LMFDB - Embedded newform 471.2.b.b.313.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(313,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("471.313");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.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:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 24x^{12} + 224x^{10} + 1027x^{8} + 2399x^{6} + 2652x^{4} + 1094x^{2} + 147 $ x^14 + 24x^12 + 224x^10 + 1027x^8 + 2399x^6 + 2652x^4 + 1094x^2 + 147
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			313.4
Root			$-1.66261i$ of defining polynomial
Character	$\chi$	$=$	471.313
Dual form			471.2.b.b.313.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.66261i q^{2} +1.00000 q^{3} -0.764270 q^{4} -1.85555i q^{5} -1.66261i q^{6} +0.948177i q^{7} -2.05454i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.66261i q^{2} +1.00000 q^{3} -0.764270 q^{4} -1.85555i q^{5} -1.66261i q^{6} +0.948177i q^{7} -2.05454i q^{8} +1.00000 q^{9} -3.08505 q^{10} +5.18060 q^{11} -0.764270 q^{12} +2.15208 q^{13} +1.57645 q^{14} -1.85555i q^{15} -4.94443 q^{16} -1.84477 q^{17} -1.66261i q^{18} -8.04487 q^{19} +1.41814i q^{20} +0.948177i q^{21} -8.61331i q^{22} +4.20591i q^{23} -2.05454i q^{24} +1.55695 q^{25} -3.57808i q^{26} +1.00000 q^{27} -0.724663i q^{28} -5.35559i q^{29} -3.08505 q^{30} -2.86427 q^{31} +4.11159i q^{32} +5.18060 q^{33} +3.06712i q^{34} +1.75939 q^{35} -0.764270 q^{36} -1.28782 q^{37} +13.3755i q^{38} +2.15208 q^{39} -3.81229 q^{40} +0.936712i q^{41} +1.57645 q^{42} -0.0513523i q^{43} -3.95938 q^{44} -1.85555i q^{45} +6.99278 q^{46} +1.22122 q^{47} -4.94443 q^{48} +6.10096 q^{49} -2.58860i q^{50} -1.84477 q^{51} -1.64477 q^{52} -0.958722i q^{53} -1.66261i q^{54} -9.61284i q^{55} +1.94806 q^{56} -8.04487 q^{57} -8.90425 q^{58} +3.20638i q^{59} +1.41814i q^{60} +13.5254i q^{61} +4.76216i q^{62} +0.948177i q^{63} -3.05290 q^{64} -3.99329i q^{65} -8.61331i q^{66} -3.65206 q^{67} +1.40990 q^{68} +4.20591i q^{69} -2.92517i q^{70} +2.98061 q^{71} -2.05454i q^{72} +12.3024i q^{73} +2.14114i q^{74} +1.55695 q^{75} +6.14845 q^{76} +4.91213i q^{77} -3.57808i q^{78} +3.34723i q^{79} +9.17462i q^{80} +1.00000 q^{81} +1.55739 q^{82} +15.2183i q^{83} -0.724663i q^{84} +3.42305i q^{85} -0.0853788 q^{86} -5.35559i q^{87} -10.6437i q^{88} +15.1938 q^{89} -3.08505 q^{90} +2.04056i q^{91} -3.21445i q^{92} -2.86427 q^{93} -2.03041i q^{94} +14.9276i q^{95} +4.11159i q^{96} -18.3611i q^{97} -10.1435i q^{98} +5.18060 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 14 q^{3} - 20 q^{4} + 14 q^{9}+O(q^{10}) $ 14 * q + 14 * q^3 - 20 * q^4 + 14 * q^9	$ 14 q + 14 q^{3} - 20 q^{4} + 14 q^{9} + 6 q^{10} - 2 q^{11} - 20 q^{12} + 24 q^{16} + 18 q^{17} - 12 q^{19} - 18 q^{25} + 14 q^{27} + 6 q^{30} - 14 q^{31} - 2 q^{33} + 16 q^{35} - 20 q^{36} - 14 q^{37} - 36 q^{40} + 24 q^{44} - 8 q^{46} + 22 q^{47} + 24 q^{48} - 48 q^{49} + 18 q^{51} - 50 q^{52} - 62 q^{56} - 12 q^{57} + 20 q^{58} - 34 q^{64} + 42 q^{67} - 56 q^{68} + 38 q^{71} - 18 q^{75} + 52 q^{76} + 14 q^{81} + 10 q^{82} + 34 q^{86} - 48 q^{89} + 6 q^{90} - 14 q^{93} - 2 q^{99}+O(q^{100}) $ 14 * q + 14 * q^3 - 20 * q^4 + 14 * q^9 + 6 * q^10 - 2 * q^11 - 20 * q^12 + 24 * q^16 + 18 * q^17 - 12 * q^19 - 18 * q^25 + 14 * q^27 + 6 * q^30 - 14 * q^31 - 2 * q^33 + 16 * q^35 - 20 * q^36 - 14 * q^37 - 36 * q^40 + 24 * q^44 - 8 * q^46 + 22 * q^47 + 24 * q^48 - 48 * q^49 + 18 * q^51 - 50 * q^52 - 62 * q^56 - 12 * q^57 + 20 * q^58 - 34 * q^64 + 42 * q^67 - 56 * q^68 + 38 * q^71 - 18 * q^75 + 52 * q^76 + 14 * q^81 + 10 * q^82 + 34 * q^86 - 48 * q^89 + 6 * q^90 - 14 * q^93 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	1.66261i		−	1.17564i	−0.808991	−	0.587821i	$-0.799986\pi$
$2$		−	1.66261i		−	1.17564i	0.808991	−	0.587821i	$-0.200014\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−0.764270			−0.382135
$5$		−	1.85555i		−	0.829826i	−0.909861	−	0.414913i	$-0.863812\pi$
$5$		−	1.85555i		−	0.829826i	0.909861	−	0.414913i	$-0.136188\pi$
$6$		−	1.66261i		−	0.678757i
$7$			0.948177i			0.358377i	0.983815	+	0.179189i	$0.0573472\pi$
$7$			0.948177i			0.358377i	−0.983815	+	0.179189i	$0.942653\pi$
$8$		−	2.05454i		−	0.726388i
$9$	1.00000			0.333333
$10$	−3.08505			−0.975578
$11$	5.18060			1.56201			0.781005	−	0.624525i	$-0.214707\pi$
$11$	5.18060			1.56201			0.781005	+	0.624525i	$0.214707\pi$
$12$	−0.764270			−0.220626
$13$	2.15208			0.596881			0.298440	−	0.954428i	$-0.403534\pi$
$13$	2.15208			0.596881			0.298440	+	0.954428i	$0.403534\pi$
$14$	1.57645			0.421323
$15$		−	1.85555i		−	0.479100i
$16$	−4.94443			−1.23611
$17$	−1.84477			−0.447421			−0.223711	−	0.974656i	$-0.571817\pi$
$17$	−1.84477			−0.447421			−0.223711	+	0.974656i	$0.571817\pi$
$18$		−	1.66261i		−	0.391881i
$19$	−8.04487			−1.84562			−0.922809	−	0.385257i	$-0.874113\pi$
$19$	−8.04487			−1.84562			−0.922809	+	0.385257i	$0.874113\pi$
$20$			1.41814i			0.317105i
$21$			0.948177i			0.206909i
$22$		−	8.61331i		−	1.83636i
$23$			4.20591i			0.876992i	0.898733	+	0.438496i	$0.144489\pi$
$23$			4.20591i			0.876992i	−0.898733	+	0.438496i	$0.855511\pi$
$24$		−	2.05454i		−	0.419380i
$25$	1.55695			0.311389
$26$		−	3.57808i		−	0.701718i
$27$	1.00000			0.192450
$28$		−	0.724663i		−	0.136949i
$29$		−	5.35559i		−	0.994507i	−0.867605	−	0.497254i	$-0.834342\pi$
$29$		−	5.35559i		−	0.994507i	0.867605	−	0.497254i	$-0.165658\pi$
$30$	−3.08505			−0.563250
$31$	−2.86427			−0.514437			−0.257219	−	0.966353i	$-0.582806\pi$
$31$	−2.86427			−0.514437			−0.257219	+	0.966353i	$0.582806\pi$
$32$			4.11159i			0.726833i
$33$	5.18060			0.901827
$34$			3.06712i			0.526007i
$35$	1.75939			0.297391
$36$	−0.764270			−0.127378
$37$	−1.28782			−0.211716			−0.105858	−	0.994381i	$-0.533759\pi$
$37$	−1.28782			−0.211716			−0.105858	+	0.994381i	$0.533759\pi$
$38$			13.3755i			2.16979i
$39$	2.15208			0.344609
$40$	−3.81229			−0.602776
$41$			0.936712i			0.146290i	0.997321	+	0.0731449i	$0.0233036\pi$
$41$			0.936712i			0.146290i	−0.997321	+	0.0731449i	$0.976696\pi$
$42$	1.57645			0.243251
$43$		−	0.0513523i		−	0.00783115i	−0.999992	−	0.00391557i	$-0.998754\pi$
$43$		−	0.0513523i		−	0.00783115i	0.999992	−	0.00391557i	$-0.00124637\pi$
$44$	−3.95938			−0.596899
$45$		−	1.85555i		−	0.276609i
$46$	6.99278			1.03103
$47$	1.22122			0.178134			0.0890668	−	0.996026i	$-0.471612\pi$
$47$	1.22122			0.178134			0.0890668	+	0.996026i	$0.471612\pi$
$48$	−4.94443			−0.713667
$49$	6.10096			0.871566
$50$		−	2.58860i		−	0.366083i
$51$	−1.84477			−0.258319
$52$	−1.64477			−0.228089
$53$		−	0.958722i		−	0.131691i	−0.997830	−	0.0658453i	$-0.979026\pi$
