LMFDB - Embedded newform 43.10.a.a.1.1

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			1.1
Root			$40.4171$ 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)

$f(q)$	$=$	$q-42.4171 q^{2} +107.942 q^{3} +1287.21 q^{4} +267.050 q^{5} -4578.58 q^{6} +1084.23 q^{7} -32882.2 q^{8} -8031.56 q^{9} +O(q^{10})$	\(q-42.4171 q^{2} +107.942 q^{3} +1287.21 q^{4} +267.050 q^{5} -4578.58 q^{6} +1084.23 q^{7} -32882.2 q^{8} -8031.56 q^{9} -11327.5 q^{10} -49756.6 q^{11} +138944. q^{12} +90530.0 q^{13} -45990.0 q^{14} +28825.8 q^{15} +735714. q^{16} +139514. q^{17} +340675. q^{18} -189921. q^{19} +343749. q^{20} +117034. q^{21} +2.11053e6 q^{22} -94945.1 q^{23} -3.54936e6 q^{24} -1.88181e6 q^{25} -3.84002e6 q^{26} -2.99156e6 q^{27} +1.39564e6 q^{28} -4.15457e6 q^{29} -1.22271e6 q^{30} +7.48504e6 q^{31} -1.43712e7 q^{32} -5.37082e6 q^{33} -5.91779e6 q^{34} +289544. q^{35} -1.03383e7 q^{36} +3.13035e6 q^{37} +8.05590e6 q^{38} +9.77197e6 q^{39} -8.78117e6 q^{40} -7.85257e6 q^{41} -4.96425e6 q^{42} -3.41880e6 q^{43} -6.40472e7 q^{44} -2.14482e6 q^{45} +4.02729e6 q^{46} -2.99064e7 q^{47} +7.94143e7 q^{48} -3.91780e7 q^{49} +7.98209e7 q^{50} +1.50594e7 q^{51} +1.16531e8 q^{52} +2.07014e7 q^{53} +1.26893e8 q^{54} -1.32875e7 q^{55} -3.56519e7 q^{56} -2.05004e7 q^{57} +1.76225e8 q^{58} -1.16826e8 q^{59} +3.71049e7 q^{60} -1.04732e8 q^{61} -3.17494e8 q^{62} -8.70808e6 q^{63} +2.32899e8 q^{64} +2.41760e7 q^{65} +2.27815e8 q^{66} -1.64575e8 q^{67} +1.79584e8 q^{68} -1.02485e7 q^{69} -1.22816e7 q^{70} -8.20184e7 q^{71} +2.64095e8 q^{72} -3.51380e8 q^{73} -1.32780e8 q^{74} -2.03126e8 q^{75} -2.44468e8 q^{76} -5.39478e7 q^{77} -4.14499e8 q^{78} +5.29284e8 q^{79} +1.96472e8 q^{80} -1.64829e8 q^{81} +3.33083e8 q^{82} -7.19804e8 q^{83} +1.50648e8 q^{84} +3.72572e7 q^{85} +1.45016e8 q^{86} -4.48452e8 q^{87} +1.63611e9 q^{88} +6.64822e8 q^{89} +9.09772e7 q^{90} +9.81556e7 q^{91} -1.22214e8 q^{92} +8.07950e8 q^{93} +1.26854e9 q^{94} -5.07183e7 q^{95} -1.55125e9 q^{96} +3.05873e8 q^{97} +1.66182e9 q^{98} +3.99623e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−42.4171	−1.87459	−0.937294	−	0.348539i	$-0.886678\pi$
$2$	−42.4171	−1.87459	−0.937294	+	0.348539i	$0.886678\pi$
$3$	107.942	0.769386	0.384693	−	0.923045i	$-0.374307\pi$
$3$	107.942	0.769386	0.384693	+	0.923045i	$0.374307\pi$
$4$	1287.21	2.51408
$5$	267.050	0.191085	0.0955426	−	0.995425i	$-0.469541\pi$
$5$	267.050	0.191085	0.0955426	+	0.995425i	$0.469541\pi$
$6$	−4578.58	−1.44228
$7$	1084.23	0.170680	0.0853398	−	0.996352i	$-0.472802\pi$
$7$	1084.23	0.170680	0.0853398	+	0.996352i	$0.472802\pi$
$8$	−32882.2	−2.83828
$9$	−8031.56	−0.408045
$10$	−11327.5	−0.358206
$11$	−49756.6	−1.02467	−0.512335	−	0.858786i	$-0.671219\pi$
$11$	−49756.6	−1.02467	−0.512335	+	0.858786i	$0.671219\pi$
$12$	138944.	1.93430
$13$	90530.0	0.879118	0.439559	−	0.898214i	$-0.355135\pi$
$13$	90530.0	0.879118	0.439559	+	0.898214i	$0.355135\pi$
$14$	−45990.0	−0.319954
$15$	28825.8	0.147018
$16$	735714.	2.80653
$17$	139514.	0.405134	0.202567	−	0.979268i	$-0.435072\pi$
$17$	139514.	0.405134	0.202567	+	0.979268i	$0.435072\pi$
$18$	340675.	0.764917
$19$	−189921.	−0.334335	−0.167168	−	0.985929i	$-0.553462\pi$
$19$	−189921.	−0.334335	−0.167168	+	0.985929i	$0.553462\pi$
$20$	343749.	0.480404
$21$	117034.	0.131318
$22$	2.11053e6	1.92083
$23$	−94945.1	−0.0707452	−0.0353726	−	0.999374i	$-0.511262\pi$
$23$	−94945.1	−0.0707452	−0.0353726	+	0.999374i	$0.511262\pi$
$24$	−3.54936e6	−2.18373
$25$	−1.88181e6	−0.963486
$26$	−3.84002e6	−1.64798
$27$	−2.99156e6	−1.08333
$28$	1.39564e6	0.429103
$29$	−4.15457e6	−1.09077	−0.545387	−	0.838184i	$-0.683617\pi$
$29$	−4.15457e6	−1.09077	−0.545387	+	0.838184i	$0.683617\pi$
$30$	−1.22271e6	−0.275599
$31$	7.48504e6	1.45568	0.727841	−	0.685745i	$-0.240524\pi$
$31$	7.48504e6	1.45568	0.727841	+	0.685745i	$0.240524\pi$
$32$	−1.43712e7	−2.42280
$33$	−5.37082e6	−0.788367
$34$	−5.91779e6	−0.759460
$35$	289544.	0.0326143
$36$	−1.03383e7	−1.02586
$37$	3.13035e6	0.274590	0.137295	−	0.990530i	$-0.456159\pi$
$37$	3.13035e6	0.274590	0.137295	+	0.990530i	$0.456159\pi$
$38$	8.05590e6	0.626741
$39$	9.77197e6	0.676381
$40$	−8.78117e6	−0.542353
$41$	−7.85257e6	−0.433995	−0.216997	−	0.976172i	$-0.569626\pi$
$41$	−7.85257e6	−0.433995	−0.216997	+	0.976172i	$0.569626\pi$
$42$	−4.96425e6	−0.246168
$43$	−3.41880e6	−0.152499
$43$	−3.41880e6	−0.152499
$44$	−6.40472e7	−2.57610
$45$	−2.14482e6	−0.0779714
$46$	4.02729e6	0.132618
$47$	−2.99064e7	−0.893973	−0.446986	−	0.894541i	$-0.647503\pi$
$47$	−2.99064e7	−0.893973	−0.446986	+	0.894541i	$0.647503\pi$
$48$	7.94143e7	2.15930
$49$	−3.91780e7	−0.970868
$50$	7.98209e7	1.80614
$51$	1.50594e7	0.311704
$52$	1.16531e8	2.21017
$53$	2.07014e7	0.360378	0.180189	−	0.983632i	$-0.442329\pi$
$53$	2.07014e7	0.360378	0.180189	+	0.983632i	$0.442329\pi$
$54$	1.26893e8	2.03080
$55$	−1.32875e7	−0.195799
$56$	−3.56519e7	−0.484437
$57$	−2.05004e7	−0.257233
$58$	1.76225e8	2.04475
$59$	−1.16826e8	−1.25518	−0.627590	−	0.778544i	$-0.715959\pi$
$59$	−1.16826e8	−1.25518	−0.627590	+	0.778544i	$0.715959\pi$
$60$	3.71049e7	0.369616
$61$	−1.04732e8	−0.968486	−0.484243	−	0.874934i	$-0.660905\pi$
$61$	−1.04732e8	−0.968486	−0.484243	+	0.874934i	$0.660905\pi$
$62$	−3.17494e8	−2.72881
$63$	−8.70808e6	−0.0696450
$64$	2.32899e8	1.73523
$65$	2.41760e7	0.167986
$66$	2.27815e8	1.47786
$67$	−1.64575e8	−0.997764	−0.498882	−	0.866670i	$-0.666256\pi$
$67$	−1.64575e8	−0.997764	−0.498882	+	0.866670i	$0.666256\pi$
$68$	1.79584e8	1.01854
$69$	−1.02485e7	−0.0544304
$70$	−1.22816e7	−0.0611385
$71$	−8.20184e7	−0.383044	−0.191522	−	0.981488i	$-0.561342\pi$
$71$	−8.20184e7	−0.383044	−0.191522	+	0.981488i	$0.561342\pi$
$72$	2.64095e8	1.15815
$73$	−3.51380e8	−1.44819	−0.724093	−	0.689702i	$-0.757741\pi$
$73$	−3.51380e8	−1.44819	−0.724093	+	0.689702i	$0.757741\pi$
$74$	−1.32780e8	−0.514744
$75$	−2.03126e8	−0.741293
$76$	−2.44468e8	−0.840546
$77$	−5.39478e7	−0.174890
$78$	−4.14499e8	−1.26794
