LMFDB - Embedded newform 37.10.a.b.1.4

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			1.4
Root			$-29.6469$ 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)

$f(q)$	$=$	$q-26.6469 q^{2} +9.79428 q^{3} +198.056 q^{4} -2462.81 q^{5} -260.987 q^{6} -4666.37 q^{7} +8365.63 q^{8} -19587.1 q^{9} +O(q^{10})$	\(q-26.6469 q^{2} +9.79428 q^{3} +198.056 q^{4} -2462.81 q^{5} -260.987 q^{6} -4666.37 q^{7} +8365.63 q^{8} -19587.1 q^{9} +65626.2 q^{10} -46335.9 q^{11} +1939.82 q^{12} -166098. q^{13} +124344. q^{14} -24121.5 q^{15} -324322. q^{16} -296546. q^{17} +521934. q^{18} +9348.59 q^{19} -487775. q^{20} -45703.8 q^{21} +1.23471e6 q^{22} +641664. q^{23} +81935.3 q^{24} +4.11232e6 q^{25} +4.42598e6 q^{26} -384622. q^{27} -924203. q^{28} +3.02464e6 q^{29} +642762. q^{30} -5.91694e6 q^{31} +4.35898e6 q^{32} -453827. q^{33} +7.90201e6 q^{34} +1.14924e7 q^{35} -3.87934e6 q^{36} +1.87416e6 q^{37} -249111. q^{38} -1.62681e6 q^{39} -2.06030e7 q^{40} +1.25513e7 q^{41} +1.21786e6 q^{42} -1.45562e7 q^{43} -9.17710e6 q^{44} +4.82393e7 q^{45} -1.70984e7 q^{46} -1.07005e7 q^{47} -3.17651e6 q^{48} -1.85786e7 q^{49} -1.09580e8 q^{50} -2.90445e6 q^{51} -3.28966e7 q^{52} -5.68114e7 q^{53} +1.02490e7 q^{54} +1.14117e8 q^{55} -3.90372e7 q^{56} +91562.8 q^{57} -8.05972e7 q^{58} +8.37659e7 q^{59} -4.77740e6 q^{60} -1.21379e8 q^{61} +1.57668e8 q^{62} +9.14006e7 q^{63} +4.98999e7 q^{64} +4.09067e8 q^{65} +1.20931e7 q^{66} -2.06880e8 q^{67} -5.87326e7 q^{68} +6.28464e6 q^{69} -3.06237e8 q^{70} -3.50597e8 q^{71} -1.63858e8 q^{72} -1.66065e8 q^{73} -4.99405e7 q^{74} +4.02772e7 q^{75} +1.85154e6 q^{76} +2.16221e8 q^{77} +4.33493e7 q^{78} -4.03611e8 q^{79} +7.98745e8 q^{80} +3.81765e8 q^{81} -3.34453e8 q^{82} +4.96138e8 q^{83} -9.05191e6 q^{84} +7.30336e8 q^{85} +3.87878e8 q^{86} +2.96242e7 q^{87} -3.87629e8 q^{88} -8.24852e8 q^{89} -1.28543e9 q^{90} +7.75074e8 q^{91} +1.27085e8 q^{92} -5.79522e7 q^{93} +2.85135e8 q^{94} -2.30238e7 q^{95} +4.26931e7 q^{96} +8.60147e8 q^{97} +4.95060e8 q^{98} +9.07584e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−26.6469	−1.17764	−0.588818	−	0.808265i	$-0.700407\pi$
$2$	−26.6469	−1.17764	−0.588818	+	0.808265i	$0.700407\pi$
$3$	9.79428	0.0698115	0.0349058	−	0.999391i	$-0.488887\pi$
$3$	9.79428	0.0698115	0.0349058	+	0.999391i	$0.488887\pi$
$4$	198.056	0.386828
$5$	−2462.81	−1.76224	−0.881122	−	0.472888i	$-0.843211\pi$
$5$	−2462.81	−1.76224	−0.881122	+	0.472888i	$0.843211\pi$
$6$	−260.987	−0.0822126
$7$	−4666.37	−0.734579	−0.367289	−	0.930107i	$-0.619714\pi$
$7$	−4666.37	−0.734579	−0.367289	+	0.930107i	$0.619714\pi$
$8$	8365.63	0.722094
$9$	−19587.1	−0.995126
$10$	65626.2	2.07528
$11$	−46335.9	−0.954224	−0.477112	−	0.878842i	$-0.658316\pi$
$11$	−46335.9	−0.954224	−0.477112	+	0.878842i	$0.658316\pi$
$12$	1939.82	0.0270050
$13$	−166098.	−1.61294	−0.806470	−	0.591275i	$-0.798625\pi$
$13$	−166098.	−1.61294	−0.806470	+	0.591275i	$0.798625\pi$
$14$	124344.	0.865067
$15$	−24121.5	−0.123025
$16$	−324322.	−1.23719
$17$	−296546.	−0.861135	−0.430567	−	0.902558i	$-0.641687\pi$
$17$	−296546.	−0.861135	−0.430567	+	0.902558i	$0.641687\pi$
$18$	521934.	1.17190
$19$	9348.59	0.0164572	0.00822858	−	0.999966i	$-0.497381\pi$
$19$	9348.59	0.0164572	0.00822858	+	0.999966i	$0.497381\pi$
$20$	−487775.	−0.681686
$21$	−45703.8	−0.0512821
$22$	1.23471e6	1.12373
$23$	641664.	0.478115	0.239058	−	0.971005i	$-0.423162\pi$
$23$	641664.	0.478115	0.239058	+	0.971005i	$0.423162\pi$
$24$	81935.3	0.0504105
$25$	4.11232e6	2.10551
$26$	4.42598e6	1.89946
$27$	−384622.	−0.139283
$28$	−924203.	−0.284156
$29$	3.02464e6	0.794113	0.397057	−	0.917794i	$-0.370032\pi$
$29$	3.02464e6	0.794113	0.397057	+	0.917794i	$0.370032\pi$
$30$	642762.	0.144879
$31$	−5.91694e6	−1.15072	−0.575360	−	0.817900i	$-0.695138\pi$
$31$	−5.91694e6	−1.15072	−0.575360	+	0.817900i	$0.695138\pi$
$32$	4.35898e6	0.734869
$33$	−453827.	−0.0666158
$34$	7.90201e6	1.01410
$35$	1.14924e7	1.29451
$36$	−3.87934e6	−0.384943
$37$	1.87416e6	0.164399
$37$	1.87416e6	0.164399
$38$	−249111.	−0.0193806
$39$	−1.62681e6	−0.112602
$40$	−2.06030e7	−1.27251
$41$	1.25513e7	0.693683	0.346841	−	0.937924i	$-0.387254\pi$
$41$	1.25513e7	0.693683	0.346841	+	0.937924i	$0.387254\pi$
$42$	1.21786e6	0.0603916
$43$	−1.45562e7	−0.649293	−0.324646	−	0.945835i	$-0.605245\pi$
$43$	−1.45562e7	−0.649293	−0.324646	+	0.945835i	$0.605245\pi$
$44$	−9.17710e6	−0.369121
$45$	4.82393e7	1.75366
$46$	−1.70984e7	−0.563046
$47$	−1.07005e7	−0.319863	−0.159931	−	0.987128i	$-0.551127\pi$
$47$	−1.07005e7	−0.319863	−0.159931	+	0.987128i	$0.551127\pi$
$48$	−3.17651e6	−0.0863702
$49$	−1.85786e7	−0.460394
$50$	−1.09580e8	−2.47952
$51$	−2.90445e6	−0.0601171
$52$	−3.28966e7	−0.623931
$53$	−5.68114e7	−0.988995	−0.494498	−	0.869179i	$-0.664648\pi$
$53$	−5.68114e7	−0.988995	−0.494498	+	0.869179i	$0.664648\pi$
$54$	1.02490e7	0.164024
$55$	1.14117e8	1.68158
$56$	−3.90372e7	−0.530435
$57$	91562.8	0.00114890
$58$	−8.05972e7	−0.935177
$59$	8.37659e7	0.899980	0.449990	−	0.893033i	$-0.351427\pi$
$59$	8.37659e7	0.899980	0.449990	+	0.893033i	$0.351427\pi$
$60$	−4.77740e6	−0.0475895
$61$	−1.21379e8	−1.12243	−0.561216	−	0.827670i	$-0.689666\pi$
$61$	−1.21379e8	−1.12243	−0.561216	+	0.827670i	$0.689666\pi$
$62$	1.57668e8	1.35513
$63$	9.14006e7	0.730999
$64$	4.98999e7	0.371783
$65$	4.09067e8	2.84240
$66$	1.20931e7	0.0784492
$67$	−2.06880e8	−1.25424	−0.627120	−	0.778922i	$-0.715767\pi$
$67$	−2.06880e8	−1.25424	−0.627120	+	0.778922i	$0.715767\pi$
$68$	−5.87326e7	−0.333111
$69$	6.28464e6	0.0333780
$70$	−3.06237e8	−1.52446
$71$	−3.50597e8	−1.63737	−0.818684	−	0.574245i	$-0.805296\pi$
$71$	−3.50597e8	−1.63737	−0.818684	+	0.574245i	$0.805296\pi$
$72$	−1.63858e8	−0.718575
$73$	−1.66065e8	−0.684425	−0.342213	−	0.939623i	$-0.611176\pi$
$73$	−1.66065e8	−0.684425	−0.342213	+	0.939623i	$0.611176\pi$
$74$	−4.99405e7	−0.193602
$75$	4.02772e7	0.146989
$76$	1.85154e6	0.00636609
$77$	2.16221e8	0.700953
$78$	4.33493e7	0.132604
$79$	−4.03611e8	−1.16585	−0.582923	−	0.812528i	$-0.698091\pi$
