LMFDB - Embedded newform 98.14.a.h.1.2

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			1.2
Root			$-338.799$ 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)

$f(q)$	$=$	$q-64.0000 q^{2} -388.685 q^{3} +4096.00 q^{4} +25902.2 q^{5} +24875.9 q^{6} -262144. q^{8} -1.44325e6 q^{9} +O(q^{10})$	\(q-64.0000 q^{2} -388.685 q^{3} +4096.00 q^{4} +25902.2 q^{5} +24875.9 q^{6} -262144. q^{8} -1.44325e6 q^{9} -1.65774e6 q^{10} -225373. q^{11} -1.59206e6 q^{12} +2.48426e7 q^{13} -1.00678e7 q^{15} +1.67772e7 q^{16} +1.22031e8 q^{17} +9.23678e7 q^{18} -2.14436e8 q^{19} +1.06095e8 q^{20} +1.44239e7 q^{22} -9.81746e8 q^{23} +1.01892e8 q^{24} -5.49779e8 q^{25} -1.58993e9 q^{26} +1.18066e9 q^{27} -2.47347e9 q^{29} +6.44340e8 q^{30} -4.88268e9 q^{31} -1.07374e9 q^{32} +8.75991e7 q^{33} -7.81000e9 q^{34} -5.91154e9 q^{36} +2.70103e10 q^{37} +1.37239e10 q^{38} -9.65596e9 q^{39} -6.79011e9 q^{40} +3.27287e10 q^{41} -5.78165e9 q^{43} -9.23127e8 q^{44} -3.73833e10 q^{45} +6.28318e10 q^{46} +1.51698e10 q^{47} -6.52106e9 q^{48} +3.51858e10 q^{50} -4.74318e10 q^{51} +1.01755e11 q^{52} +3.93259e10 q^{53} -7.55622e10 q^{54} -5.83765e9 q^{55} +8.33481e10 q^{57} +1.58302e11 q^{58} +1.44494e11 q^{59} -4.12377e10 q^{60} +1.57762e11 q^{61} +3.12491e11 q^{62} +6.87195e10 q^{64} +6.43479e11 q^{65} -5.60634e9 q^{66} -7.67214e11 q^{67} +4.99840e11 q^{68} +3.81590e11 q^{69} -1.73373e12 q^{71} +3.78338e11 q^{72} +1.58901e12 q^{73} -1.72866e12 q^{74} +2.13691e11 q^{75} -8.78329e11 q^{76} +6.17982e11 q^{78} -2.86316e11 q^{79} +4.34567e11 q^{80} +1.84210e12 q^{81} -2.09463e12 q^{82} -9.41428e10 q^{83} +3.16088e12 q^{85} +3.70025e11 q^{86} +9.61403e11 q^{87} +5.90801e10 q^{88} -3.95020e12 q^{89} +2.39253e12 q^{90} -4.02123e12 q^{92} +1.89783e12 q^{93} -9.70868e11 q^{94} -5.55436e12 q^{95} +4.17348e11 q^{96} -1.04397e13 q^{97} +3.25268e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−388.685	−0.307829	−0.153915	−	0.988084i	$-0.549188\pi$
$3$	−388.685	−0.307829	−0.153915	+	0.988084i	$0.549188\pi$
$4$	4096.00	0.500000
$5$	25902.2	0.741364	0.370682	−	0.928760i	$-0.379124\pi$
$5$	25902.2	0.741364	0.370682	+	0.928760i	$0.379124\pi$
$6$	24875.9	0.217668
$7$	0	0
$7$	0	0
$8$	−262144.	−0.353553
$9$	−1.44325e6	−0.905241
$10$	−1.65774e6	−0.524224
$11$	−225373.	−0.0383574	−0.0191787	−	0.999816i	$-0.506105\pi$
$11$	−225373.	−0.0383574	−0.0191787	+	0.999816i	$0.506105\pi$
$12$	−1.59206e6	−0.153915
$13$	2.48426e7	1.42747	0.713733	−	0.700418i	$-0.247003\pi$
$13$	2.48426e7	1.42747	0.713733	+	0.700418i	$0.247003\pi$
$14$	0	0
$15$	−1.00678e7	−0.228214
$16$	1.67772e7	0.250000
$17$	1.22031e8	1.22618	0.613088	−	0.790014i	$-0.289927\pi$
$17$	1.22031e8	1.22618	0.613088	+	0.790014i	$0.289927\pi$
$18$	9.23678e7	0.640102
$19$	−2.14436e8	−1.04568	−0.522840	−	0.852431i	$-0.675128\pi$
$19$	−2.14436e8	−1.04568	−0.522840	+	0.852431i	$0.675128\pi$
$20$	1.06095e8	0.370682
$21$	0	0
$22$	1.44239e7	0.0271228
$23$	−9.81746e8	−1.38283	−0.691414	−	0.722459i	$-0.743012\pi$
$23$	−9.81746e8	−1.38283	−0.691414	+	0.722459i	$0.743012\pi$
$24$	1.01892e8	0.108834
$25$	−5.49779e8	−0.450379
$26$	−1.58993e9	−1.00937
$27$	1.18066e9	0.586489
$28$	0	0
$29$	−2.47347e9	−0.772183	−0.386092	−	0.922460i	$-0.626175\pi$
$29$	−2.47347e9	−0.772183	−0.386092	+	0.922460i	$0.626175\pi$
$30$	6.44340e8	0.161371
$31$	−4.88268e9	−0.988114	−0.494057	−	0.869429i	$-0.664487\pi$
$31$	−4.88268e9	−0.988114	−0.494057	+	0.869429i	$0.664487\pi$
$32$	−1.07374e9	−0.176777
$33$	8.75991e7	0.0118075
$34$	−7.81000e9	−0.867038
$35$	0	0
$36$	−5.91154e9	−0.452621
$37$	2.70103e10	1.73069	0.865343	−	0.501180i	$-0.167100\pi$
$37$	2.70103e10	1.73069	0.865343	+	0.501180i	$0.167100\pi$
$38$	1.37239e10	0.739408
$39$	−9.65596e9	−0.439416
$40$	−6.79011e9	−0.262112
$41$	3.27287e10	1.07605	0.538026	−	0.842928i	$-0.319170\pi$
$41$	3.27287e10	1.07605	0.538026	+	0.842928i	$0.319170\pi$
$42$	0	0
$43$	−5.78165e9	−0.139478	−0.0697392	−	0.997565i	$-0.522217\pi$
$43$	−5.78165e9	−0.139478	−0.0697392	+	0.997565i	$0.522217\pi$
$44$	−9.23127e8	−0.0191787
$45$	−3.73833e10	−0.671113
$46$	6.28318e10	0.977807
$47$	1.51698e10	0.205279	0.102639	−	0.994719i	$-0.467271\pi$
$47$	1.51698e10	0.205279	0.102639	+	0.994719i	$0.467271\pi$
$48$	−6.52106e9	−0.0769573
$49$	0	0
$50$	3.51858e10	0.318466
$51$	−4.74318e10	−0.377453
$52$	1.01755e11	0.713733
$53$	3.93259e10	0.243717	0.121858	−	0.992548i	$-0.461115\pi$
$53$	3.93259e10	0.243717	0.121858	+	0.992548i	$0.461115\pi$
$54$	−7.55622e10	−0.414710
$55$	−5.83765e9	−0.0284368
$56$	0	0
$57$	8.33481e10	0.321891
$58$	1.58302e11	0.546016
$59$	1.44494e11	0.445977	0.222989	−	0.974821i	$-0.428419\pi$
$59$	1.44494e11	0.445977	0.222989	+	0.974821i	$0.428419\pi$
$60$	−4.12377e10	−0.114107
$61$	1.57762e11	0.392066	0.196033	−	0.980597i	$-0.437194\pi$
$61$	1.57762e11	0.392066	0.196033	+	0.980597i	$0.437194\pi$
$62$	3.12491e11	0.698702
$63$	0	0
$64$	6.87195e10	0.125000
$65$	6.43479e11	1.05827
$66$	−5.60634e9	−0.00834918
$67$	−7.67214e11	−1.03617	−0.518084	−	0.855330i	$-0.673355\pi$
$67$	−7.67214e11	−1.03617	−0.518084	+	0.855330i	$0.673355\pi$
$68$	4.99840e11	0.613088
$69$	3.81590e11	0.425675
$70$	0	0
$71$	−1.73373e12	−1.60621	−0.803106	−	0.595836i	$-0.796821\pi$
$71$	−1.73373e12	−1.60621	−0.803106	+	0.595836i	$0.796821\pi$
$72$	3.78338e11	0.320051
$73$	1.58901e12	1.22893	0.614464	−	0.788944i	$-0.289372\pi$
$73$	1.58901e12	1.22893	0.614464	+	0.788944i	$0.289372\pi$
$74$	−1.72866e12	−1.22378
$75$	2.13691e11	0.138640
$76$	−8.78329e11	−0.522840
$77$	0	0
$78$	6.17982e11	0.310714
$79$	−2.86316e11	−0.132516	−0.0662581	−	0.997803i	$-0.521106\pi$
$79$	−2.86316e11	−0.132516	−0.0662581	+	0.997803i	$0.521106\pi$
$80$	4.34567e11	0.185341
$81$	1.84210e12	0.724702
$82$	−2.09463e12	−0.760884
