LMFDB - Embedded newform 819.2.s.e.289.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(289,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("819.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			289.8
Root			$1.21707 - 2.10803i$ of defining polynomial
Character	$\chi$	$=$	819.289
Dual form			819.2.s.e.802.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.43414 q^{2} +3.92506 q^{4} +(0.613891 - 1.06329i) q^{5} +(2.20121 + 1.46788i) q^{7} +4.68588 q^{8} +O(q^{10})$	\(q+2.43414 q^{2} +3.92506 q^{4} +(0.613891 - 1.06329i) q^{5} +(2.20121 + 1.46788i) q^{7} +4.68588 q^{8} +(1.49430 - 2.58820i) q^{10} +(1.74628 - 3.02464i) q^{11} +(-2.87580 + 2.17480i) q^{13} +(5.35806 + 3.57304i) q^{14} +3.55599 q^{16} -4.52705 q^{17} +(-0.677706 - 1.17382i) q^{19} +(2.40956 - 4.17348i) q^{20} +(4.25069 - 7.36241i) q^{22} +0.673327 q^{23} +(1.74628 + 3.02464i) q^{25} +(-7.00012 + 5.29378i) q^{26} +(8.63988 + 5.76153i) q^{28} +(-2.64824 - 4.58688i) q^{29} +(4.99846 + 8.65759i) q^{31} -0.715973 q^{32} -11.0195 q^{34} +(2.91209 - 1.43940i) q^{35} -3.08236 q^{37} +(-1.64963 - 2.85725i) q^{38} +(2.87662 - 4.98245i) q^{40} +(-3.61102 - 6.25447i) q^{41} +(4.48886 - 7.77494i) q^{43} +(6.85424 - 11.8719i) q^{44} +1.63898 q^{46} +(-2.58008 + 4.46883i) q^{47} +(2.69064 + 6.46223i) q^{49} +(4.25069 + 7.36241i) q^{50} +(-11.2877 + 8.53623i) q^{52} +(4.95271 + 8.57835i) q^{53} +(-2.14405 - 3.71360i) q^{55} +(10.3146 + 6.87832i) q^{56} +(-6.44620 - 11.1651i) q^{58} -0.803443 q^{59} +(-2.32487 - 4.02680i) q^{61} +(12.1670 + 21.0738i) q^{62} -8.85475 q^{64} +(0.547016 + 4.39290i) q^{65} +(1.06068 - 1.83715i) q^{67} -17.7690 q^{68} +(7.08845 - 3.50372i) q^{70} +(2.52793 - 4.37850i) q^{71} +(-6.04227 - 10.4655i) q^{73} -7.50291 q^{74} +(-2.66004 - 4.60732i) q^{76} +(8.28373 - 4.09453i) q^{77} +(-5.90140 + 10.2215i) q^{79} +(2.18299 - 3.78105i) q^{80} +(-8.78975 - 15.2243i) q^{82} -12.6805 q^{83} +(-2.77912 + 4.81357i) q^{85} +(10.9265 - 18.9253i) q^{86} +(8.18284 - 14.1731i) q^{88} +3.10466 q^{89} +(-9.52259 + 0.565851i) q^{91} +2.64285 q^{92} +(-6.28029 + 10.8778i) q^{94} -1.66415 q^{95} +(-3.59585 + 6.22820i) q^{97} +(6.54941 + 15.7300i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{4} + q^{7} - 12 q^{8}+O(q^{10}) $ 16 * q + 12 * q^4 + q^7 - 12 * q^8	$ 16 q + 12 q^{4} + q^{7} - 12 q^{8} - 4 q^{10} + 2 q^{11} + 5 q^{13} + 7 q^{14} + 12 q^{16} - 4 q^{17} - 11 q^{19} + 20 q^{20} + 7 q^{22} + 8 q^{23} + 2 q^{25} - 33 q^{26} - q^{28} - 15 q^{29} + 3 q^{31} + 6 q^{32} - 68 q^{34} - 8 q^{37} - 2 q^{38} - 25 q^{40} - 19 q^{41} + 11 q^{43} + 16 q^{44} - 4 q^{46} - 5 q^{47} + 7 q^{49} + 7 q^{50} - 18 q^{52} - 36 q^{53} - 15 q^{55} + 51 q^{56} + 20 q^{58} - 34 q^{59} - 22 q^{61} + 6 q^{62} - 20 q^{64} + 24 q^{65} + 26 q^{67} + 10 q^{68} + 46 q^{70} - 9 q^{71} - 6 q^{73} + 30 q^{74} - 16 q^{76} + 36 q^{77} + 16 q^{79} + 28 q^{80} - q^{82} - 36 q^{83} - 4 q^{85} - 16 q^{86} + 24 q^{88} + 40 q^{89} - 10 q^{91} + 94 q^{92} - 20 q^{94} + 7 q^{97} - 18 q^{98}+O(q^{100}) $ 16 * q + 12 * q^4 + q^7 - 12 * q^8 - 4 * q^10 + 2 * q^11 + 5 * q^13 + 7 * q^14 + 12 * q^16 - 4 * q^17 - 11 * q^19 + 20 * q^20 + 7 * q^22 + 8 * q^23 + 2 * q^25 - 33 * q^26 - q^28 - 15 * q^29 + 3 * q^31 + 6 * q^32 - 68 * q^34 - 8 * q^37 - 2 * q^38 - 25 * q^40 - 19 * q^41 + 11 * q^43 + 16 * q^44 - 4 * q^46 - 5 * q^47 + 7 * q^49 + 7 * q^50 - 18 * q^52 - 36 * q^53 - 15 * q^55 + 51 * q^56 + 20 * q^58 - 34 * q^59 - 22 * q^61 + 6 * q^62 - 20 * q^64 + 24 * q^65 + 26 * q^67 + 10 * q^68 + 46 * q^70 - 9 * q^71 - 6 * q^73 + 30 * q^74 - 16 * q^76 + 36 * q^77 + 16 * q^79 + 28 * q^80 - q^82 - 36 * q^83 - 4 * q^85 - 16 * q^86 + 24 * q^88 + 40 * q^89 - 10 * q^91 + 94 * q^92 - 20 * q^94 + 7 * q^97 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	2.43414			1.72120			0.860600	−	0.509281i	$-0.170089\pi$
$2$	2.43414			1.72120			0.860600	+	0.509281i	$0.170089\pi$
$3$		0			0
$3$		0			0
$4$	3.92506			1.96253
$5$	0.613891	−	1.06329i	0.274540	−	0.475518i	−0.695479	−	0.718547i	$-0.744808\pi$
$5$	0.613891	−	1.06329i	0.274540	−	0.475518i	0.970019	+	0.243029i	$0.0781409\pi$
$6$		0			0
$7$	2.20121	+	1.46788i	0.831979	+	0.554807i
$7$	2.20121	+	1.46788i	0.831979	+	0.554807i
$8$	4.68588			1.65671
$9$		0			0
$10$	1.49430	−	2.58820i	0.472539	−	0.818462i
$11$	1.74628	−	3.02464i	0.526522	−	0.911963i	−0.473001	−	0.881062i	$-0.656829\pi$
$11$	1.74628	−	3.02464i	0.526522	−	0.911963i	0.999522	−	0.0309005i	$-0.00983750\pi$
$12$		0			0
$13$	−2.87580	+	2.17480i	−0.797604	+	0.603181i
$13$	−2.87580	+	2.17480i	−0.797604	+	0.603181i
$14$	5.35806	+	3.57304i	1.43200	+	0.954935i
$15$		0			0
$16$	3.55599			0.888997
$17$	−4.52705			−1.09797			−0.548986	−	0.835832i	$-0.684986\pi$
$17$	−4.52705			−1.09797			−0.548986	+	0.835832i	$0.684986\pi$
$18$		0			0
$19$	−0.677706	−	1.17382i	−0.155476	−	0.269293i	0.777756	−	0.628566i	$-0.216358\pi$
$19$	−0.677706	−	1.17382i	−0.155476	−	0.269293i	−0.933232	+	0.359273i	$0.883025\pi$
$20$	2.40956	−	4.17348i	0.538794	−	0.933219i
$21$		0			0
$22$	4.25069	−	7.36241i	0.906250	−	1.56967i
$23$	0.673327			0.140398			0.0701992	−	0.997533i	$-0.477636\pi$
$23$	0.673327			0.140398			0.0701992	+	0.997533i	$0.477636\pi$
$24$		0			0
$25$	1.74628	+	3.02464i	0.349255	+	0.604928i
$26$	−7.00012	+	5.29378i	−1.37284	+	1.03820i
$27$		0			0
$28$	8.63988	+	5.76153i	1.63278	+	1.08883i
$29$	−2.64824	−	4.58688i	−0.491766	−	0.851763i	0.508189	−	0.861245i	$-0.330315\pi$
$29$	−2.64824	−	4.58688i	−0.491766	−	0.851763i	−0.999955	+	0.00948238i	$0.996982\pi$
$30$		0			0
$31$	4.99846	+	8.65759i	0.897750	+	1.55495i	0.830364	+	0.557222i	$0.188133\pi$
$31$	4.99846	+	8.65759i	0.897750	+	1.55495i	0.0673864	+	0.997727i	$0.478534\pi$
$32$	−0.715973			−0.126567
$33$		0			0
$34$	−11.0195			−1.88983
$35$	2.91209	−	1.43940i	0.492233	−	0.243304i
$36$		0			0
$37$	−3.08236			−0.506737			−0.253368	−	0.967370i	$-0.581538\pi$
$37$	−3.08236			−0.506737			−0.253368	+	0.967370i	$0.581538\pi$
$38$	−1.64963	−	2.85725i	−0.267606	−	0.463507i
$39$		0			0
$40$	2.87662	−	4.98245i	0.454834	−	0.787795i
$41$	−3.61102	−	6.25447i	−0.563947	−	0.976784i	−0.997147	−	0.0754865i	$-0.975949\pi$
$41$	−3.61102	−	6.25447i	−0.563947	−	0.976784i	0.433200	−	0.901298i	$-0.357384\pi$
$42$		0			0
$43$	4.48886	−	7.77494i	0.684545	−	1.18567i	−0.289034	−	0.957319i	$-0.593334\pi$
$43$	4.48886	−	7.77494i	0.684545	−	1.18567i	0.973579	−	0.228348i	$-0.0733325\pi$
$44$	6.85424	−	11.8719i	1.03332	−	1.78975i
$45$		0			0
$46$	1.63898			0.241654
$47$	−2.58008	+	4.46883i	−0.376344	+	0.651846i	−0.990527	−	0.137317i	$-0.956152\pi$
$47$	−2.58008	+	4.46883i	−0.376344	+	0.651846i	0.614184	+	0.789163i	$0.289485\pi$
$48$		0			0
$49$	2.69064	+	6.46223i	0.384377	+	0.923176i
$50$	4.25069	+	7.36241i	0.601138	+	1.04120i
$51$		0			0
$52$	−11.2877	+	8.53623i	−1.56532	+	1.18376i
$53$	4.95271	+	8.57835i	0.680308	+	1.17833i	0.974887	+	0.222700i	$0.0714871\pi$
$53$	4.95271	+	8.57835i	0.680308	+	1.17833i	−0.294579	+	0.955627i	$0.595180\pi$
$54$		0			0
$55$	−2.14405	−	3.71360i	−0.289103	−	0.500741i
$56$	10.3146	+	6.87832i	1.37835	+	0.919154i
$57$		0			0
$58$	−6.44620	−	11.1651i	−0.846427	−	1.46605i
$59$	−0.803443			−0.104599			−0.0522997	−	0.998631i	$-0.516655\pi$
$59$	−0.803443			−0.104599			−0.0522997	+	0.998631i	$0.516655\pi$
$60$		0			0
$61$	−2.32487	−	4.02680i	−0.297669	−	0.515579i	0.677933	−	0.735124i	$-0.262876\pi$
