LMFDB - Embedded newform 289.10.a.a.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,10,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, 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("289.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	289.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:	$148.845356651$
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:	no (minimal twist has level 17)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$33.6330$ of defining polynomial
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+26.6330 q^{2} +85.9747 q^{3} +197.318 q^{4} +1460.58 q^{5} +2289.77 q^{6} +446.232 q^{7} -8380.94 q^{8} -12291.3 q^{9} +O(q^{10})$	\(q+26.6330 q^{2} +85.9747 q^{3} +197.318 q^{4} +1460.58 q^{5} +2289.77 q^{6} +446.232 q^{7} -8380.94 q^{8} -12291.3 q^{9} +38899.6 q^{10} -2565.20 q^{11} +16964.3 q^{12} +70467.9 q^{13} +11884.5 q^{14} +125573. q^{15} -324236. q^{16} -327356. q^{18} -474111. q^{19} +288198. q^{20} +38364.6 q^{21} -68319.0 q^{22} -1.74586e6 q^{23} -720549. q^{24} +180168. q^{25} +1.87677e6 q^{26} -2.74899e6 q^{27} +88049.4 q^{28} -501157. q^{29} +3.34439e6 q^{30} +510635. q^{31} -4.34435e6 q^{32} -220542. q^{33} +651757. q^{35} -2.42530e6 q^{36} +3.74847e6 q^{37} -1.26270e7 q^{38} +6.05845e6 q^{39} -1.22410e7 q^{40} +3.04327e7 q^{41} +1.02177e6 q^{42} -2.15222e7 q^{43} -506159. q^{44} -1.79525e7 q^{45} -4.64976e7 q^{46} +3.43306e6 q^{47} -2.78761e7 q^{48} -4.01545e7 q^{49} +4.79842e6 q^{50} +1.39046e7 q^{52} -2.87800e7 q^{53} -7.32138e7 q^{54} -3.74668e6 q^{55} -3.73984e6 q^{56} -4.07615e7 q^{57} -1.33473e7 q^{58} -1.37313e8 q^{59} +2.47778e7 q^{60} -1.21854e8 q^{61} +1.35997e7 q^{62} -5.48479e6 q^{63} +5.03058e7 q^{64} +1.02924e8 q^{65} -5.87371e6 q^{66} -8.31665e7 q^{67} -1.50100e8 q^{69} +1.73583e7 q^{70} -1.48492e8 q^{71} +1.03013e8 q^{72} -1.45029e8 q^{73} +9.98331e7 q^{74} +1.54899e7 q^{75} -9.35504e7 q^{76} -1.14467e6 q^{77} +1.61355e8 q^{78} +4.22172e8 q^{79} -4.73573e8 q^{80} +5.58742e6 q^{81} +8.10515e8 q^{82} -5.36072e7 q^{83} +7.57002e6 q^{84} -5.73201e8 q^{86} -4.30868e7 q^{87} +2.14988e7 q^{88} +9.26167e8 q^{89} -4.78129e8 q^{90} +3.14450e7 q^{91} -3.44490e8 q^{92} +4.39017e7 q^{93} +9.14328e7 q^{94} -6.92477e8 q^{95} -3.73504e8 q^{96} -1.44334e9 q^{97} -1.06944e9 q^{98} +3.15298e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 5 q - 33 q^{2} + 236 q^{3} + 853 q^{4} - 1480 q^{5} - 7578 q^{6} + 13202 q^{7} - 42423 q^{8} + 10981 q^{9} + 89328 q^{10} + 68036 q^{11} + 406010 q^{12} - 158862 q^{13} + 84700 q^{14} - 687324 q^{15} + 350225 q^{16} - 1911585 q^{18} - 370992 q^{19} - 1632640 q^{20} + 1783880 q^{21} - 122290 q^{22} - 1645870 q^{23} - 9678702 q^{24} + 3270239 q^{25} + 734846 q^{26} + 2998268 q^{27} - 183372 q^{28} - 3668616 q^{29} + 17048544 q^{30} + 7262362 q^{31} - 5605919 q^{32} - 11334900 q^{33} - 26503988 q^{35} + 49782133 q^{36} + 31420708 q^{37} + 18513700 q^{38} + 42449884 q^{39} + 53930464 q^{40} + 7996938 q^{41} - 44519496 q^{42} - 56908268 q^{43} - 43323054 q^{44} - 12799536 q^{45} + 32063472 q^{46} - 16903336 q^{47} + 102794498 q^{48} - 11784059 q^{49} + 85921093 q^{50} + 173619082 q^{52} - 83362982 q^{53} - 386329164 q^{54} + 6363364 q^{55} - 317409372 q^{56} - 136615904 q^{57} - 64577488 q^{58} - 37946604 q^{59} - 223158912 q^{60} + 77685452 q^{61} - 324855300 q^{62} + 191945278 q^{63} + 131623105 q^{64} + 40321288 q^{65} + 298037676 q^{66} - 304503600 q^{67} - 333409272 q^{69} - 122787392 q^{70} + 476602922 q^{71} - 1301701911 q^{72} + 289980486 q^{73} - 262289012 q^{74} + 153685772 q^{75} - 1031276084 q^{76} - 143385648 q^{77} - 691646196 q^{78} + 828240610 q^{79} - 912750944 q^{80} + 891328609 q^{81} + 1109615654 q^{82} + 194681148 q^{83} + 1541719592 q^{84} + 1164707144 q^{86} + 158149884 q^{87} + 1017979978 q^{88} + 376848106 q^{89} + 2240087472 q^{90} - 194543664 q^{91} - 2506713088 q^{92} + 3494835920 q^{93} - 2244811104 q^{94} - 1498679864 q^{95} - 2935047582 q^{96} - 692035246 q^{97} + 871744055 q^{98} - 2027106408 q^{99}+O(q^{100}) \) 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 - 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 - 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 + 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 - 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 + 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 $

$2$	26.6330	1.17702	0.588512	−	0.808488i	$-0.299714\pi$
$2$	26.6330	1.17702	0.588512	+	0.808488i	$0.299714\pi$
$3$	85.9747	0.612809	0.306404	−	0.951901i	$-0.400874\pi$
$3$	85.9747	0.612809	0.306404	+	0.951901i	$0.400874\pi$
$4$	197.318	0.385386
$5$	1460.58	1.04511	0.522553	−	0.852607i	$-0.324980\pi$
$5$	1460.58	1.04511	0.522553	+	0.852607i	$0.324980\pi$
$6$	2289.77	0.721291
$7$	446.232	0.0702456	0.0351228	−	0.999383i	$-0.488818\pi$
$7$	446.232	0.0702456	0.0351228	+	0.999383i	$0.488818\pi$
$8$	−8380.94	−0.723416
$9$	−12291.3	−0.624465
$10$	38899.6	1.23011
$11$	−2565.20	−0.0528268	−0.0264134	−	0.999651i	$-0.508409\pi$
$11$	−2565.20	−0.0528268	−0.0264134	+	0.999651i	$0.508409\pi$
$12$	16964.3	0.236168
$13$	70467.9	0.684299	0.342150	−	0.939645i	$-0.388845\pi$
$13$	70467.9	0.684299	0.342150	+	0.939645i	$0.388845\pi$
$14$	11884.5	0.0826808
$15$	125573.	0.640450
$16$	−324236.	−1.23686
$17$	0	0
$17$	0	0
$18$	−327356.	−0.735011
$19$	−474111.	−0.834620	−0.417310	−	0.908764i	$-0.637027\pi$
$19$	−474111.	−0.834620	−0.417310	+	0.908764i	$0.637027\pi$
$20$	288198.	0.402769
$21$	38364.6	0.0430471
$22$	−68319.0	−0.0621784
$23$	−1.74586e6	−1.30087	−0.650437	−	0.759561i	$-0.725414\pi$
$23$	−1.74586e6	−1.30087	−0.650437	+	0.759561i	$0.725414\pi$
$24$	−720549.	−0.443315
$25$	180168.	0.0922461
$26$	1.87677e6	0.805437
$27$	−2.74899e6	−0.995487
$28$	88049.4	0.0270717
$29$	−501157.	−0.131578	−0.0657889	−	0.997834i	$-0.520956\pi$
$29$	−501157.	−0.131578	−0.0657889	+	0.997834i	$0.520956\pi$
$30$	3.34439e6	0.753825
$31$	510635.	0.0993077	0.0496538	−	0.998766i	$-0.484188\pi$
$31$	510635.	0.0993077	0.0496538	+	0.998766i	$0.484188\pi$
$32$	−4.34435e6	−0.732403
$33$	−220542.	−0.0323727
$34$	0	0
$35$	651757.	0.0734141
$36$	−2.42530e6	−0.240660
$37$	3.74847e6	0.328811	0.164406	−	0.986393i	$-0.447429\pi$
$37$	3.74847e6	0.328811	0.164406	+	0.986393i	$0.447429\pi$
$38$	−1.26270e7	−0.982368
$39$	6.05845e6	0.419345
$40$	−1.22410e7	−0.756046
$41$	3.04327e7	1.68195	0.840975	−	0.541074i	$-0.181982\pi$
