LMFDB - Embedded newform 37.10.a.b.1.9

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			1.9
Root			$11.6755$ 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)

$f(q)$	$=$	$q+14.6755 q^{2} -208.762 q^{3} -296.629 q^{4} -1478.97 q^{5} -3063.69 q^{6} -2180.65 q^{7} -11867.1 q^{8} +23898.5 q^{9} +O(q^{10})$	\(q+14.6755 q^{2} -208.762 q^{3} -296.629 q^{4} -1478.97 q^{5} -3063.69 q^{6} -2180.65 q^{7} -11867.1 q^{8} +23898.5 q^{9} -21704.7 q^{10} -4644.07 q^{11} +61924.8 q^{12} -43227.3 q^{13} -32002.2 q^{14} +308753. q^{15} -22281.2 q^{16} +121389. q^{17} +350723. q^{18} +479056. q^{19} +438707. q^{20} +455236. q^{21} -68154.2 q^{22} -1.00798e6 q^{23} +2.47739e6 q^{24} +234239. q^{25} -634384. q^{26} -880033. q^{27} +646844. q^{28} -1.54639e6 q^{29} +4.53112e6 q^{30} -8.22507e6 q^{31} +5.74894e6 q^{32} +969504. q^{33} +1.78145e6 q^{34} +3.22512e6 q^{35} -7.08898e6 q^{36} +1.87416e6 q^{37} +7.03039e6 q^{38} +9.02421e6 q^{39} +1.75511e7 q^{40} +2.45473e7 q^{41} +6.68083e6 q^{42} +1.61688e7 q^{43} +1.37757e6 q^{44} -3.53452e7 q^{45} -1.47926e7 q^{46} -2.10476e7 q^{47} +4.65146e6 q^{48} -3.55984e7 q^{49} +3.43758e6 q^{50} -2.53414e7 q^{51} +1.28225e7 q^{52} -2.60632e7 q^{53} -1.29149e7 q^{54} +6.86846e6 q^{55} +2.58779e7 q^{56} -1.00009e8 q^{57} -2.26941e7 q^{58} +9.99275e6 q^{59} -9.15852e7 q^{60} -2.00146e8 q^{61} -1.20707e8 q^{62} -5.21142e7 q^{63} +9.57767e7 q^{64} +6.39321e7 q^{65} +1.42280e7 q^{66} +2.09766e8 q^{67} -3.60075e7 q^{68} +2.10428e8 q^{69} +4.73304e7 q^{70} +5.67724e7 q^{71} -2.83605e8 q^{72} +3.34787e8 q^{73} +2.75043e7 q^{74} -4.89002e7 q^{75} -1.42102e8 q^{76} +1.01271e7 q^{77} +1.32435e8 q^{78} +2.32299e8 q^{79} +3.29533e7 q^{80} -2.86677e8 q^{81} +3.60245e8 q^{82} -1.30030e8 q^{83} -1.35036e8 q^{84} -1.79531e8 q^{85} +2.37286e8 q^{86} +3.22827e8 q^{87} +5.51114e7 q^{88} +5.74401e8 q^{89} -5.18710e8 q^{90} +9.42636e7 q^{91} +2.98996e8 q^{92} +1.71708e9 q^{93} -3.08884e8 q^{94} -7.08511e8 q^{95} -1.20016e9 q^{96} +1.33698e9 q^{97} -5.22425e8 q^{98} -1.10986e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	14.6755	0.648573	0.324286	−	0.945959i	$-0.394876\pi$
$2$	14.6755	0.648573	0.324286	+	0.945959i	$0.394876\pi$
$3$	−208.762	−1.48801	−0.744004	−	0.668175i	$-0.767076\pi$
$3$	−208.762	−1.48801	−0.744004	+	0.668175i	$0.767076\pi$
$4$	−296.629	−0.579353
$5$	−1478.97	−1.05827	−0.529134	−	0.848538i	$-0.677483\pi$
$5$	−1478.97	−1.05827	−0.529134	+	0.848538i	$0.677483\pi$
$6$	−3063.69	−0.965082
$7$	−2180.65	−0.343277	−0.171638	−	0.985160i	$-0.554906\pi$
$7$	−2180.65	−0.343277	−0.171638	+	0.985160i	$0.554906\pi$
$8$	−11867.1	−1.02433
$9$	23898.5	1.21417
$10$	−21704.7	−0.686363
$11$	−4644.07	−0.0956383	−0.0478191	−	0.998856i	$-0.515227\pi$
$11$	−4644.07	−0.0956383	−0.0478191	+	0.998856i	$0.515227\pi$
$12$	61924.8	0.862083
$13$	−43227.3	−0.419772	−0.209886	−	0.977726i	$-0.567309\pi$
$13$	−43227.3	−0.419772	−0.209886	+	0.977726i	$0.567309\pi$
$14$	−32002.2	−0.222640
$15$	308753.	1.57471
$16$	−22281.2	−0.0849960
$17$	121389.	0.352500	0.176250	−	0.984345i	$-0.443603\pi$
$17$	121389.	0.352500	0.176250	+	0.984345i	$0.443603\pi$
$18$	350723.	0.787477
$19$	479056.	0.843324	0.421662	−	0.906753i	$-0.361447\pi$
$19$	479056.	0.843324	0.421662	+	0.906753i	$0.361447\pi$
$20$	438707.	0.613111
$21$	455236.	0.510799
$22$	−68154.2	−0.0620284
$23$	−1.00798e6	−0.751063	−0.375532	−	0.926810i	$-0.622540\pi$
$23$	−1.00798e6	−0.751063	−0.375532	+	0.926810i	$0.622540\pi$
$24$	2.47739e6	1.52420
$25$	234239.	0.119931
$26$	−634384.	−0.272252
$27$	−880033.	−0.318685
$28$	646844.	0.198879
$29$	−1.54639e6	−0.406002	−0.203001	−	0.979179i	$-0.565069\pi$
$29$	−1.54639e6	−0.406002	−0.203001	+	0.979179i	$0.565069\pi$
$30$	4.53112e6	1.02131
$31$	−8.22507e6	−1.59960	−0.799801	−	0.600265i	$-0.795062\pi$
$31$	−8.22507e6	−1.59960	−0.799801	+	0.600265i	$0.795062\pi$
$32$	5.74894e6	0.969199
$33$	969504.	0.142311
$34$	1.78145e6	0.228622
$35$	3.22512e6	0.363279
$36$	−7.08898e6	−0.703433
$37$	1.87416e6	0.164399
$37$	1.87416e6	0.164399
$38$	7.03039e6	0.546957
$39$	9.02421e6	0.624624
$40$	1.75511e7	1.08401
$41$	2.45473e7	1.35668	0.678339	−	0.734749i	$-0.262700\pi$
$41$	2.45473e7	1.35668	0.678339	+	0.734749i	$0.262700\pi$
$42$	6.68083e6	0.331290
$43$	1.61688e7	0.721223	0.360612	−	0.932716i	$-0.382568\pi$
$43$	1.61688e7	0.721223	0.360612	+	0.932716i	$0.382568\pi$
$44$	1.37757e6	0.0554084
$45$	−3.53452e7	−1.28492
$46$	−1.47926e7	−0.487119
$47$	−2.10476e7	−0.629160	−0.314580	−	0.949231i	$-0.601864\pi$
$47$	−2.10476e7	−0.629160	−0.314580	+	0.949231i	$0.601864\pi$
$48$	4.65146e6	0.126475
$49$	−3.55984e7	−0.882161
$50$	3.43758e6	0.0777836
$51$	−2.53414e7	−0.524523
$52$	1.28225e7	0.243196
$53$	−2.60632e7	−0.453719	−0.226859	−	0.973928i	$-0.572846\pi$
$53$	−2.60632e7	−0.453719	−0.226859	+	0.973928i	$0.572846\pi$
$54$	−1.29149e7	−0.206691
$55$	6.86846e6	0.101211
$56$	2.58779e7	0.351627
$57$	−1.00009e8	−1.25487
$58$	−2.26941e7	−0.263322
$59$	9.99275e6	0.107362	0.0536811	−	0.998558i	$-0.482905\pi$
$59$	9.99275e6	0.107362	0.0536811	+	0.998558i	$0.482905\pi$
$60$	−9.15852e7	−0.912314
$61$	−2.00146e8	−1.85081	−0.925405	−	0.378981i	$-0.876275\pi$
$61$	−2.00146e8	−1.85081	−0.925405	+	0.378981i	$0.876275\pi$
$62$	−1.20707e8	−1.03746
$63$	−5.21142e7	−0.416796
$64$	9.57767e7	0.713592
$65$	6.39321e7	0.444231
$66$	1.42280e7	0.0922987
$67$	2.09766e8	1.27174	0.635870	−	0.771796i	$-0.280642\pi$
$67$	2.09766e8	1.27174	0.635870	+	0.771796i	$0.280642\pi$
$68$	−3.60075e7	−0.204222
$69$	2.10428e8	1.11759
$70$	4.73304e7	0.235613
$71$	5.67724e7	0.265140	0.132570	−	0.991174i	$-0.457677\pi$
$71$	5.67724e7	0.265140	0.132570	+	0.991174i	$0.457677\pi$
$72$	−2.83605e8	−1.24370
$73$	3.34787e8	1.37980	0.689900	−	0.723904i	$-0.257654\pi$
$73$	3.34787e8	1.37980	0.689900	+	0.723904i	$0.257654\pi$
$74$	2.75043e7	0.106625
$75$	−4.89002e7	−0.178458
$76$	−1.42102e8	−0.488583
$77$	1.01271e7	0.0328304
$78$	1.32435e8	0.405114
$79$	2.32299e8	0.671004	0.335502	−	0.942040i	$-0.391094\pi$
$79$	2.32299e8	0.671004	0.335502	+	0.942040i	$0.391094\pi$
$80$	3.29533e7	0.0899485
$81$	−2.86677e8	−0.739963
$82$	3.60245e8	0.879905
$83$	−1.30030e8	−0.300740	−0.150370	−	0.988630i	$-0.548047\pi$
$83$	−1.30030e8	−0.300740	−0.150370	+	0.988630i	$0.548047\pi$
$84$	−1.35036e8	−0.295933
$85$	−1.79531e8	−0.373040
$86$	2.37286e8	0.467766
$87$	3.22827e8	0.604134
$88$	5.51114e7	0.0979647
$89$	5.74401e8	0.970421	0.485210	−	0.874397i	$-0.338743\pi$
