LMFDB - Embedded newform 98.14.a.h.1.4

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			1.4
Root			$71.3297$ 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)

$f(q)$	$=$	$q-64.0000 q^{2} +1493.71 q^{3} +4096.00 q^{4} +14356.4 q^{5} -95597.3 q^{6} -262144. q^{8} +636841. q^{9} +O(q^{10})$	\(q-64.0000 q^{2} +1493.71 q^{3} +4096.00 q^{4} +14356.4 q^{5} -95597.3 q^{6} -262144. q^{8} +636841. q^{9} -918809. q^{10} -4.28544e6 q^{11} +6.11823e6 q^{12} +5.50861e6 q^{13} +2.14443e7 q^{15} +1.67772e7 q^{16} -3.97108e7 q^{17} -4.07578e7 q^{18} +4.50229e7 q^{19} +5.88038e7 q^{20} +2.74268e8 q^{22} +7.54686e8 q^{23} -3.91567e8 q^{24} -1.01460e9 q^{25} -3.52551e8 q^{26} -1.43020e9 q^{27} -2.46353e9 q^{29} -1.37243e9 q^{30} +6.13406e9 q^{31} -1.07374e9 q^{32} -6.40119e9 q^{33} +2.54149e9 q^{34} +2.60850e9 q^{36} -1.90483e10 q^{37} -2.88147e9 q^{38} +8.22825e9 q^{39} -3.76344e9 q^{40} -4.23093e10 q^{41} -7.42867e10 q^{43} -1.75531e10 q^{44} +9.14274e9 q^{45} -4.82999e10 q^{46} +8.07016e10 q^{47} +2.50603e10 q^{48} +6.49342e10 q^{50} -5.93163e10 q^{51} +2.25633e10 q^{52} -2.21078e11 q^{53} +9.15327e10 q^{54} -6.15234e10 q^{55} +6.72511e10 q^{57} +1.57666e11 q^{58} +4.59780e11 q^{59} +8.78357e10 q^{60} +6.47850e10 q^{61} -3.92580e11 q^{62} +6.87195e10 q^{64} +7.90837e10 q^{65} +4.09676e11 q^{66} -4.14427e11 q^{67} -1.62655e11 q^{68} +1.12728e12 q^{69} -6.38110e11 q^{71} -1.66944e11 q^{72} +5.85996e11 q^{73} +1.21909e12 q^{74} -1.51551e12 q^{75} +1.84414e11 q^{76} -5.26608e11 q^{78} +2.45886e12 q^{79} +2.40860e11 q^{80} -3.15163e12 q^{81} +2.70780e12 q^{82} +3.32114e12 q^{83} -5.70103e11 q^{85} +4.75435e12 q^{86} -3.67979e12 q^{87} +1.12340e12 q^{88} -2.78406e12 q^{89} -5.85135e11 q^{90} +3.09119e12 q^{92} +9.16249e12 q^{93} -5.16490e12 q^{94} +6.46366e11 q^{95} -1.60386e12 q^{96} -7.80467e12 q^{97} -2.72914e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1493.71	1.18298	0.591490	−	0.806312i	$-0.298540\pi$
$3$	1493.71	1.18298	0.591490	+	0.806312i	$0.298540\pi$
$4$	4096.00	0.500000
$5$	14356.4	0.410904	0.205452	−	0.978667i	$-0.434134\pi$
$5$	14356.4	0.410904	0.205452	+	0.978667i	$0.434134\pi$
$6$	−95597.3	−0.836494
$7$	0	0
$7$	0	0
$8$	−262144.	−0.353553
$9$	636841.	0.399443
$10$	−918809.	−0.290553
$11$	−4.28544e6	−0.729361	−0.364681	−	0.931133i	$-0.618822\pi$
$11$	−4.28544e6	−0.729361	−0.364681	+	0.931133i	$0.618822\pi$
$12$	6.11823e6	0.591490
$13$	5.50861e6	0.316527	0.158263	−	0.987397i	$-0.449411\pi$
$13$	5.50861e6	0.316527	0.158263	+	0.987397i	$0.449411\pi$
$14$	0	0
$15$	2.14443e7	0.486091
$16$	1.67772e7	0.250000
$17$	−3.97108e7	−0.399016	−0.199508	−	0.979896i	$-0.563934\pi$
$17$	−3.97108e7	−0.399016	−0.199508	+	0.979896i	$0.563934\pi$
$18$	−4.07578e7	−0.282449
$19$	4.50229e7	0.219551	0.109775	−	0.993956i	$-0.464987\pi$
$19$	4.50229e7	0.219551	0.109775	+	0.993956i	$0.464987\pi$
$20$	5.88038e7	0.205452
$21$	0	0
$22$	2.74268e8	0.515736
$23$	7.54686e8	1.06300	0.531502	−	0.847057i	$-0.321628\pi$
$23$	7.54686e8	1.06300	0.531502	+	0.847057i	$0.321628\pi$
$24$	−3.91567e8	−0.418247
$25$	−1.01460e9	−0.831158
$26$	−3.52551e8	−0.223818
$27$	−1.43020e9	−0.710447
$28$	0	0
$29$	−2.46353e9	−0.769078	−0.384539	−	0.923109i	$-0.625640\pi$
$29$	−2.46353e9	−0.769078	−0.384539	+	0.923109i	$0.625640\pi$
$30$	−1.37243e9	−0.343719
$31$	6.13406e9	1.24136	0.620679	−	0.784065i	$-0.286857\pi$
$31$	6.13406e9	1.24136	0.620679	+	0.784065i	$0.286857\pi$
$32$	−1.07374e9	−0.176777
$33$	−6.40119e9	−0.862820
$34$	2.54149e9	0.282147
$35$	0	0
$36$	2.60850e9	0.199721
$37$	−1.90483e10	−1.22052	−0.610261	−	0.792200i	$-0.708935\pi$
$37$	−1.90483e10	−1.22052	−0.610261	+	0.792200i	$0.708935\pi$
$38$	−2.88147e9	−0.155246
$39$	8.22825e9	0.374445
$40$	−3.76344e9	−0.145276
$41$	−4.23093e10	−1.39104	−0.695522	−	0.718505i	$-0.744827\pi$
$41$	−4.23093e10	−1.39104	−0.695522	+	0.718505i	$0.744827\pi$
$42$	0	0
$43$	−7.42867e10	−1.79212	−0.896058	−	0.443937i	$-0.853581\pi$
$43$	−7.42867e10	−1.79212	−0.896058	+	0.443937i	$0.853581\pi$
$44$	−1.75531e10	−0.364681
$45$	9.14274e9	0.164133
$46$	−4.82999e10	−0.751658
$47$	8.07016e10	1.09206	0.546030	−	0.837766i	$-0.316139\pi$
$47$	8.07016e10	1.09206	0.546030	+	0.837766i	$0.316139\pi$
$48$	2.50603e10	0.295745
$49$	0	0
$50$	6.49342e10	0.587717
$51$	−5.93163e10	−0.472028
$52$	2.25633e10	0.158263
$53$	−2.21078e11	−1.37010	−0.685049	−	0.728497i	$-0.740219\pi$
$53$	−2.21078e11	−1.37010	−0.685049	+	0.728497i	$0.740219\pi$
$54$	9.15327e10	0.502362
$55$	−6.15234e10	−0.299697
$56$	0	0
$57$	6.72511e10	0.259724
$58$	1.57666e11	0.543820
$59$	4.59780e11	1.41910	0.709548	−	0.704657i	$-0.248899\pi$
$59$	4.59780e11	1.41910	0.709548	+	0.704657i	$0.248899\pi$
$60$	8.78357e10	0.243046
$61$	6.47850e10	0.161002	0.0805009	−	0.996755i	$-0.474348\pi$
$61$	6.47850e10	0.161002	0.0805009	+	0.996755i	$0.474348\pi$
$62$	−3.92580e11	−0.877772
$63$	0	0
$64$	6.87195e10	0.125000
$65$	7.90837e10	0.130062
$66$	4.09676e11	0.610106
$67$	−4.14427e11	−0.559709	−0.279855	−	0.960042i	$-0.590286\pi$
$67$	−4.14427e11	−0.559709	−0.279855	+	0.960042i	$0.590286\pi$
$68$	−1.62655e11	−0.199508
$69$	1.12728e12	1.25751
$70$	0	0
$71$	−6.38110e11	−0.591175	−0.295588	−	0.955316i	$-0.595515\pi$
$71$	−6.38110e11	−0.591175	−0.295588	+	0.955316i	$0.595515\pi$
$72$	−1.66944e11	−0.141224
$73$	5.85996e11	0.453207	0.226603	−	0.973987i	$-0.427238\pi$
$73$	5.85996e11	0.453207	0.226603	+	0.973987i	$0.427238\pi$
$74$	1.21909e12	0.863040
$75$	−1.51551e12	−0.983244
$76$	1.84414e11	0.109775
$77$	0	0
$78$	−5.26608e11	−0.264772
$79$	2.45886e12	1.13804	0.569019	−	0.822324i	$-0.307323\pi$
$79$	2.45886e12	1.13804	0.569019	+	0.822324i	$0.307323\pi$
$80$	2.40860e11	0.102726
$81$	−3.15163e12	−1.23989
$82$	2.70780e12	0.983617
