LMFDB - Embedded newform 850.2.l.e.451.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [850,2,Mod(151,850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(850, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("850.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.l (of order $8$, degree $4$, 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:	$6.78728417181$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 28x^{14} + 286x^{12} + 1412x^{10} + 3709x^{8} + 5264x^{6} + 3780x^{4} + 1072x^{2} + 4 $ x^16 + 28x^14 + 286x^12 + 1412x^10 + 3709x^8 + 5264x^6 + 3780x^4 + 1072*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 170)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			451.2
Root			$2.47571i$ of defining polynomial
Character	$\chi$	$=$	850.451
Dual form			850.2.l.e.801.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.36338 - 0.564729i) q^{3} -1.00000i q^{4} +(1.36338 - 0.564729i) q^{6} +(-1.35785 - 3.27815i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.581445 - 0.581445i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.36338 - 0.564729i) q^{3} -1.00000i q^{4} +(1.36338 - 0.564729i) q^{6} +(-1.35785 - 3.27815i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.581445 - 0.581445i) q^{9} +(-4.35013 + 1.80188i) q^{11} +(-0.564729 + 1.36338i) q^{12} +5.47699i q^{13} +(3.27815 + 1.35785i) q^{14} -1.00000 q^{16} +(-2.52894 - 3.25645i) q^{17} +0.822287 q^{18} +(0.857748 - 0.857748i) q^{19} +5.23617i q^{21} +(1.80188 - 4.35013i) q^{22} +(5.28485 - 2.18906i) q^{23} +(-0.564729 - 1.36338i) q^{24} +(-3.87282 - 3.87282i) q^{26} +(2.15856 + 5.21121i) q^{27} +(-3.27815 + 1.35785i) q^{28} +(-1.77710 + 4.29029i) q^{29} +(6.72892 + 2.78721i) q^{31} +(0.707107 - 0.707107i) q^{32} +6.94843 q^{33} +(4.09089 + 0.514430i) q^{34} +(-0.581445 + 0.581445i) q^{36} +(8.58444 + 3.55579i) q^{37} +1.21304i q^{38} +(3.09302 - 7.46720i) q^{39} +(0.0547598 + 0.132202i) q^{41} +(-3.70253 - 3.70253i) q^{42} +(0.587013 + 0.587013i) q^{43} +(1.80188 + 4.35013i) q^{44} +(-2.18906 + 5.28485i) q^{46} -5.85635i q^{47} +(1.36338 + 0.564729i) q^{48} +(-3.95275 + 3.95275i) q^{49} +(1.60888 + 5.86793i) q^{51} +5.47699 q^{52} +(-6.54226 + 6.54226i) q^{53} +(-5.21121 - 2.15856i) q^{54} +(1.35785 - 3.27815i) q^{56} +(-1.65383 + 0.685038i) q^{57} +(-1.77710 - 4.29029i) q^{58} +(-3.33507 - 3.33507i) q^{59} +(4.76261 + 11.4980i) q^{61} +(-6.72892 + 2.78721i) q^{62} +(-1.11655 + 2.69558i) q^{63} +1.00000i q^{64} +(-4.91328 + 4.91328i) q^{66} -8.66703 q^{67} +(-3.25645 + 2.52894i) q^{68} -8.44146 q^{69} +(4.75235 + 1.96849i) q^{71} -0.822287i q^{72} +(-6.17351 + 14.9042i) q^{73} +(-8.58444 + 3.55579i) q^{74} +(-0.857748 - 0.857748i) q^{76} +(11.8137 + 11.8137i) q^{77} +(3.09302 + 7.46720i) q^{78} +(9.34587 - 3.87118i) q^{79} -5.85698i q^{81} +(-0.132202 - 0.0547598i) q^{82} +(-2.40841 + 2.40841i) q^{83} +5.23617 q^{84} -0.830161 q^{86} +(4.84570 - 4.84570i) q^{87} +(-4.35013 - 1.80188i) q^{88} -2.24175i q^{89} +(17.9544 - 7.43696i) q^{91} +(-2.18906 - 5.28485i) q^{92} +(-7.60004 - 7.60004i) q^{93} +(4.14106 + 4.14106i) q^{94} +(-1.36338 + 0.564729i) q^{96} +(-1.66675 + 4.02389i) q^{97} -5.59004i q^{98} +(3.57705 + 1.48166i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 8 q^{11} - 8 q^{14} - 16 q^{16} - 8 q^{18} + 8 q^{22} - 8 q^{23} + 24 q^{27} + 8 q^{28} + 8 q^{29} + 32 q^{31} - 16 q^{33} + 16 q^{34} + 8 q^{37} - 32 q^{39} - 32 q^{41} - 32 q^{42} + 16 q^{43} + 8 q^{44} - 24 q^{46} - 8 q^{49} - 8 q^{51} + 8 q^{52} + 40 q^{53} + 16 q^{57} + 8 q^{58} + 16 q^{59} - 24 q^{61} - 32 q^{62} - 56 q^{63} - 8 q^{66} - 16 q^{67} - 16 q^{69} + 8 q^{71} - 16 q^{73} - 8 q^{74} - 24 q^{77} - 32 q^{78} + 40 q^{79} - 16 q^{82} - 32 q^{83} + 16 q^{84} + 32 q^{87} - 8 q^{88} + 24 q^{91} - 24 q^{92} + 32 q^{93} + 40 q^{94} - 24 q^{97} - 56 q^{99}+O(q^{100}) $ 16 * q - 8 * q^11 - 8 * q^14 - 16 * q^16 - 8 * q^18 + 8 * q^22 - 8 * q^23 + 24 * q^27 + 8 * q^28 + 8 * q^29 + 32 * q^31 - 16 * q^33 + 16 * q^34 + 8 * q^37 - 32 * q^39 - 32 * q^41 - 32 * q^42 + 16 * q^43 + 8 * q^44 - 24 * q^46 - 8 * q^49 - 8 * q^51 + 8 * q^52 + 40 * q^53 + 16 * q^57 + 8 * q^58 + 16 * q^59 - 24 * q^61 - 32 * q^62 - 56 * q^63 - 8 * q^66 - 16 * q^67 - 16 * q^69 + 8 * q^71 - 16 * q^73 - 8 * q^74 - 24 * q^77 - 32 * q^78 + 40 * q^79 - 16 * q^82 - 32 * q^83 + 16 * q^84 + 32 * q^87 - 8 * q^88 + 24 * q^91 - 24 * q^92 + 32 * q^93 + 40 * q^94 - 24 * q^97 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/850\mathbb{Z}\right)^\times$.

$n$	$477$	$751$
$\chi(n)$	$1$	$e\left(\frac{1}{8}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−1.36338	−	0.564729i	−0.787145	−	0.326046i	−0.0473502	−	0.998878i	$-0.515078\pi$
$3$	−1.36338	−	0.564729i	−0.787145	−	0.326046i	−0.739795	+	0.672832i	$0.765078\pi$
$4$		−	1.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$	1.36338	−	0.564729i	0.556596	−	0.230550i
$7$	−1.35785	−	3.27815i	−0.513221	−	1.23902i	−0.941999	−	0.335615i	$-0.891056\pi$
$7$	−1.35785	−	3.27815i	−0.513221	−	1.23902i	0.428779	−	0.903410i	$-0.358944\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−0.581445	−	0.581445i	−0.193815	−	0.193815i
$10$		0			0
$11$	−4.35013	+	1.80188i	−1.31161	+	0.543288i	−0.925354	−	0.379103i	$-0.876232\pi$
$11$	−4.35013	+	1.80188i	−1.31161	+	0.543288i	−0.386258	+	0.922391i	$0.626232\pi$
$12$	−0.564729	+	1.36338i	−0.163023	+	0.393573i
$13$			5.47699i			1.51904i	0.650481	+	0.759522i	$0.274567\pi$
$13$			5.47699i			1.51904i	−0.650481	+	0.759522i	$0.725433\pi$
$14$	3.27815	+	1.35785i	0.876123	+	0.362902i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−2.52894	−	3.25645i	−0.613358	−	0.789805i
$17$	−2.52894	−	3.25645i	−0.613358	−	0.789805i
$18$	0.822287			0.193815
$19$	0.857748	−	0.857748i	0.196781	−	0.196781i	−0.601838	−	0.798619i	$-0.705565\pi$
$19$	0.857748	−	0.857748i	0.196781	−	0.196781i	0.798619	+	0.601838i	$0.205565\pi$
$20$		0			0
$21$			5.23617i			1.14263i
$22$	1.80188	−	4.35013i	0.384162	−	0.927450i
$23$	5.28485	−	2.18906i	1.10197	−	0.456450i	0.243803	−	0.969825i	$-0.421605\pi$
$23$	5.28485	−	2.18906i	1.10197	−	0.456450i	0.858165	+	0.513375i	$0.171605\pi$
$24$	−0.564729	−	1.36338i	−0.115275	−	0.278298i
$25$		0			0
$26$	−3.87282	−	3.87282i	−0.759522	−	0.759522i
$27$	2.15856	+	5.21121i	0.415414	+	1.00290i
$28$	−3.27815	+	1.35785i	−0.619512	+	0.256610i
$29$	−1.77710	+	4.29029i	−0.329999	+	0.796687i	0.668593	+	0.743629i	$0.266897\pi$
$29$	−1.77710	+	4.29029i	−0.329999	+	0.796687i	−0.998591	+	0.0530586i	$0.983103\pi$
$30$		0			0
$31$	6.72892	+	2.78721i	1.20855	+	0.500598i	0.893752	−	0.448561i	$-0.148063\pi$
$31$	6.72892	+	2.78721i	1.20855	+	0.500598i	0.314798	+	0.949159i	$0.398063\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	6.94843			1.20957
$34$	4.09089	+	0.514430i	0.701581	+	0.0882239i
$35$		0			0
$36$	−0.581445	+	0.581445i	−0.0969075	+	0.0969075i
$37$	8.58444	+	3.55579i	1.41127	+	0.584569i	0.952652	−	0.304063i	$-0.0983432\pi$
$37$	8.58444	+	3.55579i	1.41127	+	0.584569i	0.458622	+	0.888631i	$0.348343\pi$
$38$			1.21304i			0.196781i
$39$	3.09302	−	7.46720i	0.495279	−	1.19571i
$40$		0			0
$41$	0.0547598	+	0.132202i	0.00855205	+	0.0206465i	0.928098	−	0.372336i	$-0.121443\pi$
$41$	0.0547598	+	0.132202i	0.00855205	+	0.0206465i	−0.919546	+	0.392983i	$0.871443\pi$
$42$	−3.70253	−	3.70253i	−0.571313	−	0.571313i
$43$	0.587013	+	0.587013i	0.0895186	+	0.0895186i	0.750448	−	0.660929i	$-0.229838\pi$
$43$	0.587013	+	0.587013i	0.0895186	+	0.0895186i	−0.660929	+	0.750448i	$0.729838\pi$
$44$	1.80188	+	4.35013i	0.271644	+	0.655806i
$45$		0			0
$46$	−2.18906	+	5.28485i	−0.322759	+	0.779209i
$47$		−	5.85635i		−	0.854236i	−0.904196	−	0.427118i	$-0.859529\pi$
$47$		−	5.85635i		−	0.854236i	0.904196	−	0.427118i	$-0.140471\pi$
$48$	1.36338	+	0.564729i	0.196786	+	0.0815116i
$49$	−3.95275	+	3.95275i	−0.564679	+	0.564679i
$50$		0			0
$51$	1.60888	+	5.86793i	0.225288	+	0.821675i
$52$	5.47699			0.759522
$53$	−6.54226	+	6.54226i	−0.898648	+	0.898648i	−0.995317	−	0.0966687i	$-0.969181\pi$
$53$	−6.54226	+	6.54226i	−0.898648	+	0.898648i	0.0966687	+	0.995317i	$0.469181\pi$
$54$	−5.21121	−	2.15856i	−0.709156	−	0.293742i
$55$		0			0
$56$	1.35785	−	3.27815i	0.181451	−	0.438061i
$57$	−1.65383	+	0.685038i	−0.219055	+	0.0907355i
