LMFDB - Embedded newform 819.2.j.h.235.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("819.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 8x^{8} + 7x^{7} + 41x^{6} + 18x^{5} + 58x^{4} + 28x^{3} + 64x^{2} + 16x + 4 $ x^10 - x^9 + 8x^8 + 7x^7 + 41x^6 + 18x^5 + 58x^4 + 28x^3 + 64x^2 + 16x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.4
Root			$-0.606661 - 1.05077i$ of defining polynomial
Character	$\chi$	$=$	819.235
Dual form			819.2.j.h.352.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.10666 + 1.91679i) q^{2} +(-1.44940 + 2.51043i) q^{4} +(-1.06140 - 1.83839i) q^{5} +(2.63169 + 0.272389i) q^{7} -1.98932 q^{8} +O(q^{10})$	\(q+(1.10666 + 1.91679i) q^{2} +(-1.44940 + 2.51043i) q^{4} +(-1.06140 - 1.83839i) q^{5} +(2.63169 + 0.272389i) q^{7} -1.98932 q^{8} +(2.34921 - 4.06896i) q^{10} +(2.39448 - 4.14736i) q^{11} +1.00000 q^{13} +(2.39028 + 5.34585i) q^{14} +(0.697291 + 1.20774i) q^{16} +(-1.88914 + 3.27208i) q^{17} +(1.78362 + 3.08931i) q^{19} +6.15355 q^{20} +10.5995 q^{22} +(2.23721 + 3.87497i) q^{23} +(0.246870 - 0.427591i) q^{25} +(1.10666 + 1.91679i) q^{26} +(-4.49818 + 6.21188i) q^{28} +5.90107 q^{29} +(1.88558 - 3.26592i) q^{31} +(-3.53265 + 6.11873i) q^{32} -8.36254 q^{34} +(-2.29251 - 5.12720i) q^{35} +(-2.81285 - 4.87200i) q^{37} +(-3.94772 + 6.83765i) q^{38} +(2.11146 + 3.65716i) q^{40} -10.3948 q^{41} +3.40733 q^{43} +(6.94110 + 12.0223i) q^{44} +(-4.95168 + 8.57655i) q^{46} +(-3.55438 - 6.15636i) q^{47} +(6.85161 + 1.43369i) q^{49} +1.09280 q^{50} +(-1.44940 + 2.51043i) q^{52} +(-6.19003 + 10.7214i) q^{53} -10.1660 q^{55} +(-5.23528 - 0.541869i) q^{56} +(6.53049 + 11.3111i) q^{58} +(2.39448 - 4.14736i) q^{59} +(-1.60348 - 2.77732i) q^{61} +8.34680 q^{62} -12.8486 q^{64} +(-1.06140 - 1.83839i) q^{65} +(1.44978 - 2.51109i) q^{67} +(-5.47622 - 9.48510i) q^{68} +(7.29075 - 10.0683i) q^{70} +2.53876 q^{71} +(-3.85035 + 6.66901i) q^{73} +(6.22574 - 10.7833i) q^{74} -10.3407 q^{76} +(7.43122 - 10.2623i) q^{77} +(2.58925 + 4.48471i) q^{79} +(1.48021 - 2.56379i) q^{80} +(-11.5035 - 19.9247i) q^{82} -3.46731 q^{83} +8.02051 q^{85} +(3.77076 + 6.53115i) q^{86} +(-4.76338 + 8.25042i) q^{88} +(1.83216 + 3.17339i) q^{89} +(2.63169 + 0.272389i) q^{91} -12.9704 q^{92} +(7.86698 - 13.6260i) q^{94} +(3.78625 - 6.55798i) q^{95} -5.40733 q^{97} +(4.83432 + 14.7197i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} - 8 q^{4} + 2 q^{5} + q^{7} - 18 q^{8}+O(q^{10}) $ 10 * q + 4 * q^2 - 8 * q^4 + 2 * q^5 + q^7 - 18 * q^8	$ 10 q + 4 q^{2} - 8 q^{4} + 2 q^{5} + q^{7} - 18 q^{8} + 5 q^{10} + 11 q^{11} + 10 q^{13} - 10 q^{14} - 10 q^{16} - 5 q^{17} - 9 q^{19} - 2 q^{20} + 16 q^{22} + 10 q^{23} - 9 q^{25} + 4 q^{26} + 37 q^{28} + 6 q^{29} + 6 q^{31} + 22 q^{32} - 44 q^{34} + 4 q^{35} - 4 q^{37} - 10 q^{38} - 28 q^{40} - 28 q^{41} + 4 q^{43} - 3 q^{46} + q^{47} - 11 q^{49} - 18 q^{50} - 8 q^{52} + 17 q^{53} + 21 q^{56} + 27 q^{58} + 11 q^{59} + 11 q^{61} + 46 q^{62} + 18 q^{64} + 2 q^{65} - 13 q^{67} - 32 q^{68} + 49 q^{70} - 30 q^{71} - 33 q^{74} + 16 q^{76} + 46 q^{77} - 2 q^{79} + 55 q^{80} - 34 q^{82} - 12 q^{83} - 44 q^{85} + 28 q^{86} + 3 q^{88} - 4 q^{89} + q^{91} - 42 q^{92} - 20 q^{94} - 12 q^{95} - 24 q^{97} + 7 q^{98}+O(q^{100}) $ 10 * q + 4 * q^2 - 8 * q^4 + 2 * q^5 + q^7 - 18 * q^8 + 5 * q^10 + 11 * q^11 + 10 * q^13 - 10 * q^14 - 10 * q^16 - 5 * q^17 - 9 * q^19 - 2 * q^20 + 16 * q^22 + 10 * q^23 - 9 * q^25 + 4 * q^26 + 37 * q^28 + 6 * q^29 + 6 * q^31 + 22 * q^32 - 44 * q^34 + 4 * q^35 - 4 * q^37 - 10 * q^38 - 28 * q^40 - 28 * q^41 + 4 * q^43 - 3 * q^46 + q^47 - 11 * q^49 - 18 * q^50 - 8 * q^52 + 17 * q^53 + 21 * q^56 + 27 * q^58 + 11 * q^59 + 11 * q^61 + 46 * q^62 + 18 * q^64 + 2 * q^65 - 13 * q^67 - 32 * q^68 + 49 * q^70 - 30 * q^71 - 33 * q^74 + 16 * q^76 + 46 * q^77 - 2 * q^79 + 55 * q^80 - 34 * q^82 - 12 * q^83 - 44 * q^85 + 28 * q^86 + 3 * q^88 - 4 * q^89 + q^91 - 42 * q^92 - 20 * q^94 - 12 * q^95 - 24 * q^97 + 7 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.10666	+	1.91679i	0.782527	+	1.35538i	0.930465	+	0.366381i	$0.119403\pi$
$2$	1.10666	+	1.91679i	0.782527	+	1.35538i	−0.147938	+	0.988997i	$0.547263\pi$
$3$		0			0
$3$		0			0
$4$	−1.44940	+	2.51043i	−0.724699	+	1.25521i
$5$	−1.06140	−	1.83839i	−0.474671	−	0.822155i	0.524908	−	0.851159i	$-0.324100\pi$
$5$	−1.06140	−	1.83839i	−0.474671	−	0.822155i	−0.999579	+	0.0290040i	$0.990766\pi$
$6$		0			0
$7$	2.63169	+	0.272389i	0.994686	+	0.102953i
$7$	2.63169	+	0.272389i	0.994686	+	0.102953i
$8$	−1.98932			−0.703331
$9$		0			0
$10$	2.34921	−	4.06896i	0.742887	−	1.28672i
$11$	2.39448	−	4.14736i	0.721962	−	1.25048i	−0.238250	−	0.971204i	$-0.576574\pi$
$11$	2.39448	−	4.14736i	0.721962	−	1.25048i	0.960212	−	0.279272i	$-0.0900930\pi$
$12$		0			0
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	2.39028	+	5.34585i	0.638829	+	1.42874i
$15$		0			0
$16$	0.697291	+	1.20774i	0.174323	+	0.301936i
$17$	−1.88914	+	3.27208i	−0.458183	+	0.793597i	−0.998865	−	0.0476304i	$-0.984833\pi$
$17$	−1.88914	+	3.27208i	−0.458183	+	0.793597i	0.540682	+	0.841227i	$0.318166\pi$
$18$		0			0
$19$	1.78362	+	3.08931i	0.409190	+	0.708737i	0.994799	−	0.101856i	$-0.0324781\pi$
$19$	1.78362	+	3.08931i	0.409190	+	0.708737i	−0.585609	+	0.810593i	$0.699145\pi$
$20$	6.15355			1.37597
$21$		0			0
$22$	10.5995			2.25982
$23$	2.23721	+	3.87497i	0.466491	+	0.807987i	0.999267	−	0.0382695i	$-0.0121845\pi$
$23$	2.23721	+	3.87497i	0.466491	+	0.807987i	−0.532776	+	0.846256i	$0.678851\pi$
$24$		0			0
$25$	0.246870	−	0.427591i	0.0493740	−	0.0855182i
$26$	1.10666	+	1.91679i	0.217034	+	0.375914i
$27$		0			0
$28$	−4.49818	+	6.21188i	−0.850076	+	1.17393i
$29$	5.90107			1.09580			0.547901	−	0.836543i	$-0.315427\pi$
$29$	5.90107			1.09580			0.547901	+	0.836543i	$0.315427\pi$
$30$		0			0
$31$	1.88558	−	3.26592i	0.338660	−	0.586577i	−0.645521	−	0.763743i	$-0.723360\pi$
$31$	1.88558	−	3.26592i	0.338660	−	0.586577i	0.984181	+	0.177166i	$0.0566929\pi$
$32$	−3.53265	+	6.11873i	−0.624490	+	1.08165i
$33$		0			0
$34$	−8.36254			−1.43416
$35$	−2.29251	−	5.12720i	−0.387505	−	0.866655i
$36$		0			0
$37$	−2.81285	−	4.87200i	−0.462429	−	0.800951i	0.536652	−	0.843804i	$-0.319689\pi$
$37$	−2.81285	−	4.87200i	−0.462429	−	0.800951i	−0.999081	+	0.0428524i	$0.986355\pi$
$38$	−3.94772	+	6.83765i	−0.640404	+	1.10921i
$39$		0			0
$40$	2.11146	+	3.65716i	0.333851	+	0.578247i
$41$	−10.3948			−1.62340			−0.811698	−	0.584077i	$-0.801457\pi$
$41$	−10.3948			−1.62340			−0.811698	+	0.584077i	$0.801457\pi$
$42$		0			0
$43$	3.40733			0.519613			0.259807	−	0.965661i	$-0.416341\pi$
$43$	3.40733			0.519613			0.259807	+	0.965661i	$0.416341\pi$
$44$	6.94110	+	12.0223i	1.04641	+	1.81244i
$45$		0			0
$46$	−4.95168	+	8.57655i	−0.730085	+	1.26454i
$47$	−3.55438	−	6.15636i	−0.518459	−	0.897998i	−0.999770	−	0.0214479i	$-0.993172\pi$
$47$	−3.55438	−	6.15636i	−0.518459	−	0.897998i	0.481311	−	0.876550i	$-0.340161\pi$
$48$		0			0
$49$	6.85161	+	1.43369i	0.978801	+	0.204813i
$50$	1.09280			0.154546
$51$		0			0
$52$	−1.44940	+	2.51043i	−0.200995	+	0.348134i
$53$	−6.19003	+	10.7214i	−0.850266	+	1.47270i	0.0307027	+	0.999529i	$0.490226\pi$
$53$	−6.19003	+	10.7214i	−0.850266	+	1.47270i	−0.880968	+	0.473175i	$0.843108\pi$
$54$		0			0
$55$	−10.1660			−1.37078
$56$	−5.23528	−	0.541869i	−0.699594	−	0.0724103i
$57$		0			0
$58$	6.53049	+	11.3111i	0.857495	+	1.48522i
$59$	2.39448	−	4.14736i	0.311734	−	0.539940i	−0.667003	−	0.745055i	$-0.732423\pi$
