LMFDB - Embedded newform 289.10.a.h.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,10,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, 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("289.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	289.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:	$148.845356651$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.07469 q^{2} -18.6108 q^{3} -502.546 q^{4} +2540.06 q^{5} +57.2223 q^{6} +10949.3 q^{7} +3119.41 q^{8} -19336.6 q^{9} +O(q^{10})$	\(q-3.07469 q^{2} -18.6108 q^{3} -502.546 q^{4} +2540.06 q^{5} +57.2223 q^{6} +10949.3 q^{7} +3119.41 q^{8} -19336.6 q^{9} -7809.90 q^{10} -55022.0 q^{11} +9352.77 q^{12} -101901. q^{13} -33665.8 q^{14} -47272.5 q^{15} +247712. q^{16} +59454.1 q^{18} -243294. q^{19} -1.27650e6 q^{20} -203776. q^{21} +169176. q^{22} +799065. q^{23} -58054.7 q^{24} +4.49879e6 q^{25} +313313. q^{26} +726185. q^{27} -5.50255e6 q^{28} -1.08920e6 q^{29} +145348. q^{30} +6.11921e6 q^{31} -2.35878e6 q^{32} +1.02400e6 q^{33} +2.78120e7 q^{35} +9.71756e6 q^{36} -1.09051e7 q^{37} +748053. q^{38} +1.89645e6 q^{39} +7.92350e6 q^{40} -2.74132e6 q^{41} +626547. q^{42} +3.55746e7 q^{43} +2.76511e7 q^{44} -4.91163e7 q^{45} -2.45687e6 q^{46} -1.19501e7 q^{47} -4.61012e6 q^{48} +7.95346e7 q^{49} -1.38324e7 q^{50} +5.12099e7 q^{52} +6.12587e7 q^{53} -2.23279e6 q^{54} -1.39759e8 q^{55} +3.41555e7 q^{56} +4.52789e6 q^{57} +3.34895e6 q^{58} -7.89274e7 q^{59} +2.37566e7 q^{60} -5.32867e7 q^{61} -1.88147e7 q^{62} -2.11724e8 q^{63} -1.19576e8 q^{64} -2.58835e8 q^{65} -3.14849e6 q^{66} -1.84553e8 q^{67} -1.48712e7 q^{69} -8.55133e7 q^{70} +1.25020e8 q^{71} -6.03190e7 q^{72} -9.89488e6 q^{73} +3.35297e7 q^{74} -8.37259e7 q^{75} +1.22267e8 q^{76} -6.02455e8 q^{77} -5.83100e6 q^{78} +3.48965e8 q^{79} +6.29205e8 q^{80} +3.67088e8 q^{81} +8.42870e6 q^{82} -1.63123e8 q^{83} +1.02407e8 q^{84} -1.09381e8 q^{86} +2.02708e7 q^{87} -1.71636e8 q^{88} +1.08465e9 q^{89} +1.51017e8 q^{90} -1.11575e9 q^{91} -4.01567e8 q^{92} -1.13883e8 q^{93} +3.67427e7 q^{94} -6.17982e8 q^{95} +4.38987e7 q^{96} +1.20151e8 q^{97} -2.44544e8 q^{98} +1.06394e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) $ 36 * q + 486 * q^3 + 9216 * q^4 + 3750 * q^5 + 11061 * q^6 + 29040 * q^7 + 24837 * q^8 + 236196 * q^9	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9} + 60000 q^{10} + 76902 q^{11} + 373248 q^{12} + 54216 q^{13} + 17373 q^{14} - 34122 q^{15} + 2359296 q^{16} - 1779435 q^{18} - 245058 q^{19} + 6439479 q^{20} - 138102 q^{21} + 267324 q^{22} + 4041462 q^{23} + 7653888 q^{24} + 16582356 q^{25} + 15822744 q^{26} + 13281612 q^{27} + 18614784 q^{28} + 4005936 q^{29} + 22471686 q^{30} + 21257064 q^{31} - 30922641 q^{32} + 35736474 q^{33} - 9039642 q^{35} + 39076761 q^{36} + 22076682 q^{37} - 27401376 q^{38} + 62736162 q^{39} - 12231630 q^{40} + 59641782 q^{41} + 150001536 q^{42} - 47951586 q^{43} - 49578936 q^{44} + 129308238 q^{45} + 140524827 q^{46} - 118557912 q^{47} + 407719119 q^{48} + 99849138 q^{49} + 435669051 q^{50} - 105017607 q^{52} + 13698846 q^{53} + 209848575 q^{54} - 365439924 q^{55} + 203095059 q^{56} - 4614108 q^{57} - 179071413 q^{58} + 343015128 q^{59} + 427179186 q^{60} + 175597116 q^{61} + 720602571 q^{62} + 587415936 q^{63} + 853082511 q^{64} + 393820182 q^{65} - 494661978 q^{66} + 502776528 q^{67} - 469106598 q^{69} - 1062525966 q^{70} + 1308709542 q^{71} - 275337849 q^{72} + 494841342 q^{73} + 1545361890 q^{74} + 1824677616 q^{75} + 242064891 q^{76} - 792768144 q^{77} + 2270624538 q^{78} + 1980107868 q^{79} + 2897000199 q^{80} + 1598298840 q^{81} + 898743654 q^{82} + 275294520 q^{83} - 2144532369 q^{84} - 2880848046 q^{86} + 1088458710 q^{87} - 2705904618 q^{88} + 148394658 q^{89} + 117916215 q^{90} + 636340896 q^{91} - 3458472327 q^{92} - 628345524 q^{93} - 200245965 q^{94} + 4878626298 q^{95} - 8390096634 q^{96} - 891786822 q^{97} + 4285627647 q^{98} - 1476187998 q^{99}+O(q^{100}) \) 36 * q + 486 * q^3 + 9216 * q^4 + 3750 * q^5 + 11061 * q^6 + 29040 * q^7 + 24837 * q^8 + 236196 * q^9 + 60000 * q^10 + 76902 * q^11 + 373248 * q^12 + 54216 * q^13 + 17373 * q^14 - 34122 * q^15 + 2359296 * q^16 - 1779435 * q^18 - 245058 * q^19 + 6439479 * q^20 - 138102 * q^21 + 267324 * q^22 + 4041462 * q^23 + 7653888 * q^24 + 16582356 * q^25 + 15822744 * q^26 + 13281612 * q^27 + 18614784 * q^28 + 4005936 * q^29 + 22471686 * q^30 + 21257064 * q^31 - 30922641 * q^32 + 35736474 * q^33 - 9039642 * q^35 + 39076761 * q^36 + 22076682 * q^37 - 27401376 * q^38 + 62736162 * q^39 - 12231630 * q^40 + 59641782 * q^41 + 150001536 * q^42 - 47951586 * q^43 - 49578936 * q^44 + 129308238 * q^45 + 140524827 * q^46 - 118557912 * q^47 + 407719119 * q^48 + 99849138 * q^49 + 435669051 * q^50 - 105017607 * q^52 + 13698846 * q^53 + 209848575 * q^54 - 365439924 * q^55 + 203095059 * q^56 - 4614108 * q^57 - 179071413 * q^58 + 343015128 * q^59 + 427179186 * q^60 + 175597116 * q^61 + 720602571 * q^62 + 587415936 * q^63 + 853082511 * q^64 + 393820182 * q^65 - 494661978 * q^66 + 502776528 * q^67 - 469106598 * q^69 - 1062525966 * q^70 + 1308709542 * q^71 - 275337849 * q^72 + 494841342 * q^73 + 1545361890 * q^74 + 1824677616 * q^75 + 242064891 * q^76 - 792768144 * q^77 + 2270624538 * q^78 + 1980107868 * q^79 + 2897000199 * q^80 + 1598298840 * q^81 + 898743654 * q^82 + 275294520 * q^83 - 2144532369 * q^84 - 2880848046 * q^86 + 1088458710 * q^87 - 2705904618 * q^88 + 148394658 * q^89 + 117916215 * q^90 + 636340896 * q^91 - 3458472327 * q^92 - 628345524 * q^93 - 200245965 * q^94 + 4878626298 * q^95 - 8390096634 * q^96 - 891786822 * q^97 + 4285627647 * q^98 - 1476187998 * 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 $

$2$	−3.07469	−0.135883	−0.0679416	−	0.997689i	$-0.521643\pi$
$2$	−3.07469	−0.135883	−0.0679416	+	0.997689i	$0.521643\pi$
$3$	−18.6108	−0.132653	−0.0663267	−	0.997798i	$-0.521128\pi$
$3$	−18.6108	−0.132653	−0.0663267	+	0.997798i	$0.521128\pi$
$4$	−502.546	−0.981536
$5$	2540.06	1.81752	0.908760	−	0.417319i	$-0.137030\pi$
$5$	2540.06	1.81752	0.908760	+	0.417319i	$0.137030\pi$
$6$	57.2223	0.0180254
$7$	10949.3	1.72364	0.861821	−	0.507213i	$-0.169324\pi$
$7$	10949.3	1.72364	0.861821	+	0.507213i	$0.169324\pi$
$8$	3119.41	0.269258
$9$	−19336.6	−0.982403
$10$	−7809.90	−0.246971
$11$	−55022.0	−1.13310	−0.566552	−	0.824026i	$-0.691723\pi$
$11$	−55022.0	−1.13310	−0.566552	+	0.824026i	$0.691723\pi$
$12$	9352.77	0.130204
$13$	−101901.	−0.989539	−0.494770	−	0.869024i	$-0.664748\pi$
$13$	−101901.	−0.989539	−0.494770	+	0.869024i	$0.664748\pi$
$14$	−33665.8	−0.234214
$15$	−47272.5	−0.241100
$16$	247712.	0.944948
$17$	0	0
$17$	0	0
$18$	59454.1	0.133492
$19$	−243294.	−0.428292	−0.214146	−	0.976802i	$-0.568697\pi$
