LMFDB - Embedded newform 2.44.a.a.1.2

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			1.2
Root			$-156187.$ 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)

$f(q)$	$=$	$q-2.09715e6 q^{2} +1.06542e8 q^{3} +4.39805e12 q^{4} -2.06968e15 q^{5} -2.23436e14 q^{6} +1.84575e18 q^{7} -9.22337e18 q^{8} -3.28246e20 q^{9} +O(q^{10})$	\(q-2.09715e6 q^{2} +1.06542e8 q^{3} +4.39805e12 q^{4} -2.06968e15 q^{5} -2.23436e14 q^{6} +1.84575e18 q^{7} -9.22337e18 q^{8} -3.28246e20 q^{9} +4.34044e21 q^{10} -3.48878e22 q^{11} +4.68578e20 q^{12} -4.35696e23 q^{13} -3.87082e24 q^{14} -2.20509e23 q^{15} +1.93428e25 q^{16} -5.00873e24 q^{17} +6.88381e26 q^{18} +2.39806e27 q^{19} -9.10256e27 q^{20} +1.96651e26 q^{21} +7.31649e28 q^{22} +3.90831e27 q^{23} -9.82680e26 q^{24} +3.14672e30 q^{25} +9.13721e29 q^{26} -6.99454e28 q^{27} +8.11771e30 q^{28} +3.01099e31 q^{29} +4.62441e29 q^{30} +4.83774e31 q^{31} -4.05648e31 q^{32} -3.71703e30 q^{33} +1.05041e31 q^{34} -3.82012e33 q^{35} -1.44364e33 q^{36} +3.30039e33 q^{37} -5.02909e33 q^{38} -4.64201e31 q^{39} +1.90894e34 q^{40} +4.18404e34 q^{41} -4.12407e32 q^{42} +3.60631e34 q^{43} -1.53438e35 q^{44} +6.79364e35 q^{45} -8.19632e33 q^{46} -1.27935e36 q^{47} +2.06083e33 q^{48} +1.22299e36 q^{49} -6.59914e36 q^{50} -5.33642e32 q^{51} -1.91621e36 q^{52} -1.39570e36 q^{53} +1.46686e35 q^{54} +7.22066e37 q^{55} -1.70241e37 q^{56} +2.55495e35 q^{57} -6.31451e37 q^{58} +1.27247e38 q^{59} -9.69808e35 q^{60} -1.47259e38 q^{61} -1.01455e38 q^{62} -6.05860e38 q^{63} +8.50706e37 q^{64} +9.01752e38 q^{65} +7.79517e36 q^{66} -2.49457e39 q^{67} -2.20286e37 q^{68} +4.16400e35 q^{69} +8.01138e39 q^{70} +2.98574e39 q^{71} +3.02753e39 q^{72} +3.76985e38 q^{73} -6.92142e39 q^{74} +3.35259e38 q^{75} +1.05468e40 q^{76} -6.43942e40 q^{77} +9.73500e37 q^{78} -3.92521e40 q^{79} -4.00335e40 q^{80} +1.07741e41 q^{81} -8.77456e40 q^{82} +3.07544e41 q^{83} +8.64880e38 q^{84} +1.03665e40 q^{85} -7.56297e40 q^{86} +3.20798e39 q^{87} +3.21783e41 q^{88} +8.59629e41 q^{89} -1.42473e42 q^{90} -8.04187e41 q^{91} +1.71889e40 q^{92} +5.15424e39 q^{93} +2.68299e42 q^{94} -4.96321e42 q^{95} -4.32187e39 q^{96} -5.70573e42 q^{97} -2.56479e42 q^{98} +1.14518e43 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.06542e8	0.00588052	0.00294026	−	0.999996i	$-0.499064\pi$
$3$	1.06542e8	0.00588052	0.00294026	+	0.999996i	$0.499064\pi$
$4$	4.39805e12	0.500000
$5$	−2.06968e15	−1.94110	−0.970552	−	0.240894i	$-0.922560\pi$
$5$	−2.06968e15	−1.94110	−0.970552	+	0.240894i	$0.922560\pi$
$6$	−2.23436e14	−0.00415815
$7$	1.84575e18	1.24901	0.624505	−	0.781021i	$-0.285301\pi$
$7$	1.84575e18	1.24901	0.624505	+	0.781021i	$0.285301\pi$
$8$	−9.22337e18	−0.353553
$9$	−3.28246e20	−0.999965
$10$	4.34044e21	1.37257
$11$	−3.48878e22	−1.42145	−0.710723	−	0.703472i	$-0.751632\pi$
$11$	−3.48878e22	−1.42145	−0.710723	+	0.703472i	$0.751632\pi$
$12$	4.68578e20	0.00294026
$13$	−4.35696e23	−0.489104	−0.244552	−	0.969636i	$-0.578641\pi$
$13$	−4.35696e23	−0.489104	−0.244552	+	0.969636i	$0.578641\pi$
$14$	−3.87082e24	−0.883183
$15$	−2.20509e23	−0.0114147
$16$	1.93428e25	0.250000
$17$	−5.00873e24	−0.0175823	−0.00879115	−	0.999961i	$-0.502798\pi$
$17$	−5.00873e24	−0.0175823	−0.00879115	+	0.999961i	$0.502798\pi$
$18$	6.88381e26	0.707082
$19$	2.39806e27	0.770295	0.385147	−	0.922855i	$-0.374151\pi$
$19$	2.39806e27	0.770295	0.385147	+	0.922855i	$0.374151\pi$
$20$	−9.10256e27	−0.970552
$21$	1.96651e26	0.00734482
$22$	7.31649e28	1.00511
$23$	3.90831e27	0.0206462	0.0103231	−	0.999947i	$-0.496714\pi$
$23$	3.90831e27	0.0206462	0.0103231	+	0.999947i	$0.496714\pi$
$24$	−9.82680e26	−0.00207908
$25$	3.14672e30	2.76788
$26$	9.13721e29	0.345849
$27$	−6.99454e28	−0.0117608
$28$	8.11771e30	0.624505
$29$	3.01099e31	1.08931	0.544657	−	0.838659i	$-0.316660\pi$
$29$	3.01099e31	1.08931	0.544657	+	0.838659i	$0.316660\pi$
$30$	4.62441e29	0.00807140
$31$	4.83774e31	0.417221	0.208610	−	0.977999i	$-0.433106\pi$
$31$	4.83774e31	0.417221	0.208610	+	0.977999i	$0.433106\pi$
$32$	−4.05648e31	−0.176777
$33$	−3.71703e30	−0.00835884
$34$	1.05041e31	0.0124326
$35$	−3.82012e33	−2.42446
$36$	−1.44364e33	−0.499983
$37$	3.30039e33	0.634203	0.317102	−	0.948392i	$-0.397290\pi$
$37$	3.30039e33	0.634203	0.317102	+	0.948392i	$0.397290\pi$
$38$	−5.02909e33	−0.544681
$39$	−4.64201e31	−0.00287619
$40$	1.90894e34	0.686284
$41$	4.18404e34	0.884591	0.442296	−	0.896869i	$-0.354164\pi$
$41$	4.18404e34	0.884591	0.442296	+	0.896869i	$0.354164\pi$
$42$	−4.12407e32	−0.00519357
$43$	3.60631e34	0.273836	0.136918	−	0.990582i	$-0.456280\pi$
$43$	3.60631e34	0.273836	0.136918	+	0.990582i	$0.456280\pi$
$44$	−1.53438e35	−0.710723
$45$	6.79364e35	1.94104
$46$	−8.19632e33	−0.0145991
$47$	−1.27935e36	−1.43511	−0.717556	−	0.696501i	$-0.754739\pi$
$47$	−1.27935e36	−1.43511	−0.717556	+	0.696501i	$0.754739\pi$
$48$	2.06083e33	0.00147013
$49$	1.22299e36	0.560024
$50$	−6.59914e36	−1.95719
$51$	−5.33642e32	−0.000103393 0
$52$	−1.91621e36	−0.244552
$53$	−1.39570e36	−0.118266	−0.0591330	−	0.998250i	$-0.518834\pi$
$53$	−1.39570e36	−0.118266	−0.0591330	+	0.998250i	$0.518834\pi$
$54$	1.46686e35	0.00831616
$55$	7.22066e37	2.75917
$56$	−1.70241e37	−0.441591
$57$	2.55495e35	0.00452973
$58$	−6.31451e37	−0.770261
$59$	1.27247e38	1.07480	0.537402	−	0.843326i	$-0.319406\pi$
$59$	1.27247e38	1.07480	0.537402	+	0.843326i	$0.319406\pi$
$60$	−9.69808e35	−0.00570734
$61$	−1.47259e38	−0.607422	−0.303711	−	0.952764i	$-0.598226\pi$
$61$	−1.47259e38	−0.607422	−0.303711	+	0.952764i	$0.598226\pi$
$62$	−1.01455e38	−0.295020
$63$	−6.05860e38	−1.24897
$64$	8.50706e37	0.125000
$65$	9.01752e38	0.949402
$66$	7.79517e36	0.00591059
$67$	−2.49457e39	−1.36895	−0.684474	−	0.729037i	$-0.739968\pi$
$67$	−2.49457e39	−1.36895	−0.684474	+	0.729037i	$0.739968\pi$
$68$	−2.20286e37	−0.00879115
$69$	4.16400e35	0.000121410 0
$70$	8.01138e39	1.71435
$71$	2.98574e39	0.470974	0.235487	−	0.971877i	$-0.424331\pi$
$71$	2.98574e39	0.470974	0.235487	+	0.971877i	$0.424331\pi$
$72$	3.02753e39	0.353541
$73$	3.76985e38	0.0327252	0.0163626	−	0.999866i	$-0.494791\pi$
$73$	3.76985e38	0.0327252	0.0163626	+	0.999866i	$0.494791\pi$