$59$	2.39448	−	4.14736i	0.311734	−	0.539940i	0.978738	+	0.205115i	$0.0657567\pi$
$60$		0			0
$61$	−1.60348	−	2.77732i	−0.205305	−	0.355599i	0.744925	−	0.667148i	$-0.232485\pi$
$61$	−1.60348	−	2.77732i	−0.205305	−	0.355599i	−0.950230	+	0.311550i	$0.899152\pi$
$62$	8.34680			1.06004
$63$		0			0
$64$	−12.8486			−1.60608
$65$	−1.06140	−	1.83839i	−0.131650	−	0.228025i
$66$		0			0
$67$	1.44978	−	2.51109i	0.177118	−	0.306778i	−0.763774	−	0.645484i	$-0.776656\pi$
$67$	1.44978	−	2.51109i	0.177118	−	0.306778i	0.940892	+	0.338706i	$0.109989\pi$
$68$	−5.47622	−	9.48510i	−0.664090	−	1.15024i
$69$		0			0
$70$	7.29075	−	10.0683i	0.871411	−	1.20340i
$71$	2.53876			0.301295			0.150648	−	0.988588i	$-0.451864\pi$
$71$	2.53876			0.301295			0.150648	+	0.988588i	$0.451864\pi$
$72$		0			0
$73$	−3.85035	+	6.66901i	−0.450650	+	0.780548i	−0.998426	−	0.0560762i	$-0.982141\pi$
$73$	−3.85035	+	6.66901i	−0.450650	+	0.780548i	0.547777	+	0.836625i	$0.315474\pi$
$74$	6.22574	−	10.7833i	0.723727	−	1.25353i
$75$		0			0
$76$	−10.3407			−1.18616
$77$	7.43122	−	10.2623i	0.846867	−	1.16950i
$78$		0			0
$79$	2.58925	+	4.48471i	0.291313	+	0.504569i	0.974120	−	0.226029i	$-0.0725745\pi$
$79$	2.58925	+	4.48471i	0.291313	+	0.504569i	−0.682807	+	0.730598i	$0.739241\pi$
$80$	1.48021	−	2.56379i	0.165492	−	0.286641i
$81$		0			0
$82$	−11.5035	−	19.9247i	−1.27035	−	2.20032i
$83$	−3.46731			−0.380587			−0.190294	−	0.981727i	$-0.560944\pi$
$83$	−3.46731			−0.380587			−0.190294	+	0.981727i	$0.560944\pi$
$84$		0			0
$85$	8.02051			0.869946
$86$	3.77076	+	6.53115i	0.406612	+	0.704272i
$87$		0			0
$88$	−4.76338	+	8.25042i	−0.507778	+	0.879498i
$89$	1.83216	+	3.17339i	0.194209	+	0.336379i	0.946641	−	0.322291i	$-0.104453\pi$
$89$	1.83216	+	3.17339i	0.194209	+	0.336379i	−0.752432	+	0.658670i	$0.771119\pi$
$90$		0			0
$91$	2.63169	+	0.272389i	0.275876	+	0.0285541i
$92$	−12.9704			−1.35226
$93$		0			0
$94$	7.86698	−	13.6260i	0.811417	−	1.40542i
$95$	3.78625	−	6.55798i	0.388461	−	0.672835i
$96$		0			0
$97$	−5.40733			−0.549031			−0.274516	−	0.961583i	$-0.588518\pi$
$97$	−5.40733			−0.549031			−0.274516	+	0.961583i	$0.588518\pi$
$98$	4.83432	+	14.7197i	0.488340	+	1.48692i
$99$		0			0
$100$	0.715625	+	1.23950i	0.0715625	+	0.123950i
$101$	4.65862	−	8.06897i	0.463550	−	0.802892i	−0.535585	−	0.844482i	$-0.679909\pi$
$101$	4.65862	−	8.06897i	0.463550	−	0.802892i	0.999135	+	0.0415891i	$0.0132420\pi$
$102$		0			0
$103$	−3.65318	−	6.32749i	−0.359958	−	0.623466i	0.627995	−	0.778217i	$-0.283876\pi$
$103$	−3.65318	−	6.32749i	−0.359958	−	0.623466i	−0.987953	+	0.154751i	$0.950542\pi$
$104$	−1.98932			−0.195069
$105$		0			0
$106$	−27.4011			−2.66143
$107$	3.37365	+	5.84333i	0.326143	+	0.564896i	0.981743	−	0.190212i	$-0.0609176\pi$
$107$	3.37365	+	5.84333i	0.326143	+	0.564896i	−0.655600	+	0.755108i	$0.727584\pi$
$108$		0			0
$109$	−2.08822	+	3.61691i	−0.200016	+	0.346437i	−0.948533	−	0.316678i	$-0.897433\pi$
$109$	−2.08822	+	3.61691i	−0.200016	+	0.346437i	0.748518	+	0.663115i	$0.230766\pi$
$110$	−11.2503	−	19.4861i	−1.07267	−	1.85792i
$111$		0			0
$112$	1.50608	+	3.36834i	0.142311	+	0.318278i
$113$	−5.90107			−0.555126			−0.277563	−	0.960707i	$-0.589527\pi$
$113$	−5.90107			−0.555126			−0.277563	+	0.960707i	$0.589527\pi$
$114$		0			0
$115$	4.74915	−	8.22577i	0.442860	−	0.767057i
$116$	−8.55300	+	14.8142i	−0.794126	+	1.37547i
$117$		0			0
$118$	10.5995			0.975763
$119$	−5.86291	+	8.09654i	−0.537452	+	0.742208i
$120$		0			0
$121$	−5.96705	−	10.3352i	−0.542459	−	0.939567i
$122$	3.54903	−	6.14709i	0.321314	−	0.556532i
$123$		0			0
$124$	5.46591	+	9.46724i	0.490853	+	0.850183i
$125$	−11.6621			−1.04309
$126$		0			0
$127$	−10.5268			−0.934100			−0.467050	−	0.884231i	$-0.654683\pi$
$127$	−10.5268			−0.934100			−0.467050	+	0.884231i	$0.654683\pi$
$128$	−7.15377	−	12.3907i	−0.632309	−	1.09519i
$129$		0			0
$130$	2.34921	−	4.06896i	0.206040	−	0.356871i
$131$	2.71204	+	4.69740i	0.236952	+	0.410413i	0.959838	−	0.280554i	$-0.0905182\pi$
$131$	2.71204	+	4.69740i	0.236952	+	0.410413i	−0.722886	+	0.690967i	$0.757185\pi$
$132$		0			0
$133$	3.85243	+	8.61596i	0.334048	+	0.747099i
$134$	6.41765			0.554400
$135$		0			0
$136$	3.75810	−	6.50922i	0.322255	−	0.558161i
$137$	11.1224	−	19.2645i	0.950248	−	1.64588i	0.205363	−	0.978686i	$-0.434163\pi$
$137$	11.1224	−	19.2645i	0.950248	−	1.64588i	0.744886	−	0.667192i	$-0.232504\pi$
$138$		0			0
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	16.1942	+	1.67616i	1.36866	+	0.141661i
$141$		0			0
$142$	2.80955	+	4.86628i	0.235772	+	0.408369i
$143$	2.39448	−	4.14736i	0.200236	−	0.346819i
$144$		0			0
$145$	−6.26338	−	10.8485i	−0.520146	−	0.900919i
$146$	−17.0441			−1.41058
$147$		0			0
$148$	16.3077			1.34049
$149$	1.47736	+	2.55887i	0.121030	+	0.209630i	0.920174	−	0.391509i	$-0.128047\pi$
$149$	1.47736	+	2.55887i	0.121030	+	0.209630i	−0.799144	+	0.601140i	$0.794714\pi$
$150$		0			0
$151$	9.27736	−	16.0689i	0.754981	−	1.30766i	−0.190403	−	0.981706i	$-0.560980\pi$
$151$	9.27736	−	16.0689i	0.754981	−	1.30766i	0.945384	−	0.325959i	$-0.105687\pi$
$152$	−3.54818	−	6.14564i	−0.287796	−	0.498477i
$153$		0			0
$154$	27.8946	+	2.88719i	2.24781	+	0.232656i
$155$	−8.00541			−0.643010
$156$		0			0
$157$	4.89982	−	8.48673i	0.391048	−	0.677315i	−0.601540	−	0.798843i	$-0.705446\pi$
$157$	4.89982	−	8.48673i	0.391048	−	0.677315i	0.992588	+	0.121528i	$0.0387793\pi$
$158$	−5.73084	+	9.92610i	−0.455921	+	0.789678i
$159$		0			0
$160$	14.9982			1.18571
$161$	4.83216	+	10.8071i	0.380828	+	0.851720i
$162$		0			0
$163$	−6.91709	−	11.9808i	−0.541788	−	0.938405i	−0.998801	−	0.0489451i	$-0.984414\pi$
$163$	−6.91709	−	11.9808i	−0.541788	−	0.938405i	0.457013	−	0.889460i	$-0.348919\pi$
$164$	15.0662	−	26.0954i	1.17647	−	2.03771i
$165$		0			0
$166$	−3.83714	−	6.64612i	−0.297820	−	0.515839i
$167$	−17.3534			−1.34285			−0.671424	−	0.741073i	$-0.734317\pi$
$167$	−17.3534			−1.34285			−0.671424	+	0.741073i	$0.734317\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	8.87598	+	15.3737i	0.680757	+	1.17911i
$171$		0			0
$172$	−4.93858	+	8.55387i	−0.376563	+	0.652226i
$173$	−1.48069	−	2.56463i	−0.112575	−	0.194985i	0.804233	−	0.594314i	$-0.202576\pi$
$173$	−1.48069	−	2.56463i	−0.112575	−	0.194985i	−0.916808	+	0.399329i	$0.869243\pi$
$174$		0			0
$175$	0.766156	−	1.05804i	0.0579160	−	0.0799806i
$176$	6.67859			0.503418
$177$		0			0
$178$	−4.05516	+	7.02374i	−0.303947	+	0.526452i
$179$	−2.83444	+	4.90939i	−0.211856	+	0.366945i	−0.952295	−	0.305178i	$-0.901284\pi$
$179$	−2.83444	+	4.90939i	−0.211856	+	0.366945i	0.740440	+	0.672123i	$0.234617\pi$
$180$		0			0
$181$	7.17645			0.533421			0.266711	−	0.963777i	$-0.414063\pi$
$181$	7.17645			0.533421			0.266711	+	0.963777i	$0.414063\pi$
$182$	2.39028	+	5.34585i	0.177179	+	0.396261i
$183$		0			0
$184$	−4.45054	−	7.70855i	−0.328098	−	0.568282i
$185$	−5.97110	+	10.3423i	−0.439004	+	0.760377i
$186$		0			0
$187$	9.04700	+	15.6699i	0.661582	+	1.14589i
$188$	20.6068			1.50291
$189$		0			0
$190$	16.7604			1.21593
$191$	5.94088	+	10.2899i	0.429867	+	0.744552i	0.996861	−	0.0791703i	$-0.0252271\pi$
$191$	5.94088	+	10.2899i	0.429867	+	0.744552i	−0.566994	+	0.823722i	$0.691894\pi$
$192$		0			0
$193$	−11.4851	+	19.8927i	−0.826714	+	1.43191i	0.0738876	+	0.997267i	$0.476459\pi$
$193$	−11.4851	+	19.8927i	−0.826714	+	1.43191i	−0.900602	+	0.434645i	$0.856874\pi$
$194$	−5.98408	−	10.3647i	−0.429632	−	0.744145i
