LMFDB - Embedded newform 289.10.a.c.1.1

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 122690 x^{10} + 5157152560 x^{8} - 87983684680032 x^{6} + \cdots + 20\!\cdots\!28 $ x^12 - 122690x^10 + 5157152560x^8 - 87983684680032x^6 + 612743619071665152x^4 - 1335826553351738886144*x^2 + 203949399568932198678528
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{17}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$12.8394$ 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)

$f(q)$	$=$	$q-39.2436 q^{2} -12.8394 q^{3} +1028.06 q^{4} -2413.73 q^{5} +503.863 q^{6} -2302.99 q^{7} -20252.0 q^{8} -19518.2 q^{9} +O(q^{10})$	\(q-39.2436 q^{2} -12.8394 q^{3} +1028.06 q^{4} -2413.73 q^{5} +503.863 q^{6} -2302.99 q^{7} -20252.0 q^{8} -19518.2 q^{9} +94723.3 q^{10} -81412.9 q^{11} -13199.6 q^{12} -59392.9 q^{13} +90377.7 q^{14} +30990.8 q^{15} +268395. q^{16} +765962. q^{18} -366131. q^{19} -2.48145e6 q^{20} +29569.0 q^{21} +3.19494e6 q^{22} -1.24935e6 q^{23} +260023. q^{24} +3.87295e6 q^{25} +2.33079e6 q^{26} +503318. q^{27} -2.36761e6 q^{28} -1.35698e6 q^{29} -1.21619e6 q^{30} +4.78110e6 q^{31} -163747. q^{32} +1.04529e6 q^{33} +5.55880e6 q^{35} -2.00658e7 q^{36} +8.36539e6 q^{37} +1.43683e7 q^{38} +762568. q^{39} +4.88828e7 q^{40} +2.02970e7 q^{41} -1.16039e6 q^{42} -2.33275e7 q^{43} -8.36973e7 q^{44} +4.71115e7 q^{45} +4.90290e7 q^{46} -3.90056e7 q^{47} -3.44602e6 q^{48} -3.50498e7 q^{49} -1.51989e8 q^{50} -6.10594e7 q^{52} -2.82011e7 q^{53} -1.97520e7 q^{54} +1.96509e8 q^{55} +4.66402e7 q^{56} +4.70090e6 q^{57} +5.32527e7 q^{58} -2.09675e7 q^{59} +3.18603e7 q^{60} +1.68828e8 q^{61} -1.87627e8 q^{62} +4.49502e7 q^{63} -1.30992e8 q^{64} +1.43358e8 q^{65} -4.10210e7 q^{66} -1.42470e8 q^{67} +1.60409e7 q^{69} -2.18147e8 q^{70} -3.49806e8 q^{71} +3.95281e8 q^{72} +2.50884e8 q^{73} -3.28288e8 q^{74} -4.97263e7 q^{75} -3.76405e8 q^{76} +1.87494e8 q^{77} -2.99259e7 q^{78} +1.12572e8 q^{79} -6.47831e8 q^{80} +3.77713e8 q^{81} -7.96528e8 q^{82} +5.17396e8 q^{83} +3.03987e7 q^{84} +9.15456e8 q^{86} +1.74228e7 q^{87} +1.64877e9 q^{88} -3.46259e7 q^{89} -1.84882e9 q^{90} +1.36781e8 q^{91} -1.28441e9 q^{92} -6.13864e7 q^{93} +1.53072e9 q^{94} +8.83741e8 q^{95} +2.10241e6 q^{96} +7.57173e8 q^{97} +1.37548e9 q^{98} +1.58903e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 30 q^{2} + 1874 q^{4} - 23550 q^{8} + 9184 q^{9}+O(q^{10}) $ 12 * q - 30 * q^2 + 1874 * q^4 - 23550 * q^8 + 9184 * q^9	$ 12 q - 30 q^{2} + 1874 q^{4} - 23550 q^{8} + 9184 q^{9} - 63204 q^{13} + 243480 q^{15} + 38978 q^{16} + 547706 q^{18} - 1110672 q^{19} - 172580 q^{21} + 4441796 q^{25} - 1336332 q^{26} - 500496 q^{30} + 1934850 q^{32} - 6557404 q^{33} + 3519864 q^{35} - 30244102 q^{36} + 28748136 q^{38} + 11901296 q^{42} - 10004616 q^{43} - 112552440 q^{47} - 121354720 q^{49} - 164889018 q^{50} - 59093180 q^{52} - 76804272 q^{53} + 300732568 q^{55} - 11618904 q^{59} - 101609232 q^{60} - 260062974 q^{64} - 18429632 q^{66} - 304208752 q^{67} - 211308236 q^{69} - 460311456 q^{70} + 493218954 q^{72} - 416024248 q^{76} - 138357828 q^{77} - 363335792 q^{81} + 845042136 q^{83} + 958037984 q^{84} + 127952904 q^{86} - 610860648 q^{87} - 938223804 q^{89} - 1635779524 q^{93} + 238629952 q^{94} - 152046078 q^{98}+O(q^{100}) $ 12 * q - 30 * q^2 + 1874 * q^4 - 23550 * q^8 + 9184 * q^9 - 63204 * q^13 + 243480 * q^15 + 38978 * q^16 + 547706 * q^18 - 1110672 * q^19 - 172580 * q^21 + 4441796 * q^25 - 1336332 * q^26 - 500496 * q^30 + 1934850 * q^32 - 6557404 * q^33 + 3519864 * q^35 - 30244102 * q^36 + 28748136 * q^38 + 11901296 * q^42 - 10004616 * q^43 - 112552440 * q^47 - 121354720 * q^49 - 164889018 * q^50 - 59093180 * q^52 - 76804272 * q^53 + 300732568 * q^55 - 11618904 * q^59 - 101609232 * q^60 - 260062974 * q^64 - 18429632 * q^66 - 304208752 * q^67 - 211308236 * q^69 - 460311456 * q^70 + 493218954 * q^72 - 416024248 * q^76 - 138357828 * q^77 - 363335792 * q^81 + 845042136 * q^83 + 958037984 * q^84 + 127952904 * q^86 - 610860648 * q^87 - 938223804 * q^89 - 1635779524 * q^93 + 238629952 * q^94 - 152046078 * q^98

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 $

$2$	−39.2436	−1.73434	−0.867169	−	0.498014i	$-0.834063\pi$
$2$	−39.2436	−1.73434	−0.867169	+	0.498014i	$0.834063\pi$
$3$	−12.8394	−0.0915163	−0.0457581	−	0.998953i	$-0.514570\pi$
$3$	−12.8394	−0.0915163	−0.0457581	+	0.998953i	$0.514570\pi$
$4$	1028.06	2.00793
$5$	−2413.73	−1.72712	−0.863561	−	0.504244i	$-0.831771\pi$
$5$	−2413.73	−1.72712	−0.863561	+	0.504244i	$0.831771\pi$
$6$	503.863	0.158720
$7$	−2302.99	−0.362536	−0.181268	−	0.983434i	$-0.558020\pi$
$7$	−2302.99	−0.362536	−0.181268	+	0.983434i	$0.558020\pi$
$8$	−20252.0	−1.74809
$9$	−19518.2	−0.991625
$10$	94723.3	2.99541
$11$	−81412.9	−1.67659	−0.838294	−	0.545219i	$-0.816447\pi$
$11$	−81412.9	−1.67659	−0.838294	+	0.545219i	$0.816447\pi$
$12$	−13199.6	−0.183758
$13$	−59392.9	−0.576752	−0.288376	−	0.957517i	$-0.593115\pi$
$13$	−59392.9	−0.576752	−0.288376	+	0.957517i	$0.593115\pi$
$14$	90377.7	0.628761
$15$	30990.8	0.158060
$16$	268395.	1.02384
$17$	0	0
$17$	0	0
$18$	765962.	1.71981
$19$	−366131.	−0.644534	−0.322267	−	0.946649i	$-0.604445\pi$
$19$	−366131.	−0.644534	−0.322267	+	0.946649i	$0.604445\pi$
$20$	−2.48145e6	−3.46794
$21$	29569.0	0.0331780
$22$	3.19494e6	2.90777
$23$	−1.24935e6	−0.930913	−0.465456	−	0.885071i	$-0.654110\pi$
$23$	−1.24935e6	−0.930913	−0.465456	+	0.885071i	$0.654110\pi$
$24$	260023.	0.159978
$25$	3.87295e6	1.98295
$26$	2.33079e6	1.00028
$27$	503318.	0.182266
$28$	−2.36761e6	−0.727947
$29$	−1.35698e6	−0.356273	−0.178136	−	0.984006i	$-0.557007\pi$
$29$	−1.35698e6	−0.356273	−0.178136	+	0.984006i	$0.557007\pi$
$30$	−1.21619e6	−0.274129
$31$	4.78110e6	0.929823	0.464911	−	0.885357i	$-0.346086\pi$
$31$	4.78110e6	0.929823	0.464911	+	0.885357i	$0.346086\pi$
$32$	−163747.	−0.0276057
$33$	1.04529e6	0.153435
$34$	0	0
$35$	5.55880e6	0.626145
$36$	−2.00658e7	−1.99111
$37$	8.36539e6	0.733801	0.366900	−	0.930260i	$-0.380419\pi$
$37$	8.36539e6	0.733801	0.366900	+	0.930260i	$0.380419\pi$
$38$	1.43683e7	1.11784
$39$	762568.	0.0527822
$40$	4.88828e7	3.01916
$41$	2.02970e7	1.12177	0.560887	−	0.827893i	$-0.310460\pi$
$41$	2.02970e7	1.12177	0.560887	+	0.827893i	$0.310460\pi$
$42$	−1.16039e6	−0.0575418
$43$	−2.33275e7	−1.04055	−0.520273	−	0.854000i	$-0.674170\pi$
$43$	−2.33275e7	−1.04055	−0.520273	+	0.854000i	$0.674170\pi$
