LMFDB - Embedded newform 5.20.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,20,Mod(1,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 20, names="a")

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

chi := DirichletCharacter("5.1");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 20 $
Character orbit:	$[\chi]$	$=$	5.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:	$11.4408348278$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 323561x^{2} - 26738538x + 10870990650 $ x^4 - 2x^3 - 323561x^2 - 26738538*x + 10870990650
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8}\cdot 3^{2}\cdot 5^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$581.867$ of defining polynomial
Character	$\chi$	$=$	5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+208.721 q^{2} -48249.1 q^{3} -480724. q^{4} -1.95312e6 q^{5} -1.00706e7 q^{6} +1.75500e8 q^{7} -2.09767e8 q^{8} +1.16572e9 q^{9} +O(q^{10})$	\(q+208.721 q^{2} -48249.1 q^{3} -480724. q^{4} -1.95312e6 q^{5} -1.00706e7 q^{6} +1.75500e8 q^{7} -2.09767e8 q^{8} +1.16572e9 q^{9} -4.07657e8 q^{10} -7.20233e9 q^{11} +2.31945e10 q^{12} +4.88586e10 q^{13} +3.66304e10 q^{14} +9.42366e10 q^{15} +2.08255e11 q^{16} -3.15530e11 q^{17} +2.43309e11 q^{18} +1.67456e12 q^{19} +9.38914e11 q^{20} -8.46771e12 q^{21} -1.50328e12 q^{22} -1.12559e13 q^{23} +1.01211e13 q^{24} +3.81470e12 q^{25} +1.01978e13 q^{26} -1.66677e11 q^{27} -8.43669e13 q^{28} +9.59543e13 q^{29} +1.96691e13 q^{30} +3.98884e13 q^{31} +1.53445e14 q^{32} +3.47506e14 q^{33} -6.58576e13 q^{34} -3.42773e14 q^{35} -5.60387e14 q^{36} -1.13986e14 q^{37} +3.49514e14 q^{38} -2.35738e15 q^{39} +4.09700e14 q^{40} +8.10592e14 q^{41} -1.76738e15 q^{42} +2.92953e15 q^{43} +3.46233e15 q^{44} -2.27679e15 q^{45} -2.34933e15 q^{46} +7.31034e15 q^{47} -1.00481e16 q^{48} +1.94013e16 q^{49} +7.96206e14 q^{50} +1.52240e16 q^{51} -2.34875e16 q^{52} -8.73883e15 q^{53} -3.47889e13 q^{54} +1.40671e16 q^{55} -3.68140e16 q^{56} -8.07959e16 q^{57} +2.00276e16 q^{58} +3.61007e16 q^{59} -4.53017e16 q^{60} +4.97095e16 q^{61} +8.32554e15 q^{62} +2.04583e17 q^{63} -7.71584e16 q^{64} -9.54269e16 q^{65} +7.25317e16 q^{66} -2.71958e17 q^{67} +1.51683e17 q^{68} +5.43086e17 q^{69} -7.15438e16 q^{70} +4.20293e17 q^{71} -2.44528e17 q^{72} -2.99464e17 q^{73} -2.37913e16 q^{74} -1.84056e17 q^{75} -8.04999e17 q^{76} -1.26401e18 q^{77} -4.92034e17 q^{78} +1.67263e18 q^{79} -4.06748e17 q^{80} -1.34682e18 q^{81} +1.69187e17 q^{82} +2.03135e18 q^{83} +4.07063e18 q^{84} +6.16269e17 q^{85} +6.11452e17 q^{86} -4.62971e18 q^{87} +1.51081e18 q^{88} -6.32365e18 q^{89} -4.75213e17 q^{90} +8.57467e18 q^{91} +5.41096e18 q^{92} -1.92458e18 q^{93} +1.52582e18 q^{94} -3.27062e18 q^{95} -7.40360e18 q^{96} -1.93684e18 q^{97} +4.04944e18 q^{98} -8.39588e18 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 420 q^{2} + 3080 q^{3} + 2084992 q^{4} - 7812500 q^{5} - 58071752 q^{6} + 214021400 q^{7} + 81737760 q^{8} + 154064548 q^{9}+O(q^{10}) $ 4 * q - 420 * q^2 + 3080 * q^3 + 2084992 * q^4 - 7812500 * q^5 - 58071752 * q^6 + 214021400 * q^7 + 81737760 * q^8 + 154064548 * q^9	$ 4 q - 420 q^{2} + 3080 q^{3} + 2084992 q^{4} - 7812500 q^{5} - 58071752 q^{6} + 214021400 q^{7} + 81737760 q^{8} + 154064548 q^{9} + 820312500 q^{10} + 11585712768 q^{11} + 105629359360 q^{12} + 14812333160 q^{13} + 185174155944 q^{14} - 6015625000 q^{15} + 1785780098944 q^{16} + 849033742440 q^{17} - 2113778999620 q^{18} + 1978167708560 q^{19} - 4072250000000 q^{20} - 1487020185552 q^{21} - 7953348762240 q^{22} - 26569906952760 q^{23} - 39774243472320 q^{24} + 15258789062500 q^{25} - 48695658207912 q^{26} - 7557605929360 q^{27} + 236612033519360 q^{28} + 116267174339640 q^{29} + 113421390625000 q^{30} + 251049672388688 q^{31} - 142495342974720 q^{32} + 359905680636160 q^{33} + 411849015040344 q^{34} - 418010546875000 q^{35} - 168308645735296 q^{36} + 53471657716520 q^{37} - 52\!\cdots\!60 q^{38}+ \cdots - 25\!\cdots\!84 q^{99}+O(q^{100}) $ 4 * q - 420 * q^2 + 3080 * q^3 + 2084992 * q^4 - 7812500 * q^5 - 58071752 * q^6 + 214021400 * q^7 + 81737760 * q^8 + 154064548 * q^9 + 820312500 * q^10 + 11585712768 * q^11 + 105629359360 * q^12 + 14812333160 * q^13 + 185174155944 * q^14 - 6015625000 * q^15 + 1785780098944 * q^16 + 849033742440 * q^17 - 2113778999620 * q^18 + 1978167708560 * q^19 - 4072250000000 * q^20 - 1487020185552 * q^21 - 7953348762240 * q^22 - 26569906952760 * q^23 - 39774243472320 * q^24 + 15258789062500 * q^25 - 48695658207912 * q^26 - 7557605929360 * q^27 + 236612033519360 * q^28 + 116267174339640 * q^29 + 113421390625000 * q^30 + 251049672388688 * q^31 - 142495342974720 * q^32 + 359905680636160 * q^33 + 411849015040344 * q^34 - 418010546875000 * q^35 - 168308645735296 * q^36 + 53471657716520 * q^37 - 5247417886886160 * q^38 - 3407032515417904 * q^39 - 159644062500000 * q^40 + 5606221897948248 * q^41 - 6858180778710960 * q^42 + 3924193112762600 * q^43 + 7741056858814464 * q^44 - 300907320312500 * q^45 - 13726548710068872 * q^46 + 9972444326989560 * q^47 + 45169928589418240 * q^48 + 40183155980030772 * q^49 - 1602172851562500 * q^50 + 21906201621258448 * q^51 - 98153899497030400 * q^52 - 7462276270800120 * q^53 - 40810202919142640 * q^54 - 22628345250000000 * q^55 - 85257126419530560 * q^56 + 24746009355310880 * q^57 - 168144043315298040 * q^58 + 186154941962838480 * q^59 - 206307342500000000 * q^60 + 248517593110644968 * q^61 - 622575860488793040 * q^62 + 375323610989436120 * q^63 + 797725889363156992 * q^64 - 28930338203125000 * q^65 + 66770019182287616 * q^66 - 83976946080676360 * q^67 + 1012065979784551680 * q^68 + 721386544222156176 * q^69 - 361668273328125000 * q^70 - 326854508200029072 * q^71 - 3247857120459936480 * q^72 + 706071038062266440 * q^73 + 1007811588432673944 * q^74 + 11749267578125000 * q^75 + 453476009937236480 * q^76 - 3188023247458540800 * q^77 - 422235733076613200 * q^78 + 1300235890504742240 * q^79 - 3487851755750000000 * q^80 - 565640020943583596 * q^81 - 3526321594330914840 * q^82 - 894716269324765080 * q^83 + 11741177868239906304 * q^84 - 1658269028203125000 * q^85 + 10889898572595403608 * q^86 - 3243563654475579280 * q^87 + 8680694316508369920 * q^88 - 4392730519471649880 * q^89 + 4128474608632812500 * q^90 - 1164625388848487312 * q^91 + 1015783757806275840 * q^92 + 589775737588352160 * q^93 + 6912955459089075144 * q^94 - 3863608805781250000 * q^95 - 34035929850443648512 * q^96 + 1437870497951780360 * q^97 + 1735173204679501740 * q^98 - 25265427652281702784 * 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 $

$2$	208.721	0.288257	0.144129	−	0.989559i	$-0.453962\pi$
$2$	208.721	0.288257	0.144129	+	0.989559i	$0.453962\pi$
$3$	−48249.1	−1.41526	−0.707632	−	0.706581i	$-0.750237\pi$
$3$	−48249.1	−1.41526	−0.707632	+	0.706581i	$0.750237\pi$
$4$	−480724.	−0.916908
$5$	−1.95312e6	−0.447214
$5$	−1.95312e6	−0.447214
$6$	−1.00706e7	−0.407960
$7$	1.75500e8	1.64379	0.821893	−	0.569642i	$-0.192918\pi$
$7$	1.75500e8	1.64379	0.821893	+	0.569642i	$0.192918\pi$
$8$	−2.09767e8	−0.552563
$9$	1.16572e9	1.00297
