LMFDB - Embedded newform 29.12.a.a.1.7

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			1.7
Root			$30.4581$ 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)

$f(q)$	$=$	$q+27.4581 q^{2} -457.582 q^{3} -1294.05 q^{4} +9990.24 q^{5} -12564.3 q^{6} +28164.0 q^{7} -91766.4 q^{8} +32234.4 q^{9} +O(q^{10})$	\(q+27.4581 q^{2} -457.582 q^{3} -1294.05 q^{4} +9990.24 q^{5} -12564.3 q^{6} +28164.0 q^{7} -91766.4 q^{8} +32234.4 q^{9} +274313. q^{10} +820236. q^{11} +592135. q^{12} -2.01616e6 q^{13} +773331. q^{14} -4.57136e6 q^{15} +130485. q^{16} -4.16146e6 q^{17} +885095. q^{18} -1.10989e7 q^{19} -1.29279e7 q^{20} -1.28873e7 q^{21} +2.25221e7 q^{22} -5.64014e7 q^{23} +4.19907e7 q^{24} +5.09768e7 q^{25} -5.53600e7 q^{26} +6.63094e7 q^{27} -3.64457e7 q^{28} +2.05111e7 q^{29} -1.25521e8 q^{30} -2.38256e8 q^{31} +1.91521e8 q^{32} -3.75325e8 q^{33} -1.14266e8 q^{34} +2.81365e8 q^{35} -4.17130e7 q^{36} -2.44550e8 q^{37} -3.04756e8 q^{38} +9.22560e8 q^{39} -9.16769e8 q^{40} -4.55274e8 q^{41} -3.53862e8 q^{42} +1.01485e9 q^{43} -1.06143e9 q^{44} +3.22029e8 q^{45} -1.54867e9 q^{46} -1.80353e9 q^{47} -5.97074e7 q^{48} -1.18412e9 q^{49} +1.39973e9 q^{50} +1.90421e9 q^{51} +2.60902e9 q^{52} +4.71738e9 q^{53} +1.82073e9 q^{54} +8.19436e9 q^{55} -2.58451e9 q^{56} +5.07868e9 q^{57} +5.63197e8 q^{58} -4.22188e9 q^{59} +5.91557e9 q^{60} -2.28265e9 q^{61} -6.54205e9 q^{62} +9.07849e8 q^{63} +4.99156e9 q^{64} -2.01420e10 q^{65} -1.03057e10 q^{66} +1.31932e10 q^{67} +5.38514e9 q^{68} +2.58083e10 q^{69} +7.72576e9 q^{70} -2.42493e10 q^{71} -2.95803e9 q^{72} +2.85298e9 q^{73} -6.71487e9 q^{74} -2.33261e10 q^{75} +1.43626e10 q^{76} +2.31011e10 q^{77} +2.53318e10 q^{78} +3.05806e9 q^{79} +1.30357e9 q^{80} -3.60522e10 q^{81} -1.25010e10 q^{82} -6.23364e10 q^{83} +1.66769e10 q^{84} -4.15739e10 q^{85} +2.78658e10 q^{86} -9.38553e9 q^{87} -7.52702e10 q^{88} +8.45655e9 q^{89} +8.84232e9 q^{90} -5.67832e10 q^{91} +7.29863e10 q^{92} +1.09022e11 q^{93} -4.95215e10 q^{94} -1.10881e11 q^{95} -8.76364e10 q^{96} +6.21636e10 q^{97} -3.25136e10 q^{98} +2.64398e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	27.4581	0.606744	0.303372	−	0.952872i	$-0.401887\pi$
$2$	27.4581	0.606744	0.303372	+	0.952872i	$0.401887\pi$
$3$	−457.582	−1.08718	−0.543591	−	0.839350i	$-0.682936\pi$
$3$	−457.582	−1.08718	−0.543591	+	0.839350i	$0.682936\pi$
$4$	−1294.05	−0.631861
$5$	9990.24	1.42969	0.714844	−	0.699284i	$-0.246498\pi$
$5$	9990.24	1.42969	0.714844	+	0.699284i	$0.246498\pi$
$6$	−12564.3	−0.659641
$7$	28164.0	0.633367	0.316683	−	0.948531i	$-0.397431\pi$
$7$	28164.0	0.633367	0.316683	+	0.948531i	$0.397431\pi$
$8$	−91766.4	−0.990123
$9$	32234.4	0.181964
$10$	274313.	0.867455
$11$	820236.	1.53560	0.767802	−	0.640687i	$-0.221350\pi$
$11$	820236.	1.53560	0.767802	+	0.640687i	$0.221350\pi$
$12$	592135.	0.686948
$13$	−2.01616e6	−1.50604	−0.753021	−	0.657997i	$-0.771404\pi$
$13$	−2.01616e6	−1.50604	−0.753021	+	0.657997i	$0.771404\pi$
$14$	773331.	0.384292
$15$	−4.57136e6	−1.55433
$16$	130485.	0.0311100
$17$	−4.16146e6	−0.710847	−0.355424	−	0.934705i	$-0.615663\pi$
$17$	−4.16146e6	−0.710847	−0.355424	+	0.934705i	$0.615663\pi$
$18$	885095.	0.110406
$19$	−1.10989e7	−1.02834	−0.514170	−	0.857688i	$-0.671900\pi$
$19$	−1.10989e7	−1.02834	−0.514170	+	0.857688i	$0.671900\pi$
$20$	−1.29279e7	−0.903364
$21$	−1.28873e7	−0.688585
$22$	2.25221e7	0.931719
$23$	−5.64014e7	−1.82720	−0.913601	−	0.406612i	$-0.866710\pi$
$23$	−5.64014e7	−1.82720	−0.913601	+	0.406612i	$0.866710\pi$
$24$	4.19907e7	1.07644
$25$	5.09768e7	1.04401
$26$	−5.53600e7	−0.913782
$27$	6.63094e7	0.889354
$28$	−3.64457e7	−0.400200
$29$	2.05111e7	0.185695
$29$	2.05111e7	0.185695
$30$	−1.25521e8	−0.943081
$31$	−2.38256e8	−1.49470	−0.747350	−	0.664430i	$-0.768674\pi$
$31$	−2.38256e8	−1.49470	−0.747350	+	0.664430i	$0.768674\pi$
$32$	1.91521e8	1.00900
$33$	−3.75325e8	−1.66948
$34$	−1.14266e8	−0.431302
$35$	2.81365e8	0.905516
$36$	−4.17130e7	−0.114976
$37$	−2.44550e8	−0.579772	−0.289886	−	0.957061i	$-0.593617\pi$
$37$	−2.44550e8	−0.579772	−0.289886	+	0.957061i	$0.593617\pi$
$38$	−3.04756e8	−0.623940
$39$	9.22560e8	1.63734
$40$	−9.16769e8	−1.41557
$41$	−4.55274e8	−0.613707	−0.306854	−	0.951757i	$-0.599276\pi$
$41$	−4.55274e8	−0.613707	−0.306854	+	0.951757i	$0.599276\pi$
$42$	−3.53862e8	−0.417795
$43$	1.01485e9	1.05275	0.526374	−	0.850253i	$-0.323551\pi$
$43$	1.01485e9	1.05275	0.526374	+	0.850253i	$0.323551\pi$
$44$	−1.06143e9	−0.970289
$45$	3.22029e8	0.260152
$46$	−1.54867e9	−1.10864
$47$	−1.80353e9	−1.14706	−0.573529	−	0.819185i	$-0.694426\pi$
$47$	−1.80353e9	−1.14706	−0.573529	+	0.819185i	$0.694426\pi$
$48$	−5.97074e7	−0.0338222
$49$	−1.18412e9	−0.598847
$50$	1.39973e9	0.633444
$51$	1.90421e9	0.772820
$52$	2.60902e9	0.951610
$53$	4.71738e9	1.54947	0.774735	−	0.632286i	$-0.217883\pi$
$53$	4.71738e9	1.54947	0.774735	+	0.632286i	$0.217883\pi$
$54$	1.82073e9	0.539610
$55$	8.19436e9	2.19543
$56$	−2.58451e9	−0.627111
$57$	5.07868e9	1.11799
$58$	5.63197e8	0.112670
$59$	−4.22188e9	−0.768812	−0.384406	−	0.923164i	$-0.625594\pi$
$59$	−4.22188e9	−0.768812	−0.384406	+	0.923164i	$0.625594\pi$
$60$	5.91557e9	0.982121
$61$	−2.28265e9	−0.346039	−0.173020	−	0.984918i	$-0.555352\pi$
$61$	−2.28265e9	−0.346039	−0.173020	+	0.984918i	$0.555352\pi$
$62$	−6.54205e9	−0.906901
$63$	9.07849e8	0.115250
$64$	4.99156e9	0.581094
$65$	−2.01420e10	−2.15317
$66$	−1.03057e10	−1.01295
$67$	1.31932e10	1.19382	0.596909	−	0.802309i	$-0.296395\pi$
$67$	1.31932e10	1.19382	0.596909	+	0.802309i	$0.296395\pi$
$68$	5.38514e9	0.449157
$69$	2.58083e10	1.98650
$70$	7.72576e9	0.549417
$71$	−2.42493e10	−1.59506	−0.797532	−	0.603276i	$-0.793862\pi$
$71$	−2.42493e10	−1.59506	−0.797532	+	0.603276i	$0.793862\pi$
$72$	−2.95803e9	−0.180167
$73$	2.85298e9	0.161073	0.0805365	−	0.996752i	$-0.474337\pi$
$73$	2.85298e9	0.161073	0.0805365	+	0.996752i	$0.474337\pi$
$74$	−6.71487e9	−0.351774
$75$	−2.33261e10	−1.13502
$76$	1.43626e10	0.649769
$77$	2.31011e10	0.972600
$78$	2.53318e10	0.993448