$44$	−8.36973e7	−3.36647
$45$	4.71115e7	1.71266
$46$	4.90290e7	1.61452
$47$	−3.90056e7	−1.16597	−0.582984	−	0.812484i	$-0.698115\pi$
$47$	−3.90056e7	−1.16597	−0.582984	+	0.812484i	$0.698115\pi$
$48$	−3.44602e6	−0.0936984
$49$	−3.50498e7	−0.868567
$50$	−1.51989e8	−3.43911
$51$	0	0
$52$	−6.10594e7	−1.15808
$53$	−2.82011e7	−0.490936	−0.245468	−	0.969405i	$-0.578942\pi$
$53$	−2.82011e7	−0.490936	−0.245468	+	0.969405i	$0.578942\pi$
$54$	−1.97520e7	−0.316111
$55$	1.96509e8	2.89567
$56$	4.66402e7	0.633745
$57$	4.70090e6	0.0589854
$58$	5.32527e7	0.617897
$59$	−2.09675e7	−0.225275	−0.112637	−	0.993636i	$-0.535930\pi$
$59$	−2.09675e7	−0.225275	−0.112637	+	0.993636i	$0.535930\pi$
$60$	3.18603e7	0.317373
$61$	1.68828e8	1.56120	0.780602	−	0.625028i	$-0.214912\pi$
$61$	1.68828e8	1.56120	0.780602	+	0.625028i	$0.214912\pi$
$62$	−1.87627e8	−1.61263
$63$	4.49502e7	0.359500
$64$	−1.30992e8	−0.975967
$65$	1.43358e8	0.996122
$66$	−4.10210e7	−0.266108
$67$	−1.42470e8	−0.863746	−0.431873	−	0.901935i	$-0.642147\pi$
$67$	−1.42470e8	−0.863746	−0.431873	+	0.901935i	$0.642147\pi$
$68$	0	0
$69$	1.60409e7	0.0851937
$70$	−2.18147e8	−1.08595
$71$	−3.49806e8	−1.63367	−0.816835	−	0.576871i	$-0.804274\pi$
$71$	−3.49806e8	−1.63367	−0.816835	+	0.576871i	$0.804274\pi$
$72$	3.95281e8	1.73345
$73$	2.50884e8	1.03400	0.516999	−	0.855986i	$-0.327049\pi$
$73$	2.50884e8	1.03400	0.516999	+	0.855986i	$0.327049\pi$
$74$	−3.28288e8	−1.27266
$75$	−4.97263e7	−0.181472
$76$	−3.76405e8	−1.29418
$77$	1.87494e8	0.607824
$78$	−2.99259e7	−0.0915422
$79$	1.12572e8	0.325170	0.162585	−	0.986695i	$-0.448017\pi$
$79$	1.12572e8	0.325170	0.162585	+	0.986695i	$0.448017\pi$
$80$	−6.47831e8	−1.76830
$81$	3.77713e8	0.974944
$82$	−7.96528e8	−1.94553
$83$	5.17396e8	1.19666	0.598331	−	0.801249i	$-0.295831\pi$
$83$	5.17396e8	1.19666	0.598331	+	0.801249i	$0.295831\pi$
$84$	3.03987e7	0.0666190
$85$	0	0
$86$	9.15456e8	1.80466
$87$	1.74228e7	0.0326047
$88$	1.64877e9	2.93082
$89$	−3.46259e7	−0.0584987	−0.0292493	−	0.999572i	$-0.509312\pi$
$89$	−3.46259e7	−0.0584987	−0.0292493	+	0.999572i	$0.509312\pi$
$90$	−1.84882e9	−2.97033
$91$	1.36781e8	0.209094
$92$	−1.28441e9	−1.86920
$93$	−6.13864e7	−0.0850939
$94$	1.53072e9	2.02218
$95$	8.83741e8	1.11319
$96$	2.10241e6	0.00252637
$97$	7.57173e8	0.868404	0.434202	−	0.900815i	$-0.357030\pi$
$97$	7.57173e8	0.868404	0.434202	+	0.900815i	$0.357030\pi$
$98$	1.37548e9	1.50639
$99$	1.58903e9	1.66255
$100$	3.98162e9	3.98162
$101$	4.87843e8	0.466481	0.233241	−	0.972419i	$-0.425067\pi$
$101$	4.87843e8	0.466481	0.233241	+	0.972419i	$0.425067\pi$
$102$	0	0
$103$	−9.38222e8	−0.821368	−0.410684	−	0.911778i	$-0.634710\pi$
$103$	−9.38222e8	−0.821368	−0.410684	+	0.911778i	$0.634710\pi$
$104$	1.20282e9	1.00821
$105$	−7.13715e7	−0.0573025
$106$	1.10671e9	0.851449
$107$	5.16803e8	0.381152	0.190576	−	0.981672i	$-0.438965\pi$
$107$	5.16803e8	0.381152	0.190576	+	0.981672i	$0.438965\pi$
$108$	5.17441e8	0.365977
$109$	2.26116e9	1.53430	0.767152	−	0.641465i	$-0.221673\pi$
$109$	2.26116e9	1.53430	0.767152	+	0.641465i	$0.221673\pi$
$110$	−7.71170e9	−5.02207
$111$	−1.07406e8	−0.0671547
$112$	−6.18111e8	−0.371181
$113$	1.75830e9	1.01447	0.507235	−	0.861808i	$-0.330668\pi$
$113$	1.75830e9	1.01447	0.507235	+	0.861808i	$0.330668\pi$
$114$	−1.84480e8	−0.102301
$115$	3.01559e9	1.60780
$116$	−1.39505e9	−0.715369
$117$	1.15924e9	0.571922
$118$	8.22840e8	0.390703
$119$	0	0
$120$	−6.27625e8	−0.276302
$121$	4.27012e9	1.81095
$122$	−6.62541e9	−2.70766
$123$	−2.60601e8	−0.102661
$124$	4.91525e9	1.86702
$125$	−4.63394e9	−1.69768
$126$	−1.76401e9	−0.623495
$127$	−3.24308e9	−1.10622	−0.553109	−	0.833109i	$-0.686559\pi$
$127$	−3.24308e9	−1.10622	−0.553109	+	0.833109i	$0.686559\pi$
$128$	5.22444e9	1.72026
$129$	2.99511e8	0.0952269
$130$	−5.62589e9	−1.72761
$131$	−1.76002e9	−0.522152	−0.261076	−	0.965318i	$-0.584077\pi$
$131$	−1.76002e9	−0.522152	−0.261076	+	0.965318i	$0.584077\pi$
$132$	1.07462e9	0.308087
$133$	8.43199e8	0.233667
$134$	5.59102e9	1.49803
$135$	−1.21487e9	−0.314796
$136$	0	0
$137$	3.29172e9	0.798326	0.399163	−	0.916880i	$-0.369301\pi$
$137$	3.29172e9	0.798326	0.399163	+	0.916880i	$0.369301\pi$
$138$	−6.29502e8	−0.147755
$139$	5.51061e9	1.25208	0.626041	−	0.779790i	$-0.284674\pi$
$139$	5.51061e9	1.25208	0.626041	+	0.779790i	$0.284674\pi$
$140$	5.71477e9	1.25725
$141$	5.00808e8	0.106705
$142$	1.37276e10	2.83334
$143$	4.83535e9	0.966976
$144$	−5.23857e9	−1.01527
$145$	3.27538e9	0.615326
$146$	−9.84557e9	−1.79330
$147$	4.50018e8	0.0794881
$148$	8.60011e9	1.47342
$149$	−4.95750e9	−0.823994	−0.411997	−	0.911185i	$-0.635169\pi$
$149$	−4.95750e9	−0.823994	−0.411997	+	0.911185i	$0.635169\pi$
$150$	1.95144e9	0.314735
$151$	5.54660e9	0.868221	0.434110	−	0.900860i	$-0.357063\pi$
$151$	5.54660e9	0.868221	0.434110	+	0.900860i	$0.357063\pi$
$152$	7.41489e9	1.12670
$153$	0	0
$154$	−7.35792e9	−1.05417
$155$	−1.15403e10	−1.60592
$156$	7.83964e8	0.105983
$157$	1.00066e10	1.31443	0.657216	−	0.753702i	$-0.271734\pi$
$157$	1.00066e10	1.31443	0.657216	+	0.753702i	$0.271734\pi$
$158$	−4.41775e9	−0.563954
$159$	3.62085e8	0.0449287
$160$	3.95240e8	0.0476783
$161$	2.87725e9	0.337490
$162$	−1.48228e10	−1.69088
$163$	−8.23046e9	−0.913229	−0.456615	−	0.889665i	$-0.650938\pi$
$163$	−8.23046e9	−0.913229	−0.456615	+	0.889665i	$0.650938\pi$
$164$	2.08665e10	2.25244
$165$	−2.52305e9	−0.265001
$166$	−2.03045e10	−2.07541
$167$	−1.36462e10	−1.35765	−0.678823	−	0.734302i	$-0.737510\pi$
$167$	−1.36462e10	−1.35765	−0.678823	+	0.734302i	$0.737510\pi$
$168$	−5.98832e8	−0.0579980
$169$	−7.07699e9	−0.667357
$170$	0	0
$171$	7.14621e9	0.639136
$172$	−2.39821e10	−2.08934
$173$	1.30021e10	1.10359	0.551793	−	0.833981i	$-0.313944\pi$
$173$	1.30021e10	1.10359	0.551793	+	0.833981i	$0.313944\pi$
$174$	−6.83732e8	−0.0565476
$175$	−8.91939e9	−0.718893
$176$	−2.18508e10	−1.71656
$177$	2.69210e8	0.0206163
$178$	1.35884e9	0.101456
$179$	−1.39913e10	−1.01864	−0.509320	−	0.860577i	$-0.670103\pi$
$179$	−1.39913e10	−1.01864	−0.509320	+	0.860577i	$0.670103\pi$
$180$	4.84334e10	3.43889
$181$	−6.83468e9	−0.473331	−0.236665	−	0.971591i	$-0.576054\pi$
$181$	−6.83468e9	−0.473331	−0.236665	+	0.971591i	$0.576054\pi$
$182$	−5.36779e9	−0.362639
$183$	−2.16765e9	−0.142876
$184$	2.53018e10	1.62732
$185$	−2.01918e10	−1.26736
$186$	2.40902e9	0.147582
$187$	0	0
$188$	−4.01000e10	−2.34118
