LMFDB - Embedded newform 1690.2.e.s.191.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1690,2,Mod(191,1690)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1690.191"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1690, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,-4,-2,-4,8,-2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.4947179416$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.22581504.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			191.1
Root			$-1.27597 - 0.609843i$ of defining polynomial
Character	$\chi$	$=$	1690.191
Dual form			1690.2.e.s.991.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.66612 + 2.88581i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-1.66612 - 2.88581i) q^{6} +(0.719687 + 1.24653i) q^{7} +1.00000 q^{8} +(-4.05193 - 7.01815i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(2.01978 - 3.49837i) q^{11} +3.33225 q^{12} -1.43937 q^{14} +(-1.66612 + 2.88581i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.15376 - 1.99837i) q^{17} +8.10387 q^{18} +(-0.199902 - 0.346241i) q^{19} +(-0.500000 - 0.866025i) q^{20} -4.79635 q^{21} +(2.01978 + 3.49837i) q^{22} +(-0.780313 + 1.35154i) q^{23} +(-1.66612 + 2.88581i) q^{24} +1.00000 q^{25} +17.0073 q^{27} +(0.719687 - 1.24653i) q^{28} +(3.93244 - 6.81119i) q^{29} +(-1.66612 - 2.88581i) q^{30} +3.10713 q^{31} +(-0.500000 - 0.866025i) q^{32} +(6.73042 + 11.6574i) q^{33} +2.30752 q^{34} +(0.719687 + 1.24653i) q^{35} +(-4.05193 + 7.01815i) q^{36} +(-3.11786 + 5.40029i) q^{37} +0.399804 q^{38} +1.00000 q^{40} +(0.380509 - 0.659061i) q^{41} +(2.39817 - 4.15376i) q^{42} +(5.50367 + 9.53264i) q^{43} -4.03957 q^{44} +(-4.05193 - 7.01815i) q^{45} +(-0.780313 - 1.35154i) q^{46} +5.84016 q^{47} +(-1.66612 - 2.88581i) q^{48} +(2.46410 - 4.26795i) q^{49} +(-0.500000 + 0.866025i) q^{50} +7.68922 q^{51} +10.6249 q^{53} +(-8.50367 + 14.7288i) q^{54} +(2.01978 - 3.49837i) q^{55} +(0.719687 + 1.24653i) q^{56} +1.33225 q^{57} +(3.93244 + 6.81119i) q^{58} +(1.73205 + 3.00000i) q^{59} +3.33225 q^{60} +(2.84624 + 4.92983i) q^{61} +(-1.55356 + 2.69085i) q^{62} +(5.83225 - 10.1017i) q^{63} +1.00000 q^{64} -13.4608 q^{66} +(5.20039 - 9.00734i) q^{67} +(-1.15376 + 1.99837i) q^{68} +(-2.60020 - 4.50367i) q^{69} -1.43937 q^{70} +(3.00000 + 5.19615i) q^{71} +(-4.05193 - 7.01815i) q^{72} -13.4608 q^{73} +(-3.11786 - 5.40029i) q^{74} +(-1.66612 + 2.88581i) q^{75} +(-0.199902 + 0.346241i) q^{76} +5.81445 q^{77} +0.931464 q^{79} +(-0.500000 + 0.866025i) q^{80} +(-16.1805 + 28.0255i) q^{81} +(0.380509 + 0.659061i) q^{82} -10.3867 q^{83} +(2.39817 + 4.15376i) q^{84} +(-1.15376 - 1.99837i) q^{85} -11.0073 q^{86} +(13.1039 + 22.6966i) q^{87} +(2.01978 - 3.49837i) q^{88} +(-0.485517 + 0.840939i) q^{89} +8.10387 q^{90} +1.56063 q^{92} +(-5.17686 + 8.96658i) q^{93} +(-2.92008 + 5.05772i) q^{94} +(-0.199902 - 0.346241i) q^{95} +3.33225 q^{96} +(-6.15919 - 10.6680i) q^{97} +(2.46410 + 4.26795i) q^{98} -32.7361 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} - 2 q^{6} + 8 q^{8} - 4 q^{9} - 4 q^{10} + 6 q^{11} + 4 q^{12} - 2 q^{15} - 4 q^{16} - 6 q^{17} + 8 q^{18} - 6 q^{19} - 4 q^{20} + 12 q^{21} + 6 q^{22} - 12 q^{23}+ \cdots - 84 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 - 2 * q^6 + 8 * q^8 - 4 * q^9 - 4 * q^10 + 6 * q^11 + 4 * q^12 - 2 * q^15 - 4 * q^16 - 6 * q^17 + 8 * q^18 - 6 * q^19 - 4 * q^20 + 12 * q^21 + 6 * q^22 - 12 * q^23 - 2 * q^24 + 8 * q^25 + 40 * q^27 - 2 * q^30 + 36 * q^31 - 4 * q^32 + 6 * q^33 + 12 * q^34 - 4 * q^36 + 6 * q^37 + 12 * q^38 + 8 * q^40 - 6 * q^42 - 4 * q^43 - 12 * q^44 - 4 * q^45 - 12 * q^46 - 2 * q^48 - 8 * q^49 - 4 * q^50 + 60 * q^53 - 20 * q^54 + 6 * q^55 - 12 * q^57 + 4 * q^60 + 26 * q^61 - 18 * q^62 + 24 * q^63 + 8 * q^64 - 12 * q^66 + 24 * q^67 - 6 * q^68 - 12 * q^69 + 24 * q^71 - 4 * q^72 - 12 * q^73 + 6 * q^74 - 2 * q^75 - 6 * q^76 + 60 * q^77 + 20 * q^79 - 4 * q^80 - 28 * q^81 - 36 * q^83 - 6 * q^84 - 6 * q^85 + 8 * q^86 + 48 * q^87 + 6 * q^88 + 8 * q^90 + 24 * q^92 + 12 * q^93 - 6 * q^95 + 4 * q^96 - 18 * q^97 - 8 * q^98 - 84 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1690\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−1.66612	+	2.88581i	−0.961937	+	1.66612i	−0.244308	+	0.969698i	$0.578561\pi$
$3$	−1.66612	+	2.88581i	−0.961937	+	1.66612i	−0.717629	+	0.696425i	$0.754773\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.66612	−	2.88581i	−0.680192	−	1.17813i
$7$	0.719687	+	1.24653i	0.272016	+	0.471146i	0.969378	−	0.245574i	$-0.0789763\pi$
$7$	0.719687	+	1.24653i	0.272016	+	0.471146i	−0.697362	+	0.716719i	$0.745643\pi$
$8$	1.00000			0.353553
$9$	−4.05193	−	7.01815i	−1.35064	−	2.33938i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	2.01978	−	3.49837i	0.608988	−	1.05480i	−0.382420	−	0.923989i	$-0.624909\pi$
$11$	2.01978	−	3.49837i	0.608988	−	1.05480i	0.991408	−	0.130809i	$-0.0417576\pi$
$12$	3.33225			0.961937
$13$		0			0
$13$		0			0
$14$	−1.43937			−0.384689
$15$	−1.66612	+	2.88581i	−0.430191	+	0.745113i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.15376	−	1.99837i	−0.279828	−	0.484676i	0.691514	−	0.722363i	$-0.256944\pi$
$17$	−1.15376	−	1.99837i	−0.279828	−	0.484676i	−0.971342	+	0.237687i	$0.923611\pi$
$18$	8.10387			1.91010
$19$	−0.199902	−	0.346241i	−0.0458607	−	0.0794331i	0.842184	−	0.539190i	$-0.181270\pi$
$19$	−0.199902	−	0.346241i	−0.0458607	−	0.0794331i	−0.888045	+	0.459757i	$0.847936\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	−4.79635			−1.04665
$22$	2.01978	+	3.49837i	0.430620	+	0.745855i
$23$	−0.780313	+	1.35154i	−0.162707	+	0.281816i	−0.935838	−	0.352429i	$-0.885356\pi$
$23$	−0.780313	+	1.35154i	−0.162707	+	0.281816i	0.773132	+	0.634245i	$0.218689\pi$
$24$	−1.66612	+	2.88581i	−0.340096	+	0.589064i
$25$	1.00000			0.200000
$26$		0			0
$27$	17.0073			3.27306
$28$	0.719687	−	1.24653i	0.136008	−	0.235573i
$29$	3.93244	−	6.81119i	0.730236	−	1.26481i	−0.226546	−	0.974000i	$-0.572743\pi$
$29$	3.93244	−	6.81119i	0.730236	−	1.26481i	0.956782	−	0.290806i	$-0.0939233\pi$
$30$	−1.66612	−	2.88581i	−0.304191	−	0.526874i
$31$	3.10713			0.558057			0.279028	−	0.960283i	$-0.409988\pi$
$31$	3.10713			0.558057			0.279028	+	0.960283i	$0.409988\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	6.73042	+	11.6574i	1.17162	+	2.02930i
$34$	2.30752			0.395736
$35$	0.719687	+	1.24653i	0.121649	+	0.210703i
$36$	−4.05193	+	7.01815i	−0.675322	+	1.16969i
$37$	−3.11786	+	5.40029i	−0.512573	+	0.887803i	0.487321	+	0.873223i	$0.337974\pi$
$37$	−3.11786	+	5.40029i	−0.512573	+	0.887803i	−0.999894	+	0.0145796i	$0.995359\pi$
$38$	0.399804			0.0648568
$39$		0			0
$40$	1.00000			0.158114
$41$	0.380509	−	0.659061i	0.0594255	−	0.102928i	−0.834782	−	0.550580i	$-0.814406\pi$
$41$	0.380509	−	0.659061i	0.0594255	−	0.102928i	0.894208	+	0.447652i	$0.147740\pi$
$42$	2.39817	−	4.15376i	0.370046	−	0.640939i
$43$	5.50367	+	9.53264i	0.839302	+	1.45371i	0.890479	+	0.455024i	$0.150369\pi$
$43$	5.50367	+	9.53264i	0.839302	+	1.45371i	−0.0511772	+	0.998690i	$0.516297\pi$
$44$	−4.03957			−0.608988
$45$	−4.05193	−	7.01815i	−0.604027	−	1.04620i
$46$	−0.780313	−	1.35154i	−0.115051	−	0.199274i
$47$	5.84016			0.851874			0.425937	−	0.904753i	$-0.359944\pi$
$47$	5.84016			0.851874			0.425937	+	0.904753i	$0.359944\pi$
$48$	−1.66612	−	2.88581i	−0.240484	−	0.416531i
$49$	2.46410	−	4.26795i	0.352015	−	0.609707i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	7.68922			1.07671
$52$		0			0
$53$	10.6249			1.45945			0.729723	−	0.683743i	$-0.239649\pi$
$53$	10.6249			1.45945			0.729723	+	0.683743i	$0.239649\pi$
$54$	−8.50367	+	14.7288i	−1.15720	+	2.00433i
$55$	2.01978	−	3.49837i	0.272348	−	0.471720i
$56$	0.719687	+	1.24653i	0.0961722	+	0.166575i
$57$	1.33225			0.176460
$58$	3.93244	+	6.81119i	0.516355	+	0.894353i
$59$	1.73205	+	3.00000i	0.225494	+	0.390567i	0.956467	−	0.291839i	$-0.0942671\pi$
$59$	1.73205	+	3.00000i	0.225494	+	0.390567i	−0.730974	+	0.682406i	$0.760934\pi$
$60$	3.33225			0.430191
$61$	2.84624	+	4.92983i	0.364424	+	0.631200i	0.988684	−	0.150016i	$-0.0479326\pi$
$61$	2.84624	+	4.92983i	0.364424	+	0.631200i	−0.624260	+	0.781217i	$0.714599\pi$
$62$	−1.55356	+	2.69085i	−0.197303	+	0.341738i
$63$	5.83225	−	10.1017i	0.734794	−	1.27270i
$64$	1.00000			0.125000
$65$		0			0
$66$	−13.4608			−1.65692
$67$	5.20039	−	9.00734i	0.635329	−	1.10042i	−0.351116	−	0.936332i	$-0.614198\pi$
