LMFDB - Embedded newform 117.3.bd.d.46.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(19,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("117.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.bd (of order $12$, degree $4$, 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:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 8 x^{10} + 8 x^{9} + 178 x^{8} - 620 x^{7} + 1088 x^{6} + 640 x^{5} + 7921 x^{4} + \cdots + 5184 $ x^12 - 4x^11 + 8x^10 + 8x^9 + 178x^8 - 620x^7 + 1088x^6 + 640x^5 + 7921x^4 - 22128x^3 + 28800x^2 - 17280*x + 5184
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			46.3
Root			$2.24591 + 2.24591i$ of defining polynomial
Character	$\chi$	$=$	117.46
Dual form			117.3.bd.d.28.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.06798 - 0.822062i) q^{2} +(5.27259 - 3.04413i) q^{4} +(5.58467 + 5.58467i) q^{5} +(-7.30003 - 1.95604i) q^{7} +(4.69005 - 4.69005i) q^{8} +(21.7246 + 12.5427i) q^{10} +(-3.01391 - 11.2481i) q^{11} +(-12.4428 - 3.76518i) q^{13} -24.0043 q^{14} +(-1.64307 + 2.84588i) q^{16} +(10.4817 - 6.05163i) q^{17} +(2.73246 - 10.1977i) q^{19} +(46.4461 + 12.4452i) q^{20} +(-18.4932 - 32.0311i) q^{22} +(3.75368 + 2.16719i) q^{23} +37.3770i q^{25} +(-41.2694 - 1.32273i) q^{26} +(-44.4444 + 11.9089i) q^{28} +(-22.1306 + 38.3313i) q^{29} +(-5.71913 - 5.71913i) q^{31} +(-9.56812 + 35.7087i) q^{32} +(27.1829 - 27.1829i) q^{34} +(-29.8444 - 51.6920i) q^{35} +(8.51041 + 31.7613i) q^{37} -33.5325i q^{38} +52.3847 q^{40} +(58.1365 - 15.5776i) q^{41} +(27.0185 - 15.5991i) q^{43} +(-50.1316 - 50.1316i) q^{44} +(13.2978 + 3.56313i) q^{46} +(-22.4086 + 22.4086i) q^{47} +(7.02906 + 4.05823i) q^{49} +(30.7262 + 114.672i) q^{50} +(-77.0675 + 18.0253i) q^{52} +54.7345 q^{53} +(45.9850 - 79.6483i) q^{55} +(-43.4114 + 25.0636i) q^{56} +(-36.3854 + 135.792i) q^{58} +(13.4735 + 3.61020i) q^{59} +(-42.0454 - 72.8249i) q^{61} +(-22.2476 - 12.8447i) q^{62} +104.274i q^{64} +(-48.4616 - 90.5162i) q^{65} +(62.2390 - 16.6769i) q^{67} +(36.8439 - 63.8155i) q^{68} +(-134.056 - 134.056i) q^{70} +(14.8017 - 55.2406i) q^{71} +(-54.9623 + 54.9623i) q^{73} +(52.2194 + 90.4467i) q^{74} +(-16.6359 - 62.0861i) q^{76} +88.0064i q^{77} -45.0309 q^{79} +(-25.0693 + 6.71729i) q^{80} +(165.555 - 95.5835i) q^{82} +(30.8346 + 30.8346i) q^{83} +(92.3333 + 24.7406i) q^{85} +(70.0685 - 70.0685i) q^{86} +(-66.8893 - 38.6186i) q^{88} +(-5.84679 - 21.8205i) q^{89} +(83.4680 + 51.8245i) q^{91} +26.3888 q^{92} +(-50.3279 + 87.1704i) q^{94} +(72.2104 - 41.6907i) q^{95} +(28.7767 - 