$19$	−243294.	−0.428292	−0.214146	+	0.976802i	$0.568697\pi$
$20$	−1.27650e6	−1.78396
$21$	−203776.	−0.228647
$22$	169176.	0.153970
$23$	799065.	0.595397	0.297699	−	0.954660i	$-0.403781\pi$
$23$	799065.	0.595397	0.297699	+	0.954660i	$0.403781\pi$
$24$	−58054.7	−0.0357180
$25$	4.49879e6	2.30338
$26$	313313.	0.134462
$27$	726185.	0.262973
$28$	−5.50255e6	−1.69182
$29$	−1.08920e6	−0.285967	−0.142984	−	0.989725i	$-0.545670\pi$
$29$	−1.08920e6	−0.285967	−0.142984	+	0.989725i	$0.545670\pi$
$30$	145348.	0.0327615
$31$	6.11921e6	1.19006	0.595028	−	0.803705i	$-0.297141\pi$
$31$	6.11921e6	1.19006	0.595028	+	0.803705i	$0.297141\pi$
$32$	−2.35878e6	−0.397660
$33$	1.02400e6	0.150310
$34$	0	0
$35$	2.78120e7	3.13275
$36$	9.71756e6	0.964264
$37$	−1.09051e7	−0.956578	−0.478289	−	0.878203i	$-0.658743\pi$
$37$	−1.09051e7	−0.956578	−0.478289	+	0.878203i	$0.658743\pi$
$38$	748053.	0.0581978
$39$	1.89645e6	0.131266
$40$	7.92350e6	0.489381
$41$	−2.74132e6	−0.151507	−0.0757534	−	0.997127i	$-0.524136\pi$
$41$	−2.74132e6	−0.151507	−0.0757534	+	0.997127i	$0.524136\pi$
$42$	626547.	0.0310693
$43$	3.55746e7	1.58684	0.793419	−	0.608676i	$-0.208299\pi$
$43$	3.55746e7	1.58684	0.793419	+	0.608676i	$0.208299\pi$
$44$	2.76511e7	1.11218
$45$	−4.91163e7	−1.78554
$46$	−2.45687e6	−0.0809045
$47$	−1.19501e7	−0.357215	−0.178607	−	0.983920i	$-0.557159\pi$
$47$	−1.19501e7	−0.357215	−0.178607	+	0.983920i	$0.557159\pi$
$48$	−4.61012e6	−0.125351
$49$	7.95346e7	1.97094
$50$	−1.38324e7	−0.312991
$51$	0	0
$52$	5.12099e7	0.971268
$53$	6.12587e7	1.06641	0.533207	−	0.845985i	$-0.320987\pi$
$53$	6.12587e7	1.06641	0.533207	+	0.845985i	$0.320987\pi$
$54$	−2.23279e6	−0.0357336
$55$	−1.39759e8	−2.05944
$56$	3.41555e7	0.464104
$57$	4.52789e6	0.0568144
$58$	3.34895e6	0.0388582
$59$	−7.89274e7	−0.847996	−0.423998	−	0.905663i	$-0.639374\pi$
$59$	−7.89274e7	−0.847996	−0.423998	+	0.905663i	$0.639374\pi$
$60$	2.37566e7	0.236649
$61$	−5.32867e7	−0.492759	−0.246379	−	0.969173i	$-0.579241\pi$
$61$	−5.32867e7	−0.492759	−0.246379	+	0.969173i	$0.579241\pi$
$62$	−1.88147e7	−0.161709
$63$	−2.11724e8	−1.69331
$64$	−1.19576e8	−0.890913
$65$	−2.58835e8	−1.79851
$66$	−3.14849e6	−0.0204246
$67$	−1.84553e8	−1.11888	−0.559441	−	0.828870i	$-0.688984\pi$
$67$	−1.84553e8	−1.11888	−0.559441	+	0.828870i	$0.688984\pi$
$68$	0	0
$69$	−1.48712e7	−0.0789815
$70$	−8.55133e7	−0.425689
$71$	1.25020e8	0.583871	0.291935	−	0.956438i	$-0.405701\pi$
$71$	1.25020e8	0.583871	0.291935	+	0.956438i	$0.405701\pi$
$72$	−6.03190e7	−0.264520
$73$	−9.89488e6	−0.0407810	−0.0203905	−	0.999792i	$-0.506491\pi$
$73$	−9.89488e6	−0.0407810	−0.0203905	+	0.999792i	$0.506491\pi$
$74$	3.35297e7	0.129983
$75$	−8.37259e7	−0.305551
$76$	1.22267e8	0.420384
$77$	−6.02455e8	−1.95306
$78$	−5.83100e6	−0.0178368
$79$	3.48965e8	1.00800	0.504000	−	0.863704i	$-0.331861\pi$
$79$	3.48965e8	1.00800	0.504000	+	0.863704i	$0.331861\pi$
$80$	6.29205e8	1.71746
$81$	3.67088e8	0.947519
$82$	8.42870e6	0.0205872
$83$	−1.63123e8	−0.377281	−0.188641	−	0.982046i	$-0.560408\pi$
$83$	−1.63123e8	−0.377281	−0.188641	+	0.982046i	$0.560408\pi$
$84$	1.02407e8	0.224425
$85$	0	0
$86$	−1.09381e8	−0.215625
$87$	2.02708e7	0.0379346
$88$	−1.71636e8	−0.305097
$89$	1.08465e9	1.83246	0.916229	−	0.400656i	$-0.131218\pi$
$89$	1.08465e9	1.83246	0.916229	+	0.400656i	$0.131218\pi$
$90$	1.51017e8	0.242625
$91$	−1.11575e9	−1.70561
$92$	−4.01567e8	−0.584404
$93$	−1.13883e8	−0.157865
$94$	3.67427e7	0.0485395
$95$	−6.17982e8	−0.778430
$96$	4.38987e7	0.0527510
$97$	1.20151e8	0.137802	0.0689009	−	0.997624i	$-0.478051\pi$
$97$	1.20151e8	0.137802	0.0689009	+	0.997624i	$0.478051\pi$
$98$	−2.44544e8	−0.267818
$99$	1.06394e9	1.11316
$100$	−2.26085e9	−2.26085
$101$	1.08867e9	1.04100	0.520498	−	0.853863i	$-0.325746\pi$
$101$	1.08867e9	1.04100	0.520498	+	0.853863i	$0.325746\pi$
$102$	0	0
$103$	−1.18252e9	−1.03524	−0.517622	−	0.855610i	$-0.673183\pi$
$103$	−1.18252e9	−1.03524	−0.517622	+	0.855610i	$0.673183\pi$
$104$	−3.17871e8	−0.266441
$105$	−5.17603e8	−0.415571
$106$	−1.88351e8	−0.144908
$107$	1.49518e9	1.10272	0.551361	−	0.834267i	$-0.314109\pi$
$107$	1.49518e9	1.10272	0.551361	+	0.834267i	$0.314109\pi$
$108$	−3.64942e8	−0.258117
$109$	2.08481e9	1.41464	0.707321	−	0.706892i	$-0.249903\pi$
$109$	2.08481e9	1.41464	0.707321	+	0.706892i	$0.249903\pi$
$110$	4.29716e8	0.279843
$111$	2.02952e8	0.126893
$112$	2.71229e9	1.62875
$113$	7.38570e8	0.426126	0.213063	−	0.977038i	$-0.431656\pi$
$113$	7.38570e8	0.426126	0.213063	+	0.977038i	$0.431656\pi$
$114$	−1.39218e7	−0.00772013
$115$	2.02967e9	1.08215
$116$	5.47373e8	0.280687
$117$	1.97042e9	0.972126
$118$	2.42677e8	0.115229
$119$	0	0
$120$	−1.47462e8	−0.0649181
$121$	6.69477e8	0.283924
$122$	1.63840e8	0.0669577
$123$	5.10180e7	0.0200979
$124$	−3.07519e9	−1.16808
$125$	6.46614e9	2.36892
$126$	6.50984e8	0.230093
$127$	−2.74828e9	−0.937441	−0.468721	−	0.883346i	$-0.655285\pi$
$127$	−2.74828e9	−0.937441	−0.468721	+	0.883346i	$0.655285\pi$
$128$	1.57535e9	0.518720
$129$	−6.62071e8	−0.210499
$130$	7.95836e8	0.244387
$131$	−5.20552e9	−1.54434	−0.772170	−	0.635416i	$-0.780829\pi$
$131$	−5.20552e9	−1.54434	−0.772170	+	0.635416i	$0.780829\pi$
$132$	−5.14609e8	−0.147535
$133$	−2.66391e9	−0.738223
$134$	5.67442e8	0.152037
$135$	1.84456e9	0.477958
$136$	0	0
$137$	6.18810e9	1.50077	0.750386	−	0.661000i	$-0.229868\pi$
$137$	6.18810e9	1.50077	0.750386	+	0.661000i	$0.229868\pi$
$138$	4.57243e7	0.0107323
$139$	−1.88233e9	−0.427690	−0.213845	−	0.976868i	$-0.568599\pi$
$139$	−1.88233e9	−0.427690	−0.213845	+	0.976868i	$0.568599\pi$
$140$	−1.39768e10	−3.07491
$141$	2.22400e8	0.0473858
$142$	−3.84397e8	−0.0793383
$143$	5.60680e9	1.12125
$144$	−4.78993e9	−0.928320
$145$	−2.76663e9	−0.519751
$146$	3.04237e7	0.00554146
$147$	−1.48020e9	−0.261452
$148$	5.48030e9	0.938915
$149$	8.74040e9	1.45276	0.726378	−	0.687295i	$-0.241202\pi$
$149$	8.74040e9	1.45276	0.726378	+	0.687295i	$0.241202\pi$
$150$	2.57431e8	0.0415193
$151$	4.41501e9	0.691091	0.345546	−	0.938402i	$-0.387694\pi$
$151$	4.41501e9	0.691091	0.345546	+	0.938402i	$0.387694\pi$
$152$	−7.58935e8	−0.115321
$153$	0	0
$154$	1.85236e9	0.265389
$155$	1.55432e10	2.16295
$156$	−9.53056e8	−0.128842
$157$	1.83214e9	0.240664	0.120332	−	0.992734i	$-0.461604\pi$
$157$	1.83214e9	0.240664	0.120332	+	0.992734i	$0.461604\pi$
$158$	−1.07296e9	−0.136970
$159$	−1.14007e9	−0.141464
$160$	−5.99144e9	−0.722756
$161$	8.74924e9	1.02625
$162$	−1.12868e9	−0.128752
$163$	3.05664e9	0.339156	0.169578	−	0.985517i	$-0.445759\pi$
$163$	3.05664e9	0.339156	0.169578	+	0.985517i	$0.445759\pi$
$164$	1.37764e9	0.148709
$165$	2.60103e9	0.273192
$166$	5.01554e8	0.0512662
$167$	−5.54078e9	−0.551248	−0.275624	−	0.961266i	$-0.588884\pi$
$167$	−5.54078e9	−0.551248	−0.275624	+	0.961266i	$0.588884\pi$
