LMFDB - Embedded newform 43.10.a.a.1.7

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			1.7
Root			$7.62988$ 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)

$f(q)$	$=$	$q-9.62988 q^{2} +189.920 q^{3} -419.265 q^{4} +636.384 q^{5} -1828.91 q^{6} -3288.51 q^{7} +8967.97 q^{8} +16386.6 q^{9} +O(q^{10})$	\(q-9.62988 q^{2} +189.920 q^{3} -419.265 q^{4} +636.384 q^{5} -1828.91 q^{6} -3288.51 q^{7} +8967.97 q^{8} +16386.6 q^{9} -6128.30 q^{10} -71891.5 q^{11} -79626.9 q^{12} -56499.0 q^{13} +31667.9 q^{14} +120862. q^{15} +128303. q^{16} +227428. q^{17} -157801. q^{18} -258196. q^{19} -266814. q^{20} -624553. q^{21} +692307. q^{22} -205452. q^{23} +1.70320e6 q^{24} -1.54814e6 q^{25} +544079. q^{26} -626056. q^{27} +1.37876e6 q^{28} +568487. q^{29} -1.16389e6 q^{30} -6.46168e6 q^{31} -5.82715e6 q^{32} -1.36536e7 q^{33} -2.19010e6 q^{34} -2.09275e6 q^{35} -6.87033e6 q^{36} -1.41255e7 q^{37} +2.48640e6 q^{38} -1.07303e7 q^{39} +5.70707e6 q^{40} -1.35846e7 q^{41} +6.01437e6 q^{42} -3.41880e6 q^{43} +3.01416e7 q^{44} +1.04282e7 q^{45} +1.97848e6 q^{46} +2.14428e7 q^{47} +2.43674e7 q^{48} -2.95393e7 q^{49} +1.49084e7 q^{50} +4.31931e7 q^{51} +2.36881e7 q^{52} +3.02124e7 q^{53} +6.02884e6 q^{54} -4.57506e7 q^{55} -2.94912e7 q^{56} -4.90366e7 q^{57} -5.47446e6 q^{58} +1.16373e8 q^{59} -5.06733e7 q^{60} -1.09646e8 q^{61} +6.22252e7 q^{62} -5.38874e7 q^{63} -9.57661e6 q^{64} -3.59551e7 q^{65} +1.31483e8 q^{66} +1.24276e8 q^{67} -9.53526e7 q^{68} -3.90194e7 q^{69} +2.01529e7 q^{70} +2.04397e8 q^{71} +1.46954e8 q^{72} +1.16000e8 q^{73} +1.36027e8 q^{74} -2.94023e8 q^{75} +1.08253e8 q^{76} +2.36416e8 q^{77} +1.03331e8 q^{78} +4.47267e8 q^{79} +8.16502e7 q^{80} -4.41438e8 q^{81} +1.30818e8 q^{82} -5.31305e8 q^{83} +2.61853e8 q^{84} +1.44731e8 q^{85} +3.29226e7 q^{86} +1.07967e8 q^{87} -6.44721e8 q^{88} +2.15750e7 q^{89} -1.00422e8 q^{90} +1.85797e8 q^{91} +8.61388e7 q^{92} -1.22720e9 q^{93} -2.06492e8 q^{94} -1.64312e8 q^{95} -1.10669e9 q^{96} +9.39408e8 q^{97} +2.84460e8 q^{98} -1.17806e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−9.62988	−0.425585	−0.212792	−	0.977097i	$-0.568256\pi$
$2$	−9.62988	−0.425585	−0.212792	+	0.977097i	$0.568256\pi$
$3$	189.920	1.35371	0.676854	−	0.736117i	$-0.263343\pi$
$3$	189.920	1.35371	0.676854	+	0.736117i	$0.263343\pi$
$4$	−419.265	−0.818878
$5$	636.384	0.455359	0.227680	−	0.973736i	$-0.426886\pi$
$5$	636.384	0.455359	0.227680	+	0.973736i	$0.426886\pi$
$6$	−1828.91	−0.576117
$7$	−3288.51	−0.517675	−0.258838	−	0.965921i	$-0.583339\pi$
$7$	−3288.51	−0.517675	−0.258838	+	0.965921i	$0.583339\pi$
$8$	8967.97	0.774086
$9$	16386.6	0.832525
$10$	−6128.30	−0.193794
$11$	−71891.5	−1.48051	−0.740254	−	0.672327i	$-0.765295\pi$
$11$	−71891.5	−1.48051	−0.740254	+	0.672327i	$0.765295\pi$
$12$	−79626.9	−1.10852
$13$	−56499.0	−0.548651	−0.274325	−	0.961637i	$-0.588455\pi$
$13$	−56499.0	−0.548651	−0.274325	+	0.961637i	$0.588455\pi$
$14$	31667.9	0.220315
$15$	120862.	0.616423
$16$	128303.	0.489439
$17$	227428.	0.660425	0.330212	−	0.943907i	$-0.392880\pi$
$17$	227428.	0.660425	0.330212	+	0.943907i	$0.392880\pi$
$18$	−157801.	−0.354310
$19$	−258196.	−0.454526	−0.227263	−	0.973833i	$-0.572978\pi$
$19$	−258196.	−0.454526	−0.227263	+	0.973833i	$0.572978\pi$
$20$	−266814.	−0.372884
$21$	−624553.	−0.700781
$22$	692307.	0.630081
$23$	−205452.	−0.153086	−0.0765429	−	0.997066i	$-0.524388\pi$
$23$	−205452.	−0.153086	−0.0765429	+	0.997066i	$0.524388\pi$
$24$	1.70320e6	1.04789
$25$	−1.54814e6	−0.792648
$26$	544079.	0.233497
$27$	−626056.	−0.226713
$28$	1.37876e6	0.423913
$29$	568487.	0.149255	0.0746276	−	0.997211i	$-0.476223\pi$
$29$	568487.	0.149255	0.0746276	+	0.997211i	$0.476223\pi$
$30$	−1.16389e6	−0.262340
$31$	−6.46168e6	−1.25666	−0.628330	−	0.777947i	$-0.716261\pi$
$31$	−6.46168e6	−1.25666	−0.628330	+	0.777947i	$0.716261\pi$
$32$	−5.82715e6	−0.982384
$33$	−1.36536e7	−2.00417
$34$	−2.19010e6	−0.281066
$35$	−2.09275e6	−0.235728
$36$	−6.87033e6	−0.681736
$37$	−1.41255e7	−1.23907	−0.619535	−	0.784969i	$-0.712679\pi$
$37$	−1.41255e7	−1.23907	−0.619535	+	0.784969i	$0.712679\pi$
$38$	2.48640e6	0.193439
$39$	−1.07303e7	−0.742713
$40$	5.70707e6	0.352487
$41$	−1.35846e7	−0.750791	−0.375395	−	0.926865i	$-0.622493\pi$
$41$	−1.35846e7	−0.750791	−0.375395	+	0.926865i	$0.622493\pi$
$42$	6.01437e6	0.298242
$43$	−3.41880e6	−0.152499
$43$	−3.41880e6	−0.152499
$44$	3.01416e7	1.21235
$45$	1.04282e7	0.379098
$46$	1.97848e6	0.0651509
$47$	2.14428e7	0.640976	0.320488	−	0.947253i	$-0.396153\pi$
$47$	2.14428e7	0.640976	0.320488	+	0.947253i	$0.396153\pi$
$48$	2.43674e7	0.662557
$49$	−2.95393e7	−0.732012
$50$	1.49084e7	0.337339
$51$	4.31931e7	0.894022
$52$	2.36881e7	0.449278
$53$	3.02124e7	0.525949	0.262975	−	0.964803i	$-0.415296\pi$
$53$	3.02124e7	0.525949	0.262975	+	0.964803i	$0.415296\pi$
$54$	6.02884e6	0.0964855
$55$	−4.57506e7	−0.674163
$56$	−2.94912e7	−0.400725
$57$	−4.90366e7	−0.615295
$58$	−5.47446e6	−0.0635207
$59$	1.16373e8	1.25031	0.625154	−	0.780501i	$-0.285036\pi$
$59$	1.16373e8	1.25031	0.625154	+	0.780501i	$0.285036\pi$
$60$	−5.06733e7	−0.504775
$61$	−1.09646e8	−1.01393	−0.506965	−	0.861967i	$-0.669233\pi$
$61$	−1.09646e8	−1.01393	−0.506965	+	0.861967i	$0.669233\pi$
$62$	6.22252e7	0.534815
$63$	−5.38874e7	−0.430977
$64$	−9.57661e6	−0.0713513
$65$	−3.59551e7	−0.249833
$66$	1.31483e8	0.852946
$67$	1.24276e8	0.753444	0.376722	−	0.926326i	$-0.377051\pi$
$67$	1.24276e8	0.753444	0.376722	+	0.926326i	$0.377051\pi$
$68$	−9.53526e7	−0.540807
$69$	−3.90194e7	−0.207233
$70$	2.01529e7	0.100322
$71$	2.04397e8	0.954578	0.477289	−	0.878746i	$-0.341620\pi$
$71$	2.04397e8	0.954578	0.477289	+	0.878746i	$0.341620\pi$
$72$	1.46954e8	0.644446
$73$	1.16000e8	0.478086	0.239043	−	0.971009i	$-0.423166\pi$
$73$	1.16000e8	0.478086	0.239043	+	0.971009i	$0.423166\pi$
$74$	1.36027e8	0.527329
$75$	−2.94023e8	−1.07301
$76$	1.08253e8	0.372201
$77$	2.36416e8	0.766422
$78$	1.03331e8	0.316087
$79$	4.47267e8	1.29195	0.645974	−	0.763359i	$-0.276451\pi$