$41$	3.04327e7	1.68195	0.840975	+	0.541074i	$0.181982\pi$
$42$	1.02177e6	0.0506675
$43$	−2.15222e7	−0.960017	−0.480008	−	0.877264i	$-0.659366\pi$
$43$	−2.15222e7	−0.960017	−0.480008	+	0.877264i	$0.659366\pi$
$44$	−506159.	−0.0203587
$45$	−1.79525e7	−0.652632
$46$	−4.64976e7	−1.53116
$47$	3.43306e6	0.102622	0.0513111	−	0.998683i	$-0.483660\pi$
$47$	3.43306e6	0.102622	0.0513111	+	0.998683i	$0.483660\pi$
$48$	−2.78761e7	−0.757961
$49$	−4.01545e7	−0.995066
$50$	4.79842e6	0.108576
$51$	0	0
$52$	1.39046e7	0.263719
$53$	−2.87800e7	−0.501013	−0.250506	−	0.968115i	$-0.580597\pi$
$53$	−2.87800e7	−0.501013	−0.250506	+	0.968115i	$0.580597\pi$
$54$	−7.32138e7	−1.17171
$55$	−3.74668e6	−0.0552096
$56$	−3.73984e6	−0.0508168
$57$	−4.07615e7	−0.511462
$58$	−1.33473e7	−0.154870
$59$	−1.37313e8	−1.47529	−0.737643	−	0.675191i	$-0.764061\pi$
$59$	−1.37313e8	−1.47529	−0.737643	+	0.675191i	$0.764061\pi$
$60$	2.47778e7	0.246821
$61$	−1.21854e8	−1.12682	−0.563410	−	0.826177i	$-0.690511\pi$
$61$	−1.21854e8	−1.12682	−0.563410	+	0.826177i	$0.690511\pi$
$62$	1.35997e7	0.116888
$63$	−5.48479e6	−0.0438659
$64$	5.03058e7	0.374808
$65$	1.02924e8	0.715165
$66$	−5.87371e6	−0.0381035
$67$	−8.31665e7	−0.504210	−0.252105	−	0.967700i	$-0.581123\pi$
$67$	−8.31665e7	−0.504210	−0.252105	+	0.967700i	$0.581123\pi$
$68$	0	0
$69$	−1.50100e8	−0.797187
$70$	1.73583e7	0.0864102
$71$	−1.48492e8	−0.693490	−0.346745	−	0.937960i	$-0.612713\pi$
$71$	−1.48492e8	−0.693490	−0.346745	+	0.937960i	$0.612713\pi$
$72$	1.03013e8	0.451748
$73$	−1.45029e8	−0.597726	−0.298863	−	0.954296i	$-0.596607\pi$
$73$	−1.45029e8	−0.597726	−0.298863	+	0.954296i	$0.596607\pi$
$74$	9.98331e7	0.387019
$75$	1.54899e7	0.0565292
$76$	−9.35504e7	−0.321651
$77$	−1.14467e6	−0.00371085
$78$	1.61355e8	0.493579
$79$	4.22172e8	1.21946	0.609729	−	0.792610i	$-0.291278\pi$
$79$	4.22172e8	1.21946	0.609729	+	0.792610i	$0.291278\pi$
$80$	−4.73573e8	−1.29265
$81$	5.58742e6	0.0144221
$82$	8.10515e8	1.97970
$83$	−5.36072e7	−0.123986	−0.0619929	−	0.998077i	$-0.519746\pi$
$83$	−5.36072e7	−0.123986	−0.0619929	+	0.998077i	$0.519746\pi$
$84$	7.57002e6	0.0165898
$85$	0	0
$86$	−5.73201e8	−1.12996
$87$	−4.30868e7	−0.0806321
$88$	2.14988e7	0.0382157
$89$	9.26167e8	1.56471	0.782355	−	0.622832i	$-0.214018\pi$
$89$	9.26167e8	1.56471	0.782355	+	0.622832i	$0.214018\pi$
$90$	−4.78129e8	−0.768164
$91$	3.14450e7	0.0480690
$92$	−3.44490e8	−0.501338
$93$	4.39017e7	0.0608566
$94$	9.14328e7	0.120789
$95$	−6.92477e8	−0.872266
$96$	−3.73504e8	−0.448823
$97$	−1.44334e9	−1.65538	−0.827688	−	0.561189i	$-0.810344\pi$
$97$	−1.44334e9	−1.65538	−0.827688	+	0.561189i	$0.810344\pi$
$98$	−1.06944e9	−1.17122
$99$	3.15298e7	0.0329885
$100$	3.55504e7	0.0355504
$101$	1.73497e9	1.65900	0.829498	−	0.558510i	$-0.188627\pi$
$101$	1.73497e9	1.65900	0.829498	+	0.558510i	$0.188627\pi$
$102$	0	0
$103$	−1.15796e9	−1.01374	−0.506871	−	0.862022i	$-0.669198\pi$
$103$	−1.15796e9	−1.01374	−0.506871	+	0.862022i	$0.669198\pi$
$104$	−5.90587e8	−0.495033
$105$	5.60346e7	0.0449888
$106$	−7.66498e8	−0.589704
$107$	−6.18767e8	−0.456352	−0.228176	−	0.973620i	$-0.573276\pi$
$107$	−6.18767e8	−0.456352	−0.228176	+	0.973620i	$0.573276\pi$
$108$	−5.42423e8	−0.383647
$109$	1.81586e9	1.23215	0.616074	−	0.787688i	$-0.288722\pi$
$109$	1.81586e9	1.23215	0.616074	+	0.787688i	$0.288722\pi$
$110$	−9.97854e7	−0.0649830
$111$	3.22274e8	0.201498
$112$	−1.44685e8	−0.0868842
$113$	2.89208e9	1.66862	0.834310	−	0.551296i	$-0.185866\pi$
$113$	2.89208e9	1.66862	0.834310	+	0.551296i	$0.185866\pi$
$114$	−1.08560e9	−0.602004
$115$	−2.54997e9	−1.35955
$116$	−9.88871e7	−0.0507083
$117$	−8.66145e8	−0.427321
$118$	−3.65705e9	−1.73645
$119$	0	0
$120$	−1.05242e9	−0.463312
$121$	−2.35137e9	−0.997209
$122$	−3.24533e9	−1.32629
$123$	2.61644e9	1.03071
$124$	1.00757e8	0.0382718
$125$	−2.58954e9	−0.948699
$126$	−1.46076e8	−0.0516313
$127$	1.38692e9	0.473081	0.236540	−	0.971622i	$-0.423986\pi$
$127$	1.38692e9	0.473081	0.236540	+	0.971622i	$0.423986\pi$
$128$	3.56410e9	1.17356
$129$	−1.85037e9	−0.588307
$130$	2.74118e9	0.841767
$131$	−5.87855e9	−1.74401	−0.872006	−	0.489496i	$-0.837181\pi$
$131$	−5.87855e9	−1.74401	−0.872006	+	0.489496i	$0.837181\pi$
$132$	−4.35169e7	−0.0124760
$133$	−2.11563e8	−0.0586284
$134$	−2.21497e9	−0.593468
$135$	−4.01511e9	−1.04039
$136$	0	0
$137$	2.25574e9	0.547075	0.273538	−	0.961861i	$-0.411806\pi$
$137$	2.25574e9	0.547075	0.273538	+	0.961861i	$0.411806\pi$
$138$	−3.99762e9	−0.938308
$139$	2.06541e9	0.469289	0.234645	−	0.972081i	$-0.424607\pi$
$139$	2.06541e9	0.469289	0.234645	+	0.972081i	$0.424607\pi$
$140$	1.28603e8	0.0282928
$141$	2.95156e8	0.0628878
$142$	−3.95479e9	−0.816254
$143$	−1.80764e8	−0.0361493
$144$	3.98530e9	0.772378
$145$	−7.31980e8	−0.137513
$146$	−3.86256e9	−0.703538
$147$	−3.45227e9	−0.609785
$148$	7.39640e8	0.126719
$149$	−3.00126e9	−0.498845	−0.249422	−	0.968395i	$-0.580241\pi$
$149$	−3.00126e9	−0.498845	−0.249422	+	0.968395i	$0.580241\pi$
$150$	4.12543e8	0.0665363
$151$	−1.05501e10	−1.65143	−0.825714	−	0.564089i	$-0.809227\pi$
$151$	−1.05501e10	−1.65143	−0.825714	+	0.564089i	$0.809227\pi$
$152$	3.97349e9	0.603777
$153$	0	0
$154$	−3.04861e7	−0.00436776
$155$	7.45823e8	0.103787
$156$	1.19544e9	0.161610
$157$	8.51695e9	1.11876	0.559378	−	0.828912i	$-0.311040\pi$
$157$	8.51695e9	1.11876	0.559378	+	0.828912i	$0.311040\pi$
$158$	1.12437e10	1.43533
$159$	−2.47435e9	−0.307025
$160$	−6.34527e9	−0.765439
$161$	−7.79059e8	−0.0913806
$162$	1.48810e8	0.0169752
$163$	6.90475e9	0.766133	0.383066	−	0.923721i	$-0.374868\pi$
$163$	6.90475e9	0.766133	0.383066	+	0.923721i	$0.374868\pi$
$164$	6.00491e9	0.648200
$165$	−3.22120e8	−0.0338329
$166$	−1.42772e9	−0.145934
$167$	8.18088e9	0.813909	0.406954	−	0.913448i	$-0.366591\pi$
$167$	8.18088e9	0.813909	0.406954	+	0.913448i	$0.366591\pi$
$168$	−3.21532e8	−0.0311410
$169$	−5.63878e9	−0.531735
$170$	0	0
$171$	5.82746e9	0.521191
$172$	−4.24671e9	−0.369977
$173$	−1.96517e9	−0.166799	−0.0833995	−	0.996516i	$-0.526578\pi$
$173$	−1.96517e9	−0.166799	−0.0833995	+	0.996516i	$0.526578\pi$
$174$	−1.14753e9	−0.0949059
$175$	8.03968e7	0.00647988
$176$	8.31731e8	0.0653395
$177$	−1.18054e10	−0.904069
$178$	2.46666e10	1.84170
$179$	−2.51083e10	−1.82801	−0.914006	−	0.405701i	$-0.867028\pi$
$179$	−2.51083e10	−1.82801	−0.914006	+	0.405701i	$0.867028\pi$
$180$	−3.54234e9	−0.251515
$181$	3.03563e9	0.210230	0.105115	−	0.994460i	$-0.466479\pi$
$181$	3.03563e9	0.210230	0.105115	+	0.994460i	$0.466479\pi$