$83$	−9.41428e10	−0.0316067	−0.0158034	−	0.999875i	$-0.505031\pi$
$83$	−9.41428e10	−0.0316067	−0.0158034	+	0.999875i	$0.505031\pi$
$84$	0	0
$85$	3.16088e12	0.909044
$86$	3.70025e11	0.0986261
$87$	9.61403e11	0.237701
$88$	5.90801e10	0.0135614
$89$	−3.95020e12	−0.842526	−0.421263	−	0.906938i	$-0.638413\pi$
$89$	−3.95020e12	−0.842526	−0.421263	+	0.906938i	$0.638413\pi$
$90$	2.39253e12	0.474549
$91$	0	0
$92$	−4.02123e12	−0.691414
$93$	1.89783e12	0.304171
$94$	−9.70868e11	−0.145154
$95$	−5.55436e12	−0.775230
$96$	4.17348e11	0.0544171
$97$	−1.04397e13	−1.27255	−0.636273	−	0.771464i	$-0.719525\pi$
$97$	−1.04397e13	−1.27255	−0.636273	+	0.771464i	$0.719525\pi$
$98$	0	0
$99$	3.25268e11	0.0347227
$100$	−2.25189e12	−0.225189
$101$	−5.54009e12	−0.519312	−0.259656	−	0.965701i	$-0.583609\pi$
$101$	−5.54009e12	−0.519312	−0.259656	+	0.965701i	$0.583609\pi$
$102$	3.03563e12	0.266900
$103$	7.84001e12	0.646956	0.323478	−	0.946236i	$-0.395148\pi$
$103$	7.84001e12	0.646956	0.323478	+	0.946236i	$0.395148\pi$
$104$	−6.51234e12	−0.504685
$105$	0	0
$106$	−2.51685e12	−0.172334
$107$	2.46028e13	1.58486	0.792428	−	0.609965i	$-0.208816\pi$
$107$	2.46028e13	1.58486	0.792428	+	0.609965i	$0.208816\pi$
$108$	4.83598e12	0.293245
$109$	−1.47603e13	−0.842989	−0.421494	−	0.906831i	$-0.638494\pi$
$109$	−1.47603e13	−0.842989	−0.421494	+	0.906831i	$0.638494\pi$
$110$	3.73610e11	0.0201079
$111$	−1.04985e13	−0.532756
$112$	0	0
$113$	2.71313e13	1.22592	0.612958	−	0.790116i	$-0.289980\pi$
$113$	2.71313e13	1.22592	0.612958	+	0.790116i	$0.289980\pi$
$114$	−5.33428e12	−0.227611
$115$	−2.54294e13	−1.02518
$116$	−1.01314e13	−0.386092
$117$	−3.58540e13	−1.29220
$118$	−9.24763e12	−0.315353
$119$	0	0
$120$	2.63922e12	0.0806857
$121$	−3.44719e13	−0.998529
$122$	−1.00968e13	−0.277233
$123$	−1.27212e13	−0.331240
$124$	−1.99995e13	−0.494057
$125$	−4.58594e13	−1.07526
$126$	0	0
$127$	1.57018e13	0.332066	0.166033	−	0.986120i	$-0.446904\pi$
$127$	1.57018e13	0.332066	0.166033	+	0.986120i	$0.446904\pi$
$128$	−4.39805e12	−0.0883883
$129$	2.24724e12	0.0429355
$130$	−4.11826e13	−0.748311
$131$	−5.21046e13	−0.900768	−0.450384	−	0.892835i	$-0.648713\pi$
$131$	−5.21046e13	−0.900768	−0.450384	+	0.892835i	$0.648713\pi$
$132$	3.58806e11	0.00590376
$133$	0	0
$134$	4.91017e13	0.732682
$135$	3.05817e13	0.434802
$136$	−3.19898e13	−0.433519
$137$	1.78930e13	0.231206	0.115603	−	0.993295i	$-0.463120\pi$
$137$	1.78930e13	0.231206	0.115603	+	0.993295i	$0.463120\pi$
$138$	−2.44218e13	−0.300998
$139$	−1.18769e14	−1.39671	−0.698357	−	0.715750i	$-0.746085\pi$
$139$	−1.18769e14	−1.39671	−0.698357	+	0.715750i	$0.746085\pi$
$140$	0	0
$141$	−5.89629e12	−0.0631909
$142$	1.10959e14	1.13576
$143$	−5.59885e12	−0.0547538
$144$	−2.42137e13	−0.226310
$145$	−6.40684e13	−0.572469
$146$	−1.01696e14	−0.868984
$147$	0	0
$148$	1.10634e14	0.865343
$149$	−6.49329e13	−0.486132	−0.243066	−	0.970010i	$-0.578153\pi$
$149$	−6.49329e13	−0.486132	−0.243066	+	0.970010i	$0.578153\pi$
$150$	−1.36762e13	−0.0980332
$151$	−2.41552e14	−1.65829	−0.829146	−	0.559033i	$-0.811173\pi$
$151$	−2.41552e14	−1.65829	−0.829146	+	0.559033i	$0.811173\pi$
$152$	5.62131e13	0.369704
$153$	−1.76121e14	−1.10999
$154$	0	0
$155$	−1.26472e14	−0.732553
$156$	−3.95508e13	−0.219708
$157$	−3.26736e14	−1.74120	−0.870602	−	0.491988i	$-0.836270\pi$
$157$	−3.26736e14	−1.74120	−0.870602	+	0.491988i	$0.836270\pi$
$158$	1.83242e13	0.0937031
$159$	−1.52854e13	−0.0750231
$160$	−2.78123e13	−0.131056
$161$	0	0
$162$	−1.17894e14	−0.512442
$163$	4.69367e14	1.96017	0.980084	−	0.198586i	$-0.0636348\pi$
$163$	4.69367e14	1.96017	0.980084	+	0.198586i	$0.0636348\pi$
$164$	1.34057e14	0.538026
$165$	2.26901e12	0.00875368
$166$	6.02514e12	0.0223493
$167$	−1.79618e14	−0.640755	−0.320378	−	0.947290i	$-0.603810\pi$
$167$	−1.79618e14	−0.640755	−0.320378	+	0.947290i	$0.603810\pi$
$168$	0	0
$169$	3.14281e14	1.03766
$170$	−2.02296e14	−0.642791
$171$	3.09484e14	0.946593
$172$	−2.36816e13	−0.0697392
$173$	−5.82178e14	−1.65103	−0.825517	−	0.564377i	$-0.809116\pi$
$173$	−5.82178e14	−1.65103	−0.825517	+	0.564377i	$0.809116\pi$
$174$	−6.15298e13	−0.168080
$175$	0	0
$176$	−3.78113e12	−0.00958935
$177$	−5.61628e13	−0.137285
$178$	2.52812e14	0.595756
$179$	−8.42500e14	−1.91437	−0.957183	−	0.289482i	$-0.906517\pi$
$179$	−8.42500e14	−1.91437	−0.957183	+	0.289482i	$0.906517\pi$
$180$	−1.53122e14	−0.335557
$181$	3.09169e14	0.653559	0.326779	−	0.945101i	$-0.394037\pi$
$181$	3.09169e14	0.653559	0.326779	+	0.945101i	$0.394037\pi$
$182$	0	0
$183$	−6.13199e13	−0.120689
$184$	2.57359e14	0.488904
$185$	6.99627e14	1.28307
$186$	−1.21461e14	−0.215081
$187$	−2.75025e13	−0.0470329
$188$	6.21356e13	0.102639
$189$	0	0
$190$	3.55479e14	0.548171
$191$	1.73956e14	0.259252	0.129626	−	0.991563i	$-0.458622\pi$
$191$	1.73956e14	0.259252	0.129626	+	0.991563i	$0.458622\pi$
$192$	−2.67103e13	−0.0384787
$193$	5.38716e13	0.0750304	0.0375152	−	0.999296i	$-0.488056\pi$
$193$	5.38716e13	0.0750304	0.0375152	+	0.999296i	$0.488056\pi$
$194$	6.68144e14	0.899826
$195$	−2.50111e14	−0.325767
$196$	0	0
$197$	−6.06639e14	−0.739435	−0.369717	−	0.929144i	$-0.620545\pi$
$197$	−6.06639e14	−0.739435	−0.369717	+	0.929144i	$0.620545\pi$
$198$	−2.08172e13	−0.0245526
$199$	−1.15850e15	−1.32236	−0.661182	−	0.750225i	$-0.729945\pi$
$199$	−1.15850e15	−1.32236	−0.661182	+	0.750225i	$0.729945\pi$
$200$	1.44121e14	0.159233
$201$	2.98205e14	0.318963
$202$	3.54566e14	0.367209
$203$	0	0
$204$	−1.94280e14	−0.188727
$205$	8.47745e14	0.797747
$206$	−5.01761e14	−0.457467
$207$	1.41690e15	1.25179
$208$	4.16790e14	0.356866
$209$	4.83280e13	0.0401096
$210$	0	0
$211$	−3.58373e14	−0.279576	−0.139788	−	0.990181i	$-0.544642\pi$
$211$	−3.58373e14	−0.279576	−0.139788	+	0.990181i	$0.544642\pi$
