LMFDB - Embedded newform 37.10.a.b.1.13

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			1.13
Root			$35.9809$ 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)

$f(q)$	$=$	$q+38.9809 q^{2} -235.969 q^{3} +1007.51 q^{4} +774.522 q^{5} -9198.30 q^{6} -1447.33 q^{7} +19315.4 q^{8} +35998.6 q^{9} +O(q^{10})$	\(q+38.9809 q^{2} -235.969 q^{3} +1007.51 q^{4} +774.522 q^{5} -9198.30 q^{6} -1447.33 q^{7} +19315.4 q^{8} +35998.6 q^{9} +30191.5 q^{10} +63229.1 q^{11} -237741. q^{12} +62568.7 q^{13} -56418.2 q^{14} -182764. q^{15} +237085. q^{16} +388942. q^{17} +1.40326e6 q^{18} +509002. q^{19} +780338. q^{20} +341526. q^{21} +2.46473e6 q^{22} +973431. q^{23} -4.55783e6 q^{24} -1.35324e6 q^{25} +2.43898e6 q^{26} -3.84998e6 q^{27} -1.45820e6 q^{28} -4.77886e6 q^{29} -7.12428e6 q^{30} +8.43437e6 q^{31} -647682. q^{32} -1.49202e7 q^{33} +1.51613e7 q^{34} -1.12099e6 q^{35} +3.62689e7 q^{36} +1.87416e6 q^{37} +1.98414e7 q^{38} -1.47643e7 q^{39} +1.49602e7 q^{40} -2.69856e7 q^{41} +1.33130e7 q^{42} -3.26248e7 q^{43} +6.37039e7 q^{44} +2.78817e7 q^{45} +3.79452e7 q^{46} +5.42568e7 q^{47} -5.59448e7 q^{48} -3.82588e7 q^{49} -5.27505e7 q^{50} -9.17785e7 q^{51} +6.30385e7 q^{52} -2.21321e7 q^{53} -1.50076e8 q^{54} +4.89724e7 q^{55} -2.79557e7 q^{56} -1.20109e8 q^{57} -1.86284e8 q^{58} +3.77128e7 q^{59} -1.84136e8 q^{60} +9.65466e7 q^{61} +3.28779e8 q^{62} -5.21019e7 q^{63} -1.46635e8 q^{64} +4.84608e7 q^{65} -5.81600e8 q^{66} +2.94576e8 q^{67} +3.91863e8 q^{68} -2.29700e8 q^{69} -4.36972e7 q^{70} -9.10691e6 q^{71} +6.95326e8 q^{72} +8.88198e6 q^{73} +7.30564e7 q^{74} +3.19323e8 q^{75} +5.12824e8 q^{76} -9.15135e7 q^{77} -5.75525e8 q^{78} -4.87262e8 q^{79} +1.83628e8 q^{80} +1.99918e8 q^{81} -1.05192e9 q^{82} -1.42007e8 q^{83} +3.44090e8 q^{84} +3.01244e8 q^{85} -1.27174e9 q^{86} +1.12767e9 q^{87} +1.22129e9 q^{88} +4.01967e8 q^{89} +1.08685e9 q^{90} -9.05576e7 q^{91} +9.80740e8 q^{92} -1.99025e9 q^{93} +2.11498e9 q^{94} +3.94234e8 q^{95} +1.52833e8 q^{96} +5.68710e7 q^{97} -1.49136e9 q^{98} +2.27616e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	38.9809	1.72273	0.861364	−	0.507989i	$-0.169611\pi$
$2$	38.9809	1.72273	0.861364	+	0.507989i	$0.169611\pi$
$3$	−235.969	−1.68194	−0.840969	−	0.541083i	$-0.818015\pi$
$3$	−235.969	−1.68194	−0.840969	+	0.541083i	$0.818015\pi$
$4$	1007.51	1.96779
$5$	774.522	0.554203	0.277101	−	0.960841i	$-0.410626\pi$
$5$	774.522	0.554203	0.277101	+	0.960841i	$0.410626\pi$
$6$	−9198.30	−2.89752
$7$	−1447.33	−0.227838	−0.113919	−	0.993490i	$-0.536340\pi$
$7$	−1447.33	−0.227838	−0.113919	+	0.993490i	$0.536340\pi$
$8$	19315.4	1.66724
$9$	35998.6	1.82892
$10$	30191.5	0.954741
$11$	63229.1	1.30212	0.651059	−	0.759027i	$-0.274325\pi$
$11$	63229.1	1.30212	0.651059	+	0.759027i	$0.274325\pi$
$12$	−237741.	−3.30970
$13$	62568.7	0.607592	0.303796	−	0.952737i	$-0.401746\pi$
$13$	62568.7	0.607592	0.303796	+	0.952737i	$0.401746\pi$
$14$	−56418.2	−0.392503
$15$	−182764.	−0.932135
$16$	237085.	0.904407
$17$	388942.	1.12944	0.564722	−	0.825281i	$-0.308983\pi$
$17$	388942.	1.12944	0.564722	+	0.825281i	$0.308983\pi$
$18$	1.40326e6	3.15073
$19$	509002.	0.896043	0.448021	−	0.894023i	$-0.352129\pi$
$19$	509002.	0.896043	0.448021	+	0.894023i	$0.352129\pi$
$20$	780338.	1.09055
$21$	341526.	0.383210
$22$	2.46473e6	2.24319
$23$	973431.	0.725320	0.362660	−	0.931921i	$-0.381869\pi$
$23$	973431.	0.725320	0.362660	+	0.931921i	$0.381869\pi$
$24$	−4.55783e6	−2.80419
$25$	−1.35324e6	−0.692859
$26$	2.43898e6	1.04672
$27$	−3.84998e6	−1.39419
$28$	−1.45820e6	−0.448338
$29$	−4.77886e6	−1.25468	−0.627341	−	0.778745i	$-0.715857\pi$
$29$	−4.77886e6	−1.25468	−0.627341	+	0.778745i	$0.715857\pi$
$30$	−7.12428e6	−1.60582
$31$	8.43437e6	1.64031	0.820154	−	0.572143i	$-0.193888\pi$
$31$	8.43437e6	1.64031	0.820154	+	0.572143i	$0.193888\pi$
$32$	−647682.	−0.109191
$33$	−1.49202e7	−2.19008
$34$	1.51613e7	1.94573
$35$	−1.12099e6	−0.126269
$36$	3.62689e7	3.59893
$37$	1.87416e6	0.164399
$37$	1.87416e6	0.164399
$38$	1.98414e7	1.54364
$39$	−1.47643e7	−1.02193
$40$	1.49602e7	0.923988
$41$	−2.69856e7	−1.49144	−0.745719	−	0.666261i	$-0.767894\pi$
$41$	−2.69856e7	−1.49144	−0.745719	+	0.666261i	$0.767894\pi$
$42$	1.33130e7	0.660167
$43$	−3.26248e7	−1.45526	−0.727629	−	0.685970i	$-0.759378\pi$
$43$	−3.26248e7	−1.45526	−0.727629	+	0.685970i	$0.759378\pi$
$44$	6.37039e7	2.56229
$45$	2.78817e7	1.01359
$46$	3.79452e7	1.24953
$47$	5.42568e7	1.62186	0.810930	−	0.585143i	$-0.198961\pi$
$47$	5.42568e7	1.62186	0.810930	+	0.585143i	$0.198961\pi$
$48$	−5.59448e7	−1.52116
$49$	−3.82588e7	−0.948090
$50$	−5.27505e7	−1.19361
$51$	−9.17785e7	−1.89966
$52$	6.30385e7	1.19561
$53$	−2.21321e7	−0.385284	−0.192642	−	0.981269i	$-0.561706\pi$
$53$	−2.21321e7	−0.385284	−0.192642	+	0.981269i	$0.561706\pi$
$54$	−1.50076e8	−2.40181
$55$	4.89724e7	0.721637
$56$	−2.79557e7	−0.379861
$57$	−1.20109e8	−1.50709
$58$	−1.86284e8	−2.16147
$59$	3.77128e7	0.405186	0.202593	−	0.979263i	$-0.435063\pi$
$59$	3.77128e7	0.405186	0.202593	+	0.979263i	$0.435063\pi$
$60$	−1.84136e8	−1.83425
$61$	9.65466e7	0.892797	0.446398	−	0.894834i	$-0.352706\pi$
$61$	9.65466e7	0.892797	0.446398	+	0.894834i	$0.352706\pi$
$62$	3.28779e8	2.82580
$63$	−5.21019e7	−0.416698
$64$	−1.46635e8	−1.09251
$65$	4.84608e7	0.336729
$66$	−5.81600e8	−3.77292
$67$	2.94576e8	1.78592	0.892958	−	0.450140i	$-0.148626\pi$
$67$	2.94576e8	1.78592	0.892958	+	0.450140i	$0.148626\pi$
$68$	3.91863e8	2.22251
$69$	−2.29700e8	−1.21994
$70$	−4.36972e7	−0.217526
$71$	−9.10691e6	−0.0425313	−0.0212656	−	0.999774i	$-0.506770\pi$
$71$	−9.10691e6	−0.0425313	−0.0212656	+	0.999774i	$0.506770\pi$
$72$	6.95326e8	3.04924
$73$	8.88198e6	0.0366064	0.0183032	−	0.999832i	$-0.494174\pi$
$73$	8.88198e6	0.0366064	0.0183032	+	0.999832i	$0.494174\pi$
$74$	7.30564e7	0.283215
$75$	3.19323e8	1.16535
$76$	5.12824e8	1.76322
$77$	−9.15135e7	−0.296672
$78$	−5.75525e8	−1.76051
$79$	−4.87262e8	−1.40747	−0.703737	−	0.710461i	$-0.748487\pi$
