LMFDB - Embedded newform 29.10.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,10,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, 10, names="a")

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

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 10 $
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:	$14.9360392488$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 4803 x^{10} + 14952 x^{9} + 8248476 x^{8} - 14809944 x^{7} - 6122244486 x^{6} + \cdots + 40\!\cdots\!38 $ x^12 - 4x^11 - 4803x^10 + 14952x^9 + 8248476x^8 - 14809944x^7 - 6122244486x^6 - 1026481216x^5 + 1899055440249x^4 + 3992697832188x^3 - 174144148490503x^2 - 282853247198664*x + 4071614738753338
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-41.0148$ 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)

$f(q)$	$=$	$q-40.0148 q^{2} -3.22123 q^{3} +1089.19 q^{4} -146.392 q^{5} +128.897 q^{6} +8248.48 q^{7} -23096.1 q^{8} -19672.6 q^{9} +O(q^{10})$	\(q-40.0148 q^{2} -3.22123 q^{3} +1089.19 q^{4} -146.392 q^{5} +128.897 q^{6} +8248.48 q^{7} -23096.1 q^{8} -19672.6 q^{9} +5857.84 q^{10} -70418.0 q^{11} -3508.52 q^{12} +16018.5 q^{13} -330062. q^{14} +471.562 q^{15} +366522. q^{16} +372336. q^{17} +787197. q^{18} +681805. q^{19} -159448. q^{20} -26570.3 q^{21} +2.81777e6 q^{22} -649778. q^{23} +74397.8 q^{24} -1.93169e6 q^{25} -640978. q^{26} +126774. q^{27} +8.98415e6 q^{28} +707281. q^{29} -18869.5 q^{30} +5.41966e6 q^{31} -2.84113e6 q^{32} +226833. q^{33} -1.48990e7 q^{34} -1.20751e6 q^{35} -2.14272e7 q^{36} +1.04945e7 q^{37} -2.72823e7 q^{38} -51599.3 q^{39} +3.38108e6 q^{40} +3.04633e7 q^{41} +1.06320e6 q^{42} +527788. q^{43} -7.66985e7 q^{44} +2.87991e6 q^{45} +2.60008e7 q^{46} +2.70093e6 q^{47} -1.18065e6 q^{48} +2.76839e7 q^{49} +7.72965e7 q^{50} -1.19938e6 q^{51} +1.74472e7 q^{52} +5.51368e7 q^{53} -5.07282e6 q^{54} +1.03086e7 q^{55} -1.90508e8 q^{56} -2.19625e6 q^{57} -2.83017e7 q^{58} -2.95096e6 q^{59} +513619. q^{60} +1.42477e8 q^{61} -2.16867e8 q^{62} -1.62269e8 q^{63} -7.39720e7 q^{64} -2.34498e6 q^{65} -9.07668e6 q^{66} -2.65283e7 q^{67} +4.05544e8 q^{68} +2.09308e6 q^{69} +4.83183e7 q^{70} +1.98120e8 q^{71} +4.54361e8 q^{72} +2.91785e8 q^{73} -4.19937e8 q^{74} +6.22243e6 q^{75} +7.42614e8 q^{76} -5.80842e8 q^{77} +2.06474e6 q^{78} +4.43550e8 q^{79} -5.36558e7 q^{80} +3.86808e8 q^{81} -1.21898e9 q^{82} -1.89412e8 q^{83} -2.89400e7 q^{84} -5.45070e7 q^{85} -2.11194e7 q^{86} -2.27831e6 q^{87} +1.62638e9 q^{88} -8.11753e8 q^{89} -1.15239e8 q^{90} +1.32128e8 q^{91} -7.07730e8 q^{92} -1.74580e7 q^{93} -1.08077e8 q^{94} -9.98106e7 q^{95} +9.15192e6 q^{96} -9.48377e8 q^{97} -1.10777e9 q^{98} +1.38531e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 16 q^{2} + 242 q^{3} + 3498 q^{4} + 1762 q^{5} + 5446 q^{6} + 12080 q^{7} + 25350 q^{8} + 43026 q^{9}+O(q^{10}) $ 12 * q + 16 * q^2 + 242 * q^3 + 3498 * q^4 + 1762 * q^5 + 5446 * q^6 + 12080 * q^7 + 25350 * q^8 + 43026 * q^9	\( 12 q + 16 q^{2} + 242 q^{3} + 3498 q^{4} + 1762 q^{5} + 5446 q^{6} + 12080 q^{7} + 25350 q^{8} + 43026 q^{9} - 46678 q^{10} + 24474 q^{11} - 14210 q^{12} + 107722 q^{13} + 677768 q^{14} + 505426 q^{15} + 1656882 q^{16} + 982120 q^{17} + 2364102 q^{18} + 2084360 q^{19} + 4689410 q^{20} + 2911344 q^{21} + 2725230 q^{22} + 3004004 q^{23} + 7893170 q^{24} + 6339542 q^{25} + 6863698 q^{26} + 7881014 q^{27} + 5116944 q^{28} + 8487372 q^{29} + 10924626 q^{30} + 17872478 q^{31} + 5122946 q^{32} - 860442 q^{33} + 15662848 q^{34} - 22252312 q^{35} - 35199980 q^{36} + 452980 q^{37} - 68665276 q^{38} - 29528222 q^{39} - 61623214 q^{40} - 69039804 q^{41} - 150603216 q^{42} + 5379186 q^{43} - 58283762 q^{44} - 63687756 q^{45} - 76817844 q^{46} - 49104062 q^{47} - 99120062 q^{48} + 73113148 q^{49} - 281373726 q^{50} + 1578252 q^{51} - 49849646 q^{52} + 2253998 q^{53} - 166064634 q^{54} + 82907066 q^{55} + 119369464 q^{56} + 69024164 q^{57} + 11316496 q^{58} + 51587572 q^{59} - 107912622 q^{60} + 251179296 q^{61} + 2421010 q^{62} + 573206808 q^{63} + 460030950 q^{64} + 301434554 q^{65} + 305189958 q^{66} + 741046264 q^{67} + 503103116 q^{68} + 1480618500 q^{69} + 666826600 q^{70} + 488700124 q^{71} + 243154096 q^{72} + 1432375020 q^{73} - 208138340 q^{74} + 462882236 q^{75} - 253709644 q^{76} + 406327616 q^{77} - 1244370462 q^{78} + 400834638 q^{79} - 440320610 q^{80} + 207205984 q^{81} - 1992598260 q^{82} + 1525085236 q^{83} - 2191854376 q^{84} - 387675996 q^{85} - 3425646378 q^{86} + 171162002 q^{87} - 3147673814 q^{88} + 691159332 q^{89} - 2412410836 q^{90} + 1569278264 q^{91} - 2491626380 q^{92} + 270455138 q^{93} - 4397366402 q^{94} + 236293724 q^{95} - 1448270346 q^{96} + 2494422276 q^{97} - 3443098784 q^{98} + 2123567852 q^{99}+O(q^{100}) \) 12 * q + 16 * q^2 + 242 * q^3 + 3498 * q^4 + 1762 * q^5 + 5446 * q^6 + 12080 * q^7 + 25350 * q^8 + 43026 * q^9 - 46678 * q^10 + 24474 * q^11 - 14210 * q^12 + 107722 * q^13 + 677768 * q^14 + 505426 * q^15 + 1656882 * q^16 + 982120 * q^17 + 2364102 * q^18 + 2084360 * q^19 + 4689410 * q^20 + 2911344 * q^21 + 2725230 * q^22 + 3004004 * q^23 + 7893170 * q^24 + 6339542 * q^25 + 6863698 * q^26 + 7881014 * q^27 + 5116944 * q^28 + 8487372 * q^29 + 10924626 * q^30 + 17872478 * q^31 + 5122946 * q^32 - 860442 * q^33 + 15662848 * q^34 - 22252312 * q^35 - 35199980 * q^36 + 452980 * q^37 - 68665276 * q^38 - 29528222 * q^39 - 61623214 * q^40 - 69039804 * q^41 - 150603216 * q^42 + 5379186 * q^43 - 58283762 * q^44 - 63687756 * q^45 - 76817844 * q^46 - 49104062 * q^47 - 99120062 * q^48 + 73113148 * q^49 - 281373726 * q^50 + 1578252 * q^51 - 49849646 * q^52 + 2253998 * q^53 - 166064634 * q^54 + 82907066 * q^55 + 119369464 * q^56 + 69024164 * q^57 + 11316496 * q^58 + 51587572 * q^59 - 107912622 * q^60 + 251179296 * q^61 + 2421010 * q^62 + 573206808 * q^63 + 460030950 * q^64 + 301434554 * q^65 + 305189958 * q^66 + 741046264 * q^67 + 503103116 * q^68 + 1480618500 * q^69 + 666826600 * q^70 + 488700124 * q^71 + 243154096 * q^72 + 1432375020 * q^73 - 208138340 * q^74 + 462882236 * q^75 - 253709644 * q^76 + 406327616 * q^77 - 1244370462 * q^78 + 400834638 * q^79 - 440320610 * q^80 + 207205984 * q^81 - 1992598260 * q^82 + 1525085236 * q^83 - 2191854376 * q^84 - 387675996 * q^85 - 3425646378 * q^86 + 171162002 * q^87 - 3147673814 * q^88 + 691159332 * q^89 - 2412410836 * q^90 + 1569278264 * q^91 - 2491626380 * q^92 + 270455138 * q^93 - 4397366402 * q^94 + 236293724 * q^95 - 1448270346 * q^96 + 2494422276 * q^97 - 3443098784 * q^98 + 2123567852 * 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 $

$2$	−40.0148	−1.76842	−0.884212	−	0.467087i	$-0.845304\pi$
$2$	−40.0148	−1.76842	−0.884212	+	0.467087i	$0.845304\pi$
$3$	−3.22123	−0.0229602	−0.0114801	−	0.999934i	$-0.503654\pi$
$3$	−3.22123	−0.0229602	−0.0114801	+	0.999934i	$0.503654\pi$
$4$	1089.19	2.12732
$5$	−146.392	−0.104749	−0.0523747	−	0.998628i	$-0.516679\pi$
$5$	−146.392	−0.104749	−0.0523747	+	0.998628i	$0.516679\pi$
$6$	128.897	0.0406034
$7$	8248.48	1.29847	0.649237	−	0.760587i	$-0.275089\pi$
