LMFDB - Embedded newform 49.26.a.d.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,26,Mod(1,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 26, names="a")

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

chi := DirichletCharacter("49.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	49.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:	$194.038422177$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 212249190 x^{5} + 97966970896 x^{4} + \cdots + 48\!\cdots\!56 $ x^7 - x^6 - 212249190x^5 + 97966970896x^4 + 13490510525162432x^3 - 12908535655668027648x^2 - 247876261380147473323520*x + 486739593081059559316115456
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{10}\cdot 5^{4}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 7)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2316.35$ of defining polynomial
Character	$\chi$	$=$	49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3512.35 q^{2} +741876. q^{3} -2.12178e7 q^{4} -1.79936e8 q^{5} +2.60573e9 q^{6} -1.92379e11 q^{8} -2.96909e11 q^{9} +O(q^{10})$	\(q+3512.35 q^{2} +741876. q^{3} -2.12178e7 q^{4} -1.79936e8 q^{5} +2.60573e9 q^{6} -1.92379e11 q^{8} -2.96909e11 q^{9} -6.31998e11 q^{10} -1.74267e13 q^{11} -1.57410e13 q^{12} -6.48062e13 q^{13} -1.33490e14 q^{15} +3.62499e13 q^{16} -3.69732e15 q^{17} -1.04285e15 q^{18} -1.11755e16 q^{19} +3.81785e15 q^{20} -6.12085e16 q^{22} +3.65404e16 q^{23} -1.42722e17 q^{24} -2.65646e17 q^{25} -2.27622e17 q^{26} -8.48852e17 q^{27} +3.09512e18 q^{29} -4.68864e17 q^{30} +3.19230e18 q^{31} +6.58250e18 q^{32} -1.29284e19 q^{33} -1.29863e19 q^{34} +6.29977e18 q^{36} +4.83471e19 q^{37} -3.92523e19 q^{38} -4.80781e19 q^{39} +3.46159e19 q^{40} +2.88257e19 q^{41} -2.18195e20 q^{43} +3.69756e20 q^{44} +5.34246e19 q^{45} +1.28342e20 q^{46} +4.24063e20 q^{47} +2.68929e19 q^{48} -9.33042e20 q^{50} -2.74295e21 q^{51} +1.37505e21 q^{52} -2.56286e21 q^{53} -2.98146e21 q^{54} +3.13568e21 q^{55} -8.29084e21 q^{57} +1.08711e22 q^{58} -1.53802e22 q^{59} +2.83237e21 q^{60} -2.77814e22 q^{61} +1.12125e22 q^{62} +2.19037e22 q^{64} +1.16610e22 q^{65} -4.54091e22 q^{66} +6.80046e22 q^{67} +7.84491e22 q^{68} +2.71084e22 q^{69} -7.25683e22 q^{71} +5.71192e22 q^{72} +3.07121e23 q^{73} +1.69812e23 q^{74} -1.97077e23 q^{75} +2.37120e23 q^{76} -1.68867e23 q^{78} +1.31075e23 q^{79} -6.52265e21 q^{80} -3.78175e23 q^{81} +1.01246e23 q^{82} +6.52147e23 q^{83} +6.65280e23 q^{85} -7.66376e23 q^{86} +2.29620e24 q^{87} +3.35253e24 q^{88} -3.16169e24 q^{89} +1.87646e23 q^{90} -7.75308e23 q^{92} +2.36829e24 q^{93} +1.48946e24 q^{94} +2.01088e24 q^{95} +4.88340e24 q^{96} +2.86205e23 q^{97} +5.17413e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 8373 q^{2} + 599172 q^{3} + 199632661 q^{4} - 485320794 q^{5} - 548762130 q^{6} + 679913241639 q^{8} + 2499178495563 q^{9}+O(q^{10}) $ 7 * q + 8373 * q^2 + 599172 * q^3 + 199632661 * q^4 - 485320794 * q^5 - 548762130 * q^6 + 679913241639 * q^8 + 2499178495563 * q^9	$ 7 q + 8373 q^{2} + 599172 q^{3} + 199632661 q^{4} - 485320794 q^{5} - 548762130 q^{6} + 679913241639 q^{8} + 2499178495563 q^{9} + 876704815140 q^{10} - 7845139606524 q^{11} + 83731581305106 q^{12} + 75871445642734 q^{13} + 12\!\cdots\!84 q^{15}+ \cdots + 29\!\cdots\!00 q^{99}+O(q^{100}) $ 7 * q + 8373 * q^2 + 599172 * q^3 + 199632661 * q^4 - 485320794 * q^5 - 548762130 * q^6 + 679913241639 * q^8 + 2499178495563 * q^9 + 876704815140 * q^10 - 7845139606524 * q^11 + 83731581305106 * q^12 + 75871445642734 * q^13 + 1250450093573784 * q^15 + 2533333214129041 * q^16 - 4930179049331550 * q^17 + 6108218172751149 * q^18 + 8822108307937204 * q^19 + 35797888210439208 * q^20 + 122308015837411896 * q^22 + 260380318250119992 * q^23 - 280838923324398306 * q^24 + 442974124902943561 * q^25 - 525030062154247104 * q^26 + 508138451607400488 * q^27 + 3074121146906357394 * q^29 + 20693674849314206160 * q^30 - 17867964278742490304 * q^31 + 41524963168122393471 * q^32 - 18631713362079899088 * q^33 - 76530595013021124150 * q^34 + 120686738791924632357 * q^36 + 37537195275383667242 * q^37 - 133898980332930749790 * q^38 + 160680068588101330968 * q^39 - 260261018010811048560 * q^40 - 349555665716732087718 * q^41 - 188918130006461199484 * q^43 - 866635019544130150704 * q^44 + 2875914312455481795918 * q^45 - 1056444907691638473648 * q^46 + 577519309883773958064 * q^47 + 1705636002072738200514 * q^48 - 3108044078925178785 * q^50 - 8568497654252614793448 * q^51 + 21223967127059853562252 * q^52 + 724118360265623334330 * q^53 + 23525683999565788877508 * q^54 + 3874297214249814234792 * q^55 + 21002099147408968606176 * q^57 - 6571075616758407948534 * q^58 + 29388013065202679743548 * q^59 + 131210151872269358361312 * q^60 - 24863323230677092393442 * q^61 - 178098511159147000538004 * q^62 + 185730465159694629378817 * q^64 - 28642507689771657088260 * q^65 + 182488465275344339797728 * q^66 + 87288896332559907446444 * q^67 - 236561584649915083645422 * q^68 + 38736311524504328113344 * q^69 + 507749245951454445426264 * q^71 - 136846012456831244000985 * q^72 + 384451815193432683470074 * q^73 - 180156332882615168418510 * q^74 + 917728597534517928543804 * q^75 + 1802955096706900507996366 * q^76 - 2701299412149008608565208 * q^78 - 512089643024553543168400 * q^79 - 1072829383400652355143456 * q^80 - 1711055088184234765637889 * q^81 + 328793973025384284153498 * q^82 - 683613625271699866065420 * q^83 - 4106127272649214828366668 * q^85 + 6352668961585470034751760 * q^86 - 6810779334667612471104168 * q^87 - 1678346430445345786597824 * q^88 - 7785138614078665124468694 * q^89 + 6907385334351120772566420 * q^90 + 4229143913695999872649632 * q^92 + 9311007684860974346150688 * q^93 - 16094575705640558287782684 * q^94 + 8670853765297953493275288 * q^95 - 20458763379770390869400514 * q^96 - 16735236191051483252826350 * q^97 + 29494988134999515624453300 * 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 $

$2$	3512.35	0.606349	0.303174	−	0.952935i	$-0.401954\pi$
$2$	3512.35	0.606349	0.303174	+	0.952935i	$0.401954\pi$
$3$	741876.	0.805964	0.402982	−	0.915208i	$-0.367974\pi$
$3$	741876.	0.805964	0.402982	+	0.915208i	$0.367974\pi$
$4$	−2.12178e7	−0.632341
$5$	−1.79936e8	−0.329604	−0.164802	−	0.986327i	$-0.552699\pi$
$5$	−1.79936e8	−0.329604	−0.164802	+	0.986327i	$0.552699\pi$
$6$	2.60573e9	0.488695
$7$	0	0
$7$	0	0
$8$	−1.92379e11	−0.989768
$9$	−2.96909e11	−0.350423
$10$	−6.31998e11	−0.199855
$11$	−1.74267e13	−1.67419	−0.837096	−	0.547055i	$-0.815749\pi$
$11$	−1.74267e13	−1.67419	−0.837096	+	0.547055i	$0.815749\pi$