$58$	−1.77710	−	4.29029i	−0.233344	−	0.563343i
$59$	−3.33507	−	3.33507i	−0.434189	−	0.434189i	0.455861	−	0.890051i	$-0.349331\pi$
$59$	−3.33507	−	3.33507i	−0.434189	−	0.434189i	−0.890051	+	0.455861i	$0.849331\pi$
$60$		0			0
$61$	4.76261	+	11.4980i	0.609790	+	1.47216i	0.863229	+	0.504812i	$0.168438\pi$
$61$	4.76261	+	11.4980i	0.609790	+	1.47216i	−0.253439	+	0.967351i	$0.581562\pi$
$62$	−6.72892	+	2.78721i	−0.854574	+	0.353976i
$63$	−1.11655	+	2.69558i	−0.140672	+	0.339611i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−4.91328	+	4.91328i	−0.604783	+	0.604783i
$67$	−8.66703			−1.05885			−0.529423	−	0.848358i	$-0.677592\pi$
$67$	−8.66703			−1.05885			−0.529423	+	0.848358i	$0.677592\pi$
$68$	−3.25645	+	2.52894i	−0.394903	+	0.306679i
$69$	−8.44146			−1.01623
$70$		0			0
$71$	4.75235	+	1.96849i	0.564000	+	0.233617i	0.646421	−	0.762981i	$-0.276265\pi$
$71$	4.75235	+	1.96849i	0.564000	+	0.233617i	−0.0824206	+	0.996598i	$0.526265\pi$
$72$		−	0.822287i		−	0.0969075i
$73$	−6.17351	+	14.9042i	−0.722555	+	1.74440i	−0.0566159	+	0.998396i	$0.518031\pi$
$73$	−6.17351	+	14.9042i	−0.722555	+	1.74440i	−0.665939	+	0.746006i	$0.731969\pi$
$74$	−8.58444	+	3.55579i	−0.997921	+	0.413353i
$75$		0			0
$76$	−0.857748	−	0.857748i	−0.0983905	−	0.0983905i
$77$	11.8137	+	11.8137i	1.34629	+	1.34629i
$78$	3.09302	+	7.46720i	0.350215	+	0.845494i
$79$	9.34587	−	3.87118i	1.05149	−	0.435542i	0.211068	−	0.977471i	$-0.432306\pi$
$79$	9.34587	−	3.87118i	1.05149	−	0.435542i	0.840424	+	0.541929i	$0.182306\pi$
$80$		0			0
$81$		−	5.85698i		−	0.650776i
$82$	−0.132202	−	0.0547598i	−0.0145993	−	0.00604721i
$83$	−2.40841	+	2.40841i	−0.264358	+	0.264358i	−0.826822	−	0.562464i	$-0.809853\pi$
$83$	−2.40841	+	2.40841i	−0.264358	+	0.264358i	0.562464	+	0.826822i	$0.309853\pi$
$84$	5.23617			0.571313
$85$		0			0
$86$	−0.830161			−0.0895186
$87$	4.84570	−	4.84570i	0.519514	−	0.519514i
$88$	−4.35013	−	1.80188i	−0.463725	−	0.192081i
$89$		−	2.24175i		−	0.237625i	−0.992917	−	0.118813i	$-0.962091\pi$
$89$		−	2.24175i		−	0.237625i	0.992917	−	0.118813i	$-0.0379088\pi$
$90$		0			0
$91$	17.9544	−	7.43696i	1.88213	−	0.779605i
$92$	−2.18906	−	5.28485i	−0.228225	−	0.550984i
$93$	−7.60004	−	7.60004i	−0.788087	−	0.788087i
$94$	4.14106	+	4.14106i	0.427118	+	0.427118i
$95$		0			0
$96$	−1.36338	+	0.564729i	−0.139149	+	0.0576374i
$97$	−1.66675	+	4.02389i	−0.169233	+	0.408564i	−0.985628	−	0.168929i	$-0.945969\pi$
$97$	−1.66675	+	4.02389i	−0.169233	+	0.408564i	0.816395	+	0.577493i	$0.195969\pi$
$98$		−	5.59004i		−	0.564679i
$99$	3.57705	+	1.48166i	0.359507	+	0.148913i
$100$		0			0
$101$	−10.7393			−1.06860			−0.534301	−	0.845294i	$-0.679425\pi$
$101$	−10.7393			−1.06860			−0.534301	+	0.845294i	$0.679425\pi$
$102$	−5.28690	−	3.01160i	−0.523482	−	0.298193i
$103$	7.43306			0.732401			0.366200	−	0.930536i	$-0.380658\pi$
$103$	7.43306			0.732401			0.366200	+	0.930536i	$0.380658\pi$
$104$	−3.87282	+	3.87282i	−0.379761	+	0.379761i
$105$		0			0
$106$		−	9.25215i		−	0.898648i
$107$	−6.01999	+	14.5335i	−0.581974	+	1.40501i	0.309046	+	0.951047i	$0.399990\pi$
$107$	−6.01999	+	14.5335i	−0.581974	+	1.40501i	−0.891020	+	0.453963i	$0.850010\pi$
$108$	5.21121	−	2.15856i	0.501449	−	0.207707i
$109$	2.46089	+	5.94112i	0.235711	+	0.569056i	0.996830	−	0.0795553i	$-0.0253500\pi$
$109$	2.46089	+	5.94112i	0.235711	+	0.569056i	−0.761120	+	0.648611i	$0.775350\pi$
$110$		0			0
$111$	−9.69577	−	9.69577i	−0.920281	−	0.920281i
$112$	1.35785	+	3.27815i	0.128305	+	0.309756i
$113$	8.90782	−	3.68974i	0.837978	−	0.347102i	0.0779218	−	0.996959i	$-0.475172\pi$
$113$	8.90782	−	3.68974i	0.837978	−	0.347102i	0.760056	+	0.649858i	$0.225172\pi$
$114$	0.685038	−	1.65383i	0.0641597	−	0.154895i
$115$		0			0
$116$	4.29029	+	1.77710i	0.398344	+	0.164999i
$117$	3.18457	−	3.18457i	0.294414	−	0.294414i
$118$	4.71650			0.434189
$119$	−7.24121	+	12.7120i	−0.663800	+	1.16531i
$120$		0			0
$121$	7.89864	−	7.89864i	0.718058	−	0.718058i
$122$	−11.4980	−	4.76261i	−1.04098	−	0.431187i
$123$		−	0.211165i		−	0.0190401i
$124$	2.78721	−	6.72892i	0.250299	−	0.604275i
$125$		0			0
$126$	−1.11655	−	2.69558i	−0.0994699	−	0.240142i
$127$	−2.26692	−	2.26692i	−0.201157	−	0.201157i	0.599339	−	0.800496i	$-0.295430\pi$
$127$	−2.26692	−	2.26692i	−0.201157	−	0.201157i	−0.800496	+	0.599339i	$0.795430\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−0.468816	−	1.13182i	−0.0412769	−	0.0996513i
$130$		0			0
$131$	−1.36747	+	3.30136i	−0.119476	+	0.288441i	−0.972292	−	0.233771i	$-0.924893\pi$
$131$	−1.36747	+	3.30136i	−0.119476	+	0.288441i	0.852815	+	0.522213i	$0.174893\pi$
$132$		−	6.94843i		−	0.604783i
$133$	−3.97653	−	1.64713i	−0.344808	−	0.142824i
$134$	6.12852	−	6.12852i	0.529423	−	0.529423i
$135$		0			0
$136$	0.514430	−	4.09089i	0.0441120	−	0.350791i
$137$	−3.30950			−0.282750			−0.141375	−	0.989956i	$-0.545152\pi$
$137$	−3.30950			−0.282750			−0.141375	+	0.989956i	$0.545152\pi$
$138$	5.96902	−	5.96902i	0.508116	−	0.508116i
$139$	−1.66295	−	0.688816i	−0.141049	−	0.0584246i	0.311042	−	0.950396i	$-0.399322\pi$
$139$	−1.66295	−	0.688816i	−0.141049	−	0.0584246i	−0.452092	+	0.891972i	$0.649322\pi$
$140$		0			0
$141$	−3.30725	+	7.98440i	−0.278520	+	0.672408i
$142$	−4.75235	+	1.96849i	−0.398808	+	0.165192i
$143$	−9.86889	−	23.8256i	−0.825278	−	1.99240i
$144$	0.581445	+	0.581445i	0.0484538	+	0.0484538i
$145$		0			0
$146$	−6.17351	−	14.9042i	−0.510924	−	1.23348i
$147$	7.62132	−	3.15686i	0.628596	−	0.260373i
$148$	3.55579	−	8.58444i	0.292284	−	0.705637i
$149$			4.16768i			0.341430i	0.985320	+	0.170715i	$0.0546077\pi$
$149$			4.16768i			0.341430i	−0.985320	+	0.170715i	$0.945392\pi$
$150$		0			0
$151$	−3.24744	+	3.24744i	−0.264273	+	0.264273i	−0.826788	−	0.562514i	$-0.809834\pi$
$151$	−3.24744	+	3.24744i	−0.264273	+	0.264273i	0.562514	+	0.826788i	$0.309834\pi$
$152$	1.21304			0.0983905
$153$	−0.423009	+	3.36389i	−0.0341982	+	0.271954i
$154$	−16.7071			−1.34629
$155$		0			0
$156$	−7.46720	−	3.09302i	−0.597854	−	0.247639i
$157$		−	15.5482i		−	1.24088i	−0.784253	−	0.620442i	$-0.786953\pi$
$157$		−	15.5482i		−	1.24088i	0.784253	−	0.620442i	$-0.213047\pi$
$158$	−3.87118	+	9.34587i	−0.307975	+	0.743517i
$159$	12.6142	−	5.22495i	1.00037	−	0.414366i
$160$		0			0
$161$	−14.3521	−	14.3521i	−1.13111	−	1.13111i
$162$	4.14151	+	4.14151i	0.325388	+	0.325388i
$163$	−3.87956	−	9.36608i	−0.303870	−	0.733608i	−0.999879	−	0.0155742i	$-0.995042\pi$
$163$	−3.87956	−	9.36608i	−0.303870	−	0.733608i	0.696008	−	0.718034i	$-0.254958\pi$
$164$	0.132202	−	0.0547598i	0.0103232	−	0.00427602i
$165$		0			0
$166$		−	3.40601i		−	0.264358i
$167$	11.5038	+	4.76501i	0.890187	+	0.368728i	0.780439	−	0.625232i	$-0.214996\pi$
$167$	11.5038	+	4.76501i	0.890187	+	0.368728i	0.109748	+	0.993959i	$0.464996\pi$
$168$	−3.70253	+	3.70253i	−0.285657	+	0.285657i
$169$	−16.9974			−1.30750
$170$		0			0
$171$	−0.997467			−0.0762782
$172$	0.587013	−	0.587013i	0.0447593	−	0.0447593i
$173$	3.27672	+	1.35726i	0.249125	+	0.103191i	0.503752	−	0.863849i	$-0.331953\pi$
$173$	3.27672	+	1.35726i	0.249125	+	0.103191i	−0.254627	+	0.967039i	$0.581953\pi$
$174$			6.85286i			0.519514i
$175$		0			0
$176$	4.35013	−	1.80188i	0.327903	−	0.135822i
$177$	2.66354	+	6.43037i	0.200204	+	0.483336i
$178$	1.58516	+	1.58516i	0.118813	+	0.118813i
$179$	−9.26485	−	9.26485i	−0.692487	−	0.692487i	0.270291	−	0.962779i	$-0.412880\pi$
$179$	−9.26485	−	9.26485i	−0.692487	−	0.692487i	−0.962779	+	0.270291i	$0.912880\pi$
$180$		0			0
$181$	1.68821	−	0.699281i	0.125484	−	0.0519772i	−0.319058	−	0.947735i	$-0.603366\pi$
$181$	1.68821	−	0.699281i	0.125484	−	0.0519772i	0.444542	+	0.895758i	$0.353366\pi$
$182$	−7.43696	+	17.9544i	−0.551264	+	1.33087i
$183$		−	18.3656i		−	1.35763i
$184$	5.28485	+	2.18906i	0.389604	+	0.161379i
$185$		0			0
$186$	10.7481			0.788087
$187$	16.8689	+	9.60913i	1.23358	+	0.702689i
$188$	−5.85635			−0.427118
$189$	14.1521	−	14.1521i	1.02942	−	1.02942i
$190$		0			0
$191$			16.8319i			1.21791i	0.793205	+	0.608955i	$0.208411\pi$
$191$			16.8319i			1.21791i	−0.793205	+	0.608955i	$0.791589\pi$
$192$	0.564729	−	1.36338i	0.0407558	−	0.0983932i
$193$	5.38504	−	2.23056i	0.387624	−	0.160559i	−0.180356	−	0.983601i	$-0.557725\pi$
$193$	5.38504	−	2.23056i	0.387624	−	0.160559i	0.567980	+	0.823042i	$0.307725\pi$
