LMFDB - Embedded newform 17.10.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,10,Mod(1,17)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, 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("17.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	17.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:	$8.75560921479$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 1596x^{3} + 5754x^{2} + 488987x - 2711704 $ x^5 - 2x^4 - 1596x^3 + 5754x^2 + 488987x - 2711704
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$5.77274$ of defining polynomial
Character	$\chi$	$=$	17.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.22726 q^{2} +177.437 q^{3} -510.494 q^{4} -1620.18 q^{5} -217.762 q^{6} -1834.42 q^{7} +1254.87 q^{8} +11801.0 q^{9} +O(q^{10})$	\(q-1.22726 q^{2} +177.437 q^{3} -510.494 q^{4} -1620.18 q^{5} -217.762 q^{6} -1834.42 q^{7} +1254.87 q^{8} +11801.0 q^{9} +1988.39 q^{10} -31779.3 q^{11} -90580.6 q^{12} -132363. q^{13} +2251.32 q^{14} -287481. q^{15} +259833. q^{16} -83521.0 q^{17} -14482.9 q^{18} -1603.79 q^{19} +827094. q^{20} -325495. q^{21} +39001.6 q^{22} +23254.0 q^{23} +222661. q^{24} +671873. q^{25} +162444. q^{26} -1.39856e6 q^{27} +936463. q^{28} +3.73267e6 q^{29} +352815. q^{30} +8.91479e6 q^{31} -961376. q^{32} -5.63884e6 q^{33} +102502. q^{34} +2.97211e6 q^{35} -6.02433e6 q^{36} -1.20475e7 q^{37} +1968.28 q^{38} -2.34861e7 q^{39} -2.03312e6 q^{40} -1.26779e7 q^{41} +399468. q^{42} +2.86352e7 q^{43} +1.62231e7 q^{44} -1.91198e7 q^{45} -28538.8 q^{46} -7.17761e6 q^{47} +4.61040e7 q^{48} -3.69885e7 q^{49} -824565. q^{50} -1.48197e7 q^{51} +6.75705e7 q^{52} -5.96065e7 q^{53} +1.71640e6 q^{54} +5.14884e7 q^{55} -2.30196e6 q^{56} -284573. q^{57} -4.58096e6 q^{58} +1.85990e8 q^{59} +1.46757e8 q^{60} -2.00037e8 q^{61} -1.09408e7 q^{62} -2.16480e7 q^{63} -1.31855e8 q^{64} +2.14453e8 q^{65} +6.92034e6 q^{66} -1.27030e8 q^{67} +4.26370e7 q^{68} +4.12613e6 q^{69} -3.64756e6 q^{70} -3.27860e8 q^{71} +1.48087e7 q^{72} -1.48678e8 q^{73} +1.47854e7 q^{74} +1.19215e8 q^{75} +818726. q^{76} +5.82968e7 q^{77} +2.88237e7 q^{78} -2.58778e8 q^{79} -4.20977e8 q^{80} -4.80436e8 q^{81} +1.55591e7 q^{82} +3.45060e8 q^{83} +1.66163e8 q^{84} +1.35319e8 q^{85} -3.51430e7 q^{86} +6.62314e8 q^{87} -3.98789e7 q^{88} +4.03936e8 q^{89} +2.34650e7 q^{90} +2.42810e8 q^{91} -1.18710e7 q^{92} +1.58182e9 q^{93} +8.80881e6 q^{94} +2.59844e6 q^{95} -1.70584e8 q^{96} -9.89973e8 q^{97} +4.53946e7 q^{98} -3.75028e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 33 q^{2} - 236 q^{3} + 853 q^{4} + 1480 q^{5} + 7578 q^{6} - 13202 q^{7} - 42423 q^{8} + 10981 q^{9}+O(q^{10}) $ 5 * q - 33 * q^2 - 236 * q^3 + 853 * q^4 + 1480 * q^5 + 7578 * q^6 - 13202 * q^7 - 42423 * q^8 + 10981 * q^9	\( 5 q - 33 q^{2} - 236 q^{3} + 853 q^{4} + 1480 q^{5} + 7578 q^{6} - 13202 q^{7} - 42423 q^{8} + 10981 q^{9} - 89328 q^{10} - 68036 q^{11} - 406010 q^{12} - 158862 q^{13} - 84700 q^{14} - 687324 q^{15} + 350225 q^{16} - 417605 q^{17} - 1911585 q^{18} - 370992 q^{19} + 1632640 q^{20} + 1783880 q^{21} + 122290 q^{22} + 1645870 q^{23} + 9678702 q^{24} + 3270239 q^{25} + 734846 q^{26} - 2998268 q^{27} + 183372 q^{28} + 3668616 q^{29} + 17048544 q^{30} - 7262362 q^{31} - 5605919 q^{32} - 11334900 q^{33} + 2756193 q^{34} - 26503988 q^{35} + 49782133 q^{36} - 31420708 q^{37} + 18513700 q^{38} - 42449884 q^{39} - 53930464 q^{40} - 7996938 q^{41} - 44519496 q^{42} - 56908268 q^{43} + 43323054 q^{44} + 12799536 q^{45} - 32063472 q^{46} - 16903336 q^{47} - 102794498 q^{48} - 11784059 q^{49} + 85921093 q^{50} + 19710956 q^{51} + 173619082 q^{52} - 83362982 q^{53} + 386329164 q^{54} + 6363364 q^{55} + 317409372 q^{56} + 136615904 q^{57} + 64577488 q^{58} - 37946604 q^{59} - 223158912 q^{60} - 77685452 q^{61} + 324855300 q^{62} - 191945278 q^{63} + 131623105 q^{64} - 40321288 q^{65} + 298037676 q^{66} - 304503600 q^{67} - 71243413 q^{68} - 333409272 q^{69} - 122787392 q^{70} - 476602922 q^{71} - 1301701911 q^{72} - 289980486 q^{73} + 262289012 q^{74} - 153685772 q^{75} - 1031276084 q^{76} - 143385648 q^{77} + 691646196 q^{78} - 828240610 q^{79} + 912750944 q^{80} + 891328609 q^{81} - 1109615654 q^{82} + 194681148 q^{83} + 1541719592 q^{84} - 123611080 q^{85} + 1164707144 q^{86} + 158149884 q^{87} - 1017979978 q^{88} + 376848106 q^{89} - 2240087472 q^{90} + 194543664 q^{91} + 2506713088 q^{92} + 3494835920 q^{93} - 2244811104 q^{94} + 1498679864 q^{95} + 2935047582 q^{96} + 692035246 q^{97} + 871744055 q^{98} + 2027106408 q^{99}+O(q^{100}) \) 5 * q - 33 * q^2 - 236 * q^3 + 853 * q^4 + 1480 * q^5 + 7578 * q^6 - 13202 * q^7 - 42423 * q^8 + 10981 * q^9 - 89328 * q^10 - 68036 * q^11 - 406010 * q^12 - 158862 * q^13 - 84700 * q^14 - 687324 * q^15 + 350225 * q^16 - 417605 * q^17 - 1911585 * q^18 - 370992 * q^19 + 1632640 * q^20 + 1783880 * q^21 + 122290 * q^22 + 1645870 * q^23 + 9678702 * q^24 + 3270239 * q^25 + 734846 * q^26 - 2998268 * q^27 + 183372 * q^28 + 3668616 * q^29 + 17048544 * q^30 - 7262362 * q^31 - 5605919 * q^32 - 11334900 * q^33 + 2756193 * q^34 - 26503988 * q^35 + 49782133 * q^36 - 31420708 * q^37 + 18513700 * q^38 - 42449884 * q^39 - 53930464 * q^40 - 7996938 * q^41 - 44519496 * q^42 - 56908268 * q^43 + 43323054 * q^44 + 12799536 * q^45 - 32063472 * q^46 - 16903336 * q^47 - 102794498 * q^48 - 11784059 * q^49 + 85921093 * q^50 + 19710956 * q^51 + 173619082 * q^52 - 83362982 * q^53 + 386329164 * q^54 + 6363364 * q^55 + 317409372 * q^56 + 136615904 * q^57 + 64577488 * q^58 - 37946604 * q^59 - 223158912 * q^60 - 77685452 * q^61 + 324855300 * q^62 - 191945278 * q^63 + 131623105 * q^64 - 40321288 * q^65 + 298037676 * q^66 - 304503600 * q^67 - 71243413 * q^68 - 333409272 * q^69 - 122787392 * q^70 - 476602922 * q^71 - 1301701911 * q^72 - 289980486 * q^73 + 262289012 * q^74 - 153685772 * q^75 - 1031276084 * q^76 - 143385648 * q^77 + 691646196 * q^78 - 828240610 * q^79 + 912750944 * q^80 + 891328609 * q^81 - 1109615654 * q^82 + 194681148 * q^83 + 1541719592 * q^84 - 123611080 * q^85 + 1164707144 * q^86 + 158149884 * q^87 - 1017979978 * q^88 + 376848106 * q^89 - 2240087472 * q^90 + 194543664 * q^91 + 2506713088 * q^92 + 3494835920 * q^93 - 2244811104 * q^94 + 1498679864 * q^95 + 2935047582 * q^96 + 692035246 * q^97 + 871744055 * q^98 + 2027106408 * 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 $

$2$	−1.22726	−0.0542379	−0.0271189	−	0.999632i	$-0.508633\pi$
$2$	−1.22726	−0.0542379	−0.0271189	+	0.999632i	$0.508633\pi$
$3$	177.437	1.26473	0.632367	−	0.774669i	$-0.282083\pi$
$3$	177.437	1.26473	0.632367	+	0.774669i	$0.282083\pi$
$4$	−510.494	−0.997058
$5$	−1620.18	−1.15931	−0.579655	−	0.814862i	$-0.696813\pi$
$5$	−1620.18	−1.15931	−0.579655	+	0.814862i	$0.696813\pi$
$6$	−217.762	−0.0685965
$7$	−1834.42	−0.288774	−0.144387	−	0.989521i	$-0.546121\pi$
$7$	−1834.42	−0.288774	−0.144387	+	0.989521i	$0.546121\pi$
$8$	1254.87	0.108316
$9$	11801.0	0.599553
$10$	1988.39	0.0628785
$11$	−31779.3	−0.654452	−0.327226	−	0.944946i	$-0.606114\pi$
$11$	−31779.3	−0.654452	−0.327226	+	0.944946i	$0.606114\pi$