$195$		0			0
$196$	−13.5299	+	15.1225i	−0.966420	+	1.08018i
$197$	−16.9216			−1.20561			−0.602806	−	0.797888i	$-0.705951\pi$
$197$	−16.9216			−1.20561			−0.602806	+	0.797888i	$0.705951\pi$
$198$		0			0
$199$	−5.02953	+	8.71140i	−0.356534	+	0.617535i	−0.987379	−	0.158374i	$-0.949375\pi$
$199$	−5.02953	+	8.71140i	−0.356534	+	0.617535i	0.630845	+	0.775909i	$0.282708\pi$
$200$	−0.491103	+	0.850616i	−0.0347262	+	0.0601476i
$201$		0			0
$202$	20.6221			1.45096
$203$	15.5298	+	1.60739i	1.08998	+	0.112817i
$204$		0			0
$205$	11.0330	+	19.1098i	0.770580	+	1.33468i
$206$	8.08566	−	14.0048i	0.563355	−	0.975759i
$207$		0			0
$208$	0.697291	+	1.20774i	0.0483484	+	0.0837419i
$209$	17.0833			1.18168
$210$		0			0
$211$	−24.4609			−1.68396			−0.841978	−	0.539512i	$-0.818609\pi$
$211$	−24.4609			−1.68396			−0.841978	+	0.539512i	$0.818609\pi$
$212$	−17.9436	−	31.0793i	−1.23237	−	2.13453i
$213$		0			0
$214$	−7.46697	+	12.9332i	−0.510431	+	0.884093i
$215$	−3.61654	−	6.26402i	−0.246646	−	0.427203i
$216$		0			0
$217$	5.85187	−	8.08129i	0.397251	−	0.548594i
$218$	−9.24382			−0.626071
$219$		0			0
$220$	14.7345	−	25.5210i	0.993402	−	1.72062i
$221$	−1.88914	+	3.27208i	−0.127077	+	0.220104i
$222$		0			0
$223$	−29.2625			−1.95956			−0.979780	−	0.200076i	$-0.935881\pi$
$223$	−29.2625			−1.95956			−0.979780	+	0.200076i	$0.935881\pi$
$224$	−10.9635	+	15.1404i	−0.732531	+	1.01161i
$225$		0			0
$226$	−6.53049	−	11.3111i	−0.434401	−	0.752405i
$227$	−5.03685	+	8.72408i	−0.334307	+	0.579038i	−0.983352	−	0.181713i	$-0.941836\pi$
$227$	−5.03685	+	8.72408i	−0.334307	+	0.579038i	0.649044	+	0.760751i	$0.275169\pi$
$228$		0			0
$229$	5.56997	+	9.64748i	0.368074	+	0.637523i	0.989264	−	0.146137i	$-0.0466839\pi$
$229$	5.56997	+	9.64748i	0.368074	+	0.637523i	−0.621190	+	0.783660i	$0.713351\pi$
$230$	21.0228			1.38620
$231$		0			0
$232$	−11.7391			−0.770711
$233$	−8.54166	−	14.7946i	−0.559583	−	0.969226i	−0.997531	−	0.0702257i	$-0.977628\pi$
$233$	−8.54166	−	14.7946i	−0.559583	−	0.969226i	0.437948	−	0.899000i	$-0.355705\pi$
$234$		0			0
$235$	−7.54522	+	13.0687i	−0.492196	+	0.852508i
$236$	6.94110	+	12.0223i	0.451827	+	0.782587i
$237$		0			0
$238$	−22.0076	−	2.27787i	−1.42654	−	0.147652i
$239$	−6.92142			−0.447710			−0.223855	−	0.974622i	$-0.571864\pi$
$239$	−6.92142			−0.447710			−0.223855	+	0.974622i	$0.571864\pi$
$240$		0			0
$241$	−3.24812	+	5.62592i	−0.209230	+	0.362397i	−0.951472	−	0.307735i	$-0.900429\pi$
$241$	−3.24812	+	5.62592i	−0.209230	+	0.362397i	0.742242	+	0.670132i	$0.233762\pi$
$242$	13.2070	−	22.8752i	0.848978	−	1.47047i
$243$		0			0
$244$	9.29634			0.595137
$245$	−4.63660	−	14.1177i	−0.296221	−	0.901945i
$246$		0			0
$247$	1.78362	+	3.08931i	0.113489	+	0.196568i
$248$	−3.75103	+	6.49697i	−0.238190	+	0.412558i
$249$		0			0
$250$	−12.9060	−	22.3538i	−0.816246	−	1.41378i
$251$	9.86804			0.622865			0.311433	−	0.950268i	$-0.399191\pi$
$251$	9.86804			0.622865			0.311433	+	0.950268i	$0.399191\pi$
$252$		0			0
$253$	21.4278			1.34716
$254$	−11.6496	−	20.1776i	−0.730959	−	1.26606i
$255$		0			0
$256$	2.98497	−	5.17012i	0.186560	−	0.323132i
$257$	3.43234	+	5.94499i	0.214104	+	0.370838i	0.952995	−	0.302986i	$-0.0979836\pi$
$257$	3.43234	+	5.94499i	0.214104	+	0.370838i	−0.738891	+	0.673825i	$0.764650\pi$
$258$		0			0
$259$	−6.07547	−	13.5878i	−0.377511	−	0.844304i
$260$	6.15355			0.381627
$261$		0			0
$262$	−6.00262	+	10.3969i	−0.370843	+	0.642320i
$263$	−0.0632753	+	0.109596i	−0.00390172	+	0.00675798i	−0.867970	−	0.496617i	$-0.834575\pi$
$263$	−0.0632753	+	0.109596i	−0.00390172	+	0.00675798i	0.864068	+	0.503375i	$0.167909\pi$
$264$		0			0
$265$	26.2803			1.61439
$266$	−12.2517	+	16.9193i	−0.751199	+	1.03739i
$267$		0			0
$268$	4.20261	+	7.27913i	0.256715	+	0.444643i
$269$	−2.12154	+	3.67462i	−0.129353	+	0.224045i	−0.923426	−	0.383777i	$-0.874623\pi$
$269$	−2.12154	+	3.67462i	−0.129353	+	0.224045i	0.794073	+	0.607822i	$0.207957\pi$
$270$		0			0
$271$	−0.783616	−	1.35726i	−0.0476013	−	0.0824479i	0.841243	−	0.540657i	$-0.181824\pi$
$271$	−0.783616	−	1.35726i	−0.0476013	−	0.0824479i	−0.888844	+	0.458209i	$0.848491\pi$
$272$	−5.26911			−0.319487
$273$		0			0
$274$	49.2348			2.97438
$275$	−1.18225	−	2.04771i	−0.0712923	−	0.123482i
$276$		0			0
$277$	6.37260	−	11.0377i	0.382892	−	0.663189i	−0.608582	−	0.793491i	$-0.708261\pi$
$277$	6.37260	−	11.0377i	0.382892	−	0.663189i	0.991474	+	0.130302i	$0.0415947\pi$
$278$	−4.42664	−	7.66717i	−0.265492	−	0.459846i
$279$		0			0
$280$	4.56054	+	10.1996i	0.272545	+	0.609546i
$281$	−4.62986			−0.276194			−0.138097	−	0.990419i	$-0.544099\pi$
$281$	−4.62986			−0.276194			−0.138097	+	0.990419i	$0.544099\pi$
$282$		0			0
$283$	−1.82416	+	3.15954i	−0.108435	+	0.187815i	−0.915136	−	0.403144i	$-0.867917\pi$
$283$	−1.82416	+	3.15954i	−0.108435	+	0.187815i	0.806701	+	0.590959i	$0.201251\pi$
$284$	−3.67967	+	6.37338i	−0.218348	+	0.378190i
$285$		0			0
$286$	10.5995			0.626762
$287$	−27.3559	−	2.83143i	−1.61477	−	0.167134i
$288$		0			0
$289$	1.36231	+	2.35959i	0.0801360	+	0.138800i
$290$	13.8629	−	24.0112i	0.814057	−	1.40999i
$291$		0			0
$292$	−11.1614	−	19.3321i	−0.653171	−	1.13132i
$293$	21.0415			1.22926			0.614630	−	0.788816i	$-0.289305\pi$
$293$	21.0415			1.22926			0.614630	+	0.788816i	$0.289305\pi$
$294$		0			0
$295$	−10.1660			−0.591886
$296$	5.59566	+	9.69196i	0.325241	+	0.563334i
$297$		0			0
$298$	−3.26988	+	5.66359i	−0.189419	+	0.328083i
$299$	2.23721	+	3.87497i	0.129381	+	0.224095i
$300$		0			0
$301$	8.96705	+	0.928120i	0.516852	+	0.0534960i
$302$	41.0676			2.36317
$303$		0			0
$304$	−2.48740	+	4.30830i	−0.142662	+	0.247098i
$305$	−3.40387	+	5.89567i	−0.194905	+	0.337585i
$306$		0			0
$307$	−4.95861			−0.283003			−0.141502	−	0.989938i	$-0.545193\pi$
$307$	−4.95861			−0.283003			−0.141502	+	0.989938i	$0.545193\pi$
$308$	14.9921	+	33.5298i	0.854253	+	1.91054i
$309$		0			0
$310$	−8.85927	−	15.3447i	−0.503173	−	0.871521i
$311$	−1.21079	+	2.09715i	−0.0686575	+	0.118918i	−0.898311	−	0.439361i	$-0.855205\pi$
$311$	−1.21079	+	2.09715i	−0.0686575	+	0.118918i	0.829653	+	0.558279i	$0.188538\pi$
$312$		0			0
$313$	−6.98026	−	12.0902i	−0.394548	−	0.683377i	0.598496	−	0.801126i	$-0.295765\pi$
$313$	−6.98026	−	12.0902i	−0.394548	−	0.683377i	−0.993043	+	0.117749i	$0.962432\pi$
$314$	21.6897			1.22402
$315$		0			0
$316$	−15.0114			−0.844457
$317$	1.53431	+	2.65750i	0.0861753	+	0.149260i	0.905891	−	0.423510i	$-0.139202\pi$
$317$	1.53431	+	2.65750i	0.0861753	+	0.149260i	−0.819716	+	0.572770i	$0.805869\pi$
$318$		0			0
$319$	14.1300	−	24.4739i	0.791127	−	1.37027i
$320$	13.6375	+	23.6208i	0.762359	+	1.32044i
$321$		0			0
$322$	−15.3674	+	21.2221i	−0.856394	+	1.18266i
$323$	−13.4780			−0.749936
$324$		0			0
$325$	0.246870	−	0.427591i	0.0136939	−	0.0237185i
$326$	15.3098	−	26.5173i	0.847929	−	1.46866i
$327$		0			0
$328$	20.6786			1.14179
$329$	−7.67710	−	17.1698i	−0.423252	−	0.946603i
$330$		0			0
$331$	−6.80261	−	11.7825i	−0.373905	−	0.647623i	0.616257	−	0.787545i	$-0.288648\pi$
$331$	−6.80261	−	11.7825i	−0.373905	−	0.647623i	−0.990162	+	0.139922i	$0.955315\pi$
$332$	5.02551	−	8.70445i	0.275811	−	0.477719i
$333$		0			0
$334$	−19.2044	−	33.2629i	−1.05082	−	1.82007i
$335$	−6.15516			−0.336292
$336$		0			0
$337$	−35.1646			−1.91554			−0.957769	−	0.287538i	$-0.907163\pi$
$337$	−35.1646			−1.91554			−0.957769	+	0.287538i	$0.907163\pi$
$338$	1.10666	+	1.91679i	0.0601944	+	0.104260i
$339$		0			0
$340$	−11.6249	+	20.1349i	−0.630449	+	1.09197i
