 q^{92} -8.35600e7 q^{93} -6.68268e8 q^{94} -1.21994e8 q^{95} -1.73765e8 q^{96} +1.16454e9 q^{97} -1.35843e9 q^{98} -4.98186e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 48 q^{2} + 3 q^{3} + 768 q^{4} + 486 q^{5} - 48 q^{6} - 13317 q^{7} - 12288 q^{8} + 22896 q^{9}+O(q^{10}) $ 3 * q - 48 * q^2 + 3 * q^3 + 768 * q^4 + 486 * q^5 - 48 * q^6 - 13317 * q^7 - 12288 * q^8 + 22896 * q^9	\( 3 q - 48 q^{2} + 3 q^{3} + 768 q^{4} + 486 q^{5} - 48 q^{6} - 13317 q^{7} - 12288 q^{8} + 22896 q^{9} - 7776 q^{10} + 55968 q^{11} + 768 q^{12} + 158181 q^{13} + 213072 q^{14} + 135660 q^{15} + 196608 q^{16} - 629091 q^{17} - 366336 q^{18} - 390963 q^{19} + 124416 q^{20} - 873405 q^{21} - 895488 q^{22} - 924627 q^{23} - 12288 q^{24} - 4805517 q^{25} - 2530896 q^{26} - 6711147 q^{27} - 3409152 q^{28} - 9839019 q^{29} - 2170560 q^{30} + 1364628 q^{31} - 3145728 q^{32} - 30339114 q^{33} + 10065456 q^{34} - 11097570 q^{35} + 5861376 q^{36} - 2289090 q^{37} + 6255408 q^{38} - 18481557 q^{39} - 1990656 q^{40} - 12899580 q^{41} + 13974480 q^{42} - 22378638 q^{43} + 14327808 q^{44} + 13005630 q^{45} + 14794032 q^{46} + 58896366 q^{47} + 196608 q^{48} + 22294974 q^{49} + 76888272 q^{50} + 85869585 q^{51} + 40494336 q^{52} + 8770629 q^{53} + 107378352 q^{54} - 73415802 q^{55} + 54546432 q^{56} - 390963 q^{57} + 157424304 q^{58} + 16426299 q^{59} + 34728960 q^{60} - 126843780 q^{61} - 21834048 q^{62} - 234650088 q^{63} + 50331648 q^{64} + 45269952 q^{65} + 485425824 q^{66} - 288075309 q^{67} - 161047296 q^{68} + 323371803 q^{69} + 177561120 q^{70} + 78122274 q^{71} - 93782016 q^{72} - 557941845 q^{73} + 36625440 q^{74} + 150154413 q^{75} - 100086528 q^{76} + 394013736 q^{77} + 295704912 q^{78} - 320222022 q^{79} + 31850496 q^{80} - 346127013 q^{81} + 206393280 q^{82} + 430491462 q^{83} - 223591680 q^{84} - 383428242 q^{85} + 358058208 q^{86} - 1044099345 q^{87} - 229244928 q^{88} + 437689644 q^{89} - 208090080 q^{90} - 1010450187 q^{91} - 236704512 q^{92} - 2684851332 q^{93} - 942341856 q^{94} - 63336006 q^{95} - 3145728 q^{96} - 384952146 q^{97} - 356719584 q^{98} + 2029897422 q^{99}+O(q^{100}) \) 3 * q - 48 * q^2 + 3 * q^3 + 768 * q^4 + 486 * q^5 - 48 * q^6 - 13317 * q^7 - 12288 * q^8 + 22896 * q^9 - 7776 * q^10 + 55968 * q^11 + 768 * q^12 + 158181 * q^13 + 213072 * q^14 + 135660 * q^15 + 196608 * q^16 - 629091 * q^17 - 366336 * q^18 - 390963 * q^19 + 124416 * q^20 - 873405 * q^21 - 895488 * q^22 - 924627 * q^23 - 12288 * q^24 - 4805517 * q^25 - 2530896 * q^26 - 6711147 * q^27 - 3409152 * q^28 - 9839019 * q^29 - 2170560 * q^30 + 1364628 * q^31 - 3145728 * q^32 - 30339114 * q^33 + 10065456 * q^34 - 11097570 * q^35 + 5861376 * q^36 - 2289090 * q^37 + 6255408 * q^38 - 18481557 * q^39 - 1990656 * q^40 - 12899580 * q^41 + 13974480 * q^42 - 22378638 * q^43 + 14327808 * q^44 + 13005630 * q^45 + 14794032 * q^46 + 58896366 * q^47 + 196608 * q^48 + 22294974 * q^49 + 76888272 * q^50 + 85869585 * q^51 + 40494336 * q^52 + 8770629 * q^53 + 107378352 * q^54 - 73415802 * q^55 + 54546432 * q^56 - 390963 * q^57 + 157424304 * q^58 + 16426299 * q^59 + 34728960 * q^60 - 126843780 * q^61 - 21834048 * q^62 - 234650088 * q^63 + 50331648 * q^64 + 45269952 * q^65 + 485425824 * q^66 - 288075309 * q^67 - 161047296 * q^68 + 323371803 * q^69 + 177561120 * q^70 + 78122274 * q^71 - 93782016 * q^72 - 557941845 * q^73 + 36625440 * q^74 + 150154413 * q^75 - 100086528 * q^76 + 394013736 * q^77 + 295704912 * q^78 - 320222022 * q^79 + 31850496 * q^80 - 346127013 * q^81 + 206393280 * q^82 + 430491462 * q^83 - 223591680 * q^84 - 383428242 * q^85 + 358058208 * q^86 - 1044099345 * q^87 - 229244928 * q^88 + 437689644 * q^89 - 208090080 * q^90 - 1010450187 * q^91 - 236704512 * q^92 - 2684851332 * q^93 - 942341856 * q^94 - 63336006 * q^95 - 3145728 * q^96 - 384952146 * q^97 - 356719584 * q^98 + 2029897422 * 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 $

$2$	−16.0000	−0.707107
$2$	−16.0000	−0.707107
$3$	165.716	1.18118	0.590592	−	0.806970i	$-0.298894\pi$
$3$	165.716	1.18118	0.590592	+	0.806970i	$0.298894\pi$
$4$	256.000	0.500000
$5$	936.105	0.669822	0.334911	−	0.942250i	$-0.391294\pi$
$5$	936.105	0.669822	0.334911	+	0.942250i	$0.391294\pi$
$6$	−2651.45	−0.835224
$7$	−11191.8	−1.76180	−0.880901	−	0.473301i	$-0.843062\pi$
$7$	−11191.8	−1.76180	−0.880901	+	0.473301i	$0.843062\pi$
$8$	−4096.00	−0.353553
$9$	7778.66	0.395197
$10$	−14977.7	−0.473636
$11$	−64045.2	−1.31892	−0.659461	−	0.751738i	$-0.729216\pi$
$11$	−64045.2	−1.31892	−0.659461	+	0.751738i	$0.729216\pi$
$12$	42423.2	0.590592
$13$	48918.1	0.475034	0.237517	−	0.971383i	$-0.423666\pi$
$13$	48918.1	0.475034	0.237517	+	0.971383i	$0.423666\pi$
$14$	179068.	1.24578
$15$	155127.	0.791183
$16$	65536.0	0.250000
$17$	−319167.	−0.926825	−0.463412	−	0.886143i	$-0.653375\pi$
$17$	−319167.	−0.926825	−0.463412	+	0.886143i	$0.653375\pi$
$18$	−124459.	−0.279446
$19$	−130321.	−0.229416
$19$	−130321.	−0.229416
$20$	239643.	0.334911
$21$	−1.85465e6	−2.08101
$22$	1.02472e6	0.932619
$23$	1.99602e6	1.48727	0.743634	−	0.668587i	$-0.233100\pi$
$23$	1.99602e6	1.48727	0.743634	+	0.668587i	$0.233100\pi$
$24$	−678771.	−0.417612
$25$	−1.07683e6	−0.551338
$26$	−782690.	−0.335900
$27$	−1.97273e6	−0.714384
$28$	−2.86509e6	−0.880901
$29$	−7.18134e6	−1.88545	−0.942724	−	0.333573i	$-0.891746\pi$
$29$	−7.18134e6	−1.88545	−0.942724	+	0.333573i	$0.891746\pi$
$30$	−2.48203e6	−0.559451
$31$	−504237.	−0.0980635	−0.0490318	−	0.998797i	$-0.515614\pi$
$31$	−504237.	−0.0980635	−0.0490318	+	0.998797i	$0.515614\pi$
$32$	−1.04858e6	−0.176777
$33$	−1.06133e7	−1.55789
$34$	5.10667e6	0.655364
$35$	−1.04767e7	−1.18009
$36$	1.99134e6	0.197598
$37$	6.41963e6	0.563122	0.281561	−	0.959543i	$-0.409148\pi$
$37$	6.41963e6	0.563122	0.281561	+	0.959543i	$0.409148\pi$
$38$	2.08514e6	0.162221
$39$	8.10650e6	0.561103
$40$	−3.83429e6	−0.236818
$41$	−8.82437e6	−0.487704	−0.243852	−	0.969812i	$-0.578411\pi$
$41$	−8.82437e6	−0.487704	−0.243852	+	0.969812i	$0.578411\pi$
$42$	2.96744e7	1.47150
$43$	5.84267e6	0.260617	0.130309	−	0.991473i	$-0.458403\pi$
$43$	5.84267e6	0.260617	0.130309	+	0.991473i	$0.458403\pi$
$44$	−1.63956e7	−0.659461
$45$	7.28164e6	0.264712
$46$	−3.19363e7	−1.05166
$47$	4.17667e7	1.24850	0.624252	−	0.781223i	$-0.285404\pi$
$47$	4.17667e7	1.24850	0.624252	+	0.781223i	$0.285404\pi$
$48$	1.08603e7	0.295296
$49$	8.49017e7	2.10394
$50$	1.72293e7	0.389855
$51$	−5.28909e7	−1.09475
$52$	1.25230e7	0.237517
$53$	−9.36845e7	−1.63090	−0.815448	−	0.578830i	$-0.803510\pi$
$53$	−9.36845e7	−1.63090	−0.815448	+	0.578830i	$0.803510\pi$
$54$	3.15638e7	0.505146
$55$	−5.99530e7	−0.883444
$56$	4.58414e7	0.622891
$57$	−2.15962e7	−0.270982