$89$	5.74401e8	0.970421	0.485210	+	0.874397i	$0.338743\pi$
$90$	−5.18710e8	−0.833361
$91$	9.42636e7	0.144098
$92$	2.98996e8	0.435131
$93$	1.71708e9	2.38022
$94$	−3.08884e8	−0.408056
$95$	−7.08511e8	−0.892463
$96$	−1.20016e9	−1.44218
$97$	1.33698e9	1.53339	0.766693	−	0.642014i	$-0.221901\pi$
$97$	1.33698e9	1.53339	0.766693	+	0.642014i	$0.221901\pi$
$98$	−5.22425e8	−0.572145
$99$	−1.10986e8	−0.116121
$100$	−6.94822e7	−0.0694822
$101$	−3.81701e8	−0.364986	−0.182493	−	0.983207i	$-0.558417\pi$
$101$	−3.81701e8	−0.364986	−0.182493	+	0.983207i	$0.558417\pi$
$102$	−3.71898e8	−0.340191
$103$	4.28260e8	0.374922	0.187461	−	0.982272i	$-0.439974\pi$
$103$	4.28260e8	0.374922	0.187461	+	0.982272i	$0.439974\pi$
$104$	5.12981e8	0.429983
$105$	−6.73283e8	−0.540562
$106$	−3.82492e8	−0.294270
$107$	1.14342e9	0.843297	0.421649	−	0.906759i	$-0.361452\pi$
$107$	1.14342e9	0.843297	0.421649	+	0.906759i	$0.361452\pi$
$108$	2.61043e8	0.184631
$109$	6.28102e8	0.426198	0.213099	−	0.977031i	$-0.431644\pi$
$109$	6.28102e8	0.426198	0.213099	+	0.977031i	$0.431644\pi$
$110$	1.00798e8	0.0656426
$111$	−3.91253e8	−0.244627
$112$	4.85875e7	0.0291772
$113$	−1.96496e8	−0.113370	−0.0566852	−	0.998392i	$-0.518053\pi$
$113$	−1.96496e8	−0.113370	−0.0566852	+	0.998392i	$0.518053\pi$
$114$	−1.46768e9	−0.813877
$115$	1.49078e9	0.794826
$116$	4.58704e8	0.235219
$117$	−1.03307e9	−0.509674
$118$	1.46649e8	0.0696321
$119$	−2.64707e8	−0.121005
$120$	−3.66399e9	−1.61302
$121$	−2.33638e9	−0.990853
$122$	−2.93724e9	−1.20038
$123$	−5.12454e9	−2.01875
$124$	2.43979e9	0.926735
$125$	2.54219e9	0.931349
$126$	−7.64804e8	−0.270323
$127$	1.34612e8	0.0459163	0.0229581	−	0.999736i	$-0.492692\pi$
$127$	1.34612e8	0.0459163	0.0229581	+	0.999736i	$0.492692\pi$
$128$	−1.53789e9	−0.506383
$129$	−3.37543e9	−1.07319
$130$	9.38237e8	0.288116
$131$	5.41212e9	1.60563	0.802817	−	0.596225i	$-0.203333\pi$
$131$	5.41212e9	1.60563	0.802817	+	0.596225i	$0.203333\pi$
$132$	−2.87583e8	−0.0824481
$133$	−1.04465e9	−0.289494
$134$	3.07842e9	0.824815
$135$	1.30155e9	0.337254
$136$	−1.44053e9	−0.361075
$137$	−6.20790e9	−1.50557	−0.752787	−	0.658265i	$-0.771291\pi$
$137$	−6.20790e9	−1.50557	−0.752787	+	0.658265i	$0.771291\pi$
$138$	3.08814e9	0.724837
$139$	5.16230e9	1.17294	0.586471	−	0.809970i	$-0.300517\pi$
$139$	5.16230e9	1.17294	0.586471	+	0.809970i	$0.300517\pi$
$140$	−9.56665e8	−0.210467
$141$	4.39393e9	0.936196
$142$	8.33165e8	0.171962
$143$	2.00751e8	0.0401462
$144$	−5.32487e8	−0.103200
$145$	2.28707e9	0.429659
$146$	4.91318e9	0.894901
$147$	7.43158e9	1.31266
$148$	−5.55930e8	−0.0952451
$149$	−6.48107e9	−1.07723	−0.538615	−	0.842552i	$-0.681052\pi$
$149$	−6.48107e9	−1.07723	−0.538615	+	0.842552i	$0.681052\pi$
$150$	−7.17636e8	−0.115743
$151$	−4.20888e9	−0.658825	−0.329413	−	0.944186i	$-0.606851\pi$
$151$	−4.20888e9	−0.658825	−0.329413	+	0.944186i	$0.606851\pi$
$152$	−5.68498e9	−0.863839
$153$	2.90101e9	0.427995
$154$	1.48620e8	0.0212929
$155$	1.21647e10	1.69281
$156$	−2.67684e9	−0.361878
$157$	−4.74215e9	−0.622913	−0.311456	−	0.950260i	$-0.600817\pi$
$157$	−4.74215e9	−0.622913	−0.311456	+	0.950260i	$0.600817\pi$
$158$	3.40910e9	0.435195
$159$	5.44101e9	0.675137
$160$	−8.50254e9	−1.02567
$161$	2.19805e9	0.257823
$162$	−4.20713e9	−0.479919
$163$	3.76338e8	0.0417575	0.0208787	−	0.999782i	$-0.493354\pi$
$163$	3.76338e8	0.0417575	0.0208787	+	0.999782i	$0.493354\pi$
$164$	−7.28145e9	−0.785996
$165$	−1.43387e9	−0.150603
$166$	−1.90826e9	−0.195052
$167$	1.64703e9	0.163862	0.0819309	−	0.996638i	$-0.473891\pi$
$167$	1.64703e9	0.163862	0.0819309	+	0.996638i	$0.473891\pi$
$168$	−5.40231e9	−0.523224
$169$	−8.73590e9	−0.823792
$170$	−2.63471e9	−0.241943
$171$	1.14487e10	1.02394
$172$	−4.79614e9	−0.417843
$173$	8.99004e9	0.763052	0.381526	−	0.924358i	$-0.375399\pi$
$173$	8.99004e9	0.763052	0.381526	+	0.924358i	$0.375399\pi$
$174$	4.73766e9	0.391825
$175$	−5.10794e8	−0.0411694
$176$	1.03475e8	0.00812887
$177$	−2.08610e9	−0.159756
$178$	8.42964e9	0.629389
$179$	1.20391e10	0.876506	0.438253	−	0.898852i	$-0.355597\pi$
$179$	1.20391e10	0.876506	0.438253	+	0.898852i	$0.355597\pi$
$180$	1.04844e10	0.744421
$181$	−3.66484e9	−0.253806	−0.126903	−	0.991915i	$-0.540504\pi$
$181$	−3.66484e9	−0.253806	−0.126903	+	0.991915i	$0.540504\pi$
$182$	1.38337e9	0.0934580
$183$	4.17827e10	2.75402
$184$	1.19618e10	0.769333
$185$	−2.77184e9	−0.173978
$186$	2.51991e10	1.54375
$187$	−5.63739e8	−0.0337125
$188$	6.24332e9	0.364506
$189$	1.91904e9	0.109397
$190$	−1.03978e10	−0.578827
$191$	−2.68267e10	−1.45854	−0.729269	−	0.684227i	$-0.760140\pi$
$191$	−2.68267e10	−1.45854	−0.729269	+	0.684227i	$0.760140\pi$
$192$	−1.99945e10	−1.06183
$193$	−2.12709e10	−1.10352	−0.551758	−	0.834005i	$-0.686043\pi$
$193$	−2.12709e10	−1.10352	−0.551758	+	0.834005i	$0.686043\pi$
$194$	1.96208e10	0.994512
$195$	−1.33466e10	−0.661019
$196$	1.05595e10	0.511083
$197$	−2.35515e10	−1.11409	−0.557046	−	0.830482i	$-0.688065\pi$
$197$	−2.35515e10	−1.11409	−0.557046	+	0.830482i	$0.688065\pi$
$198$	−1.62878e9	−0.0753129
$199$	−3.02276e10	−1.36636	−0.683180	−	0.730250i	$-0.739404\pi$
$199$	−3.02276e10	−1.36636	−0.683180	+	0.730250i	$0.739404\pi$
$200$	−2.77973e9	−0.122848
$201$	−4.37911e10	−1.89236
$202$	−5.60166e9	−0.236720
$203$	3.37213e9	0.139371
$204$	7.51699e9	0.303884
$205$	−3.63049e10	−1.43573
$206$	6.28495e9	0.243164
$207$	−2.40892e10	−0.911918
$208$	9.63156e8	0.0356789
$209$	−2.22477e9	−0.0806541
$210$	−9.88078e9	−0.350594
$211$	3.01955e10	1.04875	0.524374	−	0.851488i	$-0.324299\pi$
$211$	3.01955e10	1.04875	0.524374	+	0.851488i	$0.324299\pi$
$212$	7.73111e9	0.262864
$213$	−1.18519e10	−0.394530
$214$	1.67804e10	0.546939
$215$	−2.39132e10	−0.763247
$216$	1.04434e10	0.326438
$217$	1.79360e10	0.549107
$218$	9.21773e9	0.276420
$219$	−6.98908e10	−2.05316
$220$	−2.03738e9	−0.0586369
$221$	−5.24732e9	−0.147970
$222$	−5.74185e9	−0.158658
$223$	9.73975e8	0.0263740	0.0131870	−	0.999913i	$-0.495802\pi$
$223$	9.73975e8	0.0263740	0.0131870	+	0.999913i	$0.495802\pi$
$224$	−1.25364e10	−0.332704
$225$	5.59796e9	0.145616
$226$	−2.88368e9	−0.0735290
$227$	2.07843e10	0.519540	0.259770	−	0.965670i	$-0.416353\pi$
$227$	2.07843e10	0.519540	0.259770	+	0.965670i	$0.416353\pi$
$228$	2.96654e10	0.727016
$229$	8.03900e9	0.193171	0.0965856	−	0.995325i	$-0.469208\pi$
$229$	8.03900e9	0.193171	0.0965856	+	0.995325i	$0.469208\pi$
$230$	2.18779e10	0.515502
$231$	−2.11415e9	−0.0488519
$232$	1.83511e10	0.415878