$53$		−	0.958722i		−	0.131691i	0.997830	−	0.0658453i	$-0.0209744\pi$
$54$		−	1.66261i		−	0.226252i
$55$		−	9.61284i		−	1.29620i
$56$	1.94806			0.260321
$57$	−8.04487			−1.06557
$58$	−8.90425			−1.16919
$59$			3.20638i			0.417435i	0.977976	+	0.208717i	$0.0669289\pi$
$59$			3.20638i			0.417435i	−0.977976	+	0.208717i	$0.933071\pi$
$60$			1.41814i			0.183081i
$61$			13.5254i			1.73176i	0.500256	+	0.865878i	$0.333239\pi$
$61$			13.5254i			1.73176i	−0.500256	+	0.865878i	$0.666761\pi$
$62$			4.76216i			0.604794i
$63$			0.948177i			0.119459i
$64$	−3.05290			−0.381613
$65$		−	3.99329i		−	0.495307i
$66$		−	8.61331i		−	1.06023i
$67$	−3.65206			−0.446170			−0.223085	−	0.974799i	$-0.571613\pi$
$67$	−3.65206			−0.446170			−0.223085	+	0.974799i	$0.571613\pi$
$68$	1.40990			0.170975
$69$			4.20591i			0.506332i
$70$		−	2.92517i		−	0.349625i
$71$	2.98061			0.353733			0.176867	−	0.984235i	$-0.443404\pi$
$71$	2.98061			0.353733			0.176867	+	0.984235i	$0.443404\pi$
$72$		−	2.05454i		−	0.242129i
$73$			12.3024i			1.43989i	0.694033	+	0.719943i	$0.255832\pi$
$73$			12.3024i			1.43989i	−0.694033	+	0.719943i	$0.744168\pi$
$74$			2.14114i			0.248902i
$75$	1.55695			0.179781
$76$	6.14845			0.705276
$77$			4.91213i			0.559789i
$78$		−	3.57808i		−	0.405137i
$79$			3.34723i			0.376593i	0.982112	+	0.188296i	$0.0602965\pi$
$79$			3.34723i			0.376593i	−0.982112	+	0.188296i	$0.939703\pi$
$80$			9.17462i			1.02575i
$81$	1.00000			0.111111
$82$	1.55739			0.171985
$83$			15.2183i			1.67042i	0.549929	+	0.835211i	$0.314655\pi$
$83$			15.2183i			1.67042i	−0.549929	+	0.835211i	$0.685345\pi$
$84$		−	0.724663i		−	0.0790673i
$85$			3.42305i			0.371282i
$86$	−0.0853788			−0.00920663
$87$		−	5.35559i		−	0.574179i
$88$		−	10.6437i		−	1.13463i
$89$	15.1938			1.61054			0.805272	−	0.592905i	$-0.202019\pi$
$89$	15.1938			1.61054			0.805272	+	0.592905i	$0.202019\pi$
$90$	−3.08505			−0.325193
$91$			2.04056i			0.213908i
$92$		−	3.21445i		−	0.335129i
$93$	−2.86427			−0.297011
$94$		−	2.03041i		−	0.209421i
$95$			14.9276i			1.53154i
$96$			4.11159i			0.419637i
$97$		−	18.3611i		−	1.86429i	−0.362084	−	0.932146i	$-0.617934\pi$
$97$		−	18.3611i		−	1.86429i	0.362084	−	0.932146i	$-0.382066\pi$
$98$		−	10.1435i		−	1.02465i
$99$	5.18060			0.520670
$100$	−1.18993			−0.118993
$101$	−4.58292			−0.456018			−0.228009	−	0.973659i	$-0.573222\pi$
$101$	−4.58292			−0.456018			−0.228009	+	0.973659i	$0.573222\pi$
$102$			3.06712i			0.303691i
$103$			4.02054i			0.396156i	0.980186	+	0.198078i	$0.0634699\pi$
$103$			4.02054i			0.396156i	−0.980186	+	0.198078i	$0.936530\pi$
$104$		−	4.42153i		−	0.433567i
$105$	1.75939			0.171699
$106$	−1.59398			−0.154821
$107$		−	8.75884i		−	0.846749i	−0.905955	−	0.423375i	$-0.860845\pi$
$107$		−	8.75884i		−	0.846749i	0.905955	−	0.423375i	$-0.139155\pi$
$108$	−0.764270			−0.0735419
$109$	10.2946			0.986044			0.493022	−	0.870017i	$-0.335892\pi$
$109$	10.2946			0.986044			0.493022	+	0.870017i	$0.335892\pi$
$110$	−15.9824			−1.52386
$111$	−1.28782			−0.122234
$112$		−	4.68820i		−	0.442993i
$113$	6.05386			0.569500			0.284750	−	0.958602i	$-0.408089\pi$
$113$	6.05386			0.569500			0.284750	+	0.958602i	$0.408089\pi$
$114$			13.3755i			1.25273i
$115$	7.80425			0.727750
$116$			4.09312i			0.380036i
$117$	2.15208			0.198960
$118$	5.33095			0.490754
$119$		−	1.74916i		−	0.160346i
$120$	−3.81229			−0.348013
$121$	15.8386			1.43987
$122$	22.4875			2.03592
$123$			0.936712i			0.0844605i
$124$	2.18907			0.196585
$125$		−	12.1667i		−	1.08822i
$126$	1.57645			0.140441
$127$	−3.56745			−0.316560			−0.158280	−	0.987394i	$-0.550595\pi$
$127$	−3.56745			−0.316560			−0.158280	+	0.987394i	$0.550595\pi$
$128$			13.2990i			1.17547i
$129$		−	0.0513523i		−	0.00452131i
$130$	−6.63928			−0.582304
$131$			1.78218i			0.155710i	0.996965	+	0.0778551i	$0.0248072\pi$
$131$			1.78218i			0.155710i	−0.996965	+	0.0778551i	$0.975193\pi$
$132$	−3.95938			−0.344620
$133$		−	7.62796i		−	0.661428i
$134$			6.07195i			0.524536i
$135$		−	1.85555i		−	0.159700i
$136$			3.79014i			0.325002i
$137$			0.187329i			0.0160046i	0.999968	+	0.00800230i	$0.00254724\pi$
$137$			0.187329i			0.0160046i	−0.999968	+	0.00800230i	$0.997453\pi$
$138$	6.99278			0.595265
$139$			16.8727i			1.43112i	0.698551	+	0.715561i	$0.253829\pi$
$139$			16.8727i			1.43112i	−0.698551	+	0.715561i	$0.746171\pi$
$140$	−1.34465			−0.113643
$141$	1.22122			0.102845
$142$		−	4.95559i		−	0.415864i
$143$	11.1491			0.932333
$144$	−4.94443			−0.412036
$145$	−9.93754			−0.825268
$146$	20.4541			1.69279
$147$	6.10096			0.503199
$148$	0.984241			0.0809041
$149$		−	13.2732i		−	1.08738i	−0.839285	−	0.543692i	$-0.817026\pi$
$149$		−	13.2732i		−	1.08738i	0.839285	−	0.543692i	$-0.182974\pi$
$150$		−	2.58860i		−	0.211358i
$151$		−	21.6037i		−	1.75808i	−0.476744	−	0.879042i	$-0.658183\pi$
$151$		−	21.6037i		−	1.75808i	0.476744	−	0.879042i	$-0.341817\pi$
$152$			16.5285i			1.34064i
$153$	−1.84477			−0.149140
$154$	8.16695			0.658111
$155$			5.31478i			0.426893i
$156$	−1.64477			−0.131687
$157$	−6.45803	+	10.7375i	−0.515407	+	0.856946i
$157$	−6.45803	+	10.7375i	−0.515407	+	0.856946i
$158$	5.56513			0.442738
$159$		−	0.958722i		−	0.0760316i
$160$	7.62924			0.603144
$161$	−3.98794			−0.314294
$162$		−	1.66261i		−	0.130627i
$163$			16.3116i			1.27762i	0.769363	+	0.638812i	$0.220574\pi$
$163$			16.3116i			1.27762i	−0.769363	+	0.638812i	$0.779426\pi$
$164$		−	0.715901i		−	0.0559025i
$165$		−	9.61284i		−	0.748359i
$166$	25.3020			1.96382
$167$	−12.8059			−0.990952			−0.495476	−	0.868622i	$-0.665006\pi$
$167$	−12.8059			−0.990952			−0.495476	+	0.868622i	$0.665006\pi$
$168$	1.94806			0.150296
$169$	−8.36853			−0.643733
$170$	5.69119			0.436494
$171$	−8.04487			−0.615206
$172$			0.0392470i			0.00299256i
$173$	−15.4077			−1.17143			−0.585714	−	0.810518i	$-0.699186\pi$
$173$	−15.4077			−1.17143			−0.585714	+	0.810518i	$0.699186\pi$
$174$	−8.90425			−0.675029
$175$			1.47626i			0.111595i
$176$	−25.6151			−1.93081
$177$			3.20638i			0.241006i
$178$		−	25.2614i		−	1.89342i
$179$			3.92776i			0.293575i	0.989168	+	0.146787i	$0.0468933\pi$
$179$			3.92776i			0.293575i	−0.989168	+	0.146787i	$0.953107\pi$
$180$			1.41814i			0.105702i
$181$			4.44053i			0.330062i	0.986288	+	0.165031i	$0.0527724\pi$
$181$			4.44053i			0.330062i	−0.986288	+	0.165031i	$0.947228\pi$
$182$	3.39265			0.251480
$183$			13.5254i			0.999829i
$184$	8.64118			0.637037
$185$			2.38961i			0.175687i
$186$			4.76216i			0.349178i
$187$	−9.55699			−0.698876
$188$	−0.933343			−0.0680711
$189$			0.948177i			0.0689697i
$190$	24.8188			1.80055
$191$		−	18.7649i		−	1.35778i	−0.734240	−	0.678890i	$-0.762461\pi$