$79$	−4.03611e8	−1.16585	−0.582923	+	0.812528i	$0.698091\pi$
$80$	7.98745e8	2.18024
$81$	3.81765e8	0.985403
$82$	−3.34453e8	−0.816906
$83$	4.96138e8	1.14750	0.573748	−	0.819032i	$-0.305489\pi$
$83$	4.96138e8	1.14750	0.573748	+	0.819032i	$0.305489\pi$
$84$	−9.05191e6	−0.0198373
$85$	7.30336e8	1.51753
$86$	3.87878e8	0.764631
$87$	2.96242e7	0.0554383
$88$	−3.87629e8	−0.689039
$89$	−8.24852e8	−1.39355	−0.696773	−	0.717292i	$-0.745381\pi$
$89$	−8.24852e8	−1.39355	−0.696773	+	0.717292i	$0.745381\pi$
$90$	−1.28543e9	−2.06517
$91$	7.75074e8	1.18483
$92$	1.27085e8	0.184948
$93$	−5.79522e7	−0.0803335
$94$	2.85135e8	0.376682
$95$	−2.30238e7	−0.0290015
$96$	4.26931e7	0.0513023
$97$	8.60147e8	0.986506	0.493253	−	0.869886i	$-0.335808\pi$
$97$	8.60147e8	0.986506	0.493253	+	0.869886i	$0.335808\pi$
$98$	4.95060e8	0.542177
$99$	9.07584e8	0.949574
$100$	8.14469e8	0.814469
$101$	1.42691e9	1.36443	0.682215	−	0.731151i	$-0.261017\pi$
$101$	1.42691e9	1.36443	0.682215	+	0.731151i	$0.261017\pi$
$102$	7.73945e7	0.0707961
$103$	−9.05354e8	−0.792594	−0.396297	−	0.918122i	$-0.629705\pi$
$103$	−9.05354e8	−0.792594	−0.396297	+	0.918122i	$0.629705\pi$
$104$	−1.38951e9	−1.16469
$105$	1.12560e8	0.0903715
$106$	1.51385e9	1.16468
$107$	−2.29377e9	−1.69170	−0.845850	−	0.533421i	$-0.820906\pi$
$107$	−2.29377e9	−1.69170	−0.845850	+	0.533421i	$0.820906\pi$
$108$	−7.61767e7	−0.0538785
$109$	8.38370e8	0.568875	0.284437	−	0.958695i	$-0.408193\pi$
$109$	8.38370e8	0.568875	0.284437	+	0.958695i	$0.408193\pi$
$110$	−3.04085e9	−1.98029
$111$	1.83561e7	0.0114769
$112$	1.51341e9	0.908815
$113$	−1.05163e9	−0.606753	−0.303376	−	0.952871i	$-0.598114\pi$
$113$	−1.05163e9	−0.606753	−0.303376	+	0.952871i	$0.598114\pi$
$114$	−2.43986e6	−0.00135299
$115$	−1.58030e9	−0.842556
$116$	5.99048e8	0.307185
$117$	3.25337e9	1.60508
$118$	−2.23210e9	−1.05985
$119$	1.38379e9	0.632571
$120$	−2.01791e8	−0.0888355
$121$	−2.10933e8	−0.0894563
$122$	3.23437e9	1.32182
$123$	1.22931e8	0.0484270
$124$	−1.17189e9	−0.445131
$125$	−5.31768e9	−1.94817
$126$	−2.43554e9	−0.860851
$127$	−2.75877e9	−0.941020	−0.470510	−	0.882395i	$-0.655930\pi$
$127$	−2.75877e9	−0.941020	−0.470510	+	0.882395i	$0.655930\pi$
$128$	−3.56147e9	−1.17269
$129$	−1.42568e8	−0.0453281
$130$	−1.09004e10	−3.34731
$131$	1.01526e9	0.301201	0.150600	−	0.988595i	$-0.451879\pi$
$131$	1.01526e9	0.301201	0.150600	+	0.988595i	$0.451879\pi$
$132$	−8.98831e7	−0.0257689
$133$	−4.36240e7	−0.0120891
$134$	5.51269e9	1.47704
$135$	9.47252e8	0.245450
$136$	−2.48079e9	−0.621820
$137$	5.07256e9	1.23022	0.615112	−	0.788440i	$-0.289111\pi$
$137$	5.07256e9	1.23022	0.615112	+	0.788440i	$0.289111\pi$
$138$	−1.67466e8	−0.0393071
$139$	−7.29738e9	−1.65806	−0.829031	−	0.559203i	$-0.811107\pi$
$139$	−7.29738e9	−1.65806	−0.829031	+	0.559203i	$0.811107\pi$
$140$	2.27614e9	0.500752
$141$	−1.04804e8	−0.0223301
$142$	9.34233e9	1.92822
$143$	7.69628e9	1.53911
$144$	6.35253e9	1.23116
$145$	−7.44912e9	−1.39942
$146$	4.42512e9	0.806004
$147$	−1.81964e8	−0.0321408
$148$	3.71189e8	0.0635941
$149$	−2.94471e8	−0.0489446	−0.0244723	−	0.999701i	$-0.507791\pi$
$149$	−2.94471e8	−0.0489446	−0.0244723	+	0.999701i	$0.507791\pi$
$150$	−1.07326e9	−0.173099
$151$	−3.49004e9	−0.546304	−0.273152	−	0.961971i	$-0.588066\pi$
$151$	−3.49004e9	−0.546304	−0.273152	+	0.961971i	$0.588066\pi$
$152$	7.82068e7	0.0118836
$153$	5.80846e9	0.856938
$154$	−5.76160e9	−0.825468
$155$	1.45723e10	2.02785
$156$	−3.22199e8	−0.0435575
$157$	9.50863e9	1.24902	0.624510	−	0.781017i	$-0.285299\pi$
$157$	9.50863e9	1.24902	0.624510	+	0.781017i	$0.285299\pi$
$158$	1.07550e10	1.37294
$159$	−5.56427e8	−0.0690433
$160$	−1.07353e10	−1.29502
$161$	−2.99425e9	−0.351213
$162$	−1.01729e10	−1.16045
$163$	1.36424e10	1.51373	0.756864	−	0.653572i	$-0.226731\pi$
$163$	1.36424e10	1.51373	0.756864	+	0.653572i	$0.226731\pi$
$164$	2.48586e9	0.268336
$165$	1.11769e9	0.117393
$166$	−1.32205e10	−1.35133
$167$	1.44468e10	1.43730	0.718648	−	0.695374i	$-0.244761\pi$
$167$	1.44468e10	1.43730	0.718648	+	0.695374i	$0.244761\pi$
$168$	−3.82341e8	−0.0370305
$169$	1.69839e10	1.60158
$170$	−1.94612e10	−1.78710
$171$	−1.83112e8	−0.0163770
$172$	−2.88295e9	−0.251165
$173$	3.34009e9	0.283499	0.141749	−	0.989903i	$-0.454727\pi$
$173$	3.34009e9	0.283499	0.141749	+	0.989903i	$0.454727\pi$
$174$	−7.89392e8	−0.0652861
$175$	−1.91896e10	−1.54666
$176$	1.50278e10	1.18056
$177$	8.20427e8	0.0628290
$178$	2.19797e10	1.64109
$179$	−1.59559e9	−0.116167	−0.0580834	−	0.998312i	$-0.518499\pi$
$179$	−1.59559e9	−0.116167	−0.0580834	+	0.998312i	$0.518499\pi$
$180$	9.55407e9	0.678363
$181$	−2.80951e10	−1.94570	−0.972851	−	0.231433i	$-0.925659\pi$
$181$	−2.80951e10	−1.94570	−0.972851	+	0.231433i	$0.925659\pi$
$182$	−2.06533e10	−1.39530
$183$	−1.18882e9	−0.0783586
$184$	5.36793e9	0.345244
$185$	−4.61571e9	−0.289711
$186$	1.54425e9	0.0946037
$187$	1.37407e10	0.821716
$188$	−2.11930e9	−0.123732
$189$	1.79479e9	0.102314
$190$	6.13513e8	0.0341533
$191$	−7.08478e9	−0.385191	−0.192596	−	0.981278i	$-0.561691\pi$
$191$	−7.08478e9	−0.385191	−0.192596	+	0.981278i	$0.561691\pi$
$192$	4.88734e8	0.0259548
$193$	−3.63959e10	−1.88819	−0.944093	−	0.329679i	$-0.893059\pi$
$193$	−3.63959e10	−1.88819	−0.944093	+	0.329679i	$0.893059\pi$
$194$	−2.29202e10	−1.16175
$195$	4.00652e9	0.198432
$196$	−3.67959e9	−0.178093
$197$	−2.55653e8	−0.0120935	−0.00604675	−	0.999982i	$-0.501925\pi$
$197$	−2.55653e8	−0.0120935	−0.00604675	+	0.999982i	$0.501925\pi$
$198$	−2.41843e10	−1.11825
$199$	2.61954e10	1.18409	0.592046	−	0.805904i	$-0.298320\pi$
$199$	2.61954e10	1.18409	0.592046	+	0.805904i	$0.298320\pi$
$200$	3.44021e10	1.52037
$201$	−2.02624e9	−0.0875604
$202$	−3.80228e10	−1.60680
$203$	−1.41141e10	−0.583339
$204$	−5.75244e8	−0.0232550
$205$	−3.09115e10	−1.22244
$206$	2.41249e10	0.933388
$207$	−1.25683e10	−0.475785
$208$	5.38692e10	1.99552
$209$	−4.33175e8	−0.0157038
$210$	−2.99937e9	−0.106425
$211$	−4.65777e10	−1.61773	−0.808866	−	0.587993i	$-0.799918\pi$
$211$	−4.65777e10	−1.61773	−0.808866	+	0.587993i	$0.799918\pi$