$58$	1.14901e8	1.33321
$59$	1.84166e7	0.197868	0.0989338	−	0.995094i	$-0.468457\pi$
$59$	1.84166e7	0.197868	0.0989338	+	0.995094i	$0.468457\pi$
$60$	3.97126e7	0.395592
$61$	−2.82616e7	−0.261344	−0.130672	−	0.991426i	$-0.541713\pi$
$61$	−2.82616e7	−0.261344	−0.130672	+	0.991426i	$0.541713\pi$
$62$	8.06780e6	0.0693414
$63$	−8.70569e7	−0.696259
$64$	1.67772e7	0.125000
$65$	4.57925e7	0.318188
$66$	1.69813e8	1.10160
$67$	−2.44114e8	−1.47998	−0.739989	−	0.672619i	$-0.765169\pi$
$67$	−2.44114e8	−1.47998	−0.739989	+	0.672619i	$0.765169\pi$
$68$	−8.17067e7	−0.463412
$69$	3.30771e8	1.75674
$70$	1.67626e8	0.834452
$71$	1.69035e8	0.789432	0.394716	−	0.918803i	$-0.370843\pi$
$71$	1.69035e8	0.789432	0.394716	+	0.918803i	$0.370843\pi$
$72$	−3.18614e7	−0.139723
$73$	−3.11236e8	−1.28274	−0.641368	−	0.767233i	$-0.721633\pi$
$73$	−3.11236e8	−1.28274	−0.641368	+	0.767233i	$0.721633\pi$
$74$	−1.02714e8	−0.398187
$75$	−1.78448e8	−0.651232
$76$	−3.33622e7	−0.114708
$77$	7.16778e8	2.32368
$78$	−1.29704e8	−0.396760
$79$	7.76696e6	0.0224352	0.0112176	−	0.999937i	$-0.496429\pi$
$79$	7.76696e6	0.0224352	0.0112176	+	0.999937i	$0.496429\pi$
$80$	6.13486e7	0.167456
$81$	−4.80020e8	−1.23902
$82$	1.41190e8	0.344859
$83$	2.83143e8	0.654869	0.327435	−	0.944874i	$-0.393816\pi$
$83$	2.83143e8	0.654869	0.327435	+	0.944874i	$0.393816\pi$
$84$	−4.74790e8	−1.04051
$85$	−2.98774e8	−0.620808
$86$	−9.34826e7	−0.184284
$87$	−1.19006e9	−2.22706
$88$	2.62329e8	0.466310
$89$	8.16355e8	1.37919	0.689595	−	0.724196i	$-0.257789\pi$
$89$	8.16355e8	1.37919	0.689595	+	0.724196i	$0.257789\pi$
$90$	−1.16506e8	−0.187179
$91$	−5.47480e8	−0.836916
$92$	5.10981e8	0.743634
$93$	−8.35600e7	−0.115831
$94$	−6.68268e8	−0.882826
$95$	−1.21994e8	−0.153668
$96$	−1.73765e8	−0.208806
$97$	1.16454e9	1.33561	0.667807	−	0.744335i	$-0.267233\pi$
$97$	1.16454e9	1.33561	0.667807	+	0.744335i	$0.267233\pi$
$98$	−1.35843e9	−1.48771
$99$	−4.98186e8	−0.521234
$100$	−2.75669e8	−0.275669
$101$	−8.72197e8	−0.834005	−0.417002	−	0.908905i	$-0.636919\pi$
$101$	−8.72197e8	−0.834005	−0.417002	+	0.908905i	$0.636919\pi$
$102$	8.46255e8	0.774106
$103$	−3.82999e8	−0.335297	−0.167649	−	0.985847i	$-0.553617\pi$
$103$	−3.82999e8	−0.335297	−0.167649	+	0.985847i	$0.553617\pi$
$104$	−2.00369e8	−0.167950
$105$	−1.73615e9	−1.39391
$106$	1.49895e9	1.15322
$107$	2.15882e9	1.59217	0.796085	−	0.605185i	$-0.206901\pi$
$107$	2.15882e9	1.59217	0.796085	+	0.605185i	$0.206901\pi$
$108$	−5.05020e8	−0.357192
$109$	−5.71304e7	−0.0387657	−0.0193829	−	0.999812i	$-0.506170\pi$
$109$	−5.71304e7	−0.0387657	−0.0193829	+	0.999812i	$0.506170\pi$
$110$	9.59248e8	0.624689
$111$	1.06383e9	0.665151
$112$	−7.33463e8	−0.440450
$113$	1.46794e8	0.0846947	0.0423473	−	0.999103i	$-0.486516\pi$
$113$	1.46794e8	0.0846947	0.0423473	+	0.999103i	$0.486516\pi$
$114$	3.45540e8	0.191613
$115$	1.86848e9	0.996205
$116$	−1.83842e9	−0.942724
$117$	3.80518e8	0.187732
$118$	−2.94665e8	−0.139913
$119$	3.57204e9	1.63288
$120$	−6.35401e8	−0.279726
$121$	1.74384e9	0.739558
$122$	4.52186e8	0.184798
$123$	−1.46234e9	−0.576069
$124$	−1.29085e8	−0.0490318
$125$	−2.83636e9	−1.03912
$126$	1.39291e9	0.492329
$127$	−3.11092e9	−1.06114	−0.530569	−	0.847642i	$-0.678022\pi$
$127$	−3.11092e9	−1.06114	−0.530569	+	0.847642i	$0.678022\pi$
$128$	−2.68435e8	−0.0883883
$129$	9.68221e8	0.307837
$130$	−7.32680e8	−0.224993
$131$	4.69521e9	1.39294	0.696472	−	0.717583i	$-0.254752\pi$
$131$	4.69521e9	1.39294	0.696472	+	0.717583i	$0.254752\pi$
$132$	−2.71700e9	−0.778946
$133$	1.45852e9	0.404185
$134$	3.90582e9	1.04650
$135$	−1.84669e9	−0.478510
$136$	1.30731e9	0.327682
$137$	5.79859e9	1.40631	0.703153	−	0.711039i	$-0.251775\pi$
$137$	5.79859e9	1.40631	0.703153	+	0.711039i	$0.251775\pi$
$138$	−5.29234e9	−1.24220
$139$	4.75835e9	1.08116	0.540580	−	0.841293i	$-0.318205\pi$
$139$	4.75835e9	1.08116	0.540580	+	0.841293i	$0.318205\pi$
$140$	−2.68202e9	−0.590047
$141$	6.92140e9	1.47471
$142$	−2.70456e9	−0.558213
$143$	−3.13297e9	−0.626533
$144$	5.09782e8	0.0987992
$145$	−6.72249e9	−1.26291
$146$	4.97978e9	0.907032
$147$	1.40695e10	2.48515
$148$	1.64343e9	0.281561
$149$	−1.15543e9	−0.192045	−0.0960226	−	0.995379i	$-0.530612\pi$
$149$	−1.15543e9	−0.192045	−0.0960226	+	0.995379i	$0.530612\pi$
$150$	2.85517e9	0.460491
$151$	2.66023e9	0.416411	0.208206	−	0.978085i	$-0.433238\pi$
$151$	2.66023e9	0.416411	0.208206	+	0.978085i	$0.433238\pi$
$152$	5.33795e8	0.0811107
$153$	−2.48269e9	−0.366278
$154$	−1.14684e10	−1.64309
$155$	−4.72019e8	−0.0656851
$156$	2.07526e9	0.280552
$157$	−1.14993e10	−1.51051	−0.755255	−	0.655431i	$-0.772487\pi$
$157$	−1.14993e10	−1.51051	−0.755255	+	0.655431i	$0.772487\pi$
$158$	−1.24271e8	−0.0158640
$159$	−1.55250e10	−1.92639
$160$	−9.81577e8	−0.118409
$161$	−2.23390e10	−2.62027
$162$	7.68032e9	0.876117
$163$	−5.22994e9	−0.580300	−0.290150	−	0.956981i	$-0.593705\pi$
$163$	−5.22994e9	−0.580300	−0.290150	+	0.956981i	$0.593705\pi$
$164$	−2.25904e9	−0.243852
$165$	−9.93515e9	−1.04351
$166$	−4.53029e9	−0.463062
$167$	−4.42318e9	−0.440058	−0.220029	−	0.975493i	$-0.570615\pi$
$167$	−4.42318e9	−0.440058	−0.220029	+	0.975493i	$0.570615\pi$
$168$	7.59664e9	0.735749
$169$	−8.21151e9	−0.774343
$170$	4.78038e9	0.438977
$171$	−1.01372e9	−0.0906644
$172$	1.49572e9	0.130309
$173$	−2.71509e9	−0.230450	−0.115225	−	0.993339i	$-0.536759\pi$
$173$	−2.71509e9	−0.230450	−0.115225	+	0.993339i	$0.536759\pi$
$174$	1.90410e10	1.57477
$175$	1.20516e10	0.971349
$176$	−4.19727e9	−0.329731
$177$	3.05191e9	0.233718
$178$	−1.30617e10	−0.975234
$179$	1.67005e10	1.21588	0.607939	−	0.793984i	$-0.291997\pi$
$179$	1.67005e10	1.21588	0.607939	+	0.793984i	$0.291997\pi$
$180$	1.86410e9	0.132356
$181$	−1.80232e10	−1.24818	−0.624092	−	0.781351i	$-0.714531\pi$
$181$	−1.80232e10	−1.24818	−0.624092	+	0.781351i	$0.714531\pi$
$182$	8.75968e9	0.591789
$183$	−4.68339e9	−0.308695
$184$	−8.17569e9	−0.525829
$185$	6.00945e9	0.377191
$186$	1.33696e9	0.0819050
$187$	2.04411e10	1.22241
$188$	1.06923e10	0.624252
$189$	2.20784e10	1.25860
$190$	1.95191e9	0.108659
$191$	−2.15303e10	−1.17057	−0.585287	−	0.810826i	$-0.699018\pi$
$191$	−2.15303e10	−1.17057	−0.585287	+	0.810826i	$0.699018\pi$
$192$	2.78025e9	0.147648
$193$	−2.64164e10	−1.37046	−0.685229	−	0.728328i	$-0.740298\pi$
$193$	−2.64164e10	−1.37046	−0.685229	+	0.728328i	$0.740298\pi$
$194$	−1.86326e10	−0.944422
$195$	7.58853e9	0.375839
$196$	2.17348e10	1.05197
$197$	2.48689e10	1.17641	0.588204	−	0.808712i	$-0.299835\pi$
$197$	2.48689e10	1.17641	0.588204	+	0.808712i	$0.299835\pi$
$198$	7.97097e9	0.368568
$199$	4.77941e9	0.216041	0.108020	−	0.994149i	$-0.465549\pi$
$199$	4.77941e9	0.216041	0.108020	+	0.994149i	$0.465549\pi$
