LMFDB - Embedded newform 43.10.a.a.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,10,Mod(1,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, 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("43.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	43.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:	$22.1465409550$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2 x^{14} - 5425 x^{13} + 14888 x^{12} + 11288030 x^{11} - 37600244 x^{10} + \cdots + 52\!\cdots\!00 $ x^15 - 2x^14 - 5425x^13 + 14888x^12 + 11288030x^11 - 37600244x^10 - 11474166224x^9 + 47465836576x^8 + 5986976782464x^7 - 32493903147264x^6 - 1516975415483904x^5 + 10892588268404224x^4 + 139803541742443008x^3 - 1349125586394823680x^2 + 2103623681144094720x + 529838441422848000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	multiple of $ 2^{10}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$2.38595$ of defining polynomial
Character	$\chi$	$=$	43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.38595 q^{2} +117.920 q^{3} -492.763 q^{4} -1237.15 q^{5} -517.190 q^{6} +12549.3 q^{7} +4406.84 q^{8} -5777.96 q^{9} +O(q^{10})$	\(q-4.38595 q^{2} +117.920 q^{3} -492.763 q^{4} -1237.15 q^{5} -517.190 q^{6} +12549.3 q^{7} +4406.84 q^{8} -5777.96 q^{9} +5426.06 q^{10} +27918.0 q^{11} -58106.5 q^{12} -139652. q^{13} -55040.4 q^{14} -145884. q^{15} +232967. q^{16} -408645. q^{17} +25341.8 q^{18} -157490. q^{19} +609620. q^{20} +1.47980e6 q^{21} -122447. q^{22} -730739. q^{23} +519653. q^{24} -422597. q^{25} +612508. q^{26} -3.00235e6 q^{27} -6.18382e6 q^{28} -6.14391e6 q^{29} +639839. q^{30} +6.18625e6 q^{31} -3.27808e6 q^{32} +3.29208e6 q^{33} +1.79230e6 q^{34} -1.55253e7 q^{35} +2.84717e6 q^{36} -2.16507e7 q^{37} +690744. q^{38} -1.64677e7 q^{39} -5.45190e6 q^{40} +2.42738e7 q^{41} -6.49035e6 q^{42} -3.41880e6 q^{43} -1.37570e7 q^{44} +7.14817e6 q^{45} +3.20499e6 q^{46} -3.21569e7 q^{47} +2.74713e7 q^{48} +1.17130e8 q^{49} +1.85349e6 q^{50} -4.81873e7 q^{51} +6.88155e7 q^{52} -6.96541e7 q^{53} +1.31681e7 q^{54} -3.45386e7 q^{55} +5.53026e7 q^{56} -1.85712e7 q^{57} +2.69469e7 q^{58} -1.12041e8 q^{59} +7.18862e7 q^{60} +8.03385e7 q^{61} -2.71326e7 q^{62} -7.25091e7 q^{63} -1.04901e8 q^{64} +1.72770e8 q^{65} -1.44389e7 q^{66} -5.78429e7 q^{67} +2.01366e8 q^{68} -8.61685e7 q^{69} +6.80930e7 q^{70} +3.11039e8 q^{71} -2.54625e7 q^{72} -3.23803e7 q^{73} +9.49590e7 q^{74} -4.98325e7 q^{75} +7.76054e7 q^{76} +3.50350e8 q^{77} +7.22267e7 q^{78} +2.36871e8 q^{79} -2.88214e8 q^{80} -2.40308e8 q^{81} -1.06464e8 q^{82} +4.61987e8 q^{83} -7.29193e8 q^{84} +5.05554e8 q^{85} +1.49947e7 q^{86} -7.24488e8 q^{87} +1.23030e8 q^{88} +6.16826e8 q^{89} -3.13515e7 q^{90} -1.75253e9 q^{91} +3.60082e8 q^{92} +7.29481e8 q^{93} +1.41038e8 q^{94} +1.94838e8 q^{95} -3.86551e8 q^{96} -1.00137e9 q^{97} -5.13728e8 q^{98} -1.61309e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 32 q^{2} - 317 q^{3} + 3242 q^{4} - 4717 q^{5} + 687 q^{6} - 9680 q^{7} - 20394 q^{8} + 69516 q^{9}+O(q^{10}) $ 15 * q - 32 * q^2 - 317 * q^3 + 3242 * q^4 - 4717 * q^5 + 687 * q^6 - 9680 * q^7 - 20394 * q^8 + 69516 * q^9	\( 15 q - 32 q^{2} - 317 q^{3} + 3242 q^{4} - 4717 q^{5} + 687 q^{6} - 9680 q^{7} - 20394 q^{8} + 69516 q^{9} - 36237 q^{10} - 104484 q^{11} - 266395 q^{12} - 116174 q^{13} + 416064 q^{14} + 415388 q^{15} + 996762 q^{16} - 884265 q^{17} - 588735 q^{18} - 689535 q^{19} - 3077879 q^{20} - 2070198 q^{21} - 7276218 q^{22} - 2504077 q^{23} - 11534895 q^{24} + 1315350 q^{25} - 13343414 q^{26} - 12546986 q^{27} - 28059568 q^{28} - 18406221 q^{29} - 39503820 q^{30} - 12033699 q^{31} - 18952630 q^{32} - 14197716 q^{33} - 30383125 q^{34} - 27855546 q^{35} - 18372959 q^{36} - 8722847 q^{37} - 63941843 q^{38} - 30955510 q^{39} - 39665611 q^{40} - 18689389 q^{41} - 73185310 q^{42} - 51282015 q^{43} - 68723220 q^{44} - 216992888 q^{45} - 2067521 q^{46} - 104960741 q^{47} - 145362479 q^{48} + 92663095 q^{49} - 42446347 q^{50} + 37433407 q^{51} + 149226080 q^{52} - 215907800 q^{53} + 419158122 q^{54} + 384379852 q^{55} + 430441344 q^{56} + 258744488 q^{57} + 295963139 q^{58} + 185924544 q^{59} + 973236172 q^{60} + 247538102 q^{61} + 139798853 q^{62} + 405429926 q^{63} + 848556290 q^{64} + 94294394 q^{65} + 667230492 q^{66} + 467904656 q^{67} - 88234341 q^{68} + 163914994 q^{69} + 647526126 q^{70} - 8252944 q^{71} + 889796745 q^{72} - 715627902 q^{73} + 725122989 q^{74} - 18301762 q^{75} + 346300359 q^{76} - 1236779964 q^{77} + 2058642146 q^{78} + 560681783 q^{79} - 1157214179 q^{80} - 752010645 q^{81} + 941346367 q^{82} - 1442854698 q^{83} + 1895248718 q^{84} + 699302088 q^{85} + 109401632 q^{86} - 2094576907 q^{87} - 1464507256 q^{88} - 396710008 q^{89} + 1411356270 q^{90} - 3278076852 q^{91} + 155864647 q^{92} - 1424759183 q^{93} + 4666638949 q^{94} - 3854114395 q^{95} - 952489551 q^{96} - 3063837815 q^{97} - 6161086984 q^{98} - 6576160348 q^{99}+O(q^{100}) \) 15 * q - 32 * q^2 - 317 * q^3 + 3242 * q^4 - 4717 * q^5 + 687 * q^6 - 9680 * q^7 - 20394 * q^8 + 69516 * q^9 - 36237 * q^10 - 104484 * q^11 - 266395 * q^12 - 116174 * q^13 + 416064 * q^14 + 415388 * q^15 + 996762 * q^16 - 884265 * q^17 - 588735 * q^18 - 689535 * q^19 - 3077879 * q^20 - 2070198 * q^21 - 7276218 * q^22 - 2504077 * q^23 - 11534895 * q^24 + 1315350 * q^25 - 13343414 * q^26 - 12546986 * q^27 - 28059568 * q^28 - 18406221 * q^29 - 39503820 * q^30 - 12033699 * q^31 - 18952630 * q^32 - 14197716 * q^33 - 30383125 * q^34 - 27855546 * q^35 - 18372959 * q^36 - 8722847 * q^37 - 63941843 * q^38 - 30955510 * q^39 - 39665611 * q^40 - 18689389 * q^41 - 73185310 * q^42 - 51282015 * q^43 - 68723220 * q^44 - 216992888 * q^45 - 2067521 * q^46 - 104960741 * q^47 - 145362479 * q^48 + 92663095 * q^49 - 42446347 * q^50 + 37433407 * q^51 + 149226080 * q^52 - 215907800 * q^53 + 419158122 * q^54 + 384379852 * q^55 + 430441344 * q^56 + 258744488 * q^57 + 295963139 * q^58 + 185924544 * q^59 + 973236172 * q^60 + 247538102 * q^61 + 139798853 * q^62 + 405429926 * q^63 + 848556290 * q^64 + 94294394 * q^65 + 667230492 * q^66 + 467904656 * q^67 - 88234341 * q^68 + 163914994 * q^69 + 647526126 * q^70 - 8252944 * q^71 + 889796745 * q^72 - 715627902 * q^73 + 725122989 * q^74 - 18301762 * q^75 + 346300359 * q^76 - 1236779964 * q^77 + 2058642146 * q^78 + 560681783 * q^79 - 1157214179 * q^80 - 752010645 * q^81 + 941346367 * q^82 - 1442854698 * q^83 + 1895248718 * q^84 + 699302088 * q^85 + 109401632 * q^86 - 2094576907 * q^87 - 1464507256 * q^88 - 396710008 * q^89 + 1411356270 * q^90 - 3278076852 * q^91 + 155864647 * q^92 - 1424759183 * q^93 + 4666638949 * q^94 - 3854114395 * q^95 - 952489551 * q^96 - 3063837815 * q^97 - 6161086984 * q^98 - 6576160348 * 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 $

$2$	−4.38595	−0.193833	−0.0969167	−	0.995292i	$-0.530898\pi$
$2$	−4.38595	−0.193833	−0.0969167	+	0.995292i	$0.530898\pi$
$3$	117.920	0.840505	0.420253	−	0.907407i	$-0.361941\pi$
$3$	117.920	0.840505	0.420253	+	0.907407i	$0.361941\pi$
$4$	−492.763	−0.962429
