LMFDB - Embedded newform 29.12.a.b.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,12,Mod(1,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	29.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:	$22.2819522362$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 23517 x^{12} - 42196 x^{11} + 214206700 x^{10} + 532863376 x^{9} - 951901011680 x^{8} + \cdots + 30\!\cdots\!04 $ x^14 - 23517x^12 - 42196x^11 + 214206700x^10 + 532863376x^9 - 951901011680x^8 - 1439668569088x^7 + 2125122050961664x^6 - 3617975849298944x^5 - 2179155305696991232x^4 + 15507015861824716800x^3 + 709645914927917694976x^2 - 9478460460037847384064x + 30797548279705794248704
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$88.5004$ of defining polynomial
Character	$\chi$	$=$	29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+88.5004 q^{2} -533.955 q^{3} +5784.31 q^{4} +7590.53 q^{5} -47255.2 q^{6} -38749.2 q^{7} +330665. q^{8} +107961. q^{9} +O(q^{10})$	\(q+88.5004 q^{2} -533.955 q^{3} +5784.31 q^{4} +7590.53 q^{5} -47255.2 q^{6} -38749.2 q^{7} +330665. q^{8} +107961. q^{9} +671765. q^{10} +700680. q^{11} -3.08856e6 q^{12} +965478. q^{13} -3.42932e6 q^{14} -4.05300e6 q^{15} +1.74177e7 q^{16} -3.19468e6 q^{17} +9.55455e6 q^{18} +1.42150e7 q^{19} +4.39060e7 q^{20} +2.06903e7 q^{21} +6.20104e7 q^{22} -2.19664e7 q^{23} -1.76560e8 q^{24} +8.78802e6 q^{25} +8.54452e7 q^{26} +3.69424e7 q^{27} -2.24138e8 q^{28} -2.05111e7 q^{29} -3.58692e8 q^{30} +2.14221e8 q^{31} +8.64271e8 q^{32} -3.74131e8 q^{33} -2.82731e8 q^{34} -2.94127e8 q^{35} +6.24478e8 q^{36} -7.02398e8 q^{37} +1.25803e9 q^{38} -5.15522e8 q^{39} +2.50992e9 q^{40} +1.45772e8 q^{41} +1.83110e9 q^{42} -1.35988e9 q^{43} +4.05295e9 q^{44} +8.19478e8 q^{45} -1.94403e9 q^{46} -2.17005e9 q^{47} -9.30027e9 q^{48} -4.75823e8 q^{49} +7.77743e8 q^{50} +1.70582e9 q^{51} +5.58463e9 q^{52} -4.89523e9 q^{53} +3.26942e9 q^{54} +5.31853e9 q^{55} -1.28130e10 q^{56} -7.59016e9 q^{57} -1.81524e9 q^{58} +3.78690e9 q^{59} -2.34438e10 q^{60} -2.42972e9 q^{61} +1.89587e10 q^{62} -4.18339e9 q^{63} +4.08169e10 q^{64} +7.32849e9 q^{65} -3.31107e10 q^{66} -1.01383e10 q^{67} -1.84791e10 q^{68} +1.17291e10 q^{69} -2.60304e10 q^{70} +1.07727e10 q^{71} +3.56988e10 q^{72} +1.22630e9 q^{73} -6.21624e10 q^{74} -4.69240e9 q^{75} +8.22240e10 q^{76} -2.71508e10 q^{77} -4.56239e10 q^{78} +2.18311e10 q^{79} +1.32210e11 q^{80} -3.88505e10 q^{81} +1.29009e10 q^{82} +1.68685e10 q^{83} +1.19679e11 q^{84} -2.42493e10 q^{85} -1.20350e11 q^{86} +1.09520e10 q^{87} +2.31690e11 q^{88} +3.95893e10 q^{89} +7.25241e10 q^{90} -3.74116e10 q^{91} -1.27061e11 q^{92} -1.14384e11 q^{93} -1.92051e11 q^{94} +1.07899e11 q^{95} -4.61482e11 q^{96} +1.25723e10 q^{97} -4.21105e10 q^{98} +7.56457e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 476 q^{3} + 18362 q^{4} + 9760 q^{5} + 18454 q^{6} + 85024 q^{7} + 126588 q^{8} + 1372146 q^{9}+O(q^{10}) $ 14 * q + 476 * q^3 + 18362 * q^4 + 9760 * q^5 + 18454 * q^6 + 85024 * q^7 + 126588 * q^8 + 1372146 * q^9	\( 14 q + 476 q^{3} + 18362 q^{4} + 9760 q^{5} + 18454 q^{6} + 85024 q^{7} + 126588 q^{8} + 1372146 q^{9} + 713576 q^{10} + 398020 q^{11} - 4026800 q^{12} + 2272440 q^{13} - 7199712 q^{14} - 4763864 q^{15} + 19015138 q^{16} + 5623508 q^{17} - 204156 q^{18} + 29803300 q^{19} + 65161006 q^{20} + 51227832 q^{21} + 167334266 q^{22} + 52654304 q^{23} + 221514842 q^{24} + 194970462 q^{25} + 373581536 q^{26} + 397348256 q^{27} + 319501772 q^{28} - 287156086 q^{29} + 423014226 q^{30} + 634041348 q^{31} + 1260290884 q^{32} + 1180833420 q^{33} + 1316105060 q^{34} + 1599853768 q^{35} + 3198076132 q^{36} + 488665204 q^{37} + 1892845072 q^{38} + 1972619104 q^{39} + 1826486880 q^{40} + 198215164 q^{41} + 1011384468 q^{42} + 2193188100 q^{43} + 26522720 q^{44} - 1129321956 q^{45} - 1567525268 q^{46} - 4175934476 q^{47} - 15582938120 q^{48} + 1105222462 q^{49} - 6630582612 q^{50} + 3297462720 q^{51} - 4557341374 q^{52} - 13223081840 q^{53} - 8946135054 q^{54} - 2726359424 q^{55} - 27538267872 q^{56} - 24477013312 q^{57} + 352219640 q^{59} - 36042747924 q^{60} - 7658546476 q^{61} - 10024135594 q^{62} - 23037581736 q^{63} + 14721327762 q^{64} + 1152802884 q^{65} - 99505241364 q^{66} + 21781534280 q^{67} - 104178000188 q^{68} - 14601399408 q^{69} - 67948872984 q^{70} - 5573287168 q^{71} - 24062143544 q^{72} + 39661511924 q^{73} + 28506052056 q^{74} + 81845109044 q^{75} + 166950090320 q^{76} + 38773567192 q^{77} + 54249159006 q^{78} + 105565209020 q^{79} + 146242150550 q^{80} + 170581084750 q^{81} + 47345182756 q^{82} + 127846064024 q^{83} + 215311861496 q^{84} + 83883234552 q^{85} - 103162039382 q^{86} - 9763306924 q^{87} + 418253082102 q^{88} + 187826099404 q^{89} + 96335639960 q^{90} + 58390389864 q^{91} - 259645875396 q^{92} + 394641636020 q^{93} + 117694719934 q^{94} + 69935059424 q^{95} + 12533631786 q^{96} + 137285937500 q^{97} - 484896369168 q^{98} + 235419947204 q^{99}+O(q^{100}) \) 14 * q + 476 * q^3 + 18362 * q^4 + 9760 * q^5 + 18454 * q^6 + 85024 * q^7 + 126588 * q^8 + 1372146 * q^9 + 713576 * q^10 + 398020 * q^11 - 4026800 * q^12 + 2272440 * q^13 - 7199712 * q^14 - 4763864 * q^15 + 19015138 * q^16 + 5623508 * q^17 - 204156 * q^18 + 29803300 * q^19 + 65161006 * q^20 + 51227832 * q^21 + 167334266 * q^22 + 52654304 * q^23 + 221514842 * q^24 + 194970462 * q^25 + 373581536 * q^26 + 397348256 * q^27 + 319501772 * q^28 - 287156086 * q^29 + 423014226 * q^30 + 634041348 * q^31 + 1260290884 * q^32 + 1180833420 * q^33 + 1316105060 * q^34 + 1599853768 * q^35 + 3198076132 * q^36 + 488665204 * q^37 + 1892845072 * q^38 + 1972619104 * q^39 + 1826486880 * q^40 + 198215164 * q^41 + 1011384468 * q^42 + 2193188100 * q^43 + 26522720 * q^44 - 1129321956 * q^45 - 1567525268 * q^46 - 4175934476 * q^47 - 15582938120 * q^48 + 1105222462 * q^49 - 6630582612 * q^50 + 3297462720 * q^51 - 4557341374 * q^52 - 13223081840 * q^53 - 8946135054 * q^54 - 2726359424 * q^55 - 27538267872 * q^56 - 24477013312 * q^57 + 352219640 * q^59 - 36042747924 * q^60 - 7658546476 * q^61 - 10024135594 * q^62 - 23037581736 * q^63 + 14721327762 * q^64 + 1152802884 * q^65 - 99505241364 * q^66 + 21781534280 * q^67 - 104178000188 * q^68 - 14601399408 * q^69 - 67948872984 * q^70 - 5573287168 * q^71 - 24062143544 * q^72 + 39661511924 * q^73 + 28506052056 * q^74 + 81845109044 * q^75 + 166950090320 * q^76 + 38773567192 * q^77 + 54249159006 * q^78 + 105565209020 * q^79 + 146242150550 * q^80 + 170581084750 * q^81 + 47345182756 * q^82 + 127846064024 * q^83 + 215311861496 * q^84 + 83883234552 * q^85 - 103162039382 * q^86 - 9763306924 * q^87 + 418253082102 * q^88 + 187826099404 * q^89 + 96335639960 * q^90 + 58390389864 * q^91 - 259645875396 * q^92 + 394641636020 * q^93 + 117694719934 * q^94 + 69935059424 * q^95 + 12533631786 * q^96 + 137285937500 * q^97 - 484896369168 * q^98 + 235419947204 * 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 $

$2$	88.5004	1.95560	0.977800	−	0.209540i	$-0.0671966\pi$
$2$	88.5004	1.95560	0.977800	+	0.209540i	$0.0671966\pi$
$3$	−533.955	−1.26864	−0.634319	−	0.773072i	$-0.718719\pi$