$61$	−2.32487	−	4.02680i	−0.297669	−	0.515579i	−0.975602	+	0.219545i	$0.929543\pi$
$62$	12.1670	+	21.0738i	1.54521	+	2.67638i
$63$		0			0
$64$	−8.85475			−1.10684
$65$	0.547016	+	4.39290i	0.0678490	+	0.544873i
$66$		0			0
$67$	1.06068	−	1.83715i	0.129583	−	0.224444i	−0.793932	−	0.608006i	$-0.791970\pi$
$67$	1.06068	−	1.83715i	0.129583	−	0.224444i	0.923515	+	0.383563i	$0.125303\pi$
$68$	−17.7690			−2.15480
$69$		0			0
$70$	7.08845	−	3.50372i	0.847231	−	0.418775i
$71$	2.52793	−	4.37850i	0.300010	−	0.519632i	−0.676128	−	0.736784i	$-0.736343\pi$
$71$	2.52793	−	4.37850i	0.300010	−	0.519632i	0.976138	+	0.217152i	$0.0696767\pi$
$72$		0			0
$73$	−6.04227	−	10.4655i	−0.707194	−	1.22490i	−0.965894	−	0.258939i	$-0.916627\pi$
$73$	−6.04227	−	10.4655i	−0.707194	−	1.22490i	0.258699	−	0.965958i	$-0.416706\pi$
$74$	−7.50291			−0.872195
$75$		0			0
$76$	−2.66004	−	4.60732i	−0.305127	−	0.528496i
$77$	8.28373	−	4.09453i	0.944019	−	0.466615i
$78$		0			0
$79$	−5.90140	+	10.2215i	−0.663960	+	1.15001i	0.315607	+	0.948890i	$0.397792\pi$
$79$	−5.90140	+	10.2215i	−0.663960	+	1.15001i	−0.979566	+	0.201122i	$0.935541\pi$
$80$	2.18299	−	3.78105i	0.244066	−	0.422734i
$81$		0			0
$82$	−8.78975	−	15.2243i	−0.970665	−	1.68124i
$83$	−12.6805			−1.39187			−0.695935	−	0.718105i	$-0.745010\pi$
$83$	−12.6805			−1.39187			−0.695935	+	0.718105i	$0.745010\pi$
$84$		0			0
$85$	−2.77912	+	4.81357i	−0.301438	+	0.522105i
$86$	10.9265	−	18.9253i	1.17824	−	2.04077i
$87$		0			0
$88$	8.18284	−	14.1731i	0.872293	−	1.51086i
$89$	3.10466			0.329093			0.164546	−	0.986369i	$-0.447384\pi$
$89$	3.10466			0.329093			0.164546	+	0.986369i	$0.447384\pi$
$90$		0			0
$91$	−9.52259	+	0.565851i	−0.998239	+	0.0593173i
$92$	2.64285			0.275536
$93$		0			0
$94$	−6.28029	+	10.8778i	−0.647763	+	1.12196i
$95$	−1.66415			−0.170738
$96$		0			0
$97$	−3.59585	+	6.22820i	−0.365104	+	0.632378i	−0.988793	−	0.149294i	$-0.952300\pi$
$97$	−3.59585	+	6.22820i	−0.365104	+	0.632378i	0.623689	+	0.781672i	$0.285633\pi$
$98$	6.54941	+	15.7300i	0.661590	+	1.58897i
$99$		0			0
$100$	6.85424	+	11.8719i	0.685424	+	1.18719i
$101$	−0.772886	+	1.33868i	−0.0769050	+	0.133203i	−0.901913	−	0.431918i	$-0.857837\pi$
$101$	−0.772886	+	1.33868i	−0.0769050	+	0.133203i	0.825008	+	0.565121i	$0.191170\pi$
$102$		0			0
$103$	−2.75895	+	4.77865i	−0.271848	+	0.470854i	−0.969335	−	0.245743i	$-0.920968\pi$
$103$	−2.75895	+	4.77865i	−0.271848	+	0.470854i	0.697487	+	0.716597i	$0.254301\pi$
$104$	−13.4757	+	10.1909i	−1.32140	+	0.999296i
$105$		0			0
$106$	12.0556	+	20.8810i	1.17095	+	2.02814i
$107$	−1.44837			−0.140020			−0.0700098	−	0.997546i	$-0.522303\pi$
$107$	−1.44837			−0.140020			−0.0700098	+	0.997546i	$0.522303\pi$
$108$		0			0
$109$	−8.20485	−	14.2112i	−0.785882	−	1.36119i	−0.928471	−	0.371406i	$-0.878876\pi$
$109$	−8.20485	−	14.2112i	−0.785882	−	1.36119i	0.142588	−	0.989782i	$-0.454458\pi$
$110$	−5.21892	−	9.03943i	−0.497604	−	0.861876i
$111$		0			0
$112$	7.82747	+	5.21977i	0.739626	+	0.493222i
$113$	−5.38049	+	9.31929i	−0.506154	+	0.876685i	0.493820	+	0.869564i	$0.335600\pi$
$113$	−5.38049	+	9.31929i	−0.506154	+	0.876685i	−0.999975	+	0.00712097i	$0.997733\pi$
$114$		0			0
$115$	0.413350	−	0.715943i	0.0385451	−	0.0667620i
$116$	−10.3945	−	18.0038i	−0.965105	−	1.67161i
$117$		0			0
$118$	−1.95570			−0.180036
$119$	−9.96499	−	6.64518i	−0.913489	−	0.609163i
$120$		0			0
$121$	−0.598956	−	1.03742i	−0.0544505	−	0.0943111i
$122$	−5.65908	−	9.80181i	−0.512349	−	0.887414i
$123$		0			0
$124$	19.6193	+	33.9816i	1.76186	+	3.05164i
$125$	10.4270			0.932619
$126$		0			0
$127$	8.24568	+	14.2819i	0.731686	+	1.26732i	0.956162	+	0.292838i	$0.0945996\pi$
$127$	8.24568	+	14.2819i	0.731686	+	1.26732i	−0.224476	+	0.974480i	$0.572067\pi$
$128$	−20.1218			−1.77853
$129$		0			0
$130$	1.33152	+	10.6930i	0.116782	+	0.937835i
$131$	−3.52172	+	6.09979i	−0.307694	+	0.532942i	−0.977857	−	0.209272i	$-0.932891\pi$
$131$	−3.52172	+	6.09979i	−0.307694	+	0.532942i	0.670164	+	0.742213i	$0.266224\pi$
$132$		0			0
$133$	0.231259	−	3.57862i	0.0200527	−	0.310306i
$134$	2.58185	−	4.47189i	0.223038	−	0.386312i
$135$		0			0
$136$	−21.2132			−1.81902
$137$	19.3213			1.65073			0.825365	−	0.564600i	$-0.190969\pi$
$137$	19.3213			1.65073			0.825365	+	0.564600i	$0.190969\pi$
$138$		0			0
$139$	7.76176	−	13.4438i	0.658343	−	1.14028i	−0.322701	−	0.946501i	$-0.604591\pi$
$139$	7.76176	−	13.4438i	0.658343	−	1.14028i	0.981044	−	0.193783i	$-0.0620759\pi$
$140$	11.4301	−	5.64975i	0.966022	−	0.477491i
$141$		0			0
$142$	6.15334	−	10.6579i	0.516377	−	0.894392i
$143$	1.55604	+	12.4961i	0.130123	+	1.04497i
$144$		0			0
$145$	−6.50292			−0.540038
$146$	−14.7078	−	25.4746i	−1.21722	−	2.10829i
$147$		0			0
$148$	−12.0984			−0.994486
$149$	8.76659	+	15.1842i	0.718187	+	1.24394i	0.961717	+	0.274043i	$0.0883611\pi$
$149$	8.76659	+	15.1842i	0.718187	+	1.24394i	−0.243530	+	0.969893i	$0.578306\pi$
$150$		0			0
$151$	−7.01950	−	12.1581i	−0.571239	−	0.989415i	−0.996439	−	0.0843154i	$-0.973130\pi$
$151$	−7.01950	−	12.1581i	−0.571239	−	0.989415i	0.425200	−	0.905099i	$-0.360204\pi$
$152$	−3.17565	−	5.50038i	−0.257579	−	0.446140i
$153$		0			0
$154$	20.1638	−	9.96669i	1.62485	−	0.803138i
$155$	12.2740			0.985875
$156$		0			0
$157$	5.62295	+	9.73923i	0.448760	+	0.777275i	0.998306	−	0.0581884i	$-0.0185324\pi$
$157$	5.62295	+	9.73923i	0.448760	+	0.777275i	−0.549545	+	0.835464i	$0.685199\pi$
$158$	−14.3649	+	24.8807i	−1.14281	+	1.97940i
$159$		0			0
$160$	−0.439529	+	0.761287i	−0.0347478	+	0.0601850i
$161$	1.48213	+	0.988365i	0.116809	+	0.0778941i
$162$		0			0
$163$	−5.80397	−	10.0528i	−0.454602	−	0.787394i	0.544063	−	0.839044i	$-0.316885\pi$
$163$	−5.80397	−	10.0528i	−0.454602	−	0.787394i	−0.998665	+	0.0516501i	$0.983552\pi$
$164$	−14.1735	−	24.5492i	−1.10676	−	1.91697i
$165$		0			0
$166$	−30.8662			−2.39569
$167$	−3.44594	−	5.96855i	−0.266655	−	0.461860i	0.701341	−	0.712826i	$-0.252585\pi$
$167$	−3.44594	−	5.96855i	−0.266655	−	0.461860i	−0.967996	+	0.250966i	$0.919252\pi$
$168$		0			0
$169$	3.54048	−	12.5086i	0.272345	−	0.962200i
$170$	−6.76477	+	11.7169i	−0.518834	+	0.898648i
$171$		0			0
$172$	17.6191	−	30.5171i	1.34344	−	2.32691i
$173$	−7.91930	−	13.7166i	−0.602093	−	1.04286i	−0.992504	−	0.122215i	$-0.961000\pi$
$173$	−7.91930	−	13.7166i	−0.602093	−	1.04286i	0.390411	−	0.920641i	$-0.372333\pi$
$174$		0			0
$175$	−0.595896	+	9.22119i	−0.0450455	+	0.697056i
$176$	6.20973	−	10.7556i	0.468076	−	0.810732i
$177$		0			0
$178$	7.55718			0.566435
$179$	10.5515	−	18.2758i	0.788658	−	1.36600i	−0.138131	−	0.990414i	$-0.544109\pi$
$179$	10.5515	−	18.2758i	0.788658	−	1.36600i	0.926789	−	0.375582i	$-0.122557\pi$
$180$		0			0
$181$	15.0685			1.12003			0.560015	−	0.828483i	$-0.310796\pi$
$181$	15.0685			1.12003			0.560015	+	0.828483i	$0.310796\pi$
$182$	−23.1794	+	1.37736i	−1.71817	+	0.102097i
$183$		0			0
$184$	3.15513			0.232599
$185$	−1.89223	+	3.27744i	−0.139120	+	0.240962i
$186$		0			0
$187$	−7.90548	+	13.6927i	−0.578106	+	1.00131i
$188$	−10.1270	+	17.5404i	−0.738586	+	1.27927i
$189$		0			0
$190$	−4.05078			−0.293875
$191$	−4.74903	−	8.22556i	−0.343628	−	0.595180i	0.641476	−	0.767143i	$-0.278322\pi$
$191$	−4.74903	−	8.22556i	−0.343628	−	0.595180i	−0.985103	+	0.171963i	$0.944989\pi$
$192$		0			0
$193$	9.27175	−	16.0591i	0.667395	−	1.15596i	−0.311235	−	0.950333i	$-0.600743\pi$
$193$	9.27175	−	16.0591i	0.667395	−	1.15596i	0.978630	−	0.205629i	$-0.0659241\pi$
$194$	−8.75283	+	15.1603i	−0.628416	+	1.08845i
