LMFDB - Embedded newform 177.10.a.a.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$91.1613430010$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q+15.9818 q^{2} +81.0000 q^{3} -256.580 q^{4} +61.0966 q^{5} +1294.53 q^{6} +4757.03 q^{7} -12283.3 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+15.9818 q^{2} +81.0000 q^{3} -256.580 q^{4} +61.0966 q^{5} +1294.53 q^{6} +4757.03 q^{7} -12283.3 q^{8} +6561.00 q^{9} +976.437 q^{10} +5603.63 q^{11} -20783.0 q^{12} -73495.1 q^{13} +76026.1 q^{14} +4948.83 q^{15} -64941.2 q^{16} +430505. q^{17} +104857. q^{18} -718411. q^{19} -15676.2 q^{20} +385319. q^{21} +89556.4 q^{22} +3945.26 q^{23} -994950. q^{24} -1.94939e6 q^{25} -1.17459e6 q^{26} +531441. q^{27} -1.22056e6 q^{28} +627200. q^{29} +79091.4 q^{30} +1.02481e6 q^{31} +5.25119e6 q^{32} +453894. q^{33} +6.88027e6 q^{34} +290638. q^{35} -1.68342e6 q^{36} -1.31994e7 q^{37} -1.14815e7 q^{38} -5.95311e6 q^{39} -750470. q^{40} -7.00235e6 q^{41} +6.15811e6 q^{42} +3.11873e7 q^{43} -1.43778e6 q^{44} +400855. q^{45} +63052.5 q^{46} -7.14985e6 q^{47} -5.26024e6 q^{48} -1.77243e7 q^{49} -3.11549e7 q^{50} +3.48709e7 q^{51} +1.88574e7 q^{52} -1.00893e8 q^{53} +8.49341e6 q^{54} +342363. q^{55} -5.84322e7 q^{56} -5.81913e7 q^{57} +1.00238e7 q^{58} +1.21174e7 q^{59} -1.26977e6 q^{60} -4.94621e7 q^{61} +1.63783e7 q^{62} +3.12109e7 q^{63} +1.17174e8 q^{64} -4.49030e6 q^{65} +7.25407e6 q^{66} -2.76538e8 q^{67} -1.10459e8 q^{68} +319566. q^{69} +4.64494e6 q^{70} -2.12153e8 q^{71} -8.05910e7 q^{72} -1.63627e8 q^{73} -2.10951e8 q^{74} -1.57901e8 q^{75} +1.84330e8 q^{76} +2.66566e7 q^{77} -9.51416e7 q^{78} -5.43394e8 q^{79} -3.96769e6 q^{80} +4.30467e7 q^{81} -1.11911e8 q^{82} +5.64040e8 q^{83} -9.88654e7 q^{84} +2.63024e7 q^{85} +4.98430e8 q^{86} +5.08032e7 q^{87} -6.88313e7 q^{88} -3.74114e8 q^{89} +6.40640e6 q^{90} -3.49618e8 q^{91} -1.01228e6 q^{92} +8.30095e7 q^{93} -1.14268e8 q^{94} -4.38925e7 q^{95} +4.25346e8 q^{96} +1.37988e9 q^{97} -2.83267e8 q^{98} +3.67654e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9}+O(q^{10}) $ 21 * q - 66 * q^2 + 1701 * q^3 + 5206 * q^4 - 2964 * q^5 - 5346 * q^6 - 30775 * q^7 - 24621 * q^8 + 137781 * q^9	\( 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9} - 54663 q^{10} - 151769 q^{11} + 421686 q^{12} - 153611 q^{13} - 286771 q^{14} - 240084 q^{15} + 805530 q^{16} - 723621 q^{17} - 433026 q^{18} - 549388 q^{19} - 527311 q^{20} - 2492775 q^{21} + 2973158 q^{22} + 169962 q^{23} - 1994301 q^{24} + 8035779 q^{25} - 2337392 q^{26} + 11160261 q^{27} - 22659054 q^{28} - 16845442 q^{29} - 4427703 q^{30} - 19307976 q^{31} - 44923568 q^{32} - 12293289 q^{33} - 35547496 q^{34} - 34882596 q^{35} + 34156566 q^{36} - 41561129 q^{37} - 52335371 q^{38} - 12442491 q^{39} - 125735038 q^{40} - 68169291 q^{41} - 23228451 q^{42} - 25719587 q^{43} - 126277032 q^{44} - 19446804 q^{45} - 292814271 q^{46} - 174095332 q^{47} + 65247930 q^{48} + 7479350 q^{49} - 227877439 q^{50} - 58613301 q^{51} - 232397708 q^{52} - 228390500 q^{53} - 35075106 q^{54} - 29426208 q^{55} + 326778474 q^{56} - 44500428 q^{57} + 480343762 q^{58} + 254464581 q^{59} - 42712191 q^{60} - 183928964 q^{61} - 21753862 q^{62} - 201914775 q^{63} + 310571245 q^{64} + 5308466 q^{65} + 240825798 q^{66} - 82724114 q^{67} - 138336205 q^{68} + 13766922 q^{69} + 1030274876 q^{70} - 404721965 q^{71} - 161538381 q^{72} + 154162574 q^{73} + 36352054 q^{74} + 650898099 q^{75} + 1068940636 q^{76} - 448535481 q^{77} - 189328752 q^{78} + 272529635 q^{79} - 345587859 q^{80} + 903981141 q^{81} - 38412637 q^{82} + 432518643 q^{83} - 1835383374 q^{84} - 126211490 q^{85} - 3699273072 q^{86} - 1364480802 q^{87} + 170111045 q^{88} - 1255621070 q^{89} - 358643943 q^{90} + 1448885849 q^{91} + 1568933320 q^{92} - 1563946056 q^{93} - 1908445164 q^{94} - 2896546490 q^{95} - 3638809008 q^{96} + 1007235486 q^{97} - 9506868248 q^{98} - 995756409 q^{99}+O(q^{100}) \) 21 * q - 66 * q^2 + 1701 * q^3 + 5206 * q^4 - 2964 * q^5 - 5346 * q^6 - 30775 * q^7 - 24621 * q^8 + 137781 * q^9 - 54663 * q^10 - 151769 * q^11 + 421686 * q^12 - 153611 * q^13 - 286771 * q^14 - 240084 * q^15 + 805530 * q^16 - 723621 * q^17 - 433026 * q^18 - 549388 * q^19 - 527311 * q^20 - 2492775 * q^21 + 2973158 * q^22 + 169962 * q^23 - 1994301 * q^24 + 8035779 * q^25 - 2337392 * q^26 + 11160261 * q^27 - 22659054 * q^28 - 16845442 * q^29 - 4427703 * q^30 - 19307976 * q^31 - 44923568 * q^32 - 12293289 * q^33 - 35547496 * q^34 - 34882596 * q^35 + 34156566 * q^36 - 41561129 * q^37 - 52335371 * q^38 - 12442491 * q^39 - 125735038 * q^40 - 68169291 * q^41 - 23228451 * q^42 - 25719587 * q^43 - 126277032 * q^44 - 19446804 * q^45 - 292814271 * q^46 - 174095332 * q^47 + 65247930 * q^48 + 7479350 * q^49 - 227877439 * q^50 - 58613301 * q^51 - 232397708 * q^52 - 228390500 * q^53 - 35075106 * q^54 - 29426208 * q^55 + 326778474 * q^56 - 44500428 * q^57 + 480343762 * q^58 + 254464581 * q^59 - 42712191 * q^60 - 183928964 * q^61 - 21753862 * q^62 - 201914775 * q^63 + 310571245 * q^64 + 5308466 * q^65 + 240825798 * q^66 - 82724114 * q^67 - 138336205 * q^68 + 13766922 * q^69 + 1030274876 * q^70 - 404721965 * q^71 - 161538381 * q^72 + 154162574 * q^73 + 36352054 * q^74 + 650898099 * q^75 + 1068940636 * q^76 - 448535481 * q^77 - 189328752 * q^78 + 272529635 * q^79 - 345587859 * q^80 + 903981141 * q^81 - 38412637 * q^82 + 432518643 * q^83 - 1835383374 * q^84 - 126211490 * q^85 - 3699273072 * q^86 - 1364480802 * q^87 + 170111045 * q^88 - 1255621070 * q^89 - 358643943 * q^90 + 1448885849 * q^91 + 1568933320 * q^92 - 1563946056 * q^93 - 1908445164 * q^94 - 2896546490 * q^95 - 3638809008 * q^96 + 1007235486 * q^97 - 9506868248 * q^98 - 995756409 * 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 $

$2$	15.9818	0.706305	0.353152	−	0.935566i	$-0.385110\pi$
$2$	15.9818	0.706305	0.353152	+	0.935566i	$0.385110\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	−256.580	−0.501134
$5$	61.0966	0.0437172	0.0218586	−	0.999761i	$-0.493042\pi$
$5$	61.0966	0.0437172	0.0218586	+	0.999761i	$0.493042\pi$
$6$	1294.53	0.407785
$7$	4757.03	0.748850	0.374425	−	0.927257i	$-0.377840\pi$
$7$	4757.03	0.748850	0.374425	+	0.927257i	$0.377840\pi$
$8$	−12283.3	−1.06026
$9$	6561.00	0.333333
$10$	976.437	0.0308776
$11$	5603.63	0.115399	0.0576996	−	0.998334i	$-0.481623\pi$
$11$	5603.63	0.115399	0.0576996	+	0.998334i	$0.481623\pi$
$12$	−20783.0	−0.289330
$13$	−73495.1	−0.713696	−0.356848	−	0.934162i	$-0.616149\pi$
$13$	−73495.1	−0.713696	−0.356848	+	0.934162i	$0.616149\pi$
$14$	76026.1	0.528916
$15$	4948.83	0.0252401
$16$	−64941.2	−0.247731
$17$	430505.	1.25014	0.625069	−	0.780569i	$-0.285071\pi$
$17$	430505.	1.25014	0.625069	+	0.780569i	$0.285071\pi$
$18$	104857.	0.235435
$19$	−718411.	−1.26468	−0.632341	−	0.774690i	$-0.717906\pi$
$19$	−718411.	−1.26468	−0.632341	+	0.774690i	$0.717906\pi$
$20$	−15676.2	−0.0219082
$21$	385319.	0.432348
$22$	89556.4	0.0815070