$233$	7.31840e10	1.62673	0.813364	−	0.581756i	$-0.197634\pi$
$233$	7.31840e10	1.62673	0.813364	+	0.581756i	$0.197634\pi$
$234$	−1.51608e10	−0.330561
$235$	3.11288e10	0.665820
$236$	−2.96414e9	−0.0622006
$237$	−4.84951e10	−0.998459
$238$	−3.88471e9	−0.0784806
$239$	−5.06690e9	−0.100451	−0.0502253	−	0.998738i	$-0.515994\pi$
$239$	−5.06690e9	−0.100451	−0.0502253	+	0.998738i	$0.515994\pi$
$240$	−6.87939e9	−0.133844
$241$	−6.58949e10	−1.25827	−0.629137	−	0.777294i	$-0.716592\pi$
$241$	−6.58949e10	−1.25827	−0.629137	+	0.777294i	$0.716592\pi$
$242$	−3.42876e10	−0.642640
$243$	7.71688e10	1.41976
$244$	5.93690e10	1.07227
$245$	5.26491e10	0.933562
$246$	−7.52054e10	−1.30931
$247$	−2.07083e10	−0.354004
$248$	9.76074e10	1.63851
$249$	2.71453e10	0.447504
$250$	3.73079e10	0.604048
$251$	9.97342e10	1.58603	0.793017	−	0.609199i	$-0.208509\pi$
$251$	9.97342e10	1.58603	0.793017	+	0.609199i	$0.208509\pi$
$252$	1.54586e10	0.241472
$253$	4.68113e9	0.0718304
$254$	1.97550e9	0.0297800
$255$	3.74793e10	0.555086
$256$	−7.16070e10	−1.04202
$257$	1.19021e11	1.70186	0.850932	−	0.525276i	$-0.176038\pi$
$257$	1.19021e11	1.70186	0.850932	+	0.525276i	$0.176038\pi$
$258$	−4.95362e10	−0.696039
$259$	−4.08689e9	−0.0564344
$260$	−1.89641e10	−0.257367
$261$	−3.69564e10	−0.492955
$262$	7.94257e10	1.04137
$263$	7.42235e10	0.956622	0.478311	−	0.878190i	$-0.341249\pi$
$263$	7.42235e10	0.956622	0.478311	+	0.878190i	$0.341249\pi$
$264$	−1.15052e10	−0.145772
$265$	3.85468e10	0.480156
$266$	−1.53308e10	−0.187758
$267$	−1.19913e11	−1.44399
$268$	−6.22226e10	−0.736787
$269$	8.51230e10	0.991201	0.495601	−	0.868551i	$-0.334948\pi$
$269$	8.51230e10	0.991201	0.495601	+	0.868551i	$0.334948\pi$
$270$	1.91009e10	0.218734
$271$	−1.04532e11	−1.17730	−0.588652	−	0.808387i	$-0.700341\pi$
$271$	−1.04532e11	−1.17730	−0.588652	+	0.808387i	$0.700341\pi$
$272$	−2.70469e9	−0.0299611
$273$	−1.96786e10	−0.214419
$274$	−9.11041e10	−0.976474
$275$	−1.08782e9	−0.0114699
$276$	−6.24190e10	−0.647479
$277$	−1.88030e11	−1.91897	−0.959487	−	0.281753i	$-0.909084\pi$
$277$	−1.88030e11	−1.91897	−0.959487	+	0.281753i	$0.909084\pi$
$278$	7.57594e10	0.760738
$279$	−1.96567e11	−1.94219
$280$	−3.82727e10	−0.372116
$281$	1.45070e10	0.138803	0.0694017	−	0.997589i	$-0.477891\pi$
$281$	1.45070e10	0.138803	0.0694017	+	0.997589i	$0.477891\pi$
$282$	6.44832e10	0.607191
$283$	1.56325e11	1.44874	0.724369	−	0.689413i	$-0.242131\pi$
$283$	1.56325e11	1.44874	0.724369	+	0.689413i	$0.242131\pi$
$284$	−1.68403e10	−0.153610
$285$	1.47910e11	1.32799
$286$	2.94612e9	0.0260378
$287$	−5.35291e10	−0.465716
$288$	1.37391e11	1.17677
$289$	−1.03853e11	−0.875744
$290$	3.35640e10	0.278665
$291$	−2.79110e11	−2.28169
$292$	−9.93077e10	−0.799392
$293$	1.80405e11	1.43003	0.715014	−	0.699110i	$-0.246420\pi$
$293$	1.80405e11	1.43003	0.715014	+	0.699110i	$0.246420\pi$
$294$	1.09062e11	0.851357
$295$	−1.47790e10	−0.113618
$296$	−2.22408e10	−0.168398
$297$	4.08694e9	0.0304785
$298$	−9.51131e10	−0.698662
$299$	4.35723e10	0.315275
$300$	1.45052e10	0.103390
$301$	−3.52585e10	−0.247579
$302$	−6.17675e10	−0.427296
$303$	7.96845e10	0.543103
$304$	−1.06739e10	−0.0716792
$305$	2.96010e11	1.95865
$306$	4.25739e10	0.277586
$307$	−2.46175e11	−1.58169	−0.790843	−	0.612019i	$-0.790358\pi$
$307$	−2.46175e11	−1.58169	−0.790843	+	0.612019i	$0.790358\pi$
$308$	−3.00399e9	−0.0190204
$309$	−8.94044e10	−0.557887
$310$	1.78523e11	1.09791
$311$	2.05419e11	1.24514	0.622572	−	0.782563i	$-0.286088\pi$
$311$	2.05419e11	1.24514	0.622572	+	0.782563i	$0.286088\pi$
$312$	−1.07091e11	−0.639818
$313$	−1.53798e11	−0.905737	−0.452868	−	0.891577i	$-0.649599\pi$
$313$	−1.53798e11	−0.905737	−0.452868	+	0.891577i	$0.649599\pi$
$314$	−6.95936e10	−0.404004
$315$	7.70756e10	0.441082
$316$	−6.89065e10	−0.388748
$317$	−1.87897e11	−1.04509	−0.522543	−	0.852613i	$-0.675017\pi$
$317$	−1.87897e11	−1.04509	−0.522543	+	0.852613i	$0.675017\pi$
$318$	7.98496e10	0.437876
$319$	7.18154e9	0.0388293
$320$	−1.41651e11	−0.755172
$321$	−2.38703e11	−1.25483
$322$	3.22575e10	0.167217
$323$	5.81521e10	0.297272
$324$	8.50366e10	0.428700
$325$	−1.01255e10	−0.0503434
$326$	5.52296e9	0.0270828
$327$	−1.31124e11	−0.634186
$328$	−2.91304e11	−1.38968
$329$	4.58973e10	0.215976
$330$	−2.10428e10	−0.0976767
$331$	2.46398e11	1.12826	0.564132	−	0.825684i	$-0.309211\pi$
$331$	2.46398e11	1.12826	0.564132	+	0.825684i	$0.309211\pi$
$332$	3.85706e10	0.174235
$333$	4.47896e10	0.199608
$334$	2.41710e10	0.106276
$335$	−3.10238e11	−1.34584
$336$	−1.01432e10	−0.0434159
$337$	3.29829e11	1.39301	0.696506	−	0.717551i	$-0.254737\pi$
$337$	3.29829e11	1.39301	0.696506	+	0.717551i	$0.254737\pi$
$338$	−1.28204e11	−0.534289
$339$	4.10208e10	0.168696
$340$	5.32542e10	0.216122
$341$	3.81978e10	0.152983
$342$	1.68016e11	0.664098
$343$	1.65625e11	0.646102
$344$	−1.91876e11	−0.738768
$345$	−3.11217e11	−1.18271
$346$	1.31934e11	0.494895
$347$	1.97986e11	0.733081	0.366541	−	0.930402i	$-0.380542\pi$
$347$	1.97986e11	0.733081	0.366541	+	0.930402i	$0.380542\pi$
$348$	−9.57599e10	−0.350007
$349$	4.31807e11	1.55803	0.779014	−	0.627007i	$-0.215720\pi$
$349$	4.31807e11	1.55803	0.779014	+	0.627007i	$0.215720\pi$
$350$	−7.49616e9	−0.0267013
$351$	3.80415e10	0.133775
$352$	−2.66985e10	−0.0926925
$353$	−2.95940e11	−1.01442	−0.507210	−	0.861823i	$-0.669323\pi$
$353$	−2.95940e11	−1.01442	−0.507210	+	0.861823i	$0.669323\pi$
$354$	−3.06147e10	−0.103613
$355$	−8.39649e10	−0.280589
$356$	−1.70384e11	−0.562217
$357$	5.52607e10	0.180057
$358$	1.76680e11	0.568478
$359$	3.32064e11	1.05511	0.527554	−	0.849522i	$-0.323109\pi$
$359$	3.32064e11	1.05511	0.527554	+	0.849522i	$0.323109\pi$
$360$	4.19444e11	1.31617
$361$	−9.31935e10	−0.288804
$362$	−5.37834e10	−0.164611
$363$	4.87747e11	1.47440
$364$	−2.79613e10	−0.0834837
$365$	−4.95142e11	−1.46020
$366$	6.13184e11	1.78618
$367$	−1.58059e11	−0.454803	−0.227401	−	0.973801i	$-0.573023\pi$
$367$	−1.58059e11	−0.454803	−0.227401	+	0.973801i	$0.573023\pi$
$368$	2.24590e10	0.0638374
$369$	5.86644e11	1.64724
$370$	−4.06781e10	−0.112837
$371$	5.68348e10	0.155751
$372$	−5.09336e11	−1.37899
$373$	1.02434e10	0.0274004	0.0137002	−	0.999906i	$-0.495639\pi$
$373$	1.02434e10	0.0274004	0.0137002	+	0.999906i	$0.495639\pi$
$374$	−8.27317e9	−0.0218650
$375$	−5.30712e11	−1.38586
$376$	2.49773e11	0.644465
$377$	6.68463e10	0.170428
$378$	2.81630e10	0.0709521
$379$	2.58961e11	0.644699	0.322350	−	0.946621i	$-0.395527\pi$
$379$	2.58961e11	0.644699	0.322350	+	0.946621i	$0.395527\pi$
