LMFDB - Embedded newform 43.10.a.a.1.10

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			1.10
Root			$-17.0644$ 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)

$f(q)$	$=$	$q+15.0644 q^{2} +34.0074 q^{3} -285.063 q^{4} +1876.98 q^{5} +512.302 q^{6} -7041.18 q^{7} -12007.3 q^{8} -18526.5 q^{9} +O(q^{10})$	\(q+15.0644 q^{2} +34.0074 q^{3} -285.063 q^{4} +1876.98 q^{5} +512.302 q^{6} -7041.18 q^{7} -12007.3 q^{8} -18526.5 q^{9} +28275.7 q^{10} -2479.03 q^{11} -9694.23 q^{12} +103059. q^{13} -106071. q^{14} +63831.2 q^{15} -34931.2 q^{16} -529570. q^{17} -279091. q^{18} -431982. q^{19} -535058. q^{20} -239452. q^{21} -37345.2 q^{22} -100577. q^{23} -408337. q^{24} +1.56994e6 q^{25} +1.55253e6 q^{26} -1.29940e6 q^{27} +2.00718e6 q^{28} -7.09806e6 q^{29} +961582. q^{30} -3.27053e6 q^{31} +5.62152e6 q^{32} -84305.4 q^{33} -7.97768e6 q^{34} -1.32162e7 q^{35} +5.28121e6 q^{36} -4.41240e6 q^{37} -6.50756e6 q^{38} +3.50477e6 q^{39} -2.25375e7 q^{40} +1.81476e7 q^{41} -3.60721e6 q^{42} -3.41880e6 q^{43} +706679. q^{44} -3.47739e7 q^{45} -1.51514e6 q^{46} +5.52154e7 q^{47} -1.18792e6 q^{48} +9.22462e6 q^{49} +2.36502e7 q^{50} -1.80093e7 q^{51} -2.93783e7 q^{52} -8.53713e6 q^{53} -1.95748e7 q^{54} -4.65310e6 q^{55} +8.45456e7 q^{56} -1.46906e7 q^{57} -1.06928e8 q^{58} -1.92252e7 q^{59} -1.81959e7 q^{60} -9.01048e6 q^{61} -4.92687e7 q^{62} +1.30448e8 q^{63} +1.02570e8 q^{64} +1.93440e8 q^{65} -1.27001e6 q^{66} +1.40140e8 q^{67} +1.50961e8 q^{68} -3.42037e6 q^{69} -1.99094e8 q^{70} +2.63642e8 q^{71} +2.22453e8 q^{72} -1.09424e8 q^{73} -6.64703e7 q^{74} +5.33895e7 q^{75} +1.23142e8 q^{76} +1.74553e7 q^{77} +5.27973e7 q^{78} -6.39726e7 q^{79} -6.55653e7 q^{80} +3.20468e8 q^{81} +2.73383e8 q^{82} +4.71378e8 q^{83} +6.82588e7 q^{84} -9.93994e8 q^{85} -5.15023e7 q^{86} -2.41386e8 q^{87} +2.97665e7 q^{88} -1.07301e9 q^{89} -5.23850e8 q^{90} -7.25657e8 q^{91} +2.86708e7 q^{92} -1.11222e8 q^{93} +8.31790e8 q^{94} -8.10822e8 q^{95} +1.91173e8 q^{96} -2.81023e8 q^{97} +1.38964e8 q^{98} +4.59278e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	15.0644	0.665761	0.332880	−	0.942969i	$-0.391980\pi$
$2$	15.0644	0.665761	0.332880	+	0.942969i	$0.391980\pi$
$3$	34.0074	0.242397	0.121199	−	0.992628i	$-0.461326\pi$
$3$	34.0074	0.242397	0.121199	+	0.992628i	$0.461326\pi$
$4$	−285.063	−0.556763
$5$	1876.98	1.34306	0.671530	−	0.740978i	$-0.265638\pi$
$5$	1876.98	1.34306	0.671530	+	0.740978i	$0.265638\pi$
$6$	512.302	0.161378
$7$	−7041.18	−1.10842	−0.554210	−	0.832377i	$-0.686980\pi$
$7$	−7041.18	−1.10842	−0.554210	+	0.832377i	$0.686980\pi$
$8$	−12007.3	−1.03643
$9$	−18526.5	−0.941244
$10$	28275.7	0.894156
$11$	−2479.03	−0.0510523	−0.0255261	−	0.999674i	$-0.508126\pi$
$11$	−2479.03	−0.0510523	−0.0255261	+	0.999674i	$0.508126\pi$
$12$	−9694.23	−0.134958
$13$	103059.	1.00079	0.500393	−	0.865799i	$-0.333189\pi$
$13$	103059.	1.00079	0.500393	+	0.865799i	$0.333189\pi$
$14$	−106071.	−0.737942
$15$	63831.2	0.325554
$16$	−34931.2	−0.133252
$17$	−529570.	−1.53781	−0.768906	−	0.639361i	$-0.779199\pi$
$17$	−529570.	−1.53781	−0.768906	+	0.639361i	$0.779199\pi$
$18$	−279091.	−0.626643
$19$	−431982.	−0.760456	−0.380228	−	0.924893i	$-0.624154\pi$
$19$	−431982.	−0.760456	−0.380228	+	0.924893i	$0.624154\pi$
$20$	−535058.	−0.747766
$21$	−239452.	−0.268678
$22$	−37345.2	−0.0339886
$23$	−100577.	−0.0749419	−0.0374709	−	0.999298i	$-0.511930\pi$
$23$	−100577.	−0.0749419	−0.0374709	+	0.999298i	$0.511930\pi$
$24$	−408337.	−0.251228
$25$	1.56994e6	0.803808
$26$	1.55253e6	0.666283
$27$	−1.29940e6	−0.470552
$28$	2.00718e6	0.617127
$29$	−7.09806e6	−1.86358	−0.931792	−	0.362994i	$-0.881755\pi$
$29$	−7.09806e6	−1.86358	−0.931792	+	0.362994i	$0.881755\pi$
$30$	961582.	0.216741
$31$	−3.27053e6	−0.636049	−0.318025	−	0.948082i	$-0.603020\pi$
$31$	−3.27053e6	−0.636049	−0.318025	+	0.948082i	$0.603020\pi$
$32$	5.62152e6	0.947717
$33$	−84305.4	−0.0123749
$34$	−7.97768e6	−1.02381
$35$	−1.32162e7	−1.48867
$36$	5.28121e6	0.524050
$37$	−4.41240e6	−0.387050	−0.193525	−	0.981095i	$-0.561992\pi$
$37$	−4.41240e6	−0.387050	−0.193525	+	0.981095i	$0.561992\pi$
$38$	−6.50756e6	−0.506281
$39$	3.50477e6	0.242587
$40$	−2.25375e7	−1.39199
$41$	1.81476e7	1.00298	0.501488	−	0.865164i	$-0.332786\pi$
$41$	1.81476e7	1.00298	0.501488	+	0.865164i	$0.332786\pi$
$42$	−3.60721e6	−0.178875
$43$	−3.41880e6	−0.152499
$43$	−3.41880e6	−0.152499
$44$	706679.	0.0284240
$45$	−3.47739e7	−1.26415
$46$	−1.51514e6	−0.0498933
$47$	5.52154e7	1.65052	0.825259	−	0.564755i	$-0.191029\pi$
$47$	5.52154e7	1.65052	0.825259	+	0.564755i	$0.191029\pi$
$48$	−1.18792e6	−0.0322999
$49$	9.22462e6	0.228595
$50$	2.36502e7	0.535144
$51$	−1.80093e7	−0.372761
$52$	−2.93783e7	−0.557200
$53$	−8.53713e6	−0.148618	−0.0743089	−	0.997235i	$-0.523675\pi$
$53$	−8.53713e6	−0.148618	−0.0743089	+	0.997235i	$0.523675\pi$
$54$	−1.95748e7	−0.313275
$55$	−4.65310e6	−0.0685662
$56$	8.45456e7	1.14880
$57$	−1.46906e7	−0.184332
$58$	−1.06928e8	−1.24070
$59$	−1.92252e7	−0.206556	−0.103278	−	0.994653i	$-0.532933\pi$
$59$	−1.92252e7	−0.206556	−0.103278	+	0.994653i	$0.532933\pi$
$60$	−1.81959e7	−0.181256
$61$	−9.01048e6	−0.0833228	−0.0416614	−	0.999132i	$-0.513265\pi$
$61$	−9.01048e6	−0.0833228	−0.0416614	+	0.999132i	$0.513265\pi$
$62$	−4.92687e7	−0.423457
$63$	1.30448e8	1.04329
$64$	1.02570e8	0.764205
$65$	1.93440e8	1.34411
$66$	−1.27001e6	−0.00823873
$67$	1.40140e8	0.849625	0.424812	−	0.905281i	$-0.360340\pi$
$67$	1.40140e8	0.849625	0.424812	+	0.905281i	$0.360340\pi$
$68$	1.50961e8	0.856197
$69$	−3.42037e6	−0.0181657
$70$	−1.99094e8	−0.991100
$71$	2.63642e8	1.23127	0.615633	−	0.788033i	$-0.288900\pi$
$71$	2.63642e8	1.23127	0.615633	+	0.788033i	$0.288900\pi$
$72$	2.22453e8	0.975534
$73$	−1.09424e8	−0.450982	−0.225491	−	0.974245i	$-0.572399\pi$
$73$	−1.09424e8	−0.450982	−0.225491	+	0.974245i	$0.572399\pi$
$74$	−6.64703e7	−0.257683
$75$	5.33895e7	0.194841
$76$	1.23142e8	0.423394
$77$	1.74553e7	0.0565874
$78$	5.27973e7	0.161505