$23$	3945.26	0.00293968	0.00146984	−	0.999999i	$-0.499532\pi$
$23$	3945.26	0.00293968	0.00146984	+	0.999999i	$0.499532\pi$
$24$	−994950.	−0.612140
$25$	−1.94939e6	−0.998089
$26$	−1.17459e6	−0.504087
$27$	531441.	0.192450
$28$	−1.22056e6	−0.375274
$29$	627200.	0.164670	0.0823351	−	0.996605i	$-0.473762\pi$
$29$	627200.	0.164670	0.0823351	+	0.996605i	$0.473762\pi$
$30$	79091.4	0.0178272
$31$	1.02481e6	0.199304	0.0996518	−	0.995022i	$-0.468227\pi$
$31$	1.02481e6	0.199304	0.0996518	+	0.995022i	$0.468227\pi$
$32$	5.25119e6	0.885284
$33$	453894.	0.0666257
$34$	6.88027e6	0.882978
$35$	290638.	0.0327376
$36$	−1.68342e6	−0.167045
$37$	−1.31994e7	−1.15783	−0.578917	−	0.815386i	$-0.696525\pi$
$37$	−1.31994e7	−1.15783	−0.578917	+	0.815386i	$0.696525\pi$
$38$	−1.14815e7	−0.893251
$39$	−5.95311e6	−0.412053
$40$	−750470.	−0.0463515
$41$	−7.00235e6	−0.387005	−0.193503	−	0.981100i	$-0.561985\pi$
$41$	−7.00235e6	−0.387005	−0.193503	+	0.981100i	$0.561985\pi$
$42$	6.15811e6	0.305370
$43$	3.11873e7	1.39113	0.695567	−	0.718461i	$-0.255153\pi$
$43$	3.11873e7	1.39113	0.695567	+	0.718461i	$0.255153\pi$
$44$	−1.43778e6	−0.0578304
$45$	400855.	0.0145724
$46$	63052.5	0.00207631
$47$	−7.14985e6	−0.213726	−0.106863	−	0.994274i	$-0.534081\pi$
$47$	−7.14985e6	−0.213726	−0.106863	+	0.994274i	$0.534081\pi$
$48$	−5.26024e6	−0.143028
$49$	−1.77243e7	−0.439224
$50$	−3.11549e7	−0.704955
$51$	3.48709e7	0.721768
$52$	1.88574e7	0.357657
$53$	−1.00893e8	−1.75639	−0.878195	−	0.478303i	$-0.841252\pi$
$53$	−1.00893e8	−1.75639	−0.878195	+	0.478303i	$0.841252\pi$
$54$	8.49341e6	0.135928
$55$	342363.	0.00504493
$56$	−5.84322e7	−0.793973
$57$	−5.81913e7	−0.730165
$58$	1.00238e7	0.116307
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	−1.26977e6	−0.0126487
$61$	−4.94621e7	−0.457391	−0.228696	−	0.973498i	$-0.573446\pi$
$61$	−4.94621e7	−0.457391	−0.228696	+	0.973498i	$0.573446\pi$
$62$	1.63783e7	0.140769
$63$	3.12109e7	0.249617
$64$	1.17174e8	0.873011
$65$	−4.49030e6	−0.0312008
$66$	7.25407e6	0.0470581
$67$	−2.76538e8	−1.67656	−0.838280	−	0.545240i	$-0.816438\pi$
$67$	−2.76538e8	−1.67656	−0.838280	+	0.545240i	$0.816438\pi$
$68$	−1.10459e8	−0.626486
$69$	319566.	0.00169723
$70$	4.64494e6	0.0231227
$71$	−2.12153e8	−0.990799	−0.495400	−	0.868665i	$-0.664978\pi$
$71$	−2.12153e8	−0.990799	−0.495400	+	0.868665i	$0.664978\pi$
$72$	−8.05910e7	−0.353419
$73$	−1.63627e8	−0.674377	−0.337189	−	0.941437i	$-0.609476\pi$
$73$	−1.63627e8	−0.674377	−0.337189	+	0.941437i	$0.609476\pi$
$74$	−2.10951e8	−0.817784
$75$	−1.57901e8	−0.576247
$76$	1.84330e8	0.633775
$77$	2.66566e7	0.0864166
$78$	−9.51416e7	−0.291035
$79$	−5.43394e8	−1.56961	−0.784807	−	0.619741i	$-0.787238\pi$
$79$	−5.43394e8	−1.56961	−0.784807	+	0.619741i	$0.787238\pi$
$80$	−3.96769e6	−0.0108301
$81$	4.30467e7	0.111111
$82$	−1.11911e8	−0.273344
$83$	5.64040e8	1.30454	0.652272	−	0.757985i	$-0.273816\pi$
$83$	5.64040e8	1.30454	0.652272	+	0.757985i	$0.273816\pi$
$84$	−9.88654e7	−0.216664
$85$	2.63024e7	0.0546525
$86$	4.98430e8	0.982565
$87$	5.08032e7	0.0950724
$88$	−6.88313e7	−0.122353
$89$	−3.74114e8	−0.632047	−0.316023	−	0.948751i	$-0.602348\pi$
$89$	−3.74114e8	−0.632047	−0.316023	+	0.948751i	$0.602348\pi$
$90$	6.40640e6	0.0102925
$91$	−3.49618e8	−0.534451
$92$	−1.01228e6	−0.00147317
$93$	8.30095e7	0.115068
$94$	−1.14268e8	−0.150955
$95$	−4.38925e7	−0.0552884
$96$	4.25346e8	0.511119
$97$	1.37988e9	1.58259	0.791296	−	0.611433i	$-0.209407\pi$
$97$	1.37988e9	1.58259	0.791296	+	0.611433i	$0.209407\pi$
$98$	−2.83267e8	−0.310226
$99$	3.67654e7	0.0384664
$100$	5.00176e8	0.500176
$101$	7.62944e8	0.729536	0.364768	−	0.931099i	$-0.381148\pi$
$101$	7.62944e8	0.729536	0.364768	+	0.931099i	$0.381148\pi$
$102$	5.57301e8	0.509788
$103$	−1.73748e9	−1.52108	−0.760538	−	0.649293i	$-0.775065\pi$
$103$	−1.73748e9	−1.52108	−0.760538	+	0.649293i	$0.775065\pi$
$104$	9.02765e8	0.756702
$105$	2.35417e7	0.0189011
$106$	−1.61246e9	−1.24055
$107$	−9.32433e8	−0.687687	−0.343843	−	0.939027i	$-0.611729\pi$
$107$	−9.32433e8	−0.687687	−0.343843	+	0.939027i	$0.611729\pi$
$108$	−1.36357e8	−0.0964432
$109$	−1.28116e9	−0.869331	−0.434665	−	0.900592i	$-0.643133\pi$
$109$	−1.28116e9	−0.869331	−0.434665	+	0.900592i	$0.643133\pi$
$110$	5.47159e6	0.00356325
$111$	−1.06915e9	−0.668476
$112$	−3.08927e8	−0.185513
$113$	2.83825e8	0.163756	0.0818782	−	0.996642i	$-0.473908\pi$
$113$	2.83825e8	0.163756	0.0818782	+	0.996642i	$0.473908\pi$
$114$	−9.30004e8	−0.515719
$115$	241042.	0.000128515 0
$116$	−1.60927e8	−0.0825218
$117$	−4.82202e8	−0.237899
$118$	1.93658e8	0.0919530
$119$	2.04792e9	0.936165
$120$	−6.07881e7	−0.0267610
$121$	−2.32655e9	−0.986683
$122$	−7.90495e8	−0.323058
$123$	−5.67191e8	−0.223438
$124$	−2.62946e8	−0.0998778
$125$	−2.38431e8	−0.0873508
$126$	4.98807e8	0.176305
$127$	1.68868e9	0.576012	0.288006	−	0.957629i	$-0.407008\pi$
$127$	1.68868e9	0.576012	0.288006	+	0.957629i	$0.407008\pi$
$128$	−8.15957e8	−0.268672
$129$	2.52617e9	0.803172
$130$	−7.17634e7	−0.0220373
$131$	−3.62798e9	−1.07633	−0.538164	−	0.842840i	$-0.680882\pi$
$131$	−3.62798e9	−1.07633	−0.538164	+	0.842840i	$0.680882\pi$
$132$	−1.16460e8	−0.0333884
$133$	−3.41750e9	−0.947057
$134$	−4.41960e9	−1.18416
$135$	3.24692e7	0.00841337
$136$	−5.28804e9	−1.32547
$137$	5.88802e9	1.42800	0.713998	−	0.700148i	$-0.246883\pi$
$137$	5.88802e9	1.42800	0.713998	+	0.700148i	$0.246883\pi$
$138$	5.10725e6	0.00119876
$139$	−2.41235e9	−0.548117	−0.274058	−	0.961713i	$-0.588366\pi$
$139$	−2.41235e9	−0.548117	−0.274058	+	0.961713i	$0.588366\pi$
$140$	−7.45721e7	−0.0164059
$141$	−5.79138e8	−0.123395
$142$	−3.39059e9	−0.699806
$143$	−4.11840e8	−0.0823600
$144$	−4.26080e8	−0.0825771
$145$	3.83198e7	0.00719892
$146$	−2.61507e9	−0.476316
$147$	−1.43567e9	−0.253586
$148$	3.38671e9	0.580230
$149$	−2.91781e9	−0.484975	−0.242487	−	0.970155i	$-0.577963\pi$
$149$	−2.91781e9	−0.484975	−0.242487	+	0.970155i	$0.577963\pi$
$150$	−2.52355e9	−0.407006
$151$	8.01296e9	1.25429	0.627144	−	0.778904i	$-0.284224\pi$
$151$	8.01296e9	1.25429	0.627144	+	0.778904i	$0.284224\pi$
$152$	8.82448e9	1.34089
$153$	2.82454e9	0.416713
$154$	4.26022e8	0.0610365
$155$	6.26123e7	0.00871299
$156$	1.52745e9	0.206494
$157$	−4.74620e9	−0.623444	−0.311722	−	0.950173i	$-0.600906\pi$
$157$	−4.74620e9	−0.623444	−0.311722	+	0.950173i	$0.600906\pi$
$158$	−8.68444e9	−1.10863
$159$	−8.17236e9	−1.01405
$160$	3.20830e8	0.0387021
$161$	1.87677e7	0.00220138
$162$	6.87966e8	0.0784783
$163$	7.60267e9	0.843571	0.421786	−	0.906696i	$-0.361403\pi$
$163$	7.60267e9	0.843571	0.421786	+	0.906696i	$0.361403\pi$
$164$	1.79667e9	0.193941
$165$	2.77314e7	0.00291269
$166$	9.01440e9	0.921405
$167$	−7.86896e9	−0.782876	−0.391438	−	0.920204i	$-0.628022\pi$
$167$	−7.86896e9	−0.782876	−0.391438	+	0.920204i	$0.628022\pi$
$168$	−4.73301e9	−0.458401
$169$	−5.20297e9	−0.490638
$170$	4.20361e8	0.0386013
$171$	−4.71349e9	−0.421561
$172$	−8.00204e9	−0.697145