$12$	−1.57410e13	−0.509644
$13$	−6.48062e13	−0.771480	−0.385740	−	0.922608i	$-0.626054\pi$
$13$	−6.48062e13	−0.771480	−0.385740	+	0.922608i	$0.626054\pi$
$14$	0	0
$15$	−1.33490e14	−0.265649
$16$	3.62499e13	0.0321963
$17$	−3.69732e15	−1.53913	−0.769565	−	0.638569i	$-0.779527\pi$
$17$	−3.69732e15	−1.53913	−0.769565	+	0.638569i	$0.779527\pi$
$18$	−1.04285e15	−0.212478
$19$	−1.11755e16	−1.15837	−0.579185	−	0.815196i	$-0.696629\pi$
$19$	−1.11755e16	−1.15837	−0.579185	+	0.815196i	$0.696629\pi$
$20$	3.81785e15	0.208422
$21$	0	0
$22$	−6.12085e16	−1.01514
$23$	3.65404e16	0.347676	0.173838	−	0.984774i	$-0.444383\pi$
$23$	3.65404e16	0.347676	0.173838	+	0.984774i	$0.444383\pi$
$24$	−1.42722e17	−0.797717
$25$	−2.65646e17	−0.891361
$26$	−2.27622e17	−0.467786
$27$	−8.48852e17	−1.08839
$28$	0	0
$29$	3.09512e18	1.62444	0.812219	−	0.583353i	$-0.198260\pi$
$29$	3.09512e18	1.62444	0.812219	+	0.583353i	$0.198260\pi$
$30$	−4.68864e17	−0.161076
$31$	3.19230e18	0.727918	0.363959	−	0.931415i	$-0.381425\pi$
$31$	3.19230e18	0.727918	0.363959	+	0.931415i	$0.381425\pi$
$32$	6.58250e18	1.00929
$33$	−1.29284e19	−1.34934
$34$	−1.29863e19	−0.933250
$35$	0	0
$36$	6.29977e18	0.221587
$37$	4.83471e19	1.20739	0.603697	−	0.797214i	$-0.293694\pi$
$37$	4.83471e19	1.20739	0.603697	+	0.797214i	$0.293694\pi$
$38$	−3.92523e19	−0.702376
$39$	−4.80781e19	−0.621785
$40$	3.46159e19	0.326232
$41$	2.88257e19	0.199518	0.0997588	−	0.995012i	$-0.468193\pi$
$41$	2.88257e19	0.199518	0.0997588	+	0.995012i	$0.468193\pi$
$42$	0	0
$43$	−2.18195e20	−0.832701	−0.416350	−	0.909204i	$-0.636691\pi$
$43$	−2.18195e20	−0.832701	−0.416350	+	0.909204i	$0.636691\pi$
$44$	3.69756e20	1.05866
$45$	5.34246e19	0.115501
$46$	1.28342e20	0.210813
$47$	4.24063e20	0.532362	0.266181	−	0.963923i	$-0.414238\pi$
$47$	4.24063e20	0.532362	0.266181	+	0.963923i	$0.414238\pi$
$48$	2.68929e19	0.0259491
$49$	0	0
$50$	−9.33042e20	−0.540476
$51$	−2.74295e21	−1.24048
$52$	1.37505e21	0.487838
$53$	−2.56286e21	−0.716599	−0.358299	−	0.933607i	$-0.616643\pi$
$53$	−2.56286e21	−0.716599	−0.358299	+	0.933607i	$0.616643\pi$
$54$	−2.98146e21	−0.659945
$55$	3.13568e21	0.551821
$56$	0	0
$57$	−8.29084e21	−0.933604
$58$	1.08711e22	0.984976
$59$	−1.53802e22	−1.12541	−0.562707	−	0.826657i	$-0.690240\pi$
$59$	−1.53802e22	−1.12541	−0.562707	+	0.826657i	$0.690240\pi$
$60$	2.83237e21	0.167981
$61$	−2.77814e22	−1.34008	−0.670040	−	0.742325i	$-0.733723\pi$
$61$	−2.77814e22	−1.34008	−0.670040	+	0.742325i	$0.733723\pi$
$62$	1.12125e22	0.441372
$63$	0	0
$64$	2.19037e22	0.579786
$65$	1.16610e22	0.254283
$66$	−4.54091e22	−0.818170
$67$	6.80046e22	1.01532	0.507661	−	0.861557i	$-0.330510\pi$
$67$	6.80046e22	1.01532	0.507661	+	0.861557i	$0.330510\pi$
$68$	7.84491e22	0.973255
$69$	2.71084e22	0.280214
$70$	0	0
$71$	−7.25683e22	−0.524829	−0.262415	−	0.964955i	$-0.584519\pi$
$71$	−7.25683e22	−0.524829	−0.262415	+	0.964955i	$0.584519\pi$
$72$	5.71192e22	0.346837
$73$	3.07121e23	1.56954	0.784772	−	0.619784i	$-0.212780\pi$
$73$	3.07121e23	1.56954	0.784772	+	0.619784i	$0.212780\pi$
$74$	1.69812e23	0.732102
$75$	−1.97077e23	−0.718405
$76$	2.37120e23	0.732485
$77$	0	0
$78$	−1.68867e23	−0.377018
$79$	1.31075e23	0.249563	0.124782	−	0.992184i	$-0.460177\pi$
$79$	1.31075e23	0.249563	0.124782	+	0.992184i	$0.460177\pi$
$80$	−6.52265e21	−0.0106121
$81$	−3.78175e23	−0.526781
$82$	1.01246e23	0.120977
$83$	6.52147e23	0.669683	0.334841	−	0.942274i	$-0.391317\pi$
$83$	6.52147e23	0.669683	0.334841	+	0.942274i	$0.391317\pi$
$84$	0	0
$85$	6.65280e23	0.507304
$86$	−7.66376e23	−0.504907
$87$	2.29620e24	1.30924
$88$	3.35253e24	1.65706
$89$	−3.16169e24	−1.35689	−0.678444	−	0.734652i	$-0.737346\pi$
$89$	−3.16169e24	−1.35689	−0.678444	+	0.734652i	$0.737346\pi$
$90$	1.87646e23	0.0700338
$91$	0	0
$92$	−7.75308e23	−0.219850
$93$	2.36829e24	0.586676
$94$	1.48946e24	0.322797
$95$	2.01088e24	0.381804
$96$	4.88340e24	0.813451
$97$	2.86205e23	0.0418822	0.0209411	−	0.999781i	$-0.493334\pi$
$97$	2.86205e23	0.0418822	0.0209411	+	0.999781i	$0.493334\pi$
$98$	0	0
$99$	5.17413e24	0.586675
$100$	5.63644e24	0.563644
$101$	−1.35244e25	−1.19427	−0.597133	−	0.802143i	$-0.703693\pi$
$101$	−1.35244e25	−1.19427	−0.597133	+	0.802143i	$0.703693\pi$
$102$	−9.63419e24	−0.752165
$103$	−9.04991e24	−0.625430	−0.312715	−	0.949847i	$-0.601238\pi$
$103$	−9.04991e24	−0.625430	−0.312715	+	0.949847i	$0.601238\pi$
$104$	1.24674e25	0.763586
$105$	0	0
$106$	−9.00164e24	−0.434509
$107$	2.70603e24	0.116154	0.0580772	−	0.998312i	$-0.481503\pi$
$107$	2.70603e24	0.116154	0.0580772	+	0.998312i	$0.481503\pi$
$108$	1.80108e25	0.688235
$109$	−4.16884e25	−1.41966	−0.709830	−	0.704373i	$-0.751228\pi$
$109$	−4.16884e25	−1.41966	−0.709830	+	0.704373i	$0.751228\pi$
$110$	1.10136e25	0.334596
$111$	3.58676e25	0.973116
$112$	0	0
$113$	5.43775e25	1.18015	0.590077	−	0.807347i	$-0.299098\pi$
$113$	5.43775e25	1.18015	0.590077	+	0.807347i	$0.299098\pi$
$114$	−2.91203e25	−0.566090
$115$	−6.57493e24	−0.114596
$116$	−6.56718e25	−1.02720
$117$	1.92415e25	0.270344
$118$	−5.40207e25	−0.682393
$119$	0	0
$120$	2.56807e25	0.262931
$121$	1.95341e26	1.80292
$122$	−9.75779e25	−0.812556
$123$	2.13851e25	0.160804
$124$	−6.77338e25	−0.460293
$125$	1.01424e26	0.623401
$126$	0	0
$127$	−7.09236e25	−0.357474	−0.178737	−	0.983897i	$-0.557201\pi$
$127$	−7.09236e25	−0.357474	−0.178737	+	0.983897i	$0.557201\pi$
$128$	−1.43939e26	−0.657738
$129$	−1.61873e26	−0.671126
$130$	4.09573e25	0.154184
$131$	−3.93216e25	−0.134505	−0.0672527	−	0.997736i	$-0.521423\pi$
$131$	−3.93216e25	−0.134505	−0.0672527	+	0.997736i	$0.521423\pi$
$132$	2.74313e26	0.853242
$133$	0	0
$134$	2.38856e26	0.615639
$135$	1.52739e26	0.358739
$136$	7.11287e26	1.52338
$137$	−8.99302e25	−0.175751	−0.0878756	−	0.996131i	$-0.528008\pi$
$137$	−8.99302e25	−0.175751	−0.0878756	+	0.996131i	$0.528008\pi$
$138$	9.52142e25	0.169908
$139$	−4.04221e26	−0.659073	−0.329537	−	0.944143i	$-0.606893\pi$
$139$	−4.04221e26	−0.659073	−0.329537	+	0.944143i	$0.606893\pi$
$140$	0	0
$141$	3.14602e26	0.429064
$142$	−2.54885e26	−0.318229
$143$	1.12935e27	1.29161
$144$	−1.07629e25	−0.0112823
$145$	−5.56924e26	−0.535422
$146$	1.07872e27	0.951692
$147$	0	0
$148$	−1.02582e27	−0.763485
$149$	7.73359e26	0.529119	0.264559	−	0.964369i	$-0.414774\pi$
$149$	7.73359e26	0.529119	0.264559	+	0.964369i	$0.414774\pi$
$150$	−6.92201e26	−0.435604
$151$	2.27869e27	1.31970	0.659848	−	0.751399i	$-0.270621\pi$
$151$	2.27869e27	1.31970	0.659848	+	0.751399i	$0.270621\pi$
$152$	2.14994e27	1.14652
$153$	1.09777e27	0.539346
$154$	0	0
$155$	−5.74410e26	−0.239925
$156$	1.02011e27	0.393180