$79$	−6.39726e7	−0.184787	−0.0923937	−	0.995723i	$-0.529452\pi$
$79$	−6.39726e7	−0.184787	−0.0923937	+	0.995723i	$0.529452\pi$
$80$	−6.55653e7	−0.178966
$81$	3.20468e8	0.827183
$82$	2.73383e8	0.667742
$83$	4.71378e8	1.09023	0.545115	−	0.838362i	$-0.316486\pi$
$83$	4.71378e8	1.09023	0.545115	+	0.838362i	$0.316486\pi$
$84$	6.82588e7	0.149590
$85$	−9.93994e8	−2.06537
$86$	−5.15023e7	−0.101528
$87$	−2.41386e8	−0.451727
$88$	2.97665e7	0.0529122
$89$	−1.07301e9	−1.81279	−0.906395	−	0.422431i	$-0.861177\pi$
$89$	−1.07301e9	−1.81279	−0.906395	+	0.422431i	$0.861177\pi$
$90$	−5.23850e8	−0.841619
$91$	−7.25657e8	−1.10929
$92$	2.86708e7	0.0417249
$93$	−1.11222e8	−0.154177
$94$	8.31790e8	1.09885
$95$	−8.10822e8	−1.02134
$96$	1.91173e8	0.229724
$97$	−2.81023e8	−0.322306	−0.161153	−	0.986929i	$-0.551521\pi$
$97$	−2.81023e8	−0.322306	−0.161153	+	0.986929i	$0.551521\pi$
$98$	1.38964e8	0.152189
$99$	4.59278e7	0.0480526
$100$	−4.47531e8	−0.447531
$101$	9.66718e8	0.924387	0.462193	−	0.886779i	$-0.347063\pi$
$101$	9.66718e8	0.924387	0.462193	+	0.886779i	$0.347063\pi$
$102$	−2.71300e8	−0.248170
$103$	7.64929e8	0.669659	0.334829	−	0.942279i	$-0.391321\pi$
$103$	7.64929e8	0.669659	0.334829	+	0.942279i	$0.391321\pi$
$104$	−1.23746e9	−1.03725
$105$	−4.49447e8	−0.360850
$106$	−1.28607e8	−0.0989438
$107$	−6.83281e8	−0.503932	−0.251966	−	0.967736i	$-0.581077\pi$
$107$	−6.83281e8	−0.503932	−0.251966	+	0.967736i	$0.581077\pi$
$108$	3.70412e8	0.261986
$109$	1.06256e9	0.721001	0.360501	−	0.932759i	$-0.382606\pi$
$109$	1.06256e9	0.721001	0.360501	+	0.932759i	$0.382606\pi$
$110$	−7.00963e7	−0.0456487
$111$	−1.50054e8	−0.0938198
$112$	2.45957e8	0.147699
$113$	−2.75197e9	−1.58778	−0.793889	−	0.608062i	$-0.791947\pi$
$113$	−2.75197e9	−1.58778	−0.793889	+	0.608062i	$0.791947\pi$
$114$	−2.21305e8	−0.122721
$115$	−1.88782e8	−0.100651
$116$	2.02339e9	1.03757
$117$	−1.90932e9	−0.941983
$118$	−2.89617e8	−0.137517
$119$	3.72880e9	1.70454
$120$	−7.66441e8	−0.337414
$121$	−2.35180e9	−0.997394
$122$	−1.35738e8	−0.0554730
$123$	6.17150e8	0.243119
$124$	9.32307e8	0.354129
$125$	−7.19235e8	−0.263497
$126$	1.96513e9	0.694583
$127$	4.95413e8	0.168986	0.0844929	−	0.996424i	$-0.473073\pi$
$127$	4.95413e8	0.168986	0.0844929	+	0.996424i	$0.473073\pi$
$128$	−1.33306e9	−0.438940
$129$	−1.16264e8	−0.0369652
$130$	2.91407e9	0.894858
$131$	3.75757e9	1.11477	0.557387	−	0.830253i	$-0.311804\pi$
$131$	3.75757e9	1.11477	0.557387	+	0.830253i	$0.311804\pi$
$132$	2.40323e7	0.00688990
$133$	3.04166e9	0.842904
$134$	2.11114e9	0.565646
$135$	−2.43896e9	−0.631979
$136$	6.35871e9	1.59384
$137$	−5.56301e9	−1.34917	−0.674586	−	0.738197i	$-0.735678\pi$
$137$	−5.56301e9	−1.34917	−0.674586	+	0.738197i	$0.735678\pi$
$138$	−5.15259e7	−0.0120940
$139$	−2.23267e9	−0.507292	−0.253646	−	0.967297i	$-0.581630\pi$
$139$	−2.23267e9	−0.507292	−0.253646	+	0.967297i	$0.581630\pi$
$140$	3.76744e9	0.828838
$141$	1.87773e9	0.400081
$142$	3.97162e9	0.819728
$143$	−2.55487e8	−0.0510924
$144$	6.47154e8	0.125423
$145$	−1.33229e10	−2.50290
$146$	−1.64841e9	−0.300246
$147$	3.13705e8	0.0554107
$148$	1.25781e9	0.215495
$149$	2.53385e9	0.421156	0.210578	−	0.977577i	$-0.432465\pi$
$149$	2.53385e9	0.421156	0.210578	+	0.977577i	$0.432465\pi$
$150$	8.04282e8	0.129717
$151$	−8.68661e9	−1.35973	−0.679867	−	0.733335i	$-0.737963\pi$
$151$	−8.68661e9	−1.35973	−0.679867	+	0.733335i	$0.737963\pi$
$152$	5.18693e9	0.788160
$153$	9.81108e9	1.44746
$154$	2.62955e8	0.0376736
$155$	−6.13873e9	−0.854252
$156$	−9.99078e8	−0.135064
$157$	−1.63159e8	−0.0214320	−0.0107160	−	0.999943i	$-0.503411\pi$
$157$	−1.63159e8	−0.0214320	−0.0107160	+	0.999943i	$0.503411\pi$
$158$	−9.63712e8	−0.123024
$159$	−2.90325e8	−0.0360245
$160$	1.05515e10	1.27284
$161$	7.08183e8	0.0830671
$162$	4.82767e9	0.550706
$163$	−1.74840e10	−1.93998	−0.969991	−	0.243141i	$-0.921822\pi$
$163$	−1.74840e10	−1.93998	−0.969991	+	0.243141i	$0.921822\pi$
$164$	−5.17319e9	−0.558420
$165$	−1.58240e8	−0.0166203
$166$	7.10104e9	0.725831
$167$	1.29270e10	1.28610	0.643048	−	0.765826i	$-0.277669\pi$
$167$	1.29270e10	1.28610	0.643048	+	0.765826i	$0.277669\pi$
$168$	2.87517e9	0.278466
$169$	1.66620e7	0.00157122
$170$	−1.49740e10	−1.37504
$171$	8.00311e9	0.715774
$172$	9.74572e8	0.0849055
$173$	2.03436e10	1.72671	0.863356	−	0.504595i	$-0.168358\pi$
$173$	2.03436e10	1.72671	0.863356	+	0.504595i	$0.168358\pi$
$174$	−3.63635e9	−0.300742
$175$	−1.10542e10	−0.890957
$176$	8.65957e7	0.00680282
$177$	−6.53799e8	−0.0500685
$178$	−1.61643e10	−1.20688
$179$	−1.34136e10	−0.976581	−0.488290	−	0.872681i	$-0.662379\pi$
$179$	−1.34136e10	−0.976581	−0.488290	+	0.872681i	$0.662379\pi$
$180$	9.91274e9	0.703830
$181$	2.32509e10	1.61022	0.805111	−	0.593124i	$-0.202106\pi$
$181$	2.32509e10	1.61022	0.805111	+	0.593124i	$0.202106\pi$
$182$	−1.09316e10	−0.738522
$183$	−3.06423e8	−0.0201972
$184$	1.20766e9	0.0776721
$185$	−8.28199e9	−0.519831
$186$	−1.67550e9	−0.102645
$187$	1.31282e9	0.0785088
$188$	−1.57399e10	−0.918947
$189$	9.14934e9	0.521569
$190$	−1.22146e10	−0.679966
$191$	−2.42046e10	−1.31598	−0.657988	−	0.753029i	$-0.728592\pi$
$191$	−2.42046e10	−1.31598	−0.657988	+	0.753029i	$0.728592\pi$
$192$	3.48813e9	0.185241
$193$	−2.49753e10	−1.29570	−0.647848	−	0.761770i	$-0.724331\pi$
$193$	−2.49753e10	−1.29570	−0.647848	+	0.761770i	$0.724331\pi$
$194$	−4.23345e9	−0.214579
$195$	6.57838e9	0.325809
$196$	−2.62959e9	−0.127273
$197$	−1.22394e10	−0.578977	−0.289489	−	0.957181i	$-0.593485\pi$
$197$	−1.22394e10	−0.578977	−0.289489	+	0.957181i	$0.593485\pi$
$198$	6.91876e8	0.0319915
$199$	−2.35676e10	−1.06531	−0.532655	−	0.846332i	$-0.678806\pi$
$199$	−2.35676e10	−1.06531	−0.532655	+	0.846332i	$0.678806\pi$
$200$	−1.88507e10	−0.833092
$201$	4.76581e9	0.205946
$202$	1.45631e10	0.615420
$203$	4.99787e10	2.06563
$204$	5.13378e9	0.207540
$205$	3.40626e10	1.34706
$206$	1.15232e10	0.445832
$207$	1.86334e9	0.0705386
$208$	−3.59998e9	−0.133357
$209$	1.07090e9	0.0388230
$210$	−6.77067e9	−0.240240
$211$	−5.46004e10	−1.89638	−0.948188	−	0.317710i	$-0.897086\pi$
