LMFDB - Embedded newform 17.10.b.a.16.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,10,Mod(16,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("17.16");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	17.b (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$8.75560921479$
Analytic rank:	$0$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			16.11
Root			$-12.8394i$ of defining polynomial
Character	$\chi$	$=$	17.16
Dual form			17.10.b.a.16.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+39.2436 q^{2} -12.8394i q^{3} +1028.06 q^{4} -2413.73i q^{5} -503.863i q^{6} +2302.99i q^{7} +20252.0 q^{8} +19518.2 q^{9} +O(q^{10})$	\(q+39.2436 q^{2} -12.8394i q^{3} +1028.06 q^{4} -2413.73i q^{5} -503.863i q^{6} +2302.99i q^{7} +20252.0 q^{8} +19518.2 q^{9} -94723.3i q^{10} +81412.9i q^{11} -13199.6i q^{12} -59392.9 q^{13} +90377.7i q^{14} -30990.8 q^{15} +268395. q^{16} +(-289024. - 187225. i) q^{17} +765962. q^{18} +366131. q^{19} -2.48145e6i q^{20} +29569.0 q^{21} +3.19494e6i q^{22} +1.24935e6i q^{23} -260023. i q^{24} -3.87295e6 q^{25} -2.33079e6 q^{26} -503318. i q^{27} +2.36761e6i q^{28} -1.35698e6i q^{29} -1.21619e6 q^{30} +4.78110e6i q^{31} +163747. q^{32} +1.04529e6 q^{33} +(-1.13423e7 - 7.34738e6i) q^{34} +5.55880e6 q^{35} +2.00658e7 q^{36} +8.36539e6i q^{37} +1.43683e7 q^{38} +762568. i q^{39} -4.88828e7i q^{40} -2.02970e7i q^{41} +1.16039e6 q^{42} +2.33275e7 q^{43} +8.36973e7i q^{44} -4.71115e7i q^{45} +4.90290e7i q^{46} -3.90056e7 q^{47} -3.44602e6i q^{48} +3.50498e7 q^{49} -1.51989e8 q^{50} +(-2.40385e6 + 3.71089e6i) q^{51} -6.10594e7 q^{52} +2.82011e7 q^{53} -1.97520e7i q^{54} +1.96509e8 q^{55} +4.66402e7i q^{56} -4.70090e6i q^{57} -5.32527e7i q^{58} +2.09675e7 q^{59} -3.18603e7 q^{60} -1.68828e8i q^{61} +1.87627e8i q^{62} +4.49502e7i q^{63} -1.30992e8 q^{64} +1.43358e8i q^{65} +4.10210e7 q^{66} -1.42470e8 q^{67} +(-2.97133e8 - 1.92478e8i) q^{68} +1.60409e7 q^{69} +2.18147e8 q^{70} -3.49806e8i q^{71} +3.95281e8 q^{72} +2.50884e8i q^{73} +3.28288e8i q^{74} +4.97263e7i q^{75} +3.76405e8 q^{76} -1.87494e8 q^{77} +2.99259e7i q^{78} -1.12572e8i q^{79} -6.47831e8i q^{80} +3.77713e8 q^{81} -7.96528e8i q^{82} -5.17396e8 q^{83} +3.03987e7 q^{84} +(-4.51910e8 + 6.97624e8i) q^{85} +9.15456e8 q^{86} -1.74228e7 q^{87} +1.64877e9i q^{88} -3.46259e7 q^{89} -1.84882e9i q^{90} -1.36781e8i q^{91} +1.28441e9i q^{92} +6.13864e7 q^{93} -1.53072e9 q^{94} -8.83741e8i q^{95} -2.10241e6i q^{96} +7.57173e8i q^{97} +1.37548e9 q^{98} +1.58903e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 105960 q^{17} + 547706 q^{18} + 1110672 q^{19} - 172580 q^{21} - 4441796 q^{25} + 1336332 q^{26} - 500496 q^{30} - 1934850 q^{32} - 6557404 q^{33} - 15085546 q^{34} + 3519864 q^{35} + 30244102 q^{36} + 28748136 q^{38} - 11901296 q^{42} + 10004616 q^{43} - 112552440 q^{47} + 121354720 q^{49} - 164889018 q^{50} - 52506472 q^{51} - 59093180 q^{52} + 76804272 q^{53} + 300732568 q^{55} + 11618904 q^{59} + 101609232 q^{60} - 260062974 q^{64} + 18429632 q^{66} - 304208752 q^{67} - 444301206 q^{68} - 211308236 q^{69} + 460311456 q^{70} + 493218954 q^{72} + 416024248 q^{76} + 138357828 q^{77} - 363335792 q^{81} - 845042136 q^{83} + 958037984 q^{84} - 388949632 q^{85} + 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 - 105960 * q^17 + 547706 * q^18 + 1110672 * q^19 - 172580 * q^21 - 4441796 * q^25 + 1336332 * q^26 - 500496 * q^30 - 1934850 * q^32 - 6557404 * q^33 - 15085546 * q^34 + 3519864 * q^35 + 30244102 * q^36 + 28748136 * q^38 - 11901296 * q^42 + 10004616 * q^43 - 112552440 * q^47 + 121354720 * q^49 - 164889018 * q^50 - 52506472 * q^51 - 59093180 * q^52 + 76804272 * q^53 + 300732568 * q^55 + 11618904 * q^59 + 101609232 * q^60 - 260062974 * q^64 + 18429632 * q^66 - 304208752 * q^67 - 444301206 * q^68 - 211308236 * q^69 + 460311456 * q^70 + 493218954 * q^72 + 416024248 * q^76 + 138357828 * q^77 - 363335792 * q^81 - 845042136 * q^83 + 958037984 * q^84 - 388949632 * q^85 + 127952904 * q^86 + 610860648 * q^87 - 938223804 * q^89 + 1635779524 * q^93 - 238629952 * q^94 - 152046078 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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	$-0.165937\pi$
$2$	39.2436			1.73434			0.867169	+	0.498014i	$0.165937\pi$
$3$		−	12.8394i		−	0.0915163i	−0.998953	−	0.0457581i	$-0.985430\pi$
$3$		−	12.8394i		−	0.0915163i	0.998953	−	0.0457581i	$-0.0145704\pi$
$4$	1028.06			2.00793
$5$		−	2413.73i		−	1.72712i	−0.504244	−	0.863561i	$-0.668229\pi$
$5$		−	2413.73i		−	1.72712i	0.504244	−	0.863561i	$-0.331771\pi$
$6$		−	503.863i		−	0.158720i
$7$			2302.99i			0.362536i	0.983434	+	0.181268i	$0.0580202\pi$
$7$			2302.99i			0.362536i	−0.983434	+	0.181268i	$0.941980\pi$
$8$	20252.0			1.74809
$9$	19518.2			0.991625
$10$		−	94723.3i		−	2.99541i
$11$			81412.9i			1.67659i	0.545219	+	0.838294i	$0.316447\pi$
$11$			81412.9i			1.67659i	−0.545219	+	0.838294i	$0.683553\pi$
$12$		−	13199.6i		−	0.183758i
$13$	−59392.9			−0.576752			−0.288376	−	0.957517i	$-0.593115\pi$
$13$	−59392.9			−0.576752			−0.288376	+	0.957517i	$0.593115\pi$
$14$			90377.7i			0.628761i
$15$	−30990.8			−0.158060
$16$	268395.			1.02384
$17$	−289024.	−	187225.i	−0.839292	−	0.543680i
$17$	−289024.	−	187225.i	−0.839292	−	0.543680i
$18$	765962.			1.71981
$19$	366131.			0.644534			0.322267	−	0.946649i	$-0.395555\pi$
$19$	366131.			0.644534			0.322267	+	0.946649i	$0.395555\pi$
$20$		−	2.48145e6i		−	3.46794i
$21$	29569.0			0.0331780
$22$			3.19494e6i			2.90777i
$23$			1.24935e6i			0.930913i	0.885071	+	0.465456i	$0.154110\pi$
$23$			1.24935e6i			0.930913i	−0.885071	+	0.465456i	$0.845890\pi$
$24$		−	260023.i		−	0.159978i
$25$	−3.87295e6			−1.98295
$26$	−2.33079e6			−1.00028
$27$		−	503318.i		−	0.182266i
$28$			2.36761e6i			0.727947i
$29$		−	1.35698e6i		−	0.356273i	−0.984006	−	0.178136i	$-0.942993\pi$
$29$		−	1.35698e6i		−	0.356273i	0.984006	−	0.178136i	$-0.0570068\pi$
$30$	−1.21619e6			−0.274129
$31$			4.78110e6i			0.929823i	0.885357	+	0.464911i	$0.153914\pi$
$31$			4.78110e6i			0.929823i	−0.885357	+	0.464911i	$0.846086\pi$
$32$	163747.			0.0276057
$33$	1.04529e6			0.153435
$34$	−1.13423e7	−	7.34738e6i	−1.45562	−	0.942925i
$35$	5.55880e6			0.626145
$36$	2.00658e7			1.99111
$37$			8.36539e6i			0.733801i	0.930260	+	0.366900i	$0.119581\pi$
$37$			8.36539e6i			0.733801i	−0.930260	+	0.366900i	$0.880419\pi$
$38$	1.43683e7			1.11784
$39$			762568.i			0.0527822i
$40$		−	4.88828e7i		−	3.01916i
$41$		−	2.02970e7i		−	1.12177i	−0.827893	−	0.560887i	$-0.810460\pi$
$41$		−	2.02970e7i		−	1.12177i	0.827893	−	0.560887i	$-0.189540\pi$
$42$	1.16039e6			0.0575418
$43$	2.33275e7			1.04055			0.520273	−	0.854000i	$-0.325830\pi$
$43$	2.33275e7			1.04055			0.520273	+	0.854000i	$0.325830\pi$
$44$			8.36973e7i			3.36647i
$45$		−	4.71115e7i		−	1.71266i
$46$			4.90290e7i			1.61452i
$47$	−3.90056e7			−1.16597			−0.582984	−	0.812484i	$-0.698115\pi$
$47$	−3.90056e7			−1.16597			−0.582984	+	0.812484i	$0.698115\pi$
$48$		−	3.44602e6i		−	0.0936984i
$49$	3.50498e7			0.868567
$50$	−1.51989e8			−3.43911
$51$	−2.40385e6	+	3.71089e6i	−0.0497556	+	0.0768089i
