LMFDB - Embedded newform 43.10.a.a.1.15

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			1.15
Root			$-45.0936$ 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)

$f(q)$	$=$	$q+43.0936 q^{2} -179.621 q^{3} +1345.05 q^{4} -1330.99 q^{5} -7740.49 q^{6} -743.545 q^{7} +35899.3 q^{8} +12580.5 q^{9} +O(q^{10})$	\(q+43.0936 q^{2} -179.621 q^{3} +1345.05 q^{4} -1330.99 q^{5} -7740.49 q^{6} -743.545 q^{7} +35899.3 q^{8} +12580.5 q^{9} -57356.9 q^{10} -60876.5 q^{11} -241599. q^{12} -104090. q^{13} -32042.0 q^{14} +239072. q^{15} +858359. q^{16} -344506. q^{17} +542140. q^{18} -626694. q^{19} -1.79025e6 q^{20} +133556. q^{21} -2.62338e6 q^{22} +1.13084e6 q^{23} -6.44824e6 q^{24} -181604. q^{25} -4.48560e6 q^{26} +1.27575e6 q^{27} -1.00011e6 q^{28} +3.51526e6 q^{29} +1.03025e7 q^{30} -6.97177e6 q^{31} +1.86093e7 q^{32} +1.09347e7 q^{33} -1.48460e7 q^{34} +989648. q^{35} +1.69215e7 q^{36} +7.60065e6 q^{37} -2.70065e7 q^{38} +1.86967e7 q^{39} -4.77814e7 q^{40} +3.04443e7 q^{41} +5.75540e6 q^{42} -3.41880e6 q^{43} -8.18822e7 q^{44} -1.67445e7 q^{45} +4.87317e7 q^{46} +3.57930e7 q^{47} -1.54179e8 q^{48} -3.98007e7 q^{49} -7.82595e6 q^{50} +6.18803e7 q^{51} -1.40006e8 q^{52} -9.41168e7 q^{53} +5.49766e7 q^{54} +8.10257e7 q^{55} -2.66927e7 q^{56} +1.12567e8 q^{57} +1.51485e8 q^{58} -1.25011e8 q^{59} +3.21565e8 q^{60} +1.62742e8 q^{61} -3.00439e8 q^{62} -9.35420e6 q^{63} +3.62462e8 q^{64} +1.38542e8 q^{65} +4.71214e8 q^{66} +1.76153e8 q^{67} -4.63379e8 q^{68} -2.03121e8 q^{69} +4.26474e7 q^{70} -7.75938e7 q^{71} +4.51632e8 q^{72} -4.14592e8 q^{73} +3.27539e8 q^{74} +3.26198e7 q^{75} -8.42937e8 q^{76} +4.52644e7 q^{77} +8.05706e8 q^{78} +3.87411e8 q^{79} -1.14246e9 q^{80} -4.76773e8 q^{81} +1.31195e9 q^{82} +1.61425e7 q^{83} +1.79640e8 q^{84} +4.58532e8 q^{85} -1.47328e8 q^{86} -6.31412e8 q^{87} -2.18542e9 q^{88} -1.53813e8 q^{89} -7.21580e8 q^{90} +7.73955e7 q^{91} +1.52103e9 q^{92} +1.25227e9 q^{93} +1.54245e9 q^{94} +8.34120e8 q^{95} -3.34261e9 q^{96} +1.02217e9 q^{97} -1.71516e9 q^{98} -7.65859e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	43.0936	1.90448	0.952242	−	0.305345i	$-0.0987716\pi$
$2$	43.0936	1.90448	0.952242	+	0.305345i	$0.0987716\pi$
$3$	−179.621	−1.28030	−0.640148	−	0.768252i	$-0.721127\pi$
$3$	−179.621	−1.28030	−0.640148	+	0.768252i	$0.721127\pi$
$4$	1345.05	2.62706
$5$	−1330.99	−0.952375	−0.476188	−	0.879344i	$-0.657982\pi$
$5$	−1330.99	−0.952375	−0.476188	+	0.879344i	$0.657982\pi$
$6$	−7740.49	−2.43830
$7$	−743.545	−0.117049	−0.0585243	−	0.998286i	$-0.518640\pi$
$7$	−743.545	−0.117049	−0.0585243	+	0.998286i	$0.518640\pi$
$8$	35899.3	3.09871
$9$	12580.5	0.639157
$10$	−57356.9	−1.81378
$11$	−60876.5	−1.25367	−0.626834	−	0.779153i	$-0.715650\pi$
$11$	−60876.5	−1.25367	−0.626834	+	0.779153i	$0.715650\pi$
$12$	−241599.	−3.36341
$13$	−104090.	−1.01080	−0.505398	−	0.862887i	$-0.668654\pi$
$13$	−104090.	−1.01080	−0.505398	+	0.862887i	$0.668654\pi$
$14$	−32042.0	−0.222917
$15$	239072.	1.21932
$16$	858359.	3.27438
$17$	−344506.	−1.00041	−0.500203	−	0.865908i	$-0.666741\pi$
$17$	−344506.	−1.00041	−0.500203	+	0.865908i	$0.666741\pi$
$18$	542140.	1.21726
$19$	−626694.	−1.10323	−0.551613	−	0.834100i	$-0.685987\pi$
$19$	−626694.	−1.10323	−0.551613	+	0.834100i	$0.685987\pi$
$20$	−1.79025e6	−2.50195
$21$	133556.	0.149857
$22$	−2.62338e6	−2.38759
$23$	1.13084e6	0.842605	0.421303	−	0.906920i	$-0.361573\pi$
$23$	1.13084e6	0.842605	0.421303	+	0.906920i	$0.361573\pi$
$24$	−6.44824e6	−3.96726
$25$	−181604.	−0.0929811
$26$	−4.48560e6	−1.92504
$27$	1.27575e6	0.461986
$28$	−1.00011e6	−0.307494
$29$	3.51526e6	0.922924	0.461462	−	0.887160i	$-0.347325\pi$
$29$	3.51526e6	0.922924	0.461462	+	0.887160i	$0.347325\pi$
$30$	1.03025e7	2.32218
$31$	−6.97177e6	−1.35586	−0.677931	−	0.735125i	$-0.737123\pi$
$31$	−6.97177e6	−1.35586	−0.677931	+	0.735125i	$0.737123\pi$
$32$	1.86093e7	3.13730
$33$	1.09347e7	1.60507
$34$	−1.48460e7	−1.90526
$35$	989648.	0.111474
$36$	1.69215e7	1.67910
$37$	7.60065e6	0.666719	0.333360	−	0.942800i	$-0.391818\pi$
$37$	7.60065e6	0.666719	0.333360	+	0.942800i	$0.391818\pi$
$38$	−2.70065e7	−2.10108
$39$	1.86967e7	1.29412
$40$	−4.77814e7	−2.95113
$41$	3.04443e7	1.68259	0.841296	−	0.540575i	$-0.181793\pi$
$41$	3.04443e7	1.68259	0.841296	+	0.540575i	$0.181793\pi$
$42$	5.75540e6	0.285400
$43$	−3.41880e6	−0.152499
$43$	−3.41880e6	−0.152499
$44$	−8.18822e7	−3.29346
$45$	−1.67445e7	−0.608718
$46$	4.87317e7	1.60473
$47$	3.57930e7	1.06994	0.534968	−	0.844872i	$-0.320324\pi$
$47$	3.57930e7	1.06994	0.534968	+	0.844872i	$0.320324\pi$
$48$	−1.54179e8	−4.19217
$49$	−3.98007e7	−0.986300
$50$	−7.82595e6	−0.177081
$51$	6.18803e7	1.28082
$52$	−1.40006e8	−2.65542
$53$	−9.41168e7	−1.63842	−0.819211	−	0.573492i	$-0.805588\pi$
$53$	−9.41168e7	−1.63842	−0.819211	+	0.573492i	$0.805588\pi$
$54$	5.49766e7	0.879844
$55$	8.10257e7	1.19396
$56$	−2.66927e7	−0.362699
$57$	1.12567e8	1.41246
$58$	1.51485e8	1.75769
$59$	−1.25011e8	−1.34312	−0.671561	−	0.740949i	$-0.734376\pi$
$59$	−1.25011e8	−1.34312	−0.671561	+	0.740949i	$0.734376\pi$
$60$	3.21565e8	3.20323
$61$	1.62742e8	1.50493	0.752464	−	0.658633i	$-0.228865\pi$
$61$	1.62742e8	1.50493	0.752464	+	0.658633i	$0.228865\pi$
$62$	−3.00439e8	−2.58222
$63$	−9.35420e6	−0.0748125
$64$	3.62462e8	2.70055
$65$	1.38542e8	0.962656
$66$	4.71214e8	3.05682
$67$	1.76153e8	1.06796	0.533978	−	0.845498i	$-0.320697\pi$
$67$	1.76153e8	1.06796	0.533978	+	0.845498i	$0.320697\pi$
$68$	−4.63379e8	−2.62813
$69$	−2.03121e8	−1.07878
$70$	4.26474e7	0.212301
$71$	−7.75938e7	−0.362380	−0.181190	−	0.983448i	$-0.557995\pi$
$71$	−7.75938e7	−0.362380	−0.181190	+	0.983448i	$0.557995\pi$
$72$	4.51632e8	1.98056
$73$	−4.14592e8	−1.70871	−0.854354	−	0.519692i	$-0.826047\pi$
$73$	−4.14592e8	−1.70871	−0.854354	+	0.519692i	$0.826047\pi$
$74$	3.27539e8	1.26976
$75$	3.26198e7	0.119043
$76$	−8.42937e8	−2.89824
$77$	4.52644e7	0.146740
$78$	8.05706e8	2.46462
$79$	3.87411e8	1.11905	0.559526	−	0.828813i	$-0.310983\pi$