$200$	4.41071e9	0.194928
$201$	−4.04534e10	−1.74813
$202$	1.39552e10	0.589731
$203$	8.03718e10	3.32179
$204$	−1.35401e10	−0.547376
$205$	−8.26054e9	−0.326675
$206$	6.12798e9	0.237091
$207$	1.55264e10	0.587764
$208$	3.20590e9	0.118759
$209$	8.34643e9	0.302582
$210$	2.77783e10	0.985642
$211$	−5.52854e10	−1.92017	−0.960084	−	0.279713i	$-0.909761\pi$
$211$	−5.52854e10	−1.92017	−0.960084	+	0.279713i	$0.909761\pi$
$212$	−2.39832e10	−0.815448
$213$	2.80118e10	0.932465
$214$	−3.45411e10	−1.12583
$215$	5.46935e9	0.174567
$216$	8.08032e9	0.252573
$217$	5.64330e9	0.172768
$218$	9.14087e8	0.0274115
$219$	−5.15767e10	−1.51515
$220$	−1.53480e10	−0.441722
$221$	−1.56131e10	−0.440274
$222$	−1.70213e10	−0.470333
$223$	−5.00648e9	−0.135569	−0.0677845	−	0.997700i	$-0.521593\pi$
$223$	−5.00648e9	−0.135569	−0.0677845	+	0.997700i	$0.521593\pi$
$224$	1.17354e10	0.311445
$225$	−8.37632e9	−0.217887
$226$	−2.34871e9	−0.0598882
$227$	−7.33576e9	−0.183370	−0.0916851	−	0.995788i	$-0.529225\pi$
$227$	−7.33576e9	−0.183370	−0.0916851	+	0.995788i	$0.529225\pi$
$228$	−5.52863e9	−0.135491
$229$	2.58689e10	0.621609	0.310805	−	0.950474i	$-0.399401\pi$
$229$	2.58689e10	0.621609	0.310805	+	0.950474i	$0.399401\pi$
$230$	−2.98957e10	−0.704423
$231$	1.18781e11	2.74470
$232$	2.94148e10	0.666607
$233$	−3.11489e10	−0.692376	−0.346188	−	0.938165i	$-0.612524\pi$
$233$	−3.11489e10	−0.692376	−0.346188	+	0.938165i	$0.612524\pi$
$234$	−6.08828e9	−0.132747
$235$	3.90980e10	0.836276
$236$	4.71464e9	0.0989338
$237$	1.28711e9	0.0265001
$238$	−5.71526e10	−1.15462
$239$	−5.36117e10	−1.06284	−0.531421	−	0.847108i	$-0.678342\pi$
$239$	−5.36117e10	−1.06284	−0.531421	+	0.847108i	$0.678342\pi$
$240$	1.01664e10	0.197796
$241$	9.57350e10	1.82808	0.914038	−	0.405628i	$-0.132947\pi$
$241$	9.57350e10	1.82808	0.914038	+	0.405628i	$0.132947\pi$
$242$	−2.79014e10	−0.522946
$243$	−4.07175e10	−0.749123
$244$	−7.23497e9	−0.130672
$245$	7.94769e10	1.40927
$246$	2.33974e10	0.407342
$247$	−6.37506e9	−0.108980
$248$	2.06536e9	0.0346707
$249$	4.69212e10	0.773521
$250$	4.53817e10	0.734769
$251$	−1.16580e10	−0.185392	−0.0926959	−	0.995694i	$-0.529548\pi$
$251$	−1.16580e10	−0.185392	−0.0926959	+	0.995694i	$0.529548\pi$
$252$	−2.22866e10	−0.348129
$253$	−1.27835e11	−1.96159
$254$	4.97747e10	0.750338
$255$	−4.95115e10	−0.733288
$256$	4.29497e9	0.0625000
$257$	−2.63091e10	−0.376189	−0.188095	−	0.982151i	$-0.560231\pi$
$257$	−2.63091e10	−0.376189	−0.188095	+	0.982151i	$0.560231\pi$
$258$	−1.54915e10	−0.217674
$259$	−7.18469e10	−0.992109
$260$	1.17229e10	0.159094
$261$	−5.58612e10	−0.745123
$262$	−7.51233e10	−0.984961
$263$	8.36629e10	1.07828	0.539141	−	0.842216i	$-0.318749\pi$
$263$	8.36629e10	1.07828	0.539141	+	0.842216i	$0.318749\pi$
$264$	4.34720e10	0.550798
$265$	−8.76985e10	−1.09241
$266$	−2.33363e10	−0.285802
$267$	1.35283e11	1.62908
$268$	−6.24931e10	−0.739989
$269$	−1.02361e11	−1.19193	−0.595966	−	0.803010i	$-0.703231\pi$
$269$	−1.02361e11	−1.19193	−0.595966	+	0.803010i	$0.703231\pi$
$270$	2.95470e10	0.338358
$271$	−8.44812e9	−0.0951477	−0.0475739	−	0.998868i	$-0.515149\pi$
$271$	−8.44812e9	−0.0951477	−0.0475739	+	0.998868i	$0.515149\pi$
$272$	−2.09169e10	−0.231706
$273$	−9.07259e10	−0.988552
$274$	−9.27774e10	−0.994408
$275$	6.89660e10	0.727173
$276$	8.46775e10	0.878369
$277$	7.77514e10	0.793504	0.396752	−	0.917926i	$-0.370137\pi$
$277$	7.77514e10	0.793504	0.396752	+	0.917926i	$0.370137\pi$
$278$	−7.61336e10	−0.764496
$279$	−3.92229e9	−0.0387544
$280$	4.29124e10	0.417226
$281$	1.41860e10	0.135732	0.0678660	−	0.997694i	$-0.478381\pi$
$281$	1.41860e10	0.135732	0.0678660	+	0.997694i	$0.478381\pi$
$282$	−1.10742e11	−1.04278
$283$	−9.20528e10	−0.853097	−0.426548	−	0.904465i	$-0.640271\pi$
$283$	−9.20528e10	−0.853097	−0.426548	+	0.904465i	$0.640271\pi$
$284$	4.32730e10	0.394716
$285$	−2.02163e10	−0.181510
$286$	5.01275e10	0.443026
$287$	9.87602e10	0.859238
$288$	−8.15652e9	−0.0698616
$289$	−1.67204e10	−0.140996
$290$	1.07560e11	0.893016
$291$	1.92982e11	1.57761
$292$	−7.96765e10	−0.641368
$293$	−1.09183e11	−0.865464	−0.432732	−	0.901523i	$-0.642450\pi$
$293$	−1.09183e11	−0.865464	−0.432732	+	0.901523i	$0.642450\pi$
$294$	−2.25113e11	−1.75726
$295$	1.72398e10	0.132536
$296$	−2.62948e10	−0.199094
$297$	1.26344e11	0.942217
$298$	1.84868e10	0.135797
$299$	9.76415e10	0.706503
$300$	−4.56827e10	−0.325616
$301$	−6.53897e10	−0.459156
$302$	−4.25636e10	−0.294447
$303$	−1.44537e11	−0.985114
$304$	−8.54072e9	−0.0573539
$305$	−2.64558e10	−0.175054
$306$	3.97231e10	0.258998
$307$	2.47336e11	1.58915	0.794575	−	0.607166i	$-0.207694\pi$
$307$	2.47336e11	1.58915	0.794575	+	0.607166i	$0.207694\pi$
$308$	1.83495e11	1.16184
$309$	−6.34689e10	−0.396048
$310$	7.55230e9	0.0464464
$311$	−2.55496e10	−0.154868	−0.0774341	−	0.996997i	$-0.524673\pi$
$311$	−2.55496e10	−0.154868	−0.0774341	+	0.996997i	$0.524673\pi$
$312$	−3.32042e10	−0.198380
$313$	−1.47926e11	−0.871155	−0.435577	−	0.900151i	$-0.643456\pi$
$313$	−1.47926e11	−0.871155	−0.435577	+	0.900151i	$0.643456\pi$
$314$	1.83989e11	1.06809
$315$	−8.14943e10	−0.466369
$316$	1.98834e9	0.0112176
$317$	6.91449e10	0.384586	0.192293	−	0.981338i	$-0.438408\pi$
$317$	6.91449e10	0.384586	0.192293	+	0.981338i	$0.438408\pi$
$318$	2.48400e11	1.36216
$319$	4.59930e11	2.48676
$320$	1.57052e10	0.0837278
$321$	3.57750e11	1.88065
$322$	3.57423e11	1.85281
$323$	4.15941e10	0.212628
$324$	−1.22885e11	−0.619508
$325$	−5.26767e10	−0.261905
$326$	8.36791e10	0.410334
$327$	−9.46740e9	−0.0457895
$328$	3.61446e10	0.172430
$329$	−4.67443e11	−2.19962
$330$	1.58962e11	0.737873
$331$	−1.66086e11	−0.760514	−0.380257	−	0.924881i	$-0.624165\pi$
$331$	−1.66086e11	−0.760514	−0.380257	+	0.924881i	$0.624165\pi$
$332$	7.24846e10	0.327435
$333$	4.99361e10	0.222544
$334$	7.07708e10	0.311168
$335$	−2.28516e11	−0.991322
$336$	−1.21546e11	−0.520253
$337$	−1.36811e11	−0.577811	−0.288906	−	0.957358i	$-0.593291\pi$
$337$	−1.36811e11	−0.577811	−0.288906	+	0.957358i	$0.593291\pi$
$338$	1.31384e11	0.547543
$339$	2.43261e10	0.100040
$340$	−7.64860e10	−0.310404
$341$	3.22940e10	0.129338
$342$	1.62196e10	0.0641094
$343$	−4.98572e11	−1.94493
$344$	−2.39316e10	−0.0921421
$345$	3.09637e11	1.17670
$346$	4.34414e10	0.162953
$347$	−2.87545e11	−1.06469	−0.532345	−	0.846528i	$-0.678689\pi$
$347$	−2.87545e11	−1.06469	−0.532345	+	0.846528i	$0.678689\pi$
$348$	−3.04655e11	−1.11353
$349$	−3.68636e11	−1.33010	−0.665048	−	0.746801i	$-0.731589\pi$
$349$	−3.68636e11	−1.33010	−0.665048	+	0.746801i	$0.731589\pi$
$350$	−1.92826e11	−0.686847
$351$	−9.65025e10	−0.339357
$352$	6.71562e10	0.233155
$353$	−3.59837e11	−1.23345	−0.616723	−	0.787180i	$-0.711540\pi$
$353$	−3.59837e11	−1.23345	−0.616723	+	0.787180i	$0.711540\pi$
