LMFDB - Embedded newform 3.40.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,40,Mod(1,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 40, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 40);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 40 $
Character orbit:	$[\chi]$	$=$	3.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$28.9018654169$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 216694123x - 94580724378 $ x^3 - 216694123*x - 94580724378
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{6}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-14497.2$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+674802. q^{2} +1.16226e9 q^{3} -9.43987e10 q^{4} -4.30989e13 q^{5} +7.84296e14 q^{6} +4.52904e16 q^{7} -4.34676e17 q^{8} +1.35085e18 q^{9} +O(q^{10})$	\(q+674802. q^{2} +1.16226e9 q^{3} -9.43987e10 q^{4} -4.30989e13 q^{5} +7.84296e14 q^{6} +4.52904e16 q^{7} -4.34676e17 q^{8} +1.35085e18 q^{9} -2.90832e19 q^{10} +7.70568e18 q^{11} -1.09716e20 q^{12} -9.07516e21 q^{13} +3.05620e22 q^{14} -5.00921e22 q^{15} -2.41424e23 q^{16} -1.17059e24 q^{17} +9.11557e23 q^{18} -9.32475e24 q^{19} +4.06848e24 q^{20} +5.26393e25 q^{21} +5.19981e24 q^{22} +3.49530e26 q^{23} -5.05208e26 q^{24} +3.85224e25 q^{25} -6.12393e27 q^{26} +1.57004e27 q^{27} -4.27535e27 q^{28} -3.14567e28 q^{29} -3.38023e28 q^{30} -1.22297e29 q^{31} +7.60525e28 q^{32} +8.95602e27 q^{33} -7.89914e29 q^{34} -1.95196e30 q^{35} -1.27519e29 q^{36} -1.74197e30 q^{37} -6.29236e30 q^{38} -1.05477e31 q^{39} +1.87341e31 q^{40} +2.93451e31 q^{41} +3.55211e31 q^{42} +5.16244e31 q^{43} -7.27406e29 q^{44} -5.82202e31 q^{45} +2.35863e32 q^{46} -3.56034e31 q^{47} -2.80598e32 q^{48} +1.14168e33 q^{49} +2.59950e31 q^{50} -1.36053e33 q^{51} +8.56683e32 q^{52} -4.34269e33 q^{53} +1.05947e33 q^{54} -3.32106e32 q^{55} -1.96867e34 q^{56} -1.08378e34 q^{57} -2.12271e34 q^{58} +6.09993e34 q^{59} +4.72863e33 q^{60} +4.89141e34 q^{61} -8.25259e34 q^{62} +6.11806e34 q^{63} +1.84045e35 q^{64} +3.91129e35 q^{65} +6.04353e33 q^{66} -6.92066e35 q^{67} +1.10502e35 q^{68} +4.06245e35 q^{69} -1.31719e36 q^{70} -3.69040e35 q^{71} -5.87183e35 q^{72} +1.37872e36 q^{73} -1.17548e36 q^{74} +4.47732e34 q^{75} +8.80244e35 q^{76} +3.48993e35 q^{77} -7.11761e36 q^{78} -8.93530e36 q^{79} +1.04051e37 q^{80} +1.82480e36 q^{81} +1.98021e37 q^{82} +8.75828e36 q^{83} -4.96908e36 q^{84} +5.04510e37 q^{85} +3.48363e37 q^{86} -3.65610e37 q^{87} -3.34948e36 q^{88} +7.78454e37 q^{89} -3.92871e37 q^{90} -4.11017e38 q^{91} -3.29952e37 q^{92} -1.42141e38 q^{93} -2.40252e37 q^{94} +4.01886e38 q^{95} +8.83929e37 q^{96} -8.85026e38 q^{97} +7.70405e38 q^{98} +1.04092e37 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 1107000 q^{2} + 3486784401 q^{3} + 1005900225600 q^{4} + 9357049429290 q^{5} - 12\!\cdots\!00 q^{6}+ \cdots + 40\!\cdots\!67 q^{9}+O(q^{10}) $ 3 * q - 1107000 * q^2 + 3486784401 * q^3 + 1005900225600 * q^4 + 9357049429290 * q^5 - 1286623443969000 * q^6 + 13841884377460104 * q^7 - 1526556980351135232 * q^8 + 4052555153018976267 * q^9	$ 3 q - 1107000 q^{2} + 3486784401 q^{3} + 1005900225600 q^{4} + 9357049429290 q^{5} - 12\!\cdots\!00 q^{6}+ \cdots - 54\!\cdots\!44 q^{99}+O(q^{100}) $ 3 * q - 1107000 * q^2 + 3486784401 * q^3 + 1005900225600 * q^4 + 9357049429290 * q^5 - 1286623443969000 * q^6 + 13841884377460104 * q^7 - 1526556980351135232 * q^8 + 4052555153018976267 * q^9 - 76029599179042436880 * q^10 - 40050327611147243796 * q^11 + 1169119071861486955200 * q^12 - 13932702500978393486094 * q^13 + 64143032386415214972096 * q^14 + 10875337996478108168430 * q^15 + 1098810764821648805597184 * q^16 - 169700805136994180103018 * q^17 - 1495392851464002242523000 * q^18 - 6957470542505489016962988 * q^19 + 33307320359730090833619840 * q^20 + 16087888842591162209012568 * q^21 - 182808419494676144863843296 * q^22 - 257172639984224911978099272 * q^23 - 1774258355442000609859705344 * q^24 - 2223570708999165320980345275 * q^25 + 6420909995769964414290523056 * q^26 + 4710128697246244834921603689 * q^27 - 31489800993928145336514267648 * q^28 - 46272789498091624686435987486 * q^29 - 88366273477255858343403702960 * q^30 - 282753969983174411853352917888 * q^31 - 1118437222052144608340712062976 * q^32 - 46548952523162601127345608732 * q^33 - 2020045599738440464009480297200 * q^34 - 2778733015107044038012367571600 * q^35 + 1358822047559410249352115278400 * q^36 - 5239395449699583862273344438486 * q^37 - 4077508380452877314541820882464 * q^38 - 16193443248061716548450856539898 * q^39 - 10242585699763810314758557271040 * q^40 + 47673397400045140822464268984782 * q^41 + 74550974919263458624588661024832 * q^42 - 14936449213367655469478076825588 * q^43 + 383801287439893621552232462293248 * q^44 + 12639986293907486833224134886810 * q^45 + 646689351161727342528587792407872 * q^46 - 13040685113470292045769719198544 * q^47 + 1277105411477001534152180886908928 * q^48 - 132364363537073708245470314514213 * q^49 + 2030100946651365938753014066519800 * q^50 - 197236706729603991736995911807406 * q^51 - 16457201727541975997405015057804928 * q^52 - 11047064078175508118010662971794342 * q^53 - 1738037489283864344086071761241000 * q^54 - 1504305246366733376700435214523160 * q^55 + 6316090378583898308960601541324800 * q^56 - 8086399919341715520407790317583396 * q^57 - 23720839646010288107197368475070928 * q^58 + 35633406741119515209244171316491548 * q^59 + 38711815023138863096326248158705280 * q^60 - 26245828903346977727221409425735902 * q^61 - 98335445202496226432366585960435712 * q^62 + 18698333287122936270281907905117256 * q^63 + 922428812776307390107790824712699904 * q^64 + 260861961831082759405211612047737660 * q^65 - 212471181821833694819355024467075232 * q^66 - 200741546976450474071235708204779388 * q^67 + 1264175105126717513162323757007619200 * q^68 - 298901849820328103053611531746352024 * q^69 - 431344371239166538676321844662332800 * q^70 - 3140665348656484831244609799236867544 * q^71 - 2062152119033027062230435797305179648 * q^72 - 3825610182002392515733100347600509522 * q^73 - 2544605510256173934291855124681995024 * q^74 - 2584370554219599987738141977488018425 * q^75 - 5521658898639443517674491687212787968 * q^76 - 994601047124972255067887751426792672 * q^77 + 7462776271158562634691099091263883152 * q^78 - 1038716953120555158347640895730970000 * q^79 + 45766070974584297712698519042271272960 * q^80 + 5474401089420219382077155933569751763 * q^81 - 16726391180845396277548112611717202352 * q^82 + 69227326737654458476356626745129089940 * q^83 - 36599382298740984291406281382995119616 * q^84 + 76820078772499304751574061990694660660 * q^85 + 159762376422294357818512142478616905504 * q^86 - 53781080204234165408470505817072001962 * q^87 - 343351801449478884201073068755288881152 * q^88 + 136597710245735759116899165769855535742 * q^89 - 102704714644998585052548577575521842320 * q^90 - 259984668223904357182500109993449632208 * q^91 - 135698237299460735254844067932094260736 * q^92 - 328634043952718257237540151213237421696 * q^93 + 457887889864219720177610385758047412352 * q^94 + 462468326274179393065716948072305471640 * q^95 - 1299916486449730342986216438139082145792 * q^96 - 1338928527743499267936157260425715870618 * q^97 + 1730483839907526080834886072855293848584 * q^98 - 54102053846884316265804561020862329844 * 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 $

