LMFDB - Embedded newform 819.2.n.e.172.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(100,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("819.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.n (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 11 x^{14} - 4 x^{13} + 87 x^{12} - 35 x^{11} + 326 x^{10} - 205 x^{9} + 895 x^{8} - 481 x^{7} + \cdots + 1 $ x^16 + 11x^14 - 4x^13 + 87x^12 - 35x^11 + 326x^10 - 205x^9 + 895x^8 - 481x^7 + 1005x^6 - 544x^5 + 811x^4 - 312x^3 + 195x^2 + 13x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			172.6
Root			$-0.532778 + 0.922798i$ of defining polynomial
Character	$\chi$	$=$	819.172
Dual form			819.2.n.e.100.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.532778 - 0.922798i) q^{2} +(0.432296 + 0.748758i) q^{4} +(-1.19023 - 2.06154i) q^{5} +(2.58706 - 0.554165i) q^{7} +3.05238 q^{8} +O(q^{10})$	\(q+(0.532778 - 0.922798i) q^{2} +(0.432296 + 0.748758i) q^{4} +(-1.19023 - 2.06154i) q^{5} +(2.58706 - 0.554165i) q^{7} +3.05238 q^{8} -2.53651 q^{10} +0.666590 q^{11} +(2.19926 + 2.85714i) q^{13} +(0.866948 - 2.68258i) q^{14} +(0.761650 - 1.31922i) q^{16} +(0.707897 + 1.22611i) q^{17} -3.56270 q^{19} +(1.02906 - 1.78239i) q^{20} +(0.355145 - 0.615128i) q^{22} +(2.99126 - 5.18102i) q^{23} +(-0.333295 + 0.577284i) q^{25} +(3.80828 - 0.507250i) q^{26} +(1.53331 + 1.69752i) q^{28} +(-0.647747 - 1.12193i) q^{29} +(-3.09078 + 5.35339i) q^{31} +(2.24080 + 3.88118i) q^{32} +1.50861 q^{34} +(-4.22163 - 4.67375i) q^{35} +(3.94868 - 6.83932i) q^{37} +(-1.89813 + 3.28765i) q^{38} +(-3.63304 - 6.29260i) q^{40} +(-5.26293 - 9.11566i) q^{41} +(5.22034 - 9.04190i) q^{43} +(0.288164 + 0.499115i) q^{44} +(-3.18736 - 5.52067i) q^{46} +(5.54746 + 9.60848i) q^{47} +(6.38580 - 2.86732i) q^{49} +(0.355145 + 0.615128i) q^{50} +(-1.18858 + 2.88184i) q^{52} +(-3.39224 + 5.87554i) q^{53} +(-0.793396 - 1.37420i) q^{55} +(7.89671 - 1.69152i) q^{56} -1.38042 q^{58} +(-2.57641 - 4.46248i) q^{59} +4.83755 q^{61} +(3.29340 + 5.70433i) q^{62} +7.82199 q^{64} +(3.27249 - 7.93451i) q^{65} +5.57265 q^{67} +(-0.612042 + 1.06009i) q^{68} +(-6.56212 + 1.40565i) q^{70} +(-6.01988 + 10.4267i) q^{71} +(-4.05962 + 7.03147i) q^{73} +(-4.20754 - 7.28767i) q^{74} +(-1.54014 - 2.66760i) q^{76} +(1.72451 - 0.369401i) q^{77} +(-2.00333 - 3.46986i) q^{79} -3.62615 q^{80} -11.2159 q^{82} -8.44505 q^{83} +(1.68512 - 2.91872i) q^{85} +(-5.56257 - 9.63465i) q^{86} +2.03469 q^{88} +(0.910778 - 1.57751i) q^{89} +(7.27295 + 6.17286i) q^{91} +5.17244 q^{92} +11.8222 q^{94} +(4.24043 + 7.34465i) q^{95} +(-7.88484 + 13.6569i) q^{97} +(0.756256 - 7.42045i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{4} + q^{7} - 12 q^{8}+O(q^{10}) $ 16 * q - 6 * q^4 + q^7 - 12 * q^8	$ 16 q - 6 q^{4} + q^{7} - 12 q^{8} + 8 q^{10} - 4 q^{11} + 5 q^{13} + 7 q^{14} - 6 q^{16} + 2 q^{17} + 22 q^{19} + 20 q^{20} + 7 q^{22} - 4 q^{23} + 2 q^{25} + 6 q^{26} - 7 q^{28} - 15 q^{29} + 3 q^{31} - 3 q^{32} - 68 q^{34} + 12 q^{35} + 4 q^{37} - 2 q^{38} - 25 q^{40} - 19 q^{41} + 11 q^{43} + 16 q^{44} + 2 q^{46} - 5 q^{47} + 13 q^{49} + 7 q^{50} + 36 q^{52} - 36 q^{53} - 15 q^{55} - 39 q^{56} - 40 q^{58} + 17 q^{59} + 44 q^{61} + 6 q^{62} - 20 q^{64} + 21 q^{65} - 52 q^{67} - 5 q^{68} + 46 q^{70} - 9 q^{71} - 6 q^{73} - 15 q^{74} - 16 q^{76} + 36 q^{77} + 16 q^{79} - 56 q^{80} + 2 q^{82} - 36 q^{83} - 4 q^{85} - 16 q^{86} - 48 q^{88} - 20 q^{89} - 7 q^{91} + 94 q^{92} + 40 q^{94} + 7 q^{97} + 3 q^{98}+O(q^{100}) $ 16 * q - 6 * q^4 + q^7 - 12 * q^8 + 8 * q^10 - 4 * q^11 + 5 * q^13 + 7 * q^14 - 6 * q^16 + 2 * q^17 + 22 * q^19 + 20 * q^20 + 7 * q^22 - 4 * q^23 + 2 * q^25 + 6 * q^26 - 7 * q^28 - 15 * q^29 + 3 * q^31 - 3 * q^32 - 68 * q^34 + 12 * q^35 + 4 * q^37 - 2 * q^38 - 25 * q^40 - 19 * q^41 + 11 * q^43 + 16 * q^44 + 2 * q^46 - 5 * q^47 + 13 * q^49 + 7 * q^50 + 36 * q^52 - 36 * q^53 - 15 * q^55 - 39 * q^56 - 40 * q^58 + 17 * q^59 + 44 * q^61 + 6 * q^62 - 20 * q^64 + 21 * q^65 - 52 * q^67 - 5 * q^68 + 46 * q^70 - 9 * q^71 - 6 * q^73 - 15 * q^74 - 16 * q^76 + 36 * q^77 + 16 * q^79 - 56 * q^80 + 2 * q^82 - 36 * q^83 - 4 * q^85 - 16 * q^86 - 48 * q^88 - 20 * q^89 - 7 * q^91 + 94 * q^92 + 40 * q^94 + 7 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.532778	−	0.922798i	0.376731	−	0.652517i	−0.613854	−	0.789420i	$-0.710382\pi$
$2$	0.532778	−	0.922798i	0.376731	−	0.652517i	0.990584	+	0.136903i	$0.0437149\pi$
$3$		0			0
$3$		0			0
$4$	0.432296	+	0.748758i	0.216148	+	0.374379i
$5$	−1.19023	−	2.06154i	−0.532287	−	0.921948i	−0.999289	−	0.0376922i	$-0.987999\pi$
$5$	−1.19023	−	2.06154i	−0.532287	−	0.921948i	0.467002	−	0.884256i	$-0.345334\pi$
$6$		0			0
$7$	2.58706	−	0.554165i	0.977818	−	0.209455i
$7$	2.58706	−	0.554165i	0.977818	−	0.209455i
$8$	3.05238			1.07918
$9$		0			0
$10$	−2.53651			−0.802116
$11$	0.666590			0.200985			0.100492	−	0.994938i	$-0.467958\pi$
$11$	0.666590			0.200985			0.100492	+	0.994938i	$0.467958\pi$
$12$		0			0
$13$	2.19926	+	2.85714i	0.609965	+	0.792429i
$13$	2.19926	+	2.85714i	0.609965	+	0.792429i
$14$	0.866948	−	2.68258i	0.231702	−	0.716951i
$15$		0			0
$16$	0.761650	−	1.31922i	0.190412	−	0.329804i
$17$	0.707897	+	1.22611i	0.171690	+	0.297376i	0.939011	−	0.343887i	$-0.111744\pi$
$17$	0.707897	+	1.22611i	0.171690	+	0.297376i	−0.767321	+	0.641264i	$0.778410\pi$
$18$		0			0
$19$	−3.56270			−0.817339			−0.408670	−	0.912682i	$-0.634007\pi$
$19$	−3.56270			−0.817339			−0.408670	+	0.912682i	$0.634007\pi$
$20$	1.02906	−	1.78239i	0.230105	−	0.398554i
$21$		0			0
$22$	0.355145	−	0.615128i	0.0757171	−	0.131146i
$23$	2.99126	−	5.18102i	0.623722	−	1.08032i	−0.365065	−	0.930982i	$-0.618953\pi$
$23$	2.99126	−	5.18102i	0.623722	−	1.08032i	0.988787	−	0.149336i	$-0.0477135\pi$
$24$		0			0
$25$	−0.333295	+	0.577284i	−0.0666590	+	0.115457i
$26$	3.80828	−	0.507250i	0.746865	−	0.0994799i
$27$		0			0
$28$	1.53331	+	1.69752i	0.289769	+	0.320802i
$29$	−0.647747	−	1.12193i	−0.120284	−	0.208337i	0.799596	−	0.600538i	$-0.205047\pi$
$29$	−0.647747	−	1.12193i	−0.120284	−	0.208337i	−0.919879	+	0.392201i	$0.871714\pi$
$30$		0			0
$31$	−3.09078	+	5.35339i	−0.555120	+	0.961497i	0.442774	+	0.896633i	$0.353994\pi$
$31$	−3.09078	+	5.35339i	−0.555120	+	0.961497i	−0.997894	+	0.0648633i	$0.979339\pi$
$32$	2.24080	+	3.88118i	0.396121	+	0.686102i
$33$		0			0
$34$	1.50861			0.258724
$35$	−4.22163	−	4.67375i	−0.713586	−	0.790008i
$36$		0			0
$37$	3.94868	−	6.83932i	0.649159	−	1.12438i	−0.334165	−	0.942515i	$-0.608454\pi$
$37$	3.94868	−	6.83932i	0.649159	−	1.12438i	0.983324	−	0.181862i	$-0.0582124\pi$
$38$	−1.89813	+	3.28765i	−0.307917	+	0.533328i
$39$		0			0
$40$	−3.63304	−	6.29260i	−0.574433	−	0.994948i
$41$	−5.26293	−	9.11566i	−0.821931	−	1.42363i	−0.904242	−	0.427020i	$-0.859563\pi$
$41$	−5.26293	−	9.11566i	−0.821931	−	1.42363i	0.0823113	−	0.996607i	$-0.473770\pi$
$42$		0			0
$43$	5.22034	−	9.04190i	0.796095	−	1.37888i	−0.126047	−	0.992024i	$-0.540229\pi$
$43$	5.22034	−	9.04190i	0.796095	−	1.37888i	0.922142	−	0.386853i	$-0.126438\pi$
$44$	0.288164	+	0.499115i	0.0434424	+	0.0752444i
$45$		0			0
$46$	−3.18736	−	5.52067i	−0.469950	−	0.813978i
$47$	5.54746	+	9.60848i	0.809180	+	1.40154i	0.913433	+	0.406990i	$0.133422\pi$
$47$	5.54746	+	9.60848i	0.809180	+	1.40154i	−0.104253	+	0.994551i	$0.533245\pi$
$48$		0			0
$49$	6.38580	−	2.86732i	0.912258	−	0.409617i
$50$	0.355145	+	0.615128i	0.0502250	+	0.0869923i
$51$		0			0
$52$	−1.18858	+	2.88184i	−0.164826	+	0.399640i
$53$	−3.39224	+	5.87554i	−0.465961	+	0.807067i	−0.999244	−	0.0388691i	$-0.987624\pi$