$354$	−4.88306e10	−0.165264
$355$	1.58235e11	0.528779
$356$	2.08987e11	0.689595
$357$	5.91942e11	1.92873
$358$	−2.67207e11	−0.859755
$359$	3.97180e11	1.26201	0.631004	−	0.775779i	$-0.282643\pi$
$359$	3.97180e11	1.26201	0.631004	+	0.775779i	$0.282643\pi$
$360$	−2.98256e10	−0.0935897
$361$	1.69836e10	0.0526316
$362$	2.88371e11	0.882599
$363$	2.88981e11	0.873554
$364$	−1.40155e11	−0.418458
$365$	−2.91350e11	−0.859205
$366$	7.49342e10	0.218281
$367$	−5.36473e11	−1.54366	−0.771828	−	0.635831i	$-0.780658\pi$
$367$	−5.36473e11	−1.54366	−0.771828	+	0.635831i	$0.780658\pi$
$368$	1.30811e11	0.371817
$369$	−6.86418e10	−0.192739
$370$	−9.61512e10	−0.266715
$371$	1.04849e12	2.87332
$372$	−2.13914e10	−0.0579156
$373$	5.59186e10	0.149578	0.0747888	−	0.997199i	$-0.476172\pi$
$373$	5.59186e10	0.149578	0.0747888	+	0.997199i	$0.476172\pi$
$374$	−3.27058e11	−0.864375
$375$	−4.70029e11	−1.22739
$376$	−1.71077e11	−0.441413
$377$	−3.51298e11	−0.895652
$378$	−3.53254e11	−0.889967
$379$	−5.01348e11	−1.24814	−0.624070	−	0.781369i	$-0.714522\pi$
$379$	−5.01348e11	−1.24814	−0.624070	+	0.781369i	$0.714522\pi$
$380$	−3.12305e10	−0.0768339
$381$	−5.15528e11	−1.25340
$382$	3.44484e11	0.827721
$383$	−4.93382e11	−1.17163	−0.585813	−	0.810446i	$-0.699225\pi$
$383$	−4.93382e11	−1.17163	−0.585813	+	0.810446i	$0.699225\pi$
$384$	−4.44839e10	−0.104403
$385$	6.70979e11	1.55645
$386$	4.22662e11	0.969060
$387$	4.54481e10	0.102995
$388$	2.98122e11	0.667807
$389$	5.08678e11	1.12634	0.563171	−	0.826341i	$-0.309581\pi$
$389$	5.08678e11	1.12634	0.563171	+	0.826341i	$0.309581\pi$
$390$	−1.21417e11	−0.265758
$391$	−6.37063e11	−1.37844
$392$	−3.47758e11	−0.743857
$393$	7.78069e11	1.64533
$394$	−3.97902e11	−0.831847
$395$	7.27069e9	0.0150276
$396$	−1.27536e11	−0.260617
$397$	−8.18391e11	−1.65350	−0.826749	−	0.562571i	$-0.809812\pi$
$397$	−8.18391e11	−1.65350	−0.826749	+	0.562571i	$0.809812\pi$
$398$	−7.64706e10	−0.152764
$399$	2.41700e11	0.477417
$400$	−7.05713e10	−0.137835
$401$	5.37337e11	1.03776	0.518880	−	0.854847i	$-0.326349\pi$
$401$	5.37337e11	1.03776	0.518880	+	0.854847i	$0.326349\pi$
$402$	6.47255e11	1.23611
$403$	−2.46664e10	−0.0465835
$404$	−2.23283e11	−0.417002
$405$	−4.49349e11	−0.829920
$406$	−1.28595e12	−2.34886
$407$	−4.11147e11	−0.742714
$408$	2.16641e11	0.387053
$409$	5.07177e11	0.896200	0.448100	−	0.893983i	$-0.352101\pi$
$409$	5.07177e11	0.896200	0.448100	+	0.893983i	$0.352101\pi$
$410$	1.32169e11	0.230994
$411$	9.60917e11	1.66111
$412$	−9.80477e10	−0.167649
$413$	−2.06114e11	−0.348603
$414$	−2.48422e11	−0.415612
$415$	2.65052e11	0.438646
$416$	−5.12944e10	−0.0839750
$417$	7.88533e11	1.27705
$418$	−1.33543e11	−0.213958
$419$	8.51672e11	1.34992	0.674962	−	0.737853i	$-0.264160\pi$
$419$	8.51672e11	1.34992	0.674962	+	0.737853i	$0.264160\pi$
$420$	−4.44453e11	−0.696954
$421$	9.03027e11	1.40098	0.700489	−	0.713663i	$-0.252965\pi$
$421$	9.03027e11	1.40098	0.700489	+	0.713663i	$0.252965\pi$
$422$	8.84566e11	1.35776
$423$	3.24889e11	0.493405
$424$	3.83732e11	0.576609
$425$	3.43689e11	0.510994
$426$	−4.48189e11	−0.659352
$427$	3.16297e11	0.460436
$428$	5.52658e11	0.796085
$429$	−5.19182e11	−0.740052
$430$	−8.75095e10	−0.123438
$431$	−5.32102e11	−0.742757	−0.371379	−	0.928482i	$-0.621115\pi$
$431$	−5.32102e11	−0.742757	−0.371379	+	0.928482i	$0.621115\pi$
$432$	−1.29285e11	−0.178596
$433$	−6.26206e11	−0.856095	−0.428047	−	0.903756i	$-0.640798\pi$
$433$	−6.26206e11	−0.856095	−0.428047	+	0.903756i	$0.640798\pi$
$434$	−9.02928e10	−0.122166
$435$	−1.11402e12	−1.49174
$436$	−1.46254e10	−0.0193829
$437$	−2.60123e11	−0.341203
$438$	8.25228e11	1.07137
$439$	−2.86280e11	−0.367875	−0.183938	−	0.982938i	$-0.558884\pi$
$439$	−2.86280e11	−0.367875	−0.183938	+	0.982938i	$0.558884\pi$
$440$	2.45567e11	0.312344
$441$	6.60422e11	0.831472
$442$	2.49809e11	0.311320
$443$	2.71184e11	0.334540	0.167270	−	0.985911i	$-0.446505\pi$
$443$	2.71184e11	0.334540	0.167270	+	0.985911i	$0.446505\pi$
$444$	2.72341e11	0.332575
$445$	7.64193e11	0.923811
$446$	8.01036e10	0.0958618
$447$	−1.91472e11	−0.226841
$448$	−1.87766e11	−0.220225
$449$	1.04096e11	0.120872	0.0604359	−	0.998172i	$-0.480751\pi$
$449$	1.04096e11	0.120872	0.0604359	+	0.998172i	$0.480751\pi$
$450$	1.34021e11	0.154070
$451$	5.65159e11	0.643244
$452$	3.75793e10	0.0423473
$453$	4.40841e11	0.491859
$454$	1.17372e11	0.129662
$455$	−5.12498e11	−0.560585
$456$	8.84581e10	0.0958067
$457$	−3.01176e11	−0.322996	−0.161498	−	0.986873i	$-0.551633\pi$
$457$	−3.01176e11	−0.322996	−0.161498	+	0.986873i	$0.551633\pi$
$458$	−4.13902e11	−0.439544
$459$	6.29632e11	0.662109
$460$	4.78332e11	0.498103
$461$	7.38496e11	0.761542	0.380771	−	0.924669i	$-0.375659\pi$
$461$	7.38496e11	0.761542	0.380771	+	0.924669i	$0.375659\pi$
$462$	−1.90050e12	−1.94079
$463$	1.36551e12	1.38096	0.690478	−	0.723354i	$-0.257400\pi$
$463$	1.36551e12	1.38096	0.690478	+	0.723354i	$0.257400\pi$
$464$	−4.70636e11	−0.471362
$465$	−7.82209e10	−0.0775862
$466$	4.98383e11	0.489583
$467$	−1.96693e12	−1.91365	−0.956825	−	0.290663i	$-0.906124\pi$
$467$	−1.96693e12	−1.91365	−0.956825	+	0.290663i	$0.906124\pi$
$468$	9.74125e10	0.0938660
$469$	2.73206e12	2.60743
$470$	−6.25569e11	−0.591336
$471$	−1.90562e12	−1.78419
$472$	−7.54342e10	−0.0699567
$473$	−3.74195e11	−0.343734
$474$	−2.05937e10	−0.0187384
$475$	1.40334e11	0.126486
$476$	9.14442e11	0.816441
$477$	−7.28740e11	−0.644525
$478$	8.57787e11	0.751543
$479$	−6.78530e11	−0.588924	−0.294462	−	0.955663i	$-0.595140\pi$
$479$	−6.78530e11	−0.588924	−0.294462	+	0.955663i	$0.595140\pi$
$480$	−1.62663e11	−0.139863
$481$	3.14037e11	0.267502
$482$	−1.53176e12	−1.29265
$483$	−3.70191e12	−3.09502
$484$	4.46423e11	0.369779
$485$	1.09013e12	0.894624
$486$	6.51480e11	0.529710
$487$	−2.01095e11	−0.162002	−0.0810011	−	0.996714i	$-0.525812\pi$
$487$	−2.01095e11	−0.162002	−0.0810011	+	0.996714i	$0.525812\pi$
$488$	1.15760e11	0.0923990
$489$	−8.66683e11	−0.685441
$490$	−1.27163e12	−0.996503
$491$	−5.92335e11	−0.459940	−0.229970	−	0.973198i	$-0.573863\pi$
$491$	−5.92335e11	−0.459940	−0.229970	+	0.973198i	$0.573863\pi$
$492$	−3.74358e11	−0.288034
$493$	2.29205e12	1.74748
$494$	1.02001e11	0.0770607
$495$	−4.66354e11	−0.349134
$496$	−3.30457e10	−0.0245159
$497$	−1.89180e12	−1.39082
$498$	−7.50740e11	−0.546962
$499$	2.31617e12	1.67231	0.836157	−	0.548490i	$-0.184797\pi$
$499$	2.31617e12	1.67231	0.836157	+	0.548490i	$0.184797\pi$
$500$	−7.26108e11	−0.519560
$501$	−7.32990e11	−0.519790
$502$	1.86527e11	0.131092
$503$	−9.93417e11	−0.691952	−0.345976	−	0.938243i	$-0.612452\pi$
$503$	−9.93417e11	−0.691952	−0.345976	+	0.938243i	$0.612452\pi$
$504$	3.56585e11	0.246165
