LMFDB - Embedded newform 2.44.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,44,Mod(1,2)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2, base_ring=CyclotomicField(1))

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

N = Newforms(chi, 44, names="a")

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

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 44);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 44 $
Character orbit:	$[\chi]$	$=$	2.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$23.4220790691$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 24394519512 $ x^2 - x - 24394519512
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8}\cdot 3\cdot 5\cdot 11 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$156188.$ of defining polynomial
Character	$\chi$	$=$	2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.09715e6 q^{2} -1.30882e10 q^{3} +4.39805e12 q^{4} +1.67102e15 q^{5} +2.74479e16 q^{6} -6.70883e17 q^{7} -9.22337e18 q^{8} -1.56957e20 q^{9} +O(q^{10})$	\(q-2.09715e6 q^{2} -1.30882e10 q^{3} +4.39805e12 q^{4} +1.67102e15 q^{5} +2.74479e16 q^{6} -6.70883e17 q^{7} -9.22337e18 q^{8} -1.56957e20 q^{9} -3.50438e21 q^{10} +2.32700e22 q^{11} -5.75624e22 q^{12} -1.22318e24 q^{13} +1.40694e24 q^{14} -2.18706e25 q^{15} +1.93428e25 q^{16} +3.48170e26 q^{17} +3.29162e26 q^{18} -2.92459e27 q^{19} +7.34922e27 q^{20} +8.78063e27 q^{21} -4.88006e28 q^{22} +2.25548e29 q^{23} +1.20717e29 q^{24} +1.65544e30 q^{25} +2.56520e30 q^{26} +6.35056e30 q^{27} -2.95057e30 q^{28} +4.02623e30 q^{29} +4.58660e31 q^{30} +1.13932e32 q^{31} -4.05648e31 q^{32} -3.04561e32 q^{33} -7.30166e32 q^{34} -1.12106e33 q^{35} -6.90303e32 q^{36} -7.69200e33 q^{37} +6.13331e33 q^{38} +1.60092e34 q^{39} -1.54124e34 q^{40} +3.14341e34 q^{41} -1.84143e34 q^{42} +1.98374e35 q^{43} +1.02342e35 q^{44} -2.62278e35 q^{45} -4.73008e35 q^{46} +1.24024e36 q^{47} -2.53162e35 q^{48} -1.73373e36 q^{49} -3.47171e36 q^{50} -4.55691e36 q^{51} -5.37962e36 q^{52} +2.28375e37 q^{53} -1.33181e37 q^{54} +3.88845e37 q^{55} +6.18780e36 q^{56} +3.82776e37 q^{57} -8.44361e36 q^{58} -5.92652e37 q^{59} -9.61879e37 q^{60} +1.57810e38 q^{61} -2.38934e38 q^{62} +1.05300e38 q^{63} +8.50706e37 q^{64} -2.04396e39 q^{65} +6.38711e38 q^{66} +1.19856e39 q^{67} +1.53127e39 q^{68} -2.95201e39 q^{69} +2.35103e39 q^{70} +7.59260e39 q^{71} +1.44767e39 q^{72} -1.46070e39 q^{73} +1.61313e40 q^{74} -2.16667e40 q^{75} -1.28625e40 q^{76} -1.56114e40 q^{77} -3.35738e40 q^{78} -2.75306e40 q^{79} +3.23222e40 q^{80} -3.15951e40 q^{81} -6.59221e40 q^{82} +2.42104e41 q^{83} +3.86176e40 q^{84} +5.81799e41 q^{85} -4.16019e41 q^{86} -5.26959e40 q^{87} -2.14627e41 q^{88} -5.61520e41 q^{89} +5.50036e41 q^{90} +8.20612e41 q^{91} +9.91969e41 q^{92} -1.49117e42 q^{93} -2.60097e42 q^{94} -4.88705e42 q^{95} +5.30919e41 q^{96} +3.43039e42 q^{97} +3.63590e42 q^{98} -3.65237e42 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4194304 q^{2} - 12981630984 q^{3} + 8796093022208 q^{4} - 398662711282500 q^{5} + 27\!\cdots\!68 q^{6}+ \cdots - 48\!\cdots\!26 q^{9}+O(q^{10}) $ 2 * q - 4194304 * q^2 - 12981630984 * q^3 + 8796093022208 * q^4 - 398662711282500 * q^5 + 27224453381357568 * q^6 + 1174870033543241008 * q^7 - 18446744073709551616 * q^8 - 485202301172100019926 * q^9	$ 2 q - 4194304 q^{2} - 12981630984 q^{3} + 8796093022208 q^{4} - 398662711282500 q^{5} + 27\!\cdots\!68 q^{6}+ \cdots + 77\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q - 4194304 * q^2 - 12981630984 * q^3 + 8796093022208 * q^4 - 398662711282500 * q^5 + 27224453381357568 * q^6 + 1174870033543241008 * q^7 - 18446744073709551616 * q^8 - 485202301172100019926 * q^9 + 836056302291517440000 * q^10 - 11617807872020797407576 * q^11 - 57093816857620786446336 * q^12 - 1658879102786318366273684 * q^13 - 2463881040585274966409216 * q^14 - 22091103207013849606710000 * q^15 + 38685626227668133590597632 * q^16 + 343161409966024505905818468 * q^17 + 1017542976307671900987850752 * q^18 - 526535613098348151618559400 * q^19 - 1753337146463260382330880000 * q^20 + 8977278711349595999815289664 * q^21 + 24364309014424159324892823552 * q^22 + 229455981723979198172770632336 * q^23 + 119734412210593147537506435072 * q^24 + 4802154653491374627549005468750 * q^25 + 3478921628166533134467588947968 * q^26 + 6280615052012507617464674387760 * q^27 + 5167133052025490566355020152832 * q^28 + 34136150491106942855372319350220 * q^29 + 46328401272795508730411089920000 * q^30 + 162309856447038824698827315968704 * q^31 - 81129638414606681695789005144064 * q^32 - 308278184912318274174336905435808 * q^33 - 719661637233068224609399011803136 * q^34 - 4941179569454425103779106953980000 * q^35 - 2133942287849586742500473180258304 * q^36 - 4391607431868635112322899638873732 * q^37 + 1104225214080427022863165082828800 * q^38 + 15962811619464040671516159652622928 * q^39 + 3677014503379719437325969653760000 * q^40 + 73274473482816660070587986010183924 * q^41 - 18826718004064227950204634349436928 * q^42 + 234436585898994103006598707127282536 * q^43 - 51095659378217654576517634697723904 * q^44 + 417086449135320077301667307984347500 * q^45 - 481204070984406423406422277144707072 * q^46 - 39114598548473932831256802726900192 * q^47 - 251101262036269840544576695324114944 * q^48 - 510742495035301170011177769547783854 * q^49 - 10070848235878743282913651916800000000 * q^50 - 4557444784421248830689881595224595856 * q^51 - 7295827450352701296014973097408987136 * q^52 + 21441800128967176515730209034915502556 * q^53 - 13171404417558134374981276821639659520 * q^54 + 111091123730229295314448534371395310000 * q^55 - 10836263414321361592212563223551934464 * q^56 + 38533058136217827264209989537628772000 * q^57 - 71588696274725907423029770269952573440 * q^58 + 67981786423576245191970112954336157640 * q^59 - 97157699386045646724999078047907840000 * q^60 + 10550869229810756555782264236051582604 * q^61 - 340388440067620365294795103338399531008 * q^62 - 500560701761315054164921401424721593104 * q^63 + 170141183460469231731687303715884105728 * q^64 - 1142210409763957682754357764765378535000 * q^65 + 646506212045238093321258989908515618816 * q^66 - 1296008696996439884699343907691487049352 * q^67 + 1509239841846603493376050356400970268672 * q^68 - 2951590658050920771532689933244706114112 * q^69 + 10362404616440486515240561706753064960000 * q^70 + 10578336400277808016654999978615404825264 * q^71 + 4475201336848336536208352330925062750208 * q^72 - 1083714960819479223422811781189857230924 * q^73 + 9209868308958171863078193623463324811264 * q^74 - 21331402709079687390002224676411221875000 * q^75 - 2315728116159195691851532379784583577600 * q^76 - 80005579389320632459943851192412711459904 * q^77 - 33476442313382251822351457247817478701056 * q^78 - 66782694077687545008302637975280595820320 * q^79 - 7711258319791785377427031911322091520000 * q^80 + 76146348151673377566388577586168400203282 * q^81 - 153667708613435924300353736037229236584448 * q^82 + 549648200704305895621526521126723031888856 * q^83 + 39482489315659303774227549335190352429056 * q^84 + 592165605546979682092570996796433568995000 * q^85 - 491649154991247281108494491849394824937472 * q^86 - 49487960387866633050295824495906154497840 * q^87 + 107155364256347910730453110641601080721408 * q^88 + 298108448661015962080672472021181983545620 * q^89 - 874693680977034770753346198273990328320000 * q^90 + 16425068484305226748514962047001570578464 * q^91 + 1009158079873089899659625291358576725458944 * q^92 - 1486013428111370066200804977498842194176768 * q^93 + 82029258575129205184935866352324191453184 * q^94 - 9850264420679630550524982943635697915950000 * q^95 + 526597513881887368637740105752358303039488 * q^96 - 2275344922279044236600118263254186752839612 * q^97 + 1071104644948271919291281481762674004983808 * q^98 + 7799379619136501162487578778863682680428488 * 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 $

