LMFDB - Embedded newform 3.38.a.b.1.4

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			1.4
Root			$-101317.$ 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)

$f(q)$	$=$	$q+717293. q^{2} +3.87420e8 q^{3} +3.77070e11 q^{4} -9.63758e12 q^{5} +2.77894e14 q^{6} +1.74370e15 q^{7} +1.71886e17 q^{8} +1.50095e17 q^{9} +O(q^{10})$	\(q+717293. q^{2} +3.87420e8 q^{3} +3.77070e11 q^{4} -9.63758e12 q^{5} +2.77894e14 q^{6} +1.74370e15 q^{7} +1.71886e17 q^{8} +1.50095e17 q^{9} -6.91297e18 q^{10} +2.16917e19 q^{11} +1.46085e20 q^{12} +4.06617e20 q^{13} +1.25074e21 q^{14} -3.73380e21 q^{15} +7.14682e22 q^{16} +4.16602e21 q^{17} +1.07662e23 q^{18} -4.03822e23 q^{19} -3.63404e24 q^{20} +6.75545e23 q^{21} +1.55593e25 q^{22} -3.07818e25 q^{23} +6.65920e25 q^{24} +2.01235e25 q^{25} +2.91664e26 q^{26} +5.81497e25 q^{27} +6.57497e26 q^{28} -3.72833e26 q^{29} -2.67823e27 q^{30} -1.69414e27 q^{31} +2.76399e28 q^{32} +8.40380e27 q^{33} +2.98826e27 q^{34} -1.68050e28 q^{35} +5.65962e28 q^{36} +3.17528e28 q^{37} -2.89659e29 q^{38} +1.57532e29 q^{39} -1.65656e30 q^{40} -1.14320e29 q^{41} +4.84563e29 q^{42} +7.17875e29 q^{43} +8.17928e30 q^{44} -1.44655e30 q^{45} -2.20796e31 q^{46} +3.03496e29 q^{47} +2.76883e31 q^{48} -1.55216e31 q^{49} +1.44344e31 q^{50} +1.61400e30 q^{51} +1.53323e32 q^{52} -6.59860e31 q^{53} +4.17104e31 q^{54} -2.09055e32 q^{55} +2.99717e32 q^{56} -1.56449e32 q^{57} -2.67431e32 q^{58} -8.50758e32 q^{59} -1.40790e33 q^{60} +6.05924e32 q^{61} -1.21519e33 q^{62} +2.61720e32 q^{63} +1.00034e34 q^{64} -3.91881e33 q^{65} +6.02799e33 q^{66} -2.62114e33 q^{67} +1.57088e33 q^{68} -1.19255e34 q^{69} -1.20541e34 q^{70} +1.38853e34 q^{71} +2.57991e34 q^{72} -1.07813e34 q^{73} +2.27761e34 q^{74} +7.79624e33 q^{75} -1.52269e35 q^{76} +3.78238e34 q^{77} +1.12997e35 q^{78} +2.43825e35 q^{79} -6.88781e35 q^{80} +2.25284e34 q^{81} -8.20011e34 q^{82} -3.57499e34 q^{83} +2.54728e35 q^{84} -4.01504e34 q^{85} +5.14927e35 q^{86} -1.44443e35 q^{87} +3.72849e36 q^{88} +1.28259e36 q^{89} -1.03760e36 q^{90} +7.09018e35 q^{91} -1.16069e37 q^{92} -6.56345e35 q^{93} +2.17695e35 q^{94} +3.89187e36 q^{95} +1.07082e37 q^{96} -8.70371e36 q^{97} -1.11336e37 q^{98} +3.25581e36 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	717293.	1.93482	0.967412	−	0.253207i	$-0.0814853\pi$
$2$	717293.	1.93482	0.967412	+	0.253207i	$0.0814853\pi$
$3$	3.87420e8	0.577350
$3$	3.87420e8	0.577350
$4$	3.77070e11	2.74355
$5$	−9.63758e12	−1.12986	−0.564928	−	0.825140i	$-0.691096\pi$
$5$	−9.63758e12	−1.12986	−0.564928	+	0.825140i	$0.691096\pi$
$6$	2.77894e14	1.11707
$7$	1.74370e15	0.404723	0.202361	−	0.979311i	$-0.435138\pi$
$7$	1.74370e15	0.404723	0.202361	+	0.979311i	$0.435138\pi$
$8$	1.71886e17	3.37345
$9$	1.50095e17	0.333333
$10$	−6.91297e18	−2.18607
$11$	2.16917e19	1.17633	0.588164	−	0.808742i	$-0.299851\pi$
$11$	2.16917e19	1.17633	0.588164	+	0.808742i	$0.299851\pi$
$12$	1.46085e20	1.58399
$13$	4.06617e20	1.00285	0.501423	−	0.865202i	$-0.332810\pi$
$13$	4.06617e20	1.00285	0.501423	+	0.865202i	$0.332810\pi$
$14$	1.25074e21	0.783068
$15$	−3.73380e21	−0.652323
$16$	7.14682e22	3.78350
$17$	4.16602e21	0.0718483	0.0359241	−	0.999355i	$-0.488563\pi$
$17$	4.16602e21	0.0718483	0.0359241	+	0.999355i	$0.488563\pi$
$18$	1.07662e23	0.644941
$19$	−4.03822e23	−0.889710	−0.444855	−	0.895603i	$-0.646745\pi$
$19$	−4.03822e23	−0.889710	−0.444855	+	0.895603i	$0.646745\pi$
$20$	−3.63404e24	−3.09981
$21$	6.75545e23	0.233667
$22$	1.55593e25	2.27599
$23$	−3.07818e25	−1.97847	−0.989234	−	0.146344i	$-0.953249\pi$
$23$	−3.07818e25	−1.97847	−0.989234	+	0.146344i	$0.953249\pi$
$24$	6.65920e25	1.94766
$25$	2.01235e25	0.276575
$26$	2.91664e26	1.94033
$27$	5.81497e25	0.192450
$28$	6.57497e26	1.11038
$29$	−3.72833e26	−0.328967	−0.164483	−	0.986380i	$-0.552596\pi$
$29$	−3.72833e26	−0.328967	−0.164483	+	0.986380i	$0.552596\pi$
$30$	−2.67823e27	−1.26213
$31$	−1.69414e27	−0.435269	−0.217635	−	0.976030i	$-0.569834\pi$
$31$	−1.69414e27	−0.435269	−0.217635	+	0.976030i	$0.569834\pi$
$32$	2.76399e28	3.94695
$33$	8.40380e27	0.679153
$34$	2.98826e27	0.139014
$35$	−1.68050e28	−0.457279
$36$	5.65962e28	0.914515
$37$	3.17528e28	0.309066	0.154533	−	0.987988i	$-0.450613\pi$
$37$	3.17528e28	0.309066	0.154533	+	0.987988i	$0.450613\pi$
$38$	−2.89659e29	−1.72143
$39$	1.57532e29	0.578993
$40$	−1.65656e30	−3.81152
$41$	−1.14320e29	−0.166580	−0.0832898	−	0.996525i	$-0.526543\pi$
$41$	−1.14320e29	−0.166580	−0.0832898	+	0.996525i	$0.526543\pi$
$42$	4.84563e29	0.452104
$43$	7.17875e29	0.433394	0.216697	−	0.976239i	$-0.430472\pi$
$43$	7.17875e29	0.433394	0.216697	+	0.976239i	$0.430472\pi$
$44$	8.17928e30	3.22731
$45$	−1.44655e30	−0.376619
$46$	−2.20796e31	−3.82799
$47$	3.03496e29	0.0353462	0.0176731	−	0.999844i	$-0.494374\pi$
$47$	3.03496e29	0.0353462	0.0176731	+	0.999844i	$0.494374\pi$
$48$	2.76883e31	2.18440
$49$	−1.55216e31	−0.836199
$50$	1.44344e31	0.535123
$51$	1.61400e30	0.0414816
$52$	1.53323e32	2.75135
$53$	−6.59860e31	−0.832431	−0.416216	−	0.909266i	$-0.636644\pi$
$53$	−6.59860e31	−0.832431	−0.416216	+	0.909266i	$0.636644\pi$
$54$	4.17104e31	0.372357
$55$	−2.09055e32	−1.32908
$56$	2.99717e32	1.36531
$57$	−1.56449e32	−0.513674
$58$	−2.67431e32	−0.636492
$59$	−8.50758e32	−1.47586	−0.737928	−	0.674879i	$-0.764196\pi$
$59$	−8.50758e32	−1.47586	−0.737928	+	0.674879i	$0.764196\pi$
$60$	−1.40790e33	−1.78968
$61$	6.05924e32	0.567304	0.283652	−	0.958927i	$-0.408454\pi$
$61$	6.05924e32	0.567304	0.283652	+	0.958927i	$0.408454\pi$
$62$	−1.21519e33	−0.842170
$63$	2.61720e32	0.134908
$64$	1.00034e34	3.85315
$65$	−3.91881e33	−1.13307
$66$	6.02799e33	1.31404
$67$	−2.62114e33	−0.432619	−0.216310	−	0.976325i	$-0.569402\pi$
$67$	−2.62114e33	−0.432619	−0.216310	+	0.976325i	$0.569402\pi$
$68$	1.57088e33	0.197119
$69$	−1.19255e34	−1.14227
$70$	−1.20541e34	−0.884754
$71$	1.38853e34	0.783925	0.391963	−	0.919981i	$-0.371796\pi$
$71$	1.38853e34	0.783925	0.391963	+	0.919981i	$0.371796\pi$
$72$	2.57991e34	1.12448
$73$	−1.07813e34	−0.364079	−0.182040	−	0.983291i	$-0.558270\pi$