$67$	5.20039	−	9.00734i	0.635329	−	1.10042i	0.986445	−	0.164090i	$-0.0524688\pi$
$68$	−1.15376	+	1.99837i	−0.139914	+	0.242338i
$69$	−2.60020	−	4.50367i	−0.313027	−	0.542178i
$70$	−1.43937			−0.172038
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	0.987294	−	0.158901i	$-0.0507952\pi$
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	−0.631260	+	0.775571i	$0.717462\pi$
$72$	−4.05193	−	7.01815i	−0.477525	−	0.827097i
$73$	−13.4608			−1.57547			−0.787736	−	0.616013i	$-0.788747\pi$
$73$	−13.4608			−1.57547			−0.787736	+	0.616013i	$0.788747\pi$
$74$	−3.11786	−	5.40029i	−0.362444	−	0.627771i
$75$	−1.66612	+	2.88581i	−0.192387	+	0.333225i
$76$	−0.199902	+	0.346241i	−0.0229303	+	0.0397165i
$77$	5.81445			0.662618
$78$		0			0
$79$	0.931464			0.104798			0.0523989	−	0.998626i	$-0.483313\pi$
$79$	0.931464			0.104798			0.0523989	+	0.998626i	$0.483313\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−16.1805	+	28.0255i	−1.79784	+	3.11394i
$82$	0.380509	+	0.659061i	0.0420202	+	0.0727811i
$83$	−10.3867			−1.14008			−0.570042	−	0.821616i	$-0.693073\pi$
$83$	−10.3867			−1.14008			−0.570042	+	0.821616i	$0.693073\pi$
$84$	2.39817	+	4.15376i	0.261662	+	0.453212i
$85$	−1.15376	−	1.99837i	−0.125143	−	0.216754i
$86$	−11.0073			−1.18695
$87$	13.1039	+	22.6966i	1.40488	+	2.43333i
$88$	2.01978	−	3.49837i	0.215310	−	0.372927i
$89$	−0.485517	+	0.840939i	−0.0514647	+	0.0891394i	−0.890610	−	0.454768i	$-0.849722\pi$
$89$	−0.485517	+	0.840939i	−0.0514647	+	0.0891394i	0.839145	+	0.543907i	$0.183056\pi$
$90$	8.10387			0.854223
$91$		0			0
$92$	1.56063			0.162707
$93$	−5.17686	+	8.96658i	−0.536815	+	0.929791i
$94$	−2.92008	+	5.05772i	−0.301183	+	0.521664i
$95$	−0.199902	−	0.346241i	−0.0205095	−	0.0355235i
$96$	3.33225			0.340096
$97$	−6.15919	−	10.6680i	−0.625371	−	1.08317i	−0.988469	−	0.151424i	$-0.951614\pi$
$97$	−6.15919	−	10.6680i	−0.625371	−	1.08317i	0.363098	−	0.931751i	$-0.381719\pi$
$98$	2.46410	+	4.26795i	0.248912	+	0.431128i
$99$	−32.7361			−3.29011
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−2.41747	+	4.18718i	−0.240547	+	0.416640i	−0.960870	−	0.276999i	$-0.910660\pi$
$101$	−2.41747	+	4.18718i	−0.240547	+	0.416640i	0.720323	+	0.693639i	$0.243994\pi$
$102$	−3.84461	+	6.65906i	−0.380673	+	0.659345i
$103$	5.73205			0.564796			0.282398	−	0.959297i	$-0.408870\pi$
$103$	5.73205			0.564796			0.282398	+	0.959297i	$0.408870\pi$
$104$		0			0
$105$	−4.79635			−0.468076
$106$	−5.31246	+	9.20145i	−0.515992	+	0.893724i
$107$	6.43774	−	11.1505i	0.622360	−	1.07796i	−0.366685	−	0.930345i	$-0.619507\pi$
$107$	6.43774	−	11.1505i	0.622360	−	1.07796i	0.989045	−	0.147614i	$-0.0471594\pi$
$108$	−8.50367	−	14.7288i	−0.818266	−	1.41728i
$109$	0.214254			0.0205219			0.0102609	−	0.999947i	$-0.496734\pi$
$109$	0.214254			0.0205219			0.0102609	+	0.999947i	$0.496734\pi$
$110$	2.01978	+	3.49837i	0.192579	+	0.333556i
$111$	−10.3895	−	17.9951i	−0.986126	−	1.70802i
$112$	−1.43937			−0.136008
$113$	0.0642973	+	0.111366i	0.00604858	+	0.0104765i	0.869034	−	0.494753i	$-0.164741\pi$
$113$	0.0642973	+	0.111366i	0.00604858	+	0.0104765i	−0.862985	+	0.505229i	$0.831408\pi$
$114$	−0.666123	+	1.15376i	−0.0623882	+	0.108059i
$115$	−0.780313	+	1.35154i	−0.0727646	+	0.126032i
$116$	−7.86488			−0.730236
$117$		0			0
$118$	−3.46410			−0.318896
$119$	1.66069	−	2.87640i	0.152235	−	0.263679i
$120$	−1.66612	+	2.88581i	−0.152096	+	0.263437i
$121$	−2.65906	−	4.60563i	−0.241733	−	0.418693i
$122$	−5.69248			−0.515373
$123$	1.26795	+	2.19615i	0.114327	+	0.198020i
$124$	−1.55356	−	2.69085i	−0.139514	−	0.241646i
$125$	1.00000			0.0894427
$126$	5.83225	+	10.1017i	0.519578	+	0.899935i
$127$	8.06218	−	13.9641i	0.715403	−	1.23911i	−0.247401	−	0.968913i	$-0.579577\pi$
$127$	8.06218	−	13.9641i	0.715403	−	1.23911i	0.962804	−	0.270201i	$-0.0870900\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−36.6792			−3.22942
$130$		0			0
$131$	2.78010			0.242898			0.121449	−	0.992598i	$-0.461246\pi$
$131$	2.78010			0.242898			0.121449	+	0.992598i	$0.461246\pi$
$132$	6.73042	−	11.6574i	0.585808	−	1.01465i
$133$	0.287734	−	0.498370i	0.0249497	−	0.0432141i
$134$	5.20039	+	9.00734i	0.449245	+	0.778116i
$135$	17.0073			1.46376
$136$	−1.15376	−	1.99837i	−0.0989340	−	0.171359i
$137$	2.73368	+	4.73487i	0.233554	+	0.404528i	0.958851	−	0.283908i	$-0.0916311\pi$
$137$	2.73368	+	4.73487i	0.233554	+	0.404528i	−0.725297	+	0.688436i	$0.758298\pi$
$138$	5.20039			0.442687
$139$	0.107258	+	0.185777i	0.00909753	+	0.0157574i	0.870538	−	0.492101i	$-0.163771\pi$
$139$	0.107258	+	0.185777i	0.00909753	+	0.0157574i	−0.861441	+	0.507858i	$0.830437\pi$
$140$	0.719687	−	1.24653i	0.0608246	−	0.105351i
$141$	−9.73042	+	16.8536i	−0.819449	+	1.41933i
$142$	−6.00000			−0.503509
$143$		0			0
$144$	8.10387			0.675322
$145$	3.93244	−	6.81119i	0.326572	−	0.565639i
$146$	6.73042	−	11.6574i	0.557014	−	0.964776i
$147$	8.21099	+	14.2219i	0.677231	+	1.17300i
$148$	6.23572			0.512573
$149$	8.26469	+	14.3149i	0.677070	+	1.17272i	0.975859	+	0.218400i	$0.0700838\pi$
$149$	8.26469	+	14.3149i	0.677070	+	1.17272i	−0.298790	+	0.954319i	$0.596583\pi$
$150$	−1.66612	−	2.88581i	−0.136038	−	0.235625i
$151$	6.70830			0.545914			0.272957	−	0.962026i	$-0.411998\pi$
$151$	6.70830			0.545914			0.272957	+	0.962026i	$0.411998\pi$
$152$	−0.199902	−	0.346241i	−0.0162142	−	0.0280838i
$153$	−9.34991	+	16.1945i	−0.755896	+	1.30925i
$154$	−2.90723	+	5.03546i	−0.234271	+	0.405769i
$155$	3.10713			0.249570
$156$		0			0
$157$	5.81684			0.464234			0.232117	−	0.972688i	$-0.425435\pi$
$157$	5.81684			0.464234			0.232117	+	0.972688i	$0.425435\pi$
$158$	−0.465732	+	0.806671i	−0.0370516	+	0.0641753i
$159$	−17.7024	+	30.6615i	−1.40389	+	2.43162i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−2.24632			−0.177035
$162$	−16.1805	−	28.0255i	−1.27126	−	2.20189i
$163$	−2.08620	−	3.61341i	−0.163404	−	0.283024i	0.772683	−	0.634792i	$-0.218914\pi$
$163$	−2.08620	−	3.61341i	−0.163404	−	0.283024i	−0.936087	+	0.351768i	$0.885581\pi$
$164$	−0.761018			−0.0594255
$165$	6.73042	+	11.6574i	0.523963	+	0.907530i
$166$	5.19333	−	8.99511i	0.403080	−	0.698156i
$167$	−7.80426	+	13.5174i	−0.603912	+	1.04601i	0.388311	+	0.921528i	$0.373059\pi$
$167$	−7.80426	+	13.5174i	−0.603912	+	1.04601i	−0.992222	+	0.124477i	$0.960275\pi$
$168$	−4.79635			−0.370046
$169$		0			0
$170$	2.30752			0.176979
$171$	−1.61998	+	2.80589i	−0.123883	+	0.214572i
$172$	5.50367	−	9.53264i	0.419651	−	0.726857i
$173$	−2.90723	−	5.03546i	−0.221032	−	0.382839i	0.734089	−	0.679053i	$-0.237609\pi$
$173$	−2.90723	−	5.03546i	−0.221032	−	0.382839i	−0.955122	+	0.296214i	$0.904276\pi$
$174$	−26.2077			−1.98680
$175$	0.719687	+	1.24653i	0.0544032	+	0.0942291i
$176$	2.01978	+	3.49837i	0.152247	+	0.263700i
$177$	−11.5432			−0.867643
$178$	−0.485517	−	0.840939i	−0.0363910	−	0.0630311i
$179$	8.43611	−	14.6118i	0.630545	−	1.09214i	−0.356896	−	0.934144i	$-0.616165\pi$
$179$	8.43611	−	14.6118i	0.630545	−	1.09214i	0.987441	−	0.157991i	$-0.0505018\pi$
$180$	−4.05193	+	7.01815i	−0.302013	+	0.523102i
$181$	−12.6207			−0.938088			−0.469044	−	0.883175i	$-0.655401\pi$
$181$	−12.6207			−0.938088			−0.469044	+	0.883175i	$0.655401\pi$
$182$		0			0
$183$	−18.9688			−1.40221
$184$	−0.780313	+	1.35154i	−0.0575254	+	0.0996370i
$185$	−3.11786	+	5.40029i	−0.229230	+	0.397037i
$186$	−5.17686	−	8.96658i	−0.379586	−	0.657461i
$187$	−9.32138			−0.681647
$188$	−2.92008	−	5.05772i	−0.212969	−	0.368872i
$189$	12.2400	+	21.2002i	0.890326	+	1.54209i
$190$	0.399804			0.0290049
$191$	−0.670362	−	1.16110i	−0.0485057	−	0.0840143i	0.840753	−	0.541419i	$-0.182113\pi$
$191$	−0.670362	−	1.16110i	−0.0485057	−	0.0840143i	−0.889259	+	0.457404i	$0.848779\pi$
$192$	−1.66612	+	2.88581i	−0.120242	+	0.208265i
$193$	−8.37182	+	14.5004i	−0.602616	+	1.04376i	0.389807	+	0.920897i	$0.372542\pi$
$193$	−8.37182	+	14.5004i	−0.602616	+	1.04376i	−0.992423	+	0.122866i	$0.960792\pi$
$194$	12.3184			0.884408
$195$		0			0
$196$	−4.92820			−0.352015
$197$	−0.498370	+	0.863202i	−0.0355074	+	0.0615006i	−0.883233	−	0.468934i	$-0.844638\pi$
$197$	−0.498370	+	0.863202i	−0.0355074	+	0.0615006i	0.847726	+	0.530435i	$0.177971\pi$
$198$	16.3681	−	28.3503i	1.16323	−	2.01477i
$199$	1.30752	+	2.26469i	0.0926875	+	0.160540i	0.908641	−	0.417578i	$-0.137121\pi$
$199$	1.30752	+	2.26469i	0.0926875	+	0.160540i	−0.815954	+	0.578117i	$0.803788\pi$
$200$	1.00000			0.0707107
$201$	17.3290	+	30.0147i	1.22229	+	2.11707i