$83$	3.32114e12	1.11501	0.557506	−	0.830173i	$-0.311758\pi$
$83$	3.32114e12	1.11501	0.557506	+	0.830173i	$0.311758\pi$
$84$	0	0
$85$	−5.70103e11	−0.163957
$86$	4.75435e12	1.26722
$87$	−3.67979e12	−0.909804
$88$	1.12340e12	0.257868
$89$	−2.78406e12	−0.593804	−0.296902	−	0.954908i	$-0.595953\pi$
$89$	−2.78406e12	−0.593804	−0.296902	+	0.954908i	$0.595953\pi$
$90$	−5.85135e11	−0.116059
$91$	0	0
$92$	3.09119e12	0.531502
$93$	9.16249e12	1.46850
$94$	−5.16490e12	−0.772203
$95$	6.46366e11	0.0902143
$96$	−1.60386e12	−0.209123
$97$	−7.80467e12	−0.951345	−0.475672	−	0.879622i	$-0.657795\pi$
$97$	−7.80467e12	−0.951345	−0.475672	+	0.879622i	$0.657795\pi$
$98$	0	0
$99$	−2.72914e12	−0.291338
$100$	−4.15579e12	−0.415579
$101$	1.31661e13	1.23415	0.617076	−	0.786904i	$-0.288317\pi$
$101$	1.31661e13	1.23415	0.617076	+	0.786904i	$0.288317\pi$
$102$	3.79624e12	0.333774
$103$	−1.76879e13	−1.45960	−0.729799	−	0.683661i	$-0.760387\pi$
$103$	−1.76879e13	−1.45960	−0.729799	+	0.683661i	$0.760387\pi$
$104$	−1.44405e12	−0.111909
$105$	0	0
$106$	1.41490e13	0.968806
$107$	−1.44616e13	−0.931583	−0.465791	−	0.884895i	$-0.654230\pi$
$107$	−1.44616e13	−0.931583	−0.465791	+	0.884895i	$0.654230\pi$
$108$	−5.85809e12	−0.355224
$109$	−1.59317e13	−0.909893	−0.454947	−	0.890519i	$-0.650342\pi$
$109$	−1.59317e13	−0.909893	−0.454947	+	0.890519i	$0.650342\pi$
$110$	3.93750e12	0.211918
$111$	−2.84526e13	−1.44385
$112$	0	0
$113$	4.86885e12	0.219997	0.109998	−	0.993932i	$-0.464915\pi$
$113$	4.86885e12	0.219997	0.109998	+	0.993932i	$0.464915\pi$
$114$	−4.30407e12	−0.183653
$115$	1.08346e13	0.436793
$116$	−1.00906e13	−0.384539
$117$	3.50811e12	0.126434
$118$	−2.94259e13	−1.00345
$119$	0	0
$120$	−5.62148e12	−0.171859
$121$	−1.61577e13	−0.468032
$122$	−4.14624e12	−0.113845
$123$	−6.31978e13	−1.64558
$124$	2.51251e13	0.620679
$125$	−3.20908e13	−0.752430
$126$	0	0
$127$	1.02773e12	0.0217347	0.0108674	−	0.999941i	$-0.496541\pi$
$127$	1.02773e12	0.0217347	0.0108674	+	0.999941i	$0.496541\pi$
$128$	−4.39805e12	−0.0883883
$129$	−1.10963e14	−2.12004
$130$	−5.06136e12	−0.0919677
$131$	−6.17381e13	−1.06731	−0.533654	−	0.845703i	$-0.679182\pi$
$131$	−6.17381e13	−1.06731	−0.533654	+	0.845703i	$0.679182\pi$
$132$	−2.62193e13	−0.431410
$133$	0	0
$134$	2.65234e13	0.395774
$135$	−2.05325e13	−0.291926
$136$	1.04099e13	0.141073
$137$	−1.32352e14	−1.71020	−0.855102	−	0.518460i	$-0.826505\pi$
$137$	−1.32352e14	−1.71020	−0.855102	+	0.518460i	$0.826505\pi$
$138$	−7.21459e13	−0.889196
$139$	−1.66284e14	−1.95548	−0.977742	−	0.209810i	$-0.932716\pi$
$139$	−1.66284e14	−1.95548	−0.977742	+	0.209810i	$0.932716\pi$
$140$	0	0
$141$	1.20545e14	1.29188
$142$	4.08390e13	0.418024
$143$	−2.36068e13	−0.230862
$144$	1.06844e13	0.0998607
$145$	−3.53674e13	−0.316017
$146$	−3.75038e13	−0.320465
$147$	0	0
$148$	−7.80220e13	−0.610261
$149$	1.70896e14	1.27945	0.639723	−	0.768606i	$-0.279049\pi$
$149$	1.70896e14	1.27945	0.639723	+	0.768606i	$0.279049\pi$
$150$	9.69928e13	0.695258
$151$	2.69611e14	1.85092	0.925458	−	0.378850i	$-0.123681\pi$
$151$	2.69611e14	1.85092	0.925458	+	0.378850i	$0.123681\pi$
$152$	−1.18025e13	−0.0776229
$153$	−2.52894e13	−0.159384
$154$	0	0
$155$	8.80630e13	0.510079
$156$	3.37029e13	0.187222
$157$	−5.30818e13	−0.282877	−0.141439	−	0.989947i	$-0.545173\pi$
$157$	−5.30818e13	−0.282877	−0.141439	+	0.989947i	$0.545173\pi$
$158$	−1.57367e14	−0.804715
$159$	−3.30225e14	−1.62080
$160$	−1.54151e13	−0.0726382
$161$	0	0
$162$	2.01704e14	0.876733
$163$	2.51845e14	1.05176	0.525878	−	0.850560i	$-0.323737\pi$
$163$	2.51845e14	1.05176	0.525878	+	0.850560i	$0.323737\pi$
$164$	−1.73299e14	−0.695522
$165$	−9.18980e13	−0.354536
$166$	−2.12553e14	−0.788433
$167$	−5.21452e12	−0.0186019	−0.00930095	−	0.999957i	$-0.502961\pi$
$167$	−5.21452e12	−0.0186019	−0.00930095	+	0.999957i	$0.502961\pi$
$168$	0	0
$169$	−2.72530e14	−0.899811
$170$	3.64866e13	0.115935
$171$	2.86724e13	0.0876980
$172$	−3.04278e14	−0.896058
$173$	2.63130e14	0.746227	0.373113	−	0.927786i	$-0.378290\pi$
$173$	2.63130e14	0.746227	0.373113	+	0.927786i	$0.378290\pi$
$174$	2.35507e14	0.643329
$175$	0	0
$176$	−7.18977e13	−0.182340
$177$	6.86777e14	1.67876
$178$	1.78180e14	0.419883
$179$	−3.62070e14	−0.822713	−0.411357	−	0.911475i	$-0.634945\pi$
$179$	−3.62070e14	−0.822713	−0.411357	+	0.911475i	$0.634945\pi$
$180$	3.74487e13	0.0820663
$181$	−6.76438e14	−1.42994	−0.714969	−	0.699156i	$-0.753559\pi$
$181$	−6.76438e14	−1.42994	−0.714969	+	0.699156i	$0.753559\pi$
$182$	0	0
$183$	9.67699e13	0.190462
$184$	−1.97836e14	−0.375829
$185$	−2.73465e14	−0.501517
$186$	−5.86400e14	−1.03839
$187$	1.70178e14	0.291027
$188$	3.30554e14	0.546030
$189$	0	0
$190$	−4.13674e13	−0.0637911
$191$	−7.60361e14	−1.13319	−0.566595	−	0.823996i	$-0.691740\pi$
$191$	−7.60361e14	−1.13319	−0.566595	+	0.823996i	$0.691740\pi$
$192$	1.02647e14	0.147873
$193$	−6.42203e12	−0.00894437	−0.00447219	−	0.999990i	$-0.501424\pi$
$193$	−6.42203e12	−0.00894437	−0.00447219	+	0.999990i	$0.501424\pi$
$194$	4.99499e14	0.672702
$195$	1.18128e14	0.153861
$196$	0	0
$197$	4.19711e14	0.511588	0.255794	−	0.966731i	$-0.417663\pi$
$197$	4.19711e14	0.511588	0.255794	+	0.966731i	$0.417663\pi$
$198$	1.74665e14	0.206007
$199$	1.50769e15	1.72095	0.860475	−	0.509493i	$-0.170167\pi$
$199$	1.50769e15	1.72095	0.860475	+	0.509493i	$0.170167\pi$
$200$	2.65971e14	0.293859
$201$	−6.19034e14	−0.662125
$202$	−8.42631e14	−0.872677
$203$	0	0
$204$	−2.42960e14	−0.236014
$205$	−6.07409e14	−0.571586
$206$	1.13202e15	1.03209
$207$	4.80615e14	0.424610
$208$	9.24191e13	0.0791316
$209$	−1.92943e14	−0.160132
$210$	0	0
$211$	−9.49543e14	−0.740762	−0.370381	−	0.928880i	$-0.620773\pi$
$211$	−9.49543e14	−0.740762	−0.370381	+	0.928880i	$0.620773\pi$
