LMFDB - Embedded newform 3.38.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,38,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, 38, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 38);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 38 $
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:	$26.0142114374$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 11777633936x^{2} - 35120319927360x + 11967042111800832000 $ x^4 - x^3 - 11777633936x^2 - 35120319927360x + 11967042111800832000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{15}\cdot 3^{10}\cdot 5\cdot 7 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$105009.$ 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)

$f(q)$	$=$	$q-520663. q^{2} +3.87420e8 q^{3} +1.33651e11 q^{4} -2.63441e12 q^{5} -2.01716e14 q^{6} +8.34393e15 q^{7} +1.97212e15 q^{8} +1.50095e17 q^{9} +O(q^{10})$	\(q-520663. q^{2} +3.87420e8 q^{3} +1.33651e11 q^{4} -2.63441e12 q^{5} -2.01716e14 q^{6} +8.34393e15 q^{7} +1.97212e15 q^{8} +1.50095e17 q^{9} +1.37164e18 q^{10} -2.00696e19 q^{11} +5.17792e19 q^{12} -1.05373e20 q^{13} -4.34438e21 q^{14} -1.02062e21 q^{15} -1.93957e22 q^{16} +1.77033e22 q^{17} -7.81488e22 q^{18} +4.00776e23 q^{19} -3.52092e23 q^{20} +3.23261e24 q^{21} +1.04495e25 q^{22} -1.07722e25 q^{23} +7.64040e23 q^{24} -6.58195e25 q^{25} +5.48640e25 q^{26} +5.81497e25 q^{27} +1.11518e27 q^{28} +1.59166e27 q^{29} +5.31401e26 q^{30} +4.20936e27 q^{31} +9.82758e27 q^{32} -7.77537e27 q^{33} -9.21743e27 q^{34} -2.19813e28 q^{35} +2.00603e28 q^{36} +1.71917e29 q^{37} -2.08669e29 q^{38} -4.08238e28 q^{39} -5.19537e27 q^{40} -3.95960e29 q^{41} -1.68310e30 q^{42} +3.48956e29 q^{43} -2.68233e30 q^{44} -3.95410e29 q^{45} +5.60870e30 q^{46} -2.42346e30 q^{47} -7.51429e30 q^{48} +5.10591e31 q^{49} +3.42698e31 q^{50} +6.85860e30 q^{51} -1.40833e31 q^{52} -1.34925e32 q^{53} -3.02764e31 q^{54} +5.28715e31 q^{55} +1.64552e31 q^{56} +1.55269e32 q^{57} -8.28718e32 q^{58} +1.06678e33 q^{59} -1.36408e32 q^{60} -7.04574e32 q^{61} -2.19166e33 q^{62} +1.25238e33 q^{63} -2.45114e33 q^{64} +2.77596e32 q^{65} +4.04835e33 q^{66} +7.19450e33 q^{67} +2.36606e33 q^{68} -4.17338e33 q^{69} +1.14449e34 q^{70} +2.35209e34 q^{71} +2.96005e32 q^{72} +2.69218e33 q^{73} -8.95108e34 q^{74} -2.54998e34 q^{75} +5.35642e34 q^{76} -1.67459e35 q^{77} +2.12554e34 q^{78} +2.20044e34 q^{79} +5.10962e34 q^{80} +2.25284e34 q^{81} +2.06162e35 q^{82} -2.35934e35 q^{83} +4.32042e35 q^{84} -4.66376e34 q^{85} -1.81689e35 q^{86} +6.16641e35 q^{87} -3.95797e34 q^{88} +1.13980e35 q^{89} +2.05876e35 q^{90} -8.79227e35 q^{91} -1.43972e36 q^{92} +1.63079e36 q^{93} +1.26181e36 q^{94} -1.05581e36 q^{95} +3.80741e36 q^{96} +8.44145e36 q^{97} -2.65846e37 q^{98} -3.01234e36 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 437562 q^{2} + 1549681956 q^{3} + 346098955492 q^{4} - 4099829756904 q^{5} + 169520484007818 q^{6} + 66\!\cdots\!84 q^{7}+ \cdots + 60\!\cdots\!84 q^{9}+O(q^{10}) $ 4 * q + 437562 * q^2 + 1549681956 * q^3 + 346098955492 * q^4 - 4099829756904 * q^5 + 169520484007818 * q^6 + 6605809948153184 * q^7 + 140484113342159976 * q^8 + 600378541187996484 * q^9	$ 4 q + 437562 q^{2} + 1549681956 q^{3} + 346098955492 q^{4} - 4099829756904 q^{5} + 169520484007818 q^{6} + 66\!\cdots\!84 q^{7}+ \cdots + 31\!\cdots\!96 q^{99}+O(q^{100}) $ 4 * q + 437562 * q^2 + 1549681956 * q^3 + 346098955492 * q^4 - 4099829756904 * q^5 + 169520484007818 * q^6 + 6605809948153184 * q^7 + 140484113342159976 * q^8 + 600378541187996484 * q^9 - 21511023001649316 * q^10 + 20953708852195292976 * q^11 + 134085826579099875588 * q^12 + 51830892788989874168 * q^13 - 1809002141673235613712 * q^14 - 1588358049236498806056 * q^15 + 55184727516616371757840 * q^16 + 81101770962322537501128 * q^17 + 65675708809825529383002 * q^18 - 544604242502813077907632 * q^19 - 3566083114449076353950376 * q^20 + 2559226120354571192186976 * q^21 + 23909208610123411045457976 * q^22 - 6105434608113226892697888 * q^23 + 54426423887751042218148264 * q^24 + 95396877753446381193398716 * q^25 + 428554172265180170762299788 * q^26 + 232598948012160238761560676 * q^27 + 2469833924959492064190244448 * q^28 + 4171186009659314742454127736 * q^29 - 8333811050189225811235524 * q^30 + 8995814656808409627856220864 * q^31 + 36517476440276920084276020384 * q^32 + 8117896129881129128260185264 * q^33 + 31219088393882932122099949524 * q^34 + 42129462142584542112964223040 * q^35 + 51947596501244070980142122532 * q^36 + 55519093704269258277039732824 * q^37 - 735180697664011480109320664568 * q^38 + 20080349829617030866215028152 * q^39 - 2663133991761021855901070923152 * q^40 - 869595339264691998704372818776 * q^41 - 700844494329092219676518145168 * q^42 - 509323958833633606104562745680 * q^43 + 2838804848354890092833187324336 * q^44 - 615362452142290444090131681384 * q^45 - 14832400342987743191058839458896 * q^46 + 4297748917019550924184843821120 * q^47 + 21379694119819270371828162383760 * q^48 + 40223006658016971616433785618020 * q^49 + 102764730674385833857211828709414 * q^50 + 31420487764988998054407847811592 * q^51 + 186771330756284408934646875520568 * q^52 - 125797679190958862093479980165288 * q^53 + 25444115222524214598246503127978 * q^54 - 324441401797069196184728188134624 * q^55 + 49261177652308793436687718380480 * q^56 - 210990841941914426518569886272048 * q^57 - 758216144723951752216603559669556 * q^58 - 1322751535061383229075407129388688 * q^59 - 1381573664014504126645791751653864 * q^60 - 1210012908287761061549313720873160 * q^61 - 3774869312329378363502064838581792 * q^62 + 991496635009340824662391221351264 * q^63 + 8553618714336434539515354532145728 * q^64 + 1596939597234927778869711846229968 * q^65 + 9262917291337022257579330290870264 * q^66 + 16212837695473169417262127089269648 * q^67 + 6364770984875237153325176447214984 * q^68 - 2365370461432749730136966298227232 * q^69 + 8205699211322075854652286498656160 * q^70 + 10892424995451680587530033164573088 * q^71 + 21085911757113789886414645113381096 * q^72 - 19472416597596703966438677461737048 * q^73 - 89115306434605413664690690272305412 * q^74 + 36958705028313418437226934124692124 * q^75 - 95475877084130734100913860795365168 * q^76 - 256189314900709292482321902951864192 * q^77 + 166030666981966339429833686631556332 * q^78 + 42564929886993357285736803130555520 * q^79 - 955034489632094448517301530341944736 * q^80 + 90113598179756697647360591499090564 * q^81 + 335470244295388111217009211756354948 * q^82 - 462964612731837394872969166562146224 * q^83 + 956864266956595720700203893073695072 * q^84 + 1847677353245070936584728247586996912 * q^85 - 363370083621183428400243233525783304 * q^86 + 1616002923572170440926487227549582904 * q^87 + 4210934419609684353108607591773010656 * q^88 - 314574774231571073544391076719446552 * q^89 - 3228689152297913406320288402251236 * q^90 + 2615056540536627234228451043107657024 * q^91 - 16598538663060910484079148451607722016 * q^92 + 3485162913294081237336365108822882496 * q^93 - 573809173038711993912694394480689248 * q^94 - 8958385060094338314910240959017780256 * q^95 + 14147618579538063674464137028143247776 * q^96 + 445047507548838106214452450407795848 * q^97 - 43086999614034505592591376853854433878 * q^98 + 3145039288289754558742704694209474096 * 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 $