$191$		−	18.7649i		−	1.35778i	0.734240	−	0.678890i	$-0.237539\pi$
$192$	−3.05290			−0.220324
$193$	−9.21645			−0.663415			−0.331707	−	0.943382i	$-0.607625\pi$
$193$	−9.21645			−0.663415			−0.331707	+	0.943382i	$0.607625\pi$
$194$	−30.5274			−2.19174
$195$		−	3.99329i		−	0.285966i
$196$	−4.66278			−0.333056
$197$	−15.2713			−1.08803			−0.544017	−	0.839074i	$-0.683097\pi$
$197$	−15.2713			−1.08803			−0.544017	+	0.839074i	$0.683097\pi$
$198$		−	8.61331i		−	0.612122i
$199$	11.1866			0.792994			0.396497	−	0.918036i	$-0.370226\pi$
$199$	11.1866			0.792994			0.396497	+	0.918036i	$0.370226\pi$
$200$		−	3.19880i		−	0.226190i
$201$	−3.65206			−0.257596
$202$			7.61961i			0.536114i
$203$	5.07804			0.356409
$204$	1.40990			0.0987127
$205$	1.73811			0.121395
$206$	6.68459			0.465737
$207$			4.20591i			0.292331i
$208$	−10.6408			−0.737809
$209$	−41.6772			−2.88287
$210$		−	2.92517i		−	0.201856i
$211$			9.40401i			0.647399i	0.946160	+	0.323699i	$0.104927\pi$
$211$			9.40401i			0.647399i	−0.946160	+	0.323699i	$0.895073\pi$
$212$			0.732722i			0.0503236i
$213$	2.98061			0.204228
$214$	−14.5625			−0.995474
$215$	−0.0952865			−0.00649849
$216$		−	2.05454i		−	0.139793i
$217$		−	2.71583i		−	0.184363i
$218$		−	17.1159i		−	1.15924i
$219$			12.3024i			0.831319i
$220$			7.34681i			0.495322i
$221$	−3.97009			−0.267057
$222$			2.14114i			0.143704i
$223$			20.5618i			1.37692i	0.725276	+	0.688458i	$0.241712\pi$
$223$			20.5618i			1.37692i	−0.725276	+	0.688458i	$0.758288\pi$
$224$	−3.89851			−0.260480
$225$	1.55695			0.103796
$226$		−	10.0652i		−	0.669528i
$227$		−	14.3241i		−	0.950724i	−0.879790	−	0.475362i	$-0.842317\pi$
$227$		−	14.3241i		−	0.950724i	0.879790	−	0.475362i	$-0.157683\pi$
$228$	6.14845			0.407191
$229$		−	7.72860i		−	0.510720i	−0.966846	−	0.255360i	$-0.917806\pi$
$229$		−	7.72860i		−	0.510720i	0.966846	−	0.255360i	$-0.0821940\pi$
$230$		−	12.9754i		−	0.855574i
$231$			4.91213i			0.323194i
$232$	−11.0032			−0.722398
$233$	20.1052			1.31713			0.658566	−	0.752523i	$-0.271163\pi$
$233$	20.1052			1.31713			0.658566	+	0.752523i	$0.271163\pi$
$234$		−	3.57808i		−	0.233906i
$235$		−	2.26603i		−	0.147820i
$236$		−	2.45054i		−	0.159516i
$237$			3.34723i			0.217426i
$238$	−2.90818			−0.188509
$239$	−0.953647			−0.0616863			−0.0308432	−	0.999524i	$-0.509819\pi$
$239$	−0.953647			−0.0616863			−0.0308432	+	0.999524i	$0.509819\pi$
$240$			9.17462i			0.592219i
$241$		−	19.8937i		−	1.28146i	−0.767764	−	0.640732i	$-0.778631\pi$
$241$		−	19.8937i		−	1.28146i	0.767764	−	0.640732i	$-0.221369\pi$
$242$		−	26.3334i		−	1.69278i
$243$	1.00000			0.0641500
$244$		−	10.3371i		−	0.661764i
$245$		−	11.3206i		−	0.723248i
$246$	1.55739			0.0992953
$247$	−17.3132			−1.10161
$248$			5.88474i			0.373681i
$249$			15.2183i			0.964419i
$250$	−20.2285			−1.27936
$251$		−	13.8606i		−	0.874872i	−0.899250	−	0.437436i	$-0.855887\pi$
$251$		−	13.8606i		−	0.874872i	0.899250	−	0.437436i	$-0.144113\pi$
$252$		−	0.724663i		−	0.0456495i
$253$			21.7891i			1.36987i
$254$			5.93128i			0.372161i
$255$			3.42305i			0.214360i
$256$	16.0052			1.00032
$257$	−18.2210			−1.13660			−0.568299	−	0.822822i	$-0.692398\pi$
$257$	−18.2210			−1.13660			−0.568299	+	0.822822i	$0.692398\pi$
$258$	−0.0853788			−0.00531545
$259$		−	1.22108i		−	0.0758742i
$260$			3.05195i			0.189274i
$261$		−	5.35559i		−	0.331502i
$262$	2.96308			0.183059
$263$	−20.0832			−1.23838			−0.619192	−	0.785240i	$-0.712540\pi$
$263$	−20.0832			−1.23838			−0.619192	+	0.785240i	$0.712540\pi$
$264$		−	10.6437i		−	0.655076i
$265$	−1.77895			−0.109280
$266$	−12.6823			−0.777603
$267$	15.1938			0.929848
$268$	2.79116			0.170497
$269$		−	12.2622i		−	0.747637i	−0.927502	−	0.373818i	$-0.878048\pi$
$269$		−	12.2622i		−	0.747637i	0.927502	−	0.373818i	$-0.121952\pi$
$270$	−3.08505			−0.187750
$271$		−	7.77995i		−	0.472598i	−0.971680	−	0.236299i	$-0.924065\pi$
$271$		−	7.77995i		−	0.472598i	0.971680	−	0.236299i	$-0.0759345\pi$
$272$	9.12132			0.553061
$273$			2.04056i			0.123500i
$274$	0.311455			0.0188157
$275$	8.06592			0.486393
$276$		−	3.21445i		−	0.193487i
$277$	−20.0599			−1.20529			−0.602643	−	0.798011i	$-0.705886\pi$
$277$	−20.0599			−1.20529			−0.602643	+	0.798011i	$0.705886\pi$
$278$	28.0527			1.68249
$279$	−2.86427			−0.171479
$280$		−	3.61472i		−	0.216021i
$281$	19.2987			1.15126			0.575631	−	0.817709i	$-0.304756\pi$
$281$	19.2987			1.15126			0.575631	+	0.817709i	$0.304756\pi$
$282$		−	2.03041i		−	0.120909i
$283$	24.7780			1.47290			0.736449	−	0.676493i	$-0.236501\pi$
$283$	24.7780			1.47290			0.736449	+	0.676493i	$0.236501\pi$
$284$	−2.27799			−0.135174
$285$			14.9276i			0.884236i
$286$		−	18.5366i		−	1.09609i
$287$	−0.888169			−0.0524269
$288$			4.11159i			0.242278i
$289$	−13.5968			−0.799814
$290$			16.5222i			0.970220i
$291$		−	18.3611i		−	1.07635i
$292$		−	9.40236i		−	0.550231i
$293$		−	22.7709i		−	1.33029i	−0.746714	−	0.665145i	$-0.768370\pi$
$293$		−	22.7709i		−	1.33029i	0.746714	−	0.665145i	$-0.231630\pi$
$294$		−	10.1435i		−	0.591582i
$295$	5.94958			0.346398
$296$			2.64587i			0.153788i
$297$	5.18060			0.300609
$298$	−22.0682			−1.27838
$299$			9.05146i			0.523460i
$300$	−1.18993			−0.0687006
$301$	0.0486910			0.00280650
$302$	−35.9185			−2.06688
$303$	−4.58292			−0.263282
$304$	39.7773			2.28138
$305$	25.0971			1.43705
$306$			3.06712i			0.175336i
$307$			15.0199i			0.857230i	0.903487	+	0.428615i	$0.140998\pi$
$307$			15.0199i			0.857230i	−0.903487	+	0.428615i	$0.859002\pi$
$308$		−	3.75419i		−	0.213915i
$309$			4.02054i			0.228721i
$310$	8.83640			0.501874
$311$	11.6671			0.661582			0.330791	−	0.943704i	$-0.392684\pi$
$311$	11.6671			0.661582			0.330791	+	0.943704i	$0.392684\pi$
$312$		−	4.42153i		−	0.250320i
$313$	−27.4233			−1.55005			−0.775027	−	0.631928i	$-0.782264\pi$
$313$	−27.4233			−1.55005			−0.775027	+	0.631928i	$0.782264\pi$
$314$	17.8523	+	10.7372i	1.00746	+	0.605934i
$315$	1.75939			0.0991302
$316$		−	2.55819i		−	0.143909i
$317$	−28.3482			−1.59220			−0.796098	−	0.605168i	$-0.793106\pi$
$317$	−28.3482			−1.59220			−0.796098	+	0.605168i	$0.793106\pi$
$318$	−1.59398			−0.0893859
$319$		−	27.7452i		−	1.55343i
$320$			5.66480i			0.316672i
$321$		−	8.75884i		−	0.488871i
$322$			6.63039i			0.369497i
$323$	14.8409			0.825769
$324$	−0.764270			−0.0424595
$325$	3.35068			0.185862
$326$	27.1199			1.50203
$327$	10.2946			0.569293
$328$	1.92451			0.106263
$329$			1.15793i			0.0638390i
$330$	−15.9824			−0.879802
$331$	−2.43583			−0.133886			−0.0669428	−	0.997757i	$-0.521324\pi$
$331$	−2.43583			−0.133886			−0.0669428	+	0.997757i	$0.521324\pi$
$332$		−	11.6309i		−	0.638327i