$2$	674802.	0.910104	0.455052	−	0.890465i	$-0.349621\pi$
$2$	674802.	0.910104	0.455052	+	0.890465i	$0.349621\pi$
$3$	1.16226e9	0.577350
$3$	1.16226e9	0.577350
$4$	−9.43987e10	−0.171710
$5$	−4.30989e13	−1.01053	−0.505267	−	0.862963i	$-0.668606\pi$
$5$	−4.30989e13	−1.01053	−0.505267	+	0.862963i	$0.668606\pi$
$6$	7.84296e14	0.525449
$7$	4.52904e16	1.50174	0.750869	−	0.660451i	$-0.229635\pi$
$7$	4.52904e16	1.50174	0.750869	+	0.660451i	$0.229635\pi$
$8$	−4.34676e17	−1.06638
$9$	1.35085e18	0.333333
$10$	−2.90832e19	−0.919691
$11$	7.70568e18	0.0379886	0.0189943	−	0.999820i	$-0.493954\pi$
$11$	7.70568e18	0.0379886	0.0189943	+	0.999820i	$0.493954\pi$
$12$	−1.09716e20	−0.0991369
$13$	−9.07516e21	−1.72171	−0.860853	−	0.508854i	$-0.830069\pi$
$13$	−9.07516e21	−1.72171	−0.860853	+	0.508854i	$0.830069\pi$
$14$	3.05620e22	1.36674
$15$	−5.00921e22	−0.583432
$16$	−2.41424e23	−0.798805
$17$	−1.17059e24	−1.18754	−0.593772	−	0.804633i	$-0.702362\pi$
$17$	−1.17059e24	−1.18754	−0.593772	+	0.804633i	$0.702362\pi$
$18$	9.11557e23	0.303368
$19$	−9.32475e24	−1.08129	−0.540645	−	0.841251i	$-0.681820\pi$
$19$	−9.32475e24	−1.08129	−0.540645	+	0.841251i	$0.681820\pi$
$20$	4.06848e24	0.173519
$21$	5.26393e25	0.867029
$22$	5.19981e24	0.0345736
$23$	3.49530e26	0.976768	0.488384	−	0.872629i	$-0.337587\pi$
$23$	3.49530e26	0.976768	0.488384	+	0.872629i	$0.337587\pi$
$24$	−5.05208e26	−0.615674
$25$	3.85224e25	0.0211779
$26$	−6.12393e27	−1.56693
$27$	1.57004e27	0.192450
$28$	−4.27535e27	−0.257864
$29$	−3.14567e28	−0.957090	−0.478545	−	0.878063i	$-0.658836\pi$
$29$	−3.14567e28	−0.957090	−0.478545	+	0.878063i	$0.658836\pi$
$30$	−3.38023e28	−0.530984
$31$	−1.22297e29	−1.01359	−0.506794	−	0.862067i	$-0.669170\pi$
$31$	−1.22297e29	−1.01359	−0.506794	+	0.862067i	$0.669170\pi$
$32$	7.60525e28	0.339382
$33$	8.95602e27	0.0219328
$34$	−7.89914e29	−1.08079
$35$	−1.95196e30	−1.51756
$36$	−1.27519e29	−0.0572367
$37$	−1.74197e30	−0.458254	−0.229127	−	0.973397i	$-0.573587\pi$
$37$	−1.74197e30	−0.458254	−0.229127	+	0.973397i	$0.573587\pi$
$38$	−6.29236e30	−0.984086
$39$	−1.05477e31	−0.994027
$40$	1.87341e31	1.07761
$41$	2.93451e31	1.04292	0.521459	−	0.853276i	$-0.325388\pi$
$41$	2.93451e31	1.04292	0.521459	+	0.853276i	$0.325388\pi$
$42$	3.55211e31	0.789087
$43$	5.16244e31	0.724804	0.362402	−	0.932022i	$-0.381957\pi$
$43$	5.16244e31	0.724804	0.362402	+	0.932022i	$0.381957\pi$
$44$	−7.27406e29	−0.00652304
$45$	−5.82202e31	−0.336844
$46$	2.35863e32	0.888961
$47$	−3.56034e31	−0.0882233	−0.0441117	−	0.999027i	$-0.514046\pi$
$47$	−3.56034e31	−0.0882233	−0.0441117	+	0.999027i	$0.514046\pi$
$48$	−2.80598e32	−0.461191
$49$	1.14168e33	1.25522
$50$	2.59950e31	0.0192741
$51$	−1.36053e33	−0.685629
$52$	8.56683e32	0.295634
$53$	−4.34269e33	−1.03367	−0.516833	−	0.856087i	$-0.672889\pi$
$53$	−4.34269e33	−1.03367	−0.516833	+	0.856087i	$0.672889\pi$
$54$	1.05947e33	0.175150
$55$	−3.32106e32	−0.0383888
$56$	−1.96867e34	−1.60142
$57$	−1.08378e34	−0.624283
$58$	−2.12271e34	−0.871052
$59$	6.09993e34	1.79354	0.896769	−	0.442499i	$-0.145908\pi$
$59$	6.09993e34	1.79354	0.896769	+	0.442499i	$0.145908\pi$
$60$	4.72863e33	0.100181
$61$	4.89141e34	0.750761	0.375381	−	0.926871i	$-0.377512\pi$
$61$	4.89141e34	0.750761	0.375381	+	0.926871i	$0.377512\pi$
$62$	−8.25259e34	−0.922471
$63$	6.11806e34	0.500579
$64$	1.84045e35	1.10768
$65$	3.91129e35	1.73984
$66$	6.04353e33	0.0199611
$67$	−6.92066e35	−1.70486	−0.852430	−	0.522841i	$-0.824872\pi$
$67$	−6.92066e35	−1.70486	−0.852430	+	0.522841i	$0.824872\pi$
$68$	1.10502e35	0.203913
$69$	4.06245e35	0.563937
$70$	−1.31719e36	−1.38114
$71$	−3.69040e35	−0.293451	−0.146725	−	0.989177i	$-0.546873\pi$
$71$	−3.69040e35	−0.293451	−0.146725	+	0.989177i	$0.546873\pi$
$72$	−5.87183e35	−0.355459
$73$	1.37872e36	0.637792	0.318896	−	0.947790i	$-0.396688\pi$
$73$	1.37872e36	0.637792	0.318896	+	0.947790i	$0.396688\pi$
$74$	−1.17548e36	−0.417059
$75$	4.47732e34	0.0122271
$76$	8.80244e35	0.185668
$77$	3.48993e35	0.0570490
$78$	−7.11761e36	−0.904668
$79$	−8.93530e36	−0.885892	−0.442946	−	0.896548i	$-0.646067\pi$
$79$	−8.93530e36	−0.885892	−0.442946	+	0.896548i	$0.646067\pi$
$80$	1.04051e37	0.807220
$81$	1.82480e36	0.111111
$82$	1.98021e37	0.949164
$83$	8.75828e36	0.331433	0.165717	−	0.986173i	$-0.447006\pi$
$83$	8.75828e36	0.331433	0.165717	+	0.986173i	$0.447006\pi$
$84$	−4.96908e36	−0.148878
$85$	5.04510e37	1.20005
$86$	3.48363e37	0.659647
$87$	−3.65610e37	−0.552576
$88$	−3.34948e36	−0.0405103
$89$	7.78454e37	0.755314	0.377657	−	0.925946i	$-0.376730\pi$
$89$	7.78454e37	0.755314	0.377657	+	0.925946i	$0.376730\pi$
$90$	−3.92871e37	−0.306564
$91$	−4.11017e38	−2.58555
$92$	−3.29952e37	−0.167721
$93$	−1.42141e38	−0.585195
$94$	−2.40252e37	−0.0802924
$95$	4.01886e38	1.09268
$96$	8.83929e37	0.195942
$97$	−8.85026e38	−1.60290	−0.801451	−	0.598060i	$-0.795938\pi$
$97$	−8.85026e38	−1.60290	−0.801451	+	0.598060i	$0.795938\pi$
$98$	7.70405e38	1.14238
$99$	1.04092e37	0.0126629
$100$	−3.63647e36	−0.00363647
$101$	1.23425e39	1.01657	0.508285	−	0.861189i	$-0.330280\pi$
$101$	1.23425e39	1.01657	0.508285	+	0.861189i	$0.330280\pi$
$102$	−9.18086e38	−0.623994
$103$	1.52773e39	0.858460	0.429230	−	0.903195i	$-0.358785\pi$
$103$	1.52773e39	0.858460	0.429230	+	0.903195i	$0.358785\pi$
$104$	3.94476e39	1.83599
$105$	−2.26869e39	−0.876162
$106$	−2.93046e39	−0.940743
$107$	−2.10444e39	−0.562541	−0.281270	−	0.959629i	$-0.590756\pi$
$107$	−2.10444e39	−0.562541	−0.281270	+	0.959629i	$0.590756\pi$
$108$	−1.48210e38	−0.0330456
$109$	6.20647e39	1.15619	0.578093	−	0.815971i	$-0.303797\pi$
$109$	6.20647e39	1.15619	0.578093	+	0.815971i	$0.303797\pi$
$110$	−2.24106e38	−0.0349378
$111$	−2.02462e39	−0.264573
$112$	−1.09342e40	−1.19960
$113$	1.16705e40	1.07662	0.538309	−	0.842748i	$-0.319063\pi$
$113$	1.16705e40	1.07662	0.538309	+	0.842748i	$0.319063\pi$
$114$	−7.31336e39	−0.568163
$115$	−1.50643e40	−0.987057
$116$	2.96948e39	0.164342
$117$	−1.22592e40	−0.573902
$118$	4.11624e40	1.63231
$119$	−5.30163e40	−1.78338
$120$	2.17739e40	0.622159
$121$	−4.10854e40	−0.998557
$122$	3.30073e40	0.683271
$123$	3.41067e40	0.602129
$124$	1.15446e40	0.174043
$125$	7.67361e40	0.989132
$126$	4.12848e40	0.455580
$127$	−2.69302e40	−0.254723	−0.127361	−	0.991856i	$-0.540651\pi$
$127$	−2.69302e40	−0.254723	−0.127361	+	0.991856i	$0.540651\pi$
$128$	8.23833e40	0.668721
$129$	6.00011e40	0.418466
$130$	2.63934e41	1.58344
$131$	−3.61843e41	−1.86952	−0.934760	−	0.355279i	$-0.884386\pi$
$131$	−3.61843e41	−1.86952	−0.934760	+	0.355279i	$0.884386\pi$
$132$	−8.45436e38	−0.00376608
$133$	−4.22322e41	−1.62381
$134$	−4.67007e41	−1.55160
$135$	−6.76671e40	−0.194477
$136$	5.08826e41	1.26637
$137$	−6.70977e41	−1.44763	−0.723813	−	0.689996i	$-0.757612\pi$
$137$	−6.70977e41	−1.44763	−0.723813	+	0.689996i	$0.757612\pi$
$138$	2.74135e41	0.513242
$139$	4.97626e41	0.809309	0.404655	−	0.914470i	$-0.367392\pi$
$139$	4.97626e41	0.809309	0.404655	+	0.914470i	$0.367392\pi$
$140$	1.84263e41	0.260580
$141$	−4.13805e40	−0.0509358
$142$	−2.49029e41	−0.267071
$143$	−6.99303e40	−0.0654052
$144$	−3.26128e41	−0.266268
$145$	1.35575e42	0.967172
$146$	9.30359e41	0.580457
$147$	1.32693e42	0.724701