$212$	1.61079e14	0.121858
$213$	6.73877e14	0.494439
$214$	−1.57458e15	−1.12066
$215$	−1.49757e14	−0.103404
$216$	−3.09503e14	−0.207355
$217$	0	0
$218$	9.44656e14	0.596083
$219$	−6.17623e14	−0.378300
$220$	−2.39110e13	−0.0142184
$221$	3.03158e15	1.75032
$222$	6.71905e14	0.376715
$223$	6.64312e14	0.361735	0.180868	−	0.983507i	$-0.442109\pi$
$223$	6.64312e14	0.361735	0.180868	+	0.983507i	$0.442109\pi$
$224$	0	0
$225$	7.93467e14	0.407701
$226$	−1.73640e15	−0.866853
$227$	−1.41108e15	−0.684518	−0.342259	−	0.939606i	$-0.611192\pi$
$227$	−1.41108e15	−0.684518	−0.342259	+	0.939606i	$0.611192\pi$
$228$	3.41394e14	0.160946
$229$	−1.27260e15	−0.583126	−0.291563	−	0.956552i	$-0.594175\pi$
$229$	−1.27260e15	−0.583126	−0.291563	+	0.956552i	$0.594175\pi$
$230$	1.62748e15	0.724912
$231$	0	0
$232$	6.48406e14	0.273008
$233$	−1.44741e15	−0.592622	−0.296311	−	0.955092i	$-0.595756\pi$
$233$	−1.44741e15	−0.592622	−0.296311	+	0.955092i	$0.595756\pi$
$234$	2.29466e15	0.913724
$235$	3.92932e14	0.152186
$236$	5.91849e14	0.222989
$237$	1.11287e14	0.0407924
$238$	0	0
$239$	−5.51666e15	−1.91465	−0.957326	−	0.289009i	$-0.906674\pi$
$239$	−5.51666e15	−1.91465	−0.957326	+	0.289009i	$0.906674\pi$
$240$	−1.68910e14	−0.0570534
$241$	−2.19545e15	−0.721792	−0.360896	−	0.932606i	$-0.617529\pi$
$241$	−2.19545e15	−0.721792	−0.360896	+	0.932606i	$0.617529\pi$
$242$	2.20620e15	0.706066
$243$	−2.59835e15	−0.809574
$244$	6.46194e14	0.196033
$245$	0	0
$246$	8.14154e14	0.234222
$247$	−5.32715e15	−1.49267
$248$	1.27996e15	0.349351
$249$	3.65919e13	0.00972948
$250$	2.93500e15	0.760323
$251$	3.18963e15	0.805120	0.402560	−	0.915394i	$-0.368120\pi$
$251$	3.18963e15	0.805120	0.402560	+	0.915394i	$0.368120\pi$
$252$	0	0
$253$	2.21259e14	0.0530417
$254$	−1.00491e15	−0.234806
$255$	−1.22859e15	−0.279830
$256$	2.81475e14	0.0625000
$257$	7.52323e15	1.62869	0.814346	−	0.580379i	$-0.197096\pi$
$257$	7.52323e15	1.62869	0.814346	+	0.580379i	$0.197096\pi$
$258$	−1.43824e14	−0.0303600
$259$	0	0
$260$	2.63569e15	0.529136
$261$	3.56983e15	0.699012
$262$	3.33470e15	0.636939
$263$	2.21790e15	0.413266	0.206633	−	0.978419i	$-0.433749\pi$
$263$	2.21790e15	0.413266	0.206633	+	0.978419i	$0.433749\pi$
$264$	−2.29636e13	−0.00417459
$265$	1.01863e15	0.180683
$266$	0	0
$267$	1.53538e15	0.259354
$268$	−3.14251e15	−0.518084
$269$	−7.88167e15	−1.26832	−0.634160	−	0.773202i	$-0.718654\pi$
$269$	−7.88167e15	−1.26832	−0.634160	+	0.773202i	$0.718654\pi$
$270$	−1.95723e15	−0.307452
$271$	−1.95301e14	−0.0299506	−0.0149753	−	0.999888i	$-0.504767\pi$
$271$	−1.95301e14	−0.0299506	−0.0149753	+	0.999888i	$0.504767\pi$
$272$	2.04734e15	0.306544
$273$	0	0
$274$	−1.14515e15	−0.163488
$275$	1.23905e14	0.0172754
$276$	1.56299e15	0.212838
$277$	1.04913e16	1.39544	0.697719	−	0.716371i	$-0.254198\pi$
$277$	1.04913e16	1.39544	0.697719	+	0.716371i	$0.254198\pi$
$278$	7.60123e15	0.987626
$279$	7.04691e15	0.894482
$280$	0	0
$281$	−1.40373e16	−1.70095	−0.850475	−	0.526016i	$-0.823685\pi$
$281$	−1.40373e16	−1.70095	−0.850475	+	0.526016i	$0.823685\pi$
$282$	3.77362e14	0.0446827
$283$	1.14262e16	1.32217	0.661087	−	0.750309i	$-0.270095\pi$
$283$	1.14262e16	1.32217	0.661087	+	0.750309i	$0.270095\pi$
$284$	−7.10137e15	−0.803106
$285$	2.15890e15	0.238639
$286$	3.58326e14	0.0387168
$287$	0	0
$288$	1.54967e15	0.160026
$289$	4.98704e15	0.503509
$290$	4.10038e15	0.404797
$291$	4.05778e15	0.391727
$292$	6.50857e15	0.614464
$293$	5.81181e15	0.536626	0.268313	−	0.963332i	$-0.413534\pi$
$293$	5.81181e15	0.536626	0.268313	+	0.963332i	$0.413534\pi$
$294$	0	0
$295$	3.74272e15	0.330632
$296$	−7.08059e15	−0.611890
$297$	−2.66088e14	−0.0224962
$298$	4.15570e15	0.343747
$299$	−2.43891e16	−1.97394
$300$	8.75278e14	0.0693199
$301$	0	0
$302$	1.54593e16	1.17259
$303$	2.15335e15	0.159859
$304$	−3.59764e15	−0.261420
$305$	4.08639e15	0.290664
$306$	1.12718e16	0.784878
$307$	−9.05812e15	−0.617503	−0.308751	−	0.951143i	$-0.599911\pi$
$307$	−9.05812e15	−0.617503	−0.308751	+	0.951143i	$0.599911\pi$
$308$	0	0
$309$	−3.04730e15	−0.199152
$310$	8.09422e15	0.517993
$311$	6.95532e15	0.435888	0.217944	−	0.975961i	$-0.430065\pi$
$311$	6.95532e15	0.435888	0.217944	+	0.975961i	$0.430065\pi$
$312$	2.53125e15	0.155357
$313$	−2.28752e16	−1.37507	−0.687537	−	0.726149i	$-0.741308\pi$
$313$	−2.28752e16	−1.37507	−0.687537	+	0.726149i	$0.741308\pi$
$314$	2.09111e16	1.23122
$315$	0	0
$316$	−1.17275e15	−0.0662581
$317$	1.75517e16	0.971480	0.485740	−	0.874103i	$-0.338550\pi$
$317$	1.75517e16	0.971480	0.485740	+	0.874103i	$0.338550\pi$
$318$	9.78265e14	0.0530494
$319$	5.57454e14	0.0296189
$320$	1.77999e15	0.0926705
$321$	−9.56275e15	−0.487865
$322$	0	0
$323$	−2.61679e16	−1.28219
$324$	7.54523e15	0.362351
$325$	−1.36579e16	−0.642900
$326$	−3.00395e16	−1.38605
$327$	5.73710e15	0.259497
$328$	−8.57962e15	−0.380442
$329$	0	0
$330$	−1.45217e14	−0.00618979
$331$	3.95189e15	0.165167	0.0825834	−	0.996584i	$-0.473683\pi$
$331$	3.95189e15	0.165167	0.0825834	+	0.996584i	$0.473683\pi$
$332$	−3.85609e14	−0.0158034
$333$	−3.89825e16	−1.56669
$334$	1.14955e16	0.453082
$335$	−1.98725e16	−0.768178
$336$	0	0
$337$	−1.01379e16	−0.377012	−0.188506	−	0.982072i	$-0.560364\pi$
$337$	−1.01379e16	−0.377012	−0.188506	+	0.982072i	$0.560364\pi$
$338$	−2.01140e16	−0.733735
$339$	−1.05455e16	−0.377373
$340$	1.29470e16	0.454522
$341$	1.10042e15	0.0379015
$342$	−1.98070e16	−0.669342
$343$	0	0
$344$	1.51562e15	0.0493130
$345$	9.88403e15	0.315580
$346$	3.72594e16	1.16746
$347$	−2.30415e16	−0.708548	−0.354274	−	0.935142i	$-0.615272\pi$
$347$	−2.30415e16	−0.708548	−0.354274	+	0.935142i	$0.615272\pi$
$348$	3.93791e15	0.118850
$349$	−2.15793e16	−0.639252	−0.319626	−	0.947544i	$-0.603557\pi$
$349$	−2.15793e16	−0.639252	−0.319626	+	0.947544i	$0.603557\pi$
