LMFDB - Embedded newform 29.12.a.a.1.4

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			1.4
Root			$-20.7638$ 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)

$f(q)$	$=$	$q-23.7638 q^{2} -595.785 q^{3} -1483.28 q^{4} -5297.67 q^{5} +14158.1 q^{6} +80499.9 q^{7} +83916.8 q^{8} +177813. q^{9} +O(q^{10})$	\(q-23.7638 q^{2} -595.785 q^{3} -1483.28 q^{4} -5297.67 q^{5} +14158.1 q^{6} +80499.9 q^{7} +83916.8 q^{8} +177813. q^{9} +125893. q^{10} -48833.0 q^{11} +883716. q^{12} -930345. q^{13} -1.91299e6 q^{14} +3.15627e6 q^{15} +1.04357e6 q^{16} +506191. q^{17} -4.22552e6 q^{18} +1.04796e6 q^{19} +7.85793e6 q^{20} -4.79607e7 q^{21} +1.16046e6 q^{22} +2.83418e7 q^{23} -4.99964e7 q^{24} -2.07628e7 q^{25} +2.21086e7 q^{26} -396829. q^{27} -1.19404e8 q^{28} +2.05111e7 q^{29} -7.50052e7 q^{30} +1.94175e8 q^{31} -1.96661e8 q^{32} +2.90940e7 q^{33} -1.20290e7 q^{34} -4.26462e8 q^{35} -2.63747e8 q^{36} -7.56788e8 q^{37} -2.49035e7 q^{38} +5.54286e8 q^{39} -4.44563e8 q^{40} +5.07893e8 q^{41} +1.13973e9 q^{42} -1.48159e9 q^{43} +7.24330e7 q^{44} -9.41995e8 q^{45} -6.73509e8 q^{46} +1.66313e9 q^{47} -6.21745e8 q^{48} +4.50291e9 q^{49} +4.93404e8 q^{50} -3.01581e8 q^{51} +1.37996e9 q^{52} -8.34639e8 q^{53} +9.43018e6 q^{54} +2.58701e8 q^{55} +6.75530e9 q^{56} -6.24359e8 q^{57} -4.87424e8 q^{58} +6.60274e8 q^{59} -4.68164e9 q^{60} -7.10239e9 q^{61} -4.61435e9 q^{62} +1.43139e10 q^{63} +2.53618e9 q^{64} +4.92866e9 q^{65} -6.91385e8 q^{66} +8.27289e8 q^{67} -7.50823e8 q^{68} -1.68856e10 q^{69} +1.01344e10 q^{70} -2.25416e10 q^{71} +1.49215e10 q^{72} +6.51950e9 q^{73} +1.79842e10 q^{74} +1.23702e10 q^{75} -1.55442e9 q^{76} -3.93106e9 q^{77} -1.31720e10 q^{78} +2.48536e10 q^{79} -5.52851e9 q^{80} -3.12626e10 q^{81} -1.20695e10 q^{82} -4.41362e10 q^{83} +7.11391e10 q^{84} -2.68163e9 q^{85} +3.52083e10 q^{86} -1.22202e10 q^{87} -4.09791e9 q^{88} -7.45858e10 q^{89} +2.23854e10 q^{90} -7.48927e10 q^{91} -4.20388e10 q^{92} -1.15687e11 q^{93} -3.95223e10 q^{94} -5.55174e9 q^{95} +1.17168e11 q^{96} -1.19334e11 q^{97} -1.07007e11 q^{98} -8.68315e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−23.7638	−0.525112	−0.262556	−	0.964917i	$-0.584565\pi$
$2$	−23.7638	−0.525112	−0.262556	+	0.964917i	$0.584565\pi$
$3$	−595.785	−1.41554	−0.707771	−	0.706442i	$-0.750299\pi$
$3$	−595.785	−1.41554	−0.707771	+	0.706442i	$0.750299\pi$
$4$	−1483.28	−0.724258
$5$	−5297.67	−0.758141	−0.379070	−	0.925368i	$-0.623756\pi$
$5$	−5297.67	−0.758141	−0.379070	+	0.925368i	$0.623756\pi$
$6$	14158.1	0.743318
$7$	80499.9	1.81032	0.905162	−	0.425066i	$-0.139749\pi$
$7$	80499.9	1.81032	0.905162	+	0.425066i	$0.139749\pi$
$8$	83916.8	0.905428
$9$	177813.	1.00376
$10$	125893.	0.398109
$11$	−48833.0	−0.0914226	−0.0457113	−	0.998955i	$-0.514555\pi$
$11$	−48833.0	−0.0914226	−0.0457113	+	0.998955i	$0.514555\pi$
$12$	883716.	1.02522
$13$	−930345.	−0.694953	−0.347476	−	0.937689i	$-0.612961\pi$
$13$	−930345.	−0.694953	−0.347476	+	0.937689i	$0.612961\pi$
$14$	−1.91299e6	−0.950622
$15$	3.15627e6	1.07318
$16$	1.04357e6	0.248807
$17$	506191.	0.0864660	0.0432330	−	0.999065i	$-0.486234\pi$
$17$	506191.	0.0864660	0.0432330	+	0.999065i	$0.486234\pi$
$18$	−4.22552e6	−0.527086
$19$	1.04796e6	0.0970956	0.0485478	−	0.998821i	$-0.484541\pi$
$19$	1.04796e6	0.0970956	0.0485478	+	0.998821i	$0.484541\pi$
$20$	7.85793e6	0.549089
$21$	−4.79607e7	−2.56259
$22$	1.16046e6	0.0480071
$23$	2.83418e7	0.918171	0.459086	−	0.888392i	$-0.348177\pi$
$23$	2.83418e7	0.918171	0.459086	+	0.888392i	$0.348177\pi$
$24$	−4.99964e7	−1.28167
$25$	−2.07628e7	−0.425222
$26$	2.21086e7	0.364928
$27$	−396829.	−0.00532234
$28$	−1.19404e8	−1.31114
$29$	2.05111e7	0.185695
$29$	2.05111e7	0.185695
$30$	−7.50052e7	−0.563539
$31$	1.94175e8	1.21816	0.609081	−	0.793108i	$-0.291539\pi$
$31$	1.94175e8	1.21816	0.609081	+	0.793108i	$0.291539\pi$
$32$	−1.96661e8	−1.03608
$33$	2.90940e7	0.129413
$34$	−1.20290e7	−0.0454043
$35$	−4.26462e8	−1.37248
$36$	−2.63747e8	−0.726981
$37$	−7.56788e8	−1.79418	−0.897088	−	0.441852i	$-0.854322\pi$
$37$	−7.56788e8	−1.79418	−0.897088	+	0.441852i	$0.854322\pi$
$38$	−2.49035e7	−0.0509860
$39$	5.54286e8	0.983735
$40$	−4.44563e8	−0.686442
$41$	5.07893e8	0.684638	0.342319	−	0.939584i	$-0.388788\pi$
$41$	5.07893e8	0.684638	0.342319	+	0.939584i	$0.388788\pi$
$42$	1.13973e9	1.34565
$43$	−1.48159e9	−1.53692	−0.768461	−	0.639896i	$-0.778977\pi$
$43$	−1.48159e9	−1.53692	−0.768461	+	0.639896i	$0.778977\pi$
$44$	7.24330e7	0.0662136
$45$	−9.41995e8	−0.760991
$46$	−6.73509e8	−0.482142
$47$	1.66313e9	1.05776	0.528880	−	0.848696i	$-0.322612\pi$
$47$	1.66313e9	1.05776	0.528880	+	0.848696i	$0.322612\pi$
$48$	−6.21745e8	−0.352197
$49$	4.50291e9	2.27727
$50$	4.93404e8	0.223289
$51$	−3.01581e8	−0.122396
$52$	1.37996e9	0.503325
$53$	−8.34639e8	−0.274146	−0.137073	−	0.990561i	$-0.543769\pi$
$53$	−8.34639e8	−0.274146	−0.137073	+	0.990561i	$0.543769\pi$
$54$	9.43018e6	0.00279482
$55$	2.58701e8	0.0693112
$56$	6.75530e9	1.63912
$57$	−6.24359e8	−0.137443
$58$	−4.87424e8	−0.0975108
$59$	6.60274e8	0.120237	0.0601185	−	0.998191i	$-0.480852\pi$
$59$	6.60274e8	0.120237	0.0601185	+	0.998191i	$0.480852\pi$
$60$	−4.68164e9	−0.777259
$61$	−7.10239e9	−1.07669	−0.538345	−	0.842725i	$-0.680950\pi$
$61$	−7.10239e9	−1.07669	−0.538345	+	0.842725i	$0.680950\pi$
$62$	−4.61435e9	−0.639671
$63$	1.43139e10	1.81713
$64$	2.53618e9	0.295250
$65$	4.92866e9	0.526872
$66$	−6.91385e8	−0.0679561
$67$	8.27289e8	0.0748593	0.0374297	−	0.999299i	$-0.488083\pi$
$67$	8.27289e8	0.0748593	0.0374297	+	0.999299i	$0.488083\pi$
$68$	−7.50823e8	−0.0626237
$69$	−1.68856e10	−1.29971
$70$	1.01344e10	0.720706
$71$	−2.25416e10	−1.48273	−0.741367	−	0.671100i	$-0.765822\pi$
$71$	−2.25416e10	−1.48273	−0.741367	+	0.671100i	$0.765822\pi$
$72$	1.49215e10	0.908832
$73$	6.51950e9	0.368077	0.184039	−	0.982919i	$-0.441083\pi$
$73$	6.51950e9	0.368077	0.184039	+	0.982919i	$0.441083\pi$
$74$	1.79842e10	0.942142
$75$	1.23702e10	0.601920
$76$	−1.55442e9	−0.0703223
$77$	−3.93106e9	−0.165505
$78$	−1.31720e10	−0.516571