$202$	−2.41747	−	4.18718i	−0.170093	−	0.294609i
$203$	11.3205			0.794544
$204$	−3.84461	−	6.65906i	−0.269177	−	0.466227i
$205$	0.380509	−	0.659061i	0.0265759	−	0.0460308i
$206$	−2.86603	+	4.96410i	−0.199685	+	0.345865i
$207$	12.6471			0.879035
$208$		0			0
$209$	−1.61504			−0.111714
$210$	2.39817	−	4.15376i	0.165490	−	0.286637i
$211$	4.56691	−	7.91011i	0.314399	−	0.544555i	−0.664911	−	0.746923i	$-0.731530\pi$
$211$	4.56691	−	7.91011i	0.314399	−	0.544555i	0.979310	+	0.202368i	$0.0648638\pi$
$212$	−5.31246	−	9.20145i	−0.364861	−	0.631958i
$213$	−19.9935			−1.36993
$214$	6.43774	+	11.1505i	0.440075	+	0.762232i
$215$	5.50367	+	9.53264i	0.375347	+	0.650121i
$216$	17.0073			1.15720
$217$	2.23616	+	3.87314i	0.151800	+	0.262926i
$218$	−0.107127	+	0.185550i	−0.00725557	+	0.0125670i
$219$	22.4274	−	38.8454i	1.51550	−	2.62493i
$220$	−4.03957			−0.272348
$221$		0			0
$222$	20.7790			1.39459
$223$	−2.90595	+	5.03326i	−0.194597	+	0.337052i	−0.946768	−	0.321916i	$-0.895673\pi$
$223$	−2.90595	+	5.03326i	−0.194597	+	0.337052i	0.752171	+	0.658968i	$0.229007\pi$
$224$	0.719687	−	1.24653i	0.0480861	−	0.0832876i
$225$	−4.05193	−	7.01815i	−0.270129	−	0.467877i
$226$	−0.128595			−0.00855399
$227$	−5.77162	−	9.99674i	−0.383076	−	0.663507i	0.608424	−	0.793612i	$-0.291802\pi$
$227$	−5.77162	−	9.99674i	−0.383076	−	0.663507i	−0.991500	+	0.130105i	$0.958469\pi$
$228$	−0.666123	−	1.15376i	−0.0441151	−	0.0764096i
$229$	12.8755			0.850836			0.425418	−	0.904997i	$-0.360127\pi$
$229$	12.8755			0.850836			0.425418	+	0.904997i	$0.360127\pi$
$230$	−0.780313	−	1.35154i	−0.0514523	−	0.0891180i
$231$	−9.68759	+	16.7794i	−0.637397	+	1.10400i
$232$	3.93244	−	6.81119i	0.258177	−	0.447177i
$233$	10.4149			0.682303			0.341152	−	0.940008i	$-0.389183\pi$
$233$	10.4149			0.682303			0.341152	+	0.940008i	$0.389183\pi$
$234$		0			0
$235$	5.84016			0.380970
$236$	1.73205	−	3.00000i	0.112747	−	0.195283i
$237$	−1.55193	+	2.68803i	−0.100809	+	0.174606i
$238$	1.66069	+	2.87640i	0.107647	+	0.186449i
$239$	18.3801			1.18891			0.594456	−	0.804128i	$-0.297367\pi$
$239$	18.3801			1.18891			0.594456	+	0.804128i	$0.297367\pi$
$240$	−1.66612	−	2.88581i	−0.107548	−	0.186278i
$241$	−0.309853	−	0.536681i	−0.0199594	−	0.0345707i	0.855873	−	0.517186i	$-0.173020\pi$
$241$	−0.309853	−	0.536681i	−0.0199594	−	0.0345707i	−0.875833	+	0.482615i	$0.839687\pi$
$242$	5.31812			0.341862
$243$	−28.4065	−	49.2015i	−1.82228	−	3.15628i
$244$	2.84624	−	4.92983i	0.182212	−	0.315600i
$245$	2.46410	−	4.26795i	0.157426	−	0.272669i
$246$	−2.53590			−0.161683
$247$		0			0
$248$	3.10713			0.197303
$249$	17.3055	−	29.9739i	1.09669	−	1.89952i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	2.65376	+	4.59645i	0.167504	+	0.290125i	0.937542	−	0.347873i	$-0.113096\pi$
$251$	2.65376	+	4.59645i	0.167504	+	0.290125i	−0.770038	+	0.637998i	$0.779763\pi$
$252$	−11.6645			−0.734794
$253$	3.15213	+	5.45965i	0.198173	+	0.343245i
$254$	8.06218	+	13.9641i	0.505866	+	0.876186i
$255$	7.68922			0.481518
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−12.3686	+	21.4230i	−0.771529	+	1.33633i	0.165195	+	0.986261i	$0.447175\pi$
$257$	−12.3686	+	21.4230i	−0.771529	+	1.33633i	−0.936725	+	0.350067i	$0.886159\pi$
$258$	18.3396	−	31.7651i	1.14177	−	1.97761i
$259$	−8.97553			−0.557713
$260$		0			0
$261$	−63.7360			−3.94516
$262$	−1.39005	+	2.40764i	−0.0858775	+	0.148744i
$263$	−2.56466	+	4.44211i	−0.158143	+	0.273912i	−0.934199	−	0.356752i	$-0.883884\pi$
$263$	−2.56466	+	4.44211i	−0.158143	+	0.273912i	0.776056	+	0.630664i	$0.217218\pi$
$264$	6.73042	+	11.6574i	0.414229	+	0.717465i
$265$	10.6249			0.652684
$266$	0.287734	+	0.498370i	0.0176421	+	0.0305570i
$267$	−1.61786	−	2.80222i	−0.0990115	−	0.171493i
$268$	−10.4008			−0.635329
$269$	−3.40687	−	5.90087i	−0.207720	−	0.359782i	0.743276	−	0.668985i	$-0.233271\pi$
$269$	−3.40687	−	5.90087i	−0.207720	−	0.359782i	−0.950996	+	0.309203i	$0.899938\pi$
$270$	−8.50367	+	14.7288i	−0.517517	+	0.896366i
$271$	−11.0106	+	19.0709i	−0.668846	+	1.15848i	0.309381	+	0.950938i	$0.399878\pi$
$271$	−11.0106	+	19.0709i	−0.668846	+	1.15848i	−0.978227	+	0.207538i	$0.933455\pi$
$272$	2.30752			0.139914
$273$		0			0
$274$	−5.46736			−0.330295
$275$	2.01978	−	3.49837i	0.121798	−	0.210960i
$276$	−2.60020	+	4.50367i	−0.156513	+	0.271089i
$277$	−12.7152	−	22.0233i	−0.763980	−	1.32325i	−0.940784	−	0.339006i	$-0.889909\pi$
$277$	−12.7152	−	22.0233i	−0.763980	−	1.32325i	0.176805	−	0.984246i	$-0.443424\pi$
$278$	−0.214517			−0.0128659
$279$	−12.5899	−	21.8063i	−0.753736	−	1.30551i
$280$	0.719687	+	1.24653i	0.0430095	+	0.0744947i
$281$	25.0954			1.49707			0.748533	−	0.663098i	$-0.230759\pi$
$281$	25.0954			1.49707			0.748533	+	0.663098i	$0.230759\pi$
$282$	−9.73042	−	16.8536i	−0.579438	−	1.00362i
$283$	−0.882986	+	1.52938i	−0.0524881	+	0.0909120i	−0.891076	−	0.453855i	$-0.850048\pi$
$283$	−0.882986	+	1.52938i	−0.0524881	+	0.0909120i	0.838588	+	0.544767i	$0.183382\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$	1.33225			0.0789155
$286$		0			0
$287$	1.09539			0.0646588
$288$	−4.05193	+	7.01815i	−0.238762	+	0.413549i
$289$	5.83768	−	10.1112i	0.343393	−	0.594774i
$290$	3.93244	+	6.81119i	0.230921	+	0.399967i
$291$	41.0479			2.40627
$292$	6.73042	+	11.6574i	0.393868	+	0.682200i
$293$	9.20145	+	15.9374i	0.537555	+	0.931072i	0.999035	+	0.0439215i	$0.0139852\pi$
$293$	9.20145	+	15.9374i	0.537555	+	0.931072i	−0.461480	+	0.887150i	$0.652682\pi$
$294$	−16.4220			−0.957750
$295$	1.73205	+	3.00000i	0.100844	+	0.174667i
$296$	−3.11786	+	5.40029i	−0.181222	+	0.313886i
$297$	34.3512	−	59.4980i	1.99326	−	3.45242i
$298$	−16.5294			−0.957521
$299$		0			0
$300$	3.33225			0.192387
$301$	−7.92184	+	13.7210i	−0.456607	+	0.790867i
$302$	−3.35415	+	5.80956i	−0.193010	+	0.334303i
$303$	−8.05560	−	13.9527i	−0.462782	−	0.801563i
$304$	0.399804			0.0229303
$305$	2.84624	+	4.92983i	0.162975	+	0.282281i
$306$	−9.34991	−	16.1945i	−0.534499	−	0.925779i
$307$	−8.40730			−0.479830			−0.239915	−	0.970794i	$-0.577120\pi$
$307$	−8.40730			−0.479830			−0.239915	+	0.970794i	$0.577120\pi$
$308$	−2.90723	−	5.03546i	−0.165655	−	0.286922i
$309$	−9.55030	+	16.5416i	−0.543298	+	0.941019i
$310$	−1.55356	+	2.69085i	−0.0882365	+	0.152830i
$311$	33.6601			1.90869			0.954344	−	0.298708i	$-0.0965557\pi$
$311$	33.6601			1.90869			0.954344	+	0.298708i	$0.0965557\pi$
$312$		0			0
$313$	27.0008			1.52618			0.763088	−	0.646294i	$-0.223682\pi$
$313$	27.0008			1.52618			0.763088	+	0.646294i	$0.223682\pi$
$314$	−2.90842	+	5.03753i	−0.164132	+	0.284284i
$315$	5.83225	−	10.1017i	0.328610	−	0.569169i
$316$	−0.465732	−	0.806671i	−0.0261995	−	0.0453788i
$317$	10.2569			0.576086			0.288043	−	0.957617i	$-0.406995\pi$
$317$	10.2569			0.576086			0.288043	+	0.957617i	$0.406995\pi$
$318$	−17.7024	−	30.6615i	−0.992703	−	1.71941i
$319$	−15.8854	−	27.5143i	−0.889410	−	1.54050i
$320$	1.00000			0.0559017
$321$	21.4521	+	37.1562i	1.19734	+	2.07386i
$322$	1.12316	−	1.94537i	0.0625914	−	0.108411i
$323$	−0.461278	+	0.798957i	−0.0256662	+	0.0444551i
$324$	32.3611			1.79784
$325$		0			0
$326$	4.17240			0.231088
$327$	−0.356974	+	0.618298i	−0.0197407	+	0.0341919i
$328$	0.380509	−	0.659061i	0.0210101	−	0.0363905i
$329$	4.20308	+	7.27995i	0.231724	+	0.401357i
$330$	−13.4608			−0.740995
$331$	−2.26469	−	3.92256i	−0.124479	−	0.215603i	0.797050	−	0.603913i	$-0.206392\pi$
$331$	−2.26469	−	3.92256i	−0.124479	−	0.215603i	−0.921529	+	0.388310i	$0.873059\pi$
$332$	5.19333	+	8.99511i	0.285021	+	0.493671i
$333$	50.5335			2.76922
$334$	−7.80426	−	13.5174i	−0.427030	−	0.739638i
$335$	5.20039	−	9.00734i	0.284128	−	0.492124i
$336$	2.39817	−	4.15376i	0.130831	−	0.226606i
$337$	−6.72755			−0.366473			−0.183236	−	0.983069i	$-0.558657\pi$
$337$	−6.72755			−0.366473			−0.183236	+	0.983069i	$0.558657\pi$
$338$		0			0
$339$	−0.428509			−0.0232734
$340$	−1.15376	+	1.99837i	−0.0625714	+	0.108377i
$341$	6.27573	−	10.8699i	0.339850	−	0.588637i
$342$	−1.61998	−	2.80589i	−0.0875985	−	0.151725i
$343$	17.1691			0.927047
$344$	5.50367	+	9.53264i	0.296738	+	0.513965i
$345$	−2.60020	−	4.50367i	−0.139990	−	0.242469i
$346$	5.81445			0.312587
$347$	−1.57286	−	2.72427i	−0.0844355	−	0.146247i	0.820715	−	0.571338i	$-0.193575\pi$
$347$	−1.57286	−	2.72427i	−0.0844355	−	0.146247i	−0.905151	+	0.425091i	$0.860242\pi$
$348$	13.1039	−	22.6966i	0.702441	−	1.21666i
$349$	−5.25246	+	9.09752i	−0.281158	+	0.486979i	−0.971670	−	0.236341i	$-0.924052\pi$