$79$	3.87411e8	1.11905	0.559526	+	0.828813i	$0.310983\pi$
$80$	−1.14246e9	−3.11844
$81$	−4.76773e8	−1.23064
$82$	1.31195e9	3.20447
$83$	1.61425e7	0.0373354	0.0186677	−	0.999826i	$-0.494058\pi$
$83$	1.61425e7	0.0373354	0.0186677	+	0.999826i	$0.494058\pi$
$84$	1.79640e8	0.393683
$85$	4.58532e8	0.952763
$86$	−1.47328e8	−0.290431
$87$	−6.31412e8	−1.18162
$88$	−2.18542e9	−3.88475
$89$	−1.53813e8	−0.259859	−0.129929	−	0.991523i	$-0.541475\pi$
$89$	−1.53813e8	−0.259859	−0.129929	+	0.991523i	$0.541475\pi$
$90$	−7.21580e8	−1.15929
$91$	7.73955e7	0.118312
$92$	1.52103e9	2.21357
$93$	1.25227e9	1.73591
$94$	1.54245e9	2.03768
$95$	8.34120e8	1.05069
$96$	−3.34261e9	−4.01667
$97$	1.02217e9	1.17233	0.586167	−	0.810190i	$-0.300636\pi$
$97$	1.02217e9	1.17233	0.586167	+	0.810190i	$0.300636\pi$
$98$	−1.71516e9	−1.87839
$99$	−7.65859e8	−0.801291
$100$	−2.44267e8	−0.244267
$101$	−6.67110e8	−0.637898	−0.318949	−	0.947772i	$-0.603330\pi$
$101$	−6.67110e8	−0.637898	−0.318949	+	0.947772i	$0.603330\pi$
$102$	2.66664e9	2.43929
$103$	6.79368e7	0.0594754	0.0297377	−	0.999558i	$-0.490533\pi$
$103$	6.79368e7	0.0594754	0.0297377	+	0.999558i	$0.490533\pi$
$104$	−3.73675e9	−3.13216
$105$	−1.77761e8	−0.142720
$106$	−4.05583e9	−3.12035
$107$	−1.71864e9	−1.26753	−0.633766	−	0.773525i	$-0.718492\pi$
$107$	−1.71864e9	−1.26753	−0.633766	+	0.773525i	$0.718492\pi$
$108$	1.71595e9	1.21366
$109$	−1.49887e9	−1.01706	−0.508530	−	0.861045i	$-0.669811\pi$
$109$	−1.49887e9	−1.01706	−0.508530	+	0.861045i	$0.669811\pi$
$110$	3.49169e9	2.27388
$111$	−1.36523e9	−0.853598
$112$	−6.38229e8	−0.383262
$113$	−4.77264e8	−0.275363	−0.137681	−	0.990477i	$-0.543965\pi$
$113$	−4.77264e8	−0.275363	−0.137681	+	0.990477i	$0.543965\pi$
$114$	4.85092e9	2.69000
$115$	−1.50512e9	−0.802476
$116$	4.72821e9	2.42458
$117$	−1.30951e9	−0.646057
$118$	−5.38718e9	−2.55795
$119$	2.56156e8	0.117096
$120$	8.58252e9	3.77832
$121$	1.34800e9	0.571684
$122$	7.01314e9	2.86611
$123$	−5.46842e9	−2.15421
$124$	−9.37741e9	−3.56193
$125$	2.84129e9	1.04093
$126$	−4.03105e8	−0.142479
$127$	1.95999e9	0.668556	0.334278	−	0.942475i	$-0.391508\pi$
$127$	1.95999e9	0.668556	0.334278	+	0.942475i	$0.391508\pi$
$128$	6.09179e9	2.00586
$129$	6.14087e8	0.195243
$130$	5.97027e9	1.83336
$131$	−3.31045e9	−0.982123	−0.491061	−	0.871125i	$-0.663391\pi$
$131$	−3.31045e9	−0.982123	−0.491061	+	0.871125i	$0.663391\pi$
$132$	1.47077e10	4.21660
$133$	4.65975e8	0.129131
$134$	7.59106e9	2.03391
$135$	−1.69800e9	−0.439984
$136$	−1.23675e10	−3.09997
$137$	−6.47943e9	−1.57143	−0.785713	−	0.618591i	$-0.787704\pi$
$137$	−6.47943e9	−1.57143	−0.785713	+	0.618591i	$0.787704\pi$
$138$	−8.75321e9	−2.05453
$139$	−6.83083e9	−1.55206	−0.776028	−	0.630699i	$-0.782768\pi$
$139$	−6.83083e9	−1.55206	−0.776028	+	0.630699i	$0.782768\pi$
$140$	1.33113e9	0.292849
$141$	−6.42916e9	−1.36984
$142$	−3.34379e9	−0.690147
$143$	6.33662e9	1.26720
$144$	1.07986e10	2.09284
$145$	−4.67875e9	−0.878970
$146$	−1.78662e10	−3.25421
$147$	7.14903e9	1.26276
$148$	1.02233e10	1.75151
$149$	−5.71164e9	−0.949341	−0.474671	−	0.880164i	$-0.657433\pi$
$149$	−5.71164e9	−0.949341	−0.474671	+	0.880164i	$0.657433\pi$
$150$	1.40570e9	0.226716
$151$	6.90224e9	1.08042	0.540211	−	0.841530i	$-0.318344\pi$
$151$	6.90224e9	1.08042	0.540211	+	0.841530i	$0.318344\pi$
$152$	−2.24979e10	−3.41857
$153$	−4.33407e9	−0.639417
$154$	1.95061e9	0.279464
$155$	9.27933e9	1.29129
$156$	2.51480e10	3.39972
$157$	6.65621e8	0.0874336	0.0437168	−	0.999044i	$-0.486080\pi$
$157$	6.65621e8	0.0874336	0.0437168	+	0.999044i	$0.486080\pi$
$158$	1.66949e10	2.13122
$159$	1.69053e10	2.09766
$160$	−2.47687e10	−2.98788
$161$	−8.40827e8	−0.0986258
$162$	−2.05459e10	−2.34373
$163$	−7.03047e9	−0.780082	−0.390041	−	0.920798i	$-0.627539\pi$
$163$	−7.03047e9	−0.780082	−0.390041	+	0.920798i	$0.627539\pi$
$164$	4.09492e10	4.42027
$165$	−1.45539e10	−1.52863
$166$	6.95639e8	0.0711046
$167$	7.10666e9	0.707036	0.353518	−	0.935428i	$-0.384985\pi$
$167$	7.10666e9	0.707036	0.353518	+	0.935428i	$0.384985\pi$
$168$	4.79456e9	0.464363
$169$	2.30190e8	0.0217068
$170$	1.97598e10	1.81452
$171$	−7.88414e9	−0.705135
$172$	−4.59847e9	−0.400623
$173$	−1.52722e10	−1.29627	−0.648134	−	0.761527i	$-0.724450\pi$
$173$	−1.52722e10	−1.29627	−0.648134	+	0.761527i	$0.724450\pi$
$174$	−2.72098e10	−2.25037
$175$	1.35031e8	0.0108833
$176$	−5.22539e10	−4.10499
$177$	2.24546e10	1.71959
$178$	−6.62834e9	−0.494897
$179$	−3.28112e8	−0.0238882	−0.0119441	−	0.999929i	$-0.503802\pi$
$179$	−3.28112e8	−0.0238882	−0.0119441	+	0.999929i	$0.503802\pi$
$180$	−2.25223e10	−1.59914
$181$	1.38266e9	0.0957554	0.0478777	−	0.998853i	$-0.484754\pi$
$181$	1.38266e9	0.0957554	0.0478777	+	0.998853i	$0.484754\pi$
$182$	3.33525e9	0.225324
$183$	−2.92318e10	−1.92675
$184$	4.05961e10	2.61099
$185$	−1.01164e10	−0.634967
$186$	5.39649e10	3.30600
$187$	2.09723e10	1.25418
$188$	4.81436e10	2.81079
$189$	−9.48578e8	−0.0540748
$190$	3.59452e10	2.00101
$191$	1.10617e10	0.601411	0.300706	−	0.953717i	$-0.402778\pi$
$191$	1.10617e10	0.601411	0.300706	+	0.953717i	$0.402778\pi$
$192$	−6.51055e10	−3.45750
$193$	1.56904e10	0.814005	0.407003	−	0.913427i	$-0.366574\pi$
$193$	1.56904e10	0.814005	0.407003	+	0.913427i	$0.366574\pi$
$194$	4.40490e10	2.23269
$195$	−2.48850e10	−1.23248
$196$	−5.35342e10	−2.59107
$197$	−1.54645e10	−0.731538	−0.365769	−	0.930706i	$-0.619194\pi$
$197$	−1.54645e10	−0.731538	−0.365769	+	0.930706i	$0.619194\pi$
$198$	−3.30036e10	−1.52605
$199$	1.72181e10	0.778300	0.389150	−	0.921174i	$-0.372769\pi$
$199$	1.72181e10	0.778300	0.389150	+	0.921174i	$0.372769\pi$
$200$	−6.51944e9	−0.288121
$201$	−3.16407e10	−1.36730
$202$	−2.87482e10	−1.21487
$203$	−2.61375e9	−0.108027
$204$	8.32324e10	3.36478
$205$	−4.05209e10	−1.60246
$206$	2.92764e9	0.113270
$207$	1.42265e10	0.538557
$208$	−8.93464e10	−3.30973
$209$	3.81509e10	1.38308
$210$	−7.66036e9	−0.271808
$211$	2.45117e10	0.851337	0.425669	−	0.904879i	$-0.360039\pi$
