LMFDB - Embedded newform 98.14.a.h.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,14,Mod(1,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("98.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	98.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:	$105.086310373$
Analytic rank:	$1$
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} - 209077x^{2} - 23859426x + 2739764835 $ x^4 - 209077x^2 - 23859426x + 2739764835
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{7}\cdot 3\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 14)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$496.027$ of defining polynomial
Character	$\chi$	$=$	98.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-64.0000 q^{2} +489.405 q^{3} +4096.00 q^{4} -68192.6 q^{5} -31321.9 q^{6} -262144. q^{8} -1.35481e6 q^{9} +O(q^{10})$	\(q-64.0000 q^{2} +489.405 q^{3} +4096.00 q^{4} -68192.6 q^{5} -31321.9 q^{6} -262144. q^{8} -1.35481e6 q^{9} +4.36432e6 q^{10} +2.02729e6 q^{11} +2.00460e6 q^{12} -1.22100e7 q^{13} -3.33738e7 q^{15} +1.67772e7 q^{16} +9.52852e7 q^{17} +8.67076e7 q^{18} +2.07180e8 q^{19} -2.79317e8 q^{20} -1.29746e8 q^{22} +3.33717e8 q^{23} -1.28295e8 q^{24} +3.42952e9 q^{25} +7.81440e8 q^{26} -1.44332e9 q^{27} +4.91794e9 q^{29} +2.13592e9 q^{30} -4.39054e9 q^{31} -1.07374e9 q^{32} +9.92163e8 q^{33} -6.09825e9 q^{34} -5.54929e9 q^{36} -9.73662e9 q^{37} -1.32595e10 q^{38} -5.97564e9 q^{39} +1.78763e10 q^{40} +2.57081e10 q^{41} +2.25490e9 q^{43} +8.30376e9 q^{44} +9.23877e10 q^{45} -2.13579e10 q^{46} -1.26038e11 q^{47} +8.21085e9 q^{48} -2.19489e11 q^{50} +4.66330e10 q^{51} -5.00122e10 q^{52} -1.71319e11 q^{53} +9.23723e10 q^{54} -1.38246e11 q^{55} +1.01395e11 q^{57} -3.14748e11 q^{58} +5.50763e11 q^{59} -1.36699e11 q^{60} +4.41969e10 q^{61} +2.80995e11 q^{62} +6.87195e10 q^{64} +8.32632e11 q^{65} -6.34984e10 q^{66} -1.21412e11 q^{67} +3.90288e11 q^{68} +1.63323e11 q^{69} +1.25945e12 q^{71} +3.55154e11 q^{72} +1.45331e11 q^{73} +6.23143e11 q^{74} +1.67842e12 q^{75} +8.48608e11 q^{76} +3.82441e11 q^{78} +2.53270e12 q^{79} -1.14408e12 q^{80} +1.45363e12 q^{81} -1.64532e12 q^{82} -1.98753e11 q^{83} -6.49774e12 q^{85} -1.44314e11 q^{86} +2.40686e12 q^{87} -5.31441e11 q^{88} -5.48456e12 q^{89} -5.91281e12 q^{90} +1.36691e12 q^{92} -2.14875e12 q^{93} +8.06641e12 q^{94} -1.41281e13 q^{95} -5.25494e11 q^{96} +3.38474e12 q^{97} -2.74658e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 256 q^{2} - 182 q^{3} + 16384 q^{4} - 1792 q^{5} + 11648 q^{6} - 1048576 q^{8} - 599840 q^{9}+O(q^{10}) $ 4 * q - 256 * q^2 - 182 * q^3 + 16384 * q^4 - 1792 * q^5 + 11648 * q^6 - 1048576 * q^8 - 599840 * q^9	\( 4 q - 256 q^{2} - 182 q^{3} + 16384 q^{4} - 1792 q^{5} + 11648 q^{6} - 1048576 q^{8} - 599840 q^{9} + 114688 q^{10} + 8726914 q^{11} - 745472 q^{12} + 719208 q^{13} - 68436606 q^{15} + 67108864 q^{16} + 7943068 q^{17} + 38389760 q^{18} + 215706806 q^{19} - 7340032 q^{20} - 558522496 q^{22} + 61927978 q^{23} + 47710208 q^{24} + 1327844792 q^{25} - 46029312 q^{26} - 1634321906 q^{27} - 3162923032 q^{29} + 4379942784 q^{30} - 6113775570 q^{31} - 4294967296 q^{32} - 25235960652 q^{33} - 508356352 q^{34} - 2456944640 q^{36} + 3945652880 q^{37} - 13805235584 q^{38} + 23545599116 q^{39} + 469762048 q^{40} + 43189289976 q^{41} - 54537062128 q^{43} + 35745439744 q^{44} + 104964468168 q^{45} - 3963390592 q^{46} + 3141202722 q^{47} - 3053453312 q^{48} - 84982066688 q^{50} + 241278267462 q^{51} + 2945875968 q^{52} - 149625680376 q^{53} + 104596601984 q^{54} + 87456004874 q^{55} - 64103744980 q^{57} + 202427074048 q^{58} + 866297313938 q^{59} - 280316338176 q^{60} + 477908594184 q^{61} + 391281636480 q^{62} + 274877906944 q^{64} + 1099748343120 q^{65} + 1615101481728 q^{66} - 1895501016278 q^{67} + 32534806528 q^{68} + 1751650947816 q^{69} + 319416336064 q^{71} + 157244456960 q^{72} + 2966596192756 q^{73} - 252521784320 q^{74} + 1331079867376 q^{75} + 883535077376 q^{76} - 1506918343424 q^{78} + 6505959677634 q^{79} - 30064771072 q^{80} - 2449216493684 q^{81} - 2764114558464 q^{82} - 1689908567984 q^{83} - 8342278491232 q^{85} + 3490371976192 q^{86} + 5273311164492 q^{87} - 2287708143616 q^{88} - 9586601667468 q^{89} - 6717725962752 q^{90} + 253656997888 q^{92} + 14195747226896 q^{93} - 201036974208 q^{94} - 14384410136978 q^{95} + 195421011968 q^{96} - 22280367655784 q^{97} + 12353209992732 q^{99}+O(q^{100}) \) 4 * q - 256 * q^2 - 182 * q^3 + 16384 * q^4 - 1792 * q^5 + 11648 * q^6 - 1048576 * q^8 - 599840 * q^9 + 114688 * q^10 + 8726914 * q^11 - 745472 * q^12 + 719208 * q^13 - 68436606 * q^15 + 67108864 * q^16 + 7943068 * q^17 + 38389760 * q^18 + 215706806 * q^19 - 7340032 * q^20 - 558522496 * q^22 + 61927978 * q^23 + 47710208 * q^24 + 1327844792 * q^25 - 46029312 * q^26 - 1634321906 * q^27 - 3162923032 * q^29 + 4379942784 * q^30 - 6113775570 * q^31 - 4294967296 * q^32 - 25235960652 * q^33 - 508356352 * q^34 - 2456944640 * q^36 + 3945652880 * q^37 - 13805235584 * q^38 + 23545599116 * q^39 + 469762048 * q^40 + 43189289976 * q^41 - 54537062128 * q^43 + 35745439744 * q^44 + 104964468168 * q^45 - 3963390592 * q^46 + 3141202722 * q^47 - 3053453312 * q^48 - 84982066688 * q^50 + 241278267462 * q^51 + 2945875968 * q^52 - 149625680376 * q^53 + 104596601984 * q^54 + 87456004874 * q^55 - 64103744980 * q^57 + 202427074048 * q^58 + 866297313938 * q^59 - 280316338176 * q^60 + 477908594184 * q^61 + 391281636480 * q^62 + 274877906944 * q^64 + 1099748343120 * q^65 + 1615101481728 * q^66 - 1895501016278 * q^67 + 32534806528 * q^68 + 1751650947816 * q^69 + 319416336064 * q^71 + 157244456960 * q^72 + 2966596192756 * q^73 - 252521784320 * q^74 + 1331079867376 * q^75 + 883535077376 * q^76 - 1506918343424 * q^78 + 6505959677634 * q^79 - 30064771072 * q^80 - 2449216493684 * q^81 - 2764114558464 * q^82 - 1689908567984 * q^83 - 8342278491232 * q^85 + 3490371976192 * q^86 + 5273311164492 * q^87 - 2287708143616 * q^88 - 9586601667468 * q^89 - 6717725962752 * q^90 + 253656997888 * q^92 + 14195747226896 * q^93 - 201036974208 * q^94 - 14384410136978 * q^95 + 195421011968 * q^96 - 22280367655784 * q^97 + 12353209992732 * 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 $

$2$	−64.0000	−0.707107
$2$	−64.0000	−0.707107
$3$	489.405	0.387597	0.193798	−	0.981041i	$-0.437919\pi$
$3$	489.405	0.387597	0.193798	+	0.981041i	$0.437919\pi$
$4$	4096.00	0.500000
$5$	−68192.6	−1.95178	−0.975892	−	0.218252i	$-0.929965\pi$
$5$	−68192.6	−1.95178	−0.975892	+	0.218252i	$0.929965\pi$
$6$	−31321.9	−0.274072
$7$	0	0
$7$	0	0
$8$	−262144.	−0.353553
$9$	−1.35481e6	−0.849769
$10$	4.36432e6	1.38012
$11$	2.02729e6	0.345034	0.172517	−	0.985007i	$-0.444810\pi$