$349$	−5.25246	+	9.09752i	−0.281158	+	0.486979i	0.690513	+	0.723320i	$0.257385\pi$
$350$	−1.43937			−0.0769378
$351$		0			0
$352$	−4.03957			−0.215310
$353$	16.4988	−	28.5767i	0.878141	−	1.52099i	0.0247633	−	0.999693i	$-0.492117\pi$
$353$	16.4988	−	28.5767i	0.878141	−	1.52099i	0.853378	−	0.521292i	$-0.174550\pi$
$354$	5.77162	−	9.99674i	0.306758	−	0.531321i
$355$	3.00000	+	5.19615i	0.159223	+	0.275783i
$356$	0.971033			0.0514647
$357$	5.53383	+	9.58488i	0.292881	+	0.507285i
$358$	8.43611	+	14.6118i	0.445862	+	0.772256i
$359$	24.2487			1.27980			0.639899	−	0.768459i	$-0.278976\pi$
$359$	24.2487			1.27980			0.639899	+	0.768459i	$0.278976\pi$
$360$	−4.05193	−	7.01815i	−0.213556	−	0.369889i
$361$	9.42008	−	16.3161i	0.495794	−	0.858740i
$362$	6.31034	−	10.9298i	0.331664	−	0.574459i
$363$	17.7213			0.930127
$364$		0			0
$365$	−13.4608			−0.704573
$366$	9.48438	−	16.4274i	0.495756	−	0.858675i
$367$	9.89924	−	17.1460i	0.516736	−	0.895013i	−0.483075	−	0.875579i	$-0.660480\pi$
$367$	9.89924	−	17.1460i	0.516736	−	0.895013i	0.999811	−	0.0194340i	$-0.00618643\pi$
$368$	−0.780313	−	1.35154i	−0.0406766	−	0.0704540i
$369$	−6.16719			−0.321051
$370$	−3.11786	−	5.40029i	−0.162090	−	0.280748i
$371$	7.64662	+	13.2443i	0.396993	+	0.687611i
$372$	10.3537			0.536815
$373$	−2.39557	−	4.14924i	−0.124038	−	0.214840i	0.797319	−	0.603559i	$-0.206251\pi$
$373$	−2.39557	−	4.14924i	−0.124038	−	0.214840i	−0.921356	+	0.388719i	$0.872918\pi$
$374$	4.66069	−	8.07255i	0.240999	−	0.417422i
$375$	−1.66612	+	2.88581i	−0.0860382	+	0.149023i
$376$	5.84016			0.301183
$377$		0			0
$378$	−24.4799			−1.25911
$379$	9.74760	−	16.8833i	0.500700	−	0.867239i	−0.499299	−	0.866430i	$-0.666409\pi$
$379$	9.74760	−	16.8833i	0.500700	−	0.867239i	1.00000		0.000808945i	$-0.000257495\pi$
$380$	−0.199902	+	0.346241i	−0.0102548	+	0.0177618i
$381$	26.8652	+	46.5318i	1.37634	+	2.38390i
$382$	1.34072			0.0685974
$383$	6.43068	+	11.1383i	0.328592	+	0.569139i	0.982233	−	0.187667i	$-0.0600924\pi$
$383$	6.43068	+	11.1383i	0.328592	+	0.569139i	−0.653640	+	0.756805i	$0.726759\pi$
$384$	−1.66612	−	2.88581i	−0.0850240	−	0.147266i
$385$	5.81445			0.296332
$386$	−8.37182	−	14.5004i	−0.426114	−	0.738051i
$387$	44.6010	−	77.2512i	2.26720	−	3.92690i
$388$	−6.15919	+	10.6680i	−0.312686	+	0.541587i
$389$	−6.94233			−0.351990			−0.175995	−	0.984391i	$-0.556314\pi$
$389$	−6.94233			−0.351990			−0.175995	+	0.984391i	$0.556314\pi$
$390$		0			0
$391$	3.60117			0.182119
$392$	2.46410	−	4.26795i	0.124456	−	0.215564i
$393$	−4.63199	+	8.02284i	−0.233653	+	0.404699i
$394$	−0.498370	−	0.863202i	−0.0251075	−	0.0434875i
$395$	0.931464			0.0468670
$396$	16.3681	+	28.3503i	0.822526	+	1.42466i
$397$	2.16612	+	3.75184i	0.108715	+	0.188299i	0.915250	−	0.402887i	$-0.131993\pi$
$397$	2.16612	+	3.75184i	0.108715	+	0.188299i	−0.806535	+	0.591186i	$0.798660\pi$
$398$	−2.61504			−0.131080
$399$	0.958800	+	1.66069i	0.0480001	+	0.0831385i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−11.8616	+	20.5448i	−0.592339	+	1.02596i	0.401578	+	0.915825i	$0.368462\pi$
$401$	−11.8616	+	20.5448i	−0.592339	+	1.02596i	−0.993917	+	0.110136i	$0.964871\pi$
$402$	−34.6580			−1.72858
$403$		0			0
$404$	4.83494			0.240547
$405$	−16.1805	+	28.0255i	−0.804017	+	1.39260i
$406$	−5.66025	+	9.80385i	−0.280914	+	0.486557i
$407$	12.5948	+	21.8149i	0.624302	+	1.08132i
$408$	7.68922			0.380673
$409$	−19.1896	−	33.2373i	−0.948864	−	1.64348i	−0.747824	−	0.663897i	$-0.768901\pi$
$409$	−19.1896	−	33.2373i	−0.948864	−	1.64348i	−0.201039	−	0.979583i	$-0.564432\pi$
$410$	0.380509	+	0.659061i	0.0187920	+	0.0325487i
$411$	−18.2186			−0.898657
$412$	−2.86603	−	4.96410i	−0.141199	−	0.244564i
$413$	−2.49307	+	4.31812i	−0.122676	+	0.212481i
$414$	−6.32355	+	10.9527i	−0.310786	+	0.538297i
$415$	−10.3867			−0.509861
$416$		0			0
$417$	−0.714822			−0.0350050
$418$	0.807519	−	1.39866i	0.0394970	−	0.0684109i
$419$	19.2946	−	33.4192i	0.942602	−	1.63263i	0.182120	−	0.983276i	$-0.441704\pi$
$419$	19.2946	−	33.4192i	0.942602	−	1.63263i	0.760482	−	0.649359i	$-0.224963\pi$
$420$	2.39817	+	4.15376i	0.117019	+	0.202683i
$421$	−40.6199			−1.97969			−0.989847	−	0.142134i	$-0.954603\pi$
$421$	−40.6199			−1.97969			−0.989847	+	0.142134i	$0.954603\pi$
$422$	4.56691	+	7.91011i	0.222314	+	0.385058i
$423$	−23.6639	−	40.9871i	−1.15058	−	1.99286i
$424$	10.6249			0.515992
$425$	−1.15376	−	1.99837i	−0.0559655	−	0.0969352i
$426$	9.99674	−	17.3149i	0.484344	−	0.838908i
$427$	−4.09680	+	7.09587i	−0.198258	+	0.343393i
$428$	−12.8755			−0.622360
$429$		0			0
$430$	−11.0073			−0.530821
$431$	−5.88581	+	10.1945i	−0.283509	+	0.491053i	−0.972247	−	0.233958i	$-0.924832\pi$
$431$	−5.88581	+	10.1945i	−0.283509	+	0.491053i	0.688737	+	0.725011i	$0.258165\pi$
$432$	−8.50367	+	14.7288i	−0.409133	+	0.708639i
$433$	16.5004	+	28.5795i	0.792959	+	1.37345i	0.924127	+	0.382085i	$0.124794\pi$
$433$	16.5004	+	28.5795i	0.792959	+	1.37345i	−0.131168	+	0.991360i	$0.541873\pi$
$434$	−4.47232			−0.214678
$435$	13.1039	+	22.6966i	0.628282	+	1.08822i
$436$	−0.107127	−	0.185550i	−0.00513046	−	0.00888622i
$437$	0.623945			0.0298473
$438$	22.4274	+	38.8454i	1.07162	+	1.85611i
$439$	−0.348718	+	0.603998i	−0.0166434	+	0.0288272i	−0.874227	−	0.485517i	$-0.838631\pi$
$439$	−0.348718	+	0.603998i	−0.0166434	+	0.0288272i	0.857584	+	0.514344i	$0.171965\pi$
$440$	2.01978	−	3.49837i	0.0962895	−	0.166778i
$441$	−39.9375			−1.90179
$442$		0			0
$443$	28.6297			1.36024			0.680120	−	0.733101i	$-0.261928\pi$
$443$	28.6297			1.36024			0.680120	+	0.733101i	$0.261928\pi$
$444$	−10.3895	+	17.9951i	−0.493063	+	0.854010i
$445$	−0.485517	+	0.840939i	−0.0230157	+	0.0398644i
$446$	−2.90595	−	5.03326i	−0.137601	−	0.238332i
$447$	−55.0800			−2.60519
$448$	0.719687	+	1.24653i	0.0340020	+	0.0588932i
$449$	3.39251	+	5.87601i	0.160103	+	0.277306i	0.934905	−	0.354897i	$-0.115484\pi$
$449$	3.39251	+	5.87601i	0.160103	+	0.277306i	−0.774803	+	0.632203i	$0.782151\pi$
$450$	8.10387			0.382020
$451$	−1.53709	−	2.66232i	−0.0723788	−	0.125364i
$452$	0.0642973	−	0.111366i	0.00302429	−	0.00523823i
$453$	−11.1769	+	19.3589i	−0.525135	+	0.909560i
$454$	11.5432			0.541751
$455$		0			0
$456$	1.33225			0.0623882
$457$	−8.96940	+	15.5355i	−0.419571	+	0.726718i	−0.995896	−	0.0905021i	$-0.971153\pi$
$457$	−8.96940	+	15.5355i	−0.419571	+	0.726718i	0.576325	+	0.817220i	$0.304486\pi$
$458$	−6.43774	+	11.1505i	−0.300816	+	0.521029i
$459$	−19.6224	−	33.9870i	−0.915894	−	1.58638i
$460$	1.56063			0.0727646
$461$	−13.4486	−	23.2937i	−0.626364	−	1.08489i	−0.988275	−	0.152682i	$-0.951209\pi$
$461$	−13.4486	−	23.2937i	−0.626364	−	1.08489i	0.361911	−	0.932213i	$-0.382124\pi$
$462$	−9.68759	−	16.7794i	−0.450708	−	0.780648i
$463$	−26.8402			−1.24737			−0.623684	−	0.781677i	$-0.714365\pi$
$463$	−26.8402			−1.24737			−0.623684	+	0.781677i	$0.714365\pi$
$464$	3.93244	+	6.81119i	0.182559	+	0.316202i
$465$	−5.17686	+	8.96658i	−0.240071	+	0.415815i
$466$	−5.20745	+	9.01957i	−0.241231	+	0.417824i
$467$	−9.48726			−0.439018			−0.219509	−	0.975610i	$-0.570446\pi$
$467$	−9.48726			−0.439018			−0.219509	+	0.975610i	$0.570446\pi$
$468$		0			0
$469$	14.9706			0.691279
$470$	−2.92008	+	5.05772i	−0.134693	+	0.233295i
$471$	−9.69157	+	16.7863i	−0.446564	+	0.773471i
$472$	1.73205	+	3.00000i	0.0797241	+	0.138086i
$473$	44.4649			2.04450
$474$	−1.55193	−	2.68803i	−0.0712827	−	0.123465i
$475$	−0.199902	−	0.346241i	−0.00917214	−	0.0158866i
$476$	−3.32138			−0.152235
$477$	−43.0515	−	74.5674i	−1.97119	−	3.41420i
$478$	−9.19007	+	15.9177i	−0.420344	+	0.728057i
$479$	5.60726	−	9.71206i	0.256202	−	0.443755i	−0.709019	−	0.705189i	$-0.750862\pi$
$479$	5.60726	−	9.71206i	0.256202	−	0.443755i	0.965221	+	0.261434i	$0.0841954\pi$
$480$	3.33225			0.152096
$481$		0			0
$482$	0.619706			0.0282268
$483$	3.74265	−	6.48247i	0.170297	−	0.294962i
$484$	−2.65906	+	4.60563i	−0.120866	+	0.209347i
$485$	−6.15919	−	10.6680i	−0.279674	−	0.484410i
$486$	56.8130			2.57709
$487$	13.8643	+	24.0137i	0.628252	+	1.08816i	0.987902	+	0.155077i	$0.0495627\pi$
$487$	13.8643	+	24.0137i	0.628252	+	1.08816i	−0.359650	+	0.933087i	$0.617104\pi$
$488$	2.84624	+	4.92983i	0.128843	+	0.223163i
$489$	13.9035			0.628737
$490$	2.46410	+	4.26795i	0.111317	+	0.192806i
$491$	−13.9377	+	24.1409i	−0.629002	+	1.08946i	0.358751	+	0.933433i	$0.383203\pi$
$491$	−13.9377	+	24.1409i	−0.629002	+	1.08946i	−0.987752	+	0.156029i	$0.950131\pi$
