LMFDB - Embedded newform 819.2.ct.a.127.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(127,819)]

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, 0, 5]))

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

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

chi := DirichletCharacter("819.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.ct (of order $6$, 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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.58891012706304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.6
Root			$-1.12906 - 0.851598i$ of defining polynomial
Character	$\chi$	$=$	819.127
Dual form			819.2.ct.a.316.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.34104 - 1.35160i) q^{2} +(2.65363 - 4.59623i) q^{4} +3.25812i q^{5} +(0.866025 + 0.500000i) q^{7} -8.94020i q^{8} +O(q^{10})$	\(q+(2.34104 - 1.35160i) q^{2} +(2.65363 - 4.59623i) q^{4} +3.25812i q^{5} +(0.866025 + 0.500000i) q^{7} -8.94020i q^{8} +(4.40367 + 7.62739i) q^{10} +(1.59871 - 0.923014i) q^{11} +(3.60550 + 0.0186461i) q^{13} +2.70320 q^{14} +(-6.77628 - 11.7369i) q^{16} +(-1.07657 + 1.86467i) q^{17} +(-2.07929 - 1.20048i) q^{19} +(14.9751 + 8.64587i) q^{20} +(2.49509 - 4.32162i) q^{22} +(-0.906314 - 1.56978i) q^{23} -5.61537 q^{25} +(8.46582 - 4.82954i) q^{26} +(4.59623 - 2.65363i) q^{28} +(-1.36703 - 2.36777i) q^{29} -1.74236i q^{31} +(-16.2422 - 9.37743i) q^{32} +5.82036i q^{34} +(-1.62906 + 2.82162i) q^{35} +(-5.14042 + 2.96783i) q^{37} -6.49025 q^{38} +29.1283 q^{40} +(-3.65577 + 2.11066i) q^{41} +(-4.34111 + 7.51903i) q^{43} -9.79737i q^{44} +(-4.24343 - 2.44994i) q^{46} -5.87774i q^{47} +(0.500000 + 0.866025i) q^{49} +(-13.1458 + 7.58972i) q^{50} +(9.65339 - 16.5222i) q^{52} +9.30628 q^{53} +(3.00729 + 5.20878i) q^{55} +(4.47010 - 7.74244i) q^{56} +(-6.40054 - 3.69535i) q^{58} +(-9.31173 - 5.37613i) q^{59} +(-5.05504 + 8.75558i) q^{61} +(-2.35497 - 4.07893i) q^{62} -23.5929 q^{64} +(-0.0607514 + 11.7472i) q^{65} +(0.716130 - 0.413458i) q^{67} +(5.71365 + 9.89633i) q^{68} +8.80735i q^{70} +(2.03884 + 1.17712i) q^{71} +3.19482i q^{73} +(-8.02261 + 13.8956i) q^{74} +(-11.0353 + 6.37126i) q^{76} +1.84603 q^{77} +0.801911 q^{79} +(38.2402 - 22.0780i) q^{80} +(-5.70552 + 9.88225i) q^{82} +9.97031i q^{83} +(-6.07534 - 3.50760i) q^{85} +23.4698i q^{86} +(-8.25193 - 14.2928i) q^{88} +(-13.0886 + 7.55674i) q^{89} +(3.11313 + 1.81890i) q^{91} -9.62010 q^{92} +(-7.94435 - 13.7600i) q^{94} +(3.91130 - 6.77458i) q^{95} +(7.99489 + 4.61585i) q^{97} +(2.34104 + 1.35160i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4}+O(q^{10}) $ 12 * q + 4 * q^4	$ 12 q + 4 q^{4} + 12 q^{10} - 6 q^{11} + 4 q^{13} + 8 q^{14} - 8 q^{16} + 4 q^{17} + 12 q^{20} + 6 q^{22} + 12 q^{23} - 20 q^{25} + 42 q^{26} - 8 q^{29} - 36 q^{32} - 6 q^{35} - 42 q^{37} - 4 q^{38} + 92 q^{40} - 30 q^{41} + 2 q^{43} + 12 q^{46} + 6 q^{49} + 18 q^{50} + 2 q^{52} + 44 q^{53} - 6 q^{55} + 12 q^{56} - 12 q^{58} - 18 q^{59} + 14 q^{61} + 4 q^{62} - 52 q^{64} - 60 q^{65} - 24 q^{67} + 8 q^{68} + 24 q^{71} - 6 q^{74} - 18 q^{76} - 8 q^{77} - 56 q^{79} + 72 q^{80} + 14 q^{82} - 48 q^{85} - 14 q^{88} + 12 q^{89} + 14 q^{91} - 24 q^{92} + 4 q^{94} + 22 q^{95} + 6 q^{97}+O(q^{100}) $ 12 * q + 4 * q^4 + 12 * q^10 - 6 * q^11 + 4 * q^13 + 8 * q^14 - 8 * q^16 + 4 * q^17 + 12 * q^20 + 6 * q^22 + 12 * q^23 - 20 * q^25 + 42 * q^26 - 8 * q^29 - 36 * q^32 - 6 * q^35 - 42 * q^37 - 4 * q^38 + 92 * q^40 - 30 * q^41 + 2 * q^43 + 12 * q^46 + 6 * q^49 + 18 * q^50 + 2 * q^52 + 44 * q^53 - 6 * q^55 + 12 * q^56 - 12 * q^58 - 18 * q^59 + 14 * q^61 + 4 * q^62 - 52 * q^64 - 60 * q^65 - 24 * q^67 + 8 * q^68 + 24 * q^71 - 6 * q^74 - 18 * q^76 - 8 * q^77 - 56 * q^79 + 72 * q^80 + 14 * q^82 - 48 * q^85 - 14 * q^88 + 12 * q^89 + 14 * q^91 - 24 * q^92 + 4 * q^94 + 22 * q^95 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	2.34104	−	1.35160i	1.65536	−	0.955724i	0.680549	−	0.732702i	$-0.261741\pi$
$2$	2.34104	−	1.35160i	1.65536	−	0.955724i	0.974813	−	0.223022i	$-0.0715921\pi$
$3$		0			0
$3$		0			0
$4$	2.65363	−	4.59623i	1.32682	−	2.29811i
$5$			3.25812i			1.45708i	0.685005	+	0.728539i	$0.259800\pi$
$5$			3.25812i			1.45708i	−0.685005	+	0.728539i	$0.740200\pi$
$6$		0			0
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$		−	8.94020i		−	3.16084i
$9$		0			0
$10$	4.40367	+	7.62739i	1.39256	+	2.41199i
$11$	1.59871	−	0.923014i	0.482028	−	0.278299i	−0.239233	−	0.970962i	$-0.576896\pi$
$11$	1.59871	−	0.923014i	0.482028	−	0.278299i	0.721261	+	0.692663i	$0.243563\pi$
$12$		0			0
$13$	3.60550	+	0.0186461i	0.999987	+	0.00517151i
$13$	3.60550	+	0.0186461i	0.999987	+	0.00517151i
$14$	2.70320			0.722460
$15$		0			0
$16$	−6.77628	−	11.7369i	−1.69407	−	2.93422i
$17$	−1.07657	+	1.86467i	−0.261107	+	0.452250i	−0.966536	−	0.256530i	$-0.917421\pi$
$17$	−1.07657	+	1.86467i	−0.261107	+	0.452250i	0.705430	+	0.708780i	$0.250754\pi$
$18$		0			0
$19$	−2.07929	−	1.20048i	−0.477021	−	0.275408i	0.242153	−	0.970238i	$-0.422146\pi$
$19$	−2.07929	−	1.20048i	−0.477021	−	0.275408i	−0.719174	+	0.694830i	$0.755480\pi$
$20$	14.9751	+	8.64587i	3.34853	+	1.93328i
$21$		0			0
$22$	2.49509	−	4.32162i	0.531954	−	0.921372i
$23$	−0.906314	−	1.56978i	−0.188979	−	0.327322i	0.755931	−	0.654652i	$-0.227185\pi$
$23$	−0.906314	−	1.56978i	−0.188979	−	0.327322i	−0.944910	+	0.327329i	$0.893851\pi$
$24$		0			0
$25$	−5.61537			−1.12307
$26$	8.46582	−	4.82954i	1.66028	−	0.947151i
$27$		0			0
$28$	4.59623	−	2.65363i	0.868606	−	0.501490i
$29$	−1.36703	−	2.36777i	−0.253851	−	0.439683i	0.710732	−	0.703463i	$-0.248364\pi$
$29$	−1.36703	−	2.36777i	−0.253851	−	0.439683i	−0.964583	+	0.263780i	$0.915031\pi$
$30$		0			0
$31$		−	1.74236i		−	0.312937i	−0.987683	−	0.156468i	$-0.949989\pi$
$31$		−	1.74236i		−	0.312937i	0.987683	−	0.156468i	$-0.0500110\pi$
$32$	−16.2422	−	9.37743i	−2.87124	−	1.65771i
$33$		0			0
$34$			5.82036i			0.998183i
$35$	−1.62906	+	2.82162i	−0.275362	+	0.476940i
$36$		0			0
$37$	−5.14042	+	2.96783i	−0.845081	+	0.487908i	−0.858988	−	0.511996i	$-0.828906\pi$
$37$	−5.14042	+	2.96783i	−0.845081	+	0.487908i	0.0139073	+	0.999903i	$0.495573\pi$
$38$	−6.49025			−1.05286
$39$		0			0
$40$	29.1283			4.60558
$41$	−3.65577	+	2.11066i	−0.570935	+	0.329629i	−0.757523	−	0.652809i	$-0.773590\pi$
$41$	−3.65577	+	2.11066i	−0.570935	+	0.329629i	0.186588	+	0.982438i	$0.440257\pi$
$42$		0			0
$43$	−4.34111	+	7.51903i	−0.662014	+	1.14664i	0.318072	+	0.948067i	$0.396965\pi$
$43$	−4.34111	+	7.51903i	−0.662014	+	1.14664i	−0.980086	+	0.198575i	$0.936369\pi$
$44$		−	9.79737i		−	1.47701i
$45$		0			0
$46$	−4.24343	−	2.44994i	−0.625659	−	0.361224i
$47$		−	5.87774i		−	0.857357i	−0.903457	−	0.428678i	$-0.858979\pi$
$47$		−	5.87774i		−	0.857357i	0.903457	−	0.428678i	$-0.141021\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−13.1458	+	7.58972i	−1.85910	+	1.07335i
$51$		0			0
$52$	9.65339	−	16.5222i	1.33868	−	2.29122i
$53$	9.30628			1.27832			0.639158	−	0.769076i	$-0.279283\pi$
$53$	9.30628			1.27832			0.639158	+	0.769076i	$0.279283\pi$
$54$		0			0
$55$	3.00729	+	5.20878i	0.405503	+	0.702352i
$56$	4.47010	−	7.74244i	0.597342	−	1.03463i
$57$		0			0
$58$	−6.40054	−	3.69535i	−0.840432	−	0.485224i
$59$	−9.31173	−	5.37613i	−1.21228	−	0.699912i	−0.249028	−	0.968496i	$-0.580111\pi$
$59$	−9.31173	−	5.37613i	−1.21228	−	0.699912i	−0.963256	+	0.268584i	$0.913444\pi$
$60$		0			0
$61$	−5.05504	+	8.75558i	−0.647231	+	1.12104i	0.336550	+	0.941665i	$0.390740\pi$