$505$	−8.16468e11	−0.558635
$506$	2.04537e12	1.38706
$507$	−1.36078e12	−0.914641
$508$	−7.96395e11	−0.530569
$509$	−1.18974e12	−0.785634	−0.392817	−	0.919617i	$-0.628499\pi$
$509$	−1.18974e12	−0.785634	−0.392817	+	0.919617i	$0.628499\pi$
$510$	7.92183e11	0.518513
$511$	3.48328e12	2.25993
$512$	−6.87195e10	−0.0441942
$513$	2.57089e11	0.163891
$514$	4.20945e11	0.266006
$515$	−3.58527e11	−0.224589
$516$	2.47865e11	0.153918
$517$	−2.67496e12	−1.64668
$518$	1.14955e12	0.701527
$519$	−4.49932e11	−0.272204
$520$	−1.87566e11	−0.112497
$521$	1.77554e12	1.05575	0.527874	−	0.849323i	$-0.322989\pi$
$521$	1.77554e12	1.05575	0.527874	+	0.849323i	$0.322989\pi$
$522$	8.93780e11	0.526882
$523$	−1.82382e12	−1.06592	−0.532960	−	0.846140i	$-0.678921\pi$
$523$	−1.82382e12	−1.06592	−0.532960	+	0.846140i	$0.678921\pi$
$524$	1.20197e12	0.696472
$525$	1.99715e12	1.14734
$526$	−1.33861e12	−0.762460
$527$	1.60936e11	0.0908877
$528$	−6.95552e11	−0.389473
$529$	2.18294e12	1.21197
$530$	1.40318e12	0.772451
$531$	1.43256e11	0.0781967
$532$	3.73381e11	0.202092
$533$	−4.31672e11	−0.231676
$534$	−2.16452e12	−1.15193
$535$	2.02088e12	1.06647
$536$	9.99889e11	0.523251
$537$	2.76753e12	1.43618
$538$	1.63778e12	0.842823
$539$	−5.43755e12	−2.77494
$540$	−4.72752e11	−0.239255
$541$	−2.12345e12	−1.06575	−0.532873	−	0.846195i	$-0.678888\pi$
$541$	−2.12345e12	−1.06575	−0.532873	+	0.846195i	$0.678888\pi$
$542$	1.35170e11	0.0672796
$543$	−2.98673e12	−1.47434
$544$	3.34671e11	0.163841
$545$	−5.34801e10	−0.0259662
$546$	1.45162e12	0.699012
$547$	−2.06188e12	−0.984737	−0.492369	−	0.870387i	$-0.663869\pi$
$547$	−2.06188e12	−0.984737	−0.492369	+	0.870387i	$0.663869\pi$
$548$	1.48444e12	0.703153
$549$	−2.19837e11	−0.103282
$550$	−1.10346e12	−0.514189
$551$	9.35880e11	0.432552
$552$	−1.35484e12	−0.621101
$553$	−8.69259e10	−0.0395263
$554$	−1.24402e12	−0.561092
$555$	9.95859e11	0.445533
$556$	1.21814e12	0.540580
$557$	−3.68563e12	−1.62242	−0.811209	−	0.584756i	$-0.801190\pi$
$557$	−3.68563e12	−1.62242	−0.811209	+	0.584756i	$0.801190\pi$
$558$	6.27567e10	0.0274035
$559$	2.85812e11	0.123802
$560$	−6.86598e11	−0.295023
$561$	3.38741e12	1.44389
$562$	−2.26977e11	−0.0959771
$563$	1.91244e12	0.802231	0.401115	−	0.916028i	$-0.368623\pi$
$563$	1.91244e12	0.802231	0.401115	+	0.916028i	$0.368623\pi$
$564$	1.77188e12	0.737357
$565$	1.37415e11	0.0567303
$566$	1.47285e12	0.603230
$567$	5.37227e12	2.18290
$568$	−6.92369e11	−0.279106
$569$	−4.60869e11	−0.184320	−0.0921599	−	0.995744i	$-0.529377\pi$
$569$	−4.60869e11	−0.184320	−0.0921599	+	0.995744i	$0.529377\pi$
$570$	3.23461e11	0.128347
$571$	1.41785e12	0.558172	0.279086	−	0.960266i	$-0.409969\pi$
$571$	1.41785e12	0.558172	0.279086	+	0.960266i	$0.409969\pi$
$572$	−8.02041e11	−0.313267
$573$	−3.56790e12	−1.38266
$574$	−1.58016e12	−0.607573
$575$	−2.14938e12	−0.819988
$576$	1.30504e11	0.0493996
$577$	−5.01999e12	−1.88544	−0.942718	−	0.333590i	$-0.891740\pi$
$577$	−5.01999e12	−1.88544	−0.942718	+	0.333590i	$0.891740\pi$
$578$	2.67526e11	0.0996990
$579$	−4.37761e12	−1.61876
$580$	−1.72096e12	−0.631457
$581$	−3.16887e12	−1.15375
$582$	−3.08771e12	−1.11554
$583$	6.00004e12	2.15103
$584$	1.27482e12	0.453516
$585$	3.56204e11	0.125747
$586$	1.74692e12	0.611976
$587$	3.43500e12	1.19414	0.597070	−	0.802189i	$-0.296331\pi$
$587$	3.43500e12	1.19414	0.597070	+	0.802189i	$0.296331\pi$
$588$	3.60180e12	1.24257
$589$	6.57127e10	0.0224973
$590$	−2.75837e11	−0.0937171
$591$	4.12116e12	1.38956
$592$	4.20717e11	0.140780
$593$	8.19773e11	0.272237	0.136119	−	0.990693i	$-0.456537\pi$
$593$	8.19773e11	0.272237	0.136119	+	0.990693i	$0.456537\pi$
$594$	−2.02151e12	−0.666248
$595$	3.34380e12	1.09374
$596$	−2.95789e11	−0.0960226
$597$	7.92024e11	0.255184
$598$	−1.56226e12	−0.499573
$599$	5.59603e12	1.77607	0.888034	−	0.459777i	$-0.152071\pi$
$599$	5.59603e12	1.77607	0.888034	+	0.459777i	$0.152071\pi$
$600$	7.30923e11	0.230245
$601$	−5.95146e12	−1.86075	−0.930375	−	0.366608i	$-0.880519\pi$
$601$	−5.95146e12	−1.86075	−0.930375	+	0.366608i	$0.880519\pi$
$602$	1.04623e12	0.324672
$603$	−1.89888e12	−0.584883
$604$	6.81018e11	0.208206
$605$	1.63242e12	0.495372
$606$	2.31259e12	0.696581
$607$	4.09020e12	1.22291	0.611457	−	0.791278i	$-0.290584\pi$
$607$	4.09020e12	1.22291	0.611457	+	0.791278i	$0.290584\pi$
$608$	1.36651e11	0.0405554
$609$	1.33189e13	3.92364
$610$	4.23293e11	0.123782
$611$	2.04315e12	0.593082
$612$	−6.35569e11	−0.183139
$613$	4.35932e12	1.24694	0.623472	−	0.781846i	$-0.285722\pi$
$613$	4.35932e12	1.24694	0.623472	+	0.781846i	$0.285722\pi$
$614$	−3.95738e12	−1.12370
$615$	−1.36890e12	−0.385864
$616$	−2.93592e12	−0.821545
$617$	−7.71046e11	−0.214189	−0.107094	−	0.994249i	$-0.534155\pi$
$617$	−7.71046e11	−0.214189	−0.107094	+	0.994249i	$0.534155\pi$
$618$	1.01550e12	0.280048
$619$	5.46692e12	1.49670	0.748350	−	0.663304i	$-0.230846\pi$
$619$	5.46692e12	1.49670	0.748350	+	0.663304i	$0.230846\pi$
$620$	−1.20837e11	−0.0328425
$621$	−3.93762e12	−1.06248
$622$	4.08794e11	0.109508
$623$	−9.13644e12	−2.42986
$624$	5.31268e11	0.140276
$625$	−5.51939e11	−0.144687
$626$	2.36682e12	0.615999
$627$	1.38313e12	0.357405
$628$	−2.94382e12	−0.755255
$629$	−2.04893e12	−0.521915
$630$	1.30391e12	0.329773
$631$	3.54962e12	0.891354	0.445677	−	0.895194i	$-0.352963\pi$
$631$	3.54962e12	0.891354	0.445677	+	0.895194i	$0.352963\pi$
$632$	−3.18135e10	−0.00793202
$633$	−9.16165e12	−2.26807
$634$	−1.10632e12	−0.271943
$635$	−2.91214e12	−0.710773
$636$	−3.97440e12	−0.963195
$637$	4.15324e12	0.999446
$638$	−7.35889e12	−1.75841
$639$	1.31487e12	0.311981
$640$	−2.51284e11	−0.0592045
$641$	3.41233e12	0.798344	0.399172	−	0.916876i	$-0.369298\pi$
$641$	3.41233e12	0.798344	0.399172	+	0.916876i	$0.369298\pi$
$642$	−5.72400e12	−1.32982
$643$	−1.72117e12	−0.397076	−0.198538	−	0.980093i	$-0.563619\pi$
$643$	−1.72117e12	−0.397076	−0.198538	+	0.980093i	$0.563619\pi$
$644$	−5.71877e12	−1.31014
$645$	9.06356e11	0.206196
$646$	−6.65506e11	−0.150351
$647$	−7.85180e12	−1.76157	−0.880786	−	0.473515i	$-0.842985\pi$
$647$	−7.85180e12	−1.76157	−0.880786	+	0.473515i	$0.842985\pi$
$648$	1.96616e12	0.438058
$649$	−1.17949e12	−0.260972
$650$	8.42827e11	0.185195
$651$	9.35183e11	0.204071
$652$	−1.33886e12	−0.290150
$653$	2.61324e12	0.562432	0.281216	−	0.959645i	$-0.409262\pi$
$653$	2.61324e12	0.562432	0.281216	+	0.959645i	$0.409262\pi$
$654$	1.51478e11	0.0323781
$655$	4.39521e12	0.933025
$656$	−5.78314e11	−0.121926
$657$	−2.42100e12	−0.506934
$658$	7.47909e12	1.55536
$659$	−6.84079e12	−1.41293	−0.706467	−	0.707746i	$-0.749712\pi$
$659$	−6.84079e12	−1.41293	−0.706467	+	0.707746i	$0.749712\pi$
$660$	−2.54340e12	−0.521755
$661$	−1.82024e12	−0.370869	−0.185435	−	0.982657i	$-0.559369\pi$