$2$	−520663.	−1.40444	−0.702218	−	0.711962i	$-0.747807\pi$
$2$	−520663.	−1.40444	−0.702218	+	0.711962i	$0.747807\pi$
$3$	3.87420e8	0.577350
$3$	3.87420e8	0.577350
$4$	1.33651e11	0.972441
$5$	−2.63441e12	−0.308843	−0.154422	−	0.988005i	$-0.549351\pi$
$5$	−2.63441e12	−0.308843	−0.154422	+	0.988005i	$0.549351\pi$
$6$	−2.01716e14	−0.810852
$7$	8.34393e15	1.93668	0.968338	−	0.249642i	$-0.0803128\pi$
$7$	8.34393e15	1.93668	0.968338	+	0.249642i	$0.0803128\pi$
$8$	1.97212e15	0.0387051
$9$	1.50095e17	0.333333
$10$	1.37164e18	0.433750
$11$	−2.00696e19	−1.08836	−0.544182	−	0.838967i	$-0.683160\pi$
$11$	−2.00696e19	−1.08836	−0.544182	+	0.838967i	$0.683160\pi$
$12$	5.17792e19	0.561439
$13$	−1.05373e20	−0.259883	−0.129942	−	0.991522i	$-0.541479\pi$
$13$	−1.05373e20	−0.259883	−0.129942	+	0.991522i	$0.541479\pi$
$14$	−4.34438e21	−2.71994
$15$	−1.02062e21	−0.178311
$16$	−1.93957e22	−1.02680
$17$	1.77033e22	0.305315	0.152657	−	0.988279i	$-0.451217\pi$
$17$	1.77033e22	0.305315	0.152657	+	0.988279i	$0.451217\pi$
$18$	−7.81488e22	−0.468145
$19$	4.00776e23	0.882999	0.441499	−	0.897262i	$-0.354447\pi$
$19$	4.00776e23	0.882999	0.441499	+	0.897262i	$0.354447\pi$
$20$	−3.52092e23	−0.300332
$21$	3.23261e24	1.11814
$22$	1.04495e25	1.52854
$23$	−1.07722e25	−0.692374	−0.346187	−	0.938166i	$-0.612524\pi$
$23$	−1.07722e25	−0.692374	−0.346187	+	0.938166i	$0.612524\pi$
$24$	7.64040e23	0.0223464
$25$	−6.58195e25	−0.904616
$26$	5.48640e25	0.364989
$27$	5.81497e25	0.192450
$28$	1.11518e27	1.88330
$29$	1.59166e27	1.40439	0.702193	−	0.711986i	$-0.252204\pi$
$29$	1.59166e27	1.40439	0.702193	+	0.711986i	$0.252204\pi$
$30$	5.31401e26	0.250426
$31$	4.20936e27	1.08149	0.540747	−	0.841185i	$-0.318142\pi$
$31$	4.20936e27	1.08149	0.540747	+	0.841185i	$0.318142\pi$
$32$	9.82758e27	1.40337
$33$	−7.77537e27	−0.628367
$34$	−9.21743e27	−0.428795
$35$	−2.19813e28	−0.598129
$36$	2.00603e28	0.324147
$37$	1.71917e29	1.67335	0.836675	−	0.547700i	$-0.184496\pi$
$37$	1.71917e29	1.67335	0.836675	+	0.547700i	$0.184496\pi$
$38$	−2.08669e29	−1.24012
$39$	−4.08238e28	−0.150044
$40$	−5.19537e27	−0.0119538
$41$	−3.95960e29	−0.576965	−0.288483	−	0.957485i	$-0.593151\pi$
$41$	−3.95960e29	−0.576965	−0.288483	+	0.957485i	$0.593151\pi$
$42$	−1.68310e30	−1.57036
$43$	3.48956e29	0.210671	0.105335	−	0.994437i	$-0.466408\pi$
$43$	3.48956e29	0.210671	0.105335	+	0.994437i	$0.466408\pi$
$44$	−2.68233e30	−1.05837
$45$	−3.95410e29	−0.102948
$46$	5.60870e30	0.972395
$47$	−2.42346e30	−0.282244	−0.141122	−	0.989992i	$-0.545071\pi$
$47$	−2.42346e30	−0.282244	−0.141122	+	0.989992i	$0.545071\pi$
$48$	−7.51429e30	−0.592823
$49$	5.10591e31	2.75072
$50$	3.42698e31	1.27048
$51$	6.85860e30	0.176274
$52$	−1.40833e31	−0.252721
$53$	−1.34925e32	−1.70212	−0.851060	−	0.525068i	$-0.824040\pi$
$53$	−1.34925e32	−1.70212	−0.851060	+	0.525068i	$0.824040\pi$
$54$	−3.02764e31	−0.270284
$55$	5.28715e31	0.336134
$56$	1.64552e31	0.0749593
$57$	1.55269e32	0.509800
$58$	−8.28718e32	−1.97237
$59$	1.06678e33	1.85061	0.925304	−	0.379226i	$-0.123810\pi$
$59$	1.06678e33	1.85061	0.925304	+	0.379226i	$0.123810\pi$
$60$	−1.36408e32	−0.173397
$61$	−7.04574e32	−0.659667	−0.329833	−	0.944039i	$-0.606993\pi$
$61$	−7.04574e32	−0.659667	−0.329833	+	0.944039i	$0.606993\pi$
$62$	−2.19166e33	−1.51889
$63$	1.25238e33	0.645559
$64$	−2.45114e33	−0.944143
$65$	2.77596e32	0.0802632
$66$	4.04835e33	0.882501
$67$	7.19450e33	1.18745	0.593727	−	0.804667i	$-0.297656\pi$
$67$	7.19450e33	1.18745	0.593727	+	0.804667i	$0.297656\pi$
$68$	2.36606e33	0.296901
$69$	−4.17338e33	−0.399742
$70$	1.14449e34	0.840034
$71$	2.35209e34	1.32793	0.663964	−	0.747765i	$-0.268873\pi$
$71$	2.35209e34	1.32793	0.663964	+	0.747765i	$0.268873\pi$
$72$	2.96005e32	0.0129017
$73$	2.69218e33	0.0909140	0.0454570	−	0.998966i	$-0.485526\pi$
$73$	2.69218e33	0.0909140	0.0454570	+	0.998966i	$0.485526\pi$
$74$	−8.95108e34	−2.35011
$75$	−2.54998e34	−0.522280
$76$	5.35642e34	0.858664
$77$	−1.67459e35	−2.10781
$78$	2.12554e34	0.210727
$79$	2.20044e34	0.172349	0.0861746	−	0.996280i	$-0.472536\pi$
$79$	2.20044e34	0.172349	0.0861746	+	0.996280i	$0.472536\pi$
$80$	5.10962e34	0.317120
$81$	2.25284e34	0.111111
$82$	2.06162e35	0.810311
$83$	−2.35934e35	−0.741046	−0.370523	−	0.928823i	$-0.620822\pi$
$83$	−2.35934e35	−0.741046	−0.370523	+	0.928823i	$0.620822\pi$
$84$	4.32042e35	1.08733
$85$	−4.66376e34	−0.0942944
$86$	−1.81689e35	−0.295874
$87$	6.16641e35	0.810823
$88$	−3.95797e34	−0.0421253
$89$	1.13980e35	0.0984271	0.0492135	−	0.998788i	$-0.484329\pi$
$89$	1.13980e35	0.0984271	0.0492135	+	0.998788i	$0.484329\pi$
$90$	2.05876e35	0.144583
$91$	−8.79227e35	−0.503310
$92$	−1.43972e36	−0.673293
$93$	1.63079e36	0.624401
$94$	1.26181e36	0.396394
$95$	−1.05581e36	−0.272708
$96$	3.80741e36	0.810236
$97$	8.44145e36	1.48300	0.741498	−	0.670955i	$-0.234116\pi$
$97$	8.44145e36	1.48300	0.741498	+	0.670955i	$0.234116\pi$
$98$	−2.65846e37	−3.86321
$99$	−3.01234e36	−0.362788
$100$	−8.79685e36	−0.879685
$101$	6.86236e36	0.570858	0.285429	−	0.958400i	$-0.407864\pi$
$101$	6.86236e36	0.570858	0.285429	+	0.958400i	$0.407864\pi$
$102$	−3.57102e36	−0.247565
$103$	1.30579e37	0.755760	0.377880	−	0.925855i	$-0.376653\pi$
$103$	1.30579e37	0.755760	0.377880	+	0.925855i	$0.376653\pi$
$104$	−2.07809e35	−0.0100588
$105$	−8.51601e36	−0.345330
$106$	7.02507e37	2.39052
$107$	4.38206e37	1.25337	0.626683	−	0.779274i	$-0.284412\pi$
$107$	4.38206e37	1.25337	0.626683	+	0.779274i	$0.284412\pi$
$108$	7.77178e36	0.187146
$109$	−1.05626e37	−0.214476	−0.107238	−	0.994233i	$-0.534201\pi$
$109$	−1.05626e37	−0.214476	−0.107238	+	0.994233i	$0.534201\pi$
$110$	−2.75282e37	−0.472078
$111$	6.66041e37	0.966109
$112$	−1.61836e38	−1.98858
$113$	−6.38435e37	−0.665527	−0.332763	−	0.943010i	$-0.607981\pi$
$113$	−6.38435e37	−0.665527	−0.332763	+	0.943010i	$0.607981\pi$
$114$	−8.08428e37	−0.715981
$115$	2.83784e37	0.213835
$116$	2.12727e38	1.36568
$117$	−1.58160e37	−0.0866278
$118$	−5.55435e38	−2.59906
$119$	1.47715e38	0.591296
$120$	−2.01279e36	−0.00690154
$121$	6.27494e37	0.184536
$122$	3.66846e38	0.926460
$123$	−1.53403e38	−0.333111
$124$	5.62586e38	1.05169
$125$	3.65074e38	0.588227
$126$	−6.52068e38	−0.906646
$127$	−2.81304e38	−0.337915	−0.168957	−	0.985623i	$-0.554040\pi$
$127$	−2.81304e38	−0.337915	−0.168957	+	0.985623i	$0.554040\pi$
$128$	−7.44763e37	−0.0773809
$129$	1.35193e38	0.121631
$130$	−1.44534e38	−0.112724
$131$	1.95973e39	1.32641	0.663206	−	0.748437i	$-0.269195\pi$
$131$	1.95973e39	1.32641	0.663206	+	0.748437i	$0.269195\pi$
$132$	−1.03919e39	−0.611050
$133$	3.34405e39	1.71008
$134$	−3.74591e39	−1.66770
$135$	−1.53190e38	−0.0594369
$136$	3.49129e37	0.0118173
$137$	1.41955e39	0.419586	0.209793	−	0.977746i	$-0.432721\pi$
$137$	1.41955e39	0.419586	0.209793	+	0.977746i	$0.432721\pi$
$138$	2.17293e39	0.561412
$139$	−2.88414e39	−0.651992	−0.325996	−	0.945371i	$-0.605700\pi$
$139$	−2.88414e39	−0.651992	−0.325996	+	0.945371i	$0.605700\pi$
$140$	−2.93783e39	−0.581645
$141$	−9.38897e38	−0.162954
$142$	−1.22465e40	−1.86499
$143$	2.11480e39	0.282848
$144$	−2.91119e39	−0.342267
$145$	−4.19308e39	−0.433735
$146$	−1.40172e39	−0.127683
$147$	1.97813e40	1.58813
$148$	2.29769e40	1.62723
$149$	−1.54836e40	−0.968111	−0.484055	−	0.875037i	$-0.660837\pi$