$79$	3.05806e9	0.111814	0.0559070	−	0.998436i	$-0.482195\pi$
$79$	3.05806e9	0.111814	0.0559070	+	0.998436i	$0.482195\pi$
$80$	1.30357e9	0.0444775
$81$	−3.60522e10	−1.14885
$82$	−1.25010e10	−0.372363
$83$	−6.23364e10	−1.73705	−0.868525	−	0.495646i	$-0.834931\pi$
$83$	−6.23364e10	−1.73705	−0.868525	+	0.495646i	$0.834931\pi$
$84$	1.66769e10	0.435090
$85$	−4.15739e10	−1.01629
$86$	2.78658e10	0.638749
$87$	−9.38553e9	−0.201885
$88$	−7.52702e10	−1.52044
$89$	8.45655e9	0.160527	0.0802635	−	0.996774i	$-0.474424\pi$
$89$	8.45655e9	0.160527	0.0802635	+	0.996774i	$0.474424\pi$
$90$	8.84232e9	0.157846
$91$	−5.67832e10	−0.953877
$92$	7.29863e10	1.15454
$93$	1.09022e11	1.62501
$94$	−4.95215e10	−0.695971
$95$	−1.10881e11	−1.47021
$96$	−8.76364e10	−1.09696
$97$	6.21636e10	0.735008	0.367504	−	0.930022i	$-0.380212\pi$
$97$	6.21636e10	0.735008	0.367504	+	0.930022i	$0.380212\pi$
$98$	−3.25136e10	−0.363347
$99$	2.64398e10	0.279425
$100$	−6.59666e10	−0.659666
$101$	8.08638e9	0.0765573	0.0382786	−	0.999267i	$-0.487813\pi$
$101$	8.08638e9	0.0765573	0.0382786	+	0.999267i	$0.487813\pi$
$102$	5.22860e10	0.468904
$103$	1.33741e11	1.13674	0.568370	−	0.822773i	$-0.307574\pi$
$103$	1.33741e11	1.13674	0.568370	+	0.822773i	$0.307574\pi$
$104$	1.85016e11	1.49117
$105$	−1.28748e11	−0.984461
$106$	1.29530e11	0.940133
$107$	−6.78355e10	−0.467570	−0.233785	−	0.972288i	$-0.575111\pi$
$107$	−6.78355e10	−0.467570	−0.233785	+	0.972288i	$0.575111\pi$
$108$	−8.58078e10	−0.561948
$109$	1.42660e11	0.888090	0.444045	−	0.896004i	$-0.353543\pi$
$109$	1.42660e11	0.888090	0.444045	+	0.896004i	$0.353543\pi$
$110$	2.25002e11	1.33207
$111$	1.11902e11	0.630318
$112$	3.67497e9	0.0197040
$113$	−4.60648e10	−0.235200	−0.117600	−	0.993061i	$-0.537520\pi$
$113$	−4.60648e10	−0.235200	−0.117600	+	0.993061i	$0.537520\pi$
$114$	1.39451e11	0.678336
$115$	−5.63463e11	−2.61233
$116$	−2.65425e10	−0.117334
$117$	−6.49897e10	−0.274045
$118$	−1.15925e11	−0.466472
$119$	−1.17203e11	−0.450227
$120$	4.19497e11	1.53898
$121$	3.87476e11	1.35808
$122$	−6.26773e10	−0.209957
$123$	2.08325e11	0.667211
$124$	3.08315e11	0.944443
$125$	2.14660e10	0.0629137
$126$	2.49278e10	0.0699272
$127$	−2.44240e11	−0.655990	−0.327995	−	0.944679i	$-0.606373\pi$
$127$	−2.44240e11	−0.655990	−0.327995	+	0.944679i	$0.606373\pi$
$128$	−2.55175e11	−0.656423
$129$	−4.64376e11	−1.14453
$130$	−5.53060e11	−1.30642
$131$	6.47988e10	0.146749	0.0733744	−	0.997304i	$-0.476623\pi$
$131$	6.47988e10	0.146749	0.0733744	+	0.997304i	$0.476623\pi$
$132$	4.85691e11	1.05488
$133$	−3.12591e11	−0.651317
$134$	3.62260e11	0.724343
$135$	6.62447e11	1.27150
$136$	3.81882e11	0.703826
$137$	−2.29352e11	−0.406012	−0.203006	−	0.979177i	$-0.565071\pi$
$137$	−2.29352e11	−0.406012	−0.203006	+	0.979177i	$0.565071\pi$
$138$	7.08646e11	1.20530
$139$	−2.93273e11	−0.479393	−0.239696	−	0.970848i	$-0.577048\pi$
$139$	−2.93273e11	−0.479393	−0.239696	+	0.970848i	$0.577048\pi$
$140$	−3.64101e11	−0.572161
$141$	8.25263e11	1.24706
$142$	−6.65840e11	−0.967796
$143$	−1.65373e12	−2.31268
$144$	4.20609e9	0.00566089
$145$	2.04911e11	0.265486
$146$	7.83374e10	0.0977301
$147$	5.41830e11	0.651055
$148$	3.16460e11	0.366336
$149$	3.93354e11	0.438793	0.219396	−	0.975636i	$-0.429591\pi$
$149$	3.93354e11	0.438793	0.219396	+	0.975636i	$0.429591\pi$
$150$	−6.40490e11	−0.688669
$151$	−3.87179e11	−0.401364	−0.200682	−	0.979656i	$-0.564316\pi$
$151$	−3.87179e11	−0.401364	−0.200682	+	0.979656i	$0.564316\pi$
$152$	1.01851e12	1.01818
$153$	−1.34142e11	−0.129349
$154$	6.34314e11	0.590120
$155$	−2.38023e12	−2.13695
$156$	−1.19384e12	−1.03457
$157$	1.94053e12	1.62357	0.811786	−	0.583955i	$-0.198496\pi$
$157$	1.94053e12	1.62357	0.811786	+	0.583955i	$0.198496\pi$
$158$	8.39684e10	0.0678425
$159$	−2.15859e12	−1.68456
$160$	1.91334e12	1.44255
$161$	−1.58849e12	−1.15729
$162$	−9.89926e11	−0.697060
$163$	−2.38982e12	−1.62680	−0.813399	−	0.581707i	$-0.802385\pi$
$163$	−2.38982e12	−1.62680	−0.813399	+	0.581707i	$0.802385\pi$
$164$	5.89148e11	0.387778
$165$	−3.74959e12	−2.38683
$166$	−1.71164e12	−1.05395
$167$	1.58906e12	0.946675	0.473337	−	0.880881i	$-0.343049\pi$
$167$	1.58906e12	0.946675	0.473337	+	0.880881i	$0.343049\pi$
$168$	1.18263e12	0.681783
$169$	2.27275e12	1.26816
$170$	−1.14154e12	−0.616628
$171$	−3.57768e11	−0.187121
$172$	−1.31327e12	−0.665191
$173$	2.24583e12	1.10185	0.550926	−	0.834554i	$-0.314275\pi$
$173$	2.24583e12	1.10185	0.550926	+	0.834554i	$0.314275\pi$
$174$	−2.57709e11	−0.122492
$175$	1.43571e12	0.661238
$176$	1.07028e11	0.0477726
$177$	1.93186e12	0.835838
$178$	2.32201e11	0.0973988
$179$	4.01047e12	1.63118	0.815592	−	0.578627i	$-0.196411\pi$
$179$	4.01047e12	1.63118	0.815592	+	0.578627i	$0.196411\pi$
$180$	−4.16723e11	−0.164380
$181$	1.24801e12	0.477512	0.238756	−	0.971080i	$-0.423260\pi$
$181$	1.24801e12	0.477512	0.238756	+	0.971080i	$0.423260\pi$
$182$	−1.55916e12	−0.578759
$183$	1.04450e12	0.376208
$184$	5.17575e12	1.80915
$185$	−2.44311e12	−0.828893
$186$	2.99353e12	0.985966
$187$	−3.41338e12	−1.09158
$188$	2.33386e12	0.724781
$189$	1.86754e12	0.563287
$190$	−3.04459e12	−0.892039
$191$	2.13213e12	0.606917	0.303458	−	0.952845i	$-0.401859\pi$
$191$	2.13213e12	0.606917	0.303458	+	0.952845i	$0.401859\pi$
$192$	−2.28405e12	−0.631755
$193$	−4.63056e11	−0.124471	−0.0622355	−	0.998061i	$-0.519823\pi$
$193$	−4.63056e11	−0.124471	−0.0622355	+	0.998061i	$0.519823\pi$
$194$	1.70690e12	0.445962
$195$	9.21660e12	2.34089
$196$	1.53231e12	0.378388
$197$	4.04928e12	0.972330	0.486165	−	0.873867i	$-0.338395\pi$
$197$	4.04928e12	0.972330	0.486165	+	0.873867i	$0.338395\pi$
$198$	7.25987e11	0.169539
$199$	2.92500e11	0.0664407	0.0332204	−	0.999448i	$-0.489424\pi$
$199$	2.92500e11	0.0664407	0.0332204	+	0.999448i	$0.489424\pi$
$200$	−4.67796e12	−1.03369
$201$	−6.03697e12	−1.29790
$202$	2.22037e11	0.0464507
$203$	5.77676e11	0.117613
$204$	−2.46414e12	−0.488315
$205$	−4.54829e12	−0.877410
$206$	3.67229e12	0.689710
$207$	−1.81806e12	−0.332485
$208$	−2.63078e11	−0.0468529
$209$	−9.10376e12	−1.57912
$210$	−3.53517e12	−0.597316