$212$	−1.12518e10	−0.382571
$213$	−3.43385e9	−0.114307
$214$	6.11219e10	1.99221
$215$	3.58492e10	1.14421
$216$	−3.21761e9	−0.100575
$217$	2.76107e10	0.845295
$218$	−2.23400e10	−0.669928
$219$	−1.62649e9	−0.0477808
$220$	2.26015e10	0.650481
$221$	4.92555e10	1.38896
$222$	−4.89132e8	−0.0135157
$223$	−1.31454e10	−0.355960	−0.177980	−	0.984034i	$-0.556956\pi$
$223$	−1.31454e10	−0.355960	−0.177980	+	0.984034i	$0.556956\pi$
$224$	−2.03406e10	−0.539819
$225$	−8.05482e10	−2.09524
$226$	2.80228e10	0.714534
$227$	7.09552e10	1.77365	0.886825	−	0.462106i	$-0.152906\pi$
$227$	7.09552e10	1.77365	0.886825	+	0.462106i	$0.152906\pi$
$228$	1.81345e7	0.000444426 0
$229$	−7.39753e10	−1.77757	−0.888786	−	0.458322i	$-0.848451\pi$
$229$	−7.39753e10	−1.77757	−0.888786	+	0.458322i	$0.848451\pi$
$230$	4.21100e10	0.992225
$231$	2.11773e9	0.0489346
$232$	2.53030e10	0.573424
$233$	−4.47698e10	−0.995139	−0.497569	−	0.867424i	$-0.665774\pi$
$233$	−4.47698e10	−0.995139	−0.497569	+	0.867424i	$0.665774\pi$
$234$	−8.66921e10	−1.89020
$235$	2.63533e10	0.563677
$236$	1.65903e10	0.348138
$237$	−3.95308e9	−0.0813894
$238$	−3.68737e10	−0.744939
$239$	−8.39905e10	−1.66510	−0.832548	−	0.553952i	$-0.813119\pi$
$239$	−8.39905e10	−1.66510	−0.832548	+	0.553952i	$0.813119\pi$
$240$	7.82314e9	0.152205
$241$	7.03929e9	0.134416	0.0672082	−	0.997739i	$-0.478591\pi$
$241$	7.03929e9	0.134416	0.0672082	+	0.997739i	$0.478591\pi$
$242$	5.62071e9	0.105347
$243$	1.13096e10	0.208075
$244$	−2.40399e10	−0.434188
$245$	4.57555e10	0.811327
$246$	−3.27572e9	−0.0570295
$247$	−1.55278e9	−0.0265444
$248$	−4.94989e10	−0.830928
$249$	4.85931e9	0.0801084
$250$	1.41700e11	2.29424
$251$	4.55143e10	0.723796	0.361898	−	0.932218i	$-0.382129\pi$
$251$	4.55143e10	0.723796	0.361898	+	0.932218i	$0.382129\pi$
$252$	1.81024e10	0.282771
$253$	−2.97321e10	−0.456229
$254$	7.35126e10	1.10818
$255$	7.15312e9	0.105941
$256$	6.93534e10	1.00922
$257$	−2.11876e10	−0.302958	−0.151479	−	0.988460i	$-0.548404\pi$
$257$	−2.11876e10	−0.302958	−0.151479	+	0.988460i	$0.548404\pi$
$258$	3.79898e9	0.0533800
$259$	−8.74554e9	−0.120764
$260$	8.10182e10	1.09952
$261$	−5.92438e10	−0.790243
$262$	−2.70535e10	−0.354705
$263$	−7.66026e10	−0.987286	−0.493643	−	0.869665i	$-0.664335\pi$
$263$	−7.66026e10	−0.987286	−0.493643	+	0.869665i	$0.664335\pi$
$264$	−3.79655e9	−0.0481029
$265$	1.39916e11	1.74285
$266$	1.16244e9	0.0142365
$267$	−8.07884e9	−0.0972855
$268$	−4.09737e10	−0.485176
$269$	3.55111e10	0.413504	0.206752	−	0.978393i	$-0.433711\pi$
$269$	3.55111e10	0.413504	0.206752	+	0.978393i	$0.433711\pi$
$270$	−2.52413e10	−0.289051
$271$	−3.22739e9	−0.0363487	−0.0181744	−	0.999835i	$-0.505785\pi$
$271$	−3.22739e9	−0.0363487	−0.0181744	+	0.999835i	$0.505785\pi$
$272$	9.61764e10	1.06539
$273$	7.59129e9	0.0827149
$274$	−1.35168e11	−1.44876
$275$	−1.90548e11	−2.00912
$276$	1.24471e9	0.0129115
$277$	7.31822e10	0.746873	0.373436	−	0.927656i	$-0.378179\pi$
$277$	7.31822e10	0.746873	0.373436	+	0.927656i	$0.378179\pi$
$278$	1.94452e11	1.95259
$279$	1.15896e11	1.14511
$280$	9.61412e10	0.934756
$281$	−1.41915e10	−0.135784	−0.0678922	−	0.997693i	$-0.521627\pi$
$281$	−1.41915e10	−0.135784	−0.0678922	+	0.997693i	$0.521627\pi$
$282$	2.79269e9	0.0262967
$283$	4.77783e10	0.442784	0.221392	−	0.975185i	$-0.428940\pi$
$283$	4.77783e10	0.442784	0.221392	+	0.975185i	$0.428940\pi$
$284$	−6.94379e10	−0.633380
$285$	−2.25502e8	−0.00202464
$286$	−2.05082e11	−1.81251
$287$	−5.85690e10	−0.509565
$288$	−8.53796e10	−0.731287
$289$	−3.06486e10	−0.258447
$290$	1.98496e11	1.64801
$291$	8.42452e9	0.0688695
$292$	−3.28902e10	−0.264755
$293$	−8.34530e10	−0.661512	−0.330756	−	0.943716i	$-0.607304\pi$
$293$	−8.34530e10	−0.661512	−0.330756	+	0.943716i	$0.607304\pi$
$294$	4.84876e9	0.0378502
$295$	−2.06300e11	−1.58599
$296$	1.56785e10	0.118711
$297$	1.78218e10	0.132907
$298$	7.84674e9	0.0576390
$299$	−1.06579e11	−0.771172
$300$	7.97714e9	0.0568593
$301$	6.79248e10	0.476957
$302$	9.29988e10	0.643348
$303$	1.39756e10	0.0952530
$304$	−3.03196e9	−0.0203607
$305$	2.98934e11	1.97800
$306$	−1.54777e11	−1.00916
$307$	1.20768e11	0.775941	0.387970	−	0.921672i	$-0.373176\pi$
$307$	1.20768e11	0.775941	0.387970	+	0.921672i	$0.373176\pi$
$308$	4.28238e10	0.271148
$309$	−8.86729e9	−0.0553322
$310$	−3.88307e11	−2.38807
$311$	1.64037e11	0.994306	0.497153	−	0.867663i	$-0.334379\pi$
$311$	1.64037e11	0.994306	0.497153	+	0.867663i	$0.334379\pi$
$312$	−1.36093e10	−0.0813091
$313$	1.47010e11	0.865759	0.432879	−	0.901452i	$-0.357498\pi$
$313$	1.47010e11	0.865759	0.432879	+	0.901452i	$0.357498\pi$
$314$	−2.53375e11	−1.47089
$315$	−2.25103e11	−1.28820
$316$	−7.99375e10	−0.450982
$317$	1.72726e10	0.0960708	0.0480354	−	0.998846i	$-0.484704\pi$
$317$	1.72726e10	0.0960708	0.0480354	+	0.998846i	$0.484704\pi$
$318$	1.48270e10	0.0813079
$319$	−1.40149e11	−0.757762
$320$	−1.22894e11	−0.655173
$321$	−2.24659e10	−0.118100
$322$	7.97873e10	0.413602
$323$	−2.77228e9	−0.0141718
$324$	7.56109e10	0.381181
$325$	−6.83046e11	−3.39606
$326$	−3.63528e11	−1.78262
$327$	8.21124e9	0.0397140
$328$	1.04999e11	0.500904
$329$	4.99325e10	0.234964
$330$	−2.97829e10	−0.138247
$331$	2.56623e11	1.17508	0.587542	−	0.809194i	$-0.300096\pi$
$331$	2.56623e11	1.17508	0.587542	+	0.809194i	$0.300096\pi$
$332$	9.82630e10	0.443883
$333$	−3.67093e10	−0.163598
$334$	−3.84961e11	−1.69261
$335$	5.09505e11	2.21028
$336$	1.48228e10	0.0634458
$337$	3.12293e11	1.31895	0.659474	−	0.751728i	$-0.270779\pi$
$337$	3.12293e11	1.31895	0.659474	+	0.751728i	$0.270779\pi$
$338$	−4.52569e11	−1.88608
$339$	−1.03000e10	−0.0423583
$340$	1.44647e11	0.587023
$341$	2.74167e11	1.09805
$342$	4.87935e9	0.0192861
$343$	2.75000e11	1.07277
$344$	−1.21772e11	−0.468850
$345$	−1.54779e10	−0.0588201
$346$	−8.90030e10	−0.333858
$347$	2.11398e11	0.782743	0.391371	−	0.920233i	$-0.372001\pi$
$347$	2.11398e11	0.782743	0.391371	+	0.920233i	$0.372001\pi$
$348$	5.86724e9	0.0214451
$349$	−9.31688e10	−0.336168	−0.168084	−	0.985773i	$-0.553758\pi$
$349$	−9.31688e10	−0.336168	−0.168084	+	0.985773i	$0.553758\pi$