$7$	8248.48	1.29847	0.649237	+	0.760587i	$0.275089\pi$
$8$	−23096.1	−1.99358
$9$	−19672.6	−0.999473
$10$	5857.84	0.185241
$11$	−70418.0	−1.45016	−0.725082	−	0.688663i	$-0.758198\pi$
$11$	−70418.0	−1.45016	−0.725082	+	0.688663i	$0.758198\pi$
$12$	−3508.52	−0.0488437
$13$	16018.5	0.155552	0.0777762	−	0.996971i	$-0.475218\pi$
$13$	16018.5	0.155552	0.0777762	+	0.996971i	$0.475218\pi$
$14$	−330062.	−2.29625
$15$	471.562	0.00240507
$16$	366522.	1.39817
$17$	372336.	1.08122	0.540612	−	0.841272i	$-0.318193\pi$
$17$	372336.	1.08122	0.540612	+	0.841272i	$0.318193\pi$
$18$	787197.	1.76749
$19$	681805.	1.20024	0.600121	−	0.799909i	$-0.295119\pi$
$19$	681805.	1.20024	0.600121	+	0.799909i	$0.295119\pi$
$20$	−159448.	−0.222836
$21$	−26570.3	−0.0298132
$22$	2.81777e6	2.56450
$23$	−649778.	−0.484161	−0.242080	−	0.970256i	$-0.577830\pi$
$23$	−649778.	−0.484161	−0.242080	+	0.970256i	$0.577830\pi$
$24$	74397.8	0.0457730
$25$	−1.93169e6	−0.989028
$26$	−640978.	−0.275083
$27$	126774.	0.0459083
$28$	8.98415e6	2.76227
$29$	707281.	0.185695
$29$	707281.	0.185695
$30$	−18869.5	−0.00425318
$31$	5.41966e6	1.05401	0.527004	−	0.849863i	$-0.323315\pi$
$31$	5.41966e6	1.05401	0.527004	+	0.849863i	$0.323315\pi$
$32$	−2.84113e6	−0.478978
$33$	226833.	0.0332961
$34$	−1.48990e7	−1.91206
$35$	−1.20751e6	−0.136014
$36$	−2.14272e7	−2.12620
$37$	1.04945e7	0.920566	0.460283	−	0.887772i	$-0.347748\pi$
$37$	1.04945e7	0.920566	0.460283	+	0.887772i	$0.347748\pi$
$38$	−2.72823e7	−2.12254
$39$	−51599.3	−0.00357152
$40$	3.38108e6	0.208826
$41$	3.04633e7	1.68364	0.841821	−	0.539757i	$-0.181484\pi$
$41$	3.04633e7	1.68364	0.841821	+	0.539757i	$0.181484\pi$
$42$	1.06320e6	0.0527224
$43$	527788.	0.0235424	0.0117712	−	0.999931i	$-0.496253\pi$
$43$	527788.	0.0235424	0.0117712	+	0.999931i	$0.496253\pi$
$44$	−7.66985e7	−3.08496
$45$	2.87991e6	0.104694
$46$	2.60008e7	0.856201
$47$	2.70093e6	0.0807370	0.0403685	−	0.999185i	$-0.487147\pi$
$47$	2.70093e6	0.0807370	0.0403685	+	0.999185i	$0.487147\pi$
$48$	−1.18065e6	−0.0321023
$49$	2.76839e7	0.686032
$50$	7.72965e7	1.74902
$51$	−1.19938e6	−0.0248251
$52$	1.74472e7	0.330910
$53$	5.51368e7	0.959843	0.479922	−	0.877311i	$-0.340665\pi$
$53$	5.51368e7	0.959843	0.479922	+	0.877311i	$0.340665\pi$
$54$	−5.07282e6	−0.0811854
$55$	1.03086e7	0.151904
$56$	−1.90508e8	−2.58861
$57$	−2.19625e6	−0.0275578
$58$	−2.83017e7	−0.328388
$59$	−2.95096e6	−0.0317051	−0.0158526	−	0.999874i	$-0.505046\pi$
$59$	−2.95096e6	−0.0317051	−0.0158526	+	0.999874i	$0.505046\pi$
$60$	513619.	0.00511635
$61$	1.42477e8	1.31753	0.658767	−	0.752347i	$-0.271078\pi$
$61$	1.42477e8	1.31753	0.658767	+	0.752347i	$0.271078\pi$
$62$	−2.16867e8	−1.86393
$63$	−1.62269e8	−1.29779
$64$	−7.39720e7	−0.551134
$65$	−2.34498e6	−0.0162940
$66$	−9.07668e6	−0.0588815
$67$	−2.65283e7	−0.160832	−0.0804159	−	0.996761i	$-0.525625\pi$
$67$	−2.65283e7	−0.160832	−0.0804159	+	0.996761i	$0.525625\pi$
$68$	4.05544e8	2.30011
$69$	2.09308e6	0.0111164
$70$	4.83183e7	0.240531
$71$	1.98120e8	0.925264	0.462632	−	0.886550i	$-0.346905\pi$
$71$	1.98120e8	0.925264	0.462632	+	0.886550i	$0.346905\pi$
$72$	4.54361e8	1.99253
$73$	2.91785e8	1.20257	0.601284	−	0.799036i	$-0.294656\pi$
$73$	2.91785e8	1.20257	0.601284	+	0.799036i	$0.294656\pi$
$74$	−4.19937e8	−1.62795
$75$	6.22243e6	0.0227083
$76$	7.42614e8	2.55330
$77$	−5.80842e8	−1.88300
$78$	2.06474e6	0.00631596
$79$	4.43550e8	1.28121	0.640606	−	0.767870i	$-0.278683\pi$
$79$	4.43550e8	1.28121	0.640606	+	0.767870i	$0.278683\pi$
$80$	−5.36558e7	−0.146458
$81$	3.86808e8	0.998419
$82$	−1.21898e9	−2.97739
$83$	−1.89412e8	−0.438084	−0.219042	−	0.975715i	$-0.570293\pi$
$83$	−1.89412e8	−0.438084	−0.219042	+	0.975715i	$0.570293\pi$
$84$	−2.89400e7	−0.0634223
$85$	−5.45070e7	−0.113258
$86$	−2.11194e7	−0.0416330
$87$	−2.27831e6	−0.00426361
$88$	1.62638e9	2.89101
$89$	−8.11753e8	−1.37141	−0.685707	−	0.727877i	$-0.740507\pi$
$89$	−8.11753e8	−1.37141	−0.685707	+	0.727877i	$0.740507\pi$
$90$	−1.15239e8	−0.185144
$91$	1.32128e8	0.201981
$92$	−7.07730e8	−1.02997
$93$	−1.74580e7	−0.0242003
$94$	−1.08077e8	−0.142777
$95$	−9.98106e7	−0.125725
$96$	9.15192e6	0.0109974
$97$	−9.48377e8	−1.08770	−0.543849	−	0.839183i	$-0.683033\pi$
$97$	−9.48377e8	−1.08770	−0.543849	+	0.839183i	$0.683033\pi$
$98$	−1.10777e9	−1.21320
$99$	1.38531e9	1.44940
$100$	−2.10398e9	−2.10398
$101$	4.06380e8	0.388585	0.194292	−	0.980944i	$-0.437759\pi$
$101$	4.06380e8	0.388585	0.194292	+	0.980944i	$0.437759\pi$
$102$	4.79931e7	0.0439013
$103$	−2.00785e9	−1.75778	−0.878889	−	0.477027i	$-0.841714\pi$
$103$	−2.00785e9	−1.75778	−0.878889	+	0.477027i	$0.841714\pi$
$104$	−3.69965e8	−0.310106
$105$	3.88967e6	0.00312292
$106$	−2.20629e9	−1.69741
$107$	1.77284e9	1.30750	0.653751	−	0.756709i	$-0.273194\pi$
$107$	1.77284e9	1.30750	0.653751	+	0.756709i	$0.273194\pi$
$108$	1.38080e8	0.0976617
$109$	1.83954e9	1.24822	0.624109	−	0.781337i	$-0.285462\pi$
$109$	1.83954e9	1.24822	0.624109	+	0.781337i	$0.285462\pi$
$110$	−4.12498e8	−0.268630
$111$	−3.38053e7	−0.0211364
$112$	3.02325e9	1.81549
$113$	−1.95684e9	−1.12902	−0.564512	−	0.825425i	$-0.690936\pi$
$113$	−1.95684e9	−1.12902	−0.564512	+	0.825425i	$0.690936\pi$
$114$	8.78826e7	0.0487339
$115$	9.51221e7	0.0507156
$116$	7.70362e8	0.395033
$117$	−3.15126e8	−0.155470
$118$	1.18082e8	0.0560680
$119$	3.07121e9	1.40394
$120$	−1.08912e7	−0.00479470
$121$	2.60075e9	1.10297
$122$	−5.70121e9	−2.32996
$123$	−9.81293e7	−0.0386568
$124$	5.90303e9	2.24221
$125$	5.68706e8	0.208350
$126$	6.49318e9	2.29504
$127$	3.42597e9	1.16860	0.584302	−	0.811537i	$-0.301369\pi$
$127$	3.42597e9	1.16860	0.584302	+	0.811537i	$0.301369\pi$
$128$	4.41464e9	1.45362
$129$	−1.70013e6	−0.000540540 0
$130$	9.38339e7	0.0288147
$131$	−4.46270e9	−1.32396	−0.661982	−	0.749519i	$-0.730285\pi$
$131$	−4.46270e9	−1.32396	−0.661982	+	0.749519i	$0.730285\pi$
$132$	2.47063e8	0.0708314
$133$	5.62386e9	1.55848
$134$	1.06152e9	0.284419
$135$	−1.85586e7	−0.00480887
$136$	−8.59951e9	−2.15550
$137$	−5.70839e9	−1.38443	−0.692215	−	0.721692i	$-0.743365\pi$
$137$	−5.70839e9	−1.38443	−0.692215	+	0.721692i	$0.743365\pi$
$138$	−8.37544e7	−0.0196586
$139$	−5.22986e9	−1.18829	−0.594146	−	0.804357i	$-0.702510\pi$
$139$	−5.22986e9	−1.18829	−0.594146	+	0.804357i	$0.702510\pi$
$140$	−1.31521e9	−0.289346
$141$	−8.70031e6	−0.00185374
$142$	−7.92774e9	−1.63626
$143$	−1.12799e9	−0.225576
$144$	−7.21045e9	−1.39743
$145$	−1.03540e8	−0.0194515
$146$	−1.16757e10	−2.12665
$147$	−8.91761e7	−0.0157515
$148$	1.14305e10	1.95834
$149$	1.12763e10	1.87426	0.937129	−	0.348984i	$-0.113473\pi$
$149$	1.12763e10	1.87426	0.937129	+	0.348984i	$0.113473\pi$
$150$	−2.48990e8	−0.0401579
$151$	6.00052e9	0.939275	0.469638	−	0.882859i	$-0.344385\pi$
$151$	6.00052e9	0.939275	0.469638	+	0.882859i	$0.344385\pi$
$152$	−1.57470e10	−2.39278
$153$	−7.32483e9	−1.08065
$154$	2.32423e10	3.32994
$155$	−7.93393e8	−0.110407
$156$	−5.62013e7	−0.00759776
$157$	1.08547e10	1.42583	0.712916	−	0.701249i	$-0.247374\pi$
$157$	1.08547e10	1.42583	0.712916	+	0.701249i	$0.247374\pi$
$158$	−1.77486e10	−2.26573