$12$	−90580.6	−1.26101
$13$	−132363.	−1.28535	−0.642675	−	0.766139i	$-0.722176\pi$
$13$	−132363.	−1.28535	−0.642675	+	0.766139i	$0.722176\pi$
$14$	2251.32	0.0156625
$15$	−287481.	−1.46622
$16$	259833.	0.991183
$17$	−83521.0	−0.242536
$17$	−83521.0	−0.242536
$18$	−14482.9	−0.0325185
$19$	−1603.79	−0.00282330	−0.00141165	−	0.999999i	$-0.500449\pi$
$19$	−1603.79	−0.00282330	−0.00141165	+	0.999999i	$0.500449\pi$
$20$	827094.	1.15590
$21$	−325495.	−0.365223
$22$	39001.6	0.0354961
$23$	23254.0	0.0173270	0.00866348	−	0.999962i	$-0.497242\pi$
$23$	23254.0	0.0173270	0.00866348	+	0.999962i	$0.497242\pi$
$24$	222661.	0.136991
$25$	671873.	0.343999
$26$	162444.	0.0697147
$27$	−1.39856e6	−0.506460
$28$	936463.	0.287925
$29$	3.73267e6	0.980005	0.490002	−	0.871721i	$-0.336996\pi$
$29$	3.73267e6	0.980005	0.490002	+	0.871721i	$0.336996\pi$
$30$	352815.	0.0795246
$31$	8.91479e6	1.73374	0.866869	−	0.498536i	$-0.166129\pi$
$31$	8.91479e6	1.73374	0.866869	+	0.498536i	$0.166129\pi$
$32$	−961376.	−0.162076
$33$	−5.63884e6	−0.827707
$34$	102502.	0.0131546
$35$	2.97211e6	0.334779
$36$	−6.02433e6	−0.597789
$37$	−1.20475e7	−1.05679	−0.528395	−	0.848999i	$-0.677206\pi$
$37$	−1.20475e7	−1.05679	−0.528395	+	0.848999i	$0.677206\pi$
$38$	1968.28	0.000153130 0
$39$	−2.34861e7	−1.62563
$40$	−2.03312e6	−0.125572
$41$	−1.26779e7	−0.700680	−0.350340	−	0.936623i	$-0.613934\pi$
$41$	−1.26779e7	−0.700680	−0.350340	+	0.936623i	$0.613934\pi$
$42$	399468.	0.0198089
$43$	2.86352e7	1.27730	0.638650	−	0.769498i	$-0.279493\pi$
$43$	2.86352e7	1.27730	0.638650	+	0.769498i	$0.279493\pi$
$44$	1.62231e7	0.652526
$45$	−1.91198e7	−0.695067
$46$	−28538.8	−0.000939777 0
$47$	−7.17761e6	−0.214555	−0.107278	−	0.994229i	$-0.534213\pi$
$47$	−7.17761e6	−0.214555	−0.107278	+	0.994229i	$0.534213\pi$
$48$	4.61040e7	1.25358
$49$	−3.69885e7	−0.916609
$50$	−824565.	−0.0186578
$51$	−1.48197e7	−0.306743
$52$	6.75705e7	1.28157
$53$	−5.96065e7	−1.03765	−0.518826	−	0.854880i	$-0.673631\pi$
$53$	−5.96065e7	−1.03765	−0.518826	+	0.854880i	$0.673631\pi$
$54$	1.71640e6	0.0274693
$55$	5.14884e7	0.758712
$56$	−2.30196e6	−0.0312790
$57$	−284573.	−0.00357072
$58$	−4.58096e6	−0.0531534
$59$	1.85990e8	1.99828	0.999139	−	0.0414925i	$-0.0132113\pi$
$59$	1.85990e8	1.99828	0.999139	+	0.0414925i	$0.0132113\pi$
$60$	1.46757e8	1.46191
$61$	−2.00037e8	−1.84981	−0.924905	−	0.380198i	$-0.875856\pi$
$61$	−2.00037e8	−1.84981	−0.924905	+	0.380198i	$0.875856\pi$
$62$	−1.09408e7	−0.0940343
$63$	−2.16480e7	−0.173135
$64$	−1.31855e8	−0.982393
$65$	2.14453e8	1.49012
$66$	6.92034e6	0.0448931
$67$	−1.27030e8	−0.770137	−0.385069	−	0.922888i	$-0.625822\pi$
$67$	−1.27030e8	−0.770137	−0.385069	+	0.922888i	$0.625822\pi$
$68$	4.26370e7	0.241822
$69$	4.12613e6	0.0219140
$70$	−3.64756e6	−0.0181577
$71$	−3.27860e8	−1.53118	−0.765590	−	0.643329i	$-0.777553\pi$
$71$	−3.27860e8	−1.53118	−0.765590	+	0.643329i	$0.777553\pi$
$72$	1.48087e7	0.0649413
$73$	−1.48678e8	−0.612766	−0.306383	−	0.951908i	$-0.599119\pi$
$73$	−1.48678e8	−0.612766	−0.306383	+	0.951908i	$0.599119\pi$
$74$	1.47854e7	0.0573181
$75$	1.19215e8	0.435067
$76$	818726.	0.00281500
$77$	5.82968e7	0.188989
$78$	2.88237e7	0.0881705
$79$	−2.58778e8	−0.747491	−0.373746	−	0.927531i	$-0.621927\pi$
$79$	−2.58778e8	−0.747491	−0.373746	+	0.927531i	$0.621927\pi$
$80$	−4.20977e8	−1.14909
$81$	−4.80436e8	−1.24009
$82$	1.55591e7	0.0380034
$83$	3.45060e8	0.798073	0.399037	−	0.916935i	$-0.369345\pi$
$83$	3.45060e8	0.798073	0.399037	+	0.916935i	$0.369345\pi$
$84$	1.66163e8	0.364149
$85$	1.35319e8	0.281174
$86$	−3.51430e7	−0.0692780
$87$	6.62314e8	1.23945
$88$	−3.98789e7	−0.0708877
$89$	4.03936e8	0.682428	0.341214	−	0.939986i	$-0.389162\pi$
$89$	4.03936e8	0.682428	0.341214	+	0.939986i	$0.389162\pi$
$90$	2.34650e7	0.0376990
$91$	2.42810e8	0.371176
$92$	−1.18710e7	−0.0172760
$93$	1.58182e9	2.19272
$94$	8.80881e6	0.0116370
$95$	2.59844e6	0.00327308
$96$	−1.70584e8	−0.204983
$97$	−9.89973e8	−1.13540	−0.567702	−	0.823234i	$-0.692167\pi$
$97$	−9.89973e8	−1.13540	−0.567702	+	0.823234i	$0.692167\pi$
$98$	4.53946e7	0.0497149
$99$	−3.75028e8	−0.392378
$100$	−3.42987e8	−0.342987
$101$	−1.11917e9	−1.07017	−0.535084	−	0.844799i	$-0.679720\pi$
$101$	−1.11917e9	−1.07017	−0.535084	+	0.844799i	$0.679720\pi$
$102$	1.81877e7	0.0166371
$103$	6.58796e6	0.00576744	0.00288372	−	0.999996i	$-0.499082\pi$
$103$	6.58796e6	0.00576744	0.00288372	+	0.999996i	$0.499082\pi$
$104$	−1.66098e8	−0.139224
$105$	5.27363e8	0.423407
$106$	7.31528e7	0.0562801
$107$	1.55590e9	1.14751	0.573754	−	0.819028i	$-0.305487\pi$
$107$	1.55590e9	1.14751	0.573754	+	0.819028i	$0.305487\pi$
$108$	7.13957e8	0.504970
$109$	6.94766e8	0.471432	0.235716	−	0.971822i	$-0.424256\pi$
$109$	6.94766e8	0.471432	0.235716	+	0.971822i	$0.424256\pi$
$110$	−6.31898e7	−0.0411509
$111$	−2.13767e9	−1.33656
$112$	−4.76644e8	−0.286228
$113$	2.09735e9	1.21009	0.605047	−	0.796190i	$-0.293154\pi$
$113$	2.09735e9	1.21009	0.605047	+	0.796190i	$0.293154\pi$
$114$	349246.	0.000193669 0
$115$	−3.76758e7	−0.0200873
$116$	−1.90550e9	−0.977122
$117$	−1.56202e9	−0.770635
$118$	−2.28259e8	−0.108382
$119$	1.53213e8	0.0700381
$120$	−3.60751e8	−0.158815
$121$	−1.34802e9	−0.571693
$122$	2.45499e8	0.100330
$123$	−2.24953e9	−0.886173
$124$	−4.55095e9	−1.72864
$125$	2.07586e9	0.760508
$126$	2.65678e7	0.00939050
$127$	−4.92229e9	−1.67900	−0.839499	−	0.543361i	$-0.817151\pi$
$127$	−4.92229e9	−1.67900	−0.839499	+	0.543361i	$0.817151\pi$
$128$	6.54045e8	0.215359
$129$	5.08096e9	1.61544
$130$	−2.63190e8	−0.0808209
$131$	4.54604e9	1.34869	0.674345	−	0.738416i	$-0.264426\pi$
$131$	4.54604e9	1.34869	0.674345	+	0.738416i	$0.264426\pi$
$132$	2.87859e9	0.825272
$133$	2.94204e6	0.000815297 0
$134$	1.55899e8	0.0417706
$135$	2.26593e9	0.587143
$136$	−1.04808e8	−0.0262705
$137$	5.25313e9	1.27402	0.637010	−	0.770856i	$-0.280171\pi$
$137$	5.25313e9	1.27402	0.637010	+	0.770856i	$0.280171\pi$
$138$	−5.06384e6	−0.00118857
$139$	1.55602e9	0.353549	0.176774	−	0.984251i	$-0.443434\pi$
$139$	1.55602e9	0.353549	0.176774	+	0.984251i	$0.443434\pi$
$140$	−1.51724e9	−0.333794
$141$	−1.27358e9	−0.271356
$142$	4.02371e8	0.0830479
$143$	4.20641e9	0.841200
$144$	3.06629e9	0.594267
$145$	−6.04761e9	−1.13613
$146$	1.82467e8	0.0332351
$147$	−6.56314e9	−1.15927
$148$	6.15017e9	1.05368
$149$	2.13936e9	0.355587	0.177794	−	0.984068i	$-0.443104\pi$
$149$	2.13936e9	0.355587	0.177794	+	0.984068i	$0.443104\pi$
$150$	−1.46309e8	−0.0235971
$151$	−1.65162e9	−0.258531	−0.129266	−	0.991610i	$-0.541262\pi$
$151$	−1.65162e9	−0.258531	−0.129266	+	0.991610i	$0.541262\pi$
$152$	−2.01255e6	−0.000305809 0
$153$	−9.85631e8	−0.145413
$154$	−7.15455e7	−0.0102504
$155$	−1.44436e10	−2.00994
$156$	1.19895e10	1.62084
$157$	−4.44203e9	−0.583490	−0.291745	−	0.956496i	$-0.594236\pi$
$157$	−4.44203e9	−0.583490	−0.291745	+	0.956496i	$0.594236\pi$
$158$	3.17589e8	0.0405423
$159$	−1.05764e10	−1.31235
$160$	1.55761e9	0.187896
$161$	−4.26577e7	−0.00500358
$162$	5.89621e8	0.0672598
$163$	2.66196e9	0.295363	0.147682	−	0.989035i	$-0.452819\pi$
