LMFDB - Embedded newform 43.10.a.a.1.6

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			1.6
Root			$15.9205$ 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)

$f(q)$	$=$	$q-17.9205 q^{2} -172.986 q^{3} -190.855 q^{4} +238.484 q^{5} +3099.99 q^{6} -4524.82 q^{7} +12595.5 q^{8} +10241.0 q^{9} +O(q^{10})$	\(q-17.9205 q^{2} -172.986 q^{3} -190.855 q^{4} +238.484 q^{5} +3099.99 q^{6} -4524.82 q^{7} +12595.5 q^{8} +10241.0 q^{9} -4273.75 q^{10} +66772.1 q^{11} +33015.1 q^{12} +45566.0 q^{13} +81087.1 q^{14} -41254.2 q^{15} -128001. q^{16} +494574. q^{17} -183524. q^{18} -1.08372e6 q^{19} -45515.8 q^{20} +782728. q^{21} -1.19659e6 q^{22} +1.35193e6 q^{23} -2.17884e6 q^{24} -1.89625e6 q^{25} -816566. q^{26} +1.63333e6 q^{27} +863584. q^{28} -4.85463e6 q^{29} +739298. q^{30} +5.69784e6 q^{31} -4.15507e6 q^{32} -1.15506e7 q^{33} -8.86302e6 q^{34} -1.07910e6 q^{35} -1.95454e6 q^{36} -1.59658e7 q^{37} +1.94208e7 q^{38} -7.88225e6 q^{39} +3.00383e6 q^{40} +1.10007e7 q^{41} -1.40269e7 q^{42} -3.41880e6 q^{43} -1.27438e7 q^{44} +2.44231e6 q^{45} -2.42274e7 q^{46} +2.98409e7 q^{47} +2.21423e7 q^{48} -1.98796e7 q^{49} +3.39818e7 q^{50} -8.55541e7 q^{51} -8.69648e6 q^{52} +7.43943e6 q^{53} -2.92702e7 q^{54} +1.59241e7 q^{55} -5.69925e7 q^{56} +1.87467e8 q^{57} +8.69975e7 q^{58} +1.08119e8 q^{59} +7.87357e6 q^{60} +1.99515e8 q^{61} -1.02108e8 q^{62} -4.63386e7 q^{63} +1.39997e8 q^{64} +1.08667e7 q^{65} +2.06993e8 q^{66} -2.61727e8 q^{67} -9.43918e7 q^{68} -2.33865e8 q^{69} +1.93380e7 q^{70} +6.58887e7 q^{71} +1.28991e8 q^{72} -4.01146e8 q^{73} +2.86115e8 q^{74} +3.28024e8 q^{75} +2.06832e8 q^{76} -3.02132e8 q^{77} +1.41254e8 q^{78} +1.23252e8 q^{79} -3.05261e7 q^{80} -4.84116e8 q^{81} -1.97139e8 q^{82} -3.81346e8 q^{83} -1.49388e8 q^{84} +1.17948e8 q^{85} +6.12667e7 q^{86} +8.39780e8 q^{87} +8.41030e8 q^{88} -3.81633e8 q^{89} -4.37675e7 q^{90} -2.06178e8 q^{91} -2.58023e8 q^{92} -9.85643e8 q^{93} -5.34765e8 q^{94} -2.58449e8 q^{95} +7.18767e8 q^{96} -5.93343e8 q^{97} +3.56253e8 q^{98} +6.83813e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−17.9205	−0.791983	−0.395991	−	0.918254i	$-0.629599\pi$
$2$	−17.9205	−0.791983	−0.395991	+	0.918254i	$0.629599\pi$
$3$	−172.986	−1.23300	−0.616501	−	0.787354i	$-0.711451\pi$
$3$	−172.986	−1.23300	−0.616501	+	0.787354i	$0.711451\pi$
$4$	−190.855	−0.372763
$5$	238.484	0.170645	0.0853226	−	0.996353i	$-0.472808\pi$
$5$	238.484	0.170645	0.0853226	+	0.996353i	$0.472808\pi$
$6$	3099.99	0.976517
$7$	−4524.82	−0.712295	−0.356148	−	0.934430i	$-0.615910\pi$
$7$	−4524.82	−0.712295	−0.356148	+	0.934430i	$0.615910\pi$
$8$	12595.5	1.08720
$9$	10241.0	0.520296
$10$	−4273.75	−0.135148
$11$	66772.1	1.37508	0.687540	−	0.726146i	$-0.258690\pi$
$11$	66772.1	1.37508	0.687540	+	0.726146i	$0.258690\pi$
$12$	33015.1	0.459618
$13$	45566.0	0.442482	0.221241	−	0.975219i	$-0.428989\pi$
$13$	45566.0	0.442482	0.221241	+	0.975219i	$0.428989\pi$
$14$	81087.1	0.564126
$15$	−41254.2	−0.210406
$16$	−128001.	−0.488284
$17$	494574.	1.43619	0.718094	−	0.695947i	$-0.245015\pi$
$17$	494574.	1.43619	0.718094	+	0.695947i	$0.245015\pi$
$18$	−183524.	−0.412065
$19$	−1.08372e6	−1.90776	−0.953881	−	0.300184i	$-0.902952\pi$
$19$	−1.08372e6	−1.90776	−0.953881	+	0.300184i	$0.902952\pi$
$20$	−45515.8	−0.0636103
$21$	782728.	0.878262
$22$	−1.19659e6	−1.08904
$23$	1.35193e6	1.00735	0.503675	−	0.863893i	$-0.331981\pi$
$23$	1.35193e6	1.00735	0.503675	+	0.863893i	$0.331981\pi$
$24$	−2.17884e6	−1.34053
$25$	−1.89625e6	−0.970880
$26$	−816566.	−0.350438
$27$	1.63333e6	0.591476
$28$	863584.	0.265518
$29$	−4.85463e6	−1.27457	−0.637287	−	0.770627i	$-0.719943\pi$
$29$	−4.85463e6	−1.27457	−0.637287	+	0.770627i	$0.719943\pi$
$30$	739298.	0.166638
$31$	5.69784e6	1.10811	0.554054	−	0.832481i	$-0.313080\pi$
$31$	5.69784e6	1.10811	0.554054	+	0.832481i	$0.313080\pi$
$32$	−4.15507e6	−0.700492
$33$	−1.15506e7	−1.69548
$34$	−8.86302e6	−1.13744
$35$	−1.07910e6	−0.121550
$36$	−1.95454e6	−0.193947
$37$	−1.59658e7	−1.40050	−0.700249	−	0.713898i	$-0.746928\pi$
$37$	−1.59658e7	−1.40050	−0.700249	+	0.713898i	$0.746928\pi$
$38$	1.94208e7	1.51091
$39$	−7.88225e6	−0.545581
$40$	3.00383e6	0.185526
$41$	1.10007e7	0.607988	0.303994	−	0.952674i	$-0.401680\pi$
$41$	1.10007e7	0.607988	0.303994	+	0.952674i	$0.401680\pi$
$42$	−1.40269e7	−0.695568
$43$	−3.41880e6	−0.152499
$43$	−3.41880e6	−0.152499
$44$	−1.27438e7	−0.512580
$45$	2.44231e6	0.0887860
$46$	−2.42274e7	−0.797803
$47$	2.98409e7	0.892014	0.446007	−	0.895029i	$-0.352846\pi$
$47$	2.98409e7	0.892014	0.446007	+	0.895029i	$0.352846\pi$
$48$	2.21423e7	0.602056
$49$	−1.98796e7	−0.492635
$50$	3.39818e7	0.768920
$51$	−8.55541e7	−1.77082
$52$	−8.69648e6	−0.164941
$53$	7.43943e6	0.129509	0.0647543	−	0.997901i	$-0.479374\pi$
$53$	7.43943e6	0.129509	0.0647543	+	0.997901i	$0.479374\pi$
$54$	−2.92702e7	−0.468439
$55$	1.59241e7	0.234651
$56$	−5.69925e7	−0.774411
$57$	1.87467e8	2.35228
$58$	8.69975e7	1.00944
$59$	1.08119e8	1.16163	0.580815	−	0.814036i	$-0.302734\pi$
$59$	1.08119e8	1.16163	0.580815	+	0.814036i	$0.302734\pi$
$60$	7.87357e6	0.0784316
$61$	1.99515e8	1.84497	0.922487	−	0.386028i	$-0.126153\pi$
$61$	1.99515e8	1.84497	0.922487	+	0.386028i	$0.126153\pi$
$62$	−1.02108e8	−0.877603
$63$	−4.63386e7	−0.370604
$64$	1.39997e8	1.04306
$65$	1.08667e7	0.0755073
$66$	2.06993e8	1.34279
$67$	−2.61727e8	−1.58677	−0.793383	−	0.608723i	$-0.791682\pi$
$67$	−2.61727e8	−1.58677	−0.793383	+	0.608723i	$0.791682\pi$
$68$	−9.43918e7	−0.535358
$69$	−2.33865e8	−1.24206
$70$	1.93380e7	0.0962653
$71$	6.58887e7	0.307715	0.153857	−	0.988093i	$-0.450830\pi$
$71$	6.58887e7	0.307715	0.153857	+	0.988093i	$0.450830\pi$
$72$	1.28991e8	0.565668
$73$	−4.01146e8	−1.65329	−0.826646	−	0.562722i	$-0.809754\pi$
$73$	−4.01146e8	−1.65329	−0.826646	+	0.562722i	$0.809754\pi$
$74$	2.86115e8	1.10917
$75$	3.28024e8	1.19710
$76$	2.06832e8	0.711144
$77$	−3.02132e8	−0.979464
$78$	1.41254e8	0.432091
$79$	1.23252e8	0.356019	0.178009	−	0.984029i	$-0.443034\pi$