$182$	8.37475e8	0.0565784
$183$	−1.04763e10	−0.690526
$184$	1.46320e10	0.941072
$185$	5.47494e9	0.343642
$186$	1.16923e9	0.0716297
$187$	0	0
$188$	6.77404e8	0.0395491
$189$	−1.22668e9	−0.0699286
$190$	−1.84427e10	−1.02668
$191$	−3.15580e10	−1.71577	−0.857885	−	0.513841i	$-0.828222\pi$
$191$	−3.15580e10	−1.71577	−0.857885	+	0.513841i	$0.828222\pi$
$192$	4.32503e9	0.229685
$193$	−2.29526e9	−0.119076	−0.0595379	−	0.998226i	$-0.518963\pi$
$193$	−2.29526e9	−0.119076	−0.0595379	+	0.998226i	$0.518963\pi$
$194$	−3.84406e10	−1.94842
$195$	8.84886e9	0.438260
$196$	−7.92319e9	−0.383484
$197$	−2.65359e10	−1.25527	−0.627633	−	0.778509i	$-0.715976\pi$
$197$	−2.65359e10	−1.25527	−0.627633	+	0.778509i	$0.715976\pi$
$198$	8.39733e8	0.0388283
$199$	1.45778e10	0.658949	0.329475	−	0.944164i	$-0.393128\pi$
$199$	1.45778e10	0.658949	0.329475	+	0.944164i	$0.393128\pi$
$200$	−1.50998e9	−0.0667323
$201$	−7.15021e9	−0.308985
$202$	4.62074e10	1.95268
$203$	−2.23632e8	−0.00924276
$204$	0	0
$205$	4.44494e10	1.75782
$206$	−3.08401e10	−1.19320
$207$	2.14590e10	0.812350
$208$	−2.28482e10	−0.846385
$209$	1.21619e9	0.0440903
$210$	1.49237e9	0.0529529
$211$	−4.31184e10	−1.49759	−0.748793	−	0.662804i	$-0.769366\pi$
$211$	−4.31184e10	−1.49759	−0.748793	+	0.662804i	$0.769366\pi$
$212$	−5.67880e9	−0.193083
$213$	−1.27665e10	−0.424977
$214$	−1.64796e10	−0.537137
$215$	−3.14349e10	−1.00332
$216$	2.30391e10	0.720151
$217$	2.27861e8	0.00697593
$218$	4.83618e10	1.45027
$219$	−1.24688e10	−0.366292
$220$	−7.39286e8	−0.0212770
$221$	0	0
$222$	8.58312e9	0.237169
$223$	−3.81093e10	−1.03195	−0.515975	−	0.856604i	$-0.672570\pi$
$223$	−3.81093e10	−1.03195	−0.515975	+	0.856604i	$0.672570\pi$
$224$	−1.93859e9	−0.0514481
$225$	−2.21451e9	−0.0576045
$226$	7.70248e10	1.96401
$227$	2.78123e10	0.695216	0.347608	−	0.937640i	$-0.386994\pi$
$227$	2.78123e10	0.695216	0.347608	+	0.937640i	$0.386994\pi$
$228$	−8.04297e9	−0.197110
$229$	3.54756e10	0.852452	0.426226	−	0.904617i	$-0.359843\pi$
$229$	3.54756e10	0.852452	0.426226	+	0.904617i	$0.359843\pi$
$230$	−6.79135e10	−1.60022
$231$	−9.84130e7	−0.00227404
$232$	4.20017e9	0.0951854
$233$	−4.62674e10	−1.02843	−0.514213	−	0.857662i	$-0.671916\pi$
$233$	−4.62674e10	−1.02843	−0.514213	+	0.857662i	$0.671916\pi$
$234$	−2.30681e10	−0.502967
$235$	5.01426e9	0.107251
$236$	−2.70942e10	−0.568555
$237$	3.62961e10	0.747295
$238$	0	0
$239$	8.33772e10	1.65294	0.826469	−	0.562982i	$-0.190346\pi$
$239$	8.33772e10	1.65294	0.826469	+	0.562982i	$0.190346\pi$
$240$	−4.07153e10	−0.792149
$241$	7.31412e9	0.139664	0.0698321	−	0.997559i	$-0.477754\pi$
$241$	7.31412e9	0.139664	0.0698321	+	0.997559i	$0.477754\pi$
$242$	−6.26240e10	−1.17374
$243$	5.45887e10	1.00432
$244$	−2.40439e10	−0.434261
$245$	−5.86488e10	−1.03995
$246$	6.96838e10	1.21318
$247$	−3.34096e10	−0.571130
$248$	−4.27960e9	−0.0718407
$249$	−4.60886e9	−0.0759795
$250$	−6.89674e10	−1.11664
$251$	9.50519e10	1.51157	0.755786	−	0.654818i	$-0.227255\pi$
$251$	9.50519e10	1.51157	0.755786	+	0.654818i	$0.227255\pi$
$252$	−1.08225e9	−0.0169053
$253$	4.47849e9	0.0687210
$254$	3.69379e10	0.556827
$255$	0	0
$256$	6.91663e10	1.00650
$257$	−7.20648e10	−1.03044	−0.515222	−	0.857057i	$-0.672290\pi$
$257$	−7.20648e10	−1.03044	−0.515222	+	0.857057i	$0.672290\pi$
$258$	−4.92808e10	−0.692451
$259$	1.67269e9	0.0230975
$260$	2.03087e10	0.275615
$261$	6.15989e9	0.0821658
$262$	−1.56564e11	−2.05274
$263$	−1.71832e10	−0.221464	−0.110732	−	0.993850i	$-0.535320\pi$
$263$	−1.71832e10	−0.221464	−0.110732	+	0.993850i	$0.535320\pi$
$264$	1.84835e9	0.0234189
$265$	−4.20354e10	−0.523612
$266$	−5.63457e9	−0.0690070
$267$	7.96269e10	0.958869
$268$	−1.64102e10	−0.194316
$269$	−1.10544e10	−0.128721	−0.0643605	−	0.997927i	$-0.520501\pi$
$269$	−1.10544e10	−0.128721	−0.0643605	+	0.997927i	$0.520501\pi$
$270$	−1.06935e11	−1.22456
$271$	−1.41142e11	−1.58963	−0.794813	−	0.606855i	$-0.792431\pi$
$271$	−1.41142e11	−1.58963	−0.794813	+	0.606855i	$0.792431\pi$
$272$	0	0
$273$	2.70347e9	0.0294571
$274$	6.00773e10	0.643921
$275$	−4.62168e8	−0.00487307
$276$	−2.96174e10	−0.307225
$277$	1.12712e11	1.15030	0.575151	−	0.818047i	$-0.304943\pi$
$277$	1.12712e11	1.15030	0.575151	+	0.818047i	$0.304943\pi$
$278$	5.50082e10	0.552365
$279$	−6.27639e9	−0.0620142
$280$	−5.46234e9	−0.0531089
$281$	4.86687e10	0.465662	0.232831	−	0.972517i	$-0.425201\pi$
$281$	4.86687e10	0.465662	0.232831	+	0.972517i	$0.425201\pi$
$282$	7.86091e9	0.0740204
$283$	1.21207e11	1.12328	0.561640	−	0.827382i	$-0.310171\pi$
$283$	1.21207e11	1.12328	0.561640	+	0.827382i	$0.310171\pi$
$284$	−2.93001e10	−0.267261
$285$	−5.95355e10	−0.534532
$286$	−4.81430e9	−0.0425486
$287$	1.35800e10	0.118150
$288$	5.33979e10	0.457360
$289$	0	0
$290$	−1.94948e10	−0.161856
$291$	−1.24091e11	−1.01443
$292$	−2.86168e10	−0.230355
$293$	9.65141e10	0.765044	0.382522	−	0.923946i	$-0.375056\pi$
$293$	9.65141e10	0.765044	0.382522	+	0.923946i	$0.375056\pi$
$294$	−9.19444e10	−0.717732
$295$	−2.00556e11	−1.54183
$296$	−3.14157e10	−0.237867
$297$	7.05170e9	0.0525884
$298$	−7.99326e10	−0.587153
$299$	−1.23027e11	−0.890187
$300$	3.05643e9	0.0217856
$301$	−9.60389e9	−0.0674370
$302$	−2.80981e11	−1.94377
$303$	1.49163e11	1.01665
$304$	1.53724e11	1.03231
$305$	−1.77977e11	−1.17765
$306$	0	0
$307$	−1.31572e11	−0.845360	−0.422680	−	0.906279i	$-0.638911\pi$
$307$	−1.31572e11	−0.845360	−0.422680	+	0.906279i	$0.638911\pi$
$308$	−2.25864e8	−0.00143011
$309$	−9.95556e10	−0.621230
$310$	1.98635e10	0.122160
$311$	−3.19848e9	−0.0193875	−0.00969376	−	0.999953i	$-0.503086\pi$
$311$	−3.19848e9	−0.0193875	−0.00969376	+	0.999953i	$0.503086\pi$
$312$	−5.07755e10	−0.303360
$313$	1.59936e11	0.941882	0.470941	−	0.882165i	$-0.343914\pi$
$313$	1.59936e11	0.941882	0.470941	+	0.882165i	$0.343914\pi$
$314$	2.26832e11	1.31680
$315$	−8.01097e9	−0.0458445
$316$	8.33019e10	0.469962
$317$	−6.77437e10	−0.376792	−0.188396	−	0.982093i	$-0.560329\pi$
$317$	−6.77437e10	−0.376792	−0.188396	+	0.982093i	$0.560329\pi$
$318$	−6.58994e10	−0.361376
$319$	1.28557e9	0.00695083
$320$	7.34757e10	0.391714
$321$	−5.31983e10	−0.279657
$322$	−2.07487e10	−0.107557
$323$	0	0
$324$	1.10250e9	0.00555808
$325$	1.26961e10	0.0631239
$326$	1.83894e11	0.901757
$327$	1.56118e11	0.755071
$328$	−2.55055e11	−1.21675
$329$	1.53194e9	0.00720876
$330$	−8.57902e9	−0.0398222
$331$	1.23890e11	0.567295	0.283647	−	0.958929i	$-0.408456\pi$
$331$	1.23890e11	0.567295	0.283647	+	0.958929i	$0.408456\pi$