$211$	2.45117e10	0.851337	0.425669	+	0.904879i	$0.360039\pi$
$212$	−1.26592e11	−4.30423
$213$	1.39374e10	0.463954
$214$	−7.40625e10	−2.41400
$215$	4.55037e9	0.145236
$216$	4.57985e10	1.43156
$217$	5.18383e9	0.158702
$218$	−6.45918e10	−1.93697
$219$	7.44692e10	2.18765
$220$	1.08984e11	3.13661
$221$	3.58596e10	1.01121
$222$	−5.88327e10	−1.62566
$223$	3.43688e9	0.0930664	0.0465332	−	0.998917i	$-0.485183\pi$
$223$	3.43688e9	0.0930664	0.0465332	+	0.998917i	$0.485183\pi$
$224$	−1.38369e10	−0.367216
$225$	−2.28467e9	−0.0594295
$226$	−2.05670e10	−0.524424
$227$	1.17388e10	0.293431	0.146716	−	0.989179i	$-0.453130\pi$
$227$	1.17388e10	0.293431	0.146716	+	0.989179i	$0.453130\pi$
$228$	1.51409e11	3.71060
$229$	−8.32583e8	−0.0200064	−0.0100032	−	0.999950i	$-0.503184\pi$
$229$	−8.32583e8	−0.0200064	−0.0100032	+	0.999950i	$0.503184\pi$
$230$	−6.48612e10	−1.52830
$231$	−8.13042e9	−0.187871
$232$	1.26195e11	2.85987
$233$	−7.38751e9	−0.164209	−0.0821044	−	0.996624i	$-0.526164\pi$
$233$	−7.38751e9	−0.164209	−0.0821044	+	0.996624i	$0.526164\pi$
$234$	−5.64312e10	−1.23041
$235$	−4.76400e10	−1.01898
$236$	−1.68147e11	−3.52846
$237$	−6.95870e10	−1.43272
$238$	1.10387e10	0.223008
$239$	3.60402e10	0.714492	0.357246	−	0.934010i	$-0.383716\pi$
$239$	3.60402e10	0.714492	0.357246	+	0.934010i	$0.383716\pi$
$240$	2.05210e11	3.99252
$241$	5.35383e10	1.02232	0.511161	−	0.859485i	$-0.329216\pi$
$241$	5.35383e10	1.02232	0.511161	+	0.859485i	$0.329216\pi$
$242$	5.80902e10	1.08876
$243$	6.05277e10	1.11359
$244$	2.18897e11	3.95354
$245$	5.29742e10	0.939327
$246$	−2.35654e11	−4.10267
$247$	6.52325e10	1.11514
$248$	−2.50282e11	−4.20142
$249$	−2.89953e9	−0.0478003
$250$	1.22441e11	1.98243
$251$	8.37307e10	1.33154	0.665768	−	0.746159i	$-0.268104\pi$
$251$	8.37307e10	1.33154	0.665768	+	0.746159i	$0.268104\pi$
$252$	−1.25819e10	−0.196537
$253$	−6.88413e10	−1.05635
$254$	8.44630e10	1.27325
$255$	−8.23618e10	−1.21982
$256$	7.69365e10	1.11957
$257$	−9.28756e10	−1.32801	−0.664007	−	0.747726i	$-0.731146\pi$
$257$	−9.28756e10	−1.32801	−0.664007	+	0.747726i	$0.731146\pi$
$258$	2.64632e10	0.371838
$259$	−5.65143e9	−0.0780386
$260$	1.86346e11	2.52896
$261$	4.42238e10	0.589894
$262$	−1.42659e11	−1.87044
$263$	4.81389e10	0.620434	0.310217	−	0.950666i	$-0.399598\pi$
$263$	4.81389e10	0.620434	0.310217	+	0.950666i	$0.399598\pi$
$264$	3.92547e11	4.97363
$265$	1.25268e11	1.56039
$266$	2.00805e10	0.245928
$267$	2.76279e10	0.332696
$268$	2.36935e11	2.80558
$269$	−5.22733e10	−0.608688	−0.304344	−	0.952562i	$-0.598437\pi$
$269$	−5.22733e10	−0.608688	−0.304344	+	0.952562i	$0.598437\pi$
$270$	−7.31730e10	−0.837942
$271$	−1.23731e9	−0.0139354	−0.00696768	−	0.999976i	$-0.502218\pi$
$271$	−1.23731e9	−0.0139354	−0.00696768	+	0.999976i	$0.502218\pi$
$272$	−2.95710e11	−3.27571
$273$	−1.39018e10	−0.151475
$274$	−2.79221e11	−2.99276
$275$	1.10554e10	0.116567
$276$	−2.73209e11	−2.83403
$277$	−1.26159e10	−0.128754	−0.0643768	−	0.997926i	$-0.520506\pi$
$277$	−1.26159e10	−0.128754	−0.0643768	+	0.997926i	$0.520506\pi$
$278$	−2.94365e11	−2.95586
$279$	−8.77086e10	−0.866609
$280$	3.55276e10	0.345426
$281$	3.54512e10	0.339197	0.169599	−	0.985513i	$-0.445753\pi$
$281$	3.54512e10	0.339197	0.169599	+	0.985513i	$0.445753\pi$
$282$	−2.77055e11	−2.60883
$283$	−4.93389e10	−0.457247	−0.228624	−	0.973515i	$-0.573422\pi$
$283$	−4.93389e10	−0.457247	−0.228624	+	0.973515i	$0.573422\pi$
$284$	−1.04368e11	−0.951994
$285$	−1.49825e11	−1.34519
$286$	2.73068e11	2.41337
$287$	−2.26367e10	−0.196945
$288$	2.34115e11	2.00522
$289$	9.64955e7	0.000813704 0
$290$	−2.01624e11	−1.67398
$291$	−1.83603e11	−1.50093
$292$	−5.57648e11	−4.48888
$293$	8.58588e9	0.0680582	0.0340291	−	0.999421i	$-0.489166\pi$
$293$	8.58588e9	0.0680582	0.0340291	+	0.999421i	$0.489166\pi$
$294$	3.08077e11	2.40490
$295$	1.66388e11	1.27916
$296$	2.72858e11	2.06597
$297$	−7.76632e10	−0.579177
$298$	−2.46135e11	−1.80800
$299$	−1.17708e11	−0.851701
$300$	4.38753e10	0.312734
$301$	2.54203e9	0.0178497
$302$	2.97442e11	2.05765
$303$	1.19827e11	0.816699
$304$	−5.37928e11	−3.61238
$305$	−2.16607e11	−1.43326
$306$	−1.86770e11	−1.21776
$307$	−1.78128e11	−1.14448	−0.572241	−	0.820085i	$-0.693926\pi$
$307$	−1.78128e11	−1.14448	−0.572241	+	0.820085i	$0.693926\pi$
$308$	6.08831e10	0.385495
$309$	−1.22028e10	−0.0761461
$310$	3.99879e11	2.45924
$311$	−1.70733e11	−1.03489	−0.517447	−	0.855715i	$-0.673118\pi$
$311$	−1.70733e11	−1.03489	−0.517447	+	0.855715i	$0.673118\pi$
$312$	6.71197e11	4.01009
$313$	1.90876e11	1.12409	0.562046	−	0.827106i	$-0.310015\pi$
$313$	1.90876e11	1.12409	0.562046	+	0.827106i	$0.310015\pi$
$314$	2.86840e10	0.166516
$315$	1.24503e10	0.0712496
$316$	5.21089e11	2.93982
$317$	9.34241e10	0.519628	0.259814	−	0.965659i	$-0.416339\pi$
$317$	9.34241e10	0.519628	0.259814	+	0.965659i	$0.416339\pi$
$318$	7.28510e11	3.99497
$319$	−2.13997e11	−1.15704
$320$	−4.82431e11	−2.57194
$321$	3.08704e11	1.62282
$322$	−3.62342e10	−0.187831
$323$	2.15900e11	1.10367
$324$	−6.41286e11	−3.23295
$325$	1.89031e10	0.0939849
$326$	−3.02968e11	−1.48565
$327$	2.69229e11	1.30214
$328$	1.09293e12	5.21386
$329$	−2.66137e10	−0.125235
$330$	−6.27178e11	−2.91124
$331$	5.97363e10	0.273535	0.136767	−	0.990603i	$-0.456329\pi$
$331$	5.97363e10	0.273535	0.136767	+	0.990603i	$0.456329\pi$
$332$	2.17126e10	0.0980822
$333$	9.56202e10	0.426138
$334$	3.06251e11	1.34654
$335$	−2.34457e11	−1.01710
$336$	1.14639e11	0.490688
$337$	1.79056e11	0.756230	0.378115	−	0.925759i	$-0.376572\pi$
$337$	1.79056e11	0.756230	0.378115	+	0.925759i	$0.376572\pi$
$338$	9.91969e9	0.0413403
$339$	8.57263e10	0.352546
$340$	6.16751e11	2.50296
$341$	4.24417e11	1.69980
$342$	−3.39756e11	−1.34292
$343$	5.95984e10	0.232494
$344$	−1.22732e11	−0.472548
$345$	2.70351e11	1.02741
$346$	−6.58134e11	−2.46872
$347$	−3.88777e11	−1.43952	−0.719760	−	0.694223i	$-0.755748\pi$
$347$	−3.88777e11	−1.43952	−0.719760	+	0.694223i	$0.755748\pi$
$348$	−8.49284e11	−3.10417
$349$	−4.77801e11	−1.72398	−0.861991	−	0.506923i	$-0.830783\pi$