$159$	−1.77608e8	−0.0220382
$160$	4.15918e8	0.0501727
$161$	−5.35968e9	−0.628670
$162$	−1.54781e10	−1.76563
$163$	−1.40707e7	−0.00156125	−0.000780626	−	1.00000i	$-0.500248\pi$
$163$	−1.40707e7	−0.00156125	−0.000780626		1.00000i	$0.500248\pi$
$164$	3.31803e10	3.58164
$165$	−3.32064e7	−0.00348774
$166$	7.57931e9	0.774717
$167$	7.19083e9	0.715410	0.357705	−	0.933835i	$-0.383559\pi$
$167$	7.19083e9	0.715410	0.357705	+	0.933835i	$0.383559\pi$
$168$	6.13669e8	0.0594350
$169$	−1.03479e10	−0.975803
$170$	2.18109e9	0.200287
$171$	−1.34129e10	−1.19961
$172$	5.74860e8	0.0500823
$173$	−7.41454e9	−0.629327	−0.314664	−	0.949203i	$-0.601892\pi$
$173$	−7.41454e9	−0.629327	−0.314664	+	0.949203i	$0.601892\pi$
$174$	9.11664e7	0.00753986
$175$	−1.59336e10	−1.28423
$176$	−2.58098e10	−2.02758
$177$	9.50572e6	0.000727956 0
$178$	3.24822e10	2.42524
$179$	1.92827e10	1.40388	0.701940	−	0.712236i	$-0.252317\pi$
$179$	1.92827e10	1.40388	0.701940	+	0.712236i	$0.252317\pi$
$180$	3.13676e9	0.222718
$181$	−1.54824e10	−1.07222	−0.536110	−	0.844148i	$-0.680107\pi$
$181$	−1.54824e10	−1.07222	−0.536110	+	0.844148i	$0.680107\pi$
$182$	−5.28710e9	−0.357187
$183$	−4.58953e8	−0.0302509
$184$	1.50073e10	0.965213
$185$	−1.53631e9	−0.0964288
$186$	6.98578e8	0.0427963
$187$	−2.62192e10	−1.56795
$188$	2.94182e9	0.171753
$189$	1.04569e9	0.0596107
$190$	3.99391e9	0.222334
$191$	2.03368e10	1.10569	0.552843	−	0.833285i	$-0.313543\pi$
$191$	2.03368e10	1.10569	0.552843	+	0.833285i	$0.313543\pi$
$192$	2.38281e8	0.0126542
$193$	−2.77213e10	−1.43815	−0.719076	−	0.694931i	$-0.755435\pi$
$193$	−2.77213e10	−1.43815	−0.719076	+	0.694931i	$0.755435\pi$
$194$	3.79492e10	1.92351
$195$	7.55371e6	0.000374115 0
$196$	3.01529e10	1.45941
$197$	−2.42108e10	−1.14528	−0.572638	−	0.819808i	$-0.694080\pi$
$197$	−2.42108e10	−1.14528	−0.572638	+	0.819808i	$0.694080\pi$
$198$	−5.54329e10	−2.56315
$199$	2.35859e9	0.106614	0.0533070	−	0.998578i	$-0.483024\pi$
$199$	2.35859e9	0.106614	0.0533070	+	0.998578i	$0.483024\pi$
$200$	4.46146e10	1.97170
$201$	8.54536e7	0.00369273
$202$	−1.62612e10	−0.687183
$203$	5.83400e9	0.241120
$204$	−1.30635e9	−0.0528110
$205$	−4.45958e9	−0.176360
$206$	8.03438e10	3.10849
$207$	1.27828e10	0.483906
$208$	5.87114e9	0.217489
$209$	−4.80114e10	−1.74055
$210$	−1.55644e8	−0.00552264
$211$	−2.00478e10	−0.696299	−0.348150	−	0.937439i	$-0.613190\pi$
$211$	−2.00478e10	−0.696299	−0.348150	+	0.937439i	$0.613190\pi$
$212$	6.00543e10	2.04189
$213$	−6.38190e8	−0.0212443
$214$	−7.09399e10	−2.31222
$215$	−7.72638e7	−0.00246606
$216$	−2.92797e9	−0.0915219
$217$	4.47040e10	1.36860
$218$	−7.36090e10	−2.20738
$219$	−9.39905e8	−0.0276112
$220$	1.12280e10	0.323148
$221$	5.96427e9	0.168187
$222$	1.35271e9	0.0373781
$223$	−1.46817e9	−0.0397560	−0.0198780	−	0.999802i	$-0.506328\pi$
$223$	−1.46817e9	−0.0397560	−0.0198780	+	0.999802i	$0.506328\pi$
$224$	−2.34350e10	−0.621940
$225$	3.80015e10	0.988506
$226$	7.83028e10	1.99659
$227$	4.95206e10	1.23786	0.618928	−	0.785448i	$-0.287567\pi$
$227$	4.95206e10	1.23786	0.618928	+	0.785448i	$0.287567\pi$
$228$	−2.39213e9	−0.0586243
$229$	2.24625e10	0.539758	0.269879	−	0.962894i	$-0.413016\pi$
$229$	2.24625e10	0.539758	0.269879	+	0.962894i	$0.413016\pi$
$230$	−3.80630e9	−0.0896866
$231$	1.87103e9	0.0432340
$232$	−1.63354e10	−0.370198
$233$	3.14544e10	0.699166	0.349583	−	0.936905i	$-0.386323\pi$
$233$	3.14544e10	0.699166	0.349583	+	0.936905i	$0.386323\pi$
$234$	1.26097e10	0.274938
$235$	−3.95394e8	−0.00845715
$236$	−3.21415e9	−0.0674469
$237$	−1.42878e9	−0.0294169
$238$	−1.22894e11	−2.48276
$239$	−4.78675e10	−0.948965	−0.474482	−	0.880265i	$-0.657365\pi$
$239$	−4.78675e10	−0.948965	−0.474482	+	0.880265i	$0.657365\pi$
$240$	1.72838e8	0.00336270
$241$	−7.21425e10	−1.37757	−0.688787	−	0.724964i	$-0.741856\pi$
$241$	−7.21425e10	−1.37757	−0.688787	+	0.724964i	$0.741856\pi$
$242$	−1.04069e11	−1.95052
$243$	−3.74128e9	−0.0688323
$244$	1.55185e11	2.80282
$245$	−4.05269e9	−0.0718615
$246$	3.92663e9	0.0683615
$247$	1.09215e10	0.186701
$248$	−1.25173e11	−2.10125
$249$	6.10141e8	0.0100585
$250$	−2.27567e10	−0.368450
$251$	4.22694e10	0.672194	0.336097	−	0.941827i	$-0.390893\pi$
$251$	4.22694e10	0.672194	0.336097	+	0.941827i	$0.390893\pi$
$252$	−1.76742e11	−2.76081
$253$	4.57561e10	0.702112
$254$	−1.37090e11	−2.06658
$255$	1.75580e8	0.00260042
$256$	−1.38777e11	−2.01948
$257$	4.96385e10	0.709774	0.354887	−	0.934909i	$-0.384519\pi$
$257$	4.96385e10	0.709774	0.354887	+	0.934909i	$0.384519\pi$
$258$	6.80303e7	0.000955903 0
$259$	8.65639e10	1.19533
$260$	−2.55412e9	−0.0346626
$261$	−1.39141e10	−0.185597
$262$	1.78574e11	2.34133
$263$	3.39264e10	0.437257	0.218629	−	0.975808i	$-0.429842\pi$
$263$	3.39264e10	0.437257	0.218629	+	0.975808i	$0.429842\pi$
$264$	−5.23895e9	−0.0663783
$265$	−8.07158e9	−0.100543
$266$	−2.25038e11	−2.75606
$267$	2.61484e9	0.0314880
$268$	−2.88942e10	−0.342141
$269$	7.42881e10	0.865035	0.432518	−	0.901625i	$-0.357625\pi$
$269$	7.42881e10	0.865035	0.432518	+	0.901625i	$0.357625\pi$
$270$	7.42619e8	0.00850412
$271$	5.74689e10	0.647248	0.323624	−	0.946186i	$-0.395099\pi$
$271$	5.74689e10	0.647248	0.323624	+	0.946186i	$0.395099\pi$
$272$	1.36469e11	1.51173
$273$	−4.25616e8	−0.00463752
$274$	2.28420e11	2.44826
$275$	1.36026e11	1.43425
$276$	2.27976e9	0.0236482
$277$	−9.94296e10	−1.01474	−0.507372	−	0.861727i	$-0.669383\pi$
$277$	−9.94296e10	−1.01474	−0.507372	+	0.861727i	$0.669383\pi$
$278$	2.09272e11	2.10140
$279$	−1.06619e11	−1.05345
$280$	2.78888e10	0.271155
$281$	−1.22355e11	−1.17069	−0.585346	−	0.810783i	$-0.699042\pi$
$281$	−1.22355e11	−1.17069	−0.585346	+	0.810783i	$0.699042\pi$
$282$	3.48141e8	0.00327819
$283$	1.17242e11	1.08653	0.543266	−	0.839560i	$-0.317187\pi$
$283$	1.17242e11	1.08653	0.543266	+	0.839560i	$0.317187\pi$
$284$	2.15790e11	1.96833
$285$	3.21513e8	0.00288667
$286$	4.51364e10	0.398915
$287$	2.51276e11	2.18616
$288$	5.58924e10	0.478726
$289$	2.00466e10	0.169044
$290$	4.14314e9	0.0343984
$291$	3.05494e9	0.0249738
$292$	3.17808e11	2.55825
$293$	−2.01716e11	−1.59896	−0.799478	−	0.600696i	$-0.794890\pi$
$293$	−2.01716e11	−1.59896	−0.799478	+	0.600696i	$0.794890\pi$
$294$	3.56837e9	0.0278552
$295$	4.31996e8	0.00332109
$296$	−2.42382e11	−1.83522
$297$	−8.92714e9	−0.0665746
$298$	−4.51220e11	−3.31448
$299$	−1.04085e10	−0.0753124
$300$	6.77740e9	0.0483078
$301$	4.35345e9	0.0305692
$302$	−2.40110e11	−1.66104
$303$	−1.30904e9	−0.00892200
$304$	2.49897e11	1.67814
$305$	−2.08575e10	−0.138011
$306$	2.93102e11	1.91105
$307$	−1.12729e11	−0.724289	−0.362144	−	0.932122i	$-0.617955\pi$
$307$	−1.12729e11	−0.724289	−0.362144	+	0.932122i	$0.617955\pi$
$308$	−6.32646e11	−4.00574
$309$	6.46775e9	0.0403589
$310$	3.17475e10	0.195246
$311$	−2.64594e11	−1.60383	−0.801915	−	0.597438i	$-0.796185\pi$
$311$	−2.64594e11	−1.60383	−0.801915	+	0.597438i	$0.796185\pi$
$312$	1.19174e9	0.00712011
$313$	8.10456e10	0.477287	0.238644	−	0.971107i	$-0.423297\pi$
$313$	8.10456e10	0.477287	0.238644	+	0.971107i	$0.423297\pi$
$314$	−4.34348e11	−2.52148
$315$	2.37549e10	0.135943