$52$	−6.10594e7			−1.15808
$53$	2.82011e7			0.490936			0.245468	−	0.969405i	$-0.421058\pi$
$53$	2.82011e7			0.490936			0.245468	+	0.969405i	$0.421058\pi$
$54$		−	1.97520e7i		−	0.316111i
$55$	1.96509e8			2.89567
$56$			4.66402e7i			0.633745i
$57$		−	4.70090e6i		−	0.0589854i
$58$		−	5.32527e7i		−	0.617897i
$59$	2.09675e7			0.225275			0.112637	−	0.993636i	$-0.464070\pi$
$59$	2.09675e7			0.225275			0.112637	+	0.993636i	$0.464070\pi$
$60$	−3.18603e7			−0.317373
$61$		−	1.68828e8i		−	1.56120i	−0.625028	−	0.780602i	$-0.714912\pi$
$61$		−	1.68828e8i		−	1.56120i	0.625028	−	0.780602i	$-0.285088\pi$
$62$			1.87627e8i			1.61263i
$63$			4.49502e7i			0.359500i
$64$	−1.30992e8			−0.975967
$65$			1.43358e8i			0.996122i
$66$	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	$0.642147\pi$
$68$	−2.97133e8	−	1.92478e8i	−1.68524	−	1.09167i
$69$	1.60409e7			0.0851937
$70$	2.18147e8			1.08595
$71$		−	3.49806e8i		−	1.63367i	−0.576871	−	0.816835i	$-0.695726\pi$
$71$		−	3.49806e8i		−	1.63367i	0.576871	−	0.816835i	$-0.304274\pi$
$72$	3.95281e8			1.73345
$73$			2.50884e8i			1.03400i	0.855986	+	0.516999i	$0.172951\pi$
$73$			2.50884e8i			1.03400i	−0.855986	+	0.516999i	$0.827049\pi$
$74$			3.28288e8i			1.27266i
$75$			4.97263e7i			0.181472i
$76$	3.76405e8			1.29418
$77$	−1.87494e8			−0.607824
$78$			2.99259e7i			0.0915422i
$79$		−	1.12572e8i		−	0.325170i	−0.986695	−	0.162585i	$-0.948017\pi$
$79$		−	1.12572e8i		−	0.325170i	0.986695	−	0.162585i	$-0.0519832\pi$
$80$		−	6.47831e8i		−	1.76830i
$81$	3.77713e8			0.974944
$82$		−	7.96528e8i		−	1.94553i
$83$	−5.17396e8			−1.19666			−0.598331	−	0.801249i	$-0.704169\pi$
$83$	−5.17396e8			−1.19666			−0.598331	+	0.801249i	$0.704169\pi$
$84$	3.03987e7			0.0666190
$85$	−4.51910e8	+	6.97624e8i	−0.939003	+	1.44956i
$86$	9.15456e8			1.80466
$87$	−1.74228e7			−0.0326047
$88$			1.64877e9i			2.93082i
$89$	−3.46259e7			−0.0584987			−0.0292493	−	0.999572i	$-0.509312\pi$
$89$	−3.46259e7			−0.0584987			−0.0292493	+	0.999572i	$0.509312\pi$
$90$		−	1.84882e9i		−	2.97033i
$91$		−	1.36781e8i		−	0.209094i
$92$			1.28441e9i			1.86920i
$93$	6.13864e7			0.0850939
$94$	−1.53072e9			−2.02218
$95$		−	8.83741e8i		−	1.11319i
$96$		−	2.10241e6i		−	0.00252637i
$97$			7.57173e8i			0.868404i	0.900815	+	0.434202i	$0.142970\pi$
$97$			7.57173e8i			0.868404i	−0.900815	+	0.434202i	$0.857030\pi$
$98$	1.37548e9			1.50639
$99$			1.58903e9i			1.66255i
$100$	−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	$0.425067\pi$
$102$	−9.43358e7	+	1.45628e8i	−0.0862930	+	0.133213i
$103$	−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
$105$		−	7.13715e7i		−	0.0573025i
$106$	1.10671e9			0.851449
$107$			5.16803e8i			0.381152i	0.981672	+	0.190576i	$0.0610355\pi$
$107$			5.16803e8i			0.381152i	−0.981672	+	0.190576i	$0.938965\pi$
$108$		−	5.17441e8i		−	0.365977i
$109$		−	2.26116e9i		−	1.53430i	−0.641465	−	0.767152i	$-0.721673\pi$
$109$		−	2.26116e9i		−	1.53430i	0.641465	−	0.767152i	$-0.278327\pi$
$110$	7.71170e9			5.02207
$111$	1.07406e8			0.0671547
$112$			6.18111e8i			0.371181i
$113$		−	1.75830e9i		−	1.01447i	−0.861808	−	0.507235i	$-0.830668\pi$
$113$		−	1.75830e9i		−	1.01447i	0.861808	−	0.507235i	$-0.169332\pi$
$114$		−	1.84480e8i		−	0.102301i
$115$	3.01559e9			1.60780
$116$		−	1.39505e9i		−	0.715369i
$117$	−1.15924e9			−0.571922
$118$	8.22840e8			0.390703
$119$	4.31178e8	−	6.65620e8i	0.197104	−	0.304274i
$120$	−6.27625e8			−0.276302
$121$	−4.27012e9			−1.81095
$122$		−	6.62541e9i		−	2.70766i
$123$	−2.60601e8			−0.102661
$124$			4.91525e9i			1.86702i
$125$			4.63394e9i			1.69768i
$126$			1.76401e9i			0.623495i
$127$	3.24308e9			1.10622			0.553109	−	0.833109i	$-0.313441\pi$
$127$	3.24308e9			1.10622			0.553109	+	0.833109i	$0.313441\pi$
$128$	−5.22444e9			−1.72026
$129$		−	2.99511e8i		−	0.0952269i
$130$			5.62589e9i			1.72761i
$131$		−	1.76002e9i		−	0.522152i	−0.965318	−	0.261076i	$-0.915923\pi$
$131$		−	1.76002e9i		−	0.522152i	0.965318	−	0.261076i	$-0.0840773\pi$
$132$	1.07462e9			0.308087
$133$			8.43199e8i			0.233667i
$134$	−5.59102e9			−1.49803
$135$	−1.21487e9			−0.314796
$136$	−5.85331e9	−	3.79168e9i	−1.46716	−	0.950400i
$137$	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
$139$			5.51061e9i			1.25208i	0.779790	+	0.626041i	$0.215326\pi$
$139$			5.51061e9i			1.25208i	−0.779790	+	0.626041i	$0.784674\pi$
$140$	5.71477e9			1.25725
$141$			5.00808e8i			0.106705i
$142$		−	1.37276e10i		−	2.83334i
$143$		−	4.83535e9i		−	0.966976i
$144$	5.23857e9			1.01527
$145$	−3.27538e9			−0.615326
$146$			9.84557e9i			1.79330i
$147$		−	4.50018e8i		−	0.0794881i
$148$			8.60011e9i			1.47342i
$149$	−4.95750e9			−0.823994			−0.411997	−	0.911185i	$-0.635169\pi$
$149$	−4.95750e9			−0.823994			−0.411997	+	0.911185i	$0.635169\pi$
$150$			1.95144e9i			0.314735i
$151$	−5.54660e9			−0.868221			−0.434110	−	0.900860i	$-0.642937\pi$
$151$	−5.54660e9			−0.868221			−0.434110	+	0.900860i	$0.642937\pi$
$152$	7.41489e9			1.12670
$153$	−5.64121e9	−	3.65429e9i	−0.832263	−	0.539127i
$154$	−7.35792e9			−1.05417
$155$	1.15403e10			1.60592
$156$			7.83964e8i			0.105983i
$157$	1.00066e10			1.31443			0.657216	−	0.753702i	$-0.271734\pi$
$157$	1.00066e10			1.31443			0.657216	+	0.753702i	$0.271734\pi$
$158$		−	4.41775e9i		−	0.563954i
$159$		−	3.62085e8i		−	0.0449287i
$160$		−	3.95240e8i		−	0.0476783i
$161$	−2.87725e9			−0.337490
$162$	1.48228e10			1.69088
$163$			8.23046e9i			0.913229i	0.889665	+	0.456615i	$0.150938\pi$
$163$			8.23046e9i			0.913229i	−0.889665	+	0.456615i	$0.849062\pi$
$164$		−	2.08665e10i		−	2.25244i
$165$		−	2.52305e9i		−	0.265001i
$166$	−2.03045e10			−2.07541
$167$		−	1.36462e10i		−	1.35765i	−0.734302	−	0.678823i	$-0.762490\pi$
$167$		−	1.36462e10i		−	1.35765i	0.734302	−	0.678823i	$-0.237510\pi$
$168$	5.98832e8			0.0579980
$169$	−7.07699e9			−0.667357
$170$	−1.77346e10	+	2.73773e10i	−1.62855	+	2.51403i
$171$	7.14621e9			0.639136
$172$	2.39821e10			2.08934
$173$			1.30021e10i			1.10359i	0.833981	+	0.551793i	$0.186056\pi$
$173$			1.30021e10i			1.10359i	−0.833981	+	0.551793i	$0.813944\pi$
$174$	−6.83732e8			−0.0565476
$175$		−	8.91939e9i		−	0.718893i
$176$			2.18508e10i			1.71656i
$177$		−	2.69210e8i		−	0.0206163i
$178$	−1.35884e9			−0.101456
$179$	1.39913e10			1.01864			0.509320	−	0.860577i	$-0.329897\pi$
$179$	1.39913e10			1.01864			0.509320	+	0.860577i	$0.329897\pi$
$180$		−	4.84334e10i		−	3.43889i
$181$			6.83468e9i			0.473331i	0.971591	+	0.236665i	$0.0760545\pi$
$181$			6.83468e9i			0.473331i	−0.971591	+	0.236665i	$0.923946\pi$
$182$		−	5.36779e9i		−	0.362639i
$183$	−2.16765e9			−0.142876
$184$			2.53018e10i			1.62732i
$185$	2.01918e10			1.26736
$186$	2.40902e9			0.147582
$187$	1.52425e10	−	2.35303e10i	0.911528	−	1.40715i
$188$	−4.01000e10			−2.34118
$189$	1.15914e9			0.0660781
$190$		−	3.46812e10i		−	1.93065i
$191$	−8.16856e9			−0.444115			−0.222058	−	0.975034i	$-0.571277\pi$
$191$	−8.16856e9			−0.444115			−0.222058	+	0.975034i	$0.571277\pi$
$192$			1.68186e9i			0.0893169i
$193$			7.36391e9i			0.382033i	0.981587	+	0.191016i	$0.0611784\pi$
$193$			7.36391e9i			0.382033i	−0.981587	+	0.191016i	$0.938822\pi$
