LMFDB - Embedded newform 819.2.j.h.235.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(235,819)]

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, 4, 0]))

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

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

chi := DirichletCharacter("819.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.j (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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 8x^{8} + 7x^{7} + 41x^{6} + 18x^{5} + 58x^{4} + 28x^{3} + 64x^{2} + 16x + 4 $ x^10 - x^9 + 8x^8 + 7x^7 + 41x^6 + 18x^5 + 58x^4 + 28x^3 + 64x^2 + 16x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.3
Root			$-0.132804 - 0.230024i$ of defining polynomial
Character	$\chi$	$=$	819.235
Dual form			819.2.j.h.352.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.632804 + 1.09605i) q^{2} +(0.199118 - 0.344882i) q^{4} +(-1.45130 - 2.51373i) q^{5} +(-1.29536 + 2.30696i) q^{7} +3.03523 q^{8} +O(q^{10})$	\(q+(0.632804 + 1.09605i) q^{2} +(0.199118 - 0.344882i) q^{4} +(-1.45130 - 2.51373i) q^{5} +(-1.29536 + 2.30696i) q^{7} +3.03523 q^{8} +(1.83678 - 3.18139i) q^{10} +(1.01828 - 1.76372i) q^{11} +1.00000 q^{13} +(-3.34825 + 0.0400756i) q^{14} +(1.52247 + 2.63699i) q^{16} +(1.99933 - 3.46294i) q^{17} +(-3.48105 - 6.02935i) q^{19} -1.15592 q^{20} +2.57749 q^{22} +(-0.313640 - 0.543240i) q^{23} +(-1.71254 + 2.96621i) q^{25} +(0.632804 + 1.09605i) q^{26} +(0.537699 + 0.906101i) q^{28} -1.09606 q^{29} +(5.21624 - 9.03479i) q^{31} +(1.10838 - 1.91977i) q^{32} +5.06074 q^{34} +(7.67901 - 0.0919110i) q^{35} +(1.54268 + 2.67201i) q^{37} +(4.40565 - 7.63080i) q^{38} +(-4.40502 - 7.62973i) q^{40} +0.521150 q^{41} +0.329024 q^{43} +(-0.405516 - 0.702374i) q^{44} +(0.396945 - 0.687530i) q^{46} +(5.27284 + 9.13283i) q^{47} +(-3.64409 - 5.97667i) q^{49} -4.33482 q^{50} +(0.199118 - 0.344882i) q^{52} +(3.55950 - 6.16523i) q^{53} -5.91133 q^{55} +(-3.93171 + 7.00214i) q^{56} +(-0.693593 - 1.20134i) q^{58} +(1.01828 - 1.76372i) q^{59} +(-1.20041 - 2.07917i) q^{61} +13.2034 q^{62} +8.89542 q^{64} +(-1.45130 - 2.51373i) q^{65} +(-7.34709 + 12.7255i) q^{67} +(-0.796204 - 1.37907i) q^{68} +(4.96005 + 8.35841i) q^{70} -3.60141 q^{71} +(-1.48786 + 2.57706i) q^{73} +(-1.95243 + 3.38172i) q^{74} -2.77255 q^{76} +(2.74978 + 4.63378i) q^{77} +(4.38075 + 7.58769i) q^{79} +(4.41912 - 7.65414i) q^{80} +(0.329786 + 0.571206i) q^{82} -12.8039 q^{83} -11.6065 q^{85} +(0.208208 + 0.360627i) q^{86} +(3.09072 - 5.35328i) q^{88} +(-1.34049 - 2.32180i) q^{89} +(-1.29536 + 2.30696i) q^{91} -0.249805 q^{92} +(-6.67335 + 11.5586i) q^{94} +(-10.1041 + 17.5008i) q^{95} -2.32902 q^{97} +(4.24472 - 7.77617i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} - 8 q^{4} + 2 q^{5} + q^{7} - 18 q^{8}+O(q^{10}) $ 10 * q + 4 * q^2 - 8 * q^4 + 2 * q^5 + q^7 - 18 * q^8	$ 10 q + 4 q^{2} - 8 q^{4} + 2 q^{5} + q^{7} - 18 q^{8} + 5 q^{10} + 11 q^{11} + 10 q^{13} - 10 q^{14} - 10 q^{16} - 5 q^{17} - 9 q^{19} - 2 q^{20} + 16 q^{22} + 10 q^{23} - 9 q^{25} + 4 q^{26} + 37 q^{28} + 6 q^{29} + 6 q^{31} + 22 q^{32} - 44 q^{34} + 4 q^{35} - 4 q^{37} - 10 q^{38} - 28 q^{40} - 28 q^{41} + 4 q^{43} - 3 q^{46} + q^{47} - 11 q^{49} - 18 q^{50} - 8 q^{52} + 17 q^{53} + 21 q^{56} + 27 q^{58} + 11 q^{59} + 11 q^{61} + 46 q^{62} + 18 q^{64} + 2 q^{65} - 13 q^{67} - 32 q^{68} + 49 q^{70} - 30 q^{71} - 33 q^{74} + 16 q^{76} + 46 q^{77} - 2 q^{79} + 55 q^{80} - 34 q^{82} - 12 q^{83} - 44 q^{85} + 28 q^{86} + 3 q^{88} - 4 q^{89} + q^{91} - 42 q^{92} - 20 q^{94} - 12 q^{95} - 24 q^{97} + 7 q^{98}+O(q^{100}) $ 10 * q + 4 * q^2 - 8 * q^4 + 2 * q^5 + q^7 - 18 * q^8 + 5 * q^10 + 11 * q^11 + 10 * q^13 - 10 * q^14 - 10 * q^16 - 5 * q^17 - 9 * q^19 - 2 * q^20 + 16 * q^22 + 10 * q^23 - 9 * q^25 + 4 * q^26 + 37 * q^28 + 6 * q^29 + 6 * q^31 + 22 * q^32 - 44 * q^34 + 4 * q^35 - 4 * q^37 - 10 * q^38 - 28 * q^40 - 28 * q^41 + 4 * q^43 - 3 * q^46 + q^47 - 11 * q^49 - 18 * q^50 - 8 * q^52 + 17 * q^53 + 21 * q^56 + 27 * q^58 + 11 * q^59 + 11 * q^61 + 46 * q^62 + 18 * q^64 + 2 * q^65 - 13 * q^67 - 32 * q^68 + 49 * q^70 - 30 * q^71 - 33 * q^74 + 16 * q^76 + 46 * q^77 - 2 * q^79 + 55 * q^80 - 34 * q^82 - 12 * q^83 - 44 * q^85 + 28 * q^86 + 3 * q^88 - 4 * q^89 + q^91 - 42 * q^92 - 20 * q^94 - 12 * q^95 - 24 * q^97 + 7 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.632804	+	1.09605i	0.447460	+	0.775024i	0.998220	−	0.0596401i	$-0.0189953\pi$
$2$	0.632804	+	1.09605i	0.447460	+	0.775024i	−0.550760	+	0.834664i	$0.685662\pi$
$3$		0			0
$3$		0			0
$4$	0.199118	−	0.344882i	0.0995588	−	0.172441i
$5$	−1.45130	−	2.51373i	−0.649041	−	1.12417i	−0.983352	−	0.181709i	$-0.941837\pi$
$5$	−1.45130	−	2.51373i	−0.649041	−	1.12417i	0.334311	−	0.942463i	$-0.391496\pi$
$6$		0			0
$7$	−1.29536	+	2.30696i	−0.489599	+	0.871948i
$7$	−1.29536	+	2.30696i	−0.489599	+	0.871948i
$8$	3.03523			1.07311
$9$		0			0
$10$	1.83678	−	3.18139i	0.580840	−	1.00604i
$11$	1.01828	−	1.76372i	0.307024	−	0.531780i	−0.670686	−	0.741741i	$-0.734000\pi$
$11$	1.01828	−	1.76372i	0.307024	−	0.531780i	0.977710	+	0.209961i	$0.0673336\pi$
$12$		0			0
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	−3.34825	+	0.0400756i	−0.894856	+	0.0107107i
$15$		0			0
$16$	1.52247	+	2.63699i	0.380617	+	0.659249i
$17$	1.99933	−	3.46294i	0.484909	−	0.839887i	−0.514941	−	0.857226i	$-0.672186\pi$
$17$	1.99933	−	3.46294i	0.484909	−	0.839887i	0.999850	+	0.0173386i	$0.00551934\pi$
$18$		0			0
$19$	−3.48105	−	6.02935i	−0.798608	−	1.38323i	−0.920523	−	0.390688i	$-0.872237\pi$
$19$	−3.48105	−	6.02935i	−0.798608	−	1.38323i	0.121915	−	0.992540i	$-0.461096\pi$
$20$	−1.15592			−0.258471
$21$		0			0
$22$	2.57749			0.549523
$23$	−0.313640	−	0.543240i	−0.0653985	−	0.113273i	0.831472	−	0.555566i	$-0.187499\pi$
$23$	−0.313640	−	0.543240i	−0.0653985	−	0.113273i	−0.896871	+	0.442293i	$0.854165\pi$
$24$		0			0
$25$	−1.71254	+	2.96621i	−0.342509	+	0.593243i
$26$	0.632804	+	1.09605i	0.124103	+	0.214953i
$27$		0			0
$28$	0.537699	+	0.906101i	0.101615	+	0.171237i
$29$	−1.09606			−0.203534			−0.101767	−	0.994808i	$-0.532450\pi$
$29$	−1.09606			−0.203534			−0.101767	+	0.994808i	$0.532450\pi$
$30$		0			0
$31$	5.21624	−	9.03479i	0.936864	−	1.62270i	0.165589	−	0.986195i	$-0.447047\pi$
$31$	5.21624	−	9.03479i	0.936864	−	1.62270i	0.771275	−	0.636502i	$-0.219619\pi$
$32$	1.10838	−	1.91977i	0.195935	−	0.339370i
$33$		0			0
$34$	5.06074			0.867910
$35$	7.67901	−	0.0919110i	1.29799	−	0.0155358i
$36$		0			0
$37$	1.54268	+	2.67201i	0.253616	+	0.439275i	0.964519	−	0.264015i	$-0.0850468\pi$
$37$	1.54268	+	2.67201i	0.253616	+	0.439275i	−0.710903	+	0.703290i	$0.751713\pi$
$38$	4.40565	−	7.63080i	0.714690	−	1.23788i
$39$		0			0
$40$	−4.40502	−	7.62973i	−0.696496	−	1.20637i
$41$	0.521150			0.0813900			0.0406950	−	0.999172i	$-0.487043\pi$
$41$	0.521150			0.0813900			0.0406950	+	0.999172i	$0.487043\pi$
$42$		0			0
$43$	0.329024			0.0501757			0.0250879	−	0.999685i	$-0.492013\pi$
$43$	0.329024			0.0501757			0.0250879	+	0.999685i	$0.492013\pi$
$44$	−0.405516	−	0.702374i	−0.0611338	−	0.105887i
$45$		0			0
$46$	0.396945	−	0.687530i	0.0585264	−	0.101371i
$47$	5.27284	+	9.13283i	0.769123	+	1.33216i	0.938039	+	0.346530i	$0.112640\pi$
$47$	5.27284	+	9.13283i	0.769123	+	1.33216i	−0.168916	+	0.985630i	$0.554027\pi$
$48$		0			0
$49$	−3.64409	−	5.97667i	−0.520585	−	0.853810i
$50$	−4.33482			−0.613036
$51$		0			0
$52$	0.199118	−	0.344882i	0.0276126	−	0.0478265i
$53$	3.55950	−	6.16523i	0.488935	−	0.846860i	−0.510984	−	0.859590i	$-0.670719\pi$
