LMFDB - Embedded newform 177.12.a.d.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,12,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, 12, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 12 $
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:	$135.996742959$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q+23.0914 q^{2} +243.000 q^{3} -1514.79 q^{4} +32.6758 q^{5} +5611.21 q^{6} -80813.9 q^{7} -82269.7 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+23.0914 q^{2} +243.000 q^{3} -1514.79 q^{4} +32.6758 q^{5} +5611.21 q^{6} -80813.9 q^{7} -82269.7 q^{8} +59049.0 q^{9} +754.528 q^{10} -196616. q^{11} -368093. q^{12} -2.11622e6 q^{13} -1.86611e6 q^{14} +7940.21 q^{15} +1.20256e6 q^{16} -4.62145e6 q^{17} +1.36352e6 q^{18} +4.04501e6 q^{19} -49496.8 q^{20} -1.96378e7 q^{21} -4.54013e6 q^{22} -2.90999e7 q^{23} -1.99915e7 q^{24} -4.88271e7 q^{25} -4.88664e7 q^{26} +1.43489e7 q^{27} +1.22416e8 q^{28} +1.75499e8 q^{29} +183350. q^{30} -2.81038e8 q^{31} +1.96257e8 q^{32} -4.77776e7 q^{33} -1.06716e8 q^{34} -2.64066e6 q^{35} -8.94467e7 q^{36} -3.05876e8 q^{37} +9.34049e7 q^{38} -5.14241e8 q^{39} -2.68822e6 q^{40} -1.04911e9 q^{41} -4.53464e8 q^{42} +8.82678e8 q^{43} +2.97831e8 q^{44} +1.92947e6 q^{45} -6.71957e8 q^{46} +2.35478e9 q^{47} +2.92223e8 q^{48} +4.55357e9 q^{49} -1.12748e9 q^{50} -1.12301e9 q^{51} +3.20562e9 q^{52} -2.72305e9 q^{53} +3.31336e8 q^{54} -6.42457e6 q^{55} +6.64854e9 q^{56} +9.82937e8 q^{57} +4.05252e9 q^{58} +7.14924e8 q^{59} -1.20277e7 q^{60} -7.46101e9 q^{61} -6.48956e9 q^{62} -4.77198e9 q^{63} +2.06900e9 q^{64} -6.91491e7 q^{65} -1.10325e9 q^{66} -1.03666e9 q^{67} +7.00052e9 q^{68} -7.07128e9 q^{69} -6.09764e7 q^{70} +2.41936e9 q^{71} -4.85794e9 q^{72} +2.86219e10 q^{73} -7.06309e9 q^{74} -1.18650e10 q^{75} -6.12733e9 q^{76} +1.58893e10 q^{77} -1.18745e10 q^{78} +6.54301e9 q^{79} +3.92947e7 q^{80} +3.48678e9 q^{81} -2.42255e10 q^{82} -5.44336e10 q^{83} +2.97471e10 q^{84} -1.51009e8 q^{85} +2.03823e10 q^{86} +4.26463e10 q^{87} +1.61755e10 q^{88} +4.77033e10 q^{89} +4.45542e7 q^{90} +1.71020e11 q^{91} +4.40802e10 q^{92} -6.82922e10 q^{93} +5.43751e10 q^{94} +1.32174e8 q^{95} +4.76905e10 q^{96} +6.19173e10 q^{97} +1.05148e11 q^{98} -1.16100e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9}+O(q^{10}) $ 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9} + 616281 q^{10} + 1082362 q^{11} + 7099002 q^{12} + 503712 q^{13} + 1321669 q^{14} + 6454566 q^{15} + 34870338 q^{16} + 13513579 q^{17} + 5668704 q^{18} + 35971687 q^{19} + 96105997 q^{20} + 34586919 q^{21} - 47598882 q^{22} + 61380539 q^{23} + 80756433 q^{24} + 294744746 q^{25} + 62820734 q^{26} + 401769396 q^{27} + 148068294 q^{28} + 322339307 q^{29} + 149756283 q^{30} + 151247077 q^{31} + 466383494 q^{32} + 263013966 q^{33} + 684479860 q^{34} + 960297361 q^{35} + 1725057486 q^{36} + 863508437 q^{37} + 992640509 q^{38} + 122402016 q^{39} + 3067680252 q^{40} + 3081170377 q^{41} + 321165567 q^{42} + 2554238300 q^{43} + 4350123570 q^{44} + 1568459538 q^{45} - 1987059155 q^{46} + 6203398333 q^{47} + 8473492134 q^{48} + 10327857997 q^{49} + 17577682253 q^{50} + 3283799697 q^{51} + 32137181618 q^{52} + 14571770754 q^{53} + 1377495072 q^{54} + 18251419334 q^{55} + 33498842836 q^{56} + 8741119941 q^{57} + 11860778276 q^{58} + 20017880372 q^{59} + 23353757271 q^{60} + 2761613771 q^{61} + 13785829526 q^{62} + 8404621317 q^{63} + 86547545293 q^{64} + 32034985256 q^{65} - 11566528326 q^{66} + 39381333296 q^{67} + 38995496621 q^{68} + 14915470977 q^{69} + 8551800364 q^{70} + 26130020296 q^{71} + 19623813219 q^{72} + 41382402799 q^{73} + 23815315058 q^{74} + 71622973278 q^{75} + 10611720128 q^{76} - 8426124313 q^{77} + 15265438362 q^{78} + 59825111206 q^{79} + 4009687655 q^{80} + 97629963228 q^{81} - 39592715115 q^{82} + 35433122727 q^{83} + 35980595442 q^{84} - 8950496085 q^{85} - 182032360688 q^{86} + 78328451601 q^{87} - 220003602335 q^{88} + 102303043039 q^{89} + 36390776769 q^{90} - 111146323655 q^{91} - 163000203526 q^{92} + 36753039711 q^{93} - 81314346008 q^{94} + 208102168887 q^{95} + 113331189042 q^{96} - 171891031490 q^{97} + 72304707792 q^{98} + 63912393738 q^{99}+O(q^{100}) \) 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9 + 616281 * q^10 + 1082362 * q^11 + 7099002 * q^12 + 503712 * q^13 + 1321669 * q^14 + 6454566 * q^15 + 34870338 * q^16 + 13513579 * q^17 + 5668704 * q^18 + 35971687 * q^19 + 96105997 * q^20 + 34586919 * q^21 - 47598882 * q^22 + 61380539 * q^23 + 80756433 * q^24 + 294744746 * q^25 + 62820734 * q^26 + 401769396 * q^27 + 148068294 * q^28 + 322339307 * q^29 + 149756283 * q^30 + 151247077 * q^31 + 466383494 * q^32 + 263013966 * q^33 + 684479860 * q^34 + 960297361 * q^35 + 1725057486 * q^36 + 863508437 * q^37 + 992640509 * q^38 + 122402016 * q^39 + 3067680252 * q^40 + 3081170377 * q^41 + 321165567 * q^42 + 2554238300 * q^43 + 4350123570 * q^44 + 1568459538 * q^45 - 1987059155 * q^46 + 6203398333 * q^47 + 8473492134 * q^48 + 10327857997 * q^49 + 17577682253 * q^50 + 3283799697 * q^51 + 32137181618 * q^52 + 14571770754 * q^53 + 1377495072 * q^54 + 18251419334 * q^55 + 33498842836 * q^56 + 8741119941 * q^57 + 11860778276 * q^58 + 20017880372 * q^59 + 23353757271 * q^60 + 2761613771 * q^61 + 13785829526 * q^62 + 8404621317 * q^63 + 86547545293 * q^64 + 32034985256 * q^65 - 11566528326 * q^66 + 39381333296 * q^67 + 38995496621 * q^68 + 14915470977 * q^69 + 8551800364 * q^70 + 26130020296 * q^71 + 19623813219 * q^72 + 41382402799 * q^73 + 23815315058 * q^74 + 71622973278 * q^75 + 10611720128 * q^76 - 8426124313 * q^77 + 15265438362 * q^78 + 59825111206 * q^79 + 4009687655 * q^80 + 97629963228 * q^81 - 39592715115 * q^82 + 35433122727 * q^83 + 35980595442 * q^84 - 8950496085 * q^85 - 182032360688 * q^86 + 78328451601 * q^87 - 220003602335 * q^88 + 102303043039 * q^89 + 36390776769 * q^90 - 111146323655 * q^91 - 163000203526 * q^92 + 36753039711 * q^93 - 81314346008 * q^94 + 208102168887 * q^95 + 113331189042 * q^96 - 171891031490 * q^97 + 72304707792 * q^98 + 63912393738 * 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 $

$2$	23.0914	0.510252	0.255126	−	0.966908i	$-0.417883\pi$
$2$	23.0914	0.510252	0.255126	+	0.966908i	$0.417883\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	−1514.79	−0.739643
$5$	32.6758	0.00467617	0.00233809	−	0.999997i	$-0.499256\pi$
$5$	32.6758	0.00467617	0.00233809	+	0.999997i	$0.499256\pi$
$6$	5611.21	0.294594
$7$	−80813.9	−1.81739	−0.908693	−	0.417466i	$-0.862918\pi$
$7$	−80813.9	−1.81739	−0.908693	+	0.417466i	$0.862918\pi$
$8$	−82269.7	−0.887657
$9$	59049.0	0.333333
$10$	754.528	0.00238603
$11$	−196616.	−0.368094	−0.184047	−	0.982917i	$-0.558920\pi$
$11$	−196616.	−0.368094	−0.184047	+	0.982917i	$0.558920\pi$
$12$	−368093.	−0.427033
$13$	−2.11622e6	−1.58078	−0.790392	−	0.612602i	$-0.790123\pi$
$13$	−2.11622e6	−1.58078	−0.790392	+	0.612602i	$0.790123\pi$
$14$	−1.86611e6	−0.927325
$15$	7940.21	0.00269979
$16$	1.20256e6	0.286714
$17$	−4.62145e6	−0.789422	−0.394711	−	0.918805i	$-0.629155\pi$
