LMFDB - Embedded newform 289.10.a.h.1.27

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			1.27
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)

$f(q)$	$=$	$q+26.5808 q^{2} +204.952 q^{3} +194.540 q^{4} +2372.11 q^{5} +5447.81 q^{6} -6243.22 q^{7} -8438.34 q^{8} +22322.5 q^{9} +O(q^{10})$	\(q+26.5808 q^{2} +204.952 q^{3} +194.540 q^{4} +2372.11 q^{5} +5447.81 q^{6} -6243.22 q^{7} -8438.34 q^{8} +22322.5 q^{9} +63052.8 q^{10} +82629.5 q^{11} +39871.5 q^{12} +110834. q^{13} -165950. q^{14} +486171. q^{15} -323903. q^{16} +593351. q^{18} +562366. q^{19} +461472. q^{20} -1.27956e6 q^{21} +2.19636e6 q^{22} +1.19566e6 q^{23} -1.72946e6 q^{24} +3.67380e6 q^{25} +2.94607e6 q^{26} +540977. q^{27} -1.21456e6 q^{28} -1.98644e6 q^{29} +1.29228e7 q^{30} -9.43437e6 q^{31} -4.28917e6 q^{32} +1.69351e7 q^{33} -1.48096e7 q^{35} +4.34263e6 q^{36} -984052. q^{37} +1.49481e7 q^{38} +2.27158e7 q^{39} -2.00167e7 q^{40} -2.19605e6 q^{41} -3.40118e7 q^{42} +3.42984e6 q^{43} +1.60748e7 q^{44} +5.29516e7 q^{45} +3.17815e7 q^{46} -2.11033e7 q^{47} -6.63847e7 q^{48} -1.37586e6 q^{49} +9.76527e7 q^{50} +2.15617e7 q^{52} +2.19582e7 q^{53} +1.43796e7 q^{54} +1.96007e8 q^{55} +5.26824e7 q^{56} +1.15258e8 q^{57} -5.28011e7 q^{58} +4.21319e7 q^{59} +9.45798e7 q^{60} +6.01904e7 q^{61} -2.50773e8 q^{62} -1.39364e8 q^{63} +5.18285e7 q^{64} +2.62912e8 q^{65} +4.50150e8 q^{66} +2.11182e8 q^{67} +2.45053e8 q^{69} -3.93652e8 q^{70} +3.37272e8 q^{71} -1.88365e8 q^{72} -2.34922e8 q^{73} -2.61569e7 q^{74} +7.52955e8 q^{75} +1.09403e8 q^{76} -5.15874e8 q^{77} +6.03803e8 q^{78} +1.77751e8 q^{79} -7.68334e8 q^{80} -3.28500e8 q^{81} -5.83727e7 q^{82} +1.29416e8 q^{83} -2.48926e8 q^{84} +9.11679e7 q^{86} -4.07125e8 q^{87} -6.97256e8 q^{88} +2.82211e8 q^{89} +1.40750e9 q^{90} -6.91962e8 q^{91} +2.32603e8 q^{92} -1.93360e9 q^{93} -5.60944e8 q^{94} +1.33400e9 q^{95} -8.79076e8 q^{96} +4.77665e7 q^{97} -3.65716e7 q^{98} +1.84450e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	26.5808	1.17472	0.587359	−	0.809327i	$-0.300168\pi$
$2$	26.5808	1.17472	0.587359	+	0.809327i	$0.300168\pi$
$3$	204.952	1.46086	0.730428	−	0.682989i	$-0.239321\pi$
$3$	204.952	1.46086	0.730428	+	0.682989i	$0.239321\pi$
$4$	194.540	0.379961
$5$	2372.11	1.69735	0.848673	−	0.528917i	$-0.177402\pi$
$5$	2372.11	1.69735	0.848673	+	0.528917i	$0.177402\pi$
$6$	5447.81	1.71609
$7$	−6243.22	−0.982805	−0.491402	−	0.870933i	$-0.663516\pi$
$7$	−6243.22	−0.982805	−0.491402	+	0.870933i	$0.663516\pi$
$8$	−8438.34	−0.728370
$9$	22322.5	1.13410
$10$	63052.8	1.99390
$11$	82629.5	1.70164	0.850821	−	0.525456i	$-0.176105\pi$
$11$	82629.5	1.70164	0.850821	+	0.525456i	$0.176105\pi$
$12$	39871.5	0.555069
$13$	110834.	1.07629	0.538144	−	0.842853i	$-0.319125\pi$
$13$	110834.	1.07629	0.538144	+	0.842853i	$0.319125\pi$
$14$	−165950.	−1.15452
$15$	486171.	2.47958
$16$	−323903.	−1.23559
$17$	0	0
$17$	0	0
$18$	593351.	1.33225
$19$	562366.	0.989983	0.494992	−	0.868898i	$-0.335171\pi$
$19$	562366.	0.989983	0.494992	+	0.868898i	$0.335171\pi$
$20$	461472.	0.644926
$21$	−1.27956e6	−1.43574
$22$	2.19636e6	1.99895
$23$	1.19566e6	0.890904	0.445452	−	0.895306i	$-0.353043\pi$
$23$	1.19566e6	0.890904	0.445452	+	0.895306i	$0.353043\pi$
$24$	−1.72946e6	−1.06404
$25$	3.67380e6	1.88099
$26$	2.94607e6	1.26434
$27$	540977.	0.195903
$28$	−1.21456e6	−0.373428
$29$	−1.98644e6	−0.521535	−0.260767	−	0.965402i	$-0.583976\pi$
$29$	−1.98644e6	−0.521535	−0.260767	+	0.965402i	$0.583976\pi$
$30$	1.29228e7	2.91281
$31$	−9.43437e6	−1.83478	−0.917392	−	0.397984i	$-0.869710\pi$
$31$	−9.43437e6	−1.83478	−0.917392	+	0.397984i	$0.869710\pi$
$32$	−4.28917e6	−0.723100
$33$	1.69351e7	2.48585
$34$	0	0
$35$	−1.48096e7	−1.66816
$36$	4.34263e6	0.430915
$37$	−984052.	−0.0863197	−0.0431599	−	0.999068i	$-0.513742\pi$
$37$	−984052.	−0.0863197	−0.0431599	+	0.999068i	$0.513742\pi$
$38$	1.49481e7	1.16295
$39$	2.27158e7	1.57230
$40$	−2.00167e7	−1.23630
$41$	−2.19605e6	−0.121371	−0.0606854	−	0.998157i	$-0.519329\pi$
$41$	−2.19605e6	−0.121371	−0.0606854	+	0.998157i	$0.519329\pi$
$42$	−3.40118e7	−1.68658
$43$	3.42984e6	0.152991	0.0764954	−	0.997070i	$-0.475627\pi$
$43$	3.42984e6	0.152991	0.0764954	+	0.997070i	$0.475627\pi$
$44$	1.60748e7	0.646558
$45$	5.29516e7	1.92496
$46$	3.17815e7	1.04656
$47$	−2.11033e7	−0.630827	−0.315414	−	0.948954i	$-0.602143\pi$
$47$	−2.11033e7	−0.630827	−0.315414	+	0.948954i	$0.602143\pi$
$48$	−6.63847e7	−1.80502
$49$	−1.37586e6	−0.0340952
$50$	9.76527e7	2.20963
$51$	0	0
$52$	2.15617e7	0.408948
$53$	2.19582e7	0.382258	0.191129	−	0.981565i	$-0.438785\pi$
$53$	2.19582e7	0.382258	0.191129	+	0.981565i	$0.438785\pi$
$54$	1.43796e7	0.230131
$55$	1.96007e8	2.88828
$56$	5.26824e7	0.715846
$57$	1.15258e8	1.44622
$58$	−5.28011e7	−0.612656
$59$	4.21319e7	0.452665	0.226333	−	0.974050i	$-0.427326\pi$
$59$	4.21319e7	0.452665	0.226333	+	0.974050i	$0.427326\pi$
$60$	9.45798e7	0.942145
$61$	6.01904e7	0.556599	0.278300	−	0.960494i	$-0.410229\pi$
$61$	6.01904e7	0.556599	0.278300	+	0.960494i	$0.410229\pi$
$62$	−2.50773e8	−2.15535
$63$	−1.39364e8	−1.11460
$64$	5.18285e7	0.386153
$65$	2.62912e8	1.82684
$66$	4.50150e8	2.92018
$67$	2.11182e8	1.28032	0.640162	−	0.768240i	$-0.278867\pi$
$67$	2.11182e8	1.28032	0.640162	+	0.768240i	$0.278867\pi$
$68$	0	0
$69$	2.45053e8	1.30148
$70$	−3.93652e8	−1.95962
$71$	3.37272e8	1.57513	0.787567	−	0.616229i	$-0.211340\pi$
$71$	3.37272e8	1.57513	0.787567	+	0.616229i	$0.211340\pi$
$72$	−1.88365e8	−0.826046
$73$	−2.34922e8	−0.968211	−0.484106	−	0.875010i	$-0.660855\pi$
$73$	−2.34922e8	−0.968211	−0.484106	+	0.875010i	$0.660855\pi$
$74$	−2.61569e7	−0.101401
$75$	7.52955e8	2.74785
$76$	1.09403e8	0.376155
$77$	−5.15874e8	−1.67238
$78$	6.03803e8	1.84701
$79$	1.77751e8	0.513440	0.256720	−	0.966486i	$-0.417358\pi$
$79$	1.77751e8	0.513440	0.256720	+	0.966486i	$0.417358\pi$