$73$	−1.07813e34	−0.364079	−0.182040	+	0.983291i	$0.558270\pi$
$74$	2.27761e34	0.597987
$75$	7.79624e33	0.159680
$76$	−1.52269e35	−2.44096
$77$	3.78238e34	0.476087
$78$	1.12997e35	1.12025
$79$	2.43825e35	1.90976	0.954878	−	0.297000i	$-0.0959860\pi$
$79$	2.43825e35	1.90976	0.954878	+	0.297000i	$0.0959860\pi$
$80$	−6.88781e35	−4.27481
$81$	2.25284e34	0.111111
$82$	−8.20011e34	−0.322302
$83$	−3.57499e34	−0.112287	−0.0561436	−	0.998423i	$-0.517880\pi$
$83$	−3.57499e34	−0.112287	−0.0561436	+	0.998423i	$0.517880\pi$
$84$	2.54728e35	0.641076
$85$	−4.01504e34	−0.0811782
$86$	5.14927e35	0.838541
$87$	−1.44443e35	−0.189929
$88$	3.72849e36	3.96829
$89$	1.28259e36	1.10757	0.553785	−	0.832659i	$-0.313183\pi$
$89$	1.28259e36	1.10757	0.553785	+	0.832659i	$0.313183\pi$
$90$	−1.03760e36	−0.728691
$91$	7.09018e35	0.405875
$92$	−1.16069e37	−5.42802
$93$	−6.56345e35	−0.251303
$94$	2.17695e35	0.0683886
$95$	3.89187e36	1.00524
$96$	1.07082e37	2.27877
$97$	−8.70371e36	−1.52907	−0.764535	−	0.644582i	$-0.777031\pi$
$97$	−8.70371e36	−1.52907	−0.764535	+	0.644582i	$0.777031\pi$
$98$	−1.11336e37	−1.61790
$99$	3.25581e36	0.392109
$100$	7.58795e36	0.758795
$101$	−1.10433e37	−0.918653	−0.459327	−	0.888267i	$-0.651909\pi$
$101$	−1.10433e37	−0.918653	−0.459327	+	0.888267i	$0.651909\pi$
$102$	1.15771e36	0.0802596
$103$	−2.97966e36	−0.172456	−0.0862280	−	0.996275i	$-0.527481\pi$
$103$	−2.97966e36	−0.172456	−0.0862280	+	0.996275i	$0.527481\pi$
$104$	6.98917e37	3.38305
$105$	−6.51062e36	−0.264010
$106$	−4.73313e37	−1.61061
$107$	7.82998e36	0.223955	0.111978	−	0.993711i	$-0.464282\pi$
$107$	7.82998e36	0.223955	0.111978	+	0.993711i	$0.464282\pi$
$108$	2.19265e37	0.527996
$109$	1.17745e37	0.239085	0.119543	−	0.992829i	$-0.461857\pi$
$109$	1.17745e37	0.239085	0.119543	+	0.992829i	$0.461857\pi$
$110$	−1.49954e38	−2.57154
$111$	1.23017e37	0.178439
$112$	1.24619e38	1.53127
$113$	1.31720e38	1.37310	0.686548	−	0.727085i	$-0.259125\pi$
$113$	1.31720e38	1.37310	0.686548	+	0.727085i	$0.259125\pi$
$114$	−1.12220e38	−0.993869
$115$	2.96662e38	2.23538
$116$	−1.40584e38	−0.902535
$117$	6.10311e37	0.334282
$118$	−6.10243e38	−2.85552
$119$	7.26429e36	0.0290786
$120$	−6.41786e38	−2.20058
$121$	1.30490e38	0.383748
$122$	4.34625e38	1.09763
$123$	−4.42900e37	−0.0961747
$124$	−6.38810e38	−1.19418
$125$	5.07285e38	0.817367
$126$	1.87730e38	0.261023
$127$	1.23543e39	1.48405	0.742026	−	0.670371i	$-0.233865\pi$
$127$	1.23543e39	1.48405	0.742026	+	0.670371i	$0.233865\pi$
$128$	3.37654e39	3.50823
$129$	2.78120e38	0.250220
$130$	−2.81093e39	−2.19229
$131$	−2.21862e39	−1.50163	−0.750816	−	0.660511i	$-0.770340\pi$
$131$	−2.21862e39	−1.50163	−0.750816	+	0.660511i	$0.770340\pi$
$132$	3.16882e39	1.86329
$133$	−7.04144e38	−0.360086
$134$	−1.88012e39	−0.837042
$135$	−5.60423e38	−0.217441
$136$	7.16079e38	0.242377
$137$	1.86892e39	0.552408	0.276204	−	0.961099i	$-0.410923\pi$
$137$	1.86892e39	0.552408	0.276204	+	0.961099i	$0.410923\pi$
$138$	−8.55407e39	−2.21009
$139$	−3.65432e39	−0.826101	−0.413050	−	0.910708i	$-0.635537\pi$
$139$	−3.65432e39	−0.826101	−0.413050	+	0.910708i	$0.635537\pi$
$140$	−6.33668e39	−1.25456
$141$	1.17580e38	0.0204071
$142$	9.95980e39	1.51676
$143$	8.82022e39	1.17968
$144$	1.07270e40	1.26117
$145$	3.59321e39	0.371685
$146$	−7.73331e39	−0.704430
$147$	−6.01340e39	−0.482780
$148$	1.19730e40	0.847935
$149$	−2.36586e40	−1.47925	−0.739627	−	0.673017i	$-0.764998\pi$
$149$	−2.36586e40	−1.47925	−0.739627	+	0.673017i	$0.764998\pi$
$150$	5.59219e39	0.308954
$151$	3.03874e40	1.48464	0.742319	−	0.670047i	$-0.233726\pi$
$151$	3.03874e40	1.48464	0.742319	+	0.670047i	$0.233726\pi$
$152$	−6.94112e40	−3.00140
$153$	6.25297e38	0.0239494
$154$	2.71307e40	0.921145
$155$	1.63274e40	0.491792
$156$	5.94006e40	1.58849
$157$	−1.39003e40	−0.330280	−0.165140	−	0.986270i	$-0.552808\pi$
$157$	−1.39003e40	−0.330280	−0.165140	+	0.986270i	$0.552808\pi$
$158$	1.74894e41	3.69504
$159$	−2.55643e40	−0.480604
$160$	−2.66382e41	−4.45948
$161$	−5.36742e40	−0.800731
$162$	1.61595e40	0.214980
$163$	8.33630e40	0.989698	0.494849	−	0.868979i	$-0.335223\pi$
$163$	8.33630e40	0.989698	0.494849	+	0.868979i	$0.335223\pi$
$164$	−4.31067e40	−0.457018
$165$	−8.09924e40	−0.767346
$166$	−2.56432e40	−0.217256
$167$	−5.26775e40	−0.399365	−0.199683	−	0.979861i	$-0.563991\pi$
$167$	−5.26775e40	−0.399365	−0.199683	+	0.979861i	$0.563991\pi$
$168$	1.16116e41	0.788265
$169$	9.36904e38	0.00569890
$170$	−2.87996e40	−0.157066
$171$	−6.06115e40	−0.296570
$172$	2.70689e41	1.18904
$173$	−3.80189e41	−1.50019	−0.750096	−	0.661329i	$-0.769993\pi$
$173$	−3.80189e41	−1.50019	−0.750096	+	0.661329i	$0.769993\pi$
$174$	−1.03608e41	−0.367479
$175$	3.50892e40	0.111936
$176$	1.55027e42	4.45063
$177$	−3.29601e41	−0.852086
$178$	9.19990e41	2.14295
$179$	−5.74115e41	−1.20564	−0.602820	−	0.797877i	$-0.705956\pi$
$179$	−5.74115e41	−1.20564	−0.602820	+	0.797877i	$0.705956\pi$
$180$	−5.45451e41	−1.03327
$181$	9.26735e41	1.58453	0.792267	−	0.610174i	$-0.208900\pi$
$181$	9.26735e41	1.58453	0.792267	+	0.610174i	$0.208900\pi$
$182$	5.08574e41	0.785296
$183$	2.34747e41	0.327533
$184$	−5.29095e42	−6.67427
$185$	−3.06021e41	−0.349200
$186$	−4.70791e41	−0.486227
$187$	9.03680e40	0.0845171
$188$	1.14439e41	0.0969738
$189$	1.01396e41	0.0778890
$190$	2.79161e42	1.94497
$191$	1.34788e42	0.852183	0.426092	−	0.904680i	$-0.359890\pi$
$191$	1.34788e42	0.852183	0.426092	+	0.904680i	$0.359890\pi$
$192$	3.87551e42	2.22462
$193$	2.58423e42	1.34748	0.673738	−	0.738970i	$-0.264688\pi$
$193$	2.58423e42	1.34748	0.673738	+	0.738970i	$0.264688\pi$
$194$	−6.24311e42	−2.95848
$195$	−1.51823e42	−0.654179
$196$	−5.85274e42	−2.29415
$197$	3.24438e42	1.15746	0.578730	−	0.815519i	$-0.303549\pi$
$197$	3.24438e42	1.15746	0.578730	+	0.815519i	$0.303549\pi$
$198$	2.33537e42	0.758663
$199$	4.99334e42	1.47778	0.738890	−	0.673826i	$-0.235350\pi$
$199$	4.99334e42	1.47778	0.738890	+	0.673826i	$0.235350\pi$
$200$	3.45893e42	0.933012
$201$	−1.01548e42	−0.249773
$202$	−7.92125e42	−1.77743
$203$	−6.50109e41	−0.133140
$204$	6.08592e41	0.113807
$205$	1.10177e42	0.188211