$350$	0	0
$351$	2.93307e16	0.837193
$352$	2.41992e14	0.00678069
$353$	−1.90990e16	−0.525383	−0.262691	−	0.964880i	$-0.584610\pi$
$353$	−1.90990e16	−0.525383	−0.262691	+	0.964880i	$0.584610\pi$
$354$	3.59442e15	0.0970751
$355$	−4.49075e16	−1.19079
$356$	−1.61800e16	−0.421263
$357$	0	0
$358$	5.39200e16	1.35366
$359$	1.45493e16	0.358697	0.179349	−	0.983786i	$-0.442601\pi$
$359$	1.45493e16	0.358697	0.179349	+	0.983786i	$0.442601\pi$
$360$	9.79980e15	0.237274
$361$	3.92978e15	0.0934482
$362$	−1.97868e16	−0.462136
$363$	1.33987e16	0.307376
$364$	0	0
$365$	4.11587e16	0.911084
$366$	3.92447e15	0.0853403
$367$	−6.16872e16	−1.31785	−0.658925	−	0.752209i	$-0.728989\pi$
$367$	−6.16872e16	−1.31785	−0.658925	+	0.752209i	$0.728989\pi$
$368$	−1.64710e16	−0.345707
$369$	−4.72355e16	−0.974086
$370$	−4.47761e16	−0.907267
$371$	0	0
$372$	7.77349e15	0.152085
$373$	−7.58723e16	−1.45873	−0.729367	−	0.684123i	$-0.760185\pi$
$373$	−7.58723e16	−1.45873	−0.729367	+	0.684123i	$0.760185\pi$
$374$	1.76016e15	0.0332573
$375$	1.78249e16	0.330996
$376$	−3.97668e15	−0.0725770
$377$	−6.14476e16	−1.10227
$378$	0	0
$379$	−2.97831e16	−0.516196	−0.258098	−	0.966119i	$-0.583096\pi$
$379$	−2.97831e16	−0.516196	−0.258098	+	0.966119i	$0.583096\pi$
$380$	−2.27507e16	−0.387615
$381$	−6.10306e15	−0.102220
$382$	−1.11332e16	−0.183319
$383$	8.12688e16	1.31562	0.657812	−	0.753182i	$-0.271482\pi$
$383$	8.12688e16	1.31562	0.657812	+	0.753182i	$0.271482\pi$
$384$	1.70946e15	0.0272085
$385$	0	0
$386$	−3.44778e15	−0.0530545
$387$	8.34434e15	0.126262
$388$	−4.27612e16	−0.636273
$389$	2.64668e16	0.387284	0.193642	−	0.981072i	$-0.437970\pi$
$389$	2.64668e16	0.387284	0.193642	+	0.981072i	$0.437970\pi$
$390$	1.60071e16	0.230352
$391$	−1.19804e17	−1.69559
$392$	0	0
$393$	2.02523e16	0.277283
$394$	3.88249e16	0.522859
$395$	−7.41620e15	−0.0982427
$396$	1.33230e15	0.0173613
$397$	−8.94624e16	−1.14684	−0.573419	−	0.819262i	$-0.694383\pi$
$397$	−8.94624e16	−1.14684	−0.573419	+	0.819262i	$0.694383\pi$
$398$	7.41440e16	0.935053
$399$	0	0
$400$	−9.22376e15	−0.112595
$401$	1.15225e17	1.38391	0.691954	−	0.721942i	$-0.256750\pi$
$401$	1.15225e17	1.38391	0.691954	+	0.721942i	$0.256750\pi$
$402$	−1.90851e16	−0.225541
$403$	−1.21299e17	−1.41050
$404$	−2.26922e16	−0.259656
$405$	4.77144e16	0.537269
$406$	0	0
$407$	−6.08739e15	−0.0663846
$408$	1.24340e16	0.133450
$409$	5.04198e16	0.532598	0.266299	−	0.963890i	$-0.414199\pi$
$409$	5.04198e16	0.532598	0.266299	+	0.963890i	$0.414199\pi$
$410$	−5.42557e16	−0.564092
$411$	−6.95475e15	−0.0711721
$412$	3.21127e16	0.323478
$413$	0	0
$414$	−9.06817e16	−0.885151
$415$	−2.43851e15	−0.0234321
$416$	−2.66746e16	−0.252343
$417$	4.61638e16	0.429950
$418$	−3.09299e15	−0.0283618
$419$	−5.68881e16	−0.513606	−0.256803	−	0.966464i	$-0.582669\pi$
$419$	−5.68881e16	−0.513606	−0.256803	+	0.966464i	$0.582669\pi$
$420$	0	0
$421$	−2.24518e16	−0.196525	−0.0982623	−	0.995161i	$-0.531328\pi$
$421$	−2.24518e16	−0.196525	−0.0982623	+	0.995161i	$0.531328\pi$
$422$	2.29359e16	0.197690
$423$	−2.18938e16	−0.185827
$424$	−1.03090e16	−0.0861668
$425$	−6.70902e16	−0.552244
$426$	−4.31281e16	−0.349621
$427$	0	0
$428$	1.00773e17	0.792428
$429$	2.17619e15	0.0168548
$430$	9.58448e15	0.0731179
$431$	1.57738e17	1.18531	0.592657	−	0.805455i	$-0.298079\pi$
$431$	1.57738e17	1.18531	0.592657	+	0.805455i	$0.298079\pi$
$432$	1.98082e16	0.146622
$433$	2.52696e17	1.84258	0.921291	−	0.388873i	$-0.127136\pi$
$433$	2.52696e17	1.84258	0.921291	+	0.388873i	$0.127136\pi$
$434$	0	0
$435$	2.49025e16	0.176223
$436$	−6.04580e16	−0.421494
$437$	2.10522e17	1.44600
$438$	3.95279e16	0.267499
$439$	1.67679e17	1.11805	0.559023	−	0.829152i	$-0.311176\pi$
$439$	1.67679e17	1.11805	0.559023	+	0.829152i	$0.311176\pi$
$440$	1.53031e15	0.0100539
$441$	0	0
$442$	−1.94021e17	−1.23767
$443$	−7.88805e16	−0.495844	−0.247922	−	0.968780i	$-0.579748\pi$
$443$	−7.88805e16	−0.495844	−0.247922	+	0.968780i	$0.579748\pi$
$444$	−4.30019e16	−0.266378
$445$	−1.02319e17	−0.624619
$446$	−4.25160e16	−0.255785
$447$	2.52385e16	0.149646
$448$	0	0
$449$	−6.54338e16	−0.376878	−0.188439	−	0.982085i	$-0.560343\pi$
$449$	−6.54338e16	−0.376878	−0.188439	+	0.982085i	$0.560343\pi$
$450$	−5.07819e16	−0.288288
$451$	−7.37615e15	−0.0412745
$452$	1.11130e17	0.612958
$453$	9.38878e16	0.510471
$454$	9.03094e16	0.484028
$455$	0	0
$456$	−2.18492e16	−0.113806
$457$	−8.78797e16	−0.451267	−0.225633	−	0.974212i	$-0.572445\pi$
$457$	−8.78797e16	−0.451267	−0.225633	+	0.974212i	$0.572445\pi$
$458$	8.14466e16	0.412332
$459$	1.44077e17	0.719139
$460$	−1.04159e17	−0.512590
$461$	2.99092e17	1.45127	0.725637	−	0.688078i	$-0.241545\pi$
$461$	2.99092e17	1.45127	0.725637	+	0.688078i	$0.241545\pi$
$462$	0	0
$463$	3.52626e17	1.66356	0.831779	−	0.555106i	$-0.187322\pi$
$463$	3.52626e17	1.66356	0.831779	+	0.555106i	$0.187322\pi$
$464$	−4.14980e16	−0.193046
$465$	4.91579e16	0.225501
$466$	9.26342e16	0.419047
$467$	2.80787e17	1.25262	0.626308	−	0.779576i	$-0.284565\pi$
$467$	2.80787e17	1.25262	0.626308	+	0.779576i	$0.284565\pi$
$468$	−1.46858e17	−0.646100
$469$	0	0
$470$	−2.51476e16	−0.107612
$471$	1.26998e17	0.535994
$472$	−3.78783e16	−0.157677
$473$	1.30303e15	0.00535002
$474$	−7.12235e15	−0.0288446
$475$	1.17892e17	0.470953
$476$	0	0
$477$	−5.67569e16	−0.220622
$478$	3.53066e17	1.35386
$479$	4.04685e17	1.53086	0.765432	−	0.643517i	$-0.222525\pi$
$479$	4.04685e17	1.53086	0.765432	+	0.643517i	$0.222525\pi$
$480$	1.08102e16	0.0403429
$481$	6.71007e17	2.47050
$482$	1.40509e17	0.510384
$483$	0	0
$484$	−1.41197e17	−0.499264
$485$	−2.70412e17	−0.943420
$486$	1.66294e17	0.572455
$487$	−2.98670e17	−1.01450	−0.507251	−	0.861798i	$-0.669338\pi$
$487$	−2.98670e17	−1.01450	−0.507251	+	0.861798i	$0.669338\pi$