$173$	−1.07654e10	−0.913741	−0.456871	−	0.889533i	$-0.651030\pi$
$173$	−1.07654e10	−0.913741	−0.456871	+	0.889533i	$0.651030\pi$
$174$	8.11929e8	0.0671501
$175$	−9.27331e9	−0.747418
$176$	−3.63907e8	−0.0285880
$177$	9.81506e8	0.0751646
$178$	−5.97904e9	−0.446417
$179$	−4.69084e9	−0.341517	−0.170758	−	0.985313i	$-0.554622\pi$
$179$	−4.69084e9	−0.341517	−0.170758	+	0.985313i	$0.554622\pi$
$180$	−1.02852e8	−0.00730272
$181$	6.97407e9	0.482984	0.241492	−	0.970403i	$-0.422363\pi$
$181$	6.97407e9	0.482984	0.241492	+	0.970403i	$0.422363\pi$
$182$	−5.58755e9	−0.377485
$183$	−4.00643e9	−0.264075
$184$	−4.84609e7	−0.00311682
$185$	−8.06439e8	−0.0506173
$186$	1.32665e9	0.0812731
$187$	2.41239e9	0.144265
$188$	1.83451e9	0.107105
$189$	2.52808e9	0.144116
$190$	−7.01483e8	−0.0390504
$191$	−1.76966e10	−0.962142	−0.481071	−	0.876682i	$-0.659752\pi$
$191$	−1.76966e10	−0.962142	−0.481071	+	0.876682i	$0.659752\pi$
$192$	9.49106e9	0.504033
$193$	−1.86734e10	−0.968761	−0.484380	−	0.874858i	$-0.660955\pi$
$193$	−1.86734e10	−0.968761	−0.484380	+	0.874858i	$0.660955\pi$
$194$	2.20531e10	1.11779
$195$	−3.63715e8	−0.0180138
$196$	4.54771e9	0.220110
$197$	3.63127e10	1.71775	0.858875	−	0.512185i	$-0.171164\pi$
$197$	3.63127e10	1.71775	0.858875	+	0.512185i	$0.171164\pi$
$198$	5.87580e8	0.0271690
$199$	−5.95324e9	−0.269100	−0.134550	−	0.990907i	$-0.542959\pi$
$199$	−5.95324e9	−0.269100	−0.134550	+	0.990907i	$0.542959\pi$
$200$	2.39450e10	1.05823
$201$	−2.23996e10	−0.967962
$202$	1.21933e10	0.515274
$203$	2.98361e9	0.123313
$204$	−8.94719e9	−0.361702
$205$	−4.27820e8	−0.0169188
$206$	−2.77681e10	−1.07434
$207$	2.58848e7	0.000979894 0
$208$	4.77287e9	0.176805
$209$	−4.02571e9	−0.145943
$210$	3.76240e8	0.0133499
$211$	3.77367e10	1.31067	0.655334	−	0.755340i	$-0.272528\pi$
$211$	3.77367e10	1.31067	0.655334	+	0.755340i	$0.272528\pi$
$212$	2.58873e10	0.880186
$213$	−1.71844e10	−0.572038
$214$	−1.49020e10	−0.485716
$215$	1.90544e9	0.0608165
$216$	−6.52787e9	−0.204047
$217$	4.87504e9	0.149248
$218$	−2.04754e10	−0.614012
$219$	−1.32538e10	−0.389352
$220$	−8.78437e7	−0.00252818
$221$	−3.16400e10	−0.892219
$222$	−1.70870e10	−0.472148
$223$	1.69256e10	0.458324	0.229162	−	0.973388i	$-0.426401\pi$
$223$	1.69256e10	0.458324	0.229162	+	0.973388i	$0.426401\pi$
$224$	2.49800e10	0.662945
$225$	−1.27900e10	−0.332696
$226$	4.53605e9	0.115662
$227$	7.85769e10	1.96417	0.982084	−	0.188442i	$-0.0603437\pi$
$227$	7.85769e10	1.96417	0.982084	+	0.188442i	$0.0603437\pi$
$228$	1.49307e10	0.365910
$229$	−4.19589e10	−1.00824	−0.504121	−	0.863633i	$-0.668183\pi$
$229$	−4.19589e10	−1.00824	−0.504121	+	0.863633i	$0.668183\pi$
$230$	3.85230e6	9.07704e−5 0
$231$	2.15919e9	0.0498927
$232$	−7.70411e9	−0.174593
$233$	−3.02106e10	−0.671519	−0.335759	−	0.941948i	$-0.608993\pi$
$233$	−3.02106e10	−0.671519	−0.335759	+	0.941948i	$0.608993\pi$
$234$	−7.70647e9	−0.168029
$235$	−4.36832e8	−0.00934348
$236$	−3.10908e9	−0.0652421
$237$	−4.40149e10	−0.906217
$238$	3.27296e10	0.661218
$239$	6.22144e10	1.23339	0.616695	−	0.787202i	$-0.288471\pi$
$239$	6.22144e10	1.23339	0.616695	+	0.787202i	$0.288471\pi$
$240$	−3.21383e8	−0.00625277
$241$	1.51274e10	0.288861	0.144430	−	0.989515i	$-0.453865\pi$
$241$	1.51274e10	0.288861	0.144430	+	0.989515i	$0.453865\pi$
$242$	−3.71825e10	−0.696899
$243$	3.48678e9	0.0641500
$244$	1.26910e10	0.229214
$245$	−1.08289e9	−0.0192017
$246$	−9.06476e9	−0.157815
$247$	5.27997e10	0.902599
$248$	−1.25881e10	−0.211313
$249$	4.56872e10	0.753178
$250$	−3.81056e9	−0.0616963
$251$	2.58692e10	0.411387	0.205694	−	0.978616i	$-0.434055\pi$
$251$	2.58692e10	0.411387	0.205694	+	0.978616i	$0.434055\pi$
$252$	−8.00810e9	−0.125091
$253$	2.21078e7	0.000339237 0
$254$	2.69883e10	0.406840
$255$	2.13049e9	0.0315536
$256$	−7.30334e10	−1.06278
$257$	3.89821e10	0.557399	0.278699	−	0.960378i	$-0.410097\pi$
$257$	3.89821e10	0.557399	0.278699	+	0.960378i	$0.410097\pi$
$258$	4.03728e10	0.567284
$259$	−6.27900e10	−0.867044
$260$	1.15212e9	0.0156358
$261$	4.11506e9	0.0548901
$262$	−5.79819e10	−0.760215
$263$	−5.55292e10	−0.715682	−0.357841	−	0.933783i	$-0.616487\pi$
$263$	−5.55292e10	−0.715682	−0.357841	+	0.933783i	$0.616487\pi$
$264$	−5.57534e9	−0.0706405
$265$	−6.16424e9	−0.0767844
$266$	−5.46180e10	−0.668911
$267$	−3.03032e10	−0.364912
$268$	7.09544e10	0.840181
$269$	−1.80216e10	−0.209849	−0.104925	−	0.994480i	$-0.533460\pi$
$269$	−1.80216e10	−0.209849	−0.104925	+	0.994480i	$0.533460\pi$
$270$	5.18919e8	0.00594241
$271$	1.52363e11	1.71600	0.858001	−	0.513648i	$-0.171706\pi$
$271$	1.52363e11	1.71600	0.858001	+	0.513648i	$0.171706\pi$
$272$	−2.79575e10	−0.309698
$273$	−2.83191e10	−0.308566
$274$	9.41015e10	1.00860
$275$	−1.09237e10	−0.115179
$276$	−8.19944e7	−0.000850537 0
$277$	−4.45229e8	−0.00454386	−0.00227193	−	0.999997i	$-0.500723\pi$
$277$	−4.45229e8	−0.00454386	−0.00227193	+	0.999997i	$0.500723\pi$
$278$	−3.85538e10	−0.387138
$279$	6.72377e9	0.0664345
$280$	−3.57001e9	−0.0347103
$281$	1.75664e11	1.68075	0.840377	−	0.542002i	$-0.182334\pi$
$281$	1.75664e11	1.68075	0.840377	+	0.542002i	$0.182334\pi$
$282$	−9.25569e9	−0.0871541
$283$	−3.05315e10	−0.282950	−0.141475	−	0.989942i	$-0.545184\pi$
$283$	−3.05315e10	−0.282950	−0.141475	+	0.989942i	$0.545184\pi$
$284$	5.44342e10	0.496523
$285$	−3.55529e9	−0.0319207
$286$	−6.58196e9	−0.0581712
$287$	−3.33104e10	−0.289809
$288$	3.44530e10	0.295095
$289$	6.67466e10	0.562845
$290$	6.12421e8	0.00508463
$291$	1.11770e11	0.913710
$292$	4.19836e10	0.337953
$293$	1.77930e11	1.41041	0.705205	−	0.709003i	$-0.250855\pi$
$293$	1.77930e11	1.41041	0.705205	+	0.709003i	$0.250855\pi$
$294$	−2.29446e10	−0.179109
$295$	7.40330e8	0.00569149
$296$	1.62133e11	1.22760
$297$	2.97800e9	0.0222086
$298$	−4.66320e10	−0.342540
$299$	−2.89957e8	−0.00209804
$300$	4.05143e10	0.288777
$301$	1.48359e11	1.04175
$302$	1.28062e11	0.885909
$303$	6.17985e10	0.421198
$304$	4.66545e10	0.313301
$305$	−3.02196e9	−0.0199959
$306$	4.51414e10	0.294326
$307$	2.97466e11	1.91124	0.955620	−	0.294602i	$-0.0951870\pi$
$307$	2.97466e11	1.91124	0.955620	+	0.294602i	$0.0951870\pi$
$308$	−6.83957e9	−0.0433063
$309$	−1.40735e11	−0.878194
$310$	1.00066e9	0.00615403
$311$	1.82887e11	1.10856	0.554282	−	0.832329i	$-0.312993\pi$
$311$	1.82887e11	1.10856	0.554282	+	0.832329i	$0.312993\pi$
$312$	7.31240e10	0.436882
$313$	8.49405e10	0.500225	0.250112	−	0.968217i	$-0.419532\pi$
$313$	8.49405e10	0.500225	0.250112	+	0.968217i	$0.419532\pi$
$314$	−7.58530e10	−0.440341
$315$	1.90688e9	0.0109125
$316$	1.39424e11	0.786586
$317$	−2.29248e11	−1.27509	−0.637543	−	0.770415i	$-0.720049\pi$
$317$	−2.29248e11	−1.27509	−0.637543	+	0.770415i	$0.720049\pi$
$318$	−1.30609e11	−0.716230
$319$	3.51460e9	0.0190028
$320$	7.15891e9	0.0381656
$321$	−7.55271e10	−0.397036
$322$	2.99943e8	0.00155484
$323$	−3.09279e11	−1.58103
$324$	−1.10449e10	−0.0556815
$325$	1.43271e11	0.712332
$326$	1.21505e11	0.595818
$327$	−1.03774e11	−0.501908
$328$	8.60123e10	0.410325