$333$	−1.28782			−0.0705720
$334$			21.2912i			1.16500i
$335$			6.77657i			0.370243i
$336$		−	4.68820i		−	0.255762i
$337$			9.24995i			0.503877i	0.967743	+	0.251938i	$0.0810681\pi$
$337$			9.24995i			0.503877i	−0.967743	+	0.251938i	$0.918932\pi$
$338$			13.9136i			0.756800i
$339$	6.05386			0.328801
$340$		−	2.61613i		−	0.141880i
$341$	−14.8386			−0.803556
$342$			13.3755i			0.723263i
$343$			12.4220i			0.670727i
$344$	−0.105505			−0.00568845
$345$	7.80425			0.420167
$346$			25.6170i			1.37718i
$347$	−19.7509			−1.06028			−0.530142	−	0.847909i	$-0.677861\pi$
$347$	−19.7509			−1.06028			−0.530142	+	0.847909i	$0.677861\pi$
$348$			4.09312i			0.219414i
$349$	−21.9046			−1.17253			−0.586263	−	0.810121i	$-0.699402\pi$
$349$	−21.9046			−1.17253			−0.586263	+	0.810121i	$0.699402\pi$
$350$	2.45445			0.131196
$351$	2.15208			0.114870
$352$			21.3005i			1.13532i
$353$	4.50263			0.239651			0.119825	−	0.992795i	$-0.461767\pi$
$353$	4.50263			0.239651			0.119825	+	0.992795i	$0.461767\pi$
$354$	5.33095			0.283337
$355$		−	5.53066i		−	0.293537i
$356$	−11.6122			−0.615445
$357$		−	1.74916i		−	0.0925756i
$358$	6.53034			0.345139
$359$		−	13.0296i		−	0.687675i	−0.939029	−	0.343837i	$-0.888273\pi$
$359$		−	13.0296i		−	0.687675i	0.939029	−	0.343837i	$-0.111727\pi$
$360$	−3.81229			−0.200925
$361$	45.7199			2.40631
$362$	7.38286			0.388035
$363$	15.8386			0.831312
$364$		−	1.55954i		−	0.0817419i
$365$	22.8277			1.19485
$366$	22.4875			1.17544
$367$			7.88279i			0.411478i	0.978607	+	0.205739i	$0.0659598\pi$
$367$			7.88279i			0.411478i	−0.978607	+	0.205739i	$0.934040\pi$
$368$		−	20.7958i		−	1.08406i
$369$			0.936712i			0.0487633i
$370$	3.97298			0.206545
$371$	0.909038			0.0471949
$372$	2.18907			0.113498
$373$			5.72028i			0.296185i	0.988974	+	0.148093i	$0.0473134\pi$
$373$			5.72028i			0.296185i	−0.988974	+	0.148093i	$0.952687\pi$
$374$			15.8895i			0.821629i
$375$		−	12.1667i		−	0.628287i
$376$		−	2.50904i		−	0.129394i
$377$		−	11.5257i		−	0.593602i
$378$	1.57645			0.0810837
$379$			32.1508i			1.65148i	0.564053	+	0.825739i	$0.309241\pi$
$379$			32.1508i			1.65148i	−0.564053	+	0.825739i	$0.690759\pi$
$380$		−	11.4087i		−	0.585256i
$381$	−3.56745			−0.182766
$382$	−31.1987			−1.59626
$383$		−	31.7510i		−	1.62240i	−0.584770	−	0.811199i	$-0.698815\pi$
$383$		−	31.7510i		−	1.62240i	0.584770	−	0.811199i	$-0.301185\pi$
$384$			13.2990i			0.678659i
$385$	9.11468			0.464527
$386$			15.3234i			0.779938i
$387$		−	0.0513523i		−	0.00261038i
$388$			14.0329i			0.712411i
$389$	14.8408			0.752460			0.376230	−	0.926526i	$-0.377220\pi$
$389$	14.8408			0.752460			0.376230	+	0.926526i	$0.377220\pi$
$390$	−6.63928			−0.336193
$391$		−	7.75891i		−	0.392385i
$392$		−	12.5346i		−	0.633095i
$393$			1.78218i			0.0898993i
$394$			25.3902i			1.27914i
$395$	6.21094			0.312506
$396$	−3.95938			−0.198966
$397$		−	14.0638i		−	0.705840i	−0.935653	−	0.352920i	$-0.885189\pi$
$397$		−	14.0638i		−	0.705840i	0.935653	−	0.352920i	$-0.114811\pi$
$398$		−	18.5989i		−	0.932277i
$399$		−	7.62796i		−	0.381876i
$400$	−7.69822			−0.384911
$401$			26.3420i			1.31545i	0.753256	+	0.657727i	$0.228482\pi$
$401$			26.3420i			1.31545i	−0.753256	+	0.657727i	$0.771518\pi$
$402$			6.07195i			0.302841i
$403$	−6.16414			−0.307058
$404$	3.50259			0.174260
$405$		−	1.85555i		−	0.0922028i
$406$		−	8.44280i		−	0.419009i
$407$	−6.67167			−0.330702
$408$			3.79014i			0.187640i
$409$		−	31.2012i		−	1.54280i	−0.636352	−	0.771399i	$-0.719557\pi$
$409$		−	31.2012i		−	1.54280i	0.636352	−	0.771399i	$-0.280443\pi$
$410$		−	2.88980i		−	0.142717i
$411$			0.187329i			0.00924026i
$412$		−	3.07278i		−	0.151385i
$413$	−3.04021			−0.149599
$414$	6.99278			0.343676
$415$	28.2382			1.38616
$416$			8.84848i			0.433832i
$417$			16.8727i			0.826258i
$418$			69.2930i			3.38923i
$419$	9.65000			0.471434			0.235717	−	0.971822i	$-0.424256\pi$
$419$	9.65000			0.471434			0.235717	+	0.971822i	$0.424256\pi$
$420$	−1.34465			−0.0656120
$421$		−	20.1709i		−	0.983070i	−0.870858	−	0.491535i	$-0.836436\pi$
$421$		−	20.1709i		−	0.983070i	0.870858	−	0.491535i	$-0.163564\pi$
$422$	15.6352			0.761109
$423$	1.22122			0.0593778
$424$	−1.96973			−0.0956585
$425$	−2.87220			−0.139322
$426$		−	4.95559i		−	0.240099i
$427$	−12.8245			−0.620622
$428$			6.69412i			0.323573i
$429$	11.1491			0.538283
$430$			0.158424i			0.00763990i
$431$	15.5239			0.747762			0.373881	−	0.927477i	$-0.378027\pi$
$431$	15.5239			0.747762			0.373881	+	0.927477i	$0.378027\pi$
$432$	−4.94443			−0.237889
$433$			7.22083i			0.347011i	0.984833	+	0.173506i	$0.0555095\pi$
$433$			7.22083i			0.347011i	−0.984833	+	0.173506i	$0.944491\pi$
$434$	−4.51537			−0.216745
$435$	−9.93754			−0.476469
$436$	−7.86786			−0.376802
$437$		−	33.8359i		−	1.61859i
$438$	20.4541			0.977334
$439$			25.2189i			1.20363i	0.798635	+	0.601816i	$0.205556\pi$
$439$			25.2189i			1.20363i	−0.798635	+	0.601816i	$0.794444\pi$
$440$	−19.7499			−0.941541
$441$	6.10096			0.290522
$442$			6.60071i			0.313964i
$443$			15.8470i			0.752914i	0.926434	+	0.376457i	$0.122858\pi$
$443$			15.8470i			0.752914i	−0.926434	+	0.376457i	$0.877142\pi$
$444$	0.984241			0.0467100
$445$		−	28.1929i		−	1.33647i
$446$	34.1862			1.61876
$447$		−	13.2732i		−	0.627802i
$448$		−	2.89469i		−	0.136761i
$449$		−	32.4060i		−	1.52933i	−0.644426	−	0.764666i	$-0.722904\pi$
$449$		−	32.4060i		−	1.52933i	0.644426	−	0.764666i	$-0.277096\pi$
$450$		−	2.58860i		−	0.122028i
$451$			4.85273i			0.228506i
$452$	−4.62679			−0.217626
$453$		−	21.6037i		−	1.01503i
$454$	−23.8154			−1.11771
$455$	3.78635			0.177507
$456$			16.5285i			0.774016i
$457$	25.8272			1.20814			0.604072	−	0.796930i	$-0.293544\pi$
$457$	25.8272			1.20814			0.604072	+	0.796930i	$0.293544\pi$
$458$	−12.8496			−0.600424
$459$	−1.84477			−0.0861063
$460$	−5.96456			−0.278099
$461$	−42.1335			−1.96235			−0.981176	−	0.193116i	$-0.938141\pi$
$461$	−42.1335			−1.96235			−0.981176	+	0.193116i	$0.938141\pi$
$462$	8.16695			0.379961
$463$			0.0617504i			0.00286978i	0.999999	+	0.00143489i	$0.000456740\pi$
$463$			0.0617504i			0.00286978i	−0.999999	+	0.00143489i	$0.999543\pi$
$464$			26.4803i			1.22932i
$465$			5.31478i			0.246467i
$466$		−	33.4270i		−	1.54848i
$467$	−8.97496			−0.415312			−0.207656	−	0.978202i	$-0.566583\pi$
$467$	−8.97496			−0.415312			−0.207656	+	0.978202i	$0.566583\pi$
$468$	−1.64477			−0.0760297
$469$		−	3.46280i		−	0.159897i
$470$	−3.76753			−0.173783
$471$	−6.45803	+	10.7375i	−0.297570	+	0.494758i
$472$	6.58762			0.303220
$473$		−	0.266036i		−	0.0122323i
$474$	5.56513			0.255615
$475$	−12.5254			−0.574706
$476$			1.33683i			0.0612737i
$477$		−	0.958722i		−	0.0438968i