$5$	−1237.15	−0.885229	−0.442614	−	0.896712i	$-0.645949\pi$
$5$	−1237.15	−0.885229	−0.442614	+	0.896712i	$0.645949\pi$
$6$	−517.190	−0.162918
$7$	12549.3	1.97550	0.987750	−	0.156046i	$-0.0498748\pi$
$7$	12549.3	1.97550	0.987750	+	0.156046i	$0.0498748\pi$
$8$	4406.84	0.380384
$9$	−5777.96	−0.293551
$10$	5426.06	0.171587
$11$	27918.0	0.574933	0.287467	−	0.957791i	$-0.407187\pi$
$11$	27918.0	0.574933	0.287467	+	0.957791i	$0.407187\pi$
$12$	−58106.5	−0.808926
$13$	−139652.	−1.35613	−0.678067	−	0.735000i	$-0.737182\pi$
$13$	−139652.	−1.35613	−0.678067	+	0.735000i	$0.737182\pi$
$14$	−55040.4	−0.382918
$15$	−145884.	−0.744040
$16$	232967.	0.888697
$17$	−408645.	−1.18666	−0.593330	−	0.804959i	$-0.702187\pi$
$17$	−408645.	−1.18666	−0.593330	+	0.804959i	$0.702187\pi$
$18$	25341.8	0.0568999
$19$	−157490.	−0.277244	−0.138622	−	0.990345i	$-0.544267\pi$
$19$	−157490.	−0.277244	−0.138622	+	0.990345i	$0.544267\pi$
$20$	609620.	0.851970
$21$	1.47980e6	1.66042
$22$	−122447.	−0.111441
$23$	−730739.	−0.544487	−0.272243	−	0.962228i	$-0.587766\pi$
$23$	−730739.	−0.544487	−0.272243	+	0.962228i	$0.587766\pi$
$24$	519653.	0.319715
$25$	−422597.	−0.216370
$26$	612508.	0.262864
$27$	−3.00235e6	−1.08724
$28$	−6.18382e6	−1.90128
$29$	−6.14391e6	−1.61307	−0.806537	−	0.591184i	$-0.798661\pi$
$29$	−6.14391e6	−1.61307	−0.806537	+	0.591184i	$0.798661\pi$
$30$	639839.	0.144220
$31$	6.18625e6	1.20309	0.601547	−	0.798837i	$-0.294551\pi$
$31$	6.18625e6	1.20309	0.601547	+	0.798837i	$0.294551\pi$
$32$	−3.27808e6	−0.552644
$33$	3.29208e6	0.483234
$34$	1.79230e6	0.230015
$35$	−1.55253e7	−1.74877
$36$	2.84717e6	0.282521
$37$	−2.16507e7	−1.89917	−0.949587	−	0.313503i	$-0.898497\pi$
$37$	−2.16507e7	−1.89917	−0.949587	+	0.313503i	$0.898497\pi$
$38$	690744.	0.0537392
$39$	−1.64677e7	−1.13984
$40$	−5.45190e6	−0.336727
$41$	2.42738e7	1.34156	0.670780	−	0.741657i	$-0.265960\pi$
$41$	2.42738e7	1.34156	0.670780	+	0.741657i	$0.265960\pi$
$42$	−6.49035e6	−0.321845
$43$	−3.41880e6	−0.152499
$43$	−3.41880e6	−0.152499
$44$	−1.37570e7	−0.553332
$45$	7.14817e6	0.259859
$46$	3.20499e6	0.105540
$47$	−3.21569e7	−0.961243	−0.480622	−	0.876928i	$-0.659589\pi$
$47$	−3.21569e7	−0.961243	−0.480622	+	0.876928i	$0.659589\pi$
$48$	2.74713e7	0.746955
$49$	1.17130e8	2.90260
$50$	1.85349e6	0.0419397
$51$	−4.81873e7	−0.997395
$52$	6.88155e7	1.30518
$53$	−6.96541e7	−1.21257	−0.606283	−	0.795249i	$-0.707340\pi$
$53$	−6.96541e7	−1.21257	−0.606283	+	0.795249i	$0.707340\pi$
$54$	1.31681e7	0.210743
$55$	−3.45386e7	−0.508947
$56$	5.53026e7	0.751449
$57$	−1.85712e7	−0.233025
$58$	2.69469e7	0.312668
$59$	−1.12041e8	−1.20377	−0.601886	−	0.798582i	$-0.705584\pi$
$59$	−1.12041e8	−1.20377	−0.601886	+	0.798582i	$0.705584\pi$
$60$	7.18862e7	0.716085
$61$	8.03385e7	0.742915	0.371458	−	0.928450i	$-0.378858\pi$
$61$	8.03385e7	0.742915	0.371458	+	0.928450i	$0.378858\pi$
$62$	−2.71326e7	−0.233200
$63$	−7.25091e7	−0.579909
$64$	−1.04901e8	−0.781577
$65$	1.72770e8	1.20049
$66$	−1.44389e7	−0.0936670
$67$	−5.78429e7	−0.350682	−0.175341	−	0.984508i	$-0.556103\pi$
$67$	−5.78429e7	−0.350682	−0.175341	+	0.984508i	$0.556103\pi$
$68$	2.01366e8	1.14208
$69$	−8.61685e7	−0.457644
$70$	6.80930e7	0.338970
$71$	3.11039e8	1.45262	0.726311	−	0.687366i	$-0.241233\pi$
$71$	3.11039e8	1.45262	0.726311	+	0.687366i	$0.241233\pi$
$72$	−2.54625e7	−0.111662
$73$	−3.23803e7	−0.133453	−0.0667265	−	0.997771i	$-0.521255\pi$
$73$	−3.23803e7	−0.133453	−0.0667265	+	0.997771i	$0.521255\pi$
$74$	9.49590e7	0.368124
$75$	−4.98325e7	−0.181860
$76$	7.76054e7	0.266828
$77$	3.50350e8	1.13578
$78$	7.22267e7	0.220939
$79$	2.36871e8	0.684210	0.342105	−	0.939662i	$-0.388860\pi$
$79$	2.36871e8	0.684210	0.342105	+	0.939662i	$0.388860\pi$
$80$	−2.88214e8	−0.786701
$81$	−2.40308e8	−0.620277
$82$	−1.06464e8	−0.260039
$83$	4.61987e8	1.06851	0.534255	−	0.845324i	$-0.320592\pi$
$83$	4.61987e8	1.06851	0.534255	+	0.845324i	$0.320592\pi$
$84$	−7.29193e8	−1.59803
$85$	5.05554e8	1.05047
$86$	1.49947e7	0.0295593
$87$	−7.24488e8	−1.35580
$88$	1.23030e8	0.218696
$89$	6.16826e8	1.04210	0.521048	−	0.853527i	$-0.325541\pi$
$89$	6.16826e8	1.04210	0.521048	+	0.853527i	$0.325541\pi$
$90$	−3.13515e7	−0.0503695
$91$	−1.75253e9	−2.67904
$92$	3.60082e8	0.524029
$93$	7.29481e8	1.01121
$94$	1.41038e8	0.186321
$95$	1.94838e8	0.245425
$96$	−3.86551e8	−0.464500
$97$	−1.00137e9	−1.14848	−0.574240	−	0.818687i	$-0.694702\pi$
$97$	−1.00137e9	−1.14848	−0.574240	+	0.818687i	$0.694702\pi$
$98$	−5.13728e8	−0.562621
$99$	−1.61309e8	−0.168772
$100$	2.08240e8	0.208240
$101$	−3.05585e8	−0.292203	−0.146102	−	0.989270i	$-0.546673\pi$
$101$	−3.05585e8	−0.292203	−0.146102	+	0.989270i	$0.546673\pi$
$102$	2.11347e8	0.193328
$103$	−3.81600e8	−0.334073	−0.167036	−	0.985951i	$-0.553420\pi$
$103$	−3.81600e8	−0.334073	−0.167036	+	0.985951i	$0.553420\pi$
$104$	−6.15425e8	−0.515852
$105$	−1.83073e9	−1.46985
$106$	3.05499e8	0.235036
$107$	−1.99829e9	−1.47378	−0.736888	−	0.676015i	$-0.763705\pi$
$107$	−1.99829e9	−1.47378	−0.736888	+	0.676015i	$0.763705\pi$
$108$	1.47945e9	1.04639
$109$	5.64232e8	0.382859	0.191429	−	0.981506i	$-0.438688\pi$
$109$	5.64232e8	0.382859	0.191429	+	0.981506i	$0.438688\pi$
$110$	1.51485e8	0.0986510
$111$	−2.55305e9	−1.59627
$112$	2.92356e9	1.75562
$113$	9.01181e8	0.519947	0.259973	−	0.965616i	$-0.416286\pi$
$113$	9.01181e8	0.519947	0.259973	+	0.965616i	$0.416286\pi$
$114$	8.14523e7	0.0451681
$115$	9.04030e8	0.481995
$116$	3.02750e9	1.55247
$117$	8.06904e8	0.398094
$118$	4.91407e8	0.233331
$119$	−5.12820e9	−2.34425
$120$	−6.42887e8	−0.283021
$121$	−1.57853e9	−0.669452
$122$	−3.52361e8	−0.144002
$123$	2.86235e9	1.12759
$124$	−3.04836e9	−1.15789
$125$	2.93911e9	1.07677
$126$	3.18021e8	0.112406
$127$	3.22590e9	1.10036	0.550179	−	0.835047i	$-0.314559\pi$
$127$	3.22590e9	1.10036	0.550179	+	0.835047i	$0.314559\pi$
$128$	2.13847e9	0.704139
$129$	−4.03144e8	−0.128176
$130$	−7.57761e8	−0.232695
$131$	−3.22175e9	−0.955808	−0.477904	−	0.878412i	$-0.658603\pi$
$131$	−3.22175e9	−0.955808	−0.477904	+	0.878412i	$0.658603\pi$
$132$	−1.62222e9	−0.465079
$133$	−1.97639e9	−0.547696
$134$	2.53696e8	0.0679739
$135$	3.71434e9	0.962453
$136$	−1.80084e9	−0.451387
$137$	−4.02495e9	−0.976153	−0.488077	−	0.872801i	$-0.662301\pi$
$137$	−4.02495e9	−0.976153	−0.488077	+	0.872801i	$0.662301\pi$
$138$	3.77931e8	0.0887067
$139$	2.36428e9	0.537196	0.268598	−	0.963252i	$-0.413440\pi$
$139$	2.36428e9	0.537196	0.268598	+	0.963252i	$0.413440\pi$
$140$	7.65028e9	1.68307
$141$	−3.79193e9	−0.807930
$142$	−1.36420e9	−0.281567
$143$	−3.89881e9	−0.779686
$144$	−1.34607e9	−0.260878
$145$	7.60091e9	1.42794
$146$	1.42018e8	0.0258676
$147$	1.38120e10	2.43965
$148$	1.06687e10	1.82782
$149$	3.40025e9	0.565161	0.282581	−	0.959244i	$-0.408810\pi$
$149$	3.40025e9	0.565161	0.282581	+	0.959244i	$0.408810\pi$
$150$	2.18563e8	0.0352505
$151$	−2.71186e9	−0.424494	−0.212247	−	0.977216i	$-0.568078\pi$
$151$	−2.71186e9	−0.424494	−0.212247	+	0.977216i	$0.568078\pi$
$152$	−6.94035e8	−0.105459
$153$	2.36114e9	0.348345
$154$	−1.53662e9	−0.220152
$155$	−7.65329e9	−1.06501
$156$	8.11470e9	1.09701