$157$	−3.98503e27	−1.41803	−0.709016	−	0.705193i	$-0.750860\pi$
$157$	−3.98503e27	−1.41803	−0.709016	+	0.705193i	$0.750860\pi$
$158$	4.60381e26	0.151322
$159$	−1.90132e27	−0.577552
$160$	−1.18443e27	−0.332666
$161$	0	0
$162$	−1.32828e27	−0.319413
$163$	−8.91026e26	−0.198402	−0.0992008	−	0.995067i	$-0.531629\pi$
$163$	−8.91026e26	−0.198402	−0.0992008	+	0.995067i	$0.531629\pi$
$164$	−6.11619e26	−0.126163
$165$	2.32629e27	0.444748
$166$	2.29057e27	0.406061
$167$	−7.65107e27	−1.25825	−0.629124	−	0.777305i	$-0.716586\pi$
$167$	−7.65107e27	−1.25825	−0.629124	+	0.777305i	$0.716586\pi$
$168$	0	0
$169$	−2.85657e27	−0.404819
$170$	2.33670e27	0.307603
$171$	3.31811e27	0.405919
$172$	4.62963e27	0.526551
$173$	6.23636e27	0.659713	0.329857	−	0.944031i	$-0.393000\pi$
$173$	6.23636e27	0.659713	0.329857	+	0.944031i	$0.393000\pi$
$174$	8.06504e27	0.793855
$175$	0	0
$176$	−6.31714e26	−0.0539029
$177$	−1.14102e28	−0.907042
$178$	−1.11050e28	−0.822748
$179$	−2.22734e28	−1.53859	−0.769296	−	0.638893i	$-0.779393\pi$
$179$	−2.22734e28	−1.53859	−0.769296	+	0.638893i	$0.779393\pi$
$180$	−1.13356e27	−0.0730359
$181$	−1.82084e28	−1.09468	−0.547342	−	0.836909i	$-0.684360\pi$
$181$	−1.82084e28	−1.09468	−0.547342	+	0.836909i	$0.684360\pi$
$182$	0	0
$183$	−2.06103e28	−1.08006
$184$	−7.02961e27	−0.344119
$185$	−8.69939e27	−0.397962
$186$	8.31826e27	0.355730
$187$	6.44319e28	2.57680
$188$	−8.99770e27	−0.336634
$189$	0	0
$190$	7.06289e27	0.231506
$191$	3.90347e28	1.19821	0.599106	−	0.800670i	$-0.295523\pi$
$191$	3.90347e28	1.19821	0.599106	+	0.800670i	$0.295523\pi$
$192$	1.62498e28	0.467286
$193$	5.16606e28	1.39217	0.696086	−	0.717958i	$-0.254923\pi$
$193$	5.16606e28	1.39217	0.696086	+	0.717958i	$0.254923\pi$
$194$	1.00525e27	0.0253952
$195$	8.65098e27	0.204943
$196$	0	0
$197$	8.91024e27	0.185807	0.0929034	−	0.995675i	$-0.470385\pi$
$197$	8.91024e27	0.185807	0.0929034	+	0.995675i	$0.470385\pi$
$198$	1.81734e28	0.355730
$199$	−2.12162e28	−0.389945	−0.194973	−	0.980809i	$-0.562462\pi$
$199$	−2.12162e28	−0.389945	−0.194973	+	0.980809i	$0.562462\pi$
$200$	5.11048e28	0.882241
$201$	5.04510e28	0.818312
$202$	−4.75024e28	−0.724141
$203$	0	0
$204$	5.81995e28	0.784408
$205$	−5.18678e27	−0.0657619
$206$	−3.17864e28	−0.379229
$207$	−1.08492e28	−0.121834
$208$	−2.34921e27	−0.0248388
$209$	1.94752e29	1.93933
$210$	0	0
$211$	−1.92078e29	−1.69803	−0.849016	−	0.528366i	$-0.822805\pi$
$211$	−1.92078e29	−1.69803	−0.849016	+	0.528366i	$0.822805\pi$
$212$	5.43783e28	0.453135
$213$	−5.38367e28	−0.422993
$214$	9.50453e27	0.0704301
$215$	3.92611e28	0.274462
$216$	1.63302e29	1.07726
$217$	0	0
$218$	−1.46424e29	−0.860809
$219$	2.27846e29	1.26500
$220$	−6.65324e28	−0.348939
$221$	2.39609e29	1.18741
$222$	1.25979e29	0.590048
$223$	1.53409e29	0.679266	0.339633	−	0.940558i	$-0.389697\pi$
$223$	1.53409e29	0.679266	0.339633	+	0.940558i	$0.389697\pi$
$224$	0	0
$225$	7.88728e28	0.312353
$226$	1.90993e29	0.715585
$227$	1.70404e29	0.604166	0.302083	−	0.953282i	$-0.402318\pi$
$227$	1.70404e29	0.604166	0.302083	+	0.953282i	$0.402318\pi$
$228$	1.75914e29	0.590356
$229$	5.36965e29	1.70609	0.853046	−	0.521836i	$-0.174753\pi$
$229$	5.36965e29	1.70609	0.853046	+	0.521836i	$0.174753\pi$
$230$	−2.30934e28	−0.0694849
$231$	0	0
$232$	−5.95438e29	−1.60782
$233$	4.42341e29	1.13190	0.565951	−	0.824439i	$-0.308509\pi$
$233$	4.42341e29	1.13190	0.565951	+	0.824439i	$0.308509\pi$
$234$	6.75830e28	0.163923
$235$	−7.63042e28	−0.175469
$236$	3.26335e29	0.711645
$237$	9.72413e28	0.201139
$238$	0	0
$239$	6.15886e29	1.14690	0.573451	−	0.819240i	$-0.305604\pi$
$239$	6.15886e29	1.14690	0.573451	+	0.819240i	$0.305604\pi$
$240$	−4.83900e27	−0.00855293
$241$	−8.43150e29	−1.41479	−0.707394	−	0.706819i	$-0.750129\pi$
$241$	−8.43150e29	−1.41479	−0.707394	+	0.706819i	$0.750129\pi$
$242$	6.86107e29	1.09320
$243$	4.38664e29	0.663825
$244$	5.89461e29	0.847388
$245$	0	0
$246$	7.51118e28	0.0975033
$247$	7.24242e29	0.893659
$248$	−6.14133e29	−0.720470
$249$	4.83812e29	0.539740
$250$	3.56238e29	0.377998
$251$	−8.13920e29	−0.821600	−0.410800	−	0.911725i	$-0.634751\pi$
$251$	−8.13920e29	−0.821600	−0.410800	+	0.911725i	$0.634751\pi$
$252$	0	0
$253$	−6.36776e29	−0.582077
$254$	−2.49108e29	−0.216754
$255$	4.93555e29	0.408868
$256$	−1.24053e30	−0.978604
$257$	1.87983e30	1.41239	0.706195	−	0.708017i	$-0.250410\pi$
$257$	1.87983e30	1.41239	0.706195	+	0.708017i	$0.250410\pi$
$258$	−5.68556e29	−0.406937
$259$	0	0
$260$	−2.47420e29	−0.160794
$261$	−9.18970e29	−0.569240
$262$	−1.38111e29	−0.0815572
$263$	2.07421e30	1.16790	0.583951	−	0.811789i	$-0.301506\pi$
$263$	2.07421e30	1.16790	0.583951	+	0.811789i	$0.301506\pi$
$264$	2.48716e30	1.33553
$265$	4.61150e29	0.236194
$266$	0	0
$267$	−2.34558e30	−1.09360
$268$	−1.44291e30	−0.642029
$269$	−1.22527e30	−0.520390	−0.260195	−	0.965556i	$-0.583787\pi$
$269$	−1.22527e30	−0.520390	−0.260195	+	0.965556i	$0.583787\pi$
$270$	5.36473e29	0.217521
$271$	2.90750e30	1.12565	0.562826	−	0.826576i	$-0.309714\pi$
$271$	2.90750e30	1.12565	0.562826	+	0.826576i	$0.309714\pi$
$272$	−1.34027e29	−0.0495543
$273$	0	0
$274$	−3.15866e29	−0.106567
$275$	4.62933e30	1.49231
$276$	−5.75182e29	−0.177191
$277$	2.20820e30	0.650190	0.325095	−	0.945681i	$-0.394604\pi$
$277$	2.20820e30	0.650190	0.325095	+	0.945681i	$0.394604\pi$
$278$	−1.41976e30	−0.399628
$279$	−9.47823e29	−0.255079
$280$	0	0
$281$	−3.81840e30	−0.939838	−0.469919	−	0.882710i	$-0.655717\pi$
$281$	−3.81840e30	−0.939838	−0.469919	+	0.882710i	$0.655717\pi$
$282$	1.10499e30	0.260163
$283$	−4.96584e30	−1.11857	−0.559284	−	0.828976i	$-0.688924\pi$
$283$	−4.96584e30	−1.11857	−0.559284	+	0.828976i	$0.688924\pi$
$284$	1.53974e30	0.331871
$285$	1.49182e30	0.307720
$286$	3.96669e30	0.783164
$287$	0	0
$288$	−1.95440e30	−0.353678
$289$	7.89953e30	1.36892
$290$	−1.95611e30	−0.324652
$291$	2.12328e29	0.0337556
$292$	−6.51645e30	−0.992488
$293$	−1.07898e31	−1.57459	−0.787297	−	0.616574i	$-0.788520\pi$
$293$	−1.07898e31	−1.57459	−0.787297	+	0.616574i	$0.788520\pi$
$294$	0	0
$295$	2.76745e30	0.370941
$296$	−9.30099e30	−1.19504
$297$	1.47927e31	1.82218
$298$	2.71631e30	0.320830
$299$	−2.36804e30	−0.268225
$300$	4.18154e30	0.454277
$301$	0	0
$302$	8.00356e30	0.800196
$303$	−1.00334e31	−0.962534
$304$	−4.05110e29	−0.0372953
$305$	4.99887e30	0.441696
$306$	3.85574e30	0.327032
$307$	2.33843e31	1.90412	0.952060	−	0.305912i	$-0.0989614\pi$
$307$	2.33843e31	1.90412	0.952060	+	0.305912i	$0.0989614\pi$
$308$	0	0
$309$	−6.71390e30	−0.504074
$310$	−2.01753e30	−0.145478
$311$	2.95195e30	0.204458	0.102229	−	0.994761i	$-0.467403\pi$
