LMFDB - Embedded newform 37.10.a.b.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,10,Mod(1,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, 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("37.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	37.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:	$19.0563259381$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 6 x^{13} - 5234 x^{12} + 33102 x^{11} + 10421899 x^{10} - 66002244 x^{9} + \cdots + 51\!\cdots\!20 $ x^14 - 6x^13 - 5234x^12 + 33102x^11 + 10421899x^10 - 66002244x^9 - 9839334124x^8 + 60512691564x^7 + 4405897359639x^6 - 25392014044254x^5 - 798948725725074x^4 + 3805427076948774x^3 + 41503424166638973x^2 - 100457651820986424*x + 51865911118483920
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$39.6649$ of defining polynomial
Character	$\chi$	$=$	37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+42.6649 q^{2} +65.1896 q^{3} +1308.30 q^{4} +2393.49 q^{5} +2781.31 q^{6} -2430.73 q^{7} +33974.0 q^{8} -15433.3 q^{9} +O(q^{10})$	\(q+42.6649 q^{2} +65.1896 q^{3} +1308.30 q^{4} +2393.49 q^{5} +2781.31 q^{6} -2430.73 q^{7} +33974.0 q^{8} -15433.3 q^{9} +102118. q^{10} -73135.0 q^{11} +85287.4 q^{12} -153023. q^{13} -103707. q^{14} +156031. q^{15} +779651. q^{16} +230071. q^{17} -658462. q^{18} +9827.40 q^{19} +3.13140e6 q^{20} -158458. q^{21} -3.12030e6 q^{22} +1.66730e6 q^{23} +2.21475e6 q^{24} +3.77568e6 q^{25} -6.52870e6 q^{26} -2.28922e6 q^{27} -3.18011e6 q^{28} -3.65682e6 q^{29} +6.65705e6 q^{30} -3.59660e6 q^{31} +1.58691e7 q^{32} -4.76764e6 q^{33} +9.81599e6 q^{34} -5.81792e6 q^{35} -2.01914e7 q^{36} +1.87416e6 q^{37} +419286. q^{38} -9.97549e6 q^{39} +8.13165e7 q^{40} +2.02802e7 q^{41} -6.76060e6 q^{42} +3.31415e7 q^{43} -9.56824e7 q^{44} -3.69395e7 q^{45} +7.11354e7 q^{46} +242967. q^{47} +5.08251e7 q^{48} -3.44452e7 q^{49} +1.61089e8 q^{50} +1.49983e7 q^{51} -2.00199e8 q^{52} -4.12000e7 q^{53} -9.76694e7 q^{54} -1.75048e8 q^{55} -8.25815e7 q^{56} +640644. q^{57} -1.56018e8 q^{58} +1.40919e8 q^{59} +2.04135e8 q^{60} +7.62755e7 q^{61} -1.53449e8 q^{62} +3.75142e7 q^{63} +2.77872e8 q^{64} -3.66259e8 q^{65} -2.03411e8 q^{66} +2.37751e7 q^{67} +3.01002e8 q^{68} +1.08691e8 q^{69} -2.48221e8 q^{70} -3.19423e7 q^{71} -5.24332e8 q^{72} -3.62976e8 q^{73} +7.99610e7 q^{74} +2.46135e8 q^{75} +1.28572e7 q^{76} +1.77771e8 q^{77} -4.25604e8 q^{78} +4.39355e8 q^{79} +1.86609e9 q^{80} +1.54541e8 q^{81} +8.65255e8 q^{82} -2.46518e8 q^{83} -2.07310e8 q^{84} +5.50674e8 q^{85} +1.41398e9 q^{86} -2.38387e8 q^{87} -2.48469e9 q^{88} -3.12703e8 q^{89} -1.57602e9 q^{90} +3.71956e8 q^{91} +2.18133e9 q^{92} -2.34461e8 q^{93} +1.03662e7 q^{94} +2.35218e7 q^{95} +1.03450e9 q^{96} +2.14929e8 q^{97} -1.46960e9 q^{98} +1.12872e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 48 q^{2} + 397 q^{3} + 3498 q^{4} + 2841 q^{5} + 3375 q^{6} + 6632 q^{7} + 41046 q^{8} + 101917 q^{9}+O(q^{10}) $ 14 * q + 48 * q^2 + 397 * q^3 + 3498 * q^4 + 2841 * q^5 + 3375 * q^6 + 6632 * q^7 + 41046 * q^8 + 101917 * q^9	\( 14 q + 48 q^{2} + 397 q^{3} + 3498 q^{4} + 2841 q^{5} + 3375 q^{6} + 6632 q^{7} + 41046 q^{8} + 101917 q^{9} + 129003 q^{10} + 44949 q^{11} - 123661 q^{12} + 38913 q^{13} + 16434 q^{14} + 119816 q^{15} + 859962 q^{16} + 893196 q^{17} + 1833339 q^{18} + 1532124 q^{19} + 4974963 q^{20} + 1851132 q^{21} + 3195323 q^{22} + 5911773 q^{23} + 7885413 q^{24} + 9978791 q^{25} + 10634475 q^{26} + 13105312 q^{27} + 9469678 q^{28} + 8764377 q^{29} + 21804216 q^{30} + 13188927 q^{31} + 23982750 q^{32} + 9398618 q^{33} + 29914960 q^{34} + 29633556 q^{35} + 24297333 q^{36} + 26238254 q^{37} + 23342796 q^{38} + 40855861 q^{39} + 42889049 q^{40} + 22153785 q^{41} + 6999662 q^{42} + 1779790 q^{43} - 83674089 q^{44} - 45101798 q^{45} - 23239663 q^{46} + 40080072 q^{47} - 141884869 q^{48} - 170457752 q^{49} - 89214633 q^{50} - 127867462 q^{51} - 276889277 q^{52} - 102088122 q^{53} - 356745582 q^{54} - 206797385 q^{55} - 294922194 q^{56} - 141710762 q^{57} - 527059089 q^{58} + 56191266 q^{59} - 283393416 q^{60} - 178507397 q^{61} - 27353505 q^{62} - 291948734 q^{63} - 242330062 q^{64} - 174258810 q^{65} - 1153895008 q^{66} + 287062499 q^{67} + 308827572 q^{68} - 80094823 q^{69} - 672888452 q^{70} + 224382678 q^{71} + 105778731 q^{72} + 271440727 q^{73} + 89959728 q^{74} + 1017561832 q^{75} - 229522980 q^{76} + 671279994 q^{77} - 119785879 q^{78} + 379128625 q^{79} + 1999017183 q^{80} + 2367007018 q^{81} + 551153781 q^{82} + 1664083206 q^{83} + 1344035042 q^{84} + 1982056546 q^{85} + 520253082 q^{86} + 3606452357 q^{87} + 684092585 q^{88} + 3293434692 q^{89} + 892602798 q^{90} + 1715813946 q^{91} + 3729310881 q^{92} + 2573139250 q^{93} + 998499458 q^{94} + 878402766 q^{95} - 1221963827 q^{96} + 2385468336 q^{97} - 3234447132 q^{98} + 4029218638 q^{99}+O(q^{100}) \) 14 * q + 48 * q^2 + 397 * q^3 + 3498 * q^4 + 2841 * q^5 + 3375 * q^6 + 6632 * q^7 + 41046 * q^8 + 101917 * q^9 + 129003 * q^10 + 44949 * q^11 - 123661 * q^12 + 38913 * q^13 + 16434 * q^14 + 119816 * q^15 + 859962 * q^16 + 893196 * q^17 + 1833339 * q^18 + 1532124 * q^19 + 4974963 * q^20 + 1851132 * q^21 + 3195323 * q^22 + 5911773 * q^23 + 7885413 * q^24 + 9978791 * q^25 + 10634475 * q^26 + 13105312 * q^27 + 9469678 * q^28 + 8764377 * q^29 + 21804216 * q^30 + 13188927 * q^31 + 23982750 * q^32 + 9398618 * q^33 + 29914960 * q^34 + 29633556 * q^35 + 24297333 * q^36 + 26238254 * q^37 + 23342796 * q^38 + 40855861 * q^39 + 42889049 * q^40 + 22153785 * q^41 + 6999662 * q^42 + 1779790 * q^43 - 83674089 * q^44 - 45101798 * q^45 - 23239663 * q^46 + 40080072 * q^47 - 141884869 * q^48 - 170457752 * q^49 - 89214633 * q^50 - 127867462 * q^51 - 276889277 * q^52 - 102088122 * q^53 - 356745582 * q^54 - 206797385 * q^55 - 294922194 * q^56 - 141710762 * q^57 - 527059089 * q^58 + 56191266 * q^59 - 283393416 * q^60 - 178507397 * q^61 - 27353505 * q^62 - 291948734 * q^63 - 242330062 * q^64 - 174258810 * q^65 - 1153895008 * q^66 + 287062499 * q^67 + 308827572 * q^68 - 80094823 * q^69 - 672888452 * q^70 + 224382678 * q^71 + 105778731 * q^72 + 271440727 * q^73 + 89959728 * q^74 + 1017561832 * q^75 - 229522980 * q^76 + 671279994 * q^77 - 119785879 * q^78 + 379128625 * q^79 + 1999017183 * q^80 + 2367007018 * q^81 + 551153781 * q^82 + 1664083206 * q^83 + 1344035042 * q^84 + 1982056546 * q^85 + 520253082 * q^86 + 3606452357 * q^87 + 684092585 * q^88 + 3293434692 * q^89 + 892602798 * q^90 + 1715813946 * q^91 + 3729310881 * q^92 + 2573139250 * q^93 + 998499458 * q^94 + 878402766 * q^95 - 1221963827 * q^96 + 2385468336 * q^97 - 3234447132 * q^98 + 4029218638 * 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 $

$2$	42.6649	1.88554	0.942771	−	0.333441i	$-0.108210\pi$
$2$	42.6649	1.88554	0.942771	+	0.333441i	$0.108210\pi$
$3$	65.1896	0.464657	0.232329	−	0.972637i	$-0.425366\pi$
$3$	65.1896	0.464657	0.232329	+	0.972637i	$0.425366\pi$
$4$	1308.30	2.55527
$5$	2393.49	1.71264	0.856322	−	0.516443i	$-0.172744\pi$