$17$	−4.62145e6	−0.789422	−0.394711	+	0.918805i	$0.629155\pi$
$18$	1.36352e6	0.170084
$19$	4.04501e6	0.374779	0.187389	−	0.982286i	$-0.439997\pi$
$19$	4.04501e6	0.374779	0.187389	+	0.982286i	$0.439997\pi$
$20$	−49496.8	−0.00345870
$21$	−1.96378e7	−1.04927
$22$	−4.54013e6	−0.187821
$23$	−2.90999e7	−0.942732	−0.471366	−	0.881938i	$-0.656239\pi$
$23$	−2.90999e7	−0.942732	−0.471366	+	0.881938i	$0.656239\pi$
$24$	−1.99915e7	−0.512489
$25$	−4.88271e7	−0.999978
$26$	−4.88664e7	−0.806598
$27$	1.43489e7	0.192450
$28$	1.22416e8	1.34422
$29$	1.75499e8	1.58886	0.794432	−	0.607353i	$-0.207769\pi$
$29$	1.75499e8	1.58886	0.794432	+	0.607353i	$0.207769\pi$
$30$	183350.	0.00137757
$31$	−2.81038e8	−1.76309	−0.881547	−	0.472095i	$-0.843498\pi$
$31$	−2.81038e8	−1.76309	−0.881547	+	0.472095i	$0.843498\pi$
$32$	1.96257e8	1.03395
$33$	−4.77776e7	−0.212519
$34$	−1.06716e8	−0.402804
$35$	−2.64066e6	−0.00849841
$36$	−8.94467e7	−0.246548
$37$	−3.05876e8	−0.725163	−0.362581	−	0.931952i	$-0.618105\pi$
$37$	−3.05876e8	−0.725163	−0.362581	+	0.931952i	$0.618105\pi$
$38$	9.34049e7	0.191232
$39$	−5.14241e8	−0.912666
$40$	−2.68822e6	−0.00415084
$41$	−1.04911e9	−1.41420	−0.707100	−	0.707113i	$-0.749997\pi$
$41$	−1.04911e9	−1.41420	−0.707100	+	0.707113i	$0.749997\pi$
$42$	−4.53464e8	−0.535391
$43$	8.82678e8	0.915642	0.457821	−	0.889044i	$-0.348630\pi$
$43$	8.82678e8	0.915642	0.457821	+	0.889044i	$0.348630\pi$
$44$	2.97831e8	0.272258
$45$	1.92947e6	0.00155872
$46$	−6.71957e8	−0.481031
$47$	2.35478e9	1.49766	0.748828	−	0.662764i	$-0.230617\pi$
$47$	2.35478e9	1.49766	0.748828	+	0.662764i	$0.230617\pi$
$48$	2.92223e8	0.165534
$49$	4.55357e9	2.30289
$50$	−1.12748e9	−0.510241
$51$	−1.12301e9	−0.455773
$52$	3.20562e9	1.16921
$53$	−2.72305e9	−0.894413	−0.447206	−	0.894431i	$-0.647581\pi$
$53$	−2.72305e9	−0.894413	−0.447206	+	0.894431i	$0.647581\pi$
$54$	3.31336e8	0.0981981
$55$	−6.42457e6	−0.00172127
$56$	6.64854e9	1.61321
$57$	9.82937e8	0.216378
$58$	4.05252e9	0.810721
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	−1.20277e7	−0.00199688
$61$	−7.46101e9	−1.13106	−0.565528	−	0.824729i	$-0.691327\pi$
$61$	−7.46101e9	−1.13106	−0.565528	+	0.824729i	$0.691327\pi$
$62$	−6.48956e9	−0.899623
$63$	−4.77198e9	−0.605795
$64$	2.06900e9	0.240863
$65$	−6.91491e7	−0.00739202
$66$	−1.10325e9	−0.108438
$67$	−1.03666e9	−0.0938051	−0.0469025	−	0.998899i	$-0.514935\pi$
$67$	−1.03666e9	−0.0938051	−0.0469025	+	0.998899i	$0.514935\pi$
$68$	7.00052e9	0.583890
$69$	−7.07128e9	−0.544287
$70$	−6.09764e7	−0.00433633
$71$	2.41936e9	0.159140	0.0795702	−	0.996829i	$-0.474645\pi$
$71$	2.41936e9	0.159140	0.0795702	+	0.996829i	$0.474645\pi$
$72$	−4.85794e9	−0.295886
$73$	2.86219e10	1.61593	0.807966	−	0.589229i	$-0.200569\pi$
$73$	2.86219e10	1.61593	0.807966	+	0.589229i	$0.200569\pi$
$74$	−7.06309e9	−0.370016
$75$	−1.18650e10	−0.577338
$76$	−6.12733e9	−0.277202
$77$	1.58893e10	0.668968
$78$	−1.18745e10	−0.465690
$79$	6.54301e9	0.239237	0.119619	−	0.992820i	$-0.461833\pi$
$79$	6.54301e9	0.239237	0.119619	+	0.992820i	$0.461833\pi$
$80$	3.92947e7	0.00134072
$81$	3.48678e9	0.111111
$82$	−2.42255e10	−0.721599
$83$	−5.44336e10	−1.51683	−0.758416	−	0.651770i	$-0.774027\pi$
$83$	−5.44336e10	−1.51683	−0.758416	+	0.651770i	$0.774027\pi$
$84$	2.97471e10	0.776083
$85$	−1.51009e8	−0.00369147
$86$	2.03823e10	0.467209
$87$	4.26463e10	0.917331
$88$	1.61755e10	0.326741
$89$	4.77033e10	0.905531	0.452765	−	0.891630i	$-0.350438\pi$
$89$	4.77033e10	0.905531	0.452765	+	0.891630i	$0.350438\pi$
$90$	4.45542e7	0.000795343 0
$91$	1.71020e11	2.87289
$92$	4.40802e10	0.697285
$93$	−6.82922e10	−1.01792
$94$	5.43751e10	0.764183
$95$	1.32174e8	0.00175253
$96$	4.76905e10	0.596953
$97$	6.19173e10	0.732095	0.366048	−	0.930596i	$-0.380711\pi$
$97$	6.19173e10	0.732095	0.366048	+	0.930596i	$0.380711\pi$
$98$	1.05148e11	1.17505
$99$	−1.16100e10	−0.122698
$100$	7.39626e10	0.739626
$101$	−1.48326e11	−1.40427	−0.702133	−	0.712046i	$-0.747769\pi$
$101$	−1.48326e11	−1.40427	−0.702133	+	0.712046i	$0.747769\pi$
$102$	−2.59319e10	−0.232559
$103$	−1.07904e11	−0.917136	−0.458568	−	0.888659i	$-0.651638\pi$
$103$	−1.07904e11	−0.917136	−0.458568	+	0.888659i	$0.651638\pi$
$104$	1.74101e11	1.40319
$105$	−6.41680e8	−0.00490656
$106$	−6.28789e10	−0.456376
$107$	−1.79873e9	−0.0123981	−0.00619906	−	0.999981i	$-0.501973\pi$
$107$	−1.79873e9	−0.0123981	−0.00619906	+	0.999981i	$0.501973\pi$
$108$	−2.17356e10	−0.142344
$109$	2.47694e11	1.54195	0.770975	−	0.636865i	$-0.219769\pi$
$109$	2.47694e11	1.54195	0.770975	+	0.636865i	$0.219769\pi$
$110$	−1.48352e8	−0.000878282 0
$111$	−7.43278e10	−0.418673
$112$	−9.71839e10	−0.521069
$113$	−1.33748e10	−0.0682899	−0.0341450	−	0.999417i	$-0.510871\pi$
$113$	−1.33748e10	−0.0682899	−0.0341450	+	0.999417i	$0.510871\pi$
$114$	2.26974e10	0.110408
$115$	−9.50861e8	−0.00440838
$116$	−2.65844e11	−1.17519
$117$	−1.24961e11	−0.526928
$118$	1.65086e10	0.0664292
$119$	3.73478e11	1.43468
$120$	−6.53239e8	−0.00239649
$121$	−2.46654e11	−0.864507
$122$	−1.72285e11	−0.577124
$123$	−2.54934e11	−0.816489
$124$	4.25713e11	1.30406
$125$	−3.19096e9	−0.00935224
$126$	−1.10192e11	−0.309108
$127$	7.43211e11	1.99614	0.998072	−	0.0620676i	$-0.0197694\pi$
$127$	7.43211e11	1.99614	0.998072	+	0.0620676i	$0.0197694\pi$
$128$	−3.54159e11	−0.911052
$129$	2.14491e11	0.528646
$130$	−1.59675e9	−0.00377179
$131$	−7.58634e11	−1.71807	−0.859034	−	0.511919i	$-0.828935\pi$
$131$	−7.58634e11	−1.71807	−0.859034	+	0.511919i	$0.828935\pi$
$132$	7.23729e10	0.157188
$133$	−3.26893e11	−0.681117
$134$	−2.39380e10	−0.0478643
$135$	4.68861e8	0.000899930 0
$136$	3.80205e11	0.700736
$137$	−6.77878e11	−1.20002	−0.600010	−	0.799993i	$-0.704837\pi$
$137$	−6.77878e11	−1.20002	−0.600010	+	0.799993i	$0.704837\pi$
$138$	−1.63286e11	−0.277724
$139$	−8.19489e11	−1.33956	−0.669779	−	0.742560i	$-0.733611\pi$
$139$	−8.19489e11	−1.33956	−0.669779	+	0.742560i	$0.733611\pi$
$140$	4.00003e9	0.00628579
$141$	5.72212e11	0.864672
$142$	5.58665e10	0.0812017
$143$	4.16082e11	0.581876
$144$	7.10102e10	0.0955712
$145$	5.73457e9	0.00742980
$146$	6.60920e11	0.824533
$147$	1.10652e12	1.32957
$148$	4.63337e11	0.536361
$149$	7.79795e11	0.869873	0.434937	−	0.900461i	$-0.356771\pi$
$149$	7.79795e11	0.869873	0.434937	+	0.900461i	$0.356771\pi$
$150$	−2.73979e11	−0.294588
$151$	−2.00521e11	−0.207867	−0.103934	−	0.994584i	$-0.533143\pi$
$151$	−2.00521e11	−0.207867	−0.103934	+	0.994584i	$0.533143\pi$
$152$	−3.32782e11	−0.332675
$153$	−2.72892e11	−0.263141
$154$	3.66906e11	0.341343
$155$	−9.18313e9	−0.00824454
$156$	7.78967e11	0.675046
$157$	1.61750e11	0.135330	0.0676652	−	0.997708i	$-0.478445\pi$
$157$	1.61750e11	0.135330	0.0676652	+	0.997708i	$0.478445\pi$
$158$	1.51087e11	0.122071
$159$	−6.61700e11	−0.516389
$160$	6.41285e9	0.00483494
$161$	2.35168e12	1.71331
$162$	8.05147e10	0.0566947
$163$	−1.89658e12	−1.29104	−0.645519	−	0.763744i	$-0.723359\pi$
$163$	−1.89658e12	−1.29104	−0.645519	+	0.763744i	$0.723359\pi$
$164$	1.58918e12	1.04600
$165$	−1.56117e9	−0.000993776 0