$3$	−533.955	−1.26864	−0.634319	+	0.773072i	$0.718719\pi$
$4$	5784.31	2.82437
$5$	7590.53	1.08627	0.543134	−	0.839646i	$-0.317238\pi$
$5$	7590.53	1.08627	0.543134	+	0.839646i	$0.317238\pi$
$6$	−47255.2	−2.48095
$7$	−38749.2	−0.871413	−0.435706	−	0.900089i	$-0.643501\pi$
$7$	−38749.2	−0.871413	−0.435706	+	0.900089i	$0.643501\pi$
$8$	330665.	3.56774
$9$	107961.	0.609440
$10$	671765.	2.12431
$11$	700680.	1.31178	0.655888	−	0.754858i	$-0.272294\pi$
$11$	700680.	1.31178	0.655888	+	0.754858i	$0.272294\pi$
$12$	−3.08856e6	−3.58310
$13$	965478.	0.721197	0.360599	−	0.932721i	$-0.382572\pi$
$13$	965478.	0.721197	0.360599	+	0.932721i	$0.382572\pi$
$14$	−3.42932e6	−1.70414
$15$	−4.05300e6	−1.37808
$16$	1.74177e7	4.15271
$17$	−3.19468e6	−0.545706	−0.272853	−	0.962056i	$-0.587967\pi$
$17$	−3.19468e6	−0.545706	−0.272853	+	0.962056i	$0.587967\pi$
$18$	9.55455e6	1.19182
$19$	1.42150e7	1.31705	0.658524	−	0.752560i	$-0.271181\pi$
$19$	1.42150e7	1.31705	0.658524	+	0.752560i	$0.271181\pi$
$20$	4.39060e7	3.06803
$21$	2.06903e7	1.10551
$22$	6.20104e7	2.56531
$23$	−2.19664e7	−0.711633	−0.355816	−	0.934556i	$-0.615797\pi$
$23$	−2.19664e7	−0.711633	−0.355816	+	0.934556i	$0.615797\pi$
$24$	−1.76560e8	−4.52617
$25$	8.78802e6	0.179979
$26$	8.54452e7	1.41037
$27$	3.69424e7	0.495478
$28$	−2.24138e8	−2.46119
$29$	−2.05111e7	−0.185695
$29$	−2.05111e7	−0.185695
$30$	−3.58692e8	−2.69497
$31$	2.14221e8	1.34392	0.671960	−	0.740588i	$-0.265453\pi$
$31$	2.14221e8	1.34392	0.671960	+	0.740588i	$0.265453\pi$
$32$	8.64271e8	4.55329
$33$	−3.74131e8	−1.66417
$34$	−2.82731e8	−1.06718
$35$	−2.94127e8	−0.946588
$36$	6.24478e8	1.72129
$37$	−7.02398e8	−1.66523	−0.832614	−	0.553854i	$-0.813157\pi$
$37$	−7.02398e8	−1.66523	−0.832614	+	0.553854i	$0.813157\pi$
$38$	1.25803e9	2.57562
$39$	−5.15522e8	−0.914938
$40$	2.50992e9	3.87553
$41$	1.45772e8	0.196500	0.0982500	−	0.995162i	$-0.468676\pi$
$41$	1.45772e8	0.196500	0.0982500	+	0.995162i	$0.468676\pi$
$42$	1.83110e9	2.16193
$43$	−1.35988e9	−1.41066	−0.705332	−	0.708877i	$-0.749202\pi$
$43$	−1.35988e9	−1.41066	−0.705332	+	0.708877i	$0.749202\pi$
$44$	4.05295e9	3.70494
$45$	8.19478e8	0.662016
$46$	−1.94403e9	−1.39167
$47$	−2.17005e9	−1.38017	−0.690084	−	0.723729i	$-0.742427\pi$
$47$	−2.17005e9	−1.38017	−0.690084	+	0.723729i	$0.742427\pi$
$48$	−9.30027e9	−5.26828
$49$	−4.75823e8	−0.240639
$50$	7.77743e8	0.351966
$51$	1.70582e9	0.692303
$52$	5.58463e9	2.03693
$53$	−4.89523e9	−1.60789	−0.803944	−	0.594705i	$-0.797269\pi$
$53$	−4.89523e9	−1.60789	−0.803944	+	0.594705i	$0.797269\pi$
$54$	3.26942e9	0.968958
$55$	5.31853e9	1.42494
$56$	−1.28130e10	−3.10898
$57$	−7.59016e9	−1.67086
$58$	−1.81524e9	−0.363146
$59$	3.78690e9	0.689600	0.344800	−	0.938676i	$-0.387947\pi$
$59$	3.78690e9	0.689600	0.344800	+	0.938676i	$0.387947\pi$
$60$	−2.34438e10	−3.89221
$61$	−2.42972e9	−0.368335	−0.184167	−	0.982895i	$-0.558959\pi$
$61$	−2.42972e9	−0.368335	−0.184167	+	0.982895i	$0.558959\pi$
$62$	1.89587e10	2.62817
$63$	−4.18339e9	−0.531074
$64$	4.08169e10	4.75171
$65$	7.32849e9	0.783414
$66$	−3.31107e10	−3.25445
$67$	−1.01383e10	−0.917392	−0.458696	−	0.888593i	$-0.651683\pi$
$67$	−1.01383e10	−0.917392	−0.458696	+	0.888593i	$0.651683\pi$
$68$	−1.84791e10	−1.54128
$69$	1.17291e10	0.902804
$70$	−2.60304e10	−1.85115
$71$	1.07727e10	0.708606	0.354303	−	0.935131i	$-0.384718\pi$
$71$	1.07727e10	0.708606	0.354303	+	0.935131i	$0.384718\pi$
$72$	3.56988e10	2.17433
$73$	1.22630e9	0.0692344	0.0346172	−	0.999401i	$-0.488979\pi$
$73$	1.22630e9	0.0692344	0.0346172	+	0.999401i	$0.488979\pi$
$74$	−6.21624e10	−3.25652
$75$	−4.69240e9	−0.228328
$76$	8.22240e10	3.71983
$77$	−2.71508e10	−1.14310
$78$	−4.56239e10	−1.78925
$79$	2.18311e10	0.798227	0.399113	−	0.916902i	$-0.369318\pi$
$79$	2.18311e10	0.798227	0.399113	+	0.916902i	$0.369318\pi$
$80$	1.32210e11	4.51095
$81$	−3.88505e10	−1.23802
$82$	1.29009e10	0.384275
$83$	1.68685e10	0.470053	0.235026	−	0.971989i	$-0.424482\pi$
$83$	1.68685e10	0.470053	0.235026	+	0.971989i	$0.424482\pi$
$84$	1.19679e11	3.12236
$85$	−2.42493e10	−0.592783
$86$	−1.20350e11	−2.75870
$87$	1.09520e10	0.235580
$88$	2.31690e11	4.68008
$89$	3.95893e10	0.751506	0.375753	−	0.926720i	$-0.377384\pi$
$89$	3.95893e10	0.751506	0.375753	+	0.926720i	$0.377384\pi$
$90$	7.25241e10	1.29464
$91$	−3.74116e10	−0.628461
$92$	−1.27061e11	−2.00992
$93$	−1.14384e11	−1.70495
$94$	−1.92051e11	−2.69906
$95$	1.07899e11	1.43067
$96$	−4.61482e11	−5.77647
$97$	1.25723e10	0.148652	0.0743261	−	0.997234i	$-0.476319\pi$
$97$	1.25723e10	0.148652	0.0743261	+	0.997234i	$0.476319\pi$
$98$	−4.21105e10	−0.470595
$99$	7.56457e10	0.799449
$100$	5.08327e10	0.508327
$101$	−1.02647e11	−0.971805	−0.485902	−	0.874013i	$-0.661509\pi$
$101$	−1.02647e11	−0.971805	−0.485902	+	0.874013i	$0.661509\pi$
$102$	1.50965e11	1.35387
$103$	6.63978e10	0.564351	0.282175	−	0.959363i	$-0.408944\pi$
$103$	6.63978e10	0.564351	0.282175	+	0.959363i	$0.408944\pi$
$104$	3.19250e11	2.57305
$105$	1.57051e11	1.20088
$106$	−4.33230e11	−3.14439
$107$	2.75332e11	1.89778	0.948890	−	0.315607i	$-0.102208\pi$
$107$	2.75332e11	1.89778	0.948890	+	0.315607i	$0.102208\pi$
$108$	2.13687e11	1.39942
$109$	−1.34818e11	−0.839269	−0.419634	−	0.907693i	$-0.637842\pi$
$109$	−1.34818e11	−0.839269	−0.419634	+	0.907693i	$0.637842\pi$
$110$	4.70692e11	2.78661
$111$	3.75049e11	2.11257
$112$	−6.74923e11	−3.61872
$113$	2.25445e11	1.15109	0.575544	−	0.817770i	$-0.304790\pi$
$113$	2.25445e11	1.15109	0.575544	+	0.817770i	$0.304790\pi$
$114$	−6.71732e11	−3.26753
$115$	−1.66737e11	−0.773024
$116$	−1.18643e11	−0.524473
$117$	1.04234e11	0.439527
$118$	3.35142e11	1.34858
$119$	1.23792e11	0.475535
$120$	−1.34019e12	−4.91664
$121$	2.05640e11	0.720756
$122$	−2.15031e11	−0.720315
$123$	−7.78356e10	−0.249287
$124$	1.23912e12	3.79573
$125$	−3.03926e11	−0.890763
$126$	−3.70231e11	−1.03857
$127$	−4.99847e11	−1.34251	−0.671254	−	0.741228i	$-0.734244\pi$
$127$	−4.99847e11	−1.34251	−0.671254	+	0.741228i	$0.734244\pi$
$128$	1.84228e12	4.73915
$129$	7.26114e11	1.78962
$130$	6.48574e11	1.53204
$131$	1.71200e10	0.0387715	0.0193857	−	0.999812i	$-0.493829\pi$
$131$	1.71200e10	0.0387715	0.0193857	+	0.999812i	$0.493829\pi$
$132$	−2.16409e12	−4.70023
$133$	−5.50820e11	−1.14769
$134$	−8.97246e11	−1.79405
$135$	2.80413e11	0.538222
$136$	−1.05637e12	−1.94694
$137$	2.45152e11	0.433983	0.216992	−	0.976173i	$-0.430376\pi$
$137$	2.45152e11	0.433983	0.216992	+	0.976173i	$0.430376\pi$
$138$	1.03803e12	1.76552
$139$	−2.77389e11	−0.453427	−0.226714	−	0.973961i	$-0.572798\pi$
$139$	−2.77389e11	−0.453427	−0.226714	+	0.973961i	$0.572798\pi$
$140$	−1.70132e12	−2.67352
$141$	1.15871e12	1.75093
$142$	9.53390e11	1.38575
$143$	6.76491e11	0.946049
$144$	1.88043e12	2.53083
$145$	−1.55690e11	−0.201715
$146$	1.08528e11	0.135395
$147$	2.54068e11	0.305284
$148$	−4.06289e12	−4.70322
$149$	−1.10946e12	−1.23762	−0.618809	−	0.785541i	$-0.712385\pi$
$149$	−1.10946e12	−1.23762	−0.618809	+	0.785541i	$0.712385\pi$
$150$	−4.15279e11	−0.446518
$151$	−3.23306e11	−0.335151	−0.167575	−	0.985859i	$-0.553594\pi$