$163$	2.66196e9	0.295363	0.147682	+	0.989035i	$0.452819\pi$
$164$	6.47198e9	0.698618
$165$	9.13596e9	0.959569
$166$	−4.23479e8	−0.0432858
$167$	−1.58326e10	−1.57518	−0.787588	−	0.616203i	$-0.788670\pi$
$167$	−1.58326e10	−1.57518	−0.787588	+	0.616203i	$0.788670\pi$
$168$	−4.08454e8	−0.0395596
$169$	6.91547e9	0.652126
$170$	−1.66073e8	−0.0152503
$171$	−1.89264e7	−0.00169272
$172$	−1.46181e10	−1.27354
$173$	−1.27988e10	−1.08633	−0.543165	−	0.839626i	$-0.682774\pi$
$173$	−1.27988e10	−1.08633	−0.543165	+	0.839626i	$0.682774\pi$
$174$	−8.12834e8	−0.0672249
$175$	−1.23250e9	−0.0993382
$176$	−8.25731e9	−0.648681
$177$	3.30016e10	2.52729
$178$	−4.95735e8	−0.0370135
$179$	−8.33273e9	−0.606665	−0.303332	−	0.952885i	$-0.598099\pi$
$179$	−8.33273e9	−0.606665	−0.303332	+	0.952885i	$0.598099\pi$
$180$	9.76053e9	0.693022
$181$	−8.70236e9	−0.602676	−0.301338	−	0.953517i	$-0.597433\pi$
$181$	−8.70236e9	−0.602676	−0.301338	+	0.953517i	$0.597433\pi$
$182$	−2.97992e8	−0.0201318
$183$	−3.54941e10	−2.33952
$184$	2.91807e7	0.00187679
$185$	1.95192e10	1.22515
$186$	−1.94130e9	−0.118928
$187$	2.65424e9	0.158728
$188$	3.66413e9	0.213924
$189$	2.56556e9	0.146253
$190$	−3.18897e6	−0.000177525 0
$191$	2.29558e10	1.24808	0.624040	−	0.781392i	$-0.285490\pi$
$191$	2.29558e10	1.24808	0.624040	+	0.781392i	$0.285490\pi$
$192$	−2.33959e10	−1.24247
$193$	2.04685e10	1.06189	0.530943	−	0.847407i	$-0.321838\pi$
$193$	2.04685e10	1.06189	0.530943	+	0.847407i	$0.321838\pi$
$194$	1.21496e9	0.0615819
$195$	3.80519e10	1.88460
$196$	1.88824e10	0.913913
$197$	5.81009e9	0.274843	0.137422	−	0.990513i	$-0.456118\pi$
$197$	5.81009e9	0.274843	0.137422	+	0.990513i	$0.456118\pi$
$198$	4.60257e8	0.0212818
$199$	4.49526e9	0.203196	0.101598	−	0.994826i	$-0.467604\pi$
$199$	4.49526e9	0.203196	0.101598	+	0.994826i	$0.467604\pi$
$200$	8.43113e8	0.0372607
$201$	−2.25398e10	−0.974019
$202$	1.37352e9	0.0580436
$203$	−6.84730e9	−0.283000
$204$	7.56539e9	0.305841
$205$	2.05405e10	0.812305
$206$	−8.08516e6	−0.000312814 0
$207$	2.74420e8	0.0103884
$208$	−3.43922e10	−1.27402
$209$	5.09674e7	0.00184771
$210$	−6.47213e8	−0.0229647
$211$	3.47865e10	1.20820	0.604101	−	0.796908i	$-0.293533\pi$
$211$	3.47865e10	1.20820	0.604101	+	0.796908i	$0.293533\pi$
$212$	3.04287e10	1.03460
$213$	−5.81746e10	−1.93654
$214$	−1.90950e9	−0.0622384
$215$	−4.63944e10	−1.48079
$216$	−1.75501e9	−0.0548578
$217$	−1.63535e10	−0.500659
$218$	−8.52661e8	−0.0255695
$219$	−2.63811e10	−0.774986
$220$	−2.62845e10	−0.756480
$221$	1.10551e10	0.311743
$222$	2.62349e9	0.0724921
$223$	−2.46348e10	−0.667078	−0.333539	−	0.942736i	$-0.608243\pi$
$223$	−2.46348e10	−0.667078	−0.333539	+	0.942736i	$0.608243\pi$
$224$	1.76357e9	0.0468034
$225$	7.92877e9	0.206246
$226$	−2.57401e9	−0.0656329
$227$	4.45657e10	1.11400	0.556999	−	0.830513i	$-0.311953\pi$
$227$	4.45657e10	1.11400	0.556999	+	0.830513i	$0.311953\pi$
$228$	1.45273e8	0.00356022
$229$	6.61817e10	1.59030	0.795148	−	0.606415i	$-0.207393\pi$
$229$	6.61817e10	1.59030	0.795148	+	0.606415i	$0.207393\pi$
$230$	4.62381e7	0.00108949
$231$	1.03440e10	0.239021
$232$	4.68401e9	0.106150
$233$	−4.35721e10	−0.968516	−0.484258	−	0.874925i	$-0.660910\pi$
$233$	−4.35721e10	−0.968516	−0.484258	+	0.874925i	$0.660910\pi$
$234$	1.91700e9	0.0417976
$235$	1.16291e10	0.248736
$236$	−9.49468e10	−1.99240
$237$	−4.59169e10	−0.945378
$238$	−1.88033e8	−0.00379872
$239$	3.67128e10	0.727825	0.363912	−	0.931433i	$-0.381441\pi$
$239$	3.67128e10	0.727825	0.363912	+	0.931433i	$0.381441\pi$
$240$	−7.46970e10	−1.45329
$241$	3.62693e10	0.692568	0.346284	−	0.938130i	$-0.387443\pi$
$241$	3.62693e10	0.692568	0.346284	+	0.938130i	$0.387443\pi$
$242$	1.65438e9	0.0310074
$243$	−5.77194e10	−1.06192
$244$	1.02118e11	1.84437
$245$	5.99282e10	1.06263
$246$	2.76076e9	0.0480642
$247$	2.12283e8	0.00362893
$248$	1.11869e10	0.187792
$249$	6.12264e10	1.00935
$250$	−2.54763e9	−0.0412484
$251$	−9.34890e10	−1.48672	−0.743359	−	0.668892i	$-0.766769\pi$
$251$	−9.34890e10	−1.48672	−0.743359	+	0.668892i	$0.766769\pi$
$252$	1.10512e10	0.172626
$253$	−7.38996e8	−0.0113397
$254$	6.04094e9	0.0910653
$255$	2.40107e10	0.355610
$256$	6.67068e10	0.970712
$257$	1.91619e10	0.273993	0.136996	−	0.990572i	$-0.456255\pi$
$257$	1.91619e10	0.273993	0.136996	+	0.990572i	$0.456255\pi$
$258$	−6.23567e9	−0.0876183
$259$	2.21002e10	0.305174
$260$	−1.09477e11	−1.48574
$261$	4.40492e10	0.587564
$262$	−5.57918e9	−0.0731501
$263$	3.75028e10	0.483352	0.241676	−	0.970357i	$-0.422303\pi$
$263$	3.75028e10	0.483352	0.241676	+	0.970357i	$0.422303\pi$
$264$	−7.07600e9	−0.0896541
$265$	9.65735e10	1.20296
$266$	−3.61065e6	−4.42200e−5 0
$267$	7.16732e10	0.863090
$268$	6.48478e10	0.767872
$269$	−9.36804e10	−1.09085	−0.545423	−	0.838161i	$-0.683631\pi$
$269$	−9.36804e10	−1.09085	−0.545423	+	0.838161i	$0.683631\pi$
$270$	−2.78089e9	−0.0318454
$271$	−9.81985e10	−1.10597	−0.552985	−	0.833191i	$-0.686511\pi$
$271$	−9.81985e10	−1.10597	−0.552985	+	0.833191i	$0.686511\pi$
$272$	−2.17015e10	−0.240397
$273$	4.30836e10	0.469439
$274$	−6.44698e9	−0.0691001
$275$	−2.13517e10	−0.225131
$276$	−2.10636e9	−0.0218495
$277$	9.27606e9	0.0946683	0.0473341	−	0.998879i	$-0.484927\pi$
$277$	9.27606e9	0.0946683	0.0473341	+	0.998879i	$0.484927\pi$
$278$	−1.90965e9	−0.0191757
$279$	1.05203e11	1.03947
$280$	3.72960e9	0.0362620
$281$	−1.04165e11	−0.996649	−0.498325	−	0.866991i	$-0.666051\pi$
$281$	−1.04165e11	−0.996649	−0.498325	+	0.866991i	$0.666051\pi$
$282$	1.56301e9	0.0147177
$283$	−9.57066e10	−0.886958	−0.443479	−	0.896285i	$-0.646256\pi$
$283$	−9.57066e10	−0.886958	−0.443479	+	0.896285i	$0.646256\pi$
$284$	1.67371e11	1.52668
$285$	4.61060e8	0.00413958
$286$	−5.16237e9	−0.0456249
$287$	2.32566e10	0.202338
$288$	−1.13452e10	−0.0971730
$289$	6.97576e9	0.0588235
$290$	7.42201e9	0.0616212
$291$	−1.75658e11	−1.43598
$292$	7.58993e10	0.610963
$293$	−1.62664e11	−1.28940	−0.644698	−	0.764437i	$-0.723017\pi$
$293$	−1.62664e11	−1.28940	−0.644698	+	0.764437i	$0.723017\pi$
$294$	8.05470e9	0.0628762
$295$	−3.01338e11	−2.31662
$296$	−1.51180e10	−0.114468
$297$	4.44453e10	0.331453
$298$	−2.62556e9	−0.0192863
$299$	−3.07797e9	−0.0222712
$300$	−6.08587e10	−0.433788
$301$	−5.25292e10	−0.368851
$302$	2.02697e9	0.0140222
$303$	−1.98583e11	−1.35348
$304$	−4.16718e8	−0.00279841
$305$	3.24098e11	2.14450
$306$	1.20963e9	0.00788689
$307$	−2.26286e11	−1.45390	−0.726952	−	0.686688i	$-0.759064\pi$
$307$	−2.26286e11	−1.45390	−0.726952	+	0.686688i	$0.759064\pi$
$308$	−2.97601e10	−0.188433
$309$	1.16895e9	0.00729428
$310$	1.77261e10	0.109015
$311$	1.17225e11	0.710556	0.355278	−	0.934761i	$-0.384386\pi$
$311$	1.17225e11	0.710556	0.355278	+	0.934761i	$0.384386\pi$
$312$	−2.94720e10	−0.176082
$313$	2.85060e11	1.67876	0.839378	−	0.543549i	$-0.182920\pi$
$313$	2.85060e11	1.67876	0.839378	+	0.543549i	$0.182920\pi$
$314$	5.45154e9	0.0316472
$315$	3.50738e10	0.200718
$316$	1.32105e11	0.745292
$317$	−9.98016e9	−0.0555099	−0.0277550	−	0.999615i	$-0.508836\pi$
$317$	−9.98016e9	−0.0555099	−0.0277550	+	0.999615i	$0.508836\pi$
$318$	1.29800e10	0.0711793
$319$	−1.18622e11	−0.641365