$10$	−4.07657e8	−0.128913
$11$	−7.20233e9	−0.920964	−0.460482	−	0.887669i	$-0.652323\pi$
$11$	−7.20233e9	−0.920964	−0.460482	+	0.887669i	$0.652323\pi$
$12$	2.31945e10	1.29767
$13$	4.88586e10	1.27785	0.638924	−	0.769270i	$-0.279380\pi$
$13$	4.88586e10	1.27785	0.638924	+	0.769270i	$0.279380\pi$
$14$	3.66304e10	0.473833
$15$	9.42366e10	0.632925
$16$	2.08255e11	0.757627
$17$	−3.15530e11	−0.645321	−0.322660	−	0.946515i	$-0.604577\pi$
$17$	−3.15530e11	−0.645321	−0.322660	+	0.946515i	$0.604577\pi$
$18$	2.43309e11	0.289114
$19$	1.67456e12	1.19053	0.595265	−	0.803529i	$-0.297047\pi$
$19$	1.67456e12	1.19053	0.595265	+	0.803529i	$0.297047\pi$
$20$	9.38914e11	0.410054
$21$	−8.46771e12	−2.32639
$22$	−1.50328e12	−0.265475
$23$	−1.12559e13	−1.30306	−0.651530	−	0.758623i	$-0.725873\pi$
$23$	−1.12559e13	−1.30306	−0.651530	+	0.758623i	$0.725873\pi$
$24$	1.01211e13	0.782022
$25$	3.81470e12	0.200000
$26$	1.01978e13	0.368349
$27$	−1.66677e11	−0.00420649
$28$	−8.43669e13	−1.50720
$29$	9.59543e13	1.22824	0.614120	−	0.789212i	$-0.289511\pi$
$29$	9.59543e13	1.22824	0.614120	+	0.789212i	$0.289511\pi$
$30$	1.96691e13	0.182445
$31$	3.98884e13	0.270964	0.135482	−	0.990780i	$-0.456742\pi$
$31$	3.98884e13	0.270964	0.135482	+	0.990780i	$0.456742\pi$
$32$	1.53445e14	0.770954
$33$	3.47506e14	1.30341
$34$	−6.58576e13	−0.186018
$35$	−3.42773e14	−0.735123
$36$	−5.60387e14	−0.919633
$37$	−1.13986e14	−0.144191	−0.0720953	−	0.997398i	$-0.522969\pi$
$37$	−1.13986e14	−0.144191	−0.0720953	+	0.997398i	$0.522969\pi$
$38$	3.49514e14	0.343179
$39$	−2.35738e15	−1.80849
$40$	4.09700e14	0.247114
$41$	8.10592e14	0.386683	0.193342	−	0.981131i	$-0.438067\pi$
$41$	8.10592e14	0.386683	0.193342	+	0.981131i	$0.438067\pi$
$42$	−1.76738e15	−0.670599
$43$	2.92953e15	0.888888	0.444444	−	0.895807i	$-0.353401\pi$
$43$	2.92953e15	0.888888	0.444444	+	0.895807i	$0.353401\pi$
$44$	3.46233e15	0.844439
$45$	−2.27679e15	−0.448543
$46$	−2.34933e15	−0.375617
$47$	7.31034e15	0.952814	0.476407	−	0.879225i	$-0.341939\pi$
$47$	7.31034e15	0.952814	0.476407	+	0.879225i	$0.341939\pi$
$48$	−1.00481e16	−1.07224
$49$	1.94013e16	1.70203
$50$	7.96206e14	0.0576515
$51$	1.52240e16	0.913299
$52$	−2.34875e16	−1.17167
$53$	−8.73883e15	−0.363775	−0.181887	−	0.983319i	$-0.558221\pi$
$53$	−8.73883e15	−0.363775	−0.181887	+	0.983319i	$0.558221\pi$
$54$	−3.47889e13	−0.00121255
$55$	1.40671e16	0.411868
$56$	−3.68140e16	−0.908294
$57$	−8.07959e16	−1.68492
$58$	2.00276e16	0.354049
$59$	3.61007e16	0.542528	0.271264	−	0.962505i	$-0.412558\pi$
$59$	3.61007e16	0.542528	0.271264	+	0.962505i	$0.412558\pi$
$60$	−4.53017e16	−0.580334
$61$	4.97095e16	0.544259	0.272130	−	0.962261i	$-0.412272\pi$
$61$	4.97095e16	0.544259	0.272130	+	0.962261i	$0.412272\pi$
$62$	8.32554e15	0.0781072
$63$	2.04583e17	1.64867
$64$	−7.71584e16	−0.535394
$65$	−9.54269e16	−0.571471
$66$	7.25317e16	0.375717
$67$	−2.71958e17	−1.22121	−0.610605	−	0.791935i	$-0.709074\pi$
$67$	−2.71958e17	−1.22121	−0.610605	+	0.791935i	$0.709074\pi$
$68$	1.51683e17	0.591700
$69$	5.43086e17	1.84417
$70$	−7.15438e16	−0.211905
$71$	4.20293e17	1.08792	0.543962	−	0.839110i	$-0.316924\pi$
$71$	4.20293e17	1.08792	0.543962	+	0.839110i	$0.316924\pi$
$72$	−2.44528e17	−0.554205
$73$	−2.99464e17	−0.595357	−0.297678	−	0.954666i	$-0.596212\pi$
$73$	−2.99464e17	−0.595357	−0.297678	+	0.954666i	$0.596212\pi$
$74$	−2.37913e16	−0.0415640
$75$	−1.84056e17	−0.283053
$76$	−8.04999e17	−1.09161
$77$	−1.26401e18	−1.51387
$78$	−4.92034e17	−0.521311
$79$	1.67263e18	1.57016	0.785078	−	0.619397i	$-0.212623\pi$
$79$	1.67263e18	1.57016	0.785078	+	0.619397i	$0.212623\pi$
$80$	−4.06748e17	−0.338821
$81$	−1.34682e18	−0.997019
$82$	1.69187e17	0.111464
$83$	2.03135e18	1.19273	0.596366	−	0.802713i	$-0.296611\pi$
$83$	2.03135e18	1.19273	0.596366	+	0.802713i	$0.296611\pi$
$84$	4.07063e18	2.13309
$85$	6.16269e17	0.288596
$86$	6.11452e17	0.256228
$87$	−4.62971e18	−1.73829
$88$	1.51081e18	0.508890
$89$	−6.32365e18	−1.91321	−0.956606	−	0.291385i	$-0.905884\pi$
$89$	−6.32365e18	−1.91321	−0.956606	+	0.291385i	$0.905884\pi$
$90$	−4.75213e17	−0.129296
$91$	8.57467e18	2.10051
$92$	5.41096e18	1.19479
$93$	−1.92458e18	−0.383485
$94$	1.52582e18	0.274656
$95$	−3.27062e18	−0.532422
$96$	−7.40360e18	−1.09110
$97$	−1.93684e18	−0.258680	−0.129340	−	0.991600i	$-0.541286\pi$
$97$	−1.93684e18	−0.258680	−0.129340	+	0.991600i	$0.541286\pi$
$98$	4.04944e18	0.490623
$99$	−8.39588e18	−0.923702
$100$	−1.83382e18	−0.183382
$101$	6.98700e17	0.0635679	0.0317839	−	0.999495i	$-0.489881\pi$
$101$	6.98700e17	0.0635679	0.0317839	+	0.999495i	$0.489881\pi$
$102$	3.17757e18	0.263265
$103$	−1.27266e19	−0.961078	−0.480539	−	0.876973i	$-0.659559\pi$
$103$	−1.27266e19	−0.961078	−0.480539	+	0.876973i	$0.659559\pi$
$104$	−1.02489e19	−0.706091
$105$	1.65385e19	1.04039
$106$	−1.82397e18	−0.104861
$107$	2.66650e18	0.140216	0.0701078	−	0.997539i	$-0.477666\pi$
$107$	2.66650e18	0.140216	0.0701078	+	0.997539i	$0.477666\pi$
$108$	8.01255e16	0.00385696
$109$	2.67458e19	1.17952	0.589758	−	0.807580i	$-0.299223\pi$
$109$	2.67458e19	1.17952	0.589758	+	0.807580i	$0.299223\pi$
$110$	2.93608e18	0.118724
$111$	5.49974e18	0.204068
$112$	3.65487e19	1.24538
$113$	−1.80116e19	−0.564038	−0.282019	−	0.959409i	$-0.591004\pi$
$113$	−1.80116e19	−0.564038	−0.282019	+	0.959409i	$0.591004\pi$
$114$	−1.68638e19	−0.485689
$115$	2.19841e19	0.582746
$116$	−4.61275e19	−1.12618
$117$	5.69552e19	1.28165
$118$	7.53497e18	0.156388
$119$	−5.53754e19	−1.06077
$120$	−1.97677e19	−0.349731
$121$	−9.28547e18	−0.151825
$122$	1.03754e19	0.156887
$123$	−3.91103e19	−0.547259
$124$	−1.91753e19	−0.248449
$125$	−7.45058e18	−0.0894427
$126$	4.27007e19	0.475241
$127$	6.03395e19	0.622969	0.311484	−	0.950251i	$-0.399174\pi$
$127$	6.03395e19	0.622969	0.311484	+	0.950251i	$0.399174\pi$
$128$	−9.65541e19	−0.925286
$129$	−1.41347e20	−1.25801
$130$	−1.99176e19	−0.164731
$131$	9.68298e19	0.744615	0.372308	−	0.928109i	$-0.378567\pi$
$131$	9.68298e19	0.744615	0.372308	+	0.928109i	$0.378567\pi$
$132$	−1.67055e20	−1.19510
$133$	2.93884e20	1.95698
$134$	−5.67632e19	−0.352023
$135$	3.25541e17	0.00188120
$136$	6.61876e19	0.356580
$137$	1.31161e20	0.659113	0.329557	−	0.944136i	$-0.393101\pi$
$137$	1.31161e20	0.659113	0.329557	+	0.944136i	$0.393101\pi$
$138$	1.13353e20	0.531597
$139$	3.59681e20	1.57499	0.787493	−	0.616323i	$-0.211378\pi$
$139$	3.59681e20	1.57499	0.787493	+	0.616323i	$0.211378\pi$
$140$	1.64779e20	0.674040
$141$	−3.52718e20	−1.34848
$142$	8.77239e19	0.313602
$143$	−3.51896e20	−1.17685
$144$	2.42766e20	0.759879
$145$	−1.87411e20	−0.549286
$146$	−6.25043e19	−0.171616
$147$	−9.36094e20	−2.40882
$148$	5.47960e19	0.132209
$149$	4.94332e20	1.11879	0.559396	−	0.828901i	$-0.311033\pi$
$149$	4.94332e20	1.11879	0.559396	+	0.828901i	$0.311033\pi$
$150$	−3.84162e19	−0.0815920
$151$	3.49946e20	0.697782	0.348891	−	0.937163i	$-0.386558\pi$
$151$	3.49946e20	0.697782	0.348891	+	0.937163i	$0.386558\pi$
$152$	−3.51266e20	−0.657843
$153$	−3.67818e20	−0.647239
$154$	−2.63824e20	−0.436383
$155$	−7.79071e19	−0.121179
$156$	1.13325e21	1.65822