$380$	2.10165e11	0.517052
$381$	−2.81018e10	−0.0683238
$382$	−3.93697e11	−0.945968
$383$	5.62697e11	1.33623	0.668113	−	0.744060i	$-0.267102\pi$
$383$	5.62697e11	1.33623	0.668113	+	0.744060i	$0.267102\pi$
$384$	3.21052e11	0.753502
$385$	−1.49777e10	−0.0347434
$386$	−3.12162e11	−0.715710
$387$	3.86410e11	0.875687
$388$	−3.96586e11	−0.888372
$389$	3.79674e11	0.840694	0.420347	−	0.907363i	$-0.361908\pi$
$389$	3.79674e11	0.840694	0.420347	+	0.907363i	$0.361908\pi$
$390$	−1.95868e11	−0.428719
$391$	−1.22358e11	−0.264750
$392$	4.22448e11	0.903620
$393$	−1.12984e12	−2.38920
$394$	−3.45631e11	−0.722570
$395$	−3.43564e11	−0.710101
$396$	3.29217e10	0.0672751
$397$	9.07888e11	1.83432	0.917159	−	0.398520i	$-0.130476\pi$
$397$	9.07888e11	1.83432	0.917159	+	0.398520i	$0.130476\pi$
$398$	−4.43606e11	−0.886184
$399$	2.18083e11	0.430769
$400$	−5.21913e9	−0.0101936
$401$	−5.96464e11	−1.15195	−0.575976	−	0.817467i	$-0.695378\pi$
$401$	−5.96464e11	−1.15195	−0.575976	+	0.817467i	$0.695378\pi$
$402$	−6.42657e11	−1.22733
$403$	3.55548e11	0.671468
$404$	1.13223e11	0.211456
$405$	4.23987e11	0.783078
$406$	4.94878e10	0.0903923
$407$	−8.70373e9	−0.0157228
$408$	3.00728e11	0.537282
$409$	−9.26777e11	−1.63765	−0.818824	−	0.574045i	$-0.805373\pi$
$409$	−9.26777e11	−1.63765	−0.818824	+	0.574045i	$0.805373\pi$
$410$	−5.32793e11	−0.931175
$411$	1.29597e12	2.24031
$412$	−1.27034e11	−0.217212
$413$	−2.17907e10	−0.0368549
$414$	−3.53522e11	−0.591445
$415$	1.92311e11	0.318264
$416$	−2.48511e11	−0.406843
$417$	−1.07769e12	−1.74535
$418$	−3.26496e10	−0.0523100
$419$	−3.01045e11	−0.477165	−0.238583	−	0.971122i	$-0.576683\pi$
$419$	−3.01045e11	−0.477165	−0.238583	+	0.971122i	$0.576683\pi$
$420$	1.99715e11	0.313177
$421$	−1.27264e10	−0.0197440	−0.00987200	−	0.999951i	$-0.503142\pi$
$421$	−1.27264e10	−0.0197440	−0.00987200	+	0.999951i	$0.503142\pi$
$422$	4.43135e11	0.680190
$423$	−5.03005e11	−0.763907
$424$	3.09294e11	0.464756
$425$	2.84341e10	0.0422755
$426$	−1.73933e11	−0.255881
$427$	4.36447e11	0.635340
$428$	−3.39173e11	−0.488567
$429$	−4.19091e10	−0.0597379
$430$	−3.50939e11	−0.495021
$431$	1.37985e12	1.92612	0.963062	−	0.269281i	$-0.0867862\pi$
$431$	1.37985e12	1.92612	0.963062	+	0.269281i	$0.0867862\pi$
$432$	1.96082e10	0.0270870
$433$	1.10657e12	1.51280	0.756402	−	0.654107i	$-0.226955\pi$
$433$	1.10657e12	1.51280	0.756402	+	0.654107i	$0.226955\pi$
$434$	2.63220e11	0.356136
$435$	−4.77453e11	−0.639336
$436$	−1.86313e11	−0.246919
$437$	−4.82878e11	−0.633390
$438$	−1.02568e12	−1.33162
$439$	1.08819e11	0.139835	0.0699173	−	0.997553i	$-0.477726\pi$
$439$	1.08819e11	0.139835	0.0699173	+	0.997553i	$0.477726\pi$
$440$	−8.15084e10	−0.103673
$441$	−8.50747e11	−1.07109
$442$	−7.70072e10	−0.0959690
$443$	−1.79179e11	−0.221039	−0.110520	−	0.993874i	$-0.535252\pi$
$443$	−1.79179e11	−0.221039	−0.110520	+	0.993874i	$0.535252\pi$
$444$	1.16057e11	0.141726
$445$	−8.49524e11	−1.02697
$446$	1.42936e10	0.0171055
$447$	1.35300e12	1.60293
$448$	−2.08855e11	−0.244960
$449$	−1.50219e12	−1.74429	−0.872143	−	0.489251i	$-0.837270\pi$
$449$	−1.50219e12	−1.74429	−0.872143	+	0.489251i	$0.837270\pi$
$450$	8.21531e10	0.0944425
$451$	−1.14000e11	−0.129750
$452$	5.82863e10	0.0656816
$453$	8.78654e11	0.980338
$454$	3.05021e11	0.336960
$455$	−1.39413e11	−0.152494
$456$	1.18681e12	1.28540
$457$	3.89147e11	0.417341	0.208671	−	0.977986i	$-0.433086\pi$
$457$	3.89147e11	0.417341	0.208671	+	0.977986i	$0.433086\pi$
$458$	1.17977e11	0.125286
$459$	−1.06826e11	−0.112337
$460$	−4.42207e11	−0.460485
$461$	−1.12595e12	−1.16109	−0.580546	−	0.814228i	$-0.697161\pi$
$461$	−1.12595e12	−1.16109	−0.580546	+	0.814228i	$0.697161\pi$
$462$	−3.10262e10	−0.0316840
$463$	1.10083e11	0.111329	0.0556643	−	0.998450i	$-0.482272\pi$
$463$	1.10083e11	0.111329	0.0556643	+	0.998450i	$0.482272\pi$
$464$	3.44554e10	0.0345085
$465$	−2.53952e12	−2.51891
$466$	1.07401e12	1.05505
$467$	8.15215e11	0.793133	0.396567	−	0.918006i	$-0.370202\pi$
$467$	8.15215e11	0.793133	0.396567	+	0.918006i	$0.370202\pi$
$468$	3.06438e11	0.295281
$469$	−4.57426e11	−0.436559
$470$	4.56831e11	0.431833
$471$	9.89981e11	0.926900
$472$	−1.18585e11	−0.109974
$473$	−7.50890e10	−0.0689765
$474$	−7.11691e11	−0.647573
$475$	1.12214e11	0.101140
$476$	7.85197e10	0.0701048
$477$	−6.22872e11	−0.550891
$478$	−7.43595e10	−0.0651495
$479$	1.31217e11	0.113889	0.0569445	−	0.998377i	$-0.481864\pi$
$479$	1.31217e11	0.113889	0.0569445	+	0.998377i	$0.481864\pi$
$480$	1.77501e12	1.52621
$481$	−8.10150e10	−0.0690101
$482$	−9.67043e11	−0.816082
$483$	−4.58869e11	−0.383642
$484$	6.93038e11	0.574054
$485$	−1.97736e12	−1.62273
$486$	1.13249e12	0.920815
$487$	−9.58641e11	−0.772282	−0.386141	−	0.922440i	$-0.626192\pi$
$487$	−9.58641e11	−0.772282	−0.386141	+	0.922440i	$0.626192\pi$
$488$	2.37514e12	1.89583
$489$	−7.85651e10	−0.0621355
$490$	7.72653e11	0.605483
$491$	6.50918e10	0.0505428	0.0252714	−	0.999681i	$-0.491955\pi$
$491$	6.50918e10	0.0505428	0.0252714	+	0.999681i	$0.491955\pi$
$492$	1.52009e12	1.16957
$493$	−1.87715e11	−0.143116
$494$	−3.03905e11	−0.229597
$495$	1.64146e11	0.122887
$496$	1.83264e11	0.135960
$497$	−1.23801e11	−0.0910163
$498$	3.98371e11	0.290239
$499$	2.42420e11	0.175032	0.0875158	−	0.996163i	$-0.472107\pi$
$499$	2.42420e11	0.175032	0.0875158	+	0.996163i	$0.472107\pi$
$500$	−7.54086e11	−0.539580
$501$	−3.43837e11	−0.243828
$502$	1.46365e12	1.02866
$503$	1.40828e12	0.980919	0.490460	−	0.871464i	$-0.336829\pi$
$503$	1.40828e12	0.980919	0.490460	+	0.871464i	$0.336829\pi$
$504$	6.18442e11	0.426935
$505$	5.64525e11	0.386253
$506$	6.86980e10	0.0465872
$507$	1.82372e12	1.22581
$508$	−3.99298e10	−0.0266018
$509$	2.07053e12	1.36726	0.683630	−	0.729829i	$-0.260400\pi$
$509$	2.07053e12	1.36726	0.683630	+	0.729829i	$0.260400\pi$
$510$	5.50028e11	0.360014
$511$	−7.30054e11	−0.473654
$512$	−2.63472e11	−0.169442
$513$	−4.21585e11	−0.268755
$514$	1.74670e12	1.10378
$515$	−6.33386e11	−0.396767
$516$	1.00125e12	0.621754
$517$	9.77463e10	0.0601718
$518$	−5.99772e10	−0.0366018
$519$	−1.87678e12	−1.13543
$520$	−7.58686e11	−0.455037
$521$	2.92207e12	1.73749	0.868743	−	0.495264i	$-0.164929\pi$
$521$	2.92207e12	1.73749	0.868743	+	0.495264i	$0.164929\pi$
$522$	−5.42354e11	−0.319717
$523$	5.55233e11	0.324502	0.162251	−	0.986749i	$-0.448125\pi$
$523$	5.55233e11	0.324502	0.162251	+	0.986749i	$0.448125\pi$
$524$	−1.60539e12	−0.930230
$525$	1.06634e11	0.0612604
$526$	1.08927e12	0.620439
$527$	−9.98434e11	−0.563860