$168$	−6.35661e8	−0.0615650
$169$	−2.20706e8	−0.0208124
$170$	0	0
$171$	4.70449e9	0.420756
$172$	−1.78779e10	−1.55754
$173$	−2.19119e10	−1.85983	−0.929914	−	0.367778i	$-0.880119\pi$
$173$	−2.19119e10	−1.85983	−0.929914	+	0.367778i	$0.880119\pi$
$174$	−6.23265e7	−0.00515467
$175$	4.92588e10	3.97020
$176$	−1.36296e10	−1.07072
$177$	1.46890e9	0.112490
$178$	−3.33495e9	−0.249000
$179$	−7.29594e9	−0.531181	−0.265591	−	0.964086i	$-0.585567\pi$
$179$	−7.29594e9	−0.531181	−0.265591	+	0.964086i	$0.585567\pi$
$180$	2.46832e10	1.75257
$181$	2.75510e10	1.90802	0.954011	−	0.299770i	$-0.0969100\pi$
$181$	2.75510e10	1.90802	0.954011	+	0.299770i	$0.0969100\pi$
$182$	3.43058e9	0.231764
$183$	9.91705e8	0.0653661
$184$	2.49261e9	0.160315
$185$	−2.76995e10	−1.73860
$186$	3.50155e8	0.0214512
$187$	0	0
$188$	6.00545e9	0.350619
$189$	7.95126e9	0.453271
$190$	1.90010e9	0.105776
$191$	8.40002e9	0.456699	0.228350	−	0.973579i	$-0.426667\pi$
$191$	8.40002e9	0.456699	0.228350	+	0.973579i	$0.426667\pi$
$192$	2.22541e9	0.118183
$193$	−2.32479e10	−1.20608	−0.603040	−	0.797711i	$-0.706044\pi$
$193$	−2.32479e10	−1.20608	−0.603040	+	0.797711i	$0.706044\pi$
$194$	−3.69427e8	−0.0187250
$195$	4.81711e9	0.238578
$196$	−3.99698e10	−1.93455
$197$	−2.22594e10	−1.05297	−0.526485	−	0.850185i	$-0.676490\pi$
$197$	−2.22594e10	−1.05297	−0.526485	+	0.850185i	$0.676490\pi$
$198$	−3.27129e9	−0.151260
$199$	1.96549e10	0.888447	0.444223	−	0.895916i	$-0.353480\pi$
$199$	1.96549e10	0.888447	0.444223	+	0.895916i	$0.353480\pi$
$200$	1.40336e10	0.620202
$201$	3.43467e9	0.148423
$202$	−3.34731e9	−0.141454
$203$	−1.19260e10	−0.492905
$204$	0	0
$205$	−6.96312e9	−0.275367
$206$	3.63589e9	0.140672
$207$	−1.54512e10	−0.584920
$208$	−2.52421e10	−0.935063
$209$	1.33865e10	0.485299
$210$	1.59147e9	0.0564691
$211$	2.13271e10	0.740730	0.370365	−	0.928886i	$-0.379233\pi$
$211$	2.13271e10	0.740730	0.370365	+	0.928886i	$0.379233\pi$
$212$	−3.07853e10	−1.04672
$213$	−2.32672e9	−0.0774525
$214$	−4.59721e9	−0.149842
$215$	9.03618e10	2.88411
$216$	2.26527e9	0.0708074
$217$	6.70013e10	2.05123
$218$	−6.41013e9	−0.192226
$219$	1.84151e8	0.00540974
$220$	7.02356e10	2.02141
$221$	0	0
$222$	−6.24013e8	−0.0172427
$223$	1.60477e10	0.434552	0.217276	−	0.976110i	$-0.430283\pi$
$223$	1.60477e10	0.434552	0.217276	+	0.976110i	$0.430283\pi$
$224$	−2.58271e10	−0.685424
$225$	−8.69914e10	−2.26285
$226$	−2.27087e9	−0.0579035
$227$	6.61656e10	1.65393	0.826963	−	0.562257i	$-0.190067\pi$
$227$	6.61656e10	1.65393	0.826963	+	0.562257i	$0.190067\pi$
$228$	−2.27547e9	−0.0557654
$229$	−4.43447e10	−1.06557	−0.532786	−	0.846250i	$-0.678855\pi$
$229$	−4.43447e10	−1.06557	−0.532786	+	0.846250i	$0.678855\pi$
$230$	−6.24061e9	−0.147046
$231$	1.12122e10	0.259081
$232$	−3.39766e9	−0.0769989
$233$	−5.39484e9	−0.119916	−0.0599579	−	0.998201i	$-0.519097\pi$
$233$	−5.39484e9	−0.119916	−0.0599579	+	0.998201i	$0.519097\pi$
$234$	−6.05843e9	−0.132096
$235$	−3.03539e10	−0.649245
$236$	3.96647e10	0.832339
$237$	−6.49451e9	−0.133715
$238$	0	0
$239$	4.13971e10	0.820690	0.410345	−	0.911930i	$-0.365408\pi$
$239$	4.13971e10	0.820690	0.410345	+	0.911930i	$0.365408\pi$
$240$	−1.17100e10	−0.227827
$241$	1.66107e10	0.317183	0.158592	−	0.987344i	$-0.449305\pi$
$241$	1.66107e10	0.317183	0.158592	+	0.987344i	$0.449305\pi$
$242$	−2.05843e9	−0.0385805
$243$	−2.11253e10	−0.388664
$244$	2.67790e10	0.483660
$245$	2.02023e11	3.58223
$246$	−1.56865e8	−0.00273097
$247$	2.47919e10	0.423812
$248$	1.90883e10	0.320432
$249$	3.03585e9	0.0500476
$250$	−1.98814e10	−0.321896
$251$	3.10377e10	0.493581	0.246790	−	0.969069i	$-0.420624\pi$
$251$	3.10377e10	0.493581	0.246790	+	0.969069i	$0.420624\pi$
$252$	1.06401e11	1.66205
$253$	−4.39662e10	−0.674647
$254$	8.45010e9	0.127383
$255$	0	0
$256$	5.63793e10	0.820427
$257$	5.97981e10	0.855044	0.427522	−	0.904005i	$-0.359387\pi$
$257$	5.97981e10	0.855044	0.427522	+	0.904005i	$0.359387\pi$
$258$	2.03566e9	0.0286034
$259$	−1.19403e11	−1.64880
$260$	1.30076e11	1.76530
$261$	2.10615e10	0.280935
$262$	1.60053e10	0.209850
$263$	−3.18665e10	−0.410709	−0.205354	−	0.978688i	$-0.565835\pi$
$263$	−3.18665e10	−0.410709	−0.205354	+	0.978688i	$0.565835\pi$
$264$	3.19429e9	0.0404721
$265$	1.55601e11	1.93823
$266$	8.19069e9	0.100312
$267$	−2.01861e10	−0.243082
$268$	9.27463e10	1.09822
$269$	3.97001e10	0.462281	0.231141	−	0.972920i	$-0.425754\pi$
$269$	3.97001e10	0.462281	0.231141	+	0.972920i	$0.425754\pi$
$270$	−5.67143e9	−0.0649465
$271$	7.58840e10	0.854650	0.427325	−	0.904098i	$-0.359456\pi$
$271$	7.58840e10	0.854650	0.427325	+	0.904098i	$0.359456\pi$
$272$	0	0
$273$	2.07649e10	0.226255
$274$	−1.90265e10	−0.203930
$275$	−2.47532e11	−2.60997
$276$	7.47347e9	0.0775231
$277$	7.03115e10	0.717575	0.358788	−	0.933419i	$-0.383190\pi$
$277$	7.03115e10	0.717575	0.358788	+	0.933419i	$0.383190\pi$
$278$	5.78758e9	0.0581160
$279$	−1.18325e11	−1.16912
$280$	8.67572e10	0.843518
$281$	4.27010e10	0.408563	0.204282	−	0.978912i	$-0.434514\pi$
$281$	4.27010e10	0.408563	0.204282	+	0.978912i	$0.434514\pi$
$282$	−6.83809e8	−0.00643894
$283$	1.99849e10	0.185209	0.0926047	−	0.995703i	$-0.470481\pi$
$283$	1.99849e10	0.185209	0.0926047	+	0.995703i	$0.470481\pi$
$284$	−6.28283e10	−0.573090
$285$	1.15011e10	0.103261
$286$	−1.72391e10	−0.152359
$287$	−3.00156e10	−0.261143
$288$	4.56108e10	0.390663
$289$	0	0
$290$	8.50653e9	0.0706255
$291$	−2.23610e9	−0.0182799
$292$	4.97264e9	0.0400280
$293$	1.04039e11	0.824695	0.412347	−	0.911027i	$-0.364709\pi$
$293$	1.04039e11	0.824695	0.412347	+	0.911027i	$0.364709\pi$
$294$	4.55115e9	0.0355270
$295$	−2.00481e11	−1.54125
$296$	−3.40174e10	−0.257566
$297$	−3.99562e10	−0.297975
$298$	−2.68740e10	−0.197405
$299$	−8.14254e10	−0.589169
$300$	4.20761e10	0.299909
$301$	3.89519e11	2.73514
$302$	−1.35748e10	−0.0939077
$303$	−2.02609e10	−0.138092
$304$	−6.02670e10	−0.404714
$305$	−1.35351e11	−0.895599
$306$	0	0
$307$	1.84431e11	1.18498	0.592490	−	0.805578i	$-0.298145\pi$
$307$	1.84431e11	1.18498	0.592490	+	0.805578i	$0.298145\pi$
$308$	3.02762e11	1.91700
$309$	2.20077e10	0.137329
$310$	−4.77904e10	−0.293909
$311$	1.22863e11	0.744731	0.372365	−	0.928086i	$-0.378547\pi$
$311$	1.22863e11	0.744731	0.372365	+	0.928086i	$0.378547\pi$
$312$	5.91582e9	0.0353443
$313$	−4.77009e10	−0.280916	−0.140458	−	0.990087i	$-0.544858\pi$
$313$	−4.77009e10	−0.280916	−0.140458	+	0.990087i	$0.544858\pi$
$314$	−5.63327e9	−0.0327022
$315$	−5.37791e11	−3.07763
$316$	−1.75371e11	−0.989388
$317$	2.10729e11	1.17208	0.586041	−	0.810281i	$-0.300686\pi$
$317$	2.10729e11	1.17208	0.586041	+	0.810281i	$0.300686\pi$
$318$	3.50536e9	0.0192225
$319$	5.99300e10	0.324031
$320$	−3.03731e11	−1.61925
$321$	−2.78264e10	−0.146280
$322$	−2.69012e10	−0.139450