$79$	4.47267e8	1.29195	0.645974	+	0.763359i	$0.276451\pi$
$80$	8.16502e7	0.222870
$81$	−4.41438e8	−1.13943
$82$	1.30818e8	0.319525
$83$	−5.31305e8	−1.22883	−0.614416	−	0.788982i	$-0.710608\pi$
$83$	−5.31305e8	−1.22883	−0.614416	+	0.788982i	$0.710608\pi$
$84$	2.61853e8	0.573854
$85$	1.44731e8	0.300730
$86$	3.29226e7	0.0649010
$87$	1.07967e8	0.202048
$88$	−6.44721e8	−1.14604
$89$	2.15750e7	0.0364499	0.0182249	−	0.999834i	$-0.494198\pi$
$89$	2.15750e7	0.0364499	0.0182249	+	0.999834i	$0.494198\pi$
$90$	−1.00422e8	−0.161338
$91$	1.85797e8	0.284023
$92$	8.61388e7	0.125358
$93$	−1.22720e9	−1.70115
$94$	−2.06492e8	−0.272790
$95$	−1.64312e8	−0.206972
$96$	−1.10669e9	−1.32986
$97$	9.39408e8	1.07741	0.538705	−	0.842494i	$-0.318914\pi$
$97$	9.39408e8	1.07741	0.538705	+	0.842494i	$0.318914\pi$
$98$	2.84460e8	0.311533
$99$	−1.17806e9	−1.23256
$100$	6.49082e8	0.649082
$101$	1.98427e8	0.189738	0.0948691	−	0.995490i	$-0.469757\pi$
$101$	1.98427e8	0.189738	0.0948691	+	0.995490i	$0.469757\pi$
$102$	−4.15944e8	−0.380482
$103$	−3.43220e8	−0.300473	−0.150236	−	0.988650i	$-0.548003\pi$
$103$	−3.43220e8	−0.300473	−0.150236	+	0.988650i	$0.548003\pi$
$104$	−5.06682e8	−0.424703
$105$	−3.97455e8	−0.319107
$106$	−2.90942e8	−0.223836
$107$	1.59458e9	1.17603	0.588017	−	0.808849i	$-0.299909\pi$
$107$	1.59458e9	1.17603	0.588017	+	0.808849i	$0.299909\pi$
$108$	2.62484e8	0.185650
$109$	−1.36307e8	−0.0924912	−0.0462456	−	0.998930i	$-0.514726\pi$
$109$	−1.36307e8	−0.0924912	−0.0462456	+	0.998930i	$0.514726\pi$
$110$	4.40573e8	0.286913
$111$	−2.68271e9	−1.67734
$112$	−4.21926e8	−0.253370
$113$	6.49652e8	0.374824	0.187412	−	0.982281i	$-0.439990\pi$
$113$	6.49652e8	0.374824	0.187412	+	0.982281i	$0.439990\pi$
$114$	4.72216e8	0.261860
$115$	−1.30746e8	−0.0697090
$116$	−2.38347e8	−0.122222
$117$	−9.25826e8	−0.456765
$118$	−1.12065e9	−0.532112
$119$	−7.47897e8	−0.341885
$120$	1.08389e9	0.477165
$121$	2.81045e9	1.19190
$122$	1.05588e9	0.431513
$123$	−2.57998e9	−1.01635
$124$	2.70916e9	1.02905
$125$	−2.22815e9	−0.816299
$126$	5.18929e8	0.183417
$127$	8.75307e8	0.298568	0.149284	−	0.988794i	$-0.452303\pi$
$127$	8.75307e8	0.298568	0.149284	+	0.988794i	$0.452303\pi$
$128$	3.07572e9	1.01275
$129$	−6.49298e8	−0.206438
$130$	3.46243e8	0.106325
$131$	−5.17356e9	−1.53486	−0.767429	−	0.641134i	$-0.778464\pi$
$131$	−5.17356e9	−1.53486	−0.767429	+	0.641134i	$0.778464\pi$
$132$	5.72450e9	1.64117
$133$	8.49079e8	0.235297
$134$	−1.19676e9	−0.320654
$135$	−3.98412e8	−0.103236
$136$	2.03957e9	0.511226
$137$	2.77573e9	0.673185	0.336593	−	0.941650i	$-0.390725\pi$
$137$	2.77573e9	0.673185	0.336593	+	0.941650i	$0.390725\pi$
$138$	3.75752e8	0.0881953
$139$	−5.81753e9	−1.32182	−0.660910	−	0.750465i	$-0.729830\pi$
$139$	−5.81753e9	−1.32182	−0.660910	+	0.750465i	$0.729830\pi$
$140$	8.77419e8	0.193033
$141$	4.07242e9	0.867694
$142$	−1.96832e9	−0.406253
$143$	4.06180e9	0.812281
$144$	2.10245e9	0.407470
$145$	3.61776e8	0.0679648
$146$	−1.11707e9	−0.203466
$147$	−5.61011e9	−0.990931
$148$	5.92233e9	1.01465
$149$	−9.17312e9	−1.52468	−0.762340	−	0.647176i	$-0.775950\pi$
$149$	−9.17312e9	−1.52468	−0.762340	+	0.647176i	$0.775950\pi$
$150$	2.83140e9	0.456658
$151$	1.08986e10	1.70598	0.852990	−	0.521927i	$-0.174787\pi$
$151$	1.08986e10	1.70598	0.852990	+	0.521927i	$0.174787\pi$
$152$	−2.31550e9	−0.351842
$153$	3.72676e9	0.549820
$154$	−2.27665e9	−0.326177
$155$	−4.11211e9	−0.572232
$156$	4.49884e9	0.608191
$157$	6.31663e9	0.829730	0.414865	−	0.909883i	$-0.363829\pi$
$157$	6.31663e9	0.829730	0.414865	+	0.909883i	$0.363829\pi$
$158$	−4.30713e9	−0.549833
$159$	5.73794e9	0.711981
$160$	−3.70830e9	−0.447338
$161$	6.75629e8	0.0792487
$162$	4.25099e9	0.484923
$163$	1.41043e10	1.56498	0.782489	−	0.622665i	$-0.213950\pi$
$163$	1.41043e10	1.56498	0.782489	+	0.622665i	$0.213950\pi$
$164$	5.69555e9	0.614806
$165$	−8.68895e9	−0.912620
$166$	5.11640e9	0.522972
$167$	−9.73712e9	−0.968739	−0.484369	−	0.874864i	$-0.660951\pi$
$167$	−9.73712e9	−0.968739	−0.484369	+	0.874864i	$0.660951\pi$
$168$	−5.60097e9	−0.542465
$169$	−7.41236e9	−0.698983
$170$	−1.39375e9	−0.127986
$171$	−4.23095e9	−0.378404
$172$	1.43339e9	0.124878
$173$	−2.77504e9	−0.235539	−0.117769	−	0.993041i	$-0.537574\pi$
$173$	−2.77504e9	−0.235539	−0.117769	+	0.993041i	$0.537574\pi$
$174$	−1.03971e9	−0.0859885
$175$	5.09107e9	0.410334
$176$	−9.22393e9	−0.724618
$177$	2.21015e10	1.69255
$178$	−2.07765e8	−0.0155125
$179$	−1.51599e10	−1.10372	−0.551860	−	0.833937i	$-0.686082\pi$
$179$	−1.51599e10	−1.10372	−0.551860	+	0.833937i	$0.686082\pi$
$180$	−4.37217e9	−0.310435
$181$	−1.80133e10	−1.24750	−0.623749	−	0.781624i	$-0.714391\pi$
$181$	−1.80133e10	−1.24750	−0.623749	+	0.781624i	$0.714391\pi$
$182$	−1.78921e9	−0.120876
$183$	−2.08239e10	−1.37256
$184$	−1.84249e9	−0.118502
$185$	−8.98924e9	−0.564222
$186$	1.18178e10	0.723984
$187$	−1.63501e10	−0.977764
$188$	−8.99024e9	−0.524881
$189$	2.05879e9	0.117364
$190$	1.58230e9	0.0880843
$191$	1.94270e9	0.105623	0.0528113	−	0.998605i	$-0.483182\pi$
$191$	1.94270e9	0.105623	0.0528113	+	0.998605i	$0.483182\pi$
$192$	−1.81879e9	−0.0965888
$193$	−4.22076e8	−0.0218969	−0.0109485	−	0.999940i	$-0.503485\pi$
$193$	−4.22076e8	−0.0218969	−0.0109485	+	0.999940i	$0.503485\pi$
$194$	−9.04638e9	−0.458529
$195$	−6.82858e9	−0.338201
$196$	1.23848e10	0.599429
$197$	2.39596e10	1.13339	0.566697	−	0.823926i	$-0.308221\pi$
$197$	2.39596e10	1.13339	0.566697	+	0.823926i	$0.308221\pi$
$198$	1.13445e10	0.524558
$199$	−3.27995e10	−1.48261	−0.741307	−	0.671166i	$-0.765794\pi$
$199$	−3.27995e10	−1.48261	−0.741307	+	0.671166i	$0.765794\pi$
$200$	−1.38837e10	−0.613578
$201$	2.36025e10	1.01994
$202$	−1.91083e9	−0.0807496
$203$	−1.86947e9	−0.0772658
$204$	−1.81094e10	−0.732095
$205$	−8.64501e9	−0.341880
$206$	3.30516e9	0.127876
$207$	−3.36665e9	−0.127448
$208$	−7.24902e9	−0.268531
$209$	1.85621e10	0.672929
$210$	3.82745e9	0.135807
$211$	−7.88494e9	−0.273859	−0.136930	−	0.990581i	$-0.543723\pi$
$211$	−7.88494e9	−0.273859	−0.136930	+	0.990581i	$0.543723\pi$