$80$	−7.68334e8	−2.09723
$81$	−3.28500e8	−0.847915
$82$	−5.83727e7	−0.142576
$83$	1.29416e8	0.299321	0.149661	−	0.988737i	$-0.452182\pi$
$83$	1.29416e8	0.299321	0.149661	+	0.988737i	$0.452182\pi$
$84$	−2.48926e8	−0.545524
$85$	0	0
$86$	9.11679e7	0.179721
$87$	−4.07125e8	−0.761888
$88$	−6.97256e8	−1.23943
$89$	2.82211e8	0.476782	0.238391	−	0.971169i	$-0.423380\pi$
$89$	2.82211e8	0.476782	0.238391	+	0.971169i	$0.423380\pi$
$90$	1.40750e9	2.26129
$91$	−6.91962e8	−1.05778
$92$	2.32603e8	0.338509
$93$	−1.93360e9	−2.68036
$94$	−5.60944e8	−0.741044
$95$	1.33400e9	1.68034
$96$	−8.79076e8	−1.05635
$97$	4.77665e7	0.0547836	0.0273918	−	0.999625i	$-0.491280\pi$
$97$	4.77665e7	0.0547836	0.0273918	+	0.999625i	$0.491280\pi$
$98$	−3.65716e7	−0.0400522
$99$	1.84450e9	1.92983
$100$	7.14702e8	0.714702
$101$	8.67959e8	0.829952	0.414976	−	0.909832i	$-0.363790\pi$
$101$	8.67959e8	0.829952	0.414976	+	0.909832i	$0.363790\pi$
$102$	0	0
$103$	−1.70990e9	−1.49693	−0.748466	−	0.663173i	$-0.769209\pi$
$103$	−1.70990e9	−1.49693	−0.748466	+	0.663173i	$0.769209\pi$
$104$	−9.35257e8	−0.783937
$105$	−3.03527e9	−2.43694
$106$	5.83668e8	0.449045
$107$	4.88170e8	0.360034	0.180017	−	0.983663i	$-0.442385\pi$
$107$	4.88170e8	0.360034	0.180017	+	0.983663i	$0.442385\pi$
$108$	1.05242e8	0.0744357
$109$	1.68098e9	1.14062	0.570312	−	0.821428i	$-0.306822\pi$
$109$	1.68098e9	1.14062	0.570312	+	0.821428i	$0.306822\pi$
$110$	5.21002e9	3.39291
$111$	−2.01684e8	−0.126101
$112$	2.02219e9	1.21434
$113$	−6.53183e8	−0.376861	−0.188431	−	0.982086i	$-0.560340\pi$
$113$	−6.53183e8	−0.376861	−0.188431	+	0.982086i	$0.560340\pi$
$114$	3.06366e9	1.69890
$115$	2.83623e9	1.51217
$116$	−3.86442e8	−0.198163
$117$	2.47410e9	1.22062
$118$	1.11990e9	0.531754
$119$	0	0
$120$	−4.10248e9	−1.80605
$121$	4.46969e9	1.89559
$122$	1.59991e9	0.653847
$123$	−4.50085e8	−0.177305
$124$	−1.83536e9	−0.697147
$125$	4.08164e9	1.49534
$126$	−3.70442e9	−1.30934
$127$	−5.07472e9	−1.73099	−0.865496	−	0.500916i	$-0.832997\pi$
$127$	−5.07472e9	−1.73099	−0.865496	+	0.500916i	$0.832997\pi$
$128$	3.57370e9	1.17672
$129$	7.02954e8	0.223498
$130$	6.98840e9	2.14602
$131$	8.92114e7	0.0264667	0.0132333	−	0.999912i	$-0.495788\pi$
$131$	8.92114e7	0.0264667	0.0132333	+	0.999912i	$0.495788\pi$
$132$	3.29456e9	0.944529
$133$	−3.51097e9	−0.972960
$134$	5.61339e9	1.50402
$135$	1.28326e9	0.332516
$136$	0	0
$137$	−4.14021e9	−1.00411	−0.502053	−	0.864837i	$-0.667422\pi$
$137$	−4.14021e9	−1.00411	−0.502053	+	0.864837i	$0.667422\pi$
$138$	6.51370e9	1.52888
$139$	3.35260e9	0.761754	0.380877	−	0.924626i	$-0.375622\pi$
$139$	3.35260e9	0.761754	0.380877	+	0.924626i	$0.375622\pi$
$140$	−2.88107e9	−0.633837
$141$	−4.32518e9	−0.921548
$142$	8.96496e9	1.85034
$143$	9.15818e9	1.83146
$144$	−7.23033e9	−1.40129
$145$	−4.71205e9	−0.885226
$146$	−6.24441e9	−1.13737
$147$	−2.81986e8	−0.0498081
$148$	−1.91438e8	−0.0327982
$149$	5.04370e9	0.838323	0.419161	−	0.907912i	$-0.362324\pi$
$149$	5.04370e9	0.838323	0.419161	+	0.907912i	$0.362324\pi$
$150$	2.00142e10	3.22795
$151$	−8.59842e9	−1.34593	−0.672965	−	0.739674i	$-0.734979\pi$
$151$	−8.59842e9	−1.34593	−0.672965	+	0.739674i	$0.734979\pi$
$152$	−4.74544e9	−0.721074
$153$	0	0
$154$	−1.37124e10	−1.96458
$155$	−2.23794e10	−3.11427
$156$	4.41913e9	0.597415
$157$	−1.24814e8	−0.0163951	−0.00819756	−	0.999966i	$-0.502609\pi$
$157$	−1.24814e8	−0.0163951	−0.00819756	+	0.999966i	$0.502609\pi$
$158$	4.72476e9	0.603147
$159$	4.50040e9	0.558423
$160$	−1.01744e10	−1.22735
$161$	−7.46474e9	−0.875585
$162$	−8.73179e9	−0.996061
$163$	−1.44069e10	−1.59855	−0.799273	−	0.600969i	$-0.794782\pi$
$163$	−1.44069e10	−1.59855	−0.799273	+	0.600969i	$0.794782\pi$
$164$	−4.27219e8	−0.0461162
$165$	4.01721e10	4.21936
$166$	3.43999e9	0.351618
$167$	−5.26762e9	−0.524071	−0.262036	−	0.965058i	$-0.584394\pi$
$167$	−5.26762e9	−0.524071	−0.262036	+	0.965058i	$0.584394\pi$
$168$	1.07974e10	1.04575
$169$	1.67973e9	0.158398
$170$	0	0
$171$	1.25534e10	1.12274
$172$	6.67241e8	0.0581306
$173$	−9.75496e9	−0.827977	−0.413988	−	0.910282i	$-0.635865\pi$
$173$	−9.75496e9	−0.827977	−0.413988	+	0.910282i	$0.635865\pi$
$174$	−1.08217e10	−0.895003
$175$	−2.29363e10	−1.84864
$176$	−2.67639e10	−2.10253
$177$	8.63504e9	0.661279
$178$	7.50141e9	0.560084
$179$	−2.35794e9	−0.171670	−0.0858349	−	0.996309i	$-0.527356\pi$
$179$	−2.35794e9	−0.171670	−0.0858349	+	0.996309i	$0.527356\pi$
$180$	1.03012e10	0.731412
$181$	−1.48765e10	−1.03026	−0.515131	−	0.857111i	$-0.672257\pi$
$181$	−1.48765e10	−1.03026	−0.515131	+	0.857111i	$0.672257\pi$
$182$	−1.83929e10	−1.24259
$183$	1.23362e10	0.813112
$184$	−1.00894e10	−0.648908
$185$	−2.33428e9	−0.146515
$186$	−5.13966e10	−3.14866
$187$	0	0
$188$	−4.10544e9	−0.239690
$189$	−3.37743e9	−0.192535
$190$	3.54587e10	1.97393
$191$	1.91683e10	1.04216	0.521079	−	0.853509i	$-0.325530\pi$
$191$	1.91683e10	1.04216	0.521079	+	0.853509i	$0.325530\pi$
$192$	1.06224e10	0.564113
$193$	−2.10127e10	−1.09012	−0.545060	−	0.838397i	$-0.683493\pi$
$193$	−2.10127e10	−1.09012	−0.545060	+	0.838397i	$0.683493\pi$
$194$	1.26967e9	0.0643553
$195$	5.38844e10	2.66874
$196$	−2.67661e8	−0.0129548
$197$	4.16011e10	1.96792	0.983958	−	0.178402i	$-0.0570929\pi$
$197$	4.16011e10	1.96792	0.983958	+	0.178402i	$0.0570929\pi$
$198$	4.90283e10	2.26701
$199$	2.14454e10	0.969382	0.484691	−	0.874686i	$-0.338932\pi$
$199$	2.14454e10	0.969382	0.484691	+	0.874686i	$0.338932\pi$
$200$	−3.10008e10	−1.37005
$201$	4.32822e10	1.87037
$202$	2.30711e10	0.974959
$203$	1.24017e10	0.512567
$204$	0	0
$205$	−5.20927e9	−0.206008
$206$	−4.54504e10	−1.75847
$207$	2.66901e10	1.01038
$208$	−3.58995e10	−1.32985
$209$	4.64680e10	1.68460
$210$	−8.06800e10	−2.86272
$211$	−4.84300e10	−1.68207	−0.841034	−	0.540982i	$-0.818053\pi$
$211$	−4.84300e10	−1.68207	−0.841034	+	0.540982i	$0.818053\pi$