$211$	−8.54356e11	−0.140632	−0.0703162	−	0.997525i	$-0.522401\pi$
$211$	−8.54356e11	−0.140632	−0.0703162	+	0.997525i	$0.522401\pi$
$212$	−6.10453e12	−0.979051
$213$	1.10960e13	1.73412
$214$	−1.86264e12	−0.283695
$215$	1.01386e13	1.50510
$216$	−6.08498e12	−0.880569
$217$	−6.71024e12	−0.946693
$218$	3.91718e12	0.538844
$219$	−1.30547e12	−0.175116
$220$	−1.06039e13	−1.38721
$221$	8.39017e12	1.07057
$222$	3.07261e12	0.382442
$223$	4.19005e12	0.508794	0.254397	−	0.967100i	$-0.418123\pi$
$223$	4.19005e12	0.508794	0.254397	+	0.967100i	$0.418123\pi$
$224$	5.39399e12	0.639066
$225$	1.64321e12	0.189971
$226$	−1.26485e12	−0.142706
$227$	−1.79772e12	−0.197961	−0.0989806	−	0.995089i	$-0.531558\pi$
$227$	−1.79772e12	−0.197961	−0.0989806	+	0.995089i	$0.531558\pi$
$228$	−6.57207e12	−0.706416
$229$	5.90495e12	0.619614	0.309807	−	0.950800i	$-0.399736\pi$
$229$	5.90495e12	0.619614	0.309807	+	0.950800i	$0.399736\pi$
$230$	−1.54716e13	−1.58501
$231$	−1.05707e13	−1.05739
$232$	−1.88224e12	−0.183861
$233$	1.96123e13	1.87099	0.935496	−	0.353337i	$-0.114953\pi$
$233$	1.96123e13	1.87099	0.935496	+	0.353337i	$0.114953\pi$
$234$	−1.78450e12	−0.166276
$235$	−1.80177e13	−1.63993
$236$	5.46334e12	0.485783
$237$	−1.39931e12	−0.121562
$238$	−3.21818e12	−0.273173
$239$	−1.70534e13	−1.41456	−0.707280	−	0.706933i	$-0.750078\pi$
$239$	−1.70534e13	−1.41456	−0.707280	+	0.706933i	$0.750078\pi$
$240$	−5.96492e11	−0.0483551
$241$	−1.68533e13	−1.33534	−0.667668	−	0.744459i	$-0.732707\pi$
$241$	−1.68533e13	−1.33534	−0.667668	+	0.744459i	$0.732707\pi$
$242$	1.06394e13	0.824007
$243$	4.75034e12	0.359658
$244$	2.95387e12	0.218649
$245$	−1.18296e13	−0.856163
$246$	5.72021e12	0.404827
$247$	2.23773e13	1.54872
$248$	2.18639e13	1.47994
$249$	2.85240e13	1.88849
$250$	5.89415e11	0.0381726
$251$	−1.41324e13	−0.895383	−0.447692	−	0.894188i	$-0.647754\pi$
$251$	−1.41324e13	−0.895383	−0.447692	+	0.894188i	$0.647754\pi$
$252$	−1.17480e12	−0.0728220
$253$	−4.62624e13	−2.80586
$254$	−6.70638e12	−0.398018
$255$	1.90235e13	1.10489
$256$	−1.72293e13	−0.979375
$257$	2.09702e13	1.16673	0.583364	−	0.812211i	$-0.301736\pi$
$257$	2.09702e13	1.16673	0.583364	+	0.812211i	$0.301736\pi$
$258$	−1.27509e13	−0.694436
$259$	−6.88750e12	−0.367209
$260$	2.60647e13	1.36050
$261$	6.61164e11	0.0337899
$262$	1.77925e12	0.0890390
$263$	−3.33053e13	−1.63214	−0.816070	−	0.577953i	$-0.803852\pi$
$263$	−3.33053e13	−1.63214	−0.816070	+	0.577953i	$0.803852\pi$
$264$	3.44423e13	1.65299
$265$	4.71277e13	2.21526
$266$	−8.58315e12	−0.395183
$267$	−3.86956e12	−0.174522
$268$	−1.70727e13	−0.754328
$269$	−1.52686e13	−0.660938	−0.330469	−	0.943817i	$-0.607207\pi$
$269$	−1.52686e13	−0.660938	−0.330469	+	0.943817i	$0.607207\pi$
$270$	1.81896e13	0.771474
$271$	−1.62843e13	−0.676766	−0.338383	−	0.941009i	$-0.609880\pi$
$271$	−1.62843e13	−0.676766	−0.338383	+	0.941009i	$0.609880\pi$
$272$	−5.43006e11	−0.0221144
$273$	2.59830e13	1.03704
$274$	−6.29757e12	−0.246346
$275$	4.18130e13	1.60318
$276$	−3.33972e13	−1.25519
$277$	7.21098e12	0.265678	0.132839	−	0.991138i	$-0.457591\pi$
$277$	7.21098e12	0.265678	0.132839	+	0.991138i	$0.457591\pi$
$278$	−8.05274e12	−0.290869
$279$	−7.68003e12	−0.271982
$280$	−2.58199e13	−0.896572
$281$	−2.36856e12	−0.0806490	−0.0403245	−	0.999187i	$-0.512839\pi$
$281$	−2.36856e12	−0.0806490	−0.0403245	+	0.999187i	$0.512839\pi$
$282$	2.26602e13	0.756647
$283$	1.01047e13	0.330902	0.165451	−	0.986218i	$-0.447092\pi$
$283$	1.01047e13	0.330902	0.165451	+	0.986218i	$0.447092\pi$
$284$	3.13798e13	1.00786
$285$	5.07372e13	1.59838
$286$	−4.54083e13	−1.40321
$287$	−1.28223e13	−0.388702
$288$	6.17355e12	0.183601
$289$	−1.69542e13	−0.494696
$290$	5.62648e12	0.161082
$291$	−2.84450e13	−0.799087
$292$	−3.69190e12	−0.101776
$293$	−4.22814e12	−0.114387	−0.0571936	−	0.998363i	$-0.518215\pi$
$293$	−4.22814e12	−0.114387	−0.0571936	+	0.998363i	$0.518215\pi$
$294$	1.48776e13	0.395024
$295$	−4.21776e13	−1.09916
$296$	2.24415e13	0.574046
$297$	5.43894e13	1.36570
$298$	1.08008e13	0.266235
$299$	1.13714e14	2.75184
$300$	3.01852e13	0.717177
$301$	2.85822e13	0.666775
$302$	−1.06312e13	−0.243525
$303$	−3.70018e12	−0.0832317
$304$	−1.44824e12	−0.0319916
$305$	−2.28042e13	−0.494728
$306$	−3.68328e12	−0.0784815
$307$	4.10121e13	0.858323	0.429162	−	0.903228i	$-0.358809\pi$
$307$	4.10121e13	0.858323	0.429162	+	0.903228i	$0.358809\pi$
$308$	−2.98941e13	−0.614549
$309$	−6.11976e13	−1.23584
$310$	−6.53567e13	−1.29658
$311$	−9.97319e13	−1.94380	−0.971900	−	0.235393i	$-0.924362\pi$
$311$	−9.97319e13	−1.94380	−0.971900	+	0.235393i	$0.924362\pi$
$312$	−8.46600e13	−1.62117
$313$	−5.66854e13	−1.06654	−0.533270	−	0.845945i	$-0.679037\pi$
$313$	−5.66854e13	−1.06654	−0.533270	+	0.845945i	$0.679037\pi$
$314$	5.32832e13	0.985093
$315$	9.06963e12	0.164771
$316$	−3.95728e12	−0.0706510
$317$	2.09336e13	0.367297	0.183649	−	0.982992i	$-0.441209\pi$
$317$	2.09336e13	0.367297	0.183649	+	0.982992i	$0.441209\pi$
$318$	−5.92708e13	−1.02210
$319$	1.68240e13	0.285155
$320$	4.98669e13	0.830783
$321$	3.10403e13	0.508333
$322$	−4.36169e13	−0.702178
$323$	4.61878e13	0.730993
$324$	4.66535e13	0.725916
$325$	−1.02778e14	−1.57232
$326$	−6.56200e13	−0.987050
$327$	−6.52788e13	−0.965515
$328$	4.17788e13	0.607646
$329$	−5.07946e13	−0.726508
$330$	−1.02957e14	−1.44820
$331$	7.24918e13	1.00285	0.501424	−	0.865202i	$-0.332810\pi$
$331$	7.24918e13	1.00285	0.501424	+	0.865202i	$0.332810\pi$
$332$	8.06665e13	1.09757
$333$	−7.88290e12	−0.105498
$334$	4.36327e13	0.574390
$335$	1.31803e14	1.70679
$336$	−1.68160e12	−0.0214218
$337$	−1.03678e14	−1.29934	−0.649670	−	0.760217i	$-0.725093\pi$
$337$	−1.03678e14	−1.29934	−0.649670	+	0.760217i	$0.725093\pi$
$338$	6.24054e13	0.769450
$339$	2.10784e13	0.255705
$340$	5.37988e13	0.642154
$341$	−1.95426e14	−2.29527
$342$	−9.82362e12	−0.113535
$343$	−8.90389e13	−1.01266
$344$	−9.31290e13	−1.04235
$345$	2.57831e14	2.84007
$346$	6.16663e13	0.668543
$347$	1.05495e14	1.12569	0.562844	−	0.826563i	$-0.309707\pi$
$347$	1.05495e14	1.12569	0.562844	+	0.826563i	$0.309707\pi$
$348$	1.21454e13	0.127563