$212$	−1.26670e10	−0.430688
$213$	3.88190e10	1.29222
$214$	−1.53556e10	−0.500502
$215$	−2.17567e9	−0.0694416
$216$	−5.61445e9	−0.175495
$217$	2.12493e10	0.650542
$218$	1.31262e9	0.0393628
$219$	2.20308e10	0.647189
$220$	1.91817e10	0.552057
$221$	−1.28494e10	−0.362342
$222$	2.58342e10	0.713850
$223$	1.50654e10	0.407952	0.203976	−	0.978976i	$-0.434614\pi$
$223$	1.50654e10	0.407952	0.203976	+	0.978976i	$0.434614\pi$
$224$	1.91626e10	0.508556
$225$	−2.53687e10	−0.659899
$226$	−6.25607e9	−0.159519
$227$	2.82057e10	0.705051	0.352525	−	0.935802i	$-0.385323\pi$
$227$	2.82057e10	0.705051	0.352525	+	0.935802i	$0.385323\pi$
$228$	2.05593e10	0.503851
$229$	2.85908e10	0.687016	0.343508	−	0.939150i	$-0.388385\pi$
$229$	2.85908e10	0.687016	0.343508	+	0.939150i	$0.388385\pi$
$230$	1.25907e9	0.0296671
$231$	4.49001e10	1.03751
$232$	5.09818e9	0.115536
$233$	3.60569e10	0.801469	0.400735	−	0.916194i	$-0.368755\pi$
$233$	3.60569e10	0.801469	0.400735	+	0.916194i	$0.368755\pi$
$234$	8.91559e9	0.194392
$235$	1.36459e10	0.291874
$236$	−4.87910e10	−1.02385
$237$	8.49449e10	1.74892
$238$	7.20216e9	0.145501
$239$	−6.82558e10	−1.35316	−0.676580	−	0.736369i	$-0.736539\pi$
$239$	−6.82558e10	−1.35316	−0.676580	+	0.736369i	$0.736539\pi$
$240$	1.55070e10	0.301701
$241$	−4.14356e10	−0.791219	−0.395610	−	0.918419i	$-0.629467\pi$
$241$	−4.14356e10	−0.791219	−0.395610	+	0.918419i	$0.629467\pi$
$242$	−2.70643e10	−0.507256
$243$	−7.15151e10	−1.31574
$244$	4.59707e10	0.830285
$245$	−1.87984e10	−0.333329
$246$	2.48449e10	0.432543
$247$	1.45878e10	0.249376
$248$	−5.79482e10	−0.972764
$249$	−1.00905e11	−1.66348
$250$	2.14568e10	0.347404
$251$	−4.84151e10	−0.769927	−0.384963	−	0.922932i	$-0.625786\pi$
$251$	−4.84151e10	−0.769927	−0.384963	+	0.922932i	$0.625786\pi$
$252$	2.25931e10	0.352918
$253$	1.47702e10	0.226645
$254$	−8.42910e9	−0.127066
$255$	2.74874e10	0.407101
$256$	−2.47156e10	−0.359659
$257$	1.70355e10	0.243588	0.121794	−	0.992555i	$-0.461135\pi$
$257$	1.70355e10	0.243588	0.121794	+	0.992555i	$0.461135\pi$
$258$	6.25267e9	0.0878570
$259$	4.64518e10	0.641436
$260$	1.50747e10	0.204583
$261$	9.31556e9	0.124259
$262$	4.98207e10	0.653212
$263$	5.93948e10	0.765504	0.382752	−	0.923851i	$-0.374976\pi$
$263$	5.93948e10	0.765504	0.382752	+	0.923851i	$0.374976\pi$
$264$	−1.22445e11	−1.55140
$265$	1.92267e10	0.239496
$266$	−8.17653e9	−0.100139
$267$	4.09753e9	0.0493425
$268$	−5.21047e10	−0.616978
$269$	−1.07712e11	−1.25423	−0.627117	−	0.778925i	$-0.715765\pi$
$269$	−1.07712e11	−1.25423	−0.627117	+	0.778925i	$0.715765\pi$
$270$	3.83666e9	0.0439356
$271$	1.11447e11	1.25518	0.627592	−	0.778543i	$-0.284041\pi$
$271$	1.11447e11	1.25518	0.627592	+	0.778543i	$0.284041\pi$
$272$	2.91797e10	0.323237
$273$	3.52866e10	0.384484
$274$	−2.67299e10	−0.286497
$275$	1.11298e11	1.17352
$276$	1.63595e10	0.169699
$277$	1.47167e10	0.150194	0.0750968	−	0.997176i	$-0.476073\pi$
$277$	1.47167e10	0.150194	0.0750968	+	0.997176i	$0.476073\pi$
$278$	5.60222e10	0.562546
$279$	−1.05885e11	−1.04620
$280$	−1.87677e10	−0.182474
$281$	1.28452e11	1.22903	0.614513	−	0.788906i	$-0.289352\pi$
$281$	1.28452e11	1.22903	0.614513	+	0.788906i	$0.289352\pi$
$282$	−3.92169e10	−0.369277
$283$	−1.55862e10	−0.144445	−0.0722224	−	0.997389i	$-0.523009\pi$
$283$	−1.55862e10	−0.144445	−0.0722224	+	0.997389i	$0.523009\pi$
$284$	−8.56965e10	−0.781682
$285$	−3.12061e10	−0.280180
$286$	−3.91147e10	−0.345694
$287$	4.46730e10	0.388666
$288$	−9.54870e10	−0.817859
$289$	−6.68645e10	−0.563839
$290$	−3.48386e9	−0.0289248
$291$	1.78412e11	1.45850
$292$	−4.86349e10	−0.391494
$293$	−1.78122e11	−1.41193	−0.705965	−	0.708247i	$-0.749486\pi$
$293$	−1.78122e11	−1.41193	−0.705965	+	0.708247i	$0.749486\pi$
$294$	5.40247e10	0.421725
$295$	7.40577e10	0.569339
$296$	−1.26677e11	−0.959148
$297$	4.50081e10	0.335650
$298$	8.83360e10	0.648881
$299$	1.16078e10	0.0839906
$300$	1.23274e11	0.878667
$301$	1.12427e10	0.0789447
$302$	−1.04952e11	−0.726039
$303$	3.76853e10	0.256850
$304$	−3.31274e10	−0.222462
$305$	−6.97768e10	−0.461702
$306$	−3.58883e10	−0.233995
$307$	1.52485e11	0.979725	0.489863	−	0.871800i	$-0.337047\pi$
$307$	1.52485e11	0.979725	0.489863	+	0.871800i	$0.337047\pi$
$308$	−9.91209e10	−0.627606
$309$	−6.51843e10	−0.406752
$310$	3.95991e10	0.243533
$311$	−2.83289e11	−1.71715	−0.858574	−	0.512690i	$-0.828649\pi$
$311$	−2.83289e11	−1.71715	−0.858574	+	0.512690i	$0.828649\pi$
$312$	−9.62290e10	−0.574924
$313$	−2.44015e11	−1.43704	−0.718518	−	0.695508i	$-0.755179\pi$
$313$	−2.44015e11	−1.43704	−0.718518	+	0.695508i	$0.755179\pi$
$314$	−6.08284e10	−0.353120
$315$	−3.42931e10	−0.196250
$316$	−1.87524e11	−1.05795
$317$	−1.70636e11	−0.949084	−0.474542	−	0.880233i	$-0.657386\pi$
$317$	−1.70636e11	−0.949084	−0.474542	+	0.880233i	$0.657386\pi$
$318$	−5.52556e10	−0.303008
$319$	−4.08694e10	−0.220974
$320$	−6.09440e9	−0.0324905
$321$	3.02843e11	1.59201
$322$	−6.50623e9	−0.0337270
$323$	−5.87209e10	−0.300180
$324$	1.85079e11	0.933052
$325$	8.74684e10	0.434887
$326$	−1.35823e11	−0.666030
$327$	−2.58875e10	−0.125206
$328$	−1.21826e11	−0.581177
$329$	−7.05149e10	−0.331818
$330$	8.36736e10	0.388397
$331$	3.68117e11	1.68562	0.842811	−	0.538210i	$-0.180899\pi$
$331$	3.68117e11	1.68562	0.842811	+	0.538210i	$0.180899\pi$
$332$	2.22758e11	1.00626
$333$	−2.31469e11	−1.03156
$334$	9.37673e10	0.412280
$335$	7.90873e10	0.343088
$336$	−8.01322e10	−0.342989
$337$	−4.28944e10	−0.181162	−0.0905808	−	0.995889i	$-0.528872\pi$
$337$	−4.28944e10	−0.181162	−0.0905808	+	0.995889i	$0.528872\pi$
$338$	7.13801e10	0.297476
$339$	1.23382e11	0.507402
$340$	−6.06808e10	−0.246261
$341$	4.64540e11	1.86050
$342$	4.07435e10	0.161043
$343$	2.29843e11	0.896620
$344$	−3.06597e10	−0.118047
$345$	−2.48313e10	−0.0943656
$346$	2.67233e10	0.100242
$347$	1.60170e11	0.593059	0.296529	−	0.955024i	$-0.404171\pi$
$347$	1.60170e11	0.593059	0.296529	+	0.955024i	$0.404171\pi$
$348$	−4.52668e10	−0.165453
$349$	3.04550e11	1.09887	0.549433	−	0.835538i	$-0.314844\pi$
$349$	3.04550e11	1.09887	0.549433	+	0.835538i	$0.314844\pi$
