LMFDB - Embedded newform 17.10.b.a.16.4

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			16.4
Root			$206.667i$ of defining polynomial
Character	$\chi$	$=$	17.16
Dual form			17.10.b.a.16.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-16.7531 q^{2} +206.667i q^{3} -231.335 q^{4} +1946.29i q^{5} -3462.30i q^{6} +1633.30i q^{7} +12453.1 q^{8} -23028.2 q^{9} +O(q^{10})$	\(q-16.7531 q^{2} +206.667i q^{3} -231.335 q^{4} +1946.29i q^{5} -3462.30i q^{6} +1633.30i q^{7} +12453.1 q^{8} -23028.2 q^{9} -32606.3i q^{10} -11623.3i q^{11} -47809.2i q^{12} -163541. q^{13} -27362.8i q^{14} -402234. q^{15} -90185.0 q^{16} +(255165. - 231255. i) q^{17} +385793. q^{18} +673499. q^{19} -450244. i q^{20} -337549. q^{21} +194725. i q^{22} +1.37499e6i q^{23} +2.57365e6i q^{24} -1.83492e6 q^{25} +2.73981e6 q^{26} -691336. i q^{27} -377839. i q^{28} -4.32926e6i q^{29} +6.73865e6 q^{30} +3.45219e6i q^{31} -4.86513e6 q^{32} +2.40214e6 q^{33} +(-4.27479e6 + 3.87423e6i) q^{34} -3.17888e6 q^{35} +5.32721e6 q^{36} -5.81427e6i q^{37} -1.12832e7 q^{38} -3.37985e7i q^{39} +2.42374e7i q^{40} +2.37653e7i q^{41} +5.65499e6 q^{42} -2.46177e7 q^{43} +2.68886e6i q^{44} -4.48195e7i q^{45} -2.30353e7i q^{46} -3.94057e7 q^{47} -1.86382e7i q^{48} +3.76859e7 q^{49} +3.07406e7 q^{50} +(4.77927e7 + 5.27341e7i) q^{51} +3.78327e7 q^{52} -9.66929e7 q^{53} +1.15820e7i q^{54} +2.26222e7 q^{55} +2.03397e7i q^{56} +1.39190e8i q^{57} +7.25285e7i q^{58} +2.37253e7 q^{59} +9.30506e7 q^{60} +4.31637e7i q^{61} -5.78348e7i q^{62} -3.76120e7i q^{63} +1.27681e8 q^{64} -3.18298e8i q^{65} -4.02432e7 q^{66} +3.50040e7 q^{67} +(-5.90284e7 + 5.34973e7i) q^{68} -2.84165e8 q^{69} +5.32560e7 q^{70} -2.90407e8i q^{71} -2.86773e8 q^{72} +4.29259e8i q^{73} +9.74069e7i q^{74} -3.79217e8i q^{75} -1.55804e8 q^{76} +1.89843e7 q^{77} +5.66229e8i q^{78} -3.78639e8i q^{79} -1.75526e8i q^{80} -3.10387e8 q^{81} -3.98142e8i q^{82} +9.91655e7 q^{83} +7.80868e7 q^{84} +(4.50089e8 + 4.96625e8i) q^{85} +4.12423e8 q^{86} +8.94715e8 q^{87} -1.44746e8i q^{88} -5.39631e8 q^{89} +7.50864e8i q^{90} -2.67112e8i q^{91} -3.18083e8i q^{92} -7.13453e8 q^{93} +6.60166e8 q^{94} +1.31082e9i q^{95} -1.00546e9i q^{96} +1.21632e9i q^{97} -6.31355e8 q^{98} +2.67662e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−16.7531			−0.740388			−0.370194	−	0.928954i	$-0.620709\pi$
$2$	−16.7531			−0.740388			−0.370194	+	0.928954i	$0.620709\pi$
$3$			206.667i			1.47308i	0.676396	+	0.736538i	$0.263541\pi$
$3$			206.667i			1.47308i	−0.676396	+	0.736538i	$0.736459\pi$
$4$	−231.335			−0.451825
$5$			1946.29i			1.39265i	0.717726	+	0.696326i	$0.245183\pi$
$5$			1946.29i			1.39265i	−0.717726	+	0.696326i	$0.754817\pi$
$6$		−	3462.30i		−	1.09065i
$7$			1633.30i			0.257114i	0.991702	+	0.128557i	$0.0410345\pi$
$7$			1633.30i			0.257114i	−0.991702	+	0.128557i	$0.958966\pi$
$8$	12453.1			1.07491
$9$	−23028.2			−1.16995
$10$		−	32606.3i		−	1.03110i
$11$		−	11623.3i		−	0.239365i	−0.992812	−	0.119683i	$-0.961812\pi$
$11$		−	11623.3i		−	0.239365i	0.992812	−	0.119683i	$-0.0381877\pi$
$12$		−	47809.2i		−	0.665573i
$13$	−163541.			−1.58811			−0.794057	−	0.607844i	$-0.792035\pi$
$13$	−163541.			−1.58811			−0.794057	+	0.607844i	$0.792035\pi$
$14$		−	27362.8i		−	0.190364i
$15$	−402234.			−2.05148
$16$	−90185.0			−0.344028
$17$	255165.	−	231255.i	0.740970	−	0.671538i
$17$	255165.	−	231255.i	0.740970	−	0.671538i
$18$	385793.			0.866219
$19$	673499.			1.18562			0.592810	−	0.805342i	$-0.298019\pi$
$19$	673499.			1.18562			0.592810	+	0.805342i	$0.298019\pi$
$20$		−	450244.i		−	0.629236i
$21$	−337549.			−0.378748
$22$			194725.i			0.177223i
$23$			1.37499e6i			1.02453i	0.858828	+	0.512264i	$0.171193\pi$
$23$			1.37499e6i			1.02453i	−0.858828	+	0.512264i	$0.828807\pi$
$24$			2.57365e6i			1.58343i
$25$	−1.83492e6			−0.939480
$26$	2.73981e6			1.17582
$27$		−	691336.i		−	0.250353i
$28$		−	377839.i		−	0.116171i
$29$		−	4.32926e6i		−	1.13664i	−0.822808	−	0.568320i	$-0.807594\pi$
$29$		−	4.32926e6i		−	1.13664i	0.822808	−	0.568320i	$-0.192406\pi$
$30$	6.73865e6			1.51889
$31$			3.45219e6i			0.671378i	0.941973	+	0.335689i	$0.108969\pi$
$31$			3.45219e6i			0.671378i	−0.941973	+	0.335689i	$0.891031\pi$
$32$	−4.86513e6			−0.820200
$33$	2.40214e6			0.352603
$34$	−4.27479e6	+	3.87423e6i	−0.548605	+	0.497199i
$35$	−3.17888e6			−0.358070
$36$	5.32721e6			0.528614
$37$		−	5.81427e6i		−	0.510020i	−0.966938	−	0.255010i	$-0.917921\pi$
$37$		−	5.81427e6i		−	0.510020i	0.966938	−	0.255010i	$-0.0820788\pi$
$38$	−1.12832e7			−0.877819
$39$		−	3.37985e7i		−	2.33941i
$40$			2.42374e7i			1.49698i
$41$			2.37653e7i			1.31346i	0.754127	+	0.656729i	$0.228060\pi$
$41$			2.37653e7i			1.31346i	−0.754127	+	0.656729i	$0.771940\pi$
$42$	5.65499e6			0.280421
$43$	−2.46177e7			−1.09810			−0.549048	−	0.835791i	$-0.685010\pi$
$43$	−2.46177e7			−1.09810			−0.549048	+	0.835791i	$0.685010\pi$
$44$			2.68886e6i			0.108151i
$45$		−	4.48195e7i		−	1.62934i
$46$		−	2.30353e7i		−	0.758549i
$47$	−3.94057e7			−1.17793			−0.588963	−	0.808160i	$-0.700464\pi$
$47$	−3.94057e7			−1.17793			−0.588963	+	0.808160i	$0.700464\pi$
$48$		−	1.86382e7i		−	0.506780i
$49$	3.76859e7			0.933893
$50$	3.07406e7			0.695580
$51$	4.77927e7	+	5.27341e7i	0.989227	+	1.09150i
$52$	3.78327e7			0.717550
$53$	−9.66929e7			−1.68327			−0.841634	−	0.540048i	$-0.818406\pi$
$53$	−9.66929e7			−1.68327			−0.841634	+	0.540048i	$0.818406\pi$
$54$			1.15820e7i			0.185358i
$55$	2.26222e7			0.333352
$56$			2.03397e7i			0.276375i
$57$			1.39190e8i			1.74651i
$58$			7.25285e7i			0.841555i
$59$	2.37253e7			0.254905			0.127453	−	0.991845i	$-0.459320\pi$
$59$	2.37253e7			0.254905			0.127453	+	0.991845i	$0.459320\pi$
$60$	9.30506e7			0.926912
$61$			4.31637e7i			0.399149i	0.979883	+	0.199574i	$0.0639559\pi$
$61$			4.31637e7i			0.399149i	−0.979883	+	0.199574i	$0.936044\pi$
$62$		−	5.78348e7i		−	0.497080i
$63$		−	3.76120e7i		−	0.300811i
$64$	1.27681e8			0.951295
$65$		−	3.18298e8i		−	2.21169i
$66$	−4.02432e7			−0.261063
$67$	3.50040e7			0.212217			0.106109	−	0.994355i	$-0.466161\pi$
$67$	3.50040e7			0.212217			0.106109	+	0.994355i	$0.466161\pi$
$68$	−5.90284e7	+	5.34973e7i	−0.334789	+	0.303418i
$69$	−2.84165e8			−1.50921
$70$	5.32560e7			0.265111
$71$		−	2.90407e8i		−	1.35626i	−0.734940	−	0.678132i	$-0.762790\pi$
$71$		−	2.90407e8i		−	1.35626i	0.734940	−	0.678132i	$-0.237210\pi$
$72$	−2.86773e8			−1.25760
$73$			4.29259e8i			1.76916i	0.466392	+	0.884578i	$0.345554\pi$
$73$			4.29259e8i			1.76916i	−0.466392	+	0.884578i	$0.654446\pi$
$74$			9.74069e7i			0.377613i
$75$		−	3.79217e8i		−	1.38392i
$76$	−1.55804e8			−0.535693
$77$	1.89843e7			0.0615440
$78$			5.66229e8i			1.73207i
$79$		−	3.78639e8i		−	1.09371i	−0.837226	−	0.546856i	$-0.815824\pi$
$79$		−	3.78639e8i		−	1.09371i	0.837226	−	0.546856i	$-0.184176\pi$
$80$		−	1.75526e8i		−	0.479112i
$81$	−3.10387e8			−0.801164
$82$		−	3.98142e8i		−	0.972468i