$53$	−3.39224	+	5.87554i	−0.465961	+	0.807067i	0.533284	+	0.845936i	$0.320958\pi$
$54$		0			0
$55$	−0.793396	−	1.37420i	−0.106981	−	0.185297i
$56$	7.89671	−	1.69152i	1.05524	−	0.226039i
$57$		0			0
$58$	−1.38042			−0.181258
$59$	−2.57641	−	4.46248i	−0.335420	−	0.580965i	0.648145	−	0.761517i	$-0.275545\pi$
$59$	−2.57641	−	4.46248i	−0.335420	−	0.580965i	−0.983565	+	0.180552i	$0.942212\pi$
$60$		0			0
$61$	4.83755			0.619385			0.309692	−	0.950837i	$-0.399774\pi$
$61$	4.83755			0.619385			0.309692	+	0.950837i	$0.399774\pi$
$62$	3.29340	+	5.70433i	0.418262	+	0.724451i
$63$		0			0
$64$	7.82199			0.977749
$65$	3.27249	−	7.93451i	0.405902	−	0.984155i
$66$		0			0
$67$	5.57265			0.680808			0.340404	−	0.940279i	$-0.389436\pi$
$67$	5.57265			0.680808			0.340404	+	0.940279i	$0.389436\pi$
$68$	−0.612042	+	1.06009i	−0.0742210	+	0.128555i
$69$		0			0
$70$	−6.56212	+	1.40565i	−0.784323	+	0.168007i
$71$	−6.01988	+	10.4267i	−0.714428	+	1.23743i	0.248752	+	0.968567i	$0.419980\pi$
$71$	−6.01988	+	10.4267i	−0.714428	+	1.23743i	−0.963180	+	0.268858i	$0.913354\pi$
$72$		0			0
$73$	−4.05962	+	7.03147i	−0.475143	+	0.822971i	−0.999595	−	0.0284689i	$-0.990937\pi$
$73$	−4.05962	+	7.03147i	−0.475143	+	0.822971i	0.524452	+	0.851440i	$0.324270\pi$
$74$	−4.20754	−	7.28767i	−0.489116	−	0.847175i
$75$		0			0
$76$	−1.54014	−	2.66760i	−0.176666	−	0.305995i
$77$	1.72451	−	0.369401i	0.196526	−	0.0420971i
$78$		0			0
$79$	−2.00333	−	3.46986i	−0.225392	−	0.390390i	0.731045	−	0.682329i	$-0.239033\pi$
$79$	−2.00333	−	3.46986i	−0.225392	−	0.390390i	−0.956437	+	0.291939i	$0.905700\pi$
$80$	−3.62615			−0.405416
$81$		0			0
$82$	−11.2159			−1.23859
$83$	−8.44505			−0.926965			−0.463483	−	0.886106i	$-0.653400\pi$
$83$	−8.44505			−0.926965			−0.463483	+	0.886106i	$0.653400\pi$
$84$		0			0
$85$	1.68512	−	2.91872i	0.182777	−	0.316579i
$86$	−5.56257	−	9.63465i	−0.599827	−	1.03893i
$87$		0			0
$88$	2.03469			0.216898
$89$	0.910778	−	1.57751i	0.0965423	−	0.167216i	−0.813709	−	0.581273i	$-0.802555\pi$
$89$	0.910778	−	1.57751i	0.0965423	−	0.167216i	0.910251	+	0.414056i	$0.135888\pi$
$90$		0			0
$91$	7.27295	+	6.17286i	0.762412	+	0.647091i
$92$	5.17244			0.539264
$93$		0			0
$94$	11.8222			1.21937
$95$	4.24043	+	7.34465i	0.435059	+	0.753545i
$96$		0			0
$97$	−7.88484	+	13.6569i	−0.800584	+	1.38665i	0.118648	+	0.992936i	$0.462144\pi$
$97$	−7.88484	+	13.6569i	−0.800584	+	1.38665i	−0.919232	+	0.393716i	$0.871189\pi$
$98$	0.756256	−	7.42045i	0.0763934	−	0.749579i
$99$		0			0
$100$	−0.576328			−0.0576328
$101$	−8.97058			−0.892606			−0.446303	−	0.894882i	$-0.647260\pi$
$101$	−8.97058			−0.892606			−0.446303	+	0.894882i	$0.647260\pi$
$102$		0			0
$103$	−1.58796	−	2.75042i	−0.156466	−	0.271007i	0.777126	−	0.629345i	$-0.216677\pi$
$103$	−1.58796	−	2.75042i	−0.156466	−	0.271007i	−0.933592	+	0.358338i	$0.883344\pi$
$104$	6.71298	+	8.72109i	0.658261	+	0.855173i
$105$		0			0
$106$	3.61462	+	6.26071i	0.351083	+	0.608094i
$107$	−2.50268	+	4.33476i	−0.241943	+	0.419057i	−0.961268	−	0.275617i	$-0.911118\pi$
$107$	−2.50268	+	4.33476i	−0.241943	+	0.419057i	0.719325	+	0.694674i	$0.244451\pi$
$108$		0			0
$109$	−8.29305	+	14.3640i	−0.794330	+	1.37582i	0.128934	+	0.991653i	$0.458844\pi$
$109$	−8.29305	+	14.3640i	−0.794330	+	1.37582i	−0.923264	+	0.384167i	$0.874489\pi$
$110$	−1.69081			−0.161213
$111$		0			0
$112$	1.23937	−	3.83497i	0.117110	−	0.362371i
$113$	−3.57465	+	6.19148i	−0.336275	+	0.582446i	−0.983729	−	0.179659i	$-0.942501\pi$
$113$	−3.57465	+	6.19148i	−0.336275	+	0.582446i	0.647454	+	0.762105i	$0.275834\pi$
$114$		0			0
$115$	−14.2412			−1.32800
$116$	0.560037	−	0.970012i	0.0519981	−	0.0900633i
$117$		0			0
$118$	−5.49062			−0.505453
$119$	2.51085	+	2.77974i	0.230169	+	0.254819i
$120$		0			0
$121$	−10.5557			−0.959605
$122$	2.57734	−	4.46408i	0.233341	−	0.404159i
$123$		0			0
$124$	−5.34452			−0.479952
$125$	−10.3155			−0.922647
$126$		0			0
$127$	−5.70435	−	9.88023i	−0.506179	−	0.876728i	−0.999974	−	0.00715012i	$-0.997724\pi$
$127$	−5.70435	−	9.88023i	−0.506179	−	0.876728i	0.493795	−	0.869578i	$-0.335609\pi$
$128$	−0.314218	+	0.544241i	−0.0277732	+	0.0481046i
$129$		0			0
$130$	−5.57845	−	7.24718i	−0.489262	−	0.635619i
$131$	4.30754	+	7.46087i	0.376351	+	0.651860i	0.990528	−	0.137309i	$-0.0438452\pi$
$131$	4.30754	+	7.46087i	0.376351	+	0.651860i	−0.614177	+	0.789168i	$0.710512\pi$
$132$		0			0
$133$	−9.21693	+	1.97432i	−0.799210	+	0.171196i
$134$	2.96898	−	5.14243i	0.256481	−	0.444239i
$135$		0			0
$136$	2.16077	+	3.74257i	0.185285	+	0.320923i
$137$	4.17738	+	7.23544i	0.356898	+	0.618165i	0.987441	−	0.157989i	$-0.0505011\pi$
$137$	4.17738	+	7.23544i	0.356898	+	0.618165i	−0.630543	+	0.776154i	$0.717168\pi$
$138$		0			0
$139$	4.82663	−	8.35996i	0.409389	−	0.709083i	−0.585432	−	0.810721i	$-0.699075\pi$
$139$	4.82663	−	8.35996i	0.409389	−	0.709083i	0.994821	+	0.101638i	$0.0324085\pi$
$140$	1.67451	−	5.18142i	0.141522	−	0.437910i
$141$		0			0
$142$	6.41451	+	11.1103i	0.538294	+	0.932352i
$143$	1.46600	+	1.90454i	0.122593	+	0.159266i
$144$		0			0
$145$	−1.54194	+	2.67071i	−0.128051	+	0.221791i
$146$	4.32575	+	7.49242i	0.358002	+	0.620077i
$147$		0			0
$148$	6.82799			0.561257
$149$	−13.2608			−1.08637			−0.543183	−	0.839614i	$-0.682781\pi$
$149$	−13.2608			−1.08637			−0.543183	+	0.839614i	$0.682781\pi$
$150$		0			0
$151$	−8.22189	+	14.2407i	−0.669088	+	1.15889i	0.309072	+	0.951039i	$0.399982\pi$
$151$	−8.22189	+	14.2407i	−0.669088	+	1.15889i	−0.978160	+	0.207855i	$0.933352\pi$
$152$	−10.8747			−0.882056
$153$		0			0
$154$	0.577899	−	1.78819i	0.0465684	−	0.144096i
$155$	14.7150			1.18193
$156$		0			0
$157$	9.15038	−	15.8489i	0.730279	−	1.26488i	−0.226484	−	0.974015i	$-0.572723\pi$
$157$	9.15038	−	15.8489i	0.730279	−	1.26488i	0.956764	−	0.290866i	$-0.0939435\pi$
$158$	−4.26931			−0.339648
$159$		0			0
$160$	5.33414	−	9.23900i	0.421701	−	0.730407i
$161$	4.86745	−	15.0613i	0.383609	−	1.18700i
$162$		0			0
$163$	6.78823			0.531695			0.265847	−	0.964015i	$-0.414348\pi$
$163$	6.78823			0.531695			0.265847	+	0.964015i	$0.414348\pi$
$164$	4.55028	−	7.88132i	0.355317	−	0.615428i
$165$		0			0
$166$	−4.49934	+	7.79308i	−0.349216	+	0.604860i
$167$	−0.826837	−	1.43212i	−0.0639826	−	0.110821i	0.832260	−	0.554386i	$-0.187047\pi$
$167$	−0.826837	−	1.43212i	−0.0639826	−	0.110821i	−0.896242	+	0.443565i	$0.853714\pi$
$168$		0			0
$169$	−3.32652	+	12.5672i	−0.255886	+	0.966707i
$170$	−1.79559	−	3.11005i	−0.137716	−	0.238530i
$171$		0			0
$172$	9.02693			0.688297
$173$	11.9879			0.911421			0.455711	−	0.890128i	$-0.349385\pi$
$173$	11.9879			0.911421			0.455711	+	0.890128i	$0.349385\pi$
$174$		0			0
$175$	−0.542345	+	1.67817i	−0.0409975	+	0.126858i
$176$	0.507708	−	0.879376i	0.0382699	−	0.0662855i
$177$		0			0
$178$	−0.970485	−	1.68093i	−0.0727409	−	0.125991i
$179$	2.67017			0.199578			0.0997888	−	0.995009i	$-0.468183\pi$
$179$	2.67017			0.199578			0.0997888	+	0.995009i	$0.468183\pi$
$180$		0			0
$181$	−0.752089			−0.0559024			−0.0279512	−	0.999609i	$-0.508898\pi$
$181$	−0.752089			−0.0559024			−0.0279512	+	0.999609i	$0.508898\pi$
$182$	9.57117	−	3.42270i	0.709462	−	0.253708i
$183$		0			0
$184$	9.13048	−	15.8145i	0.673108	−	1.16586i
$185$	−18.7994			−1.38216
$186$		0			0
$187$	0.471878	+	0.817316i	0.0345071	+	0.0597681i
$188$	−4.79628	+	8.30741i	−0.349805	+	0.605880i
$189$		0			0
$190$	9.03683			0.655601
$191$	−5.15813			−0.373229			−0.186615	−	0.982433i	$-0.559752\pi$
$191$	−5.15813			−0.373229			−0.186615	+	0.982433i	$0.559752\pi$