$212$	−9.05534e14	−0.685049
$213$	−9.53150e14	−0.699349
$214$	9.25542e14	0.658728
$215$	−1.06649e15	−0.736388
$216$	3.74918e14	0.251181
$217$	0	0
$218$	1.01963e15	0.643392
$219$	8.75307e14	0.536135
$220$	−2.52000e14	−0.149849
$221$	−2.18751e14	−0.126299
$222$	1.82097e15	1.02096
$223$	6.07949e14	0.331044	0.165522	−	0.986206i	$-0.447069\pi$
$223$	6.07949e14	0.331044	0.165522	+	0.986206i	$0.447069\pi$
$224$	0	0
$225$	−6.46137e14	−0.332000
$226$	−3.11606e14	−0.155561
$227$	−2.78618e15	−1.35158	−0.675788	−	0.737096i	$-0.736197\pi$
$227$	−2.78618e15	−1.35158	−0.675788	+	0.737096i	$0.736197\pi$
$228$	2.75460e14	0.129862
$229$	1.13511e15	0.520125	0.260063	−	0.965592i	$-0.416257\pi$
$229$	1.13511e15	0.520125	0.260063	+	0.965592i	$0.416257\pi$
$230$	−6.93412e14	−0.308859
$231$	0	0
$232$	6.45799e14	0.271910
$233$	−2.03990e15	−0.835208	−0.417604	−	0.908629i	$-0.637130\pi$
$233$	−2.03990e15	−0.835208	−0.417604	+	0.908629i	$0.637130\pi$
$234$	−2.24519e14	−0.0894025
$235$	1.15858e15	0.448731
$236$	1.88326e15	0.709548
$237$	3.67281e15	1.34628
$238$	0	0
$239$	−3.57648e15	−1.24128	−0.620639	−	0.784096i	$-0.713127\pi$
$239$	−3.57648e15	−1.24128	−0.620639	+	0.784096i	$0.713127\pi$
$240$	3.59775e14	0.121523
$241$	−1.81638e15	−0.597169	−0.298584	−	0.954383i	$-0.596514\pi$
$241$	−1.81638e15	−0.597169	−0.298584	+	0.954383i	$0.596514\pi$
$242$	1.03410e15	0.330949
$243$	−2.42742e15	−0.756316
$244$	2.65359e14	0.0805009
$245$	0	0
$246$	4.04466e15	1.16360
$247$	2.48013e14	0.0694936
$248$	−1.60801e15	−0.438886
$249$	4.96081e15	1.31904
$250$	2.05381e15	0.532048
$251$	5.30330e15	1.33865	0.669325	−	0.742970i	$-0.266583\pi$
$251$	5.30330e15	1.33865	0.669325	+	0.742970i	$0.266583\pi$
$252$	0	0
$253$	−3.23416e15	−0.775314
$254$	−6.57747e13	−0.0153688
$255$	−8.51568e14	−0.193958
$256$	2.81475e14	0.0625000
$257$	−2.15610e15	−0.466771	−0.233385	−	0.972384i	$-0.574980\pi$
$257$	−2.15610e15	−0.466771	−0.233385	+	0.972384i	$0.574980\pi$
$258$	7.10161e15	1.49909
$259$	0	0
$260$	3.23927e14	0.0650310
$261$	−1.56887e15	−0.307203
$262$	3.95124e15	0.754701
$263$	5.76133e15	1.07352	0.536761	−	0.843734i	$-0.319648\pi$
$263$	5.76133e15	1.07352	0.536761	+	0.843734i	$0.319648\pi$
$264$	1.67803e15	0.305053
$265$	−3.17388e15	−0.562979
$266$	0	0
$267$	−4.15857e15	−0.702459
$268$	−1.69750e15	−0.279855
$269$	8.47718e15	1.36415	0.682074	−	0.731283i	$-0.261078\pi$
$269$	8.47718e15	1.36415	0.682074	+	0.731283i	$0.261078\pi$
$270$	1.31408e15	0.206423
$271$	−8.48599e14	−0.130137	−0.0650687	−	0.997881i	$-0.520727\pi$
$271$	−8.48599e14	−0.130137	−0.0650687	+	0.997881i	$0.520727\pi$
$272$	−6.66236e14	−0.0997540
$273$	0	0
$274$	8.47055e15	1.20930
$275$	4.34799e15	0.606214
$276$	4.61734e15	0.628757
$277$	6.95041e15	0.924468	0.462234	−	0.886758i	$-0.347048\pi$
$277$	6.95041e15	0.924468	0.462234	+	0.886758i	$0.347048\pi$
$278$	1.06422e16	1.38274
$279$	3.90642e15	0.495851
$280$	0	0
$281$	−1.13665e15	−0.137732	−0.0688661	−	0.997626i	$-0.521938\pi$
$281$	−1.13665e15	−0.137732	−0.0688661	+	0.997626i	$0.521938\pi$
$282$	−7.71486e15	−0.913501
$283$	−1.09322e16	−1.26502	−0.632508	−	0.774554i	$-0.717974\pi$
$283$	−1.09322e16	−1.26502	−0.632508	+	0.774554i	$0.717974\pi$
$284$	−2.61370e15	−0.295588
$285$	9.65483e14	0.106722
$286$	1.51083e15	0.163244
$287$	0	0
$288$	−6.83803e14	−0.0706122
$289$	−8.32763e15	−0.840786
$290$	2.26351e15	0.223458
$291$	−1.16579e16	−1.12542
$292$	2.40024e15	0.226603
$293$	−1.63957e15	−0.151388	−0.0756940	−	0.997131i	$-0.524117\pi$
$293$	−1.63957e15	−0.151388	−0.0756940	+	0.997131i	$0.524117\pi$
$294$	0	0
$295$	6.60078e15	0.583112
$296$	4.99341e15	0.431520
$297$	6.12903e15	0.518173
$298$	−1.09374e16	−0.904705
$299$	4.15727e15	0.336469
$300$	−6.20754e15	−0.491622
$301$	0	0
$302$	−1.72551e16	−1.30880
$303$	1.96663e16	1.45998
$304$	7.55359e14	0.0548877
$305$	9.30079e14	0.0661563
$306$	1.61852e15	0.112702
$307$	5.69931e15	0.388528	0.194264	−	0.980949i	$-0.437768\pi$
$307$	5.69931e15	0.388528	0.194264	+	0.980949i	$0.437768\pi$
$308$	0	0
$309$	−2.64205e16	−1.72668
$310$	−5.63603e15	−0.360680
$311$	−9.31104e15	−0.583520	−0.291760	−	0.956492i	$-0.594241\pi$
$311$	−9.31104e15	−0.583520	−0.291760	+	0.956492i	$0.594241\pi$
$312$	−2.15699e15	−0.132386
$313$	−5.64382e15	−0.339262	−0.169631	−	0.985508i	$-0.554258\pi$
$313$	−5.64382e15	−0.339262	−0.169631	+	0.985508i	$0.554258\pi$
$314$	3.39724e15	0.200024
$315$	0	0
$316$	1.00715e16	0.569019
$317$	−1.22117e16	−0.675914	−0.337957	−	0.941162i	$-0.609736\pi$
$317$	−1.22117e16	−0.675914	−0.337957	+	0.941162i	$0.609736\pi$
$318$	2.11344e16	1.14608
$319$	1.05573e16	0.560936
$320$	9.86564e14	0.0513630
$321$	−2.16014e16	−1.10204
$322$	0	0
$323$	−1.78789e15	−0.0876043
$324$	−1.29091e16	−0.619944
$325$	−5.58902e15	−0.263084
$326$	−1.61181e16	−0.743703
$327$	−2.37973e16	−1.07639
$328$	1.10911e16	0.491808
$329$	0	0
$330$	5.88147e15	0.250695
$331$	1.32873e16	0.555335	0.277667	−	0.960677i	$-0.410439\pi$
$331$	1.32873e16	0.555335	0.277667	+	0.960677i	$0.410439\pi$
$332$	1.36034e16	0.557506
$333$	−1.21308e16	−0.487529
$334$	3.33729e14	0.0131535
$335$	−5.94968e15	−0.229987
$336$	0	0
$337$	2.83215e16	1.05323	0.526614	−	0.850105i	$-0.323461\pi$
$337$	2.83215e16	1.05323	0.526614	+	0.850105i	$0.323461\pi$
$338$	1.74419e16	0.636262
$339$	7.27264e15	0.260252
$340$	−2.33514e15	−0.0819786
$341$	−2.62871e16	−0.905398
$342$	−1.83504e15	−0.0620118
$343$	0	0
$344$	1.94738e16	0.633609
$345$	1.61837e16	0.516717
$346$	−1.68403e16	−0.527662
$347$	4.84159e16	1.48883	0.744417	−	0.667715i	$-0.232727\pi$
$347$	4.84159e16	1.48883	0.744417	+	0.667715i	$0.232727\pi$
$348$	−1.50724e16	−0.454902
$349$	−3.92608e16	−1.16304	−0.581519	−	0.813533i	$-0.697541\pi$
$349$	−3.92608e16	−1.16304	−0.581519	+	0.813533i	$0.697541\pi$