$195$		0			0
$196$	10.5609	+	25.3647i	0.754352	+	1.81176i
$197$	12.8786	+	22.3065i	0.917565	+	1.58927i	0.803102	+	0.595842i	$0.203181\pi$
$197$	12.8786	+	22.3065i	0.917565	+	1.58927i	0.114463	+	0.993427i	$0.463485\pi$
$198$		0			0
$199$	17.6956			1.25441			0.627203	−	0.778856i	$-0.284200\pi$
$199$	17.6956			1.25441			0.627203	+	0.778856i	$0.284200\pi$
$200$	8.18284	+	14.1731i	0.578614	+	1.00219i
$201$		0			0
$202$	−1.88132	+	3.25854i	−0.132369	+	0.229270i
$203$	0.903681	−	13.9840i	0.0634259	−	0.981484i
$204$		0			0
$205$	−8.86709			−0.619305
$206$	−6.71569	+	11.6319i	−0.467905	+	0.810434i
$207$		0			0
$208$	−10.2263	+	7.73356i	−0.709067	+	0.536226i
$209$	−4.73385			−0.327447
$210$		0			0
$211$	−6.23896	−	10.8062i	−0.429508	−	0.743929i	0.567322	−	0.823496i	$-0.307980\pi$
$211$	−6.23896	−	10.8062i	−0.429508	−	0.743929i	−0.996830	+	0.0795669i	$0.974646\pi$
$212$	19.4397	+	33.6706i	1.33512	+	2.31250i
$213$		0			0
$214$	−3.52555			−0.241002
$215$	−5.51135	−	9.54593i	−0.375871	−	0.651027i
$216$		0			0
$217$	−1.70567	+	26.3943i	−0.115788	+	1.79176i
$218$	−19.9718	−	34.5922i	−1.35266	−	2.34288i
$219$		0			0
$220$	−8.41551	−	14.5761i	−0.567374	−	0.982720i
$221$	13.0189	−	9.84544i	0.875746	−	0.662276i
$222$		0			0
$223$	−4.65232	−	8.05805i	−0.311542	−	0.539607i	0.667154	−	0.744920i	$-0.267512\pi$
$223$	−4.65232	−	8.05805i	−0.311542	−	0.539607i	−0.978696	+	0.205313i	$0.934179\pi$
$224$	−1.57601	−	1.05096i	−0.105301	−	0.0702205i
$225$		0			0
$226$	−13.0969	+	22.6845i	−0.871193	+	1.50895i
$227$	−9.53301			−0.632728			−0.316364	−	0.948638i	$-0.602462\pi$
$227$	−9.53301			−0.632728			−0.316364	+	0.948638i	$0.602462\pi$
$228$		0			0
$229$	3.22423	−	5.58453i	0.213063	−	0.369036i	−0.739608	−	0.673037i	$-0.764989\pi$
$229$	3.22423	−	5.58453i	0.213063	−	0.369036i	0.952672	+	0.304001i	$0.0983226\pi$
$230$	1.00615	−	1.74271i	0.0663438	−	0.114911i
$231$		0			0
$232$	−12.4093	−	21.4936i	−0.814712	−	1.41112i
$233$	−12.2379	+	21.1967i	−0.801733	+	1.38864i	0.116742	+	0.993162i	$0.462755\pi$
$233$	−12.2379	+	21.1967i	−0.801733	+	1.38864i	−0.918475	+	0.395479i	$0.870579\pi$
$234$		0			0
$235$	3.16778	+	5.48675i	0.206643	+	0.357916i
$236$	−3.15356			−0.205279
$237$		0			0
$238$	−24.2562	−	16.1753i	−1.57230	−	1.04849i
$239$	−3.62130			−0.234242			−0.117121	−	0.993118i	$-0.537367\pi$
$239$	−3.62130			−0.234242			−0.117121	+	0.993118i	$0.537367\pi$
$240$		0			0
$241$	25.1298			1.61875			0.809377	−	0.587289i	$-0.199805\pi$
$241$	25.1298			1.61875			0.809377	+	0.587289i	$0.199805\pi$
$242$	−1.45795	−	2.52524i	−0.0937203	−	0.162328i
$243$		0			0
$244$	−9.12527	−	15.8054i	−0.584185	−	1.01184i
$245$	8.52299	+	1.10617i	0.544514	+	0.0706708i
$246$		0			0
$247$	4.50178	+	1.90180i	0.286441	+	0.121009i
$248$	23.4222	+	40.5684i	1.48731	+	2.57610i
$249$		0			0
$250$	25.3808			1.60523
$251$	−0.280269	+	0.485440i	−0.0176904	+	0.0306407i	−0.874735	−	0.484601i	$-0.838965\pi$
$251$	−0.280269	+	0.485440i	−0.0176904	+	0.0306407i	0.857045	+	0.515242i	$0.172298\pi$
$252$		0			0
$253$	1.17581	−	2.03657i	0.0739229	−	0.128038i
$254$	20.0712	+	34.7643i	1.25938	+	2.18131i
$255$		0			0
$256$	−31.2699			−1.95437
$257$	23.7587			1.48203			0.741013	−	0.671490i	$-0.234345\pi$
$257$	23.7587			1.48203			0.741013	+	0.671490i	$0.234345\pi$
$258$		0			0
$259$	−6.78491	−	4.52454i	−0.421594	−	0.281141i
$260$	2.14707	+	17.2424i	0.133156	+	1.06933i
$261$		0			0
$262$	−8.57237	+	14.8478i	−0.529603	+	0.917299i
$263$	−3.53761	+	6.12732i	−0.218138	+	0.377827i	−0.954239	−	0.299046i	$-0.903332\pi$
$263$	−3.53761	+	6.12732i	−0.218138	+	0.377827i	0.736100	+	0.676872i	$0.236665\pi$
$264$		0			0
$265$	12.1617			0.747088
$266$	0.562919	−	8.71088i	0.0345148	−	0.534098i
$267$		0			0
$268$	4.16323	−	7.21093i	0.254310	−	0.440478i
$269$	10.3884			0.633394			0.316697	−	0.948527i	$-0.397426\pi$
$269$	10.3884			0.633394			0.316697	+	0.948527i	$0.397426\pi$
$270$		0			0
$271$	−0.122772			−0.00745789			−0.00372894	−	0.999993i	$-0.501187\pi$
$271$	−0.122772			−0.00745789			−0.00372894	+	0.999993i	$0.501187\pi$
$272$	−16.0981			−0.976093
$273$		0			0
$274$	47.0308			2.84124
$275$	12.1979			0.735562
$276$		0			0
$277$	−5.37199			−0.322771			−0.161386	−	0.986891i	$-0.551596\pi$
$277$	−5.37199			−0.322771			−0.161386	+	0.986891i	$0.551596\pi$
$278$	18.8932	−	32.7240i	1.13314	−	1.96266i
$279$		0			0
$280$	13.6457	−	6.74488i	0.815486	−	0.403083i
$281$	14.8847			0.887945			0.443972	−	0.896040i	$-0.353569\pi$
$281$	14.8847			0.887945			0.443972	+	0.896040i	$0.353569\pi$
$282$		0			0
$283$	−2.24269	+	3.88445i	−0.133314	+	0.230906i	−0.924952	−	0.380084i	$-0.875895\pi$
$283$	−2.24269	+	3.88445i	−0.133314	+	0.230906i	0.791638	+	0.610990i	$0.209229\pi$
$284$	9.92228	−	17.1859i	0.588779	−	1.01979i
$285$		0			0
$286$	3.78763	+	30.4172i	0.223967	+	1.79861i
$287$	1.23222	−	19.0680i	0.0727356	−	1.12555i
$288$		0			0
$289$	3.49420			0.205541
$290$	−15.8291			−0.929514
$291$		0			0
$292$	−23.7163	−	41.0778i	−1.38789	−	2.40390i
$293$	11.0016	−	19.0553i	0.642719	−	1.11322i	−0.342105	−	0.939662i	$-0.611140\pi$
$293$	11.0016	−	19.0553i	0.642719	−	1.11322i	0.984823	−	0.173560i	$-0.0555269\pi$
$294$		0			0
$295$	−0.493226	+	0.854293i	−0.0287168	+	0.0497389i
$296$	−14.4436			−0.839515
$297$		0			0
$298$	21.3392	+	36.9605i	1.23614	+	2.14106i
$299$	−1.93636	+	1.46435i	−0.111982	+	0.0846857i
$300$		0			0
$301$	21.2936	−	10.5251i	1.22734	−	0.606659i
$302$	−17.0865	−	29.5947i	−0.983217	−	1.70298i
$303$		0			0
$304$	−2.40991	−	4.17409i	−0.138218	−	0.239401i
$305$	−5.70887			−0.326889
$306$		0			0
$307$	32.9959			1.88318			0.941589	−	0.336764i	$-0.109333\pi$
$307$	32.9959			1.88318			0.941589	+	0.336764i	$0.109333\pi$
$308$	32.5142	−	16.0713i	1.85267	−	0.915747i
$309$		0			0
$310$	29.8768			1.69689
$311$	−4.11532	−	7.12794i	−0.233358	−	0.404188i	0.725436	−	0.688290i	$-0.241638\pi$
$311$	−4.11532	−	7.12794i	−0.233358	−	0.404188i	−0.958794	+	0.284101i	$0.908305\pi$
$312$		0			0
$313$	7.14348	−	12.3729i	0.403773	−	0.699356i	−0.590405	−	0.807107i	$-0.701032\pi$
$313$	7.14348	−	12.3729i	0.403773	−	0.699356i	0.994178	+	0.107752i	$0.0343651\pi$
$314$	13.6871	+	23.7067i	0.772406	+	1.33785i
$315$		0			0
$316$	−23.1634	+	40.1201i	−1.30304	+	2.25693i
$317$	−4.68195	+	8.10938i	−0.262965	+	0.455468i	−0.967028	−	0.254669i	$-0.918034\pi$
$317$	−4.68195	+	8.10938i	−0.262965	+	0.455468i	0.704064	+	0.710137i	$0.251367\pi$
$318$		0			0
$319$	−18.4982			−1.03570
$320$	−5.43585	+	9.41518i	−0.303874	+	0.526324i
$321$		0			0
$322$	3.60773	+	2.40582i	0.201051	+	0.134071i
$323$	3.06801	+	5.31395i	0.170709	+	0.295676i
$324$		0			0
$325$	−11.5999	−	4.90046i	−0.643448	−	0.271829i
$326$	−14.1277	−	24.4699i	−0.782462	−	1.35526i
$327$		0			0
$328$	−16.9208	−	29.3077i	−0.934295	−	1.61825i
$329$	−12.2390	+	6.04958i	−0.674759	+	0.333524i
$330$		0			0
$331$	12.2390	+	21.1985i	0.672714	+	1.16517i	0.977132	+	0.212636i	$0.0682047\pi$
$331$	12.2390	+	21.1985i	0.672714	+	1.16517i	−0.304418	+	0.952539i	$0.598462\pi$
$332$	−49.7719			−2.73159
$333$		0			0
$334$	−8.38793	−	14.5283i	−0.458967	−	0.794954i
$335$	−1.30228	−	2.25562i	−0.0711513	−	0.123238i
$336$		0			0
$337$	−13.1685			−0.717334			−0.358667	−	0.933466i	$-0.616769\pi$
$337$	−13.1685			−0.717334			−0.358667	+	0.933466i	$0.616769\pi$
$338$	8.61805	−	30.4477i	0.468760	−	1.65614i
$339$		0			0
$340$	−10.9082	+	18.8936i	−0.591580	+	1.02465i
$341$	34.9148			1.89074
$342$		0			0