$206$	−2.13729e42	−0.333672
$207$	−4.62018e42	−0.659489
$208$	2.90602e43	3.79426
$209$	−8.75958e42	−1.04659
$210$	−4.67002e42	−0.510813
$211$	4.78475e42	0.479329	0.239665	−	0.970856i	$-0.422963\pi$
$211$	4.78475e42	0.479329	0.239665	+	0.970856i	$0.422963\pi$
$212$	−2.48814e43	−2.28381
$213$	5.37944e42	0.452599
$214$	5.61639e42	0.433314
$215$	−6.91858e42	−0.489672
$216$	9.99511e42	0.649222
$217$	−2.95407e42	−0.176164
$218$	8.44577e42	0.462588
$219$	−4.17688e42	−0.210201
$220$	−7.88285e43	−3.64640
$221$	1.69398e42	0.0720527
$222$	8.82392e42	0.345248
$223$	−2.35490e43	−0.847875	−0.423938	−	0.905691i	$-0.639352\pi$
$223$	−2.35490e43	−0.847875	−0.423938	+	0.905691i	$0.639352\pi$
$224$	4.81956e43	1.59742
$225$	3.02042e42	0.0921915
$226$	9.44818e43	2.65670
$227$	3.01075e43	0.780183	0.390092	−	0.920776i	$-0.372443\pi$
$227$	3.01075e43	0.780183	0.390092	+	0.920776i	$0.372443\pi$
$228$	−5.89922e43	−1.40929
$229$	−5.09965e43	−1.12353	−0.561764	−	0.827297i	$-0.689877\pi$
$229$	−5.09965e43	−1.12353	−0.561764	+	0.827297i	$0.689877\pi$
$230$	2.12794e44	4.32507
$231$	1.46537e43	0.274869
$232$	−6.40847e43	−1.10975
$233$	1.15459e43	0.184647	0.0923237	−	0.995729i	$-0.470571\pi$
$233$	1.15459e43	0.184647	0.0923237	+	0.995729i	$0.470571\pi$
$234$	4.37772e43	0.646777
$235$	−2.92497e42	−0.0399361
$236$	−3.20795e44	−4.04908
$237$	9.44629e43	1.10260
$238$	5.21062e42	0.0562621
$239$	−9.64335e43	−0.963533	−0.481767	−	0.876300i	$-0.660005\pi$
$239$	−9.64335e43	−0.963533	−0.481767	+	0.876300i	$0.660005\pi$
$240$	−2.66848e44	−2.46806
$241$	2.88872e43	0.247394	0.123697	−	0.992320i	$-0.460525\pi$
$241$	2.88872e43	0.247394	0.123697	+	0.992320i	$0.460525\pi$
$242$	9.35993e43	0.742486
$243$	8.72796e42	0.0641500
$244$	2.28476e44	1.55643
$245$	1.49591e44	0.944785
$246$	−3.17689e43	−0.186081
$247$	−1.64201e44	−0.892241
$248$	−2.91198e44	−1.46836
$249$	−1.38503e43	−0.0648291
$250$	3.63872e44	1.58146
$251$	3.22802e43	0.130308	0.0651542	−	0.997875i	$-0.479246\pi$
$251$	3.22802e43	0.130308	0.0651542	+	0.997875i	$0.479246\pi$
$252$	9.86867e43	0.370125
$253$	−6.67709e44	−2.32733
$254$	8.86165e44	2.87138
$255$	−1.55551e43	−0.0468683
$256$	1.04712e45	2.93465
$257$	−2.79016e44	−0.727555	−0.363777	−	0.931486i	$-0.618513\pi$
$257$	−2.79016e44	−0.727555	−0.363777	+	0.931486i	$0.618513\pi$
$258$	1.99493e44	0.484132
$259$	5.53674e43	0.125086
$260$	−1.47767e45	−3.10863
$261$	−5.59603e43	−0.109656
$262$	−1.59140e45	−2.90539
$263$	1.50410e43	0.0255916	0.0127958	−	0.999918i	$-0.495927\pi$
$263$	1.50410e43	0.0255916	0.0127958	+	0.999918i	$0.495927\pi$
$264$	1.44449e45	2.29109
$265$	6.35946e44	0.940528
$266$	−5.05078e44	−0.696703
$267$	4.96900e44	0.639456
$268$	−9.88352e44	−1.18691
$269$	1.21815e45	1.36548	0.682738	−	0.730663i	$-0.260789\pi$
$269$	1.21815e45	1.36548	0.682738	+	0.730663i	$0.260789\pi$
$270$	−4.01987e44	−0.420710
$271$	7.74428e44	0.756918	0.378459	−	0.925618i	$-0.376454\pi$
$271$	7.74428e44	0.756918	0.378459	+	0.925618i	$0.376454\pi$
$272$	2.97738e44	0.271838
$273$	2.74688e44	0.234332
$274$	1.34056e45	1.06881
$275$	4.36512e44	0.325343
$276$	−4.49675e45	−3.13387
$277$	−6.27119e44	−0.408766	−0.204383	−	0.978891i	$-0.565519\pi$
$277$	−6.27119e44	−0.408766	−0.204383	+	0.978891i	$0.565519\pi$
$278$	−2.62122e45	−1.59836
$279$	−2.54281e44	−0.145090
$280$	−2.88855e45	−1.54261
$281$	−1.10245e45	−0.551180	−0.275590	−	0.961275i	$-0.588873\pi$
$281$	−1.10245e45	−0.551180	−0.275590	+	0.961275i	$0.588873\pi$
$282$	8.43396e43	0.0394842
$283$	3.71020e45	1.62685	0.813427	−	0.581667i	$-0.197599\pi$
$283$	3.71020e45	1.62685	0.813427	+	0.581667i	$0.197599\pi$
$284$	5.23572e45	2.15073
$285$	1.50779e45	0.580378
$286$	6.32668e45	2.28246
$287$	−1.99340e44	−0.0674186
$288$	4.14860e45	1.31565
$289$	−3.34474e45	−0.994838
$290$	2.57739e45	0.719145
$291$	−3.37200e45	−0.882809
$292$	−4.06529e45	−0.998869
$293$	−1.22173e45	−0.281788	−0.140894	−	0.990025i	$-0.544998\pi$
$293$	−1.22173e45	−0.281788	−0.140894	+	0.990025i	$0.544998\pi$
$294$	−4.31337e45	−0.934094
$295$	8.19925e45	1.66750
$296$	5.45786e45	1.04262
$297$	1.26137e45	0.226384
$298$	−1.69701e46	−2.86210
$299$	−1.25164e46	−1.98410
$300$	2.93973e45	0.438091
$301$	1.25176e45	0.175404
$302$	2.17967e46	2.87251
$303$	−4.27838e45	−0.530385
$304$	−2.88604e46	−3.36621
$305$	−5.83964e45	−0.640972
$306$	4.48521e44	0.0463379
$307$	−2.41884e45	−0.235260	−0.117630	−	0.993057i	$-0.537530\pi$
$307$	−2.41884e45	−0.235260	−0.117630	+	0.993057i	$0.537530\pi$
$308$	1.42622e46	1.30617
$309$	−1.15438e45	−0.0995675
$310$	1.17115e46	0.951531
$311$	−2.34597e46	−1.79579	−0.897893	−	0.440214i	$-0.854902\pi$
$311$	−2.34597e46	−1.79579	−0.897893	+	0.440214i	$0.854902\pi$
$312$	2.70775e46	1.95321
$313$	1.37353e46	0.933832	0.466916	−	0.884302i	$-0.345365\pi$
$313$	1.37353e46	0.933832	0.466916	+	0.884302i	$0.345365\pi$
$314$	−9.97062e45	−0.639033
$315$	−2.52235e45	−0.152426
$316$	9.19392e46	5.23950
$317$	1.81588e46	0.976091	0.488046	−	0.872818i	$-0.337710\pi$
$317$	1.81588e46	0.976091	0.488046	+	0.872818i	$0.337710\pi$
$318$	−1.83371e46	−0.929885
$319$	−8.08738e45	−0.386973
$320$	−9.64082e46	−4.35351
$321$	3.03350e45	0.129301
$322$	−3.85001e46	−1.54927
$323$	−1.68233e45	−0.0639241
$324$	8.49478e45	0.304838
$325$	8.18255e45	0.277362
$326$	5.97957e46	1.91489
$327$	4.56168e45	0.138036
$328$	−1.96500e46	−0.561948
$329$	5.29205e44	0.0143054
$330$	−5.80952e46	−1.48468
$331$	6.35602e46	1.53592	0.767958	−	0.640500i	$-0.221273\pi$
$331$	6.35602e46	1.53592	0.767958	+	0.640500i	$0.221273\pi$
$332$	−1.34802e46	−0.308065
$333$	4.76593e45	0.103022
$334$	−3.77852e46	−0.772701
$335$	2.52614e46	0.488797
$336$	4.82800e46	0.884078
$337$	−8.32564e46	−1.44299	−0.721497	−	0.692417i	$-0.756546\pi$
$337$	−8.32564e46	−1.44299	−0.721497	+	0.692417i	$0.756546\pi$
$338$	6.72034e44	0.0110264
$339$	5.10310e46	0.792757
$340$	−1.51395e46	−0.222716
$341$	−3.67488e46	−0.512020
$342$	−4.34762e46	−0.573811
$343$	−5.94318e46	−0.743152
$344$	1.23392e47	1.46203
$345$	1.14933e47	1.29060
$346$	−2.72707e47	−2.90261
$347$	−2.08182e46	−0.210062	−0.105031	−	0.994469i	$-0.533494\pi$