$350$	0	0
$351$	−7.87840e15	−0.224875
$352$	4.60145e15	0.128934
$353$	−2.19079e16	−0.602649	−0.301325	−	0.953522i	$-0.597429\pi$
$353$	−2.19079e16	−0.602649	−0.301325	+	0.953522i	$0.597429\pi$
$354$	−4.39537e16	−1.18706
$355$	−9.16096e15	−0.242916
$356$	−1.14035e16	−0.296902
$357$	0	0
$358$	2.31725e16	0.581746
$359$	5.03499e16	1.24132	0.620662	−	0.784078i	$-0.286864\pi$
$359$	5.03499e16	1.24132	0.620662	+	0.784078i	$0.286864\pi$
$360$	−2.39671e15	−0.0580297
$361$	−4.00259e16	−0.951797
$362$	4.32920e16	1.01112
$363$	−2.41350e16	−0.553673
$364$	0	0
$365$	8.41279e15	0.186224
$366$	−6.19327e15	−0.134677
$367$	−8.61409e16	−1.84026	−0.920132	−	0.391609i	$-0.871919\pi$
$367$	−8.61409e16	−1.84026	−0.920132	+	0.391609i	$0.871919\pi$
$368$	1.26615e16	0.265751
$369$	−2.69443e16	−0.555643
$370$	1.75018e16	0.354626
$371$	0	0
$372$	3.75296e16	0.734251
$373$	3.30852e16	0.636102	0.318051	−	0.948074i	$-0.396972\pi$
$373$	3.30852e16	0.636102	0.318051	+	0.948074i	$0.396972\pi$
$374$	−1.08914e16	−0.205787
$375$	−4.79344e16	−0.890110
$376$	−2.11554e16	−0.386101
$377$	−1.35706e16	−0.243434
$378$	0	0
$379$	2.13699e16	0.370380	0.185190	−	0.982703i	$-0.440710\pi$
$379$	2.13699e16	0.370380	0.185190	+	0.982703i	$0.440710\pi$
$380$	2.64752e15	0.0451071
$381$	1.53513e15	0.0257118
$382$	4.86631e16	0.801287
$383$	−2.22886e16	−0.360819	−0.180410	−	0.983592i	$-0.557742\pi$
$383$	−2.22886e16	−0.360819	−0.180410	+	0.983592i	$0.557742\pi$
$384$	−6.56940e15	−0.104562
$385$	0	0
$386$	4.11010e14	0.00632463
$387$	−4.73088e16	−0.715848
$388$	−3.19679e16	−0.475672
$389$	−2.18271e16	−0.319392	−0.159696	−	0.987166i	$-0.551051\pi$
$389$	−2.18271e16	−0.319392	−0.159696	+	0.987166i	$0.551051\pi$
$390$	−7.56019e15	−0.108796
$391$	−2.99691e16	−0.424156
$392$	0	0
$393$	−9.22188e16	−1.26261
$394$	−2.68615e16	−0.361747
$395$	3.53003e16	0.467625
$396$	−1.11786e16	−0.145669
$397$	2.63258e16	0.337477	0.168738	−	0.985661i	$-0.446031\pi$
$397$	2.63258e16	0.337477	0.168738	+	0.985661i	$0.446031\pi$
$398$	−9.64924e16	−1.21690
$399$	0	0
$400$	−1.70221e16	−0.207789
$401$	−1.60087e17	−1.92272	−0.961362	−	0.275287i	$-0.911227\pi$
$401$	−1.60087e17	−1.92272	−0.961362	+	0.275287i	$0.911227\pi$
$402$	3.96182e16	0.468193
$403$	3.37901e16	0.392923
$404$	5.39284e16	0.617076
$405$	−4.52460e16	−0.509475
$406$	0	0
$407$	8.16304e16	0.890202
$408$	1.55494e16	0.166887
$409$	1.96358e16	0.207418	0.103709	−	0.994608i	$-0.466929\pi$
$409$	1.96358e16	0.207418	0.103709	+	0.994608i	$0.466929\pi$
$410$	3.88742e16	0.404172
$411$	−1.97696e17	−2.02314
$412$	−7.24495e16	−0.729799
$413$	0	0
$414$	−3.07593e16	−0.300244
$415$	4.76796e16	0.458163
$416$	−5.91482e15	−0.0559545
$417$	−2.48380e17	−2.31330
$418$	1.23483e16	0.113230
$419$	1.22382e17	1.10491	0.552454	−	0.833544i	$-0.313692\pi$
$419$	1.22382e17	1.10491	0.552454	+	0.833544i	$0.313692\pi$
$420$	0	0
$421$	−2.43087e16	−0.212778	−0.106389	−	0.994325i	$-0.533929\pi$
$421$	−2.43087e16	−0.212778	−0.106389	+	0.994325i	$0.533929\pi$
$422$	6.07707e16	0.523798
$423$	5.13941e16	0.436215
$424$	5.79542e16	0.484403
$425$	4.02904e16	0.331645
$426$	6.10016e16	0.494514
$427$	0	0
$428$	−5.92347e16	−0.465791
$429$	−3.52617e16	−0.273105
$430$	6.82553e16	0.520705
$431$	1.22888e17	0.923433	0.461717	−	0.887027i	$-0.347234\pi$
$431$	1.22888e17	0.923433	0.461717	+	0.887027i	$0.347234\pi$
$432$	−2.39948e16	−0.177612
$433$	−1.41055e17	−1.02853	−0.514267	−	0.857630i	$-0.671936\pi$
$433$	−1.41055e17	−1.02853	−0.514267	+	0.857630i	$0.671936\pi$
$434$	0	0
$435$	−5.28285e16	−0.373842
$436$	−6.52563e16	−0.454947
$437$	3.39781e16	0.233383
$438$	−5.60197e16	−0.379104
$439$	1.46988e17	0.980083	0.490042	−	0.871699i	$-0.336982\pi$
$439$	1.46988e17	0.980083	0.490042	+	0.871699i	$0.336982\pi$
$440$	1.61280e16	0.105959
$441$	0	0
$442$	1.40001e16	0.0893070
$443$	1.86887e17	1.17477	0.587386	−	0.809307i	$-0.300157\pi$
$443$	1.86887e17	1.17477	0.587386	+	0.809307i	$0.300157\pi$
$444$	−1.16542e17	−0.721927
$445$	−3.99690e16	−0.243996
$446$	−3.89087e16	−0.234083
$447$	2.55269e17	1.51356
$448$	0	0
$449$	2.15477e17	1.24108	0.620540	−	0.784175i	$-0.286913\pi$
$449$	2.15477e17	1.24108	0.620540	+	0.784175i	$0.286913\pi$
$450$	4.13528e16	0.234760
$451$	1.81314e17	1.01457
$452$	1.99428e16	0.109998
$453$	4.02719e17	2.18960
$454$	1.78315e17	0.955709
$455$	0	0
$456$	−1.76295e16	−0.0918264
$457$	−3.83908e16	−0.197139	−0.0985694	−	0.995130i	$-0.531427\pi$
$457$	−3.83908e16	−0.197139	−0.0985694	+	0.995130i	$0.531427\pi$
$458$	−7.26471e16	−0.367784
$459$	5.67943e16	0.283480
$460$	4.43784e16	0.218396
$461$	3.15284e17	1.52984	0.764921	−	0.644124i	$-0.222778\pi$
$461$	3.15284e17	1.52984	0.764921	+	0.644124i	$0.222778\pi$
$462$	0	0
$463$	−2.28642e17	−1.07865	−0.539323	−	0.842099i	$-0.681320\pi$
$463$	−2.28642e17	−1.07865	−0.539323	+	0.842099i	$0.681320\pi$
$464$	−4.13311e16	−0.192269
$465$	1.31540e17	0.603413
$466$	1.30553e17	0.590581
$467$	2.13021e17	0.950306	0.475153	−	0.879903i	$-0.342393\pi$
$467$	2.13021e17	0.950306	0.475153	+	0.879903i	$0.342393\pi$
$468$	1.43692e16	0.0632171
$469$	0	0
$470$	−7.41494e16	−0.317301
$471$	−7.92887e16	−0.334638
$472$	−1.20529e17	−0.501726
$473$	3.18351e17	1.30710
$474$	−2.35060e17	−0.951962
$475$	−4.56801e16	−0.182481
$476$	0	0
$477$	−1.40791e17	−0.547276
$478$	2.28895e17	0.877716
$479$	3.15666e16	0.119412	0.0597058	−	0.998216i	$-0.480984\pi$
$479$	3.15666e16	0.119412	0.0597058	+	0.998216i	$0.480984\pi$
$480$	−2.30256e16	−0.0859296
$481$	−1.04930e17	−0.386328
$482$	1.16249e17	0.422262
$483$	0	0
$484$	−6.61821e16	−0.234016
$485$	−1.12047e17	−0.390911
$486$	1.55355e17	0.534796
$487$	5.42988e17	1.84439	0.922193	−	0.386730i	$-0.126395\pi$
$487$	5.42988e17	1.84439	0.922193	+	0.386730i	$0.126395\pi$