$79$	2.48536e10	0.908742	0.454371	−	0.890812i	$-0.349864\pi$
$79$	2.48536e10	0.908742	0.454371	+	0.890812i	$0.349864\pi$
$80$	−5.52851e9	−0.188631
$81$	−3.12626e10	−0.996226
$82$	−1.20695e10	−0.359511
$83$	−4.41362e10	−1.22989	−0.614944	−	0.788570i	$-0.710822\pi$
$83$	−4.41362e10	−1.22989	−0.614944	+	0.788570i	$0.710822\pi$
$84$	7.11391e10	1.85598
$85$	−2.68163e9	−0.0655534
$86$	3.52083e10	0.807056
$87$	−1.22202e10	−0.262860
$88$	−4.09791e9	−0.0827766
$89$	−7.45858e10	−1.41583	−0.707915	−	0.706298i	$-0.750364\pi$
$89$	−7.45858e10	−1.41583	−0.707915	+	0.706298i	$0.750364\pi$
$90$	2.23854e10	0.399605
$91$	−7.48927e10	−1.25809
$92$	−4.20388e10	−0.664993
$93$	−1.15687e11	−1.72436
$94$	−3.95223e10	−0.555442
$95$	−5.55174e9	−0.0736122
$96$	1.17168e11	1.46661
$97$	−1.19334e11	−1.41098	−0.705490	−	0.708720i	$-0.749273\pi$
$97$	−1.19334e11	−1.41098	−0.705490	+	0.708720i	$0.749273\pi$
$98$	−1.07007e11	−1.19582
$99$	−8.68315e9	−0.0917664
$100$	3.07971e10	0.307971
$101$	−2.52198e10	−0.238767	−0.119383	−	0.992848i	$-0.538092\pi$
$101$	−2.52198e10	−0.238767	−0.119383	+	0.992848i	$0.538092\pi$
$102$	7.16672e9	0.0642717
$103$	3.15441e10	0.268110	0.134055	−	0.990974i	$-0.457200\pi$
$103$	3.15441e10	0.268110	0.134055	+	0.990974i	$0.457200\pi$
$104$	−7.80715e10	−0.629230
$105$	2.54080e11	1.94280
$106$	1.98342e10	0.143957
$107$	2.50848e11	1.72902	0.864511	−	0.502614i	$-0.167628\pi$
$107$	2.50848e11	1.72902	0.864511	+	0.502614i	$0.167628\pi$
$108$	5.88609e8	0.00385475
$109$	1.24993e11	0.778109	0.389054	−	0.921215i	$-0.372802\pi$
$109$	1.24993e11	0.778109	0.389054	+	0.921215i	$0.372802\pi$
$110$	−6.14773e9	−0.0363961
$111$	4.50883e11	2.53973
$112$	8.40076e10	0.450422
$113$	6.74405e10	0.344342	0.172171	−	0.985067i	$-0.444922\pi$
$113$	6.74405e10	0.344342	0.172171	+	0.985067i	$0.444922\pi$
$114$	1.48372e10	0.0721729
$115$	−1.50145e11	−0.696103
$116$	−3.04238e10	−0.134491
$117$	−1.65427e11	−0.697566
$118$	−1.56906e10	−0.0631379
$119$	4.07483e10	0.156531
$120$	2.64864e11	0.971687
$121$	−2.82927e11	−0.991642
$122$	1.68780e11	0.565382
$123$	−3.02595e11	−0.969134
$124$	−2.88016e11	−0.882263
$125$	3.68670e11	1.08052
$126$	−3.40154e11	−0.954197
$127$	−4.02221e11	−1.08030	−0.540150	−	0.841569i	$-0.681633\pi$
$127$	−4.02221e11	−1.08030	−0.540150	+	0.841569i	$0.681633\pi$
$128$	3.42492e11	0.881040
$129$	8.82710e11	2.17558
$130$	−1.17124e11	−0.276667
$131$	−6.76340e11	−1.53170	−0.765849	−	0.643020i	$-0.777681\pi$
$131$	−6.76340e11	−1.53170	−0.765849	+	0.643020i	$0.777681\pi$
$132$	−4.31545e10	−0.0937281
$133$	8.43607e10	0.175775
$134$	−1.96596e10	−0.0393095
$135$	2.10227e9	0.00403508
$136$	4.24779e10	0.0782887
$137$	2.81271e11	0.497923	0.248961	−	0.968513i	$-0.419911\pi$
$137$	2.81271e11	0.497923	0.248961	+	0.968513i	$0.419911\pi$
$138$	4.01267e11	0.682493
$139$	−3.80202e11	−0.621488	−0.310744	−	0.950494i	$-0.600578\pi$
$139$	−3.80202e11	−0.621488	−0.310744	+	0.950494i	$0.600578\pi$
$140$	6.32563e11	0.994030
$141$	−9.90867e11	−1.49730
$142$	5.35674e11	0.778601
$143$	4.54315e10	0.0635344
$144$	1.85561e11	0.249743
$145$	−1.08661e11	−0.140783
$146$	−1.54928e11	−0.193282
$147$	−2.68277e12	−3.22358
$148$	1.12253e12	1.29945
$149$	1.74127e12	1.94241	0.971207	−	0.238236i	$-0.0765693\pi$
$149$	1.74127e12	1.94241	0.971207	+	0.238236i	$0.0765693\pi$
$150$	−2.93963e11	−0.316075
$151$	−1.67155e12	−1.73279	−0.866394	−	0.499361i	$-0.833568\pi$
$151$	−1.67155e12	−1.73279	−0.866394	+	0.499361i	$0.833568\pi$
$152$	8.79414e10	0.0879131
$153$	9.00074e10	0.0867911
$154$	9.34170e10	0.0869084
$155$	−1.02868e12	−0.923538
$156$	−8.22161e11	−0.712478
$157$	−1.81666e12	−1.51994	−0.759969	−	0.649959i	$-0.774786\pi$
$157$	−1.81666e12	−1.51994	−0.759969	+	0.649959i	$0.774786\pi$
$158$	−5.90618e11	−0.477191
$159$	4.97266e11	0.388065
$160$	1.04184e12	0.785494
$161$	2.28151e12	1.66219
$162$	7.42920e11	0.523130
$163$	1.07869e12	0.734284	0.367142	−	0.930165i	$-0.380336\pi$
$163$	1.07869e12	0.734284	0.367142	+	0.930165i	$0.380336\pi$
$164$	−7.53347e11	−0.495854
$165$	−1.54130e11	−0.0981130
$166$	1.04885e12	0.645829
$167$	−2.12043e12	−1.26323	−0.631617	−	0.775281i	$-0.717608\pi$
$167$	−2.12043e12	−1.26323	−0.631617	+	0.775281i	$0.717608\pi$
$168$	−4.02471e12	−2.32024
$169$	−9.26619e11	−0.517040
$170$	6.37259e10	0.0344228
$171$	1.86341e11	0.0974607
$172$	2.19761e12	1.11313
$173$	1.04942e11	0.0514868	0.0257434	−	0.999669i	$-0.491805\pi$
$173$	1.04942e11	0.0514868	0.0257434	+	0.999669i	$0.491805\pi$
$174$	2.90400e11	0.138031
$175$	−1.67141e12	−0.769791
$176$	−5.09608e10	−0.0227466
$177$	−3.93382e11	−0.170201
$178$	1.77245e12	0.743469
$179$	3.02670e12	1.23105	0.615527	−	0.788116i	$-0.288943\pi$
$179$	3.02670e12	1.23105	0.615527	+	0.788116i	$0.288943\pi$
$180$	1.39724e12	0.551154
$181$	−2.56476e12	−0.981328	−0.490664	−	0.871349i	$-0.663246\pi$
$181$	−2.56476e12	−0.981328	−0.490664	+	0.871349i	$0.663246\pi$
$182$	1.77974e12	0.660638
$183$	4.23150e12	1.52410
$184$	2.37835e12	0.831338
$185$	4.00921e12	1.36024
$186$	2.74916e12	0.905481
$187$	−2.47188e10	−0.00790495
$188$	−2.46688e12	−0.766091
$189$	−3.19447e10	−0.00963516
$190$	1.31931e11	0.0386546
$191$	−3.71872e12	−1.05855	−0.529273	−	0.848452i	$-0.677535\pi$
$191$	−3.71872e12	−1.05855	−0.529273	+	0.848452i	$0.677535\pi$
$192$	−1.51102e12	−0.417939
$193$	3.83026e11	0.102959	0.0514794	−	0.998674i	$-0.483606\pi$
$193$	3.83026e11	0.102959	0.0514794	+	0.998674i	$0.483606\pi$
$194$	2.83584e12	0.740922
$195$	−2.93642e12	−0.745810
$196$	−6.67908e12	−1.64933
$197$	6.41435e12	1.54024	0.770120	−	0.637899i	$-0.220196\pi$
$197$	6.41435e12	1.54024	0.770120	+	0.637899i	$0.220196\pi$
$198$	2.06345e11	0.0481876
$199$	−1.85317e12	−0.420944	−0.210472	−	0.977600i	$-0.567500\pi$
$199$	−1.85317e12	−0.420944	−0.210472	+	0.977600i	$0.567500\pi$
$200$	−1.74235e12	−0.385008
$201$	−4.92887e11	−0.105967
$202$	5.99319e11	0.125379
$203$	1.65115e12	0.336169
$204$	4.47329e11	0.0886464
$205$	−2.69065e12	−0.519052
$206$	−7.49609e11	−0.140788
$207$	5.03953e12	0.921623
$208$	−9.70882e11	−0.172909
$209$	−5.11750e10	−0.00887674
