LMFDB - Embedded newform 29.10.a.b.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,10,Mod(1,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	29.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

Embedding invariants

Embedding label			1.11
Root			$38.0522$ 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)

$f(q)$	$=$	$q+39.0522 q^{2} -174.323 q^{3} +1013.08 q^{4} -303.923 q^{5} -6807.72 q^{6} +12556.4 q^{7} +19568.2 q^{8} +10705.6 q^{9} +O(q^{10})$	\(q+39.0522 q^{2} -174.323 q^{3} +1013.08 q^{4} -303.923 q^{5} -6807.72 q^{6} +12556.4 q^{7} +19568.2 q^{8} +10705.6 q^{9} -11868.9 q^{10} +28063.9 q^{11} -176603. q^{12} +83047.1 q^{13} +490354. q^{14} +52980.9 q^{15} +245486. q^{16} +597701. q^{17} +418079. q^{18} -124401. q^{19} -307898. q^{20} -2.18887e6 q^{21} +1.09596e6 q^{22} -1.57076e6 q^{23} -3.41119e6 q^{24} -1.86076e6 q^{25} +3.24318e6 q^{26} +1.56496e6 q^{27} +1.27206e7 q^{28} +707281. q^{29} +2.06902e6 q^{30} -4.96942e6 q^{31} -432131. q^{32} -4.89219e6 q^{33} +2.33415e7 q^{34} -3.81617e6 q^{35} +1.08456e7 q^{36} +2.43062e6 q^{37} -4.85814e6 q^{38} -1.44771e7 q^{39} -5.94722e6 q^{40} -1.97239e6 q^{41} -8.54802e7 q^{42} +1.23208e7 q^{43} +2.84309e7 q^{44} -3.25369e6 q^{45} -6.13416e7 q^{46} -1.78585e7 q^{47} -4.27940e7 q^{48} +1.17309e8 q^{49} -7.26667e7 q^{50} -1.04193e8 q^{51} +8.41332e7 q^{52} -5.50648e7 q^{53} +6.11154e7 q^{54} -8.52925e6 q^{55} +2.45705e8 q^{56} +2.16860e7 q^{57} +2.76209e7 q^{58} -4.75625e7 q^{59} +5.36737e7 q^{60} -1.26245e8 q^{61} -1.94067e8 q^{62} +1.34424e8 q^{63} -1.42565e8 q^{64} -2.52399e7 q^{65} -1.91051e8 q^{66} +2.95909e8 q^{67} +6.05517e8 q^{68} +2.73820e8 q^{69} -1.49030e8 q^{70} -1.79164e8 q^{71} +2.09490e8 q^{72} +1.11462e8 q^{73} +9.49211e7 q^{74} +3.24373e8 q^{75} -1.26028e8 q^{76} +3.52380e8 q^{77} -5.65361e8 q^{78} -4.73010e8 q^{79} -7.46089e7 q^{80} -4.83529e8 q^{81} -7.70264e7 q^{82} +8.41522e8 q^{83} -2.21749e9 q^{84} -1.81655e8 q^{85} +4.81154e8 q^{86} -1.23296e8 q^{87} +5.49159e8 q^{88} -9.29254e7 q^{89} -1.27064e8 q^{90} +1.04277e9 q^{91} -1.59130e9 q^{92} +8.66286e8 q^{93} -6.97413e8 q^{94} +3.78083e7 q^{95} +7.53305e7 q^{96} +3.59182e8 q^{97} +4.58116e9 q^{98} +3.00441e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 16 q^{2} + 242 q^{3} + 3498 q^{4} + 1762 q^{5} + 5446 q^{6} + 12080 q^{7} + 25350 q^{8} + 43026 q^{9}+O(q^{10}) $ 12 * q + 16 * q^2 + 242 * q^3 + 3498 * q^4 + 1762 * q^5 + 5446 * q^6 + 12080 * q^7 + 25350 * q^8 + 43026 * q^9	\( 12 q + 16 q^{2} + 242 q^{3} + 3498 q^{4} + 1762 q^{5} + 5446 q^{6} + 12080 q^{7} + 25350 q^{8} + 43026 q^{9} - 46678 q^{10} + 24474 q^{11} - 14210 q^{12} + 107722 q^{13} + 677768 q^{14} + 505426 q^{15} + 1656882 q^{16} + 982120 q^{17} + 2364102 q^{18} + 2084360 q^{19} + 4689410 q^{20} + 2911344 q^{21} + 2725230 q^{22} + 3004004 q^{23} + 7893170 q^{24} + 6339542 q^{25} + 6863698 q^{26} + 7881014 q^{27} + 5116944 q^{28} + 8487372 q^{29} + 10924626 q^{30} + 17872478 q^{31} + 5122946 q^{32} - 860442 q^{33} + 15662848 q^{34} - 22252312 q^{35} - 35199980 q^{36} + 452980 q^{37} - 68665276 q^{38} - 29528222 q^{39} - 61623214 q^{40} - 69039804 q^{41} - 150603216 q^{42} + 5379186 q^{43} - 58283762 q^{44} - 63687756 q^{45} - 76817844 q^{46} - 49104062 q^{47} - 99120062 q^{48} + 73113148 q^{49} - 281373726 q^{50} + 1578252 q^{51} - 49849646 q^{52} + 2253998 q^{53} - 166064634 q^{54} + 82907066 q^{55} + 119369464 q^{56} + 69024164 q^{57} + 11316496 q^{58} + 51587572 q^{59} - 107912622 q^{60} + 251179296 q^{61} + 2421010 q^{62} + 573206808 q^{63} + 460030950 q^{64} + 301434554 q^{65} + 305189958 q^{66} + 741046264 q^{67} + 503103116 q^{68} + 1480618500 q^{69} + 666826600 q^{70} + 488700124 q^{71} + 243154096 q^{72} + 1432375020 q^{73} - 208138340 q^{74} + 462882236 q^{75} - 253709644 q^{76} + 406327616 q^{77} - 1244370462 q^{78} + 400834638 q^{79} - 440320610 q^{80} + 207205984 q^{81} - 1992598260 q^{82} + 1525085236 q^{83} - 2191854376 q^{84} - 387675996 q^{85} - 3425646378 q^{86} + 171162002 q^{87} - 3147673814 q^{88} + 691159332 q^{89} - 2412410836 q^{90} + 1569278264 q^{91} - 2491626380 q^{92} + 270455138 q^{93} - 4397366402 q^{94} + 236293724 q^{95} - 1448270346 q^{96} + 2494422276 q^{97} - 3443098784 q^{98} + 2123567852 q^{99}+O(q^{100}) \) 12 * q + 16 * q^2 + 242 * q^3 + 3498 * q^4 + 1762 * q^5 + 5446 * q^6 + 12080 * q^7 + 25350 * q^8 + 43026 * q^9 - 46678 * q^10 + 24474 * q^11 - 14210 * q^12 + 107722 * q^13 + 677768 * q^14 + 505426 * q^15 + 1656882 * q^16 + 982120 * q^17 + 2364102 * q^18 + 2084360 * q^19 + 4689410 * q^20 + 2911344 * q^21 + 2725230 * q^22 + 3004004 * q^23 + 7893170 * q^24 + 6339542 * q^25 + 6863698 * q^26 + 7881014 * q^27 + 5116944 * q^28 + 8487372 * q^29 + 10924626 * q^30 + 17872478 * q^31 + 5122946 * q^32 - 860442 * q^33 + 15662848 * q^34 - 22252312 * q^35 - 35199980 * q^36 + 452980 * q^37 - 68665276 * q^38 - 29528222 * q^39 - 61623214 * q^40 - 69039804 * q^41 - 150603216 * q^42 + 5379186 * q^43 - 58283762 * q^44 - 63687756 * q^45 - 76817844 * q^46 - 49104062 * q^47 - 99120062 * q^48 + 73113148 * q^49 - 281373726 * q^50 + 1578252 * q^51 - 49849646 * q^52 + 2253998 * q^53 - 166064634 * q^54 + 82907066 * q^55 + 119369464 * q^56 + 69024164 * q^57 + 11316496 * q^58 + 51587572 * q^59 - 107912622 * q^60 + 251179296 * q^61 + 2421010 * q^62 + 573206808 * q^63 + 460030950 * q^64 + 301434554 * q^65 + 305189958 * q^66 + 741046264 * q^67 + 503103116 * q^68 + 1480618500 * q^69 + 666826600 * q^70 + 488700124 * q^71 + 243154096 * q^72 + 1432375020 * q^73 - 208138340 * q^74 + 462882236 * q^75 - 253709644 * q^76 + 406327616 * q^77 - 1244370462 * q^78 + 400834638 * q^79 - 440320610 * q^80 + 207205984 * q^81 - 1992598260 * q^82 + 1525085236 * q^83 - 2191854376 * q^84 - 387675996 * q^85 - 3425646378 * q^86 + 171162002 * q^87 - 3147673814 * q^88 + 691159332 * q^89 - 2412410836 * q^90 + 1569278264 * q^91 - 2491626380 * q^92 + 270455138 * q^93 - 4397366402 * q^94 + 236293724 * q^95 - 1448270346 * q^96 + 2494422276 * q^97 - 3443098784 * q^98 + 2123567852 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	39.0522	1.72588	0.862941	−	0.505305i	$-0.168620\pi$
$2$	39.0522	1.72588	0.862941	+	0.505305i	$0.168620\pi$
$3$	−174.323	−1.24254	−0.621269	−	0.783597i	$-0.713383\pi$
$3$	−174.323	−1.24254	−0.621269	+	0.783597i	$0.713383\pi$
$4$	1013.08	1.97867
$5$	−303.923	−0.217470	−0.108735	−	0.994071i	$-0.534680\pi$
$5$	−303.923	−0.217470	−0.108735	+	0.994071i	$0.534680\pi$
$6$	−6807.72	−2.14447
$7$	12556.4	1.97662	0.988309	−	0.152466i	$-0.0487214\pi$
$7$	12556.4	1.97662	0.988309	+	0.152466i	$0.0487214\pi$
$8$	19568.2	1.68906
$9$	10705.6	0.543903
$10$	−11868.9	−0.375327
$11$	28063.9	0.577937	0.288968	−	0.957339i	$-0.406688\pi$
$11$	28063.9	0.577937	0.288968	+	0.957339i	$0.406688\pi$
$12$	−176603.	−2.45857
$13$	83047.1	0.806454	0.403227	−	0.915100i	$-0.367889\pi$
$13$	83047.1	0.806454	0.403227	+	0.915100i	$0.367889\pi$