$350$	−4.90264e10	−0.174632
$351$	3.53715e10	0.124386
$352$	4.18923e11	1.45443
$353$	−1.58317e11	−0.542676	−0.271338	−	0.962484i	$-0.587466\pi$
$353$	−1.58317e11	−0.542676	−0.271338	+	0.962484i	$0.587466\pi$
$354$	−2.12835e11	−0.720324
$355$	1.30075e11	0.434676
$356$	−9.04566e9	−0.0298480
$357$	−1.42041e11	−0.462813
$358$	1.45988e11	0.469726
$359$	−3.29410e11	−1.04668	−0.523338	−	0.852125i	$-0.675314\pi$
$359$	−3.29410e11	−1.04668	−0.523338	+	0.852125i	$0.675314\pi$
$360$	9.35194e10	0.293454
$361$	−2.56023e11	−0.793406
$362$	1.73466e11	0.530916
$363$	5.33760e11	1.61349
$364$	−7.78984e10	−0.232580
$365$	7.38207e10	0.217701
$366$	2.00532e11	0.584142
$367$	5.66994e11	1.63148	0.815738	−	0.578421i	$-0.196331\pi$
$367$	5.66994e11	1.63148	0.815738	+	0.578421i	$0.196331\pi$
$368$	−2.63602e10	−0.0749261
$369$	−2.22605e11	−0.625052
$370$	8.65653e10	0.240124
$371$	−9.93536e10	−0.272271
$372$	5.14524e11	1.39304
$373$	−4.36684e11	−1.16809	−0.584046	−	0.811720i	$-0.698531\pi$
$373$	−4.36684e11	−1.16809	−0.584046	+	0.811720i	$0.698531\pi$
$374$	1.57450e11	0.416121
$375$	−4.23170e11	−1.10503
$376$	1.92299e11	0.496171
$377$	−3.21190e10	−0.0818890
$378$	−1.98259e10	−0.0499481
$379$	−5.72159e11	−1.42443	−0.712213	−	0.701963i	$-0.752307\pi$
$379$	−5.72159e11	−1.42443	−0.712213	+	0.701963i	$0.752307\pi$
$380$	6.88903e10	0.169485
$381$	1.66238e11	0.404174
$382$	−1.87080e10	−0.0449513
$383$	−6.60393e11	−1.56822	−0.784111	−	0.620620i	$-0.786881\pi$
$383$	−6.60393e11	−1.56822	−0.784111	+	0.620620i	$0.786881\pi$
$384$	5.84141e11	1.37097
$385$	1.50451e11	0.348997
$386$	4.06454e9	0.00931899
$387$	−5.60225e10	−0.126959
$388$	−3.93861e11	−0.882268
$389$	−5.55324e11	−1.22963	−0.614814	−	0.788672i	$-0.710769\pi$
$389$	−5.55324e11	−1.22963	−0.614814	+	0.788672i	$0.710769\pi$
$390$	6.57584e10	0.143933
$391$	−4.67254e10	−0.101102
$392$	−2.64908e11	−0.566641
$393$	−9.82561e11	−2.07775
$394$	−2.30728e11	−0.482355
$395$	2.84634e11	0.588301
$396$	4.93918e11	1.00932
$397$	−7.47227e11	−1.50972	−0.754858	−	0.655889i	$-0.772294\pi$
$397$	−7.47227e11	−1.50972	−0.754858	+	0.655889i	$0.772294\pi$
$398$	3.15855e11	0.630978
$399$	1.61257e11	0.318523
$400$	−1.98632e11	−0.387953
$401$	−4.59550e11	−0.887530	−0.443765	−	0.896143i	$-0.646357\pi$
$401$	−4.59550e11	−0.887530	−0.443765	+	0.896143i	$0.646357\pi$
$402$	−2.27289e11	−0.434072
$403$	3.65079e11	0.689468
$404$	−8.31936e10	−0.155372
$405$	−2.80924e11	−0.518849
$406$	1.80028e10	0.0328831
$407$	1.01550e12	1.83445
$408$	3.87354e11	0.692050
$409$	4.85966e11	0.858718	0.429359	−	0.903134i	$-0.358739\pi$
$409$	4.85966e11	0.858718	0.429359	+	0.903134i	$0.358739\pi$
$410$	8.32504e10	0.145499
$411$	5.27166e11	0.911296
$412$	1.43900e11	0.246050
$413$	−3.82692e11	−0.647253
$414$	3.24205e10	0.0542397
$415$	−3.38114e11	−0.559560
$416$	3.29228e11	0.538985
$417$	−1.10487e12	−1.78936
$418$	−1.78751e11	−0.286388
$419$	6.23327e11	0.987991	0.493995	−	0.869465i	$-0.335536\pi$
$419$	6.23327e11	0.987991	0.493995	+	0.869465i	$0.335536\pi$
$420$	1.66639e11	0.261310
$421$	−1.20079e11	−0.186294	−0.0931468	−	0.995652i	$-0.529693\pi$
$421$	−1.20079e11	−0.186294	−0.0931468	+	0.995652i	$0.529693\pi$
$422$	7.59311e10	0.116550
$423$	3.51375e11	0.533628
$424$	2.70944e11	0.407130
$425$	−3.52090e11	−0.523484
$426$	−3.73822e11	−0.549948
$427$	3.60571e11	0.524886
$428$	−6.68553e11	−0.963028
$429$	7.71417e11	1.09959
$430$	2.09514e10	0.0295533
$431$	−1.24998e12	−1.74485	−0.872423	−	0.488752i	$-0.837452\pi$
$431$	−1.24998e12	−1.74485	−0.872423	+	0.488752i	$0.837452\pi$
$432$	−8.03251e10	−0.110962
$433$	3.88881e10	0.0531644	0.0265822	−	0.999647i	$-0.491538\pi$
$433$	3.88881e10	0.0531644	0.0265822	+	0.999647i	$0.491538\pi$
$434$	−2.04628e11	−0.276861
$435$	6.87085e10	0.0920044
$436$	5.71490e10	0.0757390
$437$	5.30468e10	0.0695814
$438$	−2.12153e11	−0.275433
$439$	−5.52309e11	−0.709728	−0.354864	−	0.934918i	$-0.615473\pi$
$439$	−5.52309e11	−0.709728	−0.354864	+	0.934918i	$0.615473\pi$
$440$	−4.10290e11	−0.521860
$441$	−4.84049e11	−0.609418
$442$	1.23739e11	0.154207
$443$	−1.47315e12	−1.81731	−0.908656	−	0.417546i	$-0.862890\pi$
$443$	−1.47315e12	−1.81731	−0.908656	+	0.417546i	$0.862890\pi$
$444$	1.12477e12	1.37354
$445$	1.37300e10	0.0165978
$446$	−1.45078e11	−0.173618
$447$	−1.74216e12	−2.06397
$448$	3.14927e10	0.0369368
$449$	7.85918e11	0.912575	0.456288	−	0.889832i	$-0.349179\pi$
$449$	7.85918e11	0.912575	0.456288	+	0.889832i	$0.349179\pi$
$450$	2.44298e11	0.280843
$451$	9.76616e11	1.11155
$452$	−2.72377e11	−0.306935
$453$	2.06986e12	2.30940
$454$	−2.71617e11	−0.300059
$455$	1.18238e11	0.129332
$456$	−4.39759e11	−0.476291
$457$	−1.62167e12	−1.73916	−0.869579	−	0.493794i	$-0.835610\pi$
$457$	−1.62167e12	−1.73916	−0.869579	+	0.493794i	$0.835610\pi$
$458$	−2.75326e11	−0.292383
$459$	−1.42382e11	−0.149727
$460$	5.48174e10	0.0570831
$461$	−8.89063e11	−0.916808	−0.458404	−	0.888744i	$-0.651579\pi$
$461$	−8.89063e11	−0.916808	−0.458404	+	0.888744i	$0.651579\pi$
$462$	−4.32382e11	−0.441549
$463$	4.38923e11	0.443889	0.221944	−	0.975059i	$-0.428760\pi$
$463$	4.38923e11	0.443889	0.221944	+	0.975059i	$0.428760\pi$
$464$	7.29388e10	0.0730513
$465$	−7.80972e11	−0.774635
$466$	−3.47224e11	−0.341093
$467$	6.08342e11	0.591864	0.295932	−	0.955209i	$-0.404370\pi$
$467$	6.08342e11	0.591864	0.295932	+	0.955209i	$0.404370\pi$
$468$	3.88167e11	0.374035
$469$	−4.08683e11	−0.390039
$470$	−1.31408e11	−0.124217
$471$	1.19965e12	1.12321
$472$	1.04363e12	0.967846
$473$	2.45783e11	0.225775
$474$	−8.18009e11	−0.744313
$475$	3.99724e11	0.360279
$476$	3.13567e11	0.279962
$477$	4.95078e11	0.437865
$478$	6.57296e11	0.575884
$479$	2.16565e12	1.87965	0.939827	−	0.341650i	$-0.110986\pi$
$479$	2.16565e12	1.87965	0.939827	+	0.341650i	$0.110986\pi$
$480$	−7.04281e11	−0.605564
$481$	7.98077e11	0.679817
$482$	3.99020e11	0.336731
$483$	1.28315e11	0.107280
$484$	−1.17832e12	−0.976023
$485$	5.97824e11	0.490609
$486$	6.88682e11	0.559958
$487$	1.64181e12	1.32264	0.661320	−	0.750104i	$-0.269996\pi$