$149$	−1.54836e40	−0.968111	−0.484055	+	0.875037i	$0.660837\pi$
$150$	1.32768e40	0.733509
$151$	−5.65320e39	−0.276198	−0.138099	−	0.990418i	$-0.544099\pi$
$151$	−5.65320e39	−0.276198	−0.138099	+	0.990418i	$0.544099\pi$
$152$	7.90378e38	0.0341766
$153$	2.65716e39	0.101772
$154$	8.71900e40	2.96028
$155$	−1.10892e40	−0.334012
$156$	−5.45615e39	−0.145909
$157$	−6.59332e40	−1.56661	−0.783304	−	0.621638i	$-0.786467\pi$
$157$	−6.59332e40	−1.56661	−0.783304	+	0.621638i	$0.786467\pi$
$158$	−1.14569e40	−0.242053
$159$	−5.22729e40	−0.982720
$160$	−2.58899e40	−0.433421
$161$	−8.98828e40	−1.34090
$162$	−1.17297e40	−0.156048
$163$	3.78789e40	0.449704	0.224852	−	0.974393i	$-0.427810\pi$
$163$	3.78789e40	0.449704	0.224852	+	0.974393i	$0.427810\pi$
$164$	−5.29205e40	−0.561065
$165$	2.04835e40	0.194067
$166$	1.22842e41	1.04075
$167$	1.83545e41	1.39151	0.695757	−	0.718277i	$-0.255069\pi$
$167$	1.83545e41	1.39151	0.695757	+	0.718277i	$0.255069\pi$
$168$	6.37510e39	0.0432778
$169$	−1.53297e41	−0.932461
$170$	2.42825e40	0.132430
$171$	6.01543e40	0.294333
$172$	4.66384e40	0.204865
$173$	1.65118e41	0.651540	0.325770	−	0.945449i	$-0.394376\pi$
$173$	1.65118e41	0.651540	0.325770	+	0.945449i	$0.394376\pi$
$174$	−3.21062e41	−1.13875
$175$	−5.49193e41	−1.75195
$176$	3.89264e41	1.11753
$177$	4.13294e41	1.06845
$178$	−5.93454e40	−0.138235
$179$	4.97609e41	1.04498	0.522489	−	0.852646i	$-0.325004\pi$
$179$	4.97609e41	1.04498	0.522489	+	0.852646i	$0.325004\pi$
$180$	−5.28471e40	−0.100111
$181$	−7.52929e40	−0.128736	−0.0643680	−	0.997926i	$-0.520503\pi$
$181$	−7.52929e40	−0.128736	−0.0643680	+	0.997926i	$0.520503\pi$
$182$	4.57781e41	0.706867
$183$	−2.72966e41	−0.380859
$184$	−2.12441e40	−0.0267984
$185$	−4.52899e41	−0.516803
$186$	−8.49093e41	−0.876931
$187$	−3.55297e41	−0.332294
$188$	−3.23898e41	−0.274466
$189$	4.85198e41	0.372714
$190$	5.49720e41	0.383001
$191$	−3.49406e41	−0.220909	−0.110454	−	0.993881i	$-0.535231\pi$
$191$	−3.49406e41	−0.220909	−0.110454	+	0.993881i	$0.535231\pi$
$192$	−9.49620e41	−0.545101
$193$	−8.39189e41	−0.437572	−0.218786	−	0.975773i	$-0.570210\pi$
$193$	−8.39189e41	−0.437572	−0.218786	+	0.975773i	$0.570210\pi$
$194$	−4.39515e42	−2.08277
$195$	1.07546e41	0.0463400
$196$	6.82411e42	2.67491
$197$	−7.30118e41	−0.260476	−0.130238	−	0.991483i	$-0.541574\pi$
$197$	−7.30118e41	−0.260476	−0.130238	+	0.991483i	$0.541574\pi$
$198$	1.56841e42	0.509512
$199$	5.82003e41	0.172244	0.0861218	−	0.996285i	$-0.472553\pi$
$199$	5.82003e41	0.172244	0.0861218	+	0.996285i	$0.472553\pi$
$200$	−1.29804e41	−0.0350133
$201$	2.78730e42	0.685577
$202$	−3.57298e42	−0.801733
$203$	1.32807e43	2.71984
$204$	9.16661e41	0.171416
$205$	1.04312e42	0.178192
$206$	−6.79875e42	−1.06142
$207$	−1.61685e42	−0.230791
$208$	2.04379e42	0.266848
$209$	−8.04341e42	−0.961024
$210$	4.43398e42	0.484994
$211$	−1.25054e43	−1.25277	−0.626384	−	0.779515i	$-0.715466\pi$
$211$	−1.25054e43	−1.25277	−0.626384	+	0.779515i	$0.715466\pi$
$212$	−1.80330e43	−1.65521
$213$	9.11248e42	0.766680
$214$	−2.28158e43	−1.76027
$215$	−9.19292e41	−0.0650642
$216$	1.14678e41	0.00744881
$217$	3.51226e43	2.09450
$218$	5.49955e42	0.301219
$219$	1.04300e42	0.0524892
$220$	7.06634e42	0.326870
$221$	−1.86545e42	−0.0793462
$222$	−3.46783e43	−1.35684
$223$	−1.91165e43	−0.688287	−0.344143	−	0.938917i	$-0.611831\pi$
$223$	−1.91165e43	−0.688287	−0.344143	+	0.938917i	$0.611831\pi$
$224$	8.20007e43	2.71787
$225$	−9.87915e42	−0.301539
$226$	3.32410e43	0.934690
$227$	−2.06794e43	−0.535871	−0.267936	−	0.963437i	$-0.586341\pi$
$227$	−2.06794e43	−0.535871	−0.267936	+	0.963437i	$0.586341\pi$
$228$	2.07519e43	0.495750
$229$	6.73090e42	0.148292	0.0741458	−	0.997247i	$-0.476377\pi$
$229$	6.73090e42	0.148292	0.0741458	+	0.997247i	$0.476377\pi$
$230$	−1.47756e43	−0.300317
$231$	−6.48772e43	−1.21694
$232$	3.13894e42	0.0543570
$233$	−5.29076e43	−0.846123	−0.423062	−	0.906101i	$-0.639045\pi$
$233$	−5.29076e43	−0.846123	−0.423062	+	0.906101i	$0.639045\pi$
$234$	8.23479e42	0.121663
$235$	6.38437e42	0.0871692
$236$	1.42577e44	1.79961
$237$	8.52497e42	0.0995058
$238$	−7.69096e43	−0.830438
$239$	8.90649e43	0.889908	0.444954	−	0.895553i	$-0.353220\pi$
$239$	8.90649e43	0.889908	0.444954	+	0.895553i	$0.353220\pi$
$240$	1.97957e43	0.183089
$241$	−1.14469e44	−0.980331	−0.490166	−	0.871629i	$-0.663064\pi$
$241$	−1.14469e44	−0.980331	−0.490166	+	0.871629i	$0.663064\pi$
$242$	−3.26713e43	−0.259168
$243$	8.72796e42	0.0641500
$244$	−9.41672e43	−0.641487
$245$	−1.34510e44	−0.849540
$246$	7.98713e43	0.467833
$247$	−4.22311e43	−0.229477
$248$	8.30135e42	0.0418594
$249$	−9.14055e43	−0.427843
$250$	−1.90080e44	−0.826128
$251$	−1.57202e44	−0.634590	−0.317295	−	0.948327i	$-0.602774\pi$
$251$	−1.57202e44	−0.634590	−0.317295	+	0.948327i	$0.602774\pi$
$252$	1.67382e44	0.627768
$253$	2.16194e44	0.753555
$254$	1.46465e44	0.474579
$255$	−1.80684e43	−0.0544409
$256$	3.75659e44	1.05282
$257$	2.35997e44	0.615380	0.307690	−	0.951487i	$-0.400444\pi$
$257$	2.35997e44	0.615380	0.307690	+	0.951487i	$0.400444\pi$
$258$	−7.03899e43	−0.170823
$259$	1.43446e45	3.24074
$260$	3.71011e43	0.0780512
$261$	2.38899e44	0.468129
$262$	−1.02036e45	−1.86286
$263$	−1.02621e45	−1.74604	−0.873022	−	0.487680i	$-0.837843\pi$
$263$	−1.02621e45	−1.74604	−0.873022	+	0.487680i	$0.837843\pi$
$264$	−1.53340e43	−0.0243210
$265$	3.55449e44	0.525688
$266$	−1.74112e45	−2.40170
$267$	4.41583e43	0.0568269
$268$	9.61554e44	1.15473
$269$	2.39378e44	0.268328	0.134164	−	0.990959i	$-0.457165\pi$
$269$	2.39378e44	0.268328	0.134164	+	0.990959i	$0.457165\pi$
$270$	7.97605e43	0.0834753
$271$	−1.10518e45	−1.08019	−0.540094	−	0.841605i	$-0.681611\pi$
$271$	−1.10518e45	−1.08019	−0.540094	+	0.841605i	$0.681611\pi$
$272$	−3.43367e44	−0.313497
$273$	−3.40631e44	−0.290586
$274$	−7.39109e44	−0.589282
$275$	1.32097e45	0.984551
$276$	−5.57778e44	−0.388726
$277$	−2.08812e45	−1.36107	−0.680534	−	0.732717i	$-0.738252\pi$
$277$	−2.08812e45	−1.36107	−0.680534	+	0.732717i	$0.738252\pi$
$278$	1.50166e45	0.915681
$279$	6.31802e44	0.360498
$280$	−4.33498e43	−0.0231507
$281$	2.01962e45	1.00973	0.504863	−	0.863200i	$-0.331543\pi$
$281$	2.01962e45	1.00973	0.504863	+	0.863200i	$0.331543\pi$
$282$	4.88849e44	0.228858
$283$	2.43661e45	1.06841	0.534204	−	0.845356i	$-0.320612\pi$
$283$	2.43661e45	1.06841	0.534204	+	0.845356i	$0.320612\pi$
$284$	3.14360e45	1.29133
$285$	−4.09041e44	−0.157448
$286$	−1.10110e45	−0.397241
$287$	−3.30386e45	−1.11740
$288$	1.47507e45	0.467790
$289$	−3.04869e45	−0.906783
$290$	2.18318e45	0.609153
$291$	3.27039e45	0.856208
$292$	3.59813e44	0.0884084
$293$	5.41508e44	0.124898	0.0624488	−	0.998048i	$-0.480109\pi$
$293$	5.41508e44	0.124898	0.0624488	+	0.998048i	$0.480109\pi$
$294$	−1.02994e46	−2.23042
$295$	−2.81034e45	−0.571547
$296$	3.39041e44	0.0647672
$297$	−1.16704e45	−0.209456
$298$	8.06172e45	1.35965
$299$	1.13511e45	0.179936
$300$	−3.40808e45	−0.507887
$301$	2.91167e45	0.408001
$302$	2.94341e45	0.387903
$303$	2.65862e45	0.329585
$304$	−7.77333e45	−0.906663
$305$	1.85614e45	0.203734
$306$	−1.38349e45	−0.142932
$307$	3.09102e45	0.300637	0.150318	−	0.988638i	$-0.451970\pi$
$307$	3.09102e45	0.300637	0.150318	+	0.988638i	$0.451970\pi$
$308$	−2.23812e46	−2.04972
$309$	5.05889e45	0.436338
$310$	5.77372e45	0.469099
