LMFDB - Embedded newform 29.12.a.a.1.10

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:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - x^{10} - 15790 x^{9} + 14666 x^{8} + 87206462 x^{7} - 14008334 x^{6} - 203974096304 x^{5} + \cdots - 75\!\cdots\!58 $ x^11 - x^10 - 15790x^9 + 14666x^8 + 87206462x^7 - 14008334x^6 - 203974096304x^5 - 388180519304x^4 + 193065378004825x^3 + 1279291654973975x^2 - 65244901875230266*x - 758324542468966858
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$65.2743$ 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)

$f(q)$	$=$	$q+62.2743 q^{2} -384.675 q^{3} +1830.09 q^{4} +1377.47 q^{5} -23955.4 q^{6} +33050.3 q^{7} -13570.0 q^{8} -29172.4 q^{9} +O(q^{10})$	\(q+62.2743 q^{2} -384.675 q^{3} +1830.09 q^{4} +1377.47 q^{5} -23955.4 q^{6} +33050.3 q^{7} -13570.0 q^{8} -29172.4 q^{9} +85780.8 q^{10} -800438. q^{11} -703990. q^{12} +1.48554e6 q^{13} +2.05818e6 q^{14} -529877. q^{15} -4.59309e6 q^{16} -1.13043e7 q^{17} -1.81669e6 q^{18} -9.78812e6 q^{19} +2.52089e6 q^{20} -1.27136e7 q^{21} -4.98468e7 q^{22} +546284. q^{23} +5.22005e6 q^{24} -4.69307e7 q^{25} +9.25112e7 q^{26} +7.93659e7 q^{27} +6.04851e7 q^{28} +2.05111e7 q^{29} -3.29977e7 q^{30} +4.17817e6 q^{31} -2.58240e8 q^{32} +3.07908e8 q^{33} -7.03969e8 q^{34} +4.55257e7 q^{35} -5.33882e7 q^{36} +3.50598e8 q^{37} -6.09549e8 q^{38} -5.71451e8 q^{39} -1.86923e7 q^{40} +7.34075e8 q^{41} -7.91731e8 q^{42} -1.74203e9 q^{43} -1.46488e9 q^{44} -4.01841e7 q^{45} +3.40195e7 q^{46} +1.70223e9 q^{47} +1.76685e9 q^{48} -8.85005e8 q^{49} -2.92258e9 q^{50} +4.34849e9 q^{51} +2.71868e9 q^{52} +2.30025e9 q^{53} +4.94246e9 q^{54} -1.10258e9 q^{55} -4.48494e8 q^{56} +3.76524e9 q^{57} +1.27732e9 q^{58} -2.84523e8 q^{59} -9.69723e8 q^{60} +5.13866e9 q^{61} +2.60193e8 q^{62} -9.64157e8 q^{63} -6.67509e9 q^{64} +2.04629e9 q^{65} +1.91748e10 q^{66} -3.85315e9 q^{67} -2.06880e10 q^{68} -2.10142e8 q^{69} +2.83508e9 q^{70} +2.82041e10 q^{71} +3.95871e8 q^{72} -1.81192e10 q^{73} +2.18333e10 q^{74} +1.80531e10 q^{75} -1.79132e10 q^{76} -2.64547e10 q^{77} -3.55867e10 q^{78} -3.94609e10 q^{79} -6.32684e9 q^{80} -2.53622e10 q^{81} +4.57140e10 q^{82} +1.27885e10 q^{83} -2.32671e10 q^{84} -1.55713e10 q^{85} -1.08484e11 q^{86} -7.89012e9 q^{87} +1.08620e10 q^{88} +4.46844e10 q^{89} -2.50244e9 q^{90} +4.90976e10 q^{91} +9.99751e8 q^{92} -1.60724e9 q^{93} +1.06005e11 q^{94} -1.34828e10 q^{95} +9.93386e10 q^{96} -7.40280e10 q^{97} -5.51131e10 q^{98} +2.33507e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 32 q^{2} - 982 q^{3} + 9146 q^{4} - 2740 q^{5} - 28202 q^{6} - 49432 q^{7} - 150054 q^{8} + 330749 q^{9}+O(q^{10}) $ 11 * q - 32 * q^2 - 982 * q^3 + 9146 * q^4 - 2740 * q^5 - 28202 * q^6 - 49432 * q^7 - 150054 * q^8 + 330749 * q^9	\( 11 q - 32 q^{2} - 982 q^{3} + 9146 q^{4} - 2740 q^{5} - 28202 q^{6} - 49432 q^{7} - 150054 q^{8} + 330749 q^{9} - 685834 q^{10} - 612246 q^{11} + 2578538 q^{12} + 1510364 q^{13} + 3955400 q^{14} - 2462818 q^{15} + 3024818 q^{16} - 3291098 q^{17} - 27885614 q^{18} - 44121388 q^{19} - 49472662 q^{20} - 46916800 q^{21} - 43435618 q^{22} - 88684076 q^{23} - 224700678 q^{24} - 44195521 q^{25} - 324999762 q^{26} - 236304286 q^{27} - 391274848 q^{28} + 225622639 q^{29} - 494910382 q^{30} - 292235934 q^{31} - 632542514 q^{32} - 1079766410 q^{33} - 1113307936 q^{34} - 1312820120 q^{35} - 2236726492 q^{36} - 1380429338 q^{37} - 1222857284 q^{38} - 1186931090 q^{39} - 2713154106 q^{40} - 1062067494 q^{41} + 205598960 q^{42} + 74588594 q^{43} + 52891466 q^{44} + 4527996830 q^{45} - 87670324 q^{46} - 1821239394 q^{47} + 2666035542 q^{48} + 4692522003 q^{49} + 9494259926 q^{50} + 8768158380 q^{51} + 3266669866 q^{52} + 7818635688 q^{53} + 17402728558 q^{54} - 191002682 q^{55} + 11263587512 q^{56} + 15495358340 q^{57} - 656356768 q^{58} + 1230002712 q^{59} + 31834046430 q^{60} - 18602654230 q^{61} + 22075953162 q^{62} - 9964531456 q^{63} + 11813658086 q^{64} + 32245789334 q^{65} + 42677188354 q^{66} + 27481284652 q^{67} + 29588811820 q^{68} - 20565315068 q^{69} + 42862666712 q^{70} - 20347168516 q^{71} + 47061083616 q^{72} - 57740010478 q^{73} - 2640709564 q^{74} - 23544691000 q^{75} - 33350650772 q^{76} + 871959792 q^{77} - 15384525342 q^{78} - 120245016462 q^{79} - 84319695274 q^{80} - 48880047865 q^{81} - 111495532412 q^{82} - 142463983824 q^{83} - 134146226376 q^{84} - 181628566552 q^{85} + 47870165542 q^{86} - 20141948318 q^{87} - 180608014462 q^{88} - 96700717270 q^{89} - 25522461244 q^{90} - 355162031176 q^{91} - 22429477796 q^{92} - 172582115142 q^{93} + 172608565078 q^{94} - 195922150708 q^{95} + 226391047758 q^{96} - 303190852014 q^{97} - 123776497136 q^{98} - 139125462440 q^{99}+O(q^{100}) \) 11 * q - 32 * q^2 - 982 * q^3 + 9146 * q^4 - 2740 * q^5 - 28202 * q^6 - 49432 * q^7 - 150054 * q^8 + 330749 * q^9 - 685834 * q^10 - 612246 * q^11 + 2578538 * q^12 + 1510364 * q^13 + 3955400 * q^14 - 2462818 * q^15 + 3024818 * q^16 - 3291098 * q^17 - 27885614 * q^18 - 44121388 * q^19 - 49472662 * q^20 - 46916800 * q^21 - 43435618 * q^22 - 88684076 * q^23 - 224700678 * q^24 - 44195521 * q^25 - 324999762 * q^26 - 236304286 * q^27 - 391274848 * q^28 + 225622639 * q^29 - 494910382 * q^30 - 292235934 * q^31 - 632542514 * q^32 - 1079766410 * q^33 - 1113307936 * q^34 - 1312820120 * q^35 - 2236726492 * q^36 - 1380429338 * q^37 - 1222857284 * q^38 - 1186931090 * q^39 - 2713154106 * q^40 - 1062067494 * q^41 + 205598960 * q^42 + 74588594 * q^43 + 52891466 * q^44 + 4527996830 * q^45 - 87670324 * q^46 - 1821239394 * q^47 + 2666035542 * q^48 + 4692522003 * q^49 + 9494259926 * q^50 + 8768158380 * q^51 + 3266669866 * q^52 + 7818635688 * q^53 + 17402728558 * q^54 - 191002682 * q^55 + 11263587512 * q^56 + 15495358340 * q^57 - 656356768 * q^58 + 1230002712 * q^59 + 31834046430 * q^60 - 18602654230 * q^61 + 22075953162 * q^62 - 9964531456 * q^63 + 11813658086 * q^64 + 32245789334 * q^65 + 42677188354 * q^66 + 27481284652 * q^67 + 29588811820 * q^68 - 20565315068 * q^69 + 42862666712 * q^70 - 20347168516 * q^71 + 47061083616 * q^72 - 57740010478 * q^73 - 2640709564 * q^74 - 23544691000 * q^75 - 33350650772 * q^76 + 871959792 * q^77 - 15384525342 * q^78 - 120245016462 * q^79 - 84319695274 * q^80 - 48880047865 * q^81 - 111495532412 * q^82 - 142463983824 * q^83 - 134146226376 * q^84 - 181628566552 * q^85 + 47870165542 * q^86 - 20141948318 * q^87 - 180608014462 * q^88 - 96700717270 * q^89 - 25522461244 * q^90 - 355162031176 * q^91 - 22429477796 * q^92 - 172582115142 * q^93 + 172608565078 * q^94 - 195922150708 * q^95 + 226391047758 * q^96 - 303190852014 * q^97 - 123776497136 * q^98 - 139125462440 * 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 $

$2$	62.2743	1.37608	0.688041	−	0.725672i	$-0.258471\pi$
$2$	62.2743	1.37608	0.688041	+	0.725672i	$0.258471\pi$
$3$	−384.675	−0.913959	−0.456979	−	0.889477i	$-0.651069\pi$
$3$	−384.675	−0.913959	−0.456979	+	0.889477i	$0.651069\pi$
$4$	1830.09	0.893600
$5$	1377.47	0.197127	0.0985635	−	0.995131i	$-0.468575\pi$
$5$	1377.47	0.197127	0.0985635	+	0.995131i	$0.468575\pi$
$6$	−23955.4	−1.25768