$316$	4.83110e11	2.72555
$317$	1.75942e11	0.978595	0.489297	−	0.872117i	$-0.337253\pi$
$317$	1.75942e11	0.978595	0.489297	+	0.872117i	$0.337253\pi$
$318$	7.10697e9	0.0389729
$319$	−4.98053e10	−0.269289
$320$	1.08289e10	0.0577310
$321$	−5.71073e9	−0.0300206
$322$	2.14467e11	1.11175
$323$	2.53861e11	1.29773
$324$	4.21306e11	2.12396
$325$	−3.09429e10	−0.153846
$326$	5.63039e8	0.00276095
$327$	−5.92559e9	−0.0286594
$328$	−7.03583e11	−3.35647
$329$	2.22786e10	0.104835
$330$	1.32875e9	0.00616781
$331$	−2.33660e11	−1.06994	−0.534969	−	0.844872i	$-0.679677\pi$
$331$	−2.33660e11	−1.06994	−0.534969	+	0.844872i	$0.679677\pi$
$332$	−2.06306e11	−0.931944
$333$	−2.06455e11	−0.920081
$334$	−2.87740e11	−1.26515
$335$	3.88352e9	0.0168470
$336$	−9.73859e9	−0.0416840
$337$	−4.56728e11	−1.92896	−0.964480	−	0.264158i	$-0.914906\pi$
$337$	−4.56728e11	−1.92896	−0.964480	+	0.264158i	$0.914906\pi$
$338$	4.14070e11	1.72563
$339$	6.30345e9	0.0259226
$340$	−5.93684e10	−0.240935
$341$	−3.81642e11	−1.52848
$342$	5.36715e11	2.12142
$343$	−1.04506e11	−0.407679
$344$	−1.21898e10	−0.0469337
$345$	−3.06410e8	−0.00116444
$346$	2.96692e11	1.11292
$347$	−3.14644e10	−0.116503	−0.0582515	−	0.998302i	$-0.518553\pi$
$347$	−3.14644e10	−0.116503	−0.0582515	+	0.998302i	$0.518553\pi$
$348$	−2.48151e9	−0.00907005
$349$	2.94513e11	1.06265	0.531324	−	0.847169i	$-0.321695\pi$
$349$	2.94513e11	1.06265	0.531324	+	0.847169i	$0.321695\pi$
$350$	6.37579e11	2.27105
$351$	2.03072e9	0.00714116
$352$	2.00067e11	0.694596
$353$	8.12507e10	0.278510	0.139255	−	0.990257i	$-0.455529\pi$
$353$	8.12507e10	0.278510	0.139255	+	0.990257i	$0.455529\pi$
$354$	−3.80370e8	−0.00128733
$355$	−2.90031e10	−0.0969208
$356$	−8.84151e11	−2.91744
$357$	−9.89308e9	−0.0322348
$358$	−7.71596e11	−2.48265
$359$	5.34052e11	1.69691	0.848455	−	0.529267i	$-0.177533\pi$
$359$	5.34052e11	1.69691	0.848455	+	0.529267i	$0.177533\pi$
$360$	−6.65146e10	−0.208716
$361$	1.42170e11	0.440582
$362$	6.19525e11	1.89614
$363$	−8.37762e9	−0.0253245
$364$	1.43913e11	0.429678
$365$	−4.27149e10	−0.125968
$366$	1.83649e10	0.0534963
$367$	6.87598e11	1.97851	0.989253	−	0.146212i	$-0.0467083\pi$
$367$	6.87598e11	1.97851	0.989253	+	0.146212i	$0.0467083\pi$
$368$	−2.38158e11	−0.676939
$369$	−5.99293e11	−1.68275
$370$	6.14753e10	0.170527
$371$	4.54795e11	1.24633
$372$	−1.90150e10	−0.0514817
$373$	−4.32517e11	−1.15695	−0.578474	−	0.815701i	$-0.696352\pi$
$373$	−4.32517e11	−1.15695	−0.578474	+	0.815701i	$0.696352\pi$
$374$	1.04916e12	2.77280
$375$	−1.83193e9	−0.00478375
$376$	−6.23808e10	−0.160956
$377$	1.13296e10	0.0288854
$378$	−4.18431e10	−0.105417
$379$	−9.90478e10	−0.246586	−0.123293	−	0.992370i	$-0.539345\pi$
$379$	−9.90478e10	−0.246586	−0.123293	+	0.992370i	$0.539345\pi$
$380$	−1.08713e11	−0.267457
$381$	−1.10358e10	−0.0268314
$382$	−8.13773e11	−1.95532
$383$	8.46062e10	0.200913	0.100456	−	0.994941i	$-0.467970\pi$
$383$	8.46062e10	0.200913	0.100456	+	0.994941i	$0.467970\pi$
$384$	−1.42206e10	−0.0333754
$385$	8.50305e10	0.197243
$386$	1.10926e12	2.54326
$387$	−1.03830e10	−0.0235300
$388$	−1.03296e12	−2.31388
$389$	9.70273e10	0.214843	0.107421	−	0.994214i	$-0.465741\pi$
$389$	9.70273e10	0.214843	0.107421	+	0.994214i	$0.465741\pi$
$390$	−3.02261e8	−0.000661593 0
$391$	−2.41936e11	−0.523486
$392$	−6.39389e11	−1.36766
$393$	1.43754e10	0.0303985
$394$	9.68790e11	2.02533
$395$	−6.49321e10	−0.134206
$396$	1.50886e12	3.08333
$397$	−8.76558e11	−1.77102	−0.885510	−	0.464621i	$-0.846190\pi$
$397$	−8.76558e11	−1.77102	−0.885510	+	0.464621i	$0.846190\pi$
$398$	−9.43788e10	−0.188539
$399$	−1.81157e10	−0.0357831
$400$	−7.08009e11	−1.38283
$401$	−3.21027e11	−0.620001	−0.310000	−	0.950736i	$-0.600329\pi$
$401$	−3.21027e11	−0.620001	−0.310000	+	0.950736i	$0.600329\pi$
$402$	−3.41941e9	−0.00653032
$403$	8.68148e10	0.163954
$404$	4.42624e11	0.826645
$405$	−5.66255e10	−0.104584
$406$	−2.33446e11	−0.426403
$407$	−7.39004e11	−1.33497
$408$	2.77010e10	0.0494908
$409$	6.69050e11	1.18223	0.591117	−	0.806586i	$-0.298687\pi$
$409$	6.69050e11	1.18223	0.591117	+	0.806586i	$0.298687\pi$
$410$	1.78449e11	0.311880
$411$	1.83880e10	0.0317868
$412$	−2.18693e12	−3.73935
$413$	−2.43409e10	−0.0411682
$414$	−5.11503e11	−0.855750
$415$	2.77284e10	0.0458890
$416$	−4.55106e10	−0.0745062
$417$	1.68466e10	0.0272835
$418$	1.92117e12	3.07802
$419$	1.04556e12	1.65724	0.828618	−	0.559814i	$-0.189127\pi$
$419$	1.04556e12	1.65724	0.828618	+	0.559814i	$0.189127\pi$
$420$	4.23658e9	0.00664345
$421$	6.41916e11	0.995884	0.497942	−	0.867210i	$-0.334089\pi$
$421$	6.41916e11	0.995884	0.497942	+	0.867210i	$0.334089\pi$
$422$	8.02210e11	1.23135
$423$	−5.31343e10	−0.0806944
$424$	−1.27344e12	−1.91352
$425$	−7.19240e11	−1.06936
$426$	2.55371e10	0.0375688
$427$	1.17522e12	1.71078
$428$	1.93096e12	2.78148
$429$	3.63352e9	0.00517929
$430$	3.09170e9	0.00436103
$431$	8.65392e11	1.20800	0.603998	−	0.796986i	$-0.293574\pi$
$431$	8.65392e11	1.20800	0.603998	+	0.796986i	$0.293574\pi$
$432$	4.64653e10	0.0641877
$433$	−3.58591e11	−0.490235	−0.245117	−	0.969493i	$-0.578827\pi$
$433$	−3.58591e11	−0.490235	−0.245117	+	0.969493i	$0.578827\pi$
$434$	−1.78882e12	−2.42027
$435$	3.33527e8	0.000446610 0
$436$	2.00361e12	2.65536
$437$	−4.43022e11	−0.581110
$438$	3.76102e10	0.0488283
$439$	2.20723e11	0.283634	0.141817	−	0.989893i	$-0.454706\pi$
$439$	2.20723e11	0.283634	0.141817	+	0.989893i	$0.454706\pi$
$440$	−2.38089e11	−0.302832
$441$	−5.44615e11	−0.685671
$442$	−2.38660e11	−0.297426
$443$	−3.67808e10	−0.0453737	−0.0226868	−	0.999743i	$-0.507222\pi$
$443$	−3.67808e10	−0.0453737	−0.0226868	+	0.999743i	$0.507222\pi$
$444$	−3.68203e10	−0.0449639
$445$	1.18834e11	0.143655
$446$	5.87484e10	0.0703055
$447$	−3.63236e10	−0.0430334
$448$	−6.10157e11	−0.715633
$449$	1.20897e12	1.40380	0.701900	−	0.712276i	$-0.252335\pi$
$449$	1.20897e12	1.40380	0.701900	+	0.712276i	$0.252335\pi$
$450$	−1.52062e12	−1.74810
$451$	−2.14517e12	−2.44155
$452$	−2.13137e12	−2.40180
$453$	−1.93291e10	−0.0215660
$454$	−1.98156e12	−2.18905
$455$	−1.93425e10	−0.0211574
$456$	5.07248e10	0.0549387
$457$	−2.96158e11	−0.317615	−0.158807	−	0.987310i	$-0.550765\pi$
$457$	−2.96158e11	−0.317615	−0.158807	+	0.987310i	$0.550765\pi$
$458$	−8.98835e11	−0.954520
$459$	4.72024e10	0.0496372
$460$	1.03606e11	0.107888
$461$	−6.59935e11	−0.680530	−0.340265	−	0.940330i	$-0.610517\pi$
$461$	−6.59935e11	−0.680530	−0.340265	+	0.940330i	$0.610517\pi$
$462$	−7.48688e10	−0.0764561
$463$	5.99053e11	0.605830	0.302915	−	0.953018i	$-0.402040\pi$
$463$	5.99053e11	0.605830	0.302915	+	0.953018i	$0.402040\pi$
$464$	2.59234e11	0.259634
$465$	2.55570e9	0.00253497
$466$	−1.25864e12	−1.23642
$467$	1.56533e12	1.52293	0.761464	−	0.648207i	$-0.224481\pi$
$467$	1.56533e12	1.52293	0.761464	+	0.648207i	$0.224481\pi$
$468$	−3.43231e11	−0.330735
$469$	−2.18818e11	−0.208836
$470$	1.58216e10	0.0149558
$471$	−3.49654e10	−0.0327374
$472$	6.81556e10	0.0632066
$473$	−3.71658e10	−0.0341404
$474$	5.71723e10	0.0520215
$475$	−1.31704e12	−1.18707
$476$	3.34513e12	2.98663
$477$	−1.08469e12	−0.959337