$53$	3.55950	−	6.16523i	0.488935	−	0.846860i	0.999919	+	0.0127302i	$0.00405225\pi$
$54$		0			0
$55$	−5.91133			−0.797084
$56$	−3.93171	+	7.00214i	−0.525396	+	0.935700i
$57$		0			0
$58$	−0.693593	−	1.20134i	−0.0910733	−	0.157744i
$59$	1.01828	−	1.76372i	0.132569	−	0.229616i	−0.792097	−	0.610395i	$-0.791011\pi$
$59$	1.01828	−	1.76372i	0.132569	−	0.229616i	0.924666	+	0.380779i	$0.124344\pi$
$60$		0			0
$61$	−1.20041	−	2.07917i	−0.153696	−	0.266210i	0.778887	−	0.627164i	$-0.215784\pi$
$61$	−1.20041	−	2.07917i	−0.153696	−	0.266210i	−0.932584	+	0.360954i	$0.882451\pi$
$62$	13.2034			1.67684
$63$		0			0
$64$	8.89542			1.11193
$65$	−1.45130	−	2.51373i	−0.180012	−	0.311789i
$66$		0			0
$67$	−7.34709	+	12.7255i	−0.897589	+	1.55467i	−0.0670226	+	0.997751i	$0.521350\pi$
$67$	−7.34709	+	12.7255i	−0.897589	+	1.55467i	−0.830567	+	0.556919i	$0.811983\pi$
$68$	−0.796204	−	1.37907i	−0.0965539	−	0.167236i
$69$		0			0
$70$	4.96005	+	8.35841i	0.592839	+	0.999021i
$71$	−3.60141			−0.427409			−0.213704	−	0.976898i	$-0.568553\pi$
$71$	−3.60141			−0.427409			−0.213704	+	0.976898i	$0.568553\pi$
$72$		0			0
$73$	−1.48786	+	2.57706i	−0.174141	+	0.301622i	−0.939864	−	0.341550i	$-0.889048\pi$
$73$	−1.48786	+	2.57706i	−0.174141	+	0.301622i	0.765722	+	0.643171i	$0.222382\pi$
$74$	−1.95243	+	3.38172i	−0.226966	+	0.393117i
$75$		0			0
$76$	−2.77255			−0.318034
$77$	2.74978	+	4.63378i	0.313366	+	0.528068i
$78$		0			0
$79$	4.38075	+	7.58769i	0.492873	+	0.853681i	0.999966	−	0.00820995i	$-0.00261334\pi$
$79$	4.38075	+	7.58769i	0.492873	+	0.853681i	−0.507093	+	0.861891i	$0.669280\pi$
$80$	4.41912	−	7.65414i	0.494073	−	0.855759i
$81$		0			0
$82$	0.329786	+	0.571206i	0.0364188	+	0.0630792i
$83$	−12.8039			−1.40541			−0.702703	−	0.711483i	$-0.748024\pi$
$83$	−12.8039			−1.40541			−0.702703	+	0.711483i	$0.748024\pi$
$84$		0			0
$85$	−11.6065			−1.25890
$86$	0.208208	+	0.360627i	0.0224516	+	0.0388874i
$87$		0			0
$88$	3.09072	−	5.35328i	0.329471	−	0.570661i
$89$	−1.34049	−	2.32180i	−0.142092	−	0.246110i	0.786192	−	0.617982i	$-0.212050\pi$
$89$	−1.34049	−	2.32180i	−0.142092	−	0.246110i	−0.928284	+	0.371872i	$0.878716\pi$
$90$		0			0
$91$	−1.29536	+	2.30696i	−0.135790	+	0.241835i
$92$	−0.249805			−0.0260440
$93$		0			0
$94$	−6.67335	+	11.5586i	−0.688304	+	1.19218i
$95$	−10.1041	+	17.5008i	−1.03666	+	1.79554i
$96$		0			0
$97$	−2.32902			−0.236477			−0.118238	−	0.992985i	$-0.537725\pi$
$97$	−2.32902			−0.236477			−0.118238	+	0.992985i	$0.537725\pi$
$98$	4.24472	−	7.77617i	0.428782	−	0.785512i
$99$		0			0
$100$	0.681995	+	1.18125i	0.0681995	+	0.118125i
$101$	0.726620	−	1.25854i	0.0723014	−	0.125230i	−0.827608	−	0.561306i	$-0.810299\pi$
$101$	0.726620	−	1.25854i	0.0723014	−	0.125230i	0.899910	+	0.436077i	$0.143632\pi$
$102$		0			0
$103$	5.81765	+	10.0765i	0.573230	+	0.992864i	0.996231	+	0.0867346i	$0.0276432\pi$
$103$	5.81765	+	10.0765i	0.573230	+	0.992864i	−0.423001	+	0.906129i	$0.639023\pi$
$104$	3.03523			0.297628
$105$		0			0
$106$	9.00987			0.875115
$107$	9.81297	+	16.9966i	0.948656	+	1.64312i	0.748261	+	0.663405i	$0.230889\pi$
$107$	9.81297	+	16.9966i	0.948656	+	1.64312i	0.200395	+	0.979715i	$0.435777\pi$
$108$		0			0
$109$	0.553378	−	0.958479i	0.0530040	−	0.0918057i	−0.838306	−	0.545200i	$-0.816454\pi$
$109$	0.553378	−	0.958479i	0.0530040	−	0.0918057i	0.891310	+	0.453394i	$0.149787\pi$
$110$	−3.74071	−	6.47911i	−0.356663	−	0.617759i
$111$		0			0
$112$	−8.05557	+	0.0964182i	−0.761180	+	0.00911066i
$113$	1.09606			0.103109			0.0515545	−	0.998670i	$-0.483582\pi$
$113$	1.09606			0.103109			0.0515545	+	0.998670i	$0.483582\pi$
$114$		0			0
$115$	−0.910371	+	1.57681i	−0.0848926	+	0.147038i
$116$	−0.218245	+	0.378012i	−0.0202636	+	0.0350975i
$117$		0			0
$118$	2.57749			0.237277
$119$	5.39901	+	9.09812i	0.494926	+	0.834024i
$120$		0			0
$121$	3.42620	+	5.93436i	0.311473	+	0.539487i
$122$	1.51925	−	2.63141i	0.137546	−	0.238237i
$123$		0			0
$124$	−2.07729	−	3.59797i	−0.186546	−	0.323107i
$125$	−4.57134			−0.408873
$126$		0			0
$127$	5.18143			0.459778			0.229889	−	0.973217i	$-0.426164\pi$
$127$	5.18143			0.459778			0.229889	+	0.973217i	$0.426164\pi$
$128$	3.41231	+	5.91029i	0.301608	+	0.522400i
$129$		0			0
$130$	1.83678	−	3.18139i	0.161096	−	0.279027i
$131$	5.28335	+	9.15103i	0.461609	+	0.799530i	0.999041	−	0.0437770i	$-0.0139391\pi$
$131$	5.28335	+	9.15103i	0.461609	+	0.799530i	−0.537433	+	0.843307i	$0.680606\pi$
$132$		0			0
$133$	18.4187	−	0.220455i	1.59710	−	0.0191159i
$134$	−18.5971			−1.60654
$135$		0			0
$136$	6.06842	−	10.5108i	0.520363	−	0.901295i
$137$	−2.93589	+	5.08510i	−0.250830	+	0.434450i	−0.963754	−	0.266791i	$-0.914037\pi$
$137$	−2.93589	+	5.08510i	−0.250830	+	0.434450i	0.712925	+	0.701241i	$0.247370\pi$
$138$		0			0
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	1.49733	−	2.66665i	0.126547	−	0.225373i
$141$		0			0
$142$	−2.27899	−	3.94732i	−0.191248	−	0.331252i
$143$	1.01828	−	1.76372i	0.0851530	−	0.147489i
$144$		0			0
$145$	1.59072	+	2.75520i	0.132102	+	0.228807i
$146$	−3.76611			−0.311685
$147$		0			0
$148$	1.22870			0.100999
$149$	−5.05271	−	8.75155i	−0.413934	−	0.716955i	0.581382	−	0.813631i	$-0.302512\pi$
$149$	−5.05271	−	8.75155i	−0.413934	−	0.716955i	−0.995316	+	0.0966760i	$0.969179\pi$
$150$		0			0
$151$	0.0938631	−	0.162576i	0.00763847	−	0.0132302i	−0.862181	−	0.506601i	$-0.830902\pi$
$151$	0.0938631	−	0.162576i	0.00763847	−	0.0132302i	0.869819	+	0.493370i	$0.164235\pi$
$152$	−10.5658	−	18.3005i	−0.856998	−	1.48436i
$153$		0			0
$154$	−3.33878	+	5.94616i	−0.269046	+	0.479155i
$155$	−30.2813			−2.43225
$156$		0			0
$157$	6.03590	−	10.4545i	0.481717	−	0.834358i	−0.518063	−	0.855343i	$-0.673347\pi$
$157$	6.03590	−	10.4545i	0.481717	−	0.834358i	0.999780	+	0.0209844i	$0.00668003\pi$
$158$	−5.54432	+	9.60304i	−0.441082	+	0.763977i
$159$		0			0
$160$	−6.43435			−0.508680
$161$	1.65951	−	0.0198629i	0.130788	−	0.00156541i
$162$		0			0
$163$	−7.45678	−	12.9155i	−0.584060	−	1.01162i	−0.994992	−	0.0999554i	$-0.968130\pi$
$163$	−7.45678	−	12.9155i	−0.584060	−	1.01162i	0.410932	−	0.911666i	$-0.365203\pi$
$164$	0.103770	−	0.179735i	0.00810309	−	0.0140350i
$165$		0			0
$166$	−8.10234	−	14.0337i	−0.628863	−	1.08922i
$167$	−5.05664			−0.391294			−0.195647	−	0.980674i	$-0.562681\pi$
$167$	−5.05664			−0.391294			−0.195647	+	0.980674i	$0.562681\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	−7.34465	−	12.7213i	−0.563309	−	0.975680i
$171$		0			0
$172$	0.0655145	−	0.113474i	0.00499543	−	0.00865235i
$173$	−0.297807	−	0.515817i	−0.0226419	−	0.0392169i	0.854482	−	0.519480i	$-0.173874\pi$
$173$	−0.297807	−	0.515817i	−0.0226419	−	0.0392169i	−0.877124	+	0.480263i	$0.840541\pi$
$174$		0			0
$175$	−4.62457	−	7.79307i	−0.349584	−	0.589101i
$176$	6.20121			0.467434
$177$		0			0
$178$	1.69654	−	2.93849i	0.127161	−	0.220249i
$179$	4.03832	−	6.99458i	0.301838	−	0.522799i	−0.674714	−	0.738079i	$-0.735733\pi$
$179$	4.03832	−	6.99458i	0.301838	−	0.522799i	0.976552	+	0.215280i	$0.0690664\pi$
$180$		0			0
$181$	1.89324			0.140724			0.0703618	−	0.997522i	$-0.477585\pi$
$181$	1.89324			0.140724			0.0703618	+	0.997522i	$0.477585\pi$
$182$	−3.34825	+	0.0400756i	−0.248188	+	0.00297060i
$183$		0			0
$184$	−0.951968	−	1.64886i	−0.0701800	−	0.121555i
$185$	4.47780	−	7.75577i	0.329214	−	0.570216i
$186$		0			0
$187$	−4.07177	−	7.05251i	−0.297757	−	0.515730i
$188$	4.19966			0.306292
$189$		0			0
$190$	−25.5757			−1.85545
$191$	1.85087	+	3.20580i	0.133924	+	0.231964i	0.925186	−	0.379514i	$-0.123909\pi$
$191$	1.85087	+	3.20580i	0.133924	+	0.231964i	−0.791262	+	0.611478i	$0.790575\pi$