$7$	33050.3	0.743252	0.371626	−	0.928383i	$-0.378800\pi$
$7$	33050.3	0.743252	0.371626	+	0.928383i	$0.378800\pi$
$8$	−13570.0	−0.146415
$9$	−29172.4	−0.164679
$10$	85780.8	0.271263
$11$	−800438.	−1.49854	−0.749270	−	0.662265i	$-0.769595\pi$
$11$	−800438.	−1.49854	−0.749270	+	0.662265i	$0.769595\pi$
$12$	−703990.	−0.816714
$13$	1.48554e6	1.10968	0.554839	−	0.831958i	$-0.312780\pi$
$13$	1.48554e6	1.10968	0.554839	+	0.831958i	$0.312780\pi$
$14$	2.05818e6	1.02277
$15$	−529877.	−0.180166
$16$	−4.59309e6	−1.09508
$17$	−1.13043e7	−1.93097	−0.965485	−	0.260457i	$-0.916127\pi$
$17$	−1.13043e7	−1.93097	−0.965485	+	0.260457i	$0.916127\pi$
$18$	−1.81669e6	−0.226612
$19$	−9.78812e6	−0.906890	−0.453445	−	0.891284i	$-0.649805\pi$
$19$	−9.78812e6	−0.906890	−0.453445	+	0.891284i	$0.649805\pi$
$20$	2.52089e6	0.176153
$21$	−1.27136e7	−0.679302
$22$	−4.98468e7	−2.06211
$23$	546284.	0.0176977	0.00884883	−	0.999961i	$-0.497183\pi$
$23$	546284.	0.0176977	0.00884883	+	0.999961i	$0.497183\pi$
$24$	5.22005e6	0.133818
$25$	−4.69307e7	−0.961141
$26$	9.25112e7	1.52701
$27$	7.93659e7	1.06447
$28$	6.04851e7	0.664170
$29$	2.05111e7	0.185695
$29$	2.05111e7	0.185695
$30$	−3.29977e7	−0.247923
$31$	4.17817e6	0.0262118	0.0131059	−	0.999914i	$-0.495828\pi$
$31$	4.17817e6	0.0262118	0.0131059	+	0.999914i	$0.495828\pi$
$32$	−2.58240e8	−1.36050
$33$	3.07908e8	1.36960
$34$	−7.03969e8	−2.65717
$35$	4.55257e7	0.146515
$36$	−5.33882e7	−0.147157
$37$	3.50598e8	0.831190	0.415595	−	0.909550i	$-0.363573\pi$
$37$	3.50598e8	0.831190	0.415595	+	0.909550i	$0.363573\pi$
$38$	−6.09549e8	−1.24795
$39$	−5.71451e8	−1.01420
$40$	−1.86923e7	−0.0288624
$41$	7.34075e8	0.989531	0.494765	−	0.869027i	$-0.335254\pi$
$41$	7.34075e8	0.989531	0.494765	+	0.869027i	$0.335254\pi$
$42$	−7.91731e8	−0.934774
$43$	−1.74203e9	−1.80709	−0.903545	−	0.428494i	$-0.859044\pi$
$43$	−1.74203e9	−1.80709	−0.903545	+	0.428494i	$0.859044\pi$
$44$	−1.46488e9	−1.33909
$45$	−4.01841e7	−0.0324627
$46$	3.40195e7	0.0243534
$47$	1.70223e9	1.08263	0.541315	−	0.840820i	$-0.317927\pi$
$47$	1.70223e9	1.08263	0.541315	+	0.840820i	$0.317927\pi$
$48$	1.76685e9	1.00086
$49$	−8.85005e8	−0.447577
$50$	−2.92258e9	−1.32261
$51$	4.34849e9	1.76483
$52$	2.71868e9	0.991608
$53$	2.30025e9	0.755539	0.377770	−	0.925900i	$-0.376691\pi$
$53$	2.30025e9	0.755539	0.377770	+	0.925900i	$0.376691\pi$
$54$	4.94246e9	1.46480
$55$	−1.10258e9	−0.295403
$56$	−4.48494e8	−0.108823
$57$	3.76524e9	0.828860
$58$	1.27732e9	0.255532
$59$	−2.84523e8	−0.0518121	−0.0259060	−	0.999664i	$-0.508247\pi$
$59$	−2.84523e8	−0.0518121	−0.0259060	+	0.999664i	$0.508247\pi$
$60$	−9.69723e8	−0.160996
$61$	5.13866e9	0.778997	0.389499	−	0.921027i	$-0.372648\pi$
$61$	5.13866e9	0.778997	0.389499	+	0.921027i	$0.372648\pi$
$62$	2.60193e8	0.0360696
$63$	−9.64157e8	−0.122398
$64$	−6.67509e9	−0.777083
$65$	2.04629e9	0.218747
$66$	1.91748e10	1.88469
$67$	−3.85315e9	−0.348662	−0.174331	−	0.984687i	$-0.555776\pi$
$67$	−3.85315e9	−0.348662	−0.174331	+	0.984687i	$0.555776\pi$
$68$	−2.06880e10	−1.72552
$69$	−2.10142e8	−0.0161749
$70$	2.83508e9	0.201617
$71$	2.82041e10	1.85520	0.927602	−	0.373570i	$-0.121867\pi$
$71$	2.82041e10	1.85520	0.927602	+	0.373570i	$0.121867\pi$
$72$	3.95871e8	0.0241115
$73$	−1.81192e10	−1.02297	−0.511484	−	0.859293i	$-0.670904\pi$
$73$	−1.81192e10	−1.02297	−0.511484	+	0.859293i	$0.670904\pi$
$74$	2.18333e10	1.14378
$75$	1.80531e10	0.878443
$76$	−1.79132e10	−0.810396
$77$	−2.64547e10	−1.11379
$78$	−3.55867e10	−1.39562
$79$	−3.94609e10	−1.44284	−0.721419	−	0.692499i	$-0.756510\pi$
$79$	−3.94609e10	−1.44284	−0.721419	+	0.692499i	$0.756510\pi$
$80$	−6.32684e9	−0.215870
$81$	−2.53622e10	−0.808202
$82$	4.57140e10	1.36168
$83$	1.27885e10	0.356362	0.178181	−	0.983998i	$-0.442979\pi$
$83$	1.27885e10	0.356362	0.178181	+	0.983998i	$0.442979\pi$
$84$	−2.32671e10	−0.607024
$85$	−1.55713e10	−0.380646
$86$	−1.08484e11	−2.48670
$87$	−7.89012e9	−0.169718
$88$	1.08620e10	0.219409
$89$	4.46844e10	0.848225	0.424112	−	0.905610i	$-0.360586\pi$
$89$	4.46844e10	0.848225	0.424112	+	0.905610i	$0.360586\pi$
$90$	−2.50244e9	−0.0446714
$91$	4.90976e10	0.824770
$92$	9.99751e8	0.0158146
$93$	−1.60724e9	−0.0239565
$94$	1.06005e11	1.48979
$95$	−1.34828e10	−0.178772
$96$	9.93386e10	1.24344
$97$	−7.40280e10	−0.875289	−0.437644	−	0.899148i	$-0.644187\pi$
$97$	−7.40280e10	−0.875289	−0.437644	+	0.899148i	$0.644187\pi$
$98$	−5.51131e10	−0.615902
$99$	2.33507e10	0.246778
$100$	−8.58875e10	−0.858875
$101$	−8.70065e10	−0.823728	−0.411864	−	0.911245i	$-0.635122\pi$
$101$	−8.70065e10	−0.823728	−0.411864	+	0.911245i	$0.635122\pi$
$102$	2.70799e11	2.42855
$103$	−2.00277e11	−1.70227	−0.851133	−	0.524951i	$-0.824084\pi$
$103$	−2.00277e11	−1.70227	−0.851133	+	0.524951i	$0.824084\pi$
$104$	−2.01589e10	−0.162474
$105$	−1.75126e10	−0.133909
$106$	1.43246e11	1.03968
$107$	−6.27684e10	−0.432644	−0.216322	−	0.976322i	$-0.569406\pi$
$107$	−6.27684e10	−0.432644	−0.216322	+	0.976322i	$0.569406\pi$
$108$	1.45247e11	0.951209
$109$	1.65628e11	1.03107	0.515535	−	0.856868i	$-0.327593\pi$
$109$	1.65628e11	1.03107	0.515535	+	0.856868i	$0.327593\pi$
$110$	−6.86623e10	−0.406498
$111$	−1.34866e11	−0.759673
$112$	−1.51803e11	−0.813920
$113$	1.11390e11	0.568741	0.284370	−	0.958714i	$-0.408215\pi$
$113$	1.11390e11	0.568741	0.284370	+	0.958714i	$0.408215\pi$
$114$	2.34478e11	1.14058
$115$	7.52489e8	0.00348869
$116$	3.75373e10	0.165937
$117$	−4.33369e10	−0.182741
$118$	−1.77185e10	−0.0712977
$119$	−3.73611e11	−1.43520
$120$	7.19045e9	0.0263790
$121$	3.55390e11	1.24562
$122$	3.20007e11	1.07196
$123$	−2.82380e11	−0.904391
$124$	7.64644e9	0.0234229
$125$	−1.31905e11	−0.386594
$126$	−6.00422e10	−0.168430
$127$	−4.11525e11	−1.10529	−0.552644	−	0.833417i	$-0.686381\pi$
$127$	−4.11525e11	−1.10529	−0.552644	+	0.833417i	$0.686381\pi$
$128$	1.13189e11	0.291173
$129$	6.70115e11	1.65161
$130$	1.27431e11	0.301014
$131$	−9.62047e10	−0.217873	−0.108937	−	0.994049i	$-0.534745\pi$
$131$	−9.62047e10	−0.217873	−0.108937	+	0.994049i	$0.534745\pi$
$132$	5.63501e11	1.22388
$133$	−3.23500e11	−0.674047
$134$	−2.39952e11	−0.479787
$135$	1.09324e11	0.209836
$136$	1.53400e11	0.282724
$137$	−3.08367e11	−0.545890	−0.272945	−	0.962030i	$-0.587998\pi$
$137$	−3.08367e11	−0.545890	−0.272945	+	0.962030i	$0.587998\pi$
$138$	−1.30864e10	−0.0222580
$139$	6.03606e11	0.986671	0.493336	−	0.869839i	$-0.335777\pi$
$139$	6.03606e11	0.986671	0.493336	+	0.869839i	$0.335777\pi$
$140$	8.33162e10	0.130926
$141$	−6.54804e11	−0.989479
$142$	1.75639e12	2.55291
$143$	−1.18909e12	−1.66290
$144$	1.33992e11	0.180337
$145$	2.82534e10	0.0366056
$146$	−1.12836e12	−1.40769
$147$	3.40439e11	0.409067
$148$	6.41627e11	0.742751
$149$	−1.18808e12	−1.32532	−0.662660	−	0.748920i	$-0.730573\pi$
$149$	−1.18808e12	−1.32532	−0.662660	+	0.748920i	$0.730573\pi$
$150$	1.12424e12	1.20881
$151$	4.61543e11	0.478453	0.239226	−	0.970964i	$-0.423106\pi$
$151$	4.61543e11	0.478453	0.239226	+	0.970964i	$0.423106\pi$
$152$	1.32825e11	0.132782
$153$	3.29775e11	0.317991
$154$	−1.64745e12	−1.53267
$155$	5.75529e9	0.00516706
$156$	−1.04581e12	−0.906289
$157$	4.49681e11	0.376232	0.188116	−	0.982147i	$-0.439762\pi$