$210$	−6.03791e12	−1.02019
$211$	−3.00374e12	−0.494434	−0.247217	−	0.968960i	$-0.579516\pi$
$211$	−3.00374e12	−0.494434	−0.247217	+	0.968960i	$0.579516\pi$
$212$	1.23800e12	0.198552
$213$	1.34299e13	2.09887
$214$	−5.96112e12	−0.907929
$215$	7.84898e12	1.16520
$216$	−3.33006e10	−0.00481900
$217$	1.56311e13	2.20527
$218$	−2.97032e12	−0.408594
$219$	−3.88422e12	−0.521029
$220$	−3.83726e11	−0.0501992
$221$	−4.70932e11	−0.0600898
$222$	−1.07147e13	−1.33364
$223$	−7.06080e11	−0.0857388	−0.0428694	−	0.999081i	$-0.513650\pi$
$223$	−7.06080e11	−0.0857388	−0.0428694	+	0.999081i	$0.513650\pi$
$224$	−1.58312e13	−1.87564
$225$	−3.69190e12	−0.426821
$226$	−1.60265e12	−0.180818
$227$	3.18905e12	0.351171	0.175585	−	0.984464i	$-0.443818\pi$
$227$	3.18905e12	0.351171	0.175585	+	0.984464i	$0.443818\pi$
$228$	9.26099e11	0.0995441
$229$	−1.02975e13	−1.08053	−0.540266	−	0.841495i	$-0.681676\pi$
$229$	−1.02975e13	−1.08053	−0.540266	+	0.841495i	$0.681676\pi$
$230$	3.56803e12	0.365532
$231$	2.34206e12	0.234279
$232$	1.72123e12	0.168134
$233$	−6.19234e12	−0.590742	−0.295371	−	0.955383i	$-0.595443\pi$
$233$	−6.19234e12	−0.590742	−0.295371	+	0.955383i	$0.595443\pi$
$234$	3.93119e12	0.366300
$235$	−8.81070e12	−0.801931
$236$	−9.79371e11	−0.0870826
$237$	−1.48074e13	−1.28636
$238$	−9.68337e11	−0.0821965
$239$	1.38733e12	0.115078	0.0575390	−	0.998343i	$-0.481675\pi$
$239$	1.38733e12	0.115078	0.0575390	+	0.998343i	$0.481675\pi$
$240$	3.29380e12	0.267015
$241$	8.34573e12	0.661257	0.330629	−	0.943761i	$-0.392739\pi$
$241$	8.34573e12	0.661257	0.330629	+	0.943761i	$0.392739\pi$
$242$	6.72343e12	0.520723
$243$	1.86961e13	1.41552
$244$	1.05348e13	0.779800
$245$	−2.38550e13	−1.72649
$246$	7.19082e12	0.508903
$247$	−9.74963e11	−0.0674769
$248$	1.62946e13	1.10296
$249$	2.62957e13	1.74096
$250$	−8.76101e12	−0.567393
$251$	−1.99492e13	−1.26392	−0.631960	−	0.775001i	$-0.717749\pi$
$251$	−1.99492e13	−1.26392	−0.631960	+	0.775001i	$0.717749\pi$
$252$	−2.12316e13	−1.31607
$253$	−1.38401e12	−0.0839416
$254$	9.55832e12	0.567278
$255$	1.59768e12	0.0927936
$256$	−1.33330e13	−0.757894
$257$	−1.70759e13	−0.950060	−0.475030	−	0.879970i	$-0.657563\pi$
$257$	−1.70759e13	−0.950060	−0.475030	+	0.879970i	$0.657563\pi$
$258$	−2.09766e13	−1.14242
$259$	−6.09214e13	−3.24804
$260$	−7.31058e12	−0.381591
$261$	3.64715e12	0.186394
$262$	1.60724e13	0.804313
$263$	2.47821e12	0.121446	0.0607228	−	0.998155i	$-0.480659\pi$
$263$	2.47821e12	0.121446	0.0607228	+	0.998155i	$0.480659\pi$
$264$	2.44147e12	0.117174
$265$	4.42164e12	0.207841
$266$	−2.00473e12	−0.0923013
$267$	4.44371e13	2.00417
$268$	−1.22710e12	−0.0542174
$269$	3.70849e13	1.60531	0.802657	−	0.596441i	$-0.203419\pi$
$269$	3.70849e13	1.60531	0.802657	+	0.596441i	$0.203419\pi$
$270$	−4.99580e10	−0.00211887
$271$	1.89763e13	0.788642	0.394321	−	0.918973i	$-0.370980\pi$
$271$	1.89763e13	0.788642	0.394321	+	0.918973i	$0.370980\pi$
$272$	5.28247e11	0.0215134
$273$	4.46200e13	1.78088
$274$	−6.68408e12	−0.261465
$275$	1.01391e12	0.0388750
$276$	2.50461e13	0.941325
$277$	3.21867e13	1.18587	0.592935	−	0.805250i	$-0.297969\pi$
$277$	3.21867e13	1.18587	0.592935	+	0.805250i	$0.297969\pi$
$278$	9.03506e12	0.326351
$279$	3.45269e13	1.22274
$280$	−3.57873e13	−1.24268
$281$	7.67486e12	0.261328	0.130664	−	0.991427i	$-0.458289\pi$
$281$	7.67486e12	0.261328	0.130664	+	0.991427i	$0.458289\pi$
$282$	2.35468e13	0.786252
$283$	−5.46880e13	−1.79088	−0.895440	−	0.445183i	$-0.853139\pi$
$283$	−5.46880e13	−1.79088	−0.895440	+	0.445183i	$0.853139\pi$
$284$	3.34355e13	1.07388
$285$	3.30765e12	0.104201
$286$	−1.07963e12	−0.0333627
$287$	4.08853e13	1.23942
$288$	−3.49689e13	−1.03997
$289$	−3.40157e13	−0.992524
$290$	2.58221e12	0.0739269
$291$	7.10976e13	1.99730
$292$	−9.67025e12	−0.266583
$293$	−4.17914e12	−0.113062	−0.0565308	−	0.998401i	$-0.518004\pi$
$293$	−4.17914e12	−0.113062	−0.0565308	+	0.998401i	$0.518004\pi$
$294$	6.37529e13	1.69274
$295$	−3.49791e12	−0.0911566
$296$	−6.35072e13	−1.62450
$297$	1.93784e10	0.000486583 0
$298$	−4.13793e13	−1.01998
$299$	−2.63676e13	−0.638086
$300$	−1.83484e13	−0.435946
$301$	−1.19268e14	−2.78233
$302$	3.97224e13	0.909907
$303$	1.50256e13	0.337984
$304$	1.09362e12	0.0241581
$305$	3.76261e13	0.816282
$306$	−2.13892e12	−0.0455750
$307$	−1.85704e13	−0.388651	−0.194326	−	0.980937i	$-0.562252\pi$
$307$	−1.85704e13	−0.388651	−0.194326	+	0.980937i	$0.562252\pi$
$308$	5.83086e12	0.119868
$309$	−1.87935e13	−0.379521
$310$	2.44453e13	0.484961
$311$	−5.58068e13	−1.08769	−0.543845	−	0.839186i	$-0.683032\pi$
$311$	−5.58068e13	−1.08769	−0.543845	+	0.839186i	$0.683032\pi$
$312$	4.65139e13	0.890701
$313$	4.67501e13	0.879608	0.439804	−	0.898094i	$-0.355048\pi$
$313$	4.67501e13	0.879608	0.439804	+	0.898094i	$0.355048\pi$
$314$	4.31709e13	0.798137
$315$	−7.58305e13	−1.37764
$316$	−3.68649e13	−0.658164
$317$	−7.21065e13	−1.26517	−0.632584	−	0.774491i	$-0.718006\pi$
$317$	−7.21065e13	−1.26517	−0.632584	+	0.774491i	$0.718006\pi$
$318$	−1.18169e13	−0.203777
$319$	−1.00162e12	−0.0169768
$320$	−1.34358e13	−0.223841
$321$	−1.49452e14	−2.44750
$322$	−5.42174e13	−0.872834
$323$	5.30468e11	0.00839547
$324$	4.63712e13	0.721524
$325$	1.93166e13	0.295510
$326$	−2.56338e13	−0.385581
$327$	−7.44691e13	−1.10145
$328$	4.26207e13	0.619890
$329$	1.33882e14	1.91489
$330$	3.66273e12	0.0515203
$331$	7.90037e13	1.09293	0.546466	−	0.837481i	$-0.315973\pi$
$331$	7.90037e13	1.09293	0.546466	+	0.837481i	$0.315973\pi$
$332$	6.54664e13	0.890757
$333$	−1.34567e14	−1.80092
$334$	5.03896e13	0.663339
$335$	−4.38270e12	−0.0567539
$336$	−5.00505e13	−0.637591
$337$	−4.89939e13	−0.614013	−0.307006	−	0.951707i	$-0.599327\pi$
$337$	−4.89939e13	−0.614013	−0.307006	+	0.951707i	$0.599327\pi$
$338$	2.20200e13	0.271504
$339$	−4.01801e13	−0.487430
$340$	3.97761e12	0.0474776
$341$	−9.48217e12	−0.111368
$342$	−4.42817e12	−0.0511777
$343$	2.03310e14	2.31228
$344$	−1.24330e14	−1.39157
$345$	8.94543e13	0.985363
$346$	−2.49383e12	−0.0270363
$347$	1.34018e14	1.43005	0.715027	−	0.699097i	$-0.246415\pi$