$487$	1.64181e12	1.32264	0.661320	+	0.750104i	$0.269996\pi$
$488$	−9.83301e11	−0.784869
$489$	2.67869e12	2.11852
$490$	1.81026e11	0.141860
$491$	1.52108e12	1.18109	0.590547	−	0.807003i	$-0.298912\pi$
$491$	1.52108e12	1.18109	0.590547	+	0.807003i	$0.298912\pi$
$492$	1.08170e12	0.832267
$493$	1.29290e11	0.0985718
$494$	−1.40479e11	−0.106130
$495$	−7.49696e11	−0.561257
$496$	−8.29056e11	−0.615058
$497$	−6.72160e11	−0.494161
$498$	9.71707e11	0.707951
$499$	−4.02982e11	−0.290960	−0.145480	−	0.989361i	$-0.546473\pi$
$499$	−4.02982e11	−0.290960	−0.145480	+	0.989361i	$0.546473\pi$
$500$	9.34186e11	0.668449
$501$	−1.84927e12	−1.31139
$502$	4.66232e11	0.327669
$503$	−4.10239e11	−0.285747	−0.142873	−	0.989741i	$-0.545634\pi$
$503$	−4.10239e11	−0.285747	−0.142873	+	0.989741i	$0.545634\pi$
$504$	−4.83260e11	−0.333614
$505$	1.26276e11	0.0863990
$506$	−1.42236e11	−0.0964564
$507$	−1.40775e12	−0.946218
$508$	−3.66986e11	−0.244491
$509$	1.26933e12	0.838192	0.419096	−	0.907942i	$-0.362347\pi$
$509$	1.26933e12	0.838192	0.419096	+	0.907942i	$0.362347\pi$
$510$	−2.64700e11	−0.173256
$511$	−3.81467e11	−0.247493
$512$	−1.33676e12	−0.859684
$513$	1.61645e11	0.103047
$514$	−1.64050e11	−0.103667
$515$	−2.18420e11	−0.136823
$516$	2.72228e11	0.169048
$517$	−1.54156e12	−0.948970
$518$	−4.47325e11	−0.272985
$519$	−5.27036e11	−0.318850
$520$	−3.22444e11	−0.193392
$521$	2.92628e12	1.73999	0.869994	−	0.493062i	$-0.164122\pi$
$521$	2.92628e12	1.73999	0.869994	+	0.493062i	$0.164122\pi$
$522$	−8.97077e10	−0.0528826
$523$	2.35078e12	1.37390	0.686950	−	0.726705i	$-0.258949\pi$
$523$	2.35078e12	1.37390	0.686950	+	0.726705i	$0.258949\pi$
$524$	2.16909e12	1.25686
$525$	9.66895e11	0.555473
$526$	−5.71964e11	−0.325786
$527$	−1.46957e12	−0.829930
$528$	−1.75181e12	−0.980921
$529$	−1.75894e12	−0.976565
$530$	−1.85151e11	−0.101926
$531$	1.90695e12	1.04091
$532$	−3.55989e11	−0.192679
$533$	7.67516e11	0.411922
$534$	−3.94587e10	−0.0209994
$535$	1.01477e12	0.535518
$536$	1.11450e12	0.583231
$537$	−2.87917e12	−1.49411
$538$	1.03725e12	0.533782
$539$	2.12363e12	1.08375
$540$	1.67040e11	0.0845375
$541$	3.12960e12	1.57073	0.785364	−	0.619034i	$-0.212476\pi$
$541$	3.12960e12	1.57073	0.785364	+	0.619034i	$0.212476\pi$
$542$	−1.07322e12	−0.534187
$543$	−3.42109e12	−1.68875
$544$	−1.32526e12	−0.648790
$545$	−8.67439e10	−0.0421167
$546$	−3.39806e11	−0.163630
$547$	−2.95721e12	−1.41234	−0.706169	−	0.708043i	$-0.749578\pi$
$547$	−2.95721e12	−1.41234	−0.706169	+	0.708043i	$0.749578\pi$
$548$	−1.16377e12	−0.551257
$549$	−1.79672e12	−0.844121
$550$	−1.07179e12	−0.499433
$551$	−1.46781e11	−0.0678403
$552$	−3.49925e11	−0.160416
$553$	−1.47084e12	−0.668810
$554$	−1.41720e11	−0.0639201
$555$	−1.70724e12	−0.763792
$556$	2.43909e12	1.08241
$557$	−1.07910e12	−0.475021	−0.237511	−	0.971385i	$-0.576331\pi$
$557$	−1.07910e12	−0.475021	−0.237511	+	0.971385i	$0.576331\pi$
$558$	1.01966e12	0.445247
$559$	1.93159e11	0.0836684
$560$	−2.68507e11	−0.115375
$561$	−3.10522e12	−1.32361
$562$	−1.23697e12	−0.523055
$563$	1.53793e12	0.645132	0.322566	−	0.946547i	$-0.395455\pi$
$563$	1.53793e12	0.645132	0.322566	+	0.946547i	$0.395455\pi$
$564$	−1.70743e12	−0.710536
$565$	4.13428e11	0.170680
$566$	1.50093e11	0.0614735
$567$	1.45167e12	0.589853
$568$	1.83302e12	0.738925
$569$	2.07875e12	0.831377	0.415688	−	0.909507i	$-0.363541\pi$
$569$	2.07875e12	0.831377	0.415688	+	0.909507i	$0.363541\pi$
$570$	3.00511e11	0.119240
$571$	−1.16515e12	−0.458689	−0.229345	−	0.973345i	$-0.573658\pi$
$571$	−1.16515e12	−0.458689	−0.229345	+	0.973345i	$0.573658\pi$
$572$	−1.70297e12	−0.665159
$573$	3.68958e11	0.142982
$574$	−4.30195e11	−0.165410
$575$	3.18068e11	0.121343
$576$	−1.56928e11	−0.0594017
$577$	7.45248e11	0.279904	0.139952	−	0.990158i	$-0.455305\pi$
$577$	7.45248e11	0.279904	0.139952	+	0.990158i	$0.455305\pi$
$578$	6.43897e11	0.239961
$579$	−8.01607e10	−0.0296420
$580$	−1.51680e11	−0.0556548
$581$	1.74720e12	0.636136
$582$	−1.71809e12	−0.620715
$583$	−2.17202e12	−0.778672
$584$	1.04029e12	0.370080
$585$	−5.89181e11	−0.207992
$586$	1.71529e12	0.600895
$587$	−2.49286e11	−0.0866615	−0.0433308	−	0.999061i	$-0.513797\pi$
$587$	−2.49286e11	−0.0866615	−0.0433308	+	0.999061i	$0.513797\pi$
$588$	2.35212e12	0.811451
$589$	1.66838e12	0.571184
$590$	−7.13167e11	−0.242302
$591$	4.55040e12	1.53428
$592$	−1.81235e12	−0.606449
$593$	−3.10748e12	−1.03196	−0.515980	−	0.856601i	$-0.672572\pi$
$593$	−3.10748e12	−1.03196	−0.515980	+	0.856601i	$0.672572\pi$
$594$	−4.33423e11	−0.142847
$595$	−4.75950e11	−0.155681
$596$	3.84597e12	1.24853
$597$	−6.22928e12	−2.00703
$598$	−1.11782e11	−0.0357451
$599$	2.25538e12	0.715811	0.357906	−	0.933758i	$-0.383491\pi$
$599$	2.25538e12	0.715811	0.357906	+	0.933758i	$0.383491\pi$
$600$	−2.63679e12	−0.830605
$601$	6.65807e11	0.208168	0.104084	−	0.994569i	$-0.466809\pi$
$601$	6.65807e11	0.208168	0.104084	+	0.994569i	$0.466809\pi$
$602$	−1.08266e11	−0.0335977
$603$	2.03646e12	0.627260
$604$	−4.56940e12	−1.39699
$605$	1.78852e12	0.542744
$606$	−3.62904e11	−0.109311
$607$	7.48544e11	0.223804	0.111902	−	0.993719i	$-0.464306\pi$
$607$	7.48544e11	0.223804	0.111902	+	0.993719i	$0.464306\pi$
$608$	1.50455e12	0.446519
$609$	−3.55050e11	−0.104595
$610$	6.71943e11	0.196493
$611$	−1.21150e12	−0.351672
$612$	−1.56250e12	−0.450235
$613$	−2.50001e12	−0.715103	−0.357552	−	0.933893i	$-0.616388\pi$
$613$	−2.50001e12	−0.715103	−0.357552	+	0.933893i	$0.616388\pi$
$614$	−1.46841e12	−0.416956
$615$	−1.64186e12	−0.462805
$616$	2.12017e12	0.593277
$617$	1.56036e12	0.433451	0.216726	−	0.976233i	$-0.430462\pi$
$617$	1.56036e12	0.433451	0.216726	+	0.976233i	$0.430462\pi$
$618$	6.27717e11	0.173107
$619$	−1.65116e12	−0.452045	−0.226023	−	0.974122i	$-0.572572\pi$
$619$	−1.65116e12	−0.452045	−0.226023	+	0.974122i	$0.572572\pi$
$620$	1.72407e12	0.468588
$621$	1.28624e11	0.0347065
$622$	2.72804e12	0.730792
$623$	−7.09496e10	−0.0188692
$624$	−1.37673e12	−0.363512
$625$	1.60575e12	0.420939
$626$	2.34984e12	0.611580
$627$	3.52531e12	0.910949