$347$	−2.08182e46	−0.210062	−0.105031	+	0.994469i	$0.533494\pi$
$348$	−5.44652e46	−0.521079
$349$	1.34295e47	1.21840	0.609201	−	0.793016i	$-0.291490\pi$
$349$	1.34295e47	1.21840	0.609201	+	0.793016i	$0.291490\pi$
$350$	2.51693e46	0.216577
$351$	2.36447e46	0.192998
$352$	5.99555e47	4.64291
$353$	−2.08412e47	−1.53141	−0.765705	−	0.643192i	$-0.777610\pi$
$353$	−2.08412e47	−1.53141	−0.765705	+	0.643192i	$0.777610\pi$
$354$	−2.36421e47	−1.64864
$355$	−1.33820e47	−0.885723
$356$	4.83625e47	3.03867
$357$	2.81433e45	0.0167886
$358$	−4.11808e47	−2.33270
$359$	6.98095e46	0.375550	0.187775	−	0.982212i	$-0.439872\pi$
$359$	6.98095e46	0.375550	0.187775	+	0.982212i	$0.439872\pi$
$360$	−2.48641e47	−1.27051
$361$	−4.29354e46	−0.208416
$362$	6.64740e47	3.06580
$363$	5.05543e46	0.221557
$364$	2.67350e47	1.11354
$365$	1.03905e47	0.411357
$366$	1.68383e47	0.633719
$367$	4.35331e46	0.155775	0.0778875	−	0.996962i	$-0.475183\pi$
$367$	4.35331e46	0.155775	0.0778875	+	0.996962i	$0.475183\pi$
$368$	−2.19992e48	−7.48553
$369$	−1.71588e46	−0.0555265
$370$	−2.19506e47	−0.675640
$371$	−1.15060e47	−0.336904
$372$	−2.47488e47	−0.689461
$373$	4.60312e47	1.22022	0.610111	−	0.792316i	$-0.291125\pi$
$373$	4.60312e47	1.22022	0.610111	+	0.792316i	$0.291125\pi$
$374$	6.48203e46	0.163526
$375$	1.96533e47	0.471907
$376$	5.21666e46	0.119239
$377$	−1.51601e47	−0.329903
$378$	7.27304e46	0.150701
$379$	−1.24559e47	−0.245783	−0.122891	−	0.992420i	$-0.539217\pi$
$379$	−1.24559e47	−0.245783	−0.122891	+	0.992420i	$0.539217\pi$
$380$	1.46751e48	2.75793
$381$	4.78631e47	0.856818
$382$	9.66823e47	1.64882
$383$	−5.34361e47	−0.868275	−0.434137	−	0.900847i	$-0.642947\pi$
$383$	−5.34361e47	−0.868275	−0.434137	+	0.900847i	$0.642947\pi$
$384$	1.30814e48	2.02548
$385$	−3.64530e47	−0.537910
$386$	1.85365e48	2.60713
$387$	1.07749e47	0.144465
$388$	−3.28191e48	−4.19507
$389$	5.89339e47	0.718286	0.359143	−	0.933283i	$-0.383069\pi$
$389$	5.89339e47	0.718286	0.359143	+	0.933283i	$0.383069\pi$
$390$	−1.08901e48	−1.26572
$391$	−1.28238e47	−0.142149
$392$	−2.66795e48	−2.82088
$393$	−8.59538e47	−0.866968
$394$	2.32717e48	2.23948
$395$	−2.34989e48	−2.15775
$396$	1.22767e48	1.07577
$397$	6.73632e47	0.563376	0.281688	−	0.959506i	$-0.409106\pi$
$397$	6.73632e47	0.563376	0.281688	+	0.959506i	$0.409106\pi$
$398$	3.58169e48	2.85924
$399$	−2.72800e47	−0.207896
$400$	1.43819e48	1.04642
$401$	−1.51806e48	−1.05468	−0.527338	−	0.849656i	$-0.676810\pi$
$401$	−1.51806e48	−1.05468	−0.527338	+	0.849656i	$0.676810\pi$
$402$	−7.28398e47	−0.483267
$403$	−6.88867e47	−0.436508
$404$	−4.16408e48	−2.52037
$405$	−2.17119e47	−0.125540
$406$	−4.66319e47	−0.257603
$407$	6.88772e47	0.363563
$408$	2.77424e47	0.139936
$409$	3.44449e48	1.66052	0.830259	−	0.557377i	$-0.188192\pi$
$409$	3.44449e48	1.66052	0.830259	+	0.557377i	$0.188192\pi$
$410$	7.90292e47	0.364155
$411$	7.24058e47	0.318933
$412$	−1.12354e48	−0.473141
$413$	−1.48347e48	−0.597313
$414$	−3.31402e48	−1.27600
$415$	3.44543e47	0.126868
$416$	1.12389e49	3.95818
$417$	−1.41576e48	−0.476950
$418$	−6.28318e48	−2.02497
$419$	−7.49755e47	−0.231185	−0.115593	−	0.993297i	$-0.536877\pi$
$419$	−7.49755e47	−0.231185	−0.115593	+	0.993297i	$0.536877\pi$
$420$	−2.45496e48	−0.724323
$421$	5.66375e48	1.59913	0.799567	−	0.600576i	$-0.205062\pi$
$421$	5.66375e48	1.59913	0.799567	+	0.600576i	$0.205062\pi$
$422$	3.43207e48	0.927418
$423$	4.55531e46	0.0117821
$424$	−1.13421e49	−2.80817
$425$	8.38347e46	0.0198714
$426$	3.85863e48	0.875700
$427$	1.05655e48	0.229601
$428$	2.95245e48	0.614431
$429$	3.41713e48	0.681086
$430$	−4.96265e48	−0.947430
$431$	−1.73243e47	−0.0316829	−0.0158415	−	0.999875i	$-0.505043\pi$
$431$	−1.73243e47	−0.0316829	−0.0158415	+	0.999875i	$0.505043\pi$
$432$	4.15586e48	0.728134
$433$	1.13654e49	1.90792	0.953960	−	0.299934i	$-0.0969646\pi$
$433$	1.13654e49	1.90792	0.953960	+	0.299934i	$0.0969646\pi$
$434$	−2.11893e48	−0.340845
$435$	1.39208e48	0.214592
$436$	4.43981e48	0.655941
$437$	1.24304e49	1.76026
$438$	−2.99604e48	−0.406703
$439$	−1.20746e49	−1.57137	−0.785684	−	0.618629i	$-0.787689\pi$
$439$	−1.20746e49	−1.57137	−0.785684	+	0.618629i	$0.787689\pi$
$440$	−3.59336e49	−4.48360
$441$	−2.32971e48	−0.278733
$442$	1.21508e48	0.139409
$443$	−4.29789e48	−0.472919	−0.236459	−	0.971641i	$-0.575987\pi$
$443$	−4.29789e48	−0.472919	−0.236459	+	0.971641i	$0.575987\pi$
$444$	4.63860e48	0.489556
$445$	−1.23610e49	−1.25140
$446$	−1.68915e49	−1.64049
$447$	−9.16582e48	−0.854047
$448$	1.74428e49	1.55946
$449$	9.38321e48	0.804997	0.402498	−	0.915421i	$-0.368142\pi$
$449$	9.38321e48	0.804997	0.402498	+	0.915421i	$0.368142\pi$
$450$	2.16653e48	0.178374
$451$	−2.47980e48	−0.195952
$452$	4.96677e49	3.76715
$453$	1.17727e49	0.857156
$454$	2.15959e49	1.50952
$455$	−6.83323e48	−0.458580
$456$	−2.68913e49	−1.73286
$457$	−2.71199e49	−1.67818	−0.839091	−	0.543992i	$-0.816912\pi$
$457$	−2.71199e49	−1.67818	−0.839091	+	0.543992i	$0.816912\pi$
$458$	−3.65794e49	−2.17383
$459$	2.42253e47	0.0138272
$460$	1.11862e50	6.13288
$461$	3.50105e48	0.184387	0.0921937	−	0.995741i	$-0.470612\pi$
$461$	3.50105e48	0.184387	0.0921937	+	0.995741i	$0.470612\pi$
$462$	1.05110e49	0.531823
$463$	−2.14736e49	−1.04389	−0.521946	−	0.852979i	$-0.674794\pi$
$463$	−2.14736e49	−1.04389	−0.521946	+	0.852979i	$0.674794\pi$
$464$	−2.66457e49	−1.24464
$465$	6.32558e48	0.283936
$466$	8.28179e48	0.357260
$467$	−1.07777e49	−0.446853	−0.223427	−	0.974721i	$-0.571724\pi$
$467$	−1.07777e49	−0.446853	−0.223427	+	0.974721i	$0.571724\pi$
$468$	2.30130e49	0.917117
$469$	−4.57047e48	−0.175091
$470$	−2.09806e48	−0.0772693
$471$	−5.38528e48	−0.190687
$472$	−1.46233e50	−4.97873
$473$	1.55719e49	0.509813
$474$	6.77576e49	2.13333
$475$	−8.12629e48	−0.246071
$476$	2.73914e48	0.0797786
$477$	−9.90415e48	−0.277477
$478$	−6.91711e49	−1.86427
$479$	4.42983e49	1.14863	0.574314	−	0.818635i	$-0.305269\pi$
$479$	4.42983e49	1.14863	0.574314	+	0.818635i	$0.305269\pi$
$480$	−1.03202e50	−2.57468
$481$	1.29113e49	0.309945
$482$	2.07205e49	0.478664
$483$	−2.07945e49	−0.462302