$157$	−1.44059e20	−0.198378	−0.0991892	−	0.995069i	$-0.531625\pi$
$157$	−1.44059e20	−0.198378	−0.0991892	+	0.995069i	$0.531625\pi$
$158$	3.49112e20	0.452609
$159$	4.21641e20	0.514837
$160$	−2.99698e20	−0.344781
$161$	−1.97540e21	−2.14195
$162$	−2.81110e20	−0.287398
$163$	9.55973e20	0.921856	0.460928	−	0.887437i	$-0.347517\pi$
$163$	9.55973e20	0.921856	0.460928	+	0.887437i	$0.347517\pi$
$164$	−3.89671e20	−0.354553
$165$	−6.78723e20	−0.582902
$166$	4.23984e20	0.343814
$167$	1.98541e21	1.52070	0.760351	−	0.649512i	$-0.225027\pi$
$167$	1.98541e21	1.52070	0.760351	+	0.649512i	$0.225027\pi$
$168$	1.77624e21	1.28548
$169$	9.25240e20	0.632894
$170$	1.28628e20	0.0831900
$171$	1.95206e21	1.19407
$172$	−1.40829e21	−0.815028
$173$	−4.80484e20	−0.263173	−0.131586	−	0.991305i	$-0.542007\pi$
$173$	−4.80484e20	−0.263173	−0.131586	+	0.991305i	$0.542007\pi$
$174$	−9.66316e20	−0.501073
$175$	6.69478e20	0.328757
$176$	−1.49992e21	−0.697748
$177$	−1.74183e21	−0.767820
$178$	−1.31988e21	−0.551497
$179$	−2.42391e21	−0.960311	−0.480156	−	0.877183i	$-0.659420\pi$
$179$	−2.42391e21	−0.960311	−0.480156	+	0.877183i	$0.659420\pi$
$180$	1.09451e21	0.411272
$181$	−2.51267e21	−0.895753	−0.447877	−	0.894095i	$-0.647820\pi$
$181$	−2.51267e21	−0.895753	−0.447877	+	0.894095i	$0.647820\pi$
$182$	1.78971e21	0.605486
$183$	−2.39844e21	−0.770271
$184$	2.36111e21	0.720023
$185$	2.22630e20	0.0644840
$186$	−4.01700e20	−0.110542
$187$	2.27255e21	0.594317
$188$	−3.51425e21	−0.873642
$189$	−2.92518e19	−0.00691456
$190$	−6.82645e20	−0.153474
$191$	6.71163e21	1.43553	0.717763	−	0.696287i	$-0.245166\pi$
$191$	6.71163e21	1.43553	0.717763	+	0.696287i	$0.245166\pi$
$192$	3.72283e21	0.757724
$193$	−4.18140e21	−0.810080	−0.405040	−	0.914299i	$-0.632742\pi$
$193$	−4.18140e21	−0.810080	−0.405040	+	0.914299i	$0.632742\pi$
$194$	−4.04259e20	−0.0745665
$195$	4.60426e21	0.808782
$196$	−9.32665e21	−1.56060
$197$	1.00807e22	1.60716	0.803582	−	0.595194i	$-0.202925\pi$
$197$	1.00807e22	1.60716	0.803582	+	0.595194i	$0.202925\pi$
$198$	−1.75239e21	−0.266264
$199$	−6.70098e21	−0.970586	−0.485293	−	0.874352i	$-0.661287\pi$
$199$	−6.70098e21	−0.970586	−0.485293	+	0.874352i	$0.661287\pi$
$200$	−8.00196e20	−0.110513
$201$	1.31217e22	1.72834
$202$	1.45833e20	0.0183239
$203$	1.68400e22	2.01896
$204$	−7.31856e21	−0.837411
$205$	−1.58319e21	−0.172930
$206$	−2.65630e21	−0.277038
$207$	−1.31211e22	−1.30693
$208$	1.01750e22	0.968132
$209$	−1.20607e22	−1.09644
$210$	3.45192e21	0.299901
$211$	−9.23893e21	−0.767252	−0.383626	−	0.923488i	$-0.625325\pi$
$211$	−9.23893e21	−0.767252	−0.383626	+	0.923488i	$0.625325\pi$
$212$	4.20096e21	0.333548
$213$	−2.02788e22	−1.53970
$214$	5.56554e20	0.0404181
$215$	−5.72173e21	−0.397523
$216$	3.49633e19	0.00232435
$217$	7.00041e21	0.445406
$218$	5.58240e21	0.340004
$219$	1.44489e22	0.842587
$220$	−6.76237e21	−0.377645
$221$	−1.54163e22	−0.824621
$222$	1.14791e21	0.0588240
$223$	−2.54166e22	−1.24802	−0.624010	−	0.781416i	$-0.714498\pi$
$223$	−2.54166e22	−1.24802	−0.624010	+	0.781416i	$0.714498\pi$
$224$	2.69296e22	1.26728
$225$	4.44685e21	0.200594
$226$	−3.75940e21	−0.162588
$227$	−3.18017e21	−0.131888	−0.0659440	−	0.997823i	$-0.521006\pi$
$227$	−3.18017e21	−0.131888	−0.0659440	+	0.997823i	$0.521006\pi$
$228$	3.88405e22	1.54491
$229$	1.19429e22	0.455695	0.227847	−	0.973697i	$-0.426831\pi$
$229$	1.19429e22	0.455695	0.227847	+	0.973697i	$0.426831\pi$
$230$	4.58854e21	0.167981
$231$	6.09873e22	2.14252
$232$	−2.01280e22	−0.678680
$233$	−2.82197e22	−0.913422	−0.456711	−	0.889615i	$-0.650973\pi$
$233$	−2.82197e22	−0.913422	−0.456711	+	0.889615i	$0.650973\pi$
$234$	1.18877e22	0.369444
$235$	−1.42780e22	−0.426111
$236$	−1.73545e22	−0.497448
$237$	−8.07029e22	−2.22218
$238$	−1.15580e22	−0.305774
$239$	7.12199e22	1.81060	0.905298	−	0.424778i	$-0.139648\pi$
$239$	7.12199e22	1.81060	0.905298	+	0.424778i	$0.139648\pi$
$240$	1.96252e22	0.479522
$241$	−1.30761e22	−0.307126	−0.153563	−	0.988139i	$-0.549075\pi$
$241$	−1.30761e22	−0.307126	−0.153563	+	0.988139i	$0.549075\pi$
$242$	−1.93807e21	−0.0437646
$243$	6.51768e22	1.41525
$244$	−2.38965e22	−0.499036
$245$	−3.78931e22	−0.761171
$246$	−8.16313e21	−0.157751
$247$	8.18165e22	1.52132
$248$	−8.36726e21	−0.149724
$249$	−9.80108e22	−1.68803
$250$	−1.55509e21	−0.0257825
$251$	−4.61368e22	−0.736457	−0.368229	−	0.929735i	$-0.620036\pi$
$251$	−4.61368e22	−0.736457	−0.368229	+	0.929735i	$0.620036\pi$
$252$	−9.83478e22	−1.51168
$253$	8.10685e22	1.20007
$254$	1.25941e22	0.179575
$255$	−2.97344e22	−0.408440
$256$	2.03004e22	0.268674
$257$	−7.38650e22	−0.942051	−0.471025	−	0.882120i	$-0.656116\pi$
$257$	−7.38650e22	−0.942051	−0.471025	+	0.882120i	$0.656116\pi$
$258$	−2.95020e22	−0.362631
$259$	−2.00046e22	−0.237018
$260$	4.58740e22	0.523986
$261$	1.11855e23	1.23189
$262$	2.02104e22	0.214641
$263$	−5.52480e22	−0.565897	−0.282948	−	0.959135i	$-0.591312\pi$
$263$	−5.52480e22	−0.565897	−0.282948	+	0.959135i	$0.591312\pi$
$264$	−7.28952e22	−0.720214
$265$	1.70680e22	0.162685
$266$	6.13397e22	0.564113
$267$	3.05111e23	2.70770
$268$	1.30737e23	1.11974
$269$	1.52073e23	1.25720	0.628600	−	0.777729i	$-0.283628\pi$
$269$	1.52073e23	1.25720	0.628600	+	0.777729i	$0.283628\pi$
$270$	6.79471e19	0.000542269 0
$271$	4.19955e22	0.323589	0.161795	−	0.986824i	$-0.448272\pi$
$271$	4.19955e22	0.323589	0.161795	+	0.986824i	$0.448272\pi$
$272$	−6.57107e22	−0.488913
$273$	−4.13720e23	−2.97277
$274$	2.73760e22	0.189994
$275$	−2.74747e22	−0.184193
$276$	−2.61074e23	−1.69094
$277$	1.35587e23	0.848517	0.424259	−	0.905541i	$-0.360535\pi$
$277$	1.35587e23	0.848517	0.424259	+	0.905541i	$0.360535\pi$
$278$	7.50728e22	0.454001
$279$	4.64986e22	0.271769
$280$	7.19023e22	0.406202
$281$	−1.94680e23	−1.06319	−0.531596	−	0.846998i	$-0.678408\pi$
$281$	−1.94680e23	−1.06319	−0.531596	+	0.846998i	$0.678408\pi$
$282$	−7.36194e22	−0.388710
$283$	−6.12553e22	−0.312732	−0.156366	−	0.987699i	$-0.549978\pi$
$283$	−6.12553e22	−0.312732	−0.156366	+	0.987699i	$0.549978\pi$
$284$	−2.02045e23	−0.997525
$285$	1.57804e23	0.753517
$286$	−7.34479e22	−0.339236
$287$	1.42259e23	0.635625
$288$	1.78874e23	0.773246
$289$	−1.39513e23	−0.583561
$290$	−3.91165e22	−0.158336
$291$	9.34511e22	0.366101
$292$	1.43959e23	0.545887
$293$	−1.40139e23	−0.514419	−0.257209	−	0.966356i	$-0.582803\pi$
$293$	−1.40139e23	−0.514419	−0.257209	+	0.966356i	$0.582803\pi$
$294$	−1.95382e23	−0.694360
$295$	−7.05092e22	−0.242626
$296$	2.39105e22	0.0796743
$297$	1.20046e21	0.00387402
$298$	1.03177e23	0.322500
$299$	−5.49946e23	−1.66511
$300$	8.84800e22	0.259533
$301$	5.14131e23	1.46114
$302$	7.30409e22	0.201141
$303$	−3.37117e22	−0.0899653
$304$	3.48735e23	0.901979
$305$	−9.70889e22	−0.243400
$306$	−7.67712e22	−0.186571
$307$	−3.99031e23	−0.940139	−0.470069	−	0.882629i	$-0.655771\pi$
$307$	−3.99031e23	−0.940139	−0.470069	+	0.882629i	$0.655771\pi$
$308$	6.07638e23	1.38808
$309$	6.14047e23	1.36018
$310$	−1.62608e22	−0.0349306
$311$	5.36255e23	1.11724	0.558622	−	0.829422i	$-0.311330\pi$
$311$	5.36255e23	1.11724	0.558622	+	0.829422i	$0.311330\pi$
$312$	4.94500e23	0.999305
$313$	−3.21342e23	−0.629936	−0.314968	−	0.949102i	$-0.601994\pi$