$148$	1.64439e41	0.0786868
$149$	−2.36652e42	−0.993064	−0.496532	−	0.868018i	$-0.665394\pi$
$149$	−2.36652e42	−0.993064	−0.496532	+	0.868018i	$0.665394\pi$
$150$	3.02130e40	0.0111279
$151$	−1.86532e42	−0.603537	−0.301768	−	0.953381i	$-0.597577\pi$
$151$	−1.86532e42	−0.603537	−0.301768	+	0.953381i	$0.597577\pi$
$152$	4.05325e42	1.15306
$153$	−1.58129e42	−0.395848
$154$	2.35501e41	0.0519205
$155$	5.27084e42	1.02426
$156$	9.95690e41	0.170685
$157$	−7.98318e42	−1.20818	−0.604091	−	0.796915i	$-0.706464\pi$
$157$	−7.98318e42	−1.20818	−0.604091	+	0.796915i	$0.706464\pi$
$158$	−6.02955e42	−0.806254
$159$	−5.04735e42	−0.596787
$160$	−3.27778e42	−0.342957
$161$	1.58303e43	1.46685
$162$	1.23138e42	0.101123
$163$	−2.12441e43	−1.54732	−0.773661	−	0.633600i	$-0.781577\pi$
$163$	−2.12441e43	−1.54732	−0.773661	+	0.633600i	$0.781577\pi$
$164$	−2.77014e42	−0.179080
$165$	−3.85994e41	−0.0221638
$166$	5.91010e42	0.301639
$167$	−7.10435e42	−0.322517	−0.161259	−	0.986912i	$-0.551555\pi$
$167$	−7.10435e42	−0.322517	−0.161259	+	0.986912i	$0.551555\pi$
$168$	−2.28811e43	−0.924581
$169$	5.45747e43	1.96427
$170$	3.40444e43	1.09217
$171$	−1.25964e43	−0.360430
$172$	−4.87328e42	−0.124456
$173$	4.11859e43	0.939398	0.469699	−	0.882827i	$-0.344362\pi$
$173$	4.11859e43	0.939398	0.469699	+	0.882827i	$0.344362\pi$
$174$	−2.46714e43	−0.502902
$175$	1.74470e42	0.0318037
$176$	−1.86034e42	−0.0303455
$177$	7.08971e43	1.03550
$178$	5.25302e43	0.687415
$179$	−7.36813e42	−0.0864417	−0.0432208	−	0.999066i	$-0.513762\pi$
$179$	−7.36813e42	−0.0864417	−0.0432208	+	0.999066i	$0.513762\pi$
$180$	5.49591e42	0.0578396
$181$	−1.19766e44	−1.13136	−0.565680	−	0.824625i	$-0.691386\pi$
$181$	−1.19766e44	−1.13136	−0.565680	+	0.824625i	$0.691386\pi$
$182$	−2.77355e44	−2.35312
$183$	5.68509e43	0.433452
$184$	−1.51932e44	−1.04160
$185$	7.50767e43	0.463081
$186$	−9.59167e43	−0.532589
$187$	−9.02017e42	−0.0451132
$188$	3.36092e42	0.0151488
$189$	7.11079e43	0.289010
$190$	2.71193e44	0.994452
$191$	−1.31406e43	−0.0434974	−0.0217487	−	0.999763i	$-0.506923\pi$
$191$	−1.31406e43	−0.0434974	−0.0217487	+	0.999763i	$0.506923\pi$
$192$	2.13908e44	0.639519
$193$	2.21089e44	0.597309	0.298655	−	0.954361i	$-0.403462\pi$
$193$	2.21089e44	0.597309	0.298655	+	0.954361i	$0.403462\pi$
$194$	−5.97217e44	−1.45881
$195$	4.54594e44	1.00450
$196$	−1.07773e44	−0.215534
$197$	4.91464e44	0.890021	0.445010	−	0.895525i	$-0.353200\pi$
$197$	4.91464e44	0.890021	0.445010	+	0.895525i	$0.353200\pi$
$198$	7.02417e42	0.0115245
$199$	3.99025e44	0.593425	0.296712	−	0.954967i	$-0.404110\pi$
$199$	3.99025e44	0.593425	0.296712	+	0.954967i	$0.404110\pi$
$200$	−1.67448e43	−0.0225837
$201$	−8.04361e44	−0.984301
$202$	8.32876e44	0.925185
$203$	−1.42469e45	−1.43730
$204$	1.28432e44	0.117729
$205$	−1.26474e45	−1.05390
$206$	1.03091e45	0.781288
$207$	4.72163e44	0.325589
$208$	2.19096e45	1.37531
$209$	−7.18536e43	−0.0410767
$210$	−1.53092e45	−0.797399
$211$	−1.46834e45	−0.697139	−0.348569	−	0.937283i	$-0.613332\pi$
$211$	−1.46834e45	−0.697139	−0.348569	+	0.937283i	$0.613332\pi$
$212$	4.09945e44	0.177491
$213$	−4.28921e44	−0.169424
$214$	−1.42008e45	−0.511971
$215$	−2.22495e45	−0.732439
$216$	−6.82461e44	−0.205225
$217$	−5.53886e45	−1.52214
$218$	4.18813e45	1.05225
$219$	1.60243e45	0.368229
$220$	3.13504e43	0.00659175
$221$	1.06233e46	2.04460
$222$	−1.36622e45	−0.240789
$223$	−4.16612e45	−0.672647	−0.336324	−	0.941746i	$-0.609184\pi$
$223$	−4.16612e45	−0.672647	−0.336324	+	0.941746i	$0.609184\pi$
$224$	3.44445e45	0.509663
$225$	5.20381e43	0.00705931
$226$	7.87530e45	0.979834
$227$	6.75694e45	0.771340	0.385670	−	0.922637i	$-0.373970\pi$
$227$	6.75694e45	0.771340	0.385670	+	0.922637i	$0.373970\pi$
$228$	1.02307e45	0.107196
$229$	−3.02718e45	−0.291237	−0.145619	−	0.989341i	$-0.546517\pi$
$229$	−3.02718e45	−0.291237	−0.145619	+	0.989341i	$0.546517\pi$
$230$	−1.01654e46	−0.898325
$231$	4.05622e44	0.0329373
$232$	1.36735e46	1.02062
$233$	−5.18521e45	−0.355898	−0.177949	−	0.984040i	$-0.556946\pi$
$233$	−5.18521e45	−0.355898	−0.177949	+	0.984040i	$0.556946\pi$
$234$	−8.27252e45	−0.522310
$235$	1.53447e45	0.0891526
$236$	−5.75825e45	−0.307969
$237$	−1.03852e46	−0.511470
$238$	−3.57755e46	−1.62306
$239$	−3.27405e45	−0.136876	−0.0684379	−	0.997655i	$-0.521802\pi$
$239$	−3.27405e45	−0.136876	−0.0684379	+	0.997655i	$0.521802\pi$
$240$	1.20935e46	0.466048
$241$	1.09196e46	0.388037	0.194018	−	0.980998i	$-0.437848\pi$
$241$	1.09196e46	0.388037	0.194018	+	0.980998i	$0.437848\pi$
$242$	−2.77245e46	−0.908791
$243$	2.12090e45	0.0641500
$244$	−4.61742e45	−0.128913
$245$	−4.92049e46	−1.26844
$246$	2.30152e46	0.548000
$247$	8.46236e46	1.86166
$248$	5.31595e46	1.08087
$249$	1.01794e46	0.191353
$250$	5.17816e46	0.900214
$251$	−7.29218e46	−1.17279	−0.586395	−	0.810025i	$-0.699453\pi$
$251$	−7.29218e46	−1.17279	−0.586395	+	0.810025i	$0.699453\pi$
$252$	−5.77537e45	−0.0859546
$253$	2.69337e45	0.0371061
$254$	−1.81726e46	−0.231824
$255$	5.86372e46	0.692851
$256$	−4.55873e46	−0.499073
$257$	1.46128e47	1.48265	0.741326	−	0.671146i	$-0.234197\pi$
$257$	1.46128e47	1.48265	0.741326	+	0.671146i	$0.234197\pi$
$258$	4.04888e46	0.380847
$259$	−7.88943e46	−0.688177
$260$	−3.69221e46	−0.298748
$261$	−4.24934e46	−0.319030
$262$	−2.44172e47	−1.70146
$263$	2.58458e46	0.167206	0.0836032	−	0.996499i	$-0.473357\pi$
$263$	2.58458e46	0.167206	0.0836032	+	0.996499i	$0.473357\pi$
$264$	−3.89297e45	−0.0233886
$265$	1.87165e47	1.04455
$266$	−2.84983e47	−1.47784
$267$	9.04767e46	0.436081
$268$	6.53301e46	0.292742
$269$	6.48813e46	0.270365	0.135182	−	0.990821i	$-0.456838\pi$
$269$	6.48813e46	0.270365	0.135182	+	0.990821i	$0.456838\pi$
$270$	−4.56618e46	−0.176995
$271$	1.88144e47	0.678561	0.339280	−	0.940685i	$-0.389816\pi$
$271$	1.88144e47	0.678561	0.339280	+	0.940685i	$0.389816\pi$
$272$	2.82608e47	0.948616
$273$	−4.77710e47	−1.49277
$274$	−4.52776e47	−1.31749
$275$	2.96842e44	0.000804521 0
$276$	−3.83490e46	−0.0968338
$277$	−2.16676e47	−0.509865	−0.254932	−	0.966959i	$-0.582053\pi$
$277$	−2.16676e47	−0.509865	−0.254932	+	0.966959i	$0.582053\pi$
$278$	3.35799e47	0.736556
$279$	−1.65205e47	−0.337863
$280$	8.48473e47	1.61829
$281$	−2.39044e46	−0.0425309	−0.0212655	−	0.999774i	$-0.506770\pi$
$281$	−2.39044e46	−0.0425309	−0.0212655	+	0.999774i	$0.506770\pi$
$282$	−2.79236e46	−0.0463569
$283$	−2.35062e47	−0.364206	−0.182103	−	0.983279i	$-0.558290\pi$
$283$	−2.35062e47	−0.364206	−0.182103	+	0.983279i	$0.558290\pi$
$284$	3.48369e46	0.0503885
$285$	4.67097e47	0.630859
$286$	−4.71891e46	−0.0595256
$287$	1.32905e48	1.56619
$288$	1.02736e47	0.113127
$289$	3.98627e47	0.410260
$290$	9.14862e47	0.880227
$291$	−1.02863e48	−0.925436
$292$	−1.30149e47	−0.109515
$293$	−1.46388e48	−1.15236	−0.576180	−	0.817323i	$-0.695457\pi$
$293$	−1.46388e48	−1.15236	−0.576180	+	0.817323i	$0.695457\pi$
$294$	8.95412e47	0.659553
$295$	−2.62900e48	−1.81243
$296$	7.57191e47	0.488672
$297$	1.20983e46	0.00731092
$298$	−1.59693e48	−0.903792
$299$	−3.17204e48	−1.68171
$300$	−4.22653e45	−0.00209952
$301$	2.33809e48	1.08847
$302$	−1.25872e48	−0.549281
$303$	1.43453e48	0.586917
$304$	2.25122e48	0.863740
$305$	−2.10814e48	−0.758669
$306$	−1.06706e48	−0.360263
$307$	−3.04588e48	−0.964973	−0.482486	−	0.875904i	$-0.660266\pi$
$307$	−3.04588e48	−0.964973	−0.482486	+	0.875904i	$0.660266\pi$