$79$	1.23252e8	0.356019	0.178009	+	0.984029i	$0.443034\pi$
$80$	−3.05261e7	−0.0833233
$81$	−4.84116e8	−1.24959
$82$	−1.97139e8	−0.481516
$83$	−3.81346e8	−0.881998	−0.440999	−	0.897507i	$-0.645376\pi$
$83$	−3.81346e8	−0.881998	−0.440999	+	0.897507i	$0.645376\pi$
$84$	−1.49388e8	−0.327384
$85$	1.17948e8	0.245078
$86$	6.12667e7	0.120776
$87$	8.39780e8	1.57155
$88$	8.41030e8	1.49499
$89$	−3.81633e8	−0.644749	−0.322375	−	0.946612i	$-0.604481\pi$
$89$	−3.81633e8	−0.644749	−0.322375	+	0.946612i	$0.604481\pi$
$90$	−4.37675e7	−0.0703169
$91$	−2.06178e8	−0.315178
$92$	−2.58023e8	−0.375503
$93$	−9.85643e8	−1.36630
$94$	−5.34765e8	−0.706460
$95$	−2.58449e8	−0.325550
$96$	7.18767e8	0.863709
$97$	−5.93343e8	−0.680507	−0.340254	−	0.940334i	$-0.610513\pi$
$97$	−5.93343e8	−0.680507	−0.340254	+	0.940334i	$0.610513\pi$
$98$	3.56253e8	0.390159
$99$	6.83813e8	0.715449
$100$	3.61909e8	0.361909
$101$	1.22816e8	0.117438	0.0587190	−	0.998275i	$-0.481298\pi$
$101$	1.22816e8	0.117438	0.0587190	+	0.998275i	$0.481298\pi$
$102$	1.53317e9	1.40246
$103$	−1.45390e9	−1.27282	−0.636408	−	0.771353i	$-0.719580\pi$
$103$	−1.45390e9	−1.27282	−0.636408	+	0.771353i	$0.719580\pi$
$104$	5.73927e8	0.481068
$105$	1.86668e8	0.149871
$106$	−1.33319e8	−0.102569
$107$	−1.05553e9	−0.778475	−0.389237	−	0.921138i	$-0.627261\pi$
$107$	−1.05553e9	−0.778475	−0.389237	+	0.921138i	$0.627261\pi$
$108$	−3.11729e8	−0.220481
$109$	−1.48849e9	−1.01001	−0.505006	−	0.863116i	$-0.668510\pi$
$109$	−1.48849e9	−1.01001	−0.505006	+	0.863116i	$0.668510\pi$
$110$	−2.85368e8	−0.185839
$111$	2.76185e9	1.72682
$112$	5.79180e8	0.347802
$113$	−2.40872e9	−1.38974	−0.694869	−	0.719137i	$-0.744538\pi$
$113$	−2.40872e9	−1.38974	−0.694869	+	0.719137i	$0.744538\pi$
$114$	−3.35951e9	−1.86296
$115$	3.22414e8	0.171899
$116$	9.26530e8	0.475115
$117$	4.66640e8	0.230221
$118$	−1.93755e9	−0.919991
$119$	−2.23786e9	−1.02299
$120$	−5.19619e8	−0.228754
$121$	2.10057e9	0.890847
$122$	−3.57541e9	−1.46119
$123$	−1.90297e9	−0.749651
$124$	−1.08746e9	−0.413062
$125$	−9.18014e8	−0.336321
$126$	8.30412e8	0.293512
$127$	1.63138e9	0.556464	0.278232	−	0.960514i	$-0.410252\pi$
$127$	1.63138e9	0.556464	0.278232	+	0.960514i	$0.410252\pi$
$128$	−3.81431e8	−0.125595
$129$	5.91403e8	0.188031
$130$	−1.94738e8	−0.0598005
$131$	−2.34159e9	−0.694690	−0.347345	−	0.937737i	$-0.612917\pi$
$131$	−2.34159e9	−0.694690	−0.347345	+	0.937737i	$0.612917\pi$
$132$	2.20449e9	0.632012
$133$	4.90362e9	1.35889
$134$	4.69029e9	1.25669
$135$	3.89523e8	0.100933
$136$	6.22942e9	1.56143
$137$	4.87195e9	1.18157	0.590786	−	0.806828i	$-0.298818\pi$
$137$	4.87195e9	1.18157	0.590786	+	0.806828i	$0.298818\pi$
$138$	4.19098e9	0.983693
$139$	3.89560e9	0.885131	0.442566	−	0.896736i	$-0.354068\pi$
$139$	3.89560e9	0.885131	0.442566	+	0.896736i	$0.354068\pi$
$140$	2.05951e8	0.0453093
$141$	−5.16205e9	−1.09986
$142$	−1.18076e9	−0.243705
$143$	3.04254e9	0.608448
$144$	−1.31085e9	−0.254052
$145$	−1.15775e9	−0.217500
$146$	7.18875e9	1.30938
$147$	3.43888e9	0.607421
$148$	3.04715e9	0.522055
$149$	3.97719e9	0.661056	0.330528	−	0.943796i	$-0.392773\pi$
$149$	3.97719e9	0.661056	0.330528	+	0.943796i	$0.392773\pi$
$150$	−5.87836e9	−0.948081
$151$	1.04756e9	0.163977	0.0819886	−	0.996633i	$-0.473873\pi$
$151$	1.04756e9	0.163977	0.0819886	+	0.996633i	$0.473873\pi$
$152$	−1.36500e10	−2.07413
$153$	5.06492e9	0.747242
$154$	5.41436e9	0.775718
$155$	1.35884e9	0.189093
$156$	1.50437e9	0.203373
$157$	−6.06273e9	−0.796379	−0.398189	−	0.917303i	$-0.630361\pi$
$157$	−6.06273e9	−0.796379	−0.398189	+	0.917303i	$0.630361\pi$
$158$	−2.20874e9	−0.281961
$159$	−1.28691e9	−0.159684
$160$	−9.90917e8	−0.119536
$161$	−6.11726e9	−0.717530
$162$	8.67561e9	0.989652
$163$	4.36837e9	0.484702	0.242351	−	0.970189i	$-0.422081\pi$
$163$	4.36837e9	0.484702	0.242351	+	0.970189i	$0.422081\pi$
$164$	−2.09955e9	−0.226636
$165$	−2.75463e9	−0.289325
$166$	6.83392e9	0.698528
$167$	−9.06833e9	−0.902200	−0.451100	−	0.892473i	$-0.648968\pi$
$167$	−9.06833e9	−0.902200	−0.451100	+	0.892473i	$0.648968\pi$
$168$	9.85888e9	0.954851
$169$	−8.52824e9	−0.804210
$170$	−2.11369e9	−0.194098
$171$	−1.10983e10	−0.992601
$172$	6.52495e8	0.0568459
$173$	−1.41700e10	−1.20272	−0.601359	−	0.798979i	$-0.705374\pi$
$173$	−1.41700e10	−1.20272	−0.601359	+	0.798979i	$0.705374\pi$
$174$	−1.50493e10	−1.24464
$175$	8.58019e9	0.691554
$176$	−8.54688e9	−0.671430
$177$	−1.87030e10	−1.43229
$178$	6.83906e9	0.510630
$179$	2.05552e10	1.49652	0.748260	−	0.663405i	$-0.230889\pi$
$179$	2.05552e10	1.49652	0.748260	+	0.663405i	$0.230889\pi$
$180$	−4.66127e8	−0.0330962
$181$	−1.98258e10	−1.37302	−0.686511	−	0.727119i	$-0.740859\pi$
$181$	−1.98258e10	−1.37302	−0.686511	+	0.727119i	$0.740859\pi$
$182$	3.69481e9	0.249615
$183$	−3.45131e10	−2.27486
$184$	1.70283e10	1.09519
$185$	−3.80758e9	−0.238988
$186$	1.76632e10	1.08209
$187$	3.30238e10	1.97487
$188$	−5.69528e9	−0.332510
$189$	−7.39053e9	−0.421306
$190$	4.63154e9	0.257830
$191$	−1.93769e10	−1.05350	−0.526750	−	0.850020i	$-0.676590\pi$
$191$	−1.93769e10	−1.05350	−0.526750	+	0.850020i	$0.676590\pi$
$192$	−2.42175e10	−1.28610
$193$	2.44314e10	1.26748	0.633740	−	0.773546i	$-0.281519\pi$
$193$	2.44314e10	1.26748	0.633740	+	0.773546i	$0.281519\pi$
$194$	1.06330e10	0.538950
$195$	−1.87979e9	−0.0931008
$196$	3.79412e9	0.183636
$197$	−1.22473e10	−0.579354	−0.289677	−	0.957124i	$-0.593548\pi$
$197$	−1.22473e10	−0.579354	−0.289677	+	0.957124i	$0.593548\pi$
$198$	−1.22543e10	−0.566623
$199$	−2.12982e10	−0.962731	−0.481366	−	0.876520i	$-0.659859\pi$
$199$	−2.12982e10	−0.962731	−0.481366	+	0.876520i	$0.659859\pi$
$200$	−2.38843e10	−1.05555
$201$	4.52751e10	1.95649
$202$	−2.20092e9	−0.0930088
$203$	2.19663e10	0.907873
$204$	1.63284e10	0.660098
$205$	2.62350e9	0.103750
$206$	2.60546e10	1.00805
$207$	1.38451e10	0.524120
$208$	−5.83247e9	−0.216057
$209$	−7.23620e10	−2.62333
$210$	−3.34519e9	−0.118695
$211$	−3.57352e10	−1.24115	−0.620576	−	0.784146i	$-0.713101\pi$
$211$	−3.57352e10	−1.24115	−0.620576	+	0.784146i	$0.713101\pi$