$329$	−3.40120e10	−0.160048
$330$	4.43199e8	0.00205725
$331$	3.80256e11	1.74121	0.870603	−	0.491986i	$-0.163729\pi$
$331$	3.80256e11	1.74121	0.870603	+	0.491986i	$0.163729\pi$
$332$	−1.44722e11	−0.653751
$333$	−8.66013e10	−0.385945
$334$	−1.25760e11	−0.552949
$335$	−1.68956e10	−0.0732944
$336$	−2.50231e10	−0.107106
$337$	−2.10397e11	−0.888599	−0.444299	−	0.895878i	$-0.646547\pi$
$337$	−2.10397e11	−0.888599	−0.444299	+	0.895878i	$0.646547\pi$
$338$	−8.31530e10	−0.346540
$339$	2.29899e10	0.0945448
$340$	−6.74868e9	−0.0273882
$341$	5.74265e9	0.0229995
$342$	−7.53303e10	−0.297750
$343$	−2.76278e11	−1.07776
$344$	−3.83084e11	−1.47496
$345$	1.95244e7	7.41979e−5 0
$346$	−1.72051e11	−0.645380
$347$	−1.31135e10	−0.0485552	−0.0242776	−	0.999705i	$-0.507729\pi$
$347$	−1.31135e10	−0.0485552	−0.0242776	+	0.999705i	$0.507729\pi$
$348$	−1.30351e10	−0.0476440
$349$	4.66318e11	1.68255	0.841275	−	0.540608i	$-0.181806\pi$
$349$	4.66318e11	1.68255	0.841275	+	0.540608i	$0.181806\pi$
$350$	−1.48205e11	−0.527905
$351$	−3.90583e10	−0.137351
$352$	2.94257e10	0.102161
$353$	−8.93581e10	−0.306301	−0.153150	−	0.988203i	$-0.548942\pi$
$353$	−8.93581e10	−0.306301	−0.153150	+	0.988203i	$0.548942\pi$
$354$	1.56863e10	0.0530891
$355$	−1.29618e10	−0.0433150
$356$	9.59904e10	0.316740
$357$	1.65882e11	0.540495
$358$	−7.49683e10	−0.241215
$359$	3.45879e11	1.09900	0.549502	−	0.835492i	$-0.314817\pi$
$359$	3.45879e11	1.09900	0.549502	+	0.835492i	$0.314817\pi$
$360$	−4.92384e9	−0.0154505
$361$	1.93426e11	0.599422
$362$	1.11458e11	0.341134
$363$	−1.88450e11	−0.569662
$364$	8.97053e10	0.267832
$365$	−9.99708e9	−0.0294819
$366$	−6.40301e10	−0.186517
$367$	7.78994e10	0.224149	0.112074	−	0.993700i	$-0.464250\pi$
$367$	7.78994e10	0.224149	0.112074	+	0.993700i	$0.464250\pi$
$368$	−2.56210e8	−0.000728251 0
$369$	−4.59425e10	−0.129002
$370$	−1.28884e10	−0.0357512
$371$	−4.79952e11	−1.31527
$372$	−2.12986e10	−0.0576645
$373$	3.52486e11	0.942870	0.471435	−	0.881901i	$-0.343736\pi$
$373$	3.52486e11	0.942870	0.471435	+	0.881901i	$0.343736\pi$
$374$	3.85545e10	0.101895
$375$	−1.93129e10	−0.0504320
$376$	8.78240e10	0.226604
$377$	−4.60962e10	−0.117525
$378$	4.04034e10	0.101790
$379$	−7.71787e11	−1.92142	−0.960708	−	0.277562i	$-0.910473\pi$
$379$	−7.71787e11	−1.92142	−0.960708	+	0.277562i	$0.910473\pi$
$380$	1.12619e10	0.0277069
$381$	1.36783e11	0.332561
$382$	−2.82824e11	−0.679566
$383$	−5.61364e11	−1.33306	−0.666530	−	0.745478i	$-0.732221\pi$
$383$	−5.61364e11	−1.33306	−0.666530	+	0.745478i	$0.732221\pi$
$384$	−6.60925e10	−0.155118
$385$	1.62863e9	0.00377789
$386$	−2.98436e11	−0.684240
$387$	2.04620e11	0.463712
$388$	−3.54051e11	−0.793091
$389$	−1.29451e10	−0.0286636	−0.0143318	−	0.999897i	$-0.504562\pi$
$389$	−1.29451e10	−0.0286636	−0.0143318	+	0.999897i	$0.504562\pi$
$390$	−5.81283e9	−0.0127232
$391$	1.69845e9	0.00367501
$392$	2.17713e11	0.465691
$393$	−2.93867e11	−0.621418
$394$	5.80344e11	1.21326
$395$	−3.31995e10	−0.0686191
$396$	−9.43329e9	−0.0192768
$397$	−4.55778e11	−0.920866	−0.460433	−	0.887695i	$-0.652306\pi$
$397$	−4.55778e11	−0.920866	−0.460433	+	0.887695i	$0.652306\pi$
$398$	−9.51438e10	−0.190067
$399$	−2.76817e11	−0.546784
$400$	1.26596e11	0.247258
$401$	−7.04177e11	−1.35998	−0.679989	−	0.733222i	$-0.738016\pi$
$401$	−7.04177e11	−1.35998	−0.679989	+	0.733222i	$0.738016\pi$
$402$	−3.57987e11	−0.683676
$403$	−7.53184e10	−0.142242
$404$	−1.95757e11	−0.365595
$405$	2.63001e9	0.00485746
$406$	4.76836e10	0.0870967
$407$	−7.39646e10	−0.133613
$408$	−4.28331e11	−0.765260
$409$	−3.04678e11	−0.538376	−0.269188	−	0.963088i	$-0.586755\pi$
$409$	−3.04678e11	−0.538376	−0.269188	+	0.963088i	$0.586755\pi$
$410$	−6.83736e9	−0.0119498
$411$	4.76930e11	0.824454
$412$	4.45802e11	0.762263
$413$	5.76426e10	0.0974919
$414$	4.13688e8	0.000692103 0
$415$	3.44609e10	0.0570310
$416$	−3.85937e11	−0.631824
$417$	−1.95400e11	−0.316455
$418$	−6.43383e10	−0.103080
$419$	−1.10294e12	−1.74818	−0.874092	−	0.485760i	$-0.838543\pi$
$419$	−1.10294e12	−1.74818	−0.874092	+	0.485760i	$0.838543\pi$
$420$	−6.04034e9	−0.00947196
$421$	3.72442e11	0.577815	0.288908	−	0.957357i	$-0.406708\pi$
$421$	3.72442e11	0.577815	0.288908	+	0.957357i	$0.406708\pi$
$422$	6.03102e11	0.925730
$423$	−4.69102e10	−0.0712419
$424$	1.23931e12	1.86223
$425$	−8.39223e11	−1.24775
$426$	−2.74638e11	−0.404033
$427$	−2.35292e11	−0.342517
$428$	2.39244e11	0.344623
$429$	−3.33590e10	−0.0475505
$430$	3.04524e10	0.0429550
$431$	−8.30400e11	−1.15915	−0.579575	−	0.814919i	$-0.696782\pi$
$431$	−8.30400e11	−1.15915	−0.579575	+	0.814919i	$0.696782\pi$
$432$	−3.45124e10	−0.0476759
$433$	−1.15753e12	−1.58248	−0.791238	−	0.611508i	$-0.790563\pi$
$433$	−1.15753e12	−1.58248	−0.791238	+	0.611508i	$0.790563\pi$
$434$	7.79122e10	0.105415
$435$	3.10390e9	0.00415630
$436$	3.28721e11	0.435651
$437$	−2.83432e9	−0.00371776
$438$	−2.11820e11	−0.275001
$439$	4.39794e11	0.565144	0.282572	−	0.959246i	$-0.408812\pi$
$439$	4.39794e11	0.565144	0.282572	+	0.959246i	$0.408812\pi$
$440$	−4.20536e9	−0.00534892
$441$	−1.16289e11	−0.146408
$442$	−5.05666e11	−0.630178
$443$	−7.14220e11	−0.881080	−0.440540	−	0.897733i	$-0.645213\pi$
$443$	−7.14220e11	−0.881080	−0.440540	+	0.897733i	$0.645213\pi$
$444$	2.74324e11	0.334996
$445$	−2.28571e10	−0.0276313
$446$	2.70503e11	0.323717
$447$	−2.36343e11	−0.280000
$448$	5.57398e11	0.653754
$449$	−1.44352e12	−1.67616	−0.838078	−	0.545551i	$-0.816320\pi$
$449$	−1.44352e12	−1.67616	−0.838078	+	0.545551i	$0.816320\pi$
$450$	−2.04407e11	−0.234985
$451$	−3.92386e10	−0.0446601
$452$	−7.28241e10	−0.0820639
$453$	6.49050e11	0.724163
$454$	1.25580e12	1.38730
$455$	−2.13605e10	−0.0233647
$456$	7.14783e11	0.774163
$457$	9.30712e11	0.998142	0.499071	−	0.866561i	$-0.333675\pi$
$457$	9.30712e11	0.998142	0.499071	+	0.866561i	$0.333675\pi$
$458$	−6.70581e11	−0.712126
$459$	2.28788e11	0.240589
$460$	−6.18467e7	−6.44030e−5 0
$461$	−4.17109e11	−0.430125	−0.215063	−	0.976600i	$-0.568996\pi$
$461$	−4.17109e11	−0.430125	−0.215063	+	0.976600i	$0.568996\pi$
$462$	3.45078e10	0.0352394
$463$	6.97753e11	0.705646	0.352823	−	0.935690i	$-0.385222\pi$
$463$	6.97753e11	0.705646	0.352823	+	0.935690i	$0.385222\pi$
$464$	−4.07312e10	−0.0407940
$465$	5.07160e9	0.00503045
$466$	−4.82822e11	−0.474297
$467$	1.07830e12	1.04909	0.524545	−	0.851383i	$-0.324235\pi$
$467$	1.07830e12	1.04909	0.524545	+	0.851383i	$0.324235\pi$
$468$	1.23724e11	0.119219
$469$	−1.31550e12	−1.25549
$470$	−6.98138e9	−0.00659934
$471$	−3.84442e11	−0.359945
$472$	−1.48842e11	−0.138034
$473$	1.74762e11	0.160536
$474$	−7.03439e11	−0.640065
$475$	1.40046e12	1.26227
$476$	−5.25457e11	−0.469144
$477$	−6.61961e11	−0.585463
$478$	9.94302e11	0.871150
$479$	−2.23813e11	−0.194257	−0.0971283	−	0.995272i	$-0.530966\pi$
$479$	−2.23813e11	−0.194257	−0.0971283	+	0.995272i	$0.530966\pi$
$480$	2.59872e10	0.0223447
$481$	9.70092e11	0.826343
$482$	2.41764e11	0.204024
$483$	1.52018e9	0.00127097
$484$	5.96947e11	0.494460