$320$	2.13629e11	1.13890
$321$	2.76075e11	1.45129
$322$	5.23522e7	0.000271384 0
$323$	1.33950e8	0.000684751 0
$324$	2.45260e11	1.23644
$325$	−8.89312e10	−0.442159
$326$	−3.26692e9	−0.0160199
$327$	1.23277e11	0.596236
$328$	−1.59091e10	−0.0758949
$329$	1.31668e10	0.0619581
$330$	−1.12122e10	−0.0520450
$331$	−2.14841e11	−0.983766	−0.491883	−	0.870661i	$-0.663691\pi$
$331$	−2.14841e11	−0.983766	−0.491883	+	0.870661i	$0.663691\pi$
$332$	−1.76151e11	−0.795725
$333$	−1.42172e11	−0.633601
$334$	1.94308e10	0.0854342
$335$	2.05811e11	0.892828
$336$	−8.45744e10	−0.362003
$337$	−3.33228e11	−1.40737	−0.703683	−	0.710514i	$-0.748463\pi$
$337$	−3.33228e11	−1.40737	−0.703683	+	0.710514i	$0.748463\pi$
$338$	−8.48710e9	−0.0353699
$339$	3.72149e11	1.53045
$340$	−6.90797e10	−0.280347
$341$	−2.83306e11	−1.13465
$342$	2.32276e7	9.18094e−5 0
$343$	1.41878e11	0.553468
$344$	3.59335e10	0.138352
$345$	−6.68509e9	−0.0254051
$346$	1.57075e10	0.0589203
$347$	−1.63241e10	−0.0604432	−0.0302216	−	0.999543i	$-0.509621\pi$
$347$	−1.63241e10	−0.0604432	−0.0302216	+	0.999543i	$0.509621\pi$
$348$	−3.38107e11	−1.23580
$349$	1.61528e11	0.582819	0.291410	−	0.956598i	$-0.405876\pi$
$349$	1.61528e11	0.582819	0.291410	+	0.956598i	$0.405876\pi$
$350$	1.51260e9	0.00538789
$351$	1.85118e11	0.650978
$352$	3.05519e10	0.106071
$353$	2.89170e11	0.991212	0.495606	−	0.868547i	$-0.334946\pi$
$353$	2.89170e11	0.991212	0.495606	+	0.868547i	$0.334946\pi$
$354$	−4.05016e10	−0.137075
$355$	5.31194e11	1.77511
$356$	−2.06207e11	−0.680421
$357$	2.71857e10	0.0885796
$358$	1.02265e10	0.0329042
$359$	2.34120e11	0.743898	0.371949	−	0.928253i	$-0.378690\pi$
$359$	2.34120e11	0.743898	0.371949	+	0.928253i	$0.378690\pi$
$360$	−2.39928e10	−0.0752870
$361$	−3.22685e11	−0.999992
$362$	1.06801e10	0.0326878
$363$	−2.39190e11	−0.723040
$364$	−1.23953e11	−0.370084
$365$	2.40886e11	0.710385
$366$	4.35606e10	0.126890
$367$	−1.08932e11	−0.313442	−0.156721	−	0.987643i	$-0.550092\pi$
$367$	−1.08932e11	−0.313442	−0.156721	+	0.987643i	$0.550092\pi$
$368$	6.04215e9	0.0171742
$369$	−1.49612e11	−0.420094
$370$	−2.39551e10	−0.0664494
$371$	1.09344e11	0.299648
$372$	−8.07507e11	−2.18627
$373$	−6.82746e11	−1.82629	−0.913145	−	0.407635i	$-0.866353\pi$
$373$	−6.82746e11	−1.82629	−0.913145	+	0.407635i	$0.866353\pi$
$374$	−3.25745e9	−0.00860906
$375$	3.68336e11	0.961841
$376$	−9.00696e9	−0.0232398
$377$	−4.94067e11	−1.25965
$378$	−3.14861e9	−0.00793243
$379$	1.87645e11	0.467156	0.233578	−	0.972338i	$-0.424957\pi$
$379$	1.87645e11	0.467156	0.233578	+	0.972338i	$0.424957\pi$
$380$	−1.32649e9	−0.00326345
$381$	−8.73397e11	−2.12349
$382$	−2.81728e10	−0.0676932
$383$	1.01456e11	0.240925	0.120462	−	0.992718i	$-0.461562\pi$
$383$	1.01456e11	0.240925	0.120462	+	0.992718i	$0.461562\pi$
$384$	1.16052e11	0.272372
$385$	−9.44515e10	−0.219097
$386$	−2.51202e10	−0.0575945
$387$	3.37924e11	0.765808
$388$	5.05375e11	1.13206
$389$	−4.62050e11	−1.02310	−0.511548	−	0.859255i	$-0.670928\pi$
$389$	−4.62050e11	−1.02310	−0.511548	+	0.859255i	$0.670928\pi$
$390$	−4.66997e10	−0.102217
$391$	−1.94220e9	−0.00420240
$392$	−4.64157e10	−0.0992836
$393$	8.06637e11	1.70573
$394$	−7.13051e9	−0.0149069
$395$	4.19269e11	0.866574
$396$	1.91449e11	0.391224
$397$	8.72806e11	1.76344	0.881720	−	0.471774i	$-0.156386\pi$
$397$	8.72806e11	1.76344	0.881720	+	0.471774i	$0.156386\pi$
$398$	−5.51687e9	−0.0110209
$399$	5.22027e8	0.00103113
$400$	1.74575e11	0.340966
$401$	−1.68101e11	−0.324654	−0.162327	−	0.986737i	$-0.551900\pi$
$401$	−1.68101e11	−0.324654	−0.162327	+	0.986737i	$0.551900\pi$
$402$	2.76622e10	0.0528287
$403$	−1.17999e12	−2.22846
$404$	5.71332e11	1.06702
$405$	7.78395e11	1.43765
$406$	8.40343e9	0.0153493
$407$	3.82861e11	0.691618
$408$	−1.85968e10	−0.0332252
$409$	−6.99127e11	−1.23538	−0.617691	−	0.786421i	$-0.711932\pi$
$409$	−6.99127e11	−1.23538	−0.617691	+	0.786421i	$0.711932\pi$
$410$	−2.52086e10	−0.0440577
$411$	9.32102e11	1.61130
$412$	−3.36311e9	−0.00575047
$413$	−3.41185e11	−0.577052
$414$	−3.36786e8	−0.000563446 0
$415$	−5.59060e11	−0.925214
$416$	1.27251e11	0.208324
$417$	2.76097e11	0.447145
$418$	−6.25505e7	−0.000100216 0
$419$	9.68451e11	1.53502	0.767511	−	0.641036i	$-0.221495\pi$
$419$	9.68451e11	1.53502	0.767511	+	0.641036i	$0.221495\pi$
$420$	−2.69215e11	−0.422161
$421$	−5.47606e11	−0.849569	−0.424784	−	0.905295i	$-0.639650\pi$
$421$	−5.47606e11	−0.849569	−0.424784	+	0.905295i	$0.639650\pi$
$422$	−4.26921e10	−0.0655303
$423$	−8.47029e10	−0.128637
$424$	−7.47983e10	−0.112395
$425$	−5.61155e10	−0.0834320
$426$	7.13956e10	0.105034
$427$	3.66954e11	0.534178
$428$	−7.94279e11	−1.14413
$429$	7.46373e11	1.06389
$430$	5.69381e10	0.0803147
$431$	4.80670e11	0.670964	0.335482	−	0.942047i	$-0.391101\pi$
$431$	4.80670e11	0.670964	0.335482	+	0.942047i	$0.391101\pi$
$432$	−3.63392e11	−0.501994
$433$	−7.09547e11	−0.970031	−0.485016	−	0.874506i	$-0.661186\pi$
$433$	−7.09547e11	−0.970031	−0.485016	+	0.874506i	$0.661186\pi$
$434$	2.00701e10	0.0271547
$435$	−1.07307e12	−1.43690
$436$	−3.54674e11	−0.470045
$437$	−3.72946e7	−4.89192e−5 0
$438$	3.23765e10	0.0420336
$439$	1.17101e12	1.50477	0.752387	−	0.658721i	$-0.228902\pi$
$439$	1.17101e12	1.50477	0.752387	+	0.658721i	$0.228902\pi$
$440$	6.46111e10	0.0821808
$441$	−4.36501e11	−0.549555
$442$	−1.35675e10	−0.0169083
$443$	−4.75055e11	−0.586040	−0.293020	−	0.956106i	$-0.594660\pi$
$443$	−4.75055e11	−0.586040	−0.293020	+	0.956106i	$0.594660\pi$
$444$	1.09127e12	1.33263
$445$	−6.54450e11	−0.791146
$446$	3.02333e10	0.0361809
$447$	3.79603e11	0.449723
$448$	2.41877e11	0.283690
$449$	−9.33820e11	−1.08431	−0.542156	−	0.840278i	$-0.682392\pi$
$449$	−9.33820e11	−1.08431	−0.542156	+	0.840278i	$0.682392\pi$
$450$	−9.73069e9	−0.0111863
$451$	4.02895e11	0.458561
$452$	−1.07069e12	−1.20653
$453$	−2.93058e11	−0.326973
$454$	−5.46938e10	−0.0604209
$455$	−3.93397e11	−0.430308
$456$	−3.57101e8	−0.000386767 0
$457$	1.28584e12	1.37900	0.689498	−	0.724288i	$-0.257831\pi$
$457$	1.28584e12	1.37900	0.689498	+	0.724288i	$0.257831\pi$
$458$	−8.12223e10	−0.0862543
$459$	1.16809e11	0.122834
$460$	1.92332e10	0.0200282
$461$	5.18444e11	0.534623	0.267311	−	0.963610i	$-0.413865\pi$
$461$	5.18444e11	0.534623	0.267311	+	0.963610i	$0.413865\pi$
$462$	−1.26948e10	−0.0129640
$463$	−7.76808e11	−0.785596	−0.392798	−	0.919625i	$-0.628493\pi$
$463$	−7.76808e11	−0.785596	−0.392798	+	0.919625i	$0.628493\pi$
$464$	9.69869e11	0.971364
$465$	−2.56283e12	−2.54204
$466$	5.34744e10	0.0525302
$467$	8.28768e10	0.0806319	0.0403159	−	0.999187i	$-0.487164\pi$
$467$	8.28768e10	0.0806319	0.0403159	+	0.999187i	$0.487164\pi$
$468$	7.97399e11	0.768368
$469$	2.33026e11	0.222396
$470$	−1.42719e10	−0.0134909
$471$	−7.88182e11	−0.737959
$472$	2.33393e11	0.216446
$473$	−9.10008e11	−0.835930
$474$	5.63522e10	0.0512753
$475$	−1.07755e9	−0.000971213 0
$476$	−7.82143e10	−0.0698321
$477$	−7.03416e11	−0.622127
$478$	−4.50562e10	−0.0394757
$479$	−2.08230e12	−1.80731	−0.903657	−	0.428257i	$-0.859128\pi$
$479$	−2.08230e12	−1.80731	−0.903657	+	0.428257i	$0.859128\pi$
$480$	2.76378e11	0.237639