$488$	−4.13564e16	−0.138616
$489$	−1.82436e17	−0.603397
$490$	0	0
$491$	−4.17520e17	−1.34477	−0.672384	−	0.740202i	$-0.734730\pi$
$491$	−4.17520e17	−1.34477	−0.672384	+	0.740202i	$0.734730\pi$
$492$	−5.21058e16	−0.165620
$493$	−3.01841e17	−0.946833
$494$	3.40938e17	1.05548
$495$	8.42517e15	0.0257422
$496$	−8.19178e16	−0.247029
$497$	0	0
$498$	−2.34188e15	−0.00687978
$499$	−7.31558e16	−0.212127	−0.106063	−	0.994359i	$-0.533825\pi$
$499$	−7.31558e16	−0.212127	−0.106063	+	0.994359i	$0.533825\pi$
$500$	−1.87840e17	−0.537630
$501$	6.98148e16	0.197243
$502$	−2.04136e17	−0.569306
$503$	5.96999e17	1.64355	0.821773	−	0.569816i	$-0.192985\pi$
$503$	5.96999e17	1.64355	0.821773	+	0.569816i	$0.192985\pi$
$504$	0	0
$505$	−1.43501e17	−0.384999
$506$	−1.41606e16	−0.0375061
$507$	−1.22156e17	−0.319421
$508$	6.43145e16	0.166033
$509$	−2.34632e17	−0.598029	−0.299015	−	0.954248i	$-0.596658\pi$
$509$	−2.34632e17	−0.598029	−0.299015	+	0.954248i	$0.596658\pi$
$510$	7.86296e16	0.197870
$511$	0	0
$512$	−1.80144e16	−0.0441942
$513$	−2.53176e17	−0.613280
$514$	−4.81487e17	−1.15166
$515$	2.03074e17	0.479630
$516$	9.20470e15	0.0214678
$517$	−3.41886e15	−0.00787396
$518$	0	0
$519$	2.26284e17	0.508237
$520$	−1.68684e17	−0.374156
$521$	5.42280e16	0.118790	0.0593948	−	0.998235i	$-0.481083\pi$
$521$	5.42280e16	0.118790	0.0593948	+	0.998235i	$0.481083\pi$
$522$	−2.28469e17	−0.494276
$523$	−6.61963e17	−1.41440	−0.707201	−	0.707013i	$-0.750042\pi$
$523$	−6.61963e17	−1.41440	−0.707201	+	0.707013i	$0.750042\pi$
$524$	−2.13421e17	−0.450384
$525$	0	0
$526$	−1.41946e17	−0.292223
$527$	−5.95839e17	−1.21160
$528$	1.46967e15	0.00295188
$529$	4.59789e17	0.912214
$530$	−6.51921e16	−0.127762
$531$	−2.08541e17	−0.403717
$532$	0	0
$533$	8.13066e17	1.53603
$534$	−9.82645e16	−0.183391
$535$	6.37267e17	1.17496
$536$	2.01121e17	0.366341
$537$	3.27467e17	0.589298
$538$	5.04427e17	0.896837
$539$	0	0
$540$	1.25263e17	0.217401
$541$	3.19786e17	0.548374	0.274187	−	0.961676i	$-0.411591\pi$
$541$	3.19786e17	0.548374	0.274187	+	0.961676i	$0.411591\pi$
$542$	1.24993e16	0.0211782
$543$	−1.20169e17	−0.201185
$544$	−1.31030e17	−0.216759
$545$	−3.82323e17	−0.624962
$546$	0	0
$547$	−2.07693e17	−0.331516	−0.165758	−	0.986166i	$-0.553007\pi$
$547$	−2.07693e17	−0.331516	−0.165758	+	0.986166i	$0.553007\pi$
$548$	7.32897e16	0.115603
$549$	−2.27690e17	−0.354914
$550$	−7.92993e15	−0.0122155
$551$	5.30402e17	0.807457
$552$	−1.00032e17	−0.150499
$553$	0	0
$554$	−6.71443e17	−0.986724
$555$	−2.71935e17	−0.394966
$556$	−4.86479e17	−0.698357
$557$	2.65216e16	0.0376306	0.0188153	−	0.999823i	$-0.494011\pi$
$557$	2.65216e16	0.0376306	0.0188153	+	0.999823i	$0.494011\pi$
$558$	−4.51002e17	−0.632494
$559$	−1.43631e17	−0.199100
$560$	0	0
$561$	1.06898e16	0.0144781
$562$	8.98385e17	1.20275
$563$	−7.75088e17	−1.02576	−0.512881	−	0.858460i	$-0.671422\pi$
$563$	−7.75088e17	−1.02576	−0.512881	+	0.858460i	$0.671422\pi$
$564$	−2.41512e16	−0.0315954
$565$	7.02760e17	0.908850
$566$	−7.31275e17	−0.934919
$567$	0	0
$568$	4.54488e17	0.567882
$569$	1.03329e18	1.27642	0.638211	−	0.769861i	$-0.279675\pi$
$569$	1.03329e18	1.27642	0.638211	+	0.769861i	$0.279675\pi$
$570$	−1.38170e17	−0.168743
$571$	−4.71919e17	−0.569814	−0.284907	−	0.958555i	$-0.591963\pi$
$571$	−4.71919e17	−0.569814	−0.284907	+	0.958555i	$0.591963\pi$
$572$	−2.29329e16	−0.0273769
$573$	−6.76141e16	−0.0798054
$574$	0	0
$575$	5.39743e17	0.622797
$576$	−9.91792e16	−0.113155
$577$	6.65478e17	0.750742	0.375371	−	0.926875i	$-0.377515\pi$
$577$	6.65478e17	0.750742	0.375371	+	0.926875i	$0.377515\pi$
$578$	−3.19171e17	−0.356035
$579$	−2.09391e16	−0.0230966
$580$	−2.62424e17	−0.286235
$581$	0	0
$582$	−2.59698e17	−0.276993
$583$	−8.86298e15	−0.00934833
$584$	−4.16548e17	−0.434492
$585$	−9.28698e17	−0.957991
$586$	−3.71956e17	−0.379452
$587$	5.98028e16	0.0603356	0.0301678	−	0.999545i	$-0.490396\pi$
$587$	5.98028e16	0.0603356	0.0301678	+	0.999545i	$0.490396\pi$
$588$	0	0
$589$	1.04702e18	1.03325
$590$	−2.39534e17	−0.233792
$591$	2.35792e17	0.227620
$592$	4.53158e17	0.432672
$593$	1.29438e17	0.122238	0.0611189	−	0.998130i	$-0.480533\pi$
$593$	1.29438e17	0.122238	0.0611189	+	0.998130i	$0.480533\pi$
$594$	1.70297e16	0.0159072
$595$	0	0
$596$	−2.65965e17	−0.243066
$597$	4.50292e17	0.407063
$598$	1.56091e18	1.39579
$599$	−1.04882e18	−0.927740	−0.463870	−	0.885903i	$-0.653540\pi$
$599$	−1.04882e18	−0.927740	−0.463870	+	0.885903i	$0.653540\pi$
$600$	−5.60178e16	−0.0490166
$601$	−2.17964e18	−1.88669	−0.943346	−	0.331811i	$-0.892340\pi$
$601$	−2.17964e18	−1.88669	−0.943346	+	0.331811i	$0.892340\pi$
$602$	0	0
$603$	1.10728e18	0.937982
$604$	−9.89398e17	−0.829146
$605$	−8.92899e17	−0.740274
$606$	−1.37815e17	−0.113038
$607$	−2.10760e18	−1.71026	−0.855129	−	0.518415i	$-0.826522\pi$
$607$	−2.10760e18	−1.71026	−0.855129	+	0.518415i	$0.826522\pi$
$608$	2.30249e17	0.184852
$609$	0	0
$610$	−2.61529e17	−0.205530
$611$	3.76858e17	0.293028
$612$	−7.21392e17	−0.554993
$613$	−8.43304e17	−0.641935	−0.320967	−	0.947090i	$-0.604008\pi$
$613$	−8.43304e17	−0.641935	−0.320967	+	0.947090i	$0.604008\pi$
$614$	5.79720e17	0.436640
$615$	−3.29506e17	−0.245570
$616$	0	0
$617$	−1.28326e18	−0.936399	−0.468199	−	0.883623i	$-0.655097\pi$
$617$	−1.28326e18	−0.936399	−0.468199	+	0.883623i	$0.655097\pi$
$618$	1.95027e17	0.140822
$619$	1.33956e18	0.957132	0.478566	−	0.878052i	$-0.341157\pi$
$619$	1.33956e18	0.957132	0.478566	+	0.878052i	$0.341157\pi$
$620$	−5.18030e17	−0.366276
$621$	−1.15911e18	−0.811014
$622$	−4.45141e17	−0.308219
$623$	0	0
$624$	−1.62000e17	−0.109854
$625$	−5.16742e17	−0.346780
$626$	1.46401e18	0.972325
$627$	−1.87844e16	−0.0123469
$628$	−1.33831e18	−0.870602
$629$	3.29610e18	2.12213
$630$	0	0
