LMFDB - Embedded newform 17.8.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,8,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, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("17.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 8 $
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:	$5.31054543323$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 604x^{4} + 760x^{3} + 102128x^{2} - 41712x - 4749120 $ x^6 - 3x^5 - 604x^4 + 760x^3 + 102128x^2 - 41712*x - 4749120
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-8.77791$ 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)

$f(q)$	$=$	$q-6.77791 q^{2} -52.1459 q^{3} -82.0600 q^{4} +356.107 q^{5} +353.440 q^{6} +248.464 q^{7} +1423.77 q^{8} +532.198 q^{9} +O(q^{10})$	\(q-6.77791 q^{2} -52.1459 q^{3} -82.0600 q^{4} +356.107 q^{5} +353.440 q^{6} +248.464 q^{7} +1423.77 q^{8} +532.198 q^{9} -2413.66 q^{10} +6309.04 q^{11} +4279.09 q^{12} -595.847 q^{13} -1684.07 q^{14} -18569.6 q^{15} +853.516 q^{16} -4913.00 q^{17} -3607.19 q^{18} +1253.07 q^{19} -29222.2 q^{20} -12956.4 q^{21} -42762.1 q^{22} +102061. q^{23} -74243.7 q^{24} +48687.5 q^{25} +4038.59 q^{26} +86291.2 q^{27} -20389.0 q^{28} -22275.3 q^{29} +125863. q^{30} +281828. q^{31} -188027. q^{32} -328991. q^{33} +33299.9 q^{34} +88480.0 q^{35} -43672.1 q^{36} +181257. q^{37} -8493.16 q^{38} +31071.0 q^{39} +507014. q^{40} -443891. q^{41} +87817.3 q^{42} +269359. q^{43} -517720. q^{44} +189520. q^{45} -691758. q^{46} -1.23339e6 q^{47} -44507.4 q^{48} -761808. q^{49} -329999. q^{50} +256193. q^{51} +48895.2 q^{52} +1.61126e6 q^{53} -584874. q^{54} +2.24670e6 q^{55} +353755. q^{56} -65342.3 q^{57} +150980. q^{58} +1.46192e6 q^{59} +1.52382e6 q^{60} -782676. q^{61} -1.91020e6 q^{62} +132232. q^{63} +1.16518e6 q^{64} -212185. q^{65} +2.22987e6 q^{66} +220097. q^{67} +403161. q^{68} -5.32205e6 q^{69} -599709. q^{70} -3.29315e6 q^{71} +757726. q^{72} +4.05380e6 q^{73} -1.22855e6 q^{74} -2.53885e6 q^{75} -102827. q^{76} +1.56757e6 q^{77} -210596. q^{78} -2.56326e6 q^{79} +303943. q^{80} -5.66365e6 q^{81} +3.00865e6 q^{82} +292814. q^{83} +1.06320e6 q^{84} -1.74956e6 q^{85} -1.82569e6 q^{86} +1.16157e6 q^{87} +8.98261e6 q^{88} +1.06095e6 q^{89} -1.28455e6 q^{90} -148047. q^{91} -8.37510e6 q^{92} -1.46962e7 q^{93} +8.35981e6 q^{94} +446226. q^{95} +9.80485e6 q^{96} +1.57192e7 q^{97} +5.16347e6 q^{98} +3.35766e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 15 q^{2} + 40 q^{3} + 485 q^{4} - 184 q^{5} + 1882 q^{6} + 2064 q^{7} + 6729 q^{8} + 5846 q^{9}+O(q^{10}) $ 6 * q + 15 * q^2 + 40 * q^3 + 485 * q^4 - 184 * q^5 + 1882 * q^6 + 2064 * q^7 + 6729 * q^8 + 5846 * q^9	\( 6 q + 15 q^{2} + 40 q^{3} + 485 q^{4} - 184 q^{5} + 1882 q^{6} + 2064 q^{7} + 6729 q^{8} + 5846 q^{9} + 5592 q^{10} + 2000 q^{11} + 3646 q^{12} + 8708 q^{13} - 19844 q^{14} + 12552 q^{15} + 5841 q^{16} - 29478 q^{17} - 108697 q^{18} - 45400 q^{19} - 202744 q^{20} - 37896 q^{21} + 1378 q^{22} - 27208 q^{23} + 21366 q^{24} + 281826 q^{25} + 69094 q^{26} + 126520 q^{27} - 29428 q^{28} + 404808 q^{29} - 441296 q^{30} + 532984 q^{31} + 790577 q^{32} + 848728 q^{33} - 73695 q^{34} + 358952 q^{35} - 619171 q^{36} + 437968 q^{37} - 778900 q^{38} + 114856 q^{39} - 2458744 q^{40} - 441660 q^{41} - 1730952 q^{42} + 1152240 q^{43} - 1798650 q^{44} - 1089768 q^{45} - 897816 q^{46} - 90296 q^{47} + 852006 q^{48} + 692566 q^{49} - 834883 q^{50} - 196520 q^{51} + 2801826 q^{52} - 137764 q^{53} - 856340 q^{54} + 4133896 q^{55} - 191892 q^{56} - 674928 q^{57} + 4396216 q^{58} - 2050080 q^{59} + 1738352 q^{60} + 89808 q^{61} + 5080332 q^{62} - 828312 q^{63} + 14723105 q^{64} - 3447008 q^{65} - 2276164 q^{66} + 4686632 q^{67} - 2382805 q^{68} - 10069560 q^{69} + 16450144 q^{70} - 5553232 q^{71} - 7683039 q^{72} - 1436452 q^{73} + 1443964 q^{74} - 23179128 q^{75} - 5332908 q^{76} - 12631512 q^{77} - 7122876 q^{78} + 12387160 q^{79} - 26552696 q^{80} - 5930674 q^{81} + 20716762 q^{82} - 1877808 q^{83} - 7443960 q^{84} + 903992 q^{85} - 8020112 q^{86} + 19832472 q^{87} + 8442878 q^{88} - 19324324 q^{89} + 36660344 q^{90} + 14536792 q^{91} - 25909888 q^{92} - 13862632 q^{93} + 9307536 q^{94} + 3085936 q^{95} + 18152550 q^{96} - 7630812 q^{97} + 22758631 q^{98} + 25069976 q^{99}+O(q^{100}) \) 6 * q + 15 * q^2 + 40 * q^3 + 485 * q^4 - 184 * q^5 + 1882 * q^6 + 2064 * q^7 + 6729 * q^8 + 5846 * q^9 + 5592 * q^10 + 2000 * q^11 + 3646 * q^12 + 8708 * q^13 - 19844 * q^14 + 12552 * q^15 + 5841 * q^16 - 29478 * q^17 - 108697 * q^18 - 45400 * q^19 - 202744 * q^20 - 37896 * q^21 + 1378 * q^22 - 27208 * q^23 + 21366 * q^24 + 281826 * q^25 + 69094 * q^26 + 126520 * q^27 - 29428 * q^28 + 404808 * q^29 - 441296 * q^30 + 532984 * q^31 + 790577 * q^32 + 848728 * q^33 - 73695 * q^34 + 358952 * q^35 - 619171 * q^36 + 437968 * q^37 - 778900 * q^38 + 114856 * q^39 - 2458744 * q^40 - 441660 * q^41 - 1730952 * q^42 + 1152240 * q^43 - 1798650 * q^44 - 1089768 * q^45 - 897816 * q^46 - 90296 * q^47 + 852006 * q^48 + 692566 * q^49 - 834883 * q^50 - 196520 * q^51 + 2801826 * q^52 - 137764 * q^53 - 856340 * q^54 + 4133896 * q^55 - 191892 * q^56 - 674928 * q^57 + 4396216 * q^58 - 2050080 * q^59 + 1738352 * q^60 + 89808 * q^61 + 5080332 * q^62 - 828312 * q^63 + 14723105 * q^64 - 3447008 * q^65 - 2276164 * q^66 + 4686632 * q^67 - 2382805 * q^68 - 10069560 * q^69 + 16450144 * q^70 - 5553232 * q^71 - 7683039 * q^72 - 1436452 * q^73 + 1443964 * q^74 - 23179128 * q^75 - 5332908 * q^76 - 12631512 * q^77 - 7122876 * q^78 + 12387160 * q^79 - 26552696 * q^80 - 5930674 * q^81 + 20716762 * q^82 - 1877808 * q^83 - 7443960 * q^84 + 903992 * q^85 - 8020112 * q^86 + 19832472 * q^87 + 8442878 * q^88 - 19324324 * q^89 + 36660344 * q^90 + 14536792 * q^91 - 25909888 * q^92 - 13862632 * q^93 + 9307536 * q^94 + 3085936 * q^95 + 18152550 * q^96 - 7630812 * q^97 + 22758631 * q^98 + 25069976 * 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 $

$2$	−6.77791	−0.599088	−0.299544	−	0.954082i	$-0.596835\pi$
$2$	−6.77791	−0.599088	−0.299544	+	0.954082i	$0.596835\pi$
$3$	−52.1459	−1.11505	−0.557527	−	0.830159i	$-0.688250\pi$
$3$	−52.1459	−1.11505	−0.557527	+	0.830159i	$0.688250\pi$
$4$	−82.0600	−0.641094
$5$	356.107	1.27405	0.637024	−	0.770844i	$-0.280165\pi$
$5$	356.107	1.27405	0.637024	+	0.770844i	$0.280165\pi$
$6$	353.440	0.668016
$7$	248.464	0.273792	0.136896	−	0.990585i	$-0.456287\pi$
$7$	248.464	0.273792	0.136896	+	0.990585i	$0.456287\pi$
$8$	1423.77	0.983159
$9$	532.198	0.243346
$10$	−2413.66	−0.763267
$11$	6309.04	1.42919	0.714593	−	0.699540i	$-0.246612\pi$
$11$	6309.04	1.42919	0.714593	+	0.699540i	$0.246612\pi$
$12$	4279.09	0.714854
$13$	−595.847	−0.0752199	−0.0376100	−	0.999292i	$-0.511974\pi$
$13$	−595.847	−0.0752199	−0.0376100	+	0.999292i	$0.511974\pi$
$14$	−1684.07	−0.164026