$323$	0	0
$324$	−1.84479e11	−0.930024
$325$	−4.58431e11	−2.27928
$326$	−9.39821e9	−0.0460857
$327$	−3.87999e10	−0.187657
$328$	−8.55130e9	−0.0407944
$329$	−1.30845e11	−0.615710
$330$	−7.99735e9	−0.0371222
$331$	−3.32123e10	−0.152080	−0.0760400	−	0.997105i	$-0.524228\pi$
$331$	−3.32123e10	−0.152080	−0.0760400	+	0.997105i	$0.524228\pi$
$332$	8.19771e10	0.370315
$333$	2.10867e11	0.939745
$334$	1.70362e10	0.0749054
$335$	−4.68775e11	−2.03359
$336$	−5.04778e10	−0.216060
$337$	−3.00476e11	−1.26904	−0.634519	−	0.772907i	$-0.718802\pi$
$337$	−3.00476e11	−1.26904	−0.634519	+	0.772907i	$0.718802\pi$
$338$	6.78601e8	0.00282806
$339$	−1.37453e10	−0.0565271
$340$	0	0
$341$	−3.36691e11	−1.34846
$342$	−1.44648e10	−0.0571737
$343$	4.29006e11	1.67356
$344$	1.10972e11	0.427268
$345$	−3.77738e10	−0.143550
$346$	6.73723e10	0.252719
$347$	−3.76252e11	−1.39314	−0.696571	−	0.717487i	$-0.745292\pi$
$347$	−3.76252e11	−1.39314	−0.696571	+	0.717487i	$0.745292\pi$
$348$	−1.01870e10	−0.0372341
$349$	2.25550e11	0.813819	0.406909	−	0.913469i	$-0.366607\pi$
$349$	2.25550e11	0.813819	0.406909	+	0.913469i	$0.366607\pi$
$350$	−1.51455e11	−0.539484
$351$	−7.39989e10	−0.260222
$352$	1.29785e11	0.450590
$353$	7.61898e9	0.0261162	0.0130581	−	0.999915i	$-0.495843\pi$
$353$	7.61898e9	0.0261162	0.0130581	+	0.999915i	$0.495843\pi$
$354$	−4.51641e9	−0.0152855
$355$	3.17558e11	1.06120
$356$	−5.45086e11	−1.79862
$357$	0	0
$358$	2.24328e10	0.0721787
$359$	2.66775e11	0.847656	0.423828	−	0.905743i	$-0.360686\pi$
$359$	2.66775e11	0.847656	0.423828	+	0.905743i	$0.360686\pi$
$360$	−1.53214e11	−0.480770
$361$	−2.63496e11	−0.816566
$362$	−8.47107e10	−0.259268
$363$	−1.24595e10	−0.0376634
$364$	5.60715e11	1.67412
$365$	−2.51336e10	−0.0741203
$366$	−3.04918e9	−0.00888217
$367$	2.28618e11	0.657829	0.328914	−	0.944360i	$-0.393317\pi$
$367$	2.28618e11	0.657829	0.328914	+	0.944360i	$0.393317\pi$
$368$	1.97938e11	0.562619
$369$	5.30079e10	0.148841
$370$	8.51674e10	0.236247
$371$	6.70743e11	1.83812
$372$	5.72316e10	0.154950
$373$	6.18391e11	1.65415	0.827073	−	0.562095i	$-0.190005\pi$
$373$	6.18391e11	1.65415	0.827073	+	0.562095i	$0.190005\pi$
$374$	0	0
$375$	−1.20340e11	−0.314245
$376$	−3.72771e10	−0.0961828
$377$	1.10990e11	0.282976
$378$	−2.44476e10	−0.0615919
$379$	−2.10741e11	−0.524654	−0.262327	−	0.964979i	$-0.584490\pi$
$379$	−2.10741e11	−0.524654	−0.262327	+	0.964979i	$0.584490\pi$
$380$	3.10564e11	0.764057
$381$	5.11476e10	0.124355
$382$	−2.58274e10	−0.0620578
$383$	3.03050e11	0.719648	0.359824	−	0.933020i	$-0.382837\pi$
$383$	3.03050e11	0.719648	0.359824	+	0.933020i	$0.382837\pi$
$384$	−2.93185e10	−0.0688101
$385$	−1.53027e12	−3.54973
$386$	7.14800e10	0.163886
$387$	−6.87894e11	−1.55891
$388$	−6.03815e10	−0.135257
$389$	−3.07324e11	−0.680491	−0.340246	−	0.940337i	$-0.610510\pi$
$389$	−3.07324e11	−0.680491	−0.340246	+	0.940337i	$0.610510\pi$
$390$	−1.48111e10	−0.0324188
$391$	0	0
$392$	2.48101e11	0.530691
$393$	9.68787e10	0.204862
$394$	6.84408e10	0.143081
$395$	8.86394e11	1.83206
$396$	−5.34680e11	−1.09261
$397$	2.80841e11	0.567418	0.283709	−	0.958910i	$-0.408435\pi$
$397$	2.80841e11	0.567418	0.283709	+	0.958910i	$0.408435\pi$
$398$	−6.04326e10	−0.120725
$399$	4.95774e10	0.0979278
$400$	1.11441e12	2.17657
$401$	−3.13411e11	−0.605291	−0.302645	−	0.953103i	$-0.597870\pi$
$401$	−3.13411e11	−0.605291	−0.302645	+	0.953103i	$0.597870\pi$
$402$	−1.05605e10	−0.0201683
$403$	−6.23553e11	−1.17761
$404$	−5.47106e11	−1.02177
$405$	9.32427e11	1.72213
$406$	3.66688e10	0.0669776
$407$	6.00019e11	1.08390
$408$	0	0
$409$	5.95263e11	1.05185	0.525926	−	0.850531i	$-0.323719\pi$
$409$	5.95263e11	1.05185	0.525926	+	0.850531i	$0.323719\pi$
$410$	2.14094e10	0.0374177
$411$	−1.15165e11	−0.199082
$412$	5.94273e11	1.01613
$413$	−8.64204e11	−1.46164
$414$	4.75077e10	0.0794808
$415$	−4.14344e11	−0.685716
$416$	2.40362e11	0.393500
$417$	3.50316e10	0.0567346
$418$	−4.11594e10	−0.0659441
$419$	3.62055e11	0.573867	0.286934	−	0.957950i	$-0.407364\pi$
$419$	3.62055e11	0.573867	0.286934	+	0.957950i	$0.407364\pi$
$420$	2.60119e11	0.407897
$421$	1.01670e12	1.57734	0.788668	−	0.614819i	$-0.210771\pi$
$421$	1.01670e12	1.57734	0.788668	+	0.614819i	$0.210771\pi$
$422$	−6.55740e10	−0.100653
$423$	2.31074e11	0.350929
$424$	1.91091e11	0.287140
$425$	0	0
$426$	7.15393e9	0.0105245
$427$	−5.83454e11	−0.849339
$428$	−7.51397e11	−1.08236
$429$	−1.04347e11	−0.148738
$430$	−2.77834e11	−0.391902
$431$	8.42323e11	1.17579	0.587897	−	0.808936i	$-0.299956\pi$
$431$	8.42323e11	1.17579	0.587897	+	0.808936i	$0.299956\pi$
$432$	1.79885e11	0.248495
$433$	1.18575e12	1.62106	0.810529	−	0.585698i	$-0.199180\pi$
$433$	1.18575e12	1.62106	0.810529	+	0.585698i	$0.199180\pi$
$434$	−2.06008e11	−0.278728
$435$	5.14892e10	0.0689468
$436$	−1.04771e12	−1.38852
$437$	−1.94408e11	−0.255004
$438$	−5.66208e8	−0.000735093 0
$439$	−2.80153e11	−0.360002	−0.180001	−	0.983666i	$-0.557610\pi$
$439$	−2.80153e11	−0.360002	−0.180001	+	0.983666i	$0.557610\pi$
$440$	−4.35967e11	−0.554519
$441$	−1.53793e12	−1.93626
$442$	0	0
$443$	−1.03647e12	−1.27861	−0.639307	−	0.768951i	$-0.720779\pi$
$443$	−1.03647e12	−1.27861	−0.639307	+	0.768951i	$0.720779\pi$
$444$	−1.01993e11	−0.124550
$445$	2.75507e12	3.33053
$446$	−4.93418e10	−0.0590484
$447$	−1.62665e11	−0.192713
$448$	−1.30928e12	−1.53561
$449$	−9.51471e11	−1.10481	−0.552404	−	0.833576i	$-0.686290\pi$
$449$	−9.51471e11	−1.10481	−0.552404	+	0.833576i	$0.686290\pi$
$450$	2.67472e11	0.307483
$451$	1.50833e11	0.171673
$452$	−3.71165e11	−0.418258
$453$	−8.21667e10	−0.0916756
$454$	−2.03439e11	−0.224741
$455$	−2.83407e12	−3.09998
$456$	1.41244e10	0.0152977
$457$	5.23939e11	0.561899	0.280949	−	0.959723i	$-0.409351\pi$
$457$	5.23939e11	0.561899	0.280949	+	0.959723i	$0.409351\pi$
$458$	1.36346e11	0.144793
$459$	0	0
$460$	−1.02000e12	−1.06217
$461$	−1.57356e12	−1.62267	−0.811333	−	0.584585i	$-0.801257\pi$
$461$	−1.57356e12	−1.62267	−0.811333	+	0.584585i	$0.801257\pi$
$462$	−3.44739e10	−0.0352048
$463$	8.11193e11	0.820370	0.410185	−	0.912002i	$-0.365464\pi$
$463$	8.11193e11	0.820370	0.410185	+	0.912002i	$0.365464\pi$
$464$	−2.69808e11	−0.270224
$465$	−2.89270e11	−0.286923
$466$	1.65874e10	0.0162946
$467$	−1.43619e12	−1.39729	−0.698646	−	0.715467i	$-0.746214\pi$
$467$	−1.43619e12	−1.39729	−0.698646	+	0.715467i	$0.746214\pi$
$468$	−9.90228e11	−0.954177
$469$	−2.02073e12	−1.92855
$470$	9.33287e10	0.0882216
$471$	−3.40976e10	−0.0319249
$472$	−2.46207e11	−0.228329
$473$	−1.95739e12	−1.79805
$474$	1.99686e10	0.0181696
$475$	−1.09453e12	−0.986520
$476$	0	0
$477$	−1.18454e12	−1.04765
$478$	−1.27283e11	−0.111518
$479$	1.19894e11	0.104061	0.0520304	−	0.998646i	$-0.483431\pi$
$479$	1.19894e11	0.104061	0.0520304	+	0.998646i	$0.483431\pi$