$212$	4.27176e9	0.145243
$213$	6.91247e10	2.30104
$214$	1.29760e10	0.422939
$215$	8.13597e9	0.259679
$216$	−4.56495e9	−0.142690
$217$	5.89008e10	1.80323
$218$	4.46817e10	1.33991
$219$	−4.81478e10	−1.41442
$220$	3.81312e10	1.09743
$221$	0	0
$222$	−5.36092e9	−0.148133
$223$	4.89472e9	0.132543	0.0662713	−	0.997802i	$-0.478890\pi$
$223$	4.89472e9	0.132543	0.0662713	+	0.997802i	$0.478890\pi$
$224$	2.67782e10	0.710666
$225$	8.20085e10	2.13323
$226$	−1.73621e10	−0.442706
$227$	−7.30390e10	−1.82574	−0.912869	−	0.408253i	$-0.866138\pi$
$227$	−7.30390e10	−1.82574	−0.912869	+	0.408253i	$0.866138\pi$
$228$	2.24224e10	0.549509
$229$	−6.16423e10	−1.48122	−0.740609	−	0.671936i	$-0.765463\pi$
$229$	−6.16423e10	−1.48122	−0.740609	+	0.671936i	$0.765463\pi$
$230$	7.53894e10	1.77638
$231$	−1.05730e11	−2.44311
$232$	1.67622e10	0.379871
$233$	−3.99787e10	−0.888642	−0.444321	−	0.895868i	$-0.646555\pi$
$233$	−3.99787e10	−0.888642	−0.444321	+	0.895868i	$0.646555\pi$
$234$	6.57636e10	1.43388
$235$	−5.00595e10	−1.07073
$236$	8.19636e9	0.171995
$237$	3.64305e10	0.750062
$238$	0	0
$239$	6.22662e10	1.23442	0.617209	−	0.786800i	$-0.288263\pi$
$239$	6.22662e10	1.23442	0.617209	+	0.786800i	$0.288263\pi$
$240$	−1.57472e11	−3.06375
$241$	5.24041e10	1.00067	0.500333	−	0.865833i	$-0.333211\pi$
$241$	5.24041e10	1.00067	0.500333	+	0.865833i	$0.333211\pi$
$242$	1.18808e11	2.22678
$243$	−7.79749e10	−1.43459
$244$	1.17094e10	0.211486
$245$	−3.26370e9	−0.0578713
$246$	−1.19636e10	−0.208284
$247$	6.23294e10	1.06551
$248$	7.96104e10	1.33640
$249$	2.65242e10	0.437266
$250$	1.08493e11	1.75660
$251$	−1.25587e10	−0.199717	−0.0998584	−	0.995002i	$-0.531839\pi$
$251$	−1.25587e10	−0.199717	−0.0998584	+	0.995002i	$0.531839\pi$
$252$	−2.71120e10	−0.423505
$253$	9.87965e10	1.51600
$254$	−1.34890e11	−2.03343
$255$	0	0
$256$	6.84557e10	0.996161
$257$	3.80725e10	0.544393	0.272196	−	0.962242i	$-0.412250\pi$
$257$	3.80725e10	0.544393	0.272196	+	0.962242i	$0.412250\pi$
$258$	1.86851e10	0.262547
$259$	6.14365e9	0.0848354
$260$	5.11469e10	0.694127
$261$	−4.43422e10	−0.591474
$262$	2.37131e9	0.0310909
$263$	−1.29507e11	−1.66914	−0.834570	−	0.550902i	$-0.814284\pi$
$263$	−1.29507e11	−1.66914	−0.834570	+	0.550902i	$0.814284\pi$
$264$	−1.42904e11	−1.81062
$265$	5.20874e10	0.648824
$266$	−9.33245e10	−1.14295
$267$	5.78399e10	0.696509
$268$	4.10834e10	0.486474
$269$	−6.99912e10	−0.815001	−0.407500	−	0.913205i	$-0.633599\pi$
$269$	−6.99912e10	−0.815001	−0.407500	+	0.913205i	$0.633599\pi$
$270$	3.41101e10	0.390612
$271$	3.71493e10	0.418397	0.209199	−	0.977873i	$-0.432914\pi$
$271$	3.71493e10	0.418397	0.209199	+	0.977873i	$0.432914\pi$
$272$	0	0
$273$	−1.41819e11	−1.54527
$274$	−1.10050e11	−1.17954
$275$	3.03565e11	3.20077
$276$	4.76726e10	0.494513
$277$	−1.10314e11	−1.12583	−0.562915	−	0.826515i	$-0.690320\pi$
$277$	−1.10314e11	−1.12583	−0.562915	+	0.826515i	$0.690320\pi$
$278$	8.91148e10	0.894846
$279$	−2.10599e11	−2.08083
$280$	1.24969e11	1.21504
$281$	−5.01827e10	−0.480148	−0.240074	−	0.970755i	$-0.577172\pi$
$281$	−5.01827e10	−0.480148	−0.240074	+	0.970755i	$0.577172\pi$
$282$	−1.14967e11	−1.08256
$283$	−1.75840e9	−0.0162959	−0.00814795	−	0.999967i	$-0.502594\pi$
$283$	−1.75840e9	−0.0162959	−0.00814795	+	0.999967i	$0.502594\pi$
$284$	6.56129e10	0.598490
$285$	2.73406e11	2.45474
$286$	2.43432e11	2.15145
$287$	1.37104e10	0.119284
$288$	−9.57451e10	−0.820069
$289$	0	0
$290$	−1.25250e11	−1.03989
$291$	9.78986e9	0.0800310
$292$	−4.57017e10	−0.367883
$293$	−1.52956e11	−1.21245	−0.606223	−	0.795294i	$-0.707316\pi$
$293$	−1.52956e11	−1.21245	−0.606223	+	0.795294i	$0.707316\pi$
$294$	−7.49543e9	−0.0585105
$295$	9.99418e10	0.768330
$296$	8.30376e9	0.0628727
$297$	4.47007e10	0.333357
$298$	1.34066e11	0.984793
$299$	1.32520e11	0.958870
$300$	1.46480e11	1.04408
$301$	−2.14132e10	−0.150360
$302$	−2.28553e11	−1.58109
$303$	1.77890e11	1.21244
$304$	−1.82152e11	−1.22321
$305$	1.42778e11	0.944742
$306$	0	0
$307$	−4.31909e10	−0.277504	−0.138752	−	0.990327i	$-0.544309\pi$
$307$	−4.31909e10	−0.277504	−0.138752	+	0.990327i	$0.544309\pi$
$308$	−1.00358e11	−0.635440
$309$	−3.50447e11	−2.18680
$310$	−5.94863e11	−3.65838
$311$	1.43948e10	0.0872538	0.0436269	−	0.999048i	$-0.486109\pi$
$311$	1.43948e10	0.0872538	0.0436269	+	0.999048i	$0.486109\pi$
$312$	−1.91683e11	−1.14522
$313$	8.86698e10	0.522187	0.261094	−	0.965313i	$-0.415917\pi$
$313$	8.86698e10	0.522187	0.261094	+	0.965313i	$0.415917\pi$
$314$	−3.31766e9	−0.0192596
$315$	−3.30588e11	−1.89186
$316$	3.45797e10	0.195087
$317$	2.84750e11	1.58379	0.791894	−	0.610658i	$-0.209095\pi$
$317$	2.84750e11	1.58379	0.791894	+	0.610658i	$0.209095\pi$
$318$	1.19624e11	0.655990
$319$	−1.64138e11	−0.887466
$320$	1.22943e11	0.655435
$321$	1.00052e11	0.525959
$322$	−1.98419e11	−1.02856
$323$	0	0
$324$	−6.39064e10	−0.322175
$325$	4.07183e11	2.02449
$326$	−3.82946e11	−1.87784
$327$	3.44520e11	1.66629
$328$	1.85310e10	0.0884029
$329$	1.31753e11	0.619980
$330$	1.06781e12	4.95655
$331$	2.34561e11	1.07406	0.537032	−	0.843562i	$-0.319546\pi$
$331$	2.34561e11	1.07406	0.537032	+	0.843562i	$0.319546\pi$
$332$	2.51767e10	0.113731
$333$	−2.19665e10	−0.0978954
$334$	−1.40018e11	−0.615635
$335$	5.00948e11	2.17315
$336$	4.14454e11	1.77398
$337$	−2.30248e11	−0.972435	−0.486217	−	0.873838i	$-0.661624\pi$
$337$	−2.30248e11	−0.972435	−0.486217	+	0.873838i	$0.661624\pi$
$338$	4.46486e10	0.186073
$339$	−1.33871e11	−0.550541
$340$	0	0
$341$	−7.79557e11	−3.12215
$342$	3.33680e11	1.31890
$343$	2.60526e11	1.01631
$344$	−2.89421e10	−0.111434
$345$	5.81293e11	2.20907
$346$	−2.59295e11	−0.972639
$347$	−3.95650e11	−1.46497	−0.732486	−	0.680783i	$-0.761640\pi$
$347$	−3.95650e11	−1.46497	−0.732486	+	0.680783i	$0.761640\pi$
$348$	−7.92022e10	−0.289488
$349$	1.96752e10	0.0709912	0.0354956	−	0.999370i	$-0.488699\pi$