$5$	2393.49	1.71264	0.856322	+	0.516443i	$0.172744\pi$
$6$	2781.31	0.876131
$7$	−2430.73	−0.382644	−0.191322	−	0.981527i	$-0.561277\pi$
$7$	−2430.73	−0.382644	−0.191322	+	0.981527i	$0.561277\pi$
$8$	33974.0	2.93253
$9$	−15433.3	−0.784094
$10$	102118.	3.22926
$11$	−73135.0	−1.50612	−0.753058	−	0.657954i	$-0.771422\pi$
$11$	−73135.0	−1.50612	−0.753058	+	0.657954i	$0.771422\pi$
$12$	85287.4	1.18732
$13$	−153023.	−1.48597	−0.742986	−	0.669307i	$-0.766591\pi$
$13$	−153023.	−1.48597	−0.742986	+	0.669307i	$0.766591\pi$
$14$	−103707.	−0.721491
$15$	156031.	0.795792
$16$	779651.	2.97413
$17$	230071.	0.668102	0.334051	−	0.942555i	$-0.391584\pi$
$17$	230071.	0.668102	0.334051	+	0.942555i	$0.391584\pi$
$18$	−658462.	−1.47844
$19$	9827.40	0.0173001	0.00865003	−	0.999963i	$-0.497247\pi$
$19$	9827.40	0.0173001	0.00865003	+	0.999963i	$0.497247\pi$
$20$	3.13140e6	4.37627
$21$	−158458.	−0.177798
$22$	−3.12030e6	−2.83984
$23$	1.66730e6	1.24234	0.621169	−	0.783677i	$-0.286658\pi$
$23$	1.66730e6	1.24234	0.621169	+	0.783677i	$0.286658\pi$
$24$	2.21475e6	1.36262
$25$	3.77568e6	1.93315
$26$	−6.52870e6	−2.80186
$27$	−2.28922e6	−0.828992
$28$	−3.18011e6	−0.977758
$29$	−3.65682e6	−0.960093	−0.480046	−	0.877243i	$-0.659380\pi$
$29$	−3.65682e6	−0.960093	−0.480046	+	0.877243i	$0.659380\pi$
$30$	6.65705e6	1.50050
$31$	−3.59660e6	−0.699462	−0.349731	−	0.936850i	$-0.613727\pi$
$31$	−3.59660e6	−0.699462	−0.349731	+	0.936850i	$0.613727\pi$
$32$	1.58691e7	2.67533
$33$	−4.76764e6	−0.699828
$34$	9.81599e6	1.25973
$35$	−5.81792e6	−0.655333
$36$	−2.01914e7	−2.00357
$37$	1.87416e6	0.164399
$37$	1.87416e6	0.164399
$38$	419286.	0.0326200
$39$	−9.97549e6	−0.690468
$40$	8.13165e7	5.02237
$41$	2.02802e7	1.12084	0.560422	−	0.828207i	$-0.310639\pi$
$41$	2.02802e7	1.12084	0.560422	+	0.828207i	$0.310639\pi$
$42$	−6.76060e6	−0.335246
$43$	3.31415e7	1.47831	0.739153	−	0.673538i	$-0.235226\pi$
$43$	3.31415e7	1.47831	0.739153	+	0.673538i	$0.235226\pi$
$44$	−9.56824e7	−3.84853
$45$	−3.69395e7	−1.34287
$46$	7.11354e7	2.34248
$47$	242967.	0.00726285	0.00363142	−	0.999993i	$-0.498844\pi$
$47$	242967.	0.00726285	0.00363142	+	0.999993i	$0.498844\pi$
$48$	5.08251e7	1.38195
$49$	−3.44452e7	−0.853584
$50$	1.61089e8	3.64503
$51$	1.49983e7	0.310438
$52$	−2.00199e8	−3.79706
$53$	−4.12000e7	−0.717225	−0.358613	−	0.933487i	$-0.616750\pi$
$53$	−4.12000e7	−0.717225	−0.358613	+	0.933487i	$0.616750\pi$
$54$	−9.76694e7	−1.56310
$55$	−1.75048e8	−2.57944
$56$	−8.25815e7	−1.12211
$57$	640644.	0.00803860
$58$	−1.56018e8	−1.81030
$59$	1.40919e8	1.51403	0.757017	−	0.653395i	$-0.226656\pi$
$59$	1.40919e8	1.51403	0.757017	+	0.653395i	$0.226656\pi$
$60$	2.04135e8	2.03346
$61$	7.62755e7	0.705343	0.352672	−	0.935747i	$-0.385273\pi$
$61$	7.62755e7	0.705343	0.352672	+	0.935747i	$0.385273\pi$
$62$	−1.53449e8	−1.31887
$63$	3.75142e7	0.300029
$64$	2.77872e8	2.07031
$65$	−3.66259e8	−2.54494
$66$	−2.03411e8	−1.31955
$67$	2.37751e7	0.144141	0.0720703	−	0.997400i	$-0.477039\pi$
$67$	2.37751e7	0.144141	0.0720703	+	0.997400i	$0.477039\pi$
$68$	3.01002e8	1.70718
$69$	1.08691e8	0.577261
$70$	−2.48221e8	−1.23566
$71$	−3.19423e7	−0.149178	−0.0745889	−	0.997214i	$-0.523764\pi$
$71$	−3.19423e7	−0.149178	−0.0745889	+	0.997214i	$0.523764\pi$
$72$	−5.24332e8	−2.29938
$73$	−3.62976e8	−1.49598	−0.747989	−	0.663711i	$-0.768981\pi$
$73$	−3.62976e8	−1.49598	−0.747989	+	0.663711i	$0.768981\pi$
$74$	7.99610e7	0.309981
$75$	2.46135e8	0.898251
$76$	1.28572e7	0.0442063
$77$	1.77771e8	0.576306
$78$	−4.25604e8	−1.30191
$79$	4.39355e8	1.26909	0.634547	−	0.772885i	$-0.281187\pi$
$79$	4.39355e8	1.26909	0.634547	+	0.772885i	$0.281187\pi$
$80$	1.86609e9	5.09363
$81$	1.54541e8	0.398896
$82$	8.65255e8	2.11340
$83$	−2.46518e8	−0.570160	−0.285080	−	0.958504i	$-0.592020\pi$
$83$	−2.46518e8	−0.570160	−0.285080	+	0.958504i	$0.592020\pi$
$84$	−2.07310e8	−0.454322
$85$	5.50674e8	1.14422
$86$	1.41398e9	2.78741
$87$	−2.38387e8	−0.446114
$88$	−2.48469e9	−4.41672
$89$	−3.12703e8	−0.528296	−0.264148	−	0.964482i	$-0.585091\pi$
$89$	−3.12703e8	−0.528296	−0.264148	+	0.964482i	$0.585091\pi$
$90$	−1.57602e9	−2.53204
$91$	3.71956e8	0.568598
$92$	2.18133e9	3.17451
$93$	−2.34461e8	−0.325010
$94$	1.03662e7	0.0136944
$95$	2.35218e7	0.0296288
$96$	1.03450e9	1.24311
$97$	2.14929e8	0.246503	0.123251	−	0.992375i	$-0.460668\pi$
$97$	2.14929e8	0.246503	0.123251	+	0.992375i	$0.460668\pi$
$98$	−1.46960e9	−1.60947
$99$	1.12872e9	1.18094
$100$	4.93972e9	4.93972
$101$	−1.68594e9	−1.61211	−0.806056	−	0.591839i	$-0.798402\pi$
$101$	−1.68594e9	−1.61211	−0.806056	+	0.591839i	$0.798402\pi$
$102$	6.39900e8	0.585345
$103$	−3.85009e8	−0.337057	−0.168528	−	0.985697i	$-0.553902\pi$
$103$	−3.85009e8	−0.337057	−0.168528	+	0.985697i	$0.553902\pi$
$104$	−5.19879e9	−4.35765
$105$	−3.79268e8	−0.304505
$106$	−1.75779e9	−1.35236
$107$	5.71698e8	0.421638	0.210819	−	0.977525i	$-0.432387\pi$
$107$	5.71698e8	0.421638	0.210819	+	0.977525i	$0.432387\pi$
$108$	−2.99498e9	−2.11830
$109$	1.89912e9	1.28864	0.644322	−	0.764754i	$-0.277140\pi$
$109$	1.89912e9	1.28864	0.644322	+	0.764754i	$0.277140\pi$
$110$	−7.46842e9	−4.86364
$111$	1.22176e8	0.0763892
$112$	−1.89512e9	−1.13803
$113$	−1.37927e9	−0.795789	−0.397894	−	0.917431i	$-0.630259\pi$
$113$	−1.37927e9	−0.795789	−0.397894	+	0.917431i	$0.630259\pi$
$114$	2.73331e7	0.0151571
$115$	3.99068e9	2.12768
$116$	−4.78422e9	−2.45330
$117$	2.36165e9	1.16514
$118$	6.01231e9	2.85478
$119$	−5.59241e8	−0.255645
$120$	5.30099e9	2.33368
$121$	2.99078e9	1.26838
$122$	3.25429e9	1.32995
$123$	1.32206e9	0.520809
$124$	−4.70542e9	−1.78731
$125$	4.36227e9	1.59815
$126$	1.60054e9	0.565717
$127$	3.70993e9	1.26546	0.632730	−	0.774372i	$-0.281934\pi$
$127$	3.70993e9	1.26546	0.632730	+	0.774372i	$0.281934\pi$
$128$	3.73043e9	1.22833
$129$	2.16048e9	0.686905
$130$	−1.56264e10	−4.79859
$131$	6.46473e8	0.191792	0.0958958	−	0.995391i	$-0.469428\pi$
$131$	6.46473e8	0.191792	0.0958958	+	0.995391i	$0.469428\pi$
$132$	−6.23750e9	−1.78825
$133$	−2.38877e7	−0.00661976
$134$	1.01437e9	0.271783
$135$	−5.47923e9	−1.41977
$136$	7.81645e9	1.95923
$137$	8.96853e8	0.217510	0.108755	−	0.994069i	$-0.465314\pi$
$137$	8.96853e8	0.217510	0.108755	+	0.994069i	$0.465314\pi$
$138$	4.63729e9	1.08845
$139$	5.28274e8	0.120031	0.0600154	−	0.998197i	$-0.480885\pi$
$139$	5.28274e8	0.120031	0.0600154	+	0.998197i	$0.480885\pi$
$140$	−7.61158e9	−1.67455
$141$	1.58389e7	0.00337473
$142$	−1.36282e9	−0.281281
$143$	1.11913e10	2.23805
$144$	−1.20326e10	−2.33200
$145$	−8.75258e9	−1.64430
$146$	−1.54864e10	−2.82073
$147$	−2.24547e9	−0.396624
$148$	2.45196e9	0.420084
$149$	−4.61093e9	−0.766391	−0.383196	−	0.923667i	$-0.625176\pi$
$149$	−4.61093e9	−0.766391	−0.383196	+	0.923667i	$0.625176\pi$
$150$	1.05013e10	1.69369
$151$	2.91946e9	0.456990	0.228495	−	0.973545i	$-0.426620\pi$
$151$	2.91946e9	0.456990	0.228495	+	0.973545i	$0.426620\pi$
$152$	3.33876e8	0.0507329
$153$	−3.55077e9	−0.523854
$154$	7.58460e9	1.08665
$155$	−8.60843e9	−1.19793
$156$	−1.30509e10	−1.76433