$194$			2.97142e10i			1.50611i
$195$	1.84063e9			0.0911614
$196$	3.60333e10			1.74402
$197$			4.30217e9i			0.203512i	0.994809	+	0.101756i	$0.0324461\pi$
$197$			4.30217e9i			0.203512i	−0.994809	+	0.101756i	$0.967554\pi$
$198$			6.23592e10i			2.88342i
$199$		−	2.49664e10i		−	1.12854i	−0.825590	−	0.564271i	$-0.809157\pi$
$199$		−	2.49664e10i		−	1.12854i	0.825590	−	0.564271i	$-0.190843\pi$
$200$	−7.84350e10			−3.46637
$201$			1.82922e9i			0.0790468i
$202$	1.91447e10			0.809036
$203$	3.12512e9			0.129162
$204$	−2.47130e9	+	3.81501e9i	−0.0999056	+	0.154227i
$205$	−4.89915e10			−1.93744
$206$	−3.68192e10			−1.42453
$207$			2.43850e10i			0.923116i
$208$	−1.59407e10			−0.590504
$209$			2.98078e10i			1.08062i
$210$		−	2.80088e9i		−	0.0993818i
$211$			2.40166e9i			0.0834143i	0.999130	+	0.0417072i	$0.0132797\pi$
$211$			2.40166e9i			0.0834143i	−0.999130	+	0.0417072i	$0.986720\pi$
$212$	2.89924e10			0.985764
$213$	−4.49129e9			−0.149508
$214$			2.02812e10i			0.661045i
$215$		−	5.63063e10i		−	1.79715i
$216$		−	1.01932e10i		−	0.318617i
$217$	−1.10108e10			−0.337095
$218$		−	8.87359e10i		−	2.66100i
$219$	3.22119e9			0.0946276
$220$	2.02022e11			5.81430
$221$	1.71659e10	+	1.11198e10i	0.484064	+	0.313569i
$222$	4.21501e9			0.116469
$223$	1.87161e10			0.506808			0.253404	−	0.967361i	$-0.418450\pi$
$223$	1.87161e10			0.506808			0.253404	+	0.967361i	$0.418450\pi$
$224$			3.77108e8i			0.0100081i
$225$	−7.55929e10			−1.96634
$226$		−	6.90019e10i		−	1.75943i
$227$			4.09042e10i			1.02247i	0.859440	+	0.511237i	$0.170812\pi$
$227$			4.09042e10i			1.02247i	−0.859440	+	0.511237i	$0.829188\pi$
$228$		−	4.83280e9i		−	0.118438i
$229$	−3.94845e10			−0.948784			−0.474392	−	0.880314i	$-0.657332\pi$
$229$	−3.94845e10			−0.948784			−0.474392	+	0.880314i	$0.657332\pi$
$230$	1.18343e11			2.78847
$231$			2.40730e9i			0.0556258i
$232$		−	2.74815e10i		−	0.622795i
$233$			1.38741e10i			0.308392i	0.988040	+	0.154196i	$0.0492787\pi$
$233$			1.38741e10i			0.308392i	−0.988040	+	0.154196i	$0.950721\pi$
$234$	−4.54927e10			−0.991905
$235$			9.41488e10i			2.01377i
$236$	2.15558e10			0.452336
$237$	−1.44536e9			−0.0297583
$238$	1.69210e10	−	2.61213e10i	0.341845	−	0.527714i
$239$	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
$241$			5.50089e10i			1.05040i	0.850978	+	0.525201i	$0.176010\pi$
$241$			5.50089e10i			1.05040i	−0.850978	+	0.525201i	$0.823990\pi$
$242$	−1.67575e11			−3.14079
$243$		−	1.47564e10i		−	0.271489i
$244$		−	1.73565e11i		−	3.13479i
$245$		−	8.46007e10i		−	1.50012i
$246$	−1.02269e10			−0.178048
$247$	−2.17456e10			−0.371736
$248$			9.68268e10i			1.62541i
$249$			6.64304e9i			0.109514i
$250$			1.81853e11i			2.94435i
$251$	4.50601e10			0.716573			0.358287	−	0.933612i	$-0.383361\pi$
$251$	4.50601e10			0.716573			0.358287	+	0.933612i	$0.383361\pi$
$252$			4.62114e10i			0.721850i
$253$	−1.01713e11			−1.56076
$254$	1.27270e11			1.91856
$255$	8.95706e9	+	5.80224e9i	0.132658	+	0.0859340i
$256$	−1.37958e11			−2.00755
$257$	−1.80006e10			−0.257388			−0.128694	−	0.991684i	$-0.541078\pi$
$257$	−1.80006e10			−0.257388			−0.128694	+	0.991684i	$0.541078\pi$
$258$		−	1.17539e10i		−	0.165156i
$259$	−1.92654e10			−0.266030
$260$			1.47381e11i			2.00014i
$261$		−	2.64857e10i		−	0.353289i
$262$		−	6.90695e10i		−	0.905588i
$263$	3.97025e10			0.511701			0.255851	−	0.966716i	$-0.417644\pi$
$263$	3.97025e10			0.511701			0.255851	+	0.966716i	$0.417644\pi$
$264$	2.11692e10			0.268218
$265$		−	6.80698e10i		−	0.847907i
$266$			3.30901e10i			0.405258i
$267$			4.44575e8i			0.00535358i
$268$	−1.46467e11			−1.73434
$269$			1.81112e10i			0.210892i	0.994425	+	0.105446i	$0.0336271\pi$
$269$			1.81112e10i			0.210892i	−0.994425	+	0.105446i	$0.966373\pi$
$270$	−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	$0.353230\pi$
$272$	−7.75724e10	−	5.02502e10i	−0.859305	−	0.556644i
$273$	−1.75619e9			−0.0191355
$274$	1.29179e11			1.38457
$275$		−	3.15309e11i		−	3.32459i
$276$	1.64910e10			0.171063
$277$			6.92850e10i			0.707099i	0.935416	+	0.353550i	$0.115025\pi$
$277$			6.92850e10i			0.707099i	−0.935416	+	0.353550i	$0.884975\pi$
$278$			2.16256e11i			2.17153i
$279$			9.33182e10i			0.922035i
$280$	1.12577e11			1.09456
$281$	2.06595e11			1.97670			0.988352	−	0.152185i	$-0.0486309\pi$
$281$	2.06595e11			1.97670			0.988352	+	0.152185i	$0.0486309\pi$
$282$			1.96535e10i			0.185063i
$283$			1.24554e10i			0.115430i	0.998333	+	0.0577150i	$0.0183815\pi$
$283$			1.24554e10i			0.115430i	−0.998333	+	0.0577150i	$0.981619\pi$
$284$		−	3.59621e11i		−	3.28029i
$285$	−1.13467e10			−0.101875
$286$		−	1.89756e11i		−	1.67706i
$287$	4.67439e10			0.406684
$288$	3.19604e9			0.0273744
$289$	4.84815e10	+	1.08225e11i	0.408823	+	0.912614i
$290$	−1.28538e11			−1.06718
$291$	9.72163e9			0.0794732
$292$			2.57923e11i			2.07619i
$293$	2.10624e11			1.66956			0.834781	−	0.550582i	$-0.185594\pi$
$293$	2.10624e11			1.66956			0.834781	+	0.550582i	$0.185594\pi$
$294$		−	1.76603e10i		−	0.137859i
$295$		−	5.06098e10i		−	0.389077i
$296$			1.69416e11i			1.28275i
$297$	4.09766e10			0.305585
$298$	−1.94550e11			−1.42908
$299$		−	7.42025e10i		−	0.536906i
$300$			5.11216e10i			0.364384i
$301$			5.37232e10i			0.377236i
$302$	−2.17668e11			−1.50579
$303$		−	6.26360e9i		−	0.0426906i
$304$	9.82677e10			0.659902
$305$	−4.07504e11			−2.69639
$306$	−2.21381e11	−	1.43407e11i	−1.44343	−	0.935028i
$307$	−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
$309$			1.20462e10i			0.0751686i
$310$	4.52882e11			2.78520
$311$		−	1.49100e11i		−	0.903768i	−0.892077	−	0.451884i	$-0.850752\pi$
$311$		−	1.49100e11i		−	0.903768i	0.892077	−	0.451884i	$-0.149248\pi$
$312$			1.54435e10i			0.0922679i
$313$		−	2.31010e10i		−	0.136044i	−0.997684	−	0.0680222i	$-0.978331\pi$
$313$		−	2.31010e10i		−	0.136044i	0.997684	−	0.0680222i	$-0.0216689\pi$
$314$	3.92695e11			2.27967
$315$	1.08497e11			0.620901
$316$		−	1.15731e11i		−	0.652917i
$317$			1.18508e11i			0.659146i	0.944130	+	0.329573i	$0.106905\pi$
$317$			1.18508e11i			0.659146i	−0.944130	+	0.329573i	$0.893095\pi$
$318$		−	1.42095e10i		−	0.0779215i
$319$	1.10476e11			0.597322
$320$			3.16179e11i			1.68561i
$321$	6.63542e9			0.0348816
$322$	−1.12913e11			−0.585321
$323$	−1.05821e11	−	6.85489e10i	−0.540952	−	0.350420i
$324$	3.88312e11			1.95762
$325$	2.30026e11			1.14367
$326$			3.22993e11i			1.58385i
$327$	−2.90319e10			−0.140414
$328$		−	4.11055e11i		−	1.96096i
$329$		−	8.98296e10i		−	0.422706i
$330$		−	9.90135e10i		−	0.459602i
$331$	−2.01002e11			−0.920397			−0.460199	−	0.887816i	$-0.652222\pi$
$331$	−2.01002e11			−0.920397			−0.460199	+	0.887816i	$0.652222\pi$
$332$	−5.31913e11			−2.40281
$333$			1.63277e11i			0.727655i
$334$		−	5.35525e11i		−	2.35462i
$335$			3.43883e11i			1.49179i
$336$	7.93617e9			0.0339691
$337$		−	3.79448e11i		−	1.60257i	−0.598282	−	0.801286i	$-0.704150\pi$
$337$		−	3.79448e11i		−	1.60257i	0.598282	−	0.801286i	$-0.295850\pi$
$338$	−2.77726e11			−1.15742
$339$	−2.25755e10			−0.0928406
$340$	−4.64590e11	+	7.17199e11i	−1.88545	+	2.91061i
$341$	−3.89243e11			−1.55893
$342$	2.80443e11			1.10848
