LMFDB - Embedded newform 3.44.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,44,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, 44, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 44);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 44 $
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:	$35.1331186037$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 908401710x + 974756489742 $ x^3 - x^2 - 908401710*x + 974756489742
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{5}\cdot 5\cdot 11 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$29588.6$ 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)

$f(q)$	$=$	$q-1.22147e6 q^{2} +1.04604e10 q^{3} -7.30411e12 q^{4} -8.84097e14 q^{5} -1.27770e16 q^{6} +1.48034e18 q^{7} +1.96659e19 q^{8} +1.09419e20 q^{9} +O(q^{10})$	\(q-1.22147e6 q^{2} +1.04604e10 q^{3} -7.30411e12 q^{4} -8.84097e14 q^{5} -1.27770e16 q^{6} +1.48034e18 q^{7} +1.96659e19 q^{8} +1.09419e20 q^{9} +1.07990e21 q^{10} +1.46320e21 q^{11} -7.64035e22 q^{12} -4.36401e23 q^{13} -1.80819e24 q^{14} -9.24796e24 q^{15} +4.02263e25 q^{16} +3.51740e26 q^{17} -1.33652e26 q^{18} -1.50013e27 q^{19} +6.45753e27 q^{20} +1.54849e28 q^{21} -1.78725e27 q^{22} -1.10333e29 q^{23} +2.05712e29 q^{24} -3.55242e29 q^{25} +5.33051e29 q^{26} +1.14456e30 q^{27} -1.08126e31 q^{28} -3.00258e31 q^{29} +1.12961e31 q^{30} +1.83651e32 q^{31} -2.22118e32 q^{32} +1.53056e31 q^{33} -4.29639e32 q^{34} -1.30876e33 q^{35} -7.99208e32 q^{36} -9.66835e33 q^{37} +1.83236e33 q^{38} -4.56491e33 q^{39} -1.73866e34 q^{40} -5.73635e34 q^{41} -1.89143e34 q^{42} -1.24932e35 q^{43} -1.06874e34 q^{44} -9.67370e34 q^{45} +1.34768e35 q^{46} -6.52473e35 q^{47} +4.20781e35 q^{48} +7.59027e33 q^{49} +4.33917e35 q^{50} +3.67932e36 q^{51} +3.18752e36 q^{52} +2.03194e37 q^{53} -1.39805e36 q^{54} -1.29361e36 q^{55} +2.91122e37 q^{56} -1.56919e37 q^{57} +3.66756e37 q^{58} -7.05565e37 q^{59} +6.75481e37 q^{60} -4.16411e38 q^{61} -2.24324e38 q^{62} +1.61977e38 q^{63} -8.25234e37 q^{64} +3.85821e38 q^{65} -1.86953e37 q^{66} -1.46698e39 q^{67} -2.56914e39 q^{68} -1.15412e39 q^{69} +1.59861e39 q^{70} +6.58697e39 q^{71} +2.15182e39 q^{72} +8.76849e39 q^{73} +1.18096e40 q^{74} -3.71595e39 q^{75} +1.09571e40 q^{76} +2.16603e39 q^{77} +5.57590e39 q^{78} -3.63007e39 q^{79} -3.55639e40 q^{80} +1.19725e40 q^{81} +7.00677e40 q^{82} -2.43814e41 q^{83} -1.13103e41 q^{84} -3.10972e41 q^{85} +1.52600e41 q^{86} -3.14080e41 q^{87} +2.87752e40 q^{88} +6.12259e41 q^{89} +1.18161e41 q^{90} -6.46022e41 q^{91} +8.05884e41 q^{92} +1.92106e42 q^{93} +7.96976e41 q^{94} +1.32626e42 q^{95} -2.32344e42 q^{96} +8.54423e41 q^{97} -9.27128e39 q^{98} +1.60102e41 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 4857024 q^{2} + 31381059609 q^{3} - 1781058029568 q^{4} - 507753321105270 q^{5} + 50\!\cdots\!72 q^{6}+ \cdots + 32\!\cdots\!27 q^{9}+O(q^{10}) $ 3 * q + 4857024 * q^2 + 31381059609 * q^3 - 1781058029568 * q^4 - 507753321105270 * q^5 + 50806186555447872 * q^6 - 1633169303707089288 * q^7 + 11196260694472851456 * q^8 + 328256967394537077627 * q^9	$ 3 q + 4857024 q^{2} + 31381059609 q^{3} - 1781058029568 q^{4} - 507753321105270 q^{5} + 50\!\cdots\!72 q^{6}+ \cdots - 30\!\cdots\!80 q^{99}+O(q^{100}) $ 3 * q + 4857024 * q^2 + 31381059609 * q^3 - 1781058029568 * q^4 - 507753321105270 * q^5 + 50806186555447872 * q^6 - 1633169303707089288 * q^7 + 11196260694472851456 * q^8 + 328256967394537077627 * q^9 - 2286850690696789595520 * q^10 - 27750966261606959036820 * q^11 - 18630496064320497506304 * q^12 - 994786398159560287290750 * q^13 - 9473256819232835003171328 * q^14 - 5311279078757398544679810 * q^15 + 23637690650696707825729536 * q^16 - 160517621023312837046953482 * q^17 + 531450656267494684974734016 * q^18 - 3227133683900578441639486764 * q^19 - 19920520041146285724571791360 * q^20 - 17083527757073731207537789464 * q^21 - 172470540148626161048719521024 * q^22 + 114780279514038504224277444504 * q^23 + 117116841417052096124312813568 * q^24 + 1825420275602850437617559193525 * q^25 + 1775037275334840765729836075136 * q^26 + 3433683820292512484657849089281 * q^27 - 8483554335441104836174737260544 * q^28 - 28241588775620253186792106789758 * q^29 - 23921265947212925347314706450560 * q^30 - 56947467162250619768506214477136 * q^31 - 290372748061904590918491662450688 * q^32 - 290284908820945289887889881934460 * q^33 - 1778246324363072918021693922216576 * q^34 - 3641689125493658442558484764497520 * q^35 - 194881569179893810108620559091712 * q^36 - 7771759793894794226158134990367878 * q^37 - 11984574206649783949969526048471808 * q^38 - 10405817086289189756233396954772250 * q^39 - 75089135561625836440773237699379200 * q^40 - 150622420768399427659977962302801266 * q^41 - 99093612311903777628193716002563584 * q^42 - 503269829459862138385119574866599988 * q^43 - 589156491500651091472842134125289472 * q^44 - 55557855123506843126788989142931430 * q^45 + 1201666039209211956008162792803812864 * q^46 + 517590816657574666863303783889459536 * q^47 + 247258593109538461886425117709303808 * q^48 + 1183207682852736238558590379440977403 * q^49 + 5363972694460023429439963707950510400 * q^50 - 1679071011209150572675116916830702846 * q^51 + 19510568225567423700598614061466308608 * q^52 + 3147649955233970731028729152905020634 * q^53 + 5559161574524140052760934938338653248 * q^54 + 72798121427511388475535050768468313960 * q^55 + 64659225918940531158350848060065054720 * q^56 - 33756958166898605235556353943083505092 * q^57 + 165860584701603780784654252956514011264 * q^58 - 178011039218636820023529236138863835076 * q^59 - 208375675617830241670577713556023726080 * q^60 - 123533499732384273913895969461615945518 * q^61 - 685215538112102475249420816230843667456 * q^62 - 178699734292245610143928973763292053192 * q^63 - 971015593402068342273570470768658087936 * q^64 - 2575578837917643212594035173081316043940 * q^65 - 1804102767066821759775567080792024239872 * q^66 + 1292774342372783673662410484960847098148 * q^67 - 2717789569206669919054906507790539296768 * q^68 + 1200642264455907951127749596978071146312 * q^69 + 1868357626946632141981582698458836116480 * q^70 + 22400468745595901369803420176388102887816 * q^71 + 1225083527242103952511819425579970658304 * q^72 + 31313509370447648548173493799361498480654 * q^73 + 12824367911381949889146580637796075349632 * q^74 + 19094540826723419331062786999031330610575 * q^75 - 45893435926810400921777338109031978491904 * q^76 + 15925552922292610065970442499593057720544 * q^77 + 18567516848493194501297063421213806260608 * q^78 - 43825544899857898915807551182364364018080 * q^79 + 51052771545930899482561003058120286535680 * q^80 + 35917545547686059365808220080151141317043 * q^81 - 207555016724016234735599639977066643719296 * q^82 + 89911369720242570860406785197345580904468 * q^83 - 88740974765555897390939203171014875922432 * q^84 - 609771200949453596987959942886782705526220 * q^85 - 1052084075872403200090705454196607607512320 * q^86 - 295416993606868163734131771553363142894874 * q^87 - 866229044996425850996432449444164589584384 * q^88 + 65289466052051143331840751197428752211806 * q^89 - 250224890870743552579783277069120057143680 * q^90 + 1361620777581018817929645459439738348447824 * q^91 + 3753917639661643691216268373890598977257472 * q^92 - 595690620533385591184229099131314527866608 * q^93 + 7862327422462694583153035384185107177477120 * q^94 + 9328236864095865156237338173319138974757400 * q^95 - 3037401505253255729894648973244849050353664 * q^96 + 6130807410554375967448029821362307484893478 * q^97 - 2033290778553828878915746018754102329738560 * q^98 - 3036482675767738016566552437404420497075380 * 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 $