$15$	−18569.6	−1.42063
$16$	853.516	0.0520945
$17$	−4913.00	−0.242536
$17$	−4913.00	−0.242536
$18$	−3607.19	−0.145786
$19$	1253.07	0.0419118	0.0209559	−	0.999780i	$-0.493329\pi$
$19$	1253.07	0.0419118	0.0209559	+	0.999780i	$0.493329\pi$
$20$	−29222.2	−0.816784
$21$	−12956.4	−0.305293
$22$	−42762.1	−0.856209
$23$	102061.	1.74909	0.874544	−	0.484947i	$-0.161161\pi$
$23$	102061.	1.74909	0.874544	+	0.484947i	$0.161161\pi$
$24$	−74243.7	−1.09628
$25$	48687.5	0.623200
$26$	4038.59	0.0450634
$27$	86291.2	0.843710
$28$	−20389.0	−0.175526
$29$	−22275.3	−0.169602	−0.0848009	−	0.996398i	$-0.527025\pi$
$29$	−22275.3	−0.169602	−0.0848009	+	0.996398i	$0.527025\pi$
$30$	125863.	0.851084
$31$	281828.	1.69910	0.849548	−	0.527511i	$-0.176875\pi$
$31$	281828.	1.69910	0.849548	+	0.527511i	$0.176875\pi$
$32$	−188027.	−1.01437
$33$	−328991.	−1.59362
$34$	33299.9	0.145300
$35$	88480.0	0.348824
$36$	−43672.1	−0.156008
$37$	181257.	0.588288	0.294144	−	0.955761i	$-0.404966\pi$
$37$	181257.	0.588288	0.294144	+	0.955761i	$0.404966\pi$
$38$	−8493.16	−0.0251089
$39$	31071.0	0.0838743
$40$	507014.	1.25259
$41$	−443891.	−1.00585	−0.502924	−	0.864331i	$-0.667742\pi$
$41$	−443891.	−1.00585	−0.502924	+	0.864331i	$0.667742\pi$
$42$	87817.3	0.182897
$43$	269359.	0.516645	0.258323	−	0.966059i	$-0.416830\pi$
$43$	269359.	0.516645	0.258323	+	0.966059i	$0.416830\pi$
$44$	−517720.	−0.916243
$45$	189520.	0.310035
$46$	−691758.	−1.04786
$47$	−1.23339e6	−1.73284	−0.866419	−	0.499317i	$-0.833584\pi$
$47$	−1.23339e6	−1.73284	−0.866419	+	0.499317i	$0.833584\pi$
$48$	−44507.4	−0.0580882
$49$	−761808.	−0.925038
$50$	−329999.	−0.373352
$51$	256193.	0.270440
$52$	48895.2	0.0482230
$53$	1.61126e6	1.48662	0.743311	−	0.668946i	$-0.233254\pi$
$53$	1.61126e6	1.48662	0.743311	+	0.668946i	$0.233254\pi$
$54$	−584874.	−0.505457
$55$	2.24670e6	1.82085
$56$	353755.	0.269181
$57$	−65342.3	−0.0467339
$58$	150980.	0.101606
$59$	1.46192e6	0.926703	0.463351	−	0.886175i	$-0.346647\pi$
$59$	1.46192e6	0.926703	0.463351	+	0.886175i	$0.346647\pi$
$60$	1.52382e6	0.910759
$61$	−782676.	−0.441497	−0.220748	−	0.975331i	$-0.570850\pi$
$61$	−782676.	−0.441497	−0.220748	+	0.975331i	$0.570850\pi$
$62$	−1.91020e6	−1.01791
$63$	132232.	0.0666262
$64$	1.16518e6	0.555602
$65$	−212185.	−0.0958338
$66$	2.22987e6	0.954719
$67$	220097.	0.0894030	0.0447015	−	0.999000i	$-0.485766\pi$
$67$	220097.	0.0894030	0.0447015	+	0.999000i	$0.485766\pi$
$68$	403161.	0.155488
$69$	−5.32205e6	−1.95033
$70$	−599709.	−0.208977
$71$	−3.29315e6	−1.09196	−0.545981	−	0.837797i	$-0.683843\pi$
$71$	−3.29315e6	−1.09196	−0.545981	+	0.837797i	$0.683843\pi$
$72$	757726.	0.239248
$73$	4.05380e6	1.21964	0.609821	−	0.792540i	$-0.291242\pi$
$73$	4.05380e6	1.21964	0.609821	+	0.792540i	$0.291242\pi$
$74$	−1.22855e6	−0.352436
$75$	−2.53885e6	−0.694902
$76$	−102827.	−0.0268694
$77$	1.56757e6	0.391300
$78$	−210596.	−0.0502481
$79$	−2.56326e6	−0.584923	−0.292461	−	0.956277i	$-0.594474\pi$
$79$	−2.56326e6	−0.584923	−0.292461	+	0.956277i	$0.594474\pi$
$80$	303943.	0.0663709
$81$	−5.66365e6	−1.18413
$82$	3.00865e6	0.602592
$83$	292814.	0.0562107	0.0281053	−	0.999605i	$-0.491053\pi$
$83$	292814.	0.0562107	0.0281053	+	0.999605i	$0.491053\pi$
$84$	1.06320e6	0.195721
$85$	−1.74956e6	−0.309002
$86$	−1.82569e6	−0.309516
$87$	1.16157e6	0.189115
$88$	8.98261e6	1.40512
$89$	1.06095e6	0.159525	0.0797625	−	0.996814i	$-0.474584\pi$
$89$	1.06095e6	0.159525	0.0797625	+	0.996814i	$0.474584\pi$
$90$	−1.28455e6	−0.185738
$91$	−148047.	−0.0205946
$92$	−8.37510e6	−1.12133
$93$	−1.46962e7	−1.89458
$94$	8.35981e6	1.03812
$95$	446226.	0.0533977
$96$	9.80485e6	1.13108
$97$	1.57192e7	1.74876	0.874379	−	0.485243i	$-0.161269\pi$
$97$	1.57192e7	1.74876	0.874379	+	0.485243i	$0.161269\pi$
$98$	5.16347e6	0.554179
$99$	3.35766e6	0.347787
$100$	−3.99529e6	−0.399529
$101$	7.45362e6	0.719851	0.359925	−	0.932981i	$-0.382802\pi$
$101$	7.45362e6	0.719851	0.359925	+	0.932981i	$0.382802\pi$
$102$	−1.73645e6	−0.162018
$103$	5.96983e6	0.538309	0.269155	−	0.963097i	$-0.413256\pi$
$103$	5.96983e6	0.538309	0.269155	+	0.963097i	$0.413256\pi$
$104$	−848347.	−0.0739532
$105$	−4.61387e6	−0.388958
$106$	−1.09210e7	−0.890617
$107$	1.87295e7	1.47803	0.739013	−	0.673692i	$-0.235292\pi$
$107$	1.87295e7	1.47803	0.739013	+	0.673692i	$0.235292\pi$
$108$	−7.08105e6	−0.540897
$109$	−2.27165e7	−1.68015	−0.840077	−	0.542468i	$-0.817490\pi$
$109$	−2.27165e7	−1.68015	−0.840077	+	0.542468i	$0.817490\pi$
$110$	−1.52279e7	−1.09085
$111$	−9.45183e6	−0.655973
$112$	212068.	0.0142631
$113$	−1.28328e6	−0.0836654	−0.0418327	−	0.999125i	$-0.513320\pi$
$113$	−1.28328e6	−0.0836654	−0.0418327	+	0.999125i	$0.513320\pi$
$114$	442884.	0.0279977
$115$	3.63446e7	2.22842
$116$	1.82791e6	0.108731
$117$	−317108.	−0.0183045
$118$	−9.90873e6	−0.555177
$119$	−1.22071e6	−0.0664043
$120$	−2.64387e7	−1.39671
$121$	2.03168e7	1.04258
$122$	5.30491e6	0.264495
$123$	2.31471e7	1.12158
$124$	−2.31268e7	−1.08928
$125$	−1.04829e7	−0.480062
$126$	−896257.	−0.0399150
$127$	−3.27329e7	−1.41799	−0.708993	−	0.705215i	$-0.750850\pi$
$127$	−3.27329e7	−1.41799	−0.708993	+	0.705215i	$0.750850\pi$
$128$	1.61700e7	0.681514
$129$	−1.40460e7	−0.576087
$130$	1.43817e6	0.0574129
$131$	−4.75407e7	−1.84764	−0.923818	−	0.382833i	$-0.874949\pi$
$131$	−4.75407e7	−1.84764	−0.923818	+	0.382833i	$0.874949\pi$
$132$	2.69970e7	1.02166
$133$	311342.	0.0114751
$134$	−1.49180e6	−0.0535603
$135$	3.07289e7	1.07493
$136$	−6.99497e6	−0.238451
$137$	−1.17215e7	−0.389459	−0.194729	−	0.980857i	$-0.562383\pi$
$137$	−1.17215e7	−0.389459	−0.194729	+	0.980857i	$0.562383\pi$
$138$	3.60724e7	1.16842
$139$	−1.43156e7	−0.452123	−0.226062	−	0.974113i	$-0.572585\pi$
$139$	−1.43156e7	−0.452123	−0.226062	+	0.974113i	$0.572585\pi$
$140$	−7.26067e6	−0.223629
$141$	6.43163e7	1.93221
$142$	2.23207e7	0.654182
$143$	−3.75922e6	−0.107503
$144$	454239.	0.0126770
$145$	−7.93240e6	−0.216081
$146$	−2.74763e7	−0.730672
$147$	3.97252e7	1.03147
$148$	−1.48740e7	−0.377147
$149$	−4.58062e7	−1.13441	−0.567207	−	0.823575i	$-0.691976\pi$
$149$	−4.58062e7	−1.13441	−0.567207	+	0.823575i	$0.691976\pi$
$150$	1.72081e7	0.416307
$151$	7.31169e7	1.72822	0.864109	−	0.503305i	$-0.167883\pi$
$151$	7.31169e7	1.72822	0.864109	+	0.503305i	$0.167883\pi$
$152$	1.78407e6	0.0412060
$153$	−2.61469e6	−0.0590201
$154$	−1.06249e7	−0.234423
$155$	1.00361e8	2.16473
$156$	−2.54968e6	−0.0537713
$157$	−1.46130e7	−0.301363	−0.150681	−	0.988582i	$-0.548147\pi$
$157$	−1.46130e7	−0.301363	−0.150681	+	0.988582i	$0.548147\pi$
$158$	1.73736e7	0.350420
$159$	−8.40207e7	−1.65766
$160$	−6.69579e7	−1.29236
$161$	2.53585e7	0.478886
$162$	3.83877e7	0.709397
$163$	−6.26397e7	−1.13290	−0.566452	−	0.824095i	$-0.691684\pi$
$163$	−6.26397e7	−1.13290	−0.566452	+	0.824095i	$0.691684\pi$
$164$	3.64256e7	0.644843
$165$	−1.17156e8	−2.03035