$14$	490354.	3.41141
$15$	52980.9	0.270214
$16$	245486.	0.936455
$17$	597701.	1.73566	0.867828	−	0.496865i	$-0.165516\pi$
$17$	597701.	1.73566	0.867828	+	0.496865i	$0.165516\pi$
$18$	418079.	0.938711
$19$	−124401.	−0.218994	−0.109497	−	0.993987i	$-0.534924\pi$
$19$	−124401.	−0.218994	−0.109497	+	0.993987i	$0.534924\pi$
$20$	−307898.	−0.430300
$21$	−2.18887e6	−2.45602
$22$	1.09596e6	0.997450
$23$	−1.57076e6	−1.17040	−0.585200	−	0.810889i	$-0.698984\pi$
$23$	−1.57076e6	−1.17040	−0.585200	+	0.810889i	$0.698984\pi$
$24$	−3.41119e6	−2.09873
$25$	−1.86076e6	−0.952707
$26$	3.24318e6	1.39184
$27$	1.56496e6	0.566719
$28$	1.27206e7	3.91107
$29$	707281.	0.185695
$29$	707281.	0.185695
$30$	2.06902e6	0.466358
$31$	−4.96942e6	−0.966447	−0.483223	−	0.875497i	$-0.660534\pi$
$31$	−4.96942e6	−0.966447	−0.483223	+	0.875497i	$0.660534\pi$
$32$	−432131.	−0.0728518
$33$	−4.89219e6	−0.718109
$34$	2.33415e7	2.99554
$35$	−3.81617e6	−0.429854
$36$	1.08456e7	1.07620
$37$	2.43062e6	0.213211	0.106605	−	0.994301i	$-0.466002\pi$
$37$	2.43062e6	0.213211	0.106605	+	0.994301i	$0.466002\pi$
$38$	−4.85814e6	−0.377958
$39$	−1.44771e7	−1.00205
$40$	−5.94722e6	−0.367320
$41$	−1.97239e6	−0.109010	−0.0545050	−	0.998513i	$-0.517358\pi$
$41$	−1.97239e6	−0.109010	−0.0545050	+	0.998513i	$0.517358\pi$
$42$	−8.54802e7	−4.23881
$43$	1.23208e7	0.549579	0.274789	−	0.961504i	$-0.411392\pi$
$43$	1.23208e7	0.549579	0.274789	+	0.961504i	$0.411392\pi$
$44$	2.84309e7	1.14354
$45$	−3.25369e6	−0.118282
$46$	−6.13416e7	−2.01997
$47$	−1.78585e7	−0.533831	−0.266915	−	0.963720i	$-0.586004\pi$
$47$	−1.78585e7	−0.533831	−0.266915	+	0.963720i	$0.586004\pi$
$48$	−4.27940e7	−1.16358
$49$	1.17309e8	2.90702
$50$	−7.26667e7	−1.64426
$51$	−1.04193e8	−2.15662
$52$	8.41332e7	1.59570
$53$	−5.50648e7	−0.958589	−0.479294	−	0.877654i	$-0.659107\pi$
$53$	−5.50648e7	−0.958589	−0.479294	+	0.877654i	$0.659107\pi$
$54$	6.11154e7	0.978089
$55$	−8.52925e6	−0.125684
$56$	2.45705e8	3.33863
$57$	2.16860e7	0.272109
$58$	2.76209e7	0.320488
$59$	−4.75625e7	−0.511011	−0.255506	−	0.966808i	$-0.582242\pi$
$59$	−4.75625e7	−0.511011	−0.255506	+	0.966808i	$0.582242\pi$
$60$	5.36737e7	0.534664
$61$	−1.26245e8	−1.16743	−0.583713	−	0.811960i	$-0.698401\pi$
$61$	−1.26245e8	−1.16743	−0.583713	+	0.811960i	$0.698401\pi$
$62$	−1.94067e8	−1.66797
$63$	1.34424e8	1.07509
$64$	−1.42565e8	−1.06219
$65$	−2.52399e7	−0.175379
$66$	−1.91051e8	−1.23937
$67$	2.95909e8	1.79400	0.897000	−	0.442031i	$-0.145742\pi$
$67$	2.95909e8	1.79400	0.897000	+	0.442031i	$0.145742\pi$
$68$	6.05517e8	3.43428
$69$	2.73820e8	1.45427
$70$	−1.49030e8	−0.741877
$71$	−1.79164e8	−0.836733	−0.418367	−	0.908278i	$-0.637397\pi$
$71$	−1.79164e8	−0.836733	−0.418367	+	0.908278i	$0.637397\pi$
$72$	2.09490e8	0.918686
$73$	1.11462e8	0.459381	0.229690	−	0.973264i	$-0.426229\pi$
$73$	1.11462e8	0.459381	0.229690	+	0.973264i	$0.426229\pi$
$74$	9.49211e7	0.367976
$75$	3.24373e8	1.18378
$76$	−1.26028e8	−0.433316
$77$	3.52380e8	1.14236
$78$	−5.65361e8	−1.72942
$79$	−4.73010e8	−1.36631	−0.683153	−	0.730275i	$-0.739392\pi$
$79$	−4.73010e8	−1.36631	−0.683153	+	0.730275i	$0.739392\pi$
$80$	−7.46089e7	−0.203651
$81$	−4.83529e8	−1.24807
$82$	−7.70264e7	−0.188138
$83$	8.41522e8	1.94632	0.973160	−	0.230130i	$-0.0739152\pi$
$83$	8.41522e8	1.94632	0.973160	+	0.230130i	$0.0739152\pi$
$84$	−2.21749e9	−4.85965
$85$	−1.81655e8	−0.377452
$86$	4.81154e8	0.948508
$87$	−1.23296e8	−0.230734
$88$	5.49159e8	0.976172
$89$	−9.29254e7	−0.156993	−0.0784964	−	0.996914i	$-0.525012\pi$
$89$	−9.29254e7	−0.156993	−0.0784964	+	0.996914i	$0.525012\pi$
$90$	−1.27064e8	−0.204141
$91$	1.04277e9	1.59405
$92$	−1.59130e9	−2.31583
$93$	8.66286e8	1.20085
$94$	−6.97413e8	−0.921328
$95$	3.78083e7	0.0476246
$96$	7.53305e7	0.0905212
$97$	3.59182e8	0.411948	0.205974	−	0.978557i	$-0.433964\pi$
$97$	3.59182e8	0.411948	0.205974	+	0.978557i	$0.433964\pi$
$98$	4.58116e9	5.01717
$99$	3.00441e8	0.314341
$100$	−1.88509e9	−1.88509
$101$	−1.08571e9	−1.03817	−0.519085	−	0.854722i	$-0.673727\pi$
$101$	−1.08571e9	−1.03817	−0.519085	+	0.854722i	$0.673727\pi$
$102$	−4.06898e9	−3.72207
$103$	1.06363e9	0.931158	0.465579	−	0.885006i	$-0.345846\pi$
$103$	1.06363e9	0.931158	0.465579	+	0.885006i	$0.345846\pi$
$104$	1.62508e9	1.36215
$105$	6.65247e8	0.534110
$106$	−2.15040e9	−1.65441
$107$	−2.56239e8	−0.188981	−0.0944907	−	0.995526i	$-0.530122\pi$
$107$	−2.56239e8	−0.188981	−0.0944907	+	0.995526i	$0.530122\pi$
$108$	1.58543e9	1.12135
$109$	−1.84278e9	−1.25042	−0.625208	−	0.780458i	$-0.714986\pi$
$109$	−1.84278e9	−1.25042	−0.625208	+	0.780458i	$0.714986\pi$
$110$	−3.33086e8	−0.216915
$111$	−4.23713e8	−0.264922
$112$	3.08241e9	1.85101
$113$	−2.46261e9	−1.42083	−0.710415	−	0.703783i	$-0.751493\pi$
$113$	−2.46261e9	−1.42083	−0.710415	+	0.703783i	$0.751493\pi$
$114$	8.46887e8	0.469627
$115$	4.77389e8	0.254526
$116$	7.16530e8	0.367429
$117$	8.89072e8	0.438632
$118$	−1.85742e9	−0.881945
$119$	7.50495e9	3.43073
$120$	1.03674e9	0.456409
$121$	−1.57037e9	−0.665989
$122$	−4.93014e9	−2.01484
$123$	3.43834e8	0.135449
$124$	−5.03441e9	−1.91228
$125$	1.15913e9	0.424654
$126$	5.24955e9	1.85547
$127$	−1.18632e9	−0.404655	−0.202327	−	0.979318i	$-0.564851\pi$
$127$	−1.18632e9	−0.404655	−0.202327	+	0.979318i	$0.564851\pi$
$128$	−5.34622e9	−1.76036
$129$	−2.14780e9	−0.682873
$130$	−9.85676e8	−0.302684
$131$	2.44280e9	0.724716	0.362358	−	0.932039i	$-0.381972\pi$
$131$	2.44280e9	0.724716	0.362358	+	0.932039i	$0.381972\pi$
$132$	−4.95616e9	−1.42090
$133$	−1.56202e9	−0.432868
$134$	1.15559e10	3.09623
$135$	−4.75629e8	−0.123244
$136$	1.16959e10	2.93163
$137$	−3.67687e9	−0.891735	−0.445868	−	0.895099i	$-0.647105\pi$
$137$	−3.67687e9	−0.891735	−0.445868	+	0.895099i	$0.647105\pi$
$138$	1.06933e10	2.50989
$139$	1.21642e9	0.276387	0.138194	−	0.990405i	$-0.455870\pi$
$139$	1.21642e9	0.276387	0.138194	+	0.990405i	$0.455870\pi$
$140$	−3.86607e9	−0.850538
$141$	3.11315e9	0.663305
$142$	−6.99674e9	−1.44410
$143$	2.33062e9	0.466079
$144$	2.62808e9	0.509340
$145$	−2.14959e8	−0.0403831
$146$	4.35283e9	0.792836
$147$	−2.04496e10	−3.61208
$148$	2.46240e9	0.421873
$149$	−7.58956e9	−1.26147	−0.630737	−	0.775996i	$-0.717247\pi$
$149$	−7.58956e9	−1.26147	−0.630737	+	0.775996i	$0.717247\pi$
$150$	1.26675e10	2.04306
$151$	−1.34167e9	−0.210014	−0.105007	−	0.994471i	$-0.533487\pi$
$151$	−1.34167e9	−0.210014	−0.105007	+	0.994471i	$0.533487\pi$
$152$	−2.43430e9	−0.369895
$153$	6.39876e9	0.944027
$154$	1.37612e10	1.97158
$155$	1.51032e9	0.210173
$156$	−1.46664e10	−1.98272
$157$	1.16785e10	1.53405	0.767025	−	0.641617i	$-0.221736\pi$
$157$	1.16785e10	1.53405	0.767025	+	0.641617i	$0.221736\pi$
$158$	−1.84721e10	−2.35808
$159$	9.59908e9	1.19108
$160$	1.31334e8	0.0158431
$161$	−1.97230e10	−2.31343
$162$	−1.88829e10	−2.15403
$163$	8.10682e9	0.899510	0.449755	−	0.893152i	$-0.351511\pi$
$163$	8.10682e9	0.899510	0.449755	+	0.893152i	$0.351511\pi$