$157$	9.02289e9	1.18522	0.592608	−	0.805491i	$-0.298098\pi$
$157$	9.02289e9	1.18522	0.592608	+	0.805491i	$0.298098\pi$
$158$	1.87451e10	2.39293
$159$	−2.68581e9	−0.333264
$160$	3.79825e10	4.58188
$161$	−4.05276e9	−0.475373
$162$	6.59347e9	0.752136
$163$	−1.35207e10	−1.50022	−0.750108	−	0.661315i	$-0.769999\pi$
$163$	−1.35207e10	−1.50022	−0.750108	+	0.661315i	$0.769999\pi$
$164$	2.65326e10	2.86406
$165$	−1.14113e10	−1.19856
$166$	−1.05177e10	−1.07506
$167$	−1.63713e10	−1.62877	−0.814385	−	0.580325i	$-0.802926\pi$
$167$	−1.63713e10	−1.62877	−0.814385	+	0.580325i	$0.802926\pi$
$168$	−5.38346e9	−0.521398
$169$	1.28114e10	1.20811
$170$	2.34945e10	2.15748
$171$	−1.51669e8	−0.0135649
$172$	4.33590e10	3.77747
$173$	1.30889e10	1.11095	0.555476	−	0.831532i	$-0.312536\pi$
$173$	1.30889e10	1.11095	0.555476	+	0.831532i	$0.312536\pi$
$174$	−1.01708e10	−0.841167
$175$	−9.17764e9	−0.739707
$176$	−5.70198e10	−4.47939
$177$	9.18646e9	0.703507
$178$	−1.33415e10	−0.996124
$179$	−9.34511e9	−0.680371	−0.340186	−	0.940358i	$-0.610490\pi$
$179$	−9.34511e9	−0.680371	−0.340186	+	0.940358i	$0.610490\pi$
$180$	−4.83279e10	−3.43140
$181$	9.81822e9	0.679953	0.339977	−	0.940434i	$-0.389581\pi$
$181$	9.81822e9	0.679953	0.339977	+	0.940434i	$0.389581\pi$
$182$	1.58695e10	1.07212
$183$	4.97237e9	0.327743
$184$	5.66450e10	3.64319
$185$	4.48579e9	0.281557
$186$	−1.00033e10	−0.612820
$187$	−1.68263e10	−1.00624
$188$	3.17873e8	0.0185585
$189$	5.56446e9	0.317209
$190$	1.00356e9	0.0558664
$191$	−1.11840e10	−0.608058	−0.304029	−	0.952663i	$-0.598332\pi$
$191$	−1.11840e10	−0.608058	−0.304029	+	0.952663i	$0.598332\pi$
$192$	1.81144e10	0.961984
$193$	−1.06312e10	−0.551538	−0.275769	−	0.961224i	$-0.588932\pi$
$193$	−1.06312e10	−0.551538	−0.275769	+	0.961224i	$0.588932\pi$
$194$	9.16993e9	0.464792
$195$	−2.38762e10	−1.18252
$196$	−4.50646e10	−2.18114
$197$	−1.85877e10	−0.879281	−0.439641	−	0.898174i	$-0.644894\pi$
$197$	−1.85877e10	−0.879281	−0.439641	+	0.898174i	$0.644894\pi$
$198$	4.81566e10	2.22670
$199$	−7.19113e9	−0.325056	−0.162528	−	0.986704i	$-0.551965\pi$
$199$	−7.19113e9	−0.325056	−0.162528	+	0.986704i	$0.551965\pi$
$200$	1.28275e11	5.66901
$201$	1.54989e9	0.0669760
$202$	−7.19304e10	−3.03971
$203$	8.88874e9	0.367374
$204$	1.96222e10	0.793254
$205$	4.85406e10	1.91961
$206$	−1.64264e10	−0.635535
$207$	−2.57320e10	−0.974109
$208$	−1.19304e11	−4.41948
$209$	−7.18727e8	−0.0260559
$210$	−1.61815e10	−0.574157
$211$	2.21671e10	0.769905	0.384952	−	0.922936i	$-0.374218\pi$
$211$	2.21671e10	0.769905	0.384952	+	0.922936i	$0.374218\pi$
$212$	−5.39018e10	−1.83270
$213$	−2.08231e9	−0.0693166
$214$	2.43915e10	0.795016
$215$	7.93239e10	2.53181
$216$	−7.77739e10	−2.43104
$217$	8.74234e9	0.267645
$218$	8.10259e10	2.42979
$219$	−2.36623e10	−0.695117
$220$	−2.29015e11	−6.59116
$221$	−3.52061e10	−0.992781
$222$	5.21263e9	0.144035
$223$	1.99609e10	0.540515	0.270257	−	0.962788i	$-0.412891\pi$
$223$	1.99609e10	0.540515	0.270257	+	0.962788i	$0.412891\pi$
$224$	−3.85734e10	−1.02370
$225$	−5.82713e10	−1.51577
$226$	−5.88467e10	−1.50049
$227$	5.31290e10	1.32805	0.664026	−	0.747710i	$-0.268847\pi$
$227$	5.31290e10	1.32805	0.664026	+	0.747710i	$0.268847\pi$
$228$	8.38154e8	0.0205408
$229$	−1.28952e10	−0.309861	−0.154930	−	0.987925i	$-0.549515\pi$
$229$	−1.28952e10	−0.309861	−0.154930	+	0.987925i	$0.549515\pi$
$230$	1.70262e11	4.01183
$231$	1.15888e10	0.267785
$232$	−1.24237e11	−2.81550
$233$	−6.04288e10	−1.34320	−0.671602	−	0.740912i	$-0.734394\pi$
$233$	−6.04288e10	−1.34320	−0.671602	+	0.740912i	$0.734394\pi$
$234$	1.00760e11	2.19692
$235$	5.81540e8	0.0124387
$236$	1.84364e11	3.86877
$237$	2.86414e10	0.589693
$238$	−2.38600e10	−0.482030
$239$	1.34805e9	0.0267248	0.0133624	−	0.999911i	$-0.495746\pi$
$239$	1.34805e9	0.0267248	0.0133624	+	0.999911i	$0.495746\pi$
$240$	1.21650e11	2.36679
$241$	1.43633e10	0.274269	0.137134	−	0.990552i	$-0.456211\pi$
$241$	1.43633e10	0.274269	0.137134	+	0.990552i	$0.456211\pi$
$242$	1.27602e11	2.39159
$243$	5.51331e10	1.01434
$244$	9.97910e10	1.80234
$245$	−8.24443e10	−1.46188
$246$	5.64056e10	0.982006
$247$	−1.50381e9	−0.0257074
$248$	−1.22191e11	−2.05119
$249$	−1.60704e10	−0.264929
$250$	1.86116e11	3.01338
$251$	−8.75887e10	−1.39289	−0.696444	−	0.717611i	$-0.745236\pi$
$251$	−8.75887e10	−1.39289	−0.696444	+	0.717611i	$0.745236\pi$
$252$	4.90797e10	0.766654
$253$	−1.21938e11	−1.87110
$254$	1.58284e11	2.38608
$255$	3.58982e10	0.531670
$256$	1.68881e10	0.245754
$257$	9.13358e10	1.30600	0.652998	−	0.757360i	$-0.273511\pi$
$257$	9.13358e10	1.30600	0.652998	+	0.757360i	$0.273511\pi$
$258$	9.21768e10	1.29519
$259$	−4.55557e9	−0.0629063
$260$	−4.79175e11	−6.50301
$261$	5.64369e10	0.752802
$262$	2.75817e10	0.361631
$263$	1.10120e11	1.41927	0.709633	−	0.704572i	$-0.248861\pi$
$263$	1.10120e11	1.41927	0.709633	+	0.704572i	$0.248861\pi$
$264$	−1.61976e11	−2.05226
$265$	−9.86118e10	−1.22835
$266$	−1.01917e9	−0.0124818
$267$	−2.03850e10	−0.245476
$268$	3.11050e10	0.368318
$269$	1.04739e11	1.21961	0.609805	−	0.792551i	$-0.291248\pi$
$269$	1.04739e11	1.21961	0.609805	+	0.792551i	$0.291248\pi$
$270$	−2.33771e11	−2.67703
$271$	1.23245e11	1.38806	0.694029	−	0.719947i	$-0.255834\pi$
$271$	1.23245e11	1.38806	0.694029	+	0.719947i	$0.255834\pi$
$272$	1.79375e11	1.98702
$273$	2.42477e10	0.264203
$274$	3.82642e10	0.410124
$275$	−2.76135e11	−2.91155
$276$	1.42200e11	1.47506
$277$	−1.76462e11	−1.80092	−0.900458	−	0.434944i	$-0.856768\pi$
$277$	−1.76462e11	−1.80092	−0.900458	+	0.434944i	$0.856768\pi$
$278$	2.25388e10	0.226323
$279$	5.55074e10	0.548444
$280$	−1.97658e11	−1.92178
$281$	8.86579e10	0.848280	0.424140	−	0.905597i	$-0.360576\pi$
$281$	8.86579e10	0.848280	0.424140	+	0.905597i	$0.360576\pi$
$282$	6.75767e8	0.00636321
$283$	1.26268e11	1.17019	0.585093	−	0.810967i	$-0.301058\pi$
$283$	1.26268e11	1.17019	0.585093	+	0.810967i	$0.301058\pi$
$284$	−4.17901e10	−0.381190
$285$	1.53338e9	0.0137673
$286$	4.77477e11	4.21993
$287$	−4.92957e10	−0.428884
$288$	−2.44912e11	−2.09771
$289$	−6.56550e10	−0.553640
$290$	−3.73428e11	−3.10039
$291$	1.40111e10	0.114539
$292$	−4.74881e11	−3.82263
$293$	−4.64141e9	−0.0367913	−0.0183957	−	0.999831i	$-0.505856\pi$
$293$	−4.64141e9	−0.0367913	−0.0183957	+	0.999831i	$0.505856\pi$
$294$	−9.58028e10	−0.747851
$295$	3.37289e11	2.59300
$296$	6.36728e10	0.482104
$297$	1.67422e11	1.24856
$298$	−1.96725e11	−1.44506
$299$	−2.55135e11	−1.84608
$300$	3.22018e11	2.29527
$301$	−8.05579e10	−0.565665
$302$	1.24559e11	0.861673
$303$	−1.09906e11	−0.749080
$304$	7.66194e9	0.0514527
$305$	1.82565e11	1.20800
$306$	−1.51493e11	−0.987750
$307$	8.42158e10	0.541092	0.270546	−	0.962707i	$-0.412796\pi$
$307$	8.42158e10	0.541092	0.270546	+	0.962707i	$0.412796\pi$
$308$	2.32578e11	1.47262
$309$	−2.50986e10	−0.156616
$310$	−3.67278e11	−2.25875
$311$	−5.58409e10	−0.338478	−0.169239	−	0.985575i	$-0.554131\pi$
$311$	−5.58409e10	−0.338478	−0.169239	+	0.985575i	$0.554131\pi$
$312$	−3.38907e11	−2.02481
$313$	−1.94323e11	−1.14439	−0.572197	−	0.820116i	$-0.693909\pi$