$74$	−6.92142e39	−0.448449
$75$	3.35259e38	0.0162766
$76$	1.05468e40	0.385147
$77$	−6.43942e40	−1.77540
$78$	9.73500e37	0.00203377
$79$	−3.92521e40	−0.623563	−0.311781	−	0.950154i	$-0.600926\pi$
$79$	−3.92521e40	−0.623563	−0.311781	+	0.950154i	$0.600926\pi$
$80$	−4.00335e40	−0.485276
$81$	1.07741e41	0.999896
$82$	−8.77456e40	−0.625500
$83$	3.07544e41	1.68939	0.844693	−	0.535252i	$-0.179783\pi$
$83$	3.07544e41	1.68939	0.844693	+	0.535252i	$0.179783\pi$
$84$	8.64880e38	0.00367241
$85$	1.03665e40	0.0341291
$86$	−7.56297e40	−0.193631
$87$	3.20798e39	0.00640572
$88$	3.21783e41	0.502557
$89$	8.59629e41	1.05299	0.526497	−	0.850177i	$-0.323505\pi$
$89$	8.59629e41	1.05299	0.526497	+	0.850177i	$0.323505\pi$
$90$	−1.42473e42	−1.37252
$91$	−8.04187e41	−0.610896
$92$	1.71889e40	0.0103231
$93$	5.15424e39	0.00245347
$94$	2.68299e42	1.01478
$95$	−4.96321e42	−1.49522
$96$	−4.32187e39	−0.00103954
$97$	−5.70573e42	−1.09830	−0.549148	−	0.835725i	$-0.685047\pi$
$97$	−5.70573e42	−1.09830	−0.549148	+	0.835725i	$0.685047\pi$
$98$	−2.56479e42	−0.395997
$99$	1.14518e43	1.42140
$100$	1.38394e43	1.38394
$101$	−1.05999e42	−0.0855842	−0.0427921	−	0.999084i	$-0.513625\pi$
$101$	−1.05999e42	−0.0855842	−0.0427921	+	0.999084i	$0.513625\pi$
$102$	1.11913e39	7.31099e−5 0
$103$	6.46081e42	0.342205	0.171103	−	0.985253i	$-0.445267\pi$
$103$	6.46081e42	0.342205	0.171103	+	0.985253i	$0.445267\pi$
$104$	4.01859e42	0.172925
$105$	−4.07005e41	−0.0142571
$106$	2.92699e42	0.0836267
$107$	−2.23888e43	−0.522733	−0.261366	−	0.965240i	$-0.584173\pi$
$107$	−2.23888e43	−0.522733	−0.261366	+	0.965240i	$0.584173\pi$
$108$	−3.07623e41	−0.00588041
$109$	−3.44429e43	−0.540045	−0.270022	−	0.962854i	$-0.587031\pi$
$109$	−3.44429e43	−0.540045	−0.270022	+	0.962854i	$0.587031\pi$
$110$	−1.51428e44	−1.95103
$111$	3.51632e41	0.00372944
$112$	3.57020e43	0.312252
$113$	1.79557e44	1.29723	0.648613	−	0.761118i	$-0.275349\pi$
$113$	1.79557e44	1.29723	0.648613	+	0.761118i	$0.275349\pi$
$114$	−5.35811e41	−0.00320300
$115$	−8.08896e42	−0.0400764
$116$	1.32425e44	0.544657
$117$	1.43015e44	0.489087
$118$	−2.66856e44	−0.760001
$119$	−9.24487e42	−0.0219605
$120$	2.03384e42	0.00403570
$121$	6.14755e44	1.02051
$122$	3.08825e44	0.429512
$123$	4.45777e42	0.00520185
$124$	2.12766e44	0.208610
$125$	−4.15975e45	−3.43164
$126$	1.27058e45	0.883152
$127$	2.00065e45	1.17325	0.586626	−	0.809858i	$-0.300456\pi$
$127$	2.00065e45	1.17325	0.586626	+	0.809858i	$0.300456\pi$
$128$	−1.78406e44	−0.0883883
$129$	3.84224e42	0.00161030
$130$	−1.89111e45	−0.671329
$131$	−4.83548e45	−1.45582	−0.727909	−	0.685674i	$-0.759508\pi$
$131$	−4.83548e45	−1.45582	−0.727909	+	0.685674i	$0.759508\pi$
$132$	−1.63477e43	−0.00417942
$133$	4.42622e45	0.962105
$134$	5.23149e45	0.967993
$135$	1.44765e44	0.0228290
$136$	4.61974e43	0.00621628
$137$	1.55654e46	1.78924	0.894618	−	0.446832i	$-0.147448\pi$
$137$	1.55654e46	1.78924	0.894618	+	0.446832i	$0.147448\pi$
$138$	−8.73255e41	−8.58501e−5 0
$139$	−5.96200e44	−0.0501850	−0.0250925	−	0.999685i	$-0.507988\pi$
$139$	−5.96200e44	−0.0501850	−0.0250925	+	0.999685i	$0.507988\pi$
$140$	−1.68011e46	−1.21223
$141$	−1.36305e44	−0.00843920
$142$	−6.26154e45	−0.333029
$143$	1.52005e46	0.695235
$144$	−6.34919e45	−0.249991
$145$	−6.23180e46	−2.11447
$146$	−7.90594e44	−0.0231402
$147$	1.30300e44	0.00329323
$148$	1.45153e46	0.317102
$149$	2.53943e46	0.479989	0.239995	−	0.970774i	$-0.422854\pi$
$149$	2.53943e46	0.479989	0.239995	+	0.970774i	$0.422854\pi$
$150$	−7.03088e44	−0.0115093
$151$	6.65104e46	0.943812	0.471906	−	0.881649i	$-0.343566\pi$
$151$	6.65104e46	0.943812	0.471906	+	0.881649i	$0.343566\pi$
$152$	−2.21182e46	−0.272340
$153$	1.64409e45	0.0175817
$154$	1.35044e47	1.25540
$155$	−1.00126e47	−0.809869
$156$	−2.04158e44	−0.00143809
$157$	−2.40178e46	−0.147465	−0.0737327	−	0.997278i	$-0.523491\pi$
$157$	−2.40178e46	−0.147465	−0.0737327	+	0.997278i	$0.523491\pi$
$158$	8.23176e46	0.440925
$159$	−1.48701e44	−0.000695466 0
$160$	8.39563e46	0.343142
$161$	7.21377e45	0.0257873
$162$	−2.25950e47	−0.707033
$163$	−4.09519e47	−1.12264	−0.561320	−	0.827599i	$-0.689706\pi$
$163$	−4.09519e47	−1.12264	−0.561320	+	0.827599i	$0.689706\pi$
$164$	1.84016e47	0.442296
$165$	7.69306e45	0.0162254
$166$	−6.44967e47	−1.19458
$167$	8.96692e47	1.45962	0.729809	−	0.683652i	$-0.239609\pi$
$167$	8.96692e47	1.45962	0.729809	+	0.683652i	$0.239609\pi$
$168$	−1.81378e45	−0.00259679
$169$	−6.03700e47	−0.760777
$170$	−2.17401e46	−0.0241329
$171$	−7.87151e47	−0.770268
$172$	1.58607e47	0.136918
$173$	8.13600e47	0.620040	0.310020	−	0.950730i	$-0.399664\pi$
$173$	8.13600e47	0.620040	0.310020	+	0.950730i	$0.399664\pi$
$174$	−6.72763e45	−0.00452953
$175$	5.80806e48	3.45711
$176$	−6.74827e47	−0.355361
$177$	1.35572e46	0.00632040
$178$	−1.80277e48	−0.744579
$179$	−4.40713e48	−1.61367	−0.806836	−	0.590775i	$-0.798822\pi$
$179$	−4.40713e48	−1.61367	−0.806836	+	0.590775i	$0.798822\pi$
$180$	2.98788e48	0.970518
$181$	−4.00198e48	−1.15395	−0.576973	−	0.816763i	$-0.695766\pi$
$181$	−4.00198e48	−1.15395	−0.576973	+	0.816763i	$0.695766\pi$
$182$	1.68650e48	0.431969
$183$	−1.56893e46	−0.00357195
$184$	−3.60478e46	−0.00729954
$185$	−6.83076e48	−1.23105
$186$	−1.08092e46	−0.00173487
$187$	1.74743e47	0.0249923
$188$	−5.62665e48	−0.717556
$189$	−1.29102e47	−0.0146894
$190$	1.04086e49	1.05728
$191$	5.52608e48	0.501418	0.250709	−	0.968063i	$-0.419336\pi$
$191$	5.52608e48	0.501418	0.250709	+	0.968063i	$0.419336\pi$
$192$	9.06362e45	0.000735065 0
$193$	1.07272e49	0.778043	0.389022	−	0.921229i	$-0.372813\pi$
$193$	1.07272e49	0.778043	0.389022	+	0.921229i	$0.372813\pi$
$194$	1.19658e49	0.776612
$195$	9.60749e46	0.00558297
$196$	5.37876e48	0.280012
$197$	−2.18374e49	−1.01901	−0.509504	−	0.860468i	$-0.670171\pi$
$197$	−2.18374e49	−1.01901	−0.509504	+	0.860468i	$0.670171\pi$
$198$	−2.40161e49	−1.00508
$199$	3.52049e49	1.32209	0.661047	−	0.750344i	$-0.270112\pi$
$199$	3.52049e49	1.32209	0.661047	+	0.750344i	$0.270112\pi$
$200$	−2.90233e49	−0.978594
$201$	−2.65777e47	−0.00805012
$202$	2.22297e48	0.0605172
$203$	5.55755e49	1.36056
$204$	−2.34698e45	−5.16965e−5 0
$205$	−8.65963e49	−1.71708