$151$	−3.23306e11	−0.335151	−0.167575	+	0.985859i	$0.553594\pi$
$152$	4.70040e12	4.69889
$153$	−3.44900e11	−0.332575
$154$	−2.40286e12	−2.23544
$155$	1.62605e12	1.45986
$156$	−2.98194e12	−2.58412
$157$	3.07673e11	0.257419	0.128710	−	0.991682i	$-0.458916\pi$
$157$	3.07673e11	0.257419	0.128710	+	0.991682i	$0.458916\pi$
$158$	1.93206e12	1.56101
$159$	2.61383e12	2.03983
$160$	6.56028e12	4.94609
$161$	8.51182e11	0.620126
$162$	−3.43828e12	−2.42108
$163$	−2.71987e10	−0.0185147	−0.00925734	−	0.999957i	$-0.502947\pi$
$163$	−2.71987e10	−0.0185147	−0.00925734	+	0.999957i	$0.502947\pi$
$164$	8.43190e11	0.554989
$165$	−2.83985e12	−1.80773
$166$	1.49287e12	0.919235
$167$	−1.42781e12	−0.850610	−0.425305	−	0.905050i	$-0.639833\pi$
$167$	−1.42781e12	−0.850610	−0.425305	+	0.905050i	$0.639833\pi$
$168$	6.84157e12	3.94416
$169$	−8.60012e11	−0.479874
$170$	−2.14608e12	−1.15925
$171$	1.53466e12	0.802663
$172$	−7.86597e12	−3.98424
$173$	−9.84307e11	−0.482922	−0.241461	−	0.970411i	$-0.577627\pi$
$173$	−9.84307e11	−0.482922	−0.241461	+	0.970411i	$0.577627\pi$
$174$	9.69258e11	0.460700
$175$	−3.40529e11	−0.156836
$176$	1.22042e13	5.44742
$177$	−2.02203e12	−0.874852
$178$	3.50367e12	1.46965
$179$	2.05880e11	0.0837378	0.0418689	−	0.999123i	$-0.486669\pi$
$179$	2.05880e11	0.0837378	0.0418689	+	0.999123i	$0.486669\pi$
$180$	4.74012e12	1.86978
$181$	−6.96717e11	−0.266578	−0.133289	−	0.991077i	$-0.542554\pi$
$181$	−6.96717e11	−0.266578	−0.133289	+	0.991077i	$0.542554\pi$
$182$	−3.31094e12	−1.22902
$183$	1.29736e12	0.467283
$184$	−7.26352e12	−2.53892
$185$	−5.33157e12	−1.80888
$186$	−1.01231e13	−3.33419
$187$	−2.23845e12	−0.715844
$188$	−1.25523e13	−3.89811
$189$	−1.43149e12	−0.431766
$190$	9.54913e12	2.79781
$191$	−5.32603e11	−0.151607	−0.0758037	−	0.997123i	$-0.524152\pi$
$191$	−5.32603e11	−0.151607	−0.0758037	+	0.997123i	$0.524152\pi$
$192$	−2.17943e13	−6.02819
$193$	1.73960e12	0.467610	0.233805	−	0.972284i	$-0.424882\pi$
$193$	1.73960e12	0.467610	0.233805	+	0.972284i	$0.424882\pi$
$194$	1.11266e12	0.290704
$195$	−3.91308e12	−0.993868
$196$	−2.75231e12	−0.679655
$197$	1.13768e11	0.0273184	0.0136592	−	0.999907i	$-0.495652\pi$
$197$	1.13768e11	0.0273184	0.0136592	+	0.999907i	$0.495652\pi$
$198$	6.69468e12	1.56340
$199$	3.04510e12	0.691688	0.345844	−	0.938292i	$-0.387593\pi$
$199$	3.04510e12	0.691688	0.345844	+	0.938292i	$0.387593\pi$
$200$	2.90589e12	0.642117
$201$	5.41341e12	1.16384
$202$	−9.08430e12	−1.90046
$203$	7.94792e11	0.161817
$204$	9.86698e12	1.95532
$205$	1.10649e12	0.213452
$206$	5.87623e12	1.10364
$207$	−2.37151e12	−0.433698
$208$	1.68164e13	2.99492
$209$	9.96015e12	1.72767
$210$	1.38990e13	2.34844
$211$	6.23636e12	1.02654	0.513272	−	0.858226i	$-0.328433\pi$
$211$	6.23636e12	1.02654	0.513272	+	0.858226i	$0.328433\pi$
$212$	−2.83156e13	−4.54128
$213$	−5.75215e12	−0.898964
$214$	2.43670e13	3.71130
$215$	−1.03222e13	−1.53236
$216$	1.22156e13	1.76774
$217$	−8.30091e12	−1.17111
$218$	−1.19314e13	−1.64127
$219$	−6.54790e11	−0.0878334
$220$	3.07640e13	4.02456
$221$	−3.08440e12	−0.393562
$222$	3.31919e13	4.13134
$223$	−1.14837e13	−1.39445	−0.697226	−	0.716851i	$-0.745583\pi$
$223$	−1.14837e13	−1.39445	−0.697226	+	0.716851i	$0.745583\pi$
$224$	−3.34899e13	−3.96780
$225$	9.48760e11	0.109686
$226$	1.99520e13	2.25107
$227$	7.20453e12	0.793348	0.396674	−	0.917960i	$-0.370164\pi$
$227$	7.20453e12	0.793348	0.396674	+	0.917960i	$0.370164\pi$
$228$	−4.39039e13	−4.71912
$229$	9.96742e12	1.04589	0.522947	−	0.852365i	$-0.324833\pi$
$229$	9.96742e12	1.04589	0.522947	+	0.852365i	$0.324833\pi$
$230$	−1.47563e13	−1.51173
$231$	1.44973e13	1.45018
$232$	−6.78232e12	−0.662513
$233$	1.53364e12	0.146307	0.0731537	−	0.997321i	$-0.476694\pi$
$233$	1.53364e12	0.146307	0.0731537	+	0.997321i	$0.476694\pi$
$234$	9.22471e12	0.859539
$235$	−1.64719e13	−1.49923
$236$	2.19046e13	1.94769
$237$	−1.16568e13	−1.01266
$238$	1.09556e13	0.929957
$239$	−9.38203e11	−0.0778231	−0.0389115	−	0.999243i	$-0.512389\pi$
$239$	−9.38203e11	−0.0778231	−0.0389115	+	0.999243i	$0.512389\pi$
$240$	−7.05940e13	−5.72276
$241$	1.36709e12	0.108319	0.0541593	−	0.998532i	$-0.482752\pi$
$241$	1.36709e12	0.108319	0.0541593	+	0.998532i	$0.482752\pi$
$242$	1.81992e13	1.40951
$243$	1.42001e13	1.07512
$244$	−1.40543e13	−1.04031
$245$	−3.61175e12	−0.261399
$246$	−6.88848e12	−0.487506
$247$	1.37243e13	0.949852
$248$	7.08355e13	4.79476
$249$	−9.00701e12	−0.596326
$250$	−2.68975e13	−1.74198
$251$	4.23272e12	0.268173	0.134086	−	0.990970i	$-0.457190\pi$
$251$	4.23272e12	0.268173	0.134086	+	0.990970i	$0.457190\pi$
$252$	−2.41980e13	−1.49995
$253$	−1.53914e13	−0.933503
$254$	−4.42366e13	−2.62541
$255$	1.29480e13	0.752027
$256$	7.94494e13	4.51618
$257$	3.32785e13	1.85153	0.925767	−	0.378095i	$-0.123421\pi$
$257$	3.32785e13	1.85153	0.925767	+	0.378095i	$0.123421\pi$
$258$	6.42613e13	3.49978
$259$	2.72174e13	1.45110
$260$	4.23903e13	2.21265
$261$	−2.21439e12	−0.113170
$262$	1.51513e12	0.0758215
$263$	−6.16568e12	−0.302151	−0.151076	−	0.988522i	$-0.548274\pi$
$263$	−6.16568e12	−0.302151	−0.151076	+	0.988522i	$0.548274\pi$
$264$	−1.23712e14	−5.93732
$265$	−3.71574e13	−1.74660
$266$	−4.87478e13	−2.24443
$267$	−2.11389e13	−0.953389
$268$	−5.86433e13	−2.59106
$269$	1.04826e12	0.0453763	0.0226882	−	0.999743i	$-0.492778\pi$
$269$	1.04826e12	0.0453763	0.0226882	+	0.999743i	$0.492778\pi$
$270$	2.48166e13	1.05255
$271$	−4.36742e13	−1.81507	−0.907536	−	0.419975i	$-0.862039\pi$
$271$	−4.36742e13	−1.81507	−0.907536	+	0.419975i	$0.862039\pi$
$272$	−5.56441e13	−2.26616
$273$	1.99761e13	0.797289
$274$	2.16961e13	0.848698
$275$	6.15759e12	0.236092
$276$	6.78446e13	2.54985
$277$	2.77882e13	1.02382	0.511908	−	0.859040i	$-0.328939\pi$
$277$	2.77882e13	1.02382	0.511908	+	0.859040i	$0.328939\pi$
$278$	−2.45490e13	−0.886723
$279$	2.31274e13	0.819039
$280$	−9.72576e13	−3.37718
$281$	−2.28960e12	−0.0779606	−0.0389803	−	0.999240i	$-0.512411\pi$
$281$	−2.28960e12	−0.0779606	−0.0389803	+	0.999240i	$0.512411\pi$
$282$	1.02546e14	3.42413
$283$	−2.28099e12	−0.0746962	−0.0373481	−	0.999302i	$-0.511891\pi$
$283$	−2.28099e12	−0.0746962	−0.0373481	+	0.999302i	$0.511891\pi$
$284$	6.23128e13	2.00137
$285$	−5.76133e13	−1.81500
$286$	5.98697e13	1.85009
$287$	−5.64855e12	−0.171233
$288$	9.33072e13	2.77496
$289$	−2.40659e13	−0.702205
$290$	−1.37787e13	−0.394474
$291$	−6.71306e12	−0.188586
$292$	7.09332e12	0.195544
$293$	3.98684e13	1.07859	0.539295	−	0.842117i	$-0.318691\pi$
$293$	3.98684e13	1.07859	0.539295	+	0.842117i	$0.318691\pi$
$294$	2.24851e13	0.597014
$295$	2.87445e13	0.749091
$296$	−2.32258e14	−5.94110
$297$	2.58848e13	0.649957
$298$	−9.81875e13	−2.42029
$299$	−2.12081e13	−0.513228
$300$	−2.71423e13	−0.644882
$301$	5.26943e13	1.22927
$302$	−2.86127e13	−0.655421
$303$	5.48089e13	1.23287
$304$	2.47593e14	5.46931
$305$	−1.84429e13	−0.400110
$306$	−3.05238e13	−0.650384
$307$	−5.85846e13	−1.22609	−0.613045	−	0.790048i	$-0.710055\pi$
$307$	−5.85846e13	−1.22609	−0.613045	+	0.790048i	$0.710055\pi$
$308$	−1.57049e14	−3.22854
$309$	−3.54534e13	−0.715956
$310$	1.43906e14	2.85490