$485$	8.43061e10	0.0691865
$486$	5.57253e10	0.0453095
$487$	7.00426e11	0.564264	0.282132	−	0.959376i	$-0.408958\pi$
$487$	7.00426e11	0.564264	0.282132	+	0.959376i	$0.408958\pi$
$488$	6.07559e11	0.484953
$489$	6.15816e11	0.487036
$490$	−1.73066e10	−0.0135622
$491$	7.68487e11	0.596719	0.298359	−	0.954454i	$-0.403561\pi$
$491$	7.68487e11	0.596719	0.298359	+	0.954454i	$0.403561\pi$
$492$	1.45530e11	0.111972
$493$	2.70013e11	0.205861
$494$	8.43837e11	0.637510
$495$	2.24624e9	0.00168164
$496$	−6.65523e10	−0.0493737
$497$	−1.00922e12	−0.741960
$498$	7.30167e11	0.531973
$499$	2.27431e12	1.64209	0.821044	−	0.570865i	$-0.193392\pi$
$499$	2.27431e12	1.64209	0.821044	+	0.570865i	$0.193392\pi$
$500$	6.11766e10	0.0437744
$501$	−6.37385e11	−0.451994
$502$	4.13437e11	0.290565
$503$	−1.50660e11	−0.104940	−0.0524700	−	0.998623i	$-0.516709\pi$
$503$	−1.50660e11	−0.104940	−0.0524700	+	0.998623i	$0.516709\pi$
$504$	−3.83374e11	−0.264658
$505$	4.66133e10	0.0318932
$506$	3.53323e8	0.000239604 0
$507$	−4.21440e11	−0.283270
$508$	−4.33283e11	−0.288659
$509$	6.47058e11	0.427281	0.213640	−	0.976912i	$-0.431468\pi$
$509$	6.47058e11	0.427281	0.213640	+	0.976912i	$0.431468\pi$
$510$	3.40492e10	0.0222865
$511$	−7.78380e11	−0.505007
$512$	−7.49439e11	−0.481971
$513$	−3.81793e11	−0.243388
$514$	6.23006e11	0.393693
$515$	−1.06154e11	−0.0664972
$516$	−6.48165e11	−0.402497
$517$	−4.00651e10	−0.0246638
$518$	−1.00350e12	−0.612397
$519$	−8.71999e11	−0.527549
$520$	5.51559e10	0.0330809
$521$	−1.54003e12	−0.915713	−0.457857	−	0.889026i	$-0.651383\pi$
$521$	−1.54003e12	−0.915713	−0.457857	+	0.889026i	$0.651383\pi$
$522$	6.57663e10	0.0387691
$523$	2.04280e12	1.19390	0.596949	−	0.802279i	$-0.296379\pi$
$523$	2.04280e12	1.19390	0.596949	+	0.802279i	$0.296379\pi$
$524$	9.30870e11	0.539384
$525$	−7.51138e11	−0.431522
$526$	−8.87459e11	−0.505490
$527$	4.41185e11	0.249157
$528$	−2.94765e10	−0.0165053
$529$	−1.80114e12	−0.999991
$530$	−9.85160e10	−0.0542332
$531$	7.95020e10	0.0433963
$532$	8.76864e11	0.474602
$533$	5.14639e11	0.276204
$534$	−4.84302e11	−0.257739
$535$	−5.69685e10	−0.0300637
$536$	3.39682e12	1.77759
$537$	−3.79958e11	−0.197175
$538$	−2.88018e11	−0.148217
$539$	−9.93204e10	−0.0506861
$540$	−8.33097e9	−0.00421623
$541$	−3.00028e12	−1.50582	−0.752912	−	0.658121i	$-0.771352\pi$
$541$	−3.00028e12	−1.50582	−0.752912	+	0.658121i	$0.771352\pi$
$542$	2.43504e12	1.21202
$543$	5.64899e11	0.278851
$544$	2.26066e12	1.10673
$545$	−7.82747e10	−0.0380047
$546$	−4.52591e11	−0.217941
$547$	2.43565e12	1.16325	0.581625	−	0.813457i	$-0.302417\pi$
$547$	2.43565e12	1.16325	0.581625	+	0.813457i	$0.302417\pi$
$548$	−1.51075e12	−0.715617
$549$	−3.24521e11	−0.152464
$550$	−1.74581e11	−0.0813512
$551$	−4.50587e11	−0.208256
$552$	−3.92534e9	−0.00179950
$553$	−2.58494e12	−1.17540
$554$	−7.11559e9	−0.00320935
$555$	−6.53216e10	−0.0292239
$556$	6.18961e11	0.274680
$557$	1.08394e12	0.477151	0.238575	−	0.971124i	$-0.423320\pi$
$557$	1.08394e12	0.477151	0.238575	+	0.971124i	$0.423320\pi$
$558$	1.07458e11	0.0469230
$559$	−2.29211e12	−0.992848
$560$	−1.88744e10	−0.00811012
$561$	1.95404e11	0.0832914
$562$	2.80743e12	1.18712
$563$	−3.18803e12	−1.33732	−0.668659	−	0.743569i	$-0.733131\pi$
$563$	−3.18803e12	−1.33732	−0.668659	+	0.743569i	$0.733131\pi$
$564$	1.48595e11	0.0618372
$565$	1.73408e10	0.00715897
$566$	−4.87950e11	−0.199849
$567$	2.04774e11	0.0832055
$568$	2.60594e12	1.05050
$569$	2.82225e12	1.12873	0.564366	−	0.825525i	$-0.309121\pi$
$569$	2.82225e12	1.12873	0.564366	+	0.825525i	$0.309121\pi$
$570$	−5.68201e10	−0.0225458
$571$	−3.48287e12	−1.37112	−0.685559	−	0.728017i	$-0.740442\pi$
$571$	−3.48287e12	−1.37112	−0.685559	+	0.728017i	$0.740442\pi$
$572$	1.05670e11	0.0412734
$573$	−1.43342e12	−0.555493
$574$	−5.32362e11	−0.204693
$575$	−7.69086e9	−0.00293406
$576$	7.68776e11	0.291004
$577$	8.09796e11	0.304148	0.152074	−	0.988369i	$-0.451405\pi$
$577$	8.09796e11	0.304148	0.152074	+	0.988369i	$0.451405\pi$
$578$	1.06673e12	0.397540
$579$	−1.51255e12	−0.559314
$580$	−9.83211e9	−0.00360762
$581$	2.68315e12	0.976907
$582$	1.78630e12	0.645358
$583$	−5.65369e11	−0.202686
$584$	2.00989e12	0.715014
$585$	−2.94609e10	−0.0104003
$586$	2.84365e12	0.996179
$587$	2.65276e12	0.922203	0.461101	−	0.887348i	$-0.347454\pi$
$587$	2.65276e12	0.922203	0.461101	+	0.887348i	$0.347454\pi$
$588$	3.68364e11	0.127081
$589$	−7.36233e11	−0.252056
$590$	1.18318e10	0.00401993
$591$	2.94133e12	0.991744
$592$	8.57186e11	0.286832
$593$	−1.08368e12	−0.359879	−0.179940	−	0.983678i	$-0.557590\pi$
$593$	−1.08368e12	−0.359879	−0.179940	+	0.983678i	$0.557590\pi$
$594$	4.75940e10	0.0156860
$595$	1.25121e11	0.0409265
$596$	7.48654e11	0.243037
$597$	−4.82212e11	−0.155365
$598$	−4.63405e9	−0.00148186
$599$	−1.57285e12	−0.499191	−0.249595	−	0.968350i	$-0.580298\pi$
$599$	−1.57285e12	−0.499191	−0.249595	+	0.968350i	$0.580298\pi$
$600$	1.93955e12	0.610970
$601$	8.26489e10	0.0258406	0.0129203	−	0.999917i	$-0.495887\pi$
$601$	8.26489e10	0.0258406	0.0129203	+	0.999917i	$0.495887\pi$
$602$	2.37105e12	0.735793
$603$	−1.81437e12	−0.558853
$604$	−2.05597e12	−0.628566
$605$	−1.42144e11	−0.0431350
$606$	9.87654e11	0.297494
$607$	−1.82660e12	−0.546127	−0.273063	−	0.961996i	$-0.588037\pi$
$607$	−1.82660e12	−0.546127	−0.273063	+	0.961996i	$0.588037\pi$
$608$	−3.77251e12	−1.11960
$609$	2.41672e11	0.0711949
$610$	−4.82966e10	−0.0141232
$611$	5.25479e11	0.152535
$612$	−7.24723e11	−0.208829
$613$	−8.02251e11	−0.229476	−0.114738	−	0.993396i	$-0.536603\pi$
$613$	−8.02251e11	−0.229476	−0.114738	+	0.993396i	$0.536603\pi$
$614$	4.75406e12	1.34992
$615$	−3.46534e10	−0.00976806
$616$	−3.27433e11	−0.0916239
$617$	1.88160e11	0.0522691	0.0261345	−	0.999658i	$-0.491680\pi$
$617$	1.88160e11	0.0522691	0.0261345	+	0.999658i	$0.491680\pi$
$618$	−2.24921e12	−0.620272
$619$	3.64562e12	0.998076	0.499038	−	0.866580i	$-0.333687\pi$
$619$	3.64562e12	0.998076	0.499038	+	0.866580i	$0.333687\pi$
$620$	−1.60651e10	−0.00436637
$621$	2.09667e9	0.000565742 0
$622$	2.92287e12	0.782984
$623$	−1.77967e12	−0.473308
$624$	3.86602e11	0.102078
$625$	3.79284e12	0.994270
$626$	1.35751e12	0.353311
$627$	−3.26083e11	−0.0842604
$628$	1.21778e12	0.312429
$629$	−5.68241e12	−1.44745
$630$	3.04754e10	0.00770757
$631$	−6.95665e12	−1.74690	−0.873450	−	0.486914i	$-0.838123\pi$
$631$	−6.95665e12	−1.74690	−0.873450	+	0.486914i	$0.838123\pi$
$632$	6.67469e12	1.66419
$633$	3.05667e12	0.756714
$634$	−3.66381e12	−0.900599
$635$	1.03173e11	0.0251816
$636$	2.09687e12	0.508176
$637$	1.30265e12	0.313473
$638$	5.61698e10	0.0134218
$639$	−1.39193e12	−0.330266
$640$	−4.98522e10	−0.0117456
$641$	−6.18919e12	−1.44801	−0.724007	−	0.689792i	$-0.757702\pi$
$641$	−6.18919e12	−1.44801	−0.724007	+	0.689792i	$0.757702\pi$
$642$	−1.20706e12	−0.280428
$643$	2.77548e11	0.0640307	0.0320154	−	0.999487i	$-0.489807\pi$
$643$	2.77548e11	0.0640307	0.0320154	+	0.999487i	$0.489807\pi$
$644$	−4.81543e9	−0.00110319