$481$	1.59464e12	1.35835
$482$	−4.45120e10	−0.0375634
$483$	−7.56907e9	−0.00632820
$484$	6.88157e11	0.570011
$485$	1.60394e12	1.31629
$486$	7.08369e10	0.0575965
$487$	−2.69427e11	−0.217051	−0.108525	−	0.994094i	$-0.534613\pi$
$487$	−2.69427e11	−0.217051	−0.108525	+	0.994094i	$0.534613\pi$
$488$	−2.51021e11	−0.200364
$489$	4.72330e11	0.373556
$490$	−7.35477e10	−0.0576350
$491$	−5.87772e10	−0.0456396	−0.0228198	−	0.999740i	$-0.507264\pi$
$491$	−5.87772e10	−0.0456396	−0.0228198	+	0.999740i	$0.507264\pi$
$492$	1.14837e12	0.883567
$493$	−3.11756e11	−0.237686
$494$	−2.60527e8	−0.000196826 0
$495$	6.07614e11	0.454888
$496$	2.31635e12	1.71845
$497$	6.01435e11	0.442166
$498$	−7.51409e10	−0.0547450
$499$	−3.13142e11	−0.226094	−0.113047	−	0.993590i	$-0.536061\pi$
$499$	−3.13142e11	−0.226094	−0.113047	+	0.993590i	$0.536061\pi$
$500$	−1.05972e12	−0.758271
$501$	−2.80930e12	−1.99218
$502$	1.14736e11	0.0806365
$503$	7.31761e11	0.509699	0.254849	−	0.966981i	$-0.417974\pi$
$503$	7.31761e11	0.509699	0.254849	+	0.966981i	$0.417974\pi$
$504$	−2.71654e10	−0.0187534
$505$	1.81327e12	1.24066
$506$	9.06943e8	0.000615039 0
$507$	1.22706e12	0.824766
$508$	2.51280e12	1.67406
$509$	2.84601e12	1.87935	0.939673	−	0.342073i	$-0.111129\pi$
$509$	2.84601e12	1.87935	0.939673	+	0.342073i	$0.111129\pi$
$510$	−2.94675e10	−0.0192875
$511$	2.72739e11	0.176951
$512$	−4.16738e11	−0.268008
$513$	2.24300e9	0.00142989
$514$	−2.35167e10	−0.0148608
$515$	−1.06737e10	−0.00668625
$516$	−2.59380e12	−1.61069
$517$	2.28100e11	0.140416
$518$	−2.71228e10	−0.0165520
$519$	−2.27099e12	−1.37392
$520$	2.69110e11	0.161404
$521$	−1.42270e10	−0.00845949	−0.00422974	−	0.999991i	$-0.501346\pi$
$521$	−1.42270e10	−0.00845949	−0.00422974	+	0.999991i	$0.501346\pi$
$522$	−5.40599e10	−0.0318682
$523$	1.20853e12	0.706316	0.353158	−	0.935564i	$-0.385108\pi$
$523$	1.20853e12	0.706316	0.353158	+	0.935564i	$0.385108\pi$
$524$	−2.32072e12	−1.34472
$525$	−2.18692e11	−0.125636
$526$	−4.60259e10	−0.0262160
$527$	−7.44572e11	−0.420493
$528$	−1.46515e12	−0.820410
$529$	−1.80061e12	−0.999700
$530$	−1.18521e11	−0.0652460
$531$	2.19487e12	1.19807
$532$	−1.50189e9	−0.000812899 0
$533$	1.67808e12	0.900619
$534$	−8.79619e10	−0.0468122
$535$	−2.52085e12	−1.33032
$536$	−1.59405e11	−0.0834184
$537$	−1.47854e12	−0.767270
$538$	1.14971e11	0.0591652
$539$	1.17547e12	0.599876
$540$	−1.15674e12	−0.585416
$541$	2.35337e12	1.18115	0.590573	−	0.806985i	$-0.298902\pi$
$541$	2.35337e12	1.18115	0.590573	+	0.806985i	$0.298902\pi$
$542$	1.20515e11	0.0599854
$543$	−1.54412e12	−0.762224
$544$	8.02951e10	0.0393092
$545$	−1.12565e12	−0.546536
$546$	−5.28749e10	−0.0254614
$547$	1.30236e12	0.621996	0.310998	−	0.950411i	$-0.399337\pi$
$547$	1.30236e12	0.621996	0.310998	+	0.950411i	$0.399337\pi$
$548$	−2.68169e12	−1.27027
$549$	−2.36064e12	−1.10906
$550$	2.62041e10	0.0122106
$551$	−5.98642e9	−0.00276685
$552$	5.17775e9	0.00237364
$553$	4.74710e11	0.215856
$554$	−1.13842e10	−0.00513461
$555$	3.46343e12	1.54949
$556$	−7.94340e11	−0.352509
$557$	3.33519e12	1.46816	0.734078	−	0.679065i	$-0.237615\pi$
$557$	3.33519e12	1.46816	0.734078	+	0.679065i	$0.237615\pi$
$558$	−1.29112e11	−0.0563785
$559$	−3.79025e12	−1.64178
$560$	7.72251e11	0.331827
$561$	4.70961e11	0.200748
$562$	1.27838e11	0.0540561
$563$	−9.51343e11	−0.399070	−0.199535	−	0.979891i	$-0.563943\pi$
$563$	−9.51343e11	−0.399070	−0.199535	+	0.979891i	$0.563943\pi$
$564$	6.50152e11	0.270557
$565$	−3.39810e12	−1.40287
$566$	1.17457e11	0.0481067
$567$	8.81324e11	0.358106
$568$	−4.11422e11	−0.165852
$569$	−8.14899e10	−0.0325911	−0.0162955	−	0.999867i	$-0.505187\pi$
$569$	−8.14899e10	−0.0325911	−0.0162955	+	0.999867i	$0.505187\pi$
$570$	−5.65842e8	−0.000224522 0
$571$	1.06368e12	0.418744	0.209372	−	0.977836i	$-0.432858\pi$
$571$	1.06368e12	0.418744	0.209372	+	0.977836i	$0.432858\pi$
$572$	−2.14734e12	−0.838725
$573$	4.07322e12	1.57849
$574$	−2.85420e10	−0.0109744
$575$	1.56237e10	0.00596046
$576$	−1.55601e12	−0.588996
$577$	−3.44925e12	−1.29549	−0.647743	−	0.761859i	$-0.724287\pi$
$577$	−3.44925e12	−1.29549	−0.647743	+	0.761859i	$0.724287\pi$
$578$	−8.56109e9	−0.00319046
$579$	3.63187e12	1.34300
$580$	3.08727e12	1.13279
$581$	−6.32986e11	−0.230463
$582$	2.15579e11	0.0778848
$583$	1.89425e12	0.679093
$584$	−1.86572e11	−0.0663725
$585$	2.53075e12	0.893405
$586$	1.99631e11	0.0699341
$587$	−3.31180e12	−1.15131	−0.575655	−	0.817693i	$-0.695253\pi$
$587$	−3.31180e12	−1.15131	−0.575655	+	0.817693i	$0.695253\pi$
$588$	3.35044e12	1.15586
$589$	−1.42975e10	−0.00489486
$590$	3.69821e11	0.125649
$591$	1.03093e12	0.347604
$592$	−3.13033e12	−1.04747
$593$	9.22763e10	0.0306439	0.0153219	−	0.999883i	$-0.495123\pi$
$593$	9.22763e10	0.0306439	0.0153219	+	0.999883i	$0.495123\pi$
$594$	−5.45461e10	−0.0179773
$595$	−2.48233e11	−0.0811958
$596$	−1.09213e12	−0.354541
$597$	7.97627e11	0.256989
$598$	3.77748e9	0.00120794
$599$	−4.28034e11	−0.135849	−0.0679246	−	0.997690i	$-0.521638\pi$
$599$	−4.28034e11	−0.135849	−0.0679246	+	0.997690i	$0.521638\pi$
$600$	1.49600e11	0.0471249
$601$	2.92420e12	0.914266	0.457133	−	0.889398i	$-0.348876\pi$
$601$	2.92420e12	0.914266	0.457133	+	0.889398i	$0.348876\pi$
$602$	6.44671e10	0.0200057
$603$	−1.49908e12	−0.461738
$604$	8.43140e11	0.257771
$605$	2.18405e12	0.662770
$606$	2.43714e11	0.0734097
$607$	−1.45237e12	−0.434237	−0.217118	−	0.976145i	$-0.569666\pi$
$607$	−1.45237e12	−0.434237	−0.217118	+	0.976145i	$0.569666\pi$
$608$	1.54185e9	0.000457589 0
$609$	−1.21497e12	−0.357920
$610$	−3.97753e11	−0.116313
$611$	9.50050e11	0.275779
$612$	5.03158e11	0.144985
$613$	5.13743e12	1.46951	0.734757	−	0.678331i	$-0.237296\pi$
$613$	5.13743e12	1.46951	0.734757	+	0.678331i	$0.237296\pi$
$614$	2.77713e11	0.0788567
$615$	3.64465e12	1.02735
$616$	7.31548e10	0.0204706
$617$	−5.31905e12	−1.47758	−0.738790	−	0.673936i	$-0.764603\pi$
$617$	−5.31905e12	−1.47758	−0.738790	+	0.673936i	$0.764603\pi$
$618$	−1.43461e9	−0.000395626 0
$619$	−3.23470e12	−0.885577	−0.442789	−	0.896626i	$-0.646011\pi$
$619$	−3.23470e12	−0.885577	−0.442789	+	0.896626i	$0.646011\pi$
$620$	7.37337e12	2.00403
$621$	−3.25222e10	−0.00877540
$622$	−1.43866e11	−0.0385391
$623$	−7.40989e11	−0.197068
$624$	−6.10247e12	−1.61129
$625$	−4.67554e12	−1.22566
$626$	−3.49844e11	−0.0910521
$627$	9.04353e9	0.00233687
$628$	2.26763e12	0.581773
$629$	1.00622e12	0.256309
$630$	−4.30448e10	−0.0108865
$631$	−7.91021e12	−1.98635	−0.993175	−	0.116630i	$-0.962791\pi$
$631$	−7.91021e12	−1.98635	−0.993175	+	0.116630i	$0.962791\pi$
$632$	−3.24733e11	−0.0809654
$633$	6.17242e12	1.52805
$634$	1.22483e10	0.00301074
$635$	7.97501e12	1.94648
$636$	5.39919e12	1.30849
$637$	4.89591e12	1.17816
$638$	1.45580e11	0.0347863
$639$	−3.86908e12	−0.918023
$640$	−1.05967e12	−0.249668
$641$	−2.28438e12	−0.534451	−0.267225	−	0.963634i	$-0.586107\pi$
$641$	−2.28438e12	−0.534451	−0.267225	+	0.963634i	$0.586107\pi$
$642$	−3.38817e11	−0.0787150
$643$	7.52203e11	0.173534	0.0867672	−	0.996229i	$-0.472346\pi$
$643$	7.52203e11	0.173534	0.0867672	+	0.996229i	$0.472346\pi$
$644$	2.17765e10	0.00498886