$341$	−9.02997	−	15.6404i	−0.489000	−	0.846973i
$342$		0			0
$343$	17.6408	+	5.63933i	0.952514	+	0.304495i
$344$	−6.77828			−0.365460
$345$		0			0
$346$	3.27724	−	5.67635i	0.176186	−	0.305162i
$347$	−2.73551	+	4.73804i	−0.146850	+	0.254351i	−0.930062	−	0.367404i	$-0.880247\pi$
$347$	−2.73551	+	4.73804i	−0.146850	+	0.254351i	0.783212	+	0.621755i	$0.213580\pi$
$348$		0			0
$349$	4.34196			0.232420			0.116210	−	0.993225i	$-0.462925\pi$
$349$	4.34196			0.232420			0.116210	+	0.993225i	$0.462925\pi$
$350$	2.87593	+	0.297668i	0.153725	+	0.0159110i
$351$		0			0
$352$	16.9177	+	29.3023i	0.901717	+	1.56182i
$353$	13.7996	−	23.9016i	0.734479	−	1.27216i	−0.220472	−	0.975393i	$-0.570760\pi$
$353$	13.7996	−	23.9016i	0.734479	−	1.27216i	0.954951	−	0.296762i	$-0.0959068\pi$
$354$		0			0
$355$	−2.69463	−	4.66724i	−0.143016	−	0.247712i
$356$	−10.6221			−0.562971
$357$		0			0
$358$	−12.5470			−0.663132
$359$	3.31427	+	5.74049i	0.174921	+	0.302971i	0.940134	−	0.340806i	$-0.110700\pi$
$359$	3.31427	+	5.74049i	0.174921	+	0.302971i	−0.765213	+	0.643777i	$0.777366\pi$
$360$		0			0
$361$	3.13742	−	5.43418i	0.165128	−	0.286009i
$362$	7.94189	+	13.7558i	0.417417	+	0.722987i
$363$		0			0
$364$	−4.49818	+	6.21188i	−0.235769	+	0.325591i
$365$	16.3470			0.855643
$366$		0			0
$367$	−15.6037	+	27.0264i	−0.814506	+	1.41077i	0.0951768	+	0.995460i	$0.469658\pi$
$367$	−15.6037	+	27.0264i	−0.814506	+	1.41077i	−0.909682	+	0.415305i	$0.863675\pi$
$368$	−3.11998	+	5.40396i	−0.162640	+	0.281701i
$369$		0			0
$370$	−26.4319			−1.37413
$371$	−19.2107	+	26.5294i	−0.997368	+	1.37734i
$372$		0			0
$373$	7.88730	+	13.6612i	0.408389	+	0.707350i	0.994709	−	0.102729i	$-0.0327574\pi$
$373$	7.88730	+	13.6612i	0.408389	+	0.707350i	−0.586321	+	0.810079i	$0.699424\pi$
$374$	−20.0239	+	34.6825i	−1.03541	+	1.79339i
$375$		0			0
$376$	7.07080	+	12.2470i	0.364649	+	0.631590i
$377$	5.90107			0.303921
$378$		0			0
$379$	31.6512			1.62581			0.812907	−	0.582393i	$-0.197884\pi$
$379$	31.6512			1.62581			0.812907	+	0.582393i	$0.197884\pi$
$380$	10.9756	+	19.0102i	0.563035	+	0.975205i
$381$		0			0
$382$	−13.1491	+	22.7749i	−0.672766	+	1.16526i
$383$	6.19675	+	10.7331i	0.316639	+	0.548435i	0.979785	−	0.200055i	$-0.0641122\pi$
$383$	6.19675	+	10.7331i	0.316639	+	0.548435i	−0.663145	+	0.748491i	$0.730779\pi$
$384$		0			0
$385$	−26.7537	−	2.76910i	−1.36350	−	0.141126i
$386$	−50.8404			−2.58771
$387$		0			0
$388$	7.83737	−	13.5747i	0.397882	−	0.689152i
$389$	−7.03705	+	12.1885i	−0.356792	+	0.617983i	−0.987423	−	0.158100i	$-0.949463\pi$
$389$	−7.03705	+	12.1885i	−0.356792	+	0.617983i	0.630631	+	0.776083i	$0.282796\pi$
$390$		0			0
$391$	−16.9056			−0.854954
$392$	−13.6300	−	2.85207i	−0.688421	−	0.144051i
$393$		0			0
$394$	−18.7265	−	32.4352i	−0.943425	−	1.63406i
$395$	5.49644	−	9.52012i	0.276556	−	0.479009i
$396$		0			0
$397$	3.48652	+	6.03884i	0.174984	+	0.303081i	0.940156	−	0.340745i	$-0.110679\pi$
$397$	3.48652	+	6.03884i	0.174984	+	0.303081i	−0.765172	+	0.643826i	$0.777346\pi$
$398$	−22.2639			−1.11599
$399$		0			0
$400$	0.688560			0.0344280
$401$	1.36841	+	2.37016i	0.0683352	+	0.118360i	0.898169	−	0.439651i	$-0.144898\pi$
$401$	1.36841	+	2.37016i	0.0683352	+	0.118360i	−0.829833	+	0.558011i	$0.811565\pi$
$402$		0			0
$403$	1.88558	−	3.26592i	0.0939275	−	0.162687i
$404$	13.5044	+	23.3903i	0.671868	+	1.16371i
$405$		0			0
$406$	14.1052	+	31.5463i	0.700029	+	1.56561i
$407$	−26.9412			−1.33543
$408$		0			0
$409$	12.2577	−	21.2309i	0.606104	−	1.04980i	−0.385772	−	0.922594i	$-0.626065\pi$
$409$	12.2577	−	21.2309i	0.606104	−	1.04980i	0.991876	−	0.127208i	$-0.0406017\pi$
$410$	−24.4196	+	42.2961i	−1.20600	+	2.08885i
$411$		0			0
$412$	21.1796			1.04345
$413$	7.43122	−	10.2623i	0.365667	−	0.504977i
$414$		0			0
$415$	3.68020	+	6.37429i	0.180654	+	0.312902i
$416$	−3.53265	+	6.11873i	−0.173202	+	0.299995i
$417$		0			0
$418$	18.9054	+	32.7452i	0.924696	+	1.60162i
$419$	3.01252			0.147171			0.0735856	−	0.997289i	$-0.476556\pi$
$419$	3.01252			0.147171			0.0735856	+	0.997289i	$0.476556\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	−27.0699	−	46.8864i	−1.31774	−	2.28240i
$423$		0			0
$424$	12.3140	−	21.3284i	0.598018	−	1.03580i
$425$	0.932742	+	1.61556i	0.0452447	+	0.0783660i
$426$		0			0
$427$	−3.46337	−	7.74581i	−0.167604	−	0.374846i
$428$	−19.5590			−0.945421
$429$		0			0
$430$	8.00456	−	13.8643i	0.386014	−	0.668596i
$431$	−9.39711	+	16.2763i	−0.452643	+	0.784001i	−0.998549	−	0.0538455i	$-0.982852\pi$
$431$	−9.39711	+	16.2763i	−0.452643	+	0.784001i	0.545906	+	0.837846i	$0.316185\pi$
$432$		0			0
$433$	−7.76911			−0.373360			−0.186680	−	0.982421i	$-0.559773\pi$
$433$	−7.76911			−0.373360			−0.186680	+	0.982421i	$0.559773\pi$
$434$	21.9662	+	2.27358i	1.05441	+	0.109135i
$435$		0			0
$436$	−6.05333	−	10.4847i	−0.289902	−	0.502125i
$437$	−7.98066	+	13.8229i	−0.381767	+	0.661240i
$438$		0			0
$439$	18.9841	+	32.8814i	0.906060	+	1.56934i	0.819488	+	0.573096i	$0.194258\pi$
$439$	18.9841	+	32.8814i	0.906060	+	1.56934i	0.0865713	+	0.996246i	$0.472409\pi$
$440$	20.2234			0.964112
$441$		0			0
$442$	−8.36254			−0.397766
$443$	17.8135	+	30.8539i	0.846344	+	1.46591i	0.884449	+	0.466637i	$0.154535\pi$
$443$	17.8135	+	30.8539i	0.846344	+	1.46591i	−0.0381050	+	0.999274i	$0.512132\pi$
$444$		0			0
$445$	3.88930	−	6.73647i	0.184371	−	0.319339i
$446$	−32.3837	−	56.0901i	−1.53341	−	2.65594i
$447$		0			0
$448$	−33.8136	−	3.49982i	−1.59754	−	0.165351i
$449$	8.05285			0.380038			0.190019	−	0.981780i	$-0.439145\pi$
$449$	8.05285			0.380038			0.190019	+	0.981780i	$0.439145\pi$
$450$		0			0
$451$	−24.8901	+	43.1110i	−1.17203	+	2.03002i
$452$	8.55300	−	14.8142i	0.402299	−	0.696803i
$453$		0			0
$454$	−22.2963			−1.04642
$455$	−2.29251	−	5.12720i	−0.107475	−	0.240367i
$456$		0			0
$457$	−7.79881	−	13.5079i	−0.364813	−	0.631875i	0.623933	−	0.781478i	$-0.285534\pi$
$457$	−7.79881	−	13.5079i	−0.364813	−	0.631875i	−0.988746	+	0.149603i	$0.952200\pi$
$458$	−12.3281	+	21.3530i	−0.576056	+	0.997759i
$459$		0			0
$460$	13.7668	+	23.8448i	0.641880	+	1.11177i
$461$	25.6991			1.19692			0.598462	−	0.801151i	$-0.295779\pi$
$461$	25.6991			1.19692			0.598462	+	0.801151i	$0.295779\pi$
$462$		0			0
$463$	−20.5209			−0.953685			−0.476842	−	0.878989i	$-0.658219\pi$
$463$	−20.5209			−0.953685			−0.476842	+	0.878989i	$0.658219\pi$
$464$	4.11476	+	7.12698i	0.191023	+	0.330862i
$465$		0			0
$466$	18.9054	−	32.7452i	0.875778	−	1.51689i
$467$	5.91241	+	10.2406i	0.273594	+	0.473878i	0.969779	−	0.243984i	$-0.0784543\pi$
$467$	5.91241	+	10.2406i	0.273594	+	0.473878i	−0.696186	+	0.717862i	$0.745121\pi$
$468$		0			0
$469$	4.49936	−	6.21351i	0.207761	−	0.286913i
$470$	−33.4000			−1.54063
$471$		0			0
$472$	−4.76338	+	8.25042i	−0.219253	+	0.379757i
$473$	8.15878	−	14.1314i	0.375141	−	0.649764i
$474$		0			0
$475$	1.76128			0.0808133
$476$	−11.8281	−	26.4535i	−0.542140	−	1.21250i
$477$		0			0
$478$	−7.65967	−	13.2669i	−0.350345	−	0.606816i
$479$	11.3276	−	19.6200i	0.517571	−	0.896459i	−0.482221	−	0.876050i	$-0.660170\pi$
$479$	11.3276	−	19.6200i	0.517571	−	0.896459i	0.999792	−	0.0204092i	$-0.00649690\pi$
$480$		0			0
$481$	−2.81285	−	4.87200i	−0.128255	−	0.222144i
$482$	−14.3783			−0.654913
$483$		0			0
$484$	34.5945			1.57248
$485$	5.73933	+	9.94081i	0.260610	+	0.451389i
$486$		0			0
$487$	16.3584	−	28.3335i	0.741268	−	1.28391i	−0.210650	−	0.977562i	$-0.567558\pi$