$189$	−1.15914e9	−0.0660781
$190$	−3.46812e10	−1.93065
$191$	−8.16856e9	−0.444115	−0.222058	−	0.975034i	$-0.571277\pi$
$191$	−8.16856e9	−0.444115	−0.222058	+	0.975034i	$0.571277\pi$
$192$	1.68186e9	0.0893169
$193$	−7.36391e9	−0.382033	−0.191016	−	0.981587i	$-0.561178\pi$
$193$	−7.36391e9	−0.382033	−0.191016	+	0.981587i	$0.561178\pi$
$194$	−2.97142e10	−1.50611
$195$	−1.84063e9	−0.0911614
$196$	−3.60333e10	−1.74402
$197$	−4.30217e9	−0.203512	−0.101756	−	0.994809i	$-0.532446\pi$
$197$	−4.30217e9	−0.203512	−0.101756	+	0.994809i	$0.532446\pi$
$198$	−6.23592e10	−2.88342
$199$	−2.49664e10	−1.12854	−0.564271	−	0.825590i	$-0.690843\pi$
$199$	−2.49664e10	−1.12854	−0.564271	+	0.825590i	$0.690843\pi$
$200$	−7.84350e10	−3.46637
$201$	1.82922e9	0.0790468
$202$	−1.91447e10	−0.809036
$203$	3.12512e9	0.129162
$204$	0	0
$205$	−4.89915e10	−1.93744
$206$	3.68192e10	1.42453
$207$	2.43850e10	0.923116
$208$	−1.59407e10	−0.590504
$209$	2.98078e10	1.08062
$210$	2.80088e9	0.0993818
$211$	−2.40166e9	−0.0834143	−0.0417072	−	0.999130i	$-0.513280\pi$
$211$	−2.40166e9	−0.0834143	−0.0417072	+	0.999130i	$0.513280\pi$
$212$	−2.89924e10	−0.985764
$213$	4.49129e9	0.149508
$214$	−2.02812e10	−0.661045
$215$	5.63063e10	1.79715
$216$	−1.01932e10	−0.318617
$217$	−1.10108e10	−0.337095
$218$	−8.87359e10	−2.66100
$219$	−3.22119e9	−0.0946276
$220$	2.02022e11	5.81430
$221$	0	0
$222$	4.21501e9	0.116469
$223$	−1.87161e10	−0.506808	−0.253404	−	0.967361i	$-0.581550\pi$
$223$	−1.87161e10	−0.506808	−0.253404	+	0.967361i	$0.581550\pi$
$224$	3.77108e8	0.0100081
$225$	−7.55929e10	−1.96634
$226$	−6.90019e10	−1.75943
$227$	−4.09042e10	−1.02247	−0.511237	−	0.859440i	$-0.670812\pi$
$227$	−4.09042e10	−1.02247	−0.511237	+	0.859440i	$0.670812\pi$
$228$	4.83280e9	0.118438
$229$	3.94845e10	0.948784	0.474392	−	0.880314i	$-0.342668\pi$
$229$	3.94845e10	0.948784	0.474392	+	0.880314i	$0.342668\pi$
$230$	−1.18343e11	−2.78847
$231$	−2.40730e9	−0.0556258
$232$	2.74815e10	0.622795
$233$	1.38741e10	0.308392	0.154196	−	0.988040i	$-0.450721\pi$
$233$	1.38741e10	0.308392	0.154196	+	0.988040i	$0.450721\pi$
$234$	−4.54927e10	−0.991905
$235$	9.41488e10	2.01377
$236$	−2.15558e10	−0.452336
$237$	−1.44536e9	−0.0297583
$238$	0	0
$239$	2.75139e10	0.545458	0.272729	−	0.962091i	$-0.412074\pi$
$239$	2.75139e10	0.545458	0.272729	+	0.962091i	$0.412074\pi$
$240$	8.31775e9	0.161829
$241$	5.50089e10	1.05040	0.525201	−	0.850978i	$-0.323990\pi$
$241$	5.50089e10	1.05040	0.525201	+	0.850978i	$0.323990\pi$
$242$	−1.67575e11	−3.14079
$243$	−1.47564e10	−0.271489
$244$	1.73565e11	3.13479
$245$	8.46007e10	1.50012
$246$	1.02269e10	0.178048
$247$	2.17456e10	0.371736
$248$	−9.68268e10	−1.62541
$249$	−6.64304e9	−0.109514
$250$	1.81853e11	2.94435
$251$	4.50601e10	0.716573	0.358287	−	0.933612i	$-0.383361\pi$
$251$	4.50601e10	0.716573	0.358287	+	0.933612i	$0.383361\pi$
$252$	4.62114e10	0.721850
$253$	1.01713e11	1.56076
$254$	1.27270e11	1.91856
$255$	0	0
$256$	−1.37958e11	−2.00755
$257$	1.80006e10	0.257388	0.128694	−	0.991684i	$-0.458922\pi$
$257$	1.80006e10	0.257388	0.128694	+	0.991684i	$0.458922\pi$
$258$	−1.17539e10	−0.165156
$259$	−1.92654e10	−0.266030
$260$	1.47381e11	2.00014
$261$	2.64857e10	0.353289
$262$	6.90695e10	0.905588
$263$	−3.97025e10	−0.511701	−0.255851	−	0.966716i	$-0.582356\pi$
$263$	−3.97025e10	−0.511701	−0.255851	+	0.966716i	$0.582356\pi$
$264$	−2.11692e10	−0.268218
$265$	6.80698e10	0.847907
$266$	−3.30901e10	−0.405258
$267$	4.44575e8	0.00535358
$268$	−1.46467e11	−1.73434
$269$	1.81112e10	0.210892	0.105446	−	0.994425i	$-0.466373\pi$
$269$	1.81112e10	0.210892	0.105446	+	0.994425i	$0.466373\pi$
$270$	4.76760e10	0.545962
$271$	7.90096e10	0.889852	0.444926	−	0.895567i	$-0.353230\pi$
$271$	7.90096e10	0.889852	0.444926	+	0.895567i	$0.353230\pi$
$272$	0	0
$273$	−1.75619e9	−0.0191355
$274$	−1.29179e11	−1.38457
$275$	−3.15309e11	−3.32459
$276$	1.64910e10	0.171063
$277$	6.92850e10	0.707099	0.353550	−	0.935416i	$-0.384975\pi$
$277$	6.92850e10	0.707099	0.353550	+	0.935416i	$0.384975\pi$
$278$	−2.16256e11	−2.17153
$279$	−9.33182e10	−0.922035
$280$	−1.12577e11	−1.09456
$281$	−2.06595e11	−1.97670	−0.988352	−	0.152185i	$-0.951369\pi$
$281$	−2.06595e11	−1.97670	−0.988352	+	0.152185i	$0.951369\pi$
$282$	−1.96535e10	−0.185063
$283$	−1.24554e10	−0.115430	−0.0577150	−	0.998333i	$-0.518381\pi$
$283$	−1.24554e10	−0.115430	−0.0577150	+	0.998333i	$0.518381\pi$
$284$	−3.59621e11	−3.28029
$285$	−1.13467e10	−0.101875
$286$	−1.89756e11	−1.67706
$287$	−4.67439e10	−0.406684
$288$	3.19604e9	0.0273744
$289$	0	0
$290$	−1.28538e11	−1.06718
$291$	−9.72163e9	−0.0794732
$292$	2.57923e11	2.07619
$293$	2.10624e11	1.66956	0.834781	−	0.550582i	$-0.185594\pi$
$293$	2.10624e11	1.66956	0.834781	+	0.550582i	$0.185594\pi$
$294$	−1.76603e10	−0.137859
$295$	5.06098e10	0.389077
$296$	−1.69416e11	−1.28275
$297$	−4.09766e10	−0.305585
$298$	1.94550e11	1.42908
$299$	7.42025e10	0.536906
$300$	−5.11216e10	−0.364384
$301$	5.37232e10	0.377236
$302$	−2.17668e11	−1.50579
$303$	−6.26360e9	−0.0426906
$304$	−9.82677e10	−0.659902
$305$	−4.07504e11	−2.69639
$306$	0	0
$307$	−3.41297e10	−0.219286	−0.109643	−	0.993971i	$-0.534971\pi$
$307$	−3.41297e10	−0.219286	−0.109643	+	0.993971i	$0.534971\pi$
$308$	1.92754e11	1.22047
$309$	1.20462e10	0.0751686
$310$	4.52882e11	2.78520
$311$	−1.49100e11	−0.903768	−0.451884	−	0.892077i	$-0.649248\pi$
$311$	−1.49100e11	−0.903768	−0.451884	+	0.892077i	$0.649248\pi$
$312$	−1.54435e10	−0.0922679
$313$	2.31010e10	0.136044	0.0680222	−	0.997684i	$-0.478331\pi$
$313$	2.31010e10	0.136044	0.0680222	+	0.997684i	$0.478331\pi$
$314$	−3.92695e11	−2.27967
$315$	−1.08497e11	−0.620901
$316$	1.15731e11	0.652917
$317$	−1.18508e11	−0.659146	−0.329573	−	0.944130i	$-0.606905\pi$
$317$	−1.18508e11	−0.659146	−0.329573	+	0.944130i	$0.606905\pi$
$318$	−1.42095e10	−0.0779215
$319$	1.10476e11	0.597322
$320$	3.16179e11	1.68561
$321$	−6.63542e9	−0.0348816
$322$	−1.12913e11	−0.585321
$323$	0	0
$324$	3.88312e11	1.95762
$325$	−2.30026e11	−1.14367
$326$	3.22993e11	1.58385
$327$	−2.90319e10	−0.140414
$328$	−4.11055e11	−1.96096
$329$	8.98296e10	0.422706
$330$	9.90135e10	0.459602
$331$	2.01002e11	0.920397	0.460199	−	0.887816i	$-0.347778\pi$
$331$	2.01002e11	0.920397	0.460199	+	0.887816i	$0.347778\pi$
$332$	5.31913e11	2.40281
$333$	−1.63277e11	−0.727655
$334$	5.35525e11	2.35462
$335$	3.43883e11	1.49179