$349$	−6.55800e13	−0.678003	−0.339001	−	0.940786i	$-0.610089\pi$
$349$	−6.55800e13	−0.678003	−0.339001	+	0.940786i	$0.610089\pi$
$350$	3.94219e13	0.401203
$351$	−1.33691e14	−1.33940
$352$	1.57092e14	1.54942
$353$	−2.34111e13	−0.227332	−0.113666	−	0.993519i	$-0.536259\pi$
$353$	−2.34111e13	−0.227332	−0.113666	+	0.993519i	$0.536259\pi$
$354$	5.30452e13	0.507140
$355$	−2.42256e14	−2.28044
$356$	−1.09432e13	−0.101431
$357$	5.36301e13	0.489478
$358$	1.10120e14	0.989712
$359$	−7.84584e13	−0.694416	−0.347208	−	0.937788i	$-0.612870\pi$
$359$	−7.84584e13	−0.694416	−0.347208	+	0.937788i	$0.612870\pi$
$360$	−2.95515e13	−0.257582
$361$	6.69634e12	0.0574841
$362$	3.42679e13	0.289728
$363$	−1.77302e14	−1.47648
$364$	7.34804e13	0.602718
$365$	2.85019e13	0.230284
$366$	2.86800e13	0.228262
$367$	−1.84739e13	−0.144842	−0.0724212	−	0.997374i	$-0.523073\pi$
$367$	−1.84739e13	−0.144842	−0.0724212	+	0.997374i	$0.523073\pi$
$368$	−7.35951e12	−0.0568441
$369$	−1.46755e13	−0.111673
$370$	−6.70832e13	−0.502926
$371$	1.32860e14	0.981383
$372$	−1.41080e14	−1.02678
$373$	−1.14087e14	−0.818158	−0.409079	−	0.912499i	$-0.634150\pi$
$373$	−1.14087e14	−0.818158	−0.409079	+	0.912499i	$0.634150\pi$
$374$	−9.37249e13	−0.662310
$375$	−9.82245e12	−0.0683987
$376$	1.65504e14	1.13573
$377$	−4.13538e13	−0.279665
$378$	5.12791e13	0.341771
$379$	−1.39087e14	−0.913630	−0.456815	−	0.889562i	$-0.651010\pi$
$379$	−1.39087e14	−0.913630	−0.456815	+	0.889562i	$0.651010\pi$
$380$	1.43486e14	0.928966
$381$	1.11760e14	0.713180
$382$	5.85441e13	0.368243
$383$	1.07589e14	0.667078	0.333539	−	0.942736i	$-0.391757\pi$
$383$	1.07589e14	0.667078	0.333539	+	0.942736i	$0.391757\pi$
$384$	1.16764e14	0.713651
$385$	2.30786e14	1.39051
$386$	−1.27146e13	−0.0755221
$387$	3.27130e13	0.191562
$388$	−8.04430e13	−0.464423
$389$	1.72334e14	0.980953	0.490476	−	0.871454i	$-0.336823\pi$
$389$	1.72334e14	0.980953	0.490476	+	0.871454i	$0.336823\pi$
$390$	2.53070e14	1.42032
$391$	2.34712e14	1.29886
$392$	1.08662e14	0.592932
$393$	−2.96508e13	−0.159543
$394$	1.11186e14	0.589956
$395$	3.05507e13	0.159859
$396$	−3.42145e13	−0.176558
$397$	−8.40997e13	−0.428003	−0.214002	−	0.976833i	$-0.568650\pi$
$397$	−8.40997e13	−0.428003	−0.214002	+	0.976833i	$0.568650\pi$
$398$	8.03151e12	0.0403125
$399$	1.43036e14	0.708099
$400$	6.65169e12	0.0324790
$401$	1.63151e13	0.0785768	0.0392884	−	0.999228i	$-0.487491\pi$
$401$	1.63151e13	0.0785768	0.0392884	+	0.999228i	$0.487491\pi$
$402$	−1.65764e14	−0.787492
$403$	4.80362e14	2.25108
$404$	−1.04642e13	−0.0483736
$405$	−3.60170e14	−1.64250
$406$	1.58619e13	0.0713612
$407$	−2.00588e14	−0.890301
$408$	−1.74742e14	−0.765187
$409$	−9.98435e13	−0.431362	−0.215681	−	0.976464i	$-0.569197\pi$
$409$	−9.98435e13	−0.431362	−0.215681	+	0.976464i	$0.569197\pi$
$410$	−1.24888e14	−0.532363
$411$	1.04947e14	0.441409
$412$	−1.73068e14	−0.718262
$413$	−1.18905e14	−0.486940
$414$	−4.99206e13	−0.201733
$415$	−6.22756e14	−2.48344
$416$	−3.86137e14	−1.51959
$417$	1.34197e14	0.521187
$418$	−2.49972e14	−0.958124
$419$	−2.11256e14	−0.799157	−0.399578	−	0.916699i	$-0.630843\pi$
$419$	−2.11256e14	−0.799157	−0.399578	+	0.916699i	$0.630843\pi$
$420$	1.66606e14	0.622043
$421$	1.98202e14	0.730394	0.365197	−	0.930930i	$-0.381002\pi$
$421$	1.98202e14	0.730394	0.365197	+	0.930930i	$0.381002\pi$
$422$	−2.34590e13	−0.0853279
$423$	−5.81357e13	−0.208723
$424$	−4.32897e14	−1.53417
$425$	−2.12138e14	−0.742128
$426$	3.04676e14	1.05217
$427$	−6.42886e13	−0.219170
$428$	8.77827e13	0.295439
$429$	7.56717e14	2.51431
$430$	2.78386e14	0.913211
$431$	−1.18759e14	−0.384627	−0.192314	−	0.981333i	$-0.561599\pi$
$431$	−1.18759e14	−0.384627	−0.192314	+	0.981333i	$0.561599\pi$
$432$	8.65236e12	0.0276678
$433$	−3.54607e14	−1.11960	−0.559801	−	0.828627i	$-0.689122\pi$
$433$	−3.54607e14	−1.11960	−0.559801	+	0.828627i	$0.689122\pi$
$434$	−1.84250e14	−0.574401
$435$	−9.37638e13	−0.288632
$436$	−1.84610e14	−0.561150
$437$	6.25996e14	1.87899
$438$	−3.58458e13	−0.106250
$439$	1.85936e14	0.544262	0.272131	−	0.962260i	$-0.412272\pi$
$439$	1.85936e14	0.544262	0.272131	+	0.962260i	$0.412272\pi$
$440$	−7.51967e14	−2.17375
$441$	−3.81692e13	−0.108969
$442$	2.30378e14	0.649560
$443$	−5.43269e14	−1.51284	−0.756422	−	0.654084i	$-0.773054\pi$
$443$	−5.43269e14	−1.51284	−0.756422	+	0.654084i	$0.773054\pi$
$444$	−1.44806e14	−0.398273
$445$	8.44829e13	0.229503
$446$	1.15051e14	0.308708
$447$	−1.79992e14	−0.477048
$448$	1.40582e14	0.368046
$449$	1.39738e14	0.361375	0.180688	−	0.983541i	$-0.442168\pi$
$449$	1.39738e14	0.361375	0.180688	+	0.983541i	$0.442168\pi$
$450$	4.51193e13	0.115264
$451$	−3.73432e14	−0.942412
$452$	5.96102e13	0.148614
$453$	1.77166e14	0.436355
$454$	−4.93620e13	−0.120112
$455$	−5.67278e14	−1.36375
$456$	−4.66052e14	−1.10695
$457$	2.73468e14	0.641752	0.320876	−	0.947121i	$-0.396023\pi$
$457$	2.73468e14	0.641752	0.320876	+	0.947121i	$0.396023\pi$
$458$	1.62139e14	0.375947
$459$	−2.75944e14	−0.632195
$460$	7.29151e14	1.65063
$461$	2.67401e14	0.598148	0.299074	−	0.954230i	$-0.403322\pi$
$461$	2.67401e14	0.598148	0.299074	+	0.954230i	$0.403322\pi$
$462$	−2.90251e14	−0.641567
$463$	5.18177e14	1.13183	0.565917	−	0.824462i	$-0.308522\pi$
$463$	5.18177e14	1.13183	0.565917	+	0.824462i	$0.308522\pi$
$464$	2.67639e12	0.00577697
$465$	1.08915e15	2.32326
$466$	5.38518e14	1.13521
$467$	2.97457e14	0.619700	0.309850	−	0.950785i	$-0.399721\pi$
$467$	2.97457e14	0.619700	0.309850	+	0.950785i	$0.399721\pi$
$468$	8.41001e13	0.173159
$469$	3.71573e14	0.756125
$470$	−4.94732e14	−0.995020
$471$	−8.87950e14	−1.76512
$472$	3.87427e14	0.761218
$473$	8.32415e14	1.61660
$474$	−3.84225e13	−0.0737572
$475$	−5.65789e14	−1.07359
$476$	1.51667e14	0.284481
$477$	1.52062e14	0.281948
$478$	−4.68253e14	−0.858277
$479$	2.72110e13	0.0493060	0.0246530	−	0.999696i	$-0.492152\pi$
$479$	2.72110e13	0.0493060	0.0246530	+	0.999696i	$0.492152\pi$
$480$	−8.75509e14	−1.56832
$481$	4.93052e14	0.873162
$482$	−4.62759e14	−0.810207
$483$	7.26864e14	1.25818
$484$	−5.01414e14	−0.858118