$2$	−1.22147e6	−0.411849	−0.205924	−	0.978568i	$-0.566020\pi$
$2$	−1.22147e6	−0.411849	−0.205924	+	0.978568i	$0.566020\pi$
$3$	1.04604e10	0.577350
$3$	1.04604e10	0.577350
$4$	−7.30411e12	−0.830381
$5$	−8.84097e14	−0.829172	−0.414586	−	0.910010i	$-0.636074\pi$
$5$	−8.84097e14	−0.829172	−0.414586	+	0.910010i	$0.636074\pi$
$6$	−1.27770e16	−0.237781
$7$	1.48034e18	1.00174	0.500868	−	0.865524i	$-0.333014\pi$
$7$	1.48034e18	1.00174	0.500868	+	0.865524i	$0.333014\pi$
$8$	1.96659e19	0.753840
$9$	1.09419e20	0.333333
$10$	1.07990e21	0.341493
$11$	1.46320e21	0.0596158	0.0298079	−	0.999556i	$-0.490510\pi$
$11$	1.46320e21	0.0596158	0.0298079	+	0.999556i	$0.490510\pi$
$12$	−7.64035e22	−0.479420
$13$	−4.36401e23	−0.489896	−0.244948	−	0.969536i	$-0.578771\pi$
$13$	−4.36401e23	−0.489896	−0.244948	+	0.969536i	$0.578771\pi$
$14$	−1.80819e24	−0.412564
$15$	−9.24796e24	−0.478723
$16$	4.02263e25	0.519913
$17$	3.51740e26	1.23472	0.617362	−	0.786680i	$-0.288202\pi$
$17$	3.51740e26	1.23472	0.617362	+	0.786680i	$0.288202\pi$
$18$	−1.33652e26	−0.137283
$19$	−1.50013e27	−0.481865	−0.240933	−	0.970542i	$-0.577453\pi$
$19$	−1.50013e27	−0.481865	−0.240933	+	0.970542i	$0.577453\pi$
$20$	6.45753e27	0.688528
$21$	1.54849e28	0.578353
$22$	−1.78725e27	−0.0245527
$23$	−1.10333e29	−0.582850	−0.291425	−	0.956594i	$-0.594129\pi$
$23$	−1.10333e29	−0.582850	−0.291425	+	0.956594i	$0.594129\pi$
$24$	2.05712e29	0.435230
$25$	−3.55242e29	−0.312474
$26$	5.33051e29	0.201763
$27$	1.14456e30	0.192450
$28$	−1.08126e31	−0.831822
$29$	−3.00258e31	−1.08627	−0.543135	−	0.839646i	$-0.682763\pi$
$29$	−3.00258e31	−1.08627	−0.543135	+	0.839646i	$0.682763\pi$
$30$	1.12961e31	0.197161
$31$	1.83651e32	1.58386	0.791931	−	0.610611i	$-0.209076\pi$
$31$	1.83651e32	1.58386	0.791931	+	0.610611i	$0.209076\pi$
$32$	−2.22118e32	−0.967965
$33$	1.53056e31	0.0344192
$34$	−4.29639e32	−0.508519
$35$	−1.30876e33	−0.830612
$36$	−7.99208e32	−0.276794
$37$	−9.66835e33	−1.85787	−0.928935	−	0.370243i	$-0.879274\pi$
$37$	−9.66835e33	−1.85787	−0.928935	+	0.370243i	$0.879274\pi$
$38$	1.83236e33	0.198456
$39$	−4.56491e33	−0.282841
$40$	−1.73866e34	−0.625063
$41$	−5.73635e34	−1.21278	−0.606391	−	0.795167i	$-0.707383\pi$
$41$	−5.73635e34	−1.21278	−0.606391	+	0.795167i	$0.707383\pi$
$42$	−1.89143e34	−0.238194
$43$	−1.24932e35	−0.948638	−0.474319	−	0.880353i	$-0.657306\pi$
$43$	−1.24932e35	−0.948638	−0.474319	+	0.880353i	$0.657306\pi$
$44$	−1.06874e34	−0.0495038
$45$	−9.67370e34	−0.276391
$46$	1.34768e35	0.240046
$47$	−6.52473e35	−0.731912	−0.365956	−	0.930632i	$-0.619258\pi$
$47$	−6.52473e35	−0.731912	−0.365956	+	0.930632i	$0.619258\pi$
$48$	4.20781e35	0.300172
$49$	7.59027e33	0.00347569
$50$	4.33917e35	0.128692
$51$	3.67932e36	0.712868
$52$	3.18752e36	0.406800
$53$	2.03194e37	1.72179	0.860895	−	0.508783i	$-0.169904\pi$
$53$	2.03194e37	1.72179	0.860895	+	0.508783i	$0.169904\pi$
$54$	−1.39805e36	−0.0792603
$55$	−1.29361e36	−0.0494317
$56$	2.91122e37	0.755149
$57$	−1.56919e37	−0.278205
$58$	3.66756e37	0.447379
$59$	−7.05565e37	−0.595963	−0.297981	−	0.954572i	$-0.596313\pi$
$59$	−7.05565e37	−0.595963	−0.297981	+	0.954572i	$0.596313\pi$
$60$	6.75481e37	0.397522
$61$	−4.16411e38	−1.71763	−0.858816	−	0.512284i	$-0.828800\pi$
$61$	−4.16411e38	−1.71763	−0.858816	+	0.512284i	$0.828800\pi$
$62$	−2.24324e38	−0.652311
$63$	1.61977e38	0.333912
$64$	−8.25234e37	−0.121257
$65$	3.85821e38	0.406208
$66$	−1.86953e37	−0.0141755
$67$	−1.46698e39	−0.805038	−0.402519	−	0.915412i	$-0.631865\pi$
$67$	−1.46698e39	−0.805038	−0.402519	+	0.915412i	$0.631865\pi$
$68$	−2.56914e39	−1.02529
$69$	−1.15412e39	−0.336509
$70$	1.59861e39	0.342086
$71$	6.58697e39	1.03904	0.519519	−	0.854459i	$-0.326111\pi$
$71$	6.58697e39	1.03904	0.519519	+	0.854459i	$0.326111\pi$
$72$	2.15182e39	0.251280
$73$	8.76849e39	0.761173	0.380587	−	0.924745i	$-0.375722\pi$
$73$	8.76849e39	0.761173	0.380587	+	0.924745i	$0.375722\pi$
$74$	1.18096e40	0.765161
$75$	−3.71595e39	−0.180407
$76$	1.09571e40	0.400132
$77$	2.16603e39	0.0597193
$78$	5.57590e39	0.116488
$79$	−3.63007e39	−0.0576676	−0.0288338	−	0.999584i	$-0.509179\pi$
$79$	−3.63007e39	−0.0576676	−0.0288338	+	0.999584i	$0.509179\pi$
$80$	−3.55639e40	−0.431097
$81$	1.19725e40	0.111111
$82$	7.00677e40	0.499482
$83$	−2.43814e41	−1.33930	−0.669652	−	0.742675i	$-0.733557\pi$
$83$	−2.43814e41	−1.33930	−0.669652	+	0.742675i	$0.733557\pi$
$84$	−1.13103e41	−0.480253
$85$	−3.10972e41	−1.02380
$86$	1.52600e41	0.390695
$87$	−3.14080e41	−0.627158
$88$	2.87752e40	0.0449407
$89$	6.12259e41	0.749981	0.374991	−	0.927029i	$-0.377646\pi$
$89$	6.12259e41	0.749981	0.374991	+	0.927029i	$0.377646\pi$
$90$	1.18161e41	0.113831
$91$	−6.46022e41	−0.490746
$92$	8.05884e41	0.483988
$93$	1.92106e42	0.914443
$94$	7.96976e41	0.301437
$95$	1.32626e42	0.399549
$96$	−2.32344e42	−0.558855
$97$	8.54423e41	0.164468	0.0822338	−	0.996613i	$-0.473795\pi$
$97$	8.54423e41	0.164468	0.0822338	+	0.996613i	$0.473795\pi$
$98$	−9.27128e39	−0.00143146
$99$	1.60102e41	0.0198719
$100$	2.59472e42	0.259472
$101$	1.68908e43	1.36377	0.681885	−	0.731459i	$-0.261160\pi$
$101$	1.68908e43	1.36377	0.681885	+	0.731459i	$0.261160\pi$
$102$	−4.49418e42	−0.293594
$103$	−2.32882e43	−1.23349	−0.616744	−	0.787164i	$-0.711549\pi$
$103$	−2.32882e43	−1.23349	−0.616744	+	0.787164i	$0.711549\pi$
$104$	−8.58222e42	−0.369303
$105$	−1.36901e43	−0.479554
$106$	−2.48196e43	−0.709117
$107$	2.29289e43	0.535343	0.267671	−	0.963510i	$-0.413746\pi$
$107$	2.29289e43	0.535343	0.267671	+	0.963510i	$0.413746\pi$
$108$	−8.36000e42	−0.159807
$109$	−4.44751e43	−0.697344	−0.348672	−	0.937245i	$-0.613367\pi$
$109$	−4.44751e43	−0.697344	−0.348672	+	0.937245i	$0.613367\pi$
$110$	1.58011e42	0.0203584
$111$	−1.01134e44	−1.07264
$112$	5.95486e43	0.520815
$113$	1.44503e44	1.04397	0.521987	−	0.852954i	$-0.325191\pi$
$113$	1.44503e44	1.04397	0.521987	+	0.852954i	$0.325191\pi$
$114$	1.91671e43	0.114578
$115$	9.75450e43	0.483283
$116$	2.19312e44	0.902017
$117$	−4.77506e43	−0.163299
$118$	8.61827e43	0.245446
$119$	5.20694e44	1.23687
$120$	−1.81870e44	−0.360880
$121$	−6.00260e44	−0.996446
$122$	5.08633e44	0.707405
$123$	−6.00042e44	−0.700200
$124$	−1.34141e45	−1.31521
$125$	1.31917e45	1.08827
$126$	−1.97850e44	−0.137521
$127$	−1.35712e45	−0.795860	−0.397930	−	0.917416i	$-0.630271\pi$
$127$	−1.35712e45	−0.795860	−0.397930	+	0.917416i	$0.630271\pi$
$128$	2.05457e45	1.01790
$129$	−1.30683e45	−0.547696
$130$	−4.71268e44	−0.167296
$131$	−4.22352e45	−1.27157	−0.635787	−	0.771864i	$-0.719324\pi$
$131$	−4.22352e45	−1.27157	−0.635787	+	0.771864i	$0.719324\pi$
$132$	−1.11794e44	−0.0285810
$133$	−2.22070e45	−0.482702
$134$	1.79187e45	0.331554
$135$	−1.01190e45	−0.159574
$136$	6.91728e45	0.930784
$137$	1.16008e46	1.33350	0.666751	−	0.745280i	$-0.267684\pi$
$137$	1.16008e46	1.33350	0.666751	+	0.745280i	$0.267684\pi$
$138$	1.40973e45	0.138591
$139$	−3.54561e45	−0.298451	−0.149225	−	0.988803i	$-0.547678\pi$
$139$	−3.54561e45	−0.298451	−0.149225	+	0.988803i	$0.547678\pi$
$140$	9.55934e45	0.689724
$141$	−6.82510e45	−0.422569
$142$	−8.04579e45	−0.427926
