LMFDB - Embedded newform 37.10.a.b.1.6

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			1.6
Root			$-8.01135$ 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)

$f(q)$	$=$	$q-5.01135 q^{2} -80.7499 q^{3} -486.886 q^{4} +557.130 q^{5} +404.666 q^{6} -7760.08 q^{7} +5005.76 q^{8} -13162.4 q^{9} +O(q^{10})$	\(q-5.01135 q^{2} -80.7499 q^{3} -486.886 q^{4} +557.130 q^{5} +404.666 q^{6} -7760.08 q^{7} +5005.76 q^{8} -13162.4 q^{9} -2791.97 q^{10} -41662.1 q^{11} +39316.0 q^{12} -13831.9 q^{13} +38888.5 q^{14} -44988.2 q^{15} +224200. q^{16} +274297. q^{17} +65961.6 q^{18} +226307. q^{19} -271259. q^{20} +626626. q^{21} +208783. q^{22} +392869. q^{23} -404215. q^{24} -1.64273e6 q^{25} +69316.5 q^{26} +2.65227e6 q^{27} +3.77828e6 q^{28} +2.38976e6 q^{29} +225451. q^{30} +9.93724e6 q^{31} -3.68650e6 q^{32} +3.36421e6 q^{33} -1.37460e6 q^{34} -4.32337e6 q^{35} +6.40862e6 q^{36} +1.87416e6 q^{37} -1.13410e6 q^{38} +1.11693e6 q^{39} +2.78886e6 q^{40} -2.24960e7 q^{41} -3.14024e6 q^{42} +1.75526e7 q^{43} +2.02847e7 q^{44} -7.33319e6 q^{45} -1.96880e6 q^{46} -1.97393e7 q^{47} -1.81042e7 q^{48} +1.98653e7 q^{49} +8.23229e6 q^{50} -2.21495e7 q^{51} +6.73457e6 q^{52} -6.18106e7 q^{53} -1.32914e7 q^{54} -2.32112e7 q^{55} -3.88452e7 q^{56} -1.82743e7 q^{57} -1.19759e7 q^{58} -5.98396e7 q^{59} +2.19041e7 q^{60} +4.13428e7 q^{61} -4.97989e7 q^{62} +1.02142e8 q^{63} -9.63162e7 q^{64} -7.70618e6 q^{65} -1.68592e7 q^{66} -7.07839e6 q^{67} -1.33552e8 q^{68} -3.17241e7 q^{69} +2.16659e7 q^{70} +3.19253e8 q^{71} -6.58881e7 q^{72} -2.31570e8 q^{73} -9.39207e6 q^{74} +1.32650e8 q^{75} -1.10186e8 q^{76} +3.23301e8 q^{77} -5.59731e6 q^{78} +4.62203e8 q^{79} +1.24909e8 q^{80} +4.49060e7 q^{81} +1.12735e8 q^{82} +2.34443e8 q^{83} -3.05096e8 q^{84} +1.52819e8 q^{85} -8.79623e7 q^{86} -1.92973e8 q^{87} -2.08551e8 q^{88} -1.81605e8 q^{89} +3.67492e7 q^{90} +1.07337e8 q^{91} -1.91282e8 q^{92} -8.02432e8 q^{93} +9.89203e7 q^{94} +1.26083e8 q^{95} +2.97684e8 q^{96} +1.13352e9 q^{97} -9.95518e7 q^{98} +5.48375e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.01135	−0.221472	−0.110736	−	0.993850i	$-0.535321\pi$
$2$	−5.01135	−0.221472	−0.110736	+	0.993850i	$0.535321\pi$
$3$	−80.7499	−0.575568	−0.287784	−	0.957695i	$-0.592919\pi$
$3$	−80.7499	−0.575568	−0.287784	+	0.957695i	$0.592919\pi$
$4$	−486.886	−0.950950
$5$	557.130	0.398650	0.199325	−	0.979933i	$-0.436125\pi$
$5$	557.130	0.398650	0.199325	+	0.979933i	$0.436125\pi$
$6$	404.666	0.127472
$7$	−7760.08	−1.22159	−0.610795	−	0.791789i	$-0.709150\pi$
$7$	−7760.08	−1.22159	−0.610795	+	0.791789i	$0.709150\pi$
$8$	5005.76	0.432081
$9$	−13162.4	−0.668722
$10$	−2791.97	−0.0882898
$11$	−41662.1	−0.857974	−0.428987	−	0.903311i	$-0.641129\pi$
$11$	−41662.1	−0.857974	−0.428987	+	0.903311i	$0.641129\pi$
$12$	39316.0	0.547336
$13$	−13831.9	−0.134319	−0.0671595	−	0.997742i	$-0.521394\pi$
$13$	−13831.9	−0.134319	−0.0671595	+	0.997742i	$0.521394\pi$
$14$	38888.5	0.270548
$15$	−44988.2	−0.229450
$16$	224200.	0.855256
$17$	274297.	0.796528	0.398264	−	0.917271i	$-0.369613\pi$
$17$	274297.	0.796528	0.398264	+	0.917271i	$0.369613\pi$
$18$	65961.6	0.148103
$19$	226307.	0.398389	0.199194	−	0.979960i	$-0.436167\pi$
$19$	226307.	0.398389	0.199194	+	0.979960i	$0.436167\pi$
$20$	−271259.	−0.379096
$21$	626626.	0.703108
$22$	208783.	0.190017
$23$	392869.	0.292733	0.146367	−	0.989230i	$-0.453242\pi$
$23$	392869.	0.292733	0.146367	+	0.989230i	$0.453242\pi$
$24$	−404215.	−0.248692
$25$	−1.64273e6	−0.841078
$26$	69316.5	0.0297479
$27$	2.65227e6	0.960463
$28$	3.77828e6	1.16167
$29$	2.38976e6	0.627428	0.313714	−	0.949518i	$-0.398427\pi$
$29$	2.38976e6	0.627428	0.313714	+	0.949518i	$0.398427\pi$
$30$	225451.	0.0508168
$31$	9.93724e6	1.93258	0.966292	−	0.257450i	$-0.0828823\pi$
$31$	9.93724e6	1.93258	0.966292	+	0.257450i	$0.0828823\pi$
$32$	−3.68650e6	−0.621497
$33$	3.36421e6	0.493822
$34$	−1.37460e6	−0.176409
$35$	−4.32337e6	−0.486986
$36$	6.40862e6	0.635921
$37$	1.87416e6	0.164399
$37$	1.87416e6	0.164399
$38$	−1.13410e6	−0.0882321
$39$	1.11693e6	0.0773097
$40$	2.78886e6	0.172249
$41$	−2.24960e7	−1.24331	−0.621653	−	0.783293i	$-0.713539\pi$
$41$	−2.24960e7	−1.24331	−0.621653	+	0.783293i	$0.713539\pi$
$42$	−3.14024e6	−0.155719
$43$	1.75526e7	0.782951	0.391475	−	0.920189i	$-0.371965\pi$
$43$	1.75526e7	0.782951	0.391475	+	0.920189i	$0.371965\pi$
$44$	2.02847e7	0.815890
$45$	−7.33319e6	−0.266586
$46$	−1.96880e6	−0.0648323
$47$	−1.97393e7	−0.590052	−0.295026	−	0.955489i	$-0.595328\pi$
$47$	−1.97393e7	−0.590052	−0.295026	+	0.955489i	$0.595328\pi$
$48$	−1.81042e7	−0.492258
$49$	1.98653e7	0.492280
$50$	8.23229e6	0.186276
$51$	−2.21495e7	−0.458456
$52$	6.73457e6	0.127731
$53$	−6.18106e7	−1.07602	−0.538011	−	0.842938i	$-0.680824\pi$
$53$	−6.18106e7	−1.07602	−0.538011	+	0.842938i	$0.680824\pi$
$54$	−1.32914e7	−0.212716
$55$	−2.32112e7	−0.342031
$56$	−3.88452e7	−0.527826
$57$	−1.82743e7	−0.229300
$58$	−1.19759e7	−0.138958
$59$	−5.98396e7	−0.642917	−0.321458	−	0.946924i	$-0.604173\pi$
$59$	−5.98396e7	−0.642917	−0.321458	+	0.946924i	$0.604173\pi$
$60$	2.19041e7	0.218195
$61$	4.13428e7	0.382310	0.191155	−	0.981560i	$-0.438777\pi$
$61$	4.13428e7	0.382310	0.191155	+	0.981560i	$0.438777\pi$
$62$	−4.97989e7	−0.428014
$63$	1.02142e8	0.816903
$64$	−9.63162e7	−0.717612
$65$	−7.70618e6	−0.0535462
$66$	−1.68592e7	−0.109368
$67$	−7.07839e6	−0.0429139	−0.0214569	−	0.999770i	$-0.506830\pi$
$67$	−7.07839e6	−0.0429139	−0.0214569	+	0.999770i	$0.506830\pi$
$68$	−1.33552e8	−0.757458
$69$	−3.17241e7	−0.168488
$70$	2.16659e7	0.107854
$71$	3.19253e8	1.49098	0.745491	−	0.666516i	$-0.232215\pi$
$71$	3.19253e8	1.49098	0.745491	+	0.666516i	$0.232215\pi$
$72$	−6.58881e7	−0.288942
$73$	−2.31570e8	−0.954398	−0.477199	−	0.878795i	$-0.658348\pi$
$73$	−2.31570e8	−0.954398	−0.477199	+	0.878795i	$0.658348\pi$
$74$	−9.39207e6	−0.0364098
$75$	1.32650e8	0.484098
$76$	−1.10186e8	−0.378848
$77$	3.23301e8	1.04809
$78$	−5.59731e6	−0.0171220
$79$	4.62203e8	1.33509	0.667546	−	0.744569i	$-0.267345\pi$