$349$	−4.77801e11	−1.72398	−0.861991	+	0.506923i	$0.830783\pi$
$350$	5.81895e9	0.0207271
$351$	−1.32793e11	−0.466973
$352$	−1.13287e12	−3.93313
$353$	−5.04077e11	−1.72787	−0.863933	−	0.503606i	$-0.832006\pi$
$353$	−5.04077e11	−1.72787	−0.863933	+	0.503606i	$0.832006\pi$
$354$	9.67649e11	3.27494
$355$	1.03276e11	0.345122
$356$	−2.06887e11	−0.682665
$357$	−4.60108e10	−0.149918
$358$	−1.41395e10	−0.0454946
$359$	4.17951e11	1.32801	0.664004	−	0.747729i	$-0.268856\pi$
$359$	4.17951e11	1.32801	0.664004	+	0.747729i	$0.268856\pi$
$360$	−6.01115e11	−1.88624
$361$	7.00577e10	0.217107
$362$	5.95839e10	0.182365
$363$	−2.42129e11	−0.731925
$364$	1.04101e11	0.310813
$365$	5.51816e11	1.62733
$366$	−1.25970e12	−3.66947
$367$	5.55628e11	1.59877	0.799387	−	0.600817i	$-0.205158\pi$
$367$	5.55628e11	1.59877	0.799387	+	0.600817i	$0.205158\pi$
$368$	9.70662e11	2.75901
$369$	3.83005e11	1.07544
$370$	−4.35950e11	−1.20928
$371$	6.99801e10	0.191775
$372$	1.68438e12	4.56033
$373$	−6.91524e11	−1.84977	−0.924885	−	0.380247i	$-0.875839\pi$
$373$	−6.91524e11	−1.84977	−0.924885	+	0.380247i	$0.875839\pi$
$374$	9.03772e11	2.38856
$375$	−5.10354e11	−1.33270
$376$	1.28494e12	3.31542
$377$	−3.65902e11	−0.932887
$378$	−4.08776e10	−0.102985
$379$	5.21767e11	1.29897	0.649486	−	0.760373i	$-0.274984\pi$
$379$	5.21767e11	1.29897	0.649486	+	0.760373i	$0.274984\pi$
$380$	1.12194e12	2.76021
$381$	−3.52055e11	−0.855949
$382$	4.76688e11	1.14538
$383$	−6.52757e11	−1.55009	−0.775045	−	0.631906i	$-0.782273\pi$
$383$	−6.52757e11	−1.55009	−0.775045	+	0.631906i	$0.782273\pi$
$384$	−1.09421e12	−2.56809
$385$	−6.02463e10	−0.139752
$386$	6.76157e11	1.55026
$387$	−4.30103e10	−0.0974706
$388$	1.37488e12	3.07979
$389$	3.45861e11	0.765823	0.382912	−	0.923785i	$-0.374921\pi$
$389$	3.45861e11	0.765823	0.382912	+	0.923785i	$0.374921\pi$
$390$	−1.07238e12	−2.34725
$391$	−3.89579e11	−0.842948
$392$	−1.42882e12	−3.05625
$393$	5.94624e11	1.25741
$394$	−6.66419e11	−1.39320
$395$	−5.15639e11	−1.06576
$396$	−1.03012e12	−2.10504
$397$	1.97139e11	0.398305	0.199152	−	0.979969i	$-0.436181\pi$
$397$	1.97139e11	0.398305	0.199152	+	0.979969i	$0.436181\pi$
$398$	7.41990e11	1.48226
$399$	−8.36988e10	−0.165326
$400$	−1.55881e11	−0.304455
$401$	−9.67496e11	−1.86853	−0.934263	−	0.356584i	$-0.883941\pi$
$401$	−9.67496e11	−1.86853	−0.934263	+	0.356584i	$0.883941\pi$
$402$	−1.36351e12	−2.60400
$403$	7.25691e11	1.37050
$404$	−8.97300e11	−1.67580
$405$	6.34578e11	1.17203
$406$	−1.12636e11	−0.205736
$407$	−4.62701e11	−0.835845
$408$	2.22146e12	3.96888
$409$	−7.33241e11	−1.29566	−0.647831	−	0.761784i	$-0.724324\pi$
$409$	−7.33241e11	−1.29566	−0.647831	+	0.761784i	$0.724324\pi$
$410$	−1.74619e12	−3.05186
$411$	1.16384e12	2.01189
$412$	9.13786e10	0.156245
$413$	9.29516e10	0.157211
$414$	6.13071e11	1.02567
$415$	−2.14855e10	−0.0355573
$416$	−1.93704e12	−3.17116
$417$	1.22696e12	1.98709
$418$	1.64406e12	2.63405
$419$	1.00496e11	0.159289	0.0796443	−	0.996823i	$-0.474622\pi$
$419$	1.00496e11	0.159289	0.0796443	+	0.996823i	$0.474622\pi$
$420$	−2.39098e11	−0.374934
$421$	8.88132e10	0.137787	0.0688935	−	0.997624i	$-0.478053\pi$
$421$	8.88132e10	0.137787	0.0688935	+	0.997624i	$0.478053\pi$
$422$	1.05629e12	1.62136
$423$	4.50295e11	0.683858
$424$	−3.37872e12	−5.07699
$425$	6.25636e10	0.0930189
$426$	6.00614e11	0.883592
$427$	−1.21006e11	−0.176150
$428$	−2.31167e12	−3.32988
$429$	−1.13819e12	−1.62239
$430$	1.96092e11	0.276599
$431$	4.61691e11	0.644471	0.322236	−	0.946660i	$-0.395566\pi$
$431$	4.61691e11	0.644471	0.322236	+	0.946660i	$0.395566\pi$
$432$	1.09505e12	1.51272
$433$	5.27475e11	0.721119	0.360559	−	0.932736i	$-0.382586\pi$
$433$	5.27475e11	0.721119	0.360559	+	0.932736i	$0.382586\pi$
$434$	2.23390e11	0.302245
$435$	8.40400e11	1.12534
$436$	−2.01607e12	−2.67187
$437$	−7.08688e11	−0.929584
$438$	3.20914e12	4.16635
$439$	7.31485e11	0.939973	0.469986	−	0.882674i	$-0.344259\pi$
$439$	7.31485e11	0.939973	0.469986	+	0.882674i	$0.344259\pi$
$440$	2.90876e12	3.69974
$441$	−5.00714e11	−0.630400
$442$	1.54532e12	1.92583
$443$	−4.46593e11	−0.550929	−0.275464	−	0.961311i	$-0.588832\pi$
$443$	−4.46593e11	−0.550929	−0.275464	+	0.961311i	$0.588832\pi$
$444$	−1.83631e12	−2.24245
$445$	2.04723e11	0.247483
$446$	1.48108e11	0.177243
$447$	1.02593e12	1.21544
$448$	−2.69507e11	−0.316096
$449$	−3.25387e11	−0.377826	−0.188913	−	0.981994i	$-0.560496\pi$
$449$	−3.25387e11	−0.377826	−0.188913	+	0.981994i	$0.560496\pi$
$450$	−9.84546e10	−0.113183
$451$	−1.85334e12	−2.10941
$452$	−6.41945e11	−0.723394
$453$	−1.23978e12	−1.38326
$454$	5.05865e11	0.558835
$455$	−1.03012e11	−0.112678
$456$	4.04108e12	4.37679
$457$	−1.70489e12	−1.82841	−0.914203	−	0.405257i	$-0.867182\pi$
$457$	−1.70489e12	−1.82841	−0.914203	+	0.405257i	$0.867182\pi$
$458$	−3.58790e10	−0.0381018
$459$	−4.39503e11	−0.462173
$460$	−2.02447e12	−2.10815
$461$	−4.25542e11	−0.438821	−0.219411	−	0.975633i	$-0.570413\pi$
$461$	−4.25542e11	−0.438821	−0.219411	+	0.975633i	$0.570413\pi$
$462$	−3.50369e11	−0.357797
$463$	1.43391e12	1.45013	0.725065	−	0.688681i	$-0.241810\pi$
$463$	1.43391e12	1.45013	0.725065	+	0.688681i	$0.241810\pi$
$464$	3.01735e12	3.02200
$465$	−1.66676e12	−1.65323
$466$	−3.18354e11	−0.312733
$467$	−3.64292e11	−0.354424	−0.177212	−	0.984173i	$-0.556708\pi$
$467$	−3.64292e11	−0.354424	−0.177212	+	0.984173i	$0.556708\pi$
$468$	−1.76136e12	−1.69723
$469$	−1.30978e11	−0.125003
$470$	−2.05298e12	−1.94063
$471$	−1.19559e11	−0.111941
$472$	−4.48782e12	−4.16194
$473$	2.08125e11	0.191183
$474$	−2.99875e12	−2.72859
$475$	1.13810e11	0.102579
$476$	3.44543e11	0.307619
$477$	−1.18404e12	−1.04721
$478$	1.55310e12	1.36074
$479$	1.17368e12	1.01869	0.509344	−	0.860563i	$-0.329888\pi$
$479$	1.17368e12	1.01869	0.509344	+	0.860563i	$0.329888\pi$
$480$	4.44897e12	3.82537
$481$	−7.91150e11	−0.673917
$482$	2.30716e12	1.94700
$483$	1.51030e11	0.126270
$484$	1.81314e12	1.50185
$485$	−1.36050e12	−1.11650
$486$	2.60835e12	2.12082
$487$	−2.54555e11	−0.205070	−0.102535	−	0.994729i	$-0.532695\pi$