$313$	−1.94323e11	−1.14439	−0.572197	+	0.820116i	$0.693909\pi$
$314$	3.84961e11	2.23477
$315$	8.97898e10	0.513842
$316$	5.74807e11	3.24288
$317$	−1.21471e11	−0.675624	−0.337812	−	0.941214i	$-0.609687\pi$
$317$	−1.21471e11	−0.675624	−0.337812	+	0.941214i	$0.609687\pi$
$318$	−1.14590e11	−0.628383
$319$	2.67442e11	1.44601
$320$	6.65085e11	3.54570
$321$	3.72688e10	0.195917
$322$	−1.72911e11	−0.896335
$323$	2.26100e9	0.0115582
$324$	2.02185e11	1.01929
$325$	−5.77765e11	−2.87260
$326$	−5.76859e11	−2.82872
$327$	1.23803e11	0.598778
$328$	6.89001e11	3.28691
$329$	−5.90586e8	−0.00277908
$330$	−4.86863e11	−2.25993
$331$	−2.19206e11	−1.00375	−0.501877	−	0.864939i	$-0.667357\pi$
$331$	−2.19206e11	−1.00375	−0.501877	+	0.864939i	$0.667357\pi$
$332$	−3.22519e11	−1.45691
$333$	−2.89245e10	−0.128904
$334$	−6.98482e11	−3.07111
$335$	5.69056e10	0.246862
$336$	−1.23542e11	−0.528796
$337$	−4.36173e11	−1.84215	−0.921074	−	0.389388i	$-0.872687\pi$
$337$	−4.36173e11	−1.84215	−0.921074	+	0.389388i	$0.872687\pi$
$338$	5.46599e11	2.27795
$339$	−8.99144e10	−0.369769
$340$	7.20446e11	2.92379
$341$	2.63037e11	1.05347
$342$	−6.47097e9	−0.0255771
$343$	1.81815e11	0.709262
$344$	1.12595e12	4.33517
$345$	2.60151e11	0.988642
$346$	5.58437e11	2.09475
$347$	−1.13288e11	−0.419472	−0.209736	−	0.977758i	$-0.567260\pi$
$347$	−1.13288e11	−0.419472	−0.209736	+	0.977758i	$0.567260\pi$
$348$	−3.11881e11	−1.13994
$349$	3.48994e11	1.25923	0.629613	−	0.776909i	$-0.283214\pi$
$349$	3.48994e11	1.25923	0.629613	+	0.776909i	$0.283214\pi$
$350$	−3.91564e11	−1.39475
$351$	3.50302e11	1.23186
$352$	−1.16059e12	−4.02935
$353$	2.78898e11	0.956004	0.478002	−	0.878359i	$-0.341361\pi$
$353$	2.78898e11	0.956004	0.478002	+	0.878359i	$0.341361\pi$
$354$	3.91940e11	1.32649
$355$	−7.64538e10	−0.255488
$356$	−4.09109e11	−1.34994
$357$	−3.64567e10	−0.118787
$358$	−3.98709e11	−1.28287
$359$	1.92003e11	0.610076	0.305038	−	0.952340i	$-0.401331\pi$
$359$	1.92003e11	0.610076	0.305038	+	0.952340i	$0.401331\pi$
$360$	−1.25498e12	−3.93801
$361$	−3.22591e11	−0.999701
$362$	4.18894e11	1.28208
$363$	1.94968e11	0.589364
$364$	4.86629e11	1.45292
$365$	−8.68781e11	−2.56208
$366$	2.12146e11	0.617973
$367$	−5.98702e11	−1.72272	−0.861358	−	0.507999i	$-0.830385\pi$
$367$	−5.98702e11	−1.72272	−0.861358	+	0.507999i	$0.830385\pi$
$368$	1.29992e12	3.69488
$369$	−3.12991e11	−0.878847
$370$	1.91386e11	0.530887
$371$	1.00146e11	0.274442
$372$	−3.06745e11	−0.830489
$373$	−1.38574e11	−0.370675	−0.185337	−	0.982675i	$-0.559338\pi$
$373$	−1.38574e11	−0.370675	−0.185337	+	0.982675i	$0.559338\pi$
$374$	−7.17893e11	−1.89731
$375$	2.84375e11	0.742592
$376$	8.25456e9	0.0212985
$377$	5.59577e11	1.42667
$378$	2.37408e11	0.598110
$379$	7.28106e11	1.81267	0.906334	−	0.422563i	$-0.138869\pi$
$379$	7.28106e11	1.81267	0.906334	+	0.422563i	$0.138869\pi$
$380$	3.07735e10	0.0757096
$381$	2.41849e11	0.588005
$382$	−4.77163e11	−1.14652
$383$	8.64784e10	0.205359	0.102679	−	0.994715i	$-0.467258\pi$
$383$	8.64784e10	0.205359	0.102679	+	0.994715i	$0.467258\pi$
$384$	2.43185e11	0.570751
$385$	4.25494e11	0.987007
$386$	−4.53581e11	−1.03995
$387$	−5.11483e11	−1.15913
$388$	2.81191e11	0.629881
$389$	−3.64175e10	−0.0806374	−0.0403187	−	0.999187i	$-0.512837\pi$
$389$	−3.64175e10	−0.0806374	−0.0403187	+	0.999187i	$0.512837\pi$
$390$	−1.01868e12	−2.22970
$391$	3.83599e11	0.830008
$392$	−1.17024e12	−2.50316
$393$	4.21433e10	0.0891174
$394$	−7.93044e11	−1.65792
$395$	1.05159e12	2.17350
$396$	1.47670e12	3.01761
$397$	2.16429e11	0.437278	0.218639	−	0.975806i	$-0.429838\pi$
$397$	2.16429e11	0.437278	0.218639	+	0.975806i	$0.429838\pi$
$398$	−3.06809e11	−0.612907
$399$	−1.55723e9	−0.00307592
$400$	2.94371e12	5.74944
$401$	−2.80338e11	−0.541418	−0.270709	−	0.962661i	$-0.587258\pi$
$401$	−2.80338e11	−0.541418	−0.270709	+	0.962661i	$0.587258\pi$
$402$	6.61261e10	0.126286
$403$	5.50361e11	1.03938
$404$	−2.20571e12	−4.11938
$405$	3.69892e11	0.683168
$406$	3.79238e11	0.692698
$407$	−1.37067e11	−0.247604
$408$	5.09551e11	0.910369
$409$	−6.54277e11	−1.15613	−0.578065	−	0.815991i	$-0.696192\pi$
$409$	−6.54277e11	−1.15613	−0.578065	+	0.815991i	$0.696192\pi$
$410$	2.07098e12	3.61950
$411$	5.84655e10	0.101067
$412$	−5.03706e11	−0.861271
$413$	−3.42536e11	−0.579336
$414$	−1.09786e12	−1.83672
$415$	−5.90038e11	−0.976481
$416$	−2.42833e12	−3.97546
$417$	3.44380e10	0.0557732
$418$	−3.06645e10	−0.0491295
$419$	6.67807e11	1.05849	0.529246	−	0.848468i	$-0.322475\pi$
$419$	6.67807e11	1.05849	0.529246	+	0.848468i	$0.322475\pi$
$420$	−4.96196e11	−0.778092
$421$	1.99944e11	0.310197	0.155099	−	0.987899i	$-0.450430\pi$
$421$	1.99944e11	0.310197	0.155099	+	0.987899i	$0.450430\pi$
$422$	9.45757e11	1.45169
$423$	−3.74979e9	−0.00569475
$424$	−1.39973e12	−2.10328
$425$	8.68676e11	1.29154
$426$	−8.88416e10	−0.130699
$427$	−1.85405e11	−0.269895
$428$	7.47951e11	1.07740
$429$	7.29557e11	1.03992
$430$	3.38435e12	4.77384
$431$	1.33472e11	0.186313	0.0931563	−	0.995651i	$-0.470304\pi$
$431$	1.33472e11	0.186313	0.0931563	+	0.995651i	$0.470304\pi$
$432$	−1.78479e12	−2.46553
$433$	−2.57803e11	−0.352446	−0.176223	−	0.984350i	$-0.556388\pi$
$433$	−2.57803e11	−0.352446	−0.176223	+	0.984350i	$0.556388\pi$
$434$	3.72992e11	0.504656
$435$	−5.70577e11	−0.764034
$436$	2.48462e12	3.29283
$437$	1.63853e10	0.0214925
$438$	−1.00955e12	−1.31067
$439$	−1.18637e12	−1.52451	−0.762254	−	0.647278i	$-0.775907\pi$
$439$	−1.18637e12	−1.52451	−0.762254	+	0.647278i	$0.775907\pi$
$440$	−5.94709e12	−7.56427
$441$	5.31603e11	0.669290
$442$	−1.50207e12	−1.87193
$443$	−8.62950e11	−1.06456	−0.532278	−	0.846569i	$-0.678664\pi$
$443$	−8.62950e11	−1.06456	−0.532278	+	0.846569i	$0.678664\pi$
$444$	1.59842e11	0.195195
$445$	−7.48452e11	−0.904782
$446$	8.51629e11	1.01916
$447$	−3.00585e11	−0.356109
$448$	−6.75431e11	−0.792191
$449$	1.46291e12	1.69867	0.849335	−	0.527854i	$-0.177003\pi$
$449$	1.46291e12	1.69867	0.849335	+	0.527854i	$0.177003\pi$
$450$	−2.48614e12	−2.85805
$451$	−1.48319e12	−1.68812
$452$	−1.80450e12	−2.03345
$453$	1.90318e11	0.212343
$454$	2.26674e12	2.50410
$455$	8.90274e11	0.973806
$456$	2.17653e10	0.0235734
$457$	−1.69203e12	−1.81461	−0.907306	−	0.420470i	$-0.861865\pi$
$457$	−1.69203e12	−1.81461	−0.907306	+	0.420470i	$0.861865\pi$
$458$	−5.50171e11	−0.584256
$459$	−5.26684e11	−0.553851
$460$	5.22100e12	5.43680
$461$	2.52574e11	0.260456	0.130228	−	0.991484i	$-0.458429\pi$
$461$	2.52574e11	0.260456	0.130228	+	0.991484i	$0.458429\pi$
$462$	4.94437e11	0.504919
$463$	1.06985e12	1.08195	0.540975	−	0.841039i	$-0.318055\pi$
$463$	1.06985e12	1.08195	0.540975	+	0.841039i	$0.318055\pi$
$464$	−2.85105e12	−2.85544
$465$	−5.61180e11	−0.556627
$466$	−2.57819e12	−2.53267
$467$	−6.41104e11	−0.623738	−0.311869	−	0.950125i	$-0.600955\pi$
$467$	−6.41104e11	−0.623738	−0.311869	+	0.950125i	$0.600955\pi$
$468$	3.08974e12	2.97725
$469$	−5.77909e10	−0.0551545
$470$	2.48114e10	0.0234536
$471$	5.88199e11	0.550719
$472$	4.78759e12	4.43995
$473$	−2.42380e12	−2.22650