$492$	1.26795	−	2.19615i	0.0571636	−	0.0990102i
$493$	−18.1484			−0.817361
$494$		0			0
$495$	−32.7361			−1.47138
$496$	−1.55356	+	2.69085i	−0.0697571	+	0.120823i
$497$	−4.31812	+	7.47921i	−0.193694	+	0.335488i
$498$	17.3055	+	29.9739i	0.775476	+	1.34316i
$499$	−36.8040			−1.64757			−0.823786	−	0.566901i	$-0.808142\pi$
$499$	−36.8040			−1.64757			−0.823786	+	0.566901i	$0.808142\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	−26.0057	−	45.0432i	−1.16185	−	2.01238i
$502$	−5.30752			−0.236886
$503$	19.2848	+	33.4022i	0.859865	+	1.48933i	0.872057	+	0.489404i	$0.162785\pi$
$503$	19.2848	+	33.4022i	0.859865	+	1.48933i	−0.0121928	+	0.999926i	$0.503881\pi$
$504$	5.83225	−	10.1017i	0.259789	−	0.449968i
$505$	−2.41747	+	4.18718i	−0.107576	+	0.186327i
$506$	−6.30426			−0.280258
$507$		0			0
$508$	−16.1244			−0.715403
$509$	−14.4262	+	24.9870i	−0.639431	+	1.10753i	0.346126	+	0.938188i	$0.387497\pi$
$509$	−14.4262	+	24.9870i	−0.639431	+	1.10753i	−0.985558	+	0.169340i	$0.945837\pi$
$510$	−3.84461	+	6.65906i	−0.170242	+	0.294868i
$511$	−9.68759	−	16.7794i	−0.428554	−	0.742277i
$512$	1.00000			0.0441942
$513$	−3.39980	−	5.88863i	−0.150105	−	0.259990i
$514$	−12.3686	−	21.4230i	−0.545554	−	0.944927i
$515$	5.73205			0.252584
$516$	18.3396	+	31.7651i	0.807355	+	1.39838i
$517$	11.7959	−	20.4310i	0.518781	−	0.898556i
$518$	4.48777	−	7.77304i	0.197181	−	0.341528i
$519$	19.3752			0.850476
$520$		0			0
$521$	−10.6422			−0.466241			−0.233121	−	0.972448i	$-0.574894\pi$
$521$	−10.6422			−0.466241			−0.233121	+	0.972448i	$0.574894\pi$
$522$	31.8680	−	55.1970i	1.39482	−	2.41591i
$523$	−19.0759	+	33.0404i	−0.834130	+	1.44476i	0.0606070	+	0.998162i	$0.480696\pi$
$523$	−19.0759	+	33.0404i	−0.834130	+	1.44476i	−0.894737	+	0.446594i	$0.852637\pi$
$524$	−1.39005	−	2.40764i	−0.0607246	−	0.105178i
$525$	−4.79635			−0.209330
$526$	−2.56466	−	4.44211i	−0.111824	−	0.193685i
$527$	−3.58488	−	6.20919i	−0.156160	−	0.270477i
$528$	−13.4608			−0.585808
$529$	10.2822	+	17.8093i	0.447053	+	0.774319i
$530$	−5.31246	+	9.20145i	−0.230759	+	0.399686i
$531$	14.0363	−	24.3116i	0.609124	−	1.05503i
$532$	−0.575468			−0.0249497
$533$		0			0
$534$	3.23572			0.140023
$535$	6.43774	−	11.1505i	0.278328	−	0.482078i
$536$	5.20039	−	9.00734i	0.224623	−	0.389058i
$537$	28.1112	+	48.6900i	1.21309	+	2.10113i
$538$	6.81373			0.293761
$539$	−9.95391	−	17.2407i	−0.428745	−	0.742609i
$540$	−8.50367	−	14.7288i	−0.365940	−	0.633826i
$541$	1.46593			0.0630252			0.0315126	−	0.999503i	$-0.489968\pi$
$541$	1.46593			0.0630252			0.0315126	+	0.999503i	$0.489968\pi$
$542$	−11.0106	−	19.0709i	−0.472946	−	0.819166i
$543$	21.0276	−	36.4209i	0.902381	−	1.56297i
$544$	−1.15376	+	1.99837i	−0.0494670	+	0.0856794i
$545$	0.214254			0.00917765
$546$		0			0
$547$	−16.2374			−0.694262			−0.347131	−	0.937817i	$-0.612844\pi$
$547$	−16.2374			−0.694262			−0.347131	+	0.937817i	$0.612844\pi$
$548$	2.73368	−	4.73487i	0.116777	−	0.202264i
$549$	23.0656	−	39.9507i	0.984414	−	1.70505i
$550$	2.01978	+	3.49837i	0.0861239	+	0.149171i
$551$	−3.14441			−0.133957
$552$	−2.60020	−	4.50367i	−0.110672	−	0.191689i
$553$	0.670362	+	1.16110i	0.0285067	+	0.0493751i
$554$	25.4303			1.08043
$555$	−10.3895	−	17.9951i	−0.441009	−	0.763850i
$556$	0.107258	−	0.185777i	0.00454877	−	0.00787869i
$557$	16.6623	−	28.8599i	0.706004	−	1.22283i	−0.260324	−	0.965521i	$-0.583829\pi$
$557$	16.6623	−	28.8599i	0.706004	−	1.22283i	0.966328	−	0.257314i	$-0.0828373\pi$
$558$	25.1797			1.06594
$559$		0			0
$560$	−1.43937			−0.0608246
$561$	15.5306	−	26.8997i	0.655701	−	1.13571i
$562$	−12.5477	+	21.7332i	−0.529293	+	0.916762i
$563$	−3.75678	−	6.50693i	−0.158329	−	0.274234i	0.775937	−	0.630810i	$-0.217277\pi$
$563$	−3.75678	−	6.50693i	−0.158329	−	0.274234i	−0.934266	+	0.356576i	$0.883944\pi$
$564$	19.4608			0.819449
$565$	0.0642973	+	0.111366i	0.00270501	+	0.00468521i
$566$	−0.882986	−	1.52938i	−0.0371147	−	0.0642845i
$567$	−46.5797			−1.95616
$568$	3.00000	+	5.19615i	0.125877	+	0.218026i
$569$	−6.45619	+	11.1825i	−0.270658	+	0.468793i	−0.969030	−	0.246941i	$-0.920574\pi$
$569$	−6.45619	+	11.1825i	−0.270658	+	0.468793i	0.698373	+	0.715734i	$0.253908\pi$
$570$	−0.666123	+	1.15376i	−0.0279008	+	0.0483257i
$571$	−3.47470			−0.145412			−0.0727059	−	0.997353i	$-0.523163\pi$
$571$	−3.47470			−0.145412			−0.0727059	+	0.997353i	$0.523163\pi$
$572$		0			0
$573$	4.46762			0.186638
$574$	−0.547694	+	0.948635i	−0.0228603	+	0.0395952i
$575$	−0.780313	+	1.35154i	−0.0325413	+	0.0563632i
$576$	−4.05193	−	7.01815i	−0.168831	−	0.292423i
$577$	−8.80287			−0.366468			−0.183234	−	0.983069i	$-0.558657\pi$
$577$	−8.80287			−0.366468			−0.183234	+	0.983069i	$0.558657\pi$
$578$	5.83768	+	10.1112i	0.242815	+	0.420569i
$579$	−27.8970	−	48.3189i	−1.15936	−	2.00807i
$580$	−7.86488			−0.326572
$581$	−7.47514	−	12.9473i	−0.310121	−	0.537146i
$582$	−20.5239	+	35.5485i	−0.850745	+	1.47353i
$583$	21.4601	−	37.1699i	0.888785	−	1.53942i
$584$	−13.4608			−0.557014
$585$		0			0
$586$	−18.4029			−0.760217
$587$	−17.8960	+	30.9967i	−0.738646	+	1.27937i	0.214459	+	0.976733i	$0.431201\pi$
$587$	−17.8960	+	30.9967i	−0.738646	+	1.27937i	−0.953105	+	0.302639i	$0.902132\pi$
$588$	8.21099	−	14.2219i	0.338616	−	0.586500i
$589$	−0.621121	−	1.07581i	−0.0255929	−	0.0443281i
$590$	−3.46410			−0.142615
$591$	−1.66069	−	2.87640i	−0.0683117	−	0.118319i
$592$	−3.11786	−	5.40029i	−0.128143	−	0.221951i
$593$	−3.93555			−0.161613			−0.0808067	−	0.996730i	$-0.525750\pi$
$593$	−3.93555			−0.161613			−0.0808067	+	0.996730i	$0.525750\pi$
$594$	34.3512	+	59.4980i	1.40945	+	2.44123i
$595$	1.66069	−	2.87640i	0.0680817	−	0.117921i
$596$	8.26469	−	14.3149i	0.338535	−	0.586360i
$597$	−8.71395			−0.356638
$598$		0			0
$599$	−9.50704			−0.388447			−0.194223	−	0.980957i	$-0.562219\pi$
$599$	−9.50704			−0.388447			−0.194223	+	0.980957i	$0.562219\pi$
$600$	−1.66612	+	2.88581i	−0.0680192	+	0.117813i
$601$	−17.4935	+	30.2996i	−0.713574	+	1.23595i	0.249933	+	0.968263i	$0.419591\pi$
$601$	−17.4935	+	30.2996i	−0.713574	+	1.23595i	−0.963507	+	0.267683i	$0.913742\pi$
$602$	−7.92184	−	13.7210i	−0.322870	−	0.559227i
$603$	−84.2866			−3.43241
$604$	−3.35415	−	5.80956i	−0.136478	−	0.236388i
$605$	−2.65906	−	4.60563i	−0.108106	−	0.187245i
$606$	16.1112			0.654473
$607$	8.08054	+	13.9959i	0.327979	+	0.568076i	0.982111	−	0.188304i	$-0.0602991\pi$
$607$	8.08054	+	13.9959i	0.327979	+	0.568076i	−0.654132	+	0.756381i	$0.726966\pi$
$608$	−0.199902	+	0.346241i	−0.00810710	+	0.0140419i
$609$	−18.8614	+	32.6688i	−0.764301	+	1.32381i
$610$	−5.69248			−0.230482
$611$		0			0
$612$	18.6998			0.755896
$613$	4.43598	−	7.68335i	0.179168	−	0.310327i	−0.762428	−	0.647073i	$-0.775993\pi$
$613$	4.43598	−	7.68335i	0.179168	−	0.310327i	0.941596	+	0.336746i	$0.109326\pi$
$614$	4.20365	−	7.28094i	0.169646	−	0.293835i
$615$	1.26795	+	2.19615i	0.0511286	+	0.0885574i
$616$	5.81445			0.234271
$617$	−5.42453	−	9.39557i	−0.218383	−	0.378251i	0.735930	−	0.677057i	$-0.236745\pi$
$617$	−5.42453	−	9.39557i	−0.218383	−	0.378251i	−0.954314	+	0.298806i	$0.903412\pi$
$618$	−9.55030	−	16.5416i	−0.384170	−	0.665401i
$619$	5.82727			0.234218			0.117109	−	0.993119i	$-0.462637\pi$
$619$	5.82727			0.234218			0.117109	+	0.993119i	$0.462637\pi$
$620$	−1.55356	−	2.69085i	−0.0623926	−	0.108067i
$621$	−13.2711	+	22.9861i	−0.532549	+	0.922402i
$622$	−16.8300	+	29.1505i	−0.674823	+	1.16883i
$623$	−1.39768			−0.0559969
$624$		0			0
$625$	1.00000			0.0400000
$626$	−13.5004	+	23.3834i	−0.539585	+	0.934589i
$627$	2.69085	−	4.66069i	0.107462	−	0.186130i
$628$	−2.90842	−	5.03753i	−0.116059	−	0.201019i
$629$	14.3890			0.573729
$630$	5.83225	+	10.1017i	0.232362	+	0.402463i
$631$	4.71793	+	8.17169i	0.187818	+	0.325310i	0.944522	−	0.328447i	$-0.106525\pi$
$631$	4.71793	+	8.17169i	0.187818	+	0.325310i	−0.756705	+	0.653757i	$0.773192\pi$
$632$	0.931464			0.0370516
$633$	15.2181	+	26.3584i	0.604863	+	1.04765i
$634$	−5.12846	+	8.88276i	−0.203677	+	0.352779i
$635$	8.06218	−	13.9641i	0.319938	−	0.554148i
$636$	35.4049			1.40389
$637$		0			0
$638$	31.7707			1.25782
$639$	24.3116	−	42.1089i	0.961752	−	1.66580i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−20.2877	−	35.1392i	−0.801314	−	1.38792i	−0.918751	−	0.394837i	$-0.870801\pi$
$641$	−20.2877	−	35.1392i	−0.801314	−	1.38792i	0.117437	−	0.993080i	$-0.462532\pi$
$642$	−42.9043			−1.69330