$192$		0			0
$193$	−6.79373	+	11.7671i	−0.489024	+	0.847014i	−0.999920	−	0.0126285i	$-0.995980\pi$
$193$	−6.79373	+	11.7671i	−0.489024	+	0.847014i	0.510897	+	0.859642i	$0.329313\pi$
$194$	−1.47382	−	2.55272i	−0.105814	−	0.183275i
$195$		0			0
$196$	−2.78685	+	0.0667218i	−0.199061	+	0.00476585i
$197$	9.70258			0.691280			0.345640	−	0.938367i	$-0.387662\pi$
$197$	9.70258			0.691280			0.345640	+	0.938367i	$0.387662\pi$
$198$		0			0
$199$	−13.1360	+	22.7522i	−0.931185	+	1.61286i	−0.149885	+	0.988703i	$0.547891\pi$
$199$	−13.1360	+	22.7522i	−0.931185	+	1.61286i	−0.781299	+	0.624156i	$0.785443\pi$
$200$	−5.19796	+	9.00313i	−0.367551	+	0.636617i
$201$		0			0
$202$	1.83923			0.129408
$203$	1.41979	−	2.52857i	0.0996500	−	0.177471i
$204$		0			0
$205$	−0.756345	−	1.31003i	−0.0528255	−	0.0914964i
$206$	−7.36287	+	12.7529i	−0.512995	+	0.888534i
$207$		0			0
$208$	1.52247	+	2.63699i	0.105564	+	0.182843i
$209$	−14.1788			−0.980765
$210$		0			0
$211$	10.0338			0.690758			0.345379	−	0.938463i	$-0.387750\pi$
$211$	10.0338			0.690758			0.345379	+	0.938463i	$0.387750\pi$
$212$	−1.41752	−	2.45521i	−0.0973555	−	0.168625i
$213$		0			0
$214$	−12.4194	+	21.5110i	−0.848971	+	1.47046i
$215$	−0.477513	−	0.827077i	−0.0325661	−	0.0564062i
$216$		0			0
$217$	14.0860	+	23.7369i	0.956218	+	1.61137i
$218$	1.40072			0.0948688
$219$		0			0
$220$	−1.17705	+	2.03871i	−0.0793567	+	0.137450i
$221$	1.99933	−	3.46294i	0.134490	−	0.232943i
$222$		0			0
$223$	17.4961			1.17163			0.585813	−	0.810446i	$-0.300775\pi$
$223$	17.4961			1.17163			0.585813	+	0.810446i	$0.300775\pi$
$224$	2.99307	+	5.04376i	0.199983	+	0.337000i
$225$		0			0
$226$	0.693593	+	1.20134i	0.0461371	+	0.0799119i
$227$	−4.75815	+	8.24136i	−0.315810	+	0.546998i	−0.979609	−	0.200912i	$-0.935609\pi$
$227$	−4.75815	+	8.24136i	−0.315810	+	0.546998i	0.663800	+	0.747910i	$0.268943\pi$
$228$		0			0
$229$	−10.5585	−	18.2878i	−0.697725	−	1.20849i	−0.969254	−	0.246064i	$-0.920863\pi$
$229$	−10.5585	−	18.2878i	−0.697725	−	1.20849i	0.271529	−	0.962430i	$-0.412471\pi$
$230$	−2.30435			−0.151944
$231$		0			0
$232$	−3.32680			−0.218415
$233$	7.08938	+	12.2792i	0.464441	+	0.804435i	0.999176	−	0.0405847i	$-0.0129221\pi$
$233$	7.08938	+	12.2792i	0.464441	+	0.804435i	−0.534735	+	0.845020i	$0.679589\pi$
$234$		0			0
$235$	15.3050	−	26.5090i	0.998385	−	1.72925i
$236$	−0.405516	−	0.702374i	−0.0263968	−	0.0457206i
$237$		0			0
$238$	−6.55547	+	11.6749i	−0.424928	+	0.756772i
$239$	16.5275			1.06907			0.534536	−	0.845145i	$-0.320486\pi$
$239$	16.5275			1.06907			0.534536	+	0.845145i	$0.320486\pi$
$240$		0			0
$241$	6.84450	−	11.8550i	0.440893	−	0.763649i	−0.556863	−	0.830604i	$-0.687995\pi$
$241$	6.84450	−	11.8550i	0.440893	−	0.763649i	0.997756	+	0.0669552i	$0.0213284\pi$
$242$	−4.33623	+	7.51058i	−0.278744	+	0.482798i
$243$		0			0
$244$	−0.956089			−0.0612073
$245$	−9.73503	+	17.8342i	−0.621948	+	1.13938i
$246$		0			0
$247$	−3.48105	−	6.02935i	−0.221494	−	0.383639i
$248$	15.8325	−	27.4226i	1.00536	−	1.74134i
$249$		0			0
$250$	−2.89276	−	5.01042i	−0.182954	−	0.316886i
$251$	14.6603			0.925349			0.462674	−	0.886528i	$-0.346890\pi$
$251$	14.6603			0.925349			0.462674	+	0.886528i	$0.346890\pi$
$252$		0			0
$253$	−1.27750			−0.0803155
$254$	3.27883	+	5.67910i	0.205732	+	0.356339i
$255$		0			0
$256$	4.57678	−	7.92721i	0.286049	−	0.495451i
$257$	−0.876387	−	1.51795i	−0.0546675	−	0.0946869i	0.837397	−	0.546596i	$-0.184077\pi$
$257$	−0.876387	−	1.51795i	−0.0546675	−	0.0946869i	−0.892064	+	0.451909i	$0.850743\pi$
$258$		0			0
$259$	−8.16254	+	0.0976985i	−0.507195	+	0.00607069i
$260$	−1.15592			−0.0716870
$261$		0			0
$262$	−6.68666	+	11.5816i	−0.413103	+	0.715515i
$263$	13.4708	−	23.3321i	0.830645	−	1.43872i	−0.0668823	−	0.997761i	$-0.521305\pi$
$263$	13.4708	−	23.3321i	0.830645	−	1.43872i	0.897527	−	0.440959i	$-0.145361\pi$
$264$		0			0
$265$	−20.6636			−1.26936
$266$	11.8970	+	20.0483i	0.729454	+	1.22924i
$267$		0			0
$268$	2.92587	+	5.06775i	0.178726	+	0.309562i
$269$	−11.0346	+	19.1124i	−0.672789	+	1.16530i	0.304321	+	0.952570i	$0.401570\pi$
$269$	−11.0346	+	19.1124i	−0.672789	+	1.16530i	−0.977110	+	0.212735i	$0.931763\pi$
$270$		0			0
$271$	4.48105	+	7.76141i	0.272204	+	0.471472i	0.969426	−	0.245384i	$-0.0789140\pi$
$271$	4.48105	+	7.76141i	0.272204	+	0.471472i	−0.697222	+	0.716856i	$0.745581\pi$
$272$	12.1757			0.738259
$273$		0			0
$274$	−7.43137			−0.448945
$275$	3.48770	+	6.04088i	0.210316	+	0.364279i
$276$		0			0
$277$	3.76463	−	6.52052i	0.226194	−	0.391780i	−0.730483	−	0.682931i	$-0.760705\pi$
$277$	3.76463	−	6.52052i	0.226194	−	0.391780i	0.956677	+	0.291151i	$0.0940382\pi$
$278$	−2.53122	−	4.38420i	−0.151812	−	0.262947i
$279$		0			0
$280$	23.3075	−	0.278971i	1.39289	−	0.0166717i
$281$	−29.7762			−1.77630			−0.888151	−	0.459553i	$-0.848010\pi$
$281$	−29.7762			−1.77630			−0.888151	+	0.459553i	$0.848010\pi$
$282$		0			0
$283$	−0.150726	+	0.261064i	−0.00895970	+	0.0155187i	−0.870470	−	0.492221i	$-0.836185\pi$
$283$	−0.150726	+	0.261064i	−0.00895970	+	0.0155187i	0.861511	+	0.507739i	$0.169519\pi$
$284$	−0.717104	+	1.24206i	−0.0425523	+	0.0737027i
$285$		0			0
$286$	2.57749			0.152410
$287$	−0.675076	+	1.20227i	−0.0398485	+	0.0709678i
$288$		0			0
$289$	0.505347	+	0.875286i	0.0297263	+	0.0514874i
$290$	−2.01322	+	3.48701i	−0.118221	+	0.204764i
$291$		0			0
$292$	0.592520	+	1.02627i	0.0346746	+	0.0600582i
$293$	19.2471			1.12443			0.562214	−	0.826992i	$-0.309950\pi$
$293$	19.2471			1.12443			0.562214	+	0.826992i	$0.309950\pi$
$294$		0			0
$295$	−5.91133			−0.344171
$296$	4.68240	+	8.11015i	0.272159	+	0.471393i
$297$		0			0
$298$	6.39475	−	11.0760i	0.370438	−	0.641618i
$299$	−0.313640	−	0.543240i	−0.0181383	−	0.0314164i
$300$		0			0
$301$	−0.426204	+	0.759044i	−0.0245660	+	0.0437506i
$302$	0.237588			0.0136716
$303$		0			0
$304$	10.5996	−	18.3590i	0.607928	−	1.05296i
$305$	−3.48430	+	6.03499i	−0.199511	+	0.345562i
$306$		0			0
$307$	−3.57779			−0.204195			−0.102098	−	0.994774i	$-0.532555\pi$
$307$	−3.57779			−0.204195			−0.102098	+	0.994774i	$0.532555\pi$
$308$	2.14563	−	0.0256814i	0.122259	−	0.00146333i
$309$		0			0
$310$	−19.1621	−	33.1898i	−1.08834	−	1.88505i
$311$	−11.9153	+	20.6379i	−0.675655	+	1.17027i	0.300622	+	0.953743i	$0.402806\pi$
$311$	−11.9153	+	20.6379i	−0.675655	+	1.17027i	−0.976277	+	0.216526i	$0.930527\pi$
$312$		0			0
$313$	9.04068	+	15.6589i	0.511009	+	0.885094i	0.999919	+	0.0127596i	$0.00406161\pi$
$313$	9.04068	+	15.6589i	0.511009	+	0.885094i	−0.488909	+	0.872335i	$0.662605\pi$
$314$	15.2782			0.862196
$315$		0			0
$316$	3.48914			0.196279
$317$	−13.7741	−	23.8574i	−0.773630	−	1.33997i	−0.935561	−	0.353164i	$-0.885106\pi$
$317$	−13.7741	−	23.8574i	−0.773630	−	1.33997i	0.161931	−	0.986802i	$-0.448228\pi$
$318$		0			0
$319$	−1.11610	+	1.93314i	−0.0624897	+	0.108235i
$320$	−12.9099	−	22.3606i	−0.721687	−	1.25000i
$321$		0			0
$322$	1.07191	+	1.80633i	0.0597355	+	0.100663i
$323$	−27.8391			−1.54901
$324$		0			0
$325$	−1.71254	+	2.96621i	−0.0949948	+	0.164536i
$326$	9.43736	−	16.3460i	0.522687	−	0.905321i
$327$		0			0
$328$	1.58181			0.0873408
$329$	−27.8993	+	0.333930i	−1.53814	+	0.0184101i
$330$		0			0
$331$	9.09069	+	15.7455i	0.499669	+	0.865453i	1.00000		0.000381757i	$-0.000121517\pi$
$331$	9.09069	+	15.7455i	0.499669	+	0.865453i	−0.500331	+	0.865834i	$0.666788\pi$
$332$	−2.54947	+	4.41582i	−0.139921	+	0.242350i
$333$		0			0
$334$	−3.19986	−	5.54232i	−0.175089	−	0.303262i
$335$	42.6513			2.33029
$336$		0			0
$337$	−17.1381			−0.933572			−0.466786	−	0.884370i	$-0.654588\pi$
