LMFDB - Embedded newform 3.36.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,36,Mod(1,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 36, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 36);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 36 $
Character orbit:	$[\chi]$	$=$	3.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:	$23.2785391901$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{2196841}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 549210 $ x^2 - x - 549210
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{4}\cdot 3\cdot 7 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-740.587$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+218549. q^{2} +1.29140e8 q^{3} +1.34041e10 q^{4} -9.68425e11 q^{5} +2.82235e13 q^{6} -5.65365e14 q^{7} -4.57985e15 q^{8} +1.66772e16 q^{9} +O(q^{10})$	\(q+218549. q^{2} +1.29140e8 q^{3} +1.34041e10 q^{4} -9.68425e11 q^{5} +2.82235e13 q^{6} -5.65365e14 q^{7} -4.57985e15 q^{8} +1.66772e16 q^{9} -2.11649e17 q^{10} -1.62372e18 q^{11} +1.73100e18 q^{12} -2.52538e19 q^{13} -1.23560e20 q^{14} -1.25063e20 q^{15} -1.46148e21 q^{16} +4.37227e21 q^{17} +3.64479e21 q^{18} +1.72036e22 q^{19} -1.29808e22 q^{20} -7.30113e22 q^{21} -3.54863e23 q^{22} -5.13356e23 q^{23} -5.91442e23 q^{24} -1.97254e24 q^{25} -5.51920e24 q^{26} +2.15369e24 q^{27} -7.57819e24 q^{28} -3.39397e25 q^{29} -2.73323e25 q^{30} -9.89761e25 q^{31} -1.62044e26 q^{32} -2.09687e26 q^{33} +9.55557e26 q^{34} +5.47514e26 q^{35} +2.23542e26 q^{36} +4.58147e27 q^{37} +3.75982e27 q^{38} -3.26128e27 q^{39} +4.43524e27 q^{40} -2.87989e28 q^{41} -1.59566e28 q^{42} +6.85354e28 q^{43} -2.17644e28 q^{44} -1.61506e28 q^{45} -1.12194e29 q^{46} -4.79363e26 q^{47} -1.88736e29 q^{48} -5.91811e28 q^{49} -4.31096e29 q^{50} +5.64636e29 q^{51} -3.38503e29 q^{52} +2.32896e30 q^{53} +4.70688e29 q^{54} +1.57245e30 q^{55} +2.58929e30 q^{56} +2.22167e30 q^{57} -7.41751e30 q^{58} +5.75836e30 q^{59} -1.67635e30 q^{60} -2.67580e31 q^{61} -2.16312e31 q^{62} -9.42870e30 q^{63} +1.48016e31 q^{64} +2.44564e31 q^{65} -4.58270e31 q^{66} +7.66448e31 q^{67} +5.86062e31 q^{68} -6.62949e31 q^{69} +1.19659e32 q^{70} -5.08152e31 q^{71} -7.63790e31 q^{72} -2.74698e32 q^{73} +1.00128e33 q^{74} -2.54734e32 q^{75} +2.30597e32 q^{76} +9.17994e32 q^{77} -7.12750e32 q^{78} -2.13670e33 q^{79} +1.41534e33 q^{80} +2.78128e32 q^{81} -6.29399e33 q^{82} -2.22116e33 q^{83} -9.78648e32 q^{84} -4.23422e33 q^{85} +1.49784e34 q^{86} -4.38298e33 q^{87} +7.43639e33 q^{88} +2.07592e34 q^{89} -3.52970e33 q^{90} +1.42776e34 q^{91} -6.88105e33 q^{92} -1.27818e34 q^{93} -1.04765e32 q^{94} -1.66604e34 q^{95} -2.09263e34 q^{96} +1.55170e34 q^{97} -1.29340e34 q^{98} -2.70791e34 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 60912 q^{2} + 258280326 q^{3} + 57142939904 q^{4} - 1333779496740 q^{5} - 7866185608656 q^{6} - 12\!\cdots\!44 q^{7}+ \cdots + 33\!\cdots\!38 q^{9}+O(q^{10}) $ 2 * q - 60912 * q^2 + 258280326 * q^3 + 57142939904 * q^4 - 1333779496740 * q^5 - 7866185608656 * q^6 - 1201512782952944 * q^7 - 7200956480385024 * q^8 + 33354363399333138 * q^9	$ 2 q - 60912 q^{2} + 258280326 q^{3} + 57142939904 q^{4} - 1333779496740 q^{5} - 7866185608656 q^{6} - 12\!\cdots\!44 q^{7}+ \cdots - 24\!\cdots\!08 q^{99}+O(q^{100}) $ 2 * q - 60912 * q^2 + 258280326 * q^3 + 57142939904 * q^4 - 1333779496740 * q^5 - 7866185608656 * q^6 - 1201512782952944 * q^7 - 7200956480385024 * q^8 + 33354363399333138 * q^9 - 109546268366103840 * q^10 - 1474443852221320632 * q^11 + 7379448573501764352 * q^12 + 30005213658205678828 * q^13 + 54218555116626208896 * q^14 - 172244501615061568620 * q^15 - 2231841205794746859520 * q^16 + 6184381389914139549732 * q^17 - 1015840491690090050928 * q^18 - 16041801819745886283464 * q^19 - 28961016325243993797120 * q^20 - 155163556637126809489872 * q^21 - 396579699860875428206016 * q^22 + 493815500335770240457872 * q^23 - 929932693632828302118912 * q^24 - 4749434950612517913953650 * q^25 - 20961946321168144205905056 * q^26 + 4307387926151115532621494 * q^27 - 35402577540025316459804672 * q^28 - 78897034119133299270862548 * q^29 - 14146822952840393572525920 * q^30 - 121361162005932759518102048 * q^31 + 143302306271809670376062976 * q^32 - 190409919410209258491743016 * q^33 + 449143657751740113402393888 * q^34 + 779933046239496469635406560 * q^35 + 952983191632135329204869376 * q^36 + 1665586101311009800179225916 * q^37 + 13050613787750726714918949312 * q^38 + 3874878182670507651373568964 * q^39 + 5392874139550798797233971200 * q^40 - 32980805501198249253748474188 * q^41 + 7001793045385592626901490048 * q^42 + 10123013327213364172045565320 * q^43 - 15235271860221308020423891968 * q^44 - 22243683014422814226622485060 * q^45 - 393659059100782290327277976448 * q^46 - 52868797790119241441973340320 * q^47 - 288220337106450153982150901760 * q^48 - 33315801381283359525177211950 * q^49 + 344939599216803384993788031600 * q^50 + 798652020747678537457137086316 * q^51 + 2078463386549395848792119629312 * q^52 - 311667073507824309034483504068 * q^53 - 131185806678858374661520221264 * q^54 + 1517912603348115987616960289520 * q^55 + 4256698060894361051133439672320 * q^56 - 2071640901815680373226005164632 * q^57 + 5146318056193673657686145949024 * q^58 + 8206652402409843531446945489064 * q^59 - 3740030368887670373731065730560 * q^60 - 40510115780163122120323644143540 * q^61 - 15375406801958157810336643623168 * q^62 - 20037846995778288029192016929136 * q^63 - 44061412872652964817027532324864 * q^64 + 4267286913056298521798082678120 * q^65 - 51214367082524530121219703820608 * q^66 + 9614178644969763076047165071512 * q^67 + 137865760810106900938814269960704 * q^68 + 63771414205287923583278784713136 * q^69 + 54706539117989427731737467528960 * q^70 + 440682364431613985484841574021424 * q^71 - 120091659634772509086649541062656 * q^72 - 137360814802453541976117247925708 * q^73 + 1816151331037101511972964229252576 * q^74 - 613342803679997513248394335444950 * q^75 - 1223517123700955304313856844145664 * q^76 + 823032801538075311095559373941312 * q^77 - 2707029164712904493158084494364128 * q^78 - 1062176452444830588280514345530880 * q^79 + 1696790522509490100466806063759360 * q^80 + 556256778887387022514571552463522 * q^81 - 5125322741804470577254960235914848 * q^82 - 5500428376968501051342971557654344 * q^83 - 4571894634139008391745758290241536 * q^84 - 4896281708923407655277594784149640 * q^85 + 31302341732489137882852872722637888 * q^86 - 10188775846361435686566970599315324 * q^87 + 7045123450598581655224211356532736 * q^88 + 24031331951145259183892358374185236 * q^89 - 1826923022061949738940149630524960 * q^90 - 20875281935852853469733451535930528 * q^91 + 37171500488799640786609596619278336 * q^92 - 15672600243315563531207499929353824 * q^93 + 14536054971850529082624931738946304 * q^94 - 4514020436462465865986658897865200 * q^95 + 18506083190217423137341044018905088 * q^96 + 837150039420646979154473176256452 * q^97 - 20162335337791628242056365171146608 * q^98 - 24589568029451287505732827240351608 * 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 $

$2$	218549.	1.17903	0.589515	−	0.807758i	$-0.299319\pi$
$2$	218549.	1.17903	0.589515	+	0.807758i	$0.299319\pi$