$645$	−8.23209e12	−1.87280
$646$	−1.64392e8	−3.71394e−5 0
$647$	−4.59159e12	−1.03013	−0.515067	−	0.857150i	$-0.672233\pi$
$647$	−4.59159e12	−1.03013	−0.515067	+	0.857150i	$0.672233\pi$
$648$	−6.02884e11	−0.134322
$649$	−5.91064e12	−1.30778
$650$	1.09142e11	0.0239818
$651$	−2.90172e12	−0.633201
$652$	−1.35891e12	−0.294495
$653$	4.27664e12	0.920436	0.460218	−	0.887806i	$-0.347771\pi$
$653$	4.27664e12	0.920436	0.460218	+	0.887806i	$0.347771\pi$
$654$	−1.51294e11	−0.0323386
$655$	−7.36542e12	−1.56355
$656$	−3.29413e12	−0.694502
$657$	−1.75455e12	−0.367385
$658$	−1.61591e10	−0.00336048
$659$	−8.26860e12	−1.70784	−0.853920	−	0.520404i	$-0.825782\pi$
$659$	−8.26860e12	−1.70784	−0.853920	+	0.520404i	$0.825782\pi$
$660$	−4.66385e12	−0.956746
$661$	4.45784e12	0.908276	0.454138	−	0.890931i	$-0.349947\pi$
$661$	4.45784e12	0.908276	0.454138	+	0.890931i	$0.349947\pi$
$662$	2.63667e11	0.0533574
$663$	1.96159e12	0.394272
$664$	4.33005e11	0.0864442
$665$	−4.76664e9	−0.000945182 0
$666$	1.74483e11	0.0343652
$667$	8.67994e10	0.0169805
$668$	8.08246e12	1.57054
$669$	−4.37112e12	−0.843676
$670$	−2.52585e11	−0.0484251
$671$	6.35705e12	1.21061
$672$	3.12923e11	0.0591938
$673$	3.90397e12	0.733566	0.366783	−	0.930307i	$-0.380459\pi$
$673$	3.90397e12	0.733566	0.366783	+	0.930307i	$0.380459\pi$
$674$	4.08959e11	0.0763326
$675$	−9.39656e11	−0.174222
$676$	−3.53030e12	−0.650207
$677$	4.84414e12	0.886273	0.443137	−	0.896454i	$-0.353866\pi$
$677$	4.84414e12	0.886273	0.443137	+	0.896454i	$0.353866\pi$
$678$	−4.56725e11	−0.0830082
$679$	1.81603e12	0.327876
$680$	1.69808e11	0.0304557
$681$	7.90761e12	1.40891
$682$	3.47691e11	0.0615409
$683$	−3.67160e12	−0.645598	−0.322799	−	0.946468i	$-0.604624\pi$
$683$	−3.67160e12	−0.645598	−0.322799	+	0.946468i	$0.604624\pi$
$684$	9.66179e9	0.00168774
$685$	−8.51105e12	−1.47698
$686$	−1.74122e11	−0.0300189
$687$	1.17431e13	2.01130
$688$	7.44037e12	1.26604
$689$	7.88969e12	1.33375
$690$	8.20436e9	0.00137792
$691$	3.94359e12	0.658023	0.329011	−	0.944326i	$-0.393285\pi$
$691$	3.94359e12	0.658023	0.329011	+	0.944326i	$0.393285\pi$
$692$	6.53371e12	1.08314
$693$	6.87960e11	0.113309
$694$	2.00340e10	0.00327831
$695$	−2.52104e12	−0.409873
$696$	8.31117e11	0.134252
$697$	1.05887e12	0.169940
$698$	−1.98238e11	−0.0316109
$699$	−7.73131e12	−1.22492
$700$	6.29184e11	0.0990459
$701$	−9.80834e12	−1.53414	−0.767069	−	0.641564i	$-0.778286\pi$
$701$	−9.80834e12	−1.53414	−0.767069	+	0.641564i	$0.778286\pi$
$702$	−2.27188e11	−0.0353077
$703$	1.93217e10	0.00298364
$704$	4.19025e12	0.642928
$705$	2.06343e12	0.314585
$706$	−3.54887e11	−0.0537613
$707$	2.05304e12	0.309037
$708$	−1.68471e13	−2.51986
$709$	4.04313e12	0.600910	0.300455	−	0.953796i	$-0.402861\pi$
$709$	4.04313e12	0.600910	0.300455	+	0.953796i	$0.402861\pi$
$710$	−6.51915e11	−0.0962783
$711$	−3.05384e12	−0.448160
$712$	5.06886e11	0.0739180
$713$	2.07305e11	0.0300404
$714$	−3.33640e10	−0.00480437
$715$	−6.81515e12	−0.975211
$716$	4.25381e12	0.604880
$717$	6.51422e12	0.920505
$718$	−2.87327e11	−0.0403475
$719$	−4.48823e12	−0.626319	−0.313159	−	0.949701i	$-0.601387\pi$
$719$	−4.48823e12	−0.626319	−0.313159	+	0.949701i	$0.601387\pi$
$720$	−4.96795e12	−0.688939
$721$	−1.20851e10	−0.00166549
$722$	3.96020e11	0.0542374
$723$	6.43553e12	0.875915
$724$	4.44250e12	0.600903
$725$	2.50788e12	0.337121
$726$	2.93548e11	0.0392162
$727$	−1.02503e13	−1.36092	−0.680459	−	0.732786i	$-0.738220\pi$
$727$	−1.02503e13	−1.36092	−0.680459	+	0.732786i	$0.738220\pi$
$728$	3.04695e11	0.0402044
$729$	−7.85147e11	−0.102962
$730$	−2.95631e11	−0.0385298
$731$	−2.39164e12	−0.309791
$732$	1.81195e13	2.33264
$733$	−1.77332e12	−0.226892	−0.113446	−	0.993544i	$-0.536189\pi$
$733$	−1.77332e12	−0.226892	−0.113446	+	0.993544i	$0.536189\pi$
$734$	1.33688e11	0.0170004
$735$	1.06335e13	1.34395
$736$	−2.23558e10	−0.00280828
$737$	4.03691e12	0.504018
$738$	1.83613e11	0.0227850
$739$	2.07204e12	0.255563	0.127781	−	0.991802i	$-0.459214\pi$
$739$	2.07204e12	0.255563	0.127781	+	0.991802i	$0.459214\pi$
$740$	−9.96441e12	−1.22154
$741$	3.76669e10	0.00458963
$742$	−1.34193e11	−0.0162523
$743$	7.60966e12	0.916042	0.458021	−	0.888941i	$-0.348558\pi$
$743$	7.60966e12	0.916042	0.458021	+	0.888941i	$0.348558\pi$
$744$	1.98497e12	0.237507
$745$	−3.46616e12	−0.412236
$746$	8.37909e11	0.0990541
$747$	4.07205e12	0.478487
$748$	−1.35497e12	−0.158261
$749$	−2.85419e12	−0.331371
$750$	−4.52045e11	−0.0521682
$751$	−7.56877e12	−0.868252	−0.434126	−	0.900852i	$-0.642943\pi$
$751$	−7.56877e12	−0.868252	−0.434126	+	0.900852i	$0.642943\pi$
$752$	−1.86498e12	−0.212664
$753$	−1.65884e13	−1.88030
$754$	6.06350e11	0.0683207
$755$	2.67592e12	0.299718
$756$	−1.30970e12	−0.145822
$757$	−6.86633e12	−0.759965	−0.379982	−	0.924994i	$-0.624070\pi$
$757$	−6.86633e12	−0.759965	−0.379982	+	0.924994i	$0.624070\pi$
$758$	−2.30290e11	−0.0253375
$759$	−1.31125e11	−0.0143416
$760$	3.26070e9	0.000354528 0
$761$	9.51816e12	1.02878	0.514389	−	0.857557i	$-0.328019\pi$
$761$	9.51816e12	1.02878	0.514389	+	0.857557i	$0.328019\pi$
$762$	1.07189e12	0.115173
$763$	−1.27450e12	−0.136138
$764$	−1.17188e13	−1.24441
$765$	1.59690e12	0.168579
$766$	−1.24513e11	−0.0130672
$767$	−2.46182e13	−2.56849
$768$	1.18363e13	1.22769
$769$	−6.30061e12	−0.649702	−0.324851	−	0.945765i	$-0.605314\pi$
$769$	−6.30061e12	−0.649702	−0.324851	+	0.945765i	$0.605314\pi$
$770$	1.15917e11	0.0118833
$771$	3.40003e12	0.346528
$772$	−1.04490e13	−1.05876
$773$	−1.40318e13	−1.41354	−0.706768	−	0.707446i	$-0.749847\pi$
$773$	−1.40318e13	−1.41354	−0.706768	+	0.707446i	$0.749847\pi$
$774$	−4.14722e11	−0.0415358
$775$	5.98961e12	0.596404
$776$	−1.24229e12	−0.122983
$777$	3.92140e12	0.385964
$778$	5.67057e11	0.0554905
$779$	2.03327e10	0.00197823
$780$	−1.94252e13	−1.87906
$781$	1.04192e13	1.00208
$782$	2.38359e9	0.000227930 0
$783$	−5.22036e12	−0.496333
$784$	−9.61082e12	−0.908528
$785$	7.19691e12	0.676445
$786$	−9.89955e11	−0.0925154
$787$	1.03038e13	0.957440	0.478720	−	0.877968i	$-0.341101\pi$
$787$	1.03038e13	0.957440	0.478720	+	0.877968i	$0.341101\pi$
$788$	−2.96602e12	−0.274035
$789$	6.65440e12	0.611312
$790$	−5.14553e11	−0.0470011
$791$	−3.84744e12	−0.349444
$792$	−4.70610e11	−0.0425009
$793$	2.64776e13	2.37765
$794$	−1.07116e12	−0.0956452
$795$	1.71357e13	1.52143
$796$	−2.29480e12	−0.202599
$797$	1.57641e13	1.38390	0.691952	−	0.721944i	$-0.256751\pi$
$797$	1.57641e13	1.38390	0.691952	+	0.721944i	$0.256751\pi$
$798$	−6.40665e8	−5.59265e−5 0
$799$	5.99481e11	0.0520373
$800$	−6.45923e11	−0.0557540
$801$	4.76684e12	0.409152
$802$	2.06304e11	0.0176086
$803$	4.72489e12	0.401026
$804$	1.15064e13	0.971154
$805$	6.91134e10	0.00580070
$806$	1.44816e12	0.120867
$807$	−1.66224e13	−1.37963
$808$	−1.40442e12	−0.115916
$809$	1.37214e13	1.12623	0.563117	−	0.826377i	$-0.309602\pi$
$809$	1.37214e13	1.12623	0.563117	+	0.826377i	$0.309602\pi$
$810$	−9.55295e11	−0.0779750
$811$	1.55198e13	1.25977	0.629887	−	0.776687i	$-0.283101\pi$
$811$	1.55198e13	1.25977	0.629887	+	0.776687i	$0.283101\pi$
$812$	3.49550e12	0.282168
$813$	−1.74241e13	−1.39876