$631$	−2.14803e18	−1.35472	−0.677360	−	0.735652i	$-0.736876\pi$
$631$	−2.14803e18	−1.35472	−0.677360	+	0.735652i	$0.736876\pi$
$632$	7.50559e16	0.0468515
$633$	1.39294e17	0.0860616
$634$	−1.12331e18	−0.686940
$635$	4.06711e17	0.246182
$636$	−6.26089e16	−0.0375116
$637$	0	0
$638$	−3.56770e16	−0.0209437
$639$	2.50220e18	1.45401
$640$	−1.13919e17	−0.0655280
$641$	1.04871e18	0.597141	0.298570	−	0.954388i	$-0.403490\pi$
$641$	1.04871e18	0.597141	0.298570	+	0.954388i	$0.403490\pi$
$642$	6.12016e17	0.344973
$643$	−2.81734e18	−1.57205	−0.786027	−	0.618193i	$-0.787865\pi$
$643$	−2.81734e18	−1.57205	−0.786027	+	0.618193i	$0.787865\pi$
$644$	0	0
$645$	5.82085e16	0.0318309
$646$	1.67474e18	0.906645
$647$	−1.28697e18	−0.689748	−0.344874	−	0.938649i	$-0.612078\pi$
$647$	−1.28697e18	−0.689748	−0.344874	+	0.938649i	$0.612078\pi$
$648$	−4.82895e17	−0.256221
$649$	−3.25651e16	−0.0171065
$650$	8.74109e17	0.454599
$651$	0	0
$652$	1.92253e18	0.980084
$653$	−2.10910e18	−1.06454	−0.532270	−	0.846574i	$-0.678661\pi$
$653$	−2.10910e18	−1.06454	−0.532270	+	0.846574i	$0.678661\pi$
$654$	−3.67174e17	−0.183492
$655$	−1.34962e18	−0.667797
$656$	5.49096e17	0.269013
$657$	−2.29333e18	−1.11248
$658$	0	0
$659$	9.69560e17	0.461126	0.230563	−	0.973057i	$-0.425943\pi$
$659$	9.69560e17	0.461126	0.230563	+	0.973057i	$0.425943\pi$
$660$	9.29386e15	0.00437684
$661$	9.02254e16	0.0420745	0.0210373	−	0.999779i	$-0.493303\pi$
$661$	9.02254e16	0.0420745	0.0210373	+	0.999779i	$0.493303\pi$
$662$	−2.52921e17	−0.116791
$663$	−1.17833e18	−0.538801
$664$	2.46790e16	0.0111747
$665$	0	0
$666$	2.49488e18	1.10782
$667$	2.42832e18	1.06780
$668$	−7.35714e17	−0.320378
$669$	−2.58208e17	−0.111353
$670$	1.27184e18	0.543184
$671$	−3.55553e16	−0.0150386
$672$	0	0
$673$	−3.19523e18	−1.32557	−0.662787	−	0.748808i	$-0.730626\pi$
$673$	−3.19523e18	−1.32557	−0.662787	+	0.748808i	$0.730626\pi$
$674$	6.48828e17	0.266588
$675$	−6.49101e17	−0.264142
$676$	1.28729e18	0.518829
$677$	2.07313e17	0.0827560	0.0413780	−	0.999144i	$-0.486825\pi$
$677$	2.07313e17	0.0827560	0.0413780	+	0.999144i	$0.486825\pi$
$678$	6.74914e17	0.266843
$679$	0	0
$680$	−8.28605e17	−0.321395
$681$	5.48468e17	0.210715
$682$	−7.04271e16	−0.0268004
$683$	2.56411e18	0.966501	0.483251	−	0.875482i	$-0.339456\pi$
$683$	2.56411e18	0.966501	0.483251	+	0.875482i	$0.339456\pi$
$684$	1.26765e18	0.473297
$685$	4.63468e17	0.171408
$686$	0	0
$687$	4.94642e17	0.179503
$688$	−9.70000e16	−0.0348696
$689$	9.76957e17	0.347897
$690$	−6.32578e17	−0.223149
$691$	−3.39962e17	−0.118802	−0.0594009	−	0.998234i	$-0.518919\pi$
$691$	−3.39962e17	−0.118802	−0.0594009	+	0.998234i	$0.518919\pi$
$692$	−2.38460e18	−0.825517
$693$	0	0
$694$	1.47466e18	0.501019
$695$	−3.07638e18	−1.03547
$696$	−2.52026e17	−0.0840399
$697$	3.99392e18	1.31943
$698$	1.38108e18	0.452019
$699$	5.62587e17	0.182426
$700$	0	0
$701$	1.45413e18	0.462846	0.231423	−	0.972853i	$-0.425662\pi$
$701$	1.45413e18	0.462846	0.231423	+	0.972853i	$0.425662\pi$
$702$	−1.87716e18	−0.591985
$703$	−5.79198e18	−1.80975
$704$	−1.54875e16	−0.00479467
$705$	−1.52727e17	−0.0468475
$706$	1.22234e18	0.371502
$707$	0	0
$708$	−2.30043e17	−0.0686424
$709$	−3.43293e18	−1.01500	−0.507498	−	0.861653i	$-0.669429\pi$
$709$	−3.43293e18	−1.01500	−0.507498	+	0.861653i	$0.669429\pi$
$710$	2.87408e18	0.842015
$711$	4.13224e17	0.119959
$712$	1.03552e18	0.297878
$713$	4.79355e18	1.36639
$714$	0	0
$715$	−1.45023e17	−0.0405925
$716$	−3.45088e18	−0.957183
$717$	2.14425e18	0.589386
$718$	−9.31155e17	−0.253637
$719$	1.29515e18	0.349610	0.174805	−	0.984603i	$-0.444071\pi$
$719$	1.29515e18	0.349610	0.174805	+	0.984603i	$0.444071\pi$
$720$	−6.27187e17	−0.167778
$721$	0	0
$722$	−2.51506e17	−0.0660778
$723$	8.53338e17	0.222189
$724$	1.26635e18	0.326779
$725$	1.35986e18	0.347775
$726$	−8.57519e17	−0.217348
$727$	4.19685e18	1.05426	0.527132	−	0.849783i	$-0.323267\pi$
$727$	4.19685e18	1.05426	0.527132	+	0.849783i	$0.323267\pi$
$728$	0	0
$729$	−1.92696e18	−0.475492
$730$	−2.63416e18	−0.644234
$731$	−7.05542e17	−0.171025
$732$	−2.51166e17	−0.0603447
$733$	−5.79383e18	−1.37972	−0.689859	−	0.723944i	$-0.742327\pi$
$733$	−5.79383e18	−1.37972	−0.689859	+	0.723944i	$0.742327\pi$
$734$	3.94798e18	0.931861
$735$	0	0
$736$	1.05414e18	0.244452
$737$	1.72909e17	0.0397447
$738$	3.02307e18	0.688783
$739$	−3.12048e17	−0.0704746	−0.0352373	−	0.999379i	$-0.511219\pi$
$739$	−3.12048e17	−0.0704746	−0.0352373	+	0.999379i	$0.511219\pi$
$740$	2.86567e18	0.641535
$741$	2.07059e18	0.459489
$742$	0	0
$743$	−3.64180e18	−0.794124	−0.397062	−	0.917792i	$-0.629970\pi$
$743$	−3.64180e18	−0.794124	−0.397062	+	0.917792i	$0.629970\pi$
$744$	−4.97504e17	−0.107541
$745$	−1.68190e18	−0.360401
$746$	4.85583e18	1.03148
$747$	1.35871e17	0.0286117
$748$	−1.12650e17	−0.0235165
$749$	0	0
$750$	−1.14079e18	−0.234050
$751$	6.26515e18	1.27430	0.637151	−	0.770739i	$-0.280113\pi$
$751$	6.26515e18	1.27430	0.637151	+	0.770739i	$0.280113\pi$
$752$	2.54507e17	0.0513197
$753$	−1.23976e18	−0.247840
$754$	3.93265e18	0.779419
$755$	−6.25673e18	−1.22940
$756$	0	0
$757$	2.22951e18	0.430612	0.215306	−	0.976547i	$-0.430925\pi$
$757$	2.22951e18	0.430612	0.215306	+	0.976547i	$0.430925\pi$
$758$	1.90612e18	0.365006
$759$	−8.60001e16	−0.0163278
$760$	1.45604e18	0.274085
$761$	3.09582e18	0.577797	0.288899	−	0.957360i	$-0.406711\pi$
$761$	3.09582e18	0.577797	0.288899	+	0.957360i	$0.406711\pi$
$762$	3.90596e17	0.0722803
$763$	0	0
$764$	7.12524e17	0.129626
$765$	−4.56193e18	−0.822904
$766$	−5.20120e18	−0.930287
$767$	3.58962e18	0.636617
$768$	−1.09405e17	−0.0192393
$769$	−1.53830e18	−0.268238	−0.134119	−	0.990965i	$-0.542821\pi$
$769$	−1.53830e18	−0.268238	−0.134119	+	0.990965i	$0.542821\pi$
$770$	0	0
$771$	−2.92417e18	−0.501360
$772$	2.20658e17	0.0375152