$311$	2.95195e30	0.204458	0.102229	+	0.994761i	$0.467403\pi$
$312$	9.24923e30	0.615423
$313$	8.03185e29	0.0513466	0.0256733	−	0.999670i	$-0.491827\pi$
$313$	8.03185e29	0.0513466	0.0256733	+	0.999670i	$0.491827\pi$
$314$	−1.39968e31	−0.859822
$315$	0	0
$316$	−2.78113e30	−0.157809
$317$	3.17762e30	0.173325	0.0866624	−	0.996238i	$-0.472380\pi$
$317$	3.17762e30	0.173325	0.0866624	+	0.996238i	$0.472380\pi$
$318$	−6.67810e30	−0.350198
$319$	−5.39376e31	−2.71962
$320$	−3.94126e30	−0.191100
$321$	2.00754e30	0.0936163
$322$	0	0
$323$	4.13194e31	1.78288
$324$	8.02406e30	0.333105
$325$	1.72155e31	0.687667
$326$	−3.12959e30	−0.120301
$327$	−3.09276e31	−1.14419
$328$	−5.54546e30	−0.197476
$329$	0	0
$330$	8.17073e30	0.269672
$331$	−6.91341e30	−0.219706	−0.109853	−	0.993948i	$-0.535038\pi$
$331$	−6.91341e30	−0.219706	−0.109853	+	0.993948i	$0.535038\pi$
$332$	−1.38371e31	−0.423468
$333$	−1.43547e31	−0.423098
$334$	−2.68732e31	−0.762938
$335$	−1.22365e31	−0.334654
$336$	0	0
$337$	−9.99121e29	−0.0253656	−0.0126828	−	0.999920i	$-0.504037\pi$
$337$	−9.99121e29	−0.0253656	−0.0126828	+	0.999920i	$0.504037\pi$
$338$	−1.00333e31	−0.245462
$339$	4.03413e31	0.951161
$340$	−1.41158e31	−0.320789
$341$	−5.56311e31	−1.21868
$342$	1.16544e31	0.246129
$343$	0	0
$344$	4.19762e31	0.824181
$345$	−4.87778e30	−0.0923599
$346$	2.19043e31	0.400016
$347$	−8.28482e31	−1.45937	−0.729684	−	0.683785i	$-0.760333\pi$
$347$	−8.28482e31	−1.45937	−0.729684	+	0.683785i	$0.760333\pi$
$348$	−4.87203e31	−0.827885
$349$	−1.13247e32	−1.85656	−0.928280	−	0.371883i	$-0.878712\pi$
$349$	−1.13247e32	−1.85656	−0.928280	+	0.371883i	$0.878712\pi$
$350$	0	0
$351$	5.50109e31	0.839672
$352$	−1.14711e32	−1.68975
$353$	−8.37772e31	−1.19108	−0.595542	−	0.803324i	$-0.703062\pi$
$353$	−8.37772e31	−1.19108	−0.595542	+	0.803324i	$0.703062\pi$
$354$	−4.00766e31	−0.549984
$355$	1.30577e31	0.172986
$356$	6.70843e31	0.858016
$357$	0	0
$358$	−7.82319e31	−0.932923
$359$	1.18352e32	1.36299	0.681496	−	0.731822i	$-0.261330\pi$
$359$	1.18352e32	1.36299	0.681496	+	0.731822i	$0.261330\pi$
$360$	−1.02778e31	−0.114319
$361$	3.18155e31	0.341821
$362$	−6.39541e31	−0.663760
$363$	1.44919e32	1.45309
$364$	0	0
$365$	−5.52621e31	−0.517329
$366$	−7.23907e31	−0.654891
$367$	6.86714e31	0.600413	0.300206	−	0.953874i	$-0.402944\pi$
$367$	6.86714e31	0.600413	0.300206	+	0.953874i	$0.402944\pi$
$368$	1.32458e30	0.0111939
$369$	−8.55861e30	−0.0699155
$370$	−3.05553e31	−0.241304
$371$	0	0
$372$	−5.02500e31	−0.370979
$373$	−1.92434e32	−1.37379	−0.686897	−	0.726755i	$-0.741028\pi$
$373$	−1.92434e32	−1.37379	−0.686897	+	0.726755i	$0.741028\pi$
$374$	2.26307e32	1.56244
$375$	7.52443e31	0.502438
$376$	−8.15809e31	−0.526915
$377$	−2.00583e32	−1.25322
$378$	0	0
$379$	1.82303e32	1.06612	0.533058	−	0.846079i	$-0.321043\pi$
$379$	1.82303e32	1.06612	0.533058	+	0.846079i	$0.321043\pi$
$380$	−4.26665e31	−0.241430
$381$	−5.26165e31	−0.288111
$382$	1.37103e32	0.726534
$383$	−1.40193e32	−0.719020	−0.359510	−	0.933141i	$-0.617056\pi$
$383$	−1.40193e32	−0.719020	−0.359510	+	0.933141i	$0.617056\pi$
$384$	−1.06785e32	−0.530113
$385$	0	0
$386$	1.81450e32	0.844142
$387$	6.47841e31	0.291797
$388$	−6.07264e30	−0.0264839
$389$	1.13420e32	0.478984	0.239492	−	0.970898i	$-0.423019\pi$
$389$	1.13420e32	0.478984	0.239492	+	0.970898i	$0.423019\pi$
$390$	3.03853e31	0.124267
$391$	−1.35101e32	−0.535119
$392$	0	0
$393$	−2.91717e31	−0.108406
$394$	3.12959e31	0.112664
$395$	−2.35851e31	−0.0822572
$396$	−1.09784e32	−0.370979
$397$	−1.33841e31	−0.0438236	−0.0219118	−	0.999760i	$-0.506975\pi$
$397$	−1.33841e31	−0.0438236	−0.0219118	+	0.999760i	$0.506975\pi$
$398$	−7.45185e31	−0.236443
$399$	0	0
$400$	−9.62964e30	−0.0286986
$401$	−1.14160e32	−0.329770	−0.164885	−	0.986313i	$-0.552725\pi$
$401$	−1.14160e32	−0.329770	−0.164885	+	0.986313i	$0.552725\pi$
$402$	1.77201e32	0.496183
$403$	−2.06881e32	−0.561574
$404$	2.86959e32	0.755183
$405$	6.80473e31	0.173629
$406$	0	0
$407$	−8.42529e32	−2.02141
$408$	5.27687e32	1.22779
$409$	−3.89670e32	−0.879339	−0.439669	−	0.898160i	$-0.644904\pi$
$409$	−3.89670e32	−0.879339	−0.439669	+	0.898160i	$0.644904\pi$
$410$	−1.82178e31	−0.0398746
$411$	−6.67170e31	−0.141649
$412$	1.92020e32	0.395485
$413$	0	0
$414$	−3.81061e31	−0.0738737
$415$	−1.17345e32	−0.220730
$416$	−4.26587e32	−0.778647
$417$	−2.99882e32	−0.531189
$418$	6.84036e32	1.17591
$419$	4.95976e32	0.827532	0.413766	−	0.910383i	$-0.364213\pi$
$419$	4.95976e32	0.827532	0.413766	+	0.910383i	$0.364213\pi$
$420$	0	0
$421$	6.45398e32	1.01462	0.507308	−	0.861765i	$-0.330641\pi$
$421$	6.45398e32	1.01462	0.507308	+	0.861765i	$0.330641\pi$
$422$	−6.74643e32	−1.02960
$423$	−1.25908e32	−0.186552
$424$	4.93041e32	0.709266
$425$	9.82179e32	1.37192
$426$	−1.89093e32	−0.256481
$427$	0	0
$428$	−5.74162e31	−0.0734493
$429$	8.37841e32	1.04099
$430$	1.37899e32	0.166420
$431$	−4.57352e32	−0.536148	−0.268074	−	0.963398i	$-0.586387\pi$
$431$	−4.57352e32	−0.536148	−0.268074	+	0.963398i	$0.586387\pi$
$432$	−3.07708e31	−0.0350422
$433$	8.96795e32	0.992189	0.496094	−	0.868269i	$-0.334767\pi$
$433$	8.96795e32	0.992189	0.496094	+	0.868269i	$0.334767\pi$
$434$	0	0
$435$	−4.13168e32	−0.431530
$436$	8.84538e32	0.897709
$437$	−4.08357e32	−0.402738
$438$	8.00273e32	0.767029
$439$	−6.71678e32	−0.625683	−0.312841	−	0.949805i	$-0.601281\pi$
$439$	−6.71678e32	−0.625683	−0.312841	+	0.949805i	$0.601281\pi$
$440$	−6.03240e32	−0.546175
$441$	0	0
$442$	8.41590e32	0.719983
$443$	6.01735e32	0.500448	0.250224	−	0.968188i	$-0.419496\pi$
$443$	6.01735e32	0.500448	0.250224	+	0.968188i	$0.419496\pi$
$444$	−7.61032e32	−0.615341
$445$	5.68902e32	0.447236
$446$	5.38826e32	0.411872
$447$	5.73736e32	0.426450
$448$	0	0
$449$	−1.54969e33	−1.08935	−0.544674	−	0.838648i	$-0.683347\pi$
$449$	−1.54969e33	−1.08935	−0.544674	+	0.838648i	$0.683347\pi$
$450$	2.77029e32	0.189395
$451$	−5.02335e32	−0.334031
$452$	−1.15377e33	−0.746259
$453$	1.69051e33	1.06363
$454$	5.98517e32	0.366335
$455$	0	0
$456$	1.59499e33	0.924051
$457$	2.35523e33	1.32764	0.663821	−	0.747892i	$-0.268934\pi$
$457$	2.35523e33	1.32764	0.663821	+	0.747892i	$0.268934\pi$
$458$	1.88601e33	1.03449
$459$	3.13848e33	1.67518
$460$	1.39506e32	0.0724635
$461$	1.16490e33	0.588880	0.294440	−	0.955670i	$-0.404867\pi$
$461$	1.16490e33	0.588880	0.294440	+	0.955670i	$0.404867\pi$
$462$	0	0
$463$	−2.87498e33	−1.37680	−0.688402	−	0.725329i	$-0.741687\pi$
$463$	−2.87498e33	−1.37680	−0.688402	+	0.725329i	$0.741687\pi$
$464$	1.12198e32	0.0523009
$465$	−4.26141e32	−0.193371
$466$	1.55366e33	0.686327
$467$	3.23479e33	1.39118	0.695592	−	0.718437i	$-0.255142\pi$