$166$	−1.98467e6	−0.0336751
$167$	7.05687e7	1.17248	0.586239	−	0.810139i	$-0.300608\pi$
$167$	7.05687e7	1.17248	0.586239	+	0.810139i	$0.300608\pi$
$168$	−1.84469e7	−0.300152
$169$	−6.23935e7	−0.994342
$170$	1.18583e7	0.185120
$171$	666879.	0.0101991
$172$	−2.21036e7	−0.331218
$173$	−1.16141e8	−1.70540	−0.852699	−	0.522402i	$-0.825036\pi$
$173$	−1.16141e8	−1.70540	−0.852699	+	0.522402i	$0.825036\pi$
$174$	−7.87299e6	−0.113297
$175$	1.20971e7	0.170627
$176$	5.38487e6	0.0744527
$177$	−7.62330e7	−1.03332
$178$	−7.19100e6	−0.0955695
$179$	4.25745e7	0.554835	0.277418	−	0.960749i	$-0.410521\pi$
$179$	4.25745e7	0.554835	0.277418	+	0.960749i	$0.410521\pi$
$180$	−1.55520e7	−0.198761
$181$	−4.84126e7	−0.606853	−0.303427	−	0.952855i	$-0.598131\pi$
$181$	−4.84126e7	−0.606853	−0.303427	+	0.952855i	$0.598131\pi$
$182$	1.00345e6	0.0123380
$183$	4.08134e7	0.492293
$184$	1.45311e8	1.71963
$185$	6.45471e7	0.749507
$186$	9.96093e7	1.13502
$187$	−3.09963e7	−0.346629
$188$	1.01212e8	1.11091
$189$	2.14403e7	0.231001
$190$	−3.02448e6	−0.0319899
$191$	6.69571e7	0.695312	0.347656	−	0.937622i	$-0.386978\pi$
$191$	6.69571e7	0.695312	0.347656	+	0.937622i	$0.386978\pi$
$192$	−6.07594e7	−0.619526
$193$	5.06056e7	0.506697	0.253349	−	0.967375i	$-0.418468\pi$
$193$	5.06056e7	0.506697	0.253349	+	0.967375i	$0.418468\pi$
$194$	−1.06543e8	−1.04766
$195$	1.10646e7	0.106860
$196$	6.25140e7	0.593036
$197$	1.88974e7	0.176105	0.0880523	−	0.996116i	$-0.471936\pi$
$197$	1.88974e7	0.176105	0.0880523	+	0.996116i	$0.471936\pi$
$198$	−2.27579e7	−0.208355
$199$	−7.33658e7	−0.659945	−0.329973	−	0.943991i	$-0.607040\pi$
$199$	−7.33658e7	−0.659945	−0.329973	+	0.943991i	$0.607040\pi$
$200$	6.93196e7	0.612705
$201$	−1.14772e7	−0.0996892
$202$	−5.05199e7	−0.431254
$203$	−5.53462e6	−0.0464356
$204$	−2.10232e7	−0.173378
$205$	−1.58073e8	−1.28150
$206$	−4.04630e7	−0.322495
$207$	5.43165e7	0.425633
$208$	−508565.	−0.00391854
$209$	7.90564e6	0.0598998
$210$	3.12724e7	0.233020
$211$	1.55641e8	1.14061	0.570304	−	0.821434i	$-0.306825\pi$
$211$	1.55641e8	1.14061	0.570304	+	0.821434i	$0.306825\pi$
$212$	−1.32220e8	−0.953063
$213$	1.71724e8	1.21760
$214$	−1.26947e8	−0.885467
$215$	9.59208e7	0.658231
$216$	1.22859e8	0.829502
$217$	7.00242e7	0.465199
$218$	1.53970e8	1.00656
$219$	−2.11389e8	−1.35997
$220$	−1.84364e8	−1.16734
$221$	2.92740e6	0.0182435
$222$	6.40637e7	0.392985
$223$	1.05522e8	0.637202	0.318601	−	0.947889i	$-0.396787\pi$
$223$	1.05522e8	0.637202	0.318601	+	0.947889i	$0.396787\pi$
$224$	−4.67181e7	−0.277726
$225$	2.59114e7	0.151653
$226$	8.69794e6	0.0501230
$227$	−1.69209e8	−0.960138	−0.480069	−	0.877231i	$-0.659388\pi$
$227$	−1.69209e8	−0.960138	−0.480069	+	0.877231i	$0.659388\pi$
$228$	5.36199e6	0.0299608
$229$	−4.41098e7	−0.242723	−0.121361	−	0.992608i	$-0.538726\pi$
$229$	−4.41098e7	−0.242723	−0.121361	+	0.992608i	$0.538726\pi$
$230$	−2.46340e8	−1.33502
$231$	−8.17425e7	−0.436321
$232$	−3.17148e7	−0.166746
$233$	2.33697e8	1.21034	0.605170	−	0.796096i	$-0.293105\pi$
$233$	2.33697e8	1.21034	0.605170	+	0.796096i	$0.293105\pi$
$234$	2.14933e6	0.0109660
$235$	−4.39219e8	−2.20772
$236$	−1.19965e8	−0.594103
$237$	1.33664e8	0.652221
$238$	8.27383e6	0.0397820
$239$	−2.87597e7	−0.136267	−0.0681336	−	0.997676i	$-0.521704\pi$
$239$	−2.87597e7	−0.136267	−0.0681336	+	0.997676i	$0.521704\pi$
$240$	−1.58494e7	−0.0740072
$241$	2.27543e8	1.04714	0.523569	−	0.851983i	$-0.324600\pi$
$241$	2.27543e8	1.04714	0.523569	+	0.851983i	$0.324600\pi$
$242$	−1.37706e8	−0.624594
$243$	1.06617e8	0.476658
$244$	6.42264e7	0.283041
$245$	−2.71286e8	−1.17854
$246$	−1.56889e8	−0.671922
$247$	−746635.	−0.00315260
$248$	4.01257e8	1.67048
$249$	−1.52691e7	−0.0626779
$250$	7.10522e7	0.287599
$251$	−2.00505e8	−0.800326	−0.400163	−	0.916444i	$-0.631047\pi$
$251$	−2.00505e8	−0.800326	−0.400163	+	0.916444i	$0.631047\pi$
$252$	−1.08510e7	−0.0427136
$253$	6.43906e8	2.49977
$254$	2.21861e8	0.849498
$255$	9.12322e7	0.344554
$256$	−2.58742e8	−0.963889
$257$	−1.60683e8	−0.590479	−0.295239	−	0.955423i	$-0.595399\pi$
$257$	−1.60683e8	−0.590479	−0.295239	+	0.955423i	$0.595399\pi$
$258$	9.52024e7	0.345127
$259$	4.50360e7	0.161068
$260$	1.74119e7	0.0614385
$261$	−1.18549e7	−0.0412719
$262$	3.22227e8	1.10690
$263$	4.43753e7	0.150417	0.0752084	−	0.997168i	$-0.476038\pi$
$263$	4.43753e7	0.150417	0.0752084	+	0.997168i	$0.476038\pi$
$264$	−4.68406e8	−1.56678
$265$	5.73782e8	1.89403
$266$	−2.11025e6	−0.00687461
$267$	−5.53241e7	−0.177879
$268$	−1.80611e7	−0.0573157
$269$	−5.29611e8	−1.65892	−0.829458	−	0.558570i	$-0.811350\pi$
$269$	−5.29611e8	−1.65892	−0.829458	+	0.558570i	$0.811350\pi$
$270$	−2.08278e8	−0.643976
$271$	−5.88618e7	−0.179656	−0.0898279	−	0.995957i	$-0.528632\pi$
$271$	−5.88618e7	−0.179656	−0.0898279	+	0.995957i	$0.528632\pi$
$272$	−4.19332e6	−0.0126348
$273$	7.72003e6	0.0229641
$274$	7.94473e7	0.233320
$275$	3.07171e8	0.890669
$276$	4.36728e8	1.25034
$277$	3.36175e8	0.950354	0.475177	−	0.879890i	$-0.342384\pi$
$277$	3.36175e8	0.950354	0.475177	+	0.879890i	$0.342384\pi$
$278$	9.70296e7	0.270862
$279$	1.49988e8	0.413468
$280$	1.25975e8	0.342950
$281$	−5.86531e7	−0.157695	−0.0788477	−	0.996887i	$-0.525124\pi$
$281$	−5.86531e7	−0.157695	−0.0788477	+	0.996887i	$0.525124\pi$
$282$	−4.35930e8	−1.15756
$283$	−4.64309e8	−1.21774	−0.608870	−	0.793270i	$-0.708377\pi$
$283$	−4.64309e8	−1.21774	−0.608870	+	0.793270i	$0.708377\pi$
$284$	2.70236e8	0.700050
$285$	−2.32689e7	−0.0595413
$286$	2.54797e7	0.0644040
$287$	−1.10291e8	−0.275393
$288$	−1.00068e8	−0.246843
$289$	2.41376e7	0.0588235
$290$	5.37651e7	0.129451
$291$	−8.19693e8	−1.94996
$292$	−3.32655e8	−0.781904
$293$	−5.70647e8	−1.32535	−0.662676	−	0.748906i	$-0.730579\pi$
$293$	−5.70647e8	−1.32535	−0.662676	+	0.748906i	$0.730579\pi$
$294$	−2.69254e8	−0.617940
$295$	5.20599e8	1.18066
$296$	2.58068e8	0.578380
$297$	5.44415e8	1.20582
$298$	3.10470e8	0.679614
$299$	−6.08126e7	−0.131566
$300$	2.08338e8	0.445497
$301$	6.69262e7	0.141453
$302$	−4.95580e8	−1.03535
$303$	−3.88676e8	−0.802672
$304$	1.06951e6	0.00218337
$305$	−2.78717e8	−0.562488
$306$	1.77221e7	0.0353582
$307$	6.66774e7	0.131521	0.0657603	−	0.997835i	$-0.479053\pi$
$307$	6.66774e7	0.131521	0.0657603	+	0.997835i	$0.479053\pi$
$308$	−1.28635e8	−0.250860
$309$	−3.11303e8	−0.600244
$310$	−6.80238e8	−1.29686
$311$	−4.26023e8	−0.803104	−0.401552	−	0.915836i	$-0.631529\pi$
$311$	−4.26023e8	−0.803104	−0.401552	+	0.915836i	$0.631529\pi$
$312$	4.42378e7	0.0824618
$313$	5.80133e8	1.06936	0.534678	−	0.845056i	$-0.320433\pi$
$313$	5.80133e8	1.06936	0.534678	+	0.845056i	$0.320433\pi$
$314$	9.90453e7	0.180543
$315$	4.70889e7	0.0848851
$316$	2.10341e8	0.374990
$317$	−1.35626e7	−0.0239131	−0.0119566	−	0.999929i	$-0.503806\pi$
$317$	−1.35626e7	−0.0239131	−0.0119566	+	0.999929i	$0.503806\pi$
$318$	5.69484e8	0.993086