$478$			1.58554i			0.0725211i
$479$			26.8788i			1.22812i	0.789258	+	0.614062i	$0.210466\pi$
$479$			26.8788i			1.22812i	−0.789258	+	0.614062i	$0.789534\pi$
$480$	7.62924			0.348226
$481$	−2.77149			−0.126369
$482$	−33.0754			−1.50654
$483$	−3.98794			−0.181458
$484$	−12.1050			−0.550226
$485$	−34.0699			−1.54704
$486$		−	1.66261i		−	0.0754175i
$487$	29.7779			1.34936			0.674682	−	0.738109i	$-0.264281\pi$
$487$	29.7779			1.34936			0.674682	+	0.738109i	$0.264281\pi$
$488$	27.7885			1.25793
$489$			16.3116i			0.737637i
$490$	−18.8218			−0.850281
$491$			21.8336i			0.985334i	0.870218	+	0.492667i	$0.163978\pi$
$491$			21.8336i			0.985334i	−0.870218	+	0.492667i	$0.836022\pi$
$492$		−	0.715901i		−	0.0322753i
$493$			9.87980i			0.444964i
$494$			28.7851i			1.29510i
$495$		−	9.61284i		−	0.432065i
$496$	14.1622			0.635900
$497$			2.82614i			0.126770i
$498$	25.3020			1.13381
$499$		−	15.4479i		−	0.691544i	−0.938319	−	0.345772i	$-0.887617\pi$
$499$		−	15.4479i		−	0.691544i	0.938319	−	0.345772i	$-0.112383\pi$
$500$			9.29866i			0.415849i
$501$	−12.8059			−0.572126
$502$	−23.0447			−1.02854
$503$		−	20.6611i		−	0.921235i	−0.887599	−	0.460617i	$-0.847628\pi$
$503$		−	20.6611i		−	0.921235i	0.887599	−	0.460617i	$-0.152372\pi$
$504$	1.94806			0.0867737
$505$			8.50382i			0.378415i
$506$	36.2268			1.61048
$507$	−8.36853			−0.371660
$508$	2.72650			0.120969
$509$		−	10.8204i		−	0.479604i	−0.970822	−	0.239802i	$-0.922917\pi$
$509$		−	10.8204i		−	0.479604i	0.970822	−	0.239802i	$-0.0770826\pi$
$510$	5.69119			0.252010
$511$	−11.6649			−0.516023
$512$		−	0.0124320i		−	0.000549420i
$513$	−8.04487			−0.355190
$514$			30.2945i			1.33623i
$515$	7.46030			0.328740
$516$			0.0392470i			0.00172775i
$517$	6.32666			0.278246
$518$	−2.03018			−0.0892009
$519$	−15.4077			−0.676324
$520$	−8.20436			−0.359785
$521$			41.7159i			1.82761i	0.406157	+	0.913803i	$0.366868\pi$
$521$			41.7159i			1.82761i	−0.406157	+	0.913803i	$0.633132\pi$
$522$	−8.90425			−0.389728
$523$	−19.7750			−0.864701			−0.432351	−	0.901706i	$-0.642316\pi$
$523$	−19.7750			−0.864701			−0.432351	+	0.901706i	$0.642316\pi$
$524$		−	1.36207i		−	0.0595023i
$525$			1.47626i			0.0644293i
$526$			33.3905i			1.45590i
$527$	5.28390			0.230170
$528$	−25.6151			−1.11476
$529$	5.31036			0.230885
$530$			2.95770i			0.128474i
$531$			3.20638i			0.139145i
$532$			5.82982i			0.252755i
$533$			2.01588i			0.0873176i
$534$		−	25.2614i		−	1.09317i
$535$	−16.2524			−0.702654
$536$			7.50329i			0.324093i
$537$			3.92776i			0.169496i
$538$	−20.3872			−0.878954
$539$	31.6066			1.36139
$540$			1.41814i			0.0610270i
$541$			12.3635i			0.531548i	0.964035	+	0.265774i	$0.0856276\pi$
$541$			12.3635i			0.531548i	−0.964035	+	0.265774i	$0.914372\pi$
$542$	−12.9350			−0.555606
$543$			4.44053i			0.190561i
$544$		−	7.58491i		−	0.325200i
$545$		−	19.1021i		−	0.818245i
$546$	3.39265			0.145192
$547$	22.8415			0.976630			0.488315	−	0.872667i	$-0.337612\pi$
$547$	22.8415			0.976630			0.488315	+	0.872667i	$0.337612\pi$
$548$		−	0.143170i		−	0.00611592i
$549$			13.5254i			0.577252i
$550$		−	13.4105i		−	0.571825i
$551$			43.0850i			1.83548i
$552$	8.64118			0.367793
$553$	−3.17377			−0.134962
$554$			33.3519i			1.41698i
$555$			2.38961i			0.101433i
$556$		−	12.8953i		−	0.546882i
$557$	−17.9096			−0.758853			−0.379427	−	0.925222i	$-0.623879\pi$
$557$	−17.9096			−0.758853			−0.379427	+	0.925222i	$0.623879\pi$
$558$			4.76216i			0.201598i
$559$		−	0.110514i		−	0.00467426i
$560$	−8.69917			−0.367607
$561$	−9.55699			−0.403496
$562$		−	32.0862i		−	1.35347i
$563$			36.0327i			1.51860i	0.650741	+	0.759299i	$0.274458\pi$
$563$			36.0327i			1.51860i	−0.650741	+	0.759299i	$0.725542\pi$
$564$	−0.933343			−0.0393008
$565$		−	11.2332i		−	0.472585i
$566$		−	41.1961i		−	1.73160i
$567$			0.948177i			0.0398197i
$568$		−	6.12377i		−	0.256948i
$569$		−	37.7979i		−	1.58457i	−0.610151	−	0.792285i	$-0.708891\pi$
$569$		−	37.7979i		−	1.58457i	0.610151	−	0.792285i	$-0.291109\pi$
$570$	24.8188			1.03955
$571$	11.1738			0.467608			0.233804	−	0.972284i	$-0.424883\pi$
$571$	11.1738			0.467608			0.233804	+	0.972284i	$0.424883\pi$
$572$	−8.52091			−0.356277
$573$		−	18.7649i		−	0.783915i
$574$			1.47668i			0.0616353i
$575$			6.54837i			0.273086i
$576$	−3.05290			−0.127204
$577$	11.1762			0.465273			0.232637	−	0.972564i	$-0.425265\pi$
$577$	11.1762			0.465273			0.232637	+	0.972564i	$0.425265\pi$
$578$			22.6062i			0.940295i
$579$	−9.21645			−0.383023
$580$	7.59497			0.315364
$581$	−14.4296			−0.598641
$582$	−30.5274			−1.26540
$583$		−	4.96675i		−	0.205702i
$584$	25.2757			1.04592
$585$		−	3.99329i		−	0.165102i
$586$	−37.8591			−1.56395
$587$		−	21.6444i		−	0.893362i	−0.894693	−	0.446681i	$-0.852606\pi$
$587$		−	21.6444i		−	0.893362i	0.894693	−	0.446681i	$-0.147394\pi$
$588$	−4.66278			−0.192290
$589$	23.0426			0.949455
$590$		−	9.89183i		−	0.407240i
$591$	−15.2713			−0.628176
$592$	6.36753			0.261704
$593$	27.8072			1.14190			0.570952	−	0.820984i	$-0.306574\pi$
$593$	27.8072			1.14190			0.570952	+	0.820984i	$0.306574\pi$
$594$		−	8.61331i		−	0.353409i
$595$	−3.24566			−0.133059
$596$			10.1443i			0.415528i
$597$	11.1866			0.457835
$598$	15.0490			0.615401
$599$		−	5.41734i		−	0.221346i	−0.993857	−	0.110673i	$-0.964699\pi$
$599$		−	5.41734i		−	0.221346i	0.993857	−	0.110673i	$-0.0353007\pi$
$600$		−	3.19880i		−	0.130591i
$601$	−2.43791			−0.0994443			−0.0497222	−	0.998763i	$-0.515834\pi$
$601$	−2.43791			−0.0994443			−0.0497222	+	0.998763i	$0.515834\pi$
$602$		−	0.0809542i		−	0.00329945i
$603$	−3.65206			−0.148723
$604$			16.5111i			0.671826i
$605$		−	29.3893i		−	1.19484i
$606$			7.61961i			0.309525i
$607$		−	4.04993i		−	0.164382i	−0.996617	−	0.0821908i	$-0.973808\pi$
$607$		−	4.04993i		−	0.164382i	0.996617	−	0.0821908i	$-0.0261917\pi$
$608$		−	33.0772i		−	1.34146i
$609$	5.07804			0.205773
$610$		−	41.7266i		−	1.68946i
$611$	2.62817			0.106324
$612$	1.40990			0.0569918
$613$		−	41.9205i		−	1.69315i	−0.532268	−	0.846576i	$-0.678660\pi$
$613$		−	41.9205i		−	1.69315i	0.532268	−	0.846576i	$-0.321340\pi$
$614$	24.9722			1.00780
$615$	1.73811			0.0700875
$616$	10.0921			0.406624
$617$	−9.88482			−0.397948			−0.198974	−	0.980005i	$-0.563761\pi$
$617$	−9.88482			−0.397948			−0.198974	+	0.980005i	$0.563761\pi$
$618$	6.68459			0.268894
$619$	30.2104			1.21426			0.607129	−	0.794603i	$-0.292321\pi$
$619$	30.2104			1.21426			0.607129	+	0.794603i	$0.292321\pi$
$620$		−	4.06193i		−	0.163131i
$621$			4.20591i			0.168777i
$622$		−	19.3979i		−	0.777784i
$623$			14.4065i			0.577182i
$624$	−10.6408			−0.425974
$625$	−14.7912			−0.591647