$347$	1.34018e14	1.43005	0.715027	+	0.699097i	$0.246415\pi$
$348$	1.81260e13	0.190378
$349$	−1.23800e14	−1.27991	−0.639956	−	0.768412i	$-0.721047\pi$
$349$	−1.23800e14	−1.27991	−0.639956	+	0.768412i	$0.721047\pi$
$350$	3.97190e13	0.404226
$351$	3.69188e11	0.00369878
$352$	9.60354e12	0.0947211
$353$	8.30822e12	0.0806765	0.0403383	−	0.999186i	$-0.487156\pi$
$353$	8.30822e12	0.0806765	0.0403383	+	0.999186i	$0.487156\pi$
$354$	9.34826e12	0.0893743
$355$	1.19418e14	1.12412
$356$	1.10632e14	1.02543
$357$	−2.42773e13	−0.221577
$358$	−7.19260e13	−0.646441
$359$	−2.00482e14	−1.77442	−0.887210	−	0.461365i	$-0.847360\pi$
$359$	−2.00482e14	−1.77442	−0.887210	+	0.461365i	$0.847360\pi$
$360$	−7.90492e13	−0.689023
$361$	−1.15392e14	−0.990572
$362$	6.09485e13	0.515307
$363$	1.68564e14	1.40371
$364$	1.11087e14	0.911182
$365$	−3.45382e13	−0.279054
$366$	−1.00557e14	−0.800322
$367$	1.35764e13	0.106444	0.0532221	−	0.998583i	$-0.483051\pi$
$367$	1.35764e13	0.106444	0.0532221	+	0.998583i	$0.483051\pi$
$368$	2.95767e13	0.228448
$369$	9.03100e13	0.687212
$370$	−9.52743e13	−0.714277
$371$	−6.71884e13	−0.496293
$372$	1.71596e14	1.24888
$373$	−4.27855e13	−0.306830	−0.153415	−	0.988162i	$-0.549027\pi$
$373$	−4.27855e13	−0.306830	−0.153415	+	0.988162i	$0.549027\pi$
$374$	5.87414e11	0.00415098
$375$	−2.19648e14	−1.52952
$376$	1.39564e14	0.957726
$377$	−1.90824e13	−0.129050
$378$	7.59129e11	0.00505954
$379$	−8.97682e13	−0.589667	−0.294833	−	0.955549i	$-0.595264\pi$
$379$	−8.97682e13	−0.589667	−0.294833	+	0.955549i	$0.595264\pi$
$380$	8.23479e12	0.0533142
$381$	2.39638e14	1.52921
$382$	8.83710e13	0.555855
$383$	−1.56083e14	−0.967750	−0.483875	−	0.875137i	$-0.660771\pi$
$383$	−1.56083e14	−0.967750	−0.483875	+	0.875137i	$0.660771\pi$
$384$	−2.04052e14	−1.24715
$385$	2.08254e13	0.125476
$386$	−9.10217e12	−0.0540648
$387$	−2.63446e14	−1.54270
$388$	1.77006e14	1.02191
$389$	6.64866e13	0.378452	0.189226	−	0.981934i	$-0.439402\pi$
$389$	6.64866e13	0.378452	0.189226	+	0.981934i	$0.439402\pi$
$390$	6.97807e13	0.391633
$391$	1.43463e13	0.0793906
$392$	3.77870e14	2.06191
$393$	4.02954e14	2.16818
$394$	−1.52430e14	−0.808798
$395$	−1.31666e14	−0.688955
$396$	1.28795e13	0.0664625
$397$	7.81206e13	0.397574	0.198787	−	0.980043i	$-0.436300\pi$
$397$	7.81206e13	0.397574	0.198787	+	0.980043i	$0.436300\pi$
$398$	4.40385e13	0.221043
$399$	−5.02609e13	−0.248816
$400$	−2.16675e13	−0.105798
$401$	3.95314e14	1.90392	0.951958	−	0.306228i	$-0.0990670\pi$
$401$	3.95314e14	1.90392	0.951958	+	0.306228i	$0.0990670\pi$
$402$	1.17129e13	0.0556443
$403$	−1.80650e14	−0.846565
$404$	3.74080e13	0.172929
$405$	1.65619e14	0.755280
$406$	−3.92376e13	−0.176526
$407$	3.69563e13	0.164028
$408$	−2.53077e13	−0.110821
$409$	−4.19423e14	−1.81207	−0.906033	−	0.423207i	$-0.860904\pi$
$409$	−4.19423e14	−1.81207	−0.906033	+	0.423207i	$0.860904\pi$
$410$	6.39401e13	0.272560
$411$	−1.67577e14	−0.704830
$412$	−4.67887e13	−0.194181
$413$	5.31520e13	0.217668
$414$	−1.19759e14	−0.483955
$415$	2.33819e14	0.932429
$416$	1.82962e14	0.720026
$417$	2.26519e14	0.879743
$418$	1.21612e12	0.00466128
$419$	1.16987e14	0.442547	0.221273	−	0.975212i	$-0.428979\pi$
$419$	1.16987e14	0.442547	0.221273	+	0.975212i	$0.428979\pi$
$420$	−3.76872e14	−1.40709
$421$	−4.85624e14	−1.78957	−0.894785	−	0.446497i	$-0.852672\pi$
$421$	−4.85624e14	−1.78957	−0.894785	+	0.446497i	$0.852672\pi$
$422$	7.13804e13	0.259633
$423$	2.95726e14	1.06174
$424$	−7.00402e13	−0.248219
$425$	−1.05100e13	−0.0367673
$426$	−3.19147e14	−1.10214
$427$	−5.71742e14	−1.94916
$428$	−3.72078e14	−1.25226
$429$	−2.70674e13	−0.0899357
$430$	−1.86522e14	−0.611862
$431$	1.43717e14	0.465460	0.232730	−	0.972541i	$-0.425234\pi$
$431$	1.43717e14	0.465460	0.232730	+	0.972541i	$0.425234\pi$
$432$	−4.14120e11	−0.00132424
$433$	3.13984e14	0.991345	0.495672	−	0.868510i	$-0.334922\pi$
$433$	3.13984e14	0.991345	0.495672	+	0.868510i	$0.334922\pi$
$434$	−3.71455e14	−1.15801
$435$	6.47388e13	0.199285
$436$	−1.85400e14	−0.563551
$437$	2.97010e13	0.0891504
$438$	9.23041e13	0.273598
$439$	−4.69695e14	−1.37487	−0.687434	−	0.726247i	$-0.741263\pi$
$439$	−4.69695e14	−1.37487	−0.687434	+	0.726247i	$0.741263\pi$
$440$	2.17094e13	0.0627563
$441$	8.00677e14	2.28584
$442$	1.11912e13	0.0315538
$443$	−1.86393e14	−0.519050	−0.259525	−	0.965736i	$-0.583566\pi$
$443$	−1.86393e14	−0.519050	−0.259525	+	0.965736i	$0.583566\pi$
$444$	−6.68786e14	−1.83942
$445$	3.95131e14	1.07340
$446$	1.67792e13	0.0450224
$447$	−1.03742e15	−2.74957
$448$	2.04162e14	0.534498
$449$	−1.00294e14	−0.259371	−0.129685	−	0.991555i	$-0.541397\pi$
$449$	−1.00294e14	−0.259371	−0.129685	+	0.991555i	$0.541397\pi$
$450$	8.77337e13	0.224129
$451$	−2.48019e13	−0.0625914
$452$	−1.00033e14	−0.249392
$453$	9.95883e14	2.45283
$454$	−7.57840e13	−0.184404
$455$	3.96757e14	0.953810
$456$	−5.23942e13	−0.124445
$457$	2.45758e14	0.576726	0.288363	−	0.957521i	$-0.406889\pi$
$457$	2.45758e14	0.576726	0.288363	+	0.957521i	$0.406889\pi$
$458$	2.44709e14	0.567399
$459$	−2.00871e11	−0.000460202 0
$460$	2.22707e14	0.504158
$461$	−6.63539e14	−1.48426	−0.742132	−	0.670253i	$-0.766185\pi$
$461$	−6.63539e14	−1.48426	−0.742132	+	0.670253i	$0.766185\pi$
$462$	−5.56564e13	−0.123023
$463$	−1.04412e14	−0.228062	−0.114031	−	0.993477i	$-0.536376\pi$
$463$	−1.04412e14	−0.228062	−0.114031	+	0.993477i	$0.536376\pi$
$464$	2.14049e13	0.0462023
$465$	6.12871e14	1.30731
$466$	1.47154e14	0.310205
$467$	−6.80677e14	−1.41807	−0.709036	−	0.705172i	$-0.750870\pi$
$467$	−6.80677e14	−1.41807	−0.709036	+	0.705172i	$0.750870\pi$
$468$	2.45375e14	0.505218
$469$	6.65967e13	0.135520
$470$	2.09376e14	0.421104
$471$	1.08234e15	2.15154
$472$	5.54081e13	0.108866
$473$	7.23506e13	0.140510
$474$	3.51881e14	0.675484
$475$	−2.17586e13	−0.0412872
$476$	−6.04412e13	−0.113369
$477$	−1.48410e14	−0.275177
$478$	−3.29684e13	−0.0604288
$479$	−5.79575e14	−1.05018	−0.525090	−	0.851047i	$-0.675968\pi$
$479$	−5.79575e14	−1.05018	−0.525090	+	0.851047i	$0.675968\pi$
$480$	−6.20715e14	−1.11190
$481$	7.04074e14	1.24687
$482$	−1.98326e14	−0.347234
$483$	−1.35929e15	−2.35290