$2$	−2.09715e6	−0.707107
$2$	−2.09715e6	−0.707107
$3$	−1.30882e10	−0.722391	−0.361195	−	0.932490i	$-0.617631\pi$
$3$	−1.30882e10	−0.722391	−0.361195	+	0.932490i	$0.617631\pi$
$4$	4.39805e12	0.500000
$5$	1.67102e15	1.56721	0.783604	−	0.621261i	$-0.213379\pi$
$5$	1.67102e15	1.56721	0.783604	+	0.621261i	$0.213379\pi$
$6$	2.74479e16	0.510807
$7$	−6.70883e17	−0.453982	−0.226991	−	0.973897i	$-0.572889\pi$
$7$	−6.70883e17	−0.453982	−0.226991	+	0.973897i	$0.572889\pi$
$8$	−9.22337e18	−0.353553
$9$	−1.56957e20	−0.478152
$10$	−3.50438e21	−1.10818
$11$	2.32700e22	0.948097	0.474048	−	0.880499i	$-0.342792\pi$
$11$	2.32700e22	0.948097	0.474048	+	0.880499i	$0.342792\pi$
$12$	−5.75624e22	−0.361195
$13$	−1.22318e24	−1.37312	−0.686561	−	0.727072i	$-0.740881\pi$
$13$	−1.22318e24	−1.37312	−0.686561	+	0.727072i	$0.740881\pi$
$14$	1.40694e24	0.321014
$15$	−2.18706e25	−1.13214
$16$	1.93428e25	0.250000
$17$	3.48170e26	1.22219	0.611096	−	0.791556i	$-0.290729\pi$
$17$	3.48170e26	1.22219	0.611096	+	0.791556i	$0.290729\pi$
$18$	3.29162e26	0.338104
$19$	−2.92459e27	−0.939427	−0.469713	−	0.882819i	$-0.655643\pi$
$19$	−2.92459e27	−0.939427	−0.469713	+	0.882819i	$0.655643\pi$
$20$	7.34922e27	0.783604
$21$	8.78063e27	0.327952
$22$	−4.88006e28	−0.670406
$23$	2.25548e29	1.19149	0.595744	−	0.803174i	$-0.296857\pi$
$23$	2.25548e29	1.19149	0.595744	+	0.803174i	$0.296857\pi$
$24$	1.20717e29	0.255404
$25$	1.65544e30	1.45614
$26$	2.56520e30	0.970944
$27$	6.35056e30	1.06780
$28$	−2.95057e30	−0.226991
$29$	4.02623e30	0.145660	0.0728301	−	0.997344i	$-0.476797\pi$
$29$	4.02623e30	0.145660	0.0728301	+	0.997344i	$0.476797\pi$
$30$	4.58660e31	0.800541
$31$	1.13932e32	0.982587	0.491294	−	0.870994i	$-0.336524\pi$
$31$	1.13932e32	0.982587	0.491294	+	0.870994i	$0.336524\pi$
$32$	−4.05648e31	−0.176777
$33$	−3.04561e32	−0.684896
$34$	−7.30166e32	−0.864221
$35$	−1.12106e33	−0.711484
$36$	−6.90303e32	−0.239076
$37$	−7.69200e33	−1.47809	−0.739047	−	0.673654i	$-0.764724\pi$
$37$	−7.69200e33	−1.47809	−0.739047	+	0.673654i	$0.764724\pi$
$38$	6.13331e33	0.664275
$39$	1.60092e34	0.991931
$40$	−1.54124e34	−0.554091
$41$	3.14341e34	0.664581	0.332291	−	0.943177i	$-0.392179\pi$
$41$	3.14341e34	0.664581	0.332291	+	0.943177i	$0.392179\pi$
$42$	−1.84143e34	−0.231897
$43$	1.98374e35	1.50630	0.753151	−	0.657848i	$-0.228533\pi$
$43$	1.98374e35	1.50630	0.753151	+	0.657848i	$0.228533\pi$
$44$	1.02342e35	0.474048
$45$	−2.62278e35	−0.749363
$46$	−4.73008e35	−0.842510
$47$	1.24024e36	1.39124	0.695618	−	0.718412i	$-0.255131\pi$
$47$	1.24024e36	1.39124	0.695618	+	0.718412i	$0.255131\pi$
$48$	−2.53162e35	−0.180598
$49$	−1.73373e36	−0.793900
$50$	−3.47171e36	−1.02965
$51$	−4.55691e36	−0.882901
$52$	−5.37962e36	−0.686561
$53$	2.28375e37	1.93516	0.967581	−	0.252561i	$-0.0812728\pi$
$53$	2.28375e37	1.93516	0.967581	+	0.252561i	$0.0812728\pi$
$54$	−1.33181e37	−0.755051
$55$	3.88845e37	1.48586
$56$	6.18780e36	0.160507
$57$	3.82776e37	0.678633
$58$	−8.44361e36	−0.102997
$59$	−5.92652e37	−0.500589	−0.250295	−	0.968170i	$-0.580527\pi$
$59$	−5.92652e37	−0.500589	−0.250295	+	0.968170i	$0.580527\pi$
$60$	−9.61879e37	−0.566068
$61$	1.57810e38	0.650943	0.325471	−	0.945552i	$-0.394477\pi$
$61$	1.57810e38	0.650943	0.325471	+	0.945552i	$0.394477\pi$
$62$	−2.38934e38	−0.694794
$63$	1.05300e38	0.217072
$64$	8.50706e37	0.125000
$65$	−2.04396e39	−2.15197
$66$	6.38711e38	0.484295
$67$	1.19856e39	0.657736	0.328868	−	0.944376i	$-0.393333\pi$
$67$	1.19856e39	0.657736	0.328868	+	0.944376i	$0.393333\pi$
$68$	1.53127e39	0.611096
$69$	−2.95201e39	−0.860720
$70$	2.35103e39	0.503095
$71$	7.59260e39	1.19767	0.598833	−	0.800874i	$-0.295631\pi$
$71$	7.59260e39	1.19767	0.598833	+	0.800874i	$0.295631\pi$
$72$	1.44767e39	0.169052
$73$	−1.46070e39	−0.126800	−0.0634000	−	0.997988i	$-0.520194\pi$
$73$	−1.46070e39	−0.126800	−0.0634000	+	0.997988i	$0.520194\pi$
$74$	1.61313e40	1.04517
$75$	−2.16667e40	−1.05190
$76$	−1.28625e40	−0.469713
$77$	−1.56114e40	−0.430419
$78$	−3.35738e40	−0.701401
$79$	−2.75306e40	−0.437354	−0.218677	−	0.975797i	$-0.570174\pi$
$79$	−2.75306e40	−0.437354	−0.218677	+	0.975797i	$0.570174\pi$
$80$	3.23222e40	0.391802
$81$	−3.15951e40	−0.293219
$82$	−6.59221e40	−0.469930
$83$	2.42104e41	1.32991	0.664956	−	0.746883i	$-0.268450\pi$
$83$	2.42104e41	1.32991	0.664956	+	0.746883i	$0.268450\pi$
$84$	3.86176e40	0.163976
$85$	5.81799e41	1.91543
$86$	−4.16019e41	−1.06512
$87$	−5.26959e40	−0.105224
$88$	−2.14627e41	−0.335203
$89$	−5.61520e41	−0.687829	−0.343914	−	0.939001i	$-0.611753\pi$
$89$	−5.61520e41	−0.687829	−0.343914	+	0.939001i	$0.611753\pi$
$90$	5.50036e41	0.529880
$91$	8.20612e41	0.623373
$92$	9.91969e41	0.595744
$93$	−1.49117e42	−0.709812
$94$	−2.60097e42	−0.983752
$95$	−4.88705e42	−1.47228
$96$	5.30919e41	0.127702
$97$	3.43039e42	0.660314	0.330157	−	0.943926i	$-0.392898\pi$
$97$	3.43039e42	0.660314	0.330157	+	0.943926i	$0.392898\pi$
$98$	3.63590e42	0.561372
$99$	−3.65237e42	−0.453334
$100$	7.28069e42	0.728069
$101$	2.99504e42	0.241821	0.120910	−	0.992663i	$-0.461419\pi$
$101$	2.99504e42	0.241821	0.120910	+	0.992663i	$0.461419\pi$
$102$	9.55654e42	0.624305
$103$	5.24275e42	0.277689	0.138845	−	0.990314i	$-0.455661\pi$
$103$	5.24275e42	0.277689	0.138845	+	0.990314i	$0.455661\pi$
$104$	1.12819e43	0.485472
$105$	1.46726e43	0.513969
$106$	−4.78937e43	−1.36837
$107$	−3.68881e43	−0.861261	−0.430631	−	0.902528i	$-0.641709\pi$
$107$	−3.68881e43	−0.861261	−0.430631	+	0.902528i	$0.641709\pi$
$108$	2.79301e43	0.533901
$109$	−4.02750e43	−0.631490	−0.315745	−	0.948844i	$-0.602254\pi$
$109$	−4.02750e43	−0.631490	−0.315745	+	0.948844i	$0.602254\pi$
$110$	−8.15468e43	−1.05066
$111$	1.00674e44	1.06776
$112$	−1.29768e43	−0.113496
$113$	−1.40596e44	−1.01575	−0.507875	−	0.861431i	$-0.669569\pi$
$113$	−1.40596e44	−1.01575	−0.507875	+	0.861431i	$0.669569\pi$
$114$	−8.02739e43	−0.479866
$115$	3.76895e44	1.86731
$116$	1.77075e43	0.0728301
$117$	1.91987e44	0.656561
$118$	1.24288e44	0.353970
$119$	−2.33581e44	−0.554854
$120$	2.01721e44	0.400270
$121$	−6.09100e43	−0.101112
$122$	−3.30951e44	−0.460286
$123$	−4.11415e44	−0.480087
$124$	5.01080e44	0.491294
$125$	8.66540e44	0.714864
$126$	−2.20829e44	−0.153493
$127$	−2.29690e45	−1.34698	−0.673490	−	0.739196i	$-0.735206\pi$
$127$	−2.29690e45	−1.34698	−0.673490	+	0.739196i	$0.735206\pi$
$128$	−1.78406e44	−0.0883883
$129$	−2.59635e45	−1.08814
$130$	4.28650e45	1.52167
$131$	−2.63581e45	−0.793564	−0.396782	−	0.917913i	$-0.629873\pi$
$131$	−2.63581e45	−0.793564	−0.396782	+	0.917913i	$0.629873\pi$
$132$	−1.33947e45	−0.342448
$133$	1.96206e45	0.426483
$134$	−2.51356e45	−0.465089
$135$	1.06119e46	1.67347
$136$	−3.21130e45	−0.432110
$137$	8.12716e45	0.934215	0.467107	−	0.884201i	$-0.345296\pi$
$137$	8.12716e45	0.934215	0.467107	+	0.884201i	$0.345296\pi$
$138$	6.19081e45	0.608621
$139$	1.14324e46	0.962320	0.481160	−	0.876633i	$-0.340216\pi$