$337$	−17.1381			−0.933572			−0.466786	+	0.884370i	$0.654588\pi$
$338$	0.632804	+	1.09605i	0.0344200	+	0.0596172i
$339$		0			0
$340$	−2.31106	+	4.00288i	−0.125335	+	0.217086i
$341$	−10.6232	−	18.3999i	−0.575279	−	0.996412i
$342$		0			0
$343$	18.5083	−	0.664840i	0.999355	−	0.0358980i
$344$	0.998663			0.0538443
$345$		0			0
$346$	0.376907	−	0.652823i	0.0202627	−	0.0350960i
$347$	11.1344	−	19.2853i	0.597725	−	1.03529i	−0.395431	−	0.918496i	$-0.629405\pi$
$347$	11.1344	−	19.2853i	0.597725	−	1.03529i	0.993156	−	0.116794i	$-0.0372619\pi$
$348$		0			0
$349$	19.9368			1.06719			0.533595	−	0.845740i	$-0.320841\pi$
$349$	19.9368			1.06719			0.533595	+	0.845740i	$0.320841\pi$
$350$	5.61514	−	10.0002i	0.300142	−	0.534535i
$351$		0			0
$352$	−2.25728	−	3.90972i	−0.120313	−	0.208389i
$353$	11.4576	−	19.8451i	0.609825	−	1.05625i	−0.381444	−	0.924392i	$-0.624573\pi$
$353$	11.4576	−	19.8451i	0.609825	−	1.05625i	0.991269	−	0.131856i	$-0.0420937\pi$
$354$		0			0
$355$	5.22673	+	9.05296i	0.277406	+	0.480481i
$356$	−1.06766			−0.0565860
$357$		0			0
$358$	10.2219			0.540242
$359$	13.6157	+	23.5831i	0.718610	+	1.24467i	0.961551	+	0.274628i	$0.0885547\pi$
$359$	13.6157	+	23.5831i	0.718610	+	1.24467i	−0.242940	+	0.970041i	$0.578112\pi$
$360$		0			0
$361$	−14.7354	+	25.5225i	−0.775548	+	1.34329i
$362$	1.19805	+	2.07509i	0.0629682	+	0.109064i
$363$		0			0
$364$	0.537699	+	0.906101i	0.0281831	+	0.0474926i
$365$	8.63735			0.452099
$366$		0			0
$367$	5.42822	−	9.40195i	0.283351	−	0.490778i	−0.688857	−	0.724897i	$-0.741887\pi$
$367$	5.42822	−	9.40195i	0.283351	−	0.490778i	0.972208	+	0.234119i	$0.0752206\pi$
$368$	0.955014	−	1.65413i	0.0497836	−	0.0862277i
$369$		0			0
$370$	11.3343			0.589241
$371$	9.61210	+	16.1978i	0.499035	+	0.840948i
$372$		0			0
$373$	1.18572	+	2.05373i	0.0613943	+	0.106338i	0.895089	−	0.445888i	$-0.147112\pi$
$373$	1.18572	+	2.05373i	0.0613943	+	0.106338i	−0.833695	+	0.552226i	$0.813779\pi$
$374$	5.15326	−	8.92571i	0.266469	−	0.461538i
$375$		0			0
$376$	16.0043	+	27.7202i	0.825357	+	1.42956i
$377$	−1.09606			−0.0564501
$378$		0			0
$379$	−29.2197			−1.50092			−0.750458	−	0.660918i	$-0.770167\pi$
$379$	−29.2197			−1.50092			−0.750458	+	0.660918i	$0.770167\pi$
$380$	4.02381	+	6.96944i	0.206417	+	0.357525i
$381$		0			0
$382$	−2.34248	+	4.05729i	−0.119852	+	0.207589i
$383$	−1.53297	−	2.65519i	−0.0783313	−	0.135674i	0.824199	−	0.566301i	$-0.191626\pi$
$383$	−1.53297	−	2.65519i	−0.0783313	−	0.135674i	−0.902530	+	0.430627i	$0.858293\pi$
$384$		0			0
$385$	7.65729	−	13.6372i	0.390252	−	0.695015i
$386$	−17.1964			−0.875274
$387$		0			0
$388$	−0.463750	+	0.803238i	−0.0235433	+	0.0407782i
$389$	13.8705	−	24.0244i	0.703261	−	1.21808i	−0.264054	−	0.964508i	$-0.585060\pi$
$389$	13.8705	−	24.0244i	0.703261	−	1.21808i	0.967315	−	0.253576i	$-0.0816069\pi$
$390$		0			0
$391$	−2.50828			−0.126849
$392$	−11.0607	−	18.1405i	−0.558647	−	0.916236i
$393$		0			0
$394$	6.13984	+	10.6345i	0.309320	+	0.535759i
$395$	12.7156	−	22.0240i	0.639790	−	1.10815i
$396$		0			0
$397$	−8.61559	−	14.9226i	−0.432404	−	0.748946i	0.564676	−	0.825313i	$-0.309001\pi$
$397$	−8.61559	−	14.9226i	−0.432404	−	0.748946i	−0.997080	+	0.0763669i	$0.975668\pi$
$398$	−33.2500			−1.66667
$399$		0			0
$400$	−10.4292			−0.521459
$401$	8.32201	+	14.4142i	0.415582	+	0.719808i	0.995489	−	0.0948737i	$-0.0302447\pi$
$401$	8.32201	+	14.4142i	0.415582	+	0.719808i	−0.579908	+	0.814682i	$0.696911\pi$
$402$		0			0
$403$	5.21624	−	9.03479i	0.259839	−	0.450055i
$404$	−0.289366	−	0.501196i	−0.0143965	−	0.0249354i
$405$		0			0
$406$	3.66989	−	0.0439254i	0.182133	−	0.00217998i
$407$	6.28355			0.311464
$408$		0			0
$409$	6.81689	−	11.8072i	0.337073	−	0.583828i	−0.646807	−	0.762653i	$-0.723896\pi$
$409$	6.81689	−	11.8072i	0.337073	−	0.583828i	0.983881	+	0.178825i	$0.0572296\pi$
$410$	0.957237	−	1.65798i	0.0472746	−	0.0818820i
$411$		0			0
$412$	4.63359			0.228280
$413$	2.74978	+	4.63378i	0.135308	+	0.228013i
$414$		0			0
$415$	18.5822	+	32.1854i	0.912167	+	1.57992i
$416$	1.10838	−	1.91977i	0.0543426	−	0.0941242i
$417$		0			0
$418$	−8.97238	−	15.5406i	−0.438853	−	0.760116i
$419$	10.8502			0.530066			0.265033	−	0.964239i	$-0.414617\pi$
$419$	10.8502			0.530066			0.265033	+	0.964239i	$0.414617\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	6.34946	+	10.9976i	0.309087	+	0.535354i
$423$		0			0
$424$	10.8039	−	18.7129i	0.524683	−	0.908778i
$425$	6.84788	+	11.8609i	0.332171	+	0.575337i
$426$		0			0
$427$	6.35150	−	0.0760220i	0.307371	−	0.00367896i
$428$	7.81574			0.377788
$429$		0			0
$430$	0.604344	−	1.04676i	0.0291441	−	0.0504790i
$431$	0.604764	−	1.04748i	0.0291304	−	0.0504554i	−0.851093	−	0.525016i	$-0.824060\pi$
$431$	0.604764	−	1.04748i	0.0291304	−	0.0504554i	0.880223	+	0.474560i	$0.157393\pi$
$432$		0			0
$433$	−5.56422			−0.267399			−0.133700	−	0.991022i	$-0.542686\pi$
$433$	−5.56422			−0.267399			−0.133700	+	0.991022i	$0.542686\pi$
$434$	−17.1032	+	30.4597i	−0.820979	+	1.46211i
$435$		0			0
$436$	−0.220375	−	0.381700i	−0.0105540	−	0.0182801i
$437$	−2.18359	+	3.78209i	−0.104455	+	0.180922i
$438$		0			0
$439$	9.85960	+	17.0773i	0.470573	+	0.815057i	0.999434	−	0.0336522i	$-0.0107139\pi$
$439$	9.85960	+	17.0773i	0.470573	+	0.815057i	−0.528860	+	0.848709i	$0.677381\pi$
$440$	−17.9422			−0.855362
$441$		0			0
$442$	5.06074			0.240715
$443$	11.1155	+	19.2526i	0.528113	+	0.914719i	0.999463	+	0.0327726i	$0.0104337\pi$
$443$	11.1155	+	19.2526i	0.528113	+	0.914719i	−0.471350	+	0.881946i	$0.656233\pi$
$444$		0			0
$445$	−3.89091	+	6.73926i	−0.184447	+	0.319471i
$446$	11.0716	+	19.1766i	0.524256	+	0.908039i
$447$		0			0
$448$	−11.5228	+	20.5213i	−0.544399	+	0.969542i
$449$	−18.4579			−0.871082			−0.435541	−	0.900169i	$-0.643443\pi$
$449$	−18.4579			−0.871082			−0.435541	+	0.900169i	$0.643443\pi$
$450$		0			0
$451$	0.530678	−	0.919161i	0.0249886	−	0.0432816i
$452$	0.218245	−	0.378012i	0.0102654	−	0.0177802i
$453$		0			0
$454$	−12.0439			−0.565249
$455$	7.67901	−	0.0919110i	0.359997	−	0.00430886i
$456$		0			0
$457$	14.9910	+	25.9651i	0.701248	+	1.21460i	0.968029	+	0.250840i	$0.0807067\pi$
$457$	14.9910	+	25.9651i	0.701248	+	1.21460i	−0.266781	+	0.963757i	$0.585960\pi$
$458$	13.3629	−	23.1452i	0.624408	−	1.08151i
$459$		0			0
$460$	0.362542	+	0.627941i	0.0169036	+	0.0292779i
$461$	−29.1498			−1.35764			−0.678821	−	0.734304i	$-0.737509\pi$
$461$	−29.1498			−1.35764			−0.678821	+	0.734304i	$0.737509\pi$
$462$		0			0
$463$	1.55900			0.0724530			0.0362265	−	0.999344i	$-0.488466\pi$
$463$	1.55900			0.0724530			0.0362265	+	0.999344i	$0.488466\pi$
$464$	−1.66872	−	2.89031i	−0.0774685	−	0.134179i
$465$		0			0
$466$	−8.97238	+	15.5406i	−0.415637	+	0.719905i
$467$	6.21156	+	10.7587i	0.287437	+	0.497855i	0.973197	−	0.229972i	$-0.0738635\pi$
$467$	6.21156	+	10.7587i	0.287437	+	0.497855i	−0.685760	+	0.727827i	$0.740530\pi$
$468$		0			0
$469$	−19.8401	−	33.4335i	−0.916132	−	1.54382i
$470$	38.7402			1.78695
$471$		0			0
$472$	3.09072	−	5.35328i	0.142262	−	0.246405i
$473$	0.335039	−	0.580305i	0.0154051	−	0.0266825i
$474$		0			0
$475$	23.8458			1.09412
$476$	4.21281	−	0.0504237i	0.193094	−	0.00231117i
$477$		0			0
$478$	10.4587	+	18.1149i	0.478368	+	0.828557i
$479$	18.0279	−	31.2252i	0.823716	−	1.42672i	−0.0791811	−	0.996860i	$-0.525231\pi$
$479$	18.0279	−	31.2252i	0.823716	−	1.42672i	0.902897	−	0.429857i	$-0.141436\pi$
$480$		0			0
$481$	1.54268	+	2.67201i	0.0703404	+	0.121833i
$482$	17.3249			0.789128
$483$		0			0
$484$	2.72887			0.124040
$485$	3.38011	+	5.85453i	0.153483	+	0.265840i
$486$		0			0