$628$	−2.64834e12	−0.679448
$629$	−3.21253e12	−0.818313
$630$	3.30238e11	0.0835208
$631$	−9.48276e9	−0.00238124	−0.00119062	−	0.999999i	$-0.500379\pi$
$631$	−9.48276e9	−0.00238124	−0.00119062	+	0.999999i	$0.500379\pi$
$632$	4.01108e12	1.00008
$633$	−1.49751e12	−0.370726
$634$	1.64321e12	0.403916
$635$	5.57031e11	0.135956
$636$	−2.40572e12	−0.583026
$637$	1.66894e12	0.401619
$638$	3.93568e11	0.0940429
$639$	3.34936e12	0.794709
$640$	1.95734e12	0.461165
$641$	2.83779e12	0.663925	0.331963	−	0.943293i	$-0.392289\pi$
$641$	2.83779e12	0.663925	0.331963	+	0.943293i	$0.392289\pi$
$642$	−2.91634e12	−0.677533
$643$	6.64160e12	1.53223	0.766114	−	0.642704i	$-0.222188\pi$
$643$	6.64160e12	1.53223	0.766114	+	0.642704i	$0.222188\pi$
$644$	−2.83268e11	−0.0648950
$645$	−4.13203e11	−0.0940037
$646$	5.65475e11	0.127752
$647$	−1.93866e12	−0.434943	−0.217471	−	0.976067i	$-0.569781\pi$
$647$	−1.93866e12	−0.434943	−0.217471	+	0.976067i	$0.569781\pi$
$648$	−3.95880e12	−0.882015
$649$	−8.36621e12	−1.85109
$650$	−8.42310e11	−0.185081
$651$	4.03566e12	0.880644
$652$	−5.91346e12	−1.28153
$653$	3.90359e11	0.0840147	0.0420073	−	0.999117i	$-0.486625\pi$
$653$	3.90359e11	0.0840147	0.0420073	+	0.999117i	$0.486625\pi$
$654$	2.49293e11	0.0532857
$655$	−3.29237e12	−0.698912
$656$	−1.74295e12	−0.367466
$657$	1.90085e12	0.398018
$658$	6.79050e11	0.141216
$659$	4.87974e12	1.00789	0.503944	−	0.863737i	$-0.331882\pi$
$659$	4.87974e12	1.00789	0.503944	+	0.863737i	$0.331882\pi$
$660$	3.64298e12	0.747324
$661$	−8.13003e12	−1.65648	−0.828239	−	0.560376i	$-0.810657\pi$
$661$	−8.13003e12	−1.65648	−0.828239	+	0.560376i	$0.810657\pi$
$662$	−3.54492e12	−0.717375
$663$	−2.44037e12	−0.490506
$664$	−4.76473e12	−0.951222
$665$	5.40340e11	0.107145
$666$	2.22902e12	0.439015
$667$	−1.16797e11	−0.0228488
$668$	4.08244e12	0.793279
$669$	2.86122e12	0.552248
$670$	−7.61601e11	−0.146013
$671$	7.88261e12	1.50113
$672$	3.63936e12	0.688436
$673$	7.83754e12	1.47269	0.736346	−	0.676606i	$-0.236550\pi$
$673$	7.83754e12	1.47269	0.736346	+	0.676606i	$0.236550\pi$
$674$	4.13068e11	0.0770996
$675$	9.69222e11	0.179703
$676$	3.10775e12	0.572381
$677$	3.51888e12	0.643807	0.321903	−	0.946773i	$-0.395677\pi$
$677$	3.51888e12	0.643807	0.321903	+	0.946773i	$0.395677\pi$
$678$	−1.18815e12	−0.215943
$679$	−3.08925e12	−0.557749
$680$	1.29795e12	0.232791
$681$	5.35682e12	0.954433
$682$	−4.47347e12	−0.791798
$683$	9.44474e12	1.66072	0.830361	−	0.557226i	$-0.188134\pi$
$683$	9.44474e12	1.66072	0.830361	+	0.557226i	$0.188134\pi$
$684$	1.77389e12	0.309866
$685$	1.76643e12	0.306541
$686$	−2.21336e12	−0.381588
$687$	5.42997e12	0.930019
$688$	−4.38644e11	−0.0746387
$689$	−1.70697e12	−0.288562
$690$	2.39123e11	0.0401605
$691$	−3.85564e12	−0.643346	−0.321673	−	0.946851i	$-0.604245\pi$
$691$	−3.85564e12	−0.643346	−0.321673	+	0.946851i	$0.604245\pi$
$692$	1.16348e12	0.192877
$693$	3.87405e12	0.638065
$694$	−1.54241e12	−0.252397
$695$	−3.70219e12	−0.601903
$696$	9.68245e11	0.156403
$697$	−3.08951e12	−0.495841
$698$	−2.93278e12	−0.467660
$699$	6.84793e12	1.08496
$700$	−2.13451e12	−0.336014
$701$	−2.65363e12	−0.415059	−0.207529	−	0.978229i	$-0.566542\pi$
$701$	−2.65363e12	−0.415059	−0.207529	+	0.978229i	$0.566542\pi$
$702$	−3.40624e11	−0.0529368
$703$	3.64715e12	0.563189
$704$	6.88477e11	0.105636
$705$	2.59162e12	0.395113
$706$	1.52457e12	0.230954
$707$	−6.52528e11	−0.0982228
$708$	−9.26639e12	−1.38599
$709$	−8.34085e12	−1.23966	−0.619830	−	0.784736i	$-0.712798\pi$
$709$	−8.34085e12	−1.23966	−0.619830	+	0.784736i	$0.712798\pi$
$710$	−1.25260e12	−0.184991
$711$	7.32918e12	1.07558
$712$	1.93484e11	0.0282154
$713$	1.32756e12	0.192377
$714$	1.36783e12	0.196966
$715$	2.58487e12	0.369880
$716$	6.35603e12	0.903811
$717$	−1.29631e13	−1.83178
$718$	3.17218e12	0.445449
$719$	−1.03986e13	−1.45110	−0.725549	−	0.688170i	$-0.758414\pi$
$719$	−1.03986e13	−1.45110	−0.725549	+	0.688170i	$0.758414\pi$
$720$	1.33797e12	0.185545
$721$	1.12868e12	0.155547
$722$	2.46547e12	0.337662
$723$	−7.86944e12	−1.07108
$724$	7.55236e12	1.02155
$725$	−8.80098e11	−0.118307
$726$	−5.14004e12	−0.686676
$727$	−5.23334e12	−0.694822	−0.347411	−	0.937713i	$-0.612939\pi$
$727$	−5.23334e12	−0.694822	−0.347411	+	0.937713i	$0.612939\pi$
$728$	1.66623e12	0.219858
$729$	−4.89333e12	−0.641698
$730$	−7.10884e11	−0.0926501
$731$	−7.77530e11	−0.100714
$732$	8.73075e12	1.12396
$733$	−1.15223e12	−0.147425	−0.0737123	−	0.997280i	$-0.523485\pi$
$733$	−1.15223e12	−0.147425	−0.0737123	+	0.997280i	$0.523485\pi$
$734$	−5.46008e12	−0.694331
$735$	−3.57018e12	−0.451229
$736$	1.19720e12	0.150389
$737$	−8.93440e12	−1.11548
$738$	2.14366e12	0.266012
$739$	−5.82737e12	−0.718741	−0.359371	−	0.933195i	$-0.617009\pi$
$739$	−5.82737e12	−0.718741	−0.359371	+	0.933195i	$0.617009\pi$
$740$	3.76888e12	0.462029
$741$	2.77052e12	0.337582
$742$	9.56763e11	0.115874
$743$	−6.73156e12	−0.810338	−0.405169	−	0.914242i	$-0.632787\pi$
$743$	−6.73156e12	−0.810338	−0.405169	+	0.914242i	$0.632787\pi$
$744$	−1.10055e13	−1.31684
$745$	−5.83763e12	−0.694278
$746$	4.20521e12	0.497122
$747$	−8.70627e12	−1.02303
$748$	6.85504e12	0.800669
$749$	−5.24379e12	−0.608804
$750$	4.07508e12	0.470284
$751$	−1.31942e13	−1.51357	−0.756784	−	0.653665i	$-0.773231\pi$
$751$	−1.31942e13	−1.51357	−0.756784	+	0.653665i	$0.773231\pi$
$752$	2.75119e12	0.313719
$753$	−9.19500e12	−1.04226
$754$	3.09302e11	0.0348507
$755$	6.93569e12	0.776834
$756$	−8.63179e11	−0.0961065
$757$	−7.77025e12	−0.860010	−0.430005	−	0.902826i	$-0.641488\pi$
$757$	−7.77025e12	−0.860010	−0.430005	+	0.902826i	$0.641488\pi$
$758$	5.50982e12	0.606214
$759$	2.80516e12	0.306811
$760$	−1.47354e12	−0.160215
$761$	−1.84489e13	−1.99407	−0.997035	−	0.0769500i	$-0.975482\pi$
$761$	−1.84489e13	−1.99407	−0.997035	+	0.0769500i	$0.975482\pi$
$762$	−1.60085e12	−0.172010
$763$	4.48248e11	0.0478804
$764$	−8.14509e11	−0.0864920
$765$	2.37165e12	0.250365
$766$	6.35950e12	0.667411
$767$	−6.57494e12	−0.685982
$768$	−4.69399e12	−0.486874
$769$	1.24516e13	1.28397	0.641985	−	0.766717i	$-0.278111\pi$