$194$	−1.66675	−	4.02389i	−0.119666	−	0.288899i
$195$		0			0
$196$	3.95275	+	3.95275i	0.282340	+	0.282340i
$197$	−1.34760	−	3.25339i	−0.0960123	−	0.231794i	0.868575	−	0.495557i	$-0.165036\pi$
$197$	−1.34760	−	3.25339i	−0.0960123	−	0.231794i	−0.964587	+	0.263763i	$0.915036\pi$
$198$	−3.57705	+	1.48166i	−0.254210	+	0.105297i
$199$	−6.42910	+	15.5212i	−0.455747	+	1.10027i	0.514356	+	0.857577i	$0.328031\pi$
$199$	−6.42910	+	15.5212i	−0.455747	+	1.10027i	−0.970103	+	0.242694i	$0.921969\pi$
$200$		0			0
$201$	11.8164	+	4.89452i	0.833466	+	0.345233i
$202$	7.59384	−	7.59384i	0.534301	−	0.534301i
$203$	16.4773			1.15648
$204$	5.86793	−	1.60888i	0.410837	−	0.112644i
$205$		0			0
$206$	−5.25597	+	5.25597i	−0.366200	+	0.366200i
$207$	−4.34567	−	1.80003i	−0.302045	−	0.125111i
$208$		−	5.47699i		−	0.379761i
$209$	−2.18575	+	5.27687i	−0.151192	+	0.365009i
$210$		0			0
$211$	−8.73280	−	21.0828i	−0.601191	−	1.45140i	−0.872357	−	0.488870i	$-0.837409\pi$
$211$	−8.73280	−	21.0828i	−0.601191	−	1.45140i	0.271166	−	0.962533i	$-0.412591\pi$
$212$	6.54226	+	6.54226i	0.449324	+	0.449324i
$213$	−5.36758	−	5.36758i	−0.367780	−	0.367780i
$214$	−6.01999	−	14.5335i	−0.411518	−	0.993492i
$215$		0			0
$216$	−2.15856	+	5.21121i	−0.146871	+	0.354578i
$217$		−	25.8431i		−	1.75434i
$218$	−5.94112	−	2.46089i	−0.402383	−	0.166673i
$219$	16.8336	−	16.8336i	1.13751	−	1.13751i
$220$		0			0
$221$	17.8356	−	13.8510i	1.19975	−	0.931717i
$222$	13.7119			0.920281
$223$	6.41246	−	6.41246i	0.429410	−	0.429410i	−0.459017	−	0.888427i	$-0.651798\pi$
$223$	6.41246	−	6.41246i	0.429410	−	0.429410i	0.888427	+	0.459017i	$0.151798\pi$
$224$	−3.27815	−	1.35785i	−0.219031	−	0.0907255i
$225$		0			0
$226$	−3.68974	+	8.90782i	−0.245438	+	0.592540i
$227$	−14.5491	+	6.02643i	−0.965658	+	0.399988i	−0.809094	−	0.587679i	$-0.800042\pi$
$227$	−14.5491	+	6.02643i	−0.965658	+	0.399988i	−0.156564	+	0.987668i	$0.550042\pi$
$228$	0.685038	+	1.65383i	0.0453678	+	0.109527i
$229$	14.2262	+	14.2262i	0.940092	+	0.940092i	0.998304	−	0.0582124i	$-0.0185401\pi$
$229$	14.2262	+	14.2262i	0.940092	+	0.940092i	−0.0582124	+	0.998304i	$0.518540\pi$
$230$		0			0
$231$	−9.43496	−	22.7780i	−0.620775	−	1.49868i
$232$	−4.29029	+	1.77710i	−0.281672	+	0.116672i
$233$	7.37613	−	17.8076i	0.483227	−	1.16661i	−0.474841	−	0.880071i	$-0.657495\pi$
$233$	7.37613	−	17.8076i	0.483227	−	1.16661i	0.958068	−	0.286541i	$-0.0925054\pi$
$234$			4.50366i			0.294414i
$235$		0			0
$236$	−3.33507	+	3.33507i	−0.217095	+	0.217095i
$237$	−14.9281			−0.969684
$238$	−3.86845	−	14.1091i	−0.250755	−	0.914555i
$239$	14.2040			0.918778			0.459389	−	0.888235i	$-0.348068\pi$
$239$	14.2040			0.918778			0.459389	+	0.888235i	$0.348068\pi$
$240$		0			0
$241$	−4.22633	−	1.75060i	−0.272242	−	0.112766i	0.242386	−	0.970180i	$-0.422070\pi$
$241$	−4.22633	−	1.75060i	−0.272242	−	0.112766i	−0.514628	+	0.857414i	$0.672070\pi$
$242$			11.1704i			0.718058i
$243$	3.16806	−	7.64838i	0.203231	−	0.490644i
$244$	11.4980	−	4.76261i	0.736082	−	0.304895i
$245$		0			0
$246$	0.149316	+	0.149316i	0.00952007	+	0.00952007i
$247$	4.69788	+	4.69788i	0.298919	+	0.298919i
$248$	2.78721	+	6.72892i	0.176988	+	0.427287i
$249$	4.64367	−	1.92347i	0.294281	−	0.121895i
$250$		0			0
$251$			9.00712i			0.568524i	0.958747	+	0.284262i	$0.0917486\pi$
$251$			9.00712i			0.568524i	−0.958747	+	0.284262i	$0.908251\pi$
$252$	2.69558	+	1.11655i	0.169806	+	0.0703358i
$253$	−19.0453	+	19.0453i	−1.19737	+	1.19737i
$254$	3.20591			0.201157
$255$		0			0
$256$	1.00000			0.0625000
$257$	−20.2643	+	20.2643i	−1.26405	+	1.26405i	−0.314938	+	0.949112i	$0.601984\pi$
$257$	−20.2643	+	20.2643i	−1.26405	+	1.26405i	−0.949112	+	0.314938i	$0.898016\pi$
$258$	1.13182	+	0.468816i	0.0704641	+	0.0291872i
$259$		−	32.9693i		−	2.04862i
$260$		0			0
$261$	3.52785	−	1.46129i	0.218369	−	0.0904513i
$262$	−1.36747	−	3.30136i	−0.0844825	−	0.203959i
$263$	4.27498	+	4.27498i	0.263606	+	0.263606i	0.826517	−	0.562911i	$-0.190319\pi$
$263$	4.27498	+	4.27498i	0.263606	+	0.263606i	−0.562911	+	0.826517i	$0.690319\pi$
$264$	4.91328	+	4.91328i	0.302392	+	0.302392i
$265$		0			0
$266$	3.97653	−	1.64713i	0.243816	−	0.100992i
$267$	−1.26598	+	3.05635i	−0.0774769	+	0.187046i
$268$			8.66703i			0.529423i
$269$	−15.6073	−	6.46477i	−0.951596	−	0.394164i	−0.147765	−	0.989022i	$-0.547208\pi$
$269$	−15.6073	−	6.46477i	−0.951596	−	0.394164i	−0.803830	+	0.594858i	$0.797208\pi$
$270$		0			0
$271$	−22.9305			−1.39293			−0.696463	−	0.717593i	$-0.745244\pi$
$271$	−22.9305			−1.39293			−0.696463	+	0.717593i	$0.745244\pi$
$272$	2.52894	+	3.25645i	0.153339	+	0.197451i
$273$	−28.6785			−1.73570
$274$	2.34017	−	2.34017i	0.141375	−	0.141375i
$275$		0			0
$276$			8.44146i			0.508116i
$277$	−7.65435	+	18.4792i	−0.459905	+	1.11031i	0.508530	+	0.861044i	$0.330189\pi$
$277$	−7.65435	+	18.4792i	−0.459905	+	1.11031i	−0.968435	+	0.249265i	$0.919811\pi$
$278$	1.66295	−	0.688816i	0.0997370	−	0.0413124i
$279$	−2.29189	−	5.53311i	−0.137212	−	0.331259i
$280$		0			0
$281$	16.4633	+	16.4633i	0.982118	+	0.982118i	0.999843	−	0.0177247i	$-0.00564226\pi$
$281$	16.4633	+	16.4633i	0.982118	+	0.982118i	−0.0177247	+	0.999843i	$0.505642\pi$
$282$	−3.30725	−	7.98440i	−0.196944	−	0.475464i
$283$	23.2363	−	9.62478i	1.38125	−	0.572134i	0.436437	−	0.899735i	$-0.356240\pi$
$283$	23.2363	−	9.62478i	1.38125	−	0.572134i	0.944816	+	0.327601i	$0.106240\pi$
$284$	1.96849	−	4.75235i	0.116808	−	0.282000i
$285$		0			0
$286$	23.8256	+	9.86889i	1.40884	+	0.583560i
$287$	0.359022	−	0.359022i	0.0211924	−	0.0211924i
$288$	−0.822287			−0.0484538
$289$	−4.20895	+	16.4707i	−0.247585	+	0.968866i
$290$		0			0
$291$	4.54481	−	4.54481i	0.266422	−	0.266422i
$292$	14.9042	+	6.17351i	0.872201	+	0.361278i
$293$			25.5251i			1.49119i	0.666399	+	0.745595i	$0.267835\pi$
$293$			25.5251i			1.49119i	−0.666399	+	0.745595i	$0.732165\pi$
$294$	−3.15686	+	7.62132i	−0.184112	+	0.444485i
$295$		0			0
$296$	3.55579	+	8.58444i	0.206676	+	0.498961i
$297$	−18.7800	−	18.7800i	−1.08972	−	1.08972i
$298$	−2.94700	−	2.94700i	−0.170715	−	0.170715i
$299$	11.9894	+	28.9451i	0.693368	+	1.67394i
$300$		0			0
$301$	1.12724	−	2.72139i	0.0649729	−	0.156858i
$302$		−	4.59258i		−	0.264273i
$303$	14.6417	+	6.06480i	0.841145	+	0.348414i
$304$	−0.857748	+	0.857748i	−0.0491952	+	0.0491952i
$305$		0			0
$306$	−2.07951	−	2.67774i	−0.118878	−	0.153076i
$307$	14.2382			0.812616			0.406308	−	0.913736i	$-0.366816\pi$
$307$	14.2382			0.812616			0.406308	+	0.913736i	$0.366816\pi$
$308$	11.8137	−	11.8137i	0.673147	−	0.673147i
$309$	−10.1341	−	4.19766i	−0.576506	−	0.238797i
$310$		0			0
$311$	−4.65012	+	11.2264i	−0.263684	+	0.636590i	−0.999161	−	0.0409602i	$-0.986958\pi$
$311$	−4.65012	+	11.2264i	−0.263684	+	0.636590i	0.735477	+	0.677550i	$0.236958\pi$
$312$	7.46720	−	3.09302i	0.422747	−	0.175108i
$313$	8.33854	+	20.1310i	0.471322	+	1.13787i	0.963579	+	0.267422i	$0.0861719\pi$
$313$	8.33854	+	20.1310i	0.471322	+	1.13787i	−0.492257	+	0.870450i	$0.663828\pi$
$314$	10.9943	+	10.9943i	0.620442	+	0.620442i
$315$		0			0
$316$	−3.87118	−	9.34587i	−0.217771	−	0.525746i
$317$	−9.47130	+	3.92314i	−0.531961	+	0.220346i	−0.632462	−	0.774591i	$-0.717956\pi$
$317$	−9.47130	+	3.92314i	−0.531961	+	0.220346i	0.100501	+	0.994937i	$0.467956\pi$
$318$	−5.22495	+	12.6142i	−0.293001	+	0.707367i
$319$		−	21.8654i		−	1.22423i
$320$		0			0
$321$	16.4150	−	16.4150i	0.916197	−	0.916197i
$322$	20.2970			1.13111
$323$	−4.96241	−	0.624023i	−0.276116	−	0.0347216i
$324$	−5.85698			−0.325388
$325$		0			0
$326$	9.36608	+	3.87956i	0.518739	+	0.214869i
$327$		−	9.48972i		−	0.524783i
$328$	−0.0547598	+	0.132202i	−0.00302360	+	0.00729963i
$329$	−19.1980	+	7.95207i	−1.05842	+	0.438412i
$330$		0			0
$331$	−0.209438	−	0.209438i	−0.0115117	−	0.0115117i	0.701327	−	0.712839i	$-0.252591\pi$
$331$	−0.209438	−	0.209438i	−0.0115117	−	0.0115117i	−0.712839	+	0.701327i	$0.752591\pi$
$332$	2.40841	+	2.40841i	0.132179	+	0.132179i
$333$	−2.92388	−	7.05888i	−0.160228	−	0.386824i
$334$	−11.5038	+	4.76501i	−0.629457	+	0.260730i
$335$		0			0
$336$		−	5.23617i		−	0.285657i
$337$	12.9824	+	5.37748i	0.707196	+	0.292930i	0.707144	−	0.707070i	$-0.249983\pi$
$337$	12.9824	+	5.37748i	0.707196	+	0.292930i	5.22341e−5		1.00000i	$0.499983\pi$