$79$	−4.87262e8	−1.40747	−0.703737	+	0.710461i	$0.748487\pi$
$80$	1.83628e8	0.501225
$81$	1.99918e8	0.516024
$82$	−1.05192e9	−2.56934
$83$	−1.42007e8	−0.328441	−0.164220	−	0.986424i	$-0.552511\pi$
$83$	−1.42007e8	−0.328441	−0.164220	+	0.986424i	$0.552511\pi$
$84$	3.44090e8	0.754077
$85$	3.01244e8	0.625941
$86$	−1.27174e9	−2.50701
$87$	1.12767e9	2.11030
$88$	1.22129e9	2.17094
$89$	4.01967e8	0.679103	0.339551	−	0.940588i	$-0.389725\pi$
$89$	4.01967e8	0.679103	0.339551	+	0.940588i	$0.389725\pi$
$90$	1.08685e9	1.74614
$91$	−9.05576e7	−0.138433
$92$	9.80740e8	1.42728
$93$	−1.99025e9	−2.75890
$94$	2.11498e9	2.79402
$95$	3.94234e8	0.496589
$96$	1.52833e8	0.183653
$97$	5.68710e7	0.0652256	0.0326128	−	0.999468i	$-0.489617\pi$
$97$	5.68710e7	0.0652256	0.0326128	+	0.999468i	$0.489617\pi$
$98$	−1.49136e9	−1.63330
$99$	2.27616e9	2.38147
$100$	−1.36340e9	−1.36340
$101$	−4.53740e8	−0.433871	−0.216935	−	0.976186i	$-0.569606\pi$
$101$	−4.53740e8	−0.433871	−0.216935	+	0.976186i	$0.569606\pi$
$102$	−3.57761e9	−3.27259
$103$	−1.09701e8	−0.0960378	−0.0480189	−	0.998846i	$-0.515291\pi$
$103$	−1.09701e8	−0.0960378	−0.0480189	+	0.998846i	$0.515291\pi$
$104$	1.20854e9	1.01300
$105$	2.64519e8	0.212376
$106$	−8.62727e8	−0.663739
$107$	−4.23054e8	−0.312010	−0.156005	−	0.987756i	$-0.549862\pi$
$107$	−4.23054e8	−0.312010	−0.156005	+	0.987756i	$0.549862\pi$
$108$	−3.87889e9	−2.74347
$109$	2.63973e9	1.79118	0.895592	−	0.444876i	$-0.146752\pi$
$109$	2.63973e9	1.79118	0.895592	+	0.444876i	$0.146752\pi$
$110$	1.90899e9	1.24318
$111$	−4.42245e8	−0.276509
$112$	−3.43140e8	−0.206059
$113$	−1.32041e9	−0.761825	−0.380913	−	0.924611i	$-0.624390\pi$
$113$	−1.32041e9	−0.761825	−0.380913	+	0.924611i	$0.624390\pi$
$114$	−4.68196e9	−2.59630
$115$	7.53944e8	0.401975
$116$	−4.81474e9	−2.46895
$117$	2.25238e9	1.11124
$118$	1.47008e9	0.698025
$119$	−5.62928e8	−0.257331
$120$	−3.53014e9	−1.55409
$121$	1.63998e9	0.695511
$122$	3.76347e9	1.53805
$123$	6.36778e9	2.50851
$124$	8.49770e9	3.22778
$125$	−2.56085e9	−0.938187
$126$	−2.03098e9	−0.717857
$127$	2.39479e9	0.816865	0.408432	−	0.912789i	$-0.366076\pi$
$127$	2.39479e9	0.816865	0.408432	+	0.912789i	$0.366076\pi$
$128$	−5.38434e9	−1.77291
$129$	7.69847e9	2.44766
$130$	1.88905e9	0.580093
$131$	−6.33273e9	−1.87875	−0.939377	−	0.342885i	$-0.888596\pi$
$131$	−6.33273e9	−1.87875	−0.939377	+	0.342885i	$0.888596\pi$
$132$	−1.50322e10	−4.30962
$133$	−7.36695e8	−0.204153
$134$	1.14828e10	3.07665
$135$	−2.98190e9	−0.772664
$136$	7.51256e9	1.88305
$137$	−4.57649e8	−0.110992	−0.0554958	−	0.998459i	$-0.517674\pi$
$137$	−4.57649e8	−0.110992	−0.0554958	+	0.998459i	$0.517674\pi$
$138$	−8.95391e9	−2.10163
$139$	−3.15660e9	−0.717221	−0.358610	−	0.933487i	$-0.616749\pi$
$139$	−3.15660e9	−0.717221	−0.358610	+	0.933487i	$0.616749\pi$
$140$	−1.12941e9	−0.248470
$141$	−1.28029e10	−2.72787
$142$	−3.54995e8	−0.0732698
$143$	3.95616e9	0.791156
$144$	8.53473e9	1.65409
$145$	−3.70133e9	−0.695348
$146$	3.46227e8	0.0630628
$147$	9.02792e9	1.59463
$148$	1.88823e9	0.323503
$149$	−9.25042e9	−1.53753	−0.768764	−	0.639533i	$-0.779128\pi$
$149$	−9.25042e9	−1.53753	−0.768764	+	0.639533i	$0.779128\pi$
$150$	1.24475e10	2.00757
$151$	4.86792e9	0.761987	0.380993	−	0.924578i	$-0.375582\pi$
$151$	4.86792e9	0.761987	0.380993	+	0.924578i	$0.375582\pi$
$152$	9.83156e9	1.49392
$153$	1.40014e10	2.06566
$154$	−3.56728e9	−0.511085
$155$	6.53261e9	0.909063
$156$	−1.48752e10	−2.01095
$157$	−8.67879e9	−1.14002	−0.570008	−	0.821639i	$-0.693060\pi$
$157$	−8.67879e9	−1.14002	−0.570008	+	0.821639i	$0.693060\pi$
$158$	−1.89939e10	−2.42469
$159$	5.22249e9	0.648023
$160$	−5.01644e8	−0.0605139
$161$	−1.40888e9	−0.165256
$162$	7.79299e9	0.888969
$163$	1.33354e10	1.47966	0.739832	−	0.672792i	$-0.234905\pi$
$163$	1.33354e10	1.47966	0.739832	+	0.672792i	$0.234905\pi$
$164$	−2.71882e10	−2.93484
$165$	−1.15560e10	−1.21375
$166$	−5.53554e9	−0.565814
$167$	4.09736e9	0.407643	0.203821	−	0.979008i	$-0.434664\pi$
$167$	4.09736e9	0.407643	0.203821	+	0.979008i	$0.434664\pi$
$168$	6.59669e9	0.638903
$169$	−6.68966e9	−0.630832
$170$	1.17428e10	1.07833
$171$	1.83234e10	1.63879
$172$	−3.28698e10	−2.86364
$173$	4.85660e9	0.412216	0.206108	−	0.978529i	$-0.433920\pi$
$173$	4.85660e9	0.412216	0.206108	+	0.978529i	$0.433920\pi$
$174$	4.39574e10	3.63547
$175$	1.95859e9	0.157860
$176$	1.49907e10	1.17764
$177$	−8.89907e9	−0.681498
$178$	1.56690e10	1.16991
$179$	−2.47832e10	−1.80435	−0.902173	−	0.431375i	$-0.858028\pi$
$179$	−2.47832e10	−1.80435	−0.902173	+	0.431375i	$0.858028\pi$
$180$	2.80911e10	1.99454
$181$	7.57351e9	0.524498	0.262249	−	0.965000i	$-0.415536\pi$
$181$	7.57351e9	0.524498	0.262249	+	0.965000i	$0.415536\pi$
$182$	−3.53001e9	−0.238482
$183$	−2.27821e10	−1.50163
$184$	1.88022e10	1.20928
$185$	1.45158e9	0.0911104
$186$	−7.75819e10	−4.75283
$187$	2.45925e10	1.47067
$188$	5.46642e10	3.19148
$189$	5.57220e9	0.317650
$190$	1.53676e10	0.855488
$191$	3.47219e9	0.188779	0.0943895	−	0.995535i	$-0.469910\pi$
$191$	3.47219e9	0.188779	0.0943895	+	0.995535i	$0.469910\pi$
$192$	3.46013e10	1.83754
$193$	−1.98275e10	−1.02863	−0.514315	−	0.857601i	$-0.671954\pi$
$193$	−1.98275e10	−1.02863	−0.514315	+	0.857601i	$0.671954\pi$
$194$	2.21688e9	0.112366
$195$	−1.14353e10	−0.566358
$196$	−3.85461e10	−1.86564
$197$	4.73038e9	0.223768	0.111884	−	0.993721i	$-0.464311\pi$
$197$	4.73038e9	0.223768	0.111884	+	0.993721i	$0.464311\pi$
$198$	8.87267e10	4.10262
$199$	−2.39904e10	−1.08442	−0.542211	−	0.840243i	$-0.682413\pi$
$199$	−2.39904e10	−1.08442	−0.542211	+	0.840243i	$0.682413\pi$
$200$	−2.61383e10	−1.15516
$201$	−6.95110e10	−3.00380
$202$	−1.76872e10	−0.747441
$203$	6.91659e9	0.285864
$204$	−9.24676e10	−3.73813
$205$	−2.09010e10	−0.826559
$206$	−4.27623e9	−0.165447
$207$	3.50422e10	1.32655
$208$	1.48341e10	0.549510
$209$	3.21838e10	1.16675
$210$	1.03112e10	0.365866
$211$	−4.29990e10	−1.49344	−0.746719	−	0.665139i	$-0.768372\pi$
$211$	−4.29990e10	−1.49344	−0.746719	+	0.665139i	$0.768372\pi$