$139$	1.14324e46	0.962320	0.481160	+	0.876633i	$0.340216\pi$
$140$	−4.93047e45	−0.355742
$141$	−1.62324e46	−1.00502
$142$	−1.59228e46	−0.846878
$143$	−2.84634e46	−1.30185
$144$	−3.03598e45	−0.119538
$145$	6.72790e45	0.228280
$146$	3.06331e45	0.0896612
$147$	2.26914e46	0.573506
$148$	−3.38298e46	−0.739047
$149$	1.68142e46	0.317812	0.158906	−	0.987294i	$-0.449203\pi$
$149$	1.68142e46	0.317812	0.158906	+	0.987294i	$0.449203\pi$
$150$	4.54383e46	0.743806
$151$	−4.11201e46	−0.583512	−0.291756	−	0.956493i	$-0.594240\pi$
$151$	−4.11201e46	−0.583512	−0.291756	+	0.956493i	$0.594240\pi$
$152$	2.69746e46	0.332137
$153$	−5.46476e46	−0.584394
$154$	3.27395e46	0.304352
$155$	1.90383e47	1.53992
$156$	7.04093e46	0.495965
$157$	−2.41691e46	−0.148395	−0.0741973	−	0.997244i	$-0.523639\pi$
$157$	−2.41691e46	−0.148395	−0.0741973	+	0.997244i	$0.523639\pi$
$158$	5.77359e46	0.309256
$159$	−2.98901e47	−1.39794
$160$	−6.77846e46	−0.277046
$161$	−1.51316e47	−0.540914
$162$	6.62597e46	0.207337
$163$	3.22717e47	0.884684	0.442342	−	0.896846i	$-0.354148\pi$
$163$	3.22717e47	0.884684	0.442342	+	0.896846i	$0.354148\pi$
$164$	1.38249e47	0.332291
$165$	−5.08928e47	−1.07337
$166$	−5.07729e47	−0.940390
$167$	2.83162e46	0.0460926	0.0230463	−	0.999734i	$-0.492663\pi$
$167$	2.83162e46	0.0460926	0.0230463	+	0.999734i	$0.492663\pi$
$168$	−8.09870e46	−0.115949
$169$	7.02645e47	0.885466
$170$	−1.22012e48	−1.35441
$171$	4.59034e47	0.449189
$172$	8.72456e47	0.753151
$173$	1.51127e48	1.15173	0.575864	−	0.817545i	$-0.304666\pi$
$173$	1.51127e48	1.15173	0.575864	+	0.817545i	$0.304666\pi$
$174$	1.10511e47	0.0744043
$175$	−1.11060e48	−0.661061
$176$	4.50106e47	0.237024
$177$	7.75673e47	0.361621
$178$	1.17759e48	0.486368
$179$	3.10473e48	1.13680	0.568400	−	0.822753i	$-0.307563\pi$
$179$	3.10473e48	1.13680	0.568400	+	0.822753i	$0.307563\pi$
$180$	−1.15351e48	−0.374682
$181$	−3.99228e48	−1.15115	−0.575574	−	0.817750i	$-0.695221\pi$
$181$	−3.99228e48	−1.15115	−0.575574	+	0.817750i	$0.695221\pi$
$182$	−1.72095e48	−0.440791
$183$	−2.06544e48	−0.470235
$184$	−2.08031e48	−0.421255
$185$	−1.28535e49	−2.31648
$186$	3.12721e48	0.501913
$187$	8.10190e48	1.15876
$188$	5.45462e48	0.695618
$189$	−4.26048e48	−0.484763
$190$	1.02489e49	1.04106
$191$	−1.50160e48	−0.136251	−0.0681253	−	0.997677i	$-0.521702\pi$
$191$	−1.50160e48	−0.136251	−0.0681253	+	0.997677i	$0.521702\pi$
$192$	−1.11342e48	−0.0902988
$193$	7.85184e48	0.569494	0.284747	−	0.958603i	$-0.408090\pi$
$193$	7.85184e48	0.569494	0.284747	+	0.958603i	$0.408090\pi$
$194$	−7.19404e48	−0.466913
$195$	2.67517e49	1.55456
$196$	−7.62503e48	−0.396950
$197$	−2.31488e49	−1.08020	−0.540101	−	0.841600i	$-0.681614\pi$
$197$	−2.31488e49	−1.08020	−0.540101	+	0.841600i	$0.681614\pi$
$198$	7.65958e48	0.320556
$199$	2.35127e49	0.883001	0.441500	−	0.897261i	$-0.354446\pi$
$199$	2.35127e49	0.883001	0.441500	+	0.897261i	$0.354446\pi$
$200$	−1.52687e49	−0.514823
$201$	−1.56870e49	−0.475142
$202$	−6.28106e48	−0.170993
$203$	−2.70112e48	−0.0661272
$204$	−2.00415e49	−0.441450
$205$	5.25270e49	1.04154
$206$	−1.09948e49	−0.196356
$207$	−3.54012e49	−0.569712
$208$	−2.36598e49	−0.343281
$209$	−6.80551e49	−0.890667
$210$	−3.07707e49	−0.363431
$211$	9.59361e48	0.102308	0.0511540	−	0.998691i	$-0.483710\pi$
$211$	9.59361e48	0.102308	0.0511540	+	0.998691i	$0.483710\pi$
$212$	1.00440e50	0.967581
$213$	−9.93733e49	−0.865183
$214$	7.73599e49	0.609004
$215$	3.31486e50	2.36069
$216$	−5.85736e49	−0.377525
$217$	−7.64353e49	−0.446077
$218$	8.44629e49	0.446531
$219$	1.91179e49	0.0915992
$220$	1.71016e50	0.742932
$221$	−4.25876e50	−1.67822
$222$	−2.11129e50	−0.755021
$223$	5.16000e50	1.67531	0.837655	−	0.546200i	$-0.183926\pi$
$223$	5.16000e50	1.67531	0.837655	+	0.546200i	$0.183926\pi$
$224$	2.72142e49	0.0802534
$225$	−2.59832e50	−0.696255
$226$	2.94852e50	0.718244
$227$	−6.91910e50	−1.53283	−0.766415	−	0.642346i	$-0.777961\pi$
$227$	−6.91910e50	−1.53283	−0.766415	+	0.642346i	$0.777961\pi$
$228$	1.68347e50	0.339316
$229$	−6.27472e50	−1.15115	−0.575574	−	0.817749i	$-0.695221\pi$
$229$	−6.27472e50	−1.15115	−0.575574	+	0.817749i	$0.695221\pi$
$230$	−7.90405e50	−1.32039
$231$	2.04325e50	0.310931
$232$	−3.71354e49	−0.0514987
$233$	8.02437e50	1.01452	0.507258	−	0.861794i	$-0.330659\pi$
$233$	8.02437e50	1.01452	0.507258	+	0.861794i	$0.330659\pi$
$234$	−4.02625e50	−0.464259
$235$	2.07246e51	2.18035
$236$	−2.60651e50	−0.250295
$237$	3.60325e50	0.315941
$238$	4.89855e50	0.392341
$239$	5.37577e50	0.393446	0.196723	−	0.980459i	$-0.436970\pi$
$239$	5.37577e50	0.393446	0.196723	+	0.980459i	$0.436970\pi$
$240$	−4.23039e50	−0.283034
$241$	1.25831e50	0.0769880	0.0384940	−	0.999259i	$-0.487744\pi$
$241$	1.25831e50	0.0769880	0.0384940	+	0.999259i	$0.487744\pi$
$242$	1.27738e50	0.0714971
$243$	−1.67109e51	−0.855984
$244$	6.94055e50	0.325471
$245$	−2.89710e51	−1.24421
$246$	8.62800e50	0.339473
$247$	3.57731e51	1.28995
$248$	−1.05084e51	−0.347397
$249$	−3.16870e51	−0.960716
$250$	−1.81727e51	−0.505485
$251$	−3.18975e51	−0.814277	−0.407138	−	0.913366i	$-0.633473\pi$
$251$	−3.18975e51	−0.814277	−0.407138	+	0.913366i	$0.633473\pi$
$252$	4.63112e50	0.108536
$253$	5.24848e51	1.12965
$254$	4.81694e51	0.952459
$255$	−7.61469e51	−1.38369
$256$	3.74144e50	0.0625000
$257$	−3.39629e51	−0.521727	−0.260863	−	0.965376i	$-0.584007\pi$
$257$	−3.39629e51	−0.521727	−0.260863	+	0.965376i	$0.584007\pi$
$258$	5.44493e51	0.769430
$259$	5.16043e51	0.671028
$260$	−8.98944e51	−1.07598
$261$	−6.31943e50	−0.0696477
$262$	5.52770e51	0.561134
$263$	−8.01231e51	−0.749393	−0.374696	−	0.927148i	$-0.622253\pi$
$263$	−8.01231e51	−0.749393	−0.374696	+	0.927148i	$0.622253\pi$
$264$	2.80908e51	0.242147
$265$	3.81619e52	3.03280
$266$	−4.11473e51	−0.301569
$267$	7.34927e51	0.496881
$268$	5.27132e51	0.328868
$269$	−1.58737e52	−0.914120	−0.457060	−	0.889436i	$-0.651098\pi$
$269$	−1.58737e52	−0.914120	−0.457060	+	0.889436i	$0.651098\pi$
$270$	−2.22548e52	−1.18332
$271$	−2.28657e52	−1.12291	−0.561455	−	0.827507i	$-0.689758\pi$
$271$	−2.28657e52	−1.12291	−0.561455	+	0.827507i	$0.689758\pi$
$272$	6.73459e51	0.305548
$273$	−1.07403e52	−0.450319
$274$	−1.70439e52	−0.660590
$275$	3.85220e52	1.38056
$276$	−1.29831e52	−0.430360
$277$	−2.03762e52	−0.624898	−0.312449	−	0.949935i	$-0.601149\pi$
$277$	−2.03762e52	−0.624898	−0.312449	+	0.949935i	$0.601149\pi$
$278$	−2.39755e52	−0.680463
$279$	−1.78825e52	−0.469826
$280$	1.03399e52	0.251548
$281$	5.54569e52	1.24960	0.624798	−	0.780786i	$-0.285181\pi$
$281$	5.54569e52	1.24960	0.624798	+	0.780786i	$0.285181\pi$
$282$	3.40419e52	0.710653
$283$	−7.28849e52	−1.41003	−0.705016	−	0.709191i	$-0.749060\pi$
$283$	−7.28849e52	−1.41003	−0.705016	+	0.709191i	$0.749060\pi$
$284$	3.33926e52	0.598833
$285$	6.39626e52	1.06356
$286$	5.96921e52	0.920549
$287$	−2.10886e52	−0.301708
$288$	6.36692e51	0.0845261
$289$	4.00696e52	0.493755
$290$	−1.41094e52	−0.161418
$291$	−4.48975e52	−0.477005
$292$	−6.42422e51	−0.0634000
$293$	−1.02109e51	−0.00936293	−0.00468146	−	0.999989i	$-0.501490\pi$
$293$	−1.02109e51	−0.00936293	−0.00468146	+	0.999989i	$0.501490\pi$
$294$	−4.75873e52	−0.405530
$295$	−9.90333e52	−0.784527
$296$	7.09462e52	0.522585
$297$	1.47777e53	1.01238
$298$	−3.52619e52	−0.224727
$299$	−2.75886e53	−1.63606
$300$	−9.52910e52	−0.525950
$301$	−1.33085e53	−0.683834
$302$	8.62351e52	0.412606
$303$	−3.91996e52	−0.174689
$304$	−5.65698e52	−0.234857
$305$	2.63703e53	1.02016