$645$	1.54340e11	0.0351124
$646$	−4.94286e12	−1.11669
$647$	−6.51803e12	−1.46234	−0.731168	−	0.682197i	$-0.761024\pi$
$647$	−6.51803e12	−1.46234	−0.731168	+	0.682197i	$0.761024\pi$
$648$	−5.28757e11	−0.117806
$649$	6.79013e10	0.0150237
$650$	2.28973e12	0.503124
$651$	3.94879e11	0.0861686
$652$	−1.95070e12	−0.422742
$653$	7.85123e12	1.68977	0.844887	−	0.534945i	$-0.179668\pi$
$653$	7.85123e12	1.68977	0.844887	+	0.534945i	$0.179668\pi$
$654$	−1.65850e12	−0.354500
$655$	−2.21658e11	−0.0470540
$656$	4.54742e11	0.0958732
$657$	−1.07356e12	−0.224792
$658$	−5.43575e11	−0.113043
$659$	3.89784e11	0.0805081	0.0402540	−	0.999189i	$-0.487183\pi$
$659$	3.89784e11	0.0805081	0.0402540	+	0.999189i	$0.487183\pi$
$660$	−7.11534e9	−0.00145965
$661$	1.65637e12	0.337482	0.168741	−	0.985660i	$-0.446030\pi$
$661$	1.65637e12	0.337482	0.168741	+	0.985660i	$0.446030\pi$
$662$	6.07720e12	1.22982
$663$	−2.56284e12	−0.515123
$664$	−6.92829e12	−1.38315
$665$	−2.08798e11	−0.0414027
$666$	−1.38405e12	−0.272595
$667$	2.47447e9	0.000484078 0
$668$	2.01902e12	0.392326
$669$	1.37098e12	0.264614
$670$	−2.70022e11	−0.0517682
$671$	−2.77167e11	−0.0527826
$672$	2.02338e12	0.382751
$673$	8.32730e11	0.156472	0.0782360	−	0.996935i	$-0.475071\pi$
$673$	8.32730e11	0.156472	0.0782360	+	0.996935i	$0.475071\pi$
$674$	−3.36254e12	−0.627622
$675$	−1.03599e12	−0.192082
$676$	1.33498e12	0.245875
$677$	−1.03042e13	−1.88524	−0.942620	−	0.333868i	$-0.891646\pi$
$677$	−1.03042e13	−1.88524	−0.942620	+	0.333868i	$0.891646\pi$
$678$	3.67420e11	0.0667774
$679$	6.56414e12	1.18512
$680$	−3.23081e11	−0.0579457
$681$	6.36473e12	1.13401
$682$	9.17782e10	0.0162446
$683$	3.22944e12	0.567850	0.283925	−	0.958847i	$-0.408363\pi$
$683$	3.22944e12	0.567850	0.283925	+	0.958847i	$0.408363\pi$
$684$	1.20939e12	0.211258
$685$	3.59738e11	0.0624279
$686$	−4.41544e12	−0.761229
$687$	−3.39867e12	−0.582108
$688$	−2.02534e12	−0.344627
$689$	7.41517e12	1.25353
$690$	3.12036e8	5.24063e−5 0
$691$	−6.35783e12	−1.06086	−0.530430	−	0.847729i	$-0.677969\pi$
$691$	−6.35783e12	−1.06086	−0.530430	+	0.847729i	$0.677969\pi$
$692$	2.76220e12	0.457907
$693$	1.74894e11	0.0288055
$694$	−2.09578e11	−0.0342948
$695$	−1.47386e11	−0.0239621
$696$	−6.24033e11	−0.100801
$697$	−3.01455e12	−0.483810
$698$	7.45263e12	1.18839
$699$	−2.44706e12	−0.387702
$700$	2.37935e12	0.374557
$701$	−6.24586e11	−0.0976925	−0.0488463	−	0.998806i	$-0.515554\pi$
$701$	−6.24586e11	−0.0976925	−0.0488463	+	0.998806i	$0.515554\pi$
$702$	−6.24224e11	−0.0970116
$703$	9.48259e12	1.46429
$704$	6.56598e11	0.100745
$705$	−3.53834e10	−0.00539446
$706$	−1.42811e12	−0.216342
$707$	3.62935e12	0.546312
$708$	−2.51835e11	−0.0376675
$709$	−5.99601e12	−0.891157	−0.445579	−	0.895243i	$-0.647002\pi$
$709$	−5.99601e12	−0.891157	−0.445579	+	0.895243i	$0.647002\pi$
$710$	−2.07154e11	−0.0305936
$711$	−3.56521e12	−0.523204
$712$	4.59537e12	0.670132
$713$	4.04314e9	0.000585889 0
$714$	2.65110e12	0.381754
$715$	−2.51620e10	−0.00360054
$716$	1.20358e12	0.171146
$717$	5.03937e12	0.712099
$718$	5.52779e12	0.776232
$719$	−5.44093e12	−0.759265	−0.379632	−	0.925137i	$-0.623949\pi$
$719$	−5.44093e12	−0.759265	−0.379632	+	0.925137i	$0.623949\pi$
$720$	−2.60320e10	−0.00361004
$721$	−8.26522e12	−1.13906
$722$	3.09131e12	0.423375
$723$	1.22532e12	0.166774
$724$	−1.78941e12	−0.242039
$725$	−1.22266e12	−0.164356
$726$	−3.01178e12	−0.402355
$727$	3.33589e11	0.0442902	0.0221451	−	0.999755i	$-0.492950\pi$
$727$	3.33589e11	0.0442902	0.0221451	+	0.999755i	$0.492950\pi$
$728$	4.29448e12	0.566656
$729$	2.82430e11	0.0370370
$730$	−1.59772e11	−0.0208232
$731$	1.34263e13	1.73911
$732$	1.02797e12	0.132337
$733$	6.61739e12	0.846680	0.423340	−	0.905971i	$-0.360858\pi$
$733$	6.61739e12	0.846680	0.423340	+	0.905971i	$0.360858\pi$
$734$	1.24498e12	0.158317
$735$	−8.77144e10	−0.0110861
$736$	2.07173e10	0.00260245
$737$	−1.54962e12	−0.193474
$738$	−7.34245e11	−0.0911145
$739$	−5.63499e12	−0.695014	−0.347507	−	0.937677i	$-0.612972\pi$
$739$	−5.63499e12	−0.695014	−0.347507	+	0.937677i	$0.612972\pi$
$740$	2.06917e11	0.0253660
$741$	4.27677e12	0.521116
$742$	−7.67053e12	−0.928983
$743$	−1.64104e13	−1.97547	−0.987735	−	0.156140i	$-0.950095\pi$
$743$	−1.64104e13	−1.97547	−0.987735	+	0.156140i	$0.950095\pi$
$744$	−1.01963e12	−0.122002
$745$	−1.78268e11	−0.0212017
$746$	5.63337e12	0.665953
$747$	3.70067e12	0.434848
$748$	−6.18973e11	−0.0722960
$749$	−4.43561e12	−0.514974
$750$	−3.08655e11	−0.0356204
$751$	4.91387e10	0.00563694	0.00281847	−	0.999996i	$-0.499103\pi$
$751$	4.91387e10	0.00563694	0.00281847	+	0.999996i	$0.499103\pi$
$752$	4.64320e11	0.0529465
$753$	2.09540e12	0.237515
$754$	−7.36702e11	−0.0830081
$755$	4.89565e11	0.0548339
$756$	−6.48656e11	−0.0722215
$757$	−4.10791e12	−0.454663	−0.227332	−	0.973817i	$-0.573000\pi$
$757$	−4.10791e12	−0.454663	−0.227332	+	0.973817i	$0.573000\pi$
$758$	−1.23346e13	−1.35710
$759$	1.79073e9	0.000195858 0
$760$	5.39146e11	0.0586199
$761$	−3.72963e12	−0.403121	−0.201560	−	0.979476i	$-0.564601\pi$
$761$	−3.72963e12	−0.403121	−0.201560	+	0.979476i	$0.564601\pi$
$762$	2.18605e12	0.234889
$763$	−6.09453e12	−0.650998
$764$	4.54060e12	0.482162
$765$	1.72570e11	0.0182175
$766$	−8.97163e12	−0.941547
$767$	−8.90567e11	−0.0929153
$768$	−5.91570e12	−0.613594
$769$	−5.30984e12	−0.547537	−0.273768	−	0.961796i	$-0.588270\pi$
$769$	−5.30984e12	−0.547537	−0.273768	+	0.961796i	$0.588270\pi$
$770$	2.60285e10	0.00266834
$771$	3.15755e12	0.321814
$772$	4.79124e12	0.485479
$773$	1.53805e13	1.54940	0.774700	−	0.632329i	$-0.217901\pi$
$773$	1.53805e13	1.54940	0.774700	+	0.632329i	$0.217901\pi$
$774$	3.27020e12	0.327522
$775$	−1.99775e12	−0.198923
$776$	−1.69496e13	−1.67796
$777$	−5.08599e12	−0.500588
$778$	−2.06886e11	−0.0202453
$779$	5.03057e12	0.489439
$780$	9.33221e10	0.00902732
$781$	−1.18883e12	−0.114337
$782$	2.71444e10	0.00259567
$783$	3.33320e11	0.0316908
$784$	1.15104e12	0.108810
$785$	−2.89977e11	−0.0272552
$786$	−4.69653e12	−0.438910
$787$	2.05993e12	0.191410	0.0957052	−	0.995410i	$-0.469489\pi$
$787$	2.05993e12	0.191410	0.0957052	+	0.995410i	$0.469489\pi$
$788$	−9.31712e12	−0.860823
$789$	−4.49786e12	−0.413199
$790$	−5.30590e11	−0.0484660
$791$	1.35017e12	0.122629
$792$	−4.51602e11	−0.0407843
$793$	3.63522e12	0.326439
$794$	−7.28418e12	−0.650412
$795$	−4.99303e11	−0.0443315
$796$	1.52748e12	0.134855
$797$	−6.13048e12	−0.538186	−0.269093	−	0.963114i	$-0.586724\pi$
$797$	−6.13048e12	−0.538186	−0.269093	+	0.963114i	$0.586724\pi$
$798$	−4.42406e12	−0.386196
$799$	−3.07805e12	−0.267187
$800$	−1.02366e13	−0.883592
$801$	−2.45456e12	−0.210682
$802$	−1.12540e13	−0.960559
$803$	−9.16908e11	−0.0778226
$804$	5.74730e12	0.485078
$805$	1.14664e9	9.62381e−5 0
$806$	−1.20373e12	−0.100466
$807$	−1.45975e12	−0.121156
$808$	−9.37150e12	−0.773496
$809$	1.02968e13	0.845147	0.422574	−	0.906329i	$-0.361127\pi$
$809$	1.02968e13	0.845147	0.422574	+	0.906329i	$0.361127\pi$
$810$	4.20324e10	0.00343085