$157$	4.49681e11	0.376232	0.188116	+	0.982147i	$0.439762\pi$
$158$	−2.45740e12	−1.98546
$159$	−8.84846e11	−0.690532
$160$	−3.55718e11	−0.268192
$161$	1.80549e10	0.0131538
$162$	−1.57942e12	−1.11215
$163$	−1.77931e12	−1.21121	−0.605604	−	0.795766i	$-0.707068\pi$
$163$	−1.77931e12	−1.21121	−0.605604	+	0.795766i	$0.707068\pi$
$164$	1.34343e12	0.884245
$165$	4.24134e11	0.269986
$166$	7.96398e11	0.490383
$167$	5.68373e11	0.338604	0.169302	−	0.985564i	$-0.445849\pi$
$167$	5.68373e11	0.338604	0.169302	+	0.985564i	$0.445849\pi$
$168$	1.72524e11	0.0994601
$169$	4.14679e11	0.231385
$170$	−9.69695e11	−0.523801
$171$	2.85543e11	0.149346
$172$	−3.18808e12	−1.61481
$173$	−3.46675e11	−0.170086	−0.0850430	−	0.996377i	$-0.527103\pi$
$173$	−3.46675e11	−0.170086	−0.0850430	+	0.996377i	$0.527103\pi$
$174$	−4.91352e11	−0.233546
$175$	−1.55107e12	−0.714370
$176$	3.67649e12	1.64102
$177$	1.09449e11	0.0473541
$178$	2.78269e12	1.16723
$179$	−1.84659e12	−0.751068	−0.375534	−	0.926809i	$-0.622541\pi$
$179$	−1.84659e12	−0.751068	−0.375534	+	0.926809i	$0.622541\pi$
$180$	−7.35405e10	−0.0290087
$181$	1.69842e12	0.649849	0.324925	−	0.945740i	$-0.394661\pi$
$181$	1.69842e12	0.649849	0.324925	+	0.945740i	$0.394661\pi$
$182$	3.05752e12	1.13495
$183$	−1.97671e12	−0.711971
$184$	−7.41310e9	−0.00259121
$185$	4.82938e11	0.163850
$186$	−1.00090e11	−0.0329661
$187$	9.04842e12	2.89364
$188$	3.11524e12	0.967437
$189$	2.62306e12	0.791168
$190$	−8.39633e11	−0.246005
$191$	6.53577e12	1.86043	0.930215	−	0.367016i	$-0.119621\pi$
$191$	6.53577e12	1.86043	0.930215	+	0.367016i	$0.119621\pi$
$192$	2.56774e12	0.710222
$193$	2.24825e12	0.604338	0.302169	−	0.953254i	$-0.402289\pi$
$193$	2.24825e12	0.604338	0.302169	+	0.953254i	$0.402289\pi$
$194$	−4.61004e12	−1.20447
$195$	−7.87155e11	−0.199926
$196$	−1.61964e12	−0.399955
$197$	4.50505e12	1.08177	0.540885	−	0.841097i	$-0.318089\pi$
$197$	4.50505e12	1.08177	0.540885	+	0.841097i	$0.318089\pi$
$198$	1.45415e12	0.339587
$199$	−4.83401e12	−1.09803	−0.549017	−	0.835811i	$-0.684998\pi$
$199$	−4.83401e12	−1.09803	−0.549017	+	0.835811i	$0.684998\pi$
$200$	6.36852e11	0.140726
$201$	1.48221e12	0.318662
$202$	−5.41827e12	−1.13352
$203$	6.77899e11	0.138018
$204$	7.95814e12	1.57705
$205$	1.01116e12	0.195063
$206$	−1.24721e13	−2.34246
$207$	−1.59364e10	−0.00291444
$208$	−6.82324e12	−1.21519
$209$	7.83479e12	1.35901
$210$	−1.09058e12	−0.184269
$211$	−1.10099e13	−1.81229	−0.906146	−	0.422964i	$-0.860990\pi$
$211$	−1.10099e13	−1.81229	−0.906146	+	0.422964i	$0.860990\pi$
$212$	4.20966e12	0.675150
$213$	−1.08494e13	−1.69558
$214$	−3.90886e12	−0.595353
$215$	−2.39959e12	−0.356226
$216$	−1.07700e12	−0.155854
$217$	1.38090e11	0.0194820
$218$	1.03144e13	1.41884
$219$	6.96998e12	0.934951
$220$	−2.01782e12	−0.263972
$221$	−1.67931e13	−2.14276
$222$	−8.39871e12	−1.04537
$223$	−5.53451e12	−0.672051	−0.336026	−	0.941853i	$-0.609083\pi$
$223$	−5.53451e12	−0.672051	−0.336026	+	0.941853i	$0.609083\pi$
$224$	−8.53492e12	−1.01120
$225$	1.36908e12	0.158280
$226$	6.93673e12	0.782634
$227$	−4.70942e12	−0.518592	−0.259296	−	0.965798i	$-0.583490\pi$
$227$	−4.70942e12	−0.518592	−0.259296	+	0.965798i	$0.583490\pi$
$228$	6.89074e12	0.740669
$229$	−4.06336e12	−0.426374	−0.213187	−	0.977011i	$-0.568384\pi$
$229$	−4.06336e12	−0.426374	−0.213187	+	0.977011i	$0.568384\pi$
$230$	4.68607e10	0.00480072
$231$	1.01765e13	1.01796
$232$	−2.78337e11	−0.0271886
$233$	1.96315e13	1.87282	0.936411	−	0.350906i	$-0.114126\pi$
$233$	1.96315e13	1.87282	0.936411	+	0.350906i	$0.114126\pi$
$234$	−2.69878e12	−0.251466
$235$	2.34476e12	0.213415
$236$	−5.20703e11	−0.0462993
$237$	1.51796e13	1.31869
$238$	−2.32664e13	−1.97495
$239$	1.39900e13	1.16046	0.580231	−	0.814452i	$-0.302962\pi$
$239$	1.39900e13	1.16046	0.580231	+	0.814452i	$0.302962\pi$
$240$	2.43377e12	0.197296
$241$	−1.44074e13	−1.14154	−0.570772	−	0.821109i	$-0.693356\pi$
$241$	−1.44074e13	−1.14154	−0.570772	+	0.821109i	$0.693356\pi$
$242$	2.21317e13	1.71408
$243$	−4.30322e12	−0.325806
$244$	9.40423e12	0.696112
$245$	−1.21907e12	−0.0882295
$246$	−1.75850e13	−1.24451
$247$	−1.45407e13	−1.00636
$248$	−5.66980e10	−0.00383781
$249$	−4.91943e12	−0.325700
$250$	−8.21427e12	−0.531985
$251$	−2.15745e13	−1.36689	−0.683446	−	0.730001i	$-0.739520\pi$
$251$	−2.15745e13	−1.36689	−0.683446	+	0.730001i	$0.739520\pi$
$252$	−1.76450e12	−0.109375
$253$	−4.37267e11	−0.0265206
$254$	−2.56274e13	−1.52097
$255$	5.98990e12	0.347895
$256$	2.07194e13	1.17776
$257$	2.02393e13	1.12607	0.563034	−	0.826434i	$-0.309634\pi$
$257$	2.02393e13	1.12607	0.563034	+	0.826434i	$0.309634\pi$
$258$	4.17310e13	2.27274
$259$	1.15874e13	0.617783
$260$	3.74489e12	0.195473
$261$	−5.98360e11	−0.0305802
$262$	−5.99108e12	−0.299811
$263$	1.12028e13	0.548997	0.274499	−	0.961587i	$-0.411488\pi$
$263$	1.12028e13	0.548997	0.274499	+	0.961587i	$0.411488\pi$
$264$	−4.17833e12	−0.200531
$265$	3.16851e12	0.148937
$266$	−2.01458e13	−0.927544
$267$	−1.71890e13	−0.775242
$268$	−7.05162e12	−0.311564
$269$	−1.31186e13	−0.567871	−0.283935	−	0.958843i	$-0.591640\pi$
$269$	−1.31186e13	−0.567871	−0.283935	+	0.958843i	$0.591640\pi$
$270$	6.80807e12	0.288751
$271$	−1.61271e13	−0.670232	−0.335116	−	0.942177i	$-0.608775\pi$
$271$	−1.61271e13	−0.670232	−0.335116	+	0.942177i	$0.608775\pi$
$272$	5.19219e13	2.11457
$273$	−1.88866e13	−0.753806
$274$	−1.92034e13	−0.751189
$275$	3.75651e13	1.44031
$276$	−3.84579e11	−0.0144539
$277$	3.78738e13	1.39540	0.697702	−	0.716388i	$-0.254206\pi$
$277$	3.78738e13	1.39540	0.697702	+	0.716388i	$0.254206\pi$
$278$	3.75892e13	1.35774
$279$	−1.21887e11	−0.00431654
$280$	−6.17785e11	−0.0214520
$281$	−5.07029e12	−0.172643	−0.0863214	−	0.996267i	$-0.527511\pi$
$281$	−5.07029e12	−0.172643	−0.0863214	+	0.996267i	$0.527511\pi$
$282$	−4.07775e13	−1.36160
$283$	−5.45868e13	−1.78757	−0.893783	−	0.448500i	$-0.851958\pi$
$283$	−5.45868e13	−1.78757	−0.893783	+	0.448500i	$0.851958\pi$
$284$	5.16161e13	1.65781
$285$	5.18649e12	0.163391
$286$	−7.40495e13	−2.28828
$287$	2.42614e13	0.735471
$288$	7.53350e12	0.224047
$289$	9.35159e13	2.72865
$290$	1.75946e12	0.0503722
$291$	2.84767e13	0.799978
$292$	−3.31597e13	−0.914125
$293$	−3.12899e13	−0.846511	−0.423256	−	0.906010i	$-0.639113\pi$
$293$	−3.12899e13	−0.846511	−0.423256	+	0.906010i	$0.639113\pi$
$294$	2.12006e13	0.562909
$295$	−3.91921e11	−0.0102136
$296$	−4.75763e12	−0.121699
$297$	−6.35275e13	−1.59515
$298$	−7.39869e13	−1.82375
$299$	8.11529e11	0.0196387
$300$	3.30388e13	0.784977
$301$	−5.75746e13	−1.34312
$302$	2.87423e13	0.658390
$303$	3.34692e13	0.752854
$304$	4.49578e13	0.993116
$305$	7.07834e12	0.153561
$306$	2.05365e13	0.437581
$307$	−2.08032e12	−0.0435381	−0.0217691	−	0.999763i	$-0.506930\pi$
$307$	−2.08032e12	−0.0435381	−0.0217691	+	0.999763i	$0.506930\pi$
$308$	−4.84146e13	−0.995285
$309$	7.70416e13	1.55580
$310$	3.58407e11	0.00711029
$311$	3.53426e13	0.688837	0.344418	−	0.938816i	$-0.388076\pi$
$311$	3.53426e13	0.688837	0.344418	+	0.938816i	$0.388076\pi$
$312$	7.75461e12	0.148494
$313$	2.98830e13	0.562252	0.281126	−	0.959671i	$-0.409292\pi$