$79$	5.29284e8	1.52886	0.764428	−	0.644709i	$-0.223022\pi$
$79$	5.29284e8	1.52886	0.764428	+	0.644709i	$0.223022\pi$
$80$	1.96472e8	0.536285
$81$	−1.64829e8	−0.425454
$82$	3.33083e8	0.813561
$83$	−7.19804e8	−1.66480	−0.832402	−	0.554172i	$-0.813035\pi$
$83$	−7.19804e8	−1.66480	−0.832402	+	0.554172i	$0.813035\pi$
$84$	1.50648e8	0.330145
$85$	3.72572e7	0.0774151
$86$	1.45016e8	0.285872
$87$	−4.48452e8	−0.839226
$88$	1.63611e9	2.90830
$89$	6.64822e8	1.12318	0.561591	−	0.827415i	$-0.310189\pi$
$89$	6.64822e8	1.12318	0.561591	+	0.827415i	$0.310189\pi$
$90$	9.09772e7	0.146164
$91$	9.81556e7	0.150048
$92$	−1.22214e8	−0.177859
$93$	8.07950e8	1.11998
$94$	1.26854e9	1.67583
$95$	−5.07183e7	−0.0638865
$96$	−1.55125e9	−1.86407
$97$	3.05873e8	0.350807	0.175403	−	0.984497i	$-0.443877\pi$
$97$	3.05873e8	0.350807	0.175403	+	0.984497i	$0.443877\pi$
$98$	1.66182e9	1.81998
$99$	3.99623e8	0.418112
$100$	−2.42228e9	−2.42228
$101$	−1.49507e9	−1.42960	−0.714800	−	0.699328i	$-0.753482\pi$
$101$	−1.49507e9	−1.42960	−0.714800	+	0.699328i	$0.753482\pi$
$102$	−6.38778e8	−0.584317
$103$	8.69690e8	0.761372	0.380686	−	0.924704i	$-0.375688\pi$
$103$	8.69690e8	0.761372	0.380686	+	0.924704i	$0.375688\pi$
$104$	−2.97682e9	−2.49518
$105$	3.12539e7	0.0250930
$106$	−8.78094e8	−0.675561
$107$	−1.70820e9	−1.25983	−0.629915	−	0.776664i	$-0.716910\pi$
$107$	−1.70820e9	−1.25983	−0.629915	+	0.776664i	$0.716910\pi$
$108$	−3.85077e9	−2.72358
$109$	1.88987e9	1.28237	0.641183	−	0.767388i	$-0.278444\pi$
$109$	1.88987e9	1.28237	0.641183	+	0.767388i	$0.278444\pi$
$110$	5.63617e8	0.367043
$111$	3.37896e8	0.211266
$112$	7.97686e8	0.479017
$113$	−1.37931e9	−0.795809	−0.397904	−	0.917427i	$-0.630262\pi$
$113$	−1.37931e9	−0.795809	−0.397904	+	0.917427i	$0.630262\pi$
$114$	8.69569e8	0.482205
$115$	−2.53550e7	−0.0135184
$116$	−5.34780e9	−2.74230
$117$	−7.27096e8	−0.358720
$118$	4.95543e9	2.35295
$119$	1.51266e8	0.0691481
$120$	−9.47855e8	−0.417279
$121$	1.17776e8	0.0499485
$122$	4.44241e9	1.81551
$123$	−8.47621e8	−0.333909
$124$	9.63482e9	3.65971
$125$	−1.02412e9	−0.375193
$126$	3.69372e8	0.130556
$127$	−2.53906e9	−0.866078	−0.433039	−	0.901375i	$-0.642559\pi$
$127$	−2.53906e9	−0.866078	−0.433039	+	0.901375i	$0.642559\pi$
$128$	−2.52083e9	−0.830039
$129$	−3.69032e8	−0.117330
$130$	−1.02548e9	−0.314905
$131$	3.77650e9	1.12039	0.560195	−	0.828361i	$-0.310726\pi$
$131$	3.77650e9	1.12039	0.560195	+	0.828361i	$0.310726\pi$
$132$	−6.91338e9	−1.98202
$133$	−2.05919e8	−0.0570642
$134$	6.98080e9	1.87040
$135$	−7.98895e8	−0.207008
$136$	−4.58753e9	−1.14988
$137$	−1.89296e9	−0.459091	−0.229545	−	0.973298i	$-0.573724\pi$
$137$	−1.89296e9	−0.459091	−0.229545	+	0.973298i	$0.573724\pi$
$138$	4.34714e8	0.102035
$139$	4.91789e9	1.11741	0.558705	−	0.829367i	$-0.311298\pi$
$139$	4.91789e9	1.11741	0.558705	+	0.829367i	$0.311298\pi$
$140$	3.72704e8	0.0819951
$141$	−3.22816e9	−0.687810
$142$	3.47898e9	0.718050
$143$	−4.50447e9	−0.900806
$144$	−5.90893e9	−1.14519
$145$	−1.10948e9	−0.208431
$146$	1.49045e10	2.71475
$147$	−4.22895e9	−0.746973
$148$	4.02942e9	0.690343
$149$	1.00447e10	1.66955	0.834773	−	0.550594i	$-0.185599\pi$
$149$	1.00447e10	1.66955	0.834773	+	0.550594i	$0.185599\pi$
$150$	8.61602e9	1.38962
$151$	6.32434e8	0.0989963	0.0494981	−	0.998774i	$-0.484238\pi$
$151$	6.32434e8	0.0989963	0.0494981	+	0.998774i	$0.484238\pi$
$152$	6.24501e9	0.948937
$153$	−1.12052e9	−0.165313
$154$	2.28831e9	0.327847
$155$	1.99888e9	0.278159
$156$	1.25786e10	1.70048
$157$	2.92391e9	0.384075	0.192037	−	0.981388i	$-0.438490\pi$
$157$	2.92391e9	0.384075	0.192037	+	0.981388i	$0.438490\pi$
$158$	−2.24507e10	−2.86598
$159$	2.23455e9	0.277270
$160$	−3.83782e9	−0.462961
$161$	−1.02943e8	−0.0120748
$162$	6.99159e9	0.797550
$163$	−1.56060e10	−1.73160	−0.865800	−	0.500389i	$-0.833190\pi$
$163$	−1.56060e10	−1.73160	−0.865800	+	0.500389i	$0.833190\pi$
$164$	−1.01079e10	−1.09110
$165$	−1.43428e9	−0.150645
$166$	3.05320e10	3.12082
$167$	1.67291e10	1.66436	0.832182	−	0.554502i	$-0.187091\pi$
$167$	1.67291e10	1.66436	0.832182	+	0.554502i	$0.187091\pi$
$168$	−3.84834e9	−0.372719
$169$	−2.40883e9	−0.227151
$170$	−1.58034e9	−0.145121
$171$	1.52536e9	0.136424
$172$	−4.40071e9	−0.383394
$173$	1.01069e10	0.857847	0.428924	−	0.903341i	$-0.358893\pi$
$173$	1.01069e10	0.857847	0.428924	+	0.903341i	$0.358893\pi$
$174$	1.90220e10	1.57320
$175$	−2.04032e9	−0.164447
$176$	−3.66067e10	−2.87576
$177$	−1.26104e10	−0.965718
$178$	−2.81998e10	−2.10551
$179$	−1.86270e10	−1.35614	−0.678068	−	0.734999i	$-0.737183\pi$
$179$	−1.86270e10	−1.35614	−0.678068	+	0.734999i	$0.737183\pi$
$180$	−2.76084e9	−0.196027
$181$	−1.34573e10	−0.931978	−0.465989	−	0.884791i	$-0.654301\pi$
$181$	−1.34573e10	−0.931978	−0.465989	+	0.884791i	$0.654301\pi$
$182$	−4.16348e9	−0.281277
$183$	−1.13049e10	−0.745140
$184$	3.12200e9	0.200795
$185$	8.35959e8	0.0524701
$186$	−3.42709e10	−2.09951
$187$	−6.94176e9	−0.415129
$188$	−3.84959e10	−2.24752
$189$	−3.24355e9	−0.184902
$190$	2.15132e9	0.119761
$191$	−2.59444e10	−1.41056	−0.705282	−	0.708926i	$-0.749180\pi$
$191$	−2.59444e10	−1.41056	−0.705282	+	0.708926i	$0.749180\pi$
$192$	2.51395e10	1.33506
$193$	3.54739e10	1.84035	0.920176	−	0.391505i	$-0.128045\pi$
$193$	3.54739e10	1.84035	0.920176	+	0.391505i	$0.128045\pi$
$194$	−1.29742e10	−0.657618
$195$	2.60960e9	0.129246
$196$	−5.04304e10	−2.44084
$197$	1.96576e10	0.929894	0.464947	−	0.885339i	$-0.346073\pi$
$197$	1.96576e10	0.929894	0.464947	+	0.885339i	$0.346073\pi$
$198$	−1.69509e10	−0.783788
$199$	1.91082e10	0.863737	0.431869	−	0.901937i	$-0.357854\pi$
$199$	1.91082e10	0.863737	0.431869	+	0.901937i	$0.357854\pi$
$200$	6.18780e10	2.73465
$201$	−1.77646e10	−0.767666
$202$	6.34164e10	2.67991
$203$	−4.50452e9	−0.186173
$204$	1.93847e10	0.783650
$205$	−2.09702e9	−0.0829299
$206$	−3.68897e10	−1.42726
$207$	7.62557e8	0.0288673
$208$	6.66042e10	2.46727
$209$	9.44983e9	0.342583
$210$	−1.32570e9	−0.0470391
$211$	−2.94149e9	−0.102164	−0.0510818	−	0.998694i	$-0.516267\pi$