$211$	−5.46004e10	−1.89638	−0.948188	+	0.317710i	$0.897086\pi$
$212$	2.43362e9	0.0827448
$213$	8.96577e9	0.298455
$214$	−1.02932e10	−0.335498
$215$	−6.41703e9	−0.204815
$216$	1.56023e10	0.487695
$217$	2.30284e10	0.705010
$218$	1.60069e10	0.480014
$219$	−3.72122e9	−0.109317
$220$	1.32642e9	0.0381751
$221$	−5.45770e10	−1.53902
$222$	−2.26048e9	−0.0624615
$223$	2.69840e10	0.730693	0.365347	−	0.930872i	$-0.380950\pi$
$223$	2.69840e10	0.730693	0.365347	+	0.930872i	$0.380950\pi$
$224$	−3.95821e10	−1.05047
$225$	−2.90855e10	−0.756579
$226$	−4.14568e10	−1.05708
$227$	2.28428e10	0.570995	0.285498	−	0.958379i	$-0.407841\pi$
$227$	2.28428e10	0.570995	0.285498	+	0.958379i	$0.407841\pi$
$228$	4.18773e9	0.102629
$229$	4.78347e9	0.114943	0.0574716	−	0.998347i	$-0.481696\pi$
$229$	4.78347e9	0.114943	0.0574716	+	0.998347i	$0.481696\pi$
$230$	−2.84389e9	−0.0670097
$231$	5.93609e8	0.0137166
$232$	8.52286e10	1.93148
$233$	2.54149e10	0.564920	0.282460	−	0.959279i	$-0.408850\pi$
$233$	2.54149e10	0.564920	0.282460	+	0.959279i	$0.408850\pi$
$234$	−2.87629e10	−0.627135
$235$	1.03638e11	2.21674
$236$	5.48039e9	0.115003
$237$	−2.17554e9	−0.0447919
$238$	5.61723e10	1.13482
$239$	4.29227e10	0.850936	0.425468	−	0.904974i	$-0.360110\pi$
$239$	4.29227e10	0.850936	0.425468	+	0.904974i	$0.360110\pi$
$240$	−2.22970e9	−0.0433807
$241$	3.36684e10	0.642903	0.321451	−	0.946926i	$-0.395829\pi$
$241$	3.36684e10	0.642903	0.321451	+	0.946926i	$0.395829\pi$
$242$	−3.54286e10	−0.664025
$243$	3.64744e10	0.671059
$244$	2.56855e9	0.0463910
$245$	1.73145e10	0.307016
$246$	9.29703e9	0.161859
$247$	−4.45196e10	−0.761053
$248$	3.92703e10	0.659222
$249$	1.60303e10	0.264268
$250$	−1.08349e10	−0.175426
$251$	3.34718e10	0.532289	0.266145	−	0.963933i	$-0.414250\pi$
$251$	3.34718e10	0.532289	0.266145	+	0.963933i	$0.414250\pi$
$252$	−3.71860e10	−0.580867
$253$	2.49334e8	0.00382595
$254$	7.46311e9	0.112504
$255$	−3.38031e10	−0.500640
$256$	−7.25976e10	−1.05643
$257$	−3.86792e10	−0.553068	−0.276534	−	0.961004i	$-0.589186\pi$
$257$	−3.86792e10	−0.553068	−0.276534	+	0.961004i	$0.589186\pi$
$258$	−1.75146e9	−0.0246100
$259$	3.10685e10	0.429014
$260$	−5.51425e10	−0.748353
$261$	1.31502e11	1.75409
$262$	5.66057e10	0.742172
$263$	3.69446e10	0.476157	0.238078	−	0.971246i	$-0.423483\pi$
$263$	3.69446e10	0.476157	0.238078	+	0.971246i	$0.423483\pi$
$264$	1.01228e9	0.0128258
$265$	−1.60240e10	−0.199602
$266$	4.58209e10	0.561172
$267$	−3.64902e10	−0.439415
$268$	−3.99488e10	−0.473039
$269$	−1.65605e11	−1.92836	−0.964182	−	0.265242i	$-0.914548\pi$
$269$	−1.65605e11	−1.92836	−0.964182	+	0.265242i	$0.914548\pi$
$270$	−3.67416e10	−0.420747
$271$	3.88648e10	0.437718	0.218859	−	0.975756i	$-0.429766\pi$
$271$	3.88648e10	0.437718	0.218859	+	0.975756i	$0.429766\pi$
$272$	1.84985e10	0.204917
$273$	−2.46777e10	−0.268889
$274$	−8.38036e10	−0.898225
$275$	−3.89193e9	−0.0410362
$276$	9.75019e8	0.0101140
$277$	1.49820e10	0.152901	0.0764506	−	0.997073i	$-0.475641\pi$
$277$	1.49820e10	0.152901	0.0764506	+	0.997073i	$0.475641\pi$
$278$	−3.36339e10	−0.337735
$279$	6.05915e10	0.598678
$280$	1.58691e11	1.54291
$281$	−1.83669e11	−1.75734	−0.878672	−	0.477425i	$-0.841570\pi$
$281$	−1.83669e11	−1.75734	−0.878672	+	0.477425i	$0.841570\pi$
$282$	2.82870e10	0.266358
$283$	9.42540e10	0.873495	0.436748	−	0.899584i	$-0.356130\pi$
$283$	9.42540e10	0.873495	0.436748	+	0.899584i	$0.356130\pi$
$284$	−7.51544e10	−0.685523
$285$	−2.75739e10	−0.247569
$286$	−3.84876e9	−0.0340153
$287$	−1.27780e11	−1.11172
$288$	−1.04147e11	−0.892033
$289$	1.61857e11	1.36487
$290$	−2.00703e11	−1.66633
$291$	−9.55684e9	−0.0781260
$292$	3.11926e10	0.251090
$293$	−1.43511e11	−1.13758	−0.568790	−	0.822483i	$-0.692588\pi$
$293$	−1.43511e11	−1.13758	−0.568790	+	0.822483i	$0.692588\pi$
$294$	4.72579e9	0.0368903
$295$	−3.60854e10	−0.277417
$296$	5.29810e10	0.401151
$297$	3.22127e9	0.0240227
$298$	3.81711e10	0.280389
$299$	−1.03654e10	−0.0750007
$300$	−1.52193e10	−0.108480
$301$	2.40724e10	0.169032
$302$	−1.30859e11	−0.905258
$303$	3.28755e10	0.224069
$304$	1.50897e10	0.101332
$305$	−1.69125e10	−0.111907
$306$	1.47798e11	0.963659
$307$	−2.47841e11	−1.59240	−0.796198	−	0.605037i	$-0.793158\pi$
$307$	−2.47841e11	−1.59240	−0.796198	+	0.605037i	$0.793158\pi$
$308$	−4.97586e9	−0.0315057
$309$	2.60132e10	0.162323
$310$	−9.24766e10	−0.568727
$311$	−3.23810e11	−1.96276	−0.981382	−	0.192066i	$-0.938481\pi$
$311$	−3.23810e11	−1.96276	−0.981382	+	0.192066i	$0.938481\pi$
$312$	−4.20828e10	−0.251425
$313$	2.55636e11	1.50547	0.752735	−	0.658323i	$-0.228734\pi$
$313$	2.55636e11	1.50547	0.752735	+	0.658323i	$0.228734\pi$
$314$	−2.45790e9	−0.0142686
$315$	2.44849e11	1.40120
$316$	1.82362e10	0.102883
$317$	2.16477e11	1.20405	0.602025	−	0.798477i	$-0.294361\pi$
$317$	2.16477e11	1.20405	0.602025	+	0.798477i	$0.294361\pi$
$318$	−4.37359e9	−0.0239837
$319$	1.75963e10	0.0951402
$320$	1.92522e11	1.02637
$321$	−2.32366e10	−0.122152
$322$	1.06684e10	0.0553028
$323$	2.28765e11	1.16944
$324$	−9.13534e10	−0.460545
$325$	1.61796e11	0.804440
$326$	−2.63387e11	−1.29156
$327$	3.61350e10	0.174769
$328$	−2.17903e11	−1.03952
$329$	−3.88782e11	−1.82947
$330$	−2.38379e9	−0.0110651
$331$	−4.68906e10	−0.214714	−0.107357	−	0.994221i	$-0.534239\pi$
$331$	−4.68906e10	−0.214714	−0.107357	+	0.994221i	$0.534239\pi$
$332$	−1.34372e11	−0.606999
$333$	8.17463e10	0.364308
$334$	1.94738e11	0.856232
$335$	2.63041e11	1.14110
$336$	8.36436e9	0.0358019
$337$	−4.29929e11	−1.81578	−0.907888	−	0.419212i	$-0.862306\pi$
$337$	−4.29929e11	−1.81578	−0.907888	+	0.419212i	$0.862306\pi$
$338$	2.51003e8	0.00104605
$339$	−9.35871e10	−0.384873
$340$	2.83351e11	1.14992
$341$	8.10776e9	0.0324718
$342$	1.20562e11	0.476534
$343$	2.19185e11	0.855041
$344$	4.10506e10	0.158054
$345$	−6.41997e9	−0.0243976
$346$	3.06465e11	1.14958
$347$	3.36146e11	1.24465	0.622323	−	0.782761i	$-0.286189\pi$
$347$	3.36146e11	1.24465	0.622323	+	0.782761i	$0.286189\pi$
$348$	6.88102e10	0.251505
$349$	9.78546e10	0.353075	0.176537	−	0.984294i	$-0.443510\pi$