$83$	9.91655e7			0.229355			0.114678	−	0.993403i	$-0.463416\pi$
$83$	9.91655e7			0.229355			0.114678	+	0.993403i	$0.463416\pi$
$84$	7.80868e7			0.171128
$85$	4.50089e8	+	4.96625e8i	0.935219	+	1.03191i
$86$	4.12423e8			0.813017
$87$	8.94715e8			1.67436
$88$		−	1.44746e8i		−	0.257297i
$89$	−5.39631e8			−0.911679			−0.455840	−	0.890062i	$-0.650661\pi$
$89$	−5.39631e8			−0.911679			−0.455840	+	0.890062i	$0.650661\pi$
$90$			7.50864e8i			1.20634i
$91$		−	2.67112e8i		−	0.408326i
$92$		−	3.18083e8i		−	0.462908i
$93$	−7.13453e8			−0.988991
$94$	6.60166e8			0.872123
$95$			1.31082e9i			1.65116i
$96$		−	1.00546e9i		−	1.20822i
$97$			1.21632e9i			1.39500i	0.716582	+	0.697502i	$0.245705\pi$
$97$			1.21632e9i			1.39500i	−0.716582	+	0.697502i	$0.754295\pi$
$98$	−6.31355e8			−0.691443
$99$			2.67662e8i			0.280046i
$100$	4.24481e8			0.424481
$101$	1.24853e9			1.19386			0.596928	−	0.802295i	$-0.296388\pi$
$101$	1.24853e9			1.19386			0.596928	+	0.802295i	$0.296388\pi$
$102$	−8.00675e8	−	8.83458e8i	−0.732412	−	0.808137i
$103$	5.96498e7			0.0522206			0.0261103	−	0.999659i	$-0.491688\pi$
$103$	5.96498e7			0.0522206			0.0261103	+	0.999659i	$0.491688\pi$
$104$	−2.03660e9			−1.70709
$105$		−	6.56969e8i		−	0.527464i
$106$	1.61990e9			1.24627
$107$		−	1.08084e9i		−	0.797143i	−0.917137	−	0.398572i	$-0.869506\pi$
$107$		−	1.08084e9i		−	0.797143i	0.917137	−	0.398572i	$-0.130494\pi$
$108$			1.59930e8i			0.113116i
$109$			1.42610e9i			0.967678i	0.875157	+	0.483839i	$0.160758\pi$
$109$			1.42610e9i			0.967678i	−0.875157	+	0.483839i	$0.839242\pi$
$110$	−3.78992e8			−0.246810
$111$	1.20162e9			0.751299
$112$		−	1.47299e8i		−	0.0884544i
$113$		−	4.16774e8i		−	0.240463i	−0.992746	−	0.120231i	$-0.961636\pi$
$113$		−	4.16774e8i		−	0.240463i	0.992746	−	0.120231i	$-0.0383636\pi$
$114$		−	2.33186e9i		−	1.29309i
$115$	−2.67613e9			−1.42681
$116$			1.00151e9i			0.513563i
$117$	3.76605e9			1.85802
$118$	−3.97472e8			−0.188729
$119$	3.77709e8	+	4.16761e8i	0.172662	+	0.190514i
$120$	−5.00907e9			−2.20517
$121$	2.22285e9			0.942704
$122$		−	7.23125e8i		−	0.295525i
$123$	−4.91150e9			−1.93482
$124$		−	7.98611e8i		−	0.303346i
$125$			2.30059e8i			0.0842839i
$126$			6.30116e8i			0.222717i
$127$	3.27631e8			0.111755			0.0558777	−	0.998438i	$-0.482204\pi$
$127$	3.27631e8			0.111755			0.0558777	+	0.998438i	$0.482204\pi$
$128$	3.51905e8			0.115873
$129$		−	5.08767e9i		−	1.61758i
$130$			5.33247e9i			1.63751i
$131$			3.69810e8i			0.109713i	0.998494	+	0.0548565i	$0.0174701\pi$
$131$			3.69810e8i			0.109713i	−0.998494	+	0.0548565i	$0.982530\pi$
$132$	−5.55698e8			−0.159315
$133$			1.10003e9i			0.304839i
$134$	−5.86424e8			−0.157123
$135$	1.34554e9			0.348654
$136$	3.17760e9	−	2.87985e9i	0.796479	−	0.721846i
$137$	1.59553e9			0.386957			0.193478	−	0.981105i	$-0.438023\pi$
$137$	1.59553e9			0.386957			0.193478	+	0.981105i	$0.438023\pi$
$138$	4.76063e9			1.11740
$139$			6.26171e9i			1.42274i	0.702817	+	0.711371i	$0.251925\pi$
$139$			6.26171e9i			1.42274i	−0.702817	+	0.711371i	$0.748075\pi$
$140$	7.35385e8			0.161785
$141$		−	8.14384e9i		−	1.73518i
$142$			4.86521e9i			1.00416i
$143$			1.90088e9i			0.380139i
$144$	2.07679e9			0.402497
$145$	8.42600e9			1.58294
$146$		−	7.19140e9i		−	1.30986i
$147$			7.78843e9i			1.37569i
$148$			1.34504e9i			0.230440i
$149$	−6.90664e9			−1.14796			−0.573982	−	0.818868i	$-0.694602\pi$
$149$	−6.90664e9			−1.14796			−0.573982	+	0.818868i	$0.694602\pi$
$150$			6.35305e9i			1.02464i
$151$	−8.82900e9			−1.38202			−0.691012	−	0.722843i	$-0.742835\pi$
$151$	−8.82900e9			−1.38202			−0.691012	+	0.722843i	$0.742835\pi$
$152$	8.38717e9			1.27444
$153$	−5.87598e9	+	5.32538e9i	−0.866899	+	0.785668i
$154$	−3.18045e8			−0.0455665
$155$	−6.71897e9			−0.934996
$156$			7.81876e9i			1.05701i
$157$	6.94492e8			0.0912261			0.0456130	−	0.998959i	$-0.485476\pi$
$157$	6.94492e8			0.0912261			0.0456130	+	0.998959i	$0.485476\pi$
$158$			6.34336e9i			0.809772i
$159$		−	1.99832e10i		−	2.47958i
$160$		−	9.46896e9i		−	1.14225i
$161$	−2.24577e9			−0.263420
$162$	5.19994e9			0.593172
$163$		−	1.05314e10i		−	1.16854i	−0.811559	−	0.584270i	$-0.801381\pi$
$163$		−	1.05314e10i		−	1.16854i	0.811559	−	0.584270i	$-0.198619\pi$
$164$		−	5.49774e9i		−	0.593454i
$165$			4.67526e9i			0.491053i
$166$	−1.66133e9			−0.169812
$167$		−	1.06743e10i		−	1.06198i	−0.847378	−	0.530990i	$-0.821820\pi$
$167$		−	1.06743e10i		−	1.06198i	0.847378	−	0.530990i	$-0.178180\pi$
$168$	−4.20355e9			−0.407122
$169$	1.61412e10			1.52210
$170$	−7.54038e9	−	8.31999e9i	−0.692425	−	0.764016i
$171$	−1.55094e10			−1.38712
$172$	5.69494e9			0.496148
$173$			5.38138e9i			0.456758i	0.973572	+	0.228379i	$0.0733425\pi$
$173$			5.38138e9i			0.456758i	−0.973572	+	0.228379i	$0.926657\pi$
$174$	−1.49892e10			−1.23967
$175$		−	2.99698e9i		−	0.241553i
$176$			1.04824e9i			0.0823484i
$177$			4.90324e9i			0.375494i
$178$	9.04048e9			0.674996
$179$	−1.10785e10			−0.806573			−0.403286	−	0.915074i	$-0.632132\pi$
$179$	−1.10785e10			−0.806573			−0.403286	+	0.915074i	$0.632132\pi$
$180$			1.03683e10i			0.736176i
$181$			1.10717e10i			0.766761i	0.923591	+	0.383380i	$0.125240\pi$
$181$			1.10717e10i			0.766761i	−0.923591	+	0.383380i	$0.874760\pi$
$182$			4.47494e9i			0.302320i
$183$	−8.92051e9			−0.587976
$184$			1.71229e10i			1.10128i
$185$	1.13163e10			0.710281
$186$	1.19525e10			0.732237
$187$	−2.68793e9	−	2.96584e9i	−0.160743	−	0.177362i
$188$	9.11589e9			0.532217
$189$	1.12916e9			0.0643691
$190$		−	2.19603e10i		−	1.22250i
$191$	1.39536e10			0.758642			0.379321	−	0.925265i	$-0.376158\pi$
$191$	1.39536e10			0.758642			0.379321	+	0.925265i	$0.376158\pi$
$192$			2.63873e10i			1.40133i
$193$		−	4.25693e9i		−	0.220845i	−0.993885	−	0.110423i	$-0.964780\pi$
$193$		−	4.25693e9i		−	0.220845i	0.993885	−	0.110423i	$-0.0352205\pi$
$194$		−	2.03771e10i		−	1.03285i
$195$	6.57817e10			3.25799
$196$	−8.71806e9			−0.421956
$197$			3.75774e10i			1.77758i	0.458317	+	0.888789i	$0.348452\pi$
$197$			3.75774e10i			1.77758i	−0.458317	+	0.888789i	$0.651548\pi$
$198$		−	4.48417e9i		−	0.207342i
$199$		−	8.68102e9i		−	0.392403i	−0.980564	−	0.196201i	$-0.937139\pi$
$199$		−	8.68102e9i		−	0.392403i	0.980564	−	0.196201i	$-0.0628606\pi$
$200$	−2.28505e10			−1.00986
$201$			7.23416e9i			0.312612i
$202$	−2.09167e10			−0.883916
$203$	7.07099e9			0.292246
$204$	−1.10561e10	−	1.21992e10i	−0.446958	−	0.493170i
$205$	−4.62542e10			−1.82919
$206$	−9.99318e8			−0.0386635
$207$		−	3.16635e10i		−	1.19865i
$208$	1.47489e10			0.546356
$209$		−	7.82825e9i		−	0.283796i
$210$			1.10062e10i			0.390528i
$211$			3.93859e10i			1.36795i	0.729507	+	0.683974i	$0.239750\pi$
$211$			3.93859e10i			1.36795i	−0.729507	+	0.683974i	$0.760250\pi$
$212$	2.23684e10			0.760543
$213$	6.00175e10			1.99788
$214$			1.81075e10i			0.590195i
$215$		−	4.79133e10i		−	1.52927i
$216$		−	8.60930e9i		−	0.269108i
$217$	−5.63847e9			−0.172621