$336$	7.93617e9	0.0339691
$337$	−3.79448e11	−1.60257	−0.801286	−	0.598282i	$-0.795850\pi$
$337$	−3.79448e11	−1.60257	−0.801286	+	0.598282i	$0.795850\pi$
$338$	2.77726e11	1.15742
$339$	−2.25755e10	−0.0928406
$340$	0	0
$341$	−3.89243e11	−1.55893
$342$	−2.80443e11	−1.10848
$343$	1.73654e11	0.677424
$344$	4.72429e11	1.81896
$345$	−3.87183e10	−0.147140
$346$	−5.10249e11	−1.91399
$347$	−2.02768e11	−0.750789	−0.375394	−	0.926865i	$-0.622493\pi$
$347$	−2.02768e11	−0.750789	−0.375394	+	0.926865i	$0.622493\pi$
$348$	1.79116e10	0.0654679
$349$	2.76919e10	0.0999166	0.0499583	−	0.998751i	$-0.484091\pi$
$349$	2.76919e10	0.0999166	0.0499583	+	0.998751i	$0.484091\pi$
$350$	3.50029e11	1.24680
$351$	−2.98935e10	−0.105122
$352$	1.33311e10	0.0462833
$353$	2.50963e11	0.860249	0.430124	−	0.902770i	$-0.358470\pi$
$353$	2.50963e11	0.860249	0.430124	+	0.902770i	$0.358470\pi$
$354$	−1.05648e10	−0.0357557
$355$	8.44336e11	2.82155
$356$	−3.55975e10	−0.117461
$357$	0	0
$358$	5.49071e11	1.76667
$359$	−2.70942e11	−0.860898	−0.430449	−	0.902615i	$-0.641645\pi$
$359$	−2.70942e11	−0.860898	−0.430449	+	0.902615i	$0.641645\pi$
$360$	−9.54102e11	−2.99387
$361$	−1.88635e11	−0.584576
$362$	2.68217e11	0.820915
$363$	−5.48257e10	−0.165731
$364$	1.40619e11	0.419845
$365$	−6.05564e11	−1.78584
$366$	8.50662e10	0.247795
$367$	−3.18541e11	−0.916576	−0.458288	−	0.888804i	$-0.651537\pi$
$367$	−3.18541e11	−0.916576	−0.458288	+	0.888804i	$0.651537\pi$
$368$	−3.35319e11	−0.953110
$369$	−3.96161e11	−1.11238
$370$	7.92397e11	2.19804
$371$	6.49470e10	0.177982
$372$	−6.31088e10	−0.170862
$373$	−1.66138e11	−0.444406	−0.222203	−	0.975000i	$-0.571325\pi$
$373$	−1.66138e11	−0.444406	−0.222203	+	0.975000i	$0.571325\pi$
$374$	0	0
$375$	5.94970e10	0.155365
$376$	7.89941e11	2.03821
$377$	8.05949e10	0.205481
$378$	4.54888e10	0.114602
$379$	5.85960e10	0.145879	0.0729393	−	0.997336i	$-0.476762\pi$
$379$	5.85960e10	0.145879	0.0729393	+	0.997336i	$0.476762\pi$
$380$	9.08538e11	2.23520
$381$	4.16392e10	0.101237
$382$	3.20564e11	0.770246
$383$	2.93491e9	0.00696948	0.00348474	−	0.999994i	$-0.498891\pi$
$383$	2.93491e9	0.00696948	0.00348474	+	0.999994i	$0.498891\pi$
$384$	−6.70785e10	−0.157432
$385$	−4.52558e11	−1.04979
$386$	2.88986e11	0.662574
$387$	4.55311e11	1.03183
$388$	7.78418e11	1.74369
$389$	−6.42977e10	−0.142371	−0.0711856	−	0.997463i	$-0.522678\pi$
$389$	−6.42977e10	−0.142371	−0.0711856	+	0.997463i	$0.522678\pi$
$390$	7.22329e10	0.158105
$391$	0	0
$392$	7.09829e11	1.51833
$393$	2.25976e10	0.0477854
$394$	1.68833e11	0.352958
$395$	−2.71719e11	−0.561608
$396$	1.63362e12	3.33827
$397$	4.49576e11	0.908335	0.454168	−	0.890916i	$-0.349937\pi$
$397$	4.49576e11	0.908335	0.454168	+	0.890916i	$0.349937\pi$
$398$	9.79772e11	1.95727
$399$	−1.08261e10	−0.0213843
$400$	1.03948e12	2.03023
$401$	3.55995e10	0.0687534	0.0343767	−	0.999409i	$-0.489055\pi$
$401$	3.55995e10	0.0687534	0.0343767	+	0.999409i	$0.489055\pi$
$402$	−7.17852e10	−0.137094
$403$	−2.83963e11	−0.536277
$404$	5.01531e11	0.936660
$405$	−9.11697e11	−1.68385
$406$	−1.22641e11	−0.224010
$407$	−6.81051e11	−1.23028
$408$	0	0
$409$	−1.95612e11	−0.345653	−0.172826	−	0.984952i	$-0.555290\pi$
$409$	−1.95612e11	−0.345653	−0.172826	+	0.984952i	$0.555290\pi$
$410$	1.92260e12	3.36018
$411$	−4.22637e10	−0.0730599
$412$	−9.64547e11	−1.64925
$413$	4.82880e10	0.0816703
$414$	−9.56955e11	−1.60099
$415$	−1.24885e12	−2.06678
$416$	9.72539e9	0.0159216
$417$	−7.07528e10	−0.114586
$418$	−1.16977e12	−1.87416
$419$	−4.91804e10	−0.0779523	−0.0389761	−	0.999240i	$-0.512410\pi$
$419$	−4.91804e10	−0.0779523	−0.0389761	+	0.999240i	$0.512410\pi$
$420$	−7.33741e10	−0.115059
$421$	−5.58710e9	−0.00866796	−0.00433398	−	0.999991i	$-0.501380\pi$
$421$	−5.58710e9	−0.00866796	−0.00433398	+	0.999991i	$0.501380\pi$
$422$	9.42498e10	0.144669
$423$	7.61317e11	1.15620
$424$	5.71129e11	0.858198
$425$	0	0
$426$	−1.76254e11	−0.259297
$427$	−3.88810e11	−0.565994
$428$	5.31303e11	0.765324
$429$	−6.20829e10	−0.0884940
$430$	−2.20966e12	−3.11686
$431$	7.03708e11	0.982302	0.491151	−	0.871075i	$-0.336576\pi$
$431$	7.03708e11	0.982302	0.491151	+	0.871075i	$0.336576\pi$
$432$	1.35088e11	0.186612
$433$	−1.58945e11	−0.217295	−0.108648	−	0.994080i	$-0.534652\pi$
$433$	−1.58945e11	−0.217295	−0.108648	+	0.994080i	$0.534652\pi$
$434$	4.32105e11	0.584636
$435$	−4.20538e10	−0.0563124
$436$	2.32460e12	3.08077
$437$	4.57426e11	0.600005
$438$	1.26411e11	0.164116
$439$	3.36069e11	0.431855	0.215927	−	0.976409i	$-0.430723\pi$
$439$	3.36069e11	0.431855	0.215927	+	0.976409i	$0.430723\pi$
$440$	−3.97969e12	−5.06189
$441$	6.84108e11	0.861293
$442$	0	0
$443$	−1.22782e12	−1.51466	−0.757332	−	0.653030i	$-0.773498\pi$
$443$	−1.22782e12	−1.51466	−0.757332	+	0.653030i	$0.773498\pi$
$444$	−1.10420e11	−0.134842
$445$	8.35775e10	0.101034
$446$	7.34486e11	0.878975
$447$	6.36512e10	0.0754089
$448$	3.01674e11	0.353823
$449$	1.19610e12	1.38886	0.694428	−	0.719562i	$-0.255657\pi$
$449$	1.19610e12	1.38886	0.694428	+	0.719562i	$0.255657\pi$
$450$	2.96654e12	3.41031
$451$	−1.65244e12	−1.88075
$452$	1.80763e12	2.03698
$453$	−7.12148e10	−0.0794564
$454$	1.60523e12	1.77331
$455$	−3.30153e11	−0.361130
$456$	−9.52026e10	−0.103111
$457$	−5.18528e10	−0.0556096	−0.0278048	−	0.999613i	$-0.508852\pi$
$457$	−5.18528e10	−0.0556096	−0.0278048	+	0.999613i	$0.508852\pi$
$458$	−1.54951e12	−1.64551
$459$	0	0
$460$	3.10020e12	3.22835
$461$	−5.27975e11	−0.544451	−0.272226	−	0.962233i	$-0.587760\pi$
$461$	−5.27975e11	−0.544451	−0.272226	+	0.962233i	$0.587760\pi$
$462$	9.44711e10	0.0964739
$463$	−1.71882e12	−1.73827	−0.869133	−	0.494579i	$-0.835322\pi$
$463$	−1.71882e12	−1.73827	−0.869133	+	0.494579i	$0.835322\pi$
$464$	−3.64206e11	−0.364768
$465$	1.48170e11	0.146968
$466$	−5.44469e11	−0.534856
$467$	1.23791e12	1.20438	0.602188	−	0.798355i	$-0.294296\pi$
$467$	1.23791e12	1.20438	0.602188	+	0.798355i	$0.294296\pi$
$468$	1.19177e12	1.14838
$469$	3.28107e11	0.313139
$470$	−3.69474e12	−3.49256
$471$	−1.28479e11	−0.120292
$472$	4.24634e11	0.393800
$473$	1.89916e12	1.74457
$474$	5.67211e10	0.0516110
$475$	−1.41801e12	−1.27808
$476$	0	0
$477$	5.50434e11	0.486824
$478$	−1.07974e12	−0.946008
$479$	−1.00333e12	−0.870833	−0.435416	−	0.900229i	$-0.643399\pi$
$479$	−1.00333e12	−0.870833	−0.435416	+	0.900229i	$0.643399\pi$
$480$	−5.07464e9	−0.00436335
$481$	−4.96844e11	−0.423221
$482$	−2.15874e12	−1.82175