$478$	1.91541e12	1.67817
$479$	−5.20942e11	−0.452147	−0.226073	−	0.974110i	$-0.572589\pi$
$479$	−5.20942e11	−0.452147	−0.226073	+	0.974110i	$0.572589\pi$
$480$	−1.33977e9	−0.00115198
$481$	1.68107e11	0.143196
$482$	2.88677e12	2.43613
$483$	1.72648e10	0.0144344
$484$	2.83271e12	2.34638
$485$	1.38835e11	0.113936
$486$	1.49707e11	0.121725
$487$	−1.44962e12	−1.16782	−0.583909	−	0.811819i	$-0.698477\pi$
$487$	−1.44962e12	−1.16782	−0.583909	+	0.811819i	$0.698477\pi$
$488$	−3.29067e12	−2.62661
$489$	4.53251e7	3.58467e−5 0
$490$	1.62168e11	0.127082
$491$	3.83968e11	0.298146	0.149073	−	0.988826i	$-0.452371\pi$
$491$	3.83968e11	0.298146	0.149073	+	0.988826i	$0.452371\pi$
$492$	−1.06881e11	−0.0822353
$493$	2.63346e11	0.200778
$494$	−4.37022e11	−0.330166
$495$	−2.02798e11	−0.151824
$496$	1.98642e12	1.47368
$497$	1.63419e12	1.20143
$498$	−2.44147e10	−0.0177877
$499$	−1.23178e12	−0.889364	−0.444682	−	0.895689i	$-0.646683\pi$
$499$	−1.23178e12	−0.889364	−0.444682	+	0.895689i	$0.646683\pi$
$500$	6.19427e11	0.443226
$501$	−2.31633e10	−0.0164260
$502$	−1.69140e12	−1.18872
$503$	6.23381e10	0.0434208	0.0217104	−	0.999764i	$-0.493089\pi$
$503$	6.23381e10	0.0434208	0.0217104	+	0.999764i	$0.493089\pi$
$504$	3.74779e12	2.58724
$505$	−5.94907e10	−0.0407041
$506$	−1.83092e12	−1.24163
$507$	3.33330e10	0.0224047
$508$	3.73153e12	2.48599
$509$	7.46225e11	0.492765	0.246382	−	0.969173i	$-0.420758\pi$
$509$	7.46225e11	0.492765	0.246382	+	0.969173i	$0.420758\pi$
$510$	−7.02579e9	−0.00459864
$511$	2.40678e12	1.56150
$512$	3.29286e12	2.11767
$513$	8.64348e10	0.0551011
$514$	−1.98628e12	−1.25518
$515$	2.93933e11	0.184126
$516$	−1.85176e9	−0.00114990
$517$	−1.90194e11	−0.117082
$518$	−3.46384e12	−2.11385
$519$	2.38839e10	0.0144495
$520$	5.41598e10	0.0324834
$521$	7.56437e11	0.449783	0.224891	−	0.974384i	$-0.427797\pi$
$521$	7.56437e11	0.449783	0.224891	+	0.974384i	$0.427797\pi$
$522$	5.56769e11	0.328215
$523$	3.89302e11	0.227525	0.113763	−	0.993508i	$-0.463710\pi$
$523$	3.89302e11	0.227525	0.113763	+	0.993508i	$0.463710\pi$
$524$	−4.86071e12	−2.81650
$525$	5.13256e10	0.0294861
$526$	−1.35756e12	−0.773256
$527$	2.01794e12	1.13962
$528$	8.31392e10	0.0465536
$529$	−1.37894e12	−0.765588
$530$	3.22983e11	0.177803
$531$	5.80531e10	0.0316884
$532$	6.12544e12	3.31539
$533$	4.87977e11	0.261895
$534$	−1.04633e11	−0.0556841
$535$	−2.59529e11	−0.136960
$536$	6.12699e11	0.320631
$537$	−6.21141e10	−0.0322334
$538$	−2.97263e12	−1.52975
$539$	−1.94944e12	−0.994859
$540$	−2.02138e10	−0.0102300
$541$	1.11041e12	0.557308	0.278654	−	0.960392i	$-0.410112\pi$
$541$	1.11041e12	0.557308	0.278654	+	0.960392i	$0.410112\pi$
$542$	−2.29961e12	−1.14461
$543$	4.98723e10	0.0246184
$544$	−1.05786e12	−0.517882
$545$	−2.69294e11	−0.130750
$546$	1.70310e10	0.00820110
$547$	9.89223e11	0.472445	0.236222	−	0.971699i	$-0.424091\pi$
$547$	9.89223e11	0.472445	0.236222	+	0.971699i	$0.424091\pi$
$548$	−6.21751e12	−2.94512
$549$	−2.80291e12	−1.31684
$550$	−5.44306e12	−2.53636
$551$	4.82228e11	0.222879
$552$	−4.83420e10	−0.0221615
$553$	3.65862e12	1.66362
$554$	3.97866e12	1.79450
$555$	4.94881e9	0.00221403
$556$	−5.69630e12	−2.52788
$557$	1.58795e12	0.699018	0.349509	−	0.936933i	$-0.386348\pi$
$557$	1.58795e12	0.699018	0.349509	+	0.936933i	$0.386348\pi$
$558$	4.26634e12	1.86295
$559$	8.45438e9	0.00366209
$560$	−4.42579e11	−0.190171
$561$	8.44581e10	0.0360005
$562$	4.89601e12	2.07028
$563$	1.34624e12	0.564722	0.282361	−	0.959308i	$-0.408882\pi$
$563$	1.34624e12	0.564722	0.282361	+	0.959308i	$0.408882\pi$
$564$	−9.47627e9	−0.00394350
$565$	2.86466e11	0.118265
$566$	−4.69141e12	−1.92145
$567$	3.19058e12	1.29642
$568$	−4.57579e12	−1.84459
$569$	−3.38155e12	−1.35242	−0.676209	−	0.736710i	$-0.736378\pi$
$569$	−3.38155e12	−1.35242	−0.676209	+	0.736710i	$0.736378\pi$
$570$	−1.28653e10	−0.00510485
$571$	3.92602e12	1.54557	0.772787	−	0.634665i	$-0.218862\pi$
$571$	3.92602e12	1.54557	0.772787	+	0.634665i	$0.218862\pi$
$572$	−1.22860e12	−0.479873
$573$	−6.55094e10	−0.0253868
$574$	−1.00548e13	−3.86606
$575$	1.25517e12	0.478848
$576$	1.45522e12	0.550844
$577$	−3.81357e12	−1.43232	−0.716161	−	0.697935i	$-0.754102\pi$
$577$	−3.81357e12	−1.43232	−0.716161	+	0.697935i	$0.754102\pi$
$578$	−8.02160e11	−0.298941
$579$	8.92965e10	0.0330203
$580$	−1.12775e11	−0.0413795
$581$	−1.56237e12	−0.568840
$582$	−1.22243e11	−0.0441642
$583$	−3.88263e12	−1.39193
$584$	−6.73908e12	−2.39741
$585$	4.61319e10	0.0162854
$586$	8.07164e12	2.82763
$587$	−1.29227e11	−0.0449243	−0.0224622	−	0.999748i	$-0.507151\pi$
$587$	−1.29227e11	−0.0449243	−0.0224622	+	0.999748i	$0.507151\pi$
$588$	−9.71296e10	−0.0335084
$589$	3.69515e12	1.26507
$590$	−1.72863e10	−0.00587310
$591$	7.79884e10	0.0262958
$592$	3.84647e12	1.28711
$593$	−1.64180e12	−0.545224	−0.272612	−	0.962124i	$-0.587887\pi$
$593$	−1.64180e12	−0.545224	−0.272612	+	0.962124i	$0.587887\pi$
$594$	3.57218e11	0.117732
$595$	−4.49600e11	−0.147062
$596$	1.22820e13	3.98714
$597$	−7.59758e9	−0.00244788
$598$	4.16493e11	0.133184
$599$	−2.85325e12	−0.905563	−0.452781	−	0.891622i	$-0.649568\pi$
$599$	−2.85325e12	−0.905563	−0.452781	+	0.891622i	$0.649568\pi$
$600$	−1.43714e11	−0.0452708
$601$	2.91863e12	0.912522	0.456261	−	0.889846i	$-0.349188\pi$
$601$	2.91863e12	0.912522	0.456261	+	0.889846i	$0.349188\pi$
$602$	−1.74203e11	−0.0540593
$603$	5.21880e11	0.160747
$604$	6.53570e12	1.99814
$605$	−3.80729e11	−0.115536
$606$	5.23812e10	0.0157779
$607$	2.54987e12	0.762376	0.381188	−	0.924498i	$-0.375515\pi$
$607$	2.54987e12	0.762376	0.381188	+	0.924498i	$0.375515\pi$
$608$	−1.93709e12	−0.574890
$609$	−1.87926e10	−0.00553618
$610$	8.34611e11	0.244062
$611$	4.32648e10	0.0125588
$612$	−7.97812e12	−2.29890
$613$	−9.71940e11	−0.278015	−0.139007	−	0.990291i	$-0.544391\pi$
$613$	−9.71940e11	−0.278015	−0.139007	+	0.990291i	$0.544391\pi$
$614$	4.51082e12	1.28085
$615$	1.43653e10	0.00404928
$616$	1.34152e13	3.75390
$617$	7.11428e11	0.197628	0.0988138	−	0.995106i	$-0.468495\pi$
$617$	7.11428e11	0.197628	0.0988138	+	0.995106i	$0.468495\pi$
$618$	−2.58806e11	−0.0713717
$619$	−1.88527e12	−0.516138	−0.258069	−	0.966126i	$-0.583086\pi$
$619$	−1.88527e12	−0.516138	−0.258069	+	0.966126i	$0.583086\pi$
$620$	−8.64154e11	−0.234871
$621$	−8.23746e10	−0.0222270
$622$	1.05877e13	2.83625
$623$	−6.69573e12	−1.78075
$624$	−1.89123e10	−0.00499359
$625$	3.68959e12	0.967203
$626$	−3.24303e12	−0.844046
$627$	1.54656e11	0.0399633
$628$	1.18228e13	3.03320
$629$	3.90749e12	0.995337
$630$	−9.50548e11	−0.240404
$631$	2.92043e12	0.733355	0.366678	−	0.930348i	$-0.380495\pi$
$631$	2.92043e12	0.733355	0.366678	+	0.930348i	$0.380495\pi$
$632$	−1.02443e13	−2.55420
$633$	6.45786e10	0.0159872
$634$	−7.04029e12	−1.73057
$635$	−5.01534e11	−0.122411
$636$	−1.93449e11	−0.0468823
$637$	4.43454e11	0.106714
$638$	1.99295e12	0.476216
$639$	−3.89754e12	−0.924776
$640$	−6.46266e11	−0.152266
$641$	−1.73148e12	−0.405094	−0.202547	−	0.979273i	$-0.564922\pi$
$641$	−1.73148e12	−0.405094	−0.202547	+	0.979273i	$0.564922\pi$
$642$	2.28514e11	0.0530890