$166$	−1.25695e12	−0.773968
$167$	−7.97901e11	−0.475344	−0.237672	−	0.971345i	$-0.576384\pi$
$167$	−7.97901e11	−0.475344	−0.237672	+	0.971345i	$0.576384\pi$
$168$	1.61559e12	0.931390
$169$	2.68623e12	1.49888
$170$	−3.48702e9	−0.00188358
$171$	2.38854e11	0.124926
$172$	−1.33707e12	−0.677248
$173$	3.52739e12	1.73061	0.865307	−	0.501242i	$-0.167123\pi$
$173$	3.52739e12	1.73061	0.865307	+	0.501242i	$0.167123\pi$
$174$	9.84763e11	0.468070
$175$	3.94591e12	1.81735
$176$	−2.36443e11	−0.105537
$177$	1.73727e11	0.0751646
$178$	1.10153e12	0.462049
$179$	−2.73949e12	−1.11424	−0.557120	−	0.830432i	$-0.688094\pi$
$179$	−2.73949e12	−1.11424	−0.557120	+	0.830432i	$0.688094\pi$
$180$	−2.92274e9	−0.00115290
$181$	1.78794e12	0.684101	0.342050	−	0.939682i	$-0.388879\pi$
$181$	1.78794e12	0.684101	0.342050	+	0.939682i	$0.388879\pi$
$182$	3.94909e12	1.46590
$183$	−1.81303e12	−0.653015
$184$	2.39404e12	0.836823
$185$	−9.99472e9	−0.00339099
$186$	−1.57696e12	−0.519398
$187$	9.08650e11	0.290581
$188$	−3.56699e12	−1.10773
$189$	−1.15959e12	−0.349756
$190$	3.05207e9	0.000894232 0
$191$	3.55645e12	1.01236	0.506178	−	0.862429i	$-0.331058\pi$
$191$	3.55645e12	1.01236	0.506178	+	0.862429i	$0.331058\pi$
$192$	5.02767e11	0.139062
$193$	−1.22933e12	−0.330447	−0.165224	−	0.986256i	$-0.552835\pi$
$193$	−1.22933e12	−0.330447	−0.165224	+	0.986256i	$0.552835\pi$
$194$	1.42976e12	0.373553
$195$	−1.68032e10	−0.00426778
$196$	−6.89769e12	−1.70332
$197$	1.01555e12	0.243859	0.121930	−	0.992539i	$-0.461092\pi$
$197$	1.01555e12	0.243859	0.121930	+	0.992539i	$0.461092\pi$
$198$	−2.68090e11	−0.0626069
$199$	6.19152e12	1.40639	0.703194	−	0.710998i	$-0.251756\pi$
$199$	6.19152e12	1.40639	0.703194	+	0.710998i	$0.251756\pi$
$200$	4.01699e12	0.887637
$201$	−2.51909e11	−0.0541584
$202$	−3.42505e12	−0.716530
$203$	−1.41828e13	−2.88758
$204$	1.70113e12	0.337109
$205$	−3.42806e10	−0.00661305
$206$	−2.49166e12	−0.467971
$207$	−1.71832e12	−0.314244
$208$	−2.54489e12	−0.453232
$209$	−7.95312e11	−0.137954
$210$	−1.48173e10	−0.00250358
$211$	2.52523e12	0.415668	0.207834	−	0.978164i	$-0.433359\pi$
$211$	2.52523e12	0.415668	0.207834	+	0.978164i	$0.433359\pi$
$212$	4.12484e12	0.661546
$213$	5.87905e11	0.0918797
$214$	−4.15352e10	−0.00632617
$215$	2.88422e10	0.00428170
$216$	−1.18048e12	−0.170830
$217$	2.27118e13	3.20422
$218$	5.71960e12	0.786784
$219$	6.95513e12	0.932959
$220$	9.73185e9	0.00127312
$221$	9.78000e12	1.24791
$222$	−1.71633e12	−0.213629
$223$	1.21374e13	1.47384	0.736918	−	0.675983i	$-0.236281\pi$
$223$	1.21374e13	1.47384	0.736918	+	0.675983i	$0.236281\pi$
$224$	−1.58603e13	−1.87909
$225$	−2.88319e12	−0.333326
$226$	−3.08843e11	−0.0348451
$227$	4.34287e12	0.478227	0.239114	−	0.970992i	$-0.423143\pi$
$227$	4.34287e12	0.478227	0.239114	+	0.970992i	$0.423143\pi$
$228$	−1.48894e12	−0.160043
$229$	1.10467e13	1.15914	0.579572	−	0.814921i	$-0.303220\pi$
$229$	1.10467e13	1.15914	0.579572	+	0.814921i	$0.303220\pi$
$230$	−2.19567e10	−0.00224939
$231$	3.86110e12	0.386229
$232$	−1.44383e13	−1.41037
$233$	1.16025e13	1.10687	0.553433	−	0.832894i	$-0.313318\pi$
$233$	1.16025e13	1.10687	0.553433	+	0.832894i	$0.313318\pi$
$234$	−2.88551e12	−0.268866
$235$	7.69442e10	0.00700330
$236$	−1.08296e12	−0.0962933
$237$	1.58995e12	0.138124
$238$	8.62412e12	0.732051
$239$	−1.88821e13	−1.56625	−0.783127	−	0.621862i	$-0.786377\pi$
$239$	−1.88821e13	−1.56625	−0.783127	+	0.621862i	$0.786377\pi$
$240$	9.54861e9	0.000774067 0
$241$	−1.27106e13	−1.00710	−0.503548	−	0.863967i	$-0.667972\pi$
$241$	−1.27106e13	−1.00710	−0.503548	+	0.863967i	$0.667972\pi$
$242$	−5.69558e12	−0.441117
$243$	8.47289e11	0.0641500
$244$	1.13019e13	0.836576
$245$	1.48791e11	0.0107687
$246$	−5.88679e12	−0.416615
$247$	−8.56013e12	−0.592444
$248$	2.31209e13	1.56502
$249$	−1.32274e13	−0.875744
$250$	−7.36836e10	−0.00477200
$251$	−7.60243e12	−0.481667	−0.240833	−	0.970566i	$-0.577421\pi$
$251$	−7.60243e12	−0.481667	−0.240833	+	0.970566i	$0.577421\pi$
$252$	7.22854e12	0.448072
$253$	5.72150e12	0.347014
$254$	1.71618e13	1.01854
$255$	−3.66953e10	−0.00213127
$256$	−1.24153e13	−0.705730
$257$	−8.58575e10	−0.00477690	−0.00238845	−	0.999997i	$-0.500760\pi$
$257$	−8.58575e10	−0.00477690	−0.00238845	+	0.999997i	$0.500760\pi$
$258$	4.95289e12	0.269743
$259$	2.47190e13	1.31790
$260$	1.04746e11	0.00546745
$261$	1.03631e13	0.529621
$262$	−1.75179e13	−0.876648
$263$	8.70407e12	0.426546	0.213273	−	0.976993i	$-0.431588\pi$
$263$	8.70407e12	0.426546	0.213273	+	0.976993i	$0.431588\pi$
$264$	3.93065e12	0.188644
$265$	−8.89776e10	−0.00418243
$266$	−7.54841e12	−0.347542
$267$	1.15919e13	0.522808
$268$	1.57033e12	0.0693822
$269$	−3.50062e13	−1.51533	−0.757664	−	0.652644i	$-0.773660\pi$
$269$	−3.50062e13	−1.51533	−0.757664	+	0.652644i	$0.773660\pi$
$270$	1.08267e10	0.000459191 0
$271$	1.26831e13	0.527100	0.263550	−	0.964646i	$-0.415107\pi$
$271$	1.26831e13	0.527100	0.263550	+	0.964646i	$0.415107\pi$
$272$	−5.55759e12	−0.226338
$273$	4.15579e13	1.65867
$274$	−1.56531e13	−0.612313
$275$	9.60016e12	0.368086
$276$	1.07115e13	0.402578
$277$	−1.18944e13	−0.438230	−0.219115	−	0.975699i	$-0.570317\pi$
$277$	−1.18944e13	−0.438230	−0.219115	+	0.975699i	$0.570317\pi$
$278$	−1.89231e13	−0.683513
$279$	−1.65950e13	−0.587698
$280$	2.17246e11	0.00754367
$281$	−4.97437e13	−1.69376	−0.846882	−	0.531781i	$-0.821523\pi$
$281$	−4.97437e13	−1.69376	−0.846882	+	0.531781i	$0.821523\pi$
$282$	1.32132e13	0.441201
$283$	7.59641e11	0.0248762	0.0124381	−	0.999923i	$-0.496041\pi$
$283$	7.59641e11	0.0248762	0.0124381	+	0.999923i	$0.496041\pi$
$284$	−3.66482e12	−0.117707
$285$	3.21182e10	0.00101182
$286$	9.60791e12	0.296904
$287$	8.47829e13	2.57015
$288$	1.15888e13	0.344651
$289$	−1.29141e13	−0.376813
$290$	1.32419e11	0.00379107
$291$	1.50459e13	0.422675
$292$	−4.33561e13	−1.19521
$293$	8.39756e12	0.227186	0.113593	−	0.993527i	$-0.463764\pi$
$293$	8.39756e12	0.227186	0.113593	+	0.993527i	$0.463764\pi$
$294$	2.55510e13	0.678418
$295$	2.33607e10	0.000608786 0
$296$	2.51643e13	0.643696
$297$	−2.82122e12	−0.0708397
$298$	1.80065e13	0.443855
$299$	6.15818e13	1.49026
$300$	1.79729e13	0.427023
$301$	−7.13327e13	−1.66407
$302$	−4.63030e12	−0.106065
$303$	−3.60432e13	−0.810753
$304$	4.86438e12	0.107454
$305$	−2.43794e11	−0.00528901
$306$	−6.30146e12	−0.134268
$307$	−3.01401e13	−0.630787	−0.315394	−	0.948961i	$-0.602137\pi$
$307$	−3.01401e13	−0.630787	−0.315394	+	0.948961i	$0.602137\pi$
$308$	−2.40689e13	−0.494797
$309$	−2.62207e13	−0.529509
$310$	−2.12051e11	−0.00420679
$311$	5.01933e13	0.978281	0.489140	−	0.872205i	$-0.337311\pi$
$311$	5.01933e13	0.978281	0.489140	+	0.872205i	$0.337311\pi$
$312$	4.23065e13	0.810134
$313$	−4.47804e13	−0.842547	−0.421274	−	0.906934i	$-0.638417\pi$
$313$	−4.47804e13	−0.842547	−0.421274	+	0.906934i	$0.638417\pi$
$314$	3.73503e12	0.0690527
$315$	−1.55928e11	−0.00283280
$316$	−9.91127e12	−0.176950
$317$	−7.52336e13	−1.32004	−0.660018	−	0.751250i	$-0.729451\pi$
$317$	−7.52336e13	−1.32004	−0.660018	+	0.751250i	$0.729451\pi$
$318$	−1.52796e13	−0.263489
$319$	−3.45059e13	−0.584851