$488$	−1.69830e16	−0.0569227
$489$	3.76184e17	1.24421
$490$	0	0
$491$	2.87085e17	0.924658	0.462329	−	0.886708i	$-0.347014\pi$
$491$	2.87085e17	0.924658	0.462329	+	0.886708i	$0.347014\pi$
$492$	−2.58858e17	−0.822789
$493$	9.78285e16	0.306874
$494$	−1.58729e16	−0.0491394
$495$	−3.91806e16	−0.119712
$496$	1.02912e17	0.310339
$497$	0	0
$498$	−3.17492e17	−0.932701
$499$	5.29425e15	0.0153515	0.00767575	−	0.999971i	$-0.497557\pi$
$499$	5.29425e15	0.0153515	0.00767575	+	0.999971i	$0.497557\pi$
$500$	−1.31444e17	−0.376215
$501$	−7.78897e15	−0.0220057
$502$	−3.39411e17	−0.946569
$503$	9.65557e16	0.265819	0.132909	−	0.991128i	$-0.457568\pi$
$503$	9.65557e16	0.265819	0.132909	+	0.991128i	$0.457568\pi$
$504$	0	0
$505$	1.89018e17	0.507118
$506$	2.06986e17	0.548230
$507$	−4.07081e17	−1.06446
$508$	4.20958e15	0.0108674
$509$	5.40870e17	1.37857	0.689283	−	0.724492i	$-0.257926\pi$
$509$	5.40870e17	1.37857	0.689283	+	0.724492i	$0.257926\pi$
$510$	5.45003e16	0.137149
$511$	0	0
$512$	−1.80144e16	−0.0441942
$513$	−6.43917e16	−0.155979
$514$	1.37990e17	0.330057
$515$	−2.53934e17	−0.599755
$516$	−4.54503e17	−1.06002
$517$	−3.45842e17	−0.796506
$518$	0	0
$519$	3.93040e17	0.882772
$520$	−2.07313e16	−0.0459839
$521$	1.30319e17	0.285471	0.142736	−	0.989761i	$-0.454410\pi$
$521$	1.30319e17	0.285471	0.142736	+	0.989761i	$0.454410\pi$
$522$	1.00408e17	0.217225
$523$	8.68609e17	1.85594	0.927969	−	0.372658i	$-0.121554\pi$
$523$	8.68609e17	1.85594	0.927969	+	0.372658i	$0.121554\pi$
$524$	−2.52879e17	−0.533654
$525$	0	0
$526$	−3.68725e17	−0.759094
$527$	−2.43588e17	−0.495321
$528$	−1.07394e17	−0.215705
$529$	6.55140e16	0.129979
$530$	2.03128e17	0.398086
$531$	2.92807e17	0.566848
$532$	0	0
$533$	−2.33065e17	−0.440302
$534$	2.66148e17	0.496713
$535$	−2.07616e17	−0.382791
$536$	1.08640e17	0.197887
$537$	−5.40828e17	−0.973253
$538$	−5.42540e17	−0.964599
$539$	0	0
$540$	−8.41011e16	−0.145963
$541$	−5.98300e17	−1.02598	−0.512988	−	0.858396i	$-0.671461\pi$
$541$	−5.98300e17	−1.02598	−0.512988	+	0.858396i	$0.671461\pi$
$542$	5.43103e16	0.0920210
$543$	−1.01040e18	−1.69159
$544$	4.26391e16	0.0705367
$545$	−2.28722e17	−0.373879
$546$	0	0
$547$	6.94479e17	1.10851	0.554257	−	0.832345i	$-0.313002\pi$
$547$	6.94479e17	1.10851	0.554257	+	0.832345i	$0.313002\pi$
$548$	−5.42115e17	−0.855102
$549$	4.12577e16	0.0643110
$550$	−2.78271e17	−0.428658
$551$	−1.10915e17	−0.168852
$552$	−2.95510e17	−0.444598
$553$	0	0
$554$	−4.44826e17	−0.653698
$555$	−4.08477e17	−0.593285
$556$	−6.81099e17	−0.977742
$557$	8.64902e17	1.22718	0.613590	−	0.789625i	$-0.289725\pi$
$557$	8.64902e17	1.22718	0.613590	+	0.789625i	$0.289725\pi$
$558$	−2.50011e17	−0.350620
$559$	−4.09216e17	−0.567252
$560$	0	0
$561$	2.54196e17	0.344279
$562$	7.27455e16	0.0973913
$563$	1.20946e17	0.160061	0.0800307	−	0.996792i	$-0.474498\pi$
$563$	1.20946e17	0.160061	0.0800307	+	0.996792i	$0.474498\pi$
$564$	4.93751e17	0.645942
$565$	6.98991e16	0.0903976
$566$	6.99661e17	0.894501
$567$	0	0
$568$	1.67277e17	0.209012
$569$	−6.27686e17	−0.775377	−0.387688	−	0.921791i	$-0.626726\pi$
$569$	−6.27686e17	−0.775377	−0.387688	+	0.921791i	$0.626726\pi$
$570$	−6.17909e16	−0.0754637
$571$	−1.23713e18	−1.49376	−0.746882	−	0.664957i	$-0.768450\pi$
$571$	−1.23713e18	−1.49376	−0.746882	+	0.664957i	$0.768450\pi$
$572$	−9.66934e16	−0.115431
$573$	−1.13576e18	−1.34054
$574$	0	0
$575$	−7.65702e17	−0.883525
$576$	4.37634e16	0.0499304
$577$	8.44740e17	0.952972	0.476486	−	0.879182i	$-0.341910\pi$
$577$	8.44740e17	0.952972	0.476486	+	0.879182i	$0.341910\pi$
$578$	5.32969e17	0.594526
$579$	−9.59264e15	−0.0105810
$580$	−1.44865e17	−0.158009
$581$	0	0
$582$	7.46105e17	0.795794
$583$	9.47414e17	0.999296
$584$	−1.53615e17	−0.160233
$585$	5.03638e16	0.0519523
$586$	1.04933e17	0.107047
$587$	−9.19950e17	−0.928146	−0.464073	−	0.885797i	$-0.653613\pi$
$587$	−9.19950e17	−0.928146	−0.464073	+	0.885797i	$0.653613\pi$
$588$	0	0
$589$	2.76173e17	0.272541
$590$	−4.22450e17	−0.412323
$591$	6.26926e17	0.605198
$592$	−3.19578e17	−0.305131
$593$	−7.31450e16	−0.0690763	−0.0345381	−	0.999403i	$-0.510996\pi$
$593$	−7.31450e16	−0.0690763	−0.0345381	+	0.999403i	$0.510996\pi$
$594$	−3.92258e17	−0.366403
$595$	0	0
$596$	6.99991e17	0.639723
$597$	2.25205e18	2.03585
$598$	−2.66065e17	−0.237920
$599$	−3.98616e17	−0.352599	−0.176299	−	0.984337i	$-0.556413\pi$
$599$	−3.98616e17	−0.352599	−0.176299	+	0.984337i	$0.556413\pi$
$600$	3.97282e17	0.347629
$601$	2.02331e18	1.75137	0.875686	−	0.482882i	$-0.160410\pi$
$601$	2.02331e18	1.75137	0.875686	+	0.482882i	$0.160410\pi$
$602$	0	0
$603$	−2.63924e17	−0.223572
$604$	1.10432e18	0.925458
$605$	−2.31967e17	−0.192316
$606$	−1.25864e18	−1.03236
$607$	−1.82227e18	−1.47872	−0.739361	−	0.673309i	$-0.764872\pi$
$607$	−1.82227e18	−1.47872	−0.739361	+	0.673309i	$0.764872\pi$
$608$	−4.83430e16	−0.0388115
$609$	0	0
$610$	−5.95251e16	−0.0467795
$611$	4.44554e17	0.345666
$612$	−1.03586e17	−0.0796920
$613$	−1.78676e18	−1.36011	−0.680054	−	0.733162i	$-0.738044\pi$
$613$	−1.78676e18	−1.36011	−0.680054	+	0.733162i	$0.738044\pi$
$614$	−3.64756e17	−0.274731
$615$	−9.07292e17	−0.676175
$616$	0	0
$617$	8.80000e17	0.642139	0.321070	−	0.947056i	$-0.395958\pi$
$617$	8.80000e17	0.642139	0.321070	+	0.947056i	$0.395958\pi$
$618$	1.69091e18	1.22094
$619$	−9.69979e16	−0.0693064	−0.0346532	−	0.999399i	$-0.511033\pi$
$619$	−9.69979e16	−0.0693064	−0.0346532	+	0.999399i	$0.511033\pi$
$620$	3.60706e17	0.255039
$621$	−1.07935e18	−0.755209
$622$	5.95906e17	0.412611
$623$	0	0
$624$	1.38047e17	0.0936112
$625$	7.77813e17	0.521981
$626$	3.61205e17	0.239895
$627$	−2.88200e17	−0.189433
$628$	−2.17423e17	−0.141439
$629$	7.56424e17	0.487008
$630$	0	0
$631$	−8.85605e15	−0.00558533	−0.00279267	−	0.999996i	$-0.500889\pi$