$528$	−2.16017e10	−0.0120958
$529$	−7.85129e11	−0.435904
$530$	5.65695e11	0.311416
$531$	2.38812e11	0.130356
$532$	3.09874e11	0.167719
$533$	−1.06112e12	−0.569495
$534$	−1.75979e12	−0.936535
$535$	−1.69110e12	−0.892434
$536$	−2.48930e12	−1.30268
$537$	−2.51330e12	−1.30425
$538$	1.24922e12	0.642866
$539$	1.65321e11	0.0843683
$540$	−3.86076e11	−0.195390
$541$	2.08614e12	1.04702	0.523511	−	0.852019i	$-0.324622\pi$
$541$	2.08614e12	1.04702	0.523511	+	0.852019i	$0.324622\pi$
$542$	−1.53407e12	−0.763567
$543$	7.65079e11	0.377665
$544$	6.97859e11	0.341643
$545$	−9.28947e11	−0.451031
$546$	−2.88794e11	−0.139066
$547$	−7.71838e11	−0.368624	−0.184312	−	0.982868i	$-0.559006\pi$
$547$	−7.71838e11	−0.368624	−0.184312	+	0.982868i	$0.559006\pi$
$548$	1.84144e12	0.872259
$549$	−4.78318e12	−2.24720
$550$	−1.59644e10	−0.00743909
$551$	−7.40807e11	−0.342391
$552$	−2.49716e12	−1.14477
$553$	−5.06562e11	−0.230340
$554$	−2.75944e12	−1.24459
$555$	5.78653e11	0.258881
$556$	−1.53129e12	−0.679548
$557$	1.54489e12	0.680065	0.340032	−	0.940414i	$-0.389562\pi$
$557$	1.54489e12	0.680065	0.340032	+	0.940414i	$0.389562\pi$
$558$	−2.88472e12	−1.25965
$559$	−6.98934e11	−0.302749
$560$	−7.18596e10	−0.0308773
$561$	1.17687e11	0.0501645
$562$	2.12898e11	0.0900241
$563$	−4.49155e12	−1.88412	−0.942059	−	0.335447i	$-0.891113\pi$
$563$	−4.49155e12	−1.88412	−0.942059	+	0.335447i	$0.891113\pi$
$564$	−1.30337e12	−0.542388
$565$	2.90612e11	0.119976
$566$	2.29415e12	0.939611
$567$	6.25141e11	0.254012
$568$	−6.73721e11	−0.271589
$569$	−3.99341e11	−0.159712	−0.0798561	−	0.996806i	$-0.525446\pi$
$569$	−3.99341e11	−0.159712	−0.0798561	+	0.996806i	$0.525446\pi$
$570$	2.17066e12	0.861300
$571$	1.44293e12	0.568046	0.284023	−	0.958817i	$-0.408331\pi$
$571$	1.44293e12	0.568046	0.284023	+	0.958817i	$0.408331\pi$
$572$	−5.95485e10	−0.0232589
$573$	5.60040e12	2.17032
$574$	−7.85568e11	−0.302051
$575$	−2.36108e11	−0.0900754
$576$	2.28892e12	0.866422
$577$	−2.13110e12	−0.800411	−0.400206	−	0.916425i	$-0.631061\pi$
$577$	−2.13110e12	−0.800411	−0.400206	+	0.916425i	$0.631061\pi$
$578$	−1.52409e12	−0.567983
$579$	4.44055e12	1.64204
$580$	−6.78412e11	−0.248924
$581$	2.83549e11	0.103237
$582$	−4.09608e12	−1.47984
$583$	1.21039e11	0.0433929
$584$	−3.97294e12	−1.41337
$585$	1.52788e12	0.539371
$586$	2.64754e12	0.927477
$587$	1.80711e12	0.628223	0.314111	−	0.949386i	$-0.398293\pi$
$587$	1.80711e12	0.628223	0.314111	+	0.949386i	$0.398293\pi$
$588$	−2.20442e12	−0.760496
$589$	−3.94027e12	−1.34898
$590$	−2.16890e11	−0.0736894
$591$	4.91666e12	1.65778
$592$	−4.17586e10	−0.0139733
$593$	−1.19185e11	−0.0395801	−0.0197901	−	0.999804i	$-0.506300\pi$
$593$	−1.19185e11	−0.0395801	−0.0197901	+	0.999804i	$0.506300\pi$
$594$	5.99779e10	0.0197675
$595$	3.91495e11	0.128056
$596$	1.92247e12	0.624097
$597$	6.31038e12	2.03316
$598$	6.39446e11	0.204479
$599$	−3.72745e12	−1.18302	−0.591509	−	0.806298i	$-0.701468\pi$
$599$	−3.72745e12	−1.18302	−0.591509	+	0.806298i	$0.701468\pi$
$600$	5.80301e11	0.182799
$601$	−3.24268e12	−1.01384	−0.506919	−	0.861994i	$-0.669216\pi$
$601$	−3.24268e12	−1.01384	−0.506919	+	0.861994i	$0.669216\pi$
$602$	−5.17437e11	−0.160573
$603$	5.01309e12	1.54411
$604$	1.24848e12	0.381693
$605$	3.45545e12	1.04859
$606$	1.16941e12	0.352242
$607$	2.38198e12	0.712179	0.356089	−	0.934452i	$-0.384110\pi$
$607$	2.38198e12	0.712179	0.356089	+	0.934452i	$0.384110\pi$
$608$	2.75406e12	0.817350
$609$	−7.03973e11	−0.207385
$610$	4.34410e12	1.27033
$611$	9.09830e11	0.264104
$612$	−8.60525e11	−0.247960
$613$	7.43293e11	0.212612	0.106306	−	0.994333i	$-0.466098\pi$
$613$	7.43293e11	0.212612	0.106306	+	0.994333i	$0.466098\pi$
$614$	−3.61274e12	−1.02584
$615$	7.57907e12	2.13638
$616$	−1.20179e11	−0.0336290
$617$	−2.82757e12	−0.785472	−0.392736	−	0.919651i	$-0.628471\pi$
$617$	−2.82757e12	−0.785472	−0.392736	+	0.919651i	$0.628471\pi$
$618$	−1.31206e12	−0.361830
$619$	−3.73077e12	−1.02139	−0.510694	−	0.859763i	$-0.670611\pi$
$619$	−3.73077e12	−1.02139	−0.510694	+	0.859763i	$0.670611\pi$
$620$	−3.60839e12	−0.980734
$621$	8.87056e11	0.239353
$622$	3.01463e12	0.807566
$623$	−1.25257e12	−0.333123
$624$	−2.01070e11	−0.0530906
$625$	−4.21733e12	−1.10555
$626$	−2.25707e12	−0.587436
$627$	4.64446e11	0.120014
$628$	1.40666e12	0.360887
$629$	2.27503e11	0.0579507
$630$	1.13112e12	0.286074
$631$	−4.13742e12	−1.03896	−0.519478	−	0.854484i	$-0.673874\pi$
$631$	−4.13742e12	−1.03896	−0.519478	+	0.854484i	$0.673874\pi$
$632$	−2.75670e12	−0.687326
$633$	−6.30367e12	−1.56055
$634$	−2.75748e12	−0.677814
$635$	−1.99087e11	−0.0485917
$636$	−1.61396e12	−0.391143
$637$	1.53882e12	0.370306
$638$	1.05393e11	0.0251836
$639$	1.35677e12	0.321924
$640$	2.27449e12	0.535889
$641$	−3.48436e12	−0.815197	−0.407598	−	0.913161i	$-0.633634\pi$
$641$	−3.48436e12	−0.815197	−0.407598	+	0.913161i	$0.633634\pi$
$642$	−3.50310e12	−0.813851
$643$	−2.55056e12	−0.588419	−0.294209	−	0.955741i	$-0.595056\pi$
$643$	−2.55056e12	−0.588419	−0.294209	+	0.955741i	$0.595056\pi$
$644$	−6.52005e11	−0.149371
$645$	4.99217e12	1.13572
$646$	8.53412e11	0.192802
$647$	6.00643e12	1.34756	0.673779	−	0.738933i	$-0.264670\pi$
$647$	6.00643e12	1.34756	0.673779	+	0.738933i	$0.264670\pi$
$648$	3.40201e12	0.757962
$649$	−4.64070e10	−0.0102679
$650$	−1.48598e11	−0.0326514
$651$	−3.74435e12	−0.817075
$652$	−1.11633e11	−0.0241923
$653$	1.95092e12	0.419885	0.209943	−	0.977714i	$-0.432672\pi$
$653$	1.95092e12	0.419885	0.209943	+	0.977714i	$0.432672\pi$
$654$	−1.92431e12	−0.411316
$655$	−8.00439e12	−1.69919
$656$	−5.46944e11	−0.115312
$657$	8.00092e12	1.67531
$658$	6.73568e11	0.140076
$659$	9.15650e12	1.89123	0.945617	−	0.325283i	$-0.105460\pi$
$659$	9.15650e12	1.89123	0.945617	+	0.325283i	$0.105460\pi$
$660$	4.25328e11	0.0872522
$661$	4.00343e12	0.815691	0.407845	−	0.913051i	$-0.366280\pi$
$661$	4.00343e12	0.815691	0.407845	+	0.913051i	$0.366280\pi$
$662$	3.61602e12	0.731762
$663$	1.09544e12	0.220180
$664$	1.54307e12	0.308056
$665$	1.54501e12	0.306362
$666$	6.57311e11	0.129460
$667$	1.55873e12	0.304933
$668$	−4.88557e11	−0.0949339
$669$	−2.03329e11	−0.0392447
$670$	−4.55291e12	−0.872876
$671$	9.29490e11	0.177008
$672$	2.61713e12	0.495066
$673$	−6.96563e11	−0.130886	−0.0654429	−	0.997856i	$-0.520846\pi$
$673$	−6.96563e11	−0.130886	−0.0654429	+	0.997856i	$0.520846\pi$
$674$	4.84042e12	0.903470
$675$	−2.06138e11	−0.0382201
$676$	2.59132e12	0.477267
$677$	1.73767e12	0.317921	0.158961	−	0.987285i	$-0.449186\pi$