$218$		−	2.38916e10i		−	0.716457i
$219$	−8.87135e10			−2.60610
$220$	−5.23330e9			−0.150617
$221$	−4.17299e10	+	3.78197e10i	−1.17674	+	1.06648i
$222$	−2.01308e10			−0.556253
$223$	2.60341e9			0.0704971			0.0352486	−	0.999379i	$-0.488778\pi$
$223$	2.60341e9			0.0704971			0.0352486	+	0.999379i	$0.488778\pi$
$224$		−	7.94623e9i		−	0.210885i
$225$	4.22549e10			1.09915
$226$			6.98225e9i			0.178036i
$227$			6.62728e10i			1.65660i	0.560282	+	0.828302i	$0.310693\pi$
$227$			6.62728e10i			1.65660i	−0.560282	+	0.828302i	$0.689307\pi$
$228$		−	3.21994e10i		−	0.789117i
$229$	−1.37362e10			−0.330071			−0.165036	−	0.986288i	$-0.552774\pi$
$229$	−1.37362e10			−0.330071			−0.165036	+	0.986288i	$0.552774\pi$
$230$	4.48334e10			1.05639
$231$			3.92342e9i			0.0906590i
$232$		−	5.39129e10i		−	1.22179i
$233$			8.93389e9i			0.198582i	0.995058	+	0.0992908i	$0.0316574\pi$
$233$			8.93389e9i			0.198582i	−0.995058	+	0.0992908i	$0.968343\pi$
$234$	−6.30929e10			−1.37565
$235$		−	7.66948e10i		−	1.64044i
$236$	−5.48849e9			−0.115173
$237$	7.82521e10			1.61112
$238$	−6.32779e9	−	6.98203e9i	−0.127837	−	0.141054i
$239$	1.31552e10			0.260800			0.130400	−	0.991461i	$-0.458374\pi$
$239$	1.31552e10			0.260800			0.130400	+	0.991461i	$0.458374\pi$
$240$	3.62754e10			0.705768
$241$		−	3.35182e9i		−	0.0640036i	−0.999488	−	0.0320018i	$-0.989812\pi$
$241$		−	3.35182e9i		−	0.0640036i	0.999488	−	0.0320018i	$-0.0101882\pi$
$242$	−3.72395e10			−0.697967
$243$		−	7.77543e10i		−	1.43053i
$244$		−	9.98526e9i		−	0.180346i
$245$			7.33478e10i			1.30059i
$246$	8.22827e10			1.43252
$247$	−1.10145e11			−1.88290
$248$			4.29906e10i			0.721674i
$249$			2.04942e10i			0.337858i
$250$		−	3.85420e9i		−	0.0624028i
$251$	−1.16052e9			−0.0184553			−0.00922766	−	0.999957i	$-0.502937\pi$
$251$	−1.16052e9			−0.0184553			−0.00922766	+	0.999957i	$0.502937\pi$
$252$			8.70095e9i			0.135914i
$253$	1.59819e10			0.245236
$254$	−5.48883e9			−0.0827424
$255$	−1.02636e11	+	9.30185e10i	−1.52009	+	1.37765i
$256$	−7.12680e10			−1.03709
$257$	1.16697e11			1.66864			0.834319	−	0.551282i	$-0.185861\pi$
$257$	1.16697e11			1.66864			0.834319	+	0.551282i	$0.185861\pi$
$258$			8.52341e10i			1.19764i
$259$	9.49646e9			0.131133
$260$			7.36334e10i			0.999298i
$261$			9.96950e10i			1.32981i
$262$		−	6.19546e9i		−	0.0812302i
$263$	1.29675e11			1.67130			0.835652	−	0.549259i	$-0.185090\pi$
$263$	1.29675e11			1.67130			0.835652	+	0.549259i	$0.185090\pi$
$264$	2.99142e10			0.379018
$265$		−	1.88193e11i		−	2.34421i
$266$		−	1.84288e10i		−	0.225699i
$267$		−	1.11524e11i		−	1.34297i
$268$	−8.09763e9			−0.0958852
$269$		−	4.33626e10i		−	0.504928i	−0.967606	−	0.252464i	$-0.918759\pi$
$269$		−	4.33626e10i		−	0.504928i	0.967606	−	0.252464i	$-0.0812410\pi$
$270$	−2.25419e10			−0.258139
$271$	1.14864e11			1.29367			0.646834	−	0.762631i	$-0.276093\pi$
$271$	1.14864e11			1.29367			0.646834	+	0.762631i	$0.276093\pi$
$272$	−2.30120e10	+	2.08557e10i	−0.254915	+	0.231028i
$273$	5.52032e10			0.601495
$274$	−2.67300e10			−0.286498
$275$			2.13278e10i			0.224879i
$276$	6.57371e10			0.681899
$277$			9.76316e10i			0.996395i	0.867064	+	0.498197i	$0.166004\pi$
$277$			9.76316e10i			0.996395i	−0.867064	+	0.498197i	$0.833996\pi$
$278$		−	1.04903e11i		−	1.05338i
$279$		−	7.94977e10i		−	0.785481i
$280$	−3.95870e10			−0.384895
$281$	1.09933e11			1.05184			0.525921	−	0.850534i	$-0.323721\pi$
$281$	1.09933e11			1.05184			0.525921	+	0.850534i	$0.323721\pi$
$282$			1.36434e11i			1.28470i
$283$			1.55506e11i			1.44115i	0.693378	+	0.720574i	$0.256122\pi$
$283$			1.55506e11i			1.44115i	−0.693378	+	0.720574i	$0.743878\pi$
$284$			6.71812e10i			0.612795i
$285$	−2.70904e11			−2.43228
$286$		−	3.18456e10i		−	0.281450i
$287$	−3.88159e10			−0.337708
$288$	1.12035e11			0.959595
$289$	1.16302e10	−	1.18016e11i	0.0980726	−	0.995179i
$290$	−1.41161e11			−1.17199
$291$	−2.51373e11			−2.05495
$292$		−	9.93024e10i		−	0.799350i
$293$	−1.34231e11			−1.06402			−0.532010	−	0.846738i	$-0.678563\pi$
$293$	−1.34231e11			−1.06402			−0.532010	+	0.846738i	$0.678563\pi$
$294$		−	1.30480e11i		−	1.01855i
$295$			4.61764e10i			0.354994i
$296$		−	7.24059e10i		−	0.548228i
$297$	−8.03557e9			−0.0599257
$298$	1.15707e11			0.849939
$299$		−	2.24867e11i		−	1.62707i
$300$			8.77261e10i			0.625292i
$301$		−	4.02082e10i		−	0.282336i
$302$	1.47913e11			1.02323
$303$			2.58029e11i			1.75864i
$304$	−6.07394e10			−0.407887
$305$	−8.40091e10			−0.555875
$306$	9.84407e10	−	8.92164e10i	0.641842	−	0.581699i
$307$	−1.61753e11			−1.03927			−0.519637	−	0.854387i	$-0.673933\pi$
$307$	−1.61753e11			−1.03927			−0.519637	+	0.854387i	$0.673933\pi$
$308$	−4.39172e9			−0.0278072
$309$			1.23276e10i			0.0769249i
$310$	1.12563e11			0.692260
$311$		−	8.13115e10i		−	0.492867i	−0.969160	−	0.246434i	$-0.920741\pi$
$311$		−	8.13115e10i		−	0.492867i	0.969160	−	0.246434i	$-0.0792587\pi$
$312$		−	4.20897e11i		−	2.51467i
$313$			1.35663e11i			0.798935i	0.916747	+	0.399467i	$0.130805\pi$
$313$			1.35663e11i			0.798935i	−0.916747	+	0.399467i	$0.869195\pi$
$314$	−1.16349e10			−0.0675427
$315$	7.32038e10			0.418925
$316$			8.75923e10i			0.494167i
$317$		−	1.13377e11i		−	0.630604i	−0.948991	−	0.315302i	$-0.897894\pi$
$317$		−	1.13377e11i		−	0.630604i	0.948991	−	0.315302i	$-0.102106\pi$
$318$			3.34780e11i			1.83585i
$319$	−5.03201e10			−0.272072
$320$			2.48504e11i			1.32482i
$321$	2.23375e11			1.17425
$322$	3.76236e10			0.195033
$323$	1.71853e11	−	1.55750e11i	0.878509	−	0.796189i
$324$	7.18033e10			0.361986
$325$	3.00085e11			1.49200
$326$			1.76434e11i			0.865173i
$327$	−2.94728e11			−1.42546
$328$			2.95953e11i			1.41185i
$329$		−	6.43613e10i		−	0.302861i
$330$		−	7.83250e10i		−	0.363570i
$331$	1.63912e11			0.750557			0.375279	−	0.926912i	$-0.377547\pi$
$331$	1.63912e11			0.750557			0.375279	+	0.926912i	$0.377547\pi$
$332$	−2.29404e10			−0.103629
$333$			1.33892e11i			0.596699i
$334$			1.78828e11i			0.786277i
$335$			6.81279e10i			0.295545i
$336$	3.04419e10			0.130300
$337$			1.21263e11i			0.512146i	0.966657	+	0.256073i	$0.0824288\pi$
$337$			1.21263e11i			0.512146i	−0.966657	+	0.256073i	$0.917571\pi$
$338$	−2.70414e11			−1.12695
$339$	8.61334e10			0.354220
$340$	−1.04121e11	−	1.14886e11i	−0.422556	−	0.466245i
$341$	4.01257e10			0.160704
$342$	2.59831e11			1.02701
$343$			1.27462e11i			0.497230i
$344$	−3.06568e11			−1.18036
$345$		−	5.53067e11i		−	2.10180i
$346$		−	9.01547e10i		−	0.338178i
$347$		−	9.25071e10i		−	0.342525i	−0.985225	−	0.171263i	$-0.945215\pi$
$347$		−	9.25071e10i		−	0.342525i	0.985225	−	0.171263i	$-0.0547846\pi$
$348$	−2.06979e11			−0.756517
$349$	−1.54729e11			−0.558285			−0.279143	−	0.960250i	$-0.590050\pi$
$349$	−1.54729e11			−0.558285			−0.279143	+	0.960250i	$0.590050\pi$
$350$			5.02086e10i			0.178843i
$351$			1.13062e11i			0.397588i
$352$			5.65487e10i			0.196327i
$353$	−7.41434e9			−0.0254148			−0.0127074	−	0.999919i	$-0.504045\pi$