$631$	−8.85605e15	−0.00558533	−0.00279267	+	0.999996i	$0.500889\pi$
$632$	−6.44575e17	−0.402358
$633$	−1.41834e18	−0.876307
$634$	7.81550e17	0.477943
$635$	1.47545e16	0.00893089
$636$	−1.35260e18	−0.810400
$637$	0	0
$638$	−6.75666e17	−0.396641
$639$	−4.06375e17	−0.236141
$640$	−6.31401e16	−0.0363191
$641$	6.15388e17	0.350406	0.175203	−	0.984532i	$-0.443942\pi$
$641$	6.15388e17	0.350406	0.175203	+	0.984532i	$0.443942\pi$
$642$	1.38249e18	0.779263
$643$	−9.48803e17	−0.529425	−0.264713	−	0.964327i	$-0.585277\pi$
$643$	−9.48803e17	−0.529425	−0.264713	+	0.964327i	$0.585277\pi$
$644$	0	0
$645$	−1.59302e18	−0.871132
$646$	1.14425e17	0.0619456
$647$	1.81996e17	0.0975404	0.0487702	−	0.998810i	$-0.484470\pi$
$647$	1.81996e17	0.0975404	0.0487702	+	0.998810i	$0.484470\pi$
$648$	8.26181e17	0.438367
$649$	−1.97036e18	−1.03503
$650$	3.57697e17	0.186028
$651$	0	0
$652$	1.03156e18	0.525878
$653$	2.76956e18	1.39789	0.698947	−	0.715173i	$-0.253652\pi$
$653$	2.76956e18	1.39789	0.698947	+	0.715173i	$0.253652\pi$
$654$	1.52303e18	0.761120
$655$	−8.86337e17	−0.438561
$656$	−7.09833e17	−0.347761
$657$	3.73186e17	0.181030
$658$	0	0
$659$	−1.98995e18	−0.946427	−0.473213	−	0.880948i	$-0.656906\pi$
$659$	−1.98995e18	−0.946427	−0.473213	+	0.880948i	$0.656906\pi$
$660$	−3.76414e17	−0.177268
$661$	−1.16369e18	−0.542659	−0.271330	−	0.962486i	$-0.587463\pi$
$661$	−1.16369e18	−0.542659	−0.271330	+	0.962486i	$0.587463\pi$
$662$	−8.50387e17	−0.392681
$663$	−3.26750e17	−0.149409
$664$	−8.70617e17	−0.394216
$665$	0	0
$666$	7.76368e17	0.344735
$667$	−1.85919e18	−0.817533
$668$	−2.13587e16	−0.00930095
$669$	9.08098e17	0.391618
$670$	3.80780e17	0.162625
$671$	−2.77632e17	−0.117428
$672$	0	0
$673$	1.44542e18	0.599650	0.299825	−	0.953994i	$-0.403072\pi$
$673$	1.44542e18	0.599650	0.299825	+	0.953994i	$0.403072\pi$
$674$	−1.81258e18	−0.744744
$675$	1.45108e18	0.590494
$676$	−1.11628e18	−0.449905
$677$	3.81636e18	1.52343	0.761716	−	0.647911i	$-0.224357\pi$
$677$	3.81636e18	1.52343	0.761716	+	0.647911i	$0.224357\pi$
$678$	−4.65449e17	−0.184026
$679$	0	0
$680$	1.49449e17	0.0579676
$681$	−4.16173e18	−1.59889
$682$	1.68238e18	0.640213
$683$	2.28697e17	0.0862038	0.0431019	−	0.999071i	$-0.486276\pi$
$683$	2.28697e17	0.0862038	0.0431019	+	0.999071i	$0.486276\pi$
$684$	1.17442e17	0.0438490
$685$	−1.90010e18	−0.702729
$686$	0	0
$687$	1.69553e18	0.615298
$688$	−1.24632e18	−0.448029
$689$	−1.21783e18	−0.433672
$690$	−1.03576e18	−0.365374
$691$	−3.30595e18	−1.15528	−0.577642	−	0.816290i	$-0.696027\pi$
$691$	−3.30595e18	−1.15528	−0.577642	+	0.816290i	$0.696027\pi$
$692$	1.07778e18	0.373113
$693$	0	0
$694$	−3.09862e18	−1.05276
$695$	−2.38724e18	−0.803516
$696$	9.64635e17	0.321664
$697$	1.68014e18	0.555049
$698$	2.51269e18	0.822391
$699$	−3.04701e18	−0.988035
$700$	0	0
$701$	−1.97078e18	−0.627293	−0.313647	−	0.949540i	$-0.601551\pi$
$701$	−1.97078e18	−0.627293	−0.313647	+	0.949540i	$0.601551\pi$
$702$	5.04218e17	0.159011
$703$	−8.57611e17	−0.267967
$704$	−2.94493e17	−0.0911701
$705$	1.73059e18	0.530841
$706$	1.40210e18	0.426137
$707$	0	0
$708$	2.81304e18	0.839381
$709$	3.81745e18	1.12868	0.564342	−	0.825541i	$-0.309130\pi$
$709$	3.81745e18	1.12868	0.564342	+	0.825541i	$0.309130\pi$
$710$	5.86301e17	0.171768
$711$	1.56590e18	0.454582
$712$	7.29824e17	0.209941
$713$	4.62929e18	1.31957
$714$	0	0
$715$	−3.38908e17	−0.0948622
$716$	−1.48304e18	−0.411357
$717$	−5.34221e18	−1.46841
$718$	−3.22240e18	−0.877748
$719$	3.61096e18	0.974730	0.487365	−	0.873198i	$-0.337958\pi$
$719$	3.61096e18	0.974730	0.487365	+	0.873198i	$0.337958\pi$
$720$	1.53390e17	0.0410332
$721$	0	0
$722$	2.56166e18	0.673022
$723$	−2.71315e18	−0.706439
$724$	−2.77069e18	−0.714969
$725$	2.49949e18	0.639225
$726$	1.54464e18	0.391506
$727$	−3.60755e18	−0.906230	−0.453115	−	0.891452i	$-0.649687\pi$
$727$	−3.60755e18	−0.906230	−0.453115	+	0.891452i	$0.649687\pi$
$728$	0	0
$729$	1.39886e18	0.345181
$730$	−5.38419e17	−0.131681
$731$	2.94998e18	0.715083
$732$	3.96369e17	0.0952310
$733$	−1.09237e18	−0.260133	−0.130067	−	0.991505i	$-0.541519\pi$
$733$	−1.09237e18	−0.260133	−0.130067	+	0.991505i	$0.541519\pi$
$734$	5.51302e18	1.30126
$735$	0	0
$736$	−8.10337e17	−0.187914
$737$	1.77600e18	0.408230
$738$	1.72444e18	0.392899
$739$	5.28696e18	1.19404	0.597018	−	0.802228i	$-0.296352\pi$
$739$	5.28696e18	1.19404	0.597018	+	0.802228i	$0.296352\pi$
$740$	−1.12011e18	−0.250759
$741$	3.70460e17	0.0822096
$742$	0	0
$743$	−1.06272e18	−0.231736	−0.115868	−	0.993265i	$-0.536965\pi$
$743$	−1.06272e18	−0.231736	−0.115868	+	0.993265i	$0.536965\pi$
$744$	−2.40189e18	−0.519194
$745$	2.45345e18	0.525729
$746$	−2.11745e18	−0.449792
$747$	2.11504e18	0.445384
$748$	6.97049e17	0.145513
$749$	0	0
$750$	3.06780e18	0.629403
$751$	8.96376e17	0.182319	0.0911593	−	0.995836i	$-0.470943\pi$
$751$	8.96376e17	0.182319	0.0911593	+	0.995836i	$0.470943\pi$
$752$	1.35395e18	0.273015
$753$	7.92158e18	1.58360
$754$	8.68519e17	0.172134
$755$	3.87063e18	0.760549
$756$	0	0
$757$	−6.71607e18	−1.29716	−0.648578	−	0.761148i	$-0.724636\pi$
$757$	−6.71607e18	−1.29716	−0.648578	+	0.761148i	$0.724636\pi$
$758$	−1.36767e18	−0.261898
$759$	−4.83089e18	−0.917182
$760$	−1.69441e17	−0.0318956
$761$	−7.13875e18	−1.33236	−0.666181	−	0.745790i	$-0.732072\pi$
$761$	−7.13875e18	−1.33236	−0.666181	+	0.745790i	$0.732072\pi$
$762$	−9.82481e16	−0.0181810
$763$	0	0
$764$	−3.11444e18	−0.566595
$765$	−3.63065e17	−0.0654915
$766$	1.42647e18	0.255138
$767$	2.53275e18	0.449182
$768$	4.20441e17	0.0739363
$769$	9.57731e18	1.67002	0.835011	−	0.550233i	$-0.185461\pi$
$769$	9.57731e18	1.67002	0.835011	+	0.550233i	$0.185461\pi$
$770$	0	0
$771$	−3.22059e18	−0.552181
$772$	−2.63046e16	−0.00447219