$349$	9.78546e10	0.353075	0.176537	+	0.984294i	$0.443510\pi$
$350$	−1.66526e11	−0.593164
$351$	−1.33915e11	−0.470921
$352$	−1.39359e10	−0.0483831
$353$	−1.75851e11	−0.602778	−0.301389	−	0.953501i	$-0.597450\pi$
$353$	−1.75851e11	−0.602778	−0.301389	+	0.953501i	$0.597450\pi$
$354$	−9.84912e9	−0.0333336
$355$	4.94851e11	1.65366
$356$	3.05874e11	1.00929
$357$	1.26807e11	0.413176
$358$	−2.02069e11	−0.650169
$359$	5.43941e10	0.172833	0.0864165	−	0.996259i	$-0.472458\pi$
$359$	5.43941e10	0.172833	0.0864165	+	0.996259i	$0.472458\pi$
$360$	4.17541e11	1.31020
$361$	−1.36080e11	−0.421707
$362$	3.50261e11	1.07202
$363$	−7.99786e10	−0.241765
$364$	2.06858e11	0.617612
$365$	−2.05387e11	−0.605695
$366$	−4.61609e9	−0.0134465
$367$	3.85965e11	1.11058	0.555291	−	0.831656i	$-0.312607\pi$
$367$	3.85965e11	1.11058	0.555291	+	0.831656i	$0.312607\pi$
$368$	3.51329e9	0.00998616
$369$	−3.36211e11	−0.944045
$370$	−1.24764e11	−0.346083
$371$	6.01115e10	0.164731
$372$	3.17053e10	0.0858398
$373$	−1.93481e11	−0.517545	−0.258772	−	0.965938i	$-0.583318\pi$
$373$	−1.93481e11	−0.517545	−0.258772	+	0.965938i	$0.583318\pi$
$374$	1.97769e10	0.0522681
$375$	−2.44593e10	−0.0638709
$376$	−6.62989e11	−1.71065
$377$	−7.31519e11	−1.86505
$378$	1.37830e11	0.347240
$379$	1.36906e10	0.0340837	0.0170419	−	0.999855i	$-0.494575\pi$
$379$	1.36906e10	0.0340837	0.0170419	+	0.999855i	$0.494575\pi$
$380$	2.31135e11	0.568643
$381$	1.68477e10	0.0409617
$382$	−3.64629e11	−0.876125
$383$	−4.49622e11	−1.06771	−0.533855	−	0.845576i	$-0.679257\pi$
$383$	−4.49622e11	−1.06771	−0.533855	+	0.845576i	$0.679257\pi$
$384$	−4.53339e10	−0.106398
$385$	3.27633e10	0.0760002
$386$	−3.76239e11	−0.862623
$387$	6.33384e10	0.143538
$388$	8.01090e10	0.179448
$389$	3.88202e10	0.0859577	0.0429789	−	0.999076i	$-0.486315\pi$
$389$	3.88202e10	0.0859577	0.0429789	+	0.999076i	$0.486315\pi$
$390$	9.90997e10	0.216911
$391$	5.32627e10	0.115247
$392$	−1.10763e11	−0.236923
$393$	1.27785e11	0.270218
$394$	−1.84379e11	−0.385460
$395$	−1.20075e11	−0.248180
$396$	−1.30923e10	−0.0267539
$397$	−1.19424e11	−0.241288	−0.120644	−	0.992696i	$-0.538496\pi$
$397$	−1.19424e11	−0.241288	−0.120644	+	0.992696i	$0.538496\pi$
$398$	−3.55032e11	−0.709241
$399$	1.03439e11	0.204318
$400$	−5.48399e10	−0.107109
$401$	6.09718e11	1.17755	0.588775	−	0.808297i	$-0.299610\pi$
$401$	6.09718e11	1.17755	0.588775	+	0.808297i	$0.299610\pi$
$402$	7.17942e10	0.137111
$403$	−3.37058e11	−0.636549
$404$	−2.75575e11	−0.514664
$405$	6.01512e11	1.11096
$406$	7.52902e11	1.37522
$407$	1.09385e10	0.0197598
$408$	2.16243e11	0.386341
$409$	9.60444e9	0.0169714	0.00848569	−	0.999964i	$-0.497299\pi$
$409$	9.60444e9	0.0169714	0.00848569	+	0.999964i	$0.497299\pi$
$410$	5.13135e11	0.896817
$411$	−1.89183e11	−0.327035
$412$	−2.18053e11	−0.372841
$413$	1.35368e11	0.228950
$414$	2.80702e10	0.0469618
$415$	8.84768e11	1.46424
$416$	5.79348e11	0.948462
$417$	−7.59272e10	−0.122966
$418$	1.61325e10	0.0258468
$419$	3.47797e11	0.551269	0.275634	−	0.961263i	$-0.411112\pi$
$419$	3.47797e11	0.551269	0.275634	+	0.961263i	$0.411112\pi$
$420$	1.28121e11	0.200908
$421$	−3.74682e11	−0.581291	−0.290645	−	0.956831i	$-0.593870\pi$
$421$	−3.74682e11	−0.581291	−0.290645	+	0.956831i	$0.593870\pi$
$422$	−8.22524e11	−1.26253
$423$	−1.02295e12	−1.55354
$424$	1.02508e11	0.154032
$425$	−8.31393e11	−1.23611
$426$	1.35064e11	0.198700
$427$	6.34444e10	0.0923566
$428$	1.94778e11	0.280571
$429$	−8.68843e9	−0.0123846
$430$	−9.66690e10	−0.136357
$431$	−1.23917e12	−1.72975	−0.864875	−	0.501987i	$-0.832603\pi$
$431$	−1.23917e12	−1.72975	−0.864875	+	0.501987i	$0.832603\pi$
$432$	4.53898e10	0.0627020
$433$	−5.28782e11	−0.722905	−0.361453	−	0.932390i	$-0.617719\pi$
$433$	−5.28782e11	−0.722905	−0.361453	+	0.932390i	$0.617719\pi$
$434$	3.46910e11	0.469368
$435$	−4.53078e11	−0.606696
$436$	−3.02897e11	−0.401427
$437$	4.34475e10	0.0569900
$438$	−5.60580e10	−0.0727787
$439$	1.10920e12	1.42534	0.712669	−	0.701500i	$-0.247486\pi$
$439$	1.10920e12	1.42534	0.712669	+	0.701500i	$0.247486\pi$
$440$	5.58712e10	0.0710642
$441$	−1.70900e11	−0.215163
$442$	−8.22172e11	−1.02462
$443$	1.21790e12	1.50243	0.751213	−	0.660059i	$-0.229469\pi$
$443$	1.21790e12	1.50243	0.751213	+	0.660059i	$0.229469\pi$
$444$	4.27748e10	0.0522354
$445$	−2.01402e12	−2.43469
$446$	4.06500e11	0.486467
$447$	8.61697e10	0.102087
$448$	−7.22213e11	−0.847060
$449$	−9.78940e11	−1.13670	−0.568352	−	0.822785i	$-0.692419\pi$
$449$	−9.78940e11	−1.13670	−0.568352	+	0.822785i	$0.692419\pi$
$450$	−4.38156e11	−0.503701
$451$	−4.49884e10	−0.0512042
$452$	7.84482e11	0.884016
$453$	−2.95409e11	−0.329596
$454$	3.44114e11	0.380146
$455$	−1.36205e12	−1.48984
$456$	1.76394e11	0.191048
$457$	9.91411e11	1.06324	0.531619	−	0.846983i	$-0.321584\pi$
$457$	9.91411e11	1.06324	0.531619	+	0.846983i	$0.321584\pi$
$458$	7.20602e10	0.0765246
$459$	6.88126e11	0.723620
$460$	5.38146e10	0.0560390
$461$	1.84663e11	0.190426	0.0952130	−	0.995457i	$-0.469647\pi$
$461$	1.84663e11	0.190426	0.0952130	+	0.995457i	$0.469647\pi$
$462$	8.94239e9	0.00913198
$463$	8.46043e11	0.855614	0.427807	−	0.903870i	$-0.359286\pi$
$463$	8.46043e11	0.855614	0.427807	+	0.903870i	$0.359286\pi$
$464$	2.47944e11	0.248326
$465$	−2.08762e11	−0.207068
$466$	3.82861e11	0.376101
$467$	1.63330e11	0.158906	0.0794530	−	0.996839i	$-0.474683\pi$
$467$	1.63330e11	0.158906	0.0794530	+	0.996839i	$0.474683\pi$
$468$	5.44277e11	0.524461
$469$	−9.86755e11	−0.941741
$470$	1.56125e12	1.47582
$471$	−5.54862e9	−0.00519506
$472$	2.30843e11	0.214081
$473$	8.47532e9	0.00778540
$474$	−3.27733e10	−0.0298207
$475$	−6.78184e11	−0.611261
$476$	−1.06294e12	−0.949026
$477$	1.58163e11	0.139885
$478$	6.46607e11	0.566519
$479$	1.37723e12	1.19536	0.597679	−	0.801736i	$-0.296090\pi$
$479$	1.37723e12	1.19536	0.597679	+	0.801736i	$0.296090\pi$
$480$	3.58828e11	0.308533
$481$	−4.54737e11	−0.387354
$482$	5.07195e11	0.428019
$483$	2.40834e10	0.0201352
$484$	6.70411e11	0.555312
$485$	−5.27474e11	−0.432876
$486$	5.49467e11	0.446764