$487$	−3.65002	+	6.32202i	−0.165398	+	0.286478i	−0.936797	−	0.349874i	$-0.886224\pi$
$487$	−3.65002	+	6.32202i	−0.165398	+	0.286478i	0.771398	+	0.636352i	$0.219558\pi$
$488$	−3.64351	−	6.31074i	−0.164934	−	0.285674i
$489$		0			0
$490$	−25.7075	+	0.615481i	−1.16135	+	0.0278046i
$491$	−4.49178			−0.202711			−0.101356	−	0.994850i	$-0.532318\pi$
$491$	−4.49178			−0.202711			−0.101356	+	0.994850i	$0.532318\pi$
$492$		0			0
$493$	−2.19139	+	3.79560i	−0.0986954	+	0.170945i
$494$	4.40565	−	7.63080i	0.198219	−	0.343326i
$495$		0			0
$496$	31.7663			1.42635
$497$	4.66512	−	8.30829i	0.209259	−	0.372678i
$498$		0			0
$499$	−5.68369	−	9.84443i	−0.254437	−	0.440697i	0.710306	−	0.703893i	$-0.248557\pi$
$499$	−5.68369	−	9.84443i	−0.254437	−	0.440697i	−0.964742	+	0.263196i	$0.915223\pi$
$500$	−0.910235	+	1.57657i	−0.0407069	+	0.0705065i
$501$		0			0
$502$	9.27709	+	16.0684i	0.414057	+	0.717167i
$503$	−17.1080			−0.762806			−0.381403	−	0.924409i	$-0.624559\pi$
$503$	−17.1080			−0.762806			−0.381403	+	0.924409i	$0.624559\pi$
$504$		0			0
$505$	−4.21818			−0.187706
$506$	−0.808405	−	1.40020i	−0.0359380	−	0.0622464i
$507$		0			0
$508$	1.03171	−	1.78698i	0.0457749	−	0.0792845i
$509$	1.64142	+	2.84303i	0.0727547	+	0.126015i	0.900108	−	0.435667i	$-0.143488\pi$
$509$	1.64142	+	2.84303i	0.0727547	+	0.126015i	−0.827353	+	0.561682i	$0.810154\pi$
$510$		0			0
$511$	−4.01784	−	6.77065i	−0.177739	−	0.299516i
$512$	25.2340			1.11520
$513$		0			0
$514$	1.10916	−	1.92113i	0.0489231	−	0.0847373i
$515$	16.8863	−	29.2479i	0.744100	−	1.28882i
$516$		0			0
$517$	21.4770			0.944555
$518$	−5.27237	−	8.88472i	−0.231655	−	0.390372i
$519$		0			0
$520$	−4.40502	−	7.62973i	−0.193173	−	0.334586i
$521$	−2.38530	+	4.13147i	−0.104502	+	0.181003i	−0.913535	−	0.406761i	$-0.866658\pi$
$521$	−2.38530	+	4.13147i	−0.104502	+	0.181003i	0.809033	+	0.587764i	$0.199992\pi$
$522$		0			0
$523$	−12.7562	−	22.0944i	−0.557789	−	0.966119i	−0.997681	−	0.0680682i	$-0.978316\pi$
$523$	−12.7562	−	22.0944i	−0.557789	−	0.966119i	0.439892	−	0.898051i	$-0.355017\pi$
$524$	4.20803			0.183829
$525$		0			0
$526$	34.0975			1.48672
$527$	−20.8580	−	36.1271i	−0.908588	−	1.57372i
$528$		0			0
$529$	11.3033	−	19.5778i	0.491446	−	0.851210i
$530$	−13.0760	−	22.6483i	−0.567986	−	0.983780i
$531$		0			0
$532$	3.59145	−	6.39616i	0.155709	−	0.277309i
$533$	0.521150			0.0225735
$534$		0			0
$535$	28.4831	−	49.3342i	1.23143	−	2.13290i
$536$	−22.3001	+	38.6249i	−0.963216	+	1.66834i
$537$		0			0
$538$	−27.9309			−1.20418
$539$	−14.2519	+	0.341214i	−0.613871	+	0.0146971i
$540$		0			0
$541$	8.25784	+	14.3030i	0.355032	+	0.614934i	0.987123	−	0.159960i	$-0.0511366\pi$
$541$	8.25784	+	14.3030i	0.355032	+	0.614934i	−0.632091	+	0.774894i	$0.717803\pi$
$542$	−5.67125	+	9.82290i	−0.243601	+	0.421930i
$543$		0			0
$544$	−4.43203	−	7.67649i	−0.190022	−	0.329127i
$545$	−3.21247			−0.137607
$546$		0			0
$547$	23.3317			0.997591			0.498796	−	0.866720i	$-0.333776\pi$
$547$	23.3317			0.997591			0.498796	+	0.866720i	$0.333776\pi$
$548$	1.16917	+	2.02507i	0.0499446	+	0.0865066i
$549$		0			0
$550$	−4.41407	+	7.64539i	−0.188216	+	0.326001i
$551$	3.81545	+	6.60855i	0.162544	+	0.281534i
$552$		0			0
$553$	−23.1791	+	0.277434i	−0.985676	+	0.0117977i
$554$	9.52909			0.404852
$555$		0			0
$556$	−0.796470	+	1.37953i	−0.0337779	+	0.0585050i
$557$	−10.0235	+	17.3613i	−0.424711	+	0.735621i	−0.996393	−	0.0848540i	$-0.972958\pi$
$557$	−10.0235	+	17.3613i	−0.424711	+	0.735621i	0.571682	+	0.820475i	$0.306291\pi$
$558$		0			0
$559$	0.329024			0.0139162
$560$	11.9334	+	20.1096i	0.504279	+	0.849784i
$561$		0			0
$562$	−18.8425	−	32.6362i	−0.794824	−	1.37668i
$563$	−20.2642	+	35.0986i	−0.854034	+	1.47923i	0.0235047	+	0.999724i	$0.492518\pi$
$563$	−20.2642	+	35.0986i	−0.854034	+	1.47923i	−0.877539	+	0.479506i	$0.840816\pi$
$564$		0			0
$565$	−1.59072	−	2.75520i	−0.0669219	−	0.115912i
$566$	−0.381519			−0.0160364
$567$		0			0
$568$	−10.9311			−0.458659
$569$	−10.7252	−	18.5766i	−0.449623	−	0.778770i	0.548739	−	0.835994i	$-0.315108\pi$
$569$	−10.7252	−	18.5766i	−0.449623	−	0.778770i	−0.998361	+	0.0572245i	$0.981775\pi$
$570$		0			0
$571$	5.47793	−	9.48806i	0.229244	−	0.397063i	−0.728340	−	0.685216i	$-0.759708\pi$
$571$	5.47793	−	9.48806i	0.229244	−	0.397063i	0.957584	+	0.288153i	$0.0930412\pi$
$572$	−0.405516	−	0.702374i	−0.0169555	−	0.0293677i
$573$		0			0
$574$	−1.74494	+	0.0208854i	−0.0728323	+	0.000871740i
$575$	2.14849			0.0895982
$576$		0			0
$577$	−17.3708	+	30.0870i	−0.723154	+	1.25254i	0.236575	+	0.971613i	$0.423975\pi$
$577$	−17.3708	+	30.0870i	−0.723154	+	1.25254i	−0.959729	+	0.280927i	$0.909358\pi$
$578$	−0.639571	+	1.10777i	−0.0266027	+	0.0460771i
$579$		0			0
$580$	1.26696			0.0526076
$581$	16.5856	−	29.5380i	0.688086	−	1.22544i
$582$		0			0
$583$	−7.24915	−	12.5559i	−0.300229	−	0.520012i
$584$	−4.51600	+	7.82195i	−0.186874	+	0.323675i
$585$		0			0
$586$	12.1796	+	21.0958i	0.503136	+	0.871458i
$587$	22.8463			0.942967			0.471483	−	0.881875i	$-0.343719\pi$
$587$	22.8463			0.942967			0.471483	+	0.881875i	$0.343719\pi$
$588$		0			0
$589$	−72.6320			−2.99275
$590$	−3.74071	−	6.47911i	−0.154003	−	0.266741i
$591$		0			0
$592$	−4.69738	+	8.13610i	−0.193061	+	0.334392i
$593$	8.79676	+	15.2364i	0.361240	+	0.625686i	0.988165	−	0.153394i	$-0.0490202\pi$
$593$	8.79676	+	15.2364i	0.361240	+	0.625686i	−0.626925	+	0.779079i	$0.715687\pi$
$594$		0			0
$595$	15.0346	−	26.7757i	0.616359	−	1.09770i
$596$	−4.02433			−0.164843
$597$		0			0
$598$	0.396945	−	0.687530i	0.0162323	−	0.0281152i
$599$	15.5036	−	26.8531i	0.633461	−	1.09719i	−0.353378	−	0.935481i	$-0.614967\pi$
$599$	15.5036	−	26.8531i	0.633461	−	1.09719i	0.986839	−	0.161706i	$-0.0516997\pi$
$600$		0			0
$601$	−1.43754			−0.0586385			−0.0293193	−	0.999570i	$-0.509334\pi$
$601$	−1.43754			−0.0586385			−0.0293193	+	0.999570i	$0.509334\pi$
$602$	−1.10165	+	0.0131858i	−0.0449001	+	0.000537415i
$603$		0			0
$604$	−0.0373796	−	0.0647433i	−0.00152095	−	0.00263437i
$605$	9.94490	−	17.2251i	0.404318	−	0.700299i
$606$		0			0
$607$	16.5085	+	28.5936i	0.670061	+	1.16058i	0.977887	+	0.209136i	$0.0670652\pi$
$607$	16.5085	+	28.5936i	0.670061	+	1.16058i	−0.307826	+	0.951443i	$0.599601\pi$
$608$	−15.4333			−0.625901
$609$		0			0
$610$	−8.81953			−0.357092
$611$	5.27284	+	9.13283i	0.213316	+	0.369475i
$612$		0			0
$613$	21.5829	−	37.3826i	0.871723	−	1.50987i	0.0115102	−	0.999934i	$-0.496336\pi$
$613$	21.5829	−	37.3826i	0.871723	−	1.50987i	0.860213	−	0.509935i	$-0.170331\pi$
$614$	−2.26404	−	3.92143i	−0.0913692	−	0.158256i
$615$		0			0
$616$	8.34619	+	14.0646i	0.336278	+	0.566677i
$617$	−2.45772			−0.0989441			−0.0494721	−	0.998776i	$-0.515754\pi$
$617$	−2.45772			−0.0989441			−0.0494721	+	0.998776i	$0.515754\pi$
$618$		0			0
$619$	−18.8894	+	32.7175i	−0.759231	+	1.31503i	0.184013	+	0.982924i	$0.441091\pi$
$619$	−18.8894	+	32.7175i	−0.759231	+	1.31503i	−0.943243	+	0.332102i	$0.892242\pi$
$620$	−6.02954	+	10.4435i	−0.242152	+	0.419420i
$621$		0			0
$622$	−30.1602			−1.20932
$623$	7.09271	−	0.0848936i	0.284163	−	0.00340119i
$624$		0			0
$625$	15.1971	+	26.3222i	0.607884	+	1.05289i
$626$	−11.4420	+	19.8181i	−0.457313	+	0.792089i
$627$		0			0
$628$	−2.40371	−	4.16334i	−0.0959183	−	0.166135i
$629$	12.3374			0.491922
$630$		0			0
$631$	−28.4828			−1.13388			−0.566942	−	0.823758i	$-0.691874\pi$
$631$	−28.4828			−1.13388			−0.566942	+	0.823758i	$0.691874\pi$
$632$	13.2966	+	23.0303i	0.528909	+	0.916098i
$633$		0			0
$634$	17.4326	−	30.1942i	0.692337	−	1.19916i
$635$	−7.51981	−	13.0247i	−0.298415	−	0.516869i