$11$	2.02729e6	0.345034	0.172517	+	0.985007i	$0.444810\pi$
$12$	2.00460e6	0.193798
$13$	−1.22100e7	−0.701591	−0.350796	−	0.936452i	$-0.614089\pi$
$13$	−1.22100e7	−0.701591	−0.350796	+	0.936452i	$0.614089\pi$
$14$	0	0
$15$	−3.33738e7	−0.756505
$16$	1.67772e7	0.250000
$17$	9.52852e7	0.957431	0.478715	−	0.877970i	$-0.341103\pi$
$17$	9.52852e7	0.957431	0.478715	+	0.877970i	$0.341103\pi$
$18$	8.67076e7	0.600877
$19$	2.07180e8	1.01030	0.505148	−	0.863033i	$-0.331438\pi$
$19$	2.07180e8	1.01030	0.505148	+	0.863033i	$0.331438\pi$
$20$	−2.79317e8	−0.975892
$21$	0	0
$22$	−1.29746e8	−0.243976
$23$	3.33717e8	0.470054	0.235027	−	0.971989i	$-0.424482\pi$
$23$	3.33717e8	0.470054	0.235027	+	0.971989i	$0.424482\pi$
$24$	−1.28295e8	−0.137036
$25$	3.42952e9	2.80946
$26$	7.81440e8	0.496100
$27$	−1.44332e9	−0.716964
$28$	0	0
$29$	4.91794e9	1.53531	0.767655	−	0.640864i	$-0.221424\pi$
$29$	4.91794e9	1.53531	0.767655	+	0.640864i	$0.221424\pi$
$30$	2.13592e9	0.534930
$31$	−4.39054e9	−0.888520	−0.444260	−	0.895898i	$-0.646533\pi$
$31$	−4.39054e9	−0.888520	−0.444260	+	0.895898i	$0.646533\pi$
$32$	−1.07374e9	−0.176777
$33$	9.92163e8	0.133734
$34$	−6.09825e9	−0.677006
$35$	0	0
$36$	−5.54929e9	−0.424884
$37$	−9.73662e9	−0.623874	−0.311937	−	0.950103i	$-0.600978\pi$
$37$	−9.73662e9	−0.623874	−0.311937	+	0.950103i	$0.600978\pi$
$38$	−1.32595e10	−0.714388
$39$	−5.97564e9	−0.271934
$40$	1.78763e10	0.690060
$41$	2.57081e10	0.845230	0.422615	−	0.906309i	$-0.361112\pi$
$41$	2.57081e10	0.845230	0.422615	+	0.906309i	$0.361112\pi$
$42$	0	0
$43$	2.25490e9	0.0543980	0.0271990	−	0.999630i	$-0.491341\pi$
$43$	2.25490e9	0.0543980	0.0271990	+	0.999630i	$0.491341\pi$
$44$	8.30376e9	0.172517
$45$	9.23877e10	1.65857
$46$	−2.13579e10	−0.332379
$47$	−1.26038e11	−1.70555	−0.852775	−	0.522279i	$-0.825082\pi$
$47$	−1.26038e11	−1.70555	−0.852775	+	0.522279i	$0.825082\pi$
$48$	8.21085e9	0.0968992
$49$	0	0
$50$	−2.19489e11	−1.98659
$51$	4.66330e10	0.371097
$52$	−5.00122e10	−0.350796
$53$	−1.71319e11	−1.06173	−0.530863	−	0.847458i	$-0.678132\pi$
$53$	−1.71319e11	−1.06173	−0.530863	+	0.847458i	$0.678132\pi$
$54$	9.23723e10	0.506970
$55$	−1.38246e11	−0.673433
$56$	0	0
$57$	1.01395e11	0.391588
$58$	−3.14748e11	−1.08563
$59$	5.50763e11	1.69991	0.849957	−	0.526853i	$-0.176628\pi$
$59$	5.50763e11	1.69991	0.849957	+	0.526853i	$0.176628\pi$
$60$	−1.36699e11	−0.378253
$61$	4.41969e10	0.109837	0.0549184	−	0.998491i	$-0.482510\pi$
$61$	4.41969e10	0.109837	0.0549184	+	0.998491i	$0.482510\pi$
$62$	2.80995e11	0.628279
$63$	0	0
$64$	6.87195e10	0.125000
$65$	8.32632e11	1.36935
$66$	−6.34984e10	−0.0945643
$67$	−1.21412e11	−0.163975	−0.0819874	−	0.996633i	$-0.526127\pi$
$67$	−1.21412e11	−0.163975	−0.0819874	+	0.996633i	$0.526127\pi$
$68$	3.90288e11	0.478715
$69$	1.63323e11	0.182191
$70$	0	0
$71$	1.25945e12	1.16682	0.583408	−	0.812179i	$-0.301719\pi$
$71$	1.25945e12	1.16682	0.583408	+	0.812179i	$0.301719\pi$
$72$	3.55154e11	0.300439
$73$	1.45331e11	0.112398	0.0561992	−	0.998420i	$-0.482102\pi$
$73$	1.45331e11	0.112398	0.0561992	+	0.998420i	$0.482102\pi$
$74$	6.23143e11	0.441145
$75$	1.67842e12	1.08894
$76$	8.48608e11	0.505148
$77$	0	0
$78$	3.82441e11	0.192287
$79$	2.53270e12	1.17222	0.586108	−	0.810233i	$-0.300659\pi$
$79$	2.53270e12	1.17222	0.586108	+	0.810233i	$0.300659\pi$
$80$	−1.14408e12	−0.487946
$81$	1.45363e12	0.571876
$82$	−1.64532e12	−0.597668
$83$	−1.98753e11	−0.0667276	−0.0333638	−	0.999443i	$-0.510622\pi$
$83$	−1.98753e11	−0.0667276	−0.0333638	+	0.999443i	$0.510622\pi$
$84$	0	0
$85$	−6.49774e12	−1.86870
$86$	−1.44314e11	−0.0384652
$87$	2.40686e12	0.595081
$88$	−5.31441e11	−0.121988
$89$	−5.48456e12	−1.16979	−0.584894	−	0.811110i	$-0.698864\pi$
$89$	−5.48456e12	−1.16979	−0.584894	+	0.811110i	$0.698864\pi$
$90$	−5.91281e12	−1.17278
$91$	0	0
$92$	1.36691e12	0.235027
$93$	−2.14875e12	−0.344388
$94$	8.06641e12	1.20601
$95$	−1.41281e13	−1.97188
$96$	−5.25494e11	−0.0685181
$97$	3.38474e12	0.412581	0.206290	−	0.978491i	$-0.433861\pi$
$97$	3.38474e12	0.412581	0.206290	+	0.978491i	$0.433861\pi$
$98$	0	0
$99$	−2.74658e12	−0.293199
$100$	1.40473e13	1.40473
$101$	−9.42898e12	−0.883845	−0.441922	−	0.897053i	$-0.645703\pi$
$101$	−9.42898e12	−0.883845	−0.441922	+	0.897053i	$0.645703\pi$
$102$	−2.98451e12	−0.262405
$103$	−1.90520e13	−1.57217	−0.786084	−	0.618119i	$-0.787895\pi$
$103$	−1.90520e13	−1.57217	−0.786084	+	0.618119i	$0.787895\pi$
$104$	3.20078e12	0.248050
$105$	0	0
$106$	1.09644e13	0.750754
$107$	−3.76212e12	−0.242347	−0.121173	−	0.992631i	$-0.538666\pi$
$107$	−3.76212e12	−0.242347	−0.121173	+	0.992631i	$0.538666\pi$
$108$	−5.91183e12	−0.358482
$109$	−1.47028e13	−0.839705	−0.419852	−	0.907592i	$-0.637918\pi$
$109$	−1.47028e13	−0.839705	−0.419852	+	0.907592i	$0.637918\pi$
$110$	8.84773e12	0.476189
$111$	−4.76515e12	−0.241811
$112$	0	0
$113$	1.91564e13	0.865572	0.432786	−	0.901497i	$-0.357531\pi$
$113$	1.91564e13	0.865572	0.432786	+	0.901497i	$0.357531\pi$
$114$	−6.48926e12	−0.276894
$115$	−2.27570e13	−0.917445
$116$	2.01439e13	0.767655
$117$	1.65422e13	0.596190
$118$	−3.52488e13	−1.20202
$119$	0	0
$120$	8.74873e12	0.267465
$121$	−3.04128e13	−0.880951
$122$	−2.82860e12	−0.0776663
$123$	1.25817e13	0.327608
$124$	−1.79837e13	−0.444260
$125$	−1.50625e14	−3.53169
$126$	0	0
$127$	4.62943e13	0.979046	0.489523	−	0.871990i	$-0.337171\pi$
$127$	4.62943e13	0.979046	0.489523	+	0.871990i	$0.337171\pi$
$128$	−4.39805e12	−0.0883883
$129$	1.10356e12	0.0210845
$130$	−5.32884e13	−0.968280
$131$	2.11710e13	0.365997	0.182999	−	0.983113i	$-0.441420\pi$
$131$	2.11710e13	0.365997	0.182999	+	0.983113i	$0.441420\pi$
$132$	4.06390e12	0.0668671
$133$	0	0
$134$	7.77040e12	0.115948
$135$	9.84235e13	1.39936
$136$	−2.49784e13	−0.338503
$137$	−3.95915e13	−0.511586	−0.255793	−	0.966732i	$-0.582337\pi$
$137$	−3.95915e13	−0.511586	−0.255793	+	0.966732i	$0.582337\pi$
$138$	−1.04527e13	−0.128829
$139$	9.29027e11	0.0109253	0.00546264	−	0.999985i	$-0.498261\pi$
$139$	9.29027e11	0.0109253	0.00546264	+	0.999985i	$0.498261\pi$
$140$	0	0
$141$	−6.16835e13	−0.661065
$142$	−8.06049e13	−0.825063
$143$	−2.47532e13	−0.242073
$144$	−2.27299e13	−0.212442
$145$	−3.35367e14	−2.99659
$146$	−9.30119e12	−0.0794776
$147$	0	0
$148$	−3.98812e13	−0.311937
$149$	1.75704e14	1.31544	0.657719	−	0.753263i	$-0.271521\pi$
$149$	1.75704e14	1.31544	0.657719	+	0.753263i	$0.271521\pi$
$150$	−1.07419e14	−0.769996
$151$	−2.44954e14	−1.68165	−0.840823	−	0.541310i	$-0.817928\pi$
$151$	−2.44954e14	−1.68165	−0.840823	+	0.541310i	$0.817928\pi$
$152$	−5.43109e13	−0.357194
$153$	−1.29093e14	−0.813595
$154$	0	0
$155$	2.99402e14	1.73420
$156$	−2.44762e13	−0.135967
$157$	3.53611e13	0.188442	0.0942210	−	0.995551i	$-0.469964\pi$
$157$	3.53611e13	0.188442	0.0942210	+	0.995551i	$0.469964\pi$