$3$	1.29140e8	0.577350
$3$	1.29140e8	0.577350
$4$	1.34041e10	0.390109
$5$	−9.68425e11	−0.567664	−0.283832	−	0.958874i	$-0.591606\pi$
$5$	−9.68425e11	−0.567664	−0.283832	+	0.958874i	$0.591606\pi$
$6$	2.82235e13	0.680713
$7$	−5.65365e14	−0.918572	−0.459286	−	0.888288i	$-0.651895\pi$
$7$	−5.65365e14	−0.918572	−0.459286	+	0.888288i	$0.651895\pi$
$8$	−4.57985e15	−0.719079
$9$	1.66772e16	0.333333
$10$	−2.11649e17	−0.669292
$11$	−1.62372e18	−0.968588	−0.484294	−	0.874905i	$-0.660923\pi$
$11$	−1.62372e18	−0.968588	−0.484294	+	0.874905i	$0.660923\pi$
$12$	1.73100e18	0.225230
$13$	−2.52538e19	−0.809688	−0.404844	−	0.914386i	$-0.632674\pi$
$13$	−2.52538e19	−0.809688	−0.404844	+	0.914386i	$0.632674\pi$
$14$	−1.23560e20	−1.08302
$15$	−1.25063e20	−0.327741
$16$	−1.46148e21	−1.23792
$17$	4.37227e21	1.28189	0.640946	−	0.767586i	$-0.278542\pi$
$17$	4.37227e21	1.28189	0.640946	+	0.767586i	$0.278542\pi$
$18$	3.64479e21	0.393010
$19$	1.72036e22	0.720162	0.360081	−	0.932921i	$-0.382749\pi$
$19$	1.72036e22	0.720162	0.360081	+	0.932921i	$0.382749\pi$
$20$	−1.29808e22	−0.221451
$21$	−7.30113e22	−0.530338
$22$	−3.54863e23	−1.14199
$23$	−5.13356e23	−0.758895	−0.379447	−	0.925213i	$-0.623886\pi$
$23$	−5.13356e23	−0.758895	−0.379447	+	0.925213i	$0.623886\pi$
$24$	−5.91442e23	−0.415160
$25$	−1.97254e24	−0.677758
$26$	−5.51920e24	−0.954646
$27$	2.15369e24	0.192450
$28$	−7.57819e24	−0.358344
$29$	−3.39397e25	−0.868447	−0.434224	−	0.900805i	$-0.642977\pi$
$29$	−3.39397e25	−0.868447	−0.434224	+	0.900805i	$0.642977\pi$
$30$	−2.73323e25	−0.386416
$31$	−9.89761e25	−0.788317	−0.394158	−	0.919043i	$-0.628964\pi$
$31$	−9.89761e25	−0.788317	−0.394158	+	0.919043i	$0.628964\pi$
$32$	−1.62044e26	−0.740470
$33$	−2.09687e26	−0.559215
$34$	9.55557e26	1.51139
$35$	5.47514e26	0.521440
$36$	2.23542e26	0.130036
$37$	4.58147e27	1.64996	0.824982	−	0.565160i	$-0.191185\pi$
$37$	4.58147e27	1.64996	0.824982	+	0.565160i	$0.191185\pi$
$38$	3.75982e27	0.849092
$39$	−3.26128e27	−0.467474
$40$	4.43524e27	0.408195
$41$	−2.87989e28	−1.72052	−0.860259	−	0.509858i	$-0.829698\pi$
$41$	−2.87989e28	−1.72052	−0.860259	+	0.509858i	$0.829698\pi$
$42$	−1.59566e28	−0.625284
$43$	6.85354e28	1.77917	0.889583	−	0.456773i	$-0.150995\pi$
$43$	6.85354e28	1.77917	0.889583	+	0.456773i	$0.150995\pi$
$44$	−2.17644e28	−0.377855
$45$	−1.61506e28	−0.189221
$46$	−1.12194e29	−0.894759
$47$	−4.79363e26	−0.00262393	−0.00131197	−	0.999999i	$-0.500418\pi$
$47$	−4.79363e26	−0.00262393	−0.00131197	+	0.999999i	$0.500418\pi$
$48$	−1.88736e29	−0.714716
$49$	−5.91811e28	−0.156225
$50$	−4.31096e29	−0.799096
$51$	5.64636e29	0.740100
$52$	−3.38503e29	−0.315867
$53$	2.32896e30	1.55717	0.778583	−	0.627541i	$-0.215939\pi$
$53$	2.32896e30	1.55717	0.778583	+	0.627541i	$0.215939\pi$
$54$	4.70688e29	0.226904
$55$	1.57245e30	0.549832
$56$	2.58929e30	0.660526
$57$	2.22167e30	0.415786
$58$	−7.41751e30	−1.02392
$59$	5.75836e30	0.589371	0.294685	−	0.955594i	$-0.404785\pi$
$59$	5.75836e30	0.589371	0.294685	+	0.955594i	$0.404785\pi$
$60$	−1.67635e30	−0.127855
$61$	−2.67580e31	−1.52820	−0.764102	−	0.645095i	$-0.776818\pi$
$61$	−2.67580e31	−1.52820	−0.764102	+	0.645095i	$0.776818\pi$
$62$	−2.16312e31	−0.929448
$63$	−9.42870e30	−0.306191
$64$	1.48016e31	0.364889
$65$	2.44564e31	0.459630
$66$	−4.58270e31	−0.659330
$67$	7.66448e31	0.847566	0.423783	−	0.905764i	$-0.360702\pi$
$67$	7.66448e31	0.847566	0.423783	+	0.905764i	$0.360702\pi$
$68$	5.86062e31	0.500078
$69$	−6.62949e31	−0.438148
$70$	1.19659e32	0.614793
$71$	−5.08152e31	−0.203691	−0.101846	−	0.994800i	$-0.532475\pi$
$71$	−5.08152e31	−0.203691	−0.101846	+	0.994800i	$0.532475\pi$
$72$	−7.63790e31	−0.239693
$73$	−2.74698e32	−0.677181	−0.338590	−	0.940934i	$-0.609950\pi$
$73$	−2.74698e32	−0.677181	−0.338590	+	0.940934i	$0.609950\pi$
$74$	1.00128e33	1.94535
$75$	−2.54734e32	−0.391304
$76$	2.30597e32	0.280942
$77$	9.17994e32	0.889718
$78$	−7.12750e32	−0.551165
$79$	−2.13670e33	−1.32212	−0.661059	−	0.750334i	$-0.729893\pi$
$79$	−2.13670e33	−1.32212	−0.661059	+	0.750334i	$0.729893\pi$
$80$	1.41534e33	0.702724
$81$	2.78128e32	0.111111
$82$	−6.29399e33	−2.02854
$83$	−2.22116e33	−0.579046	−0.289523	−	0.957171i	$-0.593497\pi$
$83$	−2.22116e33	−0.579046	−0.289523	+	0.957171i	$0.593497\pi$
$84$	−9.78648e32	−0.206890
$85$	−4.23422e33	−0.727683
$86$	1.49784e34	2.09769
$87$	−4.38298e33	−0.501398
$88$	7.43639e33	0.696491
$89$	2.07592e34	1.59545	0.797727	−	0.603018i	$-0.206035\pi$
$89$	2.07592e34	1.59545	0.797727	+	0.603018i	$0.206035\pi$
$90$	−3.52970e33	−0.223097
$91$	1.42776e34	0.743757
$92$	−6.88105e33	−0.296052
$93$	−1.27818e34	−0.455135
$94$	−1.04765e32	−0.00309369
$95$	−1.66604e34	−0.408810
$96$	−2.09263e34	−0.427510
$97$	1.55170e34	0.264426	0.132213	−	0.991221i	$-0.457792\pi$
$97$	1.55170e34	0.264426	0.132213	+	0.991221i	$0.457792\pi$
$98$	−1.29340e34	−0.184194
$99$	−2.70791e34	−0.322863
$100$	−2.64400e34	−0.264400
$101$	−1.03897e35	−0.872929	−0.436464	−	0.899722i	$-0.643770\pi$
$101$	−1.03897e35	−0.872929	−0.436464	+	0.899722i	$0.643770\pi$
$102$	1.23401e35	0.872600
$103$	−1.94833e35	−1.16148	−0.580740	−	0.814089i	$-0.697237\pi$
$103$	−1.94833e35	−1.16148	−0.580740	+	0.814089i	$0.697237\pi$
$104$	1.15659e35	0.582229
$105$	7.07060e34	0.301053
$106$	5.08993e35	1.83594
$107$	−3.61557e35	−1.10652	−0.553262	−	0.833007i	$-0.686617\pi$
$107$	−3.61557e35	−1.10652	−0.553262	+	0.833007i	$0.686617\pi$
$108$	2.88682e34	0.0750766
$109$	−7.33560e35	−1.62357	−0.811786	−	0.583954i	$-0.801505\pi$
$109$	−7.33560e35	−1.62357	−0.811786	+	0.583954i	$0.801505\pi$
$110$	3.43658e35	0.648268
$111$	5.91651e35	0.952607
$112$	8.26271e35	1.13712
$113$	−5.95677e35	−0.701678	−0.350839	−	0.936436i	$-0.614104\pi$
$113$	−5.95677e35	−0.701678	−0.350839	+	0.936436i	$0.614104\pi$
$114$	4.85544e35	0.490223
$115$	4.97147e35	0.430797
$116$	−4.54930e35	−0.338790
$117$	−4.21162e35	−0.269896
$118$	1.25849e36	0.694885
$119$	−2.47193e36	−1.17751
$120$	5.72768e35	0.235671
$121$	−1.73778e35	−0.0618372
$122$	−5.84794e36	−1.80180
$123$	−3.71910e36	−0.993341
$124$	−1.32668e36	−0.307530
$125$	4.72874e36	0.952402
$126$	−2.06063e36	−0.361008
$127$	1.88168e36	0.287065	0.143533	−	0.989646i	$-0.454154\pi$
$127$	1.88168e36	0.287065	0.143533	+	0.989646i	$0.454154\pi$
$128$	8.80267e36	1.17068
$129$	8.85067e36	1.02720
$130$	5.34493e36	0.541918
$131$	6.22324e36	0.551784	0.275892	−	0.961189i	$-0.411027\pi$
$131$	6.22324e36	0.551784	0.275892	+	0.961189i	$0.411027\pi$
$132$	−2.81066e36	−0.218155
$133$	−9.72629e36	−0.661521
$134$	1.67507e37	0.999305
$135$	−2.08569e36	−0.109247
$136$	−2.00244e37	−0.921781
$137$	6.91179e36	0.279886	0.139943	−	0.990160i	$-0.455308\pi$
$137$	6.91179e36	0.279886	0.139943	+	0.990160i	$0.455308\pi$
$138$	−1.44887e37	−0.516589
$139$	−4.10165e37	−1.28884	−0.644421	−	0.764671i	$-0.722901\pi$
$139$	−4.10165e37	−1.28884	−0.644421	+	0.764671i	$0.722901\pi$
$140$	7.33891e36	0.203419
$141$	−6.19051e34	−0.00151493
$142$	−1.11056e37	−0.240158
$143$	4.10051e37	0.784254
$144$	−2.43734e37	−0.412641
$145$	3.28681e37	0.492986
$146$	−6.00350e37	−0.798416
$147$	−7.64266e36	−0.0901968
$148$	6.14102e37	0.643666
$149$	3.38483e37	0.315339	0.157670	−	0.987492i	$-0.449602\pi$