$350$	5.11343e11	1.82140
$351$	6.38848e10	0.224655
$352$	−2.01977e11	−0.701230
$353$	5.75708e10	0.197340	0.0986702	−	0.995120i	$-0.468541\pi$
$353$	5.75708e10	0.197340	0.0986702	+	0.995120i	$0.468541\pi$
$354$	−2.18618e10	−0.0739897
$355$	8.63456e11	2.88544
$356$	−1.63367e11	−0.539063
$357$	1.35533e10	0.0441608
$358$	4.25175e10	0.136802
$359$	−2.89497e11	−0.919853	−0.459927	−	0.887957i	$-0.652124\pi$
$359$	−2.89497e11	−0.919853	−0.459927	+	0.887957i	$0.652124\pi$
$360$	4.03552e11	1.26630
$361$	−3.22600e11	−0.999729
$362$	7.48645e11	2.29133
$363$	−2.06594e9	−0.00624508
$364$	1.53508e11	0.458326
$365$	4.08988e11	1.20612
$366$	3.16784e10	0.0922780
$367$	4.16044e11	1.19713	0.598567	−	0.801073i	$-0.295737\pi$
$367$	4.16044e11	1.19713	0.598567	+	0.801073i	$0.295737\pi$
$368$	−2.08106e11	−0.591521
$369$	−2.45843e11	−0.690302
$370$	1.22994e11	0.341175
$371$	2.65103e11	0.726495
$372$	−1.14778e10	−0.0310753
$373$	−3.26496e11	−0.873350	−0.436675	−	0.899619i	$-0.643844\pi$
$373$	−3.26496e11	−0.873350	−0.436675	+	0.899619i	$0.643844\pi$
$374$	−3.66147e11	−0.967683
$375$	−5.20829e10	−0.136005
$376$	−8.95164e10	−0.230971
$377$	−5.02385e11	−1.28086
$378$	−4.78256e10	−0.120489
$379$	3.32521e11	0.827833	0.413917	−	0.910315i	$-0.364160\pi$
$379$	3.32521e11	0.827833	0.413917	+	0.910315i	$0.364160\pi$
$380$	−4.56001e9	−0.0112186
$381$	−2.70202e10	−0.0656940
$382$	1.88787e11	0.453615
$383$	−5.45582e11	−1.29558	−0.647792	−	0.761817i	$-0.724308\pi$
$383$	−5.45582e11	−1.29558	−0.647792	+	0.761817i	$0.724308\pi$
$384$	−3.48821e10	−0.0818676
$385$	−5.32511e11	−1.23525
$386$	9.69837e11	2.22360
$387$	2.85114e11	0.646128
$388$	1.70357e11	0.381608
$389$	−4.18626e11	−0.926943	−0.463471	−	0.886112i	$-0.653396\pi$
$389$	−4.18626e11	−0.926943	−0.463471	+	0.886112i	$0.653396\pi$
$390$	−1.06761e11	−0.233681
$391$	−1.90283e11	−0.411722
$392$	−1.55421e11	−0.332448
$393$	9.94374e9	0.0210273
$394$	6.81234e9	0.0142418
$395$	9.94018e11	2.05450
$396$	1.79752e11	0.367322
$397$	−9.18511e11	−1.85578	−0.927891	−	0.372850i	$-0.878380\pi$
$397$	−9.18511e11	−1.85578	−0.927891	+	0.372850i	$0.878380\pi$
$398$	−6.98025e11	−1.39443
$399$	−4.27266e8	−0.000843957 0
$400$	−1.33372e12	−2.60492
$401$	−5.65533e11	−1.09222	−0.546108	−	0.837715i	$-0.683891\pi$
$401$	−5.65533e11	−1.09222	−0.546108	+	0.837715i	$0.683891\pi$
$402$	5.39929e10	0.103114
$403$	9.82790e11	1.85604
$404$	2.82609e11	0.527800
$405$	−9.40216e11	−1.73652
$406$	3.76097e11	0.686961
$407$	−8.68409e10	−0.156873
$408$	−2.42976e10	−0.0434102
$409$	6.16023e11	1.08853	0.544267	−	0.838912i	$-0.316808\pi$
$409$	6.16023e11	1.08853	0.544267	+	0.838912i	$0.316808\pi$
$410$	8.23694e11	1.43959
$411$	4.96821e10	0.0858838
$412$	−1.79311e11	−0.306598
$413$	−3.90883e11	−0.661107
$414$	3.34907e11	0.560302
$415$	−1.22189e12	−2.02217
$416$	−7.24016e11	−1.18530
$417$	−7.14726e10	−0.115752
$418$	1.15428e10	0.0184934
$419$	6.83891e11	1.08399	0.541993	−	0.840383i	$-0.317670\pi$
$419$	6.83891e11	1.08399	0.541993	+	0.840383i	$0.317670\pi$
$420$	2.22931e10	0.0349582
$421$	5.32579e11	0.826257	0.413128	−	0.910673i	$-0.364436\pi$
$421$	5.32579e11	0.826257	0.413128	+	0.910673i	$0.364436\pi$
$422$	1.24115e12	1.90510
$423$	2.09591e11	0.318304
$424$	−4.75263e11	−0.714147
$425$	−1.21949e12	−1.81313
$426$	9.15014e10	0.134612
$427$	5.66400e11	0.824514
$428$	−4.54295e11	−0.654397
$429$	7.53796e10	0.107447
$430$	−9.55270e11	−1.34747
$431$	−8.99709e11	−1.25590	−0.627949	−	0.778254i	$-0.716105\pi$
$431$	−8.99709e11	−1.25590	−0.627949	+	0.778254i	$0.716105\pi$
$432$	1.24742e11	0.172320
$433$	−1.63341e11	−0.223305	−0.111653	−	0.993747i	$-0.535614\pi$
$433$	−1.63341e11	−0.223305	−0.111653	+	0.993747i	$0.535614\pi$
$434$	−7.35738e11	−0.995450
$435$	−7.29588e10	−0.0976958
$436$	1.66044e11	0.220057
$437$	5.99866e9	0.00786842
$438$	4.33409e10	0.0562684
$439$	−1.38375e12	−1.77815	−0.889075	−	0.457762i	$-0.848651\pi$
$439$	−1.38375e12	−1.77815	−0.889075	+	0.457762i	$0.848651\pi$
$440$	9.54657e11	1.21426
$441$	3.63900e11	0.458150
$442$	−1.31251e12	−1.63569
$443$	7.81057e11	0.963532	0.481766	−	0.876300i	$-0.339996\pi$
$443$	7.81057e11	0.963532	0.481766	+	0.876300i	$0.339996\pi$
$444$	3.63553e9	0.00443960
$445$	2.03146e12	2.45577
$446$	3.50283e11	0.419192
$447$	−2.88414e9	−0.00341690
$448$	−2.32852e11	−0.273104
$449$	−2.47579e11	−0.287478	−0.143739	−	0.989616i	$-0.545913\pi$
$449$	−2.47579e11	−0.287478	−0.143739	+	0.989616i	$0.545913\pi$
$450$	2.14636e12	2.46744
$451$	−5.81575e11	−0.661929
$452$	−2.08282e11	−0.234709
$453$	−3.41825e10	−0.0381383
$454$	−1.89073e12	−2.08871
$455$	−1.90886e12	−2.08796
$456$	7.65980e8	0.000829613 0
$457$	1.35318e11	0.145121	0.0725607	−	0.997364i	$-0.476883\pi$
$457$	1.35318e11	0.145121	0.0725607	+	0.997364i	$0.476883\pi$
$458$	1.97121e12	2.09333
$459$	1.14058e11	0.119941
$460$	−3.12988e11	−0.325924
$461$	3.62978e11	0.374306	0.187153	−	0.982331i	$-0.440074\pi$
$461$	3.62978e11	0.374306	0.187153	+	0.982331i	$0.440074\pi$
$462$	−5.64308e10	−0.0576271
$463$	1.54578e12	1.56326	0.781632	−	0.623740i	$-0.214388\pi$
$463$	1.54578e12	1.56326	0.781632	+	0.623740i	$0.214388\pi$
$464$	−9.80958e11	−0.982471
$465$	1.42725e11	0.141567
$466$	1.19298e12	1.17191
$467$	3.89953e11	0.379391	0.189695	−	0.981843i	$-0.439250\pi$
$467$	3.89953e11	0.379391	0.189695	+	0.981843i	$0.439250\pi$
$468$	6.44349e11	0.620890
$469$	9.65377e11	0.921339
$470$	−7.02234e11	−0.663806
$471$	9.31302e10	0.0871959
$472$	7.00754e11	0.649870
$473$	6.74475e11	0.619571
$474$	1.05337e11	0.0958471
$475$	3.84444e10	0.0346507
$476$	2.74068e11	0.244696
$477$	1.11277e12	0.984175
$478$	2.23808e12	1.96088
$479$	−1.87641e12	−1.62862	−0.814308	−	0.580433i	$-0.802883\pi$
$479$	−1.87641e12	−1.62862	−0.814308	+	0.580433i	$0.802883\pi$
$480$	−1.05145e11	−0.0904072
$481$	−3.11294e11	−0.265166
$482$	−1.87575e11	−0.158294
$483$	−2.93265e10	−0.0245187
$484$	−4.17766e10	−0.0346042
$485$	−2.11838e12	−1.73847
$486$	−3.01366e11	−0.245037
$487$	1.07919e12	0.869396	0.434698	−	0.900576i	$-0.356855\pi$