$320$	6.76061e10	0.00112632
$321$	−4.37092e11	−0.00715805
$322$	5.43035e13	0.874220
$323$	−1.86938e13	−0.295858
$324$	−5.28174e12	−0.0821825
$325$	1.03329e14	1.58075
$326$	−4.37946e13	−0.658755
$327$	6.01897e13	0.890245
$328$	8.63102e13	1.25532
$329$	−1.90299e14	−2.72182
$330$	−3.60496e10	−0.000507076 0
$331$	3.77022e13	0.521571	0.260785	−	0.965397i	$-0.416019\pi$
$331$	3.77022e13	0.521571	0.260785	+	0.965397i	$0.416019\pi$
$332$	8.24554e13	1.12191
$333$	−1.80617e13	−0.241721
$334$	−1.84246e13	−0.242546
$335$	−3.38738e10	−0.000438649 0
$336$	−2.36157e13	−0.300839
$337$	−7.70482e13	−0.965602	−0.482801	−	0.875730i	$-0.660381\pi$
$337$	−7.70482e13	−0.965602	−0.482801	+	0.875730i	$0.660381\pi$
$338$	6.20287e13	0.764805
$339$	−3.25008e12	−0.0394272
$340$	2.28747e11	0.00273037
$341$	5.52565e13	0.648984
$342$	5.51546e12	0.0637439
$343$	−2.08196e14	−2.36785
$344$	−7.26177e13	−0.812776
$345$	−2.31059e11	−0.00254518
$346$	8.14524e13	0.883050
$347$	−1.50757e14	−1.60867	−0.804334	−	0.594177i	$-0.797478\pi$
$347$	−1.50757e14	−1.60867	−0.804334	+	0.594177i	$0.797478\pi$
$348$	−6.46002e13	−0.678497
$349$	8.88573e13	0.918657	0.459329	−	0.888266i	$-0.348090\pi$
$349$	8.88573e13	0.918657	0.459329	+	0.888266i	$0.348090\pi$
$350$	9.11165e13	0.927305
$351$	−3.03654e13	−0.304222
$352$	−3.85872e13	−0.380592
$353$	1.96988e13	0.191284	0.0956420	−	0.995416i	$-0.469510\pi$
$353$	1.96988e13	0.191284	0.0956420	+	0.995416i	$0.469510\pi$
$354$	4.01159e12	0.0383529
$355$	7.90545e10	0.000744168 0
$356$	−7.22603e13	−0.669769
$357$	9.07551e13	0.828315
$358$	−6.32587e13	−0.568543
$359$	−1.26180e14	−1.11679	−0.558393	−	0.829577i	$-0.688582\pi$
$359$	−1.26180e14	−1.11679	−0.558393	+	0.829577i	$0.688582\pi$
$360$	−1.58737e11	−0.00138361
$361$	−1.00128e14	−0.859541
$362$	4.12859e13	0.349064
$363$	−5.99369e13	−0.499123
$364$	−2.59059e14	−2.12491
$365$	9.35243e11	0.00755638
$366$	−4.18653e13	−0.333202
$367$	−2.20870e14	−1.73170	−0.865851	−	0.500301i	$-0.833223\pi$
$367$	−2.20870e14	−1.73170	−0.865851	+	0.500301i	$0.833223\pi$
$368$	−3.49945e13	−0.270294
$369$	−6.19491e13	−0.471400
$370$	−2.30792e11	−0.00173026
$371$	2.20060e14	1.62549
$372$	1.03448e14	0.752899
$373$	9.05981e13	0.649711	0.324856	−	0.945764i	$-0.394684\pi$
$373$	9.05981e13	0.649711	0.324856	+	0.945764i	$0.394684\pi$
$374$	2.09820e13	0.148270
$375$	−7.75403e11	−0.00539952
$376$	−1.93727e14	−1.32940
$377$	−3.71395e14	−2.51165
$378$	−2.67766e13	−0.178464
$379$	−1.24245e14	−0.816135	−0.408067	−	0.912952i	$-0.633797\pi$
$379$	−1.24245e14	−0.816135	−0.408067	+	0.912952i	$0.633797\pi$
$380$	−2.00215e11	−0.00129625
$381$	1.80600e14	1.15247
$382$	8.21233e13	0.516557
$383$	1.28435e14	0.796326	0.398163	−	0.917315i	$-0.369648\pi$
$383$	1.28435e14	0.796326	0.398163	+	0.917315i	$0.369648\pi$
$384$	−8.60606e13	−0.525996
$385$	5.19194e11	0.00312821
$386$	−2.83869e13	−0.168611
$387$	5.21212e13	0.305214
$388$	−9.37916e13	−0.541489
$389$	−2.45451e14	−1.39714	−0.698572	−	0.715539i	$-0.746181\pi$
$389$	−2.45451e14	−1.39714	−0.698572	+	0.715539i	$0.746181\pi$
$390$	−3.88010e11	−0.00217765
$391$	1.34484e14	0.744214
$392$	−3.74621e14	−2.04418
$393$	−1.84348e14	−0.991927
$394$	2.34506e13	0.124430
$395$	2.13798e11	0.00111871
$396$	1.75866e13	0.0907526
$397$	2.08288e14	1.06003	0.530013	−	0.847989i	$-0.322187\pi$
$397$	2.08288e14	1.06003	0.530013	+	0.847989i	$0.322187\pi$
$398$	1.42971e14	0.717613
$399$	−7.94350e13	−0.393243
$400$	−5.87177e13	−0.286707
$401$	−1.25727e14	−0.605528	−0.302764	−	0.953066i	$-0.597909\pi$
$401$	−1.25727e14	−0.605528	−0.302764	+	0.953066i	$0.597909\pi$
$402$	−5.81693e12	−0.0276344
$403$	5.94738e14	2.78707
$404$	2.24682e14	1.03865
$405$	1.13933e11	0.000519575 0
$406$	−3.27500e14	−1.47339
$407$	6.01399e13	0.266928
$408$	9.23899e13	0.404570
$409$	−1.28206e14	−0.553899	−0.276950	−	0.960884i	$-0.589323\pi$
$409$	−1.28206e14	−0.553899	−0.276950	+	0.960884i	$0.589323\pi$
$410$	−7.91585e11	−0.00337432
$411$	−1.64724e14	−0.692831
$412$	1.63452e14	0.678353
$413$	−5.77758e13	−0.236603
$414$	−3.96784e13	−0.160344
$415$	−1.77866e12	−0.00709297
$416$	−4.15323e14	−1.63446
$417$	−1.99136e14	−0.773394
$418$	−1.83649e13	−0.0703911
$419$	−2.42222e14	−0.916296	−0.458148	−	0.888876i	$-0.651487\pi$
$419$	−2.42222e14	−0.916296	−0.458148	+	0.888876i	$0.651487\pi$
$420$	9.72008e11	0.00362910
$421$	−4.87087e14	−1.79496	−0.897481	−	0.441053i	$-0.854605\pi$
$421$	−4.87087e14	−1.79496	−0.897481	+	0.441053i	$0.854605\pi$
$422$	5.83110e13	0.212096
$423$	1.39047e14	0.499219
$424$	2.24024e14	0.793931
$425$	2.25652e14	0.789405
$426$	1.35756e13	0.0468818
$427$	6.02954e14	2.05556
$428$	2.72470e12	0.00917017
$429$	1.01108e14	0.335946
$430$	6.66006e11	0.00218475
$431$	5.99881e13	0.194286	0.0971428	−	0.995270i	$-0.469030\pi$
$431$	5.99881e13	0.194286	0.0971428	+	0.995270i	$0.469030\pi$
$432$	1.72555e13	0.0551781
$433$	3.38430e14	1.06853	0.534264	−	0.845318i	$-0.320589\pi$
$433$	3.38430e14	1.06853	0.534264	+	0.845318i	$0.320589\pi$
$434$	5.24447e14	1.63496
$435$	1.39350e12	0.00428960
$436$	−3.75204e14	−1.14049
$437$	−1.17709e14	−0.353316
$438$	1.60604e14	0.476044
$439$	−8.87244e13	−0.259710	−0.129855	−	0.991533i	$-0.541451\pi$
$439$	−8.87244e13	−0.259710	−0.129855	+	0.991533i	$0.541451\pi$
$440$	5.28547e11	0.00152790
$441$	2.68883e14	0.767630
$442$	2.25834e14	0.636747
$443$	4.91192e14	1.36782	0.683912	−	0.729564i	$-0.260277\pi$
$443$	4.91192e14	1.36782	0.683912	+	0.729564i	$0.260277\pi$
$444$	1.12591e14	0.309668
$445$	1.55874e12	0.00423442
$446$	2.80269e14	0.752028
$447$	1.89490e14	0.502221
$448$	−1.67204e14	−0.437741
$449$	8.30943e13	0.214890	0.107445	−	0.994211i	$-0.465733\pi$
$449$	8.30943e13	0.214890	0.107445	+	0.994211i	$0.465733\pi$
$450$	−6.65768e13	−0.170080
$451$	2.06272e14	0.520558
$452$	2.02600e13	0.0505101
$453$	−4.87265e13	−0.120012
$454$	1.00283e14	0.244017
$455$	5.58821e12	0.0134341
$456$	−8.08660e13	−0.192070
$457$	−6.65893e14	−1.56266	−0.781332	−	0.624116i	$-0.785459\pi$
$457$	−6.65893e14	−1.56266	−0.781332	+	0.624116i	$0.785459\pi$
$458$	2.55084e14	0.591456
$459$	−6.63128e13	−0.151924
$460$	1.44035e12	0.00326063
$461$	1.15391e14	0.258116	0.129058	−	0.991637i	$-0.458805\pi$
$461$	1.15391e14	0.258116	0.129058	+	0.991637i	$0.458805\pi$
$462$	8.91581e13	0.197074
$463$	−6.74287e14	−1.47282	−0.736409	−	0.676536i	$-0.763480\pi$
$463$	−6.74287e14	−1.47282	−0.736409	+	0.676536i	$0.763480\pi$
$464$	2.11049e14	0.455549
$465$	−2.23150e12	−0.00475999
$466$	2.67918e14	0.564780
$467$	2.62842e14	0.547586	0.273793	−	0.961789i	$-0.411722\pi$
$467$	2.62842e14	0.547586	0.273793	+	0.961789i	$0.411722\pi$
$468$	1.89289e14	0.389738
$469$	8.37769e13	0.170480
$470$	1.77675e12	0.00357345
$471$	3.93052e13	0.0781331
$472$	−5.88166e13	−0.115563
$473$	−1.73548e14	−0.337042
$474$	3.67142e13	0.0704779
$475$	−1.97506e14	−0.374770
$476$	−5.65739e14	−1.06115
$477$	−1.60793e14	−0.298138
$478$	−4.36014e14	−0.799185
$479$	1.35085e14	0.244772	0.122386	−	0.992483i	$-0.460945\pi$
$479$	1.35085e14	0.244772	0.122386	+	0.992483i	$0.460945\pi$