$149$	3.38483e37	0.315339	0.157670	+	0.987492i	$0.449602\pi$
$150$	−5.56718e37	−0.461359
$151$	−4.14774e37	−0.305995	−0.152998	−	0.988227i	$-0.548893\pi$
$151$	−4.14774e37	−0.305995	−0.152998	+	0.988227i	$0.548893\pi$
$152$	−7.87897e37	−0.517853
$153$	7.29172e37	0.427297
$154$	2.00627e38	1.04900
$155$	9.58510e37	0.447499
$156$	−4.37144e37	−0.182366
$157$	2.79097e38	1.04115	0.520573	−	0.853817i	$-0.325718\pi$
$157$	2.79097e38	1.04115	0.520573	+	0.853817i	$0.325718\pi$
$158$	−4.66975e38	−1.55881
$159$	3.00763e38	0.899031
$160$	1.56927e38	0.420338
$161$	2.90234e38	0.697099
$162$	6.07848e37	0.131003
$163$	−9.06631e38	−1.75448	−0.877238	−	0.480056i	$-0.840616\pi$
$163$	−9.06631e38	−1.75448	−0.877238	+	0.480056i	$0.840616\pi$
$164$	−3.86023e38	−0.671190
$165$	2.03067e38	0.317446
$166$	−4.85433e38	−0.682712
$167$	−2.20471e38	−0.279134	−0.139567	−	0.990213i	$-0.544571\pi$
$167$	−2.20471e38	−0.279134	−0.139567	+	0.990213i	$0.544571\pi$
$168$	3.34381e38	0.381355
$169$	−3.35033e38	−0.344405
$170$	−9.25386e38	−0.857959
$171$	2.86907e38	0.240054
$172$	9.18652e38	0.694070
$173$	−1.20919e39	−0.825442	−0.412721	−	0.910858i	$-0.635421\pi$
$173$	−1.20919e39	−0.825442	−0.412721	+	0.910858i	$0.635421\pi$
$174$	−9.57898e38	−0.591163
$175$	1.11520e39	0.622570
$176$	2.37304e39	1.19904
$177$	7.43635e38	0.340273
$178$	4.53690e39	1.88109
$179$	2.04025e39	0.766930	0.383465	−	0.923555i	$-0.374731\pi$
$179$	2.04025e39	0.766930	0.383465	+	0.923555i	$0.374731\pi$
$180$	−2.16484e38	−0.0738170
$181$	−4.15321e39	−1.28531	−0.642656	−	0.766155i	$-0.722168\pi$
$181$	−4.15321e39	−1.28531	−0.642656	+	0.766155i	$0.722168\pi$
$182$	3.12036e39	0.876911
$183$	−3.45553e39	−0.882309
$184$	2.35109e39	0.545705
$185$	−4.43681e39	−0.936624
$186$	−2.79345e39	−0.536617
$187$	−7.09935e39	−1.24162
$188$	−6.42542e36	−0.00102362
$189$	−1.21762e39	−0.176779
$190$	−3.64111e39	−0.481998
$191$	6.52044e39	0.787396	0.393698	−	0.919240i	$-0.371196\pi$
$191$	6.52044e39	0.787396	0.393698	+	0.919240i	$0.371196\pi$
$192$	1.91149e39	0.210669
$193$	−1.97397e39	−0.198649	−0.0993246	−	0.995055i	$-0.531668\pi$
$193$	−1.97397e39	−0.198649	−0.0993246	+	0.995055i	$0.531668\pi$
$194$	3.39124e39	0.311765
$195$	3.15830e39	0.265368
$196$	−7.93267e38	−0.0609450
$197$	6.10473e39	0.429050	0.214525	−	0.976719i	$-0.431180\pi$
$197$	6.10473e39	0.429050	0.214525	+	0.976719i	$0.431180\pi$
$198$	−5.91811e39	−0.380664
$199$	−8.83517e39	−0.520338	−0.260169	−	0.965563i	$-0.583778\pi$
$199$	−8.83517e39	−0.520338	−0.260169	+	0.965563i	$0.583778\pi$
$200$	9.03392e39	0.487361
$201$	9.89792e39	0.489343
$202$	−2.27066e40	−1.02921
$203$	1.91883e40	0.797732
$204$	7.56842e39	0.288720
$205$	2.78896e40	0.976675
$206$	−4.25807e40	−1.36942
$207$	−8.56133e39	−0.252965
$208$	3.69080e40	1.00233
$209$	−2.79337e40	−0.697540
$210$	1.54527e40	0.354951
$211$	7.88511e40	1.66673	0.833364	−	0.552724i	$-0.186412\pi$
$211$	7.88511e40	1.66673	0.833364	+	0.552724i	$0.186412\pi$
$212$	3.12176e40	0.607465
$213$	−6.56228e39	−0.117601
$214$	−7.90181e40	−1.30462
$215$	−6.63714e40	−1.00997
$216$	−9.86359e39	−0.138387
$217$	5.59576e40	0.724126
$218$	−1.60319e41	−1.91424
$219$	−3.54745e40	−0.390971
$220$	2.10772e40	0.214495
$221$	−1.10416e41	−1.03793
$222$	1.29305e41	1.12315
$223$	−2.84802e40	−0.228670	−0.114335	−	0.993442i	$-0.536474\pi$
$223$	−2.84802e40	−0.228670	−0.114335	+	0.993442i	$0.536474\pi$
$224$	9.16138e40	0.680175
$225$	−3.28963e40	−0.225919
$226$	−1.30185e41	−0.827299
$227$	2.11879e41	1.24634	0.623168	−	0.782088i	$-0.285845\pi$
$227$	2.11879e41	1.24634	0.623168	+	0.782088i	$0.285845\pi$
$228$	2.97794e40	0.162202
$229$	2.44651e40	0.123432	0.0617159	−	0.998094i	$-0.480343\pi$
$229$	2.44651e40	0.123432	0.0617159	+	0.998094i	$0.480343\pi$
$230$	1.08651e41	0.507922
$231$	1.18550e41	0.513679
$232$	1.55439e41	0.624482
$233$	3.49375e41	1.30186	0.650929	−	0.759139i	$-0.274380\pi$
$233$	3.49375e41	1.30186	0.650929	+	0.759139i	$0.274380\pi$
$234$	−9.20446e40	−0.318215
$235$	4.64228e38	0.00148951
$236$	7.71854e40	0.229919
$237$	−2.75934e41	−0.763325
$238$	−5.40239e41	−1.38832
$239$	−3.32939e41	−0.795063	−0.397531	−	0.917589i	$-0.630133\pi$
$239$	−3.32939e41	−0.795063	−0.397531	+	0.917589i	$0.630133\pi$
$240$	1.82777e41	0.405718
$241$	6.93771e40	0.143192	0.0715959	−	0.997434i	$-0.477191\pi$
$241$	6.93771e40	0.143192	0.0715959	+	0.997434i	$0.477191\pi$
$242$	−3.79790e40	−0.0729078
$243$	3.59175e40	0.0641500
$244$	−3.58666e41	−0.596167
$245$	5.73125e40	0.0886835
$246$	−8.12807e41	−1.17118
$247$	−4.34455e41	−0.583106
$248$	4.53296e41	0.566862
$249$	−2.86841e41	−0.334313
$250$	1.03346e42	1.12291
$251$	3.37146e40	0.0341608	0.0170804	−	0.999854i	$-0.494563\pi$
$251$	3.37146e40	0.0341608	0.0170804	+	0.999854i	$0.494563\pi$
$252$	−1.26383e41	−0.119448
$253$	8.33546e41	0.735056
$254$	4.11240e41	0.338458
$255$	−5.46808e41	−0.420128
$256$	1.41524e42	1.01538
$257$	−2.45764e41	−0.164698	−0.0823489	−	0.996604i	$-0.526242\pi$
$257$	−2.45764e41	−0.164698	−0.0823489	+	0.996604i	$0.526242\pi$
$258$	1.93431e42	1.21110
$259$	−2.59020e42	−1.51561
$260$	3.27815e41	0.179306
$261$	−5.66019e41	−0.289482
$262$	1.36009e42	0.650569
$263$	−1.00792e42	−0.451026	−0.225513	−	0.974240i	$-0.572406\pi$
$263$	−1.00792e42	−0.451026	−0.225513	+	0.974240i	$0.572406\pi$
$264$	9.60337e41	0.402119
$265$	−2.25543e42	−0.883947
$266$	−2.12567e42	−0.779952
$267$	2.68084e42	0.921136
$268$	1.02735e42	0.330644
$269$	3.53460e42	1.06580	0.532900	−	0.846178i	$-0.321102\pi$
$269$	3.53460e42	1.06580	0.532900	+	0.846178i	$0.321102\pi$
$270$	−4.55826e41	−0.128805
$271$	2.05300e40	0.00543785	0.00271893	−	0.999996i	$-0.499135\pi$
$271$	2.05300e40	0.00543785	0.00271893	+	0.999996i	$0.499135\pi$
$272$	−6.39000e42	−1.58688
$273$	1.84381e42	0.429408
$274$	1.51057e42	0.329993
$275$	3.20285e42	0.656468
$276$	−8.88620e41	−0.170926
$277$	−3.99065e42	−0.720522	−0.360261	−	0.932851i	$-0.617312\pi$
$277$	−3.99065e42	−0.720522	−0.360261	+	0.932851i	$0.617312\pi$
$278$	−8.96412e42	−1.51958
$279$	−1.65064e42	−0.262772
$280$	−2.50753e42	−0.374956
$281$	−6.62219e42	−0.930338	−0.465169	−	0.885222i	$-0.654006\pi$
$281$	−6.62219e42	−0.930338	−0.465169	+	0.885222i	$0.654006\pi$
$282$	−1.35293e40	−0.00178614
$283$	9.02584e42	1.12002	0.560009	−	0.828487i	$-0.310798\pi$
$283$	9.02584e42	1.12002	0.560009	+	0.828487i	$0.310798\pi$
$284$	−6.81130e41	−0.0794619
$285$	−2.15152e42	−0.236026
$286$	8.96163e42	0.924658
$287$	1.62819e43	1.58042
$288$	−2.70243e42	−0.246823
$289$	7.48323e42	0.643246
$290$	7.18330e42	0.581245
$291$	2.00387e42	0.152666
$292$	−3.68206e42	−0.264175
$293$	1.83072e43	1.23719	0.618597	−	0.785708i	$-0.287701\pi$
$293$	1.83072e43	1.23719	0.618597	+	0.785708i	$0.287701\pi$
$294$	−1.67030e42	−0.106345
$295$	−5.57654e42	−0.334564
$296$	−2.09824e43	−1.18645
$297$	−3.49700e42	−0.186405
$298$	7.39753e42	0.371794
$299$	1.29642e43	0.614468
$300$	−3.41446e42	−0.152651
$301$	−3.87475e43	−1.63429
$302$	−9.06486e42	−0.360778
$303$	−1.34173e43	−0.503986
$304$	−2.51427e43	−0.891506
$305$	2.59131e43	0.867506
$306$	1.59360e43	0.503796
$307$	−5.94182e43	−1.77418	−0.887091	−	0.461595i	$-0.847277\pi$
$307$	−5.94182e43	−1.77418	−0.887091	+	0.461595i	$0.847277\pi$
$308$	1.23049e43	0.347087
$309$	−2.51608e43	−0.670580
$310$	2.09482e43	0.527614