$313$	2.98830e13	0.562252	0.281126	+	0.959671i	$0.409292\pi$
$314$	2.80036e13	0.517726
$315$	−1.32809e12	−0.0241280
$316$	−7.22170e13	−1.28932
$317$	−4.25262e13	−0.746157	−0.373079	−	0.927800i	$-0.621698\pi$
$317$	−4.25262e13	−0.746157	−0.373079	+	0.927800i	$0.621698\pi$
$318$	−5.51032e13	−0.950228
$319$	−1.64179e13	−0.278272
$320$	−9.19472e12	−0.153184
$321$	2.41454e13	0.395418
$322$	1.12435e12	0.0181007
$323$	1.10648e14	1.75118
$324$	−4.64152e13	−0.722209
$325$	−6.97176e13	−1.06656
$326$	−1.10805e14	−1.66672
$327$	−6.37129e13	−0.942356
$328$	−9.96143e12	−0.144882
$329$	5.62592e13	0.804666
$330$	2.64126e13	0.371522
$331$	3.15763e12	0.0436825	0.0218412	−	0.999761i	$-0.493047\pi$
$331$	3.15763e12	0.0436825	0.0218412	+	0.999761i	$0.493047\pi$
$332$	2.34042e13	0.318445
$333$	−1.02278e13	−0.136880
$334$	3.53950e13	0.465947
$335$	−5.30758e12	−0.0687307
$336$	5.83948e13	0.743889
$337$	−6.97371e13	−0.873976	−0.436988	−	0.899467i	$-0.643955\pi$
$337$	−6.97371e13	−0.873976	−0.436988	+	0.899467i	$0.643955\pi$
$338$	2.58239e13	0.318405
$339$	−4.28489e13	−0.519806
$340$	−2.84970e13	−0.340146
$341$	−3.34437e12	−0.0392794
$342$	1.77820e13	0.205512
$343$	−9.46009e13	−1.07591
$344$	2.36394e13	0.264585
$345$	−2.89463e11	−0.00318852
$346$	−2.15889e13	−0.234052
$347$	−1.18515e14	−1.26462	−0.632309	−	0.774716i	$-0.717893\pi$
$347$	−1.18515e14	−1.26462	−0.632309	+	0.774716i	$0.717893\pi$
$348$	−1.44396e13	−0.151660
$349$	−3.54876e13	−0.366890	−0.183445	−	0.983030i	$-0.558725\pi$
$349$	−3.54876e13	−0.366890	−0.183445	+	0.983030i	$0.558725\pi$
$350$	−9.65921e13	−0.983031
$351$	1.17901e14	1.18122
$352$	2.06706e14	2.03877
$353$	−1.48557e14	−1.44256	−0.721278	−	0.692645i	$-0.756445\pi$
$353$	−1.48557e14	−1.44256	−0.721278	+	0.692645i	$0.756445\pi$
$354$	6.81585e12	0.0651631
$355$	3.88502e13	0.365711
$356$	8.17766e13	0.757973
$357$	1.43719e14	1.31171
$358$	−1.14995e14	−1.03353
$359$	−1.39595e14	−1.23552	−0.617760	−	0.786367i	$-0.711960\pi$
$359$	−1.39595e14	−1.23552	−0.617760	+	0.786367i	$0.711960\pi$
$360$	5.45299e11	0.00475304
$361$	−2.06830e13	−0.177551
$362$	1.05768e14	0.894246
$363$	−1.36710e14	−1.13845
$364$	8.98532e13	0.737014
$365$	−2.49585e13	−0.201655
$366$	−1.23098e14	−0.979731
$367$	−2.38895e14	−1.87303	−0.936514	−	0.350631i	$-0.885967\pi$
$367$	−2.38895e14	−1.87303	−0.936514	+	0.350631i	$0.885967\pi$
$368$	−2.50914e12	−0.0193803
$369$	−2.14148e13	−0.162955
$370$	3.00746e13	0.225471
$371$	7.60238e13	0.561556
$372$	−2.94139e12	−0.0214075
$373$	−3.21648e13	−0.230665	−0.115333	−	0.993327i	$-0.536793\pi$
$373$	−3.21648e13	−0.230665	−0.115333	+	0.993327i	$0.536793\pi$
$374$	5.63484e14	3.98188
$375$	5.07404e13	0.353331
$376$	−2.30993e13	−0.158513
$377$	3.04702e13	0.206062
$378$	1.63350e14	1.08871
$379$	1.37788e14	0.905099	0.452550	−	0.891739i	$-0.350515\pi$
$379$	1.37788e14	0.905099	0.452550	+	0.891739i	$0.350515\pi$
$380$	−2.46748e13	−0.159751
$381$	1.58303e14	1.01019
$382$	4.07011e14	2.56010
$383$	−1.73711e14	−1.07704	−0.538522	−	0.842611i	$-0.681017\pi$
$383$	−1.73711e14	−1.07704	−0.538522	+	0.842611i	$0.681017\pi$
$384$	−4.35411e13	−0.266120
$385$	−3.64405e13	−0.219559
$386$	1.40008e14	0.831618
$387$	5.08193e13	0.297590
$388$	−1.35478e14	−0.782158
$389$	2.34150e14	1.33282	0.666411	−	0.745585i	$-0.267830\pi$
$389$	2.34150e14	1.33282	0.666411	+	0.745585i	$0.267830\pi$
$390$	−4.90195e13	−0.275115
$391$	−6.17538e12	−0.0341737
$392$	1.20096e13	0.0655321
$393$	3.70075e13	0.199127
$394$	2.80549e14	1.48860
$395$	−5.43560e13	−0.284422
$396$	4.27340e13	0.220521
$397$	−1.79333e14	−0.912669	−0.456334	−	0.889808i	$-0.650838\pi$
$397$	−1.79333e14	−0.912669	−0.456334	+	0.889808i	$0.650838\pi$
$398$	−3.01035e14	−1.51098
$399$	1.24442e14	0.616051
$400$	2.15557e14	1.05253
$401$	−3.03065e14	−1.45963	−0.729813	−	0.683646i	$-0.760393\pi$
$401$	−3.03065e14	−1.45963	−0.729813	+	0.683646i	$0.760393\pi$
$402$	9.23035e13	0.438506
$403$	6.20686e12	0.0290867
$404$	−1.59230e14	−0.736083
$405$	−3.49356e13	−0.159318
$406$	4.22157e13	0.189925
$407$	−2.80632e14	−1.24557
$408$	−5.90092e13	−0.258398
$409$	1.52684e14	0.659651	0.329825	−	0.944042i	$-0.393010\pi$
$409$	1.52684e14	0.659651	0.329825	+	0.944042i	$0.393010\pi$
$410$	6.29696e13	0.268423
$411$	1.18621e14	0.498921
$412$	−3.66526e14	−1.52114
$413$	−9.40356e12	−0.0385094
$414$	−9.92432e11	−0.00401050
$415$	1.76158e13	0.0702486
$416$	−3.83627e14	−1.50972
$417$	−2.32192e14	−0.901777
$418$	4.87906e14	1.87011
$419$	−2.74751e14	−1.03935	−0.519676	−	0.854363i	$-0.673947\pi$
$419$	−2.74751e14	−1.03935	−0.519676	+	0.854363i	$0.673947\pi$
$420$	−3.20496e13	−0.119661
$421$	−9.97837e13	−0.367712	−0.183856	−	0.982953i	$-0.558858\pi$
$421$	−9.97837e13	−0.367712	−0.183856	+	0.982953i	$0.558858\pi$
$422$	−6.85632e14	−2.49386
$423$	−4.96582e13	−0.178287
$424$	−3.12144e13	−0.110622
$425$	5.30520e14	1.85593
$426$	−6.75640e14	−2.33326
$427$	1.69834e14	0.578991
$428$	−1.14872e14	−0.386610
$429$	4.57411e14	1.51982
$430$	−1.49433e14	−0.490196
$431$	−9.82326e13	−0.318149	−0.159075	−	0.987267i	$-0.550851\pi$
$431$	−9.82326e13	−0.318149	−0.159075	+	0.987267i	$0.550851\pi$
$432$	−3.64535e14	−1.16568
$433$	1.34165e14	0.423601	0.211800	−	0.977313i	$-0.432067\pi$
$433$	1.34165e14	0.423601	0.211800	+	0.977313i	$0.432067\pi$
$434$	8.59945e12	0.0268088
$435$	−1.08684e13	−0.0334560
$436$	3.03115e14	0.921364
$437$	−5.34710e12	−0.0160498
$438$	4.34051e14	1.28657
$439$	1.46616e14	0.429168	0.214584	−	0.976705i	$-0.431160\pi$
$439$	1.46616e14	0.429168	0.214584	+	0.976705i	$0.431160\pi$
$440$	1.49620e13	0.0432514
$441$	2.58178e13	0.0737066
$442$	−1.04578e15	−2.94861
$443$	−1.21156e13	−0.0337385	−0.0168693	−	0.999858i	$-0.505370\pi$
$443$	−1.21156e13	−0.0337385	−0.0168693	+	0.999858i	$0.505370\pi$
$444$	−2.46818e14	−0.678844
$445$	6.15513e13	0.167208
$446$	−3.44658e14	−0.924797
$447$	4.57024e14	1.21129
$448$	−2.20614e14	−0.577569
$449$	4.14075e14	1.07084	0.535419	−	0.844586i	$-0.320154\pi$
$449$	4.14075e14	1.07084	0.535419	+	0.844586i	$0.320154\pi$
$450$	8.52587e13	0.217806
$451$	−5.87582e14	−1.48285
$452$	2.03854e14	0.508227
$453$	−1.77544e14	−0.437286
$454$	−2.93276e14	−0.713624
$455$	6.76304e13	0.162584
$456$	−5.10945e13	−0.121358
$457$	6.86418e14	1.61083	0.805415	−	0.592711i	$-0.201942\pi$
$457$	6.86418e14	1.61083	0.805415	+	0.592711i	$0.201942\pi$
$458$	−2.53043e14	−0.586725
$459$	−8.97178e14	−2.05546
$460$	1.37712e12	0.00311749
$461$	8.82601e14	1.97428	0.987142	−	0.159848i	$-0.0511003\pi$
$461$	8.82601e14	1.97428	0.987142	+	0.159848i	$0.0511003\pi$
$462$	6.33732e14	1.40080
$463$	−3.93909e14	−0.860399	−0.430200	−	0.902734i	$-0.641557\pi$
$463$	−3.93909e14	−0.860399	−0.430200	+	0.902734i	$0.641557\pi$
$464$	−9.42097e13	−0.203351
$465$	−2.21392e12	−0.00472248
$466$	1.22254e15	2.57715
$467$	−4.51731e13	−0.0941102	−0.0470551	−	0.998892i	$-0.514984\pi$
$467$	−4.51731e13	−0.0941102	−0.0470551	+	0.998892i	$0.514984\pi$
$468$	−7.93106e13	−0.163297
$469$	−1.27348e14	−0.259143
$470$	1.46019e14	0.293677
$471$	−1.72981e14	−0.343861
$472$	3.86099e12	0.00758608
$473$	1.39439e15	2.70799
$474$	9.45299e14	1.81463
$475$	4.59363e14	0.871649
$476$	−6.83743e14	−1.28249