$485$	6.21030e14	1.05083
$486$	1.30435e14	0.218221
$487$	−4.35591e14	−0.720560	−0.360280	−	0.932844i	$-0.617319\pi$
$487$	−4.35591e14	−0.720560	−0.360280	+	0.932844i	$0.617319\pi$
$488$	2.09471e14	0.342621
$489$	1.09354e15	1.76862
$490$	−3.24819e14	−0.519472
$491$	2.56952e14	0.406354	0.203177	−	0.979142i	$-0.434873\pi$
$491$	2.56952e14	0.406354	0.203177	+	0.979142i	$0.434873\pi$
$492$	−2.69583e14	−0.421585
$493$	−8.53562e13	−0.132001
$494$	6.14438e14	0.939679
$495$	2.64140e14	0.399490
$496$	−3.10887e13	−0.0465000
$497$	−6.82957e14	−1.01026
$498$	7.83216e14	1.14583
$499$	1.66560e14	0.241000	0.120500	−	0.992713i	$-0.461550\pi$
$499$	1.66560e14	0.241000	0.120500	+	0.992713i	$0.461550\pi$
$500$	−2.77781e13	−0.0397528
$501$	−7.27127e14	−1.02921
$502$	−3.88048e14	−0.543269
$503$	−4.75170e14	−0.657998	−0.328999	−	0.944330i	$-0.606711\pi$
$503$	−4.75170e14	−0.657998	−0.328999	+	0.944330i	$0.606711\pi$
$504$	−8.33101e13	−0.114112
$505$	8.07849e13	0.109453
$506$	−1.27028e15	−1.70244
$507$	−1.03997e15	−1.37872
$508$	3.16060e14	0.414495
$509$	2.49704e14	0.323950	0.161975	−	0.986795i	$-0.448214\pi$
$509$	2.49704e14	0.323950	0.161975	+	0.986795i	$0.448214\pi$
$510$	5.22349e14	0.670386
$511$	8.03513e13	0.102018
$512$	4.95135e13	0.0621926
$513$	−7.35965e14	−0.914558
$514$	5.75802e14	0.707906
$515$	1.33611e15	1.62518
$516$	6.00927e14	0.723183
$517$	−1.47932e15	−1.76143
$518$	−1.89118e14	−0.222802
$519$	−1.02765e15	−1.19791
$520$	1.84836e15	2.13190
$521$	5.63704e14	0.643344	0.321672	−	0.946851i	$-0.395755\pi$
$521$	5.63704e14	0.643344	0.321672	+	0.946851i	$0.395755\pi$
$522$	1.81543e13	0.0205018
$523$	3.19146e14	0.356640	0.178320	−	0.983973i	$-0.442934\pi$
$523$	3.19146e14	0.356640	0.178320	+	0.983973i	$0.442934\pi$
$524$	−8.38530e13	−0.0927249
$525$	−6.56956e14	−0.718886
$526$	−9.14502e14	−0.990292
$527$	9.91491e14	1.06250
$528$	−4.89742e13	−0.0519375
$529$	2.22830e15	2.33867
$530$	1.29404e15	1.34410
$531$	−1.36090e14	−0.139896
$532$	4.04509e14	0.411542
$533$	9.17906e14	0.924269
$534$	−1.06251e14	−0.105890
$535$	−6.77693e14	−0.668478
$536$	−1.21069e15	−1.18203
$537$	−1.83512e15	−1.77339
$538$	−4.19246e14	−0.401021
$539$	−9.71255e14	−0.919591
$540$	−8.57241e14	−0.803410
$541$	6.42697e14	0.596240	0.298120	−	0.954528i	$-0.403640\pi$
$541$	6.42697e14	0.596240	0.298120	+	0.954528i	$0.403640\pi$
$542$	−4.47137e14	−0.410624
$543$	−5.71065e14	−0.519142
$544$	−7.97004e14	−0.717244
$545$	1.42521e15	1.26969
$546$	7.13444e14	0.629217
$547$	8.80101e14	0.768426	0.384213	−	0.923244i	$-0.374473\pi$
$547$	8.80101e14	0.768426	0.384213	+	0.923244i	$0.374473\pi$
$548$	2.96793e14	0.256543
$549$	−7.35798e13	−0.0629667
$550$	1.14811e15	0.972720
$551$	−2.27652e14	−0.190958
$552$	−2.36833e15	−1.96688
$553$	8.61271e13	0.0708193
$554$	1.98000e14	0.161199
$555$	1.11792e15	0.901157
$556$	3.79511e14	0.302910
$557$	−1.66295e15	−1.31424	−0.657122	−	0.753784i	$-0.728227\pi$
$557$	−1.66295e15	−1.31424	−0.657122	+	0.753784i	$0.728227\pi$
$558$	−2.10879e14	−0.165023
$559$	−2.04610e15	−1.58548
$560$	3.67138e13	0.0281706
$561$	1.56190e15	1.18675
$562$	−6.50361e13	−0.0489334
$563$	−2.59049e15	−1.93012	−0.965062	−	0.262023i	$-0.915610\pi$
$563$	−2.59049e15	−1.93012	−0.965062	+	0.262023i	$0.915610\pi$
$564$	−1.06793e15	−0.787969
$565$	−4.60198e14	−0.336263
$566$	2.77457e14	0.200773
$567$	−1.01538e15	−0.727645
$568$	2.22527e15	1.57931
$569$	−1.52748e15	−1.07364	−0.536820	−	0.843697i	$-0.680375\pi$
$569$	−1.52748e15	−1.07364	−0.536820	+	0.843697i	$0.680375\pi$
$570$	1.39315e15	0.969808
$571$	1.46536e15	1.01029	0.505145	−	0.863035i	$-0.331439\pi$
$571$	1.46536e15	1.01029	0.505145	+	0.863035i	$0.331439\pi$
$572$	2.14001e15	1.46130
$573$	−9.75622e14	−0.659829
$574$	−3.52077e14	−0.235843
$575$	−2.87516e15	−1.90761
$576$	1.60900e14	0.105738
$577$	−4.85756e14	−0.316192	−0.158096	−	0.987424i	$-0.550536\pi$
$577$	−4.85756e14	−0.316192	−0.158096	+	0.987424i	$0.550536\pi$
$578$	−4.65530e14	−0.300154
$579$	2.11886e14	0.135323
$580$	−2.65166e14	−0.167750
$581$	−1.75564e15	−1.10019
$582$	−7.81045e14	−0.484841
$583$	3.86936e15	2.37937
$584$	−2.61808e14	−0.159482
$585$	−6.49263e14	−0.391799
$586$	−1.16097e14	−0.0694038
$587$	−2.96859e15	−1.75809	−0.879045	−	0.476739i	$-0.841819\pi$
$587$	−2.96859e15	−1.75809	−0.879045	+	0.476739i	$0.841819\pi$
$588$	−7.01156e14	−0.411377
$589$	2.64439e15	1.53706
$590$	−1.15812e15	−0.666910
$591$	−1.85288e15	−1.05710
$592$	−3.19100e13	−0.0180367
$593$	1.54519e15	0.865331	0.432665	−	0.901555i	$-0.357573\pi$
$593$	1.54519e15	0.865331	0.432665	+	0.901555i	$0.357573\pi$
$594$	1.49343e15	0.828628
$595$	−1.17089e15	−0.643684
$596$	−5.09021e14	−0.277256
$597$	−1.33843e14	−0.0722332
$598$	3.12238e15	1.66966
$599$	−2.08623e13	−0.0110539	−0.00552694	−	0.999985i	$-0.501759\pi$
$599$	−2.08623e13	−0.0110539	−0.00552694	+	0.999985i	$0.501759\pi$
$600$	2.14055e15	1.12381
$601$	−1.73470e15	−0.902434	−0.451217	−	0.892414i	$-0.649010\pi$
$601$	−1.73470e15	−0.902434	−0.451217	+	0.892414i	$0.649010\pi$
$602$	7.84813e14	0.404562
$603$	4.25274e14	0.217232
$604$	5.01029e14	0.253606
$605$	3.87098e15	1.94163
$606$	−1.01600e14	−0.0505003
$607$	2.55839e14	0.126017	0.0630085	−	0.998013i	$-0.479930\pi$
$607$	2.55839e14	0.126017	0.0630085	+	0.998013i	$0.479930\pi$
$608$	−2.12568e15	−1.03759
$609$	−2.64334e14	−0.127867
$610$	−6.26161e14	−0.300173
$611$	3.63621e15	1.72752
$612$	1.73587e14	0.0817304
$613$	3.22844e15	1.50647	0.753235	−	0.657751i	$-0.228492\pi$
$613$	3.22844e15	1.50647	0.753235	+	0.657751i	$0.228492\pi$
$614$	1.12611e15	0.520783
$615$	2.08122e15	0.953904
$616$	−2.11991e15	−0.962994
$617$	3.85111e15	1.73387	0.866937	−	0.498417i	$-0.166085\pi$
$617$	3.85111e15	1.73387	0.866937	+	0.498417i	$0.166085\pi$
$618$	−1.68037e15	−0.749840
$619$	−3.57668e15	−1.58191	−0.790954	−	0.611876i	$-0.790415\pi$
$619$	−3.57668e15	−1.58191	−0.790954	+	0.611876i	$0.790415\pi$
$620$	3.08014e15	1.35026
$621$	−3.73994e15	−1.62503
$622$	−2.73845e15	−1.17939
$623$	2.38170e14	0.101672
$624$	1.20380e14	0.0509376
$625$	−2.27465e15	−0.954058