$487$	1.07919e12	0.869396	0.434698	+	0.900576i	$0.356855\pi$
$488$	−1.01541e12	−0.810501
$489$	1.33618e11	0.105676
$490$	−1.21924e12	−0.955448
$491$	1.45277e11	0.112806	0.0564028	−	0.998408i	$-0.482037\pi$
$491$	1.45277e11	0.112806	0.0564028	+	0.998408i	$0.482037\pi$
$492$	2.43472e10	0.0187329
$493$	−8.96943e11	−0.683839
$494$	4.13767e10	0.0312597
$495$	−2.23521e12	−1.67338
$496$	1.91900e12	1.42366
$497$	1.63602e12	1.20278
$498$	−1.29486e11	−0.0943385
$499$	2.41264e11	0.174197	0.0870985	−	0.996200i	$-0.472241\pi$
$499$	2.41264e11	0.174197	0.0870985	+	0.996200i	$0.472241\pi$
$500$	−1.05320e12	−0.753608
$501$	1.41496e11	0.100340
$502$	−1.21281e12	−0.852369
$503$	1.13016e12	0.787200	0.393600	−	0.919282i	$-0.371229\pi$
$503$	1.13016e12	0.787200	0.393600	+	0.919282i	$0.371229\pi$
$504$	7.64624e11	0.527850
$505$	−3.51422e12	−2.40446
$506$	7.92267e11	0.537272
$507$	1.66345e11	0.111809
$508$	−5.46391e11	−0.364013
$509$	−2.11310e12	−1.39537	−0.697685	−	0.716405i	$-0.745787\pi$
$509$	−2.11310e12	−1.39537	−0.697685	+	0.716405i	$0.745787\pi$
$510$	−1.90608e11	−0.124760
$511$	7.74923e11	0.502764
$512$	−2.45765e10	−0.0158054
$513$	−3.59568e9	−0.00229220
$514$	5.64583e11	0.356775
$515$	2.22972e12	1.39674
$516$	−2.82364e10	−0.0175342
$517$	4.95817e11	0.305221
$518$	2.33041e11	0.142216
$519$	3.27138e10	0.0197915
$520$	3.42210e12	2.05248
$521$	−9.35734e11	−0.556394	−0.278197	−	0.960524i	$-0.589737\pi$
$521$	−9.35734e11	−0.556394	−0.278197	+	0.960524i	$0.589737\pi$
$522$	1.57866e12	0.930619
$523$	8.72239e11	0.509774	0.254887	−	0.966971i	$-0.417962\pi$
$523$	8.72239e11	0.509774	0.254887	+	0.966971i	$0.417962\pi$
$524$	2.01078e11	0.116513
$525$	−1.87948e11	−0.107975
$526$	2.04122e12	1.16266
$527$	1.75464e12	0.990925
$528$	1.47186e11	0.0824166
$529$	−1.38942e12	−0.771406
$530$	−3.72832e12	−2.05245
$531$	−1.64073e12	−0.895594
$532$	−8.64000e9	−0.00467640
$533$	−2.08474e12	−1.11887
$534$	2.15276e11	0.114567
$535$	5.64913e12	2.98119
$536$	−1.73068e12	−0.905680
$537$	−1.56276e10	−0.00810978
$538$	−9.46261e11	−0.486957
$539$	8.60854e11	0.439319
$540$	1.87609e11	0.0949471
$541$	2.21060e12	1.10949	0.554743	−	0.832022i	$-0.312817\pi$
$541$	2.21060e12	1.10949	0.554743	+	0.832022i	$0.312817\pi$
$542$	8.59998e10	0.0428056
$543$	−2.75171e11	−0.135832
$544$	−1.29264e12	−0.632821
$545$	−2.06475e12	−1.00250
$546$	−2.02284e11	−0.0974081
$547$	−2.96714e12	−1.41708	−0.708542	−	0.705669i	$-0.750647\pi$
$547$	−2.96714e12	−1.41708	−0.708542	+	0.705669i	$0.750647\pi$
$548$	1.00465e12	0.475885
$549$	2.37746e12	1.11696
$550$	5.07750e12	2.36602
$551$	2.82761e10	0.0130689
$552$	5.25750e10	0.0241020
$553$	1.88340e12	0.856405
$554$	−1.95008e12	−0.879544
$555$	−4.52075e10	−0.0202252
$556$	−1.44529e12	−0.641385
$557$	−1.63287e12	−0.718794	−0.359397	−	0.933185i	$-0.617018\pi$
$557$	−1.63287e12	−0.718794	−0.359397	+	0.933185i	$0.617018\pi$
$558$	−3.08826e12	−1.34853
$559$	2.41775e12	1.04727
$560$	−3.72724e12	−1.60155
$561$	1.34580e11	0.0573652
$562$	3.78159e11	0.159905
$563$	−3.59134e12	−1.50650	−0.753250	−	0.657734i	$-0.771515\pi$
$563$	−3.59134e12	−1.50650	−0.753250	+	0.657734i	$0.771515\pi$
$564$	−2.07570e10	−0.00863791
$565$	2.58998e12	1.06925
$566$	−1.27314e12	−0.521438
$567$	−1.78146e12	−0.723856
$568$	−2.93297e12	−1.18233
$569$	−1.99829e12	−0.799194	−0.399597	−	0.916691i	$-0.630850\pi$
$569$	−1.99829e12	−0.799194	−0.399597	+	0.916691i	$0.630850\pi$
$570$	6.00892e9	0.00238429
$571$	−4.51957e12	−1.77924	−0.889620	−	0.456702i	$-0.849031\pi$
$571$	−4.51957e12	−1.77924	−0.889620	+	0.456702i	$0.849031\pi$
$572$	1.52429e12	0.595370
$573$	−6.93904e10	−0.0268908
$574$	1.56068e12	0.600082
$575$	2.63873e12	1.00667
$576$	−9.77394e11	−0.369972
$577$	1.41658e12	0.532046	0.266023	−	0.963967i	$-0.414290\pi$
$577$	1.41658e12	0.532046	0.266023	+	0.963967i	$0.414290\pi$
$578$	8.16690e11	0.304356
$579$	−3.56472e11	−0.131817
$580$	−1.47534e12	−0.541336
$581$	−2.31516e12	−0.842926
$582$	−2.24487e11	−0.0811032
$583$	2.63241e12	0.943723
$584$	−1.38924e12	−0.494219
$585$	−8.01243e12	−2.82854
$586$	2.22376e12	0.779020
$587$	3.83844e12	1.33439	0.667196	−	0.744882i	$-0.267494\pi$
$587$	3.83844e12	1.33439	0.667196	+	0.744882i	$0.267494\pi$
$588$	−3.60390e10	−0.0124330
$589$	−5.53151e10	−0.0189376
$590$	5.49724e12	1.86771
$591$	−2.50393e9	−0.000844266 0
$592$	−6.07833e11	−0.203393
$593$	3.02932e12	1.00600	0.503002	−	0.864285i	$-0.332229\pi$
$593$	3.02932e12	1.00600	0.503002	+	0.864285i	$0.332229\pi$
$594$	−4.74896e11	−0.156516
$595$	−3.40802e12	−1.11475
$596$	−5.83218e10	−0.0189331
$597$	2.56565e11	0.0826633
$598$	2.84000e12	0.908160
$599$	−3.37313e12	−1.07056	−0.535281	−	0.844674i	$-0.679794\pi$
$599$	−3.37313e12	−1.07056	−0.535281	+	0.844674i	$0.679794\pi$
$600$	3.36944e11	0.106140
$601$	2.16425e12	0.676662	0.338331	−	0.941027i	$-0.390138\pi$
$601$	2.16425e12	0.676662	0.338331	+	0.941027i	$0.390138\pi$
$602$	−1.80998e12	−0.561682
$603$	4.05216e12	1.24813
$604$	−6.91224e11	−0.211326
$605$	5.19489e11	0.157644
$606$	−3.72406e11	−0.112173
$607$	−8.79897e11	−0.263077	−0.131538	−	0.991311i	$-0.541992\pi$
$607$	−8.79897e11	−0.263077	−0.131538	+	0.991311i	$0.541992\pi$
$608$	4.07503e10	0.0120939
$609$	−1.38237e11	−0.0407238
$610$	−7.96565e12	−2.32936
$611$	1.77733e12	0.515920
$612$	1.15040e12	0.331488
$613$	−9.46602e11	−0.270767	−0.135383	−	0.990793i	$-0.543227\pi$
$613$	−9.46602e11	−0.270767	−0.135383	+	0.990793i	$0.543227\pi$
$614$	−3.21809e12	−0.913777
$615$	−3.02756e11	−0.0853403
$616$	1.80882e12	0.506154
$617$	−2.99504e12	−0.831991	−0.415996	−	0.909367i	$-0.636567\pi$
$617$	−2.99504e12	−0.831991	−0.415996	+	0.909367i	$0.636567\pi$
$618$	2.36286e11	0.0651612
$619$	−4.33552e12	−1.18695	−0.593476	−	0.804851i	$-0.702245\pi$
$619$	−4.33552e12	−1.18695	−0.593476	+	0.804851i	$0.702245\pi$
$620$	2.88613e12	0.784429
$621$	−2.46798e11	−0.0665932
$622$	−4.37107e12	−1.17093
$623$	3.84907e12	1.02367
$624$	5.27610e11	0.139310
$625$	5.06458e12	1.32765
$626$	−3.91735e12	−1.01955
$627$	−4.24264e9	−0.00109631