$677$	1.73767e12	0.317921	0.158961	+	0.987285i	$0.449186\pi$
$678$	6.02002e11	0.109412
$679$	−2.91548e12	−0.526376
$680$	2.13051e12	0.382114
$681$	−4.33897e12	−0.773080
$682$	5.60573e11	0.0992207
$683$	2.89548e12	0.509128	0.254564	−	0.967056i	$-0.418068\pi$
$683$	2.89548e12	0.509128	0.254564	+	0.967056i	$0.418068\pi$
$684$	−3.39602e12	−0.593222
$685$	9.18132e12	1.59330
$686$	2.43063e12	0.419044
$687$	−1.67824e12	−0.287441
$688$	−3.60260e11	−0.0613011
$689$	1.12664e12	0.190458
$690$	−4.56727e12	−0.767072
$691$	−8.63677e12	−1.44112	−0.720560	−	0.693393i	$-0.756115\pi$
$691$	−8.63677e12	−1.44112	−0.720560	+	0.693393i	$0.756115\pi$
$692$	−2.66671e12	−0.442077
$693$	2.42022e11	0.0398617
$694$	2.90555e12	0.475457
$695$	−7.63490e12	−1.24129
$696$	−3.83101e12	−0.618830
$697$	2.97978e12	0.478229
$698$	6.33699e12	1.01049
$699$	−1.52780e13	−2.42058
$700$	1.51516e11	0.0238516
$701$	−1.05023e13	−1.64269	−0.821345	−	0.570432i	$-0.806776\pi$
$701$	−1.05023e13	−1.64269	−0.821345	+	0.570432i	$0.806776\pi$
$702$	5.58279e11	0.0867629
$703$	8.97827e11	0.138642
$704$	−4.44794e11	−0.0682467
$705$	−6.49850e12	−0.990746
$706$	−4.34308e12	−0.657925
$707$	8.32355e11	0.125291
$708$	6.18799e11	0.0925550
$709$	8.14881e11	0.121112	0.0605559	−	0.998165i	$-0.480713\pi$
$709$	8.14881e11	0.121112	0.0605559	+	0.998165i	$0.480713\pi$
$710$	−1.23223e12	−0.181982
$711$	5.55159e12	0.814712
$712$	−6.81645e12	−0.994027
$713$	8.29071e12	1.20140
$714$	8.10980e11	0.116780
$715$	−2.96905e11	−0.0424855
$716$	−3.57114e12	−0.507807
$717$	1.05778e12	0.149471
$718$	4.87321e12	0.684314
$719$	1.97539e12	0.275660	0.137830	−	0.990456i	$-0.455987\pi$
$719$	1.97539e12	0.275660	0.137830	+	0.990456i	$0.455987\pi$
$720$	7.87534e11	0.109213
$721$	−9.33886e11	−0.128702
$722$	−1.36766e12	−0.187310
$723$	1.37563e13	1.87232
$724$	1.08710e12	0.147043
$725$	−3.62225e11	−0.0486920
$726$	7.15794e12	0.956254
$727$	3.76563e12	0.499957	0.249978	−	0.968251i	$-0.419576\pi$
$727$	3.76563e12	0.499957	0.249978	+	0.968251i	$0.419576\pi$
$728$	−1.11863e12	−0.147603
$729$	−1.04672e13	−1.37265
$730$	−7.26647e12	−0.947045
$731$	1.96272e12	0.254231
$732$	−1.23940e13	−1.59555
$733$	5.26245e12	0.673318	0.336659	−	0.941627i	$-0.390703\pi$
$733$	5.26245e12	0.673318	0.336659	+	0.941627i	$0.390703\pi$
$734$	−2.31961e12	−0.294973
$735$	−1.09911e13	−1.38915
$736$	−5.79482e12	−0.727930
$737$	−9.74167e11	−0.121627
$738$	8.60931e12	1.06835
$739$	−1.29839e13	−1.60142	−0.800712	−	0.599049i	$-0.795545\pi$
$739$	−1.29839e13	−1.60142	−0.800712	+	0.599049i	$0.795545\pi$
$740$	8.22207e11	0.100795
$741$	4.32310e12	0.526761
$742$	8.34080e11	0.101016
$743$	6.61480e12	0.796282	0.398141	−	0.917324i	$-0.369655\pi$
$743$	6.61480e12	0.796282	0.398141	+	0.917324i	$0.369655\pi$
$744$	−2.03767e13	−2.43812
$745$	9.58534e12	1.14000
$746$	1.50328e11	0.0177711
$747$	−3.10752e12	−0.365149
$748$	1.67221e11	0.0195315
$749$	−2.49341e12	−0.289484
$750$	−7.78847e12	−0.898828
$751$	3.26089e12	0.374073	0.187037	−	0.982353i	$-0.440112\pi$
$751$	3.26089e12	0.374073	0.187037	+	0.982353i	$0.440112\pi$
$752$	4.68965e11	0.0534761
$753$	−2.08207e13	−2.36003
$754$	9.81004e11	0.110535
$755$	6.22483e12	0.697214
$756$	−5.69244e11	−0.0633797
$757$	1.06659e13	1.18050	0.590248	−	0.807222i	$-0.299030\pi$
$757$	1.06659e13	1.18050	0.590248	+	0.807222i	$0.299030\pi$
$758$	3.80038e12	0.418134
$759$	−9.77241e11	−0.106884
$760$	8.40794e12	0.914173
$761$	4.98641e12	0.538961	0.269480	−	0.963006i	$-0.413148\pi$
$761$	4.98641e12	0.538961	0.269480	+	0.963006i	$0.413148\pi$
$762$	−4.12409e11	−0.0443130
$763$	−1.36967e12	−0.146304
$764$	7.95759e12	0.845009
$765$	−4.29053e12	−0.452933
$766$	8.25787e12	0.866640
$767$	−4.31960e11	−0.0450676
$768$	1.49488e13	1.55053
$769$	−4.40762e12	−0.454501	−0.227251	−	0.973836i	$-0.572974\pi$
$769$	−4.40762e12	−0.454501	−0.227251	+	0.973836i	$0.572974\pi$
$770$	−2.19806e11	−0.0225336
$771$	−2.48471e13	−2.53239
$772$	6.30957e12	0.639325
$773$	9.81264e12	0.988503	0.494252	−	0.869319i	$-0.335442\pi$
$773$	9.81264e12	0.988503	0.494252	+	0.869319i	$0.335442\pi$
$774$	5.67077e12	0.567947
$775$	−1.92663e12	−0.191841
$776$	−1.58660e13	−1.57069
$777$	8.53186e11	0.0839748
$778$	5.57192e12	0.545251
$779$	1.17595e13	1.14412
$780$	3.95898e12	0.382964
$781$	−2.63655e11	−0.0253575
$782$	−1.79566e12	−0.171710
$783$	1.36087e12	0.129387
$784$	7.93174e11	0.0749802
$785$	7.01352e12	0.659209
$786$	−1.65811e13	−1.54957
$787$	3.35238e12	0.311507	0.155753	−	0.987796i	$-0.450220\pi$
$787$	3.35238e12	0.311507	0.155753	+	0.987796i	$0.450220\pi$
$788$	6.98607e12	0.645453
$789$	−1.54950e13	−1.42346
$790$	−5.04198e12	−0.460552
$791$	4.28488e11	0.0389175
$792$	1.31708e12	0.118946
$793$	8.65175e12	0.776917
$794$	1.33237e13	1.18969
$795$	−8.04711e12	−0.714476
$796$	8.96639e12	0.791606
$797$	5.38103e12	0.472392	0.236196	−	0.971705i	$-0.424099\pi$
$797$	5.38103e12	0.472392	0.236196	+	0.971705i	$0.424099\pi$
$798$	3.20049e12	0.279385
$799$	−2.55494e12	−0.221779
$800$	1.34663e12	0.116237
$801$	1.37273e13	1.17826
$802$	−8.75342e12	−0.747125
$803$	−1.55478e12	−0.131962
$804$	1.29897e13	1.09634
$805$	−3.25086e12	−0.272845
$806$	5.21785e12	0.435496
$807$	−1.77704e13	−1.47492
$808$	4.52966e12	0.373865
$809$	4.15339e12	0.340906	0.170453	−	0.985366i	$-0.445477\pi$
$809$	4.15339e12	0.340906	0.170453	+	0.985366i	$0.445477\pi$
$810$	6.22224e12	0.507883
$811$	−2.59532e12	−0.210667	−0.105333	−	0.994437i	$-0.533591\pi$
$811$	−2.59532e12	−0.210667	−0.105333	+	0.994437i	$0.533591\pi$
$812$	−1.00027e12	−0.0807451
$813$	2.18223e13	1.75184
$814$	−1.27732e11	−0.0101974
$815$	−5.56595e11	−0.0441906
$816$	5.64637e11	0.0445824
$817$	7.74575e12	0.608225
$818$	−1.36009e13	−1.06213
$819$	2.25276e12	0.174959
$820$	1.07691e13	0.831795
$821$	−9.64824e12	−0.741146	−0.370573	−	0.928803i	$-0.620839\pi$
$821$	−9.64824e12	−0.741146	−0.370573	+	0.928803i	$0.620839\pi$
$822$	1.90191e13	1.45300
$823$	1.38171e13	1.04983	0.524913	−	0.851156i	$-0.324098\pi$
$823$	1.38171e13	1.04983	0.524913	+	0.851156i	$0.324098\pi$
$824$	−5.08219e12	−0.384042
$825$	2.27096e11	0.0170674
$826$	−3.19790e11	−0.0239031
$827$	−1.15061e13	−0.855366	−0.427683	−	0.903929i	$-0.640670\pi$
$827$	−1.15061e13	−0.855366	−0.427683	+	0.903929i	$0.640670\pi$
$828$	7.14555e12	0.528323
$829$	−1.07976e13	−0.794019	−0.397009	−	0.917815i	$-0.629952\pi$
$829$	−1.07976e13	−0.794019	−0.397009	+	0.917815i	$0.629952\pi$
$830$	2.82226e12	0.206417
$831$	3.92536e13	2.85545