$206$	−1.35493e49	−0.241976
$207$	−1.28288e48	−0.0206455
$208$	−8.42759e48	−0.122276
$209$	−8.36628e49	−1.09493
$210$	8.53551e47	0.0100813
$211$	1.53515e50	1.63711	0.818554	−	0.574430i	$-0.194776\pi$
$211$	1.53515e50	1.63711	0.818554	+	0.574430i	$0.194776\pi$
$212$	−6.13834e48	−0.0591330
$213$	3.18108e47	0.00276957
$214$	4.69527e49	0.369628
$215$	−7.46391e49	−0.531544
$216$	6.45132e47	0.00415808
$217$	8.92927e49	0.521113
$218$	7.22319e49	0.381869
$219$	4.01648e46	0.000192441 0
$220$	3.17568e50	1.37959
$221$	2.18228e48	0.00859958
$222$	−7.37425e47	−0.00263711
$223$	6.20052e49	0.201314	0.100657	−	0.994921i	$-0.467906\pi$
$223$	6.20052e49	0.201314	0.100657	+	0.994921i	$0.467906\pi$
$224$	−7.48726e49	−0.220796
$225$	−1.03290e51	−2.76779
$226$	−3.76558e50	−0.917278
$227$	4.13480e50	0.916006	0.458003	−	0.888951i	$-0.348565\pi$
$227$	4.13480e50	0.916006	0.458003	+	0.888951i	$0.348565\pi$
$228$	1.12368e48	0.00226487
$229$	1.11692e50	0.204909	0.102455	−	0.994738i	$-0.467330\pi$
$229$	1.11692e50	0.204909	0.102455	+	0.994738i	$0.467330\pi$
$230$	1.69638e49	0.0283383
$231$	−6.86071e48	−0.0104403
$232$	−2.77715e50	−0.385130
$233$	−8.69051e50	−1.09874	−0.549368	−	0.835581i	$-0.685131\pi$
$233$	−8.69051e50	−1.09874	−0.549368	+	0.835581i	$0.685131\pi$
$234$	−2.99925e50	−0.345837
$235$	2.64785e51	2.78570
$236$	5.59638e50	0.537402
$237$	−4.18201e48	−0.00366687
$238$	1.93879e49	0.0155284
$239$	−3.18038e50	−0.232769	−0.116384	−	0.993204i	$-0.537130\pi$
$239$	−3.18038e50	−0.232769	−0.116384	+	0.993204i	$0.537130\pi$
$240$	−4.26526e48	−0.00285367
$241$	2.26900e51	1.38825	0.694127	−	0.719853i	$-0.255791\pi$
$241$	2.26900e51	1.38825	0.694127	+	0.719853i	$0.255791\pi$
$242$	−1.28923e51	−0.721609
$243$	3.44391e49	0.0176407
$244$	−6.47652e50	−0.303711
$245$	−2.53120e51	−1.08706
$246$	−9.34863e48	−0.00367827
$247$	−1.04482e51	−0.376755
$248$	−4.46203e50	−0.147510
$249$	3.27665e49	0.00993446
$250$	8.72362e51	2.42654
$251$	−6.50684e51	−1.66106	−0.830529	−	0.556975i	$-0.811962\pi$
$251$	−6.50684e51	−1.66106	−0.830529	+	0.556975i	$0.811962\pi$
$252$	−2.66460e51	−0.624483
$253$	−1.36352e50	−0.0293475
$254$	−4.19567e51	−0.829615
$255$	1.10447e48	0.000200696 0
$256$	3.74144e50	0.0625000
$257$	2.78532e51	0.427871	0.213935	−	0.976848i	$-0.431372\pi$
$257$	2.78532e51	0.427871	0.213935	+	0.976848i	$0.431372\pi$
$258$	−8.05777e48	−0.00113865
$259$	6.09171e51	0.792126
$260$	3.96595e51	0.474701
$261$	−9.88345e51	−1.08928
$262$	1.01407e52	1.02942
$263$	6.39160e51	0.597807	0.298903	−	0.954283i	$-0.403379\pi$
$263$	6.39160e51	0.597807	0.298903	+	0.954283i	$0.403379\pi$
$264$	3.42835e49	0.00295529
$265$	2.88865e51	0.229567
$266$	−9.28245e51	−0.680311
$267$	9.15869e49	0.00619215
$268$	−1.09712e52	−0.684474
$269$	2.28281e52	1.31461	0.657303	−	0.753626i	$-0.271697\pi$
$269$	2.28281e52	1.31461	0.657303	+	0.753626i	$0.271697\pi$
$270$	−3.03594e50	−0.0161425
$271$	1.88294e52	0.924693	0.462347	−	0.886699i	$-0.347008\pi$
$271$	1.88294e52	0.924693	0.462347	+	0.886699i	$0.347008\pi$
$272$	−9.68829e49	−0.00439558
$273$	−8.56800e49	−0.00359238
$274$	−3.26430e52	−1.26518
$275$	−1.09782e53	−3.93439
$276$	1.83135e48	6.07052e−5 0
$277$	4.61782e52	1.41619	0.708095	−	0.706117i	$-0.249555\pi$
$277$	4.61782e52	1.41619	0.708095	+	0.706117i	$0.249555\pi$
$278$	1.25032e51	0.0354862
$279$	−1.58797e52	−0.417207
$280$	3.52344e52	0.857174
$281$	5.52503e52	1.24494	0.622471	−	0.782643i	$-0.286129\pi$
$281$	5.52503e52	1.24494	0.622471	+	0.782643i	$0.286129\pi$
$282$	2.85853e50	0.00596742
$283$	4.51872e51	0.0874193	0.0437097	−	0.999044i	$-0.486082\pi$
$283$	4.51872e51	0.0874193	0.0437097	+	0.999044i	$0.486082\pi$
$284$	1.31314e52	0.235487
$285$	−5.28793e50	−0.00879267
$286$	−3.18777e52	−0.491606
$287$	7.72270e52	1.10486
$288$	1.33152e52	0.176771
$289$	−8.11277e52	−0.999691
$290$	1.30690e53	1.49516
$291$	−6.07902e50	−0.00645854
$292$	1.65800e51	0.0163626
$293$	2.13481e52	0.195752	0.0978758	−	0.995199i	$-0.468795\pi$
$293$	2.13481e52	0.195752	0.0978758	+	0.995199i	$0.468795\pi$
$294$	−2.73259e50	−0.00232867
$295$	−2.63361e53	−2.08631
$296$	−3.04407e52	−0.224225
$297$	2.44024e51	0.0167174
$298$	−5.32557e52	−0.339404
$299$	−1.70283e51	−0.0100982
$300$	1.47448e51	0.00813829
$301$	6.65635e52	0.342024
$302$	−1.39482e53	−0.667376
$303$	−1.12934e50	−0.000503280 0
$304$	4.63852e52	0.192574
$305$	3.04779e53	1.17907
$306$	−3.44791e51	−0.0124321
$307$	3.27926e52	0.110230	0.0551152	−	0.998480i	$-0.482447\pi$
$307$	3.27926e52	0.110230	0.0551152	+	0.998480i	$0.482447\pi$
$308$	−2.83209e53	−0.887700
$309$	6.88351e50	0.00201234
$310$	2.09979e53	0.572664
$311$	−1.84457e53	−0.469405	−0.234702	−	0.972067i	$-0.575412\pi$
$311$	−1.84457e53	−0.469405	−0.234702	+	0.972067i	$0.575412\pi$
$312$	4.28150e50	0.00101689
$313$	−3.25940e52	−0.0722661	−0.0361330	−	0.999347i	$-0.511504\pi$
$313$	−3.25940e52	−0.0722661	−0.0361330	+	0.999347i	$0.511504\pi$
$314$	5.03689e52	0.104274
$315$	1.25394e54	2.42437
$316$	−1.72632e53	−0.311781
$317$	2.60991e53	0.440404	0.220202	−	0.975454i	$-0.429328\pi$
$317$	2.60991e53	0.440404	0.220202	+	0.975454i	$0.429328\pi$
$318$	3.11849e50	0.000491768 0
$319$	−1.05047e54	−1.54840
$320$	−1.76069e53	−0.242638
$321$	−2.38536e51	−0.00307394
$322$	−1.51284e52	−0.0182344
$323$	−1.20112e52	−0.0135436
$324$	4.73852e53	0.499948
$325$	−1.37101e54	−1.35378
$326$	8.58823e53	0.793826
$327$	−3.66963e51	−0.00317574
$328$	−3.85909e53	−0.312750
$329$	−2.36137e54	−1.79247
$330$	−1.61335e52	−0.0114731
$331$	−1.93099e53	−0.128670	−0.0643350	−	0.997928i	$-0.520493\pi$
$331$	−1.93099e53	−0.128670	−0.0643350	+	0.997928i	$0.520493\pi$
$332$	1.35259e54	0.844693
$333$	−1.08334e54	−0.634181
$334$	−1.88050e54	−1.03211
$335$	5.16296e54	2.65727
$336$	3.80378e51	0.00183620
$337$	2.65509e54	1.20237	0.601183	−	0.799111i	$-0.294696\pi$
$337$	2.65509e54	1.20237	0.601183	+	0.799111i	$0.294696\pi$
$338$	1.26605e54	0.537951
$339$	1.91304e52	0.00762836
$340$	4.55923e52	0.0170645
$341$	−1.68778e54	−0.593057
$342$	1.65078e54	0.544662
$343$	−1.77345e54	−0.549534
$344$	−3.32623e53	−0.0968157
$345$	−8.61817e50	−0.000235670 0
$346$	−1.70624e54	−0.438435