$480$	1.55832e12	0.00279146
$481$	6.47300e14	1.14633
$482$	−2.93504e14	−0.513873
$483$	5.71458e14	0.989179
$484$	3.73628e14	0.639426
$485$	2.02319e12	0.00342340
$486$	1.95651e13	0.0327327
$487$	2.99730e14	0.495817	0.247908	−	0.968783i	$-0.420257\pi$
$487$	2.99730e14	0.495817	0.247908	+	0.968783i	$0.420257\pi$
$488$	6.13815e14	1.00399
$489$	−4.60869e14	−0.745381
$490$	3.43579e12	0.00549476
$491$	9.64896e14	1.52592	0.762961	−	0.646445i	$-0.223745\pi$
$491$	9.64896e14	1.52592	0.762961	+	0.646445i	$0.223745\pi$
$492$	3.86172e14	0.603910
$493$	−8.11062e14	−1.25428
$494$	−1.97665e14	−0.302296
$495$	−3.79364e11	−0.000573757 0
$496$	−3.37966e14	−0.505503
$497$	−1.95518e14	−0.289219
$498$	−3.05438e14	−0.446850
$499$	8.18754e14	1.18468	0.592339	−	0.805689i	$-0.298204\pi$
$499$	8.18754e14	1.18468	0.592339	+	0.805689i	$0.298204\pi$
$500$	4.83362e12	0.00691732
$501$	−1.93890e14	−0.274440
$502$	−1.75551e14	−0.245772
$503$	7.25668e14	1.00488	0.502440	−	0.864612i	$-0.332436\pi$
$503$	7.25668e14	1.00488	0.502440	+	0.864612i	$0.332436\pi$
$504$	3.92590e14	0.537738
$505$	−4.84666e12	−0.00656659
$506$	1.32117e14	0.177065
$507$	6.52753e14	0.865376
$508$	−1.12581e15	−1.47643
$509$	−1.69377e14	−0.219739	−0.109870	−	0.993946i	$-0.535043\pi$
$509$	−1.69377e14	−0.219739	−0.109870	+	0.993946i	$0.535043\pi$
$510$	−8.47345e11	−0.00108749
$511$	−2.31305e15	−2.93677
$512$	4.38630e14	0.550952
$513$	5.80415e13	0.0721262
$514$	−1.98257e12	−0.00243742
$515$	−3.52585e12	−0.00428869
$516$	−3.24908e14	−0.391009
$517$	−4.62987e14	−0.551278
$518$	5.70796e14	0.672462
$519$	8.57157e14	0.999171
$520$	5.68887e12	0.00656157
$521$	−7.53695e14	−0.860178	−0.430089	−	0.902787i	$-0.641518\pi$
$521$	−7.53695e14	−0.860178	−0.430089	+	0.902787i	$0.641518\pi$
$522$	2.39297e14	0.270240
$523$	−1.10013e15	−1.22938	−0.614689	−	0.788770i	$-0.710718\pi$
$523$	−1.10013e15	−1.22938	−0.614689	+	0.788770i	$0.710718\pi$
$524$	1.14917e15	1.27076
$525$	9.58855e14	1.04925
$526$	2.00989e14	0.217646
$527$	1.29880e15	1.39183
$528$	−5.74556e13	−0.0609321
$529$	−1.06005e14	−0.111255
$530$	−2.05462e12	−0.00213409
$531$	4.22156e13	0.0433963
$532$	4.95174e14	0.503783
$533$	2.22015e15	2.23554
$534$	2.67673e14	0.266764
$535$	−5.87749e10	−5.79757e−5 0
$536$	8.52860e13	0.0832667
$537$	−6.65697e14	−0.643306
$538$	−8.08341e14	−0.773200
$539$	−8.95302e14	−0.847679
$540$	−7.10226e11	−0.000665627 0
$541$	−2.13492e14	−0.198060	−0.0990298	−	0.995084i	$-0.531574\pi$
$541$	−2.13492e14	−0.198060	−0.0990298	+	0.995084i	$0.531574\pi$
$542$	2.92869e14	0.268954
$543$	4.34469e14	0.394966
$544$	−9.06993e14	−0.816225
$545$	8.09360e12	0.00721043
$546$	9.59629e14	0.846338
$547$	9.40079e14	0.820793	0.410397	−	0.911907i	$-0.365390\pi$
$547$	9.40079e14	0.820793	0.410397	+	0.911907i	$0.365390\pi$
$548$	1.02684e15	0.887585
$549$	−4.40565e14	−0.377018
$550$	2.21681e14	0.187817
$551$	7.09897e14	0.595472
$552$	5.81752e14	0.483140
$553$	−5.28766e14	−0.434786
$554$	−2.74657e14	−0.223608
$555$	−2.42872e12	−0.00195779
$556$	1.24135e15	0.990794
$557$	1.26663e15	1.00103	0.500513	−	0.865729i	$-0.333145\pi$
$557$	1.26663e15	1.00103	0.500513	+	0.865729i	$0.333145\pi$
$558$	−3.83202e14	−0.299874
$559$	−1.86794e15	−1.44743
$560$	−3.17556e12	−0.00243661
$561$	2.20802e14	0.167767
$562$	−1.14865e15	−0.864247
$563$	6.71361e14	0.500219	0.250109	−	0.968218i	$-0.419533\pi$
$563$	6.71361e14	0.500219	0.250109	+	0.968218i	$0.419533\pi$
$564$	−8.66779e14	−0.639548
$565$	−4.37033e11	−0.000319336 0
$566$	1.75412e13	0.0126931
$567$	−2.81781e14	−0.201932
$568$	−1.99040e14	−0.141262
$569$	7.24889e14	0.509512	0.254756	−	0.967005i	$-0.418005\pi$
$569$	7.24889e14	0.509512	0.254756	+	0.967005i	$0.418005\pi$
$570$	7.41654e11	0.000516285 0
$571$	−2.62128e15	−1.80724	−0.903619	−	0.428338i	$-0.859099\pi$
$571$	−2.62128e15	−1.80724	−0.903619	+	0.428338i	$0.859099\pi$
$572$	−6.30276e14	−0.430380
$573$	8.64217e14	0.584484
$574$	1.95776e15	1.31142
$575$	1.42086e15	0.942712
$576$	1.22172e14	0.0802878
$577$	−5.30497e14	−0.345315	−0.172658	−	0.984982i	$-0.555235\pi$
$577$	−5.30497e14	−0.345315	−0.172658	+	0.984982i	$0.555235\pi$
$578$	−2.98204e14	−0.192270
$579$	−2.98726e14	−0.190784
$580$	−8.68666e12	−0.00549540
$581$	4.39900e15	2.75667
$582$	3.47431e14	0.215671
$583$	5.35394e14	0.329228
$584$	−2.35472e15	−1.43439
$585$	−4.08318e12	−0.00246401
$586$	1.93911e14	0.115922
$587$	1.76214e15	1.04359	0.521795	−	0.853071i	$-0.325262\pi$
$587$	1.76214e15	1.04359	0.521795	+	0.853071i	$0.325262\pi$
$588$	−1.67614e15	−0.983409
$589$	−1.13680e15	−0.660770
$590$	5.39431e11	0.000310634 0
$591$	2.46780e14	0.140792
$592$	−3.67835e14	−0.207914
$593$	−2.25566e15	−1.26320	−0.631600	−	0.775294i	$-0.717601\pi$
$593$	−2.25566e15	−1.26320	−0.631600	+	0.775294i	$0.717601\pi$
$594$	−6.51459e13	−0.0361461
$595$	1.22037e13	0.00670883
$596$	−1.18122e15	−0.643395
$597$	1.50454e15	0.811979
$598$	1.42201e15	0.760406
$599$	3.85161e14	0.204078	0.102039	−	0.994780i	$-0.467463\pi$
$599$	3.85161e14	0.204078	0.102039	+	0.994780i	$0.467463\pi$
$600$	9.76128e14	0.512478
$601$	3.23146e14	0.168109	0.0840543	−	0.996461i	$-0.473213\pi$
$601$	3.23146e14	0.168109	0.0840543	+	0.996461i	$0.473213\pi$
$602$	−1.64717e15	−0.849098
$603$	−6.12139e13	−0.0312684
$604$	3.03746e14	0.153747
$605$	−8.05960e12	−0.00404259
$606$	−8.32287e14	−0.413689
$607$	2.70154e15	1.33068	0.665339	−	0.746541i	$-0.268287\pi$
$607$	2.70154e15	1.33068	0.665339	+	0.746541i	$0.268287\pi$
$608$	7.93862e14	0.387503
$609$	−3.44642e15	−1.66714
$610$	−5.62955e12	−0.00269873
$611$	−4.98323e15	−2.36747
$612$	4.13374e14	0.194630
$613$	2.58621e15	1.20679	0.603394	−	0.797443i	$-0.293815\pi$
$613$	2.58621e15	1.20679	0.603394	+	0.797443i	$0.293815\pi$
$614$	−6.95976e14	−0.321861
$615$	−8.33017e12	−0.00381804
$616$	−1.30721e15	−0.593814
$617$	4.09511e15	1.84373	0.921864	−	0.387514i	$-0.126666\pi$
$617$	4.09511e15	1.84373	0.921864	+	0.387514i	$0.126666\pi$
$618$	−6.05473e14	−0.270183
$619$	−1.43141e15	−0.633092	−0.316546	−	0.948577i	$-0.602523\pi$
$619$	−1.43141e15	−0.633092	−0.316546	+	0.948577i	$0.602523\pi$
$620$	1.39105e13	0.00609801
$621$	−4.17552e14	−0.181429
$622$	1.15903e15	0.499170
$623$	−3.85509e15	−1.64570
$624$	−6.18408e14	−0.261674
$625$	2.38403e15	0.999934
$626$	−1.03404e15	−0.429912
$627$	−1.93261e14	−0.0796475
$628$	−2.45017e14	−0.100096
$629$	1.41359e15	0.572459
$630$	−3.60060e12	−0.00144544
$631$	2.98660e15	1.18854	0.594272	−	0.804264i	$-0.297440\pi$
$631$	2.98660e15	1.18854	0.594272	+	0.804264i	$0.297440\pi$
$632$	−5.38291e14	−0.212360
$633$	6.13630e14	0.239986
$634$	−1.73725e15	−0.673552
$635$	2.42850e13	0.00933432
$636$	1.00234e15	0.381943
$637$	−9.63635e15	−3.64037
$638$	−7.96790e14	−0.298421
$639$	1.42861e14	0.0530468
$640$	−1.15724e13	−0.00426024
$641$	−3.24322e15	−1.18374	−0.591871	−	0.806032i	$-0.701611\pi$
$641$	−3.24322e15	−1.18374	−0.591871	+	0.806032i	$0.701611\pi$
$642$	−1.00931e13	−0.00365241
$643$	−7.11517e14	−0.255285	−0.127642	−	0.991820i	$-0.540741\pi$
$643$	−7.11517e14	−0.255285	−0.127642	+	0.991820i	$0.540741\pi$