$61$	−5.05504	+	8.75558i	−0.647231	+	1.12104i	−0.983781	+	0.179371i	$0.942594\pi$
$62$	−2.35497	−	4.07893i	−0.299081	−	0.518024i
$63$		0			0
$64$	−23.5929			−2.94911
$65$	−0.0607514	+	11.7472i	−0.00753529	+	1.45706i
$66$		0			0
$67$	0.716130	−	0.413458i	0.0874892	−	0.0505119i	−0.455617	−	0.890176i	$-0.650581\pi$
$67$	0.716130	−	0.413458i	0.0874892	−	0.0505119i	0.543106	+	0.839664i	$0.317248\pi$
$68$	5.71365	+	9.89633i	0.692881	+	1.20011i
$69$		0			0
$70$			8.80735i			1.05268i
$71$	2.03884	+	1.17712i	0.241965	+	0.139699i	0.616080	−	0.787684i	$-0.288720\pi$
$71$	2.03884	+	1.17712i	0.241965	+	0.139699i	−0.374114	+	0.927383i	$0.622053\pi$
$72$		0			0
$73$			3.19482i			0.373925i	0.982367	+	0.186963i	$0.0598644\pi$
$73$			3.19482i			0.373925i	−0.982367	+	0.186963i	$0.940136\pi$
$74$	−8.02261	+	13.8956i	−0.932610	+	1.61533i
$75$		0			0
$76$	−11.0353	+	6.37126i	−1.26584	+	0.730833i
$77$	1.84603			0.210374
$78$		0			0
$79$	0.801911			0.0902220			0.0451110	−	0.998982i	$-0.485636\pi$
$79$	0.801911			0.0902220			0.0451110	+	0.998982i	$0.485636\pi$
$80$	38.2402	−	22.0780i	4.27538	−	2.46839i
$81$		0			0
$82$	−5.70552	+	9.88225i	−0.630069	+	1.09131i
$83$			9.97031i			1.09438i	0.837007	+	0.547192i	$0.184303\pi$
$83$			9.97031i			1.09438i	−0.837007	+	0.547192i	$0.815697\pi$
$84$		0			0
$85$	−6.07534	−	3.50760i	−0.658963	−	0.380452i
$86$			23.4698i			2.53081i
$87$		0			0
$88$	−8.25193	−	14.2928i	−0.879658	−	1.52361i
$89$	−13.0886	+	7.55674i	−1.38739	+	0.801012i	−0.993021	−	0.117938i	$-0.962372\pi$
$89$	−13.0886	+	7.55674i	−1.38739	+	0.801012i	−0.394373	+	0.918950i	$0.629038\pi$
$90$		0			0
$91$	3.11313	+	1.81890i	0.326345	+	0.190672i
$92$	−9.62010			−1.00296
$93$		0			0
$94$	−7.94435	−	13.7600i	−0.819397	−	1.41924i
$95$	3.91130	−	6.77458i	0.401291	−	0.695057i
$96$		0			0
$97$	7.99489	+	4.61585i	0.811758	+	0.468669i	0.847566	−	0.530690i	$-0.178067\pi$
$97$	7.99489	+	4.61585i	0.811758	+	0.468669i	−0.0358079	+	0.999359i	$0.511400\pi$
$98$	2.34104	+	1.35160i	0.236480	+	0.136532i
$99$		0			0
$100$	−14.9011	+	25.8095i	−1.49011	+	2.58095i
$101$	−7.41169	−	12.8374i	−0.737491	−	1.27737i	−0.953622	−	0.301007i	$-0.902677\pi$
$101$	−7.41169	−	12.8374i	−0.737491	−	1.27737i	0.216131	−	0.976364i	$-0.430656\pi$
$102$		0			0
$103$	4.28286			0.422003			0.211001	−	0.977486i	$-0.432328\pi$
$103$	4.28286			0.422003			0.211001	+	0.977486i	$0.432328\pi$
$104$	0.166700	−	32.2339i	0.0163463	−	3.16079i
$105$		0			0
$106$	21.7863	−	12.5783i	2.11608	−	1.22172i
$107$	−9.56289	−	16.5634i	−0.924479	−	1.60124i	−0.792397	−	0.610006i	$-0.791167\pi$
$107$	−9.56289	−	16.5634i	−0.924479	−	1.60124i	−0.132082	−	0.991239i	$-0.542166\pi$
$108$		0			0
$109$		−	4.27153i		−	0.409139i	−0.978852	−	0.204569i	$-0.934421\pi$
$109$		−	4.27153i		−	0.409139i	0.978852	−	0.204569i	$-0.0655794\pi$
$110$	14.0804	+	8.12930i	1.34251	+	0.775099i
$111$		0			0
$112$		−	13.5526i		−	1.28060i
$113$	1.37488	−	2.38137i	0.129338	−	0.224020i	−0.794082	−	0.607810i	$-0.792048\pi$
$113$	1.37488	−	2.38137i	0.129338	−	0.224020i	0.923420	+	0.383790i	$0.125381\pi$
$114$		0			0
$115$	5.11454	−	2.95288i	0.476934	−	0.275358i
$116$	−14.5104			−1.34726
$117$		0			0
$118$	−29.0655			−2.67569
$119$	−1.86467	+	1.07657i	−0.170934	+	0.0986890i
$120$		0			0
$121$	−3.79609	+	6.57502i	−0.345099	+	0.597729i
$122$			27.3295i			2.47430i
$123$		0			0
$124$	−8.00828	−	4.62358i	−0.719165	−	0.415210i
$125$		−	2.00495i		−	0.179329i
$126$		0			0
$127$	−4.86719	−	8.43022i	−0.431893	−	0.748061i	0.565143	−	0.824993i	$-0.308821\pi$
$127$	−4.86719	−	8.43022i	−0.431893	−	0.748061i	−0.997036	+	0.0769320i	$0.975488\pi$
$128$	−22.7475	+	13.1333i	−2.01061	+	1.16083i
$129$		0			0
$130$	15.7352	+	27.5827i	1.38007	+	2.41916i
$131$	18.6615			1.63046			0.815230	−	0.579138i	$-0.196611\pi$
$131$	18.6615			1.63046			0.815230	+	0.579138i	$0.196611\pi$
$132$		0			0
$133$	−1.20048	−	2.07929i	−0.104095	−	0.180297i
$134$	1.11766	−	1.93584i	0.0965509	−	0.167231i
$135$		0			0
$136$	16.6706	+	9.62475i	1.42949	+	0.825315i
$137$	7.29328	+	4.21078i	0.623107	+	0.359751i	0.778078	−	0.628168i	$-0.216195\pi$
$137$	7.29328	+	4.21078i	0.623107	+	0.359751i	−0.154971	+	0.987919i	$0.549528\pi$
$138$		0			0
$139$	8.81809	−	15.2734i	0.747941	−	1.29547i	−0.200867	−	0.979619i	$-0.564376\pi$
$139$	8.81809	−	15.2734i	0.747941	−	1.29547i	0.948808	−	0.315853i	$-0.102291\pi$
$140$	8.64587	+	14.9751i	0.730709	+	1.26563i
$141$		0			0
$142$	6.36399			0.534054
$143$	5.78135	−	3.29812i	0.483461	−	0.275803i
$144$		0			0
$145$	7.71448	−	4.45396i	0.640653	−	0.369881i
$146$	4.31811	+	7.47919i	0.357370	+	0.618982i
$147$		0			0
$148$			31.5021i			2.58946i
$149$	3.48232	+	2.01052i	0.285283	+	0.164708i	0.635813	−	0.771843i	$-0.280665\pi$
$149$	3.48232	+	2.01052i	0.285283	+	0.164708i	−0.350530	+	0.936552i	$0.613998\pi$
$150$		0			0
$151$			18.9010i			1.53814i	0.639165	+	0.769069i	$0.279280\pi$
$151$			18.9010i			1.53814i	−0.639165	+	0.769069i	$0.720720\pi$
$152$	−10.7325	+	18.5892i	−0.870521	+	1.50779i
$153$		0			0
$154$	4.32162	−	2.49509i	0.348246	−	0.201060i
$155$	5.67682			0.455973
$156$		0			0
$157$	−11.5735			−0.923670			−0.461835	−	0.886966i	$-0.652809\pi$
$157$	−11.5735			−0.923670			−0.461835	+	0.886966i	$0.652809\pi$
$158$	1.87730	−	1.08386i	0.149350	−	0.0862273i
$159$		0			0
$160$	30.5528	−	52.9190i	2.41541	−	4.18362i
$161$		−	1.81263i		−	0.142855i
$162$		0			0
$163$	−3.81520	−	2.20271i	−0.298830	−	0.172529i	0.343087	−	0.939304i	$-0.388527\pi$
$163$	−3.81520	−	2.20271i	−0.298830	−	0.172529i	−0.641917	+	0.766774i	$0.721861\pi$
$164$			22.4037i			1.74943i
$165$		0			0
$166$	13.4759	+	23.3409i	1.04593	+	1.81160i
$167$	7.81076	−	4.50954i	0.604415	−	0.348959i	−0.166362	−	0.986065i	$-0.553202\pi$
$167$	7.81076	−	4.50954i	0.604415	−	0.348959i	0.770776	+	0.637106i	$0.219869\pi$
$168$		0			0
$169$	12.9993	+	0.134457i	0.999947	+	0.0103429i
$170$	−18.9635			−1.45443
$171$		0			0
$172$	23.0395	+	39.9055i	1.75674	+	3.04277i
$173$	−3.04600	+	5.27583i	−0.231583	+	0.401114i	−0.958274	−	0.285851i	$-0.907724\pi$
$173$	−3.04600	+	5.27583i	−0.231583	+	0.401114i	0.726691	+	0.686964i	$0.241057\pi$
$174$		0			0
$175$	−4.86305	−	2.80769i	−0.367612	−	0.212241i
$176$	−21.6666	−	12.5092i	−1.63318	−	0.942917i
$177$		0			0
$178$	−20.4273	+	35.3812i	−1.53109	+	2.65193i
$179$	−1.93982	−	3.35987i	−0.144989	−	0.251128i	0.784380	−	0.620281i	$-0.212981\pi$
$179$	−1.93982	−	3.35987i	−0.144989	−	0.251128i	−0.929369	+	0.369152i	$0.879648\pi$
$180$		0			0
$181$	−6.58392			−0.489379			−0.244690	−	0.969601i	$-0.578686\pi$
$181$	−6.58392			−0.489379			−0.244690	+	0.969601i	$0.578686\pi$
$182$	9.74638	+	0.0504042i	0.722450	+	0.00373621i
$183$		0			0
$184$	−14.0342	+	8.10262i	−1.03461	+	0.597333i
$185$	−9.66954	−	16.7481i	−0.710919	−	1.23135i
$186$		0			0
$187$			3.97476i			0.290663i
$188$	−27.0155	−	15.5974i	−1.97030	−	1.13756i
$189$		0			0
$190$		−	21.1460i		−	1.53410i
$191$	−6.87168	+	11.9021i	−0.497218	+	0.861206i	−0.999995	−	0.00320983i	$-0.998978\pi$
$191$	−6.87168	+	11.9021i	−0.497218	+	0.861206i	0.502777	+	0.864416i	$0.332312\pi$
$192$		0			0
$193$	19.7047	−	11.3765i	1.41838	−	0.818899i	0.422219	−	0.906494i	$-0.361251\pi$
$193$	19.7047	−	11.3765i	1.41838	−	0.818899i	0.996156	+	0.0875946i	$0.0279180\pi$
$194$	24.9551			1.79167
$195$		0			0
$196$	5.30727			0.379091
$197$	12.5809	−	7.26358i	0.896352	−	0.517509i	0.0203371	−	0.999793i	$-0.493526\pi$
$197$	12.5809	−	7.26358i	0.896352	−	0.517509i	0.876015	+	0.482284i	$0.160193\pi$