$157$	2.25484e9	0.296188	0.148094	−	0.988973i	$-0.452686\pi$
$157$	2.25484e9	0.296188	0.148094	+	0.988973i	$0.452686\pi$
$158$	−1.03890e9	−0.132623
$159$	−8.21359e9	−1.01917
$160$	4.05547e9	0.489216
$161$	−9.17024e9	−1.07563
$162$	1.05398e9	0.120231
$163$	2.12327e9	0.235592	0.117796	−	0.993038i	$-0.462417\pi$
$163$	2.12327e9	0.235592	0.117796	+	0.993038i	$0.462417\pi$
$164$	−1.19612e10	−1.29116
$165$	−4.07278e9	−0.427773
$166$	−2.02625e9	−0.207113
$167$	−7.94637e9	−0.790578	−0.395289	−	0.918557i	$-0.629355\pi$
$167$	−7.94637e9	−0.790578	−0.395289	+	0.918557i	$0.629355\pi$
$168$	6.52127e9	0.631597
$169$	8.89824e9	0.839100
$170$	−2.21733e9	−0.203616
$171$	9.09972e8	0.0813852
$172$	1.68466e9	0.146769
$173$	−1.13404e10	−0.962548	−0.481274	−	0.876570i	$-0.659826\pi$
$173$	−1.13404e10	−0.962548	−0.481274	+	0.876570i	$0.659826\pi$
$174$	3.17757e9	0.262799
$175$	−5.30328e9	−0.427438
$176$	6.50396e9	0.510941
$177$	−1.32119e10	−1.01178
$178$	−2.70537e9	−0.201993
$179$	−1.54500e10	−1.12484	−0.562420	−	0.826852i	$-0.690130\pi$
$179$	−1.54500e10	−1.12484	−0.562420	+	0.826852i	$0.690130\pi$
$180$	−3.52236e9	−0.250096
$181$	1.12851e10	0.781540	0.390770	−	0.920488i	$-0.372209\pi$
$181$	1.12851e10	0.781540	0.390770	+	0.920488i	$0.372209\pi$
$182$	7.68652e9	0.519288
$183$	9.47348e9	0.624424
$184$	−3.22025e9	−0.207114
$185$	2.67851e10	1.68120
$186$	−3.19947e9	−0.196006
$187$	−1.14086e10	−0.682250
$188$	1.58457e10	0.925128
$189$	−3.76772e10	−2.14783
$190$	−8.54551e8	−0.0475715
$191$	1.87758e10	1.02082	0.510409	−	0.859932i	$-0.329494\pi$
$191$	1.87758e10	1.02082	0.510409	+	0.859932i	$0.329494\pi$
$192$	−1.23699e10	−0.656919
$193$	2.54039e9	0.131793	0.0658966	−	0.997826i	$-0.479009\pi$
$193$	2.54039e9	0.131793	0.0658966	+	0.997826i	$0.479009\pi$
$194$	4.39197e9	0.222614
$195$	2.03730e10	1.00902
$196$	−5.77175e10	−2.79354
$197$	−2.66438e10	−1.26037	−0.630186	−	0.776444i	$-0.717021\pi$
$197$	−2.66438e10	−1.26037	−0.630186	+	0.776444i	$0.717021\pi$
$198$	7.07493e8	0.0327137
$199$	2.48904e10	1.12511	0.562553	−	0.826761i	$-0.309819\pi$
$199$	2.48904e10	1.12511	0.562553	+	0.826761i	$0.309819\pi$
$200$	−1.86232e9	−0.0823036
$201$	−6.82081e9	−0.294750
$202$	1.34028e9	0.0566388
$203$	−7.71016e10	−3.18663
$204$	2.37450e10	0.959921
$205$	−3.00302e10	−1.18759
$206$	1.67368e9	0.0647545
$207$	4.22218e9	0.159834
$208$	−3.25343e10	−1.20519
$209$	−4.39681e9	−0.159397
$210$	8.02950e9	0.284906
$211$	2.83390e10	0.984267	0.492134	−	0.870520i	$-0.336217\pi$
$211$	2.83390e10	0.984267	0.492134	+	0.870520i	$0.336217\pi$
$212$	3.43230e10	1.16701
$213$	3.66777e10	1.22094
$214$	8.76440e9	0.285667
$215$	4.22955e9	0.134996
$216$	−1.32309e10	−0.413568
$217$	7.76329e10	2.37671
$218$	−2.47470e9	−0.0742109
$219$	−3.81827e9	−0.112168
$220$	1.70194e10	0.489826
$221$	5.70682e10	1.60927
$222$	1.11975e10	0.309410
$223$	−8.66457e9	−0.234626	−0.117313	−	0.993095i	$-0.537428\pi$
$223$	−8.66457e9	−0.234626	−0.117313	+	0.993095i	$0.537428\pi$
$224$	−4.11375e10	−1.09175
$225$	2.44175e9	0.0635154
$226$	−3.95254e9	−0.100783
$227$	−1.92752e10	−0.481817	−0.240908	−	0.970548i	$-0.577445\pi$
$227$	−1.92752e10	−0.481817	−0.240908	+	0.970548i	$0.577445\pi$
$228$	9.15120e9	0.224270
$229$	−2.30675e9	−0.0554294	−0.0277147	−	0.999616i	$-0.508823\pi$
$229$	−2.30675e9	−0.0554294	−0.0277147	+	0.999616i	$0.508823\pi$
$230$	−3.96503e9	−0.0934268
$231$	4.13132e10	0.954629
$232$	−2.70753e10	−0.613588
$233$	−2.20050e10	−0.489125	−0.244562	−	0.969634i	$-0.578644\pi$
$233$	−2.20050e10	−0.489125	−0.244562	+	0.969634i	$0.578644\pi$
$234$	−3.53904e9	−0.0771639
$235$	3.97827e10	0.850920
$236$	5.52098e10	1.15854
$237$	2.79317e10	0.575083
$238$	2.24920e10	0.454394
$239$	−3.65120e10	−0.723845	−0.361922	−	0.932208i	$-0.617879\pi$
$239$	−3.65120e10	−0.723845	−0.361922	+	0.932208i	$0.617879\pi$
$240$	−3.39860e10	−0.661226
$241$	8.05560e10	1.53823	0.769115	−	0.639110i	$-0.220697\pi$
$241$	8.05560e10	1.53823	0.769115	+	0.639110i	$0.220697\pi$
$242$	6.92337e9	0.129762
$243$	3.07581e10	0.565890
$244$	−3.95879e10	−0.715003
$245$	−1.44907e11	−2.56946
$246$	−1.25541e10	−0.218564
$247$	2.19939e10	0.375980
$248$	2.72618e10	0.457638
$249$	5.44773e10	0.898088
$250$	−1.28908e10	−0.208713
$251$	2.34339e10	0.372661	0.186330	−	0.982487i	$-0.440341\pi$
$251$	2.34339e10	0.372661	0.186330	+	0.982487i	$0.440341\pi$
$252$	3.57298e10	0.558121
$253$	−2.04008e10	−0.313043
$254$	−1.41486e10	−0.213286
$255$	5.96147e10	0.882923
$256$	4.43303e10	0.645091
$257$	−1.48746e10	−0.212689	−0.106345	−	0.994329i	$-0.533915\pi$
$257$	−1.48746e10	−0.212689	−0.106345	+	0.994329i	$0.533915\pi$
$258$	1.76817e9	0.0248448
$259$	−2.71701e11	−3.75182
$260$	−8.51348e10	−1.15539
$261$	3.54993e10	0.473519
$262$	1.41304e10	0.185268
$263$	−1.29482e10	−0.166882	−0.0834410	−	0.996513i	$-0.526591\pi$
$263$	−1.29482e10	−0.166882	−0.0834410	+	0.996513i	$0.526591\pi$
$264$	1.45077e10	0.183815
$265$	8.61722e10	1.07340
$266$	8.66833e9	0.106162
$267$	7.27359e10	0.875887
$268$	2.85028e10	0.337506
$269$	1.38611e11	1.61403	0.807016	−	0.590529i	$-0.201081\pi$
$269$	1.38611e11	1.61403	0.807016	+	0.590529i	$0.201081\pi$
$270$	−1.62909e10	−0.186556
$271$	−3.55761e10	−0.400679	−0.200339	−	0.979727i	$-0.564204\pi$
$271$	−3.55761e10	−0.400679	−0.200339	+	0.979727i	$0.564204\pi$
$272$	−9.52008e10	−1.05458
$273$	−2.06658e11	−2.25175
$274$	1.76532e10	0.189211
$275$	−1.17981e10	−0.124398
$276$	4.24607e10	0.440450
$277$	1.13489e11	1.15823	0.579114	−	0.815247i	$-0.303399\pi$
$277$	1.13489e11	1.15823	0.579114	+	0.815247i	$0.303399\pi$
$278$	−1.03696e10	−0.104126
$279$	−3.57439e10	−0.353169
$280$	−6.84174e10	−0.665205
$281$	2.84629e10	0.272334	0.136167	−	0.990686i	$-0.456522\pi$
$281$	2.84629e10	0.272334	0.136167	+	0.990686i	$0.456522\pi$
$282$	1.66312e10	0.156604
$283$	1.03614e11	0.960243	0.480121	−	0.877202i	$-0.340593\pi$
$283$	1.03614e11	0.960243	0.480121	+	0.877202i	$0.340593\pi$
$284$	−1.53269e11	−1.39805
$285$	2.29753e10	0.206281
$286$	1.71000e10	0.151129
$287$	3.04618e11	2.65025
$288$	1.89406e10	0.162229
$289$	4.84032e10	0.408163
$290$	−3.33372e10	−0.276782
$291$	−1.18082e11	−0.965303
$292$	1.59558e10	0.128439
$293$	−1.91800e11	−1.52035	−0.760176	−	0.649717i	$-0.774888\pi$
$293$	−1.91800e11	−1.52035	−0.760176	+	0.649717i	$0.774888\pi$
$294$	−6.05786e10	−0.472886
$295$	1.38611e11	1.06561
$296$	−9.54114e10	−0.722416
$297$	−8.38195e10	−0.625088
$298$	−1.49133e10	−0.109547
$299$	1.02049e11	0.738397
$300$	2.45556e10	0.175027
$301$	−4.29034e10	−0.301261
$302$	1.18941e10	0.0822811
$303$	−3.60344e10	−0.245599
$304$	−3.66900e10	−0.246386
$305$	−9.93904e10	−0.657650
$306$	−1.03558e10	−0.0675209
$307$	−5.93480e10	−0.381315	−0.190657	−	0.981657i	$-0.561062\pi$
$307$	−5.93480e10	−0.381315	−0.190657	+	0.981657i	$0.561062\pi$
$308$	−1.72640e11	−1.09311
$309$	−4.49982e10	−0.280790
$310$	3.35670e10	0.206435
$311$	−1.46203e11	−0.886205	−0.443102	−	0.896471i	$-0.646122\pi$
$311$	−1.46203e11	−0.886205	−0.443102	+	0.896471i	$0.646122\pi$
$312$	−7.25707e10	−0.433577
$313$	−1.38227e11	−0.814036	−0.407018	−	0.913420i	$-0.633431\pi$