$773$	2.15650e18	0.363565	0.181783	−	0.983339i	$-0.441813\pi$
$773$	2.15650e18	0.363565	0.181783	+	0.983339i	$0.441813\pi$
$774$	3.02776e18	0.506181
$775$	−6.22360e18	−1.03176
$776$	2.04595e18	0.336351
$777$	0	0
$778$	1.39694e18	0.225844
$779$	−1.90489e18	−0.305405
$780$	4.83852e17	0.0769304
$781$	2.73458e18	0.431180
$782$	1.91802e18	0.299923
$783$	3.52333e18	0.546389
$784$	0	0
$785$	−7.62063e17	−0.116235
$786$	5.90200e18	0.892797
$787$	−2.82485e18	−0.423798	−0.211899	−	0.977292i	$-0.567965\pi$
$787$	−2.82485e18	−0.423798	−0.211899	+	0.977292i	$0.567965\pi$
$788$	1.71914e18	0.255794
$789$	8.60575e18	1.26995
$790$	−2.25922e18	−0.330661
$791$	0	0
$792$	7.15428e17	0.103004
$793$	3.56875e17	0.0509613
$794$	−1.68485e18	−0.238632
$795$	−4.74085e18	−0.665993
$796$	6.17551e18	0.860475
$797$	8.37611e18	1.15761	0.578806	−	0.815465i	$-0.303519\pi$
$797$	8.37611e18	1.15761	0.578806	+	0.815465i	$0.303519\pi$
$798$	0	0
$799$	−3.20472e18	−0.435749
$800$	1.08942e18	0.146929
$801$	−1.77300e18	−0.237191
$802$	1.02456e19	1.35957
$803$	−2.51125e18	−0.330551
$804$	−2.53556e18	−0.331062
$805$	0	0
$806$	−2.16257e18	−0.277838
$807$	1.26624e19	1.61376
$808$	−3.45141e18	−0.436338
$809$	−2.17794e18	−0.273137	−0.136569	−	0.990631i	$-0.543607\pi$
$809$	−2.17794e18	−0.273137	−0.136569	+	0.990631i	$0.543607\pi$
$810$	2.89575e18	0.360253
$811$	−1.05998e19	−1.30817	−0.654084	−	0.756422i	$-0.726946\pi$
$811$	−1.05998e19	−1.30817	−0.654084	+	0.756422i	$0.726946\pi$
$812$	0	0
$813$	−1.26756e18	−0.153950
$814$	−5.22435e18	−0.629468
$815$	3.61559e18	0.432170
$816$	−9.95162e17	−0.118007
$817$	−3.34460e18	−0.393461
$818$	−1.25669e18	−0.146667
$819$	0	0
$820$	−2.48795e18	−0.285793
$821$	1.03078e17	0.0117472	0.00587360	−	0.999983i	$-0.498130\pi$
$821$	1.03078e17	0.0117472	0.00587360	+	0.999983i	$0.498130\pi$
$822$	1.26525e19	1.43057
$823$	−1.05201e19	−1.18011	−0.590054	−	0.807363i	$-0.700894\pi$
$823$	−1.05201e19	−1.18011	−0.590054	+	0.807363i	$0.700894\pi$
$824$	4.63677e18	0.516046
$825$	6.49463e18	0.717140
$826$	0	0
$827$	1.20216e19	1.30670	0.653350	−	0.757056i	$-0.273363\pi$
$827$	1.20216e19	1.30670	0.653350	+	0.757056i	$0.273363\pi$
$828$	1.96860e18	0.212305
$829$	3.14511e18	0.336536	0.168268	−	0.985741i	$-0.446183\pi$
$829$	3.14511e18	0.336536	0.168268	+	0.985741i	$0.446183\pi$
$830$	−3.05149e18	−0.323970
$831$	1.03819e19	1.09363
$832$	3.78549e17	0.0395658
$833$	0	0
$834$	1.58963e19	1.63575
$835$	−7.48617e16	−0.00764359
$836$	−7.90294e17	−0.0800659
$837$	−8.77292e18	−0.881919
$838$	−7.83244e18	−0.781288
$839$	5.05894e18	0.500734	0.250367	−	0.968151i	$-0.419449\pi$
$839$	5.05894e18	0.500734	0.250367	+	0.968151i	$0.419449\pi$
$840$	0	0
$841$	−4.19166e18	−0.408519
$842$	1.55576e18	0.150457
$843$	−1.69782e18	−0.162934
$844$	−3.88933e18	−0.370381
$845$	−3.91255e18	−0.369736
$846$	−3.28922e18	−0.308451
$847$	0	0
$848$	−3.70907e18	−0.342525
$849$	−1.63295e19	−1.49649
$850$	−2.57859e18	−0.234509
$851$	−1.43755e19	−1.29742
$852$	−3.90410e18	−0.349674
$853$	−1.27122e19	−1.12993	−0.564967	−	0.825114i	$-0.691111\pi$
$853$	−1.27122e19	−1.12993	−0.564967	+	0.825114i	$0.691111\pi$
$854$	0	0
$855$	4.11633e17	0.0360355
$856$	3.79102e18	0.329364
$857$	1.98280e19	1.70964	0.854818	−	0.518928i	$-0.173669\pi$
$857$	1.98280e19	1.70964	0.854818	+	0.518928i	$0.173669\pi$
$858$	2.25675e18	0.193115
$859$	−6.32210e18	−0.536915	−0.268458	−	0.963292i	$-0.586514\pi$
$859$	−6.32210e18	−0.536915	−0.268458	+	0.963292i	$0.586514\pi$
$860$	−4.36834e18	−0.368194
$861$	0	0
$862$	−7.86480e18	−0.652966
$863$	−6.03231e18	−0.497065	−0.248532	−	0.968624i	$-0.579948\pi$
$863$	−6.03231e18	−0.497065	−0.248532	+	0.968624i	$0.579948\pi$
$864$	1.53566e18	0.125591
$865$	3.77760e18	0.306628
$866$	9.02754e18	0.727283
$867$	−1.24391e19	−0.994634
$868$	0	0
$869$	−1.05373e19	−0.830041
$870$	3.38102e18	0.264346
$871$	−2.28292e18	−0.177163
$872$	4.17641e18	0.321696
$873$	−4.97033e18	−0.380008
$874$	−2.17460e18	−0.165027
$875$	0	0
$876$	3.58526e18	0.268067
$877$	−3.18045e18	−0.236043	−0.118021	−	0.993011i	$-0.537655\pi$
$877$	−3.18045e18	−0.236043	−0.118021	+	0.993011i	$0.537655\pi$
$878$	−9.40724e18	−0.693024
$879$	−2.44904e18	−0.179089
$880$	−1.03219e18	−0.0749243
$881$	−2.33099e19	−1.67956	−0.839782	−	0.542924i	$-0.817317\pi$
$881$	−2.33099e19	−1.67956	−0.839782	+	0.542924i	$0.817317\pi$
$882$	0	0
$883$	−1.95630e18	−0.138896	−0.0694482	−	0.997586i	$-0.522124\pi$
$883$	−1.95630e18	−0.138896	−0.0694482	+	0.997586i	$0.522124\pi$
$884$	−8.96004e17	−0.0631496
$885$	9.85964e18	0.689810
$886$	−1.19607e19	−0.830690
$887$	−1.00657e19	−0.693967	−0.346983	−	0.937871i	$-0.612794\pi$
$887$	−1.00657e19	−0.693967	−0.346983	+	0.937871i	$0.612794\pi$
$888$	7.45869e18	0.510479
$889$	0	0
$890$	2.55802e18	0.172532
$891$	1.35061e19	0.904326
$892$	2.49016e18	0.165522
$893$	3.63342e18	0.239762
$894$	−1.63372e19	−1.07025
$895$	−5.19803e18	−0.338056
$896$	0	0
$897$	6.20974e18	0.398036
$898$	−1.37905e19	−0.877576
$899$	−1.51114e19	−0.954701
$900$	−2.64658e18	−0.166000
$901$	8.77916e18	0.546691
$902$	−1.16041e19	−0.717412
$903$	0	0
$904$	−1.27634e18	−0.0777806
$905$	−9.71121e18	−0.587567
$906$	−2.57740e19	−1.54828
$907$	−1.24818e19	−0.744439	−0.372220	−	0.928145i	$-0.621403\pi$
$907$	−1.24818e19	−0.744439	−0.372220	+	0.928145i	$0.621403\pi$
$908$	−1.14122e19	−0.675788
$909$	8.38471e18	0.492973
$910$	0	0
$911$	2.22935e19	1.29214	0.646068	−	0.763280i	$-0.276412\pi$
$911$	2.22935e19	1.29214	0.646068	+	0.763280i	$0.276412\pi$
$912$	1.12829e18	0.0649311
$913$	−1.42325e19	−0.813247
$914$	2.45701e18	0.139398
$915$	1.38927e18	0.0782616
$916$	4.64942e18	0.260063
$917$	0	0
$918$	−3.63483e18	−0.200451
$919$	2.49261e19	1.36491	0.682455	−	0.730927i	$-0.260912\pi$