$484$	4.19660e14	0.718204
$485$	6.32194e14	1.06972
$486$	−4.44291e14	−0.743307
$487$	6.09413e14	1.00810	0.504048	−	0.863675i	$-0.331843\pi$
$487$	6.09413e14	1.00810	0.504048	+	0.863675i	$0.331843\pi$
$488$	−5.96009e14	−0.974864
$489$	−6.42667e14	−1.03941
$490$	5.66885e14	0.906602
$491$	3.47139e14	0.548978	0.274489	−	0.961590i	$-0.411491\pi$
$491$	3.47139e14	0.548978	0.274489	+	0.961590i	$0.411491\pi$
$492$	4.48833e14	0.701903
$493$	1.03826e13	0.0160563
$494$	2.31689e13	0.0354329
$495$	4.60005e13	0.0695718
$496$	2.02636e14	0.303087
$497$	−1.81460e15	−2.68423
$498$	−6.24887e14	−0.914198
$499$	8.73757e14	1.26426	0.632132	−	0.774861i	$-0.282180\pi$
$499$	8.73757e14	1.26426	0.632132	+	0.774861i	$0.282180\pi$
$500$	−5.46841e14	−0.782575
$501$	1.26332e15	1.78816
$502$	4.74069e14	0.663699
$503$	−1.16225e15	−1.60944	−0.804721	−	0.593653i	$-0.797685\pi$
$503$	−1.16225e15	−1.60944	−0.804721	+	0.593653i	$0.797685\pi$
$504$	1.20118e15	1.64528
$505$	1.33606e14	0.181019
$506$	3.28895e13	0.0440787
$507$	5.52066e14	0.731893
$508$	5.96607e14	0.782416
$509$	9.89379e13	0.128356	0.0641778	−	0.997938i	$-0.479558\pi$
$509$	9.89379e13	0.128356	0.0641778	+	0.997938i	$0.479558\pi$
$510$	−3.79669e13	−0.0487270
$511$	5.24820e14	0.666339
$512$	−3.84580e14	−0.483061
$513$	−4.15861e11	−0.000516776 0
$514$	4.05789e14	0.498888
$515$	−1.67110e14	−0.203265
$516$	−1.30931e15	−1.57568
$517$	−8.12155e13	−0.0967033
$518$	1.44773e15	1.70558
$519$	−6.25229e13	−0.0728818
$520$	4.13597e14	0.477045
$521$	7.97660e14	0.910354	0.455177	−	0.890401i	$-0.349576\pi$
$521$	7.97660e14	0.910354	0.455177	+	0.890401i	$0.349576\pi$
$522$	−8.66703e13	−0.0978774
$523$	4.00131e14	0.447140	0.223570	−	0.974688i	$-0.428229\pi$
$523$	4.00131e14	0.447140	0.223570	+	0.974688i	$0.428229\pi$
$524$	1.00320e15	1.10934
$525$	9.95799e14	1.08967
$526$	−5.88919e13	−0.0637725
$527$	9.82898e13	0.105330
$528$	3.03617e13	0.0321988
$529$	−1.49555e14	−0.156962
$530$	−1.05075e14	−0.109140
$531$	1.17405e14	0.120689
$532$	−1.25131e14	−0.127306
$533$	−4.72515e14	−0.475791
$534$	−1.05600e15	−1.05241
$535$	−1.32891e15	−1.31084
$536$	6.94234e13	0.0677797
$537$	−1.80326e15	−1.74261
$538$	−8.81280e14	−0.842969
$539$	−2.19891e14	−0.208194
$540$	−3.11825e12	−0.00292244
$541$	4.56696e14	0.423684	0.211842	−	0.977304i	$-0.432054\pi$
$541$	4.56696e14	0.423684	0.211842	+	0.977304i	$0.432054\pi$
$542$	−4.50949e14	−0.414125
$543$	1.52805e15	1.38911
$544$	−9.95479e13	−0.0895856
$545$	−6.62172e14	−0.589916
$546$	−1.06034e15	−0.935161
$547$	−6.82824e13	−0.0596182	−0.0298091	−	0.999556i	$-0.509490\pi$
$547$	−6.82824e13	−0.0596182	−0.0298091	+	0.999556i	$0.509490\pi$
$548$	−4.17204e14	−0.360624
$549$	−1.26290e15	−1.08074
$550$	−2.40944e13	−0.0204137
$551$	2.14949e13	0.0180302
$552$	−1.41698e15	−1.17679
$553$	2.00072e15	1.64512
$554$	−7.64879e14	−0.622714
$555$	−2.38863e15	−1.92547
$556$	5.63946e14	0.450118
$557$	3.28321e14	0.259475	0.129737	−	0.991548i	$-0.458587\pi$
$557$	3.28321e14	0.259475	0.129737	+	0.991548i	$0.458587\pi$
$558$	−8.20492e14	−0.642076
$559$	1.37839e15	1.06809
$560$	−4.45044e14	−0.341483
$561$	1.47271e13	0.0111898
$562$	−1.82384e14	−0.137226
$563$	−7.71171e14	−0.574585	−0.287293	−	0.957843i	$-0.592755\pi$
$563$	−7.71171e14	−0.574585	−0.287293	+	0.957843i	$0.592755\pi$
$564$	1.46973e15	1.08443
$565$	−3.57278e14	−0.261059
$566$	1.29960e15	0.940412
$567$	−2.51664e15	−1.80349
$568$	−1.89162e15	−1.34251
$569$	2.18238e15	1.53396	0.766978	−	0.641674i	$-0.221760\pi$
$569$	2.18238e15	1.53396	0.766978	+	0.641674i	$0.221760\pi$
$570$	−7.86024e13	−0.0547172
$571$	8.46547e14	0.583650	0.291825	−	0.956472i	$-0.405738\pi$
$571$	8.46547e14	0.583650	0.291825	+	0.956472i	$0.405738\pi$
$572$	−6.73877e13	−0.0460153
$573$	2.21556e15	1.49842
$574$	−9.71593e14	−0.650832
$575$	−5.88455e14	−0.390427
$576$	4.50966e14	0.296360
$577$	−1.61690e15	−1.05249	−0.526244	−	0.850334i	$-0.676400\pi$
$577$	−1.61690e15	−1.05249	−0.526244	+	0.850334i	$0.676400\pi$
$578$	8.08343e14	0.521186
$579$	−2.28201e14	−0.145742
$580$	1.61175e14	0.101963
$581$	−3.55297e15	−2.22650
$582$	−1.68955e15	−1.04881
$583$	4.07580e13	0.0250631
$584$	5.47096e14	0.333267
$585$	8.76380e14	0.528853
$586$	9.93124e13	0.0593700
$587$	8.67880e14	0.513985	0.256992	−	0.966413i	$-0.417268\pi$
$587$	8.67880e14	0.513985	0.256992	+	0.966413i	$0.417268\pi$
$588$	3.97930e15	2.33470
$589$	2.03488e14	0.118278
$590$	8.31239e13	0.0478674
$591$	−3.82157e15	−2.18027
$592$	−7.89764e14	−0.446404
$593$	2.67501e15	1.49804	0.749022	−	0.662546i	$-0.230524\pi$
$593$	2.67501e15	1.49804	0.749022	+	0.662546i	$0.230524\pi$
$594$	−4.60504e11	−0.000255510 0
$595$	−2.15871e14	−0.118673
$596$	−2.58279e15	−1.40681
$597$	1.10409e15	0.595864
$598$	6.26595e14	0.335066
$599$	4.64308e14	0.246013	0.123007	−	0.992406i	$-0.460746\pi$
$599$	4.64308e14	0.246013	0.123007	+	0.992406i	$0.460746\pi$
$600$	1.03807e15	0.544995
$601$	4.46744e14	0.232407	0.116203	−	0.993225i	$-0.462928\pi$
$601$	4.46744e14	0.232407	0.116203	+	0.993225i	$0.462928\pi$
$602$	2.83427e15	1.46103
$603$	1.47103e14	0.0751408
$604$	2.47937e15	1.25499
$605$	1.49885e15	0.751804
$606$	−3.57065e14	−0.177480
$607$	3.59594e15	1.77123	0.885614	−	0.464423i	$-0.153738\pi$
$607$	3.59594e15	1.77123	0.885614	+	0.464423i	$0.153738\pi$
$608$	−2.06093e14	−0.100599
$609$	−9.83729e14	−0.475861
$610$	−8.94141e14	−0.428639
$611$	−1.54728e15	−0.735094
$612$	−1.33506e14	−0.0628591
$613$	1.78311e15	0.832044	0.416022	−	0.909355i	$-0.363424\pi$
$613$	1.78311e15	0.832044	0.416022	+	0.909355i	$0.363424\pi$
$614$	4.41304e14	0.204085
$615$	1.60305e15	0.734740
$616$	−3.29881e14	−0.149852
$617$	−4.04190e14	−0.181977	−0.0909885	−	0.995852i	$-0.529003\pi$
$617$	−4.04190e14	−0.181977	−0.0909885	+	0.995852i	$0.529003\pi$
$618$	4.46606e14	0.199291
$619$	4.73653e14	0.209489	0.104745	−	0.994499i	$-0.466597\pi$
$619$	4.73653e14	0.209489	0.104745	+	0.994499i	$0.466597\pi$
$620$	1.52582e15	0.668880
$621$	−1.12468e13	−0.00488682
$622$	1.32618e15	0.571158
$623$	−6.00415e15	−2.56311
$624$	5.78437e14	0.244760