$164$	−1.99819e9	−0.215694
$165$	1.48685e9	0.156167
$166$	3.28633e10	3.35912
$167$	−1.54754e10	−1.53964	−0.769818	−	0.638264i	$-0.779653\pi$
$167$	−1.54754e10	−1.53964	−0.769818	+	0.638264i	$0.779653\pi$
$168$	−4.28322e10	−4.14838
$169$	−3.70767e9	−0.349632
$170$	−7.09403e9	−0.651438
$171$	−1.33179e9	−0.119111
$172$	1.24819e10	1.08743
$173$	−6.47023e9	−0.549177	−0.274589	−	0.961562i	$-0.588542\pi$
$173$	−6.47023e9	−0.549177	−0.274589	+	0.961562i	$0.588542\pi$
$174$	−4.81497e9	−0.398219
$175$	−2.33643e10	−1.88314
$176$	6.88929e9	0.541212
$177$	8.29125e9	0.634951
$178$	−3.62895e9	−0.270951
$179$	−1.13283e10	−0.824756	−0.412378	−	0.911013i	$-0.635302\pi$
$179$	−1.13283e10	−0.824756	−0.412378	+	0.911013i	$0.635302\pi$
$180$	−3.29624e9	−0.234041
$181$	−1.09089e10	−0.755484	−0.377742	−	0.925911i	$-0.623299\pi$
$181$	−1.09089e10	−0.755484	−0.377742	+	0.925911i	$0.623299\pi$
$182$	4.07225e10	2.75114
$183$	2.20074e10	1.45057
$184$	−3.07369e10	−1.97688
$185$	−7.38721e8	−0.0463668
$186$	3.38304e10	2.07252
$187$	1.67738e10	1.00310
$188$	−1.80920e10	−1.05627
$189$	1.96503e10	1.12019
$190$	1.47650e9	0.0821944
$191$	7.70695e9	0.419018	0.209509	−	0.977807i	$-0.432813\pi$
$191$	7.70695e9	0.419018	0.209509	+	0.977807i	$0.432813\pi$
$192$	2.48523e10	1.31981
$193$	3.45062e10	1.79015	0.895075	−	0.445915i	$-0.147122\pi$
$193$	3.45062e10	1.79015	0.895075	+	0.445915i	$0.147122\pi$
$194$	1.40269e10	0.710973
$195$	4.39991e9	0.217915
$196$	1.18843e11	5.75202
$197$	−5.38456e9	−0.254714	−0.127357	−	0.991857i	$-0.540649\pi$
$197$	−5.38456e9	−0.254714	−0.127357	+	0.991857i	$0.540649\pi$
$198$	1.17329e10	0.542516
$199$	2.02446e10	0.915105	0.457553	−	0.889183i	$-0.348726\pi$
$199$	2.02446e10	0.915105	0.457553	+	0.889183i	$0.348726\pi$
$200$	−3.64116e10	−1.60918
$201$	−5.15839e10	−2.22911
$202$	−4.23995e10	−1.79176
$203$	8.88088e9	0.367049
$204$	−1.05556e11	−4.26723
$205$	5.99456e8	0.0237064
$206$	4.15372e10	1.60707
$207$	−1.68160e10	−0.636583
$208$	2.03869e10	0.755208
$209$	−3.49117e9	−0.126565
$210$	2.59794e10	0.921811
$211$	3.98793e10	1.38508	0.692542	−	0.721378i	$-0.256491\pi$
$211$	3.98793e10	1.38508	0.692542	+	0.721378i	$0.256491\pi$
$212$	−5.57849e10	−1.89673
$213$	3.12324e10	1.03967
$214$	−1.00067e10	−0.326159
$215$	−3.74457e9	−0.119517
$216$	3.06235e10	0.957224
$217$	−6.23978e10	−1.91030
$218$	−7.19648e10	−2.15807
$219$	−1.94304e10	−0.570798
$220$	−8.64079e9	−0.248686
$221$	4.96373e10	1.39973
$222$	−1.65470e10	−0.457225
$223$	−5.07496e10	−1.37423	−0.687117	−	0.726547i	$-0.741124\pi$
$223$	−5.07496e10	−1.37423	−0.687117	+	0.726547i	$0.741124\pi$
$224$	−5.42599e9	−0.144000
$225$	−1.99206e10	−0.518180
$226$	−9.61703e10	−2.45218
$227$	2.62916e10	0.657204	0.328602	−	0.944468i	$-0.393423\pi$
$227$	2.62916e10	0.657204	0.328602	+	0.944468i	$0.393423\pi$
$228$	2.19696e10	0.538413
$229$	−7.65160e9	−0.183862	−0.0919311	−	0.995765i	$-0.529304\pi$
$229$	−7.65160e9	−0.183862	−0.0919311	+	0.995765i	$0.529304\pi$
$230$	1.86431e10	0.439282
$231$	−6.14281e10	−1.41943
$232$	1.38402e10	0.313651
$233$	4.42227e10	0.982977	0.491488	−	0.870884i	$-0.336453\pi$
$233$	4.42227e10	0.982977	0.491488	+	0.870884i	$0.336453\pi$
$234$	3.47203e10	0.757027
$235$	5.42760e9	0.116092
$236$	−4.81845e10	−1.01112
$237$	8.24567e10	1.69769
$238$	2.93085e11	5.92103
$239$	7.09382e9	0.140634	0.0703169	−	0.997525i	$-0.477599\pi$
$239$	7.09382e9	0.140634	0.0703169	+	0.997525i	$0.477599\pi$
$240$	1.30061e10	0.253044
$241$	−6.13992e9	−0.117243	−0.0586214	−	0.998280i	$-0.518670\pi$
$241$	−6.13992e9	−0.117243	−0.0586214	+	0.998280i	$0.518670\pi$
$242$	−6.13264e10	−1.14942
$243$	5.34872e10	0.984060
$244$	−1.27896e11	−2.30995
$245$	−3.56528e10	−0.632188
$246$	1.34275e10	0.233769
$247$	−1.03311e10	−0.176609
$248$	−9.72426e10	−1.63239
$249$	−1.46697e11	−2.41838
$250$	4.52665e10	0.732903
$251$	4.48984e10	0.714002	0.357001	−	0.934104i	$-0.383799\pi$
$251$	4.48984e10	0.714002	0.357001	+	0.934104i	$0.383799\pi$
$252$	1.36182e11	2.12724
$253$	−4.40815e10	−0.676417
$254$	−4.63284e10	−0.698386
$255$	3.16667e10	0.468999
$256$	−1.35789e11	−1.97598
$257$	−9.57768e10	−1.36950	−0.684749	−	0.728779i	$-0.740088\pi$
$257$	−9.57768e10	−1.36950	−0.684749	+	0.728779i	$0.740088\pi$
$258$	−8.38763e10	−1.17856
$259$	3.05197e10	0.421436
$260$	−2.55700e10	−0.347017
$261$	7.57189e9	0.101000
$262$	9.53970e10	1.25077
$263$	1.08386e10	0.139692	0.0698460	−	0.997558i	$-0.477749\pi$
$263$	1.08386e10	0.139692	0.0698460	+	0.997558i	$0.477749\pi$
$264$	−9.57313e10	−1.21293
$265$	1.67355e10	0.208464
$266$	−6.10005e10	−0.747078
$267$	1.61991e10	0.195070
$268$	2.99779e11	3.54973
$269$	1.15477e11	1.34465	0.672324	−	0.740257i	$-0.265296\pi$
$269$	1.15477e11	1.34465	0.672324	+	0.740257i	$0.265296\pi$
$270$	−1.85744e10	−0.212705
$271$	6.85256e9	0.0771776	0.0385888	−	0.999255i	$-0.487714\pi$
$271$	6.85256e9	0.0771776	0.0385888	+	0.999255i	$0.487714\pi$
$272$	1.46727e11	1.62536
$273$	−1.81779e11	−1.98067
$274$	−1.43590e11	−1.53903
$275$	−5.22200e10	−0.550604
$276$	2.77401e11	2.87751
$277$	1.54227e11	1.57399	0.786994	−	0.616961i	$-0.211636\pi$
$277$	1.54227e11	1.57399	0.786994	+	0.616961i	$0.211636\pi$
$278$	4.75040e10	0.477011
$279$	−5.32008e10	−0.525653
$280$	−7.46755e10	−0.726051
$281$	7.42271e10	0.710205	0.355103	−	0.934827i	$-0.384446\pi$
$281$	7.42271e10	0.710205	0.355103	+	0.934827i	$0.384446\pi$
$282$	1.21575e11	1.14479
$283$	−6.42660e10	−0.595583	−0.297792	−	0.954631i	$-0.596250\pi$
$283$	−6.42660e10	−0.595583	−0.297792	+	0.954631i	$0.596250\pi$
$284$	−1.81507e11	−1.65562
$285$	−6.59087e9	−0.0591754
$286$	9.10161e10	0.804398
$287$	−2.47661e10	−0.215471
$288$	−4.62623e9	−0.0396243
$289$	2.38658e11	2.01250
$290$	−8.39463e9	−0.0696964
$291$	−6.26139e10	−0.511861
$292$	1.12919e11	0.908961
$293$	−6.98109e10	−0.553375	−0.276687	−	0.960960i	$-0.589237\pi$
$293$	−6.98109e10	−0.553375	−0.276687	+	0.960960i	$0.589237\pi$
$294$	−7.98604e11	−6.23402
$295$	1.44553e10	0.111129
$296$	4.75628e10	0.360126
$297$	4.39190e10	0.327528
$298$	−2.96389e11	−2.17716
$299$	−1.30447e11	−0.943873
$300$	3.28615e11	2.34230
$301$	1.54704e11	1.08631
$302$	−5.23952e10	−0.362460
$303$	1.89265e11	1.28997
$304$	−3.05387e10	−0.205078
$305$	3.83687e10	0.253880
$306$	2.49886e11	1.62928
$307$	5.56193e10	0.357357	0.178679	−	0.983907i	$-0.442818\pi$
$307$	5.56193e10	0.357357	0.178679	+	0.983907i	$0.442818\pi$
$308$	3.56988e11	2.26035
$309$	−1.85416e11	−1.15700
$310$	5.89814e10	0.362733
$311$	1.29454e11	0.784683	0.392341	−	0.919820i	$-0.371665\pi$
$311$	1.29454e11	0.784683	0.392341	+	0.919820i	$0.371665\pi$
$312$	−2.83290e11	−1.69253
$313$	−3.61492e10	−0.212887	−0.106444	−	0.994319i	$-0.533946\pi$
$313$	−3.61492e10	−0.212887	−0.106444	+	0.994319i	$0.533946\pi$
$314$	4.56073e11	2.64759
$315$	−4.08545e10	−0.233799
$316$	−4.79196e11	−2.70347
$317$	2.67830e11	1.48968	0.744840	−	0.667243i	$-0.232526\pi$
$317$	2.67830e11	1.48968	0.744840	+	0.667243i	$0.232526\pi$