$483$	−3.69421e10	−0.0308858
$484$	4.38993e12	3.63625
$485$	−1.82761e12	−1.49984
$486$	5.79095e11	0.470854
$487$	1.82452e12	1.46983	0.734916	−	0.678158i	$-0.237222\pi$
$487$	1.82452e12	1.46983	0.734916	+	0.678158i	$0.237222\pi$
$488$	−3.41910e12	−2.72912
$489$	1.05674e11	0.0835754
$490$	−3.32004e12	−2.60172
$491$	−3.89108e11	−0.302137	−0.151068	−	0.988523i	$-0.548271\pi$
$491$	−3.89108e11	−0.302137	−0.151068	+	0.988523i	$0.548271\pi$
$492$	−2.67913e11	−0.206135
$493$	0	0
$494$	−8.53375e11	−0.644716
$495$	−3.83548e12	−2.87142
$496$	1.28322e12	0.951994
$497$	8.05601e11	0.592265
$498$	2.60697e11	0.189934
$499$	−2.52722e12	−1.82470	−0.912349	−	0.409414i	$-0.865733\pi$
$499$	−2.52722e12	−1.82470	−0.912349	+	0.409414i	$0.865733\pi$
$500$	−4.76397e12	−3.40882
$501$	1.75208e11	0.124247
$502$	−1.76832e12	−1.24278
$503$	1.22587e12	0.853863	0.426932	−	0.904284i	$-0.359594\pi$
$503$	1.22587e12	0.853863	0.426932	+	0.904284i	$0.359594\pi$
$504$	−9.10331e11	−0.628437
$505$	−1.17752e12	−0.805670
$506$	−3.99159e12	−2.70688
$507$	9.08641e10	0.0610740
$508$	−3.33408e12	−2.22121
$509$	−2.63263e12	−1.73844	−0.869221	−	0.494424i	$-0.835379\pi$
$509$	−2.63263e12	−1.73844	−0.869221	+	0.494424i	$0.835379\pi$
$510$	0	0
$511$	−5.77783e11	−0.374862
$512$	2.73904e12	1.76150
$513$	−1.84281e11	−0.117477
$514$	−7.06407e11	−0.446397
$515$	2.26461e12	1.41860
$516$	3.07915e11	0.191209
$517$	3.17556e12	1.95485
$518$	7.56045e11	0.461385
$519$	−1.66939e11	−0.100996
$520$	−2.90329e12	−1.74131
$521$	9.50624e11	0.565248	0.282624	−	0.959231i	$-0.408795\pi$
$521$	9.50624e11	0.565248	0.282624	+	0.959231i	$0.408795\pi$
$522$	−1.03940e12	−0.612722
$523$	1.56396e12	0.914045	0.457022	−	0.889455i	$-0.348916\pi$
$523$	1.56396e12	0.914045	0.457022	+	0.889455i	$0.348916\pi$
$524$	−1.80940e12	−1.04844
$525$	1.14519e11	0.0657904
$526$	1.55807e12	0.887463
$527$	0	0
$528$	2.80551e11	0.157094
$529$	−2.40277e11	−0.133402
$530$	−2.67130e12	−1.47056
$531$	4.09247e11	0.223388
$532$	8.66858e11	0.469186
$533$	−1.20550e12	−0.646985
$534$	−1.74467e10	−0.00928492
$535$	−1.24742e12	−0.658295
$536$	2.88529e12	1.50990
$537$	1.79640e11	0.0932222
$538$	−7.10747e11	−0.365759
$539$	2.85351e12	1.45623
$540$	−1.24896e12	−0.632087
$541$	3.47453e12	1.74385	0.871924	−	0.489641i	$-0.162872\pi$
$541$	3.47453e12	1.74385	0.871924	+	0.489641i	$0.162872\pi$
$542$	−3.10062e12	−1.54330
$543$	8.77531e10	0.0433175
$544$	0	0
$545$	−5.45782e12	−2.64993
$546$	6.89191e10	0.0331874
$547$	3.19663e12	1.52669	0.763344	−	0.645993i	$-0.223556\pi$
$547$	3.19663e12	1.52669	0.763344	+	0.645993i	$0.223556\pi$
$548$	3.38408e12	1.60298
$549$	−3.29521e12	−1.54813
$550$	1.23738e13	5.76597
$551$	4.96833e11	0.229630
$552$	−3.24860e11	−0.148926
$553$	−2.59254e11	−0.117886
$554$	−2.71899e12	−1.22635
$555$	2.59250e11	0.115984
$556$	5.66523e12	2.51409
$557$	3.44273e12	1.51549	0.757747	−	0.652548i	$-0.226300\pi$
$557$	3.44273e12	1.51549	0.757747	+	0.652548i	$0.226300\pi$
$558$	3.66214e12	1.59912
$559$	1.38549e12	0.600137
$560$	1.49195e12	0.641075
$561$	0	0
$562$	8.10753e12	3.42827
$563$	3.44807e12	1.44640	0.723199	−	0.690639i	$-0.242671\pi$
$563$	3.44807e12	1.44640	0.723199	+	0.690639i	$0.242671\pi$
$564$	5.14860e11	0.214256
$565$	−4.24405e12	−1.75211
$566$	4.88794e11	0.200194
$567$	−8.69872e11	−0.353453
$568$	7.08427e12	2.85580
$569$	−2.03356e12	−0.813302	−0.406651	−	0.913584i	$-0.633304\pi$
$569$	−2.03356e12	−0.813302	−0.406651	+	0.913584i	$0.633304\pi$
$570$	4.45285e11	0.176686
$571$	2.59738e12	1.02252	0.511261	−	0.859426i	$-0.329179\pi$
$571$	2.59738e12	1.02252	0.511261	+	0.859426i	$0.329179\pi$
$572$	4.97102e12	1.94162
$573$	1.04879e11	0.0406438
$574$	1.83440e12	0.705327
$575$	−4.83868e12	−1.84596
$576$	2.55672e12	0.967793
$577$	−6.36090e11	−0.238906	−0.119453	−	0.992840i	$-0.538114\pi$
$577$	−6.36090e11	−0.238906	−0.119453	+	0.992840i	$0.538114\pi$
$578$	0	0
$579$	9.45480e10	0.0349622
$580$	3.36728e12	1.23553
$581$	−1.19156e12	−0.433833
$582$	3.81511e11	0.137833
$583$	2.29594e12	0.823097
$584$	−5.08089e12	−1.80752
$585$	−2.79809e12	−0.987779
$586$	−8.26562e12	−2.89558
$587$	1.69305e11	0.0588571	0.0294286	−	0.999567i	$-0.490631\pi$
$587$	1.69305e11	0.0588571	0.0294286	+	0.999567i	$0.490631\pi$
$588$	4.62645e11	0.159606
$589$	−1.75051e12	−0.599302
$590$	−1.98611e12	−0.674791
$591$	5.52372e10	0.0186246
$592$	2.24522e12	0.751298
$593$	3.48378e12	1.15692	0.578462	−	0.815709i	$-0.303653\pi$
$593$	3.48378e12	1.15692	0.578462	+	0.815709i	$0.303653\pi$
$594$	1.60807e12	0.529988
$595$	0	0
$596$	−5.09660e12	−1.65452
$597$	3.20554e11	0.103280
$598$	−2.91197e12	−0.931176
$599$	1.11287e12	0.353201	0.176601	−	0.984283i	$-0.443490\pi$
$599$	1.11287e12	0.353201	0.176601	+	0.984283i	$0.443490\pi$
$600$	1.00706e12	0.317229
$601$	−3.78822e12	−1.18441	−0.592203	−	0.805789i	$-0.701741\pi$
$601$	−3.78822e12	−1.18441	−0.592203	+	0.805789i	$0.701741\pi$
$602$	−2.10829e12	−0.654254
$603$	2.78074e12	0.856511
$604$	5.70223e12	1.74332
$605$	−1.03069e13	−3.12773
$606$	2.45806e11	0.0740399
$607$	−7.20412e11	−0.215393	−0.107697	−	0.994184i	$-0.534347\pi$
$607$	−7.20412e11	−0.215393	−0.107697	+	0.994184i	$0.534347\pi$
$608$	5.99529e10	0.0177928
$609$	−4.01246e10	−0.0118204
$610$	1.59919e13	4.67645
$611$	2.31665e12	0.672474
$612$	0	0
$613$	−3.71257e11	−0.106195	−0.0530973	−	0.998589i	$-0.516909\pi$
$613$	−3.71257e11	−0.106195	−0.0530973	+	0.998589i	$0.516909\pi$
$614$	1.33937e12	0.380315
$615$	6.29021e11	0.177307
$616$	−3.79712e12	−1.06253
$617$	−6.63363e11	−0.184276	−0.0921378	−	0.995746i	$-0.529370\pi$
$617$	−6.63363e11	−0.184276	−0.0921378	+	0.995746i	$0.529370\pi$
$618$	−4.72735e11	−0.130368
$619$	−1.73727e12	−0.475619	−0.237809	−	0.971312i	$-0.576429\pi$
$619$	−1.73727e12	−0.475619	−0.237809	+	0.971312i	$0.576429\pi$
$620$	−1.18641e13	−3.22457
$621$	−6.28821e11	−0.169674
$622$	5.85123e12	1.56744
$623$	7.97433e10	0.0212079
$624$	2.04669e11	0.0540408
$625$	3.62071e12	0.949148
$626$	−9.06564e11	−0.235947
$627$	−3.82714e11	−0.0988941
$628$	1.02874e13	2.63928
$629$	0	0
$630$	4.25783e12	1.07685
$631$	−5.82077e12	−1.46167	−0.730834	−	0.682556i	$-0.760869\pi$
$631$	−5.82077e12	−1.46167	−0.730834	+	0.682556i	$0.760869\pi$
$632$	−2.27982e12	−0.568425
$633$	3.08358e10	0.00763377
$634$	4.65068e12	1.14318
$635$	7.82791e12	1.91058
$636$	3.72245e11	0.0902135
$637$	2.08171e12	0.500948
$638$	−4.33546e12	−1.03596