$626$			45.5942i			1.82231i
$627$	−41.6772			−1.66443
$628$	4.93568	−	8.20635i	0.196955	−	0.327469i
$629$	2.37572			0.0947262
$630$		−	2.92517i		−	0.116542i
$631$	17.8454			0.710416			0.355208	−	0.934787i	$-0.384410\pi$
$631$	17.8454			0.710416			0.355208	+	0.934787i	$0.384410\pi$
$632$	6.87700			0.273552
$633$			9.40401i			0.373776i
$634$			47.1320i			1.87185i
$635$			6.61957i			0.262690i
$636$			0.732722i			0.0290543i
$637$	13.1298			0.520221
$638$	−46.1294			−1.82628
$639$	2.98061			0.117911
$640$	24.6768			0.975437
$641$	3.98574			0.157427			0.0787136	−	0.996897i	$-0.474919\pi$
$641$	3.98574			0.157427			0.0787136	+	0.996897i	$0.474919\pi$
$642$	−14.5625			−0.574737
$643$			0.471620i			0.0185989i	0.999957	+	0.00929944i	$0.00296015\pi$
$643$			0.471620i			0.0185989i	−0.999957	+	0.00929944i	$0.997040\pi$
$644$	3.04787			0.120103
$645$	−0.0952865			−0.00375190
$646$		−	24.6746i		−	0.970809i
$647$	8.01922			0.315268			0.157634	−	0.987498i	$-0.449613\pi$
$647$	8.01922			0.315268			0.157634	+	0.987498i	$0.449613\pi$
$648$		−	2.05454i		−	0.0807098i
$649$			16.6110i			0.652037i
$650$		−	5.57087i		−	0.218508i
$651$		−	2.71583i		−	0.106442i
$652$		−	12.4665i		−	0.488225i
$653$	−44.8929			−1.75680			−0.878398	−	0.477930i	$-0.841387\pi$
$653$	−44.8929			−1.75680			−0.878398	+	0.477930i	$0.841387\pi$
$654$		−	17.1159i		−	0.669285i
$655$	3.30693			0.129212
$656$		−	4.63151i		−	0.180830i
$657$			12.3024i			0.479962i
$658$	1.92519			0.0750518
$659$	−25.8025			−1.00512			−0.502562	−	0.864541i	$-0.667609\pi$
$659$	−25.8025			−1.00512			−0.502562	+	0.864541i	$0.667609\pi$
$660$			7.34681i			0.285974i
$661$	1.16190			0.0451925			0.0225962	−	0.999745i	$-0.492807\pi$
$661$	1.16190			0.0451925			0.0225962	+	0.999745i	$0.492807\pi$
$662$			4.04984i			0.157402i
$663$	−3.97009			−0.154186
$664$	31.2665			1.21338
$665$	−14.1540			−0.548870
$666$			2.14114i			0.0829674i
$667$	22.5251			0.872175
$668$	9.78718			0.378677
$669$			20.5618i			0.794963i
$670$	11.2668			0.435274
$671$			70.0699i			2.70502i
$672$	−3.89851			−0.150388
$673$		−	46.0707i		−	1.77589i	−0.459945	−	0.887947i	$-0.652131\pi$
$673$		−	46.0707i		−	1.77589i	0.459945	−	0.887947i	$-0.347869\pi$
$674$	15.3791			0.592379
$675$	1.55695			0.0599269
$676$	6.39582			0.245993
$677$	−22.3341			−0.858370			−0.429185	−	0.903217i	$-0.641199\pi$
$677$	−22.3341			−0.858370			−0.429185	+	0.903217i	$0.641199\pi$
$678$		−	10.0652i		−	0.386552i
$679$	17.4096			0.668120
$680$	7.03277			0.269695
$681$		−	14.3241i		−	0.548901i
$682$			24.6708i			0.944695i
$683$		−	13.3210i		−	0.509713i	−0.966979	−	0.254856i	$-0.917972\pi$
$683$		−	13.3210i		−	0.509713i	0.966979	−	0.254856i	$-0.0820282\pi$
$684$	6.14845			0.235092
$685$	0.347598			0.0132810
$686$	20.6530			0.788535
$687$		−	7.72860i		−	0.294864i
$688$			0.253908i			0.00968014i
$689$		−	2.06325i		−	0.0786035i
$690$		−	12.9754i		−	0.493966i
$691$		−	49.3055i		−	1.87567i	−0.347081	−	0.937835i	$-0.612827\pi$
$691$		−	49.3055i		−	1.87567i	0.347081	−	0.937835i	$-0.387173\pi$
$692$	11.7757			0.447644
$693$			4.91213i			0.186596i
$694$			32.8380i			1.24651i
$695$	31.3080			1.18758
$696$	−11.0032			−0.417077
$697$		−	1.72801i		−	0.0654532i
$698$			36.4188i			1.37847i
$699$	20.1052			0.760447
$700$		−	1.12826i		−	0.0426443i
$701$		−	16.3168i		−	0.616276i	−0.951342	−	0.308138i	$-0.900294\pi$
$701$		−	16.3168i		−	0.616276i	0.951342	−	0.308138i	$-0.0997058\pi$
$702$		−	3.57808i		−	0.135046i
$703$	10.3603			0.390747
$704$	−15.8159			−0.596083
$705$		−	2.26603i		−	0.0853438i
$706$		−	7.48611i		−	0.281743i
$707$		−	4.34542i		−	0.163426i
$708$		−	2.45054i		−	0.0920968i
$709$	28.6314			1.07527			0.537637	−	0.843177i	$-0.319317\pi$
$709$	28.6314			1.07527			0.537637	+	0.843177i	$0.319317\pi$
$710$	−9.19532			−0.345094
$711$			3.34723i			0.125531i
$712$		−	31.2163i		−	1.16988i
$713$		−	12.0468i		−	0.451157i
$714$	−2.90818			−0.108836
$715$		−	20.6876i		−	0.773674i
$716$		−	3.00187i		−	0.112185i
$717$	−0.953647			−0.0356146
$718$	−21.6631			−0.808460
$719$		−	3.46375i		−	0.129176i	−0.997912	−	0.0645881i	$-0.979427\pi$
$719$		−	3.46375i		−	0.129176i	0.997912	−	0.0645881i	$-0.0205733\pi$
$720$			9.17462i			0.341918i
$721$	−3.81218			−0.141973
$722$		−	76.0143i		−	2.82896i
$723$		−	19.8937i		−	0.739854i
$724$		−	3.39376i		−	0.126128i
$725$		−	8.33837i		−	0.309679i
$726$		−	26.3334i		−	0.977325i
$727$	−26.3139			−0.975930			−0.487965	−	0.872863i	$-0.662261\pi$
$727$	−26.3139			−0.975930			−0.487965	+	0.872863i	$0.662261\pi$
$728$	4.19240			0.155381
$729$	1.00000			0.0370370
$730$		−	37.9535i		−	1.40472i
$731$			0.0947329i			0.00350382i
$732$		−	10.3371i		−	0.382070i
$733$	−21.9385			−0.810317			−0.405158	−	0.914246i	$-0.632784\pi$
$733$	−21.9385			−0.810317			−0.405158	+	0.914246i	$0.632784\pi$
$734$	13.1060			0.483751
$735$		−	11.3206i		−	0.417567i
$736$	−17.2929			−0.637426
$737$	−18.9199			−0.696922
$738$	1.55739			0.0573282
$739$	−22.3359			−0.821638			−0.410819	−	0.911717i	$-0.634757\pi$
$739$	−22.3359			−0.821638			−0.410819	+	0.911717i	$0.634757\pi$
$740$		−	1.82630i		−	0.0671363i
$741$	−17.3132			−0.636017
$742$		−	1.51137i		−	0.0554843i
$743$	−13.9806			−0.512897			−0.256449	−	0.966558i	$-0.582552\pi$
$743$	−13.9806			−0.512897			−0.256449	+	0.966558i	$0.582552\pi$
$744$			5.88474i			0.215745i
$745$	−24.6291			−0.902340
$746$	9.51060			0.348208
$747$			15.2183i			0.556807i
$748$	7.30412			0.267065
$749$	8.30493			0.303456
$750$	−20.2285			−0.738641
$751$		−	32.5497i		−	1.18775i	−0.804556	−	0.593877i	$-0.797597\pi$
$751$		−	32.5497i		−	1.18775i	0.804556	−	0.593877i	$-0.202403\pi$
$752$	−6.03825			−0.220192
$753$		−	13.8606i		−	0.505107i
$754$	−19.1627			−0.697864
$755$	−40.0867			−1.45890
$756$		−	0.724663i		−	0.0263558i
$757$		−	29.6680i		−	1.07830i	−0.842209	−	0.539151i	$-0.818745\pi$
$757$		−	29.6680i		−	1.07830i	0.842209	−	0.539151i	$-0.181255\pi$
$758$	53.4543			1.94155
$759$			21.7891i			0.790895i
$760$	30.6693			1.11249
$761$		−	34.1236i		−	1.23698i	−0.785793	−	0.618489i	$-0.787745\pi$
$761$		−	34.1236i		−	1.23698i	0.785793	−	0.618489i	$-0.212255\pi$
$762$			5.93128i			0.214867i
$763$			9.76111i			0.353376i
$764$			14.3414i			0.518855i
$765$			3.42305i			0.123761i
$766$	−52.7894			−1.90736
$767$			6.90039i			0.249159i
$768$	16.0052			0.577537
$769$	−9.19160			−0.331458			−0.165729	−	0.986171i	$-0.552998\pi$
$769$	−9.19160			−0.331458			−0.165729	+	0.986171i	$0.552998\pi$
$770$		−	15.1542i		−	0.546118i
$771$	−18.2210			−0.656215
$772$	7.04386			0.253514
$773$	40.2062			1.44612			0.723059	−	0.690786i	$-0.242735\pi$