$311$	−7.91002e13	−1.54168	−0.770842	−	0.637026i	$-0.780164\pi$
$311$	−7.91002e13	−1.54168	−0.770842	+	0.637026i	$0.780164\pi$
$312$	−1.70465e14	−3.26426
$313$	−8.36875e12	−0.157459	−0.0787294	−	0.996896i	$-0.525086\pi$
$313$	−8.36875e12	−0.157459	−0.0787294	+	0.996896i	$0.525086\pi$
$314$	2.72291e13	0.503409
$315$	−3.17541e13	−0.576889
$316$	1.26278e14	2.25449
$317$	−6.25911e13	−1.09821	−0.549107	−	0.835752i	$-0.685032\pi$
$317$	−6.25911e13	−1.09821	−0.549107	+	0.835752i	$0.685032\pi$
$318$	2.31325e14	3.98909
$319$	−1.43717e13	−0.243591
$320$	3.09822e14	5.16163
$321$	−1.47015e14	−2.40759
$322$	7.53299e13	1.21272
$323$	−4.54124e13	−0.718721
$324$	−2.24723e14	−3.49664
$325$	8.48464e12	0.129800
$326$	−2.40709e12	−0.0362073
$327$	7.19865e13	1.06473
$328$	4.82017e13	0.701061
$329$	8.40879e13	1.20270
$330$	−2.51328e14	−3.53520
$331$	4.69274e13	0.649191	0.324595	−	0.945853i	$-0.394772\pi$
$331$	4.69274e13	0.649191	0.324595	+	0.945853i	$0.394772\pi$
$332$	9.75726e13	1.32760
$333$	−7.58312e13	−1.01486
$334$	−1.26362e14	−1.66345
$335$	−7.69553e13	−0.996534
$336$	3.60378e14	4.59084
$337$	2.69238e12	0.0337421	0.0168710	−	0.999858i	$-0.494630\pi$
$337$	2.69238e12	0.0337421	0.0168710	+	0.999858i	$0.494630\pi$
$338$	−7.61114e13	−0.938442
$339$	−1.20377e14	−1.46031
$340$	−1.40266e14	−1.67424
$341$	1.50100e14	1.76292
$342$	1.35818e14	1.56969
$343$	9.50577e13	1.08111
$344$	−4.49665e14	−5.03289
$345$	8.90298e13	0.980687
$346$	−8.71115e13	−0.944403
$347$	6.92937e13	0.739403	0.369702	−	0.929151i	$-0.379460\pi$
$347$	6.92937e13	0.739403	0.369702	+	0.929151i	$0.379460\pi$
$348$	6.33499e13	0.665366
$349$	3.16433e13	0.327146	0.163573	−	0.986531i	$-0.447698\pi$
$349$	3.16433e13	0.327146	0.163573	+	0.986531i	$0.447698\pi$
$350$	−3.01370e13	−0.306708
$351$	3.56671e13	0.357338
$352$	6.05577e14	5.97290
$353$	1.55460e14	1.50958	0.754792	−	0.655964i	$-0.227738\pi$
$353$	1.55460e14	1.50958	0.754792	+	0.655964i	$0.227738\pi$
$354$	−1.78950e14	−1.71086
$355$	8.17707e13	0.769736
$356$	2.28997e14	2.12253
$357$	−6.60991e13	−0.603282
$358$	1.82204e13	0.163758
$359$	1.04484e14	0.924766	0.462383	−	0.886680i	$-0.346995\pi$
$359$	1.04484e14	0.924766	0.462383	+	0.886680i	$0.346995\pi$
$360$	2.70973e14	2.36190
$361$	8.55757e13	0.734617
$362$	−6.16597e13	−0.521320
$363$	−1.09803e14	−0.914378
$364$	−2.16400e14	−1.77501
$365$	9.30829e12	0.0752072
$366$	1.14817e14	0.913819
$367$	−6.87163e13	−0.538761	−0.269381	−	0.963034i	$-0.586819\pi$
$367$	−6.87163e13	−0.538761	−0.269381	+	0.963034i	$0.586819\pi$
$368$	−3.82604e14	−2.95520
$369$	1.57376e13	0.119755
$370$	−4.71846e14	−3.53745
$371$	1.89687e14	1.40113
$372$	−6.61635e14	−4.81540
$373$	2.36862e14	1.69862	0.849312	−	0.527892i	$-0.177017\pi$
$373$	2.36862e14	1.69862	0.849312	+	0.527892i	$0.177017\pi$
$374$	−1.98104e14	−1.39991
$375$	1.62282e14	1.13006
$376$	−7.17561e14	−4.92409
$377$	−1.98031e13	−0.133923
$378$	−1.26687e14	−0.844362
$379$	1.49491e14	0.981974	0.490987	−	0.871167i	$-0.336636\pi$
$379$	1.49491e14	0.981974	0.490987	+	0.871167i	$0.336636\pi$
$380$	6.24123e14	4.04074
$381$	2.66896e14	1.70315
$382$	−4.71356e13	−0.296483
$383$	9.39433e13	0.582469	0.291234	−	0.956652i	$-0.405934\pi$
$383$	9.39433e13	0.582469	0.291234	+	0.956652i	$0.405934\pi$
$384$	−9.83693e14	−6.01226
$385$	−2.06089e14	−1.24171
$386$	1.53955e14	0.914458
$387$	−1.46813e14	−0.859716
$388$	7.27223e13	0.419849
$389$	−6.74052e13	−0.383681	−0.191841	−	0.981426i	$-0.561446\pi$
$389$	−6.74052e13	−0.383681	−0.191841	+	0.981426i	$0.561446\pi$
$390$	−3.46309e14	−1.94361
$391$	7.01757e13	0.388342
$392$	−1.57338e14	−0.858540
$393$	−9.14132e12	−0.0491870
$394$	1.00685e13	0.0534239
$395$	1.65710e14	0.867088
$396$	4.37559e14	2.25794
$397$	−5.51768e13	−0.280808	−0.140404	−	0.990094i	$-0.544840\pi$
$397$	−5.51768e13	−0.280808	−0.140404	+	0.990094i	$0.544840\pi$
$398$	2.69493e14	1.35266
$399$	2.94113e14	1.45601
$400$	1.53067e14	0.747398
$401$	−1.93621e14	−0.932519	−0.466260	−	0.884648i	$-0.654399\pi$
$401$	−1.93621e14	−0.932519	−0.466260	+	0.884648i	$0.654399\pi$
$402$	4.79089e14	2.27600
$403$	2.06826e14	0.969231
$404$	−5.93743e14	−2.74474
$405$	−2.94896e14	−1.34482
$406$	7.03393e13	0.316450
$407$	−4.92156e14	−2.18441
$408$	5.64054e14	2.46996
$409$	−1.55256e14	−0.670765	−0.335383	−	0.942082i	$-0.608866\pi$
$409$	−1.55256e14	−0.670765	−0.335383	+	0.942082i	$0.608866\pi$
$410$	9.79244e13	0.417426
$411$	−1.30900e14	−0.550567
$412$	3.84066e14	1.59394
$413$	−1.46739e14	−0.600926
$414$	−2.09879e14	−0.848139
$415$	1.28041e14	0.510603
$416$	8.34435e14	3.28382
$417$	1.48113e14	0.575235
$418$	8.81477e14	3.37864
$419$	−4.15582e14	−1.57210	−0.786049	−	0.618164i	$-0.787877\pi$
$419$	−4.15582e14	−1.57210	−0.786049	+	0.618164i	$0.787877\pi$
$420$	9.08430e14	3.39172
$421$	−2.10915e14	−0.777242	−0.388621	−	0.921398i	$-0.627048\pi$
$421$	−2.10915e14	−0.777242	−0.388621	+	0.921398i	$0.627048\pi$
$422$	5.51920e14	2.00751
$423$	−2.34280e14	−0.841131
$424$	−1.61868e15	−5.73653
$425$	−2.80749e13	−0.0982155
$426$	−5.09067e14	−1.75801
$427$	9.41499e13	0.320972
$428$	1.59261e15	5.36004
$429$	−3.61216e14	−1.20019
$430$	−9.13519e14	−2.99668
$431$	4.86383e14	1.57527	0.787633	−	0.616145i	$-0.211307\pi$
$431$	4.86383e14	1.57527	0.787633	+	0.616145i	$0.211307\pi$
$432$	6.43452e14	2.05758
$433$	−2.08963e14	−0.659760	−0.329880	−	0.944023i	$-0.607008\pi$
$433$	−2.08963e14	−0.659760	−0.329880	+	0.944023i	$0.607008\pi$
$434$	−7.34634e14	−2.29022
$435$	8.31317e13	0.255903
$436$	−7.79828e14	−2.37041
$437$	−3.12252e14	−0.937255
$438$	−5.79492e13	−0.171767
$439$	5.56034e14	1.62760	0.813798	−	0.581149i	$-0.197396\pi$
$439$	5.56034e14	1.62760	0.813798	+	0.581149i	$0.197396\pi$
$440$	1.75865e15	5.08382
$441$	−5.13701e13	−0.146655
$442$	−2.72970e14	−0.769650
$443$	−6.62988e14	−1.84623	−0.923114	−	0.384526i	$-0.874365\pi$
$443$	−6.62988e14	−1.84623	−0.923114	+	0.384526i	$0.874365\pi$
$444$	2.16940e15	5.96668
$445$	3.00504e14	0.816337
$446$	−1.01631e15	−2.72699
$447$	5.92401e14	1.57009
$448$	−1.58162e15	−4.14070
$449$	1.94558e14	0.503146	0.251573	−	0.967838i	$-0.419052\pi$
$449$	1.94558e14	0.503146	0.251573	+	0.967838i	$0.419052\pi$
$450$	8.39656e13	0.214503
$451$	1.02139e14	0.257764
$452$	1.30404e15	3.25110
$453$	1.72631e14	0.425185
$454$	6.37604e14	1.55147
$455$	−2.83974e14	−0.682677
$456$	−2.50980e15	−5.96119
$457$	−5.72155e14	−1.34269	−0.671344	−	0.741146i	$-0.734283\pi$
$457$	−5.72155e14	−1.34269	−0.671344	+	0.741146i	$0.734283\pi$
$458$	8.82120e14	2.04535
$459$	−1.18019e14	−0.270386
$460$	−9.64457e14	−2.18331
$461$	−2.04035e14	−0.456403	−0.228202	−	0.973614i	$-0.573285\pi$
$461$	−2.04035e14	−0.456403	−0.228202	+	0.973614i	$0.573285\pi$
$462$	1.28302e15	2.83597
$463$	8.93641e14	1.95195	0.975973	−	0.217893i	$-0.0699184\pi$
$463$	8.93641e14	1.95195	0.975973	+	0.217893i	$0.0699184\pi$
$464$	−3.57257e14	−0.771138
$465$	−8.68238e14	−1.85203
$466$	1.35728e14	0.286119
$467$	−6.16347e14	−1.28405	−0.642026	−	0.766683i	$-0.721906\pi$
$467$	−6.16347e14	−1.28405	−0.642026	+	0.766683i	$0.721906\pi$
$468$	6.02920e14	1.24139
$469$	3.92853e14	0.799427
$470$	−1.45777e15	−2.93190