$487$	16.3584	−	28.3335i	0.741268	−	1.28391i	0.951918	−	0.306353i	$-0.0991087\pi$
$488$	3.18984	+	5.52497i	0.144397	+	0.250104i
$489$		0			0
$490$	21.9295	−	24.5109i	0.990675	−	1.10729i
$491$	−6.17281			−0.278575			−0.139288	−	0.990252i	$-0.544481\pi$
$491$	−6.17281			−0.278575			−0.139288	+	0.990252i	$0.544481\pi$
$492$		0			0
$493$	−11.1479	+	19.3088i	−0.502078	+	0.869625i
$494$	−3.94772	+	6.83765i	−0.177616	+	0.307640i
$495$		0			0
$496$	5.25919			0.236145
$497$	6.68123	+	0.691531i	0.299694	+	0.0310194i
$498$		0			0
$499$	7.31934	+	12.6775i	0.327659	+	0.567521i	0.982047	−	0.188637i	$-0.0604071\pi$
$499$	7.31934	+	12.6775i	0.327659	+	0.567521i	−0.654388	+	0.756159i	$0.727074\pi$
$500$	16.9030	−	29.2768i	0.755925	−	1.30930i
$501$		0			0
$502$	10.9206	+	18.9150i	0.487409	+	0.844218i
$503$	−12.7787			−0.569774			−0.284887	−	0.958561i	$-0.591956\pi$
$503$	−12.7787			−0.569774			−0.284887	+	0.958561i	$0.591956\pi$
$504$		0			0
$505$	−19.7786			−0.880136
$506$	23.7134	+	41.0727i	1.05419	+	1.82591i
$507$		0			0
$508$	15.2575	−	26.4267i	0.676941	−	1.17250i
$509$	5.84263	+	10.1197i	0.258970	+	0.448549i	0.965966	−	0.258668i	$-0.0832835\pi$
$509$	5.84263	+	10.1197i	0.258970	+	0.448549i	−0.706996	+	0.707217i	$0.749950\pi$
$510$		0			0
$511$	−11.9495	+	16.5020i	−0.528615	+	0.730005i
$512$	−15.4017			−0.680664
$513$		0			0
$514$	−7.59688	+	13.1582i	−0.335084	+	0.580382i
$515$	−7.75495	+	13.4320i	−0.341724	+	0.591883i
$516$		0			0
$517$	−34.0435			−1.49723
$518$	19.3215	−	26.6825i	0.848937	−	1.17236i
$519$		0			0
$520$	2.11146	+	3.65716i	0.0925937	+	0.160377i
$521$	4.23838	−	7.34108i	0.185687	−	0.321619i	−0.758121	−	0.652114i	$-0.773882\pi$
$521$	4.23838	−	7.34108i	0.185687	−	0.321619i	0.943808	+	0.330495i	$0.107216\pi$
$522$		0			0
$523$	−16.3554	−	28.3284i	−0.715172	−	1.23871i	−0.962893	−	0.269883i	$-0.913015\pi$
$523$	−16.3554	−	28.3284i	−0.715172	−	1.23871i	0.247721	−	0.968831i	$-0.420318\pi$
$524$	−15.7233			−0.686876
$525$		0			0
$526$	−0.280097			−0.0122128
$527$	7.12425	+	12.3396i	0.310337	+	0.537520i
$528$		0			0
$529$	1.48975	−	2.58032i	0.0647716	−	0.112188i
$530$	29.0834	+	50.3739i	1.26330	+	2.18810i
$531$		0			0
$532$	−27.2135	−	2.81669i	−1.17985	−	0.122119i
$533$	−10.3948			−0.450249
$534$		0			0
$535$	7.16156	−	12.4042i	0.309621	−	0.536280i
$536$	−2.88407	+	4.99536i	−0.124573	+	0.215767i
$537$		0			0
$538$	−9.39131			−0.404888
$539$	22.3520	−	24.9831i	0.962771	−	1.07610i
$540$		0			0
$541$	14.0853	+	24.3964i	0.605573	+	1.04888i	0.991961	+	0.126547i	$0.0403893\pi$
$541$	14.0853	+	24.3964i	0.605573	+	1.04888i	−0.386388	+	0.922336i	$0.626277\pi$
$542$	1.73440	−	3.00406i	0.0744987	−	0.129035i
$543$		0			0
$544$	−13.3473	−	23.1182i	−0.572262	−	0.991187i
$545$	8.86574			0.379767
$546$		0			0
$547$	−18.5377			−0.792615			−0.396307	−	0.918118i	$-0.629709\pi$
$547$	−18.5377			−0.792615			−0.396307	+	0.918118i	$0.629709\pi$
$548$	32.2415	+	55.8438i	1.37729	+	2.38553i
$549$		0			0
$550$	2.61670	−	4.53225i	0.111576	−	0.193256i
$551$	10.5252	+	18.2303i	0.448391	+	0.776635i
$552$		0			0
$553$	5.59252	+	12.5077i	0.237818	+	0.531880i
$554$	28.2092			1.19850
$555$		0			0
$556$	5.79759	−	10.0417i	0.245873	−	0.425864i
$557$	2.00142	−	3.46655i	0.0848027	−	0.146883i	−0.820504	−	0.571640i	$-0.806307\pi$
$557$	2.00142	−	3.46655i	0.0848027	−	0.146883i	0.905307	+	0.424758i	$0.139641\pi$
$558$		0			0
$559$	3.40733			0.144115
$560$	4.59379	−	6.34392i	0.194123	−	0.268079i
$561$		0			0
$562$	−5.12368	−	8.87448i	−0.216129	−	0.374347i
$563$	−8.93100	+	15.4689i	−0.376397	+	0.651938i	−0.990535	−	0.137260i	$-0.956170\pi$
$563$	−8.93100	+	15.4689i	−0.376397	+	0.651938i	0.614138	+	0.789199i	$0.289504\pi$
$564$		0			0
$565$	6.26338	+	10.8485i	0.263503	+	0.456400i
$566$	−8.07490			−0.339413
$567$		0			0
$568$	−5.05041			−0.211910
$569$	−18.7336	−	32.4475i	−0.785353	−	1.36027i	−0.928788	−	0.370612i	$-0.879148\pi$
$569$	−18.7336	−	32.4475i	−0.785353	−	1.36027i	0.143434	−	0.989660i	$-0.454185\pi$
$570$		0			0
$571$	−8.78514	+	15.2163i	−0.367646	+	0.636782i	−0.989197	−	0.146592i	$-0.953170\pi$
$571$	−8.78514	+	15.2163i	−0.367646	+	0.636782i	0.621551	+	0.783374i	$0.286503\pi$
$572$	6.94110	+	12.0223i	0.290222	+	0.502679i
$573$		0			0
$574$	−24.8465	−	55.5691i	−1.03707	−	2.31941i
$575$	2.20920			0.0921301
$576$		0			0
$577$	17.1247	−	29.6608i	0.712910	−	1.23480i	−0.250850	−	0.968026i	$-0.580710\pi$
$577$	17.1247	−	29.6608i	0.712910	−	1.23480i	0.963760	−	0.266770i	$-0.0859565\pi$
$578$	−3.01524	+	5.22254i	−0.125417	+	0.217229i
$579$		0			0
$580$	36.3125			1.50780
$581$	−9.12490	−	0.944459i	−0.378565	−	0.0391828i
$582$		0			0
$583$	29.6438	+	51.3445i	1.22772	+	2.12647i
$584$	7.65959	−	13.2668i	0.316956	−	0.548984i
$585$		0			0
$586$	23.2859	+	40.3323i	0.961930	+	1.66611i
$587$	29.4494			1.21551			0.607754	−	0.794126i	$-0.292071\pi$
$587$	29.4494			1.21551			0.607754	+	0.794126i	$0.292071\pi$
$588$		0			0
$589$	13.4526			0.554305
$590$	−11.2503	−	19.4861i	−0.463167	−	0.802229i
$591$		0			0
$592$	3.92275	−	6.79439i	0.161224	−	0.279248i
$593$	−17.0001	−	29.4450i	−0.698109	−	1.20916i	−0.969121	−	0.246584i	$-0.920692\pi$
$593$	−17.0001	−	29.4450i	−0.698109	−	1.20916i	0.271013	−	0.962576i	$-0.412641\pi$
$594$		0			0
$595$	21.1075	+	2.18470i	0.865324	+	0.0895640i
$596$	−8.56514			−0.350842
$597$		0			0
$598$	−4.95168	+	8.57655i	−0.202489	+	0.350721i
$599$	10.7209	−	18.5691i	0.438043	−	0.758713i	−0.559495	−	0.828834i	$-0.689005\pi$
$599$	10.7209	−	18.5691i	0.438043	−	0.758713i	0.997539	+	0.0701203i	$0.0223383\pi$
$600$		0			0
$601$	40.4039			1.64811			0.824054	−	0.566511i	$-0.191707\pi$
$601$	40.4039			1.64811			0.824054	+	0.566511i	$0.191707\pi$
$602$	8.14447	+	18.2151i	0.331944	+	0.742392i
$603$		0			0
$604$	26.8931	+	46.5803i	1.09427	+	1.89533i
$605$	−12.6668	+	21.9396i	−0.514980	+	0.891971i
$606$		0			0
$607$	21.9456	+	38.0110i	0.890746	+	1.54282i	0.838983	+	0.544158i	$0.183151\pi$
$607$	21.9456	+	38.0110i	0.890746	+	1.54282i	0.0517636	+	0.998659i	$0.483516\pi$
$608$	−25.2036			−1.02214
$609$		0			0
$610$	−15.0677			−0.610074
$611$	−3.55438	−	6.15636i	−0.143795	−	0.249060i
$612$		0			0
$613$	7.15777	−	12.3976i	0.289100	−	0.500735i	−0.684496	−	0.729017i	$-0.739977\pi$
$613$	7.15777	−	12.3976i	0.289100	−	0.500735i	0.973595	+	0.228282i	$0.0733108\pi$
$614$	−5.48750	−	9.50464i	−0.221458	−	0.383576i
$615$		0			0
$616$	−14.7831	+	20.4151i	−0.595628	+	0.822547i
$617$	36.9097			1.48593			0.742965	−	0.669330i	$-0.233419\pi$
$617$	36.9097			1.48593			0.742965	+	0.669330i	$0.233419\pi$
$618$		0			0
$619$	−7.14646	+	12.3780i	−0.287240	+	0.497515i	−0.973150	−	0.230172i	$-0.926071\pi$
$619$	−7.14646	+	12.3780i	−0.287240	+	0.497515i	0.685910	+	0.727687i	$0.259405\pi$
$620$	11.6030	−	20.0970i	0.465988	−	0.807115i
$621$		0			0
$622$	−5.35973			−0.214906
$623$	3.95728	+	8.85046i	0.158545	+	0.354586i
$624$		0			0
$625$	11.1438	+	19.3016i	0.445750	+	0.772062i
$626$	15.4496	−	26.7594i	0.617489	−	1.06952i
$627$		0			0
$628$	14.2036	+	24.6013i	0.566784	+	0.981698i
$629$	21.2554			0.847510
$630$		0			0
$631$	−0.0431064			−0.00171604			−0.000858019	−	1.00000i	$-0.500273\pi$
$631$	−0.0431064			−0.00171604			−0.000858019		1.00000i	$0.500273\pi$
$632$	−5.15084	−	8.92152i	−0.204890	−	0.354879i
$633$		0			0
$634$	−3.39592	+	5.88190i	−0.134869	+	0.233600i
$635$	11.1731	+	19.3524i	0.443390	+	0.767975i
$636$		0			0
$637$	6.85161	+	1.43369i	0.271471	+	0.0568048i
$638$	62.5484			2.47632