$625$	−9.39282e14	−0.393963
$626$	−1.11096e15	−0.461892
$627$	3.04893e13	0.0125654
$628$	2.69462e15	1.10083
$629$	−3.83079e14	−0.155135
$630$	1.80202e15	0.723415
$631$	4.25063e13	0.0169158	0.00845789	−	0.999964i	$-0.497308\pi$
$631$	4.25063e13	0.0169158	0.00845789	+	0.999964i	$0.497308\pi$
$632$	2.08564e15	0.822801
$633$	1.78958e15	0.699893
$634$	1.71353e15	0.664355
$635$	2.13084e15	0.819020
$636$	−7.37584e14	−0.281059
$637$	−4.18926e15	−1.58260
$638$	2.38024e13	0.00891469
$639$	−4.00819e15	−1.48831
$640$	−1.81441e15	−0.667952
$641$	4.20206e15	1.53371	0.766855	−	0.641820i	$-0.221820\pi$
$641$	4.20206e15	1.53371	0.766855	+	0.641820i	$0.221820\pi$
$642$	3.55155e15	1.28521
$643$	2.82129e15	1.01225	0.506125	−	0.862460i	$-0.331077\pi$
$643$	2.82129e15	1.01225	0.506125	+	0.862460i	$0.331077\pi$
$644$	−3.38412e15	−1.20385
$645$	−4.67631e15	−1.64939
$646$	−1.26059e13	−0.00440856
$647$	8.24863e14	0.286028	0.143014	−	0.989721i	$-0.454321\pi$
$647$	8.24863e14	0.286028	0.143014	+	0.989721i	$0.454321\pi$
$648$	−2.62346e15	−0.902011
$649$	−3.22432e13	−0.0109924
$650$	−4.59036e14	−0.155176
$651$	−9.31278e15	−3.12165
$652$	−1.60000e15	−0.531811
$653$	3.50926e14	0.115663	0.0578313	−	0.998326i	$-0.481581\pi$
$653$	3.50926e14	0.115663	0.0578313	+	0.998326i	$0.481581\pi$
$654$	1.76967e15	0.578382
$655$	3.58303e15	1.16124
$656$	5.30023e14	0.170343
$657$	1.15925e15	0.369461
$658$	−3.18154e15	−1.00553
$659$	1.10967e15	0.347796	0.173898	−	0.984764i	$-0.444364\pi$
$659$	1.10967e15	0.347796	0.173898	+	0.984764i	$0.444364\pi$
$660$	2.28618e14	0.0710591
$661$	−2.41663e15	−0.744908	−0.372454	−	0.928051i	$-0.621483\pi$
$661$	−2.41663e15	−0.744908	−0.372454	+	0.928051i	$0.621483\pi$
$662$	−1.87743e15	−0.573911
$663$	2.80574e14	0.0850596
$664$	−3.70377e15	−1.11358
$665$	−4.46915e14	−0.133262
$666$	3.19782e15	0.945685
$667$	5.81322e14	0.170500
$668$	3.14519e15	0.914907
$669$	4.20672e14	0.121367
$670$	1.04150e14	0.0298021
$671$	3.46831e14	0.0984338
$672$	9.43199e15	2.65505
$673$	4.93288e15	1.37727	0.688633	−	0.725110i	$-0.258211\pi$
$673$	4.93288e15	1.37727	0.688633	+	0.725110i	$0.258211\pi$
$674$	1.16428e15	0.322425
$675$	8.23929e12	0.00226318
$676$	1.37444e15	0.374471
$677$	−5.77963e15	−1.56193	−0.780967	−	0.624573i	$-0.785273\pi$
$677$	−5.77963e15	−1.56193	−0.780967	+	0.624573i	$0.785273\pi$
$678$	9.54833e14	0.255955
$679$	−9.60640e15	−2.55433
$680$	−2.25034e14	−0.0593539
$681$	−1.89999e15	−0.497097
$682$	2.25333e14	0.0584804
$683$	2.53598e15	0.652879	0.326439	−	0.945218i	$-0.394151\pi$
$683$	2.53598e15	0.652879	0.326439	+	0.945218i	$0.394151\pi$
$684$	−2.76396e14	−0.0705867
$685$	−1.49008e15	−0.377495
$686$	−4.83142e15	−1.21421
$687$	6.13511e15	1.52954
$688$	−1.54615e15	−0.382397
$689$	7.76502e14	0.190518
$690$	−2.12578e15	−0.517426
$691$	−3.34143e15	−0.806870	−0.403435	−	0.915008i	$-0.632184\pi$
$691$	−3.34143e15	−0.806870	−0.403435	+	0.915008i	$0.632184\pi$
$692$	−1.55658e14	−0.0372897
$693$	−6.98993e14	−0.166127
$694$	−3.18479e15	−0.750937
$695$	2.01418e15	0.471176
$696$	−1.02548e15	−0.238000
$697$	2.57091e14	0.0591979
$698$	2.94196e15	0.672096
$699$	3.68931e15	0.836220
$700$	2.47916e15	0.557527
$701$	−6.59658e15	−1.47187	−0.735935	−	0.677052i	$-0.763257\pi$
$701$	−6.59658e15	−1.47187	−0.735935	+	0.677052i	$0.763257\pi$
$702$	−8.77332e12	−0.00194227
$703$	−7.93084e14	−0.174207
$704$	−1.23849e14	−0.0269925
$705$	5.24929e15	1.13517
$706$	−1.97435e14	−0.0423642
$707$	−2.03019e15	−0.432245
$708$	5.83495e14	0.123269
$709$	−4.27161e15	−0.895442	−0.447721	−	0.894173i	$-0.647764\pi$
$709$	−4.27161e15	−0.895442	−0.447721	+	0.894173i	$0.647764\pi$
$710$	−2.83783e15	−0.590289
$711$	4.41930e15	0.912159
$712$	−6.25900e15	−1.28193
$713$	5.50327e15	1.11848
$714$	5.76921e14	0.116353
$715$	−2.40681e14	−0.0481681
$716$	−4.48944e15	−0.891601
$717$	−8.26553e14	−0.162898
$718$	4.76423e15	0.931769
$719$	8.99730e15	1.74624	0.873118	−	0.487508i	$-0.162094\pi$
$719$	8.99730e15	1.74624	0.873118	+	0.487508i	$0.162094\pi$
$720$	−9.83040e14	−0.189340
$721$	2.53930e15	0.485367
$722$	2.74216e15	0.520161
$723$	−4.97226e15	−0.936038
$724$	3.80426e15	0.710735
$725$	−4.25869e14	−0.0789618
$726$	−4.00572e15	−0.737105
$727$	−2.23564e14	−0.0408284	−0.0204142	−	0.999792i	$-0.506499\pi$
$727$	−2.23564e14	−0.0408284	−0.0204142	+	0.999792i	$0.506499\pi$
$728$	−6.28475e15	−1.13911
$729$	−5.60079e15	−1.00751
$730$	8.20760e14	0.146535
$731$	−7.49968e14	−0.132892
$732$	−6.27650e15	−1.10384
$733$	−3.48936e15	−0.609079	−0.304539	−	0.952500i	$-0.598503\pi$
$733$	−3.48936e15	−0.609079	−0.304539	+	0.952500i	$0.598503\pi$
$734$	−3.22628e14	−0.0558951
$735$	1.42124e16	2.44393
$736$	−5.57371e15	−0.951298
$737$	−4.03990e13	−0.00684384
$738$	−2.14611e15	−0.360863
$739$	−1.54307e15	−0.257539	−0.128769	−	0.991675i	$-0.541103\pi$
$739$	−1.54307e15	−0.257539	−0.128769	+	0.991675i	$0.541103\pi$
$740$	−5.94679e15	−0.985163
$741$	5.80869e14	0.0955164
$742$	1.59665e15	0.260609
$743$	2.64447e15	0.428450	0.214225	−	0.976784i	$-0.431277\pi$
$743$	2.64447e15	0.428450	0.214225	+	0.976784i	$0.431277\pi$
$744$	−9.70807e15	−1.56128
$745$	−9.22468e15	−1.47262
$746$	1.01675e15	0.161120
$747$	−7.84800e15	−1.23451
$748$	3.66649e13	0.00572522
$749$	2.01933e16	3.13009
$750$	5.21968e15	0.803169
$751$	−7.20106e15	−1.09996	−0.549980	−	0.835178i	$-0.685365\pi$
$751$	−7.20106e15	−1.09996	−0.549980	+	0.835178i	$0.685365\pi$
$752$	1.73560e15	0.263178
$753$	1.18854e16	1.78913
$754$	4.53472e14	0.0677654
$755$	8.85530e15	1.31370
$756$	4.73830e13	0.00697834
$757$	−7.11377e15	−1.04009	−0.520047	−	0.854138i	$-0.674086\pi$
$757$	−7.11377e15	−1.04009	−0.520047	+	0.854138i	$0.674086\pi$
$758$	2.13324e15	0.309641
$759$	8.24575e14	0.118823
$760$	−4.65884e14	−0.0666505
$761$	−7.35766e15	−1.04502	−0.522509	−	0.852634i	$-0.675004\pi$
$761$	−7.35766e15	−1.04502	−0.522509	+	0.852634i	$0.675004\pi$
$762$	−5.69471e15	−0.803007
$763$	1.00619e16	1.40863
$764$	5.51590e15	0.766660
$765$	−4.76829e14	−0.0657999
$766$	3.70914e15	0.508177
$767$	−6.14282e14	−0.0835591
$768$	7.94362e15	1.07283