$318$	3.74865e11	2.05567
$319$	1.98490e10	0.107320
$320$	4.33287e10	0.230994
$321$	4.46685e10	0.234817
$322$	−7.70227e11	−3.99271
$323$	−7.43545e10	−0.380098
$324$	−4.89852e11	−2.46952
$325$	−1.54530e11	−0.768314
$326$	3.16589e11	1.55245
$327$	3.21240e11	1.55369
$328$	−3.85962e10	−0.184125
$329$	−2.24237e11	−1.05518
$330$	5.80647e10	0.269525
$331$	8.34054e10	0.381916	0.190958	−	0.981598i	$-0.438841\pi$
$331$	8.34054e10	0.381916	0.190958	+	0.981598i	$0.438841\pi$
$332$	8.52527e11	3.85112
$333$	2.60213e10	0.115966
$334$	−6.04349e11	−2.65723
$335$	−8.99337e10	−0.390140
$336$	−5.37337e11	−2.29996
$337$	−2.29807e11	−0.970572	−0.485286	−	0.874355i	$-0.661285\pi$
$337$	−2.29807e11	−0.970572	−0.485286	+	0.874355i	$0.661285\pi$
$338$	−1.44793e11	−0.603424
$339$	4.29290e11	1.76544
$340$	−1.84031e11	−0.746852
$341$	−1.39461e11	−0.558545
$342$	−5.20094e10	−0.205572
$343$	9.66275e11	3.76944
$344$	2.41095e11	0.928273
$345$	−8.32201e10	−0.316259
$346$	−2.52677e11	−0.947815
$347$	2.41953e11	0.895877	0.447939	−	0.894064i	$-0.352158\pi$
$347$	2.41953e11	0.895877	0.447939	+	0.894064i	$0.352158\pi$
$348$	−1.24908e11	−0.456545
$349$	1.45432e11	0.524743	0.262372	−	0.964967i	$-0.415495\pi$
$349$	1.45432e11	0.524743	0.262372	+	0.964967i	$0.415495\pi$
$350$	−9.12429e11	−3.25007
$351$	1.29966e11	0.457033
$352$	−1.21273e10	−0.0421037
$353$	−4.49577e11	−1.54105	−0.770527	−	0.637408i	$-0.780007\pi$
$353$	−4.49577e11	−1.54105	−0.770527	+	0.637408i	$0.780007\pi$
$354$	3.23792e11	1.09585
$355$	5.44519e10	0.181964
$356$	−9.41406e10	−0.310636
$357$	−1.30829e12	−4.26281
$358$	−4.42395e11	−1.42343
$359$	4.14994e10	0.131861	0.0659305	−	0.997824i	$-0.478998\pi$
$359$	4.14994e10	0.131861	0.0659305	+	0.997824i	$0.478998\pi$
$360$	−6.36688e10	−0.199786
$361$	−3.07212e11	−0.952042
$362$	−4.26015e11	−1.30388
$363$	2.73752e11	0.827517
$364$	1.05641e12	3.15410
$365$	−3.38758e10	−0.0999013
$366$	8.59439e11	2.50351
$367$	7.31152e10	0.210383	0.105191	−	0.994452i	$-0.466454\pi$
$367$	7.31152e10	0.210383	0.105191	+	0.994452i	$0.466454\pi$
$368$	−3.85599e11	−1.09603
$369$	−2.11157e10	−0.0592908
$370$	−2.88487e10	−0.0800236
$371$	−6.91413e11	−1.89476
$372$	8.77615e11	2.37608
$373$	−4.59195e11	−1.22831	−0.614155	−	0.789186i	$-0.710503\pi$
$373$	−4.59195e11	−1.22831	−0.614155	+	0.789186i	$0.710503\pi$
$374$	6.55054e11	1.73123
$375$	−2.02063e11	−0.527650
$376$	−3.49458e11	−0.901674
$377$	5.87377e10	0.149755
$378$	7.67387e11	1.93331
$379$	4.94507e11	1.23111	0.615553	−	0.788095i	$-0.288933\pi$
$379$	4.94507e11	1.23111	0.615553	+	0.788095i	$0.288933\pi$
$380$	3.83028e10	0.0942332
$381$	2.06803e11	0.502799
$382$	3.00974e11	0.723175
$383$	−3.88013e11	−0.921407	−0.460703	−	0.887554i	$-0.652403\pi$
$383$	−3.88013e11	−0.921407	−0.460703	+	0.887554i	$0.652403\pi$
$384$	9.31970e11	2.18732
$385$	−1.07096e11	−0.248429
$386$	1.34755e12	3.08959
$387$	1.31902e11	0.298917
$388$	3.63879e11	0.815107
$389$	−5.58300e11	−1.23622	−0.618108	−	0.786093i	$-0.712101\pi$
$389$	−5.58300e11	−1.23622	−0.618108	+	0.786093i	$0.712101\pi$
$390$	1.71826e11	0.376096
$391$	−9.38843e11	−2.03141
$392$	2.29552e12	4.91013
$393$	−4.25838e11	−0.900487
$394$	−2.10279e11	−0.439606
$395$	1.43759e11	0.297130
$396$	3.04370e11	0.621977
$397$	3.28328e11	0.663363	0.331681	−	0.943391i	$-0.392384\pi$
$397$	3.28328e11	0.663363	0.331681	+	0.943391i	$0.392384\pi$
$398$	7.90598e11	1.57936
$399$	2.72297e11	0.537855
$400$	−4.56790e11	−0.892168
$401$	−3.43192e11	−0.662807	−0.331403	−	0.943489i	$-0.607522\pi$
$401$	−3.43192e11	−0.662807	−0.331403	+	0.943489i	$0.607522\pi$
$402$	−2.01447e12	−3.84719
$403$	−4.12696e11	−0.779395
$404$	−1.09991e12	−2.05419
$405$	1.46956e11	0.271418
$406$	3.46818e11	0.633482
$407$	6.82125e10	0.123222
$408$	−2.03887e12	−3.64267
$409$	7.00955e11	1.23861	0.619306	−	0.785150i	$-0.287414\pi$
$409$	7.00955e11	1.23861	0.619306	+	0.785150i	$0.287414\pi$
$410$	2.34101e10	0.0409144
$411$	6.40965e11	1.10802
$412$	1.07754e12	1.84245
$413$	−5.97212e11	−1.01007
$414$	−6.56701e11	−1.09867
$415$	−2.55758e11	−0.423265
$416$	−3.58872e10	−0.0587516
$417$	−2.12051e11	−0.343422
$418$	−1.36338e11	−0.218436
$419$	7.92426e11	1.25602	0.628008	−	0.778207i	$-0.283870\pi$
$419$	7.92426e11	1.25602	0.628008	+	0.778207i	$0.283870\pi$
$420$	6.73947e11	1.05683
$421$	1.65206e11	0.256304	0.128152	−	0.991755i	$-0.459095\pi$
$421$	1.65206e11	0.256304	0.128152	+	0.991755i	$0.459095\pi$
$422$	1.55737e12	2.39049
$423$	−1.91186e11	−0.290352
$424$	−1.07752e12	−1.61912
$425$	−1.11217e12	−1.65357
$426$	1.21969e12	1.79435
$427$	−1.58518e12	−2.30755
$428$	−2.59590e11	−0.373931
$429$	−4.06282e11	−0.579122
$430$	−1.46234e11	−0.206272
$431$	−3.28492e10	−0.0458540	−0.0229270	−	0.999737i	$-0.507299\pi$
$431$	−3.28492e10	−0.0458540	−0.0229270	+	0.999737i	$0.507299\pi$
$432$	3.84177e11	0.530707
$433$	8.09178e11	1.10624	0.553119	−	0.833102i	$-0.313438\pi$
$433$	8.09178e11	1.10624	0.553119	+	0.833102i	$0.313438\pi$
$434$	−2.43677e12	−3.29694
$435$	3.74724e10	0.0501776
$436$	−1.86688e12	−2.47416
$437$	1.95404e11	0.256311
$438$	−7.58799e11	−0.985130
$439$	5.06639e11	0.651041	0.325520	−	0.945535i	$-0.394461\pi$
$439$	5.06639e11	0.651041	0.325520	+	0.945535i	$0.394461\pi$
$440$	−1.66902e11	−0.212288
$441$	1.25586e12	1.58113
$442$	1.93845e12	2.41576
$443$	8.85491e11	1.09236	0.546182	−	0.837667i	$-0.316081\pi$
$443$	8.85491e11	1.09236	0.546182	+	0.837667i	$0.316081\pi$
$444$	−4.29254e11	−0.524193
$445$	2.82422e10	0.0341411
$446$	−1.98188e12	−2.37176
$447$	1.32304e12	1.56743
$448$	−1.79009e12	−2.09954
$449$	8.52412e11	0.989786	0.494893	−	0.868954i	$-0.335207\pi$
$449$	8.52412e11	0.989786	0.494893	+	0.868954i	$0.335207\pi$
$450$	−7.77943e11	−0.894317
$451$	−5.53530e10	−0.0630009
$452$	−2.49481e12	−2.81135
$453$	2.33884e11	0.260951
$454$	1.02674e12	1.13426
$455$	−3.16922e11	−0.346658
$456$	4.24356e11	0.459609
$457$	−5.14407e11	−0.551675	−0.275838	−	0.961204i	$-0.588955\pi$
$457$	−5.14407e11	−0.551675	−0.275838	+	0.961204i	$0.588955\pi$
$458$	−2.98812e11	−0.317324
$459$	9.35380e11	0.983629
$460$	4.83632e11	0.503623
$461$	−1.41708e12	−1.46131	−0.730653	−	0.682749i	$-0.760784\pi$
$461$	−1.41708e12	−1.46131	−0.730653	+	0.682749i	$0.760784\pi$
$462$	−2.39890e12	−2.44976
$463$	4.59102e11	0.464296	0.232148	−	0.972681i	$-0.425425\pi$
$463$	4.59102e11	0.464296	0.232148	+	0.972681i	$0.425425\pi$
$464$	1.73628e11	0.173895
$465$	−2.63284e11	−0.261148
$466$	1.72699e12	1.69650
$467$	−4.47905e11	−0.435772	−0.217886	−	0.975974i	$-0.569916\pi$
$467$	−4.47905e11	−0.435772	−0.217886	+	0.975974i	$0.569916\pi$
$468$	9.00699e11	0.867907
$469$	3.71555e12	3.54605
$470$	2.11960e11	0.200361
$471$	−2.03584e12	−1.90612
$472$	−9.30712e11	−0.863130
$473$	3.45768e11	0.317622
$474$	3.22012e12	2.93001
$475$	2.31480e11	0.208637
$476$	7.60309e12	6.78827
$477$	−5.89503e11	−0.521379
$478$	2.77030e11	0.242717
$479$	−1.37894e12	−1.19684	−0.598421	−	0.801182i	$-0.704205\pi$