$811$	1.95327e13	1.58551	0.792754	−	0.609541i	$-0.208646\pi$
$811$	1.95327e13	1.58551	0.792754	+	0.609541i	$0.208646\pi$
$812$	−7.65536e11	−0.0617964
$813$	1.23414e13	0.990734
$814$	−1.18209e12	−0.0943716
$815$	4.64497e11	0.0368786
$816$	−2.26456e12	−0.178804
$817$	−2.24053e13	−1.75934
$818$	−4.86931e12	−0.380258
$819$	−2.29385e12	−0.178150
$820$	1.09770e11	0.00847857
$821$	−4.94835e12	−0.380116	−0.190058	−	0.981773i	$-0.560868\pi$
$821$	−4.94835e12	−0.380116	−0.190058	+	0.981773i	$0.560868\pi$
$822$	7.62222e12	0.582315
$823$	−7.29946e12	−0.554615	−0.277308	−	0.960781i	$-0.589442\pi$
$823$	−7.29946e12	−0.554615	−0.277308	+	0.960781i	$0.589442\pi$
$824$	2.13420e13	1.61273
$825$	−8.84818e11	−0.0664984
$826$	9.21236e11	0.0688590
$827$	−6.55140e12	−0.487034	−0.243517	−	0.969897i	$-0.578301\pi$
$827$	−6.55140e12	−0.487034	−0.243517	+	0.969897i	$0.578301\pi$
$828$	−6.64155e9	−0.000491058 0
$829$	6.85363e12	0.503994	0.251997	−	0.967728i	$-0.418913\pi$
$829$	6.85363e12	0.503994	0.251997	+	0.967728i	$0.418913\pi$
$830$	5.50749e11	0.0402812
$831$	−3.60636e10	−0.00262340
$832$	−8.61169e12	−0.623065
$833$	−7.63039e12	−0.549091
$834$	−3.12286e12	−0.223514
$835$	−4.80767e11	−0.0342251
$836$	1.03292e12	0.0731371
$837$	5.44625e11	0.0383560
$838$	−1.76270e13	−1.23475
$839$	−1.69365e12	−0.118003	−0.0590017	−	0.998258i	$-0.518792\pi$
$839$	−1.69365e12	−0.118003	−0.0590017	+	0.998258i	$0.518792\pi$
$840$	−2.89171e11	−0.0200400
$841$	−1.41138e13	−0.972884
$842$	5.95231e12	0.408114
$843$	1.42288e13	0.970384
$844$	−9.68249e12	−0.656820
$845$	−3.17884e11	−0.0214493
$846$	−7.49711e11	−0.0503185
$847$	−1.10674e13	−0.738877
$848$	6.55214e12	0.435113
$849$	−2.47305e12	−0.163361
$850$	−1.34123e13	−0.881291
$851$	−5.20751e10	−0.00340367
$852$	4.40917e12	0.286668
$853$	5.29571e12	0.342495	0.171247	−	0.985228i	$-0.445220\pi$
$853$	5.29571e12	0.342495	0.171247	+	0.985228i	$0.445220\pi$
$854$	−3.76041e12	−0.241922
$855$	−2.87978e11	−0.0184295
$856$	1.14534e13	0.729125
$857$	1.96625e12	0.124516	0.0622579	−	0.998060i	$-0.480170\pi$
$857$	1.96625e12	0.124516	0.0622579	+	0.998060i	$0.480170\pi$
$858$	−5.33139e11	−0.0335852
$859$	9.30080e12	0.582842	0.291421	−	0.956595i	$-0.405872\pi$
$859$	9.30080e12	0.582842	0.291421	+	0.956595i	$0.405872\pi$
$860$	−4.88898e11	−0.0304772
$861$	−2.69814e12	−0.167321
$862$	−1.32713e13	−0.818713
$863$	1.38352e13	0.849059	0.424530	−	0.905414i	$-0.360439\pi$
$863$	1.38352e13	0.849059	0.424530	+	0.905414i	$0.360439\pi$
$864$	2.79070e12	0.170373
$865$	−6.57730e11	−0.0399462
$866$	−1.84995e13	−1.11771
$867$	5.40648e12	0.324959
$868$	−1.25084e12	−0.0747934
$869$	−3.04498e12	−0.181132
$870$	4.96061e10	0.00293561
$871$	2.03242e13	1.19655
$872$	1.57370e13	0.921715
$873$	9.05340e12	0.527531
$874$	−4.52976e10	−0.00262587
$875$	−1.13422e12	−0.0654126
$876$	3.40067e12	0.195117
$877$	−5.14801e11	−0.0293860	−0.0146930	−	0.999892i	$-0.504677\pi$
$877$	−5.14801e11	−0.0293860	−0.0146930	+	0.999892i	$0.504677\pi$
$878$	7.02872e12	0.399164
$879$	1.44123e13	0.814301
$880$	−2.22335e10	−0.00124979
$881$	−1.48523e13	−0.830621	−0.415310	−	0.909680i	$-0.636327\pi$
$881$	−1.48523e13	−0.830621	−0.415310	+	0.909680i	$0.636327\pi$
$882$	−1.85851e12	−0.103409
$883$	7.61722e12	0.421671	0.210835	−	0.977522i	$-0.432382\pi$
$883$	7.61722e12	0.421671	0.210835	+	0.977522i	$0.432382\pi$
$884$	8.11821e12	0.447121
$885$	5.99667e10	0.00328598
$886$	−1.14146e13	−0.622311
$887$	−1.19196e13	−0.646556	−0.323278	−	0.946304i	$-0.604785\pi$
$887$	−1.19196e13	−0.646556	−0.323278	+	0.946304i	$0.604785\pi$
$888$	1.31328e13	0.708757
$889$	8.03311e12	0.431346
$890$	−3.65299e11	−0.0195161
$891$	2.41218e11	0.0128221
$892$	−4.34279e12	−0.229682
$893$	5.13653e12	0.270295
$894$	−3.77719e12	−0.197765
$895$	−2.86595e11	−0.0149302
$896$	−3.88153e12	−0.201195
$897$	−2.34865e10	−0.00121130
$898$	−2.30701e13	−1.18388
$899$	6.42760e11	0.0328194
$900$	3.28165e12	0.166725
$901$	−4.34351e13	−2.19573
$902$	−6.27106e11	−0.0315436
$903$	1.20171e13	0.601455
$904$	−3.48632e12	−0.173624
$905$	4.26092e11	0.0211147
$906$	1.03730e13	0.511480
$907$	8.17267e12	0.400988	0.200494	−	0.979695i	$-0.435745\pi$
$907$	8.17267e12	0.400988	0.200494	+	0.979695i	$0.435745\pi$
$908$	−2.01613e13	−0.984311
$909$	5.00568e12	0.243179
$910$	−3.41380e11	−0.0165026
$911$	−3.55337e12	−0.170926	−0.0854630	−	0.996341i	$-0.527237\pi$
$911$	−3.55337e12	−0.170926	−0.0854630	+	0.996341i	$0.527237\pi$
$912$	3.77901e12	0.180885
$913$	3.16067e12	0.150543
$914$	1.48745e13	0.704992
$915$	−2.44779e11	−0.0115446
$916$	1.07658e13	0.505264
$917$	−1.72584e13	−0.806007
$918$	3.65645e12	0.169929
$919$	−2.00027e12	−0.0925060	−0.0462530	−	0.998930i	$-0.514728\pi$
$919$	−2.00027e12	−0.0925060	−0.0462530	+	0.998930i	$0.514728\pi$
$920$	−2.96080e9	−0.000136259 0
$921$	2.40948e13	1.10346
$922$	−6.66617e12	−0.303799
$923$	1.55922e13	0.707130
$924$	−5.54006e11	−0.0250029
$925$	2.57308e13	1.15562
$926$	1.11514e13	0.498401
$927$	−1.13996e13	−0.507026
$928$	3.29355e12	0.145780
$929$	1.77193e13	0.780507	0.390253	−	0.920707i	$-0.372387\pi$
$929$	1.77193e13	0.780507	0.390253	+	0.920707i	$0.372387\pi$
$930$	8.10535e10	0.00355303
$931$	1.27333e13	0.555479
$932$	7.75146e12	0.336521
$933$	1.48138e13	0.640030
$934$	1.72332e13	0.740977
$935$	1.47389e11	0.00630685
$936$	5.92304e12	0.252234
$937$	2.49060e13	1.05554	0.527771	−	0.849387i	$-0.323028\pi$
$937$	2.49060e13	1.05554	0.527771	+	0.849387i	$0.323028\pi$
$938$	−2.10241e13	−0.886759
$939$	6.88018e12	0.288805
$940$	1.12082e11	0.00468233
$941$	−3.15204e13	−1.31050	−0.655252	−	0.755410i	$-0.727438\pi$
$941$	−3.15204e13	−1.31050	−0.655252	+	0.755410i	$0.727438\pi$
$942$	−6.14409e12	−0.254231
$943$	−2.76261e10	−0.00113767
$944$	−7.86917e11	−0.0322519
$945$	1.54457e11	0.00630035
$946$	2.79302e12	0.113387
$947$	−3.38266e13	−1.36673	−0.683367	−	0.730075i	$-0.739485\pi$
$947$	−3.38266e13	−1.36673	−0.683367	+	0.730075i	$0.739485\pi$
$948$	1.12934e13	0.454136
$949$	1.20258e13	0.481301
$950$	2.23820e13	0.891544
$951$	−1.85691e13	−0.736171
$952$	−2.51553e13	−0.992577
$953$	1.17005e13	0.459503	0.229751	−	0.973249i	$-0.426209\pi$
$953$	1.17005e13	0.459503	0.229751	+	0.973249i	$0.426209\pi$
$954$	−1.05794e13	−0.413515
$955$	−1.08120e12	−0.0420621
$956$	−1.59630e13	−0.618094
$957$	2.84683e11	0.0109713
$958$	−3.57695e12	−0.137204
$959$	2.80095e13	1.06935
$960$	5.79872e11	0.0220349
$961$	−2.53894e13	−0.960278
$962$	1.55039e13	0.583650
$963$	−6.11769e12	−0.229229
$964$	−3.88140e12	−0.144758
$965$	−1.14088e12	−0.0423515
$966$	2.42954e10	0.000897690 0
$967$	5.41005e13	1.98968	0.994838	−	0.101475i	$-0.0323563\pi$
$967$	5.41005e13	1.98968	0.994838	+	0.101475i	$0.0323563\pi$
$968$	2.85778e13	1.04614
$969$	−2.50516e13	−0.912807
$970$	1.34737e12	0.0488667
$971$	1.68712e12	0.0609059	0.0304529	−	0.999536i	$-0.490305\pi$
$971$	1.68712e12	0.0609059	0.0304529	+	0.999536i	$0.490305\pi$
$972$	−8.94641e11	−0.0321477