$158$	−1.62093e14	−0.828882
$159$	−8.38443e13	−0.411521
$160$	7.32212e13	0.345030
$161$	0	0
$162$	−9.30324e13	−0.404377
$163$	−6.66239e13	−0.278234	−0.139117	−	0.990276i	$-0.544426\pi$
$163$	−6.66239e13	−0.278234	−0.139117	+	0.990276i	$0.544426\pi$
$164$	1.05300e14	0.422615
$165$	−6.76581e13	−0.261020
$166$	1.27202e13	0.0471836
$167$	−3.09178e14	−1.10294	−0.551469	−	0.834195i	$-0.685933\pi$
$167$	−3.09178e14	−1.10294	−0.551469	+	0.834195i	$0.685933\pi$
$168$	0	0
$169$	−1.53791e14	−0.507770
$170$	4.15855e14	1.32137
$171$	−2.80688e14	−0.858519
$172$	9.23608e12	0.0271990
$173$	1.04184e13	0.0295461	0.0147730	−	0.999891i	$-0.495297\pi$
$173$	1.04184e13	0.0295461	0.0147730	+	0.999891i	$0.495297\pi$
$174$	−1.54039e14	−0.420786
$175$	0	0
$176$	3.40122e13	0.0862586
$177$	2.69546e14	0.658881
$178$	3.51012e14	0.827165
$179$	4.38819e14	0.997104	0.498552	−	0.866860i	$-0.333865\pi$
$179$	4.38819e14	0.997104	0.498552	+	0.866860i	$0.333865\pi$
$180$	3.78420e14	0.829283
$181$	−1.08144e13	−0.0228607	−0.0114304	−	0.999935i	$-0.503638\pi$
$181$	−1.08144e13	−0.0228607	−0.0114304	+	0.999935i	$0.503638\pi$
$182$	0	0
$183$	2.16302e13	0.0425724
$184$	−8.74820e13	−0.166189
$185$	6.63965e14	1.21767
$186$	1.37520e14	0.243519
$187$	1.93170e14	0.330347
$188$	−5.16250e14	−0.852775
$189$	0	0
$190$	9.04199e14	1.39433
$191$	5.97656e14	0.890706	0.445353	−	0.895355i	$-0.353078\pi$
$191$	5.97656e14	0.890706	0.445353	+	0.895355i	$0.353078\pi$
$192$	3.36316e13	0.0484496
$193$	−4.55645e14	−0.634606	−0.317303	−	0.948324i	$-0.602777\pi$
$193$	−4.55645e14	−0.634606	−0.317303	+	0.948324i	$0.602777\pi$
$194$	−2.16623e14	−0.291739
$195$	4.07494e14	0.530757
$196$	0	0
$197$	−8.49836e14	−1.03587	−0.517934	−	0.855421i	$-0.673299\pi$
$197$	−8.49836e14	−1.03587	−0.517934	+	0.855421i	$0.673299\pi$
$198$	1.75781e14	0.207323
$199$	−1.45385e15	−1.65949	−0.829743	−	0.558145i	$-0.811513\pi$
$199$	−1.45385e15	−1.65949	−0.829743	+	0.558145i	$0.811513\pi$
$200$	−8.99029e14	−0.993296
$201$	−5.94198e13	−0.0635561
$202$	6.03455e14	0.624972
$203$	0	0
$204$	1.91009e14	0.185548
$205$	−1.75310e15	−1.64971
$206$	1.21933e15	1.11169
$207$	−4.52122e14	−0.399437
$208$	−2.04850e14	−0.175398
$209$	4.20012e14	0.348587
$210$	0	0
$211$	−1.00855e14	−0.0786797	−0.0393399	−	0.999226i	$-0.512526\pi$
$211$	−1.00855e14	−0.0786797	−0.0393399	+	0.999226i	$0.512526\pi$
$212$	−7.01723e14	−0.530863
$213$	6.16382e14	0.452254
$214$	2.40775e14	0.171365
$215$	−1.53767e14	−0.106173
$216$	3.78357e14	0.253485
$217$	0	0
$218$	9.40977e14	0.593761
$219$	7.11257e13	0.0435652
$220$	−5.66255e14	−0.336716
$221$	−1.16343e15	−0.671725
$222$	3.04969e14	0.170987
$223$	−7.82121e14	−0.425885	−0.212942	−	0.977065i	$-0.568305\pi$
$223$	−7.82121e14	−0.425885	−0.212942	+	0.977065i	$0.568305\pi$
$224$	0	0
$225$	−4.64634e15	−2.38740
$226$	−1.22601e15	−0.612052
$227$	2.80471e14	0.136057	0.0680284	−	0.997683i	$-0.478329\pi$
$227$	2.80471e14	0.136057	0.0680284	+	0.997683i	$0.478329\pi$
$228$	4.15313e14	0.195794
$229$	−3.07496e15	−1.40899	−0.704496	−	0.709708i	$-0.748827\pi$
$229$	−3.07496e15	−1.40899	−0.704496	+	0.709708i	$0.748827\pi$
$230$	1.45645e15	0.648731
$231$	0	0
$232$	−1.28921e15	−0.542814
$233$	3.10634e15	1.27185	0.635925	−	0.771751i	$-0.280619\pi$
$233$	3.10634e15	1.27185	0.635925	+	0.771751i	$0.280619\pi$
$234$	−1.05870e15	−0.421570
$235$	8.59483e15	3.32887
$236$	2.25593e15	0.849957
$237$	1.23952e15	0.454347
$238$	0	0
$239$	5.08395e15	1.76447	0.882237	−	0.470805i	$-0.156037\pi$
$239$	5.08395e15	1.76447	0.882237	+	0.470805i	$0.156037\pi$
$240$	−5.59919e14	−0.189126
$241$	−2.13772e15	−0.702815	−0.351407	−	0.936223i	$-0.614297\pi$
$241$	−2.13772e15	−0.702815	−0.351407	+	0.936223i	$0.614297\pi$
$242$	1.94642e15	0.622927
$243$	3.01253e15	0.938621
$244$	1.81030e14	0.0549184
$245$	0	0
$246$	−8.05227e14	−0.231654
$247$	−2.52967e15	−0.708815
$248$	1.15095e15	0.314139
$249$	−9.72706e13	−0.0258634
$250$	9.64000e15	2.49728
$251$	−1.27798e15	−0.322585	−0.161293	−	0.986907i	$-0.551566\pi$
$251$	−1.27798e15	−0.322585	−0.161293	+	0.986907i	$0.551566\pi$
$252$	0	0
$253$	6.76540e14	0.162185
$254$	−2.96283e15	−0.692290
$255$	−3.18003e15	−0.724302
$256$	2.81475e14	0.0625000
$257$	−4.69629e15	−1.01669	−0.508346	−	0.861153i	$-0.669743\pi$
$257$	−4.69629e15	−1.01669	−0.508346	+	0.861153i	$0.669743\pi$
$258$	−7.06278e13	−0.0149090
$259$	0	0
$260$	3.41046e15	0.684677
$261$	−6.66285e15	−1.30466
$262$	−1.35494e15	−0.258799
$263$	9.45035e15	1.76090	0.880452	−	0.474136i	$-0.157239\pi$
$263$	9.45035e15	1.76090	0.880452	+	0.474136i	$0.157239\pi$
$264$	−2.60090e14	−0.0472822
$265$	1.16827e16	2.07226
$266$	0	0
$267$	−2.68417e15	−0.453406
$268$	−4.97305e14	−0.0819874
$269$	3.47304e15	0.558881	0.279441	−	0.960163i	$-0.409851\pi$
$269$	3.47304e15	0.558881	0.279441	+	0.960163i	$0.409851\pi$
$270$	−6.29911e15	−0.989497
$271$	4.67678e15	0.717210	0.358605	−	0.933489i	$-0.383253\pi$
$271$	4.67678e15	0.717210	0.358605	+	0.933489i	$0.383253\pi$
$272$	1.59862e15	0.239358
$273$	0	0
$274$	2.53386e15	0.361746
$275$	6.95262e15	0.969362
$276$	6.68971e14	0.0910957
$277$	−7.16300e15	−0.952745	−0.476372	−	0.879244i	$-0.658049\pi$
$277$	−7.16300e15	−0.952745	−0.476372	+	0.879244i	$0.658049\pi$
$278$	−5.94578e13	−0.00772534
$279$	5.94834e15	0.755037
$280$	0	0
$281$	−3.65564e15	−0.442968	−0.221484	−	0.975164i	$-0.571090\pi$
$281$	−3.65564e15	−0.442968	−0.221484	+	0.975164i	$0.571090\pi$
$282$	3.94774e15	0.467444
$283$	4.06133e14	0.0469955	0.0234978	−	0.999724i	$-0.492520\pi$
$283$	4.06133e14	0.0469955	0.0234978	+	0.999724i	$0.492520\pi$
$284$	5.15872e15	0.583408
$285$	−6.91437e15	−0.764295
$286$	1.58420e15	0.171171
$287$	0	0
$288$	1.45471e15	0.150219
$289$	−8.25311e14	−0.0833262
$290$	2.14635e16	2.11891
$291$	1.65651e15	0.159915
$292$	5.95276e14	0.0561992
$293$	−1.50550e15	−0.139008	−0.0695041	−	0.997582i	$-0.522142\pi$
$293$	−1.50550e15	−0.139008	−0.0695041	+	0.997582i	$0.522142\pi$
$294$	0	0
$295$	−3.75579e16	−3.31786
$296$	2.55240e15	0.220573
$297$	−2.92602e15	−0.247377
$298$	−1.12450e16	−0.930155
$299$	−4.07469e15	−0.329786
$300$	6.87483e15	0.544470
$301$	0	0
$302$	1.56771e16	1.18910
$303$	−4.61459e15	−0.342575
$304$	3.47590e15	0.252574
$305$	−3.01390e15	−0.214378
$306$	8.26195e15	0.575298
$307$	−1.99255e16	−1.35835	−0.679173	−	0.733978i	$-0.737661\pi$
$307$	−1.99255e16	−1.35835	−0.679173	+	0.733978i	$0.737661\pi$
$308$	0	0
$309$	−9.32415e15	−0.609367
$310$	−1.91618e16	−1.22627
$311$	−4.42021e13	−0.00277013	−0.00138506	−	0.999999i	$-0.500441\pi$
$311$	−4.42021e13	−0.00277013	−0.00138506	+	0.999999i	$0.500441\pi$
$312$	1.56648e15	0.0961433
$313$	4.24997e15	0.255475	0.127737	−	0.991808i	$-0.459229\pi$
$313$	4.24997e15	0.255475	0.127737	+	0.991808i	$0.459229\pi$