$487$	−2.54555e11	−0.205070	−0.102535	+	0.994729i	$0.532695\pi$
$488$	5.84233e12	4.66333
$489$	1.26282e12	0.998735
$490$	2.28285e12	1.78893
$491$	−1.23895e11	−0.0962028	−0.0481014	−	0.998842i	$-0.515317\pi$
$491$	−1.23895e11	−0.0962028	−0.0481014	+	0.998842i	$0.515317\pi$
$492$	−7.35532e12	−5.65925
$493$	−1.21103e12	−0.923300
$494$	2.81110e12	2.12376
$495$	1.01935e12	0.763130
$496$	−5.98429e12	−4.43961
$497$	5.76945e10	0.0424161
$498$	−1.24951e11	−0.0910349
$499$	−1.43556e12	−1.03650	−0.518250	−	0.855229i	$-0.673416\pi$
$499$	−1.43556e12	−1.03650	−0.518250	+	0.855229i	$0.673416\pi$
$500$	3.82169e12	2.73458
$501$	−1.27650e12	−0.905215
$502$	3.60825e12	2.53589
$503$	−2.19255e12	−1.52719	−0.763595	−	0.645695i	$-0.776568\pi$
$503$	−2.19255e12	−1.52719	−0.763595	+	0.645695i	$0.776568\pi$
$504$	−3.35809e11	−0.231822
$505$	8.87914e11	0.607519
$506$	−2.96662e12	−2.01180
$507$	−4.13468e10	−0.0277911
$508$	2.63630e12	1.75633
$509$	8.92806e11	0.589559	0.294779	−	0.955565i	$-0.404754\pi$
$509$	8.92806e11	0.589559	0.294779	+	0.955565i	$0.404754\pi$
$510$	−3.54926e12	−2.32312
$511$	3.08268e11	0.200002
$512$	1.96471e11	0.126352
$513$	−7.99505e11	−0.509674
$514$	−4.00234e12	−2.52918
$515$	−9.04228e10	−0.0566429
$516$	8.25980e11	0.512916
$517$	−2.17895e12	−1.34135
$518$	−2.43540e11	−0.148623
$519$	2.74320e12	1.65961
$520$	4.97356e12	2.98299
$521$	1.73495e12	1.03161	0.515807	−	0.856705i	$-0.327492\pi$
$521$	1.73495e12	1.03161	0.515807	+	0.856705i	$0.327492\pi$
$522$	1.90576e12	1.12344
$523$	2.26368e12	1.32299	0.661497	−	0.749948i	$-0.269921\pi$
$523$	2.26368e12	1.32299	0.661497	+	0.749948i	$0.269921\pi$
$524$	−4.45273e12	−2.58009
$525$	−2.42543e10	−0.0139339
$526$	2.07448e12	1.18161
$527$	2.40182e12	1.35641
$528$	9.38587e12	5.25560
$529$	−5.22364e11	−0.290017
$530$	5.39825e12	2.97174
$531$	−1.57271e12	−0.858466
$532$	6.26762e11	0.339235
$533$	−3.16894e12	−1.70076
$534$	1.19059e12	0.633615
$535$	2.28749e12	1.20717
$536$	6.32376e12	3.30928
$537$	5.89356e10	0.0305839
$538$	−2.25264e12	−1.15924
$539$	2.42293e12	1.23649
$540$	−2.28391e12	−1.15586
$541$	7.85800e11	0.394388	0.197194	−	0.980364i	$-0.436817\pi$
$541$	7.85800e11	0.394388	0.197194	+	0.980364i	$0.436817\pi$
$542$	−5.33202e10	−0.0265397
$543$	−2.48355e11	−0.122595
$544$	−6.41102e12	−3.13857
$545$	1.99498e12	0.968622
$546$	−5.99079e11	−0.288481
$547$	−8.14762e11	−0.389124	−0.194562	−	0.980890i	$-0.562329\pi$
$547$	−8.14762e11	−0.389124	−0.194562	+	0.980890i	$0.562329\pi$
$548$	−8.71518e12	−4.12823
$549$	2.04738e12	0.961886
$550$	4.76417e11	0.222001
$551$	−2.20299e12	−1.01819
$552$	−7.29190e12	−3.34283
$553$	−2.88058e11	−0.130984
$554$	−5.43664e11	−0.245209
$555$	1.81710e12	0.812946
$556$	−9.18784e12	−4.07734
$557$	2.73409e12	1.20355	0.601775	−	0.798666i	$-0.294460\pi$
$557$	2.73409e12	1.20355	0.601775	+	0.798666i	$0.294460\pi$
$558$	−3.77968e12	−1.65044
$559$	3.55862e11	0.154145
$560$	8.49473e11	0.365009
$561$	−3.76706e12	−1.60572
$562$	1.52772e12	0.645996
$563$	9.71533e11	0.407540	0.203770	−	0.979019i	$-0.434681\pi$
$563$	9.71533e11	0.407540	0.203770	+	0.979019i	$0.434681\pi$
$564$	−8.64757e12	−3.59864
$565$	6.35231e11	0.262249
$566$	−2.12619e12	−0.870820
$567$	3.54503e11	0.144044
$568$	−2.78556e12	−1.12291
$569$	2.53670e12	1.01453	0.507265	−	0.861790i	$-0.330657\pi$
$569$	2.53670e12	1.01453	0.507265	+	0.861790i	$0.330657\pi$
$570$	−6.45650e12	−2.56189
$571$	4.31961e12	1.70052	0.850261	−	0.526361i	$-0.176444\pi$
$571$	4.31961e12	1.70052	0.850261	+	0.526361i	$0.176444\pi$
$572$	8.52310e12	3.32901
$573$	−1.98691e12	−0.769984
$574$	−9.75497e11	−0.375079
$575$	−2.05364e11	−0.0783464
$576$	4.55996e12	1.72608
$577$	1.89784e12	0.712801	0.356401	−	0.934333i	$-0.384004\pi$
$577$	1.89784e12	0.712801	0.356401	+	0.934333i	$0.384004\pi$
$578$	4.15833e9	0.00154969
$579$	−2.81832e12	−1.04217
$580$	−6.29318e12	−2.30911
$581$	−1.20027e10	−0.00437005
$582$	−7.91211e12	−2.85850
$583$	5.72950e12	2.05404
$584$	−1.48835e13	−5.29479
$585$	1.74293e12	0.615289
$586$	3.69996e11	0.129616
$587$	2.77649e12	0.965216	0.482608	−	0.875837i	$-0.339690\pi$
$587$	2.77649e12	0.965216	0.482608	+	0.875837i	$0.339690\pi$
$588$	9.61583e12	3.31733
$589$	4.36917e12	1.49582
$590$	7.17026e12	2.43613
$591$	2.77773e12	0.936585
$592$	6.52409e12	2.18309
$593$	−2.88583e11	−0.0958352	−0.0479176	−	0.998851i	$-0.515258\pi$
$593$	−2.88583e11	−0.0958352	−0.0479176	+	0.998851i	$0.515258\pi$
$594$	−3.34678e12	−1.10303
$595$	−3.40940e11	−0.111520
$596$	−7.68246e12	−2.49397
$597$	−3.09273e12	−0.996455
$598$	−5.07247e12	−1.62205
$599$	2.66006e12	0.844250	0.422125	−	0.906538i	$-0.361284\pi$
$599$	2.66006e12	0.844250	0.422125	+	0.906538i	$0.361284\pi$
$600$	1.17103e12	0.368880
$601$	3.96050e12	1.23827	0.619134	−	0.785286i	$-0.287484\pi$
$601$	3.96050e12	1.23827	0.619134	+	0.785286i	$0.287484\pi$
$602$	1.09545e11	0.0339946
$603$	2.21610e12	0.682592
$604$	9.28388e12	2.83833
$605$	−1.79417e12	−0.544458
$606$	5.16376e12	1.55539
$607$	6.64259e12	1.98604	0.993020	−	0.117944i	$-0.0376303\pi$
$607$	6.64259e12	1.98604	0.993020	+	0.117944i	$0.0376303\pi$
$608$	−1.16623e13	−3.46115
$609$	4.69484e11	0.138307
$610$	−9.33438e12	−2.72962
$611$	−3.72569e12	−1.08149
$612$	−5.82956e12	−1.67979
$613$	−5.81304e12	−1.66277	−0.831383	−	0.555700i	$-0.812450\pi$
$613$	−5.81304e12	−1.66277	−0.831383	+	0.555700i	$0.812450\pi$
$614$	−7.67616e12	−2.17965
$615$	7.27839e12	2.05162
$616$	1.62496e12	0.454705
$617$	−4.96503e12	−1.37924	−0.689618	−	0.724173i	$-0.742222\pi$
$617$	−4.96503e12	−1.37924	−0.689618	+	0.724173i	$0.742222\pi$
$618$	−5.25864e11	−0.145019
$619$	−1.48949e11	−0.0407784	−0.0203892	−	0.999792i	$-0.506491\pi$
$619$	−1.48949e11	−0.0407784	−0.0203892	+	0.999792i	$0.506491\pi$
$620$	1.24812e13	3.39230
$621$	1.44266e12	0.389271
$622$	−7.35749e12	−1.97094
$623$	1.14367e11	0.0304161
$624$	1.60485e13	4.23743
$625$	−3.42702e12	−0.898373
$626$	8.22552e12	2.14081
$627$	−6.85269e12	−1.77075