$198$		0			0
$199$	11.9202	−	20.6464i	0.845001	−	1.46358i	−0.0406192	−	0.999175i	$-0.512933\pi$
$199$	11.9202	−	20.6464i	0.845001	−	1.46358i	0.885620	−	0.464410i	$-0.153734\pi$
$200$			50.2025i			3.54985i
$201$		0			0
$202$	−34.7021	−	20.0353i	−2.44163	−	1.40968i
$203$		−	2.73406i		−	0.191894i
$204$		0			0
$205$	−6.87678	−	11.9109i	−0.480295	−	0.831896i
$206$	10.0263	−	5.78871i	0.698568	−	0.403318i
$207$		0			0
$208$	−24.2131	−	42.4437i	−1.67887	−	2.94294i
$209$	−4.43223			−0.306584
$210$		0			0
$211$	−2.15764	−	3.73714i	−0.148538	−	0.257275i	0.782149	−	0.623091i	$-0.214123\pi$
$211$	−2.15764	−	3.73714i	−0.148538	−	0.257275i	−0.930687	+	0.365816i	$0.880790\pi$
$212$	24.6955	−	42.7738i	1.69609	−	2.93772i
$213$		0			0
$214$	−44.7741	−	25.8504i	−3.06070	−	1.76709i
$215$	−24.4979	−	14.1439i	−1.67075	−	0.964605i
$216$		0			0
$217$	0.871180	−	1.50893i	0.0591395	−	0.102433i
$218$	−5.77339	−	9.99981i	−0.391024	−	0.677273i
$219$		0			0
$220$	31.9210			2.15212
$221$	−3.91635	+	6.70301i	−0.263442	+	0.450893i
$222$		0			0
$223$	−20.2604	+	11.6973i	−1.35674	+	0.783312i	−0.989182	−	0.146691i	$-0.953138\pi$
$223$	−20.2604	+	11.6973i	−1.35674	+	0.783312i	−0.367553	+	0.930003i	$0.619804\pi$
$224$	−9.37743	−	16.2422i	−0.626556	−	1.08523i
$225$		0			0
$226$		−	7.43315i		−	0.494446i
$227$	23.1427	+	13.3614i	1.53603	+	0.886829i	0.999065	+	0.0432270i	$0.0137639\pi$
$227$	23.1427	+	13.3614i	1.53603	+	0.886829i	0.536968	+	0.843602i	$0.319569\pi$
$228$		0			0
$229$		−	3.00670i		−	0.198688i	−0.995053	−	0.0993442i	$-0.968326\pi$
$229$		−	3.00670i		−	0.198688i	0.995053	−	0.0993442i	$-0.0316745\pi$
$230$	7.98222	−	13.8256i	0.526332	−	0.911634i
$231$		0			0
$232$	−21.1683	+	12.2215i	−1.38977	+	0.802383i
$233$	−11.7148			−0.767462			−0.383731	−	0.923445i	$-0.625361\pi$
$233$	−11.7148			−0.767462			−0.383731	+	0.923445i	$0.625361\pi$
$234$		0			0
$235$	19.1504			1.24924
$236$	−49.4199	+	28.5326i	−3.21696	+	1.85731i
$237$		0			0
$238$	−2.91018	+	5.04058i	−0.188639	+	0.326732i
$239$		−	1.42797i		−	0.0923677i	−0.998933	−	0.0461838i	$-0.985294\pi$
$239$		−	1.42797i		−	0.0923677i	0.998933	−	0.0461838i	$-0.0147060\pi$
$240$		0			0
$241$	−2.32068	−	1.33984i	−0.149488	−	0.0863069i	0.423390	−	0.905947i	$-0.360840\pi$
$241$	−2.32068	−	1.33984i	−0.149488	−	0.0863069i	−0.572878	+	0.819640i	$0.694173\pi$
$242$			20.5232i			1.31928i
$243$		0			0
$244$	26.8284	+	46.4682i	1.71751	+	2.97482i
$245$	−2.82162	+	1.62906i	−0.180267	+	0.104077i
$246$		0			0
$247$	−7.47450	−	4.36710i	−0.475591	−	0.277872i
$248$	−15.5770			−0.989143
$249$		0			0
$250$	−2.70989	−	4.69367i	−0.171389	−	0.296854i
$251$	−5.46696	+	9.46906i	−0.345072	+	0.597681i	−0.985367	−	0.170447i	$-0.945479\pi$
$251$	−5.46696	+	9.46906i	−0.345072	+	0.597681i	0.640295	+	0.768129i	$0.278812\pi$
$252$		0			0
$253$	−2.89786	−	1.67308i	−0.182187	−	0.105186i
$254$	−22.7885	−	13.1570i	−1.42988	−	0.825541i
$255$		0			0
$256$	−11.9089	+	20.6268i	−0.744307	+	1.28918i
$257$	−2.07569	−	3.59520i	−0.129478	−	0.224262i	0.793996	−	0.607922i	$-0.207997\pi$
$257$	−2.07569	−	3.59520i	−0.129478	−	0.224262i	−0.923474	+	0.383660i	$0.874663\pi$
$258$		0			0
$259$	−5.93565			−0.368823
$260$	53.8315	+	31.4519i	3.33849	+	1.95057i
$261$		0			0
$262$	43.6872	−	25.2228i	2.69900	−	1.55827i
$263$	2.02680	+	3.51052i	0.124978	+	0.216468i	0.921724	−	0.387846i	$-0.126781\pi$
$263$	2.02680	+	3.51052i	0.124978	+	0.216468i	−0.796747	+	0.604314i	$0.793447\pi$
$264$		0			0
$265$			30.3210i			1.86260i
$266$	−5.62072	−	3.24513i	−0.344629	−	0.198971i
$267$		0			0
$268$		−	4.38866i		−	0.268080i
$269$	2.00011	−	3.46430i	0.121949	−	0.211222i	−0.798587	−	0.601879i	$-0.794419\pi$
$269$	2.00011	−	3.46430i	0.121949	−	0.211222i	0.920536	+	0.390657i	$0.127752\pi$
$270$		0			0
$271$	−2.41189	+	1.39251i	−0.146512	+	0.0845888i	−0.571464	−	0.820627i	$-0.693624\pi$
$271$	−2.41189	+	1.39251i	−0.146512	+	0.0845888i	0.424952	+	0.905216i	$0.360291\pi$
$272$	29.1806			1.76933
$273$		0			0
$274$	22.7651			1.37529
$275$	−8.97733	+	5.18306i	−0.541353	+	0.312551i
$276$		0			0
$277$	8.34618	−	14.4560i	0.501474	−	0.868578i	−0.498525	−	0.866875i	$-0.666125\pi$
$277$	8.34618	−	14.4560i	0.501474	−	0.868578i	0.999999	−	0.00170243i	$-0.000541901\pi$
$278$		−	47.6741i		−	2.85930i
$279$		0			0
$280$	25.2258	+	14.5641i	1.50753	+	0.870373i
$281$		−	13.3731i		−	0.797774i	−0.917000	−	0.398887i	$-0.869397\pi$
$281$		−	13.3731i		−	0.797774i	0.917000	−	0.398887i	$-0.130603\pi$
$282$		0			0
$283$	−9.44312	−	16.3560i	−0.561335	−	0.972261i	−0.997380	−	0.0723362i	$-0.976955\pi$
$283$	−9.44312	−	16.3560i	−0.561335	−	0.972261i	0.436045	−	0.899925i	$-0.356379\pi$
$284$	10.8207	−	6.24731i	0.642088	−	0.370710i
$285$		0			0
$286$	9.07663	−	15.5351i	0.536712	−	0.918609i
$287$	−4.22131			−0.249176
$288$		0			0
$289$	6.18199	+	10.7075i	0.363647	+	0.629855i
$290$	12.0399	−	20.8537i	0.707008	−	1.22457i
$291$		0			0
$292$	14.6841	+	8.47789i	0.859324	+	0.496131i
$293$	2.95999	+	1.70895i	0.172925	+	0.0998380i	0.583964	−	0.811779i	$-0.301501\pi$
$293$	2.95999	+	1.70895i	0.172925	+	0.0998380i	−0.411040	+	0.911617i	$0.634834\pi$
$294$		0			0
$295$	17.5161	−	30.3388i	1.01983	−	1.76639i
$296$	26.5329	+	45.9564i	1.54220	+	2.67116i
$297$		0			0
$298$	10.8697			0.629663
$299$	−3.23845	−	5.67675i	−0.187284	−	0.328295i
$300$		0			0
$301$	−7.51903	+	4.34111i	−0.433390	+	0.250218i
$302$	25.5465	+	44.2479i	1.47004	+	2.54618i
$303$		0			0
$304$			32.5391i			1.86625i
$305$	−28.5268	−	16.4699i	−1.63344	−	0.943066i
$306$		0			0
$307$		−	16.3679i		−	0.934165i	−0.884214	−	0.467083i	$-0.845305\pi$
$307$		−	16.3679i		−	0.934165i	0.884214	−	0.467083i	$-0.154695\pi$
$308$	4.89868	−	8.48477i	0.279128	−	0.483464i
$309$		0			0
$310$	13.2896	−	7.67278i	0.754801	−	0.435785i
$311$	23.6979			1.34378			0.671891	−	0.740650i	$-0.265482\pi$
$311$	23.6979			1.34378			0.671891	+	0.740650i	$0.265482\pi$
$312$		0			0
$313$	−5.18025			−0.292805			−0.146403	−	0.989225i	$-0.546769\pi$
$313$	−5.18025			−0.292805			−0.146403	+	0.989225i	$0.546769\pi$
$314$	−27.0941	+	15.6428i	−1.52901	+	0.882774i
$315$		0			0
$316$	2.12798	−	3.68577i	0.119708	−	0.207341i
$317$			6.06537i			0.340665i	0.985387	+	0.170332i	$0.0544842\pi$
$317$			6.06537i			0.340665i	−0.985387	+	0.170332i	$0.945516\pi$
$318$		0			0
$319$	−4.37096	−	2.52358i	−0.244727	−	0.141293i
$320$		−	76.8686i		−	4.29709i
$321$		0			0
$322$	−2.44994	−	4.24343i	−0.136530	−	0.236477i
$323$	4.47700	−	2.58480i	0.249107	−	0.143822i
$324$		0			0
$325$	−20.2462	−	0.104705i	−1.12306	−	0.00580799i
$326$	−11.9087			−0.659562
$327$		0			0
$328$	18.8697	+	32.6833i	1.04190	+	1.80463i
$329$	2.93887	−	5.09027i	0.162025	−	0.280636i
$330$		0			0
$331$	14.9605	+	8.63743i	0.822301	+	0.474756i	0.851209	−	0.524826i	$-0.175870\pi$
$331$	14.9605	+	8.63743i	0.822301	+	0.474756i	−0.0289082	+	0.999582i	$0.509203\pi$
$332$	45.8258	+	26.4576i	2.51502	+	1.45205i
$333$		0			0
$334$	12.1902	−	21.1140i	0.667017	−	1.15531i
$335$	1.34710	+	2.33324i	0.0735998	+	0.127479i
$336$		0			0
$337$	−8.35464			−0.455106			−0.227553	−	0.973766i	$-0.573073\pi$
$337$	−8.35464			−0.455106			−0.227553	+	0.973766i	$0.573073\pi$
$338$	30.6136	−	17.2551i	1.66516	−	0.938552i
$339$		0			0
$340$	−32.2435	+	18.6158i	−1.74865	+	1.00958i
$341$	−1.60822	−	2.78552i	−0.0870901	−	0.150844i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	67.2216	+	38.8104i	3.62435	+	2.09252i
$345$		0			0
$346$			16.4679i			0.885318i