$639$	6.82756e12	1.61999
$640$	−1.26104e13	−2.97110
$641$	−7.79878e12	−1.82459	−0.912296	−	0.409532i	$-0.865692\pi$
$641$	−7.79878e12	−1.82459	−0.912296	+	0.409532i	$0.865692\pi$
$642$	2.60398e11	0.0604964
$643$	−2.47918e12	−0.571950	−0.285975	−	0.958237i	$-0.592317\pi$
$643$	−2.47918e12	−0.571950	−0.285975	+	0.958237i	$0.592317\pi$
$644$	2.95798e12	0.677655
$645$	−7.22938e11	−0.164468
$646$	0	0
$647$	2.78295e12	0.624362	0.312181	−	0.950023i	$-0.398941\pi$
$647$	2.78295e12	0.624362	0.312181	+	0.950023i	$0.398941\pi$
$648$	−7.64945e12	−1.70429
$649$	1.70703e12	0.377693
$650$	9.02704e12	1.98351
$651$	1.41372e11	0.0308496
$652$	−8.46139e12	−1.83370
$653$	2.01770e12	0.434257	0.217128	−	0.976143i	$-0.430331\pi$
$653$	2.01770e12	0.434257	0.217128	+	0.976143i	$0.430331\pi$
$654$	1.13931e12	0.243525
$655$	4.24821e12	0.901820
$656$	5.44761e12	1.14852
$657$	−4.89678e12	−1.02534
$658$	−3.52524e12	−0.733114
$659$	3.26107e12	0.673559	0.336779	−	0.941584i	$-0.390662\pi$
$659$	3.26107e12	0.673559	0.336779	+	0.941584i	$0.390662\pi$
$660$	−2.59384e12	−0.532103
$661$	3.23725e12	0.659583	0.329792	−	0.944054i	$-0.393022\pi$
$661$	3.23725e12	0.659583	0.329792	+	0.944054i	$0.393022\pi$
$662$	−7.88806e12	−1.59628
$663$	0	0
$664$	−1.04783e13	−2.09187
$665$	−2.03525e12	−0.403572
$666$	6.40757e12	1.26200
$667$	1.69534e12	0.331659
$668$	−1.40291e13	−2.72606
$669$	2.40303e11	0.0463811
$670$	−1.34952e13	−2.58728
$671$	−1.37448e13	−2.61750
$672$	−4.84183e9	−0.000915900 0
$673$	−2.71466e12	−0.510091	−0.255046	−	0.966929i	$-0.582090\pi$
$673$	−2.71466e12	−0.510091	−0.255046	+	0.966929i	$0.582090\pi$
$674$	1.48909e13	2.77940
$675$	1.94933e12	0.361425
$676$	−7.27556e12	−1.34000
$677$	7.38964e10	0.0135199	0.00675997	−	0.999977i	$-0.497848\pi$
$677$	7.38964e10	0.0135199	0.00675997	+	0.999977i	$0.497848\pi$
$678$	8.85942e11	0.161017
$679$	−1.74376e12	−0.314828
$680$	0	0
$681$	5.25185e11	0.0935729
$682$	1.52753e13	2.70371
$683$	5.15673e12	0.906737	0.453368	−	0.891323i	$-0.350222\pi$
$683$	5.15673e12	0.906737	0.453368	+	0.891323i	$0.350222\pi$
$684$	7.34672e12	1.28334
$685$	−7.94532e12	−1.37881
$686$	−6.81479e12	−1.17488
$687$	−5.06957e11	−0.0868292
$688$	−6.26099e12	−1.06536
$689$	1.67495e12	0.283148
$690$	1.51945e12	0.255190
$691$	9.13711e12	1.52461	0.762303	−	0.647220i	$-0.224069\pi$
$691$	9.13711e12	1.52461	0.762303	+	0.647220i	$0.224069\pi$
$692$	1.33669e13	2.21592
$693$	−3.65953e12	−0.602734
$694$	7.95736e12	1.30212
$695$	−1.33011e13	−2.16250
$696$	−3.52846e11	−0.0569959
$697$	0	0
$698$	−1.08673e12	−0.173289
$699$	−1.78135e11	−0.0282229
$700$	−9.16966e12	−1.44348
$701$	1.05802e11	0.0165487	0.00827433	−	0.999966i	$-0.497366\pi$
$701$	1.05802e11	0.0165487	0.00827433	+	0.999966i	$0.497366\pi$
$702$	1.17313e12	0.182318
$703$	−3.06283e12	−0.472960
$704$	1.06644e13	1.63629
$705$	−1.20881e12	−0.184293
$706$	−9.84870e12	−1.49196
$707$	−1.12350e12	−0.169116
$708$	2.76763e11	0.0413961
$709$	−5.40312e12	−0.803038	−0.401519	−	0.915851i	$-0.631518\pi$
$709$	−5.40312e12	−0.803038	−0.401519	+	0.915851i	$0.631518\pi$
$710$	−3.31348e13	−4.89352
$711$	−2.19721e12	−0.322447
$712$	7.01244e11	0.102261
$713$	−5.97327e12	−0.865584
$714$	0	0
$715$	−1.16712e13	−1.67009
$716$	−1.43839e13	−2.04536
$717$	−3.53261e11	−0.0499183
$718$	1.06327e13	1.49309
$719$	1.25578e13	1.75240	0.876202	−	0.481944i	$-0.160069\pi$
$719$	1.25578e13	1.75240	0.876202	+	0.481944i	$0.160069\pi$
$720$	1.26445e13	1.75349
$721$	2.16072e12	0.297776
$722$	7.40273e12	1.01385
$723$	−7.06280e11	−0.0961290
$724$	−7.02645e12	−0.950413
$725$	−5.25552e12	−0.706472
$726$	2.15156e12	0.287434
$727$	3.74144e12	0.496746	0.248373	−	0.968665i	$-0.420104\pi$
$727$	3.74144e12	0.496746	0.248373	+	0.968665i	$0.420104\pi$
$728$	−2.77010e12	−0.365514
$729$	−7.24507e12	−0.950099
$730$	2.37645e13	3.09725
$731$	0	0
$732$	−2.22847e12	−0.286884
$733$	−7.03096e12	−0.899594	−0.449797	−	0.893131i	$-0.648504\pi$
$733$	−7.03096e12	−0.899594	−0.449797	+	0.893131i	$0.648504\pi$
$734$	1.25007e13	1.58965
$735$	−1.08622e12	−0.137286
$736$	2.04577e11	0.0256984
$737$	1.15989e13	1.44815
$738$	1.55468e13	1.92924
$739$	4.06712e12	0.501634	0.250817	−	0.968035i	$-0.419301\pi$
$739$	4.06712e12	0.501634	0.250817	+	0.968035i	$0.419301\pi$
$740$	−2.07583e13	−2.54477
$741$	−2.79200e11	−0.0340199
$742$	−2.54875e12	−0.308681
$743$	1.05121e13	1.26543	0.632716	−	0.774384i	$-0.281940\pi$
$743$	1.05121e13	1.26543	0.632716	+	0.774384i	$0.281940\pi$
$744$	1.24320e12	0.148752
$745$	1.19660e13	1.42314
$746$	6.51986e12	0.770750
$747$	−1.00986e13	−1.18664
$748$	0	0
$749$	−1.19019e12	−0.138181
$750$	−2.33487e12	−0.269456
$751$	−9.86339e12	−1.13148	−0.565739	−	0.824584i	$-0.691409\pi$
$751$	−9.86339e12	−1.13148	−0.565739	+	0.824584i	$0.691409\pi$
$752$	−1.04689e13	−1.19377
$753$	−5.78544e11	−0.0655781
$754$	−3.16283e12	−0.356373
$755$	−1.33880e13	−1.49952
$756$	−1.19166e12	−0.132680
$757$	1.58167e13	1.75060	0.875298	−	0.483584i	$-0.160665\pi$
$757$	1.58167e13	1.75060	0.875298	+	0.483584i	$0.160665\pi$
$758$	−2.29952e12	−0.253003
$759$	−1.30594e12	−0.142835
$760$	−1.78975e13	−1.94595
$761$	−2.52570e12	−0.272992	−0.136496	−	0.990641i	$-0.543584\pi$
$761$	−2.52570e12	−0.272992	−0.136496	+	0.990641i	$0.543584\pi$
$762$	−1.63407e12	−0.175579
$763$	−5.20743e12	−0.556241
$764$	−8.39776e12	−0.891751
$765$	0	0
$766$	−1.15176e11	−0.0120874
$767$	1.24532e12	0.129928
$768$	1.77129e12	0.183723
$769$	−1.30319e13	−1.34382	−0.671909	−	0.740634i	$-0.734525\pi$
$769$	−1.30319e13	−1.34382	−0.671909	+	0.740634i	$0.734525\pi$
$770$	1.77600e13	1.82068
$771$	−2.31116e11	−0.0235552
$772$	−7.57053e12	−0.767094
$773$	1.55200e13	1.56345	0.781724	−	0.623624i	$-0.214340\pi$
$773$	1.55200e13	1.56345	0.781724	+	0.623624i	$0.214340\pi$
$774$	−1.78680e13	−1.78954
$775$	1.85170e13	1.84379
$776$	−1.53343e13	−1.51805
$777$	2.47356e11	0.0243460
$778$	2.52327e12	0.246920
$779$	−7.43138e12	−0.723021
$780$	−1.89228e12	−0.183045
$781$	2.84787e13	2.73899
$782$	0	0
$783$	−6.82993e11	−0.0649364
$784$	−9.40718e12	−0.889278
$785$	−2.41532e13	−2.27019
$786$	−8.86810e11	−0.0828760
$787$	8.13448e12	0.755864	0.377932	−	0.925833i	$-0.376635\pi$
$787$	8.13448e12	0.755864	0.377932	+	0.925833i	$0.376635\pi$
$788$	−4.42288e12	−0.408637
$789$	5.09755e11	0.0468290
$790$	1.06632e13	0.974018
$791$	−4.04935e12	−0.367782
$792$	−3.21810e13	−2.90627