$349$	1.96752e10	0.0709912	0.0354956	+	0.999370i	$0.488699\pi$
$350$	−6.09667e11	−2.17163
$351$	5.99587e10	0.210849
$352$	−3.54412e11	−1.23046
$353$	−3.77116e11	−1.29267	−0.646336	−	0.763053i	$-0.723700\pi$
$353$	−3.77116e11	−1.29267	−0.646336	+	0.763053i	$0.723700\pi$
$354$	2.29527e11	0.776816
$355$	8.00047e11	2.67355
$356$	5.49015e10	0.181159
$357$	0	0
$358$	−6.26760e10	−0.201664
$359$	−1.70850e11	−0.542864	−0.271432	−	0.962458i	$-0.587497\pi$
$359$	−1.70850e11	−0.542864	−0.271432	+	0.962458i	$0.587497\pi$
$360$	−4.46824e11	−1.40209
$361$	−6.43229e9	−0.0199335
$362$	−3.95430e11	−1.21027
$363$	9.16074e11	2.76918
$364$	−1.34614e11	−0.401916
$365$	−5.57261e11	−1.64339
$366$	3.27905e11	0.955177
$367$	5.44356e11	1.56634	0.783169	−	0.621809i	$-0.213602\pi$
$367$	5.44356e11	1.56634	0.783169	+	0.621809i	$0.213602\pi$
$368$	−3.87276e11	−1.10079
$369$	−4.90213e10	−0.137647
$370$	−6.20472e10	−0.172113
$371$	−1.37090e11	−0.375684
$372$	−3.76162e11	−1.01843
$373$	1.31625e11	0.352086	0.176043	−	0.984383i	$-0.443670\pi$
$373$	1.31625e11	0.352086	0.176043	+	0.984383i	$0.443670\pi$
$374$	0	0
$375$	8.36543e11	2.18448
$376$	1.78077e11	0.459476
$377$	−2.20165e11	−0.561322
$378$	−8.97750e10	−0.226174
$379$	−4.36513e11	−1.08673	−0.543363	−	0.839498i	$-0.682849\pi$
$379$	−4.36513e11	−1.08673	−0.543363	+	0.839498i	$0.682849\pi$
$380$	2.59516e11	0.638466
$381$	−1.04008e12	−2.52873
$382$	5.09509e11	1.22424
$383$	−4.54186e11	−1.07855	−0.539274	−	0.842131i	$-0.681301\pi$
$383$	−4.54186e11	−1.07855	−0.539274	+	0.842131i	$0.681301\pi$
$384$	7.32439e11	1.71902
$385$	−1.22371e12	−2.83861
$386$	−5.58535e11	−1.28058
$387$	7.65626e10	0.173507
$388$	9.29251e9	0.0208157
$389$	−3.33633e11	−0.738746	−0.369373	−	0.929281i	$-0.620428\pi$
$389$	−3.33633e11	−0.738746	−0.369373	+	0.929281i	$0.620428\pi$
$390$	1.43229e12	3.13502
$391$	0	0
$392$	1.16100e10	0.0248339
$393$	1.82841e10	0.0386640
$394$	1.10579e12	2.31174
$395$	4.21645e11	0.871486
$396$	3.58829e11	0.733263
$397$	−6.05717e9	−0.0122381	−0.00611903	−	0.999981i	$-0.501948\pi$
$397$	−6.05717e9	−0.0122381	−0.00611903	+	0.999981i	$0.501948\pi$
$398$	5.70036e11	1.13875
$399$	−7.19582e11	−1.42135
$400$	−1.18995e12	−2.32413
$401$	−5.77300e11	−1.11494	−0.557470	−	0.830197i	$-0.688228\pi$
$401$	−5.77300e11	−1.11494	−0.557470	+	0.830197i	$0.688228\pi$
$402$	1.15048e12	2.19716
$403$	−1.04565e12	−1.97476
$404$	1.68853e11	0.315350
$405$	−7.79239e11	−1.43921
$406$	3.29649e11	0.602121
$407$	−8.13117e10	−0.146885
$408$	0	0
$409$	4.95915e11	0.876299	0.438150	−	0.898902i	$-0.355634\pi$
$409$	4.95915e11	0.876299	0.438150	+	0.898902i	$0.355634\pi$
$410$	−1.38467e11	−0.242002
$411$	−8.48545e11	−1.46685
$412$	−3.32644e11	−0.568777
$413$	−2.63039e11	−0.444882
$414$	7.09444e11	1.18691
$415$	3.06990e11	0.508052
$416$	−4.75387e11	−0.778264
$417$	6.87124e11	1.11281
$418$	1.23516e12	1.97893
$419$	2.71184e10	0.0429835	0.0214917	−	0.999769i	$-0.493158\pi$
$419$	2.71184e10	0.0429835	0.0214917	+	0.999769i	$0.493158\pi$
$420$	−5.90482e11	−0.925944
$421$	4.56222e10	0.0707794	0.0353897	−	0.999374i	$-0.488733\pi$
$421$	4.56222e10	0.0707794	0.0353897	+	0.999374i	$0.488733\pi$
$422$	−1.28731e12	−1.97596
$423$	−4.71079e11	−0.715422
$424$	−1.85291e11	−0.278425
$425$	0	0
$426$	1.83739e12	2.70308
$427$	−3.75781e11	−0.547028
$428$	9.49687e10	0.136799
$429$	1.87699e12	2.67550
$430$	2.16261e11	0.305049
$431$	4.84347e11	0.676097	0.338049	−	0.941129i	$-0.390233\pi$
$431$	4.84347e11	0.676097	0.338049	+	0.941129i	$0.390233\pi$
$432$	−1.75224e11	−0.242056
$433$	−3.69939e11	−0.505748	−0.252874	−	0.967499i	$-0.581376\pi$
$433$	−3.69939e11	−0.505748	−0.252874	+	0.967499i	$0.581376\pi$
$434$	1.56563e12	2.11829
$435$	−9.65747e11	−1.29319
$436$	3.27017e11	0.433393
$437$	6.72396e11	0.881980
$438$	−1.27981e12	−1.66154
$439$	4.40589e11	0.566165	0.283083	−	0.959096i	$-0.408643\pi$
$439$	4.40589e11	0.566165	0.283083	+	0.959096i	$0.408643\pi$
$440$	−1.65397e12	−2.10373
$441$	−3.07127e10	−0.0386674
$442$	0	0
$443$	−5.93995e11	−0.732767	−0.366383	−	0.930464i	$-0.619404\pi$
$443$	−5.93995e11	−0.732767	−0.366383	+	0.930464i	$0.619404\pi$
$444$	−3.92356e10	−0.0479134
$445$	6.69438e11	0.809264
$446$	1.30106e11	0.155700
$447$	1.03372e12	1.22467
$448$	−3.23577e11	−0.379512
$449$	1.04989e12	1.21909	0.609546	−	0.792751i	$-0.291352\pi$
$449$	1.04989e12	1.21909	0.609546	+	0.792751i	$0.291352\pi$
$450$	2.17985e12	2.50594
$451$	−1.81458e11	−0.206530
$452$	−1.27070e11	−0.143193
$453$	−1.76227e12	−1.96621
$454$	−1.94144e12	−2.14473
$455$	−1.64141e12	−1.79542
$456$	−9.72589e11	−1.05339
$457$	−1.90102e11	−0.203875	−0.101937	−	0.994791i	$-0.532504\pi$
$457$	−1.90102e11	−0.203875	−0.101937	+	0.994791i	$0.532504\pi$
$458$	−1.63850e12	−1.74001
$459$	0	0
$460$	5.51761e11	0.574568
$461$	−1.73350e11	−0.178760	−0.0893798	−	0.995998i	$-0.528489\pi$
$461$	−1.73350e11	−0.178760	−0.0893798	+	0.995998i	$0.528489\pi$
$462$	−2.81038e12	−2.86996
$463$	−8.10491e11	−0.819660	−0.409830	−	0.912162i	$-0.634412\pi$
$463$	−8.10491e11	−0.819660	−0.409830	+	0.912162i	$0.634412\pi$
$464$	6.43412e11	0.644404
$465$	−4.58671e12	−4.54950
$466$	−1.06267e12	−1.04390
$467$	1.10255e12	1.07269	0.536343	−	0.844000i	$-0.319805\pi$
$467$	1.10255e12	1.07269	0.536343	+	0.844000i	$0.319805\pi$
$468$	4.81312e11	0.463789
$469$	−1.31845e12	−1.25831
$470$	−1.33062e12	−1.25781
$471$	−2.55809e10	−0.0239509
$472$	−3.55524e11	−0.329708
$473$	2.83406e11	0.260336
$474$	9.68352e11	0.881111
$475$	2.06602e12	1.86215
$476$	0	0
$477$	4.90163e11	0.433519
$478$	1.65509e12	1.45009
$479$	−1.26632e12	−1.09909	−0.549546	−	0.835463i	$-0.685199\pi$
$479$	−1.26632e12	−1.09909	−0.549546	+	0.835463i	$0.685199\pi$
$480$	−2.08527e12	−1.79298
$481$	−1.09067e11	−0.0929050
$482$	1.39294e12	1.17550
$483$	−1.52992e12	−1.27910
$484$	8.69535e11	0.720249