$661$	−1.82024e12	−0.370869	−0.185435	+	0.982657i	$0.559369\pi$
$662$	2.65738e12	0.537765
$663$	−2.58733e12	−0.520044
$664$	−1.15975e12	−0.231531
$665$	1.36533e12	0.270732
$666$	−7.98978e11	−0.157362
$667$	−1.43341e13	−2.80417
$668$	−1.13233e12	−0.220029
$669$	−8.29652e11	−0.160132
$670$	3.65625e12	0.700970
$671$	1.81002e12	0.344693
$672$	1.94474e12	0.367875
$673$	7.55008e11	0.141868	0.0709339	−	0.997481i	$-0.477402\pi$
$673$	7.55008e11	0.141868	0.0709339	+	0.997481i	$0.477402\pi$
$674$	2.18897e12	0.408574
$675$	2.12431e12	0.393867
$676$	−2.10215e12	−0.387171
$677$	2.54203e12	0.465084	0.232542	−	0.972586i	$-0.425296\pi$
$677$	2.54203e12	0.465084	0.232542	+	0.972586i	$0.425296\pi$
$678$	−3.89218e11	−0.0707390
$679$	−1.30332e13	−2.35309
$680$	1.22378e12	0.219489
$681$	−1.21565e12	−0.216594
$682$	−5.16704e11	−0.0914559
$683$	−6.52575e11	−0.114746	−0.0573730	−	0.998353i	$-0.518272\pi$
$683$	−6.52575e11	−0.114746	−0.0573730	+	0.998353i	$0.518272\pi$
$684$	−2.59513e11	−0.0453322
$685$	5.42809e12	0.941975
$686$	7.97715e12	1.37527
$687$	4.28687e12	0.734235
$688$	3.82905e11	0.0651543
$689$	−4.58287e12	−0.774732
$690$	−4.95419e12	−0.832054
$691$	4.92319e11	0.0821478	0.0410739	−	0.999156i	$-0.486922\pi$
$691$	4.92319e11	0.0821478	0.0410739	+	0.999156i	$0.486922\pi$
$692$	−6.95062e11	−0.115225
$693$	5.57557e12	0.918311
$694$	4.60072e12	0.752849
$695$	4.45432e12	0.724185
$696$	4.87449e12	0.787386
$697$	2.81645e12	0.452016
$698$	5.89817e12	0.940519
$699$	−5.16187e12	−0.817823
$700$	3.08522e12	0.485674
$701$	−8.13700e12	−1.27272	−0.636361	−	0.771392i	$-0.719561\pi$
$701$	−8.13700e12	−1.27272	−0.636361	+	0.771392i	$0.719561\pi$
$702$	1.54404e12	0.239962
$703$	−8.36613e11	−0.129189
$704$	−1.07450e12	−0.164865
$705$	6.47915e12	0.987796
$706$	5.75740e12	0.872178
$707$	9.76142e12	1.46935
$708$	7.81289e11	0.116859
$709$	−6.01945e12	−0.894641	−0.447321	−	0.894374i	$-0.647622\pi$
$709$	−6.01945e12	−0.894641	−0.447321	+	0.894374i	$0.647622\pi$
$710$	−2.53176e12	−0.373903
$711$	6.04165e10	0.00886630
$712$	−3.34379e12	−0.487617
$713$	−1.00647e12	−0.145847
$714$	−9.47108e12	−1.36382
$715$	−2.93279e12	−0.419666
$716$	4.27532e12	0.607939
$717$	−8.88430e12	−1.25541
$718$	−6.35488e12	−0.892375
$719$	1.46528e12	0.204475	0.102237	−	0.994760i	$-0.467400\pi$
$719$	1.46528e12	0.204475	0.102237	+	0.994760i	$0.467400\pi$
$720$	4.77210e11	0.0661779
$721$	4.28643e12	0.590727
$722$	−2.71737e11	−0.0372161
$723$	1.58648e13	2.15930
$724$	−4.61394e12	−0.624092
$725$	7.73311e12	1.03952
$726$	−4.62370e12	−0.617696
$727$	6.70236e11	0.0889862	0.0444931	−	0.999010i	$-0.485833\pi$
$727$	6.70236e11	0.0889862	0.0444931	+	0.999010i	$0.485833\pi$
$728$	2.24248e12	0.295894
$729$	2.70071e12	0.354164
$730$	4.66160e12	0.607550
$731$	−1.86479e12	−0.241546
$732$	−1.19895e12	−0.154348
$733$	−1.35697e13	−1.73622	−0.868108	−	0.496375i	$-0.834664\pi$
$733$	−1.35697e13	−1.73622	−0.868108	+	0.496375i	$0.834664\pi$
$734$	8.58357e12	1.09153
$735$	1.31706e13	1.66461
$736$	−2.09298e12	−0.262914
$737$	1.56343e13	1.95198
$738$	1.09827e12	0.136287
$739$	9.97461e12	1.23026	0.615129	−	0.788427i	$-0.289104\pi$
$739$	9.97461e12	1.23026	0.615129	+	0.788427i	$0.289104\pi$
$740$	1.53842e12	0.188596
$741$	−1.05645e12	−0.128726
$742$	−1.67759e13	−2.03174
$743$	1.33724e13	1.60976	0.804880	−	0.593438i	$-0.202230\pi$
$743$	1.33724e13	1.60976	0.804880	+	0.593438i	$0.202230\pi$
$744$	3.42262e11	0.0409525
$745$	−1.08160e12	−0.128636
$746$	−8.94697e11	−0.105767
$747$	2.20247e12	0.258802
$748$	5.23292e12	0.611205
$749$	−2.41610e13	−2.80509
$750$	7.52046e12	0.867898
$751$	7.93956e12	0.910787	0.455393	−	0.890290i	$-0.349499\pi$
$751$	7.93956e12	0.910787	0.455393	+	0.890290i	$0.349499\pi$
$752$	2.73722e12	0.312126
$753$	−1.93190e12	−0.218982
$754$	5.62077e12	0.633322
$755$	2.49025e12	0.278921
$756$	5.65206e12	0.629301
$757$	−1.38452e13	−1.53238	−0.766190	−	0.642614i	$-0.777850\pi$
$757$	−1.38452e13	−1.53238	−0.766190	+	0.642614i	$0.777850\pi$
$758$	8.02157e12	0.882568
$759$	−2.11843e13	−2.31700
$760$	4.99688e11	0.0543297
$761$	4.23304e10	0.00457532	0.00228766	−	0.999997i	$-0.499272\pi$
$761$	4.23304e10	0.00457532	0.00228766	+	0.999997i	$0.499272\pi$
$762$	8.24844e12	0.886287
$763$	6.39390e11	0.0682976
$764$	−5.51174e12	−0.585287
$765$	−2.32406e12	−0.245341
$766$	7.89411e12	0.828464
$767$	9.00904e11	0.0939938
$768$	7.11743e11	0.0738240
$769$	1.20995e13	1.24767	0.623836	−	0.781555i	$-0.285573\pi$
$769$	1.20995e13	1.24767	0.623836	+	0.781555i	$0.285573\pi$
$770$	−1.07357e13	−1.10058
$771$	−4.35982e12	−0.444349
$772$	−6.76260e12	−0.685229
$773$	7.75119e11	0.0780838	0.0390419	−	0.999238i	$-0.487569\pi$
$773$	7.75119e11	0.0780838	0.0390419	+	0.999238i	$0.487569\pi$
$774$	−7.27170e11	−0.0728285
$775$	5.42979e11	0.0540662
$776$	−4.76995e12	−0.472211
$777$	−1.19062e13	−1.17186
$778$	−8.13885e12	−0.796443
$779$	1.15000e12	0.111887
$780$	1.94266e12	0.187920
$781$	−1.08259e13	−1.04120
$782$	1.01930e13	0.974703
$783$	1.41669e13	1.34693
$784$	5.56412e12	0.525986
$785$	−1.07646e13	−1.01177
$786$	−1.24491e13	−1.16342
$787$	−1.31883e13	−1.22547	−0.612733	−	0.790290i	$-0.709930\pi$
$787$	−1.31883e13	−1.22547	−0.612733	+	0.790290i	$0.709930\pi$
$788$	6.36643e12	0.588204
$789$	1.38643e13	1.27365
$790$	−1.16331e11	−0.0106261
$791$	−1.64289e12	−0.149215
$792$	2.04057e12	0.184284
$793$	−1.38250e12	−0.124147
$794$	1.30943e13	1.16920
$795$	−1.45330e13	−1.29034
$796$	1.22353e12	0.108020
$797$	1.39760e13	1.22693	0.613467	−	0.789720i	$-0.289774\pi$
$797$	1.39760e13	1.22693	0.613467	+	0.789720i	$0.289774\pi$
$798$	−3.86719e12	−0.337585
$799$	−1.33306e13	−1.15715
$800$	1.12914e12	0.0974638
$801$	6.35015e12	0.545051
$802$	−8.59739e12	−0.733808
$803$	1.99332e13	1.69183
$804$	−1.03561e13	−0.874063
$805$	−2.09116e13	−1.75512
$806$	3.94662e11	0.0329395
$807$	−1.69629e13	−1.40789
$808$	3.57252e12	0.294865
$809$	1.20948e13	0.992725	0.496363	−	0.868115i	$-0.334669\pi$
$809$	1.20948e13	0.992725	0.496363	+	0.868115i	$0.334669\pi$
$810$	7.18959e12	0.586842
$811$	5.13281e12	0.416641	0.208320	−	0.978061i	$-0.433200\pi$
$811$	5.13281e12	0.416641	0.208320	+	0.978061i	$0.433200\pi$
$812$	2.05752e13	1.66089
$813$	−1.39999e12	−0.112387
$814$	6.57834e12	0.525178
$815$	−4.89577e12	−0.388698
$816$	−3.46626e12	−0.273688
$817$	−7.61422e11	−0.0597897
$818$	−8.11484e12	−0.633709
$819$	−4.25866e12	−0.330747
$820$	−2.11470e12	−0.163338
$821$	−1.64939e13	−1.26701	−0.633503	−	0.773741i	$-0.718383\pi$
$821$	−1.64939e13	−1.26701	−0.633503	+	0.773741i	$0.718383\pi$
$822$	−1.53747e13	−1.17458
$823$	2.20650e13	1.67651	0.838254	−	0.545280i	$-0.183577\pi$
$823$	2.20650e13	1.67651	0.838254	+	0.545280i	$0.183577\pi$