$308$	−3.29445e46	−0.00979590
$309$	1.77562e48	0.495632
$310$	3.55677e48	0.932187
$311$	6.35606e48	1.56444	0.782222	−	0.622999i	$-0.214086\pi$
$311$	6.35606e48	1.56444	0.782222	+	0.622999i	$0.214086\pi$
$312$	4.58484e48	1.06001
$313$	5.57167e48	1.21024	0.605119	−	0.796135i	$-0.293125\pi$
$313$	5.57167e48	1.21024	0.605119	+	0.796135i	$0.293125\pi$
$314$	−5.38706e48	−1.09957
$315$	−2.63681e48	−0.505852
$316$	8.43481e47	0.152117
$317$	−1.01793e48	−0.172608	−0.0863039	−	0.996269i	$-0.527506\pi$
$317$	−1.01793e48	−0.172608	−0.0863039	+	0.996269i	$0.527506\pi$
$318$	−3.40596e48	−0.543138
$319$	−2.42396e47	−0.0363586
$320$	−7.93212e48	−1.11935
$321$	−2.44592e48	−0.324783
$322$	1.06823e49	1.33499
$323$	1.09154e49	1.28408
$324$	−1.72259e47	−0.0190789
$325$	−3.49597e47	−0.0364622
$326$	−1.43356e49	−1.40822
$327$	7.21354e48	0.667524
$328$	−1.27556e49	−1.11215
$329$	−1.61249e48	−0.132488
$330$	−2.60469e47	−0.0201713
$331$	−1.67237e49	−1.22092	−0.610460	−	0.792047i	$-0.709015\pi$
$331$	−1.67237e49	−1.22092	−0.610460	+	0.792047i	$0.709015\pi$
$332$	−8.26770e47	−0.0569104
$333$	−2.35314e48	−0.152751
$334$	−4.79403e48	−0.293524
$335$	2.98272e49	1.72282
$336$	−1.27084e49	−0.692587
$337$	−2.19412e49	−1.12844	−0.564219	−	0.825625i	$-0.690823\pi$
$337$	−2.19412e49	−1.12844	−0.564219	+	0.825625i	$0.690823\pi$
$338$	3.68271e49	1.78769
$339$	1.35642e49	0.621585
$340$	−4.76250e48	−0.206061
$341$	−9.42379e47	−0.0385048
$342$	−8.50004e48	−0.328029
$343$	1.05134e49	0.383271
$344$	−2.24399e49	−0.772915
$345$	−1.75087e49	−0.569877
$346$	2.77923e49	0.854950
$347$	4.13352e48	0.120197	0.0600987	−	0.998192i	$-0.480858\pi$
$347$	4.13352e48	0.120197	0.0600987	+	0.998192i	$0.480858\pi$
$348$	3.45131e48	0.0948830
$349$	1.88917e48	0.0491106	0.0245553	−	0.999698i	$-0.492183\pi$
$349$	1.88917e48	0.0491106	0.0245553	+	0.999698i	$0.492183\pi$
$350$	1.17732e48	0.0289447
$351$	−1.42484e49	−0.331342
$352$	5.86037e47	0.0128927
$353$	8.09424e49	1.68488	0.842440	−	0.538790i	$-0.181118\pi$
$353$	8.09424e49	1.68488	0.842440	+	0.538790i	$0.181118\pi$
$354$	4.78415e49	0.942413
$355$	1.59052e49	0.296542
$356$	−7.34850e48	−0.129695
$357$	−6.16188e49	−1.02963
$358$	−4.97203e48	−0.0786709
$359$	−2.98600e49	−0.447454	−0.223727	−	0.974652i	$-0.571822\pi$
$359$	−2.98600e49	−0.447454	−0.223727	+	0.974652i	$0.571822\pi$
$360$	2.53069e49	0.359204
$361$	1.25822e49	0.169187
$362$	−8.08181e49	−1.02965
$363$	−4.77520e49	−0.576517
$364$	3.87995e49	0.443966
$365$	−5.94210e49	−0.644510
$366$	3.83631e49	0.394487
$367$	−1.14457e50	−1.11598	−0.557989	−	0.829848i	$-0.688427\pi$
$367$	−1.14457e50	−1.11598	−0.557989	+	0.829848i	$0.688427\pi$
$368$	−8.43849e49	−0.780247
$369$	3.96409e49	0.347639
$370$	5.06619e49	0.421452
$371$	−1.96682e50	−1.55229
$372$	1.34179e49	0.100484
$373$	2.01495e49	0.143200	0.0715999	−	0.997433i	$-0.477190\pi$
$373$	2.01495e49	0.143200	0.0715999	+	0.997433i	$0.477190\pi$
$374$	−6.08682e48	−0.0410577
$375$	8.91874e49	0.571076
$376$	1.54760e49	0.0940795
$377$	2.85475e50	1.64783
$378$	4.79837e49	0.263029
$379$	1.35411e50	0.705003	0.352501	−	0.935811i	$-0.385331\pi$
$379$	1.35411e50	0.705003	0.352501	+	0.935811i	$0.385331\pi$
$380$	−3.79375e49	−0.187624
$381$	−3.13000e49	−0.147064
$382$	−8.86727e48	−0.0395872
$383$	2.72274e50	1.15513	0.577563	−	0.816346i	$-0.304004\pi$
$383$	2.72274e50	1.15513	0.577563	+	0.816346i	$0.304004\pi$
$384$	9.57509e49	0.386086
$385$	−1.50412e49	−0.0576499
$386$	1.49191e50	0.543614
$387$	6.97370e49	0.241601
$388$	8.35453e49	0.275235
$389$	−5.88064e50	−1.84250	−0.921250	−	0.388971i	$-0.872831\pi$
$389$	−5.88064e50	−1.84250	−0.921250	+	0.388971i	$0.872831\pi$
$390$	3.06761e50	0.914198
$391$	−4.09155e50	−1.15995
$392$	−4.96260e50	−1.33854
$393$	−4.20557e50	−1.07937
$394$	3.31640e50	0.810012
$395$	3.85101e50	0.895224
$396$	−9.82618e47	−0.00217435
$397$	−4.79977e50	−1.01113	−0.505564	−	0.862789i	$-0.668715\pi$
$397$	−4.79977e50	−1.01113	−0.505564	+	0.862789i	$0.668715\pi$
$398$	2.69263e50	0.540078
$399$	−4.90848e50	−0.937510
$400$	−9.30025e48	−0.0169171
$401$	4.38176e50	0.759160	0.379580	−	0.925159i	$-0.376069\pi$
$401$	4.38176e50	0.759160	0.379580	+	0.925159i	$0.376069\pi$
$402$	−5.42784e50	−0.895817
$403$	1.10986e51	1.74510
$404$	−1.16512e50	−0.174556
$405$	−7.86468e49	−0.112281
$406$	−9.61382e50	−1.30809
$407$	−1.34230e49	−0.0174084
$408$	5.91389e50	0.731140
$409$	1.42901e50	0.168434	0.0842171	−	0.996447i	$-0.473161\pi$
$409$	1.42901e50	0.168434	0.0842171	+	0.996447i	$0.473161\pi$
$410$	−8.53448e50	−0.959162
$411$	−7.79851e50	−0.835788
$412$	−1.44216e50	−0.147406
$413$	2.76268e51	2.69343
$414$	3.18616e50	0.296320
$415$	−3.77472e50	−0.334924
$416$	−6.90189e50	−0.584316
$417$	5.78372e50	0.467255
$418$	−4.84869e49	−0.0373841
$419$	1.68767e51	1.24198	0.620990	−	0.783818i	$-0.286731\pi$
$419$	1.68767e51	1.24198	0.620990	+	0.783818i	$0.286731\pi$
$420$	2.14162e50	0.150446
$421$	−1.90313e51	−1.27635	−0.638173	−	0.769893i	$-0.720309\pi$
$421$	−1.90313e51	−1.27635	−0.638173	+	0.769893i	$0.720309\pi$
$422$	−9.90840e50	−0.634469
$423$	−4.80949e49	−0.0294078
$424$	1.88767e51	1.10228
$425$	−4.50939e49	−0.0251497
$426$	−2.89436e50	−0.154193
$427$	2.21534e51	1.12745
$428$	1.98657e50	0.0965940
$429$	−8.12773e49	−0.0377617
$430$	−1.50140e51	−0.666596
$431$	1.43665e51	0.609599	0.304800	−	0.952416i	$-0.401410\pi$
$431$	1.43665e51	0.609599	0.304800	+	0.952416i	$0.401410\pi$
$432$	−3.79046e50	−0.153730
$433$	−1.17620e51	−0.456002	−0.228001	−	0.973661i	$-0.573219\pi$
$433$	−1.17620e51	−0.456002	−0.228001	+	0.973661i	$0.573219\pi$
$434$	−3.73763e51	−1.38531
$435$	1.57574e51	0.558397
$436$	−5.85882e50	−0.198529
$437$	−3.25928e51	−1.05617
$438$	1.08132e51	0.335127
$439$	−4.19657e51	−1.24405	−0.622023	−	0.782999i	$-0.713689\pi$
$439$	−4.19657e51	−1.24405	−0.622023	+	0.782999i	$0.713689\pi$
$440$	1.44359e50	0.0409370
$441$	1.54223e51	0.418406
$442$	7.16859e51	1.86080
$443$	−4.75225e51	−1.18039	−0.590196	−	0.807260i	$-0.700950\pi$
$443$	−4.75225e51	−1.18039	−0.590196	+	0.807260i	$0.700950\pi$
$444$	1.91121e50	0.0454299
$445$	−3.35505e51	−0.763270
$446$	−2.81131e51	−0.612179
$447$	−2.75051e51	−0.573346
$448$	8.33546e51	1.66344
$449$	−1.67282e51	−0.319628	−0.159814	−	0.987147i	$-0.551089\pi$
$449$	−1.67282e51	−0.319628	−0.159814	+	0.987147i	$0.551089\pi$
$450$	3.51154e49	0.00642471
$451$	2.26124e50	0.0396190
$452$	−1.10168e51	−0.184866
$453$	−2.16799e51	−0.348452
$454$	4.55959e51	0.701999
$455$	1.77144e52	2.61279
$456$	4.71094e51	0.665722
$457$	1.91726e51	0.259607	0.129803	−	0.991540i	$-0.458565\pi$
$457$	1.91726e51	0.259607	0.129803	+	0.991540i	$0.458565\pi$
$458$	−2.04275e51	−0.265056
$459$	−1.83787e51	−0.228543
$460$	1.42205e51	0.169488
$461$	−1.60914e52	−1.83833	−0.919167	−	0.393868i	$-0.871137\pi$
$461$	−1.60914e52	−1.83833	−0.919167	+	0.393868i	$0.871137\pi$
$462$	2.73714e50	0.0299763
$463$	8.40375e51	0.882356	0.441178	−	0.897420i	$-0.354561\pi$
$463$	8.40375e51	0.882356	0.441178	+	0.897420i	$0.354561\pi$
$464$	7.59442e51	0.764529
$465$	6.12610e51	0.591359
$466$	−3.49899e51	−0.323905
$467$	1.10748e52	0.983238	0.491619	−	0.870811i	$-0.336405\pi$
$467$	1.10748e52	0.983238	0.491619	+	0.870811i	$0.336405\pi$
$468$	1.15725e51	0.0985448
$469$	−3.13439e52	−2.56025
$470$	1.03546e51	0.0811382
$471$	−9.27854e51	−0.697544