$769$	1.24516e13	1.28397	0.641985	+	0.766717i	$0.278111\pi$
$770$	−1.44883e12	−0.148528
$771$	3.23538e12	0.329747
$772$	1.76962e11	0.0179309
$773$	−1.48775e13	−1.49873	−0.749365	−	0.662157i	$-0.769641\pi$
$773$	−1.48775e13	−1.49873	−0.749365	+	0.662157i	$0.769641\pi$
$774$	5.39489e11	0.0540317
$775$	1.00036e13	0.996090
$776$	8.42459e12	0.834009
$777$	8.82212e12	0.868317
$778$	5.34771e12	0.523310
$779$	3.50748e12	0.341254
$780$	2.86299e12	0.276945
$781$	−1.46944e13	−1.41326
$782$	4.49960e11	0.0430273
$783$	−3.55905e11	−0.0338381
$784$	−3.79000e12	−0.358275
$785$	4.01980e12	0.377825
$786$	9.46195e12	0.884258
$787$	1.10622e13	1.02791	0.513956	−	0.857816i	$-0.328179\pi$
$787$	1.10622e13	1.02791	0.513956	+	0.857816i	$0.328179\pi$
$788$	−1.00454e13	−0.928112
$789$	1.12802e13	1.03627
$790$	−2.74099e12	−0.250372
$791$	−2.13638e12	−0.194037
$792$	−1.05648e13	−0.954107
$793$	6.19488e12	0.556293
$794$	7.19570e12	0.642512
$795$	3.65153e12	0.324207
$796$	1.37517e13	1.21408
$797$	−5.04498e12	−0.442891	−0.221446	−	0.975173i	$-0.571077\pi$
$797$	−5.04498e12	−0.442891	−0.221446	+	0.975173i	$0.571077\pi$
$798$	−1.55289e12	−0.135558
$799$	4.87670e12	0.423316
$800$	9.02124e12	0.778684
$801$	3.53541e11	0.0303454
$802$	4.42541e12	0.377719
$803$	−8.33943e12	−0.707810
$804$	−9.89571e12	−0.835208
$805$	4.29960e11	0.0360866
$806$	−3.51566e12	−0.293427
$807$	−2.04566e13	−1.69787
$808$	1.77949e12	0.146874
$809$	1.42809e11	0.0117216	0.00586079	−	0.999983i	$-0.498134\pi$
$809$	1.42809e11	0.0117216	0.00586079	+	0.999983i	$0.498134\pi$
$810$	2.70526e12	0.220814
$811$	2.03598e13	1.65264	0.826322	−	0.563197i	$-0.190429\pi$
$811$	2.03598e13	1.65264	0.826322	+	0.563197i	$0.190429\pi$
$812$	7.83805e11	0.0632712
$813$	2.11660e13	1.69915
$814$	−9.77918e12	−0.780715
$815$	8.97577e12	0.712627
$816$	5.54182e12	0.437569
$817$	8.82721e11	0.0693145
$818$	−4.67979e12	−0.365457
$819$	3.04458e12	0.236456
$820$	3.62455e12	0.279958
$821$	−1.84922e11	−0.0142051	−0.00710255	−	0.999975i	$-0.502261\pi$
$821$	−1.84922e11	−0.0142051	−0.00710255	+	0.999975i	$0.502261\pi$
$822$	−5.07655e12	−0.387834
$823$	2.87069e12	0.218116	0.109058	−	0.994035i	$-0.465217\pi$
$823$	2.87069e12	0.218116	0.109058	+	0.994035i	$0.465217\pi$
$824$	−3.07799e12	−0.232592
$825$	2.11377e13	1.58861
$826$	3.68528e12	0.275461
$827$	2.25945e13	1.67969	0.839844	−	0.542828i	$-0.182647\pi$
$827$	2.25945e13	1.67969	0.839844	+	0.542828i	$0.182647\pi$
$828$	1.41152e12	0.104364
$829$	−1.25049e12	−0.0919570	−0.0459785	−	0.998942i	$-0.514641\pi$
$829$	−1.25049e12	−0.0919570	−0.0459785	+	0.998942i	$0.514641\pi$
$830$	3.25600e12	0.238140
$831$	2.79500e12	0.203318
$832$	5.41069e11	0.0391469
$833$	−6.71806e12	−0.483439
$834$	1.06397e13	0.761523
$835$	−6.19655e12	−0.441124
$836$	−7.78245e12	−0.551046
$837$	4.04537e12	0.284901
$838$	−6.00256e12	−0.420474
$839$	−9.40360e12	−0.655187	−0.327594	−	0.944819i	$-0.606238\pi$
$839$	−9.40360e12	−0.655187	−0.327594	+	0.944819i	$0.606238\pi$
$840$	−3.56437e12	−0.247016
$841$	−1.41840e13	−0.977723
$842$	1.15635e12	0.0792837
$843$	2.43955e13	1.66374
$844$	3.30588e12	0.224257
$845$	−4.71711e12	−0.318288
$846$	−3.38370e12	−0.227104
$847$	−9.24217e12	−0.617019
$848$	3.87635e12	0.257420
$849$	−2.96013e12	−0.195536
$850$	3.39058e12	0.222787
$851$	2.90211e12	0.189684
$852$	−1.62755e13	−1.05817
$853$	4.97590e12	0.321811	0.160905	−	0.986970i	$-0.448559\pi$
$853$	4.97590e12	0.321811	0.160905	+	0.986970i	$0.448559\pi$
$854$	−3.47225e12	−0.223384
$855$	−2.69251e12	−0.172310
$856$	1.43002e13	0.910352
$857$	−2.45954e13	−1.55755	−0.778773	−	0.627306i	$-0.784158\pi$
$857$	−2.45954e13	−1.55755	−0.778773	+	0.627306i	$0.784158\pi$
$858$	−7.42865e12	−0.467969
$859$	4.12964e12	0.258787	0.129394	−	0.991593i	$-0.458697\pi$
$859$	4.12964e12	0.258787	0.129394	+	0.991593i	$0.458697\pi$
$860$	9.12183e11	0.0568642
$861$	8.48429e12	0.526140
$862$	1.20372e13	0.742579
$863$	−5.44656e11	−0.0334252	−0.0167126	−	0.999860i	$-0.505320\pi$
$863$	−5.44656e11	−0.0334252	−0.0167126	+	0.999860i	$0.505320\pi$
$864$	3.64812e12	0.222719
$865$	−1.76599e12	−0.107255
$866$	−3.74488e11	−0.0226260
$867$	−1.26989e13	−0.763274
$868$	−8.90909e12	−0.532715
$869$	−3.21547e13	−1.91274
$870$	−6.61654e11	−0.0391557
$871$	−7.02148e12	−0.413377
$872$	−1.22240e12	−0.0715961
$873$	1.53937e13	0.896971
$874$	−5.10835e11	−0.0296128
$875$	7.32728e12	0.422578
$876$	−9.23673e12	−0.529968
$877$	2.79747e13	1.59686	0.798431	−	0.602087i	$-0.205664\pi$
$877$	2.79747e13	1.59686	0.798431	+	0.602087i	$0.205664\pi$
$878$	5.31867e12	0.302049
$879$	−3.38289e13	−1.91134
$880$	−5.86996e12	−0.329961
$881$	2.31406e13	1.29415	0.647073	−	0.762428i	$-0.275993\pi$
$881$	2.31406e13	1.29415	0.647073	+	0.762428i	$0.275993\pi$
$882$	4.66133e12	0.259359
$883$	−2.00961e13	−1.11247	−0.556235	−	0.831025i	$-0.687754\pi$
$883$	−2.00961e13	−1.11247	−0.556235	+	0.831025i	$0.687754\pi$
$884$	5.38733e12	0.296714
$885$	1.40650e13	0.770719
$886$	1.41862e13	0.773420
$887$	1.62218e12	0.0879916	0.0439958	−	0.999032i	$-0.485991\pi$
$887$	1.62218e12	0.0879916	0.0439958	+	0.999032i	$0.485991\pi$
$888$	−2.40585e13	−1.29841
$889$	−2.87845e12	−0.154561
$890$	−1.32218e11	−0.00706376
$891$	3.17356e13	1.68693
$892$	−6.31641e12	−0.334063
$893$	−5.53646e12	−0.291340
$894$	1.67768e13	0.878395
$895$	−9.64754e12	−0.502589
$896$	−1.01145e13	−0.524276
$897$	2.20456e12	0.113699
$898$	−7.56829e12	−0.388378
$899$	−3.67338e12	−0.187563
$900$	1.06362e13	0.540377
$901$	6.87113e12	0.347350
$902$	−9.40470e12	−0.473059
$903$	2.13522e12	0.106868
$904$	5.82606e12	0.290146
$905$	−1.14634e13	−0.568060
$906$	−1.99325e13	−0.982844
$907$	3.75549e13	1.84261	0.921306	−	0.388839i	$-0.127124\pi$
$907$	3.75549e13	1.84261	0.921306	+	0.388839i	$0.127124\pi$
$908$	−1.18257e13	−0.577350
$909$	3.25154e12	0.157962
$910$	−1.13862e12	−0.0550419
$911$	−1.18903e13	−0.571951	−0.285975	−	0.958237i	$-0.592318\pi$
$911$	−1.18903e13	−0.571951	−0.285975	+	0.958237i	$0.592318\pi$
$912$	−6.29156e12	−0.301149
$913$	3.81963e13	1.81929