$824$	1.56876e12	0.118545
$825$	1.14287e13	0.858925
$826$	3.29782e12	0.246500
$827$	1.76939e13	1.31537	0.657687	−	0.753291i	$-0.271535\pi$
$827$	1.76939e13	1.31537	0.657687	+	0.753291i	$0.271535\pi$
$828$	3.97475e12	0.293882
$829$	−2.45533e13	−1.80557	−0.902784	−	0.430094i	$-0.858480\pi$
$829$	−2.45533e13	−1.80557	−0.902784	+	0.430094i	$0.858480\pi$
$830$	−4.24083e12	−0.310169
$831$	1.28846e13	0.937275
$832$	8.20710e11	0.0593793
$833$	−2.70978e13	−1.94999
$834$	−1.26165e13	−0.903010
$835$	−4.14056e12	−0.294761
$836$	2.13669e12	0.151291
$837$	9.94727e11	0.0700550
$838$	−1.36267e13	−0.954540
$839$	−1.83603e13	−1.27923	−0.639617	−	0.768693i	$-0.720907\pi$
$839$	−1.83603e13	−1.27923	−0.639617	+	0.768693i	$0.720907\pi$
$840$	7.11125e12	0.492821
$841$	3.70645e13	2.55492
$842$	−1.44484e13	−0.990641
$843$	2.35085e12	0.160325
$844$	−1.41531e13	−0.960084
$845$	−7.68684e12	−0.518672
$846$	−5.19823e12	−0.348890
$847$	−1.95166e13	−1.30295
$848$	−6.13971e12	−0.407724
$849$	−1.52546e13	−1.00766
$850$	−5.49903e12	−0.361327
$851$	1.28137e13	0.837513
$852$	7.17102e12	0.466233
$853$	8.77657e12	0.567615	0.283808	−	0.958881i	$-0.408402\pi$
$853$	8.77657e12	0.567615	0.283808	+	0.958881i	$0.408402\pi$
$854$	−5.06075e12	−0.325578
$855$	−9.48951e11	−0.0607290
$856$	−8.84252e12	−0.562917
$857$	8.66615e11	0.0548798	0.0274399	−	0.999623i	$-0.491265\pi$
$857$	8.66615e11	0.0548798	0.0274399	+	0.999623i	$0.491265\pi$
$858$	8.30692e12	0.523296
$859$	−1.34151e12	−0.0840666	−0.0420333	−	0.999116i	$-0.513384\pi$
$859$	−1.34151e12	−0.0840666	−0.0420333	+	0.999116i	$0.513384\pi$
$860$	1.40015e12	0.0872835
$861$	1.63661e13	1.01492
$862$	8.51362e12	0.525209
$863$	1.65463e13	1.01543	0.507717	−	0.861524i	$-0.330489\pi$
$863$	1.65463e13	1.01543	0.507717	+	0.861524i	$0.330489\pi$
$864$	2.06856e12	0.126286
$865$	−2.54160e12	−0.154360
$866$	1.00193e13	0.605350
$867$	−2.77083e12	−0.166542
$868$	1.44469e12	0.0863842
$869$	−4.97436e11	−0.0295902
$870$	1.78243e13	1.05482
$871$	−1.19416e13	−0.703040
$872$	2.34006e11	0.0137058
$873$	9.05855e12	0.527830
$874$	4.16197e12	0.241267
$875$	3.17438e13	1.83072
$876$	−1.32036e13	−0.757574
$877$	−1.11057e12	−0.0633937	−0.0316968	−	0.999498i	$-0.510091\pi$
$877$	−1.11057e12	−0.0633937	−0.0316968	+	0.999498i	$0.510091\pi$
$878$	4.58048e12	0.260127
$879$	−1.80933e13	−1.02227
$880$	−3.92908e12	−0.220861
$881$	3.74048e12	0.209187	0.104594	−	0.994515i	$-0.466646\pi$
$881$	3.74048e12	0.209187	0.104594	+	0.994515i	$0.466646\pi$
$882$	−1.05668e13	−0.587940
$883$	−2.60258e13	−1.44072	−0.720362	−	0.693599i	$-0.756024\pi$
$883$	−2.60258e13	−1.44072	−0.720362	+	0.693599i	$0.756024\pi$
$884$	−3.99694e12	−0.220137
$885$	2.85691e12	0.156550
$886$	−4.33895e12	−0.236555
$887$	−1.09720e13	−0.595154	−0.297577	−	0.954698i	$-0.596178\pi$
$887$	−1.09720e13	−0.595154	−0.297577	+	0.954698i	$0.596178\pi$
$888$	−4.35746e12	−0.235166
$889$	3.48166e13	1.86951
$890$	−1.22271e13	−0.653233
$891$	3.07430e13	1.63417
$892$	−1.28166e12	−0.0677845
$893$	−5.44308e12	−0.286427
$894$	3.06355e12	0.160401
$895$	1.56334e13	0.814422
$896$	3.00426e12	0.155723
$897$	1.61807e13	0.834511
$898$	−1.66554e12	−0.0854693
$899$	3.62110e12	0.184894
$900$	−2.14434e12	−0.108944
$901$	2.99010e13	1.51156
$902$	−9.04254e12	−0.454842
$903$	−1.08361e13	−0.542348
$904$	−6.01269e11	−0.0299441
$905$	−1.68716e13	−0.836061
$906$	−7.05346e12	−0.347797
$907$	2.28042e12	0.111887	0.0559437	−	0.998434i	$-0.482183\pi$
$907$	2.28042e12	0.111887	0.0559437	+	0.998434i	$0.482183\pi$
$908$	−1.87795e12	−0.0916851
$909$	−6.78453e12	−0.329596
$910$	8.19998e12	0.396393
$911$	3.61939e13	1.74102	0.870509	−	0.492153i	$-0.163790\pi$
$911$	3.61939e13	1.74102	0.870509	+	0.492153i	$0.163790\pi$
$912$	−1.41533e12	−0.0677456
$913$	−1.81340e13	−0.863722
$914$	4.81881e12	0.228393
$915$	−4.38414e12	−0.206771
$916$	6.62243e12	0.310805
$917$	−5.25476e13	−2.45409
$918$	−1.00741e13	−0.468182
$919$	2.03447e13	0.940875	0.470438	−	0.882433i	$-0.344096\pi$
$919$	2.03447e13	0.940875	0.470438	+	0.882433i	$0.344096\pi$
$920$	−7.65331e12	−0.352212
$921$	4.09875e13	1.87708
$922$	−1.18159e13	−0.538492
$923$	8.26889e12	0.375007
$924$	3.04080e13	1.37235
$925$	−6.91287e12	−0.310471
$926$	−2.18481e13	−0.976483
$927$	−2.97922e12	−0.132508
$928$	7.53018e12	0.333303
$929$	3.15812e13	1.39110	0.695550	−	0.718478i	$-0.255161\pi$
$929$	3.15812e13	1.39110	0.695550	+	0.718478i	$0.255161\pi$
$930$	1.25153e12	0.0548617
$931$	−1.10645e13	−0.482678
$932$	−7.97413e12	−0.346188
$933$	−4.23397e12	−0.182928
$934$	3.14709e13	1.35316
$935$	1.91350e13	0.818797
$936$	−1.55860e12	−0.0663733
$937$	3.69060e12	0.156412	0.0782058	−	0.996937i	$-0.475081\pi$
$937$	3.69060e12	0.156412	0.0782058	+	0.996937i	$0.475081\pi$
$938$	−4.37129e13	−1.84373
$939$	−2.45137e13	−1.02899
$940$	1.00091e13	0.418138
$941$	9.74870e12	0.405316	0.202658	−	0.979250i	$-0.435042\pi$
$941$	9.74870e12	0.405316	0.202658	+	0.979250i	$0.435042\pi$
$942$	3.04899e13	1.26161
$943$	−1.76136e13	−0.725347
$944$	1.20695e12	0.0494669
$945$	2.06677e13	0.843040
$946$	5.98711e12	0.243057
$947$	1.04232e13	0.421140	0.210570	−	0.977579i	$-0.432468\pi$
$947$	1.04232e13	0.421140	0.210570	+	0.977579i	$0.432468\pi$
$948$	3.29499e11	0.0132500
$949$	−1.52251e13	−0.609344
$950$	−2.24534e12	−0.0894389
$951$	1.14584e13	0.454267
$952$	−1.46311e13	−0.577311
$953$	6.13632e12	0.240985	0.120493	−	0.992714i	$-0.461553\pi$
$953$	6.13632e12	0.240985	0.120493	+	0.992714i	$0.461553\pi$
$954$	1.16598e13	0.455748
$955$	−2.01546e13	−0.784076
$956$	−1.37246e13	−0.531421
$957$	7.62176e13	2.93732
$958$	1.08565e13	0.416432
$959$	−6.48964e13	−2.47763
$960$	2.60260e12	0.0988979
$961$	−2.61854e13	−0.990384
$962$	−5.02458e12	−0.189153
$963$	1.67927e13	0.629220
$964$	2.45082e13	0.914038
$965$	−2.47285e13	−0.917963
$966$	5.92306e13	2.18851
$967$	−3.58499e13	−1.31847	−0.659234	−	0.751938i	$-0.729119\pi$
$967$	−3.58499e13	−1.31847	−0.659234	+	0.751938i	$0.729119\pi$
$968$	−7.14276e12	−0.261473
$969$	6.89280e12	0.251153
$970$	−1.74421e13	−0.632594
$971$	3.91644e13	1.41386	0.706928	−	0.707285i	$-0.250080\pi$
$971$	3.91644e13	1.41386	0.706928	+	0.707285i	$0.250080\pi$
$972$	−1.04237e13	−0.374561
$973$	−5.32543e13	−1.90479
$974$	3.21752e12	0.114553
$975$	−8.72935e12	−0.309358
$976$	−1.85215e12	−0.0653360
$977$	3.46561e12	0.121690	0.0608450	−	0.998147i	$-0.480620\pi$
$977$	3.46561e12	0.121690	0.0608450	+	0.998147i	$0.480620\pi$
$978$	1.38669e13	0.484680
$979$	−5.22836e13	−1.81904
$980$	2.03461e13	0.704634
$981$	−4.44398e11	−0.0153201
$982$	9.47736e12	0.325226
$983$	−3.96438e13	−1.35421	−0.677103	−	0.735889i	$-0.736765\pi$
$983$	−3.96438e13	−1.35421	−0.677103	+	0.735889i	$0.736765\pi$