$832$	−4.14017e12	−0.299546
$833$	−4.32125e12	−0.310962
$834$	−1.58157e13	−1.13198
$835$	−2.43592e12	−0.173410
$836$	6.59930e11	0.0467272
$837$	7.23834e12	0.509770
$838$	−4.41800e12	−0.309476
$839$	−1.66712e13	−1.16155	−0.580775	−	0.814064i	$-0.697250\pi$
$839$	−1.66712e13	−1.16155	−0.580775	+	0.814064i	$0.697250\pi$
$840$	7.98988e12	0.553712
$841$	−1.21158e13	−0.835162
$842$	−1.86766e11	−0.0128054
$843$	−3.02851e12	−0.206541
$844$	−8.95687e12	−0.607596
$845$	1.29202e13	0.871792
$846$	−7.38186e12	−0.495449
$847$	5.09483e12	0.340137
$848$	5.80720e11	0.0385643
$849$	−3.26347e13	−2.15573
$850$	4.17285e11	0.0274187
$851$	−1.88912e12	−0.123474
$852$	3.51562e12	0.228572
$853$	−2.00958e13	−1.29967	−0.649836	−	0.760075i	$-0.725162\pi$
$853$	−2.00958e13	−1.29967	−0.649836	+	0.760075i	$0.725162\pi$
$854$	6.40509e12	0.412064
$855$	−1.69323e13	−1.08360
$856$	−1.35691e13	−0.863811
$857$	−8.22213e12	−0.520679	−0.260340	−	0.965517i	$-0.583835\pi$
$857$	−8.22213e12	−0.520679	−0.260340	+	0.965517i	$0.583835\pi$
$858$	−6.15038e11	−0.0387444
$859$	−2.42849e13	−1.52183	−0.760916	−	0.648850i	$-0.775250\pi$
$859$	−2.42849e13	−1.52183	−0.760916	+	0.648850i	$0.775250\pi$
$860$	7.09336e12	0.442190
$861$	1.11748e13	0.692990
$862$	2.02500e13	1.24923
$863$	1.52380e13	0.935145	0.467572	−	0.883955i	$-0.345129\pi$
$863$	1.52380e13	0.935145	0.467572	+	0.883955i	$0.345129\pi$
$864$	−5.05926e12	−0.308870
$865$	−1.32960e13	−0.807513
$866$	1.62395e13	0.981163
$867$	2.16805e13	1.30311
$868$	−5.32034e12	−0.318127
$869$	−1.07881e12	−0.0641736
$870$	−7.00687e12	−0.414656
$871$	−9.06761e12	−0.533840
$872$	−7.45372e12	−0.436565
$873$	3.19517e13	1.86179
$874$	−7.08649e12	−0.410799
$875$	−5.54362e12	−0.319711
$876$	2.07316e13	1.18950
$877$	1.22720e12	0.0700512	0.0350256	−	0.999386i	$-0.488849\pi$
$877$	1.22720e12	0.0700512	0.0350256	+	0.999386i	$0.488849\pi$
$878$	1.59698e12	0.0906929
$879$	−3.76617e13	−2.12789
$880$	−1.53037e11	−0.00860252
$881$	−7.25699e12	−0.405850	−0.202925	−	0.979194i	$-0.565045\pi$
$881$	−7.25699e12	−0.405850	−0.202925	+	0.979194i	$0.565045\pi$
$882$	−1.24852e13	−0.694681
$883$	2.31876e13	1.28361	0.641804	−	0.766869i	$-0.278186\pi$
$883$	2.31876e13	1.28361	0.641804	+	0.766869i	$0.278186\pi$
$884$	1.55651e12	0.0857267
$885$	3.08530e12	0.169064
$886$	−2.62954e12	−0.143360
$887$	3.42062e13	1.85545	0.927723	−	0.373269i	$-0.121763\pi$
$887$	3.42062e13	1.85545	0.927723	+	0.373269i	$0.121763\pi$
$888$	4.64302e12	0.250578
$889$	−2.93541e11	−0.0157620
$890$	−1.24672e13	−0.666062
$891$	1.33135e12	0.0707687
$892$	−2.88909e11	−0.0152799
$893$	−1.00830e13	−0.530586
$894$	1.98560e13	1.03962
$895$	−1.78055e13	−0.927578
$896$	3.35359e12	0.173830
$897$	−9.09622e12	−0.469132
$898$	−2.20455e13	−1.13130
$899$	1.27192e13	0.649442
$900$	−1.66052e12	−0.0843631
$901$	−3.16379e12	−0.159936
$902$	−1.67300e12	−0.0841525
$903$	7.36063e12	0.368400
$904$	2.33182e12	0.116128
$905$	5.42020e12	0.268594
$906$	1.28947e13	0.635820
$907$	−1.45806e13	−0.715388	−0.357694	−	0.933839i	$-0.616437\pi$
$907$	−1.45806e13	−0.715388	−0.357694	+	0.933839i	$0.616437\pi$
$908$	−6.16523e12	−0.300998
$909$	−9.12207e12	−0.443155
$910$	−2.04597e12	−0.0989036
$911$	8.34928e12	0.401621	0.200810	−	0.979630i	$-0.435642\pi$
$911$	8.34928e12	0.401621	0.200810	+	0.979630i	$0.435642\pi$
$912$	2.22831e12	0.106659
$913$	6.03867e11	0.0287623
$914$	5.71094e12	0.270676
$915$	−6.17956e13	−2.91449
$916$	−2.38460e12	−0.111914
$917$	−1.18019e13	−0.551177
$918$	−1.56773e12	−0.0728585
$919$	−2.40071e13	−1.11025	−0.555123	−	0.831768i	$-0.687329\pi$
$919$	−2.40071e13	−1.11025	−0.555123	+	0.831768i	$0.687329\pi$
$920$	−1.76911e13	−0.814161
$921$	5.13918e13	2.35356
$922$	−1.65240e13	−0.753052
$923$	−2.45412e12	−0.111298
$924$	6.27118e11	0.0283025
$925$	4.39002e11	0.0197165
$926$	1.61553e12	0.0722047
$927$	1.02348e13	0.455218
$928$	−8.89011e12	−0.393497
$929$	−7.49834e12	−0.330289	−0.165145	−	0.986269i	$-0.552809\pi$
$929$	−7.49834e12	−0.330289	−0.165145	+	0.986269i	$0.552809\pi$
$930$	−3.72688e13	−1.63370
$931$	−1.70536e13	−0.743948
$932$	−2.17085e13	−0.942450
$933$	−4.28837e13	−1.85278
$934$	1.19637e13	0.514405
$935$	8.33756e11	0.0356768
$936$	1.22595e13	0.522072
$937$	−2.06752e13	−0.876239	−0.438119	−	0.898917i	$-0.644355\pi$
$937$	−2.06752e13	−0.876239	−0.438119	+	0.898917i	$0.644355\pi$
$938$	−6.71296e12	−0.283140
$939$	3.21072e13	1.34774
$940$	−9.23370e12	−0.385745
$941$	1.33241e13	0.553967	0.276983	−	0.960875i	$-0.410665\pi$
$941$	1.33241e13	0.553967	0.276983	+	0.960875i	$0.410665\pi$
$942$	1.45285e13	0.601162
$943$	−2.47432e13	−1.01895
$944$	−2.22650e11	−0.00912535
$945$	−2.83822e12	−0.115772
$946$	−1.10197e12	−0.0447363
$947$	2.92921e13	1.18352	0.591760	−	0.806115i	$-0.298434\pi$
$947$	2.92921e13	1.18352	0.591760	+	0.806115i	$0.298434\pi$
$948$	1.43850e13	0.578461
$949$	−1.44720e13	−0.579201
$950$	1.64679e12	0.0655968
$951$	3.92256e13	1.55510
$952$	3.14129e12	0.123949
$953$	9.71157e12	0.381392	0.190696	−	0.981649i	$-0.438926\pi$
$953$	9.71157e12	0.381392	0.190696	+	0.981649i	$0.438926\pi$
$954$	−9.14097e12	−0.357293
$955$	3.96761e13	1.54352
$956$	1.50299e12	0.0581964
$957$	−1.49923e12	−0.0577783
$958$	1.92568e12	0.0738652
$959$	1.35372e13	0.516829
$960$	2.95714e13	1.12370
$961$	4.12122e13	1.55873
$962$	−1.18894e12	−0.0447580
$963$	2.73261e13	1.02391
$964$	1.95463e13	0.728986
$965$	3.14591e13	1.16781
$966$	−6.73414e12	−0.248820
$967$	2.92185e13	1.07458	0.537289	−	0.843398i	$-0.319448\pi$
$967$	2.92185e13	1.07458	0.537289	+	0.843398i	$0.319448\pi$
$968$	2.77260e13	1.01496
$969$	−1.21399e13	−0.442343
$970$	−2.90187e13	−1.05246
$971$	1.66211e12	0.0600030	0.0300015	−	0.999550i	$-0.490449\pi$
$971$	1.66211e12	0.0600030	0.0300015	+	0.999550i	$0.490449\pi$
$972$	−2.28905e13	−0.822541
$973$	−1.12572e13	−0.402644
$974$	−1.40686e13	−0.500881
$975$	2.11383e12	0.0749115
$976$	4.45948e12	0.157311
$977$	3.76753e13	1.32291	0.661457	−	0.749983i	$-0.269938\pi$
$977$	3.76753e13	1.32291	0.661457	+	0.749983i	$0.269938\pi$
$978$	−1.15298e12	−0.0402994
$979$	−2.66756e12	−0.0928094
$980$	−1.56172e13	−0.540863
$981$	1.50107e13	0.517476
$982$	9.55256e11	0.0327807
$983$	−4.44517e13	−1.51844	−0.759220	−	0.650834i	$-0.774420\pi$
$983$	−4.44517e13	−1.51844	−0.759220	+	0.650834i	$0.774420\pi$
$984$	6.08133e13	2.06786
$985$	3.48321e13	1.17901
$986$	−2.75481e12	−0.0928210
$987$	−9.58161e12	−0.321374
$988$	6.14268e12	0.205093
$989$	−1.62978e13	−0.541684