$472$	−2.65150e52	−1.91259
$473$	3.97802e50	0.0275343
$474$	−7.00792e51	−0.465491
$475$	−3.59212e50	−0.0228995
$476$	5.00467e51	0.306225
$477$	−5.86634e51	−0.344555
$478$	−2.20934e51	−0.124571
$479$	1.97798e51	0.107073	0.0535366	−	0.998566i	$-0.482951\pi$
$479$	1.97798e51	0.107073	0.0535366	+	0.998566i	$0.482951\pi$
$480$	−3.80964e51	−0.198006
$481$	1.58086e52	0.788978
$482$	7.36854e51	0.353154
$483$	1.83990e52	0.846886
$484$	3.87841e51	0.171462
$485$	3.81436e52	1.61979
$486$	1.43118e51	0.0583832
$487$	2.25402e52	0.883372	0.441686	−	0.897170i	$-0.354380\pi$
$487$	2.25402e52	0.883372	0.441686	+	0.897170i	$0.354380\pi$
$488$	−2.12618e52	−0.800596
$489$	−2.46912e52	−0.893347
$490$	−3.32036e52	−1.15441
$491$	−4.66673e52	−1.55928	−0.779639	−	0.626230i	$-0.784597\pi$
$491$	−4.66673e52	−1.55928	−0.779639	+	0.626230i	$0.784597\pi$
$492$	−3.21962e51	−0.103392
$493$	3.68228e52	1.13659
$494$	5.71041e52	1.69431
$495$	−4.48626e50	−0.0127963
$496$	2.95254e52	0.809659
$497$	−1.67140e52	−0.440686
$498$	6.86908e51	0.174151
$499$	3.75021e52	0.914312	0.457156	−	0.889386i	$-0.348868\pi$
$499$	3.75021e52	0.914312	0.457156	+	0.889386i	$0.348868\pi$
$500$	−7.24379e51	−0.169844
$501$	−8.25711e51	−0.186206
$502$	−4.92078e52	−1.06736
$503$	2.28011e52	0.475751	0.237876	−	0.971296i	$-0.423549\pi$
$503$	2.28011e52	0.475751	0.237876	+	0.971296i	$0.423549\pi$
$504$	−2.65938e52	−0.533807
$505$	−5.31949e52	−1.02728
$506$	1.81749e51	0.0337704
$507$	6.34301e52	1.13407
$508$	2.54218e51	0.0437385
$509$	−5.18105e52	−0.857869	−0.428935	−	0.903336i	$-0.641111\pi$
$509$	−5.18105e52	−0.857869	−0.428935	+	0.903336i	$0.641111\pi$
$510$	3.95685e52	0.630566
$511$	6.24425e52	0.957796
$512$	−7.60531e52	−1.12293
$513$	−1.46403e52	−0.208094
$514$	9.86077e52	1.34937
$515$	−6.58433e52	−0.867503
$516$	−5.66403e51	−0.0718548
$517$	−2.74349e50	−0.00335148
$518$	−5.32380e52	−0.626313
$519$	4.78688e52	0.542362
$520$	−1.70015e53	−1.85533
$521$	−5.14369e52	−0.540679	−0.270339	−	0.962765i	$-0.587136\pi$
$521$	−5.14369e52	−0.540679	−0.270339	+	0.962765i	$0.587136\pi$
$522$	−2.86746e52	−0.290351
$523$	−6.41449e52	−0.625719	−0.312859	−	0.949799i	$-0.601287\pi$
$523$	−6.41449e52	−0.625719	−0.312859	+	0.949799i	$0.601287\pi$
$524$	3.41575e52	0.321016
$525$	2.02779e51	0.0183619
$526$	1.74408e52	0.152175
$527$	1.43159e53	1.20368
$528$	−2.16220e51	−0.0175200
$529$	−5.88070e51	−0.0459244
$530$	1.26299e53	0.950652
$531$	8.24010e52	0.597846
$532$	3.98666e52	0.278825
$533$	−2.66311e53	−1.79560
$534$	6.10538e52	0.396879
$535$	9.06992e52	0.568466
$536$	3.00825e53	1.81803
$537$	−8.56369e51	−0.0499071
$538$	4.37820e52	0.246060
$539$	8.79739e51	0.0476840
$540$	6.38768e51	0.0333937
$541$	1.24083e53	0.625700	0.312850	−	0.949803i	$-0.398716\pi$
$541$	1.24083e53	0.625700	0.312850	+	0.949803i	$0.398716\pi$
$542$	1.26960e53	0.617561
$543$	−1.39199e53	−0.653191
$544$	−8.90261e52	−0.403031
$545$	−2.67492e53	−1.16836
$546$	−3.22359e53	−1.35858
$547$	2.54604e53	1.03541	0.517705	−	0.855559i	$-0.326787\pi$
$547$	2.54604e53	1.03541	0.517705	+	0.855559i	$0.326787\pi$
$548$	6.33393e52	0.248572
$549$	6.60756e52	0.250254
$550$	2.00309e50	0.000732198 0
$551$	2.93326e53	1.03489
$552$	−1.76585e53	−0.601371
$553$	−4.04683e53	−1.33038
$554$	−1.46213e53	−0.464030
$555$	8.72588e52	0.267360
$556$	−4.69752e52	−0.138967
$557$	−5.48790e53	−1.56758	−0.783790	−	0.621026i	$-0.786716\pi$
$557$	−5.48790e53	−1.56758	−0.783790	+	0.621026i	$0.786716\pi$
$558$	−1.11480e53	−0.307490
$559$	−4.68500e53	−1.24790
$560$	4.71251e53	1.21223
$561$	−1.04838e52	−0.0260461
$562$	−1.61307e52	−0.0387076
$563$	6.31928e53	1.46472	0.732359	−	0.680918i	$-0.238419\pi$
$563$	6.31928e53	1.46472	0.732359	+	0.680918i	$0.238419\pi$
$564$	3.90626e51	0.00874619
$565$	−5.02987e53	−1.08796
$566$	−1.58620e53	−0.331465
$567$	8.26459e52	0.166860
$568$	1.60413e53	0.312930
$569$	4.35425e52	0.0820775	0.0410388	−	0.999158i	$-0.486933\pi$
$569$	4.35425e52	0.0820775	0.0410388	+	0.999158i	$0.486933\pi$
$570$	3.15198e53	0.574147
$571$	6.53474e53	1.15034	0.575168	−	0.818036i	$-0.304937\pi$
$571$	6.53474e53	1.15034	0.575168	+	0.818036i	$0.304937\pi$
$572$	6.60133e51	0.0112307
$573$	−1.52728e52	−0.0251132
$574$	8.96845e53	1.42540
$575$	1.34647e52	0.0206859
$576$	2.48617e53	0.369226
$577$	−6.13059e53	−0.880185	−0.440092	−	0.897953i	$-0.645054\pi$
$577$	−6.13059e53	−0.880185	−0.440092	+	0.897953i	$0.645054\pi$
$578$	2.68994e53	0.373379
$579$	2.56963e53	0.344857
$580$	−1.27981e53	−0.166073
$581$	3.96666e53	0.497726
$582$	−6.94122e53	−0.842243
$583$	−3.34634e52	−0.0392675
$584$	−5.99295e53	−0.680127
$585$	5.28357e53	0.579947
$586$	−9.87831e53	−1.04877
$587$	3.72203e53	0.382241	0.191121	−	0.981567i	$-0.438788\pi$
$587$	3.72203e53	0.382241	0.191121	+	0.981567i	$0.438788\pi$
$588$	−1.25260e53	−0.124438
$589$	1.14039e54	1.09598
$590$	−1.77405e54	−1.64950
$591$	5.71209e53	0.513854
$592$	4.20553e53	0.366056
$593$	−2.12008e54	−1.78560	−0.892802	−	0.450450i	$-0.851264\pi$
$593$	−2.12008e54	−1.78560	−0.892802	+	0.450450i	$0.851264\pi$
$594$	8.16392e51	0.00665370
$595$	2.28494e54	1.80217
$596$	2.23396e53	0.170519
$597$	4.63772e53	0.342614
$598$	−2.14050e54	−1.53053
$599$	−2.24993e54	−1.55721	−0.778603	−	0.627517i	$-0.784071\pi$
$599$	−2.24993e54	−1.55721	−0.778603	+	0.627517i	$0.784071\pi$
$600$	−1.94618e52	−0.0130387
$601$	4.73602e53	0.307158	0.153579	−	0.988136i	$-0.450920\pi$
$601$	4.73602e53	0.307158	0.153579	+	0.988136i	$0.450920\pi$
$602$	1.57775e54	0.990617
$603$	−9.34878e53	−0.568287
$604$	1.76084e53	0.103633
$605$	1.77073e54	1.00908
$606$	9.68020e53	0.534156
$607$	7.49804e53	0.400653	0.200326	−	0.979729i	$-0.435800\pi$
$607$	7.49804e53	0.400653	0.200326	+	0.979729i	$0.435800\pi$
$608$	−7.09171e53	−0.366971
$609$	−1.65586e54	−0.829825
$610$	−1.42258e54	−0.690468
$611$	3.23107e53	0.151895
$612$	1.49272e53	0.0679711
$613$	5.17668e53	0.228335	0.114167	−	0.993462i	$-0.463580\pi$
$613$	5.17668e53	0.228335	0.114167	+	0.993462i	$0.463580\pi$
$614$	−2.05537e54	−0.878226
$615$	−1.46996e54	−0.608471
$616$	−1.51699e53	−0.0608358
$617$	1.54418e54	0.599981	0.299991	−	0.953942i	$-0.403016\pi$
$617$	1.54418e54	0.599981	0.299991	+	0.953942i	$0.403016\pi$
$618$	1.19819e54	0.451077
$619$	−8.41718e53	−0.307043	−0.153521	−	0.988145i	$-0.549061\pi$
$619$	−8.41718e53	−0.307043	−0.153521	+	0.988145i	$0.549061\pi$
$620$	−4.97561e53	−0.175877
$621$	5.48777e53	0.187979
$622$	4.28908e54	1.42381
$623$	3.52565e54	1.13428
$624$	2.54647e54	0.794034
$625$	−3.37731e54	−1.02073
$626$	3.75977e54	1.10144
$627$	−8.35126e52	−0.0237157
$628$	7.53601e53	0.207457
$629$	2.03912e54	0.544196
$630$	−1.77933e54	−0.460378
$631$	−2.69722e54	−0.676619	−0.338309	−	0.941035i	$-0.609855\pi$
$631$	−2.69722e54	−0.676619	−0.338309	+	0.941035i	$0.609855\pi$
$632$	3.88396e54	0.944696
$633$	−1.70660e54	−0.402493
$634$	−6.86898e53	−0.157091
$635$	1.16066e54	0.257406
$636$	4.76463e53	0.102474
$637$	−1.03609e55	−2.16112
$638$	−1.63569e53	−0.0330901
$639$	−4.98518e53	−0.0978169
$640$	−3.55063e54	−0.675765
$641$	−1.64292e54	−0.303308	−0.151654	−	0.988434i	$-0.548460\pi$
$641$	−1.64292e54	−0.303308	−0.151654	+	0.988434i	$0.548460\pi$
$642$	−1.65051e54	−0.295586
$643$	1.12355e54	0.195199	0.0975995	−	0.995226i	$-0.468884\pi$
$643$	1.12355e54	0.195199	0.0975995	+	0.995226i	$0.468884\pi$