$311$	9.43273e42	0.224559	0.112280	−	0.993677i	$-0.464185\pi$
$311$	9.43273e42	0.224559	0.112280	+	0.993677i	$0.464185\pi$
$312$	1.49362e43	0.336150
$313$	5.95209e43	1.26661	0.633306	−	0.773902i	$-0.281697\pi$
$313$	5.95209e43	1.26661	0.633306	+	0.773902i	$0.281697\pi$
$314$	6.09965e43	1.22754
$315$	9.13099e42	0.173813
$316$	−2.86405e43	−0.515770
$317$	−1.09193e44	−1.86062	−0.930311	−	0.366772i	$-0.880463\pi$
$317$	−1.09193e44	−1.86062	−0.930311	+	0.366772i	$0.880463\pi$
$318$	6.57315e43	1.05998
$319$	5.51086e43	0.841168
$320$	−1.43343e43	−0.207134
$321$	−4.66916e43	−0.638852
$322$	6.34303e43	0.821901
$323$	7.52186e43	0.923169
$324$	3.72805e42	0.0433455
$325$	4.98140e43	0.548773
$326$	−1.98144e44	−2.06858
$327$	−9.47320e43	−0.937370
$328$	1.31895e44	1.23719
$329$	2.71015e41	0.00241027
$330$	4.43801e43	0.374278
$331$	−6.64486e43	−0.531491	−0.265746	−	0.964043i	$-0.585618\pi$
$331$	−6.64486e43	−0.531491	−0.265746	+	0.964043i	$0.585618\pi$
$332$	−2.97726e43	−0.225891
$333$	7.64059e43	0.549988
$334$	−4.81837e43	−0.329107
$335$	−7.42248e43	−0.481132
$336$	1.06705e44	0.656518
$337$	−1.32087e44	−0.771504	−0.385752	−	0.922602i	$-0.626058\pi$
$337$	−1.32087e44	−0.771504	−0.385752	+	0.922602i	$0.626058\pi$
$338$	−7.32211e43	−0.406064
$339$	−7.69258e43	−0.405114
$340$	−5.67557e43	−0.283876
$341$	1.60709e44	0.763554
$342$	6.27033e43	0.283031
$343$	2.47630e44	1.06208
$344$	−3.13882e44	−1.27936
$345$	6.42016e43	0.248721
$346$	−2.64267e44	−0.973220
$347$	1.51937e44	0.531983	0.265991	−	0.963975i	$-0.414301\pi$
$347$	1.51937e44	0.531983	0.265991	+	0.963975i	$0.414301\pi$
$348$	−5.87498e43	−0.195600
$349$	−4.35219e44	−1.37804	−0.689022	−	0.724741i	$-0.741960\pi$
$349$	−4.35219e44	−1.37804	−0.689022	+	0.724741i	$0.741960\pi$
$350$	2.43727e44	0.734028
$351$	−5.43889e43	−0.155825
$352$	2.63113e44	0.717210
$353$	3.37356e44	0.875045	0.437523	−	0.899207i	$-0.355856\pi$
$353$	3.37356e44	0.875045	0.437523	+	0.899207i	$0.355856\pi$
$354$	1.62521e44	0.401192
$355$	4.92107e43	0.115628
$356$	2.78257e44	0.622402
$357$	−3.19226e44	−0.679836
$358$	4.45896e44	0.904233
$359$	8.65151e44	1.67086	0.835428	−	0.549600i	$-0.185220\pi$
$359$	8.65151e44	1.67086	0.835428	+	0.549600i	$0.185220\pi$
$360$	7.39673e43	0.136065
$361$	−2.74696e44	−0.481367
$362$	−9.07681e44	−1.51542
$363$	−2.24417e43	−0.0357017
$364$	1.91378e44	0.290147
$365$	2.66024e44	0.384411
$366$	−7.55204e44	−1.04027
$367$	2.11463e44	0.277701	0.138851	−	0.990313i	$-0.455659\pi$
$367$	2.11463e44	0.277701	0.138851	+	0.990313i	$0.455659\pi$
$368$	7.50261e44	0.939454
$369$	−4.80285e44	−0.573506
$370$	−9.69661e44	−1.10431
$371$	−1.31671e45	−1.43037
$372$	−1.71328e44	−0.177552
$373$	−8.06525e44	−0.797468	−0.398734	−	0.917067i	$-0.630550\pi$
$373$	−8.06525e44	−0.797468	−0.398734	+	0.917067i	$0.630550\pi$
$374$	−1.55156e45	−1.46391
$375$	6.10670e44	0.549870
$376$	2.19541e42	0.00188681
$377$	8.57107e44	0.703172
$378$	−2.66111e44	−0.208428
$379$	1.62962e45	1.21871	0.609356	−	0.792897i	$-0.291428\pi$
$379$	1.62962e45	1.21871	0.609356	+	0.792897i	$0.291428\pi$
$380$	−2.23316e44	−0.159480
$381$	2.43000e44	0.165737
$382$	1.42504e45	0.928362
$383$	3.08699e45	1.92113	0.960565	−	0.278055i	$-0.0896896\pi$
$383$	3.08699e45	1.92113	0.960565	+	0.278055i	$0.0896896\pi$
$384$	1.13678e45	0.675895
$385$	−8.89009e44	−0.505060
$386$	−4.31409e44	−0.234213
$387$	1.14298e45	0.593056
$388$	2.07991e44	0.103155
$389$	−2.76724e45	−1.31199	−0.655993	−	0.754767i	$-0.727750\pi$
$389$	−2.76724e45	−1.31199	−0.655993	+	0.754767i	$0.727750\pi$
$390$	6.90245e44	0.312876
$391$	−2.24453e45	−0.972821
$392$	2.71040e44	0.112338
$393$	8.03671e44	0.318573
$394$	1.33418e45	0.505862
$395$	2.06924e45	0.750518
$396$	−3.62969e44	−0.125952
$397$	−3.58547e45	−1.19045	−0.595226	−	0.803558i	$-0.702938\pi$
$397$	−3.58547e45	−1.19045	−0.595226	+	0.803558i	$0.702938\pi$
$398$	−1.93092e45	−0.613494
$399$	−1.25605e45	−0.381929
$400$	2.88283e45	0.839013
$401$	−4.26941e45	−1.18944	−0.594718	−	0.803934i	$-0.702736\pi$
$401$	−4.26941e45	−1.18944	−0.594718	+	0.803934i	$0.702736\pi$
$402$	2.16318e45	0.576949
$403$	2.49952e45	0.638291
$404$	−1.39264e45	−0.340538
$405$	−2.69347e44	−0.0630737
$406$	4.19360e45	0.940549
$407$	−7.43902e45	−1.59813
$408$	−2.58595e45	−0.532190
$409$	−8.56530e43	−0.0168883	−0.00844413	−	0.999964i	$-0.502688\pi$
$409$	−8.56530e43	−0.0168883	−0.00844413	+	0.999964i	$0.502688\pi$
$410$	6.09526e45	1.15153
$411$	8.92590e44	0.161592
$412$	−2.61156e45	−0.453104
$413$	−3.25557e45	−0.541379
$414$	−1.87107e45	−0.298253
$415$	2.15103e45	0.328704
$416$	4.09221e45	0.599550
$417$	−5.29688e45	−0.744113
$418$	−6.10490e45	−0.822420
$419$	5.67787e45	0.733567	0.366783	−	0.930306i	$-0.380459\pi$
$419$	5.67787e45	0.733567	0.366783	+	0.930306i	$0.380459\pi$
$420$	9.47748e44	0.117444
$421$	4.40748e45	0.523907	0.261953	−	0.965081i	$-0.415633\pi$
$421$	4.40748e45	0.523907	0.261953	+	0.965081i	$0.415633\pi$
$422$	1.72329e46	1.96512
$423$	−7.99443e42	−0.000874644 0
$424$	−1.06663e46	−1.11973
$425$	−8.62447e45	−0.868812
$426$	−1.43418e45	−0.138655
$427$	1.51280e46	1.40377
$428$	−4.84633e45	−0.431666
$429$	5.29540e45	0.452789
$430$	−1.45054e46	−1.19078
$431$	2.36863e46	1.86700	0.933500	−	0.358578i	$-0.116738\pi$
$431$	2.36863e46	1.86700	0.933500	+	0.358578i	$0.116738\pi$
$432$	−3.14759e45	−0.238239
$433$	6.19663e45	0.450420	0.225210	−	0.974310i	$-0.427693\pi$
$433$	6.19663e45	0.450420	0.225210	+	0.974310i	$0.427693\pi$
$434$	1.22295e46	0.853765
$435$	4.24459e45	0.284626
$436$	−9.83268e45	−0.633371
$437$	−8.83155e45	−0.546527
$438$	−7.75292e45	−0.460966
$439$	−4.03275e45	−0.230394	−0.115197	−	0.993343i	$-0.536750\pi$
$439$	−4.03275e45	−0.230394	−0.115197	+	0.993343i	$0.536750\pi$
$440$	−7.20159e45	−0.395373
$441$	−9.86974e44	−0.0520751
$442$	−2.41314e46	−1.22375
$443$	9.72231e44	0.0473919	0.0236959	−	0.999719i	$-0.492457\pi$
$443$	9.72231e44	0.0473919	0.0236959	+	0.999719i	$0.492457\pi$
$444$	7.93053e45	0.371621
$445$	−2.01037e46	−0.905681
$446$	−6.22433e45	−0.269608
$447$	4.37118e45	0.182061
$448$	−8.36833e45	−0.335177
$449$	−3.45806e46	−1.33205	−0.666027	−	0.745928i	$-0.732006\pi$
$449$	−3.45806e46	−1.33205	−0.666027	+	0.745928i	$0.732006\pi$
$450$	−7.18947e45	−0.266365
$451$	4.67614e46	1.66647
$452$	−7.98448e45	−0.273731
$453$	−5.35640e45	−0.176667
$454$	4.63060e46	1.46947
$455$	−1.38268e46	−0.422204
$456$	−1.01749e46	−0.298983
$457$	3.54182e46	1.00160	0.500799	−	0.865564i	$-0.333040\pi$
$457$	3.54182e46	1.00160	0.500799	+	0.865564i	$0.333040\pi$
$458$	5.34684e45	0.145530
$459$	9.41654e45	0.246700
$460$	6.66379e45	0.168058
$461$	7.06935e45	0.171638	0.0858189	−	0.996311i	$-0.472649\pi$
$461$	7.06935e45	0.171638	0.0858189	+	0.996311i	$0.472649\pi$
$462$	2.59090e46	0.605642
$463$	−6.22902e44	−0.0140201	−0.00701007	−	0.999975i	$-0.502231\pi$
$463$	−6.22902e44	−0.0140201	−0.00701007	+	0.999975i	$0.502231\pi$
$464$	4.96023e46	1.07507
$465$	1.23782e46	0.258363
$466$	7.63557e46	1.53493
$467$	−6.28266e46	−1.21646	−0.608231	−	0.793760i	$-0.708120\pi$
$467$	−6.28266e46	−1.21646	−0.608231	+	0.793760i	$0.708120\pi$
$468$	−5.64528e45	−0.105289
$469$	−4.33323e46	−0.778551
$470$	1.01457e44	0.00175618
$471$	3.60427e46	0.601106
$472$	−2.63724e46	−0.423804