$479$	−1.37894e12	−1.19684	−0.598421	+	0.801182i	$0.704205\pi$
$480$	−2.28947e10	−0.0196856
$481$	2.01856e11	0.171945
$482$	−2.39778e11	−0.202347
$483$	3.43818e12	2.87453
$484$	−1.59090e12	−1.31777
$485$	−1.09164e11	−0.0895861
$486$	2.08879e12	1.69837
$487$	3.37768e11	0.272106	0.136053	−	0.990702i	$-0.456558\pi$
$487$	3.37768e11	0.272106	0.136053	+	0.990702i	$0.456558\pi$
$488$	−2.47038e12	−1.97186
$489$	−1.41321e12	−1.11768
$490$	−1.39232e12	−1.09108
$491$	−6.52851e11	−0.506929	−0.253465	−	0.967345i	$-0.581570\pi$
$491$	−6.52851e11	−0.506929	−0.253465	+	0.967345i	$0.581570\pi$
$492$	3.48331e11	0.268009
$493$	4.22742e11	0.322303
$494$	−4.03454e11	−0.304806
$495$	−9.13111e10	−0.0683597
$496$	−1.21992e12	−0.905034
$497$	−2.24964e12	−1.65390
$498$	−5.72885e12	−4.17383
$499$	−2.59483e12	−1.87351	−0.936756	−	0.349983i	$-0.886187\pi$
$499$	−2.59483e12	−1.87351	−0.936756	+	0.349983i	$0.886187\pi$
$500$	1.17428e12	0.840250
$501$	2.69772e12	1.91306
$502$	1.75338e12	1.23228
$503$	1.75074e12	1.21946	0.609728	−	0.792611i	$-0.291279\pi$
$503$	1.75074e12	1.21946	0.609728	+	0.792611i	$0.291279\pi$
$504$	2.63043e12	1.81589
$505$	3.29973e11	0.225771
$506$	−1.72148e12	−1.16742
$507$	6.46334e11	0.434431
$508$	−1.20183e12	−0.800677
$509$	−5.48195e11	−0.361997	−0.180999	−	0.983483i	$-0.557933\pi$
$509$	−5.48195e11	−0.361997	−0.180999	+	0.983483i	$0.557933\pi$
$510$	1.23666e12	0.809437
$511$	1.39955e12	0.908020
$512$	−2.56559e12	−1.64995
$513$	−1.94683e11	−0.124108
$514$	−3.74030e12	−2.36359
$515$	−3.23262e11	−0.202499
$516$	−2.17589e12	−1.35118
$517$	−5.01177e11	−0.308520
$518$	1.19186e12	0.727348
$519$	1.12791e12	0.682374
$520$	−4.93900e11	−0.296226
$521$	−1.01468e12	−0.603333	−0.301667	−	0.953413i	$-0.597543\pi$
$521$	−1.01468e12	−0.603333	−0.301667	+	0.953413i	$0.597543\pi$
$522$	2.95699e11	0.174314
$523$	−8.43857e11	−0.493187	−0.246593	−	0.969119i	$-0.579311\pi$
$523$	−8.43857e11	−0.493187	−0.246593	+	0.969119i	$0.579311\pi$
$524$	2.47475e12	1.43397
$525$	4.07295e12	2.33987
$526$	4.23271e11	0.241092
$527$	−2.97022e12	−1.67742
$528$	−1.20096e12	−0.672477
$529$	6.66127e11	0.369834
$530$	6.53557e11	0.359784
$531$	−5.09186e11	−0.277940
$532$	−1.58245e12	−0.856501
$533$	−1.63802e11	−0.0879115
$534$	6.32610e11	0.336667
$535$	7.78770e10	0.0410977
$536$	5.79041e12	3.03018
$537$	1.97478e12	1.02479
$538$	4.50962e12	2.32070
$539$	3.29213e12	1.68007
$540$	−4.81849e11	−0.243859
$541$	4.12072e11	0.206817	0.103408	−	0.994639i	$-0.467025\pi$
$541$	4.12072e11	0.206817	0.103408	+	0.994639i	$0.467025\pi$
$542$	2.67608e11	0.133199
$543$	1.90167e12	0.938719
$544$	−2.58285e11	−0.126446
$545$	5.60064e11	0.271928
$546$	−7.09888e12	−3.41840
$547$	9.82744e11	0.469351	0.234675	−	0.972074i	$-0.424597\pi$
$547$	9.82744e11	0.469351	0.234675	+	0.972074i	$0.424597\pi$
$548$	−3.72496e12	−1.76445
$549$	−1.35153e12	−0.634966
$550$	−2.03931e12	−0.950278
$551$	−8.79864e10	−0.0406662
$552$	5.35816e12	2.45635
$553$	−5.93928e12	−2.70067
$554$	6.02291e12	2.71652
$555$	1.28776e11	0.0576126
$556$	1.23233e12	0.546878
$557$	−3.03366e12	−1.33542	−0.667711	−	0.744420i	$-0.732726\pi$
$557$	−3.03366e12	−1.33542	−0.667711	+	0.744420i	$0.732726\pi$
$558$	−2.07761e12	−0.907215
$559$	1.02320e12	0.443210
$560$	−9.36816e11	−0.402539
$561$	−2.92406e12	−1.24639
$562$	2.89873e12	1.22573
$563$	−6.32277e11	−0.265228	−0.132614	−	0.991168i	$-0.542337\pi$
$563$	−6.32277e11	−0.265228	−0.132614	+	0.991168i	$0.542337\pi$
$564$	3.15386e12	1.31246
$565$	7.48443e11	0.308987
$566$	−2.50973e12	−1.02791
$567$	−6.07136e12	−2.46696
$568$	−3.50591e12	−1.41330
$569$	2.07332e11	0.0829203	0.0414601	−	0.999140i	$-0.486799\pi$
$569$	2.07332e11	0.0829203	0.0414601	+	0.999140i	$0.486799\pi$
$570$	−2.57388e11	−0.102130
$571$	−2.07283e12	−0.816022	−0.408011	−	0.912977i	$-0.633777\pi$
$571$	−2.07283e12	−0.816022	−0.408011	+	0.912977i	$0.633777\pi$
$572$	2.36110e12	0.922216
$573$	−1.34350e12	−0.520646
$574$	−9.67171e11	−0.371878
$575$	2.92280e12	1.11505
$576$	−1.52624e12	−0.577727
$577$	4.41168e12	1.65696	0.828482	−	0.560015i	$-0.189205\pi$
$577$	4.41168e12	1.65696	0.828482	+	0.560015i	$0.189205\pi$
$578$	9.32014e12	3.47334
$579$	−6.01524e12	−2.22433
$580$	−2.17770e11	−0.0799047
$581$	1.05665e13	3.84713
$582$	−2.44521e12	−0.883411
$583$	−1.54533e12	−0.554004
$584$	2.18110e12	0.775923
$585$	−2.70209e11	−0.0953892
$586$	−2.72627e12	−0.955059
$587$	−3.80914e11	−0.132421	−0.0662103	−	0.997806i	$-0.521091\pi$
$587$	−3.80914e11	−0.132421	−0.0662103	+	0.997806i	$0.521091\pi$
$588$	−2.07171e13	−7.14710
$589$	6.18201e11	0.211646
$590$	5.64513e11	0.191796
$591$	9.38655e11	0.316492
$592$	5.96683e11	0.199662
$593$	−5.02082e12	−1.66736	−0.833679	−	0.552249i	$-0.813770\pi$
$593$	−5.02082e12	−1.66736	−0.833679	+	0.552249i	$0.813770\pi$
$594$	1.71513e12	0.565274
$595$	−2.28093e12	−0.746079
$596$	−7.68881e12	−2.49604
$597$	−3.52911e12	−1.13705
$598$	−5.09424e12	−1.62901
$599$	−9.35713e11	−0.296977	−0.148488	−	0.988914i	$-0.547441\pi$
$599$	−9.35713e11	−0.296977	−0.148488	+	0.988914i	$0.547441\pi$
$600$	6.34740e12	1.99947
$601$	−9.60230e11	−0.300220	−0.150110	−	0.988669i	$-0.547963\pi$
$601$	−9.60230e11	−0.300220	−0.150110	+	0.988669i	$0.547963\pi$
$602$	6.04154e12	1.87484
$603$	3.16790e12	0.975761
$604$	−1.35921e12	−0.415549
$605$	4.77271e11	0.144832
$606$	7.39123e12	2.22633
$607$	2.48935e12	0.744280	0.372140	−	0.928177i	$-0.378624\pi$
$607$	2.48935e12	0.744280	0.372140	+	0.928177i	$0.378624\pi$
$608$	5.37575e10	0.0159541
$609$	−1.54814e12	−0.456072
$610$	1.49838e12	0.438166
$611$	−1.48309e12	−0.430510
$612$	6.48244e12	1.86792
$613$	2.89387e12	0.827764	0.413882	−	0.910331i	$-0.364173\pi$
$613$	2.89387e12	0.827764	0.413882	+	0.910331i	$0.364173\pi$
$614$	2.17206e12	0.616756
$615$	−1.04499e11	−0.0294561
$616$	6.89544e12	1.92952
$617$	6.00234e11	0.166739	0.0833695	−	0.996519i	$-0.473432\pi$
$617$	6.00234e11	0.166739	0.0833695	+	0.996519i	$0.473432\pi$
$618$	−7.24090e12	−1.99684
$619$	3.13032e12	0.857000	0.428500	−	0.903542i	$-0.359042\pi$
$619$	3.13032e12	0.857000	0.428500	+	0.903542i	$0.359042\pi$
$620$	1.53007e12	0.415862
$621$	−2.45818e12	−0.663287
$622$	5.05547e12	1.35427
$623$	−1.16681e12	−0.310315
$624$	−3.55392e12	−0.938375
$625$	3.28200e12	0.860358
$626$	−1.41171e12	−0.367418
$627$	6.08593e11	0.157262
$628$	1.18313e13	3.03538
$629$	1.45278e12	0.370060
$630$	−1.59546e12	−0.403509
$631$	−5.17362e10	−0.0129916	−0.00649579	−	0.999979i	$-0.502068\pi$
$631$	−5.17362e10	−0.0129916	−0.00649579	+	0.999979i	$0.502068\pi$
$632$	−9.25595e12	−2.30778
$633$	−6.95189e12	−1.72102
$634$	1.04594e13	2.57101
$635$	3.60550e11	0.0880001
$636$	9.72461e12	2.35676
$637$	9.74214e12	2.34437
$638$	7.75149e11	0.185222
$639$	−1.91806e12	−0.455101
$640$	1.62484e12	0.382825
$641$	5.21430e11	0.121993	0.0609965	−	0.998138i	$-0.480572\pi$
$641$	5.21430e11	0.121993	0.0609965	+	0.998138i	$0.480572\pi$
$642$	1.74441e12	0.405266