$79$	4.62203e8	1.33509	0.667546	+	0.744569i	$0.267345\pi$
$80$	1.24909e8	0.340948
$81$	4.49060e7	0.115910
$82$	1.12735e8	0.275358
$83$	2.34443e8	0.542232	0.271116	−	0.962547i	$-0.412607\pi$
$83$	2.34443e8	0.542232	0.271116	+	0.962547i	$0.412607\pi$
$84$	−3.05096e8	−0.668620
$85$	1.52819e8	0.317536
$86$	−8.79623e7	−0.173402
$87$	−1.92973e8	−0.361127
$88$	−2.08551e8	−0.370715
$89$	−1.81605e8	−0.306812	−0.153406	−	0.988163i	$-0.549024\pi$
$89$	−1.81605e8	−0.306812	−0.153406	+	0.988163i	$0.549024\pi$
$90$	3.67492e7	0.0590413
$91$	1.07337e8	0.164083
$92$	−1.91282e8	−0.278375
$93$	−8.02432e8	−1.11233
$94$	9.89203e7	0.130680
$95$	1.26083e8	0.158818
$96$	2.97684e8	0.357714
$97$	1.13352e9	1.30004	0.650019	−	0.759918i	$-0.274761\pi$
$97$	1.13352e9	1.30004	0.650019	+	0.759918i	$0.274761\pi$
$98$	−9.95518e7	−0.109026
$99$	5.48375e8	0.573746
$100$	7.99824e8	0.799824
$101$	1.46930e9	1.40496	0.702481	−	0.711703i	$-0.252076\pi$
$101$	1.46930e9	1.40496	0.702481	+	0.711703i	$0.252076\pi$
$102$	1.10999e8	0.101535
$103$	4.13686e8	0.362162	0.181081	−	0.983468i	$-0.442040\pi$
$103$	4.13686e8	0.362162	0.181081	+	0.983468i	$0.442040\pi$
$104$	−6.92393e7	−0.0580367
$105$	3.49112e8	0.280294
$106$	3.09754e8	0.238309
$107$	6.05593e8	0.446636	0.223318	−	0.974746i	$-0.428311\pi$
$107$	6.05593e8	0.446636	0.223318	+	0.974746i	$0.428311\pi$
$108$	−1.29135e9	−0.913352
$109$	−2.65476e9	−1.80138	−0.900692	−	0.434457i	$-0.856940\pi$
$109$	−2.65476e9	−1.80138	−0.900692	+	0.434457i	$0.856940\pi$
$110$	1.16319e8	0.0757504
$111$	−1.51338e8	−0.0946228
$112$	−1.73981e9	−1.04477
$113$	−1.99867e8	−0.115316	−0.0576578	−	0.998336i	$-0.518363\pi$
$113$	−1.99867e8	−0.115316	−0.0576578	+	0.998336i	$0.518363\pi$
$114$	9.15788e7	0.0507836
$115$	2.18879e8	0.116698
$116$	−1.16354e9	−0.596653
$117$	1.82062e8	0.0898220
$118$	2.99877e8	0.142388
$119$	−2.12857e9	−0.973030
$120$	−2.25200e8	−0.0991410
$121$	−6.22216e8	−0.263881
$122$	−2.07183e8	−0.0846710
$123$	1.81655e9	0.715607
$124$	−4.83831e9	−1.83779
$125$	−2.00336e9	−0.733945
$126$	−5.11867e8	−0.180921
$127$	6.46022e8	0.220359	0.110179	−	0.993912i	$-0.464857\pi$
$127$	6.46022e8	0.220359	0.110179	+	0.993912i	$0.464857\pi$
$128$	2.37016e9	0.780428
$129$	−1.41737e9	−0.450641
$130$	3.86183e7	0.0118590
$131$	−8.52345e8	−0.252869	−0.126434	−	0.991975i	$-0.540353\pi$
$131$	−8.52345e8	−0.252869	−0.126434	+	0.991975i	$0.540353\pi$
$132$	−1.63799e9	−0.469600
$133$	−1.75616e9	−0.486668
$134$	3.54723e7	0.00950423
$135$	1.47766e9	0.382888
$136$	1.37307e9	0.344165
$137$	6.14685e9	1.49077	0.745384	−	0.666635i	$-0.232266\pi$
$137$	6.14685e9	1.49077	0.745384	+	0.666635i	$0.232266\pi$
$138$	1.58981e8	0.0373154
$139$	−3.44217e9	−0.782106	−0.391053	−	0.920368i	$-0.627889\pi$
$139$	−3.44217e9	−0.782106	−0.391053	+	0.920368i	$0.627889\pi$
$140$	2.10499e9	0.463100
$141$	1.59394e9	0.339615
$142$	−1.59989e9	−0.330211
$143$	5.76267e8	0.115242
$144$	−2.95102e9	−0.571928
$145$	1.33141e9	0.250124
$146$	1.16048e9	0.211373
$147$	−1.60412e9	−0.283341
$148$	−9.12504e8	−0.156335
$149$	1.15781e10	1.92441	0.962206	−	0.272321i	$-0.0877913\pi$
$149$	1.15781e10	1.92441	0.962206	+	0.272321i	$0.0877913\pi$
$150$	−6.64757e8	−0.107214
$151$	4.98356e9	0.780087	0.390044	−	0.920796i	$-0.372460\pi$
$151$	4.98356e9	0.780087	0.390044	+	0.920796i	$0.372460\pi$
$152$	1.13284e9	0.172136
$153$	−3.61042e9	−0.532655
$154$	−1.62018e9	−0.232123
$155$	5.53633e9	0.770424
$156$	−5.43816e8	−0.0735177
$157$	−2.52347e9	−0.331474	−0.165737	−	0.986170i	$-0.553000\pi$
$157$	−2.52347e9	−0.331474	−0.165737	+	0.986170i	$0.553000\pi$
$158$	−2.31626e9	−0.295686
$159$	4.99120e9	0.619324
$160$	−2.05386e9	−0.247759
$161$	−3.04869e9	−0.357600
$162$	−2.25039e8	−0.0256709
$163$	1.21081e10	1.34348	0.671742	−	0.740785i	$-0.265546\pi$
$163$	1.21081e10	1.34348	0.671742	+	0.740785i	$0.265546\pi$
$164$	1.09530e10	1.18232
$165$	1.87430e9	0.196862
$166$	−1.17487e9	−0.120089
$167$	−1.42256e10	−1.41529	−0.707647	−	0.706566i	$-0.750243\pi$
$167$	−1.42256e10	−1.41529	−0.707647	+	0.706566i	$0.750243\pi$
$168$	3.13674e9	0.303800
$169$	−1.04132e10	−0.981958
$170$	−7.65829e8	−0.0703253
$171$	−2.97876e9	−0.266411
$172$	−8.54614e9	−0.744547
$173$	1.07034e10	0.908477	0.454238	−	0.890880i	$-0.349911\pi$
$173$	1.07034e10	0.908477	0.454238	+	0.890880i	$0.349911\pi$
$174$	9.67055e8	0.0799797
$175$	1.27477e10	1.02745
$176$	−9.34065e9	−0.733787
$177$	4.83205e9	0.370042
$178$	9.10085e8	0.0679504
$179$	4.96832e9	0.361719	0.180859	−	0.983509i	$-0.442112\pi$
$179$	4.96832e9	0.361719	0.180859	+	0.983509i	$0.442112\pi$
$180$	3.57043e9	0.253510
$181$	1.41677e10	0.981173	0.490587	−	0.871392i	$-0.336783\pi$
$181$	1.41677e10	0.981173	0.490587	+	0.871392i	$0.336783\pi$
$182$	−5.37902e8	−0.0363398
$183$	−3.33843e9	−0.220045
$184$	1.96661e9	0.126485
$185$	1.04415e9	0.0655376
$186$	4.02126e9	0.246351
$187$	−1.14278e10	−0.683400
$188$	9.61078e9	0.561110
$189$	−2.05818e10	−1.17329
$190$	−6.31843e8	−0.0351737
$191$	2.48156e9	0.134920	0.0674598	−	0.997722i	$-0.478511\pi$
$191$	2.48156e9	0.134920	0.0674598	+	0.997722i	$0.478511\pi$
$192$	7.77753e9	0.413034
$193$	−1.76304e9	−0.0914648	−0.0457324	−	0.998954i	$-0.514562\pi$
$193$	−1.76304e9	−0.0914648	−0.0457324	+	0.998954i	$0.514562\pi$
$194$	−5.68046e9	−0.287922
$195$	6.22273e8	0.0308195
$196$	−9.67214e9	−0.468134
$197$	−2.50390e10	−1.18446	−0.592228	−	0.805771i	$-0.701751\pi$
$197$	−2.50390e10	−1.18446	−0.592228	+	0.805771i	$0.701751\pi$
$198$	−2.74810e9	−0.127069
$199$	2.88737e9	0.130516	0.0652579	−	0.997868i	$-0.479213\pi$
$199$	2.88737e9	0.130516	0.0652579	+	0.997868i	$0.479213\pi$
$200$	−8.22313e9	−0.363414
$201$	5.71579e8	0.0246999
$202$	−7.36317e9	−0.311160
$203$	−1.85448e10	−0.766459
$204$	1.07843e10	0.435969
$205$	−1.25332e10	−0.495644
$206$	−2.07312e9	−0.0802089
$207$	−5.17111e9	−0.195757
$208$	−3.10112e9	−0.114877
$209$	−9.42844e9	−0.341807
$210$	−1.74952e9	−0.0620773
$211$	−1.82058e10	−0.632323	−0.316162	−	0.948705i	$-0.602394\pi$
$211$	−1.82058e10	−0.632323	−0.316162	+	0.948705i	$0.602394\pi$