$332$	−1.05776e10	−0.0477824
$333$	−4.60738e10	−0.205331
$334$	2.17881e11	0.957990
$335$	−1.21471e11	−0.526953
$336$	−1.24392e10	−0.0532434
$337$	1.66091e11	0.701476	0.350738	−	0.936474i	$-0.385931\pi$
$337$	1.66091e11	0.701476	0.350738	+	0.936474i	$0.385931\pi$
$338$	−1.50178e11	−0.625865
$339$	2.48646e11	1.02254
$340$	0	0
$341$	−1.30988e9	−0.00524611
$342$	1.55203e11	0.613454
$343$	−3.59253e10	−0.140145
$344$	1.80376e11	0.694491
$345$	−2.19233e11	−0.833144
$346$	−5.23385e10	−0.196327
$347$	3.59340e11	1.33052	0.665262	−	0.746610i	$-0.268320\pi$
$347$	3.59340e11	1.33052	0.665262	+	0.746610i	$0.268320\pi$
$348$	−8.50179e9	−0.0310745
$349$	4.55698e11	1.64423	0.822116	−	0.569321i	$-0.192794\pi$
$349$	4.55698e11	1.64423	0.822116	+	0.569321i	$0.192794\pi$
$350$	2.14121e9	0.00762698
$351$	−1.93715e11	−0.681211
$352$	1.11441e10	0.0386905
$353$	−2.35070e11	−0.805772	−0.402886	−	0.915250i	$-0.631993\pi$
$353$	−2.35070e11	−0.805772	−0.402886	+	0.915250i	$0.631993\pi$
$354$	−3.14414e11	−1.06411
$355$	−2.16884e11	−0.724770
$356$	1.82749e11	0.603018
$357$	0	0
$358$	−6.68710e11	−2.15161
$359$	8.46696e10	0.269031	0.134516	−	0.990911i	$-0.457052\pi$
$359$	8.46696e10	0.269031	0.134516	+	0.990911i	$0.457052\pi$
$360$	1.50459e11	0.472124
$361$	−9.79067e10	−0.303410
$362$	8.08479e10	0.247446
$363$	−2.02158e11	−0.611099
$364$	6.20465e9	0.0185251
$365$	−2.11827e11	−0.624687
$366$	−2.79017e11	−0.812765
$367$	−3.10781e10	−0.0894246	−0.0447123	−	0.999000i	$-0.514237\pi$
$367$	−3.10781e10	−0.0894246	−0.0447123	+	0.999000i	$0.514237\pi$
$368$	5.66072e11	1.60900
$369$	−3.74059e11	−1.05032
$370$	1.45814e11	0.404476
$371$	−1.28425e10	−0.0351940
$372$	8.66258e9	0.0234533
$373$	−6.64364e11	−1.77712	−0.888559	−	0.458763i	$-0.848293\pi$
$373$	−6.64364e11	−1.77712	−0.888559	+	0.458763i	$0.848293\pi$
$374$	0	0
$375$	−2.22635e11	−0.581371
$376$	−2.87723e10	−0.0742385
$377$	−3.53155e10	−0.0900386
$378$	−3.26703e10	−0.0823076
$379$	1.05029e11	0.261475	0.130738	−	0.991417i	$-0.458265\pi$
$379$	1.05029e11	0.261475	0.130738	+	0.991417i	$0.458265\pi$
$380$	−1.36638e11	−0.336159
$381$	1.19240e11	0.289908
$382$	−8.40485e11	−2.01950
$383$	6.90072e11	1.63870	0.819351	−	0.573293i	$-0.194334\pi$
$383$	6.90072e11	1.63870	0.819351	+	0.573293i	$0.194334\pi$
$384$	3.06423e11	0.719168
$385$	−1.67189e9	−0.00387823
$386$	−6.11297e10	−0.140155
$387$	2.64537e11	0.599497
$388$	−2.84797e11	−0.637959
$389$	1.43485e11	0.317712	0.158856	−	0.987302i	$-0.449219\pi$
$389$	1.43485e11	0.317712	0.158856	+	0.987302i	$0.449219\pi$
$390$	2.35672e11	0.515842
$391$	0	0
$392$	3.36532e11	0.719846
$393$	−5.05407e11	−1.06875
$394$	−7.06731e11	−1.47748
$395$	6.16615e11	1.27446
$396$	6.22138e9	0.0127133
$397$	4.59121e11	0.927620	0.463810	−	0.885935i	$-0.346482\pi$
$397$	4.59121e11	0.927620	0.463810	+	0.885935i	$0.346482\pi$
$398$	3.88250e11	0.775599
$399$	−1.81891e10	−0.0359280
$400$	−5.84171e10	−0.114096
$401$	1.18477e11	0.228815	0.114408	−	0.993434i	$-0.463503\pi$
$401$	1.18477e11	0.228815	0.114408	+	0.993434i	$0.463503\pi$
$402$	−1.90432e11	−0.363682
$403$	3.59834e10	0.0679562
$404$	3.42340e11	0.639354
$405$	8.16088e9	0.0150726
$406$	−5.95600e9	−0.0108790
$407$	−9.61558e9	−0.0173700
$408$	0	0
$409$	3.44816e11	0.609301	0.304651	−	0.952464i	$-0.401460\pi$
$409$	3.44816e11	0.609301	0.304651	+	0.952464i	$0.401460\pi$
$410$	1.18382e12	2.06899
$411$	1.93937e11	0.335253
$412$	−2.28487e11	−0.390682
$413$	−6.12732e10	−0.103632
$414$	5.71518e11	0.956156
$415$	−7.82976e10	−0.129578
$416$	−3.06137e11	−0.501183
$417$	1.77573e11	0.287585
$418$	3.23908e10	0.0518953
$419$	−1.06432e12	−1.68697	−0.843487	−	0.537150i	$-0.819501\pi$
$419$	−1.06432e12	−1.68697	−0.843487	+	0.537150i	$0.819501\pi$
$420$	1.10566e10	0.0173381
$421$	8.40482e11	1.30394	0.651972	−	0.758243i	$-0.273942\pi$
$421$	8.40482e11	1.30394	0.651972	+	0.758243i	$0.273942\pi$
$422$	−1.14837e12	−1.76269
$423$	−4.21970e10	−0.0640840
$424$	2.41203e11	0.362441
$425$	0	0
$426$	−3.40012e11	−0.500208
$427$	−5.43750e10	−0.0791542
$428$	−1.22094e11	−0.175872
$429$	−1.55411e10	−0.0221526
$430$	−8.37206e11	−1.18093
$431$	7.86921e11	1.09846	0.549229	−	0.835672i	$-0.314922\pi$
$431$	7.86921e11	1.09846	0.549229	+	0.835672i	$0.314922\pi$
$432$	8.91321e11	1.23128
$433$	−7.27832e11	−0.995029	−0.497514	−	0.867456i	$-0.665754\pi$
$433$	−7.27832e11	−0.995029	−0.497514	+	0.867456i	$0.665754\pi$
$434$	6.06864e9	0.00821084
$435$	−6.29317e10	−0.0842690
$436$	3.58301e11	0.474853
$437$	8.27733e11	1.08573
$438$	−3.32083e11	−0.431135
$439$	5.63619e11	0.724261	0.362130	−	0.932127i	$-0.382050\pi$
$439$	5.63619e11	0.724261	0.362130	+	0.932127i	$0.382050\pi$
$440$	3.14007e10	0.0399395
$441$	4.93553e11	0.621384
$442$	0	0
$443$	2.48083e11	0.306041	0.153021	−	0.988223i	$-0.451100\pi$
$443$	2.48083e11	0.306041	0.153021	+	0.988223i	$0.451100\pi$
$444$	6.35903e10	0.0776547
$445$	1.35274e12	1.63529
$446$	−1.01496e12	−1.21463
$447$	−2.58033e11	−0.305697
$448$	2.24481e10	0.0263286
$449$	1.36225e12	1.58178	0.790891	−	0.611957i	$-0.209617\pi$
$449$	1.36225e12	1.58178	0.790891	+	0.611957i	$0.209617\pi$
$450$	−5.89791e10	−0.0678019
$451$	−7.80660e10	−0.0888520
$452$	5.70658e11	0.643063
$453$	−9.07040e11	−1.01201
$454$	7.40724e11	0.818286
$455$	4.59279e10	0.0502372
$456$	3.41620e11	0.370000
$457$	9.81977e11	1.05312	0.526560	−	0.850138i	$-0.323481\pi$
$457$	9.81977e11	1.05312	0.526560	+	0.850138i	$0.323481\pi$
$458$	9.44822e11	1.00336
$459$	0	0
$460$	−5.03155e11	−0.523952
$461$	7.36336e11	0.759314	0.379657	−	0.925127i	$-0.376042\pi$
$461$	7.36336e11	0.759314	0.379657	+	0.925127i	$0.376042\pi$
$462$	−2.62103e9	−0.00267660
$463$	1.79548e11	0.181579	0.0907894	−	0.995870i	$-0.471061\pi$
$463$	1.79548e11	0.181579	0.0907894	+	0.995870i	$0.471061\pi$
$464$	1.62493e11	0.162744
$465$	6.41219e10	0.0636016
$466$	−1.23224e12	−1.21048
$467$	1.13676e11	0.110596	0.0552982	−	0.998470i	$-0.482389\pi$
$467$	1.13676e11	0.110596	0.0552982	+	0.998470i	$0.482389\pi$
$468$	−1.70906e11	−0.164684
$469$	−3.71115e10	−0.0354186
$470$	1.33545e11	0.126237
$471$	7.32242e11	0.685584
$472$	1.15081e12	1.06724
$473$	5.52088e10	0.0507146
$474$	9.66674e11	0.879584
$475$	−8.54197e10	−0.0769904
$476$	0	0
$477$	3.53745e11	0.312865
$478$	2.22059e12	1.94555
$479$	5.35347e11	0.464649	0.232325	−	0.972638i	$-0.425367\pi$
$479$	5.35347e11	0.464649	0.232325	+	0.972638i	$0.425367\pi$
$480$	−5.45533e11	−0.469068
$481$	2.64147e11	0.225005
$482$	1.94797e11	0.164388