$353$	−7.41434e9			−0.0254148			−0.0127074	+	0.999919i	$0.504045\pi$
$354$		−	8.21443e10i		−	0.278012i
$355$	5.65216e11			1.88881
$356$	1.24835e11			0.411920
$357$	−8.61307e10	+	7.80599e10i	−0.280641	+	0.254344i
$358$	1.85599e11			0.597177
$359$	−3.11894e11			−0.991019			−0.495509	−	0.868603i	$-0.665019\pi$
$359$	−3.11894e11			−0.991019			−0.495509	+	0.868603i	$0.665019\pi$
$360$		−	5.58143e11i		−	1.75140i
$361$	1.30913e11			0.405694
$362$		−	1.85485e11i		−	0.567701i
$363$			4.59389e11i			1.38868i
$364$			6.17922e10i			0.184492i
$365$	−8.35462e11			−2.46382
$366$	1.49446e11			0.435331
$367$		−	3.42287e11i		−	0.984902i	−0.870340	−	0.492451i	$-0.836101\pi$
$367$		−	3.42287e11i		−	0.984902i	0.870340	−	0.492451i	$-0.163899\pi$
$368$		−	1.24003e11i		−	0.352467i
$369$		−	5.47272e11i		−	1.53668i
$370$	−1.89582e11			−0.525883
$371$		−	1.57929e11i		−	0.432791i
$372$	1.65046e11			0.446851
$373$	2.39957e11			0.641866			0.320933	−	0.947102i	$-0.396004\pi$
$373$	2.39957e11			0.641866			0.320933	+	0.947102i	$0.396004\pi$
$374$	4.50312e10	+	4.96870e10i	0.119012	+	0.131317i
$375$	−4.75456e10			−0.124157
$376$	−4.90724e11			−1.26617
$377$			7.08012e11i			1.80511i
$378$	−1.89169e10			−0.0476581
$379$			7.31981e11i			1.82231i	0.412060	+	0.911157i	$0.364809\pi$
$379$			7.31981e11i			1.82231i	−0.412060	+	0.911157i	$0.635191\pi$
$380$		−	3.03239e11i		−	0.746034i
$381$			6.77105e10i			0.164624i
$382$	−2.33766e11			−0.561689
$383$	−3.51103e10			−0.0833758			−0.0416879	−	0.999131i	$-0.513274\pi$
$383$	−3.51103e10			−0.0833758			−0.0416879	+	0.999131i	$0.513274\pi$
$384$			7.27271e10i			0.170689i
$385$			3.69489e10i			0.0857094i
$386$			7.13166e10i			0.163511i
$387$	5.66902e11			1.28472
$388$		−	2.81377e11i		−	0.630299i
$389$	−4.06726e10			−0.0900593			−0.0450297	−	0.998986i	$-0.514338\pi$
$389$	−4.06726e10			−0.0900593			−0.0450297	+	0.998986i	$0.514338\pi$
$390$	−1.10205e12			−2.41217
$391$	3.17973e11	+	3.50849e11i	0.688010	+	0.759145i
$392$	4.69308e11			1.00385
$393$	−7.64275e10			−0.161616
$394$		−	6.29537e11i		−	1.31610i
$395$	7.36941e11			1.52316
$396$		−	6.19196e10i		−	0.126532i
$397$			8.82945e11i			1.78392i	0.452110	+	0.891962i	$0.350672\pi$
$397$			8.82945e11i			1.78392i	−0.452110	+	0.891962i	$0.649328\pi$
$398$			1.45434e11i			0.290530i
$399$	−2.27339e11			−0.449051
$400$	1.65482e11			0.323208
$401$		−	5.06461e11i		−	0.978130i	−0.872247	−	0.489065i	$-0.837338\pi$
$401$		−	5.06461e11i		−	0.978130i	0.872247	−	0.489065i	$-0.162662\pi$
$402$		−	1.21194e11i		−	0.231454i
$403$		−	5.64575e11i		−	1.06622i
$404$	−2.88827e11			−0.539414
$405$		−	6.04104e11i		−	1.11574i
$406$	−1.18461e11			−0.216375
$407$	−6.75807e10			−0.122081
$408$	5.95169e11	+	6.56705e11i	1.06333	+	1.17327i
$409$	5.97268e11			1.05539			0.527697	−	0.849433i	$-0.323056\pi$
$409$	5.97268e11			1.05539			0.527697	+	0.849433i	$0.323056\pi$
$410$	7.74900e11			1.35431
$411$			3.29743e11i			0.570016i
$412$	−1.37991e10			−0.0235946
$413$			3.87506e10i			0.0655396i
$414$			5.30461e11i			0.887466i
$415$			1.93005e11i			0.319412i
$416$	7.95648e11			1.30257
$417$	−1.29409e12			−2.09581
$418$			1.31147e11i			0.210119i
$419$		−	6.76816e11i		−	1.07277i	−0.843972	−	0.536386i	$-0.819789\pi$
$419$		−	6.76816e11i		−	1.07277i	0.843972	−	0.536386i	$-0.180211\pi$
$420$			1.51980e11i			0.238322i
$421$	4.95533e11			0.768782			0.384391	−	0.923170i	$-0.374411\pi$
$421$	4.95533e11			0.768782			0.384391	+	0.923170i	$0.374411\pi$
$422$		−	6.59834e11i		−	1.01281i
$423$	9.07440e11			1.37812
$424$	−1.20413e12			−1.80937
$425$	−4.68207e11	+	4.24334e11i	−0.696126	+	0.630897i
$426$	−1.00548e12			−1.47921
$427$	−7.04994e10			−0.102627
$428$			2.50037e11i			0.360169i
$429$	−3.92849e11			−0.559973
$430$			8.02695e11i			1.13225i
$431$		−	1.02852e11i		−	0.143571i	−0.997420	−	0.0717854i	$-0.977130\pi$
$431$		−	1.02852e11i		−	0.143571i	0.997420	−	0.0717854i	$-0.0228697\pi$
$432$			6.23481e10i			0.0861284i
$433$	−2.70612e10			−0.0369957			−0.0184978	−	0.999829i	$-0.505888\pi$
$433$	−2.70612e10			−0.0369957			−0.0184978	+	0.999829i	$0.505888\pi$
$434$	9.44617e10			0.127806
$435$			1.74138e12i			2.33180i
$436$		−	3.29906e11i		−	0.437222i
$437$			9.26053e11i			1.21470i
$438$	1.48622e12			1.92953
$439$		−	5.59050e11i		−	0.718390i	−0.933263	−	0.359195i	$-0.883051\pi$
$439$		−	5.59050e11i		−	0.718390i	0.933263	−	0.359195i	$-0.116949\pi$
$440$	2.81718e11			0.358325
$441$	−8.67838e11			−1.09261
$442$	6.99104e11	−	6.33595e11i	0.871247	−	0.789608i
$443$	4.39616e11			0.542321			0.271161	−	0.962534i	$-0.412593\pi$
$443$	4.39616e11			0.542321			0.271161	+	0.962534i	$0.412593\pi$
$444$	−2.77976e11			−0.339456
$445$		−	1.05028e12i		−	1.26965i
$446$	−4.36152e10			−0.0521952
$447$		−	1.42737e12i		−	1.69104i
$448$			2.08541e11i			0.244591i
$449$		−	3.20262e11i		−	0.371874i	−0.982562	−	0.185937i	$-0.940468\pi$
$449$		−	3.20262e11i		−	0.371874i	0.982562	−	0.185937i	$-0.0595321\pi$
$450$	−7.07899e11			−0.813795
$451$	2.76230e11			0.314396
$452$			9.64143e10i			0.108647i
$453$		−	1.82466e12i		−	2.03583i
$454$		−	1.11027e12i		−	1.22653i
$455$	5.19877e11			0.568656
$456$			1.73335e12i			1.87735i
$457$	−1.12742e12			−1.20910			−0.604550	−	0.796567i	$-0.706647\pi$
$457$	−1.12742e12			−1.20910			−0.604550	+	0.796567i	$0.706647\pi$
$458$	2.30124e11			0.244381
$459$	−1.59875e11	−	1.76405e11i	−0.168121	−	0.185504i
$460$	6.19081e11			0.644670
$461$	−1.06579e12			−1.09905			−0.549523	−	0.835478i	$-0.685191\pi$
$461$	−1.06579e12			−1.09905			−0.549523	+	0.835478i	$0.685191\pi$
$462$		−	6.57294e10i		−	0.0671229i
$463$	2.47213e11			0.250010			0.125005	−	0.992156i	$-0.460105\pi$
$463$	2.47213e11			0.250010			0.125005	+	0.992156i	$0.460105\pi$
$464$			3.90434e11i			0.391036i
$465$		−	1.38859e12i		−	1.37732i
$466$		−	1.49670e11i		−	0.147027i
$467$	−1.64486e12			−1.60030			−0.800151	−	0.599799i	$-0.795247\pi$
$467$	−1.64486e12			−1.60030			−0.800151	+	0.599799i	$0.795247\pi$
$468$	−8.71218e11			−0.839499
$469$			5.71721e10i			0.0545640i
$470$			1.28487e12i			1.21456i
$471$			1.43528e11i			0.134383i
$472$	2.95455e11			0.274001
$473$			2.86138e11i			0.262846i
$474$	−1.31096e12			−1.19286
$475$	−1.23582e12			−1.11387
$476$	−8.73772e10	−	9.64113e10i	−0.0780130	−	0.0860789i
$477$	2.22666e12			1.96934
$478$	−2.20390e11			−0.193093
$479$		−	5.67060e11i		−	0.492175i	−0.969248	−	0.246087i	$-0.920855\pi$
$479$		−	5.67060e11i		−	0.492175i	0.969248	−	0.246087i	$-0.0791450\pi$
$480$	1.95692e12			1.68263
$481$			9.50872e11i			0.809970i
$482$			5.61533e10i			0.0473875i
$483$		−	4.64127e11i		−	0.388038i
$484$	−5.14222e11			−0.425938
$485$	−2.36732e12			−1.94276
$486$			1.30262e12i			1.05915i
$487$			2.01812e12i			1.62580i	0.582402	+	0.812901i	$0.302113\pi$
$487$			2.01812e12i			1.62580i	−0.582402	+	0.812901i	$0.697887\pi$
$488$			5.37524e11i			0.429051i
$489$	2.17650e12			1.72135
$490$		−	1.22880e12i		−	0.962939i