$639$		0			0
$640$	−15.1860	+	26.3029i	−0.600279	+	1.03971i
$641$	21.3328	−	36.9494i	0.842594	−	1.45942i	−0.0451008	−	0.998982i	$-0.514361\pi$
$641$	21.3328	−	36.9494i	0.842594	−	1.45942i	0.887695	−	0.460433i	$-0.152306\pi$
$642$		0			0
$643$	−5.49737			−0.216795			−0.108398	−	0.994108i	$-0.534572\pi$
$643$	−5.49737			−0.216795			−0.108398	+	0.994108i	$0.534572\pi$
$644$	−34.1342	−	3.53301i	−1.34508	−	0.139220i
$645$		0			0
$646$	−14.9156	−	25.8345i	−0.586845	−	1.01645i
$647$	−19.0933	+	33.0706i	−0.750637	+	1.30014i	0.196877	+	0.980428i	$0.436920\pi$
$647$	−19.0933	+	33.0706i	−0.750637	+	1.30014i	−0.947514	+	0.319713i	$0.896413\pi$
$648$		0			0
$649$	−11.4671	−	19.8615i	−0.450121	−	0.779633i
$650$	1.09280			0.0428633
$651$		0			0
$652$	40.1024			1.57053
$653$	19.2510	+	33.3437i	0.753349	+	1.30484i	0.946191	+	0.323608i	$0.104896\pi$
$653$	19.2510	+	33.3437i	0.753349	+	1.30484i	−0.192843	+	0.981230i	$0.561771\pi$
$654$		0			0
$655$	5.75711	−	9.97161i	0.224949	−	0.389623i
$656$	−7.24820	−	12.5543i	−0.282995	−	0.490161i
$657$		0			0
$658$	24.4151	−	33.7166i	0.951798	−	1.31441i
$659$	−19.4843			−0.759002			−0.379501	−	0.925191i	$-0.623904\pi$
$659$	−19.4843			−0.759002			−0.379501	+	0.925191i	$0.623904\pi$
$660$		0			0
$661$	20.8334	−	36.0844i	0.810324	−	1.40352i	−0.102314	−	0.994752i	$-0.532625\pi$
$661$	20.8334	−	36.0844i	0.810324	−	1.40352i	0.912638	−	0.408770i	$-0.134042\pi$
$662$	15.0564	−	26.0784i	0.585182	−	1.01356i
$663$		0			0
$664$	6.89760			0.267679
$665$	11.7506	−	16.2273i	0.455668	−	0.629266i
$666$		0			0
$667$	13.2020	+	22.8665i	0.511182	+	0.885393i
$668$	25.1520	−	43.5645i	0.973160	−	1.68556i
$669$		0			0
$670$	−6.81168	−	11.7982i	−0.263158	−	0.455803i
$671$	−15.3580			−0.592890
$672$		0			0
$673$	−14.3157			−0.551830			−0.275915	−	0.961182i	$-0.588981\pi$
$673$	−14.3157			−0.551830			−0.275915	+	0.961182i	$0.588981\pi$
$674$	−38.9153	−	67.4033i	−1.49896	−	2.59628i
$675$		0			0
$676$	−1.44940	+	2.51043i	−0.0557460	+	0.0965550i
$677$	−14.7641	−	25.5721i	−0.567429	−	0.982815i	−0.996819	−	0.0796963i	$-0.974605\pi$
$677$	−14.7641	−	25.5721i	−0.567429	−	0.982815i	0.429391	−	0.903119i	$-0.358728\pi$
$678$		0			0
$679$	−14.2304	−	1.47290i	−0.546114	−	0.0565247i
$680$	−15.9554			−0.611860
$681$		0			0
$682$	19.9862	−	34.6172i	0.765312	−	1.32556i
$683$	23.5349	−	40.7637i	0.900539	−	1.55978i	0.0737441	−	0.997277i	$-0.476505\pi$
$683$	23.5349	−	40.7637i	0.900539	−	1.55978i	0.826795	−	0.562503i	$-0.190161\pi$
$684$		0			0
$685$	−47.2210			−1.80422
$686$	8.71296	+	40.0546i	0.332662	+	1.52929i
$687$		0			0
$688$	2.37590	+	4.11518i	0.0905804	+	0.156890i
$689$	−6.19003	+	10.7214i	−0.235821	+	0.408454i
$690$		0			0
$691$	15.4334	+	26.7314i	0.587113	+	1.01691i	0.994608	+	0.103703i	$0.0330690\pi$
$691$	15.4334	+	26.7314i	0.587113	+	1.01691i	−0.407495	+	0.913207i	$0.633598\pi$
$692$	8.58442			0.326331
$693$		0			0
$694$	−12.1091			−0.459656
$695$	4.24559	+	7.35358i	0.161044	+	0.278937i
$696$		0			0
$697$	19.6372	−	34.0127i	0.743813	−	1.28832i
$698$	4.80508	+	8.32264i	0.181875	+	0.315017i
$699$		0			0
$700$	1.54568	+	3.45691i	0.0584211	+	0.130659i
$701$	−6.48958			−0.245108			−0.122554	−	0.992462i	$-0.539108\pi$
$701$	−6.48958			−0.245108			−0.122554	+	0.992462i	$0.539108\pi$
$702$		0			0
$703$	10.0341	−	17.3795i	0.378443	−	0.655482i
$704$	−30.7657	+	53.2878i	−1.15953	+	2.00836i
$705$		0			0
$706$	61.0860			2.29900
$707$	14.4580	−	19.9661i	0.543747	−	0.750902i
$708$		0			0
$709$	6.68689	+	11.5820i	0.251131	+	0.434972i	0.963838	−	0.266490i	$-0.0858641\pi$
$709$	6.68689	+	11.5820i	0.251131	+	0.434972i	−0.712706	+	0.701463i	$0.752531\pi$
$710$	5.96409	−	10.3301i	0.223828	−	0.387682i
$711$		0			0
$712$	−3.64475	−	6.31290i	−0.136593	−	0.236586i
$713$	16.8738			0.631929
$714$		0			0
$715$	−10.1660			−0.380186
$716$	−8.21645	−	14.2313i	−0.307063	−	0.531849i
$717$		0			0
$718$	−7.33555	+	12.7055i	−0.273760	+	0.474167i
$719$	−8.37048	−	14.4981i	−0.312166	−	0.540688i	0.666665	−	0.745358i	$-0.267721\pi$
$719$	−8.37048	−	14.4981i	−0.312166	−	0.540688i	−0.978831	+	0.204670i	$0.934388\pi$
$720$		0			0
$721$	−7.89050	−	17.6471i	−0.293858	−	0.657212i
$722$	13.8883			0.516868
$723$		0			0
$724$	−10.4015	+	18.0160i	−0.386570	+	0.669558i
$725$	1.45680	−	2.52325i	0.0541041	−	0.0937110i
$726$		0			0
$727$	38.8138			1.43952			0.719761	−	0.694221i	$-0.244251\pi$
$727$	38.8138			1.43952			0.719761	+	0.694221i	$0.244251\pi$
$728$	−5.23528	−	0.541869i	−0.194032	−	0.0200830i
$729$		0			0
$730$	18.0906	+	31.3339i	0.669564	+	1.15972i
$731$	−6.43692	+	11.1491i	−0.238078	+	0.412364i
$732$		0			0
$733$	−18.8639	−	32.6733i	−0.696756	−	1.20682i	−0.969585	−	0.244754i	$-0.921293\pi$
$733$	−18.8639	−	32.6733i	−0.696756	−	1.20682i	0.272830	−	0.962062i	$-0.412040\pi$
$734$	−69.0719			−2.54949
$735$		0			0
$736$	−31.6132			−1.16528
$737$	−6.94292	−	12.0255i	−0.255746	−	0.442965i
$738$		0			0
$739$	4.61476	−	7.99300i	0.169757	−	0.294027i	−0.768578	−	0.639757i	$-0.779035\pi$
$739$	4.61476	−	7.99300i	0.169757	−	0.294027i	0.938334	+	0.345729i	$0.112368\pi$
$740$	−17.3090	−	29.9801i	−0.636291	−	1.10209i
$741$		0			0
$742$	−72.1111	−	7.46375i	−2.64728	−	0.274003i
$743$	3.56327			0.130724			0.0653619	−	0.997862i	$-0.479180\pi$
$743$	3.56327			0.130724			0.0653619	+	0.997862i	$0.479180\pi$
$744$		0			0
$745$	3.13614	−	5.43195i	0.114899	−	0.199011i
$746$	−17.4571	+	30.2366i	−0.639151	+	1.10704i
$747$		0			0
$748$	−52.4508			−1.91779
$749$	7.28674	+	16.2968i	0.266252	+	0.595472i
$750$		0			0
$751$	−25.6053	−	44.3496i	−0.934350	−	1.61834i	−0.775789	−	0.630992i	$-0.782648\pi$
$751$	−25.6053	−	44.3496i	−0.934350	−	1.61834i	−0.158561	−	0.987349i	$-0.550685\pi$
$752$	4.95687	−	8.58555i	0.180758	−	0.313083i
$753$		0			0
$754$	6.53049	+	11.3111i	0.237826	+	0.411927i
$755$	−39.3879			−1.43347
$756$		0			0
$757$	25.2305			0.917019			0.458509	−	0.888690i	$-0.348384\pi$
$757$	25.2305			0.917019			0.458509	+	0.888690i	$0.348384\pi$
$758$	35.0272	+	60.6688i	1.27224	+	2.20359i
$759$		0			0
$760$	−7.53207	+	13.0459i	−0.273217	+	0.473226i
$761$	1.82372	+	3.15878i	0.0661099	+	0.114506i	0.897186	−	0.441653i	$-0.145608\pi$
$761$	1.82372	+	3.15878i	0.0661099	+	0.114506i	−0.831076	+	0.556159i	$0.812275\pi$
$762$		0			0
$763$	−6.48077	+	8.94978i	−0.234620	+	0.324004i
$764$	−34.4428			−1.24610
$765$		0			0
$766$	−13.7154	+	23.7558i	−0.495558	+	0.858331i
$767$	2.39448	−	4.14736i	0.0864596	−	0.149752i
$768$		0			0
$769$	21.9882			0.792914			0.396457	−	0.918053i	$-0.370240\pi$
$769$	21.9882			0.792914			0.396457	+	0.918053i	$0.370240\pi$
$770$	−24.2995	−	54.3458i	−0.875693	−	1.95849i
$771$		0			0
$772$	−33.2929	−	57.6650i	−1.19824	−	2.07541i
$773$	10.9295	−	18.9305i	0.393108	−	0.680882i	−0.599750	−	0.800187i	$-0.704733\pi$
$773$	10.9295	−	18.9305i	0.393108	−	0.680882i	0.992858	+	0.119305i	$0.0380667\pi$
$774$		0			0
$775$	−0.930986	−	1.61252i	−0.0334420	−	0.0579233i
$776$	10.7569			0.386151
$777$		0			0
$778$	−31.1505			−1.11680
$779$	−18.5404	−	32.1128i	−0.664277	−	1.15056i
$780$		0			0
$781$	6.07900	−	10.5291i	0.217524	−	0.376762i
$782$	−18.7088	−	32.4046i	−0.669025	−	1.15879i
$783$		0			0
$784$	3.04603	+	9.27468i	0.108787	+	0.331239i
$785$	−20.8026			−0.742477
$786$		0			0
$787$	−19.9336	+	34.5261i	−0.710557	+	1.23072i	0.254091	+	0.967180i	$0.418224\pi$
$787$	−19.9336	+	34.5261i	−0.710557	+	1.23072i	−0.964648	+	0.263541i	$0.915109\pi$
$788$	24.5261	−	42.4804i	0.873706	−	1.51330i