$212$	−1.41985e9	−0.0482761
$213$	−1.13978e10	−0.379413
$214$	1.89157e10	0.616538
$215$	−8.15329e8	−0.0260231
$216$	2.05727e10	0.643056
$217$	−2.57817e10	−0.789301
$218$	2.66745e10	0.799912
$219$	6.93925e10	2.03851
$220$	−3.03919e9	−0.0874692
$221$	2.25357e10	0.635487
$222$	−4.94938e10	−1.36761
$223$	1.10106e10	0.298153	0.149076	−	0.988826i	$-0.452370\pi$
$223$	1.10106e10	0.298153	0.149076	+	0.988826i	$0.452370\pi$
$224$	1.88009e10	0.498958
$225$	−1.94195e10	−0.505145
$226$	4.31655e10	1.10065
$227$	1.50858e10	0.377096	0.188548	−	0.982064i	$-0.439622\pi$
$227$	1.50858e10	0.377096	0.188548	+	0.982064i	$0.439622\pi$
$228$	−3.57790e10	−0.876843
$229$	1.14580e10	0.275327	0.137664	−	0.990479i	$-0.456041\pi$
$229$	1.14580e10	0.275327	0.137664	+	0.990479i	$0.456041\pi$
$230$	−5.77783e9	−0.136141
$231$	5.22644e10	1.20768
$232$	−6.11466e10	−1.38572
$233$	−1.02658e10	−0.228187	−0.114094	−	0.993470i	$-0.536396\pi$
$233$	−1.02658e10	−0.228187	−0.114094	+	0.993470i	$0.536396\pi$
$234$	−8.36244e9	−0.182331
$235$	7.11658e9	0.152218
$236$	−2.06350e10	−0.433013
$237$	−2.13208e10	−0.438972
$238$	4.01036e10	0.810190
$239$	3.71284e10	0.736064	0.368032	−	0.929813i	$-0.380032\pi$
$239$	3.71284e10	0.736064	0.368032	+	0.929813i	$0.380032\pi$
$240$	5.28057e9	0.102738
$241$	4.83626e10	0.923492	0.461746	−	0.887012i	$-0.347223\pi$
$241$	4.83626e10	0.923492	0.461746	+	0.887012i	$0.347223\pi$
$242$	−3.76433e10	−0.705536
$243$	5.15962e10	0.949269
$244$	−3.80783e10	−0.687739
$245$	−4.74096e9	−0.0840658
$246$	3.41022e10	0.593710
$247$	−4.93806e10	−0.844150
$248$	7.17672e10	1.20474
$249$	6.59673e10	1.08751
$250$	1.64513e10	0.266360
$251$	3.34140e10	0.531369	0.265684	−	0.964060i	$-0.414402\pi$
$251$	3.34140e10	0.531369	0.265684	+	0.964060i	$0.414402\pi$
$252$	8.84395e9	0.138148
$253$	9.02715e10	1.38519
$254$	−2.92351e10	−0.440710
$255$	−2.04033e10	−0.302182
$256$	−6.48432e10	−0.943593
$257$	−8.20412e10	−1.17309	−0.586547	−	0.809915i	$-0.699513\pi$
$257$	−8.20412e10	−1.17309	−0.586547	+	0.809915i	$0.699513\pi$
$258$	−1.05983e10	−0.148917
$259$	7.22423e10	0.997569
$260$	−2.07397e9	−0.0281464
$261$	−4.97162e10	−0.663156
$262$	4.19626e10	0.550182
$263$	4.19397e10	0.540536	0.270268	−	0.962785i	$-0.412888\pi$
$263$	4.19397e10	0.540536	0.270268	+	0.962785i	$0.412888\pi$
$264$	−1.45486e11	−1.84333
$265$	1.77418e9	0.0221000
$266$	−8.78754e10	−1.07622
$267$	6.60170e10	0.794977
$268$	4.99520e10	0.591488
$269$	1.06374e11	1.23866	0.619328	−	0.785132i	$-0.287405\pi$
$269$	1.06374e11	1.23866	0.619328	+	0.785132i	$0.287405\pi$
$270$	−6.98046e9	−0.0799368
$271$	−8.12651e10	−0.915255	−0.457628	−	0.889144i	$-0.651301\pi$
$271$	−8.12651e10	−0.915255	−0.457628	+	0.889144i	$0.651301\pi$
$272$	−6.33058e10	−0.701267
$273$	3.56658e10	0.388615
$274$	−8.73079e10	−0.935785
$275$	−1.26617e11	−1.33504
$276$	4.46343e10	0.462996
$277$	2.01089e10	0.205225	0.102612	−	0.994721i	$-0.467280\pi$
$277$	2.01089e10	0.205225	0.102612	+	0.994721i	$0.467280\pi$
$278$	−6.98112e10	−0.701009
$279$	5.83514e10	0.576544
$280$	−1.35918e10	−0.132149
$281$	−1.16967e11	−1.11914	−0.559572	−	0.828782i	$-0.689035\pi$
$281$	−1.16967e11	−1.11914	−0.559572	+	0.828782i	$0.689035\pi$
$282$	9.25066e10	0.871067
$283$	−9.10743e10	−0.844028	−0.422014	−	0.906589i	$-0.638677\pi$
$283$	−9.10743e10	−0.844028	−0.422014	+	0.906589i	$0.638677\pi$
$284$	−1.25752e10	−0.114705
$285$	4.47079e10	0.401404
$286$	−5.45238e10	−0.481880
$287$	−4.97764e10	−0.433067
$288$	−4.25520e10	−0.364463
$289$	1.26015e11	1.06263
$290$	2.07475e10	0.172256
$291$	1.02640e11	0.839067
$292$	7.65607e10	0.616287
$293$	−7.51554e10	−0.595739	−0.297869	−	0.954607i	$-0.596276\pi$
$293$	−7.51554e10	−0.595739	−0.297869	+	0.954607i	$0.596276\pi$
$294$	−6.16266e10	−0.481067
$295$	2.57846e10	0.198226
$296$	−2.01098e11	−1.52263
$297$	1.09061e11	0.813328
$298$	−7.12733e10	−0.523545
$299$	6.16021e10	0.445734
$300$	−6.26049e10	−0.446234
$301$	1.54695e10	0.108624
$302$	−1.87729e10	−0.129867
$303$	−2.12454e10	−0.144801
$304$	1.38716e11	0.931530
$305$	4.75810e10	0.314836
$306$	−9.07661e10	−0.591803
$307$	2.57354e10	0.165352	0.0826759	−	0.996576i	$-0.473653\pi$
$307$	2.57354e10	0.165352	0.0826759	+	0.996576i	$0.473653\pi$
$308$	5.76634e10	0.365108
$309$	2.51503e11	1.56939
$310$	−2.43511e10	−0.149759
$311$	5.97715e10	0.362304	0.181152	−	0.983455i	$-0.442017\pi$
$311$	5.97715e10	0.362304	0.181152	+	0.983455i	$0.442017\pi$
$312$	−9.92811e10	−0.593159
$313$	−6.89838e10	−0.406254	−0.203127	−	0.979152i	$-0.565110\pi$
$313$	−6.89838e10	−0.406254	−0.203127	+	0.979152i	$0.565110\pi$
$314$	1.08647e11	0.630718
$315$	−1.10510e10	−0.0632418
$316$	−2.35233e10	−0.132711
$317$	−3.11421e11	−1.73213	−0.866067	−	0.499928i	$-0.833360\pi$
$317$	−3.11421e11	−1.73213	−0.866067	+	0.499928i	$0.833360\pi$
$318$	2.30622e10	0.126467
$319$	−3.24154e11	−1.75264
$320$	3.33871e10	0.177993
$321$	1.82592e11	0.959861
$322$	1.09624e11	0.568271
$323$	−5.35978e11	−2.73990
$324$	9.23959e10	0.465801
$325$	−8.64045e10	−0.429597
$326$	−7.82835e10	−0.383876
$327$	2.57487e11	1.24535
$328$	1.38560e11	0.661007
$329$	−1.35025e11	−0.635378
$330$	4.93645e10	0.229140
$331$	−1.00401e11	−0.459738	−0.229869	−	0.973222i	$-0.573830\pi$
$331$	−1.00401e11	−0.459738	−0.229869	+	0.973222i	$0.573830\pi$
$332$	7.27818e10	0.328777
$333$	−1.63505e11	−0.728674
$334$	1.62509e11	0.714527
$335$	−6.24178e10	−0.270774
$336$	−1.00190e11	−0.428841
$337$	−3.46652e11	−1.46406	−0.732030	−	0.681273i	$-0.761427\pi$
$337$	−3.46652e11	−1.46406	−0.732030	+	0.681273i	$0.761427\pi$
$338$	1.52831e11	0.636920
$339$	4.16673e11	1.71355
$340$	−2.25109e10	−0.0913562
$341$	3.80457e11	1.52374
$342$	1.98888e11	0.786123
$343$	2.72544e11	1.06320
$344$	−4.30616e10	−0.165797
$345$	−5.57730e10	−0.211952
$346$	2.53935e11	0.952531
$347$	4.59014e10	0.169959	0.0849794	−	0.996383i	$-0.472918\pi$
$347$	4.59014e10	0.169959	0.0849794	+	0.996383i	$0.472918\pi$
$348$	−1.60276e11	−0.585818
$349$	−5.52760e11	−1.99445	−0.997224	−	0.0744645i	$-0.976275\pi$