$477$	−6.71038e13	−0.124422
$478$	8.71221e14	1.59689
$479$	−4.93799e14	−0.894756	−0.447378	−	0.894345i	$-0.647642\pi$
$479$	−4.93799e14	−0.894756	−0.447378	+	0.894345i	$0.647642\pi$
$480$	1.36836e14	0.245116
$481$	5.20829e14	0.922353
$482$	−8.97213e14	−1.57086
$483$	−6.94525e12	−0.0120220
$484$	6.50397e14	1.11309
$485$	−1.01971e14	−0.172543
$486$	−2.67980e14	−0.448336
$487$	5.62413e14	0.930350	0.465175	−	0.885219i	$-0.345991\pi$
$487$	5.62413e14	0.930350	0.465175	+	0.885219i	$0.345991\pi$
$488$	−6.97319e13	−0.114057
$489$	6.84454e14	1.10699
$490$	−7.59165e13	−0.121411
$491$	−6.06349e14	−0.958902	−0.479451	−	0.877569i	$-0.659164\pi$
$491$	−6.06349e14	−0.958902	−0.479451	+	0.877569i	$0.659164\pi$
$492$	−5.16782e14	−0.808163
$493$	−2.31865e14	−0.358572
$494$	−9.05511e14	−1.38483
$495$	3.21649e13	0.0486467
$496$	−1.91907e13	−0.0287040
$497$	9.32154e14	1.37888
$498$	−3.06354e14	−0.448190
$499$	−9.66448e14	−1.39838	−0.699191	−	0.714935i	$-0.746456\pi$
$499$	−9.66448e14	−1.39838	−0.699191	+	0.714935i	$0.746456\pi$
$500$	−2.41398e14	−0.345460
$501$	−2.18639e14	−0.309470
$502$	−1.34353e15	−1.88095
$503$	5.10073e14	0.706331	0.353166	−	0.935561i	$-0.385105\pi$
$503$	5.10073e14	0.706331	0.353166	+	0.935561i	$0.385105\pi$
$504$	1.30837e13	0.0179210
$505$	−1.19849e14	−0.162379
$506$	−2.72305e13	−0.0364946
$507$	−1.59517e14	−0.211476
$508$	−7.53128e14	−0.987685
$509$	−5.21410e12	−0.00676443	−0.00338222	−	0.999994i	$-0.501077\pi$
$509$	−5.21410e12	−0.00676443	−0.00338222	+	0.999994i	$0.501077\pi$
$510$	3.73017e14	0.478732
$511$	−5.98843e14	−0.760323
$512$	1.05847e15	1.32952
$513$	−7.76842e14	−0.965356
$514$	1.26039e15	1.54956
$515$	−2.75876e14	−0.335562
$516$	1.22637e15	1.47587
$517$	−1.36253e15	−1.62236
$518$	7.21596e14	0.850120
$519$	1.33357e14	0.155452
$520$	−2.77682e13	−0.0320280
$521$	4.21554e14	0.481112	0.240556	−	0.970635i	$-0.422670\pi$
$521$	4.21554e14	0.481112	0.240556	+	0.970635i	$0.422670\pi$
$522$	−3.72625e13	−0.0420808
$523$	8.60935e14	0.962080	0.481040	−	0.876699i	$-0.340259\pi$
$523$	8.60935e14	0.962080	0.481040	+	0.876699i	$0.340259\pi$
$524$	−1.76064e14	−0.194692
$525$	5.96659e14	0.652905
$526$	6.97648e14	0.755465
$527$	−4.72314e13	−0.0506142
$528$	−1.41425e15	−1.49982
$529$	−9.52511e14	−0.999687
$530$	1.97317e14	0.204950
$531$	8.30022e12	0.00853238
$532$	−5.92035e14	−0.602329
$533$	1.09050e15	1.09806
$534$	−1.07043e15	−1.06680
$535$	−8.64614e13	−0.0852858
$536$	5.22874e13	0.0510494
$537$	7.10337e14	0.686446
$538$	−8.16951e14	−0.781436
$539$	7.08392e14	0.670711
$540$	2.00073e14	0.187509
$541$	−2.89790e14	−0.268842	−0.134421	−	0.990924i	$-0.542918\pi$
$541$	−2.89790e14	−0.268842	−0.134421	+	0.990924i	$0.542918\pi$
$542$	−1.00430e15	−0.922293
$543$	−6.53339e14	−0.593936
$544$	2.91923e15	2.62709
$545$	2.28147e14	0.203252
$546$	−1.17615e15	−1.03730
$547$	2.01239e15	1.75704	0.878520	−	0.477705i	$-0.158531\pi$
$547$	2.01239e15	1.75704	0.878520	+	0.477705i	$0.158531\pi$
$548$	−5.64340e14	−0.487807
$549$	−1.49907e14	−0.128285
$550$	2.33934e15	1.98198
$551$	−2.00766e14	−0.168405
$552$	2.85163e12	0.00236826
$553$	−1.30419e15	−1.07239
$554$	2.35857e15	1.92019
$555$	−1.85774e14	−0.149752
$556$	1.10466e15	0.881689
$557$	1.45243e15	1.14787	0.573933	−	0.818902i	$-0.305417\pi$
$557$	1.45243e15	1.14787	0.573933	+	0.818902i	$0.305417\pi$
$558$	−7.59046e12	−0.00593991
$559$	−2.58786e15	−2.00529
$560$	−2.09104e14	−0.160446
$561$	−3.48070e15	−2.64466
$562$	−3.15749e14	−0.237571
$563$	−1.90166e15	−1.41689	−0.708447	−	0.705764i	$-0.750604\pi$
$563$	−1.90166e15	−1.41689	−0.708447	+	0.705764i	$0.750604\pi$
$564$	−1.19835e15	−0.884198
$565$	1.53436e14	0.112114
$566$	−3.39935e15	−2.45984
$567$	−8.38229e14	−0.600697
$568$	−3.82731e14	−0.271630
$569$	1.27765e15	0.898041	0.449020	−	0.893522i	$-0.351773\pi$
$569$	1.27765e15	0.898041	0.449020	+	0.893522i	$0.351773\pi$
$570$	3.22985e14	0.224839
$571$	8.73926e14	0.602527	0.301263	−	0.953541i	$-0.402592\pi$
$571$	8.73926e14	0.602527	0.301263	+	0.953541i	$0.402592\pi$
$572$	−2.17614e15	−1.48596
$573$	−2.51414e15	−1.70036
$574$	1.51086e15	1.01207
$575$	−2.56375e13	−0.0170099
$576$	1.94729e14	0.127969
$577$	1.90100e15	1.23741	0.618706	−	0.785623i	$-0.287657\pi$
$577$	1.90100e15	1.23741	0.618706	+	0.785623i	$0.287657\pi$
$578$	5.82364e15	3.75484
$579$	−8.64846e14	−0.552340
$580$	5.17064e13	0.0327107
$581$	4.22665e14	0.264867
$582$	1.77337e15	1.10083
$583$	−1.84121e15	−1.13221
$584$	2.45878e14	0.149778
$585$	−5.96952e13	−0.0360232
$586$	−1.94856e15	−1.16487
$587$	−5.70371e14	−0.337791	−0.168895	−	0.985634i	$-0.554020\pi$
$587$	−5.70371e14	−0.337791	−0.168895	+	0.985634i	$0.554020\pi$
$588$	6.23035e14	0.365542
$589$	−4.08964e13	−0.0237712
$590$	−2.44066e13	−0.0140547
$591$	−1.73298e15	−0.988693
$592$	−1.61033e15	−0.910219
$593$	6.76252e14	0.378711	0.189355	−	0.981909i	$-0.439360\pi$
$593$	6.76252e14	0.378711	0.189355	+	0.981909i	$0.439360\pi$
$594$	−3.95613e15	−2.19505
$595$	−5.14637e14	−0.282916
$596$	−2.17430e15	−1.18431
$597$	1.85952e15	1.00356
$598$	5.05375e13	0.0270244
$599$	−5.41473e14	−0.286899	−0.143449	−	0.989658i	$-0.545819\pi$
$599$	−5.41473e14	−0.286899	−0.143449	+	0.989658i	$0.545819\pi$
$600$	−2.44981e14	−0.128617
$601$	2.86332e15	1.48957	0.744785	−	0.667305i	$-0.232552\pi$
$601$	2.86332e15	1.48957	0.744785	+	0.667305i	$0.232552\pi$
$602$	−3.58542e15	−1.84825
$603$	1.12406e14	0.0574174
$604$	8.44666e14	0.427545
$605$	4.89538e14	0.245545
$606$	2.08427e15	1.03599
$607$	2.24665e15	1.10662	0.553310	−	0.832976i	$-0.313365\pi$
$607$	2.24665e15	1.10662	0.553310	+	0.832976i	$0.313365\pi$
$608$	2.52769e15	1.23383
$609$	−2.60771e14	−0.126143
$610$	4.40799e14	0.211313
$611$	2.52874e15	1.20137
$612$	6.03518e14	0.284157
$613$	−1.37966e15	−0.643783	−0.321891	−	0.946777i	$-0.604319\pi$
$613$	−1.37966e15	−0.643783	−0.321891	+	0.946777i	$0.604319\pi$
$614$	−1.29551e14	−0.0599120
$615$	−3.88969e14	−0.178280
$616$	3.58992e14	0.163076
$617$	−1.77458e15	−0.798966	−0.399483	−	0.916741i	$-0.630810\pi$
$617$	−1.77458e15	−0.798966	−0.399483	+	0.916741i	$0.630810\pi$
$618$	4.79772e15	2.14091
$619$	−6.71770e14	−0.297113	−0.148557	−	0.988904i	$-0.547463\pi$
$619$	−6.71770e14	−0.297113	−0.148557	+	0.988904i	$0.547463\pi$
$620$	1.05327e13	0.00461728
$621$	4.33563e13	0.0188386
$622$	2.20094e15	0.947895
$623$	1.47683e15	0.630445
$624$	2.62473e15	1.11063
$625$	2.10984e15	0.884933
$626$	1.86095e15	0.773705
$627$	−3.01384e15	−1.24208
$628$	8.22957e14	0.336201
$629$	−3.96328e15	−1.60500
$630$	−8.27062e13	−0.0332021
$631$	3.94122e15	1.56845	0.784223	−	0.620479i	$-0.213062\pi$
$631$	3.94122e15	1.56845	0.784223	+	0.620479i	$0.213062\pi$
$632$	5.35486e14	0.211253
$633$	4.23521e15	1.65636
$634$	−2.64829e15	−1.02677
$635$	−5.66862e14	−0.217882
$636$	−1.61935e15	−0.617059
$637$	−1.31471e15	−0.496666
$638$	−1.02241e15	−0.382925
$639$	−8.22783e14	−0.305514
$640$	1.55915e14	0.0573980
$641$	−2.71163e15	−0.989716	−0.494858	−	0.868974i	$-0.664780\pi$
$641$	−2.71163e15	−0.989716	−0.494858	+	0.868974i	$0.664780\pi$
$642$	1.50364e15	0.544128
$643$	1.11976e15	0.401757	0.200879	−	0.979616i	$-0.435620\pi$