$338$	12.0190	−	12.0190i	0.653748	−	0.653748i
$339$	−14.2284			−0.772782
$340$		0			0
$341$	−34.2939			−1.85712
$342$	0.705316	−	0.705316i	0.0381391	−	0.0381391i
$343$	−4.62206	−	1.91452i	−0.249568	−	0.103374i
$344$			0.830161i			0.0447593i
$345$		0			0
$346$	−3.27672	+	1.35726i	−0.176158	+	0.0729669i
$347$	4.26669	+	10.3007i	0.229048	+	0.552971i	0.996062	−	0.0886594i	$-0.0282583\pi$
$347$	4.26669	+	10.3007i	0.229048	+	0.552971i	−0.767014	+	0.641631i	$0.778258\pi$
$348$	−4.84570	−	4.84570i	−0.259757	−	0.259757i
$349$	−1.77671	−	1.77671i	−0.0951051	−	0.0951051i	0.657953	−	0.753059i	$-0.271422\pi$
$349$	−1.77671	−	1.77671i	−0.0951051	−	0.0951051i	−0.753059	+	0.657953i	$0.771422\pi$
$350$		0			0
$351$	−28.5418	+	11.8224i	−1.52345	+	0.631033i
$352$	−1.80188	+	4.35013i	−0.0960406	+	0.231862i
$353$		−	10.0823i		−	0.536629i	−0.963331	−	0.268314i	$-0.913533\pi$
$353$		−	10.0823i		−	0.536629i	0.963331	−	0.268314i	$-0.0864666\pi$
$354$	−6.43037	−	2.66354i	−0.341770	−	0.141566i
$355$		0			0
$356$	−2.24175			−0.118813
$357$	17.0513	−	13.2420i	0.902452	−	0.700838i
$358$	13.1025			0.692487
$359$	−17.4429	+	17.4429i	−0.920599	+	0.920599i	−0.997072	−	0.0764723i	$-0.975634\pi$
$359$	−17.4429	+	17.4429i	−0.920599	+	0.920599i	0.0764723	+	0.997072i	$0.475634\pi$
$360$		0			0
$361$			17.5285i			0.922555i
$362$	−0.699281	+	1.68821i	−0.0367534	+	0.0887306i
$363$	−15.2294	+	6.30823i	−0.799337	+	0.331096i
$364$	−7.43696	−	17.9544i	−0.389803	−	0.941067i
$365$		0			0
$366$	12.9865	+	12.9865i	0.678813	+	0.678813i
$367$	−11.3939	−	27.5072i	−0.594755	−	1.43587i	−0.878863	−	0.477073i	$-0.841698\pi$
$367$	−11.3939	−	27.5072i	−0.594755	−	1.43587i	0.284108	−	0.958792i	$-0.408302\pi$
$368$	−5.28485	+	2.18906i	−0.275492	+	0.114112i
$369$	0.0450283	−	0.108708i	0.00234408	−	0.00565911i
$370$		0			0
$371$	30.3299	+	12.5631i	1.57465	+	0.652242i
$372$	−7.60004	+	7.60004i	−0.394043	+	0.394043i
$373$	−20.8039			−1.07718			−0.538592	−	0.842567i	$-0.681044\pi$
$373$	−20.8039			−1.07718			−0.538592	+	0.842567i	$0.681044\pi$
$374$	−18.7228	+	5.13346i	−0.968134	+	0.265445i
$375$		0			0
$376$	4.14106	−	4.14106i	0.213559	−	0.213559i
$377$	−23.4979	−	9.73315i	−1.21020	−	0.501283i
$378$			20.0142i			1.02942i
$379$	3.99706	−	9.64974i	0.205315	−	0.495674i	−0.787359	−	0.616494i	$-0.788552\pi$
$379$	3.99706	−	9.64974i	0.205315	−	0.495674i	0.992674	+	0.120820i	$0.0385524\pi$
$380$		0			0
$381$	1.81047	+	4.37087i	0.0927533	+	0.223926i
$382$	−11.9019	−	11.9019i	−0.608955	−	0.608955i
$383$	14.2495	+	14.2495i	0.728113	+	0.728113i	0.970244	−	0.242130i	$-0.0778462\pi$
$383$	14.2495	+	14.2495i	0.728113	+	0.728113i	−0.242130	+	0.970244i	$0.577846\pi$
$384$	0.564729	+	1.36338i	0.0288187	+	0.0695745i
$385$		0			0
$386$	−2.23056	+	5.38504i	−0.113532	+	0.274091i
$387$		−	0.682631i		−	0.0347001i
$388$	4.02389	+	1.66675i	0.204282	+	0.0846164i
$389$	−13.9058	+	13.9058i	−0.705051	+	0.705051i	−0.965490	−	0.260440i	$-0.916133\pi$
$389$	−13.9058	+	13.9058i	−0.705051	+	0.705051i	0.260440	+	0.965490i	$0.416133\pi$
$390$		0			0
$391$	−20.4936	−	11.6739i	−1.03641	−	0.590373i
$392$	−5.59004			−0.282340
$393$	3.72875	−	3.72875i	0.188090	−	0.188090i
$394$	3.25339	+	1.34760i	0.163903	+	0.0678909i
$395$		0			0
$396$	1.48166	−	3.57705i	0.0744564	−	0.179754i
$397$	22.1250	−	9.16446i	1.11042	−	0.459951i	0.249338	−	0.968416i	$-0.419787\pi$
$397$	22.1250	−	9.16446i	1.11042	−	0.459951i	0.861083	+	0.508465i	$0.169787\pi$
$398$	−6.42910	−	15.5212i	−0.322262	−	0.778009i
$399$	4.49132	+	4.49132i	0.224847	+	0.224847i
$400$		0			0
$401$	−8.81734	−	21.2869i	−0.440317	−	1.06302i	−0.975838	−	0.218497i	$-0.929885\pi$
$401$	−8.81734	−	21.2869i	−0.440317	−	1.06302i	0.535521	−	0.844522i	$-0.320115\pi$
$402$	−11.8164	+	4.89452i	−0.589350	+	0.244117i
$403$	−15.2655	+	36.8543i	−0.760431	+	1.83584i
$404$			10.7393i			0.534301i
$405$		0			0
$406$	−11.6512	+	11.6512i	−0.578239	+	0.578239i
$407$	−43.7505			−2.16863
$408$	−3.01160	+	5.28690i	−0.149097	+	0.261741i
$409$	12.7488			0.630389			0.315195	−	0.949027i	$-0.397930\pi$
$409$	12.7488			0.630389			0.315195	+	0.949027i	$0.397930\pi$
$410$		0			0
$411$	4.51209	+	1.86897i	0.222565	+	0.0921895i
$412$		−	7.43306i		−	0.366200i
$413$	−6.40432	+	15.4614i	−0.315136	+	0.760806i
$414$	4.34567	−	1.80003i	0.213578	−	0.0884669i
$415$		0			0
$416$	3.87282	+	3.87282i	0.189881	+	0.189881i
$417$	1.87823	+	1.87823i	0.0919773	+	0.0919773i
$418$	−2.18575	−	5.27687i	−0.106909	−	0.258100i
$419$	25.2883	−	10.4748i	1.23541	−	0.511725i	0.333136	−	0.942879i	$-0.391893\pi$
$419$	25.2883	−	10.4748i	1.23541	−	0.511725i	0.902279	+	0.431153i	$0.141893\pi$
$420$		0			0
$421$		−	33.6813i		−	1.64153i	−0.571268	−	0.820764i	$-0.693548\pi$
$421$		−	33.6813i		−	1.64153i	0.571268	−	0.820764i	$-0.306452\pi$
$422$	21.0828	+	8.73280i	1.02630	+	0.425106i
$423$	−3.40514	+	3.40514i	−0.165564	+	0.165564i
$424$	−9.25215			−0.449324
$425$		0			0
$426$	7.59090			0.367780
$427$	31.2251	−	31.2251i	1.51109	−	1.51109i
$428$	14.5335	+	6.01999i	0.702505	+	0.290987i
$429$			38.0565i			1.83739i
$430$		0			0
$431$	−16.7963	+	6.95725i	−0.809049	+	0.335119i	−0.748575	−	0.663051i	$-0.769261\pi$
$431$	−16.7963	+	6.95725i	−0.809049	+	0.335119i	−0.0604746	+	0.998170i	$0.519261\pi$
$432$	−2.15856	−	5.21121i	−0.103854	−	0.250725i
$433$	5.73034	+	5.73034i	0.275382	+	0.275382i	0.831262	−	0.555880i	$-0.187619\pi$
$433$	5.73034	+	5.73034i	0.275382	+	0.275382i	−0.555880	+	0.831262i	$0.687619\pi$
$434$	18.2738	+	18.2738i	0.877170	+	0.877170i
$435$		0			0
$436$	5.94112	−	2.46089i	0.284528	−	0.117855i
$437$	2.65541	−	6.41073i	0.127026	−	0.306667i
$438$			23.8064i			1.13751i
$439$	22.1522	+	9.17574i	1.05727	+	0.437934i	0.842480	−	0.538727i	$-0.181095\pi$
$439$	22.1522	+	9.17574i	1.05727	+	0.437934i	0.214786	+	0.976661i	$0.431095\pi$
$440$		0			0
$441$	4.59662			0.218887
$442$	−2.81753	+	22.4058i	−0.134016	+	1.06573i
$443$	−0.244075			−0.0115964			−0.00579819	−	0.999983i	$-0.501846\pi$
$443$	−0.244075			−0.0115964			−0.00579819	+	0.999983i	$0.501846\pi$
$444$	−9.69577	+	9.69577i	−0.460141	+	0.460141i
$445$		0			0
$446$			9.06859i			0.429410i
$447$	2.35361	−	5.68212i	0.111322	−	0.268755i
$448$	3.27815	−	1.35785i	0.154878	−	0.0641526i
$449$	−0.0315454	−	0.0761574i	−0.00148872	−	0.00359409i	0.923133	−	0.384480i	$-0.125619\pi$
$449$	−0.0315454	−	0.0761574i	−0.00148872	−	0.00359409i	−0.924622	+	0.380886i	$0.875619\pi$
$450$		0			0
$451$	−0.476424	−	0.476424i	−0.0224339	−	0.0224339i
$452$	−3.68974	−	8.90782i	−0.173551	−	0.418989i
$453$	6.26141	−	2.59356i	0.294187	−	0.121856i
$454$	6.02643	−	14.5491i	0.282835	−	0.682823i
$455$		0			0
$456$	−1.65383	−	0.685038i	−0.0774476	−	0.0320799i
$457$	−17.2461	+	17.2461i	−0.806737	+	0.806737i	−0.984139	−	0.177402i	$-0.943231\pi$
$457$	−17.2461	+	17.2461i	−0.806737	+	0.806737i	0.177402	+	0.984139i	$0.443231\pi$
$458$	−20.1188			−0.940092
$459$	11.5112	−	20.2081i	0.537297	−	0.943232i
$460$		0			0
$461$	20.5839	−	20.5839i	0.958687	−	0.958687i	−0.0404924	−	0.999180i	$-0.512893\pi$
$461$	20.5839	−	20.5839i	0.958687	−	0.958687i	0.999180	+	0.0404924i	$0.0128926\pi$
$462$	22.7780	+	9.43496i	1.05973	+	0.438954i
$463$			27.9762i			1.30016i	0.759865	+	0.650081i	$0.225265\pi$
$463$			27.9762i			1.30016i	−0.759865	+	0.650081i	$0.774735\pi$
$464$	1.77710	−	4.29029i	0.0824997	−	0.199172i
$465$		0			0
$466$	7.37613	+	17.8076i	0.341693	+	0.824919i
$467$	−22.1173	−	22.1173i	−1.02347	−	1.02347i	−0.999718	−	0.0237504i	$-0.992439\pi$
$467$	−22.1173	−	22.1173i	−1.02347	−	1.02347i	−0.0237504	−	0.999718i	$-0.507561\pi$
$468$	−3.18457	−	3.18457i	−0.147207	−	0.147207i
$469$	11.7686	+	28.4118i	0.543422	+	1.31194i
$470$		0			0
$471$	−8.78053	+	21.1981i	−0.404586	+	0.976756i
$472$		−	4.71650i		−	0.217095i
$473$	−3.61131	−	1.49585i	−0.166048	−	0.0687793i
$474$	10.5558	−	10.5558i	0.484842	−	0.484842i
$475$		0			0
$476$	12.7120	+	7.24121i	0.582655	+	0.331900i
$477$	7.60792			0.348343
$478$	−10.0437	+	10.0437i	−0.459389	+	0.459389i
$479$	−11.1564	−	4.62112i	−0.509748	−	0.211144i	0.112959	−	0.993600i	$-0.463967\pi$
$479$	−11.1564	−	4.62112i	−0.509748	−	0.211144i	−0.622707	+	0.782455i	$0.713967\pi$
$480$		0			0
$481$	−19.4751	+	47.0169i	−0.887986	+	2.14379i
$482$	4.22633	−	1.75060i	0.192504	−	0.0797378i