$212$	−2.22982e10	−0.758157
$213$	2.14895e9	0.0715350
$214$	−1.64910e10	−0.537509
$215$	−2.52687e10	−0.806509
$216$	−7.43638e10	−2.32445
$217$	−1.22073e10	−0.373725
$218$	1.02899e11	3.08572
$219$	−2.09588e9	−0.0615697
$220$	4.93401e10	1.42003
$221$	2.43356e10	0.686241
$222$	−1.72391e10	−0.476350
$223$	−6.61217e10	−1.79049	−0.895245	−	0.445574i	$-0.852999\pi$
$223$	−6.61217e10	−1.79049	−0.895245	+	0.445574i	$0.852999\pi$
$224$	9.37410e8	0.0248779
$225$	−4.87148e10	−1.26718
$226$	−5.14707e10	−1.31242
$227$	6.71383e9	0.167824	0.0839120	−	0.996473i	$-0.473259\pi$
$227$	6.71383e9	0.167824	0.0839120	+	0.996473i	$0.473259\pi$
$228$	−1.21011e11	−2.96563
$229$	−2.85296e10	−0.685545	−0.342773	−	0.939418i	$-0.611366\pi$
$229$	−2.85296e10	−0.685545	−0.342773	+	0.939418i	$0.611366\pi$
$230$	2.93894e10	0.692493
$231$	2.15944e10	0.498985
$232$	−9.23054e10	−2.09185
$233$	5.73412e10	1.27457	0.637287	−	0.770626i	$-0.280057\pi$
$233$	5.73412e10	1.27457	0.637287	+	0.770626i	$0.280057\pi$
$234$	8.77999e10	1.91436
$235$	4.20231e10	0.898840
$236$	3.79960e10	0.797321
$237$	1.14979e11	2.36728
$238$	−2.19434e10	−0.443311
$239$	−2.19186e10	−0.434532	−0.217266	−	0.976112i	$-0.569714\pi$
$239$	−2.19186e10	−0.434532	−0.217266	+	0.976112i	$0.569714\pi$
$240$	−4.33305e10	−0.843030
$241$	7.47661e10	1.42767	0.713835	−	0.700314i	$-0.246957\pi$
$241$	7.47661e10	1.42767	0.713835	+	0.700314i	$0.246957\pi$
$242$	6.39278e10	1.19818
$243$	2.86046e10	0.526269
$244$	9.72715e10	1.75684
$245$	−2.96323e10	−0.525434
$246$	2.48222e11	4.32147
$247$	3.18476e10	0.544428
$248$	1.62913e11	2.73478
$249$	3.35092e10	0.552417
$250$	−9.98243e10	−1.61624
$251$	6.49612e10	1.03305	0.516526	−	0.856271i	$-0.327225\pi$
$251$	6.49612e10	1.03305	0.516526	+	0.856271i	$0.327225\pi$
$252$	−5.24931e10	−0.819973
$253$	6.15492e10	0.944453
$254$	9.33509e10	1.40724
$255$	−7.10845e10	−1.05280
$256$	−1.34809e11	−1.96173
$257$	−4.80681e10	−0.687319	−0.343659	−	0.939094i	$-0.611667\pi$
$257$	−4.80681e10	−0.687319	−0.343659	+	0.939094i	$0.611667\pi$
$258$	3.00093e11	4.21665
$259$	−2.71253e9	−0.0374564
$260$	4.88247e10	0.662612
$261$	−1.72032e11	−2.29471
$262$	−2.46855e11	−3.23658
$263$	2.28787e10	0.294871	0.147435	−	0.989072i	$-0.452898\pi$
$263$	2.28787e10	0.294871	0.147435	+	0.989072i	$0.452898\pi$
$264$	−2.88188e11	−3.65139
$265$	−1.71418e10	−0.213525
$266$	−2.87170e10	−0.351700
$267$	−9.48520e10	−1.14221
$268$	2.96788e11	3.51431
$269$	−4.39549e10	−0.511826	−0.255913	−	0.966700i	$-0.582376\pi$
$269$	−4.39549e10	−0.511826	−0.255913	+	0.966700i	$0.582376\pi$
$270$	−1.16237e11	−1.33109
$271$	−7.77386e10	−0.875538	−0.437769	−	0.899087i	$-0.644231\pi$
$271$	−7.77386e10	−0.875538	−0.437769	+	0.899087i	$0.644231\pi$
$272$	9.22124e10	1.02148
$273$	2.13688e10	0.232835
$274$	−1.78396e10	−0.191208
$275$	−8.55642e10	−0.902184
$276$	−2.31425e11	−2.40059
$277$	1.18881e11	1.21326	0.606630	−	0.794984i	$-0.292521\pi$
$277$	1.18881e11	1.21326	0.606630	+	0.794984i	$0.292521\pi$
$278$	−1.23047e11	−1.23558
$279$	3.03626e11	2.99999
$280$	−2.16523e10	−0.210520
$281$	2.01709e10	0.192996	0.0964979	−	0.995333i	$-0.469236\pi$
$281$	2.01709e10	0.192996	0.0964979	+	0.995333i	$0.469236\pi$
$282$	−4.99070e11	−4.69938
$283$	1.17813e11	1.09183	0.545915	−	0.837841i	$-0.316182\pi$
$283$	1.17813e11	1.09183	0.545915	+	0.837841i	$0.316182\pi$
$284$	−9.17529e9	−0.0836927
$285$	−9.30271e10	−0.835233
$286$	1.54215e11	1.36295
$287$	3.90571e10	0.339807
$288$	−2.33156e10	−0.199701
$289$	3.26882e10	0.275645
$290$	−1.44281e11	−1.19790
$291$	−1.34198e10	−0.109705
$292$	8.94867e9	0.0720337
$293$	−9.96143e10	−0.789618	−0.394809	−	0.918763i	$-0.629189\pi$
$293$	−9.96143e10	−0.789618	−0.394809	+	0.918763i	$0.629189\pi$
$294$	3.51916e11	2.74711
$295$	2.92094e10	0.224555
$296$	3.62001e10	0.274092
$297$	−2.43431e11	−1.81540
$298$	−3.60589e11	−2.64874
$299$	6.09063e10	0.440699
$300$	3.21721e11	2.29316
$301$	4.72189e10	0.331564
$302$	1.89756e11	1.31270
$303$	1.07069e11	0.729744
$304$	1.20677e11	0.810388
$305$	7.47775e10	0.494791
$306$	5.45786e11	3.55857
$307$	−2.85145e10	−0.183208	−0.0916038	−	0.995796i	$-0.529199\pi$
$307$	−2.85145e10	−0.183208	−0.0916038	+	0.995796i	$0.529199\pi$
$308$	−9.22006e10	−0.583789
$309$	2.58860e10	0.161530
$310$	2.54647e11	1.56607
$311$	−4.99899e10	−0.303012	−0.151506	−	0.988456i	$-0.548412\pi$
$311$	−4.99899e10	−0.303012	−0.151506	+	0.988456i	$0.548412\pi$
$312$	−2.85178e11	−1.70380
$313$	−1.24731e11	−0.734553	−0.367277	−	0.930112i	$-0.619710\pi$
$313$	−1.24731e11	−0.734553	−0.367277	+	0.930112i	$0.619710\pi$
$314$	−3.38307e11	−1.96394
$315$	−4.03541e10	−0.230935
$316$	−4.90920e11	−2.76961
$317$	8.74242e10	0.486256	0.243128	−	0.969994i	$-0.421826\pi$
$317$	8.74242e10	0.486256	0.243128	+	0.969994i	$0.421826\pi$
$318$	2.03577e11	1.11637
$319$	−3.02163e11	−1.63374
$320$	−1.13572e11	−0.605474
$321$	9.98279e10	0.524783
$322$	−5.49193e10	−0.284691
$323$	1.97973e11	1.01203
$324$	2.01419e11	1.01543
$325$	−8.46705e10	−0.420976
$326$	5.19827e11	2.54906
$327$	−6.22896e11	−3.01266
$328$	−5.21237e11	−2.48658
$329$	−7.85275e10	−0.369522
$330$	−4.50462e11	−2.09096
$331$	−3.27495e11	−1.49961	−0.749805	−	0.661659i	$-0.769853\pi$
$331$	−3.27495e11	−1.49961	−0.749805	+	0.661659i	$0.769853\pi$
$332$	−1.43073e11	−0.646302
$333$	6.74672e10	0.300672
$334$	1.59719e11	0.702257
$335$	2.28156e11	0.989760
$336$	8.09707e10	0.346578
$337$	2.53387e11	1.07016	0.535081	−	0.844801i	$-0.320281\pi$
$337$	2.53387e11	1.07016	0.535081	+	0.844801i	$0.320281\pi$
$338$	−2.60769e11	−1.08675
$339$	3.11576e11	1.28134
$340$	3.03506e11	1.23172
$341$	5.33298e11	2.13587
$342$	7.14261e11	2.82319
$343$	1.13778e11	0.443849
$344$	−6.30160e11	−2.42626
$345$	−1.77908e11	−0.676097
$346$	1.89315e11	0.710136
$347$	−3.68863e10	−0.136579	−0.0682893	−	0.997666i	$-0.521754\pi$
$347$	−3.68863e10	−0.136579	−0.0682893	+	0.997666i	$0.521754\pi$
$348$	1.13613e12	4.15262
$349$	1.95134e10	0.0704075	0.0352037	−	0.999380i	$-0.488792\pi$