$793$	−1.00272e13	−0.900428
$794$	−1.76430e13	−1.57536
$795$	−8.73974e11	−0.0775973
$796$	−2.56670e13	−2.26603
$797$	−1.96859e13	−1.72820	−0.864098	−	0.503324i	$-0.832110\pi$
$797$	−1.96859e13	−1.72820	−0.864098	+	0.503324i	$0.832110\pi$
$798$	4.24857e11	0.0370877
$799$	0	0
$800$	−6.34184e11	−0.0547407
$801$	6.75834e11	0.0580087
$802$	−1.39705e12	−0.119242
$803$	−2.04252e13	−1.73359
$804$	1.88055e12	0.158720
$805$	−6.94489e12	−0.582886
$806$	1.11437e13	0.930086
$807$	−2.32536e11	−0.0193001
$808$	−9.87980e12	−0.815449
$809$	−9.92022e12	−0.814241	−0.407120	−	0.913375i	$-0.633467\pi$
$809$	−9.92022e12	−0.814241	−0.407120	+	0.913375i	$0.633467\pi$
$810$	3.57783e13	2.92036
$811$	1.77102e13	1.43757	0.718784	−	0.695233i	$-0.244699\pi$
$811$	1.77102e13	1.43757	0.718784	+	0.695233i	$0.244699\pi$
$812$	3.21280e12	0.259347
$813$	−1.01443e12	−0.0814360
$814$	2.67269e13	2.13372
$815$	1.98661e13	1.57726
$816$	0	0
$817$	8.54095e12	0.670667
$818$	7.67651e12	0.599479
$819$	−2.66972e12	−0.207342
$820$	−5.03661e13	−3.89024
$821$	−1.68690e13	−1.29582	−0.647912	−	0.761715i	$-0.724358\pi$
$821$	−1.68690e13	−1.29582	−0.647912	+	0.761715i	$0.724358\pi$
$822$	1.65858e12	0.126710
$823$	−4.79642e12	−0.364433	−0.182216	−	0.983258i	$-0.558327\pi$
$823$	−4.79642e12	−0.364433	−0.182216	+	0.983258i	$0.558327\pi$
$824$	1.90009e13	1.43582
$825$	4.04837e12	0.304255
$826$	−1.89500e12	−0.141644
$827$	−1.43263e12	−0.106502	−0.0532510	−	0.998581i	$-0.516958\pi$
$827$	−1.43263e12	−0.106502	−0.0532510	+	0.998581i	$0.516958\pi$
$828$	2.50692e13	1.85355
$829$	1.06309e13	0.781763	0.390881	−	0.920441i	$-0.372170\pi$
$829$	1.06309e13	0.781763	0.390881	+	0.920441i	$0.372170\pi$
$830$	4.90094e13	3.58450
$831$	−8.89577e11	−0.0647111
$832$	7.77999e12	0.562891
$833$	0	0
$834$	2.77659e12	0.198731
$835$	3.29381e13	2.34482
$836$	3.06442e13	2.16980
$837$	2.40642e12	0.169475
$838$	1.93001e12	0.135196
$839$	2.10767e13	1.46850	0.734251	−	0.678878i	$-0.237534\pi$
$839$	2.10767e13	1.46850	0.734251	+	0.678878i	$0.237534\pi$
$840$	1.44542e12	0.100170
$841$	−1.26658e13	−0.873070
$842$	2.19258e11	0.0150332
$843$	2.65255e12	0.180901
$844$	−2.46905e12	−0.167490
$845$	1.70819e13	1.15261
$846$	−2.98768e13	−2.00525
$847$	−9.83406e12	−0.656534
$848$	−7.56903e12	−0.502642
$849$	1.59920e11	0.0105637
$850$	0	0
$851$	−1.04513e13	−0.683105
$852$	4.61731e12	0.300200
$853$	8.83863e12	0.571629	0.285814	−	0.958285i	$-0.407736\pi$
$853$	8.83863e12	0.571629	0.285814	+	0.958285i	$0.407736\pi$
$854$	1.52583e13	0.981624
$855$	−1.72490e13	−1.10387
$856$	−1.04663e13	−0.666286
$857$	2.77034e13	1.75436	0.877181	−	0.480161i	$-0.159422\pi$
$857$	2.77034e13	1.75436	0.877181	+	0.480161i	$0.159422\pi$
$858$	2.43635e12	0.153479
$859$	1.52744e13	0.957183	0.478592	−	0.878038i	$-0.341147\pi$
$859$	1.52744e13	0.957183	0.478592	+	0.878038i	$0.341147\pi$
$860$	5.78862e13	3.60855
$861$	6.00163e11	0.0372182
$862$	−2.76160e13	−1.70364
$863$	5.46258e12	0.335235	0.167618	−	0.985852i	$-0.446393\pi$
$863$	5.46258e12	0.335235	0.167618	+	0.985852i	$0.446393\pi$
$864$	−8.24168e10	−0.00503157
$865$	−3.13835e13	−1.90603
$866$	6.23756e12	0.376863
$867$	0	0
$868$	−1.13198e13	−0.676861
$869$	−9.16486e12	−0.545176
$870$	1.65034e12	0.0976647
$871$	8.46168e12	0.498167
$872$	−4.57929e13	−2.68210
$873$	−1.47786e13	−0.861131
$874$	−1.79510e13	−1.04061
$875$	1.06719e13	0.615471
$876$	−3.31157e12	−0.190005
$877$	7.13412e12	0.407232	0.203616	−	0.979051i	$-0.434731\pi$
$877$	7.13412e12	0.407232	0.203616	+	0.979051i	$0.434731\pi$
$878$	−1.31885e13	−0.748982
$879$	−2.70428e12	−0.152792
$880$	5.27419e13	2.96472
$881$	6.08084e12	0.340073	0.170036	−	0.985438i	$-0.445611\pi$
$881$	6.08084e12	0.340073	0.170036	+	0.985438i	$0.445611\pi$
$882$	−2.68468e13	−1.49377
$883$	3.80818e12	0.210812	0.105406	−	0.994429i	$-0.466386\pi$
$883$	3.80818e12	0.210812	0.105406	+	0.994429i	$0.466386\pi$
$884$	0	0
$885$	−6.49799e11	−0.0356069
$886$	4.81839e13	2.62694
$887$	1.70080e13	0.922568	0.461284	−	0.887253i	$-0.347389\pi$
$887$	1.70080e13	0.922568	0.461284	+	0.887253i	$0.347389\pi$
$888$	2.17519e12	0.117392
$889$	7.46880e12	0.401045
$890$	−3.27988e12	−0.175228
$891$	−3.07508e13	−1.63458
$892$	−1.92412e13	−1.01763
$893$	1.42812e13	0.751506
$894$	−2.49790e12	−0.130784
$895$	3.37713e13	1.75932
$896$	−1.20318e13	−0.623657
$897$	−9.52714e11	−0.0491356
$898$	−4.69391e13	−2.40875
$899$	−6.48785e12	−0.331270
$900$	−7.77139e13	−3.94828
$901$	0	0
$902$	6.48477e13	3.26186
$903$	−6.89773e11	−0.0345232
$904$	−3.56090e13	−1.77338
$905$	1.64971e13	0.817500
$906$	2.79473e12	0.137804
$907$	−3.06959e13	−1.50608	−0.753039	−	0.657975i	$-0.771413\pi$
$907$	−3.06959e13	−1.50608	−0.753039	+	0.657975i	$0.771413\pi$
$908$	−4.20519e13	−2.05305
$909$	−9.52180e12	−0.462574
$910$	1.29564e13	0.626322
$911$	−3.61989e13	−1.74126	−0.870629	−	0.491940i	$-0.836288\pi$
$911$	−3.61989e13	−1.74126	−0.870629	+	0.491940i	$0.836288\pi$
$912$	1.26170e12	0.0603918
$913$	−4.21227e13	−2.00631
$914$	2.03489e12	0.0964458
$915$	5.23210e12	0.246764
$916$	4.05924e13	1.90509
$917$	4.05332e12	0.189299
$918$	0	0
$919$	−1.22396e13	−0.566040	−0.283020	−	0.959114i	$-0.591336\pi$
$919$	−1.22396e13	−0.566040	−0.283020	+	0.959114i	$0.591336\pi$
$920$	−6.10717e13	−2.81057
$921$	4.38204e11	0.0200682
$922$	2.07196e13	0.944262
$923$	2.07760e13	0.942223
$924$	−2.47485e12	−0.111693
$925$	3.23988e13	1.45509
$926$	6.74527e13	3.01474
$927$	1.83124e13	0.814489
$928$	2.22201e11	0.00983514
$929$	−2.58941e13	−1.14059	−0.570295	−	0.821440i	$-0.693171\pi$
$929$	−2.58941e13	−1.14059	−0.570295	+	0.821440i	$0.693171\pi$
$930$	−5.81472e12	−0.254892
$931$	1.28328e13	0.559821
$932$	1.42634e13	0.619229
$933$	1.91436e12	0.0827095
$934$	−4.85799e13	−2.08879
$935$	0	0
$936$	−2.34769e13	−0.999768
$937$	4.81953e12	0.204257	0.102128	−	0.994771i	$-0.467435\pi$
$937$	4.81953e12	0.204257	0.102128	+	0.994771i	$0.467435\pi$
$938$	−1.28761e13	−0.543089
$939$	−2.96602e11	−0.0124503
$940$	9.67905e13	4.04350
$941$	1.82547e13	0.758966	0.379483	−	0.925199i	$-0.376102\pi$
$941$	1.82547e13	0.758966	0.379483	+	0.925199i	$0.376102\pi$
$942$	5.04196e12	0.208627
$943$	−2.53581e13	−1.04427
$944$	−5.62757e12	−0.230646
$945$	2.79785e12	0.114125
$946$	−7.45300e13	−3.02567
$947$	5.09493e12	0.205856	0.102928	−	0.994689i	$-0.467179\pi$
$947$	5.09493e12	0.205856	0.102928	+	0.994689i	$0.467179\pi$
$948$	−1.48592e12	−0.0597526