$343$	−3.56314	+	18.1743i	−0.192391	+	0.981318i
$344$	21.0343	−	36.4324i	1.13409	−	1.96430i
$345$		0			0
$346$	−19.2767	−	33.3882i	−1.03632	−	1.79496i
$347$	−14.6733			−0.787705			−0.393853	−	0.919174i	$-0.628858\pi$
$347$	−14.6733			−0.787705			−0.393853	+	0.919174i	$0.628858\pi$
$348$		0			0
$349$	12.1698	+	21.0787i	0.651433	+	1.12831i	0.982775	+	0.184804i	$0.0591652\pi$
$349$	12.1698	+	21.0787i	0.651433	+	1.12831i	−0.331342	+	0.943511i	$0.607502\pi$
$350$	−1.45050	+	22.4457i	−0.0775324	+	1.19977i
$351$		0			0
$352$	−1.25029	+	2.16556i	−0.0666404	+	0.115425i
$353$	−0.334813	+	0.579912i	−0.0178203	+	0.0308656i	−0.874798	−	0.484488i	$-0.839006\pi$
$353$	−0.334813	+	0.579912i	−0.0178203	+	0.0308656i	0.856978	+	0.515353i	$0.172339\pi$
$354$		0			0
$355$	−3.10375	−	5.37585i	−0.164730	−	0.285320i
$356$	12.1860			0.645855
$357$		0			0
$358$	25.6840	−	44.4859i	1.35744	−	2.35115i
$359$	−17.8146	+	30.8557i	−0.940216	+	1.62850i	−0.175158	+	0.984540i	$0.556044\pi$
$359$	−17.8146	+	30.8557i	−0.940216	+	1.62850i	−0.765058	+	0.643962i	$0.777290\pi$
$360$		0			0
$361$	8.58143	−	14.8635i	0.451654	−	0.782288i
$362$	36.6788			1.92779
$363$		0			0
$364$	−37.3768	+	2.22100i	−1.95908	+	0.116412i
$365$	−14.8372			−0.776614
$366$		0			0
$367$	−5.11118	+	8.85282i	−0.266801	+	0.462113i	−0.968034	−	0.250819i	$-0.919300\pi$
$367$	−5.11118	+	8.85282i	−0.266801	+	0.462113i	0.701233	+	0.712932i	$0.252633\pi$
$368$	2.39434			0.124814
$369$		0			0
$370$	−4.60597	+	7.97777i	−0.239453	+	0.414745i
$371$	−1.69006	+	26.1527i	−0.0877433	+	1.35778i
$372$		0			0
$373$	−2.47554	−	4.28776i	−0.128179	−	0.222012i	0.794792	−	0.606881i	$-0.207580\pi$
$373$	−2.47554	−	4.28776i	−0.128179	−	0.222012i	−0.922971	+	0.384870i	$0.874246\pi$
$374$	−19.2431	+	33.3300i	−0.995036	+	1.72345i
$375$		0			0
$376$	−12.0900	+	20.9404i	−0.623492	+	1.07992i
$377$	17.5914	+	7.43158i	0.906002	+	0.382746i
$378$		0			0
$379$	6.33641	+	10.9750i	0.325479	+	0.563747i	0.981609	−	0.190901i	$-0.0611410\pi$
$379$	6.33641	+	10.9750i	0.325479	+	0.563747i	−0.656130	+	0.754648i	$0.727808\pi$
$380$	−6.53189			−0.335079
$381$		0			0
$382$	−11.5598	−	20.0222i	−0.591452	−	1.02442i
$383$	−11.8951	−	20.6029i	−0.607810	−	1.05276i	−0.991601	−	0.129338i	$-0.958715\pi$
$383$	−11.8951	−	20.6029i	−0.607810	−	1.05276i	0.383790	−	0.923420i	$-0.374619\pi$
$384$		0			0
$385$	0.731631	−	11.3216i	0.0372874	−	0.577003i
$386$	22.5688	−	39.0903i	1.14872	−	1.98964i
$387$		0			0
$388$	−14.1139	+	24.4461i	−0.716527	+	1.24106i
$389$	−12.7721	−	22.1218i	−0.647569	−	1.12162i	−0.983702	−	0.179808i	$-0.942452\pi$
$389$	−12.7721	−	22.1218i	−0.647569	−	1.12162i	0.336133	−	0.941815i	$-0.390881\pi$
$390$		0			0
$391$	−3.04819			−0.154153
$392$	12.6080	+	30.2812i	0.636801	+	1.52943i
$393$		0			0
$394$	31.3485	+	54.2971i	1.57931	+	2.73545i
$395$	7.24564	+	12.5498i	0.364568	+	0.631450i
$396$		0			0
$397$	1.06368	+	1.84235i	0.0533846	+	0.0924648i	0.891483	−	0.453055i	$-0.149666\pi$
$397$	1.06368	+	1.84235i	0.0533846	+	0.0924648i	−0.838098	+	0.545519i	$0.816332\pi$
$398$	43.0736			2.15908
$399$		0			0
$400$	6.20973	+	10.7556i	0.310487	+	0.537779i
$401$	−0.587289			−0.0293278			−0.0146639	−	0.999892i	$-0.504668\pi$
$401$	−0.587289			−0.0293278			−0.0146639	+	0.999892i	$0.504668\pi$
$402$		0			0
$403$	−33.2031	−	14.0269i	−1.65397	−	0.698728i
$404$	−3.03362	+	5.25439i	−0.150928	+	0.261416i
$405$		0			0
$406$	2.19969	−	34.0391i	0.109169	−	1.68933i
$407$	−5.38265	+	9.32302i	−0.266808	+	0.462125i
$408$		0			0
$409$	−4.34455			−0.214824			−0.107412	−	0.994215i	$-0.534256\pi$
$409$	−4.34455			−0.214824			−0.107412	+	0.994215i	$0.534256\pi$
$410$	−21.5838			−1.06595
$411$		0			0
$412$	−10.8291	+	18.7565i	−0.533510	+	0.924066i
$413$	−1.76855	−	1.17936i	−0.0870244	−	0.0580325i
$414$		0			0
$415$	−7.78446	+	13.4831i	−0.382124	+	0.661859i
$416$	2.05900	−	1.55710i	0.100951	−	0.0763430i
$417$		0			0
$418$	−11.5229			−0.563602
$419$	4.72818	+	8.18946i	0.230987	+	0.400081i	0.958099	−	0.286438i	$-0.0924712\pi$
$419$	4.72818	+	8.18946i	0.230987	+	0.400081i	−0.727112	+	0.686519i	$0.759138\pi$
$420$		0			0
$421$	−11.9569			−0.582741			−0.291371	−	0.956610i	$-0.594111\pi$
$421$	−11.9569			−0.582741			−0.291371	+	0.956610i	$0.594111\pi$
$422$	−15.1865	−	26.3039i	−0.739269	−	1.28045i
$423$		0			0
$424$	23.2078	+	40.1971i	1.12707	+	1.95214i
$425$	−7.90548	−	13.6927i	−0.383472	−	0.664193i
$426$		0			0
$427$	0.793336	−	12.2765i	0.0383922	−	0.594100i
$428$	−5.68496			−0.274793
$429$		0			0
$430$	−13.4154	−	23.2362i	−0.646949	−	1.12055i
$431$	−13.2352	+	22.9241i	−0.637519	+	1.10422i	0.348456	+	0.937325i	$0.386706\pi$
$431$	−13.2352	+	22.9241i	−0.637519	+	1.10422i	−0.985975	+	0.166891i	$0.946627\pi$
$432$		0			0
$433$	4.13088	−	7.15489i	0.198517	−	0.343842i	−0.749531	−	0.661970i	$-0.769721\pi$
$433$	4.13088	−	7.15489i	0.198517	−	0.343842i	0.948048	+	0.318128i	$0.103054\pi$
$434$	−4.15184	+	64.2476i	−0.199295	+	3.08398i
$435$		0			0
$436$	−32.2046	−	55.7799i	−1.54232	−	2.67137i
$437$	−0.456318	−	0.790366i	−0.0218286	−	0.0378083i
$438$		0			0
$439$	35.1043			1.67544			0.837719	−	0.546102i	$-0.183889\pi$
$439$	35.1043			1.67544			0.837719	+	0.546102i	$0.183889\pi$
$440$	−10.0467	−	17.4015i	−0.478960	−	0.829582i
$441$		0			0
$442$	31.6899	−	23.9652i	1.50734	−	1.13991i
$443$	−0.192275	+	0.333030i	−0.00913525	+	0.0158227i	−0.870557	−	0.492068i	$-0.836241\pi$
$443$	−0.192275	+	0.333030i	−0.00913525	+	0.0158227i	0.861422	+	0.507890i	$0.169575\pi$
$444$		0			0
$445$	1.90592	−	3.30115i	0.0903493	−	0.156490i
$446$	−11.3244	−	19.6145i	−0.536227	−	0.928772i
$447$		0			0
$448$	−19.4912	−	12.9977i	−0.920871	−	0.614085i
$449$	18.9728	−	32.8619i	0.895382	−	1.55085i	0.0620505	−	0.998073i	$-0.480236\pi$
$449$	18.9728	−	32.8619i	0.895382	−	1.55085i	0.833331	−	0.552774i	$-0.186431\pi$
$450$		0			0
$451$	−25.2233			−1.18772
$452$	−21.1188	+	36.5788i	−0.993343	+	1.72052i
$453$		0			0
$454$	−23.2047			−1.08905
$455$	−5.24417	+	10.4727i	−0.245851	+	0.490966i
$456$		0			0
$457$	−14.3895			−0.673112			−0.336556	−	0.941663i	$-0.609262\pi$
$457$	−14.3895			−0.673112			−0.336556	+	0.941663i	$0.609262\pi$
$458$	7.84825	−	13.5936i	0.366725	−	0.635186i
$459$		0			0
$460$	1.62242	−	2.81012i	0.0756459	−	0.131022i
$461$	−1.79501	+	3.10905i	−0.0836019	+	0.144803i	−0.904795	−	0.425848i	$-0.859976\pi$
$461$	−1.79501	+	3.10905i	−0.0836019	+	0.144803i	0.821193	+	0.570651i	$0.193309\pi$
$462$		0			0
$463$	4.69484			0.218188			0.109094	−	0.994031i	$-0.465205\pi$
$463$	4.69484			0.218188			0.109094	+	0.994031i	$0.465205\pi$
$464$	−9.41710	−	16.3109i	−0.437178	−	0.757214i
$465$		0			0
$466$	−29.7889	+	51.5958i	−1.37994	+	2.39013i
$467$	−20.0343	+	34.7003i	−0.927075	+	1.60574i	−0.138885	+	0.990309i	$0.544352\pi$
$467$	−20.0343	+	34.7003i	−0.927075	+	1.60574i	−0.788190	+	0.615432i	$0.788982\pi$
$468$		0			0
$469$	5.03150	−	2.48700i	0.232333	−	0.114839i
$470$	7.71083	+	13.3556i	0.355674	+	0.616046i
$471$		0			0
$472$	−3.76484			−0.173291
$473$	−15.6776	−	27.1544i	−0.720856	−	1.24856i
$474$		0			0
$475$	2.36692	−	4.09963i	0.108602	−	0.188104i
$476$	−39.1132	−	26.0827i	−1.79275	−	1.19550i
$477$		0			0
$478$	−8.81476			−0.403178
$479$	10.2350	−	17.7276i	0.467650	−	0.809993i	−0.531667	−	0.846954i	$-0.678434\pi$
$479$	10.2350	−	17.7276i	0.467650	−	0.809993i	0.999317	+	0.0369602i	$0.0117675\pi$
$480$		0			0
$481$	8.86425	−	6.70352i	0.404175	−	0.305654i