$343$			1.73654e11i			0.677424i
$344$	4.72429e11			1.81896
$345$		−	3.87183e10i		−	0.147140i
$346$			5.10249e11i			1.91399i
$347$			2.02768e11i			0.750789i	0.926865	+	0.375394i	$0.122493\pi$
$347$			2.02768e11i			0.750789i	−0.926865	+	0.375394i	$0.877507\pi$
$348$	−1.79116e10			−0.0654679
$349$	−2.76919e10			−0.0999166			−0.0499583	−	0.998751i	$-0.515909\pi$
$349$	−2.76919e10			−0.0999166			−0.0499583	+	0.998751i	$0.515909\pi$
$350$		−	3.50029e11i		−	1.24680i
$351$			2.98935e10i			0.105122i
$352$			1.33311e10i			0.0462833i
$353$	2.50963e11			0.860249			0.430124	−	0.902770i	$-0.358470\pi$
$353$	2.50963e11			0.860249			0.430124	+	0.902770i	$0.358470\pi$
$354$		−	1.05648e10i		−	0.0357557i
$355$	−8.44336e11			−2.82155
$356$	−3.55975e10			−0.117461
$357$	−8.54615e9	−	5.53606e9i	−0.0278460	−	0.0180382i
$358$	5.49071e11			1.76667
$359$	2.70942e11			0.860898			0.430449	−	0.902615i	$-0.358355\pi$
$359$	2.70942e11			0.860898			0.430449	+	0.902615i	$0.358355\pi$
$360$		−	9.54102e11i		−	2.99387i
$361$	−1.88635e11			−0.584576
$362$			2.68217e11i			0.820915i
$363$			5.48257e10i			0.165731i
$364$		−	1.40619e11i		−	0.419845i
$365$	6.05564e11			1.78584
$366$	−8.50662e10			−0.247795
$367$			3.18541e11i			0.916576i	0.888804	+	0.458288i	$0.151537\pi$
$367$			3.18541e11i			0.916576i	−0.888804	+	0.458288i	$0.848463\pi$
$368$			3.35319e11i			0.953110i
$369$		−	3.96161e11i		−	1.11238i
$370$	7.92397e11			2.19804
$371$			6.49470e10i			0.177982i
$372$	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	$0.571325\pi$
$374$	5.98172e11	−	9.23412e11i	1.58090	−	2.44047i
$375$	5.94970e10			0.155365
$376$	−7.89941e11			−2.03821
$377$			8.05949e10i			0.205481i
$378$	4.54888e10			0.114602
$379$			5.85960e10i			0.145879i	0.997336	+	0.0729393i	$0.0232379\pi$
$379$			5.85960e10i			0.145879i	−0.997336	+	0.0729393i	$0.976762\pi$
$380$		−	9.08538e11i		−	2.23520i
$381$		−	4.16392e10i		−	0.101237i
$382$	−3.20564e11			−0.770246
$383$	−2.93491e9			−0.00696948			−0.00348474	−	0.999994i	$-0.501109\pi$
$383$	−2.93491e9			−0.00696948			−0.00348474	+	0.999994i	$0.501109\pi$
$384$			6.70785e10i			0.157432i
$385$			4.52558e11i			1.04979i
$386$			2.88986e11i			0.662574i
$387$	4.55311e11			1.03183
$388$			7.78418e11i			1.74369i
$389$	6.42977e10			0.142371			0.0711856	−	0.997463i	$-0.477322\pi$
$389$	6.42977e10			0.142371			0.0711856	+	0.997463i	$0.477322\pi$
$390$	7.22329e10			0.158105
$391$	2.33910e11	−	3.61092e11i	0.506119	−	0.781308i
$392$	7.09829e11			1.51833
$393$	−2.25976e10			−0.0477854
$394$			1.68833e11i			0.352958i
$395$	−2.71719e11			−0.561608
$396$			1.63362e12i			3.33827i
$397$		−	4.49576e11i		−	0.908335i	−0.890916	−	0.454168i	$-0.849937\pi$
$397$		−	4.49576e11i		−	0.908335i	0.890916	−	0.454168i	$-0.150063\pi$
$398$		−	9.79772e11i		−	1.95727i
$399$	1.08261e10			0.0213843
$400$	−1.03948e12			−2.03023
$401$		−	3.55995e10i		−	0.0687534i	−0.999409	−	0.0343767i	$-0.989055\pi$
$401$		−	3.55995e10i		−	0.0687534i	0.999409	−	0.0343767i	$-0.0109446\pi$
$402$			7.17852e10i			0.137094i
$403$		−	2.83963e11i		−	0.536277i
$404$	5.01531e11			0.936660
$405$		−	9.11697e11i		−	1.68385i
$406$	1.22641e11			0.224010
$407$	−6.81051e11			−1.23028
$408$	−4.86828e10	+	7.51528e10i	−0.0869771	+	0.134269i
$409$	−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
$411$		−	4.22637e10i		−	0.0730599i
$412$	−9.64547e11			−1.64925
$413$			4.82880e10i			0.0816703i
$414$			9.56955e11i			1.60099i
$415$			1.24885e12i			2.06678i
$416$	−9.72539e9			−0.0159216
$417$	7.07528e10			0.114586
$418$			1.16977e12i			1.87416i
$419$			4.91804e10i			0.0779523i	0.999240	+	0.0389761i	$0.0124096\pi$
$419$			4.91804e10i			0.0779523i	−0.999240	+	0.0389761i	$0.987590\pi$
$420$		−	7.33741e10i		−	0.115059i
$421$	−5.58710e9			−0.00866796			−0.00433398	−	0.999991i	$-0.501380\pi$
$421$	−5.58710e9			−0.00866796			−0.00433398	+	0.999991i	$0.501380\pi$
$422$			9.42498e10i			0.144669i
$423$	−7.61317e11			−1.15620
$424$	5.71129e11			0.858198
$425$	1.11938e12	+	7.25114e11i	1.66428	+	1.07809i
$426$	−1.76254e11			−0.259297
$427$	3.88810e11			0.565994
$428$			5.31303e11i			0.765324i
$429$	−6.20829e10			−0.0884940
$430$		−	2.20966e12i		−	3.11686i
$431$		−	7.03708e11i		−	0.982302i	−0.871075	−	0.491151i	$-0.836576\pi$
$431$		−	7.03708e11i		−	0.982302i	0.871075	−	0.491151i	$-0.163424\pi$
$432$		−	1.35088e11i		−	0.186612i
$433$	1.58945e11			0.217295			0.108648	−	0.994080i	$-0.465348\pi$
$433$	1.58945e11			0.217295			0.108648	+	0.994080i	$0.465348\pi$
$434$	−4.32105e11			−0.584636
$435$			4.20538e10i			0.0563124i
$436$		−	2.32460e12i		−	3.08077i
$437$			4.57426e11i			0.600005i
$438$	1.26411e11			0.164116
$439$			3.36069e11i			0.431855i	0.976409	+	0.215927i	$0.0692775\pi$
$439$			3.36069e11i			0.431855i	−0.976409	+	0.215927i	$0.930723\pi$
$440$	3.97969e12			5.06189
$441$	6.84108e11			0.861293
$442$	6.73653e11	+	4.36382e11i	0.839530	+	0.543834i
$443$	−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
$445$			8.35775e10i			0.101034i
$446$	7.34486e11			0.878975
$447$			6.36512e10i			0.0754089i
$448$		−	3.01674e11i		−	0.353823i
$449$		−	1.19610e12i		−	1.38886i	−0.719562	−	0.694428i	$-0.755657\pi$
$449$		−	1.19610e12i		−	1.38886i	0.719562	−	0.694428i	$-0.244343\pi$
$450$	−2.96654e12			−3.41031
$451$	1.65244e12			1.88075
$452$		−	1.80763e12i		−	2.03698i
$453$			7.12148e10i			0.0794564i
$454$			1.60523e12i			1.77331i
$455$	−3.30153e11			−0.361130
$456$		−	9.52026e10i		−	0.103111i
$457$	5.18528e10			0.0556096			0.0278048	−	0.999613i	$-0.491148\pi$
$457$	5.18528e10			0.0556096			0.0278048	+	0.999613i	$0.491148\pi$
$458$	−1.54951e12			−1.64551
$459$	−9.42338e10	+	1.45471e11i	−0.0990945	+	0.152975i
$460$	3.10020e12			3.22835
$461$	5.27975e11			0.544451			0.272226	−	0.962233i	$-0.412240\pi$
$461$	5.27975e11			0.544451			0.272226	+	0.962233i	$0.412240\pi$
$462$			9.44711e10i			0.0964739i
$463$	−1.71882e12			−1.73827			−0.869133	−	0.494579i	$-0.835322\pi$
$463$	−1.71882e12			−1.73827			−0.869133	+	0.494579i	$0.835322\pi$
$464$		−	3.64206e11i		−	0.364768i
$465$		−	1.48170e11i		−	0.146968i
$466$			5.44469e11i			0.534856i
$467$	−1.23791e12			−1.20438			−0.602188	−	0.798355i	$-0.705704\pi$
$467$	−1.23791e12			−1.20438			−0.602188	+	0.798355i	$0.705704\pi$
$468$	−1.19177e12			−1.14838
$469$		−	3.28107e11i		−	0.313139i
$470$			3.69474e12i			3.49256i
$471$		−	1.28479e11i		−	0.120292i
$472$	4.24634e11			0.393800
$473$			1.89916e12i			1.74457i
$474$	−5.67211e10			−0.0516110
$475$	−1.41801e12			−1.27808
$476$	4.43276e11	−	6.84296e11i	0.395770	−	0.610960i
$477$	5.50434e11			0.486824
$478$	1.07974e12			0.946008
$479$		−	1.00333e12i		−	0.870833i	−0.900229	−	0.435416i	$-0.856601\pi$
$479$		−	1.00333e12i		−	0.870833i	0.900229	−	0.435416i	$-0.143399\pi$
$480$	−5.07464e9			−0.00436335
$481$		−	4.96844e11i		−	0.423221i
$482$			2.15874e12i			1.82175i
$483$			3.69421e10i			0.0308858i
$484$	−4.38993e12			−3.63625
$485$	1.82761e12			1.49984
$486$		−	5.79095e11i		−	0.470854i
$487$		−	1.82452e12i		−	1.46983i	−0.678158	−	0.734916i	$-0.737222\pi$
$487$		−	1.82452e12i		−	1.46983i	0.678158	−	0.734916i	$-0.262778\pi$