$347$	3.27098e54	0.789941	0.394970	−	0.918694i	$-0.370755\pi$
$347$	3.27098e54	0.789941	0.394970	+	0.918694i	$0.370755\pi$
$348$	1.41089e52	0.00320286
$349$	2.42552e54	0.517676	0.258838	−	0.965921i	$-0.416660\pi$
$349$	2.42552e54	0.517676	0.258838	+	0.965921i	$0.416660\pi$
$350$	−1.21804e55	−2.44455
$351$	3.04749e52	0.00575227
$352$	1.41522e54	0.251279
$353$	−5.87621e54	−0.981615	−0.490807	−	0.871268i	$-0.663298\pi$
$353$	−5.87621e54	−0.981615	−0.490807	+	0.871268i	$0.663298\pi$
$354$	−2.84315e52	−0.00446920
$355$	−6.17953e54	−0.914209
$356$	3.78069e54	0.526497
$357$	−9.84971e50	−0.000129139 0
$358$	9.24241e54	1.14104
$359$	1.22420e55	1.42338	0.711690	−	0.702494i	$-0.247930\pi$
$359$	1.22420e55	1.42338	0.711690	+	0.702494i	$0.247930\pi$
$360$	−6.26603e54	−0.686260
$361$	−3.94114e54	−0.406646
$362$	8.39276e54	0.815963
$363$	6.54975e52	0.00600112
$364$	−3.53685e54	−0.305448
$365$	−7.80238e53	−0.0635230
$366$	3.29029e52	0.00252575
$367$	6.65116e54	0.481479	0.240739	−	0.970590i	$-0.422610\pi$
$367$	6.65116e54	0.481479	0.240739	+	0.970590i	$0.422610\pi$
$368$	7.55977e52	0.00516155
$369$	−1.37339e55	−0.884561
$370$	1.43251e55	0.870486
$371$	−2.57611e54	−0.147715
$372$	2.26686e52	0.00122674
$373$	1.69267e55	0.864632	0.432316	−	0.901722i	$-0.357697\pi$
$373$	1.69267e55	0.864632	0.432316	+	0.901722i	$0.357697\pi$
$374$	−3.66463e53	−0.0176722
$375$	−4.43189e53	−0.0201798
$376$	1.17999e55	0.507389
$377$	−1.31188e55	−0.532788
$378$	2.70746e53	0.0103870
$379$	−4.11600e55	−1.49188	−0.745938	−	0.666016i	$-0.767998\pi$
$379$	−4.11600e55	−1.49188	−0.745938	+	0.666016i	$0.767998\pi$
$380$	−2.18284e55	−0.747611
$381$	2.13154e53	0.00689933
$382$	−1.15890e55	−0.354556
$383$	−4.06771e55	−1.17646	−0.588229	−	0.808694i	$-0.700175\pi$
$383$	−4.06771e55	−1.17646	−0.588229	+	0.808694i	$0.700175\pi$
$384$	−1.90078e52	−0.000519769 0
$385$	1.33275e56	3.44623
$386$	−2.24965e55	−0.550160
$387$	−1.18375e55	−0.273827
$388$	−2.50941e55	−0.549148
$389$	−3.95636e55	−0.819180	−0.409590	−	0.912270i	$-0.634328\pi$
$389$	−3.95636e55	−0.819180	−0.409590	+	0.912270i	$0.634328\pi$
$390$	−2.01484e53	−0.00394776
$391$	−1.95757e52	−0.000363008 0
$392$	−1.12801e55	−0.197998
$393$	−5.15184e53	−0.00856096
$394$	4.57964e55	0.720547
$395$	8.12393e55	1.21040
$396$	5.03653e55	0.710698
$397$	1.01362e56	1.35481	0.677404	−	0.735611i	$-0.263105\pi$
$397$	1.01362e56	1.35481	0.677404	+	0.735611i	$0.263105\pi$
$398$	−7.38301e55	−0.934862
$399$	4.71580e53	0.00565768
$400$	6.08663e55	0.691970
$401$	−6.40929e54	−0.0690567	−0.0345284	−	0.999404i	$-0.510993\pi$
$401$	−6.40929e54	−0.0690567	−0.0345284	+	0.999404i	$0.510993\pi$
$402$	5.57375e53	0.00569230
$403$	−2.10778e55	−0.204065
$404$	−4.66190e54	−0.0427921
$405$	−2.22991e56	−1.94090
$406$	−1.16550e56	−0.962063
$407$	−1.15143e56	−0.901486
$408$	4.92198e51	3.65550e−5 0
$409$	−1.48591e55	−0.104699	−0.0523495	−	0.998629i	$-0.516671\pi$
$409$	−1.48591e55	−0.104699	−0.0523495	+	0.998629i	$0.516671\pi$
$410$	1.81606e56	1.21416
$411$	1.65837e54	0.0105216
$412$	2.84150e55	0.171103
$413$	2.34866e56	1.34244
$414$	2.69040e54	0.0145986
$415$	−6.36519e56	−3.27927
$416$	1.76739e55	0.0864623
$417$	−6.35206e52	−0.000295114 0
$418$	1.75454e56	0.774234
$419$	3.48862e56	1.46235	0.731177	−	0.682187i	$-0.238971\pi$
$419$	3.48862e56	1.46235	0.731177	+	0.682187i	$0.238971\pi$
$420$	−1.79003e54	−0.00712853
$421$	3.31748e56	1.25529	0.627645	−	0.778500i	$-0.284019\pi$
$421$	3.31748e56	1.25529	0.627645	+	0.778500i	$0.284019\pi$
$422$	−3.21944e56	−1.15761
$423$	4.19942e56	1.43506
$424$	1.28730e55	0.0418134
$425$	−1.57611e55	−0.0486657
$426$	−6.67120e53	−0.00195838
$427$	−2.71804e56	−0.758676
$428$	−9.84670e55	−0.261366
$429$	1.61949e54	0.00408834
$430$	1.56529e56	0.375859
$431$	3.50172e56	0.799872	0.399936	−	0.916543i	$-0.369032\pi$
$431$	3.50172e56	0.799872	0.399936	+	0.916543i	$0.369032\pi$
$432$	−1.35294e54	−0.00294021
$433$	−6.19424e56	−1.28085	−0.640425	−	0.768020i	$-0.721242\pi$
$433$	−6.19424e56	−1.28085	−0.640425	+	0.768020i	$0.721242\pi$
$434$	−1.87260e56	−0.368482
$435$	−6.63951e54	−0.0124342
$436$	−1.51481e56	−0.270022
$437$	9.37234e54	0.0159037
$438$	−8.42318e52	−0.000136076 0
$439$	9.86613e56	1.51761	0.758804	−	0.651319i	$-0.225784\pi$
$439$	9.86613e56	1.51761	0.758804	+	0.651319i	$0.225784\pi$
$440$	−6.65988e56	−0.975515
$441$	−4.01441e56	−0.560005
$442$	−4.57658e54	−0.00608082
$443$	4.08147e56	0.516579	0.258290	−	0.966068i	$-0.416841\pi$
$443$	4.08147e56	0.516579	0.258290	+	0.966068i	$0.416841\pi$
$444$	1.54649e54	0.00186472
$445$	−1.77916e57	−2.04397
$446$	−1.30034e56	−0.142350
$447$	2.70557e54	0.00282258
$448$	1.57019e56	0.156126
$449$	7.25652e56	0.687753	0.343876	−	0.939015i	$-0.388260\pi$
$449$	7.25652e56	0.687753	0.343876	+	0.939015i	$0.388260\pi$
$450$	2.16614e57	1.95712
$451$	−1.45972e57	−1.25740
$452$	7.89700e56	0.648613
$453$	7.08618e54	0.00555010
$454$	−8.67130e56	−0.647714
$455$	1.66441e57	1.18581
$456$	−2.35652e54	−0.00160150
$457$	5.03696e56	0.326565	0.163283	−	0.986579i	$-0.447792\pi$
$457$	5.03696e56	0.326565	0.163283	+	0.986579i	$0.447792\pi$
$458$	−2.34236e56	−0.144893
$459$	3.50337e53	0.000206782 0
$460$	−3.55756e55	−0.0200382
$461$	7.57000e56	0.406936	0.203468	−	0.979082i	$-0.434779\pi$
$461$	7.57000e56	0.406936	0.203468	+	0.979082i	$0.434779\pi$
$462$	1.43880e55	0.00738238
$463$	6.94436e56	0.340127	0.170063	−	0.985433i	$-0.445603\pi$
$463$	6.94436e56	0.340127	0.170063	+	0.985433i	$0.445603\pi$
$464$	5.82411e56	0.272328
$465$	−1.06676e55	−0.00476245
$466$	1.82253e57	0.776923
$467$	−3.37517e57	−1.37399	−0.686994	−	0.726663i	$-0.741070\pi$
$467$	−3.37517e57	−1.37399	−0.686994	+	0.726663i	$0.741070\pi$
$468$	6.28988e56	0.244544
$469$	−4.60436e57	−1.70983
$470$	−5.55295e57	−1.96979
$471$	−2.55891e54	−0.000867173 0
$472$	−1.17365e57	−0.380001
$473$	−1.25816e57	−0.389243
$474$	8.77031e54	0.00259287
$475$	7.54600e57	2.13208
$476$	−4.06594e55	−0.0109802
$477$	4.58132e56	0.118262
$478$	6.66975e56	0.164592
$479$	2.97595e57	0.702121	0.351060	−	0.936353i	$-0.385821\pi$
$479$	2.97595e57	0.702121	0.351060	+	0.936353i	$0.385821\pi$
$480$	8.94490e54	0.00201785
$481$	−1.43797e57	−0.310192