$192$		0			0
$193$	2.84627			0.204879			0.102439	−	0.994739i	$-0.467335\pi$
$193$	2.84627			0.204879			0.102439	+	0.994739i	$0.467335\pi$
$194$	8.40173	+	14.5522i	0.603209	+	1.04479i
$195$		0			0
$196$	4.90748	+	3.54189i	0.350535	+	0.252992i
$197$	0.483548	+	0.837530i	0.0344514	+	0.0596716i	0.882737	−	0.469867i	$-0.155698\pi$
$197$	0.483548	+	0.837530i	0.0344514	+	0.0596716i	−0.848286	+	0.529539i	$0.822365\pi$
$198$		0			0
$199$	−4.69085	−	8.12478i	−0.332525	−	0.575951i	0.650481	−	0.759522i	$-0.274567\pi$
$199$	−4.69085	−	8.12478i	−0.332525	−	0.575951i	−0.983006	+	0.183572i	$0.941234\pi$
$200$	−1.01734	+	1.76209i	−0.0719371	+	0.124599i
$201$		0			0
$202$	−4.77933	+	8.27804i	−0.336272	+	0.582441i
$203$	−2.29750	−	2.54355i	−0.161253	−	0.178522i
$204$		0			0
$205$	−12.5282	+	21.6995i	−0.875007	+	1.51556i
$206$	−3.38411			−0.235782
$207$		0			0
$208$	5.44425	−	0.725155i	0.377491	−	0.0502805i
$209$	−2.37486			−0.164273
$210$		0			0
$211$	10.3756	+	17.9711i	0.714288	+	1.23718i	0.963233	+	0.268666i	$0.0865827\pi$
$211$	10.3756	+	17.9711i	0.714288	+	1.23718i	−0.248945	+	0.968518i	$0.580084\pi$
$212$	−5.86581			−0.402865
$213$		0			0
$214$	2.66674	+	4.61893i	0.182295	+	0.315744i
$215$	−24.8536			−1.69500
$216$		0			0
$217$	−5.02939	+	15.5624i	−0.341417	+	1.05644i
$218$	8.83670	+	15.3056i	0.598497	+	1.03663i
$219$		0			0
$220$	0.685963	−	1.18812i	0.0462476	−	0.0801032i
$221$	−1.94633	+	4.71911i	−0.130925	+	0.317441i
$222$		0			0
$223$	−4.05504	−	7.02354i	−0.271546	−	0.470331i	0.697712	−	0.716378i	$-0.254201\pi$
$223$	−4.05504	−	7.02354i	−0.271546	−	0.470331i	−0.969258	+	0.246047i	$0.920868\pi$
$224$	7.94791	+	8.79909i	0.531042	+	0.587914i
$225$		0			0
$226$	3.80899	+	6.59737i	0.253370	+	0.438850i
$227$	1.09865	+	1.90291i	0.0729197	+	0.126301i	0.900180	−	0.435519i	$-0.143435\pi$
$227$	1.09865	+	1.90291i	0.0729197	+	0.126301i	−0.827260	+	0.561819i	$0.810102\pi$
$228$		0			0
$229$	−10.1545	−	17.5882i	−0.671030	−	1.16226i	−0.977612	−	0.210414i	$-0.932519\pi$
$229$	−10.1545	−	17.5882i	−0.671030	−	1.16226i	0.306582	−	0.951844i	$-0.400815\pi$
$230$	−7.58738	+	13.1417i	−0.500297	+	0.866540i
$231$		0			0
$232$	−1.97717	−	3.42456i	−0.129808	−	0.224833i
$233$	10.7709	+	18.6557i	0.705624	+	1.22218i	0.966466	+	0.256795i	$0.0826665\pi$
$233$	10.7709	+	18.6557i	0.705624	+	1.22218i	−0.260842	+	0.965382i	$0.584000\pi$
$234$		0			0
$235$	13.2055	−	22.8726i	0.861432	−	1.49204i
$236$	2.22754	−	3.85822i	0.145001	−	0.251149i
$237$		0			0
$238$	3.90287	−	0.836018i	0.252985	−	0.0541910i
$239$	17.3697			1.12355			0.561775	−	0.827290i	$-0.310119\pi$
$239$	17.3697			1.12355			0.561775	+	0.827290i	$0.310119\pi$
$240$		0			0
$241$	5.25156	+	9.09597i	0.338283	+	0.585923i	0.984110	−	0.177561i	$-0.0568206\pi$
$241$	5.25156	+	9.09597i	0.338283	+	0.585923i	−0.645827	+	0.763484i	$0.723487\pi$
$242$	−5.62382	+	9.74074i	−0.361513	+	0.626159i
$243$		0			0
$244$	2.09125	+	3.62216i	0.133879	+	0.231885i
$245$	−13.5117	−	9.75181i	−0.863229	−	0.623020i
$246$		0			0
$247$	−7.83530	−	10.1791i	−0.498548	−	0.647683i
$248$	−9.43424	+	16.3406i	−0.599075	+	1.03763i
$249$		0			0
$250$	−5.49587	+	9.51913i	−0.347590	+	0.602043i
$251$	0.706938	−	1.22445i	0.0446215	−	0.0772867i	−0.842852	−	0.538145i	$-0.819125\pi$
$251$	0.706938	−	1.22445i	0.0446215	−	0.0772867i	0.887474	+	0.460859i	$0.152458\pi$
$252$		0			0
$253$	1.99395	−	3.45362i	0.125358	−	0.217127i
$254$	−12.1566			−0.762773
$255$		0			0
$256$	8.15681	+	14.1280i	0.509801	+	0.883001i
$257$	−6.87362	+	11.9055i	−0.428765	+	0.742642i	−0.996764	−	0.0803871i	$-0.974384\pi$
$257$	−6.87362	+	11.9055i	−0.428765	+	0.742642i	0.567999	+	0.823029i	$0.307718\pi$
$258$		0			0
$259$	6.42538	−	19.8820i	0.399254	−	1.23541i
$260$	7.35571	−	0.979756i	0.456182	−	0.0607619i
$261$		0			0
$262$	9.17984			0.567133
$263$	−7.97741			−0.491908			−0.245954	−	0.969281i	$-0.579101\pi$
$263$	−7.97741			−0.491908			−0.245954	+	0.969281i	$0.579101\pi$
$264$		0			0
$265$	16.1502			0.992099
$266$	−3.08868	+	9.55725i	−0.189379	+	0.585992i
$267$		0			0
$268$	2.40903	+	4.17257i	0.147155	+	0.254880i
$269$	13.8192	+	23.9355i	0.842569	+	1.45937i	0.887716	+	0.460392i	$0.152291\pi$
$269$	13.8192	+	23.9355i	0.842569	+	1.45937i	−0.0451470	+	0.998980i	$0.514376\pi$
$270$		0			0
$271$	−5.15953	+	8.93656i	−0.313419	+	0.542857i	−0.979100	−	0.203379i	$-0.934808\pi$
$271$	−5.15953	+	8.93656i	−0.313419	+	0.542857i	0.665681	+	0.746236i	$0.268141\pi$
$272$	2.15668			0.130768
$273$		0			0
$274$	8.90247			0.537818
$275$	−0.222171	+	0.384812i	−0.0133974	+	0.0232050i
$276$		0			0
$277$	1.07784	+	1.86687i	0.0647611	+	0.112170i	0.896588	−	0.442866i	$-0.146038\pi$
$277$	1.07784	+	1.86687i	0.0647611	+	0.112170i	−0.831827	+	0.555035i	$0.812705\pi$
$278$	−5.14304	−	8.90801i	−0.308459	−	0.534267i
$279$		0			0
$280$	−12.8860	−	14.2661i	−0.770088	−	0.852561i
$281$	2.60596			0.155458			0.0777292	−	0.996975i	$-0.475233\pi$
$281$	2.60596			0.155458			0.0777292	+	0.996975i	$0.475233\pi$
$282$		0			0
$283$	1.73242			0.102982			0.0514909	−	0.998673i	$-0.483603\pi$
$283$	1.73242			0.102982			0.0514909	+	0.998673i	$0.483603\pi$
$284$	−10.4095			−0.617688
$285$		0			0
$286$	2.53856	−	0.338128i	0.150108	−	0.0199939i
$287$	−18.6671	−	20.6663i	−1.10188	−	1.21989i
$288$		0			0
$289$	7.49776	−	12.9865i	0.441045	−	0.763912i
$290$	1.64302	+	2.84579i	0.0964814	+	0.167111i
$291$		0			0
$292$	−7.01982			−0.410804
$293$	16.4196	−	28.4396i	0.959243	−	1.66146i	0.234898	−	0.972020i	$-0.424524\pi$
$293$	16.4196	−	28.4396i	0.959243	−	1.66146i	0.724345	−	0.689438i	$-0.242142\pi$
$294$		0			0
$295$	−6.13305	+	10.6227i	−0.357080	+	0.618480i
$296$	12.0529	−	20.8762i	0.700559	−	1.21340i
$297$		0			0
$298$	−7.06506	+	12.2370i	−0.409268	+	0.708873i
$299$	21.3815	−	2.84794i	1.23652	−	0.164701i
$300$		0			0
$301$	8.49466	−	26.2849i	0.489624	−	1.51504i
$302$	8.76088	+	15.1743i	0.504132	+	0.873182i
$303$		0			0
$304$	−2.71353	+	4.69997i	−0.155632	+	0.269562i
$305$	−5.75780	−	9.97280i	−0.329691	−	0.571041i
$306$		0			0
$307$	−29.4618			−1.68147			−0.840737	−	0.541444i	$-0.817878\pi$
$307$	−29.4618			−1.68147			−0.840737	+	0.541444i	$0.817878\pi$
$308$	1.02209	+	1.13155i	0.0582390	+	0.0644762i
$309$		0			0
$310$	7.83980	−	13.5789i	0.445271	−	0.771232i
$311$	3.53099	−	6.11585i	0.200224	−	0.346798i	−0.748377	−	0.663274i	$-0.769166\pi$
$311$	3.53099	−	6.11585i	0.200224	−	0.346798i	0.948601	+	0.316476i	$0.102500\pi$
$312$		0			0
$313$	8.17883	+	14.1661i	0.462295	+	0.800718i	0.999075	−	0.0430043i	$-0.0136929\pi$
$313$	8.17883	+	14.1661i	0.462295	+	0.800718i	−0.536780	+	0.843722i	$0.680360\pi$
$314$	−9.75023	−	16.8879i	−0.550237	−	0.953039i
$315$		0			0
$316$	1.73206	−	3.00001i	0.0974359	−	0.168764i
$317$	9.48109	+	16.4217i	0.532511	+	0.922337i	0.999279	+	0.0379568i	$0.0120849\pi$
$317$	9.48109	+	16.4217i	0.532511	+	0.922337i	−0.466768	+	0.884380i	$0.654582\pi$
$318$		0			0
$319$	−0.431782	−	0.747868i	−0.0241751	−	0.0418726i
$320$	−9.30997	−	16.1253i	−0.520443	−	0.901434i
$321$		0			0
$322$	−11.3053	−	12.5160i	−0.630017	−	0.697489i
$323$	−2.52203	−	4.36828i	−0.140329	−	0.243057i
$324$		0			0
$325$	−2.38239	+	0.317326i	−0.132151	+	0.0176021i
$326$	3.61662	−	6.26416i	0.200306	−	0.346940i
$327$		0			0
$328$	−16.0645	−	27.8245i	−0.887011	−	1.53635i
$329$	19.6763	+	21.7835i	1.08479	+	1.20097i
$330$		0			0
$331$	−19.0379			−1.04642			−0.523208	−	0.852205i	$-0.675265\pi$
$331$	−19.0379			−1.04642			−0.523208	+	0.852205i	$0.675265\pi$