$471$	−1.64283e14	−0.326572
$472$	1.25219e15	2.46031
$473$	−9.52839e14	−1.85048
$474$	−1.03163e15	−1.98036
$475$	1.24922e14	0.237041
$476$	7.16049e14	1.34309
$477$	−5.28492e14	−0.979912
$478$	−8.30313e13	−0.152191
$479$	9.39250e14	1.70191	0.850954	−	0.525240i	$-0.176025\pi$
$479$	9.39250e14	1.70191	0.850954	+	0.525240i	$0.176025\pi$
$480$	−3.50289e15	−6.27480
$481$	−6.78150e14	−1.20096
$482$	1.20988e14	0.211828
$483$	−4.54492e14	−0.786715
$484$	1.18949e15	2.03568
$485$	9.54307e13	0.161476
$486$	1.25672e15	2.10251
$487$	−6.17233e14	−1.02103	−0.510516	−	0.859868i	$-0.670546\pi$
$487$	−6.17233e14	−1.02103	−0.510516	+	0.859868i	$0.670546\pi$
$488$	−8.03425e14	−1.31412
$489$	1.45229e13	0.0234884
$490$	−3.19641e14	−0.511192
$491$	−4.40633e14	−0.696833	−0.348417	−	0.937340i	$-0.613281\pi$
$491$	−4.40633e14	−0.696833	−0.348417	+	0.937340i	$0.613281\pi$
$492$	−4.50225e14	−0.704080
$493$	6.55266e13	0.101335
$494$	1.21460e15	1.85753
$495$	5.74191e14	0.868416
$496$	3.73124e15	5.58090
$497$	−4.17435e14	−0.617488
$498$	−7.97123e14	−1.16618
$499$	6.22862e14	0.901236	0.450618	−	0.892717i	$-0.351204\pi$
$499$	6.22862e14	0.901236	0.450618	+	0.892717i	$0.351204\pi$
$500$	−1.75800e15	−2.51585
$501$	7.62387e14	1.07912
$502$	3.74598e14	0.524439
$503$	−1.56955e14	−0.217346	−0.108673	−	0.994078i	$-0.534660\pi$
$503$	−1.56955e14	−0.217346	−0.108673	+	0.994078i	$0.534660\pi$
$504$	−1.38330e15	−1.89474
$505$	−7.79146e14	−1.05564
$506$	−1.36215e15	−1.82556
$507$	4.59207e14	0.608786
$508$	−2.89127e15	−3.79174
$509$	2.64123e13	0.0342656	0.0171328	−	0.999853i	$-0.494546\pi$
$509$	2.64123e13	0.0342656	0.0171328	+	0.999853i	$0.494546\pi$
$510$	1.14591e15	1.47066
$511$	−4.75183e13	−0.0603318
$512$	3.25832e15	4.09269
$513$	5.25136e14	0.652569
$514$	2.94516e15	3.62086
$515$	5.03995e14	0.613036
$516$	4.20007e15	5.05456
$517$	−1.52051e15	−1.81047
$518$	2.40875e15	2.83777
$519$	5.25575e14	0.612653
$520$	2.42328e15	2.79502
$521$	2.90398e14	0.331425	0.165713	−	0.986174i	$-0.447008\pi$
$521$	2.90398e14	0.331425	0.165713	+	0.986174i	$0.447008\pi$
$522$	−1.95975e14	−0.221316
$523$	1.46202e15	1.63378	0.816888	−	0.576796i	$-0.195697\pi$
$523$	1.46202e15	1.63378	0.816888	+	0.576796i	$0.195697\pi$
$524$	9.90277e13	0.109505
$525$	1.81827e14	0.198968
$526$	−5.45665e14	−0.590887
$527$	−6.84369e14	−0.733385
$528$	−6.51651e15	−6.91080
$529$	−4.70287e14	−0.493579
$530$	−3.28844e15	−3.41565
$531$	4.08835e14	0.420270
$532$	−3.18612e15	−3.24151
$533$	1.40740e14	0.141715
$534$	−1.87080e15	−1.86445
$535$	2.08992e15	2.06150
$536$	−3.35239e15	−3.27302
$537$	−1.09930e14	−0.106233
$538$	9.27710e13	0.0887380
$539$	−3.33399e14	−0.315665
$540$	1.62199e15	1.52014
$541$	−4.88748e13	−0.0453420	−0.0226710	−	0.999743i	$-0.507217\pi$
$541$	−4.88748e13	−0.0453420	−0.0226710	+	0.999743i	$0.507217\pi$
$542$	−3.86518e15	−3.54955
$543$	3.72015e14	0.338191
$544$	−2.76107e15	−2.48476
$545$	−1.02334e15	−0.911671
$546$	1.76789e15	1.55918
$547$	4.50612e14	0.393434	0.196717	−	0.980460i	$-0.436972\pi$
$547$	4.50612e14	0.393434	0.196717	+	0.980460i	$0.436972\pi$
$548$	1.41804e15	1.22573
$549$	−2.62314e14	−0.224478
$550$	5.44949e14	0.461701
$551$	−2.91566e14	−0.244570
$552$	3.87839e15	3.22097
$553$	−8.45938e14	−0.695585
$554$	2.45927e15	2.00218
$555$	2.84682e15	2.29482
$556$	−1.60450e15	−1.28065
$557$	−1.37188e15	−1.08421	−0.542105	−	0.840311i	$-0.682373\pi$
$557$	−1.37188e15	−1.08421	−0.542105	+	0.840311i	$0.682373\pi$
$558$	2.04679e15	1.60171
$559$	−1.31293e15	−1.01737
$560$	−5.12302e15	−3.93090
$561$	1.19523e15	0.908147
$562$	−2.02630e14	−0.152460
$563$	1.74160e15	1.29763	0.648816	−	0.760945i	$-0.275264\pi$
$563$	1.74160e15	1.29763	0.648816	+	0.760945i	$0.275264\pi$
$564$	6.70234e15	4.94529
$565$	1.71125e15	1.25039
$566$	−2.01869e14	−0.146076
$567$	1.50543e15	1.07883
$568$	3.56217e15	2.52812
$569$	−2.66782e15	−1.87516	−0.937581	−	0.347767i	$-0.886940\pi$
$569$	−2.66782e15	−1.87516	−0.937581	+	0.347767i	$0.886940\pi$
$570$	−5.09880e15	−3.54941
$571$	−6.97870e14	−0.481145	−0.240572	−	0.970631i	$-0.577335\pi$
$571$	−6.97870e14	−0.481145	−0.240572	+	0.970631i	$0.577335\pi$
$572$	3.91304e15	2.67200
$573$	2.84386e14	0.192335
$574$	−4.99899e14	−0.334863
$575$	−1.93041e14	−0.128079
$576$	4.40661e15	2.89588
$577$	1.14127e15	0.742887	0.371444	−	0.928456i	$-0.378863\pi$
$577$	1.14127e15	0.742887	0.371444	+	0.928456i	$0.378863\pi$
$578$	−2.12984e15	−1.37323
$579$	−9.28866e14	−0.593227
$580$	−9.00563e14	−0.569718
$581$	−6.53641e14	−0.409610
$582$	−5.94108e14	−0.368798
$583$	−3.42999e15	−2.10919
$584$	4.05496e14	0.247011
$585$	7.91188e14	0.477444
$586$	3.52836e15	2.10929
$587$	2.09404e15	1.24015	0.620076	−	0.784542i	$-0.287102\pi$
$587$	2.09404e15	1.24015	0.620076	+	0.784542i	$0.287102\pi$
$588$	1.46961e15	0.862236
$589$	3.04515e15	1.77001
$590$	2.54390e15	1.46492
$591$	−6.07469e13	−0.0346572
$592$	−1.22342e16	−6.91520
$593$	2.31610e15	1.29705	0.648525	−	0.761194i	$-0.275386\pi$
$593$	2.31610e15	1.29705	0.648525	+	0.761194i	$0.275386\pi$
$594$	2.29081e15	1.27106
$595$	9.39644e14	0.516559
$596$	−6.41746e15	−3.49549
$597$	−1.62595e15	−0.877501
$598$	−1.87692e15	−1.00367
$599$	−2.97037e14	−0.157385	−0.0786925	−	0.996899i	$-0.525075\pi$
$599$	−2.97037e14	−0.157385	−0.0786925	+	0.996899i	$0.525075\pi$
$600$	−1.55161e15	−0.814614
$601$	1.91682e15	0.997176	0.498588	−	0.866839i	$-0.333852\pi$
$601$	1.91682e15	0.997176	0.498588	+	0.866839i	$0.333852\pi$
$602$	4.66346e15	2.40396
$603$	−1.09454e15	−0.559096
$604$	−1.87010e15	−0.946590
$605$	1.56092e15	0.782935
$606$	4.85061e15	2.41100
$607$	8.66928e14	0.427017	0.213509	−	0.976941i	$-0.431511\pi$
$607$	8.66928e14	0.427017	0.213509	+	0.976941i	$0.431511\pi$
$608$	1.22856e16	5.99690
$609$	−4.24383e14	−0.205287
$610$	−1.63220e15	−0.782456
$611$	−2.09514e15	−0.995374
$612$	−1.99501e15	−0.939317
$613$	2.09731e15	0.978655	0.489328	−	0.872100i	$-0.337242\pi$
$613$	2.09731e15	0.978655	0.489328	+	0.872100i	$0.337242\pi$
$614$	−5.18475e15	−2.39774
$615$	−5.90813e14	−0.270793
$616$	−8.97782e15	−4.07828
$617$	−2.97271e15	−1.33840	−0.669198	−	0.743084i	$-0.733362\pi$
$617$	−2.97271e15	−1.33840	−0.669198	+	0.743084i	$0.733362\pi$
$618$	−3.13764e15	−1.40012
$619$	1.49974e15	0.663312	0.331656	−	0.943400i	$-0.392393\pi$
$619$	1.49974e15	0.663312	0.331656	+	0.943400i	$0.392393\pi$
$620$	9.40560e15	4.12318
$621$	−8.11492e14	−0.352599
$622$	−7.00040e15	−3.01492
$623$	−1.53405e15	−0.654872
$624$	−8.97921e15	−3.79947
$625$	−2.73606e15	−1.14759
$626$	−7.40638e14	−0.307926
$627$	−5.31827e15	−2.19179
$628$	1.77968e15	0.727048
$629$	2.24394e15	0.908725
$630$	−2.81025e15	−1.12816
$631$	6.21245e14	0.247230	0.123615	−	0.992330i	$-0.460551\pi$
$631$	6.21245e14	0.247230	0.123615	+	0.992330i	$0.460551\pi$
$632$	7.21878e15	2.84787
$633$	−3.32993e15	−1.30231
$634$	−5.53934e15	−2.14767
$635$	−3.79410e15	−1.45832
$636$	1.51192e16	5.76123
$637$	−4.59397e14	−0.173549
$638$	−1.27190e15	−0.476366
$639$	1.16303e15	0.431853
$640$	1.39839e16	5.14799
$641$	−3.52150e15	−1.28531	−0.642655	−	0.766155i	$-0.722167\pi$