$313$	−3.21342e23	−0.629936	−0.314968	+	0.949102i	$0.601994\pi$
$314$	−3.00681e22	−0.0571840
$315$	−3.99576e23	−0.737308
$316$	−8.04073e23	−1.43969
$317$	−1.25795e23	−0.218575	−0.109288	−	0.994010i	$-0.534857\pi$
$317$	−1.25795e23	−0.218575	−0.109288	+	0.994010i	$0.534857\pi$
$318$	8.80051e22	0.148406
$319$	−6.91095e23	−1.13117
$320$	1.50700e23	0.239436
$321$	−1.28656e23	−0.198442
$322$	−4.12307e23	−0.617433
$323$	−5.28373e23	−0.768274
$324$	6.47451e23	0.914174
$325$	1.86381e23	0.255569
$326$	1.99531e23	0.265732
$327$	−1.29046e24	−1.66933
$328$	−1.70035e23	−0.213667
$329$	1.28296e24	1.56622
$330$	−1.41664e23	−0.168026
$331$	1.01808e24	1.17332	0.586659	−	0.809834i	$-0.300443\pi$
$331$	1.01808e24	1.17332	0.586659	+	0.809834i	$0.300443\pi$
$332$	−9.76518e23	−1.09362
$333$	−1.32876e23	−0.144619
$334$	4.14396e23	0.438354
$335$	5.31167e23	0.546142
$336$	−1.76344e24	−1.76254
$337$	−2.03982e23	−0.198202	−0.0991008	−	0.995077i	$-0.531597\pi$
$337$	−2.03982e23	−0.198202	−0.0991008	+	0.995077i	$0.531597\pi$
$338$	1.93117e23	0.182436
$339$	8.69046e23	0.798262
$340$	−2.96255e23	−0.264616
$341$	−2.87290e23	−0.249548
$342$	4.07435e23	0.344199
$343$	1.40441e24	1.15399
$344$	−6.14517e23	−0.491166
$345$	−1.06071e24	−0.824740
$346$	−1.00287e23	−0.0758615
$347$	1.36477e24	1.00445	0.502225	−	0.864737i	$-0.332515\pi$
$347$	1.36477e24	1.00445	0.502225	+	0.864737i	$0.332515\pi$
$348$	2.22561e24	1.59385
$349$	6.53594e23	0.455477	0.227738	−	0.973722i	$-0.426867\pi$
$349$	6.53594e23	0.455477	0.227738	+	0.973722i	$0.426867\pi$
$350$	1.39734e23	0.0947666
$351$	−8.14360e21	−0.00537525
$352$	−1.10516e24	−0.710021
$353$	−1.83791e24	−1.14938	−0.574692	−	0.818370i	$-0.694878\pi$
$353$	−1.83791e24	−1.14938	−0.574692	+	0.818370i	$0.694878\pi$
$354$	−3.63555e23	−0.221330
$355$	−8.20886e23	−0.486534
$356$	3.03993e24	1.75424
$357$	2.67181e24	1.50127
$358$	−5.05919e23	−0.276817
$359$	−1.24769e24	−0.664829	−0.332414	−	0.943133i	$-0.607863\pi$
$359$	−1.24769e24	−0.664829	−0.332414	+	0.943133i	$0.607863\pi$
$360$	4.77594e23	0.247848
$361$	8.25721e23	0.417364
$362$	−5.24445e23	−0.258207
$363$	4.48016e23	0.214872
$364$	−4.12205e24	−1.92597
$365$	5.84891e23	0.266252
$366$	−5.00604e23	−0.222036
$367$	−3.50209e24	−1.51356	−0.756780	−	0.653670i	$-0.773228\pi$
$367$	−3.50209e24	−1.51356	−0.756780	+	0.653670i	$0.773228\pi$
$368$	−2.34409e24	−0.987234
$369$	9.44920e23	0.387833
$370$	4.64674e22	0.0185880
$371$	−1.53366e24	−0.597967
$372$	9.25192e23	0.351620
$373$	−4.15733e23	−0.154021	−0.0770106	−	0.997030i	$-0.524538\pi$
$373$	−4.15733e23	−0.154021	−0.0770106	+	0.997030i	$0.524538\pi$
$374$	4.74328e23	0.171316
$375$	3.59484e23	0.126585
$376$	−1.53347e24	−0.526489
$377$	4.68819e24	1.56950
$378$	−6.10544e21	−0.00199317
$379$	−4.28981e24	−1.36573	−0.682866	−	0.730543i	$-0.739267\pi$
$379$	−4.28981e24	−1.36573	−0.682866	+	0.730543i	$0.739267\pi$
$380$	1.57226e24	0.488181
$381$	−2.91133e24	−0.881665
$382$	1.40086e24	0.413801
$383$	6.02881e23	0.173718	0.0868588	−	0.996221i	$-0.472317\pi$
$383$	6.02881e23	0.173718	0.0868588	+	0.996221i	$0.472317\pi$
$384$	4.65865e24	1.30952
$385$	2.46877e24	0.677022
$386$	−8.72745e23	−0.233511
$387$	3.41500e24	0.891530
$388$	9.31087e23	0.237186
$389$	4.29842e24	1.06853	0.534266	−	0.845317i	$-0.320588\pi$
$389$	4.29842e24	1.06853	0.534266	+	0.845317i	$0.320588\pi$
$390$	9.61005e23	0.233137
$391$	3.55156e24	0.840892
$392$	−4.06974e24	−0.940478
$393$	−4.67195e24	−1.05383
$394$	2.10404e24	0.463277
$395$	−3.26686e24	−0.702195
$396$	4.03610e24	0.846949
$397$	2.35387e24	0.482251	0.241125	−	0.970494i	$-0.422483\pi$
$397$	2.35387e24	0.482251	0.241125	+	0.970494i	$0.422483\pi$
$398$	−1.39863e24	−0.279778
$399$	−1.41797e25	−2.76964
$400$	7.94430e23	0.151525
$401$	−3.35639e24	−0.625173	−0.312587	−	0.949889i	$-0.601195\pi$
$401$	−3.35639e24	−0.625173	−0.312587	+	0.949889i	$0.601195\pi$
$402$	2.73877e24	0.498205
$403$	1.94889e24	0.346250
$404$	−3.35882e23	−0.0582859
$405$	2.63052e24	0.445880
$406$	3.51485e24	0.581981
$407$	8.20968e23	0.132794
$408$	−3.19349e24	−0.504655
$409$	5.55551e24	0.857733	0.428867	−	0.903368i	$-0.358913\pi$
$409$	5.55551e24	0.857733	0.428867	+	0.903368i	$0.358913\pi$
$410$	−3.30444e23	−0.0498484
$411$	−6.32841e24	−0.932819
$412$	6.11797e24	0.881219
$413$	6.33567e24	0.891799
$414$	−2.73865e24	−0.376733
$415$	−3.96748e24	−0.533406
$416$	7.49712e24	0.985162
$417$	−1.73543e25	−2.22902
$418$	−2.51732e24	−0.316056
$419$	−8.86611e24	−1.08818	−0.544089	−	0.839027i	$-0.683125\pi$
$419$	−8.86611e24	−1.08818	−0.544089	+	0.839027i	$0.683125\pi$
$420$	−7.95044e24	−0.953945
$421$	−5.31841e24	−0.623881	−0.311941	−	0.950102i	$-0.600979\pi$
$421$	−5.31841e24	−0.623881	−0.311941	+	0.950102i	$0.600979\pi$
$422$	−1.92835e24	−0.221166
$423$	8.52178e24	0.955646
$424$	1.83311e24	0.201008
$425$	−1.20365e24	−0.129064
$426$	−4.23260e24	−0.443829
$427$	8.72400e24	0.894646
$428$	−1.28185e24	−0.128565
$429$	1.69787e25	1.66556
$430$	−1.19424e24	−0.114589
$431$	5.73236e24	0.538021	0.269010	−	0.963137i	$-0.413303\pi$
$431$	5.73236e24	0.538021	0.269010	+	0.963137i	$0.413303\pi$
$432$	−3.47113e22	−0.00318695
$433$	1.14471e25	1.02816	0.514079	−	0.857743i	$-0.328134\pi$
$433$	1.14471e25	1.02816	0.514079	+	0.857743i	$0.328134\pi$
$434$	1.46113e24	0.128392
$435$	9.04241e24	0.777385
$436$	−1.28573e25	−1.08151
$437$	−1.88486e25	−1.55133
$438$	3.01578e24	0.242882
$439$	2.47099e25	1.94741	0.973706	−	0.227807i	$-0.0731556\pi$
$439$	2.47099e25	1.94741	0.973706	+	0.227807i	$0.0731556\pi$
$440$	−2.95080e24	−0.227583
$441$	2.26164e25	1.70709
$442$	−3.21771e24	−0.237703
$443$	−2.61954e24	−0.189404	−0.0947022	−	0.995506i	$-0.530190\pi$
$443$	−2.61954e24	−0.189404	−0.0947022	+	0.995506i	$0.530190\pi$
$444$	−2.64386e24	−0.187111
$445$	1.23509e25	0.855614
$446$	−5.30497e24	−0.359751
$447$	−2.38511e25	−1.58338
$448$	−1.35413e25	−0.880073
$449$	4.02342e24	0.256009	0.128004	−	0.991774i	$-0.459143\pi$
$449$	4.02342e24	0.256009	0.128004	+	0.991774i	$0.459143\pi$
$450$	9.28150e23	0.0578228
$451$	−5.83815e24	−0.356122
$452$	8.65862e24	0.517170
$453$	−1.68846e25	−0.987546
$454$	−6.63768e23	−0.0380177
$455$	−1.67474e25	−0.939375
$456$	1.69483e25	0.931021
$457$	−5.67034e24	−0.305074	−0.152537	−	0.988298i	$-0.548744\pi$
$457$	−5.67034e24	−0.305074	−0.152537	+	0.988298i	$0.548744\pi$
$458$	2.49274e24	0.131357
$459$	5.25915e22	0.00271453
$460$	−1.05683e25	−0.534325
$461$	−2.04179e25	−1.01124	−0.505618	−	0.862758i	$-0.668735\pi$
$461$	−2.04179e25	−1.01124	−0.505618	+	0.862758i	$0.668735\pi$
$462$	1.27293e25	0.617598
$463$	2.83894e25	1.34939	0.674695	−	0.738097i	$-0.264275\pi$
$463$	2.83894e25	1.34939	0.674695	+	0.738097i	$0.264275\pi$
$464$	1.99830e25	0.930549
$465$	3.75895e24	0.171500
$466$	−5.89004e24	−0.263301
$467$	1.70349e25	0.746157	0.373078	−	0.927800i	$-0.378302\pi$
$467$	1.70349e25	0.746157	0.373078	+	0.927800i	$0.378302\pi$
$468$	−2.73797e25	−1.17515
$469$	−4.77285e25	−2.00741
$470$	−2.98011e24	−0.122830
$471$	6.95073e24	0.280758
$472$	−7.57273e24	−0.299781
$473$	−2.10994e25	−0.818634
$474$	−1.68444e25	−0.640561