$306$	1.14604e53	0.413229
$307$	3.90717e53	1.31337	0.656685	−	0.754165i	$-0.271958\pi$
$307$	3.90717e53	1.31337	0.656685	+	0.754165i	$0.271958\pi$
$308$	−6.86597e52	−0.215209
$309$	−6.86181e52	−0.200600
$310$	−3.99263e53	−1.08889
$311$	6.19128e53	1.57555	0.787775	−	0.615964i	$-0.211233\pi$
$311$	6.19128e53	1.57555	0.787775	+	0.615964i	$0.211233\pi$
$312$	−1.47659e53	−0.350701
$313$	−4.24265e53	−0.940663	−0.470331	−	0.882490i	$-0.655866\pi$
$313$	−4.24265e53	−0.940663	−0.470331	+	0.882490i	$0.655866\pi$
$314$	5.06863e52	0.104931
$315$	1.75958e53	0.340197
$316$	−1.21081e53	−0.218677
$317$	8.62450e52	0.145532	0.0727662	−	0.997349i	$-0.476817\pi$
$317$	8.62450e52	0.145532	0.0727662	+	0.997349i	$0.476817\pi$
$318$	6.26841e53	0.988495
$319$	9.36901e52	0.138100
$320$	1.42155e53	0.195901
$321$	4.82798e53	0.622167
$322$	3.17333e53	0.382484
$323$	−1.01826e54	−1.14816
$324$	−1.38957e53	−0.146609
$325$	−2.02490e54	−1.99946
$326$	−6.76786e53	−0.625566
$327$	5.27127e53	0.456182
$328$	−2.89928e53	−0.234965
$329$	−8.32053e53	−0.631596
$330$	1.06730e54	0.758990
$331$	−1.53215e54	−1.02094	−0.510471	−	0.859895i	$-0.670529\pi$
$331$	−1.53215e54	−1.02094	−0.510471	+	0.859895i	$0.670529\pi$
$332$	1.06478e54	0.664956
$333$	1.20731e54	0.706754
$334$	−5.93834e52	−0.0325924
$335$	2.00282e54	1.03081
$336$	1.69842e53	0.0819881
$337$	−2.50480e53	−0.113431	−0.0567153	−	0.998390i	$-0.518063\pi$
$337$	−2.50480e53	−0.113431	−0.0567153	+	0.998390i	$0.518063\pi$
$338$	−1.47355e54	−0.626119
$339$	1.84015e54	0.733769
$340$	2.55878e54	0.957715
$341$	2.65120e54	0.931588
$342$	−9.62665e53	−0.317624
$343$	2.62821e54	0.814399
$344$	−1.82967e54	−0.532558
$345$	−4.93286e54	−1.34893
$346$	−3.16936e54	−0.814395
$347$	5.16597e54	1.24758	0.623789	−	0.781593i	$-0.285592\pi$
$347$	5.16597e54	1.24758	0.623789	+	0.781593i	$0.285592\pi$
$348$	−2.31759e53	−0.0526118
$349$	−7.76485e54	−1.65724	−0.828622	−	0.559809i	$-0.810874\pi$
$349$	−7.76485e54	−1.65724	−0.828622	+	0.559809i	$0.810874\pi$
$350$	2.32911e54	0.467441
$351$	−7.76790e54	−1.46622
$352$	−9.43941e53	−0.167601
$353$	2.07986e54	0.347439	0.173719	−	0.984795i	$-0.444421\pi$
$353$	2.07986e54	0.347439	0.173719	+	0.984795i	$0.444421\pi$
$354$	−1.62670e54	−0.255705
$355$	1.26874e55	1.87699
$356$	−2.46959e54	−0.343914
$357$	3.05715e54	0.400821
$358$	−6.51109e54	−0.803838
$359$	−6.95386e54	−0.808528	−0.404264	−	0.914642i	$-0.632472\pi$
$359$	−6.95386e54	−0.808528	−0.404264	+	0.914642i	$0.632472\pi$
$360$	2.41908e54	0.264940
$361$	−1.13857e54	−0.117478
$362$	8.37241e54	0.813985
$363$	7.97201e53	0.0730425
$364$	3.60909e54	0.311687
$365$	−2.44086e54	−0.198722
$366$	4.33155e54	0.332506
$367$	6.70860e54	0.485637	0.242818	−	0.970072i	$-0.421928\pi$
$367$	6.70860e54	0.485637	0.242818	+	0.970072i	$0.421928\pi$
$368$	4.36273e54	0.297872
$369$	−4.93379e54	−0.317771
$370$	2.69557e55	1.63800
$371$	−1.53213e55	−0.878529
$372$	−6.55822e54	−0.354906
$373$	8.81171e54	0.450112	0.225056	−	0.974346i	$-0.427744\pi$
$373$	8.81171e54	0.450112	0.225056	+	0.974346i	$0.427744\pi$
$374$	−1.69909e55	−0.819365
$375$	−1.13414e55	−0.516411
$376$	−1.14392e55	−0.491876
$377$	−4.92481e54	−0.200009
$378$	8.93488e54	0.342779
$379$	1.20095e55	0.435293	0.217647	−	0.976028i	$-0.430162\pi$
$379$	1.20095e55	0.435293	0.217647	+	0.976028i	$0.430162\pi$
$380$	−2.14935e55	−0.736138
$381$	3.00622e55	0.973046
$382$	3.14909e54	0.0963437
$383$	−3.24831e55	−0.939471	−0.469736	−	0.882807i	$-0.655651\pi$
$383$	−3.24831e55	−0.939471	−0.469736	+	0.882807i	$0.655651\pi$
$384$	2.33501e54	0.0638509
$385$	−2.60870e55	−0.674556
$386$	−1.64665e55	−0.402693
$387$	−3.11361e55	−0.720241
$388$	1.50870e55	0.330157
$389$	3.93519e55	0.814797	0.407398	−	0.913251i	$-0.366436\pi$
$389$	3.93519e55	0.814797	0.407398	+	0.913251i	$0.366436\pi$
$390$	−5.61025e55	−1.09924
$391$	7.85290e55	1.45623
$392$	1.59908e55	0.280686
$393$	3.44980e55	0.573263
$394$	4.85466e55	0.763819
$395$	−4.60042e55	−0.685425
$396$	−1.60633e55	−0.226667
$397$	1.07339e56	1.43470	0.717352	−	0.696711i	$-0.245354\pi$
$397$	1.07339e56	1.43470	0.717352	+	0.696711i	$0.245354\pi$
$398$	−4.93097e55	−0.624376
$399$	−2.56798e55	−0.308087
$400$	3.20208e55	0.364035
$401$	1.40659e56	1.51552	0.757761	−	0.652532i	$-0.226293\pi$
$401$	1.40659e56	1.51552	0.757761	+	0.652532i	$0.226293\pi$
$402$	3.28979e55	0.335976
$403$	−1.39360e56	−1.34921
$404$	1.31723e55	0.120910
$405$	−5.27960e55	−0.459535
$406$	5.66467e54	0.0467590
$407$	−1.78992e56	−1.40138
$408$	4.20301e55	0.312152
$409$	−2.32188e56	−1.63602	−0.818008	−	0.575206i	$-0.804922\pi$
$409$	−2.32188e56	−1.63602	−0.818008	+	0.575206i	$0.804922\pi$
$410$	−1.10157e56	−0.736478
$411$	−1.06370e56	−0.674868
$412$	2.30579e55	0.138845
$413$	3.97600e55	0.227259
$414$	7.42417e55	0.402848
$415$	4.04560e56	2.08425
$416$	4.96182e55	0.242736
$417$	−1.49629e56	−0.695171
$418$	1.42722e56	0.629797
$419$	2.81206e56	1.17875	0.589376	−	0.807859i	$-0.299374\pi$
$419$	2.81206e56	1.17875	0.589376	+	0.807859i	$0.299374\pi$
$420$	6.45308e55	0.256985
$421$	−3.32075e56	−1.25652	−0.628262	−	0.778002i	$-0.716233\pi$
$421$	−3.32075e56	−1.25652	−0.628262	+	0.778002i	$0.716233\pi$
$422$	−2.01193e55	−0.0723427
$423$	−1.94663e56	−0.665222
$424$	−2.10639e56	−0.684183
$425$	5.76374e56	1.77968
$426$	2.08401e56	0.611777
$427$	−1.05872e56	−0.295516
$428$	−1.62236e56	−0.430631
$429$	3.72534e56	0.940447
$430$	−6.95177e56	−1.66926
$431$	4.47425e56	1.02202	0.511009	−	0.859575i	$-0.329272\pi$
$431$	4.47425e56	1.02202	0.511009	+	0.859575i	$0.329272\pi$
$432$	1.22838e56	0.266951
$433$	3.38743e55	0.0700455	0.0350228	−	0.999387i	$-0.488850\pi$
$433$	3.38743e55	0.0700455	0.0350228	+	0.999387i	$0.488850\pi$
$434$	1.60296e56	0.315424
$435$	−8.80560e55	−0.164907
$436$	−1.77132e56	−0.315745
$437$	−6.59635e56	−1.11932
$438$	−4.00931e55	−0.0647704
$439$	−8.47461e56	−1.30356	−0.651782	−	0.758406i	$-0.725978\pi$
$439$	−8.47461e56	−1.30356	−0.651782	+	0.758406i	$0.725978\pi$
$440$	−3.58647e56	−0.525332
$441$	2.72121e56	0.379605
$442$	8.93126e56	1.18668
$443$	7.14165e56	0.903896	0.451948	−	0.892044i	$-0.350729\pi$
$443$	7.14165e56	0.903896	0.451948	+	0.892044i	$0.350729\pi$
$444$	4.42770e56	0.533881
$445$	−9.38311e56	−1.07797
$446$	−1.08213e57	−1.18462
$447$	−2.20067e56	−0.229585
$448$	−5.70724e55	−0.0567478
$449$	−5.19514e55	−0.0492380	−0.0246190	−	0.999697i	$-0.507837\pi$
$449$	−5.19514e55	−0.0492380	−0.0246190	+	0.999697i	$0.507837\pi$
$450$	5.44907e56	0.492327
$451$	7.31470e56	0.630087
$452$	−6.18349e56	−0.507875
$453$	5.38187e56	0.421524
$454$	1.45104e57	1.08387
$455$	1.37126e57	0.976955
$456$	−3.53048e56	−0.239933
$457$	−2.34455e57	−1.52006	−0.760030	−	0.649888i	$-0.774816\pi$
$457$	−2.34455e57	−1.52006	−0.760030	+	0.649888i	$0.774816\pi$
$458$	1.31590e57	0.813985
$459$	2.21108e57	1.30506
$460$	1.65760e57	0.933655
$461$	−1.16136e57	−0.624306	−0.312153	−	0.950032i	$-0.601050\pi$
$461$	−1.16136e57	−0.624306	−0.312153	+	0.950032i	$0.601050\pi$
$462$	−4.28500e56	−0.219861
$463$	−1.42613e57	−0.698504	−0.349252	−	0.937029i	$-0.613564\pi$
$463$	−1.42613e57	−0.698504	−0.349252	+	0.937029i	$0.613564\pi$
$464$	7.78785e55	0.0364151
$465$	−2.49177e57	−1.11242
$466$	−1.68283e57	−0.717371
$467$	1.93948e57	0.789535	0.394768	−	0.918781i	$-0.370825\pi$
$467$	1.93948e57	0.789535	0.394768	+	0.918781i	$0.370825\pi$
$468$	8.44367e56	0.328281
$469$	−8.04093e56	−0.298600
$470$	−4.34626e57	−1.54174