$349$	1.95134e10	0.0704075	0.0352037	+	0.999380i	$0.488792\pi$
$350$	7.63474e10	0.271950
$351$	−2.40888e11	−0.847099
$352$	−4.09524e10	−0.142179
$353$	−2.08386e11	−0.714303	−0.357152	−	0.934046i	$-0.616252\pi$
$353$	−2.08386e11	−0.714303	−0.357152	+	0.934046i	$0.616252\pi$
$354$	−3.46893e11	−1.17404
$355$	−7.05351e9	−0.0235710
$356$	4.04985e11	1.33633
$357$	1.32834e11	0.432815
$358$	−9.66073e11	−3.10839
$359$	4.75019e11	1.50934	0.754669	−	0.656106i	$-0.227798\pi$
$359$	4.75019e11	1.50934	0.754669	+	0.656106i	$0.227798\pi$
$360$	5.38545e11	1.68990
$361$	−6.36042e10	−0.197108
$362$	2.95222e11	0.903567
$363$	−3.86985e11	−1.16981
$364$	−9.12375e10	−0.272406
$365$	6.87929e9	0.0202874
$366$	−8.88064e11	−2.58690
$367$	8.25540e10	0.237542	0.118771	−	0.992922i	$-0.462105\pi$
$367$	8.25540e10	0.237542	0.118771	+	0.992922i	$0.462105\pi$
$368$	2.30786e11	0.655985
$369$	−9.71445e11	−2.72772
$370$	5.65838e10	0.156958
$371$	3.20324e10	0.0877824
$372$	−2.00520e12	−5.42893
$373$	2.96328e11	0.792653	0.396326	−	0.918110i	$-0.370285\pi$
$373$	2.96328e11	0.792653	0.396326	+	0.918110i	$0.370285\pi$
$374$	9.58637e11	2.53356
$375$	6.04283e11	1.57797
$376$	1.04799e12	2.70403
$377$	−2.99007e11	−0.762334
$378$	2.17209e11	0.547224
$379$	4.16002e11	1.03566	0.517832	−	0.855482i	$-0.326739\pi$
$379$	4.16002e11	1.03566	0.517832	+	0.855482i	$0.326739\pi$
$380$	3.97194e11	0.977184
$381$	−5.65097e11	−1.37392
$382$	1.35349e11	0.325215
$383$	3.09735e10	0.0735523	0.0367761	−	0.999324i	$-0.488291\pi$
$383$	3.09735e10	0.0735523	0.0367761	+	0.999324i	$0.488291\pi$
$384$	1.27054e12	2.98193
$385$	−7.08792e10	−0.164417
$386$	−7.72892e11	−1.77205
$387$	−1.17445e12	−2.66155
$388$	5.72980e10	0.128350
$389$	7.11486e11	1.57541	0.787704	−	0.616054i	$-0.211270\pi$
$389$	7.11486e11	1.57541	0.787704	+	0.616054i	$0.211270\pi$
$390$	−4.45757e11	−0.975680
$391$	3.78608e11	0.819209
$392$	−7.38983e11	−1.58069
$393$	1.49433e12	3.15995
$394$	1.84395e11	0.385492
$395$	−3.77395e11	−0.780026
$396$	2.29325e12	4.68623
$397$	4.02764e11	0.813754	0.406877	−	0.913483i	$-0.366618\pi$
$397$	4.02764e11	0.813754	0.406877	+	0.913483i	$0.366618\pi$
$398$	−9.35166e11	−1.86816
$399$	1.73838e11	0.343373
$400$	−3.20833e11	−0.626627
$401$	4.99751e10	0.0965170	0.0482585	−	0.998835i	$-0.484633\pi$
$401$	4.99751e10	0.0965170	0.0482585	+	0.998835i	$0.484633\pi$
$402$	−2.70960e12	−5.17473
$403$	5.27728e11	0.996637
$404$	−4.57147e11	−0.853767
$405$	1.54841e11	0.285982
$406$	2.69615e11	0.492467
$407$	1.18502e11	0.214067
$408$	−1.77273e12	−3.16718
$409$	−1.94549e11	−0.343775	−0.171888	−	0.985117i	$-0.554987\pi$
$409$	−1.94549e11	−0.343775	−0.171888	+	0.985117i	$0.554987\pi$
$410$	−8.14738e11	−1.42394
$411$	1.07991e11	0.186681
$412$	−1.10524e11	−0.188982
$413$	−5.45829e10	−0.0923169
$414$	1.36597e12	2.28529
$415$	−1.09987e11	−0.182023
$416$	−4.05246e10	−0.0663435
$417$	7.44861e11	1.20632
$418$	1.25455e12	2.01000
$419$	1.15616e12	1.83254	0.916272	−	0.400556i	$-0.131183\pi$
$419$	1.15616e12	1.83254	0.916272	+	0.400556i	$0.131183\pi$
$420$	2.66506e11	0.417912
$421$	−8.71617e11	−1.35225	−0.676124	−	0.736788i	$-0.736341\pi$
$421$	−8.71617e11	−1.35225	−0.676124	+	0.736788i	$0.736341\pi$
$422$	−1.67614e12	−2.57279
$423$	1.95317e12	2.96625
$424$	−4.27489e11	−0.642360
$425$	−5.26332e11	−0.782546
$426$	8.37681e10	0.123235
$427$	−1.39735e11	−0.203413
$428$	−4.26231e11	−0.613971
$429$	−9.33534e11	−1.33068
$430$	−9.84994e11	−1.38939
$431$	1.58320e11	0.220998	0.110499	−	0.993876i	$-0.464755\pi$
$431$	1.58320e11	0.220998	0.110499	+	0.993876i	$0.464755\pi$
$432$	−9.12773e11	−1.26092
$433$	−1.24195e11	−0.169789	−0.0848945	−	0.996390i	$-0.527055\pi$
$433$	−1.24195e11	−0.169789	−0.0848945	+	0.996390i	$0.527055\pi$
$434$	−4.75852e11	−0.643826
$435$	8.73402e11	1.16953
$436$	2.65955e12	3.52468
$437$	4.95479e11	0.649918
$438$	−8.16991e10	−0.106068
$439$	6.38585e11	0.820594	0.410297	−	0.911952i	$-0.365425\pi$
$439$	6.38585e11	0.820594	0.410297	+	0.911952i	$0.365425\pi$
$440$	9.45919e11	1.20314
$441$	−1.37726e12	−1.73398
$442$	9.48623e11	1.18221
$443$	8.64410e11	1.06636	0.533179	−	0.846002i	$-0.320997\pi$
$443$	8.64410e11	1.06636	0.533179	+	0.846002i	$0.320997\pi$
$444$	−4.45565e11	−0.544112
$445$	3.11332e11	0.376361
$446$	−2.57748e12	−3.08453
$447$	2.18282e12	2.58603
$448$	2.12229e11	0.248916
$449$	−9.35376e11	−1.08612	−0.543060	−	0.839694i	$-0.682734\pi$
$449$	−9.35376e11	−1.08612	−0.543060	+	0.839694i	$0.682734\pi$
$450$	−1.89894e12	−2.18301
$451$	−1.70628e12	−1.94203
$452$	−1.33032e12	−1.49911
$453$	−1.14868e12	−1.28162
$454$	2.61711e11	0.289115
$455$	−7.01389e10	−0.0767198
$456$	−2.31995e12	−2.51268
$457$	−1.09025e12	−1.16924	−0.584619	−	0.811308i	$-0.698756\pi$
$457$	−1.09025e12	−1.16924	−0.584619	+	0.811308i	$0.698756\pi$
$458$	−1.11211e12	−1.18101
$459$	−1.49742e12	−1.57466
$460$	7.59605e11	0.791002
$461$	2.10918e11	0.217500	0.108750	−	0.994069i	$-0.465315\pi$
$461$	2.10918e11	0.217500	0.108750	+	0.994069i	$0.465315\pi$
$462$	8.41768e11	0.859615
$463$	−1.51627e12	−1.53342	−0.766710	−	0.641994i	$-0.778107\pi$
$463$	−1.51627e12	−1.53342	−0.766710	+	0.641994i	$0.778107\pi$
$464$	−1.13300e12	−1.13474
$465$	−1.54150e12	−1.52899
$466$	2.23521e12	2.19574
$467$	8.29112e11	0.806654	0.403327	−	0.915056i	$-0.367854\pi$
$467$	8.29112e11	0.806654	0.403327	+	0.915056i	$0.367854\pi$
$468$	2.26930e12	2.18668
$469$	−4.26349e11	−0.406900
$470$	1.63810e12	1.54846
$471$	2.04793e12	1.91744
$472$	7.28436e11	0.675542
$473$	−2.06284e12	−1.89492
$474$	4.48198e12	4.07819
$475$	−6.88803e11	−0.620831
$476$	−5.67155e11	−0.506373
$477$	−7.96723e11	−0.704652
$478$	−8.54404e11	−0.748579
$479$	1.58605e12	1.37660	0.688298	−	0.725428i	$-0.258358\pi$
$479$	1.58605e12	1.37660	0.688298	+	0.725428i	$0.258358\pi$
$480$	1.18373e11	0.101781
$481$	1.17264e11	0.0998875
$482$	2.91445e12	2.45949
$483$	3.32452e11	0.277950
$484$	1.65229e12	1.36862
$485$	4.40478e10	0.0361482
$486$	1.11503e12	0.906618
$487$	−2.23757e12	−1.80259	−0.901295	−	0.433206i	$-0.857382\pi$