$311$	−2.15029e46	−1.64600	−0.823001	−	0.568040i	$-0.807702\pi$
$311$	−2.15029e46	−1.64600	−0.823001	+	0.568040i	$0.807702\pi$
$312$	−8.05093e43	−0.00580746
$313$	−1.50052e42	−0.000102017 0	−5.10083e−5	−	1.00000i	$-0.500016\pi$
$313$	−1.50052e42	−0.000102017 0	−5.10083e−5		1.00000i	$0.500016\pi$
$314$	3.43290e46	2.20020
$315$	−3.29928e45	−0.199376
$316$	2.94092e45	0.167599
$317$	−7.41293e45	−0.398468	−0.199234	−	0.979952i	$-0.563845\pi$
$317$	−7.41293e45	−0.398468	−0.199234	+	0.979952i	$0.563845\pi$
$318$	2.72166e46	1.38017
$319$	−3.19439e46	−1.52848
$320$	6.45729e45	0.291592
$321$	1.69770e46	0.723632
$322$	4.67987e46	1.88321
$323$	7.09504e45	0.269593
$324$	3.01095e45	0.108049
$325$	6.93561e45	0.235095
$326$	−1.97221e46	−0.631580
$327$	−4.09216e45	−0.123828
$328$	−7.80880e44	−0.0223315
$329$	−2.02212e46	−0.546616
$330$	−1.06650e46	−0.272554
$331$	−2.02313e46	−0.488883	−0.244441	−	0.969664i	$-0.578605\pi$
$331$	−2.02313e46	−0.488883	−0.244441	+	0.969664i	$0.578605\pi$
$332$	−3.15328e46	−0.720623
$333$	2.58038e46	0.557783
$334$	−9.55651e46	−1.95429
$335$	−1.89532e46	−0.366737
$336$	−6.26987e46	−1.14811
$337$	1.40951e46	0.244295	0.122148	−	0.992512i	$-0.461022\pi$
$337$	1.40951e46	0.244295	0.122148	+	0.992512i	$0.461022\pi$
$338$	7.98163e46	1.30958
$339$	−2.47343e46	−0.384242
$340$	−6.23317e45	−0.0916957
$341$	−8.44801e46	−1.17706
$342$	−3.13201e46	−0.413372
$343$	2.71153e47	3.39057
$344$	6.88183e44	0.00815404
$345$	1.09944e46	0.123458
$346$	−8.59708e46	−0.915046
$347$	1.91978e46	0.193711	0.0968557	−	0.995298i	$-0.469121\pi$
$347$	1.91978e46	0.193711	0.0968557	+	0.995298i	$0.469121\pi$
$348$	8.24148e46	0.788477
$349$	1.61862e47	1.46851	0.734253	−	0.678876i	$-0.237533\pi$
$349$	1.61862e47	1.46851	0.734253	+	0.678876i	$0.237533\pi$
$350$	2.85945e47	2.46050
$351$	−6.12743e45	−0.0500146
$352$	−1.97236e47	−1.52738
$353$	−9.35860e46	−0.687668	−0.343834	−	0.939030i	$-0.611726\pi$
$353$	−9.35860e46	−0.687668	−0.343834	+	0.939030i	$0.611726\pi$
$354$	−2.15187e47	−1.50057
$355$	−6.19636e46	−0.410121
$356$	1.52336e46	0.0957145
$357$	5.72277e46	0.341385
$358$	−2.59086e47	−1.46760
$359$	3.05449e47	1.64321	0.821603	−	0.570060i	$-0.193080\pi$
$359$	3.05449e47	1.64321	0.821603	+	0.570060i	$0.193080\pi$
$360$	−7.79797e44	−0.00398460
$361$	−4.53862e46	−0.220313
$362$	3.92022e46	0.180802
$363$	2.43104e46	0.106542
$364$	−1.17510e47	−0.489439
$365$	−7.09229e45	−0.0280781
$366$	1.42124e47	0.534892
$367$	−3.45206e47	−1.23526	−0.617628	−	0.786471i	$-0.711906\pi$
$367$	−3.45206e47	−1.23526	−0.617628	+	0.786471i	$0.711906\pi$
$368$	2.08935e47	0.710929
$369$	−5.94314e46	−0.192322
$370$	2.35808e47	0.725816
$371$	−1.12581e48	−3.29646
$372$	2.17957e47	0.607193
$373$	5.25222e47	1.39229	0.696145	−	0.717901i	$-0.254897\pi$
$373$	5.25222e47	1.39229	0.696145	+	0.717901i	$0.254897\pi$
$374$	1.84990e47	0.466685
$375$	1.41437e47	0.339613
$376$	−4.77935e45	−0.0109243
$377$	−1.67718e47	−0.364977
$378$	−2.52625e47	−0.523452
$379$	1.07624e47	0.212365	0.106183	−	0.994347i	$-0.466137\pi$
$379$	1.07624e47	0.212365	0.106183	+	0.994347i	$0.466137\pi$
$380$	−1.41110e47	−0.265192
$381$	−1.08983e47	−0.195095
$382$	1.81923e47	0.310252
$383$	3.92097e44	0.000637112 0	0.000318556	−	1.00000i	$-0.499899\pi$
$383$	3.92097e44	0.000637112 0	0.000318556		1.00000i	$0.499899\pi$
$384$	−2.88536e46	−0.0446759
$385$	4.41156e47	0.650982
$386$	4.36935e47	0.614542
$387$	5.23764e46	0.0702236
$388$	1.12821e48	1.44213
$389$	−1.07652e48	−1.31206	−0.656029	−	0.754736i	$-0.727765\pi$
$389$	−1.07652e48	−1.31206	−0.656029	+	0.754736i	$0.727765\pi$
$390$	−5.59955e46	−0.0650815
$391$	−1.90704e47	−0.211392
$392$	1.00695e47	0.106467
$393$	7.59241e47	0.765804
$394$	3.80145e47	0.365822
$395$	−5.79687e46	−0.0532288
$396$	−4.02603e47	−0.352790
$397$	−9.91329e47	−0.829074	−0.414537	−	0.910032i	$-0.636056\pi$
$397$	−9.91329e47	−0.829074	−0.414537	+	0.910032i	$0.636056\pi$
$398$	−3.03027e47	−0.241905
$399$	1.29555e48	0.987317
$400$	1.27661e48	0.928859
$401$	5.74839e47	0.399370	0.199685	−	0.979860i	$-0.436008\pi$
$401$	5.74839e47	0.399370	0.199685	+	0.979860i	$0.436008\pi$
$402$	−1.45124e48	−0.962849
$403$	−4.43553e47	−0.281062
$404$	9.17163e47	0.555125
$405$	−5.93490e46	−0.0343159
$406$	−6.91477e48	−3.81985
$407$	−3.45030e48	−1.82121
$408$	1.35260e46	0.00682269
$409$	−1.42222e48	−0.685623	−0.342812	−	0.939404i	$-0.611379\pi$
$409$	−1.42222e48	−0.685623	−0.342812	+	0.939404i	$0.611379\pi$
$410$	−5.43114e47	−0.250259
$411$	5.49964e47	0.242248
$412$	1.74520e48	0.734932
$413$	8.90118e48	3.58403
$414$	8.41836e47	0.324132
$415$	6.21545e47	0.228867
$416$	−1.03556e48	−0.364712
$417$	−1.11737e48	−0.376428
$418$	4.18791e48	1.34970
$419$	−2.58159e47	−0.0796026	−0.0398013	−	0.999208i	$-0.512672\pi$
$419$	−2.58159e47	−0.0796026	−0.0398013	+	0.999208i	$0.512672\pi$
$420$	−1.13818e48	−0.335813
$421$	2.31697e48	0.654186	0.327093	−	0.944992i	$-0.393931\pi$
$421$	2.31697e48	0.654186	0.327093	+	0.944992i	$0.393931\pi$
$422$	6.51108e48	1.75943
$423$	−3.63748e47	−0.0940814
$424$	−2.66089e47	−0.0658808
$425$	−1.16522e48	−0.276193
$426$	−4.74453e48	−1.07675
$427$	−5.87892e48	−1.27756
$428$	5.85668e48	1.21883
$429$	8.19317e47	0.163302
$430$	4.78642e47	0.0913785
$431$	−3.89804e48	−0.712881	−0.356441	−	0.934318i	$-0.616010\pi$
$431$	−3.89804e48	−0.712881	−0.356441	+	0.934318i	$0.616010\pi$
$432$	−1.12785e48	−0.197608
$433$	9.77220e48	1.64046	0.820231	−	0.572032i	$-0.193845\pi$
$433$	9.77220e48	1.64046	0.820231	+	0.572032i	$0.193845\pi$
$434$	−1.82870e49	−2.94160
$435$	−1.62448e48	−0.250417
$436$	−1.41170e48	−0.208566
$437$	−4.31725e48	−0.611365
$438$	−5.43054e47	−0.0737177
$439$	−1.19379e48	−0.155359	−0.0776793	−	0.996978i	$-0.524751\pi$
$439$	−1.19379e48	−0.155359	−0.0776793	+	0.996978i	$0.524751\pi$
$440$	1.04269e47	0.0130101
$441$	7.66370e48	0.916905
$442$	9.71271e47	0.111437
$443$	−1.49848e48	−0.164886	−0.0824429	−	0.996596i	$-0.526272\pi$
$443$	−1.49848e48	−0.164886	−0.0824429	+	0.996596i	$0.526272\pi$
$444$	8.90173e48	0.939484
$445$	−3.00271e47	−0.0303985
$446$	9.95328e48	0.966655
$447$	−5.99865e48	−0.558939
$448$	−2.04521e49	−1.82850
$449$	9.14003e48	0.784134	0.392067	−	0.919937i	$-0.371760\pi$
$449$	9.14003e48	0.784134	0.392067	+	0.919937i	$0.371760\pi$
$450$	5.14371e48	0.423492
$451$	7.94675e48	0.627948
$452$	−8.53277e48	−0.647185
$453$	−2.19016e48	−0.159463
$454$	1.07670e49	0.752597
$455$	2.31624e48	0.155444
$456$	3.06209e47	0.0197319
$457$	−7.21363e48	−0.446379	−0.223190	−	0.974775i	$-0.571647\pi$
$457$	−7.21363e48	−0.446379	−0.223190	+	0.974775i	$0.571647\pi$
$458$	−3.50453e48	−0.208266
$459$	1.02944e48	0.0587579
$460$	3.79281e48	0.207942
$461$	−3.62582e48	−0.190959	−0.0954793	−	0.995431i	$-0.530438\pi$
$461$	−3.62582e48	−0.190959	−0.0954793	+	0.995431i	$0.530438\pi$
$462$	3.37792e49	1.70912
$463$	−2.42342e49	−1.17810	−0.589048	−	0.808098i	$-0.700497\pi$
$463$	−2.42342e49	−1.17810	−0.589048	+	0.808098i	$0.700497\pi$
$464$	−3.08713e49	−1.44202
$465$	−4.29617e48	−0.192842
$466$	2.75471e49	1.18833
$467$	2.11890e49	0.878514	0.439257	−	0.898362i	$-0.355242\pi$
$467$	2.11890e49	0.878514	0.439257	+	0.898362i	$0.355242\pi$
$468$	−2.11382e48	−0.0842404
$469$	6.00304e49	2.29971
$470$	−3.32411e48	−0.122424
$471$	−2.55439e49	−0.904482
$472$	2.10383e48	0.0716280