$484$	4.92037e49	1.05283
$485$	8.38827e49	1.72763
$486$	6.26051e48	0.124119
$487$	8.17887e48	0.156102	0.0780508	−	0.996949i	$-0.475130\pi$
$487$	8.17887e48	0.156102	0.0780508	+	0.996949i	$0.475130\pi$
$488$	1.04150e50	1.91378
$489$	3.22965e49	0.571402
$490$	1.07301e50	1.82799
$491$	−8.00334e49	−1.31300	−0.656498	−	0.754328i	$-0.727963\pi$
$491$	−8.00334e49	−1.31300	−0.656498	+	0.754328i	$0.727963\pi$
$492$	−1.67004e49	−0.263860
$493$	−1.55323e48	−0.0236357
$494$	−1.17780e50	−1.72633
$495$	−3.13781e49	−0.443027
$496$	−1.21077e50	−1.64684
$497$	2.42117e49	0.317273
$498$	−9.93469e48	−0.125433
$499$	−2.89490e49	−0.352187	−0.176094	−	0.984373i	$-0.556346\pi$
$499$	−2.89490e49	−0.352187	−0.176094	+	0.984373i	$0.556346\pi$
$500$	1.91282e50	2.24248
$501$	−2.04083e49	−0.230574
$502$	2.31544e49	0.252124
$503$	−6.85440e49	−0.719385	−0.359693	−	0.933071i	$-0.617118\pi$
$503$	−6.85440e49	−0.719385	−0.359693	+	0.933071i	$0.617118\pi$
$504$	4.49859e49	0.455105
$505$	1.06430e50	1.03795
$506$	−4.78943e50	−4.50297
$507$	3.62976e47	0.00329026
$508$	4.65844e50	4.07157
$509$	5.38706e49	0.454018	0.227009	−	0.973893i	$-0.427105\pi$
$509$	5.38706e49	0.454018	0.227009	+	0.973893i	$0.427105\pi$
$510$	−1.11575e49	−0.0906818
$511$	−1.87993e49	−0.147351
$512$	2.87022e50	2.16981
$513$	−2.34821e49	−0.171225
$514$	−2.00136e50	−1.40769
$515$	2.87167e49	0.194850
$516$	1.04871e50	0.686490
$517$	6.58333e48	0.0415787
$518$	3.97146e49	0.242019
$519$	−1.47293e50	−0.866136
$520$	−6.73587e50	−3.82236
$521$	3.05490e50	1.67301	0.836506	−	0.547958i	$-0.184595\pi$
$521$	3.05490e50	1.67301	0.836506	+	0.547958i	$0.184595\pi$
$522$	−4.01399e49	−0.212164
$523$	−2.66823e50	−1.36126	−0.680631	−	0.732626i	$-0.738294\pi$
$523$	−2.66823e50	−1.36126	−0.680631	+	0.732626i	$0.738294\pi$
$524$	−8.36574e50	−4.11980
$525$	1.35943e49	0.0646263
$526$	1.07888e49	0.0495152
$527$	−7.05782e48	−0.0312733
$528$	6.00605e50	2.56957
$529$	7.05455e50	2.91433
$530$	4.56159e50	1.81976
$531$	−1.27694e50	−0.491952
$532$	−2.65512e50	−0.987912
$533$	−4.64846e49	−0.167054
$534$	3.56423e50	1.23724
$535$	−7.54621e49	−0.253037
$536$	−4.50536e50	−1.45942
$537$	−2.22424e50	−0.696076
$538$	8.73771e50	2.64196
$539$	−3.36690e50	−0.983645
$540$	−2.11319e50	−0.596559
$541$	−3.15729e50	−0.861322	−0.430661	−	0.902514i	$-0.641720\pi$
$541$	−3.15729e50	−0.861322	−0.430661	+	0.902514i	$0.641720\pi$
$542$	5.55491e50	1.46450
$543$	3.59036e50	0.914832
$544$	1.15148e50	0.283581
$545$	−1.13478e50	−0.270132
$546$	1.97032e50	0.453391
$547$	1.90478e50	0.423720	0.211860	−	0.977300i	$-0.432048\pi$
$547$	1.90478e50	0.423720	0.211860	+	0.977300i	$0.432048\pi$
$548$	7.04713e50	1.51556
$549$	9.09459e49	0.189101
$550$	3.13107e50	0.629481
$551$	1.50558e50	0.292685
$552$	−2.04982e51	−3.85339
$553$	4.25158e50	0.772922
$554$	−4.49828e50	−0.790890
$555$	−1.18559e50	−0.201610
$556$	−1.37794e51	−2.26645
$557$	1.91249e50	0.304283	0.152142	−	0.988359i	$-0.451383\pi$
$557$	1.91249e50	0.304283	0.152142	+	0.988359i	$0.451383\pi$
$558$	−1.82394e50	−0.280723
$559$	2.91901e50	0.434627
$560$	−1.20103e51	−1.73011
$561$	3.50104e49	0.0487960
$562$	−7.90782e50	−1.06644
$563$	−4.86098e50	−0.634335	−0.317167	−	0.948370i	$-0.602732\pi$
$563$	−4.86098e50	−0.634335	−0.317167	+	0.948370i	$0.602732\pi$
$564$	4.43361e49	0.0559878
$565$	−1.26946e51	−1.55140
$566$	2.66130e51	3.14768
$567$	3.92828e49	0.0449692
$568$	2.38668e51	2.64454
$569$	−9.00352e50	−0.965685	−0.482842	−	0.875707i	$-0.660396\pi$
$569$	−9.00352e50	−0.965685	−0.482842	+	0.875707i	$0.660396\pi$
$570$	1.08153e51	1.12293
$571$	−1.09945e51	−1.10512	−0.552560	−	0.833473i	$-0.686349\pi$
$571$	−1.09945e51	−1.10512	−0.552560	+	0.833473i	$0.686349\pi$
$572$	3.32584e51	3.23649
$573$	5.22195e50	0.492008
$574$	−1.42985e50	−0.130443
$575$	−6.19436e50	−0.547194
$576$	1.50145e51	1.28438
$577$	−8.24476e50	−0.683007	−0.341504	−	0.939880i	$-0.610936\pi$
$577$	−8.24476e50	−0.683007	−0.341504	+	0.939880i	$0.610936\pi$
$578$	−2.39916e51	−1.92484
$579$	1.00118e51	0.777966
$580$	1.35489e51	1.01973
$581$	−6.23371e49	−0.0454452
$582$	−2.41871e51	−1.70808
$583$	−1.43135e51	−0.979213
$584$	−1.85314e51	−1.22821
$585$	−5.88192e50	−0.377690
$586$	−8.76336e50	−0.545211
$587$	2.47843e51	1.49407	0.747035	−	0.664784i	$-0.231477\pi$
$587$	2.47843e51	1.49407	0.747035	+	0.664784i	$0.231477\pi$
$588$	−2.26747e51	−1.32453
$589$	6.84131e50	0.387263
$590$	5.88127e51	3.22633
$591$	1.25694e51	0.668260
$592$	2.26932e51	1.16935
$593$	−2.66024e50	−0.132864	−0.0664322	−	0.997791i	$-0.521162\pi$
$593$	−2.66024e50	−0.132864	−0.0664322	+	0.997791i	$0.521162\pi$
$594$	9.04769e50	0.438014
$595$	−7.00102e49	−0.0328547
$596$	−8.92094e51	−4.05840
$597$	1.93452e51	0.853196
$598$	−8.97793e51	−3.83888
$599$	7.18446e50	0.297850	0.148925	−	0.988848i	$-0.452419\pi$
$599$	7.18446e50	0.297850	0.148925	+	0.988848i	$0.452419\pi$
$600$	1.34006e51	0.538675
$601$	4.14069e51	1.61397	0.806984	−	0.590574i	$-0.201099\pi$
$601$	4.14069e51	1.61397	0.806984	+	0.590574i	$0.201099\pi$
$602$	8.97877e50	0.339377
$603$	−3.93419e50	−0.144206
$604$	1.14582e52	4.07317
$605$	−1.25760e51	−0.433580
$606$	−3.06885e51	−1.02620
$607$	2.73180e51	0.886049	0.443025	−	0.896509i	$-0.353905\pi$
$607$	2.73180e51	0.886049	0.443025	+	0.896509i	$0.353905\pi$
$608$	−1.11616e52	−3.51164
$609$	−2.51866e50	−0.0768686
$610$	−4.18873e51	−1.24017
$611$	1.23407e50	0.0354467
$612$	2.35781e50	0.0657063
$613$	4.36236e51	1.17951	0.589756	−	0.807581i	$-0.299224\pi$
$613$	4.36236e51	1.17951	0.589756	+	0.807581i	$0.299224\pi$
$614$	−1.73502e51	−0.455187
$615$	4.26848e50	0.108664
$616$	6.50136e51	1.60606
$617$	−3.01014e51	−0.721624	−0.360812	−	0.932639i	$-0.617500\pi$
$617$	−3.01014e51	−0.721624	−0.360812	+	0.932639i	$0.617500\pi$
$618$	−8.28030e50	−0.192646
$619$	−1.23535e51	−0.278942	−0.139471	−	0.990226i	$-0.544540\pi$
$619$	−1.23535e51	−0.278942	−0.139471	+	0.990226i	$0.544540\pi$
$620$	6.15658e51	1.34925
$621$	−1.78995e51	−0.380756
$622$	−1.68274e52	−3.47453
$623$	2.23644e51	0.448259
$624$	1.12585e52	2.19062
$625$	−6.35318e51	−1.20008