$347$	14.4110	−	24.9606i	0.773623	−	1.33995i	−0.161942	−	0.986800i	$-0.551776\pi$
$347$	14.4110	−	24.9606i	0.773623	−	1.33995i	0.935565	−	0.353154i	$-0.114891\pi$
$348$		0			0
$349$	−10.1516	+	5.86103i	−0.543403	+	0.313734i	−0.746457	−	0.665434i	$-0.768247\pi$
$349$	−10.1516	+	5.86103i	−0.543403	+	0.313734i	0.203054	+	0.979167i	$0.434913\pi$
$350$	−15.1794			−0.811376
$351$		0			0
$352$	−34.6220			−1.84536
$353$	−15.4466	+	8.91811i	−0.822141	+	0.474663i	−0.851154	−	0.524916i	$-0.824097\pi$
$353$	−15.4466	+	8.91811i	−0.822141	+	0.474663i	0.0290134	+	0.999579i	$0.490763\pi$
$354$		0			0
$355$	−3.83521	+	6.64278i	−0.203552	+	0.352562i
$356$			80.2113i			4.25119i
$357$		0			0
$358$	−9.08239	−	5.24372i	−0.480019	−	0.277139i
$359$			5.68162i			0.299864i	0.988696	+	0.149932i	$0.0479055\pi$
$359$			5.68162i			0.299864i	−0.988696	+	0.149932i	$0.952094\pi$
$360$		0			0
$361$	−6.61771	−	11.4622i	−0.348300	−	0.603274i
$362$	−15.4132	+	8.89882i	−0.810100	+	0.467712i
$363$		0			0
$364$	16.6212	−	9.48199i	0.871188	−	0.496991i
$365$	−10.4091			−0.544838
$366$		0			0
$367$	9.81580	+	17.0015i	0.512381	+	0.887469i	0.999897	+	0.0143554i	$0.00456964\pi$
$367$	9.81580	+	17.0015i	0.512381	+	0.887469i	−0.487516	+	0.873114i	$0.662097\pi$
$368$	−12.2829	+	21.2746i	−0.640289	+	1.10901i
$369$		0			0
$370$	−45.2735	−	26.1387i	−2.35366	−	1.35888i
$371$	8.05947	+	4.65314i	0.418427	+	0.241579i
$372$		0			0
$373$	−16.0323	+	27.7687i	−0.830119	+	1.43781i	0.0678240	+	0.997697i	$0.478394\pi$
$373$	−16.0323	+	27.7687i	−0.830119	+	1.43781i	−0.897943	+	0.440111i	$0.854939\pi$
$374$	5.37227	+	9.30505i	0.277794	+	0.481153i
$375$		0			0
$376$	−52.5482			−2.70997
$377$	−4.88468	−	8.56248i	−0.251574	−	0.440990i
$378$		0			0
$379$	−16.4745	+	9.51154i	−0.846237	+	0.488575i	−0.859379	−	0.511339i	$-0.829150\pi$
$379$	−16.4745	+	9.51154i	−0.846237	+	0.488575i	0.0131425	+	0.999914i	$0.495816\pi$
$380$	−20.7583	−	35.9545i	−1.06488	−	1.84443i
$381$		0			0
$382$			37.1510i			1.90081i
$383$	−0.606070	−	0.349915i	−0.0309687	−	0.0178798i	0.484436	−	0.874827i	$-0.339025\pi$
$383$	−0.606070	−	0.349915i	−0.0309687	−	0.0178798i	−0.515404	+	0.856947i	$0.672358\pi$
$384$		0			0
$385$			6.01459i			0.306532i
$386$	30.7529	−	53.2657i	1.56528	−	2.71115i
$387$		0			0
$388$	42.4310	−	24.4976i	2.15411	−	1.24368i
$389$	−20.0547			−1.01681			−0.508407	−	0.861117i	$-0.669765\pi$
$389$	−20.0547			−1.01681			−0.508407	+	0.861117i	$0.669765\pi$
$390$		0			0
$391$	3.90284			0.197375
$392$	7.74244	−	4.47010i	0.391052	−	0.225774i
$393$		0			0
$394$	19.6349	−	34.0086i	0.989192	−	1.71333i
$395$			2.61272i			0.131460i
$396$		0			0
$397$	−19.2953	−	11.1401i	−0.968403	−	0.559108i	−0.0696541	−	0.997571i	$-0.522190\pi$
$397$	−19.2953	−	11.1401i	−0.968403	−	0.559108i	−0.898749	+	0.438463i	$0.855523\pi$
$398$		−	64.4453i		−	3.23035i
$399$		0			0
$400$	38.0513	+	65.9069i	1.90257	+	3.29534i
$401$	4.16341	−	2.40374i	0.207911	−	0.120037i	−0.392429	−	0.919782i	$-0.628365\pi$
$401$	4.16341	−	2.40374i	0.207911	−	0.120037i	0.600340	+	0.799745i	$0.295032\pi$
$402$		0			0
$403$	0.0324883	−	6.28208i	0.00161836	−	0.312933i
$404$	−78.6717			−3.91406
$405$		0			0
$406$	−3.69535	−	6.40054i	−0.183397	−	0.317653i
$407$	−5.47869	+	9.48937i	−0.271568	+	0.470370i
$408$		0			0
$409$	31.8727	+	18.4017i	1.57601	+	0.909907i	0.995409	+	0.0957164i	$0.0305142\pi$
$409$	31.8727	+	18.4017i	1.57601	+	0.909907i	0.580597	+	0.814191i	$0.302819\pi$
$410$	−32.1976	−	18.5893i	−1.59013	−	0.918060i
$411$		0			0
$412$	11.3651	−	19.6850i	0.559921	−	0.969811i
$413$	−5.37613	−	9.31173i	−0.264542	−	0.458200i
$414$		0			0
$415$	−32.4845			−1.59460
$416$	−58.3864	−	34.1132i	−2.86263	−	1.67254i
$417$		0			0
$418$	−10.3760	+	5.99059i	−0.507507	+	0.293009i
$419$	14.6334	+	25.3457i	0.714887	+	1.23822i	0.963003	+	0.269490i	$0.0868552\pi$
$419$	14.6334	+	25.3457i	0.714887	+	1.23822i	−0.248116	+	0.968730i	$0.579812\pi$
$420$		0			0
$421$		−	7.53862i		−	0.367410i	−0.982981	−	0.183705i	$-0.941191\pi$
$421$		−	7.53862i		−	0.367410i	0.982981	−	0.183705i	$-0.0588091\pi$
$422$	−10.1022	−	5.83251i	−0.491768	−	0.283922i
$423$		0			0
$424$		−	83.2000i		−	4.04055i
$425$	6.04534	−	10.4708i	0.293242	−	0.507910i
$426$		0			0
$427$	−8.75558	+	5.05504i	−0.423712	+	0.244630i
$428$	−101.506			−4.90646
$429$		0			0
$430$	−76.4674			−3.68759
$431$	27.0426	−	15.6131i	1.30260	−	0.752055i	0.321748	−	0.946825i	$-0.395730\pi$
$431$	27.0426	−	15.6131i	1.30260	−	0.752055i	0.980849	+	0.194771i	$0.0623963\pi$
$432$		0			0
$433$	2.94202	−	5.09573i	0.141384	−	0.244885i	−0.786634	−	0.617420i	$-0.788178\pi$
$433$	2.94202	−	5.09573i	0.141384	−	0.244885i	0.928018	+	0.372535i	$0.121511\pi$
$434$		−	4.70994i		−	0.226084i
$435$		0			0
$436$	−19.6329	−	11.3351i	−0.940247	−	0.542852i
$437$			4.35204i			0.208186i
$438$		0			0
$439$	−4.97821	−	8.62251i	−0.237597	−	0.411530i	0.722427	−	0.691447i	$-0.243026\pi$
$439$	−4.97821	−	8.62251i	−0.237597	−	0.411530i	−0.960024	+	0.279917i	$0.909693\pi$
$440$	46.5676	−	26.8858i	2.22002	−	1.28173i
$441$		0			0
$442$	−0.108527	+	20.9853i	−0.00516212	+	0.998170i
$443$	35.8813			1.70477			0.852385	−	0.522915i	$-0.175155\pi$
$443$	35.8813			1.70477			0.852385	+	0.522915i	$0.175155\pi$
$444$		0			0
$445$	−24.6208	−	42.6444i	−1.16714	−	2.02154i
$446$	−31.6202	+	54.7678i	−1.49726	+	2.59333i
$447$		0			0
$448$	−20.4321	−	11.7965i	−0.965324	−	0.557330i
$449$	−3.46001	−	1.99764i	−0.163288	−	0.0942744i	0.416129	−	0.909306i	$-0.363386\pi$
$449$	−3.46001	−	1.99764i	−0.163288	−	0.0942744i	−0.579417	+	0.815031i	$0.696720\pi$
$450$		0			0
$451$	−3.89633	+	6.74864i	−0.183471	+	0.317781i
$452$	−7.29687	−	12.6386i	−0.343216	−	0.594467i
$453$		0			0
$454$	72.2371			3.39026
$455$	−5.92620	+	10.1430i	−0.277825	+	0.475510i
$456$		0			0
$457$	35.6995	−	20.6111i	1.66995	−	0.964147i	0.702291	−	0.711890i	$-0.252160\pi$
$457$	35.6995	−	20.6111i	1.66995	−	0.964147i	0.967660	−	0.252257i	$-0.0811729\pi$
$458$	−4.06385	−	7.03880i	−0.189891	−	0.328901i
$459$		0			0
$460$		−	31.3435i		−	1.46140i
$461$	−21.4139	−	12.3633i	−0.997343	−	0.575816i	−0.0898818	−	0.995952i	$-0.528649\pi$
$461$	−21.4139	−	12.3633i	−0.997343	−	0.575816i	−0.907461	+	0.420136i	$0.861982\pi$
$462$		0			0
$463$		−	24.4057i		−	1.13423i	−0.823639	−	0.567115i	$-0.808060\pi$
$463$		−	24.4057i		−	1.13423i	0.823639	−	0.567115i	$-0.191940\pi$
$464$	−18.5268	+	32.0893i	−0.860084	+	1.48971i
$465$		0			0
$466$	−27.4248	+	15.8337i	−1.27043	+	0.733482i
$467$	−4.44860			−0.205857			−0.102928	−	0.994689i	$-0.532821\pi$
$467$	−4.44860			−0.205857			−0.102928	+	0.994689i	$0.532821\pi$
$468$		0			0
$469$	0.826916			0.0381834
$470$	44.8318	−	25.8837i	2.06794	−	1.19392i
$471$		0			0
$472$	−48.0637	+	83.2487i	−2.21231	+	3.83183i
$473$			16.0276i			0.736951i
$474$		0			0
$475$	11.6760	+	6.74113i	0.535730	+	0.309304i
$476$			11.4273i			0.523769i
$477$		0			0
$478$	−1.93004	−	3.34293i	−0.0882780	−	0.152902i
$479$	27.4328	−	15.8383i	1.25343	−	0.723671i	0.281645	−	0.959519i	$-0.409120\pi$
$479$	27.4328	−	15.8383i	1.25343	−	0.723671i	0.971790	+	0.235848i	$0.0757868\pi$
$480$		0			0
$481$	−18.5892	+	10.6047i	−0.847593	+	0.483531i
$482$	−7.24372			−0.329942
$483$		0			0
$484$	20.1469	+	34.8954i	0.915767	+	1.58616i
$485$	−15.0390	+	26.0483i	−0.682887	+	1.18279i
$486$		0			0
$487$	23.3096	+	13.4578i	1.05626	+	0.609832i	0.924395	−	0.381436i	$-0.124570\pi$
$487$	23.3096	+	13.4578i	1.05626	+	0.609832i	0.131864	+	0.991268i	$0.457904\pi$
$488$	78.2766	+	45.1930i	3.54341	+	2.04579i
$489$		0			0