$643$	−8.07709e12	−1.86340	−0.931699	−	0.363232i	$-0.881673\pi$
$643$	−8.07709e12	−1.86340	−0.931699	+	0.363232i	$0.881673\pi$
$644$	−5.83770e12	−1.33738
$645$	2.48885e8	5.66212e−5 0
$646$	−1.01582e13	−2.29494
$647$	−5.93240e12	−1.33095	−0.665475	−	0.746420i	$-0.731771\pi$
$647$	−5.93240e12	−1.33095	−0.665475	+	0.746420i	$0.731771\pi$
$648$	−8.93375e12	−1.99043
$649$	2.07801e11	0.0459776
$650$	1.23817e12	0.272064
$651$	−1.44002e11	−0.0314234
$652$	−1.53257e10	−0.00332128
$653$	6.02910e12	1.29761	0.648804	−	0.760956i	$-0.275270\pi$
$653$	6.02910e12	1.29761	0.648804	+	0.760956i	$0.275270\pi$
$654$	2.37112e11	0.0506819
$655$	6.53302e11	0.138685
$656$	1.11655e13	2.35402
$657$	−5.74017e12	−1.20193
$658$	−8.91473e11	−0.185392
$659$	−4.57146e12	−0.944213	−0.472107	−	0.881541i	$-0.656506\pi$
$659$	−4.57146e12	−0.944213	−0.472107	+	0.881541i	$0.656506\pi$
$660$	−3.61681e10	−0.00741955
$661$	−2.52106e12	−0.513661	−0.256830	−	0.966456i	$-0.582678\pi$
$661$	−2.52106e12	−0.513661	−0.256830	+	0.966456i	$0.582678\pi$
$662$	9.34987e12	1.89210
$663$	−1.92123e10	−0.00386161
$664$	4.37468e12	0.873354
$665$	−8.23286e11	−0.163250
$666$	8.26126e12	1.62709
$667$	−4.59576e11	−0.0899064
$668$	7.83217e12	1.52191
$669$	4.72930e9	0.000912807 0
$670$	−1.55398e11	−0.0297927
$671$	−1.00330e13	−1.91064
$672$	7.54895e10	0.0142799
$673$	7.32733e12	1.37682	0.688411	−	0.725321i	$-0.258309\pi$
$673$	7.32733e12	1.37682	0.688411	+	0.725321i	$0.258309\pi$
$674$	1.82759e13	3.41122
$675$	−2.44888e11	−0.0454046
$676$	−1.12708e13	−2.07585
$677$	−4.68628e12	−0.857392	−0.428696	−	0.903449i	$-0.641027\pi$
$677$	−4.68628e12	−0.857392	−0.428696	+	0.903449i	$0.641027\pi$
$678$	−2.52231e11	−0.0458422
$679$	−7.82267e12	−1.41235
$680$	1.25890e12	0.225788
$681$	−1.59517e11	−0.0284214
$682$	1.52713e13	2.70301
$683$	−6.83665e12	−1.20213	−0.601064	−	0.799201i	$-0.705256\pi$
$683$	−6.83665e12	−1.20213	−0.601064	+	0.799201i	$0.705256\pi$
$684$	−1.46092e13	−2.55195
$685$	8.35661e11	0.145018
$686$	4.18179e12	0.720948
$687$	−7.23570e10	−0.0123930
$688$	1.93446e11	0.0329163
$689$	8.83209e11	0.149306
$690$	1.22610e10	0.00205922
$691$	3.74759e12	0.625318	0.312659	−	0.949865i	$-0.398780\pi$
$691$	3.74759e12	0.625318	0.312659	+	0.949865i	$0.398780\pi$
$692$	−8.07583e12	−1.33878
$693$	1.14267e13	1.88201
$694$	1.25904e12	0.206027
$695$	7.65608e11	0.124473
$696$	5.26201e10	0.00849983
$697$	1.13426e13	1.82039
$698$	−1.17849e13	−1.87921
$699$	−1.01322e11	−0.0160530
$700$	−1.73546e13	−2.73196
$701$	−4.20066e12	−0.657031	−0.328516	−	0.944499i	$-0.606548\pi$
$701$	−4.20066e12	−0.657031	−0.328516	+	0.944499i	$0.606548\pi$
$702$	−8.12590e10	−0.0126286
$703$	7.15522e12	1.10490
$704$	5.20896e12	0.799235
$705$	1.27365e9	0.000194178 0
$706$	−3.25123e12	−0.492524
$707$	3.35202e12	0.504567
$708$	1.03535e10	0.00154860
$709$	3.55808e12	0.528820	0.264410	−	0.964410i	$-0.414823\pi$
$709$	3.55808e12	0.528820	0.264410	+	0.964410i	$0.414823\pi$
$710$	1.16056e12	0.171397
$711$	−8.72580e12	−1.28054
$712$	1.87483e13	2.73402
$713$	−3.52157e12	−0.510310
$714$	3.95870e11	0.0570047
$715$	1.65129e11	0.0236290
$716$	2.10025e13	2.98650
$717$	1.54192e11	0.0217884
$718$	−2.13700e13	−3.00086
$719$	8.51832e12	1.18870	0.594352	−	0.804205i	$-0.297409\pi$
$719$	8.51832e12	1.18870	0.594352	+	0.804205i	$0.297409\pi$
$720$	1.05555e12	0.146380
$721$	−1.65617e13	−2.28243
$722$	−5.68892e12	−0.779135
$723$	2.32388e11	0.0316294
$724$	−1.68632e13	−2.28095
$725$	−1.36625e12	−0.183658
$726$	3.35229e11	0.0447844
$727$	−8.63567e11	−0.114654	−0.0573272	−	0.998355i	$-0.518258\pi$
$727$	−8.63567e11	−0.114654	−0.0573272	+	0.998355i	$0.518258\pi$
$728$	−3.05165e12	−0.402664
$729$	−7.60149e12	−0.996838
$730$	1.70923e12	0.222765
$731$	1.96515e11	0.0254546
$732$	−4.99886e11	−0.0643533
$733$	2.45258e12	0.313802	0.156901	−	0.987614i	$-0.449850\pi$
$733$	2.45258e12	0.313802	0.156901	+	0.987614i	$0.449850\pi$
$734$	−2.75141e13	−3.49884
$735$	1.30547e10	0.00164996
$736$	1.84610e12	0.231902
$737$	1.86807e12	0.233232
$738$	2.39806e13	2.97582
$739$	6.49968e12	0.801663	0.400832	−	0.916152i	$-0.368721\pi$
$739$	6.49968e12	0.801663	0.400832	+	0.916152i	$0.368721\pi$
$740$	−1.67333e12	−0.205135
$741$	−3.51807e10	−0.00428669
$742$	−1.81986e13	−2.20404
$743$	3.68596e12	0.443711	0.221856	−	0.975080i	$-0.428789\pi$
$743$	3.68596e12	0.443711	0.221856	+	0.975080i	$0.428789\pi$
$744$	4.03211e11	0.0482452
$745$	−1.65076e12	−0.196327
$746$	1.73071e13	2.04597
$747$	3.72624e12	0.437853
$748$	−2.85576e13	−3.33553
$749$	1.46232e13	1.69776
$750$	7.33045e10	0.00845969
$751$	6.43220e11	0.0737870	0.0368935	−	0.999319i	$-0.488254\pi$
$751$	6.43220e11	0.0737870	0.0368935	+	0.999319i	$0.488254\pi$
$752$	9.89949e11	0.112884
$753$	−1.36160e11	−0.0154337
$754$	−4.53352e11	−0.0510816
$755$	−8.78427e11	−0.0983886
$756$	1.13895e12	0.126811
$757$	1.48021e12	0.163830	0.0819150	−	0.996639i	$-0.473896\pi$
$757$	1.48021e12	0.163830	0.0819150	+	0.996639i	$0.473896\pi$
$758$	3.96338e12	0.436068
$759$	−1.47391e11	−0.0161207
$760$	2.30523e12	0.250642
$761$	3.22241e11	0.0348297	0.0174149	−	0.999848i	$-0.494456\pi$
$761$	3.22241e11	0.0348297	0.0174149	+	0.999848i	$0.494456\pi$
$762$	4.41598e11	0.0474492
$763$	1.51734e13	1.62078
$764$	2.21506e13	2.35215
$765$	1.07230e12	0.113198
$766$	−3.38550e12	−0.355299
$767$	−4.72700e10	−0.00493181
$768$	4.47034e11	0.0463676
$769$	1.57040e13	1.61936	0.809679	−	0.586873i	$-0.199641\pi$
$769$	1.57040e13	1.61936	0.809679	+	0.586873i	$0.199641\pi$
$770$	−3.40248e12	−0.348809
$771$	−1.59897e11	−0.0162966
$772$	−3.01937e13	−3.05941
$773$	1.39133e12	0.140160	0.0700798	−	0.997541i	$-0.477675\pi$
$773$	1.39133e12	0.140160	0.0700798	+	0.997541i	$0.477675\pi$
$774$	4.15473e11	0.0416111
$775$	−1.04691e13	−1.04244
$776$	2.19038e13	2.16841
$777$	−2.78842e11	−0.0274450
$778$	−3.88253e12	−0.379933
$779$	2.07700e13	2.02078
$780$	8.22741e9	0.000795862 0
$781$	−1.39512e13	−1.34178
$782$	9.68103e12	0.925745
$783$	8.96645e10	0.00852496
$784$	1.01468e13	0.959190
$785$	−1.58904e12	−0.149355
$786$	−5.75228e11	−0.0537575
$787$	3.88863e12	0.361335	0.180668	−	0.983544i	$-0.442174\pi$
$787$	3.88863e12	0.361335	0.180668	+	0.983544i	$0.442174\pi$
$788$	−2.63701e13	−2.43637
$789$	−1.09285e11	−0.0100395
$790$	2.59825e12	0.237333
$791$	−1.61410e13	−1.46601
$792$	−3.19952e13	−2.88949
$793$	2.28228e12	0.204946
$794$	3.50753e13	3.13191
$795$	2.60004e10	0.00230849
$796$	2.56895e12	0.226802
$797$	1.03788e13	0.911142	0.455571	−	0.890200i	$-0.349435\pi$
$797$	1.03788e13	0.911142	0.455571	+	0.890200i	$0.349435\pi$
$798$	7.24898e11	0.0632797
$799$	1.00565e12	0.0872947
$800$	5.48819e12	0.473723
$801$	1.59693e13	1.37069
$802$	1.28459e13	1.09642
$803$	−2.05469e13	−1.74392
$804$	9.30750e10	0.00785563
$805$	7.84613e11	0.0658528
$806$	−3.47388e12	−0.289940
$807$	−2.39299e11	−0.0198614
$808$	−9.38578e12	−0.774675
$809$	−4.15938e10	−0.00341397	−0.00170699	−	0.999999i	$-0.500543\pi$
$809$	−4.15938e10	−0.00341397	−0.00170699	+	0.999999i	$0.500543\pi$
$810$	2.26586e12	0.184948
$811$	8.84040e12	0.717592	0.358796	−	0.933416i	$-0.383187\pi$