$143$	−6.38542e44	−0.0292055
$144$	4.40152e45	0.173304
$145$	2.65457e46	0.900704
$146$	−1.07104e46	−0.313488
$147$	7.93969e43	0.00200669
$148$	7.06186e46	1.54274
$149$	−7.81974e46	−1.47804	−0.739022	−	0.673681i	$-0.764712\pi$
$149$	−7.81974e46	−1.47804	−0.739022	+	0.673681i	$0.764712\pi$
$150$	4.53892e45	0.0743003
$151$	−1.13420e47	−1.60947	−0.804736	−	0.593633i	$-0.797693\pi$
$151$	−1.13420e47	−1.60947	−0.804736	+	0.593633i	$0.797693\pi$
$152$	−2.95014e46	−0.363249
$153$	3.84870e46	0.411574
$154$	−2.64574e45	−0.0245953
$155$	−1.62365e47	−1.31329
$156$	3.33426e46	0.234866
$157$	−6.59354e46	−0.404833	−0.202417	−	0.979300i	$-0.564879\pi$
$157$	−6.59354e46	−0.404833	−0.202417	+	0.979300i	$0.564879\pi$
$158$	4.43402e45	0.0237503
$159$	2.12548e47	0.994076
$160$	1.96374e47	0.802610
$161$	−1.63330e47	−0.583862
$162$	−1.46241e46	−0.0457610
$163$	3.98621e47	1.09276	0.546382	−	0.837536i	$-0.316005\pi$
$163$	3.98621e47	1.09276	0.546382	+	0.837536i	$0.316005\pi$
$164$	4.18989e47	1.00707
$165$	−1.35316e46	−0.0285394
$166$	2.97811e47	0.551590
$167$	−5.79083e47	−0.942619	−0.471310	−	0.881968i	$-0.656219\pi$
$167$	−5.79083e47	−0.942619	−0.471310	+	0.881968i	$0.656219\pi$
$168$	3.04524e47	0.435985
$169$	−6.03086e47	−0.760002
$170$	3.79843e47	0.421650
$171$	−1.64142e47	−0.160622
$172$	9.12513e47	0.787730
$173$	−2.23477e48	−1.70311	−0.851554	−	0.524267i	$-0.824340\pi$
$173$	−2.23477e48	−1.70311	−0.851554	+	0.524267i	$0.824340\pi$
$174$	3.83640e47	0.258294
$175$	−5.25878e47	−0.313016
$176$	5.88591e46	0.0309950
$177$	−7.38046e47	−0.344079
$178$	−7.47856e47	−0.308879
$179$	1.61027e47	0.0589603	0.0294801	−	0.999565i	$-0.490615\pi$
$179$	1.61027e47	0.0589603	0.0294801	+	0.999565i	$0.490615\pi$
$180$	7.06577e47	0.229509
$181$	−7.92049e47	−0.228383	−0.114191	−	0.993459i	$-0.536428\pi$
$181$	−7.92049e47	−0.228383	−0.114191	+	0.993459i	$0.536428\pi$
$182$	7.89096e47	0.202113
$183$	−4.35580e48	−0.991676
$184$	−2.16980e48	−0.439376
$185$	8.54775e48	1.54049
$186$	−2.34651e48	−0.376612
$187$	5.14666e47	0.0736090
$188$	4.76573e48	0.607765
$189$	1.69434e48	0.192784
$190$	−1.61998e48	−0.164554
$191$	9.55527e48	0.867013	0.433507	−	0.901150i	$-0.357276\pi$
$191$	9.55527e48	0.867013	0.433507	+	0.901150i	$0.357276\pi$
$192$	−8.63224e47	−0.0700079
$193$	2.03467e48	0.147574	0.0737872	−	0.997274i	$-0.476491\pi$
$193$	2.03467e48	0.147574	0.0737872	+	0.997274i	$0.476491\pi$
$194$	−1.04365e48	−0.0677358
$195$	4.03582e48	0.234524
$196$	−5.54401e46	−0.00288615
$197$	2.76148e49	1.28860	0.644300	−	0.764773i	$-0.277149\pi$
$197$	2.76148e49	1.28860	0.644300	+	0.764773i	$0.277149\pi$
$198$	−1.95560e47	−0.00818422
$199$	−3.48688e49	−1.30947	−0.654735	−	0.755858i	$-0.727220\pi$
$199$	−3.48688e49	−1.30947	−0.654735	+	0.755858i	$0.727220\pi$
$200$	−6.98615e48	−0.235555
$201$	−1.53451e49	−0.464789
$202$	−2.06316e49	−0.561667
$203$	−4.44484e49	−1.08816
$204$	−2.68742e49	−0.591952
$205$	5.07148e49	1.00560
$206$	2.84458e49	0.508011
$207$	−1.20725e49	−0.194283
$208$	−1.75548e49	−0.254703
$209$	−2.19499e48	−0.0287268
$210$	1.67221e49	0.197504
$211$	1.86123e49	0.198484	0.0992422	−	0.995063i	$-0.468358\pi$
$211$	1.86123e49	0.198484	0.0992422	+	0.995063i	$0.468358\pi$
$212$	−1.48415e50	−1.42974
$213$	6.89021e49	0.599889
$214$	−2.80069e49	−0.220480
$215$	1.10452e50	0.786584
$216$	2.25088e49	0.145077
$217$	2.71866e50	1.58661
$218$	5.43249e49	0.287200
$219$	9.17215e49	0.439463
$220$	9.44867e48	0.0410471
$221$	−1.53500e50	−0.604886
$222$	1.23533e50	0.441766
$223$	2.85176e50	0.925889	0.462945	−	0.886387i	$-0.346793\pi$
$223$	2.85176e50	0.925889	0.462945	+	0.886387i	$0.346793\pi$
$224$	−3.28810e50	−0.969646
$225$	−3.88702e49	−0.104158
$226$	−1.76506e50	−0.429959
$227$	−6.18346e50	−1.36986	−0.684929	−	0.728609i	$-0.740167\pi$
$227$	−6.18346e50	−1.36986	−0.684929	+	0.728609i	$0.740167\pi$
$228$	1.14615e50	0.231016
$229$	−3.54720e50	−0.650762	−0.325381	−	0.945583i	$-0.605493\pi$
$229$	−3.54720e50	−0.650762	−0.325381	+	0.945583i	$0.605493\pi$
$230$	−1.19148e50	−0.199040
$231$	2.26575e49	0.0344789
$232$	−5.90484e50	−0.818873
$233$	8.36113e50	1.05709	0.528546	−	0.848905i	$-0.322738\pi$
$233$	8.36113e50	1.05709	0.528546	+	0.848905i	$0.322738\pi$
$234$	5.83258e49	0.0672543
$235$	5.76849e50	0.606881
$236$	5.15352e50	0.494876
$237$	−3.79718e49	−0.0332944
$238$	−6.36012e50	−0.509402
$239$	−1.78108e51	−1.30355	−0.651775	−	0.758412i	$-0.725976\pi$
$239$	−1.78108e51	−1.30355	−0.651775	+	0.758412i	$0.725976\pi$
$240$	−3.72011e50	−0.248894
$241$	−2.31617e50	−0.141711	−0.0708557	−	0.997487i	$-0.522573\pi$
$241$	−2.31617e50	−0.141711	−0.0708557	+	0.997487i	$0.522573\pi$
$242$	7.33199e50	0.410385
$243$	1.25237e50	0.0641500
$244$	3.04151e51	1.42629
$245$	−6.71053e48	−0.00288195
$246$	7.32933e50	0.288376
$247$	6.54657e50	0.236064
$248$	3.61166e51	1.19398
$249$	−2.55038e51	−0.773247
$250$	−1.61133e51	−0.448201
$251$	3.21256e51	0.820100	0.410050	−	0.912063i	$-0.365511\pi$
$251$	3.21256e51	0.820100	0.410050	+	0.912063i	$0.365511\pi$
$252$	−1.18310e51	−0.277274
$253$	−1.61439e50	−0.0347471
$254$	1.65767e51	0.327774
$255$	−3.25288e51	−0.591090
$256$	−1.78371e51	−0.297966
$257$	6.07157e51	0.932693	0.466347	−	0.884602i	$-0.345570\pi$
$257$	6.07157e51	0.932693	0.466347	+	0.884602i	$0.345570\pi$
$258$	1.59625e51	0.225568
$259$	−1.43124e52	−1.86110
$260$	−2.81807e51	−0.337307
$261$	−3.28539e51	−0.362090
$262$	5.15890e51	0.523696
$263$	−6.37529e51	−0.596281	−0.298141	−	0.954522i	$-0.596366\pi$
$263$	−6.37529e51	−0.596281	−0.298141	+	0.954522i	$0.596366\pi$
$264$	3.00998e50	0.0259465
$265$	−1.79643e52	−1.42766
$266$	2.71251e51	0.198800
$267$	6.40445e51	0.433002
$268$	1.07150e52	0.668488
$269$	−1.13773e52	−0.655186	−0.327593	−	0.944819i	$-0.606237\pi$
$269$	−1.13773e52	−0.655186	−0.327593	+	0.944819i	$0.606237\pi$
$270$	1.23601e51	0.0657204
$271$	3.06013e52	1.50280	0.751399	−	0.659848i	$-0.229379\pi$
$271$	3.06013e52	1.50280	0.751399	+	0.659848i	$0.229379\pi$
$272$	1.41492e52	0.641948
$273$	−6.75761e51	−0.283333
$274$	−1.41700e52	−0.549201
$275$	−5.19790e50	−0.0186284
$276$	8.42983e51	0.279430
$277$	3.79780e52	1.16471	0.582354	−	0.812936i	$-0.302132\pi$
$277$	3.79780e52	1.16471	0.582354	+	0.812936i	$0.302132\pi$
$278$	4.33085e51	0.122917
$279$	2.00949e52	0.527954
$280$	−2.57380e52	−0.626148
$281$	1.86684e51	0.0420651	0.0210325	−	0.999779i	$-0.493305\pi$
$281$	1.86684e51	0.0420651	0.0210325	+	0.999779i	$0.493305\pi$
$282$	8.33665e51	0.174035
$283$	2.48229e52	0.480224	0.240112	−	0.970745i	$-0.422816\pi$
$283$	2.48229e52	0.480224	0.240112	+	0.970745i	$0.422816\pi$
$284$	−4.81119e52	−0.862797
$285$	1.38731e52	0.230680
$286$	7.79960e50	0.0120282
$287$	−8.49174e52	−1.21489
$288$	−2.43040e52	−0.322655
$289$	4.25680e52	0.524541
$290$	−3.24248e52	−0.370954
$291$	8.93756e51	0.0949555
$292$	−6.40460e52	−0.632063
$293$	−2.43606e52	−0.223374	−0.111687	−	0.993743i	$-0.535625\pi$
$293$	−2.43606e52	−0.223374	−0.111687	+	0.993743i	$0.535625\pi$
$294$	−9.69809e49	−0.000826454 0
$295$	6.23788e52	0.494156
$296$	−1.90137e53	−1.40054
$297$	1.67472e51	0.0114731
$298$	9.55157e52	0.608731
$299$	4.81494e52	0.285536
$300$	2.71417e52	0.149806
$301$	−1.84941e53	−0.950285
$302$	1.38538e53	0.662859
$303$	1.76684e53	0.787373
$304$	−6.03445e52	−0.250528
$305$	3.68147e53	1.42421
$306$	−4.70107e52	−0.169506
$307$	−2.77366e51	−0.00932348	−0.00466174	−	0.999989i	$-0.501484\pi$