$773$	−1.33220e18	−0.224597	−0.112298	−	0.993675i	$-0.535821\pi$
$773$	−1.33220e18	−0.224597	−0.112298	+	0.993675i	$0.535821\pi$
$774$	−5.34038e17	−0.0892804
$775$	2.68439e18	0.445026
$776$	2.73672e18	0.449913
$777$	0	0
$778$	−1.69388e18	−0.273851
$779$	−7.01820e18	−1.12521
$780$	−1.02445e18	−0.162884
$781$	3.90736e17	0.0616101
$782$	7.66744e18	1.19896
$783$	−2.92033e18	−0.452877
$784$	0	0
$785$	−8.46319e18	−1.29087
$786$	−1.29615e18	−0.196069
$787$	−9.04527e17	−0.135702	−0.0678509	−	0.997695i	$-0.521614\pi$
$787$	−9.04527e17	−0.135702	−0.0678509	+	0.997695i	$0.521614\pi$
$788$	−2.48479e18	−0.369717
$789$	−8.62066e17	−0.127215
$790$	4.74637e17	0.0694681
$791$	0	0
$792$	−8.52672e16	−0.0122763
$793$	3.91923e18	0.559661
$794$	5.72559e18	0.810937
$795$	−3.95925e17	−0.0556195
$796$	−4.74522e18	−0.661182
$797$	1.22176e19	1.68853	0.844264	−	0.535927i	$-0.180038\pi$
$797$	1.22176e19	1.68853	0.844264	+	0.535927i	$0.180038\pi$
$798$	0	0
$799$	1.85119e18	0.251708
$800$	5.90321e17	0.0796165
$801$	5.70111e18	0.762690
$802$	−7.37438e18	−0.978570
$803$	−3.58119e17	−0.0471385
$804$	1.22145e18	0.159482
$805$	0	0
$806$	7.76311e18	0.997373
$807$	3.06349e18	0.390426
$808$	1.45230e18	0.183604
$809$	1.42866e19	1.79169	0.895846	−	0.444365i	$-0.146571\pi$
$809$	1.42866e19	1.79169	0.895846	+	0.444365i	$0.146571\pi$
$810$	−3.05372e18	−0.379906
$811$	5.74123e18	0.708548	0.354274	−	0.935142i	$-0.384728\pi$
$811$	5.74123e18	0.708548	0.354274	+	0.935142i	$0.384728\pi$
$812$	0	0
$813$	7.59108e16	0.00921966
$814$	3.89593e17	0.0469410
$815$	1.21576e19	1.45320
$816$	−7.95773e17	−0.0943633
$817$	1.23979e18	0.145850
$818$	−3.22687e18	−0.376604
$819$	0	0
$820$	3.47236e18	0.398873
$821$	4.92909e18	0.561741	0.280871	−	0.959746i	$-0.409377\pi$
$821$	4.92909e18	0.561741	0.280871	+	0.959746i	$0.409377\pi$
$822$	4.45104e17	0.0503263
$823$	1.14451e19	1.28387	0.641937	−	0.766758i	$-0.278131\pi$
$823$	1.14451e19	1.28387	0.641937	+	0.766758i	$0.278131\pi$
$824$	−2.05521e18	−0.228734
$825$	−4.81601e16	−0.00531786
$826$	0	0
$827$	−1.52462e16	−0.00165720	−0.000828600	−	1.00000i	$-0.500264\pi$
$827$	−1.52462e16	−0.00165720	−0.000828600		1.00000i	$0.500264\pi$
$828$	5.80363e18	0.625897
$829$	−8.73738e18	−0.934925	−0.467463	−	0.884013i	$-0.654832\pi$
$829$	−8.73738e18	−0.934925	−0.467463	+	0.884013i	$0.654832\pi$
$830$	1.56064e17	0.0165690
$831$	−4.07781e18	−0.429557
$832$	1.70717e18	0.178433
$833$	0	0
$834$	−2.95449e18	−0.304020
$835$	−4.65250e18	−0.475033
$836$	1.97952e17	0.0200548
$837$	−5.76478e18	−0.579518
$838$	3.64084e18	0.363175
$839$	1.82185e18	0.180327	0.0901635	−	0.995927i	$-0.471261\pi$
$839$	1.82185e18	0.180327	0.0901635	+	0.995927i	$0.471261\pi$
$840$	0	0
$841$	−4.14255e18	−0.403733
$842$	1.43691e18	0.138964
$843$	5.45608e18	0.523602
$844$	−1.46790e18	−0.139788
$845$	8.14056e18	0.769282
$846$	1.40120e18	0.131399
$847$	0	0
$848$	6.59778e17	0.0609291
$849$	−4.44119e18	−0.407004
$850$	4.29377e18	0.390495
$851$	−2.65173e19	−2.39324
$852$	2.76020e18	0.247220
$853$	−1.25797e19	−1.11816	−0.559078	−	0.829115i	$-0.688845\pi$
$853$	−1.25797e19	−1.11816	−0.559078	+	0.829115i	$0.688845\pi$
$854$	0	0
$855$	8.01632e18	0.701770
$856$	−6.44948e18	−0.560332
$857$	−4.02067e17	−0.0346676	−0.0173338	−	0.999850i	$-0.505518\pi$
$857$	−4.02067e17	−0.0346676	−0.0173338	+	0.999850i	$0.505518\pi$
$858$	−1.39276e17	−0.0119182
$859$	−9.34722e18	−0.793829	−0.396914	−	0.917856i	$-0.629919\pi$
$859$	−9.34722e18	−0.793829	−0.396914	+	0.917856i	$0.629919\pi$
$860$	−6.13406e17	−0.0517021
$861$	0	0
$862$	−1.00952e19	−0.838144
$863$	1.64045e19	1.35174	0.675869	−	0.737022i	$-0.263769\pi$
$863$	1.64045e19	1.35174	0.675869	+	0.737022i	$0.263769\pi$
$864$	−1.26772e18	−0.103678
$865$	−1.50797e19	−1.22402
$866$	−1.61725e19	−1.30290
$867$	−1.93839e18	−0.154995
$868$	0	0
$869$	6.45277e16	0.00508297
$870$	−1.59376e18	−0.124608
$871$	−1.90596e19	−1.47909
$872$	3.86931e18	0.298041
$873$	1.50671e19	1.15196
$874$	−1.34734e19	−1.02247
$875$	0	0
$876$	−2.52978e18	−0.189150
$877$	−2.46782e18	−0.183154	−0.0915769	−	0.995798i	$-0.529191\pi$
$877$	−2.46782e18	−0.183154	−0.0915769	+	0.995798i	$0.529191\pi$
$878$	−1.07315e19	−0.790578
$879$	−2.25897e18	−0.165189
$880$	−9.79395e16	−0.00710920
$881$	−3.32748e18	−0.239757	−0.119879	−	0.992789i	$-0.538251\pi$
$881$	−3.32748e18	−0.239757	−0.119879	+	0.992789i	$0.538251\pi$
$882$	0	0
$883$	8.38821e18	0.595559	0.297779	−	0.954635i	$-0.403754\pi$
$883$	8.38821e18	0.595559	0.297779	+	0.954635i	$0.403754\pi$
$884$	1.24173e19	0.875162
$885$	−1.45474e18	−0.101778
$886$	5.04835e18	0.350615
$887$	−2.10367e19	−1.45035	−0.725176	−	0.688564i	$-0.758242\pi$
$887$	−2.10367e19	−1.45035	−0.725176	+	0.688564i	$0.758242\pi$
$888$	2.75212e18	0.188358
$889$	0	0
$890$	6.54840e18	0.441672
$891$	−4.15158e17	−0.0277977
$892$	2.72102e18	0.180868
$893$	−3.25295e18	−0.214656
$894$	−1.61526e18	−0.105815
$895$	−2.18226e19	−1.41924
$896$	0	0
$897$	9.47970e18	0.607637
$898$	4.18776e18	0.266493
$899$	1.20772e19	0.763005
$900$	3.25004e18	0.203851
$901$	4.79898e18	0.298840
$902$	4.72074e17	0.0291855
$903$	0	0
$904$	−7.11230e18	−0.433427
$905$	8.00815e18	0.484525
$906$	−6.00882e18	−0.360957
$907$	−1.23567e19	−0.736982	−0.368491	−	0.929631i	$-0.620125\pi$
$907$	−1.23567e19	−0.736982	−0.368491	+	0.929631i	$0.620125\pi$
$908$	−5.77980e18	−0.342259
$909$	7.99572e18	0.470102
$910$	0	0
$911$	2.86402e19	1.65999	0.829997	−	0.557768i	$-0.188342\pi$
$911$	2.86402e19	1.65999	0.829997	+	0.557768i	$0.188342\pi$
$912$	1.39835e18	0.0804728
$913$	2.12172e16	0.00121235
$914$	5.62430e18	0.319094
$915$	−1.58832e18	−0.0894749
$916$	−5.21258e18	−0.291563
$917$	0	0
$918$	−9.22094e18	−0.508508
$919$	1.55535e18	0.0851681	0.0425840	−	0.999093i	$-0.486441\pi$