$643$	1.11976e15	0.401757	0.200879	+	0.979616i	$0.435620\pi$
$644$	3.30421e13	0.0117542
$645$	9.23062e14	0.325576
$646$	6.89054e15	2.40976
$647$	−5.20369e14	−0.180442	−0.0902210	−	0.995922i	$-0.528757\pi$
$647$	−5.20369e14	−0.180442	−0.0902210	+	0.995922i	$0.528757\pi$
$648$	3.44166e14	0.118333
$649$	2.27743e14	0.0776425
$650$	−4.34162e15	−1.46767
$651$	−5.31196e13	−0.0178057
$652$	−3.25629e15	−1.08234
$653$	6.45444e14	0.212734	0.106367	−	0.994327i	$-0.466078\pi$
$653$	6.45444e14	0.212734	0.106367	+	0.994327i	$0.466078\pi$
$654$	−3.96768e15	−1.29676
$655$	−1.32519e14	−0.0429487
$656$	−3.37168e15	−1.08361
$657$	5.28580e14	0.168462
$658$	3.50350e15	1.10729
$659$	−4.90862e14	−0.153847	−0.0769236	−	0.997037i	$-0.524510\pi$
$659$	−4.90862e14	−0.153847	−0.0769236	+	0.997037i	$0.524510\pi$
$660$	7.76204e14	0.241259
$661$	−1.13195e15	−0.348915	−0.174458	−	0.984665i	$-0.555817\pi$
$661$	−1.13195e15	−0.348915	−0.174458	+	0.984665i	$0.555817\pi$
$662$	1.96639e14	0.0601106
$663$	6.45987e15	1.95839
$664$	−1.73541e14	−0.0521768
$665$	−4.45611e14	−0.132873
$666$	−6.36930e14	−0.188358
$667$	1.12049e13	0.00328637
$668$	1.04017e15	0.302577
$669$	2.12899e15	0.614227
$670$	−3.30526e14	−0.0945790
$671$	−4.11318e15	−1.16736
$672$	3.28317e15	0.924192
$673$	−1.66789e15	−0.465676	−0.232838	−	0.972516i	$-0.574801\pi$
$673$	−1.66789e15	−0.465676	−0.232838	+	0.972516i	$0.574801\pi$
$674$	−4.34283e15	−1.20266
$675$	−3.72470e15	−1.02310
$676$	7.58901e14	0.206766
$677$	3.40687e15	0.920699	0.460349	−	0.887738i	$-0.347724\pi$
$677$	3.40687e15	0.920699	0.460349	+	0.887738i	$0.347724\pi$
$678$	−2.66839e15	−0.715295
$679$	−2.44665e15	−0.650560
$680$	2.11304e14	0.0557324
$681$	1.81160e15	0.473971
$682$	−2.08268e14	−0.0540517
$683$	1.01334e15	0.260882	0.130441	−	0.991456i	$-0.458361\pi$
$683$	1.01334e15	0.260882	0.130441	+	0.991456i	$0.458361\pi$
$684$	5.22570e14	0.133455
$685$	−4.24765e14	−0.107610
$686$	−5.89121e15	−1.48055
$687$	1.56307e15	0.389688
$688$	8.00132e15	1.97891
$689$	3.41712e15	0.838405
$690$	−1.80261e13	−0.00438766
$691$	−3.43978e15	−0.830618	−0.415309	−	0.909680i	$-0.636327\pi$
$691$	−3.43978e15	−0.830618	−0.415309	+	0.909680i	$0.636327\pi$
$692$	−6.34447e14	−0.151989
$693$	7.71748e14	0.183418
$694$	−7.38041e15	−1.74022
$695$	8.31448e14	0.194500
$696$	1.07069e14	0.0248493
$697$	−8.29823e15	−1.91076
$698$	−2.20996e15	−0.504871
$699$	−7.55175e15	−1.71168
$700$	−2.83861e15	−0.638361
$701$	−1.06049e15	−0.236622	−0.118311	−	0.992977i	$-0.537748\pi$
$701$	−1.06049e15	−0.236622	−0.118311	+	0.992977i	$0.537748\pi$
$702$	7.34223e15	1.62545
$703$	−3.43170e15	−0.753797
$704$	5.34300e15	1.16449
$705$	−9.01971e14	−0.195053
$706$	−9.25130e15	−1.98507
$707$	−2.87559e15	−0.612237
$708$	2.00301e14	0.0423156
$709$	2.55303e15	0.535181	0.267591	−	0.963533i	$-0.413773\pi$
$709$	2.55303e15	0.535181	0.267591	+	0.963533i	$0.413773\pi$
$710$	2.41937e15	0.503248
$711$	1.15117e15	0.237605
$712$	−6.06369e14	−0.124193
$713$	2.28247e12	0.000463888 0
$714$	8.94999e15	1.80502
$715$	−1.63793e15	−0.327802
$716$	−3.37944e15	−0.671155
$717$	−5.38161e15	−1.06061
$718$	−8.69317e15	−1.70018
$719$	2.96226e15	0.574929	0.287464	−	0.957791i	$-0.407188\pi$
$719$	2.96226e15	0.574929	0.287464	+	0.957791i	$0.407188\pi$
$720$	1.84569e14	0.0355493
$721$	−6.61923e15	−1.26521
$722$	−1.28802e15	−0.244325
$723$	5.54217e15	1.04332
$724$	3.10826e15	0.580705
$725$	−9.62603e14	−0.178479
$726$	−8.51350e15	−1.56659
$727$	1.27741e15	0.233287	0.116643	−	0.993174i	$-0.462787\pi$
$727$	1.27741e15	0.233287	0.116643	+	0.993174i	$0.462787\pi$
$728$	−6.66257e14	−0.120759
$729$	6.14818e15	1.10597
$730$	−1.55428e15	−0.277493
$731$	1.96925e16	3.48944
$732$	−3.61757e15	−0.636218
$733$	7.57379e15	1.32203	0.661015	−	0.750372i	$-0.270126\pi$
$733$	7.57379e15	1.32203	0.661015	+	0.750372i	$0.270126\pi$
$734$	−1.48770e16	−2.57744
$735$	4.68944e14	0.0806381
$736$	−1.41073e14	−0.0240777
$737$	3.08421e15	0.522483
$738$	−1.33359e15	−0.224240
$739$	−3.67278e15	−0.612986	−0.306493	−	0.951873i	$-0.599156\pi$
$739$	−3.67278e15	−0.612986	−0.306493	+	0.951873i	$0.599156\pi$
$740$	8.83820e14	0.146416
$741$	5.59343e15	0.919767
$742$	4.73433e15	0.772747
$743$	7.23474e15	1.17215	0.586077	−	0.810256i	$-0.300672\pi$
$743$	7.23474e15	1.17215	0.586077	+	0.810256i	$0.300672\pi$
$744$	2.18103e13	0.00350760
$745$	−1.63654e15	−0.261257
$746$	−2.00304e15	−0.317414
$747$	−3.73073e14	−0.0586854
$748$	1.65594e16	2.58575
$749$	−2.07451e15	−0.321563
$750$	3.15982e15	0.486212
$751$	−2.47237e15	−0.377654	−0.188827	−	0.982010i	$-0.560469\pi$
$751$	−2.47237e15	−0.377654	−0.188827	+	0.982010i	$0.560469\pi$
$752$	−7.81850e15	−1.18556
$753$	8.29914e15	1.24928
$754$	1.89751e15	0.283558
$755$	6.35760e14	0.0943159
$756$	4.80045e15	0.706988
$757$	1.07908e15	0.157771	0.0788854	−	0.996884i	$-0.474864\pi$
$757$	1.07908e15	0.157771	0.0788854	+	0.996884i	$0.474864\pi$
$758$	8.58066e15	1.24549
$759$	1.68206e14	0.0242388
$760$	1.82962e14	0.0261750
$761$	8.35973e15	1.18734	0.593672	−	0.804707i	$-0.297678\pi$
$761$	8.35973e15	1.18734	0.593672	+	0.804707i	$0.297678\pi$
$762$	9.85822e15	1.39010
$763$	5.47406e15	0.766345
$764$	1.19611e16	1.66248
$765$	4.54254e14	0.0626846
$766$	−1.08177e16	−1.48210
$767$	−4.22671e14	−0.0574947
$768$	−7.97022e15	−1.07643
$769$	8.47458e15	1.13638	0.568190	−	0.822898i	$-0.307644\pi$
$769$	8.47458e15	1.13638	0.568190	+	0.822898i	$0.307644\pi$
$770$	−2.26931e15	−0.302130
$771$	−7.78556e15	−1.02918
$772$	4.11451e15	0.540036
$773$	−1.35997e16	−1.77232	−0.886159	−	0.463381i	$-0.846636\pi$
$773$	−1.35997e16	−1.77232	−0.886159	+	0.463381i	$0.846636\pi$
$774$	3.16474e15	0.409508
$775$	−1.96085e14	−0.0251932
$776$	1.00456e15	0.128156
$777$	−4.45737e15	−0.564629
$778$	1.45816e16	1.83407
$779$	−7.18522e15	−0.897395
$780$	−1.44057e15	−0.178654
$781$	−2.25757e16	−2.78010
$782$	−3.84568e14	−0.0470257
$783$	1.62788e15	0.197667
$784$	4.06491e15	0.490132
$785$	6.19420e14	0.0741655
$786$	2.30462e15	0.274015
$787$	6.33252e15	0.747680	0.373840	−	0.927493i	$-0.378041\pi$
$787$	6.33252e15	0.747680	0.373840	+	0.927493i	$0.378041\pi$
$788$	8.24465e15	0.966670
$789$	−4.30944e15	−0.501761
$790$	−3.38499e15	−0.391388
$791$	3.68147e15	0.422718
$792$	−3.16870e14	−0.0361321
$793$	7.63370e15	0.864436
$794$	−1.11679e16	−1.25591
$795$	−1.21885e15	−0.136122
$796$	−8.84669e15	−0.981203
$797$	−1.53574e16	−1.69159	−0.845796	−	0.533507i	$-0.820874\pi$
$797$	−1.53574e16	−1.69159	−0.845796	+	0.533507i	$0.820874\pi$
$798$	7.74956e15	0.847737
$799$	−1.92426e16	−2.09053
$800$	1.21194e16	1.30763
$801$	−1.30355e15	−0.139685
$802$	−1.88732e16	−2.00857
$803$	1.45033e16	1.53296
$804$	2.71258e15	0.284757
$805$	2.48700e13	0.00259297
$806$	3.86528e14	0.0400256
$807$	5.04639e15	0.519010
$808$	1.18068e15	0.120606
$809$	−8.68168e15	−0.880819	−0.440410	−	0.897797i	$-0.645167\pi$
$809$	−8.68168e15	−0.880819	−0.440410	+	0.897797i	$0.645167\pi$
$810$	−2.17559e15	−0.219235
$811$	−1.24520e16	−1.24630	−0.623151	−	0.782102i	$-0.714148\pi$
$811$	−1.24520e16	−1.24630	−0.623151	+	0.782102i	$0.714148\pi$
$812$	1.24062e15	0.123333
$813$	6.20368e15	0.612564
$814$	−1.74762e16	−1.71401