$626$	−1.55647e15	−0.647117
$627$	4.16572e15	1.71679
$628$	−2.51114e15	−1.02587
$629$	1.01768e15	0.412130
$630$	2.49035e14	0.0999741
$631$	2.99953e15	1.19369	0.596845	−	0.802357i	$-0.296421\pi$
$631$	2.99953e15	1.19369	0.596845	+	0.802357i	$0.296421\pi$
$632$	−2.80627e14	−0.110710
$633$	3.90938e14	0.152893
$634$	5.74797e14	0.222856
$635$	−2.44002e15	−0.937860
$636$	2.79332e15	1.06441
$637$	2.38737e15	0.901888
$638$	4.61955e14	0.173016
$639$	−7.81661e14	−0.290244
$640$	−2.54926e15	−0.938479
$641$	−1.92000e15	−0.700779	−0.350390	−	0.936604i	$-0.613951\pi$
$641$	−1.92000e15	−0.700779	−0.350390	+	0.936604i	$0.613951\pi$
$642$	8.52308e14	0.308428
$643$	−6.57468e14	−0.235893	−0.117946	−	0.993020i	$-0.537631\pi$
$643$	−6.57468e14	−0.235893	−0.117946	+	0.993020i	$0.537631\pi$
$644$	2.05559e15	0.731246
$645$	−4.63923e15	−1.63632
$646$	1.26823e15	0.443526
$647$	3.89397e15	1.35026	0.675132	−	0.737697i	$-0.264087\pi$
$647$	3.89397e15	1.35026	0.675132	+	0.737697i	$0.264087\pi$
$648$	3.30838e15	1.13751
$649$	−3.46294e15	−1.18059
$650$	−2.82208e15	−0.953994
$651$	3.07048e15	1.02923
$652$	3.09255e15	1.02791
$653$	1.13595e15	0.374400	0.187200	−	0.982322i	$-0.440059\pi$
$653$	1.13595e15	0.374400	0.187200	+	0.982322i	$0.440059\pi$
$654$	−1.79243e15	−0.585821
$655$	6.47356e14	0.209805
$656$	−5.94062e13	−0.0190924
$657$	9.19640e13	0.0293095
$658$	−1.39473e15	−0.440805
$659$	1.83420e15	0.574881	0.287440	−	0.957799i	$-0.407196\pi$
$659$	1.83420e15	0.574881	0.287440	+	0.957799i	$0.407196\pi$
$660$	4.85217e15	1.50815
$661$	−6.16892e15	−1.90152	−0.950761	−	0.309925i	$-0.899696\pi$
$661$	−6.16892e15	−1.90152	−0.950761	+	0.309925i	$0.899696\pi$
$662$	1.99049e15	0.608472
$663$	−3.83919e15	−1.16390
$664$	5.72039e15	1.71989
$665$	−3.12286e15	−0.931179
$666$	−2.16450e14	−0.0640101
$667$	−1.15686e15	−0.339303
$668$	−2.05633e15	−0.598167
$669$	−1.91729e15	−0.553152
$670$	3.61907e15	1.03558
$671$	−1.87231e15	−0.531379
$672$	−2.46819e15	−0.694781
$673$	4.64828e15	1.29780	0.648902	−	0.760872i	$-0.275228\pi$
$673$	4.64828e15	1.29780	0.648902	+	0.760872i	$0.275228\pi$
$674$	−2.84680e15	−0.788367
$675$	3.38024e15	0.928490
$676$	−2.94106e15	−0.801303
$677$	−4.11808e15	−1.11290	−0.556451	−	0.830881i	$-0.687837\pi$
$677$	−4.11808e15	−1.11290	−0.556451	+	0.830881i	$0.687837\pi$
$678$	5.78774e14	0.155148
$679$	1.75078e15	0.465529
$680$	3.81509e15	1.00625
$681$	8.22605e14	0.215220
$682$	−5.36603e15	−1.39264
$683$	−1.25755e14	−0.0323751	−0.0161876	−	0.999869i	$-0.505153\pi$
$683$	−1.25755e14	−0.0323751	−0.0161876	+	0.999869i	$0.505153\pi$
$684$	4.62970e14	0.118234
$685$	−2.29128e15	−0.580470
$686$	−2.44484e15	−0.614423
$687$	−2.70200e15	−0.673632
$688$	1.32422e14	0.0327509
$689$	−9.51100e15	−2.33357
$690$	7.07954e15	1.72320
$691$	−7.66811e14	−0.185165	−0.0925825	−	0.995705i	$-0.529512\pi$
$691$	−7.66811e14	−0.185165	−0.0925825	+	0.995705i	$0.529512\pi$
$692$	−2.90622e15	−0.696218
$693$	7.44651e14	0.176978
$694$	2.89668e15	0.683005
$695$	−2.92987e15	−0.685382
$696$	8.61277e14	0.199890
$697$	1.89460e15	0.436252
$698$	−1.80070e15	−0.411374
$699$	−8.97426e15	−2.03411
$700$	−1.85789e15	−0.417811
$701$	1.21260e15	0.270563	0.135281	−	0.990807i	$-0.456806\pi$
$701$	1.21260e15	0.270563	0.135281	+	0.990807i	$0.456806\pi$
$702$	−3.67089e15	−0.812676
$703$	2.71424e15	0.596203
$704$	4.09426e15	0.892331
$705$	8.24458e15	1.78291
$706$	−6.42825e14	−0.137933
$707$	2.27745e14	0.0484888
$708$	−2.49993e15	−0.528134
$709$	−3.37885e15	−0.708296	−0.354148	−	0.935189i	$-0.615229\pi$
$709$	−3.37885e15	−0.708296	−0.354148	+	0.935189i	$0.615229\pi$
$710$	−6.65190e15	−1.38365
$711$	9.85745e13	0.0203461
$712$	−7.76027e14	−0.158941
$713$	1.34379e16	2.73112
$714$	1.47258e15	0.296988
$715$	−1.65212e16	−3.30641
$716$	−5.18975e15	−1.03068
$717$	7.80331e15	1.53788
$718$	−2.15432e15	−0.421333
$719$	−1.75792e15	−0.341185	−0.170592	−	0.985342i	$-0.554568\pi$
$719$	−1.75792e15	−0.341185	−0.170592	+	0.985342i	$0.554568\pi$
$720$	4.20199e13	0.00809330
$721$	3.76669e15	0.719973
$722$	1.83869e14	0.0348781
$723$	7.71175e15	1.45175
$724$	−1.61498e15	−0.301721
$725$	1.04559e15	0.193867
$726$	−4.86838e15	−0.895846
$727$	2.56923e15	0.469205	0.234603	−	0.972091i	$-0.424621\pi$
$727$	2.56923e15	0.469205	0.234603	+	0.972091i	$0.424621\pi$
$728$	5.21079e15	0.944455
$729$	4.21287e15	0.757839
$730$	7.82610e14	0.139723
$731$	−4.22324e15	−0.748343
$732$	−1.35164e15	−0.237711
$733$	7.65401e15	1.33603	0.668017	−	0.744146i	$-0.267143\pi$
$733$	7.65401e15	1.33603	0.668017	+	0.744146i	$0.267143\pi$
$734$	−5.07259e14	−0.0878824
$735$	5.41301e15	0.930805
$736$	−1.08020e16	−1.84364
$737$	1.08215e16	1.83323
$738$	−4.02961e14	−0.0677568
$739$	−1.10369e16	−1.84206	−0.921031	−	0.389490i	$-0.872651\pi$
$739$	−1.10369e16	−1.84206	−0.921031	+	0.389490i	$0.872651\pi$
$740$	3.16151e15	0.523745
$741$	−1.02394e16	−1.68374
$742$	3.64809e15	0.595449
$743$	7.30257e15	1.18314	0.591572	−	0.806253i	$-0.298508\pi$
$743$	7.30257e15	1.18314	0.591572	+	0.806253i	$0.298508\pi$
$744$	−1.00045e16	−1.60896
$745$	3.92971e15	0.627337
$746$	−3.13261e15	−0.496413
$747$	−2.00938e15	−0.316081
$748$	4.41709e15	0.689727
$749$	−1.91052e15	−0.296143
$750$	−2.69706e14	−0.0415005
$751$	7.71607e15	1.17863	0.589313	−	0.807905i	$-0.299398\pi$
$751$	7.71607e15	1.17863	0.589313	+	0.807905i	$0.299398\pi$
$752$	−2.35333e14	−0.0356849
$753$	6.46671e15	0.973444
$754$	−1.13550e15	−0.169685
$755$	−3.86801e15	−0.573825
$756$	−2.41669e15	−0.355919
$757$	−1.00894e16	−1.47516	−0.737578	−	0.675262i	$-0.764031\pi$
$757$	−1.00894e16	−1.47516	−0.737578	+	0.675262i	$0.764031\pi$
$758$	−3.81906e15	−0.554340
$759$	2.11689e16	3.05048
$760$	1.01752e16	1.45568
$761$	−3.81428e15	−0.541748	−0.270874	−	0.962615i	$-0.587313\pi$
$761$	−3.81428e15	−0.541748	−0.270874	+	0.962615i	$0.587313\pi$
$762$	3.06872e15	0.432718
$763$	4.01788e15	0.562487
$764$	−2.75908e15	−0.383487
$765$	−1.34011e15	−0.184928
$766$	2.95420e15	0.404746
$767$	8.51200e15	1.15786
$768$	7.88384e15	1.06476
$769$	6.91913e15	0.927805	0.463903	−	0.885886i	$-0.346449\pi$