$319$	−1.40536e8	−0.242393
$320$	4.14930e8	0.707864
$321$	−9.76665e8	−1.64808
$322$	−1.71877e8	−0.286895
$323$	−6.15631e6	−0.0101651
$324$	4.64759e8	0.759137
$325$	−2.90103e7	−0.0468770
$326$	4.24566e8	0.678709
$327$	1.18457e9	1.87346
$328$	−6.31997e8	−0.988909
$329$	−3.06454e8	−0.474437
$330$	7.94073e8	1.21636
$331$	1.02459e9	1.55293	0.776465	−	0.630161i	$-0.217011\pi$
$331$	1.02459e9	1.55293	0.776465	+	0.630161i	$0.217011\pi$
$332$	−2.40283e7	−0.0360363
$333$	9.64648e7	0.143157
$334$	−4.78308e8	−0.702417
$335$	7.83781e7	0.113904
$336$	−1.10585e7	−0.0159041
$337$	5.13594e8	0.730997	0.365498	−	0.930812i	$-0.380899\pi$
$337$	5.13594e8	0.730997	0.365498	+	0.930812i	$0.380899\pi$
$338$	4.22897e8	0.595698
$339$	6.69177e7	0.0932915
$340$	1.43568e8	0.198099
$341$	1.77806e9	2.42833
$342$	−4.52004e6	−0.00611014
$343$	−3.93903e8	−0.527060
$344$	3.83505e8	0.507945
$345$	−1.89522e9	−2.48481
$346$	7.87196e8	1.02168
$347$	−5.84214e8	−0.750618	−0.375309	−	0.926900i	$-0.622463\pi$
$347$	−5.84214e8	−0.750618	−0.375309	+	0.926900i	$0.622463\pi$
$348$	−9.53181e7	−0.121241
$349$	−3.24241e7	−0.0408300	−0.0204150	−	0.999792i	$-0.506499\pi$
$349$	−3.24241e7	−0.0408300	−0.0204150	+	0.999792i	$0.506499\pi$
$350$	−8.19931e7	−0.102221
$351$	−5.14163e7	−0.0634638
$352$	−1.18627e9	−1.44972
$353$	−1.48909e8	−0.180181	−0.0900906	−	0.995934i	$-0.528716\pi$
$353$	−1.48909e8	−0.180181	−0.0900906	+	0.995934i	$0.528716\pi$
$354$	5.16700e8	0.619052
$355$	−1.17272e9	−1.39121
$356$	−8.70613e7	−0.102270
$357$	6.36548e7	0.0740444
$358$	−2.88566e8	−0.332395
$359$	−9.80370e8	−1.11830	−0.559151	−	0.829066i	$-0.688873\pi$
$359$	−9.80370e8	−1.11830	−0.559151	+	0.829066i	$0.688873\pi$
$360$	2.69832e8	0.304814
$361$	−8.92302e8	−0.998243
$362$	3.28136e8	0.363558
$363$	−1.05944e9	−1.16253
$364$	1.21487e7	0.0132031
$365$	1.44359e9	1.55388
$366$	−2.76629e8	−0.294927
$367$	8.10002e8	0.855372	0.427686	−	0.903927i	$-0.359329\pi$
$367$	8.10002e8	0.855372	0.427686	+	0.903927i	$0.359329\pi$
$368$	8.71105e7	0.0911178
$369$	−2.36238e8	−0.244769
$370$	−4.37494e8	−0.449021
$371$	4.00341e8	0.407025
$372$	1.20597e9	1.21461
$373$	−1.12406e9	−1.12153	−0.560763	−	0.827976i	$-0.689492\pi$
$373$	−1.12406e9	−1.12153	−0.560763	+	0.827976i	$0.689492\pi$
$374$	2.10090e8	0.207661
$375$	5.46641e8	0.535295
$376$	−1.75606e9	−1.70366
$377$	1.32727e7	0.0127574
$378$	−1.45320e8	−0.138390
$379$	1.41305e9	1.33328	0.666639	−	0.745380i	$-0.267732\pi$
$379$	1.41305e9	1.33328	0.666639	+	0.745380i	$0.267732\pi$
$380$	−3.66173e7	−0.0342329
$381$	1.70689e9	1.58113
$382$	−4.53829e8	−0.416553
$383$	−1.39556e9	−1.26926	−0.634632	−	0.772814i	$-0.718848\pi$
$383$	−1.39556e9	−1.26926	−0.634632	+	0.772814i	$0.718848\pi$
$384$	−8.43199e8	−0.759926
$385$	5.58224e8	0.498535
$386$	−3.43000e8	−0.303556
$387$	1.43352e8	0.125724
$388$	−1.28992e9	−1.12112
$389$	1.03347e9	0.890169	0.445084	−	0.895489i	$-0.353174\pi$
$389$	1.03347e9	0.890169	0.445084	+	0.895489i	$0.353174\pi$
$390$	−7.49949e7	−0.0640185
$391$	−5.01425e8	−0.424216
$392$	−1.08464e9	−0.909460
$393$	2.47906e9	2.06021
$394$	−1.28085e8	−0.105502
$395$	−9.12798e8	−0.745220
$396$	−2.75529e8	−0.222964
$397$	9.92977e8	0.796476	0.398238	−	0.917282i	$-0.369622\pi$
$397$	9.92977e8	0.796476	0.398238	+	0.917282i	$0.369622\pi$
$398$	4.97267e8	0.395365
$399$	−1.62352e7	−0.0127954
$400$	4.15556e7	0.0324653
$401$	3.32662e8	0.257631	0.128816	−	0.991669i	$-0.458882\pi$
$401$	3.32662e8	0.257631	0.128816	+	0.991669i	$0.458882\pi$
$402$	7.77911e7	0.0597226
$403$	−1.67926e8	−0.127806
$404$	−6.11644e8	−0.461492
$405$	−2.01687e9	−1.50864
$406$	3.75131e7	0.0278190
$407$	1.14356e9	0.840773
$408$	3.64759e8	0.265886
$409$	6.64898e8	0.480533	0.240267	−	0.970707i	$-0.422765\pi$
$409$	6.64898e8	0.480533	0.240267	+	0.970707i	$0.422765\pi$
$410$	1.07140e9	0.767731
$411$	6.11229e8	0.434268
$412$	−4.89884e8	−0.345107
$413$	3.63234e8	0.253724
$414$	−3.68152e8	−0.254992
$415$	1.04273e8	0.0716151
$416$	1.12035e8	0.0763007
$417$	7.46499e8	0.504142
$418$	−5.35837e7	−0.0358852
$419$	2.06771e8	0.137322	0.0686611	−	0.997640i	$-0.478127\pi$
$419$	2.06771e8	0.137322	0.0686611	+	0.997640i	$0.478127\pi$
$420$	3.78614e8	0.249359
$421$	1.08403e9	0.708037	0.354018	−	0.935238i	$-0.384815\pi$
$421$	1.08403e9	0.708037	0.354018	+	0.935238i	$0.384815\pi$
$422$	−1.05492e9	−0.683325
$423$	−6.56408e8	−0.421679
$424$	2.29406e9	1.46159
$425$	−2.39202e8	−0.151148
$426$	−1.16393e9	−0.729448
$427$	−1.94467e8	−0.120878
$428$	−1.53694e9	−0.947553
$429$	1.96028e8	0.119872
$430$	−6.50142e8	−0.394338
$431$	1.11437e9	0.670437	0.335219	−	0.942140i	$-0.391190\pi$
$431$	1.11437e9	0.670437	0.335219	+	0.942140i	$0.391190\pi$
$432$	7.36509e7	0.0439526
$433$	−2.47401e9	−1.46451	−0.732257	−	0.681028i	$-0.761533\pi$
$433$	−2.47401e9	−1.46451	−0.732257	+	0.681028i	$0.761533\pi$
$434$	−4.74617e8	−0.278695
$435$	4.13642e8	0.240942
$436$	1.86412e9	1.07714
$437$	1.27889e8	0.0733074
$438$	1.43278e9	0.814739
$439$	9.88561e8	0.557671	0.278835	−	0.960339i	$-0.410052\pi$
$439$	9.88561e8	0.557671	0.278835	+	0.960339i	$0.410052\pi$
$440$	3.19877e9	1.79019
$441$	−4.05433e8	−0.225104
$442$	−1.98416e7	−0.0109295
$443$	1.95995e8	0.107110	0.0535552	−	0.998565i	$-0.482945\pi$
$443$	1.95995e8	0.107110	0.0535552	+	0.998565i	$0.482945\pi$
$444$	7.75617e8	0.420540
$445$	3.77811e8	0.203243
$446$	−7.15220e8	−0.381740
$447$	2.38860e9	1.26493
$448$	2.89506e8	0.152119
$449$	−2.81643e9	−1.46838	−0.734188	−	0.678947i	$-0.762437\pi$
$449$	−2.81643e9	−1.46838	−0.734188	+	0.678947i	$0.762437\pi$
$450$	−1.75625e8	−0.0908536
$451$	−2.80052e9	−1.43754
$452$	1.05306e8	0.0536374
$453$	−3.81275e9	−1.92706
$454$	1.14688e9	0.575207
$455$	−5.27205e7	−0.0262385
$456$	−9.30322e7	−0.0459469
$457$	−2.69617e9	−1.32142	−0.660709	−	0.750642i	$-0.729744\pi$
$457$	−2.69617e9	−1.32142	−0.660709	+	0.750642i	$0.729744\pi$
$458$	2.98972e8	0.145412
$459$	−4.23949e8	−0.204630
$460$	−2.98244e9	−1.42863
$461$	−1.57512e9	−0.748792	−0.374396	−	0.927269i	$-0.622150\pi$
$461$	−1.57512e9	−0.748792	−0.374396	+	0.927269i	$0.622150\pi$
$462$	5.54043e8	0.261395
$463$	5.31323e8	0.248785	0.124393	−	0.992233i	$-0.460302\pi$
$463$	5.31323e8	0.248785	0.124393	+	0.992233i	$0.460302\pi$
$464$	−1.90123e7	−0.00883532
$465$	−5.23342e9	−2.41379
$466$	−1.58398e9	−0.725101
$467$	−1.82463e9	−0.829022	−0.414511	−	0.910044i	$-0.636047\pi$
$467$	−1.82463e9	−0.829022	−0.414511	+	0.910044i	$0.636047\pi$
$468$	2.60219e7	0.0117349
$469$	5.46862e7	0.0244778
$470$	2.97699e9	1.32262
$471$	7.62006e8	0.336036
$472$	2.08143e9	0.911097
$473$	1.69940e9	0.738382
$474$	−9.05961e8	−0.390738
$475$	6.10086e7	0.0261194
$476$	1.00171e8	0.0425714
$477$	8.57510e8	0.361763
$478$	1.94931e8	0.0816361
$479$	2.68719e9	1.11718	0.558591	−	0.829443i	$-0.311342\pi$
$479$	2.68719e9	1.11718	0.558591	+	0.829443i	$0.311342\pi$
$480$	3.49158e9	1.44105