$471$	3.16330e56	0.107199
$472$	5.46625e56	0.176985
$473$	4.61614e57	1.42812
$474$	−7.55657e56	−0.223404
$475$	−4.84148e57	−1.36794
$476$	−1.02730e57	−0.277427
$477$	−3.58450e57	−0.925301
$478$	−1.12738e57	−0.278209
$479$	6.92746e56	0.163441	0.0817204	−	0.996655i	$-0.473959\pi$
$479$	6.92746e56	0.163441	0.0817204	+	0.996655i	$0.473959\pi$
$480$	8.87177e56	0.200135
$481$	9.40872e57	2.02961
$482$	−2.63888e56	−0.0544387
$483$	1.98045e57	0.390751
$484$	−2.67885e56	−0.0505561
$485$	5.73224e57	1.03485
$486$	3.50454e57	0.605272
$487$	4.52567e57	0.747843	0.373922	−	0.927460i	$-0.378013\pi$
$487$	4.52567e57	0.747843	0.373922	+	0.927460i	$0.378013\pi$
$488$	−1.45554e57	−0.230143
$489$	−4.22377e57	−0.639087
$490$	6.07566e57	0.879787
$491$	−7.11420e57	−0.985993	−0.492997	−	0.870031i	$-0.664098\pi$
$491$	−7.11420e57	−0.985993	−0.492997	+	0.870031i	$0.664098\pi$
$492$	−1.80942e57	−0.240044
$493$	1.40181e57	0.178025
$494$	−7.50216e57	−0.912131
$495$	−6.10319e57	−0.710469
$496$	2.20377e57	0.245647
$497$	−5.09374e57	−0.543719
$498$	6.64524e57	0.679329
$499$	−1.31361e58	−1.28619	−0.643093	−	0.765788i	$-0.722349\pi$
$499$	−1.31361e58	−1.28619	−0.643093	+	0.765788i	$0.722349\pi$
$500$	3.81108e57	0.357432
$501$	−3.70607e56	−0.0332968
$502$	6.68940e57	0.575781
$503$	3.98333e57	0.328500	0.164250	−	0.986419i	$-0.447480\pi$
$503$	3.98333e57	0.328500	0.164250	+	0.986419i	$0.447480\pi$
$504$	−9.71217e56	−0.0767467
$505$	5.00477e57	0.378983
$506$	−1.10069e58	−0.798781
$507$	−9.19634e57	−0.639652
$508$	−1.01019e58	−0.673490
$509$	9.54927e57	0.610292	0.305146	−	0.952306i	$-0.401295\pi$
$509$	9.54927e57	0.610292	0.305146	+	0.952306i	$0.401295\pi$
$510$	1.59692e58	0.978415
$511$	9.79958e56	0.0575649
$512$	−7.84638e56	−0.0441942
$513$	−1.85728e58	−1.00312
$514$	7.12254e57	0.368916
$515$	8.76074e57	0.435197
$516$	−1.14189e58	−0.544069
$517$	2.88603e58	1.31903
$518$	−1.08222e58	−0.474489
$519$	−1.97797e58	−0.831998
$520$	1.88522e58	0.760836
$521$	2.55219e58	0.988331	0.494165	−	0.869368i	$-0.335474\pi$
$521$	2.55219e58	0.988331	0.494165	+	0.869368i	$0.335474\pi$
$522$	1.32528e57	0.0492484
$523$	−2.20883e57	−0.0787726	−0.0393863	−	0.999224i	$-0.512540\pi$
$523$	−2.20883e57	−0.0787726	−0.0393863	+	0.999224i	$0.512540\pi$
$524$	−1.15924e58	−0.396782
$525$	1.45358e58	0.477544
$526$	1.68030e58	0.529901
$527$	3.96679e58	1.20091
$528$	−5.89107e57	−0.171224
$529$	1.50376e58	0.419645
$530$	−8.00313e58	−2.14451
$531$	9.30207e57	0.239358
$532$	8.62922e57	0.213241
$533$	−3.84497e58	−0.912552
$534$	−1.54125e58	−0.351348
$535$	−6.16407e58	−1.34978
$536$	−1.10548e58	−0.232545
$537$	−4.06353e58	−0.821213
$538$	3.32895e58	0.646381
$539$	−4.03438e58	−0.752694
$540$	4.66717e58	0.836734
$541$	5.96044e57	0.102692	0.0513460	−	0.998681i	$-0.483649\pi$
$541$	5.96044e57	0.102692	0.0513460	+	0.998681i	$0.483649\pi$
$542$	4.79529e58	0.794017
$543$	5.22516e58	0.831579
$544$	−1.41235e58	−0.216055
$545$	−6.73004e58	−0.989675
$546$	2.25241e58	0.318423
$547$	6.80993e58	0.925583	0.462792	−	0.886467i	$-0.346848\pi$
$547$	6.80993e58	0.925583	0.462792	+	0.886467i	$0.346848\pi$
$548$	3.57436e58	0.467107
$549$	−2.47693e58	−0.311249
$550$	−8.07864e58	−0.976204
$551$	−1.17751e58	−0.136837
$552$	2.72275e58	0.304311
$553$	1.84698e58	0.198551
$554$	4.27321e58	0.441870
$555$	1.68229e59	1.67340
$556$	5.02802e58	0.481160
$557$	1.69579e59	1.56130	0.780649	−	0.624970i	$-0.214889\pi$
$557$	1.69579e59	1.56130	0.780649	+	0.624970i	$0.214889\pi$
$558$	3.75022e58	0.332217
$559$	−2.42647e59	−2.06834
$560$	−2.16844e58	−0.177871
$561$	−1.06039e59	−0.837075
$562$	−1.16302e59	−0.883598
$563$	6.74574e58	0.493286	0.246643	−	0.969106i	$-0.420672\pi$
$563$	6.74574e58	0.493286	0.246643	+	0.969106i	$0.420672\pi$
$564$	−7.13910e58	−0.502508
$565$	−2.34939e59	−1.59189
$566$	1.52851e59	0.997044
$567$	2.11966e58	0.133116
$568$	−7.00294e58	−0.423439
$569$	4.53105e58	0.263806	0.131903	−	0.991263i	$-0.457891\pi$
$569$	4.53105e58	0.263806	0.131903	+	0.991263i	$0.457891\pi$
$570$	−1.34139e59	−0.752049
$571$	3.40361e58	0.183765	0.0918826	−	0.995770i	$-0.470712\pi$
$571$	3.40361e58	0.183765	0.0918826	+	0.995770i	$0.470712\pi$
$572$	−1.25183e59	−0.650927
$573$	1.96533e58	0.0984261
$574$	4.42260e58	0.213340
$575$	3.73380e59	1.73497
$576$	−1.33524e58	−0.0597690
$577$	−1.63805e59	−0.706393	−0.353197	−	0.935549i	$-0.614905\pi$
$577$	−1.63805e59	−0.706393	−0.353197	+	0.935549i	$0.614905\pi$
$578$	−8.40321e58	−0.349138
$579$	−1.02766e59	−0.411397
$580$	2.95896e58	0.114140
$581$	−1.62423e59	−0.603756
$582$	9.41569e58	0.337293
$583$	5.31427e59	1.83472
$584$	1.34726e58	0.0448306
$585$	3.20814e59	1.02897
$586$	2.14139e57	0.00662059
$587$	−2.59001e59	−0.771937	−0.385968	−	0.922512i	$-0.626133\pi$
$587$	−2.59001e59	−0.771937	−0.385968	+	0.922512i	$0.626133\pi$
$588$	9.97977e58	0.286753
$589$	−3.33206e59	−0.923068
$590$	2.07688e59	0.554744
$591$	3.02976e59	0.780328
$592$	−1.48785e59	−0.369524
$593$	1.64400e59	0.393755	0.196877	−	0.980428i	$-0.436920\pi$
$593$	1.64400e59	0.393755	0.196877	+	0.980428i	$0.436920\pi$
$594$	−3.09911e59	−0.715861
$595$	−3.90319e59	−0.869571
$596$	7.39495e58	0.158906
$597$	−3.07738e59	−0.637871
$598$	5.78575e59	1.15687
$599$	−3.26024e59	−0.628887	−0.314443	−	0.949276i	$-0.601818\pi$
$599$	−3.26024e59	−0.628887	−0.314443	+	0.949276i	$0.601818\pi$
$600$	1.99840e59	0.371903
$601$	2.19604e59	0.394312	0.197156	−	0.980372i	$-0.436829\pi$
$601$	2.19604e59	0.394312	0.197156	+	0.980372i	$0.436829\pi$
$602$	2.79100e59	0.483544
$603$	−1.88122e59	−0.314498
$604$	−1.80848e59	−0.291756
$605$	−1.01782e59	−0.158464
$606$	8.22075e58	0.123524
$607$	−6.75055e59	−0.978999	−0.489500	−	0.872003i	$-0.662821\pi$
$607$	−6.75055e59	−0.978999	−0.489500	+	0.872003i	$0.662821\pi$
$608$	1.18636e59	0.166069
$609$	3.53528e58	0.0477696
$610$	−5.53026e59	−0.721364
$611$	−1.51704e60	−1.91034
$612$	−2.40343e59	−0.292197
$613$	1.52637e60	1.79168	0.895838	−	0.444380i	$-0.146576\pi$
$613$	1.52637e60	1.79168	0.895838	+	0.444380i	$0.146576\pi$
$614$	−8.19392e59	−0.928692
$615$	−6.87482e59	−0.752396
$616$	1.43990e59	0.152176
$617$	1.10660e60	1.12943	0.564717	−	0.825285i	$-0.308985\pi$
$617$	1.10660e60	1.12943	0.564717	+	0.825285i	$0.308985\pi$
$618$	1.43902e59	0.141846
$619$	1.89230e60	1.80153	0.900763	−	0.434310i	$-0.143008\pi$
$619$	1.89230e60	1.80153	0.900763	+	0.434310i	$0.143008\pi$
$620$	8.37315e59	0.769959
$621$	1.43235e60	1.27228
$622$	−1.29841e60	−1.11408
$623$	3.76714e59	0.312262
$624$	3.09664e59	0.247983
$625$	−4.34010e59	−0.335799
$626$	8.89748e59	0.665149
$627$	8.90717e59	0.643410
$628$	−1.06297e59	−0.0741973
$629$	−2.67812e60	−1.80652
$630$	−3.69010e59	−0.240556
$631$	1.45280e60	0.915321	0.457660	−	0.889127i	$-0.348688\pi$
$631$	1.45280e60	0.915321	0.457660	+	0.889127i	$0.348688\pi$
$632$	2.53925e59	0.154628
$633$	−1.25563e59	−0.0739063
$634$	−1.80869e59	−0.102907
$635$	−3.83816e60	−2.11100
$636$	−1.31458e60	−0.698971
$637$	2.12067e60	1.09012
$638$	−1.96482e59	−0.0976515
$639$	−1.19171e60	−0.572667
$640$	−2.98120e59	−0.138523
$641$	5.68468e59	0.255422	0.127711	−	0.991811i	$-0.459237\pi$
$641$	5.68468e59	0.255422	0.127711	+	0.991811i	$0.459237\pi$
$642$	−1.01250e60	−0.439939
$643$	2.49248e60	1.04736	0.523681	−	0.851915i	$-0.324559\pi$
$643$	2.49248e60	1.04736	0.523681	+	0.851915i	$0.324559\pi$
$644$	−6.65495e59	−0.270457
$645$	−4.33855e60	−1.70534
$646$	2.13544e60	0.811872
$647$	−1.39608e60	−0.513414	−0.256707	−	0.966489i	$-0.582638\pi$