$473$	−7.00341e48	−0.229286
$474$	−4.43864e48	−0.139750
$475$	−2.63789e49	−0.798775
$476$	1.97423e49	0.575001
$477$	−2.02516e49	−0.567374
$478$	−4.63728e49	−1.24982
$479$	−3.96549e49	−1.02823	−0.514115	−	0.857721i	$-0.671879\pi$
$479$	−3.96549e49	−1.02823	−0.514115	+	0.857721i	$0.671879\pi$
$480$	−1.00303e49	−0.250236
$481$	−1.81154e49	−0.434876
$482$	5.95998e49	1.37681
$483$	−3.48224e49	−0.774171
$484$	8.38653e48	0.179450
$485$	−2.22382e49	−0.458013
$486$	−4.54433e48	−0.0900946
$487$	−3.49809e49	−0.667644	−0.333822	−	0.942636i	$-0.608338\pi$
$487$	−3.49809e49	−0.667644	−0.333822	+	0.942636i	$0.608338\pi$
$488$	−1.38950e48	−0.0255325
$489$	1.46751e49	0.259636
$490$	7.00347e49	1.19312
$491$	1.54468e49	0.253414	0.126707	−	0.991940i	$-0.459559\pi$
$491$	1.54468e49	0.253414	0.126707	+	0.991940i	$0.459559\pi$
$492$	−2.05025e49	−0.323931
$493$	2.81775e49	0.428780
$494$	2.19882e49	0.322285
$495$	7.93573e48	0.112045
$496$	−8.16434e49	−1.11048
$497$	1.96257e50	2.57177
$498$	4.75915e49	0.600878
$499$	−8.88148e49	−1.08050	−0.540250	−	0.841504i	$-0.681670\pi$
$499$	−8.88148e49	−1.08050	−0.540250	+	0.841504i	$0.681670\pi$
$500$	4.87926e49	0.572016
$501$	7.11090e49	0.803391
$502$	8.18491e49	0.891240
$503$	−4.16645e49	−0.437279	−0.218639	−	0.975806i	$-0.570162\pi$
$503$	−4.16645e49	−0.437279	−0.218639	+	0.975806i	$0.570162\pi$
$504$	2.46984e48	0.0249864
$505$	−1.80782e49	−0.176305
$506$	−1.12564e50	−1.05832
$507$	−5.93905e49	−0.538356
$508$	−3.75966e49	−0.328602
$509$	1.88211e50	1.58623	0.793114	−	0.609074i	$-0.208459\pi$
$509$	1.88211e50	1.58623	0.793114	+	0.609074i	$0.208459\pi$
$510$	9.40753e48	0.0764588
$511$	2.24633e49	0.176071
$512$	−1.85356e50	−1.40124
$513$	2.33050e49	0.169933
$514$	−1.22875e50	−0.864262
$515$	−3.43998e49	−0.233411
$516$	1.80687e49	0.118279
$517$	4.86378e49	0.307184
$518$	−7.46872e50	−4.55141
$519$	6.39700e49	0.376167
$520$	5.47453e47	0.00310660
$521$	2.50866e50	1.37386	0.686931	−	0.726723i	$-0.258957\pi$
$521$	2.50866e50	1.37386	0.686931	+	0.726723i	$0.258957\pi$
$522$	−1.24386e50	−0.657457
$523$	1.68115e49	0.0857682	0.0428841	−	0.999080i	$-0.486345\pi$
$523$	1.68115e49	0.0857682	0.0428841	+	0.999080i	$0.486345\pi$
$524$	2.61921e50	1.28986
$525$	−2.12769e50	−1.01149
$526$	5.34310e50	2.45221
$527$	7.45193e49	0.330196
$528$	1.50809e50	0.645207
$529$	−1.26023e50	−0.520618
$530$	−1.85069e50	−0.738295
$531$	1.60119e50	0.616869
$532$	4.46936e50	1.66295
$533$	4.17236e49	0.149944
$534$	−2.29916e49	−0.0798098
$535$	−1.15441e50	−0.387094
$536$	1.41884e49	0.0459606
$537$	1.92784e50	0.603318
$538$	−1.24635e50	−0.376850
$539$	−1.02474e51	−2.99378
$540$	−2.04740e49	−0.0577988
$541$	9.81522e49	0.267763	0.133882	−	0.990997i	$-0.457256\pi$
$541$	9.81522e49	0.267763	0.133882	+	0.990997i	$0.457256\pi$
$542$	5.75425e50	1.51706
$543$	−2.91700e49	−0.0743258
$544$	1.73980e50	0.428470
$545$	2.78261e49	0.0662396
$546$	1.77354e50	0.408110
$547$	−6.05828e50	−1.34767	−0.673836	−	0.738881i	$-0.735354\pi$
$547$	−6.05828e50	−1.34767	−0.673836	+	0.738881i	$0.735354\pi$
$548$	1.89725e50	0.408023
$549$	−1.05753e50	−0.219889
$550$	−6.87781e50	−1.38274
$551$	6.37898e50	1.24007
$552$	−8.23041e48	−0.0154721
$553$	1.83604e50	0.333785
$554$	1.08721e51	1.91153
$555$	−1.75462e50	−0.298376
$556$	−3.85469e50	−0.634023
$557$	1.04564e50	0.166365	0.0831826	−	0.996534i	$-0.473492\pi$
$557$	1.04564e50	0.166365	0.0831826	+	0.996534i	$0.473492\pi$
$558$	−3.28956e50	−0.506297
$559$	−3.67706e49	−0.0547498
$560$	4.26343e50	0.614159
$561$	−1.37649e50	−0.191850
$562$	−1.05154e51	−1.41809
$563$	−6.57533e50	−0.858050	−0.429025	−	0.903293i	$-0.641143\pi$
$563$	−6.57533e50	−0.858050	−0.429025	+	0.903293i	$0.641143\pi$
$564$	−1.25485e50	−0.158463
$565$	1.68190e50	0.205543
$566$	−1.26865e51	−1.50051
$567$	1.87975e50	0.215186
$568$	4.63860e49	0.0513976
$569$	−2.74695e50	−0.294628	−0.147314	−	0.989090i	$-0.547063\pi$
$569$	−2.74695e50	−0.294628	−0.147314	+	0.989090i	$0.547063\pi$
$570$	2.12973e50	0.221126
$571$	−2.57528e50	−0.258855	−0.129428	−	0.991589i	$-0.541314\pi$
$571$	−2.57528e50	−0.258855	−0.129428	+	0.991589i	$0.541314\pi$
$572$	2.82646e50	0.275053
$573$	−1.35367e50	−0.127542
$574$	1.72020e51	1.56931
$575$	7.09023e50	0.626332
$576$	−3.67902e50	−0.314714
$577$	1.01888e51	0.844058	0.422029	−	0.906582i	$-0.361318\pi$
$577$	1.01888e51	0.844058	0.422029	+	0.906582i	$0.361318\pi$
$578$	1.58734e51	1.27352
$579$	−3.25119e50	−0.252632
$580$	−5.60410e50	−0.421782
$581$	−1.96861e51	−1.43517
$582$	−1.70277e51	−1.20249
$583$	2.70790e51	1.85253
$584$	5.30929e48	0.00351884
$585$	4.16657e49	0.0267544
$586$	−2.81943e50	−0.175411
$587$	2.83210e51	1.70728	0.853638	−	0.520867i	$-0.174391\pi$
$587$	2.83210e51	1.70728	0.853638	+	0.520867i	$0.174391\pi$
$588$	2.64380e51	1.54436
$589$	1.68701e51	0.954958
$590$	1.46324e51	0.802702
$591$	−2.82863e50	−0.150386
$592$	−3.33445e51	−1.71820
$593$	−3.45126e51	−1.72372	−0.861858	−	0.507150i	$-0.830699\pi$
$593$	−3.45126e51	−1.72372	−0.861858	+	0.507150i	$0.830699\pi$
$594$	6.07636e50	0.294167
$595$	−3.89141e50	−0.182618
$596$	−2.06940e51	−0.941430
$597$	2.25480e50	0.0994449
$598$	−5.91007e50	−0.252709
$599$	−4.18318e51	−1.73425	−0.867123	−	0.498094i	$-0.834034\pi$
$599$	−4.18318e51	−1.73425	−0.867123	+	0.498094i	$0.834034\pi$
$600$	−5.02887e49	−0.0202149
$601$	−2.49077e51	−0.970860	−0.485430	−	0.874276i	$-0.661337\pi$
$601$	−2.49077e51	−0.970860	−0.485430	+	0.874276i	$0.661337\pi$
$602$	−1.51600e51	−0.573011
$603$	1.07986e51	0.395818
$604$	−7.55557e50	−0.268586
$605$	−1.65307e50	−0.0569925
$606$	−1.38424e51	−0.462881
$607$	1.98679e50	0.0644409	0.0322204	−	0.999481i	$-0.489742\pi$
$607$	1.98679e50	0.0644409	0.0322204	+	0.999481i	$0.489742\pi$
$608$	3.93866e51	1.23917
$609$	5.14521e51	1.57030
$610$	−9.66421e50	−0.286131
$611$	2.55368e50	0.0733505
$612$	3.55133e50	0.0989669
$613$	3.22821e50	0.0872856	0.0436428	−	0.999047i	$-0.486104\pi$
$613$	3.22821e50	0.0872856	0.0436428	+	0.999047i	$0.486104\pi$
$614$	−1.60938e51	−0.422225
$615$	4.04126e50	0.102879
$616$	−3.30250e50	−0.0815830
$617$	2.17195e51	0.520683	0.260342	−	0.965517i	$-0.416165\pi$
$617$	2.17195e51	0.520683	0.260342	+	0.965517i	$0.416165\pi$
$618$	−2.63398e51	−0.612809
$619$	3.90977e51	0.882824	0.441412	−	0.897305i	$-0.354478\pi$
$619$	3.90977e51	0.882824	0.441412	+	0.897305i	$0.354478\pi$
$620$	−1.48208e51	−0.324807
$621$	−6.26402e50	−0.133247
$622$	1.11958e52	2.31171
$623$	9.51044e50	0.190621
$624$	7.91805e50	0.154065
$625$	3.82724e51	0.722946
$626$	7.81264e47	0.000143276 0
$627$	−3.11618e51	−0.554847
$628$	−8.81205e51	−1.52343
$629$	3.04349e51	0.510899
$630$	1.71781e51	0.280011
$631$	−7.04074e51	−1.11449	−0.557244	−	0.830349i	$-0.688141\pi$
$631$	−7.04074e51	−1.11449	−0.557244	+	0.830349i	$0.688141\pi$
$632$	4.33954e49	0.00667080
$633$	−4.84483e51	−0.723286
$634$	3.85964e51	0.559623
$635$	7.41069e50	0.104363
$636$	−6.98634e51	−0.955637
$637$	−5.38026e51	−0.714865
$638$	1.66320e52	2.14666
$639$	3.53036e51	0.442643
$640$	1.96201e50	0.0238985
$641$	−1.31488e52	−1.55601	−0.778003	−	0.628260i	$-0.783767\pi$
$641$	−1.31488e52	−1.55601	−0.778003	+	0.628260i	$0.783767\pi$
$642$	−8.83929e51	−1.01629
$643$	1.39124e52	1.55417	0.777084	−	0.629397i	$-0.216698\pi$
$643$	1.39124e52	1.55417	0.777084	+	0.629397i	$0.216698\pi$