$643$	−8.23393e12	−1.89958	−0.949791	−	0.312886i	$-0.898704\pi$
$643$	−8.23393e12	−1.89958	−0.949791	+	0.312886i	$0.898704\pi$
$644$	−1.99809e13	−4.57751
$645$	6.52765e11	0.148504
$646$	−2.90371e12	−0.656005
$647$	1.70875e12	0.383363	0.191681	−	0.981457i	$-0.438606\pi$
$647$	1.70875e12	0.383363	0.191681	+	0.981457i	$0.438606\pi$
$648$	−9.46179e12	−2.10807
$649$	−1.33479e12	−0.295332
$650$	−6.03476e12	−1.32602
$651$	1.08774e13	2.37362
$652$	8.21283e12	1.77983
$653$	−2.18310e12	−0.469855	−0.234927	−	0.972013i	$-0.575485\pi$
$653$	−2.18310e12	−0.469855	−0.234927	+	0.972013i	$0.575485\pi$
$654$	1.25451e13	2.68149
$655$	−7.42424e11	−0.157604
$656$	−4.84195e11	−0.102083
$657$	1.19327e12	0.249858
$658$	−8.75697e12	−1.82111
$659$	−9.29839e11	−0.192054	−0.0960270	−	0.995379i	$-0.530614\pi$
$659$	−9.29839e11	−0.192054	−0.0960270	+	0.995379i	$0.530614\pi$
$660$	1.50629e12	0.309002
$661$	3.04031e12	0.619457	0.309728	−	0.950825i	$-0.399762\pi$
$661$	3.04031e12	0.619457	0.309728	+	0.950825i	$0.399762\pi$
$662$	3.25717e12	0.659142
$663$	−8.65294e12	−1.73921
$664$	1.64671e13	3.28746
$665$	4.74735e11	0.0941356
$666$	1.01619e12	0.200143
$667$	−1.11097e12	−0.217338
$668$	−1.56778e13	−3.04643
$669$	8.84683e12	1.70754
$670$	−3.51211e12	−0.673336
$671$	−3.54292e12	−0.674698
$672$	9.45877e11	0.178926
$673$	−5.56575e12	−1.04582	−0.522909	−	0.852389i	$-0.675153\pi$
$673$	−5.56575e12	−1.04582	−0.522909	+	0.852389i	$0.675153\pi$
$674$	−8.97446e12	−1.67509
$675$	−2.91202e12	−0.539917
$676$	−3.75616e12	−0.691805
$677$	−4.47427e12	−0.818602	−0.409301	−	0.912399i	$-0.634227\pi$
$677$	−4.47427e12	−0.818602	−0.409301	+	0.912399i	$0.634227\pi$
$678$	1.67647e13	3.04693
$679$	4.51002e12	0.814263
$680$	−3.55466e12	−0.637541
$681$	−4.58324e12	−0.816602
$682$	−5.44627e12	−0.963983
$683$	4.63330e12	0.814699	0.407350	−	0.913272i	$-0.366453\pi$
$683$	4.63330e12	0.814699	0.407350	+	0.913272i	$0.366453\pi$
$684$	−1.34921e12	−0.235682
$685$	1.11749e12	0.193925
$686$	3.77352e13	6.50561
$687$	1.33385e12	0.228456
$688$	3.02458e12	0.514656
$689$	−4.57297e12	−0.773058
$690$	−3.24993e12	−0.545825
$691$	−2.98447e12	−0.497984	−0.248992	−	0.968506i	$-0.580099\pi$
$691$	−2.98447e12	−0.497984	−0.248992	+	0.968506i	$0.580099\pi$
$692$	−6.55485e12	−1.08664
$693$	3.77245e12	0.621332
$694$	9.44881e12	1.54618
$695$	−3.69699e11	−0.0601058
$696$	−2.41267e12	−0.389724
$697$	−1.17890e12	−0.189204
$698$	5.67946e12	0.905644
$699$	−7.70904e12	−1.22139
$700$	−2.36699e13	−3.72610
$701$	−1.62837e12	−0.254696	−0.127348	−	0.991858i	$-0.540647\pi$
$701$	−1.62837e12	−0.254696	−0.127348	+	0.991858i	$0.540647\pi$
$702$	5.07546e12	0.788784
$703$	−3.02371e11	−0.0466919
$704$	−4.00091e12	−0.613878
$705$	−9.46157e11	−0.144249
$706$	−1.75570e13	−2.65968
$707$	−1.36326e13	−2.05207
$708$	8.39968e12	1.25636
$709$	2.54476e12	0.378215	0.189108	−	0.981956i	$-0.439440\pi$
$709$	2.54476e12	0.378215	0.189108	+	0.981956i	$0.439440\pi$
$710$	2.12647e12	0.314048
$711$	−5.06387e12	−0.743138
$712$	−1.81838e12	−0.265171
$713$	7.80575e12	1.13113
$714$	−5.10915e13	−7.35711
$715$	−7.08330e11	−0.101358
$716$	−1.14764e13	−1.63192
$717$	−1.23662e12	−0.174743
$718$	1.62064e12	0.227576
$719$	−1.15794e12	−0.161587	−0.0807936	−	0.996731i	$-0.525745\pi$
$719$	−1.15794e12	−0.161587	−0.0807936	+	0.996731i	$0.525745\pi$
$720$	−7.98735e11	−0.110766
$721$	1.33553e13	1.84054
$722$	−1.19973e13	−1.64311
$723$	1.07033e12	0.145679
$724$	−1.10515e13	−1.49485
$725$	−1.31608e12	−0.176913
$726$	1.06906e13	1.42820
$727$	7.34504e12	0.975190	0.487595	−	0.873070i	$-0.337874\pi$
$727$	7.34504e12	0.975190	0.487595	+	0.873070i	$0.337874\pi$
$728$	2.04051e13	2.69245
$729$	1.93235e11	0.0253403
$730$	−1.32292e12	−0.172418
$731$	7.36413e12	0.953879
$732$	2.22952e13	2.87020
$733$	−2.29808e12	−0.294033	−0.147017	−	0.989134i	$-0.546967\pi$
$733$	−2.29808e12	−0.294033	−0.147017	+	0.989134i	$0.546967\pi$
$734$	2.85531e12	0.363096
$735$	6.21511e12	0.785518
$736$	6.78773e11	0.0852657
$737$	8.30436e12	1.03682
$738$	−8.24616e11	−0.102329
$739$	5.12224e12	0.631771	0.315886	−	0.948797i	$-0.397698\pi$
$739$	5.12224e12	0.631771	0.315886	+	0.948797i	$0.397698\pi$
$740$	−7.48381e11	−0.0917445
$741$	1.80096e12	0.219443
$742$	−2.70012e13	−3.27014
$743$	−5.17123e11	−0.0622507	−0.0311254	−	0.999515i	$-0.509909\pi$
$743$	−5.17123e11	−0.0622507	−0.0311254	+	0.999515i	$0.509909\pi$
$744$	1.69516e13	2.02831
$745$	2.30664e12	0.274332
$746$	−1.79326e13	−2.11992
$747$	9.00903e12	1.05861
$748$	1.69931e13	1.98480
$749$	−3.21743e12	−0.373544
$750$	−7.89100e12	−0.910661
$751$	1.20684e13	1.38443	0.692214	−	0.721692i	$-0.256635\pi$
$751$	1.20684e13	1.38443	0.692214	+	0.721692i	$0.256635\pi$
$752$	−4.38400e12	−0.499909
$753$	−7.82685e12	−0.887175
$754$	2.29384e12	0.258459
$755$	4.07764e11	0.0456718
$756$	1.99072e13	2.21648
$757$	−7.03407e12	−0.778530	−0.389265	−	0.921126i	$-0.627271\pi$
$757$	−7.03407e12	−0.778530	−0.389265	+	0.921126i	$0.627271\pi$
$758$	1.93116e13	2.12474
$759$	7.68444e12	0.840474
$760$	7.39840e11	0.0804409
$761$	1.40627e13	1.51998	0.759989	−	0.649936i	$-0.225204\pi$
$761$	1.40627e13	1.51998	0.759989	+	0.649936i	$0.225204\pi$
$762$	8.07612e12	0.867772
$763$	−2.31386e13	−2.47159
$764$	7.80774e12	0.829097
$765$	−1.94473e12	−0.205297
$766$	−1.51528e13	−1.59024
$767$	−3.94993e12	−0.412107
$768$	2.36711e13	2.45524
$769$	−1.16542e12	−0.120175	−0.0600875	−	0.998193i	$-0.519138\pi$
$769$	−1.16542e12	−0.120175	−0.0600875	+	0.998193i	$0.519138\pi$
$770$	−4.18235e12	−0.428758
$771$	1.66961e13	1.70165
$772$	3.49575e13	3.54211
$773$	−9.54640e12	−0.961683	−0.480842	−	0.876808i	$-0.659669\pi$
$773$	−9.54640e12	−0.961683	−0.480842	+	0.876808i	$0.659669\pi$
$774$	5.15106e12	0.515896
$775$	9.24687e12	0.920741
$776$	7.02855e12	0.695805
$777$	−5.32030e12	−0.523650
$778$	−2.18029e13	−2.13356
$779$	2.45368e11	0.0238726
$780$	4.45745e12	0.431182
$781$	−5.02802e12	−0.483579
$782$	−3.66639e13	−3.50597
$783$	1.10687e12	0.105237
$784$	2.87976e13	2.72229
$785$	−3.54937e12	−0.333609
$786$	−1.66299e13	−1.55413
$787$	5.09173e12	0.473128	0.236564	−	0.971616i	$-0.423979\pi$
$787$	5.09173e12	0.473128	0.236564	+	0.971616i	$0.423979\pi$
$788$	−5.45498e12	−0.503994
$789$	−1.88942e12	−0.173573
$790$	5.61409e12	0.512811
$791$	−3.09214e13	−2.80844
$792$	5.87910e12	0.530942
$793$	−1.04843e13	−0.941475
$794$	1.28220e13	1.14489
$795$	−2.91738e12	−0.259025
$796$	2.05094e13	1.81069
$797$	−5.95236e11	−0.0522549	−0.0261274	−	0.999659i	$-0.508318\pi$
$797$	−5.95236e11	−0.0522549	−0.0261274	+	0.999659i	$0.508318\pi$
$798$	1.06338e13	0.928274
$799$	−1.06740e13	−0.926546
$800$	8.04090e11	0.0694064
$801$	−9.94826e11	−0.0853887
$802$	−1.34024e13	−1.14393
$803$	3.12804e12	0.265493
$804$	−5.22585e13	−4.41067
$805$	5.99427e12	0.503101
$806$	−1.61167e13	−1.34514
$807$	−2.01303e13	−1.67078
$808$	−2.12454e13	−1.75354
$809$	6.15645e12	0.505315	0.252657	−	0.967556i	$-0.418695\pi$
$809$	6.15645e12	0.505315	0.252657	+	0.967556i	$0.418695\pi$