$481$	−1.08002e8	−0.0442509
$482$	−1.54227e9	−0.627328
$483$	−1.32234e9	−0.533984
$484$	−1.66720e9	−0.668388
$485$	5.59773e9	2.22800
$486$	−7.22643e8	−0.285560
$487$	3.03986e8	0.119262	0.0596310	−	0.998220i	$-0.481008\pi$
$487$	3.03986e8	0.119262	0.0596310	+	0.998220i	$0.481008\pi$
$488$	−1.11435e9	−0.434062
$489$	3.26640e9	1.26325
$490$	1.83875e9	0.706051
$491$	−2.22822e9	−0.849519	−0.424760	−	0.905306i	$-0.639641\pi$
$491$	−2.22822e9	−0.849519	−0.424760	+	0.905306i	$0.639641\pi$
$492$	−1.89945e9	−0.719035
$493$	1.09439e8	0.0411345
$494$	5.06062e6	0.00188869
$495$	1.19569e9	0.443098
$496$	2.40545e8	0.0885135
$497$	−8.18231e8	−0.298971
$498$	1.03492e8	0.0375496
$499$	3.51713e9	1.26717	0.633587	−	0.773671i	$-0.281582\pi$
$499$	3.51713e9	1.26717	0.633587	+	0.773671i	$0.281582\pi$
$500$	8.60228e8	0.307764
$501$	−3.67987e9	−1.30738
$502$	1.35900e9	0.479466
$503$	−1.54401e9	−0.540957	−0.270479	−	0.962726i	$-0.587182\pi$
$503$	−1.54401e9	−0.540957	−0.270479	+	0.962726i	$0.587182\pi$
$504$	1.88268e8	0.0655042
$505$	2.65429e9	0.917125
$506$	−4.36433e9	−1.49758
$507$	3.25357e9	1.10875
$508$	2.68606e9	0.909062
$509$	−1.53211e9	−0.514964	−0.257482	−	0.966283i	$-0.582893\pi$
$509$	−1.53211e9	−0.514964	−0.257482	+	0.966283i	$0.582893\pi$
$510$	−6.18363e8	−0.206418
$511$	1.00722e9	0.333928
$512$	−3.16031e8	−0.104060
$513$	1.08129e8	0.0353614
$514$	1.08910e9	0.353749
$515$	2.12590e9	0.685832
$516$	1.15261e9	0.369326
$517$	−7.78151e9	−2.47655
$518$	−3.05250e8	−0.0964942
$519$	6.05630e9	1.90161
$520$	−3.02103e8	−0.0942199
$521$	−3.77662e9	−1.16996	−0.584980	−	0.811047i	$-0.698898\pi$
$521$	−3.77662e9	−1.16996	−0.584980	+	0.811047i	$0.698898\pi$
$522$	8.03512e7	0.0247255
$523$	−2.58826e9	−0.791136	−0.395568	−	0.918437i	$-0.629452\pi$
$523$	−2.58826e9	−0.791136	−0.395568	+	0.918437i	$0.629452\pi$
$524$	3.90119e9	1.18451
$525$	−6.30815e8	−0.190259
$526$	−3.00772e8	−0.0901129
$527$	−1.38462e9	−0.412091
$528$	−2.80799e8	−0.0830189
$529$	7.01158e9	2.05931
$530$	−3.88904e9	−1.13469
$531$	7.78029e8	0.225509
$532$	−2.55487e7	−0.00735662
$533$	2.64491e8	0.0756598
$534$	3.74981e8	0.106565
$535$	6.66970e9	1.88308
$536$	3.13367e8	0.0878974
$537$	−2.22009e9	−0.618671
$538$	3.58966e9	0.993836
$539$	−4.80628e9	−1.32205
$540$	−2.52162e9	−0.689129
$541$	−3.44603e9	−0.935684	−0.467842	−	0.883812i	$-0.654968\pi$
$541$	−3.44603e9	−0.935684	−0.467842	+	0.883812i	$0.654968\pi$
$542$	3.98960e8	0.107630
$543$	2.52452e9	0.676674
$544$	9.23778e8	0.246021
$545$	−8.08952e9	−2.14060
$546$	−5.23257e7	−0.0137575
$547$	−2.57628e9	−0.673035	−0.336518	−	0.941677i	$-0.609249\pi$
$547$	−2.57628e9	−0.673035	−0.336518	+	0.941677i	$0.609249\pi$
$548$	9.61867e8	0.249679
$549$	−4.16538e8	−0.107437
$550$	−2.08198e9	−0.533589
$551$	−2.79124e7	−0.00710831
$552$	−7.57736e9	−1.91748
$553$	−6.36880e8	−0.160147
$554$	−2.27856e9	−0.569346
$555$	−3.36587e9	−0.835741
$556$	1.17474e9	0.289853
$557$	5.84528e9	1.43322	0.716609	−	0.697476i	$-0.245693\pi$
$557$	5.84528e9	1.43322	0.716609	+	0.697476i	$0.245693\pi$
$558$	−1.01661e9	−0.247704
$559$	−1.60497e8	−0.0388620
$560$	7.55191e7	0.0181718
$561$	1.61633e9	0.386510
$562$	3.97546e8	0.0944735
$563$	−3.69708e7	−0.00873131	−0.00436566	−	0.999990i	$-0.501390\pi$
$563$	−3.69708e7	−0.00873131	−0.00436566	+	0.999990i	$0.501390\pi$
$564$	−5.27779e9	−1.23873
$565$	−4.56985e8	−0.106594
$566$	3.14704e9	0.729533
$567$	−1.40722e9	−0.324205
$568$	−4.68868e9	−1.07357
$569$	7.36933e9	1.67701	0.838504	−	0.544896i	$-0.183431\pi$
$569$	7.36933e9	1.67701	0.838504	+	0.544896i	$0.183431\pi$
$570$	1.57714e8	0.0356705
$571$	−3.06832e9	−0.689723	−0.344862	−	0.938654i	$-0.612074\pi$
$571$	−3.06832e9	−0.689723	−0.344862	+	0.938654i	$0.612074\pi$
$572$	3.08482e8	0.0689197
$573$	−3.49154e9	−0.775311
$574$	7.47542e8	0.164985
$575$	4.96908e9	1.09003
$576$	6.20107e8	0.135203
$577$	3.71530e9	0.805152	0.402576	−	0.915387i	$-0.368115\pi$
$577$	3.71530e9	0.805152	0.402576	+	0.915387i	$0.368115\pi$
$578$	−1.63602e8	−0.0352405
$579$	−2.63888e9	−0.564995
$580$	6.50932e8	0.138528
$581$	7.27539e7	0.0153900
$582$	5.55581e9	1.16820
$583$	1.01655e10	2.12466
$584$	5.77166e9	1.19910
$585$	−1.12925e8	−0.0233208
$586$	3.86779e9	0.794002
$587$	−1.81251e9	−0.369867	−0.184934	−	0.982751i	$-0.559207\pi$
$587$	−1.81251e9	−0.369867	−0.184934	+	0.982751i	$0.559207\pi$
$588$	−3.25985e9	−0.661267
$589$	3.53149e8	0.0712122
$590$	−3.52857e9	−0.707322
$591$	−9.85424e8	−0.196366
$592$	1.54706e8	0.0306465
$593$	4.16833e9	0.820864	0.410432	−	0.911891i	$-0.365378\pi$
$593$	4.16833e9	0.820864	0.410432	+	0.911891i	$0.365378\pi$
$594$	−3.68999e9	−0.722392
$595$	−4.34702e8	−0.0846024
$596$	3.75885e9	0.727266
$597$	3.82573e9	0.735875
$598$	4.12182e8	0.0788197
$599$	−3.92805e9	−0.746764	−0.373382	−	0.927678i	$-0.621802\pi$
$599$	−3.92805e9	−0.746764	−0.373382	+	0.927678i	$0.621802\pi$
$600$	−3.61474e9	−0.683199
$601$	−1.21250e8	−0.0227836	−0.0113918	−	0.999935i	$-0.503626\pi$
$601$	−1.21250e8	−0.0227836	−0.0113918	+	0.999935i	$0.503626\pi$
$602$	−4.53619e8	−0.0847430
$603$	1.17135e8	0.0217559
$604$	−5.99997e9	−1.10795
$605$	7.23498e9	1.32829
$606$	2.63441e9	0.480871
$607$	−6.82334e9	−1.23833	−0.619166	−	0.785260i	$-0.712529\pi$
$607$	−6.82334e9	−1.23833	−0.619166	+	0.785260i	$0.712529\pi$
$608$	−2.35610e8	−0.0425140
$609$	2.88608e8	0.0517782
$610$	1.88912e9	0.336980
$611$	7.34912e8	0.130344
$612$	2.14561e8	0.0378374
$613$	−2.16247e9	−0.379173	−0.189587	−	0.981864i	$-0.560715\pi$
$613$	−2.16247e9	−0.379173	−0.189587	+	0.981864i	$0.560715\pi$
$614$	−4.51933e8	−0.0787925
$615$	8.24285e9	1.42894
$616$	2.23186e9	0.384710
$617$	−5.21256e9	−0.893415	−0.446708	−	0.894680i	$-0.647404\pi$
$617$	−5.21256e9	−0.893415	−0.446708	+	0.894680i	$0.647404\pi$
$618$	2.10998e9	0.359599
$619$	−8.17938e8	−0.138613	−0.0693064	−	0.997595i	$-0.522079\pi$
$619$	−8.17938e8	−0.138613	−0.0693064	+	0.997595i	$0.522079\pi$
$620$	−8.23562e9	−1.38780
$621$	8.80695e9	1.47572
$622$	2.88754e9	0.481130
$623$	2.63608e8	0.0436767
$624$	2.65196e7	0.00436939
$625$	−7.53675e9	−1.23482
$626$	−3.93209e9	−0.640638
$627$	−4.12247e8	−0.0667915
$628$	1.19914e9	0.193202
$629$	−8.90517e8	−0.142681
$630$	−3.19164e8	−0.0508536
$631$	8.82496e9	1.39833	0.699165	−	0.714960i	$-0.253555\pi$
$631$	8.82496e9	1.39833	0.699165	+	0.714960i	$0.253555\pi$
$632$	−3.64949e9	−0.575072
$633$	−8.11607e9	−1.27184
$634$	9.19262e7	0.0143261
$635$	−1.16564e10	−1.80658
$636$	6.89474e9	1.06272
$637$	4.53921e8	0.0695813
$638$	9.52538e8	0.145215
$639$	−1.75261e9	−0.265725
$640$	5.75826e9	0.868282
$641$	5.64109e9	0.845980	0.422990	−	0.906134i	$-0.360981\pi$
$641$	5.64109e9	0.845980	0.422990	+	0.906134i	$0.360981\pi$
$642$	6.61974e9	0.987344
$643$	−9.86940e9	−1.46404	−0.732019	−	0.681284i	$-0.761422\pi$
$643$	−9.86940e9	−1.46404	−0.732019	+	0.681284i	$0.761422\pi$