$474$	1.22198e12	1.11189
$475$	3.71051e10	0.0334436
$476$	−7.31653e11	−0.653242
$477$	6.35852e11	0.562372
$478$	5.75143e10	0.0503907
$479$	1.18417e12	1.02779	0.513897	−	0.857852i	$-0.328201\pi$
$479$	1.18417e12	1.02779	0.513897	+	0.857852i	$0.328201\pi$
$480$	2.47607e12	2.12900
$481$	−2.86789e11	−0.244292
$482$	6.12807e11	0.517145
$483$	−2.64198e11	−0.220885
$484$	3.91284e12	3.24106
$485$	5.14431e11	0.422172
$486$	2.35225e12	1.91259
$487$	−1.29277e12	−1.04146	−0.520728	−	0.853723i	$-0.674339\pi$
$487$	−1.29277e12	−1.04146	−0.520728	+	0.853723i	$0.674339\pi$
$488$	2.59138e12	2.06844
$489$	−8.81407e11	−0.697086
$490$	−3.51748e12	−2.75645
$491$	1.12506e12	0.873593	0.436796	−	0.899560i	$-0.356113\pi$
$491$	1.12506e12	0.873593	0.436796	+	0.899560i	$0.356113\pi$
$492$	1.72965e12	1.33081
$493$	−8.41331e11	−0.641440
$494$	−6.41602e10	−0.0484724
$495$	2.70157e12	2.02252
$496$	−2.80409e12	−2.08029
$497$	7.76431e10	0.0570820
$498$	−6.85642e11	−0.499535
$499$	2.49604e11	0.180218	0.0901092	−	0.995932i	$-0.471278\pi$
$499$	2.49604e11	0.180218	0.0901092	+	0.995932i	$0.471278\pi$
$500$	5.70715e12	4.08371
$501$	−1.06724e12	−0.756820
$502$	−3.73697e12	−2.62635
$503$	−3.65178e10	−0.0254360	−0.0127180	−	0.999919i	$-0.504048\pi$
$503$	−3.65178e10	−0.0254360	−0.0127180	+	0.999919i	$0.504048\pi$
$504$	1.27451e12	0.879842
$505$	−4.03528e12	−2.76097
$506$	−5.20249e12	−3.52805
$507$	8.35172e11	0.561358
$508$	4.85369e12	3.23359
$509$	−1.30112e12	−0.859187	−0.429593	−	0.903022i	$-0.641343\pi$
$509$	−1.30112e12	−0.859187	−0.429593	+	0.903022i	$0.641343\pi$
$510$	1.53160e12	1.00249
$511$	8.82296e11	0.572427
$512$	−1.18945e12	−0.764947
$513$	−2.24971e10	−0.0143416
$514$	3.89684e12	2.46251
$515$	−9.21516e11	−0.577258
$516$	2.82655e12	1.75523
$517$	−1.77694e10	−0.0109387
$518$	−1.94363e11	−0.118612
$519$	8.53260e11	0.516212
$520$	−1.24433e13	−7.46310
$521$	−6.92794e11	−0.411940	−0.205970	−	0.978558i	$-0.566035\pi$
$521$	−6.92794e11	−0.411940	−0.205970	+	0.978558i	$0.566035\pi$
$522$	2.40788e12	1.41944
$523$	8.09195e11	0.472929	0.236464	−	0.971640i	$-0.424011\pi$
$523$	8.09195e11	0.472929	0.236464	+	0.971640i	$0.424011\pi$
$524$	8.45780e11	0.490079
$525$	−5.98287e11	−0.343710
$526$	4.69825e12	2.67609
$527$	−8.27475e11	−0.467312
$528$	−3.71710e12	−2.08138
$529$	9.78750e11	0.543402
$530$	−4.20727e12	−2.31611
$531$	−2.17485e12	−1.18715
$532$	−3.12522e10	−0.0169153
$533$	−3.10333e12	−1.66554
$534$	−8.69724e11	−0.462856
$535$	1.36835e12	0.722115
$536$	8.07737e11	0.422696
$537$	−6.09204e11	−0.316139
$538$	4.46867e12	2.29963
$539$	2.51915e12	1.28560
$540$	−7.16846e12	−3.62789
$541$	−1.54936e12	−0.777615	−0.388807	−	0.921319i	$-0.627113\pi$
$541$	−1.54936e12	−0.777615	−0.388807	+	0.921319i	$0.627113\pi$
$542$	5.25824e12	2.61724
$543$	6.40046e11	0.315945
$544$	3.65102e12	1.78739
$545$	4.54553e12	2.20699
$546$	1.03453e12	0.498166
$547$	2.61193e12	1.24744	0.623718	−	0.781649i	$-0.285621\pi$
$547$	2.61193e12	1.24744	0.623718	+	0.781649i	$0.285621\pi$
$548$	1.17335e12	0.555796
$549$	−1.17718e12	−0.553055
$550$	−1.17813e13	−5.48984
$551$	−3.59371e10	−0.0166097
$552$	3.69267e12	1.69283
$553$	−1.06795e12	−0.485611
$554$	−7.52876e12	−3.39570
$555$	2.92427e11	0.130827
$556$	6.91140e11	0.306711
$557$	−1.83949e12	−0.809744	−0.404872	−	0.914373i	$-0.632684\pi$
$557$	−1.83949e12	−0.809744	−0.404872	+	0.914373i	$0.632684\pi$
$558$	2.36822e12	1.03411
$559$	−5.07140e12	−2.19672
$560$	−4.53595e12	−1.94905
$561$	−1.09690e12	−0.467556
$562$	3.78259e12	1.59947
$563$	3.14922e12	1.32104	0.660520	−	0.750809i	$-0.270336\pi$
$563$	3.14922e12	1.32104	0.660520	+	0.750809i	$0.270336\pi$
$564$	2.07220e10	0.00862336
$565$	−3.30128e12	−1.36290
$566$	5.38722e12	2.20643
$567$	−3.75646e11	−0.152635
$568$	−1.08521e12	−0.437468
$569$	−1.61011e12	−0.643946	−0.321973	−	0.946749i	$-0.604346\pi$
$569$	−1.61011e12	−0.643946	−0.321973	+	0.946749i	$0.604346\pi$
$570$	6.54215e10	0.0259587
$571$	−2.71862e12	−1.07025	−0.535127	−	0.844772i	$-0.679736\pi$
$571$	−2.71862e12	−1.07025	−0.535127	+	0.844772i	$0.679736\pi$
$572$	1.46416e13	5.71881
$573$	−7.29078e11	−0.282539
$574$	−2.10320e12	−0.808679
$575$	6.29521e12	2.40162
$576$	−4.28849e12	−1.62332
$577$	−3.98473e11	−0.149661	−0.0748303	−	0.997196i	$-0.523842\pi$
$577$	−3.98473e11	−0.149661	−0.0748303	+	0.997196i	$0.523842\pi$
$578$	−2.80117e12	−1.04391
$579$	−6.93045e11	−0.256276
$580$	−1.14510e13	−4.20162
$581$	5.99217e11	0.218168
$582$	5.97784e11	0.215969
$583$	3.01316e12	1.08022
$584$	−1.23318e13	−4.38700
$585$	5.65258e12	1.99547
$586$	−1.98025e11	−0.0693716
$587$	−7.40176e11	−0.257314	−0.128657	−	0.991689i	$-0.541067\pi$
$587$	−7.40176e11	−0.257314	−0.128657	+	0.991689i	$0.541067\pi$
$588$	−2.93774e12	−1.01348
$589$	−3.53452e10	−0.0121007
$590$	1.43904e13	4.88922
$591$	−1.21173e12	−0.408564
$592$	1.46119e12	0.488944
$593$	5.44376e11	0.180781	0.0903905	−	0.995906i	$-0.471188\pi$
$593$	5.44376e11	0.180781	0.0903905	+	0.995906i	$0.471188\pi$
$594$	7.14305e12	2.35421
$595$	−1.33854e12	−0.437829
$596$	−6.03247e12	−1.95834
$597$	−4.68787e11	−0.151040
$598$	−1.08853e13	−3.48086
$599$	−2.07562e12	−0.658759	−0.329379	−	0.944198i	$-0.606840\pi$
$599$	−2.07562e12	−0.658759	−0.329379	+	0.944198i	$0.606840\pi$
$600$	8.36220e12	2.63415
$601$	−6.73776e11	−0.210659	−0.105330	−	0.994437i	$-0.533590\pi$
$601$	−6.73776e11	−0.210659	−0.105330	+	0.994437i	$0.533590\pi$
$602$	−3.43700e12	−1.06658
$603$	−3.66929e11	−0.113020
$604$	3.81952e12	1.16773
$605$	7.15842e12	2.17229
$606$	−4.68912e12	−1.41242
$607$	−7.25227e11	−0.216833	−0.108416	−	0.994106i	$-0.534578\pi$
$607$	−7.25227e11	−0.216833	−0.108416	+	0.994106i	$0.534578\pi$
$608$	1.55952e11	0.0462833
$609$	5.79453e11	0.170703
$610$	7.78911e12	2.27774
$611$	−3.71795e10	−0.0107924
$612$	−4.64546e12	−1.33859
$613$	6.47836e12	1.85307	0.926537	−	0.376204i	$-0.122771\pi$
$613$	6.47836e12	1.85307	0.926537	+	0.376204i	$0.122771\pi$
$614$	3.59306e12	1.02025
$615$	3.16434e12	0.891959
$616$	6.03960e12	1.69003
$617$	8.39807e10	0.0233290	0.0116645	−	0.999932i	$-0.496287\pi$
$617$	8.39807e10	0.0233290	0.0116645	+	0.999932i	$0.496287\pi$
$618$	−1.07083e12	−0.295306
$619$	5.75912e12	1.57670	0.788348	−	0.615230i	$-0.210937\pi$
$619$	5.75912e12	1.57670	0.788348	+	0.615230i	$0.210937\pi$
$620$	−1.12624e13	−3.06103
$621$	−3.81682e12	−1.02989
$622$	−2.38245e12	−0.638214
$623$	7.60095e11	0.202149
$624$	−7.77740e12	−2.05354
$625$	3.06669e12	0.803914
$626$	−8.29079e12	−2.15780
$627$	−4.68535e10	−0.0121071
$628$	1.18046e13	3.02854
$629$	4.31191e11	0.109835
$630$	3.83088e12	0.968871
$631$	7.49831e11	0.188292	0.0941459	−	0.995558i	$-0.469988\pi$
$631$	7.49831e11	0.188292	0.0941459	+	0.995558i	$0.469988\pi$
$632$	1.49266e13	3.72165
$633$	1.44506e12	0.357742
$634$	−5.18254e12	−1.27392
$635$	8.87968e12	2.16728
$636$	−3.51384e12	−0.851579
$637$	5.27089e12	1.26840
$638$	1.14104e13	2.72651
$639$	4.92976e11	0.116969
$640$	8.92875e12	2.10369
$641$	−4.93088e12	−1.15362	−0.576810	−	0.816878i	$-0.695703\pi$