$488$		−	3.41910e12i		−	2.72912i
$489$	1.05674e11			0.0835754
$490$		−	3.32004e12i		−	2.60172i
$491$	3.89108e11			0.302137			0.151068	−	0.988523i	$-0.451729\pi$
$491$	3.89108e11			0.302137			0.151068	+	0.988523i	$0.451729\pi$
$492$	−2.67913e11			−0.206135
$493$	−2.54060e11	+	3.92199e11i	−0.193698	+	0.299017i
$494$	−8.53375e11			−0.644716
$495$	3.83548e12			2.87142
$496$			1.28322e12i			0.951994i
$497$	8.05601e11			0.592265
$498$			2.60697e11i			0.189934i
$499$			2.52722e12i			1.82470i	0.409414	+	0.912349i	$0.365733\pi$
$499$			2.52722e12i			1.82470i	−0.409414	+	0.912349i	$0.634267\pi$
$500$			4.76397e12i			3.40882i
$501$	−1.75208e11			−0.124247
$502$	1.76832e12			1.24278
$503$		−	1.22587e12i		−	0.853863i	−0.904284	−	0.426932i	$-0.859594\pi$
$503$		−	1.22587e12i		−	0.853863i	0.904284	−	0.426932i	$-0.140406\pi$
$504$			9.10331e11i			0.628437i
$505$		−	1.17752e12i		−	0.805670i
$506$	−3.99159e12			−2.70688
$507$			9.08641e10i			0.0610740i
$508$	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	$0.835379\pi$
$510$	3.51507e11	+	2.27701e11i	0.230075	+	0.149039i
$511$	−5.77783e11			−0.374862
$512$	−2.73904e12			−1.76150
$513$		−	1.84281e11i		−	0.117477i
$514$	−7.06407e11			−0.446397
$515$			2.26461e12i			1.41860i
$516$		−	3.07915e11i		−	0.191209i
$517$		−	3.17556e12i		−	1.95485i
$518$	−7.56045e11			−0.461385
$519$	1.66939e11			0.100996
$520$			2.90329e12i			1.74131i
$521$		−	9.50624e11i		−	0.565248i	−0.959231	−	0.282624i	$-0.908795\pi$
$521$		−	9.50624e11i		−	0.565248i	0.959231	−	0.282624i	$-0.0912049\pi$
$522$		−	1.03940e12i		−	0.612722i
$523$	1.56396e12			0.914045			0.457022	−	0.889455i	$-0.348916\pi$
$523$	1.56396e12			0.914045			0.457022	+	0.889455i	$0.348916\pi$
$524$		−	1.80940e12i		−	1.04844i
$525$	−1.14519e11			−0.0657904
$526$	1.55807e12			0.887463
$527$	8.95141e11	−	1.38185e12i	0.505526	−	0.780393i
$528$	2.80551e11			0.157094
$529$	2.40277e11			0.133402
$530$		−	2.67130e12i		−	1.47056i
$531$	4.09247e11			0.223388
$532$			8.66858e11i			0.469186i
$533$			1.20550e12i			0.646985i
$534$			1.74467e10i			0.00928492i
$535$	1.24742e12			0.658295
$536$	−2.88529e12			−1.50990
$537$		−	1.79640e11i		−	0.0932222i
$538$			7.10747e11i			0.365759i
$539$			2.85351e12i			1.45623i
$540$	−1.24896e12			−0.632087
$541$			3.47453e12i			1.74385i	0.489641	+	0.871924i	$0.337128\pi$
$541$			3.47453e12i			1.74385i	−0.489641	+	0.871924i	$0.662872\pi$
$542$	3.10062e12			1.54330
$543$	8.77531e10			0.0433175
$544$	−4.73267e10	−	3.06575e10i	−0.0231692	−	0.0150086i
$545$	−5.45782e12			−2.64993
$546$	−6.89191e10			−0.0331874
$547$			3.19663e12i			1.52669i	0.645993	+	0.763344i	$0.276444\pi$
$547$			3.19663e12i			1.52669i	−0.645993	+	0.763344i	$0.723556\pi$
$548$	3.38408e12			1.60298
$549$		−	3.29521e12i		−	1.54813i
$550$		−	1.23738e13i		−	5.76597i
$551$		−	4.96833e11i		−	0.229630i
$552$	3.24860e11			0.148926
$553$	2.59254e11			0.117886
$554$			2.71899e12i			1.22635i
$555$		−	2.59250e11i		−	0.115984i
$556$			5.66523e12i			2.51409i
$557$	3.44273e12			1.51549			0.757747	−	0.652548i	$-0.226300\pi$
$557$	3.44273e12			1.51549			0.757747	+	0.652548i	$0.226300\pi$
$558$			3.66214e12i			1.59912i
$559$	−1.38549e12			−0.600137
$560$	1.49195e12			0.641075
$561$	−3.02114e11	−	1.95705e11i	−0.128777	−	0.0834197i
$562$	8.10753e12			3.42827
$563$	−3.44807e12			−1.44640			−0.723199	−	0.690639i	$-0.757329\pi$
$563$	−3.44807e12			−1.44640			−0.723199	+	0.690639i	$0.757329\pi$
$564$			5.14860e11i			0.214256i
$565$	−4.24405e12			−1.75211
$566$			4.88794e11i			0.200194i
$567$			8.69872e11i			0.353453i
$568$		−	7.08427e12i		−	2.85580i
$569$	2.03356e12			0.813302			0.406651	−	0.913584i	$-0.366696\pi$
$569$	2.03356e12			0.813302			0.406651	+	0.913584i	$0.366696\pi$
$570$	−4.45285e11			−0.176686
$571$		−	2.59738e12i		−	1.02252i	−0.859426	−	0.511261i	$-0.829179\pi$
$571$		−	2.59738e12i		−	1.02252i	0.859426	−	0.511261i	$-0.170821\pi$
$572$		−	4.97102e12i		−	1.94162i
$573$			1.04879e11i			0.0406438i
$574$	1.83440e12			0.705327
$575$		−	4.83868e12i		−	1.84596i
$576$	−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	$0.538114\pi$
$578$	1.90259e12	+	4.24713e12i	0.709038	+	1.58278i
$579$	9.45480e10			0.0349622
$580$	−3.36728e12			−1.23553
$581$		−	1.19156e12i		−	0.433833i
$582$	3.81511e11			0.137833
$583$			2.29594e12i			0.823097i
$584$			5.08089e12i			1.80752i
$585$			2.79809e12i			0.987779i
$586$	8.26562e12			2.89558
$587$	−1.69305e11			−0.0588571			−0.0294286	−	0.999567i	$-0.509369\pi$
$587$	−1.69305e11			−0.0588571			−0.0294286	+	0.999567i	$0.509369\pi$
$588$		−	4.62645e11i		−	0.159606i
$589$			1.75051e12i			0.599302i
$590$		−	1.98611e12i		−	0.674791i
$591$	5.52372e10			0.0186246
$592$			2.24522e12i			0.751298i
$593$	−3.48378e12			−1.15692			−0.578462	−	0.815709i	$-0.696347\pi$
$593$	−3.48378e12			−1.15692			−0.578462	+	0.815709i	$0.696347\pi$
$594$	1.60807e12			0.529988
$595$	−1.60662e12	−	1.04075e12i	−0.525519	−	0.340423i
$596$	−5.09660e12			−1.65452
$597$	−3.20554e11			−0.103280
$598$		−	2.91197e12i		−	0.931176i
$599$	1.11287e12			0.353201			0.176601	−	0.984283i	$-0.443490\pi$
$599$	1.11287e12			0.353201			0.176601	+	0.984283i	$0.443490\pi$
$600$			1.00706e12i			0.317229i
$601$			3.78822e12i			1.18441i	0.805789	+	0.592203i	$0.201741\pi$
$601$			3.78822e12i			1.18441i	−0.805789	+	0.592203i	$0.798259\pi$
$602$			2.10829e12i			0.654254i
$603$	−2.78074e12			−0.856511
$604$	−5.70223e12			−1.74332
$605$			1.03069e13i			3.12773i
$606$		−	2.45806e11i		−	0.0740399i
$607$		−	7.20412e11i		−	0.215393i	−0.994184	−	0.107697i	$-0.965653\pi$
$607$		−	7.20412e11i		−	0.215393i	0.994184	−	0.107697i	$-0.0343475\pi$
$608$	5.99529e10			0.0177928
$609$		−	4.01246e10i		−	0.0118204i
$610$	−1.59919e13			−4.67645
$611$	2.31665e12			0.672474
$612$	−5.79949e12	−	3.75682e12i	−1.67112	−	1.08253i
$613$	−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
$615$			6.29021e11i			0.177307i
$616$	−3.79712e12			−1.06253
$617$		−	6.63363e11i		−	0.184276i	−0.995746	−	0.0921378i	$-0.970630\pi$
$617$		−	6.63363e11i		−	0.184276i	0.995746	−	0.0921378i	$-0.0293700\pi$
$618$			4.72735e11i			0.130368i
$619$			1.73727e12i			0.475619i	0.971312	+	0.237809i	$0.0764293\pi$
$619$			1.73727e12i			0.475619i	−0.971312	+	0.237809i	$0.923571\pi$
$620$	1.18641e13			3.22457
$621$	6.28821e11			0.169674
$622$		−	5.85123e12i		−	1.56744i
$623$		−	7.97433e10i		−	0.0212079i
$624$			2.04669e11i			0.0540408i
$625$	3.62071e12			0.949148
$626$		−	9.06564e11i		−	0.235947i
$627$	3.82714e11			0.0988941
$628$	1.02874e13			2.63928
$629$	1.56621e12	−	2.41779e12i	0.398953	−	0.615873i
$630$	4.25783e12			1.07685
$631$	5.82077e12			1.46167			0.730834	−	0.682556i	$-0.239131\pi$
$631$	5.82077e12			1.46167			0.730834	+	0.682556i	$0.239131\pi$
$632$		−	2.27982e12i		−	0.568425i
$633$	3.08358e10			0.00763377
$634$			4.65068e12i			1.14318i
$635$		−	7.82791e12i		−	1.91058i
$636$		−	3.72245e11i		−	0.0902135i
$637$	−2.08171e12			−0.500948
$638$	4.33546e12			1.03596
$639$		−	6.82756e12i		−	1.61999i
$640$			1.26104e13i			2.97110i
$641$		−	7.79878e12i		−	1.82459i	−0.409532	−	0.912296i	$-0.634308\pi$