$487$	−2.23757e12	−1.80259	−0.901295	+	0.433206i	$0.857382\pi$
$488$	1.86483e12	1.48851
$489$	−3.14676e12	−2.48870
$490$	−1.15509e12	−0.905180
$491$	−2.05134e12	−1.59283	−0.796417	−	0.604748i	$-0.793274\pi$
$491$	−2.05134e12	−1.59283	−0.796417	+	0.604748i	$0.793274\pi$
$492$	6.41560e12	4.93621
$493$	−1.85870e12	−1.41709
$494$	1.24145e12	0.937901
$495$	1.76294e12	1.31982
$496$	1.99966e12	1.48351
$497$	1.31807e10	0.00969026
$498$	1.30622e12	0.951664
$499$	1.27419e12	0.919988	0.459994	−	0.887922i	$-0.347852\pi$
$499$	1.27419e12	0.919988	0.459994	+	0.887922i	$0.347852\pi$
$500$	−2.58008e12	−1.84616
$501$	−9.66851e11	−0.685630
$502$	2.53225e12	1.77967
$503$	−2.09133e11	−0.145669	−0.0728343	−	0.997344i	$-0.523204\pi$
$503$	−2.09133e11	−0.145669	−0.0728343	+	0.997344i	$0.523204\pi$
$504$	−1.00637e12	−0.694734
$505$	−3.51431e11	−0.240453
$506$	2.39924e12	1.62703
$507$	1.57856e12	1.06102
$508$	2.41277e12	1.60742
$509$	−8.42197e10	−0.0556139	−0.0278070	−	0.999613i	$-0.508852\pi$
$509$	−8.42197e10	−0.0556139	−0.0278070	+	0.999613i	$0.508852\pi$
$510$	−2.77093e12	−1.81368
$511$	−1.28552e10	−0.00834034
$512$	−2.49820e12	−1.60662
$513$	−1.95965e12	−1.24925
$514$	−1.87374e12	−1.18406
$515$	−8.49657e10	−0.0532244
$516$	7.75627e12	4.81647
$517$	3.43061e12	2.11185
$518$	−1.05737e11	−0.0645271
$519$	−1.14601e12	−0.693322
$520$	9.36038e11	0.561408
$521$	6.10415e11	0.362957	0.181479	−	0.983395i	$-0.441912\pi$
$521$	6.10415e11	0.362957	0.181479	+	0.983395i	$0.441912\pi$
$522$	−6.70597e12	−3.95316
$523$	−1.40360e12	−0.820324	−0.410162	−	0.912013i	$-0.634528\pi$
$523$	−1.40360e12	−0.820324	−0.410162	+	0.912013i	$0.634528\pi$
$524$	−6.38028e12	−3.69699
$525$	−4.62167e11	−0.265511
$526$	8.91834e11	0.507982
$527$	3.28048e12	1.85264
$528$	−3.53734e12	−1.98073
$529$	−8.53585e11	−0.473910
$530$	−6.68201e11	−0.367846
$531$	1.35761e12	0.741052
$532$	−7.42227e11	−0.401730
$533$	−1.68845e12	−0.906185
$534$	−3.69741e12	−1.96772
$535$	−3.27665e11	−0.172917
$536$	5.68984e12	2.97755
$537$	5.84809e12	3.03480
$538$	−1.71340e12	−0.881736
$539$	−2.41907e12	−1.23452
$540$	−3.00429e12	−1.52044
$541$	−2.69217e11	−0.135119	−0.0675593	−	0.997715i	$-0.521521\pi$
$541$	−2.69217e11	−0.135119	−0.0675593	+	0.997715i	$0.521521\pi$
$542$	−3.03032e12	−1.50831
$543$	−1.78712e12	−0.882173
$544$	−2.51911e11	−0.123325
$545$	2.04453e12	0.992680
$546$	8.32976e11	0.401112
$547$	3.74178e11	0.178704	0.0893521	−	0.996000i	$-0.471520\pi$
$547$	3.74178e11	0.178704	0.0893521	+	0.996000i	$0.471520\pi$
$548$	−4.61085e11	−0.218408
$549$	3.47554e12	1.63285
$550$	−3.33537e12	−1.55422
$551$	−2.43245e12	−1.12425
$552$	−4.43674e12	−2.03394
$553$	7.05229e11	0.320676
$554$	4.63409e12	2.09012
$555$	−3.42528e11	−0.153242
$556$	−3.18030e12	−1.41134
$557$	2.72560e12	1.19981	0.599906	−	0.800070i	$-0.295205\pi$
$557$	2.72560e12	1.19981	0.599906	+	0.800070i	$0.295205\pi$
$558$	1.18356e13	5.16816
$559$	−2.04129e12	−0.884203
$560$	−2.65770e11	−0.114198
$561$	−5.80308e12	−2.47358
$562$	7.86281e11	0.332479
$563$	3.42118e12	1.43512	0.717561	−	0.696496i	$-0.245259\pi$
$563$	3.42118e12	1.43512	0.717561	+	0.696496i	$0.245259\pi$
$564$	−1.28991e13	−5.36788
$565$	−1.02269e12	−0.422206
$566$	4.59246e12	1.88092
$567$	−2.89348e11	−0.117570
$568$	−1.75903e11	−0.0709098
$569$	−2.87261e12	−1.14887	−0.574437	−	0.818549i	$-0.694779\pi$
$569$	−2.87261e12	−1.14887	−0.574437	+	0.818549i	$0.694779\pi$
$570$	−3.62628e12	−1.43888
$571$	7.00838e11	0.275902	0.137951	−	0.990439i	$-0.455948\pi$
$571$	7.00838e11	0.275902	0.137951	+	0.990439i	$0.455948\pi$
$572$	3.98587e12	1.55683
$573$	−8.19331e11	−0.317515
$574$	1.52248e12	0.585394
$575$	−1.31729e12	−0.502545
$576$	−5.27864e12	−1.99812
$577$	−5.05198e12	−1.89745	−0.948725	−	0.316103i	$-0.897625\pi$
$577$	−5.05198e12	−1.89745	−0.948725	+	0.316103i	$0.897625\pi$
$578$	1.27421e12	0.474862
$579$	4.67868e12	1.73009
$580$	−3.72912e12	−1.36830
$581$	2.05531e11	0.0748314
$582$	−5.23116e11	−0.188993
$583$	−1.39939e12	−0.501685
$584$	1.71559e11	0.0610316
$585$	1.74452e12	0.615850
$586$	−3.88305e12	−1.36030
$587$	2.66984e12	0.928139	0.464070	−	0.885799i	$-0.346389\pi$
$587$	2.66984e12	0.928139	0.464070	+	0.885799i	$0.346389\pi$
$588$	9.09570e12	3.13789
$589$	4.29312e12	1.46979
$590$	1.13861e12	0.386848
$591$	−1.11623e12	−0.376365
$592$	4.44335e11	0.148684
$593$	6.87496e11	0.228309	0.114155	−	0.993463i	$-0.463584\pi$
$593$	6.87496e11	0.228309	0.114155	+	0.993463i	$0.463584\pi$
$594$	−9.48916e12	−3.12744
$595$	−4.36000e11	−0.142613
$596$	−9.31987e12	−3.02553
$597$	5.66100e12	1.82393
$598$	2.37418e12	0.759204
$599$	−3.90668e11	−0.123990	−0.0619951	−	0.998076i	$-0.519746\pi$
$599$	−3.90668e11	−0.123990	−0.0619951	+	0.998076i	$0.519746\pi$
$600$	6.16785e12	1.94291
$601$	−2.78012e12	−0.869217	−0.434608	−	0.900620i	$-0.643113\pi$
$601$	−2.78012e12	−0.869217	−0.434608	+	0.900620i	$0.643113\pi$
$602$	1.84064e12	0.571194
$603$	1.06043e13	3.26630
$604$	4.90447e12	1.49943
$605$	1.27020e12	0.385454
$606$	4.17363e12	1.25715
$607$	−2.39533e12	−0.716171	−0.358086	−	0.933689i	$-0.616570\pi$
$607$	−2.39533e12	−0.716171	−0.358086	+	0.933689i	$0.616570\pi$
$608$	−3.29672e11	−0.0978398
$609$	−1.63211e12	−0.480807
$610$	2.91489e12	0.852389
$611$	3.39477e12	0.985429
$612$	1.41065e13	4.06479
$613$	−5.20010e12	−1.48744	−0.743720	−	0.668491i	$-0.766940\pi$
$613$	−5.20010e12	−1.48744	−0.743720	+	0.668491i	$0.766940\pi$
$614$	−1.11152e12	−0.315617
$615$	4.93199e12	1.39022
$616$	−1.76762e12	−0.494623
$617$	−3.38516e11	−0.0940363	−0.0470182	−	0.998894i	$-0.514972\pi$
$617$	−3.38516e11	−0.0940363	−0.0470182	+	0.998894i	$0.514972\pi$
$618$	1.00906e12	0.278272
$619$	6.50681e12	1.78139	0.890697	−	0.454597i	$-0.150217\pi$
$619$	6.50681e12	1.78139	0.890697	+	0.454597i	$0.150217\pi$
$620$	6.58166e12	1.78885
$621$	−3.74769e12	−1.01123
$622$	−1.94865e12	−0.522008
$623$	−5.81779e11	−0.154726
$624$	−3.50039e12	−0.924243
$625$	6.59611e11	0.172913
$626$	−4.86210e12	−1.26543