$814$	−4.69871e11	−0.0375119
$815$	−4.31286e12	−0.342418
$816$	−3.85065e12	−0.304039
$817$	−4.59250e10	−0.00360620
$818$	8.58013e11	0.0670045
$819$	2.86540e12	0.222540
$820$	−1.04858e13	−0.809915
$821$	3.40134e12	0.261280	0.130640	−	0.991430i	$-0.458297\pi$
$821$	3.40134e12	0.261280	0.130640	+	0.991430i	$0.458297\pi$
$822$	−1.14393e12	−0.0873933
$823$	4.01848e12	0.305325	0.152663	−	0.988278i	$-0.451215\pi$
$823$	4.01848e12	0.305325	0.152663	+	0.988278i	$0.451215\pi$
$824$	8.26702e9	0.000624707 0
$825$	−3.78858e12	−0.284731
$826$	4.18724e11	0.0312981
$827$	−4.31147e12	−0.320517	−0.160258	−	0.987075i	$-0.551233\pi$
$827$	−4.31147e12	−0.320517	−0.160258	+	0.987075i	$0.551233\pi$
$828$	−1.40090e11	−0.0103579
$829$	4.42248e12	0.325215	0.162608	−	0.986691i	$-0.448010\pi$
$829$	4.42248e12	0.325215	0.162608	+	0.986691i	$0.448010\pi$
$830$	6.86114e11	0.0501816
$831$	1.64592e12	0.119730
$832$	1.74527e13	1.26272
$833$	3.08932e12	0.222310
$834$	−3.38843e11	−0.0242522
$835$	2.56518e13	1.82612
$836$	−2.60186e10	−0.00184228
$837$	−1.24679e13	−0.878068
$838$	−1.18854e12	−0.0832563
$839$	1.12787e13	0.785835	0.392917	−	0.919574i	$-0.371466\pi$
$839$	1.12787e13	0.785835	0.392917	+	0.919574i	$0.371466\pi$
$840$	6.61771e11	0.0458618
$841$	−5.74353e11	−0.0395910
$842$	6.72056e11	0.0460788
$843$	−1.84827e13	−1.26050
$844$	−1.77583e13	−1.20465
$845$	−1.12043e13	−0.756016
$846$	1.03953e11	0.00697701
$847$	2.47285e12	0.165090
$848$	−1.54877e13	−1.02850
$849$	−1.69819e13	−1.12177
$850$	6.88685e10	0.00452518
$851$	−2.80152e11	−0.0183110
$852$	2.96978e13	1.93084
$853$	−3.07683e12	−0.198991	−0.0994954	−	0.995038i	$-0.531723\pi$
$853$	−3.07683e12	−0.198991	−0.0994954	+	0.995038i	$0.531723\pi$
$854$	−4.50349e11	−0.0289727
$855$	3.06642e10	0.00196238
$856$	1.95246e12	0.124294
$857$	−3.10840e13	−1.96845	−0.984223	−	0.176930i	$-0.943383\pi$
$857$	−3.10840e13	−1.96845	−0.984223	+	0.176930i	$0.943383\pi$
$858$	−9.15996e11	−0.0577033
$859$	−7.61893e12	−0.477446	−0.238723	−	0.971088i	$-0.576729\pi$
$859$	−7.61893e12	−0.477446	−0.238723	+	0.971088i	$0.576729\pi$
$860$	2.36840e13	1.47643
$861$	4.12659e12	0.255904
$862$	−5.89908e11	−0.0363917
$863$	−2.61427e13	−1.60436	−0.802179	−	0.597083i	$-0.796326\pi$
$863$	−2.61427e13	−1.60436	−0.802179	+	0.597083i	$0.796326\pi$
$864$	1.34454e12	0.0820849
$865$	2.07364e13	1.25939
$866$	8.70801e11	0.0526124
$867$	1.23776e12	0.0743961
$868$	8.34837e12	0.499186
$869$	8.22380e12	0.489197
$870$	1.31694e12	0.0779345
$871$	1.68140e13	0.989896
$872$	8.71840e11	0.0510638
$873$	−1.16827e13	−0.680735
$874$	4.57703e7	2.65327e−6 0
$875$	−3.80802e12	−0.219615
$876$	1.34674e13	0.772706
$877$	−3.00641e13	−1.71613	−0.858065	−	0.513541i	$-0.828333\pi$
$877$	−3.00641e13	−1.71613	−0.858065	+	0.513541i	$0.828333\pi$
$878$	−1.43714e12	−0.0816158
$879$	−2.88626e13	−1.63074
$880$	1.33784e13	0.752023
$881$	−2.06409e13	−1.15435	−0.577175	−	0.816620i	$-0.695845\pi$
$881$	−2.06409e13	−1.15435	−0.577175	+	0.816620i	$0.695845\pi$
$882$	5.35702e11	0.0298067
$883$	1.85711e13	1.02805	0.514026	−	0.857774i	$-0.328153\pi$
$883$	1.85711e13	1.02805	0.514026	+	0.857774i	$0.328153\pi$
$884$	−5.64356e12	−0.310826
$885$	−5.34687e13	−2.92991
$886$	5.83017e11	0.0317855
$887$	1.35590e11	0.00735482	0.00367741	−	0.999993i	$-0.498829\pi$
$887$	1.35590e11	0.00735482	0.00367741	+	0.999993i	$0.498829\pi$
$888$	−2.68250e12	−0.144771
$889$	9.02957e12	0.484852
$890$	8.03182e11	0.0429101
$891$	1.52679e13	0.811578
$892$	1.25759e13	0.665115
$893$	1.15114e10	0.000605754 0
$894$	−4.65872e11	−0.0243920
$895$	1.35006e13	0.703313
$896$	−1.19980e12	−0.0621901
$897$	−5.46146e11	−0.0281672
$898$	1.14604e12	0.0588108
$899$	3.32759e13	1.69907
$900$	−4.04759e12	−0.205639
$901$	4.97839e12	0.251668
$902$	−4.94458e11	−0.0248714
$903$	−9.32064e12	−0.466499
$904$	2.63190e12	0.131073
$905$	1.40994e13	0.698688
$906$	3.59660e11	0.0177343
$907$	−1.36972e13	−0.672045	−0.336022	−	0.941854i	$-0.609082\pi$
$907$	−1.36972e13	−0.672045	−0.336022	+	0.941854i	$0.609082\pi$
$908$	−2.27505e13	−1.11072
$909$	−1.32074e13	−0.641622
$910$	4.82802e11	0.0233390
$911$	−2.24844e13	−1.08156	−0.540778	−	0.841165i	$-0.681870\pi$
$911$	−2.24844e13	−1.08156	−0.540778	+	0.841165i	$0.681870\pi$
$912$	−7.39413e10	−0.00353924
$913$	−1.09658e13	−0.522300
$914$	−1.57806e12	−0.0747938
$915$	5.75070e13	2.71223
$916$	−3.37853e13	−1.58562
$917$	−8.33936e12	−0.389467
$918$	−1.43356e11	−0.00666228
$919$	9.66637e12	0.447037	0.223519	−	0.974700i	$-0.428246\pi$
$919$	9.66637e12	0.447037	0.223519	+	0.974700i	$0.428246\pi$
$920$	−4.72781e10	−0.00217578
$921$	−4.01516e13	−1.83880
$922$	−6.36267e11	−0.0289968
$923$	4.33966e13	1.96810
$924$	−5.28056e12	−0.238318
$925$	−8.09439e12	−0.363535
$926$	9.53348e11	0.0426091
$927$	7.77444e10	0.00345788
$928$	−3.58850e12	−0.158835
$929$	8.19216e12	0.360851	0.180425	−	0.983589i	$-0.442253\pi$
$929$	8.19216e12	0.360851	0.180425	+	0.983589i	$0.442253\pi$
$930$	3.14527e12	0.137875
$931$	5.93219e10	0.00258786
$932$	2.22433e13	0.965667
$933$	2.08001e13	0.898665
$934$	−1.01712e11	−0.00437330
$935$	−4.30036e12	−0.184015
$936$	−1.96012e12	−0.0834723
$937$	3.49872e12	0.148279	0.0741396	−	0.997248i	$-0.476379\pi$
$937$	3.49872e12	0.148279	0.0741396	+	0.997248i	$0.476379\pi$
$938$	−2.85984e11	−0.0120623
$939$	5.05803e13	2.12318
$940$	−5.93656e12	−0.248004
$941$	−1.51926e12	−0.0631655	−0.0315827	−	0.999501i	$-0.510055\pi$
$941$	−1.51926e12	−0.0631655	−0.0315827	+	0.999501i	$0.510055\pi$
$942$	9.67307e11	0.0400254
$943$	−2.94811e11	−0.0121406
$944$	4.83263e13	1.98066
$945$	−4.15668e12	−0.169552
$946$	1.11682e12	0.0453391
$947$	−2.12785e13	−0.859738	−0.429869	−	0.902891i	$-0.641440\pi$
$947$	−2.12785e13	−0.859738	−0.429869	+	0.902891i	$0.641440\pi$
$948$	2.34403e13	0.942597
$949$	1.96795e13	0.787619
$950$	1.32243e9	5.26765e−5 0
$951$	−1.77085e12	−0.0702053
$952$	1.92262e11	0.00758626
$953$	9.61359e12	0.377544	0.188772	−	0.982021i	$-0.439549\pi$
$953$	9.61359e12	0.377544	0.188772	+	0.982021i	$0.439549\pi$
$954$	8.63276e11	0.0337429
$955$	−3.71927e13	−1.44691
$956$	−1.87417e13	−0.725684
$957$	−2.10479e13	−0.811157
$958$	2.55553e12	0.0980249
$959$	−9.63648e12	−0.367904
$960$	3.79057e13	1.44040
$961$	5.30339e13	2.00585
$962$	−1.95705e12	−0.0736738
$963$	1.83612e13	0.687992
$964$	−1.85153e13	−0.690531
$965$	−3.31627e13	−1.23106
$966$	9.28924e9	0.000343228 0
$967$	−1.08700e13	−0.399772	−0.199886	−	0.979819i	$-0.564057\pi$
$967$	−1.08700e13	−0.399772	−0.199886	+	0.979819i	$0.564057\pi$
$968$	−1.69159e12	−0.0619236
$969$	2.37678e10	0.000866028 0
$970$	−1.96846e12	−0.0713925
$971$	2.79438e13	1.00879	0.504393	−	0.863474i	$-0.331716\pi$
$971$	2.79438e13	1.00879	0.504393	+	0.863474i	$0.331716\pi$
$972$	2.94654e13	1.05880
$973$	−2.85441e12	−0.102096
$974$	3.30658e11	0.0117724
$975$	−1.57797e13	−0.559214
$976$	−5.19763e13	−1.83350
$977$	−1.49620e13	−0.525369	−0.262685	−	0.964882i	$-0.584608\pi$
$977$	−1.49620e13	−0.525369	−0.262685	+	0.964882i	$0.584608\pi$
$978$	−5.79674e11	−0.0202609
$979$	−1.28368e13	−0.446616
$980$	−3.05930e13	−1.05951