$212$	3.00947e10	1.02324
$213$	−2.57797e10	−0.858161
$214$	−3.03484e9	−0.0989176
$215$	9.77910e9	0.312123
$216$	1.32766e10	0.414998
$217$	−7.71138e10	−2.36082
$218$	1.33039e10	0.398957
$219$	1.86993e10	0.549321
$220$	1.13012e10	0.325254
$221$	−3.79406e9	−0.106989
$222$	7.58409e8	0.0209563
$223$	4.25562e10	1.15237	0.576184	−	0.817320i	$-0.304541\pi$
$223$	4.25562e10	1.15237	0.576184	+	0.817320i	$0.304541\pi$
$224$	2.86075e10	0.759214
$225$	2.16224e10	0.562447
$226$	1.00160e9	0.0255392
$227$	−2.20447e10	−0.551047	−0.275524	−	0.961294i	$-0.588851\pi$
$227$	−2.20447e10	−0.551047	−0.275524	+	0.961294i	$0.588851\pi$
$228$	8.89751e9	0.218053
$229$	−2.32919e10	−0.559687	−0.279844	−	0.960046i	$-0.590283\pi$
$229$	−2.32919e10	−0.559687	−0.279844	+	0.960046i	$0.590283\pi$
$230$	−1.09688e9	−0.0258454
$231$	−2.61066e10	−0.603248
$232$	1.19626e10	0.271100
$233$	1.08068e10	0.240212	0.120106	−	0.992761i	$-0.461677\pi$
$233$	1.08068e10	0.240212	0.120106	+	0.992761i	$0.461677\pi$
$234$	−9.12375e8	−0.0198931
$235$	−1.09973e10	−0.235224
$236$	2.91351e10	0.611382
$237$	−3.73229e10	−0.768436
$238$	1.06670e10	0.215499
$239$	7.79226e10	1.54480	0.772401	−	0.635135i	$-0.219055\pi$
$239$	7.79226e10	1.54480	0.772401	+	0.635135i	$0.219055\pi$
$240$	−1.00864e10	−0.196238
$241$	9.04959e10	1.72803	0.864017	−	0.503463i	$-0.167941\pi$
$241$	9.04959e10	1.72803	0.864017	+	0.503463i	$0.167941\pi$
$242$	3.11814e9	0.0584422
$243$	−5.58307e10	−1.02718
$244$	−2.01292e10	−0.363558
$245$	1.10675e10	0.196247
$246$	−9.10337e9	−0.158487
$247$	−3.13026e9	−0.0535112
$248$	4.97435e10	0.835033
$249$	−1.89312e10	−0.312091
$250$	1.00395e10	0.162549
$251$	2.33943e9	0.0372030	0.0186015	−	0.999827i	$-0.494079\pi$
$251$	2.33943e9	0.0372030	0.0186015	+	0.999827i	$0.494079\pi$
$252$	−4.97314e10	−0.776834
$253$	−1.63677e10	−0.251158
$254$	−3.23744e9	−0.0488033
$255$	−1.23401e10	−0.182763
$256$	3.74362e10	0.544769
$257$	7.48255e10	1.06992	0.534959	−	0.844878i	$-0.320327\pi$
$257$	7.48255e10	1.06992	0.534959	+	0.844878i	$0.320327\pi$
$258$	7.10295e9	0.0998045
$259$	−1.45436e10	−0.200828
$260$	3.75203e9	0.0509198
$261$	−3.14551e10	−0.419575
$262$	4.27140e9	0.0560034
$263$	1.40183e11	1.80673	0.903367	−	0.428868i	$-0.141087\pi$
$263$	1.40183e11	1.80673	0.903367	+	0.428868i	$0.141087\pi$
$264$	1.68405e10	0.213371
$265$	−3.44365e10	−0.428956
$266$	8.80074e9	0.107783
$267$	1.46646e10	0.176591
$268$	3.44637e9	0.0408090
$269$	−6.21510e10	−0.723707	−0.361854	−	0.932235i	$-0.617856\pi$
$269$	−6.21510e10	−0.723707	−0.361854	+	0.932235i	$0.617856\pi$
$270$	−7.40505e9	−0.0847991
$271$	−3.11198e10	−0.350489	−0.175245	−	0.984525i	$-0.556072\pi$
$271$	−3.11198e10	−0.350489	−0.175245	+	0.984525i	$0.556072\pi$
$272$	6.14975e10	0.681235
$273$	−8.66745e9	−0.0944407
$274$	−3.08040e10	−0.330164
$275$	6.84397e10	0.721623
$276$	1.54460e10	0.160224
$277$	1.94755e10	0.198761	0.0993803	−	0.995050i	$-0.468314\pi$
$277$	1.94755e10	0.198761	0.0993803	+	0.995050i	$0.468314\pi$
$278$	1.72499e10	0.173215
$279$	−1.30798e11	−1.29236
$280$	−2.16418e10	−0.210418
$281$	1.32347e11	1.26630	0.633148	−	0.774031i	$-0.281762\pi$
$281$	1.32347e11	1.26630	0.633148	+	0.774031i	$0.281762\pi$
$282$	−7.98781e9	−0.0752154
$283$	−1.07006e11	−0.991672	−0.495836	−	0.868416i	$-0.665138\pi$
$283$	−1.07006e11	−0.991672	−0.495836	+	0.868416i	$0.665138\pi$
$284$	−1.55440e11	−1.41785
$285$	−1.01812e10	−0.0914103
$286$	−2.88787e9	−0.0255230
$287$	1.74571e11	1.51881
$288$	4.85233e10	0.415608
$289$	−4.33490e10	−0.365543
$290$	−6.67215e9	−0.0553955
$291$	−9.15316e10	−0.748260
$292$	1.12748e11	0.907585
$293$	1.50742e11	1.19490	0.597449	−	0.801907i	$-0.296181\pi$
$293$	1.50742e11	1.19490	0.597449	+	0.801907i	$0.296181\pi$
$294$	8.03881e9	0.0627521
$295$	−3.33384e10	−0.256299
$296$	9.38161e9	0.0710337
$297$	−1.10499e11	−0.824052
$298$	−5.80217e10	−0.426204
$299$	−5.43413e9	−0.0393197
$300$	−6.45857e10	−0.460353
$301$	−1.36210e11	−0.956444
$302$	−2.49743e10	−0.172768
$303$	−1.18646e11	−0.808651
$304$	5.07381e10	0.340725
$305$	2.30333e10	0.152408
$306$	1.80931e10	0.117968
$307$	8.00511e9	0.0514333	0.0257167	−	0.999669i	$-0.491813\pi$
$307$	8.00511e9	0.0514333	0.0257167	+	0.999669i	$0.491813\pi$
$308$	−1.57411e11	−0.996683
$309$	−3.34051e10	−0.208449
$310$	−2.77445e10	−0.170627
$311$	−3.02914e11	−1.83611	−0.918054	−	0.396455i	$-0.870240\pi$
$311$	−3.02914e11	−1.83611	−0.918054	+	0.396455i	$0.870240\pi$
$312$	5.59107e9	0.0334041
$313$	1.49790e11	0.882134	0.441067	−	0.897474i	$-0.354600\pi$
$313$	1.49790e11	0.882134	0.441067	+	0.897474i	$0.354600\pi$
$314$	1.26460e10	0.0734124
$315$	5.69062e10	0.325658
$316$	−2.25040e11	−1.26961
$317$	1.85636e11	1.03251	0.516256	−	0.856434i	$-0.327325\pi$
$317$	1.85636e11	1.03251	0.516256	+	0.856434i	$0.327325\pi$
$318$	−2.50126e10	−0.137163
$319$	−9.95626e10	−0.538317
$320$	−5.36606e10	−0.286076
$321$	−4.89016e10	−0.257070
$322$	1.52781e10	0.0791985
$323$	6.20754e10	0.317328
$324$	−2.18641e10	−0.110225
$325$	2.27221e10	0.112973
$326$	−6.06780e10	−0.297545
$327$	2.14372e11	1.03682
$328$	−1.12610e11	−0.537209
$329$	1.53178e11	0.720802
$330$	−9.39278e9	−0.0435995
$331$	3.51664e11	1.61028	0.805141	−	0.593083i	$-0.202089\pi$
$331$	3.51664e11	1.61028	0.805141	+	0.593083i	$0.202089\pi$
$332$	−1.14147e11	−0.515636
$333$	−2.46685e10	−0.109937
$334$	7.12894e10	0.313448
$335$	−3.94358e9	−0.0171076
$336$	1.40490e11	0.601337
$337$	−5.13643e10	−0.216934	−0.108467	−	0.994100i	$-0.534594\pi$
$337$	−5.13643e10	−0.216934	−0.108467	+	0.994100i	$0.534594\pi$
$338$	5.21840e10	0.217477
$339$	1.61392e10	0.0663719
$340$	−7.44055e10	−0.301960
$341$	−4.14006e11	−1.65811
$342$	1.49276e10	0.0590027
$343$	1.58991e11	0.620225
$344$	8.78644e10	0.338298
$345$	−1.76745e10	−0.0671677
$346$	−5.36384e10	−0.201202
$347$	7.76426e10	0.287487	0.143743	−	0.989615i	$-0.454086\pi$
$347$	7.76426e10	0.287487	0.143743	+	0.989615i	$0.454086\pi$
$348$	9.39560e10	0.343414
$349$	−2.73199e11	−0.985745	−0.492872	−	0.870102i	$-0.664053\pi$