$641$		−	7.79878e12i		−	1.82459i	0.409532	−	0.912296i	$-0.365692\pi$
$642$	2.60398e11			0.0604964
$643$		−	2.47918e12i		−	0.571950i	−0.958237	−	0.285975i	$-0.907683\pi$
$643$		−	2.47918e12i		−	0.571950i	0.958237	−	0.285975i	$-0.0923175\pi$
$644$	−2.95798e12			−0.677655
$645$	−7.22938e11			−0.164468
$646$	−4.15278e12	−	2.69011e12i	−0.938194	−	0.607747i
$647$	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
$649$			1.70703e12i			0.377693i
$650$	9.02704e12			1.98351
$651$			1.41372e11i			0.0308496i
$652$			8.46139e12i			1.83370i
$653$		−	2.01770e12i		−	0.434257i	−0.976143	−	0.217128i	$-0.930331\pi$
$653$		−	2.01770e12i		−	0.434257i	0.976143	−	0.217128i	$-0.0696690\pi$
$654$	−1.13931e12			−0.243525
$655$	−4.24821e12			−0.901820
$656$		−	5.44761e12i		−	1.14852i
$657$			4.89678e12i			1.02534i
$658$		−	3.52524e12i		−	0.733114i
$659$	3.26107e12			0.673559			0.336779	−	0.941584i	$-0.390662\pi$
$659$	3.26107e12			0.673559			0.336779	+	0.941584i	$0.390662\pi$
$660$		−	2.59384e12i		−	0.532103i
$661$	−3.23725e12			−0.659583			−0.329792	−	0.944054i	$-0.606978\pi$
$661$	−3.23725e12			−0.659583			−0.329792	+	0.944054i	$0.606978\pi$
$662$	−7.88806e12			−1.59628
$663$	1.42772e11	−	2.20400e11i	0.0286967	−	0.0442997i
$664$	−1.04783e13			−2.09187
$665$	2.03525e12			0.403572
$666$			6.40757e12i			1.26200i
$667$	1.69534e12			0.331659
$668$		−	1.40291e13i		−	2.72606i
$669$		−	2.40303e11i		−	0.0463811i
$670$			1.34952e13i			2.58728i
$671$	1.37448e13			2.61750
$672$	4.84183e9			0.000915900
$673$			2.71466e12i			0.510091i	0.966929	+	0.255046i	$0.0820905\pi$
$673$			2.71466e12i			0.510091i	−0.966929	+	0.255046i	$0.917910\pi$
$674$		−	1.48909e13i		−	2.77940i
$675$			1.94933e12i			0.361425i
$676$	−7.27556e12			−1.34000
$677$			7.38964e10i			0.0135199i	0.999977	+	0.00675997i	$0.00215178\pi$
$677$			7.38964e10i			0.0135199i	−0.999977	+	0.00675997i	$0.997848\pi$
$678$	−8.85942e11			−0.161017
$679$	−1.74376e12			−0.314828
$680$	−9.15208e12	+	1.41283e13i	−1.64146	+	2.53396i
$681$	5.25185e11			0.0935729
$682$	−1.52753e13			−2.70371
$683$			5.15673e12i			0.906737i	0.891323	+	0.453368i	$0.149778\pi$
$683$			5.15673e12i			0.906737i	−0.891323	+	0.453368i	$0.850222\pi$
$684$	7.34672e12			1.28334
$685$		−	7.94532e12i		−	1.37881i
$686$			6.81479e12i			1.17488i
$687$			5.06957e11i			0.0868292i
$688$	6.26099e12			1.06536
$689$	−1.67495e12			−0.283148
$690$		−	1.51945e12i		−	0.255190i
$691$		−	9.13711e12i		−	1.52461i	−0.647220	−	0.762303i	$-0.724069\pi$
$691$		−	9.13711e12i		−	1.52461i	0.647220	−	0.762303i	$-0.275931\pi$
$692$			1.33669e13i			2.21592i
$693$	−3.65953e12			−0.602734
$694$			7.95736e12i			1.30212i
$695$	1.33011e13			2.16250
$696$	−3.52846e11			−0.0569959
$697$	−3.80011e12	+	5.86632e12i	−0.609886	+	0.941496i
$698$	−1.08673e12			−0.173289
$699$	1.78135e11			0.0282229
$700$		−	9.16966e12i		−	1.44348i
$701$	1.05802e11			0.0165487			0.00827433	−	0.999966i	$-0.497366\pi$
$701$	1.05802e11			0.0165487			0.00827433	+	0.999966i	$0.497366\pi$
$702$			1.17313e12i			0.182318i
$703$			3.06283e12i			0.472960i
$704$		−	1.06644e13i		−	1.63629i
$705$	1.20881e12			0.184293
$706$	9.84870e12			1.49196
$707$			1.12350e12i			0.169116i
$708$		−	2.76763e11i		−	0.0413961i
$709$		−	5.40312e12i		−	0.803038i	−0.915851	−	0.401519i	$-0.868482\pi$
$709$		−	5.40312e12i		−	0.803038i	0.915851	−	0.401519i	$-0.131518\pi$
$710$	−3.31348e13			−4.89352
$711$		−	2.19721e12i		−	0.322447i
$712$	−7.01244e11			−0.102261
$713$	−5.97327e12			−0.865584
$714$	−3.35381e11	−	2.17255e11i	−0.0482944	−	0.0312844i
$715$	−1.16712e13			−1.67009
$716$	1.43839e13			2.04536
$717$		−	3.53261e11i		−	0.0499183i
$718$	1.06327e13			1.49309
$719$			1.25578e13i			1.75240i	0.481944	+	0.876202i	$0.339931\pi$
$719$			1.25578e13i			1.75240i	−0.481944	+	0.876202i	$0.660069\pi$
$720$		−	1.26445e13i		−	1.75349i
$721$		−	2.16072e12i		−	0.297776i
$722$	−7.40273e12			−1.01385
$723$	7.06280e11			0.0961290
$724$			7.02645e12i			0.950413i
$725$			5.25552e12i			0.706472i
$726$			2.15156e12i			0.287434i
$727$	3.74144e12			0.496746			0.248373	−	0.968665i	$-0.420104\pi$
$727$	3.74144e12			0.496746			0.248373	+	0.968665i	$0.420104\pi$
$728$		−	2.77010e12i		−	0.365514i
$729$	7.24507e12			0.950099
$730$	2.37645e13			3.09725
$731$	−6.74221e12	−	4.36750e12i	−0.873322	−	0.565724i
$732$	−2.22847e12			−0.286884
$733$	7.03096e12			0.899594			0.449797	−	0.893131i	$-0.351496\pi$
$733$	7.03096e12			0.899594			0.449797	+	0.893131i	$0.351496\pi$
$734$			1.25007e13i			1.58965i
$735$	−1.08622e12			−0.137286
$736$			2.04577e11i			0.0256984i
$737$		−	1.15989e13i		−	1.44815i
$738$		−	1.55468e13i		−	1.92924i
$739$	−4.06712e12			−0.501634			−0.250817	−	0.968035i	$-0.580699\pi$
$739$	−4.06712e12			−0.501634			−0.250817	+	0.968035i	$0.580699\pi$
$740$	2.07583e13			2.54477
$741$			2.79200e11i			0.0340199i
$742$			2.54875e12i			0.308681i
$743$			1.05121e13i			1.26543i	0.774384	+	0.632716i	$0.218060\pi$
$743$			1.05121e13i			1.26543i	−0.774384	+	0.632716i	$0.781940\pi$
$744$	1.24320e12			0.148752
$745$			1.19660e13i			1.42314i
$746$	−6.51986e12			−0.770750
$747$	−1.00986e13			−1.18664
$748$	1.56702e13	−	2.41905e13i	1.83028	−	2.82545i
$749$	−1.19019e12			−0.138181
$750$	2.33487e12			0.269456
$751$		−	9.86339e12i		−	1.13148i	−0.824584	−	0.565739i	$-0.808591\pi$
$751$		−	9.86339e12i		−	1.13148i	0.824584	−	0.565739i	$-0.191409\pi$
$752$	−1.04689e13			−1.19377
$753$		−	5.78544e11i		−	0.0655781i
$754$			3.16283e12i			0.356373i
$755$			1.33880e13i			1.49952i
$756$	1.19166e12			0.132680
$757$	−1.58167e13			−1.75060			−0.875298	−	0.483584i	$-0.839335\pi$
$757$	−1.58167e13			−1.75060			−0.875298	+	0.483584i	$0.839335\pi$
$758$			2.29952e12i			0.253003i
$759$			1.30594e12i			0.142835i
$760$		−	1.78975e13i		−	1.94595i
$761$	−2.52570e12			−0.272992			−0.136496	−	0.990641i	$-0.543584\pi$
$761$	−2.52570e12			−0.272992			−0.136496	+	0.990641i	$0.543584\pi$
$762$		−	1.63407e12i		−	0.175579i
$763$	5.20743e12			0.556241
$764$	−8.39776e12			−0.891751
$765$	−8.82045e12	+	1.36163e13i	−0.931138	+	1.43742i
$766$	−1.15176e11			−0.0120874
$767$	−1.24532e12			−0.129928
$768$			1.77129e12i			0.183723i
$769$	−1.30319e13			−1.34382			−0.671909	−	0.740634i	$-0.734525\pi$
$769$	−1.30319e13			−1.34382			−0.671909	+	0.740634i	$0.734525\pi$
$770$			1.77600e13i			1.82068i
$771$			2.31116e11i			0.0235552i
$772$			7.57053e12i			0.767094i
$773$	−1.55200e13			−1.56345			−0.781724	−	0.623624i	$-0.785660\pi$
$773$	−1.55200e13			−1.56345			−0.781724	+	0.623624i	$0.785660\pi$
$774$	1.78680e13			1.78954
$775$		−	1.85170e13i		−	1.84379i
$776$			1.53343e13i			1.51805i
$777$			2.47356e11i			0.0243460i
$778$	2.52327e12			0.246920
$779$		−	7.43138e12i		−	0.723021i
$780$	1.89228e12			0.183045
$781$	2.84787e13			2.73899
$782$	9.17945e12	−	1.41705e13i	0.877781	−	1.35505i
$783$	−6.82993e11			−0.0649364
$784$	9.40718e12			0.889278
$785$		−	2.41532e13i		−	2.27019i
$786$	−8.86810e11			−0.0828760
$787$			8.13448e12i			0.755864i	0.925833	+	0.377932i	$0.123365\pi$
$787$			8.13448e12i			0.755864i	−0.925833	+	0.377932i	$0.876635\pi$