$467$	3.23479e33	1.39118	0.695592	+	0.718437i	$0.255142\pi$
$468$	−4.08264e32	−0.170950
$469$	0	0
$470$	−2.68007e32	−0.106395
$471$	−2.95640e33	−1.14288
$472$	2.95883e33	1.11390
$473$	3.80241e33	1.39410
$474$	3.41545e32	0.121960
$475$	2.96873e33	1.03253
$476$	0	0
$477$	7.60935e32	0.251112
$478$	2.16320e33	0.695423
$479$	−1.29113e32	−0.0404367	−0.0202184	−	0.999796i	$-0.506436\pi$
$479$	−1.29113e32	−0.0404367	−0.0202184	+	0.999796i	$0.506436\pi$
$480$	−8.78699e32	−0.268117
$481$	−3.13319e33	−0.931480
$482$	−2.96143e33	−0.857855
$483$	0	0
$484$	−4.14472e33	−1.14006
$485$	−5.14985e31	−0.0138046
$486$	1.54074e33	0.402509
$487$	−4.41145e33	−1.12323	−0.561615	−	0.827399i	$-0.689820\pi$
$487$	−4.41145e33	−1.12323	−0.561615	+	0.827399i	$0.689820\pi$
$488$	5.34456e33	1.32637
$489$	−6.61031e32	−0.159905
$490$	0	0
$491$	−7.89520e32	−0.181487	−0.0907433	−	0.995874i	$-0.528924\pi$
$491$	−7.89520e32	−0.181487	−0.0907433	+	0.995874i	$0.528924\pi$
$492$	−4.53745e32	−0.101683
$493$	−1.14437e34	−2.50022
$494$	2.54379e33	0.541869
$495$	−9.31013e32	−0.193371
$496$	1.15720e32	0.0234363
$497$	0	0
$498$	1.69932e33	0.327271
$499$	−5.31903e33	−0.999024	−0.499512	−	0.866307i	$-0.666487\pi$
$499$	−5.31903e33	−0.999024	−0.499512	+	0.866307i	$0.666487\pi$
$500$	−2.15201e33	−0.394202
$501$	−5.67615e33	−1.01410
$502$	−2.85877e33	−0.498176
$503$	−8.37476e33	−1.42355	−0.711775	−	0.702408i	$-0.752108\pi$
$503$	−8.37476e33	−1.42355	−0.711775	+	0.702408i	$0.752108\pi$
$504$	0	0
$505$	2.43353e33	0.393635
$506$	−2.23658e33	−0.352942
$507$	−2.11922e33	−0.326269
$508$	1.50485e33	0.226045
$509$	−1.19348e34	−1.74922	−0.874610	−	0.484827i	$-0.838883\pi$
$509$	−1.19348e34	−1.74922	−0.874610	+	0.484827i	$0.838883\pi$
$510$	1.73354e33	0.247917
$511$	0	0
$512$	4.72614e32	0.0643624
$513$	9.48636e33	1.26076
$514$	6.60262e33	0.856401
$515$	1.62840e33	0.206144
$516$	3.43461e33	0.424381
$517$	−7.39000e33	−0.891277
$518$	0	0
$519$	4.62661e33	0.531705
$520$	−2.24333e33	−0.251681
$521$	6.49088e33	0.710938	0.355469	−	0.934688i	$-0.384321\pi$
$521$	6.49088e33	0.710938	0.355469	+	0.934688i	$0.384321\pi$
$522$	−3.22774e33	−0.345158
$523$	1.56822e34	1.63733	0.818663	−	0.574274i	$-0.194715\pi$
$523$	1.56822e34	1.63733	0.818663	+	0.574274i	$0.194715\pi$
$524$	8.34319e32	0.0850533
$525$	0	0
$526$	7.28535e33	0.708156
$527$	−1.18030e34	−1.12036
$528$	−4.68653e32	−0.0434438
$529$	−9.71057e33	−0.879121
$530$	1.61972e33	0.143216
$531$	4.56653e33	0.394370
$532$	0	0
$533$	−1.86808e33	−0.153924
$534$	−8.23850e33	−0.663105
$535$	−4.86913e32	−0.0382850
$536$	−1.30827e34	−1.00493
$537$	−1.65241e34	−1.24005
$538$	−4.30358e33	−0.315538
$539$	0	0
$540$	−3.24079e33	−0.226845
$541$	−7.15188e32	−0.0489164	−0.0244582	−	0.999701i	$-0.507786\pi$
$541$	−7.15188e32	−0.0489164	−0.0244582	+	0.999701i	$0.507786\pi$
$542$	1.02122e34	0.682538
$543$	−1.35083e34	−0.882275
$544$	−2.43376e34	−1.55343
$545$	7.50124e33	0.467926
$546$	0	0
$547$	−9.83424e33	−0.586002	−0.293001	−	0.956112i	$-0.594654\pi$
$547$	−9.83424e33	−0.586002	−0.293001	+	0.956112i	$0.594654\pi$
$548$	1.90813e33	0.111135
$549$	8.24855e33	0.469595
$550$	1.62598e34	0.904861
$551$	−3.45896e34	−1.88170
$552$	−5.21510e33	−0.277347
$553$	0	0
$554$	7.75595e33	0.394242
$555$	−6.45386e33	−0.320743
$556$	8.57669e33	0.416759
$557$	1.80009e34	0.855270	0.427635	−	0.903952i	$-0.359347\pi$
$557$	1.80009e34	0.855270	0.427635	+	0.903952i	$0.359347\pi$
$558$	−3.32909e33	−0.154667
$559$	1.41404e34	0.642412
$560$	0	0
$561$	4.78004e34	2.07681
$562$	−1.34116e34	−0.569869
$563$	8.53627e33	0.354743	0.177371	−	0.984144i	$-0.443241\pi$
$563$	8.53627e33	0.354743	0.177371	+	0.984144i	$0.443241\pi$
$564$	−6.67518e33	−0.271315
$565$	−9.78446e33	−0.388984
$566$	−1.74418e34	−0.678242
$567$	0	0
$568$	1.39606e34	0.519459
$569$	1.39739e34	0.508643	0.254321	−	0.967120i	$-0.418148\pi$
$569$	1.39739e34	0.508643	0.254321	+	0.967120i	$0.418148\pi$
$570$	5.23979e33	0.186586
$571$	−3.83262e34	−1.33519	−0.667597	−	0.744523i	$-0.732677\pi$
$571$	−3.83262e34	−1.33519	−0.667597	+	0.744523i	$0.732677\pi$
$572$	−2.39625e34	−0.816735
$573$	2.89589e34	0.965715
$574$	0	0
$575$	−9.70681e33	−0.309905
$576$	−6.50340e33	−0.203170
$577$	2.95244e34	0.902574	0.451287	−	0.892379i	$-0.350965\pi$
$577$	2.95244e34	0.902574	0.451287	+	0.892379i	$0.350965\pi$
$578$	2.77459e34	0.830043
$579$	3.83257e34	1.12204
$580$	1.18167e34	0.338569
$581$	0	0
$582$	7.45770e32	0.0204676
$583$	4.46620e34	1.19972
$584$	−5.90837e34	−1.55349
$585$	−3.46225e33	−0.0891065
$586$	−3.78976e34	−0.954753
$587$	−1.96038e34	−0.483464	−0.241732	−	0.970343i	$-0.577716\pi$
$587$	−1.96038e34	−0.483464	−0.241732	+	0.970343i	$0.577716\pi$
$588$	0	0
$589$	−3.56756e34	−0.843199
$590$	9.72026e33	0.224920
$591$	6.61029e33	0.149753
$592$	1.75258e33	0.0388737
$593$	7.06996e33	0.153544	0.0767721	−	0.997049i	$-0.475539\pi$
$593$	7.06996e33	0.153544	0.0767721	+	0.997049i	$0.475539\pi$
$594$	5.19570e34	1.10488
$595$	0	0
$596$	−1.64090e34	−0.334583
$597$	−1.57398e34	−0.314282
$598$	−8.31739e33	−0.162638
$599$	−5.49008e34	−1.05134	−0.525671	−	0.850688i	$-0.676186\pi$
$599$	−5.49008e34	−1.05134	−0.525671	+	0.850688i	$0.676186\pi$
$600$	3.79134e34	0.711054
$601$	−2.28050e34	−0.418890	−0.209445	−	0.977820i	$-0.567166\pi$
$601$	−2.28050e34	−0.418890	−0.209445	+	0.977820i	$0.567166\pi$
$602$	0	0
$603$	−2.01912e34	−0.355792
$604$	−4.83490e34	−0.834498
$605$	−3.51489e34	−0.594251
$606$	−3.52409e34	−0.583632
$607$	−1.40795e33	−0.0228417	−0.0114208	−	0.999935i	$-0.503635\pi$
$607$	−1.40795e33	−0.0228417	−0.0114208	+	0.999935i	$0.503635\pi$
$608$	−7.35628e34	−1.16913
$609$	0	0
$610$	1.75578e34	0.267822
$611$	−2.74819e34	−0.410707
$612$	−2.32923e34	−0.341051
$613$	7.82318e33	0.112235	0.0561174	−	0.998424i	$-0.482128\pi$
$613$	7.82318e33	0.112235	0.0561174	+	0.998424i	$0.482128\pi$
$614$	8.21337e34	1.15456
$615$	−3.84794e33	−0.0530017
$616$	0	0
$617$	4.23299e34	0.559864	0.279932	−	0.960020i	$-0.409688\pi$
$617$	4.23299e34	0.559864	0.279932	+	0.960020i	$0.409688\pi$
$618$	−2.35816e34	−0.305645
$619$	1.02723e35	1.30478	0.652389	−	0.757884i	$-0.273767\pi$
$619$	1.02723e35	1.30478	0.652389	+	0.757884i	$0.273767\pi$
$620$	1.21877e34	0.151714
$621$	−3.10174e34	−0.378408
$622$	1.03683e34	0.123973
$623$	0	0
$624$	−1.74282e33	−0.0200192
$625$	6.09189e34	0.685885
$626$	2.82107e33	0.0311339
$627$	1.44482e35	1.56303
$628$	8.45537e34	0.896679
$629$	−1.78755e35	−1.85834
$630$	0	0
$631$	3.63627e33	0.0363320	0.0181660	−	0.999835i	$-0.494217\pi$
$631$	3.63627e33	0.0363320	0.0181660	+	0.999835i	$0.494217\pi$
$632$	−2.52161e34	−0.247010