$349$	−2.73199e11	−0.985745	−0.492872	+	0.870102i	$0.664053\pi$
$350$	−6.38833e10	−0.227552
$351$	−3.66860e10	−0.129008
$352$	1.53587e11	0.533228
$353$	−6.08844e10	−0.208699	−0.104349	−	0.994541i	$-0.533276\pi$
$353$	−6.08844e10	−0.208699	−0.104349	+	0.994541i	$0.533276\pi$
$354$	−2.42151e10	−0.0819541
$355$	1.77865e11	0.594379
$356$	8.84210e10	0.291763
$357$	1.71882e11	0.560045
$358$	−2.48980e10	−0.0801107
$359$	4.64024e11	1.47440	0.737200	−	0.675675i	$-0.236148\pi$
$359$	4.64024e11	1.47440	0.737200	+	0.675675i	$0.236148\pi$
$360$	−3.67082e10	−0.115187
$361$	−2.71473e11	−0.841286
$362$	−7.09992e10	−0.217303
$363$	5.02439e10	0.151881
$364$	−5.22609e10	−0.156034
$365$	−1.29015e11	−0.380470
$366$	1.67300e10	0.0487339
$367$	1.20513e11	0.346767	0.173384	−	0.984854i	$-0.444530\pi$
$367$	1.20513e11	0.346767	0.173384	+	0.984854i	$0.444530\pi$
$368$	8.80813e10	0.250362
$369$	2.96103e11	0.831426
$370$	−5.23260e9	−0.0145148
$371$	4.79655e11	1.31446
$372$	3.90693e11	1.05777
$373$	8.82896e10	0.236167	0.118084	−	0.993004i	$-0.462325\pi$
$373$	8.82896e10	0.236167	0.118084	+	0.993004i	$0.462325\pi$
$374$	5.72686e10	0.151354
$375$	1.61771e11	0.422435
$376$	−9.88101e10	−0.254951
$377$	−3.30550e10	−0.0842755
$378$	1.03143e11	0.259851
$379$	3.63126e11	0.904026	0.452013	−	0.892011i	$-0.350706\pi$
$379$	3.63126e11	0.904026	0.452013	+	0.892011i	$0.350706\pi$
$380$	−6.13879e10	−0.151028
$381$	−5.21662e10	−0.126831
$382$	−1.24360e10	−0.0298809
$383$	3.84226e11	0.912414	0.456207	−	0.889874i	$-0.349208\pi$
$383$	3.84226e11	0.912414	0.456207	+	0.889874i	$0.349208\pi$
$384$	−1.91390e11	−0.449189
$385$	1.80121e11	0.417821
$386$	8.83519e9	0.0202569
$387$	−2.31036e11	−0.523576
$388$	−5.51895e11	−1.23627
$389$	−5.61787e11	−1.24394	−0.621968	−	0.783042i	$-0.713667\pi$
$389$	−5.61787e11	−1.24394	−0.621968	+	0.783042i	$0.713667\pi$
$390$	−3.11843e9	−0.00682566
$391$	1.07763e11	0.233170
$392$	9.94410e10	0.212705
$393$	6.88268e10	0.145543
$394$	1.25479e11	0.262324
$395$	2.57507e11	0.532234
$396$	−2.66996e11	−0.545604
$397$	−3.56910e11	−0.721109	−0.360555	−	0.932738i	$-0.617413\pi$
$397$	−3.56910e11	−0.721109	−0.360555	+	0.932738i	$0.617413\pi$
$398$	−1.44696e10	−0.0289056
$399$	1.41810e11	0.280110
$400$	−3.68301e11	−0.719337
$401$	9.30288e9	0.0179667	0.00898334	−	0.999960i	$-0.497140\pi$
$401$	9.30288e9	0.0179667	0.00898334	+	0.999960i	$0.497140\pi$
$402$	−2.86438e9	−0.00547033
$403$	−1.37451e11	−0.259583
$404$	−7.15382e11	−1.33605
$405$	2.50185e10	0.0462075
$406$	9.29342e10	0.169749
$407$	−7.80815e10	−0.141050
$408$	−1.10875e11	−0.198090
$409$	−7.02687e11	−1.24167	−0.620836	−	0.783941i	$-0.713207\pi$
$409$	−7.02687e11	−1.24167	−0.620836	+	0.783941i	$0.713207\pi$
$410$	6.28082e10	0.109771
$411$	−4.96358e11	−0.858038
$412$	−2.01418e11	−0.344398
$413$	4.64361e11	0.785380
$414$	2.59142e10	0.0433548
$415$	1.30615e11	0.216161
$416$	5.09913e10	0.0834788
$417$	2.77955e11	0.450155
$418$	4.72492e10	0.0757009
$419$	−8.94772e11	−1.41824	−0.709119	−	0.705089i	$-0.750907\pi$
$419$	−8.94772e11	−1.41824	−0.709119	+	0.705089i	$0.750907\pi$
$420$	−1.69978e11	−0.266545
$421$	1.49728e11	0.232292	0.116146	−	0.993232i	$-0.462946\pi$
$421$	1.49728e11	0.232292	0.116146	+	0.993232i	$0.462946\pi$
$422$	9.12356e10	0.140042
$423$	2.59817e11	0.394581
$424$	−3.09409e11	−0.464929
$425$	−4.50596e11	−0.669942
$426$	1.29191e11	0.190059
$427$	−3.20823e11	−0.467026
$428$	−2.94855e11	−0.424729
$429$	−4.65335e10	−0.0663297
$430$	−4.90064e10	−0.0691266
$431$	−5.29202e11	−0.738710	−0.369355	−	0.929288i	$-0.620421\pi$
$431$	−5.29202e11	−0.738710	−0.369355	+	0.929288i	$0.620421\pi$
$432$	5.94639e11	0.821441
$433$	1.76117e11	0.240772	0.120386	−	0.992727i	$-0.461587\pi$
$433$	1.76117e11	0.240772	0.120386	+	0.992727i	$0.461587\pi$
$434$	3.86444e11	0.522857
$435$	−1.07511e11	−0.143963
$436$	1.29257e12	1.71303
$437$	8.89091e10	0.116622
$438$	−9.37085e10	−0.121659
$439$	7.40629e11	0.951723	0.475861	−	0.879520i	$-0.342136\pi$
$439$	7.40629e11	0.951723	0.475861	+	0.879520i	$0.342136\pi$
$440$	−1.16190e11	−0.147785
$441$	−2.61476e11	−0.329199
$442$	1.90133e10	0.0236951
$443$	2.15106e11	0.265360	0.132680	−	0.991159i	$-0.457642\pi$
$443$	2.15106e11	0.265360	0.132680	+	0.991159i	$0.457642\pi$
$444$	7.36846e10	0.0899815
$445$	−1.01178e11	−0.122311
$446$	−2.13264e11	−0.255217
$447$	−9.34929e11	−1.10763
$448$	7.47422e11	0.876627
$449$	−1.08175e12	−1.25608	−0.628040	−	0.778181i	$-0.716142\pi$
$449$	−1.08175e12	−1.25608	−0.628040	+	0.778181i	$0.716142\pi$
$450$	−1.08357e11	−0.124566
$451$	9.37231e11	1.06672
$452$	9.73125e10	0.109659
$453$	−4.02422e11	−0.448993
$454$	1.10474e11	0.122042
$455$	5.98006e10	0.0654115
$456$	−9.14768e10	−0.0990762
$457$	−1.10702e12	−1.18722	−0.593610	−	0.804753i	$-0.702298\pi$
$457$	−1.10702e12	−1.18722	−0.593610	+	0.804753i	$0.702298\pi$
$458$	1.16724e11	0.123955
$459$	7.27509e11	0.765035
$460$	−1.06569e11	−0.110974
$461$	−4.82228e9	−0.00497277	−0.00248639	−	0.999997i	$-0.500791\pi$
$461$	−4.82228e9	−0.00497277	−0.00248639	+	0.999997i	$0.500791\pi$
$462$	1.30829e11	0.133603
$463$	−7.30180e11	−0.738440	−0.369220	−	0.929342i	$-0.620375\pi$
$463$	−7.30180e11	−0.738440	−0.369220	+	0.929342i	$0.620375\pi$
$464$	5.35785e11	0.536612
$465$	−4.47059e11	−0.443431
$466$	−5.41565e10	−0.0532003
$467$	1.23496e12	1.20150	0.600752	−	0.799435i	$-0.294868\pi$
$467$	1.23496e12	1.20150	0.600752	+	0.799435i	$0.294868\pi$
$468$	−8.86435e10	−0.0854162
$469$	5.49289e10	0.0524231
$470$	5.51114e10	0.0520956
$471$	2.03770e11	0.190786
$472$	−2.99543e11	−0.277792
$473$	−7.31280e11	−0.671751
$474$	1.87038e11	0.170187
$475$	−3.71762e11	−0.335076
$476$	1.03637e12	0.925303
$477$	8.13578e11	0.719559
$478$	−3.90497e11	−0.342131
$479$	−1.11004e12	−0.963452	−0.481726	−	0.876322i	$-0.659990\pi$
$479$	−1.11004e12	−0.963452	−0.481726	+	0.876322i	$0.659990\pi$
$480$	1.65849e11	0.142602
$481$	−2.59232e10	−0.0220819
$482$	−4.53506e11	−0.382711
$483$	2.46182e11	0.205823
$484$	3.02949e11	0.250937
$485$	6.31517e11	0.518260
$486$	2.79787e11	0.227491