$644$	−3.56229e15	−1.26724
$645$	7.00865e12	0.00247204
$646$	−4.31666e14	−0.150962
$647$	2.83929e15	0.984546	0.492273	−	0.870441i	$-0.336166\pi$
$647$	2.83929e15	0.984546	0.492273	+	0.870441i	$0.336166\pi$
$648$	−2.86857e14	−0.0986285
$649$	−1.40565e14	−0.0479217
$650$	2.38600e15	0.806581
$651$	5.51896e15	1.84996
$652$	2.87292e15	0.954907
$653$	2.12909e15	0.701733	0.350866	−	0.936425i	$-0.385887\pi$
$653$	2.12909e15	0.701733	0.350866	+	0.936425i	$0.385887\pi$
$654$	1.38986e15	0.454250
$655$	−2.47889e13	−0.00803398
$656$	−1.26163e15	−0.405471
$657$	1.69010e15	0.538644
$658$	−4.39427e15	−1.38881
$659$	−3.01446e15	−0.944799	−0.472399	−	0.881385i	$-0.656612\pi$
$659$	−3.01446e15	−0.944799	−0.472399	+	0.881385i	$0.656612\pi$
$660$	2.36484e12	0.000735039 0
$661$	−6.64300e14	−0.204765	−0.102383	−	0.994745i	$-0.532647\pi$
$661$	−6.64300e14	−0.204765	−0.102383	+	0.994745i	$0.532647\pi$
$662$	8.70597e14	0.266133
$663$	2.37654e15	0.720478
$664$	4.47824e15	1.34643
$665$	−1.06815e13	−0.00318502
$666$	−4.17069e14	−0.123339
$667$	−5.10702e15	−1.49787
$668$	1.20865e15	0.351585
$669$	2.94939e15	0.850919
$670$	−7.82192e11	−0.000223822 0
$671$	1.46695e15	0.416334
$672$	−3.85406e15	−1.08489
$673$	3.38199e15	0.944257	0.472128	−	0.881530i	$-0.343486\pi$
$673$	3.38199e15	0.944257	0.472128	+	0.881530i	$0.343486\pi$
$674$	−1.77915e15	−0.492701
$675$	−7.00615e14	−0.192446
$676$	−4.06906e15	−1.10863
$677$	3.81617e15	1.03131	0.515656	−	0.856796i	$-0.327548\pi$
$677$	3.81617e15	1.03131	0.515656	+	0.856796i	$0.327548\pi$
$678$	−7.50489e13	−0.0201178
$679$	−5.00378e15	−1.33050
$680$	1.24235e13	0.00327676
$681$	1.05532e15	0.276105
$682$	1.27595e15	0.331146
$683$	−2.73376e14	−0.0703796	−0.0351898	−	0.999381i	$-0.511204\pi$
$683$	−2.73376e14	−0.0703796	−0.0351898	+	0.999381i	$0.511204\pi$
$684$	−3.61813e14	−0.0924007
$685$	−2.21502e13	−0.00561150
$686$	−4.80753e15	−1.20820
$687$	2.68435e15	0.669232
$688$	1.06148e15	0.262527
$689$	5.76257e15	1.41387
$690$	−5.33548e12	−0.00129868
$691$	7.82046e14	0.188844	0.0944219	−	0.995532i	$-0.469900\pi$
$691$	7.82046e14	0.188844	0.0944219	+	0.995532i	$0.469900\pi$
$692$	−5.34325e15	−1.28004
$693$	9.38246e14	0.222989
$694$	−3.48120e15	−0.820827
$695$	−2.67774e13	−0.00626401
$696$	−3.50850e15	−0.814275
$697$	4.84842e15	1.11640
$698$	2.05184e15	0.468747
$699$	2.81941e15	0.639049
$700$	−5.97721e15	−1.34419
$701$	4.73443e15	1.05638	0.528189	−	0.849127i	$-0.322871\pi$
$701$	4.73443e15	1.05638	0.528189	+	0.849127i	$0.322871\pi$
$702$	−7.01180e14	−0.155230
$703$	−1.23727e15	−0.271775
$704$	−4.06798e14	−0.0886603
$705$	1.86974e13	0.00404336
$706$	4.54872e14	0.0976031
$707$	1.19868e16	2.55209
$708$	−2.63159e14	−0.0555949
$709$	−3.55437e15	−0.745089	−0.372544	−	0.928014i	$-0.621515\pi$
$709$	−3.55437e15	−0.745089	−0.372544	+	0.928014i	$0.621515\pi$
$710$	1.82548e12	0.000379713 0
$711$	3.86358e14	0.0797457
$712$	−3.92453e15	−0.803800
$713$	8.17818e15	1.66213
$714$	2.09566e15	0.422650
$715$	1.35958e13	0.00272095
$716$	4.14975e15	0.824139
$717$	−4.58835e15	−0.904277
$718$	−2.91366e15	−0.569842
$719$	4.65529e15	0.903520	0.451760	−	0.892140i	$-0.350796\pi$
$719$	4.65529e15	0.903520	0.451760	+	0.892140i	$0.350796\pi$
$720$	2.32031e12	0.000446908 0
$721$	8.72017e15	1.66679
$722$	−2.31210e15	−0.438583
$723$	−3.08867e15	−0.581447
$724$	−2.70834e15	−0.505990
$725$	−8.56912e15	−1.58883
$726$	−1.38403e15	−0.254679
$727$	1.70435e15	0.311257	0.155628	−	0.987816i	$-0.450260\pi$
$727$	1.70435e15	0.311257	0.155628	+	0.987816i	$0.450260\pi$
$728$	−1.40698e16	−2.55014
$729$	2.05891e14	0.0370370
$730$	2.15961e13	0.00385566
$731$	−4.07925e15	−0.722828
$732$	2.74635e15	0.482998
$733$	2.90878e15	0.507737	0.253869	−	0.967239i	$-0.418297\pi$
$733$	2.90878e15	0.507737	0.253869	+	0.967239i	$0.418297\pi$
$734$	−5.10019e15	−0.883605
$735$	3.61563e13	0.00621732
$736$	−5.71107e15	−0.974741
$737$	2.03824e14	0.0345291
$738$	−1.43049e15	−0.240533
$739$	−8.19566e15	−1.36785	−0.683926	−	0.729551i	$-0.739729\pi$
$739$	−8.19566e15	−1.36785	−0.683926	+	0.729551i	$0.739729\pi$
$740$	1.51399e13	0.00250812
$741$	−2.08011e15	−0.342047
$742$	5.08149e15	0.829411
$743$	5.72916e15	0.928223	0.464111	−	0.885777i	$-0.346374\pi$
$743$	5.72916e15	0.928223	0.464111	+	0.885777i	$0.346374\pi$
$744$	5.61838e15	0.903566
$745$	2.54804e13	0.00406768
$746$	2.09204e15	0.331517
$747$	−3.21425e15	−0.505611
$748$	−1.37641e15	−0.214926
$749$	1.45363e14	0.0225322
$750$	−1.79051e13	−0.00275512
$751$	−1.03765e16	−1.58501	−0.792504	−	0.609866i	$-0.791223\pi$
$751$	−1.03765e16	−1.58501	−0.792504	+	0.609866i	$0.791223\pi$
$752$	2.83177e15	0.429398
$753$	−1.84739e15	−0.278090
$754$	−8.57603e15	−1.28157
$755$	−6.55217e12	−0.000972024 0
$756$	1.75654e15	0.258694
$757$	−4.55421e15	−0.665864	−0.332932	−	0.942951i	$-0.608038\pi$
$757$	−4.55421e15	−0.665864	−0.332932	+	0.942951i	$0.608038\pi$
$758$	−2.86898e15	−0.416435
$759$	1.39032e15	0.200349
$760$	−1.08739e13	−0.00155564
$761$	−6.12924e15	−0.870544	−0.435272	−	0.900299i	$-0.643348\pi$
$761$	−6.12924e15	−0.870544	−0.435272	+	0.900299i	$0.643348\pi$
$762$	4.17031e15	0.588053
$763$	−2.00172e16	−2.80232
$764$	−5.38727e15	−0.748781
$765$	−8.91695e12	−0.00123049
$766$	2.96575e15	0.406327
$767$	−1.51294e15	−0.205800
$768$	−3.01692e15	−0.407453
$769$	−5.25841e14	−0.0705115	−0.0352557	−	0.999378i	$-0.511225\pi$
$769$	−5.25841e14	−0.0705115	−0.0352557	+	0.999378i	$0.511225\pi$
$770$	1.19889e13	0.00159618
$771$	−2.08634e13	−0.00275794
$772$	1.86217e15	0.244413
$773$	−4.59777e14	−0.0599184	−0.0299592	−	0.999551i	$-0.509538\pi$
$773$	−4.59777e14	−0.0599184	−0.0299592	+	0.999551i	$0.509538\pi$
$774$	1.20355e15	0.155736
$775$	1.37223e16	1.76306
$776$	−5.09392e15	−0.649849
$777$	6.00672e15	0.760890
$778$	−5.66780e15	−0.712896
$779$	−4.24367e15	−0.530012
$780$	2.54533e13	0.00315663
$781$	−4.75685e14	−0.0585785
$782$	3.10542e15	0.379737
$783$	2.51822e15	0.305777
$784$	5.47595e15	0.660270
$785$	5.28530e12	0.000632829 0
$786$	−4.25685e15	−0.506133
$787$	1.58443e16	1.87074	0.935369	−	0.353674i	$-0.115068\pi$
$787$	1.58443e16	1.87074	0.935369	+	0.353674i	$0.115068\pi$
$788$	−1.53835e15	−0.180369
$789$	2.11509e15	0.246267
$790$	4.93689e12	0.000570827 0
$791$	1.08087e15	0.124109
$792$	9.55148e14	0.108914
$793$	1.57891e16	1.78795
$794$	4.80966e15	0.540881
$795$	−2.16216e13	−0.00241473
$796$	−9.37884e15	−1.04022
$797$	1.10469e16	1.21680	0.608400	−	0.793631i	$-0.291812\pi$
$797$	1.10469e16	1.21680	0.608400	+	0.793631i	$0.291812\pi$
$798$	−1.83426e15	−0.200653
$799$	−1.08825e16	−1.18228
$800$	−9.58266e15	−1.03393
$801$	2.81683e15	0.301844
$802$	−2.90321e15	−0.308972
$803$	−5.62752e15	−0.594814
$804$	3.81589e14	0.0400578
$805$	7.68429e13	0.00801173
$806$	1.37333e16	1.42211
$807$	−8.50650e15	−0.874876
$808$	1.22027e16	1.24651
$809$	−1.65576e16	−1.67989	−0.839947	−	0.542669i	$-0.817414\pi$
$809$	−1.65576e16	−1.67989	−0.839947	+	0.542669i	$0.817414\pi$
$810$	2.63088e12	0.000265114 0
$811$	−4.97584e15	−0.498025	−0.249013	−	0.968500i	$-0.580106\pi$
$811$	−4.97584e15	−0.498025	−0.249013	+	0.968500i	$0.580106\pi$