$626$	9.85225e51	1.80680
$627$	−3.39364e51	−0.604250
$628$	−5.24140e51	−0.906138
$629$	1.32283e50	0.0222058
$630$	−1.80926e51	−0.294918
$631$	1.05432e52	1.66890	0.834450	−	0.551083i	$-0.185785\pi$
$631$	1.05432e52	1.66890	0.834450	+	0.551083i	$0.185785\pi$
$632$	4.19101e52	6.44247
$633$	1.85371e51	0.276741
$634$	1.30252e52	1.88857
$635$	−1.19066e52	−1.67677
$636$	−9.63955e51	−1.31856
$637$	−6.31137e51	−0.838579
$638$	−5.80102e51	−0.748724
$639$	2.08410e51	0.261308
$640$	−3.25417e52	−3.96379
$641$	−8.08669e51	−0.956968	−0.478484	−	0.878096i	$-0.658813\pi$
$641$	−8.08669e51	−0.956968	−0.478484	+	0.878096i	$0.658813\pi$
$642$	2.17590e51	0.250174
$643$	5.36035e51	0.598812	0.299406	−	0.954126i	$-0.403211\pi$
$643$	5.36035e51	0.598812	0.299406	+	0.954126i	$0.403211\pi$
$644$	−2.02389e52	−2.19684
$645$	−2.68040e51	−0.282713
$646$	−1.20672e51	−0.123682
$647$	−6.77154e51	−0.674463	−0.337232	−	0.941422i	$-0.609491\pi$
$647$	−6.77154e51	−0.674463	−0.337232	+	0.941422i	$0.609491\pi$
$648$	3.87231e51	0.374828
$649$	−1.84544e52	−1.73609
$650$	5.86928e51	0.536646
$651$	−1.14447e51	−0.101708
$652$	3.14337e52	2.71528
$653$	−9.50332e51	−0.797961	−0.398981	−	0.916959i	$-0.630636\pi$
$653$	−9.50332e51	−0.797961	−0.398981	+	0.916959i	$0.630636\pi$
$654$	3.27206e51	0.267075
$655$	2.13821e52	1.69663
$656$	−8.17026e51	−0.630253
$657$	−1.61821e51	−0.121360
$658$	3.79595e50	0.0276784
$659$	1.31463e52	0.932018	0.466009	−	0.884780i	$-0.345691\pi$
$659$	1.31463e52	0.932018	0.466009	+	0.884780i	$0.345691\pi$
$660$	−3.05398e52	−2.10525
$661$	1.11659e52	0.748459	0.374229	−	0.927336i	$-0.377907\pi$
$661$	1.11659e52	0.748459	0.374229	+	0.927336i	$0.377907\pi$
$662$	4.55913e52	2.97173
$663$	6.56281e50	0.0415996
$664$	−6.14490e51	−0.378796
$665$	6.78625e51	0.406845
$666$	3.41857e51	0.199329
$667$	1.14765e52	0.650850
$668$	−1.98631e52	−1.09568
$669$	−9.12335e51	−0.489521
$670$	1.81198e52	0.945737
$671$	1.31435e52	0.667336
$672$	1.86720e52	0.922271
$673$	−2.40983e52	−1.15800	−0.578998	−	0.815329i	$-0.696556\pi$
$673$	−2.40983e52	−1.15800	−0.578998	+	0.815329i	$0.696556\pi$
$674$	−5.97192e52	−2.79194
$675$	1.17017e51	0.0532268
$676$	3.53278e50	0.0156352
$677$	2.62781e52	1.13163	0.565814	−	0.824533i	$-0.308562\pi$
$677$	2.62781e52	1.13163	0.565814	+	0.824533i	$0.308562\pi$
$678$	3.66042e52	1.53385
$679$	−1.51767e52	−0.618850
$680$	−6.90127e51	−0.273851
$681$	1.16643e52	0.450439
$682$	−2.63596e52	−0.990668
$683$	2.18094e52	0.797741	0.398870	−	0.917007i	$-0.369402\pi$
$683$	2.18094e52	0.797741	0.398870	+	0.917007i	$0.369402\pi$
$684$	−2.28548e52	−0.813653
$685$	−1.80119e52	−0.624142
$686$	−4.26300e52	−1.43787
$687$	−1.97571e52	−0.648669
$688$	5.13053e52	1.63974
$689$	−2.68311e52	−0.834800
$690$	8.24406e52	2.49708
$691$	2.89991e51	0.0855148	0.0427574	−	0.999085i	$-0.486386\pi$
$691$	2.89991e51	0.0855148	0.0427574	+	0.999085i	$0.486386\pi$
$692$	−1.43358e53	−4.11585
$693$	5.67714e51	0.158696
$694$	−1.49327e52	−0.406433
$695$	3.52188e52	0.933375
$696$	−2.48277e52	−0.640717
$697$	−4.76260e50	−0.0119684
$698$	9.63291e52	2.35740
$699$	4.47312e51	0.106606
$700$	1.32311e52	0.307102
$701$	−7.75630e51	−0.175336	−0.0876681	−	0.996150i	$-0.527941\pi$
$701$	−7.75630e51	−0.175336	−0.0876681	+	0.996150i	$0.527941\pi$
$702$	1.69602e52	0.373417
$703$	−1.28225e52	−0.274979
$704$	2.16990e53	4.53257
$705$	−1.13319e51	−0.0230571
$706$	−1.49493e53	−2.96301
$707$	−1.92561e52	−0.371800
$708$	−1.24283e53	−2.33774
$709$	−2.37217e52	−0.434700	−0.217350	−	0.976094i	$-0.569741\pi$
$709$	−2.37217e52	−0.434700	−0.217350	+	0.976094i	$0.569741\pi$
$710$	−9.59884e52	−1.71372
$711$	3.65969e52	0.636585
$712$	2.20458e53	3.73634
$713$	5.21487e52	0.861166
$714$	2.01870e51	0.0324829
$715$	−8.50056e52	−1.33286
$716$	−2.16481e53	−3.30773
$717$	−3.73603e52	−0.556296
$718$	5.00739e52	0.726623
$719$	1.39711e53	1.97581	0.987904	−	0.155068i	$-0.0495598\pi$
$719$	1.39711e53	1.97581	0.987904	+	0.155068i	$0.0495598\pi$
$720$	−1.03382e53	−1.42494
$721$	−5.19563e51	−0.0697969
$722$	−3.07972e52	−0.403249
$723$	1.11915e52	0.142833
$724$	3.49444e53	4.34724
$725$	−7.50269e51	−0.0909838
$726$	3.62623e52	0.428674
$727$	1.82625e52	0.210462	0.105231	−	0.994448i	$-0.466442\pi$
$727$	1.82625e52	0.210462	0.105231	+	0.994448i	$0.466442\pi$
$728$	1.21870e53	1.36920
$729$	3.38139e51	0.0370370
$730$	7.45305e52	0.795904
$731$	2.99068e51	0.0311386
$732$	8.85162e52	0.898602
$733$	−2.47287e52	−0.244781	−0.122390	−	0.992482i	$-0.539056\pi$
$733$	−2.47287e52	−0.244781	−0.122390	+	0.992482i	$0.539056\pi$
$734$	3.12260e52	0.301397
$735$	5.79546e52	0.545472
$736$	−8.50805e53	−7.80891
$737$	−5.68569e52	−0.508902
$738$	−1.23079e52	−0.107434
$739$	−3.06278e52	−0.260732	−0.130366	−	0.991466i	$-0.541615\pi$
$739$	−3.06278e52	−0.260732	−0.130366	+	0.991466i	$0.541615\pi$
$740$	−1.15391e53	−0.958045
$741$	−6.36149e52	−0.515136
$742$	−8.25316e52	−0.651850
$743$	2.58567e52	0.199196	0.0995978	−	0.995028i	$-0.468244\pi$
$743$	2.58567e52	0.199196	0.0995978	+	0.995028i	$0.468244\pi$
$744$	−1.12816e53	−0.847759
$745$	2.28011e53	1.67134
$746$	3.30179e53	2.36092
$747$	−5.36587e51	−0.0374291
$748$	3.40751e52	0.231877
$749$	1.36531e52	0.0906398
$750$	1.40971e53	0.913057
$751$	−1.09214e53	−0.690141	−0.345071	−	0.938577i	$-0.612145\pi$
$751$	−1.09214e53	−0.690141	−0.345071	+	0.938577i	$0.612145\pi$
$752$	2.16903e52	0.133732
$753$	1.25060e52	0.0752336
$754$	−1.08742e53	−0.638304
$755$	−2.92862e53	−1.67743
$756$	3.82333e52	0.213692
$757$	5.53806e52	0.302054	0.151027	−	0.988530i	$-0.451742\pi$
$757$	5.53806e52	0.302054	0.151027	+	0.988530i	$0.451742\pi$
$758$	−8.93456e52	−0.475546
$759$	−2.58684e53	−1.34368
$760$	6.68956e53	3.39114
$761$	1.91021e53	0.945072	0.472536	−	0.881311i	$-0.343339\pi$
$761$	1.91021e53	0.945072	0.472536	+	0.881311i	$0.343339\pi$
$762$	3.43319e53	1.65779
$763$	2.05312e52	0.0967632
$764$	5.08244e53	2.33800
$765$	−6.02635e51	−0.0270594
$766$	−3.83293e53	−1.67996
$767$	−3.45933e53	−1.48006
$768$	4.05675e53	1.69432
$769$	−3.71712e52	−0.151555	−0.0757773	−	0.997125i	$-0.524144\pi$