$487$	2.02968e12	1.63511	0.817555	−	0.575850i	$-0.195329\pi$
$487$	2.02968e12	1.63511	0.817555	+	0.575850i	$0.195329\pi$
$488$	2.06952e11	0.165189
$489$	−9.77731e11	−0.773267
$490$	−5.54633e10	−0.0434634
$491$	−6.33964e11	−0.492264	−0.246132	−	0.969236i	$-0.579160\pi$
$491$	−6.33964e11	−0.492264	−0.246132	+	0.969236i	$0.579160\pi$
$492$	−8.84454e11	−0.680507
$493$	6.55505e11	0.499764
$494$	1.56868e10	0.0118512
$495$	3.05516e11	0.228724
$496$	2.22793e12	1.65285
$497$	−2.47743e12	−1.82137
$498$	9.48710e10	0.0691196
$499$	−6.34178e11	−0.457888	−0.228944	−	0.973440i	$-0.573527\pi$
$499$	−6.34178e11	−0.457888	−0.228944	+	0.973440i	$0.573527\pi$
$500$	9.75408e11	0.697945
$501$	1.14872e12	0.814597
$502$	−1.17237e10	−0.00823944
$503$	3.33194e11	0.232082	0.116041	−	0.993244i	$-0.462980\pi$
$503$	3.33194e11	0.232082	0.116041	+	0.993244i	$0.462980\pi$
$504$	5.11297e11	0.352969
$505$	8.18591e11	0.560087
$506$	8.20244e10	0.0556245
$507$	8.40863e11	0.565184
$508$	−3.14539e11	−0.209550
$509$	4.79181e10	0.0316424	0.0158212	−	0.999875i	$-0.494964\pi$
$509$	4.79181e10	0.0316424	0.0158212	+	0.999875i	$0.494964\pi$
$510$	6.18407e10	0.0404770
$511$	1.79700e12	1.16588
$512$	−1.40113e12	−0.901079
$513$	6.00228e11	0.382638
$514$	−3.74977e11	−0.236957
$515$	2.30477e11	0.144376
$516$	6.90100e11	0.428537
$517$	8.22379e11	0.506250
$518$	7.28832e10	0.0444778
$519$	−8.64298e11	−0.522890
$520$	−3.85753e10	−0.0231363
$521$	−2.52197e12	−1.49958	−0.749791	−	0.661675i	$-0.769846\pi$
$521$	−2.52197e12	−1.49958	−0.749791	+	0.661675i	$0.769846\pi$
$522$	1.57633e11	0.0929241
$523$	1.64865e12	0.963540	0.481770	−	0.876298i	$-0.339994\pi$
$523$	1.64865e12	0.963540	0.481770	+	0.876298i	$0.339994\pi$
$524$	4.14995e11	0.240465
$525$	−1.02938e12	−0.591369
$526$	−7.02505e11	−0.400142
$527$	2.72576e12	1.53936
$528$	7.54257e11	0.422345
$529$	−1.64681e12	−0.914307
$530$	1.72573e11	0.0950019
$531$	7.87636e11	0.429932
$532$	8.55052e11	0.462797
$533$	3.11163e11	0.167000
$534$	−7.34893e10	−0.0391101
$535$	3.37394e11	0.178051
$536$	−3.54327e10	−0.0185423
$537$	−4.01192e11	−0.208194
$538$	3.11460e11	0.160281
$539$	−8.27630e11	−0.422364
$540$	−7.19451e11	−0.364107
$541$	−5.60834e11	−0.281480	−0.140740	−	0.990047i	$-0.544948\pi$
$541$	−5.60834e11	−0.281480	−0.140740	+	0.990047i	$0.544948\pi$
$542$	1.55952e11	0.0776237
$543$	−1.14404e12	−0.564732
$544$	−1.01120e12	−0.495040
$545$	−1.47905e12	−0.718121
$546$	4.34356e10	0.0209160
$547$	−3.72560e12	−1.77932	−0.889659	−	0.456625i	$-0.849058\pi$
$547$	−3.72560e12	−1.77932	−0.889659	+	0.456625i	$0.849058\pi$
$548$	−2.99282e12	−1.41765
$549$	−5.44172e11	−0.255659
$550$	−3.42975e11	−0.159820
$551$	5.40821e11	0.249960
$552$	−1.58804e11	−0.0728005
$553$	−3.58674e12	−1.63093
$554$	−9.75986e10	−0.0440200
$555$	−8.43151e10	−0.0377213
$556$	1.67594e12	0.743743
$557$	−1.77269e12	−0.780343	−0.390171	−	0.920742i	$-0.627584\pi$
$557$	−1.77269e12	−0.780343	−0.390171	+	0.920742i	$0.627584\pi$
$558$	6.55476e11	0.286222
$559$	−2.42787e11	−0.105165
$560$	−9.69301e11	−0.416498
$561$	9.22794e11	0.393343
$562$	−6.63236e11	−0.280449
$563$	2.82521e12	1.18512	0.592561	−	0.805526i	$-0.298117\pi$
$563$	2.82521e12	1.18512	0.592561	+	0.805526i	$0.298117\pi$
$564$	−7.76070e11	−0.322957
$565$	−1.11352e11	−0.0459705
$566$	5.36243e11	0.219628
$567$	−3.48474e11	−0.141595
$568$	1.59811e12	0.644225
$569$	−3.08563e12	−1.23407	−0.617034	−	0.786937i	$-0.711666\pi$
$569$	−3.08563e12	−1.23407	−0.617034	+	0.786937i	$0.711666\pi$
$570$	5.10213e10	0.0202449
$571$	2.61226e12	1.02838	0.514190	−	0.857676i	$-0.328093\pi$
$571$	2.61226e12	1.02838	0.514190	+	0.857676i	$0.328093\pi$
$572$	−2.80577e11	−0.109590
$573$	−2.00386e11	−0.0776554
$574$	−8.74835e11	−0.336374
$575$	−6.45378e11	−0.246212
$576$	1.26776e12	0.479882
$577$	3.09050e12	1.16075	0.580373	−	0.814350i	$-0.302907\pi$
$577$	3.09050e12	1.16075	0.580373	+	0.814350i	$0.302907\pi$
$578$	2.17237e11	0.0809577
$579$	1.42365e11	0.0526442
$580$	−6.48245e11	−0.237855
$581$	−1.81930e12	−0.662385
$582$	4.58697e11	0.165719
$583$	2.57516e12	0.923199
$584$	−1.15919e12	−0.412378
$585$	1.01432e11	0.0358075
$586$	−7.55422e11	−0.264637
$587$	1.88219e12	0.654321	0.327161	−	0.944969i	$-0.393908\pi$
$587$	1.88219e12	0.654321	0.327161	+	0.944969i	$0.393908\pi$
$588$	7.81025e11	0.269443
$589$	2.24887e12	0.769920
$590$	1.67070e11	0.0567630
$591$	2.02190e12	0.681735
$592$	4.20187e11	0.140603
$593$	−4.14376e12	−1.37610	−0.688048	−	0.725666i	$-0.741532\pi$
$593$	−4.14376e12	−1.37610	−0.688048	+	0.725666i	$0.741532\pi$
$594$	5.53749e11	0.182505
$595$	−1.18589e12	−0.387898
$596$	−5.63721e12	−1.83002
$597$	−2.33155e11	−0.0751208
$598$	2.72323e10	0.00870821
$599$	−6.79304e11	−0.215597	−0.107799	−	0.994173i	$-0.534380\pi$
$599$	−6.79304e11	−0.215597	−0.107799	+	0.994173i	$0.534380\pi$
$600$	6.64017e11	0.209170
$601$	1.23321e12	0.385567	0.192784	−	0.981241i	$-0.438248\pi$
$601$	1.23321e12	0.385567	0.192784	+	0.981241i	$0.438248\pi$
$602$	6.82595e11	0.211826
$603$	9.31689e10	0.0286974
$604$	−2.42643e12	−0.741824
$605$	−3.46655e11	−0.105196
$606$	5.94576e11	0.179094
$607$	−2.27029e12	−0.678786	−0.339393	−	0.940645i	$-0.610222\pi$
$607$	−2.27029e12	−0.678786	−0.339393	+	0.940645i	$0.610222\pi$
$608$	−8.34281e11	−0.247597
$609$	1.49749e12	0.441149
$610$	−1.15428e11	−0.0337541
$611$	2.73032e11	0.0792552
$612$	1.75786e12	0.506529
$613$	3.36091e12	0.961357	0.480679	−	0.876897i	$-0.340390\pi$
$613$	3.36091e12	0.961357	0.480679	+	0.876897i	$0.340390\pi$
$614$	−4.01164e10	−0.0113911
$615$	1.01206e12	0.285277
$616$	1.61837e12	0.452861
$617$	8.69025e11	0.241407	0.120703	−	0.992689i	$-0.461485\pi$
$617$	8.69025e11	0.241407	0.120703	+	0.992689i	$0.461485\pi$
$618$	1.67405e11	0.0461657
$619$	−5.95420e12	−1.63010	−0.815052	−	0.579388i	$-0.803292\pi$
$619$	−5.95420e12	−1.63010	−0.815052	+	0.579388i	$0.803292\pi$
$620$	−2.69557e12	−0.732634
$621$	1.04199e12	0.281159
$622$	1.51801e12	0.406647
$623$	1.40927e12	0.374799
$624$	2.50415e11	0.0661196
$625$	2.09233e12	0.548491
$626$	−7.50652e11	−0.195368