$313$	−1.38227e11	−0.814036	−0.407018	+	0.913420i	$0.633431\pi$
$314$	−9.88963e9	−0.0574112
$315$	8.97042e10	0.513352
$316$	−1.16721e11	−0.658504
$317$	5.56681e10	0.309628	0.154814	−	0.987944i	$-0.450522\pi$
$317$	5.56681e10	0.309628	0.154814	+	0.987944i	$0.450522\pi$
$318$	3.60244e10	0.197549
$319$	−1.71526e11	−0.927409
$320$	1.29778e11	0.691874
$321$	−2.35638e11	−1.23872
$322$	4.02202e10	0.208494
$323$	6.43577e10	0.328995
$324$	1.18415e11	0.596973
$325$	5.90166e10	0.293426
$326$	−9.31255e9	−0.0456656
$327$	6.65341e10	0.321795
$328$	1.06971e11	0.510308
$329$	−4.03545e11	−1.89894
$330$	1.78630e10	0.0829167
$331$	2.09845e11	0.960888	0.480444	−	0.877025i	$-0.340476\pi$
$331$	2.09845e11	0.960888	0.480444	+	0.877025i	$0.340476\pi$
$332$	−2.27650e11	−1.02836
$333$	1.25097e11	0.557504
$334$	3.48524e10	0.153240
$335$	7.15600e10	0.310434
$336$	3.44745e11	1.47561
$337$	2.40308e11	1.01493	0.507463	−	0.861673i	$-0.330583\pi$
$337$	2.40308e11	1.01493	0.507463	+	0.861673i	$0.330583\pi$
$338$	−3.90272e10	−0.162646
$339$	1.06267e11	0.437018
$340$	−2.49118e11	−1.01100
$341$	1.72708e11	0.691699
$342$	−3.99109e9	−0.0157752
$343$	9.63491e11	3.75858
$344$	−1.50661e10	−0.0580081
$345$	1.06603e11	0.405120
$346$	4.97386e10	0.186574
$347$	1.62927e10	0.0603266	0.0301633	−	0.999545i	$-0.490397\pi$
$347$	1.62927e10	0.0603266	0.0301633	+	0.999545i	$0.490397\pi$
$348$	3.57001e11	1.30486
$349$	−1.41443e11	−0.510347	−0.255174	−	0.966895i	$-0.582133\pi$
$349$	−1.41443e11	−0.510347	−0.255174	+	0.966895i	$0.582133\pi$
$350$	2.32599e10	0.0828518
$351$	4.19284e11	1.47444
$352$	−9.15176e10	−0.317733
$353$	3.15790e10	0.108246	0.0541230	−	0.998534i	$-0.482764\pi$
$353$	3.15790e10	0.108246	0.0541230	+	0.998534i	$0.482764\pi$
$354$	5.79466e10	0.196116
$355$	−3.84801e11	−1.28590
$356$	−3.03949e11	−1.00294
$357$	−6.04715e11	−1.97035
$358$	6.77631e10	0.218032
$359$	9.18482e10	0.291840	0.145920	−	0.989296i	$-0.453386\pi$
$359$	9.18482e10	0.291840	0.145920	+	0.989296i	$0.453386\pi$
$360$	3.15009e10	0.0988465
$361$	−2.97885e11	−0.923136
$362$	−4.94958e10	−0.151489
$363$	−1.86140e11	−0.562678
$364$	8.63584e11	2.57839
$365$	4.00591e10	0.118136
$366$	−4.15502e10	−0.121034
$367$	2.61752e11	0.753169	0.376584	−	0.926382i	$-0.377098\pi$
$367$	2.61752e11	0.753169	0.376584	+	0.926382i	$0.377098\pi$
$368$	−1.70238e11	−0.483884
$369$	−1.40253e11	−0.393816
$370$	−1.17478e11	−0.325874
$371$	−8.74107e11	−2.39542
$372$	−3.59461e11	−0.973215
$373$	2.92272e11	0.781803	0.390902	−	0.920433i	$-0.372163\pi$
$373$	2.92272e11	0.781803	0.390902	+	0.920433i	$0.372163\pi$
$374$	5.00374e10	0.132243
$375$	3.46579e11	0.905027
$376$	−1.41710e11	−0.365642
$377$	8.58011e11	2.18754
$378$	1.65251e11	0.416322
$379$	4.04776e11	1.00772	0.503859	−	0.863786i	$-0.331913\pi$
$379$	4.04776e11	1.00772	0.503859	+	0.863786i	$0.331913\pi$
$380$	−9.60092e10	−0.236204
$381$	3.80397e11	0.924857
$382$	−8.23497e10	−0.197869
$383$	−6.03567e11	−1.43328	−0.716640	−	0.697443i	$-0.754321\pi$
$383$	−6.03567e11	−1.43328	−0.716640	+	0.697443i	$0.754321\pi$
$384$	2.52168e11	0.591833
$385$	−4.33434e11	−1.00543
$386$	−1.11420e10	−0.0255459
$387$	1.97537e10	0.0447660
$388$	4.93440e11	1.10533
$389$	−4.00613e11	−0.887057	−0.443529	−	0.896260i	$-0.646274\pi$
$389$	−4.00613e11	−0.887057	−0.443529	+	0.896260i	$0.646274\pi$
$390$	−8.93549e10	−0.195581
$391$	2.98613e11	0.646121
$392$	5.16175e11	1.10410
$393$	−3.79907e11	−0.803362
$394$	1.16859e11	0.244302
$395$	−2.93044e11	−0.605683
$396$	7.94872e10	0.162431
$397$	−7.65107e11	−1.54584	−0.772920	−	0.634503i	$-0.781205\pi$
$397$	−7.65107e11	−1.54584	−0.772920	+	0.634503i	$0.781205\pi$
$398$	−1.09168e11	−0.218083
$399$	−2.33055e11	−0.460341
$400$	−9.84510e10	−0.192287
$401$	5.13976e11	0.992643	0.496322	−	0.868139i	$-0.334684\pi$
$401$	5.13976e11	0.992643	0.496322	+	0.868139i	$0.334684\pi$
$402$	2.99157e10	0.0571324
$403$	−8.63924e11	−1.63156
$404$	1.50581e11	0.281225
$405$	2.97296e11	0.549088
$406$	3.38164e11	0.617675
$407$	−6.04445e11	−1.09190
$408$	−2.12354e11	−0.379393
$409$	3.29917e11	0.582975	0.291488	−	0.956575i	$-0.405850\pi$
$409$	3.29917e11	0.582975	0.291488	+	0.956575i	$0.405850\pi$
$410$	1.31711e11	0.230194
$411$	−4.74621e11	−0.820462
$412$	1.88039e11	0.321521
$413$	−1.40603e12	−2.37805
$414$	−1.85183e10	−0.0309812
$415$	−5.71545e11	−0.945875
$416$	4.57792e11	0.749459
$417$	2.78795e11	0.451516
$418$	1.92842e10	0.0308964
$419$	1.13273e11	0.179541	0.0897707	−	0.995962i	$-0.471387\pi$
$419$	1.13273e11	0.179541	0.0897707	+	0.995962i	$0.471387\pi$
$420$	9.02118e11	1.41463
$421$	−5.70807e11	−0.885564	−0.442782	−	0.896629i	$-0.646008\pi$
$421$	−5.70807e11	−0.885564	−0.442782	+	0.896629i	$0.646008\pi$
$422$	−1.24293e11	−0.190784
$423$	1.85801e11	0.282173
$424$	−3.06955e11	−0.461241
$425$	1.72692e11	0.256757
$426$	−1.60866e11	−0.236658
$427$	1.00819e12	1.46763
$428$	9.84684e11	1.41840
$429$	−4.59746e11	−0.655331
$430$	−1.85506e10	−0.0261668
$431$	−5.38814e11	−0.752127	−0.376064	−	0.926594i	$-0.622723\pi$
$431$	−5.38814e11	−0.752127	−0.376064	+	0.926594i	$0.622723\pi$
$432$	−6.99447e11	−0.966224
$433$	−8.64588e11	−1.18199	−0.590995	−	0.806675i	$-0.701265\pi$
$433$	−8.64588e11	−1.18199	−0.590995	+	0.806675i	$0.701265\pi$
$434$	−3.40494e11	−0.460687
$435$	8.96297e11	1.20019
$436$	−2.78033e11	−0.368474
$437$	1.15084e11	0.150956
$438$	1.67468e10	0.0217419
$439$	−3.81449e10	−0.0490170	−0.0245085	−	0.999700i	$-0.507802\pi$
$439$	−3.81449e10	−0.0490170	−0.0245085	+	0.999700i	$0.507802\pi$
$440$	−1.52206e11	−0.193596
$441$	−6.76774e11	−0.852059
$442$	−2.50298e11	−0.311931
$443$	4.04411e11	0.498891	0.249446	−	0.968389i	$-0.419752\pi$
$443$	4.04411e11	0.498891	0.249446	+	0.968389i	$0.419752\pi$
$444$	1.25805e12	1.53629
$445$	−7.63103e11	−0.922494
$446$	3.80024e10	0.0454783
$447$	4.00956e11	0.475021
$448$	−1.31644e12	−1.54400
$449$	5.23002e11	0.607288	0.303644	−	0.952786i	$-0.401797\pi$
$449$	5.23002e11	0.607288	0.303644	+	0.952786i	$0.401797\pi$
$450$	−1.07094e10	−0.0123114
$451$	6.77675e11	0.771307
$452$	−4.44069e11	−0.500412
$453$	−3.19782e11	−0.356789
$454$	8.45400e10	0.0933923
$455$	2.16814e12	2.37157
$456$	−8.18403e10	−0.0886392
$457$	−1.62214e12	−1.73966	−0.869832	−	0.493347i	$-0.835773\pi$
$457$	−1.62214e12	−1.73966	−0.869832	+	0.493347i	$0.835773\pi$
$458$	1.01173e10	0.0107441
$459$	1.22690e12	1.29018
$460$	−4.45473e11	−0.463886
$461$	−5.64486e11	−0.582102	−0.291051	−	0.956708i	$-0.594005\pi$
$461$	−5.64486e11	−0.582102	−0.291051	+	0.956708i	$0.594005\pi$
$462$	−1.81198e11	−0.185039
$463$	−1.76040e11	−0.178031	−0.0890156	−	0.996030i	$-0.528372\pi$
$463$	−1.76040e11	−0.178031	−0.0890156	+	0.996030i	$0.528372\pi$
$464$	−1.43133e12	−1.43353
$465$	−9.02473e11	−0.895150
$466$	9.65129e10	0.0948088
$467$	1.36802e11	0.133097	0.0665483	−	0.997783i	$-0.478801\pi$
$467$	1.36802e11	0.133097	0.0665483	+	0.997783i	$0.478801\pi$
$468$	−3.97613e11	−0.383137
$469$	−7.25885e11	−0.692772
$470$	−1.74485e11	−0.164937
$471$	2.65890e11	0.248948
$472$	−4.93748e11	−0.457896
$473$	−9.54461e10	−0.0876765
$474$	−1.22507e11	−0.111470