$812$	2.14839e16	2.13578
$813$	3.08198e15	0.304321
$814$	1.38871e15	0.136201
$815$	−6.19722e13	−0.00603712
$816$	−1.35049e15	−0.130676
$817$	3.57044e15	0.343163
$818$	−2.96046e15	−0.282628
$819$	1.00986e16	0.957631
$820$	5.19278e13	0.00489129
$821$	−1.06268e16	−0.994295	−0.497147	−	0.867666i	$-0.665619\pi$
$821$	−1.06268e16	−0.994295	−0.497147	+	0.867666i	$0.665619\pi$
$822$	−3.80371e15	−0.353519
$823$	4.84440e15	0.447240	0.223620	−	0.974676i	$-0.428213\pi$
$823$	4.84440e15	0.447240	0.223620	+	0.974676i	$0.428213\pi$
$824$	8.87725e15	0.814102
$825$	2.33284e15	0.212514
$826$	−1.33412e15	−0.120727
$827$	−1.28296e16	−1.15327	−0.576636	−	0.817001i	$-0.695635\pi$
$827$	−1.28296e16	−1.15327	−0.576636	+	0.817001i	$0.695635\pi$
$828$	2.60289e15	0.232428
$829$	−4.09240e15	−0.363018	−0.181509	−	0.983389i	$-0.558098\pi$
$829$	−4.09240e15	−0.363018	−0.181509	+	0.983389i	$0.558098\pi$
$830$	−4.10717e13	−0.00361921
$831$	−2.89033e15	−0.253012
$832$	−4.37846e15	−0.380753
$833$	−2.10441e16	−1.81795
$834$	−4.59832e15	−0.394626
$835$	−2.60720e13	−0.00222279
$836$	1.20473e15	0.102036
$837$	−4.03259e15	−0.339308
$838$	−5.59323e15	−0.467542
$839$	−2.34497e13	−0.00194736	−0.000973681	−	1.00000i	$-0.500310\pi$
$839$	−2.34497e13	−0.00194736	−0.000973681		1.00000i	$0.500310\pi$
$840$	5.27908e13	0.00435534
$841$	1.85995e16	1.52449
$842$	−1.12475e16	−0.915883
$843$	−1.20877e16	−0.977895
$844$	−3.82518e15	−0.307446
$845$	8.77745e13	0.00700900
$846$	3.21080e15	0.254728
$847$	1.99331e16	1.57114
$848$	−3.27464e15	−0.256440
$849$	1.84593e14	0.0143623
$850$	5.21061e15	0.402796
$851$	8.90095e15	0.683634
$852$	−8.90552e14	−0.0679581
$853$	1.55756e16	1.18094	0.590468	−	0.807061i	$-0.298943\pi$
$853$	1.55756e16	1.18094	0.590468	+	0.807061i	$0.298943\pi$
$854$	1.39230e16	1.04886
$855$	7.80473e12	0.000584176 0
$856$	1.47981e14	0.0110053
$857$	−5.14979e15	−0.380535	−0.190268	−	0.981732i	$-0.560936\pi$
$857$	−5.14979e15	−0.380535	−0.190268	+	0.981732i	$0.560936\pi$
$858$	2.33472e15	0.171417
$859$	1.33478e16	0.973748	0.486874	−	0.873472i	$-0.338137\pi$
$859$	1.33478e16	0.973748	0.486874	+	0.873472i	$0.338137\pi$
$860$	−4.36898e13	−0.00316693
$861$	2.06023e16	1.48388
$862$	1.38521e15	0.0991347
$863$	−1.56635e16	−1.11386	−0.556929	−	0.830560i	$-0.688020\pi$
$863$	−1.56635e16	−1.11386	−0.556929	+	0.830560i	$0.688020\pi$
$864$	2.81608e15	0.198984
$865$	1.15260e14	0.00809265
$866$	7.81482e15	0.545219
$867$	−3.13812e15	−0.217553
$868$	−3.44035e16	−2.36998
$869$	−1.28646e15	−0.0880617
$870$	3.21779e13	0.00218878
$871$	2.19381e15	0.148285
$872$	−2.03777e16	−1.36872
$873$	3.65615e15	0.244032
$874$	−2.71807e15	−0.180280
$875$	2.57874e14	0.0169966
$876$	−1.05355e16	−0.690056
$877$	2.79689e15	0.182045	0.0910223	−	0.995849i	$-0.470987\pi$
$877$	2.79689e15	0.182045	0.0910223	+	0.995849i	$0.470987\pi$
$878$	−2.04877e15	−0.132518
$879$	2.04061e15	0.131166
$880$	−7.72595e12	−0.000493512 0
$881$	2.21053e16	1.40323	0.701615	−	0.712556i	$-0.252462\pi$
$881$	2.21053e16	1.40323	0.701615	+	0.712556i	$0.252462\pi$
$882$	6.20889e15	0.391685
$883$	1.88831e16	1.18383	0.591916	−	0.805999i	$-0.298372\pi$
$883$	1.88831e16	1.18383	0.591916	+	0.805999i	$0.298372\pi$
$884$	−1.48146e16	−0.923004
$885$	5.67665e12	0.000351483 0
$886$	1.13423e16	0.697936
$887$	−6.82286e15	−0.417240	−0.208620	−	0.977997i	$-0.566897\pi$
$887$	−6.82286e15	−0.417240	−0.208620	+	0.977997i	$0.566897\pi$
$888$	6.11493e15	0.371638
$889$	−6.00618e16	−3.62776
$890$	3.59935e13	0.00216062
$891$	−6.85556e14	−0.0408993
$892$	−1.83856e16	−1.09011
$893$	9.52511e15	0.561289
$894$	4.37559e15	0.256260
$895$	−8.95150e13	−0.00521038
$896$	2.86210e16	1.65573
$897$	1.49644e16	0.860400
$898$	1.91876e15	0.109648
$899$	−4.93220e16	−2.80132
$900$	4.36742e15	0.246542
$901$	1.25844e16	0.706069
$902$	4.76311e15	0.265616
$903$	−1.73338e16	−0.960754
$904$	1.10034e15	0.0606180
$905$	5.84222e13	0.00319897
$906$	−1.12516e15	−0.0612365
$907$	3.32482e16	1.79857	0.899285	−	0.437362i	$-0.144087\pi$
$907$	3.32482e16	1.79857	0.899285	+	0.437362i	$0.144087\pi$
$908$	−6.57852e15	−0.353717
$909$	−8.75849e15	−0.468088
$910$	1.29039e14	0.00685480
$911$	3.33817e16	1.76261	0.881307	−	0.472544i	$-0.156664\pi$
$911$	3.33817e16	1.76261	0.881307	+	0.472544i	$0.156664\pi$
$912$	1.18205e15	0.0620387
$913$	1.07025e16	0.558337
$914$	−1.53764e16	−0.797353
$915$	−5.92420e13	−0.00305361
$916$	−1.67334e16	−0.857353
$917$	6.13082e16	3.12239
$918$	−1.53125e15	−0.0775198
$919$	−3.87899e15	−0.195201	−0.0976007	−	0.995226i	$-0.531117\pi$
$919$	−3.87899e15	−0.195201	−0.0976007	+	0.995226i	$0.531117\pi$
$920$	7.82271e13	0.00391313
$921$	−7.32403e15	−0.364185
$922$	2.66453e15	0.131705
$923$	−5.11991e15	−0.251566
$924$	−5.84874e15	−0.285671
$925$	1.49350e16	0.725147
$926$	−1.55702e16	−0.751509
$927$	−6.37164e15	−0.305712
$928$	3.44430e16	1.64281
$929$	2.71315e16	1.28643	0.643217	−	0.765684i	$-0.277599\pi$
$929$	2.71315e16	1.28643	0.643217	+	0.765684i	$0.277599\pi$
$930$	−5.15284e13	−0.00242879
$931$	1.84192e16	0.863074
$932$	−1.75754e16	−0.818684
$933$	1.21970e16	0.564811
$934$	6.06940e15	0.279407
$935$	2.96908e13	0.00135881
$936$	1.02805e16	0.467731
$937$	−1.07760e15	−0.0487404	−0.0243702	−	0.999703i	$-0.507758\pi$
$937$	−1.07760e15	−0.0487404	−0.0243702	+	0.999703i	$0.507758\pi$
$938$	1.93452e15	0.0869878
$939$	−1.08816e16	−0.486445
$940$	−1.16554e14	−0.00517994
$941$	3.70173e16	1.63554	0.817771	−	0.575544i	$-0.195210\pi$
$941$	3.70173e16	1.63554	0.817771	+	0.575544i	$0.195210\pi$
$942$	9.07611e14	0.0398676
$943$	3.05291e16	1.33321
$944$	8.59742e14	0.0373269
$945$	−3.78905e13	−0.00163552
$946$	−4.00747e15	−0.171977
$947$	−1.04889e16	−0.447513	−0.223756	−	0.974645i	$-0.571832\pi$
$947$	−1.04889e16	−0.447513	−0.223756	+	0.974645i	$0.571832\pi$
$948$	−2.40844e15	−0.102162
$949$	−6.05703e16	−2.55444
$950$	−4.56068e15	−0.191227
$951$	−1.82818e16	−0.762123
$952$	−3.07259e16	−1.27351
$953$	3.94046e15	0.162381	0.0811906	−	0.996699i	$-0.474128\pi$
$953$	3.94046e15	0.162381	0.0811906	+	0.996699i	$0.474128\pi$
$954$	−3.71294e15	−0.152125
$955$	1.16210e14	0.00473395
$956$	2.86024e16	1.15847
$957$	−8.38494e15	−0.337664
$958$	3.11930e15	0.124896
$959$	5.47820e16	2.18090
$960$	1.64283e13	0.000650280 0
$961$	5.35739e16	2.10850
$962$	1.49471e16	0.584915
$963$	−1.06213e14	−0.00413270
$964$	1.92538e16	0.744891
$965$	−4.01692e13	−0.00154523
$966$	1.31958e16	0.504731
$967$	−1.48756e16	−0.565756	−0.282878	−	0.959156i	$-0.591289\pi$
$967$	−1.48756e16	−0.565756	−0.282878	+	0.959156i	$0.591289\pi$
$968$	2.02921e16	0.767385
$969$	−4.54260e15	−0.170814
$970$	4.67184e13	0.00174680
$971$	1.88583e16	0.701126	0.350563	−	0.936539i	$-0.385990\pi$
$971$	1.88583e16	0.701126	0.350563	+	0.936539i	$0.385990\pi$
$972$	−1.28346e15	−0.0474481
$973$	6.62261e16	2.43449
$974$	6.92119e15	0.252992
$975$	2.51089e16	0.912646
$976$	−8.97235e15	−0.324289
$977$	−1.93781e16	−0.696450	−0.348225	−	0.937411i	$-0.613216\pi$
$977$	−1.93781e16	−0.696450	−0.348225	+	0.937411i	$0.613216\pi$
$978$	−1.06421e16	−0.380333