$475$	6.38793e24	0.238106
$476$	2.66203e25	0.972627
$477$	−1.01870e25	−0.364856
$478$	1.48651e25	0.521917
$479$	−5.92093e24	−0.203799	−0.101900	−	0.994795i	$-0.532492\pi$
$479$	−5.92093e24	−0.203799	−0.101900	+	0.994795i	$0.532492\pi$
$480$	1.44602e25	0.487957
$481$	−5.56921e24	−0.184253
$482$	−2.72925e24	−0.0885313
$483$	9.53114e25	3.03143
$484$	4.46375e24	0.139209
$485$	3.78290e24	0.115685
$486$	1.36037e25	0.407957
$487$	4.99276e25	1.46830	0.734151	−	0.678986i	$-0.237580\pi$
$487$	4.99276e25	1.46830	0.734151	+	0.678986i	$0.237580\pi$
$488$	−1.04274e25	−0.300737
$489$	−4.61248e25	−1.30467
$490$	−7.90907e24	−0.219413
$491$	−1.62806e25	−0.442992	−0.221496	−	0.975161i	$-0.571094\pi$
$491$	−1.62806e25	−0.442992	−0.221496	+	0.975161i	$0.571094\pi$
$492$	1.88013e25	0.501786
$493$	−3.02765e25	−0.792609
$494$	1.70768e25	0.438531
$495$	1.63982e25	0.413092
$496$	8.30697e24	0.205289
$497$	7.37614e25	1.78831
$498$	−2.04569e25	−0.486587
$499$	1.03784e25	0.242202	0.121101	−	0.992640i	$-0.461358\pi$
$499$	1.03784e25	0.242202	0.121101	+	0.992640i	$0.461358\pi$
$500$	3.58167e24	0.0820107
$501$	−9.57944e25	−2.15220
$502$	−9.62971e24	−0.212289
$503$	−7.01202e25	−1.51687	−0.758433	−	0.651751i	$-0.774035\pi$
$503$	−7.01202e25	−1.51687	−0.758433	+	0.651751i	$0.774035\pi$
$504$	−4.29147e25	−0.910994
$505$	−1.36465e24	−0.0284284
$506$	1.69207e25	0.345930
$507$	−4.46420e25	−0.895712
$508$	−2.90066e25	−0.571205
$509$	5.95755e25	1.15146	0.575730	−	0.817640i	$-0.304718\pi$
$509$	5.95755e25	1.15146	0.575730	+	0.817640i	$0.304718\pi$
$510$	−6.20619e24	−0.117736
$511$	−5.25559e25	−0.978639
$512$	5.48593e25	1.00273
$513$	−2.79110e23	−0.00500795
$514$	−1.54172e25	−0.271553
$515$	2.48566e25	0.429807
$516$	6.79489e25	1.15348
$517$	−5.26515e25	−0.877507
$518$	−4.17537e24	−0.0683222
$519$	2.31829e25	0.372459
$520$	2.00174e25	0.315773
$521$	4.46697e25	0.691919	0.345959	−	0.938250i	$-0.387554\pi$
$521$	4.46697e25	0.691919	0.345959	+	0.938250i	$0.387554\pi$
$522$	2.33465e25	0.355102
$523$	−6.95288e25	−1.03848	−0.519241	−	0.854628i	$-0.673785\pi$
$523$	−6.95288e25	−1.03848	−0.519241	+	0.854628i	$0.673785\pi$
$524$	−4.65484e25	−0.682743
$525$	−3.23017e25	−0.465278
$526$	−1.15314e25	−0.163124
$527$	−1.25860e25	−0.174858
$528$	7.23699e25	0.987497
$529$	5.20791e25	0.697966
$530$	3.56245e24	0.0468951
$531$	4.20832e25	0.544140
$532$	−1.41277e26	−1.79437
$533$	3.96044e25	0.494122
$534$	6.36829e25	0.780514
$535$	−5.20801e24	−0.0627063
$536$	5.70476e25	0.674796
$537$	1.16951e26	1.35909
$538$	3.17407e25	0.362397
$539$	−1.39734e26	−1.56751
$540$	−1.56495e23	−0.00172489
$541$	−1.10337e25	−0.119494	−0.0597471	−	0.998214i	$-0.519029\pi$
$541$	−1.10337e25	−0.119494	−0.0597471	+	0.998214i	$0.519029\pi$
$542$	8.76532e24	0.0932770
$543$	1.21234e26	1.26773
$544$	−4.84166e25	−0.497513
$545$	−5.22379e25	−0.527496
$546$	−8.63519e25	−0.856923
$547$	2.58325e25	0.251934	0.125967	−	0.992034i	$-0.459797\pi$
$547$	2.58325e25	0.251934	0.125967	+	0.992034i	$0.459797\pi$
$548$	−6.30523e25	−0.604346
$549$	5.79472e25	0.545877
$550$	−5.73454e24	−0.0530949
$551$	1.60681e26	1.46226
$552$	−1.13921e26	−1.01902
$553$	2.93546e26	2.58100
$554$	2.82998e25	0.244591
$555$	−1.07417e25	−0.0912618
$556$	−1.72907e26	−1.44412
$557$	−1.79240e26	−1.47167	−0.735837	−	0.677159i	$-0.763211\pi$
$557$	−1.79240e26	−1.47167	−0.735837	+	0.677159i	$0.763211\pi$
$558$	9.70521e24	0.0783394
$559$	1.43132e26	1.13586
$560$	−7.13842e25	−0.556949
$561$	−1.09649e26	−0.841116
$562$	−4.06338e25	−0.306473
$563$	−1.87169e26	−1.38804	−0.694022	−	0.719954i	$-0.744163\pi$
$563$	−1.87169e26	−1.38804	−0.694022	+	0.719954i	$0.744163\pi$
$564$	1.69560e26	1.23643
$565$	3.51790e25	0.252245
$566$	−1.27852e25	−0.0901473
$567$	−2.36367e26	−1.63889
$568$	−8.81635e25	−0.601146
$569$	−1.83047e26	−1.22743	−0.613713	−	0.789529i	$-0.710325\pi$
$569$	−1.83047e26	−1.22743	−0.613713	+	0.789529i	$0.710325\pi$
$570$	3.29370e25	0.217207
$571$	2.09660e26	1.35979	0.679895	−	0.733310i	$-0.262025\pi$
$571$	2.09660e26	1.35979	0.679895	+	0.733310i	$0.262025\pi$
$572$	1.69165e26	1.07906
$573$	−3.23830e26	−2.03165
$574$	2.96923e25	0.183223
$575$	−4.29377e25	−0.260612
$576$	−8.99448e25	−0.536986
$577$	4.57673e25	0.268772	0.134386	−	0.990929i	$-0.457094\pi$
$577$	4.57673e25	0.268772	0.134386	+	0.990929i	$0.457094\pi$
$578$	−2.91193e25	−0.168216
$579$	2.01749e26	1.14648
$580$	9.00928e25	0.503645
$581$	3.56501e26	1.96059
$582$	1.95052e25	0.105531
$583$	6.29400e25	0.335023
$584$	6.28176e25	0.328972
$585$	−1.11241e26	−0.573169
$586$	−2.92499e25	−0.148285
$587$	1.17955e26	0.588378	0.294189	−	0.955747i	$-0.404951\pi$
$587$	1.17955e26	0.588378	0.294189	+	0.955747i	$0.404951\pi$
$588$	4.50002e26	2.20867
$589$	6.67955e25	0.322591
$590$	−1.47167e25	−0.0699387
$591$	−4.86383e26	−2.27456
$592$	−2.37382e25	−0.109243
$593$	−8.10305e25	−0.366969	−0.183484	−	0.983023i	$-0.558738\pi$
$593$	−8.10305e25	−0.366969	−0.183484	+	0.983023i	$0.558738\pi$
$594$	2.50561e23	0.00111672
$595$	1.08155e26	0.474390
$596$	−2.37637e26	−1.02583
$597$	3.23316e26	1.37363
$598$	−1.14785e26	−0.479981
$599$	1.14902e26	0.472902	0.236451	−	0.971643i	$-0.424016\pi$
$599$	1.14902e26	0.472902	0.236451	+	0.971643i	$0.424016\pi$
$600$	3.86088e25	0.156404
$601$	1.40104e26	0.558654	0.279327	−	0.960196i	$-0.409889\pi$
$601$	1.40104e26	0.558654	0.279327	+	0.960196i	$0.409889\pi$
$602$	1.07310e26	0.421185
$603$	−3.17025e26	−1.22484
$604$	−1.68227e26	−0.639802
$605$	1.81357e25	0.0678982
$606$	−7.03632e24	−0.0259332
$607$	−2.24823e26	−0.815734	−0.407867	−	0.913041i	$-0.633727\pi$
$607$	−2.24823e26	−0.815734	−0.407867	+	0.913041i	$0.633727\pi$
$608$	2.56953e26	0.917845
$609$	−8.12513e26	−2.85737
$610$	−2.02644e25	−0.0701619
$611$	3.57173e26	1.21755
$612$	1.76819e26	0.593458
$613$	5.55576e26	1.83599	0.917993	−	0.396597i	$-0.129809\pi$
$613$	5.55576e26	1.83599	0.917993	+	0.396597i	$0.129809\pi$
$614$	−8.32860e25	−0.271002
$615$	7.63874e25	0.244742
$616$	2.65147e26	0.836507
$617$	−4.29518e26	−1.33436	−0.667178	−	0.744898i	$-0.732498\pi$
$617$	−4.29518e26	−1.33436	−0.667178	+	0.744898i	$0.732498\pi$
$618$	1.28164e26	0.392081
$619$	−1.93785e26	−0.583793	−0.291896	−	0.956450i	$-0.594286\pi$
$619$	−1.93785e26	−0.583793	−0.291896	+	0.956450i	$0.594286\pi$
$620$	3.74518e25	0.111110
$621$	1.87609e24	0.00548131
$622$	1.11928e26	0.322054
$623$	−1.10980e27	−3.14491
$624$	−4.90937e26	−1.37016
$625$	1.45519e25	0.0400000
$626$	−6.70707e25	−0.181584
$627$	5.81919e26	1.55175
$628$	6.92527e25	0.181895
$629$	3.59661e25	0.0930491
$630$	−8.33997e25	−0.212534
$631$	−5.20159e26	−1.30574	−0.652871	−	0.757469i	$-0.726436\pi$
$631$	−5.20159e26	−1.30574	−0.652871	+	0.757469i	$0.726436\pi$
$632$	−3.50862e26	−0.867609
$633$	4.45770e26	1.08586
$634$	−2.62560e25	−0.0630059
$635$	−1.17851e26	−0.278600
$636$	−2.02693e26	−0.472058
$637$	9.47918e26	2.17493
$638$	−1.44246e26	−0.326067
$639$	4.89943e26	1.09116
$640$	1.88582e26	0.413800
$641$	7.75770e26	1.67719	0.838593	−	0.544758i	$-0.183378\pi$
$641$	7.75770e26	1.67719	0.838593	+	0.544758i	$0.183378\pi$
$642$	−2.68532e25	−0.0572023