107.396i) q^{97} +(24.9011 + 6.67223i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 12 q^{4} - 4 q^{5} - 32 q^{7} + 24 q^{8} + 30 q^{10} - 22 q^{11} + 2 q^{13} - 92 q^{14} + 52 q^{16} + 6 q^{17} + 4 q^{19} + 208 q^{20} - 98 q^{22} + 18 q^{23} + 44 q^{26} - 78 q^{28} - 128 q^{29}+ \cdots + 350 q^{98}+O(q^{100}) $ 12 * q + 2 * q^2 - 12 * q^4 - 4 * q^5 - 32 * q^7 + 24 * q^8 + 30 * q^10 - 22 * q^11 + 2 * q^13 - 92 * q^14 + 52 * q^16 + 6 * q^17 + 4 * q^19 + 208 * q^20 - 98 * q^22 + 18 * q^23 + 44 * q^26 - 78 * q^28 - 128 * q^29 - 66 * q^31 - 358 * q^32 + 336 * q^34 - 14 * q^35 - 36 * q^37 - 12 * q^40 + 326 * q^41 + 60 * q^43 + 236 * q^44 - 138 * q^46 - 40 * q^47 + 78 * q^49 + 40 * q^50 - 392 * q^52 - 80 * q^53 + 166 * q^55 + 102 * q^56 + 250 * q^58 + 164 * q^59 - 98 * q^61 - 228 * q^62 - 514 * q^65 - 230 * q^67 - 78 * q^68 - 92 * q^70 - 70 * q^71 + 106 * q^73 + 16 * q^74 + 534 * q^76 + 16 * q^79 - 124 * q^80 - 156 * q^82 + 176 * q^83 + 90 * q^85 + 612 * q^86 - 318 * q^88 + 476 * q^89 + 106 * q^91 - 228 * q^92 - 374 * q^94 + 234 * q^95 - 306 * q^97 + 350 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$1$

Coefficient data

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

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

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

$2$	3.06798	−	0.822062i	1.53399	−	0.411031i	0.609670	−	0.792655i	$-0.291302\pi$
$2$	3.06798	−	0.822062i	1.53399	−	0.411031i	0.924317	+	0.381624i	$0.124635\pi$
$3$		0			0
$3$		0			0
$4$	5.27259	−	3.04413i	1.31815	−	0.761032i
$5$	5.58467	+	5.58467i	1.11693	+	1.11693i	0.992189	+	0.124744i	$0.0398110\pi$
$5$	5.58467	+	5.58467i	1.11693	+	1.11693i	0.124744	+	0.992189i	$0.460189\pi$
$6$		0			0
$7$	−7.30003	−	1.95604i	−1.04286	−	0.279434i	−0.303562	−	0.952812i	$-0.598176\pi$
$7$	−7.30003	−	1.95604i	−1.04286	−	0.279434i	−0.739299	+	0.673378i	$0.764843\pi$
$8$	4.69005	−	4.69005i	0.586256	−	0.586256i
$9$		0			0
$10$	21.7246	+	12.5427i	2.17246	+	1.25427i
$11$	−3.01391	−	11.2481i	−0.273992	−	1.02255i	−0.956514	−	0.291686i	$-0.905784\pi$
$11$	−3.01391	−	11.2481i	−0.273992	−	1.02255i	0.682523	−	0.730865i	$-0.260883\pi$
$12$		0			0
$13$	−12.4428	−	3.76518i	−0.957139	−	0.289629i
$13$	−12.4428	−	3.76518i	−0.957139	−	0.289629i
$14$	−24.0043			−1.71459
$15$		0			0
$16$	−1.64307	+	2.84588i	−0.102692	+	0.177868i
$17$	10.4817	−	6.05163i	0.616573	−	0.355978i	−0.158961	−	0.987285i	$-0.550814\pi$
$17$	10.4817	−	6.05163i	0.616573	−	0.355978i	0.775533	+	0.631307i	$0.217481\pi$
$18$		0			0
$19$	2.73246	−	10.1977i	0.143814	−	0.536720i	−0.855992	−	0.516989i	$-0.827053\pi$