$641$	−4.93088e12	−1.15362	−0.576810	+	0.816878i	$0.695703\pi$
$642$	1.59007e12	0.369410
$643$	−1.70883e12	−0.394229	−0.197115	−	0.980380i	$-0.563157\pi$
$643$	−1.70883e12	−0.394229	−0.197115	+	0.980380i	$0.563157\pi$
$644$	−5.30222e12	−1.21471
$645$	5.17110e12	1.17642
$646$	9.64657e10	0.0217935
$647$	−3.00189e12	−0.673481	−0.336740	−	0.941598i	$-0.609324\pi$
$647$	−3.00189e12	−0.673481	−0.336740	+	0.941598i	$0.609324\pi$
$648$	5.25037e12	1.16977
$649$	−1.03061e13	−2.28031
$650$	−2.46503e13	−5.41642
$651$	5.69910e11	0.124363
$652$	−1.76891e13	−3.83346
$653$	−3.48391e12	−0.749821	−0.374911	−	0.927061i	$-0.622327\pi$
$653$	−3.48391e12	−0.749821	−0.374911	+	0.927061i	$0.622327\pi$
$654$	5.28204e12	1.12902
$655$	1.54733e12	0.328471
$656$	1.58115e13	3.33354
$657$	5.60193e12	1.17299
$658$	−2.51973e10	−0.00524008
$659$	7.64257e11	0.157854	0.0789269	−	0.996880i	$-0.474851\pi$
$659$	7.64257e11	0.157854	0.0789269	+	0.996880i	$0.474851\pi$
$660$	−1.49294e13	−3.06263
$661$	−1.74904e12	−0.356364	−0.178182	−	0.983998i	$-0.557022\pi$
$661$	−1.74904e12	−0.356364	−0.178182	+	0.983998i	$0.557022\pi$
$662$	−9.35243e12	−1.89262
$663$	−2.29507e12	−0.461303
$664$	−8.37519e12	−1.67201
$665$	−5.71751e10	−0.0113373
$666$	−1.23406e12	−0.243054
$667$	−6.09704e12	−1.19276
$668$	−2.14186e13	−4.16195
$669$	1.30124e12	0.251154
$670$	2.42788e12	0.465468
$671$	−5.57841e12	−1.06233
$672$	−2.51458e12	−0.475668
$673$	6.83842e12	1.28496	0.642478	−	0.766305i	$-0.277907\pi$
$673$	6.83842e12	1.28496	0.642478	+	0.766305i	$0.277907\pi$
$674$	−1.86093e13	−3.47345
$675$	−8.64336e12	−1.60256
$676$	1.67612e13	3.08705
$677$	2.78168e12	0.508931	0.254465	−	0.967082i	$-0.418100\pi$
$677$	2.78168e12	0.508931	0.254465	+	0.967082i	$0.418100\pi$
$678$	−3.83619e12	−0.697215
$679$	−5.22433e11	−0.0943228
$680$	1.87086e13	3.35546
$681$	3.46346e12	0.617089
$682$	1.12225e13	1.98636
$683$	−3.44683e12	−0.606075	−0.303037	−	0.952979i	$-0.598001\pi$
$683$	−3.44683e12	−0.606075	−0.303037	+	0.952979i	$0.598001\pi$
$684$	−1.98429e11	−0.0346619
$685$	2.14661e12	0.372517
$686$	7.75714e12	1.33734
$687$	−8.40630e11	−0.143979
$688$	2.58388e13	4.39668
$689$	6.30453e12	1.06578
$690$	1.10993e13	1.86413
$691$	−1.03041e12	−0.171933	−0.0859664	−	0.996298i	$-0.527398\pi$
$691$	−1.03041e12	−0.171933	−0.0859664	+	0.996298i	$0.527398\pi$
$692$	1.71242e13	2.83878
$693$	−2.74360e12	−0.451878
$694$	−4.83345e12	−0.790932
$695$	1.26442e12	0.205570
$696$	−8.09896e12	−1.30824
$697$	4.66590e12	0.748838
$698$	1.48898e13	2.37432
$699$	−3.93933e12	−0.624130
$700$	−1.20071e13	−1.89015
$701$	3.45573e12	0.540517	0.270258	−	0.962788i	$-0.412891\pi$
$701$	3.45573e12	0.540517	0.270258	+	0.962788i	$0.412891\pi$
$702$	1.49456e13	2.32272
$703$	1.84181e10	0.00284411
$704$	−2.03222e13	−3.11812
$705$	3.79103e10	0.00577972
$706$	1.18992e13	1.80259
$707$	4.09805e12	0.616865
$708$	1.20186e13	1.79765
$709$	−9.36848e12	−1.39239	−0.696195	−	0.717852i	$-0.745125\pi$
$709$	−9.36848e12	−1.39239	−0.696195	+	0.717852i	$0.745125\pi$
$710$	−3.26190e12	−0.481734
$711$	−6.78070e12	−0.995088
$712$	−1.06238e13	−1.54924
$713$	−5.99662e12	−0.868968
$714$	−1.55542e12	−0.223979
$715$	2.67863e13	3.83297
$716$	−1.22262e13	−1.73853
$717$	8.78786e10	0.0124179
$718$	8.19181e12	1.15032
$719$	−3.71547e12	−0.518483	−0.259241	−	0.965813i	$-0.583472\pi$
$719$	−3.71547e12	−0.518483	−0.259241	+	0.965813i	$0.583472\pi$
$720$	−2.87999e13	−3.99388
$721$	9.35851e11	0.128973
$722$	−1.37633e13	−1.88498
$723$	9.36335e11	0.127441
$724$	1.28452e13	1.73746
$725$	−1.38070e13	−1.85600
$726$	8.31830e12	1.11127
$727$	5.50761e12	0.731237	0.365619	−	0.930765i	$-0.380857\pi$
$727$	5.50761e12	0.731237	0.365619	+	0.930765i	$0.380857\pi$
$728$	1.26368e13	1.66743
$729$	5.52284e11	0.0724250
$730$	−3.70665e13	−4.83091
$731$	7.62492e12	0.987659
$732$	6.50534e12	0.837471
$733$	−1.19209e13	−1.52525	−0.762627	−	0.646838i	$-0.776091\pi$
$733$	−1.19209e13	−1.52525	−0.762627	+	0.646838i	$0.776091\pi$
$734$	−2.55436e13	−3.24825
$735$	−5.37451e12	−0.679275
$736$	2.64586e13	3.32366
$737$	−1.73880e12	−0.217093
$738$	−1.33537e13	−1.65710
$739$	−8.89307e12	−1.09686	−0.548431	−	0.836196i	$-0.684775\pi$
$739$	−8.89307e12	−1.09686	−0.548431	+	0.836196i	$0.684775\pi$
$740$	5.86875e12	0.719454
$741$	−9.80331e10	−0.0119451
$742$	4.27272e12	0.517472
$743$	−3.81881e12	−0.459704	−0.229852	−	0.973226i	$-0.573824\pi$
$743$	−3.81881e12	−0.459704	−0.229852	+	0.973226i	$0.573824\pi$
$744$	−7.96557e12	−0.953101
$745$	−1.10362e13	−1.31255
$746$	−5.91227e12	−0.698923
$747$	3.80458e12	0.447059
$748$	−2.20138e13	−2.57121
$749$	−1.38964e12	−0.161337
$750$	1.21328e13	1.40019
$751$	8.01902e12	0.919902	0.459951	−	0.887944i	$-0.347867\pi$
$751$	8.01902e12	0.919902	0.459951	+	0.887944i	$0.347867\pi$
$752$	1.89429e11	0.0216007
$753$	−5.70987e12	−0.647216
$754$	2.38743e13	2.69005
$755$	6.98770e12	0.782660
$756$	7.27998e12	0.810554
$757$	−9.18364e12	−1.01644	−0.508222	−	0.861226i	$-0.669697\pi$
$757$	−9.18364e12	−1.01644	−0.508222	+	0.861226i	$0.669697\pi$
$758$	3.10646e13	3.41786
$759$	−7.94911e12	−0.869422
$760$	7.99130e11	0.0868873
$761$	1.41280e13	1.52704	0.763519	−	0.645786i	$-0.223470\pi$
$761$	1.41280e13	1.52704	0.763519	+	0.645786i	$0.223470\pi$
$762$	1.03185e13	1.10871
$763$	−4.61624e12	−0.493092
$764$	−1.46319e13	−1.55375
$765$	−8.49873e12	−0.897176
$766$	3.68960e12	0.387213
$767$	−2.15638e13	−2.24981
$768$	1.10093e12	0.114191
$769$	5.63638e12	0.581208	0.290604	−	0.956843i	$-0.406144\pi$
$769$	5.63638e12	0.581208	0.290604	+	0.956843i	$0.406144\pi$
$770$	1.81537e13	1.86104
$771$	5.95414e12	0.606841
$772$	−1.39088e13	−1.40933
$773$	−1.30136e12	−0.131096	−0.0655480	−	0.997849i	$-0.520880\pi$
$773$	−1.30136e12	−0.131096	−0.0655480	+	0.997849i	$0.520880\pi$
$774$	−2.18224e13	−2.18559
$775$	−1.35796e13	−1.35216
$776$	7.30200e12	0.722876
$777$	−2.96976e11	−0.0292299
$778$	−1.55375e12	−0.152045
$779$	1.99302e11	0.0193907
$780$	−3.12372e13	−3.02167
$781$	2.33610e12	0.224679
$782$	1.63662e13	1.56501
$783$	8.37127e12	0.795909
$784$	−2.68552e13	−2.53867
$785$	2.15962e13	2.02985
$786$	1.79804e12	0.168035
$787$	−1.46399e13	−1.36036	−0.680179	−	0.733046i	$-0.738098\pi$
$787$	−1.46399e13	−1.36036	−0.680179	+	0.733046i	$0.738098\pi$
$788$	−2.43183e13	−2.24680
$789$	7.17865e12	0.659472
$790$	4.48661e13	4.09823
$791$	3.35264e12	0.304504
$792$	3.83470e13	3.46313
$793$	−1.16719e13	−1.04812
$794$	9.23392e12	0.824506
$795$	−6.42846e12	−0.570762
$796$	−9.40814e12	−0.830606
$797$	−1.26651e13	−1.11185	−0.555926	−	0.831232i	$-0.687636\pi$
$797$	−1.26651e13	−1.11185	−0.555926	+	0.831232i	$0.687636\pi$
$798$	−6.64392e10	−0.00579978
$799$	5.58998e10	0.00485232
$800$	5.99166e13	5.17180
$801$	4.82604e12	0.414233
$802$	−1.19606e13	−1.02087
$803$	2.65463e13	2.25312
$804$	2.02772e12	0.171142
$805$	−9.70025e12	−0.814144
$806$	2.34811e13	1.95980
$807$	6.82787e12	0.566701
$808$	−5.72781e13	−4.72756
$809$	1.44662e13	1.18737	0.593687	−	0.804696i	$-0.297672\pi$
$809$	1.44662e13	1.18737	0.593687	+	0.804696i	$0.297672\pi$