$643$	−4.62866e26	−0.971519	−0.485759	−	0.874093i	$-0.661457\pi$
$643$	−4.62866e26	−0.971519	−0.485759	+	0.874093i	$0.661457\pi$
$644$	9.49622e26	1.96397
$645$	2.76068e26	0.562600
$646$	−1.10282e26	−0.221461
$647$	4.34133e26	0.859076	0.429538	−	0.903049i	$-0.358676\pi$
$647$	4.34133e26	0.859076	0.429538	+	0.903049i	$0.358676\pi$
$648$	2.82519e26	0.550915
$649$	−2.60010e26	−0.499649
$650$	3.89015e25	0.0736698
$651$	−3.37764e26	−0.630367
$652$	−4.59559e26	−0.845257
$653$	−9.04704e26	−1.63995	−0.819976	−	0.572397i	$-0.806013\pi$
$653$	−9.04704e26	−1.63995	−0.819976	+	0.572397i	$0.806013\pi$
$654$	−2.69346e26	−0.481196
$655$	−1.89121e26	−0.333002
$656$	1.68810e26	0.292962
$657$	−3.49090e26	−0.597127
$658$	2.67781e26	0.451475
$659$	4.60505e26	0.765285	0.382643	−	0.923896i	$-0.375014\pi$
$659$	4.60505e26	0.765285	0.382643	+	0.923896i	$0.375014\pi$
$660$	3.26278e26	0.534467
$661$	2.42000e25	0.0390753	0.0195376	−	0.999809i	$-0.493781\pi$
$661$	2.42000e25	0.0390753	0.0195376	+	0.999809i	$0.493781\pi$
$662$	2.12494e26	0.338217
$663$	7.43825e26	1.16706
$664$	−4.26109e26	−0.659059
$665$	−5.73993e26	−0.875187
$666$	−2.77339e25	−0.0416875
$667$	−1.08005e27	−1.60047
$668$	−9.54435e26	−1.39434
$669$	1.22633e27	1.76628
$670$	1.10866e26	0.157429
$671$	−3.58024e26	−0.501243
$672$	−1.29933e27	−1.79354
$673$	1.08717e27	1.47963	0.739817	−	0.672809i	$-0.234912\pi$
$673$	1.08717e27	1.47963	0.739817	+	0.672809i	$0.234912\pi$
$674$	−4.25752e25	−0.0571330
$675$	−6.35822e23	−0.000841298 0
$676$	−4.44785e26	−0.580305
$677$	9.58678e26	1.23333	0.616667	−	0.787224i	$-0.288483\pi$
$677$	9.58678e26	1.23333	0.616667	+	0.787224i	$0.288483\pi$
$678$	1.81388e26	0.230105
$679$	−3.39916e26	−0.425215
$680$	−1.29273e26	−0.159468
$681$	1.53441e26	0.186656
$682$	−5.99633e25	−0.0719340
$683$	1.34004e27	1.58533	0.792666	−	0.609656i	$-0.208692\pi$
$683$	1.34004e27	1.58533	0.792666	+	0.609656i	$0.208692\pi$
$684$	−9.38400e26	−1.09485
$685$	−2.56174e26	−0.294764
$686$	2.93130e26	0.332645
$687$	−5.76236e26	−0.644928
$688$	6.10089e26	0.673446
$689$	−4.26967e26	−0.464848
$690$	−2.21393e26	−0.237737
$691$	−1.08388e27	−1.14799	−0.573997	−	0.818858i	$-0.694608\pi$
$691$	−1.08388e27	−1.14799	−0.573997	+	0.818858i	$0.694608\pi$
$692$	2.30980e26	0.241305
$693$	−1.47347e27	−1.51837
$694$	2.84855e26	0.289540
$695$	−7.02502e26	−0.704355
$696$	9.71159e26	0.960512
$697$	−2.55766e26	−0.249535
$698$	1.36418e26	0.131295
$699$	1.36158e27	1.29273
$700$	−3.21834e26	−0.301440
$701$	1.36260e27	1.25907	0.629533	−	0.776974i	$-0.283246\pi$
$701$	1.36260e27	1.25907	0.629533	+	0.776974i	$0.283246\pi$
$702$	−1.69974e24	−0.00154945
$703$	−1.90877e26	−0.171663
$704$	5.55721e26	0.493079
$705$	6.88901e26	0.603060
$706$	−3.83610e26	−0.331319
$707$	1.22622e26	0.104492
$708$	8.37338e26	0.704020
$709$	2.26436e26	0.187848	0.0939240	−	0.995579i	$-0.470059\pi$
$709$	2.26436e26	0.187848	0.0939240	+	0.995579i	$0.470059\pi$
$710$	−1.71336e26	−0.140247
$711$	1.94981e27	1.57482
$712$	1.32649e27	1.05717
$713$	−4.48979e26	−0.353082
$714$	5.57663e26	0.432751
$715$	6.87296e26	0.526304
$716$	1.16523e27	0.880517
$717$	−3.43630e27	−2.56247
$718$	−2.60419e26	−0.191642
$719$	−6.82192e26	−0.495430	−0.247715	−	0.968833i	$-0.579680\pi$
$719$	−6.82192e26	−0.495430	−0.247715	+	0.968833i	$0.579680\pi$
$720$	−4.74153e26	−0.339828
$721$	−2.23351e27	−1.57981
$722$	1.72345e26	0.120308
$723$	6.30911e26	0.434665
$724$	1.20790e27	0.821323
$725$	3.66037e26	0.245648
$726$	9.35101e25	0.0619385
$727$	−8.76419e26	−0.572974	−0.286487	−	0.958084i	$-0.592487\pi$
$727$	−8.76419e26	−0.572974	−0.286487	+	0.958084i	$0.592487\pi$
$728$	−1.79868e27	−1.16066
$729$	−1.57936e27	−1.00594
$730$	1.22079e26	0.0767490
$731$	−9.24353e26	−0.573618
$732$	1.15299e27	0.706267
$733$	−2.50275e26	−0.151332	−0.0756658	−	0.997133i	$-0.524108\pi$
$733$	−2.50275e26	−0.151332	−0.0756658	+	0.997133i	$0.524108\pi$
$734$	−7.30958e26	−0.436295
$735$	1.82831e27	1.07726
$736$	−1.72716e27	−1.00460
$737$	1.95873e27	1.12469
$738$	1.97224e26	0.111796
$739$	9.14648e25	0.0511837	0.0255918	−	0.999672i	$-0.491853\pi$
$739$	9.14648e25	0.0511837	0.0255918	+	0.999672i	$0.491853\pi$
$740$	−1.07023e26	−0.0591258
$741$	−3.94757e27	−2.15306
$742$	−3.20107e26	−0.172368
$743$	−1.81890e27	−0.966977	−0.483489	−	0.875351i	$-0.660631\pi$
$743$	−1.81890e27	−0.966977	−0.483489	+	0.875351i	$0.660631\pi$
$744$	4.03713e26	0.211900
$745$	−9.65492e26	−0.500339
$746$	−8.67720e25	−0.0443977
$747$	2.36798e27	1.19628
$748$	−1.09247e27	−0.544934
$749$	4.67970e26	0.230484
$750$	7.50317e25	0.0364891
$751$	4.04881e27	1.94423	0.972116	−	0.234502i	$-0.0753459\pi$
$751$	4.04881e27	1.94423	0.972116	+	0.234502i	$0.0753459\pi$
$752$	1.52242e27	0.721878
$753$	2.22606e27	1.04228
$754$	9.78522e26	0.452421
$755$	−6.83488e26	−0.312058
$756$	1.40620e25	0.00634002
$757$	2.04779e26	0.0911747	0.0455874	−	0.998960i	$-0.485484\pi$
$757$	2.04779e26	0.0911747	0.0455874	+	0.998960i	$0.485484\pi$
$758$	−8.95372e26	−0.393683
$759$	−3.91148e27	−1.69842
$760$	6.86067e26	0.294196
$761$	1.54497e27	0.654283	0.327142	−	0.944975i	$-0.393915\pi$
$761$	1.54497e27	0.654283	0.327142	+	0.944975i	$0.393915\pi$
$762$	−6.07654e26	−0.254146
$763$	4.69388e27	1.93887
$764$	−3.22644e27	−1.31625
$765$	7.18395e26	0.289454
$766$	1.25834e26	0.0500753
$767$	1.76383e27	0.693268
$768$	−9.79478e26	−0.380245
$769$	−4.84871e27	−1.85920	−0.929600	−	0.368570i	$-0.879848\pi$
$769$	−4.84871e27	−1.85920	−0.929600	+	0.368570i	$0.879848\pi$
$770$	5.15282e26	0.195157
$771$	3.56392e27	1.33325
$772$	2.01010e27	0.742768
$773$	−1.50395e27	−0.548946	−0.274473	−	0.961595i	$-0.588503\pi$
$773$	−1.50395e27	−0.548946	−0.274473	+	0.961595i	$0.588503\pi$
$774$	7.12780e26	0.256990
$775$	1.52162e26	0.0541927
$776$	4.06285e26	0.142937
$777$	9.65203e26	0.335443
$778$	8.97168e26	0.308012
$779$	1.35738e27	0.460359
$780$	−2.21338e27	−0.741578
$781$	−3.02709e27	−1.00194
$782$	7.41284e26	0.242393
$783$	−1.59934e25	−0.00516658
$784$	4.04041e27	1.28950
$785$	2.81366e26	0.0887175
$786$	−9.75133e26	−0.303773
$787$	−2.98654e27	−0.919196	−0.459598	−	0.888127i	$-0.652006\pi$
$787$	−2.98654e27	−0.919196	−0.459598	+	0.888127i	$0.652006\pi$
$788$	−4.84602e27	−1.47362
$789$	2.66567e27	0.800893
$790$	−6.81860e26	−0.202413
$791$	−3.16104e27	−0.927157
$792$	1.76117e27	0.510403
$793$	2.42874e27	0.695480
$794$	4.91301e26	0.139012
$795$	−8.23517e26	−0.230242
$796$	3.22132e27	0.889937
$797$	1.07867e27	0.294465	0.147232	−	0.989102i	$-0.452963\pi$
$797$	1.07867e27	0.294465	0.147232	+	0.989102i	$0.452963\pi$
$798$	−2.95959e27	−0.798369
$799$	−2.30663e27	−0.614871
$800$	5.85347e26	0.154191
$801$	−7.37158e27	−1.91890
$802$	−7.00547e26	−0.180211
$803$	2.15684e27	0.548302
$804$	−6.30792e27	−1.58472
$805$	3.85821e27	0.957910
$806$	4.06774e26	0.0998091
$807$	−7.33737e27	−1.77927
$808$	−1.46564e26	−0.0351252
$809$	6.10584e27	1.44622	0.723110	−	0.690733i	$-0.242712\pi$
$809$	6.10584e27	1.44622	0.723110	+	0.690733i	$0.242712\pi$
$810$	5.49043e26	0.128528
$811$	2.16906e27	0.501849	0.250924	−	0.968007i	$-0.419265\pi$
$811$	2.16906e27	0.501849	0.250924	+	0.968007i	$0.419265\pi$