$769$	6.91913e15	0.927805	0.463903	+	0.885886i	$0.346449\pi$
$770$	6.33695e15	0.843687
$771$	−9.59558e15	−1.26845
$772$	5.99218e14	0.0786484
$773$	4.63161e15	0.603593	0.301797	−	0.953372i	$-0.402414\pi$
$773$	4.63161e15	0.603593	0.301797	+	0.953372i	$0.402414\pi$
$774$	8.98237e14	0.116229
$775$	−1.21455e16	−1.56047
$776$	−5.70454e15	−0.727748
$777$	3.15160e15	0.399222
$778$	4.73197e15	0.595188
$779$	5.05306e15	0.631100
$780$	−1.19268e16	−1.47911
$781$	−1.98902e16	−2.44939
$782$	6.44474e15	0.788077
$783$	1.36008e15	0.165149
$784$	−1.54509e14	−0.0186301
$785$	1.93863e16	2.32120
$786$	−8.14154e14	−0.0968016
$787$	2.98178e15	0.352058	0.176029	−	0.984385i	$-0.443675\pi$
$787$	2.98178e15	0.352058	0.176029	+	0.984385i	$0.443675\pi$
$788$	−5.23998e15	−0.614378
$789$	1.52399e16	1.77443
$790$	8.38865e14	0.0969936
$791$	−1.29737e15	−0.148968
$792$	−2.42629e15	−0.276665
$793$	4.60220e15	0.521150
$794$	−2.30922e15	−0.259688
$795$	−2.15648e16	−2.40839
$796$	−3.78511e14	−0.0419813
$797$	−5.13438e15	−0.565545	−0.282772	−	0.959187i	$-0.591254\pi$
$797$	−5.13438e15	−0.565545	−0.282772	+	0.959187i	$0.591254\pi$
$798$	3.92750e15	0.429635
$799$	7.50531e15	0.815383
$800$	9.76311e15	1.05340
$801$	2.72591e14	0.0292101
$802$	4.47981e14	0.0476760
$803$	2.34012e15	0.247344
$804$	7.81215e15	0.820091
$805$	−1.58694e16	−1.65456
$806$	1.31898e16	1.36583
$807$	6.98663e15	0.718560
$808$	−7.42058e14	−0.0758011
$809$	−1.70412e16	−1.72896	−0.864478	−	0.502670i	$-0.832351\pi$
$809$	−1.70412e16	−1.72896	−0.864478	+	0.502670i	$0.832351\pi$
$810$	−9.88960e15	−0.996578
$811$	1.29797e16	1.29913	0.649563	−	0.760308i	$-0.274952\pi$
$811$	1.29797e16	1.29913	0.649563	+	0.760308i	$0.274952\pi$
$812$	−7.47543e14	−0.0743153
$813$	7.45141e15	0.735767
$814$	−5.50778e15	−0.540185
$815$	−2.38749e16	−2.32581
$816$	2.48470e14	0.0240424
$817$	−1.12637e16	−1.08258
$818$	−2.74152e15	−0.261726
$819$	−1.83037e15	−0.173571
$820$	5.88573e15	0.554401
$821$	1.93401e15	0.180955	0.0904775	−	0.995899i	$-0.471161\pi$
$821$	1.93401e15	0.180955	0.0904775	+	0.995899i	$0.471161\pi$
$822$	2.88165e15	0.267822
$823$	−4.38449e15	−0.404781	−0.202391	−	0.979305i	$-0.564871\pi$
$823$	−4.38449e15	−0.404781	−0.202391	+	0.979305i	$0.564871\pi$
$824$	−1.22730e16	−1.12551
$825$	−1.91329e16	−1.74295
$826$	−3.26491e15	−0.295448
$827$	6.99123e15	0.628453	0.314227	−	0.949348i	$-0.398255\pi$
$827$	6.99123e15	0.628453	0.314227	+	0.949348i	$0.398255\pi$
$828$	2.35267e15	0.210084
$829$	−1.75858e16	−1.55995	−0.779977	−	0.625808i	$-0.784770\pi$
$829$	−1.75858e16	−1.55995	−0.779977	+	0.625808i	$0.784770\pi$
$830$	−1.70997e16	−1.50681
$831$	−3.29962e15	−0.288840
$832$	−1.00638e16	−0.875152
$833$	4.92764e15	0.425688
$834$	3.68479e15	0.316227
$835$	1.58751e16	1.35345
$836$	1.17807e16	0.997787
$837$	−1.57986e16	−1.32932
$838$	−5.80069e15	−0.484884
$839$	−1.58820e16	−1.31890	−0.659452	−	0.751746i	$-0.729212\pi$
$839$	−1.58820e16	−1.31890	−0.659452	+	0.751746i	$0.729212\pi$
$840$	1.18147e16	0.974737
$841$	4.20707e14	0.0344828
$842$	5.44226e15	0.443162
$843$	1.08381e15	0.0876802
$844$	1.10558e15	0.0888602
$845$	2.27053e16	1.81308
$846$	−1.59630e15	−0.126642
$847$	1.09129e16	0.860163
$848$	6.15545e14	0.0482040
$849$	−4.62374e15	−0.359750
$850$	−5.82490e15	−0.450282
$851$	1.37929e16	1.05936
$852$	−1.43589e16	−1.09573
$853$	−1.91284e16	−1.45031	−0.725153	−	0.688588i	$-0.758231\pi$
$853$	−1.91284e16	−1.45031	−0.725153	+	0.688588i	$0.758231\pi$
$854$	−1.76524e15	−0.132980
$855$	−3.57419e15	−0.267524
$856$	6.22502e15	0.462951
$857$	1.22456e16	0.904868	0.452434	−	0.891798i	$-0.350556\pi$
$857$	1.22456e16	0.904868	0.452434	+	0.891798i	$0.350556\pi$
$858$	2.07780e16	1.52554
$859$	1.71244e15	0.124926	0.0624630	−	0.998047i	$-0.480104\pi$
$859$	1.71244e15	0.124926	0.0624630	+	0.998047i	$0.480104\pi$
$860$	−1.31198e16	−0.951014
$861$	5.86727e15	0.422589
$862$	−3.26089e15	−0.233371
$863$	2.12302e16	1.50972	0.754858	−	0.655888i	$-0.227706\pi$
$863$	2.12302e16	1.50972	0.754858	+	0.655888i	$0.227706\pi$
$864$	1.26996e16	0.897357
$865$	2.24364e16	1.57530
$866$	−9.73684e15	−0.679312
$867$	7.75793e15	0.537825
$868$	8.68339e15	0.598179
$869$	2.50833e15	0.171702
$870$	−2.57458e15	−0.175126
$871$	−2.65996e16	−1.79794
$872$	−1.30914e16	−0.879318
$873$	2.00381e15	0.133745
$874$	1.71887e16	1.14006
$875$	6.04568e14	0.0398475
$876$	1.68935e15	0.110649
$877$	−1.92397e16	−1.25228	−0.626140	−	0.779711i	$-0.715366\pi$
$877$	−1.92397e16	−1.25228	−0.626140	+	0.779711i	$0.715366\pi$
$878$	5.10544e15	0.330228
$879$	1.93472e15	0.124360
$880$	1.06924e15	0.0682998
$881$	1.96899e16	1.24990	0.624952	−	0.780663i	$-0.285119\pi$
$881$	1.96899e16	1.24990	0.624952	+	0.780663i	$0.285119\pi$
$882$	−1.04805e15	−0.0661160
$883$	−2.17436e16	−1.36316	−0.681582	−	0.731741i	$-0.738708\pi$
$883$	−2.17436e16	−1.36316	−0.681582	+	0.731741i	$0.738708\pi$
$884$	−1.08573e16	−0.676449
$885$	1.92997e16	1.19499
$886$	−1.49171e16	−0.917909
$887$	3.10400e16	1.89820	0.949100	−	0.314975i	$-0.101996\pi$
$887$	3.10400e16	1.89820	0.949100	+	0.314975i	$0.101996\pi$
$888$	−1.02688e16	−0.624092
$889$	−6.87879e15	−0.415482
$890$	2.31974e15	0.139250
$891$	−2.95713e16	−1.76418
$892$	−5.42214e15	−0.321488
$893$	2.00173e16	1.17957
$894$	−4.94224e15	−0.289446
$895$	4.00655e16	2.33208
$896$	−7.18676e15	−0.415756
$897$	−5.20336e16	−2.99175
$898$	3.83693e15	0.219262
$899$	−4.88690e15	−0.277559
$900$	−2.12639e15	−0.120036
$901$	−1.96312e16	−1.10144
$902$	−1.02537e16	−0.571803
$903$	−1.30787e16	−0.724906
$904$	4.22720e15	0.232877
$905$	1.24679e16	0.682693
$906$	4.86465e15	0.264756
$907$	3.65942e15	0.197958	0.0989788	−	0.995090i	$-0.468442\pi$
$907$	3.65942e15	0.197958	0.0989788	+	0.995090i	$0.468442\pi$
$908$	2.32634e15	0.125084
$909$	2.60659e14	0.0139307
$910$	−1.55764e16	−0.827445
$911$	−1.86890e16	−0.986815	−0.493407	−	0.869798i	$-0.664249\pi$
$911$	−1.86890e16	−0.986815	−0.493407	+	0.869798i	$0.664249\pi$
$912$	6.62689e14	0.0347807
$913$	−5.11306e16	−2.66742
$914$	7.50892e15	0.389380
$915$	1.04348e16	0.537859