$644$	−1.20129e52	−1.30395
$645$	−3.56153e50	−0.0375648
$646$	−3.69413e51	−0.378626
$647$	1.43133e52	1.42564	0.712821	−	0.701346i	$-0.247417\pi$
$647$	1.43133e52	1.42564	0.712821	+	0.701346i	$0.247417\pi$
$648$	4.44287e49	0.00430057
$649$	−2.14099e52	−2.01413
$650$	−3.61112e51	−0.330175
$651$	1.36072e52	1.20926
$652$	5.06256e51	0.437310
$653$	5.93896e51	0.498674	0.249337	−	0.968417i	$-0.419787\pi$
$653$	5.93896e51	0.498674	0.249337	+	0.968417i	$0.419787\pi$
$654$	2.13064e51	0.173909
$655$	−5.16274e51	−0.409653
$656$	7.67992e51	0.592428
$657$	4.04081e50	0.0303047
$658$	1.05284e52	0.767687
$659$	−1.23688e52	−0.876898	−0.438449	−	0.898756i	$-0.644472\pi$
$659$	−1.23688e52	−0.876898	−0.438449	+	0.898756i	$0.644472\pi$
$660$	2.73765e51	0.188718
$661$	−2.33294e52	−1.56378	−0.781891	−	0.623415i	$-0.785745\pi$
$661$	−2.33294e52	−1.56378	−0.781891	+	0.623415i	$0.785745\pi$
$662$	1.05337e52	0.686605
$663$	−7.22713e50	−0.0458106
$664$	−4.65289e50	−0.0286823
$665$	−8.80959e51	−0.528147
$666$	−1.34351e52	−0.783371
$667$	−1.71457e52	−0.972361
$668$	2.45310e52	1.35316
$669$	−7.40614e51	−0.397382
$670$	9.86826e51	0.515058
$671$	1.41405e52	0.717958
$672$	3.17687e52	1.56916
$673$	1.92388e52	0.924484	0.462242	−	0.886754i	$-0.347045\pi$
$673$	1.92388e52	0.924484	0.462242	+	0.886754i	$0.347045\pi$
$674$	−7.33880e51	−0.343097
$675$	−3.82739e51	−0.174093
$676$	−2.04884e52	−0.906763
$677$	−6.78443e51	−0.292162	−0.146081	−	0.989273i	$-0.546666\pi$
$677$	−6.78443e51	−0.292162	−0.146081	+	0.989273i	$0.546666\pi$
$678$	1.28782e52	0.539644
$679$	7.04349e52	2.87208
$680$	−9.19749e49	−0.00364968
$681$	−8.01164e51	−0.309385
$682$	4.39857e52	1.65310
$683$	−1.97532e52	−0.722528	−0.361264	−	0.932464i	$-0.617655\pi$
$683$	−1.97532e52	−0.722528	−0.361264	+	0.932464i	$0.617655\pi$
$684$	8.03970e51	0.286221
$685$	−3.73968e51	−0.129586
$686$	−1.41179e53	−4.76184
$687$	2.60769e51	0.0856162
$688$	−6.76824e51	−0.216317
$689$	1.42175e52	0.442353
$690$	−5.72438e51	−0.173388
$691$	−2.82676e52	−0.833575	−0.416788	−	0.909004i	$-0.636844\pi$
$691$	−2.82676e52	−0.833575	−0.416788	+	0.909004i	$0.636844\pi$
$692$	2.20682e52	0.633584
$693$	−2.51348e52	−0.702603
$694$	−9.99557e51	−0.272055
$695$	7.59799e51	0.201363
$696$	1.21609e51	0.0313830
$697$	−7.00977e51	−0.176156
$698$	−8.42758e52	−2.06242
$699$	−2.04975e52	−0.488510
$700$	−7.34004e52	−1.70367
$701$	6.97961e52	1.57778	0.788892	−	0.614532i	$-0.210655\pi$
$701$	6.97961e52	1.57778	0.788892	+	0.614532i	$0.210655\pi$
$702$	3.19033e51	0.0702423
$703$	6.89002e52	1.47757
$704$	4.91933e52	1.02757
$705$	2.47344e51	0.0503271
$706$	4.87268e52	0.965785
$707$	5.72591e52	1.10557
$708$	5.52373e52	1.03900
$709$	−2.71632e52	−0.497766	−0.248883	−	0.968534i	$-0.580063\pi$
$709$	−2.71632e52	−0.497766	−0.248883	+	0.968534i	$0.580063\pi$
$710$	3.22622e52	0.575989
$711$	3.30275e51	0.0574497
$712$	2.24783e50	0.00380963
$713$	−4.53441e52	−0.748798
$714$	−2.97964e52	−0.479453
$715$	−5.57124e51	−0.0873555
$716$	6.65060e52	1.01618
$717$	3.45056e52	0.513789
$718$	−1.59036e53	−2.30778
$719$	1.18694e53	1.67860	0.839298	−	0.543672i	$-0.182967\pi$
$719$	1.18694e53	1.67860	0.839298	+	0.543672i	$0.182967\pi$
$720$	7.66926e51	0.105707
$721$	1.08954e53	1.46366
$722$	2.36309e52	0.309416
$723$	−4.43477e52	−0.565995
$724$	−1.00630e52	−0.125188
$725$	−1.04762e53	−1.27043
$726$	−1.26575e52	−0.149631
$727$	−5.48820e52	−0.632475	−0.316237	−	0.948680i	$-0.602420\pi$
$727$	−5.48820e52	−0.632475	−0.316237	+	0.948680i	$0.602420\pi$
$728$	−1.73394e51	−0.0194807
$729$	3.38139e51	0.0370370
$730$	3.69269e51	0.0394340
$731$	6.17765e51	0.0643209
$732$	−3.64823e52	−0.370363
$733$	−1.43675e53	−1.42219	−0.711097	−	0.703094i	$-0.751801\pi$
$733$	−1.43675e53	−1.42219	−0.711097	+	0.703094i	$0.751801\pi$
$734$	1.79736e53	1.73484
$735$	−5.21121e52	−0.490482
$736$	−1.05865e53	−0.971656
$737$	−1.44391e53	−1.29238
$738$	3.09438e52	0.270104
$739$	−1.14941e53	−0.978484	−0.489242	−	0.872148i	$-0.662727\pi$
$739$	−1.14941e53	−0.978484	−0.489242	+	0.872148i	$0.662727\pi$
$740$	−6.05306e52	−0.502560
$741$	−1.63612e52	−0.132488
$742$	5.86167e53	4.62966
$743$	−7.23269e52	−0.557195	−0.278597	−	0.960408i	$-0.589870\pi$
$743$	−7.23269e52	−0.557195	−0.278597	+	0.960408i	$0.589870\pi$
$744$	3.21611e51	0.0241675
$745$	4.07900e52	0.298994
$746$	−2.73464e53	−1.95538
$747$	−3.54124e52	−0.247015
$748$	−4.74859e52	−0.323136
$749$	3.65636e53	2.42737
$750$	−7.36411e52	−0.476965
$751$	−1.89145e53	−1.19524	−0.597621	−	0.801779i	$-0.703887\pi$
$751$	−1.89145e53	−1.19524	−0.597621	+	0.801779i	$0.703887\pi$
$752$	4.70046e52	0.289808
$753$	−6.09031e52	−0.366380
$754$	8.73247e52	0.512586
$755$	1.48928e52	0.0853018
$756$	6.48473e52	0.362442
$757$	1.52507e53	0.831796	0.415898	−	0.909411i	$-0.363467\pi$
$757$	1.52507e53	0.831796	0.415898	+	0.909411i	$0.363467\pi$
$758$	−5.60358e52	−0.298253
$759$	8.37581e52	0.435065
$760$	−2.08218e51	−0.0105552
$761$	−1.93715e53	−0.958399	−0.479199	−	0.877706i	$-0.659073\pi$
$761$	−1.93715e53	−0.958399	−0.479199	+	0.877706i	$0.659073\pi$
$762$	5.67434e52	0.273999
$763$	−8.81334e52	−0.415372
$764$	−4.66986e52	−0.214821
$765$	−7.00005e51	−0.0314315
$766$	−2.04150e50	−0.000894783 0
$767$	−1.12411e53	−0.480942
$768$	1.45538e53	0.607846
$769$	3.76633e53	1.53561	0.767805	−	0.640683i	$-0.221349\pi$
$769$	3.76633e53	1.53561	0.767805	+	0.640683i	$0.221349\pi$
$770$	−2.29694e53	−0.914263
$771$	9.14300e52	0.355290
$772$	−1.12159e53	−0.425513
$773$	2.46250e53	0.912127	0.456064	−	0.889947i	$-0.349259\pi$
$773$	2.46250e53	0.912127	0.456064	+	0.889947i	$0.349259\pi$
$774$	−2.72705e52	−0.0986245
$775$	−2.77058e53	−0.978337
$776$	1.66475e52	0.0573995
$777$	5.55741e53	1.87104
$778$	5.60503e53	1.84270
$779$	−1.58691e53	−0.509460
$780$	1.43737e52	0.0450629
$781$	−4.72055e53	−1.44527
$782$	9.92923e52	0.296887
$783$	9.25545e52	0.270274
$784$	−9.90327e53	−2.82443
$785$	1.73695e53	0.483836
$786$	−3.95309e53	−1.07552
$787$	3.69252e53	0.981275	0.490638	−	0.871364i	$-0.336764\pi$
$787$	3.69252e53	0.981275	0.490638	+	0.871364i	$0.336764\pi$
$788$	−9.75812e52	−0.253298
$789$	−3.97575e53	−1.00808
$790$	3.01822e52	0.0747565
$791$	−5.32706e53	−1.28891
$792$	−5.94069e51	−0.0140418
$793$	7.42433e52	0.171436
$794$	5.16148e53	1.16438
$795$	1.37708e53	0.303506
$796$	7.77854e52	0.167497
$797$	5.45878e53	1.14846	0.574231	−	0.818694i	$-0.305301\pi$
$797$	5.45878e53	1.14846	0.574231	+	0.818694i	$0.305301\pi$
$798$	−6.74547e53	−1.38662
$799$	−4.29031e52	−0.0861733
$800$	−6.46846e53	−1.26951
$801$	1.71078e52	0.0328090
$802$	−2.99297e53	−0.560889
$803$	−5.40309e52	−0.0989475
$804$	3.72526e53	0.666683
$805$	2.36788e53	0.414129
$806$	2.30942e53	0.394734
$807$	9.27399e52	0.154920
$808$	1.35334e52	0.0220951
$809$	−1.10283e54	−1.75979	−0.879893	−	0.475171i	$-0.842386\pi$
$809$	−1.10283e54	−1.75979	−0.879893	+	0.475171i	$0.842386\pi$
$810$	3.09008e52	0.0481945
$811$	7.85452e53	1.19739	0.598693	−	0.800979i	$-0.295687\pi$
$811$	7.85452e53	1.19739	0.598693	+	0.800979i	$0.295687\pi$
$812$	1.77498e54	2.64489
$813$	−4.28168e53	−0.623647
$814$	1.79645e54	2.55778
$815$	−9.97884e52	−0.138888
$816$	−1.33027e53	−0.180998
$817$	1.39853e53	0.186022
$818$	7.40497e53	0.962914
$819$	−1.31967e53	−0.167770
$820$	1.39414e53	0.173281
$821$	1.01998e54	1.23949	0.619744	−	0.784804i	$-0.287236\pi$