$482$	−4.75845e57	−0.981644
$483$	7.68572e53	0.000151643 0
$484$	2.70372e57	0.510254
$485$	1.18091e58	2.13190
$486$	−7.22240e55	−0.0124739
$487$	−6.28542e57	−1.03863	−0.519316	−	0.854582i	$-0.673813\pi$
$487$	−6.28542e57	−1.03863	−0.519316	+	0.854582i	$0.673813\pi$
$488$	1.35822e57	0.214756
$489$	−4.36311e55	−0.00660170
$490$	5.30831e57	0.768671
$491$	5.70226e57	0.790305	0.395153	−	0.918615i	$-0.370692\pi$
$491$	5.70226e57	0.790305	0.395153	+	0.918615i	$0.370692\pi$
$492$	1.96055e55	0.00260093
$493$	−1.50812e56	−0.0191526
$494$	2.19115e57	0.266406
$495$	−2.37015e58	−2.75908
$496$	9.35755e56	0.104305
$497$	5.51093e57	0.588251
$498$	−6.87163e55	−0.00702472
$499$	−7.55319e57	−0.739552	−0.369776	−	0.929121i	$-0.620566\pi$
$499$	−7.55319e57	−0.739552	−0.369776	+	0.929121i	$0.620566\pi$
$500$	−1.82948e58	−1.71582
$501$	9.55357e55	0.00858330
$502$	1.36458e58	1.17455
$503$	1.01823e57	0.0839718	0.0419859	−	0.999118i	$-0.486632\pi$
$503$	1.01823e57	0.0839718	0.0419859	+	0.999118i	$0.486632\pi$
$504$	5.58807e57	0.441576
$505$	2.19385e57	0.166128
$506$	2.85951e56	0.0207518
$507$	−6.43197e55	−0.00447376
$508$	8.79896e57	0.586626
$509$	−1.61549e58	−1.03246	−0.516229	−	0.856451i	$-0.672665\pi$
$509$	−1.61549e58	−1.03246	−0.516229	+	0.856451i	$0.672665\pi$
$510$	−2.31624e54	−0.000141914 0
$511$	6.95820e56	0.0408741
$512$	−7.84638e56	−0.0441942
$513$	−1.67733e56	−0.00905930
$514$	−5.84123e57	−0.302550
$515$	−1.33718e58	−0.664256
$516$	1.68984e55	0.000805149 0
$517$	4.46337e58	2.03993
$518$	−1.27752e58	−0.560117
$519$	8.66829e55	0.00364616
$520$	−8.31720e57	−0.335664
$521$	2.87022e58	1.11148	0.555742	−	0.831355i	$-0.312434\pi$
$521$	2.87022e58	1.11148	0.555742	+	0.831355i	$0.312434\pi$
$522$	2.07271e58	0.770234
$523$	3.54622e58	1.26468	0.632339	−	0.774692i	$-0.282095\pi$
$523$	3.54622e58	1.26468	0.632339	+	0.774692i	$0.282095\pi$
$524$	−2.12667e58	−0.727909
$525$	6.18805e56	0.0203296
$526$	−1.34042e58	−0.422713
$527$	−2.42309e56	−0.00733571
$528$	−7.18977e55	−0.00208971
$529$	−3.58189e58	−0.999574
$530$	−6.05794e57	−0.162328
$531$	−4.17683e58	−1.07477
$532$	1.94667e58	0.481053
$533$	−1.82297e58	−0.432657
$534$	−1.92072e56	−0.00437851
$535$	4.63377e58	1.01468
$536$	2.30083e58	0.483996
$537$	−4.69546e56	−0.00948923
$538$	−4.78740e58	−0.929567
$539$	−4.26673e58	−0.796044
$540$	6.36682e56	0.0114145
$541$	−6.62227e58	−1.14095	−0.570473	−	0.821316i	$-0.693240\pi$
$541$	−6.62227e58	−1.14095	−0.570473	+	0.821316i	$0.693240\pi$
$542$	−3.94882e58	−0.653857
$543$	−4.26381e56	−0.00678580
$544$	2.03178e56	0.00310814
$545$	7.12858e58	1.04828
$546$	1.79684e56	0.00254020
$547$	−4.90873e58	−0.667178	−0.333589	−	0.942719i	$-0.608260\pi$
$547$	−4.90873e58	−0.667178	−0.333589	+	0.942719i	$0.608260\pi$
$548$	6.84573e58	0.894618
$549$	4.83371e58	0.607401
$550$	2.30229e59	2.78204
$551$	7.22053e58	0.839092
$552$	−3.84062e54	−4.29250e−5 0
$553$	−7.24496e58	−0.778836
$554$	−9.68427e58	−1.00140
$555$	−7.27766e56	−0.00723923
$556$	−2.62212e57	−0.0250925
$557$	2.53254e58	0.233168	0.116584	−	0.993181i	$-0.462806\pi$
$557$	2.53254e58	0.233168	0.116584	+	0.993181i	$0.462806\pi$
$558$	3.33021e58	0.295010
$559$	−1.57125e58	−0.133934
$560$	−7.38919e58	−0.606114
$561$	1.86176e55	0.000146968 0
$562$	−1.15868e59	−0.880307
$563$	2.25761e59	1.65089	0.825445	−	0.564483i	$-0.190924\pi$
$563$	2.25761e59	1.65089	0.825445	+	0.564483i	$0.190924\pi$
$564$	−5.99476e56	−0.00421960
$565$	−3.71626e59	−2.51805
$566$	−9.47645e57	−0.0618148
$567$	1.98864e59	1.24888
$568$	−2.75386e58	−0.166514
$569$	−2.32353e59	−1.35280	−0.676402	−	0.736533i	$-0.736462\pi$
$569$	−2.32353e59	−1.35280	−0.676402	+	0.736533i	$0.736462\pi$
$570$	1.10896e57	0.00621736
$571$	−7.96462e57	−0.0430020	−0.0215010	−	0.999769i	$-0.506845\pi$
$571$	−7.96462e57	−0.0430020	−0.0215010	+	0.999769i	$0.506845\pi$
$572$	6.68523e58	0.347618
$573$	5.88762e56	0.00294860
$574$	−1.61957e59	−0.781256
$575$	1.22983e58	0.0571463
$576$	−2.79240e58	−0.124996
$577$	2.06427e59	0.890199	0.445099	−	0.895481i	$-0.353168\pi$
$577$	2.06427e59	0.890199	0.445099	+	0.895481i	$0.353168\pi$
$578$	1.70137e59	0.706888
$579$	1.14290e57	0.00457530
$580$	−2.74077e59	−1.05723
$581$	5.67651e59	2.11006
$582$	1.27486e57	0.00456688
$583$	4.86928e58	0.168109
$584$	−3.47707e57	−0.0115701
$585$	−2.95996e59	−0.949369
$586$	−4.47702e58	−0.138417
$587$	−2.18486e59	−0.651185	−0.325593	−	0.945510i	$-0.605564\pi$
$587$	−2.18486e59	−0.651185	−0.325593	+	0.945510i	$0.605564\pi$
$588$	5.73066e56	0.00164662
$589$	1.16012e59	0.321383
$590$	5.52308e59	1.47524
$591$	−2.32661e57	−0.00599229
$592$	6.38389e58	0.158551
$593$	1.66747e56	0.000399375 0	0.000199688	−	1.00000i	$-0.499936\pi$
$593$	1.66747e56	0.000399375 0	0.000199688		1.00000i	$0.499936\pi$
$594$	−5.11755e57	−0.0118210
$595$	1.91340e58	0.0426275
$596$	1.11685e59	0.239995
$597$	3.75082e57	0.00777460
$598$	3.57110e57	0.00714047
$599$	−8.31418e59	−1.60377	−0.801887	−	0.597476i	$-0.796170\pi$
$599$	−8.31418e59	−1.60377	−0.801887	+	0.597476i	$0.796170\pi$
$600$	−3.09222e57	−0.00575464
$601$	3.62301e58	0.0650531	0.0325265	−	0.999471i	$-0.489645\pi$
$601$	3.62301e58	0.0650531	0.0325265	+	0.999471i	$0.489645\pi$
$602$	−1.39594e59	−0.241847
$603$	8.18831e59	1.36890
$604$	2.92516e59	0.471906
$605$	−1.27235e60	−1.98091
$606$	2.36840e56	0.000355872 0
$607$	−8.13623e59	−1.17996	−0.589979	−	0.807419i	$-0.700864\pi$
$607$	−8.13623e59	−1.17996	−0.589979	+	0.807419i	$0.700864\pi$
$608$	−9.72767e58	−0.136170
$609$	5.92114e57	0.00800081
$610$	−6.39169e59	−0.833727
$611$	5.57408e59	0.701920
$612$	7.23080e57	0.00879085
$613$	1.45687e60	1.71010	0.855050	−	0.518545i	$-0.173526\pi$
$613$	1.45687e60	1.71010	0.855050	+	0.518545i	$0.173526\pi$
$614$	−6.87711e58	−0.0779446
$615$	−9.22618e57	−0.0100973
$616$	5.93931e59	0.627698
$617$	−8.99399e59	−0.917955	−0.458978	−	0.888448i	$-0.651784\pi$
$617$	−8.99399e59	−0.917955	−0.458978	+	0.888448i	$0.651784\pi$
$618$	−1.44358e57	−0.00142294
$619$	−1.01581e60	−0.967078	−0.483539	−	0.875323i	$-0.660649\pi$
$619$	−1.01581e60	−0.967078	−0.483539	+	0.875323i	$0.660649\pi$
$620$	−4.40358e59	−0.404934
$621$	−2.73368e56	−0.000242817 0
$622$	3.86835e59	0.331919