$769$	−3.71712e52	−0.151555	−0.0757773	+	0.997125i	$0.524144\pi$
$770$	−2.61475e53	−1.04076
$771$	−1.08096e53	−0.420054
$772$	9.74436e53	3.69686
$773$	−1.53846e53	−0.569858	−0.284929	−	0.958549i	$-0.591970\pi$
$773$	−1.53846e53	−0.569858	−0.284929	+	0.958549i	$0.591970\pi$
$774$	7.72877e52	0.279514
$775$	−3.40920e52	−0.120384
$776$	−1.49604e54	−5.15825
$777$	2.14505e52	0.0722184
$778$	4.22728e53	1.38976
$779$	4.61650e52	0.148207
$780$	−5.72478e53	−1.79477
$781$	3.01195e53	0.922153
$782$	−9.19839e52	−0.275034
$783$	−2.16802e52	−0.0633096
$784$	−1.10930e54	−3.16376
$785$	1.33966e53	0.373169
$786$	−6.16541e53	−1.67743
$787$	1.23159e53	0.327292	0.163646	−	0.986519i	$-0.447675\pi$
$787$	1.23159e53	0.327292	0.163646	+	0.986519i	$0.447675\pi$
$788$	1.22336e54	3.17554
$789$	5.82721e51	0.0147753
$790$	−1.68556e54	−4.17486
$791$	2.29680e53	0.555723
$792$	5.59626e53	1.32276
$793$	2.46379e53	0.568918
$794$	4.83192e53	1.09003
$795$	2.46378e53	0.543014
$796$	1.88284e54	4.05436
$797$	−1.87818e53	−0.395147	−0.197574	−	0.980288i	$-0.563306\pi$
$797$	−1.87818e53	−0.395147	−0.197574	+	0.980288i	$0.563306\pi$
$798$	−1.95677e53	−0.402242
$799$	1.26437e51	0.00253956
$800$	5.56209e53	1.09163
$801$	1.92509e53	0.369190
$802$	−1.08890e54	−2.04061
$803$	−2.33863e53	−0.428277
$804$	−3.82908e53	−0.685263
$805$	5.17289e53	0.904711
$806$	−4.94119e53	−0.844566
$807$	4.71937e53	0.788358
$808$	−1.89818e54	−3.09904
$809$	1.37996e53	0.220201	0.110100	−	0.993920i	$-0.464883\pi$
$809$	1.37996e53	0.220201	0.110100	+	0.993920i	$0.464883\pi$
$810$	−1.55738e53	−0.242897
$811$	2.88787e53	0.440243	0.220121	−	0.975472i	$-0.429355\pi$
$811$	2.88787e53	0.440243	0.220121	+	0.975472i	$0.429355\pi$
$812$	−2.45137e53	−0.365276
$813$	3.00029e53	0.437007
$814$	4.94051e53	0.703430
$815$	−8.03418e53	−1.11822
$816$	1.15350e53	0.156946
$817$	−2.89894e53	−0.385595
$818$	2.47071e54	3.21281
$819$	1.06420e53	0.135292
$820$	4.15445e53	0.516365
$821$	9.46819e53	1.15058	0.575292	−	0.817948i	$-0.304888\pi$
$821$	9.46819e53	1.15058	0.575292	+	0.817948i	$0.304888\pi$
$822$	5.19361e53	0.617079
$823$	−9.45005e53	−1.09783	−0.548917	−	0.835877i	$-0.684960\pi$
$823$	−9.45005e53	−1.09783	−0.548917	+	0.835877i	$0.684960\pi$
$824$	−5.12161e53	−0.581772
$825$	1.69114e53	0.187837
$826$	−1.06408e54	−1.15570
$827$	6.22799e53	0.661449	0.330724	−	0.943727i	$-0.392707\pi$
$827$	6.22799e53	0.661449	0.330724	+	0.943727i	$0.392707\pi$
$828$	−1.74213e54	−1.80934
$829$	−3.74356e53	−0.380212	−0.190106	−	0.981764i	$-0.560883\pi$
$829$	−3.74356e53	−0.380212	−0.190106	+	0.981764i	$0.560883\pi$
$830$	2.47138e53	0.245468
$831$	−2.42959e53	−0.236001
$832$	4.06754e54	3.86412
$833$	−6.46634e52	−0.0600795
$834$	−1.01551e54	−0.922814
$835$	5.07683e53	0.451225
$836$	−3.30297e54	−2.87137
$837$	−9.85138e52	−0.0837676
$838$	−5.37794e53	−0.447303
$839$	−1.42400e54	−1.15855	−0.579274	−	0.815133i	$-0.696664\pi$
$839$	−1.42400e54	−1.15855	−0.579274	+	0.815133i	$0.696664\pi$
$840$	−1.11908e54	−0.890626
$841$	−1.14547e54	−0.891781
$842$	4.06257e54	3.09405
$843$	−4.27113e53	−0.318224
$844$	1.80419e54	1.31506
$845$	−9.02949e51	−0.00643893
$846$	3.26749e52	0.0227962
$847$	2.27535e53	0.155312
$848$	−4.71590e54	−3.14950
$849$	1.43741e54	0.939264
$850$	6.01340e52	0.0384477
$851$	−9.77409e53	−0.611476
$852$	2.02842e54	1.24173
$853$	−1.93589e54	−1.15964	−0.579821	−	0.814744i	$-0.696877\pi$
$853$	−1.93589e54	−1.15964	−0.579821	+	0.814744i	$0.696877\pi$
$854$	7.57855e53	0.444238
$855$	5.84149e53	0.335081
$856$	1.34586e54	0.755502
$857$	−2.55656e54	−1.40447	−0.702233	−	0.711947i	$-0.747813\pi$
$857$	−2.55656e54	−1.40447	−0.702233	+	0.711947i	$0.747813\pi$
$858$	2.45108e54	1.31778
$859$	−1.64382e54	−0.864927	−0.432464	−	0.901651i	$-0.642356\pi$
$859$	−1.64382e54	−0.864927	−0.432464	+	0.901651i	$0.642356\pi$
$860$	−2.60879e54	−1.34344
$861$	−7.72284e52	−0.0389241
$862$	−1.24266e53	−0.0613009
$863$	−1.78555e54	−0.862128	−0.431064	−	0.902321i	$-0.641862\pi$
$863$	−1.78555e54	−0.862128	−0.431064	+	0.902321i	$0.641862\pi$
$864$	1.60725e54	0.759590
$865$	3.66411e54	1.69500
$866$	8.15235e54	3.69149
$867$	−1.29582e54	−0.574370
$868$	−1.11389e54	−0.483313
$869$	5.28898e54	2.24650
$870$	9.98532e53	0.415198
$871$	−1.06580e54	−0.433850
$872$	2.02387e54	0.806543
$873$	−1.30638e54	−0.509690
$874$	8.91621e54	3.40580
$875$	8.84553e53	0.330807
$876$	−1.57498e54	−0.576697
$877$	−1.18991e54	−0.426602	−0.213301	−	0.976987i	$-0.568421\pi$
$877$	−1.18991e54	−0.426602	−0.213301	+	0.976987i	$0.568421\pi$
$878$	−8.66099e54	−3.04032
$879$	−4.73322e53	−0.162691
$880$	−1.49408e55	−5.02858
$881$	6.27215e53	0.206710	0.103355	−	0.994645i	$-0.467042\pi$
$881$	6.27215e53	0.206710	0.103355	+	0.994645i	$0.467042\pi$
$882$	−1.67109e54	−0.539300
$883$	−7.94118e53	−0.250964	−0.125482	−	0.992096i	$-0.540048\pi$
$883$	−7.94118e53	−0.250964	−0.125482	+	0.992096i	$0.540048\pi$
$884$	6.38748e53	0.197680
$885$	3.17656e54	0.962734
$886$	−3.08285e54	−0.915014
$887$	4.43676e54	1.28967	0.644836	−	0.764321i	$-0.276926\pi$
$887$	4.43676e54	1.28967	0.644836	+	0.764321i	$0.276926\pi$
$888$	2.11449e54	0.601956
$889$	2.15422e54	0.600630
$890$	−8.86648e54	−2.42123
$891$	4.88679e53	0.130703
$892$	−8.87961e54	−2.32618
$893$	−1.22558e53	−0.0314478
$894$	−6.57457e54	−1.65243
$895$	5.53308e54	1.36220
$896$	5.88767e54	1.41986
$897$	−4.84912e54	−1.14552
$898$	6.73051e54	1.55753
$899$	6.31632e53	0.143189
$900$	1.13891e54	0.252932
$901$	−2.74899e53	−0.0598087
$902$	−1.77874e54	−0.379133
$903$	4.84957e53	0.101270
$904$	2.26408e55	4.63207
$905$	−8.93148e54	−1.79030
$906$	8.44449e54	1.65845
$907$	8.87474e54	1.70774	0.853868	−	0.520490i	$-0.174251\pi$
$907$	8.87474e54	1.70774	0.853868	+	0.520490i	$0.174251\pi$
$908$	1.13526e55	2.14047
$909$	−1.65753e54	−0.306218
$910$	−4.90142e54	−0.887271
$911$	2.41119e54	0.427702	0.213851	−	0.976866i	$-0.431399\pi$
$911$	2.41119e54	0.427702	0.213851	+	0.976866i	$0.431399\pi$
$912$	−1.11811e55	−1.94348
$913$	−7.75476e53	−0.132087
$914$	−1.94529e55	−3.24699
$915$	−2.26240e54	−0.370065
$916$	−1.92293e55	−3.08245