$483$	11.4623	+	27.6724i	0.521552	+	1.25914i
$484$	−7.89864	−	7.89864i	−0.359029	−	0.359029i
$485$		0			0
$486$	3.16806	+	7.64838i	0.143706	+	0.346937i
$487$	−4.63377	+	1.91937i	−0.209976	+	0.0869749i	−0.485192	−	0.874407i	$-0.661250\pi$
$487$	−4.63377	+	1.91937i	−0.209976	+	0.0869749i	0.275217	+	0.961382i	$0.411250\pi$
$488$	−4.76261	+	11.4980i	−0.215593	+	0.520488i
$489$			14.9604i			0.676532i
$490$		0			0
$491$	−18.6988	+	18.6988i	−0.843865	+	0.843865i	−0.989359	−	0.145494i	$-0.953523\pi$
$491$	−18.6988	+	18.6988i	−0.843865	+	0.843865i	0.145494	+	0.989359i	$0.453523\pi$
$492$	−0.211165			−0.00952007
$493$	18.4653	−	5.06285i	0.831635	−	0.228019i
$494$	−6.64381			−0.298919
$495$		0			0
$496$	−6.72892	−	2.78721i	−0.302138	−	0.125150i
$497$		−	18.2518i		−	0.818707i
$498$	−1.92347	+	4.64367i	−0.0861929	+	0.208088i
$499$	−27.6595	+	11.4569i	−1.23821	+	0.512882i	−0.903154	−	0.429317i	$-0.858754\pi$
$499$	−27.6595	+	11.4569i	−1.23821	+	0.512882i	−0.335053	+	0.942199i	$0.608754\pi$
$500$		0			0
$501$	−12.9930	−	12.9930i	−0.580484	−	0.580484i
$502$	−6.36899	−	6.36899i	−0.284262	−	0.284262i
$503$	−13.0499	−	31.5052i	−0.581865	−	1.40475i	−0.891120	−	0.453768i	$-0.850080\pi$
$503$	−13.0499	−	31.5052i	−0.581865	−	1.40475i	0.309255	−	0.950979i	$-0.399920\pi$
$504$	−2.69558	+	1.11655i	−0.120071	+	0.0497349i
$505$		0			0
$506$		−	26.9342i		−	1.19737i
$507$	23.1739	+	9.59895i	1.02919	+	0.426304i
$508$	−2.26692	+	2.26692i	−0.100578	+	0.100578i
$509$	28.0939			1.24524			0.622620	−	0.782525i	$-0.286068\pi$
$509$	28.0939			1.24524			0.622620	+	0.782525i	$0.286068\pi$
$510$		0			0
$511$	57.2409			2.53219
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	6.32141	+	2.61841i	0.279097	+	0.115606i
$514$		−	28.6580i		−	1.26405i
$515$		0			0
$516$	−1.13182	+	0.468816i	−0.0498257	+	0.0206385i
$517$	10.5524	+	25.4758i	0.464096	+	1.12043i
$518$	23.3129	+	23.3129i	1.02431	+	1.02431i
$519$	−3.70092	−	3.70092i	−0.162452	−	0.162452i
$520$		0			0
$521$	17.6215	−	7.29907i	0.772013	−	0.319778i	0.0383252	−	0.999265i	$-0.487798\pi$
$521$	17.6215	−	7.29907i	0.772013	−	0.319778i	0.733687	+	0.679487i	$0.237798\pi$
$522$	−1.46129	+	3.52785i	−0.0639587	+	0.154410i
$523$			6.69653i			0.292819i	0.989224	+	0.146409i	$0.0467717\pi$
$523$			6.69653i			0.292819i	−0.989224	+	0.146409i	$0.953228\pi$
$524$	3.30136	+	1.36747i	0.144221	+	0.0597381i
$525$		0			0
$526$	−6.04573			−0.263606
$527$	−7.94061	−	28.9611i	−0.345899	−	1.26157i
$528$	−6.94843			−0.302392
$529$	6.87423	−	6.87423i	0.298879	−	0.298879i
$530$		0			0
$531$			3.87832i			0.168305i
$532$	−1.64713	+	3.97653i	−0.0714122	+	0.172404i
$533$	−0.724069	+	0.299919i	−0.0313629	+	0.0129909i
$534$	−1.26598	−	3.05635i	−0.0547844	−	0.132261i
$535$		0			0
$536$	−6.12852	−	6.12852i	−0.264712	−	0.264712i
$537$	7.39935	+	17.8636i	0.319305	+	0.770871i
$538$	15.6073	−	6.46477i	0.672880	−	0.278716i
$539$	10.0726	−	24.3174i	0.433857	−	1.04742i
$540$		0			0
$541$	−6.32639	−	2.62047i	−0.271993	−	0.112663i	0.242518	−	0.970147i	$-0.422027\pi$
$541$	−6.32639	−	2.62047i	−0.271993	−	0.112663i	−0.514511	+	0.857484i	$0.672027\pi$
$542$	16.2143	−	16.2143i	0.696463	−	0.696463i
$543$	−2.69657			−0.115721
$544$	−4.09089	−	0.514430i	−0.175395	−	0.0220560i
$545$		0			0
$546$	20.2787	−	20.2787i	0.867850	−	0.867850i
$547$	3.26202	+	1.35117i	0.139474	+	0.0577719i	0.451329	−	0.892358i	$-0.350950\pi$
$547$	3.26202	+	1.35117i	0.139474	+	0.0577719i	−0.311855	+	0.950130i	$0.600950\pi$
$548$			3.30950i			0.141375i
$549$	3.91624	−	9.45463i	0.167141	−	0.403514i
$550$		0			0
$551$	2.15569	+	5.20429i	0.0918355	+	0.221710i
$552$	−5.96902	−	5.96902i	−0.254058	−	0.254058i
$553$	−25.3806	−	25.3806i	−1.07929	−	1.07929i
$554$	−7.65435	−	18.4792i	−0.325202	−	0.785108i
$555$		0			0
$556$	−0.688816	+	1.66295i	−0.0292123	+	0.0705247i
$557$			45.7591i			1.93888i	0.245338	+	0.969438i	$0.421101\pi$
$557$			45.7591i			1.93888i	−0.245338	+	0.969438i	$0.578899\pi$
$558$	5.53311	+	2.29189i	0.234235	+	0.0970234i
$559$	−3.21506	+	3.21506i	−0.135983	+	0.135983i
$560$		0			0
$561$	−17.5721	−	22.6272i	−0.741897	−	0.955322i
$562$	−23.2826			−0.982118
$563$	7.05601	−	7.05601i	0.297375	−	0.297375i	−0.542610	−	0.839985i	$-0.682564\pi$
$563$	7.05601	−	7.05601i	0.297375	−	0.297375i	0.839985	+	0.542610i	$0.182564\pi$
$564$	7.98440	+	3.30725i	0.336204	+	0.139260i
$565$		0			0
$566$	−9.62478	+	23.2363i	−0.404560	+	0.976693i
$567$	−19.2001	+	7.95293i	−0.806327	+	0.333992i
$568$	1.96849	+	4.75235i	0.0825959	+	0.199404i
$569$	−9.56020	−	9.56020i	−0.400784	−	0.400784i	0.477725	−	0.878509i	$-0.341462\pi$
$569$	−9.56020	−	9.56020i	−0.400784	−	0.400784i	−0.878509	+	0.477725i	$0.841462\pi$
$570$		0			0
$571$	6.49469	+	15.6796i	0.271794	+	0.656169i	0.999560	−	0.0296562i	$-0.00944125\pi$
$571$	6.49469	+	15.6796i	0.271794	+	0.656169i	−0.727766	+	0.685826i	$0.759441\pi$
$572$	−23.8256	+	9.86889i	−0.996199	+	0.412639i
$573$	9.50543	−	22.9481i	0.397095	−	0.958673i
$574$			0.507734i			0.0211924i
$575$		0			0
$576$	0.581445	−	0.581445i	0.0242269	−	0.0242269i
$577$	9.67374			0.402723			0.201361	−	0.979517i	$-0.435463\pi$
$577$	9.67374			0.402723			0.201361	+	0.979517i	$0.435463\pi$
$578$	−8.67039	−	14.6227i	−0.360641	−	0.608226i
$579$	−8.60150			−0.357466
$580$		0			0
$581$	11.1654	+	4.62487i	0.463220	+	0.191872i
$582$			6.42734i			0.266422i
$583$	16.6713	−	40.2480i	0.690453	−	1.66690i
$584$	−14.9042	+	6.17351i	−0.616739	+	0.255462i
$585$		0			0
$586$	−18.0489	−	18.0489i	−0.745595	−	0.745595i
$587$	−3.24694	−	3.24694i	−0.134015	−	0.134015i	0.636917	−	0.770932i	$-0.280209\pi$
$587$	−3.24694	−	3.24694i	−0.134015	−	0.134015i	−0.770932	+	0.636917i	$0.780209\pi$
$588$	−3.15686	−	7.62132i	−0.130187	−	0.314298i
$589$	8.16245	−	3.38100i	0.336328	−	0.139312i
$590$		0			0
$591$			5.19661i			0.213760i
$592$	−8.58444	−	3.55579i	−0.352818	−	0.146142i
$593$	0.550724	−	0.550724i	0.0226155	−	0.0226155i	−0.695709	−	0.718324i	$-0.744910\pi$
$593$	0.550724	−	0.550724i	0.0226155	−	0.0226155i	0.718324	+	0.695709i	$0.244910\pi$
$594$	26.5589			1.08972
$595$		0			0
$596$	4.16768			0.170715
$597$	17.5306	−	17.5306i	0.717478	−	0.717478i
$598$	−28.9451	−	11.9894i	−1.18365	−	0.490285i
$599$			10.4846i			0.428391i	0.976791	+	0.214196i	$0.0687130\pi$
$599$			10.4846i			0.428391i	−0.976791	+	0.214196i	$0.931287\pi$
$600$		0			0
$601$	−14.1755	+	5.87170i	−0.578233	+	0.239512i	−0.652579	−	0.757721i	$-0.726313\pi$
$601$	−14.1755	+	5.87170i	−0.578233	+	0.239512i	0.0743464	+	0.997232i	$0.476313\pi$
$602$	1.12724	+	2.72139i	0.0459428	+	0.110916i
$603$	5.03940	+	5.03940i	0.205220	+	0.205220i
$604$	3.24744	+	3.24744i	0.132137	+	0.132137i
$605$		0			0
$606$	−14.6417	+	6.06480i	−0.594779	+	0.246366i
$607$	−8.27458	+	19.9766i	−0.335855	+	0.810825i	0.662250	+	0.749283i	$0.269602\pi$
$607$	−8.27458	+	19.9766i	−0.335855	+	0.810825i	−0.998105	+	0.0615418i	$0.980398\pi$
$608$		−	1.21304i		−	0.0491952i
$609$	−22.4647	−	9.30519i	−0.910316	−	0.377065i
$610$		0			0
$611$	32.0752			1.29762
$612$	3.36389	+	0.423009i	0.135977	+	0.0170991i
$613$	18.6071			0.751535			0.375768	−	0.926714i	$-0.377379\pi$
$613$	18.6071			0.751535			0.375768	+	0.926714i	$0.377379\pi$
$614$	−10.0679	+	10.0679i	−0.406308	+	0.406308i
$615$		0			0
$616$			16.7071i			0.673147i
$617$	−2.18286	+	5.26989i	−0.0878787	+	0.212158i	−0.961709	−	0.274074i	$-0.911629\pi$
$617$	−2.18286	+	5.26989i	−0.0878787	+	0.212158i	0.873830	+	0.486231i	$0.161629\pi$
$618$	10.1341	−	4.19766i	0.407651	−	0.168855i
$619$	11.1868	+	27.0073i	0.449635	+	1.08552i	0.972459	+	0.233075i	$0.0748787\pi$
$619$	11.1868	+	27.0073i	0.449635	+	1.08552i	−0.522823	+	0.852441i	$0.675121\pi$
$620$		0			0
$621$	22.8153	+	22.8153i	0.915546	+	0.915546i
$622$	−4.65012	−	11.2264i	−0.186453	−	0.450137i
$623$	−7.34881	+	3.04397i	−0.294424	+	0.121954i
$624$	−3.09302	+	7.46720i	−0.123820	+	0.298927i
$625$		0			0
$626$	−20.1310	−	8.33854i	−0.804597	−	0.333275i
$627$	5.96000	−	5.96000i	0.238020	−	0.238020i
$628$	−15.5482			−0.620442
$629$	−10.1303	−	36.9472i	−0.403920	−	1.47318i
$630$		0			0
$631$	30.9574	−	30.9574i	1.23239	−	1.23239i	0.269351	−	0.963042i	$-0.413191\pi$
$631$	30.9574	−	30.9574i	1.23239	−	1.23239i	0.963042	−	0.269351i	$-0.0868092\pi$