$623$	1.58666e60	1.31520
$624$	−8.97895e56	−0.000719047 0
$625$	5.03195e60	3.89328
$626$	6.83546e58	0.0510998
$627$	−8.91364e57	−0.00643877
$628$	−1.05631e59	−0.0737327
$629$	−1.65308e58	−0.0111508
$630$	−2.62970e60	−1.71429
$631$	−1.44520e60	−0.910534	−0.455267	−	0.890355i	$-0.650456\pi$
$631$	−1.44520e60	−0.910534	−0.455267	+	0.890355i	$0.650456\pi$
$632$	3.62037e59	0.220463
$633$	1.63558e58	0.00962704
$634$	−5.47338e59	−0.311413
$635$	−4.14071e60	−2.27740
$636$	−6.53994e56	−0.000347733 0
$637$	−5.32851e59	−0.273910
$638$	2.20299e60	1.09488
$639$	−9.80055e59	−0.470958
$640$	3.69244e59	0.171571
$641$	−1.14193e59	−0.0513089	−0.0256545	−	0.999671i	$-0.508167\pi$
$641$	−1.14193e59	−0.0513089	−0.0256545	+	0.999671i	$0.508167\pi$
$642$	5.00246e57	0.00217360
$643$	−1.22490e59	−0.0514712	−0.0257356	−	0.999669i	$-0.508193\pi$
$643$	−1.22490e59	−0.0514712	−0.0257356	+	0.999669i	$0.508193\pi$
$644$	3.17265e58	0.0128937
$645$	−7.95223e57	−0.00312575
$646$	2.51893e58	0.00957674
$647$	2.04374e60	0.751594	0.375797	−	0.926702i	$-0.377369\pi$
$647$	2.04374e60	0.751594	0.375797	+	0.926702i	$0.377369\pi$
$648$	−9.93740e59	−0.353517
$649$	−4.43936e60	−1.52778
$650$	2.87522e60	0.957269
$651$	9.51346e57	0.00306441
$652$	−1.80108e60	−0.561320
$653$	−6.31762e59	−0.190511	−0.0952555	−	0.995453i	$-0.530367\pi$
$653$	−6.31762e59	−0.190511	−0.0952555	+	0.995453i	$0.530367\pi$
$654$	7.69576e57	0.00224559
$655$	1.00079e61	2.82589
$656$	8.09311e59	0.221148
$657$	−1.23744e59	−0.0327241
$658$	4.95214e60	1.26747
$659$	−6.26841e60	−1.55282	−0.776409	−	0.630229i	$-0.782961\pi$
$659$	−6.26841e60	−1.55282	−0.776409	+	0.630229i	$0.782961\pi$
$660$	3.38344e58	0.00811268
$661$	4.90303e60	1.13798	0.568989	−	0.822345i	$-0.307335\pi$
$661$	4.90303e60	1.13798	0.568989	+	0.822345i	$0.307335\pi$
$662$	4.04957e59	0.0909834
$663$	2.32506e56	5.05700e−5 0
$664$	−2.83660e60	−0.597288
$665$	−9.16087e60	−1.86755
$666$	2.27193e60	0.448434
$667$	1.17679e59	0.0224902
$668$	3.94369e60	0.729809
$669$	6.60618e57	0.00118383
$670$	−1.08275e61	−1.87897
$671$	5.13754e60	0.863417
$672$	−7.97711e57	−0.00129839
$673$	6.30665e60	0.994203	0.497102	−	0.867692i	$-0.334398\pi$
$673$	6.30665e60	0.994203	0.497102	+	0.867692i	$0.334398\pi$
$674$	−5.56813e60	−0.850201
$675$	−2.20098e59	−0.0325526
$676$	−2.65510e60	−0.380388
$677$	9.09208e60	1.26185	0.630924	−	0.775845i	$-0.282676\pi$
$677$	9.09208e60	1.26185	0.630924	+	0.775845i	$0.282676\pi$
$678$	−4.01194e58	−0.00539407
$679$	−1.05314e61	−1.37178
$680$	−9.56139e58	−0.0120664
$681$	4.40531e58	0.00538659
$682$	3.53953e60	0.419355
$683$	9.34804e60	1.07319	0.536593	−	0.843841i	$-0.319711\pi$
$683$	9.34804e60	1.07319	0.536593	+	0.843841i	$0.319711\pi$
$684$	−3.46193e60	−0.385134
$685$	−3.22154e61	−3.47309
$686$	3.71919e60	0.388579
$687$	1.19000e58	0.00120497
$688$	6.97561e59	0.0684590
$689$	6.08100e59	0.0578445
$690$	1.80736e57	0.000166644 0
$691$	1.90200e61	1.69993	0.849967	−	0.526836i	$-0.176622\pi$
$691$	1.90200e61	1.69993	0.849967	+	0.526836i	$0.176622\pi$
$692$	3.57825e60	0.310020
$693$	2.11371e61	1.77534
$694$	−6.85975e60	−0.558572
$695$	1.23395e60	0.0974143
$696$	−2.95884e58	−0.00226477
$697$	−2.09567e59	−0.0155532
$698$	−5.08668e60	−0.366052
$699$	−9.25908e58	−0.00646113
$700$	2.55441e61	1.72855
$701$	−2.19436e61	−1.44002	−0.720012	−	0.693962i	$-0.755864\pi$
$701$	−2.19436e61	−1.44002	−0.720012	+	0.693962i	$0.755864\pi$
$702$	−6.39105e58	−0.00406747
$703$	7.91452e60	0.488523
$704$	−2.96792e60	−0.177681
$705$	2.82108e59	0.0163814
$706$	1.23233e61	0.694106
$707$	−1.95649e60	−0.106896
$708$	5.96252e58	0.00316020
$709$	−3.13056e61	−1.60964	−0.804818	−	0.593522i	$-0.797737\pi$
$709$	−3.13056e61	−1.60964	−0.804818	+	0.593522i	$0.797737\pi$
$710$	1.29594e61	0.646444
$711$	1.28843e61	0.623541
$712$	−7.92868e60	−0.372289
$713$	1.89074e59	0.00861403
$714$	2.06563e57	9.13149e−5 0
$715$	−3.14601e61	−1.34952
$716$	−1.93827e61	−0.806836
$717$	−3.38846e58	−0.00136880
$718$	−2.56733e61	−1.00648
$719$	−4.08353e61	−1.55369	−0.776845	−	0.629691i	$-0.783181\pi$
$719$	−4.08353e61	−1.55369	−0.776845	+	0.629691i	$0.783181\pi$
$720$	1.31408e61	0.485259
$721$	1.19251e61	0.427418
$722$	8.26516e60	0.287542
$723$	2.41745e59	0.00816365
$724$	−1.76009e61	−0.576973
$725$	9.47474e61	3.01509
$726$	−1.37358e59	−0.00424343
$727$	3.27882e61	0.983395	0.491698	−	0.870766i	$-0.336377\pi$
$727$	3.27882e61	0.983395	0.491698	+	0.870766i	$0.336377\pi$
$728$	7.41732e60	0.215984
$729$	−3.53632e61	−0.999793
$730$	1.63628e60	0.0449175
$731$	−1.80630e59	−0.00481467
$732$	−6.90024e58	−0.00178598
$733$	8.88787e60	0.223389	0.111695	−	0.993743i	$-0.464372\pi$
$733$	8.88787e60	0.223389	0.111695	+	0.993743i	$0.464372\pi$
$734$	−1.39485e61	−0.340457
$735$	−2.69680e59	−0.00639250
$736$	−1.58540e59	−0.00364977
$737$	8.70299e61	1.94589
$738$	2.88021e61	0.625479
$739$	−4.67983e61	−0.987131	−0.493565	−	0.869709i	$-0.664307\pi$
$739$	−4.67983e61	−0.987131	−0.493565	+	0.869709i	$0.664307\pi$
$740$	−3.00420e61	−0.615527
$741$	−1.11318e59	−0.00221551
$742$	5.40250e60	0.104451
$743$	7.75880e61	1.45725	0.728627	−	0.684911i	$-0.240159\pi$
$743$	7.75880e61	1.45725	0.728627	+	0.684911i	$0.240159\pi$
$744$	−4.75395e58	−0.000867434 0
$745$	−5.25581e61	−0.931709
$746$	−3.54978e61	−0.611387
$747$	−1.00950e62	−1.68933
$748$	7.68529e59	0.0124961
$749$	−4.13242e61	−0.652898
$750$	9.29436e59	0.0142693
$751$	8.12743e61	1.21254	0.606268	−	0.795260i	$-0.292666\pi$
$751$	8.12743e61	1.21254	0.606268	+	0.795260i	$0.292666\pi$
$752$	−2.47463e61	−0.358778
$753$	−6.93254e59	−0.00976788
$754$	2.75121e61	0.376738
$755$	−1.37655e62	−1.83204
$756$	−5.67796e59	−0.00734469
$757$	5.81763e61	0.731450	0.365725	−	0.930723i	$-0.380821\pi$
$757$	5.81763e61	0.731450	0.365725	+	0.930723i	$0.380821\pi$
$758$	8.63188e61	1.05492
$759$	−1.45273e58	−0.000172578 0
$760$	4.57776e61	0.528641
$761$	−8.00450e61	−0.898595	−0.449298	−	0.893382i	$-0.648326\pi$
$761$	−8.00450e61	−0.898595	−0.449298	+	0.893382i	$0.648326\pi$
$762$	−4.47017e59	−0.00487856
$763$	−6.35730e61	−0.674521
$764$	2.43040e61	0.250709
$765$	−3.40275e60	−0.0341279
$766$	8.53061e61	0.831882
$767$	−5.54410e61	−0.525691