$349$	−5.52760e11	−1.99445	−0.997224	+	0.0744645i	$0.976275\pi$
$350$	−1.53762e11	−0.547698
$351$	7.44243e10	0.261718
$352$	−2.77443e11	−0.963234
$353$	−3.24055e11	−1.11079	−0.555395	−	0.831586i	$-0.687433\pi$
$353$	−3.24055e11	−1.11079	−0.555395	+	0.831586i	$0.687433\pi$
$354$	3.35168e11	1.13435
$355$	1.57134e10	0.0525100
$356$	7.28365e10	0.240339
$357$	3.87117e11	1.26135
$358$	−3.68360e11	−1.18522
$359$	2.90617e11	0.923413	0.461707	−	0.887033i	$-0.347237\pi$
$359$	2.90617e11	0.923413	0.461707	+	0.887033i	$0.347237\pi$
$360$	3.07622e10	0.0965285
$361$	8.51753e11	2.63956
$362$	3.55289e11	1.08741
$363$	−3.63368e11	−1.09842
$364$	3.93500e10	0.117487
$365$	−9.56668e10	−0.282126
$366$	6.18493e11	1.80165
$367$	−1.08398e11	−0.311906	−0.155953	−	0.987764i	$-0.549845\pi$
$367$	−1.08398e11	−0.311906	−0.155953	+	0.987764i	$0.549845\pi$
$368$	−1.73048e11	−0.491872
$369$	1.12658e11	0.316334
$370$	6.82339e10	0.189275
$371$	−3.36621e10	−0.0922483
$372$	1.88115e11	0.509307
$373$	−4.17071e11	−1.11563	−0.557815	−	0.829965i	$-0.688360\pi$
$373$	−4.17071e11	−1.11563	−0.557815	+	0.829965i	$0.688360\pi$
$374$	−5.91803e11	−1.56407
$375$	1.58803e11	0.414685
$376$	3.75862e11	0.969802
$377$	−2.21206e11	−0.563976
$378$	1.32442e11	0.333667
$379$	−2.63908e11	−0.657015	−0.328508	−	0.944501i	$-0.606546\pi$
$379$	−2.63908e11	−0.657015	−0.328508	+	0.944501i	$0.606546\pi$
$380$	4.93262e10	0.121353
$381$	−2.82204e11	−0.686122
$382$	3.47245e11	0.834354
$383$	8.16196e11	1.93821	0.969103	−	0.246658i	$-0.0793325\pi$
$383$	8.16196e11	1.93821	0.969103	+	0.246658i	$0.0793325\pi$
$384$	6.59820e10	0.154858
$385$	−7.20536e10	−0.167141
$386$	−4.37824e11	−1.00382
$387$	−3.50119e10	−0.0793444
$388$	1.13242e11	0.253668
$389$	6.95765e11	1.54060	0.770299	−	0.637683i	$-0.220107\pi$
$389$	6.95765e11	1.54060	0.770299	+	0.637683i	$0.220107\pi$
$390$	3.36868e10	0.0737342
$391$	6.68631e11	1.44674
$392$	−2.50394e11	−0.535595
$393$	4.05062e11	0.856554
$394$	2.19479e11	0.458838
$395$	2.93937e10	0.0607528
$396$	−1.30509e11	−0.266693
$397$	2.39129e10	0.0483143	0.0241571	−	0.999708i	$-0.492310\pi$
$397$	2.39129e10	0.0483143	0.0241571	+	0.999708i	$0.492310\pi$
$398$	3.81676e11	0.762466
$399$	−8.48255e11	−1.67552
$400$	2.42721e11	0.474065
$401$	−1.31846e11	−0.254634	−0.127317	−	0.991862i	$-0.540637\pi$
$401$	−1.31846e11	−0.254634	−0.127317	+	0.991862i	$0.540637\pi$
$402$	−8.11353e11	−1.54950
$403$	2.59627e11	0.490318
$404$	−2.34400e10	−0.0437766
$405$	−1.15454e11	−0.213236
$406$	−3.93648e11	−0.719020
$407$	−1.06607e12	−1.92580
$408$	−1.07760e12	−1.92525
$409$	2.22821e11	0.393732	0.196866	−	0.980430i	$-0.436924\pi$
$409$	2.22821e11	0.393732	0.196866	+	0.980430i	$0.436924\pi$
$410$	−4.70145e10	−0.0821683
$411$	−8.42777e11	−1.45688
$412$	2.77483e11	0.474459
$413$	−4.89219e11	−0.827423
$414$	−2.48112e11	−0.415094
$415$	−9.09449e10	−0.150509
$416$	−1.89330e11	−0.309955
$417$	−6.73882e11	−1.09137
$418$	1.29677e12	2.07763
$419$	−8.93132e11	−1.41564	−0.707820	−	0.706393i	$-0.750321\pi$
$419$	−8.93132e11	−1.41564	−0.707820	+	0.706393i	$0.750321\pi$
$420$	−3.56265e10	−0.0558665
$421$	4.93105e11	0.765014	0.382507	−	0.923953i	$-0.375061\pi$
$421$	4.93105e11	0.765014	0.382507	+	0.923953i	$0.375061\pi$
$422$	6.40393e11	0.982971
$423$	3.05600e11	0.464111
$424$	9.37036e10	0.140802
$425$	−9.37836e11	−1.39437
$426$	2.04254e11	0.300489
$427$	−9.02768e11	−1.31417
$428$	2.01453e11	0.290187
$429$	−5.26315e11	−0.750218
$430$	1.46111e10	0.0206099
$431$	1.09242e12	1.52490	0.762449	−	0.647048i	$-0.223997\pi$
$431$	1.09242e12	1.52490	0.762449	+	0.647048i	$0.223997\pi$
$432$	−2.09068e11	−0.288808
$433$	−6.73980e11	−0.921406	−0.460703	−	0.887554i	$-0.652403\pi$
$433$	−6.73980e11	−0.921406	−0.460703	+	0.887554i	$0.652403\pi$
$434$	4.62021e11	0.625112
$435$	2.00274e11	0.268178
$436$	2.84085e11	0.376495
$437$	−1.46511e12	−1.92178
$438$	−1.24355e12	−1.61447
$439$	2.78225e11	0.357524	0.178762	−	0.983892i	$-0.442791\pi$
$439$	2.78225e11	0.357524	0.178762	+	0.983892i	$0.442791\pi$
$440$	2.00572e11	0.255114
$441$	−2.03587e11	−0.256316
$442$	−4.03852e11	−0.503294
$443$	3.25574e11	0.401636	0.200818	−	0.979629i	$-0.435640\pi$
$443$	3.25574e11	0.401636	0.200818	+	0.979629i	$0.435640\pi$
$444$	−5.27113e11	−0.643695
$445$	−9.10133e10	−0.110023
$446$	−1.97316e11	−0.236132
$447$	−6.87996e11	−0.815083
$448$	−6.33463e11	−0.742968
$449$	9.27680e11	1.07718	0.538592	−	0.842567i	$-0.318956\pi$
$449$	9.27680e11	1.07718	0.538592	+	0.842567i	$0.318956\pi$
$450$	3.48007e11	0.400066
$451$	7.34544e11	0.836032
$452$	4.59715e11	0.518043
$453$	−1.81213e11	−0.202184
$454$	−2.70346e11	−0.298654
$455$	−4.91700e10	−0.0537835
$456$	2.36125e12	2.55741
$457$	1.08416e12	1.16271	0.581355	−	0.813650i	$-0.302523\pi$
$457$	1.08416e12	1.16271	0.581355	+	0.813650i	$0.302523\pi$
$458$	−2.05333e11	−0.218055
$459$	8.07803e11	0.849471
$460$	−6.15343e10	−0.0640777
$461$	5.03578e11	0.519293	0.259647	−	0.965704i	$-0.416394\pi$
$461$	5.03578e11	0.519293	0.259647	+	0.965704i	$0.416394\pi$
$462$	−9.36606e11	−0.956463
$463$	−1.27085e12	−1.28523	−0.642613	−	0.766191i	$-0.722150\pi$
$463$	−1.27085e12	−1.28523	−0.642613	+	0.766191i	$0.722150\pi$
$464$	6.21396e11	0.622354
$465$	−2.35060e11	−0.233153
$466$	1.83968e11	0.180720
$467$	1.68815e12	1.64243	0.821214	−	0.570621i	$-0.193297\pi$
$467$	1.68815e12	1.64243	0.821214	+	0.570621i	$0.193297\pi$
$468$	−8.90606e10	−0.0858181
$469$	1.18427e12	1.13025
$470$	−1.27533e11	−0.120554
$471$	1.04876e12	0.981937
$472$	1.36181e12	1.26293
$473$	−2.28281e11	−0.209698
$474$	3.82081e11	0.347658
$475$	2.05500e12	1.85221
$476$	4.27106e11	0.381333
$477$	7.61871e10	0.0673828
$478$	−6.65360e11	−0.582950
$479$	−1.34770e12	−1.16972	−0.584862	−	0.811133i	$-0.698851\pi$
$479$	−1.34770e12	−1.16972	−0.584862	+	0.811133i	$0.698851\pi$
$480$	1.71414e11	0.147388
$481$	−7.27496e11	−0.619695
$482$	−8.66684e11	−0.731390
$483$	1.05820e12	0.884717
$484$	−4.00904e11	−0.332075
$485$	−1.41503e11	−0.116125
$486$	−9.24631e11	−0.751805
$487$	4.15547e11	0.334765	0.167382	−	0.985892i	$-0.446469\pi$