$475$	6.65549e10	0.0599872
$476$	2.52699e12	2.25617
$477$	4.02458e11	0.355949
$478$	1.60140e11	0.140305
$479$	−4.86473e11	−0.422230	−0.211115	−	0.977461i	$-0.567709\pi$
$479$	−4.86473e11	−0.422230	−0.211115	+	0.977461i	$0.567709\pi$
$480$	4.78219e11	0.411189
$481$	3.02357e12	2.57554
$482$	−3.53315e11	−0.298160
$483$	−1.08135e12	−0.904075
$484$	7.77843e11	0.644300
$485$	1.23884e12	1.01667
$486$	−1.34904e11	−0.109688
$487$	−8.10600e11	−0.653020	−0.326510	−	0.945194i	$-0.605873\pi$
$487$	−8.10600e11	−0.653020	−0.326510	+	0.945194i	$0.605873\pi$
$488$	3.54039e11	0.282593
$489$	2.50375e11	0.198016
$490$	6.35556e11	0.498048
$491$	1.12030e12	0.869893	0.434947	−	0.900456i	$-0.356767\pi$
$491$	1.12030e12	0.869893	0.434947	+	0.900456i	$0.356767\pi$
$492$	−1.41046e12	−1.08522
$493$	2.51068e12	1.91417
$494$	−9.64640e10	−0.0728776
$495$	1.99563e11	0.149402
$496$	1.44119e12	1.06919
$497$	3.90331e12	2.86966
$498$	−2.38935e11	−0.174079
$499$	1.93337e12	1.39593	0.697963	−	0.716134i	$-0.254090\pi$
$499$	1.93337e12	1.39593	0.697963	+	0.716134i	$0.254090\pi$
$500$	−1.44829e12	−1.03631
$501$	−9.37033e11	−0.664485
$502$	−1.02780e11	−0.0722341
$503$	−9.53953e11	−0.664463	−0.332232	−	0.943198i	$-0.607802\pi$
$503$	−9.53953e11	−0.664463	−0.332232	+	0.943198i	$0.607802\pi$
$504$	−3.19536e11	−0.220588
$505$	3.78052e11	0.258667
$506$	8.94768e10	0.0606783
$507$	1.04928e12	0.705268
$508$	−1.58961e12	−1.05902
$509$	−2.27539e12	−1.50254	−0.751270	−	0.659995i	$-0.770558\pi$
$509$	−2.27539e12	−1.50254	−0.751270	+	0.659995i	$0.770558\pi$
$510$	−2.61467e11	−0.171140
$511$	−4.06349e11	−0.263636
$512$	−1.28933e12	−0.829180
$513$	4.72840e11	0.301430
$514$	6.52392e10	0.0412263
$515$	4.72095e11	0.295731
$516$	1.98655e11	0.123360
$517$	−8.97755e11	−0.552650
$518$	1.19167e12	0.727228
$519$	−1.33726e12	−0.809027
$520$	7.61370e11	0.456647
$521$	8.63866e11	0.513661	0.256830	−	0.966456i	$-0.417322\pi$
$521$	8.63866e11	0.513661	0.256830	+	0.966456i	$0.417322\pi$
$522$	−1.55698e11	−0.0917837
$523$	−3.96246e11	−0.231583	−0.115792	−	0.993274i	$-0.536940\pi$
$523$	−3.96246e11	−0.231583	−0.115792	+	0.993274i	$0.536940\pi$
$524$	1.58756e12	0.919897
$525$	−6.25361e11	−0.359264
$526$	5.67903e10	0.0323473
$527$	−2.52798e12	−1.42767
$528$	7.66945e11	0.429449
$529$	−1.26717e12	−0.703534
$530$	−3.77947e11	−0.208061
$531$	6.47369e11	0.353368
$532$	9.73891e11	0.527118
$533$	−3.38989e12	−1.81933
$534$	−3.19016e11	−0.169776
$535$	2.47217e12	1.30463
$536$	−2.54904e11	−0.133394
$537$	−1.82186e12	−0.945434
$538$	−6.07941e11	−0.312854
$539$	3.27004e12	1.66880
$540$	−1.83029e12	−0.926292
$541$	−3.00813e12	−1.50976	−0.754881	−	0.655862i	$-0.772305\pi$
$541$	−3.00813e12	−1.50976	−0.754881	+	0.655862i	$0.772305\pi$
$542$	1.56035e11	0.0776650
$543$	1.33073e12	0.656888
$544$	1.33957e12	0.655800
$545$	−6.98037e11	−0.338918
$546$	9.06392e11	0.436465
$547$	−1.67014e12	−0.797645	−0.398823	−	0.917028i	$-0.630581\pi$
$547$	−1.67014e12	−0.797645	−0.398823	+	0.917028i	$0.630581\pi$
$548$	1.98335e12	0.939478
$549$	−4.64192e11	−0.218083
$550$	5.17457e10	0.0241125
$551$	9.67606e11	0.447215
$552$	−3.79731e11	−0.174081
$553$	2.97255e12	1.35166
$554$	−4.97756e11	−0.224503
$555$	3.15849e12	1.41306
$556$	−1.16503e12	−0.517012
$557$	−3.27102e12	−1.43991	−0.719954	−	0.694022i	$-0.755837\pi$
$557$	−3.27102e12	−1.43991	−0.719954	+	0.694022i	$0.755837\pi$
$558$	1.56771e11	0.0684560
$559$	4.77443e11	0.206809
$560$	−3.61687e12	−1.55413
$561$	−1.34529e12	−0.573435
$562$	−1.24837e11	−0.0527874
$563$	−3.16570e12	−1.32795	−0.663976	−	0.747754i	$-0.731132\pi$
$563$	−3.16570e12	−1.32795	−0.663976	+	0.747754i	$0.731132\pi$
$564$	1.86852e12	0.777575
$565$	−1.11489e12	−0.460272
$566$	−4.54448e11	−0.186127
$567$	−3.01569e12	−1.22536
$568$	1.37070e12	0.552555
$569$	−3.41258e12	−1.36483	−0.682414	−	0.730966i	$-0.739070\pi$
$569$	−3.41258e12	−1.36483	−0.682414	+	0.730966i	$0.739070\pi$
$570$	−1.00768e11	−0.0399841
$571$	5.10789e11	0.201085	0.100542	−	0.994933i	$-0.467942\pi$
$571$	5.10789e11	0.201085	0.100542	+	0.994933i	$0.467942\pi$
$572$	1.92119e12	0.750393
$573$	2.21403e12	0.858002
$574$	−1.33604e12	−0.513707
$575$	3.08808e11	0.117810
$576$	6.06116e11	0.229432
$577$	3.29567e12	1.23781	0.618903	−	0.785467i	$-0.287577\pi$
$577$	3.29567e12	1.23781	0.618903	+	0.785467i	$0.287577\pi$
$578$	−2.12294e11	−0.0791157
$579$	2.99562e11	0.110773
$580$	−3.74545e12	−1.37429
$581$	5.79759e12	2.11084
$582$	5.17900e11	0.187108
$583$	−1.94460e12	−0.697144
$584$	−1.42695e11	−0.0507634
$585$	−9.98258e11	−0.352404
$586$	8.41226e11	0.294695
$587$	3.75472e12	1.30529	0.652644	−	0.757665i	$-0.273660\pi$
$587$	3.75472e12	1.30529	0.652644	+	0.757665i	$0.273660\pi$
$588$	−6.80603e12	−2.34799
$589$	−9.74274e11	−0.333551
$590$	−6.07942e11	−0.206551
$591$	−3.14183e12	−1.05935
$592$	−5.04390e12	−1.68779
$593$	−7.28844e11	−0.242041	−0.121020	−	0.992650i	$-0.538617\pi$
$593$	−7.28844e11	−0.242041	−0.121020	+	0.992650i	$0.538617\pi$
$594$	3.67628e11	0.121163
$595$	6.34432e12	2.07520
$596$	−1.67552e12	−0.543927
$597$	2.93507e12	0.945658
$598$	−4.47583e11	−0.143126
$599$	1.79149e12	0.568582	0.284291	−	0.958738i	$-0.408242\pi$
$599$	1.79149e12	0.568582	0.284291	+	0.958738i	$0.408242\pi$
$600$	−2.19604e11	−0.0691767
$601$	3.67032e11	0.114754	0.0573772	−	0.998353i	$-0.481726\pi$
$601$	3.67032e11	0.114754	0.0573772	+	0.998353i	$0.481726\pi$
$602$	1.88172e11	0.0583944
$603$	3.34213e11	0.102943
$604$	1.33631e12	0.408545
$605$	1.95287e12	0.592618
$606$	1.58045e11	0.0476052
$607$	−3.38377e12	−1.01170	−0.505850	−	0.862622i	$-0.668821\pi$
$607$	−3.38377e12	−1.01170	−0.505850	+	0.862622i	$0.668821\pi$
$608$	5.16266e11	0.153217
$609$	−9.09179e12	−2.67838
$610$	4.35921e11	0.127475
$611$	4.49078e12	1.30357
$612$	−1.16348e12	−0.335257
$613$	3.01980e11	0.0863786	0.0431893	−	0.999067i	$-0.486248\pi$
$613$	3.01980e11	0.0863786	0.0431893	+	0.999067i	$0.486248\pi$
$614$	2.60298e11	0.0739116
$615$	−3.54115e12	−0.998174
$616$	1.54394e12	0.432033
$617$	3.65251e12	1.01463	0.507315	−	0.861761i	$-0.330638\pi$
$617$	3.65251e12	1.01463	0.507315	+	0.861761i	$0.330638\pi$
$618$	1.97360e11	0.0544265
$619$	1.83928e10	0.00503546	0.00251773	−	0.999997i	$-0.499199\pi$
$619$	1.83928e10	0.00503546	0.00251773	+	0.999997i	$0.499199\pi$
$620$	3.77126e12	1.02500
$621$	2.19393e12	0.591986
$622$	6.41239e11	0.171776
$623$	7.74071e12	2.05866
$624$	−3.83643e12	−1.01297
$625$	−2.81072e12	−0.736815
$626$	6.06257e11	0.157787
$627$	−5.18471e11	−0.133974
$628$	−1.11110e12	−0.285060
$629$	8.84747e12	2.25367
$630$	−3.93438e11	−0.0995049
$631$	−3.45921e12	−0.868650	−0.434325	−	0.900756i	$-0.643013\pi$
$631$	−3.45921e12	−0.868650	−0.434325	+	0.900756i	$0.643013\pi$
$632$	1.04385e12	0.260263
$633$	3.34172e12	0.827282
$634$	−2.44157e11	−0.0600162
$635$	−3.99091e12	−0.974069
$636$	4.04736e12	0.980877
$637$	−1.63575e13	−3.93631
$638$	7.52304e11	0.179763
$639$	−1.79717e12	−0.426418
$640$	−2.64560e12	−0.623325
$641$	−1.71702e12	−0.401710	−0.200855	−	0.979621i	$-0.564372\pi$
$641$	−1.71702e12	−0.401710	−0.200855	+	0.979621i	$0.564372\pi$