$984$	5.98973e12	0.203671
$985$	2.32799e13	0.787985
$986$	−3.66727e13	−1.23566
$987$	−7.74626e13	−2.59815
$988$	−1.63202e12	−0.0544902
$989$	1.16621e13	0.387608
$990$	7.46167e12	0.246875
$991$	−2.46380e13	−0.811472	−0.405736	−	0.913990i	$-0.632985\pi$
$991$	−2.46380e13	−0.811472	−0.405736	+	0.913990i	$0.632985\pi$
$992$	5.28731e11	0.0173353
$993$	−2.75231e13	−0.898308
$994$	3.02688e13	0.983460
$995$	4.47403e12	0.144709
$996$	1.20118e13	0.386761
$997$	3.98049e13	1.27588	0.637938	−	0.770088i	$-0.279788\pi$
$997$	3.98049e13	1.27588	0.637938	+	0.770088i	$0.279788\pi$
$998$	−3.70587e13	−1.18250
$999$	−1.26642e13	−0.402285

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.10.a.c.1.3	✓	3
3.2	odd	2		342.10.a.e.1.1		3
4.3	odd	2		304.10.a.c.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.a.c.1.3	✓	3	1.1	even	1	trivial
304.10.a.c.1.1		3	4.3	odd	2
342.10.a.e.1.1		3	3.2	odd	2

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	38.a (trivial)

\(f(q)\)	\(=\)	\(q-16.0000 q^{2} +165.716 q^{3} +256.000 q^{4} +936.105 q^{5} -2651.45 q^{6} -11191.8 q^{7} -4096.00 q^{8} +7778.66 q^{9} +O(q^{10})\)	\(q-16.0000 q^{2} +165.716 q^{3} +256.000 q^{4} +936.105 q^{5} -2651.45 q^{6} -11191.8 q^{7} -4096.00 q^{8} +7778.66 q^{9} -14977.7 q^{10} -64045.2 q^{11} +42423.2 q^{12} +48918.1 q^{13} +179068. q^{14} +155127. q^{15} +65536.0 q^{16} -319167. q^{17} -124459. q^{18} -130321. q^{19} +239643. q^{20} -1.85465e6 q^{21} +1.02472e6 q^{22} +1.99602e6 q^{23} -678771. q^{24} -1.07683e6 q^{25} -782690. q^{26} -1.97273e6 q^{27} -2.86509e6 q^{28} -7.18134e6 q^{29} -2.48203e6 q^{30} -504237. q^{31} -1.04858e6 q^{32} -1.06133e7 q^{33} +5.10667e6 q^{34} -1.04767e7 q^{35} +1.99134e6 q^{36} +6.41963e6 q^{37} +2.08514e6 q^{38} +8.10650e6 q^{39} -3.83429e6 q^{40} -8.82437e6 q^{41} +2.96744e7 q^{42} +5.84267e6 q^{43} -1.63956e7 q^{44} +7.28164e6 q^{45} -3.19363e7 q^{46} +4.17667e7 q^{47} +1.08603e7 q^{48} +8.49017e7 q^{49} +1.72293e7 q^{50} -5.28909e7 q^{51} +1.25230e7 q^{52} -9.36845e7 q^{53} +3.15638e7 q^{54} -5.99530e7 q^{55} +4.58414e7 q^{56} -2.15962e7 q^{57} +1.14901e8 q^{58} +1.84166e7 q^{59} +3.97126e7 q^{60} -2.82616e7 q^{61} +8.06780e6 q^{62} -8.70569e7 q^{63} +1.67772e7 q^{64} +4.57925e7 q^{65} +1.69813e8 q^{66} -2.44114e8 q^{67} -8.17067e7 q^{68} +3.30771e8 q^{69} +1.67626e8 q^{70} +1.69035e8 q^{71} -3.18614e7 q^{72} -3.11236e8 q^{73} -1.02714e8 q^{74} -1.78448e8 q^{75} -3.33622e7 q^{76} +7.16778e8 q^{77} -1.29704e8 q^{78} +7.76696e6 q^{79} +6.13486e7 q^{80} -4.80020e8 q^{81} +1.41190e8 q^{82} +2.83143e8 q^{83} -4.74790e8 q^{84} -2.98774e8 q^{85} -9.34826e7 q^{86} -1.19006e9 q^{87} +2.62329e8 q^{88} +8.16355e8 q^{89} -1.16506e8 q^{90} -5.47480e8 q^{91} +5.10981e8 q^{92} -8.35600e7 q^{93} -6.68268e8 q^{94} -1.21994e8 q^{95} -1.73765e8 q^{96} +1.16454e9 q^{97} -1.35843e9 q^{98} -4.98186e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 48 q^{2} + 3 q^{3} + 768 q^{4} + 486 q^{5} - 48 q^{6} - 13317 q^{7} - 12288 q^{8} + 22896 q^{9}+O(q^{10}) \) 3 * q - 48 * q^2 + 3 * q^3 + 768 * q^4 + 486 * q^5 - 48 * q^6 - 13317 * q^7 - 12288 * q^8 + 22896 * q^9	\( 3 q - 48 q^{2} + 3 q^{3} + 768 q^{4} + 486 q^{5} - 48 q^{6} - 13317 q^{7} - 12288 q^{8} + 22896 q^{9} - 7776 q^{10} + 55968 q^{11} + 768 q^{12} + 158181 q^{13} + 213072 q^{14} + 135660 q^{15} + 196608 q^{16} - 629091 q^{17} - 366336 q^{18} - 390963 q^{19} + 124416 q^{20} - 873405 q^{21} - 895488 q^{22} - 924627 q^{23} - 12288 q^{24} - 4805517 q^{25} - 2530896 q^{26} - 6711147 q^{27} - 3409152 q^{28} - 9839019 q^{29} - 2170560 q^{30} + 1364628 q^{31} - 3145728 q^{32} - 30339114 q^{33} + 10065456 q^{34} - 11097570 q^{35} + 5861376 q^{36} - 2289090 q^{37} + 6255408 q^{38} - 18481557 q^{39} - 1990656 q^{40} - 12899580 q^{41} + 13974480 q^{42} - 22378638 q^{43} + 14327808 q^{44} + 13005630 q^{45} + 14794032 q^{46} + 58896366 q^{47} + 196608 q^{48} + 22294974 q^{49} + 76888272 q^{50} + 85869585 q^{51} + 40494336 q^{52} + 8770629 q^{53} + 107378352 q^{54} - 73415802 q^{55} + 54546432 q^{56} - 390963 q^{57} + 157424304 q^{58} + 16426299 q^{59} + 34728960 q^{60} - 126843780 q^{61} - 21834048 q^{62} - 234650088 q^{63} + 50331648 q^{64} + 45269952 q^{65} + 485425824 q^{66} - 288075309 q^{67} - 161047296 q^{68} + 323371803 q^{69} + 177561120 q^{70} + 78122274 q^{71} - 93782016 q^{72} - 557941845 q^{73} + 36625440 q^{74} + 150154413 q^{75} - 100086528 q^{76} + 394013736 q^{77} + 295704912 q^{78} - 320222022 q^{79} + 31850496 q^{80} - 346127013 q^{81} + 206393280 q^{82} + 430491462 q^{83} - 223591680 q^{84} - 383428242 q^{85} + 358058208 q^{86} - 1044099345 q^{87} - 229244928 q^{88} + 437689644 q^{89} - 208090080 q^{90} - 1010450187 q^{91} - 236704512 q^{92} - 2684851332 q^{93} - 942341856 q^{94} - 63336006 q^{95} - 3145728 q^{96} - 384952146 q^{97} - 356719584 q^{98} + 2029897422 q^{99}+O(q^{100}) \) 3 * q - 48 * q^2 + 3 * q^3 + 768 * q^4 + 486 * q^5 - 48 * q^6 - 13317 * q^7 - 12288 * q^8 + 22896 * q^9 - 7776 * q^10 + 55968 * q^11 + 768 * q^12 + 158181 * q^13 + 213072 * q^14 + 135660 * q^15 + 196608 * q^16 - 629091 * q^17 - 366336 * q^18 - 390963 * q^19 + 124416 * q^20 - 873405 * q^21 - 895488 * q^22 - 924627 * q^23 - 12288 * q^24 - 4805517 * q^25 - 2530896 * q^26 - 6711147 * q^27 - 3409152 * q^28 - 9839019 * q^29 - 2170560 * q^30 + 1364628 * q^31 - 3145728 * q^32 - 30339114 * q^33 + 10065456 * q^34 - 11097570 * q^35 + 5861376 * q^36 - 2289090 * q^37 + 6255408 * q^38 - 18481557 * q^39 - 1990656 * q^40 - 12899580 * q^41 + 13974480 * q^42 - 22378638 * q^43 + 14327808 * q^44 + 13005630 * q^45 + 14794032 * q^46 + 58896366 * q^47 + 196608 * q^48 + 22294974 * q^49 + 76888272 * q^50 + 85869585 * q^51 + 40494336 * q^52 + 8770629 * q^53 + 107378352 * q^54 - 73415802 * q^55 + 54546432 * q^56 - 390963 * q^57 + 157424304 * q^58 + 16426299 * q^59 + 34728960 * q^60 - 126843780 * q^61 - 21834048 * q^62 - 234650088 * q^63 + 50331648 * q^64 + 45269952 * q^65 + 485425824 * q^66 - 288075309 * q^67 - 161047296 * q^68 + 323371803 * q^69 + 177561120 * q^70 + 78122274 * q^71 - 93782016 * q^72 - 557941845 * q^73 + 36625440 * q^74 + 150154413 * q^75 - 100086528 * q^76 + 394013736 * q^77 + 295704912 * q^78 - 320222022 * q^79 + 31850496 * q^80 - 346127013 * q^81 + 206393280 * q^82 + 430491462 * q^83 - 223591680 * q^84 - 383428242 * q^85 + 358058208 * q^86 - 1044099345 * q^87 - 229244928 * q^88 + 437689644 * q^89 - 208090080 * q^90 - 1010450187 * q^91 - 236704512 * q^92 - 2684851332 * q^93 - 942341856 * q^94 - 63336006 * q^95 - 3145728 * q^96 - 384952146 * q^97 - 356719584 * q^98 + 2029897422 * q^99

Introduction

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