$768$	3.98622e58	0.000367532 0
$769$	1.59678e62	1.43162	0.715810	−	0.698296i	$-0.246058\pi$
$769$	1.59678e62	1.43162	0.715810	+	0.698296i	$0.246058\pi$
$770$	−2.79499e62	−2.43685
$771$	2.96754e59	0.00251610
$772$	4.71787e61	0.389022
$773$	5.71876e61	0.458609	0.229304	−	0.973355i	$-0.426355\pi$
$773$	5.71876e61	0.458609	0.229304	+	0.973355i	$0.426355\pi$
$774$	2.48251e61	0.193625
$775$	1.52230e62	1.15482
$776$	5.26261e61	0.388306
$777$	6.49025e59	0.00465811
$778$	8.29708e61	0.579247
$779$	1.00336e62	0.681396
$780$	4.22542e59	0.00279149
$781$	−1.04166e62	−0.669464
$782$	4.10531e58	0.000256685 0
$783$	−2.10605e60	−0.0128112
$784$	2.36560e61	0.140006
$785$	4.97091e61	0.286246
$786$	1.08042e60	0.00605351
$787$	−2.96283e62	−1.61529	−0.807643	−	0.589671i	$-0.799257\pi$
$787$	−2.96283e62	−1.61529	−0.807643	+	0.589671i	$0.799257\pi$
$788$	−9.60420e61	−0.509504
$789$	6.80976e59	0.00351541
$790$	−1.70371e62	−0.855882
$791$	3.31418e62	1.62025
$792$	−1.05624e62	−0.502540
$793$	6.41602e61	0.297093
$794$	−2.12571e62	−0.957994
$795$	3.07764e59	0.00134997
$796$	1.54833e62	0.661047
$797$	−1.51741e62	−0.630594	−0.315297	−	0.948993i	$-0.602104\pi$
$797$	−1.51741e62	−0.630594	−0.315297	+	0.948993i	$0.602104\pi$
$798$	−9.88975e59	−0.00400058
$799$	6.40793e60	0.0252326
$800$	−1.27646e62	−0.489297
$801$	−2.82169e62	−1.05296
$802$	1.34413e61	0.0488305
$803$	−1.31521e61	−0.0465171
$804$	−1.16890e60	−0.00402506
$805$	−1.49302e61	−0.0500558
$806$	4.42034e61	0.144295
$807$	2.43216e60	0.00773057
$808$	9.77672e60	0.0302586
$809$	−2.93763e62	−0.885327	−0.442663	−	0.896688i	$-0.645966\pi$
$809$	−2.93763e62	−0.885327	−0.442663	+	0.896688i	$0.645966\pi$
$810$	4.67645e62	1.37242
$811$	3.67101e62	1.04915	0.524575	−	0.851364i	$-0.324224\pi$
$811$	3.67101e62	1.04915	0.524575	+	0.851364i	$0.324224\pi$
$812$	2.44424e62	0.680281
$813$	2.00613e60	0.00543767
$814$	2.41473e62	0.637447
$815$	8.47574e62	2.17916
$816$	−1.03221e58	−2.58483e−5 0
$817$	8.64812e61	0.210935
$818$	3.11619e61	0.0740334
$819$	2.63971e62	0.610875
$820$	−3.80854e62	−0.858541
$821$	−7.97990e62	−1.75235	−0.876173	−	0.481997i	$-0.839912\pi$
$821$	−7.97990e62	−1.75235	−0.876173	+	0.481997i	$0.839912\pi$
$822$	−3.47786e60	−0.00743992
$823$	−6.36565e62	−1.32662	−0.663309	−	0.748345i	$-0.730849\pi$
$823$	−6.36565e62	−1.32662	−0.663309	+	0.748345i	$0.730849\pi$
$824$	−5.95905e61	−0.120988
$825$	−1.16964e61	−0.0231363
$826$	−4.92551e62	−0.949248
$827$	−3.36234e62	−0.631355	−0.315677	−	0.948867i	$-0.602232\pi$
$827$	−3.36234e62	−0.631355	−0.315677	+	0.948867i	$0.602232\pi$
$828$	−5.64219e60	−0.0103227
$829$	5.67452e62	1.01159	0.505797	−	0.862652i	$-0.331198\pi$
$829$	5.67452e62	1.01159	0.505797	+	0.862652i	$0.331198\pi$
$830$	1.33488e63	2.31879
$831$	4.91993e60	0.00832793
$832$	−3.70649e61	−0.0611380
$833$	−6.12562e60	−0.00984651
$834$	1.33212e59	0.000208677 0
$835$	−1.85587e63	−2.83327
$836$	−3.67953e62	−0.547466
$837$	−3.38377e60	−0.00490687
$838$	−7.31618e62	−1.03404
$839$	8.37436e62	1.15364	0.576819	−	0.816872i	$-0.304294\pi$
$839$	8.37436e62	1.15364	0.576819	+	0.816872i	$0.304294\pi$
$840$	3.75396e60	0.00504063
$841$	1.42571e62	0.186603
$842$	−6.95727e62	−0.887624
$843$	5.88650e60	0.00732090
$844$	6.75165e62	0.818554
$845$	1.24947e63	1.47675
$846$	−8.80681e62	−1.01474
$847$	1.13469e63	1.27462
$848$	−2.69967e61	−0.0295665
$849$	4.81436e59	0.000514071 0
$850$	3.30533e61	0.0344119
$851$	1.28989e61	0.0130939
$852$	1.39905e60	0.00138479
$853$	−1.18819e63	−1.14678	−0.573392	−	0.819281i	$-0.694373\pi$
$853$	−1.18819e63	−1.14678	−0.573392	+	0.819281i	$0.694373\pi$
$854$	5.70014e62	0.536465
$855$	1.62915e63	1.49517
$856$	2.06500e62	0.184814
$857$	2.67982e62	0.233894	0.116947	−	0.993138i	$-0.462689\pi$
$857$	2.67982e62	0.233894	0.116947	+	0.993138i	$0.462689\pi$
$858$	−3.39632e60	−0.00289090
$859$	−3.65813e62	−0.303673	−0.151837	−	0.988406i	$-0.548519\pi$
$859$	−3.65813e62	−0.303673	−0.151837	+	0.988406i	$0.548519\pi$
$860$	−3.28266e62	−0.265772
$861$	8.22795e60	0.00649716
$862$	−7.34365e62	−0.565595
$863$	−9.90631e61	−0.0744183	−0.0372091	−	0.999307i	$-0.511847\pi$
$863$	−9.90631e61	−0.0744183	−0.0372091	+	0.999307i	$0.511847\pi$
$864$	2.83732e60	0.00207904
$865$	−1.68389e63	−1.20356
$866$	1.29903e63	0.905698
$867$	−8.64354e60	−0.00587870
$868$	3.92714e62	0.260556
$869$	1.36942e63	0.886361
$870$	1.39241e61	0.00879229
$871$	1.08687e63	0.669559
$872$	3.17679e62	0.190935
$873$	1.87288e63	1.09826
$874$	−1.96552e61	−0.0112456
$875$	−7.67786e63	−4.28615
$876$	1.76647e59	9.62205e−5 0
$877$	1.85432e63	0.985585	0.492793	−	0.870147i	$-0.335976\pi$
$877$	1.85432e63	0.985585	0.492793	+	0.870147i	$0.335976\pi$
$878$	−2.06908e63	−1.07311
$879$	2.27448e60	0.00115112
$880$	1.39668e63	0.689793
$881$	−8.58814e62	−0.413920	−0.206960	−	0.978349i	$-0.566357\pi$
$881$	−8.58814e62	−0.413920	−0.206960	+	0.978349i	$0.566357\pi$
$882$	8.41882e62	0.395983
$883$	−2.94353e63	−1.35118	−0.675589	−	0.737278i	$-0.736111\pi$
$883$	−2.94353e63	−1.35118	−0.675589	+	0.737278i	$0.736111\pi$
$884$	9.59778e60	0.00429979
$885$	−2.80591e61	−0.0122686
$886$	−8.55947e62	−0.365277
$887$	−2.64455e62	−0.110152	−0.0550762	−	0.998482i	$-0.517540\pi$
$887$	−2.64455e62	−0.110152	−0.0550762	+	0.998482i	$0.517540\pi$
$888$	−3.24323e60	−0.00131856
$889$	3.69271e63	1.46540
$890$	3.73117e63	1.44530
$891$	−3.75886e63	−1.42130
$892$	2.72702e62	0.100657
$893$	−3.06796e63	−1.10546
$894$	−5.67399e60	−0.00199587
$895$	9.12135e63	3.13230
$896$	−3.29293e62	−0.110398
$897$	−1.81424e59	−5.93823e−5 0
$898$	−1.52180e63	−0.486315
$899$	1.45664e63	0.454484
$900$	−4.54272e63	−1.38389
$901$	6.99067e60	0.00207939
$902$	3.06125e63	0.889115
$903$	7.09183e60	0.00201128
$904$	−1.65612e63	−0.458639
$905$	8.28283e63	2.23993
$906$	−1.48608e61	−0.00392451
$907$	3.70525e63	0.955566	0.477783	−	0.878478i	$-0.341441\pi$
$907$	3.70525e63	0.955566	0.477783	+	0.878478i	$0.341441\pi$
$908$	1.81850e63	0.458003
$909$	3.47938e62	0.0855813
$910$	−3.49052e63	−0.838496
$911$	−3.20223e63	−0.751289	−0.375644	−	0.926764i	$-0.622579\pi$
$911$	−3.20223e63	−0.751289	−0.375644	+	0.926764i	$0.622579\pi$
$912$	4.94198e60	0.00113243