$636$		0			0
$637$	−3.64409	−	5.97667i	−0.144384	−	0.236804i
$638$	−2.82509			−0.111847
$639$		0			0
$640$	9.90456	−	17.1552i	0.391512	−	0.678119i
$641$	−13.5961	+	23.5492i	−0.537014	+	0.930136i	0.462049	+	0.886854i	$0.347114\pi$
$641$	−13.5961	+	23.5492i	−0.537014	+	0.930136i	−0.999063	+	0.0432812i	$0.986219\pi$
$642$		0			0
$643$	−37.1664			−1.46570			−0.732849	−	0.680391i	$-0.761810\pi$
$643$	−37.1664			−1.46570			−0.732849	+	0.680391i	$0.761810\pi$
$644$	0.323587	−	0.576289i	0.0127511	−	0.0227090i
$645$		0			0
$646$	−17.6167	−	30.5130i	−0.693120	−	1.20052i
$647$	9.41593	−	16.3089i	0.370178	−	0.641168i	−0.619414	−	0.785064i	$-0.712630\pi$
$647$	9.41593	−	16.3089i	0.370178	−	0.641168i	0.989593	+	0.143896i	$0.0459632\pi$
$648$		0			0
$649$	−2.07380	−	3.59192i	−0.0814036	−	0.140995i
$650$	−4.33482			−0.170026
$651$		0			0
$652$	−5.93910			−0.232593
$653$	−13.0092	−	22.5326i	−0.509090	−	0.881770i	−0.999945	−	0.0105286i	$-0.996649\pi$
$653$	−13.0092	−	22.5326i	−0.509090	−	0.881770i	0.490854	−	0.871242i	$-0.336685\pi$
$654$		0			0
$655$	15.3355	−	26.5618i	0.599206	−	1.03786i
$656$	0.793435	+	1.37427i	0.0309784	+	0.0536562i
$657$		0			0
$658$	−18.0208	−	30.3676i	−0.702523	−	1.18385i
$659$	33.3339			1.29851			0.649253	−	0.760573i	$-0.275082\pi$
$659$	33.3339			1.29851			0.649253	+	0.760573i	$0.275082\pi$
$660$		0			0
$661$	−3.14920	+	5.45458i	−0.122490	+	0.212159i	−0.920749	−	0.390156i	$-0.872421\pi$
$661$	−3.14920	+	5.45458i	−0.122490	+	0.212159i	0.798259	+	0.602314i	$0.205755\pi$
$662$	−11.5053	+	19.9277i	−0.447164	+	0.774511i
$663$		0			0
$664$	−38.8626			−1.50816
$665$	−27.2852	−	45.9795i	−1.05807	−	1.78301i
$666$		0			0
$667$	0.343769	+	0.595426i	0.0133108	+	0.0230550i
$668$	−1.00687	+	1.74394i	−0.0389568	+	0.0674752i
$669$		0			0
$670$	26.9899	+	46.7479i	1.04271	+	1.80603i
$671$	−4.88941			−0.188754
$672$		0			0
$673$	18.3188			0.706137			0.353068	−	0.935598i	$-0.385138\pi$
$673$	18.3188			0.706137			0.353068	+	0.935598i	$0.385138\pi$
$674$	−10.8451	−	18.7842i	−0.417736	−	0.723541i
$675$		0			0
$676$	0.199118	−	0.344882i	0.00765837	−	0.0132647i
$677$	12.1696	+	21.0783i	0.467715	+	0.810106i	0.999319	−	0.0368866i	$-0.0117440\pi$
$677$	12.1696	+	21.0783i	0.467715	+	0.810106i	−0.531604	+	0.846993i	$0.678411\pi$
$678$		0			0
$679$	3.01692	−	5.37296i	0.115779	−	0.206195i
$680$	−35.2284			−1.35095
$681$		0			0
$682$	13.4448	−	23.2871i	0.514829	−	0.891709i
$683$	5.88409	−	10.1916i	0.225149	−	0.389969i	−0.731215	−	0.682147i	$-0.761047\pi$
$683$	5.88409	−	10.1916i	0.225149	−	0.389969i	0.956364	+	0.292178i	$0.0943799\pi$
$684$		0			0
$685$	17.0434			0.651195
$686$	12.4408	+	19.8653i	0.474994	+	0.758461i
$687$		0			0
$688$	0.500929	+	0.867635i	0.0190977	+	0.0330783i
$689$	3.55950	−	6.16523i	0.135606	−	0.234877i
$690$		0			0
$691$	−0.588923	−	1.02004i	−0.0224037	−	0.0388043i	0.854606	−	0.519277i	$-0.173799\pi$
$691$	−0.588923	−	1.02004i	−0.0224037	−	0.0388043i	−0.877010	+	0.480472i	$0.840465\pi$
$692$	−0.237195			−0.00901679
$693$		0			0
$694$	28.1835			1.06983
$695$	5.80520	+	10.0549i	0.220204	+	0.381404i
$696$		0			0
$697$	1.04195	−	1.80471i	0.0394668	−	0.0683584i
$698$	12.6161	+	21.8517i	0.477525	+	0.827097i
$699$		0			0
$700$	−3.60852	+	0.0431908i	−0.136389	+	0.00163246i
$701$	31.2867			1.18168			0.590841	−	0.806788i	$-0.298796\pi$
$701$	31.2867			1.18168			0.590841	+	0.806788i	$0.298796\pi$
$702$		0			0
$703$	10.7403	−	18.6028i	0.405079	−	0.701617i
$704$	9.05804	−	15.6890i	0.341388	−	0.591301i
$705$		0			0
$706$	29.0016			1.09149
$707$	1.96217	+	3.30654i	0.0737950	+	0.124355i
$708$		0			0
$709$	−7.68738	−	13.3149i	−0.288706	−	0.500053i	0.684795	−	0.728735i	$-0.259892\pi$
$709$	−7.68738	−	13.3149i	−0.288706	−	0.500053i	−0.973501	+	0.228682i	$0.926558\pi$
$710$	−6.61499	+	11.4575i	−0.248256	+	0.429992i
$711$		0			0
$712$	−4.06870	−	7.04719i	−0.152481	−	0.264105i
$713$	−6.54409			−0.245078
$714$		0			0
$715$	−5.91133			−0.221071
$716$	−1.60820	−	2.78549i	−0.0601013	−	0.104098i
$717$		0			0
$718$	−17.2322	+	29.8470i	−0.643099	+	1.11388i
$719$	−5.57087	−	9.64904i	−0.207759	−	0.359848i	0.743250	−	0.669014i	$-0.233283\pi$
$719$	−5.57087	−	9.64904i	−0.207759	−	0.359848i	−0.951008	+	0.309166i	$0.899950\pi$
$720$		0			0
$721$	−30.7819	+	0.368433i	−1.14638	+	0.0137211i
$722$	−37.2985			−1.38811
$723$		0			0
$724$	0.376978	−	0.652945i	0.0140103	−	0.0242665i
$725$	1.87706	−	3.25116i	0.0697121	−	0.120745i
$726$		0			0
$727$	−6.24735			−0.231702			−0.115851	−	0.993267i	$-0.536959\pi$
$727$	−6.24735			−0.231702			−0.115851	+	0.993267i	$0.536959\pi$
$728$	−3.93171	+	7.00214i	−0.145719	+	0.259516i
$729$		0			0
$730$	5.46575	+	9.46696i	0.202296	+	0.350388i
$731$	0.657828	−	1.13939i	0.0243307	−	0.0421419i
$732$		0			0
$733$	−15.4834	−	26.8181i	−0.571894	−	0.990550i	−0.996371	−	0.0851111i	$-0.972875\pi$
$733$	−15.4834	−	26.8181i	−0.571894	−	0.990550i	0.424477	−	0.905439i	$-0.360458\pi$
$734$	13.7400			0.507153
$735$		0			0
$736$	−1.39053			−0.0512554
$737$	14.9628	+	25.9163i	0.551162	+	0.954641i
$738$		0			0
$739$	−1.16872	+	2.02429i	−0.0429921	+	0.0744646i	−0.886721	−	0.462305i	$-0.847022\pi$
$739$	−1.16872	+	2.02429i	−0.0429921	+	0.0744646i	0.843729	+	0.536770i	$0.180356\pi$
$740$	−1.78322	−	3.08862i	−0.0655523	−	0.113540i
$741$		0			0
$742$	−11.6710	+	20.7854i	−0.428456	+	0.763055i
$743$	−24.3612			−0.893726			−0.446863	−	0.894603i	$-0.647459\pi$
$743$	−24.3612			−0.893726			−0.446863	+	0.894603i	$0.647459\pi$
$744$		0			0
$745$	−14.6660	+	25.4022i	−0.537321	+	0.930666i
$746$	−1.50066	+	2.59922i	−0.0549430	+	0.0951641i
$747$		0			0
$748$	−3.24304			−0.118577
$749$	−51.9216	+	0.621457i	−1.89718	+	0.0227075i
$750$		0			0
$751$	6.01266	+	10.4142i	0.219405	+	0.380021i	0.954626	−	0.297806i	$-0.0962550\pi$
$751$	6.01266	+	10.4142i	0.219405	+	0.380021i	−0.735221	+	0.677827i	$0.762922\pi$
$752$	−16.0555	+	27.8089i	−0.585483	+	1.01409i
$753$		0			0
$754$	−0.693593	−	1.20134i	−0.0252592	−	0.0437502i
$755$	−0.544894			−0.0198307
$756$		0			0
$757$	25.9905			0.944641			0.472321	−	0.881427i	$-0.343416\pi$
$757$	25.9905			0.944641			0.472321	+	0.881427i	$0.343416\pi$
$758$	−18.4904	−	32.0263i	−0.671600	−	1.16325i
$759$		0			0
$760$	−30.6682	+	53.1189i	−1.11245	+	1.92683i
$761$	6.66350	+	11.5415i	0.241552	+	0.418380i	0.961156	−	0.276004i	$-0.0890103\pi$
$761$	6.66350	+	11.5415i	0.241552	+	0.418380i	−0.719605	+	0.694384i	$0.755677\pi$
$762$		0			0
$763$	1.49435	+	2.51819i	0.0540990	+	0.0911647i
$764$	1.47416			0.0533334
$765$		0			0
$766$	1.94014	−	3.36043i	0.0701002	−	0.121417i
$767$	1.01828	−	1.76372i	0.0367680	−	0.0636841i
$768$		0			0
$769$	9.24486			0.333378			0.166689	−	0.986010i	$-0.446692\pi$
$769$	9.24486			0.333378			0.166689	+	0.986010i	$0.446692\pi$
$770$	19.7926	−	0.236900i	0.713275	−	0.00853728i
$771$		0			0
$772$	2.70550	+	4.68607i	0.0973732	+	0.168655i
$773$	−5.07097	+	8.78317i	−0.182390	+	0.315909i	−0.942694	−	0.333659i	$-0.891717\pi$
$773$	−5.07097	+	8.78317i	−0.182390	+	0.315909i	0.760304	+	0.649568i	$0.225050\pi$
$774$		0			0
$775$	17.8661	+	30.9450i	0.641768	+	1.11158i
$776$	−7.06912			−0.253766
$777$		0			0
$778$	35.1092			1.25873
$779$	−1.81415	−	3.14220i	−0.0649987	−	0.112581i
$780$		0			0
$781$	−3.66725	+	6.35186i	−0.131225	+	0.227288i
$782$	−1.58725	−	2.74920i	−0.0567600	−	0.0983112i
$783$		0			0
$784$	10.2124	−	18.7088i	0.364729	−	0.668170i
$785$	−35.0396			−1.25062
$786$		0			0
$787$	−22.6411	+	39.2156i	−0.807070	+	1.39789i	0.107815	+	0.994171i	$0.465614\pi$
$787$	−22.6411	+	39.2156i	−0.807070	+	1.39789i	−0.914885	+	0.403715i	$0.867719\pi$