$485$	1.13308e11	0.0929868
$486$	−2.07264e12	−1.68523
$487$	1.15988e12	0.934400	0.467200	−	0.884152i	$-0.345263\pi$
$487$	1.15988e12	0.934400	0.467200	+	0.884152i	$0.345263\pi$
$488$	−5.07907e11	−0.405410
$489$	−2.95272e12	−2.33524
$490$	−8.67519e10	−0.0679824
$491$	−5.92953e11	−0.460420	−0.230210	−	0.973141i	$-0.573941\pi$
$491$	−5.92953e11	−0.460420	−0.230210	+	0.973141i	$0.573941\pi$
$492$	−8.75597e10	−0.0673692
$493$	0	0
$494$	1.65677e12	1.25167
$495$	4.37536e12	3.27560
$496$	3.05582e12	2.26704
$497$	−2.10566e12	−1.54805
$498$	7.05035e11	0.513664
$499$	−2.80366e11	−0.202429	−0.101214	−	0.994865i	$-0.532273\pi$
$499$	−2.80366e11	−0.202429	−0.101214	+	0.994865i	$0.532273\pi$
$500$	7.94044e11	0.568172
$501$	−1.07961e12	−0.765593
$502$	−3.33822e11	−0.234611
$503$	2.37709e12	1.65573	0.827866	−	0.560926i	$-0.189555\pi$
$503$	2.37709e12	1.65573	0.827866	+	0.560926i	$0.189555\pi$
$504$	1.17600e12	0.811842
$505$	2.05890e12	1.40872
$506$	2.62609e12	1.78087
$507$	3.44265e11	0.231396
$508$	−9.87236e11	−0.657710
$509$	−7.61106e11	−0.502591	−0.251296	−	0.967910i	$-0.580857\pi$
$509$	−7.61106e11	−0.502591	−0.251296	+	0.967910i	$0.580857\pi$
$510$	0	0
$511$	1.46667e12	0.951563
$512$	−1.01257e10	−0.00651191
$513$	3.04227e11	0.193941
$514$	1.01200e12	0.639508
$515$	−4.05607e12	−2.54081
$516$	1.36753e11	0.0849205
$517$	−1.74376e12	−1.07344
$518$	1.63303e11	0.0996577
$519$	−1.99930e12	−1.20956
$520$	−2.21854e12	−1.33061
$521$	1.80892e12	1.07560	0.537800	−	0.843073i	$-0.319256\pi$
$521$	1.80892e12	1.07560	0.537800	+	0.843073i	$0.319256\pi$
$522$	−1.17865e12	−0.694815
$523$	2.49717e11	0.145946	0.0729728	−	0.997334i	$-0.476751\pi$
$523$	2.49717e11	0.145946	0.0729728	+	0.997334i	$0.476751\pi$
$524$	1.73552e10	0.0100563
$525$	−4.70086e12	−2.70060
$526$	−3.44241e12	−1.96077
$527$	0	0
$528$	−5.48533e12	−3.07150
$529$	−3.71559e11	−0.206290
$530$	1.38453e12	0.762185
$531$	9.40491e11	0.513369
$532$	−6.83025e11	−0.369687
$533$	−2.43397e11	−0.130630
$534$	1.53743e12	0.818202
$535$	1.15799e12	0.611103
$536$	−1.78202e12	−0.932550
$537$	−4.83266e11	−0.250785
$538$	−1.86042e12	−0.957396
$539$	−1.13687e11	−0.0580177
$540$	2.49645e11	0.126343
$541$	−1.08050e12	−0.542297	−0.271148	−	0.962538i	$-0.587403\pi$
$541$	−1.08050e12	−0.542297	−0.271148	+	0.962538i	$0.587403\pi$
$542$	9.87459e11	0.491499
$543$	−3.04898e12	−1.50507
$544$	0	0
$545$	3.98747e12	1.93603
$546$	−3.76968e12	−1.81525
$547$	−2.42243e12	−1.15693	−0.578466	−	0.815707i	$-0.696348\pi$
$547$	−2.42243e12	−1.15693	−0.578466	+	0.815707i	$0.696348\pi$
$548$	−8.05437e11	−0.381521
$549$	1.34360e12	0.631240
$550$	8.06900e12	3.76000
$551$	−1.11710e12	−0.516311
$552$	−2.06784e12	−0.947962
$553$	−1.10974e12	−0.504611
$554$	−2.93225e12	−1.32253
$555$	−4.78417e11	−0.214037
$556$	6.52215e11	0.289437
$557$	−1.69897e12	−0.747890	−0.373945	−	0.927451i	$-0.621995\pi$
$557$	−1.69897e12	−0.747890	−0.373945	+	0.927451i	$0.621995\pi$
$558$	−5.59789e12	−2.44439
$559$	3.80143e11	0.164662
$560$	4.79688e12	2.06116
$561$	0	0
$562$	−1.33390e12	−0.564038
$563$	−2.39306e12	−1.00384	−0.501921	−	0.864913i	$-0.667373\pi$
$563$	−2.39306e12	−1.00384	−0.501921	+	0.864913i	$0.667373\pi$
$564$	−8.41421e11	−0.350153
$565$	−1.54942e12	−0.639665
$566$	−4.67397e10	−0.0191431
$567$	2.05089e12	0.833335
$568$	−2.84602e12	−1.14728
$569$	−2.71831e12	−1.08716	−0.543581	−	0.839357i	$-0.682932\pi$
$569$	−2.71831e12	−1.08716	−0.543581	+	0.839357i	$0.682932\pi$
$570$	7.26735e12	2.88363
$571$	−1.20499e12	−0.474374	−0.237187	−	0.971464i	$-0.576225\pi$
$571$	−1.20499e12	−0.474374	−0.237187	+	0.971464i	$0.576225\pi$
$572$	1.78163e12	0.695883
$573$	3.92859e12	1.52244
$574$	3.64434e11	0.140125
$575$	4.39260e12	1.67578
$576$	1.15694e12	0.437936
$577$	2.39602e12	0.899910	0.449955	−	0.893051i	$-0.351440\pi$
$577$	2.39602e12	0.899910	0.449955	+	0.893051i	$0.351440\pi$
$578$	0	0
$579$	−4.30661e12	−1.59251
$580$	−9.16684e11	−0.336352
$581$	−8.07974e11	−0.294175
$582$	2.60223e11	0.0940138
$583$	1.81440e12	0.650465
$584$	1.98235e12	0.705216
$585$	5.86885e12	2.07182
$586$	−4.06570e12	−1.42428
$587$	−1.88643e12	−0.655796	−0.327898	−	0.944713i	$-0.606340\pi$
$587$	−1.88643e12	−0.655796	−0.327898	+	0.944713i	$0.606340\pi$
$588$	−5.48577e10	−0.0189252
$589$	−5.30557e12	−1.81641
$590$	2.65653e12	0.902571
$591$	8.52624e12	2.87484
$592$	3.18737e11	0.106656
$593$	1.28573e12	0.426976	0.213488	−	0.976946i	$-0.431518\pi$
$593$	1.28573e12	0.426976	0.213488	+	0.976946i	$0.431518\pi$
$594$	1.18818e12	0.391601
$595$	0	0
$596$	9.81203e11	0.318530
$597$	4.39528e12	1.41613
$598$	3.52248e12	1.12640
$599$	4.18407e12	1.32794	0.663969	−	0.747760i	$-0.268871\pi$
$599$	4.18407e12	1.32794	0.663969	+	0.747760i	$0.268871\pi$
$600$	−6.35369e12	−2.00145
$601$	2.40265e12	0.751199	0.375599	−	0.926782i	$-0.377437\pi$
$601$	2.40265e12	0.751199	0.375599	+	0.926782i	$0.377437\pi$
$602$	−5.69181e11	−0.176631
$603$	4.71411e12	1.45202
$604$	−1.67274e12	−0.511401
$605$	1.06026e13	3.21747
$606$	4.72847e12	1.42428
$607$	1.65529e12	0.494908	0.247454	−	0.968900i	$-0.420406\pi$
$607$	1.65529e12	0.494908	0.247454	+	0.968900i	$0.420406\pi$
$608$	−2.41208e12	−0.715857
$609$	2.54177e12	0.748787
$610$	3.79517e12	1.10981
$611$	−2.33897e12	−0.678952
$612$	0	0
$613$	−1.56192e11	−0.0446772	−0.0223386	−	0.999750i	$-0.507111\pi$
$613$	−1.56192e11	−0.0446772	−0.0223386	+	0.999750i	$0.507111\pi$
$614$	−1.14805e12	−0.325989
$615$	−1.06765e12	−0.300949
$616$	4.35312e12	1.21811
$617$	−1.41213e12	−0.392277	−0.196138	−	0.980576i	$-0.562840\pi$
$617$	−1.41213e12	−0.392277	−0.196138	+	0.980576i	$0.562840\pi$
$618$	−9.31518e12	−2.56888
$619$	−2.21421e12	−0.606193	−0.303096	−	0.952960i	$-0.598020\pi$
$619$	−2.21421e12	−0.606193	−0.303096	+	0.952960i	$0.598020\pi$
$620$	−4.35369e12	−1.18330
$621$	6.46822e11	0.174531
$622$	3.82626e11	0.102499