$332$	−3.65076	−	6.32330i	−0.200362	−	0.347036i
$333$		0			0
$334$	−1.76208			−0.0964168
$335$	−6.63274	−	11.4882i	−0.362385	−	0.627669i
$336$		0			0
$337$	1.90388			0.103711			0.0518555	−	0.998655i	$-0.483486\pi$
$337$	1.90388			0.103711			0.0518555	+	0.998655i	$0.483486\pi$
$338$	9.82468	+	9.76523i	0.534392	+	0.531158i
$339$		0			0
$340$	2.91388			0.158028
$341$	−2.06028	+	3.56852i	−0.111571	+	0.193246i
$342$		0			0
$343$	14.9315	−	10.9567i	0.806226	−	0.591608i
$344$	15.9345	−	27.5993i	0.859130	−	1.48806i
$345$		0			0
$346$	6.38687	−	11.0624i	0.343360	−	0.594718i
$347$	−10.4403	−	18.0831i	−0.560462	−	0.970749i	−0.997456	−	0.0712845i	$-0.977290\pi$
$347$	−10.4403	−	18.0831i	−0.560462	−	0.970749i	0.436994	−	0.899465i	$-0.356043\pi$
$348$		0			0
$349$	−4.79951	−	8.31300i	−0.256912	−	0.444984i	0.708501	−	0.705710i	$-0.249372\pi$
$349$	−4.79951	−	8.31300i	−0.256912	−	0.444984i	−0.965413	+	0.260725i	$0.916038\pi$
$350$	1.25966	+	1.39457i	0.0673319	+	0.0745428i
$351$		0			0
$352$	1.49370	+	2.58716i	0.0796143	+	0.137896i
$353$	−10.8140			−0.575569			−0.287785	−	0.957695i	$-0.592919\pi$
$353$	−10.8140			−0.575569			−0.287785	+	0.957695i	$0.592919\pi$
$354$		0			0
$355$	28.6602			1.52112
$356$	1.57490			0.0834696
$357$		0			0
$358$	1.42260	−	2.46402i	0.0751870	−	0.130228i
$359$	−14.4945	−	25.1052i	−0.764990	−	1.32500i	−0.940252	−	0.340479i	$-0.889411\pi$
$359$	−14.4945	−	25.1052i	−0.764990	−	1.32500i	0.175262	−	0.984522i	$-0.443923\pi$
$360$		0			0
$361$	−6.30717			−0.331956
$362$	−0.400696	+	0.694027i	−0.0210601	+	0.0364772i
$363$		0			0
$364$	−1.47791	+	8.11418i	−0.0774637	+	0.425299i
$365$	19.3275			1.01165
$366$		0			0
$367$	−32.5733			−1.70031			−0.850156	−	0.526530i	$-0.823493\pi$
$367$	−32.5733			−1.70031			−0.850156	+	0.526530i	$0.823493\pi$
$368$	−4.55659	−	7.89224i	−0.237529	−	0.411412i
$369$		0			0
$370$	−10.0159	+	17.3480i	−0.520701	+	0.901880i
$371$	−5.51994	+	17.0803i	−0.286581	+	0.886763i
$372$		0			0
$373$	−23.8778			−1.23634			−0.618172	−	0.786043i	$-0.712126\pi$
$373$	−23.8778			−1.23634			−0.618172	+	0.786043i	$0.712126\pi$
$374$	1.00562			0.0519996
$375$		0			0
$376$	16.9330	+	29.3287i	0.873250	+	1.51251i
$377$	1.78095	−	4.31812i	0.0917237	−	0.222395i
$378$		0			0
$379$	−4.89406	−	8.47676i	−0.251391	−	0.435422i	0.712518	−	0.701654i	$-0.247555\pi$
$379$	−4.89406	−	8.47676i	−0.251391	−	0.435422i	−0.963909	+	0.266232i	$0.914221\pi$
$380$	−3.66624	+	6.35012i	−0.188074	+	0.325754i
$381$		0			0
$382$	−2.74814	+	4.75992i	−0.140607	+	0.243539i
$383$	−14.8568			−0.759146			−0.379573	−	0.925162i	$-0.623929\pi$
$383$	−14.8568			−0.759146			−0.379573	+	0.925162i	$0.623929\pi$
$384$		0			0
$385$	−2.81410	−	3.11548i	−0.143420	−	0.158779i
$386$	1.51643	−	2.62653i	0.0771841	−	0.133687i
$387$		0			0
$388$	−13.6343			−0.692178
$389$	9.62735	−	16.6751i	0.488126	−	0.845459i	−0.511781	−	0.859116i	$-0.671014\pi$
$389$	9.62735	−	16.6751i	0.488126	−	0.845459i	0.999907	+	0.0136568i	$0.00434723\pi$
$390$		0			0
$391$	8.47003			0.428348
$392$	19.4919	−	8.75215i	0.984490	−	0.442051i
$393$		0			0
$394$	1.03050			0.0519156
$395$	−4.76884	+	8.25987i	−0.239946	+	0.415599i
$396$		0			0
$397$	38.3010			1.92227			0.961136	−	0.276074i	$-0.0890335\pi$
$397$	38.3010			1.92227			0.961136	+	0.276074i	$0.0890335\pi$
$398$	−9.99671			−0.501090
$399$		0			0
$400$	0.507708	+	0.879376i	0.0253854	+	0.0439688i
$401$	17.8057	−	30.8404i	0.889175	−	1.54010i	0.0483236	−	0.998832i	$-0.484612\pi$
$401$	17.8057	−	30.8404i	0.889175	−	1.54010i	0.840852	−	0.541265i	$-0.182055\pi$
$402$		0			0
$403$	−22.0928	+	2.94269i	−1.10052	+	0.146586i
$404$	−3.87794	−	6.71680i	−0.192935	−	0.334173i
$405$		0			0
$406$	−3.57124	+	0.764981i	−0.177238	+	0.0379654i
$407$	2.63215	−	4.55902i	0.130471	−	0.225982i
$408$		0			0
$409$	1.58236	+	2.74072i	0.0782426	+	0.135520i	0.902492	−	0.430707i	$-0.141736\pi$
$409$	1.58236	+	2.74072i	0.0782426	+	0.135520i	−0.824249	+	0.566227i	$0.808402\pi$
$410$	13.3495	+	23.1220i	0.659284	+	1.14191i
$411$		0			0
$412$	1.37293	−	2.37799i	0.0676396	−	0.117155i
$413$	−9.13829	−	10.1170i	−0.449666	−	0.497823i
$414$		0			0
$415$	10.0516	+	17.4098i	0.493412	+	0.854614i
$416$	−6.16099	+	14.9380i	−0.302067	+	0.732396i
$417$		0			0
$418$	−1.26527	+	2.19152i	−0.0618865	+	0.107191i
$419$	−11.0530	−	19.1444i	−0.539975	−	0.935265i	−0.998905	−	0.0467918i	$-0.985100\pi$
$419$	−11.0530	−	19.1444i	−0.539975	−	0.935265i	0.458929	−	0.888473i	$-0.348233\pi$
$420$		0			0
$421$	7.75012			0.377718			0.188859	−	0.982004i	$-0.439521\pi$
$421$	7.75012			0.377718			0.188859	+	0.982004i	$0.439521\pi$
$422$	22.1116			1.07638
$423$		0			0
$424$	−10.3544	+	17.9344i	−0.502855	+	0.870971i
$425$	−0.943755			−0.0457789
$426$		0			0
$427$	12.5151	−	2.68080i	0.605646	−	0.129733i
$428$	−4.32759			−0.209182
$429$		0			0
$430$	−13.2415	+	22.9349i	−0.638560	+	1.10602i
$431$	34.5590			1.66465			0.832324	−	0.554290i	$-0.187010\pi$
$431$	34.5590			1.66465			0.832324	+	0.554290i	$0.187010\pi$
$432$		0			0
$433$	−12.2389	+	21.1985i	−0.588166	+	1.01873i	0.406306	+	0.913737i	$0.366817\pi$
$433$	−12.2389	+	21.1985i	−0.588166	+	1.01873i	−0.994473	+	0.104997i	$0.966517\pi$
$434$	11.6814	+	12.9324i	0.560724	+	0.620774i
$435$		0			0
$436$	−14.3402			−0.686771
$437$	−10.6570	+	18.4584i	−0.509792	+	0.882986i
$438$		0			0
$439$	5.36348	−	9.28983i	0.255985	−	0.443379i	−0.709177	−	0.705030i	$-0.750934\pi$
$439$	5.36348	−	9.28983i	0.255985	−	0.443379i	0.965163	+	0.261651i	$0.0842669\pi$
$440$	−2.42175	−	4.19459i	−0.115452	−	0.199969i
$441$		0			0
$442$	3.31782	+	4.31031i	0.157813	+	0.205020i
$443$	−19.9363	−	34.5306i	−0.947200	−	1.64060i	−0.751284	−	0.659979i	$-0.770565\pi$
$443$	−19.9363	−	34.5306i	−0.947200	−	1.64060i	−0.195916	−	0.980621i	$-0.562768\pi$
$444$		0			0
$445$	−4.33614			−0.205553
$446$	−8.64174			−0.409198
$447$		0			0
$448$	20.2360	−	4.33467i	0.956061	−	0.204794i
$449$	−15.2790	+	26.4640i	−0.721060	+	1.24891i	0.239515	+	0.970893i	$0.423012\pi$
$449$	−15.2790	+	26.4640i	−0.721060	+	1.24891i	−0.960575	+	0.278021i	$0.910322\pi$
$450$		0			0
$451$	−3.50822	−	6.07641i	−0.165195	−	0.286127i
$452$	−6.18123			−0.290741
$453$		0			0
$454$	2.34134			0.109884
$455$	4.06910	−	22.3406i	0.190762	−	1.04734i
$456$		0			0
$457$	8.01733	−	13.8864i	0.375035	−	0.649579i	−0.615297	−	0.788295i	$-0.710964\pi$
$457$	8.01733	−	13.8864i	0.375035	−	0.649579i	0.990332	+	0.138716i	$0.0442974\pi$
$458$	−21.6404			−1.01119
$459$		0			0
$460$	−6.15640	−	10.6632i	−0.287043	−	0.497174i
$461$	−19.7152	+	34.1477i	−0.918227	+	1.59042i	−0.116121	+	0.993235i	$0.537046\pi$
$461$	−19.7152	+	34.1477i	−0.918227	+	1.59042i	−0.802106	+	0.597181i	$0.796287\pi$
$462$		0			0
$463$	−25.9972			−1.20819			−0.604096	−	0.796912i	$-0.706466\pi$
$463$	−25.9972			−1.20819			−0.604096	+	0.796912i	$0.706466\pi$
$464$	−1.97342			−0.0916140
$465$		0			0
$466$	22.9539			1.06332
$467$	10.4162	+	18.0413i	0.482003	+	0.834854i	0.999787	−	0.0206579i	$-0.00657608\pi$
$467$	10.4162	+	18.0413i	0.482003	+	0.834854i	−0.517784	+	0.855512i	$0.673243\pi$
$468$		0			0
$469$	14.4168	−	3.08817i	0.665706	−	0.142598i
$470$	−14.0712	−	24.3720i	−0.649056	−	1.12420i
$471$		0			0
$472$	−7.86419	−	13.6212i	−0.361979	−	0.626966i
$473$	3.47983	−	6.02724i	0.160003	−	0.277133i
$474$		0			0
$475$	1.18743	−	2.05669i	0.0544831	−	0.0943674i
$476$	−0.995929	+	3.08169i	−0.0456483	+	0.141249i
$477$		0			0
$478$	9.25417	−	16.0287i	0.423276	−	0.733135i
$479$	30.8878			1.41130			0.705650	−	0.708560i	$-0.250655\pi$