$491$	1.15865e12			0.899672			0.449836	−	0.893111i	$-0.351482\pi$
$491$	1.15865e12			0.899672			0.449836	+	0.893111i	$0.351482\pi$
$492$	1.13620e12			0.874202
$493$	−1.00116e12	−	1.10468e12i	−0.763297	−	0.842216i
$494$	1.84526e12			1.39408
$495$	−5.20949e11			−0.390006
$496$		−	3.11336e11i		−	0.230973i
$497$	4.74322e11			0.348714
$498$		−	3.43341e11i		−	0.250146i
$499$		−	2.89972e11i		−	0.209365i	−0.994506	−	0.104682i	$-0.966617\pi$
$499$		−	2.89972e11i		−	0.209365i	0.994506	−	0.104682i	$-0.0333826\pi$
$500$		−	5.32206e10i		−	0.0380816i
$501$	2.20603e12			1.56438
$502$	1.94423e10			0.0136641
$503$			3.27029e11i			0.227788i	0.993493	+	0.113894i	$0.0363324\pi$
$503$			3.27029e11i			0.227788i	−0.993493	+	0.113894i	$0.963668\pi$
$504$		−	4.68387e11i		−	0.323346i
$505$			2.43000e12i			1.66262i
$506$	−2.67745e11			−0.181570
$507$			3.33584e12i			2.24218i
$508$	−7.57924e10			−0.0504939
$509$	5.42106e11			0.357976			0.178988	−	0.983851i	$-0.442718\pi$
$509$	5.42106e11			0.357976			0.178988	+	0.983851i	$0.442718\pi$
$510$	1.71947e12	−	1.55835e12i	1.12545	−	1.01999i
$511$	−7.01109e11			−0.454875
$512$	1.01378e12			0.651973
$513$		−	4.65614e11i		−	0.296823i
$514$	−1.95504e12			−1.23544
$515$			1.16096e11i			0.0727251i
$516$			1.17695e12i			0.730863i
$517$			4.58022e11i			0.281954i
$518$	−1.59095e11			−0.0970895
$519$	−1.11215e12			−0.672839
$520$		−	3.96381e12i		−	2.37738i
$521$			7.31594e11i			0.435011i	0.976059	+	0.217506i	$0.0697920\pi$
$521$			7.31594e11i			0.435011i	−0.976059	+	0.217506i	$0.930208\pi$
$522$		−	1.67020e12i		−	0.984579i
$523$	−6.27765e11			−0.366893			−0.183447	−	0.983030i	$-0.558725\pi$
$523$	−6.27765e11			−0.366893			−0.183447	+	0.983030i	$0.558725\pi$
$524$		−	8.55499e10i		−	0.0495711i
$525$	6.19376e11			0.355826
$526$	−2.17245e12			−1.23741
$527$	7.98336e11	+	8.80878e11i	0.450856	+	0.497471i
$528$	−2.16637e11			−0.121305
$529$	−8.94434e10			−0.0496590
$530$			3.15280e12i			1.73562i
$531$	−5.46351e11			−0.298227
$532$		−	2.54474e11i		−	0.137734i
$533$		−	3.88660e12i		−	2.08592i
$534$			1.86837e12i			0.994321i
$535$	2.10364e12			1.11014
$536$	4.35909e11			0.228115
$537$		−	2.28957e12i		−	1.18814i
$538$			7.26456e11i			0.373843i
$539$		−	4.38033e11i		−	0.223541i
$540$	−3.11270e11			−0.157531
$541$		−	9.88955e11i		−	0.496351i	−0.968715	−	0.248176i	$-0.920169\pi$
$541$		−	9.88955e11i		−	0.496351i	0.968715	−	0.248176i	$-0.0798310\pi$
$542$	−1.92433e12			−0.957816
$543$	−2.28815e12			−1.12950
$544$	−1.24141e12	+	1.12509e12i	−0.607743	+	0.550796i
$545$	−2.77561e12			−1.34764
$546$	−9.24822e11			−0.445340
$547$			1.80571e12i			0.862394i	0.902258	+	0.431197i	$0.141909\pi$
$547$			1.80571e12i			0.862394i	−0.902258	+	0.431197i	$0.858091\pi$
$548$	−3.69101e11			−0.174837
$549$		−	9.93982e11i		−	0.466985i
$550$		−	3.57305e11i		−	0.166497i
$551$		−	2.91575e12i		−	1.34762i
$552$	−3.53874e12			−1.62227
$553$	6.18432e11			0.281209
$554$		−	1.63563e12i		−	0.737719i
$555$			2.33869e12i			1.04630i
$556$		−	1.44855e12i		−	0.642831i
$557$	3.45273e12			1.51990			0.759949	−	0.649982i	$-0.225224\pi$
$557$	3.45273e12			1.51990			0.759949	+	0.649982i	$0.225224\pi$
$558$			1.33183e12i			0.581560i
$559$	4.02601e12			1.74390
$560$	2.86687e11			0.123186
$561$	6.12942e11	−	5.55507e11i	0.261268	−	0.236786i
$562$	−1.84172e12			−0.778771
$563$	6.22962e11			0.261321			0.130660	−	0.991427i	$-0.458290\pi$
$563$	6.22962e11			0.261321			0.130660	+	0.991427i	$0.458290\pi$
$564$			1.88395e12i			0.783996i
$565$	8.11163e11			0.334881
$566$		−	2.60521e12i		−	1.06701i
$567$		−	5.06956e11i		−	0.205990i
$568$		−	3.61648e12i		−	1.45787i
$569$	−6.19292e11			−0.247680			−0.123840	−	0.992302i	$-0.539521\pi$
$569$	−6.19292e11			−0.247680			−0.123840	+	0.992302i	$0.539521\pi$
$570$	4.53847e12			1.80083
$571$		−	7.93244e11i		−	0.312280i	−0.987735	−	0.156140i	$-0.950095\pi$
$571$		−	7.93244e11i		−	0.312280i	0.987735	−	0.156140i	$-0.0499051\pi$
$572$		−	4.39739e11i		−	0.171756i
$573$			2.88375e12i			1.11754i
$574$	6.50286e11			0.250035
$575$		−	2.52300e12i		−	0.962524i
$576$	−2.94025e12			−1.11297
$577$	1.65552e12			0.621790			0.310895	−	0.950444i	$-0.399371\pi$
$577$	1.65552e12			0.621790			0.310895	+	0.950444i	$0.399371\pi$
$578$	−1.94842e11	+	1.97713e12i	−0.0726118	+	0.736819i
$579$	8.79765e11			0.325322
$580$	−1.94923e12			−0.715214
$581$			1.61967e11i			0.0589704i
$582$	4.21128e12			1.52146
$583$			1.12389e12i			0.402916i
$584$			5.34562e12i			1.90169i
$585$			7.32983e12i			2.58757i
$586$	2.24879e12			0.787788
$587$	−1.55182e12			−0.539473			−0.269736	−	0.962934i	$-0.586937\pi$
$587$	−1.55182e12			−0.539473			−0.269736	+	0.962934i	$0.586937\pi$
$588$		−	1.80173e12i		−	0.621574i
$589$			2.32505e12i			0.795999i
$590$		−	7.73596e11i		−	0.262833i
$591$	−7.76600e12			−2.61851
$592$			5.24360e11i			0.175461i
$593$	−6.74726e10			−0.0224069			−0.0112034	−	0.999937i	$-0.503566\pi$
$593$	−6.74726e10			−0.0224069			−0.0112034	+	0.999937i	$0.503566\pi$
$594$	1.34621e11			0.0443682
$595$	−8.11138e11	+	7.35132e11i	−0.265319	+	0.240458i
$596$	1.59774e12			0.518680
$597$	1.79408e12			0.578039
$598$			3.76722e12i			1.20466i
$599$	−2.69514e12			−0.855384			−0.427692	−	0.903925i	$-0.640673\pi$
$599$	−2.69514e12			−0.855384			−0.427692	+	0.903925i	$0.640673\pi$
$600$		−	4.72245e12i		−	1.48760i
$601$		−	2.33770e11i		−	0.0730893i	−0.999332	−	0.0365447i	$-0.988365\pi$
$601$		−	2.33770e11i		−	0.0730893i	0.999332	−	0.0365447i	$-0.0116351\pi$
$602$			6.73611e11i			0.209038i
$603$	−8.06078e11			−0.248284
$604$	2.04245e12			0.624433
$605$			4.32631e12i			1.31286i
$606$		−	4.32278e12i		−	1.30208i
$607$		−	4.93542e12i		−	1.47562i	−0.675008	−	0.737811i	$-0.735860\pi$
$607$		−	4.93542e12i		−	1.47562i	0.675008	−	0.737811i	$-0.264140\pi$
$608$	−3.27666e12			−0.972445
$609$			1.46134e12i			0.430500i
$610$	1.40741e12			0.411563
$611$	6.44444e12			1.87068
$612$	1.35932e12	−	1.23194e12i	0.391687	−	0.354985i
$613$	9.23540e11			0.264170			0.132085	−	0.991238i	$-0.457833\pi$
$613$	9.23540e11			0.264170			0.132085	+	0.991238i	$0.457833\pi$
$614$	2.70986e12			0.769467
$615$		−	9.55921e12i		−	2.69453i
$616$	2.36414e11			0.0661546
$617$			6.93577e12i			1.92669i	0.268268	+	0.963344i	$0.413549\pi$
$617$			6.93577e12i			1.92669i	−0.268268	+	0.963344i	$0.586451\pi$
$618$		−	2.06526e11i		−	0.0569543i
$619$		−	4.16055e12i		−	1.13905i	−0.821974	−	0.569525i	$-0.807127\pi$
$619$		−	4.16055e12i		−	1.13905i	0.821974	−	0.569525i	$-0.192873\pi$
$620$	1.55433e12			0.422455
$621$	9.50579e11			0.256493
$622$			1.36222e12i			0.364913i
$623$		−	8.81381e11i		−	0.234405i
$624$			3.04812e12i			0.804824i
$625$	−4.03159e12			−1.05686
$626$		−	2.27277e12i		−	0.591522i
$627$	1.61784e12			0.418053
$628$	−1.60660e11			−0.0412183
$629$	−1.34458e12	−	1.48360e12i	−0.342498	−	0.377910i
$630$	−1.22639e12			−0.310167
$631$	6.87945e12			1.72751			0.863757	−	0.503909i	$-0.168105\pi$