$643$	−2.93598	−	5.08527i	−0.115784	−	0.200543i	0.802309	−	0.596909i	$-0.203605\pi$
$643$	−2.93598	−	5.08527i	−0.115784	−	0.200543i	−0.918093	+	0.396365i	$0.870271\pi$
$644$	1.12316	+	1.94537i	0.0442588	+	0.0766585i
$645$	−36.6792			−1.44424
$646$	−0.461278	−	0.798957i	−0.0181487	−	0.0314345i
$647$	−19.3652	+	33.5416i	−0.761326	+	1.31866i	0.180841	+	0.983512i	$0.442118\pi$
$647$	−19.3652	+	33.5416i	−0.761326	+	1.31866i	−0.942167	+	0.335143i	$0.891215\pi$
$648$	−16.1805	+	28.0255i	−0.635631	+	1.10095i
$649$	13.9935			0.549292
$650$		0			0
$651$	−14.9029			−0.584089
$652$	−2.08620	+	3.61341i	−0.0817020	+	0.141512i
$653$	6.45492	−	11.1802i	0.252601	−	0.437517i	−0.711641	−	0.702544i	$-0.752047\pi$
$653$	6.45492	−	11.1802i	0.252601	−	0.437517i	0.964241	+	0.265027i	$0.0853808\pi$
$654$	−0.356974	−	0.618298i	−0.0139588	−	0.0241774i
$655$	2.78010			0.108627
$656$	0.380509	+	0.659061i	0.0148564	+	0.0257320i
$657$	54.5424	+	94.4703i	2.12790	+	3.68564i
$658$	−8.40617			−0.327707
$659$	3.20654	+	5.55389i	0.124909	+	0.216349i	0.921697	−	0.387910i	$-0.126803\pi$
$659$	3.20654	+	5.55389i	0.124909	+	0.216349i	−0.796788	+	0.604259i	$0.793469\pi$
$660$	6.73042	−	11.6574i	0.261981	−	0.453765i
$661$	−3.49470	+	6.05300i	−0.135928	+	0.235434i	−0.925952	−	0.377642i	$-0.876735\pi$
$661$	−3.49470	+	6.05300i	−0.135928	+	0.235434i	0.790024	+	0.613076i	$0.210068\pi$
$662$	4.52938			0.176039
$663$		0			0
$664$	−10.3867			−0.403080
$665$	0.287734	−	0.498370i	0.0111578	−	0.0193260i
$666$	−25.2667	+	43.7633i	−0.979066	+	1.69579i
$667$	6.13707	+	10.6297i	0.237628	+	0.411584i
$668$	15.6085			0.603912
$669$	−9.68335	−	16.7721i	−0.374380	−	0.648445i
$670$	5.20039	+	9.00734i	0.200909	+	0.347984i
$671$	22.9952			0.887719
$672$	2.39817	+	4.15376i	0.0925116	+	0.160235i
$673$	23.3083	−	40.3712i	0.898470	−	1.55620i	0.0690207	−	0.997615i	$-0.478013\pi$
$673$	23.3083	−	40.3712i	0.898470	−	1.55620i	0.829450	−	0.558581i	$-0.188654\pi$
$674$	3.36377	−	5.82623i	0.129568	−	0.224418i
$675$	17.0073			0.654613
$676$		0			0
$677$	6.85102			0.263306			0.131653	−	0.991296i	$-0.457972\pi$
$677$	6.85102			0.263306			0.131653	+	0.991296i	$0.457972\pi$
$678$	0.214254	−	0.371100i	0.00822839	−	0.0142520i
$679$	8.86538	−	15.3553i	0.340222	−	0.589282i
$680$	−1.15376	−	1.99837i	−0.0442446	−	0.0766340i
$681$	38.4649			1.47398
$682$	6.27573	+	10.8699i	0.240310	+	0.416229i
$683$	12.2614	+	21.2374i	0.469171	+	0.812627i	0.999379	−	0.0352402i	$-0.0112196\pi$
$683$	12.2614	+	21.2374i	0.469171	+	0.812627i	−0.530208	+	0.847867i	$0.677886\pi$
$684$	3.23996			0.123883
$685$	2.73368	+	4.73487i	0.104449	+	0.180910i
$686$	−8.58457	+	14.8689i	−0.327760	+	0.567698i
$687$	−21.4521	+	37.1562i	−0.818451	+	1.41760i
$688$	−11.0073			−0.419651
$689$		0			0
$690$	5.20039			0.197976
$691$	−5.03484	+	8.72060i	−0.191534	+	0.331747i	−0.945759	−	0.324869i	$-0.894680\pi$
$691$	−5.03484	+	8.72060i	−0.191534	+	0.331747i	0.754225	+	0.656617i	$0.228013\pi$
$692$	−2.90723	+	5.03546i	−0.110516	+	0.191420i
$693$	−23.5598	−	40.8067i	−0.894961	−	1.55012i
$694$	3.14572			0.119410
$695$	0.107258	+	0.185777i	0.00406854	+	0.00704692i
$696$	13.1039	+	22.6966i	0.496701	+	0.860311i
$697$	−1.75606			−0.0665156
$698$	−5.25246	−	9.09752i	−0.198808	−	0.344346i
$699$	−17.3525	+	30.0554i	−0.656333	+	1.13680i
$700$	0.719687	−	1.24653i	0.0272016	−	0.0471146i
$701$	10.4149			0.393366			0.196683	−	0.980467i	$-0.436983\pi$
$701$	10.4149			0.393366			0.196683	+	0.980467i	$0.436983\pi$
$702$		0			0
$703$	2.49307			0.0940279
$704$	2.01978	−	3.49837i	0.0761235	−	0.131850i
$705$	−9.73042	+	16.8536i	−0.366469	+	0.634743i
$706$	16.4988	+	28.5767i	0.620940	+	1.07550i
$707$	−6.95928			−0.261731
$708$	5.77162	+	9.99674i	0.216911	+	0.375700i
$709$	0.187896	+	0.325446i	0.00705660	+	0.0122224i	0.869532	−	0.493876i	$-0.164420\pi$
$709$	0.187896	+	0.325446i	0.00705660	+	0.0122224i	−0.862476	+	0.506099i	$0.831087\pi$
$710$	−6.00000			−0.225176
$711$	−3.77423	−	6.53716i	−0.141545	−	0.245163i
$712$	−0.485517	+	0.840939i	−0.0181955	+	0.0315155i
$713$	−2.42453	+	4.19941i	−0.0907994	+	0.157269i
$714$	−11.0677			−0.414197
$715$		0			0
$716$	−16.8722			−0.630545
$717$	−30.6236	+	53.0416i	−1.14366	+	1.98087i
$718$	−12.1244	+	21.0000i	−0.452477	+	0.783713i
$719$	9.66547	+	16.7411i	0.360461	+	0.624337i	0.988037	−	0.154218i	$-0.0492860\pi$
$719$	9.66547	+	16.7411i	0.360461	+	0.624337i	−0.627576	+	0.778556i	$0.715953\pi$
$720$	8.10387			0.302013
$721$	4.12528	+	7.14520i	0.153634	+	0.266101i
$722$	9.42008	+	16.3161i	0.350579	+	0.607221i
$723$	2.06501			0.0767987
$724$	6.31034	+	10.9298i	0.234522	+	0.406204i
$725$	3.93244	−	6.81119i	0.146047	−	0.252961i
$726$	−8.86065	+	15.3471i	−0.328849	+	0.569584i
$727$	−31.3390			−1.16230			−0.581150	−	0.813797i	$-0.697397\pi$
$727$	−31.3390			−1.16230			−0.581150	+	0.813797i	$0.697397\pi$
$728$		0			0
$729$	92.2317			3.41599
$730$	6.73042	−	11.6574i	0.249104	−	0.431461i
$731$	12.6998	−	21.9967i	0.469720	−	0.813579i
$732$	9.48438	+	16.4274i	0.350553	+	0.607175i
$733$	−19.6207			−0.724707			−0.362353	−	0.932041i	$-0.618027\pi$
$733$	−19.6207			−0.724707			−0.362353	+	0.932041i	$0.618027\pi$
$734$	9.89924	+	17.1460i	0.365387	+	0.632870i
$735$	8.21099	+	14.2219i	0.302867	+	0.524581i
$736$	1.56063			0.0575254
$737$	−21.0073	−	36.3858i	−0.773815	−	1.34029i
$738$	3.08359	−	5.34094i	0.113509	−	0.196603i
$739$	−5.98141	+	10.3601i	−0.220030	+	0.381103i	−0.954817	−	0.297195i	$-0.903949\pi$
$739$	−5.98141	+	10.3601i	−0.220030	+	0.381103i	0.734787	+	0.678298i	$0.237282\pi$
$740$	6.23572			0.229230
$741$		0			0
$742$	−15.2932			−0.561432
$743$	9.96162	−	17.2540i	0.365457	−	0.632989i	−0.623393	−	0.781909i	$-0.714246\pi$
$743$	9.96162	−	17.2540i	0.365457	−	0.632989i	0.988849	+	0.148920i	$0.0475795\pi$
$744$	−5.17686	+	8.96658i	−0.189793	+	0.328731i
$745$	8.26469	+	14.3149i	0.302795	+	0.524456i
$746$	4.79113			0.175416
$747$	42.0860	+	72.8952i	1.53985	+	2.66709i
$748$	4.66069	+	8.07255i	0.170412	+	0.295162i
$749$	18.5326			0.677168
$750$	−1.66612	−	2.88581i	−0.0608382	−	0.105375i
$751$	−21.4608	+	37.1713i	−0.783117	+	1.35640i	0.147000	+	0.989136i	$0.453038\pi$
$751$	−21.4608	+	37.1713i	−0.783117	+	1.35640i	−0.930117	+	0.367262i	$0.880295\pi$
$752$	−2.92008	+	5.05772i	−0.106484	+	0.184436i
$753$	−17.6860			−0.644512
$754$		0			0
$755$	6.70830			0.244140
$756$	12.2400	−	21.2002i	0.445163	−	0.771045i
$757$	17.8750	−	30.9604i	0.649678	−	1.12528i	−0.333522	−	0.942742i	$-0.608237\pi$
$757$	17.8750	−	30.9604i	0.649678	−	1.12528i	0.983200	−	0.182533i	$-0.0584295\pi$
$758$	9.74760	+	16.8833i	0.354049	+	0.613230i
$759$	−21.0073			−0.762518
$760$	−0.199902	−	0.346241i	−0.00725121	−	0.0125595i
$761$	−15.0822	−	26.1232i	−0.546731	−	0.946965i	−0.998496	−	0.0548284i	$-0.982539\pi$
$761$	−15.0822	−	26.1232i	−0.546731	−	0.946965i	0.451765	−	0.892137i	$-0.350795\pi$
$762$	−53.7303			−1.94644
$763$	0.154196	+	0.267076i	0.00558227	+	0.00966878i
$764$	−0.670362	+	1.16110i	−0.0242529	+	0.0420072i
$765$	−9.34991	+	16.1945i	−0.338047	+	0.585514i
$766$	−12.8614			−0.464700
$767$		0			0
$768$	3.33225			0.120242
$769$	12.1380	−	21.0236i	0.437708	−	0.758132i	−0.559805	−	0.828625i	$-0.689124\pi$
$769$	12.1380	−	21.0236i	0.437708	−	0.758132i	0.997512	+	0.0704928i	$0.0224572\pi$
$770$	−2.90723	+	5.03546i	−0.104769	+	0.181465i
$771$	−41.2151	−	71.3866i	−1.48432	−	2.57093i
$772$	16.7436			0.602616
$773$	−22.2667	−	38.5671i	−0.800879	−	1.38716i	−0.919038	−	0.394168i	$-0.871033\pi$
$773$	−22.2667	−	38.5671i	−0.800879	−	1.38716i	0.118160	−	0.992995i	$-0.462300\pi$
$774$	44.6010	+	77.2512i	1.60315	+	2.77674i
$775$	3.10713			0.111611
$776$	−6.15919	−	10.6680i	−0.221102	−	0.382960i
$777$	14.9543	−	25.9017i	0.536484	−	0.929218i
$778$	3.47116	−	6.01223i	0.124447	−	0.215549i
$779$	−0.304258			−0.0109012
$780$		0			0
$781$	24.2374			0.867283
$782$	−1.80059	+	3.11871i	−0.0643889	+	0.111525i
$783$	66.8804	−	115.840i	2.39011	−	4.13979i
$784$	2.46410	+	4.26795i	0.0880036	+	0.152427i
$785$	5.81684			0.207612
$786$	−4.63199	−	8.02284i	−0.165217	−	0.286165i
$787$	8.71015	+	15.0864i	0.310483	+	0.537773i	0.978467	−	0.206403i	$-0.0661758\pi$
$787$	8.71015	+	15.0864i	0.310483	+	0.537773i	−0.667984	+	0.744176i	$0.732842\pi$
$788$	0.996740			0.0355074
$789$	−8.54606	−	14.8022i	−0.304248	−	0.526973i
$790$	−0.465732	+	0.806671i	−0.0165700	+	0.0287001i
$791$	−0.0925479	+	0.160298i	−0.00329062	+	0.00569953i
$792$	−32.7361			−1.16323