$314$	−2.26311e15	−0.133249
$315$	0	0
$316$	1.03739e16	0.586108
$317$	1.10064e16	0.609201	0.304601	−	0.952480i	$-0.401477\pi$
$317$	1.10064e16	0.609201	0.304601	+	0.952480i	$0.401477\pi$
$318$	5.36604e15	0.290990
$319$	9.97006e15	0.529735
$320$	−4.68616e15	−0.243973
$321$	−1.84120e15	−0.0939329
$322$	0	0
$323$	1.97412e16	0.967289
$324$	5.95408e15	0.285938
$325$	−4.18745e16	−1.97110
$326$	4.26393e15	0.196741
$327$	−7.19560e15	−0.325467
$328$	−6.73923e15	−0.298834
$329$	0	0
$330$	4.33012e15	0.184569
$331$	4.23352e16	1.76937	0.884687	−	0.466186i	$-0.154372\pi$
$331$	4.23352e16	1.76937	0.884687	+	0.466186i	$0.154372\pi$
$332$	−8.14092e14	−0.0333638
$333$	1.31912e16	0.530149
$334$	1.97874e16	0.779896
$335$	8.27943e15	0.320043
$336$	0	0
$337$	2.81461e16	1.04670	0.523352	−	0.852117i	$-0.324681\pi$
$337$	2.81461e16	1.04670	0.523352	+	0.852117i	$0.324681\pi$
$338$	9.84262e15	0.359048
$339$	9.37521e15	0.335493
$340$	−2.66147e16	−0.934350
$341$	−8.90089e15	−0.306570
$342$	1.79641e16	0.607064
$343$	0	0
$344$	−5.91109e14	−0.0192326
$345$	−1.11374e16	−0.355599
$346$	−6.66775e14	−0.0208922
$347$	−2.74045e16	−0.842713	−0.421357	−	0.906895i	$-0.638446\pi$
$347$	−2.74045e16	−0.842713	−0.421357	+	0.906895i	$0.638446\pi$
$348$	9.85851e15	0.297540
$349$	−5.20113e16	−1.54075	−0.770375	−	0.637591i	$-0.779931\pi$
$349$	−5.20113e16	−1.54075	−0.770375	+	0.637591i	$0.779931\pi$
$350$	0	0
$351$	1.76229e16	0.503016
$352$	−2.17678e15	−0.0609940
$353$	2.05371e16	0.564942	0.282471	−	0.959276i	$-0.408846\pi$
$353$	2.05371e16	0.564942	0.282471	+	0.959276i	$0.408846\pi$
$354$	−1.72509e16	−0.465899
$355$	−8.58852e16	−2.27737
$356$	−2.24648e16	−0.584894
$357$	0	0
$358$	−2.80844e16	−0.705059
$359$	4.89402e15	0.120657	0.0603285	−	0.998179i	$-0.480785\pi$
$359$	4.89402e15	0.120657	0.0603285	+	0.998179i	$0.480785\pi$
$360$	−2.42189e16	−0.586392
$361$	8.70459e14	0.0206991
$362$	6.92118e14	0.0161650
$363$	−1.48842e16	−0.341454
$364$	0	0
$365$	−9.91050e15	−0.219377
$366$	−1.38433e15	−0.0301032
$367$	1.20744e14	0.00257951	0.00128976	−	0.999999i	$-0.499589\pi$
$367$	1.20744e14	0.00257951	0.00128976	+	0.999999i	$0.499589\pi$
$368$	5.59885e15	0.117514
$369$	−3.48295e16	−0.718250
$370$	−4.24937e16	−0.861021
$371$	0	0
$372$	−8.80129e15	−0.172194
$373$	−1.47457e16	−0.283504	−0.141752	−	0.989902i	$-0.545273\pi$
$373$	−1.47457e16	−0.283504	−0.141752	+	0.989902i	$0.545273\pi$
$374$	−1.23629e16	−0.233590
$375$	−7.37166e16	−1.36887
$376$	3.30400e16	0.603003
$377$	−6.00480e16	−1.07716
$378$	0	0
$379$	2.32876e15	0.0403617	0.0201809	−	0.999796i	$-0.493576\pi$
$379$	2.32876e15	0.0403617	0.0201809	+	0.999796i	$0.493576\pi$
$380$	−5.78688e16	−0.985941
$381$	2.26566e16	0.379475
$382$	−3.82500e16	−0.629824
$383$	−3.73695e16	−0.604958	−0.302479	−	0.953156i	$-0.597814\pi$
$383$	−3.73695e16	−0.604958	−0.302479	+	0.953156i	$0.597814\pi$
$384$	−2.15242e15	−0.0342590
$385$	0	0
$386$	2.91613e16	0.448734
$387$	−3.05495e15	−0.0462257
$388$	1.38639e16	0.206290
$389$	4.80620e15	0.0703282	0.0351641	−	0.999382i	$-0.488805\pi$
$389$	4.80620e15	0.0703282	0.0351641	+	0.999382i	$0.488805\pi$
$390$	−2.60796e16	−0.375302
$391$	3.17983e16	0.450044
$392$	0	0
$393$	1.03612e16	0.141859
$394$	5.43895e16	0.732469
$395$	−1.72711e17	−2.28791
$396$	−1.12500e16	−0.146600
$397$	2.36633e16	0.303345	0.151672	−	0.988431i	$-0.451534\pi$
$397$	2.36633e16	0.303345	0.151672	+	0.988431i	$0.451534\pi$
$398$	9.30462e16	1.17343
$399$	0	0
$400$	5.75378e16	0.702366
$401$	5.28863e16	0.635191	0.317596	−	0.948226i	$-0.397125\pi$
$401$	5.28863e16	0.635191	0.317596	+	0.948226i	$0.397125\pi$
$402$	3.80287e15	0.0449409
$403$	5.36086e16	0.623378
$404$	−3.86211e16	−0.441922
$405$	−9.91269e16	−1.11618
$406$	0	0
$407$	−1.97389e16	−0.215258
$408$	−1.22246e16	−0.131203
$409$	−4.35394e16	−0.459919	−0.229959	−	0.973200i	$-0.573859\pi$
$409$	−4.35394e16	−0.459919	−0.229959	+	0.973200i	$0.573859\pi$
$410$	1.12199e17	1.16652
$411$	−1.93763e16	−0.198289
$412$	−7.80371e16	−0.786084
$413$	0	0
$414$	2.89358e16	0.282445
$415$	1.35535e16	0.130238
$416$	1.31104e16	0.124025
$417$	4.54670e14	0.00423460
$418$	−2.68808e16	−0.246488
$419$	5.69881e16	0.514509	0.257255	−	0.966344i	$-0.417182\pi$
$419$	5.69881e16	0.514509	0.257255	+	0.966344i	$0.417182\pi$
$420$	0	0
$421$	6.97807e16	0.610803	0.305402	−	0.952224i	$-0.401209\pi$
$421$	6.97807e16	0.610803	0.305402	+	0.952224i	$0.401209\pi$
$422$	6.45474e15	0.0556350
$423$	1.70757e17	1.44932
$424$	4.49103e16	0.375377
$425$	3.26783e17	2.68987
$426$	−3.94484e16	−0.319792
$427$	0	0
$428$	−1.54096e16	−0.121173
$429$	−1.21143e16	−0.0938267
$430$	9.84112e15	0.0750757
$431$	−2.52192e17	−1.89509	−0.947545	−	0.319622i	$-0.896444\pi$
$431$	−2.52192e17	−1.89509	−0.947545	+	0.319622i	$0.896444\pi$
$432$	−2.42149e16	−0.179241
$433$	−1.42066e16	−0.103590	−0.0517952	−	0.998658i	$-0.516494\pi$
$433$	−1.42066e16	−0.103590	−0.0517952	+	0.998658i	$0.516494\pi$
$434$	0	0
$435$	−1.64130e17	−1.16147
$436$	−6.02225e16	−0.419852
$437$	6.91395e16	0.474894
$438$	−4.55205e15	−0.0308053
$439$	−5.42647e16	−0.361825	−0.180912	−	0.983499i	$-0.557905\pi$
$439$	−5.42647e16	−0.361825	−0.180912	+	0.983499i	$0.557905\pi$
$440$	3.62403e16	0.238094
$441$	0	0
$442$	7.44597e16	0.474981
$443$	−2.45341e17	−1.54222	−0.771110	−	0.636702i	$-0.780298\pi$
$443$	−2.45341e17	−1.54222	−0.771110	+	0.636702i	$0.780298\pi$
$444$	−1.95180e16	−0.120906
$445$	3.74006e17	2.28317
$446$	5.00557e16	0.301146
$447$	8.59903e16	0.509859
$448$	0	0
$449$	−3.17982e17	−1.83148	−0.915739	−	0.401773i	$-0.868394\pi$
$449$	−3.17982e17	−1.83148	−0.915739	+	0.401773i	$0.868394\pi$
$450$	2.97366e17	1.68814
$451$	5.21177e16	0.291634
$452$	7.84644e16	0.432786
$453$	−1.19882e17	−0.651800
$454$	−1.79502e16	−0.0962066
$455$	0	0
$456$	−2.65800e16	−0.138447
$457$	4.77041e16	0.244963	0.122481	−	0.992471i	$-0.460915\pi$
$457$	4.77041e16	0.244963	0.122481	+	0.992471i	$0.460915\pi$
$458$	1.96797e17	0.996307
$459$	−1.37527e17	−0.686444
$460$	−9.32129e16	−0.458722
$461$	3.80845e17	1.84796	0.923979	−	0.382444i	$-0.124917\pi$
$461$	3.80845e17	1.84796	0.923979	+	0.382444i	$0.124917\pi$
$462$	0	0
$463$	3.17540e17	1.49803	0.749017	−	0.662550i	$-0.230526\pi$
$463$	3.17540e17	1.49803	0.749017	+	0.662550i	$0.230526\pi$
$464$	8.25093e16	0.383827
$465$	1.46529e17	0.672170
$466$	−1.98806e17	−0.899333
$467$	2.70007e17	1.20452	0.602261	−	0.798299i	$-0.294267\pi$
$467$	2.70007e17	1.20452	0.602261	+	0.798299i	$0.294267\pi$
$468$	6.77568e16	0.298095
$469$	0	0
$470$	−5.50069e17	−2.35386
$471$	1.73059e16	0.0730395
$472$	−1.44379e17	−0.601010
$473$	4.57133e15	0.0187692
$474$	−7.93290e16	−0.321272
$475$	7.10527e17	2.83839
$476$	0	0
$477$	2.32104e17	0.902222
$478$	−3.25373e17	−1.24767