$490$	−4.40367	+	7.62739i	−0.198938	+	0.344570i
$491$	−4.86358	−	8.42396i	−0.219490	−	0.380168i	0.735162	−	0.677891i	$-0.237106\pi$
$491$	−4.86358	−	8.42396i	−0.219490	−	0.380168i	−0.954652	+	0.297723i	$0.903773\pi$
$492$		0			0
$493$	5.88682			0.265129
$494$	−23.4006	−	0.121018i	−1.05284	−	0.00544487i
$495$		0			0
$496$	−20.4498	+	11.8067i	−0.918225	+	0.530137i
$497$	1.17712	+	2.03884i	0.0528012	+	0.0914543i
$498$		0			0
$499$			7.87525i			0.352545i	0.984341	+	0.176272i	$0.0564039\pi$
$499$			7.87525i			0.352545i	−0.984341	+	0.176272i	$0.943596\pi$
$500$	−9.21523	−	5.32042i	−0.412118	−	0.237936i
$501$		0			0
$502$			29.5565i			1.31917i
$503$	−4.87603	+	8.44553i	−0.217411	+	0.376568i	−0.954016	−	0.299756i	$-0.903095\pi$
$503$	−4.87603	+	8.44553i	−0.217411	+	0.376568i	0.736604	+	0.676324i	$0.236428\pi$
$504$		0			0
$505$	41.8259	−	24.1482i	1.86123	−	1.07458i
$506$	−9.04533			−0.402114
$507$		0			0
$508$	−51.6630			−2.29217
$509$	19.9407	−	11.5128i	0.883857	−	0.510295i	0.0119288	−	0.999929i	$-0.496203\pi$
$509$	19.9407	−	11.5128i	0.883857	−	0.510295i	0.871928	+	0.489634i	$0.162870\pi$
$510$		0			0
$511$	−1.59741	+	2.76680i	−0.0706653	+	0.122396i
$512$			11.8512i			0.523752i
$513$		0			0
$514$	−9.71853	−	5.61100i	−0.428666	−	0.247490i
$515$			13.9541i			0.614891i
$516$		0			0
$517$	−5.42524	−	9.39679i	−0.238602	−	0.413270i
$518$	−13.8956	+	8.02261i	−0.610537	+	0.352493i
$519$		0			0
$520$	105.022	+	0.543130i	4.60552	+	0.0238178i
$521$	−0.486481			−0.0213131			−0.0106566	−	0.999943i	$-0.503392\pi$
$521$	−0.486481			−0.0213131			−0.0106566	+	0.999943i	$0.503392\pi$
$522$		0			0
$523$	17.3135	+	29.9878i	0.757065	+	1.31128i	0.944341	+	0.328968i	$0.106701\pi$
$523$	17.3135	+	29.9878i	0.757065	+	1.31128i	−0.187275	+	0.982307i	$0.559966\pi$
$524$	49.5207	−	85.7724i	2.16332	−	3.74698i
$525$		0			0
$526$	9.48962	+	5.47883i	0.413767	+	0.238888i
$527$	3.24893	+	1.87577i	0.141526	+	0.0817099i
$528$		0			0
$529$	9.85719	−	17.0732i	0.428574	−	0.742311i
$530$	40.9818	+	70.9826i	1.78014	+	3.08329i
$531$		0			0
$532$	−12.7425			−0.552458
$533$	−13.2202	+	7.54182i	−0.572632	+	0.326672i
$534$		0			0
$535$	53.9656	−	31.1571i	2.33314	−	1.34704i
$536$	−3.69639	−	6.40234i	−0.159660	−	0.276539i
$537$		0			0
$538$		−	10.8134i		−	0.466198i
$539$	1.59871	+	0.923014i	0.0688612	+	0.0397570i
$540$		0			0
$541$			22.5384i			0.969002i	0.874791	+	0.484501i	$0.160999\pi$
$541$			22.5384i			0.969002i	−0.874791	+	0.484501i	$0.839001\pi$
$542$	−3.76422	+	6.51982i	−0.161687	+	0.280050i
$543$		0			0
$544$	34.9717	−	20.1909i	1.49940	−	0.865678i
$545$	13.9172			0.596146
$546$		0			0
$547$	39.3716			1.68341			0.841704	−	0.539940i	$-0.181553\pi$
$547$	39.3716			1.68341			0.841704	+	0.539940i	$0.181553\pi$
$548$	38.7074	−	22.3477i	1.65350	−	0.954648i
$549$		0			0
$550$	−14.0108	+	24.2675i	−0.597424	+	1.03477i
$551$			6.56436i			0.279651i
$552$		0			0
$553$	0.694475	+	0.400955i	0.0295321	+	0.0170504i
$554$		−	45.1227i		−	1.91708i
$555$		0			0
$556$	−46.8000	−	81.0600i	−1.98476	−	3.43771i
$557$	−0.629579	+	0.363487i	−0.0266761	+	0.0154015i	−0.513279	−	0.858222i	$-0.671569\pi$
$557$	−0.629579	+	0.363487i	−0.0266761	+	0.0154015i	0.486603	+	0.873623i	$0.338236\pi$
$558$		0			0
$559$	−15.7921	+	27.0289i	−0.667935	+	1.14320i
$560$	44.1559			1.86593
$561$		0			0
$562$	−18.0751	−	31.3070i	−0.762452	−	1.32061i
$563$	−20.8038	+	36.0333i	−0.876777	+	1.51862i	−0.0219200	+	0.999760i	$0.506978\pi$
$563$	−20.8038	+	36.0333i	−0.876777	+	1.51862i	−0.854857	+	0.518863i	$0.826355\pi$
$564$		0			0
$565$	7.75879	+	4.47954i	0.326415	+	0.188456i
$566$	−44.2134	−	25.5266i	−1.85843	−	1.07296i
$567$		0			0
$568$	10.5237	−	18.2276i	0.441565	−	0.764813i
$569$	12.6944	+	21.9873i	0.532177	+	0.921757i	0.999294	+	0.0375618i	$0.0119591\pi$
$569$	12.6944	+	21.9873i	0.532177	+	0.921757i	−0.467118	+	0.884195i	$0.654708\pi$
$570$		0			0
$571$	−16.9992			−0.711393			−0.355697	−	0.934602i	$-0.615756\pi$
$571$	−16.9992			−0.711393			−0.355697	+	0.934602i	$0.615756\pi$
$572$	0.182683	−	35.3244i	0.00763836	−	1.47699i
$573$		0			0
$574$	−9.88225	+	5.70552i	−0.412477	+	0.238144i
$575$	5.08929	+	8.81490i	0.212238	+	0.367607i
$576$		0			0
$577$		−	15.9759i		−	0.665084i	−0.943088	−	0.332542i	$-0.892094\pi$
$577$		−	15.9759i		−	0.665084i	0.943088	−	0.332542i	$-0.107906\pi$
$578$	28.9445	+	16.7111i	1.20393	+	0.695092i
$579$		0			0
$580$		−	47.2767i		−	1.96306i
$581$	−4.98516	+	8.63454i	−0.206819	+	0.358221i
$582$		0			0
$583$	14.8780	−	8.58982i	0.616184	−	0.355754i
$584$	28.5623			1.18192
$585$		0			0
$586$	9.23926			0.381670
$587$	13.8404	−	7.99075i	0.571254	−	0.329814i	−0.186396	−	0.982475i	$-0.559681\pi$
$587$	13.8404	−	7.99075i	0.571254	−	0.329814i	0.757650	+	0.652661i	$0.226347\pi$
$588$		0			0
$589$	−2.09166	+	3.62287i	−0.0861855	+	0.149278i
$590$		−	94.6989i		−	3.89869i
$591$		0			0
$592$	69.6660	+	40.2217i	2.86325	+	1.65310i
$593$			29.0532i			1.19307i	0.802586	+	0.596536i	$0.203457\pi$
$593$			29.0532i			1.19307i	−0.802586	+	0.596536i	$0.796543\pi$
$594$		0			0
$595$	−3.50760	−	6.07534i	−0.143797	−	0.249065i
$596$	18.4816	−	10.6704i	0.757037	−	0.437075i
$597$		0			0
$598$	−15.2540	−	8.91240i	−0.623783	−	0.364455i
$599$	−3.45554			−0.141190			−0.0705948	−	0.997505i	$-0.522490\pi$
$599$	−3.45554			−0.141190			−0.0705948	+	0.997505i	$0.522490\pi$
$600$		0			0
$601$	−7.76518	−	13.4497i	−0.316748	−	0.548624i	0.663059	−	0.748567i	$-0.269258\pi$
$601$	−7.76518	−	13.4497i	−0.316748	−	0.548624i	−0.979808	+	0.199943i	$0.935924\pi$
$602$	−11.7349	+	20.3254i	−0.478278	+	0.828402i
$603$		0			0
$604$	86.8732	+	50.1563i	3.53482	+	2.04083i
$605$	−21.4222	−	12.3681i	−0.870938	−	0.502836i
$606$		0			0
$607$	−7.73922	+	13.4047i	−0.314125	+	0.544081i	−0.979251	−	0.202650i	$-0.935044\pi$
$607$	−7.73922	+	13.4047i	−0.314125	+	0.544081i	0.665126	+	0.746731i	$0.268378\pi$
$608$	22.5148	+	38.9967i	0.913095	+	1.58153i
$609$		0			0
$610$	−89.0429			−3.60524
$611$	0.109597	−	21.1922i	0.00443383	−	0.857345i
$612$		0			0
$613$	−6.17669	+	3.56611i	−0.249474	+	0.144034i	−0.619523	−	0.784978i	$-0.712674\pi$
$613$	−6.17669	+	3.56611i	−0.249474	+	0.144034i	0.370049	+	0.929012i	$0.379341\pi$
$614$	−22.1228	−	38.3178i	−0.892804	−	1.54638i
$615$		0			0
$616$		−	16.5039i		−	0.664959i
$617$	4.30142	+	2.48342i	0.173168	+	0.0999789i	0.584079	−	0.811697i	$-0.301456\pi$
$617$	4.30142	+	2.48342i	0.173168	+	0.0999789i	−0.410911	+	0.911676i	$0.634789\pi$
$618$		0			0
$619$		−	42.3570i		−	1.70247i	−0.524784	−	0.851235i	$-0.675854\pi$
$619$		−	42.3570i		−	1.70247i	0.524784	−	0.851235i	$-0.324146\pi$
$620$	15.0642	−	26.0920i	0.604993	−	1.04788i
$621$		0			0
$622$	55.4776	−	32.0300i	2.22445	−	1.28429i
$623$	−15.1135			−0.605508
$624$		0			0
$625$	−21.5445			−0.861779
$626$	−12.1272	+	7.00162i	−0.484699	+	0.279841i
$627$		0			0
$628$	−30.7120	+	53.1947i	−1.22554	+	2.12270i
$629$		−	12.7803i		−	0.509583i
$630$		0			0
$631$	−5.42803	−	3.13387i	−0.216086	−	0.124758i	0.388050	−	0.921638i	$-0.373149\pi$
$631$	−5.42803	−	3.13387i	−0.216086	−	0.124758i	−0.604137	+	0.796881i	$0.706482\pi$
$632$		−	7.16924i		−	0.285177i
$633$		0			0
$634$	8.19794	+	14.1992i	0.325582	+	0.563924i
$635$	27.4667	−	15.8579i	1.08998	−	0.629302i
$636$		0			0
$637$	1.78660	+	3.13178i	0.0707878	+	0.124086i
$638$	−13.6434			−0.540149
$639$		0			0
$640$	−42.7898	−	74.1142i	−1.69142	−	2.92962i
$641$	15.7818	−	27.3350i	0.623345	−	1.07967i	−0.365513	−	0.930806i	$-0.619106\pi$