$482$	61.1696			2.78620
$483$		0			0
$484$	−2.35094	−	4.07195i	−0.106861	−	0.185088i
$485$	4.41492	+	7.64687i	0.200471	+	0.347227i
$486$		0			0
$487$	33.5937			1.52228			0.761138	−	0.648590i	$-0.224641\pi$
$487$	33.5937			1.52228			0.761138	+	0.648590i	$0.224641\pi$
$488$	−10.8941	−	18.8691i	−0.493151	−	0.854163i
$489$		0			0
$490$	20.7462	+	2.69259i	0.937218	+	0.121639i
$491$	−20.2312	−	35.0415i	−0.913021	−	1.58140i	−0.809773	−	0.586743i	$-0.800410\pi$
$491$	−20.2312	−	35.0415i	−0.913021	−	1.58140i	−0.103248	−	0.994656i	$-0.532923\pi$
$492$		0			0
$493$	11.9887	+	20.7651i	0.539944	+	0.935211i
$494$	10.9580	+	4.62926i	0.493023	+	0.208280i
$495$		0			0
$496$	17.7745	+	30.7863i	0.798097	+	1.38234i
$497$	11.9916	−	5.92729i	0.537898	−	0.265875i
$498$		0			0
$499$	−2.38204	+	4.12581i	−0.106635	+	0.184697i	−0.914405	−	0.404801i	$-0.867341\pi$
$499$	−2.38204	+	4.12581i	−0.106635	+	0.184697i	0.807770	+	0.589498i	$0.200674\pi$
$500$	40.9266			1.83029
$501$		0			0
$502$	−0.682215	+	1.18163i	−0.0304487	+	0.0527388i
$503$	0.350346	−	0.606817i	0.0156212	−	0.0270567i	−0.858109	−	0.513467i	$-0.828361\pi$
$503$	0.350346	−	0.606817i	0.0156212	−	0.0270567i	0.873730	+	0.486411i	$0.161694\pi$
$504$		0			0
$505$	0.948935	+	1.64360i	0.0422271	+	0.0731394i
$506$	2.86210	−	4.95731i	0.127236	−	0.220379i
$507$		0			0
$508$	32.3648	+	56.0575i	1.43596	+	2.48715i
$509$	−26.8914			−1.19194			−0.595970	−	0.803007i	$-0.703232\pi$
$509$	−26.8914			−1.19194			−0.595970	+	0.803007i	$0.703232\pi$
$510$		0			0
$511$	2.06185	−	31.9061i	0.0912111	−	1.41144i
$512$	−35.8718			−1.58533
$513$		0			0
$514$	57.8321			2.55087
$515$	3.38739	+	5.86714i	0.149266	+	0.258537i
$516$		0			0
$517$	9.01107	+	15.6076i	0.396306	+	0.686423i
$518$	−16.5155	−	11.0134i	−0.725648	−	0.483900i
$519$		0			0
$520$	2.56325	+	20.5846i	0.112406	+	0.902695i
$521$	15.4700	+	26.7948i	0.677753	+	1.17390i	0.975656	+	0.219306i	$0.0703794\pi$
$521$	15.4700	+	26.7948i	0.677753	+	1.17390i	−0.297903	+	0.954596i	$0.596287\pi$
$522$		0			0
$523$	−1.70226			−0.0744347			−0.0372173	−	0.999307i	$-0.511849\pi$
$523$	−1.70226			−0.0744347			−0.0372173	+	0.999307i	$0.511849\pi$
$524$	−13.8230	+	23.9421i	−0.603859	+	1.04591i
$525$		0			0
$526$	−8.61105	+	14.9148i	−0.375460	+	0.650315i
$527$	−22.6283	−	39.1933i	−0.985704	−	1.70729i
$528$		0			0
$529$	−22.5466			−0.980288
$530$	29.6034			1.28589
$531$		0			0
$532$	0.907707	−	14.0463i	0.0393541	−	0.608984i
$533$	23.9868	+	10.1334i	1.03898	+	0.438925i
$534$		0			0
$535$	−0.889144	+	1.54004i	−0.0384410	+	0.0665818i
$536$	4.97021	−	8.60866i	0.214681	−	0.371838i
$537$		0			0
$538$	25.2870			1.09020
$539$	24.2445	+	3.14662i	1.04429	+	0.135535i
$540$		0			0
$541$	1.00845	−	1.74668i	0.0433566	−	0.0750958i	−0.843533	−	0.537078i	$-0.819528\pi$
$541$	1.00845	−	1.74668i	0.0433566	−	0.0750958i	0.886889	+	0.461982i	$0.152862\pi$
$542$	−0.298846			−0.0128365
$543$		0			0
$544$	3.24124			0.138967
$545$	−20.1475			−0.863026
$546$		0			0
$547$	−2.08074			−0.0889658			−0.0444829	−	0.999010i	$-0.514164\pi$
$547$	−2.08074			−0.0889658			−0.0444829	+	0.999010i	$0.514164\pi$
$548$	75.8373			3.23961
$549$		0			0
$550$	29.6915			1.26605
$551$	−3.58945	+	6.21712i	−0.152916	+	0.264858i
$552$		0			0
$553$	−27.9942	+	13.8372i	−1.19044	+	0.588416i
$554$	−13.0762			−0.555554
$555$		0			0
$556$	30.4654	−	52.7676i	1.29202	−	2.23784i
$557$	9.81703	−	17.0036i	0.415961	−	0.720465i	−0.579568	−	0.814924i	$-0.696779\pi$
$557$	9.81703	−	17.0036i	0.415961	−	0.720465i	0.995529	+	0.0944586i	$0.0301120\pi$
$558$		0			0
$559$	3.99986	+	32.1216i	0.169176	+	1.35860i
$560$	10.3553	−	5.11850i	0.437593	−	0.216296i
$561$		0			0
$562$	36.2314			1.52833
$563$	23.3397			0.983652			0.491826	−	0.870693i	$-0.336330\pi$
$563$	23.3397			0.983652			0.491826	+	0.870693i	$0.336330\pi$
$564$		0			0
$565$	6.60607	+	11.4421i	0.277920	+	0.481371i
$566$	−5.45902	+	9.45531i	−0.229460	+	0.397436i
$567$		0			0
$568$	11.8456	−	20.5171i	0.497029	−	0.860880i
$569$	21.6413			0.907250			0.453625	−	0.891193i	$-0.350131\pi$
$569$	21.6413			0.907250			0.453625	+	0.891193i	$0.350131\pi$
$570$		0			0
$571$	−3.91282	−	6.77720i	−0.163746	−	0.283617i	0.772463	−	0.635060i	$-0.219025\pi$
$571$	−3.91282	−	6.77720i	−0.163746	−	0.283617i	−0.936209	+	0.351443i	$0.885691\pi$
$572$	6.10756	+	49.0478i	0.255370	+	2.05079i
$573$		0			0
$574$	2.99940	−	46.4142i	0.125193	−	1.93729i
$575$	1.17581	+	2.03657i	0.0490349	+	0.0849309i
$576$		0			0
$577$	5.92244	+	10.2580i	0.246555	+	0.427045i	0.962568	−	0.271042i	$-0.0873682\pi$
$577$	5.92244	+	10.2580i	0.246555	+	0.427045i	−0.716013	+	0.698087i	$0.754035\pi$
$578$	8.50538			0.353777
$579$		0			0
$580$	−25.5244			−1.05984
$581$	−27.9125	−	18.6135i	−1.15801	−	0.772219i
$582$		0			0
$583$	34.5952			1.43279
$584$	−28.3134	−	49.0402i	−1.17161	−	2.02930i
$585$		0			0
$586$	26.7794	−	46.3833i	1.10625	−	1.91608i
$587$	2.24869	+	3.89484i	0.0928134	+	0.160757i	0.908694	−	0.417463i	$-0.137081\pi$
$587$	2.24869	+	3.89484i	0.0928134	+	0.160757i	−0.815881	+	0.578220i	$0.803747\pi$
$588$		0			0
$589$	6.77497	−	11.7346i	0.279158	−	0.483516i
$590$	−1.20058	+	2.07947i	−0.0494273	+	0.0856106i
$591$		0			0
$592$	−10.9608			−0.450487
$593$	−17.8835	+	30.9751i	−0.734388	+	1.27200i	0.220604	+	0.975363i	$0.429197\pi$
$593$	−17.8835	+	30.9751i	−0.734388	+	1.27200i	−0.954992	+	0.296633i	$0.904136\pi$
$594$		0			0
$595$	−13.1832	+	6.51626i	−0.540457	+	0.267141i
$596$	34.4094	+	59.5988i	1.40946	+	2.44126i
$597$		0			0
$598$	−4.71337	+	3.56445i	−0.192744	+	0.145761i
$599$	9.70429	+	16.8083i	0.396507	+	0.686769i	0.993292	−	0.115631i	$-0.0368891\pi$
$599$	9.70429	+	16.8083i	0.396507	+	0.686769i	−0.596786	+	0.802401i	$0.703556\pi$
$600$		0			0
$601$	−20.4135	−	35.3571i	−0.832682	−	1.44225i	−0.895904	−	0.444248i	$-0.853471\pi$
$601$	−20.4135	−	35.3571i	−0.832682	−	1.44225i	0.0632213	−	0.998000i	$-0.479863\pi$
$602$	51.8318	−	25.6197i	2.11251	−	1.04418i
$603$		0			0
$604$	−27.5520	−	47.7214i	−1.12107	−	1.94176i
$605$	−1.47077			−0.0597955
$606$		0			0
$607$	−0.471345	−	0.816393i	−0.0191313	−	0.0331364i	0.856301	−	0.516477i	$-0.172757\pi$
$607$	−0.471345	−	0.816393i	−0.0191313	−	0.0331364i	−0.875433	+	0.483340i	$0.839423\pi$
$608$	0.485219	+	0.840424i	0.0196782	+	0.0340837i
$609$		0			0
$610$	−13.8962			−0.562642
$611$	−2.29902	−	18.4626i	−0.0930082	−	0.746919i
$612$		0			0
$613$	−0.460547	+	0.797690i	−0.0186013	+	0.0322184i	−0.875176	−	0.483804i	$-0.839255\pi$
$613$	−0.460547	+	0.797690i	−0.0186013	+	0.0322184i	0.856575	+	0.516023i	$0.172588\pi$
$614$	80.3169			3.24133
$615$		0			0
$616$	38.8166	−	19.1865i	1.56396	−	0.773045i
$617$	−12.3732	+	21.4311i	−0.498127	+	0.862782i	−0.999998	−	0.00216105i	$-0.999312\pi$
$617$	−12.3732	+	21.4311i	−0.498127	+	0.862782i	0.501870	+	0.864943i	$0.332645\pi$
$618$		0			0
$619$	−12.0229	−	20.8243i	−0.483242	−	0.836999i	0.516573	−	0.856243i	$-0.327207\pi$
$619$	−12.0229	−	20.8243i	−0.483242	−	0.836999i	−0.999815	+	0.0192441i	$0.993874\pi$
$620$	48.1764			1.93481
$621$		0			0
$622$	−10.0173	−	17.3504i	−0.401656	−	0.695689i
$623$	6.83400	+	4.55727i	0.273798	+	0.182583i
$624$		0			0
$625$	−2.33033	+	4.03626i	−0.0932133	+	0.161450i
$626$	17.3883	−	30.1174i	0.694975	−	1.20373i
$627$		0			0
$628$	22.0704	+	38.2271i	0.880706	+	1.52543i
$629$	13.9540			0.556382
$630$		0			0
$631$	−14.7428	+	25.5353i	−0.586902	+	1.01654i	0.407734	+	0.913101i	$0.366319\pi$