$480$	1.11505e11	0.0958760
$481$	1.11124e12	0.946571
$482$	−5.10726e10	−0.0430999
$483$	−1.62830e11	−0.136136
$484$	−3.36443e11	−0.278681
$485$	3.05191e11	0.250458
$486$	6.49537e10	0.0528130
$487$	1.21696e12	0.980386	0.490193	−	0.871614i	$-0.336926\pi$
$487$	1.21696e12	0.980386	0.490193	+	0.871614i	$0.336926\pi$
$488$	−1.66223e11	−0.132679
$489$	−5.68864e10	−0.0449902
$490$	−6.21157e11	−0.486765
$491$	1.10228e12	0.855904	0.427952	−	0.903802i	$-0.359235\pi$
$491$	1.10228e12	0.855904	0.427952	+	0.903802i	$0.359235\pi$
$492$	−2.56389e10	−0.0197268
$493$	0	0
$494$	−7.62273e10	−0.0575890
$495$	2.70248e12	2.02320
$496$	1.51580e12	1.12454
$497$	1.36889e12	1.00638
$498$	−9.33430e9	−0.00680064
$499$	−1.83821e12	−1.32722	−0.663610	−	0.748078i	$-0.730977\pi$
$499$	−1.83821e12	−1.32722	−0.663610	+	0.748078i	$0.730977\pi$
$500$	−3.24953e12	−2.32518
$501$	1.03118e11	0.0731250
$502$	−9.54314e10	−0.0670694
$503$	1.35686e12	0.945104	0.472552	−	0.881303i	$-0.343333\pi$
$503$	1.35686e12	0.945104	0.472552	+	0.881303i	$0.343333\pi$
$504$	−6.60453e11	−0.455937
$505$	2.76528e12	1.89203
$506$	1.35182e11	0.0916732
$507$	4.10750e9	0.00276084
$508$	1.38114e12	0.920132
$509$	−1.97514e12	−1.30427	−0.652137	−	0.758101i	$-0.726127\pi$
$509$	−1.97514e12	−1.30427	−0.652137	+	0.758101i	$0.726127\pi$
$510$	0	0
$511$	−1.08342e11	−0.0702918
$512$	−9.79930e11	−0.630203
$513$	−1.76677e11	−0.112629
$514$	−1.83861e11	−0.116186
$515$	−3.00368e12	−1.88158
$516$	3.32721e11	0.206613
$517$	6.57516e11	0.404761
$518$	3.67128e11	0.224044
$519$	4.07797e11	0.246713
$520$	−8.07412e11	−0.484262
$521$	−1.99095e12	−1.18383	−0.591917	−	0.805999i	$-0.701629\pi$
$521$	−1.99095e12	−1.18383	−0.591917	+	0.805999i	$0.701629\pi$
$522$	−6.47574e10	−0.0381744
$523$	−3.10464e11	−0.181448	−0.0907242	−	0.995876i	$-0.528918\pi$
$523$	−3.10464e11	−0.181448	−0.0907242	+	0.995876i	$0.528918\pi$
$524$	2.61601e12	1.51583
$525$	−9.16744e11	−0.526661
$526$	9.79796e10	0.0558084
$527$	0	0
$528$	2.53658e11	0.142035
$529$	−1.16265e12	−0.645502
$530$	−4.78424e11	−0.263373
$531$	1.52619e12	0.833074
$532$	1.33874e12	0.724592
$533$	2.79343e11	0.149922
$534$	6.20661e10	0.0330308
$535$	3.79785e12	2.00422
$536$	−5.75696e11	−0.301267
$537$	1.35783e11	0.0704630
$538$	−1.22065e11	−0.0628163
$539$	−4.37616e12	−2.23328
$540$	−9.26975e11	−0.469133
$541$	−8.59585e11	−0.431421	−0.215711	−	0.976457i	$-0.569207\pi$
$541$	−8.59585e11	−0.431421	−0.215711	+	0.976457i	$0.569207\pi$
$542$	−2.33320e11	−0.116133
$543$	−5.12745e11	−0.253106
$544$	0	0
$545$	5.29554e12	2.57114
$546$	−6.38457e10	−0.0307443
$547$	−2.41617e12	−1.15394	−0.576971	−	0.816765i	$-0.695765\pi$
$547$	−2.41617e12	−1.15394	−0.576971	+	0.816765i	$0.695765\pi$
$548$	−3.10980e12	−1.47306
$549$	1.03038e12	0.484088
$550$	7.61085e11	0.354651
$551$	2.64996e11	0.122478
$552$	−4.63894e10	−0.0212664
$553$	3.82094e12	1.73743
$554$	−2.16186e11	−0.0975065
$555$	5.15509e11	0.230631
$556$	9.45958e11	0.419793
$557$	1.61258e12	0.709859	0.354929	−	0.934893i	$-0.384505\pi$
$557$	1.61258e12	0.709859	0.354929	+	0.934893i	$0.384505\pi$
$558$	3.63812e11	0.158863
$559$	−3.62509e12	−1.57024
$560$	6.88938e12	2.96029
$561$	0	0
$562$	−1.31292e11	−0.0555169
$563$	4.85659e10	0.0203725	0.0101862	−	0.999948i	$-0.496758\pi$
$563$	4.85659e10	0.0203725	0.0101862	+	0.999948i	$0.496758\pi$
$564$	−1.11766e11	−0.0465108
$565$	1.87601e12	0.774493
$566$	−6.14473e10	−0.0251669
$567$	4.01938e12	1.63318
$568$	3.89989e11	0.157212
$569$	−2.08971e12	−0.835758	−0.417879	−	0.908503i	$-0.637226\pi$
$569$	−2.08971e12	−0.835758	−0.417879	+	0.908503i	$0.637226\pi$
$570$	−3.53623e10	−0.0140315
$571$	1.98387e12	0.780999	0.390500	−	0.920603i	$-0.372302\pi$
$571$	1.98387e12	0.780999	0.390500	+	0.920603i	$0.372302\pi$
$572$	−2.81767e12	−1.10055
$573$	−1.56331e11	−0.0605827
$574$	9.22887e10	0.0354850
$575$	3.59482e12	1.37143
$576$	2.31220e12	0.875235
$577$	−1.30195e12	−0.488992	−0.244496	−	0.969650i	$-0.578623\pi$
$577$	−1.30195e12	−0.488992	−0.244496	+	0.969650i	$0.578623\pi$
$578$	0	0
$579$	4.32661e11	0.159991
$580$	1.39036e12	0.510155
$581$	−1.78610e12	−0.650297
$582$	6.87532e9	0.00248393
$583$	−3.37058e12	−1.20836
$584$	−3.08662e10	−0.0109806
$585$	5.00499e12	1.76686
$586$	−3.19888e11	−0.112062
$587$	8.77295e11	0.304982	0.152491	−	0.988305i	$-0.451270\pi$
$587$	8.77295e11	0.304982	0.152491	+	0.988305i	$0.451270\pi$
$588$	7.43869e11	0.256625
$589$	−1.48877e12	−0.509692
$590$	6.16415e11	0.209430
$591$	4.14265e11	0.139680
$592$	−2.70132e12	−0.903917
$593$	1.76865e12	0.587348	0.293674	−	0.955906i	$-0.405122\pi$
$593$	1.76865e12	0.587348	0.293674	+	0.955906i	$0.405122\pi$
$594$	1.22853e11	0.0404899
$595$	0	0
$596$	−4.39245e12	−1.42593
$597$	−3.65792e11	−0.117856
$598$	2.50358e11	0.0800582
$599$	−4.78571e12	−1.51889	−0.759444	−	0.650573i	$-0.774529\pi$
$599$	−4.78571e12	−1.51889	−0.759444	+	0.650573i	$0.774529\pi$
$600$	−2.61176e11	−0.0822720
$601$	2.40341e12	0.751439	0.375719	−	0.926734i	$-0.377396\pi$
$601$	2.40341e12	0.751439	0.375719	+	0.926734i	$0.377396\pi$
$602$	−1.19765e12	−0.371660
$603$	3.56863e12	1.09919
$604$	−2.21875e12	−0.678331
$605$	1.70051e12	0.516037
$606$	6.22960e10	0.0187644
$607$	3.97836e11	0.118947	0.0594737	−	0.998230i	$-0.481058\pi$
$607$	3.97836e11	0.118947	0.0594737	+	0.998230i	$0.481058\pi$
$608$	5.73877e11	0.170315
$609$	2.21952e11	0.0653856
$610$	4.16163e11	0.121697
$611$	1.21772e12	0.353478
$612$	0	0
$613$	−2.43845e12	−0.697497	−0.348748	−	0.937216i	$-0.613393\pi$
$613$	−2.43845e12	−0.697497	−0.348748	+	0.937216i	$0.613393\pi$
$614$	−5.67068e11	−0.161019
$615$	1.29589e11	0.0365283
$616$	−1.87931e12	−0.525878
$617$	5.95149e12	1.65326	0.826632	−	0.562743i	$-0.190254\pi$
$617$	5.95149e12	1.65326	0.826632	+	0.562743i	$0.190254\pi$
$618$	−6.76667e10	−0.0186607
$619$	5.90632e12	1.61700	0.808499	−	0.588498i	$-0.200280\pi$
$619$	5.90632e12	1.61700	0.808499	+	0.588498i	$0.200280\pi$
$620$	−7.81116e12	−2.12301
$621$	5.80269e11	0.156573
$622$	−3.77765e11	−0.101196
$623$	1.18762e13	3.15850
$624$	4.69775e11	0.124039
$625$	7.63770e12	2.00218
$626$	1.46665e11	0.0381718
$627$	−2.49134e11	−0.0643767
$628$	−9.20737e11	−0.236220
$629$	0	0
$630$	1.65354e12	0.418198
$631$	5.67619e12	1.42536	0.712680	−	0.701489i	$-0.247481\pi$
$631$	5.67619e12	1.42536	0.712680	+	0.701489i	$0.247481\pi$
$632$	1.08857e12	0.271412
$633$	−3.96913e11	−0.0982604
$634$	−6.47926e11	−0.159266
$635$	−6.98080e12	−1.70382
$636$	5.72938e11	0.138852
$637$	−8.10465e12	−1.95032
$638$	−1.84266e11	−0.0440303
$639$	−2.41747e12	−0.573597
$640$	4.00150e12	0.942785
$641$	−1.49036e12	−0.348681	−0.174341	−	0.984685i	$-0.555779\pi$
$641$	−1.49036e12	−0.348681	−0.174341	+	0.984685i	$0.555779\pi$
$642$	8.55576e10	0.0198770
$643$	8.89423e11	0.205191	0.102596	−	0.994723i	$-0.467285\pi$