$307$	−2.77366e51	−0.00932348	−0.00466174	+	0.999989i	$0.501484\pi$
$308$	−1.58209e52	−0.0495897
$309$	−2.43602e53	−0.712155
$310$	1.98324e53	0.540878
$311$	4.97151e53	1.26514	0.632572	−	0.774501i	$-0.281999\pi$
$311$	4.97151e53	1.26514	0.632572	+	0.774501i	$0.281999\pi$
$312$	−8.97730e52	−0.213217
$313$	−4.32278e53	−0.958429	−0.479215	−	0.877698i	$-0.659078\pi$
$313$	−4.32278e53	−0.958429	−0.479215	+	0.877698i	$0.659078\pi$
$314$	8.05381e52	0.166730
$315$	−1.43204e53	−0.276871
$316$	2.65144e52	0.0478861
$317$	2.29417e53	0.387125	0.193563	−	0.981088i	$-0.437996\pi$
$317$	2.29417e53	0.387125	0.193563	+	0.981088i	$0.437996\pi$
$318$	−2.59621e53	−0.409409
$319$	−4.39337e52	−0.0647588
$320$	7.29587e52	0.100543
$321$	2.39844e53	0.309080
$322$	1.99503e53	0.240463
$323$	−5.27654e53	−0.594970
$324$	−8.74485e52	−0.0922645
$325$	1.55028e53	0.153080
$326$	−4.86903e53	−0.450053
$327$	−4.65225e53	−0.402612
$328$	−1.12810e54	−0.914243
$329$	−9.65882e53	−0.733183
$330$	1.65285e52	0.0117539
$331$	−1.97700e54	−1.31736	−0.658681	−	0.752422i	$-0.728885\pi$
$331$	−1.97700e54	−1.31736	−0.658681	+	0.752422i	$0.728885\pi$
$332$	1.78084e54	1.11213
$333$	−1.05790e54	−0.619290
$334$	7.07332e53	0.388217
$335$	1.29695e54	0.667515
$336$	6.22899e53	0.300693
$337$	3.64300e54	1.64974	0.824872	−	0.565319i	$-0.191247\pi$
$337$	3.64300e54	1.64974	0.824872	+	0.565319i	$0.191247\pi$
$338$	7.36651e53	0.313006
$339$	1.51155e54	0.602738
$340$	2.27137e54	0.850142
$341$	2.68718e53	0.0944231
$342$	2.00495e53	0.0661519
$343$	−3.22155e54	−0.998255
$344$	−2.45689e54	−0.715121
$345$	1.02036e54	0.279024
$346$	2.72971e54	0.701423
$347$	−4.88799e54	−1.18045	−0.590224	−	0.807240i	$-0.700961\pi$
$347$	−4.88799e54	−1.18045	−0.590224	+	0.807240i	$0.700961\pi$
$348$	2.29408e54	0.520780
$349$	2.09870e54	0.447923	0.223962	−	0.974598i	$-0.428101\pi$
$349$	2.09870e54	0.447923	0.223962	+	0.974598i	$0.428101\pi$
$350$	6.42344e53	0.128915
$351$	−4.99488e53	−0.0942805
$352$	−3.25004e53	−0.0577060
$353$	−4.91912e54	−0.821734	−0.410867	−	0.911695i	$-0.634774\pi$
$353$	−4.91912e54	−0.821734	−0.410867	+	0.911695i	$0.634774\pi$
$354$	9.01501e53	0.141709
$355$	−5.82352e54	−0.861541
$356$	−4.47201e54	−0.622770
$357$	5.44664e54	0.714106
$358$	−1.96690e53	−0.0242827
$359$	−8.13508e53	−0.0945869	−0.0472935	−	0.998881i	$-0.515060\pi$
$359$	−8.13508e53	−0.0945869	−0.0472935	+	0.998881i	$0.515060\pi$
$360$	−1.90242e54	−0.208354
$361$	−7.44143e54	−0.767806
$362$	9.67464e53	0.0940591
$363$	−6.27893e54	−0.575298
$364$	4.71861e54	0.407506
$365$	−7.75219e54	−0.631143
$366$	5.32048e54	0.408420
$367$	1.94351e55	1.40691	0.703455	−	0.710740i	$-0.251640\pi$
$367$	1.94351e55	1.40691	0.703455	+	0.710740i	$0.251640\pi$
$368$	−4.43829e54	−0.303031
$369$	−6.27665e54	−0.404260
$370$	−1.04408e55	−0.634450
$371$	3.00796e55	1.72478
$372$	−1.40316e55	−0.759335
$373$	2.61183e55	1.33415	0.667075	−	0.744991i	$-0.267546\pi$
$373$	2.61183e55	1.33415	0.667075	+	0.744991i	$0.267546\pi$
$374$	−6.28648e53	−0.0303158
$375$	1.37990e55	0.628311
$376$	−1.28315e55	−0.551744
$377$	1.31033e55	0.532159
$378$	−2.06958e54	−0.0793980
$379$	−1.70034e55	−0.616302	−0.308151	−	0.951337i	$-0.599710\pi$
$379$	−1.70034e55	−0.616302	−0.308151	+	0.951337i	$0.599710\pi$
$380$	−9.68712e54	−0.331778
$381$	−1.41959e55	−0.459490
$382$	−1.16715e55	−0.357078
$383$	6.50840e55	1.88235	0.941175	−	0.337919i	$-0.109723\pi$
$383$	6.50840e55	1.88235	0.941175	+	0.337919i	$0.109723\pi$
$384$	2.14916e55	0.587688
$385$	−1.91498e54	−0.0495175
$386$	−2.48528e54	−0.0607783
$387$	−1.36699e55	−0.316213
$388$	−6.24079e54	−0.136571
$389$	−3.77716e55	−0.782075	−0.391038	−	0.920375i	$-0.627884\pi$
$389$	−3.77716e55	−0.782075	−0.391038	+	0.920375i	$0.627884\pi$
$390$	−4.92963e54	−0.0965885
$391$	−3.88085e55	−0.719659
$392$	1.49269e53	0.00262012
$393$	−4.41795e55	−0.734144
$394$	−3.37306e55	−0.530708
$395$	3.20933e54	0.0478164
$396$	−1.16940e54	−0.0165013
$397$	1.25028e55	0.167114	0.0835569	−	0.996503i	$-0.473372\pi$
$397$	1.25028e55	0.167114	0.0835569	+	0.996503i	$0.473372\pi$
$398$	4.25912e55	0.539304
$399$	−2.32293e55	−0.278688
$400$	−1.42901e55	−0.162459
$401$	1.06687e56	1.14949	0.574746	−	0.818332i	$-0.305101\pi$
$401$	1.06687e56	1.14949	0.574746	+	0.818332i	$0.305101\pi$
$402$	1.87436e55	0.191423
$403$	−8.01455e55	−0.775927
$404$	−1.23372e56	−1.13245
$405$	−1.05849e55	−0.0921302
$406$	5.42923e55	0.448155
$407$	−1.41467e55	−0.110758
$408$	7.23572e55	0.537388
$409$	1.13698e56	0.801124	0.400562	−	0.916270i	$-0.368815\pi$
$409$	1.13698e56	0.801124	0.400562	+	0.916270i	$0.368815\pi$
$410$	−6.19466e55	−0.414157
$411$	1.21348e56	0.769898
$412$	1.70099e56	1.02426
$413$	−1.04448e56	−0.596997
$414$	1.47462e55	0.0800154
$415$	2.15555e56	1.11051
$416$	9.69326e55	0.474202
$417$	−3.70883e55	−0.172311
$418$	2.68111e54	0.0118311
$419$	−2.17540e56	−0.911881	−0.455940	−	0.890010i	$-0.650697\pi$
$419$	−2.17540e56	−0.911881	−0.455940	+	0.890010i	$0.650697\pi$
$420$	9.99941e55	0.398212
$421$	−1.38105e56	−0.522572	−0.261286	−	0.965261i	$-0.584147\pi$
$421$	−1.38105e56	−0.522572	−0.261286	+	0.965261i	$0.584147\pi$
$422$	−2.27343e55	−0.0817456
$423$	−7.13930e55	−0.243971
$424$	3.99600e56	1.29795
$425$	−1.24953e56	−0.385819
$426$	−8.41618e55	−0.247063
$427$	−6.16429e56	−1.72062
$428$	−1.67475e56	−0.444538
$429$	−6.67938e54	−0.0168618
$430$	−1.34913e56	−0.323954
$431$	−1.40065e56	−0.319940	−0.159970	−	0.987122i	$-0.551140\pi$
$431$	−1.40065e56	−0.319940	−0.159970	+	0.987122i	$0.551140\pi$
$432$	4.60415e55	0.100057
$433$	−3.59607e56	−0.743599	−0.371800	−	0.928313i	$-0.621259\pi$
$433$	−3.59607e56	−0.743599	−0.371800	+	0.928313i	$0.621259\pi$
$434$	−3.32076e56	−0.653444
$435$	2.77677e56	0.520022
$436$	3.24851e56	0.579061
$437$	1.65514e56	0.280855
$438$	−1.12035e56	−0.180992
$439$	2.54990e56	0.392225	0.196112	−	0.980581i	$-0.437168\pi$
$439$	2.54990e56	0.392225	0.196112	+	0.980581i	$0.437168\pi$
$440$	−2.54400e55	−0.0372636
$441$	8.30520e53	0.00115856
$442$	1.87495e56	0.249121
$443$	1.35904e57	1.72010	0.860049	−	0.510211i	$-0.170433\pi$
$443$	1.35904e57	1.72010	0.860049	+	0.510211i	$0.170433\pi$
$444$	7.38696e56	0.890701
$445$	−5.41296e56	−0.621863
$446$	−3.48334e56	−0.381326
$447$	−8.17972e56	−0.853349
$448$	−1.22163e56	−0.121468
$449$	1.61899e57	1.53443	0.767216	−	0.641388i	$-0.221641\pi$
$449$	1.61899e57	1.53443	0.767216	+	0.641388i	$0.221641\pi$
$450$	4.74787e55	0.0428973
$451$	−8.39342e55	−0.0723009
$452$	−1.05546e57	−0.866895
$453$	−1.18641e57	−0.929229
$454$	7.55291e56	0.564175
$455$	5.71145e56	0.406913
$456$	−3.08595e56	−0.209722
$457$	9.28707e56	0.602116	0.301058	−	0.953606i	$-0.402660\pi$
$457$	9.28707e56	0.602116	0.301058	+	0.953606i	$0.402660\pi$
$458$	4.33279e56	0.268016
$459$	4.02588e56	0.237623
$460$	−7.12479e56	−0.401309
$461$	2.44925e57	1.31663	0.658313	−	0.752744i	$-0.271270\pi$
$461$	2.44925e57	1.31663	0.658313	+	0.752744i	$0.271270\pi$
$462$	−2.76754e55	−0.0142001
$463$	−1.26241e57	−0.618315	−0.309157	−	0.951011i	$-0.600047\pi$
$463$	−1.26241e57	−0.618315	−0.309157	+	0.951011i	$0.600047\pi$
$464$	−1.20783e57	−0.564765
$465$	−1.69840e57	−0.758230
$466$	−1.02129e57	−0.435362
$467$	2.72382e56	0.110883	0.0554415	−	0.998462i	$-0.482343\pi$
$467$	2.72382e56	0.110883	0.0554415	+	0.998462i	$0.482343\pi$
$468$	3.48775e56	0.135600
$469$	−2.17163e57	−0.806436
$470$	−7.04604e56	−0.249943
$471$	−6.89707e56	−0.233730
$472$	−1.38756e57	−0.449260
$473$	−1.82800e56	−0.0565537