$623$	−1.76191e12	−0.468583
$624$	−7.35769e12	−1.94272
$625$	2.50673e12	0.657124
$626$	2.35692e12	0.613423
$627$	9.52374e12	2.46095
$628$	−2.42813e10	−0.00622951
$629$	0	0
$630$	−8.78731e12	−2.22241
$631$	5.77311e12	1.44970	0.724849	−	0.688908i	$-0.241909\pi$
$631$	5.77311e12	1.44970	0.724849	+	0.688908i	$0.241909\pi$
$632$	−1.49992e12	−0.373974
$633$	−9.92586e12	−2.45726
$634$	7.56889e12	1.86050
$635$	−1.20378e13	−2.93809
$636$	8.75508e11	0.212179
$637$	−1.52493e11	−0.0366962
$638$	−4.36293e12	−1.04252
$639$	7.52876e12	1.78636
$640$	8.47722e12	1.99730
$641$	−4.73882e12	−1.10869	−0.554344	−	0.832288i	$-0.687031\pi$
$641$	−4.73882e12	−1.10869	−0.554344	+	0.832288i	$0.687031\pi$
$642$	2.65946e12	0.617853
$643$	6.93341e12	1.59955	0.799774	−	0.600301i	$-0.204952\pi$
$643$	6.93341e12	1.59955	0.799774	+	0.600301i	$0.204952\pi$
$644$	−1.45219e12	−0.332688
$645$	1.66749e12	0.379353
$646$	0	0
$647$	5.27307e12	1.18302	0.591512	−	0.806296i	$-0.298531\pi$
$647$	5.27307e12	1.18302	0.591512	+	0.806296i	$0.298531\pi$
$648$	2.77199e12	0.617596
$649$	3.48134e12	0.770274
$650$	1.08233e13	2.37820
$651$	1.20719e13	2.63427
$652$	−2.80271e12	−0.607385
$653$	5.48140e12	1.17973	0.589864	−	0.807503i	$-0.299181\pi$
$653$	5.48140e12	1.17973	0.589864	+	0.807503i	$0.299181\pi$
$654$	9.15763e12	1.95742
$655$	2.11620e11	0.0449231
$656$	7.11305e11	0.149965
$657$	−5.24404e12	−1.09805
$658$	3.50209e12	0.728301
$659$	−1.18012e12	−0.243749	−0.121874	−	0.992546i	$-0.538891\pi$
$659$	−1.18012e12	−0.243749	−0.121874	+	0.992546i	$0.538891\pi$
$660$	7.81508e12	1.60319
$661$	7.91914e12	1.61351	0.806755	−	0.590886i	$-0.201222\pi$
$661$	7.91914e12	1.61351	0.806755	+	0.590886i	$0.201222\pi$
$662$	6.23483e12	1.26172
$663$	0	0
$664$	−1.09206e12	−0.218017
$665$	−8.32843e12	−1.65145
$666$	−5.83888e11	−0.114999
$667$	−2.37509e12	−0.464638
$668$	−1.02476e12	−0.199127
$669$	1.00318e12	0.193626
$670$	1.33156e13	2.55284
$671$	4.97350e12	0.947133
$672$	5.48826e12	1.03818
$673$	−4.57851e12	−0.860312	−0.430156	−	0.902755i	$-0.641541\pi$
$673$	−4.57851e12	−0.860312	−0.430156	+	0.902755i	$0.641541\pi$
$674$	−6.12017e12	−1.14234
$675$	1.98744e12	0.368491
$676$	3.26775e11	0.0601850
$677$	2.03823e12	0.372909	0.186455	−	0.982464i	$-0.440300\pi$
$677$	2.03823e12	0.372909	0.186455	+	0.982464i	$0.440300\pi$
$678$	−3.55841e12	−0.646730
$679$	−2.98217e11	−0.0538416
$680$	0	0
$681$	−1.49695e13	−2.66714
$682$	−2.07213e13	−3.66764
$683$	−6.08765e12	−1.07042	−0.535212	−	0.844718i	$-0.679768\pi$
$683$	−6.08765e12	−1.07042	−0.535212	+	0.844718i	$0.679768\pi$
$684$	2.44215e12	0.426598
$685$	−9.82104e12	−1.70432
$686$	6.92500e12	1.19388
$687$	−1.26337e13	−2.16385
$688$	−1.11093e12	−0.189034
$689$	2.43372e12	0.411420
$690$	1.54512e13	2.59503
$691$	9.24898e12	1.54327	0.771636	−	0.636064i	$-0.219439\pi$
$691$	9.24898e12	1.54327	0.771636	+	0.636064i	$0.219439\pi$
$692$	−1.89773e12	−0.314599
$693$	−1.15156e13	−1.89665
$694$	−1.05167e13	−1.72093
$695$	7.95275e12	1.29296
$696$	3.43546e12	0.554936
$697$	0	0
$698$	5.22983e11	0.0833946
$699$	−8.19373e12	−1.29818
$700$	−4.46204e12	−0.702413
$701$	5.92651e11	0.0926974	0.0463487	−	0.998925i	$-0.485241\pi$
$701$	5.92651e11	0.0926974	0.0463487	+	0.998925i	$0.485241\pi$
$702$	1.59375e12	0.247687
$703$	−5.53397e11	−0.0854551
$704$	4.28257e12	0.657093
$705$	−1.02598e13	−1.56419
$706$	−1.00241e13	−1.51853
$707$	−5.41886e12	−0.815681
$708$	1.67986e12	0.251261
$709$	1.07708e13	1.60082	0.800408	−	0.599456i	$-0.204616\pi$
$709$	1.07708e13	1.60082	0.800408	+	0.599456i	$0.204616\pi$
$710$	2.12659e13	3.14067
$711$	3.96785e12	0.582293
$712$	−2.38140e12	−0.347274
$713$	−1.12803e13	−1.63462
$714$	0	0
$715$	2.17243e13	3.10862
$716$	−4.58714e11	−0.0652279
$717$	1.27616e13	1.80331
$718$	−4.54134e12	−0.637712
$719$	7.91653e12	1.10473	0.552363	−	0.833604i	$-0.313726\pi$
$719$	7.91653e12	1.10473	0.552363	+	0.833604i	$0.313726\pi$
$720$	−1.71512e13	−2.37847
$721$	1.06752e13	1.47119
$722$	−1.70976e11	−0.0234162
$723$	1.07404e13	1.46183
$724$	−2.89408e12	−0.391460
$725$	−7.29777e12	−0.981000
$726$	2.43500e13	3.25300
$727$	−8.90450e12	−1.18224	−0.591119	−	0.806585i	$-0.701313\pi$
$727$	−8.90450e12	−1.18224	−0.591119	+	0.806585i	$0.701313\pi$
$728$	5.83901e12	0.770457
$729$	−9.51529e12	−1.24781
$730$	−1.48125e13	−1.93052
$731$	0	0
$732$	2.39988e12	0.308951
$733$	−1.21085e13	−1.54926	−0.774628	−	0.632417i	$-0.782063\pi$
$733$	−1.21085e13	−1.54926	−0.774628	+	0.632417i	$0.782063\pi$
$734$	1.44694e13	1.84001
$735$	−6.68904e11	−0.0845417
$736$	−5.12837e12	−0.644213
$737$	1.74499e13	2.17865
$738$	−1.30303e12	−0.161696
$739$	−6.25896e12	−0.771973	−0.385987	−	0.922504i	$-0.626139\pi$
$739$	−6.25896e12	−0.771973	−0.385987	+	0.922504i	$0.626139\pi$
$740$	−4.54112e11	−0.0556699
$741$	1.27746e13	1.55655
$742$	−3.64397e12	−0.441323
$743$	−8.59497e12	−1.03465	−0.517326	−	0.855788i	$-0.673073\pi$
$743$	−8.59497e12	−1.03465	−0.517326	+	0.855788i	$0.673073\pi$
$744$	1.63164e13	1.95229
$745$	1.19642e13	1.42292
$746$	3.49870e12	0.413601
$747$	2.88890e12	0.339461
$748$	0	0
$749$	−3.04775e12	−0.353843
$750$	2.22360e13	2.56614
$751$	1.13458e13	1.30153	0.650767	−	0.759277i	$-0.274447\pi$
$751$	1.13458e13	1.30153	0.650767	+	0.759277i	$0.274447\pi$
$752$	6.83542e12	0.779444
$753$	−2.57395e12	−0.291758
$754$	−5.85217e12	−0.659395
$755$	−2.03964e13	−2.28451
$756$	−6.57047e11	−0.0731557
$757$	−1.34405e13	−1.48759	−0.743797	−	0.668406i	$-0.766977\pi$
$757$	−1.34405e13	−1.48759	−0.743797	+	0.668406i	$0.766977\pi$
$758$	−1.16029e13	−1.27660
$759$	2.02486e13	2.21466
$760$	−1.12567e13	−1.22391
$761$	2.20957e12	0.238823	0.119412	−	0.992845i	$-0.461899\pi$
$761$	2.20957e12	0.238823	0.119412	+	0.992845i	$0.461899\pi$
$762$	−2.76461e13	−2.97054
$763$	−1.04947e13	−1.12101
$764$	3.72901e12	0.395980
$765$	0	0