$641$	−3.52150e15	−1.28531	−0.642655	+	0.766155i	$0.722167\pi$
$642$	−1.30109e16	−4.70829
$643$	−5.37057e14	−0.192690	−0.0963451	−	0.995348i	$-0.530715\pi$
$643$	−5.37057e14	−0.192690	−0.0963451	+	0.995348i	$0.530715\pi$
$644$	4.92350e15	1.75147
$645$	5.51159e15	1.94401
$646$	−4.01901e15	−1.40553
$647$	1.58376e15	0.549180	0.274590	−	0.961561i	$-0.411458\pi$
$647$	1.58376e15	0.549180	0.274590	+	0.961561i	$0.411458\pi$
$648$	−1.28465e16	−4.41695
$649$	2.65340e15	0.904601
$650$	7.50894e14	0.253837
$651$	4.43231e15	1.48571
$652$	−1.57326e14	−0.0522923
$653$	5.91836e15	1.95065	0.975323	−	0.220782i	$-0.0708609\pi$
$653$	5.91836e15	1.95065	0.975323	+	0.220782i	$0.0708609\pi$
$654$	6.37083e15	2.08218
$655$	1.29950e14	0.0421162
$656$	2.53901e15	0.816007
$657$	1.32392e14	0.0421943
$658$	7.44181e15	2.35199
$659$	−2.26135e15	−0.708757	−0.354378	−	0.935102i	$-0.615307\pi$
$659$	−2.26135e15	−0.708757	−0.354378	+	0.935102i	$0.615307\pi$
$660$	−1.64266e16	−5.10571
$661$	1.54295e15	0.475603	0.237801	−	0.971314i	$-0.423573\pi$
$661$	1.54295e15	0.475603	0.237801	+	0.971314i	$0.423573\pi$
$662$	4.15309e15	1.26956
$663$	1.64693e15	0.499287
$664$	5.57782e15	1.67703
$665$	−4.18102e15	−1.24670
$666$	−6.71109e15	−1.98465
$667$	4.50556e14	0.132147
$668$	−8.25891e15	−2.40244
$669$	6.13175e15	1.76905
$670$	−6.81057e15	−1.94882
$671$	−1.70246e15	−0.483173
$672$	1.78821e16	5.03369
$673$	4.31175e15	1.20385	0.601923	−	0.798554i	$-0.294401\pi$
$673$	4.31175e15	1.20385	0.601923	+	0.798554i	$0.294401\pi$
$674$	2.38276e14	0.0659860
$675$	3.24651e14	0.0891755
$676$	−4.97458e15	−1.35534
$677$	−4.37830e15	−1.18323	−0.591613	−	0.806222i	$-0.701509\pi$
$677$	−4.37830e15	−1.18323	−0.591613	+	0.806222i	$0.701509\pi$
$678$	−1.06534e16	−2.85579
$679$	−4.87169e14	−0.129537
$680$	−8.01841e15	−2.11490
$681$	−3.84689e15	−1.00647
$682$	1.32839e16	3.44757
$683$	4.66287e15	1.20044	0.600218	−	0.799836i	$-0.295080\pi$
$683$	4.66287e15	1.20044	0.600218	+	0.799836i	$0.295080\pi$
$684$	8.87694e15	2.26702
$685$	1.86084e15	0.471422
$686$	8.41264e15	2.11422
$687$	−5.32215e15	−1.32686
$688$	−2.36860e16	−5.85807
$689$	−4.72624e15	−1.15961
$690$	7.87917e15	1.91783
$691$	2.12155e15	0.512300	0.256150	−	0.966637i	$-0.417546\pi$
$691$	2.12155e15	0.512300	0.256150	+	0.966637i	$0.417546\pi$
$692$	−5.69354e15	−1.36395
$693$	−2.93122e15	−0.696651
$694$	6.13251e15	1.44598
$695$	−2.10553e15	−0.492544
$696$	3.62145e15	0.840489
$697$	−4.65695e14	−0.107231
$698$	2.80044e15	0.639766
$699$	−8.18894e14	−0.185611
$700$	−1.96973e15	−0.442962
$701$	−2.00228e15	−0.446761	−0.223381	−	0.974731i	$-0.571709\pi$
$701$	−2.00228e15	−0.446761	−0.223381	+	0.974731i	$0.571709\pi$
$702$	3.15655e15	0.698810
$703$	−9.98458e15	−2.19319
$704$	2.85995e16	6.23318
$705$	8.79522e15	1.90198
$706$	1.37583e16	2.95214
$707$	3.97750e15	0.846843
$708$	−1.16961e16	−2.47091
$709$	1.67594e14	0.0351322	0.0175661	−	0.999846i	$-0.494408\pi$
$709$	1.67594e14	0.0351322	0.0175661	+	0.999846i	$0.494408\pi$
$710$	7.23674e15	1.50530
$711$	2.35690e15	0.486472
$712$	1.30908e16	2.68118
$713$	−4.70567e15	−0.956377
$714$	−5.84979e15	−1.17978
$715$	5.13493e15	1.02766
$716$	1.19087e15	0.236507
$717$	5.00958e14	0.0987292
$718$	9.24690e15	1.80847
$719$	−5.40408e14	−0.104885	−0.0524424	−	0.998624i	$-0.516701\pi$
$719$	−5.40408e14	−0.104885	−0.0524424	+	0.998624i	$0.516701\pi$
$720$	1.42734e16	2.74916
$721$	−2.57287e15	−0.491783
$722$	7.57348e15	1.43662
$723$	−7.29964e14	−0.137417
$724$	−4.03003e15	−0.752916
$725$	−1.80252e14	−0.0334212
$726$	−9.71756e15	−1.78816
$727$	2.08415e15	0.380618	0.190309	−	0.981724i	$-0.439051\pi$
$727$	2.08415e15	0.380618	0.190309	+	0.981724i	$0.439051\pi$
$728$	−1.23707e16	−2.24219
$729$	−6.99990e14	−0.125919
$730$	8.23787e14	0.147075
$731$	4.34438e15	0.769808
$732$	7.50435e15	1.31978
$733$	−9.37069e15	−1.63568	−0.817842	−	0.575442i	$-0.804830\pi$
$733$	−9.37069e15	−1.63568	−0.817842	+	0.575442i	$0.804830\pi$
$734$	−6.08142e15	−1.05360
$735$	1.92851e15	0.331621
$736$	−1.89849e16	−3.24027
$737$	−7.10372e15	−1.20341
$738$	1.39278e15	0.234193
$739$	2.41068e15	0.402342	0.201171	−	0.979556i	$-0.435525\pi$
$739$	2.41068e15	0.402342	0.201171	+	0.979556i	$0.435525\pi$
$740$	−3.08395e16	−5.10896
$741$	−7.32814e15	−1.20502
$742$	1.67873e16	2.74006
$743$	8.03930e15	1.30251	0.651253	−	0.758861i	$-0.274244\pi$
$743$	8.03930e15	1.30251	0.651253	+	0.758861i	$0.274244\pi$
$744$	−3.78229e16	−6.08281
$745$	−8.42138e15	−1.34439
$746$	2.09624e16	3.32183
$747$	1.82113e15	0.286469
$748$	−1.29479e16	−2.02181
$749$	−1.06689e16	−1.65375
$750$	1.43621e16	2.20994
$751$	−4.62590e15	−0.706604	−0.353302	−	0.935509i	$-0.614941\pi$
$751$	−4.62590e15	−0.706604	−0.353302	+	0.935509i	$0.614941\pi$
$752$	−3.77974e16	−5.73143
$753$	−2.26008e15	−0.340214
$754$	−1.75258e15	−0.261900
$755$	−2.45406e15	−0.364063
$756$	−8.28019e15	−1.21947
$757$	2.86149e15	0.418375	0.209187	−	0.977876i	$-0.432918\pi$
$757$	2.86149e15	0.418375	0.209187	+	0.977876i	$0.432918\pi$
$758$	1.32300e16	1.92035
$759$	8.21832e15	1.18428
$760$	3.56785e16	5.10425
$761$	8.19939e15	1.16457	0.582285	−	0.812984i	$-0.302159\pi$
$761$	8.19939e15	1.16457	0.582285	+	0.812984i	$0.302159\pi$
$762$	2.36204e16	3.33069
$763$	5.22408e15	0.731350
$764$	−3.08074e15	−0.428196
$765$	−2.61797e15	−0.361266
$766$	8.31402e15	1.13908
$767$	3.65617e15	0.497338
$768$	−4.24224e16	−5.72939
$769$	1.21122e16	1.62416	0.812081	−	0.583544i	$-0.198334\pi$
$769$	1.21122e16	1.62416	0.812081	+	0.583544i	$0.198334\pi$
$770$	−1.82389e16	−2.42829
$771$	−1.77692e16	−2.34892
$772$	1.00624e16	1.32070
$773$	6.80802e15	0.887224	0.443612	−	0.896219i	$-0.353697\pi$
$773$	6.80802e15	0.887224	0.443612	+	0.896219i	$0.353697\pi$
$774$	−1.29930e16	−1.68126
$775$	1.88258e15	0.241877
$776$	4.15723e15	0.530353
$777$	−1.45328e16	−1.84092
$778$	−5.96539e15	−0.750327
$779$	2.07215e15	0.258800
$780$	−2.26345e16	−2.80705
$781$	7.54823e15	0.929532
$782$	6.21058e15	0.759442
$783$	−7.57732e14	−0.0920080
$784$	−8.28774e15	−0.999305
$785$	2.33540e15	0.279626
$786$	−8.09010e14	−0.0961900
$787$	1.08444e16	1.28040	0.640198	−	0.768210i	$-0.278852\pi$
$787$	1.08444e16	1.28040	0.640198	+	0.768210i	$0.278852\pi$
$788$	6.58069e14	0.0771574
$789$	3.29219e15	0.383320
$790$	1.46654e16	1.69568
$791$	−8.73582e15	−1.00307
$792$	2.50134e16	2.85223
$793$	−2.34584e15	−0.265642
$794$	−4.88317e15	−0.549148
$795$	1.98404e16	2.21580
$796$	1.76138e16	1.95358
$797$	3.00226e15	0.330695	0.165348	−	0.986235i	$-0.447125\pi$
$797$	3.00226e15	0.330695	0.165348	+	0.986235i	$0.447125\pi$
$798$	2.60291e16	2.84737
$799$	6.93264e15	0.753167
$800$	7.59523e15	0.819495
$801$	4.27408e15	0.457998
$802$	−1.71355e16	−1.82364
$803$	8.59246e14	0.0908201
$804$	3.13129e16	3.28711
$805$	6.46092e15	0.673623
$806$	1.83042e16	1.89543
$807$	−5.59721e14	−0.0575661
$808$	−3.39418e16	−3.46715
$809$	1.78054e15	0.180649	0.0903244	−	0.995912i	$-0.471210\pi$
$809$	1.78054e15	0.180649	0.0903244	+	0.995912i	$0.471210\pi$
$810$	−2.60984e16	−2.62994
$811$	−1.87967e16	−1.88133	−0.940667	−	0.339332i	$-0.889799\pi$
$811$	−1.87967e16	−1.88133	−0.940667	+	0.339332i	$0.889799\pi$