$479$	30.8878			1.41130			0.705650	+	0.708560i	$0.250655\pi$
$480$		0			0
$481$	28.2251	−	3.75948i	1.28695	−	0.171418i
$482$	11.1917			0.509766
$483$		0			0
$484$	−4.56317	−	7.90363i	−0.207417	−	0.359256i
$485$	37.5391			1.70456
$486$		0			0
$487$	−11.2136	−	19.4224i	−0.508135	−	0.880115i	−0.999956	−	0.00941874i	$-0.997002\pi$
$487$	−11.2136	−	19.4224i	−0.508135	−	0.880115i	0.491821	−	0.870696i	$-0.336331\pi$
$488$	14.7660			0.668428
$489$		0			0
$490$	−16.1977	+	7.27299i	−0.731736	+	0.328560i
$491$	6.66716	+	11.5479i	0.300885	+	0.521147i	0.976337	−	0.216257i	$-0.0693848\pi$
$491$	6.66716	+	11.5479i	0.300885	+	0.521147i	−0.675452	+	0.737404i	$0.736051\pi$
$492$		0			0
$493$	0.917077	−	1.58842i	0.0413031	−	0.0715390i
$494$	−13.5678	+	1.80718i	−0.610443	+	0.0813089i
$495$		0			0
$496$	4.70818	+	8.15481i	0.211404	+	0.366162i
$497$	−9.79568	+	30.3106i	−0.439396	+	1.35962i
$498$		0			0
$499$	−15.2608	−	26.4324i	−0.683165	−	1.18328i	−0.974010	−	0.226507i	$-0.927269\pi$
$499$	−15.2608	−	26.4324i	−0.683165	−	1.18328i	0.290844	−	0.956770i	$-0.406064\pi$
$500$	−4.45935	−	7.72382i	−0.199428	−	0.345420i
$501$		0			0
$502$	−0.753281	−	1.30472i	−0.0336206	−	0.0582326i
$503$	12.1432	−	21.0327i	0.541441	−	0.937803i	−0.457381	−	0.889271i	$-0.651212\pi$
$503$	12.1432	−	21.0327i	0.541441	−	0.937803i	0.998822	−	0.0485320i	$-0.0154543\pi$
$504$		0			0
$505$	10.6771	+	18.4932i	0.475123	+	0.822937i
$506$	−2.12466	−	3.68002i	−0.0944528	−	0.163597i
$507$		0			0
$508$	4.93193	−	8.54236i	0.218819	−	0.379006i
$509$	11.7319	−	20.3202i	0.520007	−	0.900678i	−0.479723	−	0.877420i	$-0.659263\pi$
$509$	11.7319	−	20.3202i	0.520007	−	0.900678i	0.999729	−	0.0232579i	$-0.00740389\pi$
$510$		0			0
$511$	−6.60590	+	20.4406i	−0.292228	+	0.904237i
$512$	16.1262			0.712684
$513$		0			0
$514$	7.32422	+	12.6859i	0.323058	+	0.559552i
$515$	−3.78007	+	6.54727i	−0.166570	+	0.288507i
$516$		0			0
$517$	3.69788	+	6.40492i	0.162633	+	0.281688i
$518$	−14.9237	−	16.5220i	−0.655712	−	0.725935i
$519$		0			0
$520$	9.98888	−	24.2192i	0.438041	−	1.06208i
$521$	−2.93601	+	5.08531i	−0.128629	+	0.222791i	−0.923146	−	0.384451i	$-0.874391\pi$
$521$	−2.93601	+	5.08531i	−0.128629	+	0.222791i	0.794517	+	0.607242i	$0.207724\pi$
$522$		0			0
$523$	−5.03484	+	8.72060i	−0.220158	+	0.381325i	−0.954856	−	0.297070i	$-0.903991\pi$
$523$	−5.03484	+	8.72060i	−0.220158	+	0.381325i	0.734698	+	0.678395i	$0.237324\pi$
$524$	−3.72426	+	6.45061i	−0.162695	+	0.281796i
$525$		0			0
$526$	−4.25019	+	7.36154i	−0.185317	+	0.320978i
$527$	−8.75182			−0.381235
$528$		0			0
$529$	−6.39532	−	11.0770i	−0.278057	−	0.481610i
$530$	8.60447	−	14.9034i	0.373754	−	0.647361i
$531$		0			0
$532$	−5.46273	−	6.04776i	−0.236839	−	0.262204i
$533$	14.4702	−	35.0846i	0.626773	−	1.51968i
$534$		0			0
$535$	11.9150			0.515132
$536$	17.0099			0.734714
$537$		0			0
$538$	29.4502			1.26969
$539$	4.25671	−	1.91133i	0.183350	−	0.0823267i
$540$		0			0
$541$	19.5150	+	33.8010i	0.839015	+	1.45322i	0.890719	+	0.454555i	$0.150202\pi$
$541$	19.5150	+	33.8010i	0.839015	+	1.45322i	−0.0517032	+	0.998662i	$0.516465\pi$
$542$	5.49776	+	9.52240i	0.236149	+	0.409022i
$543$		0			0
$544$	−3.17252	+	5.49496i	−0.136020	+	0.235594i
$545$	39.4825			1.69125
$546$		0			0
$547$	−30.9149			−1.32183			−0.660913	−	0.750462i	$-0.729831\pi$
$547$	−30.9149			−1.32183			−0.660913	+	0.750462i	$0.729831\pi$
$548$	−3.61173	+	6.25570i	−0.154285	+	0.267230i
$549$		0			0
$550$	0.236736	+	0.410039i	0.0100945	+	0.0174841i
$551$	2.30773	+	3.99710i	0.0983125	+	0.170282i
$552$		0			0
$553$	−7.10561	−	7.86658i	−0.302161	−	0.334521i
$554$	2.29700			0.0975901
$555$		0			0
$556$	8.34612			0.353954
$557$	10.8223			0.458556			0.229278	−	0.973361i	$-0.426363\pi$
$557$	10.8223			0.458556			0.229278	+	0.973361i	$0.426363\pi$
$558$		0			0
$559$	37.3149	−	4.97021i	1.57825	−	0.210218i
$560$	−9.38109	+	2.00949i	−0.396423	+	0.0849163i
$561$		0			0
$562$	1.38840	−	2.40477i	0.0585659	−	0.101439i
$563$	−16.5581	−	28.6794i	−0.697839	−	1.20869i	−0.969214	−	0.246219i	$-0.920812\pi$
$563$	−16.5581	−	28.6794i	−0.697839	−	1.20869i	0.271375	−	0.962474i	$-0.412522\pi$
$564$		0			0
$565$	17.0186			0.715980
$566$	0.922996	−	1.59868i	0.0387964	−	0.0671974i
$567$		0			0
$568$	−18.3750	+	31.8264i	−0.770996	+	1.33540i
$569$	−12.7080	+	22.0110i	−0.532749	+	0.922748i	0.466520	+	0.884511i	$0.345508\pi$
$569$	−12.7080	+	22.0110i	−0.532749	+	0.922748i	−0.999269	+	0.0382374i	$0.987826\pi$
$570$		0			0
$571$	19.9266	−	34.5138i	0.833901	−	1.44436i	−0.0610215	−	0.998136i	$-0.519436\pi$
$571$	19.9266	−	34.5138i	0.833901	−	1.44436i	0.894922	−	0.446222i	$-0.147231\pi$
$572$	−0.792295	+	1.92101i	−0.0331275	+	0.0803214i
$573$		0			0
$574$	−29.0162	+	6.21545i	−1.21111	+	0.259428i
$575$	1.99395	+	3.45362i	0.0831534	+	0.144026i
$576$		0			0
$577$	−3.99457	+	6.91879i	−0.166296	+	0.288033i	−0.937115	−	0.349021i	$-0.886514\pi$
$577$	−3.99457	+	6.91879i	−0.166296	+	0.288033i	0.770819	+	0.637054i	$0.219847\pi$
$578$	−7.98928	−	13.8378i	−0.332310	−	0.575578i
$579$		0			0
$580$	−2.66629			−0.110712
$581$	−21.8479	+	4.67995i	−0.906404	+	0.194157i
$582$		0			0
$583$	−2.26124	+	3.91658i	−0.0936509	+	0.162208i
$584$	−12.3915	+	21.4627i	−0.512764	+	0.888134i
$585$		0			0
$586$	−17.4960	−	30.3039i	−0.722753	−	1.25184i
$587$	−7.56713	−	13.1067i	−0.312329	−	0.540969i	0.666537	−	0.745472i	$-0.267776\pi$
$587$	−7.56713	−	13.1067i	−0.312329	−	0.540969i	−0.978866	+	0.204502i	$0.934442\pi$
$588$		0			0
$589$	11.0115	−	19.0725i	0.453722	−	0.785869i
$590$	6.53510	+	11.3191i	0.269046	+	0.466001i
$591$		0			0
$592$	−6.01502	−	10.4183i	−0.247216	−	0.428190i
$593$	10.5712	+	18.3099i	0.434109	+	0.751898i	0.997222	−	0.0744812i	$-0.0237301\pi$
$593$	10.5712	+	18.3099i	0.434109	+	0.751898i	−0.563114	+	0.826379i	$0.690397\pi$
$594$		0			0
$595$	2.74207	−	8.48474i	0.112414	−	0.347840i
$596$	−5.73259	−	9.92913i	−0.234816	−	0.406713i
$597$		0			0
$598$	8.76350	−	21.2481i	0.358366	−	0.868900i
$599$	−4.21779	+	7.30543i	−0.172334	+	0.298492i	−0.939236	−	0.343273i	$-0.888464\pi$
$599$	−4.21779	+	7.30543i	−0.172334	+	0.298492i	0.766901	+	0.641765i	$0.221798\pi$
$600$		0			0
$601$	8.61342	+	14.9189i	0.351349	+	0.608554i	0.986486	−	0.163845i	$-0.0523898\pi$
$601$	8.61342	+	14.9189i	0.351349	+	0.608554i	−0.635137	+	0.772399i	$0.719056\pi$
$602$	−19.7299	−	21.8429i	−0.804131	−	0.890249i
$603$		0			0
$604$	−14.2171			−0.578488
$605$	12.5637	+	21.7609i	0.510785	+	0.884706i
$606$		0			0
$607$	16.5854			0.673180			0.336590	−	0.941651i	$-0.390726\pi$
$607$	16.5854			0.673180			0.336590	+	0.941651i	$0.390726\pi$
$608$	−7.98330	−	13.8275i	−0.323766	−	0.560779i
$609$		0			0
$610$	−12.2705			−0.496818
$611$	−15.2525	+	36.9814i	−0.617050	+	1.49611i
$612$		0			0
$613$	−17.2057			−0.694934			−0.347467	−	0.937692i	$-0.612958\pi$
$613$	−17.2057			−0.694934			−0.347467	+	0.937692i	$0.612958\pi$
$614$	−15.6966	+	27.1873i	−0.633463	+	1.09719i
$615$		0			0
$616$	5.26387	−	1.12755i	0.212087	−	0.0454304i
$617$	−24.1220	+	41.7805i	−0.971115	+	1.68202i	−0.278913	+	0.960316i	$0.589974\pi$
$617$	−24.1220	+	41.7805i	−0.971115	+	1.68202i	−0.692202	+	0.721704i	$0.743359\pi$
$618$		0			0
$619$	18.8263	−	32.6081i	0.756694	−	1.31063i	−0.187834	−	0.982201i	$-0.560147\pi$
$619$	18.8263	−	32.6081i	0.756694	−	1.31063i	0.944528	−	0.328431i	$-0.106520\pi$
$620$	6.36121	+	11.0179i	0.255472	+	0.442491i
$621$		0			0
$622$	−3.76246	−	6.51678i	−0.150861	−	0.261299i
$623$	1.48204	−	4.58585i	0.0593766	−	0.183728i
$624$		0			0