$487$	−2.11605e12	−1.70469	−0.852347	−	0.522977i	$-0.824821\pi$
$487$	−2.11605e12	−1.70469	−0.852347	+	0.522977i	$0.824821\pi$
$488$	1.08192e11	0.0863583
$489$	−5.94586e11	−0.470246
$490$	2.60833e11	0.204399
$491$	−1.23880e11	−0.0961907	−0.0480954	−	0.998843i	$-0.515315\pi$
$491$	−1.23880e11	−0.0961907	−0.0480954	+	0.998843i	$0.515315\pi$
$492$	−1.75927e11	−0.135359
$493$	3.75892e12	2.86584
$494$	−6.70663e11	−0.506679
$495$	8.62056e10	0.0645375
$496$	1.14244e11	0.0847549
$497$	−1.85635e12	−1.36476
$498$	2.41488e11	0.175939
$499$	−2.30366e10	−0.0166328	−0.00831641	−	0.999965i	$-0.502647\pi$
$499$	−2.30366e10	−0.0166328	−0.00831641	+	0.999965i	$0.502647\pi$
$500$	2.05027e11	0.146705
$501$	4.39613e11	0.311746
$502$	5.04234e11	0.354377
$503$	1.75621e12	1.22327	0.611633	−	0.791142i	$-0.290513\pi$
$503$	1.75621e12	1.22327	0.611633	+	0.791142i	$0.290513\pi$
$504$	−1.56633e12	−1.08130
$505$	1.81451e12	1.24151
$506$	3.75608e9	0.00254717
$507$	5.66629e8	0.000380858 0
$508$	−1.41224e11	−0.0940850
$509$	1.05347e12	0.695650	0.347825	−	0.937559i	$-0.386920\pi$
$509$	1.05347e12	0.695650	0.347825	+	0.937559i	$0.386920\pi$
$510$	−5.09225e11	−0.333307
$511$	7.70473e11	0.499877
$512$	−4.11115e11	−0.264392
$513$	5.61319e11	0.357834
$514$	−5.82681e11	−0.368211
$515$	1.43576e12	0.899392
$516$	3.31426e10	0.0205809
$517$	−1.36881e11	−0.0842627
$518$	4.68030e11	0.285620
$519$	6.91831e11	0.418550
$520$	−2.32269e12	−1.39308
$521$	−7.44126e11	−0.442463	−0.221231	−	0.975221i	$-0.571008\pi$
$521$	−7.44126e11	−0.442463	−0.221231	+	0.975221i	$0.571008\pi$
$522$	1.98101e12	1.16780
$523$	9.32642e11	0.545076	0.272538	−	0.962145i	$-0.412137\pi$
$523$	9.32642e11	0.545076	0.272538	+	0.962145i	$0.412137\pi$
$524$	−1.07114e12	−0.620664
$525$	−3.75925e11	−0.215965
$526$	5.56549e11	0.317006
$527$	1.73198e12	0.978125
$528$	2.94489e9	0.00164898
$529$	−1.79104e12	−0.994384
$530$	−2.41393e11	−0.132887
$531$	3.56176e11	0.194419
$532$	−8.67064e11	−0.469298
$533$	1.87027e12	1.00376
$534$	−5.49704e11	−0.292545
$535$	−1.28251e12	−0.676811
$536$	−1.68271e12	−0.880577
$537$	−4.56163e11	−0.236720
$538$	−2.49475e12	−1.28383
$539$	−2.28681e10	−0.0116703
$540$	6.95256e11	0.351862
$541$	1.74928e12	0.877952	0.438976	−	0.898499i	$-0.355341\pi$
$541$	1.74928e12	0.877952	0.438976	+	0.898499i	$0.355341\pi$
$542$	5.85477e11	0.291416
$543$	7.90701e11	0.390313
$544$	−2.97699e12	−1.45741
$545$	1.99441e12	0.968347
$546$	−3.71756e11	−0.179015
$547$	−2.83590e12	−1.35440	−0.677202	−	0.735797i	$-0.736808\pi$
$547$	−2.83590e12	−1.35440	−0.677202	+	0.735797i	$0.736808\pi$
$548$	1.58581e12	0.751168
$549$	1.66933e11	0.0784270
$550$	−5.86297e10	−0.0273203
$551$	3.06623e12	1.41717
$552$	4.10694e10	0.0188275
$553$	4.50443e11	0.204822
$554$	2.25695e11	0.101796
$555$	−2.81649e11	−0.126005
$556$	6.36450e11	0.282441
$557$	−4.44074e11	−0.195482	−0.0977410	−	0.995212i	$-0.531162\pi$
$557$	−4.44074e11	−0.195482	−0.0977410	+	0.995212i	$0.531162\pi$
$558$	9.12777e11	0.398576
$559$	−3.52338e11	−0.152618
$560$	4.61657e11	0.198369
$561$	4.46456e10	0.0190303
$562$	−2.76687e12	−1.16997
$563$	2.66977e11	0.111992	0.0559959	−	0.998431i	$-0.482167\pi$
$563$	2.66977e11	0.111992	0.0559959	+	0.998431i	$0.482167\pi$
$564$	−5.35271e11	−0.222750
$565$	−5.16539e12	−2.13248
$566$	1.41988e12	0.581539
$567$	−2.25647e12	−0.916866
$568$	−3.16563e12	−1.27612
$569$	1.98776e12	0.794985	0.397492	−	0.917606i	$-0.369881\pi$
$569$	1.98776e12	0.794985	0.397492	+	0.917606i	$0.369881\pi$
$570$	−4.15386e11	−0.164822
$571$	1.77358e11	0.0698215	0.0349107	−	0.999390i	$-0.488885\pi$
$571$	1.77358e11	0.0698215	0.0349107	+	0.999390i	$0.488885\pi$
$572$	7.28297e10	0.0284463
$573$	−8.23135e11	−0.318989
$574$	−1.92494e12	−0.740139
$575$	−1.57900e11	−0.0602389
$576$	−1.90026e12	−0.719303
$577$	−2.44961e12	−0.920039	−0.460020	−	0.887909i	$-0.652158\pi$
$577$	−2.44961e12	−0.920039	−0.460020	+	0.887909i	$0.652158\pi$
$578$	2.43828e12	0.908675
$579$	−8.49344e11	−0.314073
$580$	3.79787e12	1.39352
$581$	−3.31906e12	−1.20843
$582$	−1.43968e11	−0.0520132
$583$	2.11638e10	0.00758727
$584$	1.31389e12	0.467412
$585$	−3.58377e12	−1.26514
$586$	−2.16192e12	−0.757356
$587$	−3.96669e12	−1.37898	−0.689488	−	0.724297i	$-0.742164\pi$
$587$	−3.96669e12	−1.37898	−0.689488	+	0.724297i	$0.742164\pi$
$588$	−8.94256e10	−0.0308506
$589$	1.41281e12	0.483687
$590$	−5.43606e11	−0.184693
$591$	−4.16229e11	−0.140342
$592$	1.54131e11	0.0515752
$593$	−1.37473e12	−0.456531	−0.228265	−	0.973599i	$-0.573305\pi$
$593$	−1.37473e12	−0.456531	−0.228265	+	0.973599i	$0.573305\pi$
$594$	4.85266e10	0.0159934
$595$	6.99889e12	2.28930
$596$	−7.22307e11	−0.234484
$597$	−8.01471e11	−0.258228
$598$	−1.56149e11	−0.0499325
$599$	−1.83622e12	−0.582779	−0.291389	−	0.956605i	$-0.594118\pi$
$599$	−1.83622e12	−0.582779	−0.291389	+	0.956605i	$0.594118\pi$
$600$	−6.41063e11	−0.201939
$601$	2.11756e12	0.662064	0.331032	−	0.943620i	$-0.392603\pi$
$601$	2.11756e12	0.662064	0.331032	+	0.943620i	$0.392603\pi$
$602$	3.62637e11	0.112535
$603$	−2.59631e12	−0.799704
$604$	2.47623e12	0.757050
$605$	−4.41429e12	−1.33956
$606$	4.95252e11	0.149176
$607$	6.21202e12	1.85731	0.928654	−	0.370947i	$-0.120967\pi$
$607$	6.21202e12	1.85731	0.928654	+	0.370947i	$0.120967\pi$
$608$	−2.42839e12	−0.720697
$609$	1.69965e12	0.500703
$610$	−2.54778e11	−0.0745035
$611$	5.69045e12	1.65181
$612$	−2.79677e12	−0.805890
$613$	1.80823e12	0.517228	0.258614	−	0.965981i	$-0.416734\pi$
$613$	1.80823e12	0.517228	0.258614	+	0.965981i	$0.416734\pi$
$614$	−3.73359e12	−1.06015
$615$	1.15838e12	0.326523
$616$	−2.09591e11	−0.0586489
$617$	−5.17980e11	−0.143890	−0.0719449	−	0.997409i	$-0.522921\pi$
$617$	−5.17980e11	−0.143890	−0.0719449	+	0.997409i	$0.522921\pi$
$618$	3.91875e11	0.108068
$619$	4.80654e12	1.31591	0.657953	−	0.753059i	$-0.271423\pi$
$619$	4.80654e12	1.31591	0.657953	+	0.753059i	$0.271423\pi$
$620$	1.74992e12	0.475616
$621$	1.30691e11	0.0352640
$622$	−4.87801e12	−1.30673
$623$	7.55524e12	2.00933
$624$	−1.22426e11	−0.0323253