$487$	4.15547e11	0.334765	0.167382	+	0.985892i	$0.446469\pi$
$488$	2.51299e12	2.00587
$489$	−7.55665e11	−0.597640
$490$	8.49606e10	0.0665787
$491$	2.51440e11	0.195239	0.0976197	−	0.995224i	$-0.468877\pi$
$491$	2.51440e11	0.195239	0.0976197	+	0.995224i	$0.468877\pi$
$492$	3.63191e11	0.279442
$493$	−2.40097e12	−1.83053
$494$	8.84925e11	0.668552
$495$	1.63078e11	0.122088
$496$	−7.29327e11	−0.541072
$497$	−2.98134e11	−0.219184
$498$	−1.18217e12	−0.861286
$499$	−1.18872e12	−0.858273	−0.429137	−	0.903240i	$-0.641182\pi$
$499$	−1.18872e12	−0.858273	−0.429137	+	0.903240i	$0.641182\pi$
$500$	1.75207e11	0.125368
$501$	1.56869e12	1.11242
$502$	−5.98796e11	−0.420835
$503$	−2.74830e10	−0.0191430	−0.00957148	−	0.999954i	$-0.503047\pi$
$503$	−2.74830e10	−0.0191430	−0.00957148	+	0.999954i	$0.503047\pi$
$504$	−5.83659e11	−0.402923
$505$	2.92896e10	0.0200402
$506$	−1.61771e12	−1.09704
$507$	1.47526e12	0.991593
$508$	−3.11356e11	−0.207430
$509$	−2.56804e12	−1.69579	−0.847894	−	0.530165i	$-0.822130\pi$
$509$	−2.56804e12	−1.69579	−0.847894	+	0.530165i	$0.822130\pi$
$510$	3.65637e11	0.239323
$511$	1.81511e12	1.17763
$512$	1.35732e12	0.872904
$513$	−1.77007e12	−1.12840
$514$	1.47022e12	0.929070
$515$	−3.46730e11	−0.217200
$516$	−1.12872e11	−0.0700911
$517$	1.99254e12	1.22659
$518$	−1.29462e12	−0.790057
$519$	2.45121e12	1.48295
$520$	1.36872e11	0.0820920
$521$	−5.58805e11	−0.332269	−0.166135	−	0.986103i	$-0.553129\pi$
$521$	−5.58805e11	−0.332269	−0.166135	+	0.986103i	$0.553129\pi$
$522$	8.90940e11	0.525208
$523$	−1.74645e12	−1.02070	−0.510350	−	0.859967i	$-0.670484\pi$
$523$	−1.74645e12	−1.02070	−0.510350	+	0.859967i	$0.670484\pi$
$524$	4.46905e11	0.258955
$525$	−1.48425e12	−0.852687
$526$	−7.51581e11	−0.428095
$527$	2.81800e12	1.59145
$528$	1.47849e12	0.827875
$529$	2.65711e10	0.0147523
$530$	−3.17943e10	−0.0175028
$531$	1.10724e12	0.604391
$532$	−9.35880e11	−0.506545
$533$	5.01260e11	0.269024
$534$	−1.18306e12	−0.629608
$535$	−2.51727e11	−0.132843
$536$	−3.29660e12	−1.72514
$537$	−3.55575e12	−1.84521
$538$	−1.90628e12	−0.980994
$539$	−1.32740e12	−0.677413
$540$	−7.43424e10	−0.0376240
$541$	1.23556e12	0.620122	0.310061	−	0.950717i	$-0.399650\pi$
$541$	1.23556e12	0.620122	0.310061	+	0.950717i	$0.399650\pi$
$542$	1.45631e12	0.724866
$543$	3.42958e12	1.69294
$544$	−2.05499e12	−1.00604
$545$	−3.54981e11	−0.172354
$546$	−6.39149e11	−0.307776
$547$	−1.66722e11	−0.0796251	−0.0398126	−	0.999207i	$-0.512676\pi$
$547$	−1.66722e11	−0.0796251	−0.0398126	+	0.999207i	$0.512676\pi$
$548$	−9.29835e11	−0.440447
$549$	2.04323e12	0.959933
$550$	2.26904e12	1.05733
$551$	5.26104e12	2.43158
$552$	−2.94565e12	−1.35038
$553$	−5.57694e11	−0.253590
$554$	−3.60362e11	−0.162534
$555$	6.58656e11	0.294673
$556$	−7.43494e11	−0.329945
$557$	5.10355e11	0.224659	0.112330	−	0.993671i	$-0.464169\pi$
$557$	5.10355e11	0.224659	0.112330	+	0.993671i	$0.464169\pi$
$558$	−1.04569e12	−0.456613
$559$	−1.55781e11	−0.0674778
$560$	1.38125e11	0.0593508
$561$	−5.71263e12	−2.43502
$562$	2.09612e12	0.886343
$563$	6.39701e11	0.268342	0.134171	−	0.990958i	$-0.457163\pi$
$563$	6.39701e11	0.268342	0.134171	+	0.990958i	$0.457163\pi$
$564$	9.85202e11	0.409986
$565$	−5.74440e11	−0.237152
$566$	1.63210e12	0.668456
$567$	2.19054e12	0.890076
$568$	8.29903e11	0.334549
$569$	2.50583e12	1.00218	0.501090	−	0.865395i	$-0.332933\pi$
$569$	2.50583e12	1.00218	0.501090	+	0.865395i	$0.332933\pi$
$570$	−8.01189e11	−0.317905
$571$	−2.06826e12	−0.814220	−0.407110	−	0.913379i	$-0.633463\pi$
$571$	−2.06826e12	−0.814220	−0.407110	+	0.913379i	$0.633463\pi$
$572$	−5.80683e11	−0.226807
$573$	3.35193e12	1.29897
$574$	8.92019e11	0.342982
$575$	−2.56360e12	−0.978015
$576$	1.43371e12	0.542701
$577$	−1.61115e12	−0.605124	−0.302562	−	0.953130i	$-0.597842\pi$
$577$	−1.61115e12	−0.605124	−0.302562	+	0.953130i	$0.597842\pi$
$578$	−2.25826e12	−0.841587
$579$	−4.22629e12	−1.56281
$580$	2.20962e11	0.0810760
$581$	1.72552e12	0.628243
$582$	−1.83936e12	−0.664527
$583$	4.96747e11	0.178085
$584$	−5.05265e12	−1.79747
$585$	1.11286e11	0.0392862
$586$	1.34682e12	0.471815
$587$	2.54415e12	0.884446	0.442223	−	0.896905i	$-0.354190\pi$
$587$	2.54415e12	0.884446	0.442223	+	0.896905i	$0.354190\pi$
$588$	−6.56328e11	−0.226424
$589$	−6.17484e12	−2.11401
$590$	−4.62074e11	−0.156992
$591$	2.11861e12	0.714345
$592$	2.04363e12	0.683841
$593$	1.32235e11	0.0439137	0.0219569	−	0.999759i	$-0.493010\pi$
$593$	1.32235e11	0.0439137	0.0219569	+	0.999759i	$0.493010\pi$
$594$	−1.95443e12	−0.644142
$595$	−5.33693e11	−0.174568
$596$	−7.59066e11	−0.246417
$597$	3.68429e12	1.18705
$598$	−1.10394e12	−0.353013
$599$	2.32737e12	0.738660	0.369330	−	0.929298i	$-0.379587\pi$
$599$	2.32737e12	0.738660	0.369330	+	0.929298i	$0.379587\pi$
$600$	4.13163e12	1.30149
$601$	−5.87945e12	−1.83824	−0.919119	−	0.393981i	$-0.871098\pi$
$601$	−5.87945e12	−1.83824	−0.919119	+	0.393981i	$0.871098\pi$
$602$	−2.77221e11	−0.0860284
$603$	−2.68035e12	−0.825588
$604$	−1.99932e11	−0.0611247
$605$	5.00952e11	0.152019
$606$	3.80728e11	0.114680
$607$	−2.28556e12	−0.683351	−0.341675	−	0.939818i	$-0.610994\pi$
$607$	−2.28556e12	−0.683351	−0.341675	+	0.939818i	$0.610994\pi$
$608$	4.50292e12	1.33637
$609$	−3.79986e12	−1.11941
$610$	−8.52676e11	−0.249345
$611$	1.35973e12	0.394700
$612$	−9.66665e11	−0.278545
$613$	−2.72675e12	−0.779960	−0.389980	−	0.920823i	$-0.627518\pi$
$613$	−2.72675e12	−0.779960	−0.389980	+	0.920823i	$0.627518\pi$
$614$	−4.61192e11	−0.130956
$615$	−4.53828e11	−0.127924
$616$	−3.80551e12	−1.06488
$617$	1.68755e12	0.468784	0.234392	−	0.972142i	$-0.424690\pi$
$617$	1.68755e12	0.468784	0.234392	+	0.972142i	$0.424690\pi$
$618$	−4.50706e12	−1.24293
$619$	−5.29229e12	−1.44889	−0.724445	−	0.689332i	$-0.757904\pi$
$619$	−5.29229e12	−1.44889	−0.724445	+	0.689332i	$0.757904\pi$
$620$	−2.59341e11	−0.0704871
$621$	2.20816e12	0.595823
$622$	−1.07114e12	−0.286938
$623$	1.72682e12	0.459252
$624$	1.00893e12	0.266399
$625$	3.48468e12	0.913489
$626$	1.23623e12	0.321746