$644$	−2.08091e9	−0.307011
$645$	−5.00188e9	−0.733963
$646$	4.17269e7	0.00608979
$647$	1.06687e10	1.54862	0.774312	−	0.632804i	$-0.218096\pi$
$647$	1.06687e10	1.54862	0.774312	+	0.632804i	$0.218096\pi$
$648$	−8.06372e9	−1.16419
$649$	9.22329e9	1.32443
$650$	1.96629e8	0.0280835
$651$	−3.65148e9	−0.518722
$652$	5.14021e9	0.726297
$653$	6.95822e9	0.977918	0.488959	−	0.872307i	$-0.337377\pi$
$653$	6.95822e9	0.977918	0.488959	+	0.872307i	$0.337377\pi$
$654$	−8.02893e9	−1.12237
$655$	−1.69296e10	−2.35398
$656$	−3.78868e8	−0.0523991
$657$	2.15742e9	0.296795
$658$	2.07711e9	0.284230
$659$	6.19278e9	0.842921	0.421460	−	0.906847i	$-0.361518\pi$
$659$	6.19278e9	0.842921	0.421460	+	0.906847i	$0.361518\pi$
$660$	9.61383e9	1.30164
$661$	−5.38789e9	−0.725627	−0.362813	−	0.931862i	$-0.618184\pi$
$661$	−5.38789e9	−0.725627	−0.362813	+	0.931862i	$0.618184\pi$
$662$	−6.94457e9	−0.930341
$663$	−1.52652e8	−0.0203425
$664$	4.16899e8	0.0552640
$665$	1.10871e8	0.0146199
$666$	−6.53829e8	−0.0857639
$667$	−2.27343e9	−0.296648
$668$	−5.79086e9	−0.751667
$669$	−5.50256e9	−0.710515
$670$	−5.31240e8	−0.0682384
$671$	−4.93794e9	−0.630982
$672$	2.43616e9	0.309680
$673$	−3.45950e9	−0.437482	−0.218741	−	0.975783i	$-0.570195\pi$
$673$	−3.45950e9	−0.437482	−0.218741	+	0.975783i	$0.570195\pi$
$674$	−3.48109e9	−0.437932
$675$	4.20130e9	0.525800
$676$	5.12001e9	0.637466
$677$	−5.23201e9	−0.648050	−0.324025	−	0.946049i	$-0.605036\pi$
$677$	−5.23201e9	−0.648050	−0.324025	+	0.946049i	$0.605036\pi$
$678$	−4.53562e8	−0.0558898
$679$	3.90567e9	0.478796
$680$	−2.49096e9	−0.303798
$681$	8.82357e9	1.07061
$682$	−1.20516e10	−1.45478
$683$	−1.66770e9	−0.200284	−0.100142	−	0.994973i	$-0.531930\pi$
$683$	−1.66770e9	−0.200284	−0.100142	+	0.994973i	$0.531930\pi$
$684$	−5.47241e7	−0.00653856
$685$	−4.17412e9	−0.496189
$686$	2.66984e9	0.315755
$687$	2.30015e9	0.270649
$688$	2.29902e8	0.0269144
$689$	−9.60065e8	−0.111824
$690$	1.28456e10	1.48862
$691$	−4.14982e9	−0.478472	−0.239236	−	0.970961i	$-0.576897\pi$
$691$	−4.14982e9	−0.478472	−0.239236	+	0.970961i	$0.576897\pi$
$692$	9.53057e9	1.09332
$693$	8.34258e8	0.0952213
$694$	3.95975e9	0.449686
$695$	−5.09788e9	−0.576027
$696$	1.65380e9	0.185930
$697$	2.18083e9	0.243954
$698$	2.19768e8	0.0244608
$699$	−1.21864e10	−1.34960
$700$	−9.92688e8	−0.109388
$701$	−1.69844e10	−1.86224	−0.931122	−	0.364707i	$-0.881169\pi$
$701$	−1.69844e10	−1.86224	−0.931122	+	0.364707i	$0.881169\pi$
$702$	3.48495e8	0.0380204
$703$	2.27127e8	0.0246562
$704$	7.35118e9	0.794059
$705$	2.29035e10	2.46173
$706$	1.00929e9	0.107944
$707$	1.85196e9	0.197089
$708$	6.25568e9	0.662457
$709$	−8.73648e8	−0.0920607	−0.0460304	−	0.998940i	$-0.514657\pi$
$709$	−8.73648e8	−0.0920607	−0.0460304	+	0.998940i	$0.514657\pi$
$710$	7.94856e9	0.833459
$711$	−1.36416e9	−0.142339
$712$	1.51054e9	0.156839
$713$	2.87636e10	2.97187
$714$	−4.31446e8	−0.0443591
$715$	−1.33869e9	−0.136964
$716$	−3.49366e9	−0.355701
$717$	1.49970e9	0.151945
$718$	6.64486e9	0.669962
$719$	−2.28358e8	−0.0229121	−0.0114561	−	0.999934i	$-0.503647\pi$
$719$	−2.28358e8	−0.0229121	−0.0114561	+	0.999934i	$0.503647\pi$
$720$	1.61758e8	0.0161511
$721$	1.48329e9	0.147385
$722$	6.04794e9	0.598036
$723$	−1.18655e10	−1.16762
$724$	3.97274e9	0.389050
$725$	−1.08453e9	−0.105696
$726$	7.18079e9	0.696457
$727$	−1.17491e9	−0.113405	−0.0567026	−	0.998391i	$-0.518059\pi$
$727$	−1.17491e9	−0.113405	−0.0567026	+	0.998391i	$0.518059\pi$
$728$	−2.10784e8	−0.0202478
$729$	6.82674e9	0.652630
$730$	−9.78450e9	−0.930912
$731$	−1.32336e9	−0.125305
$732$	−3.34914e9	−0.315606
$733$	−3.87932e9	−0.363824	−0.181912	−	0.983315i	$-0.558229\pi$
$733$	−3.87932e9	−0.363824	−0.181912	+	0.983315i	$0.558229\pi$
$734$	−5.49012e9	−0.512443
$735$	1.41464e10	1.31414
$736$	−1.91902e10	−1.77422
$737$	1.38860e9	0.127774
$738$	1.60120e9	0.146638
$739$	−1.01598e10	−0.926035	−0.463018	−	0.886349i	$-0.653233\pi$
$739$	−1.01598e10	−0.926035	−0.463018	+	0.886349i	$0.653233\pi$
$740$	−5.29673e9	−0.480504
$741$	3.89340e7	0.00351532
$742$	−2.71347e9	−0.243844
$743$	−2.57660e9	−0.230455	−0.115227	−	0.993339i	$-0.536760\pi$
$743$	−2.57660e9	−0.230455	−0.115227	+	0.993339i	$0.536760\pi$
$744$	−2.09239e10	−1.86268
$745$	−1.63119e10	−1.44530
$746$	7.61879e9	0.671893
$747$	1.55835e8	0.0136786
$748$	2.54356e9	0.222221
$749$	4.65360e9	0.404672
$750$	−3.70508e9	−0.320689
$751$	−2.86683e9	−0.246980	−0.123490	−	0.992346i	$-0.539409\pi$
$751$	−2.86683e9	−0.246980	−0.123490	+	0.992346i	$0.539409\pi$
$752$	−1.05272e9	−0.0902713
$753$	1.04555e10	0.892407
$754$	−8.99609e7	−0.00764282
$755$	2.60375e10	2.20183
$756$	−1.75939e9	−0.148093
$757$	1.12562e10	0.943099	0.471550	−	0.881840i	$-0.343695\pi$
$757$	1.12562e10	0.943099	0.471550	+	0.881840i	$0.343695\pi$
$758$	−9.57754e9	−0.798751
$759$	−3.35771e10	−2.78738
$760$	6.35322e8	0.0524984
$761$	−1.05472e10	−0.867545	−0.433773	−	0.901022i	$-0.642818\pi$
$761$	−1.05472e10	−0.867545	−0.433773	+	0.901022i	$0.642818\pi$
$762$	−1.15691e10	−0.947237
$763$	−5.64424e9	−0.460013
$764$	−5.49450e9	−0.445760
$765$	−9.31110e8	−0.0751945
$766$	9.45896e9	0.760401
$767$	−8.71078e8	−0.0697065
$768$	1.34923e10	1.07479
$769$	−1.70020e10	−1.34821	−0.674107	−	0.738633i	$-0.735472\pi$
$769$	−1.70020e10	−1.34821	−0.674107	+	0.738633i	$0.735472\pi$
$770$	−3.78359e9	−0.298667
$771$	8.37897e9	0.658416
$772$	−4.15270e9	−0.324840
$773$	1.64749e10	1.28291	0.641454	−	0.767161i	$-0.278331\pi$
$773$	1.64749e10	1.28291	0.641454	+	0.767161i	$0.278331\pi$
$774$	−9.71629e8	−0.0753195
$775$	1.37215e10	1.05888
$776$	2.23805e10	1.71931
$777$	−2.34844e9	−0.179600
$778$	−7.00473e9	−0.533289
$779$	−5.56224e8	−0.0421569
$780$	−9.07961e8	−0.0685072
$781$	−2.07766e10	−1.56062
$782$	3.39861e9	0.254143
$783$	−1.92216e9	−0.143095
$784$	−6.50216e8	−0.0481894
$785$	−5.20378e9	−0.383951
$786$	−1.68028e10	−1.23425
$787$	1.53623e10	1.12343	0.561713	−	0.827332i	$-0.310142\pi$
$787$	1.53623e10	1.12343	0.561713	+	0.827332i	$0.310142\pi$
$788$	−1.55072e9	−0.112900
$789$	−2.31399e9	−0.167723
$790$	6.18686e9	0.446453
$791$	−3.18849e8	−0.0229069
$792$	4.78052e9	0.341930
$793$	4.66355e8	0.0332094
$794$	−6.73031e9	−0.477159
$795$	−2.99204e10	−2.11194
$796$	6.02039e9	0.423087
$797$	1.48850e10	1.04146	0.520732	−	0.853720i	$-0.325659\pi$
$797$	1.48850e10	1.04146	0.520732	+	0.853720i	$0.325659\pi$
$798$	1.10041e8	0.00766556
$799$	6.05965e9	0.420275
$800$	−9.15457e9	−0.632154
$801$	5.64634e8	0.0388198
$802$	−2.25475e9	−0.154344
$803$	2.55756e10	1.74310
$804$	9.41815e8	0.0639101
$805$	9.03034e9	0.610124
$806$	1.13819e9	0.0765670
$807$	2.76171e10	1.84978
$808$	1.06122e10	0.707728
$809$	−5.16211e9	−0.342774	−0.171387	−	0.985204i	$-0.554825\pi$
$809$	−5.16211e9	−0.342774	−0.171387	+	0.985204i	$0.554825\pi$
$810$	1.36701e10	0.903807
$811$	1.73293e10	1.14080	0.570399	−	0.821367i	$-0.306788\pi$