$789$		0			0
$790$	24.3308			0.865651
$791$	−15.5298	−	1.60739i	−0.552176	−	0.0571521i
$792$		0			0
$793$	−1.60348	−	2.77732i	−0.0569414	−	0.0986254i
$794$	−7.71680	+	13.3659i	−0.273859	+	0.474338i
$795$		0			0
$796$	−14.5796	−	25.2526i	−0.516759	−	0.895053i
$797$	40.1971			1.42385			0.711927	−	0.702253i	$-0.247822\pi$
$797$	40.1971			1.42385			0.711927	+	0.702253i	$0.247822\pi$
$798$		0			0
$799$	26.8589			0.950198
$800$	1.74421	+	3.02106i	0.0616671	+	0.106811i
$801$		0			0
$802$	−3.02873	+	5.24592i	−0.106948	+	0.185240i
$803$	18.4392	+	31.9376i	0.650704	+	1.12705i
$804$		0			0
$805$	14.7389	−	20.3541i	0.519478	−	0.717387i
$806$	8.34680			0.294003
$807$		0			0
$808$	−9.26749	+	16.0518i	−0.326029	+	0.564699i
$809$	1.26924	−	2.19840i	0.0446243	−	0.0772915i	−0.842851	−	0.538148i	$-0.819124\pi$
$809$	1.26924	−	2.19840i	0.0446243	−	0.0772915i	0.887475	+	0.460856i	$0.152458\pi$
$810$		0			0
$811$	−41.7062			−1.46450			−0.732251	−	0.681035i	$-0.761530\pi$
$811$	−41.7062			−1.46450			−0.732251	+	0.681035i	$0.761530\pi$
$812$	−26.5441	+	36.6567i	−0.931515	+	1.28640i
$813$		0			0
$814$	−29.8148	−	51.6407i	−1.04501	−	1.81001i
$815$	−14.6836	+	25.4327i	−0.514343	+	0.890868i
$816$		0			0
$817$	6.07737	+	10.5263i	0.212620	+	0.368269i
$818$	54.2604			1.89717
$819$		0			0
$820$	−63.9650			−2.23375
$821$	15.9652	+	27.6525i	0.557189	+	0.965079i	0.997730	+	0.0673467i	$0.0214534\pi$
$821$	15.9652	+	27.6525i	0.557189	+	0.965079i	−0.440541	+	0.897733i	$0.645213\pi$
$822$		0			0
$823$	17.1266	−	29.6641i	0.596995	−	1.03402i	−0.396267	−	0.918135i	$-0.629695\pi$
$823$	17.1266	−	29.6641i	0.596995	−	1.03402i	0.993262	−	0.115890i	$-0.0369720\pi$
$824$	7.26734	+	12.5874i	0.253170	+	0.438503i
$825$		0			0
$826$	27.8946	+	2.88719i	0.970578	+	0.100458i
$827$	−36.9755			−1.28576			−0.642882	−	0.765965i	$-0.722261\pi$
$827$	−36.9755			−1.28576			−0.642882	+	0.765965i	$0.722261\pi$
$828$		0			0
$829$	9.99473	−	17.3114i	0.347131	−	0.601249i	−0.638607	−	0.769533i	$-0.720489\pi$
$829$	9.99473	−	17.3114i	0.347131	−	0.601249i	0.985739	+	0.168284i	$0.0538225\pi$
$830$	−8.14547	+	14.1084i	−0.282733	+	0.489708i
$831$		0			0
$832$	−12.8486			−0.445446
$833$	−17.6348	+	19.7106i	−0.611009	+	0.682932i
$834$		0			0
$835$	18.4189	+	31.9024i	0.637412	+	1.10403i
$836$	−24.7605	+	42.8865i	−0.856360	+	1.48326i
$837$		0			0
$838$	3.33384	+	5.77438i	0.115166	+	0.199473i
$839$	−12.8147			−0.442411			−0.221206	−	0.975227i	$-0.570999\pi$
$839$	−12.8147			−0.442411			−0.221206	+	0.975227i	$0.570999\pi$
$840$		0			0
$841$	5.82265			0.200781
$842$	−11.0666	−	19.1679i	−0.381381	−	0.660571i
$843$		0			0
$844$	35.4535	−	61.4073i	1.22036	−	2.11373i
$845$	−1.06140	−	1.83839i	−0.0365132	−	0.0632427i
$846$		0			0
$847$	−12.8882	−	28.8245i	−0.442845	−	0.990422i
$848$	−17.2650			−0.592882
$849$		0			0
$850$	−2.06446	+	3.57575i	−0.0708104	+	0.122647i
$851$	12.5859	−	21.7994i	0.431439	−	0.747274i
$852$		0			0
$853$	−30.1839			−1.03348			−0.516739	−	0.856143i	$-0.672854\pi$
$853$	−30.1839			−1.03348			−0.516739	+	0.856143i	$0.672854\pi$
$854$	11.0143	−	15.2105i	0.376903	−	0.520494i
$855$		0			0
$856$	−6.71127	−	11.6243i	−0.229386	−	0.397309i
$857$	−26.6164	+	46.1009i	−0.909197	+	1.57478i	−0.0940154	+	0.995571i	$0.529970\pi$
$857$	−26.6164	+	46.1009i	−0.909197	+	1.57478i	−0.815182	+	0.579205i	$0.803363\pi$
$858$		0			0
$859$	6.13597	+	10.6278i	0.209357	+	0.362616i	0.951512	−	0.307611i	$-0.0995297\pi$
$859$	6.13597	+	10.6278i	0.209357	+	0.362616i	−0.742155	+	0.670228i	$0.766196\pi$
$860$	20.9672			0.714975
$861$		0			0
$862$	−41.5977			−1.41682
$863$	12.2226	+	21.1702i	0.416064	+	0.720643i	0.995539	−	0.0943460i	$-0.0300760\pi$
$863$	12.2226	+	21.1702i	0.416064	+	0.720643i	−0.579476	+	0.814989i	$0.696743\pi$
$864$		0			0
$865$	−3.14320	+	5.44418i	−0.106872	+	0.185108i
$866$	−8.59778	−	14.8918i	−0.292164	−	0.506043i
$867$		0			0
$868$	11.8058	+	26.4037i	0.400716	+	0.896200i
$869$	24.7996			0.841268
$870$		0			0
$871$	1.44978	−	2.51109i	0.0491238	−	0.0850850i
$872$	4.15415	−	7.19519i	0.140677	−	0.243660i
$873$		0			0
$874$	−35.3276			−1.19497
$875$	−30.6910	−	3.17663i	−1.03755	−	0.107390i
$876$		0			0
$877$	26.4376	+	45.7913i	0.892736	+	1.54626i	0.836582	+	0.547842i	$0.184550\pi$
$877$	26.4376	+	45.7913i	0.892736	+	1.54626i	0.0561539	+	0.998422i	$0.482116\pi$
$878$	−42.0178	+	72.7770i	−1.41803	+	2.45611i
$879$		0			0
$880$	−7.08864	−	12.2779i	−0.238958	−	0.413887i
$881$	−55.0118			−1.85339			−0.926697	−	0.375809i	$-0.877365\pi$
$881$	−55.0118			−1.85339			−0.926697	+	0.375809i	$0.877365\pi$
$882$		0			0
$883$	44.1730			1.48654			0.743269	−	0.668992i	$-0.233274\pi$
$883$	44.1730			1.48654			0.743269	+	0.668992i	$0.233274\pi$
$884$	−5.47622	−	9.48510i	−0.184185	−	0.319018i
$885$		0			0
$886$	−39.4270	+	68.2895i	−1.32457	+	2.29423i
$887$	−2.54330	−	4.40512i	−0.0853955	−	0.147909i	0.820164	−	0.572128i	$-0.193882\pi$
$887$	−2.54330	−	4.40512i	−0.0853955	−	0.147909i	−0.905560	+	0.424219i	$0.860549\pi$
$888$		0			0
$889$	−27.7032	−	2.86738i	−0.929136	−	0.0961688i
$890$	17.2165			0.577100
$891$		0			0
$892$	42.4130	−	73.4614i	1.42009	−	2.45967i
$893$	12.6793	−	21.9612i	0.424296	−	0.734903i
$894$		0			0
$895$	12.0339			0.402248
$896$	−15.4514	−	34.5571i	−0.516196	−	1.15447i
$897$		0			0
$898$	8.91178	+	15.4356i	0.297390	+	0.515094i
$899$	11.1270	−	19.2724i	0.371105	−	0.642772i
$900$		0			0
$901$	−23.3876	−	40.5086i	−0.779155	−	1.34954i
$902$	−110.180			−3.66859
$903$		0			0
$904$	11.7391			0.390437
$905$	−7.61706	−	13.1931i	−0.253200	−	0.438555i
$906$		0			0
$907$	9.06264	−	15.6969i	0.300920	−	0.521209i	−0.675425	−	0.737429i	$-0.736040\pi$
$907$	9.06264	−	15.6969i	0.300920	−	0.521209i	0.976345	+	0.216220i	$0.0693730\pi$
$908$	−14.6008	−	25.2893i	−0.484544	−	0.839255i
$909$		0			0
$910$	7.29075	−	10.0683i	0.241686	−	0.333763i
$911$	9.65804			0.319985			0.159993	−	0.987118i	$-0.448853\pi$
$911$	9.65804			0.319985			0.159993	+	0.987118i	$0.448853\pi$
$912$		0			0
$913$	−8.30241	+	14.3802i	−0.274770	+	0.475915i
$914$	17.2613	−	29.8974i	0.570952	−	0.988918i
$915$		0			0
$916$	−32.2924			−1.06697
$917$	5.85774	+	13.1008i	0.193440	+	0.432628i
$918$		0			0
$919$	−23.8801	−	41.3616i	−0.787733	−	1.36439i	−0.927353	−	0.374188i	$-0.877922\pi$
$919$	−23.8801	−	41.3616i	−0.787733	−	1.36439i	0.139620	−	0.990205i	$-0.455412\pi$
$920$	−9.44758	+	16.3637i	−0.311477	+	0.539495i
$921$		0			0
$922$	28.4401	+	49.2598i	0.936626	+	1.62228i
$923$	2.53876			0.0835643
$924$		0			0
$925$	−2.77763			−0.0913279
$926$	−22.7096	−	39.3342i	−0.746285	−	1.29260i
$927$		0			0
$928$	−20.8464	+	36.1071i	−0.684317	+	1.18527i
$929$	16.9905	+	29.4285i	0.557442	+	0.965517i	0.997709	+	0.0676505i	$0.0215503\pi$
$929$	16.9905	+	29.4285i	0.557442	+	0.965517i	−0.440267	+	0.897867i	$0.645116\pi$
$930$		0			0
$931$	7.79153	+	23.7239i	0.255357	+	0.777520i
$932$	49.5210			1.62212
$933$		0			0
$934$	−13.0861	+	22.6657i	−0.428189	+	0.741645i
$935$	19.2049	−	33.2639i	0.628068	−	1.08785i
$936$		0			0
$937$	−24.7948			−0.810012			−0.405006	−	0.914314i	$-0.632731\pi$
$937$	−24.7948			−0.810012			−0.405006	+	0.914314i	$0.632731\pi$
$938$	16.8893	+	1.74810i	0.551454	+	0.0570774i
$939$		0			0
$940$	−21.8720	−	37.8835i	−0.713387	−	1.23562i
$941$	−4.12098	+	7.13774i	−0.134340	+	0.232684i	−0.925345	−	0.379126i	$-0.876225\pi$
$941$	−4.12098	+	7.13774i	−0.134340	+	0.232684i	0.791005	+	0.611810i	$0.209558\pi$