$631$	−14.7428	+	25.5353i	−0.586902	+	1.01654i	−0.994635	+	0.103443i	$0.967014\pi$
$632$	−27.6533	+	47.8969i	−1.09999	+	1.90523i
$633$		0			0
$634$	−11.3965	+	19.7394i	−0.452615	+	0.783952i
$635$	20.2478			0.803510
$636$		0			0
$637$	−21.7918	−	12.7325i	−0.863423	−	0.504480i
$638$	−45.0273			−1.78265
$639$		0			0
$640$	−12.3526	+	21.3953i	−0.488279	+	0.845725i
$641$	−2.18539			−0.0863178			−0.0431589	−	0.999068i	$-0.513742\pi$
$641$	−2.18539			−0.0863178			−0.0431589	+	0.999068i	$0.513742\pi$
$642$		0			0
$643$	5.19137	−	8.99172i	0.204728	−	0.354599i	−0.745318	−	0.666709i	$-0.767702\pi$
$643$	5.19137	−	8.99172i	0.204728	−	0.354599i	0.950046	+	0.312110i	$0.101036\pi$
$644$	5.81747	+	3.87940i	0.229240	+	0.152870i
$645$		0			0
$646$	7.46798	+	12.9349i	0.293824	+	0.508918i
$647$	−6.06580	+	10.5063i	−0.238471	+	0.413045i	−0.960276	−	0.279052i	$-0.909980\pi$
$647$	−6.06580	+	10.5063i	−0.238471	+	0.413045i	0.721804	+	0.692097i	$0.243313\pi$
$648$		0			0
$649$	−1.40303	+	2.43012i	−0.0550738	+	0.0953907i
$650$	−28.2359	−	11.9284i	−1.10750	−	0.467872i
$651$		0			0
$652$	−22.7810	−	39.4578i	−0.892171	−	1.54529i
$653$	24.0253			0.940183			0.470091	−	0.882618i	$-0.344221\pi$
$653$	24.0253			0.940183			0.470091	+	0.882618i	$0.344221\pi$
$654$		0			0
$655$	4.32390	+	7.48922i	0.168949	+	0.292628i
$656$	−12.8407	−	22.2408i	−0.501347	−	0.868358i
$657$		0			0
$658$	−29.7916	+	14.7255i	−1.16140	+	0.574062i
$659$	−10.4678	+	18.1307i	−0.407766	+	0.706272i	−0.994639	−	0.103407i	$-0.967026\pi$
$659$	−10.4678	+	18.1307i	−0.407766	+	0.706272i	0.586873	+	0.809679i	$0.300359\pi$
$660$		0			0
$661$	10.7390	−	18.6005i	0.417699	−	0.723476i	−0.578009	−	0.816031i	$-0.696170\pi$
$661$	10.7390	−	18.6005i	0.417699	−	0.723476i	0.995708	+	0.0925549i	$0.0295034\pi$
$662$	29.7914	+	51.6002i	1.15787	+	2.00550i
$663$		0			0
$664$	−59.4194			−2.30592
$665$	−3.66314	−	2.44278i	−0.142051	−	0.0947269i
$666$		0			0
$667$	−1.78313	−	3.08847i	−0.0690431	−	0.119586i
$668$	−13.5255	−	23.4269i	−0.523319	−	0.906415i
$669$		0			0
$670$	−3.16995	−	5.49051i	−0.122466	−	0.212117i
$671$	−16.2395			−0.626918
$672$		0			0
$673$	−0.483978	−	0.838274i	−0.0186560	−	0.0323131i	0.856547	−	0.516070i	$-0.172605\pi$
$673$	−0.483978	−	0.838274i	−0.0186560	−	0.0323131i	−0.875203	+	0.483756i	$0.839272\pi$
$674$	−32.0541			−1.23468
$675$		0			0
$676$	13.8966	−	49.0970i	0.534485	−	1.88835i
$677$	23.4146	−	40.5552i	0.899895	−	1.55866i	0.0722691	−	0.997385i	$-0.476976\pi$
$677$	23.4146	−	40.5552i	0.899895	−	1.55866i	0.827626	−	0.561279i	$-0.189691\pi$
$678$		0			0
$679$	−17.0575	+	8.43128i	−0.654606	+	0.323563i
$680$	−13.0226	+	22.5558i	−0.499394	+	0.864976i
$681$		0			0
$682$	84.9876			3.25434
$683$	−17.8803			−0.684170			−0.342085	−	0.939669i	$-0.611133\pi$
$683$	−17.8803			−0.684170			−0.342085	+	0.939669i	$0.611133\pi$
$684$		0			0
$685$	11.8612	−	20.5442i	0.453192	−	0.784952i
$686$	−8.67319	+	44.2388i	−0.331144	+	1.68905i
$687$		0			0
$688$	15.9623	−	27.6476i	0.608558	−	1.05405i
$689$	−32.8992	−	13.8985i	−1.25336	−	0.529490i
$690$		0			0
$691$	−33.2164			−1.26361			−0.631806	−	0.775127i	$-0.717686\pi$
$691$	−33.2164			−1.26361			−0.631806	+	0.775127i	$0.717686\pi$
$692$	−31.0837	−	53.8386i	−1.18163	−	2.04664i
$693$		0			0
$694$	−35.7170			−1.35580
$695$	−9.52974	−	16.5060i	−0.361484	−	0.626108i
$696$		0			0
$697$	16.3473	+	28.3143i	0.619197	+	1.07248i
$698$	29.6230	+	51.3085i	1.12125	+	1.94206i
$699$		0			0
$700$	−2.33893	+	36.1937i	−0.0884032	+	1.36799i
$701$	−29.1267			−1.10010			−0.550050	−	0.835132i	$-0.685391\pi$
$701$	−29.1267			−1.10010			−0.550050	+	0.835132i	$0.685391\pi$
$702$		0			0
$703$	2.08893	+	3.61814i	0.0787856	+	0.136461i
$704$	−15.4628	+	26.7824i	−0.582778	+	1.00940i
$705$		0			0
$706$	−0.814982	+	1.41159i	−0.0306723	+	0.0531259i
$707$	−3.66630	+	1.81220i	−0.137886	+	0.0681549i
$708$		0			0
$709$	−5.70074	−	9.87397i	−0.214096	−	0.370825i	0.738897	−	0.673819i	$-0.235347\pi$
$709$	−5.70074	−	9.87397i	−0.214096	−	0.370825i	−0.952992	+	0.302994i	$0.902014\pi$
$710$	−7.55497	−	13.0856i	−0.283533	−	0.491093i
$711$		0			0
$712$	14.5480			0.545211
$713$	3.36560	+	5.82939i	0.126043	+	0.218312i
$714$		0			0
$715$	14.2422	+	6.01670i	0.532628	+	0.225012i
$716$	41.4154	−	71.7336i	1.54777	−	2.68081i
$717$		0			0
$718$	−43.3632	+	75.1073i	−1.61830	+	2.80298i
$719$	−18.1259	−	31.3949i	−0.675980	−	1.17083i	−0.976181	−	0.216956i	$-0.930387\pi$
$719$	−18.1259	−	31.3949i	−0.675980	−	1.17083i	0.300201	−	0.953876i	$-0.402946\pi$
$720$		0			0
$721$	−13.0875	+	6.46898i	−0.487405	+	0.240917i
$722$	20.8884	−	36.1798i	0.777387	−	1.34647i
$723$		0			0
$724$	59.1446			2.19809
$725$	9.24911	−	16.0199i	0.343503	−	0.594965i
$726$		0			0
$727$	4.46075			0.165440			0.0827200	−	0.996573i	$-0.473639\pi$
$727$	4.46075			0.165440			0.0827200	+	0.996573i	$0.473639\pi$
$728$	−44.6217	+	2.65151i	−1.65379	+	0.0982714i
$729$		0			0
$730$	−36.1159			−1.33671
$731$	−20.3213	+	35.1975i	−0.751611	+	1.30183i
$732$		0			0
$733$	5.24983	−	9.09297i	0.193907	−	0.335856i	−0.752635	−	0.658438i	$-0.771217\pi$
$733$	5.24983	−	9.09297i	0.193907	−	0.335856i	0.946542	+	0.322582i	$0.104551\pi$
$734$	−12.4413	+	21.5490i	−0.459218	+	0.795390i
$735$		0			0
$736$	−0.482084			−0.0177698
$737$	−3.70448	−	6.41634i	−0.136456	−	0.236349i
$738$		0			0
$739$	2.32461	−	4.02635i	0.0855123	−	0.148112i	−0.820097	−	0.572224i	$-0.806081\pi$
$739$	2.32461	−	4.02635i	0.0855123	−	0.148112i	0.905609	+	0.424113i	$0.139414\pi$
$740$	−7.42713	+	12.8642i	−0.273027	+	0.472896i
$741$		0			0
$742$	−4.11384	+	63.6596i	−0.151024	+	2.33702i
$743$	−9.95236	−	17.2380i	−0.365117	−	0.632400i	0.623678	−	0.781681i	$-0.285638\pi$
$743$	−9.95236	−	17.2380i	−0.365117	−	0.632400i	−0.988795	+	0.149281i	$0.952304\pi$
$744$		0			0
$745$	21.5269			0.788686
$746$	−6.02582	−	10.4370i	−0.220621	−	0.382127i
$747$		0			0
$748$	−31.0295	+	53.7447i	−1.13455	+	1.96510i
$749$	−3.18817	−	2.12604i	−0.116493	−	0.0776839i
$750$		0			0
$751$	−41.9901			−1.53224			−0.766120	−	0.642697i	$-0.777815\pi$
$751$	−41.9901			−1.53224			−0.766120	+	0.642697i	$0.777815\pi$
$752$	−9.17474	+	15.8911i	−0.334568	+	0.579489i
$753$		0			0
$754$	42.8199	+	18.0895i	1.55941	+	0.658782i
$755$	−17.2368			−0.627313
$756$		0			0
$757$	21.8795	+	37.8965i	0.795225	+	1.37737i	0.922696	+	0.385528i	$0.125981\pi$
$757$	21.8795	+	37.8965i	0.795225	+	1.37737i	−0.127471	+	0.991842i	$0.540686\pi$
$758$	15.4237	+	26.7147i	0.560215	+	0.970321i
$759$		0			0
$760$	−7.79801			−0.282864
$761$	6.01947	+	10.4260i	0.218206	+	0.377943i	0.954259	−	0.298980i	$-0.0966463\pi$
$761$	6.01947	+	10.4260i	0.218206	+	0.377943i	−0.736054	+	0.676923i	$0.763313\pi$
$762$		0			0
$763$	2.79981	−	43.3256i	0.101360	−	1.56849i
$764$	−18.6402	−	32.2858i	−0.674380	−	1.16806i
$765$		0			0
$766$	−28.9544	−	50.1504i	−1.04616	−	1.81201i
$767$	2.31054	−	1.74733i	0.0834289	−	0.0630924i
$768$		0			0
$769$	13.1918	+	22.8489i	0.475708	+	0.823951i	0.999613	−	0.0278261i	$-0.00885848\pi$
$769$	13.1918	+	22.8489i	0.475708	+	0.823951i	−0.523905	+	0.851777i	$0.675525\pi$
$770$	1.78090	−	27.5584i	0.0641790	−	0.993137i
$771$		0			0
$772$	36.3922	−	63.0331i	1.30978	−	2.26861i
$773$	9.88877			0.355674			0.177837	−	0.984060i	$-0.443090\pi$
$773$	9.88877			0.355674			0.177837	+	0.984060i	$0.443090\pi$
$774$		0			0
$775$	−17.4574	+	30.2371i	−0.627088	+	1.08615i
$776$	−16.8497	+	29.1846i	−0.604870	+	1.04767i
$777$		0			0