$627$	7.61346e11	0.196733
$628$	1.22864e12	0.315215
$629$	5.14077e11	0.130948
$630$	−2.85177e11	−0.0721242
$631$	3.88933e11	0.0976660	0.0488330	−	0.998807i	$-0.484450\pi$
$631$	3.88933e11	0.0976660	0.0488330	+	0.998807i	$0.484450\pi$
$632$	2.31368e12	0.576868
$633$	1.47012e12	0.363945
$634$	−9.30286e11	−0.228673
$635$	3.59918e11	0.0878459
$636$	−2.43015e12	−0.588946
$637$	−2.74775e11	−0.0661226
$638$	4.98942e11	0.119222
$639$	−4.20215e12	−0.997052
$640$	1.32049e12	0.311117
$641$	4.00334e12	0.936616	0.468308	−	0.883565i	$-0.344864\pi$
$641$	4.00334e12	0.936616	0.468308	+	0.883565i	$0.344864\pi$
$642$	2.45063e11	0.0569338
$643$	8.27928e12	1.91004	0.955022	−	0.296535i	$-0.0958311\pi$
$643$	8.27928e12	1.91004	0.955022	+	0.296535i	$0.0958311\pi$
$644$	1.48437e12	0.340060
$645$	−7.89662e11	−0.179648
$646$	−3.11081e11	−0.0702793
$647$	3.94109e12	0.884193	0.442097	−	0.896967i	$-0.354235\pi$
$647$	3.94109e12	0.884193	0.442097	+	0.896967i	$0.354235\pi$
$648$	2.24789e11	0.0500826
$649$	2.49305e12	0.551606
$650$	−1.13868e11	−0.0250203
$651$	6.22694e12	1.35881
$652$	−5.89528e12	−1.27759
$653$	6.62319e12	1.42547	0.712735	−	0.701434i	$-0.247456\pi$
$653$	6.62319e12	1.42547	0.712735	+	0.701434i	$0.247456\pi$
$654$	−1.07429e12	−0.229627
$655$	−4.74867e11	−0.100806
$656$	−5.04361e12	−1.06335
$657$	3.04803e12	0.638227
$658$	−7.67630e11	−0.159638
$659$	−6.40199e12	−1.32230	−0.661151	−	0.750253i	$-0.729932\pi$
$659$	−6.40199e12	−1.32230	−0.661151	+	0.750253i	$0.729932\pi$
$660$	−9.12573e11	−0.187206
$661$	−1.63899e12	−0.333941	−0.166971	−	0.985962i	$-0.553398\pi$
$661$	−1.63899e12	−0.333941	−0.166971	+	0.985962i	$0.553398\pi$
$662$	−1.76231e12	−0.356633
$663$	3.06370e11	0.0615793
$664$	1.17357e12	0.234288
$665$	−9.78411e11	−0.194010
$666$	1.23623e11	0.0243480
$667$	9.38863e11	0.183669
$668$	6.92625e12	1.34587
$669$	−3.43641e12	−0.663266
$670$	1.97626e10	0.00378886
$671$	−1.72243e12	−0.328012
$672$	−2.31006e12	−0.436979
$673$	−5.07685e12	−0.953953	−0.476976	−	0.878916i	$-0.658267\pi$
$673$	−5.07685e12	−0.953953	−0.476976	+	0.878916i	$0.658267\pi$
$674$	2.57404e11	0.0480448
$675$	−4.35696e12	−0.807824
$676$	5.07003e12	0.933793
$677$	8.18905e12	1.49825	0.749126	−	0.662428i	$-0.230474\pi$
$677$	8.18905e12	1.49825	0.749126	+	0.662428i	$0.230474\pi$
$678$	−8.08793e10	−0.0146995
$679$	−8.79621e12	−1.58811
$680$	7.64976e11	0.137201
$681$	1.78011e12	0.317165
$682$	2.07473e12	0.367225
$683$	1.04429e13	1.83624	0.918120	−	0.396303i	$-0.129707\pi$
$683$	1.04429e13	1.83624	0.918120	+	0.396303i	$0.129707\pi$
$684$	1.45032e12	0.253344
$685$	3.42459e12	0.594294
$686$	−7.96759e11	−0.137363
$687$	1.88082e12	0.322138
$688$	3.93531e12	0.669623
$689$	8.54959e11	0.144530
$690$	8.85728e10	0.0148758
$691$	−5.72108e12	−0.954612	−0.477306	−	0.878737i	$-0.658387\pi$
$691$	−5.72108e12	−0.954612	−0.477306	+	0.878737i	$0.658387\pi$
$692$	−5.21133e12	−0.863916
$693$	−4.25544e12	−0.700882
$694$	−3.89094e11	−0.0636703
$695$	−1.91773e12	−0.311786
$696$	−9.65979e11	−0.156036
$697$	−6.17059e12	−0.990328
$698$	1.36909e12	0.218315
$699$	−8.72647e11	−0.138258
$700$	−6.20670e12	−0.977056
$701$	4.40737e12	0.689364	0.344682	−	0.938720i	$-0.387987\pi$
$701$	4.40737e12	0.689364	0.344682	+	0.938720i	$0.387987\pi$
$702$	1.83846e11	0.0285718
$703$	4.24136e11	0.0654947
$704$	4.01274e12	0.615692
$705$	8.88034e11	0.135387
$706$	3.05113e11	0.0462210
$707$	−1.14019e13	−1.71629
$708$	−2.35266e12	−0.351892
$709$	1.82952e12	0.271913	0.135956	−	0.990715i	$-0.456589\pi$
$709$	1.82952e12	0.271913	0.135956	+	0.990715i	$0.456589\pi$
$710$	−8.91345e11	−0.131639
$711$	−6.08372e12	−0.892804
$712$	−9.09072e11	−0.132568
$713$	3.90403e12	0.565732
$714$	−8.61359e11	−0.124034
$715$	3.21056e11	0.0459413
$716$	−2.41901e12	−0.343976
$717$	−6.29225e12	−0.889139
$718$	−2.32538e12	−0.326539
$719$	8.08941e12	1.12885	0.564426	−	0.825484i	$-0.309098\pi$
$719$	8.08941e12	1.12885	0.564426	+	0.825484i	$0.309098\pi$
$720$	−1.64410e12	−0.227999
$721$	−3.21024e12	−0.442414
$722$	1.36044e12	0.186322
$723$	−7.30754e12	−0.994600
$724$	−6.89806e12	−0.933047
$725$	−3.92574e12	−0.527716
$726$	−2.51790e11	−0.0336375
$727$	−1.41851e13	−1.88334	−0.941669	−	0.336541i	$-0.890743\pi$
$727$	−1.41851e13	−1.88334	−0.941669	+	0.336541i	$0.890743\pi$
$728$	5.37303e11	0.0708970
$729$	3.62445e12	0.475300
$730$	6.46537e11	0.0842636
$731$	4.81464e12	0.623642
$732$	1.62544e12	0.209252
$733$	−3.22278e12	−0.412347	−0.206173	−	0.978515i	$-0.566101\pi$
$733$	−3.22278e12	−0.412347	−0.206173	+	0.978515i	$0.566101\pi$
$734$	−6.03934e11	−0.0767993
$735$	−8.93704e11	−0.112954
$736$	−1.44831e12	−0.181933
$737$	2.94901e11	0.0368190
$738$	−1.48387e12	−0.184138
$739$	−6.03232e10	−0.00744019	−0.00372010	−	0.999993i	$-0.501184\pi$
$739$	−6.03232e10	−0.00744019	−0.00372010	+	0.999993i	$0.501184\pi$
$740$	−5.08383e11	−0.0623230
$741$	2.52769e11	0.0307993
$742$	−2.40372e12	−0.291116
$743$	1.32585e13	1.59604	0.798021	−	0.602630i	$-0.205880\pi$
$743$	1.32585e13	1.59604	0.798021	+	0.602630i	$0.205880\pi$
$744$	−4.01678e12	−0.480618
$745$	6.45049e12	0.767167
$746$	−4.42450e11	−0.0523045
$747$	−3.08584e12	−0.362602
$748$	5.56404e12	0.649880
$749$	−4.69946e12	−0.545606
$750$	−8.10691e11	−0.0935577
$751$	6.39838e12	0.733991	0.366995	−	0.930223i	$-0.380387\pi$
$751$	6.39838e12	0.733991	0.366995	+	0.930223i	$0.380387\pi$
$752$	−4.42555e12	−0.504646
$753$	−1.88909e11	−0.0214129
$754$	1.65650e11	0.0186647
$755$	2.77649e12	0.310981
$756$	1.00210e13	1.11574
$757$	1.23763e13	1.36981	0.684906	−	0.728631i	$-0.259843\pi$
$757$	1.23763e13	1.36981	0.684906	+	0.728631i	$0.259843\pi$
$758$	−1.81975e12	−0.200217
$759$	1.32169e12	0.144558
$760$	6.31139e11	0.0686221
$761$	2.06556e12	0.223258	0.111629	−	0.993750i	$-0.464393\pi$
$761$	2.06556e12	0.223258	0.111629	+	0.993750i	$0.464393\pi$
$762$	2.61423e11	0.0280896
$763$	2.06012e13	2.20055
$764$	−1.20824e12	−0.128302
$765$	−2.01147e12	−0.212343
$766$	−1.92549e12	−0.202074
$767$	8.27697e11	0.0863559
$768$	−3.02297e12	−0.313551