$769$	−5.70882e15	−0.765511	−0.382756	−	0.923850i	$-0.625025\pi$
$769$	−5.70882e15	−0.765511	−0.382756	+	0.923850i	$0.625025\pi$
$770$	−4.94892e14	−0.0658888
$771$	1.01736e16	1.34485
$772$	−5.68135e14	−0.0745687
$773$	−2.55574e15	−0.333065	−0.166533	−	0.986036i	$-0.553257\pi$
$773$	−2.55574e15	−0.333065	−0.166533	+	0.986036i	$0.553257\pi$
$774$	6.26050e15	0.810090
$775$	−4.03163e15	−0.517990
$776$	−1.00141e16	−1.27754
$777$	3.62961e16	4.59774
$778$	−1.57998e15	−0.198730
$779$	5.32251e14	0.0664753
$780$	4.35554e15	0.540159
$781$	1.10077e15	0.135556
$782$	−3.40924e14	−0.0416889
$783$	−8.13942e12	−0.000988334 0
$784$	4.69912e15	0.566602
$785$	9.62407e15	1.15233
$786$	−9.57573e15	−1.13854
$787$	1.39857e16	1.65129	0.825643	−	0.564193i	$-0.190813\pi$
$787$	1.39857e16	1.65129	0.825643	+	0.564193i	$0.190813\pi$
$788$	−9.51427e15	−1.11553
$789$	−1.47648e15	−0.171911
$790$	3.12890e15	0.361778
$791$	5.42896e15	0.623370
$792$	−7.28662e14	−0.0830878
$793$	6.60767e15	0.748248
$794$	−1.85645e15	−0.208771
$795$	−2.63435e15	−0.294208
$796$	2.74878e15	0.304872
$797$	1.33077e15	0.146582	0.0732912	−	0.997311i	$-0.476650\pi$
$797$	1.33077e15	0.146582	0.0732912	+	0.997311i	$0.476650\pi$
$798$	1.19439e15	0.130656
$799$	8.41860e14	0.0914603
$800$	4.08323e15	0.440564
$801$	−1.32623e16	−1.42115
$802$	−9.39417e15	−0.999769
$803$	−3.18367e14	−0.0336506
$804$	7.31089e14	0.0767471
$805$	−1.20867e16	−1.26017
$806$	4.29294e15	0.444541
$807$	−2.20947e16	−2.27239
$808$	−2.11636e15	−0.216186
$809$	−1.93263e15	−0.196079	−0.0980396	−	0.995183i	$-0.531257\pi$
$809$	−1.93263e15	−0.196079	−0.0980396	+	0.995183i	$0.531257\pi$
$810$	−3.93574e15	−0.396606
$811$	−2.88987e15	−0.289243	−0.144622	−	0.989487i	$-0.546196\pi$
$811$	−2.88987e15	−0.289243	−0.144622	+	0.989487i	$0.546196\pi$
$812$	−2.44911e15	−0.243473
$813$	−1.13058e16	−1.11636
$814$	−8.78223e14	−0.0861332
$815$	−5.71453e15	−0.556691
$816$	−3.14722e14	−0.0304531
$817$	−1.55265e15	−0.149228
$818$	9.96710e15	0.951537
$819$	−1.33169e16	−1.26282
$820$	3.99098e15	0.375927
$821$	−1.15152e16	−1.07742	−0.538710	−	0.842491i	$-0.681088\pi$
$821$	−1.15152e16	−1.07742	−0.538710	+	0.842491i	$0.681088\pi$
$822$	3.98228e15	0.370115
$823$	2.15934e15	0.199353	0.0996763	−	0.995020i	$-0.468219\pi$
$823$	2.15934e15	0.199353	0.0996763	+	0.995020i	$0.468219\pi$
$824$	2.64708e15	0.242755
$825$	−6.04073e14	−0.0550292
$826$	−1.26310e15	−0.114300
$827$	9.76712e15	0.877984	0.438992	−	0.898491i	$-0.355336\pi$
$827$	9.76712e15	0.877984	0.438992	+	0.898491i	$0.355336\pi$
$828$	−7.47504e15	−0.667493
$829$	1.75825e16	1.55966	0.779831	−	0.625991i	$-0.215305\pi$
$829$	1.75825e16	1.55966	0.779831	+	0.625991i	$0.215305\pi$
$830$	−5.55644e15	−0.489629
$831$	−1.91763e16	−1.67865
$832$	−2.35952e15	−0.205185
$833$	2.27933e15	0.196907
$834$	−5.38295e15	−0.461963
$835$	1.12333e16	0.957709
$836$	7.59069e13	0.00642905
$837$	−7.70544e13	−0.00648347
$838$	−2.78005e15	−0.232387
$839$	−6.59993e15	−0.548085	−0.274043	−	0.961718i	$-0.588361\pi$
$839$	−6.59993e15	−0.548085	−0.274043	+	0.961718i	$0.588361\pi$
$840$	2.13216e16	1.75907
$841$	4.20707e14	0.0344828
$842$	1.15403e16	0.939724
$843$	−4.57257e15	−0.369921
$844$	4.45539e15	0.358098
$845$	4.90892e15	0.391989
$846$	−7.02758e15	−0.557531
$847$	−2.27756e16	−1.79519
$848$	−8.71007e14	−0.0682094
$849$	3.25823e16	2.53507
$850$	2.49757e14	0.0193069
$851$	−2.14487e16	−1.64736
$852$	−1.99204e16	−1.52013
$853$	1.50817e14	0.0114349	0.00571744	−	0.999984i	$-0.498180\pi$
$853$	1.50817e14	0.0114349	0.00571744	+	0.999984i	$0.498180\pi$
$854$	1.35868e16	1.02352
$855$	−9.87173e14	−0.0738889
$856$	2.10504e16	1.56550
$857$	1.33286e16	0.984894	0.492447	−	0.870343i	$-0.336103\pi$
$857$	1.33286e16	0.984894	0.492447	+	0.870343i	$0.336103\pi$
$858$	6.43226e14	0.0472263
$859$	−8.76363e15	−0.639325	−0.319662	−	0.947532i	$-0.603569\pi$
$859$	−8.76363e15	−0.639325	−0.319662	+	0.947532i	$0.603569\pi$
$860$	−1.16422e16	−0.843908
$861$	−2.43589e16	−1.75445
$862$	−3.41526e15	−0.244418
$863$	−2.04820e16	−1.45651	−0.728256	−	0.685305i	$-0.759669\pi$
$863$	−2.04820e16	−1.45651	−0.728256	+	0.685305i	$0.759669\pi$
$864$	7.80407e13	0.00551437
$865$	−5.55949e14	−0.0390343
$866$	−7.46147e15	−0.520567
$867$	2.02660e16	1.40496
$868$	−2.31853e16	−1.59718
$869$	−1.21368e15	−0.0830796
$870$	−1.53844e15	−0.104647
$871$	−7.69664e14	−0.0520237
$872$	1.04890e16	0.704521
$873$	−2.12192e16	−1.41628
$874$	−7.05810e14	−0.0468139
$875$	2.96779e16	1.95609
$876$	5.76139e15	0.377359
$877$	−2.58409e16	−1.68194	−0.840969	−	0.541083i	$-0.818014\pi$
$877$	−2.58409e16	−1.68194	−0.840969	+	0.541083i	$0.818014\pi$
$878$	1.11618e16	0.721959
$879$	2.48987e15	0.160043
$880$	2.69974e14	0.0172451
$881$	−2.22834e15	−0.141453	−0.0707267	−	0.997496i	$-0.522532\pi$
$881$	−2.22834e15	−0.141453	−0.0707267	+	0.997496i	$0.522532\pi$
$882$	−1.90272e16	−1.20032
$883$	5.86667e15	0.367797	0.183898	−	0.982945i	$-0.441128\pi$
$883$	5.86667e15	0.367797	0.183898	+	0.982945i	$0.441128\pi$
$884$	6.98524e14	0.0435205
$885$	2.08401e15	0.129036
$886$	4.42941e15	0.272559
$887$	1.54439e16	0.944443	0.472221	−	0.881480i	$-0.343452\pi$
$887$	1.54439e16	0.944443	0.472221	+	0.881480i	$0.343452\pi$
$888$	3.78367e16	2.29954
$889$	−3.23788e16	−1.95569
$890$	−9.38983e15	−0.563654
$891$	1.52665e15	0.0910776
$892$	1.04731e15	0.0620970
$893$	1.74289e15	0.102704
$894$	2.46532e16	1.44383
$895$	−1.60344e16	−0.933313
$896$	2.75706e16	1.59497
$897$	1.57094e16	0.903237
$898$	2.38337e15	0.136199
$899$	3.98276e15	0.226207
$900$	5.47612e15	0.309129
$901$	−4.22487e14	−0.0237043
$902$	5.89389e14	0.0328675
$903$	7.10581e16	3.93850
$904$	5.65939e15	0.311776
$905$	1.35872e16	0.743985
$906$	−2.36660e16	−1.28801
$907$	−1.11131e16	−0.601165	−0.300583	−	0.953756i	$-0.597181\pi$
$907$	−1.11131e16	−0.601165	−0.300583	+	0.953756i	$0.597181\pi$
$908$	−4.73025e15	−0.254338
$909$	−4.48441e15	−0.239664
$910$	−9.42846e15	−0.500856
$911$	−3.61381e16	−1.90816	−0.954078	−	0.299559i	$-0.903161\pi$
$911$	−3.61381e16	−1.90816	−0.954078	+	0.299559i	$0.903161\pi$
$912$	−6.51564e14	−0.0341968