$642$	1.03349e12	0.240105
$643$	−5.95110e11	−0.137293	−0.0686464	−	0.997641i	$-0.521868\pi$
$643$	−5.95110e11	−0.137293	−0.0686464	+	0.997641i	$0.521868\pi$
$644$	4.51876e12	1.03522
$645$	4.98747e11	0.113465
$646$	−2.82270e11	−0.0637702
$647$	−2.77664e12	−0.622946	−0.311473	−	0.950255i	$-0.600822\pi$
$647$	−2.77664e12	−0.622946	−0.311473	+	0.950255i	$0.600822\pi$
$648$	−1.05900e12	−0.235944
$649$	−3.12797e12	−0.692088
$650$	−2.58844e11	−0.0568758
$651$	9.15444e12	1.99764
$652$	−1.04627e12	−0.226740
$653$	2.92497e12	0.629523	0.314761	−	0.949171i	$-0.398075\pi$
$653$	2.92497e12	0.629523	0.314761	+	0.949171i	$0.398075\pi$
$654$	−2.91815e11	−0.0623747
$655$	3.98577e12	0.846109
$656$	5.65498e12	1.19224
$657$	1.87092e11	0.0391752
$658$	1.76993e12	0.368077
$659$	−3.06130e12	−0.632299	−0.316149	−	0.948709i	$-0.602390\pi$
$659$	−3.06130e12	−0.632299	−0.316149	+	0.948709i	$0.602390\pi$
$660$	2.00692e12	0.411701
$661$	7.09295e12	1.44517	0.722587	−	0.691280i	$-0.242953\pi$
$661$	7.09295e12	1.44517	0.722587	+	0.691280i	$0.242953\pi$
$662$	−9.20370e11	−0.186252
$663$	6.72947e12	1.35260
$664$	2.03590e12	0.406444
$665$	2.44508e12	0.484836
$666$	−5.48669e11	−0.108063
$667$	4.48960e12	0.878297
$668$	3.91568e12	0.760875
$669$	−1.02172e12	−0.197204
$670$	−3.13859e11	−0.0601724
$671$	2.24289e12	0.427127
$672$	−4.85092e12	−0.917620
$673$	3.65617e12	0.687003	0.343502	−	0.939152i	$-0.388387\pi$
$673$	3.65617e12	0.687003	0.343502	+	0.939152i	$0.388387\pi$
$674$	−1.05398e12	−0.196727
$675$	1.26878e12	0.235245
$676$	−4.38473e12	−0.807574
$677$	−1.69929e12	−0.310898	−0.155449	−	0.987844i	$-0.549682\pi$
$677$	−1.69929e12	−0.310898	−0.155449	+	0.987844i	$0.549682\pi$
$678$	−4.66082e11	−0.0847088
$679$	−1.25665e13	−2.26882
$680$	2.22790e12	0.399581
$681$	−2.27292e12	−0.404970
$682$	−7.57488e11	−0.134074
$683$	−3.57423e12	−0.628477	−0.314239	−	0.949344i	$-0.601749\pi$
$683$	−3.57423e12	−0.628477	−0.314239	+	0.949344i	$0.601749\pi$
$684$	−4.48401e11	−0.0783274
$685$	4.97945e12	0.864119
$686$	−4.22582e12	−0.728539
$687$	−2.72011e11	−0.0465887
$688$	−7.96467e11	−0.135525
$689$	9.72735e12	1.64440
$690$	−4.67555e11	−0.0785257
$691$	9.20422e11	0.153580	0.0767902	−	0.997047i	$-0.475533\pi$
$691$	9.20422e11	0.153580	0.0767902	+	0.997047i	$0.475533\pi$
$692$	5.58815e12	0.926384
$693$	−2.02431e12	−0.333409
$694$	−7.14588e10	−0.0116933
$695$	−2.92496e12	−0.475541
$696$	−3.19271e12	−0.515724
$697$	−9.91937e12	−1.59198
$698$	6.20360e11	0.0989224
$699$	−2.59482e12	−0.411112
$700$	2.61326e12	0.411379
$701$	3.78617e11	0.0592200	0.0296100	−	0.999562i	$-0.490573\pi$
$701$	3.78617e11	0.0592200	0.0296100	+	0.999562i	$0.490573\pi$
$702$	−1.83896e12	−0.285796
$703$	3.40978e12	0.526535
$704$	−2.92864e12	−0.449354
$705$	4.69116e12	0.715203
$706$	−1.38504e11	−0.0209817
$707$	−3.83486e12	−0.577248
$708$	6.51032e12	0.973762
$709$	−4.49168e12	−0.667576	−0.333788	−	0.942648i	$-0.608327\pi$
$709$	−4.49168e12	−0.667576	−0.333788	+	0.942648i	$0.608327\pi$
$710$	1.68772e12	0.249251
$711$	−1.36863e12	−0.200850
$712$	2.71826e12	0.396397
$713$	−4.52054e12	−0.655069
$714$	2.65225e12	0.381920
$715$	4.82339e12	0.690201
$716$	7.61321e12	1.08258
$717$	−4.30549e12	−0.608395
$718$	−4.02842e11	−0.0565684
$719$	−8.71449e12	−1.21608	−0.608039	−	0.793907i	$-0.708044\pi$
$719$	−8.71449e12	−1.21608	−0.608039	+	0.793907i	$0.708044\pi$
$720$	1.66529e12	0.230936
$721$	−4.78880e12	−0.659961
$722$	1.30651e12	0.178935
$723$	9.49914e12	1.29289
$724$	−5.56087e12	−0.752176
$725$	2.59640e12	0.349020
$726$	8.16401e11	0.109066
$727$	1.20858e13	1.60461	0.802306	−	0.596913i	$-0.203606\pi$
$727$	1.20858e13	1.60461	0.802306	+	0.596913i	$0.203606\pi$
$728$	−7.72313e12	−1.01907
$729$	8.35698e12	1.09591
$730$	−1.75697e11	−0.0228988
$731$	1.39708e12	0.180964
$732$	−4.66819e12	−0.600964
$733$	−2.17693e12	−0.278534	−0.139267	−	0.990255i	$-0.544475\pi$
$733$	−2.17693e12	−0.278534	−0.139267	+	0.990255i	$0.544475\pi$
$734$	−1.14803e12	−0.145989
$735$	−1.70874e13	−2.15965
$736$	2.39542e12	0.300907
$737$	−1.61486e12	−0.201619
$738$	6.15142e11	0.0763346
$739$	1.41514e13	1.74542	0.872709	−	0.488240i	$-0.162361\pi$
$739$	1.41514e13	1.74542	0.872709	+	0.488240i	$0.162361\pi$
$740$	−1.31987e13	−1.61804
$741$	2.59351e12	0.316014
$742$	3.83379e12	0.464313
$743$	−1.36261e13	−1.64030	−0.820148	−	0.572152i	$-0.806109\pi$
$743$	−1.36261e13	−1.64030	−0.820148	+	0.572152i	$0.806109\pi$
$744$	3.21471e12	0.384648
$745$	−4.20660e12	−0.500297
$746$	−1.28189e12	−0.151540
$747$	−2.66934e12	−0.313661
$748$	5.62172e12	0.656617
$749$	−2.50770e13	−2.91144
$750$	−1.52008e12	−0.175425
$751$	−1.39601e13	−1.60143	−0.800715	−	0.599046i	$-0.795547\pi$
$751$	−1.39601e13	−1.60143	−0.800715	+	0.599046i	$0.795547\pi$
$752$	−7.49148e12	−0.854254
$753$	2.76332e12	0.313223
$754$	−3.76319e12	−0.424019
$755$	3.35497e12	0.375774
$756$	1.85660e13	2.06714
$757$	6.22034e12	0.688467	0.344233	−	0.938884i	$-0.388139\pi$
$757$	6.22034e12	0.688467	0.344233	+	0.938884i	$0.388139\pi$
$758$	−1.77533e12	−0.195329
$759$	−2.40565e12	−0.263115
$760$	8.58622e11	0.0933557
$761$	−7.99871e12	−0.864548	−0.432274	−	0.901742i	$-0.642289\pi$
$761$	−7.99871e12	−0.864548	−0.432274	+	0.901742i	$0.642289\pi$
$762$	−1.66840e12	−0.179268
$763$	7.08070e12	0.756338
$764$	−9.25202e12	−0.982464
$765$	−2.92107e12	−0.308365
$766$	2.64721e12	0.277818
$767$	1.56468e13	1.63248
$768$	5.22741e12	0.542202
$769$	−1.87310e13	−1.93149	−0.965745	−	0.259493i	$-0.916444\pi$
$769$	−1.87310e13	−1.93149	−0.965745	+	0.259493i	$0.916444\pi$
$770$	1.90102e12	0.194885
$771$	−1.75401e12	−0.178767
$772$	−1.25181e12	−0.126842
$773$	−7.45839e12	−0.751342	−0.375671	−	0.926753i	$-0.622588\pi$
$773$	−7.45839e12	−0.751342	−0.375671	+	0.926753i	$0.622588\pi$
$774$	−8.66387e10	−0.00867716
$775$	−2.61429e12	−0.260313
$776$	−4.41289e12	−0.436863
$777$	−3.20388e13	−3.15342
$778$	1.75707e12	0.171941
$779$	−3.82288e12	−0.371939
$780$	−1.00391e13	−0.971108
$781$	8.68360e12	0.835161
$782$	−1.30970e12	−0.125240
$783$	1.84462e13	1.75379
$784$	2.72875e13	2.57953
$785$	−2.78957e12	−0.262194
$786$	1.66626e12	0.155718
$787$	−1.24079e13	−1.15295	−0.576476	−	0.817114i	$-0.695573\pi$
$787$	−1.24079e13	−1.15295	−0.576476	+	0.817114i	$0.695573\pi$
$788$	1.31291e13	1.21302
$789$	−1.52685e12	−0.140265
$790$	1.28527e12	0.117402
$791$	1.13092e13	1.02715
$792$	−7.10863e11	−0.0641982
$793$	−1.12194e13	−1.00749
$794$	3.35572e12	0.299636
$795$	1.01614e13	0.902197
$796$	−1.22651e13	−1.08283
$797$	4.11416e12	0.361176	0.180588	−	0.983559i	$-0.442200\pi$
$797$	4.11416e12	0.361176	0.180588	+	0.983559i	$0.442200\pi$
$798$	1.02217e12	0.0892295
$799$	1.31408e13	1.14067
$800$	1.38531e12	0.119575
$801$	−3.56399e12	−0.305908
$802$	−2.25427e12	−0.192408
$803$	−9.03993e11	−0.0767265
$804$	3.36105e12	0.283676
$805$	1.13449e13	0.952181
$806$	3.78913e12	0.316251
$807$	1.63450e13	1.35660
$808$	−1.34666e12	−0.111150
$809$	1.87181e13	1.53636	0.768182	−	0.640231i	$-0.221162\pi$
$809$	1.87181e13	1.53636	0.768182	+	0.640231i	$0.221162\pi$
$810$	−1.30393e12	−0.106432