$632$	9.34587	+	3.87118i	0.371759	+	0.153987i
$633$			33.6755i			1.33848i
$634$	3.92314	−	9.47130i	0.155808	−	0.376153i
$635$		0			0
$636$	−5.22495	−	12.6142i	−0.207183	−	0.500184i
$637$	−21.6492	−	21.6492i	−0.857773	−	0.857773i
$638$	15.4612	+	15.4612i	0.612115	+	0.612115i
$639$	−1.61866	−	3.90780i	−0.0640333	−	0.154590i
$640$		0			0
$641$	−16.6913	+	40.2963i	−0.659265	+	1.59161i	0.139676	+	0.990197i	$0.455394\pi$
$641$	−16.6913	+	40.2963i	−0.659265	+	1.59161i	−0.798941	+	0.601410i	$0.794606\pi$
$642$			23.2143i			0.916197i
$643$	5.12401	+	2.12244i	0.202071	+	0.0837007i	0.481424	−	0.876488i	$-0.340120\pi$
$643$	5.12401	+	2.12244i	0.202071	+	0.0837007i	−0.279353	+	0.960189i	$0.590120\pi$
$644$	−14.3521	+	14.3521i	−0.565553	+	0.565553i
$645$		0			0
$646$	3.95020	−	3.06770i	0.155419	−	0.120697i
$647$	25.3893			0.998155			0.499078	−	0.866557i	$-0.333672\pi$
$647$	25.3893			0.998155			0.499078	+	0.866557i	$0.333672\pi$
$648$	4.14151	−	4.14151i	0.162694	−	0.162694i
$649$	20.5174	+	8.49858i	0.805378	+	0.333598i
$650$		0			0
$651$	−14.5943	+	35.2338i	−0.571996	+	1.38092i
$652$	−9.36608	+	3.87956i	−0.366804	+	0.151935i
$653$	−15.0457	−	36.3236i	−0.588784	−	1.42145i	−0.884666	−	0.466226i	$-0.845613\pi$
$653$	−15.0457	−	36.3236i	−0.588784	−	1.42145i	0.295882	−	0.955225i	$-0.404387\pi$
$654$	6.71024	+	6.71024i	0.262391	+	0.262391i
$655$		0			0
$656$	−0.0547598	−	0.132202i	−0.00213801	−	0.00516162i
$657$	12.2555	−	5.07640i	0.478133	−	0.198049i
$658$	7.95207	−	19.1980i	0.310004	−	0.748415i
$659$		−	39.5179i		−	1.53940i	−0.638408	−	0.769698i	$-0.720407\pi$
$659$		−	39.5179i		−	1.53940i	0.638408	−	0.769698i	$-0.279593\pi$
$660$		0			0
$661$	−2.21986	+	2.21986i	−0.0863427	+	0.0863427i	−0.748959	−	0.662616i	$-0.769446\pi$
$661$	−2.21986	+	2.21986i	−0.0863427	+	0.0863427i	0.662616	+	0.748959i	$0.269446\pi$
$662$	0.296190			0.0115117
$663$	−32.1386	+	8.81183i	−1.24816	+	0.342223i
$664$	−3.40601			−0.132179
$665$		0			0
$666$	7.05888	+	2.92388i	0.273526	+	0.113298i
$667$			26.5637i			1.02855i
$668$	4.76501	−	11.5038i	0.184364	−	0.445093i
$669$	−12.3639	+	5.12129i	−0.478016	+	0.198001i
$670$		0			0
$671$	−41.4359	−	41.4359i	−1.59962	−	1.59962i
$672$	3.70253	+	3.70253i	0.142828	+	0.142828i
$673$	8.91195	+	21.5153i	0.343530	+	0.829355i	0.997353	+	0.0727079i	$0.0231641\pi$
$673$	8.91195	+	21.5153i	0.343530	+	0.829355i	−0.653823	+	0.756647i	$0.726836\pi$
$674$	−12.9824	+	5.37748i	−0.500063	+	0.207133i
$675$		0			0
$676$			16.9974i			0.653748i
$677$	38.1349	+	15.7960i	1.46564	+	0.607089i	0.965861	−	0.259062i	$-0.0834134\pi$
$677$	38.1349	+	15.7960i	1.46564	+	0.607089i	0.499782	+	0.866151i	$0.333413\pi$
$678$	10.0610	−	10.0610i	0.386391	−	0.386391i
$679$	15.4541			0.593075
$680$		0			0
$681$	23.2392			0.890528
$682$	24.2494	−	24.2494i	0.928559	−	0.928559i
$683$	−5.77636	−	2.39265i	−0.221026	−	0.0915521i	0.269423	−	0.963022i	$-0.413167\pi$
$683$	−5.77636	−	2.39265i	−0.221026	−	0.0915521i	−0.490449	+	0.871470i	$0.663167\pi$
$684$			0.997467i			0.0381391i
$685$		0			0
$686$	4.62206	−	1.91452i	0.176471	−	0.0730968i
$687$	−11.3617	−	27.4295i	−0.433476	−	1.04650i
$688$	−0.587013	−	0.587013i	−0.0223796	−	0.0223796i
$689$	−35.8319	−	35.8319i	−1.36509	−	1.36509i
$690$		0			0
$691$	−29.6992	+	12.3018i	−1.12981	+	0.467983i	−0.867716	−	0.497060i	$-0.834413\pi$
$691$	−29.6992	+	12.3018i	−1.12981	+	0.467983i	−0.262094	+	0.965042i	$0.584413\pi$
$692$	1.35726	−	3.27672i	0.0515954	−	0.124562i
$693$		−	13.7380i		−	0.521864i
$694$	−10.3007	−	4.26669i	−0.391010	−	0.161961i
$695$		0			0
$696$	6.85286			0.259757
$697$	0.292025	−	0.512653i	0.0110612	−	0.0194181i
$698$	2.51265			0.0951051
$699$	−20.1129	+	20.1129i	−0.760739	+	0.760739i
$700$		0			0
$701$			12.7609i			0.481972i	0.970529	+	0.240986i	$0.0774708\pi$
$701$			12.7609i			0.481972i	−0.970529	+	0.240986i	$0.922529\pi$
$702$	11.8224	−	28.5418i	0.446208	−	1.07724i
$703$	10.4133	−	4.31332i	0.392744	−	0.162680i
$704$	−1.80188	−	4.35013i	−0.0679109	−	0.163952i
$705$		0			0
$706$	7.12929	+	7.12929i	0.268314	+	0.268314i
$707$	14.5824	+	35.2051i	0.548429	+	1.32402i
$708$	6.43037	−	2.66354i	0.241668	−	0.100102i
$709$	12.8274	−	30.9681i	0.481744	−	1.16303i	−0.477036	−	0.878884i	$-0.658289\pi$
$709$	12.8274	−	30.9681i	0.481744	−	1.16303i	0.958780	−	0.284149i	$-0.0917110\pi$
$710$		0			0
$711$	−7.68499	−	3.18323i	−0.288210	−	0.119380i
$712$	1.58516	−	1.58516i	0.0594063	−	0.0594063i
$713$	41.6627			1.56028
$714$	−2.69364	+	21.4206i	−0.100807	+	0.801645i
$715$		0			0
$716$	−9.26485	+	9.26485i	−0.346244	+	0.346244i
$717$	−19.3653	−	8.02139i	−0.723212	−	0.299564i
$718$		−	24.6679i		−	0.920599i
$719$	−10.9707	+	26.4857i	−0.409140	+	0.987750i	0.576225	+	0.817291i	$0.304525\pi$
$719$	−10.9707	+	26.4857i	−0.409140	+	0.987750i	−0.985365	+	0.170459i	$0.945475\pi$
$720$		0			0
$721$	−10.0930	−	24.3667i	−0.375883	−	0.907463i
$722$	−12.3945	−	12.3945i	−0.461277	−	0.461277i
$723$	4.77346	+	4.77346i	0.177527	+	0.177527i
$724$	−0.699281	−	1.68821i	−0.0259886	−	0.0627420i
$725$		0			0
$726$	6.30823	−	15.2294i	0.234120	−	0.565216i
$727$			21.0302i			0.779966i	0.920822	+	0.389983i	$0.127519\pi$
$727$			21.0302i			0.779966i	−0.920822	+	0.389983i	$0.872481\pi$
$728$	17.9544	+	7.43696i	0.665435	+	0.275632i
$729$	−21.0631	+	21.0631i	−0.780113	+	0.780113i
$730$		0			0
$731$	0.427059	−	3.39610i	0.0157954	−	0.125609i
$732$	−18.3656			−0.678813
$733$	6.38248	−	6.38248i	0.235742	−	0.235742i	−0.579342	−	0.815084i	$-0.696690\pi$
$733$	6.38248	−	6.38248i	0.235742	−	0.235742i	0.815084	+	0.579342i	$0.196690\pi$
$734$	27.5072	+	11.3939i	1.01531	+	0.420555i
$735$		0			0
$736$	2.18906	−	5.28485i	0.0806897	−	0.194802i
$737$	37.7027	−	15.6170i	1.38880	−	0.575258i
$738$	0.0450283	+	0.108708i	0.00165751	+	0.00400160i
$739$	10.1850	+	10.1850i	0.374662	+	0.374662i	0.869172	−	0.494510i	$-0.164653\pi$
$739$	10.1850	+	10.1850i	0.374662	+	0.374662i	−0.494510	+	0.869172i	$0.664653\pi$
$740$		0			0
$741$	−3.75195	−	9.05801i	−0.137831	−	0.332754i
$742$	−30.3299	+	12.5631i	−1.11345	+	0.461205i
$743$	−12.6717	+	30.5921i	−0.464879	+	1.12232i	0.501492	+	0.865162i	$0.332785\pi$
$743$	−12.6717	+	30.5921i	−0.464879	+	1.12232i	−0.966370	+	0.257154i	$0.917215\pi$
$744$		−	10.7481i		−	0.394043i
$745$		0			0
$746$	14.7106	−	14.7106i	0.538592	−	0.538592i
$747$	2.80072			0.102473
$748$	9.60913	−	16.8689i	0.351344	−	0.616789i
$749$	55.8174			2.03952
$750$		0			0
$751$	−5.92242	−	2.45315i	−0.216112	−	0.0895166i	0.272001	−	0.962297i	$-0.412315\pi$
$751$	−5.92242	−	2.45315i	−0.216112	−	0.0895166i	−0.488113	+	0.872780i	$0.662315\pi$
$752$			5.85635i			0.213559i
$753$	5.08658	−	12.2801i	0.185365	−	0.447511i
$754$	23.4979	−	9.73315i	0.855743	−	0.354460i
$755$		0			0
$756$	−14.1521	−	14.1521i	−0.514708	−	0.514708i
$757$	−34.6660	−	34.6660i	−1.25996	−	1.25996i	−0.951112	−	0.308847i	$-0.900057\pi$
$757$	−34.6660	−	34.6660i	−1.25996	−	1.25996i	−0.308847	−	0.951112i	$-0.599943\pi$
$758$	3.99706	+	9.64974i	0.145180	+	0.350495i
$759$	36.7214	−	15.2105i	1.33290	−	0.552107i
$760$		0			0
$761$		−	42.6819i		−	1.54722i	−0.633662	−	0.773610i	$-0.718449\pi$
$761$		−	42.6819i		−	1.54722i	0.633662	−	0.773610i	$-0.281551\pi$
$762$	−4.37087	−	1.81047i	−0.158340	−	0.0655865i
$763$	16.1344	−	16.1344i	0.584103	−	0.584103i
$764$	16.8319			0.608955
$765$		0			0
$766$	−20.1518			−0.728113
$767$	18.2662	−	18.2662i	0.659553	−	0.659553i
$768$	−1.36338	−	0.564729i	−0.0491966	−	0.0203779i
$769$		−	14.6429i		−	0.528035i	−0.964518	−	0.264018i	$-0.914952\pi$
$769$		−	14.6429i		−	0.528035i	0.964518	−	0.264018i	$-0.0850477\pi$
$770$		0			0
$771$	39.0716	−	16.1840i	1.40713	−	0.582853i
$772$	−2.23056	−	5.38504i	−0.0802795	−	0.193812i
$773$	−10.5010	−	10.5010i	−0.377696	−	0.377696i	0.492575	−	0.870270i	$-0.336056\pi$
$773$	−10.5010	−	10.5010i	−0.377696	−	0.377696i	−0.870270	+	0.492575i	$0.836056\pi$
$774$	0.482693	+	0.482693i	0.0173500	+	0.0173500i
$775$		0			0
$776$	−4.02389	+	1.66675i	−0.144449	+	0.0598328i
$777$	−18.6187	+	44.9496i	−0.667944	+	1.61256i
$778$		−	19.6657i		−	0.705051i
$779$	0.160366	+	0.0664258i	0.00574571	+	0.00237995i
$780$		0			0
$781$	−24.2203			−0.866670
$782$	22.7458	−	6.23650i	0.813390	−	0.223017i
$783$	−26.1936			−0.936083
$784$	3.95275	−	3.95275i	0.141170	−	0.141170i