$949$	−1.49007e13	−0.596360
$950$	5.56478e13	2.21662
$951$	1.52157e12	0.0603226
$952$	0	0
$953$	5.88769e12	0.231221	0.115610	−	0.993295i	$-0.463118\pi$
$953$	5.88769e12	0.231221	0.115610	+	0.993295i	$0.463118\pi$
$954$	−2.16010e13	−0.844318
$955$	1.97167e13	0.767041
$956$	2.82859e13	1.09524
$957$	−1.41844e12	−0.0546647
$958$	3.93743e13	1.51032
$959$	−7.58081e12	−0.289422
$960$	−4.05954e12	−0.154261
$961$	−3.58071e12	−0.135430
$962$	1.94979e13	0.734009
$963$	−1.00870e13	−0.377959
$964$	5.65523e13	2.10913
$965$	1.77745e13	0.659817
$966$	1.44974e12	0.0535664
$967$	−4.68118e13	−1.72161	−0.860807	−	0.508931i	$-0.830041\pi$
$967$	−4.68118e13	−1.72161	−0.860807	+	0.508931i	$0.830041\pi$
$968$	−8.64784e13	−3.16569
$969$	0	0
$970$	7.17219e13	2.60123
$971$	−4.48543e13	−1.61926	−0.809632	−	0.586938i	$-0.800333\pi$
$971$	−4.48543e13	−1.61926	−0.809632	+	0.586938i	$0.800333\pi$
$972$	−1.51705e13	−0.545131
$973$	−1.26909e13	−0.453925
$974$	−7.16006e13	−2.54918
$975$	2.95339e12	0.104665
$976$	4.53125e13	1.59843
$977$	3.39602e13	1.19246	0.596231	−	0.802813i	$-0.296664\pi$
$977$	3.39602e13	1.19246	0.596231	+	0.802813i	$0.296664\pi$
$978$	−4.14703e12	−0.144948
$979$	2.81900e12	0.0980782
$980$	8.69745e13	3.01214
$981$	−4.41336e13	−1.52145
$982$	1.52700e13	0.524007
$983$	1.74563e13	0.596297	0.298148	−	0.954520i	$-0.403631\pi$
$983$	1.74563e13	0.596297	0.298148	+	0.954520i	$0.403631\pi$
$984$	5.27770e12	0.179459
$985$	1.03843e13	0.351490
$986$	0	0
$987$	−1.15336e12	−0.0386845
$988$	2.23557e13	0.746419
$989$	2.91443e13	0.968657
$990$	1.50518e14	4.98001
$991$	−4.90669e13	−1.61606	−0.808029	−	0.589143i	$-0.799466\pi$
$991$	−4.90669e13	−1.61606	−0.808029	+	0.589143i	$0.799466\pi$
$992$	−7.82890e11	−0.0256684
$993$	−2.58075e12	−0.0842314
$994$	−3.16147e13	−1.02719
$995$	6.02622e13	1.94913
$996$	−6.82943e12	−0.219896
$997$	4.75402e12	0.152382	0.0761908	−	0.997093i	$-0.475724\pi$
$997$	4.75402e12	0.152382	0.0761908	+	0.997093i	$0.475724\pi$
$998$	9.91772e13	3.16464
$999$	4.21045e12	0.133747

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.c.1.1		12
17.4	even	4		17.10.b.a.16.12	yes	12
17.13	even	4		17.10.b.a.16.11	✓	12
17.16	even	2	inner	289.10.a.c.1.2		12
51.38	odd	4		153.10.d.b.118.1		12
51.47	odd	4		153.10.d.b.118.2		12
68.47	odd	4		272.10.b.c.33.7		12
68.55	odd	4		272.10.b.c.33.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.b.a.16.11	✓	12	17.13	even	4
17.10.b.a.16.12	yes	12	17.4	even	4
153.10.d.b.118.1		12	51.38	odd	4
153.10.d.b.118.2		12	51.47	odd	4
272.10.b.c.33.6		12	68.55	odd	4
272.10.b.c.33.7		12	68.47	odd	4
289.10.a.c.1.1		12	1.1	even	1	trivial
289.10.a.c.1.2		12	17.16	even	2	inner

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)

\(f(q)\)	\(=\)	\(q-39.2436 q^{2} -12.8394 q^{3} +1028.06 q^{4} -2413.73 q^{5} +503.863 q^{6} -2302.99 q^{7} -20252.0 q^{8} -19518.2 q^{9} +O(q^{10})\)	\(q-39.2436 q^{2} -12.8394 q^{3} +1028.06 q^{4} -2413.73 q^{5} +503.863 q^{6} -2302.99 q^{7} -20252.0 q^{8} -19518.2 q^{9} +94723.3 q^{10} -81412.9 q^{11} -13199.6 q^{12} -59392.9 q^{13} +90377.7 q^{14} +30990.8 q^{15} +268395. q^{16} +765962. q^{18} -366131. q^{19} -2.48145e6 q^{20} +29569.0 q^{21} +3.19494e6 q^{22} -1.24935e6 q^{23} +260023. q^{24} +3.87295e6 q^{25} +2.33079e6 q^{26} +503318. q^{27} -2.36761e6 q^{28} -1.35698e6 q^{29} -1.21619e6 q^{30} +4.78110e6 q^{31} -163747. q^{32} +1.04529e6 q^{33} +5.55880e6 q^{35} -2.00658e7 q^{36} +8.36539e6 q^{37} +1.43683e7 q^{38} +762568. q^{39} +4.88828e7 q^{40} +2.02970e7 q^{41} -1.16039e6 q^{42} -2.33275e7 q^{43} -8.36973e7 q^{44} +4.71115e7 q^{45} +4.90290e7 q^{46} -3.90056e7 q^{47} -3.44602e6 q^{48} -3.50498e7 q^{49} -1.51989e8 q^{50} -6.10594e7 q^{52} -2.82011e7 q^{53} -1.97520e7 q^{54} +1.96509e8 q^{55} +4.66402e7 q^{56} +4.70090e6 q^{57} +5.32527e7 q^{58} -2.09675e7 q^{59} +3.18603e7 q^{60} +1.68828e8 q^{61} -1.87627e8 q^{62} +4.49502e7 q^{63} -1.30992e8 q^{64} +1.43358e8 q^{65} -4.10210e7 q^{66} -1.42470e8 q^{67} +1.60409e7 q^{69} -2.18147e8 q^{70} -3.49806e8 q^{71} +3.95281e8 q^{72} +2.50884e8 q^{73} -3.28288e8 q^{74} -4.97263e7 q^{75} -3.76405e8 q^{76} +1.87494e8 q^{77} -2.99259e7 q^{78} +1.12572e8 q^{79} -6.47831e8 q^{80} +3.77713e8 q^{81} -7.96528e8 q^{82} +5.17396e8 q^{83} +3.03987e7 q^{84} +9.15456e8 q^{86} +1.74228e7 q^{87} +1.64877e9 q^{88} -3.46259e7 q^{89} -1.84882e9 q^{90} +1.36781e8 q^{91} -1.28441e9 q^{92} -6.13864e7 q^{93} +1.53072e9 q^{94} +8.83741e8 q^{95} +2.10241e6 q^{96} +7.57173e8 q^{97} +1.37548e9 q^{98} +1.58903e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 30 q^{2} + 1874 q^{4} - 23550 q^{8} + 9184 q^{9}+O(q^{10}) \) 12 * q - 30 * q^2 + 1874 * q^4 - 23550 * q^8 + 9184 * q^9	\( 12 q - 30 q^{2} + 1874 q^{4} - 23550 q^{8} + 9184 q^{9} - 63204 q^{13} + 243480 q^{15} + 38978 q^{16} + 547706 q^{18} - 1110672 q^{19} - 172580 q^{21} + 4441796 q^{25} - 1336332 q^{26} - 500496 q^{30} + 1934850 q^{32} - 6557404 q^{33} + 3519864 q^{35} - 30244102 q^{36} + 28748136 q^{38} + 11901296 q^{42} - 10004616 q^{43} - 112552440 q^{47} - 121354720 q^{49} - 164889018 q^{50} - 59093180 q^{52} - 76804272 q^{53} + 300732568 q^{55} - 11618904 q^{59} - 101609232 q^{60} - 260062974 q^{64} - 18429632 q^{66} - 304208752 q^{67} - 211308236 q^{69} - 460311456 q^{70} + 493218954 q^{72} - 416024248 q^{76} - 138357828 q^{77} - 363335792 q^{81} + 845042136 q^{83} + 958037984 q^{84} + 127952904 q^{86} - 610860648 q^{87} - 938223804 q^{89} - 1635779524 q^{93} + 238629952 q^{94} - 152046078 q^{98}+O(q^{100}) \) 12 * q - 30 * q^2 + 1874 * q^4 - 23550 * q^8 + 9184 * q^9 - 63204 * q^13 + 243480 * q^15 + 38978 * q^16 + 547706 * q^18 - 1110672 * q^19 - 172580 * q^21 + 4441796 * q^25 - 1336332 * q^26 - 500496 * q^30 + 1934850 * q^32 - 6557404 * q^33 + 3519864 * q^35 - 30244102 * q^36 + 28748136 * q^38 + 11901296 * q^42 - 10004616 * q^43 - 112552440 * q^47 - 121354720 * q^49 - 164889018 * q^50 - 59093180 * q^52 - 76804272 * q^53 + 300732568 * q^55 - 11618904 * q^59 - 101609232 * q^60 - 260062974 * q^64 - 18429632 * q^66 - 304208752 * q^67 - 211308236 * q^69 - 460311456 * q^70 + 493218954 * q^72 - 416024248 * q^76 - 138357828 * q^77 - 363335792 * q^81 + 845042136 * q^83 + 958037984 * q^84 + 127952904 * q^86 - 610860648 * q^87 - 938223804 * q^89 - 1635779524 * q^93 + 238629952 * q^94 - 152046078 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more