$479$	4.00091e16	0.151348	0.0756742	−	0.997133i	$-0.475889\pi$
$479$	4.00091e16	0.151348	0.0756742	+	0.997133i	$0.475889\pi$
$480$	3.58348e16	0.133733
$481$	1.18884e17	0.437704
$482$	1.36814e17	0.496965
$483$	0	0
$484$	−1.24571e17	−0.440476
$485$	−2.30814e17	−0.805269
$486$	−1.92802e17	−0.663706
$487$	1.06218e17	0.360795	0.180398	−	0.983594i	$-0.442262\pi$
$487$	1.06218e17	0.360795	0.180398	+	0.983594i	$0.442262\pi$
$488$	−1.15860e16	−0.0388332
$489$	−3.26060e16	−0.107843
$490$	0	0
$491$	2.75703e16	0.0887998	0.0443999	−	0.999014i	$-0.485862\pi$
$491$	2.75703e16	0.0887998	0.0443999	+	0.999014i	$0.485862\pi$
$492$	5.15345e16	0.163804
$493$	4.68607e17	1.46995
$494$	1.61899e17	0.501208
$495$	1.87296e17	0.572262
$496$	−7.36611e16	−0.222130
$497$	0	0
$498$	6.22532e15	0.0182882
$499$	4.60971e17	1.33666	0.668329	−	0.743866i	$-0.267010\pi$
$499$	4.60971e17	1.33666	0.668329	+	0.743866i	$0.267010\pi$
$500$	−6.16960e17	−1.76584
$501$	−1.51313e17	−0.427495
$502$	8.17907e16	0.228102
$503$	−5.56693e17	−1.53258	−0.766291	−	0.642494i	$-0.777900\pi$
$503$	−5.56693e17	−1.53258	−0.766291	+	0.642494i	$0.777900\pi$
$504$	0	0
$505$	6.42986e17	1.72507
$506$	−4.32986e16	−0.114682
$507$	−7.52660e16	−0.196810
$508$	1.89621e17	0.489523
$509$	4.92984e17	1.25651	0.628257	−	0.778006i	$-0.283768\pi$
$509$	4.92984e17	1.25651	0.628257	+	0.778006i	$0.283768\pi$
$510$	2.03522e17	0.512159
$511$	0	0
$512$	−1.80144e16	−0.0441942
$513$	−2.99026e17	−0.724346
$514$	3.00563e17	0.718910
$515$	1.29921e18	3.06854
$516$	4.52018e15	0.0105422
$517$	−2.55514e17	−0.588473
$518$	0	0
$519$	5.09879e15	0.0114520
$520$	−2.18269e17	−0.484140
$521$	−5.79596e17	−1.26964	−0.634819	−	0.772661i	$-0.718925\pi$
$521$	−5.79596e17	−1.26964	−0.634819	+	0.772661i	$0.718925\pi$
$522$	4.26422e17	0.922533
$523$	−1.24323e17	−0.265638	−0.132819	−	0.991140i	$-0.542403\pi$
$523$	−1.24323e17	−0.265638	−0.132819	+	0.991140i	$0.542403\pi$
$524$	8.67164e16	0.182999
$525$	0	0
$526$	−6.04822e17	−1.24515
$527$	−4.18354e17	−0.850697
$528$	1.66457e16	0.0334335
$529$	−3.92669e17	−0.779049
$530$	−7.47692e17	−1.46531
$531$	−7.46177e17	−1.44453
$532$	0	0
$533$	−3.13896e17	−0.593006
$534$	1.71787e17	0.320606
$535$	2.56548e17	0.473009
$536$	3.18275e16	0.0579738
$537$	2.14760e17	0.386474
$538$	−2.22274e17	−0.395189
$539$	0	0
$540$	4.03143e17	0.699680
$541$	8.19126e16	0.140465	0.0702325	−	0.997531i	$-0.477626\pi$
$541$	8.19126e16	0.140465	0.0702325	+	0.997531i	$0.477626\pi$
$542$	−2.99314e17	−0.507144
$543$	−5.29259e15	−0.00886074
$544$	−1.02312e17	−0.169251
$545$	1.00262e18	1.63892
$546$	0	0
$547$	−3.99955e17	−0.638402	−0.319201	−	0.947687i	$-0.603414\pi$
$547$	−3.99955e17	−0.638402	−0.319201	+	0.947687i	$0.603414\pi$
$548$	−1.62167e17	−0.255793
$549$	−5.98782e16	−0.0933359
$550$	−4.44968e17	−0.685442
$551$	1.01890e18	1.55112
$552$	−4.28141e16	−0.0644144
$553$	0	0
$554$	4.58432e17	0.673692
$555$	3.24948e17	0.471964
$556$	3.80530e15	0.00546264
$557$	−1.04640e18	−1.48470	−0.742352	−	0.670010i	$-0.766290\pi$
$557$	−1.04640e18	−1.48470	−0.742352	+	0.670010i	$0.766290\pi$
$558$	−3.80694e17	−0.533892
$559$	−2.75324e16	−0.0381651
$560$	0	0
$561$	9.45384e16	0.128041
$562$	2.33961e17	0.313226
$563$	6.76618e17	0.895445	0.447722	−	0.894173i	$-0.352235\pi$
$563$	6.76618e17	0.895445	0.447722	+	0.894173i	$0.352235\pi$
$564$	−2.52655e17	−0.330533
$565$	−1.30632e18	−1.68941
$566$	−2.59925e16	−0.0332309
$567$	0	0
$568$	−3.30158e17	−0.412532
$569$	−1.15236e18	−1.42350	−0.711749	−	0.702434i	$-0.752097\pi$
$569$	−1.15236e18	−1.42350	−0.711749	+	0.702434i	$0.752097\pi$
$570$	4.42520e17	0.540438
$571$	−1.39160e18	−1.68027	−0.840137	−	0.542375i	$-0.817525\pi$
$571$	−1.39160e18	−1.68027	−0.840137	+	0.542375i	$0.817525\pi$
$572$	−1.01389e17	−0.121037
$573$	2.92496e17	0.345235
$574$	0	0
$575$	1.14449e18	1.32060
$576$	−9.31016e16	−0.106221
$577$	−1.27932e18	−1.44324	−0.721618	−	0.692291i	$-0.756601\pi$
$577$	−1.27932e18	−1.44324	−0.721618	+	0.692291i	$0.756601\pi$
$578$	5.28199e16	0.0589205
$579$	−2.22995e17	−0.245971
$580$	−1.37366e18	−1.49830
$581$	0	0
$582$	−1.06017e17	−0.113077
$583$	−3.47312e17	−0.366332
$584$	−3.80977e16	−0.0397388
$585$	−1.12805e18	−1.16364
$586$	9.63518e16	0.0982936
$587$	−5.72711e17	−0.577813	−0.288907	−	0.957357i	$-0.593292\pi$
$587$	−5.72711e17	−0.577813	−0.288907	+	0.957357i	$0.593292\pi$
$588$	0	0
$589$	−9.09632e17	−0.897669
$590$	2.40371e18	2.34608
$591$	−4.15914e17	−0.401499
$592$	−1.63353e17	−0.155968
$593$	−1.04895e18	−0.990598	−0.495299	−	0.868723i	$-0.664941\pi$
$593$	−1.04895e18	−0.990598	−0.495299	+	0.868723i	$0.664941\pi$
$594$	1.87265e17	0.174922
$595$	0	0
$596$	7.19683e17	0.657719
$597$	−7.11520e17	−0.643211
$598$	2.60780e17	0.233194
$599$	7.68590e17	0.679861	0.339931	−	0.940450i	$-0.389596\pi$
$599$	7.68590e17	0.679861	0.339931	+	0.940450i	$0.389596\pi$
$600$	−4.39989e17	−0.384998
$601$	−9.28666e16	−0.0803851	−0.0401926	−	0.999192i	$-0.512797\pi$
$601$	−9.28666e16	−0.0803851	−0.0401926	+	0.999192i	$0.512797\pi$
$602$	0	0
$603$	1.64490e17	0.139341
$604$	−1.00333e18	−0.840823
$605$	2.07393e18	1.71943
$606$	2.95334e17	0.242237
$607$	1.57067e18	1.27456	0.637278	−	0.770634i	$-0.280060\pi$
$607$	1.57067e18	1.27456	0.637278	+	0.770634i	$0.280060\pi$
$608$	−2.22458e17	−0.178597
$609$	0	0
$610$	1.92890e17	0.151588
$611$	1.53892e18	1.19660
$612$	−5.28765e17	−0.406797
$613$	1.28930e18	0.981435	0.490718	−	0.871319i	$-0.336735\pi$
$613$	1.28930e18	0.981435	0.490718	+	0.871319i	$0.336735\pi$
$614$	1.27523e18	0.960495
$615$	−8.57976e17	−0.639421
$616$	0	0
$617$	8.41398e17	0.613971	0.306985	−	0.951714i	$-0.400680\pi$
$617$	8.41398e17	0.613971	0.306985	+	0.951714i	$0.400680\pi$
$618$	5.96746e17	0.430888
$619$	−1.17850e18	−0.842055	−0.421028	−	0.907048i	$-0.638330\pi$
$619$	−1.17850e18	−0.842055	−0.421028	+	0.907048i	$0.638330\pi$
$620$	1.22635e18	0.867100
$621$	−4.81660e17	−0.337012
$622$	2.82893e15	0.00195878
$623$	0	0
$624$	−1.00255e17	−0.0679836
$625$	6.08508e18	4.08363
$626$	−2.71998e17	−0.180648
$627$	2.05556e17	0.135111
$628$	1.44839e17	0.0942210
$629$	−9.27755e17	−0.597316
$630$	0	0
$631$	−1.91515e17	−0.120785	−0.0603923	−	0.998175i	$-0.519235\pi$
$631$	−1.91515e17	−0.120785	−0.0603923	+	0.998175i	$0.519235\pi$
$632$	−6.63932e17	−0.414441
$633$	−4.93591e16	−0.0304960
$634$	−7.04411e17	−0.430770
$635$	−3.15693e18	−1.91089
$636$	−3.43426e17	−0.205761
$637$	0	0
$638$	−6.38084e17	−0.374579
$639$	−1.70631e18	−0.991524
$640$	2.99914e17	0.172515
$641$	−1.46353e18	−0.833344	−0.416672	−	0.909057i	$-0.636804\pi$
$641$	−1.46353e18	−0.833344	−0.416672	+	0.909057i	$0.636804\pi$
$642$	1.17837e17	0.0664206
$643$	−1.79993e18	−1.00435	−0.502173	−	0.864767i	$-0.667466\pi$
$643$	−1.79993e18	−1.00435	−0.502173	+	0.864767i	$0.667466\pi$