$474$	4.63814e55	0.0137123
$475$	5.32908e56	0.150570
$476$	−3.80320e57	−1.02707
$477$	2.22333e57	0.573930
$478$	2.17553e57	0.536866
$479$	6.71590e56	0.158449	0.0792247	−	0.996857i	$-0.474756\pi$
$479$	6.71590e56	0.158449	0.0792247	+	0.996857i	$0.474756\pi$
$480$	2.05414e57	0.463387
$481$	4.21928e57	0.910162
$482$	2.82913e56	0.0583636
$483$	−1.70849e57	−0.337093
$484$	4.38436e57	0.827429
$485$	−7.55392e56	−0.136372
$486$	−1.52973e56	−0.0264201
$487$	6.52355e56	0.107798	0.0538991	−	0.998546i	$-0.482835\pi$
$487$	6.52355e56	0.107798	0.0538991	+	0.998546i	$0.482835\pi$
$488$	−8.18909e57	−1.29482
$489$	4.16971e57	0.630907
$490$	8.19671e54	0.00118693
$491$	9.15403e57	1.26870	0.634352	−	0.773045i	$-0.281267\pi$
$491$	9.15403e57	1.26870	0.634352	+	0.773045i	$0.281267\pi$
$492$	4.38277e57	0.581432
$493$	−1.05613e58	−1.34124
$494$	−7.99644e56	−0.0972226
$495$	−1.41546e56	−0.0164772
$496$	7.38760e57	0.823469
$497$	9.75096e57	1.04084
$498$	3.11521e57	0.318461
$499$	8.05141e57	0.788334	0.394167	−	0.919039i	$-0.371033\pi$
$499$	8.05141e57	0.788334	0.394167	+	0.919039i	$0.371033\pi$
$500$	−9.63535e57	−0.903675
$501$	−6.05741e57	−0.544221
$502$	−3.92405e57	−0.337757
$503$	−1.27336e58	−1.05012	−0.525059	−	0.851066i	$-0.675957\pi$
$503$	−1.27336e58	−1.05012	−0.525059	+	0.851066i	$0.675957\pi$
$504$	3.18543e57	0.251716
$505$	−1.49331e58	−1.13080
$506$	1.97193e56	0.0143105
$507$	−6.30849e57	−0.438787
$508$	9.91251e57	0.660867
$509$	−2.89502e58	−1.85021	−0.925103	−	0.379717i	$-0.876021\pi$
$509$	−2.89502e58	−1.85021	−0.925103	+	0.379717i	$0.876021\pi$
$510$	3.97329e57	0.243440
$511$	1.29803e58	0.762495
$512$	−1.58935e58	−0.895188
$513$	−1.71699e57	−0.0927350
$514$	−7.41624e57	−0.384128
$515$	2.05890e58	1.02277
$516$	9.54521e57	0.454796
$517$	−9.54699e56	−0.0436335
$518$	1.74822e58	0.766490
$519$	−2.33765e58	−0.983290
$520$	7.58751e57	0.306216
$521$	−4.03859e57	−0.156393	−0.0781967	−	0.996938i	$-0.524916\pi$
$521$	−4.03859e57	−0.156393	−0.0781967	+	0.996938i	$0.524916\pi$
$522$	4.01301e57	0.149126
$523$	−1.88422e58	−0.671963	−0.335981	−	0.941869i	$-0.609068\pi$
$523$	−1.88422e58	−0.671963	−0.335981	+	0.941869i	$0.609068\pi$
$524$	3.08490e58	1.05589
$525$	−5.50087e57	−0.180720
$526$	7.78722e57	0.245578
$527$	6.45974e58	1.95563
$528$	6.15687e56	0.0178950
$529$	−2.36608e58	−0.660286
$530$	2.19429e58	0.587980
$531$	−7.72023e57	−0.198654
$532$	1.62202e58	0.400826
$533$	2.50335e58	0.594136
$534$	−7.82284e57	−0.178331
$535$	−2.02714e58	−0.443891
$536$	−2.88495e58	−0.606870
$537$	1.68440e57	0.0340407
$538$	1.38970e58	0.269837
$539$	1.11061e55	0.000207206 0
$540$	7.39104e57	0.132507
$541$	−2.61000e58	−0.449675	−0.224838	−	0.974396i	$-0.572185\pi$
$541$	−2.61000e58	−0.449675	−0.224838	+	0.974396i	$0.572185\pi$
$542$	−3.73786e58	−0.618926
$543$	−8.28512e57	−0.131857
$544$	−7.81278e58	−1.19517
$545$	3.93202e58	0.578218
$546$	8.25422e57	0.116690
$547$	4.86896e58	0.661772	0.330886	−	0.943671i	$-0.392652\pi$
$547$	4.86896e58	0.661772	0.330886	+	0.943671i	$0.392652\pi$
$548$	−8.47331e58	−1.10731
$549$	−4.55632e58	−0.572544
$550$	6.34907e56	0.00767207
$551$	4.50425e58	0.523436
$552$	−2.26969e58	−0.253674
$553$	−5.37373e57	−0.0577678
$554$	−4.63889e58	−0.479683
$555$	8.94125e58	0.889404
$556$	2.58975e58	0.247828
$557$	1.92712e58	0.177428	0.0887138	−	0.996057i	$-0.471724\pi$
$557$	1.92712e58	0.177428	0.0887138	+	0.996057i	$0.471724\pi$
$558$	−2.45453e58	−0.217437
$559$	5.45203e58	0.464734
$560$	−5.26467e58	−0.431845
$561$	5.38358e57	0.0424981
$562$	−2.28029e57	−0.0173244
$563$	−1.21276e59	−0.886841	−0.443420	−	0.896314i	$-0.646235\pi$
$563$	−1.21276e59	−0.886841	−0.443420	+	0.896314i	$0.646235\pi$
$564$	4.98513e58	0.350893
$565$	−1.27754e59	−0.865633
$566$	−3.03204e58	−0.197780
$567$	1.77234e58	0.111304
$568$	1.29539e59	0.783268
$569$	1.02783e59	0.598420	0.299210	−	0.954187i	$-0.403277\pi$
$569$	1.02783e59	0.598420	0.299210	+	0.954187i	$0.403277\pi$
$570$	−1.69456e58	−0.0950052
$571$	2.10956e59	1.13898	0.569488	−	0.821999i	$-0.307141\pi$
$571$	2.10956e59	1.13898	0.569488	+	0.821999i	$0.307141\pi$
$572$	4.66398e57	0.0242517
$573$	9.99515e58	0.500570
$574$	1.03724e59	0.500350
$575$	3.91949e58	0.182125
$576$	−9.02963e57	−0.0404191
$577$	2.50403e59	1.07984	0.539921	−	0.841716i	$-0.318454\pi$
$577$	2.50403e59	1.07984	0.539921	+	0.841716i	$0.318454\pi$
$578$	−5.19955e58	−0.216032
$579$	2.12833e58	0.0852021
$580$	−1.93893e59	−0.747927
$581$	−3.60927e59	−1.34163
$582$	−1.09170e58	−0.0391073
$583$	2.97314e58	0.102646
$584$	1.72440e59	0.573803
$585$	4.22161e58	0.135403
$586$	2.97557e58	0.0919965
$587$	−1.76752e59	−0.526800	−0.263400	−	0.964687i	$-0.584844\pi$
$587$	−1.76752e59	−0.526800	−0.263400	+	0.964687i	$0.584844\pi$
$588$	−5.79923e56	−0.00166632
$589$	−2.75500e59	−0.763208
$590$	−7.61938e58	−0.203517
$591$	2.88861e59	0.743973
$592$	−3.88922e59	−0.965930
$593$	−6.37698e59	−1.52735	−0.763676	−	0.645600i	$-0.776607\pi$
$593$	−6.37698e59	−1.52735	−0.763676	+	0.645600i	$0.776607\pi$
$594$	−2.04562e57	−0.00472516
$595$	−4.60344e59	−1.02558
$596$	5.71162e59	1.22734
$597$	−3.64740e59	−0.756023
$598$	−5.88131e58	−0.117598
$599$	5.75228e59	1.10959	0.554796	−	0.831986i	$-0.312796\pi$
$599$	5.75228e59	1.10959	0.554796	+	0.831986i	$0.312796\pi$
$600$	−7.30776e58	−0.135998
$601$	−3.64629e59	−0.654711	−0.327355	−	0.944901i	$-0.606157\pi$
$601$	−3.64629e59	−0.654711	−0.327355	+	0.944901i	$0.606157\pi$
$602$	2.25900e59	0.391374
$603$	−1.60516e59	−0.268346
$604$	8.28428e59	1.33647
$605$	5.30688e59	0.826225
$606$	−2.15814e59	−0.324279
$607$	5.14767e59	0.746542	0.373271	−	0.927722i	$-0.378236\pi$
$607$	5.14767e59	0.746542	0.373271	+	0.927722i	$0.378236\pi$
$608$	3.33206e59	0.466429
$609$	−4.64946e59	−0.628247
$610$	−4.49681e59	−0.586560
$611$	2.84740e59	0.358560
$612$	−2.81113e59	−0.341763
$613$	−1.37174e59	−0.161017	−0.0805083	−	0.996754i	$-0.525654\pi$
$613$	−1.37174e59	−0.161017	−0.0805083	+	0.996754i	$0.525654\pi$
$614$	3.38794e57	0.00383986
$615$	5.30495e59	0.580586
$616$	4.25970e58	0.0450188
$617$	−7.62052e59	−0.777774	−0.388887	−	0.921285i	$-0.627140\pi$
$617$	−7.62052e59	−0.777774	−0.388887	+	0.921285i	$0.627140\pi$
$618$	2.97553e59	0.293300
$619$	1.72119e60	1.63862	0.819311	−	0.573349i	$-0.194356\pi$
$619$	1.72119e60	1.63862	0.819311	+	0.573349i	$0.194356\pi$
$620$	1.18593e60	1.09053
$621$	−1.26283e59	−0.112170
$622$	−6.07255e59	−0.521048
$623$	9.06352e59	0.751283
$624$	−1.83629e59	−0.147053
$625$	−7.62410e59	−0.589886
$626$	5.28015e59	0.394728
$627$	−2.29603e58	−0.0165854
$628$	4.81599e59	0.336166
$629$	−3.40074e60	−2.29395
$630$	1.74919e59	0.114029
$631$	−2.19924e60	−1.38561	−0.692807	−	0.721123i	$-0.743626\pi$
$631$	−2.19924e60	−1.38561	−0.692807	+	0.721123i	$0.743626\pi$
$632$	−7.13885e58	−0.0434722
$633$	1.94691e59	0.114595
$634$	−2.80226e59	−0.159437
$635$	1.19982e60	0.659905
$636$	−1.55248e60	−0.825461
$637$	−3.31240e57	−0.00170273
$638$	5.36637e58	0.0266708
$639$	7.20740e59	0.346346
$640$	−1.81644e60	−0.844018
$641$	−3.07540e60	−1.38183	−0.690914	−	0.722937i	$-0.742791\pi$
$641$	−3.07540e60	−1.38183	−0.690914	+	0.722937i	$0.742791\pi$
$642$	−2.92963e59	−0.127294
$643$	3.88562e60	1.63277	0.816385	−	0.577508i	$-0.195975\pi$
$643$	3.88562e60	1.63277	0.816385	+	0.577508i	$0.195975\pi$
$644$	1.19298e60	0.484828
$645$	1.15536e60	0.454134
$646$	6.44514e59	0.245038
$647$	3.66567e59	0.134807	0.0674034	−	0.997726i	$-0.478529\pi$