$19$	2.73246	−	10.1977i	0.143814	−	0.536720i	0.999805	−	0.0197301i	$-0.00628070\pi$
$20$	46.4461	+	12.4452i	2.32230	+	0.622259i
$21$		0			0
$22$	−18.4932	−	32.0311i	−0.840599	−	1.45596i
$23$	3.75368	+	2.16719i	0.163204	+	0.0942256i	0.579377	−	0.815060i	$-0.303296\pi$
$23$	3.75368	+	2.16719i	0.163204	+	0.0942256i	−0.416174	+	0.909285i	$0.636629\pi$
$24$		0			0
$25$			37.3770i			1.49508i
$26$	−41.2694	−	1.32273i	−1.58729	−	0.0508743i
$27$		0			0
$28$	−44.4444	+	11.9089i	−1.58730	+	0.425316i
$29$	−22.1306	+	38.3313i	−0.763123	+	1.32177i	0.178111	+	0.984010i	$0.443002\pi$
$29$	−22.1306	+	38.3313i	−0.763123	+	1.32177i	−0.941233	+	0.337757i	$0.890332\pi$
$30$		0			0
$31$	−5.71913	−	5.71913i	−0.184488	−	0.184488i	0.608820	−	0.793308i	$-0.291643\pi$
$31$	−5.71913	−	5.71913i	−0.184488	−	0.184488i	−0.793308	+	0.608820i	$0.791643\pi$
$32$	−9.56812	+	35.7087i	−0.299004	+	1.11590i
$33$		0			0
$34$	27.1829	−	27.1829i	0.799497	−	0.799497i
$35$	−29.8444	−	51.6920i	−0.852697	−	1.47691i
$36$		0			0
$37$	8.51041	+	31.7613i	0.230011	+	0.858413i	0.980335	+	0.197342i	$0.0632309\pi$
$37$	8.51041	+	31.7613i	0.230011	+	0.858413i	−0.750324	+	0.661071i	$0.770102\pi$
$38$		−	33.5325i		−	0.882433i
$39$		0			0
$40$	52.3847			1.30962
$41$	58.1365	−	15.5776i	1.41796	−	0.379942i	0.533202	−	0.845988i	$-0.320989\pi$
$41$	58.1365	−	15.5776i	1.41796	−	0.379942i	0.884760	+	0.466046i	$0.154322\pi$
$42$		0			0
$43$	27.0185	−	15.5991i	0.628336	−	0.362770i	−0.151771	−	0.988416i	$-0.548498\pi$
$43$	27.0185	−	15.5991i	0.628336	−	0.362770i	0.780107	+	0.625646i	$0.215164\pi$
$44$	−50.1316	−	50.1316i	−1.13936	−	1.13936i
$45$		0			0
$46$	13.2978	+	3.56313i	0.289082	+	0.0774592i
$47$	−22.4086	+	22.4086i	−0.476779	+	0.476779i	−0.904100	−	0.427321i	$-0.859458\pi$
$47$	−22.4086	+	22.4086i	−0.476779	+	0.476779i	0.427321	+	0.904100i	$0.359458\pi$
$48$		0			0
$49$	7.02906	+	4.05823i	0.143450	+	0.0828210i
$50$	30.7262	+	114.672i	0.614524	+	2.29343i
$51$		0			0
$52$	−77.0675	+	18.0253i	−1.48207	+	0.346640i
$53$	54.7345			1.03273			0.516363	−	0.856370i	$-0.327286\pi$
$53$	54.7345			1.03273			0.516363	+	0.856370i	$0.327286\pi$
$54$		0			0
$55$	45.9850	−	79.6483i	0.836090	−	1.44815i
$56$	−43.4114	+	25.0636i	−0.775203	+	0.447564i
$57$		0			0
$58$	−36.3854	+	135.792i	−0.627334	+	2.34124i
$59$	13.4735	+	3.61020i	0.228364	+	0.0611899i	0.371186	−	0.928558i	$-0.378951\pi$
$59$	13.4735	+	3.61020i	0.228364	+	0.0611899i	−0.142822	+	0.989748i	$0.545618\pi$
$60$		0			0
$61$	−42.0454	−	72.8249i	−0.689270	−	1.19385i	−0.972074	−	0.234673i	$-0.924598\pi$