$815$	−2.45093e15	−0.238762
$816$	−1.99730e16	−1.93263
$817$	1.70512e16	1.63883
$818$	9.50827e15	0.907733
$819$	−1.43230e15	−0.135823
$820$	1.85052e15	0.174309
$821$	1.60834e16	1.50484	0.752420	−	0.658684i	$-0.228887\pi$
$821$	1.60834e16	1.50484	0.752420	+	0.658684i	$0.228887\pi$
$822$	7.38704e15	0.686555
$823$	9.49861e15	0.876922	0.438461	−	0.898750i	$-0.355524\pi$
$823$	9.49861e15	0.876922	0.438461	+	0.898750i	$0.355524\pi$
$824$	2.71777e15	0.249238
$825$	−1.44504e16	−1.31638
$826$	−5.85601e14	−0.0529921
$827$	2.12819e15	0.191306	0.0956532	−	0.995415i	$-0.469506\pi$
$827$	2.12819e15	0.191306	0.0956532	+	0.995415i	$0.469506\pi$
$828$	−2.91652e13	−0.00260434
$829$	−1.90510e15	−0.168993	−0.0844965	−	0.996424i	$-0.526928\pi$
$829$	−1.90510e15	−0.168993	−0.0844965	+	0.996424i	$0.526928\pi$
$830$	1.09701e15	0.0966678
$831$	−1.45691e16	−1.27534
$832$	−9.91614e15	−0.862312
$833$	1.00044e16	0.864258
$834$	−1.44596e16	−1.24092
$835$	7.82914e14	0.0667481
$836$	1.43384e16	1.21441
$837$	3.31604e14	0.0279017
$838$	−1.71100e16	−1.43023
$839$	2.03621e15	0.169095	0.0845477	−	0.996419i	$-0.473055\pi$
$839$	2.03621e15	0.169095	0.0845477	+	0.996419i	$0.473055\pi$
$840$	2.37646e14	0.0196063
$841$	4.20707e14	0.0344828
$842$	−6.21396e15	−0.506002
$843$	1.95041e15	0.157788
$844$	−2.01491e16	−1.61946
$845$	5.71207e14	0.0456122
$846$	−3.09243e15	−0.245337
$847$	1.17457e16	0.925810
$848$	−1.05652e16	−0.827375
$849$	2.09981e16	1.63376
$850$	3.30378e16	2.55392
$851$	1.91526e14	0.0147101
$852$	−1.98554e16	−1.51517
$853$	−1.08461e16	−0.822343	−0.411172	−	0.911558i	$-0.634880\pi$
$853$	−1.08461e16	−0.822343	−0.411172	+	0.911558i	$0.634880\pi$
$854$	1.05763e16	0.796739
$855$	3.93326e14	0.0294401
$856$	8.51770e14	0.0633456
$857$	2.23715e16	1.65311	0.826553	−	0.562859i	$-0.190299\pi$
$857$	2.23715e16	1.65311	0.826553	+	0.562859i	$0.190299\pi$
$858$	2.84850e16	2.09139
$859$	1.15245e16	0.840738	0.420369	−	0.907353i	$-0.361901\pi$
$859$	1.15245e16	0.840738	0.420369	+	0.907353i	$0.361901\pi$
$860$	−4.39147e15	−0.318324
$861$	−9.33274e15	−0.672190
$862$	−6.11737e15	−0.437799
$863$	−6.38998e15	−0.454402	−0.227201	−	0.973848i	$-0.572957\pi$
$863$	−6.38998e15	−0.454402	−0.227201	+	0.973848i	$0.572957\pi$
$864$	−2.04955e16	−1.44821
$865$	−4.77533e14	−0.0335286
$866$	8.35505e15	0.582909
$867$	−3.59732e16	−2.49387
$868$	2.52717e14	0.0174091
$869$	3.15860e16	2.16215
$870$	−6.76821e14	−0.0460382
$871$	−5.72402e15	−0.386902
$872$	−2.24758e15	−0.150964
$873$	2.15958e15	0.144142
$874$	−3.32987e14	−0.0220859
$875$	−4.35949e15	−0.287337
$876$	1.27557e16	0.835472
$877$	−1.02607e16	−0.667849	−0.333924	−	0.942600i	$-0.608373\pi$
$877$	−1.02607e16	−0.667849	−0.333924	+	0.942600i	$0.608373\pi$
$878$	9.13044e15	0.590571
$879$	1.20364e16	0.773676
$880$	5.06424e15	0.323489
$881$	−7.21654e15	−0.458101	−0.229051	−	0.973415i	$-0.573562\pi$
$881$	−7.21654e15	−0.458101	−0.229051	+	0.973415i	$0.573562\pi$
$882$	1.60778e15	0.101426
$883$	8.51122e15	0.533591	0.266795	−	0.963753i	$-0.414035\pi$
$883$	8.51122e15	0.533591	0.266795	+	0.963753i	$0.414035\pi$
$884$	−3.07329e16	−1.91477
$885$	1.50762e14	0.00933478
$886$	−7.54494e14	−0.0464269
$887$	−1.37601e16	−0.841477	−0.420739	−	0.907182i	$-0.638229\pi$
$887$	−1.37601e16	−0.841477	−0.420739	+	0.907182i	$0.638229\pi$
$888$	1.83014e15	0.111228
$889$	−1.36010e16	−0.821507
$890$	3.83307e15	0.230092
$891$	2.03009e16	1.21112
$892$	−1.01287e16	−0.600545
$893$	−1.66616e16	−0.981825
$894$	2.84609e16	1.66683
$895$	−2.54362e15	−0.148056
$896$	3.74094e15	0.216415
$897$	−3.12175e14	−0.0179490
$898$	2.57862e16	1.47356
$899$	8.56991e13	0.00486741
$900$	2.50555e15	0.141439
$901$	−2.60027e16	−1.45892
$902$	−3.65913e16	−2.04052
$903$	2.21475e16	1.22756
$904$	−1.51157e15	−0.0832723
$905$	2.33952e15	0.128103
$906$	−1.10564e16	−0.601741
$907$	−1.86017e15	−0.100626	−0.0503132	−	0.998733i	$-0.516022\pi$
$907$	−1.86017e15	−0.100626	−0.0503132	+	0.998733i	$0.516022\pi$
$908$	−8.61868e15	−0.463413
$909$	2.53819e15	0.135651
$910$	4.21164e15	0.223729
$911$	1.78581e15	0.0942939	0.0471469	−	0.998888i	$-0.484987\pi$
$911$	1.78581e15	0.0942939	0.0471469	+	0.998888i	$0.484987\pi$
$912$	−1.72941e16	−0.907667
$913$	−1.02364e16	−0.534023
$914$	4.27462e16	2.21663
$915$	−2.72286e15	−0.140349
$916$	−7.43633e15	−0.381008
$917$	−3.17959e15	−0.161935
$918$	−5.58711e16	−2.82848
$919$	−1.41640e15	−0.0712770	−0.0356385	−	0.999365i	$-0.511346\pi$
$919$	−1.41640e15	−0.0712770	−0.0356385	+	0.999365i	$0.511346\pi$
$920$	−1.02113e13	−0.000510797 0
$921$	8.00247e14	0.0397920
$922$	5.49634e16	2.71677
$923$	4.18984e16	2.05868
$924$	1.86239e16	0.909649
$925$	−1.64538e16	−0.798891
$926$	−2.45304e16	−1.18398
$927$	5.84258e15	0.280328
$928$	−5.29681e15	−0.252639
$929$	−3.39995e16	−1.61208	−0.806039	−	0.591862i	$-0.798393\pi$
$929$	−3.39995e16	−1.61208	−0.806039	+	0.591862i	$0.798393\pi$
$930$	−1.37870e14	−0.00649851
$931$	8.66254e15	0.405903
$932$	3.59275e16	1.67355
$933$	−1.35954e16	−0.629568
$934$	−2.81312e15	−0.129503
$935$	1.24639e16	0.570414
$936$	5.88084e14	0.0267561
$937$	−7.34935e14	−0.0332415	−0.0166208	−	0.999862i	$-0.505291\pi$
$937$	−7.34935e14	−0.0332415	−0.0166208	+	0.999862i	$0.505291\pi$
$938$	−7.93049e15	−0.356603
$939$	−1.14953e16	−0.513875
$940$	4.29114e15	0.190708
$941$	−3.19965e16	−1.41371	−0.706854	−	0.707360i	$-0.749886\pi$
$941$	−3.19965e16	−1.41371	−0.706854	+	0.707360i	$0.749886\pi$
$942$	−1.07723e16	−0.473180
$943$	4.01014e14	0.0175124
$944$	1.30684e15	0.0567383
$945$	3.61318e15	0.155961
$946$	8.68347e16	3.72642
$947$	3.54537e16	1.51264	0.756321	−	0.654201i	$-0.226995\pi$
$947$	3.54537e16	1.51264	0.756321	+	0.654201i	$0.226995\pi$
$948$	2.77801e16	1.17839
$949$	−2.69168e16	−1.13517
$950$	2.86065e16	1.19946
$951$	1.63587e16	0.681957
$952$	5.06992e15	0.210135
$953$	1.61742e16	0.666519	0.333260	−	0.942835i	$-0.391851\pi$
$953$	1.61742e16	0.666519	0.333260	+	0.942835i	$0.391851\pi$
$954$	−4.17884e15	−0.171214
$955$	9.00281e15	0.366741
$956$	2.56031e16	1.03699
$957$	6.31555e15	0.254329
$958$	−3.07510e16	−1.23126
$959$	−1.01916e16	−0.405733
$960$	3.53698e15	0.140004
$961$	−2.53910e16	−0.999313
$962$	3.24343e16	1.26923
$963$	1.83111e15	0.0712474
$964$	−2.63669e16	−1.02008
$965$	3.09689e15	0.119131
$966$	−4.32511e14	−0.0165433
$967$	2.66442e16	1.01335	0.506673	−	0.862138i	$-0.330875\pi$
$967$	2.66442e16	1.01335	0.506673	+	0.862138i	$0.330875\pi$
$968$	−4.82266e15	−0.182378
$969$	−4.25635e16	−1.60050
$970$	−6.35018e15	−0.237433
$971$	−3.55781e16	−1.32275	−0.661374	−	0.750056i	$-0.730026\pi$
$971$	−3.55781e16	−1.32275	−0.661374	+	0.750056i	$0.730026\pi$
$972$	−7.87529e15	−0.291140
$973$	1.99494e16	0.733345
$974$	3.50239e16	1.28024
$975$	2.68186e16	0.974789
$976$	−2.36024e16	−0.853064
$977$	8.11999e15	0.291834	0.145917	−	0.989297i	$-0.453387\pi$
$977$	8.11999e15	0.291834	0.145917	+	0.989297i	$0.453387\pi$
$978$	4.26239e16	1.52331
$979$	−3.57671e16	−1.27110
$980$	−2.23100e15	−0.0788418
$981$	−4.83177e15	−0.169796
$982$	−3.77600e16	−1.31953
$983$	1.07762e15	0.0374472	0.0187236	−	0.999825i	$-0.494040\pi$
$983$	1.07762e15	0.0374472	0.0187236	+	0.999825i	$0.494040\pi$