$981$	8.19893e12	0.282648
$982$	7.21350e10	0.00247540
$983$	2.54966e13	0.870946	0.435473	−	0.900202i	$-0.356581\pi$
$983$	2.54966e13	0.870946	0.435473	+	0.900202i	$0.356581\pi$
$984$	−2.82286e12	−0.0959869
$985$	−9.41343e12	−0.318629
$986$	3.82607e11	0.0128916
$987$	2.33628e12	0.0783605
$988$	−1.08369e11	−0.00361826
$989$	6.65884e11	0.0221317
$990$	−7.45702e11	−0.0246721
$991$	−9.59893e12	−0.316149	−0.158074	−	0.987427i	$-0.550529\pi$
$991$	−9.59893e12	−0.316149	−0.158074	+	0.987427i	$0.550529\pi$
$992$	−8.57047e12	−0.280997
$993$	−3.81209e13	−1.24420
$994$	−7.38119e11	−0.0239821
$995$	−7.28315e12	−0.235568
$996$	−3.12557e13	−1.00638
$997$	−3.17533e13	−1.01780	−0.508898	−	0.860827i	$-0.669947\pi$
$997$	−3.17533e13	−1.01780	−0.508898	+	0.860827i	$0.669947\pi$
$998$	3.84308e11	0.0122629
$999$	1.68492e13	0.535222

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.10.a.a.1.3	✓	5
3.2	odd	2		153.10.a.c.1.3		5
4.3	odd	2		272.10.a.f.1.1		5
17.16	even	2		289.10.a.a.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.a.a.1.3	✓	5	1.1	even	1	trivial
153.10.a.c.1.3		5	3.2	odd	2
272.10.a.f.1.1		5	4.3	odd	2
289.10.a.a.1.3		5	17.16	even	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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	17.a (trivial)

\(f(q)\)	\(=\)	\(q-1.22726 q^{2} +177.437 q^{3} -510.494 q^{4} -1620.18 q^{5} -217.762 q^{6} -1834.42 q^{7} +1254.87 q^{8} +11801.0 q^{9} +O(q^{10})\)	\(q-1.22726 q^{2} +177.437 q^{3} -510.494 q^{4} -1620.18 q^{5} -217.762 q^{6} -1834.42 q^{7} +1254.87 q^{8} +11801.0 q^{9} +1988.39 q^{10} -31779.3 q^{11} -90580.6 q^{12} -132363. q^{13} +2251.32 q^{14} -287481. q^{15} +259833. q^{16} -83521.0 q^{17} -14482.9 q^{18} -1603.79 q^{19} +827094. q^{20} -325495. q^{21} +39001.6 q^{22} +23254.0 q^{23} +222661. q^{24} +671873. q^{25} +162444. q^{26} -1.39856e6 q^{27} +936463. q^{28} +3.73267e6 q^{29} +352815. q^{30} +8.91479e6 q^{31} -961376. q^{32} -5.63884e6 q^{33} +102502. q^{34} +2.97211e6 q^{35} -6.02433e6 q^{36} -1.20475e7 q^{37} +1968.28 q^{38} -2.34861e7 q^{39} -2.03312e6 q^{40} -1.26779e7 q^{41} +399468. q^{42} +2.86352e7 q^{43} +1.62231e7 q^{44} -1.91198e7 q^{45} -28538.8 q^{46} -7.17761e6 q^{47} +4.61040e7 q^{48} -3.69885e7 q^{49} -824565. q^{50} -1.48197e7 q^{51} +6.75705e7 q^{52} -5.96065e7 q^{53} +1.71640e6 q^{54} +5.14884e7 q^{55} -2.30196e6 q^{56} -284573. q^{57} -4.58096e6 q^{58} +1.85990e8 q^{59} +1.46757e8 q^{60} -2.00037e8 q^{61} -1.09408e7 q^{62} -2.16480e7 q^{63} -1.31855e8 q^{64} +2.14453e8 q^{65} +6.92034e6 q^{66} -1.27030e8 q^{67} +4.26370e7 q^{68} +4.12613e6 q^{69} -3.64756e6 q^{70} -3.27860e8 q^{71} +1.48087e7 q^{72} -1.48678e8 q^{73} +1.47854e7 q^{74} +1.19215e8 q^{75} +818726. q^{76} +5.82968e7 q^{77} +2.88237e7 q^{78} -2.58778e8 q^{79} -4.20977e8 q^{80} -4.80436e8 q^{81} +1.55591e7 q^{82} +3.45060e8 q^{83} +1.66163e8 q^{84} +1.35319e8 q^{85} -3.51430e7 q^{86} +6.62314e8 q^{87} -3.98789e7 q^{88} +4.03936e8 q^{89} +2.34650e7 q^{90} +2.42810e8 q^{91} -1.18710e7 q^{92} +1.58182e9 q^{93} +8.80881e6 q^{94} +2.59844e6 q^{95} -1.70584e8 q^{96} -9.89973e8 q^{97} +4.53946e7 q^{98} -3.75028e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 33 q^{2} - 236 q^{3} + 853 q^{4} + 1480 q^{5} + 7578 q^{6} - 13202 q^{7} - 42423 q^{8} + 10981 q^{9}+O(q^{10}) \) 5 * q - 33 * q^2 - 236 * q^3 + 853 * q^4 + 1480 * q^5 + 7578 * q^6 - 13202 * q^7 - 42423 * q^8 + 10981 * q^9	\( 5 q - 33 q^{2} - 236 q^{3} + 853 q^{4} + 1480 q^{5} + 7578 q^{6} - 13202 q^{7} - 42423 q^{8} + 10981 q^{9} - 89328 q^{10} - 68036 q^{11} - 406010 q^{12} - 158862 q^{13} - 84700 q^{14} - 687324 q^{15} + 350225 q^{16} - 417605 q^{17} - 1911585 q^{18} - 370992 q^{19} + 1632640 q^{20} + 1783880 q^{21} + 122290 q^{22} + 1645870 q^{23} + 9678702 q^{24} + 3270239 q^{25} + 734846 q^{26} - 2998268 q^{27} + 183372 q^{28} + 3668616 q^{29} + 17048544 q^{30} - 7262362 q^{31} - 5605919 q^{32} - 11334900 q^{33} + 2756193 q^{34} - 26503988 q^{35} + 49782133 q^{36} - 31420708 q^{37} + 18513700 q^{38} - 42449884 q^{39} - 53930464 q^{40} - 7996938 q^{41} - 44519496 q^{42} - 56908268 q^{43} + 43323054 q^{44} + 12799536 q^{45} - 32063472 q^{46} - 16903336 q^{47} - 102794498 q^{48} - 11784059 q^{49} + 85921093 q^{50} + 19710956 q^{51} + 173619082 q^{52} - 83362982 q^{53} + 386329164 q^{54} + 6363364 q^{55} + 317409372 q^{56} + 136615904 q^{57} + 64577488 q^{58} - 37946604 q^{59} - 223158912 q^{60} - 77685452 q^{61} + 324855300 q^{62} - 191945278 q^{63} + 131623105 q^{64} - 40321288 q^{65} + 298037676 q^{66} - 304503600 q^{67} - 71243413 q^{68} - 333409272 q^{69} - 122787392 q^{70} - 476602922 q^{71} - 1301701911 q^{72} - 289980486 q^{73} + 262289012 q^{74} - 153685772 q^{75} - 1031276084 q^{76} - 143385648 q^{77} + 691646196 q^{78} - 828240610 q^{79} + 912750944 q^{80} + 891328609 q^{81} - 1109615654 q^{82} + 194681148 q^{83} + 1541719592 q^{84} - 123611080 q^{85} + 1164707144 q^{86} + 158149884 q^{87} - 1017979978 q^{88} + 376848106 q^{89} - 2240087472 q^{90} + 194543664 q^{91} + 2506713088 q^{92} + 3494835920 q^{93} - 2244811104 q^{94} + 1498679864 q^{95} + 2935047582 q^{96} + 692035246 q^{97} + 871744055 q^{98} + 2027106408 q^{99}+O(q^{100}) \) 5 * q - 33 * q^2 - 236 * q^3 + 853 * q^4 + 1480 * q^5 + 7578 * q^6 - 13202 * q^7 - 42423 * q^8 + 10981 * q^9 - 89328 * q^10 - 68036 * q^11 - 406010 * q^12 - 158862 * q^13 - 84700 * q^14 - 687324 * q^15 + 350225 * q^16 - 417605 * q^17 - 1911585 * q^18 - 370992 * q^19 + 1632640 * q^20 + 1783880 * q^21 + 122290 * q^22 + 1645870 * q^23 + 9678702 * q^24 + 3270239 * q^25 + 734846 * q^26 - 2998268 * q^27 + 183372 * q^28 + 3668616 * q^29 + 17048544 * q^30 - 7262362 * q^31 - 5605919 * q^32 - 11334900 * q^33 + 2756193 * q^34 - 26503988 * q^35 + 49782133 * q^36 - 31420708 * q^37 + 18513700 * q^38 - 42449884 * q^39 - 53930464 * q^40 - 7996938 * q^41 - 44519496 * q^42 - 56908268 * q^43 + 43323054 * q^44 + 12799536 * q^45 - 32063472 * q^46 - 16903336 * q^47 - 102794498 * q^48 - 11784059 * q^49 + 85921093 * q^50 + 19710956 * q^51 + 173619082 * q^52 - 83362982 * q^53 + 386329164 * q^54 + 6363364 * q^55 + 317409372 * q^56 + 136615904 * q^57 + 64577488 * q^58 - 37946604 * q^59 - 223158912 * q^60 - 77685452 * q^61 + 324855300 * q^62 - 191945278 * q^63 + 131623105 * q^64 - 40321288 * q^65 + 298037676 * q^66 - 304503600 * q^67 - 71243413 * q^68 - 333409272 * q^69 - 122787392 * q^70 - 476602922 * q^71 - 1301701911 * q^72 - 289980486 * q^73 + 262289012 * q^74 - 153685772 * q^75 - 1031276084 * q^76 - 143385648 * q^77 + 691646196 * q^78 - 828240610 * q^79 + 912750944 * q^80 + 891328609 * q^81 - 1109615654 * q^82 + 194681148 * q^83 + 1541719592 * q^84 - 123611080 * q^85 + 1164707144 * q^86 + 158149884 * q^87 - 1017979978 * q^88 + 376848106 * q^89 - 2240087472 * q^90 + 194543664 * q^91 + 2506713088 * q^92 + 3494835920 * q^93 - 2244811104 * q^94 + 1498679864 * q^95 + 2935047582 * q^96 + 692035246 * q^97 + 871744055 * q^98 + 2027106408 * q^99

Introduction

L-functions

Modular forms

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