$917$	−3.86860e54	−0.607745
$918$	1.73766e53	0.0267532
$919$	−9.87356e54	−1.48983	−0.744915	−	0.667159i	$-0.767510\pi$
$919$	−9.87356e54	−1.48983	−0.744915	+	0.667159i	$0.767510\pi$
$920$	5.09920e55	7.54096
$921$	−9.37110e53	−0.135827
$922$	2.51128e54	0.356757
$923$	5.64599e54	0.786156
$924$	5.52547e54	0.754116
$925$	6.38977e53	0.0854797
$926$	−1.54028e55	−2.01975
$927$	−4.47231e53	−0.0574853
$928$	−1.03051e55	−1.29841
$929$	−6.84483e54	−0.845418	−0.422709	−	0.906265i	$-0.638921\pi$
$929$	−6.84483e54	−0.845418	−0.422709	+	0.906265i	$0.638921\pi$
$930$	4.53729e54	0.549366
$931$	6.26798e54	0.743975
$932$	4.35361e54	0.506589
$933$	−9.08875e54	−1.03680
$934$	−7.73078e54	−0.864582
$935$	−8.70929e53	−0.0954922
$936$	1.04904e55	1.12768
$937$	−9.21588e53	−0.0971302	−0.0485651	−	0.998820i	$-0.515465\pi$
$937$	−9.21588e53	−0.0971302	−0.0485651	+	0.998820i	$0.515465\pi$
$938$	−3.27837e54	−0.338770
$939$	5.32134e54	0.539148
$940$	−1.10292e54	−0.109566
$941$	1.10225e55	1.07367	0.536835	−	0.843687i	$-0.319620\pi$
$941$	1.10225e55	1.07367	0.536835	+	0.843687i	$0.319620\pi$
$942$	−3.86282e54	−0.368946
$943$	3.51898e54	0.329572
$944$	−6.08022e55	−5.58390
$945$	−9.77209e53	−0.0880033
$946$	1.11696e55	0.986399
$947$	2.12495e55	1.84024	0.920120	−	0.391636i	$-0.128091\pi$
$947$	2.12495e55	1.84024	0.920120	+	0.391636i	$0.128091\pi$
$948$	3.56191e55	3.02503
$949$	−4.38384e54	−0.365115
$950$	−5.82893e54	−0.476104
$951$	7.03509e54	0.563547
$952$	1.24863e54	0.0980955
$953$	1.66851e55	1.28562	0.642808	−	0.766028i	$-0.277769\pi$
$953$	1.66851e55	1.28562	0.642808	+	0.766028i	$0.277769\pi$
$954$	−7.10417e54	−0.536869
$955$	−1.29903e55	−0.962844
$956$	−3.63622e55	−2.64350
$957$	−3.13322e54	−0.223419
$958$	3.17748e55	2.22240
$959$	3.25883e54	0.223572
$960$	−3.73505e55	−2.51350
$961$	−1.22788e55	−0.810541
$962$	9.26115e54	0.599689
$963$	1.17524e54	0.0746517
$964$	1.08925e55	0.678737
$965$	−2.49057e55	−1.52245
$966$	−1.49157e55	−0.894474
$967$	−1.94586e55	−1.14478	−0.572389	−	0.819982i	$-0.693983\pi$
$967$	−1.94586e55	−1.14478	−0.572389	+	0.819982i	$0.693983\pi$
$968$	2.24293e55	1.29456
$969$	−6.51769e53	−0.0369066
$970$	6.01685e55	3.34266
$971$	−1.46805e55	−0.800173	−0.400087	−	0.916477i	$-0.631020\pi$
$971$	−1.46805e55	−0.800173	−0.400087	+	0.916477i	$0.631020\pi$
$972$	3.29105e54	0.175999
$973$	−6.37204e54	−0.334342
$974$	5.86664e54	0.302029
$975$	3.17009e54	0.160135
$976$	4.33043e55	2.14639
$977$	2.32343e55	1.13001	0.565003	−	0.825089i	$-0.308875\pi$
$977$	2.32343e55	1.13001	0.565003	+	0.825089i	$0.308875\pi$
$978$	2.31661e55	1.10556
$979$	2.78215e55	1.30287
$980$	5.64063e55	2.59206
$981$	1.76729e54	0.0796950
$982$	−5.74073e55	−2.54042
$983$	1.19994e55	0.521097	0.260549	−	0.965461i	$-0.416097\pi$
$983$	1.19994e55	0.521097	0.260549	+	0.965461i	$0.416097\pi$
$984$	−7.61281e54	−0.324441
$985$	−3.12679e55	−1.30776
$986$	−1.11412e54	−0.0457309
$987$	2.05025e53	0.00825923
$988$	−6.19153e55	−2.44790
$989$	−2.20975e55	−0.857455
$990$	−2.25073e55	−0.857180
$991$	−3.02946e54	−0.113241	−0.0566203	−	0.998396i	$-0.518032\pi$
$991$	−3.02946e54	−0.113241	−0.0566203	+	0.998396i	$0.518032\pi$
$992$	−4.68258e55	−1.71799
$993$	2.46245e55	0.886762
$994$	1.73669e55	0.613867
$995$	−4.81238e55	−1.66968
$996$	−5.22252e54	−0.177862
$997$	−3.34593e55	−1.11855	−0.559277	−	0.828981i	$-0.688921\pi$
$997$	−3.34593e55	−1.11855	−0.559277	+	0.828981i	$0.688921\pi$
$998$	−2.07649e55	−0.681421
$999$	1.84642e54	0.0594797

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.38.a.b.1.4	✓	4	1.1	even	1	trivial
9.38.a.c.1.1		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)

\(f(q)\)	\(=\)	\(q+717293. q^{2} +3.87420e8 q^{3} +3.77070e11 q^{4} -9.63758e12 q^{5} +2.77894e14 q^{6} +1.74370e15 q^{7} +1.71886e17 q^{8} +1.50095e17 q^{9} +O(q^{10})\)	\(q+717293. q^{2} +3.87420e8 q^{3} +3.77070e11 q^{4} -9.63758e12 q^{5} +2.77894e14 q^{6} +1.74370e15 q^{7} +1.71886e17 q^{8} +1.50095e17 q^{9} -6.91297e18 q^{10} +2.16917e19 q^{11} +1.46085e20 q^{12} +4.06617e20 q^{13} +1.25074e21 q^{14} -3.73380e21 q^{15} +7.14682e22 q^{16} +4.16602e21 q^{17} +1.07662e23 q^{18} -4.03822e23 q^{19} -3.63404e24 q^{20} +6.75545e23 q^{21} +1.55593e25 q^{22} -3.07818e25 q^{23} +6.65920e25 q^{24} +2.01235e25 q^{25} +2.91664e26 q^{26} +5.81497e25 q^{27} +6.57497e26 q^{28} -3.72833e26 q^{29} -2.67823e27 q^{30} -1.69414e27 q^{31} +2.76399e28 q^{32} +8.40380e27 q^{33} +2.98826e27 q^{34} -1.68050e28 q^{35} +5.65962e28 q^{36} +3.17528e28 q^{37} -2.89659e29 q^{38} +1.57532e29 q^{39} -1.65656e30 q^{40} -1.14320e29 q^{41} +4.84563e29 q^{42} +7.17875e29 q^{43} +8.17928e30 q^{44} -1.44655e30 q^{45} -2.20796e31 q^{46} +3.03496e29 q^{47} +2.76883e31 q^{48} -1.55216e31 q^{49} +1.44344e31 q^{50} +1.61400e30 q^{51} +1.53323e32 q^{52} -6.59860e31 q^{53} +4.17104e31 q^{54} -2.09055e32 q^{55} +2.99717e32 q^{56} -1.56449e32 q^{57} -2.67431e32 q^{58} -8.50758e32 q^{59} -1.40790e33 q^{60} +6.05924e32 q^{61} -1.21519e33 q^{62} +2.61720e32 q^{63} +1.00034e34 q^{64} -3.91881e33 q^{65} +6.02799e33 q^{66} -2.62114e33 q^{67} +1.57088e33 q^{68} -1.19255e34 q^{69} -1.20541e34 q^{70} +1.38853e34 q^{71} +2.57991e34 q^{72} -1.07813e34 q^{73} +2.27761e34 q^{74} +7.79624e33 q^{75} -1.52269e35 q^{76} +3.78238e34 q^{77} +1.12997e35 q^{78} +2.43825e35 q^{79} -6.88781e35 q^{80} +2.25284e34 q^{81} -8.20011e34 q^{82} -3.57499e34 q^{83} +2.54728e35 q^{84} -4.01504e34 q^{85} +5.14927e35 q^{86} -1.44443e35 q^{87} +3.72849e36 q^{88} +1.28259e36 q^{89} -1.03760e36 q^{90} +7.09018e35 q^{91} -1.16069e37 q^{92} -6.56345e35 q^{93} +2.17695e35 q^{94} +3.89187e36 q^{95} +1.07082e37 q^{96} -8.70371e36 q^{97} -1.11336e37 q^{98} +3.25581e36 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 437562 q^{2} + 1549681956 q^{3} + 346098955492 q^{4} - 4099829756904 q^{5} + 169520484007818 q^{6} + 66\!\cdots\!84 q^{7}+ \cdots + 60\!\cdots\!84 q^{9}+O(q^{10}) \) 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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Groups

Database

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