$625$	−4.41628e12	−1.15770
$626$	3.85101e12	1.00228
$627$	3.64184e10	0.00941058
$628$	4.65106e10	0.0119326
$629$	2.33667e12	0.595210
$630$	3.68852e12	0.932867
$631$	6.50796e12	1.63423	0.817114	−	0.576476i	$-0.195572\pi$
$631$	6.50796e12	1.63423	0.817114	+	0.576476i	$0.195572\pi$
$632$	7.68138e11	0.191519
$633$	−1.85681e12	−0.459676
$634$	3.26110e12	0.801609
$635$	9.29881e11	0.226958
$636$	8.27609e10	0.0200571
$637$	9.50680e11	0.228774
$638$	2.65079e11	0.0633406
$639$	−4.88436e12	−1.15892
$640$	−2.50213e12	−0.589522
$641$	−3.48179e12	−0.814595	−0.407297	−	0.913296i	$-0.633529\pi$
$641$	−3.48179e12	−0.814595	−0.407297	+	0.913296i	$0.633529\pi$
$642$	−3.50046e11	−0.0813238
$643$	−1.58721e12	−0.366172	−0.183086	−	0.983097i	$-0.558609\pi$
$643$	−1.58721e12	−0.366172	−0.183086	+	0.983097i	$0.558609\pi$
$644$	−2.01876e11	−0.0462487
$645$	−2.18226e11	−0.0496465
$646$	3.44621e12	0.778566
$647$	−1.50095e12	−0.336741	−0.168371	−	0.985724i	$-0.553851\pi$
$647$	−1.50095e12	−0.336741	−0.168371	+	0.985724i	$0.553851\pi$
$648$	−3.84795e12	−0.857319
$649$	4.76599e10	0.0105451
$650$	2.43737e12	0.535564
$651$	7.83136e11	0.170892
$652$	4.98405e12	1.08011
$653$	−6.01788e12	−1.29519	−0.647596	−	0.761984i	$-0.724226\pi$
$653$	−6.01788e12	−1.29519	−0.647596	+	0.761984i	$0.724226\pi$
$654$	5.44354e11	0.116354
$655$	7.05290e12	1.49721
$656$	−6.33917e11	−0.133649
$657$	2.02724e12	0.424484
$658$	−5.85678e12	−1.21799
$659$	6.45564e12	1.33338	0.666691	−	0.745334i	$-0.267710\pi$
$659$	6.45564e12	1.33338	0.666691	+	0.745334i	$0.267710\pi$
$660$	4.51082e10	0.00925354
$661$	6.32975e12	1.28967	0.644837	−	0.764320i	$-0.276925\pi$
$661$	6.32975e12	1.28967	0.644837	+	0.764320i	$0.276925\pi$
$662$	−7.06380e11	−0.142948
$663$	−1.85602e12	−0.373054
$664$	−5.65998e12	−1.12995
$665$	5.70914e12	1.13207
$666$	1.23146e12	0.242542
$667$	7.13904e11	0.139660
$668$	−3.68500e12	−0.716051
$669$	9.17656e11	0.177118
$670$	3.96257e12	0.759697
$671$	2.23373e10	0.00425382
$672$	−1.34608e12	−0.254631
$673$	−2.05876e12	−0.386846	−0.193423	−	0.981115i	$-0.561959\pi$
$673$	−2.05876e12	−0.386846	−0.193423	+	0.981115i	$0.561959\pi$
$674$	−6.47664e12	−1.20887
$675$	−2.03998e12	−0.378233
$676$	−4.74970e9	−0.000874795 0
$677$	1.82789e12	0.334427	0.167213	−	0.985921i	$-0.446523\pi$
$677$	1.82789e12	0.334427	0.167213	+	0.985921i	$0.446523\pi$
$678$	−1.40984e12	−0.256233
$679$	1.97873e12	0.357250
$680$	1.19352e13	2.14062
$681$	7.76823e11	0.138408
$682$	1.22139e11	0.0216184
$683$	−5.70420e11	−0.100300	−0.0501501	−	0.998742i	$-0.515970\pi$
$683$	−5.70420e11	−0.100300	−0.0501501	+	0.998742i	$0.515970\pi$
$684$	−2.28139e12	−0.398517
$685$	−1.04417e13	−1.81202
$686$	3.30190e12	0.569253
$687$	1.62673e11	0.0278619
$688$	1.19423e11	0.0203208
$689$	−8.79829e11	−0.148734
$690$	−9.67133e10	−0.0162430
$691$	7.86912e11	0.131303	0.0656515	−	0.997843i	$-0.479087\pi$
$691$	7.86912e11	0.131303	0.0656515	+	0.997843i	$0.479087\pi$
$692$	−5.79919e12	−0.961369
$693$	−3.23386e11	−0.0532625
$694$	5.06386e12	0.828636
$695$	−4.19068e12	−0.681323
$696$	2.89840e12	0.468184
$697$	−9.61040e12	−1.54239
$698$	1.47413e12	0.235063
$699$	8.64294e11	0.136935
$700$	3.15114e12	0.496052
$701$	5.46260e12	0.854415	0.427207	−	0.904154i	$-0.359497\pi$
$701$	5.46260e12	0.854415	0.427207	+	0.904154i	$0.359497\pi$
$702$	−2.01736e12	−0.313521
$703$	1.90607e12	0.294334
$704$	−2.54274e11	−0.0390144
$705$	3.52447e12	0.537332
$706$	−2.64909e12	−0.401306
$707$	−6.80684e12	−1.02461
$708$	1.86374e11	0.0278763
$709$	−7.21721e12	−1.07266	−0.536329	−	0.844009i	$-0.680189\pi$
$709$	−7.21721e12	−1.07266	−0.536329	+	0.844009i	$0.680189\pi$
$710$	7.45466e12	1.10094
$711$	1.18519e12	0.173930
$712$	1.28839e13	1.87883
$713$	3.28941e11	0.0476667
$714$	1.91027e12	0.275076
$715$	−4.79544e11	−0.0686201
$716$	3.82373e12	0.543724
$717$	1.45969e12	0.206264
$718$	8.19416e11	0.115065
$719$	−9.38428e12	−1.30955	−0.654773	−	0.755825i	$-0.727236\pi$
$719$	−9.38428e12	−1.30955	−0.654773	+	0.755825i	$0.727236\pi$
$720$	1.21470e12	0.168450
$721$	−5.38600e12	−0.742263
$722$	−2.04996e12	−0.280756
$723$	1.14497e12	0.155838
$724$	−6.62795e12	−0.896512
$725$	−1.11435e13	−1.49796
$726$	−1.20483e12	−0.160958
$727$	−1.35930e13	−1.80472	−0.902362	−	0.430980i	$-0.858168\pi$
$727$	−1.35930e13	−1.80472	−0.902362	+	0.430980i	$0.858168\pi$
$728$	8.71319e12	1.14970
$729$	−5.06737e12	−0.664521
$730$	−3.09403e12	−0.403248
$731$	1.81050e12	0.234514
$732$	8.73496e10	0.0112450
$733$	−1.32485e13	−1.69512	−0.847559	−	0.530701i	$-0.821929\pi$
$733$	−1.32485e13	−1.69512	−0.847559	+	0.530701i	$0.821929\pi$
$734$	5.81435e12	0.739382
$735$	5.88819e11	0.0744198
$736$	−5.65397e11	−0.0710237
$737$	−3.47413e11	−0.0433753
$738$	−5.06483e12	−0.628508
$739$	−6.06380e10	−0.00747903	−0.00373951	−	0.999993i	$-0.501190\pi$
$739$	−6.06380e10	−0.00747903	−0.00373951	+	0.999993i	$0.501190\pi$
$740$	2.36089e12	0.289423
$741$	−1.51399e12	−0.184477
$742$	9.05546e11	0.109671
$743$	8.45052e12	1.01726	0.508632	−	0.860984i	$-0.330151\pi$
$743$	8.45052e12	1.01726	0.508632	+	0.860984i	$0.330151\pi$
$744$	1.33548e12	0.159793
$745$	4.75600e12	0.565638
$746$	−2.91468e12	−0.344561
$747$	−8.73298e12	−1.02617
$748$	−3.74236e11	−0.0437108
$749$	4.81110e12	0.558569
$750$	−3.68466e11	−0.0425227
$751$	5.00951e12	0.574666	0.287333	−	0.957831i	$-0.407231\pi$
$751$	5.00951e12	0.574666	0.287333	+	0.957831i	$0.407231\pi$
$752$	−1.92874e12	−0.219935
$753$	1.13829e12	0.129025
$754$	−1.10199e13	−1.24167
$755$	−1.63046e13	−1.82620
$756$	−2.60814e12	−0.290390
$757$	5.80549e12	0.642551	0.321276	−	0.946986i	$-0.395888\pi$
$757$	5.80549e12	0.642551	0.321276	+	0.946986i	$0.395888\pi$
$758$	2.06242e11	0.0226916
$759$	8.47920e9	0.000927400 0
$760$	9.73578e12	1.05855
$761$	1.32066e13	1.42745	0.713723	−	0.700429i	$-0.247008\pi$
$761$	1.32066e13	1.42745	0.713723	+	0.700429i	$0.247008\pi$
$762$	2.53801e11	0.0272707
$763$	−7.48171e12	−0.799172
$764$	6.89983e12	0.732686
$765$	1.84152e13	1.94402
$766$	−6.77331e12	−0.710839
$767$	−1.98133e12	−0.206718