$644$	0	0
$645$	−7.52545e16	−0.0411523
$646$	−1.26343e18	−0.683977
$647$	2.26478e18	1.21380	0.606902	−	0.794777i	$-0.292412\pi$
$647$	2.26478e18	1.21380	0.606902	+	0.794777i	$0.292412\pi$
$648$	−3.81061e17	−0.202189
$649$	1.11655e18	0.586528
$650$	2.67997e18	1.39377
$651$	0	0
$652$	−2.72891e17	−0.139117
$653$	−1.82611e18	−0.921703	−0.460851	−	0.887477i	$-0.652456\pi$
$653$	−1.82611e18	−0.921703	−0.460851	+	0.887477i	$0.652456\pi$
$654$	4.60518e17	0.230140
$655$	−1.44370e18	−0.714348
$656$	4.31311e17	0.211308
$657$	−1.96895e17	−0.0955126
$658$	0	0
$659$	1.72001e18	0.818044	0.409022	−	0.912525i	$-0.365870\pi$
$659$	1.72001e18	0.818044	0.409022	+	0.912525i	$0.365870\pi$
$660$	−2.77128e17	−0.130510
$661$	1.58382e17	0.0738578	0.0369289	−	0.999318i	$-0.488242\pi$
$661$	1.58382e17	0.0738578	0.0369289	+	0.999318i	$0.488242\pi$
$662$	−2.70945e18	−1.25114
$663$	−5.69390e17	−0.260358
$664$	5.21019e16	0.0235918
$665$	0	0
$666$	−8.44238e17	−0.374872
$667$	1.64120e18	0.721679
$668$	−1.26639e18	−0.551469
$669$	−3.82774e17	−0.165072
$670$	−5.29883e17	−0.226305
$671$	8.95997e16	0.0378975
$672$	0	0
$673$	−2.70067e18	−1.12040	−0.560201	−	0.828356i	$-0.689276\pi$
$673$	−2.70067e18	−1.12040	−0.560201	+	0.828356i	$0.689276\pi$
$674$	−1.80135e18	−0.740132
$675$	−4.94989e18	−2.01429
$676$	−6.29927e17	−0.253885
$677$	−2.43456e18	−0.971838	−0.485919	−	0.874004i	$-0.661515\pi$
$677$	−2.43456e18	−0.971838	−0.485919	+	0.874004i	$0.661515\pi$
$678$	−6.00014e17	−0.237229
$679$	0	0
$680$	1.70334e18	0.660685
$681$	1.37264e17	0.0527351
$682$	5.69657e17	0.216778
$683$	1.47514e17	0.0556032	0.0278016	−	0.999613i	$-0.491149\pi$
$683$	1.47514e17	0.0556032	0.0278016	+	0.999613i	$0.491149\pi$
$684$	−1.14970e18	−0.429259
$685$	2.69985e18	0.998506
$686$	0	0
$687$	−1.50490e18	−0.546120
$688$	3.78310e16	0.0135995
$689$	2.09181e18	0.744898
$690$	7.12794e17	0.251446
$691$	−2.57754e18	−0.900738	−0.450369	−	0.892842i	$-0.648708\pi$
$691$	−2.57754e18	−0.900738	−0.450369	+	0.892842i	$0.648708\pi$
$692$	4.26736e16	0.0147730
$693$	0	0
$694$	1.75389e18	0.595888
$695$	−6.33528e16	−0.0213238
$696$	−6.30944e17	−0.210393
$697$	2.44960e18	0.809250
$698$	3.32872e18	1.08947
$699$	1.52026e18	0.492965
$700$	0	0
$701$	−1.66664e18	−0.530486	−0.265243	−	0.964182i	$-0.585452\pi$
$701$	−1.66664e18	−0.530486	−0.265243	+	0.964182i	$0.585452\pi$
$702$	−1.12787e18	−0.355686
$703$	−2.01723e18	−0.630298
$704$	1.39314e17	0.0431293
$705$	4.20635e18	1.29026
$706$	−1.31438e18	−0.399475
$707$	0	0
$708$	1.10406e18	0.329440
$709$	−5.16125e18	−1.52600	−0.763000	−	0.646398i	$-0.776274\pi$
$709$	−5.16125e18	−1.52600	−0.763000	+	0.646398i	$0.776274\pi$
$710$	5.49666e18	1.61035
$711$	−3.43132e18	−0.996113
$712$	1.43775e18	0.413582
$713$	−1.46520e18	−0.417653
$714$	0	0
$715$	1.68798e18	0.472475
$716$	1.79740e18	0.498552
$717$	2.48811e18	0.683904
$718$	−3.13218e17	−0.0853173
$719$	3.61985e18	0.977131	0.488565	−	0.872527i	$-0.337520\pi$
$719$	3.61985e18	0.977131	0.488565	+	0.872527i	$0.337520\pi$
$720$	1.55001e18	0.414641
$721$	0	0
$722$	−5.57094e16	−0.0146365
$723$	−1.04621e18	−0.272409
$724$	−4.42956e16	−0.0114304
$725$	1.68662e19	4.31340
$726$	9.52588e17	0.241444
$727$	−4.45477e18	−1.11906	−0.559528	−	0.828811i	$-0.689018\pi$
$727$	−4.45477e18	−1.11906	−0.559528	+	0.828811i	$0.689018\pi$
$728$	0	0
$729$	−8.43212e17	−0.208069
$730$	6.34272e17	0.155123
$731$	2.14859e17	0.0520823
$732$	8.85972e16	0.0212862
$733$	−1.49899e18	−0.356964	−0.178482	−	0.983943i	$-0.557119\pi$
$733$	−1.49899e18	−0.356964	−0.178482	+	0.983943i	$0.557119\pi$
$734$	−7.72764e15	−0.00182399
$735$	0	0
$736$	−3.58326e17	−0.0830946
$737$	−2.46138e17	−0.0565769
$738$	2.22909e18	0.507880
$739$	1.99135e18	0.449737	0.224869	−	0.974389i	$-0.427805\pi$
$739$	1.99135e18	0.449737	0.224869	+	0.974389i	$0.427805\pi$
$740$	2.71960e18	0.608834
$741$	−1.23803e18	−0.274734
$742$	0	0
$743$	−3.75670e18	−0.819179	−0.409590	−	0.912270i	$-0.634328\pi$
$743$	−3.75670e18	−0.819179	−0.409590	+	0.912270i	$0.634328\pi$
$744$	5.63283e17	0.121759
$745$	−1.19817e19	−2.56745
$746$	9.43726e17	0.200467
$747$	2.69272e17	0.0567031
$748$	7.91225e17	0.165173
$749$	0	0
$750$	4.71786e18	0.967937
$751$	−9.25720e18	−1.88287	−0.941435	−	0.337196i	$-0.890522\pi$
$751$	−9.25720e18	−1.88287	−0.941435	+	0.337196i	$0.890522\pi$
$752$	−2.11456e18	−0.426387
$753$	−6.25449e17	−0.125033
$754$	3.84307e18	0.761667
$755$	1.67040e19	3.28221
$756$	0	0
$757$	9.65926e17	0.186561	0.0932805	−	0.995640i	$-0.470265\pi$
$757$	9.65926e17	0.186561	0.0932805	+	0.995640i	$0.470265\pi$
$758$	−1.49041e17	−0.0285401
$759$	3.31102e17	0.0628623
$760$	3.70360e18	0.697165
$761$	5.53203e18	1.03249	0.516243	−	0.856442i	$-0.327330\pi$
$761$	5.53203e18	1.03249	0.516243	+	0.856442i	$0.327330\pi$
$762$	−1.45002e18	−0.268329
$763$	0	0
$764$	2.44800e18	0.445353
$765$	8.80318e18	1.58796
$766$	2.39165e18	0.427770
$767$	−6.72482e18	−1.19264
$768$	1.37755e17	0.0242248
$769$	5.13853e18	0.896021	0.448010	−	0.894028i	$-0.352133\pi$
$769$	5.13853e18	0.896021	0.448010	+	0.894028i	$0.352133\pi$
$770$	0	0
$771$	−2.29839e18	−0.394067
$772$	−1.86632e18	−0.317303
$773$	−8.25185e18	−1.39118	−0.695592	−	0.718437i	$-0.744858\pi$
$773$	−8.25185e18	−1.39118	−0.695592	+	0.718437i	$0.744858\pi$
$774$	1.95517e17	0.0326865
$775$	−1.50575e19	−2.49627
$776$	−8.87289e17	−0.145869
$777$	0	0
$778$	−3.07597e17	−0.0497295
$779$	5.32620e18	0.853933
$780$	1.66909e18	0.265379
$781$	2.55327e18	0.402592
$782$	−2.03509e18	−0.318229
$783$	−7.09815e18	−1.10076
$784$	0	0
$785$	−2.41136e18	−0.367798
$786$	−6.63116e17	−0.100310
$787$	9.79973e18	1.47021	0.735103	−	0.677955i	$-0.237134\pi$
$787$	9.79973e18	1.47021	0.735103	+	0.677955i	$0.237134\pi$
$788$	−3.48093e18	−0.517934
$789$	4.62505e18	0.682520
$790$	1.10535e19	1.61780
$791$	0	0
$792$	7.19999e17	0.103662
$793$	−5.39644e17	−0.0770605
$794$	−1.51445e18	−0.214497
$795$	5.71756e18	0.803201
$796$	−5.95496e18	−0.829743
$797$	4.47372e18	0.618287	0.309143	−	0.951015i	$-0.399958\pi$
$797$	4.47372e18	0.618287	0.309143	+	0.951015i	$0.399958\pi$
$798$	0	0
$799$	−1.20095e19	−1.63295
$800$	−3.68242e18	−0.496648
$801$	7.43052e18	0.994049
$802$	−3.38472e18	−0.449148
$803$	2.94627e17	0.0387813
$804$	−2.43384e17	−0.0317780
$805$	0	0
$806$	−3.43095e18	−0.440795
$807$	1.69972e18	0.216620
$808$	2.47175e18	0.312486
$809$	−4.55457e17	−0.0571192	−0.0285596	−	0.999592i	$-0.509092\pi$
$809$	−4.55457e17	−0.0571192	−0.0285596	+	0.999592i	$0.509092\pi$
$810$	6.34412e18	0.789258
$811$	−2.22500e17	−0.0274596	−0.0137298	−	0.999906i	$-0.504370\pi$
$811$	−2.22500e17	−0.0274596	−0.0137298	+	0.999906i	$0.504370\pi$
$812$	0	0
$813$	2.28884e18	0.277988
$814$	1.26329e18	0.152210
$815$	4.54325e18	0.543053
$816$	7.82372e17	0.0927742