$647$	−1.39608e60	−0.513414	−0.256707	+	0.966489i	$0.582638\pi$
$648$	2.91413e59	0.103669
$649$	−1.37910e60	−0.474607
$650$	4.24653e60	1.41383
$651$	1.00040e60	0.322242
$652$	1.41932e60	0.442342
$653$	5.68894e60	1.71553	0.857764	−	0.514044i	$-0.171853\pi$
$653$	5.68894e60	1.71553	0.857764	+	0.514044i	$0.171853\pi$
$654$	−1.10547e60	−0.322570
$655$	−4.40450e60	−1.24368
$656$	6.08024e59	0.166145
$657$	2.29267e59	0.0606297
$658$	1.74494e60	0.446606
$659$	−4.23342e60	−1.04871	−0.524354	−	0.851500i	$-0.675693\pi$
$659$	−4.23342e60	−1.04871	−0.524354	+	0.851500i	$0.675693\pi$
$660$	−2.23829e60	−0.536687
$661$	3.85976e60	0.895837	0.447919	−	0.894074i	$-0.352165\pi$
$661$	3.85976e60	0.895837	0.447919	+	0.894074i	$0.352165\pi$
$662$	3.21316e60	0.721914
$663$	5.57394e60	1.21233
$664$	−2.23301e60	−0.470195
$665$	3.27864e60	0.668387
$666$	−2.53191e60	−0.499750
$667$	9.08106e59	0.173553
$668$	1.24536e59	0.0230463
$669$	−6.75350e60	−1.21023
$670$	−4.20021e60	−0.728891
$671$	3.67223e60	0.617157
$672$	−3.56185e59	−0.0579743
$673$	−1.01477e61	−1.59972	−0.799859	−	0.600188i	$-0.795093\pi$
$673$	−1.01477e61	−1.59972	−0.799859	+	0.600188i	$0.795093\pi$
$674$	5.25295e59	0.0802075
$675$	1.05130e61	1.55487
$676$	3.09027e60	0.442733
$677$	−1.06619e61	−1.47971	−0.739856	−	0.672765i	$-0.765107\pi$
$677$	−1.06619e61	−1.47971	−0.739856	+	0.672765i	$0.765107\pi$
$678$	−3.85907e60	−0.518853
$679$	−2.30139e60	−0.299771
$680$	−5.36615e60	−0.677207
$681$	9.05584e60	1.10730
$682$	−5.55997e60	−0.658732
$683$	3.19343e60	0.366617	0.183308	−	0.983055i	$-0.441319\pi$
$683$	3.19343e60	0.366617	0.183308	+	0.983055i	$0.441319\pi$
$684$	2.01885e60	0.224594
$685$	1.35807e61	1.46411
$686$	−5.51176e60	−0.575867
$687$	8.21246e60	0.831579
$688$	3.83710e60	0.376575
$689$	−2.79344e61	−2.65722
$690$	1.03450e61	0.953835
$691$	−1.60049e61	−1.43045	−0.715227	−	0.698892i	$-0.753677\pi$
$691$	−1.60049e61	−1.43045	−0.715227	+	0.698892i	$0.753677\pi$
$692$	6.64663e60	0.575864
$693$	2.45031e60	0.205806
$694$	−1.08338e61	−0.882171
$695$	1.91038e61	1.50815
$696$	4.86034e59	0.0372022
$697$	1.09444e61	0.812246
$698$	1.62841e61	1.17185
$699$	−1.05024e61	−0.732876
$700$	−4.88449e60	−0.330530
$701$	1.23383e61	0.809686	0.404843	−	0.914386i	$-0.367326\pi$
$701$	1.23383e61	0.809686	0.404843	+	0.914386i	$0.367326\pi$
$702$	1.62905e61	1.03678
$703$	2.24960e61	1.38856
$704$	1.97959e60	0.118512
$705$	−2.71247e61	−1.57507
$706$	−4.36178e60	−0.245676
$707$	−2.00932e60	−0.109782
$708$	3.41145e60	0.180810
$709$	−2.92969e61	−1.50635	−0.753177	−	0.657818i	$-0.771480\pi$
$709$	−2.92969e61	−1.50635	−0.753177	+	0.657818i	$0.771480\pi$
$710$	−2.66074e61	−1.32723
$711$	4.32111e60	0.209122
$712$	5.17911e60	0.243184
$713$	2.56972e61	1.17074
$714$	−6.41131e60	−0.283423
$715$	−4.75629e61	−2.04027
$716$	1.36547e61	0.568400
$717$	−7.03590e60	−0.284222
$718$	1.45833e61	0.571716
$719$	−1.74774e61	−0.664976	−0.332488	−	0.943108i	$-0.607888\pi$
$719$	−1.74774e61	−0.664976	−0.332488	+	0.943108i	$0.607888\pi$
$720$	−5.07319e60	−0.187341
$721$	−3.51727e60	−0.126066
$722$	2.38776e60	0.0830693
$723$	−1.64690e60	−0.0556154
$724$	−1.75582e61	−0.575574
$725$	6.66517e60	0.212102
$726$	−1.67185e60	−0.0516488
$727$	1.29440e61	0.388220	0.194110	−	0.980980i	$-0.437818\pi$
$727$	1.29440e61	0.388220	0.194110	+	0.980980i	$0.437818\pi$
$728$	−7.56881e60	−0.220396
$729$	3.22429e61	0.911574
$730$	5.11885e60	0.140518
$731$	6.90677e61	1.84099
$732$	−9.08391e60	−0.235117
$733$	6.07862e61	1.52781	0.763905	−	0.645329i	$-0.223280\pi$
$733$	6.07862e61	1.52781	0.763905	+	0.645329i	$0.223280\pi$
$734$	−1.40690e61	−0.343397
$735$	3.79177e61	0.898803
$736$	−9.14930e60	−0.210627
$737$	2.78904e61	0.623597
$738$	1.03469e61	0.224698
$739$	−8.38473e61	−1.76862	−0.884308	−	0.466904i	$-0.845369\pi$
$739$	−8.38473e61	−1.76862	−0.884308	+	0.466904i	$0.845369\pi$
$740$	−5.65302e61	−1.15824
$741$	−4.68205e61	−0.931846
$742$	3.21311e61	0.621214
$743$	−4.40042e61	−0.826485	−0.413243	−	0.910621i	$-0.635604\pi$
$743$	−4.40042e61	−0.826485	−0.413243	+	0.910621i	$0.635604\pi$
$744$	1.37536e61	0.250956
$745$	2.80968e61	0.498078
$746$	−1.84795e61	−0.318277
$747$	−3.79998e61	−0.635900
$748$	3.56325e61	0.579379
$749$	2.47476e61	0.390997
$750$	2.37847e61	0.365158
$751$	−3.97940e61	−0.593689	−0.296845	−	0.954926i	$-0.595934\pi$
$751$	−3.97940e61	−0.593689	−0.296845	+	0.954926i	$0.595934\pi$
$752$	2.39897e61	0.347809
$753$	4.17480e61	0.588226
$754$	1.03281e61	0.141428
$755$	−6.87125e61	−0.914485
$756$	−1.87378e61	−0.242382
$757$	−3.21616e61	−0.404368	−0.202184	−	0.979348i	$-0.564804\pi$
$757$	−3.21616e61	−0.404368	−0.202184	+	0.979348i	$0.564804\pi$
$758$	−2.51858e61	−0.307799
$759$	−6.86931e61	−0.816046
$760$	4.50751e61	0.520528
$761$	2.87614e61	0.322879	0.161439	−	0.986883i	$-0.448386\pi$
$761$	2.87614e61	0.322879	0.161439	+	0.986883i	$0.448386\pi$
$762$	−6.30450e61	−0.688048
$763$	2.70198e61	0.286685
$764$	−6.60413e60	−0.0681253
$765$	−9.13173e61	−0.915866
$766$	6.81219e61	0.664306
$767$	7.24922e61	0.687370
$768$	−4.89687e60	−0.0451494
$769$	1.35777e61	0.121734	0.0608669	−	0.998146i	$-0.480613\pi$
$769$	1.35777e61	0.121734	0.0608669	+	0.998146i	$0.480613\pi$
$770$	5.47083e61	0.476983
$771$	4.44513e61	0.376890
$772$	3.45327e61	0.284747
$773$	−3.10392e61	−0.248915	−0.124458	−	0.992225i	$-0.539719\pi$
$773$	−3.10392e61	−0.248915	−0.124458	+	0.992225i	$0.539719\pi$
$774$	6.52970e61	0.509287
$775$	1.88608e62	1.43078
$776$	−3.16397e61	−0.233456
$777$	−6.75406e61	−0.484744
$778$	−8.25269e61	−0.576148
$779$	−9.19319e61	−0.624325
$780$	1.17655e62	0.777281
$781$	1.76679e62	1.13550
$782$	−1.64687e62	−1.02971
$783$	2.55688e61	0.155536
$784$	−3.35352e61	−0.198475
$785$	−4.03871e61	−0.232565
$786$	−7.23475e61	−0.405358
$787$	8.37357e61	0.456514	0.228257	−	0.973601i	$-0.426697\pi$
$787$	8.37357e61	0.456514	0.228257	+	0.973601i	$0.426697\pi$
$788$	−1.01810e62	−0.540101
$789$	1.04867e62	0.541354
$790$	9.64778e61	0.484669
$791$	9.43236e61	0.461133
$792$	3.36872e61	0.160278
$793$	−1.93030e62	−0.893824
$794$	−2.25106e62	−1.01449
$795$	−4.99470e62	−2.19087
$796$	1.03410e62	0.441500
$797$	−1.76667e62	−0.734180	−0.367090	−	0.930185i	$-0.619646\pi$
$797$	−1.76667e62	−0.734180	−0.367090	+	0.930185i	$0.619646\pi$
$798$	5.38543e61	0.217850
$799$	4.31813e62	1.70036
$800$	−6.71525e61	−0.257411
$801$	8.81344e61	0.328887
$802$	−2.94983e62	−1.07164
$803$	−3.39904e61	−0.120219
$804$	−6.89920e61	−0.237571
$805$	−2.52852e62	−0.847725
$806$	2.92260e62	0.954037
$807$	2.07757e62	0.660352
$808$	−2.76244e61	−0.0854965
$809$	4.77106e62	1.43788	0.718938	−	0.695074i	$-0.244628\pi$
$809$	4.77106e62	1.43788	0.718938	+	0.695074i	$0.244628\pi$
$810$	1.10721e62	0.324940
$811$	−5.23958e62	−1.49743	−0.748717	−	0.662890i	$-0.769330\pi$
$811$	−5.23958e62	−1.49743	−0.748717	+	0.662890i	$0.769330\pi$
$812$	−1.18797e61	−0.0330636
$813$	2.99270e62	0.811179
$814$	3.75374e62	0.990923
$815$	5.39266e62	1.38648
$816$	−8.81435e61	−0.220725
$817$	−5.80162e62	−1.41506
$818$	4.86933e62	1.15684
$819$	−1.28801e62	−0.298067
$820$	2.31016e62	0.520768
$821$	−1.29314e62	−0.283968	−0.141984	−	0.989869i	$-0.545348\pi$
$821$	−1.29314e62	−0.283968	−0.141984	+	0.989869i	$0.545348\pi$
$822$	2.23073e62	0.477204
$823$	4.99113e62	1.04016	0.520082	−	0.854116i	$-0.325901\pi$
$823$	4.99113e62	1.04016	0.520082	+	0.854116i	$0.325901\pi$
$824$	−4.83559e61	−0.0981780