$810$	1.57814e13	1.28814
$811$	1.27666e13	1.03629	0.518147	−	0.855292i	$-0.326622\pi$
$811$	1.27666e13	1.03629	0.518147	+	0.855292i	$0.326622\pi$
$812$	1.16291e13	0.938738
$813$	8.03429e12	0.644971
$814$	−5.84795e12	−0.466868
$815$	−3.23616e13	−2.56934
$816$	1.16934e13	0.923285
$817$	3.25695e11	0.0255748
$818$	−2.79147e13	−2.17993
$819$	−5.74051e12	−0.445834
$820$	6.35055e13	4.90511
$821$	2.26267e13	1.73811	0.869055	−	0.494715i	$-0.164728\pi$
$821$	2.26267e13	1.73811	0.869055	+	0.494715i	$0.164728\pi$
$822$	2.49443e12	0.190567
$823$	3.00789e12	0.228541	0.114270	−	0.993450i	$-0.463547\pi$
$823$	3.00789e12	0.228541	0.114270	+	0.993450i	$0.463547\pi$
$824$	−1.30803e13	−0.988428
$825$	−1.80011e13	−1.35287
$826$	−1.46143e13	−1.09236
$827$	1.11435e13	0.828413	0.414207	−	0.910183i	$-0.364059\pi$
$827$	1.11435e13	0.828413	0.414207	+	0.910183i	$0.364059\pi$
$828$	−3.36652e13	−2.48911
$829$	1.88281e13	1.38456	0.692280	−	0.721629i	$-0.256606\pi$
$829$	1.88281e13	1.38456	0.692280	+	0.721629i	$0.256606\pi$
$830$	−2.51739e13	−1.84120
$831$	−1.15035e13	−0.836808
$832$	−4.25207e13	−3.07642
$833$	−7.92485e12	−0.570281
$834$	1.46929e12	0.105163
$835$	−3.91846e13	−2.78950
$836$	−9.40309e11	−0.0665798
$837$	8.23340e12	0.579849
$838$	2.84919e13	1.99583
$839$	1.46603e13	1.02144	0.510721	−	0.859746i	$-0.329378\pi$
$839$	1.46603e13	1.02144	0.510721	+	0.859746i	$0.329378\pi$
$840$	−1.28853e13	−0.892969
$841$	−1.13478e12	−0.0782223
$842$	8.53058e12	0.584890
$843$	5.77958e12	0.394159
$844$	2.90011e13	1.96731
$845$	3.06641e13	2.06907
$846$	−1.59984e11	−0.0107377
$847$	−7.26978e12	−0.485340
$848$	−3.21216e13	−2.13312
$849$	8.23137e12	0.543735
$850$	3.70620e13	2.43525
$851$	3.12480e12	0.204239
$852$	−2.72428e12	−0.177122
$853$	−1.15003e13	−0.743767	−0.371884	−	0.928279i	$-0.621288\pi$
$853$	−1.15003e13	−0.743767	−0.371884	+	0.928279i	$0.621288\pi$
$854$	−7.91028e12	−0.508899
$855$	−3.63019e11	−0.0232318
$856$	1.94229e13	1.23646
$857$	1.05442e13	0.667727	0.333863	−	0.942621i	$-0.391648\pi$
$857$	1.05442e13	0.667727	0.333863	+	0.942621i	$0.391648\pi$
$858$	3.11265e13	1.96082
$859$	1.10874e13	0.694801	0.347400	−	0.937717i	$-0.387064\pi$
$859$	1.10874e13	0.694801	0.347400	+	0.937717i	$0.387064\pi$
$860$	1.03779e14	6.46946
$861$	−3.21356e12	−0.199284
$862$	5.69457e12	0.351300
$863$	−3.33933e12	−0.204933	−0.102466	−	0.994736i	$-0.532673\pi$
$863$	−3.33933e12	−0.204933	−0.102466	+	0.994736i	$0.532673\pi$
$864$	−3.63278e13	−2.21782
$865$	3.13282e13	1.90267
$866$	−1.09992e13	−0.664552
$867$	−4.28002e12	−0.257253
$868$	1.14376e13	0.683905
$869$	−3.21322e13	−1.91140
$870$	−2.43437e13	−1.44062
$871$	−3.63814e12	−0.214189
$872$	6.45207e13	3.77898
$873$	−3.31707e12	−0.193281
$874$	6.99076e11	0.0405250
$875$	−1.06035e13	−0.611523
$876$	−3.09573e13	−1.77621
$877$	−2.15296e13	−1.22896	−0.614479	−	0.788933i	$-0.710634\pi$
$877$	−2.15296e13	−1.22896	−0.614479	+	0.788933i	$0.710634\pi$
$878$	−5.06164e13	−2.87452
$879$	−3.02571e11	−0.0170953
$880$	−1.36476e14	−7.67160
$881$	−2.44987e13	−1.37010	−0.685049	−	0.728497i	$-0.740219\pi$
$881$	−2.44987e13	−1.37010	−0.685049	+	0.728497i	$0.740219\pi$
$882$	2.26808e13	1.26197
$883$	2.35249e13	1.30228	0.651142	−	0.758956i	$-0.274290\pi$
$883$	2.35249e13	1.30228	0.651142	+	0.758956i	$0.274290\pi$
$884$	−4.60601e13	−2.53682
$885$	2.19877e13	1.20486
$886$	−3.68177e13	−2.00727
$887$	4.53738e11	0.0246121	0.0123060	−	0.999924i	$-0.496083\pi$
$887$	4.53738e11	0.0246121	0.0123060	+	0.999924i	$0.496083\pi$
$888$	4.15080e12	0.224013
$889$	−9.01781e12	−0.484221
$890$	−3.19327e13	−1.70600
$891$	−1.13023e13	−0.600784
$892$	2.61148e13	1.38116
$893$	2.38773e9	0.000125648 0
$894$	−1.28244e13	−0.671459
$895$	−2.23675e13	−1.16523
$896$	−9.06765e12	−0.470012
$897$	−1.66322e13	−0.857794
$898$	6.24150e13	3.20291
$899$	1.31521e13	0.671548
$900$	−7.62362e13	−3.87320
$901$	−9.47894e12	−0.479179
$902$	−6.32804e13	−3.18302
$903$	−5.25154e12	−0.262840
$904$	−4.68595e13	−2.33367
$905$	2.34998e13	1.16452
$906$	8.11993e12	0.400383
$907$	2.88276e13	1.41441	0.707205	−	0.707009i	$-0.249956\pi$
$907$	2.88276e13	1.41441	0.707205	+	0.707009i	$0.249956\pi$
$908$	6.95085e13	3.39353
$909$	2.60196e13	1.26405
$910$	3.79835e13	1.83615
$911$	−3.91719e13	−1.88426	−0.942131	−	0.335244i	$-0.891181\pi$
$911$	−3.91719e13	−1.88426	−0.942131	+	0.335244i	$0.891181\pi$
$912$	4.99479e11	0.0239078
$913$	1.80291e13	0.858727
$914$	−7.21902e13	−3.42153
$915$	1.19013e13	0.561307
$916$	−1.68707e13	−0.791778
$917$	−1.57140e12	−0.0733879
$918$	−2.24709e13	−1.04431
$919$	1.52842e13	0.706843	0.353421	−	0.935464i	$-0.385018\pi$
$919$	1.52842e13	0.706843	0.353421	+	0.935464i	$0.385018\pi$
$920$	1.35579e14	6.23948
$921$	5.49000e12	0.251422
$922$	1.07760e13	0.491100
$923$	4.88790e12	0.221674
$924$	1.51616e13	0.684262
$925$	7.07623e12	0.317808
$926$	4.56450e13	2.04006
$927$	5.94196e12	0.264284
$928$	−5.80304e13	−2.56856
$929$	3.59478e12	0.158344	0.0791720	−	0.996861i	$-0.474772\pi$
$929$	3.59478e12	0.158344	0.0791720	+	0.996861i	$0.474772\pi$
$930$	−2.39427e13	−1.04954
$931$	−3.38507e11	−0.0147670
$932$	−7.90588e13	−3.43225
$933$	−3.64024e12	−0.157276
$934$	−2.73527e13	−1.17608
$935$	−4.02736e13	−1.72333
$936$	8.02346e13	3.41681
$937$	−1.45718e13	−0.617566	−0.308783	−	0.951132i	$-0.599922\pi$
$937$	−1.45718e13	−0.617566	−0.308783	+	0.951132i	$0.599922\pi$
$938$	−2.46564e12	−0.103996
$939$	−1.26679e13	−0.531751
$940$	7.60827e11	0.0317842
$941$	1.94320e12	0.0807912	0.0403956	−	0.999184i	$-0.487138\pi$
$941$	1.94320e12	0.0807912	0.0403956	+	0.999184i	$0.487138\pi$
$942$	2.50955e13	1.03840
$943$	3.38133e13	1.39247
$944$	1.09868e14	4.50294
$945$	1.33185e13	0.543266
$946$	−1.03412e14	−4.19816
$947$	−1.11009e13	−0.448523	−0.224261	−	0.974529i	$-0.571997\pi$
$947$	−1.11009e13	−0.448523	−0.224261	+	0.974529i	$0.571997\pi$
$948$	3.74714e13	1.50683
$949$	5.55436e13	2.22298
$950$	1.58309e12	0.0630593
$951$	−7.91863e12	−0.313933
$952$	−1.89997e13	−0.749686
$953$	2.85961e13	1.12302	0.561512	−	0.827469i	$-0.310220\pi$
$953$	2.85961e13	1.12302	0.561512	+	0.827469i	$0.310220\pi$
$954$	2.71286e13	1.06038
$955$	−2.67687e13	−1.04139
$956$	1.76365e12	0.0682890
$957$	1.74344e13	0.671899
$958$	5.05227e13	1.93795
$959$	−2.18000e12	−0.0832287
$960$	4.33566e13	1.64754
$961$	−1.35041e13	−0.510753
$962$	−1.22358e13	−0.460623
$963$	−8.82319e12	−0.330604
$964$	1.87914e13	0.700830
$965$	−2.54458e13	−0.944588
$966$	−1.12720e13	−0.416489
$967$	−1.44855e13	−0.532740	−0.266370	−	0.963871i	$-0.585824\pi$
$967$	−1.44855e13	−0.532740	−0.266370	+	0.963871i	$0.585824\pi$
$968$	1.01609e14	3.71957
$969$	1.47394e11	0.00537060
$970$	2.19482e13	0.796023
$971$	−4.70916e13	−1.70003	−0.850015	−	0.526758i	$-0.823407\pi$
$971$	−4.70916e13	−1.70003	−0.850015	+	0.526758i	$0.823407\pi$
$972$	7.21306e13	2.59192
$973$	−1.28409e12	−0.0459290
$974$	−5.51560e13	−1.96371
$975$	−3.76642e13	−1.33478
$976$	5.94682e13	2.09778
$977$	1.77800e12	0.0624320	0.0312160	−	0.999513i	$-0.490062\pi$
$977$	1.77800e12	0.0624320	0.0312160	+	0.999513i	$0.490062\pi$