$627$	−7.59439e12	−1.96241
$628$	−8.74395e12	−2.24331
$629$	7.28940e11	0.185680
$630$	−1.57304e12	−0.397838
$631$	−1.32536e12	−0.332814	−0.166407	−	0.986057i	$-0.553217\pi$
$631$	−1.32536e12	−0.332814	−0.166407	+	0.986057i	$0.553217\pi$
$632$	−9.41163e12	−2.34659
$633$	1.01465e13	2.51187
$634$	3.40787e12	0.837686
$635$	1.85482e12	0.452709
$636$	5.26170e12	1.27517
$637$	−2.39380e12	−0.576052
$638$	−1.17786e13	−2.81449
$639$	−3.27836e11	−0.0777863
$640$	−4.17029e12	−0.982553
$641$	−3.77644e12	−0.883531	−0.441766	−	0.897131i	$-0.645648\pi$
$641$	−3.77644e12	−0.883531	−0.441766	+	0.897131i	$0.645648\pi$
$642$	3.89138e12	0.904057
$643$	−3.24115e11	−0.0747739	−0.0373869	−	0.999301i	$-0.511903\pi$
$643$	−3.24115e11	−0.0747739	−0.0373869	+	0.999301i	$0.511903\pi$
$644$	−1.41946e12	−0.325189
$645$	5.96263e12	1.35650
$646$	7.71714e12	1.74345
$647$	−5.43954e12	−1.22037	−0.610187	−	0.792257i	$-0.708906\pi$
$647$	−5.43954e12	−1.22037	−0.610187	+	0.792257i	$0.708906\pi$
$648$	3.86149e12	0.860336
$649$	2.38455e12	0.527600
$650$	−3.30053e12	−0.725226
$651$	2.88056e12	0.628582
$652$	1.34356e13	2.91167
$653$	6.91737e12	1.48879	0.744393	−	0.667742i	$-0.232739\pi$
$653$	6.91737e12	1.48879	0.744393	+	0.667742i	$0.232739\pi$
$654$	−2.42810e13	−5.19000
$655$	−4.90484e12	−1.04121
$656$	−6.39788e12	−1.34887
$657$	3.19739e11	0.0669501
$658$	−3.06107e12	−0.636586
$659$	−5.19839e12	−1.07370	−0.536852	−	0.843677i	$-0.680387\pi$
$659$	−5.19839e12	−1.07370	−0.536852	+	0.843677i	$0.680387\pi$
$660$	−1.16428e13	−2.38841
$661$	−3.41806e12	−0.696423	−0.348211	−	0.937416i	$-0.613211\pi$
$661$	−3.41806e12	−0.696423	−0.348211	+	0.937416i	$0.613211\pi$
$662$	−1.27660e13	−2.58342
$663$	−5.74246e12	−1.15422
$664$	−2.74291e12	−0.547589
$665$	−5.70587e11	−0.113142
$666$	2.62993e12	0.517977
$667$	−4.65189e12	−0.910046
$668$	4.12812e12	0.802155
$669$	1.56027e13	3.01149
$670$	8.89371e12	1.70509
$671$	6.10456e12	1.16253
$672$	−2.21200e11	−0.0418431
$673$	−5.22993e12	−0.982717	−0.491358	−	0.870958i	$-0.663499\pi$
$673$	−5.22993e12	−0.982717	−0.491358	+	0.870958i	$0.663499\pi$
$674$	9.87725e12	1.84360
$675$	5.20996e12	0.965977
$676$	−6.73989e12	−1.24135
$677$	−2.71165e11	−0.0496117	−0.0248059	−	0.999692i	$-0.507897\pi$
$677$	−2.71165e11	−0.0496117	−0.0248059	+	0.999692i	$0.507897\pi$
$678$	1.21455e13	2.20741
$679$	−8.23111e10	−0.0148609
$680$	5.81864e12	1.04359
$681$	−1.58426e12	−0.282270
$682$	2.07884e13	3.67953
$683$	−6.83276e12	−1.20144	−0.600721	−	0.799459i	$-0.705120\pi$
$683$	−6.83276e12	−1.20144	−0.600721	+	0.799459i	$0.705120\pi$
$684$	1.84610e13	3.22479
$685$	−3.54459e11	−0.0615118
$686$	4.43518e12	0.764632
$687$	6.73212e12	1.15304
$688$	−7.73486e12	−1.31615
$689$	−1.38477e12	−0.234095
$690$	−6.93500e12	−1.16473
$691$	9.89589e12	1.65122	0.825608	−	0.564244i	$-0.190832\pi$
$691$	9.89589e12	1.65122	0.825608	+	0.564244i	$0.190832\pi$
$692$	4.89307e12	0.811155
$693$	−3.29436e12	−0.542589
$694$	−1.43786e12	−0.235288
$695$	−2.44486e12	−0.397486
$696$	2.17813e13	3.51837
$697$	−1.04958e13	−1.68450
$698$	7.60650e11	0.121293
$699$	−1.35308e13	−2.14376
$700$	1.97329e12	0.310635
$701$	9.15078e12	1.43129	0.715644	−	0.698465i	$-0.246133\pi$
$701$	9.15078e12	1.43129	0.715644	+	0.698465i	$0.246133\pi$
$702$	−9.39004e12	−1.45932
$703$	9.53953e11	0.147309
$704$	−9.27159e12	−1.42258
$705$	−9.91616e12	−1.51179
$706$	−8.12307e12	−1.23055
$707$	6.56712e11	0.0988524
$708$	−8.96589e12	−1.34105
$709$	5.58442e12	0.829985	0.414993	−	0.909825i	$-0.363784\pi$
$709$	5.58442e12	0.829985	0.414993	+	0.909825i	$0.363784\pi$
$710$	−2.74952e11	−0.0406064
$711$	−1.75407e13	−2.57415
$712$	7.76413e12	1.13223
$713$	8.21028e12	1.18975
$714$	5.17798e12	0.745622
$715$	3.06414e12	0.438461
$716$	−2.49693e13	−3.55057
$717$	5.17211e12	0.730856
$718$	1.85167e13	2.60018
$719$	7.53737e11	0.105182	0.0525908	−	0.998616i	$-0.483252\pi$
$719$	7.53737e11	0.105182	0.0525908	+	0.998616i	$0.483252\pi$
$720$	6.61033e12	0.916700
$721$	1.58773e11	0.0218811
$722$	−2.47935e12	−0.339563
$723$	−1.76425e13	−2.40125
$724$	7.63037e12	1.03210
$725$	6.46695e12	0.869317
$726$	−1.50850e13	−2.01526
$727$	1.43246e13	1.90186	0.950929	−	0.309409i	$-0.100131\pi$
$727$	1.43246e13	1.90186	0.950929	+	0.309409i	$0.100131\pi$
$728$	−1.74915e12	−0.230800
$729$	−1.06848e13	−1.40118
$730$	2.68161e11	0.0349496
$731$	−1.26892e13	−1.64363
$732$	−2.29531e13	−2.95489
$733$	1.34469e13	1.72050	0.860252	−	0.509870i	$-0.170306\pi$
$733$	1.34469e13	1.72050	0.860252	+	0.509870i	$0.170306\pi$
$734$	3.21803e12	0.409220
$735$	6.99232e12	0.883748
$736$	−6.30473e11	−0.0791984
$737$	1.86258e13	2.32547
$738$	−3.78678e13	−4.69911
$739$	1.18493e13	1.46148	0.730740	−	0.682656i	$-0.239175\pi$
$739$	1.18493e13	1.46148	0.730740	+	0.682656i	$0.239175\pi$
$740$	1.46248e12	0.179286
$741$	−7.51506e12	−0.915695
$742$	1.24865e12	0.151225
$743$	−3.23328e12	−0.389218	−0.194609	−	0.980881i	$-0.562344\pi$
$743$	−3.23328e12	−0.389218	−0.194609	+	0.980881i	$0.562344\pi$
$744$	−3.84425e13	−4.59974
$745$	−7.16465e12	−0.852102
$746$	1.15511e13	1.36552
$747$	−5.11204e12	−0.600691
$748$	2.47771e13	2.89397
$749$	6.12300e11	0.0710879
$750$	2.35555e13	2.71842
$751$	−1.55020e13	−1.77831	−0.889155	−	0.457606i	$-0.848707\pi$
$751$	−1.55020e13	−1.77831	−0.889155	+	0.457606i	$0.848707\pi$
$752$	1.28635e13	1.46682
$753$	−1.53289e13	−1.73753
$754$	−1.16556e13	−1.31329
$755$	3.77031e12	0.422295
$756$	5.61404e12	0.625068
$757$	−4.12422e12	−0.456468	−0.228234	−	0.973606i	$-0.573295\pi$
$757$	−4.12422e12	−0.456468	−0.228234	+	0.973606i	$0.573295\pi$
$758$	1.62161e13	1.78417
$759$	−1.45237e13	−1.58851
$760$	7.61476e12	0.827933
$761$	1.00368e13	1.08484	0.542420	−	0.840107i	$-0.317508\pi$
$761$	1.00368e13	1.08484	0.542420	+	0.840107i	$0.317508\pi$
$762$	−2.20280e13	−2.36688
$763$	−3.82056e12	−0.408101
$764$	3.49826e12	0.371477
$765$	1.08444e13	1.14480
$766$	1.20738e12	0.126711
$767$	2.35964e12	0.246188
$768$	3.18108e13	3.29951