$788$	1.93195	−	3.34624i	0.0688230	−	0.119205i
$789$		0			0
$790$	32.1859			1.14512
$791$	−1.41979	+	2.52857i	−0.0504821	+	0.0899056i
$792$		0			0
$793$	−1.20041	−	2.07917i	−0.0426277	−	0.0738334i
$794$	10.9040	−	18.8862i	0.386967	−	0.670247i
$795$		0			0
$796$	5.23121	+	9.06072i	0.185415	+	0.321149i
$797$	−27.0784			−0.959165			−0.479583	−	0.877497i	$-0.659212\pi$
$797$	−27.0784			−0.959165			−0.479583	+	0.877497i	$0.659212\pi$
$798$		0			0
$799$	42.1686			1.49182
$800$	3.79629	+	6.57536i	0.134219	+	0.232474i
$801$		0			0
$802$	−10.5324	+	18.2427i	−0.371912	+	0.644171i
$803$	3.03013	+	5.24834i	0.106931	+	0.185210i
$804$		0			0
$805$	−2.45837	−	4.14272i	−0.0866463	−	0.146012i
$806$	13.2034			0.465071
$807$		0			0
$808$	2.20546	−	3.81996i	0.0775877	−	0.134386i
$809$	−12.8899	+	22.3260i	−0.453185	+	0.784939i	−0.998582	−	0.0532388i	$-0.983046\pi$
$809$	−12.8899	+	22.3260i	−0.453185	+	0.784939i	0.545397	+	0.838178i	$0.316379\pi$
$810$		0			0
$811$	−25.7829			−0.905362			−0.452681	−	0.891673i	$-0.649532\pi$
$811$	−25.7829			−0.905362			−0.452681	+	0.891673i	$0.649532\pi$
$812$	−0.589352	−	0.993144i	−0.0206822	−	0.0348525i
$813$		0			0
$814$	3.97626	+	6.88708i	0.139368	+	0.241392i
$815$	−21.6440	+	37.4886i	−0.758158	+	1.31317i
$816$		0			0
$817$	−1.14535	−	1.98380i	−0.0400707	−	0.0694045i
$818$	17.2550			0.603308
$819$		0			0
$820$	−0.602407			−0.0210370
$821$	−0.855366	−	1.48154i	−0.0298525	−	0.0517060i	0.850713	−	0.525630i	$-0.176170\pi$
$821$	−0.855366	−	1.48154i	−0.0298525	−	0.0517060i	−0.880566	+	0.473924i	$0.842837\pi$
$822$		0			0
$823$	20.1887	−	34.9678i	0.703733	−	1.21890i	−0.263414	−	0.964683i	$-0.584849\pi$
$823$	20.1887	−	34.9678i	0.703733	−	1.21890i	0.967147	−	0.254218i	$-0.0818181\pi$
$824$	17.6579	+	30.5844i	0.615142	+	1.06546i
$825$		0			0
$826$	−3.33878	+	5.94616i	−0.116171	+	0.206893i
$827$	−19.5698			−0.680509			−0.340254	−	0.940333i	$-0.610513\pi$
$827$	−19.5698			−0.680509			−0.340254	+	0.940333i	$0.610513\pi$
$828$		0			0
$829$	−20.7871	+	36.0043i	−0.721966	+	1.25048i	0.238244	+	0.971205i	$0.423428\pi$
$829$	−20.7871	+	36.0043i	−0.721966	+	1.25048i	−0.960211	+	0.279277i	$0.909905\pi$
$830$	−23.5178	+	40.7341i	−0.816316	+	1.41390i
$831$		0			0
$832$	8.89542			0.308393
$833$	−27.9826	+	0.669951i	−0.969540	+	0.0232124i
$834$		0			0
$835$	7.33870	+	12.7110i	0.253966	+	0.439882i
$836$	−2.82324	+	4.89000i	−0.0976438	+	0.169124i
$837$		0			0
$838$	6.86604	+	11.8923i	0.237183	+	0.410814i
$839$	−45.8480			−1.58285			−0.791425	−	0.611266i	$-0.790660\pi$
$839$	−45.8480			−1.58285			−0.791425	+	0.611266i	$0.790660\pi$
$840$		0			0
$841$	−27.7986			−0.958574
$842$	−6.32804	−	10.9605i	−0.218079	−	0.377723i
$843$		0			0
$844$	1.99791	−	3.46049i	0.0687710	−	0.119115i
$845$	−1.45130	−	2.51373i	−0.0499262	−	0.0864748i
$846$		0			0
$847$	−18.1285	+	0.216982i	−0.622902	+	0.00745559i
$848$	21.6769			0.744388
$849$		0			0
$850$	−8.66674	+	15.0112i	−0.297267	+	0.514881i
$851$	0.967695	−	1.67610i	0.0331722	−	0.0574559i
$852$		0			0
$853$	40.0236			1.37038			0.685191	−	0.728364i	$-0.259719\pi$
$853$	40.0236			1.37038			0.685191	+	0.728364i	$0.259719\pi$
$854$	4.10258	+	6.91345i	0.140387	+	0.236573i
$855$		0			0
$856$	29.7846	+	51.5884i	1.01802	+	1.76326i
$857$	16.4351	−	28.4664i	0.561412	−	0.972395i	−0.435961	−	0.899966i	$-0.643591\pi$
$857$	16.4351	−	28.4664i	0.561412	−	0.972395i	0.997374	−	0.0724294i	$-0.0230752\pi$
$858$		0			0
$859$	17.0252	+	29.4885i	0.580891	+	1.00613i	0.995374	+	0.0960762i	$0.0306292\pi$
$859$	17.0252	+	29.4885i	0.580891	+	1.00613i	−0.414483	+	0.910057i	$0.636037\pi$
$860$	−0.380325			−0.0129690
$861$		0			0
$862$	1.53079			0.0521388
$863$	−7.03208	−	12.1799i	−0.239375	−	0.414609i	0.721160	−	0.692768i	$-0.243609\pi$
$863$	−7.03208	−	12.1799i	−0.239375	−	0.414609i	−0.960535	+	0.278159i	$0.910276\pi$
$864$		0			0
$865$	−0.864415	+	1.49721i	−0.0293910	+	0.0509067i
$866$	−3.52106	−	6.09866i	−0.119651	−	0.207241i
$867$		0			0
$868$	10.9912	−	0.131555i	0.373066	−	0.00446527i
$869$	17.8434			0.605295
$870$		0			0
$871$	−7.34709	+	12.7255i	−0.248947	+	0.431188i
$872$	1.67963	−	2.90920i	0.0568794	−	0.0985180i
$873$		0			0
$874$	−5.52715			−0.186959
$875$	5.92153	−	10.5459i	0.200184	−	0.356516i
$876$		0			0
$877$	−25.5335	−	44.2252i	−0.862204	−	1.49338i	−0.869797	−	0.493409i	$-0.835751\pi$
$877$	−25.5335	−	44.2252i	−0.862204	−	1.49338i	0.00759373	−	0.999971i	$-0.497583\pi$
$878$	−12.4784	+	21.6132i	−0.421125	+	0.729411i
$879$		0			0
$880$	−8.99982	−	15.5881i	−0.303384	−	0.525476i
$881$	18.4203			0.620597			0.310298	−	0.950639i	$-0.399571\pi$
$881$	18.4203			0.620597			0.310298	+	0.950639i	$0.399571\pi$
$882$		0			0
$883$	0.126678			0.00426305			0.00213153	−	0.999998i	$-0.499322\pi$
$883$	0.126678			0.00426305			0.00213153	+	0.999998i	$0.499322\pi$
$884$	−0.796204	−	1.37907i	−0.0267792	−	0.0463830i
$885$		0			0
$886$	−14.0679	+	24.3663i	−0.472619	+	0.818601i
$887$	1.93735	+	3.35559i	0.0650498	+	0.112670i	0.896716	−	0.442606i	$-0.145946\pi$
$887$	1.93735	+	3.35559i	0.0650498	+	0.112670i	−0.831666	+	0.555276i	$0.812613\pi$
$888$		0			0
$889$	−6.71181	+	11.9533i	−0.225107	+	0.400902i
$890$	−9.84874			−0.330131
$891$		0			0
$892$	3.48378	−	6.03409i	0.116646	−	0.202036i
$893$	36.7100	−	63.5837i	1.22845	−	2.12775i
$894$		0			0
$895$	−23.4433			−0.783622
$896$	−18.0549	+	0.216102i	−0.603173	+	0.00721945i
$897$		0			0
$898$	−11.6802	−	20.2308i	−0.389775	−	0.675109i
$899$	−5.71733	+	9.90270i	−0.190684	+	0.330274i
$900$		0			0
$901$	−14.2332	−	24.6527i	−0.474178	−	0.821300i
$902$	1.34326			0.0447257
$903$		0			0
$904$	3.32680			0.110648
$905$	−2.74766	−	4.75909i	−0.0913355	−	0.158198i
$906$		0			0
$907$	23.3871	−	40.5076i	0.776555	−	1.34503i	−0.157362	−	0.987541i	$-0.550299\pi$
$907$	23.3871	−	40.5076i	0.776555	−	1.34503i	0.933916	−	0.357491i	$-0.116368\pi$
$908$	1.89486	+	3.28200i	0.0628832	+	0.108917i
$909$		0			0
$910$	4.96005	+	8.35841i	0.164424	+	0.277079i
$911$	−5.93675			−0.196693			−0.0983467	−	0.995152i	$-0.531355\pi$
$911$	−5.93675			−0.196693			−0.0983467	+	0.995152i	$0.531355\pi$
$912$		0			0
$913$	−13.0379	+	22.5824i	−0.431493	+	0.747368i
$914$	−18.9727	+	32.8617i	−0.627561	+	1.08697i
$915$		0			0
$916$	−8.40952			−0.277858
$917$	−27.9549	+	0.334595i	−0.923151	+	0.0110493i
$918$		0			0
$919$	4.29351	+	7.43657i	0.141630	+	0.245310i	0.928110	−	0.372305i	$-0.121432\pi$
$919$	4.29351	+	7.43657i	0.141630	+	0.245310i	−0.786481	+	0.617615i	$0.788099\pi$
$920$	−2.76318	+	4.78597i	−0.0910995	+	0.157789i
$921$		0			0
$922$	−18.4461	−	31.9496i	−0.607490	−	1.05220i
$923$	−3.60141			−0.118542
$924$		0			0
$925$	−10.5677			−0.347463
$926$	0.986543	+	1.70874i	0.0324198	+	0.0561528i
$927$		0			0
$928$	−1.21485	+	2.10418i	−0.0398794	+	0.0690732i
$929$	−4.22972	−	7.32610i	−0.138773	−	0.240361i	0.788260	−	0.615343i	$-0.210982\pi$
$929$	−4.22972	−	7.32610i	−0.138773	−	0.240361i	−0.927032	+	0.374981i	$0.877649\pi$
$930$		0			0
$931$	−23.3502	+	42.7766i	−0.765271	+	1.40195i
$932$	5.64648			0.184957
$933$		0			0
$934$	−7.86141	+	13.6164i	−0.257233	+	0.445541i
$935$	−11.8187	+	20.4706i	−0.386513	+	0.669460i
$936$		0			0
$937$	−33.3596			−1.08981			−0.544905	−	0.838498i	$-0.683434\pi$
$937$	−33.3596			−1.08981			−0.544905	+	0.838498i	$0.683434\pi$
$938$	24.0899	−	42.9026i	0.786562	−	1.40082i
$939$		0			0
$940$	−6.09497	−	10.5568i	−0.198796	−	0.344325i
$941$	−6.70187	+	11.6080i	−0.218475	+	0.378409i	−0.954342	−	0.298717i	$-0.903441\pi$
$941$	−6.70187	+	11.6080i	−0.218475	+	0.378409i	0.735867	+	0.677126i	$0.236775\pi$