$211$	−2.94149e9	−0.102164	−0.0510818	+	0.998694i	$0.516267\pi$
$212$	2.66471e10	0.906020
$213$	−8.85322e9	−0.294709
$214$	7.24570e10	2.36166
$215$	−9.12989e8	−0.0291402
$216$	9.83690e10	3.07480
$217$	8.11554e9	0.248455
$218$	−8.01627e10	−2.40391
$219$	−3.79286e10	−1.11421
$220$	−1.71038e10	−0.492255
$221$	1.26302e10	0.356161
$222$	−1.43326e10	−0.396037
$223$	−4.30635e7	−0.00116610	−0.000583052	−	1.00000i	$-0.500186\pi$
$223$	−4.30635e7	−0.00116610	−0.000583052		1.00000i	$0.500186\pi$
$224$	−1.55817e10	−0.413523
$225$	1.51139e10	0.393146
$226$	5.85063e10	1.49181
$227$	−5.87731e10	−1.46914	−0.734569	−	0.678534i	$-0.762615\pi$
$227$	−5.87731e10	−1.46914	−0.734569	+	0.678534i	$0.762615\pi$
$228$	−2.63884e10	−0.646704
$229$	−4.67848e9	−0.112420	−0.0562101	−	0.998419i	$-0.517902\pi$
$229$	−4.67848e9	−0.112420	−0.0562101	+	0.998419i	$0.517902\pi$
$230$	1.07549e9	0.0253414
$231$	−5.82323e9	−0.134558
$232$	1.36611e11	3.09592
$233$	−6.22080e10	−1.38275	−0.691377	−	0.722494i	$-0.742996\pi$
$233$	−6.22080e10	−1.38275	−0.691377	+	0.722494i	$0.742996\pi$
$234$	3.08413e10	0.672452
$235$	−7.98650e9	−0.170825
$236$	−1.50380e11	−3.15563
$237$	5.71318e10	1.17628
$238$	−6.41627e9	−0.129624
$239$	8.17154e10	1.61999	0.809997	−	0.586434i	$-0.199469\pi$
$239$	8.17154e10	1.61999	0.809997	+	0.586434i	$0.199469\pi$
$240$	2.12076e10	0.412610
$241$	−7.26673e9	−0.138759	−0.0693796	−	0.997590i	$-0.522102\pi$
$241$	−7.26673e9	−0.138759	−0.0693796	+	0.997590i	$0.522102\pi$
$242$	−4.99571e9	−0.0936328
$243$	4.10909e10	0.755992
$244$	−1.34812e11	−2.43485
$245$	−1.04625e10	−0.185519
$246$	3.59536e10	0.625942
$247$	−1.71935e10	−0.293920
$248$	−2.46124e11	−4.13164
$249$	−7.76970e10	−1.28088
$250$	4.34401e10	0.703333
$251$	6.85052e10	1.08941	0.544706	−	0.838627i	$-0.316641\pi$
$251$	6.85052e10	1.08941	0.544706	+	0.838627i	$0.316641\pi$
$252$	−1.12091e10	−0.175093
$253$	4.72415e9	0.0724905
$254$	1.07700e11	1.62354
$255$	4.02162e9	0.0595621
$256$	−1.23178e10	−0.179247
$257$	1.40768e10	0.201281	0.100641	−	0.994923i	$-0.467911\pi$
$257$	1.40768e10	0.201281	0.100641	+	0.994923i	$0.467911\pi$
$258$	1.56533e10	0.219946
$259$	3.39403e9	0.0468670
$260$	3.11196e10	0.422332
$261$	3.33676e10	0.445085
$262$	−1.60188e11	−2.10027
$263$	4.75236e10	0.612503	0.306252	−	0.951951i	$-0.400925\pi$
$263$	4.75236e10	0.612503	0.306252	+	0.951951i	$0.400925\pi$
$264$	1.76604e11	2.23761
$265$	5.52830e9	0.0688629
$266$	8.73448e9	0.106972
$267$	7.17621e10	0.864161
$268$	−2.11843e11	−2.50846
$269$	3.74937e10	0.436589	0.218294	−	0.975883i	$-0.429951\pi$
$269$	3.74937e10	0.436589	0.218294	+	0.975883i	$0.429951\pi$
$270$	3.38868e10	0.388055
$271$	9.32440e10	1.05017	0.525084	−	0.851050i	$-0.324034\pi$
$271$	9.32440e10	1.05017	0.525084	+	0.851050i	$0.324034\pi$
$272$	1.02643e11	1.13702
$273$	1.05951e10	0.115444
$274$	8.02938e10	0.860606
$275$	9.36325e10	0.987256
$276$	−1.31920e10	−0.136842
$277$	−1.14756e11	−1.17116	−0.585582	−	0.810614i	$-0.699134\pi$
$277$	−1.14756e11	−1.17116	−0.585582	+	0.810614i	$0.699134\pi$
$278$	−2.08603e11	−2.09468
$279$	−6.01166e10	−0.593985
$280$	−9.52084e9	−0.0925686
$281$	1.15044e11	1.10074	0.550372	−	0.834920i	$-0.314486\pi$
$281$	1.15044e11	1.10074	0.550372	+	0.834920i	$0.314486\pi$
$282$	1.36929e11	1.28936
$283$	−3.96421e10	−0.367382	−0.183691	−	0.982984i	$-0.558805\pi$
$283$	−3.96421e10	−0.367382	−0.183691	+	0.982984i	$0.558805\pi$
$284$	−1.05575e11	−0.963004
$285$	−5.47463e9	−0.0491533
$286$	1.91066e11	1.68864
$287$	−8.51402e9	−0.0740740
$288$	1.15423e11	0.988613
$289$	−9.91236e10	−0.835866
$290$	4.70607e10	0.390722
$291$	3.30164e10	0.269906
$292$	−4.52300e11	−3.64086
$293$	1.46620e11	1.16222	0.581109	−	0.813825i	$-0.302619\pi$
$293$	1.46620e11	1.16222	0.581109	+	0.813825i	$0.302619\pi$
$294$	1.79380e11	1.40027
$295$	−3.11984e10	−0.239846
$296$	−1.02933e11	−0.779364
$297$	1.48850e11	1.11006
$298$	−4.26067e11	−3.12971
$299$	−8.59537e9	−0.0621934
$300$	−2.61466e11	−1.86367
$301$	−3.70678e9	−0.0260284
$302$	−2.68260e10	−0.185577
$303$	−1.61380e11	−1.09991
$304$	−1.39728e11	−0.938320
$305$	−2.79685e10	−0.185063
$306$	4.75291e10	0.309894
$307$	2.04547e11	1.31423	0.657114	−	0.753792i	$-0.271777\pi$
$307$	2.04547e11	1.31423	0.657114	+	0.753792i	$0.271777\pi$
$308$	−6.94422e10	−0.439688
$309$	9.38760e10	0.585789
$310$	−8.47866e10	−0.521434
$311$	2.05452e11	1.24534	0.622671	−	0.782483i	$-0.286047\pi$
$311$	2.05452e11	1.24534	0.622671	+	0.782483i	$0.286047\pi$
$312$	−3.21323e11	−1.91976
$313$	2.06361e11	1.21528	0.607642	−	0.794211i	$-0.292116\pi$
$313$	2.06361e11	1.21528	0.607642	+	0.794211i	$0.292116\pi$
$314$	−1.24024e11	−0.719982
$315$	−2.32549e9	−0.0133081
$316$	6.81299e11	3.84367
$317$	−2.13970e10	−0.119011	−0.0595053	−	0.998228i	$-0.518952\pi$
$317$	−2.13970e10	−0.119011	−0.0595053	+	0.998228i	$0.518952\pi$
$318$	−9.47831e10	−0.519767
$319$	2.06717e11	1.11768
$320$	6.21955e10	0.331577
$321$	−1.84386e11	−0.969296
$322$	4.36653e9	0.0226352
$323$	−2.64967e10	−0.135450
$324$	−2.12170e11	−1.06963
$325$	−1.70360e11	−0.847018
$326$	6.61962e11	3.24604
$327$	2.03996e11	0.986634
$328$	2.58209e11	1.23180
$329$	−3.24256e10	−0.152583
$330$	6.08378e10	0.282398
$331$	1.60601e11	0.735396	0.367698	−	0.929945i	$-0.380146\pi$
$331$	1.60601e11	0.735396	0.367698	+	0.929945i	$0.380146\pi$
$332$	−9.26539e11	−4.18545
$333$	−2.51416e10	−0.112045
$334$	−7.09600e11	−3.12000
$335$	−4.39498e10	−0.190658
$336$	8.61037e10	0.368549
$337$	−3.08563e11	−1.30320	−0.651598	−	0.758564i	$-0.725901\pi$
$337$	−3.08563e11	−1.30320	−0.651598	+	0.758564i	$0.725901\pi$
$338$	1.02175e11	0.425815
$339$	−1.48885e11	−0.612284
$340$	4.79579e10	0.194628
$341$	−3.72431e11	−1.49159
$342$	−6.47014e10	−0.255739
$343$	−8.62309e10	−0.336387
$344$	1.12418e11	0.432834
$345$	−2.73687e9	−0.0104008
$346$	−4.28705e11	−1.60811
$347$	1.34264e11	0.497138	0.248569	−	0.968614i	$-0.420040\pi$
$347$	1.34264e11	0.497138	0.248569	+	0.968614i	$0.420040\pi$
$348$	−5.77251e11	−2.10988