$483$	−6.69794e10	−0.0559989
$484$	−4.63966e11	−0.384311
$485$	−2.10812e12	−1.73004
$486$	1.45386e12	1.18211
$487$	−9.30784e11	−0.749840	−0.374920	−	0.927057i	$-0.622330\pi$
$487$	−9.30784e11	−0.749840	−0.374920	+	0.927057i	$0.622330\pi$
$488$	1.02125e12	0.815159
$489$	5.93634e11	0.469493
$490$	−1.56200e12	−1.22404
$491$	1.40150e12	1.08824	0.544122	−	0.839006i	$-0.316863\pi$
$491$	1.40150e12	1.08824	0.544122	+	0.839006i	$0.316863\pi$
$492$	5.16270e11	0.397223
$493$	0	0
$494$	−8.89798e11	−0.672233
$495$	4.60517e10	0.0344765
$496$	−1.65566e11	−0.122830
$497$	−6.62617e10	−0.0487146
$498$	−1.22748e11	−0.0894298
$499$	−9.65319e11	−0.696977	−0.348488	−	0.937313i	$-0.613305\pi$
$499$	−9.65319e11	−0.696977	−0.348488	+	0.937313i	$0.613305\pi$
$500$	−5.10963e11	−0.365615
$501$	7.03348e11	0.498771
$502$	2.53152e12	1.77916
$503$	1.35251e12	0.942076	0.471038	−	0.882113i	$-0.343879\pi$
$503$	1.35251e12	0.942076	0.471038	+	0.882113i	$0.343879\pi$
$504$	4.59677e10	0.0317333
$505$	2.53406e12	1.73383
$506$	1.19276e11	0.0808862
$507$	−4.84792e11	−0.325852
$508$	2.73664e11	0.182319
$509$	−1.24943e12	−0.825053	−0.412527	−	0.910946i	$-0.635354\pi$
$509$	−1.24943e12	−0.825053	−0.412527	+	0.910946i	$0.635354\pi$
$510$	0	0
$511$	−6.47166e10	−0.0419876
$512$	1.72851e10	0.0111162
$513$	1.30332e12	0.830853
$514$	−1.91930e12	−1.21286
$515$	−1.69130e12	−1.05947
$516$	−3.65110e11	−0.226725
$517$	−8.80649e9	−0.00542120
$518$	4.45487e10	0.0271864
$519$	−1.68955e11	−0.102216
$520$	−8.62599e11	−0.517361
$521$	−2.83113e11	−0.168341	−0.0841706	−	0.996451i	$-0.526824\pi$
$521$	−2.83113e11	−0.168341	−0.0841706	+	0.996451i	$0.526824\pi$
$522$	1.64057e11	0.0967111
$523$	6.03608e11	0.352774	0.176387	−	0.984321i	$-0.443559\pi$
$523$	6.03608e11	0.352774	0.176387	+	0.984321i	$0.443559\pi$
$524$	−1.15994e12	−0.672118
$525$	6.91209e9	0.00397093
$526$	−4.57640e11	−0.260668
$527$	0	0
$528$	7.15078e10	0.0400406
$529$	1.24689e12	0.692271
$530$	−1.11953e12	−0.616303
$531$	1.68776e12	0.921265
$532$	−4.17452e10	−0.0225946
$533$	2.14453e12	1.15096
$534$	2.12070e12	1.12861
$535$	−9.03758e11	−0.476936
$536$	6.97013e11	0.364754
$537$	−2.15868e12	−1.12022
$538$	−2.94412e11	−0.151508
$539$	1.03004e11	0.0525661
$540$	−7.92253e11	−0.400951
$541$	7.92682e11	0.397843	0.198921	−	0.980015i	$-0.436256\pi$
$541$	7.92682e11	0.397843	0.198921	+	0.980015i	$0.436256\pi$
$542$	−3.75904e12	−1.87103
$543$	2.60987e11	0.128831
$544$	0	0
$545$	2.65221e12	1.28773
$546$	7.20017e10	0.0346717
$547$	−5.81013e10	−0.0277487	−0.0138744	−	0.999904i	$-0.504416\pi$
$547$	−5.81013e10	−0.0277487	−0.0138744	+	0.999904i	$0.504416\pi$
$548$	4.45098e11	0.210835
$549$	1.49775e12	0.703660
$550$	−1.23089e10	−0.00573572
$551$	2.37604e11	0.109817
$552$	1.25798e12	0.576697
$553$	1.88386e11	0.0856616
$554$	3.00187e12	1.35393
$555$	4.70707e11	0.210587
$556$	4.07543e11	0.180857
$557$	−8.04975e11	−0.354351	−0.177176	−	0.984179i	$-0.556696\pi$
$557$	−8.04975e11	−0.354351	−0.177176	+	0.984179i	$0.556696\pi$
$558$	−1.67159e11	−0.0729922
$559$	−1.51662e12	−0.656939
$560$	−2.11323e11	−0.0908032
$561$	0	0
$562$	1.29619e12	0.548096
$563$	−3.22746e12	−1.35386	−0.676929	−	0.736048i	$-0.736690\pi$
$563$	−3.22746e12	−1.35386	−0.676929	+	0.736048i	$0.736690\pi$
$564$	5.82396e10	0.0242361
$565$	4.22411e12	1.74388
$566$	3.22810e12	1.32213
$567$	2.49329e9	0.00101309
$568$	1.24450e12	0.501681
$569$	−2.00792e12	−0.803048	−0.401524	−	0.915848i	$-0.631519\pi$
$569$	−2.00792e12	−0.803048	−0.401524	+	0.915848i	$0.631519\pi$
$570$	−1.58561e12	−0.629157
$571$	−3.16004e11	−0.124403	−0.0622013	−	0.998064i	$-0.519812\pi$
$571$	−3.16004e11	−0.124403	−0.0622013	+	0.998064i	$0.519812\pi$
$572$	−3.56680e10	−0.0139314
$573$	−2.71319e12	−1.05144
$574$	3.61677e11	0.139065
$575$	−3.14549e11	−0.120001
$576$	−6.18327e11	−0.234054
$577$	−1.81033e12	−0.679932	−0.339966	−	0.940438i	$-0.610416\pi$
$577$	−1.81033e12	−0.679932	−0.339966	+	0.940438i	$0.610416\pi$
$578$	0	0
$579$	−1.97334e11	−0.0729707
$580$	−1.44432e11	−0.0529955
$581$	−2.39212e10	−0.00870945
$582$	−3.30492e12	−1.19401
$583$	7.38264e10	0.0264669
$584$	1.21548e12	0.432404
$585$	−1.26507e12	−0.446596
$586$	2.57046e12	0.900475
$587$	2.94820e12	1.02491	0.512455	−	0.858714i	$-0.328736\pi$
$587$	2.94820e12	1.02491	0.512455	+	0.858714i	$0.328736\pi$
$588$	−6.81194e11	−0.235003
$589$	−2.42098e11	−0.0828842
$590$	−5.34141e12	−1.81477
$591$	−2.28142e12	−0.769238
$592$	−1.21539e12	−0.406695
$593$	4.46478e12	1.48270	0.741350	−	0.671118i	$-0.234186\pi$
$593$	4.46478e12	1.48270	0.741350	+	0.671118i	$0.234186\pi$
$594$	1.87808e11	0.0618978
$595$	0	0
$596$	−5.92202e11	−0.192248
$597$	1.25332e12	0.403810
$598$	−3.27659e12	−1.04777
$599$	3.15817e12	1.00234	0.501170	−	0.865349i	$-0.332903\pi$
$599$	3.15817e12	1.00234	0.501170	+	0.865349i	$0.332903\pi$
$600$	−1.29820e11	−0.0408941
$601$	−5.98536e12	−1.87135	−0.935675	−	0.352863i	$-0.885208\pi$
$601$	−5.98536e12	−1.87135	−0.935675	+	0.352863i	$0.885208\pi$
$602$	−2.55781e11	−0.0793749
$603$	1.02223e12	0.314862
$604$	−2.08172e12	−0.636437
$605$	−3.43436e12	−1.04219
$606$	3.97267e12	1.19662
$607$	−1.60857e11	−0.0480939	−0.0240469	−	0.999711i	$-0.507655\pi$
$607$	−1.60857e11	−0.0480939	−0.0240469	+	0.999711i	$0.507655\pi$
$608$	2.05970e12	0.611278
$609$	−1.92267e10	−0.00566405
$610$	−4.74007e12	−1.38612
$611$	2.41920e11	0.0702243
$612$	0	0
$613$	−4.87119e12	−1.39336	−0.696679	−	0.717383i	$-0.745340\pi$
$613$	−4.87119e12	−1.39336	−0.696679	+	0.717383i	$0.745340\pi$
$614$	−3.50417e12	−0.995009
$615$	3.82152e12	1.07721
$616$	9.59344e9	0.00268449
$617$	−3.48094e12	−0.966970	−0.483485	−	0.875353i	$-0.660629\pi$
$617$	−3.48094e12	−0.966970	−0.483485	+	0.875353i	$0.660629\pi$
$618$	−2.65147e12	−0.731203
$619$	−2.25847e12	−0.618310	−0.309155	−	0.951012i	$-0.600046\pi$
$619$	−2.25847e12	−0.618310	−0.309155	+	0.951012i	$0.600046\pi$
$620$	1.47164e11	0.0399981
$621$	4.79935e12	1.29500
$622$	−8.51852e10	−0.0228196
$623$	4.13285e11	0.109914
$624$	−1.96437e12	−0.518672
$625$	−4.13413e12	−1.08374
$626$	4.25958e12	1.10862
$627$	1.04561e11	0.0270189
$628$	1.68054e12	0.431153
$629$	0	0
$630$	−2.13356e11	−0.0539601
$631$	−6.76730e12	−1.69935	−0.849676	−	0.527305i	$-0.823203\pi$
$631$	−6.76730e12	−1.69935	−0.849676	+	0.527305i	$0.823203\pi$
$632$	−3.53819e12	−0.882175
$633$	−3.70709e12	−0.917734
$634$	−1.80422e12	−0.443494
$635$	2.02571e12	0.494419
$636$	−4.88233e11	−0.118323
$637$	−2.82960e12	−0.680923