$766$	−1.20726e13	−1.26699
$767$	4.66966e12	0.487199
$768$	1.40302e13	1.45525
$769$	6.08633e12	0.627605	0.313803	−	0.949488i	$-0.398397\pi$
$769$	6.08633e12	0.627605	0.313803	+	0.949488i	$0.398397\pi$
$770$	−3.25273e13	−3.33457
$771$	7.80306e12	0.795280
$772$	−4.08782e12	−0.414204
$773$	−6.60486e11	−0.0665359	−0.0332680	−	0.999446i	$-0.510591\pi$
$773$	−6.60486e11	−0.0665359	−0.0332680	+	0.999446i	$0.510591\pi$
$774$	2.03510e12	0.203822
$775$	−3.46600e13	−3.45121
$776$	−4.03070e11	−0.0399027
$777$	1.25916e12	0.123932
$778$	−8.86823e12	−0.867818
$779$	−1.23498e12	−0.120155
$780$	1.04827e13	1.01402
$781$	2.78686e13	2.68031
$782$	0	0
$783$	−1.07462e12	−0.102170
$784$	4.45646e11	0.0421277
$785$	−2.96073e11	−0.0278282
$786$	4.86006e11	0.0454193
$787$	4.67412e12	0.434324	0.217162	−	0.976136i	$-0.430320\pi$
$787$	4.67412e12	0.434324	0.217162	+	0.976136i	$0.430320\pi$
$788$	8.09308e12	0.747732
$789$	−2.65428e13	−2.43837
$790$	1.12077e13	1.02375
$791$	4.07796e12	0.370381
$792$	−1.55645e13	−1.40563
$793$	6.67115e12	0.599062
$794$	−1.61005e11	−0.0143763
$795$	1.06755e13	0.947838
$796$	4.17199e12	0.368328
$797$	−4.83102e12	−0.424108	−0.212054	−	0.977258i	$-0.568015\pi$
$797$	−4.83102e12	−0.424108	−0.212054	+	0.977258i	$0.568015\pi$
$798$	−1.91271e13	−1.66969
$799$	0	0
$800$	−1.57576e13	−1.36014
$801$	6.29967e12	0.540719
$802$	−1.53451e13	−1.30974
$803$	−1.94115e13	−1.64755
$804$	8.42014e12	0.710668
$805$	−1.77072e13	−1.48617
$806$	−2.77943e13	−2.31978
$807$	−1.43449e13	−1.19060
$808$	−7.32413e12	−0.604512
$809$	1.13819e13	0.934213	0.467106	−	0.884201i	$-0.345297\pi$
$809$	1.13819e13	0.934213	0.467106	+	0.884201i	$0.345297\pi$
$810$	−2.07128e13	−1.69066
$811$	1.59699e13	1.29631	0.648154	−	0.761510i	$-0.275541\pi$
$811$	1.59699e13	1.29631	0.648154	+	0.761510i	$0.275541\pi$
$812$	2.41264e12	0.194756
$813$	7.61384e12	0.611218
$814$	−2.16133e12	−0.172549
$815$	−3.41747e13	−2.71329
$816$	0	0
$817$	1.92882e12	0.151458
$818$	1.31818e13	1.02940
$819$	−1.54463e13	−1.19963
$820$	−1.01341e12	−0.0782752
$821$	−6.88013e12	−0.528509	−0.264254	−	0.964453i	$-0.585126\pi$
$821$	−6.88013e12	−0.528509	−0.264254	+	0.964453i	$0.585126\pi$
$822$	−2.25550e13	−1.72314
$823$	2.46473e13	1.87271	0.936353	−	0.351061i	$-0.114179\pi$
$823$	2.46473e13	1.87271	0.936353	+	0.351061i	$0.114179\pi$
$824$	1.44287e13	1.09032
$825$	6.22163e13	4.67586
$826$	−6.99179e12	−0.522610
$827$	2.43084e13	1.80709	0.903547	−	0.428489i	$-0.140954\pi$
$827$	2.43084e13	1.80709	0.903547	+	0.428489i	$0.140954\pi$
$828$	5.19229e12	0.383904
$829$	−1.07060e11	−0.00787282	−0.00393641	−	0.999992i	$-0.501253\pi$
$829$	−1.07060e11	−0.00787282	−0.00393641	+	0.999992i	$0.501253\pi$
$830$	8.16006e12	0.596818
$831$	−2.26092e13	−1.64468
$832$	5.74437e12	0.415612
$833$	0	0
$834$	1.82643e13	1.30724
$835$	−1.24954e13	−0.889530
$836$	9.03990e12	0.640082
$837$	−5.10377e12	−0.359440
$838$	7.20830e11	0.0504934
$839$	2.29541e12	0.159930	0.0799652	−	0.996798i	$-0.474519\pi$
$839$	2.29541e12	0.159930	0.0799652	+	0.996798i	$0.474519\pi$
$840$	2.56126e13	1.77500
$841$	−1.05612e13	−0.728001
$842$	1.21268e12	0.0831458
$843$	−1.02851e13	−0.701427
$844$	−9.42159e12	−0.639121
$845$	3.98451e12	0.268856
$846$	−1.25217e13	−0.840419
$847$	−2.79052e13	−1.86299
$848$	−7.11233e12	−0.472314
$849$	−3.60388e11	−0.0238060
$850$	0	0
$851$	−1.17659e12	−0.0769026
$852$	1.34475e13	0.874308
$853$	−8.93269e12	−0.577713	−0.288856	−	0.957372i	$-0.593275\pi$
$853$	−8.93269e12	−0.577713	−0.288856	+	0.957372i	$0.593275\pi$
$854$	−9.98858e12	−0.642604
$855$	2.97782e13	1.90568
$856$	−4.11934e12	−0.262238
$857$	1.66952e13	1.05725	0.528626	−	0.848855i	$-0.322707\pi$
$857$	1.66952e13	1.05725	0.528626	+	0.848855i	$0.322707\pi$
$858$	4.98920e13	3.14295
$859$	−8.71639e12	−0.546220	−0.273110	−	0.961983i	$-0.588052\pi$
$859$	−8.71639e12	−0.546220	−0.273110	+	0.961983i	$0.588052\pi$
$860$	1.58277e12	0.0986678
$861$	2.80998e12	0.174256
$862$	1.28744e13	0.794223
$863$	−3.01729e12	−0.185169	−0.0925844	−	0.995705i	$-0.529513\pi$
$863$	−3.01729e12	−0.185169	−0.0925844	+	0.995705i	$0.529513\pi$
$864$	−2.32034e12	−0.141658
$865$	−2.31399e13	−1.40536
$866$	−9.83328e12	−0.594112
$867$	0	0
$868$	1.14586e13	0.685160
$869$	1.46875e13	0.873691
$870$	−2.56703e13	−1.51913
$871$	2.34062e13	1.37800
$872$	−1.41846e13	−0.830796
$873$	1.06627e12	0.0621302
$874$	1.78728e13	1.03608
$875$	−2.54826e13	−1.46963
$876$	−9.36668e12	−0.537424
$877$	2.25993e13	1.29002	0.645012	−	0.764173i	$-0.276853\pi$
$877$	2.25993e13	1.29002	0.645012	+	0.764173i	$0.276853\pi$
$878$	1.17112e13	0.665084
$879$	−3.13487e13	−1.77121
$880$	−6.34871e13	−3.56873
$881$	−2.64062e13	−1.47678	−0.738388	−	0.674376i	$-0.764413\pi$
$881$	−2.64062e13	−1.47678	−0.738388	+	0.674376i	$0.764413\pi$
$882$	−8.16369e11	−0.0454232
$883$	−8.21138e12	−0.454562	−0.227281	−	0.973829i	$-0.572984\pi$
$883$	−8.21138e12	−0.454562	−0.227281	+	0.973829i	$0.572984\pi$
$884$	0	0
$885$	2.04833e13	1.12242
$886$	−1.57889e13	−0.860794
$887$	2.49193e12	0.135170	0.0675848	−	0.997714i	$-0.478471\pi$
$887$	2.49193e12	0.135170	0.0675848	+	0.997714i	$0.478471\pi$
$888$	1.70188e12	0.0918480
$889$	3.16825e13	1.70123
$890$	1.77942e13	0.950656
$891$	−2.71438e13	−1.44285
$892$	9.52219e11	0.0503611
$893$	−1.18678e13	−0.624508
$894$	2.74771e13	1.43864
$895$	−5.59330e12	−0.291383
$896$	−2.23114e13	−1.15649
$897$	2.71602e13	1.40077
$898$	2.79070e13	1.43209
$899$	1.87408e13	0.956904
$900$	1.59540e13	0.810545
$901$	0	0
$902$	−4.82331e12	−0.242614
$903$	−4.38869e12	−0.219654
$904$	5.51178e12	0.274495
$905$	−3.52888e13	−1.74871
$906$	−4.68425e13	−2.30974
$907$	2.95913e13	1.45188	0.725940	−	0.687758i	$-0.241405\pi$
$907$	2.95913e13	1.45188	0.725940	+	0.687758i	$0.241405\pi$
$908$	−1.42090e13	−0.693710
$909$	1.93750e13	0.941250
$910$	−4.36301e13	−2.10911