$773$	40.2062			1.44612			0.723059	+	0.690786i	$0.242735\pi$
$774$	−0.0853788			−0.00306888
$775$	−4.45951			−0.160190
$776$	−37.7236			−1.35420
$777$		−	1.22108i		−	0.0438060i
$778$		−	24.6745i		−	0.884623i
$779$		−	7.53572i		−	0.269995i
$780$			3.05195i			0.109277i
$781$	15.4413			0.552535
$782$	−12.9000			−0.461304
$783$		−	5.35559i		−	0.191393i
$784$	−30.1658			−1.07735
$785$	19.9239	+	11.9832i	0.711116	+	0.427698i
$786$	2.96308			0.105689
$787$		−	24.2272i		−	0.863607i	−0.901968	−	0.431804i	$-0.857877\pi$
$787$		−	24.2272i		−	0.863607i	0.901968	−	0.431804i	$-0.142123\pi$
$788$	11.6714			0.415776
$789$	−20.0832			−0.714981
$790$		−	10.3264i		−	0.367396i
$791$			5.74014i			0.204096i
$792$		−	10.6437i		−	0.378208i
$793$			29.1079i			1.03365i
$794$	−23.3826			−0.829816
$795$	−1.77895			−0.0630929
$796$	−8.54955			−0.303031
$797$	39.7328			1.40741			0.703704	−	0.710494i	$-0.251528\pi$
$797$	39.7328			1.40741			0.703704	+	0.710494i	$0.251528\pi$
$798$	−12.6823			−0.448949
$799$	−2.25287			−0.0797007
$800$			6.40152i			0.226328i
$801$	15.1938			0.536848
$802$	43.7964			1.54650
$803$			63.7338i			2.24912i
$804$	2.79116			0.0984366
$805$			7.39981i			0.260809i
$806$			10.2486i			0.360990i
$807$		−	12.2622i		−	0.431648i
$808$			9.41578i			0.331246i
$809$			38.8549i			1.36607i	0.730387	+	0.683033i	$0.239340\pi$
$809$			38.8549i			1.36607i	−0.730387	+	0.683033i	$0.760660\pi$
$810$	−3.08505			−0.108398
$811$		−	5.45752i		−	0.191640i	−0.995399	−	0.0958198i	$-0.969453\pi$
$811$		−	5.45752i		−	0.191640i	0.995399	−	0.0958198i	$-0.0305473\pi$
$812$	−3.88100			−0.136196
$813$		−	7.77995i		−	0.272855i
$814$			11.0924i			0.388788i
$815$	30.2670			1.06021
$816$	9.12132			0.319310
$817$			0.413122i			0.0144533i
$818$	−51.8754			−1.81378
$819$			2.04056i			0.0713028i
$820$	−1.32839			−0.0463893
$821$	42.6751			1.48937			0.744686	−	0.667415i	$-0.232599\pi$
$821$	42.6751			1.48937			0.744686	+	0.667415i	$0.232599\pi$
$822$	0.311455			0.0108632
$823$		−	15.3052i		−	0.533506i	−0.963765	−	0.266753i	$-0.914049\pi$
$823$		−	15.3052i		−	0.533506i	0.963765	−	0.266753i	$-0.0859507\pi$
$824$	8.26034			0.287763
$825$	8.06592			0.280819
$826$			5.05469i			0.175875i
$827$	16.4588			0.572329			0.286165	−	0.958180i	$-0.407620\pi$
$827$	16.4588			0.572329			0.286165	+	0.958180i	$0.407620\pi$
$828$		−	3.21445i		−	0.111710i
$829$	45.9078			1.59444			0.797221	−	0.603687i	$-0.206302\pi$
$829$	45.9078			1.59444			0.797221	+	0.603687i	$0.206302\pi$
$830$		−	46.9491i		−	1.62963i
$831$	−20.0599			−0.695872
$832$	−6.57010			−0.227777
$833$	−11.2548			−0.389957
$834$	28.0527			0.971384
$835$			23.7620i			0.822317i
$836$	31.8527			1.10165
$837$	−2.86427			−0.0990035
$838$		−	16.0442i		−	0.554237i
$839$			51.1787i			1.76689i	0.468539	+	0.883443i	$0.344780\pi$
$839$			51.1787i			1.76689i	−0.468539	+	0.883443i	$0.655220\pi$
$840$		−	3.61472i		−	0.124720i
$841$	0.317695			0.0109550
$842$	−33.5363			−1.15574
$843$	19.2987			0.664682
$844$		−	7.18720i		−	0.247394i
$845$			15.5282i			0.534186i
$846$		−	2.03041i		−	0.0698071i
$847$			15.0178i			0.516018i
$848$			4.74033i			0.162784i
$849$	24.7780			0.850379
$850$			4.77535i			0.163793i
$851$		−	5.41644i		−	0.185673i
$852$	−2.27799			−0.0780427
$853$	−47.5724			−1.62885			−0.814425	−	0.580269i	$-0.802947\pi$
$853$	−47.5724			−1.62885			−0.814425	+	0.580269i	$0.802947\pi$
$854$			21.3222i			0.729629i
$855$			14.9276i			0.510514i
$856$	−17.9954			−0.615069
$857$			27.0365i			0.923548i	0.886998	+	0.461774i	$0.152787\pi$
$857$			27.0365i			0.923548i	−0.886998	+	0.461774i	$0.847213\pi$
$858$		−	18.5366i		−	0.632828i
$859$		−	37.5771i		−	1.28211i	−0.767493	−	0.641057i	$-0.778496\pi$
$859$		−	37.5771i		−	1.28211i	0.767493	−	0.641057i	$-0.221504\pi$
$860$	0.0728246			0.00248330
$861$	−0.888169			−0.0302687
$862$		−	25.8103i		−	0.879101i
$863$			22.9205i			0.780222i	0.920768	+	0.390111i	$0.127563\pi$
$863$			22.9205i			0.780222i	−0.920768	+	0.390111i	$0.872437\pi$
$864$			4.11159i			0.139879i
$865$			28.5898i			0.972081i
$866$	12.0054			0.407961
$867$	−13.5968			−0.461773
$868$			2.07563i			0.0704514i
$869$			17.3407i			0.588241i
$870$			16.5222i			0.560157i
$871$	−7.85954			−0.266310
$872$		−	21.1506i		−	0.716251i
$873$		−	18.3611i		−	0.621430i
$874$	−56.2560			−1.90289
$875$	11.5362			0.389995
$876$		−	9.40236i		−	0.317676i
$877$			12.4486i			0.420358i	0.977663	+	0.210179i	$0.0674047\pi$
$877$			12.4486i			0.420358i	−0.977663	+	0.210179i	$0.932595\pi$
$878$	41.9292			1.41504
$879$		−	22.7709i		−	0.768044i
$880$			47.5300i			1.60224i
$881$			24.3022i			0.818761i	0.912364	+	0.409381i	$0.134255\pi$
$881$			24.3022i			0.818761i	−0.912364	+	0.409381i	$0.865745\pi$
$882$		−	10.1435i		−	0.341550i
$883$			17.2499i			0.580507i	0.956950	+	0.290253i	$0.0937396\pi$
$883$			17.2499i			0.580507i	−0.956950	+	0.290253i	$0.906260\pi$
$884$	3.03422			0.102052
$885$	5.94958			0.199993
$886$	26.3474			0.885157
$887$			18.8361i			0.632455i	0.948683	+	0.316227i	$0.102416\pi$
$887$			18.8361i			0.632455i	−0.948683	+	0.316227i	$0.897584\pi$
$888$			2.64587i			0.0887895i
$889$		−	3.38257i		−	0.113448i
$890$	−46.8738			−1.57121
$891$	5.18060			0.173557
$892$		−	15.7147i		−	0.526168i
$893$	−9.82457			−0.328767
$894$	−22.0682			−0.738071
$895$	7.28815			0.243616
$896$	−12.6098			−0.421263
$897$			9.05146i			0.302219i
$898$	−53.8785			−1.79795
$899$			15.3398i			0.511612i
$900$	−1.18993			−0.0396643
$901$			1.76862i			0.0589212i
$902$	8.06820			0.268642
$903$	0.0486910			0.00162034
$904$		−	12.4379i		−	0.413678i
$905$	8.23961			0.273894
$906$	−35.9185			−1.19331
$907$	−47.5393			−1.57852			−0.789258	−	0.614061i	$-0.789535\pi$
$907$	−47.5393			−1.57852			−0.789258	+	0.614061i	$0.789535\pi$
$908$			10.9475i			0.363305i
$909$	−4.58292			−0.152006
$910$		−	6.29522i		−	0.208684i
$911$	−0.316553			−0.0104879			−0.00524393	−	0.999986i	$-0.501669\pi$
$911$	−0.316553			−0.0104879			−0.00524393	+	0.999986i	$0.501669\pi$
$912$	39.7773			1.31716
$913$			78.8398i			2.60922i
$914$		−	42.9405i		−	1.42035i
$915$	25.0971			0.829684
$916$			5.90673i			0.195164i
$917$	−1.68983			−0.0558030
$918$			3.06712i			0.101230i
$919$		−	23.0906i		−	0.761689i	−0.924639	−	0.380844i	$-0.875633\pi$
$919$		−	23.0906i		−	0.761689i	0.924639	−	0.380844i	$-0.124367\pi$
$920$		−	16.0341i		−	0.528629i
$921$			15.0199i			0.494922i
$922$			70.0515i			2.30702i
$923$	6.41452			0.211136
$924$		−	3.75419i		−	0.123504i
$925$	−2.00506			−0.0659261
$926$	0.102667			0.00337384
$927$			4.02054i			0.132052i
$928$	22.0200			0.722840
$929$	−20.3673			−0.668230			−0.334115	−	0.942532i	$-0.608437\pi$