$647$	3.66567e59	0.134807	0.0674034	+	0.997726i	$0.478529\pi$
$648$	2.35450e59	0.0837600
$649$	−1.03238e59	−0.0355288
$650$	−1.89362e59	−0.0630456
$651$	2.84381e60	0.916030
$652$	−2.91157e60	−0.907410
$653$	−2.33400e60	−0.703829	−0.351915	−	0.936032i	$-0.614469\pi$
$653$	−2.33400e60	−0.703829	−0.351915	+	0.936032i	$0.614469\pi$
$654$	5.68258e59	0.165815
$655$	3.73400e60	1.05435
$656$	−2.30752e60	−0.630540
$657$	9.59439e59	0.253724
$658$	1.17980e60	0.301960
$659$	−3.08702e60	−0.764721	−0.382360	−	0.924013i	$-0.624889\pi$
$659$	−3.08702e60	−0.764721	−0.382360	+	0.924013i	$0.624889\pi$
$660$	9.88364e58	0.0236986
$661$	5.93115e60	1.37660	0.688300	−	0.725426i	$-0.258357\pi$
$661$	5.93115e60	1.37660	0.688300	+	0.725426i	$0.258357\pi$
$662$	2.41485e60	0.542554
$663$	−1.60566e60	−0.349231
$664$	−4.79482e60	−1.00962
$665$	1.96331e60	0.400243
$666$	1.29219e60	0.255054
$667$	3.31284e60	0.633132
$668$	4.22968e60	0.782733
$669$	2.98305e60	0.534562
$670$	−1.58419e60	−0.274915
$671$	−6.09292e59	−0.102398
$672$	−3.43947e60	−0.559825
$673$	−3.82992e60	−0.603763	−0.301881	−	0.953346i	$-0.597615\pi$
$673$	−3.82992e60	−0.603763	−0.301881	+	0.953346i	$0.597615\pi$
$674$	−4.44982e60	−0.679445
$675$	−4.06596e59	−0.0601356
$676$	4.40500e60	0.631091
$677$	−3.89712e60	−0.540863	−0.270432	−	0.962739i	$-0.587166\pi$
$677$	−3.89712e60	−0.540863	−0.270432	+	0.962739i	$0.587166\pi$
$678$	−1.84631e60	−0.248237
$679$	1.26484e60	0.164753
$680$	−6.11554e60	−0.771780
$681$	−6.46812e60	−0.790888
$682$	−3.28231e59	−0.0388880
$683$	1.22609e61	1.40759	0.703797	−	0.710401i	$-0.251486\pi$
$683$	1.22609e61	1.40759	0.703797	+	0.710401i	$0.251486\pi$
$684$	1.19891e60	0.133377
$685$	−1.02562e61	−1.10570
$686$	3.93503e60	0.411130
$687$	−3.71049e60	−0.375718
$688$	−5.02553e60	−0.493209
$689$	−8.86742e60	−0.843498
$690$	−1.24633e60	−0.114916
$691$	−5.01752e60	−0.448447	−0.224223	−	0.974538i	$-0.571985\pi$
$691$	−5.01752e60	−0.448447	−0.224223	+	0.974538i	$0.571985\pi$
$692$	1.63230e61	1.41423
$693$	2.37005e59	0.0199064
$694$	5.97053e60	0.486166
$695$	3.13466e60	0.247467
$696$	−6.17667e60	−0.472777
$697$	−2.01770e61	−1.49745
$698$	−2.56350e60	−0.184477
$699$	8.74603e60	0.610312
$700$	3.84107e60	0.259923
$701$	1.42916e61	0.937874	0.468937	−	0.883232i	$-0.344637\pi$
$701$	1.42916e61	0.937874	0.468937	+	0.883232i	$0.344637\pi$
$702$	6.10109e59	0.0388293
$703$	1.45038e61	0.895243
$704$	−1.20748e59	−0.00722884
$705$	6.03405e60	0.350383
$706$	6.00855e60	0.338430
$707$	2.50041e61	1.36614
$708$	5.39077e60	0.285717
$709$	4.09729e59	0.0210670	0.0105335	−	0.999945i	$-0.496647\pi$
$709$	4.09729e59	0.0210670	0.0105335	+	0.999945i	$0.496647\pi$
$710$	7.11325e60	0.354825
$711$	−3.97198e59	−0.0192225
$712$	1.20406e61	0.565366
$713$	−2.02628e61	−0.923154
$714$	−6.65291e60	−0.294103
$715$	5.64533e59	0.0242164
$716$	−1.17616e60	−0.0489595
$717$	−1.86307e61	−0.752606
$718$	9.93675e59	0.0389555
$719$	−2.67487e61	−1.01773	−0.508864	−	0.860847i	$-0.669934\pi$
$719$	−2.67487e61	−1.01773	−0.508864	+	0.860847i	$0.669934\pi$
$720$	−3.89137e60	−0.143699
$721$	−3.44744e61	−1.23563
$722$	9.08948e60	0.316220
$723$	−2.42280e60	−0.0818171
$724$	5.78521e60	0.189644
$725$	1.06664e61	0.339431
$726$	7.66952e60	0.236936
$727$	−2.69955e60	−0.0809659	−0.0404829	−	0.999180i	$-0.512890\pi$
$727$	−2.69955e60	−0.0809659	−0.0404829	+	0.999180i	$0.512890\pi$
$728$	−1.27046e61	−0.369944
$729$	1.31002e60	0.0370370
$730$	9.46907e60	0.259936
$731$	−4.39434e61	−1.17130
$732$	3.18152e61	0.823468
$733$	−2.80157e61	−0.704151	−0.352075	−	0.935972i	$-0.614524\pi$
$733$	−2.80157e61	−0.704151	−0.352075	+	0.935972i	$0.614524\pi$
$734$	−2.37394e61	−0.579434
$735$	−7.01945e58	−0.00166389
$736$	2.45070e61	0.564179
$737$	−2.14649e60	−0.0479929
$738$	7.66674e60	0.166494
$739$	5.72171e61	1.20690	0.603449	−	0.797402i	$-0.293793\pi$
$739$	5.72171e61	1.20690	0.603449	+	0.797402i	$0.293793\pi$
$740$	−6.24337e61	−1.27920
$741$	6.84794e60	0.136291
$742$	−3.67414e61	−0.710348
$743$	−2.53630e60	−0.0476366	−0.0238183	−	0.999716i	$-0.507582\pi$
$743$	−2.53630e60	−0.0476366	−0.0238183	+	0.999716i	$0.507582\pi$
$744$	3.77793e61	0.689343
$745$	6.91340e61	1.22555
$746$	−3.19027e61	−0.549468
$747$	−2.66778e61	−0.446435
$748$	−3.75917e60	−0.0611234
$749$	3.39425e61	0.536272
$750$	−1.68550e61	−0.258769
$751$	6.37711e61	0.951405	0.475703	−	0.879606i	$-0.342194\pi$
$751$	6.37711e61	0.951405	0.475703	+	0.879606i	$0.342194\pi$
$752$	−2.62466e61	−0.380530
$753$	3.36046e61	0.473485
$754$	−1.60053e61	−0.219169
$755$	1.00274e62	1.33453
$756$	−1.23756e61	−0.160084
$757$	−2.56176e61	−0.322090	−0.161045	−	0.986947i	$-0.551486\pi$
$757$	−2.56176e61	−0.322090	−0.161045	+	0.986947i	$0.551486\pi$
$758$	2.07692e61	0.253823
$759$	−1.68871e60	−0.0200612
$760$	2.60820e61	0.301196
$761$	1.22342e62	1.37342	0.686712	−	0.726929i	$-0.259053\pi$
$761$	1.22342e62	1.37342	0.686712	+	0.726929i	$0.259053\pi$
$762$	1.73399e61	0.189240
$763$	−6.58382e61	−0.698554
$764$	−6.97927e61	−0.719951
$765$	−3.40262e61	−0.341266
$766$	−7.94981e61	−0.775244
$767$	3.07909e61	0.291960
$768$	−1.86583e61	−0.172031
$769$	−5.11370e61	−0.458479	−0.229239	−	0.973370i	$-0.573624\pi$
$769$	−5.11370e61	−0.458479	−0.229239	+	0.973370i	$0.573624\pi$
$770$	2.33909e60	0.0203937
$771$	6.35108e61	0.538491
$772$	−1.48614e61	−0.122543
$773$	−1.07353e62	−0.860903	−0.430452	−	0.902614i	$-0.641646\pi$
$773$	−1.07353e62	−0.860903	−0.430452	+	0.902614i	$0.641646\pi$
$774$	1.66973e61	0.130232
$775$	−6.52405e61	−0.494915
$776$	1.68030e61	0.123982
$777$	−1.49713e62	−1.07450
$778$	4.61368e61	0.322097
$779$	8.60525e61	0.584397
$780$	−2.94781e61	−0.194744
$781$	9.63806e60	0.0619430
$782$	4.74034e61	0.296391
$783$	−3.43664e61	−0.209053
$784$	3.05328e59	0.00180706
$785$	5.82932e61	0.335676
$786$	5.39639e61	0.302356
$787$	−1.80931e62	−0.986406	−0.493203	−	0.869914i	$-0.664174\pi$
$787$	−1.80931e62	−0.986406	−0.493203	+	0.869914i	$0.664174\pi$
$788$	−2.01701e62	−1.07003
$789$	−6.66878e61	−0.344263
$790$	−3.92010e60	−0.0196931
$791$	2.13913e62	1.04579
$792$	3.14855e60	0.0149802
$793$	1.81722e62	0.841461
$794$	−1.52718e61	−0.0688256
$795$	−1.87913e62	−0.824260
$796$	2.54685e62	1.08736
$797$	8.36111e61	0.347464	0.173732	−	0.984793i	$-0.444417\pi$
$797$	8.36111e61	0.347464	0.173732	+	0.984793i	$0.444417\pi$
$798$	2.83739e61	0.114777
$799$	−2.29501e62	−0.903708
$800$	7.89057e61	0.302464
$801$	6.69928e61	0.249994
$802$	−1.30314e62	−0.473417
$803$	1.28301e61	0.0453779
$804$	1.12083e62	0.385952
$805$	1.44400e62	0.484122
$806$	9.78953e61	0.319564
$807$	−1.19010e62	−0.378272
$808$	3.32173e62	1.02806
$809$	1.30597e62	0.393585	0.196793	−	0.980445i	$-0.436947\pi$
$809$	1.30597e62	0.393585	0.196793	+	0.980445i	$0.436947\pi$
$810$	1.29291e61	0.0379437
$811$	−2.29199e61	−0.0655036	−0.0327518	−	0.999464i	$-0.510427\pi$
$811$	−2.29199e61	−0.0655036	−0.0327518	+	0.999464i	$0.510427\pi$
$812$	3.24656e62	0.903583
$813$	3.20101e62	0.867641
$814$	1.72798e61	0.0456157
$815$	−3.52419e62	−0.906089
$816$	1.48005e62	0.370629
$817$	1.87413e62	0.457116
$818$	−1.38878e62	−0.329942
$819$	−7.06870e61	−0.163582
$820$	−3.70427e62	−0.835034
$821$	−3.14859e62	−0.691414	−0.345707	−	0.938343i	$-0.612361\pi$
$821$	−3.14859e62	−0.691414	−0.345707	+	0.938343i	$0.612361\pi$
$822$	−1.48223e62	−0.317082
$823$	−8.04910e62	−1.67745	−0.838727	−	0.544552i	$-0.816700\pi$
$823$	−8.04910e62	−1.67745	−0.838727	+	0.544552i	$0.816700\pi$