$778$	−31.0890	−	53.8478i	−1.11460	−	1.93054i
$779$	−4.89442	+	8.47738i	−0.175361	+	0.303734i
$780$		0			0
$781$	−8.82892	−	15.2921i	−0.315924	−	0.547196i
$782$	−7.41973			−0.265329
$783$		0			0
$784$	9.56788	+	22.9796i	0.341710	+	0.820700i
$785$	13.8075			0.492811
$786$		0			0
$787$	−38.4666			−1.37119			−0.685593	−	0.727985i	$-0.740457\pi$
$787$	−38.4666			−1.37119			−0.685593	+	0.727985i	$0.740457\pi$
$788$	50.5495	+	87.5542i	1.80075	+	3.11899i
$789$		0			0
$790$	17.6369	+	30.5481i	0.627494	+	1.08685i
$791$	−25.5232	+	12.6158i	−0.907501	+	0.448565i
$792$		0			0
$793$	15.4434	+	6.52414i	0.548410	+	0.231679i
$794$	2.58915	+	4.48454i	0.0918856	+	0.159151i
$795$		0			0
$796$	69.4562			2.46181
$797$	−4.91617	+	8.51506i	−0.174140	+	0.301619i	−0.939863	−	0.341551i	$-0.889048\pi$
$797$	−4.91617	+	8.51506i	−0.174140	+	0.301619i	0.765723	+	0.643170i	$0.222381\pi$
$798$		0			0
$799$	11.6802	−	20.2306i	0.413214	−	0.715709i
$800$	−1.25029	−	2.16556i	−0.0442043	−	0.0765640i
$801$		0			0
$802$	−1.42955			−0.0504790
$803$	−42.2059			−1.48941
$804$		0			0
$805$	1.96079	−	0.969190i	0.0691087	−	0.0341595i
$806$	−80.8212	−	34.1434i	−2.84681	−	1.20265i
$807$		0			0
$808$	−3.62165	+	6.27288i	−0.127409	+	0.220679i
$809$	−10.6278	+	18.4078i	−0.373653	+	0.647185i	−0.990124	−	0.140192i	$-0.955228\pi$
$809$	−10.6278	+	18.4078i	−0.373653	+	0.647185i	0.616472	+	0.787377i	$0.288561\pi$
$810$		0			0
$811$	35.9695			1.26306			0.631531	−	0.775351i	$-0.282427\pi$
$811$	35.9695			1.26306			0.631531	+	0.775351i	$0.282427\pi$
$812$	3.54700	−	54.8880i	0.124475	−	1.92619i
$813$		0			0
$814$	−13.1021	+	22.6936i	−0.459230	+	0.795409i
$815$	−14.2520			−0.499227
$816$		0			0
$817$	−12.1685			−0.425723
$818$	−10.5753			−0.369756
$819$		0			0
$820$	−34.8039			−1.21540
$821$	−36.8113			−1.28472			−0.642362	−	0.766401i	$-0.722045\pi$
$821$	−36.8113			−1.28472			−0.642362	+	0.766401i	$0.722045\pi$
$822$		0			0
$823$	−37.6324			−1.31178			−0.655892	−	0.754855i	$-0.727707\pi$
$823$	−37.6324			−1.31178			−0.655892	+	0.754855i	$0.727707\pi$
$824$	−12.9281	+	22.3922i	−0.450373	+	0.780068i
$825$		0			0
$826$	−4.30490	−	2.87073i	−0.149787	−	0.0998856i
$827$	28.9693			1.00736			0.503681	−	0.863890i	$-0.331979\pi$
$827$	28.9693			1.00736			0.503681	+	0.863890i	$0.331979\pi$
$828$		0			0
$829$	−4.43056	+	7.67395i	−0.153880	+	0.266527i	−0.932650	−	0.360781i	$-0.882510\pi$
$829$	−4.43056	+	7.67395i	−0.153880	+	0.266527i	0.778771	+	0.627308i	$0.215843\pi$
$830$	−18.9485	+	32.8198i	−0.657713	+	1.13919i
$831$		0			0
$832$	25.4645	−	19.2573i	0.882824	−	0.667628i
$833$	−12.1807	−	29.2549i	−0.422035	−	1.01362i
$834$		0			0
$835$	−8.46174			−0.292831
$836$	−18.5806			−0.642625
$837$		0			0
$838$	11.5091	+	19.9343i	0.397575	+	0.688620i
$839$	−15.9655	+	27.6530i	−0.551190	+	0.954689i	0.446999	+	0.894534i	$0.352493\pi$
$839$	−15.9655	+	27.6530i	−0.551190	+	0.954689i	−0.998189	+	0.0601547i	$0.980841\pi$
$840$		0			0
$841$	0.473666	−	0.820413i	0.0163333	−	0.0282901i
$842$	−29.1047			−1.00301
$843$		0			0
$844$	−24.4883	−	42.4150i	−0.842922	−	1.45998i
$845$	−11.1268	−	11.4435i	−0.382774	−	0.393668i
$846$		0			0
$847$	0.204387	−	3.16278i	0.00702281	−	0.108674i
$848$	17.6118	+	30.5045i	0.604791	+	1.04753i
$849$		0			0
$850$	−19.2431	−	33.3300i	−0.660032	−	1.14321i
$851$	−2.07544			−0.0711450
$852$		0			0
$853$	5.62395			0.192560			0.0962801	−	0.995354i	$-0.469306\pi$
$853$	5.62395			0.192560			0.0962801	+	0.995354i	$0.469306\pi$
$854$	1.93109	−	29.8827i	0.0660807	−	1.02256i
$855$		0			0
$856$	−6.78691			−0.231972
$857$	−23.8452	−	41.3011i	−0.814537	−	1.41082i	−0.909660	−	0.415354i	$-0.863658\pi$
$857$	−23.8452	−	41.3011i	−0.814537	−	1.41082i	0.0951229	−	0.995466i	$-0.469676\pi$
$858$		0			0
$859$	−24.8420	+	43.0276i	−0.847598	+	1.46808i	0.0357469	+	0.999361i	$0.488619\pi$
$859$	−24.8420	+	43.0276i	−0.847598	+	1.46808i	−0.883345	+	0.468723i	$0.844714\pi$
$860$	−21.6324	−	37.4684i	−0.737658	−	1.27766i
$861$		0			0
$862$	−32.2165	+	55.8006i	−1.09730	+	1.90058i
$863$	−11.4553	+	19.8412i	−0.389944	+	0.675402i	−0.992442	−	0.122718i	$-0.960839\pi$
$863$	−11.4553	+	19.8412i	−0.389944	+	0.675402i	0.602498	+	0.798121i	$0.294172\pi$
$864$		0			0
$865$	−19.4463			−0.661195
$866$	10.0552	−	17.4160i	0.341688	−	0.591821i
$867$		0			0
$868$	−6.69485	+	103.599i	−0.227238	+	3.51639i
$869$	20.6109	+	35.6992i	0.699179	+	1.21101i
$870$		0			0
$871$	0.945132	+	7.59005i	0.0320246	+	0.257179i
$872$	−38.4470	−	66.5921i	−1.30198	−	2.25509i
$873$		0			0
$874$	−1.11074	−	1.92387i	−0.0375715	−	0.0650757i
$875$	22.9520	+	15.3056i	0.775920	+	0.517424i
$876$		0			0
$877$	16.1524	+	27.9767i	0.545427	+	0.944707i	0.998580	+	0.0532742i	$0.0169657\pi$
$877$	16.1524	+	27.9767i	0.545427	+	0.944707i	−0.453153	+	0.891433i	$0.649701\pi$
$878$	85.4490			2.88376
$879$		0			0
$880$	−7.62420	−	13.2055i	−0.257012	−	0.445157i
$881$	−18.8690	−	32.6821i	−0.635714	−	1.10109i	−0.986363	−	0.164582i	$-0.947373\pi$
$881$	−18.8690	−	32.6821i	−0.635714	−	1.10109i	0.350650	−	0.936507i	$-0.385961\pi$
$882$		0			0
$883$	−34.3867			−1.15720			−0.578602	−	0.815610i	$-0.696401\pi$
$883$	−34.3867			−1.15720			−0.578602	+	0.815610i	$0.696401\pi$
$884$	51.1000	−	38.6439i	1.71868	−	1.29974i
$885$		0			0
$886$	−0.468025	+	0.810643i	−0.0157236	+	0.0272341i
$887$	−23.6793			−0.795073			−0.397536	−	0.917586i	$-0.630135\pi$
$887$	−23.6793			−0.795073			−0.397536	+	0.917586i	$0.630135\pi$
$888$		0			0
$889$	−2.81374	+	43.5412i	−0.0943699	+	1.46033i
$890$	4.63929	−	8.03548i	0.155509	−	0.269350i
$891$		0			0
$892$	−18.2606	−	31.6284i	−0.611412	−	1.05900i
$893$	6.99415			0.234050
$894$		0			0
$895$	−12.9550	−	22.4387i	−0.433037	−	0.750043i
$896$	−44.2923	−	29.5365i	−1.47970	−	0.986744i
$897$		0			0
$898$	46.1825	−	79.9905i	1.54113	−	2.66932i
$899$	26.4742	−	45.8547i	0.882965	−	1.52934i
$900$		0			0
$901$	−22.4212	−	38.8346i	−0.746958	−	1.29377i
$902$	−61.3973			−2.04431
$903$		0			0
$904$	−25.2123	+	43.6691i	−0.838550	+	1.45241i
$905$	9.25039	−	16.0221i	0.307493	−	0.532594i
$906$		0			0
$907$	4.63367	−	8.02574i	0.153858	−	0.266490i	−0.778784	−	0.627292i	$-0.784163\pi$
$907$	4.63367	−	8.02574i	0.153858	−	0.266490i	0.932643	+	0.360801i	$0.117497\pi$
$908$	−37.4177			−1.24175
$909$		0			0
$910$	−12.7651	+	25.4920i	−0.423158	+	0.845050i
$911$	10.2739			0.340390			0.170195	−	0.985410i	$-0.445560\pi$
$911$	10.2739			0.340390			0.170195	+	0.985410i	$0.445560\pi$
$912$		0			0
$913$	−22.1437	+	38.3540i	−0.732849	+	1.26933i
$914$	−35.0261			−1.15856
$915$		0			0
$916$	12.6553	−	21.9196i	0.418143	−	0.724245i
$917$	−16.7058	+	8.25745i	−0.551675	+	0.272685i
$918$		0			0
$919$	2.31603	+	4.01148i	0.0763987	+	0.132326i	0.901694	−	0.432375i	$-0.142324\pi$
$919$	2.31603	+	4.01148i	0.0763987	+	0.132326i	−0.825295	+	0.564702i	$0.808991\pi$
$920$	1.93691	−	3.35482i	0.0638579	−	0.110605i
$921$		0			0
$922$	−4.36931	+	7.56787i	−0.143896	+	0.249235i
$923$	2.25254	+	18.0894i	0.0741434	+	0.595421i
$924$		0			0
$925$	−5.38265	−	9.32302i	−0.176980	−	0.306539i
$926$	11.4279			0.375545
$927$		0			0
$928$	1.89607	+	3.28408i	0.0622414	+	0.107805i
$929$	1.54518	+	2.67633i	0.0506958	+	0.0878076i	0.890260	−	0.455453i	$-0.150523\pi$
$929$	1.54518	+	2.67633i	0.0506958	+	0.0878076i	−0.839564	+	0.543261i	$0.817189\pi$
$930$		0			0
$931$	5.76204	−	7.53783i	0.188843	−	0.247042i
$932$	−48.0346	+	83.1983i	−1.57342	+	2.72525i
$933$		0			0
$934$	−48.7663	+	84.4657i	−1.59568	+	2.76380i