$641$	15.7818	−	27.3350i	0.623345	−	1.07967i	0.988858	−	0.148860i	$-0.0475602\pi$
$642$		0			0
$643$	15.8053	+	9.12520i	0.623300	+	0.359863i	0.778153	−	0.628075i	$-0.216157\pi$
$643$	15.8053	+	9.12520i	0.623300	+	0.359863i	−0.154852	+	0.987938i	$0.549490\pi$
$644$	−8.33125	−	4.81005i	−0.328297	−	0.189543i
$645$		0			0
$646$	6.98721	−	12.1022i	0.274908	−	0.476155i
$647$	−11.5137	−	19.9423i	−0.452649	−	0.784011i	0.545901	−	0.837850i	$-0.316188\pi$
$647$	−11.5137	−	19.9423i	−0.452649	−	0.784011i	−0.998550	+	0.0538387i	$0.982854\pi$
$648$		0			0
$649$	−19.8490			−0.779140
$650$	−47.5387	+	27.1197i	−1.86462	+	1.06372i
$651$		0			0
$652$	−20.2483	+	11.6904i	−0.792985	+	0.457830i
$653$	14.4062	+	24.9523i	0.563759	+	0.976459i	0.997164	+	0.0752597i	$0.0239786\pi$
$653$	14.4062	+	24.9523i	0.563759	+	0.976459i	−0.433405	+	0.901199i	$0.642688\pi$
$654$		0			0
$655$			60.8014i			2.37571i
$656$	49.5450	+	28.6048i	1.93441	+	1.11683i
$657$		0			0
$658$		−	15.8887i		−	0.619406i
$659$	−15.6114	+	27.0397i	−0.608134	+	1.05332i	0.383414	+	0.923577i	$0.374748\pi$
$659$	−15.6114	+	27.0397i	−0.608134	+	1.05332i	−0.991548	+	0.129742i	$0.958585\pi$
$660$		0			0
$661$	−23.0000	+	13.2791i	−0.894598	+	0.516496i	−0.875444	−	0.483320i	$-0.839431\pi$
$661$	−23.0000	+	13.2791i	−0.894598	+	0.516496i	−0.0191541	+	0.999817i	$0.506097\pi$
$662$	46.6973			1.81494
$663$		0			0
$664$	89.1366			3.45917
$665$	6.77458	−	3.91130i	0.262707	−	0.151674i
$666$		0			0
$667$	−2.47792	+	4.29188i	−0.0959454	+	0.166182i
$668$		−	47.8667i		−	1.85202i
$669$		0			0
$670$	6.30721	+	3.64147i	0.243669	+	0.140682i
$671$			18.6635i			0.720495i
$672$		0			0
$673$	−9.86930	−	17.0941i	−0.380434	−	0.658930i	0.610691	−	0.791869i	$-0.290892\pi$
$673$	−9.86930	−	17.0941i	−0.380434	−	0.658930i	−0.991124	+	0.132939i	$0.957559\pi$
$674$	−19.5585	+	11.2921i	−0.753366	+	0.434956i
$675$		0			0
$676$	35.1134	−	59.3910i	1.35052	−	2.28427i
$677$	13.1440			0.505163			0.252582	−	0.967576i	$-0.418720\pi$
$677$	13.1440			0.505163			0.252582	+	0.967576i	$0.418720\pi$
$678$		0			0
$679$	4.61585	+	7.99489i	0.177140	+	0.306816i
$680$	−31.3586	+	54.3147i	−1.20255	+	2.08287i
$681$		0			0
$682$	−7.52981	−	4.34734i	−0.288331	−	0.166468i
$683$	5.85654	+	3.38128i	0.224094	+	0.129381i	0.607845	−	0.794056i	$-0.292034\pi$
$683$	5.85654	+	3.38128i	0.224094	+	0.129381i	−0.383750	+	0.923437i	$0.625368\pi$
$684$		0			0
$685$	−13.7192	+	23.7624i	−0.524185	+	0.907915i
$686$	1.35160	+	2.34104i	0.0516043	+	0.0893812i
$687$		0			0
$688$	117.666			4.48599
$689$	33.5538	+	0.173526i	1.27830	+	0.00661082i
$690$		0			0
$691$	7.94223	−	4.58545i	0.302137	−	0.174439i	−0.341266	−	0.939967i	$-0.610856\pi$
$691$	7.94223	−	4.58545i	0.302137	−	0.174439i	0.643402	+	0.765528i	$0.277522\pi$
$692$	16.1659	+	28.0002i	0.614537	+	1.06441i
$693$		0			0
$694$		−	77.9115i		−	2.95748i
$695$	49.7626	+	28.7304i	1.88760	+	1.08981i
$696$		0			0
$697$		−	9.08908i		−	0.344273i
$698$	−15.8435	+	27.4418i	−0.599686	+	1.03869i
$699$		0			0
$700$	−25.8095	+	14.9011i	−0.975509	+	0.563210i
$701$	−47.4700			−1.79292			−0.896459	−	0.443127i	$-0.853869\pi$
$701$	−47.4700			−1.79292			−0.896459	+	0.443127i	$0.853869\pi$
$702$		0			0
$703$	14.2512			0.537495
$704$	−37.7181	+	21.7766i	−1.42156	+	0.820736i
$705$		0			0
$706$	−24.1074	+	41.7552i	−0.907294	+	1.57148i
$707$		−	14.8234i		−	0.557491i
$708$		0			0
$709$	30.2866	+	17.4860i	1.13744	+	0.656699i	0.945795	−	0.324766i	$-0.105285\pi$
$709$	30.2866	+	17.4860i	1.13744	+	0.656699i	0.191642	+	0.981465i	$0.438619\pi$
$710$			20.7347i			0.778158i
$711$		0			0
$712$	67.5587	+	117.015i	2.53187	+	4.38533i
$713$	−2.73512	+	1.57912i	−0.102431	+	0.0591387i
$714$		0			0
$715$	10.7457	+	18.8364i	0.401866	+	0.704440i
$716$	−20.5903			−0.769496
$717$		0			0
$718$	7.67926	+	13.3009i	0.286588	+	0.496384i
$719$	4.18051	−	7.24085i	0.155907	−	0.270038i	−0.777482	−	0.628905i	$-0.783503\pi$
$719$	4.18051	−	7.24085i	0.155907	−	0.270038i	0.933389	+	0.358867i	$0.116837\pi$
$720$		0			0
$721$	3.70907	+	2.14143i	0.138133	+	0.0797511i
$722$	−30.9846	−	17.8890i	−1.15313	−	0.665758i
$723$		0			0
$724$	−17.4713	+	30.2612i	−0.649317	+	1.12465i
$725$	7.67639	+	13.2959i	0.285094	+	0.493797i
$726$		0			0
$727$	−27.4014			−1.01626			−0.508131	−	0.861280i	$-0.669663\pi$
$727$	−27.4014			−1.01626			−0.508131	+	0.861280i	$0.669663\pi$
$728$	16.2613	−	27.8320i	0.602685	−	1.03152i
$729$		0			0
$730$	−24.3681	+	14.0689i	−0.901905	+	0.520715i
$731$	−9.34703	−	16.1895i	−0.345712	−	0.598791i
$732$		0			0
$733$		−	12.1569i		−	0.449026i	−0.974471	−	0.224513i	$-0.927921\pi$
$733$		−	12.1569i		−	0.449026i	0.974471	−	0.224513i	$-0.0720792\pi$
$734$	45.9583	+	26.5340i	1.69635	+	0.979389i
$735$		0			0
$736$			33.9956i			1.25309i
$737$	0.763255	−	1.32200i	0.0281148	−	0.0486963i
$738$		0			0
$739$	−41.9537	+	24.2220i	−1.54329	+	0.891019i	−0.544662	+	0.838656i	$0.683342\pi$
$739$	−41.9537	+	24.2220i	−1.54329	+	0.891019i	−0.998628	+	0.0523634i	$0.983325\pi$
$740$	−102.638			−3.77304
$741$		0			0
$742$	25.1567			0.923531
$743$	14.7143	−	8.49532i	0.539816	−	0.311663i	−0.205188	−	0.978722i	$-0.565781\pi$
$743$	14.7143	−	8.49532i	0.539816	−	0.311663i	0.745004	+	0.667060i	$0.232447\pi$
$744$		0			0
$745$	−6.55052	+	11.3458i	−0.239993	+	0.415679i
$746$			86.6767i			3.17346i
$747$		0			0
$748$	18.2689	+	10.5475i	0.667977	+	0.385657i
$749$		−	19.1258i		−	0.698841i
$750$		0			0
$751$	21.5162	+	37.2671i	0.785136	+	1.35990i	0.928918	+	0.370287i	$0.120741\pi$
$751$	21.5162	+	37.2671i	0.785136	+	1.35990i	−0.143781	+	0.989610i	$0.545926\pi$
$752$	−68.9863	+	39.8292i	−2.51567	+	1.45242i
$753$		0			0
$754$	−23.0083	−	13.4430i	−0.837911	−	0.489563i
$755$	−61.5817			−2.24119
$756$		0			0
$757$	−14.5892	−	25.2693i	−0.530255	−	0.918428i	−0.999377	−	0.0352949i	$-0.988763\pi$
$757$	−14.5892	−	25.2693i	−0.530255	−	0.918428i	0.469122	−	0.883133i	$-0.344570\pi$
$758$	−25.7116	+	44.5337i	−0.933886	+	1.61754i
$759$		0			0
$760$	−60.5661	−	34.9678i	−2.19696	−	1.26842i
$761$	25.4829	+	14.7126i	0.923754	+	0.533330i	0.884831	−	0.465912i	$-0.154274\pi$
$761$	25.4829	+	14.7126i	0.923754	+	0.533330i	0.0389234	+	0.999242i	$0.487607\pi$
$762$		0			0
$763$	2.13577	−	3.69925i	0.0773199	−	0.133922i
$764$	36.4699	+	63.1677i	1.31943	+	2.28533i
$765$		0			0
$766$	−1.89178			−0.0683526
$767$	−33.4732	−	19.5573i	−1.20865	−	0.706172i
$768$		0			0
$769$	14.8839	−	8.59322i	0.536727	−	0.309879i	−0.207024	−	0.978336i	$-0.566378\pi$
$769$	14.8839	−	8.59322i	0.536727	−	0.309879i	0.743751	+	0.668456i	$0.233045\pi$
$770$	8.12930	+	14.0804i	0.292960	+	0.507421i
$771$		0			0
$772$		−	120.756i		−	4.34612i
$773$	−19.0180	−	10.9801i	−0.684031	−	0.394926i	0.117341	−	0.993092i	$-0.462563\pi$
$773$	−19.0180	−	10.9801i	−0.684031	−	0.394926i	−0.801372	+	0.598166i	$0.795896\pi$
$774$		0			0
$775$			9.78399i			0.351451i
$776$	41.2666	−	71.4759i	1.48139	−	2.56584i
$777$		0			0
$778$	−46.9488	+	27.1059i	−1.68320	+	0.971794i
$779$	10.1352			0.363131
$780$		0			0
$781$	4.34600			0.155512
$782$	9.13669	−	5.27507i	0.326727	−	0.188636i
$783$		0			0
$784$	6.77628	−	11.7369i	0.242010	−	0.419174i
$785$		−	37.7081i		−	1.34586i
$786$		0			0
$787$	−2.02275	−	1.16784i	−0.0721033	−	0.0416289i	0.463515	−	0.886089i	$-0.346588\pi$
$787$	−2.02275	−	1.16784i	−0.0721033	−	0.0416289i	−0.535618	+	0.844460i	$0.679921\pi$
$788$		−	77.0996i		−	2.74656i
$789$		0			0
$790$	3.53135	+	6.11648i	0.125640	+	0.217615i
$791$	2.38137	−	1.37488i	0.0846716	−	0.0488852i
$792$		0			0