$919$	2.49261e19	1.36491	0.682455	+	0.730927i	$0.260912\pi$
$920$	−2.84022e18	−0.154430
$921$	8.51310e18	0.459621
$922$	−2.01782e19	−1.08176
$923$	−3.51510e18	−0.187123
$924$	0	0
$925$	1.93264e19	1.01445
$926$	1.46331e19	0.762718
$927$	−1.12644e19	−0.583026
$928$	2.64519e18	0.135955
$929$	3.10241e19	1.58343	0.791713	−	0.610893i	$-0.209190\pi$
$929$	3.10241e19	1.58343	0.791713	+	0.610893i	$0.209190\pi$
$930$	−8.41858e18	−0.426678
$931$	0	0
$932$	−8.35542e18	−0.417604
$933$	−1.39080e19	−0.690293
$934$	−1.36334e19	−0.671968
$935$	2.44314e18	0.119584
$936$	−9.19629e17	−0.0447013
$937$	4.17037e17	0.0201311	0.0100655	−	0.999949i	$-0.496796\pi$
$937$	4.17037e17	0.0201311	0.0100655	+	0.999949i	$0.496796\pi$
$938$	0	0
$939$	−8.43023e18	−0.401340
$940$	4.74556e18	0.224366
$941$	−1.91878e18	−0.0900934	−0.0450467	−	0.998985i	$-0.514344\pi$
$941$	−1.91878e18	−0.0900934	−0.0450467	+	0.998985i	$0.514344\pi$
$942$	5.07448e18	0.236625
$943$	−3.19302e19	−1.47869
$944$	7.71382e18	0.354774
$945$	0	0
$946$	−2.03745e19	−0.924259
$947$	3.50323e19	1.57832	0.789158	−	0.614190i	$-0.210517\pi$
$947$	3.50323e19	1.57832	0.789158	+	0.614190i	$0.210517\pi$
$948$	1.50438e19	0.673139
$949$	3.22802e18	0.143452
$950$	2.92353e18	0.129034
$951$	−1.82407e19	−0.799593
$952$	0	0
$953$	3.82110e19	1.65228	0.826142	−	0.563462i	$-0.190531\pi$
$953$	3.82110e19	1.65228	0.826142	+	0.563462i	$0.190531\pi$
$954$	9.01064e18	0.386983
$955$	−1.09160e19	−0.465632
$956$	−1.46492e19	−0.620639
$957$	1.57695e19	0.663576
$958$	−2.02026e18	−0.0844368
$959$	0	0
$960$	1.47364e18	0.0607614
$961$	1.32091e19	0.540969
$962$	6.71551e18	0.273175
$963$	−9.20973e18	−0.372114
$964$	−7.43991e18	−0.298584
$965$	−9.21972e16	−0.00367528
$966$	0	0
$967$	3.71357e19	1.46056	0.730281	−	0.683147i	$-0.239389\pi$
$967$	3.71357e19	1.46056	0.730281	+	0.683147i	$0.239389\pi$
$968$	4.23566e18	0.165474
$969$	−2.67059e18	−0.103634
$970$	7.17100e18	0.276416
$971$	−1.19385e19	−0.457114	−0.228557	−	0.973531i	$-0.573401\pi$
$971$	−1.19385e19	−0.457114	−0.228557	+	0.973531i	$0.573401\pi$
$972$	−9.94270e18	−0.378158
$973$	0	0
$974$	−3.47512e19	−1.30418
$975$	−8.34836e18	−0.311223
$976$	1.08691e18	0.0402504
$977$	−8.06557e18	−0.296702	−0.148351	−	0.988935i	$-0.547397\pi$
$977$	−8.06557e18	−0.296702	−0.148351	+	0.988935i	$0.547397\pi$
$978$	−2.40758e19	−0.879787
$979$	1.19309e19	0.433098
$980$	0	0
$981$	−1.01460e19	−0.363450
$982$	−1.83735e19	−0.653832
$983$	2.65628e19	0.939021	0.469511	−	0.882927i	$-0.344430\pi$
$983$	2.65628e19	0.939021	0.469511	+	0.882927i	$0.344430\pi$
$984$	1.65669e19	0.581800
$985$	6.02554e18	0.210213
$986$	−6.26103e18	−0.216993
$987$	0	0
$988$	1.01586e18	0.0347468
$989$	−5.60631e19	−1.90503
$990$	2.50756e18	0.0846492
$991$	3.73728e19	1.25336	0.626682	−	0.779275i	$-0.284413\pi$
$991$	3.73728e19	1.25336	0.626682	+	0.779275i	$0.284413\pi$
$992$	−6.58640e18	−0.219443
$993$	1.98473e19	0.656950
$994$	0	0
$995$	2.16450e19	0.707145
$996$	2.03195e19	0.659519
$997$	1.49700e18	0.0482729	0.0241364	−	0.999709i	$-0.492316\pi$
$997$	1.49700e18	0.0482729	0.0241364	+	0.999709i	$0.492316\pi$
$998$	−3.38832e17	−0.0108551
$999$	2.72429e19	0.867117

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.14.a.h.1.4		4
7.2	even	3		14.14.c.b.11.1	yes	8
7.3	odd	6		98.14.c.o.79.4		8
7.4	even	3		14.14.c.b.9.1	✓	8
7.5	odd	6		98.14.c.o.67.4		8
7.6	odd	2		98.14.a.j.1.1		4
21.2	odd	6		126.14.g.b.109.2		8
21.11	odd	6		126.14.g.b.37.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.14.c.b.9.1	✓	8	7.4	even	3
14.14.c.b.11.1	yes	8	7.2	even	3
98.14.a.h.1.4		4	1.1	even	1	trivial
98.14.a.j.1.1		4	7.6	odd	2
98.14.c.o.67.4		8	7.5	odd	6
98.14.c.o.79.4		8	7.3	odd	6
126.14.g.b.37.2		8	21.11	odd	6
126.14.g.b.109.2		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)

\(f(q)\)	\(=\)	\(q-64.0000 q^{2} +1493.71 q^{3} +4096.00 q^{4} +14356.4 q^{5} -95597.3 q^{6} -262144. q^{8} +636841. q^{9} +O(q^{10})\)	\(q-64.0000 q^{2} +1493.71 q^{3} +4096.00 q^{4} +14356.4 q^{5} -95597.3 q^{6} -262144. q^{8} +636841. q^{9} -918809. q^{10} -4.28544e6 q^{11} +6.11823e6 q^{12} +5.50861e6 q^{13} +2.14443e7 q^{15} +1.67772e7 q^{16} -3.97108e7 q^{17} -4.07578e7 q^{18} +4.50229e7 q^{19} +5.88038e7 q^{20} +2.74268e8 q^{22} +7.54686e8 q^{23} -3.91567e8 q^{24} -1.01460e9 q^{25} -3.52551e8 q^{26} -1.43020e9 q^{27} -2.46353e9 q^{29} -1.37243e9 q^{30} +6.13406e9 q^{31} -1.07374e9 q^{32} -6.40119e9 q^{33} +2.54149e9 q^{34} +2.60850e9 q^{36} -1.90483e10 q^{37} -2.88147e9 q^{38} +8.22825e9 q^{39} -3.76344e9 q^{40} -4.23093e10 q^{41} -7.42867e10 q^{43} -1.75531e10 q^{44} +9.14274e9 q^{45} -4.82999e10 q^{46} +8.07016e10 q^{47} +2.50603e10 q^{48} +6.49342e10 q^{50} -5.93163e10 q^{51} +2.25633e10 q^{52} -2.21078e11 q^{53} +9.15327e10 q^{54} -6.15234e10 q^{55} +6.72511e10 q^{57} +1.57666e11 q^{58} +4.59780e11 q^{59} +8.78357e10 q^{60} +6.47850e10 q^{61} -3.92580e11 q^{62} +6.87195e10 q^{64} +7.90837e10 q^{65} +4.09676e11 q^{66} -4.14427e11 q^{67} -1.62655e11 q^{68} +1.12728e12 q^{69} -6.38110e11 q^{71} -1.66944e11 q^{72} +5.85996e11 q^{73} +1.21909e12 q^{74} -1.51551e12 q^{75} +1.84414e11 q^{76} -5.26608e11 q^{78} +2.45886e12 q^{79} +2.40860e11 q^{80} -3.15163e12 q^{81} +2.70780e12 q^{82} +3.32114e12 q^{83} -5.70103e11 q^{85} +4.75435e12 q^{86} -3.67979e12 q^{87} +1.12340e12 q^{88} -2.78406e12 q^{89} -5.85135e11 q^{90} +3.09119e12 q^{92} +9.16249e12 q^{93} -5.16490e12 q^{94} +6.46366e11 q^{95} -1.60386e12 q^{96} -7.80467e12 q^{97} -2.72914e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 256 q^{2} - 182 q^{3} + 16384 q^{4} - 1792 q^{5} + 11648 q^{6} - 1048576 q^{8} - 599840 q^{9}+O(q^{10}) \) 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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