$824$	−4.57983e62	−0.929853
$825$	−5.43718e60	−0.0107551
$826$	1.27580e62	0.245873
$827$	−7.55224e62	−1.41810	−0.709050	−	0.705158i	$-0.750876\pi$
$827$	−7.55224e62	−1.41810	−0.709050	+	0.705158i	$0.750876\pi$
$828$	8.81790e61	0.161329
$829$	4.48039e62	0.798718	0.399359	−	0.916795i	$-0.369233\pi$
$829$	4.48039e62	0.798718	0.399359	+	0.916795i	$0.369233\pi$
$830$	−2.63294e62	−0.457363
$831$	3.97263e62	0.672444
$832$	3.60133e61	0.0594034
$833$	2.66980e60	0.00429152
$834$	4.53023e61	0.0709659
$835$	5.11965e62	0.781593
$836$	1.60324e61	0.0238541
$837$	2.10200e62	0.304814
$838$	2.65719e62	0.375557
$839$	−9.00857e62	−1.24100	−0.620502	−	0.784205i	$-0.713071\pi$
$839$	−9.00857e62	−1.24100	−0.620502	+	0.784205i	$0.713071\pi$
$840$	−2.69229e62	−0.361507
$841$	1.37512e62	0.179981
$842$	1.68692e62	0.215220
$843$	1.95278e61	0.0242863
$844$	−1.35946e62	−0.164818
$845$	5.33186e62	0.630172
$846$	8.72043e61	0.100479
$847$	−8.88588e62	−0.998176
$848$	8.17375e62	0.895180
$849$	2.59656e62	0.277257
$850$	1.52626e62	0.158899
$851$	1.06674e63	1.08286
$852$	−5.03268e62	−0.498136
$853$	3.94807e62	0.381048	0.190524	−	0.981682i	$-0.438981\pi$
$853$	3.94807e62	0.381048	0.190524	+	0.981682i	$0.438981\pi$
$854$	7.52949e62	0.708633
$855$	1.45118e62	0.133183
$856$	4.50917e62	0.403563
$857$	9.25891e62	0.808113	0.404056	−	0.914734i	$-0.367600\pi$
$857$	9.25891e62	0.808113	0.404056	+	0.914734i	$0.367600\pi$
$858$	8.15865e60	0.00694451
$859$	−1.13513e62	−0.0942309	−0.0471155	−	0.998889i	$-0.515003\pi$
$859$	−1.13513e62	−0.0942309	−0.0471155	+	0.998889i	$0.515003\pi$
$860$	−8.06750e62	−0.653164
$861$	−8.88266e62	−0.701415
$862$	1.71085e62	0.131767
$863$	−1.90326e63	−1.42977	−0.714885	−	0.699242i	$-0.753521\pi$
$863$	−1.90326e63	−1.42977	−0.714885	+	0.699242i	$0.753521\pi$
$864$	−2.54228e62	−0.186285
$865$	1.97576e63	1.41217
$866$	4.39249e62	0.306250
$867$	4.45276e62	0.302844
$868$	−1.98574e63	−1.31749
$869$	−5.31151e60	−0.00343790
$870$	−3.39175e62	−0.214170
$871$	6.40192e62	0.394385
$872$	−8.74642e62	−0.525686
$873$	9.34901e61	0.0548226
$874$	−2.02170e62	−0.115670
$875$	1.95282e63	1.09016
$876$	−6.69944e62	−0.364922
$877$	−3.05610e63	−1.62434	−0.812170	−	0.583421i	$-0.801714\pi$
$877$	−3.05610e63	−1.62434	−0.812170	+	0.583421i	$0.801714\pi$
$878$	−3.11462e62	−0.161537
$879$	−2.54820e62	−0.128965
$880$	−5.20371e61	−0.0257002
$881$	1.33139e63	0.641687	0.320843	−	0.947132i	$-0.396034\pi$
$881$	1.33139e63	0.641687	0.320843	+	0.947132i	$0.396034\pi$
$882$	−1.01445e60	−0.000477153 0
$883$	3.18228e62	0.146077	0.0730387	−	0.997329i	$-0.476730\pi$
$883$	3.18228e62	0.146077	0.0730387	+	0.997329i	$0.476730\pi$
$884$	1.12118e63	0.502285
$885$	6.52504e62	0.285301
$886$	−1.66003e63	−0.708421
$887$	1.09631e62	0.0456641	0.0228320	−	0.999739i	$-0.492732\pi$
$887$	1.09631e62	0.0456641	0.0228320	+	0.999739i	$0.492732\pi$
$888$	−1.98890e63	−0.808600
$889$	−2.00899e63	−0.797242
$890$	6.61177e62	0.256114
$891$	1.75182e61	0.00662397
$892$	−2.08296e63	−0.768840
$893$	9.78793e62	0.352683
$894$	9.99128e62	0.351451
$895$	−1.42364e62	−0.0488882
$896$	3.04147e63	1.01967
$897$	5.03660e62	0.164854
$898$	−1.97755e63	−0.631954
$899$	−5.51427e63	−1.72050
$900$	2.83912e62	0.0864908
$901$	7.14715e63	2.12593
$902$	1.02523e62	0.0297770
$903$	−1.93455e63	−0.548647
$904$	2.84178e63	0.786989
$905$	7.00248e62	0.189368
$906$	1.44916e63	0.382702
$907$	5.74551e63	1.48174	0.740870	−	0.671648i	$-0.234413\pi$
$907$	5.74551e63	1.48174	0.740870	+	0.671648i	$0.234413\pi$
$908$	4.51647e63	1.13750
$909$	1.84818e63	0.454590
$910$	−6.97637e62	−0.167587
$911$	−5.00178e63	−1.17349	−0.586745	−	0.809772i	$-0.699591\pi$
$911$	−5.00178e63	−1.17349	−0.586745	+	0.809772i	$0.699591\pi$
$912$	−6.31225e62	−0.144642
$913$	−3.56748e62	−0.0798436
$914$	−1.13439e63	−0.247981
$915$	3.85095e63	0.822270
$916$	2.59091e63	0.540380
$917$	−6.25224e63	−1.27378
$918$	−4.91749e62	−0.0978646
$919$	−4.87365e63	−0.947482	−0.473741	−	0.880664i	$-0.657097\pi$
$919$	−4.87365e63	−0.947482	−0.473741	+	0.880664i	$0.657097\pi$
$920$	1.91831e63	0.364318
$921$	−2.90135e61	−0.00538292
$922$	−2.99168e63	−0.542251
$923$	−2.87456e63	−0.509020
$924$	−1.65493e62	−0.0286306
$925$	3.43460e63	0.580536
$926$	1.54200e63	0.254652
$927$	−2.54817e63	−0.411163
$928$	6.66928e63	1.05147
$929$	−7.28764e63	−1.12266	−0.561331	−	0.827591i	$-0.689711\pi$
$929$	−7.28764e63	−1.12266	−0.561331	+	0.827591i	$0.689711\pi$
$930$	2.07454e63	0.312276
$931$	−1.13864e61	−0.00167482
$932$	−6.10705e63	−0.877788
$933$	5.20038e63	0.730432
$934$	−3.32706e62	−0.0456670
$935$	−4.55014e62	−0.0610345
$936$	−9.39058e62	−0.123101
$937$	−1.27714e64	−1.63621	−0.818103	−	0.575072i	$-0.804974\pi$
$937$	−1.27714e64	−1.63621	−0.818103	+	0.575072i	$0.804974\pi$
$938$	2.65258e63	0.332130
$939$	−4.52178e63	−0.553349
$940$	−4.21337e63	−0.503942
$941$	2.91347e63	0.340592	0.170296	−	0.985393i	$-0.445528\pi$
$941$	2.91347e63	0.340592	0.170296	+	0.985393i	$0.445528\pi$
$942$	8.42457e62	0.0962616
$943$	6.32908e63	0.706870
$944$	−2.83823e63	−0.309848
$945$	−1.49796e63	−0.159851
$946$	2.23284e62	0.0232916
$947$	−7.13938e63	−0.728008	−0.364004	−	0.931397i	$-0.618591\pi$
$947$	−7.13938e63	−0.728008	−0.364004	+	0.931397i	$0.618591\pi$
$948$	2.77350e62	0.0276470
$949$	−3.82658e63	−0.372895
$950$	−6.50931e62	−0.0620122
$951$	2.39978e63	0.223507
$952$	1.02399e64	0.932400
$953$	1.57816e64	1.40493	0.702466	−	0.711718i	$-0.252083\pi$
$953$	1.57816e64	1.40493	0.702466	+	0.711718i	$0.252083\pi$
$954$	−2.71573e63	−0.236372
$955$	−8.44779e63	−0.718903
$956$	1.30092e64	1.08244
$957$	−4.59563e62	−0.0373885
$958$	−8.20326e62	−0.0652572
$959$	1.71730e64	1.33582
$960$	7.63174e62	0.0580486
$961$	2.02830e64	1.50862
$962$	−5.15372e63	−0.374849
$963$	2.50886e63	0.178448
$964$	1.69176e63	0.117674
$965$	−1.79884e63	−0.122365
$966$	2.08687e63	0.138831
$967$	−1.41648e64	−0.921597	−0.460799	−	0.887505i	$-0.652437\pi$
$967$	−1.41648e64	−0.921597	−0.460799	+	0.887505i	$0.652437\pi$
$968$	−1.18046e64	−0.751161
$969$	−5.51945e63	−0.343506
$970$	9.22689e62	0.0561646
$971$	3.18091e64	1.89382	0.946908	−	0.321505i	$-0.104189\pi$
$971$	3.18091e64	1.89382	0.946908	+	0.321505i	$0.104189\pi$
$972$	−9.14742e62	−0.0532689
$973$	−5.24870e63	−0.298969
$974$	−7.96832e62	−0.0443965
$975$	1.62165e63	0.0883806
$976$	−1.67507e64	−0.893019
$977$	−2.23211e64	−1.16408	−0.582039	−	0.813161i	$-0.697745\pi$
$977$	−2.23211e64	−1.16408	−0.582039	+	0.813161i	$0.697745\pi$
$978$	−5.09318e63	−0.259838
$979$	8.95858e62	0.0447107
$980$	4.90144e61	0.00239311
$981$	−4.86642e63	−0.232448
$982$	−1.11814e64	−0.522514
$983$	9.61367e63	0.439530	0.219765	−	0.975553i	$-0.429471\pi$
$983$	9.61367e63	0.439530	0.219765	+	0.975553i	$0.429471\pi$
$984$	−1.18004e64	−0.527838
$985$	−2.44141e64	−1.06847
$986$	1.29003e64	0.552389
$987$	−1.01035e64	−0.423303
$988$	−4.78168e63	−0.196023
$989$	1.37841e64	0.552914
$990$	1.72894e62	0.00678613
$991$	5.07104e64	1.94766	0.973830	−	0.227278i	$-0.0729825\pi$
$991$	5.07104e64	1.94766	0.973830	+	0.227278i	$0.0729825\pi$
$992$	−4.07923e64	−1.53312
$993$	−2.06801e64	−0.760580
$994$	−1.19105e64	−0.428669
$995$	3.08274e64	1.08578
$996$	1.86282e64	0.642090
$997$	5.61838e63	0.189524	0.0947622	−	0.995500i	$-0.469791\pi$
$997$	5.61838e63	0.189524	0.0947622	+	0.995500i	$0.469791\pi$
$998$	−9.83455e63	−0.324674
$999$	−1.10660e64	−0.357547

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.44.a.a.1.1	✓	3