$628$	8.95296e11	0.229693
$629$	−2.61847e12	−0.666990
$630$	5.36527e11	0.135694
$631$	−6.80747e11	−0.170944	−0.0854719	−	0.996341i	$-0.527240\pi$
$631$	−6.80747e11	−0.170944	−0.0854719	+	0.996341i	$0.527240\pi$
$632$	1.39078e13	3.46762
$633$	−4.40280e12	−1.08996
$634$	4.02598e12	0.989622
$635$	−2.60872e12	−0.636716
$636$	2.27386e13	5.51069
$637$	4.14285e12	0.996947
$638$	−9.22187e12	−2.20357
$639$	−9.76171e11	−0.231618
$640$	−8.10808e12	−1.91033
$641$	−3.88893e12	−0.909848	−0.454924	−	0.890530i	$-0.650334\pi$
$641$	−3.88893e12	−0.909848	−0.454924	+	0.890530i	$0.650334\pi$
$642$	1.33031e13	3.09063
$643$	−3.00480e11	−0.0693213	−0.0346606	−	0.999399i	$-0.511035\pi$
$643$	−3.00480e11	−0.0693213	−0.0346606	+	0.999399i	$0.511035\pi$
$644$	−1.13096e12	−0.259096
$645$	−8.17340e11	−0.185945
$646$	9.30389e12	2.10193
$647$	−2.32257e12	−0.521074	−0.260537	−	0.965464i	$-0.583900\pi$
$647$	−2.32257e12	−0.521074	−0.260537	+	0.965464i	$0.583900\pi$
$648$	−1.71158e13	−3.81338
$649$	7.61026e12	1.68383
$650$	8.14602e11	0.178993
$651$	−9.31122e11	−0.203185
$652$	−9.45636e12	−2.04932
$653$	−5.89953e12	−1.26972	−0.634860	−	0.772627i	$-0.718942\pi$
$653$	−5.89953e12	−1.26972	−0.634860	+	0.772627i	$0.718942\pi$
$654$	1.16020e13	2.47990
$655$	4.40615e12	0.935349
$656$	2.61321e13	5.50944
$657$	−5.21578e12	−1.09213
$658$	−1.14688e12	−0.238507
$659$	−2.83678e12	−0.585924	−0.292962	−	0.956124i	$-0.594641\pi$
$659$	−2.83678e12	−0.585924	−0.292962	+	0.956124i	$0.594641\pi$
$660$	−1.95758e13	−4.01579
$661$	6.55557e12	1.33568	0.667842	−	0.744303i	$-0.267218\pi$
$661$	6.55557e12	1.33568	0.667842	+	0.744303i	$0.267218\pi$
$662$	2.57425e12	0.520942
$663$	−6.44111e12	−1.29464
$664$	5.79505e11	0.115691
$665$	−6.20206e11	−0.122981
$666$	4.12061e12	0.811574
$667$	3.97518e12	0.777661
$668$	9.55884e12	1.85742
$669$	−6.17335e11	−0.119153
$670$	−1.01036e13	−1.93704
$671$	−9.90718e12	−1.88668
$672$	2.48539e12	0.470145
$673$	−7.59974e11	−0.142801	−0.0714004	−	0.997448i	$-0.522747\pi$
$673$	−7.59974e11	−0.142801	−0.0714004	+	0.997448i	$0.522747\pi$
$674$	7.71615e12	1.44023
$675$	−2.31681e11	−0.0429559
$676$	3.09618e11	0.0570250
$677$	−7.68314e12	−1.40569	−0.702845	−	0.711343i	$-0.748087\pi$
$677$	−7.68314e12	−1.40569	−0.702845	+	0.711343i	$0.748087\pi$
$678$	3.69425e12	0.671418
$679$	−7.60031e11	−0.137220
$680$	1.64610e13	2.95233
$681$	−2.10852e12	−0.375679
$682$	1.82896e13	3.23725
$683$	−3.85374e12	−0.677624	−0.338812	−	0.940854i	$-0.610025\pi$
$683$	−3.85374e12	−0.677624	−0.338812	+	0.940854i	$0.610025\pi$
$684$	−1.06046e13	−1.85243
$685$	8.62402e12	1.49659
$686$	2.56831e12	0.442780
$687$	1.49549e11	0.0256141
$688$	−2.93456e12	−0.499338
$689$	9.79660e12	1.65611
$690$	1.16504e13	1.95668
$691$	1.15096e11	0.0192048	0.00960239	−	0.999954i	$-0.496943\pi$
$691$	1.15096e11	0.0192048	0.00960239	+	0.999954i	$0.496943\pi$
$692$	−2.05420e13	−3.40537
$693$	5.69451e11	0.0937900
$694$	−1.67538e13	−2.74154
$695$	9.09174e12	1.47814
$696$	−2.26672e13	−3.66148
$697$	−1.04882e13	−1.68328
$698$	−2.05902e13	−3.28330
$699$	1.32695e12	0.210236
$700$	1.81624e11	0.0285911
$701$	−2.15689e12	−0.337362	−0.168681	−	0.985671i	$-0.553951\pi$
$701$	−2.15689e12	−0.337362	−0.168681	+	0.985671i	$0.553951\pi$
$702$	−5.72250e12	−0.889342
$703$	−4.76328e12	−0.735542
$704$	−2.20654e13	−3.38559
$705$	8.55712e12	1.30460
$706$	−2.17224e13	−3.29069
$707$	4.96027e11	0.0746651
$708$	3.02027e13	4.51747
$709$	9.13106e12	1.35710	0.678552	−	0.734552i	$-0.262608\pi$
$709$	9.13106e12	1.35710	0.678552	+	0.734552i	$0.262608\pi$
$710$	4.45054e12	0.657279
$711$	4.87384e12	0.715250
$712$	−5.52177e12	−0.805227
$713$	−7.88393e12	−1.14246
$714$	−1.98277e12	−0.285516
$715$	−8.43395e12	−1.20685
$716$	−4.41328e11	−0.0627556
$717$	−6.47357e12	−0.914760
$718$	1.80110e13	2.52917
$719$	7.17755e12	1.00160	0.500802	−	0.865562i	$-0.333038\pi$
$719$	7.17755e12	1.00160	0.500802	+	0.865562i	$0.333038\pi$
$720$	−1.43728e13	−1.99317
$721$	−5.05141e10	−0.00696151
$722$	3.01904e12	0.413477
$723$	−9.61658e12	−1.30888
$724$	1.85976e12	0.251555
$725$	−6.38384e11	−0.0858145
$726$	−1.04342e13	−1.39394
$727$	1.54751e12	0.205461	0.102730	−	0.994709i	$-0.467242\pi$
$727$	1.54751e12	0.205461	0.102730	+	0.994709i	$0.467242\pi$
$728$	2.77844e12	0.366615
$729$	−1.48769e12	−0.195091
$730$	2.37797e13	3.09923
$731$	1.17780e12	0.152561
$732$	−3.93184e13	−5.06170
$733$	5.60399e12	0.717017	0.358508	−	0.933527i	$-0.383285\pi$
$733$	5.60399e12	0.717017	0.358508	+	0.933527i	$0.383285\pi$
$734$	2.39440e13	3.04484
$735$	−9.51525e12	−1.20262
$736$	2.10441e13	2.64350
$737$	−1.07236e13	−1.33886
$738$	1.65051e13	2.04816
$739$	−1.36939e12	−0.168899	−0.0844494	−	0.996428i	$-0.526913\pi$
$739$	−1.36939e12	−0.168899	−0.0844494	+	0.996428i	$0.526913\pi$
$740$	−1.36070e13	−1.66810
$741$	−1.17171e13	−1.42770
$742$	3.01569e12	0.365232
$743$	−4.16784e12	−0.501720	−0.250860	−	0.968023i	$-0.580713\pi$
$743$	−4.16784e12	−0.501720	−0.250860	+	0.968023i	$0.580713\pi$
$744$	4.49557e13	5.37906
$745$	7.60210e12	0.904129
$746$	−2.98002e13	−3.52286
$747$	2.03082e11	0.0238632
$748$	2.82089e13	3.29480
$749$	1.27789e12	0.148363
$750$	−2.19930e13	−2.53810
$751$	−4.35477e12	−0.499557	−0.249779	−	0.968303i	$-0.580358\pi$
$751$	−4.35477e12	−0.499557	−0.249779	+	0.968303i	$0.580358\pi$
$752$	3.07233e13	3.50338
$753$	−1.50397e13	−1.70476
$754$	−1.57680e13	−1.77667
$755$	−9.18677e12	−1.02897
$756$	−1.27589e12	−0.142058
$757$	1.07979e13	1.19511	0.597556	−	0.801827i	$-0.296138\pi$
$757$	1.07979e13	1.19511	0.597556	+	0.801827i	$0.296138\pi$
$758$	2.24848e13	2.47387
$759$	1.23653e13	1.35244
$760$	2.99443e13	3.25577
$761$	−1.64930e13	−1.78266	−0.891328	−	0.453359i	$-0.850226\pi$
$761$	−1.64930e13	−1.78266	−0.891328	+	0.453359i	$0.850226\pi$
$762$	−1.51713e13	−1.63014
$763$	1.11448e12	0.119045
$764$	1.48786e13	1.57994
$765$	5.76858e12	0.608965
$766$	−2.81296e13	−2.95212
$767$	1.30124e13	1.35762
$768$	−1.38194e13	−1.43339
$769$	1.66475e13	1.71665	0.858323	−	0.513109i	$-0.171506\pi$