$973$	−1.14756e13	−0.410457
$974$	1.11941e13	0.398542
$975$	1.16049e13	0.411265
$976$	3.21213e12	0.113310
$977$	−9.67341e12	−0.339668	−0.169834	−	0.985473i	$-0.554323\pi$
$977$	−9.67341e12	−0.339668	−0.169834	+	0.985473i	$0.554323\pi$
$978$	9.84188e12	0.343996
$979$	−2.09640e12	−0.0729376
$980$	2.77849e11	0.00962260
$981$	−8.40571e12	−0.289777
$982$	1.22818e13	0.421465
$983$	3.21482e13	1.09816	0.549080	−	0.835770i	$-0.314978\pi$
$983$	3.21482e13	1.09816	0.549080	+	0.835770i	$0.314978\pi$
$984$	6.96700e12	0.236901
$985$	2.21858e12	0.0750952
$986$	4.31530e12	0.145400
$987$	−2.75498e12	−0.0924039
$988$	−1.35474e13	−0.452323
$989$	1.23042e11	0.00408949
$990$	3.58991e10	0.00118775
$991$	−3.41521e13	−1.12483	−0.562413	−	0.826856i	$-0.690127\pi$
$991$	−3.41521e13	−1.12483	−0.562413	+	0.826856i	$0.690127\pi$
$992$	5.38146e12	0.176440
$993$	3.08007e13	1.00529
$994$	−1.61291e13	−0.524050
$995$	−3.63723e11	−0.0117643
$996$	−1.17225e13	−0.377443
$997$	3.99927e13	1.28190	0.640948	−	0.767584i	$-0.278541\pi$
$997$	3.99927e13	1.28190	0.640948	+	0.767584i	$0.278541\pi$
$998$	3.63476e13	1.15981
$999$	−7.01471e12	−0.222825

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.a.1.15	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.a.1.15	✓	21	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+15.9818 q^{2} +81.0000 q^{3} -256.580 q^{4} +61.0966 q^{5} +1294.53 q^{6} +4757.03 q^{7} -12283.3 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+15.9818 q^{2} +81.0000 q^{3} -256.580 q^{4} +61.0966 q^{5} +1294.53 q^{6} +4757.03 q^{7} -12283.3 q^{8} +6561.00 q^{9} +976.437 q^{10} +5603.63 q^{11} -20783.0 q^{12} -73495.1 q^{13} +76026.1 q^{14} +4948.83 q^{15} -64941.2 q^{16} +430505. q^{17} +104857. q^{18} -718411. q^{19} -15676.2 q^{20} +385319. q^{21} +89556.4 q^{22} +3945.26 q^{23} -994950. q^{24} -1.94939e6 q^{25} -1.17459e6 q^{26} +531441. q^{27} -1.22056e6 q^{28} +627200. q^{29} +79091.4 q^{30} +1.02481e6 q^{31} +5.25119e6 q^{32} +453894. q^{33} +6.88027e6 q^{34} +290638. q^{35} -1.68342e6 q^{36} -1.31994e7 q^{37} -1.14815e7 q^{38} -5.95311e6 q^{39} -750470. q^{40} -7.00235e6 q^{41} +6.15811e6 q^{42} +3.11873e7 q^{43} -1.43778e6 q^{44} +400855. q^{45} +63052.5 q^{46} -7.14985e6 q^{47} -5.26024e6 q^{48} -1.77243e7 q^{49} -3.11549e7 q^{50} +3.48709e7 q^{51} +1.88574e7 q^{52} -1.00893e8 q^{53} +8.49341e6 q^{54} +342363. q^{55} -5.84322e7 q^{56} -5.81913e7 q^{57} +1.00238e7 q^{58} +1.21174e7 q^{59} -1.26977e6 q^{60} -4.94621e7 q^{61} +1.63783e7 q^{62} +3.12109e7 q^{63} +1.17174e8 q^{64} -4.49030e6 q^{65} +7.25407e6 q^{66} -2.76538e8 q^{67} -1.10459e8 q^{68} +319566. q^{69} +4.64494e6 q^{70} -2.12153e8 q^{71} -8.05910e7 q^{72} -1.63627e8 q^{73} -2.10951e8 q^{74} -1.57901e8 q^{75} +1.84330e8 q^{76} +2.66566e7 q^{77} -9.51416e7 q^{78} -5.43394e8 q^{79} -3.96769e6 q^{80} +4.30467e7 q^{81} -1.11911e8 q^{82} +5.64040e8 q^{83} -9.88654e7 q^{84} +2.63024e7 q^{85} +4.98430e8 q^{86} +5.08032e7 q^{87} -6.88313e7 q^{88} -3.74114e8 q^{89} +6.40640e6 q^{90} -3.49618e8 q^{91} -1.01228e6 q^{92} +8.30095e7 q^{93} -1.14268e8 q^{94} -4.38925e7 q^{95} +4.25346e8 q^{96} +1.37988e9 q^{97} -2.83267e8 q^{98} +3.67654e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9}+O(q^{10}) \) 21 * q - 66 * q^2 + 1701 * q^3 + 5206 * q^4 - 2964 * q^5 - 5346 * q^6 - 30775 * q^7 - 24621 * q^8 + 137781 * q^9	\( 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9} - 54663 q^{10} - 151769 q^{11} + 421686 q^{12} - 153611 q^{13} - 286771 q^{14} - 240084 q^{15} + 805530 q^{16} - 723621 q^{17} - 433026 q^{18} - 549388 q^{19} - 527311 q^{20} - 2492775 q^{21} + 2973158 q^{22} + 169962 q^{23} - 1994301 q^{24} + 8035779 q^{25} - 2337392 q^{26} + 11160261 q^{27} - 22659054 q^{28} - 16845442 q^{29} - 4427703 q^{30} - 19307976 q^{31} - 44923568 q^{32} - 12293289 q^{33} - 35547496 q^{34} - 34882596 q^{35} + 34156566 q^{36} - 41561129 q^{37} - 52335371 q^{38} - 12442491 q^{39} - 125735038 q^{40} - 68169291 q^{41} - 23228451 q^{42} - 25719587 q^{43} - 126277032 q^{44} - 19446804 q^{45} - 292814271 q^{46} - 174095332 q^{47} + 65247930 q^{48} + 7479350 q^{49} - 227877439 q^{50} - 58613301 q^{51} - 232397708 q^{52} - 228390500 q^{53} - 35075106 q^{54} - 29426208 q^{55} + 326778474 q^{56} - 44500428 q^{57} + 480343762 q^{58} + 254464581 q^{59} - 42712191 q^{60} - 183928964 q^{61} - 21753862 q^{62} - 201914775 q^{63} + 310571245 q^{64} + 5308466 q^{65} + 240825798 q^{66} - 82724114 q^{67} - 138336205 q^{68} + 13766922 q^{69} + 1030274876 q^{70} - 404721965 q^{71} - 161538381 q^{72} + 154162574 q^{73} + 36352054 q^{74} + 650898099 q^{75} + 1068940636 q^{76} - 448535481 q^{77} - 189328752 q^{78} + 272529635 q^{79} - 345587859 q^{80} + 903981141 q^{81} - 38412637 q^{82} + 432518643 q^{83} - 1835383374 q^{84} - 126211490 q^{85} - 3699273072 q^{86} - 1364480802 q^{87} + 170111045 q^{88} - 1255621070 q^{89} - 358643943 q^{90} + 1448885849 q^{91} + 1568933320 q^{92} - 1563946056 q^{93} - 1908445164 q^{94} - 2896546490 q^{95} - 3638809008 q^{96} + 1007235486 q^{97} - 9506868248 q^{98} - 995756409 q^{99}+O(q^{100}) \) 21 * q - 66 * q^2 + 1701 * q^3 + 5206 * q^4 - 2964 * q^5 - 5346 * q^6 - 30775 * q^7 - 24621 * q^8 + 137781 * q^9 - 54663 * q^10 - 151769 * q^11 + 421686 * q^12 - 153611 * q^13 - 286771 * q^14 - 240084 * q^15 + 805530 * q^16 - 723621 * q^17 - 433026 * q^18 - 549388 * q^19 - 527311 * q^20 - 2492775 * q^21 + 2973158 * q^22 + 169962 * q^23 - 1994301 * q^24 + 8035779 * q^25 - 2337392 * q^26 + 11160261 * q^27 - 22659054 * q^28 - 16845442 * q^29 - 4427703 * q^30 - 19307976 * q^31 - 44923568 * q^32 - 12293289 * q^33 - 35547496 * q^34 - 34882596 * q^35 + 34156566 * q^36 - 41561129 * q^37 - 52335371 * q^38 - 12442491 * q^39 - 125735038 * q^40 - 68169291 * q^41 - 23228451 * q^42 - 25719587 * q^43 - 126277032 * q^44 - 19446804 * q^45 - 292814271 * q^46 - 174095332 * q^47 + 65247930 * q^48 + 7479350 * q^49 - 227877439 * q^50 - 58613301 * q^51 - 232397708 * q^52 - 228390500 * q^53 - 35075106 * q^54 - 29426208 * q^55 + 326778474 * q^56 - 44500428 * q^57 + 480343762 * q^58 + 254464581 * q^59 - 42712191 * q^60 - 183928964 * q^61 - 21753862 * q^62 - 201914775 * q^63 + 310571245 * q^64 + 5308466 * q^65 + 240825798 * q^66 - 82724114 * q^67 - 138336205 * q^68 + 13766922 * q^69 + 1030274876 * q^70 - 404721965 * q^71 - 161538381 * q^72 + 154162574 * q^73 + 36352054 * q^74 + 650898099 * q^75 + 1068940636 * q^76 - 448535481 * q^77 - 189328752 * q^78 + 272529635 * q^79 - 345587859 * q^80 + 903981141 * q^81 - 38412637 * q^82 + 432518643 * q^83 - 1835383374 * q^84 - 126211490 * q^85 - 3699273072 * q^86 - 1364480802 * q^87 + 170111045 * q^88 - 1255621070 * q^89 - 358643943 * q^90 + 1448885849 * q^91 + 1568933320 * q^92 - 1563946056 * q^93 - 1908445164 * q^94 - 2896546490 * q^95 - 3638809008 * q^96 + 1007235486 * q^97 - 9506868248 * q^98 - 995756409 * q^99

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