$812$	−8.09537e27	−1.85120
$813$	−2.02625e27	−0.457965
$814$	1.71353e26	0.0382789
$815$	−1.86713e27	−0.412267
$816$	3.17048e27	0.691941
$817$	4.90566e27	1.05825
$818$	1.15955e27	0.247248
$819$	9.99563e27	2.10675
$820$	7.61076e26	0.158561
$821$	3.35524e27	0.690977	0.345488	−	0.938423i	$-0.387713\pi$
$821$	3.35524e27	0.690977	0.345488	+	0.938423i	$0.387713\pi$
$822$	−1.32087e27	−0.268892
$823$	4.08390e27	0.821820	0.410910	−	0.911676i	$-0.365211\pi$
$823$	4.08390e27	0.821820	0.410910	+	0.911676i	$0.365211\pi$
$824$	2.66961e27	0.531056
$825$	1.32563e27	0.260682
$826$	1.32238e27	0.257068
$827$	−1.62181e27	−0.311673	−0.155836	−	0.987783i	$-0.549807\pi$
$827$	−1.62181e27	−0.311673	−0.155836	+	0.987783i	$0.549807\pi$
$828$	6.30765e27	1.19834
$829$	3.98329e27	0.748125	0.374063	−	0.927403i	$-0.377965\pi$
$829$	3.98329e27	0.748125	0.374063	+	0.927403i	$0.377965\pi$
$830$	−8.28095e26	−0.153758
$831$	−6.54196e27	−1.20088
$832$	−3.76985e27	−0.684152
$833$	−6.12168e27	−1.09836
$834$	−3.62220e27	−0.642532
$835$	−3.87776e27	−0.680079
$836$	5.79787e27	1.00533
$837$	−6.64848e24	−0.00113981
$838$	−1.85054e27	−0.313675
$839$	−6.04374e27	−1.01290	−0.506450	−	0.862269i	$-0.669043\pi$
$839$	−6.04374e27	−1.01290	−0.506450	+	0.862269i	$0.669043\pi$
$840$	−3.46922e27	−0.574882
$841$	3.10397e27	0.508576
$842$	−1.11006e27	−0.179838
$843$	9.39315e27	1.50470
$844$	4.44137e27	0.703500
$845$	−1.80711e27	−0.283039
$846$	1.77867e27	0.275472
$847$	−1.62960e27	−0.249568
$848$	−1.81991e27	−0.275606
$849$	2.95551e27	0.442599
$850$	−2.51227e26	−0.0372037
$851$	1.28302e27	0.187889
$852$	9.74849e27	1.41176
$853$	−7.74231e27	−1.10880	−0.554402	−	0.832249i	$-0.687053\pi$
$853$	−7.74231e27	−1.10880	−0.554402	+	0.832249i	$0.687053\pi$
$854$	1.82088e27	0.257888
$855$	−3.81261e27	−0.534004
$856$	−5.59343e26	−0.0774779
$857$	−5.49676e27	−0.752990	−0.376495	−	0.926419i	$-0.622871\pi$
$857$	−5.49676e27	−0.752990	−0.376495	+	0.926419i	$0.622871\pi$
$858$	3.54380e27	0.480109
$859$	−1.01985e28	−1.36647	−0.683235	−	0.730199i	$-0.739427\pi$
$859$	−1.01985e28	−1.36647	−0.683235	+	0.730199i	$0.739427\pi$
$860$	2.75057e27	0.364492
$861$	−6.86386e27	−0.899577
$862$	1.19646e27	0.155088
$863$	1.03036e28	1.32095	0.660477	−	0.750846i	$-0.270354\pi$
$863$	1.03036e28	1.32095	0.660477	+	0.750846i	$0.270354\pi$
$864$	−2.55758e25	−0.00324301
$865$	9.38445e26	0.117694
$866$	2.38924e27	0.296374
$867$	6.73140e27	0.825893
$868$	−3.36526e27	−0.408396
$869$	−1.20468e28	−1.44606
$870$	1.88734e27	0.224087
$871$	−1.32875e28	−1.56052
$872$	−5.61038e27	−0.651757
$873$	−2.25781e27	−0.259449
$874$	−3.93409e27	−0.447183
$875$	−1.30757e27	−0.147025
$876$	−6.94592e27	−0.772575
$877$	−1.69807e28	−1.86836	−0.934179	−	0.356805i	$-0.883866\pi$
$877$	−1.69807e28	−1.86836	−0.934179	+	0.356805i	$0.883866\pi$
$878$	5.15746e27	0.561356
$879$	6.76159e27	0.728039
$880$	2.92954e27	0.312042
$881$	1.75003e28	1.84406	0.922031	−	0.387116i	$-0.126529\pi$
$881$	1.75003e28	1.84406	0.922031	+	0.387116i	$0.126529\pi$
$882$	4.72050e27	0.492081
$883$	−1.48487e28	−1.53130	−0.765652	−	0.643255i	$-0.777584\pi$
$883$	−1.48487e28	−1.53130	−0.765652	+	0.643255i	$0.777584\pi$
$884$	7.41100e27	0.756102
$885$	3.40201e27	0.343380
$886$	−5.46752e26	−0.0545972
$887$	2.78064e27	0.274708	0.137354	−	0.990522i	$-0.456140\pi$
$887$	2.78064e27	0.274708	0.137354	+	0.990522i	$0.456140\pi$
$888$	−1.15366e27	−0.112760
$889$	1.05896e28	1.02403
$890$	2.57788e27	0.246637
$891$	9.70028e27	0.918219
$892$	1.22184e28	1.14432
$893$	1.22416e28	1.13435
$894$	−4.97821e27	−0.456422
$895$	4.73419e27	0.429464
$896$	−1.69452e28	−1.52097
$897$	2.65344e28	2.35657
$898$	8.39770e26	0.0737964
$899$	3.82747e27	0.332809
$900$	−2.13771e27	−0.183927
$901$	2.75736e27	0.234751
$902$	−1.21854e27	−0.102655
$903$	−2.48064e28	−2.06790
$904$	3.77824e27	0.311666
$905$	4.90755e27	0.400593
$906$	−3.52416e27	−0.284667
$907$	1.01693e28	0.812871	0.406435	−	0.913679i	$-0.366772\pi$
$907$	1.01693e28	0.812871	0.406435	+	0.913679i	$0.366772\pi$
$908$	1.52879e27	0.120929
$909$	8.14486e26	0.0637568
$910$	−3.49553e27	−0.270782
$911$	−1.27159e28	−0.974815	−0.487407	−	0.873175i	$-0.662057\pi$
$911$	−1.27159e28	−0.974815	−0.487407	+	0.873175i	$0.662057\pi$
$912$	−1.68262e28	−1.27654
$913$	−1.46305e28	−1.09846
$914$	−1.18352e27	−0.0879398
$915$	4.68445e27	0.344476
$916$	−5.74125e27	−0.417830
$917$	1.69936e28	1.22399
$918$	1.09769e25	0.000782484 0
$919$	−1.87980e28	−1.32622	−0.663108	−	0.748524i	$-0.730763\pi$
$919$	−1.87980e28	−1.32622	−0.663108	+	0.748524i	$0.730763\pi$
$920$	−4.61153e27	−0.322004
$921$	1.92529e28	1.33054
$922$	−4.26164e27	−0.291496
$923$	2.05349e28	1.39020
$924$	−2.93180e28	−1.96449
$925$	−4.34824e26	−0.0288381
$926$	5.92546e27	0.388971
$927$	−1.48356e28	−0.963934
$928$	1.47237e28	0.946918
$929$	−2.46587e28	−1.56971	−0.784856	−	0.619678i	$-0.787263\pi$
$929$	−2.46587e28	−1.56971	−0.784856	+	0.619678i	$0.787263\pi$
$930$	7.84570e26	0.0494361
$931$	3.24885e28	2.02632
$932$	1.35659e28	0.837524
$933$	−2.58738e28	−1.58119
$934$	3.55554e27	0.215085
$935$	−4.43858e27	−0.265787
$936$	−1.19473e28	−0.708189
$937$	−6.64369e27	−0.389837	−0.194919	−	0.980819i	$-0.562444\pi$
$937$	−6.64369e27	−0.389837	−0.194919	+	0.980819i	$0.562444\pi$
$938$	−9.96192e27	−0.578650
$939$	1.55045e28	0.891525
$940$	6.86378e27	0.390705
$941$	1.61710e27	0.0911247	0.0455623	−	0.998961i	$-0.485492\pi$
$941$	1.61710e27	0.0911247	0.0455623	+	0.998961i	$0.485492\pi$
$942$	1.45076e27	0.0809305
$943$	−9.12392e27	−0.503872
$944$	7.51816e27	0.411034
$945$	5.71323e25	0.00309229
$946$	−4.40388e27	−0.235977
$947$	−2.61067e28	−1.38493	−0.692463	−	0.721453i	$-0.743474\pi$
$947$	−2.61067e28	−1.38493	−0.692463	+	0.721453i	$0.743474\pi$
$948$	3.87958e28	2.03754
$949$	−1.46314e28	−0.760775
$950$	1.33329e27	0.0686358
$951$	6.06950e27	0.309342
$952$	1.16159e28	0.586141
$953$	1.18996e28	0.594495	0.297247	−	0.954800i	$-0.403931\pi$
$953$	1.18996e28	0.594495	0.297247	+	0.954800i	$0.403931\pi$
$954$	−2.12623e27	−0.105172
$955$	−1.31087e28	−0.641987
$956$	−3.42371e28	−1.66015
$957$	3.33447e28	1.60090
$958$	−1.23582e27	−0.0587466
$959$	2.30188e28	1.08344
$960$	−7.27115e27	−0.338865
$961$	−2.00796e28	−0.926579
$962$	−1.16241e27	−0.0531124
$963$	3.10838e27	0.140632
$964$	6.28600e27	0.281606
$965$	8.16680e27	0.362279
$966$	1.98935e28	0.873831
$967$	−1.79063e28	−0.778849	−0.389425	−	0.921058i	$-0.627326\pi$
$967$	−1.79063e28	−0.778849	−0.389425	+	0.921058i	$0.627326\pi$
$968$	1.94778e27	0.0838928
$969$	2.54935e28	1.08731
$970$	7.89569e26	0.0333471
$971$	−2.14214e28	−0.895913	−0.447956	−	0.894055i	$-0.647848\pi$
$971$	−2.14214e28	−0.895913	−0.447956	+	0.894055i	$0.647848\pi$
$972$	−3.13320e28	−1.29766
$973$	6.31239e28	2.58894
$974$	1.04209e28	0.423249
$975$	−8.99270e27	−0.361698
$976$	1.03523e28	0.412346
$977$	5.44608e27	0.214825	0.107413	−	0.994215i	$-0.465743\pi$
$977$	5.44608e27	0.214825	0.107413	+	0.994215i	$0.465743\pi$
$978$	−9.62721e27	−0.376081
$979$	4.55451e28	1.76200
$980$	1.82161e28	0.697923
$981$	3.11780e28	1.18302
$982$	−3.39809e27	−0.127696
$983$	−4.72241e28	−1.75754	−0.878769	−	0.477247i	$-0.841635\pi$