$625$	13.9443	+	24.1522i	0.557772	+	0.966090i
$626$	17.4300			0.696642
$627$		0			0
$628$	15.8227			0.631393
$629$	11.1810			0.445817
$630$		0			0
$631$	−9.79240	+	16.9609i	−0.389829	+	0.675204i	−0.992426	−	0.122841i	$-0.960799\pi$
$631$	−9.79240	+	16.9609i	−0.389829	+	0.675204i	0.602597	+	0.798046i	$0.294133\pi$
$632$	−6.11491	−	10.5913i	−0.243238	−	0.421301i
$633$		0			0
$634$	20.2053			0.802454
$635$	−13.5790	+	23.5195i	−0.538865	+	0.933342i
$636$		0			0
$637$	22.2364	+	11.9392i	0.881037	+	0.473047i
$638$	−0.920175			−0.0364301
$639$		0			0
$640$	1.49597			0.0591332
$641$	−6.96205	−	12.0586i	−0.274984	−	0.476287i	0.695147	−	0.718868i	$-0.255339\pi$
$641$	−6.96205	−	12.0586i	−0.274984	−	0.476287i	−0.970131	+	0.242581i	$0.922006\pi$
$642$		0			0
$643$	10.3893	−	17.9948i	0.409714	−	0.709645i	−0.585144	−	0.810930i	$-0.698962\pi$
$643$	10.3893	−	17.9948i	0.409714	−	0.709645i	0.994858	+	0.101284i	$0.0322952\pi$
$644$	13.3814	−	2.86639i	0.527303	−	0.112951i
$645$		0			0
$646$	−5.37472			−0.211465
$647$	7.92761			0.311666			0.155833	−	0.987783i	$-0.450194\pi$
$647$	7.92761			0.311666			0.155833	+	0.987783i	$0.450194\pi$
$648$		0			0
$649$	−1.71741	−	2.97464i	−0.0674143	−	0.116765i
$650$	−0.976455	+	2.36752i	−0.0382997	+	0.0928620i
$651$		0			0
$652$	2.93452	+	5.08274i	0.114925	+	0.199055i
$653$	18.1324	−	31.4063i	0.709576	−	1.22902i	−0.255439	−	0.966825i	$-0.582220\pi$
$653$	18.1324	−	31.4063i	0.709576	−	1.22902i	0.965015	−	0.262196i	$-0.0844468\pi$
$654$		0			0
$655$	10.2539	−	17.7603i	0.400654	−	0.693953i
$656$	−16.0340			−0.626023
$657$		0			0
$658$	30.5849	−	6.55147i	1.19232	−	0.255403i
$659$	−11.6108	+	20.1105i	−0.452293	+	0.783395i	−0.998528	−	0.0542371i	$-0.982727\pi$
$659$	−11.6108	+	20.1105i	−0.452293	+	0.783395i	0.546235	+	0.837632i	$0.316061\pi$
$660$		0			0
$661$	−18.8730			−0.734074			−0.367037	−	0.930206i	$-0.619628\pi$
$661$	−18.8730			−0.734074			−0.367037	+	0.930206i	$0.619628\pi$
$662$	−10.1430	+	17.5681i	−0.394217	+	0.682804i
$663$		0			0
$664$	−25.7775			−1.00036
$665$	15.0404	+	16.6512i	0.583242	+	0.645705i
$666$		0			0
$667$	−7.75033			−0.300094
$668$	0.714876	−	1.23820i	0.0276594	−	0.0479075i
$669$		0			0
$670$	−14.1351			−0.546087
$671$	3.22466			0.124487
$672$		0			0
$673$	−6.68396	−	11.5770i	−0.257648	−	0.446259i	0.707964	−	0.706249i	$-0.249614\pi$
$673$	−6.68396	−	11.5770i	−0.257648	−	0.446259i	−0.965611	+	0.259990i	$0.916281\pi$
$674$	1.01435	−	1.75690i	0.0390711	−	0.0676732i
$675$		0			0
$676$	−10.8478	+	2.94198i	−0.417224	+	0.113153i
$677$	−10.5600	−	18.2904i	−0.405853	−	0.702958i	0.588567	−	0.808448i	$-0.299692\pi$
$677$	−10.5600	−	18.2904i	−0.405853	−	0.702958i	−0.994420	+	0.105490i	$0.966359\pi$
$678$		0			0
$679$	−12.8304	+	39.7009i	−0.492385	+	1.52358i
$680$	5.14363	−	8.90903i	0.197249	−	0.341646i
$681$		0			0
$682$	2.19535	+	3.80245i	0.0840642	+	0.145603i
$683$	−16.9165	−	29.3002i	−0.647291	−	1.12114i	−0.983767	−	0.179449i	$-0.942568\pi$
$683$	−16.9165	−	29.3002i	−0.647291	−	1.12114i	0.336476	−	0.941692i	$-0.390765\pi$
$684$		0			0
$685$	9.94409	−	17.2237i	0.379944	−	0.658083i
$686$	−2.15567	−	19.6163i	−0.0823039	−	0.748953i
$687$		0			0
$688$	−7.95214	−	13.7735i	−0.303173	−	0.525110i
$689$	−24.2477	+	3.22971i	−0.923763	+	0.123042i
$690$		0			0
$691$	−13.1762	+	22.8218i	−0.501245	+	0.868181i	0.498754	+	0.866743i	$0.333791\pi$
$691$	−13.1762	+	22.8218i	−0.501245	+	0.868181i	−0.999999	+	0.00143773i	$0.999542\pi$
$692$	5.18231	+	8.97602i	0.197002	+	0.341217i
$693$		0			0
$694$	−22.2493			−0.844573
$695$	−22.9792			−0.871650
$696$		0			0
$697$	7.45122	−	12.9059i	0.282235	−	0.488846i
$698$	−10.2283			−0.387146
$699$		0			0
$700$	−1.49100	+	0.319381i	−0.0563544	+	0.0120715i
$701$	−11.2115			−0.423453			−0.211727	−	0.977329i	$-0.567909\pi$
$701$	−11.2115			−0.423453			−0.211727	+	0.977329i	$0.567909\pi$
$702$		0			0
$703$	−14.0680	+	24.3664i	−0.530583	+	0.918997i
$704$	5.21407			0.196513
$705$		0			0
$706$	−5.76144	+	9.97910i	−0.216835	+	0.375569i
$707$	−23.2075	+	4.97118i	−0.872807	+	0.186961i
$708$		0			0
$709$	11.5011			0.431934			0.215967	−	0.976401i	$-0.430710\pi$
$709$	11.5011			0.431934			0.215967	+	0.976401i	$0.430710\pi$
$710$	15.2695	−	26.4475i	0.573054	−	0.992558i
$711$		0			0
$712$	2.78004	−	4.81517i	0.104186	−	0.180456i
$713$	18.4907	+	32.0268i	0.692481	+	1.19941i
$714$		0			0
$715$	2.18141	−	5.28907i	0.0815800	−	0.197800i
$716$	1.15430	+	1.99931i	0.0431383	+	0.0747176i
$717$		0			0
$718$	−30.8894			−1.15278
$719$	−24.1105			−0.899170			−0.449585	−	0.893238i	$-0.648428\pi$
$719$	−24.1105			−0.899170			−0.449585	+	0.893238i	$0.648428\pi$
$720$		0			0
$721$	−5.63234	−	6.23553i	−0.209759	−	0.232223i
$722$	−3.36032	+	5.82024i	−0.125058	+	0.216607i
$723$		0			0
$724$	−0.325125	−	0.563133i	−0.0120832	−	0.0209287i
$725$	0.863564			0.0320720
$726$		0			0
$727$	27.2156			1.00937			0.504686	−	0.863303i	$-0.331608\pi$
$727$	27.2156			1.00937			0.504686	+	0.863303i	$0.331608\pi$
$728$	22.1998	+	18.8419i	0.822780	+	0.698328i
$729$		0			0
$730$	10.2973	−	17.8354i	0.381119	−	0.660118i
$731$	14.7819			0.546727
$732$		0			0
$733$	−0.965303	−	1.67195i	−0.0356543	−	0.0617550i	0.847648	−	0.530560i	$-0.178018\pi$
$733$	−0.965303	−	1.67195i	−0.0356543	−	0.0617550i	−0.883302	+	0.468805i	$0.844685\pi$
$734$	−17.3543	+	30.0586i	−0.640560	+	1.10948i
$735$		0			0
$736$	26.8113			0.988278
$737$	3.71468			0.136832
$738$		0			0
$739$	22.7217			0.835832			0.417916	−	0.908486i	$-0.362761\pi$
$739$	22.7217			0.835832			0.417916	+	0.908486i	$0.362761\pi$
$740$	−8.12688	−	14.0762i	−0.298750	−	0.517450i
$741$		0			0
$742$	12.8207	+	14.1938i	0.470664	+	0.521070i
$743$	−10.9451	−	18.9574i	−0.401535	−	0.695480i	0.592376	−	0.805662i	$-0.298190\pi$
$743$	−10.9451	−	18.9574i	−0.401535	−	0.695480i	−0.993911	+	0.110182i	$0.964857\pi$
$744$		0			0
$745$	15.7834	+	27.3376i	0.578259	+	1.00157i
$746$	−12.7215	+	22.0344i	−0.465769	+	0.806735i
$747$		0			0
$748$	−0.407981	+	0.706644i	−0.0149173	+	0.0258375i
$749$	−4.07241	+	12.6012i	−0.148803	+	0.460438i
$750$		0			0
$751$	−12.3385	+	21.3710i	−0.450240	+	0.779839i	−0.998401	−	0.0565344i	$-0.981995\pi$
$751$	−12.3385	+	21.3710i	−0.450240	+	0.779839i	0.548161	+	0.836373i	$0.315328\pi$
$752$	16.9009			0.616311
$753$		0			0
$754$	−3.03590	−	3.94406i	−0.110561	−	0.143634i
$755$	39.1438			1.42459
$756$		0			0
$757$	1.04346	+	1.80733i	0.0379252	+	0.0656884i	0.884365	−	0.466796i	$-0.154592\pi$
$757$	1.04346	+	1.80733i	0.0379252	+	0.0656884i	−0.846440	+	0.532484i	$0.821258\pi$
$758$	−10.4298			−0.378827
$759$		0			0
$760$	12.9434	+	22.4187i	0.469507	+	0.813210i
$761$	21.5976			0.782911			0.391455	−	0.920197i	$-0.371972\pi$
$761$	21.5976			0.782911			0.391455	+	0.920197i	$0.371972\pi$
$762$		0			0
$763$	−13.4946	+	41.7563i	−0.488539	+	1.51168i
$764$	−2.22984	−	3.86219i	−0.0806727	−	0.139729i
$765$		0			0
$766$	−7.91537	+	13.7098i	−0.285994	+	0.495356i
$767$	7.08373	−	17.1753i	0.255779	−	0.620165i
$768$		0			0
$769$	2.39533	+	4.14883i	0.0863777	+	0.149611i	0.905977	−	0.423326i	$-0.139137\pi$
$769$	2.39533	+	4.14883i	0.0863777	+	0.149611i	−0.819600	+	0.572937i	$0.805804\pi$
$770$	−4.37425	+	0.936990i	−0.157637	+	0.0337668i
$771$		0			0
$772$	1.23043	+	2.13116i	0.0442841	+	0.0767023i
$773$	5.29480	+	9.17087i	0.190441	+	0.329853i	0.945396	−	0.325923i	$-0.105675\pi$
$773$	5.29480	+	9.17087i	0.190441	+	0.329853i	−0.754956	+	0.655776i	$0.772342\pi$
$774$		0			0
$775$	−2.06028	−	3.56852i	−0.0740076	−	0.128185i
$776$	−24.0675	+	41.6862i	−0.863974	+	1.49645i