$628$	1.88324e12	0.483156
$629$	−5.55774e11	−0.141570
$630$	5.99828e12	1.51703
$631$	3.55404e12	0.892464	0.446232	−	0.894917i	$-0.352766\pi$
$631$	3.55404e12	0.892464	0.446232	+	0.894917i	$0.352766\pi$
$632$	−3.37646e12	−0.841850
$633$	−4.56195e11	−0.112936
$634$	−4.60261e11	−0.113136
$635$	6.79433e12	1.65831
$636$	−1.10204e11	−0.0267079
$637$	3.08585e12	0.742588
$638$	3.73454e12	0.892369
$639$	6.86718e12	1.62939
$640$	8.77124e12	2.06658
$641$	−2.97399e12	−0.695789	−0.347895	−	0.937534i	$-0.613103\pi$
$641$	−2.97399e12	−0.695789	−0.347895	+	0.937534i	$0.613103\pi$
$642$	5.98645e11	0.139079
$643$	−5.75976e12	−1.32879	−0.664393	−	0.747383i	$-0.731310\pi$
$643$	−5.75976e12	−1.32879	−0.664393	+	0.747383i	$0.731310\pi$
$644$	−5.93028e11	−0.135859
$645$	3.51117e11	0.0798792
$646$	7.38727e10	0.0166893
$647$	−1.82254e12	−0.408891	−0.204446	−	0.978878i	$-0.565539\pi$
$647$	−1.82254e12	−0.408891	−0.204446	+	0.978878i	$0.565539\pi$
$648$	3.19371e12	0.711553
$649$	−3.88137e12	−0.858783
$650$	1.82010e13	3.99932
$651$	2.70427e11	0.0590113
$652$	2.70197e12	0.585552
$653$	−2.56506e12	−0.552062	−0.276031	−	0.961149i	$-0.589019\pi$
$653$	−2.56506e12	−0.552062	−0.276031	+	0.961149i	$0.589019\pi$
$654$	−2.18804e11	−0.0467687
$655$	−2.50039e12	−0.530790
$656$	−4.07066e12	−0.858219
$657$	3.25273e12	0.681090
$658$	−1.33055e12	−0.276703
$659$	−1.91454e12	−0.395438	−0.197719	−	0.980259i	$-0.563353\pi$
$659$	−1.91454e12	−0.395438	−0.197719	+	0.980259i	$0.563353\pi$
$660$	2.21365e11	0.0454110
$661$	5.04668e12	1.02825	0.514125	−	0.857715i	$-0.328117\pi$
$661$	5.04668e12	1.02825	0.514125	+	0.857715i	$0.328117\pi$
$662$	−6.83819e12	−1.38382
$663$	4.82422e11	0.0969654
$664$	4.15050e12	0.828599
$665$	1.07438e11	0.0213039
$666$	9.78189e11	0.192659
$667$	1.94080e12	0.379678
$668$	2.86127e12	0.555986
$669$	−1.28750e11	−0.0248501
$670$	−1.35767e13	−2.60291
$671$	5.62421e12	1.07105
$672$	−1.99222e11	−0.0376856
$673$	6.22823e12	1.17030	0.585150	−	0.810925i	$-0.301036\pi$
$673$	6.22823e12	1.17030	0.585150	+	0.810925i	$0.301036\pi$
$674$	−8.32163e12	−1.55324
$675$	−1.58169e12	−0.293261
$676$	3.36377e12	0.619535
$677$	−7.10203e12	−1.29937	−0.649686	−	0.760203i	$-0.725100\pi$
$677$	−7.10203e12	−1.29937	−0.649686	+	0.760203i	$0.725100\pi$
$678$	2.74463e11	0.0498827
$679$	−4.01377e12	−0.724667
$680$	6.10972e12	1.09580
$681$	6.94955e11	0.123821
$682$	−7.30569e12	−1.29310
$683$	6.95652e12	1.22320	0.611602	−	0.791166i	$-0.290526\pi$
$683$	6.95652e12	1.22320	0.611602	+	0.791166i	$0.290526\pi$
$684$	−3.62663e10	−0.00633507
$685$	−1.24928e13	−2.16796
$686$	−7.32788e12	−1.26334
$687$	−7.24535e11	−0.124095
$688$	4.72091e12	0.803300
$689$	9.43624e12	1.59519
$690$	4.12437e11	0.0692687
$691$	9.25287e11	0.154392	0.0771961	−	0.997016i	$-0.475403\pi$
$691$	9.25287e11	0.154392	0.0771961	+	0.997016i	$0.475403\pi$
$692$	6.61525e11	0.109665
$693$	−4.23513e12	−0.697537
$694$	−5.63311e12	−0.921787
$695$	1.79721e13	2.92191
$696$	2.47825e11	0.0400316
$697$	−3.72203e12	−0.597354
$698$	2.48266e12	0.395884
$699$	−4.38488e11	−0.0694721
$700$	−3.80062e12	−0.598292
$701$	−5.07495e12	−0.793781	−0.396890	−	0.917866i	$-0.629911\pi$
$701$	−5.07495e12	−0.793781	−0.396890	+	0.917866i	$0.629911\pi$
$702$	−1.70233e12	−0.264562
$703$	1.75208e10	0.00270554
$704$	−2.31216e12	−0.354765
$705$	2.58112e11	0.0393511
$706$	−1.53408e12	−0.232395
$707$	−6.65851e12	−1.00228
$708$	1.62490e11	0.0243040
$709$	2.37979e12	0.353697	0.176848	−	0.984238i	$-0.443410\pi$
$709$	2.37979e12	0.353697	0.176848	+	0.984238i	$0.443410\pi$
$710$	−2.30084e13	−3.39800
$711$	7.90555e12	1.16016
$712$	−6.90041e12	−1.00627
$713$	−3.79669e12	−0.550177
$714$	−3.61152e11	−0.0520053
$715$	−1.89545e13	−2.71228
$716$	−3.16016e11	−0.0449366
$717$	−8.22626e11	−0.116243
$718$	7.71418e12	1.08325
$719$	−4.60105e12	−0.642063	−0.321031	−	0.947069i	$-0.604029\pi$
$719$	−4.60105e12	−0.642063	−0.321031	+	0.947069i	$0.604029\pi$
$720$	−1.56451e13	−2.16961
$721$	4.22472e12	0.582223
$722$	8.59629e12	1.17732
$723$	6.89448e10	0.00938380
$724$	−5.56439e12	−0.752652
$725$	1.24383e13	1.67201
$726$	5.50508e10	0.00735443
$727$	1.94690e11	0.0258487	0.0129243	−	0.999916i	$-0.495886\pi$
$727$	1.94690e11	0.0258487	0.0129243	+	0.999916i	$0.495886\pi$
$728$	6.48398e12	0.855560
$729$	−7.40352e12	−0.970877
$730$	−1.08982e13	−1.42038
$731$	4.31658e12	0.559129
$732$	−2.35453e11	−0.0303113
$733$	5.51145e12	0.705177	0.352589	−	0.935778i	$-0.385302\pi$
$733$	5.51145e12	0.705177	0.352589	+	0.935778i	$0.385302\pi$
$734$	−1.10863e13	−1.40979
$735$	4.48142e11	0.0566399
$736$	2.79700e12	0.351352
$737$	9.58595e12	1.19683
$738$	6.55095e12	0.812925
$739$	7.91334e12	0.976022	0.488011	−	0.872837i	$-0.337723\pi$
$739$	7.91334e12	0.976022	0.488011	+	0.872837i	$0.337723\pi$
$740$	−9.14168e11	−0.112068
$741$	−1.52084e10	−0.00185311
$742$	−7.06418e12	−0.855547
$743$	1.10198e13	1.32655	0.663277	−	0.748374i	$-0.269165\pi$
$743$	1.10198e13	1.32655	0.663277	+	0.748374i	$0.269165\pi$
$744$	−4.84807e11	−0.0580083
$745$	7.25227e11	0.0862524
$746$	8.70010e12	1.02849
$747$	−9.71789e12	−1.14190
$748$	2.72143e12	0.317863
$749$	1.07036e13	1.24269
$750$	1.38785e12	0.160164
$751$	−2.86454e12	−0.328606	−0.164303	−	0.986410i	$-0.552537\pi$
$751$	−2.86454e12	−0.328606	−0.164303	+	0.986410i	$0.552537\pi$
$752$	3.47041e12	0.395732
$753$	4.45780e11	0.0505293
$754$	1.33870e13	1.50839
$755$	8.59532e12	0.962722
$756$	3.55469e11	0.0395780
$757$	−9.28213e12	−1.02734	−0.513672	−	0.857986i	$-0.671715\pi$
$757$	−9.28213e12	−1.02734	−0.513672	+	0.857986i	$0.671715\pi$
$758$	−8.86065e12	−0.974887
$759$	−2.91204e11	−0.0318500
$760$	−1.92609e11	−0.0209418
$761$	5.61208e12	0.606586	0.303293	−	0.952897i	$-0.401914\pi$
$761$	5.61208e12	0.606586	0.303293	+	0.952897i	$0.401914\pi$
$762$	7.20003e11	0.0773637
$763$	−3.91215e12	−0.417883
$764$	−1.40318e12	−0.149003
$765$	−1.43051e13	−1.51013
$766$	1.45381e13	1.52573
$767$	−1.39133e13	−1.45161
$768$	6.79267e11	0.0704555
$769$	−1.87629e12	−0.193478	−0.0967390	−	0.995310i	$-0.530841\pi$