$785$		0			0
$786$			5.27324i			0.188090i
$787$	−8.22589	+	19.8591i	−0.293221	+	0.707899i	0.706779	+	0.707435i	$0.250148\pi$
$787$	−8.22589	+	19.8591i	−0.293221	+	0.707899i	−1.00000		0.000464022i	$0.999852\pi$
$788$	−3.25339	+	1.34760i	−0.115897	+	0.0480061i
$789$	−3.41420	−	8.24261i	−0.121549	−	0.293445i
$790$		0			0
$791$	−24.1911	−	24.1911i	−0.860135	−	0.860135i
$792$	1.48166	+	3.57705i	0.0526486	+	0.127105i
$793$	−62.9743	+	26.0848i	−2.23628	+	0.926298i
$794$	−9.16446	+	22.1250i	−0.325235	+	0.785186i
$795$		0			0
$796$	15.5212	+	6.42910i	0.550135	+	0.227874i
$797$	−14.8934	+	14.8934i	−0.527550	+	0.527550i	−0.919841	−	0.392291i	$-0.871683\pi$
$797$	−14.8934	+	14.8934i	−0.527550	+	0.527550i	0.392291	+	0.919841i	$0.371683\pi$
$798$	−6.35168			−0.224847
$799$	−19.0709	+	14.8103i	−0.674680	+	0.523952i
$800$		0			0
$801$	−1.30346	+	1.30346i	−0.0460554	+	0.0460554i
$802$	21.2869	+	8.81734i	0.751668	+	0.311351i
$803$		−	75.9590i		−	2.68053i
$804$	4.89452	−	11.8164i	0.172617	−	0.416733i
$805$		0			0
$806$	−15.2655	−	36.8543i	−0.537706	−	1.29814i
$807$	17.6278	+	17.6278i	0.620529	+	0.620529i
$808$	−7.59384	−	7.59384i	−0.267150	−	0.267150i
$809$	−6.98690	−	16.8679i	−0.245646	−	0.593042i	0.752179	−	0.658959i	$-0.229003\pi$
$809$	−6.98690	−	16.8679i	−0.245646	−	0.593042i	−0.997825	+	0.0659166i	$0.979003\pi$
$810$		0			0
$811$	−5.56638	+	13.4384i	−0.195462	+	0.471887i	−0.990975	−	0.134050i	$-0.957202\pi$
$811$	−5.56638	+	13.4384i	−0.195462	+	0.471887i	0.795512	+	0.605937i	$0.207202\pi$
$812$		−	16.4773i		−	0.578239i
$813$	31.2628	+	12.9495i	1.09644	+	0.454158i
$814$	30.9363	−	30.9363i	1.08432	−	1.08432i
$815$		0			0
$816$	−1.60888	−	5.86793i	−0.0563221	−	0.205419i
$817$	1.00702			0.0352311
$818$	−9.01479	+	9.01479i	−0.315195	+	0.315195i
$819$	−14.7637	−	6.11532i	−0.515885	−	0.213686i
$820$		0			0
$821$	15.6230	−	37.7172i	0.545246	−	1.31634i	−0.375733	−	0.926728i	$-0.622609\pi$
$821$	15.6230	−	37.7172i	0.545246	−	1.31634i	0.920979	−	0.389613i	$-0.127391\pi$
$822$	−4.51209	+	1.86897i	−0.157377	+	0.0651878i
$823$	−0.697439	−	1.68377i	−0.0243112	−	0.0586925i	0.911258	−	0.411837i	$-0.135113\pi$
$823$	−0.697439	−	1.68377i	−0.0243112	−	0.0586925i	−0.935569	+	0.353144i	$0.885113\pi$
$824$	5.25597	+	5.25597i	0.183100	+	0.183100i
$825$		0			0
$826$	−6.40432	−	15.4614i	−0.222835	−	0.537971i
$827$	−42.9008	+	17.7701i	−1.49181	+	0.617927i	−0.971709	−	0.236180i	$-0.924104\pi$
$827$	−42.9008	+	17.7701i	−1.49181	+	0.617927i	−0.520098	+	0.854107i	$0.674104\pi$
$828$	−1.80003	+	4.34567i	−0.0625555	+	0.151022i
$829$			34.9749i			1.21473i	0.794424	+	0.607364i	$0.207773\pi$
$829$			34.9749i			1.21473i	−0.794424	+	0.607364i	$0.792227\pi$
$830$		0			0
$831$	20.8715	−	20.8715i	0.724025	−	0.724025i
$832$	−5.47699			−0.189881
$833$	22.8682	+	2.87568i	0.792337	+	0.0996365i
$834$	−2.65622			−0.0919773
$835$		0			0
$836$	5.27687	+	2.18575i	0.182504	+	0.0755958i
$837$			41.0822i			1.42001i
$838$	−10.4748	+	25.2883i	−0.361845	+	0.873570i
$839$	39.6860	−	16.4385i	1.37011	−	0.567520i	0.428294	−	0.903639i	$-0.359115\pi$
$839$	39.6860	−	16.4385i	1.37011	−	0.567520i	0.941819	+	0.336120i	$0.109115\pi$
$840$		0			0
$841$	5.25756	+	5.25756i	0.181295	+	0.181295i
$842$	23.8163	+	23.8163i	0.820764	+	0.820764i
$843$	−13.1484	−	31.7430i	−0.452854	−	1.09329i
$844$	−21.0828	+	8.73280i	−0.725701	+	0.300595i
$845$		0			0
$846$		−	4.81560i		−	0.165564i
$847$	−36.6181	−	15.1677i	−1.25821	−	0.521169i
$848$	6.54226	−	6.54226i	0.224662	−	0.224662i
$849$	−37.1152			−1.27379
$850$		0			0
$851$	53.1513			1.82200
$852$	−5.36758	+	5.36758i	−0.183890	+	0.183890i
$853$	8.59031	+	3.55822i	0.294127	+	0.121831i	0.524867	−	0.851184i	$-0.324115\pi$
$853$	8.59031	+	3.55822i	0.294127	+	0.121831i	−0.230741	+	0.973015i	$0.574115\pi$
$854$			44.1590i			1.51109i
$855$		0			0
$856$	−14.5335	+	6.01999i	−0.496746	+	0.205759i
$857$	11.8527	+	28.6150i	0.404881	+	0.977469i	0.986463	+	0.163982i	$0.0524338\pi$
$857$	11.8527	+	28.6150i	0.404881	+	0.977469i	−0.581582	+	0.813488i	$0.697566\pi$
$858$	−26.9100	−	26.9100i	−0.918693	−	0.918693i
$859$	13.1008	+	13.1008i	0.446994	+	0.446994i	0.894354	−	0.447360i	$-0.147636\pi$
$859$	13.1008	+	13.1008i	0.446994	+	0.446994i	−0.447360	+	0.894354i	$0.647636\pi$
$860$		0			0
$861$	−0.692232	+	0.286732i	−0.0235912	+	0.00977179i
$862$	6.95725	−	16.7963i	0.236965	−	0.572084i
$863$		−	18.5377i		−	0.631030i	−0.948921	−	0.315515i	$-0.897823\pi$
$863$		−	18.5377i		−	0.631030i	0.948921	−	0.315515i	$-0.102177\pi$
$864$	5.21121	+	2.15856i	0.177289	+	0.0734356i
$865$		0			0
$866$	−8.10392			−0.275382
$867$	15.0399	−	20.0789i	0.510781	−	0.681914i
$868$	−25.8431			−0.877170
$869$	−33.6803	+	33.6803i	−1.14253	+	1.14253i
$870$		0			0
$871$		−	47.4693i		−	1.60843i
$872$	−2.46089	+	5.94112i	−0.0833363	+	0.201192i
$873$	3.30880	−	1.37055i	0.111986	−	0.0463860i
$874$	2.65541	+	6.41073i	0.0898207	+	0.216846i
$875$		0			0
$876$	−16.8336	−	16.8336i	−0.568756	−	0.568756i
$877$	−16.3998	−	39.5926i	−0.553781	−	1.33695i	−0.914619	−	0.404318i	$-0.867509\pi$
$877$	−16.3998	−	39.5926i	−0.553781	−	1.33695i	0.360837	−	0.932629i	$-0.382491\pi$
$878$	−22.1522	+	9.17574i	−0.747600	+	0.309666i
$879$	14.4147	−	34.8003i	0.486197	−	1.17378i
$880$		0			0
$881$	37.7646	+	15.6426i	1.27232	+	0.527014i	0.913670	−	0.406457i	$-0.133236\pi$
$881$	37.7646	+	15.6426i	1.27232	+	0.527014i	0.358653	+	0.933471i	$0.383236\pi$
$882$	−3.25030	+	3.25030i	−0.109443	+	0.109443i
$883$	−52.3174			−1.76062			−0.880310	−	0.474398i	$-0.842666\pi$
$883$	−52.3174			−1.76062			−0.880310	+	0.474398i	$0.842666\pi$
$884$	−13.8510	−	17.8356i	−0.465859	−	0.599875i
$885$		0			0
$886$	0.172587	−	0.172587i	0.00579819	−	0.00579819i
$887$	13.9607	+	5.78272i	0.468755	+	0.194165i	0.604542	−	0.796573i	$-0.293356\pi$
$887$	13.9607	+	5.78272i	0.468755	+	0.194165i	−0.135787	+	0.990738i	$0.543356\pi$
$888$		−	13.7119i		−	0.460141i
$889$	−4.35317	+	10.5095i	−0.146000	+	0.352476i
$890$		0			0
$891$	10.5536	+	25.4786i	0.353558	+	0.853565i
$892$	−6.41246	−	6.41246i	−0.214705	−	0.214705i
$893$	−5.02327	−	5.02327i	−0.168097	−	0.168097i
$894$	2.35361	+	5.68212i	0.0787165	+	0.190038i
$895$		0			0
$896$	−1.35785	+	3.27815i	−0.0453627	+	0.109515i
$897$		−	46.2338i		−	1.54370i
$898$	0.0761574	+	0.0315454i	0.00254140	+	0.00105268i
$899$	−23.9159	+	23.9159i	−0.797640	+	0.797640i
$900$		0			0
$901$	37.8495	+	4.75958i	1.26095	+	0.158565i
$902$	0.673765			0.0224339
$903$	−3.07370	+	3.07370i	−0.102286	+	0.102286i
$904$	8.90782	+	3.68974i	0.296270	+	0.122719i
$905$		0			0
$906$	−2.59356	+	6.26141i	−0.0861653	+	0.208022i
$907$	23.1561	−	9.59155i	0.768884	−	0.318482i	0.0364638	−	0.999335i	$-0.488391\pi$
$907$	23.1561	−	9.59155i	0.768884	−	0.318482i	0.732420	+	0.680853i	$0.238391\pi$
$908$	6.02643	+	14.5491i	0.199994	+	0.482829i
$909$	6.24432	+	6.24432i	0.207111	+	0.207111i
$910$		0			0
$911$	−1.10387	−	2.66499i	−0.0365730	−	0.0882950i	0.904538	−	0.426394i	$-0.140216\pi$
$911$	−1.10387	−	2.66499i	−0.0365730	−	0.0882950i	−0.941111	+	0.338099i	$0.890216\pi$
$912$	1.65383	−	0.685038i	0.0547637	−	0.0226839i
$913$	6.13723	−	14.8166i	0.203113	−	0.490357i
$914$		−	24.3896i		−	0.806737i
$915$		0			0
$916$	14.2262	−	14.2262i	0.470046	−	0.470046i
$917$	12.6792			0.418703
$918$	6.14961	+	22.4289i	0.202967	+	0.740265i
$919$	−48.0746			−1.58584			−0.792918	−	0.609328i	$-0.791439\pi$
$919$	−48.0746			−1.58584			−0.792918	+	0.609328i	$0.791439\pi$
$920$		0			0
$921$	−19.4120	−	8.04071i	−0.639647	−	0.264950i
$922$			29.1100i			0.958687i
$923$	−10.7814	+	26.0286i	−0.354874	+	0.856741i
$924$	−22.7780	+	9.43496i	−0.749341	+	0.310387i
$925$		0			0
$926$	−19.7821	−	19.7821i	−0.650081	−	0.650081i
$927$	−4.32191	−	4.32191i	−0.141950	−	0.141950i
$928$	1.77710	+	4.29029i	0.0583361	+	0.140836i
$929$	25.3430	−	10.4974i	0.831478	−	0.344409i	0.0739901	−	0.997259i	$-0.476427\pi$
$929$	25.3430	−	10.4974i	0.831478	−	0.344409i	0.757487	+	0.652850i	$0.226427\pi$
$930$		0			0
$931$			6.78094i			0.222236i
$932$	−17.8076	−	7.37613i	−0.583306	−	0.241613i
$933$	12.6797	−	12.6797i	0.415116	−	0.415116i
$934$	31.2786			1.02347
$935$		0			0
$936$	4.50366			0.147207
$937$	10.3762	−	10.3762i	0.338975	−	0.338975i	−0.517007	−	0.855981i	$-0.672954\pi$