$911$	−2.96554e12	−0.142650	−0.0713250	−	0.997453i	$-0.522723\pi$
$911$	−2.96554e12	−0.142650	−0.0713250	+	0.997453i	$0.522723\pi$
$912$	−3.73325e13	−1.78694
$913$	1.06936e13	0.509338
$914$	−5.05307e12	−0.239496
$915$	2.92628e13	1.38013
$916$	−1.19919e13	−0.562806
$917$	−5.56966e11	−0.0260116
$918$	0	0
$919$	1.87888e13	0.868918	0.434459	−	0.900692i	$-0.356940\pi$
$919$	1.87888e13	0.868918	0.434459	+	0.900692i	$0.356940\pi$
$920$	−2.39331e13	−1.10142
$921$	−8.85209e12	−0.405394
$922$	−4.60778e12	−0.209992
$923$	3.73813e13	1.69530
$924$	−2.05687e13	−0.928287
$925$	−3.61521e12	−0.162366
$926$	−2.15435e13	−0.962869
$927$	−3.81692e13	−1.69767
$928$	8.52016e12	0.377122
$929$	−4.36911e13	−1.92452	−0.962259	−	0.272135i	$-0.912270\pi$
$929$	−4.36911e13	−1.92452	−0.962259	+	0.272135i	$0.912270\pi$
$930$	−1.21919e14	−5.34437
$931$	−7.73738e11	−0.0337536
$932$	−7.77746e12	−0.337650
$933$	2.95025e12	0.127465
$934$	2.93067e13	1.26010
$935$	0	0
$936$	−2.08773e13	−0.889064
$937$	6.48044e12	0.274648	0.137324	−	0.990526i	$-0.456150\pi$
$937$	6.48044e12	0.274648	0.137324	+	0.990526i	$0.456150\pi$
$938$	−3.50456e13	−1.47816
$939$	1.81731e13	0.762841
$940$	−9.73858e12	−0.406837
$941$	7.36913e12	0.306382	0.153191	−	0.988197i	$-0.451045\pi$
$941$	7.36913e12	0.306382	0.153191	+	0.988197i	$0.451045\pi$
$942$	−6.79962e11	−0.0281356
$943$	−2.62572e12	−0.108130
$944$	−1.36466e13	−0.559309
$945$	−8.01166e12	−0.326798
$946$	7.53316e12	0.305821
$947$	1.63100e11	0.00658988	0.00329494	−	0.999995i	$-0.498951\pi$
$947$	1.63100e11	0.00658988	0.00329494	+	0.999995i	$0.498951\pi$
$948$	7.08719e12	0.284995
$949$	−2.60374e13	−1.04208
$950$	5.49165e13	2.18749
$951$	5.83602e13	2.31369
$952$	0	0
$953$	3.44725e13	1.35380	0.676901	−	0.736074i	$-0.263322\pi$
$953$	3.44725e13	1.35380	0.676901	+	0.736074i	$0.263322\pi$
$954$	1.30289e13	0.509262
$955$	4.54694e13	1.76890
$956$	1.21133e13	0.469031
$957$	−3.36405e13	−1.29646
$958$	−3.36599e13	−1.29112
$959$	2.58482e13	0.986839
$960$	2.51975e13	0.957496
$961$	6.25677e13	2.36644
$962$	−2.89908e12	−0.109137
$963$	1.08972e13	0.408316
$964$	1.01947e13	0.380214
$965$	−4.98446e13	−1.85031
$966$	−4.06664e13	−1.50259
$967$	4.11357e13	1.51286	0.756431	−	0.654073i	$-0.226941\pi$
$967$	4.11357e13	1.51286	0.756431	+	0.654073i	$0.226941\pi$
$968$	−3.77168e13	−1.38069
$969$	0	0
$970$	3.01181e12	0.109233
$971$	−2.31458e12	−0.0835577	−0.0417789	−	0.999127i	$-0.513302\pi$
$971$	−2.31458e12	−0.0835577	−0.0417789	+	0.999127i	$0.513302\pi$
$972$	−1.51693e13	−0.545087
$973$	−2.09310e13	−0.748656
$974$	3.08306e13	1.09766
$975$	8.34532e13	2.95748
$976$	−1.94958e13	−0.687729
$977$	−4.08077e13	−1.43290	−0.716450	−	0.697638i	$-0.754234\pi$
$977$	−4.08077e13	−1.43290	−0.716450	+	0.697638i	$0.754234\pi$
$978$	−7.84857e13	−2.74325
$979$	2.33190e13	0.811312
$980$	−6.34922e11	−0.0219889
$981$	3.75236e13	1.29358
$982$	−1.57612e13	−0.540863
$983$	3.41341e13	1.16600	0.582998	−	0.812473i	$-0.301879\pi$
$983$	3.41341e13	1.16600	0.582998	+	0.812473i	$0.301879\pi$
$984$	3.79797e12	0.129144
$985$	9.86825e13	3.34023
$986$	0	0
$987$	2.70030e13	0.905701
$988$	1.21256e13	0.404852
$989$	4.10090e12	0.136300
$990$	1.16301e14	3.84790
$991$	2.85414e13	0.940035	0.470017	−	0.882657i	$-0.344248\pi$
$991$	2.85414e13	0.940035	0.470017	+	0.882657i	$0.344248\pi$
$992$	4.04656e13	1.32673
$993$	4.80739e13	1.56905
$994$	−5.59702e13	−1.81852
$995$	5.08709e13	1.64538
$996$	5.16003e12	0.166144
$997$	−4.47702e13	−1.43503	−0.717515	−	0.696544i	$-0.754720\pi$
$997$	−4.47702e13	−1.43503	−0.717515	+	0.696544i	$0.754720\pi$
$998$	−7.45235e12	−0.237797
$999$	−5.32349e11	−0.0169103

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.h.1.27	yes	36
17.16	even	2		289.10.a.g.1.27	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.27	✓	36	17.16	even	2
289.10.a.h.1.27	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)

\(f(q)\)	\(=\)	\(q+26.5808 q^{2} +204.952 q^{3} +194.540 q^{4} +2372.11 q^{5} +5447.81 q^{6} -6243.22 q^{7} -8438.34 q^{8} +22322.5 q^{9} +O(q^{10})\)	\(q+26.5808 q^{2} +204.952 q^{3} +194.540 q^{4} +2372.11 q^{5} +5447.81 q^{6} -6243.22 q^{7} -8438.34 q^{8} +22322.5 q^{9} +63052.8 q^{10} +82629.5 q^{11} +39871.5 q^{12} +110834. q^{13} -165950. q^{14} +486171. q^{15} -323903. q^{16} +593351. q^{18} +562366. q^{19} +461472. q^{20} -1.27956e6 q^{21} +2.19636e6 q^{22} +1.19566e6 q^{23} -1.72946e6 q^{24} +3.67380e6 q^{25} +2.94607e6 q^{26} +540977. q^{27} -1.21456e6 q^{28} -1.98644e6 q^{29} +1.29228e7 q^{30} -9.43437e6 q^{31} -4.28917e6 q^{32} +1.69351e7 q^{33} -1.48096e7 q^{35} +4.34263e6 q^{36} -984052. q^{37} +1.49481e7 q^{38} +2.27158e7 q^{39} -2.00167e7 q^{40} -2.19605e6 q^{41} -3.40118e7 q^{42} +3.42984e6 q^{43} +1.60748e7 q^{44} +5.29516e7 q^{45} +3.17815e7 q^{46} -2.11033e7 q^{47} -6.63847e7 q^{48} -1.37586e6 q^{49} +9.76527e7 q^{50} +2.15617e7 q^{52} +2.19582e7 q^{53} +1.43796e7 q^{54} +1.96007e8 q^{55} +5.26824e7 q^{56} +1.15258e8 q^{57} -5.28011e7 q^{58} +4.21319e7 q^{59} +9.45798e7 q^{60} +6.01904e7 q^{61} -2.50773e8 q^{62} -1.39364e8 q^{63} +5.18285e7 q^{64} +2.62912e8 q^{65} +4.50150e8 q^{66} +2.11182e8 q^{67} +2.45053e8 q^{69} -3.93652e8 q^{70} +3.37272e8 q^{71} -1.88365e8 q^{72} -2.34922e8 q^{73} -2.61569e7 q^{74} +7.52955e8 q^{75} +1.09403e8 q^{76} -5.15874e8 q^{77} +6.03803e8 q^{78} +1.77751e8 q^{79} -7.68334e8 q^{80} -3.28500e8 q^{81} -5.83727e7 q^{82} +1.29416e8 q^{83} -2.48926e8 q^{84} +9.11679e7 q^{86} -4.07125e8 q^{87} -6.97256e8 q^{88} +2.82211e8 q^{89} +1.40750e9 q^{90} -6.91962e8 q^{91} +2.32603e8 q^{92} -1.93360e9 q^{93} -5.60944e8 q^{94} +1.33400e9 q^{95} -8.79076e8 q^{96} +4.77665e7 q^{97} -3.65716e7 q^{98} +1.84450e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 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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