$769$	−9.71416e12	−1.00170	−0.500849	−	0.865535i	$-0.666979\pi$
$769$	−9.71416e12	−1.00170	−0.500849	+	0.865535i	$0.666979\pi$
$770$	−2.76293e12	−0.283245
$771$	1.13426e13	1.15603
$772$	−1.99763e13	−2.02413
$773$	−1.39666e13	−1.40696	−0.703482	−	0.710713i	$-0.748373\pi$
$773$	−1.39666e13	−1.40696	−0.703482	+	0.710713i	$0.748373\pi$
$774$	−4.57810e13	−4.58513
$775$	−1.14137e13	−1.13650
$776$	1.09848e12	0.108747
$777$	6.40075e11	0.0629994
$778$	2.77343e13	2.71400
$779$	−1.37357e13	−1.33639
$780$	−1.15211e13	−1.11447
$781$	−5.75822e11	−0.0553808
$782$	1.47585e13	1.41127
$783$	1.83985e13	1.74926
$784$	−9.07060e12	−0.857459
$785$	−6.72191e12	−0.631800
$786$	5.82503e13	5.44373
$787$	1.38403e13	1.28605	0.643026	−	0.765845i	$-0.277679\pi$
$787$	1.38403e13	1.28605	0.643026	+	0.765845i	$0.277679\pi$
$788$	4.76590e12	0.440329
$789$	−5.39869e12	−0.495954
$790$	−1.47112e13	−1.34377
$791$	1.91107e12	0.173573
$792$	4.39649e13	3.97047
$793$	6.04079e12	0.542456
$794$	1.57001e13	1.40188
$795$	4.04494e12	0.359136
$796$	−2.41705e13	−2.13391
$797$	7.15665e12	0.628271	0.314136	−	0.949378i	$-0.398285\pi$
$797$	7.15665e12	0.628271	0.314136	+	0.949378i	$0.398285\pi$
$798$	6.77634e12	0.591537
$799$	2.11027e13	1.83180
$800$	8.76469e11	0.0756540
$801$	1.44703e13	1.24202
$802$	1.94807e12	0.166273
$803$	5.61600e11	0.0476658
$804$	−7.00329e13	−5.91085
$805$	−1.09121e12	−0.0915852
$806$	2.05713e13	1.71693
$807$	1.03720e13	0.860859
$808$	−8.76414e12	−0.723366
$809$	−2.46970e12	−0.202711	−0.101355	−	0.994850i	$-0.532318\pi$
$809$	−2.46970e12	−0.202711	−0.101355	+	0.994850i	$0.532318\pi$
$810$	6.03585e12	0.492669
$811$	−4.26438e11	−0.0346148	−0.0173074	−	0.999850i	$-0.505509\pi$
$811$	−4.26438e11	−0.0346148	−0.0173074	+	0.999850i	$0.505509\pi$
$812$	6.96853e12	0.562521
$813$	1.83439e13	1.47260
$814$	4.61930e12	0.368779
$815$	1.03286e13	0.820034
$816$	−2.17593e13	−1.71806
$817$	−1.66061e13	−1.30397
$818$	−7.58370e12	−0.592231
$819$	−3.25995e12	−0.253182
$820$	−2.10579e13	−1.62649
$821$	1.00527e13	0.772216	0.386108	−	0.922454i	$-0.373819\pi$
$821$	1.00527e13	0.772216	0.386108	+	0.922454i	$0.373819\pi$
$822$	4.20959e12	0.321600
$823$	−2.22362e13	−1.68951	−0.844757	−	0.535150i	$-0.820255\pi$
$823$	−2.22362e13	−1.68951	−0.844757	+	0.535150i	$0.820255\pi$
$824$	−2.11891e12	−0.160118
$825$	2.01906e13	1.51742
$826$	−2.12769e12	−0.159037
$827$	2.01733e13	1.49969	0.749846	−	0.661612i	$-0.230127\pi$
$827$	2.01733e13	1.49969	0.749846	+	0.661612i	$0.230127\pi$
$828$	3.53053e13	2.61038
$829$	−1.68052e13	−1.23580	−0.617899	−	0.786257i	$-0.712016\pi$
$829$	−1.68052e13	−1.23580	−0.617899	+	0.786257i	$0.712016\pi$
$830$	−4.28740e12	−0.313576
$831$	−2.80523e13	−2.04063
$832$	−9.17474e12	−0.663802
$833$	−1.48805e13	−1.07081
$834$	2.90353e13	2.07816
$835$	3.17349e12	0.225917
$836$	3.24254e13	2.29592
$837$	−3.24722e13	−2.28690
$838$	4.50681e13	3.15697
$839$	−9.07284e12	−0.632142	−0.316071	−	0.948736i	$-0.602364\pi$
$839$	−9.07284e12	−0.632142	−0.316071	+	0.948736i	$0.602364\pi$
$840$	5.10929e12	0.354082
$841$	8.33037e12	0.574225
$842$	−3.39764e13	−2.32955
$843$	−4.75973e12	−0.324607
$844$	−4.33219e13	−2.93877
$845$	−5.18129e12	−0.349609
$846$	7.61362e13	5.11004
$847$	−2.37359e12	−0.158464
$848$	−5.24718e12	−0.348453
$849$	−2.78003e13	−1.83639
$850$	−2.05169e13	−1.34811
$851$	1.82437e12	0.119242
$852$	2.16509e12	0.140766
$853$	2.23098e13	1.44286	0.721430	−	0.692487i	$-0.243485\pi$
$853$	2.23098e13	1.44286	0.721430	+	0.692487i	$0.243485\pi$
$854$	−5.44699e12	−0.350426
$855$	1.41919e13	0.908222
$856$	−8.17144e12	−0.520196
$857$	−5.22612e12	−0.330952	−0.165476	−	0.986214i	$-0.552916\pi$
$857$	−5.22612e12	−0.330952	−0.165476	+	0.986214i	$0.552916\pi$
$858$	−3.63900e13	−2.29239
$859$	−1.19351e13	−0.747926	−0.373963	−	0.927444i	$-0.622001\pi$
$859$	−1.19351e13	−0.747926	−0.373963	+	0.927444i	$0.622001\pi$
$860$	−2.54584e13	−1.58704
$861$	−9.21629e12	−0.571534
$862$	6.17145e12	0.380719
$863$	3.53492e12	0.216936	0.108468	−	0.994100i	$-0.465406\pi$
$863$	3.53492e12	0.216936	0.108468	+	0.994100i	$0.465406\pi$
$864$	2.49356e12	0.152233
$865$	3.76154e12	0.228451
$866$	−4.84124e12	−0.292500
$867$	−7.71341e12	−0.463618
$868$	−1.22990e13	−0.735412
$869$	−3.08091e13	−1.83270
$870$	3.40460e13	2.01479
$871$	1.84312e13	1.08511
$872$	5.09873e13	2.98633
$873$	2.04728e12	0.119292
$874$	1.93142e13	1.11963
$875$	3.70640e12	0.213755
$876$	−2.11161e12	−0.121156
$877$	8.33035e12	0.475516	0.237758	−	0.971324i	$-0.423587\pi$
$877$	8.33035e12	0.475516	0.237758	+	0.971324i	$0.423587\pi$
$878$	2.48926e13	1.41366
$879$	2.35059e13	1.32809
$880$	1.16106e13	0.652654
$881$	2.69573e11	0.0150760	0.00753798	−	0.999972i	$-0.497601\pi$
$881$	2.69573e11	0.0150760	0.00753798	+	0.999972i	$0.497601\pi$
$882$	−5.36870e13	−2.98717
$883$	5.13539e12	0.284283	0.142141	−	0.989846i	$-0.454601\pi$
$883$	5.13539e12	0.284283	0.142141	+	0.989846i	$0.454601\pi$
$884$	2.45183e13	1.35038
$885$	−6.89252e12	−0.377688
$886$	3.36955e13	1.83705
$887$	1.01778e13	0.552075	0.276037	−	0.961147i	$-0.410979\pi$
$887$	1.01778e13	0.552075	0.276037	+	0.961147i	$0.410979\pi$
$888$	−8.54211e12	−0.461006
$889$	−3.46605e12	−0.186113
$890$	1.21360e13	0.648367
$891$	1.26407e13	0.671924
$892$	−6.66181e13	−3.52331
$893$	2.76168e13	1.45326
$894$	8.50881e13	4.45502
$895$	−1.91952e13	−0.999973
$896$	7.79292e12	0.403937
$897$	−1.43720e13	−0.741228
$898$	−3.64618e13	−1.87109
$899$	−4.03067e13	−2.05806
$900$	−4.90805e13	−2.49355
$901$	−8.60809e12	−0.435156
$902$	−6.65122e13	−3.34558
$903$	−1.11422e13	−0.557670
$904$	−2.55042e13	−1.27014
$905$	5.86585e12	0.290678
$906$	−4.47766e13	−2.20787
$907$	−4.31613e12	−0.211769	−0.105884	−	0.994378i	$-0.533767\pi$
$907$	−4.31613e12	−0.211769	−0.105884	+	0.994378i	$0.533767\pi$
$908$	6.76424e12	0.330242
$909$	−1.63340e13	−0.793515
$910$	−2.73407e12	−0.132167
$911$	3.18600e13	1.53254	0.766272	−	0.642517i	$-0.222110\pi$
$911$	3.18600e13	1.53254	0.766272	+	0.642517i	$0.222110\pi$
$912$	−2.84761e13	−1.36302