$929$	−20.3673			−0.668230			−0.334115	+	0.942532i	$0.608437\pi$
$930$	8.83640			0.289757
$931$	−49.0814			−1.60858
$932$	−15.3658			−0.503323
$933$	11.6671			0.381965
$934$			14.9219i			0.488258i
$935$			17.7334i			0.579946i
$936$		−	4.42153i		−	0.144522i
$937$			42.5596i			1.39036i	0.718835	+	0.695181i	$0.244676\pi$
$937$			42.5596i			1.39036i	−0.718835	+	0.695181i	$0.755324\pi$
$938$	−5.75728			−0.187982
$939$	−27.4233			−0.894924
$940$			1.73186i			0.0564871i
$941$	23.9270			0.779996			0.389998	−	0.920816i	$-0.372476\pi$
$941$	23.9270			0.779996			0.389998	+	0.920816i	$0.372476\pi$
$942$	17.8523	+	10.7372i	0.581658	+	0.349836i
$943$	−3.93972			−0.128295
$944$		−	15.8537i		−	0.515994i
$945$	1.75939			0.0572328
$946$	−0.442313			−0.0143808
$947$		−	10.2660i		−	0.333601i	−0.985991	−	0.166800i	$-0.946656\pi$
$947$		−	10.2660i		−	0.333601i	0.985991	−	0.166800i	$-0.0533436\pi$
$948$		−	2.55819i		−	0.0830861i
$949$			26.4758i			0.859441i
$950$			20.8249i			0.675649i
$951$	−28.3482			−0.919254
$952$	−3.59372			−0.116473
$953$	−50.6371			−1.64030			−0.820148	−	0.572151i	$-0.806109\pi$
$953$	−50.6371			−1.64030			−0.820148	+	0.572151i	$0.806109\pi$
$954$	−1.59398			−0.0516070
$955$	−34.8191			−1.12672
$956$	0.728844			0.0235725
$957$		−	27.7452i		−	0.896873i
$958$	44.6890			1.44384
$959$	−0.177621			−0.00573569
$960$			5.66480i			0.182831i
$961$	−22.7960			−0.735354
$962$			4.60791i			0.148565i
$963$		−	8.75884i		−	0.282250i
$964$			15.2041i			0.489693i
$965$			17.1016i			0.550518i
$966$			6.63039i			0.213329i
$967$	−7.19667			−0.231429			−0.115715	−	0.993282i	$-0.536916\pi$
$967$	−7.19667			−0.231429			−0.115715	+	0.993282i	$0.536916\pi$
$968$		−	32.5410i		−	1.04591i
$969$	14.8409			0.476758
$970$			56.6450i			1.81876i
$971$			1.23786i			0.0397247i	0.999803	+	0.0198624i	$0.00632280\pi$
$971$			1.23786i			0.0397247i	−0.999803	+	0.0198624i	$0.993677\pi$
$972$	−0.764270			−0.0245140
$973$	−15.9983			−0.512881
$974$		−	49.5090i		−	1.58637i
$975$	3.35068			0.107308
$976$		−	66.8756i		−	2.14064i
$977$	37.4266			1.19738			0.598692	−	0.800979i	$-0.295687\pi$
$977$	37.4266			1.19738			0.598692	+	0.800979i	$0.295687\pi$
$978$	27.1199			0.867197
$979$	78.7132			2.51569
$980$			8.65201i			0.276378i
$981$	10.2946			0.328681
$982$	36.3007			1.15840
$983$		−	15.8593i		−	0.505834i	−0.967488	−	0.252917i	$-0.918610\pi$
$983$		−	15.8593i		−	0.505834i	0.967488	−	0.252917i	$-0.0813900\pi$
$984$	1.92451			0.0613511
$985$			28.3366i			0.902878i
$986$	16.4262			0.523118
$987$			1.15793i			0.0368575i
$988$	13.2320			0.420965
$989$	0.215983			0.00686785
$990$	−15.9824			−0.507954
$991$	26.8582			0.853178			0.426589	−	0.904446i	$-0.359715\pi$
$991$	26.8582			0.853178			0.426589	+	0.904446i	$0.359715\pi$
$992$		−	11.7767i		−	0.373910i
$993$	−2.43583			−0.0772989
$994$	4.69877			0.149036
$995$		−	20.7572i		−	0.658047i
$996$		−	11.6309i		−	0.368538i
$997$		−	8.02275i		−	0.254083i	−0.991897	−	0.127042i	$-0.959452\pi$
$997$		−	8.02275i		−	0.254083i	0.991897	−	0.127042i	$-0.0405481\pi$
$998$	−25.6838			−0.813008
$999$	−1.28782			−0.0407448

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.b.b.313.4	✓	14
3.2	odd	2		1413.2.b.e.784.11		14
157.156	even	2	inner	471.2.b.b.313.11	yes	14
471.470	odd	2		1413.2.b.e.784.4		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.b.b.313.4	✓	14	1.1	even	1	trivial
471.2.b.b.313.11	yes	14	157.156	even	2	inner
1413.2.b.e.784.4		14	471.470	odd	2
1413.2.b.e.784.11		14	3.2	odd	2

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:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.66261i q^{2} +1.00000 q^{3} -0.764270 q^{4} -1.85555i q^{5} -1.66261i q^{6} +0.948177i q^{7} -2.05454i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.66261i q^{2} +1.00000 q^{3} -0.764270 q^{4} -1.85555i q^{5} -1.66261i q^{6} +0.948177i q^{7} -2.05454i q^{8} +1.00000 q^{9} -3.08505 q^{10} +5.18060 q^{11} -0.764270 q^{12} +2.15208 q^{13} +1.57645 q^{14} -1.85555i q^{15} -4.94443 q^{16} -1.84477 q^{17} -1.66261i q^{18} -8.04487 q^{19} +1.41814i q^{20} +0.948177i q^{21} -8.61331i q^{22} +4.20591i q^{23} -2.05454i q^{24} +1.55695 q^{25} -3.57808i q^{26} +1.00000 q^{27} -0.724663i q^{28} -5.35559i q^{29} -3.08505 q^{30} -2.86427 q^{31} +4.11159i q^{32} +5.18060 q^{33} +3.06712i q^{34} +1.75939 q^{35} -0.764270 q^{36} -1.28782 q^{37} +13.3755i q^{38} +2.15208 q^{39} -3.81229 q^{40} +0.936712i q^{41} +1.57645 q^{42} -0.0513523i q^{43} -3.95938 q^{44} -1.85555i q^{45} +6.99278 q^{46} +1.22122 q^{47} -4.94443 q^{48} +6.10096 q^{49} -2.58860i q^{50} -1.84477 q^{51} -1.64477 q^{52} -0.958722i q^{53} -1.66261i q^{54} -9.61284i q^{55} +1.94806 q^{56} -8.04487 q^{57} -8.90425 q^{58} +3.20638i q^{59} +1.41814i q^{60} +13.5254i q^{61} +4.76216i q^{62} +0.948177i q^{63} -3.05290 q^{64} -3.99329i q^{65} -8.61331i q^{66} -3.65206 q^{67} +1.40990 q^{68} +4.20591i q^{69} -2.92517i q^{70} +2.98061 q^{71} -2.05454i q^{72} +12.3024i q^{73} +2.14114i q^{74} +1.55695 q^{75} +6.14845 q^{76} +4.91213i q^{77} -3.57808i q^{78} +3.34723i q^{79} +9.17462i q^{80} +1.00000 q^{81} +1.55739 q^{82} +15.2183i q^{83} -0.724663i q^{84} +3.42305i q^{85} -0.0853788 q^{86} -5.35559i q^{87} -10.6437i q^{88} +15.1938 q^{89} -3.08505 q^{90} +2.04056i q^{91} -3.21445i q^{92} -2.86427 q^{93} -2.03041i q^{94} +14.9276i q^{95} +4.11159i q^{96} -18.3611i q^{97} -10.1435i q^{98} +5.18060 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 14 q^{3} - 20 q^{4} + 14 q^{9}+O(q^{10}) \) 14 * q + 14 * q^3 - 20 * q^4 + 14 * q^9	\( 14 q + 14 q^{3} - 20 q^{4} + 14 q^{9} + 6 q^{10} - 2 q^{11} - 20 q^{12} + 24 q^{16} + 18 q^{17} - 12 q^{19} - 18 q^{25} + 14 q^{27} + 6 q^{30} - 14 q^{31} - 2 q^{33} + 16 q^{35} - 20 q^{36} - 14 q^{37} - 36 q^{40} + 24 q^{44} - 8 q^{46} + 22 q^{47} + 24 q^{48} - 48 q^{49} + 18 q^{51} - 50 q^{52} - 62 q^{56} - 12 q^{57} + 20 q^{58} - 34 q^{64} + 42 q^{67} - 56 q^{68} + 38 q^{71} - 18 q^{75} + 52 q^{76} + 14 q^{81} + 10 q^{82} + 34 q^{86} - 48 q^{89} + 6 q^{90} - 14 q^{93} - 2 q^{99}+O(q^{100}) \) 14 * q + 14 * q^3 - 20 * q^4 + 14 * q^9 + 6 * q^10 - 2 * q^11 - 20 * q^12 + 24 * q^16 + 18 * q^17 - 12 * q^19 - 18 * q^25 + 14 * q^27 + 6 * q^30 - 14 * q^31 - 2 * q^33 + 16 * q^35 - 20 * q^36 - 14 * q^37 - 36 * q^40 + 24 * q^44 - 8 * q^46 + 22 * q^47 + 24 * q^48 - 48 * q^49 + 18 * q^51 - 50 * q^52 - 62 * q^56 - 12 * q^57 + 20 * q^58 - 34 * q^64 + 42 * q^67 - 56 * q^68 + 38 * q^71 - 18 * q^75 + 52 * q^76 + 14 * q^81 + 10 * q^82 + 34 * q^86 - 48 * q^89 + 6 * q^90 - 14 * q^93 - 2 * q^99

Introduction

L-functions

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