$788$			4.42288e12i			0.408637i
$789$		−	5.09755e11i		−	0.0468290i
$790$	−1.06632e13			−0.974018
$791$	4.04935e12			0.367782
$792$			3.21810e13i			2.90627i
$793$			1.00272e13i			0.900428i
$794$		−	1.76430e13i		−	1.57536i
$795$	−8.73974e11			−0.0775973
$796$		−	2.56670e13i		−	2.26603i
$797$	1.96859e13			1.72820			0.864098	−	0.503324i	$-0.167890\pi$
$797$	1.96859e13			1.72820			0.864098	+	0.503324i	$0.167890\pi$
$798$	4.24857e11			0.0370877
$799$	1.12735e13	+	7.30282e12i	0.978588	+	0.633914i
$800$	−6.34184e11			−0.0547407
$801$	−6.75834e11			−0.0580087
$802$		−	1.39705e12i		−	0.119242i
$803$	−2.04252e13			−1.73359
$804$			1.88055e12i			0.158720i
$805$			6.94489e12i			0.582886i
$806$		−	1.11437e13i		−	0.930086i
$807$	2.32536e11			0.0193001
$808$	9.87980e12			0.815449
$809$			9.92022e12i			0.814241i	0.913375	+	0.407120i	$0.133467\pi$
$809$			9.92022e12i			0.814241i	−0.913375	+	0.407120i	$0.866533\pi$
$810$		−	3.57783e13i		−	2.92036i
$811$			1.77102e13i			1.43757i	0.695233	+	0.718784i	$0.255301\pi$
$811$			1.77102e13i			1.43757i	−0.695233	+	0.718784i	$0.744699\pi$
$812$	3.21280e12			0.259347
$813$		−	1.01443e12i		−	0.0814360i
$814$	−2.67269e13			−2.13372
$815$	1.98661e13			1.57726
$816$	−6.45181e11	+	9.95982e11i	−0.0509420	+	0.0786404i
$817$	8.54095e12			0.670667
$818$	−7.67651e12			−0.599479
$819$		−	2.66972e12i		−	0.207342i
$820$	−5.03661e13			−3.89024
$821$		−	1.68690e13i		−	1.29582i	−0.761715	−	0.647912i	$-0.775642\pi$
$821$		−	1.68690e13i		−	1.29582i	0.761715	−	0.647912i	$-0.224358\pi$
$822$		−	1.65858e12i		−	0.126710i
$823$			4.79642e12i			0.364433i	0.983258	+	0.182216i	$0.0583272\pi$
$823$			4.79642e12i			0.364433i	−0.983258	+	0.182216i	$0.941673\pi$
$824$	−1.90009e13			−1.43582
$825$	−4.04837e12			−0.304255
$826$			1.89500e12i			0.141644i
$827$			1.43263e12i			0.106502i	0.998581	+	0.0532510i	$0.0169584\pi$
$827$			1.43263e12i			0.106502i	−0.998581	+	0.0532510i	$0.983042\pi$
$828$			2.50692e13i			1.85355i
$829$	1.06309e13			0.781763			0.390881	−	0.920441i	$-0.372170\pi$
$829$	1.06309e13			0.781763			0.390881	+	0.920441i	$0.372170\pi$
$830$			4.90094e13i			3.58450i
$831$	8.89577e11			0.0647111
$832$	7.77999e12			0.562891
$833$	−1.01302e13	−	6.56220e12i	−0.728982	−	0.472223i
$834$	2.77659e12			0.198731
$835$	−3.29381e13			−2.34482
$836$			3.06442e13i			2.16980i
$837$	2.40642e12			0.169475
$838$			1.93001e12i			0.135196i
$839$		−	2.10767e13i		−	1.46850i	−0.678878	−	0.734251i	$-0.737534\pi$
$839$		−	2.10767e13i		−	1.46850i	0.678878	−	0.734251i	$-0.262466\pi$
$840$		−	1.44542e12i		−	0.100170i
$841$	1.26658e13			0.873070
$842$	−2.19258e11			−0.0150332
$843$		−	2.65255e12i		−	0.180901i
$844$			2.46905e12i			0.167490i
$845$			1.70819e13i			1.15261i
$846$	−2.98768e13			−2.00525
$847$		−	9.83406e12i		−	0.656534i
$848$	7.56903e12			0.502642
$849$	1.59920e11			0.0105637
$850$	4.39283e13	+	2.84561e13i	2.88642	+	1.86978i
$851$	−1.04513e13			−0.683105
$852$	−4.61731e12			−0.300200
$853$			8.83863e12i			0.571629i	0.958285	+	0.285814i	$0.0922641\pi$
$853$			8.83863e12i			0.571629i	−0.958285	+	0.285814i	$0.907736\pi$
$854$	1.52583e13			0.981624
$855$		−	1.72490e13i		−	1.10387i
$856$			1.04663e13i			0.666286i
$857$		−	2.77034e13i		−	1.75436i	−0.480161	−	0.877181i	$-0.659422\pi$
$857$		−	2.77034e13i		−	1.75436i	0.480161	−	0.877181i	$-0.340578\pi$
$858$	−2.43635e12			−0.153479
$859$	−1.52744e13			−0.957183			−0.478592	−	0.878038i	$-0.658853\pi$
$859$	−1.52744e13			−0.957183			−0.478592	+	0.878038i	$0.658853\pi$
$860$		−	5.78862e13i		−	3.60855i
$861$		−	6.00163e11i		−	0.0372182i
$862$		−	2.76160e13i		−	1.70364i
$863$	5.46258e12			0.335235			0.167618	−	0.985852i	$-0.446393\pi$
$863$	5.46258e12			0.335235			0.167618	+	0.985852i	$0.446393\pi$
$864$		−	8.24168e10i		−	0.00503157i
$865$	3.13835e13			1.90603
$866$	6.23756e12			0.376863
$867$	1.38954e12	−	6.22472e11i	0.0835190	−	0.0374140i
$868$	−1.13198e13			−0.676861
$869$	9.16486e12			0.545176
$870$			1.65034e12i			0.0976647i
$871$	8.46168e12			0.498167
$872$		−	4.57929e13i		−	2.68210i
$873$			1.47786e13i			0.861131i
$874$			1.79510e13i			1.04061i
$875$	−1.06719e13			−0.615471
$876$	3.31157e12			0.190005
$877$		−	7.13412e12i		−	0.407232i	−0.979051	−	0.203616i	$-0.934731\pi$
$877$		−	7.13412e12i		−	0.407232i	0.979051	−	0.203616i	$-0.0652695\pi$
$878$			1.31885e13i			0.748982i
$879$		−	2.70428e12i		−	0.152792i
$880$	5.27419e13			2.96472
$881$			6.08084e12i			0.340073i	0.985438	+	0.170036i	$0.0543885\pi$
$881$			6.08084e12i			0.340073i	−0.985438	+	0.170036i	$0.945611\pi$
$882$	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	$0.466386\pi$
$884$	1.76476e13	+	1.14318e13i	0.971965	+	0.629623i
$885$	−6.49799e11			−0.0356069
$886$	−4.81839e13			−2.62694
$887$			1.70080e13i			0.922568i	0.887253	+	0.461284i	$0.152611\pi$
$887$			1.70080e13i			0.922568i	−0.887253	+	0.461284i	$0.847389\pi$
$888$	2.17519e12			0.117392
$889$			7.46880e12i			0.401045i
$890$			3.27988e12i			0.175228i
$891$			3.07508e13i			1.63458i
$892$	1.92412e13			1.01763
$893$	−1.42812e13			−0.751506
$894$			2.49790e12i			0.130784i
$895$		−	3.37713e13i		−	1.75932i
$896$		−	1.20318e13i		−	0.623657i
$897$	−9.52714e11			−0.0491356
$898$		−	4.69391e13i		−	2.40875i
$899$	6.48785e12			0.331270
$900$	−7.77139e13			−3.94828
$901$	−8.15079e12	−	5.27995e12i	−0.412039	−	0.266912i
$902$	6.48477e13			3.26186
$903$	6.89773e11			0.0345232
$904$		−	3.56090e13i		−	1.77338i
$905$	1.64971e13			0.817500
$906$			2.79473e12i			0.137804i
$907$			3.06959e13i			1.50608i	0.657975	+	0.753039i	$0.271413\pi$
$907$			3.06959e13i			1.50608i	−0.657975	+	0.753039i	$0.728587\pi$
$908$			4.20519e13i			2.05305i
$909$	9.52180e12			0.462574
$910$	−1.29564e13			−0.626322
$911$			3.61989e13i			1.74126i	0.491940	+	0.870629i	$0.336288\pi$
$911$			3.61989e13i			1.74126i	−0.491940	+	0.870629i	$0.663712\pi$
$912$		−	1.26170e12i		−	0.0603918i
$913$		−	4.21227e13i		−	2.00631i
$914$	2.03489e12			0.0964458
$915$			5.23210e12i			0.246764i
$916$	−4.05924e13			−1.90509
$917$	4.05332e12			0.189299
$918$	−3.69807e12	+	5.70880e12i	−0.171863	+	0.265310i
$919$	−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
$921$			4.38204e11i			0.0200682i
$922$	2.07196e13			0.944262
$923$			2.07760e13i			0.942223i
$924$			2.47485e12i			0.111693i
$925$		−	3.23988e13i		−	1.45509i
$926$	−6.74527e13			−3.01474
$927$	−1.83124e13			−0.814489
$928$		−	2.22201e11i		−	0.00983514i
$929$			2.58941e13i			1.14059i	0.821440	+	0.570295i	$0.193171\pi$
$929$			2.58941e13i			1.14059i	−0.821440	+	0.570295i	$0.806829\pi$
$930$		−	5.81472e12i		−	0.254892i
$931$	1.28328e13			0.559821
$932$			1.42634e13i			0.619229i
$933$	−1.91436e12			−0.0827095
$934$	−4.85799e13			−2.08879
$935$	−5.67956e13	−	3.67913e13i	−2.43032	−	1.57432i
$936$	−2.34769e13			−0.999768
$937$	−4.81953e12			−0.204257			−0.102128	−	0.994771i	$-0.532565\pi$
$937$	−4.81953e12			−0.204257			−0.102128	+	0.994771i	$0.532565\pi$
$938$		−	1.28761e13i		−	0.543089i
$939$	−2.96602e11			−0.0124503
$940$			9.67905e13i			4.04350i
$941$		−	1.82547e13i		−	0.758966i	−0.925199	−	0.379483i	$-0.876102\pi$