$811$	−1.17522e13	−0.953949	−0.476975	−	0.878917i	$-0.658267\pi$
$811$	−1.17522e13	−0.953949	−0.476975	+	0.878917i	$0.658267\pi$
$812$	3.79928e13	3.06690
$813$	−4.19512e12	−0.336773
$814$	2.65107e12	0.211646
$815$	−2.62679e12	−0.208553
$816$	−1.12260e13	−0.886382
$817$	5.38428e11	0.0422793
$818$	−1.44700e12	−0.113000
$819$	1.01261e13	0.786435
$820$	1.47978e13	1.14297
$821$	2.29795e13	1.76521	0.882605	−	0.470115i	$-0.155787\pi$
$821$	2.29795e13	1.76521	0.882605	+	0.470115i	$0.155787\pi$
$822$	2.08166e12	0.159033
$823$	7.89246e12	0.599671	0.299836	−	0.953991i	$-0.403068\pi$
$823$	7.89246e12	0.599671	0.299836	+	0.953991i	$0.403068\pi$
$824$	−1.68165e12	−0.127076
$825$	−1.39122e12	−0.104557
$826$	6.16680e12	0.460946
$827$	−1.43874e13	−1.06957	−0.534784	−	0.844989i	$-0.679607\pi$
$827$	−1.43874e13	−1.06957	−0.534784	+	0.844989i	$0.679607\pi$
$828$	−2.08054e12	−0.153829
$829$	−1.40139e12	−0.103053	−0.0515267	−	0.998672i	$-0.516409\pi$
$829$	−1.40139e12	−0.103053	−0.0515267	+	0.998672i	$0.516409\pi$
$830$	2.50677e12	0.183342
$831$	1.33826e13	0.973496
$832$	1.46497e13	1.05992
$833$	−4.78648e13	−3.44440
$834$	−1.22278e12	−0.0875189
$835$	9.83081e12	0.699842
$836$	2.16659e12	0.153408
$837$	−1.85733e13	−1.30805
$838$	−4.96811e11	−0.0348011
$839$	−2.01539e13	−1.40420	−0.702101	−	0.712078i	$-0.747754\pi$
$839$	−2.01539e13	−1.40420	−0.702101	+	0.712078i	$0.747754\pi$
$840$	−8.06775e12	−0.559108
$841$	2.32405e13	1.60200
$842$	2.50353e12	0.171652
$843$	3.35634e12	0.228898
$844$	−1.39644e13	−0.947287
$845$	−1.10084e13	−0.742796
$846$	−8.14914e11	−0.0546947
$847$	−1.98094e13	−1.32250
$848$	−1.62271e13	−1.07760
$849$	1.22182e13	0.807089
$850$	−7.57420e11	−0.0497682
$851$	1.58210e13	1.03407
$852$	−1.80734e13	−1.17506
$853$	−1.31259e13	−0.848907	−0.424453	−	0.905450i	$-0.639534\pi$
$853$	−1.31259e13	−0.848907	−0.424453	+	0.905450i	$0.639534\pi$
$854$	−4.42187e12	−0.284476
$855$	−1.12577e12	−0.0720445
$856$	−8.80615e12	−0.560601
$857$	−8.66664e12	−0.548829	−0.274414	−	0.961612i	$-0.588484\pi$
$857$	−8.66664e12	−0.548829	−0.274414	+	0.961612i	$0.588484\pi$
$858$	2.01643e12	0.127025
$859$	1.00716e13	0.631143	0.315571	−	0.948902i	$-0.397804\pi$
$859$	1.00716e13	0.631143	0.315571	+	0.948902i	$0.397804\pi$
$860$	−2.08417e12	−0.129924
$861$	3.59204e13	2.22755
$862$	2.36321e12	0.145787
$863$	−8.56376e12	−0.525552	−0.262776	−	0.964857i	$-0.584638\pi$
$863$	−8.56376e12	−0.525552	−0.262776	+	0.964857i	$0.584638\pi$
$864$	9.84195e12	0.600854
$865$	1.40298e13	0.852075
$866$	3.79204e12	0.229109
$867$	5.70769e12	0.343063
$868$	−3.82546e13	−2.28742
$869$	6.61296e12	0.393375
$870$	−3.93111e12	−0.232637
$871$	8.07788e12	0.475571
$872$	2.48648e12	0.145634
$873$	5.78589e12	0.337137
$874$	−5.04754e11	−0.0292603
$875$	3.68837e13	2.12715
$876$	1.88151e12	0.107954
$877$	−1.86361e12	−0.106379	−0.0531896	−	0.998584i	$-0.516939\pi$
$877$	−1.86361e12	−0.106379	−0.0531896	+	0.998584i	$0.516939\pi$
$878$	1.67302e11	0.00950113
$879$	−2.26170e13	−1.27786
$880$	−8.04635e12	−0.452300
$881$	1.12984e13	0.631868	0.315934	−	0.948781i	$-0.397682\pi$
$881$	1.12984e13	0.631868	0.315934	+	0.948781i	$0.397682\pi$
$882$	2.96830e12	0.165158
$883$	−1.69207e13	−0.936690	−0.468345	−	0.883546i	$-0.655150\pi$
$883$	−1.69207e13	−0.936690	−0.468345	+	0.883546i	$0.655150\pi$
$884$	−2.81211e13	−1.54881
$885$	1.63450e13	0.895654
$886$	−1.77373e12	−0.0967018
$887$	1.15592e13	0.627004	0.313502	−	0.949588i	$-0.398498\pi$
$887$	1.15592e13	0.627004	0.313502	+	0.949588i	$0.398498\pi$
$888$	−1.12509e13	−0.607195
$889$	4.04827e13	2.17376
$890$	3.34693e12	0.178810
$891$	−6.70893e12	−0.356618
$892$	4.26959e12	0.225810
$893$	5.06439e12	0.266499
$894$	−1.75857e12	−0.0920750
$895$	1.91139e13	0.995741
$896$	2.68362e13	1.39103
$897$	1.20336e13	0.620627
$898$	−2.29386e12	−0.117713
$899$	−3.80078e13	−1.94068
$900$	−1.20320e12	−0.0611291
$901$	2.84638e13	1.43890
$902$	−2.97225e12	−0.149505
$903$	−5.05916e12	−0.253211
$904$	3.97136e12	0.197780
$905$	−1.39613e13	−0.691842
$906$	1.40255e12	0.0691577
$907$	−8.82407e12	−0.432948	−0.216474	−	0.976288i	$-0.569456\pi$
$907$	−8.82407e12	−0.432948	−0.216474	+	0.976288i	$0.569456\pi$
$908$	9.49810e12	0.463714
$909$	1.76565e12	0.0857765
$910$	−9.50934e12	−0.459689
$911$	−9.12800e12	−0.439079	−0.219540	−	0.975604i	$-0.570456\pi$
$911$	−9.12800e12	−0.439079	−0.219540	+	0.975604i	$0.570456\pi$
$912$	−4.32647e12	−0.207089
$913$	1.28978e13	0.614321
$914$	7.11463e12	0.337205
$915$	−1.17201e13	−0.552759
$916$	1.13668e12	0.0533468
$917$	−4.04306e13	−1.88820
$918$	−5.38110e12	−0.250080
$919$	−1.89826e13	−0.877881	−0.438940	−	0.898516i	$-0.644646\pi$
$919$	−1.89826e13	−0.877881	−0.438940	+	0.898516i	$0.644646\pi$
$920$	3.98392e12	0.183343
$921$	−6.99830e12	−0.320497
$922$	2.47581e12	0.112831
$923$	−4.34373e13	−1.96995
$924$	−2.03576e13	−0.918763
$925$	9.14953e12	0.410924
$926$	7.72101e11	0.0345084
$927$	2.20487e12	0.0980673
$928$	2.01403e13	0.891455
$929$	1.66439e13	0.733136	0.366568	−	0.930391i	$-0.380533\pi$
$929$	1.66439e13	0.733136	0.366568	+	0.930391i	$0.380533\pi$
$930$	3.95820e12	0.173510
$931$	−1.84469e13	−0.804729
$932$	1.08433e13	0.470748
$933$	−1.72402e13	−0.744860
$934$	−6.00008e11	−0.0257986
$935$	1.41141e13	0.603948
$936$	3.55590e12	0.151429
$937$	1.20784e13	0.511896	0.255948	−	0.966691i	$-0.417612\pi$
$937$	1.20784e13	0.511896	0.255948	+	0.966691i	$0.417612\pi$
$938$	3.18370e12	0.134282
$939$	−1.62997e13	−0.684201
$940$	−1.96035e13	−0.818950
$941$	−1.09033e13	−0.453320	−0.226660	−	0.973974i	$-0.572781\pi$
$941$	−1.09033e13	−0.453320	−0.226660	+	0.973974i	$0.572781\pi$
$942$	−1.16618e12	−0.0482544
$943$	−1.77378e13	−0.730461
$944$	−2.61019e13	−1.06979
$945$	4.66122e13	1.90133
$946$	4.18622e11	0.0169946
$947$	2.49583e13	1.00842	0.504209	−	0.863582i	$-0.331784\pi$
$947$	2.49583e13	1.00842	0.504209	+	0.863582i	$0.331784\pi$
$948$	−1.37637e13	−0.553476
$949$	4.52198e12	0.180980
$950$	−2.91907e11	−0.0116275
$951$	6.56436e12	0.260244
$952$	−2.25992e13	−0.891715
$953$	−1.44768e13	−0.568530	−0.284265	−	0.958746i	$-0.591750\pi$
$953$	−1.44768e13	−0.568530	−0.284265	+	0.958746i	$0.591750\pi$
$954$	−1.76516e12	−0.0689949
$955$	−2.32284e13	−0.903657
$956$	1.79918e13	0.696649
$957$	−2.02263e13	−0.779492
$958$	2.13365e12	0.0818423
$959$	−5.05102e13	−1.92839
$960$	1.53034e13	0.581524
$961$	1.18301e13	0.447437
$962$	−1.32612e13	−0.499225
$963$	1.15460e13	0.432628
$964$	−3.96951e13	−1.48044
$965$	−3.14284e12	−0.116667
$966$	4.74275e12	0.175240
$967$	−1.31877e12	−0.0485007	−0.0242504	−	0.999706i	$-0.507720\pi$
$967$	−1.31877e12	−0.0485007	−0.0242504	+	0.999706i	$0.507720\pi$
$968$	−6.95635e12	−0.254649
$969$	7.58903e12	0.276522
$970$	−5.43351e12	−0.197064
$971$	−5.24865e13	−1.89479	−0.947394	−	0.320069i	$-0.896294\pi$
$971$	−5.24865e13	−1.89479	−0.947394	+	0.320069i	$0.896294\pi$
$972$	−1.51565e13	−0.544628
$973$	2.96700e13	1.06123
$974$	3.55525e12	0.126577
$975$	6.95922e12	0.246626
$976$	1.87162e13	0.660227
$977$	5.15657e13	1.81065	0.905327	−	0.424714i	$-0.139625\pi$
$977$	5.15657e13	1.81065	0.905327	+	0.424714i	$0.139625\pi$