$811$	8.84040e12	0.717592	0.358796	+	0.933416i	$0.383187\pi$
$812$	6.35432e12	0.512940
$813$	−1.85120e11	−0.0148610
$814$	2.95711e13	2.36079
$815$	2.05984e9	0.000163540 0
$816$	−4.39600e11	−0.0347098
$817$	3.59849e11	0.0282566
$818$	−2.67719e13	−2.09069
$819$	−2.59931e12	−0.201874
$820$	−4.85732e12	−0.375175
$821$	1.09261e13	0.839308	0.419654	−	0.907684i	$-0.362151\pi$
$821$	1.09261e13	0.839308	0.419654	+	0.907684i	$0.362151\pi$
$822$	−7.35794e11	−0.0562125
$823$	1.55823e12	0.118395	0.0591974	−	0.998246i	$-0.481146\pi$
$823$	1.55823e12	0.118395	0.0591974	+	0.998246i	$0.481146\pi$
$824$	4.63735e13	3.50427
$825$	−4.38171e11	−0.0329307
$826$	9.73999e11	0.0728029
$827$	−1.24014e13	−0.921926	−0.460963	−	0.887419i	$-0.652496\pi$
$827$	−1.24014e13	−0.921926	−0.460963	+	0.887419i	$0.652496\pi$
$828$	1.39229e13	1.02942
$829$	1.60188e13	1.17797	0.588985	−	0.808144i	$-0.299528\pi$
$829$	1.60188e13	1.17797	0.588985	+	0.808144i	$0.299528\pi$
$830$	−1.10955e12	−0.0811512
$831$	3.20286e11	0.0232988
$832$	−1.18492e12	−0.0857303
$833$	1.03077e13	0.741754
$834$	−6.74113e11	−0.0482487
$835$	−1.05268e12	−0.0749388
$836$	−5.22934e13	−3.70270
$837$	6.87069e11	0.0483878
$838$	−4.18378e13	−2.93070
$839$	−7.02598e12	−0.489529	−0.244764	−	0.969583i	$-0.578711\pi$
$839$	−7.02598e12	−0.489529	−0.244764	+	0.969583i	$0.578711\pi$
$840$	−8.98361e10	−0.00622578
$841$	5.00246e11	0.0344828
$842$	−2.56862e13	−1.76114
$843$	3.94133e11	0.0268794
$844$	−2.18358e13	−1.48125
$845$	1.51485e12	0.102215
$846$	2.12616e12	0.142702
$847$	2.14523e13	1.43218
$848$	2.02089e13	1.34202
$849$	−3.77662e11	−0.0249470
$850$	2.87803e13	1.89108
$851$	−6.81911e12	−0.445702
$852$	−6.95109e11	−0.0451933
$853$	−6.86612e12	−0.444059	−0.222030	−	0.975040i	$-0.571268\pi$
$853$	−6.86612e12	−0.444059	−0.222030	+	0.975040i	$0.571268\pi$
$854$	−4.70264e13	−3.02539
$855$	1.96354e12	0.125658
$856$	−4.09457e13	−2.60661
$857$	−1.29717e13	−0.821452	−0.410726	−	0.911759i	$-0.634725\pi$
$857$	−1.29717e13	−0.821452	−0.410726	+	0.911759i	$0.634725\pi$
$858$	−1.45395e11	−0.00915917
$859$	9.68624e12	0.606997	0.303498	−	0.952832i	$-0.401845\pi$
$859$	9.68624e12	0.606997	0.303498	+	0.952832i	$0.401845\pi$
$860$	−8.41548e10	−0.00524609
$861$	−8.09418e11	−0.0501948
$862$	−3.46285e13	−2.13625
$863$	−1.74142e13	−1.06870	−0.534348	−	0.845265i	$-0.679443\pi$
$863$	−1.74142e13	−1.06870	−0.534348	+	0.845265i	$0.679443\pi$
$864$	−3.60180e11	−0.0219891
$865$	1.08543e12	0.0659217
$866$	1.43490e13	0.866943
$867$	−6.45746e10	−0.00388128
$868$	4.86910e13	2.91145
$869$	−3.12339e13	−1.85797
$870$	−1.33460e10	−0.000789796 0
$871$	−4.24943e11	−0.0250178
$872$	−4.24862e13	−2.48842
$873$	1.86571e13	1.08712
$874$	1.77274e13	1.02765
$875$	4.69096e12	0.270536
$876$	−1.02373e12	−0.0587379
$877$	−1.57762e13	−0.900540	−0.450270	−	0.892893i	$-0.648672\pi$
$877$	−1.57762e13	−0.900540	−0.450270	+	0.892893i	$0.648672\pi$
$878$	−8.83221e12	−0.501584
$879$	6.49774e11	0.0367124
$880$	3.77834e12	0.212387
$881$	−2.09362e13	−1.17086	−0.585431	−	0.810722i	$-0.699075\pi$
$881$	−2.09362e13	−1.17086	−0.585431	+	0.810722i	$0.699075\pi$
$882$	2.17927e13	1.21256
$883$	−2.22338e13	−1.23081	−0.615405	−	0.788211i	$-0.711007\pi$
$883$	−2.22338e13	−1.23081	−0.615405	+	0.788211i	$0.711007\pi$
$884$	6.49621e12	0.357788
$885$	−1.39156e9	−7.62530e−5 0
$886$	1.47178e12	0.0802398
$887$	−3.27791e13	−1.77804	−0.889019	−	0.457870i	$-0.848613\pi$
$887$	−3.27791e13	−1.77804	−0.889019	+	0.457870i	$0.848613\pi$
$888$	7.80769e11	0.0421371
$889$	2.82591e13	1.51740
$890$	−4.75512e12	−0.254043
$891$	−2.72383e13	−1.44787
$892$	−1.59911e12	−0.0845738
$893$	1.84151e12	0.0969039
$894$	1.45348e12	0.0761012
$895$	−2.82283e12	−0.147056
$896$	3.64141e13	1.88748
$897$	3.35281e10	0.00172919
$898$	−4.83765e13	−2.48251
$899$	3.83322e12	0.195725
$900$	4.13908e13	2.10287
$901$	2.05294e13	1.03780
$902$	8.58385e13	4.31770
$903$	−1.40235e10	−0.000701876 0
$904$	4.51954e13	2.25080
$905$	2.26649e12	0.112314
$906$	7.73450e11	0.0381378
$907$	−4.94213e12	−0.242483	−0.121241	−	0.992623i	$-0.538688\pi$
$907$	−4.94213e12	−0.242483	−0.121241	+	0.992623i	$0.538688\pi$
$908$	5.39373e13	2.63331
$909$	−7.99456e12	−0.388380
$910$	7.73988e11	0.0374152
$911$	6.77428e12	0.325860	0.162930	−	0.986638i	$-0.447906\pi$
$911$	6.77428e12	0.325860	0.162930	+	0.986638i	$0.447906\pi$
$912$	−8.04974e11	−0.0385305
$913$	1.33381e13	0.635293
$914$	1.18507e13	0.561677
$915$	6.71869e10	0.00316876
$916$	2.44659e13	1.14824
$917$	−3.68105e13	−1.71913
$918$	−1.88880e12	−0.0877795
$919$	1.05639e13	0.488546	0.244273	−	0.969707i	$-0.421451\pi$
$919$	1.05639e13	0.488546	0.244273	+	0.969707i	$0.421451\pi$
$920$	−2.19695e12	−0.101105
$921$	3.63125e11	0.0166298
$922$	2.64072e13	1.20346
$923$	3.17359e12	0.143927
$924$	2.03790e12	0.0919727
$925$	−2.02722e13	−0.910465
$926$	−2.39710e13	−1.07136
$927$	3.94997e13	1.75685
$928$	−2.00948e12	−0.0889440
$929$	−1.90200e13	−0.837797	−0.418899	−	0.908033i	$-0.637584\pi$
$929$	−1.90200e13	−0.837797	−0.418899	+	0.908033i	$0.637584\pi$
$930$	−1.02266e11	−0.00448289
$931$	1.88750e13	0.823405
$932$	3.42598e13	1.48735
$933$	8.52319e11	0.0368243
$934$	−6.26364e13	−2.69318
$935$	3.83828e12	0.164242
$936$	7.27818e12	0.309943
$937$	2.95545e13	1.25255	0.626275	−	0.779602i	$-0.284579\pi$
$937$	2.95545e13	1.25255	0.626275	+	0.779602i	$0.284579\pi$
$938$	8.75596e12	0.369310
$939$	−2.61066e11	−0.0109586
$940$	−4.30658e11	−0.0179911
$941$	−2.30623e13	−0.958848	−0.479424	−	0.877583i	$-0.659154\pi$
$941$	−2.30623e13	−0.958848	−0.479424	+	0.877583i	$0.659154\pi$
$942$	1.39914e12	0.0578936
$943$	−1.97944e13	−0.815153
$944$	−1.08159e12	−0.0443292
$945$	−1.53080e11	−0.00624419
$946$	1.48718e12	0.0603746
$947$	−1.96143e13	−0.792496	−0.396248	−	0.918144i	$-0.629688\pi$
$947$	−1.96143e13	−0.792496	−0.396248	+	0.918144i	$0.629688\pi$
$948$	−1.55621e12	−0.0625792
$949$	4.67395e12	0.187062
$950$	5.27011e13	2.09925
$951$	−5.66750e11	−0.0224688
$952$	−7.09329e13	−2.79886
$953$	1.46400e13	0.574941	0.287471	−	0.957789i	$-0.407186\pi$
$953$	1.46400e13	0.574941	0.287471	+	0.957789i	$0.407186\pi$
$954$	4.34035e13	1.69651
$955$	−2.97714e12	−0.115820
$956$	−5.21367e13	−2.01875
$957$	1.60434e11	0.00618292
$958$	2.08454e13	0.799587
$959$	−4.70855e13	−1.79764
$960$	−3.48824e10	−0.00132552
$961$	2.93307e12	0.110935
$962$	−6.72676e12	−0.253232
$963$	−3.48764e13	−1.30681
$964$	−7.85768e13	−2.93054
$965$	4.05816e12	0.150646
$966$	−6.90847e11	−0.0255261
$967$	3.56210e13	1.31005	0.655024	−	0.755608i	$-0.272658\pi$
$967$	3.56210e13	1.31005	0.655024	+	0.755608i	$0.272658\pi$
$968$	−6.00672e13	−2.19886
$969$	−8.17744e11	−0.0297962
$970$	−5.55544e12	−0.201486
$971$	4.88501e13	1.76351	0.881757	−	0.471704i	$-0.156361\pi$
$971$	4.88501e13	1.76351	0.881757	+	0.471704i	$0.156361\pi$
$972$	−4.07496e12	−0.146428
$973$	−4.31384e13	−1.54297
$974$	5.80065e13	2.06519
$975$	9.96741e10	0.00353233
$976$	5.22211e13	1.84214
$977$	5.58411e12	0.196078	0.0980389	−	0.995183i	$-0.468743\pi$
$977$	5.58411e12	0.196078	0.0980389	+	0.995183i	$0.468743\pi$