$942$		0			0
$943$	−23.2554	−	40.2796i	−0.757301	−	1.31168i
$944$	6.67859			0.217370
$945$		0			0
$946$	36.1160			1.17423
$947$	9.98643	+	17.2970i	0.324515	+	0.562077i	0.981414	−	0.191902i	$-0.0614655\pi$
$947$	9.98643	+	17.2970i	0.324515	+	0.562077i	−0.656899	+	0.753979i	$0.728132\pi$
$948$		0			0
$949$	−3.85035	+	6.66901i	−0.124988	+	0.216485i
$950$	1.94914	+	3.37602i	0.0632386	+	0.109532i
$951$		0			0
$952$	11.6632	−	16.1066i	0.378007	−	0.522018i
$953$	21.5341			0.697557			0.348778	−	0.937205i	$-0.386597\pi$
$953$	21.5341			0.697557			0.348778	+	0.937205i	$0.386597\pi$
$954$		0			0
$955$	12.6113	−	21.8434i	0.408091	−	0.706835i
$956$	10.0319	−	17.3757i	0.324455	−	0.561972i
$957$		0			0
$958$	50.1432			1.62005
$959$	34.5181	−	47.6686i	1.11465	−	1.53930i
$960$		0			0
$961$	8.38917	+	14.5305i	0.270618	+	0.468725i
$962$	6.22574	−	10.7833i	0.200726	−	0.347667i
$963$		0			0
$964$	−9.41564	−	16.3084i	−0.303257	−	0.525257i
$965$	48.7610			1.56967
$966$		0			0
$967$	43.2887			1.39207			0.696036	−	0.718007i	$-0.254945\pi$
$967$	43.2887			1.39207			0.696036	+	0.718007i	$0.254945\pi$
$968$	11.8704	+	20.5601i	0.381528	+	0.660827i
$969$		0			0
$970$	−12.7030	+	22.0022i	−0.407868	+	0.706449i
$971$	−26.3356	−	45.6147i	−0.845151	−	1.46384i	−0.885490	−	0.464658i	$-0.846177\pi$
$971$	−26.3356	−	45.6147i	−0.845151	−	1.46384i	0.0403390	−	0.999186i	$-0.487156\pi$
$972$		0			0
$973$	−10.5268	−	1.08956i	−0.337473	−	0.0349296i
$974$	72.4127			2.32025
$975$		0			0
$976$	2.23619	−	3.87319i	0.0715787	−	0.123978i
$977$	7.70305	−	13.3421i	0.246442	−	0.426851i	−0.716094	−	0.698004i	$-0.754072\pi$
$977$	7.70305	−	13.3421i	0.246442	−	0.426851i	0.962536	+	0.271153i	$0.0874051\pi$
$978$		0			0
$979$	17.5483			0.560845
$980$	42.1617	+	8.82227i	1.34681	+	0.281817i
$981$		0			0
$982$	−6.83121	−	11.8320i	−0.217993	−	0.377575i
$983$	3.79073	−	6.56574i	0.120906	−	0.209415i	−0.799219	−	0.601039i	$-0.794754\pi$
$983$	3.79073	−	6.56574i	0.120906	−	0.209415i	0.920125	+	0.391625i	$0.128087\pi$
$984$		0			0
$985$	17.9605	+	31.1085i	0.572270	+	0.991201i
$986$	−49.3480			−1.57156
$987$		0			0
$988$	−10.3407			−0.328981
$989$	7.62293	+	13.2033i	0.242395	+	0.419841i
$990$		0			0
$991$	9.50923	−	16.4705i	0.302071	−	0.523202i	−0.674534	−	0.738244i	$-0.735655\pi$
$991$	9.50923	−	16.4705i	0.302071	−	0.523202i	0.976605	+	0.215042i	$0.0689888\pi$
$992$	13.3222	+	23.0747i	0.422980	+	0.732623i
$993$		0			0
$994$	6.06834	+	13.5718i	0.192476	+	0.430472i
$995$	21.3533			0.676946
$996$		0			0
$997$	−23.0499	+	39.9236i	−0.729998	+	1.26439i	0.226885	+	0.973922i	$0.427146\pi$
$997$	−23.0499	+	39.9236i	−0.729998	+	1.26439i	−0.956883	+	0.290473i	$0.906187\pi$
$998$	−16.2001	+	28.0593i	−0.512804	+	0.888202i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.j.h.235.4		10
3.2	odd	2		91.2.e.c.53.2	✓	10
7.2	even	3	inner	819.2.j.h.352.4		10
7.3	odd	6		5733.2.a.bm.1.2		5
7.4	even	3		5733.2.a.bl.1.2		5
12.11	even	2		1456.2.r.p.417.5		10
21.2	odd	6		91.2.e.c.79.2	yes	10
21.5	even	6		637.2.e.m.79.2		10
21.11	odd	6		637.2.a.l.1.4		5
21.17	even	6		637.2.a.k.1.4		5
21.20	even	2		637.2.e.m.508.2		10
39.38	odd	2		1183.2.e.f.508.4		10
84.23	even	6		1456.2.r.p.625.5		10
273.38	even	6		8281.2.a.bx.1.2		5
273.116	odd	6		8281.2.a.bw.1.2		5
273.233	odd	6		1183.2.e.f.170.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.c.53.2	✓	10	3.2	odd	2
91.2.e.c.79.2	yes	10	21.2	odd	6
637.2.a.k.1.4		5	21.17	even	6
637.2.a.l.1.4		5	21.11	odd	6
637.2.e.m.79.2		10	21.5	even	6
637.2.e.m.508.2		10	21.20	even	2
819.2.j.h.235.4		10	1.1	even	1	trivial
819.2.j.h.352.4		10	7.2	even	3	inner
1183.2.e.f.170.4		10	273.233	odd	6
1183.2.e.f.508.4		10	39.38	odd	2
1456.2.r.p.417.5		10	12.11	even	2
1456.2.r.p.625.5		10	84.23	even	6
5733.2.a.bl.1.2		5	7.4	even	3
5733.2.a.bm.1.2		5	7.3	odd	6
8281.2.a.bw.1.2		5	273.116	odd	6
8281.2.a.bx.1.2		5	273.38	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.10666 + 1.91679i) q^{2} +(-1.44940 + 2.51043i) q^{4} +(-1.06140 - 1.83839i) q^{5} +(2.63169 + 0.272389i) q^{7} -1.98932 q^{8} +O(q^{10})\)	\(q+(1.10666 + 1.91679i) q^{2} +(-1.44940 + 2.51043i) q^{4} +(-1.06140 - 1.83839i) q^{5} +(2.63169 + 0.272389i) q^{7} -1.98932 q^{8} +(2.34921 - 4.06896i) q^{10} +(2.39448 - 4.14736i) q^{11} +1.00000 q^{13} +(2.39028 + 5.34585i) q^{14} +(0.697291 + 1.20774i) q^{16} +(-1.88914 + 3.27208i) q^{17} +(1.78362 + 3.08931i) q^{19} +6.15355 q^{20} +10.5995 q^{22} +(2.23721 + 3.87497i) q^{23} +(0.246870 - 0.427591i) q^{25} +(1.10666 + 1.91679i) q^{26} +(-4.49818 + 6.21188i) q^{28} +5.90107 q^{29} +(1.88558 - 3.26592i) q^{31} +(-3.53265 + 6.11873i) q^{32} -8.36254 q^{34} +(-2.29251 - 5.12720i) q^{35} +(-2.81285 - 4.87200i) q^{37} +(-3.94772 + 6.83765i) q^{38} +(2.11146 + 3.65716i) q^{40} -10.3948 q^{41} +3.40733 q^{43} +(6.94110 + 12.0223i) q^{44} +(-4.95168 + 8.57655i) q^{46} +(-3.55438 - 6.15636i) q^{47} +(6.85161 + 1.43369i) q^{49} +1.09280 q^{50} +(-1.44940 + 2.51043i) q^{52} +(-6.19003 + 10.7214i) q^{53} -10.1660 q^{55} +(-5.23528 - 0.541869i) q^{56} +(6.53049 + 11.3111i) q^{58} +(2.39448 - 4.14736i) q^{59} +(-1.60348 - 2.77732i) q^{61} +8.34680 q^{62} -12.8486 q^{64} +(-1.06140 - 1.83839i) q^{65} +(1.44978 - 2.51109i) q^{67} +(-5.47622 - 9.48510i) q^{68} +(7.29075 - 10.0683i) q^{70} +2.53876 q^{71} +(-3.85035 + 6.66901i) q^{73} +(6.22574 - 10.7833i) q^{74} -10.3407 q^{76} +(7.43122 - 10.2623i) q^{77} +(2.58925 + 4.48471i) q^{79} +(1.48021 - 2.56379i) q^{80} +(-11.5035 - 19.9247i) q^{82} -3.46731 q^{83} +8.02051 q^{85} +(3.77076 + 6.53115i) q^{86} +(-4.76338 + 8.25042i) q^{88} +(1.83216 + 3.17339i) q^{89} +(2.63169 + 0.272389i) q^{91} -12.9704 q^{92} +(7.86698 - 13.6260i) q^{94} +(3.78625 - 6.55798i) q^{95} -5.40733 q^{97} +(4.83432 + 14.7197i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} - 8 q^{4} + 2 q^{5} + q^{7} - 18 q^{8}+O(q^{10}) \) 10 * q + 4 * q^2 - 8 * q^4 + 2 * q^5 + q^7 - 18 * q^8	\( 10 q + 4 q^{2} - 8 q^{4} + 2 q^{5} + q^{7} - 18 q^{8} + 5 q^{10} + 11 q^{11} + 10 q^{13} - 10 q^{14} - 10 q^{16} - 5 q^{17} - 9 q^{19} - 2 q^{20} + 16 q^{22} + 10 q^{23} - 9 q^{25} + 4 q^{26} + 37 q^{28} + 6 q^{29} + 6 q^{31} + 22 q^{32} - 44 q^{34} + 4 q^{35} - 4 q^{37} - 10 q^{38} - 28 q^{40} - 28 q^{41} + 4 q^{43} - 3 q^{46} + q^{47} - 11 q^{49} - 18 q^{50} - 8 q^{52} + 17 q^{53} + 21 q^{56} + 27 q^{58} + 11 q^{59} + 11 q^{61} + 46 q^{62} + 18 q^{64} + 2 q^{65} - 13 q^{67} - 32 q^{68} + 49 q^{70} - 30 q^{71} - 33 q^{74} + 16 q^{76} + 46 q^{77} - 2 q^{79} + 55 q^{80} - 34 q^{82} - 12 q^{83} - 44 q^{85} + 28 q^{86} + 3 q^{88} - 4 q^{89} + q^{91} - 42 q^{92} - 20 q^{94} - 12 q^{95} - 24 q^{97} + 7 q^{98}+O(q^{100}) \) 10 * q + 4 * q^2 - 8 * q^4 + 2 * q^5 + q^7 - 18 * q^8 + 5 * q^10 + 11 * q^11 + 10 * q^13 - 10 * q^14 - 10 * q^16 - 5 * q^17 - 9 * q^19 - 2 * q^20 + 16 * q^22 + 10 * q^23 - 9 * q^25 + 4 * q^26 + 37 * q^28 + 6 * q^29 + 6 * q^31 + 22 * q^32 - 44 * q^34 + 4 * q^35 - 4 * q^37 - 10 * q^38 - 28 * q^40 - 28 * q^41 + 4 * q^43 - 3 * q^46 + q^47 - 11 * q^49 - 18 * q^50 - 8 * q^52 + 17 * q^53 + 21 * q^56 + 27 * q^58 + 11 * q^59 + 11 * q^61 + 46 * q^62 + 18 * q^64 + 2 * q^65 - 13 * q^67 - 32 * q^68 + 49 * q^70 - 30 * q^71 - 33 * q^74 + 16 * q^76 + 46 * q^77 - 2 * q^79 + 55 * q^80 - 34 * q^82 - 12 * q^83 - 44 * q^85 + 28 * q^86 + 3 * q^88 - 4 * q^89 + q^91 - 42 * q^92 - 20 * q^94 - 12 * q^95 - 24 * q^97 + 7 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more