$821$	1.01998e54	1.23949	0.619744	+	0.784804i	$0.287236\pi$
$822$	−2.86346e53	−0.340222
$823$	−1.92578e52	−0.0223722	−0.0111861	−	0.999937i	$-0.503561\pi$
$823$	−1.92578e52	−0.0223722	−0.0111861	+	0.999937i	$0.503561\pi$
$824$	2.57517e52	0.0292518
$825$	5.11771e53	0.568431
$826$	−4.63452e54	−5.03354
$827$	−5.47526e53	−0.581504	−0.290752	−	0.956798i	$-0.593905\pi$
$827$	−5.47526e53	−0.581504	−0.290752	+	0.956798i	$0.593905\pi$
$828$	−2.16095e53	−0.224431
$829$	−1.39168e53	−0.141346	−0.0706728	−	0.997500i	$-0.522515\pi$
$829$	−1.39168e53	−0.141346	−0.0706728	+	0.997500i	$0.522515\pi$
$830$	−3.23616e53	−0.321429
$831$	−8.08980e53	−0.785813
$832$	2.58284e53	0.245367
$833$	9.03912e53	0.839835
$834$	5.81776e53	0.528669
$835$	−4.83532e53	−0.429759
$836$	−1.07501e54	−0.934539
$837$	2.44773e53	0.208134
$838$	1.34414e53	0.111797
$839$	−1.43760e54	−1.16961	−0.584804	−	0.811174i	$-0.698829\pi$
$839$	−1.43760e54	−1.16961	−0.584804	+	0.811174i	$0.698829\pi$
$840$	−1.67946e52	−0.0133660
$841$	1.24890e54	0.972302
$842$	−1.20636e54	−0.918762
$843$	7.82443e53	0.582965
$844$	−1.67136e54	−1.21824
$845$	4.03848e53	0.287984
$846$	1.89390e53	0.132131
$847$	5.23577e53	0.357386
$848$	2.61697e54	1.74774
$849$	9.43992e53	0.616845
$850$	6.06687e53	0.387895
$851$	−1.85193e54	−1.15858
$852$	1.21789e54	0.745550
$853$	1.36560e54	0.818024	0.409012	−	0.912529i	$-0.365873\pi$
$853$	1.36560e54	0.818024	0.409012	+	0.912529i	$0.365873\pi$
$854$	3.06094e54	1.79425
$855$	−1.58471e53	−0.0909027
$856$	8.64194e52	0.0485117
$857$	−3.06618e54	−1.68443	−0.842213	−	0.539145i	$-0.818747\pi$
$857$	−3.06618e54	−1.68443	−0.842213	+	0.539145i	$0.818747\pi$
$858$	−4.26588e53	−0.229347
$859$	−2.99741e53	−0.157715	−0.0788575	−	0.996886i	$-0.525127\pi$
$859$	−2.99741e53	−0.157715	−0.0788575	+	0.996886i	$0.525127\pi$
$860$	−1.22865e53	−0.0632711
$861$	−1.27998e54	−0.645128
$862$	2.02957e54	1.00120
$863$	−4.97031e53	−0.239985	−0.119992	−	0.992775i	$-0.538287\pi$
$863$	−4.97031e53	−0.239985	−0.119992	+	0.992775i	$0.538287\pi$
$864$	5.71471e53	0.270079
$865$	−4.34988e53	−0.201224
$866$	−5.08802e54	−2.30392
$867$	−1.18113e54	−0.523531
$868$	4.69418e54	2.03678
$869$	−4.41620e53	−0.187579
$870$	8.45809e53	0.351695
$871$	−7.58108e53	−0.308599
$872$	−2.08307e52	−0.00830134
$873$	1.26702e54	0.494332
$874$	2.24783e54	0.858624
$875$	3.04615e54	1.13921
$876$	1.39399e53	0.0510426
$877$	5.81431e53	0.208452	0.104226	−	0.994554i	$-0.466764\pi$
$877$	5.81431e53	0.208452	0.104226	+	0.994554i	$0.466764\pi$
$878$	6.21564e53	0.218191
$879$	2.09791e53	0.0721096
$880$	−1.02548e54	−0.345142
$881$	−2.08913e54	−0.688510	−0.344255	−	0.938876i	$-0.611869\pi$
$881$	−2.08913e54	−0.688510	−0.344255	+	0.938876i	$0.611869\pi$
$882$	−3.99021e54	−1.28774
$883$	−3.47147e54	−1.09709	−0.548543	−	0.836122i	$-0.684817\pi$
$883$	−3.47147e54	−1.09709	−0.548543	+	0.836122i	$0.684817\pi$
$884$	−2.49320e53	−0.0771595
$885$	−1.08879e54	−0.329983
$886$	7.80205e53	0.231572
$887$	5.12164e54	1.48875	0.744376	−	0.667761i	$-0.232747\pi$
$887$	5.12164e54	1.48875	0.744376	+	0.667761i	$0.232747\pi$
$888$	1.31351e53	0.0373934
$889$	−2.34718e54	−0.654431
$890$	1.56340e53	0.0426928
$891$	−4.52136e53	−0.120929
$892$	−2.55495e54	−0.669318
$893$	−9.71264e53	−0.249221
$894$	3.12328e54	0.784994
$895$	−1.31090e54	−0.322734
$896$	−6.21425e53	−0.149862
$897$	4.39763e53	0.103886
$898$	−4.75888e54	−1.10127
$899$	6.69985e54	1.51884
$900$	−1.32036e54	−0.293228
$901$	−2.38862e54	−0.519683
$902$	−4.13758e54	−0.881913
$903$	1.12804e54	0.235560
$904$	−1.25907e53	−0.0257593
$905$	1.98352e53	0.0397592
$906$	1.14034e54	0.223956
$907$	−6.23293e53	−0.119938	−0.0599691	−	0.998200i	$-0.519100\pi$
$907$	−6.23293e53	−0.119938	−0.0599691	+	0.998200i	$0.519100\pi$
$908$	−2.76383e54	−0.521103
$909$	1.03000e54	0.190286
$910$	−1.20598e54	−0.218311
$911$	2.11014e54	0.374302	0.187151	−	0.982331i	$-0.440075\pi$
$911$	2.11014e54	0.374302	0.187151	+	0.982331i	$0.440075\pi$
$912$	−3.01155e54	−0.523462
$913$	4.73509e54	0.806527
$914$	3.75587e54	0.626911
$915$	7.19105e53	0.117626
$916$	8.99593e53	0.144205
$917$	1.63519e55	2.56883
$918$	−5.35991e53	−0.0825217
$919$	1.59651e52	0.00240899	0.00120450	−	0.999999i	$-0.499617\pi$
$919$	1.59651e52	0.00240899	0.00120450	+	0.999999i	$0.499617\pi$
$920$	5.59657e52	0.00827651
$921$	1.19752e54	0.173573
$922$	1.88783e54	0.268189
$923$	−2.47847e54	−0.345106
$924$	−8.67092e54	−1.18341
$925$	−1.13155e55	−1.51374
$926$	1.26179e55	1.65456
$927$	1.95992e54	0.251920
$928$	1.56421e55	1.97087
$929$	−4.23691e54	−0.523309	−0.261654	−	0.965162i	$-0.584268\pi$
$929$	−4.23691e54	−0.523309	−0.261654	+	0.965162i	$0.584268\pi$
$930$	2.23686e54	0.270834
$931$	2.04633e55	2.42888
$932$	−7.07117e54	−0.822805
$933$	−8.33068e54	−0.950320
$934$	−1.10323e55	−1.23382
$935$	9.35998e53	0.102627
$936$	−3.11910e52	−0.00335294
$937$	−1.28910e55	−1.35863	−0.679317	−	0.733845i	$-0.737724\pi$
$937$	−1.28910e55	−1.35863	−0.679317	+	0.733845i	$0.737724\pi$
$938$	−3.12556e55	−3.22980
$939$	−5.81331e50	−5.88993e−5 0
$940$	8.53279e53	0.0847668
$941$	−4.90525e54	−0.477807	−0.238904	−	0.971043i	$-0.576788\pi$
$941$	−4.90525e54	−0.477807	−0.238904	+	0.971043i	$0.576788\pi$
$942$	1.32998e55	1.27029
$943$	4.26537e54	0.399476
$944$	−2.06910e55	−1.90020
$945$	−1.27821e54	−0.115110
$946$	3.64642e54	0.322018
$947$	−7.97016e54	−0.690228	−0.345114	−	0.938561i	$-0.612160\pi$
$947$	−7.97016e54	−0.690228	−0.345114	+	0.938561i	$0.612160\pi$
$948$	1.13937e54	0.0967635
$949$	−2.83683e53	−0.0236270
$950$	1.37345e55	1.12183
$951$	−2.87192e54	−0.230056
$952$	2.91311e53	0.0228862
$953$	−1.23666e55	−0.952864	−0.476432	−	0.879211i	$-0.658070\pi$
$953$	−1.23666e55	−0.952864	−0.476432	+	0.879211i	$0.658070\pi$
$954$	1.05443e55	0.796840
$955$	9.20478e53	0.0682262
$956$	1.19036e55	0.865383
$957$	−1.23757e55	−0.882470
$958$	2.06469e55	1.44408
$959$	1.18447e55	0.812603
$960$	2.50169e54	0.168351
$961$	2.56972e54	0.169630
$962$	9.43205e54	0.610755
$963$	6.57723e54	0.417789
$964$	−1.52989e55	−0.953314
$965$	2.21077e54	0.135141
$966$	1.81308e55	1.08727
$967$	−1.79944e55	−1.05864	−0.529318	−	0.848424i	$-0.677552\pi$
$967$	−1.79944e55	−1.05864	−0.529318	+	0.848424i	$0.677552\pi$
$968$	1.23749e53	0.00714247
$969$	2.74876e54	0.155649
$970$	1.15786e55	0.643250
$971$	1.81554e55	0.989577	0.494789	−	0.869013i	$-0.335245\pi$
$971$	1.81554e55	0.989577	0.494789	+	0.869013i	$0.335245\pi$
$972$	1.16650e54	0.0623821
$973$	−2.40651e55	−1.26270
$974$	1.82133e55	0.937664
$975$	2.68700e54	0.135732
$976$	1.36657e55	0.677346
$977$	−1.52699e54	−0.0742656	−0.0371328	−	0.999310i	$-0.511822\pi$
$977$	−1.52699e54	−0.0742656	−0.0371328	+	0.999310i	$0.511822\pi$
$978$	−7.64076e54	−0.364643
$979$	−2.28754e54	−0.107124
$980$	−1.79775e55	−0.826127
$981$	−1.58539e54	−0.0714922
$982$	−8.04259e54	−0.355904
$983$	−3.38697e55	−1.47086	−0.735431	−	0.677600i	$-0.763020\pi$
$983$	−3.38697e55	−1.47086	−0.735431	+	0.677600i	$0.763020\pi$
$984$	−3.02529e53	−0.0128931
$985$	1.92343e54	0.0804462
$986$	−1.46710e55	−0.602194
$987$	−7.83409e54	−0.315589
$988$	−5.64424e54	−0.223152
$989$	−3.75903e54	−0.145863
$990$	−4.13184e54	−0.157359
$991$	4.67890e55	1.74897	0.874483	−	0.485057i	$-0.161201\pi$
$991$	4.67890e55	1.74897	0.874483	+	0.485057i	$0.161201\pi$
$992$	4.13678e55	1.51774