$769$	−1.87629e12	−0.193478	−0.0967390	+	0.995310i	$0.530841\pi$
$770$	1.41897e13	1.45468
$771$	−2.07517e11	−0.0211500
$772$	−7.20843e12	−0.730403
$773$	−3.19448e12	−0.321805	−0.160903	−	0.986970i	$-0.551440\pi$
$773$	−3.19448e12	−0.321805	−0.160903	+	0.986970i	$0.551440\pi$
$774$	−7.59739e12	−0.760904
$775$	−2.43323e13	−2.42285
$776$	7.19567e12	0.712350
$777$	−8.56563e10	−0.00843072
$778$	1.11551e13	1.09160
$779$	1.17337e11	0.0114161
$780$	7.93515e11	0.0767590
$781$	1.62452e13	1.56242
$782$	5.07044e12	0.484859
$783$	−1.16334e12	−0.110606
$784$	6.02544e12	0.569596
$785$	−2.34180e13	−2.20108
$786$	−2.64970e11	−0.0247625
$787$	6.28832e12	0.584317	0.292158	−	0.956370i	$-0.405627\pi$
$787$	6.28832e12	0.584317	0.292158	+	0.956370i	$0.405627\pi$
$788$	−5.06335e10	−0.00467811
$789$	−7.50268e11	−0.0689239
$790$	−2.64875e13	−2.41946
$791$	4.90732e12	0.445708
$792$	7.59251e12	0.685681
$793$	2.01608e13	1.81041
$794$	2.44755e13	2.18544
$795$	1.37038e12	0.121671
$796$	5.18815e12	0.458040
$797$	−4.35894e12	−0.382665	−0.191333	−	0.981525i	$-0.561281\pi$
$797$	−4.35894e12	−0.382665	−0.191333	+	0.981525i	$0.561281\pi$
$798$	1.13853e10	0.000993875 0
$799$	3.17319e12	0.275445
$800$	1.79255e13	1.54727
$801$	1.61564e13	1.38675
$802$	1.50697e13	1.28623
$803$	7.69478e12	0.653095
$804$	−4.01308e11	−0.0338708
$805$	7.37427e12	0.618924
$806$	−2.61883e13	−2.18574
$807$	3.47806e11	0.0288673
$808$	1.19370e13	0.985247
$809$	1.11674e13	0.916609	0.458305	−	0.888795i	$-0.348457\pi$
$809$	1.11674e13	0.916609	0.458305	+	0.888795i	$0.348457\pi$
$810$	2.50538e13	2.04499
$811$	−1.94879e13	−1.58187	−0.790937	−	0.611898i	$-0.790406\pi$
$811$	−1.94879e13	−1.58187	−0.790937	+	0.611898i	$0.790406\pi$
$812$	−2.79538e12	−0.225652
$813$	−3.16099e10	−0.00253756
$814$	2.31404e12	0.184740
$815$	−3.35988e13	−2.66756
$816$	9.41979e11	0.0743764
$817$	−1.36080e11	−0.0106855
$818$	−1.64151e13	−1.28190
$819$	−1.51814e13	−1.17906
$820$	−6.12220e12	−0.472874
$821$	2.05237e13	1.57657	0.788283	−	0.615312i	$-0.210970\pi$
$821$	2.05237e13	1.57657	0.788283	+	0.615312i	$0.210970\pi$
$822$	−1.32387e12	−0.101140
$823$	−1.34411e13	−1.02126	−0.510630	−	0.859800i	$-0.670588\pi$
$823$	−1.34411e13	−1.02126	−0.510630	+	0.859800i	$0.670588\pi$
$824$	−7.57385e12	−0.572327
$825$	−1.86628e12	−0.140260
$826$	1.04158e13	0.778543
$827$	1.46026e13	1.08557	0.542784	−	0.839873i	$-0.317370\pi$
$827$	1.46026e13	1.08557	0.542784	+	0.839873i	$0.317370\pi$
$828$	−2.48923e12	−0.184047
$829$	6.76121e12	0.497198	0.248599	−	0.968607i	$-0.420030\pi$
$829$	6.76121e12	0.497198	0.248599	+	0.968607i	$0.420030\pi$
$830$	3.25597e13	2.38138
$831$	7.16767e11	0.0521403
$832$	−8.28826e12	−0.599665
$833$	5.50939e12	0.396461
$834$	1.90452e12	0.136313
$835$	−3.55796e13	−2.53287
$836$	−8.57929e10	−0.00607468
$837$	2.27579e12	0.160275
$838$	−1.82236e13	−1.27654
$839$	−2.26203e13	−1.57605	−0.788026	−	0.615642i	$-0.788897\pi$
$839$	−2.26203e13	−1.57605	−0.788026	+	0.615642i	$0.788897\pi$
$840$	9.41634e11	0.0652567
$841$	−5.35870e12	−0.369384
$842$	−1.41916e13	−0.973030
$843$	−1.38996e11	−0.00947932
$844$	−9.22499e12	−0.625784
$845$	−4.18282e13	−2.82237
$846$	−5.58496e12	−0.374846
$847$	9.84293e11	0.0657127
$848$	1.84252e13	1.22358
$849$	4.67954e11	0.0309114
$850$	3.24956e13	2.13520
$851$	1.20258e12	0.0786017
$852$	−6.80095e11	−0.0442172
$853$	−1.28121e13	−0.828606	−0.414303	−	0.910139i	$-0.635975\pi$
$853$	−1.28121e13	−0.828606	−0.414303	+	0.910139i	$0.635975\pi$
$854$	−1.50928e13	−0.970978
$855$	4.50969e11	0.0288602
$856$	−1.91888e13	−1.22157
$857$	2.24166e13	1.41957	0.709783	−	0.704420i	$-0.248793\pi$
$857$	2.24166e13	1.41957	0.709783	+	0.704420i	$0.248793\pi$
$858$	−2.00863e12	−0.126534
$859$	3.20784e12	0.201022	0.100511	−	0.994936i	$-0.467952\pi$
$859$	3.20784e12	0.201022	0.100511	+	0.994936i	$0.467952\pi$
$860$	7.10015e12	0.442614
$861$	−5.73641e11	−0.0355735
$862$	2.39744e13	1.47899
$863$	7.07914e12	0.434442	0.217221	−	0.976122i	$-0.430301\pi$
$863$	7.07914e12	0.434442	0.217221	+	0.976122i	$0.430301\pi$
$864$	−1.67656e12	−0.102355
$865$	−8.22601e12	−0.499594
$866$	4.35252e12	0.262972
$867$	−3.00181e11	−0.0180425
$868$	5.46846e12	0.326984
$869$	1.87017e13	1.11248
$870$	1.94412e12	0.115050
$871$	3.43622e13	2.02302
$872$	7.01349e12	0.410781
$873$	−1.68478e13	−0.981698
$874$	−1.59846e11	−0.00926614
$875$	2.48143e13	1.43109
$876$	−3.22136e11	−0.0184829
$877$	1.24073e13	0.708239	0.354120	−	0.935200i	$-0.384781\pi$
$877$	1.24073e13	0.708239	0.354120	+	0.935200i	$0.384781\pi$
$878$	3.68727e13	2.09401
$879$	−8.17362e11	−0.0461811
$880$	−3.70106e13	−2.08043
$881$	−1.98848e13	−1.11206	−0.556031	−	0.831162i	$-0.687676\pi$
$881$	−1.98848e13	−1.11206	−0.556031	+	0.831162i	$0.687676\pi$
$882$	−9.69679e12	−0.539534
$883$	−1.64716e13	−0.911830	−0.455915	−	0.890023i	$-0.650688\pi$
$883$	−1.64716e13	−0.911830	−0.455915	+	0.890023i	$0.650688\pi$
$884$	9.75535e12	0.537288
$885$	−2.02056e12	−0.110720
$886$	−2.08127e13	−1.13469
$887$	−2.57254e12	−0.139542	−0.0697710	−	0.997563i	$-0.522227\pi$
$887$	−2.57254e12	−0.139542	−0.0697710	+	0.997563i	$0.522227\pi$
$888$	1.53560e11	0.00828743
$889$	1.28735e13	0.691253
$890$	−5.41320e13	−2.89200
$891$	−1.76894e13	−0.940295
$892$	−2.60352e12	−0.137695
$893$	−1.00035e11	−0.00526403
$894$	7.68532e10	0.00402386
$895$	3.92963e12	0.204714
$896$	1.66192e13	0.861437
$897$	−1.04386e12	−0.0538367
$898$	6.59720e12	0.338545
$899$	−1.78966e13	−0.913802
$900$	−1.59531e13	−0.810499
$901$	1.68472e13	0.851659
$902$	1.54972e13	0.779512
$903$	6.65274e11	0.0332971
$904$	−8.79758e12	−0.438132
$905$	6.91928e13	3.42880
$906$	9.10856e11	0.0449131
$907$	−2.18450e13	−1.07181	−0.535907	−	0.844277i	$-0.680030\pi$
$907$	−2.18450e13	−1.07181	−0.535907	+	0.844277i	$0.680030\pi$
$908$	1.40531e13	0.686097
$909$	−2.79491e13	−1.35778
$910$	5.08652e13	2.45886
$911$	3.24827e12	0.156250	0.0781250	−	0.996944i	$-0.475107\pi$
$911$	3.24827e12	0.156250	0.0781250	+	0.996944i	$0.475107\pi$
$912$	−2.96959e10	−0.00142141
$913$	−2.29890e13	−1.09497
$914$	−3.60579e12	−0.170900