$913$	−1.07295e64	−2.40137
$914$	−1.05633e63	−0.230916
$915$	3.24719e61	0.00693353
$916$	4.91229e62	0.102455
$917$	−8.92510e63	−1.81833
$918$	−7.34711e59	−0.000146217 0
$919$	2.79540e63	0.543452	0.271726	−	0.962375i	$-0.412406\pi$
$919$	2.79540e63	0.543452	0.271726	+	0.962375i	$0.412406\pi$
$920$	7.46074e61	0.0141692
$921$	3.49380e60	0.000648211 0
$922$	−1.58754e63	−0.287747
$923$	−1.30087e63	−0.230356
$924$	−3.01737e61	−0.00522013
$925$	1.03854e64	1.75540
$926$	−1.45634e63	−0.240506
$927$	−2.12073e63	−0.342194
$928$	−1.22140e63	−0.192565
$929$	−4.76577e62	−0.0734168	−0.0367084	−	0.999326i	$-0.511687\pi$
$929$	−4.76577e62	−0.0734168	−0.0367084	+	0.999326i	$0.511687\pi$
$930$	2.23717e61	0.00336756
$931$	2.93279e63	0.431384
$932$	−3.82213e63	−0.549368
$933$	−1.96525e61	−0.00276034
$934$	7.07824e63	0.971556
$935$	−3.61663e62	−0.0485126
$936$	−1.31908e63	−0.172919
$937$	−8.61288e63	−1.10344	−0.551718	−	0.834031i	$-0.686028\pi$
$937$	−8.61288e63	−1.10344	−0.551718	+	0.834031i	$0.686028\pi$
$938$	9.65603e63	1.20903
$939$	−3.47264e60	−0.000424962 0
$940$	1.16454e64	1.39285
$941$	3.45409e63	0.403791	0.201895	−	0.979407i	$-0.435290\pi$
$941$	3.45409e63	0.403791	0.201895	+	0.979407i	$0.435290\pi$
$942$	5.36642e60	0.000613184 0
$943$	1.63525e62	0.0182635
$944$	2.46131e63	0.268701
$945$	2.67200e62	0.0285136
$946$	2.63855e63	0.275237
$947$	3.46532e63	0.353361	0.176680	−	0.984268i	$-0.443464\pi$
$947$	3.46532e63	0.353361	0.176680	+	0.984268i	$0.443464\pi$
$948$	−1.83927e61	−0.00183344
$949$	−1.64251e62	−0.0160060
$950$	−1.58251e64	−1.50761
$951$	2.78066e61	0.00258981
$952$	8.52689e61	0.00776419
$953$	−7.53482e63	−0.670773	−0.335387	−	0.942081i	$-0.608867\pi$
$953$	−7.53482e63	−0.670773	−0.335387	+	0.942081i	$0.608867\pi$
$954$	−9.60772e62	−0.0836239
$955$	−1.14372e64	−0.973303
$956$	−1.39875e63	−0.116384
$957$	−1.11919e62	−0.00910539
$958$	−6.24101e63	−0.496474
$959$	2.87298e64	2.23477
$960$	−1.87588e61	−0.00142684
$961$	−1.11044e64	−0.825927
$962$	3.01564e63	0.219339
$963$	7.34903e63	0.522715
$964$	9.97919e63	0.694127
$965$	−2.22019e64	−1.51026
$966$	−1.61181e60	−0.000107228 0
$967$	9.70611e63	0.631504	0.315752	−	0.948842i	$-0.397743\pi$
$967$	9.70611e63	0.631504	0.315752	+	0.948842i	$0.397743\pi$
$968$	−5.67011e63	−0.360804
$969$	−1.27970e60	−7.96431e−5 0
$970$	−2.47654e64	−1.50748
$971$	−6.64214e63	−0.395453	−0.197726	−	0.980257i	$-0.563356\pi$
$971$	−6.64214e63	−0.395453	−0.197726	+	0.980257i	$0.563356\pi$
$972$	1.51465e62	0.00882037
$973$	−1.10044e63	−0.0626815
$974$	1.31815e64	0.734423
$975$	−1.46071e62	−0.00796094
$976$	−2.84840e63	−0.151855
$977$	1.54974e64	0.808213	0.404107	−	0.914712i	$-0.367582\pi$
$977$	1.54974e64	0.808213	0.404107	+	0.914712i	$0.367582\pi$
$978$	9.15011e61	0.00466811
$979$	−2.99905e64	−1.49677
$980$	−1.11323e64	−0.543532
$981$	1.13057e64	0.540026
$982$	−1.19585e64	−0.558830
$983$	3.96381e64	1.81222	0.906112	−	0.423037i	$-0.139036\pi$
$983$	3.96381e64	1.81222	0.906112	+	0.423037i	$0.139036\pi$
$984$	−4.11157e61	−0.00183913
$985$	4.51965e64	1.97800
$986$	3.16277e62	0.0135430
$987$	−2.51586e62	−0.0105406
$988$	−4.59518e63	−0.188377
$989$	1.40946e62	0.00565368
$990$	4.97056e64	1.95096
$991$	−2.80505e63	−0.107735	−0.0538676	−	0.998548i	$-0.517155\pi$
$991$	−2.80505e63	−0.107735	−0.0538676	+	0.998548i	$0.517155\pi$
$992$	−1.96242e63	−0.0737549
$993$	−2.05732e61	−0.000756646 0
$994$	−1.15573e64	−0.415956
$995$	−7.28631e64	−2.56632
$996$	1.44109e62	0.00496723
$997$	−1.59618e64	−0.538437	−0.269219	−	0.963079i	$-0.586765\pi$
$997$	−1.59618e64	−0.538437	−0.269219	+	0.963079i	$0.586765\pi$
$998$	1.58402e64	0.522942
$999$	−2.30847e62	−0.00745876

Twists

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

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

\(f(q)\)	\(=\)	\(q-2.09715e6 q^{2} +1.06542e8 q^{3} +4.39805e12 q^{4} -2.06968e15 q^{5} -2.23436e14 q^{6} +1.84575e18 q^{7} -9.22337e18 q^{8} -3.28246e20 q^{9} +O(q^{10})\)	\(q-2.09715e6 q^{2} +1.06542e8 q^{3} +4.39805e12 q^{4} -2.06968e15 q^{5} -2.23436e14 q^{6} +1.84575e18 q^{7} -9.22337e18 q^{8} -3.28246e20 q^{9} +4.34044e21 q^{10} -3.48878e22 q^{11} +4.68578e20 q^{12} -4.35696e23 q^{13} -3.87082e24 q^{14} -2.20509e23 q^{15} +1.93428e25 q^{16} -5.00873e24 q^{17} +6.88381e26 q^{18} +2.39806e27 q^{19} -9.10256e27 q^{20} +1.96651e26 q^{21} +7.31649e28 q^{22} +3.90831e27 q^{23} -9.82680e26 q^{24} +3.14672e30 q^{25} +9.13721e29 q^{26} -6.99454e28 q^{27} +8.11771e30 q^{28} +3.01099e31 q^{29} +4.62441e29 q^{30} +4.83774e31 q^{31} -4.05648e31 q^{32} -3.71703e30 q^{33} +1.05041e31 q^{34} -3.82012e33 q^{35} -1.44364e33 q^{36} +3.30039e33 q^{37} -5.02909e33 q^{38} -4.64201e31 q^{39} +1.90894e34 q^{40} +4.18404e34 q^{41} -4.12407e32 q^{42} +3.60631e34 q^{43} -1.53438e35 q^{44} +6.79364e35 q^{45} -8.19632e33 q^{46} -1.27935e36 q^{47} +2.06083e33 q^{48} +1.22299e36 q^{49} -6.59914e36 q^{50} -5.33642e32 q^{51} -1.91621e36 q^{52} -1.39570e36 q^{53} +1.46686e35 q^{54} +7.22066e37 q^{55} -1.70241e37 q^{56} +2.55495e35 q^{57} -6.31451e37 q^{58} +1.27247e38 q^{59} -9.69808e35 q^{60} -1.47259e38 q^{61} -1.01455e38 q^{62} -6.05860e38 q^{63} +8.50706e37 q^{64} +9.01752e38 q^{65} +7.79517e36 q^{66} -2.49457e39 q^{67} -2.20286e37 q^{68} +4.16400e35 q^{69} +8.01138e39 q^{70} +2.98574e39 q^{71} +3.02753e39 q^{72} +3.76985e38 q^{73} -6.92142e39 q^{74} +3.35259e38 q^{75} +1.05468e40 q^{76} -6.43942e40 q^{77} +9.73500e37 q^{78} -3.92521e40 q^{79} -4.00335e40 q^{80} +1.07741e41 q^{81} -8.77456e40 q^{82} +3.07544e41 q^{83} +8.64880e38 q^{84} +1.03665e40 q^{85} -7.56297e40 q^{86} +3.20798e39 q^{87} +3.21783e41 q^{88} +8.59629e41 q^{89} -1.42473e42 q^{90} -8.04187e41 q^{91} +1.71889e40 q^{92} +5.15424e39 q^{93} +2.68299e42 q^{94} -4.96321e42 q^{95} -4.32187e39 q^{96} -5.70573e42 q^{97} -2.56479e42 q^{98} +1.14518e43 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4194304 q^{2} - 12981630984 q^{3} + 8796093022208 q^{4} - 398662711282500 q^{5} + 27\!\cdots\!68 q^{6}+ \cdots - 48\!\cdots\!26 q^{9}+O(q^{10}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

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