$812$	4.59732e15	0.457032
$813$	2.33200e16	2.30267
$814$	−4.35560e16	−4.27182
$815$	−2.06453e14	−0.0201119
$816$	2.97114e16	2.87493
$817$	−1.93307e16	−1.85791
$818$	−1.37402e16	−1.31175
$819$	−4.03897e15	−0.383009
$820$	6.40026e15	0.602867
$821$	8.15422e14	0.0762949	0.0381474	−	0.999272i	$-0.487854\pi$
$821$	8.15422e14	0.0762949	0.0381474	+	0.999272i	$0.487854\pi$
$822$	−1.15847e16	−1.07669
$823$	9.06704e15	0.837079	0.418540	−	0.908199i	$-0.362542\pi$
$823$	9.06704e15	0.837079	0.418540	+	0.908199i	$0.362542\pi$
$824$	2.19554e16	2.01346
$825$	−3.28787e15	−0.299515
$826$	−1.29865e16	−1.17517
$827$	−1.59791e16	−1.43639	−0.718194	−	0.695843i	$-0.755031\pi$
$827$	−1.59791e16	−1.43639	−0.718194	+	0.695843i	$0.755031\pi$
$828$	−1.37175e16	−1.22492
$829$	−3.44649e15	−0.305722	−0.152861	−	0.988248i	$-0.548849\pi$
$829$	−3.44649e15	−0.305722	−0.152861	+	0.988248i	$0.548849\pi$
$830$	1.13317e16	0.998536
$831$	−1.48377e16	−1.29885
$832$	3.94078e16	3.42692
$833$	1.52010e15	0.131318
$834$	1.31081e16	1.12493
$835$	−1.08379e16	−0.923991
$836$	5.76126e16	4.87959
$837$	7.91385e15	0.665883
$838$	−3.67792e16	−3.07439
$839$	−1.85653e16	−1.54174	−0.770870	−	0.636992i	$-0.780178\pi$
$839$	−1.85653e16	−1.54174	−0.770870	+	0.636992i	$0.780178\pi$
$840$	5.19312e16	4.28442
$841$	4.20707e14	0.0344828
$842$	−1.86661e16	−1.51997
$843$	1.22254e15	0.0989037
$844$	3.60730e16	2.89934
$845$	−6.52794e15	−0.521272
$846$	−2.07339e16	−1.64492
$847$	−7.96840e15	−0.628076
$848$	−8.52637e16	−6.67709
$849$	1.21795e15	0.0947624
$850$	−2.48464e15	−0.192070
$851$	1.54292e16	1.18503
$852$	−3.32722e16	−2.53901
$853$	−1.82394e16	−1.38290	−0.691449	−	0.722425i	$-0.743027\pi$
$853$	−1.82394e16	−1.38290	−0.691449	+	0.722425i	$0.743027\pi$
$854$	8.33230e15	0.627692
$855$	1.16489e16	0.871907
$856$	9.10427e16	6.77079
$857$	1.04154e16	0.769626	0.384813	−	0.922994i	$-0.374266\pi$
$857$	1.04154e16	0.769626	0.384813	+	0.922994i	$0.374266\pi$
$858$	−3.19677e16	−2.34710
$859$	5.89745e15	0.430231	0.215116	−	0.976589i	$-0.430987\pi$
$859$	5.89745e15	0.430231	0.215116	+	0.976589i	$0.430987\pi$
$860$	−5.97069e16	−4.32795
$861$	3.01607e15	0.217232
$862$	4.30451e16	3.08059
$863$	−1.69219e16	−1.20334	−0.601671	−	0.798744i	$-0.705498\pi$
$863$	−1.69219e16	−1.20334	−0.601671	+	0.798744i	$0.705498\pi$
$864$	3.19283e16	2.25606
$865$	−7.47141e15	−0.524583
$866$	−1.84933e16	−1.29023
$867$	1.28501e16	0.890843
$868$	−4.80151e16	−3.30765
$869$	1.52966e16	1.04709
$870$	7.35718e15	0.500444
$871$	−9.78834e15	−0.661621
$872$	−4.45795e16	−2.99429
$873$	1.35732e15	0.0905947
$874$	−2.76344e16	−1.83290
$875$	1.17769e16	0.776223
$876$	−3.78751e15	−0.248074
$877$	1.33236e16	0.867209	0.433605	−	0.901103i	$-0.357241\pi$
$877$	1.33236e16	0.867209	0.433605	+	0.901103i	$0.357241\pi$
$878$	4.92092e16	3.18293
$879$	−2.12879e16	−1.36834
$880$	9.26366e16	5.91736
$881$	1.70185e15	0.108032	0.0540161	−	0.998540i	$-0.482798\pi$
$881$	1.70185e15	0.108032	0.0540161	+	0.998540i	$0.482798\pi$
$882$	−4.54627e15	−0.286799
$883$	−2.82141e16	−1.76882	−0.884408	−	0.466715i	$-0.845437\pi$
$883$	−2.82141e16	−1.76882	−0.884408	+	0.466715i	$0.845437\pi$
$884$	−1.78411e16	−1.11157
$885$	−1.53483e16	−0.950324
$886$	−5.86747e16	−3.61048
$887$	1.74126e16	1.06484	0.532420	−	0.846480i	$-0.321283\pi$
$887$	1.74126e16	1.06484	0.532420	+	0.846480i	$0.321283\pi$
$888$	1.24015e17	7.53710
$889$	1.93687e16	1.16988
$890$	2.65947e16	1.59643
$891$	−2.72217e16	−1.62401
$892$	−6.64251e16	−3.93845
$893$	−3.08473e16	−1.81775
$894$	5.24277e16	3.07047
$895$	1.56274e15	0.0909618
$896$	−7.13869e16	−4.12976
$897$	1.13242e16	0.651100
$898$	1.72185e16	0.983953
$899$	−4.39392e15	−0.249560
$900$	5.48792e15	0.309795
$901$	1.56387e16	0.877435
$902$	9.03937e15	0.504083
$903$	−2.81364e16	−1.55950
$904$	7.45468e16	4.10679
$905$	−5.28845e15	−0.289575
$906$	1.52779e16	0.831491
$907$	2.06747e15	0.111840	0.0559202	−	0.998435i	$-0.482191\pi$
$907$	2.06747e15	0.111840	0.0559202	+	0.998435i	$0.482191\pi$
$908$	4.16733e16	2.24071
$909$	−1.10818e16	−0.592257
$910$	−2.51318e16	−1.33504
$911$	8.20176e15	0.433068	0.216534	−	0.976275i	$-0.430525\pi$
$911$	8.20176e15	0.433068	0.216534	+	0.976275i	$0.430525\pi$
$912$	−1.32203e17	−6.93858
$913$	1.18194e16	0.616604
$914$	−5.06360e16	−2.62576
$915$	9.84766e15	0.507595
$916$	5.76547e16	2.95399
$917$	−6.63388e14	−0.0337860
$918$	−1.04448e16	−0.528766
$919$	3.82365e16	1.92417	0.962083	−	0.272758i	$-0.0879359\pi$
$919$	3.82365e16	1.92417	0.962083	+	0.272758i	$0.0879359\pi$
$920$	−5.51340e16	−2.75795
$921$	3.12815e16	1.55546
$922$	−1.80571e16	−0.892543
$923$	1.04008e16	0.511045
$924$	8.38569e16	4.09584
$925$	−6.17269e15	−0.299705
$926$	7.90876e16	3.81722
$927$	7.16835e15	0.343938
$928$	−1.77272e16	−0.845525
$929$	−3.91173e16	−1.85474	−0.927369	−	0.374149i	$-0.877935\pi$
$929$	−3.91173e16	−1.85474	−0.927369	+	0.374149i	$0.877935\pi$
$930$	−7.68394e16	−3.62183
$931$	−6.76382e15	−0.316934
$932$	8.87106e15	0.413226
$933$	4.22359e16	1.95584
$934$	−5.45470e16	−2.51109
$935$	−1.69910e16	−0.777599
$936$	3.44664e16	1.56812
$937$	2.63472e16	1.19170	0.595849	−	0.803097i	$-0.296816\pi$
$937$	2.63472e16	1.19170	0.595849	+	0.803097i	$0.296816\pi$
$938$	3.47676e16	1.56336
$939$	4.46853e15	0.199758
$940$	−9.52784e16	−4.23439
$941$	1.90496e15	0.0841673	0.0420837	−	0.999114i	$-0.486600\pi$
$941$	1.90496e15	0.0841673	0.0420837	+	0.999114i	$0.486600\pi$
$942$	−1.45391e16	−0.638643
$943$	−3.20208e15	−0.139836
$944$	6.59590e16	2.86371
$945$	−1.08658e16	−0.469014
$946$	−8.43266e16	−3.61879
$947$	−1.77371e16	−0.756761	−0.378380	−	0.925650i	$-0.623519\pi$
$947$	−1.77371e16	−0.756761	−0.378380	+	0.925650i	$0.623519\pi$
$948$	−6.74266e16	−2.86013
$949$	1.18397e15	0.0499317
$950$	1.10556e16	0.463557
$951$	3.34208e16	1.39323
$952$	4.09336e16	1.69659
$953$	1.23784e16	0.510098	0.255049	−	0.966928i	$-0.417908\pi$
$953$	1.23784e16	0.510098	0.255049	+	0.966928i	$0.417908\pi$
$954$	−4.67717e16	−1.91632
$955$	−4.04274e15	−0.164686
$956$	−5.42686e15	−0.219801
$957$	7.67386e15	0.309028
$958$	8.31240e16	3.32825
$959$	−9.49947e15	−0.378179
$960$	−1.65431e17	−6.54823
$961$	2.04823e16	0.806120
$962$	−6.00165e16	−2.34859
$963$	2.97250e16	1.15658
$964$	7.90768e15	0.305932
$965$	1.32045e16	0.507950
$966$	−4.02227e16	−1.53850
$967$	−2.25207e16	−0.856518	−0.428259	−	0.903656i	$-0.640873\pi$
$967$	−2.25207e16	−0.856518	−0.428259	+	0.903656i	$0.640873\pi$
$968$	6.79980e16	2.57147
$969$	2.42482e16	0.911797
$970$	8.44565e15	0.315783
$971$	−1.12109e16	−0.416808	−0.208404	−	0.978043i	$-0.566827\pi$
$971$	−1.12109e16	−0.416808	−0.208404	+	0.978043i	$0.566827\pi$
$972$	8.21381e16	3.03655
$973$	1.07486e16	0.395122
$974$	−5.46253e16	−1.99673
$975$	−4.53042e15	−0.164669
$976$	−4.23202e16	−1.52959
$977$	4.15299e16	1.49259	0.746295	−	0.665615i	$-0.231831\pi$
$977$	4.15299e16	1.49259	0.746295	+	0.665615i	$0.231831\pi$
$978$	1.28528e15	0.0459339
$979$	2.77394e16	0.985808
$980$	−2.08915e16	−0.738288
$981$	−1.45550e16	−0.511484
$982$	−3.89962e16	−1.36273
$983$	3.65502e16	1.27012	0.635062	−	0.772462i	$-0.280975\pi$