$631$	6.87945e12			1.72751			0.863757	+	0.503909i	$0.168105\pi$
$632$		−	4.71524e12i		−	1.17565i
$633$	−8.13975e12			−2.01509
$634$			1.89941e12i			0.466892i
$635$			6.37665e11i			0.155636i
$636$			4.62281e12i			1.12034i
$637$	−6.16319e12			−1.48313
$638$	8.43017e11			0.201439
$639$			6.68754e12i			1.58677i
$640$			6.84909e11i			0.161370i
$641$			3.56709e11i			0.0834550i	0.999129	+	0.0417275i	$0.0132861\pi$
$641$			3.56709e11i			0.0834550i	−0.999129	+	0.0417275i	$0.986714\pi$
$642$	−3.74221e12			−0.869402
$643$			6.44704e11i			0.148734i	0.997231	+	0.0743672i	$0.0236937\pi$
$643$			6.44704e11i			0.148734i	−0.997231	+	0.0743672i	$0.976306\pi$
$644$	5.19525e11			0.119020
$645$	9.90208e12			2.25272
$646$	−2.87907e12	+	2.60929e12i	−0.650437	+	0.589489i
$647$	−6.40320e12			−1.43657			−0.718287	−	0.695747i	$-0.755073\pi$
$647$	−6.40320e12			−1.43657			−0.718287	+	0.695747i	$0.755073\pi$
$648$	−3.86530e12			−0.861183
$649$		−	2.75766e11i		−	0.0610153i
$650$	−5.02734e12			−1.10466
$651$		−	1.16528e12i		−	0.254283i
$652$			2.43629e12i			0.527976i
$653$		−	2.26464e12i		−	0.487404i	−0.969850	−	0.243702i	$-0.921638\pi$
$653$		−	2.26464e12i		−	0.487404i	0.969850	−	0.243702i	$-0.0783619\pi$
$654$	4.93759e12			1.05540
$655$	−7.19758e11			−0.152792
$656$		−	2.14327e12i		−	0.451867i
$657$		−	9.88504e12i		−	2.06983i
$658$			1.07825e12i			0.224235i
$659$	5.66256e12			1.16958			0.584788	−	0.811186i	$-0.301178\pi$
$659$	5.66256e12			1.16958			0.584788	+	0.811186i	$0.301178\pi$
$660$		−	1.08155e12i		−	0.221870i
$661$	3.57090e12			0.727563			0.363782	−	0.931484i	$-0.381485\pi$
$661$	3.57090e12			0.727563			0.363782	+	0.931484i	$0.381485\pi$
$662$	−2.74602e12			−0.555704
$663$	−7.81607e12	−	8.62418e12i	−1.57100	−	1.73343i
$664$	1.23492e12			0.246537
$665$	−2.14097e12			−0.424535
$666$		−	2.24310e12i		−	0.441789i
$667$	5.95269e12			1.16452
$668$			2.46934e12i			0.479829i
$669$			5.38039e11i			0.103848i
$670$		−	1.14135e12i		−	0.218818i
$671$	5.01703e11			0.0955422
$672$	1.64222e12			0.310649
$673$			7.77167e12i			1.46031i	0.683279	+	0.730157i	$0.260553\pi$
$673$			7.77167e12i			1.46031i	−0.683279	+	0.730157i	$0.739447\pi$
$674$		−	2.03153e12i		−	0.379187i
$675$			1.26855e12i			0.235201i
$676$	−3.73401e12			−0.687726
$677$		−	7.80583e12i		−	1.42814i	−0.700076	−	0.714069i	$-0.746850\pi$
$677$		−	7.80583e12i		−	1.42814i	0.700076	−	0.714069i	$-0.253150\pi$
$678$	−1.44300e12			−0.262260
$679$	−1.98662e12			−0.358675
$680$	5.60502e12	+	6.18454e12i	1.00528	+	1.10922i
$681$	−1.36964e13			−2.44030
$682$	−6.72229e11			−0.118984
$683$		−	1.18413e12i		−	0.208212i	−0.994566	−	0.104106i	$-0.966802\pi$
$683$		−	1.18413e12i		−	0.208212i	0.994566	−	0.104106i	$-0.0331981\pi$
$684$	3.58787e12			0.626735
$685$			3.10536e12i			0.538896i
$686$		−	2.13538e12i		−	0.368143i
$687$		−	2.83882e12i		−	0.486220i
$688$	2.22015e12			0.377776
$689$	1.58133e13			2.67322
$690$			9.26557e12i			1.55615i
$691$		−	1.71186e12i		−	0.285639i	−0.989749	−	0.142820i	$-0.954383\pi$
$691$		−	1.71186e12i		−	0.285639i	0.989749	−	0.142820i	$-0.0456169\pi$
$692$		−	1.24490e12i		−	0.206375i
$693$	−4.37173e11			−0.0720036
$694$			1.54978e12i			0.253601i
$695$	−1.21871e13			−1.98138
$696$	1.11420e13			1.79979
$697$	5.49584e12	+	6.06407e12i	0.882037	+	0.973233i
$698$	2.59218e12			0.413348
$699$	−1.84634e12			−0.292526
$700$			6.93305e11i			0.109140i
$701$	−3.61533e12			−0.565480			−0.282740	−	0.959197i	$-0.591243\pi$
$701$	−3.61533e12			−0.565480			−0.282740	+	0.959197i	$0.591243\pi$
$702$		−	1.89413e12i		−	0.294370i
$703$		−	3.91590e12i		−	0.604690i
$704$		−	1.48406e12i		−	0.227707i
$705$	1.58503e13			2.41650
$706$	1.24213e11			0.0188168
$707$			2.03922e12i			0.306957i
$708$		−	1.13429e12i		−	0.169658i
$709$			4.40149e12i			0.654172i	0.944995	+	0.327086i	$0.106067\pi$
$709$			4.40149e12i			0.654172i	−0.944995	+	0.327086i	$0.893933\pi$
$710$	−9.46911e12			−1.39845
$711$			8.71936e12i			1.27959i
$712$	−6.72010e12			−0.979977
$713$	−4.74673e12			−0.687846
$714$	1.44295e12	−	1.30774e12i	0.207783	−	0.188313i
$715$	−3.69966e12			−0.529401
$716$	2.56285e12			0.364430
$717$			2.71875e12i			0.384178i
$718$	5.22518e12			0.733739
$719$			6.79671e12i			0.948459i	0.880401	+	0.474230i	$0.157273\pi$
$719$			6.79671e12i			0.948459i	−0.880401	+	0.474230i	$0.842727\pi$
$720$			4.04205e12i			0.560538i
$721$			9.74262e10i			0.0134266i
$722$	−2.19319e12			−0.300371
$723$	6.92710e11			0.0942821
$724$		−	2.56126e12i		−	0.346442i
$725$			7.94386e12i			1.06785i
$726$		−	7.69617e12i		−	1.02816i
$727$	−2.72583e10			−0.00361904			−0.00180952	−	0.999998i	$-0.500576\pi$
$727$	−2.72583e10			−0.00361904			−0.00180952	+	0.999998i	$0.500576\pi$
$728$		−	3.32638e12i		−	0.438915i
$729$	9.95988e12			1.30611
$730$	1.39966e13			1.82418
$731$	−6.28158e12	+	5.69297e12i	−0.813656	+	0.737413i
$732$	2.06362e12			0.265663
$733$	3.31700e12			0.424403			0.212201	−	0.977226i	$-0.431937\pi$
$733$	3.31700e12			0.424403			0.212201	+	0.977226i	$0.431937\pi$
$734$			5.73436e12i			0.729210i
$735$	−1.51585e13			−1.91586
$736$		−	6.68950e12i		−	0.840318i
$737$		−	4.06860e11i		−	0.0507974i
$738$			9.16848e12i			1.13774i
$739$	7.15630e12			0.882650			0.441325	−	0.897347i	$-0.354509\pi$
$739$	7.15630e12			0.882650			0.441325	+	0.897347i	$0.354509\pi$
$740$	−2.61784e12			−0.320923
$741$		−	2.27632e13i		−	2.77365i
$742$			2.64579e12i			0.320434i
$743$		−	9.58156e12i		−	1.15342i	−0.816950	−	0.576709i	$-0.804337\pi$
$743$		−	9.58156e12i		−	1.15342i	0.816950	−	0.576709i	$-0.195663\pi$
$744$	−8.88473e12			−1.06308
$745$		−	1.34423e13i		−	1.59872i
$746$	−4.02002e12			−0.475230
$747$	−2.28360e12			−0.268335
$748$	6.21812e11	+	6.86103e11i	0.0726277	+	0.0801368i
$749$	1.76535e12			0.204956
$750$	7.96535e11			0.0919240
$751$			1.53884e13i			1.76528i	0.470047	+	0.882641i	$0.344237\pi$
$751$			1.53884e13i			1.76528i	−0.470047	+	0.882641i	$0.655763\pi$
$752$	3.55380e12			0.405240
$753$		−	2.39841e11i		−	0.0271861i
$754$		−	1.18614e13i		−	1.33648i
$755$		−	1.71838e13i		−	1.92468i
$756$	−2.61214e11			−0.0290836
$757$	−1.07153e13			−1.18597			−0.592983	−	0.805215i	$-0.702050\pi$
$757$	−1.07153e13			−1.18597			−0.592983	+	0.805215i	$0.702050\pi$
$758$		−	1.22629e13i		−	1.34922i
$759$			3.30292e12i			0.361252i
$760$			1.63239e13i			1.77485i
$761$	−2.41871e12			−0.261428			−0.130714	−	0.991420i	$-0.541727\pi$
$761$	−2.41871e12			−0.261428			−0.130714	+	0.991420i	$0.541727\pi$
$762$		−	1.13436e12i		−	0.121886i
$763$	−2.32925e12			−0.248803
$764$	−3.22795e12			−0.342774
$765$	−1.03647e13	−	1.14364e13i	−1.09416	−	1.20729i
$766$	5.88206e11			0.0617305
$767$	−3.88007e12			−0.404818
$768$		−	1.47287e13i		−	1.52771i
$769$	1.04607e13			1.07868			0.539339	−	0.842089i	$-0.318674\pi$
$769$	1.04607e13			1.07868			0.539339	+	0.842089i	$0.318674\pi$
$770$		−	6.19008e11i		−	0.0634582i
$771$			2.41175e13i			2.45803i