$810$	5.73894e12	0.468435
$811$	6.32134e12	0.513116	0.256558	−	0.966529i	$-0.417412\pi$
$811$	6.32134e12	0.513116	0.256558	+	0.966529i	$0.417412\pi$
$812$	8.99701e12	0.726267
$813$	−1.19456e12	−0.0958962
$814$	2.66385e12	0.212667
$815$	−2.46385e12	−0.195616
$816$	−2.55780e13	−2.01958
$817$	−1.53272e12	−0.120355
$818$	2.73739e13	2.13770
$819$	1.11635e13	0.867008
$820$	6.07295e11	0.0469070
$821$	5.23991e12	0.402513	0.201257	−	0.979539i	$-0.435498\pi$
$821$	5.23991e12	0.402513	0.201257	+	0.979539i	$0.435498\pi$
$822$	2.50311e13	1.91230
$823$	−1.68486e13	−1.28016	−0.640082	−	0.768306i	$-0.721100\pi$
$823$	−1.68486e13	−1.28016	−0.640082	+	0.768306i	$0.721100\pi$
$824$	2.08133e13	1.57278
$825$	9.10316e12	0.684147
$826$	−2.33225e13	−1.74327
$827$	1.54030e13	1.14507	0.572535	−	0.819881i	$-0.305960\pi$
$827$	1.54030e13	1.14507	0.572535	+	0.819881i	$0.305960\pi$
$828$	−1.70359e13	−1.25959
$829$	−2.97263e12	−0.218598	−0.109299	−	0.994009i	$-0.534861\pi$
$829$	−2.97263e12	−0.218598	−0.109299	+	0.994009i	$0.534861\pi$
$830$	−9.98792e12	−0.730506
$831$	−2.68854e13	−1.95574
$832$	−1.18396e13	−0.856606
$833$	7.01154e13	5.04558
$834$	−8.28106e12	−0.592705
$835$	4.70333e12	0.334824
$836$	−3.53683e12	−0.250430
$837$	−7.77697e12	−0.547704
$838$	3.09460e13	2.16774
$839$	−1.22129e13	−0.850919	−0.425459	−	0.904977i	$-0.639888\pi$
$839$	−1.22129e13	−0.850919	−0.425459	+	0.904977i	$0.639888\pi$
$840$	1.30177e13	0.902146
$841$	5.00246e11	0.0344828
$842$	6.45166e12	0.442351
$843$	−1.29395e13	−0.882457
$844$	4.04008e13	2.74062
$845$	1.12685e12	0.0760344
$846$	−7.46624e12	−0.501113
$847$	−1.97181e13	−1.31641
$848$	−1.35176e13	−0.897676
$849$	1.12031e13	0.740035
$850$	−4.34329e13	−2.85387
$851$	−3.81791e12	−0.249542
$852$	3.16408e13	2.05717
$853$	2.74191e13	1.77330	0.886650	−	0.462442i	$-0.153027\pi$
$853$	2.74191e13	1.77330	0.886650	+	0.462442i	$0.153027\pi$
$854$	−6.19046e13	−3.98256
$855$	4.04762e11	0.0259031
$856$	−5.01414e12	−0.319201
$857$	2.36396e13	1.49702	0.748508	−	0.663125i	$-0.230770\pi$
$857$	2.36396e13	1.49702	0.748508	+	0.663125i	$0.230770\pi$
$858$	−1.58662e13	−0.999495
$859$	2.55139e13	1.59885	0.799426	−	0.600764i	$-0.205137\pi$
$859$	2.55139e13	1.59885	0.799426	+	0.600764i	$0.205137\pi$
$860$	−3.79354e12	−0.236484
$861$	4.31731e12	0.267731
$862$	−1.28284e12	−0.0791386
$863$	1.89660e13	1.16393	0.581966	−	0.813213i	$-0.302284\pi$
$863$	1.89660e13	1.16393	0.581966	+	0.813213i	$0.302284\pi$
$864$	−6.76269e11	−0.0412865
$865$	1.96645e12	0.119429
$866$	3.16002e13	1.90923
$867$	−4.16037e13	−2.50061
$868$	−6.32138e13	−3.77984
$869$	−1.32745e13	−0.789639
$870$	1.46338e12	0.0866005
$871$	2.45744e13	1.44678
$872$	−3.60599e13	−2.11203
$873$	3.84527e12	0.224059
$874$	7.63096e12	0.442362
$875$	1.45544e13	0.839379
$876$	−1.96845e13	−1.12942
$877$	−2.76003e13	−1.57549	−0.787744	−	0.616003i	$-0.788751\pi$
$877$	−2.76003e13	−1.57549	−0.787744	+	0.616003i	$0.788751\pi$
$878$	1.97854e13	1.12362
$879$	1.21697e13	0.687589
$880$	−2.09381e12	−0.117697
$881$	9.02572e12	0.504766	0.252383	−	0.967627i	$-0.418786\pi$
$881$	9.02572e12	0.504766	0.252383	+	0.967627i	$0.418786\pi$
$882$	4.90443e13	2.72885
$883$	1.30038e13	0.719861	0.359931	−	0.932979i	$-0.382800\pi$
$883$	1.30038e13	0.719861	0.359931	+	0.932979i	$0.382800\pi$
$884$	5.02864e13	2.76959
$885$	−2.51990e12	−0.138083
$886$	3.45804e13	1.88529
$887$	−1.10687e13	−0.600399	−0.300199	−	0.953876i	$-0.597053\pi$
$887$	−1.10687e13	−0.600399	−0.300199	+	0.953876i	$0.597053\pi$
$888$	−8.29131e12	−0.447471
$889$	−1.48958e13	−0.799848
$890$	1.10292e12	0.0589236
$891$	−1.35697e13	−0.721307
$892$	−5.14132e13	−2.71915
$893$	2.22161e12	0.116906
$894$	5.16676e13	2.70520
$895$	3.44292e12	0.179359
$896$	−6.71290e13	−3.47956
$897$	2.27399e13	1.17280
$898$	3.32886e13	1.70825
$899$	−3.51478e12	−0.179465
$900$	−2.01811e13	−1.02530
$901$	−3.29122e13	−1.66378
$902$	−2.16166e12	−0.108732
$903$	−2.69685e13	−1.34978
$904$	−4.81888e13	−2.39987
$905$	3.31545e12	0.164295
$906$	9.13371e12	0.450371
$907$	2.97715e13	1.46072	0.730362	−	0.683061i	$-0.239352\pi$
$907$	2.97715e13	1.46072	0.730362	+	0.683061i	$0.239352\pi$
$908$	2.66354e13	1.30039
$909$	−1.16232e13	−0.564664
$910$	−1.23765e13	−0.598290
$911$	1.78394e13	0.858119	0.429059	−	0.903276i	$-0.358845\pi$
$911$	1.78394e13	0.858119	0.429059	+	0.903276i	$0.358845\pi$
$912$	5.32361e12	0.254818
$913$	2.36164e13	1.12485
$914$	−2.00887e13	−0.952126
$915$	−6.68856e12	−0.315455
$916$	−7.75166e12	−0.363802
$917$	3.06727e13	1.43249
$918$	3.65287e13	1.69763
$919$	−4.33224e12	−0.200351	−0.100176	−	0.994970i	$-0.531941\pi$
$919$	−4.33224e12	−0.200351	−0.100176	+	0.994970i	$0.531941\pi$
$920$	9.34165e12	0.429911
$921$	−9.69574e12	−0.444030
$922$	−5.53403e13	−2.52204
$923$	−1.48790e13	−0.674787
$924$	−6.22314e13	−2.80857
$925$	−4.52279e12	−0.203127
$926$	1.79290e13	0.801319
$927$	1.13868e13	0.506459
$928$	−3.05638e11	−0.0135282
$929$	−3.94834e13	−1.73918	−0.869588	−	0.493779i	$-0.835615\pi$
$929$	−3.94834e13	−1.73918	−0.869588	+	0.493779i	$0.835615\pi$
$930$	−1.02818e13	−0.450710
$931$	−1.45933e13	−0.636620
$932$	4.48010e13	1.94498
$933$	−2.25669e13	−0.974999
$934$	−1.74917e13	−0.752091
$935$	−5.09794e12	−0.218144
$936$	1.73975e13	0.740878
$937$	−9.51098e12	−0.403085	−0.201543	−	0.979480i	$-0.564595\pi$
$937$	−9.51098e12	−0.403085	−0.201543	+	0.979480i	$0.564595\pi$
$938$	1.45100e14	6.12006
$939$	6.30166e12	0.264521
$940$	5.49857e12	0.229707
$941$	2.78154e13	1.15646	0.578232	−	0.815872i	$-0.303743\pi$
$941$	2.78154e13	1.15646	0.578232	+	0.815872i	$0.303743\pi$
$942$	−7.95041e13	−3.28973
$943$	3.09815e12	0.127585
$944$	−1.16759e13	−0.478539
$945$	−5.97217e12	−0.243606
$946$	1.35030e13	0.548177
$947$	−1.51421e13	−0.611804	−0.305902	−	0.952063i	$-0.598958\pi$
$947$	−1.51421e13	−0.611804	−0.305902	+	0.952063i	$0.598958\pi$
$948$	8.35350e13	3.35916
$949$	9.25657e12	0.370469
$950$	9.03981e12	0.360083
$951$	−4.66891e13	−1.85099
$952$	1.46858e14	5.79471
$953$	7.81405e11	0.0306872	0.0153436	−	0.999882i	$-0.495116\pi$
$953$	7.81405e11	0.0306872	0.0153436	+	0.999882i	$0.495116\pi$
$954$	−2.30214e13	−0.899838
$955$	−2.34232e12	−0.0911236
$956$	7.18659e12	0.278267
$957$	−3.46015e12	−0.133349
$958$	−5.38508e13	−2.06561
$959$	−4.61681e13	−1.76262
$960$	−7.55320e12	−0.287019
$961$	−1.74450e12	−0.0659805
$962$	7.88292e12	0.296756
$963$	−2.74320e12	−0.102787
$964$	−6.22021e12	−0.231984
$965$	−1.04872e13	−0.389303
$966$	1.34269e14	4.96109
$967$	4.15674e13	1.52874	0.764370	−	0.644778i	$-0.223050\pi$
$967$	4.15674e13	1.52874	0.764370	+	0.644778i	$0.223050\pi$
$968$	−3.07293e13	−1.12490
$969$	1.29617e13	0.472287
$970$	−4.26309e12	−0.154615
$971$	2.30558e13	0.832327	0.416163	−	0.909290i	$-0.363374\pi$
$971$	2.30558e13	0.832327	0.416163	+	0.909290i	$0.363374\pi$
$972$	5.41867e13	1.94713
$973$	1.52738e13	0.546312
$974$	1.31906e13	0.469623
$975$	2.69383e13	0.954660
$976$	−3.09914e13	−1.09324