$993$	−7.83800e54	−0.282257
$994$	−1.02184e56	−3.61188
$995$	−1.53323e54	−0.0531962
$996$	−1.22165e55	−0.416052
$997$	4.89388e55	1.63603	0.818017	−	0.575193i	$-0.195073\pi$
$997$	4.89388e55	1.63603	0.818017	+	0.575193i	$0.195073\pi$
$998$	4.62426e55	1.51749
$999$	9.99693e54	0.322036

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.38.a.b.1.1	✓	4
3.2	odd	2		9.38.a.c.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.38.a.b.1.1	✓	4	1.1	even	1	trivial
9.38.a.c.1.4		4	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:	\( k \)	\(=\)	\( 38 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q-520663. q^{2} +3.87420e8 q^{3} +1.33651e11 q^{4} -2.63441e12 q^{5} -2.01716e14 q^{6} +8.34393e15 q^{7} +1.97212e15 q^{8} +1.50095e17 q^{9} +O(q^{10})\)	\(q-520663. q^{2} +3.87420e8 q^{3} +1.33651e11 q^{4} -2.63441e12 q^{5} -2.01716e14 q^{6} +8.34393e15 q^{7} +1.97212e15 q^{8} +1.50095e17 q^{9} +1.37164e18 q^{10} -2.00696e19 q^{11} +5.17792e19 q^{12} -1.05373e20 q^{13} -4.34438e21 q^{14} -1.02062e21 q^{15} -1.93957e22 q^{16} +1.77033e22 q^{17} -7.81488e22 q^{18} +4.00776e23 q^{19} -3.52092e23 q^{20} +3.23261e24 q^{21} +1.04495e25 q^{22} -1.07722e25 q^{23} +7.64040e23 q^{24} -6.58195e25 q^{25} +5.48640e25 q^{26} +5.81497e25 q^{27} +1.11518e27 q^{28} +1.59166e27 q^{29} +5.31401e26 q^{30} +4.20936e27 q^{31} +9.82758e27 q^{32} -7.77537e27 q^{33} -9.21743e27 q^{34} -2.19813e28 q^{35} +2.00603e28 q^{36} +1.71917e29 q^{37} -2.08669e29 q^{38} -4.08238e28 q^{39} -5.19537e27 q^{40} -3.95960e29 q^{41} -1.68310e30 q^{42} +3.48956e29 q^{43} -2.68233e30 q^{44} -3.95410e29 q^{45} +5.60870e30 q^{46} -2.42346e30 q^{47} -7.51429e30 q^{48} +5.10591e31 q^{49} +3.42698e31 q^{50} +6.85860e30 q^{51} -1.40833e31 q^{52} -1.34925e32 q^{53} -3.02764e31 q^{54} +5.28715e31 q^{55} +1.64552e31 q^{56} +1.55269e32 q^{57} -8.28718e32 q^{58} +1.06678e33 q^{59} -1.36408e32 q^{60} -7.04574e32 q^{61} -2.19166e33 q^{62} +1.25238e33 q^{63} -2.45114e33 q^{64} +2.77596e32 q^{65} +4.04835e33 q^{66} +7.19450e33 q^{67} +2.36606e33 q^{68} -4.17338e33 q^{69} +1.14449e34 q^{70} +2.35209e34 q^{71} +2.96005e32 q^{72} +2.69218e33 q^{73} -8.95108e34 q^{74} -2.54998e34 q^{75} +5.35642e34 q^{76} -1.67459e35 q^{77} +2.12554e34 q^{78} +2.20044e34 q^{79} +5.10962e34 q^{80} +2.25284e34 q^{81} +2.06162e35 q^{82} -2.35934e35 q^{83} +4.32042e35 q^{84} -4.66376e34 q^{85} -1.81689e35 q^{86} +6.16641e35 q^{87} -3.95797e34 q^{88} +1.13980e35 q^{89} +2.05876e35 q^{90} -8.79227e35 q^{91} -1.43972e36 q^{92} +1.63079e36 q^{93} +1.26181e36 q^{94} -1.05581e36 q^{95} +3.80741e36 q^{96} +8.44145e36 q^{97} -2.65846e37 q^{98} -3.01234e36 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 437562 q^{2} + 1549681956 q^{3} + 346098955492 q^{4} - 4099829756904 q^{5} + 169520484007818 q^{6} + 66\!\cdots\!84 q^{7}+ \cdots + 60\!\cdots\!84 q^{9}+O(q^{10}) \) 4 * q + 437562 * q^2 + 1549681956 * q^3 + 346098955492 * q^4 - 4099829756904 * q^5 + 169520484007818 * q^6 + 6605809948153184 * q^7 + 140484113342159976 * q^8 + 600378541187996484 * q^9	\( 4 q + 437562 q^{2} + 1549681956 q^{3} + 346098955492 q^{4} - 4099829756904 q^{5} + 169520484007818 q^{6} + 66\!\cdots\!84 q^{7}+ \cdots + 31\!\cdots\!96 q^{99}+O(q^{100}) \) 4 * q + 437562 * q^2 + 1549681956 * q^3 + 346098955492 * q^4 - 4099829756904 * q^5 + 169520484007818 * q^6 + 6605809948153184 * q^7 + 140484113342159976 * q^8 + 600378541187996484 * q^9 - 21511023001649316 * q^10 + 20953708852195292976 * q^11 + 134085826579099875588 * q^12 + 51830892788989874168 * q^13 - 1809002141673235613712 * q^14 - 1588358049236498806056 * q^15 + 55184727516616371757840 * q^16 + 81101770962322537501128 * q^17 + 65675708809825529383002 * q^18 - 544604242502813077907632 * q^19 - 3566083114449076353950376 * q^20 + 2559226120354571192186976 * q^21 + 23909208610123411045457976 * q^22 - 6105434608113226892697888 * q^23 + 54426423887751042218148264 * q^24 + 95396877753446381193398716 * q^25 + 428554172265180170762299788 * q^26 + 232598948012160238761560676 * q^27 + 2469833924959492064190244448 * q^28 + 4171186009659314742454127736 * q^29 - 8333811050189225811235524 * q^30 + 8995814656808409627856220864 * q^31 + 36517476440276920084276020384 * q^32 + 8117896129881129128260185264 * q^33 + 31219088393882932122099949524 * q^34 + 42129462142584542112964223040 * q^35 + 51947596501244070980142122532 * q^36 + 55519093704269258277039732824 * q^37 - 735180697664011480109320664568 * q^38 + 20080349829617030866215028152 * q^39 - 2663133991761021855901070923152 * q^40 - 869595339264691998704372818776 * q^41 - 700844494329092219676518145168 * q^42 - 509323958833633606104562745680 * q^43 + 2838804848354890092833187324336 * q^44 - 615362452142290444090131681384 * q^45 - 14832400342987743191058839458896 * q^46 + 4297748917019550924184843821120 * q^47 + 21379694119819270371828162383760 * q^48 + 40223006658016971616433785618020 * q^49 + 102764730674385833857211828709414 * q^50 + 31420487764988998054407847811592 * q^51 + 186771330756284408934646875520568 * q^52 - 125797679190958862093479980165288 * q^53 + 25444115222524214598246503127978 * q^54 - 324441401797069196184728188134624 * q^55 + 49261177652308793436687718380480 * q^56 - 210990841941914426518569886272048 * q^57 - 758216144723951752216603559669556 * q^58 - 1322751535061383229075407129388688 * q^59 - 1381573664014504126645791751653864 * q^60 - 1210012908287761061549313720873160 * q^61 - 3774869312329378363502064838581792 * q^62 + 991496635009340824662391221351264 * q^63 + 8553618714336434539515354532145728 * q^64 + 1596939597234927778869711846229968 * q^65 + 9262917291337022257579330290870264 * q^66 + 16212837695473169417262127089269648 * q^67 + 6364770984875237153325176447214984 * q^68 - 2365370461432749730136966298227232 * q^69 + 8205699211322075854652286498656160 * q^70 + 10892424995451680587530033164573088 * q^71 + 21085911757113789886414645113381096 * q^72 - 19472416597596703966438677461737048 * q^73 - 89115306434605413664690690272305412 * q^74 + 36958705028313418437226934124692124 * q^75 - 95475877084130734100913860795365168 * q^76 - 256189314900709292482321902951864192 * q^77 + 166030666981966339429833686631556332 * q^78 + 42564929886993357285736803130555520 * q^79 - 955034489632094448517301530341944736 * q^80 + 90113598179756697647360591499090564 * q^81 + 335470244295388111217009211756354948 * q^82 - 462964612731837394872969166562146224 * q^83 + 956864266956595720700203893073695072 * q^84 + 1847677353245070936584728247586996912 * q^85 - 363370083621183428400243233525783304 * q^86 + 1616002923572170440926487227549582904 * q^87 + 4210934419609684353108607591773010656 * q^88 - 314574774231571073544391076719446552 * q^89 - 3228689152297913406320288402251236 * q^90 + 2615056540536627234228451043107657024 * q^91 - 16598538663060910484079148451607722016 * q^92 + 3485162913294081237336365108822882496 * q^93 - 573809173038711993912694394480689248 * q^94 - 8958385060094338314910240959017780256 * q^95 + 14147618579538063674464137028143247776 * q^96 + 445047507548838106214452450407795848 * q^97 - 43086999614034505592591376853854433878 * q^98 + 3145039288289754558742704694209474096 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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