$811$	1.73293e10	1.14080	0.570399	+	0.821367i	$0.306788\pi$
$812$	4.54170e8	0.0297696
$813$	3.06940e9	0.200326
$814$	−7.75095e9	−0.503697
$815$	−2.23065e10	−1.44337
$816$	2.18665e8	0.0140885
$817$	3.37525e8	0.0216535
$818$	−4.50662e9	−0.287882
$819$	−7.87901e7	−0.00501162
$820$	1.29714e10	0.821561
$821$	−6.66915e9	−0.420600	−0.210300	−	0.977637i	$-0.567444\pi$
$821$	−6.66915e9	−0.420600	−0.210300	+	0.977637i	$0.567444\pi$
$822$	−4.14285e9	−0.260165
$823$	1.81553e10	1.13528	0.567641	−	0.823276i	$-0.307856\pi$
$823$	1.81553e10	1.13528	0.567641	+	0.823276i	$0.307856\pi$
$824$	8.49965e9	0.529244
$825$	−1.60177e10	−0.993145
$826$	−2.46197e9	−0.152003
$827$	−2.47744e10	−1.52312	−0.761558	−	0.648097i	$-0.775565\pi$
$827$	−2.47744e10	−1.52312	−0.761558	+	0.648097i	$0.775565\pi$
$828$	−4.45721e9	−0.272871
$829$	1.33189e10	0.811944	0.405972	−	0.913886i	$-0.366933\pi$
$829$	1.33189e10	0.811944	0.405972	+	0.913886i	$0.366933\pi$
$830$	−7.06755e8	−0.0429038
$831$	−1.75301e10	−1.05970
$832$	−6.94269e8	−0.0417923
$833$	3.74277e9	0.224355
$834$	−5.05970e9	−0.302026
$835$	2.51300e10	1.49379
$836$	−6.48737e8	−0.0384014
$837$	2.43193e10	1.43355
$838$	−1.40147e9	−0.0822680
$839$	−3.09944e9	−0.181182	−0.0905912	−	0.995888i	$-0.528876\pi$
$839$	−3.09944e9	−0.181182	−0.0905912	+	0.995888i	$0.528876\pi$
$840$	−6.56908e9	−0.382408
$841$	−1.67537e10	−0.971235
$842$	−7.34749e9	−0.424176
$843$	3.05852e9	0.175839
$844$	−1.27719e10	−0.731237
$845$	−2.22188e10	−1.26684
$846$	4.44907e9	0.252623
$847$	5.04801e9	0.285449
$848$	1.37524e9	0.0774448
$849$	2.42118e10	1.35785
$850$	1.62129e9	0.0905511
$851$	1.84993e10	1.02897
$852$	−1.40917e10	−0.780594
$853$	2.47088e10	1.36311	0.681554	−	0.731768i	$-0.261304\pi$
$853$	2.47088e10	1.36311	0.681554	+	0.731768i	$0.261304\pi$
$854$	1.31808e9	0.0724168
$855$	2.37480e8	0.0129941
$856$	2.66664e10	1.45313
$857$	−1.58319e10	−0.859210	−0.429605	−	0.903017i	$-0.641347\pi$
$857$	−1.58319e10	−0.859210	−0.429605	+	0.903017i	$0.641347\pi$
$858$	−1.32866e9	−0.0718139
$859$	2.16654e9	0.116625	0.0583125	−	0.998298i	$-0.481428\pi$
$859$	2.16654e9	0.116625	0.0583125	+	0.998298i	$0.481428\pi$
$860$	−7.87126e9	−0.421988
$861$	5.75123e9	0.307078
$862$	−7.55308e9	−0.401651
$863$	8.37277e9	0.443436	0.221718	−	0.975111i	$-0.428834\pi$
$863$	8.37277e9	0.443436	0.221718	+	0.975111i	$0.428834\pi$
$864$	−1.62251e10	−0.855833
$865$	−4.13588e10	−2.17276
$866$	1.67686e10	0.877373
$867$	−1.25868e9	−0.0655914
$868$	−5.74618e9	−0.298236
$869$	−1.61717e10	−0.835964
$870$	−2.80363e9	−0.144345
$871$	−1.31144e8	−0.00672489
$872$	−3.23430e10	−1.65186
$873$	8.36573e9	0.425554
$874$	−8.66819e8	−0.0439176
$875$	−2.60463e9	−0.131437
$876$	1.73466e10	0.871865
$877$	2.75083e10	1.37710	0.688549	−	0.725190i	$-0.258248\pi$
$877$	2.75083e10	1.37710	0.688549	+	0.725190i	$0.258248\pi$
$878$	−6.70038e9	−0.334094
$879$	2.97569e10	1.47784
$880$	1.91759e9	0.0948564
$881$	6.49119e9	0.319822	0.159911	−	0.987131i	$-0.448879\pi$
$881$	6.49119e9	0.319822	0.159911	+	0.987131i	$0.448879\pi$
$882$	2.74799e9	0.134857
$883$	−2.72832e10	−1.33362	−0.666810	−	0.745228i	$-0.732341\pi$
$883$	−2.72832e10	−1.33362	−0.666810	+	0.745228i	$0.732341\pi$
$884$	−2.40222e8	−0.0116958
$885$	−2.71471e10	−1.31650
$886$	−1.32844e9	−0.0641686
$887$	−2.32690e10	−1.11956	−0.559778	−	0.828643i	$-0.689114\pi$
$887$	−2.32690e10	−1.11956	−0.559778	+	0.828643i	$0.689114\pi$
$888$	−1.34572e10	−0.644926
$889$	−8.13297e9	−0.388233
$890$	−2.56077e9	−0.121760
$891$	−3.57322e10	−1.69234
$892$	−8.65915e9	−0.408506
$893$	−1.54552e9	−0.0726264
$894$	−1.61897e10	−0.757807
$895$	1.51611e10	0.706887
$896$	4.01767e9	0.186593
$897$	3.17113e9	0.146703
$898$	1.90895e10	0.879686
$899$	−6.27780e9	−0.288170
$900$	−2.12629e9	−0.0972239
$901$	−7.91612e9	−0.360559
$902$	1.89817e10	0.861216
$903$	−3.48993e9	−0.157728
$904$	−1.82709e9	−0.0822565
$905$	−1.72401e10	−0.773161
$906$	2.58425e10	1.15448
$907$	1.21988e10	0.542864	0.271432	−	0.962458i	$-0.412503\pi$
$907$	1.21988e10	0.542864	0.271432	+	0.962458i	$0.412503\pi$
$908$	1.38853e10	0.615538
$909$	3.96680e9	0.175173
$910$	3.57335e8	0.0157192
$911$	−2.25430e10	−0.987866	−0.493933	−	0.869500i	$-0.664441\pi$
$911$	−2.25430e10	−0.987866	−0.493933	+	0.869500i	$0.664441\pi$
$912$	−5.57707e7	−0.00243458
$913$	1.84738e9	0.0803355
$914$	1.82744e10	0.791646
$915$	1.45339e10	0.627205
$916$	3.61965e9	0.155608
$917$	−1.18122e10	−0.505868
$918$	2.87348e9	0.122591
$919$	−4.74349e8	−0.0201601	−0.0100801	−	0.999949i	$-0.503209\pi$
$919$	−4.74349e8	−0.0201601	−0.0100801	+	0.999949i	$0.503209\pi$
$920$	5.17462e10	2.19089
$921$	−3.47695e9	−0.146653
$922$	1.06760e10	0.448593
$923$	1.96221e9	0.0821373
$924$	6.70779e9	0.279722
$925$	8.82497e9	0.366621
$926$	−3.60126e9	−0.149044
$927$	3.17713e9	0.130995
$928$	4.18836e9	0.172039
$929$	2.12890e10	0.871164	0.435582	−	0.900149i	$-0.356543\pi$
$929$	2.12890e10	0.871164	0.435582	+	0.900149i	$0.356543\pi$
$930$	3.54716e10	1.44607
$931$	−9.54596e8	−0.0387700
$932$	−1.91772e10	−0.775942
$933$	2.22154e10	0.895504
$934$	1.23672e10	0.496657
$935$	−1.10380e10	−0.441622
$936$	−4.51488e8	−0.0179962
$937$	−3.77211e10	−1.49794	−0.748971	−	0.662602i	$-0.769452\pi$
$937$	−3.77211e10	−1.49794	−0.748971	+	0.662602i	$0.769452\pi$
$938$	−3.70658e8	−0.0146644
$939$	−3.02516e10	−1.19239
$940$	3.60423e10	1.41536
$941$	−4.40770e10	−1.72444	−0.862221	−	0.506532i	$-0.830927\pi$
$941$	−4.40770e10	−1.72444	−0.862221	+	0.506532i	$0.830927\pi$
$942$	−5.16481e9	−0.201315
$943$	−4.53038e10	−1.75932
$944$	1.24777e9	0.0482761
$945$	7.63504e9	0.294307
$946$	−1.15184e10	−0.442356
$947$	−9.51014e9	−0.363883	−0.181942	−	0.983309i	$-0.558238\pi$
$947$	−9.51014e9	−0.363883	−0.181942	+	0.983309i	$0.558238\pi$
$948$	−1.09684e10	−0.418135
$949$	−2.41544e9	−0.0917413
$950$	−4.13511e8	−0.0156478
$951$	7.07235e8	0.0266644
$952$	−1.73800e9	−0.0652861
$953$	9.43137e9	0.352980	0.176490	−	0.984302i	$-0.443526\pi$
$953$	9.43137e9	0.352980	0.176490	+	0.984302i	$0.443526\pi$
$954$	−5.81212e9	−0.216728
$955$	2.38439e10	0.885861
$956$	2.36002e9	0.0873601
$957$	7.32837e9	0.270281
$958$	−1.82135e10	−0.669291
$959$	−2.91238e9	−0.106631
$960$	−2.16369e10	−0.789306
$961$	5.19144e10	1.88693
$962$	7.32025e8	0.0265102
$963$	9.96777e9	0.359672
$964$	−1.86722e10	−0.671314
$965$	1.80210e10	0.645557
$966$	8.96270e9	0.319904
$967$	4.78178e10	1.70058	0.850290	−	0.526314i	$-0.176426\pi$
$967$	4.78178e10	1.70058	0.850290	+	0.526314i	$0.176426\pi$
$968$	2.89265e10	1.02502
$969$	3.21027e8	0.0113346
$970$	−3.79409e10	−1.33477
$971$	3.61403e10	1.26685	0.633424	−	0.773805i	$-0.281649\pi$
$971$	3.61403e10	1.26685	0.633424	+	0.773805i	$0.281649\pi$
$972$	−8.74903e9	−0.305582
$973$	−3.55691e9	−0.123788
$974$	−2.06039e9	−0.0714484
$975$	1.51277e9	0.0522705
$976$	−6.68026e8	−0.0229995
$977$	−1.36900e10	−0.469649	−0.234825	−	0.972038i	$-0.575452\pi$