$793$		0			0
$794$	−4.33225			−0.153746
$795$	−17.7024	+	30.6615i	−0.627841	+	1.08745i
$796$	1.30752	−	2.26469i	0.0463438	−	0.0802698i
$797$	−16.4801	−	28.5444i	−0.583756	−	1.01110i	−0.995029	−	0.0995834i	$-0.968249\pi$
$797$	−16.4801	−	28.5444i	−0.583756	−	1.01110i	0.411273	−	0.911512i	$-0.365084\pi$
$798$	−1.91760			−0.0678823
$799$	−6.73813	−	11.6708i	−0.238378	−	0.412883i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	7.86912			0.278042
$802$	−11.8616	−	20.5448i	−0.418847	−	0.725464i
$803$	−27.1880	+	47.0910i	−0.959444	+	1.66181i
$804$	17.3290	−	30.0147i	0.611146	−	1.05854i
$805$	−2.24632			−0.0791725
$806$		0			0
$807$	22.7050			0.799255
$808$	−2.41747	+	4.18718i	−0.0850463	+	0.147304i
$809$	−12.6664	+	21.9389i	−0.445327	+	0.771329i	−0.998075	−	0.0620195i	$-0.980246\pi$
$809$	−12.6664	+	21.9389i	−0.445327	+	0.771329i	0.552748	+	0.833348i	$0.313579\pi$
$810$	−16.1805	−	28.0255i	−0.568526	−	0.984716i
$811$	42.4806			1.49170			0.745848	−	0.666117i	$-0.232045\pi$
$811$	42.4806			1.49170			0.745848	+	0.666117i	$0.232045\pi$
$812$	−5.66025	−	9.80385i	−0.198636	−	0.344048i
$813$	−36.6900	−	63.5490i	−1.28678	−	2.22876i
$814$	−25.1896			−0.882896
$815$	−2.08620	−	3.61341i	−0.0730765	−	0.126572i
$816$	−3.84461	+	6.65906i	−0.134588	+	0.233114i
$817$	2.20039	−	3.81119i	0.0769820	−	0.133337i
$818$	38.3792			1.34190
$819$		0			0
$820$	−0.761018			−0.0265759
$821$	−8.87640	+	15.3744i	−0.309789	+	0.536569i	−0.978316	−	0.207118i	$-0.933592\pi$
$821$	−8.87640	+	15.3744i	−0.309789	+	0.536569i	0.668527	+	0.743687i	$0.266925\pi$
$822$	9.10930	−	15.7778i	0.317723	−	0.550313i
$823$	−16.2840	−	28.2048i	−0.567626	−	0.983157i	−0.996800	−	0.0799351i	$-0.974529\pi$
$823$	−16.2840	−	28.2048i	−0.567626	−	0.983157i	0.429174	−	0.903222i	$-0.358805\pi$
$824$	5.73205			0.199685
$825$	6.73042	+	11.6574i	0.234323	+	0.405860i
$826$	−2.49307	−	4.31812i	−0.0867449	−	0.150247i
$827$	−26.6419			−0.926429			−0.463215	−	0.886246i	$-0.653304\pi$
$827$	−26.6419			−0.926429			−0.463215	+	0.886246i	$0.653304\pi$
$828$	−6.32355	−	10.9527i	−0.219759	−	0.380633i
$829$	8.58281	−	14.8659i	0.298093	−	0.516313i	−0.677606	−	0.735425i	$-0.736983\pi$
$829$	8.58281	−	14.8659i	0.298093	−	0.516313i	0.975700	+	0.219112i	$0.0703160\pi$
$830$	5.19333	−	8.99511i	0.180263	−	0.312225i
$831$	84.7401			2.93960
$832$		0			0
$833$	−11.3719			−0.394014
$834$	0.357411	−	0.619054i	0.0123761	−	0.0214361i
$835$	−7.80426	+	13.5174i	−0.270077	+	0.467788i
$836$	0.807519	+	1.39866i	0.0279286	+	0.0483738i
$837$	52.8440			1.82656
$838$	19.2946	+	33.4192i	0.666520	+	1.15445i
$839$	22.5138	+	38.9951i	0.777264	+	1.34626i	0.933513	+	0.358543i	$0.116726\pi$
$839$	22.5138	+	38.9951i	0.777264	+	1.34626i	−0.156249	+	0.987718i	$0.549940\pi$
$840$	−4.79635			−0.165490
$841$	−16.4282	−	28.4545i	−0.566490	−	0.981189i
$842$	20.3100	−	35.1779i	0.699928	−	1.21231i
$843$	−41.8120	+	72.4205i	−1.44008	+	2.49430i
$844$	−9.13381			−0.314399
$845$		0			0
$846$	47.3279			1.62717
$847$	3.82738	−	6.62922i	0.131510	−	0.227783i
$848$	−5.31246	+	9.20145i	−0.182431	+	0.315979i
$849$	−2.94233	−	5.09626i	−0.100980	−	0.174903i
$850$	2.30752			0.0791472
$851$	−4.86582	−	8.42784i	−0.166798	−	0.288903i
$852$	9.99674	+	17.3149i	0.342483	+	0.593197i
$853$	−31.0013			−1.06146			−0.530731	−	0.847540i	$-0.678083\pi$
$853$	−31.0013			−1.06146			−0.530731	+	0.847540i	$0.678083\pi$
$854$	−4.09680	−	7.09587i	−0.140190	−	0.242816i
$855$	−1.61998	+	2.80589i	−0.0554022	+	0.0959594i
$856$	6.43774	−	11.1505i	0.220038	−	0.381116i
$857$	27.3813			0.935326			0.467663	−	0.883907i	$-0.345096\pi$
$857$	27.3813			0.935326			0.467663	+	0.883907i	$0.345096\pi$
$858$		0			0
$859$	8.36050			0.285256			0.142628	−	0.989776i	$-0.454445\pi$
$859$	8.36050			0.285256			0.142628	+	0.989776i	$0.454445\pi$
$860$	5.50367	−	9.53264i	0.187674	−	0.325060i
$861$	−1.82505	+	3.16108i	−0.0621976	+	0.107729i
$862$	−5.88581	−	10.1945i	−0.200471	−	0.347227i
$863$	40.2398			1.36978			0.684889	−	0.728647i	$-0.259850\pi$
$863$	40.2398			1.36978			0.684889	+	0.728647i	$0.259850\pi$
$864$	−8.50367	−	14.7288i	−0.289301	−	0.501084i
$865$	−2.90723	−	5.03546i	−0.0988486	−	0.171211i
$866$	−33.0008			−1.12141
$867$	19.4526	+	33.6929i	0.660644	+	1.14427i
$868$	2.23616	−	3.87314i	0.0759002	−	0.131463i
$869$	1.88136	−	3.25860i	0.0638206	−	0.110541i
$870$	−26.2077			−0.888525
$871$		0			0
$872$	0.214254			0.00725557
$873$	−49.9133	+	86.4523i	−1.68931	+	2.92597i
$874$	−0.311973	+	0.540352i	−0.0105526	+	0.0182777i
$875$	0.719687	+	1.24653i	0.0243299	+	0.0421405i
$876$	−44.8548			−1.51550
$877$	−26.0338	−	45.0918i	−0.879098	−	1.52264i	−0.852333	−	0.523000i	$-0.824813\pi$
$877$	−26.0338	−	45.0918i	−0.879098	−	1.52264i	−0.0267652	−	0.999642i	$-0.508521\pi$
$878$	−0.348718	−	0.603998i	−0.0117687	−	0.0203839i
$879$	−61.3230			−2.06837
$880$	2.01978	+	3.49837i	0.0680869	+	0.117930i
$881$	17.2542	−	29.8852i	0.581310	−	1.00686i	−0.414015	−	0.910270i	$-0.635874\pi$
$881$	17.2542	−	29.8852i	0.581310	−	1.00686i	0.995324	−	0.0965881i	$-0.0307929\pi$
$882$	19.9688	−	34.5869i	0.672383	−	1.16460i
$883$	28.2064			0.949222			0.474611	−	0.880196i	$-0.342589\pi$
$883$	28.2064			0.949222			0.474611	+	0.880196i	$0.342589\pi$
$884$		0			0
$885$	−11.5432			−0.388022
$886$	−14.3149	+	24.7941i	−0.480917	+	0.832973i
$887$	−1.06098	+	1.83768i	−0.0356244	+	0.0617032i	−0.883288	−	0.468831i	$-0.844675\pi$
$887$	−1.06098	+	1.83768i	−0.0356244	+	0.0617032i	0.847664	+	0.530534i	$0.178009\pi$
$888$	−10.3895	−	17.9951i	−0.348648	−	0.603876i
$889$	23.2090			0.778404
$890$	−0.485517	−	0.840939i	−0.0162746	−	0.0281884i
$891$	65.3624	+	113.211i	2.18972	+	3.79271i
$892$	5.81191			0.194597
$893$	−1.16746	−	2.02210i	−0.0390676	−	0.0676670i
$894$	27.5400	−	47.7006i	0.921075	−	1.59535i
$895$	8.43611	−	14.6118i	0.281988	−	0.488418i
$896$	−1.43937			−0.0480861
$897$		0			0
$898$	−6.78503			−0.226419
$899$	12.2186	−	21.1632i	0.407513	−	0.705833i
$900$	−4.05193	+	7.01815i	−0.135064	+	0.233938i
$901$	−12.2586	−	21.2325i	−0.408393	−	0.707358i
$902$	3.07418			0.102359
$903$	−26.3975	−	45.7218i	−0.878455	−	1.52153i
$904$	0.0642973	+	0.111366i	0.00213850	+	0.00370398i
$905$	−12.6207			−0.419526
$906$	−11.1769	−	19.3589i	−0.371326	−	0.643156i
$907$	−14.7272	+	25.5082i	−0.489007	+	0.846986i	−0.999920	−	0.0126471i	$-0.995974\pi$
$907$	−14.7272	+	25.5082i	−0.489007	+	0.846986i	0.510913	+	0.859633i	$0.329308\pi$
$908$	−5.77162	+	9.99674i	−0.191538	+	0.331753i
$909$	39.1817			1.29958
$910$		0			0
$911$	19.9986			0.662582			0.331291	−	0.943529i	$-0.392516\pi$
$911$	19.9986			0.662582			0.331291	+	0.943529i	$0.392516\pi$
$912$	−0.666123	+	1.15376i	−0.0220575	+	0.0382048i
$913$	−20.9788	+	36.3364i	−0.694297	+	1.20256i
$914$	−8.96940	−	15.5355i	−0.296681	−	0.513867i
$915$	−18.9688			−0.627088
$916$	−6.43774	−	11.1505i	−0.212709	−	0.368423i
$917$	2.00080	+	3.46549i	0.0660722	+	0.114440i
$918$	39.2448			1.29527
$919$	14.8564	+	25.7321i	0.490068	+	0.848822i	0.999935	−	0.0114312i	$-0.00363874\pi$
$919$	14.8564	+	25.7321i	0.490068	+	0.848822i	−0.509867	+	0.860253i	$0.670305\pi$
$920$	−0.780313	+	1.35154i	−0.0257262	+	0.0445590i
$921$	14.0076	−	24.2619i	0.461566	−	0.799456i
$922$	26.8972			0.885813
$923$		0			0
$924$	19.3752			0.637397
$925$	−3.11786	+	5.40029i	−0.102515	+	0.177561i
$926$	13.4201	−	23.2443i	0.441011	−	0.763854i
$927$	−23.2259	−	40.2284i	−0.762838	−	1.32127i
$928$	−7.86488			−0.258177
$929$	−4.61504	−	7.99348i	−0.151414	−	0.262258i	0.780333	−	0.625364i	$-0.215049\pi$
$929$	−4.61504	−	7.99348i	−0.151414	−	0.262258i	−0.931748	+	0.363106i	$0.881716\pi$
$930$	−5.17686	−	8.96658i	−0.169756	−	0.294026i
$931$	−1.97032			−0.0645745
$932$	−5.20745	−	9.01957i	−0.170576	−	0.295446i
$933$	−56.0819	+	97.1366i	−1.83604	+	3.18011i
$934$	4.74363	−	8.21621i	0.155216	−	0.268843i
$935$	−9.32138			−0.304842
$936$		0			0
$937$	−4.58731			−0.149861			−0.0749305	−	0.997189i	$-0.523873\pi$
$937$	−4.58731			−0.149861			−0.0749305	+	0.997189i	$0.523873\pi$
$938$	−7.48531	+	12.9649i	−0.244404	+	0.423320i
$939$	−44.9867	+	77.9192i	−1.46809	+	2.54280i
$940$	−2.92008	−	5.05772i	−0.0952425	−	0.164965i
$941$	9.00734			0.293631			0.146815	−	0.989164i	$-0.453098\pi$
$941$	9.00734			0.293631			0.146815	+	0.989164i	$0.453098\pi$
$942$	−9.69157	−	16.7863i	−0.315768	−	0.546927i
$943$	0.593832	+	1.02855i	0.0193378	+	0.0334941i
$944$	−3.46410			−0.112747