$638$	3.42385e10	0.00818130
$639$	1.82516e12	0.433060
$640$	5.20566e12	1.22649
$641$	−7.28070e12	−1.70338	−0.851691	−	0.524045i	$-0.824422\pi$
$641$	−7.28070e12	−1.70338	−0.851691	+	0.524045i	$0.824422\pi$
$642$	−1.41683e12	−0.329163
$643$	6.62565e12	1.52855	0.764274	−	0.644892i	$-0.223098\pi$
$643$	6.62565e12	1.52855	0.764274	+	0.644892i	$0.223098\pi$
$644$	−1.53722e11	−0.0352168
$645$	−2.70261e12	−0.614843
$646$	0	0
$647$	−6.36313e12	−1.42758	−0.713792	−	0.700358i	$-0.753024\pi$
$647$	−6.36313e12	−1.42758	−0.713792	+	0.700358i	$0.753024\pi$
$648$	−4.68279e10	−0.0104332
$649$	3.52234e11	0.0779346
$650$	3.38135e11	0.0742984
$651$	1.95903e10	0.00427491
$652$	1.36243e12	0.295257
$653$	−5.95209e12	−1.28103	−0.640516	−	0.767945i	$-0.721280\pi$
$653$	−5.95209e12	−1.28103	−0.640516	+	0.767945i	$0.721280\pi$
$654$	4.15789e12	0.888737
$655$	−8.58609e12	−1.82268
$656$	−9.86739e12	−2.08034
$657$	1.78260e12	0.373259
$658$	4.08002e10	0.00848488
$659$	−5.45445e12	−1.12659	−0.563296	−	0.826255i	$-0.690467\pi$
$659$	−5.45445e12	−1.12659	−0.563296	+	0.826255i	$0.690467\pi$
$660$	−6.35599e10	−0.0130387
$661$	−2.82523e12	−0.575634	−0.287817	−	0.957685i	$-0.592930\pi$
$661$	−2.82523e12	−0.575634	−0.287817	+	0.957685i	$0.592930\pi$
$662$	3.29955e12	0.667720
$663$	0	0
$664$	4.49279e11	0.0896932
$665$	−3.09005e11	−0.0612728
$666$	−1.22708e12	−0.241680
$667$	8.74951e11	0.171166
$668$	1.61423e12	0.313669
$669$	−3.27643e12	−0.632388
$670$	−3.23515e12	−0.620237
$671$	3.12579e11	0.0595263
$672$	−1.66669e11	−0.0315278
$673$	2.66233e12	0.500259	0.250129	−	0.968212i	$-0.419527\pi$
$673$	2.66233e12	0.500259	0.250129	+	0.968212i	$0.419527\pi$
$674$	4.42352e12	0.825654
$675$	−4.95280e11	−0.0918298
$676$	−1.11263e12	−0.204923
$677$	6.37169e12	1.16575	0.582875	−	0.812562i	$-0.301928\pi$
$677$	6.37169e12	1.16575	0.582875	+	0.812562i	$0.301928\pi$
$678$	6.62219e12	1.20356
$679$	−6.44065e11	−0.116283
$680$	0	0
$681$	2.39115e12	0.426035
$682$	−3.48861e10	−0.00617479
$683$	−7.29274e12	−1.28232	−0.641161	−	0.767406i	$-0.721547\pi$
$683$	−7.29274e12	−1.28232	−0.641161	+	0.767406i	$0.721547\pi$
$684$	1.14986e12	0.200860
$685$	3.29469e12	0.571752
$686$	−9.56798e11	−0.164954
$687$	3.05000e12	0.522390
$688$	6.97828e12	1.18741
$689$	−2.02806e12	−0.342843
$690$	−5.83884e12	−0.980631
$691$	−8.91264e12	−1.48715	−0.743576	−	0.668652i	$-0.766872\pi$
$691$	−8.91264e12	−1.48715	−0.743576	+	0.668652i	$0.766872\pi$
$692$	−3.87764e11	−0.0642820
$693$	1.40696e10	0.00231730
$694$	9.57030e12	1.56606
$695$	3.01670e12	0.490457
$696$	3.61108e11	0.0583305
$697$	0	0
$698$	1.21366e13	1.93530
$699$	−3.97782e12	−0.630229
$700$	1.58637e10	0.00249726
$701$	3.09782e12	0.484534	0.242267	−	0.970210i	$-0.422109\pi$
$701$	3.09782e12	0.484534	0.242267	+	0.970210i	$0.422109\pi$
$702$	−5.15922e12	−0.801802
$703$	−1.77719e12	−0.274432
$704$	−1.29045e11	−0.0197999
$705$	4.31099e11	0.0657244
$706$	−6.26064e12	−0.948413
$707$	7.74197e11	0.116537
$708$	−2.32942e12	−0.348415
$709$	−5.42374e12	−0.806104	−0.403052	−	0.915177i	$-0.632051\pi$
$709$	−5.42374e12	−0.806104	−0.403052	+	0.915177i	$0.632051\pi$
$710$	−5.77628e12	−0.853072
$711$	−5.18906e12	−0.761509
$712$	−7.76215e12	−1.13194
$713$	−8.91499e11	−0.129187
$714$	0	0
$715$	−2.64020e11	−0.0377799
$716$	−4.95432e12	−0.704490
$717$	7.16833e12	1.01294
$718$	2.25501e12	0.316656
$719$	5.08993e12	0.710284	0.355142	−	0.934812i	$-0.384433\pi$
$719$	5.08993e12	0.710284	0.355142	+	0.934812i	$0.384433\pi$
$720$	5.82085e12	0.807217
$721$	−5.16720e11	−0.0712109
$722$	−2.60755e12	−0.357121
$723$	6.28829e11	0.0855875
$724$	5.98982e11	0.0810197
$725$	−9.02925e10	−0.0121375
$726$	−5.38408e12	−0.719278
$727$	8.07173e12	1.07167	0.535836	−	0.844322i	$-0.319997\pi$
$727$	8.07173e12	1.07167	0.535836	+	0.844322i	$0.319997\pi$
$728$	−2.63539e11	−0.0347739
$729$	4.58327e12	0.601037
$730$	−5.64158e12	−0.735272
$731$	0	0
$732$	−2.06717e12	−0.266119
$733$	6.29376e12	0.805272	0.402636	−	0.915360i	$-0.368094\pi$
$733$	6.29376e12	0.805272	0.402636	+	0.915360i	$0.368094\pi$
$734$	−8.27703e11	−0.105255
$735$	−5.04232e12	−0.637290
$736$	7.58464e12	0.952763
$737$	2.13339e11	0.0266358
$738$	−9.96232e12	−1.23625
$739$	−9.33473e11	−0.115134	−0.0575668	−	0.998342i	$-0.518334\pi$
$739$	−9.33473e11	−0.115134	−0.0575668	+	0.998342i	$0.518334\pi$
$740$	1.08030e12	0.132435
$741$	−2.87238e12	−0.349993
$742$	−3.42035e11	−0.0414241
$743$	1.42665e13	1.71739	0.858694	−	0.512489i	$-0.171276\pi$
$743$	1.42665e13	1.71739	0.858694	+	0.512489i	$0.171276\pi$
$744$	−3.67937e11	−0.0440246
$745$	−4.38358e12	−0.521346
$746$	−1.76940e13	−2.09171
$747$	6.58905e11	0.0774248
$748$	0	0
$749$	−2.76113e11	−0.0320567
$750$	−5.92945e12	−0.684288
$751$	−1.42997e13	−1.64039	−0.820197	−	0.572081i	$-0.806136\pi$
$751$	−1.42997e13	−1.64039	−0.820197	+	0.572081i	$0.806136\pi$
$752$	−1.11312e12	−0.126930
$753$	8.17206e12	0.926305
$754$	−9.40557e11	−0.105978
$755$	−1.54092e13	−1.72592
$756$	−2.42046e11	−0.0269495
$757$	−6.04819e12	−0.669413	−0.334706	−	0.942322i	$-0.608637\pi$
$757$	−6.04819e12	−0.669413	−0.334706	+	0.942322i	$0.608637\pi$
$758$	2.79723e12	0.307763
$759$	3.85037e11	0.0421128
$760$	5.80361e12	0.631011
$761$	5.22191e12	0.564414	0.282207	−	0.959353i	$-0.408933\pi$
$761$	5.22191e12	0.564414	0.282207	+	0.959353i	$0.408933\pi$
$762$	3.17573e12	0.341229
$763$	8.10294e11	0.0865530
$764$	−6.22695e12	−0.661234
$765$	0	0
$766$	1.83787e13	1.92879
$767$	−9.67612e12	−1.00954
$768$	5.94655e12	0.616793
$769$	−8.85529e12	−0.913134	−0.456567	−	0.889689i	$-0.650921\pi$
$769$	−8.85529e12	−0.913134	−0.456567	+	0.889689i	$0.650921\pi$
$770$	−4.45274e10	−0.00456477
$771$	−6.19575e12	−0.631465
$772$	−4.52895e11	−0.0458902
$773$	5.21750e12	0.525599	0.262799	−	0.964850i	$-0.415354\pi$
$773$	5.21750e12	0.525599	0.262799	+	0.964850i	$0.415354\pi$
$774$	7.04542e12	0.705623
$775$	9.20002e10	0.00916075
$776$	1.20966e13	1.19752
$777$	1.43809e11	0.0141544
$778$	3.82144e12	0.373955
$779$	−1.44285e13	−1.40379
$780$	1.74604e12	0.168899
$781$	3.80911e11	0.0366348
$782$	0	0
$783$	1.37767e12	0.130984
$784$	1.30195e13	1.23076
$785$	1.24397e13	1.16922
$786$	−1.34605e13	−1.25794
$787$	1.22879e13	1.14181	0.570903	−	0.821017i	$-0.306593\pi$
$787$	1.22879e13	1.14181	0.570903	+	0.821017i	$0.306593\pi$
$788$	−5.23600e12	−0.483762
$789$	−1.47732e12	−0.135715
$790$	1.64223e13	1.50007
$791$	1.29054e12	0.117213
$792$	−2.64249e11	−0.0238644
$793$	−8.58678e12	−0.771082
$794$	1.22278e13	1.09183