$817$	4.67170e17	0.0549581
$818$	2.78652e18	0.325212
$819$	0	0
$820$	−7.18071e18	−0.824854
$821$	−7.94825e18	−0.905818	−0.452909	−	0.891557i	$-0.649614\pi$
$821$	−7.94825e18	−0.905818	−0.452909	+	0.891557i	$0.649614\pi$
$822$	1.24008e18	0.140212
$823$	−1.39010e19	−1.55936	−0.779682	−	0.626175i	$-0.784619\pi$
$823$	−1.39010e19	−1.55936	−0.779682	+	0.626175i	$0.784619\pi$
$824$	4.99437e18	0.555846
$825$	3.40264e18	0.375721
$826$	0	0
$827$	−9.22759e18	−1.00300	−0.501502	−	0.865157i	$-0.667219\pi$
$827$	−9.22759e18	−1.00300	−0.501502	+	0.865157i	$0.667219\pi$
$828$	−1.85189e18	−0.199719
$829$	1.55663e19	1.66564	0.832821	−	0.553542i	$-0.186724\pi$
$829$	1.55663e19	1.66564	0.832821	+	0.553542i	$0.186724\pi$
$830$	−8.67422e17	−0.0920922
$831$	−3.50561e18	−0.369281
$832$	−8.39065e17	−0.0876989
$833$	0	0
$834$	−2.90989e16	−0.00299431
$835$	2.10836e19	2.15270
$836$	1.72037e18	0.174294
$837$	6.33695e18	0.637037
$838$	−3.64724e18	−0.363813
$839$	−1.58146e19	−1.56532	−0.782662	−	0.622447i	$-0.786139\pi$
$839$	−1.58146e19	−1.56532	−0.782662	+	0.622447i	$0.786139\pi$
$840$	0	0
$841$	1.39255e19	1.35718
$842$	−4.46596e18	−0.431903
$843$	−1.78909e18	−0.171693
$844$	−4.13103e17	−0.0393399
$845$	1.04874e19	0.991058
$846$	−1.09284e19	−1.02483
$847$	0	0
$848$	−2.87426e18	−0.265431
$849$	1.98764e17	0.0182153
$850$	−2.09141e19	−1.90202
$851$	−3.24928e18	−0.293255
$852$	2.52470e18	0.226127
$853$	−5.27149e18	−0.468560	−0.234280	−	0.972169i	$-0.575273\pi$
$853$	−5.27149e18	−0.468560	−0.234280	+	0.972169i	$0.575273\pi$
$854$	0	0
$855$	1.91409e19	1.67564
$856$	9.86216e17	0.0856826
$857$	−3.12438e18	−0.269395	−0.134697	−	0.990887i	$-0.543006\pi$
$857$	−3.12438e18	−0.269395	−0.134697	+	0.990887i	$0.543006\pi$
$858$	7.75316e17	0.0663455
$859$	−3.96920e18	−0.337091	−0.168546	−	0.985694i	$-0.553907\pi$
$859$	−3.96920e18	−0.337091	−0.168546	+	0.985694i	$0.553907\pi$
$860$	−6.29832e17	−0.0530866
$861$	0	0
$862$	1.61403e19	1.34003
$863$	−2.58283e18	−0.212826	−0.106413	−	0.994322i	$-0.533937\pi$
$863$	−2.58283e18	−0.212826	−0.106413	+	0.994322i	$0.533937\pi$
$864$	1.54975e18	0.126743
$865$	−7.10454e17	−0.0576676
$866$	9.09224e17	0.0732495
$867$	−4.03911e17	−0.0322970
$868$	0	0
$869$	5.13450e18	0.404455
$870$	1.05043e19	0.821283
$871$	1.48245e18	0.115043
$872$	3.85424e18	0.296880
$873$	−4.58567e18	−0.350598
$874$	−4.42493e18	−0.335801
$875$	0	0
$876$	2.91331e17	0.0217826
$877$	−1.30589e19	−0.969191	−0.484595	−	0.874738i	$-0.661033\pi$
$877$	−1.30589e19	−0.969191	−0.484595	+	0.874738i	$0.661033\pi$
$878$	3.47294e18	0.255849
$879$	−7.36798e17	−0.0538791
$880$	−2.31938e18	−0.168358
$881$	1.15631e19	0.833164	0.416582	−	0.909098i	$-0.363228\pi$
$881$	1.15631e19	0.833164	0.416582	+	0.909098i	$0.363228\pi$
$882$	0	0
$883$	2.08991e19	1.48383	0.741914	−	0.670495i	$-0.233918\pi$
$883$	2.08991e19	1.48383	0.741914	+	0.670495i	$0.233918\pi$
$884$	−4.76542e18	−0.335862
$885$	−1.83810e19	−1.28599
$886$	1.57018e19	1.09051
$887$	5.90131e18	0.406860	0.203430	−	0.979089i	$-0.434791\pi$
$887$	5.90131e18	0.406860	0.203430	+	0.979089i	$0.434791\pi$
$888$	1.24915e18	0.0854933
$889$	0	0
$890$	−2.39364e19	−1.61445
$891$	2.94693e18	0.197317
$892$	−3.20357e18	−0.212942
$893$	−2.61125e19	−1.72311
$894$	−5.50338e18	−0.360525
$895$	−2.99242e19	−1.94613
$896$	0	0
$897$	−1.99417e18	−0.127824
$898$	2.03509e19	1.29505
$899$	−2.15924e19	−1.36415
$900$	−1.90314e19	−1.19370
$901$	−1.63242e19	−1.01653
$902$	−3.33553e18	−0.206216
$903$	0	0
$904$	−5.02172e18	−0.306026
$905$	7.37458e17	0.0446192
$906$	7.67243e18	0.460892
$907$	6.15456e18	0.367070	0.183535	−	0.983013i	$-0.441246\pi$
$907$	6.15456e18	0.367070	0.183535	+	0.983013i	$0.441246\pi$
$908$	1.14881e18	0.0680284
$909$	1.27744e19	0.751064
$910$	0	0
$911$	−6.88604e18	−0.399117	−0.199558	−	0.979886i	$-0.563951\pi$
$911$	−6.88604e18	−0.399117	−0.199558	+	0.979886i	$0.563951\pi$
$912$	1.70112e18	0.0978969
$913$	−4.02929e17	−0.0230233
$914$	−3.05306e18	−0.173215
$915$	−1.47502e18	−0.0830921
$916$	−1.25950e19	−0.704496
$917$	0	0
$918$	8.80172e18	0.485389
$919$	−2.18107e19	−1.19431	−0.597157	−	0.802124i	$-0.703703\pi$
$919$	−2.18107e19	−1.19431	−0.597157	+	0.802124i	$0.703703\pi$
$920$	5.96562e18	0.324366
$921$	−9.75165e18	−0.526490
$922$	−2.43741e19	−1.30670
$923$	−1.53779e19	−0.818628
$924$	0	0
$925$	−3.33919e19	−1.75275
$926$	−2.03226e19	−1.05927
$927$	2.58118e19	1.33598
$928$	−5.28059e18	−0.271407
$929$	−8.25018e18	−0.421077	−0.210538	−	0.977586i	$-0.567522\pi$
$929$	−8.25018e18	−0.421077	−0.210538	+	0.977586i	$0.567522\pi$
$930$	−9.37786e18	−0.475296
$931$	0	0
$932$	1.27236e19	0.635925
$933$	−2.16327e16	−0.00107369
$934$	−1.72804e19	−0.851726
$935$	−1.31728e19	−0.644765
$936$	−4.33644e18	−0.210785
$937$	−2.57007e19	−1.24061	−0.620307	−	0.784359i	$-0.712992\pi$
$937$	−2.57007e19	−1.24061	−0.620307	+	0.784359i	$0.712992\pi$
$938$	0	0
$939$	2.07996e18	0.0990212
$940$	3.52044e19	1.66443
$941$	1.56024e19	0.732586	0.366293	−	0.930500i	$-0.380627\pi$
$941$	1.56024e19	0.732586	0.366293	+	0.930500i	$0.380627\pi$
$942$	−1.10758e18	−0.0516467
$943$	8.57925e18	0.397304
$944$	9.24027e18	0.424978
$945$	0	0
$946$	−2.92565e17	−0.0132718
$947$	2.49878e19	1.12578	0.562889	−	0.826533i	$-0.309690\pi$
$947$	2.49878e19	1.12578	0.562889	+	0.826533i	$0.309690\pi$
$948$	5.07706e18	0.227174
$949$	−1.77449e18	−0.0788577
$950$	−4.54738e19	−2.00705
$951$	5.38659e18	0.236124
$952$	0	0
$953$	8.45730e18	0.365702	0.182851	−	0.983141i	$-0.441467\pi$
$953$	8.45730e18	0.365702	0.182851	+	0.983141i	$0.441467\pi$
$954$	−1.48547e19	−0.637967
$955$	−4.07557e19	−1.73847
$956$	2.08239e19	0.882237
$957$	4.87939e18	0.205323
$958$	−2.56058e18	−0.107020
$959$	0	0
$960$	−2.29343e18	−0.0945632
$961$	−5.14066e18	−0.210532
$962$	−7.60859e18	−0.309504
$963$	5.09694e18	0.205939
$964$	−8.75612e18	−0.351407
$965$	3.10716e19	1.23861
$966$	0	0
$967$	8.33453e18	0.327800	0.163900	−	0.986477i	$-0.447593\pi$
$967$	8.33453e18	0.327800	0.163900	+	0.986477i	$0.447593\pi$
$968$	7.97254e18	0.311463
$969$	9.66142e18	0.374918
$970$	1.47721e19	0.569411
$971$	7.32843e18	0.280599	0.140299	−	0.990109i	$-0.455193\pi$
$971$	7.32843e18	0.280599	0.140299	+	0.990109i	$0.455193\pi$
$972$	1.23393e19	0.469311
$973$	0	0
$974$	−6.79797e18	−0.255121
$975$	−2.04936e19	−0.763990
$976$	7.41501e17	0.0274592
$977$	9.91268e18	0.364650	0.182325	−	0.983238i	$-0.441638\pi$
$977$	9.91268e18	0.364650	0.182325	+	0.983238i	$0.441638\pi$
$978$	2.08679e18	0.0762563
$979$	−1.11188e19	−0.403617
$980$	0	0
$981$	1.99194e19	0.713555
$982$	−1.76450e18	−0.0627909
$983$	−2.72015e19	−0.961601	−0.480800	−	0.876830i	$-0.659654\pi$
$983$	−2.72015e19	−0.961601	−0.480800	+	0.876830i	$0.659654\pi$
$984$	−3.29821e18	−0.115827