$768$	−2.46885e12	−0.256076
$769$	−8.98106e12	−0.926102	−0.463051	−	0.886332i	$-0.653245\pi$
$769$	−8.98106e12	−0.926102	−0.463051	+	0.886332i	$0.653245\pi$
$770$	4.93561e11	0.0505979
$771$	−1.31538e12	−0.134062
$772$	7.11952e12	0.721395
$773$	−3.75046e12	−0.377813	−0.188906	−	0.981995i	$-0.560494\pi$
$773$	−3.75046e12	−0.377813	−0.188906	+	0.981995i	$0.560494\pi$
$774$	9.54158e11	0.0955621
$775$	−5.13453e12	−0.511262
$776$	3.37432e12	0.334048
$777$	1.05656e12	0.103992
$778$	5.84805e11	0.0572272
$779$	−7.83941e12	−0.762719
$780$	−1.87525e12	−0.181399
$781$	−6.53577e11	−0.0628589
$782$	8.02373e11	0.0767266
$783$	9.22325e12	0.876912
$784$	−3.22228e11	−0.0304607
$785$	−3.06247e11	−0.0287845
$786$	1.92501e12	0.179900
$787$	8.97788e12	0.834233	0.417117	−	0.908853i	$-0.363041\pi$
$787$	8.97788e12	0.834233	0.417117	+	0.908853i	$0.363041\pi$
$788$	3.48899e12	0.322353
$789$	1.25639e12	0.115419
$790$	−1.80887e12	−0.165229
$791$	1.93771e13	1.75993
$792$	−5.51469e11	−0.0498032
$793$	−9.28611e11	−0.0833882
$794$	−1.79906e12	−0.160640
$795$	−5.44936e11	−0.0483830
$796$	6.71823e12	0.593125
$797$	−9.78357e12	−0.858884	−0.429442	−	0.903094i	$-0.641290\pi$
$797$	−9.78357e12	−0.858884	−0.429442	+	0.903094i	$0.641290\pi$
$798$	1.55825e12	0.136027
$799$	−2.92405e13	−2.53819
$800$	8.82544e12	0.761783
$801$	1.98791e13	1.70628
$802$	9.18507e12	0.783967
$803$	2.71265e11	0.0230236
$804$	−1.35855e12	−0.114663
$805$	1.32925e12	0.111564
$806$	−5.07759e12	−0.423789
$807$	−5.63180e12	−0.467430
$808$	−1.16077e13	−0.958063
$809$	−2.21862e13	−1.82102	−0.910511	−	0.413485i	$-0.864311\pi$
$809$	−2.21862e13	−1.82102	−0.910511	+	0.413485i	$0.864311\pi$
$810$	9.06145e12	0.739631
$811$	2.78479e12	0.226047	0.113023	−	0.993592i	$-0.463946\pi$
$811$	2.78479e12	0.226047	0.113023	+	0.993592i	$0.463946\pi$
$812$	−1.42471e13	−1.15007
$813$	1.32169e12	0.106102
$814$	1.64782e11	0.0131553
$815$	−3.28172e13	−2.60551
$816$	6.29087e11	0.0496712
$817$	1.47686e12	0.115968
$818$	1.44685e11	0.0112989
$819$	1.34439e13	1.04411
$820$	−9.70998e12	−0.749991
$821$	1.16501e13	0.894920	0.447460	−	0.894304i	$-0.352329\pi$
$821$	1.16501e13	0.894920	0.447460	+	0.894304i	$0.352329\pi$
$822$	−2.84994e12	−0.217727
$823$	8.62542e11	0.0655361	0.0327681	−	0.999463i	$-0.489568\pi$
$823$	8.62542e11	0.0655361	0.0327681	+	0.999463i	$0.489568\pi$
$824$	−9.18473e12	−0.694055
$825$	−1.32354e11	−0.00994706
$826$	2.03925e12	0.152426
$827$	3.07127e12	0.228320	0.114160	−	0.993462i	$-0.463582\pi$
$827$	3.07127e12	0.228320	0.114160	+	0.993462i	$0.463582\pi$
$828$	−5.31170e11	−0.0392733
$829$	1.65764e13	1.21897	0.609487	−	0.792796i	$-0.291375\pi$
$829$	1.65764e13	1.21897	0.609487	+	0.792796i	$0.291375\pi$
$830$	1.33285e13	0.974835
$831$	5.09498e11	0.0370628
$832$	1.05707e13	0.764805
$833$	−4.88509e12	−0.351536
$834$	−1.14380e12	−0.0818659
$835$	2.42637e13	1.72730
$836$	−3.05272e11	−0.0216152
$837$	4.24974e12	0.299294
$838$	5.23937e12	0.367013
$839$	9.91022e12	0.690486	0.345243	−	0.938513i	$-0.387797\pi$
$839$	9.91022e12	0.690486	0.345243	+	0.938513i	$0.387797\pi$
$840$	5.39665e12	0.373996
$841$	3.58753e13	2.47294
$842$	−5.64437e12	−0.387000
$843$	−6.24609e12	−0.425975
$844$	1.55645e13	1.05583
$845$	3.12742e10	0.00211024
$846$	−1.54102e13	−1.03429
$847$	1.65595e13	1.10553
$848$	2.98213e11	0.0198036
$849$	3.20533e12	0.211733
$850$	−1.25245e13	−0.822951
$851$	4.43787e11	0.0290062
$852$	−2.55580e12	−0.166169
$853$	−2.84458e13	−1.83970	−0.919852	−	0.392266i	$-0.871691\pi$
$853$	−2.84458e13	−1.83970	−0.919852	+	0.392266i	$0.871691\pi$
$854$	9.55755e11	0.0614874
$855$	1.50217e13	0.961327
$856$	8.20436e12	0.522291
$857$	−9.16254e12	−0.580232	−0.290116	−	0.956991i	$-0.593694\pi$
$857$	−9.16254e12	−0.580232	−0.290116	+	0.956991i	$0.593694\pi$
$858$	−1.30886e11	−0.00824520
$859$	−1.59098e13	−0.997002	−0.498501	−	0.866889i	$-0.666116\pi$
$859$	−1.59098e13	−0.997002	−0.498501	+	0.866889i	$0.666116\pi$
$860$	1.82926e12	0.114033
$861$	−4.34547e12	−0.269477
$862$	−1.86674e13	−1.15160
$863$	−6.71369e12	−0.412015	−0.206007	−	0.978550i	$-0.566047\pi$
$863$	−6.71369e12	−0.412015	−0.206007	+	0.978550i	$0.566047\pi$
$864$	−7.30463e12	−0.445950
$865$	3.81845e13	2.31908
$866$	−7.96581e12	−0.481282
$867$	5.50432e12	0.330840
$868$	−6.56454e12	−0.392523
$869$	1.58590e11	0.00943381
$870$	−6.82537e12	−0.403914
$871$	1.44427e13	0.850292
$872$	−1.27585e13	−0.747268
$873$	5.20636e12	0.303368
$874$	6.54513e11	0.0379417
$875$	5.06426e12	0.292065
$876$	1.06078e12	0.0608635
$877$	4.21446e12	0.240571	0.120286	−	0.992739i	$-0.461619\pi$
$877$	4.21446e12	0.240571	0.120286	+	0.992739i	$0.461619\pi$
$878$	1.67094e13	0.948934
$879$	−4.88044e12	−0.275746
$880$	1.62539e11	0.00913660
$881$	−8.50983e12	−0.475915	−0.237957	−	0.971276i	$-0.576478\pi$
$881$	−8.50983e12	−0.475915	−0.237957	+	0.971276i	$0.576478\pi$
$882$	−2.57451e12	−0.143247
$883$	2.12668e13	1.17728	0.588639	−	0.808396i	$-0.299664\pi$
$883$	2.12668e13	1.17728	0.588639	+	0.808396i	$0.299664\pi$
$884$	1.55579e13	0.856869
$885$	−1.22717e12	−0.0672450
$886$	1.83469e13	1.00026
$887$	−2.61674e13	−1.41940	−0.709700	−	0.704504i	$-0.751170\pi$
$887$	−2.61674e13	−1.41940	−0.709700	+	0.704504i	$0.751170\pi$
$888$	1.80174e12	0.0972377
$889$	−3.48829e12	−0.187307
$890$	−3.03400e13	−1.62092
$891$	−7.94450e11	−0.0422296
$892$	−7.69214e12	−0.406823
$893$	−2.38521e13	−1.25515
$894$	1.29810e12	0.0679655
$895$	−2.51772e13	−1.31161
$896$	9.38632e12	0.486530
$897$	−3.52500e11	−0.0181800
$898$	−1.47472e13	−0.756773
$899$	2.32144e13	1.18533
$900$	8.29118e12	0.421235
$901$	4.52101e12	0.228546
$902$	−6.77725e11	−0.0340898
$903$	8.18639e11	0.0409730
$904$	3.30437e13	1.64562
$905$	4.36415e13	2.16262
$906$	−4.45017e12	−0.219432
$907$	1.63634e13	0.802861	0.401431	−	0.915889i	$-0.368513\pi$
$907$	1.63634e13	0.802861	0.401431	+	0.915889i	$0.368513\pi$
$908$	−6.51162e12	−0.317909
$909$	−1.79099e13	−0.870073
$910$	−2.05185e13	−0.991878
$911$	−3.39916e13	−1.63508	−0.817540	−	0.575872i	$-0.804663\pi$