$633$	−1.42498e35	−1.36855
$634$	1.11609e34	0.105095
$635$	1.27617e34	0.117825
$636$	4.03419e34	0.365210
$637$	0	0
$638$	−1.89448e35	−1.64904
$639$	2.15462e34	0.183912
$640$	2.58997e34	0.216793
$641$	1.07688e35	0.883979	0.441990	−	0.897020i	$-0.354273\pi$
$641$	1.07688e35	0.883979	0.441990	+	0.897020i	$0.354273\pi$
$642$	7.05118e33	0.0567641
$643$	1.30773e35	1.03248	0.516238	−	0.856445i	$-0.327332\pi$
$643$	1.30773e35	1.03248	0.516238	+	0.856445i	$0.327332\pi$
$644$	0	0
$645$	2.91269e34	0.221206
$646$	1.45128e35	1.08105
$647$	−1.01463e35	−0.741314	−0.370657	−	0.928770i	$-0.620867\pi$
$647$	−1.01463e35	−0.741314	−0.370657	+	0.928770i	$0.620867\pi$
$648$	7.27531e34	0.521391
$649$	2.68026e35	1.88416
$650$	6.04669e34	0.416966
$651$	0	0
$652$	1.89057e34	0.125458
$653$	4.63913e34	0.302010	0.151005	−	0.988533i	$-0.451749\pi$
$653$	4.63913e34	0.302010	0.151005	+	0.988533i	$0.451749\pi$
$654$	−1.08629e35	−0.693781
$655$	7.07536e33	0.0443335
$656$	1.04493e33	0.00642374
$657$	−9.11870e34	−0.550004
$658$	0	0
$659$	−1.40098e35	−0.813514	−0.406757	−	0.913536i	$-0.633340\pi$
$659$	−1.40098e35	−0.813514	−0.406757	+	0.913536i	$0.633340\pi$
$660$	−4.93588e34	−0.281232
$661$	5.35455e34	0.299367	0.149684	−	0.988734i	$-0.452174\pi$
$661$	5.35455e34	0.299367	0.149684	+	0.988734i	$0.452174\pi$
$662$	−2.42823e34	−0.133219
$663$	1.77760e35	0.957007
$664$	−1.25460e35	−0.662831
$665$	0	0
$666$	−5.04187e34	−0.256545
$667$	1.13097e35	0.564778
$668$	1.62339e35	0.795642
$669$	1.13810e35	0.547464
$670$	−4.29788e34	−0.202917
$671$	4.84137e35	2.24355
$672$	0	0
$673$	−4.22346e34	−0.188573	−0.0942867	−	0.995545i	$-0.530057\pi$
$673$	−4.22346e34	−0.188573	−0.0942867	+	0.995545i	$0.530057\pi$
$674$	−3.50926e33	−0.0153804
$675$	2.25494e35	0.970150
$676$	6.06103e34	0.255984
$677$	2.08680e35	0.865210	0.432605	−	0.901584i	$-0.357594\pi$
$677$	2.08680e35	0.865210	0.432605	+	0.901584i	$0.357594\pi$
$678$	1.41693e35	0.576735
$679$	0	0
$680$	−1.27986e35	−0.502113
$681$	1.26418e35	0.486936
$682$	−1.95396e35	−0.738943
$683$	1.56234e35	0.580117	0.290059	−	0.957009i	$-0.406325\pi$
$683$	1.56234e35	0.580117	0.290059	+	0.957009i	$0.406325\pi$
$684$	−7.04031e34	−0.256679
$685$	1.61817e34	0.0579284
$686$	0	0
$687$	3.98361e35	1.37505
$688$	−7.90953e33	−0.0268099
$689$	1.66089e35	0.552841
$690$	−1.71325e34	−0.0560023
$691$	−3.12977e35	−1.00470	−0.502351	−	0.864664i	$-0.667532\pi$
$691$	−3.12977e35	−1.00470	−0.502351	+	0.864664i	$0.667532\pi$
$692$	−1.32322e35	−0.417164
$693$	0	0
$694$	−2.90992e35	−0.884886
$695$	7.27339e34	0.217233
$696$	−4.41741e35	−1.29584
$697$	−1.06578e35	−0.307084
$698$	−3.97763e35	−1.12572
$699$	3.28162e35	0.912271
$700$	0	0
$701$	−1.60689e32	−0.000431032 0	−0.000215516	−	1.00000i	$-0.500069\pi$
$701$	−1.60689e32	−0.000431032 0	−0.000215516		1.00000i	$0.500069\pi$
$702$	1.93217e35	0.509134
$703$	−5.40304e35	−1.39861
$704$	−3.81708e35	−0.970673
$705$	−5.66082e34	−0.141421
$706$	−2.94255e35	−0.722212
$707$	0	0
$708$	2.42100e35	0.573560
$709$	−1.33925e33	−0.00311733	−0.00155866	−	0.999999i	$-0.500496\pi$
$709$	−1.33925e33	−0.00311733	−0.00155866	+	0.999999i	$0.500496\pi$
$710$	4.58630e34	0.104890
$711$	−3.89173e34	−0.0874527
$712$	6.08244e35	1.34301
$713$	1.16648e35	0.253080
$714$	0	0
$715$	−2.03212e35	−0.425719
$716$	4.72593e35	0.972915
$717$	4.56911e35	0.924361
$718$	4.15692e35	0.826449
$719$	−2.42723e32	−0.000474241 0	−0.000237120	−	1.00000i	$-0.500075\pi$
$719$	−2.42723e32	−0.000474241 0	−0.000237120		1.00000i	$0.500075\pi$
$720$	1.93663e33	0.00371870
$721$	0	0
$722$	1.11747e35	0.207263
$723$	−6.25512e35	−1.14027
$724$	3.86342e35	0.692213
$725$	−8.22208e35	−1.44796
$726$	5.09006e35	0.881079
$727$	−8.12562e35	−1.38254	−0.691268	−	0.722599i	$-0.742948\pi$
$727$	−8.12562e35	−1.38254	−0.691268	+	0.722599i	$0.742948\pi$
$728$	0	0
$729$	6.45858e35	1.06180
$730$	−1.94100e35	−0.313682
$731$	8.06736e35	1.28163
$732$	4.37307e35	0.682964
$733$	−1.19990e36	−1.84224	−0.921121	−	0.389277i	$-0.872725\pi$
$733$	−1.19990e36	−1.84224	−0.921121	+	0.389277i	$0.872725\pi$
$734$	2.41198e35	0.364060
$735$	0	0
$736$	2.40527e35	0.350906
$737$	−1.18509e36	−1.69984
$738$	−3.00608e34	−0.0423932
$739$	−6.35621e35	−0.881339	−0.440670	−	0.897669i	$-0.645259\pi$
$739$	−6.35621e35	−0.881339	−0.440670	+	0.897669i	$0.645259\pi$
$740$	1.84582e35	0.251648
$741$	5.37297e35	0.720256
$742$	0	0
$743$	8.42134e35	1.09149	0.545746	−	0.837950i	$-0.316246\pi$
$743$	8.42134e35	1.09149	0.545746	+	0.837950i	$0.316246\pi$
$744$	−4.55610e35	−0.580673
$745$	−1.39155e35	−0.174400
$746$	−6.75896e35	−0.832999
$747$	−1.93628e35	−0.234672
$748$	−1.36711e36	−1.62942
$749$	0	0
$750$	2.64284e35	0.304653
$751$	1.97273e35	0.223650	0.111825	−	0.993728i	$-0.464330\pi$
$751$	1.97273e35	0.223650	0.111825	+	0.993728i	$0.464330\pi$
$752$	1.53722e34	0.0171401
$753$	−6.03828e35	−0.662180
$754$	−7.04518e35	−0.759889
$755$	−4.10019e35	−0.434978
$756$	0	0
$757$	−1.65208e36	−1.69564	−0.847820	−	0.530284i	$-0.822085\pi$
$757$	−1.65208e36	−1.69564	−0.847820	+	0.530284i	$0.822085\pi$
$758$	6.40312e35	0.646438
$759$	−4.72409e35	−0.469133
$760$	−3.86851e35	−0.377897
$761$	−7.60662e35	−0.730943	−0.365471	−	0.930823i	$-0.619092\pi$
$761$	−7.60662e35	−0.730943	−0.365471	+	0.930823i	$0.619092\pi$
$762$	−1.84807e35	−0.174696
$763$	0	0
$764$	−8.28232e35	−0.757678
$765$	−1.97528e35	−0.177771
$766$	−4.92406e35	−0.435977
$767$	9.96733e35	0.868234
$768$	−9.20318e35	−0.788719
$769$	1.87332e36	1.57955	0.789775	−	0.613397i	$-0.210197\pi$
$769$	1.87332e36	1.57955	0.789775	+	0.613397i	$0.210197\pi$
$770$	0	0
$771$	1.39460e36	1.13834
$772$	−1.09613e36	−0.880328
$773$	9.35829e35	0.739525	0.369762	−	0.929126i	$-0.379439\pi$
$773$	9.35829e35	0.739525	0.369762	+	0.929126i	$0.379439\pi$
$774$	2.27544e35	0.176931
$775$	−8.48023e35	−0.648838
$776$	−5.50598e34	−0.0414537
$777$	0	0
$778$	3.98371e35	0.290431
$779$	−3.22142e35	−0.231115
$780$	−1.83555e35	−0.129594
$781$	1.26462e36	0.878665
$782$	−4.74523e35	−0.324469
$783$	−2.62730e36	−1.76802
$784$	0	0
$785$	7.17050e35	0.467389
$786$	−1.02461e35	−0.0657321
$787$	−6.40628e35	−0.404503	−0.202251	−	0.979334i	$-0.564826\pi$
$787$	−6.40628e35	−0.404503	−0.202251	+	0.979334i	$0.564826\pi$
$788$	−1.89056e35	−0.117493
$789$	1.53881e36	0.941286
$790$	−8.28390e34	−0.0498765
$791$	0	0
$792$	−9.95396e35	−0.580672
$793$	1.80041e36	1.03384
$794$	−4.70097e34	−0.0265724
$795$	3.42116e35	0.190364
$796$	4.50161e35	0.246578
$797$	2.26218e35	0.121983	0.0609914	−	0.998138i	$-0.480574\pi$
$797$	2.26218e35	0.121983	0.0609914	+	0.998138i	$0.480574\pi$
$798$	0	0
$799$	−1.56790e36	−0.819374