$825$	−5.04182e62	−0.997304
$826$	−8.33827e61	−0.160696
$827$	−9.44817e61	−0.177410	−0.0887052	−	0.996058i	$-0.528273\pi$
$827$	−9.44817e61	−0.177410	−0.0887052	+	0.996058i	$0.528273\pi$
$828$	−1.55696e62	−0.284856
$829$	−8.58776e62	−1.53094	−0.765469	−	0.643473i	$-0.777493\pi$
$829$	−8.58776e62	−1.53094	−0.765469	+	0.643473i	$0.777493\pi$
$830$	−8.48425e62	−1.47379
$831$	2.66688e62	0.451420
$832$	−1.04057e62	−0.171640
$833$	−6.03633e62	−0.970299
$834$	3.13795e62	0.491560
$835$	4.73169e61	0.0722366
$836$	−2.99310e62	−0.445334
$837$	7.23535e62	1.04921
$838$	−5.89731e62	−0.833504
$839$	1.14529e63	1.57773	0.788863	−	0.614569i	$-0.210670\pi$
$839$	1.14529e63	1.57773	0.788863	+	0.614569i	$0.210670\pi$
$840$	−1.35331e62	−0.181716
$841$	−7.47826e62	−0.978783
$842$	6.96411e62	0.888496
$843$	−7.25830e62	−0.902697
$844$	4.21932e61	0.0511540
$845$	1.17413e63	1.38771
$846$	4.08239e62	0.470383
$847$	4.08635e61	0.0459031
$848$	4.41741e62	0.483790
$849$	9.53930e62	1.01859
$850$	−1.20874e63	−1.25843
$851$	−1.73491e63	−1.76113
$852$	−4.37048e62	−0.432592
$853$	3.37317e62	0.325562	0.162781	−	0.986662i	$-0.447954\pi$
$853$	3.37317e62	0.325562	0.162781	+	0.986662i	$0.447954\pi$
$854$	2.22029e62	0.208962
$855$	7.67055e62	0.703972
$856$	3.40233e62	0.304502
$857$	7.32198e62	0.639059	0.319530	−	0.947576i	$-0.396475\pi$
$857$	7.32198e62	0.639059	0.319530	+	0.947576i	$0.396475\pi$
$858$	−7.81261e62	−0.664996
$859$	1.05145e63	0.872844	0.436422	−	0.899742i	$-0.356246\pi$
$859$	1.05145e63	0.872844	0.436422	+	0.899742i	$0.356246\pi$
$860$	1.45789e63	1.18034
$861$	2.76011e62	0.217951
$862$	−9.38318e62	−0.722677
$863$	−1.87788e63	−1.41071	−0.705353	−	0.708856i	$-0.749211\pi$
$863$	−1.87788e63	−1.41071	−0.705353	+	0.708856i	$0.749211\pi$
$864$	−2.57609e62	−0.188763
$865$	2.52536e63	1.80500
$866$	−7.10395e61	−0.0495297
$867$	−5.24438e62	−0.356684
$868$	−3.36166e62	−0.223038
$869$	−6.40636e62	−0.414654
$870$	1.84667e62	0.116607
$871$	−1.46606e63	−0.903152
$872$	3.71472e62	0.223265
$873$	−5.38422e62	−0.315731
$874$	1.38335e63	0.791476
$875$	−5.81347e62	−0.324535
$876$	8.40814e61	0.0457996
$877$	−1.22772e63	−0.652541	−0.326270	−	0.945276i	$-0.605792\pi$
$877$	−1.22772e63	−0.652541	−0.326270	+	0.945276i	$0.605792\pi$
$878$	1.77726e63	0.921760
$879$	1.33642e61	0.00676369
$880$	7.52136e62	0.371466
$881$	−2.09648e63	−1.01044	−0.505219	−	0.862991i	$-0.668588\pi$
$881$	−2.09648e63	−1.01044	−0.505219	+	0.862991i	$0.668588\pi$
$882$	−5.70678e62	−0.268421
$883$	−3.97564e63	−1.82495	−0.912477	−	0.409128i	$-0.865833\pi$
$883$	−3.97564e63	−1.82495	−0.912477	+	0.409128i	$0.865833\pi$
$884$	−1.87302e63	−0.839110
$885$	1.29617e63	0.566735
$886$	−1.49771e63	−0.639151
$887$	2.03352e63	0.847012	0.423506	−	0.905893i	$-0.360799\pi$
$887$	2.03352e63	0.847012	0.423506	+	0.905893i	$0.360799\pi$
$888$	−9.28556e62	−0.377511
$889$	1.54095e63	0.611505
$890$	1.96778e63	0.762240
$891$	−7.35217e62	−0.278000
$892$	2.26939e63	0.837655
$893$	−3.62719e63	−1.30696
$894$	4.61514e62	0.162341
$895$	5.18807e63	1.78160
$896$	1.19689e62	0.0401267
$897$	3.61084e63	1.18187
$898$	1.08950e62	0.0348165
$899$	4.58718e62	0.143124
$900$	−1.14275e63	−0.348128
$901$	7.95133e63	2.36514
$902$	−1.53400e63	−0.445539
$903$	1.74184e63	0.493995
$904$	1.29677e63	0.359122
$905$	−6.67117e63	−1.80409
$906$	−1.12866e63	−0.298062
$907$	−6.09664e63	−1.57229	−0.786147	−	0.618039i	$-0.787927\pi$
$907$	−6.09664e63	−1.57229	−0.786147	+	0.618039i	$0.787927\pi$
$908$	−3.04305e63	−0.766415
$909$	−4.70092e62	−0.115627
$910$	−2.87574e63	−0.690811
$911$	4.57893e63	1.07428	0.537141	−	0.843492i	$-0.319504\pi$
$911$	4.57893e63	1.07428	0.537141	+	0.843492i	$0.319504\pi$
$912$	7.40396e62	0.169658
$913$	5.63375e63	1.26089
$914$	4.91687e63	1.07484
$915$	−3.45140e63	−0.736955
$916$	−2.75965e63	−0.575574
$917$	1.76832e63	0.360264
$918$	−4.63696e63	−0.922818
$919$	4.02894e63	0.783262	0.391631	−	0.920122i	$-0.371911\pi$
$919$	4.02894e63	0.783262	0.391631	+	0.920122i	$0.371911\pi$
$920$	−3.47624e63	−0.660194
$921$	−5.11377e63	−0.948766
$922$	2.43555e63	0.441451
$923$	−9.28714e63	−1.64454
$924$	8.98630e62	0.155465
$925$	−1.27336e64	−2.15231
$926$	2.99082e63	0.493917
$927$	−8.22885e62	−0.132778
$928$	−1.63323e62	−0.0257493
$929$	7.64195e63	1.17724	0.588622	−	0.808408i	$-0.299671\pi$
$929$	7.64195e63	1.17724	0.588622	+	0.808408i	$0.299671\pi$
$930$	5.22562e63	0.786601
$931$	5.07046e63	0.745811
$932$	3.52916e63	0.507258
$933$	−8.10325e63	−1.13816
$934$	−4.06738e63	−0.558286
$935$	1.35384e64	1.81601
$936$	−1.77077e63	−0.232129
$937$	4.86207e63	0.622903	0.311451	−	0.950262i	$-0.399185\pi$
$937$	4.86207e63	0.622903	0.311451	+	0.950262i	$0.399185\pi$
$938$	1.68630e63	0.211142
$939$	5.55285e63	0.679526
$940$	9.11478e63	1.09018
$941$	−3.00329e63	−0.351092	−0.175546	−	0.984471i	$-0.556169\pi$
$941$	−3.00329e63	−0.351092	−0.175546	+	0.984471i	$0.556169\pi$
$942$	−6.63391e62	−0.0758011
$943$	7.08989e63	0.791841
$944$	−1.14636e63	−0.125147
$945$	−7.11935e63	−0.759725
$946$	−9.68075e63	−1.00983
$947$	−1.08153e64	−1.10284	−0.551422	−	0.834226i	$-0.685915\pi$
$947$	−1.08153e64	−1.10284	−0.551422	+	0.834226i	$0.685915\pi$
$948$	1.58473e63	0.157970
$949$	1.78670e63	0.174112
$950$	1.01533e64	0.967276
$951$	−1.12879e63	−0.105131
$952$	2.15441e63	0.196170
$953$	−1.03034e64	−0.917237	−0.458619	−	0.888633i	$-0.651656\pi$
$953$	−1.03034e64	−0.917237	−0.458619	+	0.888633i	$0.651656\pi$
$954$	7.51724e63	0.654287
$955$	−2.50921e63	−0.213533
$956$	2.36429e63	0.196723
$957$	−1.22623e63	−0.0997622
$958$	−1.45279e63	−0.115570
$959$	−5.45237e63	−0.424117
$960$	−1.86054e63	−0.141517
$961$	−4.64150e62	−0.0345227
$962$	−1.97315e64	−1.43515
$963$	5.78983e63	0.411814
$964$	5.53413e62	0.0384940
$965$	1.31206e64	0.892515
$966$	−4.15331e63	−0.276303
$967$	2.18440e63	0.142122	0.0710612	−	0.997472i	$-0.477361\pi$
$967$	2.18440e63	0.142122	0.0710612	+	0.997472i	$0.477361\pi$
$968$	5.61796e62	0.0357486
$969$	1.33271e64	0.829420
$970$	−1.20214e64	−0.731749
$971$	−8.26509e63	−0.492078	−0.246039	−	0.969260i	$-0.579129\pi$
$971$	−8.26509e63	−0.492078	−0.246039	+	0.969260i	$0.579129\pi$
$972$	−7.34955e63	−0.427992
$973$	−7.66980e63	−0.436876
$974$	−9.49103e63	−0.528805
$975$	2.65023e64	1.44439
$976$	3.05249e63	0.162736
$977$	−1.47278e64	−0.768078	−0.384039	−	0.923317i	$-0.625467\pi$
$977$	−1.47278e64	−0.768078	−0.384039	+	0.923317i	$0.625467\pi$
$978$	8.85790e63	0.451903
$979$	−1.30665e64	−0.652128
$980$	−1.27416e64	−0.622103
$981$	6.32144e63	0.301948
$982$	1.49196e64	0.697202
$983$	3.00159e64	1.37231	0.686153	−	0.727457i	$-0.259298\pi$
$983$	3.00159e64	1.37231	0.686153	+	0.727457i	$0.259298\pi$
$984$	3.79463e63	0.169736
$985$	−3.86822e64	−1.69290
$986$	−2.93981e63	−0.125883
$987$	1.08901e64	0.456259
$988$	1.57332e64	0.644974
$989$	4.47427e64	1.79474
$990$	1.27993e64	0.502377
$991$	−3.15959e64	−1.21352	−0.606760	−	0.794885i	$-0.707531\pi$
$991$	−3.15959e64	−1.21352	−0.606760	+	0.794885i	$0.707531\pi$
$992$	−4.62165e63	−0.173698
$993$	2.00531e64	0.737518
$994$	1.06824e64	0.384468
$995$	3.92902e64	1.38385
$996$	−1.39361e64	−0.480358
$997$	−1.16979e64	−0.394605	−0.197302	−	0.980343i	$-0.563218\pi$
$997$	−1.16979e64	−0.394605	−0.197302	+	0.980343i	$0.563218\pi$
$998$	2.75483e64	0.909470
$999$	−4.88485e64	−1.57831

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.44.a.a.1.1	✓	2
3.2	odd	2		18.44.a.e.1.1		2