$942$		0			0
$943$	−0.163454	−	0.283110i	−0.00532278	−	0.00921933i
$944$	6.20121			0.201832
$945$		0			0
$946$	0.848057			0.0275727
$947$	21.5397	+	37.3078i	0.699946	+	1.21234i	0.968485	+	0.249073i	$0.0801259\pi$
$947$	21.5397	+	37.3078i	0.699946	+	1.21234i	−0.268539	+	0.963269i	$0.586541\pi$
$948$		0			0
$949$	−1.48786	+	2.57706i	−0.0482981	+	0.0836548i
$950$	15.0897	+	26.1362i	0.489575	+	0.847969i
$951$		0			0
$952$	16.3872	+	27.6149i	0.531113	+	0.895003i
$953$	−16.7332			−0.542040			−0.271020	−	0.962574i	$-0.587361\pi$
$953$	−16.7332			−0.542040			−0.271020	+	0.962574i	$0.587361\pi$
$954$		0			0
$955$	5.37234	−	9.30517i	0.173845	−	0.301108i
$956$	3.29091	−	5.70002i	0.106436	−	0.184352i
$957$		0			0
$958$	45.6325			1.47432
$959$	−7.92809	−	13.3600i	−0.256011	−	0.431417i
$960$		0			0
$961$	−38.9183	−	67.4085i	−1.25543	−	2.17447i
$962$	−1.95243	+	3.38172i	−0.0629490	+	0.109031i
$963$		0			0
$964$	−2.72572	−	4.72109i	−0.0877896	−	0.152056i
$965$	39.4390			1.26959
$966$		0			0
$967$	44.7594			1.43937			0.719683	−	0.694303i	$-0.244287\pi$
$967$	44.7594			1.43937			0.719683	+	0.694303i	$0.244287\pi$
$968$	10.3993	+	18.0121i	0.334246	+	0.578932i
$969$		0			0
$970$	−4.27790	+	7.40954i	−0.137355	+	0.237906i
$971$	−2.10129	−	3.63955i	−0.0674337	−	0.116799i	0.830337	−	0.557261i	$-0.188148\pi$
$971$	−2.10129	−	3.63955i	−0.0674337	−	0.116799i	−0.897771	+	0.440463i	$0.854814\pi$
$972$		0			0
$973$	5.18143	−	9.22783i	0.166109	−	0.295830i
$974$	−9.23899			−0.296036
$975$		0			0
$976$	3.65517	−	6.33093i	0.116999	−	0.202648i
$977$	−12.8449	+	22.2481i	−0.410946	+	0.711779i	−0.994993	−	0.0999403i	$-0.968135\pi$
$977$	−12.8449	+	22.2481i	−0.410946	+	0.711779i	0.584048	+	0.811719i	$0.301468\pi$
$978$		0			0
$979$	−5.45999			−0.174502
$980$	4.21227	+	6.90854i	0.134556	+	0.220685i
$981$		0			0
$982$	−2.84242	−	4.92321i	−0.0907051	−	0.157106i
$983$	−15.9122	+	27.5607i	−0.507520	+	0.879051i	0.492442	+	0.870345i	$0.336104\pi$
$983$	−15.9122	+	27.5607i	−0.507520	+	0.879051i	−0.999962	+	0.00870538i	$0.997229\pi$
$984$		0			0
$985$	−14.0814	−	24.3896i	−0.448669	−	0.777118i
$986$	−5.54689			−0.176649
$987$		0			0
$988$	−2.77255			−0.0882067
$989$	−0.103195	−	0.178739i	−0.00328141	−	0.00568358i
$990$		0			0
$991$	−4.73739	+	8.20540i	−0.150488	+	0.260653i	−0.931407	−	0.363979i	$-0.881418\pi$
$991$	−4.73739	+	8.20540i	−0.150488	+	0.260653i	0.780919	+	0.624632i	$0.214751\pi$
$992$	−11.5631	−	20.0279i	−0.367129	−	0.635887i
$993$		0			0
$994$	12.0584	−	0.144329i	0.382469	−	0.00457783i
$995$	76.2570			2.41751
$996$		0			0
$997$	−10.9755	+	19.0102i	−0.347599	+	0.602059i	−0.985822	−	0.167792i	$-0.946336\pi$
$997$	−10.9755	+	19.0102i	−0.347599	+	0.602059i	0.638224	+	0.769851i	$0.279670\pi$
$998$	7.19332	−	12.4592i	0.227701	−	0.394389i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.j.h.235.3		10
3.2	odd	2		91.2.e.c.53.3	✓	10
7.2	even	3	inner	819.2.j.h.352.3		10
7.3	odd	6		5733.2.a.bm.1.3		5
7.4	even	3		5733.2.a.bl.1.3		5
12.11	even	2		1456.2.r.p.417.1		10
21.2	odd	6		91.2.e.c.79.3	yes	10
21.5	even	6		637.2.e.m.79.3		10
21.11	odd	6		637.2.a.l.1.3		5
21.17	even	6		637.2.a.k.1.3		5
21.20	even	2		637.2.e.m.508.3		10
39.38	odd	2		1183.2.e.f.508.3		10
84.23	even	6		1456.2.r.p.625.1		10
273.38	even	6		8281.2.a.bx.1.3		5
273.116	odd	6		8281.2.a.bw.1.3		5
273.233	odd	6		1183.2.e.f.170.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.c.53.3	✓	10	3.2	odd	2
91.2.e.c.79.3	yes	10	21.2	odd	6
637.2.a.k.1.3		5	21.17	even	6
637.2.a.l.1.3		5	21.11	odd	6
637.2.e.m.79.3		10	21.5	even	6
637.2.e.m.508.3		10	21.20	even	2
819.2.j.h.235.3		10	1.1	even	1	trivial
819.2.j.h.352.3		10	7.2	even	3	inner
1183.2.e.f.170.3		10	273.233	odd	6
1183.2.e.f.508.3		10	39.38	odd	2
1456.2.r.p.417.1		10	12.11	even	2
1456.2.r.p.625.1		10	84.23	even	6
5733.2.a.bl.1.3		5	7.4	even	3
5733.2.a.bm.1.3		5	7.3	odd	6
8281.2.a.bw.1.3		5	273.116	odd	6
8281.2.a.bx.1.3		5	273.38	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.632804 + 1.09605i) q^{2} +(0.199118 - 0.344882i) q^{4} +(-1.45130 - 2.51373i) q^{5} +(-1.29536 + 2.30696i) q^{7} +3.03523 q^{8} +O(q^{10})\)	\(q+(0.632804 + 1.09605i) q^{2} +(0.199118 - 0.344882i) q^{4} +(-1.45130 - 2.51373i) q^{5} +(-1.29536 + 2.30696i) q^{7} +3.03523 q^{8} +(1.83678 - 3.18139i) q^{10} +(1.01828 - 1.76372i) q^{11} +1.00000 q^{13} +(-3.34825 + 0.0400756i) q^{14} +(1.52247 + 2.63699i) q^{16} +(1.99933 - 3.46294i) q^{17} +(-3.48105 - 6.02935i) q^{19} -1.15592 q^{20} +2.57749 q^{22} +(-0.313640 - 0.543240i) q^{23} +(-1.71254 + 2.96621i) q^{25} +(0.632804 + 1.09605i) q^{26} +(0.537699 + 0.906101i) q^{28} -1.09606 q^{29} +(5.21624 - 9.03479i) q^{31} +(1.10838 - 1.91977i) q^{32} +5.06074 q^{34} +(7.67901 - 0.0919110i) q^{35} +(1.54268 + 2.67201i) q^{37} +(4.40565 - 7.63080i) q^{38} +(-4.40502 - 7.62973i) q^{40} +0.521150 q^{41} +0.329024 q^{43} +(-0.405516 - 0.702374i) q^{44} +(0.396945 - 0.687530i) q^{46} +(5.27284 + 9.13283i) q^{47} +(-3.64409 - 5.97667i) q^{49} -4.33482 q^{50} +(0.199118 - 0.344882i) q^{52} +(3.55950 - 6.16523i) q^{53} -5.91133 q^{55} +(-3.93171 + 7.00214i) q^{56} +(-0.693593 - 1.20134i) q^{58} +(1.01828 - 1.76372i) q^{59} +(-1.20041 - 2.07917i) q^{61} +13.2034 q^{62} +8.89542 q^{64} +(-1.45130 - 2.51373i) q^{65} +(-7.34709 + 12.7255i) q^{67} +(-0.796204 - 1.37907i) q^{68} +(4.96005 + 8.35841i) q^{70} -3.60141 q^{71} +(-1.48786 + 2.57706i) q^{73} +(-1.95243 + 3.38172i) q^{74} -2.77255 q^{76} +(2.74978 + 4.63378i) q^{77} +(4.38075 + 7.58769i) q^{79} +(4.41912 - 7.65414i) q^{80} +(0.329786 + 0.571206i) q^{82} -12.8039 q^{83} -11.6065 q^{85} +(0.208208 + 0.360627i) q^{86} +(3.09072 - 5.35328i) q^{88} +(-1.34049 - 2.32180i) q^{89} +(-1.29536 + 2.30696i) q^{91} -0.249805 q^{92} +(-6.67335 + 11.5586i) q^{94} +(-10.1041 + 17.5008i) q^{95} -2.32902 q^{97} +(4.24472 - 7.77617i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} - 8 q^{4} + 2 q^{5} + q^{7} - 18 q^{8}+O(q^{10}) \) 10 * q + 4 * q^2 - 8 * q^4 + 2 * q^5 + q^7 - 18 * q^8	\( 10 q + 4 q^{2} - 8 q^{4} + 2 q^{5} + q^{7} - 18 q^{8} + 5 q^{10} + 11 q^{11} + 10 q^{13} - 10 q^{14} - 10 q^{16} - 5 q^{17} - 9 q^{19} - 2 q^{20} + 16 q^{22} + 10 q^{23} - 9 q^{25} + 4 q^{26} + 37 q^{28} + 6 q^{29} + 6 q^{31} + 22 q^{32} - 44 q^{34} + 4 q^{35} - 4 q^{37} - 10 q^{38} - 28 q^{40} - 28 q^{41} + 4 q^{43} - 3 q^{46} + q^{47} - 11 q^{49} - 18 q^{50} - 8 q^{52} + 17 q^{53} + 21 q^{56} + 27 q^{58} + 11 q^{59} + 11 q^{61} + 46 q^{62} + 18 q^{64} + 2 q^{65} - 13 q^{67} - 32 q^{68} + 49 q^{70} - 30 q^{71} - 33 q^{74} + 16 q^{76} + 46 q^{77} - 2 q^{79} + 55 q^{80} - 34 q^{82} - 12 q^{83} - 44 q^{85} + 28 q^{86} + 3 q^{88} - 4 q^{89} + q^{91} - 42 q^{92} - 20 q^{94} - 12 q^{95} - 24 q^{97} + 7 q^{98}+O(q^{100}) \) 10 * q + 4 * q^2 - 8 * q^4 + 2 * q^5 + q^7 - 18 * q^8 + 5 * q^10 + 11 * q^11 + 10 * q^13 - 10 * q^14 - 10 * q^16 - 5 * q^17 - 9 * q^19 - 2 * q^20 + 16 * q^22 + 10 * q^23 - 9 * q^25 + 4 * q^26 + 37 * q^28 + 6 * q^29 + 6 * q^31 + 22 * q^32 - 44 * q^34 + 4 * q^35 - 4 * q^37 - 10 * q^38 - 28 * q^40 - 28 * q^41 + 4 * q^43 - 3 * q^46 + q^47 - 11 * q^49 - 18 * q^50 - 8 * q^52 + 17 * q^53 + 21 * q^56 + 27 * q^58 + 11 * q^59 + 11 * q^61 + 46 * q^62 + 18 * q^64 + 2 * q^65 - 13 * q^67 - 32 * q^68 + 49 * q^70 - 30 * q^71 - 33 * q^74 + 16 * q^76 + 46 * q^77 - 2 * q^79 + 55 * q^80 - 34 * q^82 - 12 * q^83 - 44 * q^85 + 28 * q^86 + 3 * q^88 - 4 * q^89 + q^91 - 42 * q^92 - 20 * q^94 - 12 * q^95 - 24 * q^97 + 7 * q^98

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