$644$	−1.49436e54	−0.251873
$645$	−2.58598e54	−0.422874
$646$	7.36575e54	1.16865
$647$	−1.06644e55	−1.64174	−0.820870	−	0.571115i	$-0.806511\pi$
$647$	−1.06644e55	−1.64174	−0.820870	+	0.571115i	$0.806511\pi$
$648$	−7.93198e53	−0.118486
$649$	4.70041e53	0.0681341
$650$	−2.35909e53	−0.0331844
$651$	−6.43761e54	−0.878810
$652$	2.00542e54	0.265691
$653$	2.11443e54	0.271886	0.135943	−	0.990717i	$-0.456594\pi$
$653$	2.11443e54	0.271886	0.135943	+	0.990717i	$0.456594\pi$
$654$	4.86771e54	0.607517
$655$	1.55950e55	1.88921
$656$	−7.08461e54	−0.833089
$657$	1.86244e54	0.212597
$658$	−1.08811e54	−0.120578
$659$	1.16605e55	1.25445	0.627225	−	0.778838i	$-0.284191\pi$
$659$	1.16605e55	1.25445	0.627225	+	0.778838i	$0.284191\pi$
$660$	3.64373e52	0.00380575
$661$	−1.41645e54	−0.143639	−0.0718197	−	0.997418i	$-0.522881\pi$
$661$	−1.41645e54	−0.143639	−0.0718197	+	0.997418i	$0.522881\pi$
$662$	−1.12852e55	−1.11116
$663$	1.23470e55	1.18045
$664$	−3.80702e54	−0.353433
$665$	1.82016e55	1.64092
$666$	−1.58790e54	−0.139020
$667$	−1.09951e55	−0.934855
$668$	6.70641e53	0.0553795
$669$	−4.84213e54	−0.388353
$670$	2.01275e55	1.56794
$671$	3.76916e53	0.0285204
$672$	4.00335e54	0.294254
$673$	2.36621e55	1.68951	0.844753	−	0.535156i	$-0.179747\pi$
$673$	2.36621e55	1.68951	0.844753	+	0.535156i	$0.179747\pi$
$674$	−1.48060e55	−1.02700
$675$	6.04819e52	0.00407570
$676$	−5.15178e54	−0.337285
$677$	−1.89149e55	−1.20316	−0.601581	−	0.798812i	$-0.705462\pi$
$677$	−1.89149e55	−1.20316	−0.601581	+	0.798812i	$0.705462\pi$
$678$	9.15316e54	0.565708
$679$	−4.00832e55	−2.40714
$680$	−2.19298e55	−1.27971
$681$	7.85333e54	0.445333
$682$	−6.35919e53	−0.0350434
$683$	−7.86138e54	−0.421012	−0.210506	−	0.977593i	$-0.567511\pi$
$683$	−7.86138e54	−0.421012	−0.210506	+	0.977593i	$0.567511\pi$
$684$	1.18908e54	0.0618895
$685$	2.89183e55	1.46288
$686$	7.09443e54	0.348817
$687$	−3.51838e54	−0.168146
$688$	−1.24634e55	−0.578977
$689$	3.94106e55	1.77967
$690$	−1.18149e55	−0.518648
$691$	−2.28466e55	−0.974987	−0.487493	−	0.873127i	$-0.662089\pi$
$691$	−2.28466e55	−0.974987	−0.487493	+	0.873127i	$0.662089\pi$
$692$	−3.88789e54	−0.161304
$693$	4.71438e53	0.0190163
$694$	2.78931e54	0.109392
$695$	−2.14471e55	−0.817834
$696$	1.58922e55	0.589255
$697$	−3.43510e55	−1.23851
$698$	1.27481e54	0.0446958
$699$	−6.02657e54	−0.205478
$700$	−1.64697e53	−0.00546102
$701$	1.34200e55	0.432763	0.216382	−	0.976309i	$-0.430574\pi$
$701$	1.34200e55	0.432763	0.216382	+	0.976309i	$0.430574\pi$
$702$	−9.61483e54	−0.301556
$703$	1.62434e55	0.495505
$704$	1.41819e54	0.0420792
$705$	1.78345e54	0.0514723
$706$	5.46200e55	1.53342
$707$	5.58998e55	1.52662
$708$	−6.69260e54	−0.177806
$709$	2.37185e55	0.613034	0.306517	−	0.951865i	$-0.400836\pi$
$709$	2.37185e55	0.613034	0.306517	+	0.951865i	$0.400836\pi$
$710$	1.07328e55	0.269884
$711$	−1.20703e55	−0.295297
$712$	−3.38375e55	−0.805451
$713$	−4.27463e55	−0.990040
$714$	−4.15805e55	−0.937075
$715$	3.01392e54	0.0660942
$716$	6.95542e53	0.0148429
$717$	−3.80531e54	−0.0790253
$718$	−2.01496e55	−0.407230
$719$	2.91345e55	0.573052	0.286526	−	0.958072i	$-0.407499\pi$
$719$	2.91345e55	0.573052	0.286526	+	0.958072i	$0.407499\pi$
$720$	1.40558e55	0.269073
$721$	6.91914e55	1.28918
$722$	8.49052e54	0.153978
$723$	1.26914e55	0.224033
$724$	1.13057e55	0.194266
$725$	−1.21179e54	−0.0202692
$726$	−3.22231e55	−0.524691
$727$	−6.49549e55	−1.02965	−0.514827	−	0.857294i	$-0.672144\pi$
$727$	−6.49549e55	−1.02965	−0.514827	+	0.857294i	$0.672144\pi$
$728$	1.78660e56	2.75718
$729$	2.46503e54	0.0370370
$730$	−4.00974e55	−0.586571
$731$	−6.04309e55	−0.860736
$732$	−5.36665e54	−0.0744282
$733$	−1.85011e55	−0.249844	−0.124922	−	0.992167i	$-0.539868\pi$
$733$	−1.85011e55	−0.249844	−0.124922	+	0.992167i	$0.539868\pi$
$734$	−7.72360e55	−1.01566
$735$	−5.71890e55	−0.732334
$736$	2.65826e55	0.331498
$737$	−5.33284e54	−0.0647653
$738$	2.67497e55	0.316388
$739$	−1.25445e56	−1.44507	−0.722533	−	0.691337i	$-0.757022\pi$
$739$	−1.25445e56	−1.44507	−0.722533	+	0.691337i	$0.757022\pi$
$740$	−7.08715e54	−0.0795157
$741$	9.83547e55	1.07483
$742$	−1.32722e56	−1.41275
$743$	−1.55554e56	−1.61287	−0.806435	−	0.591323i	$-0.798606\pi$
$743$	−1.55554e56	−1.61287	−0.806435	+	0.591323i	$0.798606\pi$
$744$	6.17852e55	0.624040
$745$	1.01994e56	1.00352
$746$	1.35969e55	0.130327
$747$	1.18311e55	0.110478
$748$	8.51492e53	0.00774639
$749$	−9.53111e55	−0.844789
$750$	6.01838e55	0.519739
$751$	−3.51389e55	−0.295671	−0.147836	−	0.989012i	$-0.547231\pi$
$751$	−3.51389e55	−0.295671	−0.147836	+	0.989012i	$0.547231\pi$
$752$	8.59552e54	0.0704733
$753$	−8.47542e55	−0.677110
$754$	1.92639e56	1.49969
$755$	8.03933e55	0.609894
$756$	−6.71249e54	−0.0496259
$757$	2.06718e56	1.48939	0.744694	−	0.667406i	$-0.232595\pi$
$757$	2.06718e56	1.48939	0.744694	+	0.667406i	$0.232595\pi$
$758$	9.13759e55	0.641626
$759$	3.13039e54	0.0214232
$760$	−1.74690e56	−1.16521
$761$	2.29387e56	1.49131	0.745654	−	0.666334i	$-0.232137\pi$
$761$	2.29387e56	1.49131	0.745654	+	0.666334i	$0.232137\pi$
$762$	−2.11213e55	−0.133844
$763$	2.81093e56	1.73629
$764$	1.24045e54	0.00746895
$765$	6.81518e55	0.400018
$766$	1.83731e56	1.05129
$767$	−5.53578e56	−3.08794
$768$	−5.29843e55	−0.288140
$769$	−6.24542e55	−0.331130	−0.165565	−	0.986199i	$-0.552945\pi$
$769$	−6.24542e55	−0.331130	−0.165565	+	0.986199i	$0.552945\pi$
$770$	−1.01498e55	−0.0524674
$771$	1.69840e56	0.856009
$772$	−2.08705e55	−0.102564
$773$	−2.48233e56	−1.18948	−0.594742	−	0.803917i	$-0.702746\pi$
$773$	−2.48233e56	−1.18948	−0.594742	+	0.803917i	$0.702746\pi$
$774$	4.70586e55	0.219882
$775$	−4.71116e54	−0.0214657
$776$	3.84700e56	1.70930
$777$	−9.16958e55	−0.397319
$778$	−3.96827e56	−1.67687
$779$	−2.73636e56	−1.12770
$780$	−4.29131e55	−0.172482
$781$	−2.84370e54	−0.0111478
$782$	−2.76098e56	−1.05568
$783$	−4.93884e55	−0.184192
$784$	−2.75628e56	−1.00268
$785$	3.44066e56	1.22091
$786$	−2.83792e56	−0.982338
$787$	3.71812e56	1.25550	0.627749	−	0.778416i	$-0.283976\pi$
$787$	3.71812e56	1.25550	0.627749	+	0.778416i	$0.283976\pi$
$788$	−4.63935e55	−0.152826
$789$	3.00396e55	0.0965366
$790$	2.59867e56	0.814747
$791$	5.28563e56	1.61680
$792$	−4.52465e54	−0.0135034
$793$	−4.43903e56	−1.29259
$794$	−3.23889e56	−0.920231
$795$	2.17535e56	0.603073
$796$	−3.76675e55	−0.101897
$797$	4.19694e56	1.10789	0.553944	−	0.832554i	$-0.313122\pi$
$797$	4.19694e56	1.10789	0.553944	+	0.832554i	$0.313122\pi$
$798$	−3.31225e56	−0.853231
$799$	4.16769e55	0.104769
$800$	2.92973e54	0.00718742
$801$	1.05158e56	0.251771
$802$	2.95682e56	0.690914
$803$	1.06239e55	0.0242288
$804$	7.59307e55	0.169015
$805$	−6.82270e56	−1.48230
$806$	7.48936e56	1.58822
$807$	7.54091e55	0.156095
$808$	−5.36501e56	−1.08405
$809$	−2.18181e56	−0.430349	−0.215175	−	0.976576i	$-0.569032\pi$
$809$	−2.18181e56	−0.430349	−0.215175	+	0.976576i	$0.569032\pi$
$810$	−5.30710e55	−0.102188
$811$	4.74906e56	0.892690	0.446345	−	0.894861i	$-0.352725\pi$
$811$	4.74906e56	0.892690	0.446345	+	0.894861i	$0.352725\pi$
$812$	1.34489e56	0.246799
$813$	2.18672e56	0.391767
$814$	−9.05788e54	−0.0158435
$815$	9.15598e56	1.56362
$816$	3.28464e56	0.547684
$817$	−4.81385e56	−0.783723
$818$	9.64297e55	0.153293
$819$	−5.55224e56	−0.861850
$820$	1.19390e56	0.180966
$821$	2.22668e56	0.329584	0.164792	−	0.986328i	$-0.447305\pi$