$978$	−1.81368e9	−6.33921e−5 0
$979$	5.71621e13	1.98878
$980$	−4.41414e12	−0.152872
$981$	−3.61886e13	−1.24756
$982$	−1.53644e13	−0.527248
$983$	7.99790e12	0.273203	0.136601	−	0.990626i	$-0.456382\pi$
$983$	7.99790e12	0.273203	0.136601	+	0.990626i	$0.456382\pi$
$984$	2.26640e12	0.0770653
$985$	3.54426e12	0.119967
$986$	−1.05378e13	−0.355061
$987$	−7.17643e10	−0.00240703
$988$	1.18956e13	0.397172
$989$	−3.42945e11	−0.0113983
$990$	8.11492e12	0.268488
$991$	−3.79199e13	−1.24892	−0.624462	−	0.781055i	$-0.714682\pi$
$991$	−3.79199e13	−1.24892	−0.624462	+	0.781055i	$0.714682\pi$
$992$	−1.53979e13	−0.504847
$993$	7.52673e11	0.0245660
$994$	−6.53918e13	−2.12464
$995$	−3.45279e11	−0.0111678
$996$	6.64558e11	0.0213976
$997$	−2.34070e12	−0.0750270	−0.0375135	−	0.999296i	$-0.511944\pi$
$997$	−2.34070e12	−0.0750270	−0.0375135	+	0.999296i	$0.511944\pi$
$998$	4.92893e13	1.57277
$999$	1.33043e12	0.0422617

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.10.a.b.1.2	✓	12
3.2	odd	2		261.10.a.e.1.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.10.a.b.1.2	✓	12	1.1	even	1	trivial
261.10.a.e.1.11		12	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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q-40.0148 q^{2} -3.22123 q^{3} +1089.19 q^{4} -146.392 q^{5} +128.897 q^{6} +8248.48 q^{7} -23096.1 q^{8} -19672.6 q^{9} +O(q^{10})\)	\(q-40.0148 q^{2} -3.22123 q^{3} +1089.19 q^{4} -146.392 q^{5} +128.897 q^{6} +8248.48 q^{7} -23096.1 q^{8} -19672.6 q^{9} +5857.84 q^{10} -70418.0 q^{11} -3508.52 q^{12} +16018.5 q^{13} -330062. q^{14} +471.562 q^{15} +366522. q^{16} +372336. q^{17} +787197. q^{18} +681805. q^{19} -159448. q^{20} -26570.3 q^{21} +2.81777e6 q^{22} -649778. q^{23} +74397.8 q^{24} -1.93169e6 q^{25} -640978. q^{26} +126774. q^{27} +8.98415e6 q^{28} +707281. q^{29} -18869.5 q^{30} +5.41966e6 q^{31} -2.84113e6 q^{32} +226833. q^{33} -1.48990e7 q^{34} -1.20751e6 q^{35} -2.14272e7 q^{36} +1.04945e7 q^{37} -2.72823e7 q^{38} -51599.3 q^{39} +3.38108e6 q^{40} +3.04633e7 q^{41} +1.06320e6 q^{42} +527788. q^{43} -7.66985e7 q^{44} +2.87991e6 q^{45} +2.60008e7 q^{46} +2.70093e6 q^{47} -1.18065e6 q^{48} +2.76839e7 q^{49} +7.72965e7 q^{50} -1.19938e6 q^{51} +1.74472e7 q^{52} +5.51368e7 q^{53} -5.07282e6 q^{54} +1.03086e7 q^{55} -1.90508e8 q^{56} -2.19625e6 q^{57} -2.83017e7 q^{58} -2.95096e6 q^{59} +513619. q^{60} +1.42477e8 q^{61} -2.16867e8 q^{62} -1.62269e8 q^{63} -7.39720e7 q^{64} -2.34498e6 q^{65} -9.07668e6 q^{66} -2.65283e7 q^{67} +4.05544e8 q^{68} +2.09308e6 q^{69} +4.83183e7 q^{70} +1.98120e8 q^{71} +4.54361e8 q^{72} +2.91785e8 q^{73} -4.19937e8 q^{74} +6.22243e6 q^{75} +7.42614e8 q^{76} -5.80842e8 q^{77} +2.06474e6 q^{78} +4.43550e8 q^{79} -5.36558e7 q^{80} +3.86808e8 q^{81} -1.21898e9 q^{82} -1.89412e8 q^{83} -2.89400e7 q^{84} -5.45070e7 q^{85} -2.11194e7 q^{86} -2.27831e6 q^{87} +1.62638e9 q^{88} -8.11753e8 q^{89} -1.15239e8 q^{90} +1.32128e8 q^{91} -7.07730e8 q^{92} -1.74580e7 q^{93} -1.08077e8 q^{94} -9.98106e7 q^{95} +9.15192e6 q^{96} -9.48377e8 q^{97} -1.10777e9 q^{98} +1.38531e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 16 q^{2} + 242 q^{3} + 3498 q^{4} + 1762 q^{5} + 5446 q^{6} + 12080 q^{7} + 25350 q^{8} + 43026 q^{9}+O(q^{10}) \) 12 * q + 16 * q^2 + 242 * q^3 + 3498 * q^4 + 1762 * q^5 + 5446 * q^6 + 12080 * q^7 + 25350 * q^8 + 43026 * q^9	\( 12 q + 16 q^{2} + 242 q^{3} + 3498 q^{4} + 1762 q^{5} + 5446 q^{6} + 12080 q^{7} + 25350 q^{8} + 43026 q^{9} - 46678 q^{10} + 24474 q^{11} - 14210 q^{12} + 107722 q^{13} + 677768 q^{14} + 505426 q^{15} + 1656882 q^{16} + 982120 q^{17} + 2364102 q^{18} + 2084360 q^{19} + 4689410 q^{20} + 2911344 q^{21} + 2725230 q^{22} + 3004004 q^{23} + 7893170 q^{24} + 6339542 q^{25} + 6863698 q^{26} + 7881014 q^{27} + 5116944 q^{28} + 8487372 q^{29} + 10924626 q^{30} + 17872478 q^{31} + 5122946 q^{32} - 860442 q^{33} + 15662848 q^{34} - 22252312 q^{35} - 35199980 q^{36} + 452980 q^{37} - 68665276 q^{38} - 29528222 q^{39} - 61623214 q^{40} - 69039804 q^{41} - 150603216 q^{42} + 5379186 q^{43} - 58283762 q^{44} - 63687756 q^{45} - 76817844 q^{46} - 49104062 q^{47} - 99120062 q^{48} + 73113148 q^{49} - 281373726 q^{50} + 1578252 q^{51} - 49849646 q^{52} + 2253998 q^{53} - 166064634 q^{54} + 82907066 q^{55} + 119369464 q^{56} + 69024164 q^{57} + 11316496 q^{58} + 51587572 q^{59} - 107912622 q^{60} + 251179296 q^{61} + 2421010 q^{62} + 573206808 q^{63} + 460030950 q^{64} + 301434554 q^{65} + 305189958 q^{66} + 741046264 q^{67} + 503103116 q^{68} + 1480618500 q^{69} + 666826600 q^{70} + 488700124 q^{71} + 243154096 q^{72} + 1432375020 q^{73} - 208138340 q^{74} + 462882236 q^{75} - 253709644 q^{76} + 406327616 q^{77} - 1244370462 q^{78} + 400834638 q^{79} - 440320610 q^{80} + 207205984 q^{81} - 1992598260 q^{82} + 1525085236 q^{83} - 2191854376 q^{84} - 387675996 q^{85} - 3425646378 q^{86} + 171162002 q^{87} - 3147673814 q^{88} + 691159332 q^{89} - 2412410836 q^{90} + 1569278264 q^{91} - 2491626380 q^{92} + 270455138 q^{93} - 4397366402 q^{94} + 236293724 q^{95} - 1448270346 q^{96} + 2494422276 q^{97} - 3443098784 q^{98} + 2123567852 q^{99}+O(q^{100}) \) 12 * q + 16 * q^2 + 242 * q^3 + 3498 * q^4 + 1762 * q^5 + 5446 * q^6 + 12080 * q^7 + 25350 * q^8 + 43026 * q^9 - 46678 * q^10 + 24474 * q^11 - 14210 * q^12 + 107722 * q^13 + 677768 * q^14 + 505426 * q^15 + 1656882 * q^16 + 982120 * q^17 + 2364102 * q^18 + 2084360 * q^19 + 4689410 * q^20 + 2911344 * q^21 + 2725230 * q^22 + 3004004 * q^23 + 7893170 * q^24 + 6339542 * q^25 + 6863698 * q^26 + 7881014 * q^27 + 5116944 * q^28 + 8487372 * q^29 + 10924626 * q^30 + 17872478 * q^31 + 5122946 * q^32 - 860442 * q^33 + 15662848 * q^34 - 22252312 * q^35 - 35199980 * q^36 + 452980 * q^37 - 68665276 * q^38 - 29528222 * q^39 - 61623214 * q^40 - 69039804 * q^41 - 150603216 * q^42 + 5379186 * q^43 - 58283762 * q^44 - 63687756 * q^45 - 76817844 * q^46 - 49104062 * q^47 - 99120062 * q^48 + 73113148 * q^49 - 281373726 * q^50 + 1578252 * q^51 - 49849646 * q^52 + 2253998 * q^53 - 166064634 * q^54 + 82907066 * q^55 + 119369464 * q^56 + 69024164 * q^57 + 11316496 * q^58 + 51587572 * q^59 - 107912622 * q^60 + 251179296 * q^61 + 2421010 * q^62 + 573206808 * q^63 + 460030950 * q^64 + 301434554 * q^65 + 305189958 * q^66 + 741046264 * q^67 + 503103116 * q^68 + 1480618500 * q^69 + 666826600 * q^70 + 488700124 * q^71 + 243154096 * q^72 + 1432375020 * q^73 - 208138340 * q^74 + 462882236 * q^75 - 253709644 * q^76 + 406327616 * q^77 - 1244370462 * q^78 + 400834638 * q^79 - 440320610 * q^80 + 207205984 * q^81 - 1992598260 * q^82 + 1525085236 * q^83 - 2191854376 * q^84 - 387675996 * q^85 - 3425646378 * q^86 + 171162002 * q^87 - 3147673814 * q^88 + 691159332 * q^89 - 2412410836 * q^90 + 1569278264 * q^91 - 2491626380 * q^92 + 270455138 * q^93 - 4397366402 * q^94 + 236293724 * q^95 - 1448270346 * q^96 + 2494422276 * q^97 - 3443098784 * q^98 + 2123567852 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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