$795$	−3.61399e12	−0.320874
$796$	2.87645e12	0.253950
$797$	1.04691e13	0.919063	0.459532	−	0.888161i	$-0.348017\pi$
$797$	1.04691e13	0.919063	0.459532	+	0.888161i	$0.348017\pi$
$798$	−4.84430e11	−0.0422881
$799$	0	0
$800$	−7.82714e11	−0.0675613
$801$	−1.13838e13	−0.977107
$802$	3.15540e12	0.269321
$803$	3.72029e11	0.0315760
$804$	−1.41086e12	−0.119078
$805$	−1.13788e12	−0.0955024
$806$	9.58345e11	0.0799861
$807$	−9.50398e11	−0.0788814
$808$	−1.45407e13	−1.20014
$809$	1.43675e13	1.17927	0.589634	−	0.807671i	$-0.299272\pi$
$809$	1.43675e13	1.17927	0.589634	+	0.807671i	$0.299272\pi$
$810$	2.17349e11	0.0177409
$811$	1.55011e12	0.125825	0.0629127	−	0.998019i	$-0.479961\pi$
$811$	1.55011e12	0.125825	0.0629127	+	0.998019i	$0.479961\pi$
$812$	−4.41265e10	−0.00356203
$813$	−1.21347e13	−0.974137
$814$	−2.56092e11	−0.0204450
$815$	1.00849e13	0.800690
$816$	0	0
$817$	1.02039e13	0.801249
$818$	9.18348e12	0.717163
$819$	−3.86501e11	−0.0300174
$820$	8.77065e12	0.677438
$821$	1.37949e13	1.05968	0.529839	−	0.848098i	$-0.322252\pi$
$821$	1.37949e13	1.05968	0.529839	+	0.848098i	$0.322252\pi$
$822$	5.16513e12	0.394601
$823$	1.07251e13	0.814899	0.407449	−	0.913228i	$-0.366418\pi$
$823$	1.07251e13	0.814899	0.407449	+	0.913228i	$0.366418\pi$
$824$	9.70482e12	0.733357
$825$	−3.97347e10	−0.00298626
$826$	−1.63189e12	−0.121978
$827$	−1.65480e13	−1.23019	−0.615093	−	0.788454i	$-0.710882\pi$
$827$	−1.65480e13	−1.23019	−0.615093	+	0.788454i	$0.710882\pi$
$828$	4.23424e12	0.313068
$829$	1.03812e13	0.763398	0.381699	−	0.924287i	$-0.375339\pi$
$829$	1.03812e13	0.763398	0.381699	+	0.924287i	$0.375339\pi$
$830$	−2.08530e12	−0.152517
$831$	9.69040e12	0.704916
$832$	3.54494e12	0.256481
$833$	0	0
$834$	4.72931e12	0.338494
$835$	1.19488e13	0.850621
$836$	2.39976e11	0.0169918
$837$	−1.40373e12	−0.0988595
$838$	−2.83460e13	−1.98561
$839$	6.25038e12	0.435489	0.217745	−	0.976006i	$-0.430130\pi$
$839$	6.25038e12	0.435489	0.217745	+	0.976006i	$0.430130\pi$
$840$	−4.69623e11	−0.0325456
$841$	−1.42560e13	−0.982687
$842$	2.23846e13	1.53477
$843$	4.18428e12	0.285362
$844$	−8.50802e12	−0.577149
$845$	−8.23589e12	−0.555719
$846$	−1.12383e12	−0.0754284
$847$	−1.04925e12	−0.0700496
$848$	9.33151e12	0.619685
$849$	1.04207e13	0.688356
$850$	0	0
$851$	−6.54432e12	−0.427742
$852$	−2.51906e12	−0.163780
$853$	2.08264e13	1.34693	0.673464	−	0.739220i	$-0.264806\pi$
$853$	2.08264e13	1.34693	0.673464	+	0.739220i	$0.264806\pi$
$854$	−1.44817e12	−0.0931664
$855$	8.51147e12	0.544700
$856$	5.18585e12	0.330132
$857$	−2.34103e12	−0.148249	−0.0741246	−	0.997249i	$-0.523616\pi$
$857$	−2.34103e12	−0.148249	−0.0741246	+	0.997249i	$0.523616\pi$
$858$	−4.13908e11	−0.0260742
$859$	−1.14439e13	−0.717139	−0.358569	−	0.933503i	$-0.616735\pi$
$859$	−1.14439e13	−0.717139	−0.358569	+	0.933503i	$0.616735\pi$
$860$	−6.20266e12	−0.386665
$861$	1.16754e12	0.0724031
$862$	2.09581e13	1.29291
$863$	−1.65044e13	−1.01286	−0.506431	−	0.862281i	$-0.669035\pi$
$863$	−1.65044e13	−1.01286	−0.506431	+	0.862281i	$0.669035\pi$
$864$	1.19426e13	0.729097
$865$	−2.87029e12	−0.174323
$866$	−1.93844e13	−1.17117
$867$	0	0
$868$	4.49611e10	0.00268843
$869$	−1.08295e12	−0.0644201
$870$	−1.67606e12	−0.0991867
$871$	−5.86056e12	−0.345031
$872$	−1.52186e13	−0.891355
$873$	1.77406e13	1.03372
$874$	2.20450e13	1.27794
$875$	−1.15554e12	−0.0666419
$876$	−2.46032e12	−0.141164
$877$	1.42710e11	0.00814620	0.00407310	−	0.999992i	$-0.498703\pi$
$877$	1.42710e11	0.00814620	0.00407310	+	0.999992i	$0.498703\pi$
$878$	1.50109e13	0.852473
$879$	8.29777e12	0.468826
$880$	1.21481e12	0.0682867
$881$	−2.11785e13	−1.18441	−0.592206	−	0.805786i	$-0.701743\pi$
$881$	−2.11785e13	−1.18441	−0.592206	+	0.805786i	$0.701743\pi$
$882$	1.31448e13	0.731384
$883$	1.83970e13	1.01841	0.509207	−	0.860644i	$-0.329939\pi$
$883$	1.83970e13	1.01841	0.509207	+	0.860644i	$0.329939\pi$
$884$	0	0
$885$	−1.72427e13	−0.944847
$886$	6.60720e12	0.360218
$887$	1.18951e13	0.645225	0.322613	−	0.946531i	$-0.395439\pi$
$887$	1.18951e13	0.645225	0.322613	+	0.946531i	$0.395439\pi$
$888$	−2.70096e12	−0.145767
$889$	6.18888e11	0.0332318
$890$	3.60276e13	1.92477
$891$	−1.43329e10	−0.000761874 0
$892$	−7.51963e12	−0.397699
$893$	−1.62765e12	−0.0856505
$894$	−6.87219e12	−0.359812
$895$	−3.66727e13	−1.91047
$896$	1.59042e12	0.0824375
$897$	−1.05772e13	−0.545514
$898$	3.62807e13	1.86180
$899$	−2.55908e11	−0.0130667
$900$	−4.36962e11	−0.0222000
$901$	0	0
$902$	−2.07913e12	−0.104581
$903$	−8.25692e11	−0.0413260
$904$	−2.42384e13	−1.20711
$905$	4.43377e12	0.219713
$906$	−2.41572e13	−1.19116
$907$	−3.91571e13	−1.92122	−0.960612	−	0.277893i	$-0.910364\pi$
$907$	−3.91571e13	−1.92122	−0.960612	+	0.277893i	$0.910364\pi$
$908$	5.48785e12	0.267927
$909$	−2.13251e13	−1.03599
$910$	1.22320e12	0.0591304
$911$	2.83393e13	1.36319	0.681595	−	0.731730i	$-0.261287\pi$
$911$	2.83393e13	1.36319	0.681595	+	0.731730i	$0.261287\pi$
$912$	1.32164e13	0.632609
$913$	1.37513e11	0.00654977
$914$	2.61530e13	1.23955
$915$	−1.53015e13	−0.721672
$916$	6.99996e12	0.328523
$917$	−2.62319e12	−0.122509
$918$	0	0
$919$	−1.73995e13	−0.804668	−0.402334	−	0.915493i	$-0.631801\pi$
$919$	−1.73995e13	−0.804668	−0.402334	+	0.915493i	$0.631801\pi$
$920$	2.13712e13	0.983520
$921$	−1.13119e13	−0.518044
$922$	1.96108e13	0.893731
$923$	−1.04639e13	−0.474554
$924$	−1.94186e10	−0.000876384 0
$925$	6.75356e11	0.0303316
$926$	4.78189e12	0.213723
$927$	1.42329e13	0.633047
$928$	2.17720e12	0.0963680
$929$	3.95509e13	1.74215	0.871074	−	0.491151i	$-0.163424\pi$
$929$	3.95509e13	1.74215	0.871074	+	0.491151i	$0.163424\pi$
$930$	1.70776e12	0.0748607
$931$	1.90377e13	0.830501
$932$	−9.12937e12	−0.396341
$933$	−2.74988e11	−0.0118808
$934$	3.02752e12	0.130175
$935$	0	0
$936$	7.25911e12	0.309131
$937$	4.31185e13	1.82741	0.913704	−	0.406381i	$-0.133210\pi$
$937$	4.31185e13	1.82741	0.913704	+	0.406381i	$0.133210\pi$
$938$	−9.88392e11	−0.0416885
$939$	1.37504e13	0.577194
$940$	9.89402e11	0.0413330
$941$	−1.23028e13	−0.511505	−0.255753	−	0.966742i	$-0.582323\pi$
$941$	−1.23028e13	−0.511505	−0.255753	+	0.966742i	$0.582323\pi$
$942$	1.95018e13	0.806949
$943$	−5.31313e13	−2.18800
$944$	4.45217e13	1.82473
$945$	−1.79167e12	−0.0730828
$946$	1.47038e12	0.0596923
$947$	−3.99251e13	−1.61314	−0.806568	−	0.591142i	$-0.798677\pi$
$947$	−3.99251e13	−1.61314	−0.806568	+	0.591142i	$0.798677\pi$
$948$	7.16186e12	0.287997
$949$	−1.02199e13	−0.409024
$950$	−2.27498e12	−0.0906196