$800$	−1.74862e36	−0.899642
$801$	9.38735e35	0.475485
$802$	−4.00971e35	−0.199955
$803$	−5.35209e36	−2.62772
$804$	−1.07046e36	−0.517452
$805$	0	0
$806$	−7.26637e35	−0.340510
$807$	−9.08999e35	−0.419415
$808$	2.60181e36	1.18205
$809$	−1.49375e36	−0.668223	−0.334112	−	0.942534i	$-0.608436\pi$
$809$	−1.49375e36	−0.668223	−0.334112	+	0.942534i	$0.608436\pi$
$810$	2.39006e35	0.105280
$811$	3.50563e36	1.52057	0.760283	−	0.649592i	$-0.225060\pi$
$811$	3.50563e36	1.52057	0.760283	+	0.649592i	$0.225060\pi$
$812$	0	0
$813$	2.15701e36	0.907234
$814$	−2.95925e36	−1.22568
$815$	1.60328e35	0.0653941
$816$	−9.94315e34	−0.0399390
$817$	2.43844e36	0.964575
$818$	−1.36866e36	−0.533186
$819$	0	0
$820$	1.10052e35	0.0415839
$821$	4.78835e36	1.78195	0.890976	−	0.454050i	$-0.150021\pi$
$821$	4.78835e36	1.78195	0.890976	+	0.454050i	$0.150021\pi$
$822$	−2.34333e35	−0.0858888
$823$	−1.62799e36	−0.587698	−0.293849	−	0.955852i	$-0.594936\pi$
$823$	−1.62799e36	−0.587698	−0.293849	+	0.955852i	$0.594936\pi$
$824$	1.74101e36	0.619031
$825$	3.43438e36	1.20275
$826$	0	0
$827$	4.35770e35	0.148060	0.0740301	−	0.997256i	$-0.476414\pi$
$827$	4.35770e35	0.148060	0.0740301	+	0.997256i	$0.476414\pi$
$828$	2.30196e35	0.0770404
$829$	1.44084e36	0.474989	0.237494	−	0.971389i	$-0.423674\pi$
$829$	1.44084e36	0.474989	0.237494	+	0.971389i	$0.423674\pi$
$830$	−4.12155e35	−0.133840
$831$	1.63821e36	0.524030
$832$	−1.41949e36	−0.447293
$833$	0	0
$834$	−1.05329e36	−0.322086
$835$	1.37670e36	0.414724
$836$	−4.13221e36	−1.22632
$837$	−2.70979e36	−0.792260
$838$	1.74204e36	0.501773
$839$	−1.61008e36	−0.456901	−0.228450	−	0.973556i	$-0.573366\pi$
$839$	−1.61008e36	−0.456901	−0.228450	+	0.973556i	$0.573366\pi$
$840$	0	0
$841$	5.94943e36	1.63880
$842$	2.26686e36	0.615211
$843$	−2.83278e36	−0.757475
$844$	4.07547e36	1.07374
$845$	5.14000e35	0.133430
$846$	−4.42233e35	−0.113115
$847$	0	0
$848$	−9.29032e34	−0.0230718
$849$	−3.68404e36	−0.901525
$850$	3.44975e36	0.831862
$851$	1.76662e36	0.419782
$852$	1.14230e36	0.267476
$853$	9.55672e35	0.220519	0.110259	−	0.993903i	$-0.464832\pi$
$853$	9.55672e35	0.220519	0.110259	+	0.993903i	$0.464832\pi$
$854$	0	0
$855$	−5.97047e35	−0.133793
$856$	−5.20585e35	−0.114966
$857$	6.29123e35	0.136923	0.0684613	−	0.997654i	$-0.478191\pi$
$857$	6.29123e35	0.136923	0.0684613	+	0.997654i	$0.478191\pi$
$858$	2.94279e36	0.631201
$859$	2.95344e36	0.624329	0.312165	−	0.950028i	$-0.398946\pi$
$859$	2.95344e36	0.624329	0.312165	+	0.950028i	$0.398946\pi$
$860$	−8.33036e35	−0.173553
$861$	0	0
$862$	−1.60638e36	−0.325093
$863$	7.13098e36	1.42238	0.711188	−	0.703002i	$-0.248158\pi$
$863$	7.13098e36	1.42238	0.711188	+	0.703002i	$0.248158\pi$
$864$	−5.58757e36	−1.09850
$865$	−1.12215e36	−0.217444
$866$	3.14985e36	0.601613
$867$	5.86047e36	1.10330
$868$	0	0
$869$	−2.28420e36	−0.417817
$870$	−1.45119e36	−0.261658
$871$	−4.40712e36	−0.783300
$872$	8.01999e36	1.40513
$873$	−8.49767e34	−0.0146765
$874$	−1.43429e36	−0.244200
$875$	0	0
$876$	−4.83439e36	−0.799909
$877$	8.80567e36	1.43637	0.718187	−	0.695850i	$-0.244972\pi$
$877$	8.80567e36	1.43637	0.718187	+	0.695850i	$0.244972\pi$
$878$	−2.35916e36	−0.379382
$879$	−8.00470e36	−1.26907
$880$	1.13668e35	0.0177666
$881$	9.59803e36	1.47905	0.739525	−	0.673129i	$-0.235050\pi$
$881$	9.59803e36	1.47905	0.739525	+	0.673129i	$0.235050\pi$
$882$	0	0
$883$	−9.16459e36	−1.37279	−0.686395	−	0.727229i	$-0.740808\pi$
$883$	−9.16459e36	−1.37279	−0.686395	+	0.727229i	$0.740808\pi$
$884$	−5.08399e36	−0.750846
$885$	2.05311e36	0.298965
$886$	2.11350e36	0.303446
$887$	1.59262e36	0.225459	0.112729	−	0.993626i	$-0.464041\pi$
$887$	1.59262e36	0.225459	0.112729	+	0.993626i	$0.464041\pi$
$888$	−6.90018e36	−0.963159
$889$	0	0
$890$	1.99818e36	0.271181
$891$	6.59033e36	0.881934
$892$	−3.25501e36	−0.429528
$893$	−4.73912e36	−0.616672
$894$	2.01516e36	0.258578
$895$	4.00778e36	0.507126
$896$	0	0
$897$	−1.75679e36	−0.216180
$898$	−5.44306e36	−0.660525
$899$	9.88057e36	1.18246
$900$	−1.67351e36	−0.197514
$901$	9.47569e36	1.10294
$902$	−1.76438e36	−0.202539
$903$	0	0
$904$	−1.04611e37	−1.16808
$905$	3.27634e36	0.360812
$906$	5.93765e36	0.644929
$907$	1.15729e37	1.23980	0.619900	−	0.784681i	$-0.287173\pi$
$907$	1.15729e37	1.23980	0.619900	+	0.784681i	$0.287173\pi$
$908$	−3.61560e36	−0.382039
$909$	4.01552e36	0.418498
$910$	0	0
$911$	1.04056e37	1.05509	0.527544	−	0.849528i	$-0.323113\pi$
$911$	1.04056e37	1.05509	0.527544	+	0.849528i	$0.323113\pi$
$912$	−3.00542e35	−0.0300586
$913$	−1.13647e37	−1.12118
$914$	8.27238e36	0.805014
$915$	3.70854e36	0.355991
$916$	−1.13932e37	−1.07883
$917$	0	0
$918$	1.10234e37	1.01574
$919$	4.11564e36	0.374105	0.187052	−	0.982350i	$-0.440107\pi$
$919$	4.11564e36	0.374105	0.187052	+	0.982350i	$0.440107\pi$
$920$	1.26488e36	0.113423
$921$	1.73482e37	1.53465
$922$	4.09153e36	0.357066
$923$	4.70288e36	0.404895
$924$	0	0
$925$	−1.28432e37	−1.07622
$926$	−1.00979e37	−0.834824
$927$	2.68700e36	0.219165
$928$	2.03736e37	1.63953
$929$	2.99150e36	0.237516	0.118758	−	0.992923i	$-0.462109\pi$
$929$	2.99150e36	0.237516	0.118758	+	0.992923i	$0.462109\pi$
$930$	−1.49675e36	−0.117250
$931$	0	0
$932$	−9.38553e36	−0.715748
$933$	2.18998e36	0.164786
$934$	1.13617e37	0.843543
$935$	−1.15936e37	−0.849324
$936$	−3.70167e36	−0.267578
$937$	−1.54202e37	−1.09988	−0.549938	−	0.835205i	$-0.685349\pi$
$937$	−1.54202e37	−1.09988	−0.549938	+	0.835205i	$0.685349\pi$
$938$	0	0
$939$	5.95864e35	0.0413835
$940$	1.61901e36	0.110956
$941$	−1.67751e37	−1.13448	−0.567239	−	0.823553i	$-0.691988\pi$
$941$	−1.67751e37	−1.13448	−0.567239	+	0.823553i	$0.691988\pi$
$942$	−1.03839e37	−0.692985
$943$	1.05330e36	0.0693675
$944$	−5.57530e35	−0.0362342
$945$	0	0
$946$	1.33554e37	0.845312
$947$	−5.11310e36	−0.319382	−0.159691	−	0.987167i	$-0.551050\pi$
$947$	−5.11310e36	−0.319382	−0.159691	+	0.987167i	$0.551050\pi$
$948$	−2.06325e36	−0.127188
$949$	−1.99033e37	−1.21087
$950$	1.04272e37	0.626071
$951$	2.35740e36	0.139693
$952$	0	0
$953$	3.65122e36	0.210755	0.105377	−	0.994432i	$-0.466395\pi$
$953$	3.65122e36	0.210755	0.105377	+	0.994432i	$0.466395\pi$
$954$	2.67267e36	0.152262
$955$	−7.02374e36	−0.394936
$956$	−1.30678e37	−0.725233
$957$	−4.00150e37	−2.19192
$958$	−4.53490e35	−0.0245188
$959$	0	0
$960$	−2.92393e36	−0.154020
$961$	−9.04200e36	−0.470135
$962$	−1.10049e37	−0.564802
$963$	−8.03446e35	−0.0407032
$964$	1.78898e37	0.894629
$965$	−9.29560e36	−0.458866
$966$	0	0
$967$	3.46438e37	1.66646	0.833231	−	0.552926i	$-0.186489\pi$
$967$	3.46438e37	1.66646	0.833231	+	0.552926i	$0.186489\pi$
$968$	−3.75796e37	−1.78447