$769$	−1.33067e13	−1.37215	−0.686076	−	0.727529i	$-0.740668\pi$
$769$	−1.33067e13	−1.37215	−0.686076	+	0.727529i	$0.740668\pi$
$770$	−9.02648e11	−0.0925359
$771$	−6.04216e12	−0.615811
$772$	8.58399e11	0.0869784
$773$	1.16520e13	1.17379	0.586897	−	0.809662i	$-0.300350\pi$
$773$	1.16520e13	1.17379	0.586897	+	0.809662i	$0.300350\pi$
$774$	1.15780e12	0.115958
$775$	−1.63242e13	−1.62545
$776$	5.67413e12	0.561722
$777$	1.17440e12	0.115590
$778$	2.81531e12	0.275497
$779$	−5.09101e12	−0.495320
$780$	−3.02976e11	−0.0293078
$781$	−1.33007e13	−1.27922
$782$	−5.40036e11	−0.0516408
$783$	6.33829e12	0.602621
$784$	4.45380e12	0.421026
$785$	−1.40590e12	−0.132142
$786$	−3.44915e11	−0.0322337
$787$	2.04268e11	0.0189808	0.00949039	−	0.999955i	$-0.496979\pi$
$787$	2.04268e11	0.0189808	0.00949039	+	0.999955i	$0.496979\pi$
$788$	1.21911e13	1.12636
$789$	−1.13198e13	−1.03990
$790$	−1.29046e12	−0.117875
$791$	1.55098e12	0.140868
$792$	2.74504e12	0.247905
$793$	−5.71850e11	−0.0513515
$794$	1.78860e12	0.159706
$795$	2.78075e12	0.246893
$796$	−1.40582e12	−0.124114
$797$	4.74583e12	0.416629	0.208314	−	0.978062i	$-0.433202\pi$
$797$	4.74583e12	0.416629	0.208314	+	0.978062i	$0.433202\pi$
$798$	−7.10659e11	−0.0620367
$799$	−5.41442e12	−0.469993
$800$	6.05592e12	0.522728
$801$	2.39037e12	0.205172
$802$	−4.66200e10	−0.00397912
$803$	9.64770e12	0.818849
$804$	−2.78294e11	−0.0234883
$805$	−1.69852e12	−0.142557
$806$	6.88815e11	0.0574904
$807$	5.01869e12	0.416543
$808$	7.35497e12	0.607058
$809$	7.05649e12	0.579189	0.289595	−	0.957149i	$-0.406480\pi$
$809$	7.05649e12	0.579189	0.289595	+	0.957149i	$0.406480\pi$
$810$	−1.25376e11	−0.0102337
$811$	1.15520e13	0.937696	0.468848	−	0.883279i	$-0.344669\pi$
$811$	1.15520e13	0.937696	0.468848	+	0.883279i	$0.344669\pi$
$812$	9.02919e12	0.728864
$813$	2.51292e12	0.201730
$814$	3.91293e11	0.0312387
$815$	6.74580e12	0.535580
$816$	−4.96592e12	−0.392097
$817$	3.97229e12	0.311919
$818$	3.52141e12	0.274996
$819$	−1.41282e12	−0.109726
$820$	6.10224e12	0.471332
$821$	−1.01996e13	−0.783501	−0.391750	−	0.920072i	$-0.628130\pi$
$821$	−1.01996e13	−0.783501	−0.391750	+	0.920072i	$0.628130\pi$
$822$	2.48742e12	0.190032
$823$	−1.56251e13	−1.18720	−0.593599	−	0.804761i	$-0.702293\pi$
$823$	−1.56251e13	−1.18720	−0.593599	+	0.804761i	$0.702293\pi$
$824$	2.07082e12	0.156484
$825$	−5.52650e12	−0.415343
$826$	−2.32707e12	−0.173940
$827$	−2.15862e13	−1.60473	−0.802363	−	0.596836i	$-0.796424\pi$
$827$	−2.15862e13	−1.60473	−0.802363	+	0.596836i	$0.796424\pi$
$828$	2.51775e12	0.186155
$829$	5.93446e12	0.436401	0.218201	−	0.975904i	$-0.429981\pi$
$829$	5.93446e12	0.436401	0.218201	+	0.975904i	$0.429981\pi$
$830$	−6.54557e11	−0.0478736
$831$	−1.57265e12	−0.114400
$832$	1.33224e12	0.0963889
$833$	5.44899e12	0.392115
$834$	−1.39293e12	−0.0996968
$835$	−7.92551e12	−0.564206
$836$	4.59058e12	0.325042
$837$	2.63562e13	1.85617
$838$	4.48401e12	0.314101
$839$	−1.13565e13	−0.791256	−0.395628	−	0.918411i	$-0.629473\pi$
$839$	−1.13565e13	−0.791256	−0.395628	+	0.918411i	$0.629473\pi$
$840$	1.74757e12	0.121110
$841$	−8.79618e12	−0.606334
$842$	−7.50341e11	−0.0514463
$843$	−1.06870e13	−0.728839
$844$	8.86416e12	0.601308
$845$	−5.80149e12	−0.391457
$846$	−1.30203e12	−0.0873887
$847$	4.82845e12	0.322354
$848$	−1.38579e13	−0.920275
$849$	8.64071e12	0.570775
$850$	2.25809e12	0.148374
$851$	7.36299e11	0.0481251
$852$	1.25518e13	0.816068
$853$	−1.85007e13	−1.19651	−0.598257	−	0.801304i	$-0.704140\pi$
$853$	−1.85007e13	−1.19651	−0.598257	+	0.801304i	$0.704140\pi$
$854$	1.60776e12	0.103433
$855$	−1.65955e12	−0.106205
$856$	3.03146e12	0.192983
$857$	1.96567e13	1.24479	0.622396	−	0.782702i	$-0.286159\pi$
$857$	1.96567e13	1.24479	0.622396	+	0.782702i	$0.286159\pi$
$858$	2.33196e11	0.0146902
$859$	−5.75458e12	−0.360616	−0.180308	−	0.983610i	$-0.557709\pi$
$859$	−5.75458e12	−0.360616	−0.180308	+	0.983610i	$0.557709\pi$
$860$	−4.76131e12	−0.296813
$861$	−1.40966e13	−0.874178
$862$	2.65202e12	0.163604
$863$	−2.78321e13	−1.70804	−0.854018	−	0.520243i	$-0.825841\pi$
$863$	−2.78321e13	−1.70804	−0.854018	+	0.520243i	$0.825841\pi$
$864$	−9.77758e12	−0.596924
$865$	5.96318e12	0.362164
$866$	−8.82583e11	−0.0533243
$867$	3.50043e12	0.210395
$868$	3.75457e13	2.24502
$869$	−1.92564e13	−1.14547
$870$	5.38775e11	0.0318839
$871$	9.79077e10	0.00576415
$872$	−1.32891e13	−0.778345
$873$	−1.49199e13	−0.869364
$874$	−4.45554e11	−0.0258285
$875$	1.55462e13	0.896580
$876$	−9.10442e12	−0.522377
$877$	1.39390e13	0.795672	0.397836	−	0.917457i	$-0.369761\pi$
$877$	1.39390e13	0.795672	0.397836	+	0.917457i	$0.369761\pi$
$878$	−3.71155e12	−0.210780
$879$	−1.21724e13	−0.687745
$880$	−5.20396e12	−0.292524
$881$	2.10534e13	1.17742	0.588709	−	0.808345i	$-0.299636\pi$
$881$	2.10534e13	1.17742	0.588709	+	0.808345i	$0.299636\pi$
$882$	1.31035e12	0.0729084
$883$	−1.60235e13	−0.887023	−0.443512	−	0.896269i	$-0.646268\pi$
$883$	−1.60235e13	−0.887023	−0.443512	+	0.896269i	$0.646268\pi$
$884$	1.84727e12	0.101741
$885$	2.69208e12	0.147517
$886$	−1.07797e12	−0.0587699
$887$	−7.95565e12	−0.431538	−0.215769	−	0.976444i	$-0.569226\pi$
$887$	−7.95565e12	−0.431538	−0.215769	+	0.976444i	$0.569226\pi$
$888$	−7.57564e11	−0.0408847
$889$	−5.01318e12	−0.269188
$890$	5.07036e11	0.0270884
$891$	−1.87088e12	−0.0994479
$892$	−2.07200e13	−1.09584
$893$	−4.46714e12	−0.235070
$894$	4.68525e12	0.245309
$895$	2.76800e12	0.144199
$896$	−1.83926e13	−0.953362
$897$	4.38806e11	0.0226311
$898$	5.42101e12	0.278187
$899$	2.37477e13	1.21256
$900$	−1.05276e13	−0.534859
$901$	−1.69545e13	−0.857082
$902$	−4.69679e12	−0.236250
$903$	1.09989e13	0.550499
$904$	−1.00049e12	−0.0498257
$905$	7.89325e12	0.391144
$906$	2.01668e12	0.0994395
$907$	6.51759e12	0.319782	0.159891	−	0.987135i	$-0.448886\pi$
$907$	6.51759e12	0.319782	0.159891	+	0.987135i	$0.448886\pi$
$908$	1.07333e13	0.524018
$909$	−1.93396e13	−0.939528
$910$	−2.99681e11	−0.0144868
$911$	1.94390e13	0.935063	0.467532	−	0.883976i	$-0.345143\pi$
$911$	1.94390e13	0.935063	0.467532	+	0.883976i	$0.345143\pi$