$643$	8.89423e11	0.205191	0.102596	+	0.994723i	$0.467285\pi$
$644$	−4.39690e12	−1.00730
$645$	−1.68170e12	−0.382587
$646$	0	0
$647$	1.62659e12	0.364929	0.182465	−	0.983212i	$-0.441593\pi$
$647$	1.62659e12	0.364929	0.182465	+	0.983212i	$0.441593\pi$
$648$	1.14510e12	0.255127
$649$	4.34275e12	0.960867
$650$	1.40953e12	0.309717
$651$	−1.24695e12	−0.272103
$652$	−1.53610e12	−0.332894
$653$	−5.76853e12	−1.24153	−0.620763	−	0.783998i	$-0.713177\pi$
$653$	−5.76853e12	−1.24153	−0.620763	+	0.783998i	$0.713177\pi$
$654$	1.19297e11	0.0254995
$655$	−1.32223e13	−2.80687
$656$	−6.79059e11	−0.143166
$657$	1.91334e11	0.0400634
$658$	4.02308e11	0.0836648
$659$	−2.19347e12	−0.453050	−0.226525	−	0.974005i	$-0.572737\pi$
$659$	−2.19347e12	−0.453050	−0.226525	+	0.974005i	$0.572737\pi$
$660$	−1.30714e12	−0.268147
$661$	−3.13563e12	−0.638879	−0.319439	−	0.947607i	$-0.603495\pi$
$661$	−3.13563e12	−0.638879	−0.319439	+	0.947607i	$0.603495\pi$
$662$	1.02117e11	0.0206651
$663$	0	0
$664$	−5.08850e11	−0.101586
$665$	−6.76650e12	−1.34173
$666$	−6.48351e11	−0.127696
$667$	−8.70341e11	−0.170264
$668$	2.78450e12	0.541070
$669$	−2.98661e11	−0.0576449
$670$	1.44134e12	0.276331
$671$	2.93194e12	0.558346
$672$	4.80662e11	0.0909239
$673$	3.23212e12	0.607323	0.303662	−	0.952780i	$-0.401791\pi$
$673$	3.23212e12	0.607323	0.303662	+	0.952780i	$0.401791\pi$
$674$	9.23869e11	0.172441
$675$	3.26695e12	0.605726
$676$	1.10915e11	0.0204282
$677$	−6.52077e12	−1.19303	−0.596513	−	0.802603i	$-0.703448\pi$
$677$	−6.52077e12	−1.19303	−0.596513	+	0.802603i	$0.703448\pi$
$678$	4.22626e10	0.00768109
$679$	1.31558e12	0.237521
$680$	0	0
$681$	−1.23139e12	−0.219399
$682$	1.03522e12	0.183233
$683$	−2.88073e11	−0.0506534	−0.0253267	−	0.999679i	$-0.508063\pi$
$683$	−2.88073e11	−0.0506534	−0.0253267	+	0.999679i	$0.508063\pi$
$684$	−2.36422e12	−0.412987
$685$	1.57181e13	2.72768
$686$	−1.31906e12	−0.227408
$687$	8.25290e11	0.141352
$688$	8.81228e12	1.49948
$689$	−6.24231e12	−1.05526
$690$	1.16143e11	0.0195061
$691$	6.08618e12	1.01553	0.507766	−	0.861495i	$-0.330471\pi$
$691$	6.08618e12	1.01553	0.507766	+	0.861495i	$0.330471\pi$
$692$	1.10117e13	1.82549
$693$	1.16495e13	1.91870
$694$	1.15686e12	0.189305
$695$	−4.78124e12	−0.777335
$696$	6.32331e10	0.0102142
$697$	0	0
$698$	−6.93495e11	−0.110584
$699$	1.00402e11	0.0159073
$700$	−2.47548e13	−3.89689
$701$	−1.78933e12	−0.279872	−0.139936	−	0.990161i	$-0.544690\pi$
$701$	−1.78933e12	−0.279872	−0.139936	+	0.990161i	$0.544690\pi$
$702$	2.27524e11	0.0353598
$703$	2.65314e12	0.409695
$704$	6.57933e12	1.00950
$705$	5.64909e11	0.0861246
$706$	−2.34260e10	−0.00354876
$707$	1.19202e13	1.79430
$708$	−7.38190e11	−0.110413
$709$	−7.74406e12	−1.15096	−0.575481	−	0.817815i	$-0.695185\pi$
$709$	−7.74406e12	−1.15096	−0.575481	+	0.817815i	$0.695185\pi$
$710$	−9.76393e11	−0.144199
$711$	−6.74782e12	−0.990262
$712$	3.38347e12	0.493403
$713$	4.88964e12	0.708556
$714$	0	0
$715$	1.42416e13	2.03789
$716$	3.66655e12	0.521373
$717$	−7.70432e11	−0.108867
$718$	−8.20249e11	−0.115182
$719$	7.67138e12	1.07052	0.535258	−	0.844688i	$-0.320214\pi$
$719$	7.67138e12	1.07052	0.535258	+	0.844688i	$0.320214\pi$
$720$	−1.21667e13	−1.68724
$721$	−1.29479e13	−1.78439
$722$	8.10167e11	0.110958
$723$	−3.09137e11	−0.0420755
$724$	−1.38456e13	−1.87279
$725$	−4.90008e12	−0.658691
$726$	3.83090e10	0.00511783
$727$	−8.22639e12	−1.09221	−0.546103	−	0.837718i	$-0.683889\pi$
$727$	−8.22639e12	−1.09221	−0.546103	+	0.837718i	$0.683889\pi$
$728$	−3.48048e12	−0.459249
$729$	−6.83224e12	−0.895961
$730$	7.72780e10	0.0100717
$731$	0	0
$732$	−4.98378e11	−0.0641592
$733$	9.55042e11	0.122195	0.0610977	−	0.998132i	$-0.480540\pi$
$733$	9.55042e11	0.122195	0.0610977	+	0.998132i	$0.480540\pi$
$734$	−7.02929e11	−0.0893880
$735$	−3.75980e12	−0.475195
$736$	−1.88482e12	−0.236766
$737$	1.01545e13	1.26781
$738$	−1.62983e11	−0.0202250
$739$	−3.28401e12	−0.405046	−0.202523	−	0.979278i	$-0.564914\pi$
$739$	−3.28401e12	−0.405046	−0.202523	+	0.979278i	$0.564914\pi$
$740$	1.39203e13	1.70650
$741$	−4.61396e11	−0.0562201
$742$	−2.06232e12	−0.249769
$743$	−2.11148e12	−0.254178	−0.127089	−	0.991891i	$-0.540563\pi$
$743$	−2.11148e12	−0.254178	−0.127089	+	0.991891i	$0.540563\pi$
$744$	−3.55249e11	−0.0425064
$745$	2.22011e13	2.64041
$746$	−1.90136e12	−0.224771
$747$	3.15426e12	0.370642
$748$	0	0
$749$	1.63712e13	1.90070
$750$	3.70007e11	0.0427007
$751$	3.55572e12	0.407895	0.203947	−	0.978982i	$-0.434623\pi$
$751$	3.55572e12	0.407895	0.203947	+	0.978982i	$0.434623\pi$
$752$	−2.96018e12	−0.337549
$753$	−5.77636e11	−0.0654752
$754$	−3.41261e11	−0.0384517
$755$	1.12144e13	1.25607
$756$	−3.99587e12	−0.444901
$757$	−8.12210e12	−0.898953	−0.449476	−	0.893292i	$-0.648389\pi$
$757$	−8.12210e12	−0.898953	−0.449476	+	0.893292i	$0.648389\pi$
$758$	6.47963e11	0.0712917
$759$	8.18244e11	0.0894942
$760$	−1.92774e12	−0.209598
$761$	1.55670e13	1.68258	0.841289	−	0.540586i	$-0.181797\pi$
$761$	1.55670e13	1.68258	0.841289	+	0.540586i	$0.181797\pi$
$762$	−1.57263e11	−0.0168977
$763$	2.28273e13	2.43834
$764$	−4.22140e12	−0.448267
$765$	0	0
$766$	−9.31785e11	−0.0977881
$767$	8.04278e12	0.839125
$768$	−1.04926e12	−0.108833
$769$	−1.59487e13	−1.64458	−0.822292	−	0.569066i	$-0.807305\pi$
$769$	−1.59487e13	−1.64458	−0.822292	+	0.569066i	$0.807305\pi$
$770$	4.70511e12	0.482350
$771$	−1.11289e12	−0.113425
$772$	1.16831e13	1.18381
$773$	−4.36572e12	−0.439793	−0.219896	−	0.975523i	$-0.570572\pi$
$773$	−4.36572e12	−0.439793	−0.219896	+	0.975523i	$0.570572\pi$
$774$	2.11506e12	0.211830
$775$	2.75290e13	2.74115
$776$	3.74801e11	0.0371042
$777$	2.22219e12	0.218719
$778$	9.44924e11	0.0924674
$779$	6.66946e11	0.0648892
$780$	−2.42082e12	−0.234173
$781$	−6.87885e12	−0.661586
$782$	0	0
$783$	−7.90961e11	−0.0752016
$784$	1.97017e13	1.86244
$785$	4.65376e12	0.437411
$786$	−2.97872e11	−0.0278373
$787$	−1.29316e13	−1.20162	−0.600808	−	0.799393i	$-0.705154\pi$
$787$	−1.29316e13	−1.20162	−0.600808	+	0.799393i	$0.705154\pi$
$788$	1.11864e13	1.03353
$789$	5.93060e11	0.0544819
$790$	−2.72538e12	−0.248946
$791$	8.08685e12	0.734489
$792$	3.31887e12	0.299728
$793$	5.42996e12	0.487604
$794$	−8.63499e11	−0.0771027
$795$	−2.89585e12	−0.257113
$796$	−9.87748e12	−0.872042
$797$	7.30256e12	0.641081	0.320540	−	0.947235i	$-0.396135\pi$
$797$	7.30256e12	0.641081	0.320540	+	0.947235i	$0.396135\pi$
$798$	−1.52435e11	−0.0133067
$799$	0	0
$800$	−1.06116e13	−0.915962
$801$	−2.09734e13	−1.80021
$802$	9.63640e11	0.0822489
$803$	5.44437e11	0.0462091
$804$	−1.72608e12	−0.145683
$805$	2.22236e13	1.86523
$806$	1.91723e12	0.160017
$807$	−7.38849e11	−0.0613232
$808$	3.39600e12	0.280296
$809$	−2.08963e13	−1.71514	−0.857571	−	0.514365i	$-0.828027\pi$