$983$	−4.72241e28	−1.75754	−0.878769	+	0.477247i	$0.841635\pi$
$984$	8.20405e27	0.302395
$985$	−1.96888e28	−0.718746
$986$	−6.31932e27	−0.228475
$987$	−6.19018e28	−2.21662
$988$	−3.93311e28	−1.39491
$989$	−3.29744e28	−1.15827
$990$	3.42264e27	0.119077
$991$	1.05475e27	0.0363454	0.0181727	−	0.999835i	$-0.494215\pi$
$991$	1.05475e27	0.0363454	0.0181727	+	0.999835i	$0.494215\pi$
$992$	6.12069e27	0.208901
$993$	−4.91214e28	−1.66055
$994$	1.53955e28	0.515494
$995$	1.30878e28	0.434059
$996$	4.71161e28	1.54777
$997$	5.09592e28	1.65813	0.829065	−	0.559153i	$-0.188874\pi$
$997$	5.09592e28	1.65813	0.829065	+	0.559153i	$0.188874\pi$
$998$	2.16619e27	0.0698164
$999$	1.89989e25	0.000606536 0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.20.a.b.1.3	✓	4
3.2	odd	2		45.20.a.f.1.2		4
4.3	odd	2		80.20.a.g.1.4		4
5.2	odd	4		25.20.b.c.24.5		8
5.3	odd	4		25.20.b.c.24.4		8
5.4	even	2		25.20.a.c.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.20.a.b.1.3	✓	4	1.1	even	1	trivial
25.20.a.c.1.2		4	5.4	even	2
25.20.b.c.24.4		8	5.3	odd	4
25.20.b.c.24.5		8	5.2	odd	4
45.20.a.f.1.2		4	3.2	odd	2
80.20.a.g.1.4		4	4.3	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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	5.a (trivial)

\(f(q)\)	\(=\)	\(q+208.721 q^{2} -48249.1 q^{3} -480724. q^{4} -1.95312e6 q^{5} -1.00706e7 q^{6} +1.75500e8 q^{7} -2.09767e8 q^{8} +1.16572e9 q^{9} +O(q^{10})\)	\(q+208.721 q^{2} -48249.1 q^{3} -480724. q^{4} -1.95312e6 q^{5} -1.00706e7 q^{6} +1.75500e8 q^{7} -2.09767e8 q^{8} +1.16572e9 q^{9} -4.07657e8 q^{10} -7.20233e9 q^{11} +2.31945e10 q^{12} +4.88586e10 q^{13} +3.66304e10 q^{14} +9.42366e10 q^{15} +2.08255e11 q^{16} -3.15530e11 q^{17} +2.43309e11 q^{18} +1.67456e12 q^{19} +9.38914e11 q^{20} -8.46771e12 q^{21} -1.50328e12 q^{22} -1.12559e13 q^{23} +1.01211e13 q^{24} +3.81470e12 q^{25} +1.01978e13 q^{26} -1.66677e11 q^{27} -8.43669e13 q^{28} +9.59543e13 q^{29} +1.96691e13 q^{30} +3.98884e13 q^{31} +1.53445e14 q^{32} +3.47506e14 q^{33} -6.58576e13 q^{34} -3.42773e14 q^{35} -5.60387e14 q^{36} -1.13986e14 q^{37} +3.49514e14 q^{38} -2.35738e15 q^{39} +4.09700e14 q^{40} +8.10592e14 q^{41} -1.76738e15 q^{42} +2.92953e15 q^{43} +3.46233e15 q^{44} -2.27679e15 q^{45} -2.34933e15 q^{46} +7.31034e15 q^{47} -1.00481e16 q^{48} +1.94013e16 q^{49} +7.96206e14 q^{50} +1.52240e16 q^{51} -2.34875e16 q^{52} -8.73883e15 q^{53} -3.47889e13 q^{54} +1.40671e16 q^{55} -3.68140e16 q^{56} -8.07959e16 q^{57} +2.00276e16 q^{58} +3.61007e16 q^{59} -4.53017e16 q^{60} +4.97095e16 q^{61} +8.32554e15 q^{62} +2.04583e17 q^{63} -7.71584e16 q^{64} -9.54269e16 q^{65} +7.25317e16 q^{66} -2.71958e17 q^{67} +1.51683e17 q^{68} +5.43086e17 q^{69} -7.15438e16 q^{70} +4.20293e17 q^{71} -2.44528e17 q^{72} -2.99464e17 q^{73} -2.37913e16 q^{74} -1.84056e17 q^{75} -8.04999e17 q^{76} -1.26401e18 q^{77} -4.92034e17 q^{78} +1.67263e18 q^{79} -4.06748e17 q^{80} -1.34682e18 q^{81} +1.69187e17 q^{82} +2.03135e18 q^{83} +4.07063e18 q^{84} +6.16269e17 q^{85} +6.11452e17 q^{86} -4.62971e18 q^{87} +1.51081e18 q^{88} -6.32365e18 q^{89} -4.75213e17 q^{90} +8.57467e18 q^{91} +5.41096e18 q^{92} -1.92458e18 q^{93} +1.52582e18 q^{94} -3.27062e18 q^{95} -7.40360e18 q^{96} -1.93684e18 q^{97} +4.04944e18 q^{98} -8.39588e18 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 420 q^{2} + 3080 q^{3} + 2084992 q^{4} - 7812500 q^{5} - 58071752 q^{6} + 214021400 q^{7} + 81737760 q^{8} + 154064548 q^{9}+O(q^{10}) \) 4 * q - 420 * q^2 + 3080 * q^3 + 2084992 * q^4 - 7812500 * q^5 - 58071752 * q^6 + 214021400 * q^7 + 81737760 * q^8 + 154064548 * q^9	\( 4 q - 420 q^{2} + 3080 q^{3} + 2084992 q^{4} - 7812500 q^{5} - 58071752 q^{6} + 214021400 q^{7} + 81737760 q^{8} + 154064548 q^{9} + 820312500 q^{10} + 11585712768 q^{11} + 105629359360 q^{12} + 14812333160 q^{13} + 185174155944 q^{14} - 6015625000 q^{15} + 1785780098944 q^{16} + 849033742440 q^{17} - 2113778999620 q^{18} + 1978167708560 q^{19} - 4072250000000 q^{20} - 1487020185552 q^{21} - 7953348762240 q^{22} - 26569906952760 q^{23} - 39774243472320 q^{24} + 15258789062500 q^{25} - 48695658207912 q^{26} - 7557605929360 q^{27} + 236612033519360 q^{28} + 116267174339640 q^{29} + 113421390625000 q^{30} + 251049672388688 q^{31} - 142495342974720 q^{32} + 359905680636160 q^{33} + 411849015040344 q^{34} - 418010546875000 q^{35} - 168308645735296 q^{36} + 53471657716520 q^{37} - 52\!\cdots\!60 q^{38}+ \cdots - 25\!\cdots\!84 q^{99}+O(q^{100}) \) 4 * q - 420 * q^2 + 3080 * q^3 + 2084992 * q^4 - 7812500 * q^5 - 58071752 * q^6 + 214021400 * q^7 + 81737760 * q^8 + 154064548 * q^9 + 820312500 * q^10 + 11585712768 * q^11 + 105629359360 * q^12 + 14812333160 * q^13 + 185174155944 * q^14 - 6015625000 * q^15 + 1785780098944 * q^16 + 849033742440 * q^17 - 2113778999620 * q^18 + 1978167708560 * q^19 - 4072250000000 * q^20 - 1487020185552 * q^21 - 7953348762240 * q^22 - 26569906952760 * q^23 - 39774243472320 * q^24 + 15258789062500 * q^25 - 48695658207912 * q^26 - 7557605929360 * q^27 + 236612033519360 * q^28 + 116267174339640 * q^29 + 113421390625000 * q^30 + 251049672388688 * q^31 - 142495342974720 * q^32 + 359905680636160 * q^33 + 411849015040344 * q^34 - 418010546875000 * q^35 - 168308645735296 * q^36 + 53471657716520 * q^37 - 5247417886886160 * q^38 - 3407032515417904 * q^39 - 159644062500000 * q^40 + 5606221897948248 * q^41 - 6858180778710960 * q^42 + 3924193112762600 * q^43 + 7741056858814464 * q^44 - 300907320312500 * q^45 - 13726548710068872 * q^46 + 9972444326989560 * q^47 + 45169928589418240 * q^48 + 40183155980030772 * q^49 - 1602172851562500 * q^50 + 21906201621258448 * q^51 - 98153899497030400 * q^52 - 7462276270800120 * q^53 - 40810202919142640 * q^54 - 22628345250000000 * q^55 - 85257126419530560 * q^56 + 24746009355310880 * q^57 - 168144043315298040 * q^58 + 186154941962838480 * q^59 - 206307342500000000 * q^60 + 248517593110644968 * q^61 - 622575860488793040 * q^62 + 375323610989436120 * q^63 + 797725889363156992 * q^64 - 28930338203125000 * q^65 + 66770019182287616 * q^66 - 83976946080676360 * q^67 + 1012065979784551680 * q^68 + 721386544222156176 * q^69 - 361668273328125000 * q^70 - 326854508200029072 * q^71 - 3247857120459936480 * q^72 + 706071038062266440 * q^73 + 1007811588432673944 * q^74 + 11749267578125000 * q^75 + 453476009937236480 * q^76 - 3188023247458540800 * q^77 - 422235733076613200 * q^78 + 1300235890504742240 * q^79 - 3487851755750000000 * q^80 - 565640020943583596 * q^81 - 3526321594330914840 * q^82 - 894716269324765080 * q^83 + 11741177868239906304 * q^84 - 1658269028203125000 * q^85 + 10889898572595403608 * q^86 - 3243563654475579280 * q^87 + 8680694316508369920 * q^88 - 4392730519471649880 * q^89 + 4128474608632812500 * q^90 - 1164625388848487312 * q^91 + 1015783757806275840 * q^92 + 589775737588352160 * q^93 + 6912955459089075144 * q^94 - 3863608805781250000 * q^95 - 34035929850443648512 * q^96 + 1437870497951780360 * q^97 + 1735173204679501740 * q^98 - 25265427652281702784 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more