$777$		0			0
$778$	−10.2585	−	17.7682i	−0.367784	−	0.637021i
$779$	18.7502	+	32.4764i	0.671797	+	1.16359i
$780$		0			0
$781$	−4.01279	+	6.95036i	−0.143589	+	0.248703i
$782$	4.51265	−	7.81613i	0.161372	−	0.279504i
$783$		0			0
$784$	1.08113	−	10.6081i	0.0386118	−	0.378862i
$785$	−43.5642			−1.55487
$786$		0			0
$787$	15.1155	+	26.1808i	0.538810	+	0.933246i	0.998968	+	0.0454093i	$0.0144592\pi$
$787$	15.1155	+	26.1808i	0.538810	+	0.933246i	−0.460159	+	0.887837i	$0.652207\pi$
$788$	−0.418072	+	0.724121i	−0.0148932	+	0.0257958i
$789$		0			0
$790$	5.08146	+	8.80135i	0.180790	+	0.313138i
$791$	−5.81676	+	17.9987i	−0.206820	+	0.639960i
$792$		0			0
$793$	10.6390	+	13.8216i	0.377803	+	0.490818i
$794$	20.4059	−	35.3441i	0.724179	−	1.25432i
$795$		0			0
$796$	4.05567	−	7.02462i	0.143749	−	0.248981i
$797$	4.57126	−	7.91765i	0.161922	−	0.280457i	−0.773636	−	0.633630i	$-0.781564\pi$
$797$	4.57126	−	7.91765i	0.161922	−	0.280457i	0.935558	+	0.353173i	$0.114897\pi$
$798$		0			0
$799$	−7.85406	+	13.6036i	−0.277857	+	0.481262i
$800$	−2.98739			−0.105620
$801$		0			0
$802$	−18.9730	−	32.8622i	−0.669960	−	1.16040i
$803$	−2.70610	+	4.68711i	−0.0954963	+	0.165404i
$804$		0			0
$805$	−36.8428	+	7.89196i	−1.29854	+	0.278155i
$806$	−9.05505	+	21.9550i	−0.318951	+	0.773332i
$807$		0			0
$808$	−27.3816			−0.963283
$809$	34.3902			1.20909			0.604547	−	0.796569i	$-0.293354\pi$
$809$	34.3902			1.20909			0.604547	+	0.796569i	$0.293354\pi$
$810$		0			0
$811$	−11.9106			−0.418237			−0.209119	−	0.977890i	$-0.567060\pi$
$811$	−11.9106			−0.418237			−0.209119	+	0.977890i	$0.567060\pi$
$812$	0.911304	−	2.81984i	0.0319805	−	0.0989568i
$813$		0			0
$814$	−2.80470	−	4.85789i	−0.0983049	−	0.170269i
$815$	−8.07955	−	13.9942i	−0.283014	−	0.490195i
$816$		0			0
$817$	−18.5985	+	32.2136i	−0.650680	+	1.12701i
$818$	3.37218			0.117906
$819$		0			0
$820$	−21.6635			−0.756523
$821$	1.47638	−	2.55717i	0.0515261	−	0.0892458i	−0.839112	−	0.543959i	$-0.816925\pi$
$821$	1.47638	−	2.55717i	0.0515261	−	0.0892458i	0.890638	+	0.454713i	$0.150258\pi$
$822$		0			0
$823$	21.1527	+	36.6376i	0.737338	+	1.27711i	0.953690	+	0.300791i	$0.0972507\pi$
$823$	21.1527	+	36.6376i	0.737338	+	1.27711i	−0.216352	+	0.976315i	$0.569416\pi$
$824$	−4.84705	−	8.39534i	−0.168855	−	0.292466i
$825$		0			0
$826$	−14.2046	+	3.04271i	−0.494241	+	0.105869i
$827$	23.0380			0.801109			0.400554	−	0.916273i	$-0.368818\pi$
$827$	23.0380			0.801109			0.400554	+	0.916273i	$0.368818\pi$
$828$		0			0
$829$	16.4790			0.572338			0.286169	−	0.958179i	$-0.407618\pi$
$829$	16.4790			0.572338			0.286169	+	0.958179i	$0.407618\pi$
$830$	21.4210			0.743533
$831$		0			0
$832$	17.2026	+	22.3486i	0.596392	+	0.774797i
$833$	8.03616	+	5.79996i	0.278436	+	0.200957i
$834$		0			0
$835$	−1.96825	+	3.40911i	−0.0681142	+	0.117977i
$836$	−1.02664	−	1.77820i	−0.0355072	−	0.0615002i
$837$		0			0
$838$	−23.5552			−0.813701
$839$	8.66147	−	15.0021i	0.299027	−	0.517930i	−0.676887	−	0.736087i	$-0.736671\pi$
$839$	8.66147	−	15.0021i	0.299027	−	0.517930i	0.975914	+	0.218157i	$0.0700046\pi$
$840$		0			0
$841$	13.6608	−	23.6613i	0.471064	−	0.815906i
$842$	4.12909	−	7.15179i	0.142298	−	0.246467i
$843$		0			0
$844$	−8.97068	+	15.5377i	−0.308784	+	0.534829i
$845$	29.8671	−	8.10009i	1.02746	−	0.278652i
$846$		0			0
$847$	−27.3082	+	5.84957i	−0.938320	+	0.200994i
$848$	5.16740	+	8.95020i	0.177449	+	0.307351i
$849$		0			0
$850$	−0.502812	+	0.870896i	−0.0172463	+	0.0298715i
$851$	−23.6231	−	40.9164i	−0.809789	−	1.40260i
$852$		0			0
$853$	−47.0511			−1.61100			−0.805499	−	0.592597i	$-0.798103\pi$
$853$	−47.0511			−1.61100			−0.805499	+	0.592597i	$0.798103\pi$
$854$	4.19390	−	12.9771i	0.143512	−	0.444069i
$855$		0			0
$856$	−7.63912	+	13.2314i	−0.261100	+	0.452238i
$857$	11.3602	−	19.6764i	0.388056	−	0.672133i	−0.604132	−	0.796884i	$-0.706480\pi$
$857$	11.3602	−	19.6764i	0.388056	−	0.672133i	0.992188	+	0.124751i	$0.0398133\pi$
$858$		0			0
$859$	−18.8507	−	32.6504i	−0.643177	−	1.11402i	−0.984719	−	0.174149i	$-0.944282\pi$
$859$	−18.8507	−	32.6504i	−0.643177	−	1.11402i	0.341542	−	0.939867i	$-0.389051\pi$
$860$	−10.7441	−	18.6094i	−0.366371	−	0.634574i
$861$		0			0
$862$	18.4123	−	31.8910i	0.627124	−	1.08621i
$863$	19.9474	+	34.5499i	0.679018	+	1.17609i	0.975277	+	0.220986i	$0.0709276\pi$
$863$	19.9474	+	34.5499i	0.679018	+	1.17609i	−0.296259	+	0.955108i	$0.595739\pi$
$864$		0			0
$865$	−14.2683	−	24.7135i	−0.485138	−	0.840283i
$866$	13.0413	+	22.5882i	0.443161	+	0.767577i
$867$		0			0
$868$	−13.8266	+	2.96175i	−0.469306	+	0.100528i
$869$	−1.33540	−	2.31298i	−0.0453003	−	0.0784624i
$870$		0			0
$871$	12.2557	+	15.9219i	0.415269	+	0.539492i
$872$	−25.3135	+	43.8443i	−0.857225	+	1.48476i
$873$		0			0
$874$	11.3556	+	19.6685i	0.384109	+	0.665296i
$875$	−26.6869	+	5.71649i	−0.902181	+	0.193253i
$876$		0			0
$877$	−15.2544			−0.515106			−0.257553	−	0.966264i	$-0.582916\pi$
$877$	−15.2544			−0.515106			−0.257553	+	0.966264i	$0.582916\pi$
$878$	−5.71509	−	9.89883i	−0.192875	−	0.334069i
$879$		0			0
$880$	−2.41716			−0.0814824
$881$	25.8195	+	44.7207i	0.869881	+	1.50668i	0.862117	+	0.506709i	$0.169138\pi$
$881$	25.8195	+	44.7207i	0.869881	+	1.50668i	0.00776438	+	0.999970i	$0.497528\pi$
$882$		0			0
$883$	27.4588			0.924062			0.462031	−	0.886864i	$-0.347121\pi$
$883$	27.4588			0.924062			0.462031	+	0.886864i	$0.347121\pi$
$884$	−4.37486	+	0.582716i	−0.147142	+	0.0195989i
$885$		0			0
$886$	−42.4864			−1.42736
$887$	16.4316	−	28.4603i	0.551718	−	0.955604i	−0.446432	−	0.894817i	$-0.647306\pi$
$887$	16.4316	−	28.4603i	0.551718	−	0.955604i	0.998151	−	0.0607868i	$-0.0193610\pi$
$888$		0			0
$889$	−20.2328	−	22.3996i	−0.678586	−	0.751260i
$890$	−2.31020	+	4.00138i	−0.0774381	+	0.134127i
$891$		0			0
$892$	3.50595	−	6.07249i	0.117388	−	0.203322i
$893$	−19.7639	−	34.2321i	−0.661375	−	1.14553i
$894$		0			0
$895$	−3.17811	−	5.50465i	−0.106233	−	0.184000i
$896$	−0.511302	+	1.58212i	−0.0170814	+	0.0528548i
$897$		0			0
$898$	16.2806	+	28.1989i	0.543291	+	0.941008i
$899$	8.00817			0.267088
$900$		0			0
$901$	−9.60544			−0.320004
$902$	−7.47640			−0.248937
$903$		0			0
$904$	−10.9112	+	18.8988i	−0.362901	+	0.628564i
$905$	0.895159	+	1.55046i	0.0297561	+	0.0515391i
$906$		0			0
$907$	44.8192			1.48820			0.744098	−	0.668071i	$-0.232880\pi$
$907$	44.8192			1.48820			0.744098	+	0.668071i	$0.232880\pi$
$908$	−0.949880	+	1.64524i	−0.0315229	+	0.0545992i
$909$		0			0
$910$	−18.4479	−	15.6575i	−0.611543	−	0.519042i
$911$	−31.4169			−1.04089			−0.520445	−	0.853895i	$-0.674234\pi$
$911$	−31.4169			−1.04089			−0.520445	+	0.853895i	$0.674234\pi$
$912$		0			0
$913$	−5.62939			−0.186306
$914$	−8.54291	−	14.7968i	−0.282574	−	0.489433i
$915$		0			0
$916$	8.77952	−	15.2066i	0.290084	−	0.502439i
$917$	15.2784	+	16.9147i	0.504538	+	0.558572i
$918$		0			0
$919$	37.3862			1.23326			0.616628	−	0.787255i	$-0.288498\pi$
$919$	37.3862			1.23326			0.616628	+	0.787255i	$0.288498\pi$
$920$	−43.4695			−1.43315
$921$		0			0
$922$	21.0076	+	36.3863i	0.691849	+	1.19832i
$923$	−43.0299	+	5.73144i	−1.41635	+	0.188653i
$924$		0			0
$925$	2.63215	+	4.55902i	0.0865446	+	0.149900i
$926$	−13.8507	+	23.9902i	−0.455163	+	0.788366i
$927$		0			0
$928$	2.90295	−	5.02805i	0.0952938	−	0.165054i
$929$	23.1574			0.759768			0.379884	−	0.925034i	$-0.375964\pi$
$929$	23.1574			0.759768			0.379884	+	0.925034i	$0.375964\pi$
$930$		0			0
$931$	−22.7507	+	10.2154i	−0.745624	+	0.334796i
$932$	−9.31241	+	16.1296i	−0.305038	+	0.528342i
$933$		0			0