$473$	−1.11282e47	−1.72328
$474$	−6.03052e46	−0.899982
$475$	−3.39346e46	−0.488095
$476$	−3.31339e46	−0.459358
$477$	3.88406e46	0.519056
$478$	−7.27636e46	−0.937402
$479$	1.10146e47	1.36804	0.684020	−	0.729463i	$-0.260230\pi$
$479$	1.10146e47	1.36804	0.684020	+	0.729463i	$0.260230\pi$
$480$	2.02656e46	0.242682
$481$	−1.15699e47	−1.33596
$482$	1.51623e46	0.168827
$483$	3.74808e46	0.402471
$484$	−2.32932e45	−0.0241233
$485$	−1.50271e46	−0.150105
$486$	7.84975e45	0.0756347
$487$	8.13246e46	0.755901	0.377951	−	0.925826i	$-0.376629\pi$
$487$	8.13246e46	0.755901	0.377951	+	0.925826i	$0.376629\pi$
$488$	1.22548e47	1.09890
$489$	−1.17082e47	−1.01295
$490$	1.25256e46	0.104560
$491$	1.83224e47	1.47590	0.737950	−	0.674855i	$-0.235794\pi$
$491$	1.83224e47	1.47590	0.737950	+	0.674855i	$0.235794\pi$
$492$	−4.98510e46	−0.387512
$493$	−1.48394e47	−1.11326
$494$	−9.49498e46	−0.687499
$495$	2.62241e46	0.183277
$496$	1.44652e47	0.975876
$497$	2.87291e46	0.187105
$498$	−6.26889e46	−0.394164
$499$	9.12339e45	0.0553856	0.0276928	−	0.999616i	$-0.491184\pi$
$499$	9.12339e45	0.0553856	0.0276928	+	0.999616i	$0.491184\pi$
$500$	6.33843e46	0.371541
$501$	−2.84716e46	−0.161158
$502$	7.36830e45	0.0402766
$503$	−1.87342e47	−0.989001	−0.494500	−	0.869177i	$-0.664649\pi$
$503$	−1.87342e47	−0.989001	−0.494500	+	0.869177i	$0.664649\pi$
$504$	4.31820e46	0.220175
$505$	1.00616e47	0.495530
$506$	1.82171e47	0.866653
$507$	−4.32662e46	−0.198842
$508$	2.52221e46	0.111987
$509$	1.22247e47	0.524418	0.262209	−	0.965011i	$-0.415549\pi$
$509$	1.22247e47	0.524418	0.262209	+	0.965011i	$0.415549\pi$
$510$	−1.19504e47	−0.495343
$511$	1.55304e47	0.622039
$512$	6.84151e45	0.0264806
$513$	3.70512e46	0.138595
$514$	−5.37115e46	−0.194184
$515$	1.88681e47	0.659329
$516$	1.18635e47	0.400721
$517$	7.78352e44	0.00254151
$518$	−5.66086e47	−1.78695
$519$	−1.56154e47	−0.476569
$520$	−1.12007e47	−0.330510
$521$	−6.28279e46	−0.179264	−0.0896318	−	0.995975i	$-0.528569\pi$
$521$	−6.28279e46	−0.179264	−0.0896318	+	0.995975i	$0.528569\pi$
$522$	−1.23703e47	−0.341308
$523$	−2.46925e47	−0.658849	−0.329425	−	0.944182i	$-0.606855\pi$
$523$	−2.46925e47	−0.658849	−0.329425	+	0.944182i	$0.606855\pi$
$524$	8.34167e46	0.215256
$525$	1.44017e47	0.359441
$526$	−2.20281e47	−0.531773
$527$	−4.32751e47	−1.01054
$528$	3.06455e47	0.692265
$529$	−1.94053e47	−0.424079
$530$	−4.92922e47	−1.04220
$531$	9.60332e46	0.196457
$532$	−1.30372e47	−0.258065
$533$	7.27282e47	1.39308
$534$	5.85896e47	1.08605
$535$	3.50141e47	0.628133
$536$	−3.51022e47	−0.609467
$537$	2.63478e47	0.442787
$538$	7.72485e47	1.25661
$539$	9.60935e46	0.151318
$540$	−2.79567e46	−0.0426182
$541$	1.20408e47	0.177706	0.0888529	−	0.996045i	$-0.471680\pi$
$541$	1.20408e47	0.177706	0.0888529	+	0.996045i	$0.471680\pi$
$542$	4.48683e45	0.00641139
$543$	−5.36346e47	−0.742075
$544$	−7.08499e47	−0.949202
$545$	7.10398e47	0.921643
$546$	4.02964e47	0.506285
$547$	8.44104e47	1.02711	0.513556	−	0.858056i	$-0.328328\pi$
$547$	8.44104e47	1.02711	0.513556	+	0.858056i	$0.328328\pi$
$548$	9.26461e46	0.109186
$549$	−4.46248e47	−0.509402
$550$	6.99980e47	0.773995
$551$	−5.83884e47	−0.625423
$552$	3.03621e47	0.315063
$553$	1.20802e48	1.21446
$554$	−8.72153e47	−0.849517
$555$	−5.72970e47	−0.540760
$556$	−5.49787e47	−0.502789
$557$	−1.28303e48	−1.13703	−0.568514	−	0.822674i	$-0.692481\pi$
$557$	−1.28303e48	−1.13703	−0.568514	+	0.822674i	$0.692481\pi$
$558$	−3.60747e47	−0.309816
$559$	−1.73078e48	−1.44057
$560$	−8.00182e47	−0.645503
$561$	−9.16811e47	−0.716852
$562$	−1.44727e48	−1.09690
$563$	2.05838e48	1.51227	0.756133	−	0.654418i	$-0.227086\pi$
$563$	2.05838e48	1.51227	0.756133	+	0.654418i	$0.227086\pi$
$564$	−8.29779e44	−0.000590987 0
$565$	5.76868e47	0.398317
$566$	1.97259e48	1.32053
$567$	−1.57244e47	−0.102064
$568$	2.32726e47	0.146470
$569$	−4.38677e47	−0.267720	−0.133860	−	0.991000i	$-0.542737\pi$
$569$	−4.38677e47	−0.267720	−0.133860	+	0.991000i	$0.542737\pi$
$570$	−4.70213e47	−0.278282
$571$	−2.36363e48	−1.35658	−0.678292	−	0.734792i	$-0.737280\pi$
$571$	−2.36363e48	−1.35658	−0.678292	+	0.734792i	$0.737280\pi$
$572$	5.49634e47	0.305945
$573$	8.42051e47	0.454603
$574$	3.55840e48	1.86336
$575$	1.01261e48	0.514347
$576$	2.46850e47	0.121630
$577$	−1.45741e48	−0.696632	−0.348316	−	0.937377i	$-0.613246\pi$
$577$	−1.45741e48	−0.696632	−0.348316	+	0.937377i	$0.613246\pi$
$578$	1.63546e48	0.758406
$579$	−2.54918e47	−0.114690
$580$	4.40566e47	0.192318
$581$	1.25577e48	0.531896
$582$	4.37945e47	0.179998
$583$	−3.78159e48	−1.50825
$584$	1.25807e48	0.486946
$585$	4.07864e47	0.153210
$586$	4.00102e48	1.45869
$587$	−2.31218e48	−0.818190	−0.409095	−	0.912492i	$-0.634156\pi$
$587$	−2.31218e48	−0.818190	−0.409095	+	0.912492i	$0.634156\pi$
$588$	−1.02443e47	−0.0351866
$589$	−1.70274e48	−0.567716
$590$	−1.21875e48	−0.394461
$591$	7.88366e47	0.247712
$592$	−6.69573e48	−2.04253
$593$	4.31701e48	1.27857	0.639287	−	0.768968i	$-0.279230\pi$
$593$	4.31701e48	1.27857	0.639287	+	0.768968i	$0.279230\pi$
$594$	−7.64266e47	−0.219777
$595$	2.39388e48	0.668429
$596$	4.53705e47	0.123017
$597$	−1.14097e48	−0.300418
$598$	2.83331e48	0.724476
$599$	−2.66626e48	−0.662114	−0.331057	−	0.943611i	$-0.607405\pi$
$599$	−2.66626e48	−0.662114	−0.331057	+	0.943611i	$0.607405\pi$
$600$	1.16664e48	0.281378
$601$	7.51112e48	1.75955	0.879775	−	0.475391i	$-0.157693\pi$
$601$	7.51112e48	1.75955	0.879775	+	0.475391i	$0.157693\pi$
$602$	−8.46824e48	−1.92688
$603$	1.27822e48	0.282522
$604$	−5.55966e47	−0.119372
$605$	1.68291e47	0.0351027
$606$	−2.93234e48	−0.594214
$607$	−4.81557e48	−0.948081	−0.474040	−	0.880503i	$-0.657205\pi$
$607$	−4.81557e48	−0.948081	−0.474040	+	0.880503i	$0.657205\pi$
$608$	−2.78773e48	−0.533258
$609$	2.47799e48	0.460571
$610$	5.66329e48	1.02281
$611$	1.21057e46	0.00212457
$612$	9.77387e47	0.166693
$613$	1.36361e48	0.226012	0.113006	−	0.993594i	$-0.463952\pi$
$613$	1.36361e48	0.226012	0.113006	+	0.993594i	$0.463952\pi$
$614$	−1.29858e49	−2.09181
$615$	3.60167e48	0.563884
$616$	−4.20428e48	−0.639777
$617$	1.76559e48	0.261156	0.130578	−	0.991438i	$-0.458317\pi$
$617$	1.76559e48	0.261156	0.130578	+	0.991438i	$0.458317\pi$
$618$	−5.49887e48	−0.790634
$619$	7.44879e48	1.04112	0.520559	−	0.853826i	$-0.325724\pi$
$619$	7.44879e48	1.04112	0.520559	+	0.853826i	$0.325724\pi$
$620$	1.28479e48	0.174573
$621$	−1.10561e48	−0.146049
$622$	2.06152e48	0.264762
$623$	−1.17365e49	−1.46554
$624$	4.76630e48	0.578697
$625$	1.16140e48	0.137114
$626$	1.30083e49	1.49337
$627$	−3.60737e48	−0.402725
$628$	3.74104e48	0.406161
$629$	2.00314e49	2.11507
$630$	1.99557e48	0.204931
$631$	4.61699e48	0.461153	0.230576	−	0.973054i	$-0.425939\pi$
$631$	4.61699e48	0.461153	0.230576	+	0.973054i	$0.425939\pi$
$632$	9.78578e48	0.950706
$633$	1.01828e49	0.962286
$634$	−2.38641e49	−2.19373
$635$	−1.82227e48	−0.162956
$636$	4.03144e48	0.350720
$637$	1.49455e48	0.126494
$638$	1.20440e49	0.991761
$639$	−8.47454e47	−0.0678971
$640$	−8.52472e48	−0.664555
$641$	−2.29073e49	−1.73763	−0.868816	−	0.495134i	$-0.835119\pi$
$641$	−2.29073e49	−1.73763	−0.868816	+	0.495134i	$0.835119\pi$
$642$	−1.02044e49	−0.753225
$643$	−1.75961e49	−1.26394	−0.631969	−	0.774994i	$-0.717753\pi$
$643$	−1.75961e49	−1.26394	−0.631969	+	0.774994i	$0.717753\pi$