$937$	10.3762	−	10.3762i	0.338975	−	0.338975i	0.855981	+	0.517007i	$0.172954\pi$
$938$	−28.4118	−	11.7686i	−0.927679	−	0.384257i
$939$		−	32.1552i		−	1.04934i
$940$		0			0
$941$	22.8397	−	9.46050i	0.744552	−	0.308404i	0.0220356	−	0.999757i	$-0.492985\pi$
$941$	22.8397	−	9.46050i	0.744552	−	0.308404i	0.722517	+	0.691354i	$0.242985\pi$
$942$	−8.78053	−	21.1981i	−0.286085	−	0.690671i
$943$	0.578795	+	0.578795i	0.0188482	+	0.0188482i
$944$	3.33507	+	3.33507i	0.108547	+	0.108547i
$945$		0			0
$946$	3.61131	−	1.49585i	0.117414	−	0.0486343i
$947$	2.49335	−	6.01947i	0.0810228	−	0.195606i	−0.878177	−	0.478336i	$-0.841240\pi$
$947$	2.49335	−	6.01947i	0.0810228	−	0.195606i	0.959200	+	0.282730i	$0.0912400\pi$
$948$			14.9281i			0.484842i
$949$	−81.6301	−	33.8123i	−2.64982	−	1.09759i
$950$		0			0
$951$	15.1285			0.490574
$952$	−14.1091	+	3.86845i	−0.457277	+	0.125377i
$953$	−13.6944			−0.443607			−0.221803	−	0.975091i	$-0.571194\pi$
$953$	−13.6944			−0.443607			−0.221803	+	0.975091i	$0.571194\pi$
$954$	−5.37961	+	5.37961i	−0.174171	+	0.174171i
$955$		0			0
$956$		−	14.2040i		−	0.459389i
$957$	−12.3480	+	29.8108i	−0.399155	+	0.963646i
$958$	11.1564	−	4.62112i	0.360446	−	0.149302i
$959$	4.49382	+	10.8490i	0.145113	+	0.350334i
$960$		0			0
$961$	15.5896	+	15.5896i	0.502889	+	0.502889i
$962$	−19.4751	−	47.0169i	−0.627901	−	1.51589i
$963$	11.9507	−	4.95016i	0.385107	−	0.159517i
$964$	−1.75060	+	4.22633i	−0.0563832	+	0.136121i
$965$		0			0
$966$	−27.6724	−	11.4623i	−0.890344	−	0.368793i
$967$	−11.5376	+	11.5376i	−0.371026	+	0.371026i	−0.867851	−	0.496825i	$-0.834499\pi$
$967$	−11.5376	+	11.5376i	−0.371026	+	0.371026i	0.496825	+	0.867851i	$0.334499\pi$
$968$	11.1704			0.359029
$969$	6.41322	+	3.65319i	0.206022	+	0.117357i
$970$		0			0
$971$	−19.0136	+	19.0136i	−0.610176	+	0.610176i	−0.942992	−	0.332816i	$-0.892001\pi$
$971$	−19.0136	+	19.0136i	−0.610176	+	0.610176i	0.332816	+	0.942992i	$0.392001\pi$
$972$	−7.64838	−	3.16806i	−0.245322	−	0.101616i
$973$			6.38671i			0.204748i
$974$	1.91937	−	4.63377i	0.0615005	−	0.148475i
$975$		0			0
$976$	−4.76261	−	11.4980i	−0.152448	−	0.368041i
$977$	14.1423	+	14.1423i	0.452451	+	0.452451i	0.896167	−	0.443716i	$-0.146340\pi$
$977$	14.1423	+	14.1423i	0.452451	+	0.452451i	−0.443716	+	0.896167i	$0.646340\pi$
$978$	−10.5786	−	10.5786i	−0.338266	−	0.338266i
$979$	4.03937	+	9.75191i	0.129099	+	0.311672i
$980$		0			0
$981$	2.02356	−	4.88531i	0.0646073	−	0.155976i
$982$		−	26.4441i		−	0.843865i
$983$	26.6406	+	11.0349i	0.849704	+	0.351959i	0.764672	−	0.644419i	$-0.222901\pi$
$983$	26.6406	+	11.0349i	0.849704	+	0.351959i	0.0850316	+	0.996378i	$0.472901\pi$
$984$	0.149316	−	0.149316i	0.00476003	−	0.00476003i
$985$		0			0
$986$	−9.47696	+	16.6369i	−0.301808	+	0.529827i
$987$	30.6648			0.976072
$988$	4.69788	−	4.69788i	0.149460	−	0.149460i
$989$	4.38728	+	1.81727i	0.139507	+	0.0577858i
$990$		0			0
$991$	−10.2929	+	24.8494i	−0.326966	+	0.789366i	0.671848	+	0.740689i	$0.265501\pi$
$991$	−10.2929	+	24.8494i	−0.326966	+	0.789366i	−0.998815	+	0.0486775i	$0.984499\pi$
$992$	6.72892	−	2.78721i	0.213644	−	0.0884941i
$993$	0.167267	+	0.403818i	0.00530805	+	0.0128148i
$994$	12.9060	+	12.9060i	0.409353	+	0.409353i
$995$		0			0
$996$	−1.92347	−	4.64367i	−0.0609476	−	0.147140i
$997$	−28.1434	+	11.6574i	−0.891310	+	0.369193i	−0.780872	−	0.624690i	$-0.785225\pi$
$997$	−28.1434	+	11.6574i	−0.891310	+	0.369193i	−0.110437	+	0.993883i	$0.535225\pi$
$998$	11.4569	−	27.6595i	0.362663	−	0.875545i
$999$			52.4108i			1.65820i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.l.e.451.2		16
5.2	odd	4		850.2.o.g.349.2		16
5.3	odd	4		850.2.o.j.349.3		16
5.4	even	2		170.2.k.b.111.3	✓	16
17.2	even	8	inner	850.2.l.e.801.2		16
85.2	odd	8		850.2.o.j.699.3		16
85.19	even	8		170.2.k.b.121.3	yes	16
85.24	odd	16		2890.2.b.r.2311.5		16
85.44	odd	16		2890.2.b.r.2311.12		16
85.53	odd	8		850.2.o.g.699.2		16
85.74	odd	16		2890.2.a.bi.1.7		8
85.79	odd	16		2890.2.a.bj.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.k.b.111.3	✓	16	5.4	even	2
170.2.k.b.121.3	yes	16	85.19	even	8
850.2.l.e.451.2		16	1.1	even	1	trivial
850.2.l.e.801.2		16	17.2	even	8	inner
850.2.o.g.349.2		16	5.2	odd	4
850.2.o.g.699.2		16	85.53	odd	8
850.2.o.j.349.3		16	5.3	odd	4
850.2.o.j.699.3		16	85.2	odd	8
2890.2.a.bi.1.7		8	85.74	odd	16
2890.2.a.bj.1.2		8	85.79	odd	16
2890.2.b.r.2311.5		16	85.24	odd	16
2890.2.b.r.2311.12		16	85.44	odd	16

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:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.l (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.36338 - 0.564729i) q^{3} -1.00000i q^{4} +(1.36338 - 0.564729i) q^{6} +(-1.35785 - 3.27815i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.581445 - 0.581445i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.36338 - 0.564729i) q^{3} -1.00000i q^{4} +(1.36338 - 0.564729i) q^{6} +(-1.35785 - 3.27815i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.581445 - 0.581445i) q^{9} +(-4.35013 + 1.80188i) q^{11} +(-0.564729 + 1.36338i) q^{12} +5.47699i q^{13} +(3.27815 + 1.35785i) q^{14} -1.00000 q^{16} +(-2.52894 - 3.25645i) q^{17} +0.822287 q^{18} +(0.857748 - 0.857748i) q^{19} +5.23617i q^{21} +(1.80188 - 4.35013i) q^{22} +(5.28485 - 2.18906i) q^{23} +(-0.564729 - 1.36338i) q^{24} +(-3.87282 - 3.87282i) q^{26} +(2.15856 + 5.21121i) q^{27} +(-3.27815 + 1.35785i) q^{28} +(-1.77710 + 4.29029i) q^{29} +(6.72892 + 2.78721i) q^{31} +(0.707107 - 0.707107i) q^{32} +6.94843 q^{33} +(4.09089 + 0.514430i) q^{34} +(-0.581445 + 0.581445i) q^{36} +(8.58444 + 3.55579i) q^{37} +1.21304i q^{38} +(3.09302 - 7.46720i) q^{39} +(0.0547598 + 0.132202i) q^{41} +(-3.70253 - 3.70253i) q^{42} +(0.587013 + 0.587013i) q^{43} +(1.80188 + 4.35013i) q^{44} +(-2.18906 + 5.28485i) q^{46} -5.85635i q^{47} +(1.36338 + 0.564729i) q^{48} +(-3.95275 + 3.95275i) q^{49} +(1.60888 + 5.86793i) q^{51} +5.47699 q^{52} +(-6.54226 + 6.54226i) q^{53} +(-5.21121 - 2.15856i) q^{54} +(1.35785 - 3.27815i) q^{56} +(-1.65383 + 0.685038i) q^{57} +(-1.77710 - 4.29029i) q^{58} +(-3.33507 - 3.33507i) q^{59} +(4.76261 + 11.4980i) q^{61} +(-6.72892 + 2.78721i) q^{62} +(-1.11655 + 2.69558i) q^{63} +1.00000i q^{64} +(-4.91328 + 4.91328i) q^{66} -8.66703 q^{67} +(-3.25645 + 2.52894i) q^{68} -8.44146 q^{69} +(4.75235 + 1.96849i) q^{71} -0.822287i q^{72} +(-6.17351 + 14.9042i) q^{73} +(-8.58444 + 3.55579i) q^{74} +(-0.857748 - 0.857748i) q^{76} +(11.8137 + 11.8137i) q^{77} +(3.09302 + 7.46720i) q^{78} +(9.34587 - 3.87118i) q^{79} -5.85698i q^{81} +(-0.132202 - 0.0547598i) q^{82} +(-2.40841 + 2.40841i) q^{83} +5.23617 q^{84} -0.830161 q^{86} +(4.84570 - 4.84570i) q^{87} +(-4.35013 - 1.80188i) q^{88} -2.24175i q^{89} +(17.9544 - 7.43696i) q^{91} +(-2.18906 - 5.28485i) q^{92} +(-7.60004 - 7.60004i) q^{93} +(4.14106 + 4.14106i) q^{94} +(-1.36338 + 0.564729i) q^{96} +(-1.66675 + 4.02389i) q^{97} -5.59004i q^{98} +(3.57705 + 1.48166i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 8 q^{11} - 8 q^{14} - 16 q^{16} - 8 q^{18} + 8 q^{22} - 8 q^{23} + 24 q^{27} + 8 q^{28} + 8 q^{29} + 32 q^{31} - 16 q^{33} + 16 q^{34} + 8 q^{37} - 32 q^{39} - 32 q^{41} - 32 q^{42} + 16 q^{43} + 8 q^{44} - 24 q^{46} - 8 q^{49} - 8 q^{51} + 8 q^{52} + 40 q^{53} + 16 q^{57} + 8 q^{58} + 16 q^{59} - 24 q^{61} - 32 q^{62} - 56 q^{63} - 8 q^{66} - 16 q^{67} - 16 q^{69} + 8 q^{71} - 16 q^{73} - 8 q^{74} - 24 q^{77} - 32 q^{78} + 40 q^{79} - 16 q^{82} - 32 q^{83} + 16 q^{84} + 32 q^{87} - 8 q^{88} + 24 q^{91} - 24 q^{92} + 32 q^{93} + 40 q^{94} - 24 q^{97} - 56 q^{99}+O(q^{100}) \) 16 * q - 8 * q^11 - 8 * q^14 - 16 * q^16 - 8 * q^18 + 8 * q^22 - 8 * q^23 + 24 * q^27 + 8 * q^28 + 8 * q^29 + 32 * q^31 - 16 * q^33 + 16 * q^34 + 8 * q^37 - 32 * q^39 - 32 * q^41 - 32 * q^42 + 16 * q^43 + 8 * q^44 - 24 * q^46 - 8 * q^49 - 8 * q^51 + 8 * q^52 + 40 * q^53 + 16 * q^57 + 8 * q^58 + 16 * q^59 - 24 * q^61 - 32 * q^62 - 56 * q^63 - 8 * q^66 - 16 * q^67 - 16 * q^69 + 8 * q^71 - 16 * q^73 - 8 * q^74 - 24 * q^77 - 32 * q^78 + 40 * q^79 - 16 * q^82 - 32 * q^83 + 16 * q^84 + 32 * q^87 - 8 * q^88 + 24 * q^91 - 24 * q^92 + 32 * q^93 + 40 * q^94 - 24 * q^97 - 56 * q^99

Introduction

L-functions

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