$809$	−2.08963e13	−1.71514	−0.857571	+	0.514365i	$0.828027\pi$
$810$	−2.86692e12	−0.234009
$811$	−8.60451e12	−0.698445	−0.349222	−	0.937040i	$-0.613554\pi$
$811$	−8.60451e12	−0.698445	−0.349222	+	0.937040i	$0.613554\pi$
$812$	5.99338e12	0.483804
$813$	−1.41226e12	−0.113372
$814$	−1.84487e12	−0.147284
$815$	7.76405e12	0.616423
$816$	0	0
$817$	−8.65509e12	−0.679630
$818$	−1.83025e12	−0.142929
$819$	2.15748e13	1.67560
$820$	3.49929e12	0.270282
$821$	−1.33422e13	−1.02491	−0.512453	−	0.858716i	$-0.671263\pi$
$821$	−1.33422e13	−1.02491	−0.512453	+	0.858716i	$0.671263\pi$
$822$	3.54097e11	0.0270520
$823$	−9.21038e12	−0.699807	−0.349903	−	0.936786i	$-0.613786\pi$
$823$	−9.21038e12	−0.699807	−0.349903	+	0.936786i	$0.613786\pi$
$824$	−3.68878e12	−0.278747
$825$	4.60677e12	0.346221
$826$	2.65716e12	0.198613
$827$	1.73042e13	1.28640	0.643202	−	0.765696i	$-0.277605\pi$
$827$	1.73042e13	1.28640	0.643202	+	0.765696i	$0.277605\pi$
$828$	7.76496e12	0.574120
$829$	−1.69425e13	−1.24590	−0.622949	−	0.782263i	$-0.714065\pi$
$829$	−1.69425e13	−1.24590	−0.622949	+	0.782263i	$0.714065\pi$
$830$	1.27398e12	0.0931773
$831$	−1.30855e12	−0.0951889
$832$	1.21849e13	0.881593
$833$	0	0
$834$	−1.07711e11	−0.00770928
$835$	−1.40739e13	−1.00190
$836$	−6.72735e12	−0.476339
$837$	4.44368e12	0.312952
$838$	−1.11321e12	−0.0779790
$839$	−2.51719e13	−1.75383	−0.876915	−	0.480645i	$-0.840402\pi$
$839$	−2.51719e13	−1.75383	−0.876915	+	0.480645i	$0.840402\pi$
$840$	−1.61462e12	−0.111896
$841$	−1.33208e13	−0.918223
$842$	−3.12604e12	−0.214334
$843$	−7.94698e11	−0.0541973
$844$	−1.07178e13	−0.727053
$845$	−5.60606e11	−0.0378270
$846$	−7.10480e11	−0.0476854
$847$	7.33034e12	0.489383
$848$	1.51745e13	1.00771
$849$	−3.71934e11	−0.0245687
$850$	0	0
$851$	−8.71385e12	−0.569544
$852$	1.16928e12	0.0760224
$853$	−1.68384e13	−1.08901	−0.544503	−	0.838759i	$-0.683282\pi$
$853$	−1.68384e13	−1.08901	−0.544503	+	0.838759i	$0.683282\pi$
$854$	1.79394e12	0.115411
$855$	1.19497e13	0.764732
$856$	4.66408e12	0.296916
$857$	1.45946e13	0.924225	0.462113	−	0.886821i	$-0.347092\pi$
$857$	1.45946e13	0.924225	0.462113	+	0.886821i	$0.347092\pi$
$858$	3.20834e11	0.0202110
$859$	−2.05283e13	−1.28642	−0.643211	−	0.765689i	$-0.722398\pi$
$859$	−2.05283e13	−1.28642	−0.643211	+	0.765689i	$0.722398\pi$
$860$	−4.54110e13	−2.83086
$861$	5.58614e11	0.0346416
$862$	−2.58988e12	−0.159771
$863$	2.15891e13	1.32491	0.662453	−	0.749104i	$-0.269515\pi$
$863$	2.15891e13	1.32491	0.662453	+	0.749104i	$0.269515\pi$
$864$	−1.71291e12	−0.104574
$865$	−5.56576e13	−3.38027
$866$	−3.64582e12	−0.220275
$867$	0	0
$868$	−3.36713e13	−2.01336
$869$	−1.92008e13	−1.14217
$870$	−1.58313e11	−0.00936872
$871$	1.88061e13	1.10718
$872$	6.50338e12	0.380903
$873$	−2.32332e12	−0.135377
$874$	5.97743e11	0.0346508
$875$	7.08000e13	4.08317
$876$	−9.25446e10	−0.00530985
$877$	1.82834e13	1.04366	0.521830	−	0.853049i	$-0.325250\pi$
$877$	1.82834e13	1.04366	0.521830	+	0.853049i	$0.325250\pi$
$878$	8.61383e11	0.0489182
$879$	−1.93625e12	−0.109399
$880$	−3.46201e13	−1.94606
$881$	1.70514e12	0.0953604	0.0476802	−	0.998863i	$-0.484817\pi$
$881$	1.70514e12	0.0953604	0.0476802	+	0.998863i	$0.484817\pi$
$882$	4.72866e12	0.263105
$883$	−2.21871e13	−1.22822	−0.614112	−	0.789219i	$-0.710486\pi$
$883$	−2.21871e13	−1.22822	−0.614112	+	0.789219i	$0.710486\pi$
$884$	0	0
$885$	3.73110e12	0.204452
$886$	3.18682e12	0.173742
$887$	2.47842e13	1.34437	0.672186	−	0.740382i	$-0.265356\pi$
$887$	2.47842e13	1.34437	0.672186	+	0.740382i	$0.265356\pi$
$888$	6.33090e11	0.0341670
$889$	−3.00919e13	−1.61581
$890$	−8.47099e12	−0.452563
$891$	−2.01979e13	−1.07364
$892$	−8.06474e12	−0.426529
$893$	2.90738e12	0.152992
$894$	5.00145e11	0.0261865
$895$	−1.85321e13	−0.965433
$896$	1.72491e13	0.894088
$897$	1.51539e12	0.0781553
$898$	2.92548e12	0.150125
$899$	−6.66504e12	−0.340317
$900$	4.37172e13	2.22107
$901$	0	0
$902$	−4.63764e11	−0.0233275
$903$	−7.24925e12	−0.362826
$904$	2.30390e12	0.114738
$905$	6.99812e13	3.46787
$906$	2.52637e11	0.0124572
$907$	−2.81679e13	−1.38204	−0.691021	−	0.722835i	$-0.742839\pi$
$907$	−2.81679e13	−1.38204	−0.691021	+	0.722835i	$0.742839\pi$
$908$	−3.32513e13	−1.62339
$909$	−2.10512e13	−1.02268
$910$	8.71388e12	0.421236
$911$	2.22649e12	0.107100	0.0535498	−	0.998565i	$-0.482946\pi$
$911$	2.22649e12	0.107100	0.0535498	+	0.998565i	$0.482946\pi$
$912$	1.12161e12	0.0536867
$913$	8.97539e12	0.427499
$914$	−1.61095e12	−0.0763527
$915$	2.51899e12	0.118804
$916$	2.22853e13	1.04590
$917$	−5.69970e13	−2.66189
$918$	0	0
$919$	2.93520e13	1.35743	0.678715	−	0.734402i	$-0.262537\pi$
$919$	2.93520e13	1.35743	0.678715	+	0.734402i	$0.262537\pi$
$920$	6.33139e12	0.291376
$921$	−3.43240e12	−0.157192
$922$	4.83820e12	0.220493
$923$	−1.27396e13	−0.577763
$924$	−5.63463e12	−0.254297
$925$	−4.90596e13	−2.20336
$926$	−2.49416e12	−0.111475
$927$	2.28660e13	1.01703
$928$	2.56918e12	0.113718
$929$	−7.11576e12	−0.313437	−0.156719	−	0.987643i	$-0.550092\pi$
$929$	−7.11576e12	−0.313437	−0.156719	+	0.987643i	$0.550092\pi$
$930$	8.89416e11	0.0389881
$931$	−1.93503e13	−0.844139
$932$	2.71115e12	0.117702
$933$	−2.28657e12	−0.0987911
$934$	4.41585e12	0.189869
$935$	0	0
$936$	6.14656e12	0.261752
$937$	1.06889e13	0.453007	0.226503	−	0.974010i	$-0.427271\pi$
$937$	1.06889e13	0.453007	0.226503	+	0.974010i	$0.427271\pi$
$938$	6.21312e12	0.262058
$939$	8.87750e11	0.0372645
$940$	1.52542e13	0.637257
$941$	1.96244e13	0.815910	0.407955	−	0.913002i	$-0.366242\pi$
$941$	1.96244e13	0.815910	0.407955	+	0.913002i	$0.366242\pi$
$942$	1.04839e11	0.00433806
$943$	−2.19049e12	−0.0902067
$944$	−1.95513e13	−0.801312
$945$	2.01967e13	0.823829
$946$	6.01836e12	0.244325
$947$	−1.29410e13	−0.522870	−0.261435	−	0.965221i	$-0.584196\pi$
$947$	−1.29410e13	−0.522870	−0.261435	+	0.965221i	$0.584196\pi$
$948$	3.26379e12	0.131246
$949$	1.00830e12	0.0403544
$950$	3.36533e12	0.134052
$951$	−3.92183e12	−0.155481
$952$	0	0
$953$	−1.09666e13	−0.430680	−0.215340	−	0.976539i	$-0.569086\pi$
$953$	−1.09666e13	−0.430680	−0.215340	+	0.976539i	$0.569086\pi$
$954$	3.64208e12	0.142358
$955$	2.13366e13	0.830060
$956$	−2.08040e13	−0.805537
$957$	−1.11534e12	−0.0429838
$958$	−3.68636e11	−0.0141401
$959$	6.77556e13	2.58679
$960$	5.65267e12	0.214799
$961$	1.10051e13	0.416235
$962$	−3.41670e12	−0.128623
$963$	−2.89117e13	−1.08332
$964$	−8.34763e12	−0.311327
$965$	−5.90511e13	−2.19207
$966$	5.00651e11	0.0184986
$967$	3.26302e13	1.20005	0.600027	−	0.799980i	$-0.295157\pi$
$967$	3.26302e13	1.20005	0.600027	+	0.799980i	$0.295157\pi$
$968$	2.08838e12	0.0764486
$969$	0	0
$970$	−9.38368e11	−0.0340330
$971$	1.49723e13	0.540507	0.270253	−	0.962789i	$-0.412893\pi$
$971$	1.49723e13	0.540507	0.270253	+	0.962789i	$0.412893\pi$
$972$	1.06164e13	0.381488