$772$			9.84774e11i			0.0997835i
$773$	6.75781e12			0.680767			0.340383	−	0.940287i	$-0.389443\pi$
$773$	6.75781e12			0.680767			0.340383	+	0.940287i	$0.389443\pi$
$774$	−9.49734e12			−0.951191
$775$		−	6.33450e12i		−	0.630746i
$776$			1.51470e13i			1.49951i
$777$			1.96260e12i			0.193169i
$778$	6.81391e11			0.0666789
$779$			1.60059e13i			1.55726i
$780$	−1.52176e13			−1.47204
$781$	−3.37547e12			−0.324642
$782$	−5.32703e12	−	5.87780e12i	−0.509395	−	0.562062i
$783$	−2.99297e12			−0.284561
$784$	−3.39870e12			−0.321286
$785$			1.35168e12i			0.127046i
$786$	1.28040e12			0.119658
$787$		−	1.52232e13i		−	1.41456i	−0.706935	−	0.707279i	$-0.749922\pi$
$787$		−	1.52232e13i		−	1.41456i	0.706935	−	0.707279i	$-0.250078\pi$
$788$		−	8.69295e12i		−	0.803155i
$789$			2.67995e13i			2.46196i
$790$	−1.23460e13			−1.12773
$791$	6.80718e11			0.0618263
$792$			3.33324e12i			0.301025i
$793$		−	7.05904e12i		−	0.633893i
$794$		−	1.47920e13i		−	1.32080i
$795$	3.88932e13			3.45319
$796$			2.00822e12i			0.177298i
$797$	1.41512e13			1.24231			0.621155	−	0.783688i	$-0.286664\pi$
$797$	1.41512e13			1.24231			0.621155	+	0.783688i	$0.286664\pi$
$798$	3.80863e12			0.332472
$799$	−1.00549e13	+	9.11275e12i	−0.872808	+	0.791023i
$800$	8.92713e12			0.770561
$801$	1.24267e13			1.06662
$802$			8.48478e12i			0.724196i
$803$	4.98938e12			0.423474
$804$		−	1.67351e12i		−	0.141246i
$805$		−	4.37093e12i		−	0.366853i
$806$			9.45836e12i			0.789420i
$807$	8.96161e12			0.743798
$808$	1.55481e13			1.28329
$809$		−	1.28851e13i		−	1.05760i	−0.848748	−	0.528798i	$-0.822643\pi$
$809$		−	1.28851e13i		−	1.05760i	0.848748	−	0.528798i	$-0.177357\pi$
$810$			1.01206e13i			0.826083i
$811$		−	4.50010e12i		−	0.365282i	−0.983180	−	0.182641i	$-0.941535\pi$
$811$		−	4.50010e12i		−	0.365282i	0.983180	−	0.182641i	$-0.0584646\pi$
$812$	−1.63577e12			−0.132044
$813$			2.37386e13i			1.90567i
$814$	1.13218e12			0.0903873
$815$	2.04972e13			1.62737
$816$	−4.31018e12	−	4.75582e12i	−0.340322	−	0.375509i
$817$	−1.65800e13			−1.30192
$818$	−1.00061e13			−0.781401
$819$			6.15110e12i			0.477722i
$820$	1.07002e13			0.826474
$821$		−	7.07667e12i		−	0.543606i	−0.962353	−	0.271803i	$-0.912380\pi$
$821$		−	7.07667e12i		−	0.543606i	0.962353	−	0.271803i	$-0.0876200\pi$
$822$		−	5.52421e12i		−	0.422033i
$823$		−	2.16722e13i		−	1.64666i	−0.567563	−	0.823330i	$-0.692114\pi$
$823$		−	2.16722e13i		−	1.64666i	0.567563	−	0.823330i	$-0.307886\pi$
$824$	7.42827e11			0.0561326
$825$	−4.40774e12			−0.331263
$826$		−	6.49192e11i		−	0.0485247i
$827$			9.53709e12i			0.708992i	0.935058	+	0.354496i	$0.115347\pi$
$827$			9.53709e12i			0.708992i	−0.935058	+	0.354496i	$0.884653\pi$
$828$			7.32486e12i			0.541580i
$829$	−1.85810e13			−1.36639			−0.683194	−	0.730237i	$-0.739410\pi$
$829$	−1.85810e13			−1.36639			−0.683194	+	0.730237i	$0.739410\pi$
$830$		−	3.23342e12i		−	0.236489i
$831$	−2.01772e13			−1.46776
$832$	−2.08810e13			−1.51076
$833$	9.61612e12	−	8.71506e12i	0.691986	−	0.627145i
$834$	2.16799e13			1.55171
$835$	2.07753e13			1.47897
$836$			1.81094e12i			0.128226i
$837$	2.38662e12			0.168081
$838$			1.13388e13i			0.794268i
$839$			1.59920e12i			0.111422i	0.998447	+	0.0557112i	$0.0177426\pi$
$839$			1.59920e12i			0.111422i	−0.998447	+	0.0557112i	$0.982257\pi$
$840$		−	8.18133e12i		−	0.566979i
$841$	−4.23537e12			−0.291951
$842$	−8.30170e12			−0.569197
$843$			2.27195e13i			1.54944i
$844$		−	9.11132e12i		−	0.618073i
$845$			3.14154e13i			2.11976i
$846$	−1.52024e13			−1.02034
$847$			3.63058e12i			0.242382i
$848$	8.72025e12			0.579092
$849$	−3.21380e13			−2.12292
$850$	7.84391e12	−	7.10891e12i	0.515403	−	0.467108i
$851$	7.99456e12			0.522530
$852$	−1.38841e13			−0.902693
$853$			3.66406e10i			0.00236969i	0.999999	+	0.00118485i	$0.000377148\pi$
$853$			3.66406e10i			0.00236969i	−0.999999	+	0.00118485i	$0.999623\pi$
$854$	1.18108e12			0.0759835
$855$		−	3.01859e13i		−	1.93177i
$856$		−	1.34599e13i		−	0.856860i
$857$			1.12995e13i			0.715559i	0.933806	+	0.357779i	$0.116466\pi$
$857$			1.12995e13i			0.715559i	−0.933806	+	0.357779i	$0.883534\pi$
$858$	6.58142e12			0.414598
$859$	−1.13307e13			−0.710049			−0.355025	−	0.934857i	$-0.615528\pi$
$859$	−1.13307e13			−0.710049			−0.355025	+	0.934857i	$0.615528\pi$
$860$			1.10840e13i			0.690961i
$861$		−	8.02196e12i		−	0.497470i
$862$			1.72309e12i			0.106298i
$863$	5.46870e12			0.335610			0.167805	−	0.985820i	$-0.446332\pi$
$863$	5.46870e12			0.335610			0.167805	+	0.985820i	$0.446332\pi$
$864$			3.36344e12i			0.205339i
$865$	−1.04737e13			−0.636105
$866$	4.53358e11			0.0273912
$867$	2.43900e13	+	2.40358e12i	1.46597	+	0.144468i
$868$	1.30437e12			0.0779944
$869$	−4.40102e12			−0.261797
$870$		−	2.91734e13i		−	1.72643i
$871$	−5.72459e12			−0.337025
$872$			1.77594e13i			1.04017i
$873$		−	2.80097e13i		−	1.63209i
$874$		−	1.55142e13i		−	0.899351i
$875$	−3.75756e11			−0.0216705
$876$	2.05225e13			1.17750
$877$		−	2.29940e12i		−	0.131255i	−0.997844	−	0.0656275i	$-0.979095\pi$
$877$		−	2.29940e12i		−	0.131255i	0.997844	−	0.0656275i	$-0.0209049\pi$
$878$			9.36580e12i			0.531887i
$879$		−	2.77412e13i		−	1.56738i
$880$	−2.04019e12			−0.114683
$881$		−	1.11997e13i		−	0.626348i	−0.949696	−	0.313174i	$-0.898608\pi$
$881$		−	1.11997e13i		−	0.626348i	0.949696	−	0.313174i	$-0.101392\pi$
$882$	1.45390e13			0.808955
$883$	−3.12943e13			−1.73238			−0.866188	−	0.499718i	$-0.833437\pi$
$883$	−3.12943e13			−1.73238			−0.866188	+	0.499718i	$0.833437\pi$
$884$	9.65357e12	−	8.74900e12i	0.531683	−	0.481862i
$885$	−9.54313e12			−0.522933
$886$	−7.36491e12			−0.401528
$887$			1.69578e13i			0.919840i	0.887960	+	0.459920i	$0.152122\pi$
$887$			1.69578e13i			0.919840i	−0.887960	+	0.459920i	$0.847878\pi$
$888$	1.49639e13			0.807582
$889$			5.35121e11i			0.0287338i
$890$			1.75954e13i			0.940035i
$891$			3.60771e12i			0.191771i
$892$	−6.02260e11			−0.0318524
$893$	−2.65397e13			−1.39657
$894$			2.39129e13i			1.25203i
$895$		−	2.15620e13i		−	1.12328i
$896$			5.74767e11i			0.0297924i
$897$	4.64726e13			2.39679
$898$			5.36536e12i			0.275331i
$899$	1.49454e13			0.763115
$900$	−9.77502e12			−0.496622
$901$	−2.46726e13	+	2.23607e13i	−1.24725	+	1.13038i
$902$	−4.62770e12			−0.232775
$903$	8.30970e12			0.415902
$904$		−	5.19014e12i		−	0.258477i
$905$	−2.15487e13			−1.06783
$906$			3.05687e13i			1.50730i
$907$			1.21182e13i			0.594575i	0.954788	+	0.297288i	$0.0960820\pi$
$907$			1.21182e13i			0.594575i	−0.954788	+	0.297288i	$0.903918\pi$
$908$		−	1.53312e13i		−	0.748496i
$909$	−2.87513e13			−1.39675
$910$	−8.70954e12			−0.421026
$911$		−	1.52506e13i		−	0.733594i	−0.930301	−	0.366797i	$-0.880454\pi$
$911$		−	1.52506e13i		−	0.733594i	0.930301	−	0.366797i	$-0.119546\pi$
$912$		−	1.25528e13i		−	0.600848i
$913$		−	1.15263e12i		−	0.0548997i
$914$	1.88877e13			0.895203
$915$		−	1.73619e13i		−	0.818846i
$916$	3.17767e12			0.149135
$917$	−6.04012e11			−0.0282087