$913$	−8.97895e12	−0.427668
$914$	−4.24989e13	−2.01428
$915$	−1.76452e13	−0.832208
$916$	−2.87438e13	−1.34901
$917$	9.16556e12	0.428052
$918$	−5.83708e13	−2.71271
$919$	−4.19797e11	−0.0194142	−0.00970711	−	0.999953i	$-0.503090\pi$
$919$	−4.19797e11	−0.0194142	−0.00970711	+	0.999953i	$0.503090\pi$
$920$	1.45627e13	0.670188
$921$	6.72856e12	0.308144
$922$	8.22178e12	0.374694
$923$	−5.69808e11	−0.0258417
$924$	2.17565e13	0.981897
$925$	−2.53619e12	−0.113905
$926$	−5.91054e13	−2.64166
$927$	−3.94907e12	−0.175645
$928$	3.09518e12	0.137000
$929$	2.28353e13	1.00586	0.502929	−	0.864328i	$-0.332256\pi$
$929$	2.28353e13	1.00586	0.502929	+	0.864328i	$0.332256\pi$
$930$	−6.00889e13	−2.63403
$931$	−1.94738e13	−0.849529
$932$	5.77718e13	2.50809
$933$	1.17961e13	0.509648
$934$	3.23195e13	1.38964
$935$	1.90474e13	0.815050
$936$	4.35056e13	1.85269
$937$	4.47463e13	1.89639	0.948197	−	0.317683i	$-0.102905\pi$
$937$	4.47463e13	1.89639	0.948197	+	0.317683i	$0.102905\pi$
$938$	−1.66195e13	−0.700978
$939$	2.94326e13	1.23547
$940$	4.23386e13	1.76873
$941$	−1.74843e13	−0.726934	−0.363467	−	0.931607i	$-0.618407\pi$
$941$	−1.74843e13	−0.726934	−0.363467	+	0.931607i	$0.618407\pi$
$942$	7.98301e13	3.30322
$943$	−2.62686e13	−1.08177
$944$	8.94113e12	0.366453
$945$	4.31579e12	0.176043
$946$	−8.04113e13	−3.26443
$947$	1.26242e13	0.510069	0.255034	−	0.966932i	$-0.417913\pi$
$947$	1.26242e13	0.510069	0.255034	+	0.966932i	$0.417913\pi$
$948$	1.15842e14	4.65832
$949$	5.55734e11	0.0222417
$950$	−2.68501e13	−1.06952
$951$	−2.06294e13	−0.817853
$952$	−1.08732e13	−0.429032
$953$	2.46694e13	0.968816	0.484408	−	0.874842i	$-0.339035\pi$
$953$	2.46694e13	0.968816	0.484408	+	0.874842i	$0.339035\pi$
$954$	−3.10570e13	−1.21392
$955$	2.68929e12	0.104622
$956$	−2.20831e13	−0.855067
$957$	7.13013e13	2.74786
$958$	6.18255e13	2.37150
$959$	6.62370e11	0.0252881
$960$	2.67995e13	1.01837
$961$	4.46990e13	1.69061
$962$	4.57104e12	0.172079
$963$	−1.52294e13	−0.570642
$964$	7.53275e13	2.80936
$965$	−1.53568e13	−0.570070
$966$	1.29593e13	0.478832
$967$	−2.81285e13	−1.03449	−0.517246	−	0.855837i	$-0.673043\pi$
$967$	−2.81285e13	−1.03449	−0.517246	+	0.855837i	$0.673043\pi$
$968$	3.16767e13	1.15958
$969$	−4.67155e13	−1.70217
$970$	1.71702e12	0.0622735
$971$	−6.47677e12	−0.233815	−0.116907	−	0.993143i	$-0.537298\pi$
$971$	−6.47677e12	−0.233815	−0.116907	+	0.993143i	$0.537298\pi$
$972$	2.88194e13	1.03559
$973$	4.56864e12	0.163410
$974$	−8.72225e13	−3.10537
$975$	1.99796e13	0.708055
$976$	2.28897e13	0.807452
$977$	1.47124e13	0.516604	0.258302	−	0.966064i	$-0.416837\pi$
$977$	1.47124e13	0.516604	0.258302	+	0.966064i	$0.416837\pi$
$978$	−1.22663e14	−4.28736
$979$	2.54160e13	0.884272
$980$	−2.98548e13	−1.03394
$981$	9.50266e13	3.27593
$982$	−7.99629e13	−2.74402
$983$	−4.87088e12	−0.166386	−0.0831930	−	0.996533i	$-0.526512\pi$
$983$	−4.87088e12	−0.166386	−0.0831930	+	0.996533i	$0.526512\pi$
$984$	1.22996e14	4.18228
$985$	3.66379e12	0.124013
$986$	−7.24538e13	−2.44127
$987$	1.85301e13	0.621513
$988$	3.20867e13	1.07132
$989$	−3.17580e13	−1.05553
$990$	6.87208e13	2.27368
$991$	−1.19901e13	−0.394902	−0.197451	−	0.980313i	$-0.563266\pi$
$991$	−1.19901e13	−0.394902	−0.197451	+	0.980313i	$0.563266\pi$
$992$	−5.46279e12	−0.179107
$993$	7.72787e13	2.52225
$994$	5.13796e11	0.0166937
$995$	−1.85811e13	−0.600989
$996$	3.37608e13	1.08704
$997$	−3.88448e13	−1.24510	−0.622550	−	0.782580i	$-0.713903\pi$
$997$	−3.88448e13	−1.24510	−0.622550	+	0.782580i	$0.713903\pi$
$998$	4.96691e13	1.58489
$999$	−7.21549e12	−0.229203

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.10.a.b.1.13	✓	14
3.2	odd	2		333.10.a.d.1.2		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.10.a.b.1.13	✓	14	1.1	even	1	trivial
333.10.a.d.1.2		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)

\(f(q)\)	\(=\)	\(q+38.9809 q^{2} -235.969 q^{3} +1007.51 q^{4} +774.522 q^{5} -9198.30 q^{6} -1447.33 q^{7} +19315.4 q^{8} +35998.6 q^{9} +O(q^{10})\)	\(q+38.9809 q^{2} -235.969 q^{3} +1007.51 q^{4} +774.522 q^{5} -9198.30 q^{6} -1447.33 q^{7} +19315.4 q^{8} +35998.6 q^{9} +30191.5 q^{10} +63229.1 q^{11} -237741. q^{12} +62568.7 q^{13} -56418.2 q^{14} -182764. q^{15} +237085. q^{16} +388942. q^{17} +1.40326e6 q^{18} +509002. q^{19} +780338. q^{20} +341526. q^{21} +2.46473e6 q^{22} +973431. q^{23} -4.55783e6 q^{24} -1.35324e6 q^{25} +2.43898e6 q^{26} -3.84998e6 q^{27} -1.45820e6 q^{28} -4.77886e6 q^{29} -7.12428e6 q^{30} +8.43437e6 q^{31} -647682. q^{32} -1.49202e7 q^{33} +1.51613e7 q^{34} -1.12099e6 q^{35} +3.62689e7 q^{36} +1.87416e6 q^{37} +1.98414e7 q^{38} -1.47643e7 q^{39} +1.49602e7 q^{40} -2.69856e7 q^{41} +1.33130e7 q^{42} -3.26248e7 q^{43} +6.37039e7 q^{44} +2.78817e7 q^{45} +3.79452e7 q^{46} +5.42568e7 q^{47} -5.59448e7 q^{48} -3.82588e7 q^{49} -5.27505e7 q^{50} -9.17785e7 q^{51} +6.30385e7 q^{52} -2.21321e7 q^{53} -1.50076e8 q^{54} +4.89724e7 q^{55} -2.79557e7 q^{56} -1.20109e8 q^{57} -1.86284e8 q^{58} +3.77128e7 q^{59} -1.84136e8 q^{60} +9.65466e7 q^{61} +3.28779e8 q^{62} -5.21019e7 q^{63} -1.46635e8 q^{64} +4.84608e7 q^{65} -5.81600e8 q^{66} +2.94576e8 q^{67} +3.91863e8 q^{68} -2.29700e8 q^{69} -4.36972e7 q^{70} -9.10691e6 q^{71} +6.95326e8 q^{72} +8.88198e6 q^{73} +7.30564e7 q^{74} +3.19323e8 q^{75} +5.12824e8 q^{76} -9.15135e7 q^{77} -5.75525e8 q^{78} -4.87262e8 q^{79} +1.83628e8 q^{80} +1.99918e8 q^{81} -1.05192e9 q^{82} -1.42007e8 q^{83} +3.44090e8 q^{84} +3.01244e8 q^{85} -1.27174e9 q^{86} +1.12767e9 q^{87} +1.22129e9 q^{88} +4.01967e8 q^{89} +1.08685e9 q^{90} -9.05576e7 q^{91} +9.80740e8 q^{92} -1.99025e9 q^{93} +2.11498e9 q^{94} +3.94234e8 q^{95} +1.52833e8 q^{96} +5.68710e7 q^{97} -1.49136e9 q^{98} +2.27616e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 48 q^{2} + 397 q^{3} + 3498 q^{4} + 2841 q^{5} + 3375 q^{6} + 6632 q^{7} + 41046 q^{8} + 101917 q^{9}+O(q^{10}) \) 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

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