$349$	2.70503e11	0.976016	0.488008	−	0.872839i	$-0.337724\pi$
$349$	2.70503e11	0.976016	0.488008	+	0.872839i	$0.337724\pi$
$350$	8.65445e10	0.308271
$351$	−2.70826e11	−0.952375
$352$	7.15062e11	2.48257
$353$	1.67866e10	0.0575408	0.0287704	−	0.999586i	$-0.490841\pi$
$353$	1.67866e10	0.0575408	0.0287704	+	0.999586i	$0.490841\pi$
$354$	5.34898e11	1.81032
$355$	−2.19030e10	−0.0731940
$356$	8.55766e11	2.82377
$357$	1.63279e10	0.0532016
$358$	7.90102e11	2.54220
$359$	4.80875e11	1.52794	0.763972	−	0.645250i	$-0.223247\pi$
$359$	4.80875e11	1.52794	0.763972	+	0.645250i	$0.223247\pi$
$360$	7.05264e10	0.221305
$361$	−2.86618e11	−0.888220
$362$	5.70821e11	1.74707
$363$	1.27129e10	0.0384296
$364$	1.26347e11	0.377232
$365$	−9.38359e10	−0.276727
$366$	4.79522e11	1.39683
$367$	−5.91797e11	−1.70285	−0.851424	−	0.524479i	$-0.824260\pi$
$367$	−5.91797e11	−1.70285	−0.851424	+	0.524479i	$0.824260\pi$
$368$	−6.98524e10	−0.198548
$369$	6.30683e10	0.177089
$370$	−3.54589e10	−0.0983599
$371$	2.24452e10	0.0615092
$372$	1.04000e12	2.81573
$373$	−5.20908e11	−1.39338	−0.696692	−	0.717370i	$-0.745346\pi$
$373$	−5.20908e11	−1.39338	−0.696692	+	0.717370i	$0.745346\pi$
$374$	2.94450e11	0.778195
$375$	−1.10545e11	−0.288668
$376$	9.83388e11	2.53735
$377$	−3.76113e11	−0.958919
$378$	1.37582e11	0.346616
$379$	−9.96613e10	−0.248113	−0.124057	−	0.992275i	$-0.539590\pi$
$379$	−9.96613e10	−0.248113	−0.124057	+	0.992275i	$0.539590\pi$
$380$	−6.52852e10	−0.160616
$381$	−2.74071e11	−0.666348
$382$	1.10049e12	2.64423
$383$	−3.57401e11	−0.848714	−0.424357	−	0.905495i	$-0.639500\pi$
$383$	−3.57401e11	−0.848714	−0.424357	+	0.905495i	$0.639500\pi$
$384$	−2.72103e11	−0.638621
$385$	−1.44067e10	−0.0334189
$386$	−1.50470e12	−3.44990
$387$	2.74583e10	0.0622263
$388$	3.93722e11	0.881956
$389$	−4.67526e11	−1.03522	−0.517610	−	0.855617i	$-0.673178\pi$
$389$	−4.67526e11	−1.03522	−0.517610	+	0.855617i	$0.673178\pi$
$390$	−1.10692e11	−0.242284
$391$	−1.32462e10	−0.0286613
$392$	1.28826e12	2.75560
$393$	4.07643e11	0.862012
$394$	−8.33820e11	−1.74317
$395$	1.41345e11	0.292142
$396$	5.14399e11	1.05117
$397$	−9.97116e10	−0.201460	−0.100730	−	0.994914i	$-0.532118\pi$
$397$	−9.97116e10	−0.201460	−0.100730	+	0.994914i	$0.532118\pi$
$398$	−8.10516e11	−1.61915
$399$	−2.22273e10	−0.0439044
$400$	−1.38447e12	−2.70405
$401$	−4.32588e11	−0.835459	−0.417729	−	0.908572i	$-0.637174\pi$
$401$	−4.32588e11	−0.835459	−0.417729	+	0.908572i	$0.637174\pi$
$402$	7.53521e11	1.43906
$403$	6.77621e11	1.27972
$404$	−1.92447e12	−3.59413
$405$	−4.40176e10	−0.0812979
$406$	1.91069e11	0.348998
$407$	−1.55756e11	−0.281364
$408$	−4.95187e11	−0.884705
$409$	−8.08953e11	−1.42945	−0.714724	−	0.699406i	$-0.753448\pi$
$409$	−8.08953e11	−1.42945	−0.714724	+	0.699406i	$0.753448\pi$
$410$	8.89497e10	0.155459
$411$	−2.04329e11	−0.353218
$412$	1.11947e12	1.91415
$413$	−1.26667e11	−0.214234
$414$	−3.23454e10	−0.0541142
$415$	−1.92223e11	−0.318119
$416$	−1.30102e12	−2.12993
$417$	5.30846e11	0.859719
$418$	−4.00835e11	−0.642202
$419$	7.28742e11	1.15508	0.577538	−	0.816364i	$-0.304014\pi$
$419$	7.28742e11	1.15508	0.577538	+	0.816364i	$0.304014\pi$
$420$	4.02304e10	0.0630859
$421$	−6.26279e11	−0.971625	−0.485812	−	0.874063i	$-0.661476\pi$
$421$	−6.26279e11	−0.971625	−0.485812	+	0.874063i	$0.661476\pi$
$422$	1.24769e11	0.191515
$423$	2.40195e11	0.364781
$424$	−6.80707e11	−1.02285
$425$	−2.62539e11	−0.390341
$426$	3.75528e11	0.552457
$427$	−1.13553e11	−0.165301
$428$	−2.19881e12	−3.16732
$429$	−4.86220e11	−0.693067
$430$	3.87264e10	0.0546259
$431$	9.36909e11	1.30782	0.653912	−	0.756570i	$-0.273127\pi$
$431$	9.36909e11	1.30782	0.653912	+	0.756570i	$0.273127\pi$
$432$	−2.20093e12	−3.04039
$433$	−2.08675e11	−0.285282	−0.142641	−	0.989774i	$-0.545560\pi$
$433$	−2.08675e11	−0.285282	−0.142641	+	0.989774i	$0.545560\pi$
$434$	−3.44237e11	−0.465752
$435$	−1.19759e11	−0.160364
$436$	2.43266e12	3.22397
$437$	1.80321e10	0.0236526
$438$	1.60882e12	2.08869
$439$	4.01235e10	0.0515594	0.0257797	−	0.999668i	$-0.491793\pi$
$439$	4.01235e10	0.0515594	0.0257797	+	0.999668i	$0.491793\pi$
$440$	4.36921e11	0.555733
$441$	3.14661e11	0.396158
$442$	−5.35738e11	−0.667655
$443$	−4.49679e11	−0.554735	−0.277367	−	0.960764i	$-0.589462\pi$
$443$	−4.49679e11	−0.554735	−0.277367	+	0.960764i	$0.589462\pi$
$444$	4.34943e11	0.531140
$445$	1.77540e11	0.214624
$446$	1.82663e9	0.00218597
$447$	1.08424e12	1.28453
$448$	2.52516e11	0.296168
$449$	2.85367e11	0.331357	0.165678	−	0.986180i	$-0.447019\pi$
$449$	2.85367e11	0.331357	0.165678	+	0.986180i	$0.447019\pi$
$450$	−6.41086e11	−0.736987
$451$	3.90717e11	0.444701
$452$	−1.77546e12	−2.00073
$453$	6.82661e10	0.0761663
$454$	2.49299e12	2.75403
$455$	2.62124e10	0.0286719
$456$	6.74098e11	0.730099
$457$	3.04646e11	0.326718	0.163359	−	0.986567i	$-0.447767\pi$
$457$	3.04646e11	0.326718	0.163359	+	0.986567i	$0.447767\pi$
$458$	1.98447e11	0.210742
$459$	−4.17366e11	−0.438894
$460$	−3.26373e10	−0.0339863
$461$	6.14100e11	0.633265	0.316632	−	0.948548i	$-0.397448\pi$
$461$	6.14100e11	0.633265	0.316632	+	0.948548i	$0.397448\pi$
$462$	2.47004e11	0.252241
$463$	−1.91905e11	−0.194076	−0.0970382	−	0.995281i	$-0.530937\pi$
$463$	−1.91905e11	−0.194076	−0.0970382	+	0.995281i	$0.530937\pi$
$464$	−3.05657e12	−3.06129
$465$	2.15763e11	0.214012
$466$	2.63868e12	2.59209
$467$	3.82929e11	0.372556	0.186278	−	0.982497i	$-0.440357\pi$
$467$	3.82929e11	0.372556	0.186278	+	0.982497i	$0.440357\pi$
$468$	−9.35926e11	−0.901852
$469$	−1.78438e11	−0.170298
$470$	3.38764e11	0.320226
$471$	3.15613e11	0.295502
$472$	3.84150e12	3.56255
$473$	1.70108e11	0.156261
$474$	−2.42337e12	−2.20504
$475$	3.57395e11	0.322127
$476$	1.94711e11	0.173844
$477$	−1.66265e11	−0.147051
$478$	−3.46613e12	−3.03682
$479$	−1.69714e11	−0.147302	−0.0736510	−	0.997284i	$-0.523465\pi$
$479$	−1.69714e11	−0.147302	−0.0736510	+	0.997284i	$0.523465\pi$
$480$	−4.14261e11	−0.356196
$481$	2.83391e11	0.241397
$482$	3.08233e11	0.260117