$941$		−	1.82547e13i		−	0.758966i	0.925199	−	0.379483i	$-0.123898\pi$
$942$		−	5.04196e12i		−	0.208627i
$943$	2.53581e13			1.04427
$944$	5.62757e12			0.230646
$945$		−	2.79785e12i		−	0.114125i
$946$			7.45300e13i			3.02567i
$947$			5.09493e12i			0.205856i	0.994689	+	0.102928i	$0.0328211\pi$
$947$			5.09493e12i			0.205856i	−0.994689	+	0.102928i	$0.967179\pi$
$948$	−1.48592e12			−0.0597526
$949$		−	1.49007e13i		−	0.596360i
$950$	−5.56478e13			−2.21662
$951$	1.52157e12			0.0603226
$952$	8.73221e12	−	1.34801e13i	0.344555	−	0.531897i
$953$	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
$955$			1.97167e13i			0.767041i
$956$	2.82859e13			1.09524
$957$		−	1.41844e12i		−	0.0546647i
$958$		−	3.93743e13i		−	1.51032i
$959$			7.58081e12i			0.289422i
$960$	4.05954e12			0.154261
$961$	3.58071e12			0.135430
$962$		−	1.94979e13i		−	0.734009i
$963$			1.00870e13i			0.377959i
$964$			5.65523e13i			2.10913i
$965$	1.77745e13			0.659817
$966$			1.44974e12i			0.0535664i
$967$	4.68118e13			1.72161			0.860807	−	0.508931i	$-0.169959\pi$
$967$	4.68118e13			1.72161			0.860807	+	0.508931i	$0.169959\pi$
$968$	−8.64784e13			−3.16569
$969$	−8.80126e11	+	1.35867e12i	−0.0320692	+	0.0495060i
$970$	7.17219e13			2.60123
$971$	4.48543e13			1.61926			0.809632	−	0.586938i	$-0.199667\pi$
$971$	4.48543e13			1.61926			0.809632	+	0.586938i	$0.199667\pi$
$972$		−	1.51705e13i		−	0.545131i
$973$	−1.26909e13			−0.453925
$974$		−	7.16006e13i		−	2.54918i
$975$		−	2.95339e12i		−	0.104665i
$976$		−	4.53125e13i		−	1.59843i
$977$	−3.39602e13			−1.19246			−0.596231	−	0.802813i	$-0.703336\pi$
$977$	−3.39602e13			−1.19246			−0.596231	+	0.802813i	$0.703336\pi$
$978$	4.14703e12			0.144948
$979$		−	2.81900e12i		−	0.0980782i
$980$		−	8.69745e13i		−	3.01214i
$981$		−	4.41336e13i		−	1.52145i
$982$	1.52700e13			0.524007
$983$			1.74563e13i			0.596297i	0.954520	+	0.298148i	$0.0963690\pi$
$983$			1.74563e13i			0.596297i	−0.954520	+	0.298148i	$0.903631\pi$
$984$	−5.27770e12			−0.179459
$985$	1.03843e13			0.351490
$986$	−9.97024e12	+	1.53913e13i	−0.335938	+	0.518596i
$987$	−1.15336e12			−0.0386845
$988$	−2.23557e13			−0.746419
$989$			2.91443e13i			0.968657i
$990$	1.50518e14			4.98001
$991$		−	4.90669e13i		−	1.61606i	−0.589143	−	0.808029i	$-0.700534\pi$
$991$		−	4.90669e13i		−	1.61606i	0.589143	−	0.808029i	$-0.299466\pi$
$992$			7.82890e11i			0.0256684i
$993$			2.58075e12i			0.0842314i
$994$	3.16147e13			1.02719
$995$	−6.02622e13			−1.94913
$996$			6.82943e12i			0.219896i
$997$		−	4.75402e12i		−	0.152382i	−0.997093	−	0.0761908i	$-0.975724\pi$
$997$		−	4.75402e12i		−	0.152382i	0.997093	−	0.0761908i	$-0.0242758\pi$
$998$			9.91772e13i			3.16464i
$999$	4.21045e12			0.133747

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.b.a.16.11	✓	12	1.1	even	1	trivial
17.10.b.a.16.12	yes	12	17.16	even	2	inner
153.10.d.b.118.1		12	51.50	odd	2
153.10.d.b.118.2		12	3.2	odd	2
272.10.b.c.33.6		12	68.67	odd	2
272.10.b.c.33.7		12	4.3	odd	2
289.10.a.c.1.1		12	17.4	even	4
289.10.a.c.1.2		12	17.13	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	17.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+39.2436 q^{2} -12.8394i q^{3} +1028.06 q^{4} -2413.73i q^{5} -503.863i q^{6} +2302.99i q^{7} +20252.0 q^{8} +19518.2 q^{9} +O(q^{10})\)	\(q+39.2436 q^{2} -12.8394i q^{3} +1028.06 q^{4} -2413.73i q^{5} -503.863i q^{6} +2302.99i q^{7} +20252.0 q^{8} +19518.2 q^{9} -94723.3i q^{10} +81412.9i q^{11} -13199.6i q^{12} -59392.9 q^{13} +90377.7i q^{14} -30990.8 q^{15} +268395. q^{16} +(-289024. - 187225. i) q^{17} +765962. q^{18} +366131. q^{19} -2.48145e6i q^{20} +29569.0 q^{21} +3.19494e6i q^{22} +1.24935e6i q^{23} -260023. i q^{24} -3.87295e6 q^{25} -2.33079e6 q^{26} -503318. i q^{27} +2.36761e6i q^{28} -1.35698e6i q^{29} -1.21619e6 q^{30} +4.78110e6i q^{31} +163747. q^{32} +1.04529e6 q^{33} +(-1.13423e7 - 7.34738e6i) q^{34} +5.55880e6 q^{35} +2.00658e7 q^{36} +8.36539e6i q^{37} +1.43683e7 q^{38} +762568. i q^{39} -4.88828e7i q^{40} -2.02970e7i q^{41} +1.16039e6 q^{42} +2.33275e7 q^{43} +8.36973e7i q^{44} -4.71115e7i q^{45} +4.90290e7i q^{46} -3.90056e7 q^{47} -3.44602e6i q^{48} +3.50498e7 q^{49} -1.51989e8 q^{50} +(-2.40385e6 + 3.71089e6i) q^{51} -6.10594e7 q^{52} +2.82011e7 q^{53} -1.97520e7i q^{54} +1.96509e8 q^{55} +4.66402e7i q^{56} -4.70090e6i q^{57} -5.32527e7i q^{58} +2.09675e7 q^{59} -3.18603e7 q^{60} -1.68828e8i q^{61} +1.87627e8i q^{62} +4.49502e7i q^{63} -1.30992e8 q^{64} +1.43358e8i q^{65} +4.10210e7 q^{66} -1.42470e8 q^{67} +(-2.97133e8 - 1.92478e8i) q^{68} +1.60409e7 q^{69} +2.18147e8 q^{70} -3.49806e8i q^{71} +3.95281e8 q^{72} +2.50884e8i q^{73} +3.28288e8i q^{74} +4.97263e7i q^{75} +3.76405e8 q^{76} -1.87494e8 q^{77} +2.99259e7i q^{78} -1.12572e8i q^{79} -6.47831e8i q^{80} +3.77713e8 q^{81} -7.96528e8i q^{82} -5.17396e8 q^{83} +3.03987e7 q^{84} +(-4.51910e8 + 6.97624e8i) q^{85} +9.15456e8 q^{86} -1.74228e7 q^{87} +1.64877e9i q^{88} -3.46259e7 q^{89} -1.84882e9i q^{90} -1.36781e8i q^{91} +1.28441e9i q^{92} +6.13864e7 q^{93} -1.53072e9 q^{94} -8.83741e8i q^{95} -2.10241e6i q^{96} +7.57173e8i q^{97} +1.37548e9 q^{98} +1.58903e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 30 q^{2} + 1874 q^{4} + 23550 q^{8} - 9184 q^{9}+O(q^{10}) \) 12 * q + 30 * q^2 + 1874 * q^4 + 23550 * q^8 - 9184 * q^9	\( 12 q + 30 q^{2} + 1874 q^{4} + 23550 q^{8} - 9184 q^{9} - 63204 q^{13} - 243480 q^{15} + 38978 q^{16} - 105960 q^{17} + 547706 q^{18} + 1110672 q^{19} - 172580 q^{21} - 4441796 q^{25} + 1336332 q^{26} - 500496 q^{30} - 1934850 q^{32} - 6557404 q^{33} - 15085546 q^{34} + 3519864 q^{35} + 30244102 q^{36} + 28748136 q^{38} - 11901296 q^{42} + 10004616 q^{43} - 112552440 q^{47} + 121354720 q^{49} - 164889018 q^{50} - 52506472 q^{51} - 59093180 q^{52} + 76804272 q^{53} + 300732568 q^{55} + 11618904 q^{59} + 101609232 q^{60} - 260062974 q^{64} + 18429632 q^{66} - 304208752 q^{67} - 444301206 q^{68} - 211308236 q^{69} + 460311456 q^{70} + 493218954 q^{72} + 416024248 q^{76} + 138357828 q^{77} - 363335792 q^{81} - 845042136 q^{83} + 958037984 q^{84} - 388949632 q^{85} + 127952904 q^{86} + 610860648 q^{87} - 938223804 q^{89} + 1635779524 q^{93} - 238629952 q^{94} - 152046078 q^{98}+O(q^{100}) \) 12 * q + 30 * q^2 + 1874 * q^4 + 23550 * q^8 - 9184 * q^9 - 63204 * q^13 - 243480 * q^15 + 38978 * q^16 - 105960 * q^17 + 547706 * q^18 + 1110672 * q^19 - 172580 * q^21 - 4441796 * q^25 + 1336332 * q^26 - 500496 * q^30 - 1934850 * q^32 - 6557404 * q^33 - 15085546 * q^34 + 3519864 * q^35 + 30244102 * q^36 + 28748136 * q^38 - 11901296 * q^42 + 10004616 * q^43 - 112552440 * q^47 + 121354720 * q^49 - 164889018 * q^50 - 52506472 * q^51 - 59093180 * q^52 + 76804272 * q^53 + 300732568 * q^55 + 11618904 * q^59 + 101609232 * q^60 - 260062974 * q^64 + 18429632 * q^66 - 304208752 * q^67 - 444301206 * q^68 - 211308236 * q^69 + 460311456 * q^70 + 493218954 * q^72 + 416024248 * q^76 + 138357828 * q^77 - 363335792 * q^81 - 845042136 * q^83 + 958037984 * q^84 - 388949632 * q^85 + 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

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