$793$	−18.3892	+	31.4740i	−0.653020	+	1.11767i
$794$	−60.2280			−2.13741
$795$		0			0
$796$	−63.2637	−	109.576i	−2.24232	−	3.88382i
$797$	−13.9020	+	24.0790i	−0.492434	+	0.852921i	−0.999962	−	0.00871411i	$-0.997226\pi$
$797$	−13.9020	+	24.0790i	−0.492434	+	0.852921i	0.507528	+	0.861635i	$0.330560\pi$
$798$		0			0
$799$	10.9601	+	6.32780i	0.387739	+	0.223861i
$800$	91.2059	+	52.6577i	3.22461	+	1.86173i
$801$		0			0
$802$	6.49779	−	11.2545i	0.229445	−	0.397410i
$803$	2.94886	+	5.10758i	0.104063	+	0.180243i
$804$		0			0
$805$	5.90576			0.208151
$806$	−8.41479	−	14.7505i	−0.296398	−	0.519564i
$807$		0			0
$808$	−114.769	+	66.2620i	−4.03756	+	2.33109i
$809$	7.51017	+	13.0080i	0.264043	+	0.457337i	0.967313	−	0.253587i	$-0.0816104\pi$
$809$	7.51017	+	13.0080i	0.264043	+	0.457337i	−0.703269	+	0.710924i	$0.748277\pi$
$810$		0			0
$811$			43.6933i			1.53428i	0.641481	+	0.767139i	$0.278320\pi$
$811$			43.6933i			1.53428i	−0.641481	+	0.767139i	$0.721680\pi$
$812$	−12.5664	−	7.25520i	−0.440993	−	0.254608i
$813$		0			0
$814$			29.6199i			1.03818i
$815$	7.17670	−	12.4304i	0.251389	−	0.435418i
$816$		0			0
$817$	18.0529	−	10.4228i	0.631590	−	0.364648i
$818$	99.4870			3.47848
$819$		0			0
$820$	−72.9939			−2.54906
$821$	−15.6492	+	9.03506i	−0.546160	+	0.315326i	−0.747572	−	0.664181i	$-0.768780\pi$
$821$	−15.6492	+	9.03506i	−0.546160	+	0.315326i	0.201412	+	0.979507i	$0.435447\pi$
$822$		0			0
$823$	2.22775	−	3.85857i	0.0776544	−	0.134501i	−0.824583	−	0.565741i	$-0.808590\pi$
$823$	2.22775	−	3.85857i	0.0776544	−	0.134501i	0.902238	+	0.431239i	$0.141924\pi$
$824$		−	38.2896i		−	1.33388i
$825$		0			0
$826$	−25.1714	−	14.5327i	−0.875826	−	0.505658i
$827$		−	11.8352i		−	0.411549i	−0.978599	−	0.205774i	$-0.934029\pi$
$827$		−	11.8352i		−	0.411549i	0.978599	−	0.205774i	$-0.0659713\pi$
$828$		0			0
$829$	−1.76947	−	3.06482i	−0.0614563	−	0.106445i	0.833660	−	0.552278i	$-0.186241\pi$
$829$	−1.76947	−	3.06482i	−0.0614563	−	0.106445i	−0.895117	+	0.445832i	$0.852908\pi$
$830$	−76.0474	+	43.9060i	−2.63964	+	1.52400i
$831$		0			0
$832$	−85.0643	−	0.439917i	−2.94907	−	0.0152514i
$833$	−2.15314			−0.0746019
$834$		0			0
$835$	14.6927	+	25.4484i	0.508460	+	0.880679i
$836$	−11.7615	+	20.3715i	−0.406781	+	0.704565i
$837$		0			0
$838$	68.5145	+	39.5569i	2.36679	+	1.36647i
$839$	28.9991	+	16.7426i	1.00116	+	0.578020i	0.908591	−	0.417686i	$-0.137159\pi$
$839$	28.9991	+	16.7426i	1.00116	+	0.578020i	0.0925687	+	0.995706i	$0.470492\pi$
$840$		0			0
$841$	10.7625	−	18.6411i	0.371119	−	0.642797i
$842$	−10.1892	−	17.6482i	−0.351143	−	0.608197i
$843$		0			0
$844$	−22.9023			−0.788330
$845$	−0.438079	+	42.3533i	−0.0150704	+	1.45700i
$846$		0			0
$847$	−6.57502	+	3.79609i	−0.225920	+	0.130435i
$848$	−63.0620	−	109.227i	−2.16556	−	3.75086i
$849$		0			0
$850$		−	32.6835i		−	1.12103i
$851$	9.31768	+	5.37956i	0.319406	+	0.184409i
$852$		0			0
$853$			22.0871i			0.756248i	0.925755	+	0.378124i	$0.123431\pi$
$853$			22.0871i			0.756248i	−0.925755	+	0.378124i	$0.876569\pi$
$854$	−13.6648	+	23.6680i	−0.467598	+	0.809904i
$855$		0			0
$856$	−148.080	+	85.4941i	−5.06127	+	2.92213i
$857$	−6.89363			−0.235482			−0.117741	−	0.993044i	$-0.537565\pi$
$857$	−6.89363			−0.235482			−0.117741	+	0.993044i	$0.537565\pi$
$858$		0			0
$859$	−37.4834			−1.27892			−0.639459	−	0.768825i	$-0.720842\pi$
$859$	−37.4834			−1.27892			−0.639459	+	0.768825i	$0.720842\pi$
$860$	−130.017	+	75.0654i	−4.43355	+	2.55971i
$861$		0			0
$862$	42.2052	−	73.1015i	1.43751	−	2.48985i
$863$			17.5248i			0.596552i	0.954480	+	0.298276i	$0.0964115\pi$
$863$			17.5248i			0.596552i	−0.954480	+	0.298276i	$0.903588\pi$
$864$		0			0
$865$	−17.1893	−	9.92425i	−0.584454	−	0.337435i
$866$		−	15.9057i		−	0.540498i
$867$		0			0
$868$	−4.62358	−	8.00828i	−0.156935	−	0.271819i
$869$	1.28202	−	0.740175i	0.0434896	−	0.0251087i
$870$		0			0
$871$	2.58972	−	1.47737i	0.0877493	−	0.0500588i
$872$	−38.1883			−1.29322
$873$		0			0
$874$	5.88221	+	10.1883i	0.198969	+	0.344624i
$875$	1.00248	−	1.73634i	0.0338899	−	0.0586990i
$876$		0			0
$877$	−40.4859	−	23.3745i	−1.36711	−	0.789302i	−0.376553	−	0.926395i	$-0.622891\pi$
$877$	−40.4859	−	23.3745i	−1.36711	−	0.789302i	−0.990558	+	0.137093i	$0.956224\pi$
$878$	−23.3083	−	13.4571i	−0.786618	−	0.454154i
$879$		0			0
$880$	40.7565	−	70.5924i	1.37390	−	2.37967i
$881$	1.45937	+	2.52771i	0.0491675	+	0.0851606i	0.889562	−	0.456815i	$-0.151010\pi$
$881$	1.45937	+	2.52771i	0.0491675	+	0.0851606i	−0.840394	+	0.541976i	$0.817677\pi$
$882$		0			0
$883$	28.5505			0.960801			0.480400	−	0.877049i	$-0.340491\pi$
$883$	28.5505			0.960801			0.480400	+	0.877049i	$0.340491\pi$
$884$	20.4160	+	35.7878i	0.686666	+	1.20367i
$885$		0			0
$886$	83.9993	−	48.4970i	2.82201	−	1.62929i
$887$	0.211457	+	0.366254i	0.00710004	+	0.0122976i	0.869554	−	0.493839i	$-0.164407\pi$
$887$	0.211457	+	0.366254i	0.00710004	+	0.0122976i	−0.862454	+	0.506136i	$0.831073\pi$
$888$		0			0
$889$		−	9.73438i		−	0.326480i
$890$	−115.276	−	66.5548i	−3.86407	−	2.23092i
$891$		0			0
$892$			124.162i			4.15725i
$893$	−7.05610	+	12.2215i	−0.236123	+	0.408978i
$894$		0			0
$895$	10.9469	−	6.32018i	0.365914	−	0.211260i
$896$	−26.2666			−0.877504
$897$		0			0
$898$	−10.8000			−0.360401
$899$	−4.12550	+	2.38186i	−0.137593	+	0.0794394i
$900$		0			0
$901$	−10.0189	+	17.3532i	−0.333777	+	0.578118i
$902$			21.0651i			0.701391i
$903$		0			0
$904$	−21.2899	−	12.2917i	−0.708091	−	0.408816i
$905$		−	21.4512i		−	0.713063i
$906$		0			0
$907$	−11.2142	−	19.4236i	−0.372361	−	0.644949i	0.617567	−	0.786518i	$-0.288118\pi$
$907$	−11.2142	−	19.4236i	−0.372361	−	0.644949i	−0.989928	+	0.141570i	$0.954785\pi$
$908$	122.824	−	70.9127i	4.07607	−	2.35332i
$909$		0			0
$910$	−0.164223	+	31.7549i	−0.00544394	+	1.05267i
$911$	32.5788			1.07938			0.539692	−	0.841863i	$-0.318541\pi$
$911$	32.5788			1.07938			0.539692	+	0.841863i	$0.318541\pi$
$912$		0			0
$913$	9.20274	+	15.9396i	0.304566	+	0.527524i
$914$	55.7159	−	96.5027i	1.84292	−	3.19203i
$915$		0			0
$916$	−13.8195	−	7.97869i	−0.456609	−	0.263623i
$917$	16.1613	+	9.33073i	0.533693	+	0.308128i
$918$		0			0
$919$	4.93957	−	8.55558i	0.162941	−	0.282223i	−0.772981	−	0.634429i	$-0.781235\pi$
$919$	4.93957	−	8.55558i	0.162941	−	0.282223i	0.935922	+	0.352207i	$0.114569\pi$
$920$	−26.3993	−	45.7250i	−0.870361	−	1.50751i
$921$		0			0
$922$	−66.8408			−2.20129
$923$	7.32908	+	4.28214i	0.241240	+	0.140948i
$924$		0			0
$925$	28.8654	−	16.6654i	0.949088	−	0.547956i
$926$	−32.9867	−	57.1346i	−1.08401	−	1.87756i
$927$		0			0
$928$			51.2769i			1.68325i
$929$	−25.9060	−	14.9568i	−0.849947	−	0.490717i	0.0106859	−	0.999943i	$-0.496599\pi$
$929$	−25.9060	−	14.9568i	−0.849947	−	0.490717i	−0.860633	+	0.509226i	$0.829932\pi$
$930$		0			0
$931$		−	2.40096i		−	0.0786881i
$932$	−31.0868	+	53.8439i	−1.01828	+	1.76371i
$933$		0			0
$934$	−10.4143	+	6.01273i	−0.340768	+	0.196742i
$935$	−12.9502			−0.423518
$936$		0			0
$937$	−31.8296			−1.03983			−0.519914	−	0.854219i	$-0.674036\pi$
$937$	−31.8296			−1.03983			−0.519914	+	0.854219i	$0.674036\pi$
$938$	1.93584	−	1.11766i	0.0632074	−	0.0364928i
$939$		0			0
$940$	50.8182	−	88.0197i	1.65751	−	2.87089i
$941$			42.0885i			1.37205i	0.727580	+	0.686023i	$0.240645\pi$
$941$			42.0885i			1.37205i	−0.727580	+	0.686023i	$0.759355\pi$
$942$		0			0
$943$	6.62654	+	3.82584i	0.215790	+	0.124586i
$944$			145.721i			4.74280i
$945$		0			0
$946$	21.6629	+	37.5213i	0.704322	+	1.21992i