$483$	−1.11118e10	−0.00929016
$484$	1.51602e11	0.125575
$485$	8.16831e10	0.0670339
$486$	−1.74296e12	−1.41717
$487$	2.46356e11	0.198465	0.0992324	−	0.995064i	$-0.468361\pi$
$487$	2.46356e11	0.198465	0.0992324	+	0.995064i	$0.468361\pi$
$488$	3.44380e12	2.74884
$489$	−1.68454e12	−1.33227
$490$	4.43788e11	0.347771
$491$	1.01928e12	0.791458	0.395729	−	0.918367i	$-0.370492\pi$
$491$	1.01928e12	0.791458	0.395729	+	0.918367i	$0.370492\pi$
$492$	−1.09107e12	−0.839475
$493$	−5.79622e11	−0.441910
$494$	7.29300e11	0.550979
$495$	1.06719e11	0.0798950
$496$	5.50685e12	4.08541
$497$	−8.89271e10	−0.0653778
$498$	3.29568e12	2.40112
$499$	1.06244e12	0.767101	0.383550	−	0.923520i	$-0.374701\pi$
$499$	1.06244e12	0.767101	0.383550	+	0.923520i	$0.374701\pi$
$500$	−1.31825e12	−0.943266
$501$	1.80577e12	1.28054
$502$	−2.90579e12	−2.04220
$503$	−2.56713e12	−1.78810	−0.894051	−	0.447965i	$-0.852149\pi$
$503$	−2.56713e12	−1.78810	−0.894051	+	0.447965i	$0.852149\pi$
$504$	2.86341e11	0.197672
$505$	−3.99257e11	−0.273175
$506$	−2.00385e11	−0.135890
$507$	−2.60013e11	−0.174767
$508$	−3.26831e12	−2.17739
$509$	2.54412e12	1.67999	0.839997	−	0.542590i	$-0.182556\pi$
$509$	2.54412e12	1.67999	0.839997	+	0.542590i	$0.182556\pi$
$510$	−1.70585e11	−0.111654
$511$	−3.80978e11	−0.247176
$512$	1.81315e12	1.16605
$513$	5.68160e11	0.362195
$514$	−5.97095e11	−0.377320
$515$	2.32250e11	0.145487
$516$	−4.75021e11	−0.294978
$517$	1.48804e12	0.916027
$518$	−1.43965e11	−0.0878563
$519$	1.09096e12	0.660015
$520$	−7.94959e11	−0.476793
$521$	−1.73418e12	−1.03116	−0.515579	−	0.856842i	$-0.672423\pi$
$521$	−1.73418e12	−1.03116	−0.515579	+	0.856842i	$0.672423\pi$
$522$	−1.41536e12	−0.834352
$523$	1.03596e12	0.605457	0.302729	−	0.953077i	$-0.402102\pi$
$523$	1.03596e12	0.605457	0.302729	+	0.953077i	$0.402102\pi$
$524$	4.86115e12	2.81675
$525$	−2.20236e11	−0.126524
$526$	−2.01581e12	−1.14819
$527$	1.04427e12	0.589747
$528$	−3.95139e12	−2.21257
$529$	−1.79214e12	−0.994995
$530$	−2.34495e11	−0.129090
$531$	9.38296e11	0.512170
$532$	−2.65061e11	−0.143464
$533$	−7.10892e11	−0.381532
$534$	−3.04394e12	−1.61995
$535$	−4.56175e11	−0.240735
$536$	5.41159e12	2.83194
$537$	−2.01063e12	−1.04339
$538$	−1.59037e12	−0.818424
$539$	1.94937e12	0.994820
$540$	−1.02835e12	−0.520436
$541$	−2.94842e12	−1.47980	−0.739898	−	0.672719i	$-0.765126\pi$
$541$	−2.94842e12	−1.47980	−0.739898	+	0.672719i	$0.765126\pi$
$542$	−3.95514e12	−1.96863
$543$	−1.45261e12	−0.717050
$544$	−2.00499e12	−0.981559
$545$	5.04688e11	0.245041
$546$	−4.49413e11	−0.216411
$547$	2.32179e12	1.10887	0.554435	−	0.832227i	$-0.312935\pi$
$547$	2.32179e12	1.10887	0.554435	+	0.832227i	$0.312935\pi$
$548$	−2.43663e12	−1.15419
$549$	8.41158e11	0.395186
$550$	−3.97162e12	−1.85070
$551$	7.89040e11	0.364684
$552$	3.36994e11	0.154489
$553$	5.73867e11	0.260944
$554$	4.86763e12	2.19545
$555$	9.02350e10	0.0403698
$556$	6.33036e12	2.80926
$557$	2.16532e12	0.953176	0.476588	−	0.879127i	$-0.341873\pi$
$557$	2.16532e12	0.953176	0.476588	+	0.879127i	$0.341873\pi$
$558$	2.54997e12	1.11348
$559$	−3.09504e11	−0.134064
$560$	2.13022e11	0.0915330
$561$	−7.49307e11	−0.319394
$562$	−4.87984e12	−2.06344
$563$	−1.91225e12	−0.802154	−0.401077	−	0.916044i	$-0.631364\pi$
$563$	−1.91225e12	−0.802154	−0.401077	+	0.916044i	$0.631364\pi$
$564$	−4.15531e12	−1.72921
$565$	−3.68344e11	−0.152067
$566$	1.68150e12	0.688690
$567$	−1.78714e11	−0.0726163
$568$	2.69694e12	1.08719
$569$	2.85153e12	1.14044	0.570220	−	0.821492i	$-0.306858\pi$
$569$	2.85153e12	1.14044	0.570220	+	0.821492i	$0.306858\pi$
$570$	2.32218e11	0.0921423
$571$	−2.16577e12	−0.852608	−0.426304	−	0.904580i	$-0.640185\pi$
$571$	−2.16577e12	−0.852608	−0.426304	+	0.904580i	$0.640185\pi$
$572$	−5.79819e12	−2.26470
$573$	−2.80048e12	−1.08527
$574$	3.61140e11	0.138858
$575$	1.78669e11	0.0681621
$576$	−1.87054e12	−0.708052
$577$	−2.81611e12	−1.05769	−0.528845	−	0.848718i	$-0.677375\pi$
$577$	−2.81611e12	−1.05769	−0.528845	+	0.848718i	$0.677375\pi$
$578$	4.20454e12	1.56691
$579$	3.82912e12	1.41594
$580$	−1.42813e12	−0.524012
$581$	−7.80436e11	−0.284148
$582$	−1.40046e12	−0.505962
$583$	−1.03003e12	−0.369269
$584$	1.15541e13	4.11036
$585$	−1.94171e11	−0.0685461
$586$	−6.21918e12	−2.17868
$587$	−1.61735e12	−0.562255	−0.281128	−	0.959670i	$-0.590708\pi$
$587$	−1.61735e12	−0.562255	−0.281128	+	0.959670i	$0.590708\pi$
$588$	−5.44355e12	−1.87795
$589$	−1.42157e12	−0.486686
$590$	1.32334e12	0.449613
$591$	2.12188e12	0.715447
$592$	2.30304e12	0.770645
$593$	2.81752e12	0.935665	0.467833	−	0.883817i	$-0.345035\pi$
$593$	2.81752e12	0.935665	0.467833	+	0.883817i	$0.345035\pi$
$594$	−6.31379e12	−2.08090
$595$	4.03956e10	0.0132132
$596$	1.29296e13	4.19738
$597$	2.06258e12	0.664547
$598$	3.64591e11	0.116587
$599$	1.84733e12	0.586305	0.293152	−	0.956066i	$-0.405296\pi$
$599$	1.84733e12	0.586305	0.293152	+	0.956066i	$0.405296\pi$
$600$	6.67922e12	2.10400
$601$	1.93095e12	0.603720	0.301860	−	0.953352i	$-0.402392\pi$
$601$	1.93095e12	0.603720	0.301860	+	0.953352i	$0.402392\pi$
$602$	1.57231e11	0.0487925
$603$	1.32180e12	0.407133
$604$	8.14075e11	0.248885
$605$	3.14520e10	0.00954441
$606$	6.84529e12	2.06189
$607$	2.77322e12	0.829155	0.414578	−	0.910014i	$-0.363929\pi$
$607$	2.77322e12	0.829155	0.414578	+	0.910014i	$0.363929\pi$
$608$	2.72939e12	0.810027
$609$	−4.86226e11	−0.143239
$610$	1.18634e12	0.346918
$611$	−2.70743e12	−0.785908
$612$	−1.44234e12	−0.415611
$613$	−6.12373e12	−1.75164	−0.875819	−	0.482640i	$-0.839678\pi$
$613$	−6.12373e12	−1.75164	−0.875819	+	0.482640i	$0.839678\pi$
$614$	−8.67629e12	−2.46364
$615$	−2.26357e11	−0.0638051
$616$	1.77392e12	0.496388
$617$	−5.57842e12	−1.54963	−0.774815	−	0.632188i	$-0.782157\pi$
$617$	−5.57842e12	−1.54963	−0.774815	+	0.632188i	$0.782157\pi$
$618$	−3.98195e12	−1.09811
$619$	−1.98413e12	−0.543203	−0.271602	−	0.962410i	$-0.587553\pi$
$619$	−1.98413e12	−0.543203	−0.271602	+	0.962410i	$0.587553\pi$
$620$	2.57298e12	0.699315
$621$	2.84034e11	0.0766404