$627$	1.25176e13	3.23457
$628$	1.15710e12	0.296861
$629$	−7.89626e12	−2.01138
$630$	1.98040e11	0.0500864
$631$	−2.78836e12	−0.700191	−0.350095	−	0.936714i	$-0.613851\pi$
$631$	−2.78836e12	−0.700191	−0.350095	+	0.936714i	$0.613851\pi$
$632$	1.55243e12	0.387065
$633$	6.18167e12	1.53034
$634$	5.58083e12	1.37182
$635$	3.89057e11	0.0949579
$636$	2.45614e11	0.0595245
$637$	−9.05833e11	−0.217982
$638$	5.80901e12	1.38806
$639$	6.74765e11	0.160103
$640$	−9.09650e10	−0.0214321
$641$	5.16942e12	1.20943	0.604715	−	0.796442i	$-0.293287\pi$
$641$	5.16942e12	1.20943	0.604715	+	0.796442i	$0.293287\pi$
$642$	−3.27214e12	−0.760194
$643$	−3.58293e12	−0.826589	−0.413294	−	0.910598i	$-0.635622\pi$
$643$	−3.58293e12	−0.826589	−0.413294	+	0.910598i	$0.635622\pi$
$644$	1.16751e12	0.267469
$645$	1.41040e11	0.0320866
$646$	9.60500e12	2.16996
$647$	3.89598e12	0.874074	0.437037	−	0.899444i	$-0.356028\pi$
$647$	3.89598e12	0.874074	0.437037	+	0.899444i	$0.356028\pi$
$648$	−6.09770e12	−1.35856
$649$	7.21933e12	1.59733
$650$	1.54841e12	0.340233
$651$	4.45986e12	0.973210
$652$	−8.33725e11	−0.180679
$653$	−6.62700e10	−0.0142629	−0.00713145	−	0.999975i	$-0.502270\pi$
$653$	−6.62700e10	−0.0142629	−0.00713145	+	0.999975i	$0.502270\pi$
$654$	−4.61430e12	−0.986294
$655$	−5.58432e11	−0.118545
$656$	−1.40810e12	−0.296871
$657$	−4.10813e12	−0.860201
$658$	2.41971e12	0.503208
$659$	1.84962e12	0.382030	0.191015	−	0.981587i	$-0.438822\pi$
$659$	1.84962e12	0.382030	0.191015	+	0.981587i	$0.438822\pi$
$660$	5.25735e11	0.107850
$661$	−3.74337e12	−0.762705	−0.381352	−	0.924430i	$-0.624542\pi$
$661$	−3.74337e12	−0.762705	−0.381352	+	0.924430i	$0.624542\pi$
$662$	1.79923e12	0.364104
$663$	−3.89835e12	−0.783557
$664$	−4.80325e12	−0.958913
$665$	1.16943e12	0.231888
$666$	2.93010e12	0.577097
$667$	−6.56314e12	−1.28394
$668$	1.73073e12	0.336307
$669$	−1.90467e12	−0.367623
$670$	1.11856e12	0.214448
$671$	1.33220e13	2.53699
$672$	−3.25229e12	−0.615216
$673$	2.59774e12	0.488122	0.244061	−	0.969760i	$-0.421520\pi$
$673$	2.59774e12	0.488122	0.244061	+	0.969760i	$0.421520\pi$
$674$	6.21218e12	1.15951
$675$	−3.09721e12	−0.574253
$676$	1.62766e12	0.299780
$677$	−7.57984e12	−1.38679	−0.693396	−	0.720557i	$-0.743886\pi$
$677$	−7.57984e12	−1.38679	−0.693396	+	0.720557i	$0.743886\pi$
$678$	−7.46700e12	−1.35710
$679$	2.68477e12	0.484722
$680$	1.48562e12	0.266450
$681$	−2.60963e12	−0.464961
$682$	−6.81798e12	−1.20677
$683$	−9.09946e12	−1.60001	−0.800004	−	0.599994i	$-0.795170\pi$
$683$	−9.09946e12	−1.60001	−0.800004	+	0.599994i	$0.795170\pi$
$684$	2.11817e12	0.370005
$685$	1.16188e12	0.201630
$686$	−4.88414e12	−0.842034
$687$	−1.98207e12	−0.339479
$688$	4.37609e11	0.0744626
$689$	3.38985e11	0.0573052
$690$	9.99481e11	0.167862
$691$	1.40526e10	0.00234480	0.00117240	−	0.999999i	$-0.499627\pi$
$691$	1.40526e10	0.00234480	0.00117240	+	0.999999i	$0.499627\pi$
$692$	2.70442e12	0.448329
$693$	−3.09413e12	−0.509611
$694$	−8.22578e11	−0.134604
$695$	9.29037e11	0.151043
$696$	1.05775e13	1.70860
$697$	5.44068e12	0.873184
$698$	9.90576e12	1.57957
$699$	1.77583e12	0.281355
$700$	−1.63757e12	−0.257786
$701$	−9.00853e12	−1.40904	−0.704519	−	0.709685i	$-0.748837\pi$
$701$	−9.00853e12	−1.40904	−0.704519	+	0.709685i	$0.748837\pi$
$702$	−1.33372e12	−0.207276
$703$	1.73024e13	2.67182
$704$	9.34793e12	1.43429
$705$	−1.23106e12	−0.187685
$706$	5.80723e12	0.879727
$707$	−5.55720e11	−0.0836505
$708$	3.56956e12	0.533906
$709$	−1.15494e13	−1.71653	−0.858264	−	0.513209i	$-0.828457\pi$
$709$	−1.15494e13	−1.71653	−0.858264	+	0.513209i	$0.828457\pi$
$710$	−2.81592e11	−0.0415870
$711$	1.26222e12	0.185235
$712$	−4.80687e12	−0.700974
$713$	7.70309e12	1.11625
$714$	−6.93734e12	−0.998966
$715$	7.25596e11	0.103829
$716$	−3.92306e12	−0.557848
$717$	−6.42268e12	−0.907569
$718$	−5.20801e12	−0.731327
$719$	−2.80308e12	−0.391161	−0.195580	−	0.980688i	$-0.562659\pi$
$719$	−2.80308e12	−0.391161	−0.195580	+	0.980688i	$0.562659\pi$
$720$	−3.12617e11	−0.0433528
$721$	6.57861e12	0.906621
$722$	−1.52639e13	−2.09048
$723$	−8.36603e12	−1.13867
$724$	3.78386e12	0.511813
$725$	9.20559e12	1.23746
$726$	6.51175e12	0.869927
$727$	−5.45780e12	−0.724625	−0.362312	−	0.932057i	$-0.618013\pi$
$727$	−5.45780e12	−0.724625	−0.362312	+	0.932057i	$0.618013\pi$
$728$	−2.59692e12	−0.342663
$729$	6.03463e11	0.0791366
$730$	1.71440e12	0.223439
$731$	−1.69085e12	−0.219016
$732$	6.58700e12	0.847984
$733$	−3.95238e12	−0.505697	−0.252849	−	0.967506i	$-0.581367\pi$
$733$	−3.95238e12	−0.505697	−0.252849	+	0.967506i	$0.581367\pi$
$734$	1.94255e12	0.247024
$735$	8.20118e11	0.103653
$736$	−5.61738e12	−0.705640
$737$	−1.74761e13	−2.18193
$738$	−2.01890e12	−0.250531
$739$	2.12821e11	0.0262491	0.0131246	−	0.999914i	$-0.495822\pi$
$739$	2.12821e11	0.0262491	0.0131246	+	0.999914i	$0.495822\pi$
$740$	7.26696e11	0.0890861
$741$	8.54212e12	1.04084
$742$	6.03242e11	0.0730591
$743$	−4.10800e12	−0.494516	−0.247258	−	0.968950i	$-0.579530\pi$
$743$	−4.10800e12	−0.494516	−0.247258	+	0.968950i	$0.579530\pi$
$744$	−1.24147e13	−1.48545
$745$	9.48495e11	0.112806
$746$	7.47413e12	0.883560
$747$	−3.90536e12	−0.458900
$748$	−6.30274e12	−0.736161
$749$	4.77609e12	0.554504
$750$	−2.84583e12	−0.328423
$751$	5.19165e12	0.595560	0.297780	−	0.954634i	$-0.403754\pi$
$751$	5.19165e12	0.595560	0.297780	+	0.954634i	$0.403754\pi$
$752$	−3.81966e12	−0.435556
$753$	−5.78013e12	−0.655179
$754$	3.96412e12	0.446659
$755$	2.49826e11	0.0279819
$756$	1.41052e12	0.157047
$757$	−1.20035e13	−1.32854	−0.664272	−	0.747491i	$-0.731258\pi$
$757$	−1.20035e13	−1.32854	−0.664272	+	0.747491i	$0.731258\pi$
$758$	4.72936e12	0.520345
$759$	−1.56157e13	−1.70794
$760$	−3.25530e12	−0.353940
$761$	−1.27185e12	−0.137469	−0.0687345	−	0.997635i	$-0.521896\pi$
$761$	−1.27185e12	−0.137469	−0.0687345	+	0.997635i	$0.521896\pi$
$762$	5.05725e12	0.543397
$763$	6.73515e12	0.719427
$764$	3.69818e12	0.392706
$765$	1.20790e12	0.127513
$766$	−1.46267e13	−1.53502
$767$	4.92654e12	0.514000
$768$	1.12169e13	1.16345