$644$	3.89031e48	0.271945
$645$	−8.57121e48	−0.583105
$646$	1.64390e49	1.08844
$647$	−1.34530e49	−0.866950	−0.433475	−	0.901166i	$-0.642713\pi$
$647$	−1.34530e49	−0.866950	−0.433475	+	0.901166i	$0.642713\pi$
$648$	−1.27379e48	−0.0798976
$649$	−9.34996e48	−0.570857
$650$	1.08868e49	0.647019
$651$	7.22638e48	0.418074
$652$	−1.21525e49	−0.684438
$653$	−1.55134e49	−0.850601	−0.425300	−	0.905052i	$-0.639832\pi$
$653$	−1.55134e49	−0.850601	−0.425300	+	0.905052i	$0.639832\pi$
$654$	−2.07036e49	−1.10519
$655$	−6.02675e48	−0.313228
$656$	4.20892e49	2.12987
$657$	−4.58118e48	−0.225727
$658$	5.92302e46	0.00284178
$659$	−1.67026e46	−0.000780348 0	−0.000390174	−	1.00000i	$-0.500124\pi$
$659$	−1.67026e46	−0.000780348 0	−0.000390174		1.00000i	$0.500124\pi$
$660$	2.72192e48	0.123839
$661$	3.86727e49	1.71348	0.856740	−	0.515748i	$-0.172486\pi$
$661$	3.86727e49	1.71348	0.856740	+	0.515748i	$0.172486\pi$
$662$	−1.45223e49	−0.626644
$663$	−1.42592e49	−0.599250
$664$	1.01726e49	0.416380
$665$	9.41918e48	0.375521
$666$	1.66985e49	0.648451
$667$	1.74232e49	0.659060
$668$	−2.95520e48	−0.108893
$669$	−3.67794e48	−0.132022
$670$	−1.62218e49	−0.567269
$671$	4.34475e49	1.48020
$672$	1.18310e49	0.392699
$673$	1.92251e49	0.621734	0.310867	−	0.950453i	$-0.399381\pi$
$673$	1.92251e49	0.621734	0.310867	+	0.950453i	$0.399381\pi$
$674$	−2.88676e49	−0.909626
$675$	−4.24824e48	−0.130435
$676$	−4.49080e48	−0.134356
$677$	−2.27583e49	−0.663495	−0.331747	−	0.943368i	$-0.607638\pi$
$677$	−2.27583e49	−0.663495	−0.331747	+	0.943368i	$0.607638\pi$
$678$	−1.68121e49	−0.477641
$679$	−8.77279e48	−0.242894
$680$	1.93921e49	0.523261
$681$	2.73621e49	0.719573
$682$	3.51229e49	0.900253
$683$	−7.47926e49	−1.86851	−0.934257	−	0.356599i	$-0.883936\pi$
$683$	−7.47926e49	−1.86851	−0.934257	+	0.356599i	$0.883936\pi$
$684$	3.84572e48	0.0936473
$685$	−6.69355e48	−0.158881
$686$	5.41193e49	1.25222
$687$	3.15943e48	0.0712634
$688$	−1.00163e50	−2.20247
$689$	−5.88151e49	−1.26082
$690$	1.40312e49	0.293249
$691$	5.04033e49	1.02705	0.513527	−	0.858073i	$-0.328339\pi$
$691$	5.04033e49	1.02705	0.513527	+	0.858073i	$0.328339\pi$
$692$	−1.62080e49	−0.322013
$693$	1.53096e49	0.296573
$694$	3.32057e49	0.627223
$695$	3.97214e49	0.731628
$696$	2.00734e49	0.360545
$697$	−1.25917e50	−2.20552
$698$	−9.51168e49	−1.62475
$699$	4.51184e49	0.751628
$700$	1.49482e49	0.242870
$701$	3.72125e48	0.0589690	0.0294845	−	0.999565i	$-0.490613\pi$
$701$	3.72125e48	0.0589690	0.0294845	+	0.999565i	$0.490613\pi$
$702$	−1.18867e49	−0.183722
$703$	7.88175e49	1.18824
$704$	−2.40337e49	−0.353427
$705$	5.99504e46	0.000859969 0
$706$	7.37288e49	1.03170
$707$	5.87397e49	0.801848
$708$	9.96773e48	0.132744
$709$	−5.15574e49	−0.669857	−0.334928	−	0.942244i	$-0.608712\pi$
$709$	−5.15574e49	−0.669857	−0.334928	+	0.942244i	$0.608712\pi$
$710$	1.07550e49	0.136329
$711$	−3.56342e49	−0.440706
$712$	−9.50738e49	−1.14726
$713$	5.08100e49	0.598249
$714$	−6.97665e49	−0.801546
$715$	−3.97103e49	−0.445193
$716$	2.73477e49	0.299187
$717$	−4.29958e49	−0.459030
$718$	1.89078e50	1.96999
$719$	−3.36048e49	−0.341700	−0.170850	−	0.985297i	$-0.554651\pi$
$719$	−3.36048e49	−0.341700	−0.170850	+	0.985297i	$0.554651\pi$
$720$	2.36038e49	0.234241
$721$	1.10152e50	1.06690
$722$	−6.00346e49	−0.567546
$723$	8.95937e48	0.0826718
$724$	−5.56699e49	−0.501412
$725$	6.69473e49	0.588597
$726$	−4.90461e48	−0.0420934
$727$	1.31541e50	1.10207	0.551033	−	0.834484i	$-0.314234\pi$
$727$	1.31541e50	1.10207	0.551033	+	0.834484i	$0.314234\pi$
$728$	−6.53893e49	−0.534820
$729$	4.63840e48	0.0370370
$730$	5.81394e49	0.453232
$731$	2.99655e50	2.28070
$732$	−4.63182e49	−0.344197
$733$	−2.25359e50	−1.63514	−0.817570	−	0.575829i	$-0.804680\pi$
$733$	−2.25359e50	−1.63514	−0.817570	+	0.575829i	$0.804680\pi$
$734$	4.62151e49	0.327418
$735$	7.40134e48	0.0512014
$736$	8.31861e49	0.561939
$737$	−1.24450e50	−0.820943
$738$	−1.04966e50	−0.676180
$739$	−1.93424e50	−1.21684	−0.608419	−	0.793616i	$-0.708196\pi$
$739$	−1.93424e50	−1.21684	−0.608419	+	0.793616i	$0.708196\pi$
$740$	−5.94712e49	−0.365386
$741$	−5.61056e49	−0.336657
$742$	−2.87767e50	−1.68645
$743$	8.43115e49	0.482595	0.241297	−	0.970451i	$-0.422427\pi$
$743$	8.43115e49	0.482595	0.241297	+	0.970451i	$0.422427\pi$
$744$	5.85387e49	0.327278
$745$	−3.27796e49	−0.179006
$746$	−1.76266e50	−0.940238
$747$	−3.70427e49	−0.193015
$748$	−9.51601e49	−0.484370
$749$	2.04412e50	1.01642
$750$	1.33462e50	0.648312
$751$	−2.50076e50	−1.18679	−0.593394	−	0.804912i	$-0.702212\pi$
$751$	−2.50076e50	−1.18679	−0.593394	+	0.804912i	$0.702212\pi$
$752$	7.00581e47	0.00324823
$753$	4.35391e48	0.0197227
$754$	1.87320e50	0.829060
$755$	4.01678e49	0.173702
$756$	−1.63211e49	−0.0689633
$757$	−8.14773e49	−0.336402	−0.168201	−	0.985753i	$-0.553796\pi$
$757$	−8.14773e49	−0.336402	−0.168201	+	0.985753i	$0.553796\pi$
$758$	3.56153e50	1.43690
$759$	1.07644e50	0.424385
$760$	7.63019e49	0.293966
$761$	−3.09181e50	−1.16408	−0.582038	−	0.813161i	$-0.697745\pi$
$761$	−3.09181e50	−1.16408	−0.582038	+	0.813161i	$0.697745\pi$
$762$	5.31076e49	0.195409
$763$	4.14729e50	1.49137
$764$	8.74004e49	0.307171
$765$	−7.06149e49	−0.242561
$766$	6.74660e50	2.26507
$767$	−1.45420e50	−0.477206
$768$	1.82764e50	0.586231
$769$	−9.48513e49	−0.297394	−0.148697	−	0.988883i	$-0.547508\pi$
$769$	−9.48513e49	−0.297394	−0.148697	+	0.988883i	$0.547508\pi$
$770$	−1.94292e50	−0.595481
$771$	−3.17380e49	−0.0950884
$772$	−2.64592e49	−0.0774950
$773$	1.05155e50	0.301086	0.150543	−	0.988603i	$-0.451898\pi$
$773$	1.05155e50	0.301086	0.150543	+	0.988603i	$0.451898\pi$
$774$	2.49797e50	0.699230
$775$	1.95234e50	0.534288
$776$	−7.10657e49	−0.190143
$777$	−3.34499e50	−0.875038
$778$	−6.04779e50	−1.54687
$779$	−4.95444e50	−1.23905
$780$	4.23341e49	0.103522
$781$	8.25096e49	0.197293
$782$	−4.90541e50	−1.14698
$783$	−7.30958e49	−0.167133
$784$	8.64922e49	0.193395
$785$	−2.70285e50	−0.591021
$786$	1.75642e50	0.375606
$787$	−1.75648e50	−0.367354	−0.183677	−	0.982987i	$-0.558800\pi$
$787$	−1.75648e50	−0.367354	−0.183677	+	0.982987i	$0.558800\pi$
$788$	8.18282e49	0.167376
$789$	−1.30163e50	−0.260400
$790$	4.52230e50	0.884882
$791$	3.36775e50	0.644542
$792$	1.24018e50	0.232164
$793$	6.75741e50	1.23737
$794$	−7.83602e50	−1.40358
$795$	−2.91266e50	−0.510347
$796$	−1.18427e50	−0.202989
$797$	5.53388e49	0.0927917	0.0463959	−	0.998923i	$-0.485226\pi$
$797$	5.53388e49	0.0927917	0.0463959	+	0.998923i	$0.485226\pi$
$798$	−2.74510e50	−0.450305
$799$	−2.09591e48	−0.00336359
$800$	3.19637e50	0.501859
$801$	3.46204e50	0.531818
$802$	−9.33077e50	−1.40238
$803$	4.46032e50	0.655909
$804$	1.32672e50	0.190897
$805$	−2.81069e50	−0.395718
$806$	5.46269e50	0.752563
$807$	4.56459e50	0.615340
$808$	4.75832e50	0.627704
$809$	4.98563e50	0.643607	0.321803	−	0.946807i	$-0.395711\pi$
$809$	4.98563e50	0.643607	0.321803	+	0.946807i	$0.395711\pi$
$810$	−5.88655e49	−0.0743658
$811$	−1.07303e51	−1.32662	−0.663309	−	0.748346i	$-0.730848\pi$
$811$	−1.07303e51	−1.32662	−0.663309	+	0.748346i	$0.730848\pi$
$812$	2.57202e50	0.311203
$813$	2.65125e48	0.00313955
$814$	−1.62579e51	−1.88425
$815$	8.78004e50	0.995952
$816$	−8.25206e50	−0.916188
$817$	1.17905e51	1.28129
$818$	−1.87194e49	−0.0199117