$622$	−8.71468e12	−2.33451
$623$	7.20822e11	0.191704
$624$	7.18938e12	1.89828
$625$	3.40192e12	0.891793
$626$	−8.75322e12	−2.27816
$627$	1.02003e12	0.263579
$628$	3.76369e12	0.965596
$629$	4.36729e11	0.111246
$630$	9.86405e10	0.0249473
$631$	−5.57032e12	−1.39878	−0.699388	−	0.714743i	$-0.746544\pi$
$631$	−5.57032e12	−1.39878	−0.699388	+	0.714743i	$0.746544\pi$
$632$	−1.74040e13	−4.33932
$633$	−3.17510e11	−0.0786033
$634$	9.07598e11	0.223096
$635$	−6.78056e11	−0.165495
$636$	2.87633e12	0.697079
$637$	−3.54679e12	−0.853508
$638$	−8.76835e12	−2.09520
$639$	6.58735e11	0.156299
$640$	−6.73187e11	−0.158608
$641$	−5.38235e12	−1.25925	−0.629623	−	0.776901i	$-0.716791\pi$
$641$	−5.38235e12	−1.25925	−0.629623	+	0.776901i	$0.716791\pi$
$642$	7.82114e12	1.81703
$643$	7.27179e11	0.167761	0.0838807	−	0.996476i	$-0.473269\pi$
$643$	7.27179e11	0.167761	0.0838807	+	0.996476i	$0.473269\pi$
$644$	−1.32509e11	−0.0303570
$645$	−9.85498e10	−0.0224201
$646$	1.12391e12	0.253914
$647$	1.81068e12	0.406231	0.203116	−	0.979155i	$-0.434893\pi$
$647$	1.81068e12	0.406231	0.203116	+	0.979155i	$0.434893\pi$
$648$	5.41995e12	1.20756
$649$	5.81288e12	1.28615
$650$	7.22618e12	1.58781
$651$	8.76006e11	0.191158
$652$	−2.00882e13	−4.35339
$653$	−3.82339e12	−0.822886	−0.411443	−	0.911435i	$-0.634975\pi$
$653$	−3.82339e12	−0.822886	−0.411443	+	0.911435i	$0.634975\pi$
$654$	−8.65291e12	−1.84953
$655$	1.00851e12	0.214090
$656$	−5.77724e12	−1.21802
$657$	2.82213e12	0.590926
$658$	1.37540e12	0.286030
$659$	3.40517e12	0.703323	0.351661	−	0.936127i	$-0.385617\pi$
$659$	3.40517e12	0.703323	0.351661	+	0.936127i	$0.385617\pi$
$660$	−1.84621e12	−0.378734
$661$	1.30545e12	0.265982	0.132991	−	0.991117i	$-0.457542\pi$
$661$	1.30545e12	0.265982	0.132991	+	0.991117i	$0.457542\pi$
$662$	−6.81221e12	−1.37857
$663$	1.36333e12	0.274025
$664$	2.36687e13	4.72518
$665$	−5.49905e10	−0.0109041
$666$	1.06643e12	0.210039
$667$	3.94456e11	0.0771671
$668$	2.15339e13	4.18435
$669$	−4.64836e9	−0.000897185 0
$670$	1.86422e12	0.357405
$671$	5.21109e12	0.992379
$672$	−1.68192e12	−0.318159
$673$	−1.13952e12	−0.214119	−0.107059	−	0.994253i	$-0.534143\pi$
$673$	−1.13952e12	−0.214119	−0.107059	+	0.994253i	$0.534143\pi$
$674$	1.30884e13	2.44296
$675$	5.62955e12	1.04377
$676$	−3.10067e12	−0.571077
$677$	−2.85019e12	−0.521464	−0.260732	−	0.965411i	$-0.583964\pi$
$677$	−2.85019e12	−0.521464	−0.260732	+	0.965411i	$0.583964\pi$
$678$	6.31528e12	1.14778
$679$	3.31637e11	0.0598755
$680$	−1.22510e12	−0.219726
$681$	−6.34408e12	−1.13033
$682$	1.57974e13	2.79613
$683$	6.16518e12	1.08406	0.542029	−	0.840360i	$-0.317656\pi$
$683$	6.16518e12	1.08406	0.542029	+	0.840360i	$0.317656\pi$
$684$	1.96346e12	0.342981
$685$	−5.05514e11	−0.0877254
$686$	3.65766e12	0.630587
$687$	−5.05003e11	−0.0864946
$688$	−2.51526e12	−0.427991
$689$	1.87410e12	0.316815
$690$	1.16090e11	0.0194973
$691$	9.71088e12	1.62034	0.810172	−	0.586192i	$-0.199374\pi$
$691$	9.71088e12	1.62034	0.810172	+	0.586192i	$0.199374\pi$
$692$	1.30097e13	2.15670
$693$	4.33285e11	0.0713632
$694$	−5.69509e12	−0.931929
$695$	1.31332e12	0.213520
$696$	1.47461e13	2.38196
$697$	−1.09555e12	−0.175826
$698$	−1.14739e13	−1.82963
$699$	−6.71485e12	−1.06387
$700$	−2.62632e12	−0.413435
$701$	3.33352e12	0.521402	0.260701	−	0.965420i	$-0.416046\pi$
$701$	3.33352e12	0.521402	0.260701	+	0.965420i	$0.416046\pi$
$702$	1.14876e13	1.78531
$703$	−5.94520e11	−0.0918052
$704$	−1.15882e13	−1.77804
$705$	−8.62078e11	−0.131430
$706$	−7.12037e11	−0.107865
$707$	−1.62100e12	−0.244004
$708$	−1.62323e13	−2.42789
$709$	−6.12092e12	−0.909723	−0.454861	−	0.890562i	$-0.650311\pi$
$709$	−6.12092e12	−0.909723	−0.454861	+	0.890562i	$0.650311\pi$
$710$	9.29061e11	0.137209
$711$	−4.25097e12	−0.623842
$712$	−2.18608e13	−3.18791
$713$	−7.10668e11	−0.102983
$714$	−6.92584e11	−0.0997311
$715$	−1.20292e12	−0.172131
$716$	−2.39768e13	−3.40944
$717$	8.82051e12	1.24640
$718$	−2.03973e13	−2.86427
$719$	2.16423e12	0.302012	0.151006	−	0.988533i	$-0.451749\pi$
$719$	2.16423e12	0.302012	0.151006	+	0.988533i	$0.451749\pi$
$720$	−1.57798e12	−0.218829
$721$	9.42947e11	0.129951
$722$	1.21575e13	1.66505
$723$	−7.84384e11	−0.106759
$724$	−1.73224e13	−2.34307
$725$	7.81810e12	1.05095
$726$	−5.39246e11	−0.0720398
$727$	1.22681e13	1.62882	0.814412	−	0.580287i	$-0.197060\pi$
$727$	1.22681e13	1.62882	0.814412	+	0.580287i	$0.197060\pi$
$728$	−3.22757e12	−0.425877
$729$	7.67976e12	1.00710
$730$	3.98025e12	0.518749
$731$	−4.76972e11	−0.0617824
$732$	−1.45518e13	−1.87334
$733$	−1.22993e13	−1.57367	−0.786833	−	0.617166i	$-0.788281\pi$
$733$	−1.22993e13	−1.57367	−0.786833	+	0.617166i	$0.788281\pi$
$734$	2.51023e13	3.19214
$735$	−1.12934e12	−0.142735
$736$	1.36447e12	0.171402
$737$	8.18871e12	1.02238
$738$	−2.67518e12	−0.331970
$739$	2.39881e12	0.295867	0.147933	−	0.988997i	$-0.452738\pi$
$739$	2.39881e12	0.295867	0.147933	+	0.988997i	$0.452738\pi$
$740$	1.07605e12	0.131914
$741$	−1.85590e12	−0.226138
$742$	−9.52059e11	−0.115304
$743$	−9.39278e12	−1.13069	−0.565346	−	0.824854i	$-0.691258\pi$
$743$	−9.39278e12	−1.13069	−0.565346	+	0.824854i	$0.691258\pi$
$744$	−2.65671e13	−3.17882
$745$	2.68243e12	0.319026
$746$	2.20954e13	2.61202
$747$	5.78115e12	0.679316
$748$	−8.93551e12	−1.04367
$749$	−1.85209e12	−0.215027
$750$	4.68900e12	0.541134
$751$	−1.66561e13	−1.91070	−0.955352	−	0.295469i	$-0.904524\pi$
$751$	−1.66561e13	−1.91070	−0.955352	+	0.295469i	$0.904524\pi$
$752$	−2.20026e13	−2.50896
$753$	7.39458e12	0.838178
$754$	1.59536e13	1.79758
$755$	1.68891e11	0.0189167
$756$	−4.17513e12	−0.464860
$757$	−1.58067e13	−1.74949	−0.874743	−	0.484587i	$-0.838970\pi$
$757$	−1.58067e13	−1.74949	−0.874743	+	0.484587i	$0.838970\pi$
$758$	4.22734e12	0.465111
$759$	5.09933e11	0.0557732
$760$	1.66773e12	0.181328
$761$	−1.76096e13	−1.90335	−0.951673	−	0.307112i	$-0.900637\pi$
$761$	−1.76096e13	−1.90335	−0.951673	+	0.307112i	$0.900637\pi$
$762$	1.16253e13	1.24913
$763$	2.04906e12	0.218874
$764$	−3.33959e13	−3.54628