$978$	−1.09813e12	−0.0383822
$979$	1.72206e13	0.599135
$980$	7.14050e13	2.47293
$981$	−3.26011e12	−0.112388
$982$	−4.91356e12	−0.168614
$983$	2.11520e13	0.722537	0.361269	−	0.932462i	$-0.382344\pi$
$983$	2.11520e13	0.722537	0.361269	+	0.932462i	$0.382344\pi$
$984$	1.26139e13	0.428917
$985$	3.29623e13	1.11572
$986$	−1.10117e13	−0.371030
$987$	−4.75859e13	−1.59607
$988$	−1.08378e13	−0.361854
$989$	2.49825e12	0.0830334
$990$	−8.75272e11	−0.0289591
$991$	−4.73443e13	−1.55932	−0.779661	−	0.626201i	$-0.784609\pi$
$991$	−4.73443e13	−1.55932	−0.779661	+	0.626201i	$0.784609\pi$
$992$	−2.02791e13	−0.664883
$993$	2.47449e13	0.807632
$994$	−1.71197e13	−0.556235
$995$	−3.07931e13	−0.995977
$996$	−2.68444e13	−0.864345
$997$	−1.49776e13	−0.480081	−0.240041	−	0.970763i	$-0.577161\pi$
$997$	−1.49776e13	−0.480081	−0.240041	+	0.970763i	$0.577161\pi$
$998$	−8.47966e12	−0.270577
$999$	6.50030e13	2.06485

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.a.a.1.8	✓	15
3.2	odd	2		387.10.a.c.1.8		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.a.a.1.8	✓	15	1.1	even	1	trivial
387.10.a.c.1.8		15	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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	43.a (trivial)

\(f(q)\)	\(=\)	\(q-4.38595 q^{2} +117.920 q^{3} -492.763 q^{4} -1237.15 q^{5} -517.190 q^{6} +12549.3 q^{7} +4406.84 q^{8} -5777.96 q^{9} +O(q^{10})\)	\(q-4.38595 q^{2} +117.920 q^{3} -492.763 q^{4} -1237.15 q^{5} -517.190 q^{6} +12549.3 q^{7} +4406.84 q^{8} -5777.96 q^{9} +5426.06 q^{10} +27918.0 q^{11} -58106.5 q^{12} -139652. q^{13} -55040.4 q^{14} -145884. q^{15} +232967. q^{16} -408645. q^{17} +25341.8 q^{18} -157490. q^{19} +609620. q^{20} +1.47980e6 q^{21} -122447. q^{22} -730739. q^{23} +519653. q^{24} -422597. q^{25} +612508. q^{26} -3.00235e6 q^{27} -6.18382e6 q^{28} -6.14391e6 q^{29} +639839. q^{30} +6.18625e6 q^{31} -3.27808e6 q^{32} +3.29208e6 q^{33} +1.79230e6 q^{34} -1.55253e7 q^{35} +2.84717e6 q^{36} -2.16507e7 q^{37} +690744. q^{38} -1.64677e7 q^{39} -5.45190e6 q^{40} +2.42738e7 q^{41} -6.49035e6 q^{42} -3.41880e6 q^{43} -1.37570e7 q^{44} +7.14817e6 q^{45} +3.20499e6 q^{46} -3.21569e7 q^{47} +2.74713e7 q^{48} +1.17130e8 q^{49} +1.85349e6 q^{50} -4.81873e7 q^{51} +6.88155e7 q^{52} -6.96541e7 q^{53} +1.31681e7 q^{54} -3.45386e7 q^{55} +5.53026e7 q^{56} -1.85712e7 q^{57} +2.69469e7 q^{58} -1.12041e8 q^{59} +7.18862e7 q^{60} +8.03385e7 q^{61} -2.71326e7 q^{62} -7.25091e7 q^{63} -1.04901e8 q^{64} +1.72770e8 q^{65} -1.44389e7 q^{66} -5.78429e7 q^{67} +2.01366e8 q^{68} -8.61685e7 q^{69} +6.80930e7 q^{70} +3.11039e8 q^{71} -2.54625e7 q^{72} -3.23803e7 q^{73} +9.49590e7 q^{74} -4.98325e7 q^{75} +7.76054e7 q^{76} +3.50350e8 q^{77} +7.22267e7 q^{78} +2.36871e8 q^{79} -2.88214e8 q^{80} -2.40308e8 q^{81} -1.06464e8 q^{82} +4.61987e8 q^{83} -7.29193e8 q^{84} +5.05554e8 q^{85} +1.49947e7 q^{86} -7.24488e8 q^{87} +1.23030e8 q^{88} +6.16826e8 q^{89} -3.13515e7 q^{90} -1.75253e9 q^{91} +3.60082e8 q^{92} +7.29481e8 q^{93} +1.41038e8 q^{94} +1.94838e8 q^{95} -3.86551e8 q^{96} -1.00137e9 q^{97} -5.13728e8 q^{98} -1.61309e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 32 q^{2} - 317 q^{3} + 3242 q^{4} - 4717 q^{5} + 687 q^{6} - 9680 q^{7} - 20394 q^{8} + 69516 q^{9}+O(q^{10}) \) 15 * q - 32 * q^2 - 317 * q^3 + 3242 * q^4 - 4717 * q^5 + 687 * q^6 - 9680 * q^7 - 20394 * q^8 + 69516 * q^9	\( 15 q - 32 q^{2} - 317 q^{3} + 3242 q^{4} - 4717 q^{5} + 687 q^{6} - 9680 q^{7} - 20394 q^{8} + 69516 q^{9} - 36237 q^{10} - 104484 q^{11} - 266395 q^{12} - 116174 q^{13} + 416064 q^{14} + 415388 q^{15} + 996762 q^{16} - 884265 q^{17} - 588735 q^{18} - 689535 q^{19} - 3077879 q^{20} - 2070198 q^{21} - 7276218 q^{22} - 2504077 q^{23} - 11534895 q^{24} + 1315350 q^{25} - 13343414 q^{26} - 12546986 q^{27} - 28059568 q^{28} - 18406221 q^{29} - 39503820 q^{30} - 12033699 q^{31} - 18952630 q^{32} - 14197716 q^{33} - 30383125 q^{34} - 27855546 q^{35} - 18372959 q^{36} - 8722847 q^{37} - 63941843 q^{38} - 30955510 q^{39} - 39665611 q^{40} - 18689389 q^{41} - 73185310 q^{42} - 51282015 q^{43} - 68723220 q^{44} - 216992888 q^{45} - 2067521 q^{46} - 104960741 q^{47} - 145362479 q^{48} + 92663095 q^{49} - 42446347 q^{50} + 37433407 q^{51} + 149226080 q^{52} - 215907800 q^{53} + 419158122 q^{54} + 384379852 q^{55} + 430441344 q^{56} + 258744488 q^{57} + 295963139 q^{58} + 185924544 q^{59} + 973236172 q^{60} + 247538102 q^{61} + 139798853 q^{62} + 405429926 q^{63} + 848556290 q^{64} + 94294394 q^{65} + 667230492 q^{66} + 467904656 q^{67} - 88234341 q^{68} + 163914994 q^{69} + 647526126 q^{70} - 8252944 q^{71} + 889796745 q^{72} - 715627902 q^{73} + 725122989 q^{74} - 18301762 q^{75} + 346300359 q^{76} - 1236779964 q^{77} + 2058642146 q^{78} + 560681783 q^{79} - 1157214179 q^{80} - 752010645 q^{81} + 941346367 q^{82} - 1442854698 q^{83} + 1895248718 q^{84} + 699302088 q^{85} + 109401632 q^{86} - 2094576907 q^{87} - 1464507256 q^{88} - 396710008 q^{89} + 1411356270 q^{90} - 3278076852 q^{91} + 155864647 q^{92} - 1424759183 q^{93} + 4666638949 q^{94} - 3854114395 q^{95} - 952489551 q^{96} - 3063837815 q^{97} - 6161086984 q^{98} - 6576160348 q^{99}+O(q^{100}) \) 15 * q - 32 * q^2 - 317 * q^3 + 3242 * q^4 - 4717 * q^5 + 687 * q^6 - 9680 * q^7 - 20394 * q^8 + 69516 * q^9 - 36237 * q^10 - 104484 * q^11 - 266395 * q^12 - 116174 * q^13 + 416064 * q^14 + 415388 * q^15 + 996762 * q^16 - 884265 * q^17 - 588735 * q^18 - 689535 * q^19 - 3077879 * q^20 - 2070198 * q^21 - 7276218 * q^22 - 2504077 * q^23 - 11534895 * q^24 + 1315350 * q^25 - 13343414 * q^26 - 12546986 * q^27 - 28059568 * q^28 - 18406221 * q^29 - 39503820 * q^30 - 12033699 * q^31 - 18952630 * q^32 - 14197716 * q^33 - 30383125 * q^34 - 27855546 * q^35 - 18372959 * q^36 - 8722847 * q^37 - 63941843 * q^38 - 30955510 * q^39 - 39665611 * q^40 - 18689389 * q^41 - 73185310 * q^42 - 51282015 * q^43 - 68723220 * q^44 - 216992888 * q^45 - 2067521 * q^46 - 104960741 * q^47 - 145362479 * q^48 + 92663095 * q^49 - 42446347 * q^50 + 37433407 * q^51 + 149226080 * q^52 - 215907800 * q^53 + 419158122 * q^54 + 384379852 * q^55 + 430441344 * q^56 + 258744488 * q^57 + 295963139 * q^58 + 185924544 * q^59 + 973236172 * q^60 + 247538102 * q^61 + 139798853 * q^62 + 405429926 * q^63 + 848556290 * q^64 + 94294394 * q^65 + 667230492 * q^66 + 467904656 * q^67 - 88234341 * q^68 + 163914994 * q^69 + 647526126 * q^70 - 8252944 * q^71 + 889796745 * q^72 - 715627902 * q^73 + 725122989 * q^74 - 18301762 * q^75 + 346300359 * q^76 - 1236779964 * q^77 + 2058642146 * q^78 + 560681783 * q^79 - 1157214179 * q^80 - 752010645 * q^81 + 941346367 * q^82 - 1442854698 * q^83 + 1895248718 * q^84 + 699302088 * q^85 + 109401632 * q^86 - 2094576907 * q^87 - 1464507256 * q^88 - 396710008 * q^89 + 1411356270 * q^90 - 3278076852 * q^91 + 155864647 * q^92 - 1424759183 * q^93 + 4666638949 * q^94 - 3854114395 * q^95 - 952489551 * q^96 - 3063837815 * q^97 - 6161086984 * q^98 - 6576160348 * q^99

Introduction

L-functions

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