$985$	5.79525e19	2.02179
$986$	−2.99908e19	−1.03941
$987$	0	0
$988$	−1.03615e19	−0.354408
$989$	7.52500e17	0.0255700
$990$	−1.19870e19	−0.404651
$991$	−1.12757e19	−0.378150	−0.189075	−	0.981963i	$-0.560549\pi$
$991$	−1.12757e19	−0.378150	−0.189075	+	0.981963i	$0.560549\pi$
$992$	4.71431e18	0.157070
$993$	2.07190e19	0.685803
$994$	0	0
$995$	9.91415e19	3.23896
$996$	−3.98420e17	−0.0129317
$997$	3.35653e19	1.08236	0.541180	−	0.840907i	$-0.317978\pi$
$997$	3.35653e19	1.08236	0.541180	+	0.840907i	$0.317978\pi$
$998$	−2.95022e19	−0.945160
$999$	1.40530e19	0.447295

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.14.a.h.1.3		4
7.2	even	3		14.14.c.b.11.2	yes	8
7.3	odd	6		98.14.c.o.79.3		8
7.4	even	3		14.14.c.b.9.2	✓	8
7.5	odd	6		98.14.c.o.67.3		8
7.6	odd	2		98.14.a.j.1.2		4
21.2	odd	6		126.14.g.b.109.1		8
21.11	odd	6		126.14.g.b.37.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.14.c.b.9.2	✓	8	7.4	even	3
14.14.c.b.11.2	yes	8	7.2	even	3
98.14.a.h.1.3		4	1.1	even	1	trivial
98.14.a.j.1.2		4	7.6	odd	2
98.14.c.o.67.3		8	7.5	odd	6
98.14.c.o.79.3		8	7.3	odd	6
126.14.g.b.37.1		8	21.11	odd	6
126.14.g.b.109.1		8	21.2	odd	6

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	98.a (trivial)

\(f(q)\)	\(=\)	\(q-64.0000 q^{2} +489.405 q^{3} +4096.00 q^{4} -68192.6 q^{5} -31321.9 q^{6} -262144. q^{8} -1.35481e6 q^{9} +O(q^{10})\)	\(q-64.0000 q^{2} +489.405 q^{3} +4096.00 q^{4} -68192.6 q^{5} -31321.9 q^{6} -262144. q^{8} -1.35481e6 q^{9} +4.36432e6 q^{10} +2.02729e6 q^{11} +2.00460e6 q^{12} -1.22100e7 q^{13} -3.33738e7 q^{15} +1.67772e7 q^{16} +9.52852e7 q^{17} +8.67076e7 q^{18} +2.07180e8 q^{19} -2.79317e8 q^{20} -1.29746e8 q^{22} +3.33717e8 q^{23} -1.28295e8 q^{24} +3.42952e9 q^{25} +7.81440e8 q^{26} -1.44332e9 q^{27} +4.91794e9 q^{29} +2.13592e9 q^{30} -4.39054e9 q^{31} -1.07374e9 q^{32} +9.92163e8 q^{33} -6.09825e9 q^{34} -5.54929e9 q^{36} -9.73662e9 q^{37} -1.32595e10 q^{38} -5.97564e9 q^{39} +1.78763e10 q^{40} +2.57081e10 q^{41} +2.25490e9 q^{43} +8.30376e9 q^{44} +9.23877e10 q^{45} -2.13579e10 q^{46} -1.26038e11 q^{47} +8.21085e9 q^{48} -2.19489e11 q^{50} +4.66330e10 q^{51} -5.00122e10 q^{52} -1.71319e11 q^{53} +9.23723e10 q^{54} -1.38246e11 q^{55} +1.01395e11 q^{57} -3.14748e11 q^{58} +5.50763e11 q^{59} -1.36699e11 q^{60} +4.41969e10 q^{61} +2.80995e11 q^{62} +6.87195e10 q^{64} +8.32632e11 q^{65} -6.34984e10 q^{66} -1.21412e11 q^{67} +3.90288e11 q^{68} +1.63323e11 q^{69} +1.25945e12 q^{71} +3.55154e11 q^{72} +1.45331e11 q^{73} +6.23143e11 q^{74} +1.67842e12 q^{75} +8.48608e11 q^{76} +3.82441e11 q^{78} +2.53270e12 q^{79} -1.14408e12 q^{80} +1.45363e12 q^{81} -1.64532e12 q^{82} -1.98753e11 q^{83} -6.49774e12 q^{85} -1.44314e11 q^{86} +2.40686e12 q^{87} -5.31441e11 q^{88} -5.48456e12 q^{89} -5.91281e12 q^{90} +1.36691e12 q^{92} -2.14875e12 q^{93} +8.06641e12 q^{94} -1.41281e13 q^{95} -5.25494e11 q^{96} +3.38474e12 q^{97} -2.74658e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 256 q^{2} - 182 q^{3} + 16384 q^{4} - 1792 q^{5} + 11648 q^{6} - 1048576 q^{8} - 599840 q^{9}+O(q^{10}) \) 4 * q - 256 * q^2 - 182 * q^3 + 16384 * q^4 - 1792 * q^5 + 11648 * q^6 - 1048576 * q^8 - 599840 * q^9	\( 4 q - 256 q^{2} - 182 q^{3} + 16384 q^{4} - 1792 q^{5} + 11648 q^{6} - 1048576 q^{8} - 599840 q^{9} + 114688 q^{10} + 8726914 q^{11} - 745472 q^{12} + 719208 q^{13} - 68436606 q^{15} + 67108864 q^{16} + 7943068 q^{17} + 38389760 q^{18} + 215706806 q^{19} - 7340032 q^{20} - 558522496 q^{22} + 61927978 q^{23} + 47710208 q^{24} + 1327844792 q^{25} - 46029312 q^{26} - 1634321906 q^{27} - 3162923032 q^{29} + 4379942784 q^{30} - 6113775570 q^{31} - 4294967296 q^{32} - 25235960652 q^{33} - 508356352 q^{34} - 2456944640 q^{36} + 3945652880 q^{37} - 13805235584 q^{38} + 23545599116 q^{39} + 469762048 q^{40} + 43189289976 q^{41} - 54537062128 q^{43} + 35745439744 q^{44} + 104964468168 q^{45} - 3963390592 q^{46} + 3141202722 q^{47} - 3053453312 q^{48} - 84982066688 q^{50} + 241278267462 q^{51} + 2945875968 q^{52} - 149625680376 q^{53} + 104596601984 q^{54} + 87456004874 q^{55} - 64103744980 q^{57} + 202427074048 q^{58} + 866297313938 q^{59} - 280316338176 q^{60} + 477908594184 q^{61} + 391281636480 q^{62} + 274877906944 q^{64} + 1099748343120 q^{65} + 1615101481728 q^{66} - 1895501016278 q^{67} + 32534806528 q^{68} + 1751650947816 q^{69} + 319416336064 q^{71} + 157244456960 q^{72} + 2966596192756 q^{73} - 252521784320 q^{74} + 1331079867376 q^{75} + 883535077376 q^{76} - 1506918343424 q^{78} + 6505959677634 q^{79} - 30064771072 q^{80} - 2449216493684 q^{81} - 2764114558464 q^{82} - 1689908567984 q^{83} - 8342278491232 q^{85} + 3490371976192 q^{86} + 5273311164492 q^{87} - 2287708143616 q^{88} - 9586601667468 q^{89} - 6717725962752 q^{90} + 253656997888 q^{92} + 14195747226896 q^{93} - 201036974208 q^{94} - 14384410136978 q^{95} + 195421011968 q^{96} - 22280367655784 q^{97} + 12353209992732 q^{99}+O(q^{100}) \) 4 * q - 256 * q^2 - 182 * q^3 + 16384 * q^4 - 1792 * q^5 + 11648 * q^6 - 1048576 * q^8 - 599840 * q^9 + 114688 * q^10 + 8726914 * q^11 - 745472 * q^12 + 719208 * q^13 - 68436606 * q^15 + 67108864 * q^16 + 7943068 * q^17 + 38389760 * q^18 + 215706806 * q^19 - 7340032 * q^20 - 558522496 * q^22 + 61927978 * q^23 + 47710208 * q^24 + 1327844792 * q^25 - 46029312 * q^26 - 1634321906 * q^27 - 3162923032 * q^29 + 4379942784 * q^30 - 6113775570 * q^31 - 4294967296 * q^32 - 25235960652 * q^33 - 508356352 * q^34 - 2456944640 * q^36 + 3945652880 * q^37 - 13805235584 * q^38 + 23545599116 * q^39 + 469762048 * q^40 + 43189289976 * q^41 - 54537062128 * q^43 + 35745439744 * q^44 + 104964468168 * q^45 - 3963390592 * q^46 + 3141202722 * q^47 - 3053453312 * q^48 - 84982066688 * q^50 + 241278267462 * q^51 + 2945875968 * q^52 - 149625680376 * q^53 + 104596601984 * q^54 + 87456004874 * q^55 - 64103744980 * q^57 + 202427074048 * q^58 + 866297313938 * q^59 - 280316338176 * q^60 + 477908594184 * q^61 + 391281636480 * q^62 + 274877906944 * q^64 + 1099748343120 * q^65 + 1615101481728 * q^66 - 1895501016278 * q^67 + 32534806528 * q^68 + 1751650947816 * q^69 + 319416336064 * q^71 + 157244456960 * q^72 + 2966596192756 * q^73 - 252521784320 * q^74 + 1331079867376 * q^75 + 883535077376 * q^76 - 1506918343424 * q^78 + 6505959677634 * q^79 - 30064771072 * q^80 - 2449216493684 * q^81 - 2764114558464 * q^82 - 1689908567984 * q^83 - 8342278491232 * q^85 + 3490371976192 * q^86 + 5273311164492 * q^87 - 2287708143616 * q^88 - 9586601667468 * q^89 - 6717725962752 * q^90 + 253656997888 * q^92 + 14195747226896 * q^93 - 201036974208 * q^94 - 14384410136978 * q^95 + 195421011968 * q^96 - 22280367655784 * q^97 + 12353209992732 * q^99

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