$973$	−2.06103e13	−0.737185
$974$	−3.74178e12	−0.133218
$975$	8.53174e12	0.302355
$976$	−1.31998e13	−0.465631
$977$	1.12933e13	0.396548	0.198274	−	0.980147i	$-0.436466\pi$
$977$	1.12933e13	0.396548	0.198274	+	0.980147i	$0.436466\pi$
$978$	1.74908e11	0.00611342
$979$	−5.96795e13	−2.07636
$980$	−1.01526e14	−3.51608
$981$	−4.03132e13	−1.38975
$982$	−3.38916e12	−0.116303
$983$	−5.44159e13	−1.85881	−0.929404	−	0.369063i	$-0.879679\pi$
$983$	−5.44159e13	−1.85881	−0.929404	+	0.369063i	$0.879679\pi$
$984$	1.59146e11	0.00541151
$985$	−5.65403e13	−1.91379
$986$	0	0
$987$	2.43513e12	0.0816761
$988$	−1.24591e13	−0.415987
$989$	2.84264e13	0.944798
$990$	−8.30927e12	−0.274919
$991$	−3.13975e13	−1.03410	−0.517052	−	0.855954i	$-0.672971\pi$
$991$	−3.13975e13	−1.03410	−0.517052	+	0.855954i	$0.672971\pi$
$992$	−1.44339e13	−0.473238
$993$	6.18105e11	0.0201740
$994$	−4.20890e12	−0.136751
$995$	4.99246e13	1.61477
$996$	−1.52566e12	−0.0491235
$997$	3.75262e11	0.0120284	0.00601419	−	0.999982i	$-0.498086\pi$
$997$	3.75262e11	0.0120284	0.00601419	+	0.999982i	$0.498086\pi$
$998$	5.65193e12	0.180347
$999$	−7.91910e12	−0.251554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.h.1.18	yes	36
17.16	even	2		289.10.a.g.1.18	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.18	✓	36	17.16	even	2
289.10.a.h.1.18	yes	36	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q-3.07469 q^{2} -18.6108 q^{3} -502.546 q^{4} +2540.06 q^{5} +57.2223 q^{6} +10949.3 q^{7} +3119.41 q^{8} -19336.6 q^{9} +O(q^{10})\)	\(q-3.07469 q^{2} -18.6108 q^{3} -502.546 q^{4} +2540.06 q^{5} +57.2223 q^{6} +10949.3 q^{7} +3119.41 q^{8} -19336.6 q^{9} -7809.90 q^{10} -55022.0 q^{11} +9352.77 q^{12} -101901. q^{13} -33665.8 q^{14} -47272.5 q^{15} +247712. q^{16} +59454.1 q^{18} -243294. q^{19} -1.27650e6 q^{20} -203776. q^{21} +169176. q^{22} +799065. q^{23} -58054.7 q^{24} +4.49879e6 q^{25} +313313. q^{26} +726185. q^{27} -5.50255e6 q^{28} -1.08920e6 q^{29} +145348. q^{30} +6.11921e6 q^{31} -2.35878e6 q^{32} +1.02400e6 q^{33} +2.78120e7 q^{35} +9.71756e6 q^{36} -1.09051e7 q^{37} +748053. q^{38} +1.89645e6 q^{39} +7.92350e6 q^{40} -2.74132e6 q^{41} +626547. q^{42} +3.55746e7 q^{43} +2.76511e7 q^{44} -4.91163e7 q^{45} -2.45687e6 q^{46} -1.19501e7 q^{47} -4.61012e6 q^{48} +7.95346e7 q^{49} -1.38324e7 q^{50} +5.12099e7 q^{52} +6.12587e7 q^{53} -2.23279e6 q^{54} -1.39759e8 q^{55} +3.41555e7 q^{56} +4.52789e6 q^{57} +3.34895e6 q^{58} -7.89274e7 q^{59} +2.37566e7 q^{60} -5.32867e7 q^{61} -1.88147e7 q^{62} -2.11724e8 q^{63} -1.19576e8 q^{64} -2.58835e8 q^{65} -3.14849e6 q^{66} -1.84553e8 q^{67} -1.48712e7 q^{69} -8.55133e7 q^{70} +1.25020e8 q^{71} -6.03190e7 q^{72} -9.89488e6 q^{73} +3.35297e7 q^{74} -8.37259e7 q^{75} +1.22267e8 q^{76} -6.02455e8 q^{77} -5.83100e6 q^{78} +3.48965e8 q^{79} +6.29205e8 q^{80} +3.67088e8 q^{81} +8.42870e6 q^{82} -1.63123e8 q^{83} +1.02407e8 q^{84} -1.09381e8 q^{86} +2.02708e7 q^{87} -1.71636e8 q^{88} +1.08465e9 q^{89} +1.51017e8 q^{90} -1.11575e9 q^{91} -4.01567e8 q^{92} -1.13883e8 q^{93} +3.67427e7 q^{94} -6.17982e8 q^{95} +4.38987e7 q^{96} +1.20151e8 q^{97} -2.44544e8 q^{98} +1.06394e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 36 * q + 486 * q^3 + 9216 * q^4 + 3750 * q^5 + 11061 * q^6 + 29040 * q^7 + 24837 * q^8 + 236196 * q^9	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9} + 60000 q^{10} + 76902 q^{11} + 373248 q^{12} + 54216 q^{13} + 17373 q^{14} - 34122 q^{15} + 2359296 q^{16} - 1779435 q^{18} - 245058 q^{19} + 6439479 q^{20} - 138102 q^{21} + 267324 q^{22} + 4041462 q^{23} + 7653888 q^{24} + 16582356 q^{25} + 15822744 q^{26} + 13281612 q^{27} + 18614784 q^{28} + 4005936 q^{29} + 22471686 q^{30} + 21257064 q^{31} - 30922641 q^{32} + 35736474 q^{33} - 9039642 q^{35} + 39076761 q^{36} + 22076682 q^{37} - 27401376 q^{38} + 62736162 q^{39} - 12231630 q^{40} + 59641782 q^{41} + 150001536 q^{42} - 47951586 q^{43} - 49578936 q^{44} + 129308238 q^{45} + 140524827 q^{46} - 118557912 q^{47} + 407719119 q^{48} + 99849138 q^{49} + 435669051 q^{50} - 105017607 q^{52} + 13698846 q^{53} + 209848575 q^{54} - 365439924 q^{55} + 203095059 q^{56} - 4614108 q^{57} - 179071413 q^{58} + 343015128 q^{59} + 427179186 q^{60} + 175597116 q^{61} + 720602571 q^{62} + 587415936 q^{63} + 853082511 q^{64} + 393820182 q^{65} - 494661978 q^{66} + 502776528 q^{67} - 469106598 q^{69} - 1062525966 q^{70} + 1308709542 q^{71} - 275337849 q^{72} + 494841342 q^{73} + 1545361890 q^{74} + 1824677616 q^{75} + 242064891 q^{76} - 792768144 q^{77} + 2270624538 q^{78} + 1980107868 q^{79} + 2897000199 q^{80} + 1598298840 q^{81} + 898743654 q^{82} + 275294520 q^{83} - 2144532369 q^{84} - 2880848046 q^{86} + 1088458710 q^{87} - 2705904618 q^{88} + 148394658 q^{89} + 117916215 q^{90} + 636340896 q^{91} - 3458472327 q^{92} - 628345524 q^{93} - 200245965 q^{94} + 4878626298 q^{95} - 8390096634 q^{96} - 891786822 q^{97} + 4285627647 q^{98} - 1476187998 q^{99}+O(q^{100}) \) 36 * q + 486 * q^3 + 9216 * q^4 + 3750 * q^5 + 11061 * q^6 + 29040 * q^7 + 24837 * q^8 + 236196 * q^9 + 60000 * q^10 + 76902 * q^11 + 373248 * q^12 + 54216 * q^13 + 17373 * q^14 - 34122 * q^15 + 2359296 * q^16 - 1779435 * q^18 - 245058 * q^19 + 6439479 * q^20 - 138102 * q^21 + 267324 * q^22 + 4041462 * q^23 + 7653888 * q^24 + 16582356 * q^25 + 15822744 * q^26 + 13281612 * q^27 + 18614784 * q^28 + 4005936 * q^29 + 22471686 * q^30 + 21257064 * q^31 - 30922641 * q^32 + 35736474 * q^33 - 9039642 * q^35 + 39076761 * q^36 + 22076682 * q^37 - 27401376 * q^38 + 62736162 * q^39 - 12231630 * q^40 + 59641782 * q^41 + 150001536 * q^42 - 47951586 * q^43 - 49578936 * q^44 + 129308238 * q^45 + 140524827 * q^46 - 118557912 * q^47 + 407719119 * q^48 + 99849138 * q^49 + 435669051 * q^50 - 105017607 * q^52 + 13698846 * q^53 + 209848575 * q^54 - 365439924 * q^55 + 203095059 * q^56 - 4614108 * q^57 - 179071413 * q^58 + 343015128 * q^59 + 427179186 * q^60 + 175597116 * q^61 + 720602571 * q^62 + 587415936 * q^63 + 853082511 * q^64 + 393820182 * q^65 - 494661978 * q^66 + 502776528 * q^67 - 469106598 * q^69 - 1062525966 * q^70 + 1308709542 * q^71 - 275337849 * q^72 + 494841342 * q^73 + 1545361890 * q^74 + 1824677616 * q^75 + 242064891 * q^76 - 792768144 * q^77 + 2270624538 * q^78 + 1980107868 * q^79 + 2897000199 * q^80 + 1598298840 * q^81 + 898743654 * q^82 + 275294520 * q^83 - 2144532369 * q^84 - 2880848046 * q^86 + 1088458710 * q^87 - 2705904618 * q^88 + 148394658 * q^89 + 117916215 * q^90 + 636340896 * q^91 - 3458472327 * q^92 - 628345524 * q^93 - 200245965 * q^94 + 4878626298 * q^95 - 8390096634 * q^96 - 891786822 * q^97 + 4285627647 * q^98 - 1476187998 * q^99

Introduction

L-functions

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