$912$	−4.09710e12	−0.196110
$913$	−9.76738e12	−0.465221
$914$	5.54764e12	0.262936
$915$	−1.85994e12	−0.0877210
$916$	1.13405e13	0.532235
$917$	6.61427e12	0.308901
$918$	−3.64580e12	−0.169434
$919$	−1.65728e13	−0.766435	−0.383217	−	0.923658i	$-0.625184\pi$
$919$	−1.65728e13	−0.766435	−0.383217	+	0.923658i	$0.625184\pi$
$920$	1.09566e12	0.0504231
$921$	−6.46412e11	−0.0296034
$922$	2.41661e10	0.00110133
$923$	−4.41588e12	−0.200267
$924$	1.27109e13	0.573659
$925$	−3.07874e12	−0.138272
$926$	3.65918e12	0.163544
$927$	−5.44512e12	−0.242186
$928$	−8.80985e12	−0.389944
$929$	−2.80460e13	−1.23538	−0.617690	−	0.786422i	$-0.711931\pi$
$929$	−2.80460e13	−1.23538	−0.617690	+	0.786422i	$0.711931\pi$
$930$	2.24036e12	0.0982077
$931$	4.49566e12	0.196119
$932$	−5.26168e12	−0.228430
$933$	2.44603e13	1.05680
$934$	−6.18879e12	−0.266100
$935$	−6.36676e12	−0.272437
$936$	9.11359e11	0.0388104
$937$	−2.45511e13	−1.04050	−0.520251	−	0.854013i	$-0.674162\pi$
$937$	−2.45511e13	−1.04050	−0.520251	+	0.854013i	$0.674162\pi$
$938$	−2.75268e11	−0.0116103
$939$	−1.20956e13	−0.507728
$940$	5.35445e12	0.223686
$941$	2.57484e13	1.07053	0.535263	−	0.844686i	$-0.320213\pi$
$941$	2.57484e13	1.07053	0.535263	+	0.844686i	$0.320213\pi$
$942$	−1.02116e12	−0.0422538
$943$	−8.83798e12	−0.363957
$944$	−1.34161e13	−0.549859
$945$	−1.14667e13	−0.467732
$946$	3.66470e12	0.148774
$947$	3.20045e13	1.29311	0.646556	−	0.762867i	$-0.276209\pi$
$947$	3.20045e13	1.29311	0.646556	+	0.762867i	$0.276209\pi$
$948$	1.81720e13	0.730744
$949$	3.20306e12	0.128194
$950$	1.86303e12	0.0742101
$951$	−1.49901e13	−0.594281
$952$	−1.06551e13	−0.420428
$953$	3.87308e13	1.52103	0.760517	−	0.649318i	$-0.224946\pi$
$953$	3.87308e13	1.52103	0.760517	+	0.649318i	$0.224946\pi$
$954$	−4.07712e12	−0.159362
$955$	1.38255e12	0.0537856
$956$	−3.79395e13	−1.46903
$957$	8.03967e12	0.309838
$958$	5.56281e12	0.213378
$959$	−4.77001e13	−1.82111
$960$	4.33309e12	0.164656
$961$	7.23091e13	2.73488
$962$	1.29910e11	0.00489053
$963$	−7.97109e12	−0.298675
$964$	−4.40612e13	−1.64327
$965$	−9.82241e11	−0.0364624
$966$	−1.23370e12	−0.0455841
$967$	−3.70138e13	−1.36127	−0.680635	−	0.732622i	$-0.738296\pi$
$967$	−3.70138e13	−1.36127	−0.680635	+	0.732622i	$0.738296\pi$
$968$	−3.11467e12	−0.114018
$969$	−5.01259e12	−0.182644
$970$	−3.16475e12	−0.114780
$971$	3.26137e13	1.17737	0.588686	−	0.808361i	$-0.299645\pi$
$971$	3.26137e13	1.17737	0.588686	+	0.808361i	$0.299645\pi$
$972$	2.71832e13	0.976794
$973$	2.67115e13	0.955412
$974$	−1.01714e13	−0.362132
$975$	−1.83481e12	−0.0650235
$976$	9.26906e12	0.326973
$977$	2.93187e13	1.02948	0.514741	−	0.857346i	$-0.327888\pi$
$977$	2.93187e13	1.02948	0.514741	+	0.857346i	$0.327888\pi$
$978$	4.89975e12	0.171257
$979$	7.56605e12	0.263237
$980$	−5.38864e12	−0.186622
$981$	3.49432e13	1.20463
$982$	3.17701e12	0.109023
$983$	4.92057e13	1.68083	0.840416	−	0.541942i	$-0.182311\pi$
$983$	4.92057e13	1.68083	0.840416	+	0.541942i	$0.182311\pi$
$984$	9.09323e12	0.309201
$985$	−1.39500e13	−0.472183
$986$	−3.28496e12	−0.110684
$987$	−1.23691e13	−0.414870
$988$	1.52408e12	0.0508865
$989$	6.89588e12	0.229196
$990$	−1.53105e12	−0.0506559
$991$	−1.54085e12	−0.0507492	−0.0253746	−	0.999678i	$-0.508078\pi$
$991$	−1.54085e12	−0.0507492	−0.0253746	+	0.999678i	$0.508078\pi$
$992$	−3.66336e13	−1.20109
$993$	−2.83969e13	−0.926827
$994$	1.24153e13	0.403382
$995$	1.60864e12	0.0520301
$996$	9.21736e12	0.296783
$997$	4.54090e13	1.45551	0.727753	−	0.685839i	$-0.240565\pi$
$997$	4.54090e13	1.45551	0.727753	+	0.685839i	$0.240565\pi$
$998$	3.17809e12	0.101409
$999$	4.97078e12	0.157899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.10.a.b.1.6	✓	14
3.2	odd	2		333.10.a.d.1.9		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.10.a.b.1.6	✓	14	1.1	even	1	trivial
333.10.a.d.1.9		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)

\(f(q)\)	\(=\)	\(q-5.01135 q^{2} -80.7499 q^{3} -486.886 q^{4} +557.130 q^{5} +404.666 q^{6} -7760.08 q^{7} +5005.76 q^{8} -13162.4 q^{9} +O(q^{10})\)	\(q-5.01135 q^{2} -80.7499 q^{3} -486.886 q^{4} +557.130 q^{5} +404.666 q^{6} -7760.08 q^{7} +5005.76 q^{8} -13162.4 q^{9} -2791.97 q^{10} -41662.1 q^{11} +39316.0 q^{12} -13831.9 q^{13} +38888.5 q^{14} -44988.2 q^{15} +224200. q^{16} +274297. q^{17} +65961.6 q^{18} +226307. q^{19} -271259. q^{20} +626626. q^{21} +208783. q^{22} +392869. q^{23} -404215. q^{24} -1.64273e6 q^{25} +69316.5 q^{26} +2.65227e6 q^{27} +3.77828e6 q^{28} +2.38976e6 q^{29} +225451. q^{30} +9.93724e6 q^{31} -3.68650e6 q^{32} +3.36421e6 q^{33} -1.37460e6 q^{34} -4.32337e6 q^{35} +6.40862e6 q^{36} +1.87416e6 q^{37} -1.13410e6 q^{38} +1.11693e6 q^{39} +2.78886e6 q^{40} -2.24960e7 q^{41} -3.14024e6 q^{42} +1.75526e7 q^{43} +2.02847e7 q^{44} -7.33319e6 q^{45} -1.96880e6 q^{46} -1.97393e7 q^{47} -1.81042e7 q^{48} +1.98653e7 q^{49} +8.23229e6 q^{50} -2.21495e7 q^{51} +6.73457e6 q^{52} -6.18106e7 q^{53} -1.32914e7 q^{54} -2.32112e7 q^{55} -3.88452e7 q^{56} -1.82743e7 q^{57} -1.19759e7 q^{58} -5.98396e7 q^{59} +2.19041e7 q^{60} +4.13428e7 q^{61} -4.97989e7 q^{62} +1.02142e8 q^{63} -9.63162e7 q^{64} -7.70618e6 q^{65} -1.68592e7 q^{66} -7.07839e6 q^{67} -1.33552e8 q^{68} -3.17241e7 q^{69} +2.16659e7 q^{70} +3.19253e8 q^{71} -6.58881e7 q^{72} -2.31570e8 q^{73} -9.39207e6 q^{74} +1.32650e8 q^{75} -1.10186e8 q^{76} +3.23301e8 q^{77} -5.59731e6 q^{78} +4.62203e8 q^{79} +1.24909e8 q^{80} +4.49060e7 q^{81} +1.12735e8 q^{82} +2.34443e8 q^{83} -3.05096e8 q^{84} +1.52819e8 q^{85} -8.79623e7 q^{86} -1.92973e8 q^{87} -2.08551e8 q^{88} -1.81605e8 q^{89} +3.67492e7 q^{90} +1.07337e8 q^{91} -1.91282e8 q^{92} -8.02432e8 q^{93} +9.89203e7 q^{94} +1.26083e8 q^{95} +2.97684e8 q^{96} +1.13352e9 q^{97} -9.95518e7 q^{98} +5.48375e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 48 q^{2} + 397 q^{3} + 3498 q^{4} + 2841 q^{5} + 3375 q^{6} + 6632 q^{7} + 41046 q^{8} + 101917 q^{9}+O(q^{10}) \) 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

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