$978$	−3.76052e13	−1.31439
$979$	2.28695e13	0.795674
$980$	−1.07862e14	−3.73551
$981$	−2.93097e13	−1.01042
$982$	4.80006e13	1.64720
$983$	4.28444e13	1.46354	0.731768	−	0.681554i	$-0.238695\pi$
$983$	4.28444e13	1.46354	0.731768	+	0.681554i	$0.238695\pi$
$984$	4.49157e13	1.52728
$985$	−4.44895e13	−1.50590
$986$	−3.58953e13	−1.20946
$987$	−3.85001e10	−0.00129132
$988$	−1.96744e12	−0.0656893
$989$	5.52570e13	1.83655
$990$	1.15262e14	3.81355
$991$	−2.28138e13	−0.751391	−0.375695	−	0.926743i	$-0.622596\pi$
$991$	−2.28138e13	−0.751391	−0.375695	+	0.926743i	$0.622596\pi$
$992$	−5.70747e13	−1.87129
$993$	−1.42900e13	−0.466401
$994$	3.31264e12	0.107630
$995$	−1.72119e13	−0.556705
$996$	−2.10249e13	−0.676965
$997$	5.16080e13	1.65420	0.827102	−	0.562052i	$-0.189988\pi$
$997$	5.16080e13	1.65420	0.827102	+	0.562052i	$0.189988\pi$
$998$	1.06493e13	0.339809
$999$	−4.29036e12	−0.136285

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.10.a.b.1.14	✓	14
3.2	odd	2		333.10.a.d.1.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.10.a.b.1.14	✓	14	1.1	even	1	trivial
333.10.a.d.1.1		14	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	37.a (trivial)

\(f(q)\)	\(=\)	\(q+42.6649 q^{2} +65.1896 q^{3} +1308.30 q^{4} +2393.49 q^{5} +2781.31 q^{6} -2430.73 q^{7} +33974.0 q^{8} -15433.3 q^{9} +O(q^{10})\)	\(q+42.6649 q^{2} +65.1896 q^{3} +1308.30 q^{4} +2393.49 q^{5} +2781.31 q^{6} -2430.73 q^{7} +33974.0 q^{8} -15433.3 q^{9} +102118. q^{10} -73135.0 q^{11} +85287.4 q^{12} -153023. q^{13} -103707. q^{14} +156031. q^{15} +779651. q^{16} +230071. q^{17} -658462. q^{18} +9827.40 q^{19} +3.13140e6 q^{20} -158458. q^{21} -3.12030e6 q^{22} +1.66730e6 q^{23} +2.21475e6 q^{24} +3.77568e6 q^{25} -6.52870e6 q^{26} -2.28922e6 q^{27} -3.18011e6 q^{28} -3.65682e6 q^{29} +6.65705e6 q^{30} -3.59660e6 q^{31} +1.58691e7 q^{32} -4.76764e6 q^{33} +9.81599e6 q^{34} -5.81792e6 q^{35} -2.01914e7 q^{36} +1.87416e6 q^{37} +419286. q^{38} -9.97549e6 q^{39} +8.13165e7 q^{40} +2.02802e7 q^{41} -6.76060e6 q^{42} +3.31415e7 q^{43} -9.56824e7 q^{44} -3.69395e7 q^{45} +7.11354e7 q^{46} +242967. q^{47} +5.08251e7 q^{48} -3.44452e7 q^{49} +1.61089e8 q^{50} +1.49983e7 q^{51} -2.00199e8 q^{52} -4.12000e7 q^{53} -9.76694e7 q^{54} -1.75048e8 q^{55} -8.25815e7 q^{56} +640644. q^{57} -1.56018e8 q^{58} +1.40919e8 q^{59} +2.04135e8 q^{60} +7.62755e7 q^{61} -1.53449e8 q^{62} +3.75142e7 q^{63} +2.77872e8 q^{64} -3.66259e8 q^{65} -2.03411e8 q^{66} +2.37751e7 q^{67} +3.01002e8 q^{68} +1.08691e8 q^{69} -2.48221e8 q^{70} -3.19423e7 q^{71} -5.24332e8 q^{72} -3.62976e8 q^{73} +7.99610e7 q^{74} +2.46135e8 q^{75} +1.28572e7 q^{76} +1.77771e8 q^{77} -4.25604e8 q^{78} +4.39355e8 q^{79} +1.86609e9 q^{80} +1.54541e8 q^{81} +8.65255e8 q^{82} -2.46518e8 q^{83} -2.07310e8 q^{84} +5.50674e8 q^{85} +1.41398e9 q^{86} -2.38387e8 q^{87} -2.48469e9 q^{88} -3.12703e8 q^{89} -1.57602e9 q^{90} +3.71956e8 q^{91} +2.18133e9 q^{92} -2.34461e8 q^{93} +1.03662e7 q^{94} +2.35218e7 q^{95} +1.03450e9 q^{96} +2.14929e8 q^{97} -1.46960e9 q^{98} +1.12872e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 48 q^{2} + 397 q^{3} + 3498 q^{4} + 2841 q^{5} + 3375 q^{6} + 6632 q^{7} + 41046 q^{8} + 101917 q^{9}+O(q^{10}) \) 14 * q + 48 * q^2 + 397 * q^3 + 3498 * q^4 + 2841 * q^5 + 3375 * q^6 + 6632 * q^7 + 41046 * q^8 + 101917 * q^9	\( 14 q + 48 q^{2} + 397 q^{3} + 3498 q^{4} + 2841 q^{5} + 3375 q^{6} + 6632 q^{7} + 41046 q^{8} + 101917 q^{9} + 129003 q^{10} + 44949 q^{11} - 123661 q^{12} + 38913 q^{13} + 16434 q^{14} + 119816 q^{15} + 859962 q^{16} + 893196 q^{17} + 1833339 q^{18} + 1532124 q^{19} + 4974963 q^{20} + 1851132 q^{21} + 3195323 q^{22} + 5911773 q^{23} + 7885413 q^{24} + 9978791 q^{25} + 10634475 q^{26} + 13105312 q^{27} + 9469678 q^{28} + 8764377 q^{29} + 21804216 q^{30} + 13188927 q^{31} + 23982750 q^{32} + 9398618 q^{33} + 29914960 q^{34} + 29633556 q^{35} + 24297333 q^{36} + 26238254 q^{37} + 23342796 q^{38} + 40855861 q^{39} + 42889049 q^{40} + 22153785 q^{41} + 6999662 q^{42} + 1779790 q^{43} - 83674089 q^{44} - 45101798 q^{45} - 23239663 q^{46} + 40080072 q^{47} - 141884869 q^{48} - 170457752 q^{49} - 89214633 q^{50} - 127867462 q^{51} - 276889277 q^{52} - 102088122 q^{53} - 356745582 q^{54} - 206797385 q^{55} - 294922194 q^{56} - 141710762 q^{57} - 527059089 q^{58} + 56191266 q^{59} - 283393416 q^{60} - 178507397 q^{61} - 27353505 q^{62} - 291948734 q^{63} - 242330062 q^{64} - 174258810 q^{65} - 1153895008 q^{66} + 287062499 q^{67} + 308827572 q^{68} - 80094823 q^{69} - 672888452 q^{70} + 224382678 q^{71} + 105778731 q^{72} + 271440727 q^{73} + 89959728 q^{74} + 1017561832 q^{75} - 229522980 q^{76} + 671279994 q^{77} - 119785879 q^{78} + 379128625 q^{79} + 1999017183 q^{80} + 2367007018 q^{81} + 551153781 q^{82} + 1664083206 q^{83} + 1344035042 q^{84} + 1982056546 q^{85} + 520253082 q^{86} + 3606452357 q^{87} + 684092585 q^{88} + 3293434692 q^{89} + 892602798 q^{90} + 1715813946 q^{91} + 3729310881 q^{92} + 2573139250 q^{93} + 998499458 q^{94} + 878402766 q^{95} - 1221963827 q^{96} + 2385468336 q^{97} - 3234447132 q^{98} + 4029218638 q^{99}+O(q^{100}) \) 14 * q + 48 * q^2 + 397 * q^3 + 3498 * q^4 + 2841 * q^5 + 3375 * q^6 + 6632 * q^7 + 41046 * q^8 + 101917 * q^9 + 129003 * q^10 + 44949 * q^11 - 123661 * q^12 + 38913 * q^13 + 16434 * q^14 + 119816 * q^15 + 859962 * q^16 + 893196 * q^17 + 1833339 * q^18 + 1532124 * q^19 + 4974963 * q^20 + 1851132 * q^21 + 3195323 * q^22 + 5911773 * q^23 + 7885413 * q^24 + 9978791 * q^25 + 10634475 * q^26 + 13105312 * q^27 + 9469678 * q^28 + 8764377 * q^29 + 21804216 * q^30 + 13188927 * q^31 + 23982750 * q^32 + 9398618 * q^33 + 29914960 * q^34 + 29633556 * q^35 + 24297333 * q^36 + 26238254 * q^37 + 23342796 * q^38 + 40855861 * q^39 + 42889049 * q^40 + 22153785 * q^41 + 6999662 * q^42 + 1779790 * q^43 - 83674089 * q^44 - 45101798 * q^45 - 23239663 * q^46 + 40080072 * q^47 - 141884869 * q^48 - 170457752 * q^49 - 89214633 * q^50 - 127867462 * q^51 - 276889277 * q^52 - 102088122 * q^53 - 356745582 * q^54 - 206797385 * q^55 - 294922194 * q^56 - 141710762 * q^57 - 527059089 * q^58 + 56191266 * q^59 - 283393416 * q^60 - 178507397 * q^61 - 27353505 * q^62 - 291948734 * q^63 - 242330062 * q^64 - 174258810 * q^65 - 1153895008 * q^66 + 287062499 * q^67 + 308827572 * q^68 - 80094823 * q^69 - 672888452 * q^70 + 224382678 * q^71 + 105778731 * q^72 + 271440727 * q^73 + 89959728 * q^74 + 1017561832 * q^75 - 229522980 * q^76 + 671279994 * q^77 - 119785879 * q^78 + 379128625 * q^79 + 1999017183 * q^80 + 2367007018 * q^81 + 551153781 * q^82 + 1664083206 * q^83 + 1344035042 * q^84 + 1982056546 * q^85 + 520253082 * q^86 + 3606452357 * q^87 + 684092585 * q^88 + 3293434692 * q^89 + 892602798 * q^90 + 1715813946 * q^91 + 3729310881 * q^92 + 2573139250 * q^93 + 998499458 * q^94 + 878402766 * q^95 - 1221963827 * q^96 + 2385468336 * q^97 - 3234447132 * q^98 + 4029218638 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more