$769$	1.49703e13	1.54370	0.771849	−	0.635806i	$-0.219332\pi$
$769$	1.49703e13	1.54370	0.771849	+	0.635806i	$0.219332\pi$
$770$	1.29124e12	0.132373
$771$	1.41919e13	1.44643
$772$	−4.66286e12	−0.472470
$773$	1.59529e13	1.60706	0.803529	−	0.595266i	$-0.202953\pi$
$773$	1.59529e13	1.60706	0.803529	+	0.595266i	$0.202953\pi$
$774$	6.27431e11	0.0628394
$775$	−1.08045e13	−1.07584
$776$	−7.47346e12	−0.739851
$777$	−1.24969e13	−1.23000
$778$	−1.24685e13	−1.22013
$779$	−1.19217e13	−1.15990
$780$	3.58767e11	0.0347046
$781$	4.39953e12	0.423133
$782$	−1.19822e13	−1.14579
$783$	−7.92922e12	−0.753881
$784$	2.54460e12	0.240546
$785$	−1.44586e12	−0.135898
$786$	−7.25892e12	−0.678376
$787$	−4.64442e12	−0.431564	−0.215782	−	0.976442i	$-0.569230\pi$
$787$	−4.64442e12	−0.431564	−0.215782	+	0.976442i	$0.569230\pi$
$788$	2.33747e12	0.215962
$789$	−7.25496e12	−0.666482
$790$	−5.26750e11	−0.0481152
$791$	1.08990e13	0.989904
$792$	8.61298e12	0.777840
$793$	9.09107e12	0.816368
$794$	−4.28532e11	−0.0382641
$795$	−3.06908e11	−0.0272494
$796$	4.06487e12	0.358871
$797$	1.24077e13	1.08925	0.544625	−	0.838680i	$-0.316672\pi$
$797$	1.24077e13	1.08925	0.544625	+	0.838680i	$0.316672\pi$
$798$	1.52012e13	1.32698
$799$	1.47585e13	1.28110
$800$	7.87905e12	0.680094
$801$	−3.90830e12	−0.335460
$802$	2.36275e12	0.201666
$803$	−2.67854e13	−2.27341
$804$	−8.64097e12	−0.729306
$805$	−1.45887e12	−0.122443
$806$	−4.65266e12	−0.388323
$807$	−1.84012e13	−1.52727
$808$	1.54693e12	0.127679
$809$	−9.50544e12	−0.780196	−0.390098	−	0.920773i	$-0.627559\pi$
$809$	−9.50544e12	−0.780196	−0.390098	+	0.920773i	$0.627559\pi$
$810$	2.06899e12	0.168879
$811$	−6.56385e12	−0.532801	−0.266400	−	0.963862i	$-0.585834\pi$
$811$	−6.56385e12	−0.532801	−0.266400	+	0.963862i	$0.585834\pi$
$812$	−4.19238e12	−0.338422
$813$	1.40577e13	1.12851
$814$	1.91045e13	1.52520
$815$	1.04179e12	0.0827121
$816$	1.09510e13	0.864664
$817$	3.70501e12	0.290931
$818$	−3.99306e12	−0.311829
$819$	−2.11146e12	−0.163986
$820$	−5.00708e11	−0.0386743
$821$	3.96939e12	0.304915	0.152458	−	0.988310i	$-0.451281\pi$
$821$	3.96939e12	0.304915	0.152458	+	0.988310i	$0.451281\pi$
$822$	1.51030e13	1.15383
$823$	2.57352e13	1.95537	0.977683	−	0.210086i	$-0.0673743\pi$
$823$	2.57352e13	1.95537	0.977683	+	0.210086i	$0.0673743\pi$
$824$	−1.83126e13	−1.38381
$825$	2.19029e13	1.64611
$826$	8.76706e12	0.655305
$827$	−1.59944e13	−1.18903	−0.594516	−	0.804084i	$-0.702656\pi$
$827$	−1.59944e13	−1.18903	−0.594516	+	0.804084i	$0.702656\pi$
$828$	−2.64241e12	−0.195373
$829$	5.84546e12	0.429856	0.214928	−	0.976630i	$-0.431048\pi$
$829$	5.84546e12	0.429856	0.214928	+	0.976630i	$0.431048\pi$
$830$	1.62978e12	0.119200
$831$	−3.47855e12	−0.253043
$832$	6.37911e12	0.461536
$833$	−9.83194e12	−0.707516
$834$	1.20763e13	0.864346
$835$	−2.16265e12	−0.153956
$836$	1.38106e13	0.977881
$837$	9.30646e12	0.655420
$838$	1.60054e13	1.12116
$839$	−2.45685e12	−0.171178	−0.0855892	−	0.996331i	$-0.527277\pi$
$839$	−2.45685e12	−0.171178	−0.0855892	+	0.996331i	$0.527277\pi$
$840$	2.35118e12	0.162941
$841$	9.06028e12	0.624539
$842$	−8.83669e12	−0.605878
$843$	2.02337e13	1.37991
$844$	6.82023e12	0.462656
$845$	−2.03385e12	−0.137234
$846$	−5.47652e12	−0.367568
$847$	−9.50471e12	−0.634546
$848$	−9.52253e11	−0.0632370
$849$	1.57545e13	1.04069
$850$	1.68065e13	1.10431
$851$	−2.15847e13	−1.41079
$852$	2.17532e12	0.141431
$853$	1.38158e11	0.00893523	0.00446761	−	0.999990i	$-0.498578\pi$
$853$	1.38158e11	0.00893523	0.00446761	+	0.999990i	$0.498578\pi$
$854$	1.61781e13	1.04080
$855$	−2.64677e12	−0.169383
$856$	−1.32950e13	−0.846361
$857$	−4.58334e12	−0.290248	−0.145124	−	0.989414i	$-0.546358\pi$
$857$	−4.58334e12	−0.290248	−0.145124	+	0.989414i	$0.546358\pi$
$858$	9.43183e12	0.594160
$859$	1.34992e13	0.845938	0.422969	−	0.906144i	$-0.360988\pi$
$859$	1.34992e13	0.845938	0.422969	+	0.906144i	$0.360988\pi$
$860$	1.55609e11	0.00970047
$861$	8.61060e12	0.533973
$862$	−1.95767e13	−1.20769
$863$	1.87111e13	1.14829	0.574144	−	0.818754i	$-0.305335\pi$
$863$	1.87111e13	1.14829	0.574144	+	0.818754i	$0.305335\pi$
$864$	−6.78661e12	−0.414325
$865$	−3.37932e12	−0.205238
$866$	1.20781e13	0.729738
$867$	−2.17988e13	−1.31023
$868$	4.92056e12	0.294222
$869$	8.22981e12	0.489554
$870$	−3.58902e12	−0.212392
$871$	−1.19259e13	−0.702115
$872$	−1.87483e13	−1.09809
$873$	−6.07641e12	−0.354065
$874$	2.62556e13	1.52202
$875$	4.15385e12	0.239560
$876$	−1.32439e13	−0.759884
$877$	−2.55346e13	−1.45757	−0.728786	−	0.684741i	$-0.759915\pi$
$877$	−2.55346e13	−1.45757	−0.728786	+	0.684741i	$0.759915\pi$
$878$	−4.98593e12	−0.283153
$879$	1.30008e13	0.734548
$880$	−2.03829e12	−0.114576
$881$	3.99929e12	0.223662	0.111831	−	0.993727i	$-0.464329\pi$
$881$	3.99929e12	0.223662	0.111831	+	0.993727i	$0.464329\pi$
$882$	3.64838e12	0.202998
$883$	−1.35158e12	−0.0748204	−0.0374102	−	0.999300i	$-0.511911\pi$
$883$	−1.35158e12	−0.0748204	−0.0374102	+	0.999300i	$0.511911\pi$
$884$	−4.30105e12	−0.236886
$885$	−4.46036e12	−0.244414
$886$	−5.83445e12	−0.318089
$887$	−1.75151e13	−0.950074	−0.475037	−	0.879966i	$-0.657565\pi$
$887$	−1.75151e13	−0.950074	−0.475037	+	0.879966i	$0.657565\pi$
$888$	3.47870e13	1.87741
$889$	−7.38168e12	−0.396367
$890$	1.63101e12	0.0871365
$891$	−3.23255e13	−1.71828
$892$	−2.10143e12	−0.111140
$893$	−3.23391e13	−1.70175
$894$	1.23292e13	0.645532
$895$	4.90208e12	0.255374
$896$	1.72591e12	0.0894604
$897$	−1.06563e13	−0.549591
$898$	−1.66245e13	−0.853111
$899$	−2.76609e13	−1.41237
$900$	3.70630e12	0.188300
$901$	3.67935e12	0.185999
$902$	−1.31634e13	−0.662123
$903$	−2.67599e12	−0.133934
$904$	−3.03391e13	−1.51093
$905$	−4.72814e12	−0.234300
$906$	3.24743e12	0.160126
$907$	3.20478e13	1.57241	0.786204	−	0.617967i	$-0.212044\pi$
$907$	3.20478e13	1.57241	0.786204	+	0.617967i	$0.212044\pi$
$908$	−2.87920e12	−0.140568
$909$	1.25776e12	0.0611025
$910$	8.81153e11	0.0425956
$911$	3.17963e13	1.52948	0.764740	−	0.644340i	$-0.222868\pi$
$911$	3.17963e13	1.52948	0.764740	+	0.644340i	$0.222868\pi$
$912$	−2.39959e13	−1.14858