$916$	−7.64131e15	−0.391510
$917$	1.82499e15	0.0929458
$918$	−7.57689e15	−0.383580
$919$	−8.05474e14	−0.0405337	−0.0202668	−	0.999795i	$-0.506452\pi$
$919$	−8.05474e14	−0.0405337	−0.0202668	+	0.999795i	$0.506452\pi$
$920$	5.17070e16	2.58652
$921$	−1.87664e16	−0.933153
$922$	7.34234e15	0.362923
$923$	4.88905e16	2.40223
$924$	1.36790e16	0.668126
$925$	−1.24664e16	−0.605285
$926$	1.42282e16	0.686734
$927$	4.31107e15	0.206846
$928$	3.92831e15	0.187366
$929$	1.95360e15	0.0926297	0.0463148	−	0.998927i	$-0.485252\pi$
$929$	1.95360e15	0.0926297	0.0463148	+	0.998927i	$0.485252\pi$
$930$	2.99061e16	1.40962
$931$	1.31424e16	0.615818
$932$	−2.53794e16	−1.18221
$933$	4.56355e16	2.11326
$934$	8.16761e15	0.376000
$935$	−3.41005e16	−1.56062
$936$	5.96388e15	0.271339
$937$	−1.32425e16	−0.598964	−0.299482	−	0.954102i	$-0.596814\pi$
$937$	−1.32425e16	−0.598964	−0.299482	+	0.954102i	$0.596814\pi$
$938$	1.02027e16	0.458775
$939$	2.59382e16	1.15952
$940$	2.33158e16	1.03621
$941$	2.17167e16	0.959511	0.479756	−	0.877402i	$-0.340725\pi$
$941$	2.17167e16	0.959511	0.479756	+	0.877402i	$0.340725\pi$
$942$	−2.43814e16	−1.07098
$943$	2.56781e16	1.12137
$944$	−5.50891e14	−0.0239177
$945$	1.86572e16	0.805324
$946$	2.28565e16	0.980865
$947$	−2.98709e16	−1.27445	−0.637225	−	0.770678i	$-0.719918\pi$
$947$	−2.98709e16	−1.27445	−0.637225	+	0.770678i	$0.719918\pi$
$948$	1.81078e15	0.0768104
$949$	−5.75207e15	−0.242583
$950$	−1.55355e16	−0.651396
$951$	−9.57884e15	−0.399319
$952$	1.07553e16	0.445780
$953$	−3.61993e16	−1.49173	−0.745863	−	0.666099i	$-0.767963\pi$
$953$	−3.61993e16	−1.49173	−0.745863	+	0.666099i	$0.767963\pi$
$954$	4.17533e15	0.171070
$955$	2.13004e16	0.867701
$956$	2.20679e16	0.893806
$957$	−7.69836e15	−0.310015
$958$	7.47164e14	0.0299161
$959$	−6.45947e15	−0.257155
$960$	−2.28182e16	−0.903212
$961$	3.13573e16	1.23413
$962$	1.35383e16	0.529786
$963$	−2.18664e15	−0.0850808
$964$	2.18090e16	0.843747
$965$	−4.62604e15	−0.177955
$966$	1.99583e16	0.763395
$967$	−3.95775e15	−0.150523	−0.0752616	−	0.997164i	$-0.523979\pi$
$967$	−3.95775e15	−0.150523	−0.0752616	+	0.997164i	$0.523979\pi$
$968$	−3.55573e16	−1.34467
$969$	−2.11347e16	−0.794722
$970$	1.70523e16	0.637586
$971$	−3.84988e16	−1.43134	−0.715668	−	0.698441i	$-0.753878\pi$
$971$	−3.84988e16	−1.43134	−0.715668	+	0.698441i	$0.753878\pi$
$972$	−6.14718e15	−0.227254
$973$	−8.25976e15	−0.303631
$974$	−1.19605e16	−0.437196
$975$	4.70292e16	1.70939
$976$	−2.97851e14	−0.0107653
$977$	−2.81728e16	−1.01254	−0.506268	−	0.862376i	$-0.668975\pi$
$977$	−2.81728e16	−1.01254	−0.506268	+	0.862376i	$0.668975\pi$
$978$	3.00265e16	1.07310
$979$	6.93637e15	0.246506
$980$	1.53081e16	0.540976
$981$	4.59856e15	0.161600
$982$	7.05543e15	0.246553
$983$	−1.45405e16	−0.505282	−0.252641	−	0.967560i	$-0.581299\pi$
$983$	−1.45405e16	−0.505282	−0.252641	+	0.967560i	$0.581299\pi$
$984$	−1.91173e16	−0.660621
$985$	4.04533e16	1.39013
$986$	−2.34372e15	−0.0800909
$987$	2.32427e16	0.789846
$988$	−2.89574e16	−0.978579
$989$	−5.72388e16	−1.92358
$990$	7.25279e15	0.242388
$991$	4.13728e16	1.37502	0.687511	−	0.726174i	$-0.258703\pi$
$991$	4.13728e16	1.37502	0.687511	+	0.726174i	$0.258703\pi$
$992$	−4.56309e16	−1.50815
$993$	−3.31710e16	−1.09028
$994$	−1.87527e16	−0.612970
$995$	2.92215e15	0.0949895
$996$	−3.69116e16	−1.19326
$997$	−5.41765e16	−1.74176	−0.870879	−	0.491498i	$-0.836450\pi$
$997$	−5.41765e16	−1.74176	−0.870879	+	0.491498i	$0.836450\pi$
$998$	4.57342e15	0.146225
$999$	−1.62159e16	−0.515623

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.12.a.a.1.7	✓	11
3.2	odd	2		261.12.a.a.1.5		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.12.a.a.1.7	✓	11	1.1	even	1	trivial
261.12.a.a.1.5		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)

\(f(q)\)	\(=\)	\(q+27.4581 q^{2} -457.582 q^{3} -1294.05 q^{4} +9990.24 q^{5} -12564.3 q^{6} +28164.0 q^{7} -91766.4 q^{8} +32234.4 q^{9} +O(q^{10})\)	\(q+27.4581 q^{2} -457.582 q^{3} -1294.05 q^{4} +9990.24 q^{5} -12564.3 q^{6} +28164.0 q^{7} -91766.4 q^{8} +32234.4 q^{9} +274313. q^{10} +820236. q^{11} +592135. q^{12} -2.01616e6 q^{13} +773331. q^{14} -4.57136e6 q^{15} +130485. q^{16} -4.16146e6 q^{17} +885095. q^{18} -1.10989e7 q^{19} -1.29279e7 q^{20} -1.28873e7 q^{21} +2.25221e7 q^{22} -5.64014e7 q^{23} +4.19907e7 q^{24} +5.09768e7 q^{25} -5.53600e7 q^{26} +6.63094e7 q^{27} -3.64457e7 q^{28} +2.05111e7 q^{29} -1.25521e8 q^{30} -2.38256e8 q^{31} +1.91521e8 q^{32} -3.75325e8 q^{33} -1.14266e8 q^{34} +2.81365e8 q^{35} -4.17130e7 q^{36} -2.44550e8 q^{37} -3.04756e8 q^{38} +9.22560e8 q^{39} -9.16769e8 q^{40} -4.55274e8 q^{41} -3.53862e8 q^{42} +1.01485e9 q^{43} -1.06143e9 q^{44} +3.22029e8 q^{45} -1.54867e9 q^{46} -1.80353e9 q^{47} -5.97074e7 q^{48} -1.18412e9 q^{49} +1.39973e9 q^{50} +1.90421e9 q^{51} +2.60902e9 q^{52} +4.71738e9 q^{53} +1.82073e9 q^{54} +8.19436e9 q^{55} -2.58451e9 q^{56} +5.07868e9 q^{57} +5.63197e8 q^{58} -4.22188e9 q^{59} +5.91557e9 q^{60} -2.28265e9 q^{61} -6.54205e9 q^{62} +9.07849e8 q^{63} +4.99156e9 q^{64} -2.01420e10 q^{65} -1.03057e10 q^{66} +1.31932e10 q^{67} +5.38514e9 q^{68} +2.58083e10 q^{69} +7.72576e9 q^{70} -2.42493e10 q^{71} -2.95803e9 q^{72} +2.85298e9 q^{73} -6.71487e9 q^{74} -2.33261e10 q^{75} +1.43626e10 q^{76} +2.31011e10 q^{77} +2.53318e10 q^{78} +3.05806e9 q^{79} +1.30357e9 q^{80} -3.60522e10 q^{81} -1.25010e10 q^{82} -6.23364e10 q^{83} +1.66769e10 q^{84} -4.15739e10 q^{85} +2.78658e10 q^{86} -9.38553e9 q^{87} -7.52702e10 q^{88} +8.45655e9 q^{89} +8.84232e9 q^{90} -5.67832e10 q^{91} +7.29863e10 q^{92} +1.09022e11 q^{93} -4.95215e10 q^{94} -1.10881e11 q^{95} -8.76364e10 q^{96} +6.21636e10 q^{97} -3.25136e10 q^{98} +2.64398e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 32 q^{2} - 982 q^{3} + 9146 q^{4} - 2740 q^{5} - 28202 q^{6} - 49432 q^{7} - 150054 q^{8} + 330749 q^{9}+O(q^{10}) \) 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

Fields

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Database

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