$765$	−2.99234e11	−0.0315889
$766$	1.51599e13	1.59099
$767$	−1.05763e13	−1.10345
$768$	−1.32960e12	−0.137910
$769$	−1.26882e13	−1.30838	−0.654188	−	0.756332i	$-0.726989\pi$
$769$	−1.26882e13	−1.30838	−0.654188	+	0.756332i	$0.726989\pi$
$770$	6.11092e11	0.0626467
$771$	1.51947e12	0.154863
$772$	4.56623e13	4.62680
$773$	1.57233e12	0.158393	0.0791965	−	0.996859i	$-0.474765\pi$
$773$	1.57233e12	0.158393	0.0791965	+	0.996859i	$0.474765\pi$
$774$	−1.16470e12	−0.116649
$775$	−1.40854e13	−1.40253
$776$	−1.00577e13	−0.995687
$777$	3.66358e11	0.0360588
$778$	1.98311e13	1.94061
$779$	1.49137e12	0.145100
$780$	3.35910e12	0.324936
$781$	4.08096e12	0.392494
$782$	5.61865e11	0.0537281
$783$	1.24286e13	1.18167
$784$	−2.88238e13	−2.72477
$785$	7.80830e11	0.0733910
$786$	−1.72910e13	−1.61592
$787$	−7.00350e12	−0.650772	−0.325386	−	0.945581i	$-0.605494\pi$
$787$	−7.00350e12	−0.650772	−0.325386	+	0.945581i	$0.605494\pi$
$788$	2.53035e13	2.33783
$789$	5.12978e12	0.471251
$790$	−5.99544e12	−0.547645
$791$	−1.49549e12	−0.135828
$792$	−1.31405e13	−1.18672
$793$	−9.48135e12	−0.851414
$794$	4.22948e12	0.377654
$795$	5.96735e11	0.0529822
$796$	2.45963e13	2.17151
$797$	6.34176e12	0.556734	0.278367	−	0.960475i	$-0.410207\pi$
$797$	6.34176e12	0.556734	0.278367	+	0.960475i	$0.410207\pi$
$798$	9.42816e11	0.0823026
$799$	−4.17238e12	−0.362179
$800$	2.70438e13	2.33434
$801$	−5.33956e12	−0.458309
$802$	1.83491e13	1.56614
$803$	1.74835e13	1.48391
$804$	−2.28667e13	−1.92997
$805$	−2.74908e10	−0.00230731
$806$	−2.87427e13	−2.39894
$807$	4.04713e12	0.335905
$808$	4.91611e13	4.05761
$809$	−1.84767e13	−1.51654	−0.758272	−	0.651938i	$-0.773956\pi$
$809$	−1.84767e13	−1.51654	−0.758272	+	0.651938i	$0.773956\pi$
$810$	1.86710e12	0.152400
$811$	9.90436e12	0.803956	0.401978	−	0.915649i	$-0.368323\pi$
$811$	9.90436e12	0.803956	0.401978	+	0.915649i	$0.368323\pi$
$812$	−5.79826e12	−0.468054
$813$	1.00649e13	0.807985
$814$	6.60671e12	0.527443
$815$	−4.16758e12	−0.330883
$816$	1.10794e13	0.874807
$817$	6.49302e11	0.0509856
$818$	3.43135e13	2.67963
$819$	−7.88342e11	−0.0612262
$820$	−2.69931e12	−0.208493
$821$	−6.67366e12	−0.512649	−0.256324	−	0.966591i	$-0.582512\pi$
$821$	−6.67366e12	−0.512649	−0.256324	+	0.966591i	$0.582512\pi$
$822$	8.66706e12	0.662138
$823$	−1.21283e13	−0.921512	−0.460756	−	0.887527i	$-0.652422\pi$
$823$	−1.21283e13	−0.921512	−0.460756	+	0.887527i	$0.652422\pi$
$824$	−2.85973e13	−2.16099
$825$	1.01069e13	0.759581
$826$	5.37284e12	0.401600
$827$	−1.18283e13	−0.879318	−0.439659	−	0.898165i	$-0.644901\pi$
$827$	−1.18283e13	−0.879318	−0.439659	+	0.898165i	$0.644901\pi$
$828$	9.81571e11	0.0725747
$829$	7.07948e12	0.520602	0.260301	−	0.965527i	$-0.416178\pi$
$829$	7.07948e12	0.520602	0.260301	+	0.965527i	$0.416178\pi$
$830$	8.15356e12	0.596343
$831$	−1.23870e13	−0.901076
$832$	2.10843e13	1.52547
$833$	−5.46590e12	−0.393332
$834$	−2.25170e13	−1.61162
$835$	4.46750e12	0.318035
$836$	1.21639e13	0.861282
$837$	−2.23920e13	−1.57699
$838$	−3.09111e13	−2.16529
$839$	−2.29506e12	−0.159906	−0.0799532	−	0.996799i	$-0.525477\pi$
$839$	−2.29506e12	−0.159906	−0.0799532	+	0.996799i	$0.525477\pi$
$840$	−1.02770e12	−0.0712210
$841$	2.75328e12	0.189788
$842$	2.65649e13	1.82140
$843$	1.24181e13	0.846897
$844$	−3.78632e12	−0.256848
$845$	−6.43276e11	−0.0434053
$846$	−1.01884e13	−0.683815
$847$	1.27697e11	0.00852519
$848$	1.52303e13	1.01141
$849$	−4.27904e12	−0.282659
$850$	1.11362e13	0.731729
$851$	−2.97211e11	−0.0194260
$852$	−1.13960e13	−0.740922
$853$	1.07725e13	0.696700	0.348350	−	0.937365i	$-0.386742\pi$
$853$	1.07725e13	0.696700	0.348350	+	0.937365i	$0.386742\pi$
$854$	4.81661e12	0.309871
$855$	4.07347e11	0.0260686
$856$	5.61694e13	3.57575
$857$	1.70306e13	1.07849	0.539246	−	0.842148i	$-0.318709\pi$
$857$	1.70306e13	1.07849	0.539246	+	0.842148i	$0.318709\pi$
$858$	2.06241e13	1.29922
$859$	1.68432e13	1.05549	0.527747	−	0.849402i	$-0.323037\pi$
$859$	1.68432e13	1.05549	0.527747	+	0.849402i	$0.323037\pi$
$860$	−1.17521e12	−0.0732609
$861$	−9.19019e11	−0.0569915
$862$	−3.97409e13	−2.45163
$863$	2.85773e13	1.75377	0.876886	−	0.480699i	$-0.159617\pi$
$863$	2.85773e13	1.75377	0.876886	+	0.480699i	$0.159617\pi$
$864$	4.29923e13	2.62469
$865$	2.69904e12	0.163922
$866$	8.85139e12	0.534787
$867$	−1.06996e13	−0.643104
$868$	1.04464e13	0.624637
$869$	−2.63354e13	−1.56657
$870$	5.07982e12	0.300616
$871$	−1.48990e13	−0.877153
$872$	−6.21429e13	−3.63971
$873$	−2.45663e12	−0.143145
$874$	−7.64868e11	−0.0443389
$875$	−1.11038e12	−0.0640378
$876$	−4.88221e13	−2.80123
$877$	−1.62714e12	−0.0928807	−0.0464404	−	0.998921i	$-0.514788\pi$
$877$	−1.62714e12	−0.0928807	−0.0464404	+	0.998921i	$0.514788\pi$
$878$	−1.70192e12	−0.0966527
$879$	1.58264e13	0.894195
$880$	−9.77579e12	−0.549516
$881$	9.31457e12	0.520920	0.260460	−	0.965485i	$-0.416126\pi$
$881$	9.31457e12	0.520920	0.260460	+	0.965485i	$0.416126\pi$
$882$	−1.33470e13	−0.742634
$883$	−1.11738e12	−0.0618553	−0.0309277	−	0.999522i	$-0.509846\pi$
$883$	−1.11738e12	−0.0618553	−0.0309277	+	0.999522i	$0.509846\pi$
$884$	1.62578e13	0.895417
$885$	−3.36761e12	−0.184534
$886$	1.90741e13	1.03990
$887$	−1.85575e13	−1.00661	−0.503307	−	0.864108i	$-0.667884\pi$
$887$	−1.85575e13	−1.00661	−0.503307	+	0.864108i	$0.667884\pi$
$888$	−1.11107e13	−0.599632
$889$	−2.75294e12	−0.147822
$890$	−7.53075e12	−0.402331
$891$	8.20136e12	0.435950
$892$	−5.54318e10	−0.00293168
$893$	5.67986e12	0.298886
$894$	−4.59904e13	−2.40796
$895$	−4.97432e12	−0.259138
$896$	−2.73317e12	−0.141671
$897$	−9.27800e11	−0.0478507
$898$	−1.21045e13	−0.621158
$899$	−3.10971e13	−1.58782
$900$	1.94547e13	0.988402
$901$	2.88814e12	0.146001
$902$	−1.65731e13	−0.833632
$903$	−4.00117e11	−0.0200259
$904$	4.53547e13	2.25873
$905$	−3.59378e12	−0.178087
$906$	−2.89565e12	−0.142781
$907$	−1.49318e13	−0.732620	−0.366310	−	0.930493i	$-0.619379\pi$
$907$	−1.49318e13	−0.732620	−0.366310	+	0.930493i	$0.619379\pi$
$908$	−7.56533e13	−3.69353