$918$	2.67839e12	+	2.95532e12i	0.124475	+	0.137345i
$919$	−3.47751e12			−0.160823			−0.0804116	−	0.996762i	$-0.525623\pi$
$919$	−3.47751e12			−0.160823			−0.0804116	+	0.996762i	$0.525623\pi$
$920$	−3.33262e13			−1.53370
$921$		−	3.34290e13i		−	1.53093i
$922$	1.78552e13			0.813721
$923$			4.74935e13i			2.15390i
$924$		−	9.07623e11i		−	0.0409621i
$925$			1.06687e13i			0.479154i
$926$	−4.14158e12			−0.185104
$927$	−1.37363e12			−0.0610956
$928$			2.10624e13i			0.932272i
$929$		−	1.36859e13i		−	0.602841i	−0.953491	−	0.301421i	$-0.902539\pi$
$929$		−	1.36859e13i		−	0.602841i	0.953491	−	0.301421i	$-0.0974609\pi$
$930$			2.32631e13i			1.01975i
$931$	2.53814e13			1.10724
$932$		−	2.06672e12i		−	0.0897242i
$933$	1.68044e13			0.726031
$934$	2.75564e13			1.18484
$935$	5.77240e12	−	5.23150e12i	0.247004	−	0.223859i
$936$	4.68991e13			1.99721
$937$	2.71915e13			1.15241			0.576203	−	0.817307i	$-0.304534\pi$
$937$	2.71915e13			1.15241			0.576203	+	0.817307i	$0.304534\pi$
$938$		−	9.57808e11i		−	0.0403985i
$939$	−2.80370e13			−1.17689
$940$			1.77422e13i			0.741193i
$941$			1.67036e13i			0.694476i	0.937777	+	0.347238i	$0.112880\pi$
$941$			1.67036e13i			0.694476i	−0.937777	+	0.347238i	$0.887120\pi$
$942$		−	2.40454e12i		−	0.0994955i
$943$	−3.26770e13			−1.34568
$944$	−2.13967e12			−0.0876946
$945$			2.19767e12i			0.0896438i
$946$		−	4.79370e12i		−	0.194608i
$947$		−	2.14351e13i		−	0.866067i	−0.901378	−	0.433033i	$-0.857443\pi$
$947$		−	2.14351e13i		−	0.866067i	0.901378	−	0.433033i	$-0.142557\pi$
$948$	−1.81024e13			−0.727946
$949$		−	7.02014e13i		−	2.80962i
$950$	2.07037e13			0.824693
$951$	2.34312e13			0.928927
$952$	4.70366e12	+	5.18998e12i	0.185597	+	0.204786i
$953$	−9.22579e12			−0.362314			−0.181157	−	0.983454i	$-0.557984\pi$
$953$	−9.22579e12			−0.362314			−0.181157	+	0.983454i	$0.557984\pi$
$954$	−3.73034e13			−1.45808
$955$			2.71578e13i			1.05652i
$956$	−3.04326e12			−0.117836
$957$		−	1.03995e13i		−	0.400782i
$958$			9.50000e12i			0.364400i
$959$			2.60598e12i			0.0994919i
$960$	−5.13574e13			−1.95156
$961$	1.45220e13			0.549251
$962$		−	1.59300e13i		−	0.599692i
$963$			2.48899e13i			0.932619i
$964$			7.75392e11i			0.0289184i
$965$	8.28521e12			0.307561
$966$			7.77555e12i			0.287299i
$967$	5.20219e13			1.91323			0.956614	−	0.291359i	$-0.0941073\pi$
$967$	5.20219e13			1.91323			0.956614	+	0.291359i	$0.0941073\pi$
$968$	2.76814e13			1.01333
$969$	3.21883e13	+	3.55163e13i	1.17285	+	1.29411i
$970$	3.96598e13			1.43839
$971$	8.53408e12			0.308085			0.154042	−	0.988064i	$-0.450771\pi$
$971$	8.53408e12			0.308085			0.154042	+	0.988064i	$0.450771\pi$
$972$			1.79873e13i			0.646349i
$973$	−1.02273e13			−0.365807
$974$		−	3.38098e13i		−	1.20372i
$975$			6.20176e13i			2.19783i
$976$		−	3.89272e12i		−	0.137318i
$977$	1.09077e13			0.383008			0.191504	−	0.981492i	$-0.438663\pi$
$977$	1.09077e13			0.383008			0.191504	+	0.981492i	$0.438663\pi$
$978$	−3.64630e13			−1.27447
$979$			6.27227e12i			0.218224i
$980$		−	1.69679e13i		−	0.587638i
$981$		−	3.28405e13i		−	1.13214i
$982$	−1.94109e13			−0.666106
$983$		−	3.83440e12i		−	0.130981i	−0.997853	−	0.0654903i	$-0.979139\pi$
$983$		−	3.83440e12i		−	0.130981i	0.997853	−	0.0654903i	$-0.0208611\pi$
$984$	−6.11636e13			−2.07977
$985$	−7.31365e13			−2.47555
$986$	1.67726e13	+	1.85067e13i	0.565136	+	0.623567i
$987$	1.33014e13			0.446137
$988$	2.54803e13			0.850742
$989$		−	3.38491e13i		−	1.12503i
$990$	8.72749e12			0.288756
$991$		−	3.67907e13i		−	1.21173i	−0.795566	−	0.605867i	$-0.792827\pi$
$991$		−	3.67907e13i		−	1.21173i	0.795566	−	0.605867i	$-0.207173\pi$
$992$		−	1.67954e13i		−	0.550664i
$993$			3.38751e13i			1.10563i
$994$	−7.94636e12			−0.258184
$995$	1.68958e13			0.546480
$996$		−	4.74102e12i		−	0.152653i
$997$			2.49866e13i			0.800901i	0.916318	+	0.400451i	$0.131146\pi$
$997$			2.49866e13i			0.800901i	−0.916318	+	0.400451i	$0.868854\pi$
$998$			4.85792e12i			0.155011i
$999$	−4.01961e12			−0.127685

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.10.b.a.16.4	yes	12
3.2	odd	2		153.10.d.b.118.9		12
4.3	odd	2		272.10.b.c.33.2		12
17.4	even	4		289.10.a.c.1.10		12
17.13	even	4		289.10.a.c.1.9		12
17.16	even	2	inner	17.10.b.a.16.3	✓	12
51.50	odd	2		153.10.d.b.118.10		12
68.67	odd	2		272.10.b.c.33.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.b.a.16.3	✓	12	17.16	even	2	inner
17.10.b.a.16.4	yes	12	1.1	even	1	trivial
153.10.d.b.118.9		12	3.2	odd	2
153.10.d.b.118.10		12	51.50	odd	2
272.10.b.c.33.2		12	4.3	odd	2
272.10.b.c.33.11		12	68.67	odd	2
289.10.a.c.1.9		12	17.13	even	4
289.10.a.c.1.10		12	17.4	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)

\(f(q)\)	\(=\)	\(q-16.7531 q^{2} +206.667i q^{3} -231.335 q^{4} +1946.29i q^{5} -3462.30i q^{6} +1633.30i q^{7} +12453.1 q^{8} -23028.2 q^{9} +O(q^{10})\)	\(q-16.7531 q^{2} +206.667i q^{3} -231.335 q^{4} +1946.29i q^{5} -3462.30i q^{6} +1633.30i q^{7} +12453.1 q^{8} -23028.2 q^{9} -32606.3i q^{10} -11623.3i q^{11} -47809.2i q^{12} -163541. q^{13} -27362.8i q^{14} -402234. q^{15} -90185.0 q^{16} +(255165. - 231255. i) q^{17} +385793. q^{18} +673499. q^{19} -450244. i q^{20} -337549. q^{21} +194725. i q^{22} +1.37499e6i q^{23} +2.57365e6i q^{24} -1.83492e6 q^{25} +2.73981e6 q^{26} -691336. i q^{27} -377839. i q^{28} -4.32926e6i q^{29} +6.73865e6 q^{30} +3.45219e6i q^{31} -4.86513e6 q^{32} +2.40214e6 q^{33} +(-4.27479e6 + 3.87423e6i) q^{34} -3.17888e6 q^{35} +5.32721e6 q^{36} -5.81427e6i q^{37} -1.12832e7 q^{38} -3.37985e7i q^{39} +2.42374e7i q^{40} +2.37653e7i q^{41} +5.65499e6 q^{42} -2.46177e7 q^{43} +2.68886e6i q^{44} -4.48195e7i q^{45} -2.30353e7i q^{46} -3.94057e7 q^{47} -1.86382e7i q^{48} +3.76859e7 q^{49} +3.07406e7 q^{50} +(4.77927e7 + 5.27341e7i) q^{51} +3.78327e7 q^{52} -9.66929e7 q^{53} +1.15820e7i q^{54} +2.26222e7 q^{55} +2.03397e7i q^{56} +1.39190e8i q^{57} +7.25285e7i q^{58} +2.37253e7 q^{59} +9.30506e7 q^{60} +4.31637e7i q^{61} -5.78348e7i q^{62} -3.76120e7i q^{63} +1.27681e8 q^{64} -3.18298e8i q^{65} -4.02432e7 q^{66} +3.50040e7 q^{67} +(-5.90284e7 + 5.34973e7i) q^{68} -2.84165e8 q^{69} +5.32560e7 q^{70} -2.90407e8i q^{71} -2.86773e8 q^{72} +4.29259e8i q^{73} +9.74069e7i q^{74} -3.79217e8i q^{75} -1.55804e8 q^{76} +1.89843e7 q^{77} +5.66229e8i q^{78} -3.78639e8i q^{79} -1.75526e8i q^{80} -3.10387e8 q^{81} -3.98142e8i q^{82} +9.91655e7 q^{83} +7.80868e7 q^{84} +(4.50089e8 + 4.96625e8i) q^{85} +4.12423e8 q^{86} +8.94715e8 q^{87} -1.44746e8i q^{88} -5.39631e8 q^{89} +7.50864e8i q^{90} -2.67112e8i q^{91} -3.18083e8i q^{92} -7.13453e8 q^{93} +6.60166e8 q^{94} +1.31082e9i q^{95} -1.00546e9i q^{96} +1.21632e9i q^{97} -6.31355e8 q^{98} +2.67662e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 30 q^{2} + 1874 q^{4} + 23550 q^{8} - 9184 q^{9}+O(q^{10}) \) 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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