$983$	3.65502e16	1.27012	0.635062	+	0.772462i	$0.280975\pi$
$984$	−2.57375e16	−0.889393
$985$	8.63559e14	0.0296751
$986$	5.79913e15	0.198171
$987$	−4.48991e16	−1.52579
$988$	7.93855e16	2.68274
$989$	2.98717e16	1.00387
$990$	5.08161e16	1.69828
$991$	−5.53106e16	−1.83824	−0.919122	−	0.393974i	$-0.871100\pi$
$991$	−5.53106e16	−1.83824	−0.919122	+	0.393974i	$0.871100\pi$
$992$	1.85145e17	6.11925
$993$	−2.50571e16	−0.823587
$994$	−3.69432e16	−1.20756
$995$	2.31139e16	0.751358
$996$	−5.20993e16	−1.68425
$997$	3.47259e16	1.11643	0.558213	−	0.829697i	$-0.311487\pi$
$997$	3.47259e16	1.11643	0.558213	+	0.829697i	$0.311487\pi$
$998$	5.51235e16	1.76246
$999$	−2.59483e16	−0.825084

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.12.a.b.1.14	✓	14
3.2	odd	2		261.12.a.e.1.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.12.a.b.1.14	✓	14	1.1	even	1	trivial
261.12.a.e.1.1		14	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q+88.5004 q^{2} -533.955 q^{3} +5784.31 q^{4} +7590.53 q^{5} -47255.2 q^{6} -38749.2 q^{7} +330665. q^{8} +107961. q^{9} +O(q^{10})\)	\(q+88.5004 q^{2} -533.955 q^{3} +5784.31 q^{4} +7590.53 q^{5} -47255.2 q^{6} -38749.2 q^{7} +330665. q^{8} +107961. q^{9} +671765. q^{10} +700680. q^{11} -3.08856e6 q^{12} +965478. q^{13} -3.42932e6 q^{14} -4.05300e6 q^{15} +1.74177e7 q^{16} -3.19468e6 q^{17} +9.55455e6 q^{18} +1.42150e7 q^{19} +4.39060e7 q^{20} +2.06903e7 q^{21} +6.20104e7 q^{22} -2.19664e7 q^{23} -1.76560e8 q^{24} +8.78802e6 q^{25} +8.54452e7 q^{26} +3.69424e7 q^{27} -2.24138e8 q^{28} -2.05111e7 q^{29} -3.58692e8 q^{30} +2.14221e8 q^{31} +8.64271e8 q^{32} -3.74131e8 q^{33} -2.82731e8 q^{34} -2.94127e8 q^{35} +6.24478e8 q^{36} -7.02398e8 q^{37} +1.25803e9 q^{38} -5.15522e8 q^{39} +2.50992e9 q^{40} +1.45772e8 q^{41} +1.83110e9 q^{42} -1.35988e9 q^{43} +4.05295e9 q^{44} +8.19478e8 q^{45} -1.94403e9 q^{46} -2.17005e9 q^{47} -9.30027e9 q^{48} -4.75823e8 q^{49} +7.77743e8 q^{50} +1.70582e9 q^{51} +5.58463e9 q^{52} -4.89523e9 q^{53} +3.26942e9 q^{54} +5.31853e9 q^{55} -1.28130e10 q^{56} -7.59016e9 q^{57} -1.81524e9 q^{58} +3.78690e9 q^{59} -2.34438e10 q^{60} -2.42972e9 q^{61} +1.89587e10 q^{62} -4.18339e9 q^{63} +4.08169e10 q^{64} +7.32849e9 q^{65} -3.31107e10 q^{66} -1.01383e10 q^{67} -1.84791e10 q^{68} +1.17291e10 q^{69} -2.60304e10 q^{70} +1.07727e10 q^{71} +3.56988e10 q^{72} +1.22630e9 q^{73} -6.21624e10 q^{74} -4.69240e9 q^{75} +8.22240e10 q^{76} -2.71508e10 q^{77} -4.56239e10 q^{78} +2.18311e10 q^{79} +1.32210e11 q^{80} -3.88505e10 q^{81} +1.29009e10 q^{82} +1.68685e10 q^{83} +1.19679e11 q^{84} -2.42493e10 q^{85} -1.20350e11 q^{86} +1.09520e10 q^{87} +2.31690e11 q^{88} +3.95893e10 q^{89} +7.25241e10 q^{90} -3.74116e10 q^{91} -1.27061e11 q^{92} -1.14384e11 q^{93} -1.92051e11 q^{94} +1.07899e11 q^{95} -4.61482e11 q^{96} +1.25723e10 q^{97} -4.21105e10 q^{98} +7.56457e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 476 q^{3} + 18362 q^{4} + 9760 q^{5} + 18454 q^{6} + 85024 q^{7} + 126588 q^{8} + 1372146 q^{9}+O(q^{10}) \) 14 * q + 476 * q^3 + 18362 * q^4 + 9760 * q^5 + 18454 * q^6 + 85024 * q^7 + 126588 * q^8 + 1372146 * q^9	\( 14 q + 476 q^{3} + 18362 q^{4} + 9760 q^{5} + 18454 q^{6} + 85024 q^{7} + 126588 q^{8} + 1372146 q^{9} + 713576 q^{10} + 398020 q^{11} - 4026800 q^{12} + 2272440 q^{13} - 7199712 q^{14} - 4763864 q^{15} + 19015138 q^{16} + 5623508 q^{17} - 204156 q^{18} + 29803300 q^{19} + 65161006 q^{20} + 51227832 q^{21} + 167334266 q^{22} + 52654304 q^{23} + 221514842 q^{24} + 194970462 q^{25} + 373581536 q^{26} + 397348256 q^{27} + 319501772 q^{28} - 287156086 q^{29} + 423014226 q^{30} + 634041348 q^{31} + 1260290884 q^{32} + 1180833420 q^{33} + 1316105060 q^{34} + 1599853768 q^{35} + 3198076132 q^{36} + 488665204 q^{37} + 1892845072 q^{38} + 1972619104 q^{39} + 1826486880 q^{40} + 198215164 q^{41} + 1011384468 q^{42} + 2193188100 q^{43} + 26522720 q^{44} - 1129321956 q^{45} - 1567525268 q^{46} - 4175934476 q^{47} - 15582938120 q^{48} + 1105222462 q^{49} - 6630582612 q^{50} + 3297462720 q^{51} - 4557341374 q^{52} - 13223081840 q^{53} - 8946135054 q^{54} - 2726359424 q^{55} - 27538267872 q^{56} - 24477013312 q^{57} + 352219640 q^{59} - 36042747924 q^{60} - 7658546476 q^{61} - 10024135594 q^{62} - 23037581736 q^{63} + 14721327762 q^{64} + 1152802884 q^{65} - 99505241364 q^{66} + 21781534280 q^{67} - 104178000188 q^{68} - 14601399408 q^{69} - 67948872984 q^{70} - 5573287168 q^{71} - 24062143544 q^{72} + 39661511924 q^{73} + 28506052056 q^{74} + 81845109044 q^{75} + 166950090320 q^{76} + 38773567192 q^{77} + 54249159006 q^{78} + 105565209020 q^{79} + 146242150550 q^{80} + 170581084750 q^{81} + 47345182756 q^{82} + 127846064024 q^{83} + 215311861496 q^{84} + 83883234552 q^{85} - 103162039382 q^{86} - 9763306924 q^{87} + 418253082102 q^{88} + 187826099404 q^{89} + 96335639960 q^{90} + 58390389864 q^{91} - 259645875396 q^{92} + 394641636020 q^{93} + 117694719934 q^{94} + 69935059424 q^{95} + 12533631786 q^{96} + 137285937500 q^{97} - 484896369168 q^{98} + 235419947204 q^{99}+O(q^{100}) \) 14 * q + 476 * q^3 + 18362 * q^4 + 9760 * q^5 + 18454 * q^6 + 85024 * q^7 + 126588 * q^8 + 1372146 * q^9 + 713576 * q^10 + 398020 * q^11 - 4026800 * q^12 + 2272440 * q^13 - 7199712 * q^14 - 4763864 * q^15 + 19015138 * q^16 + 5623508 * q^17 - 204156 * q^18 + 29803300 * q^19 + 65161006 * q^20 + 51227832 * q^21 + 167334266 * q^22 + 52654304 * q^23 + 221514842 * q^24 + 194970462 * q^25 + 373581536 * q^26 + 397348256 * q^27 + 319501772 * q^28 - 287156086 * q^29 + 423014226 * q^30 + 634041348 * q^31 + 1260290884 * q^32 + 1180833420 * q^33 + 1316105060 * q^34 + 1599853768 * q^35 + 3198076132 * q^36 + 488665204 * q^37 + 1892845072 * q^38 + 1972619104 * q^39 + 1826486880 * q^40 + 198215164 * q^41 + 1011384468 * q^42 + 2193188100 * q^43 + 26522720 * q^44 - 1129321956 * q^45 - 1567525268 * q^46 - 4175934476 * q^47 - 15582938120 * q^48 + 1105222462 * q^49 - 6630582612 * q^50 + 3297462720 * q^51 - 4557341374 * q^52 - 13223081840 * q^53 - 8946135054 * q^54 - 2726359424 * q^55 - 27538267872 * q^56 - 24477013312 * q^57 + 352219640 * q^59 - 36042747924 * q^60 - 7658546476 * q^61 - 10024135594 * q^62 - 23037581736 * q^63 + 14721327762 * q^64 + 1152802884 * q^65 - 99505241364 * q^66 + 21781534280 * q^67 - 104178000188 * q^68 - 14601399408 * q^69 - 67948872984 * q^70 - 5573287168 * q^71 - 24062143544 * q^72 + 39661511924 * q^73 + 28506052056 * q^74 + 81845109044 * q^75 + 166950090320 * q^76 + 38773567192 * q^77 + 54249159006 * q^78 + 105565209020 * q^79 + 146242150550 * q^80 + 170581084750 * q^81 + 47345182756 * q^82 + 127846064024 * q^83 + 215311861496 * q^84 + 83883234552 * q^85 - 103162039382 * q^86 - 9763306924 * q^87 + 418253082102 * q^88 + 187826099404 * q^89 + 96335639960 * q^90 + 58390389864 * q^91 - 259645875396 * q^92 + 394641636020 * q^93 + 117694719934 * q^94 + 69935059424 * q^95 + 12533631786 * q^96 + 137285937500 * q^97 - 484896369168 * q^98 + 235419947204 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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