$977$	−1.36900e10	−0.469649	−0.234825	+	0.972038i	$0.575452\pi$
$978$	−2.21394e10	−0.756797
$979$	6.69356e9	0.227991
$980$	2.22617e10	0.755556
$981$	−1.20897e10	−0.408859
$982$	1.51027e10	0.508937
$983$	1.39614e10	0.468805	0.234403	−	0.972140i	$-0.424687\pi$
$983$	1.39614e10	0.468805	0.234403	+	0.972140i	$0.424687\pi$
$984$	3.29561e10	1.10269
$985$	6.72951e9	0.224366
$986$	−7.41764e8	−0.0246432
$987$	1.59803e10	0.529024
$988$	6.12689e7	0.00202111
$989$	2.74910e10	0.903657
$990$	−8.10426e9	−0.265454
$991$	1.85305e10	0.604824	0.302412	−	0.953177i	$-0.402208\pi$
$991$	1.85305e10	0.604824	0.302412	+	0.953177i	$0.402208\pi$
$992$	−5.29913e10	−1.72351
$993$	−5.34281e10	−1.73160
$994$	5.54589e9	0.179110
$995$	−2.61261e10	−0.840802
$996$	1.25298e9	0.0401824
$997$	−8.42274e9	−0.269166	−0.134583	−	0.990902i	$-0.542969\pi$
$997$	−8.42274e9	−0.269166	−0.134583	+	0.990902i	$0.542969\pi$
$998$	−2.38388e10	−0.759149
$999$	1.56409e10	0.496344

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.8.a.c.1.3	✓	6
3.2	odd	2		153.8.a.h.1.4		6
4.3	odd	2		272.8.a.i.1.5		6
5.4	even	2		425.8.a.c.1.4		6
17.16	even	2		289.8.a.c.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.8.a.c.1.3	✓	6	1.1	even	1	trivial
153.8.a.h.1.4		6	3.2	odd	2
272.8.a.i.1.5		6	4.3	odd	2
289.8.a.c.1.3		6	17.16	even	2
425.8.a.c.1.4		6	5.4	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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	17.a (trivial)

\(f(q)\)	\(=\)	\(q-6.77791 q^{2} -52.1459 q^{3} -82.0600 q^{4} +356.107 q^{5} +353.440 q^{6} +248.464 q^{7} +1423.77 q^{8} +532.198 q^{9} +O(q^{10})\)	\(q-6.77791 q^{2} -52.1459 q^{3} -82.0600 q^{4} +356.107 q^{5} +353.440 q^{6} +248.464 q^{7} +1423.77 q^{8} +532.198 q^{9} -2413.66 q^{10} +6309.04 q^{11} +4279.09 q^{12} -595.847 q^{13} -1684.07 q^{14} -18569.6 q^{15} +853.516 q^{16} -4913.00 q^{17} -3607.19 q^{18} +1253.07 q^{19} -29222.2 q^{20} -12956.4 q^{21} -42762.1 q^{22} +102061. q^{23} -74243.7 q^{24} +48687.5 q^{25} +4038.59 q^{26} +86291.2 q^{27} -20389.0 q^{28} -22275.3 q^{29} +125863. q^{30} +281828. q^{31} -188027. q^{32} -328991. q^{33} +33299.9 q^{34} +88480.0 q^{35} -43672.1 q^{36} +181257. q^{37} -8493.16 q^{38} +31071.0 q^{39} +507014. q^{40} -443891. q^{41} +87817.3 q^{42} +269359. q^{43} -517720. q^{44} +189520. q^{45} -691758. q^{46} -1.23339e6 q^{47} -44507.4 q^{48} -761808. q^{49} -329999. q^{50} +256193. q^{51} +48895.2 q^{52} +1.61126e6 q^{53} -584874. q^{54} +2.24670e6 q^{55} +353755. q^{56} -65342.3 q^{57} +150980. q^{58} +1.46192e6 q^{59} +1.52382e6 q^{60} -782676. q^{61} -1.91020e6 q^{62} +132232. q^{63} +1.16518e6 q^{64} -212185. q^{65} +2.22987e6 q^{66} +220097. q^{67} +403161. q^{68} -5.32205e6 q^{69} -599709. q^{70} -3.29315e6 q^{71} +757726. q^{72} +4.05380e6 q^{73} -1.22855e6 q^{74} -2.53885e6 q^{75} -102827. q^{76} +1.56757e6 q^{77} -210596. q^{78} -2.56326e6 q^{79} +303943. q^{80} -5.66365e6 q^{81} +3.00865e6 q^{82} +292814. q^{83} +1.06320e6 q^{84} -1.74956e6 q^{85} -1.82569e6 q^{86} +1.16157e6 q^{87} +8.98261e6 q^{88} +1.06095e6 q^{89} -1.28455e6 q^{90} -148047. q^{91} -8.37510e6 q^{92} -1.46962e7 q^{93} +8.35981e6 q^{94} +446226. q^{95} +9.80485e6 q^{96} +1.57192e7 q^{97} +5.16347e6 q^{98} +3.35766e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 15 q^{2} + 40 q^{3} + 485 q^{4} - 184 q^{5} + 1882 q^{6} + 2064 q^{7} + 6729 q^{8} + 5846 q^{9}+O(q^{10}) \) 6 * q + 15 * q^2 + 40 * q^3 + 485 * q^4 - 184 * q^5 + 1882 * q^6 + 2064 * q^7 + 6729 * q^8 + 5846 * q^9	\( 6 q + 15 q^{2} + 40 q^{3} + 485 q^{4} - 184 q^{5} + 1882 q^{6} + 2064 q^{7} + 6729 q^{8} + 5846 q^{9} + 5592 q^{10} + 2000 q^{11} + 3646 q^{12} + 8708 q^{13} - 19844 q^{14} + 12552 q^{15} + 5841 q^{16} - 29478 q^{17} - 108697 q^{18} - 45400 q^{19} - 202744 q^{20} - 37896 q^{21} + 1378 q^{22} - 27208 q^{23} + 21366 q^{24} + 281826 q^{25} + 69094 q^{26} + 126520 q^{27} - 29428 q^{28} + 404808 q^{29} - 441296 q^{30} + 532984 q^{31} + 790577 q^{32} + 848728 q^{33} - 73695 q^{34} + 358952 q^{35} - 619171 q^{36} + 437968 q^{37} - 778900 q^{38} + 114856 q^{39} - 2458744 q^{40} - 441660 q^{41} - 1730952 q^{42} + 1152240 q^{43} - 1798650 q^{44} - 1089768 q^{45} - 897816 q^{46} - 90296 q^{47} + 852006 q^{48} + 692566 q^{49} - 834883 q^{50} - 196520 q^{51} + 2801826 q^{52} - 137764 q^{53} - 856340 q^{54} + 4133896 q^{55} - 191892 q^{56} - 674928 q^{57} + 4396216 q^{58} - 2050080 q^{59} + 1738352 q^{60} + 89808 q^{61} + 5080332 q^{62} - 828312 q^{63} + 14723105 q^{64} - 3447008 q^{65} - 2276164 q^{66} + 4686632 q^{67} - 2382805 q^{68} - 10069560 q^{69} + 16450144 q^{70} - 5553232 q^{71} - 7683039 q^{72} - 1436452 q^{73} + 1443964 q^{74} - 23179128 q^{75} - 5332908 q^{76} - 12631512 q^{77} - 7122876 q^{78} + 12387160 q^{79} - 26552696 q^{80} - 5930674 q^{81} + 20716762 q^{82} - 1877808 q^{83} - 7443960 q^{84} + 903992 q^{85} - 8020112 q^{86} + 19832472 q^{87} + 8442878 q^{88} - 19324324 q^{89} + 36660344 q^{90} + 14536792 q^{91} - 25909888 q^{92} - 13862632 q^{93} + 9307536 q^{94} + 3085936 q^{95} + 18152550 q^{96} - 7630812 q^{97} + 22758631 q^{98} + 25069976 q^{99}+O(q^{100}) \) 6 * q + 15 * q^2 + 40 * q^3 + 485 * q^4 - 184 * q^5 + 1882 * q^6 + 2064 * q^7 + 6729 * q^8 + 5846 * q^9 + 5592 * q^10 + 2000 * q^11 + 3646 * q^12 + 8708 * q^13 - 19844 * q^14 + 12552 * q^15 + 5841 * q^16 - 29478 * q^17 - 108697 * q^18 - 45400 * q^19 - 202744 * q^20 - 37896 * q^21 + 1378 * q^22 - 27208 * q^23 + 21366 * q^24 + 281826 * q^25 + 69094 * q^26 + 126520 * q^27 - 29428 * q^28 + 404808 * q^29 - 441296 * q^30 + 532984 * q^31 + 790577 * q^32 + 848728 * q^33 - 73695 * q^34 + 358952 * q^35 - 619171 * q^36 + 437968 * q^37 - 778900 * q^38 + 114856 * q^39 - 2458744 * q^40 - 441660 * q^41 - 1730952 * q^42 + 1152240 * q^43 - 1798650 * q^44 - 1089768 * q^45 - 897816 * q^46 - 90296 * q^47 + 852006 * q^48 + 692566 * q^49 - 834883 * q^50 - 196520 * q^51 + 2801826 * q^52 - 137764 * q^53 - 856340 * q^54 + 4133896 * q^55 - 191892 * q^56 - 674928 * q^57 + 4396216 * q^58 - 2050080 * q^59 + 1738352 * q^60 + 89808 * q^61 + 5080332 * q^62 - 828312 * q^63 + 14723105 * q^64 - 3447008 * q^65 - 2276164 * q^66 + 4686632 * q^67 - 2382805 * q^68 - 10069560 * q^69 + 16450144 * q^70 - 5553232 * q^71 - 7683039 * q^72 - 1436452 * q^73 + 1443964 * q^74 - 23179128 * q^75 - 5332908 * q^76 - 12631512 * q^77 - 7122876 * q^78 + 12387160 * q^79 - 26552696 * q^80 - 5930674 * q^81 + 20716762 * q^82 - 1877808 * q^83 - 7443960 * q^84 + 903992 * q^85 - 8020112 * q^86 + 19832472 * q^87 + 8442878 * q^88 - 19324324 * q^89 + 36660344 * q^90 + 14536792 * q^91 - 25909888 * q^92 - 13862632 * q^93 + 9307536 * q^94 + 3085936 * q^95 + 18152550 * q^96 - 7630812 * q^97 + 22758631 * q^98 + 25069976 * q^99

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