$913$	−2.54633e13	−1.21282
$914$	−1.94287e13	−0.920846
$915$	−8.23082e12	−0.388194
$916$	−2.18682e12	−0.102632
$917$	1.05953e13	0.494824
$918$	−1.44763e13	−0.672766
$919$	6.46550e12	0.299008	0.149504	−	0.988761i	$-0.452232\pi$
$919$	6.46550e12	0.299008	0.149504	+	0.988761i	$0.452232\pi$
$920$	4.06098e12	0.186890
$921$	−4.45186e12	−0.203879
$922$	−9.02438e12	−0.411271
$923$	3.00228e12	0.136158
$924$	−9.97492e12	−0.450180
$925$	3.02751e13	1.35972
$926$	2.27743e13	1.01788
$927$	−1.48893e13	−0.662241
$928$	2.01713e13	0.892829
$929$	3.58746e12	0.158022	0.0790109	−	0.996874i	$-0.474824\pi$
$929$	3.58746e12	0.158022	0.0790109	+	0.996874i	$0.474824\pi$
$930$	4.21240e12	0.184653
$931$	2.15439e13	0.939831
$932$	1.95928e12	0.0850598
$933$	−1.03396e13	−0.446721
$934$	−3.02526e13	−1.30077
$935$	7.87563e12	0.337002
$936$	5.87758e12	0.250298
$937$	4.03654e13	1.71073	0.855364	−	0.518027i	$-0.173333\pi$
$937$	4.03654e13	1.71073	0.855364	+	0.518027i	$0.173333\pi$
$938$	−2.12227e13	−0.895135
$939$	1.19332e13	0.500912
$940$	−1.35823e12	−0.0567413
$941$	−1.34172e13	−0.557840	−0.278920	−	0.960314i	$-0.589977\pi$
$941$	−1.34172e13	−0.557840	−0.278920	+	0.960314i	$0.589977\pi$
$942$	−1.87944e13	−0.777677
$943$	1.48723e13	0.612456
$944$	−1.38393e13	−0.567205
$945$	−1.76252e12	−0.0718938
$946$	4.09091e12	0.166077
$947$	−8.00627e12	−0.323486	−0.161743	−	0.986833i	$-0.551712\pi$
$947$	−8.00627e12	−0.323486	−0.161743	+	0.986833i	$0.551712\pi$
$948$	4.06919e12	0.163633
$949$	−1.82786e13	−0.731552
$950$	−3.68266e13	−1.46692
$951$	5.38714e13	2.13573
$952$	−2.81870e13	−1.11220
$953$	−2.74035e13	−1.07619	−0.538094	−	0.842885i	$-0.680855\pi$
$953$	−2.74035e13	−1.07619	−0.538094	+	0.842885i	$0.680855\pi$
$954$	−1.36531e12	−0.0533660
$955$	−4.62108e12	−0.179775
$956$	−7.08614e12	−0.274378
$957$	5.60739e13	2.16101
$958$	2.41515e13	0.926402
$959$	−2.20447e13	−0.841628
$960$	−5.77549e12	−0.219466
$961$	6.02571e12	0.227904
$962$	1.30371e13	0.490788
$963$	−1.08097e13	−0.405037
$964$	−9.23024e12	−0.344244
$965$	5.82650e12	0.216289
$966$	−1.89634e13	−0.700680
$967$	−1.14021e13	−0.419341	−0.209671	−	0.977772i	$-0.567239\pi$
$967$	−1.14021e13	−0.419341	−0.209671	+	0.977772i	$0.567239\pi$
$968$	2.64578e13	0.968534
$969$	9.27164e13	3.37831
$970$	2.53580e12	0.0919692
$971$	3.11540e13	1.12467	0.562337	−	0.826908i	$-0.309902\pi$
$971$	3.11540e13	1.12467	0.562337	+	0.826908i	$0.309902\pi$
$972$	−9.84738e12	−0.353853
$973$	−1.76269e13	−0.630475
$974$	−7.44682e12	−0.265128
$975$	1.49467e13	0.529694
$976$	−2.55380e13	−0.900872
$977$	−4.42114e13	−1.55242	−0.776209	−	0.630475i	$-0.782860\pi$
$977$	−4.42114e13	−1.55242	−0.776209	+	0.630475i	$0.782860\pi$
$978$	1.35419e13	0.473320
$979$	−2.54824e13	−0.886582
$980$	9.04836e11	0.0313367
$981$	−1.52436e13	−0.525505
$982$	−4.50594e12	−0.154626
$983$	1.16477e13	0.397877	0.198939	−	0.980012i	$-0.436251\pi$
$983$	1.16477e13	0.397877	0.198939	+	0.980012i	$0.436251\pi$
$984$	−2.39689e13	−0.815024
$985$	−2.92079e12	−0.0988639
$986$	4.30267e13	1.44975
$987$	2.33573e13	0.783422
$988$	9.42452e12	0.314668
$989$	−4.62199e12	−0.153619
$990$	−2.92245e12	−0.0966915
$991$	4.19672e12	0.138222	0.0691112	−	0.997609i	$-0.477984\pi$
$991$	4.19672e12	0.138222	0.0691112	+	0.997609i	$0.477984\pi$
$992$	−2.36749e13	−0.776222
$993$	1.73678e13	0.566858
$994$	5.34273e12	0.173590
$995$	−5.07929e12	−0.164285
$996$	−1.25902e13	−0.405383
$997$	3.39392e13	1.08786	0.543930	−	0.839131i	$-0.316936\pi$
$997$	3.39392e13	1.08786	0.543930	+	0.839131i	$0.316936\pi$
$998$	2.13024e13	0.679737
$999$	−2.60774e13	−0.828362

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.a.a.1.6	✓	15
3.2	odd	2		387.10.a.c.1.10		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.a.a.1.6	✓	15	1.1	even	1	trivial
387.10.a.c.1.10		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)

\(f(q)\)	\(=\)	\(q-17.9205 q^{2} -172.986 q^{3} -190.855 q^{4} +238.484 q^{5} +3099.99 q^{6} -4524.82 q^{7} +12595.5 q^{8} +10241.0 q^{9} +O(q^{10})\)	\(q-17.9205 q^{2} -172.986 q^{3} -190.855 q^{4} +238.484 q^{5} +3099.99 q^{6} -4524.82 q^{7} +12595.5 q^{8} +10241.0 q^{9} -4273.75 q^{10} +66772.1 q^{11} +33015.1 q^{12} +45566.0 q^{13} +81087.1 q^{14} -41254.2 q^{15} -128001. q^{16} +494574. q^{17} -183524. q^{18} -1.08372e6 q^{19} -45515.8 q^{20} +782728. q^{21} -1.19659e6 q^{22} +1.35193e6 q^{23} -2.17884e6 q^{24} -1.89625e6 q^{25} -816566. q^{26} +1.63333e6 q^{27} +863584. q^{28} -4.85463e6 q^{29} +739298. q^{30} +5.69784e6 q^{31} -4.15507e6 q^{32} -1.15506e7 q^{33} -8.86302e6 q^{34} -1.07910e6 q^{35} -1.95454e6 q^{36} -1.59658e7 q^{37} +1.94208e7 q^{38} -7.88225e6 q^{39} +3.00383e6 q^{40} +1.10007e7 q^{41} -1.40269e7 q^{42} -3.41880e6 q^{43} -1.27438e7 q^{44} +2.44231e6 q^{45} -2.42274e7 q^{46} +2.98409e7 q^{47} +2.21423e7 q^{48} -1.98796e7 q^{49} +3.39818e7 q^{50} -8.55541e7 q^{51} -8.69648e6 q^{52} +7.43943e6 q^{53} -2.92702e7 q^{54} +1.59241e7 q^{55} -5.69925e7 q^{56} +1.87467e8 q^{57} +8.69975e7 q^{58} +1.08119e8 q^{59} +7.87357e6 q^{60} +1.99515e8 q^{61} -1.02108e8 q^{62} -4.63386e7 q^{63} +1.39997e8 q^{64} +1.08667e7 q^{65} +2.06993e8 q^{66} -2.61727e8 q^{67} -9.43918e7 q^{68} -2.33865e8 q^{69} +1.93380e7 q^{70} +6.58887e7 q^{71} +1.28991e8 q^{72} -4.01146e8 q^{73} +2.86115e8 q^{74} +3.28024e8 q^{75} +2.06832e8 q^{76} -3.02132e8 q^{77} +1.41254e8 q^{78} +1.23252e8 q^{79} -3.05261e7 q^{80} -4.84116e8 q^{81} -1.97139e8 q^{82} -3.81346e8 q^{83} -1.49388e8 q^{84} +1.17948e8 q^{85} +6.12667e7 q^{86} +8.39780e8 q^{87} +8.41030e8 q^{88} -3.81633e8 q^{89} -4.37675e7 q^{90} -2.06178e8 q^{91} -2.58023e8 q^{92} -9.85643e8 q^{93} -5.34765e8 q^{94} -2.58449e8 q^{95} +7.18767e8 q^{96} -5.93343e8 q^{97} +3.56253e8 q^{98} +6.83813e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 32 q^{2} - 317 q^{3} + 3242 q^{4} - 4717 q^{5} + 687 q^{6} - 9680 q^{7} - 20394 q^{8} + 69516 q^{9}+O(q^{10}) \) 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

Modular forms

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