4.3	odd	2		16.44.a.a.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.44.a.a.1.1	✓	2	1.1	even	1	trivial
16.44.a.a.1.2		2	4.3	odd	2
18.44.a.e.1.1		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 44 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q-2.09715e6 q^{2} -1.30882e10 q^{3} +4.39805e12 q^{4} +1.67102e15 q^{5} +2.74479e16 q^{6} -6.70883e17 q^{7} -9.22337e18 q^{8} -1.56957e20 q^{9} +O(q^{10})\)	\(q-2.09715e6 q^{2} -1.30882e10 q^{3} +4.39805e12 q^{4} +1.67102e15 q^{5} +2.74479e16 q^{6} -6.70883e17 q^{7} -9.22337e18 q^{8} -1.56957e20 q^{9} -3.50438e21 q^{10} +2.32700e22 q^{11} -5.75624e22 q^{12} -1.22318e24 q^{13} +1.40694e24 q^{14} -2.18706e25 q^{15} +1.93428e25 q^{16} +3.48170e26 q^{17} +3.29162e26 q^{18} -2.92459e27 q^{19} +7.34922e27 q^{20} +8.78063e27 q^{21} -4.88006e28 q^{22} +2.25548e29 q^{23} +1.20717e29 q^{24} +1.65544e30 q^{25} +2.56520e30 q^{26} +6.35056e30 q^{27} -2.95057e30 q^{28} +4.02623e30 q^{29} +4.58660e31 q^{30} +1.13932e32 q^{31} -4.05648e31 q^{32} -3.04561e32 q^{33} -7.30166e32 q^{34} -1.12106e33 q^{35} -6.90303e32 q^{36} -7.69200e33 q^{37} +6.13331e33 q^{38} +1.60092e34 q^{39} -1.54124e34 q^{40} +3.14341e34 q^{41} -1.84143e34 q^{42} +1.98374e35 q^{43} +1.02342e35 q^{44} -2.62278e35 q^{45} -4.73008e35 q^{46} +1.24024e36 q^{47} -2.53162e35 q^{48} -1.73373e36 q^{49} -3.47171e36 q^{50} -4.55691e36 q^{51} -5.37962e36 q^{52} +2.28375e37 q^{53} -1.33181e37 q^{54} +3.88845e37 q^{55} +6.18780e36 q^{56} +3.82776e37 q^{57} -8.44361e36 q^{58} -5.92652e37 q^{59} -9.61879e37 q^{60} +1.57810e38 q^{61} -2.38934e38 q^{62} +1.05300e38 q^{63} +8.50706e37 q^{64} -2.04396e39 q^{65} +6.38711e38 q^{66} +1.19856e39 q^{67} +1.53127e39 q^{68} -2.95201e39 q^{69} +2.35103e39 q^{70} +7.59260e39 q^{71} +1.44767e39 q^{72} -1.46070e39 q^{73} +1.61313e40 q^{74} -2.16667e40 q^{75} -1.28625e40 q^{76} -1.56114e40 q^{77} -3.35738e40 q^{78} -2.75306e40 q^{79} +3.23222e40 q^{80} -3.15951e40 q^{81} -6.59221e40 q^{82} +2.42104e41 q^{83} +3.86176e40 q^{84} +5.81799e41 q^{85} -4.16019e41 q^{86} -5.26959e40 q^{87} -2.14627e41 q^{88} -5.61520e41 q^{89} +5.50036e41 q^{90} +8.20612e41 q^{91} +9.91969e41 q^{92} -1.49117e42 q^{93} -2.60097e42 q^{94} -4.88705e42 q^{95} +5.30919e41 q^{96} +3.43039e42 q^{97} +3.63590e42 q^{98} -3.65237e42 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4194304 q^{2} - 12981630984 q^{3} + 8796093022208 q^{4} - 398662711282500 q^{5} + 27\!\cdots\!68 q^{6}+ \cdots - 48\!\cdots\!26 q^{9}+O(q^{10}) \) 2 * q - 4194304 * q^2 - 12981630984 * q^3 + 8796093022208 * q^4 - 398662711282500 * q^5 + 27224453381357568 * q^6 + 1174870033543241008 * q^7 - 18446744073709551616 * q^8 - 485202301172100019926 * q^9	\( 2 q - 4194304 q^{2} - 12981630984 q^{3} + 8796093022208 q^{4} - 398662711282500 q^{5} + 27\!\cdots\!68 q^{6}+ \cdots + 77\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q - 4194304 * q^2 - 12981630984 * q^3 + 8796093022208 * q^4 - 398662711282500 * q^5 + 27224453381357568 * q^6 + 1174870033543241008 * q^7 - 18446744073709551616 * q^8 - 485202301172100019926 * q^9 + 836056302291517440000 * q^10 - 11617807872020797407576 * q^11 - 57093816857620786446336 * q^12 - 1658879102786318366273684 * q^13 - 2463881040585274966409216 * q^14 - 22091103207013849606710000 * q^15 + 38685626227668133590597632 * q^16 + 343161409966024505905818468 * q^17 + 1017542976307671900987850752 * q^18 - 526535613098348151618559400 * q^19 - 1753337146463260382330880000 * q^20 + 8977278711349595999815289664 * q^21 + 24364309014424159324892823552 * q^22 + 229455981723979198172770632336 * q^23 + 119734412210593147537506435072 * q^24 + 4802154653491374627549005468750 * q^25 + 3478921628166533134467588947968 * q^26 + 6280615052012507617464674387760 * q^27 + 5167133052025490566355020152832 * q^28 + 34136150491106942855372319350220 * q^29 + 46328401272795508730411089920000 * q^30 + 162309856447038824698827315968704 * q^31 - 81129638414606681695789005144064 * q^32 - 308278184912318274174336905435808 * q^33 - 719661637233068224609399011803136 * q^34 - 4941179569454425103779106953980000 * q^35 - 2133942287849586742500473180258304 * q^36 - 4391607431868635112322899638873732 * q^37 + 1104225214080427022863165082828800 * q^38 + 15962811619464040671516159652622928 * q^39 + 3677014503379719437325969653760000 * q^40 + 73274473482816660070587986010183924 * q^41 - 18826718004064227950204634349436928 * q^42 + 234436585898994103006598707127282536 * q^43 - 51095659378217654576517634697723904 * q^44 + 417086449135320077301667307984347500 * q^45 - 481204070984406423406422277144707072 * q^46 - 39114598548473932831256802726900192 * q^47 - 251101262036269840544576695324114944 * q^48 - 510742495035301170011177769547783854 * q^49 - 10070848235878743282913651916800000000 * q^50 - 4557444784421248830689881595224595856 * q^51 - 7295827450352701296014973097408987136 * q^52 + 21441800128967176515730209034915502556 * q^53 - 13171404417558134374981276821639659520 * q^54 + 111091123730229295314448534371395310000 * q^55 - 10836263414321361592212563223551934464 * q^56 + 38533058136217827264209989537628772000 * q^57 - 71588696274725907423029770269952573440 * q^58 + 67981786423576245191970112954336157640 * q^59 - 97157699386045646724999078047907840000 * q^60 + 10550869229810756555782264236051582604 * q^61 - 340388440067620365294795103338399531008 * q^62 - 500560701761315054164921401424721593104 * q^63 + 170141183460469231731687303715884105728 * q^64 - 1142210409763957682754357764765378535000 * q^65 + 646506212045238093321258989908515618816 * q^66 - 1296008696996439884699343907691487049352 * q^67 + 1509239841846603493376050356400970268672 * q^68 - 2951590658050920771532689933244706114112 * q^69 + 10362404616440486515240561706753064960000 * q^70 + 10578336400277808016654999978615404825264 * q^71 + 4475201336848336536208352330925062750208 * q^72 - 1083714960819479223422811781189857230924 * q^73 + 9209868308958171863078193623463324811264 * q^74 - 21331402709079687390002224676411221875000 * q^75 - 2315728116159195691851532379784583577600 * q^76 - 80005579389320632459943851192412711459904 * q^77 - 33476442313382251822351457247817478701056 * q^78 - 66782694077687545008302637975280595820320 * q^79 - 7711258319791785377427031911322091520000 * q^80 + 76146348151673377566388577586168400203282 * q^81 - 153667708613435924300353736037229236584448 * q^82 + 549648200704305895621526521126723031888856 * q^83 + 39482489315659303774227549335190352429056 * q^84 + 592165605546979682092570996796433568995000 * q^85 - 491649154991247281108494491849394824937472 * q^86 - 49487960387866633050295824495906154497840 * q^87 + 107155364256347910730453110641601080721408 * q^88 + 298108448661015962080672472021181983545620 * q^89 - 874693680977034770753346198273990328320000 * q^90 + 16425068484305226748514962047001570578464 * q^91 + 1009158079873089899659625291358576725458944 * q^92 - 1486013428111370066200804977498842194176768 * q^93 + 82029258575129205184935866352324191453184 * q^94 - 9850264420679630550524982943635697915950000 * q^95 + 526597513881887368637740105752358303039488 * q^96 - 2275344922279044236600118263254186752839612 * q^97 + 1071104644948271919291281481762674004983808 * q^98 + 7799379619136501162487578778863682680428488 * q^99

Introduction

L-functions

Modular forms

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Properties

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