3.2	odd	2		9.44.a.a.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.44.a.a.1.1	✓	3	1.1	even	1	trivial
9.44.a.a.1.3		3	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 44 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q-1.22147e6 q^{2} +1.04604e10 q^{3} -7.30411e12 q^{4} -8.84097e14 q^{5} -1.27770e16 q^{6} +1.48034e18 q^{7} +1.96659e19 q^{8} +1.09419e20 q^{9} +O(q^{10})\)	\(q-1.22147e6 q^{2} +1.04604e10 q^{3} -7.30411e12 q^{4} -8.84097e14 q^{5} -1.27770e16 q^{6} +1.48034e18 q^{7} +1.96659e19 q^{8} +1.09419e20 q^{9} +1.07990e21 q^{10} +1.46320e21 q^{11} -7.64035e22 q^{12} -4.36401e23 q^{13} -1.80819e24 q^{14} -9.24796e24 q^{15} +4.02263e25 q^{16} +3.51740e26 q^{17} -1.33652e26 q^{18} -1.50013e27 q^{19} +6.45753e27 q^{20} +1.54849e28 q^{21} -1.78725e27 q^{22} -1.10333e29 q^{23} +2.05712e29 q^{24} -3.55242e29 q^{25} +5.33051e29 q^{26} +1.14456e30 q^{27} -1.08126e31 q^{28} -3.00258e31 q^{29} +1.12961e31 q^{30} +1.83651e32 q^{31} -2.22118e32 q^{32} +1.53056e31 q^{33} -4.29639e32 q^{34} -1.30876e33 q^{35} -7.99208e32 q^{36} -9.66835e33 q^{37} +1.83236e33 q^{38} -4.56491e33 q^{39} -1.73866e34 q^{40} -5.73635e34 q^{41} -1.89143e34 q^{42} -1.24932e35 q^{43} -1.06874e34 q^{44} -9.67370e34 q^{45} +1.34768e35 q^{46} -6.52473e35 q^{47} +4.20781e35 q^{48} +7.59027e33 q^{49} +4.33917e35 q^{50} +3.67932e36 q^{51} +3.18752e36 q^{52} +2.03194e37 q^{53} -1.39805e36 q^{54} -1.29361e36 q^{55} +2.91122e37 q^{56} -1.56919e37 q^{57} +3.66756e37 q^{58} -7.05565e37 q^{59} +6.75481e37 q^{60} -4.16411e38 q^{61} -2.24324e38 q^{62} +1.61977e38 q^{63} -8.25234e37 q^{64} +3.85821e38 q^{65} -1.86953e37 q^{66} -1.46698e39 q^{67} -2.56914e39 q^{68} -1.15412e39 q^{69} +1.59861e39 q^{70} +6.58697e39 q^{71} +2.15182e39 q^{72} +8.76849e39 q^{73} +1.18096e40 q^{74} -3.71595e39 q^{75} +1.09571e40 q^{76} +2.16603e39 q^{77} +5.57590e39 q^{78} -3.63007e39 q^{79} -3.55639e40 q^{80} +1.19725e40 q^{81} +7.00677e40 q^{82} -2.43814e41 q^{83} -1.13103e41 q^{84} -3.10972e41 q^{85} +1.52600e41 q^{86} -3.14080e41 q^{87} +2.87752e40 q^{88} +6.12259e41 q^{89} +1.18161e41 q^{90} -6.46022e41 q^{91} +8.05884e41 q^{92} +1.92106e42 q^{93} +7.96976e41 q^{94} +1.32626e42 q^{95} -2.32344e42 q^{96} +8.54423e41 q^{97} -9.27128e39 q^{98} +1.60102e41 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 4857024 q^{2} + 31381059609 q^{3} - 1781058029568 q^{4} - 507753321105270 q^{5} + 50\!\cdots\!72 q^{6}+ \cdots + 32\!\cdots\!27 q^{9}+O(q^{10}) \) 3 * q + 4857024 * q^2 + 31381059609 * q^3 - 1781058029568 * q^4 - 507753321105270 * q^5 + 50806186555447872 * q^6 - 1633169303707089288 * q^7 + 11196260694472851456 * q^8 + 328256967394537077627 * q^9	\( 3 q + 4857024 q^{2} + 31381059609 q^{3} - 1781058029568 q^{4} - 507753321105270 q^{5} + 50\!\cdots\!72 q^{6}+ \cdots - 30\!\cdots\!80 q^{99}+O(q^{100}) \) 3 * q + 4857024 * q^2 + 31381059609 * q^3 - 1781058029568 * q^4 - 507753321105270 * q^5 + 50806186555447872 * q^6 - 1633169303707089288 * q^7 + 11196260694472851456 * q^8 + 328256967394537077627 * q^9 - 2286850690696789595520 * q^10 - 27750966261606959036820 * q^11 - 18630496064320497506304 * q^12 - 994786398159560287290750 * q^13 - 9473256819232835003171328 * q^14 - 5311279078757398544679810 * q^15 + 23637690650696707825729536 * q^16 - 160517621023312837046953482 * q^17 + 531450656267494684974734016 * q^18 - 3227133683900578441639486764 * q^19 - 19920520041146285724571791360 * q^20 - 17083527757073731207537789464 * q^21 - 172470540148626161048719521024 * q^22 + 114780279514038504224277444504 * q^23 + 117116841417052096124312813568 * q^24 + 1825420275602850437617559193525 * q^25 + 1775037275334840765729836075136 * q^26 + 3433683820292512484657849089281 * q^27 - 8483554335441104836174737260544 * q^28 - 28241588775620253186792106789758 * q^29 - 23921265947212925347314706450560 * q^30 - 56947467162250619768506214477136 * q^31 - 290372748061904590918491662450688 * q^32 - 290284908820945289887889881934460 * q^33 - 1778246324363072918021693922216576 * q^34 - 3641689125493658442558484764497520 * q^35 - 194881569179893810108620559091712 * q^36 - 7771759793894794226158134990367878 * q^37 - 11984574206649783949969526048471808 * q^38 - 10405817086289189756233396954772250 * q^39 - 75089135561625836440773237699379200 * q^40 - 150622420768399427659977962302801266 * q^41 - 99093612311903777628193716002563584 * q^42 - 503269829459862138385119574866599988 * q^43 - 589156491500651091472842134125289472 * q^44 - 55557855123506843126788989142931430 * q^45 + 1201666039209211956008162792803812864 * q^46 + 517590816657574666863303783889459536 * q^47 + 247258593109538461886425117709303808 * q^48 + 1183207682852736238558590379440977403 * q^49 + 5363972694460023429439963707950510400 * q^50 - 1679071011209150572675116916830702846 * q^51 + 19510568225567423700598614061466308608 * q^52 + 3147649955233970731028729152905020634 * q^53 + 5559161574524140052760934938338653248 * q^54 + 72798121427511388475535050768468313960 * q^55 + 64659225918940531158350848060065054720 * q^56 - 33756958166898605235556353943083505092 * q^57 + 165860584701603780784654252956514011264 * q^58 - 178011039218636820023529236138863835076 * q^59 - 208375675617830241670577713556023726080 * q^60 - 123533499732384273913895969461615945518 * q^61 - 685215538112102475249420816230843667456 * q^62 - 178699734292245610143928973763292053192 * q^63 - 971015593402068342273570470768658087936 * q^64 - 2575578837917643212594035173081316043940 * q^65 - 1804102767066821759775567080792024239872 * q^66 + 1292774342372783673662410484960847098148 * q^67 - 2717789569206669919054906507790539296768 * q^68 + 1200642264455907951127749596978071146312 * q^69 + 1868357626946632141981582698458836116480 * q^70 + 22400468745595901369803420176388102887816 * q^71 + 1225083527242103952511819425579970658304 * q^72 + 31313509370447648548173493799361498480654 * q^73 + 12824367911381949889146580637796075349632 * q^74 + 19094540826723419331062786999031330610575 * q^75 - 45893435926810400921777338109031978491904 * q^76 + 15925552922292610065970442499593057720544 * q^77 + 18567516848493194501297063421213806260608 * q^78 - 43825544899857898915807551182364364018080 * q^79 + 51052771545930899482561003058120286535680 * q^80 + 35917545547686059365808220080151141317043 * q^81 - 207555016724016234735599639977066643719296 * q^82 + 89911369720242570860406785197345580904468 * q^83 - 88740974765555897390939203171014875922432 * q^84 - 609771200949453596987959942886782705526220 * q^85 - 1052084075872403200090705454196607607512320 * q^86 - 295416993606868163734131771553363142894874 * q^87 - 866229044996425850996432449444164589584384 * q^88 + 65289466052051143331840751197428752211806 * q^89 - 250224890870743552579783277069120057143680 * q^90 + 1361620777581018817929645459439738348447824 * q^91 + 3753917639661643691216268373890598977257472 * q^92 - 595690620533385591184229099131314527866608 * q^93 + 7862327422462694583153035384185107177477120 * q^94 + 9328236864095865156237338173319138974757400 * q^95 - 3037401505253255729894648973244849050353664 * q^96 + 6130807410554375967448029821362307484893478 * q^97 - 2033290778553828878915746018754102329738560 * q^98 - 3036482675767738016566552437404420497075380 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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