$945$	12.2400	+	21.2002i	0.398166	+	0.689644i
$946$	−22.2325	+	38.5078i	−0.722840	+	1.25200i
$947$	27.3144	−	47.3100i	0.887600	−	1.53737i	0.0448946	−	0.998992i	$-0.485705\pi$
$947$	27.3144	−	47.3100i	0.887600	−	1.53737i	0.842705	−	0.538376i	$-0.180962\pi$
$948$	3.10387			0.100809
$949$		0			0
$950$	0.399804			0.0129714
$951$	−17.0893	+	29.5995i	−0.554159	+	0.959831i
$952$	1.66069	−	2.87640i	0.0538233	−	0.0932247i
$953$	9.46862	+	16.4001i	0.306719	+	0.531252i	0.977643	−	0.210274i	$-0.0674356\pi$
$953$	9.46862	+	16.4001i	0.306719	+	0.531252i	−0.670924	+	0.741526i	$0.734102\pi$
$954$	86.1030			2.78769
$955$	−0.670362	−	1.16110i	−0.0216924	−	0.0375724i
$956$	−9.19007	−	15.9177i	−0.297228	−	0.514814i
$957$	105.868			3.42223
$958$	5.60726	+	9.71206i	0.181162	+	0.313782i
$959$	−3.93479	+	6.81525i	−0.127061	+	0.220076i
$960$	−1.66612	+	2.88581i	−0.0537739	+	0.0931391i
$961$	−21.3458			−0.688573
$962$		0			0
$963$	−104.341			−3.36235
$964$	−0.309853	+	0.536681i	−0.00997970	+	0.0172853i
$965$	−8.37182	+	14.5004i	−0.269498	+	0.466785i
$966$	3.74265	+	6.48247i	0.120418	+	0.208570i
$967$	−19.1583			−0.616089			−0.308044	−	0.951372i	$-0.599675\pi$
$967$	−19.1583			−0.616089			−0.308044	+	0.951372i	$0.599675\pi$
$968$	−2.65906	−	4.60563i	−0.0854654	−	0.148030i
$969$	−1.53709	−	2.66232i	−0.0493785	−	0.0855261i
$970$	12.3184			0.395519
$971$	−11.1876	−	19.3775i	−0.359027	−	0.621853i	0.628772	−	0.777590i	$-0.283558\pi$
$971$	−11.1876	−	19.3775i	−0.359027	−	0.621853i	−0.987799	+	0.155737i	$0.950225\pi$
$972$	−28.4065	+	49.2015i	−0.911139	+	1.57814i
$973$	−0.154385	+	0.267402i	−0.00494935	+	0.00857253i
$974$	−27.7286			−0.888483
$975$		0			0
$976$	−5.69248			−0.182212
$977$	−2.26299	+	3.91962i	−0.0723996	+	0.125400i	−0.899952	−	0.435988i	$-0.856399\pi$
$977$	−2.26299	+	3.91962i	−0.0723996	+	0.125400i	0.827553	+	0.561388i	$0.189732\pi$
$978$	−6.95174	+	12.0408i	−0.222292	+	0.385021i
$979$	1.96128	+	3.39703i	0.0626827	+	0.108570i
$980$	−4.92820			−0.157426
$981$	−0.868145	−	1.50367i	−0.0277177	−	0.0480085i
$982$	−13.9377	−	24.1409i	−0.444771	−	0.770366i
$983$	12.1598			0.387839			0.193919	−	0.981017i	$-0.437880\pi$
$983$	12.1598			0.387839			0.193919	+	0.981017i	$0.437880\pi$
$984$	1.26795	+	2.19615i	0.0404207	+	0.0700108i
$985$	−0.498370	+	0.863202i	−0.0158794	+	0.0275039i
$986$	9.07418	−	15.7169i	0.288981	−	0.500530i
$987$	−28.0114			−0.891613
$988$		0			0
$989$	−17.1783			−0.546240
$990$	16.3681	−	28.3503i	0.520211	−	0.901032i
$991$	28.1367	−	48.7341i	0.893790	−	1.54809i	0.0584955	−	0.998288i	$-0.481370\pi$
$991$	28.1367	−	48.7341i	0.893790	−	1.54809i	0.835295	−	0.549802i	$-0.185297\pi$
$992$	−1.55356	−	2.69085i	−0.0493257	−	0.0854346i
$993$	15.0930			0.478962
$994$	−4.31812	−	7.47921i	−0.136962	−	0.237226i
$995$	1.30752	+	2.26469i	0.0414511	+	0.0717955i
$996$	−34.6109			−1.09669
$997$	2.33056	+	4.03665i	0.0738097	+	0.127842i	0.900568	−	0.434715i	$-0.143151\pi$
$997$	2.33056	+	4.03665i	0.0738097	+	0.127842i	−0.826758	+	0.562557i	$0.809818\pi$
$998$	18.4020	−	31.8732i	0.582504	−	1.00893i
$999$	−53.0265	+	91.8446i	−1.67769	+	2.90584i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.e.s.191.1		8
13.2	odd	12		1690.2.l.j.361.1		8
13.3	even	3	inner	1690.2.e.s.991.1		8
13.4	even	6		1690.2.a.t.1.4		4
13.5	odd	4		130.2.l.b.121.3	yes	8
13.6	odd	12		1690.2.d.k.1351.4		8
13.7	odd	12		1690.2.d.k.1351.8		8
13.8	odd	4		1690.2.l.j.1161.1		8
13.9	even	3		1690.2.a.u.1.4		4
13.10	even	6		1690.2.e.t.991.1		8
13.11	odd	12		130.2.l.b.101.3	✓	8
13.12	even	2		1690.2.e.t.191.1		8
39.5	even	4		1170.2.bs.g.901.1		8
39.11	even	12		1170.2.bs.g.361.1		8
52.11	even	12		1040.2.da.d.881.4		8
52.31	even	4		1040.2.da.d.641.4		8
65.4	even	6		8450.2.a.cm.1.1		4
65.9	even	6		8450.2.a.ci.1.1		4
65.18	even	4		650.2.n.e.199.1		8
65.24	odd	12		650.2.m.c.101.2		8
65.37	even	12		650.2.n.e.49.1		8
65.44	odd	4		650.2.m.c.251.2		8
65.57	even	4		650.2.n.d.199.4		8
65.63	even	12		650.2.n.d.49.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.l.b.101.3	✓	8	13.11	odd	12
130.2.l.b.121.3	yes	8	13.5	odd	4
650.2.m.c.101.2		8	65.24	odd	12
650.2.m.c.251.2		8	65.44	odd	4
650.2.n.d.49.4		8	65.63	even	12
650.2.n.d.199.4		8	65.57	even	4
650.2.n.e.49.1		8	65.37	even	12
650.2.n.e.199.1		8	65.18	even	4
1040.2.da.d.641.4		8	52.31	even	4
1040.2.da.d.881.4		8	52.11	even	12
1170.2.bs.g.361.1		8	39.11	even	12
1170.2.bs.g.901.1		8	39.5	even	4
1690.2.a.t.1.4		4	13.4	even	6
1690.2.a.u.1.4		4	13.9	even	3
1690.2.d.k.1351.4		8	13.6	odd	12
1690.2.d.k.1351.8		8	13.7	odd	12
1690.2.e.s.191.1		8	1.1	even	1	trivial
1690.2.e.s.991.1		8	13.3	even	3	inner
1690.2.e.t.191.1		8	13.12	even	2
1690.2.e.t.991.1		8	13.10	even	6
1690.2.l.j.361.1		8	13.2	odd	12
1690.2.l.j.1161.1		8	13.8	odd	4
8450.2.a.ci.1.1		4	65.9	even	6
8450.2.a.cm.1.1		4	65.4	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.66612 + 2.88581i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-1.66612 - 2.88581i) q^{6} +(0.719687 + 1.24653i) q^{7} +1.00000 q^{8} +(-4.05193 - 7.01815i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(2.01978 - 3.49837i) q^{11} +3.33225 q^{12} -1.43937 q^{14} +(-1.66612 + 2.88581i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.15376 - 1.99837i) q^{17} +8.10387 q^{18} +(-0.199902 - 0.346241i) q^{19} +(-0.500000 - 0.866025i) q^{20} -4.79635 q^{21} +(2.01978 + 3.49837i) q^{22} +(-0.780313 + 1.35154i) q^{23} +(-1.66612 + 2.88581i) q^{24} +1.00000 q^{25} +17.0073 q^{27} +(0.719687 - 1.24653i) q^{28} +(3.93244 - 6.81119i) q^{29} +(-1.66612 - 2.88581i) q^{30} +3.10713 q^{31} +(-0.500000 - 0.866025i) q^{32} +(6.73042 + 11.6574i) q^{33} +2.30752 q^{34} +(0.719687 + 1.24653i) q^{35} +(-4.05193 + 7.01815i) q^{36} +(-3.11786 + 5.40029i) q^{37} +0.399804 q^{38} +1.00000 q^{40} +(0.380509 - 0.659061i) q^{41} +(2.39817 - 4.15376i) q^{42} +(5.50367 + 9.53264i) q^{43} -4.03957 q^{44} +(-4.05193 - 7.01815i) q^{45} +(-0.780313 - 1.35154i) q^{46} +5.84016 q^{47} +(-1.66612 - 2.88581i) q^{48} +(2.46410 - 4.26795i) q^{49} +(-0.500000 + 0.866025i) q^{50} +7.68922 q^{51} +10.6249 q^{53} +(-8.50367 + 14.7288i) q^{54} +(2.01978 - 3.49837i) q^{55} +(0.719687 + 1.24653i) q^{56} +1.33225 q^{57} +(3.93244 + 6.81119i) q^{58} +(1.73205 + 3.00000i) q^{59} +3.33225 q^{60} +(2.84624 + 4.92983i) q^{61} +(-1.55356 + 2.69085i) q^{62} +(5.83225 - 10.1017i) q^{63} +1.00000 q^{64} -13.4608 q^{66} +(5.20039 - 9.00734i) q^{67} +(-1.15376 + 1.99837i) q^{68} +(-2.60020 - 4.50367i) q^{69} -1.43937 q^{70} +(3.00000 + 5.19615i) q^{71} +(-4.05193 - 7.01815i) q^{72} -13.4608 q^{73} +(-3.11786 - 5.40029i) q^{74} +(-1.66612 + 2.88581i) q^{75} +(-0.199902 + 0.346241i) q^{76} +5.81445 q^{77} +0.931464 q^{79} +(-0.500000 + 0.866025i) q^{80} +(-16.1805 + 28.0255i) q^{81} +(0.380509 + 0.659061i) q^{82} -10.3867 q^{83} +(2.39817 + 4.15376i) q^{84} +(-1.15376 - 1.99837i) q^{85} -11.0073 q^{86} +(13.1039 + 22.6966i) q^{87} +(2.01978 - 3.49837i) q^{88} +(-0.485517 + 0.840939i) q^{89} +8.10387 q^{90} +1.56063 q^{92} +(-5.17686 + 8.96658i) q^{93} +(-2.92008 + 5.05772i) q^{94} +(-0.199902 - 0.346241i) q^{95} +3.33225 q^{96} +(-6.15919 - 10.6680i) q^{97} +(2.46410 + 4.26795i) q^{98} -32.7361 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} - 2 q^{6} + 8 q^{8} - 4 q^{9} - 4 q^{10} + 6 q^{11} + 4 q^{12} - 2 q^{15} - 4 q^{16} - 6 q^{17} + 8 q^{18} - 6 q^{19} - 4 q^{20} + 12 q^{21} + 6 q^{22} - 12 q^{23}+ \cdots - 84 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 - 2 * q^6 + 8 * q^8 - 4 * q^9 - 4 * q^10 + 6 * q^11 + 4 * q^12 - 2 * q^15 - 4 * q^16 - 6 * q^17 + 8 * q^18 - 6 * q^19 - 4 * q^20 + 12 * q^21 + 6 * q^22 - 12 * q^23 - 2 * q^24 + 8 * q^25 + 40 * q^27 - 2 * q^30 + 36 * q^31 - 4 * q^32 + 6 * q^33 + 12 * q^34 - 4 * q^36 + 6 * q^37 + 12 * q^38 + 8 * q^40 - 6 * q^42 - 4 * q^43 - 12 * q^44 - 4 * q^45 - 12 * q^46 - 2 * q^48 - 8 * q^49 - 4 * q^50 + 60 * q^53 - 20 * q^54 + 6 * q^55 - 12 * q^57 + 4 * q^60 + 26 * q^61 - 18 * q^62 + 24 * q^63 + 8 * q^64 - 12 * q^66 + 24 * q^67 - 6 * q^68 - 12 * q^69 + 24 * q^71 - 4 * q^72 - 12 * q^73 + 6 * q^74 - 2 * q^75 - 6 * q^76 + 60 * q^77 + 20 * q^79 - 4 * q^80 - 28 * q^81 - 36 * q^83 - 6 * q^84 - 6 * q^85 + 8 * q^86 + 48 * q^87 + 6 * q^88 + 8 * q^90 + 24 * q^92 + 12 * q^93 - 6 * q^95 + 4 * q^96 - 18 * q^97 - 8 * q^98 - 84 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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