$914$	1.56165e13	0.740159
$915$	−1.32520e13	−0.625010
$916$	−1.19871e13	−0.562582
$917$	1.70133e13	0.794558
$918$	1.37113e12	0.0637214
$919$	−2.35907e11	−0.0109099	−0.00545495	−	0.999985i	$-0.501736\pi$
$919$	−2.35907e11	−0.0109099	−0.00545495	+	0.999985i	$0.501736\pi$
$920$	−1.17253e12	−0.0539608
$921$	2.89599e13	1.32626
$922$	8.56157e12	0.390179
$923$	−1.15482e13	−0.523730
$924$	−1.88250e13	−0.849595
$925$	2.18683e13	0.982147
$926$	−4.22678e12	−0.188912
$927$	−5.62420e12	−0.250151
$928$	−3.31266e12	−0.146626
$929$	−1.46785e11	−0.00646562	−0.00323281	−	0.999995i	$-0.501029\pi$
$929$	−1.46785e11	−0.00646562	−0.00323281	+	0.999995i	$0.501029\pi$
$930$	7.52066e12	0.329673
$931$	7.62694e12	0.332718
$932$	−1.51174e13	−0.656305
$933$	−5.38022e13	−2.32452
$934$	−5.85826e12	−0.251888
$935$	−1.04050e13	−0.445234
$936$	−8.30278e12	−0.353576
$937$	2.39861e13	1.01656	0.508279	−	0.861193i	$-0.330282\pi$
$937$	2.39861e13	1.01656	0.508279	+	0.861193i	$0.330282\pi$
$938$	3.93556e12	0.165995
$939$	−4.63434e13	−1.94533
$940$	−5.72124e12	−0.239010
$941$	−1.94273e12	−0.0807716	−0.0403858	−	0.999184i	$-0.512859\pi$
$941$	−1.94273e12	−0.0807716	−0.0403858	+	0.999184i	$0.512859\pi$
$942$	−1.15525e13	−0.478022
$943$	2.79098e12	0.114935
$944$	1.49310e13	0.611949
$945$	1.31018e12	0.0534426
$946$	−2.36686e12	−0.0960865
$947$	3.34211e12	0.135035	0.0675173	−	0.997718i	$-0.478492\pi$
$947$	3.34211e12	0.135035	0.0675173	+	0.997718i	$0.478492\pi$
$948$	−3.56145e13	−1.43215
$949$	−6.55390e12	−0.262302
$950$	−3.84929e12	−0.153329
$951$	−3.24072e13	−1.28478
$952$	−6.70712e12	−0.264649
$953$	−2.86874e13	−1.12661	−0.563304	−	0.826250i	$-0.690470\pi$
$953$	−2.86874e13	−1.12661	−0.563304	+	0.826250i	$0.690470\pi$
$954$	−4.76754e12	−0.186349
$955$	1.23631e12	0.0480962
$956$	2.86173e13	1.10807
$957$	−7.76192e12	−0.299134
$958$	−2.08549e13	−0.799952
$959$	−9.12800e12	−0.348491
$960$	−1.15745e12	−0.0439826
$961$	1.53137e13	0.579196
$962$	−7.68539e12	−0.289320
$963$	2.61297e13	0.979077
$964$	1.73725e13	0.647912
$965$	−2.68603e11	−0.00997097
$966$	−1.23566e12	−0.0456565
$967$	−3.93409e13	−1.44685	−0.723427	−	0.690401i	$-0.757434\pi$
$967$	−3.93409e13	−1.44685	−0.723427	+	0.690401i	$0.757434\pi$
$968$	2.52040e13	0.922636
$969$	−1.11523e13	−0.406356
$970$	−5.75697e12	−0.208796
$971$	−1.16162e13	−0.419353	−0.209676	−	0.977771i	$-0.567241\pi$
$971$	−1.16162e13	−0.419353	−0.209676	+	0.977771i	$0.567241\pi$
$972$	2.99838e13	1.07743
$973$	1.91310e13	0.684274
$974$	−1.58104e13	−0.562895
$975$	1.66120e13	0.588710
$976$	−1.40679e13	−0.496256
$977$	3.35215e13	1.17706	0.588530	−	0.808476i	$-0.299707\pi$
$977$	3.35215e13	1.17706	0.588530	+	0.808476i	$0.299707\pi$
$978$	−2.57955e13	−0.901610
$979$	−1.55106e12	−0.0539643
$980$	7.88150e12	0.272955
$981$	−2.23361e12	−0.0770012
$982$	−1.46478e13	−0.502655
$983$	−5.05172e13	−1.72563	−0.862817	−	0.505516i	$-0.831302\pi$
$983$	−5.05172e13	−1.72563	−0.862817	+	0.505516i	$0.831302\pi$
$984$	−2.31372e13	−0.786744
$985$	1.52475e13	0.516102
$986$	−1.24504e12	−0.0419507
$987$	−1.33922e13	−0.449184
$988$	−6.11617e12	−0.204208
$989$	7.02399e11	0.0233454
$990$	7.21948e12	0.238862
$991$	5.31629e13	1.75096	0.875482	−	0.483250i	$-0.160544\pi$
$991$	5.31629e13	1.75096	0.875482	+	0.483250i	$0.160544\pi$
$992$	3.76532e13	1.23452
$993$	6.99128e13	2.28184
$994$	6.47282e12	0.210307
$995$	−2.08731e13	−0.675122
$996$	4.23061e13	1.36219
$997$	−4.26532e13	−1.36717	−0.683586	−	0.729870i	$-0.739581\pi$
$997$	−4.26532e13	−1.36717	−0.683586	+	0.729870i	$0.739581\pi$
$998$	3.88067e12	0.123828
$999$	8.84335e12	0.280913

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.10.a.a.1.7	✓	15
3.2	odd	2		387.10.a.c.1.9		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.10.a.a.1.7	✓	15	1.1	even	1	trivial
387.10.a.c.1.9		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)

\(f(q)\)	\(=\)	\(q-9.62988 q^{2} +189.920 q^{3} -419.265 q^{4} +636.384 q^{5} -1828.91 q^{6} -3288.51 q^{7} +8967.97 q^{8} +16386.6 q^{9} +O(q^{10})\)	\(q-9.62988 q^{2} +189.920 q^{3} -419.265 q^{4} +636.384 q^{5} -1828.91 q^{6} -3288.51 q^{7} +8967.97 q^{8} +16386.6 q^{9} -6128.30 q^{10} -71891.5 q^{11} -79626.9 q^{12} -56499.0 q^{13} +31667.9 q^{14} +120862. q^{15} +128303. q^{16} +227428. q^{17} -157801. q^{18} -258196. q^{19} -266814. q^{20} -624553. q^{21} +692307. q^{22} -205452. q^{23} +1.70320e6 q^{24} -1.54814e6 q^{25} +544079. q^{26} -626056. q^{27} +1.37876e6 q^{28} +568487. q^{29} -1.16389e6 q^{30} -6.46168e6 q^{31} -5.82715e6 q^{32} -1.36536e7 q^{33} -2.19010e6 q^{34} -2.09275e6 q^{35} -6.87033e6 q^{36} -1.41255e7 q^{37} +2.48640e6 q^{38} -1.07303e7 q^{39} +5.70707e6 q^{40} -1.35846e7 q^{41} +6.01437e6 q^{42} -3.41880e6 q^{43} +3.01416e7 q^{44} +1.04282e7 q^{45} +1.97848e6 q^{46} +2.14428e7 q^{47} +2.43674e7 q^{48} -2.95393e7 q^{49} +1.49084e7 q^{50} +4.31931e7 q^{51} +2.36881e7 q^{52} +3.02124e7 q^{53} +6.02884e6 q^{54} -4.57506e7 q^{55} -2.94912e7 q^{56} -4.90366e7 q^{57} -5.47446e6 q^{58} +1.16373e8 q^{59} -5.06733e7 q^{60} -1.09646e8 q^{61} +6.22252e7 q^{62} -5.38874e7 q^{63} -9.57661e6 q^{64} -3.59551e7 q^{65} +1.31483e8 q^{66} +1.24276e8 q^{67} -9.53526e7 q^{68} -3.90194e7 q^{69} +2.01529e7 q^{70} +2.04397e8 q^{71} +1.46954e8 q^{72} +1.16000e8 q^{73} +1.36027e8 q^{74} -2.94023e8 q^{75} +1.08253e8 q^{76} +2.36416e8 q^{77} +1.03331e8 q^{78} +4.47267e8 q^{79} +8.16502e7 q^{80} -4.41438e8 q^{81} +1.30818e8 q^{82} -5.31305e8 q^{83} +2.61853e8 q^{84} +1.44731e8 q^{85} +3.29226e7 q^{86} +1.07967e8 q^{87} -6.44721e8 q^{88} +2.15750e7 q^{89} -1.00422e8 q^{90} +1.85797e8 q^{91} +8.61388e7 q^{92} -1.22720e9 q^{93} -2.06492e8 q^{94} -1.64312e8 q^{95} -1.10669e9 q^{96} +9.39408e8 q^{97} +2.84460e8 q^{98} -1.17806e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 32 q^{2} - 317 q^{3} + 3242 q^{4} - 4717 q^{5} + 687 q^{6} - 9680 q^{7} - 20394 q^{8} + 69516 q^{9}+O(q^{10}) \) 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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