$990$	2.40893e12	0.0797012
$991$	−1.33325e12	−0.0439116	−0.0219558	−	0.999759i	$-0.506989\pi$
$991$	−1.33325e12	−0.0439116	−0.0219558	+	0.999759i	$0.506989\pi$
$992$	−4.72855e13	−1.55033
$993$	−5.14385e13	−1.67887
$994$	−1.81684e12	−0.0590307
$995$	4.47059e13	1.44598
$996$	−8.05207e12	−0.259263
$997$	4.45739e13	1.42874	0.714369	−	0.699769i	$-0.246714\pi$
$997$	4.45739e13	1.42874	0.714369	+	0.699769i	$0.246714\pi$
$998$	3.55765e12	0.113521
$999$	−1.64932e12	−0.0523916

Twists

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

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

\(f(q)\)	\(=\)	\(q+14.6755 q^{2} -208.762 q^{3} -296.629 q^{4} -1478.97 q^{5} -3063.69 q^{6} -2180.65 q^{7} -11867.1 q^{8} +23898.5 q^{9} +O(q^{10})\)	\(q+14.6755 q^{2} -208.762 q^{3} -296.629 q^{4} -1478.97 q^{5} -3063.69 q^{6} -2180.65 q^{7} -11867.1 q^{8} +23898.5 q^{9} -21704.7 q^{10} -4644.07 q^{11} +61924.8 q^{12} -43227.3 q^{13} -32002.2 q^{14} +308753. q^{15} -22281.2 q^{16} +121389. q^{17} +350723. q^{18} +479056. q^{19} +438707. q^{20} +455236. q^{21} -68154.2 q^{22} -1.00798e6 q^{23} +2.47739e6 q^{24} +234239. q^{25} -634384. q^{26} -880033. q^{27} +646844. q^{28} -1.54639e6 q^{29} +4.53112e6 q^{30} -8.22507e6 q^{31} +5.74894e6 q^{32} +969504. q^{33} +1.78145e6 q^{34} +3.22512e6 q^{35} -7.08898e6 q^{36} +1.87416e6 q^{37} +7.03039e6 q^{38} +9.02421e6 q^{39} +1.75511e7 q^{40} +2.45473e7 q^{41} +6.68083e6 q^{42} +1.61688e7 q^{43} +1.37757e6 q^{44} -3.53452e7 q^{45} -1.47926e7 q^{46} -2.10476e7 q^{47} +4.65146e6 q^{48} -3.55984e7 q^{49} +3.43758e6 q^{50} -2.53414e7 q^{51} +1.28225e7 q^{52} -2.60632e7 q^{53} -1.29149e7 q^{54} +6.86846e6 q^{55} +2.58779e7 q^{56} -1.00009e8 q^{57} -2.26941e7 q^{58} +9.99275e6 q^{59} -9.15852e7 q^{60} -2.00146e8 q^{61} -1.20707e8 q^{62} -5.21142e7 q^{63} +9.57767e7 q^{64} +6.39321e7 q^{65} +1.42280e7 q^{66} +2.09766e8 q^{67} -3.60075e7 q^{68} +2.10428e8 q^{69} +4.73304e7 q^{70} +5.67724e7 q^{71} -2.83605e8 q^{72} +3.34787e8 q^{73} +2.75043e7 q^{74} -4.89002e7 q^{75} -1.42102e8 q^{76} +1.01271e7 q^{77} +1.32435e8 q^{78} +2.32299e8 q^{79} +3.29533e7 q^{80} -2.86677e8 q^{81} +3.60245e8 q^{82} -1.30030e8 q^{83} -1.35036e8 q^{84} -1.79531e8 q^{85} +2.37286e8 q^{86} +3.22827e8 q^{87} +5.51114e7 q^{88} +5.74401e8 q^{89} -5.18710e8 q^{90} +9.42636e7 q^{91} +2.98996e8 q^{92} +1.71708e9 q^{93} -3.08884e8 q^{94} -7.08511e8 q^{95} -1.20016e9 q^{96} +1.33698e9 q^{97} -5.22425e8 q^{98} -1.10986e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 48 q^{2} + 397 q^{3} + 3498 q^{4} + 2841 q^{5} + 3375 q^{6} + 6632 q^{7} + 41046 q^{8} + 101917 q^{9}+O(q^{10}) \) 14 * q + 48 * q^2 + 397 * q^3 + 3498 * q^4 + 2841 * q^5 + 3375 * q^6 + 6632 * q^7 + 41046 * q^8 + 101917 * q^9	\( 14 q + 48 q^{2} + 397 q^{3} + 3498 q^{4} + 2841 q^{5} + 3375 q^{6} + 6632 q^{7} + 41046 q^{8} + 101917 q^{9} + 129003 q^{10} + 44949 q^{11} - 123661 q^{12} + 38913 q^{13} + 16434 q^{14} + 119816 q^{15} + 859962 q^{16} + 893196 q^{17} + 1833339 q^{18} + 1532124 q^{19} + 4974963 q^{20} + 1851132 q^{21} + 3195323 q^{22} + 5911773 q^{23} + 7885413 q^{24} + 9978791 q^{25} + 10634475 q^{26} + 13105312 q^{27} + 9469678 q^{28} + 8764377 q^{29} + 21804216 q^{30} + 13188927 q^{31} + 23982750 q^{32} + 9398618 q^{33} + 29914960 q^{34} + 29633556 q^{35} + 24297333 q^{36} + 26238254 q^{37} + 23342796 q^{38} + 40855861 q^{39} + 42889049 q^{40} + 22153785 q^{41} + 6999662 q^{42} + 1779790 q^{43} - 83674089 q^{44} - 45101798 q^{45} - 23239663 q^{46} + 40080072 q^{47} - 141884869 q^{48} - 170457752 q^{49} - 89214633 q^{50} - 127867462 q^{51} - 276889277 q^{52} - 102088122 q^{53} - 356745582 q^{54} - 206797385 q^{55} - 294922194 q^{56} - 141710762 q^{57} - 527059089 q^{58} + 56191266 q^{59} - 283393416 q^{60} - 178507397 q^{61} - 27353505 q^{62} - 291948734 q^{63} - 242330062 q^{64} - 174258810 q^{65} - 1153895008 q^{66} + 287062499 q^{67} + 308827572 q^{68} - 80094823 q^{69} - 672888452 q^{70} + 224382678 q^{71} + 105778731 q^{72} + 271440727 q^{73} + 89959728 q^{74} + 1017561832 q^{75} - 229522980 q^{76} + 671279994 q^{77} - 119785879 q^{78} + 379128625 q^{79} + 1999017183 q^{80} + 2367007018 q^{81} + 551153781 q^{82} + 1664083206 q^{83} + 1344035042 q^{84} + 1982056546 q^{85} + 520253082 q^{86} + 3606452357 q^{87} + 684092585 q^{88} + 3293434692 q^{89} + 892602798 q^{90} + 1715813946 q^{91} + 3729310881 q^{92} + 2573139250 q^{93} + 998499458 q^{94} + 878402766 q^{95} - 1221963827 q^{96} + 2385468336 q^{97} - 3234447132 q^{98} + 4029218638 q^{99}+O(q^{100}) \) 14 * q + 48 * q^2 + 397 * q^3 + 3498 * q^4 + 2841 * q^5 + 3375 * q^6 + 6632 * q^7 + 41046 * q^8 + 101917 * q^9 + 129003 * q^10 + 44949 * q^11 - 123661 * q^12 + 38913 * q^13 + 16434 * q^14 + 119816 * q^15 + 859962 * q^16 + 893196 * q^17 + 1833339 * q^18 + 1532124 * q^19 + 4974963 * q^20 + 1851132 * q^21 + 3195323 * q^22 + 5911773 * q^23 + 7885413 * q^24 + 9978791 * q^25 + 10634475 * q^26 + 13105312 * q^27 + 9469678 * q^28 + 8764377 * q^29 + 21804216 * q^30 + 13188927 * q^31 + 23982750 * q^32 + 9398618 * q^33 + 29914960 * q^34 + 29633556 * q^35 + 24297333 * q^36 + 26238254 * q^37 + 23342796 * q^38 + 40855861 * q^39 + 42889049 * q^40 + 22153785 * q^41 + 6999662 * q^42 + 1779790 * q^43 - 83674089 * q^44 - 45101798 * q^45 - 23239663 * q^46 + 40080072 * q^47 - 141884869 * q^48 - 170457752 * q^49 - 89214633 * q^50 - 127867462 * q^51 - 276889277 * q^52 - 102088122 * q^53 - 356745582 * q^54 - 206797385 * q^55 - 294922194 * q^56 - 141710762 * q^57 - 527059089 * q^58 + 56191266 * q^59 - 283393416 * q^60 - 178507397 * q^61 - 27353505 * q^62 - 291948734 * q^63 - 242330062 * q^64 - 174258810 * q^65 - 1153895008 * q^66 + 287062499 * q^67 + 308827572 * q^68 - 80094823 * q^69 - 672888452 * q^70 + 224382678 * q^71 + 105778731 * q^72 + 271440727 * q^73 + 89959728 * q^74 + 1017561832 * q^75 - 229522980 * q^76 + 671279994 * q^77 - 119785879 * q^78 + 379128625 * q^79 + 1999017183 * q^80 + 2367007018 * q^81 + 551153781 * q^82 + 1664083206 * q^83 + 1344035042 * q^84 + 1982056546 * q^85 + 520253082 * q^86 + 3606452357 * q^87 + 684092585 * q^88 + 3293434692 * q^89 + 892602798 * q^90 + 1715813946 * q^91 + 3729310881 * q^92 + 2573139250 * q^93 + 998499458 * q^94 + 878402766 * q^95 - 1221963827 * q^96 + 2385468336 * q^97 - 3234447132 * q^98 + 4029218638 * q^99

Introduction

L-functions

Modular forms

Varieties

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