$984$	3.83191e15	0.132417
$985$	6.20555e15	0.213246
$986$	−1.44392e16	−0.493425
$987$	−2.16415e16	−0.735432
$988$	−2.66108e16	−0.899279
$989$	−9.51645e14	−0.0319812
$990$	2.00305e15	0.0669418
$991$	1.71972e16	0.571547	0.285773	−	0.958297i	$-0.407750\pi$
$991$	1.71972e16	0.571547	0.285773	+	0.958297i	$0.407750\pi$
$992$	−1.07897e15	−0.0356612
$993$	−1.21466e15	−0.0399240
$994$	5.80493e16	1.89746
$995$	−6.65869e15	−0.216452
$996$	−9.00301e15	−0.291046
$997$	3.20573e16	1.03063	0.515316	−	0.857000i	$-0.327674\pi$
$997$	3.20573e16	1.03063	0.515316	+	0.857000i	$0.327674\pi$
$998$	−6.01849e16	−1.92429
$999$	2.78255e16	0.884776

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.12.a.a.1.10	✓	11
3.2	odd	2		261.12.a.a.1.2		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.12.a.a.1.10	✓	11	1.1	even	1	trivial
261.12.a.a.1.2		11	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)

\(f(q)\)	\(=\)	\(q+62.2743 q^{2} -384.675 q^{3} +1830.09 q^{4} +1377.47 q^{5} -23955.4 q^{6} +33050.3 q^{7} -13570.0 q^{8} -29172.4 q^{9} +O(q^{10})\)	\(q+62.2743 q^{2} -384.675 q^{3} +1830.09 q^{4} +1377.47 q^{5} -23955.4 q^{6} +33050.3 q^{7} -13570.0 q^{8} -29172.4 q^{9} +85780.8 q^{10} -800438. q^{11} -703990. q^{12} +1.48554e6 q^{13} +2.05818e6 q^{14} -529877. q^{15} -4.59309e6 q^{16} -1.13043e7 q^{17} -1.81669e6 q^{18} -9.78812e6 q^{19} +2.52089e6 q^{20} -1.27136e7 q^{21} -4.98468e7 q^{22} +546284. q^{23} +5.22005e6 q^{24} -4.69307e7 q^{25} +9.25112e7 q^{26} +7.93659e7 q^{27} +6.04851e7 q^{28} +2.05111e7 q^{29} -3.29977e7 q^{30} +4.17817e6 q^{31} -2.58240e8 q^{32} +3.07908e8 q^{33} -7.03969e8 q^{34} +4.55257e7 q^{35} -5.33882e7 q^{36} +3.50598e8 q^{37} -6.09549e8 q^{38} -5.71451e8 q^{39} -1.86923e7 q^{40} +7.34075e8 q^{41} -7.91731e8 q^{42} -1.74203e9 q^{43} -1.46488e9 q^{44} -4.01841e7 q^{45} +3.40195e7 q^{46} +1.70223e9 q^{47} +1.76685e9 q^{48} -8.85005e8 q^{49} -2.92258e9 q^{50} +4.34849e9 q^{51} +2.71868e9 q^{52} +2.30025e9 q^{53} +4.94246e9 q^{54} -1.10258e9 q^{55} -4.48494e8 q^{56} +3.76524e9 q^{57} +1.27732e9 q^{58} -2.84523e8 q^{59} -9.69723e8 q^{60} +5.13866e9 q^{61} +2.60193e8 q^{62} -9.64157e8 q^{63} -6.67509e9 q^{64} +2.04629e9 q^{65} +1.91748e10 q^{66} -3.85315e9 q^{67} -2.06880e10 q^{68} -2.10142e8 q^{69} +2.83508e9 q^{70} +2.82041e10 q^{71} +3.95871e8 q^{72} -1.81192e10 q^{73} +2.18333e10 q^{74} +1.80531e10 q^{75} -1.79132e10 q^{76} -2.64547e10 q^{77} -3.55867e10 q^{78} -3.94609e10 q^{79} -6.32684e9 q^{80} -2.53622e10 q^{81} +4.57140e10 q^{82} +1.27885e10 q^{83} -2.32671e10 q^{84} -1.55713e10 q^{85} -1.08484e11 q^{86} -7.89012e9 q^{87} +1.08620e10 q^{88} +4.46844e10 q^{89} -2.50244e9 q^{90} +4.90976e10 q^{91} +9.99751e8 q^{92} -1.60724e9 q^{93} +1.06005e11 q^{94} -1.34828e10 q^{95} +9.93386e10 q^{96} -7.40280e10 q^{97} -5.51131e10 q^{98} +2.33507e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 32 q^{2} - 982 q^{3} + 9146 q^{4} - 2740 q^{5} - 28202 q^{6} - 49432 q^{7} - 150054 q^{8} + 330749 q^{9}+O(q^{10}) \) 11 * q - 32 * q^2 - 982 * q^3 + 9146 * q^4 - 2740 * q^5 - 28202 * q^6 - 49432 * q^7 - 150054 * q^8 + 330749 * q^9	\( 11 q - 32 q^{2} - 982 q^{3} + 9146 q^{4} - 2740 q^{5} - 28202 q^{6} - 49432 q^{7} - 150054 q^{8} + 330749 q^{9} - 685834 q^{10} - 612246 q^{11} + 2578538 q^{12} + 1510364 q^{13} + 3955400 q^{14} - 2462818 q^{15} + 3024818 q^{16} - 3291098 q^{17} - 27885614 q^{18} - 44121388 q^{19} - 49472662 q^{20} - 46916800 q^{21} - 43435618 q^{22} - 88684076 q^{23} - 224700678 q^{24} - 44195521 q^{25} - 324999762 q^{26} - 236304286 q^{27} - 391274848 q^{28} + 225622639 q^{29} - 494910382 q^{30} - 292235934 q^{31} - 632542514 q^{32} - 1079766410 q^{33} - 1113307936 q^{34} - 1312820120 q^{35} - 2236726492 q^{36} - 1380429338 q^{37} - 1222857284 q^{38} - 1186931090 q^{39} - 2713154106 q^{40} - 1062067494 q^{41} + 205598960 q^{42} + 74588594 q^{43} + 52891466 q^{44} + 4527996830 q^{45} - 87670324 q^{46} - 1821239394 q^{47} + 2666035542 q^{48} + 4692522003 q^{49} + 9494259926 q^{50} + 8768158380 q^{51} + 3266669866 q^{52} + 7818635688 q^{53} + 17402728558 q^{54} - 191002682 q^{55} + 11263587512 q^{56} + 15495358340 q^{57} - 656356768 q^{58} + 1230002712 q^{59} + 31834046430 q^{60} - 18602654230 q^{61} + 22075953162 q^{62} - 9964531456 q^{63} + 11813658086 q^{64} + 32245789334 q^{65} + 42677188354 q^{66} + 27481284652 q^{67} + 29588811820 q^{68} - 20565315068 q^{69} + 42862666712 q^{70} - 20347168516 q^{71} + 47061083616 q^{72} - 57740010478 q^{73} - 2640709564 q^{74} - 23544691000 q^{75} - 33350650772 q^{76} + 871959792 q^{77} - 15384525342 q^{78} - 120245016462 q^{79} - 84319695274 q^{80} - 48880047865 q^{81} - 111495532412 q^{82} - 142463983824 q^{83} - 134146226376 q^{84} - 181628566552 q^{85} + 47870165542 q^{86} - 20141948318 q^{87} - 180608014462 q^{88} - 96700717270 q^{89} - 25522461244 q^{90} - 355162031176 q^{91} - 22429477796 q^{92} - 172582115142 q^{93} + 172608565078 q^{94} - 195922150708 q^{95} + 226391047758 q^{96} - 303190852014 q^{97} - 123776497136 q^{98} - 139125462440 q^{99}+O(q^{100}) \) 11 * q - 32 * q^2 - 982 * q^3 + 9146 * q^4 - 2740 * q^5 - 28202 * q^6 - 49432 * q^7 - 150054 * q^8 + 330749 * q^9 - 685834 * q^10 - 612246 * q^11 + 2578538 * q^12 + 1510364 * q^13 + 3955400 * q^14 - 2462818 * q^15 + 3024818 * q^16 - 3291098 * q^17 - 27885614 * q^18 - 44121388 * q^19 - 49472662 * q^20 - 46916800 * q^21 - 43435618 * q^22 - 88684076 * q^23 - 224700678 * q^24 - 44195521 * q^25 - 324999762 * q^26 - 236304286 * q^27 - 391274848 * q^28 + 225622639 * q^29 - 494910382 * q^30 - 292235934 * q^31 - 632542514 * q^32 - 1079766410 * q^33 - 1113307936 * q^34 - 1312820120 * q^35 - 2236726492 * q^36 - 1380429338 * q^37 - 1222857284 * q^38 - 1186931090 * q^39 - 2713154106 * q^40 - 1062067494 * q^41 + 205598960 * q^42 + 74588594 * q^43 + 52891466 * q^44 + 4527996830 * q^45 - 87670324 * q^46 - 1821239394 * q^47 + 2666035542 * q^48 + 4692522003 * q^49 + 9494259926 * q^50 + 8768158380 * q^51 + 3266669866 * q^52 + 7818635688 * q^53 + 17402728558 * q^54 - 191002682 * q^55 + 11263587512 * q^56 + 15495358340 * q^57 - 656356768 * q^58 + 1230002712 * q^59 + 31834046430 * q^60 - 18602654230 * q^61 + 22075953162 * q^62 - 9964531456 * q^63 + 11813658086 * q^64 + 32245789334 * q^65 + 42677188354 * q^66 + 27481284652 * q^67 + 29588811820 * q^68 - 20565315068 * q^69 + 42862666712 * q^70 - 20347168516 * q^71 + 47061083616 * q^72 - 57740010478 * q^73 - 2640709564 * q^74 - 23544691000 * q^75 - 33350650772 * q^76 + 871959792 * q^77 - 15384525342 * q^78 - 120245016462 * q^79 - 84319695274 * q^80 - 48880047865 * q^81 - 111495532412 * q^82 - 142463983824 * q^83 - 134146226376 * q^84 - 181628566552 * q^85 + 47870165542 * q^86 - 20141948318 * q^87 - 180608014462 * q^88 - 96700717270 * q^89 - 25522461244 * q^90 - 355162031176 * q^91 - 22429477796 * q^92 - 172582115142 * q^93 + 172608565078 * q^94 - 195922150708 * q^95 + 226391047758 * q^96 - 303190852014 * q^97 - 123776497136 * q^98 - 139125462440 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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