$913$	2.15531e15	0.112440
$914$	−5.84016e15	−0.302845
$915$	−2.24171e16	−1.15548
$916$	1.52741e16	0.782583
$917$	−5.44454e16	−2.77287
$918$	4.77347e12	0.000241657 0
$919$	1.56063e15	0.0785351	0.0392675	−	0.999229i	$-0.487498\pi$
$919$	1.56063e15	0.0785351	0.0392675	+	0.999229i	$0.487498\pi$
$920$	−1.25997e16	−0.630271
$921$	1.10640e16	0.550152
$922$	1.57682e16	0.779405
$923$	2.09714e16	1.03043
$924$	−3.47394e15	−0.169678
$925$	1.57131e16	0.762924
$926$	2.48122e15	0.119758
$927$	5.60895e15	0.269118
$928$	−4.03374e15	−0.192395
$929$	−3.93856e16	−1.86746	−0.933729	−	0.357982i	$-0.883465\pi$
$929$	−3.93856e16	−1.86746	−0.933729	+	0.357982i	$0.883465\pi$
$930$	−1.45642e16	−0.686482
$931$	4.71887e15	0.221113
$932$	9.18498e15	0.427849
$933$	3.32489e16	1.53967
$934$	1.61755e16	0.744646
$935$	1.30952e14	0.00599306
$936$	−1.38821e16	−0.631596
$937$	2.61331e16	1.18201	0.591007	−	0.806666i	$-0.298731\pi$
$937$	2.61331e16	1.18201	0.591007	+	0.806666i	$0.298731\pi$
$938$	−1.58259e15	−0.0711629
$939$	−2.78530e16	−1.24512
$940$	1.30687e16	0.580805
$941$	8.78306e15	0.388063	0.194032	−	0.980995i	$-0.437844\pi$
$941$	8.78306e15	0.388063	0.194032	+	0.980995i	$0.437844\pi$
$942$	−2.57206e16	−1.12980
$943$	1.43946e16	0.628615
$944$	6.89044e14	0.0299158
$945$	1.69233e14	0.00730481
$946$	−1.71933e15	−0.0737832
$947$	1.87878e16	0.801586	0.400793	−	0.916169i	$-0.368735\pi$
$947$	1.87878e16	0.801586	0.400793	+	0.916169i	$0.368735\pi$
$948$	2.19636e16	0.931659
$949$	−6.06539e15	−0.255796
$950$	5.17068e14	0.0216804
$951$	4.29600e16	1.79090
$952$	3.41947e15	0.141728
$953$	1.66665e16	0.686807	0.343404	−	0.939188i	$-0.388420\pi$
$953$	1.66665e16	0.686807	0.343404	+	0.939188i	$0.388420\pi$
$954$	3.52679e15	0.144498
$955$	1.97005e16	0.802527
$956$	−2.05781e15	−0.0833462
$957$	5.96751e14	0.0240313
$958$	1.37729e16	0.551462
$959$	2.26423e16	0.901401
$960$	8.00487e15	0.316857
$961$	1.22956e16	0.483918
$962$	−1.67315e16	−0.654745
$963$	4.46041e16	1.73552
$964$	−1.23790e16	−0.478921
$965$	−2.02915e15	−0.0780572
$966$	3.23019e16	1.23553
$967$	1.23857e16	0.471057	0.235528	−	0.971867i	$-0.424318\pi$
$967$	1.23857e16	0.471057	0.235528	+	0.971867i	$0.424318\pi$
$968$	−2.37423e16	−0.897860
$969$	−3.16045e14	−0.0118841
$970$	−1.50233e16	−0.561723
$971$	−2.59670e16	−0.965421	−0.482710	−	0.875780i	$-0.660348\pi$
$971$	−2.59670e16	−0.965421	−0.482710	+	0.875780i	$0.660348\pi$
$972$	−2.77316e16	−1.02520
$973$	−3.06062e16	−1.12510
$974$	−1.44820e16	−0.529363
$975$	−1.15085e16	−0.418306
$976$	−7.41186e15	−0.267888
$977$	−4.38632e16	−1.57645	−0.788225	−	0.615387i	$-0.789000\pi$
$977$	−4.38632e16	−1.57645	−0.788225	+	0.615387i	$0.789000\pi$
$978$	1.52722e16	0.545806
$979$	3.64225e15	0.129439
$980$	3.53836e16	1.25043
$981$	2.22254e16	0.781035
$982$	−8.24936e15	−0.288275
$983$	9.95512e15	0.345941	0.172971	−	0.984927i	$-0.444663\pi$
$983$	9.95512e15	0.345941	0.172971	+	0.984927i	$0.444663\pi$
$984$	−2.53928e16	−0.877480
$985$	−3.39811e16	−1.16772
$986$	−2.46729e14	−0.00843137
$987$	−7.97647e16	−2.71061
$988$	1.44614e15	0.0488707
$989$	−4.19909e16	−1.41116
$990$	−1.09315e15	−0.0365330
$991$	1.41215e16	0.469327	0.234663	−	0.972077i	$-0.424601\pi$
$991$	1.41215e16	0.469327	0.234663	+	0.972077i	$0.424601\pi$
$992$	−3.81867e16	−1.26211
$993$	−4.70692e16	−1.54709
$994$	4.31218e16	1.40952
$995$	9.81751e15	0.319135
$996$	−3.90039e16	−1.26090
$997$	−1.95475e16	−0.628445	−0.314223	−	0.949349i	$-0.601744\pi$
$997$	−1.95475e16	−0.628445	−0.314223	+	0.949349i	$0.601744\pi$
$998$	−2.07638e16	−0.663880
$999$	3.00316e14	0.00954922

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.12.a.a.1.4	✓	11
3.2	odd	2		261.12.a.a.1.8		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.12.a.a.1.4	✓	11	1.1	even	1	trivial
261.12.a.a.1.8		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)

\(f(q)\)	\(=\)	\(q-23.7638 q^{2} -595.785 q^{3} -1483.28 q^{4} -5297.67 q^{5} +14158.1 q^{6} +80499.9 q^{7} +83916.8 q^{8} +177813. q^{9} +O(q^{10})\)	\(q-23.7638 q^{2} -595.785 q^{3} -1483.28 q^{4} -5297.67 q^{5} +14158.1 q^{6} +80499.9 q^{7} +83916.8 q^{8} +177813. q^{9} +125893. q^{10} -48833.0 q^{11} +883716. q^{12} -930345. q^{13} -1.91299e6 q^{14} +3.15627e6 q^{15} +1.04357e6 q^{16} +506191. q^{17} -4.22552e6 q^{18} +1.04796e6 q^{19} +7.85793e6 q^{20} -4.79607e7 q^{21} +1.16046e6 q^{22} +2.83418e7 q^{23} -4.99964e7 q^{24} -2.07628e7 q^{25} +2.21086e7 q^{26} -396829. q^{27} -1.19404e8 q^{28} +2.05111e7 q^{29} -7.50052e7 q^{30} +1.94175e8 q^{31} -1.96661e8 q^{32} +2.90940e7 q^{33} -1.20290e7 q^{34} -4.26462e8 q^{35} -2.63747e8 q^{36} -7.56788e8 q^{37} -2.49035e7 q^{38} +5.54286e8 q^{39} -4.44563e8 q^{40} +5.07893e8 q^{41} +1.13973e9 q^{42} -1.48159e9 q^{43} +7.24330e7 q^{44} -9.41995e8 q^{45} -6.73509e8 q^{46} +1.66313e9 q^{47} -6.21745e8 q^{48} +4.50291e9 q^{49} +4.93404e8 q^{50} -3.01581e8 q^{51} +1.37996e9 q^{52} -8.34639e8 q^{53} +9.43018e6 q^{54} +2.58701e8 q^{55} +6.75530e9 q^{56} -6.24359e8 q^{57} -4.87424e8 q^{58} +6.60274e8 q^{59} -4.68164e9 q^{60} -7.10239e9 q^{61} -4.61435e9 q^{62} +1.43139e10 q^{63} +2.53618e9 q^{64} +4.92866e9 q^{65} -6.91385e8 q^{66} +8.27289e8 q^{67} -7.50823e8 q^{68} -1.68856e10 q^{69} +1.01344e10 q^{70} -2.25416e10 q^{71} +1.49215e10 q^{72} +6.51950e9 q^{73} +1.79842e10 q^{74} +1.23702e10 q^{75} -1.55442e9 q^{76} -3.93106e9 q^{77} -1.31720e10 q^{78} +2.48536e10 q^{79} -5.52851e9 q^{80} -3.12626e10 q^{81} -1.20695e10 q^{82} -4.41362e10 q^{83} +7.11391e10 q^{84} -2.68163e9 q^{85} +3.52083e10 q^{86} -1.22202e10 q^{87} -4.09791e9 q^{88} -7.45858e10 q^{89} +2.23854e10 q^{90} -7.48927e10 q^{91} -4.20388e10 q^{92} -1.15687e11 q^{93} -3.95223e10 q^{94} -5.55174e9 q^{95} +1.17168e11 q^{96} -1.19334e11 q^{97} -1.07007e11 q^{98} -8.68315e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 32 q^{2} - 982 q^{3} + 9146 q^{4} - 2740 q^{5} - 28202 q^{6} - 49432 q^{7} - 150054 q^{8} + 330749 q^{9}+O(q^{10}) \) 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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