$977$	−2.15282e13	−0.755930	−0.377965	−	0.925820i	$-0.623376\pi$
$977$	−2.15282e13	−0.755930	−0.377965	+	0.925820i	$0.623376\pi$
$978$	−5.51889e13	−1.92898
$979$	−2.60785e12	−0.0907319
$980$	−3.61190e13	−1.25089
$981$	−1.97281e13	−0.680105
$982$	−2.54953e13	−0.874900
$983$	−1.12766e13	−0.385200	−0.192600	−	0.981277i	$-0.561692\pi$
$983$	−1.12766e13	−0.385200	−0.192600	+	0.981277i	$0.561692\pi$
$984$	6.72822e12	0.228782
$985$	1.63649e12	0.0553925
$986$	1.65090e13	0.556257
$987$	3.90898e13	1.31110
$988$	−1.04662e13	−0.349450
$989$	−1.93529e13	−0.643226
$990$	−3.56590e12	−0.117981
$991$	4.73642e13	1.55998	0.779990	−	0.625792i	$-0.215224\pi$
$991$	4.73642e13	1.55998	0.779990	+	0.625792i	$0.215224\pi$
$992$	2.14744e12	0.0704074
$993$	−1.45395e13	−0.474546
$994$	−8.78536e13	−2.85444
$995$	−6.15281e12	−0.199008
$996$	−1.48615e14	−4.78516
$997$	−1.70262e12	−0.0545745	−0.0272873	−	0.999628i	$-0.508687\pi$
$997$	−1.70262e12	−0.0545745	−0.0272873	+	0.999628i	$0.508687\pi$
$998$	−1.01334e14	−3.23346
$999$	3.80383e12	0.120830

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q+39.0522 q^{2} -174.323 q^{3} +1013.08 q^{4} -303.923 q^{5} -6807.72 q^{6} +12556.4 q^{7} +19568.2 q^{8} +10705.6 q^{9} +O(q^{10})\)	\(q+39.0522 q^{2} -174.323 q^{3} +1013.08 q^{4} -303.923 q^{5} -6807.72 q^{6} +12556.4 q^{7} +19568.2 q^{8} +10705.6 q^{9} -11868.9 q^{10} +28063.9 q^{11} -176603. q^{12} +83047.1 q^{13} +490354. q^{14} +52980.9 q^{15} +245486. q^{16} +597701. q^{17} +418079. q^{18} -124401. q^{19} -307898. q^{20} -2.18887e6 q^{21} +1.09596e6 q^{22} -1.57076e6 q^{23} -3.41119e6 q^{24} -1.86076e6 q^{25} +3.24318e6 q^{26} +1.56496e6 q^{27} +1.27206e7 q^{28} +707281. q^{29} +2.06902e6 q^{30} -4.96942e6 q^{31} -432131. q^{32} -4.89219e6 q^{33} +2.33415e7 q^{34} -3.81617e6 q^{35} +1.08456e7 q^{36} +2.43062e6 q^{37} -4.85814e6 q^{38} -1.44771e7 q^{39} -5.94722e6 q^{40} -1.97239e6 q^{41} -8.54802e7 q^{42} +1.23208e7 q^{43} +2.84309e7 q^{44} -3.25369e6 q^{45} -6.13416e7 q^{46} -1.78585e7 q^{47} -4.27940e7 q^{48} +1.17309e8 q^{49} -7.26667e7 q^{50} -1.04193e8 q^{51} +8.41332e7 q^{52} -5.50648e7 q^{53} +6.11154e7 q^{54} -8.52925e6 q^{55} +2.45705e8 q^{56} +2.16860e7 q^{57} +2.76209e7 q^{58} -4.75625e7 q^{59} +5.36737e7 q^{60} -1.26245e8 q^{61} -1.94067e8 q^{62} +1.34424e8 q^{63} -1.42565e8 q^{64} -2.52399e7 q^{65} -1.91051e8 q^{66} +2.95909e8 q^{67} +6.05517e8 q^{68} +2.73820e8 q^{69} -1.49030e8 q^{70} -1.79164e8 q^{71} +2.09490e8 q^{72} +1.11462e8 q^{73} +9.49211e7 q^{74} +3.24373e8 q^{75} -1.26028e8 q^{76} +3.52380e8 q^{77} -5.65361e8 q^{78} -4.73010e8 q^{79} -7.46089e7 q^{80} -4.83529e8 q^{81} -7.70264e7 q^{82} +8.41522e8 q^{83} -2.21749e9 q^{84} -1.81655e8 q^{85} +4.81154e8 q^{86} -1.23296e8 q^{87} +5.49159e8 q^{88} -9.29254e7 q^{89} -1.27064e8 q^{90} +1.04277e9 q^{91} -1.59130e9 q^{92} +8.66286e8 q^{93} -6.97413e8 q^{94} +3.78083e7 q^{95} +7.53305e7 q^{96} +3.59182e8 q^{97} +4.58116e9 q^{98} +3.00441e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 16 q^{2} + 242 q^{3} + 3498 q^{4} + 1762 q^{5} + 5446 q^{6} + 12080 q^{7} + 25350 q^{8} + 43026 q^{9}+O(q^{10}) \) 12 * q + 16 * q^2 + 242 * q^3 + 3498 * q^4 + 1762 * q^5 + 5446 * q^6 + 12080 * q^7 + 25350 * q^8 + 43026 * q^9	\( 12 q + 16 q^{2} + 242 q^{3} + 3498 q^{4} + 1762 q^{5} + 5446 q^{6} + 12080 q^{7} + 25350 q^{8} + 43026 q^{9} - 46678 q^{10} + 24474 q^{11} - 14210 q^{12} + 107722 q^{13} + 677768 q^{14} + 505426 q^{15} + 1656882 q^{16} + 982120 q^{17} + 2364102 q^{18} + 2084360 q^{19} + 4689410 q^{20} + 2911344 q^{21} + 2725230 q^{22} + 3004004 q^{23} + 7893170 q^{24} + 6339542 q^{25} + 6863698 q^{26} + 7881014 q^{27} + 5116944 q^{28} + 8487372 q^{29} + 10924626 q^{30} + 17872478 q^{31} + 5122946 q^{32} - 860442 q^{33} + 15662848 q^{34} - 22252312 q^{35} - 35199980 q^{36} + 452980 q^{37} - 68665276 q^{38} - 29528222 q^{39} - 61623214 q^{40} - 69039804 q^{41} - 150603216 q^{42} + 5379186 q^{43} - 58283762 q^{44} - 63687756 q^{45} - 76817844 q^{46} - 49104062 q^{47} - 99120062 q^{48} + 73113148 q^{49} - 281373726 q^{50} + 1578252 q^{51} - 49849646 q^{52} + 2253998 q^{53} - 166064634 q^{54} + 82907066 q^{55} + 119369464 q^{56} + 69024164 q^{57} + 11316496 q^{58} + 51587572 q^{59} - 107912622 q^{60} + 251179296 q^{61} + 2421010 q^{62} + 573206808 q^{63} + 460030950 q^{64} + 301434554 q^{65} + 305189958 q^{66} + 741046264 q^{67} + 503103116 q^{68} + 1480618500 q^{69} + 666826600 q^{70} + 488700124 q^{71} + 243154096 q^{72} + 1432375020 q^{73} - 208138340 q^{74} + 462882236 q^{75} - 253709644 q^{76} + 406327616 q^{77} - 1244370462 q^{78} + 400834638 q^{79} - 440320610 q^{80} + 207205984 q^{81} - 1992598260 q^{82} + 1525085236 q^{83} - 2191854376 q^{84} - 387675996 q^{85} - 3425646378 q^{86} + 171162002 q^{87} - 3147673814 q^{88} + 691159332 q^{89} - 2412410836 q^{90} + 1569278264 q^{91} - 2491626380 q^{92} + 270455138 q^{93} - 4397366402 q^{94} + 236293724 q^{95} - 1448270346 q^{96} + 2494422276 q^{97} - 3443098784 q^{98} + 2123567852 q^{99}+O(q^{100}) \) 12 * q + 16 * q^2 + 242 * q^3 + 3498 * q^4 + 1762 * q^5 + 5446 * q^6 + 12080 * q^7 + 25350 * q^8 + 43026 * q^9 - 46678 * q^10 + 24474 * q^11 - 14210 * q^12 + 107722 * q^13 + 677768 * q^14 + 505426 * q^15 + 1656882 * q^16 + 982120 * q^17 + 2364102 * q^18 + 2084360 * q^19 + 4689410 * q^20 + 2911344 * q^21 + 2725230 * q^22 + 3004004 * q^23 + 7893170 * q^24 + 6339542 * q^25 + 6863698 * q^26 + 7881014 * q^27 + 5116944 * q^28 + 8487372 * q^29 + 10924626 * q^30 + 17872478 * q^31 + 5122946 * q^32 - 860442 * q^33 + 15662848 * q^34 - 22252312 * q^35 - 35199980 * q^36 + 452980 * q^37 - 68665276 * q^38 - 29528222 * q^39 - 61623214 * q^40 - 69039804 * q^41 - 150603216 * q^42 + 5379186 * q^43 - 58283762 * q^44 - 63687756 * q^45 - 76817844 * q^46 - 49104062 * q^47 - 99120062 * q^48 + 73113148 * q^49 - 281373726 * q^50 + 1578252 * q^51 - 49849646 * q^52 + 2253998 * q^53 - 166064634 * q^54 + 82907066 * q^55 + 119369464 * q^56 + 69024164 * q^57 + 11316496 * q^58 + 51587572 * q^59 - 107912622 * q^60 + 251179296 * q^61 + 2421010 * q^62 + 573206808 * q^63 + 460030950 * q^64 + 301434554 * q^65 + 305189958 * q^66 + 741046264 * q^67 + 503103116 * q^68 + 1480618500 * q^69 + 666826600 * q^70 + 488700124 * q^71 + 243154096 * q^72 + 1432375020 * q^73 - 208138340 * q^74 + 462882236 * q^75 - 253709644 * q^76 + 406327616 * q^77 - 1244370462 * q^78 + 400834638 * q^79 - 440320610 * q^80 + 207205984 * q^81 - 1992598260 * q^82 + 1525085236 * q^83 - 2191854376 * q^84 - 387675996 * q^85 - 3425646378 * q^86 + 171162002 * q^87 - 3147673814 * q^88 + 691159332 * q^89 - 2412410836 * q^90 + 1569278264 * q^91 - 2491626380 * q^92 + 270455138 * q^93 - 4397366402 * q^94 + 236293724 * q^95 - 1448270346 * q^96 + 2494422276 * q^97 - 3443098784 * q^98 + 2123567852 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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