$769$	1.66475e13	1.71665	0.858323	+	0.513109i	$0.171506\pi$
$770$	−2.59623e12	−0.266155
$771$	1.66824e13	1.70025
$772$	2.11045e13	2.13844
$773$	1.53370e12	0.154502	0.0772509	−	0.997012i	$-0.475386\pi$
$773$	1.53370e12	0.154502	0.0772509	+	0.997012i	$0.475386\pi$
$774$	−1.85347e12	−0.185631
$775$	1.26610e12	0.126070
$776$	3.66952e13	3.63272
$777$	1.01511e12	0.0999124
$778$	1.49044e13	1.45850
$779$	−1.90793e13	−1.85628
$780$	−3.34717e13	−3.23781
$781$	4.72364e12	0.454304
$782$	−1.67884e13	−1.60538
$783$	4.48459e12	0.426378
$784$	−3.41633e13	−3.22952
$785$	−8.85931e11	−0.0832696
$786$	2.56245e13	2.39471
$787$	−5.66934e12	−0.526801	−0.263400	−	0.964687i	$-0.584844\pi$
$787$	−5.66934e12	−0.526801	−0.263400	+	0.964687i	$0.584844\pi$
$788$	−2.08005e13	−1.92179
$789$	−8.64674e12	−0.794339
$790$	−2.22207e13	−2.02972
$791$	3.54867e11	0.0322308
$792$	−2.74938e13	−2.48297
$793$	−1.69398e13	−1.52117
$794$	8.49542e12	0.758565
$795$	−2.25007e13	−1.99776
$796$	2.31593e13	2.04464
$797$	1.69239e13	1.48572	0.742860	−	0.669446i	$-0.233469\pi$
$797$	1.69239e13	1.48572	0.742860	+	0.669446i	$0.233469\pi$
$798$	−3.60688e12	−0.314861
$799$	−1.23309e13	−1.07037
$800$	−3.37952e12	−0.291709
$801$	−1.93505e12	−0.166091
$802$	−4.16928e13	−3.55858
$803$	2.52389e13	2.14215
$804$	−4.25584e13	−3.59198
$805$	1.11913e12	0.0939287
$806$	3.12726e13	2.61009
$807$	9.38936e12	0.779301
$808$	−2.39488e13	−1.97666
$809$	1.54138e13	1.26515	0.632575	−	0.774499i	$-0.281998\pi$
$809$	1.54138e13	1.26515	0.632575	+	0.774499i	$0.281998\pi$
$810$	2.73462e13	2.23211
$811$	−6.33063e12	−0.513870	−0.256935	−	0.966429i	$-0.582713\pi$
$811$	−6.33063e12	−0.513870	−0.256935	+	0.966429i	$0.582713\pi$
$812$	−3.51564e12	−0.283793
$813$	2.22247e11	0.0178414
$814$	−1.99394e13	−1.59185
$815$	9.35745e12	0.742931
$816$	5.31155e13	4.19388
$817$	2.14254e12	0.168240
$818$	−3.15979e13	−2.46757
$819$	9.73676e11	0.0756201
$820$	−5.45028e13	−4.20975
$821$	−1.35648e13	−1.04200	−0.521000	−	0.853557i	$-0.674441\pi$
$821$	−1.35648e13	−1.04200	−0.521000	+	0.853557i	$0.674441\pi$
$822$	5.01539e13	3.83161
$823$	6.80965e11	0.0517399	0.0258700	−	0.999665i	$-0.491764\pi$
$823$	6.80965e11	0.0517399	0.0258700	+	0.999665i	$0.491764\pi$
$824$	2.43888e12	0.184297
$825$	−1.98578e12	−0.149241
$826$	4.00562e12	0.299405
$827$	2.18527e13	1.62454	0.812270	−	0.583281i	$-0.198231\pi$
$827$	2.18527e13	1.62454	0.812270	+	0.583281i	$0.198231\pi$
$828$	1.91354e13	1.41482
$829$	−8.42772e12	−0.619747	−0.309874	−	0.950778i	$-0.600287\pi$
$829$	−8.42772e12	−0.619747	−0.309874	+	0.950778i	$0.600287\pi$
$830$	−9.25885e11	−0.0677183
$831$	2.26607e12	0.164843
$832$	−3.77286e13	−2.72970
$833$	1.37116e13	0.986701
$834$	5.28740e13	3.78438
$835$	−9.45886e12	−0.673364
$836$	5.13151e13	3.63343
$837$	−8.89424e12	−0.626389
$838$	4.33072e12	0.303363
$839$	−1.21585e13	−0.847130	−0.423565	−	0.905866i	$-0.639221\pi$
$839$	−1.21585e13	−0.847130	−0.423565	+	0.905866i	$0.639221\pi$
$840$	−6.38149e12	−0.442247
$841$	−2.15012e12	−0.148211
$842$	3.82728e12	0.262413
$843$	−6.36776e12	−0.434273
$844$	3.29695e13	2.23651
$845$	−3.06379e11	−0.0206730
$846$	1.94048e13	1.30240
$847$	−1.00230e12	−0.0669149
$848$	−8.07860e13	−5.36482
$849$	8.86229e12	0.585411
$850$	2.69609e12	0.177153
$851$	8.59508e12	0.561781
$852$	1.87466e13	1.21883
$853$	1.08092e13	0.699072	0.349536	−	0.936923i	$-0.386339\pi$
$853$	1.08092e13	0.699072	0.349536	+	0.936923i	$0.386339\pi$
$854$	−5.21459e12	−0.335475
$855$	1.04937e13	0.671553
$856$	−6.16981e13	−3.92771
$857$	5.36363e12	0.339660	0.169830	−	0.985473i	$-0.445678\pi$
$857$	5.36363e12	0.339660	0.169830	+	0.985473i	$0.445678\pi$
$858$	−4.90486e13	−3.08982
$859$	−9.61783e12	−0.602709	−0.301355	−	0.953512i	$-0.597439\pi$
$859$	−9.61783e12	−0.602709	−0.301355	+	0.953512i	$0.597439\pi$
$860$	6.12050e12	0.381543
$861$	4.06602e12	0.252148
$862$	1.98959e13	1.22738
$863$	1.95919e13	1.20234	0.601171	−	0.799121i	$-0.294701\pi$
$863$	1.95919e13	1.20234	0.601171	+	0.799121i	$0.294701\pi$
$864$	2.37408e13	1.44939
$865$	2.03271e13	1.23453
$866$	2.27308e13	1.37336
$867$	−1.73326e10	−0.00104178
$868$	6.97253e12	0.416919
$869$	−2.35842e13	−1.40292
$870$	3.62158e13	2.14320
$871$	−1.83357e13	−1.07948
$872$	−5.38085e13	−3.15157
$873$	1.28595e13	0.749305
$874$	−3.05399e13	−1.77038
$875$	−2.11263e12	−0.121839
$876$	1.00165e14	5.74709
$877$	1.92311e13	1.09775	0.548877	−	0.835903i	$-0.315056\pi$
$877$	1.92311e13	1.09775	0.548877	+	0.835903i	$0.315056\pi$
$878$	3.15223e13	1.79016
$879$	−1.54220e12	−0.0871346
$880$	6.95492e13	3.90949
$881$	1.63419e13	0.913925	0.456963	−	0.889486i	$-0.348937\pi$
$881$	1.63419e13	0.913925	0.456963	+	0.889486i	$0.348937\pi$
$882$	−2.15776e13	−1.20059
$883$	−3.37986e13	−1.87101	−0.935503	−	0.353319i	$-0.885053\pi$
$883$	−3.37986e13	−1.87101	−0.935503	+	0.353319i	$0.885053\pi$
$884$	4.82331e13	2.65650
$885$	−2.98868e13	−1.63770
$886$	−1.92453e13	−1.04924
$887$	−1.58038e13	−0.857244	−0.428622	−	0.903484i	$-0.641001\pi$
$887$	−1.58038e13	−0.857244	−0.428622	+	0.903484i	$0.641001\pi$
$888$	−4.90108e13	−2.64505
$889$	−1.45734e12	−0.0782535
$890$	8.82222e12	0.471328
$891$	2.90243e13	1.54281
$892$	4.62279e12	0.244491
$893$	−2.24313e13	−1.18038
$894$	4.42108e13	2.31478
$895$	4.36712e11	0.0227505
$896$	−4.52952e12	−0.234783
$897$	2.11428e13	1.09043
$898$	−1.40221e13	−0.719564
$899$	−2.45076e13	−1.25136
$900$	−3.07301e12	−0.156125
$901$	3.24238e13	1.63909
$902$	−7.98671e13	−4.01734
$903$	−4.56601e11	−0.0228530
$904$	−1.71334e13	−0.853269
$905$	−1.84031e12	−0.0911951
$906$	−5.34267e13	−2.63440
$907$	−8.09983e12	−0.397414	−0.198707	−	0.980059i	$-0.563674\pi$
$907$	−8.09983e12	−0.397414	−0.198707	+	0.980059i	$0.563674\pi$
$908$	1.57893e13	0.770861
$909$	−8.39260e12	−0.407717
$910$	−4.43916e12	−0.214593
$911$	−4.04038e12	−0.194352	−0.0971760	−	0.995267i	$-0.530981\pi$
$911$	−4.04038e12	−0.194352	−0.0971760	+	0.995267i	$0.530981\pi$
$912$	9.66230e13	4.62491
$913$	−9.82701e11	−0.0468062