$821$	2.22668e56	0.329584	0.164792	+	0.986328i	$0.447305\pi$
$822$	−5.26244e56	−0.760654
$823$	−5.24389e56	−0.740213	−0.370107	−	0.928989i	$-0.620679\pi$
$823$	−5.24389e56	−0.740213	−0.370107	+	0.928989i	$0.620679\pi$
$824$	−6.64067e56	−0.915443
$825$	3.45008e53	0.000464490 0
$826$	1.86426e57	2.45130
$827$	−7.47674e56	−0.960185	−0.480092	−	0.877218i	$-0.659397\pi$
$827$	−7.47674e56	−0.960185	−0.480092	+	0.877218i	$0.659397\pi$
$828$	−4.45716e55	−0.0559070
$829$	8.89160e56	1.08935	0.544674	−	0.838648i	$-0.316653\pi$
$829$	8.89160e56	1.08935	0.544674	+	0.838648i	$0.316653\pi$
$830$	−2.54718e56	−0.304816
$831$	−2.51834e56	−0.294371
$832$	−1.67023e57	−1.90710
$833$	−1.33643e57	−1.49063
$834$	3.90286e56	0.425251
$835$	3.06189e56	0.325915
$836$	6.78288e54	0.00705329
$837$	−1.92011e56	−0.195065
$838$	1.13884e57	1.13033
$839$	8.13975e56	0.789320	0.394660	−	0.918827i	$-0.370862\pi$
$839$	8.13975e56	0.789320	0.394660	+	0.918827i	$0.370862\pi$
$840$	9.86147e56	0.934320
$841$	−9.07171e55	−0.0839783
$842$	−1.28424e57	−1.16161
$843$	−2.77832e55	−0.0245553
$844$	1.38610e56	0.119706
$845$	−2.35211e57	−1.98496
$846$	−3.24545e55	−0.0267641
$847$	−1.86077e57	−1.49957
$848$	1.04843e57	0.825697
$849$	−2.73203e56	−0.210274
$850$	−3.04294e55	−0.0228889
$851$	−6.08869e56	−0.447608
$852$	4.04895e55	0.0290918
$853$	2.27332e57	1.59645	0.798223	−	0.602362i	$-0.205773\pi$
$853$	2.27332e57	1.59645	0.798223	+	0.602362i	$0.205773\pi$
$854$	1.49491e57	1.02609
$855$	5.42889e56	0.364226
$856$	9.14753e56	0.599881
$857$	7.35063e56	0.471193	0.235596	−	0.971851i	$-0.424296\pi$
$857$	7.35063e56	0.471193	0.235596	+	0.971851i	$0.424296\pi$
$858$	−5.48460e55	−0.0343671
$859$	−2.20018e57	−1.34770	−0.673848	−	0.738870i	$-0.735360\pi$
$859$	−2.20018e57	−1.34770	−0.673848	+	0.738870i	$0.735360\pi$
$860$	2.10033e56	0.125767
$861$	1.54470e57	0.904240
$862$	9.69454e56	0.554799
$863$	1.59256e57	0.891016	0.445508	−	0.895278i	$-0.353023\pi$
$863$	1.59256e57	0.891016	0.445508	+	0.895278i	$0.353023\pi$
$864$	1.19406e56	0.0653141
$865$	−1.77507e57	−0.949293
$866$	−7.93701e56	−0.415010
$867$	4.63309e56	0.236864
$868$	5.22861e56	0.261368
$869$	−6.88526e55	−0.0336538
$870$	1.06331e57	0.508199
$871$	6.28061e57	2.93527
$872$	−2.69780e57	−1.23293
$873$	−1.19554e57	−0.534301
$874$	−2.19937e57	−0.961224
$875$	3.47541e57	1.48542
$876$	−1.51267e56	−0.0632287
$877$	−4.57607e57	−1.87068	−0.935342	−	0.353745i	$-0.884908\pi$
$877$	−4.57607e57	−1.87068	−0.935342	+	0.353745i	$0.884908\pi$
$878$	−2.83185e57	−1.13221
$879$	−1.70142e57	−0.665315
$880$	8.01784e55	0.0306652
$881$	2.25056e57	0.841898	0.420949	−	0.907084i	$-0.361697\pi$
$881$	2.25056e57	0.841898	0.420949	+	0.907084i	$0.361697\pi$
$882$	1.04070e57	0.380793
$883$	−3.31542e56	−0.118660	−0.0593300	−	0.998238i	$-0.518896\pi$
$883$	−3.31542e56	−0.118660	−0.0593300	+	0.998238i	$0.518896\pi$
$884$	−1.00282e57	−0.351079
$885$	−3.05559e57	−1.04641
$886$	−3.20683e57	−1.07428
$887$	1.34789e56	0.0441717	0.0220858	−	0.999756i	$-0.492969\pi$
$887$	1.34789e56	0.0441717	0.0220858	+	0.999756i	$0.492969\pi$
$888$	8.80055e56	0.282135
$889$	−1.21968e57	−0.382527
$890$	−2.26399e57	−0.694656
$891$	1.40613e55	0.00422096
$892$	3.93277e56	0.115500
$893$	3.31993e56	0.0953950
$894$	−1.85605e57	−0.521805
$895$	3.17558e56	0.0873522
$896$	3.73117e57	1.00424
$897$	−3.68674e57	−0.970934
$898$	−1.12882e57	−0.290895
$899$	3.84705e57	0.970095
$900$	−4.91233e54	−0.00121216
$901$	5.08350e57	1.22752
$902$	1.52589e56	0.0360575
$903$	2.71747e57	0.628426
$904$	−5.07291e57	−1.14808
$905$	5.16177e57	1.14328
$906$	−1.46297e57	−0.317128
$907$	3.17933e57	0.674517	0.337259	−	0.941412i	$-0.390500\pi$
$907$	3.17933e57	0.674517	0.337259	+	0.941412i	$0.390500\pi$
$908$	−6.37846e56	−0.132447
$909$	1.66729e57	0.338857
$910$	1.19537e58	2.37791
$911$	1.42416e56	0.0277300	0.0138650	−	0.999904i	$-0.495586\pi$
$911$	1.42416e56	0.0277300	0.0138650	+	0.999904i	$0.495586\pi$
$912$	2.61651e57	0.498681
$913$	6.74885e55	0.0125907
$914$	1.29377e57	0.236269
$915$	−2.45021e57	−0.438018
$916$	2.85762e56	0.0500084
$917$	−1.63880e58	−2.80753
$918$	−1.24020e57	−0.207998
$919$	−1.61610e57	−0.265348	−0.132674	−	0.991160i	$-0.542356\pi$
$919$	−1.61610e57	−0.265348	−0.132674	+	0.991160i	$0.542356\pi$
$920$	6.54811e57	1.05258
$921$	−3.54011e57	−0.557127
$922$	−1.08585e58	−1.67308
$923$	3.34909e57	0.505236
$924$	−3.82901e55	−0.00565566
$925$	−6.71048e55	−0.00970487
$926$	5.67087e57	0.803036
$927$	2.06373e57	0.286153
$928$	−2.39237e57	−0.324819
$929$	3.89998e57	0.518508	0.259254	−	0.965809i	$-0.416523\pi$
$929$	3.89998e57	0.518508	0.259254	+	0.965809i	$0.416523\pi$
$930$	4.13390e57	0.538199
$931$	−1.06458e58	−1.35725
$932$	4.89477e56	0.0611114
$933$	7.38740e57	0.903232
$934$	7.47332e57	0.894849
$935$	3.88759e56	0.0455884
$936$	5.32878e57	0.611996
$937$	−2.52619e57	−0.284148	−0.142074	−	0.989856i	$-0.545377\pi$
$937$	−2.52619e57	−0.284148	−0.142074	+	0.989856i	$0.545377\pi$
$938$	−2.11509e58	−2.33010
$939$	6.47574e57	0.698732
$940$	−1.44852e56	−0.0153084
$941$	−7.20442e57	−0.745763	−0.372882	−	0.927879i	$-0.621630\pi$
$941$	−7.20442e57	−0.745763	−0.372882	+	0.927879i	$0.621630\pi$
$942$	−6.26117e57	−0.634838
$943$	1.02570e58	1.01869
$944$	−1.47267e58	−1.43269
$945$	−3.06467e57	−0.292054
$946$	2.68437e56	0.0250591
$947$	−3.57570e56	−0.0326992	−0.0163496	−	0.999866i	$-0.505204\pi$
$947$	−3.57570e56	−0.0326992	−0.0163496	+	0.999866i	$0.505204\pi$
$948$	9.80345e56	0.0878246
$949$	−1.25121e58	−1.09809
$950$	−2.42397e56	−0.0208409
$951$	−1.18310e57	−0.0996551
$952$	2.30449e58	1.90176
$953$	2.36891e58	1.91530	0.957652	−	0.287929i	$-0.0929668\pi$
$953$	2.36891e58	1.91530	0.957652	+	0.287929i	$0.0929668\pi$
$954$	−3.95861e57	−0.313581
$955$	5.66343e56	0.0439556
$956$	3.09066e56	0.0235030
$957$	−2.81727e56	−0.0209916
$958$	1.33475e57	0.0974477
$959$	−3.03888e58	−2.17396
$960$	−9.21919e57	−0.646255
$961$	3.98317e56	0.0273604
$962$	1.06677e58	0.718052
$963$	−2.84279e57	−0.187514
$964$	−1.03079e57	−0.0666299
$965$	−9.52868e57	−0.603601
$966$	1.24157e58	0.770755
$967$	−4.76265e57	−0.289756	−0.144878	−	0.989450i	$-0.546279\pi$
$967$	−4.76265e57	−0.289756	−0.144878	+	0.989450i	$0.546279\pi$
$968$	1.78589e58	1.06484
$969$	1.26866e58	0.741363
$970$	2.57394e58	1.47417
$971$	3.36164e56	0.0188702	0.00943510	−	0.999955i	$-0.496997\pi$
$971$	3.36164e56	0.0188702	0.00943510	+	0.999955i	$0.496997\pi$
$972$	−2.00210e56	−0.0110152
$973$	2.25377e58	1.21537
$974$	1.52102e58	0.803961
$975$	−4.06323e56	−0.0210514
$976$	−1.18090e58	−0.599712
$977$	6.50958e57	0.324048	0.162024	−	0.986787i	$-0.448198\pi$
$977$	6.50958e57	0.324048	0.162024	+	0.986787i	$0.448198\pi$
$978$	−1.66617e58	−0.813038
$979$	5.99852e56	0.0286934
$980$	4.64488e57	0.217804
$981$	8.38402e57	0.385395
$982$	−3.14911e58	−1.41910
$983$	−1.98360e58	−0.876315	−0.438158	−	0.898898i	$-0.644369\pi$
$983$	−1.98360e58	−0.876315	−0.438158	+	0.898898i	$0.644369\pi$
$984$	−1.48254e58	−0.642097
$985$	−2.11815e58	−0.899396
$986$	2.48481e58	1.03441
$987$	−1.87414e57	−0.0764922
$988$	−7.98836e57	−0.319666
$989$	1.80443e58	0.707965
$990$	−3.02734e56	−0.0116459
$991$	8.49263e57	0.320336	0.160168	−	0.987090i	$-0.448796\pi$
$991$	8.49263e57	0.320336	0.160168	+	0.987090i	$0.448796\pi$
$992$	−9.30097e57	−0.343994
$993$	−1.94373e58	−0.704898