$934$	22.1980			0.726342
$935$	1.12329	−	1.94559i	0.0367354	−	0.0636275i
$936$		0			0
$937$	−20.1142			−0.657103			−0.328552	−	0.944486i	$-0.606560\pi$
$937$	−20.1142			−0.657103			−0.328552	+	0.944486i	$0.606560\pi$
$938$	4.83120	−	14.9491i	0.157744	−	0.488106i
$939$		0			0
$940$	22.8347			0.744787
$941$	−9.41116	+	16.3006i	−0.306795	+	0.531384i	−0.977659	−	0.210196i	$-0.932590\pi$
$941$	−9.41116	+	16.3006i	−0.306795	+	0.531384i	0.670864	+	0.741580i	$0.265923\pi$
$942$		0			0
$943$	−62.9712			−2.05062
$944$	−7.84929			−0.255473
$945$		0			0
$946$	−3.70795	−	6.42236i	−0.120556	−	0.208809i
$947$	−12.6734	+	21.9511i	−0.411832	+	0.713313i	−0.995090	−	0.0989733i	$-0.968444\pi$
$947$	−12.6734	+	21.9511i	−0.411832	+	0.713313i	0.583258	+	0.812287i	$0.301777\pi$
$948$		0			0
$949$	−29.0181	+	3.86510i	−0.941966	+	0.125467i
$950$	−1.26527	−	2.19152i	−0.0410509	−	0.0711022i
$951$		0			0
$952$	7.66406	+	8.48484i	0.248394	+	0.274995i
$953$	0.132751	−	0.229931i	0.00430021	−	0.00744818i	−0.863867	−	0.503719i	$-0.831965\pi$
$953$	0.132751	−	0.229931i	0.00430021	−	0.00744818i	0.868168	+	0.496271i	$0.165298\pi$
$954$		0			0
$955$	6.13937	+	10.6337i	0.198665	+	0.344098i
$956$	7.50883	+	13.0057i	0.242853	+	0.420634i
$957$		0			0
$958$	16.4563	−	28.5032i	0.531680	−	0.920897i
$959$	14.8168	+	16.4036i	0.478459	+	0.529699i
$960$		0			0
$961$	−3.60583	−	6.24549i	−0.116317	−	0.201467i
$962$	11.5684	−	28.0490i	0.372982	−	0.904336i
$963$		0			0
$964$	−4.54045	+	7.86430i	−0.146238	+	0.253292i
$965$	−3.38771	−	5.86769i	−0.109054	−	0.188888i
$966$		0			0
$967$	15.3845			0.494732			0.247366	−	0.968922i	$-0.420435\pi$
$967$	15.3845			0.494732			0.247366	+	0.968922i	$0.420435\pi$
$968$	−32.2199			−1.03559
$969$		0			0
$970$	20.0000	−	34.6410i	0.642161	−	1.11226i
$971$	46.5181			1.49284			0.746418	−	0.665478i	$-0.231772\pi$
$971$	46.5181			1.49284			0.746418	+	0.665478i	$0.231772\pi$
$972$		0			0
$973$	7.85400	−	24.3025i	0.251788	−	0.779103i
$974$	−23.8973			−0.765720
$975$		0			0
$976$	3.68452	−	6.38177i	0.117939	−	0.204276i
$977$	−10.5495			−0.337507			−0.168754	−	0.985658i	$-0.553974\pi$
$977$	−10.5495			−0.337507			−0.168754	+	0.985658i	$0.553974\pi$
$978$		0			0
$979$	0.607116	−	1.05156i	0.0194035	−	0.0336079i
$980$	1.46071	−	14.3326i	0.0466607	−	0.457839i
$981$		0			0
$982$	14.2085			0.453410
$983$	16.6152	−	28.7783i	0.529942	−	0.917887i	−0.469448	−	0.882960i	$-0.655547\pi$
$983$	16.6152	−	28.7783i	0.529942	−	0.917887i	0.999390	−	0.0349264i	$-0.0111197\pi$
$984$		0			0
$985$	1.15107	−	1.99371i	0.0366761	−	0.0635248i
$986$	−0.977196	−	1.69255i	−0.0311203	−	0.0539019i
$987$		0			0
$988$	4.23455	−	10.2671i	0.134719	−	0.326641i
$989$	−31.2309	−	54.0934i	−0.993083	−	1.72007i
$990$		0			0
$991$	43.7630			1.39018			0.695089	−	0.718923i	$-0.255365\pi$
$991$	43.7630			1.39018			0.695089	+	0.718923i	$0.255365\pi$
$992$	−27.7033			−0.879580
$993$		0			0
$994$	22.7517	+	25.1883i	0.721639	+	0.798923i
$995$	−11.1664	+	19.3407i	−0.353998	+	0.613142i
$996$		0			0
$997$	−26.0411	−	45.1045i	−0.824729	−	1.42847i	−0.902126	−	0.431473i	$-0.857994\pi$
$997$	−26.0411	−	45.1045i	−0.824729	−	1.42847i	0.0773967	−	0.997000i	$-0.475339\pi$
$998$	−32.5224			−1.02948
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.n.e.172.6		16
3.2	odd	2		273.2.j.b.172.3	yes	16
7.2	even	3		819.2.s.e.289.3		16
13.9	even	3		819.2.s.e.802.3		16
21.2	odd	6		273.2.l.b.16.6	yes	16
39.35	odd	6		273.2.l.b.256.6	yes	16
91.9	even	3	inner	819.2.n.e.100.6		16
273.191	odd	6		273.2.j.b.100.3	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.b.100.3	✓	16	273.191	odd	6
273.2.j.b.172.3	yes	16	3.2	odd	2
273.2.l.b.16.6	yes	16	21.2	odd	6
273.2.l.b.256.6	yes	16	39.35	odd	6
819.2.n.e.100.6		16	91.9	even	3	inner
819.2.n.e.172.6		16	1.1	even	1	trivial
819.2.s.e.289.3		16	7.2	even	3
819.2.s.e.802.3		16	13.9	even	3

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.n (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.532778 - 0.922798i) q^{2} +(0.432296 + 0.748758i) q^{4} +(-1.19023 - 2.06154i) q^{5} +(2.58706 - 0.554165i) q^{7} +3.05238 q^{8} +O(q^{10})\)	\(q+(0.532778 - 0.922798i) q^{2} +(0.432296 + 0.748758i) q^{4} +(-1.19023 - 2.06154i) q^{5} +(2.58706 - 0.554165i) q^{7} +3.05238 q^{8} -2.53651 q^{10} +0.666590 q^{11} +(2.19926 + 2.85714i) q^{13} +(0.866948 - 2.68258i) q^{14} +(0.761650 - 1.31922i) q^{16} +(0.707897 + 1.22611i) q^{17} -3.56270 q^{19} +(1.02906 - 1.78239i) q^{20} +(0.355145 - 0.615128i) q^{22} +(2.99126 - 5.18102i) q^{23} +(-0.333295 + 0.577284i) q^{25} +(3.80828 - 0.507250i) q^{26} +(1.53331 + 1.69752i) q^{28} +(-0.647747 - 1.12193i) q^{29} +(-3.09078 + 5.35339i) q^{31} +(2.24080 + 3.88118i) q^{32} +1.50861 q^{34} +(-4.22163 - 4.67375i) q^{35} +(3.94868 - 6.83932i) q^{37} +(-1.89813 + 3.28765i) q^{38} +(-3.63304 - 6.29260i) q^{40} +(-5.26293 - 9.11566i) q^{41} +(5.22034 - 9.04190i) q^{43} +(0.288164 + 0.499115i) q^{44} +(-3.18736 - 5.52067i) q^{46} +(5.54746 + 9.60848i) q^{47} +(6.38580 - 2.86732i) q^{49} +(0.355145 + 0.615128i) q^{50} +(-1.18858 + 2.88184i) q^{52} +(-3.39224 + 5.87554i) q^{53} +(-0.793396 - 1.37420i) q^{55} +(7.89671 - 1.69152i) q^{56} -1.38042 q^{58} +(-2.57641 - 4.46248i) q^{59} +4.83755 q^{61} +(3.29340 + 5.70433i) q^{62} +7.82199 q^{64} +(3.27249 - 7.93451i) q^{65} +5.57265 q^{67} +(-0.612042 + 1.06009i) q^{68} +(-6.56212 + 1.40565i) q^{70} +(-6.01988 + 10.4267i) q^{71} +(-4.05962 + 7.03147i) q^{73} +(-4.20754 - 7.28767i) q^{74} +(-1.54014 - 2.66760i) q^{76} +(1.72451 - 0.369401i) q^{77} +(-2.00333 - 3.46986i) q^{79} -3.62615 q^{80} -11.2159 q^{82} -8.44505 q^{83} +(1.68512 - 2.91872i) q^{85} +(-5.56257 - 9.63465i) q^{86} +2.03469 q^{88} +(0.910778 - 1.57751i) q^{89} +(7.27295 + 6.17286i) q^{91} +5.17244 q^{92} +11.8222 q^{94} +(4.24043 + 7.34465i) q^{95} +(-7.88484 + 13.6569i) q^{97} +(0.756256 - 7.42045i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{4} + q^{7} - 12 q^{8}+O(q^{10}) \) 16 * q - 6 * q^4 + q^7 - 12 * q^8	\( 16 q - 6 q^{4} + q^{7} - 12 q^{8} + 8 q^{10} - 4 q^{11} + 5 q^{13} + 7 q^{14} - 6 q^{16} + 2 q^{17} + 22 q^{19} + 20 q^{20} + 7 q^{22} - 4 q^{23} + 2 q^{25} + 6 q^{26} - 7 q^{28} - 15 q^{29} + 3 q^{31} - 3 q^{32} - 68 q^{34} + 12 q^{35} + 4 q^{37} - 2 q^{38} - 25 q^{40} - 19 q^{41} + 11 q^{43} + 16 q^{44} + 2 q^{46} - 5 q^{47} + 13 q^{49} + 7 q^{50} + 36 q^{52} - 36 q^{53} - 15 q^{55} - 39 q^{56} - 40 q^{58} + 17 q^{59} + 44 q^{61} + 6 q^{62} - 20 q^{64} + 21 q^{65} - 52 q^{67} - 5 q^{68} + 46 q^{70} - 9 q^{71} - 6 q^{73} - 15 q^{74} - 16 q^{76} + 36 q^{77} + 16 q^{79} - 56 q^{80} + 2 q^{82} - 36 q^{83} - 4 q^{85} - 16 q^{86} - 48 q^{88} - 20 q^{89} - 7 q^{91} + 94 q^{92} + 40 q^{94} + 7 q^{97} + 3 q^{98}+O(q^{100}) \) 16 * q - 6 * q^4 + q^7 - 12 * q^8 + 8 * q^10 - 4 * q^11 + 5 * q^13 + 7 * q^14 - 6 * q^16 + 2 * q^17 + 22 * q^19 + 20 * q^20 + 7 * q^22 - 4 * q^23 + 2 * q^25 + 6 * q^26 - 7 * q^28 - 15 * q^29 + 3 * q^31 - 3 * q^32 - 68 * q^34 + 12 * q^35 + 4 * q^37 - 2 * q^38 - 25 * q^40 - 19 * q^41 + 11 * q^43 + 16 * q^44 + 2 * q^46 - 5 * q^47 + 13 * q^49 + 7 * q^50 + 36 * q^52 - 36 * q^53 - 15 * q^55 - 39 * q^56 - 40 * q^58 + 17 * q^59 + 44 * q^61 + 6 * q^62 - 20 * q^64 + 21 * q^65 - 52 * q^67 - 5 * q^68 + 46 * q^70 - 9 * q^71 - 6 * q^73 - 15 * q^74 - 16 * q^76 + 36 * q^77 + 16 * q^79 - 56 * q^80 + 2 * q^82 - 36 * q^83 - 4 * q^85 - 16 * q^86 - 48 * q^88 - 20 * q^89 - 7 * q^91 + 94 * q^92 + 40 * q^94 + 7 * q^97 + 3 * q^98

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