$915$	2.92784e12	0.138087
$916$	−1.46513e13	−0.687615
$917$	−4.73758e12	−0.221256
$918$	−3.03929e12	−0.141247
$919$	−3.85651e13	−1.78351	−0.891753	−	0.452523i	$-0.850524\pi$
$919$	−3.85651e13	−1.78351	−0.891753	+	0.452523i	$0.850524\pi$
$920$	−1.32202e13	−0.608405
$921$	1.18283e12	0.0541696
$922$	−9.67224e12	−0.440796
$923$	5.82334e13	2.64098
$924$	4.19428e11	0.0189293
$925$	7.70714e12	0.346143
$926$	−4.11901e13	−1.84096
$927$	1.77332e13	0.788731
$928$	1.31843e13	0.583569
$929$	−3.50045e13	−1.54189	−0.770944	−	0.636903i	$-0.780215\pi$
$929$	−3.50045e13	−1.54189	−0.770944	+	0.636903i	$0.780215\pi$
$930$	−3.80319e12	−0.166715
$931$	−1.73683e11	−0.00757678
$932$	−8.86693e12	−0.384947
$933$	1.60662e12	0.0694140
$934$	−1.03910e13	−0.446785
$935$	−3.38408e13	−1.44806
$936$	2.72165e13	1.15902
$937$	7.36793e12	0.312261	0.156130	−	0.987736i	$-0.450098\pi$
$937$	7.36793e12	0.312261	0.156130	+	0.987736i	$0.450098\pi$
$938$	−2.57243e13	−1.08500
$939$	1.43986e12	0.0604399
$940$	5.21943e12	0.218046
$941$	−2.82173e13	−1.17317	−0.586586	−	0.809887i	$-0.699528\pi$
$941$	−2.82173e13	−1.17317	−0.586586	+	0.809887i	$0.699528\pi$
$942$	−2.48163e12	−0.102685
$943$	8.05371e12	0.331660
$944$	−2.71672e13	−1.11345
$945$	−4.42023e12	−0.180303
$946$	−1.79727e13	−0.729629
$947$	−1.59713e13	−0.645307	−0.322653	−	0.946517i	$-0.604575\pi$
$947$	−1.59713e13	−0.645307	−0.322653	+	0.946517i	$0.604575\pi$
$948$	−7.82931e11	−0.0314837
$949$	2.75831e13	1.10394
$950$	−1.02442e12	−0.0408059
$951$	1.69173e11	0.00670685
$952$	1.15763e13	0.456776
$953$	−4.81575e13	−1.89124	−0.945619	−	0.325276i	$-0.894543\pi$
$953$	−4.81575e13	−1.89124	−0.945619	+	0.325276i	$0.894543\pi$
$954$	−2.96518e13	−1.15900
$955$	1.74485e13	0.678801
$956$	−1.66348e13	−0.644106
$957$	−1.37266e12	−0.0529005
$958$	5.00006e13	1.91792
$959$	−2.36704e13	−0.903697
$960$	−1.20366e12	−0.0457386
$961$	8.57059e12	0.324157
$962$	8.29500e12	0.312269
$963$	4.49283e13	1.68346
$964$	1.39417e12	0.0519960
$965$	8.96363e13	3.32745
$966$	7.81459e11	0.0288742
$967$	−1.91510e13	−0.704323	−0.352161	−	0.935939i	$-0.614553\pi$
$967$	−1.91510e13	−0.704323	−0.352161	+	0.935939i	$0.614553\pi$
$968$	−1.76459e12	−0.0645958
$969$	−2.71525e10	−0.000989357 0
$970$	5.64482e13	2.04728
$971$	3.39138e13	1.22430	0.612152	−	0.790740i	$-0.290304\pi$
$971$	3.39138e13	1.22430	0.612152	+	0.790740i	$0.290304\pi$
$972$	2.23994e12	0.0804893
$973$	3.40523e13	1.21798
$974$	−2.87570e13	−1.02383
$975$	−6.68995e12	−0.237084
$976$	3.93660e13	1.38866
$977$	1.56963e13	0.551153	0.275577	−	0.961279i	$-0.411131\pi$
$977$	1.56963e13	0.551153	0.275577	+	0.961279i	$0.411131\pi$
$978$	−3.56050e12	−0.124447
$979$	3.82203e13	1.32975
$980$	9.06215e12	0.313844
$981$	−1.64212e13	−0.566102
$982$	−3.87118e12	−0.132844
$983$	−3.21169e13	−1.09709	−0.548546	−	0.836120i	$-0.684819\pi$
$983$	−3.21169e13	−1.09709	−0.548546	+	0.836120i	$0.684819\pi$
$984$	1.02839e12	0.0349689
$985$	6.29624e11	0.0213117
$986$	2.39007e13	0.805314
$987$	4.89053e11	0.0164032
$988$	−3.07537e11	−0.0102681
$989$	−9.34021e12	−0.310437
$990$	5.95613e13	1.97063
$991$	−1.77507e13	−0.584633	−0.292316	−	0.956322i	$-0.594426\pi$
$991$	−1.77507e13	−0.584633	−0.292316	+	0.956322i	$0.594426\pi$
$992$	−2.57918e13	−0.845629
$993$	2.51343e12	0.0820344
$994$	−4.35948e13	−1.41643
$995$	−6.45143e13	−2.08666
$996$	9.62416e11	0.0309882
$997$	2.10154e12	0.0673613	0.0336806	−	0.999433i	$-0.489277\pi$
$997$	2.10154e12	0.0673613	0.0336806	+	0.999433i	$0.489277\pi$
$998$	−6.42894e12	−0.205141
$999$	−7.20844e11	−0.0228979

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.10.a.b.1.4	✓	14
3.2	odd	2		333.10.a.d.1.11		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.10.a.b.1.4	✓	14	1.1	even	1	trivial
333.10.a.d.1.11		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)

\(f(q)\)	\(=\)	\(q-26.6469 q^{2} +9.79428 q^{3} +198.056 q^{4} -2462.81 q^{5} -260.987 q^{6} -4666.37 q^{7} +8365.63 q^{8} -19587.1 q^{9} +O(q^{10})\)	\(q-26.6469 q^{2} +9.79428 q^{3} +198.056 q^{4} -2462.81 q^{5} -260.987 q^{6} -4666.37 q^{7} +8365.63 q^{8} -19587.1 q^{9} +65626.2 q^{10} -46335.9 q^{11} +1939.82 q^{12} -166098. q^{13} +124344. q^{14} -24121.5 q^{15} -324322. q^{16} -296546. q^{17} +521934. q^{18} +9348.59 q^{19} -487775. q^{20} -45703.8 q^{21} +1.23471e6 q^{22} +641664. q^{23} +81935.3 q^{24} +4.11232e6 q^{25} +4.42598e6 q^{26} -384622. q^{27} -924203. q^{28} +3.02464e6 q^{29} +642762. q^{30} -5.91694e6 q^{31} +4.35898e6 q^{32} -453827. q^{33} +7.90201e6 q^{34} +1.14924e7 q^{35} -3.87934e6 q^{36} +1.87416e6 q^{37} -249111. q^{38} -1.62681e6 q^{39} -2.06030e7 q^{40} +1.25513e7 q^{41} +1.21786e6 q^{42} -1.45562e7 q^{43} -9.17710e6 q^{44} +4.82393e7 q^{45} -1.70984e7 q^{46} -1.07005e7 q^{47} -3.17651e6 q^{48} -1.85786e7 q^{49} -1.09580e8 q^{50} -2.90445e6 q^{51} -3.28966e7 q^{52} -5.68114e7 q^{53} +1.02490e7 q^{54} +1.14117e8 q^{55} -3.90372e7 q^{56} +91562.8 q^{57} -8.05972e7 q^{58} +8.37659e7 q^{59} -4.77740e6 q^{60} -1.21379e8 q^{61} +1.57668e8 q^{62} +9.14006e7 q^{63} +4.98999e7 q^{64} +4.09067e8 q^{65} +1.20931e7 q^{66} -2.06880e8 q^{67} -5.87326e7 q^{68} +6.28464e6 q^{69} -3.06237e8 q^{70} -3.50597e8 q^{71} -1.63858e8 q^{72} -1.66065e8 q^{73} -4.99405e7 q^{74} +4.02772e7 q^{75} +1.85154e6 q^{76} +2.16221e8 q^{77} +4.33493e7 q^{78} -4.03611e8 q^{79} +7.98745e8 q^{80} +3.81765e8 q^{81} -3.34453e8 q^{82} +4.96138e8 q^{83} -9.05191e6 q^{84} +7.30336e8 q^{85} +3.87878e8 q^{86} +2.96242e7 q^{87} -3.87629e8 q^{88} -8.24852e8 q^{89} -1.28543e9 q^{90} +7.75074e8 q^{91} +1.27085e8 q^{92} -5.79522e7 q^{93} +2.85135e8 q^{94} -2.30238e7 q^{95} +4.26931e7 q^{96} +8.60147e8 q^{97} +4.95060e8 q^{98} +9.07584e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 48 q^{2} + 397 q^{3} + 3498 q^{4} + 2841 q^{5} + 3375 q^{6} + 6632 q^{7} + 41046 q^{8} + 101917 q^{9}+O(q^{10}) \) 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

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Database

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