$935$	9.70621	+	16.8116i	0.317427	+	0.549800i
$936$		0			0
$937$	−41.8382			−1.36680			−0.683398	−	0.730046i	$-0.739498\pi$
$937$	−41.8382			−1.36680			−0.683398	+	0.730046i	$0.739498\pi$
$938$	12.2474	−	6.05372i	0.399892	−	0.197661i
$939$		0			0
$940$	12.4337	+	21.5358i	0.405543	+	0.702422i
$941$	18.9382	+	32.8019i	0.617368	+	1.06931i	0.989964	+	0.141319i	$0.0451344\pi$
$941$	18.9382	+	32.8019i	0.617368	+	1.06931i	−0.372596	+	0.927994i	$0.621532\pi$
$942$		0			0
$943$	−2.43140	−	4.21131i	−0.0791772	−	0.137139i
$944$	−2.85703			−0.0929885
$945$		0			0
$946$	−38.1615	−	66.0977i	−1.24074	−	2.14902i
$947$	0.781555			0.0253971			0.0126986	−	0.999919i	$-0.495958\pi$
$947$	0.781555			0.0253971			0.0126986	+	0.999919i	$0.495958\pi$
$948$		0			0
$949$	40.1368	+	16.9560i	1.30290	+	0.550416i
$950$	5.76143	−	9.97909i	0.186926	−	0.323765i
$951$		0			0
$952$	−46.6947	−	31.1385i	−1.51338	−	1.00921i
$953$	−14.6233	+	25.3283i	−0.473695	+	0.820463i	−0.999547	−	0.0301129i	$-0.990413\pi$
$953$	−14.6233	+	25.3283i	−0.473695	+	0.820463i	0.525852	+	0.850576i	$0.323747\pi$
$954$		0			0
$955$	−11.6615			−0.377359
$956$	−14.2138			−0.459708
$957$		0			0
$958$	24.9135	−	43.1515i	0.804919	−	1.39416i
$959$	42.5302	+	28.3614i	1.37337	+	0.915837i
$960$		0			0
$961$	−34.4692	+	59.7025i	−1.11191	+	1.92589i
$962$	21.5769	−	16.3173i	0.695666	−	0.526092i
$963$		0			0
$964$	98.6361			3.17686
$965$	−11.3837	−	19.7171i	−0.366454	−	0.634717i
$966$		0			0
$967$	−30.4010			−0.977631			−0.488816	−	0.872387i	$-0.662571\pi$
$967$	−30.4010			−0.977631			−0.488816	+	0.872387i	$0.662571\pi$
$968$	−2.80663	−	4.86123i	−0.0902087	−	0.156246i
$969$		0			0
$970$	10.7466	+	18.6136i	0.345051	+	0.597647i
$971$	4.45931	+	7.72376i	0.143106	+	0.247867i	0.928665	−	0.370920i	$-0.120958\pi$
$971$	4.45931	+	7.72376i	0.143106	+	0.247867i	−0.785559	+	0.618787i	$0.787624\pi$
$972$		0			0
$973$	36.8191	−	18.1992i	1.18037	−	0.583438i
$974$	81.7719			2.62014
$975$		0			0
$976$	−8.26721	−	14.3192i	−0.264627	−	0.458348i
$977$	11.8031	−	20.4436i	0.377615	−	0.654048i	−0.613100	−	0.790005i	$-0.710078\pi$
$977$	11.8031	−	20.4436i	0.377615	−	0.654048i	0.990715	+	0.135957i	$0.0434111\pi$
$978$		0			0
$979$	5.42158	−	9.39046i	0.173275	−	0.300120i
$980$	33.4533	+	4.34180i	1.06863	+	0.138694i
$981$		0			0
$982$	−49.2457	−	85.2960i	−1.57149	−	2.72190i
$983$	10.1644	+	17.6053i	0.324195	+	0.561523i	0.981349	−	0.192234i	$-0.0615732\pi$
$983$	10.1644	+	17.6053i	0.324195	+	0.561523i	−0.657154	+	0.753756i	$0.728240\pi$
$984$		0			0
$985$	31.6243			1.00763
$986$	29.1823	+	50.5452i	0.929353	+	1.60969i
$987$		0			0
$988$	17.6698	+	7.46469i	0.562150	+	0.237484i
$989$	3.02247	−	5.23508i	0.0961091	−	0.166466i
$990$		0			0
$991$	22.6402	−	39.2140i	0.719190	−	1.24567i	−0.242131	−	0.970244i	$-0.577846\pi$
$991$	22.6402	−	39.2140i	0.719190	−	1.24567i	0.961321	−	0.275430i	$-0.0888204\pi$
$992$	−3.57876	−	6.19860i	−0.113626	−	0.196806i
$993$		0			0
$994$	29.1894	−	14.4279i	0.925830	−	0.457625i
$995$	10.8632	−	18.8155i	0.344385	−	0.596493i
$996$		0			0
$997$	−19.3021			−0.611303			−0.305652	−	0.952143i	$-0.598874\pi$
$997$	−19.3021			−0.611303			−0.305652	+	0.952143i	$0.598874\pi$
$998$	−5.79823	+	10.0428i	−0.183540	+	0.317900i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.s.e.289.8		16
3.2	odd	2		273.2.l.b.16.1	yes	16
7.4	even	3		819.2.n.e.172.1		16
13.9	even	3		819.2.n.e.100.1		16
21.11	odd	6		273.2.j.b.172.8	yes	16
39.35	odd	6		273.2.j.b.100.8	✓	16
91.74	even	3	inner	819.2.s.e.802.8		16
273.74	odd	6		273.2.l.b.256.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.b.100.8	✓	16	39.35	odd	6
273.2.j.b.172.8	yes	16	21.11	odd	6
273.2.l.b.16.1	yes	16	3.2	odd	2
273.2.l.b.256.1	yes	16	273.74	odd	6
819.2.n.e.100.1		16	13.9	even	3
819.2.n.e.172.1		16	7.4	even	3
819.2.s.e.289.8		16	1.1	even	1	trivial
819.2.s.e.802.8		16	91.74	even	3	inner

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.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.43414 q^{2} +3.92506 q^{4} +(0.613891 - 1.06329i) q^{5} +(2.20121 + 1.46788i) q^{7} +4.68588 q^{8} +O(q^{10})\)	\(q+2.43414 q^{2} +3.92506 q^{4} +(0.613891 - 1.06329i) q^{5} +(2.20121 + 1.46788i) q^{7} +4.68588 q^{8} +(1.49430 - 2.58820i) q^{10} +(1.74628 - 3.02464i) q^{11} +(-2.87580 + 2.17480i) q^{13} +(5.35806 + 3.57304i) q^{14} +3.55599 q^{16} -4.52705 q^{17} +(-0.677706 - 1.17382i) q^{19} +(2.40956 - 4.17348i) q^{20} +(4.25069 - 7.36241i) q^{22} +0.673327 q^{23} +(1.74628 + 3.02464i) q^{25} +(-7.00012 + 5.29378i) q^{26} +(8.63988 + 5.76153i) q^{28} +(-2.64824 - 4.58688i) q^{29} +(4.99846 + 8.65759i) q^{31} -0.715973 q^{32} -11.0195 q^{34} +(2.91209 - 1.43940i) q^{35} -3.08236 q^{37} +(-1.64963 - 2.85725i) q^{38} +(2.87662 - 4.98245i) q^{40} +(-3.61102 - 6.25447i) q^{41} +(4.48886 - 7.77494i) q^{43} +(6.85424 - 11.8719i) q^{44} +1.63898 q^{46} +(-2.58008 + 4.46883i) q^{47} +(2.69064 + 6.46223i) q^{49} +(4.25069 + 7.36241i) q^{50} +(-11.2877 + 8.53623i) q^{52} +(4.95271 + 8.57835i) q^{53} +(-2.14405 - 3.71360i) q^{55} +(10.3146 + 6.87832i) q^{56} +(-6.44620 - 11.1651i) q^{58} -0.803443 q^{59} +(-2.32487 - 4.02680i) q^{61} +(12.1670 + 21.0738i) q^{62} -8.85475 q^{64} +(0.547016 + 4.39290i) q^{65} +(1.06068 - 1.83715i) q^{67} -17.7690 q^{68} +(7.08845 - 3.50372i) q^{70} +(2.52793 - 4.37850i) q^{71} +(-6.04227 - 10.4655i) q^{73} -7.50291 q^{74} +(-2.66004 - 4.60732i) q^{76} +(8.28373 - 4.09453i) q^{77} +(-5.90140 + 10.2215i) q^{79} +(2.18299 - 3.78105i) q^{80} +(-8.78975 - 15.2243i) q^{82} -12.6805 q^{83} +(-2.77912 + 4.81357i) q^{85} +(10.9265 - 18.9253i) q^{86} +(8.18284 - 14.1731i) q^{88} +3.10466 q^{89} +(-9.52259 + 0.565851i) q^{91} +2.64285 q^{92} +(-6.28029 + 10.8778i) q^{94} -1.66415 q^{95} +(-3.59585 + 6.22820i) q^{97} +(6.54941 + 15.7300i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4} + q^{7} - 12 q^{8}+O(q^{10}) \) 16 * q + 12 * q^4 + q^7 - 12 * q^8	\( 16 q + 12 q^{4} + q^{7} - 12 q^{8} - 4 q^{10} + 2 q^{11} + 5 q^{13} + 7 q^{14} + 12 q^{16} - 4 q^{17} - 11 q^{19} + 20 q^{20} + 7 q^{22} + 8 q^{23} + 2 q^{25} - 33 q^{26} - q^{28} - 15 q^{29} + 3 q^{31} + 6 q^{32} - 68 q^{34} - 8 q^{37} - 2 q^{38} - 25 q^{40} - 19 q^{41} + 11 q^{43} + 16 q^{44} - 4 q^{46} - 5 q^{47} + 7 q^{49} + 7 q^{50} - 18 q^{52} - 36 q^{53} - 15 q^{55} + 51 q^{56} + 20 q^{58} - 34 q^{59} - 22 q^{61} + 6 q^{62} - 20 q^{64} + 24 q^{65} + 26 q^{67} + 10 q^{68} + 46 q^{70} - 9 q^{71} - 6 q^{73} + 30 q^{74} - 16 q^{76} + 36 q^{77} + 16 q^{79} + 28 q^{80} - q^{82} - 36 q^{83} - 4 q^{85} - 16 q^{86} + 24 q^{88} + 40 q^{89} - 10 q^{91} + 94 q^{92} - 20 q^{94} + 7 q^{97} - 18 q^{98}+O(q^{100}) \) 16 * q + 12 * q^4 + q^7 - 12 * q^8 - 4 * q^10 + 2 * q^11 + 5 * q^13 + 7 * q^14 + 12 * q^16 - 4 * q^17 - 11 * q^19 + 20 * q^20 + 7 * q^22 + 8 * q^23 + 2 * q^25 - 33 * q^26 - q^28 - 15 * q^29 + 3 * q^31 + 6 * q^32 - 68 * q^34 - 8 * q^37 - 2 * q^38 - 25 * q^40 - 19 * q^41 + 11 * q^43 + 16 * q^44 - 4 * q^46 - 5 * q^47 + 7 * q^49 + 7 * q^50 - 18 * q^52 - 36 * q^53 - 15 * q^55 + 51 * q^56 + 20 * q^58 - 34 * q^59 - 22 * q^61 + 6 * q^62 - 20 * q^64 + 24 * q^65 + 26 * q^67 + 10 * q^68 + 46 * q^70 - 9 * q^71 - 6 * q^73 + 30 * q^74 - 16 * q^76 + 36 * q^77 + 16 * q^79 + 28 * q^80 - q^82 - 36 * q^83 - 4 * q^85 - 16 * q^86 + 24 * q^88 + 40 * q^89 - 10 * q^91 + 94 * q^92 - 20 * q^94 + 7 * q^97 - 18 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more