$819$	2.38110e50	0.247919
$820$	3.73834e50	0.381010
$821$	−2.21488e50	−0.220976	−0.110488	−	0.993877i	$-0.535241\pi$
$821$	−2.21488e50	−0.220976	−0.110488	+	0.993877i	$0.535241\pi$
$822$	1.95075e50	0.190522
$823$	1.24351e51	1.18892	0.594459	−	0.804126i	$-0.297366\pi$
$823$	1.24351e51	1.18892	0.594459	+	0.804126i	$0.297366\pi$
$824$	8.92306e50	0.835195
$825$	4.13616e50	0.379012
$826$	−7.11504e50	−0.638302
$827$	1.45573e49	0.0127860	0.00639299	−	0.999980i	$-0.497965\pi$
$827$	1.45573e49	0.0127860	0.00639299	+	0.999980i	$0.497965\pi$
$828$	−1.14757e50	−0.0986840
$829$	−9.35859e50	−0.787964	−0.393982	−	0.919118i	$-0.628903\pi$
$829$	−9.35859e50	−0.787964	−0.393982	+	0.919118i	$0.628903\pi$
$830$	4.70106e50	0.387551
$831$	−5.15353e50	−0.415994
$832$	−3.73797e50	−0.295446
$833$	−2.58756e50	−0.200264
$834$	−1.15763e51	−0.877331
$835$	2.13510e50	0.158454
$836$	−3.74426e50	−0.272117
$837$	−2.13164e50	−0.151712
$838$	1.24089e51	0.864897
$839$	−7.95070e50	−0.542714	−0.271357	−	0.962479i	$-0.587472\pi$
$839$	−7.95070e50	−0.542714	−0.271357	+	0.962479i	$0.587472\pi$
$840$	−3.23823e50	−0.216481
$841$	−3.75414e50	−0.245799
$842$	9.63252e50	0.617701
$843$	−8.55190e50	−0.537131
$844$	1.05692e51	0.650206
$845$	3.24454e50	0.195506
$846$	−1.74718e48	−0.00103123
$847$	9.82478e49	0.0568019
$848$	−3.40374e51	−1.92765
$849$	1.16560e51	0.646642
$850$	−1.88487e51	−1.02435
$851$	−2.35192e51	−1.25215
$852$	−8.79612e49	−0.0458773
$853$	−2.54840e50	−0.130214	−0.0651072	−	0.997878i	$-0.520739\pi$
$853$	−2.54840e50	−0.130214	−0.0651072	+	0.997878i	$0.520739\pi$
$854$	3.30622e51	1.65508
$855$	−2.77848e50	−0.136270
$856$	1.65588e51	0.795678
$857$	−2.64469e51	−1.24512	−0.622558	−	0.782573i	$-0.713907\pi$
$857$	−2.64469e51	−1.24512	−0.622558	+	0.782573i	$0.713907\pi$
$858$	1.15731e51	0.533852
$859$	−1.92463e51	−0.869894	−0.434947	−	0.900456i	$-0.643233\pi$
$859$	−1.92463e51	−0.869894	−0.434947	+	0.900456i	$0.643233\pi$
$860$	−8.89646e50	−0.393998
$861$	2.10265e51	0.912456
$862$	5.17661e51	2.20125
$863$	−1.08280e51	−0.451190	−0.225595	−	0.974221i	$-0.572433\pi$
$863$	−1.08280e51	−0.451190	−0.225595	+	0.974221i	$0.572433\pi$
$864$	−3.48992e50	−0.142503
$865$	1.17101e51	0.468573
$866$	1.35427e51	0.531058
$867$	9.66386e50	0.371378
$868$	7.50059e50	0.282488
$869$	3.46941e51	1.28059
$870$	9.27653e50	0.335582
$871$	−1.93557e51	−0.686264
$872$	3.35959e51	1.16748
$873$	2.58780e50	0.0881419
$874$	−1.93013e51	−0.644371
$875$	−2.67347e51	−0.874850
$876$	−4.75502e50	−0.152521
$877$	1.72464e51	0.542258	0.271129	−	0.962543i	$-0.412603\pi$
$877$	1.72464e51	0.542258	0.271129	+	0.962543i	$0.412603\pi$
$878$	−8.81354e50	−0.271642
$879$	2.36419e51	0.714295
$880$	−2.29811e51	−0.680650
$881$	8.76279e50	0.254428	0.127214	−	0.991875i	$-0.459397\pi$
$881$	8.76279e50	0.254428	0.127214	+	0.991875i	$0.459397\pi$
$882$	−2.15702e50	−0.0613981
$883$	−2.14016e51	−0.597221	−0.298610	−	0.954375i	$-0.596523\pi$
$883$	−2.14016e51	−0.597221	−0.298610	+	0.954375i	$0.596523\pi$
$884$	−1.48003e51	−0.404907
$885$	−7.20155e50	−0.193161
$886$	2.12480e50	0.0558764
$887$	−3.78615e51	−0.976189	−0.488095	−	0.872791i	$-0.662308\pi$
$887$	−3.78615e51	−0.976189	−0.488095	+	0.872791i	$0.662308\pi$
$888$	−2.70967e51	−0.684999
$889$	−1.06384e51	−0.263690
$890$	−4.39365e51	−1.06782
$891$	−4.51603e50	−0.107621
$892$	−3.81751e50	−0.0892061
$893$	−8.24675e48	−0.00188965
$894$	9.55318e50	0.214655
$895$	−1.97583e51	−0.435358
$896$	−4.97672e51	−1.07536
$897$	1.67420e51	0.354763
$898$	−7.55757e51	−1.57053
$899$	3.35922e51	0.684612
$900$	−4.40944e50	−0.0881333
$901$	1.01829e52	1.99612
$902$	1.02197e52	1.96482
$903$	−5.00386e51	−0.943559
$904$	2.72811e51	0.504562
$905$	4.02207e51	0.729625
$906$	−1.17064e51	−0.208295
$907$	5.56638e51	0.971506	0.485753	−	0.874096i	$-0.338545\pi$
$907$	5.56638e51	0.971506	0.485753	+	0.874096i	$0.338545\pi$
$908$	2.84004e51	0.486208
$909$	−1.73271e51	−0.290976
$910$	−3.02184e51	−0.497790
$911$	−4.53769e51	−0.733268	−0.366634	−	0.930365i	$-0.619490\pi$
$911$	−4.53769e51	−0.733268	−0.366634	+	0.930365i	$0.619490\pi$
$912$	−3.24693e51	−0.514711
$913$	3.60654e51	0.560857
$914$	7.74063e51	1.18091
$915$	3.34642e51	0.500855
$916$	3.27932e50	0.0481519
$917$	−3.51840e51	−0.506853
$918$	2.05798e51	0.290867
$919$	−9.66145e50	−0.133974	−0.0669870	−	0.997754i	$-0.521339\pi$
$919$	−9.66145e50	−0.133974	−0.0669870	+	0.997754i	$0.521339\pi$
$920$	−2.27686e51	−0.309777
$921$	−7.67328e51	−1.02432
$922$	1.54500e51	0.202366
$923$	1.28328e51	0.164926
$924$	1.58905e51	0.200391
$925$	−9.03710e51	−1.11828
$926$	−1.36135e50	−0.0165302
$927$	−3.24927e51	−0.387160
$928$	5.49972e51	0.643059
$929$	1.12588e52	1.29187	0.645935	−	0.763392i	$-0.276468\pi$
$929$	1.12588e52	1.29187	0.645935	+	0.763392i	$0.276468\pi$
$930$	2.70525e51	0.304618
$931$	−1.01812e51	−0.112508
$932$	4.68305e51	0.507867
$933$	1.21814e51	0.129649
$934$	−1.37307e52	−1.43424
$935$	6.87519e51	0.704825
$936$	1.92886e51	0.194076
$937$	−9.93521e51	−0.981147	−0.490574	−	0.871400i	$-0.663213\pi$
$937$	−9.93521e51	−0.981147	−0.490574	+	0.871400i	$0.663213\pi$
$938$	−9.47024e51	−0.917934
$939$	7.68654e51	0.731279
$940$	6.22254e48	0.000581072 0
$941$	−7.86741e51	−0.721129	−0.360565	−	0.932734i	$-0.617416\pi$
$941$	−7.86741e51	−0.721129	−0.360565	+	0.932734i	$0.617416\pi$
$942$	7.87710e51	0.708721
$943$	1.47841e52	1.30569
$944$	−8.41574e51	−0.729596
$945$	1.17918e51	0.100351
$946$	−2.43206e52	−2.03180
$947$	1.76717e52	1.44928	0.724641	−	0.689127i	$-0.242006\pi$
$947$	1.76717e52	1.44928	0.724641	+	0.689127i	$0.242006\pi$
$948$	−3.69864e51	−0.297780
$949$	6.93715e51	0.548305
$950$	−7.41639e51	−0.575479
$951$	−1.41012e52	−1.07423
$952$	1.13211e52	0.846722
$953$	−2.15077e52	−1.57931	−0.789656	−	0.613550i	$-0.789741\pi$
$953$	−2.15077e52	−1.57931	−0.789656	+	0.613550i	$0.789741\pi$
$954$	8.48858e51	0.611982
$955$	−6.31456e51	−0.446976
$956$	−4.46273e51	−0.310162
$957$	7.11674e51	0.485648
$958$	2.40724e52	1.61296
$959$	−3.90769e51	−0.257095
$960$	−1.85113e51	−0.119589
$961$	−5.96747e51	−0.378557
$962$	−2.52860e52	−1.57513
$963$	−6.02976e51	−0.368841
$964$	9.29935e50	0.0558605
$965$	1.91164e51	0.112766
$966$	8.19140e51	0.474524
$967$	5.62647e51	0.320091	0.160045	−	0.987110i	$-0.448836\pi$
$967$	5.62647e51	0.320091	0.160045	+	0.987110i	$0.448836\pi$
$968$	7.95875e50	0.0444658
$969$	9.71375e51	0.532992
$970$	−3.28416e51	−0.176978
$971$	3.42787e51	0.181421	0.0907104	−	0.995877i	$-0.471086\pi$
$971$	3.42787e51	0.181421	0.0907104	+	0.995877i	$0.471086\pi$
$972$	4.81441e50	0.0250255
$973$	2.31893e52	1.18389
$974$	1.77734e52	0.891230
$975$	6.43299e51	0.316834
$976$	3.91064e52	1.89180
$977$	1.18458e52	0.562872	0.281436	−	0.959580i	$-0.409189\pi$
$977$	1.18458e52	0.562872	0.281436	+	0.959580i	$0.409189\pi$
$978$	−2.55883e52	−1.19429
$979$	−3.37070e52	−1.54534
$980$	7.68220e50	0.0345963
$981$	−1.22337e52	−0.541191
$982$	4.00436e52	1.74013
$983$	2.75159e52	1.17462	0.587311	−	0.809362i	$-0.300187\pi$
$983$	2.75159e52	1.17462	0.587311	+	0.809362i	$0.300187\pi$
$984$	1.70329e52	0.714291
$985$	−5.91197e51	−0.243556
$986$	−3.24314e52	−1.31256
$987$	3.49990e49	0.00139157
$988$	−5.82346e51	−0.227475
$989$	−3.51830e52	−1.35020
$990$	5.73125e51	0.216089