$911$	−3.39916e13	−1.63508	−0.817540	+	0.575872i	$0.804663\pi$
$912$	5.13159e11	0.0245627
$913$	−1.16856e12	−0.0556587
$914$	1.49350e13	0.707862
$915$	−5.75150e11	−0.0271260
$916$	−1.36359e12	−0.0639961
$917$	−2.64577e13	−1.23564
$918$	1.03662e13	0.481758
$919$	−2.19737e12	−0.101621	−0.0508106	−	0.998708i	$-0.516180\pi$
$919$	−2.19737e12	−0.101621	−0.0508106	+	0.998708i	$0.516180\pi$
$920$	2.26676e12	0.104318
$921$	−8.42843e12	−0.385992
$922$	2.78185e12	0.126778
$923$	2.71707e13	1.23223
$924$	−1.69216e11	−0.00763690
$925$	−6.92719e12	−0.311114
$926$	1.27452e13	0.569634
$927$	−1.41715e13	−0.630312
$928$	−3.99019e13	−1.76615
$929$	−1.08879e12	−0.0479596	−0.0239798	−	0.999712i	$-0.507634\pi$
$929$	−1.08879e12	−0.0479596	−0.0239798	+	0.999712i	$0.507634\pi$
$930$	−3.14488e12	−0.137858
$931$	−3.98487e12	−0.173836
$932$	−7.24484e12	−0.314526
$933$	−1.10119e13	−0.475768
$934$	2.46048e12	0.105793
$935$	2.46414e12	0.105442
$936$	2.29258e13	0.976300
$937$	3.72812e13	1.58002	0.790008	−	0.613096i	$-0.210076\pi$
$937$	3.72812e13	1.58002	0.790008	+	0.613096i	$0.210076\pi$
$938$	−1.48649e13	−0.626974
$939$	8.69350e12	0.364922
$940$	−2.95434e13	−1.23420
$941$	1.01973e13	0.423966	0.211983	−	0.977273i	$-0.432008\pi$
$941$	1.01973e13	0.423966	0.211983	+	0.977273i	$0.432008\pi$
$942$	−8.35868e10	−0.00345867
$943$	−1.82523e12	−0.0751649
$944$	6.71561e11	0.0275240
$945$	1.71732e13	0.700498
$946$	1.27676e11	0.00518321
$947$	−1.73267e13	−0.700070	−0.350035	−	0.936737i	$-0.613830\pi$
$947$	−1.73267e13	−0.700070	−0.350035	+	0.936737i	$0.613830\pi$
$948$	6.20165e11	0.0249385
$949$	−1.12771e13	−0.451336
$950$	−1.02165e13	−0.406953
$951$	7.36180e12	0.291858
$952$	−4.47728e13	−1.76664
$953$	−3.24945e13	−1.27612	−0.638060	−	0.769986i	$-0.720263\pi$
$953$	−3.24945e13	−1.27612	−0.638060	+	0.769986i	$0.720263\pi$
$954$	2.38264e12	0.0931302
$955$	−4.54316e13	−1.76743
$956$	−1.22357e13	−0.473769
$957$	5.98405e11	0.0230617
$958$	2.07473e13	0.795822
$959$	3.91701e13	1.49545
$960$	6.54716e12	0.248790
$961$	−1.57432e13	−0.595441
$962$	−6.85037e12	−0.257885
$963$	1.26588e13	0.474323
$964$	−9.59759e12	−0.357944
$965$	−4.68782e13	−1.74020
$966$	3.62803e11	0.0134052
$967$	−2.07087e13	−0.761611	−0.380805	−	0.924655i	$-0.624353\pi$
$967$	−2.07087e13	−0.761611	−0.380805	+	0.924655i	$0.624353\pi$
$968$	2.82388e13	1.03373
$969$	7.77968e12	0.283468
$970$	−7.94611e12	−0.288192
$971$	3.71042e13	1.33948	0.669740	−	0.742596i	$-0.266406\pi$
$971$	3.71042e13	1.33948	0.669740	+	0.742596i	$0.266406\pi$
$972$	−1.03975e13	−0.373621
$973$	1.57206e13	0.562292
$974$	−3.18772e13	−1.13492
$975$	5.50227e12	0.194994
$976$	3.14747e11	0.0111029
$977$	−1.12430e13	−0.394783	−0.197392	−	0.980325i	$-0.563247\pi$
$977$	−1.12430e13	−0.394783	−0.197392	+	0.980325i	$0.563247\pi$
$978$	−8.95711e12	−0.313071
$979$	2.66002e12	0.0925471
$980$	−4.93570e12	−0.170935
$981$	−1.96856e13	−0.678638
$982$	−1.86618e12	−0.0640400
$983$	−7.97289e12	−0.272349	−0.136174	−	0.990685i	$-0.543481\pi$
$983$	−7.97289e12	−0.272349	−0.136174	+	0.990685i	$0.543481\pi$
$984$	−7.41031e12	−0.251976
$985$	−2.29731e13	−0.777601
$986$	5.66261e13	1.90796
$987$	−1.32214e13	−0.443457
$988$	1.26909e13	0.423726
$989$	3.43854e11	0.0114285
$990$	1.29864e12	0.0429665
$991$	2.75569e13	0.907609	0.453804	−	0.891101i	$-0.350066\pi$
$991$	2.75569e13	0.907609	0.453804	+	0.891101i	$0.350066\pi$
$992$	−1.83854e13	−0.602795
$993$	−1.59462e12	−0.0520459
$994$	−2.79649e13	−0.908603
$995$	−4.42359e13	−1.43077
$996$	−4.56964e12	−0.147135
$997$	1.33441e13	0.427722	0.213861	−	0.976864i	$-0.431396\pi$
$997$	1.33441e13	0.427722	0.213861	+	0.976864i	$0.431396\pi$
$998$	−3.47033e11	−0.0110735
$999$	5.73349e12	0.182127

Twists

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

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

\(f(q)\)	\(=\)	\(q+15.0644 q^{2} +34.0074 q^{3} -285.063 q^{4} +1876.98 q^{5} +512.302 q^{6} -7041.18 q^{7} -12007.3 q^{8} -18526.5 q^{9} +O(q^{10})\)	\(q+15.0644 q^{2} +34.0074 q^{3} -285.063 q^{4} +1876.98 q^{5} +512.302 q^{6} -7041.18 q^{7} -12007.3 q^{8} -18526.5 q^{9} +28275.7 q^{10} -2479.03 q^{11} -9694.23 q^{12} +103059. q^{13} -106071. q^{14} +63831.2 q^{15} -34931.2 q^{16} -529570. q^{17} -279091. q^{18} -431982. q^{19} -535058. q^{20} -239452. q^{21} -37345.2 q^{22} -100577. q^{23} -408337. q^{24} +1.56994e6 q^{25} +1.55253e6 q^{26} -1.29940e6 q^{27} +2.00718e6 q^{28} -7.09806e6 q^{29} +961582. q^{30} -3.27053e6 q^{31} +5.62152e6 q^{32} -84305.4 q^{33} -7.97768e6 q^{34} -1.32162e7 q^{35} +5.28121e6 q^{36} -4.41240e6 q^{37} -6.50756e6 q^{38} +3.50477e6 q^{39} -2.25375e7 q^{40} +1.81476e7 q^{41} -3.60721e6 q^{42} -3.41880e6 q^{43} +706679. q^{44} -3.47739e7 q^{45} -1.51514e6 q^{46} +5.52154e7 q^{47} -1.18792e6 q^{48} +9.22462e6 q^{49} +2.36502e7 q^{50} -1.80093e7 q^{51} -2.93783e7 q^{52} -8.53713e6 q^{53} -1.95748e7 q^{54} -4.65310e6 q^{55} +8.45456e7 q^{56} -1.46906e7 q^{57} -1.06928e8 q^{58} -1.92252e7 q^{59} -1.81959e7 q^{60} -9.01048e6 q^{61} -4.92687e7 q^{62} +1.30448e8 q^{63} +1.02570e8 q^{64} +1.93440e8 q^{65} -1.27001e6 q^{66} +1.40140e8 q^{67} +1.50961e8 q^{68} -3.42037e6 q^{69} -1.99094e8 q^{70} +2.63642e8 q^{71} +2.22453e8 q^{72} -1.09424e8 q^{73} -6.64703e7 q^{74} +5.33895e7 q^{75} +1.23142e8 q^{76} +1.74553e7 q^{77} +5.27973e7 q^{78} -6.39726e7 q^{79} -6.55653e7 q^{80} +3.20468e8 q^{81} +2.73383e8 q^{82} +4.71378e8 q^{83} +6.82588e7 q^{84} -9.93994e8 q^{85} -5.15023e7 q^{86} -2.41386e8 q^{87} +2.97665e7 q^{88} -1.07301e9 q^{89} -5.23850e8 q^{90} -7.25657e8 q^{91} +2.86708e7 q^{92} -1.11222e8 q^{93} +8.31790e8 q^{94} -8.10822e8 q^{95} +1.91173e8 q^{96} -2.81023e8 q^{97} +1.38964e8 q^{98} +4.59278e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 32 q^{2} - 317 q^{3} + 3242 q^{4} - 4717 q^{5} + 687 q^{6} - 9680 q^{7} - 20394 q^{8} + 69516 q^{9}+O(q^{10}) \) 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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Database

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