$969$	3.06539e37	1.43694
$970$	−1.80881e35	−0.00837038
$971$	−3.41475e37	−1.55998	−0.779989	−	0.625793i	$-0.784775\pi$
$971$	−3.41475e37	−1.55998	−0.779989	+	0.625793i	$0.784775\pi$
$972$	−9.30750e36	−0.419764
$973$	0	0
$974$	−1.54945e37	−0.681070
$975$	1.27718e37	0.554234
$976$	−1.00707e36	−0.0431457
$977$	−1.78260e37	−0.754003	−0.377001	−	0.926213i	$-0.623045\pi$
$977$	−1.78260e37	−0.754003	−0.377001	+	0.926213i	$0.623045\pi$
$978$	−2.32177e36	−0.0969579
$979$	5.50977e37	2.27169
$980$	0	0
$981$	1.23777e37	0.497481
$982$	−2.77307e36	−0.110044
$983$	3.32401e37	1.30240	0.651199	−	0.758907i	$-0.274266\pi$
$983$	3.32401e37	1.30240	0.651199	+	0.758907i	$0.274266\pi$
$984$	−4.11404e36	−0.159159
$985$	−1.60327e36	−0.0612427
$986$	−4.01941e37	−1.51601
$987$	0	0
$988$	−1.53669e37	−0.565097
$989$	−7.97292e36	−0.289510
$990$	−3.27004e36	−0.117250
$991$	−5.13817e37	−1.81923	−0.909616	−	0.415450i	$-0.863624\pi$
$991$	−5.13817e37	−1.81923	−0.909616	+	0.415450i	$0.863624\pi$
$992$	2.10133e37	0.734681
$993$	−5.12889e36	−0.177075
$994$	0	0
$995$	3.81755e36	0.128528
$996$	−1.02654e37	−0.341300
$997$	−2.55608e37	−0.839238	−0.419619	−	0.907700i	$-0.637836\pi$
$997$	−2.55608e37	−0.839238	−0.419619	+	0.907700i	$0.637836\pi$
$998$	−1.86823e37	−0.605757
$999$	−4.10396e37	−1.31412

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.26.a.d.1.4		7
7.6	odd	2		7.26.a.b.1.4	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.26.a.b.1.4	✓	7	7.6	odd	2
49.26.a.d.1.4		7	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	49.a (trivial)

\(f(q)\)	\(=\)	\(q+3512.35 q^{2} +741876. q^{3} -2.12178e7 q^{4} -1.79936e8 q^{5} +2.60573e9 q^{6} -1.92379e11 q^{8} -2.96909e11 q^{9} +O(q^{10})\)	\(q+3512.35 q^{2} +741876. q^{3} -2.12178e7 q^{4} -1.79936e8 q^{5} +2.60573e9 q^{6} -1.92379e11 q^{8} -2.96909e11 q^{9} -6.31998e11 q^{10} -1.74267e13 q^{11} -1.57410e13 q^{12} -6.48062e13 q^{13} -1.33490e14 q^{15} +3.62499e13 q^{16} -3.69732e15 q^{17} -1.04285e15 q^{18} -1.11755e16 q^{19} +3.81785e15 q^{20} -6.12085e16 q^{22} +3.65404e16 q^{23} -1.42722e17 q^{24} -2.65646e17 q^{25} -2.27622e17 q^{26} -8.48852e17 q^{27} +3.09512e18 q^{29} -4.68864e17 q^{30} +3.19230e18 q^{31} +6.58250e18 q^{32} -1.29284e19 q^{33} -1.29863e19 q^{34} +6.29977e18 q^{36} +4.83471e19 q^{37} -3.92523e19 q^{38} -4.80781e19 q^{39} +3.46159e19 q^{40} +2.88257e19 q^{41} -2.18195e20 q^{43} +3.69756e20 q^{44} +5.34246e19 q^{45} +1.28342e20 q^{46} +4.24063e20 q^{47} +2.68929e19 q^{48} -9.33042e20 q^{50} -2.74295e21 q^{51} +1.37505e21 q^{52} -2.56286e21 q^{53} -2.98146e21 q^{54} +3.13568e21 q^{55} -8.29084e21 q^{57} +1.08711e22 q^{58} -1.53802e22 q^{59} +2.83237e21 q^{60} -2.77814e22 q^{61} +1.12125e22 q^{62} +2.19037e22 q^{64} +1.16610e22 q^{65} -4.54091e22 q^{66} +6.80046e22 q^{67} +7.84491e22 q^{68} +2.71084e22 q^{69} -7.25683e22 q^{71} +5.71192e22 q^{72} +3.07121e23 q^{73} +1.69812e23 q^{74} -1.97077e23 q^{75} +2.37120e23 q^{76} -1.68867e23 q^{78} +1.31075e23 q^{79} -6.52265e21 q^{80} -3.78175e23 q^{81} +1.01246e23 q^{82} +6.52147e23 q^{83} +6.65280e23 q^{85} -7.66376e23 q^{86} +2.29620e24 q^{87} +3.35253e24 q^{88} -3.16169e24 q^{89} +1.87646e23 q^{90} -7.75308e23 q^{92} +2.36829e24 q^{93} +1.48946e24 q^{94} +2.01088e24 q^{95} +4.88340e24 q^{96} +2.86205e23 q^{97} +5.17413e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 8373 q^{2} + 599172 q^{3} + 199632661 q^{4} - 485320794 q^{5} - 548762130 q^{6} + 679913241639 q^{8} + 2499178495563 q^{9}+O(q^{10}) \) 7 * q + 8373 * q^2 + 599172 * q^3 + 199632661 * q^4 - 485320794 * q^5 - 548762130 * q^6 + 679913241639 * q^8 + 2499178495563 * q^9	\( 7 q + 8373 q^{2} + 599172 q^{3} + 199632661 q^{4} - 485320794 q^{5} - 548762130 q^{6} + 679913241639 q^{8} + 2499178495563 q^{9} + 876704815140 q^{10} - 7845139606524 q^{11} + 83731581305106 q^{12} + 75871445642734 q^{13} + 12\!\cdots\!84 q^{15}+ \cdots + 29\!\cdots\!00 q^{99}+O(q^{100}) \) 7 * q + 8373 * q^2 + 599172 * q^3 + 199632661 * q^4 - 485320794 * q^5 - 548762130 * q^6 + 679913241639 * q^8 + 2499178495563 * q^9 + 876704815140 * q^10 - 7845139606524 * q^11 + 83731581305106 * q^12 + 75871445642734 * q^13 + 1250450093573784 * q^15 + 2533333214129041 * q^16 - 4930179049331550 * q^17 + 6108218172751149 * q^18 + 8822108307937204 * q^19 + 35797888210439208 * q^20 + 122308015837411896 * q^22 + 260380318250119992 * q^23 - 280838923324398306 * q^24 + 442974124902943561 * q^25 - 525030062154247104 * q^26 + 508138451607400488 * q^27 + 3074121146906357394 * q^29 + 20693674849314206160 * q^30 - 17867964278742490304 * q^31 + 41524963168122393471 * q^32 - 18631713362079899088 * q^33 - 76530595013021124150 * q^34 + 120686738791924632357 * q^36 + 37537195275383667242 * q^37 - 133898980332930749790 * q^38 + 160680068588101330968 * q^39 - 260261018010811048560 * q^40 - 349555665716732087718 * q^41 - 188918130006461199484 * q^43 - 866635019544130150704 * q^44 + 2875914312455481795918 * q^45 - 1056444907691638473648 * q^46 + 577519309883773958064 * q^47 + 1705636002072738200514 * q^48 - 3108044078925178785 * q^50 - 8568497654252614793448 * q^51 + 21223967127059853562252 * q^52 + 724118360265623334330 * q^53 + 23525683999565788877508 * q^54 + 3874297214249814234792 * q^55 + 21002099147408968606176 * q^57 - 6571075616758407948534 * q^58 + 29388013065202679743548 * q^59 + 131210151872269358361312 * q^60 - 24863323230677092393442 * q^61 - 178098511159147000538004 * q^62 + 185730465159694629378817 * q^64 - 28642507689771657088260 * q^65 + 182488465275344339797728 * q^66 + 87288896332559907446444 * q^67 - 236561584649915083645422 * q^68 + 38736311524504328113344 * q^69 + 507749245951454445426264 * q^71 - 136846012456831244000985 * q^72 + 384451815193432683470074 * q^73 - 180156332882615168418510 * q^74 + 917728597534517928543804 * q^75 + 1802955096706900507996366 * q^76 - 2701299412149008608565208 * q^78 - 512089643024553543168400 * q^79 - 1072829383400652355143456 * q^80 - 1711055088184234765637889 * q^81 + 328793973025384284153498 * q^82 - 683613625271699866065420 * q^83 - 4106127272649214828366668 * q^85 + 6352668961585470034751760 * q^86 - 6810779334667612471104168 * q^87 - 1678346430445345786597824 * q^88 - 7785138614078665124468694 * q^89 + 6907385334351120772566420 * q^90 + 4229143913695999872649632 * q^92 + 9311007684860974346150688 * q^93 - 16094575705640558287782684 * q^94 + 8670853765297953493275288 * q^95 - 20458763379770390869400514 * q^96 - 16735236191051483252826350 * q^97 + 29494988134999515624453300 * q^99

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