$909$	1.20077e13	0.583342
$910$	−1.11185e12	−0.0537479
$911$	−2.77113e13	−1.33298	−0.666490	−	0.745514i	$-0.732204\pi$
$911$	−2.77113e13	−1.33298	−0.666490	+	0.745514i	$0.732204\pi$
$912$	−1.50825e13	−0.721930
$913$	3.58151e13	1.70587
$914$	−1.29222e13	−0.612462
$915$	−3.01897e12	−0.142385
$916$	−6.02218e12	−0.282634
$917$	4.09461e12	0.191228
$918$	1.77034e13	0.822745
$919$	2.32626e13	1.07582	0.537909	−	0.843003i	$-0.319214\pi$
$919$	2.32626e13	1.07582	0.537909	+	0.843003i	$0.319214\pi$
$920$	8.33728e11	0.0383689
$921$	2.20792e13	1.01115
$922$	−2.60484e13	−1.18711
$923$	−7.42512e12	−0.336741
$924$	−7.49572e12	−0.338290
$925$	−5.89072e12	−0.264564
$926$	8.14007e12	0.363813
$927$	−6.98497e12	−0.310674
$928$	5.97061e13	2.64273
$929$	−2.61747e13	−1.15295	−0.576476	−	0.817114i	$-0.695572\pi$
$929$	−2.61747e13	−1.15295	−0.576476	+	0.817114i	$0.695572\pi$
$930$	−9.15202e12	−0.401184
$931$	7.44074e12	0.324595
$932$	−8.00748e13	−3.47636
$933$	2.21769e13	0.958149
$934$	−1.62427e13	−0.698390
$935$	−1.85380e12	−0.0793249
$936$	2.39085e13	1.01815
$937$	1.82019e12	0.0771417	0.0385709	−	0.999256i	$-0.487719\pi$
$937$	1.82019e12	0.0771417	0.0385709	+	0.999256i	$0.487719\pi$
$938$	7.56882e12	0.319239
$939$	2.22750e13	0.935022
$940$	−1.02803e13	−0.429468
$941$	3.78437e13	1.57340	0.786702	−	0.617332i	$-0.211787\pi$
$941$	3.78437e13	1.57340	0.786702	+	0.617332i	$0.211787\pi$
$942$	−1.33874e13	−0.553944
$943$	7.45562e11	0.0307030
$944$	−8.59507e13	−3.52270
$945$	−8.66189e11	−0.0353321
$946$	−7.21549e12	−0.292925
$947$	1.25246e13	0.506045	0.253022	−	0.967460i	$-0.418575\pi$
$947$	1.25246e13	0.506045	0.253022	+	0.967460i	$0.418575\pi$
$948$	7.35407e13	2.95726
$949$	−3.18104e13	−1.27313
$950$	−1.51597e13	−0.603856
$951$	−2.30963e12	−0.0915652
$952$	−4.97396e12	−0.196262
$953$	6.72806e12	0.264224	0.132112	−	0.991235i	$-0.457824\pi$
$953$	6.72806e12	0.264224	0.132112	+	0.991235i	$0.457824\pi$
$954$	7.05246e12	0.275659
$955$	−6.92844e12	−0.269538
$956$	1.05185e14	4.07280
$957$	2.23135e13	0.859930
$958$	7.19879e12	0.276131
$959$	−2.05241e12	−0.0783574
$960$	6.71349e12	0.255110
$961$	2.95863e13	1.11901
$962$	−1.20206e13	−0.452521
$963$	1.37195e13	0.514068
$964$	−9.35380e12	−0.348852
$965$	9.47329e12	0.351664
$966$	4.71331e11	0.0174152
$967$	4.50859e13	1.65814	0.829071	−	0.559143i	$-0.188870\pi$
$967$	4.50859e13	1.65814	0.829071	+	0.559143i	$0.188870\pi$
$968$	−3.87272e12	−0.141768
$969$	−2.86010e12	−0.104214
$970$	−3.46476e12	−0.125661
$971$	6.75879e12	0.243996	0.121998	−	0.992530i	$-0.461070\pi$
$971$	6.75879e12	0.243996	0.121998	+	0.992530i	$0.461070\pi$
$972$	5.28926e13	1.90063
$973$	5.33214e12	0.190719
$974$	−1.04497e13	−0.372040
$975$	−1.83890e13	−0.651684
$976$	−7.70525e13	−2.71808
$977$	2.58525e13	0.907772	0.453886	−	0.891060i	$-0.350037\pi$
$977$	2.58525e13	0.907772	0.453886	+	0.891060i	$0.350037\pi$
$978$	7.14534e13	2.49746
$979$	−3.30793e13	−1.15089
$980$	−1.34674e13	−0.466409
$981$	−1.51786e13	−0.523263
$982$	−4.32350e13	−1.48366
$983$	1.85340e13	0.633109	0.316554	−	0.948574i	$-0.397474\pi$
$983$	1.85340e13	0.633109	0.316554	+	0.948574i	$0.397474\pi$
$984$	2.78716e13	0.947728
$985$	5.24957e12	0.177689
$986$	2.45859e13	0.828399
$987$	−3.50007e12	−0.117395
$988$	−2.21317e13	−0.738939
$989$	3.24598e11	0.0107885
$990$	−4.52672e12	−0.149770
$991$	−4.66998e12	−0.153809	−0.0769047	−	0.997038i	$-0.524504\pi$
$991$	−4.66998e12	−0.153809	−0.0769047	+	0.997038i	$0.524504\pi$
$992$	−1.07569e14	−3.52683
$993$	1.73355e13	0.565803
$994$	3.77203e12	0.122556
$995$	5.10285e12	0.165047
$996$	−1.00012e14	−3.22023
$997$	3.66040e13	1.17328	0.586639	−	0.809849i	$-0.300451\pi$
$997$	3.66040e13	1.17328	0.586639	+	0.809849i	$0.300451\pi$
$998$	−4.50657e13	−1.43800
$999$	−9.36463e12	−0.297472

Twists

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

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

\(f(q)\)	\(=\)	\(q-42.4171 q^{2} +107.942 q^{3} +1287.21 q^{4} +267.050 q^{5} -4578.58 q^{6} +1084.23 q^{7} -32882.2 q^{8} -8031.56 q^{9} +O(q^{10})\)	\(q-42.4171 q^{2} +107.942 q^{3} +1287.21 q^{4} +267.050 q^{5} -4578.58 q^{6} +1084.23 q^{7} -32882.2 q^{8} -8031.56 q^{9} -11327.5 q^{10} -49756.6 q^{11} +138944. q^{12} +90530.0 q^{13} -45990.0 q^{14} +28825.8 q^{15} +735714. q^{16} +139514. q^{17} +340675. q^{18} -189921. q^{19} +343749. q^{20} +117034. q^{21} +2.11053e6 q^{22} -94945.1 q^{23} -3.54936e6 q^{24} -1.88181e6 q^{25} -3.84002e6 q^{26} -2.99156e6 q^{27} +1.39564e6 q^{28} -4.15457e6 q^{29} -1.22271e6 q^{30} +7.48504e6 q^{31} -1.43712e7 q^{32} -5.37082e6 q^{33} -5.91779e6 q^{34} +289544. q^{35} -1.03383e7 q^{36} +3.13035e6 q^{37} +8.05590e6 q^{38} +9.77197e6 q^{39} -8.78117e6 q^{40} -7.85257e6 q^{41} -4.96425e6 q^{42} -3.41880e6 q^{43} -6.40472e7 q^{44} -2.14482e6 q^{45} +4.02729e6 q^{46} -2.99064e7 q^{47} +7.94143e7 q^{48} -3.91780e7 q^{49} +7.98209e7 q^{50} +1.50594e7 q^{51} +1.16531e8 q^{52} +2.07014e7 q^{53} +1.26893e8 q^{54} -1.32875e7 q^{55} -3.56519e7 q^{56} -2.05004e7 q^{57} +1.76225e8 q^{58} -1.16826e8 q^{59} +3.71049e7 q^{60} -1.04732e8 q^{61} -3.17494e8 q^{62} -8.70808e6 q^{63} +2.32899e8 q^{64} +2.41760e7 q^{65} +2.27815e8 q^{66} -1.64575e8 q^{67} +1.79584e8 q^{68} -1.02485e7 q^{69} -1.22816e7 q^{70} -8.20184e7 q^{71} +2.64095e8 q^{72} -3.51380e8 q^{73} -1.32780e8 q^{74} -2.03126e8 q^{75} -2.44468e8 q^{76} -5.39478e7 q^{77} -4.14499e8 q^{78} +5.29284e8 q^{79} +1.96472e8 q^{80} -1.64829e8 q^{81} +3.33083e8 q^{82} -7.19804e8 q^{83} +1.50648e8 q^{84} +3.72572e7 q^{85} +1.45016e8 q^{86} -4.48452e8 q^{87} +1.63611e9 q^{88} +6.64822e8 q^{89} +9.09772e7 q^{90} +9.81556e7 q^{91} -1.22214e8 q^{92} +8.07950e8 q^{93} +1.26854e9 q^{94} -5.07183e7 q^{95} -1.55125e9 q^{96} +3.05873e8 q^{97} +1.66182e9 q^{98} +3.99623e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 32 q^{2} - 317 q^{3} + 3242 q^{4} - 4717 q^{5} + 687 q^{6} - 9680 q^{7} - 20394 q^{8} + 69516 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more