$914$	−7.34696e13	−3.48217
$915$	3.89071e13	1.83499
$916$	−1.11987e12	−0.0525579
$917$	2.46147e12	0.114956
$918$	−1.89398e13	−0.880202
$919$	−1.35982e13	−0.628869	−0.314435	−	0.949279i	$-0.601815\pi$
$919$	−1.35982e13	−0.628869	−0.314435	+	0.949279i	$0.601815\pi$
$920$	−5.40329e13	−2.48664
$921$	3.19954e13	1.46528
$922$	−1.83381e13	−0.835728
$923$	8.07672e12	0.366292
$924$	−1.09359e13	−0.493548
$925$	−1.38031e12	−0.0619923
$926$	6.17922e13	2.76175
$927$	8.54680e11	0.0380141
$928$	6.54165e13	2.89549
$929$	−1.80722e13	−0.796049	−0.398024	−	0.917375i	$-0.630304\pi$
$929$	−1.80722e13	−0.796049	−0.398024	+	0.917375i	$0.630304\pi$
$930$	−7.18265e13	−3.14856
$931$	2.49429e13	1.08811
$932$	−9.93660e12	−0.431386
$933$	3.06672e13	1.32497
$934$	−1.56986e13	−0.674995
$935$	−2.79138e13	−1.19445
$936$	−4.70103e13	−2.00194
$937$	−2.82959e13	−1.19921	−0.599606	−	0.800295i	$-0.704676\pi$
$937$	−2.82959e13	−1.19921	−0.599606	+	0.800295i	$0.704676\pi$
$938$	−5.64430e12	−0.238066
$939$	−3.42852e13	−1.43917
$940$	−6.40784e13	−2.67692
$941$	1.67782e13	0.697579	0.348789	−	0.937201i	$-0.386593\pi$
$941$	1.67782e13	0.697579	0.348789	+	0.937201i	$0.386593\pi$
$942$	−5.15223e12	−0.213190
$943$	3.44275e13	1.41776
$944$	−1.07305e14	−4.39789
$945$	1.26254e12	0.0514995
$946$	8.96883e12	0.364104
$947$	−9.22630e12	−0.372780	−0.186390	−	0.982476i	$-0.559679\pi$
$947$	−9.22630e12	−0.372780	−0.186390	+	0.982476i	$0.559679\pi$
$948$	−9.35983e13	−3.76383
$949$	4.31548e13	1.72715
$950$	4.90448e12	0.195360
$951$	−1.67809e13	−0.665277
$952$	9.19581e12	0.362847
$953$	−2.41710e13	−0.949241	−0.474620	−	0.880191i	$-0.657415\pi$
$953$	−2.41710e13	−0.949241	−0.474620	+	0.880191i	$0.657415\pi$
$954$	−5.10245e13	−1.99439
$955$	−1.47229e13	−0.572769
$956$	4.84761e13	1.87701
$957$	3.84382e13	1.48135
$958$	5.05782e13	1.94007
$959$	4.81775e12	0.183933
$960$	8.66545e13	3.29284
$961$	2.21660e13	0.838364
$962$	−3.40935e13	−1.28346
$963$	−2.16215e13	−0.810152
$964$	7.20119e13	2.68570
$965$	−2.08837e13	−0.775239
$966$	6.50841e12	0.240479
$967$	4.39048e13	1.61470	0.807352	−	0.590070i	$-0.200900\pi$
$967$	4.39048e13	1.61470	0.807352	+	0.590070i	$0.200900\pi$
$968$	4.83923e13	1.77148
$969$	−3.87800e13	−1.41303
$970$	−5.86286e13	−2.12636
$971$	−1.38873e13	−0.501339	−0.250670	−	0.968073i	$-0.580651\pi$
$971$	−1.38873e13	−0.501339	−0.250670	+	0.968073i	$0.580651\pi$
$972$	8.14130e13	2.92547
$973$	5.07904e12	0.181666
$974$	−1.09697e13	−0.390552
$975$	−3.39538e12	−0.120328
$976$	1.39691e14	4.92771
$977$	−1.29967e13	−0.456359	−0.228179	−	0.973619i	$-0.573277\pi$
$977$	−1.29967e13	−0.456359	−0.228179	+	0.973619i	$0.573277\pi$
$978$	5.44192e13	1.90208
$979$	9.36359e12	0.325777
$980$	7.12532e13	2.46767
$981$	−1.88566e13	−0.650061
$982$	−5.33909e12	−0.183217
$983$	−1.69991e12	−0.0580679	−0.0290340	−	0.999578i	$-0.509243\pi$
$983$	−1.69991e12	−0.0580679	−0.0290340	+	0.999578i	$0.509243\pi$
$984$	−1.96312e14	−6.67528
$985$	2.05830e13	0.696699
$986$	−5.21875e13	−1.75841
$987$	4.78037e12	0.160337
$988$	8.77412e13	2.92953
$989$	−3.86610e12	−0.128496
$990$	4.39273e13	1.45337
$991$	−3.65973e13	−1.20536	−0.602681	−	0.797982i	$-0.705901\pi$
$991$	−3.65973e13	−1.20536	−0.602681	+	0.797982i	$0.705901\pi$
$992$	−1.29740e14	−4.25374
$993$	−1.07299e13	−0.350205
$994$	2.48626e12	0.0807808
$995$	−2.29171e13	−0.741234
$996$	−3.90003e12	−0.125574
$997$	−7.31096e12	−0.234340	−0.117170	−	0.993112i	$-0.537382\pi$
$997$	−7.31096e12	−0.234340	−0.117170	+	0.993112i	$0.537382\pi$
$998$	−6.18635e13	−1.97400
$999$	9.69652e12	0.308015

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.a.a.1.15	✓	15
3.2	odd	2		387.10.a.c.1.1		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.a.a.1.15	✓	15	1.1	even	1	trivial
387.10.a.c.1.1		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)

\(f(q)\)	\(=\)	\(q+43.0936 q^{2} -179.621 q^{3} +1345.05 q^{4} -1330.99 q^{5} -7740.49 q^{6} -743.545 q^{7} +35899.3 q^{8} +12580.5 q^{9} +O(q^{10})\)	\(q+43.0936 q^{2} -179.621 q^{3} +1345.05 q^{4} -1330.99 q^{5} -7740.49 q^{6} -743.545 q^{7} +35899.3 q^{8} +12580.5 q^{9} -57356.9 q^{10} -60876.5 q^{11} -241599. q^{12} -104090. q^{13} -32042.0 q^{14} +239072. q^{15} +858359. q^{16} -344506. q^{17} +542140. q^{18} -626694. q^{19} -1.79025e6 q^{20} +133556. q^{21} -2.62338e6 q^{22} +1.13084e6 q^{23} -6.44824e6 q^{24} -181604. q^{25} -4.48560e6 q^{26} +1.27575e6 q^{27} -1.00011e6 q^{28} +3.51526e6 q^{29} +1.03025e7 q^{30} -6.97177e6 q^{31} +1.86093e7 q^{32} +1.09347e7 q^{33} -1.48460e7 q^{34} +989648. q^{35} +1.69215e7 q^{36} +7.60065e6 q^{37} -2.70065e7 q^{38} +1.86967e7 q^{39} -4.77814e7 q^{40} +3.04443e7 q^{41} +5.75540e6 q^{42} -3.41880e6 q^{43} -8.18822e7 q^{44} -1.67445e7 q^{45} +4.87317e7 q^{46} +3.57930e7 q^{47} -1.54179e8 q^{48} -3.98007e7 q^{49} -7.82595e6 q^{50} +6.18803e7 q^{51} -1.40006e8 q^{52} -9.41168e7 q^{53} +5.49766e7 q^{54} +8.10257e7 q^{55} -2.66927e7 q^{56} +1.12567e8 q^{57} +1.51485e8 q^{58} -1.25011e8 q^{59} +3.21565e8 q^{60} +1.62742e8 q^{61} -3.00439e8 q^{62} -9.35420e6 q^{63} +3.62462e8 q^{64} +1.38542e8 q^{65} +4.71214e8 q^{66} +1.76153e8 q^{67} -4.63379e8 q^{68} -2.03121e8 q^{69} +4.26474e7 q^{70} -7.75938e7 q^{71} +4.51632e8 q^{72} -4.14592e8 q^{73} +3.27539e8 q^{74} +3.26198e7 q^{75} -8.42937e8 q^{76} +4.52644e7 q^{77} +8.05706e8 q^{78} +3.87411e8 q^{79} -1.14246e9 q^{80} -4.76773e8 q^{81} +1.31195e9 q^{82} +1.61425e7 q^{83} +1.79640e8 q^{84} +4.58532e8 q^{85} -1.47328e8 q^{86} -6.31412e8 q^{87} -2.18542e9 q^{88} -1.53813e8 q^{89} -7.21580e8 q^{90} +7.73955e7 q^{91} +1.52103e9 q^{92} +1.25227e9 q^{93} +1.54245e9 q^{94} +8.34120e8 q^{95} -3.34261e9 q^{96} +1.02217e9 q^{97} -1.71516e9 q^{98} -7.65859e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 32 q^{2} - 317 q^{3} + 3242 q^{4} - 4717 q^{5} + 687 q^{6} - 9680 q^{7} - 20394 q^{8} + 69516 q^{9}+O(q^{10}) \) 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

Varieties

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