$979$	−9.37921e15	−0.333320
$980$	−2.25387e14	−0.00796500
$981$	1.46261e16	0.513983
$982$	2.22808e16	0.778605
$983$	4.98162e16	1.73112	0.865558	−	0.500809i	$-0.166964\pi$
$983$	4.98162e16	1.73112	0.865558	+	0.500809i	$0.166964\pi$
$984$	2.09734e16	0.724762
$985$	3.31840e13	0.00114033
$986$	−1.87285e16	−0.640001
$987$	−4.62427e16	−1.57144
$988$	1.29668e16	0.438197
$989$	−2.56858e16	−0.863206
$990$	−8.76004e12	−0.000292761 0
$991$	−9.60040e15	−0.319069	−0.159534	−	0.987192i	$-0.550999\pi$
$991$	−9.60040e15	−0.319069	−0.159534	+	0.987192i	$0.550999\pi$
$992$	−5.51557e16	−1.82296
$993$	9.16164e15	0.301129
$994$	−4.51479e15	−0.147575
$995$	2.02313e14	0.00657652
$996$	2.00367e16	0.647737
$997$	2.54447e16	0.818039	0.409020	−	0.912526i	$-0.365871\pi$
$997$	2.54447e16	0.818039	0.409020	+	0.912526i	$0.365871\pi$
$998$	1.89062e16	0.604485
$999$	−4.38898e15	−0.139558

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.d.1.16	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.d.1.16	✓	28	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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+23.0914 q^{2} +243.000 q^{3} -1514.79 q^{4} +32.6758 q^{5} +5611.21 q^{6} -80813.9 q^{7} -82269.7 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+23.0914 q^{2} +243.000 q^{3} -1514.79 q^{4} +32.6758 q^{5} +5611.21 q^{6} -80813.9 q^{7} -82269.7 q^{8} +59049.0 q^{9} +754.528 q^{10} -196616. q^{11} -368093. q^{12} -2.11622e6 q^{13} -1.86611e6 q^{14} +7940.21 q^{15} +1.20256e6 q^{16} -4.62145e6 q^{17} +1.36352e6 q^{18} +4.04501e6 q^{19} -49496.8 q^{20} -1.96378e7 q^{21} -4.54013e6 q^{22} -2.90999e7 q^{23} -1.99915e7 q^{24} -4.88271e7 q^{25} -4.88664e7 q^{26} +1.43489e7 q^{27} +1.22416e8 q^{28} +1.75499e8 q^{29} +183350. q^{30} -2.81038e8 q^{31} +1.96257e8 q^{32} -4.77776e7 q^{33} -1.06716e8 q^{34} -2.64066e6 q^{35} -8.94467e7 q^{36} -3.05876e8 q^{37} +9.34049e7 q^{38} -5.14241e8 q^{39} -2.68822e6 q^{40} -1.04911e9 q^{41} -4.53464e8 q^{42} +8.82678e8 q^{43} +2.97831e8 q^{44} +1.92947e6 q^{45} -6.71957e8 q^{46} +2.35478e9 q^{47} +2.92223e8 q^{48} +4.55357e9 q^{49} -1.12748e9 q^{50} -1.12301e9 q^{51} +3.20562e9 q^{52} -2.72305e9 q^{53} +3.31336e8 q^{54} -6.42457e6 q^{55} +6.64854e9 q^{56} +9.82937e8 q^{57} +4.05252e9 q^{58} +7.14924e8 q^{59} -1.20277e7 q^{60} -7.46101e9 q^{61} -6.48956e9 q^{62} -4.77198e9 q^{63} +2.06900e9 q^{64} -6.91491e7 q^{65} -1.10325e9 q^{66} -1.03666e9 q^{67} +7.00052e9 q^{68} -7.07128e9 q^{69} -6.09764e7 q^{70} +2.41936e9 q^{71} -4.85794e9 q^{72} +2.86219e10 q^{73} -7.06309e9 q^{74} -1.18650e10 q^{75} -6.12733e9 q^{76} +1.58893e10 q^{77} -1.18745e10 q^{78} +6.54301e9 q^{79} +3.92947e7 q^{80} +3.48678e9 q^{81} -2.42255e10 q^{82} -5.44336e10 q^{83} +2.97471e10 q^{84} -1.51009e8 q^{85} +2.03823e10 q^{86} +4.26463e10 q^{87} +1.61755e10 q^{88} +4.77033e10 q^{89} +4.45542e7 q^{90} +1.71020e11 q^{91} +4.40802e10 q^{92} -6.82922e10 q^{93} +5.43751e10 q^{94} +1.32174e8 q^{95} +4.76905e10 q^{96} +6.19173e10 q^{97} +1.05148e11 q^{98} -1.16100e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9}+O(q^{10}) \) 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9} + 616281 q^{10} + 1082362 q^{11} + 7099002 q^{12} + 503712 q^{13} + 1321669 q^{14} + 6454566 q^{15} + 34870338 q^{16} + 13513579 q^{17} + 5668704 q^{18} + 35971687 q^{19} + 96105997 q^{20} + 34586919 q^{21} - 47598882 q^{22} + 61380539 q^{23} + 80756433 q^{24} + 294744746 q^{25} + 62820734 q^{26} + 401769396 q^{27} + 148068294 q^{28} + 322339307 q^{29} + 149756283 q^{30} + 151247077 q^{31} + 466383494 q^{32} + 263013966 q^{33} + 684479860 q^{34} + 960297361 q^{35} + 1725057486 q^{36} + 863508437 q^{37} + 992640509 q^{38} + 122402016 q^{39} + 3067680252 q^{40} + 3081170377 q^{41} + 321165567 q^{42} + 2554238300 q^{43} + 4350123570 q^{44} + 1568459538 q^{45} - 1987059155 q^{46} + 6203398333 q^{47} + 8473492134 q^{48} + 10327857997 q^{49} + 17577682253 q^{50} + 3283799697 q^{51} + 32137181618 q^{52} + 14571770754 q^{53} + 1377495072 q^{54} + 18251419334 q^{55} + 33498842836 q^{56} + 8741119941 q^{57} + 11860778276 q^{58} + 20017880372 q^{59} + 23353757271 q^{60} + 2761613771 q^{61} + 13785829526 q^{62} + 8404621317 q^{63} + 86547545293 q^{64} + 32034985256 q^{65} - 11566528326 q^{66} + 39381333296 q^{67} + 38995496621 q^{68} + 14915470977 q^{69} + 8551800364 q^{70} + 26130020296 q^{71} + 19623813219 q^{72} + 41382402799 q^{73} + 23815315058 q^{74} + 71622973278 q^{75} + 10611720128 q^{76} - 8426124313 q^{77} + 15265438362 q^{78} + 59825111206 q^{79} + 4009687655 q^{80} + 97629963228 q^{81} - 39592715115 q^{82} + 35433122727 q^{83} + 35980595442 q^{84} - 8950496085 q^{85} - 182032360688 q^{86} + 78328451601 q^{87} - 220003602335 q^{88} + 102303043039 q^{89} + 36390776769 q^{90} - 111146323655 q^{91} - 163000203526 q^{92} + 36753039711 q^{93} - 81314346008 q^{94} + 208102168887 q^{95} + 113331189042 q^{96} - 171891031490 q^{97} + 72304707792 q^{98} + 63912393738 q^{99}+O(q^{100}) \) 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9 + 616281 * q^10 + 1082362 * q^11 + 7099002 * q^12 + 503712 * q^13 + 1321669 * q^14 + 6454566 * q^15 + 34870338 * q^16 + 13513579 * q^17 + 5668704 * q^18 + 35971687 * q^19 + 96105997 * q^20 + 34586919 * q^21 - 47598882 * q^22 + 61380539 * q^23 + 80756433 * q^24 + 294744746 * q^25 + 62820734 * q^26 + 401769396 * q^27 + 148068294 * q^28 + 322339307 * q^29 + 149756283 * q^30 + 151247077 * q^31 + 466383494 * q^32 + 263013966 * q^33 + 684479860 * q^34 + 960297361 * q^35 + 1725057486 * q^36 + 863508437 * q^37 + 992640509 * q^38 + 122402016 * q^39 + 3067680252 * q^40 + 3081170377 * q^41 + 321165567 * q^42 + 2554238300 * q^43 + 4350123570 * q^44 + 1568459538 * q^45 - 1987059155 * q^46 + 6203398333 * q^47 + 8473492134 * q^48 + 10327857997 * q^49 + 17577682253 * q^50 + 3283799697 * q^51 + 32137181618 * q^52 + 14571770754 * q^53 + 1377495072 * q^54 + 18251419334 * q^55 + 33498842836 * q^56 + 8741119941 * q^57 + 11860778276 * q^58 + 20017880372 * q^59 + 23353757271 * q^60 + 2761613771 * q^61 + 13785829526 * q^62 + 8404621317 * q^63 + 86547545293 * q^64 + 32034985256 * q^65 - 11566528326 * q^66 + 39381333296 * q^67 + 38995496621 * q^68 + 14915470977 * q^69 + 8551800364 * q^70 + 26130020296 * q^71 + 19623813219 * q^72 + 41382402799 * q^73 + 23815315058 * q^74 + 71622973278 * q^75 + 10611720128 * q^76 - 8426124313 * q^77 + 15265438362 * q^78 + 59825111206 * q^79 + 4009687655 * q^80 + 97629963228 * q^81 - 39592715115 * q^82 + 35433122727 * q^83 + 35980595442 * q^84 - 8950496085 * q^85 - 182032360688 * q^86 + 78328451601 * q^87 - 220003602335 * q^88 + 102303043039 * q^89 + 36390776769 * q^90 - 111146323655 * q^91 - 163000203526 * q^92 + 36753039711 * q^93 - 81314346008 * q^94 + 208102168887 * q^95 + 113331189042 * q^96 - 171891031490 * q^97 + 72304707792 * q^98 + 63912393738 * q^99

Introduction

L-functions

Modular forms

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Database

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