$994$	−1.12786e58	−0.401071
$995$	−1.71975e58	−0.599676
$996$	−9.60923e56	−0.0328573
$997$	−3.24438e57	−0.108787	−0.0543934	−	0.998520i	$-0.517323\pi$
$997$	−3.24438e57	−0.108787	−0.0543934	+	0.998520i	$0.517323\pi$
$998$	2.53065e58	0.832120
$999$	−2.73496e57	−0.0881910

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.40.a.a.1.3	✓	3
3.2	odd	2		9.40.a.d.1.1		3

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 40 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q+674802. q^{2} +1.16226e9 q^{3} -9.43987e10 q^{4} -4.30989e13 q^{5} +7.84296e14 q^{6} +4.52904e16 q^{7} -4.34676e17 q^{8} +1.35085e18 q^{9} +O(q^{10})\)	\(q+674802. q^{2} +1.16226e9 q^{3} -9.43987e10 q^{4} -4.30989e13 q^{5} +7.84296e14 q^{6} +4.52904e16 q^{7} -4.34676e17 q^{8} +1.35085e18 q^{9} -2.90832e19 q^{10} +7.70568e18 q^{11} -1.09716e20 q^{12} -9.07516e21 q^{13} +3.05620e22 q^{14} -5.00921e22 q^{15} -2.41424e23 q^{16} -1.17059e24 q^{17} +9.11557e23 q^{18} -9.32475e24 q^{19} +4.06848e24 q^{20} +5.26393e25 q^{21} +5.19981e24 q^{22} +3.49530e26 q^{23} -5.05208e26 q^{24} +3.85224e25 q^{25} -6.12393e27 q^{26} +1.57004e27 q^{27} -4.27535e27 q^{28} -3.14567e28 q^{29} -3.38023e28 q^{30} -1.22297e29 q^{31} +7.60525e28 q^{32} +8.95602e27 q^{33} -7.89914e29 q^{34} -1.95196e30 q^{35} -1.27519e29 q^{36} -1.74197e30 q^{37} -6.29236e30 q^{38} -1.05477e31 q^{39} +1.87341e31 q^{40} +2.93451e31 q^{41} +3.55211e31 q^{42} +5.16244e31 q^{43} -7.27406e29 q^{44} -5.82202e31 q^{45} +2.35863e32 q^{46} -3.56034e31 q^{47} -2.80598e32 q^{48} +1.14168e33 q^{49} +2.59950e31 q^{50} -1.36053e33 q^{51} +8.56683e32 q^{52} -4.34269e33 q^{53} +1.05947e33 q^{54} -3.32106e32 q^{55} -1.96867e34 q^{56} -1.08378e34 q^{57} -2.12271e34 q^{58} +6.09993e34 q^{59} +4.72863e33 q^{60} +4.89141e34 q^{61} -8.25259e34 q^{62} +6.11806e34 q^{63} +1.84045e35 q^{64} +3.91129e35 q^{65} +6.04353e33 q^{66} -6.92066e35 q^{67} +1.10502e35 q^{68} +4.06245e35 q^{69} -1.31719e36 q^{70} -3.69040e35 q^{71} -5.87183e35 q^{72} +1.37872e36 q^{73} -1.17548e36 q^{74} +4.47732e34 q^{75} +8.80244e35 q^{76} +3.48993e35 q^{77} -7.11761e36 q^{78} -8.93530e36 q^{79} +1.04051e37 q^{80} +1.82480e36 q^{81} +1.98021e37 q^{82} +8.75828e36 q^{83} -4.96908e36 q^{84} +5.04510e37 q^{85} +3.48363e37 q^{86} -3.65610e37 q^{87} -3.34948e36 q^{88} +7.78454e37 q^{89} -3.92871e37 q^{90} -4.11017e38 q^{91} -3.29952e37 q^{92} -1.42141e38 q^{93} -2.40252e37 q^{94} +4.01886e38 q^{95} +8.83929e37 q^{96} -8.85026e38 q^{97} +7.70405e38 q^{98} +1.04092e37 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 1107000 q^{2} + 3486784401 q^{3} + 1005900225600 q^{4} + 9357049429290 q^{5} - 12\!\cdots\!00 q^{6}+ \cdots + 40\!\cdots\!67 q^{9}+O(q^{10}) \) 3 * q - 1107000 * q^2 + 3486784401 * q^3 + 1005900225600 * q^4 + 9357049429290 * q^5 - 1286623443969000 * q^6 + 13841884377460104 * q^7 - 1526556980351135232 * q^8 + 4052555153018976267 * q^9	\( 3 q - 1107000 q^{2} + 3486784401 q^{3} + 1005900225600 q^{4} + 9357049429290 q^{5} - 12\!\cdots\!00 q^{6}+ \cdots - 54\!\cdots\!44 q^{99}+O(q^{100}) \) 3 * q - 1107000 * q^2 + 3486784401 * q^3 + 1005900225600 * q^4 + 9357049429290 * q^5 - 1286623443969000 * q^6 + 13841884377460104 * q^7 - 1526556980351135232 * q^8 + 4052555153018976267 * q^9 - 76029599179042436880 * q^10 - 40050327611147243796 * q^11 + 1169119071861486955200 * q^12 - 13932702500978393486094 * q^13 + 64143032386415214972096 * q^14 + 10875337996478108168430 * q^15 + 1098810764821648805597184 * q^16 - 169700805136994180103018 * q^17 - 1495392851464002242523000 * q^18 - 6957470542505489016962988 * q^19 + 33307320359730090833619840 * q^20 + 16087888842591162209012568 * q^21 - 182808419494676144863843296 * q^22 - 257172639984224911978099272 * q^23 - 1774258355442000609859705344 * q^24 - 2223570708999165320980345275 * q^25 + 6420909995769964414290523056 * q^26 + 4710128697246244834921603689 * q^27 - 31489800993928145336514267648 * q^28 - 46272789498091624686435987486 * q^29 - 88366273477255858343403702960 * q^30 - 282753969983174411853352917888 * q^31 - 1118437222052144608340712062976 * q^32 - 46548952523162601127345608732 * q^33 - 2020045599738440464009480297200 * q^34 - 2778733015107044038012367571600 * q^35 + 1358822047559410249352115278400 * q^36 - 5239395449699583862273344438486 * q^37 - 4077508380452877314541820882464 * q^38 - 16193443248061716548450856539898 * q^39 - 10242585699763810314758557271040 * q^40 + 47673397400045140822464268984782 * q^41 + 74550974919263458624588661024832 * q^42 - 14936449213367655469478076825588 * q^43 + 383801287439893621552232462293248 * q^44 + 12639986293907486833224134886810 * q^45 + 646689351161727342528587792407872 * q^46 - 13040685113470292045769719198544 * q^47 + 1277105411477001534152180886908928 * q^48 - 132364363537073708245470314514213 * q^49 + 2030100946651365938753014066519800 * q^50 - 197236706729603991736995911807406 * q^51 - 16457201727541975997405015057804928 * q^52 - 11047064078175508118010662971794342 * q^53 - 1738037489283864344086071761241000 * q^54 - 1504305246366733376700435214523160 * q^55 + 6316090378583898308960601541324800 * q^56 - 8086399919341715520407790317583396 * q^57 - 23720839646010288107197368475070928 * q^58 + 35633406741119515209244171316491548 * q^59 + 38711815023138863096326248158705280 * q^60 - 26245828903346977727221409425735902 * q^61 - 98335445202496226432366585960435712 * q^62 + 18698333287122936270281907905117256 * q^63 + 922428812776307390107790824712699904 * q^64 + 260861961831082759405211612047737660 * q^65 - 212471181821833694819355024467075232 * q^66 - 200741546976450474071235708204779388 * q^67 + 1264175105126717513162323757007619200 * q^68 - 298901849820328103053611531746352024 * q^69 - 431344371239166538676321844662332800 * q^70 - 3140665348656484831244609799236867544 * q^71 - 2062152119033027062230435797305179648 * q^72 - 3825610182002392515733100347600509522 * q^73 - 2544605510256173934291855124681995024 * q^74 - 2584370554219599987738141977488018425 * q^75 - 5521658898639443517674491687212787968 * q^76 - 994601047124972255067887751426792672 * q^77 + 7462776271158562634691099091263883152 * q^78 - 1038716953120555158347640895730970000 * q^79 + 45766070974584297712698519042271272960 * q^80 + 5474401089420219382077155933569751763 * q^81 - 16726391180845396277548112611717202352 * q^82 + 69227326737654458476356626745129089940 * q^83 - 36599382298740984291406281382995119616 * q^84 + 76820078772499304751574061990694660660 * q^85 + 159762376422294357818512142478616905504 * q^86 - 53781080204234165408470505817072001962 * q^87 - 343351801449478884201073068755288881152 * q^88 + 136597710245735759116899165769855535742 * q^89 - 102704714644998585052548577575521842320 * q^90 - 259984668223904357182500109993449632208 * q^91 - 135698237299460735254844067932094260736 * q^92 - 328634043952718257237540151213237421696 * q^93 + 457887889864219720177610385758047412352 * q^94 + 462468326274179393065716948072305471640 * q^95 - 1299916486449730342986216438139082145792 * q^96 - 1338928527743499267936157260425715870618 * q^97 + 1730483839907526080834886072855293848584 * q^98 - 54102053846884316265804561020862329844 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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