$951$	−5.82424e12	−0.230902
$952$	0	0
$953$	−4.12885e13	−1.62148	−0.810739	−	0.585408i	$-0.800934\pi$
$953$	−4.12885e13	−1.62148	−0.810739	+	0.585408i	$0.800934\pi$
$954$	9.42129e12	0.368250
$955$	−4.60930e13	−1.79316
$956$	1.64518e13	0.637019
$957$	1.10526e11	0.00425953
$958$	1.42579e13	0.546904
$959$	1.00658e12	0.0384296
$960$	6.31705e12	0.240046
$961$	−2.61789e13	−0.990138
$962$	7.03503e12	0.264837
$963$	7.60548e12	0.284976
$964$	1.44320e12	0.0538246
$965$	−3.35241e12	−0.124447
$966$	−1.78386e12	−0.0659120
$967$	−3.74952e13	−1.37898	−0.689488	−	0.724297i	$-0.742164\pi$
$967$	−3.74952e13	−1.37898	−0.689488	+	0.724297i	$0.742164\pi$
$968$	1.97067e13	0.721397
$969$	0	0
$970$	−5.61455e13	−2.03630
$971$	−1.85734e13	−0.670508	−0.335254	−	0.942128i	$-0.608822\pi$
$971$	−1.85734e13	−0.670508	−0.335254	+	0.942128i	$0.608822\pi$
$972$	1.07713e13	0.387053
$973$	9.21653e11	0.0329655
$974$	−2.47896e13	−0.882580
$975$	1.09154e12	0.0386829
$976$	3.95094e13	1.39372
$977$	−5.09643e13	−1.78954	−0.894769	−	0.446530i	$-0.852660\pi$
$977$	−5.09643e13	−1.78954	−0.894769	+	0.446530i	$0.852660\pi$
$978$	1.58103e13	0.552604
$979$	−2.37580e12	−0.0826586
$980$	−1.15724e13	−0.400782
$981$	−2.23194e13	−0.769434
$982$	3.73262e13	1.28089
$983$	−1.27845e12	−0.0436710	−0.0218355	−	0.999762i	$-0.506951\pi$
$983$	−1.27845e12	−0.0436710	−0.0218355	+	0.999762i	$0.506951\pi$
$984$	−2.19283e13	−0.745635
$985$	−3.87578e13	−1.31189
$986$	0	0
$987$	1.31708e11	0.00441759
$988$	−6.59230e12	−0.220105
$989$	3.75748e13	1.24886
$990$	1.22650e12	0.0405796
$991$	−1.53850e13	−0.506719	−0.253360	−	0.967372i	$-0.581536\pi$
$991$	−1.53850e13	−0.506719	−0.253360	+	0.967372i	$0.581536\pi$
$992$	−2.21838e12	−0.0727332
$993$	1.06514e13	0.347643
$994$	−1.76475e12	−0.0573383
$995$	2.12920e13	0.688672
$996$	−9.09410e11	−0.0292815
$997$	−3.56093e13	−1.14139	−0.570696	−	0.821162i	$-0.693326\pi$
$997$	−3.56093e13	−1.14139	−0.570696	+	0.821162i	$0.693326\pi$
$998$	−2.57094e13	−0.820359
$999$	−1.03045e13	−0.327327

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.a.1.5		5
17.16	even	2		17.10.a.a.1.5	✓	5
51.50	odd	2		153.10.a.c.1.1		5
68.67	odd	2		272.10.a.f.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.a.a.1.5	✓	5	17.16	even	2
153.10.a.c.1.1		5	51.50	odd	2
272.10.a.f.1.4		5	68.67	odd	2
289.10.a.a.1.5		5	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q+26.6330 q^{2} +85.9747 q^{3} +197.318 q^{4} +1460.58 q^{5} +2289.77 q^{6} +446.232 q^{7} -8380.94 q^{8} -12291.3 q^{9} +O(q^{10})\)	\(q+26.6330 q^{2} +85.9747 q^{3} +197.318 q^{4} +1460.58 q^{5} +2289.77 q^{6} +446.232 q^{7} -8380.94 q^{8} -12291.3 q^{9} +38899.6 q^{10} -2565.20 q^{11} +16964.3 q^{12} +70467.9 q^{13} +11884.5 q^{14} +125573. q^{15} -324236. q^{16} -327356. q^{18} -474111. q^{19} +288198. q^{20} +38364.6 q^{21} -68319.0 q^{22} -1.74586e6 q^{23} -720549. q^{24} +180168. q^{25} +1.87677e6 q^{26} -2.74899e6 q^{27} +88049.4 q^{28} -501157. q^{29} +3.34439e6 q^{30} +510635. q^{31} -4.34435e6 q^{32} -220542. q^{33} +651757. q^{35} -2.42530e6 q^{36} +3.74847e6 q^{37} -1.26270e7 q^{38} +6.05845e6 q^{39} -1.22410e7 q^{40} +3.04327e7 q^{41} +1.02177e6 q^{42} -2.15222e7 q^{43} -506159. q^{44} -1.79525e7 q^{45} -4.64976e7 q^{46} +3.43306e6 q^{47} -2.78761e7 q^{48} -4.01545e7 q^{49} +4.79842e6 q^{50} +1.39046e7 q^{52} -2.87800e7 q^{53} -7.32138e7 q^{54} -3.74668e6 q^{55} -3.73984e6 q^{56} -4.07615e7 q^{57} -1.33473e7 q^{58} -1.37313e8 q^{59} +2.47778e7 q^{60} -1.21854e8 q^{61} +1.35997e7 q^{62} -5.48479e6 q^{63} +5.03058e7 q^{64} +1.02924e8 q^{65} -5.87371e6 q^{66} -8.31665e7 q^{67} -1.50100e8 q^{69} +1.73583e7 q^{70} -1.48492e8 q^{71} +1.03013e8 q^{72} -1.45029e8 q^{73} +9.98331e7 q^{74} +1.54899e7 q^{75} -9.35504e7 q^{76} -1.14467e6 q^{77} +1.61355e8 q^{78} +4.22172e8 q^{79} -4.73573e8 q^{80} +5.58742e6 q^{81} +8.10515e8 q^{82} -5.36072e7 q^{83} +7.57002e6 q^{84} -5.73201e8 q^{86} -4.30868e7 q^{87} +2.14988e7 q^{88} +9.26167e8 q^{89} -4.78129e8 q^{90} +3.14450e7 q^{91} -3.44490e8 q^{92} +4.39017e7 q^{93} +9.14328e7 q^{94} -6.92477e8 q^{95} -3.73504e8 q^{96} -1.44334e9 q^{97} -1.06944e9 q^{98} +3.15298e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 33 q^{2} + 236 q^{3} + 853 q^{4} - 1480 q^{5} - 7578 q^{6} + 13202 q^{7} - 42423 q^{8} + 10981 q^{9}+O(q^{10}) \) 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	\( 5 q - 33 q^{2} + 236 q^{3} + 853 q^{4} - 1480 q^{5} - 7578 q^{6} + 13202 q^{7} - 42423 q^{8} + 10981 q^{9} + 89328 q^{10} + 68036 q^{11} + 406010 q^{12} - 158862 q^{13} + 84700 q^{14} - 687324 q^{15} + 350225 q^{16} - 1911585 q^{18} - 370992 q^{19} - 1632640 q^{20} + 1783880 q^{21} - 122290 q^{22} - 1645870 q^{23} - 9678702 q^{24} + 3270239 q^{25} + 734846 q^{26} + 2998268 q^{27} - 183372 q^{28} - 3668616 q^{29} + 17048544 q^{30} + 7262362 q^{31} - 5605919 q^{32} - 11334900 q^{33} - 26503988 q^{35} + 49782133 q^{36} + 31420708 q^{37} + 18513700 q^{38} + 42449884 q^{39} + 53930464 q^{40} + 7996938 q^{41} - 44519496 q^{42} - 56908268 q^{43} - 43323054 q^{44} - 12799536 q^{45} + 32063472 q^{46} - 16903336 q^{47} + 102794498 q^{48} - 11784059 q^{49} + 85921093 q^{50} + 173619082 q^{52} - 83362982 q^{53} - 386329164 q^{54} + 6363364 q^{55} - 317409372 q^{56} - 136615904 q^{57} - 64577488 q^{58} - 37946604 q^{59} - 223158912 q^{60} + 77685452 q^{61} - 324855300 q^{62} + 191945278 q^{63} + 131623105 q^{64} + 40321288 q^{65} + 298037676 q^{66} - 304503600 q^{67} - 333409272 q^{69} - 122787392 q^{70} + 476602922 q^{71} - 1301701911 q^{72} + 289980486 q^{73} - 262289012 q^{74} + 153685772 q^{75} - 1031276084 q^{76} - 143385648 q^{77} - 691646196 q^{78} + 828240610 q^{79} - 912750944 q^{80} + 891328609 q^{81} + 1109615654 q^{82} + 194681148 q^{83} + 1541719592 q^{84} + 1164707144 q^{86} + 158149884 q^{87} + 1017979978 q^{88} + 376848106 q^{89} + 2240087472 q^{90} - 194543664 q^{91} - 2506713088 q^{92} + 3494835920 q^{93} - 2244811104 q^{94} - 1498679864 q^{95} - 2935047582 q^{96} - 692035246 q^{97} + 871744055 q^{98} - 2027106408 q^{99}+O(q^{100}) \) 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 - 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 - 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 + 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 - 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 + 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

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