$947$	−52.2540	+	30.1689i	−1.69803	+	0.980357i	−0.750397	+	0.660988i	$0.770138\pi$
$947$	−52.2540	+	30.1689i	−1.69803	+	0.980357i	−0.947630	+	0.319369i	$0.896529\pi$
$948$		0			0
$949$	−0.0595711	+	11.5189i	−0.00193376	+	0.373920i
$950$	36.4452			1.18244
$951$		0			0
$952$	9.62475	+	16.6706i	0.311940	+	0.540296i
$953$	8.68770	−	15.0475i	0.281422	−	0.487438i	−0.690313	−	0.723511i	$-0.742527\pi$
$953$	8.68770	−	15.0475i	0.281422	−	0.487438i	0.971735	+	0.236073i	$0.0758605\pi$
$954$		0			0
$955$	−38.7785	−	22.3888i	−1.25484	−	0.724484i
$956$	−6.56328	−	3.78931i	−0.212272	−	0.122555i
$957$		0			0
$958$	42.8140	−	74.1561i	1.38326	−	2.39588i
$959$	4.21078	+	7.29328i	0.135973	+	0.235512i
$960$		0			0
$961$	27.9642			0.902070
$962$	−29.1847	+	49.9510i	−0.940951	+	1.61048i
$963$		0			0
$964$	−12.3165	+	7.11091i	−0.396686	+	0.229027i
$965$	37.0661	+	64.2003i	1.19320	+	2.06668i
$966$		0			0
$967$			18.8630i			0.606594i	0.952896	+	0.303297i	$0.0980874\pi$
$967$			18.8630i			0.606594i	−0.952896	+	0.303297i	$0.901913\pi$
$968$	58.7820	+	33.9378i	1.88932	+	1.09080i
$969$		0			0
$970$			81.3068i			2.61061i
$971$	−0.782231	+	1.35486i	−0.0251030	+	0.0434797i	−0.878304	−	0.478103i	$-0.841325\pi$
$971$	−0.782231	+	1.35486i	−0.0251030	+	0.0434797i	0.853201	+	0.521582i	$0.174658\pi$
$972$		0			0
$973$	15.2734	−	8.81809i	0.489642	−	0.282695i
$974$	72.7582			2.33132
$975$		0			0
$976$	137.017			4.38582
$977$	24.1409	−	13.9378i	0.772336	−	0.445909i	−0.0613710	−	0.998115i	$-0.519547\pi$
$977$	24.1409	−	13.9378i	0.772336	−	0.445909i	0.833707	+	0.552206i	$0.186214\pi$
$978$		0			0
$979$	−13.9499	+	24.1620i	−0.445842	+	0.772221i
$980$			17.2917i			0.552364i
$981$		0			0
$982$	−22.7716	−	13.1472i	−0.726672	−	0.419544i
$983$		−	33.4239i		−	1.06606i	−0.846097	−	0.533029i	$-0.821054\pi$
$983$		−	33.4239i		−	1.06606i	0.846097	−	0.533029i	$-0.178946\pi$
$984$		0			0
$985$	23.6657	+	40.9901i	0.754051	+	1.30605i
$986$	13.7813	−	7.95661i	0.438885	−	0.253390i
$987$		0			0
$988$	−39.9068	+	22.7658i	−1.26960	+	0.724277i
$989$	15.7376			0.500428
$990$		0			0
$991$	9.45548	+	16.3774i	0.300363	+	0.520244i	0.976218	−	0.216790i	$-0.0695588\pi$
$991$	9.45548	+	16.3774i	0.300363	+	0.520244i	−0.675855	+	0.737035i	$0.736225\pi$
$992$	−16.3388	+	28.2997i	−0.518759	+	0.898517i
$993$		0			0
$994$	5.51138	+	3.18199i	0.174810	+	0.100927i
$995$	67.2685	+	38.8375i	2.13256	+	1.23123i
$996$		0			0
$997$	−21.7888	+	37.7393i	−0.690057	+	1.19521i	0.281762	+	0.959484i	$0.409081\pi$
$997$	−21.7888	+	37.7393i	−0.690057	+	1.19521i	−0.971819	+	0.235730i	$0.924252\pi$
$998$	10.6442	+	18.4363i	0.336936	+	0.583589i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.ct.a.127.6		12
3.2	odd	2		91.2.q.a.36.1	✓	12
12.11	even	2		1456.2.cc.c.673.4		12
13.4	even	6	inner	819.2.ct.a.316.6		12
21.2	odd	6		637.2.u.h.361.6		12
21.5	even	6		637.2.u.i.361.6		12
21.11	odd	6		637.2.k.h.569.1		12
21.17	even	6		637.2.k.g.569.1		12
21.20	even	2		637.2.q.h.491.1		12
39.2	even	12		1183.2.a.m.1.1		6
39.11	even	12		1183.2.a.p.1.6		6
39.17	odd	6		91.2.q.a.43.1	yes	12
39.23	odd	6		1183.2.c.i.337.12		12
39.29	odd	6		1183.2.c.i.337.1		12
156.95	even	6		1456.2.cc.c.225.4		12
273.17	even	6		637.2.u.i.30.6		12
273.41	odd	12		8281.2.a.by.1.1		6
273.95	odd	6		637.2.u.h.30.6		12
273.167	odd	12		8281.2.a.ch.1.6		6
273.173	even	6		637.2.k.g.459.6		12
273.212	odd	6		637.2.k.h.459.6		12
273.251	even	6		637.2.q.h.589.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.1	✓	12	3.2	odd	2
91.2.q.a.43.1	yes	12	39.17	odd	6
637.2.k.g.459.6		12	273.173	even	6
637.2.k.g.569.1		12	21.17	even	6
637.2.k.h.459.6		12	273.212	odd	6
637.2.k.h.569.1		12	21.11	odd	6
637.2.q.h.491.1		12	21.20	even	2
637.2.q.h.589.1		12	273.251	even	6
637.2.u.h.30.6		12	273.95	odd	6
637.2.u.h.361.6		12	21.2	odd	6
637.2.u.i.30.6		12	273.17	even	6
637.2.u.i.361.6		12	21.5	even	6
819.2.ct.a.127.6		12	1.1	even	1	trivial
819.2.ct.a.316.6		12	13.4	even	6	inner
1183.2.a.m.1.1		6	39.2	even	12
1183.2.a.p.1.6		6	39.11	even	12
1183.2.c.i.337.1		12	39.29	odd	6
1183.2.c.i.337.12		12	39.23	odd	6
1456.2.cc.c.225.4		12	156.95	even	6
1456.2.cc.c.673.4		12	12.11	even	2
8281.2.a.by.1.1		6	273.41	odd	12
8281.2.a.ch.1.6		6	273.167	odd	12

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.ct (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.34104 - 1.35160i) q^{2} +(2.65363 - 4.59623i) q^{4} +3.25812i q^{5} +(0.866025 + 0.500000i) q^{7} -8.94020i q^{8} +O(q^{10})\)	\(q+(2.34104 - 1.35160i) q^{2} +(2.65363 - 4.59623i) q^{4} +3.25812i q^{5} +(0.866025 + 0.500000i) q^{7} -8.94020i q^{8} +(4.40367 + 7.62739i) q^{10} +(1.59871 - 0.923014i) q^{11} +(3.60550 + 0.0186461i) q^{13} +2.70320 q^{14} +(-6.77628 - 11.7369i) q^{16} +(-1.07657 + 1.86467i) q^{17} +(-2.07929 - 1.20048i) q^{19} +(14.9751 + 8.64587i) q^{20} +(2.49509 - 4.32162i) q^{22} +(-0.906314 - 1.56978i) q^{23} -5.61537 q^{25} +(8.46582 - 4.82954i) q^{26} +(4.59623 - 2.65363i) q^{28} +(-1.36703 - 2.36777i) q^{29} -1.74236i q^{31} +(-16.2422 - 9.37743i) q^{32} +5.82036i q^{34} +(-1.62906 + 2.82162i) q^{35} +(-5.14042 + 2.96783i) q^{37} -6.49025 q^{38} +29.1283 q^{40} +(-3.65577 + 2.11066i) q^{41} +(-4.34111 + 7.51903i) q^{43} -9.79737i q^{44} +(-4.24343 - 2.44994i) q^{46} -5.87774i q^{47} +(0.500000 + 0.866025i) q^{49} +(-13.1458 + 7.58972i) q^{50} +(9.65339 - 16.5222i) q^{52} +9.30628 q^{53} +(3.00729 + 5.20878i) q^{55} +(4.47010 - 7.74244i) q^{56} +(-6.40054 - 3.69535i) q^{58} +(-9.31173 - 5.37613i) q^{59} +(-5.05504 + 8.75558i) q^{61} +(-2.35497 - 4.07893i) q^{62} -23.5929 q^{64} +(-0.0607514 + 11.7472i) q^{65} +(0.716130 - 0.413458i) q^{67} +(5.71365 + 9.89633i) q^{68} +8.80735i q^{70} +(2.03884 + 1.17712i) q^{71} +3.19482i q^{73} +(-8.02261 + 13.8956i) q^{74} +(-11.0353 + 6.37126i) q^{76} +1.84603 q^{77} +0.801911 q^{79} +(38.2402 - 22.0780i) q^{80} +(-5.70552 + 9.88225i) q^{82} +9.97031i q^{83} +(-6.07534 - 3.50760i) q^{85} +23.4698i q^{86} +(-8.25193 - 14.2928i) q^{88} +(-13.0886 + 7.55674i) q^{89} +(3.11313 + 1.81890i) q^{91} -9.62010 q^{92} +(-7.94435 - 13.7600i) q^{94} +(3.91130 - 6.77458i) q^{95} +(7.99489 + 4.61585i) q^{97} +(2.34104 + 1.35160i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4}+O(q^{10}) \) 12 * q + 4 * q^4	\( 12 q + 4 q^{4} + 12 q^{10} - 6 q^{11} + 4 q^{13} + 8 q^{14} - 8 q^{16} + 4 q^{17} + 12 q^{20} + 6 q^{22} + 12 q^{23} - 20 q^{25} + 42 q^{26} - 8 q^{29} - 36 q^{32} - 6 q^{35} - 42 q^{37} - 4 q^{38} + 92 q^{40} - 30 q^{41} + 2 q^{43} + 12 q^{46} + 6 q^{49} + 18 q^{50} + 2 q^{52} + 44 q^{53} - 6 q^{55} + 12 q^{56} - 12 q^{58} - 18 q^{59} + 14 q^{61} + 4 q^{62} - 52 q^{64} - 60 q^{65} - 24 q^{67} + 8 q^{68} + 24 q^{71} - 6 q^{74} - 18 q^{76} - 8 q^{77} - 56 q^{79} + 72 q^{80} + 14 q^{82} - 48 q^{85} - 14 q^{88} + 12 q^{89} + 14 q^{91} - 24 q^{92} + 4 q^{94} + 22 q^{95} + 6 q^{97}+O(q^{100}) \) 12 * q + 4 * q^4 + 12 * q^10 - 6 * q^11 + 4 * q^13 + 8 * q^14 - 8 * q^16 + 4 * q^17 + 12 * q^20 + 6 * q^22 + 12 * q^23 - 20 * q^25 + 42 * q^26 - 8 * q^29 - 36 * q^32 - 6 * q^35 - 42 * q^37 - 4 * q^38 + 92 * q^40 - 30 * q^41 + 2 * q^43 + 12 * q^46 + 6 * q^49 + 18 * q^50 + 2 * q^52 + 44 * q^53 - 6 * q^55 + 12 * q^56 - 12 * q^58 - 18 * q^59 + 14 * q^61 + 4 * q^62 - 52 * q^64 - 60 * q^65 - 24 * q^67 + 8 * q^68 + 24 * q^71 - 6 * q^74 - 18 * q^76 - 8 * q^77 - 56 * q^79 + 72 * q^80 + 14 * q^82 - 48 * q^85 - 14 * q^88 + 12 * q^89 + 14 * q^91 - 24 * q^92 + 4 * q^94 + 22 * q^95 + 6 * q^97

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