$991$	−3.30440e52	−1.22406	−0.612031	−	0.790834i	$-0.709647\pi$
$991$	−3.30440e52	−1.22406	−0.612031	+	0.790834i	$0.709647\pi$
$992$	1.60384e52	0.583725
$993$	−8.58119e51	−0.306857
$994$	6.27873e51	0.220602
$995$	8.55620e51	0.295377
$996$	−3.84483e51	−0.130418
$997$	−4.71253e52	−1.57068	−0.785342	−	0.619062i	$-0.787513\pi$
$997$	−4.71253e52	−1.57068	−0.785342	+	0.619062i	$0.787513\pi$
$998$	1.99391e51	0.0653012
$999$	9.86707e51	0.317536

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.36.a.a.1.2	✓	2
3.2	odd	2		9.36.a.a.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.36.a.a.1.2	✓	2	1.1	even	1	trivial
9.36.a.a.1.1		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 36 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q+218549. q^{2} +1.29140e8 q^{3} +1.34041e10 q^{4} -9.68425e11 q^{5} +2.82235e13 q^{6} -5.65365e14 q^{7} -4.57985e15 q^{8} +1.66772e16 q^{9} +O(q^{10})\)	\(q+218549. q^{2} +1.29140e8 q^{3} +1.34041e10 q^{4} -9.68425e11 q^{5} +2.82235e13 q^{6} -5.65365e14 q^{7} -4.57985e15 q^{8} +1.66772e16 q^{9} -2.11649e17 q^{10} -1.62372e18 q^{11} +1.73100e18 q^{12} -2.52538e19 q^{13} -1.23560e20 q^{14} -1.25063e20 q^{15} -1.46148e21 q^{16} +4.37227e21 q^{17} +3.64479e21 q^{18} +1.72036e22 q^{19} -1.29808e22 q^{20} -7.30113e22 q^{21} -3.54863e23 q^{22} -5.13356e23 q^{23} -5.91442e23 q^{24} -1.97254e24 q^{25} -5.51920e24 q^{26} +2.15369e24 q^{27} -7.57819e24 q^{28} -3.39397e25 q^{29} -2.73323e25 q^{30} -9.89761e25 q^{31} -1.62044e26 q^{32} -2.09687e26 q^{33} +9.55557e26 q^{34} +5.47514e26 q^{35} +2.23542e26 q^{36} +4.58147e27 q^{37} +3.75982e27 q^{38} -3.26128e27 q^{39} +4.43524e27 q^{40} -2.87989e28 q^{41} -1.59566e28 q^{42} +6.85354e28 q^{43} -2.17644e28 q^{44} -1.61506e28 q^{45} -1.12194e29 q^{46} -4.79363e26 q^{47} -1.88736e29 q^{48} -5.91811e28 q^{49} -4.31096e29 q^{50} +5.64636e29 q^{51} -3.38503e29 q^{52} +2.32896e30 q^{53} +4.70688e29 q^{54} +1.57245e30 q^{55} +2.58929e30 q^{56} +2.22167e30 q^{57} -7.41751e30 q^{58} +5.75836e30 q^{59} -1.67635e30 q^{60} -2.67580e31 q^{61} -2.16312e31 q^{62} -9.42870e30 q^{63} +1.48016e31 q^{64} +2.44564e31 q^{65} -4.58270e31 q^{66} +7.66448e31 q^{67} +5.86062e31 q^{68} -6.62949e31 q^{69} +1.19659e32 q^{70} -5.08152e31 q^{71} -7.63790e31 q^{72} -2.74698e32 q^{73} +1.00128e33 q^{74} -2.54734e32 q^{75} +2.30597e32 q^{76} +9.17994e32 q^{77} -7.12750e32 q^{78} -2.13670e33 q^{79} +1.41534e33 q^{80} +2.78128e32 q^{81} -6.29399e33 q^{82} -2.22116e33 q^{83} -9.78648e32 q^{84} -4.23422e33 q^{85} +1.49784e34 q^{86} -4.38298e33 q^{87} +7.43639e33 q^{88} +2.07592e34 q^{89} -3.52970e33 q^{90} +1.42776e34 q^{91} -6.88105e33 q^{92} -1.27818e34 q^{93} -1.04765e32 q^{94} -1.66604e34 q^{95} -2.09263e34 q^{96} +1.55170e34 q^{97} -1.29340e34 q^{98} -2.70791e34 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 60912 q^{2} + 258280326 q^{3} + 57142939904 q^{4} - 1333779496740 q^{5} - 7866185608656 q^{6} - 12\!\cdots\!44 q^{7}+ \cdots + 33\!\cdots\!38 q^{9}+O(q^{10}) \) 2 * q - 60912 * q^2 + 258280326 * q^3 + 57142939904 * q^4 - 1333779496740 * q^5 - 7866185608656 * q^6 - 1201512782952944 * q^7 - 7200956480385024 * q^8 + 33354363399333138 * q^9	\( 2 q - 60912 q^{2} + 258280326 q^{3} + 57142939904 q^{4} - 1333779496740 q^{5} - 7866185608656 q^{6} - 12\!\cdots\!44 q^{7}+ \cdots - 24\!\cdots\!08 q^{99}+O(q^{100}) \) 2 * q - 60912 * q^2 + 258280326 * q^3 + 57142939904 * q^4 - 1333779496740 * q^5 - 7866185608656 * q^6 - 1201512782952944 * q^7 - 7200956480385024 * q^8 + 33354363399333138 * q^9 - 109546268366103840 * q^10 - 1474443852221320632 * q^11 + 7379448573501764352 * q^12 + 30005213658205678828 * q^13 + 54218555116626208896 * q^14 - 172244501615061568620 * q^15 - 2231841205794746859520 * q^16 + 6184381389914139549732 * q^17 - 1015840491690090050928 * q^18 - 16041801819745886283464 * q^19 - 28961016325243993797120 * q^20 - 155163556637126809489872 * q^21 - 396579699860875428206016 * q^22 + 493815500335770240457872 * q^23 - 929932693632828302118912 * q^24 - 4749434950612517913953650 * q^25 - 20961946321168144205905056 * q^26 + 4307387926151115532621494 * q^27 - 35402577540025316459804672 * q^28 - 78897034119133299270862548 * q^29 - 14146822952840393572525920 * q^30 - 121361162005932759518102048 * q^31 + 143302306271809670376062976 * q^32 - 190409919410209258491743016 * q^33 + 449143657751740113402393888 * q^34 + 779933046239496469635406560 * q^35 + 952983191632135329204869376 * q^36 + 1665586101311009800179225916 * q^37 + 13050613787750726714918949312 * q^38 + 3874878182670507651373568964 * q^39 + 5392874139550798797233971200 * q^40 - 32980805501198249253748474188 * q^41 + 7001793045385592626901490048 * q^42 + 10123013327213364172045565320 * q^43 - 15235271860221308020423891968 * q^44 - 22243683014422814226622485060 * q^45 - 393659059100782290327277976448 * q^46 - 52868797790119241441973340320 * q^47 - 288220337106450153982150901760 * q^48 - 33315801381283359525177211950 * q^49 + 344939599216803384993788031600 * q^50 + 798652020747678537457137086316 * q^51 + 2078463386549395848792119629312 * q^52 - 311667073507824309034483504068 * q^53 - 131185806678858374661520221264 * q^54 + 1517912603348115987616960289520 * q^55 + 4256698060894361051133439672320 * q^56 - 2071640901815680373226005164632 * q^57 + 5146318056193673657686145949024 * q^58 + 8206652402409843531446945489064 * q^59 - 3740030368887670373731065730560 * q^60 - 40510115780163122120323644143540 * q^61 - 15375406801958157810336643623168 * q^62 - 20037846995778288029192016929136 * q^63 - 44061412872652964817027532324864 * q^64 + 4267286913056298521798082678120 * q^65 - 51214367082524530121219703820608 * q^66 + 9614178644969763076047165071512 * q^67 + 137865760810106900938814269960704 * q^68 + 63771414205287923583278784713136 * q^69 + 54706539117989427731737467528960 * q^70 + 440682364431613985484841574021424 * q^71 - 120091659634772509086649541062656 * q^72 - 137360814802453541976117247925708 * q^73 + 1816151331037101511972964229252576 * q^74 - 613342803679997513248394335444950 * q^75 - 1223517123700955304313856844145664 * q^76 + 823032801538075311095559373941312 * q^77 - 2707029164712904493158084494364128 * q^78 - 1062176452444830588280514345530880 * q^79 + 1696790522509490100466806063759360 * q^80 + 556256778887387022514571552463522 * q^81 - 5125322741804470577254960235914848 * q^82 - 5500428376968501051342971557654344 * q^83 - 4571894634139008391745758290241536 * q^84 - 4896281708923407655277594784149640 * q^85 + 31302341732489137882852872722637888 * q^86 - 10188775846361435686566970599315324 * q^87 + 7045123450598581655224211356532736 * q^88 + 24031331951145259183892358374185236 * q^89 - 1826923022061949738940149630524960 * q^90 - 20875281935852853469733451535930528 * q^91 + 37171500488799640786609596619278336 * q^92 - 15672600243315563531207499929353824 * q^93 + 14536054971850529082624931738946304 * q^94 - 4514020436462465865986658897865200 * q^95 + 18506083190217423137341044018905088 * q^96 + 837150039420646979154473176256452 * q^97 - 20162335337791628242056365171146608 * q^98 - 24589568029451287505732827240351608 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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