$919$	1.55535e18	0.0851681	0.0425840	+	0.999093i	$0.486441\pi$
$920$	6.66616e18	0.362456
$921$	3.52076e18	0.190085
$922$	−1.91419e19	−1.02621
$923$	−4.30705e19	−2.29281
$924$	0	0
$925$	−1.48497e19	−0.779465
$926$	−2.25681e19	−1.17631
$927$	−1.13151e19	−0.585651
$928$	2.65587e18	0.136504
$929$	9.49029e18	0.484370	0.242185	−	0.970230i	$-0.422136\pi$
$929$	9.49029e18	0.484370	0.242185	+	0.970230i	$0.422136\pi$
$930$	−3.14610e18	−0.159453
$931$	0	0
$932$	−5.92859e18	−0.296311
$933$	−2.70343e18	−0.134179
$934$	−1.79704e19	−0.885733
$935$	−7.12376e17	−0.0348685
$936$	9.39892e18	0.456862
$937$	2.37142e19	1.14473	0.572363	−	0.820001i	$-0.306027\pi$
$937$	2.37142e19	1.14473	0.572363	+	0.820001i	$0.306027\pi$
$938$	0	0
$939$	8.89125e18	0.423288
$940$	1.60945e18	0.0760932
$941$	9.77251e17	0.0458853	0.0229427	−	0.999737i	$-0.492696\pi$
$941$	9.77251e17	0.0458853	0.0229427	+	0.999737i	$0.492696\pi$
$942$	−8.12785e18	−0.379005
$943$	−3.21312e19	−1.48800
$944$	2.42421e18	0.111494
$945$	0	0
$946$	−8.33937e16	−0.00378304
$947$	−3.83155e19	−1.72624	−0.863118	−	0.505002i	$-0.831492\pi$
$947$	−3.83155e19	−1.72624	−0.863118	+	0.505002i	$0.831492\pi$
$948$	4.55830e17	0.0203962
$949$	3.94751e19	1.75425
$950$	−7.54511e18	−0.333014
$951$	−6.82209e18	−0.299050
$952$	0	0
$953$	2.21709e19	0.958693	0.479347	−	0.877626i	$-0.340874\pi$
$953$	2.21709e19	0.958693	0.479347	+	0.877626i	$0.340874\pi$
$954$	3.63244e18	0.156003
$955$	4.50584e18	0.192200
$956$	−2.25962e19	−0.957326
$957$	−2.16674e17	−0.00911758
$958$	−2.58999e19	−1.08248
$959$	0	0
$960$	−6.91855e17	−0.0285267
$961$	−5.76995e17	−0.0236303
$962$	−4.29444e19	−1.74690
$963$	−3.55079e19	−1.43468
$964$	−8.99254e18	−0.360896
$965$	1.39539e18	0.0556248
$966$	0	0
$967$	−1.43421e19	−0.564080	−0.282040	−	0.959403i	$-0.591011\pi$
$967$	−1.43421e19	−0.564080	−0.282040	+	0.959403i	$0.591011\pi$
$968$	9.03661e18	0.353033
$969$	1.01711e19	0.394695
$970$	1.73064e19	0.667099
$971$	4.60781e19	1.76429	0.882144	−	0.470979i	$-0.156099\pi$
$971$	4.60781e19	1.76429	0.882144	+	0.470979i	$0.156099\pi$
$972$	−1.06428e19	−0.404787
$973$	0	0
$974$	1.91149e19	0.717362
$975$	5.30864e18	0.197904
$976$	2.64681e18	0.0980165
$977$	−8.55166e18	−0.314583	−0.157292	−	0.987552i	$-0.550276\pi$
$977$	−8.55166e18	−0.314583	−0.157292	+	0.987552i	$0.550276\pi$
$978$	1.16759e19	0.426666
$979$	8.90266e17	0.0323171
$980$	0	0
$981$	2.13027e19	0.763108
$982$	2.67213e19	0.950895
$983$	1.20315e19	0.425327	0.212663	−	0.977126i	$-0.431786\pi$
$983$	1.20315e19	0.425327	0.212663	+	0.977126i	$0.431786\pi$
$984$	3.33477e18	0.117111
$985$	−1.57133e19	−0.548191
$986$	1.93178e19	0.669512
$987$	0	0
$988$	−2.18200e19	−0.746337
$989$	5.67611e18	0.192875
$990$	−5.39211e17	−0.0182025
$991$	−2.35156e19	−0.788637	−0.394318	−	0.918974i	$-0.629019\pi$
$991$	−2.35156e19	−0.788637	−0.394318	+	0.918974i	$0.629019\pi$
$992$	5.24274e18	0.174676
$993$	−1.53604e18	−0.0508432
$994$	0	0
$995$	−3.00077e19	−0.980354
$996$	1.49881e17	0.00486474
$997$	4.40987e19	1.42202	0.711012	−	0.703179i	$-0.248237\pi$
$997$	4.40987e19	1.42202	0.711012	+	0.703179i	$0.248237\pi$
$998$	4.68197e18	0.149996
$999$	3.18900e19	1.01503

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.14.a.h.1.2		4
7.2	even	3		14.14.c.b.11.3	yes	8
7.3	odd	6		98.14.c.o.79.2		8
7.4	even	3		14.14.c.b.9.3	✓	8
7.5	odd	6		98.14.c.o.67.2		8
7.6	odd	2		98.14.a.j.1.3		4
21.2	odd	6		126.14.g.b.109.3		8
21.11	odd	6		126.14.g.b.37.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.14.c.b.9.3	✓	8	7.4	even	3
14.14.c.b.11.3	yes	8	7.2	even	3
98.14.a.h.1.2		4	1.1	even	1	trivial
98.14.a.j.1.3		4	7.6	odd	2
98.14.c.o.67.2		8	7.5	odd	6
98.14.c.o.79.2		8	7.3	odd	6
126.14.g.b.37.3		8	21.11	odd	6
126.14.g.b.109.3		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)

\(f(q)\)	\(=\)	\(q-64.0000 q^{2} -388.685 q^{3} +4096.00 q^{4} +25902.2 q^{5} +24875.9 q^{6} -262144. q^{8} -1.44325e6 q^{9} +O(q^{10})\)	\(q-64.0000 q^{2} -388.685 q^{3} +4096.00 q^{4} +25902.2 q^{5} +24875.9 q^{6} -262144. q^{8} -1.44325e6 q^{9} -1.65774e6 q^{10} -225373. q^{11} -1.59206e6 q^{12} +2.48426e7 q^{13} -1.00678e7 q^{15} +1.67772e7 q^{16} +1.22031e8 q^{17} +9.23678e7 q^{18} -2.14436e8 q^{19} +1.06095e8 q^{20} +1.44239e7 q^{22} -9.81746e8 q^{23} +1.01892e8 q^{24} -5.49779e8 q^{25} -1.58993e9 q^{26} +1.18066e9 q^{27} -2.47347e9 q^{29} +6.44340e8 q^{30} -4.88268e9 q^{31} -1.07374e9 q^{32} +8.75991e7 q^{33} -7.81000e9 q^{34} -5.91154e9 q^{36} +2.70103e10 q^{37} +1.37239e10 q^{38} -9.65596e9 q^{39} -6.79011e9 q^{40} +3.27287e10 q^{41} -5.78165e9 q^{43} -9.23127e8 q^{44} -3.73833e10 q^{45} +6.28318e10 q^{46} +1.51698e10 q^{47} -6.52106e9 q^{48} +3.51858e10 q^{50} -4.74318e10 q^{51} +1.01755e11 q^{52} +3.93259e10 q^{53} -7.55622e10 q^{54} -5.83765e9 q^{55} +8.33481e10 q^{57} +1.58302e11 q^{58} +1.44494e11 q^{59} -4.12377e10 q^{60} +1.57762e11 q^{61} +3.12491e11 q^{62} +6.87195e10 q^{64} +6.43479e11 q^{65} -5.60634e9 q^{66} -7.67214e11 q^{67} +4.99840e11 q^{68} +3.81590e11 q^{69} -1.73373e12 q^{71} +3.78338e11 q^{72} +1.58901e12 q^{73} -1.72866e12 q^{74} +2.13691e11 q^{75} -8.78329e11 q^{76} +6.17982e11 q^{78} -2.86316e11 q^{79} +4.34567e11 q^{80} +1.84210e12 q^{81} -2.09463e12 q^{82} -9.41428e10 q^{83} +3.16088e12 q^{85} +3.70025e11 q^{86} +9.61403e11 q^{87} +5.90801e10 q^{88} -3.95020e12 q^{89} +2.39253e12 q^{90} -4.02123e12 q^{92} +1.89783e12 q^{93} -9.70868e11 q^{94} -5.55436e12 q^{95} +4.17348e11 q^{96} -1.04397e13 q^{97} +3.25268e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 256 q^{2} - 182 q^{3} + 16384 q^{4} - 1792 q^{5} + 11648 q^{6} - 1048576 q^{8} - 599840 q^{9}+O(q^{10}) \) 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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