$61$	−42.0454	−	72.8249i	−0.689270	−	1.19385i	0.282805	−	0.959177i	$-0.408735\pi$
$62$	−22.2476	−	12.8447i	−0.358832	−	0.207172i
$63$		0			0
$64$			104.274i			1.62929i
$65$	−48.4616	−	90.5162i	−0.745564	−	1.39256i
$66$		0			0
$67$	62.2390	−	16.6769i	0.928940	−	0.248909i	0.237537	−	0.971378i	$-0.423660\pi$
$67$	62.2390	−	16.6769i	0.928940	−	0.248909i	0.691403	+	0.722470i	$0.256993\pi$
$68$	36.8439	−	63.8155i	0.541822	−	0.938463i
$69$		0			0
$70$	−134.056	−	134.056i	−1.91508	−	1.91508i
$71$	14.8017	−	55.2406i	0.208474	−	0.778036i	−0.779888	−	0.625919i	$-0.784724\pi$
$71$	14.8017	−	55.2406i	0.208474	−	0.778036i	0.988362	−	0.152117i	$-0.0486092\pi$
$72$		0			0
$73$	−54.9623	+	54.9623i	−0.752909	+	0.752909i	−0.975021	−	0.222113i	$-0.928705\pi$
$73$	−54.9623	+	54.9623i	−0.752909	+	0.752909i	0.222113	+	0.975021i	$0.428705\pi$
$74$	52.2194	+	90.4467i	0.705668	+	1.22225i
$75$		0			0
$76$	−16.6359	−	62.0861i	−0.218894	−	0.816922i
$77$			88.0064i			1.14294i
$78$		0			0
$79$	−45.0309			−0.570012			−0.285006	−	0.958526i	$-0.591996\pi$
$79$	−45.0309			−0.570012			−0.285006	+	0.958526i	$0.591996\pi$
$80$	−25.0693	+	6.71729i	−0.313366	+	0.0839662i
$81$		0			0
$82$	165.555	−	95.5835i	2.01897	−	1.16565i
$83$	30.8346	+	30.8346i	0.371501	+	0.371501i	0.868024	−	0.496523i	$-0.165390\pi$
$83$	30.8346	+	30.8346i	0.371501	+	0.371501i	−0.496523	+	0.868024i	$0.665390\pi$
$84$		0			0
$85$	92.3333	+	24.7406i	1.08627	+	0.291066i
$86$	70.0685	−	70.0685i	0.814750	−	0.814750i
$87$		0			0
$88$	−66.8893	−	38.6186i	−0.760106	−	0.438847i
$89$	−5.84679	−	21.8205i	−0.0656942	−	0.245174i	0.925268	−	0.379313i	$-0.123840\pi$
$89$	−5.84679	−	21.8205i	−0.0656942	−	0.245174i	−0.990963	+	0.134139i	$0.957173\pi$
$90$		0			0
$91$	83.4680	+	51.8245i	0.917231	+	0.569500i
$92$	26.3888			0.286835
$93$		0			0
$94$	−50.3279	+	87.1704i	−0.535403	+	0.927345i
$95$	72.2104	−	41.6907i	0.760110	−	0.438850i
$96$		0			0
$97$	28.7767	−	107.396i	0.296667	−	1.10718i	−0.643217	−	0.765684i	$-0.722401\pi$
$97$	28.7767	−	107.396i	0.296667	−	1.10718i	0.939884	−	0.341493i	$-0.110933\pi$
$98$	24.9011	+	6.67223i	0.254093	+	0.0680840i
$99$		0			0
$100$	113.780	+	197.073i	1.13780	+	1.97073i
$101$	−26.0181	−	15.0216i	−0.257605	−	0.148728i	0.365637	−	0.930758i	$-0.380851\pi$
$101$	−26.0181	−	15.0216i	−0.257605	−	0.148728i	−0.623242	+	0.782029i	$0.714185\pi$
$102$		0			0
$103$			122.717i			1.19143i	0.803197	+	0.595713i	$0.203131\pi$
$103$			122.717i			1.19143i	−0.803197	+	0.595713i	$0.796869\pi$
$104$	−76.0163	+	40.6985i	−0.730926	+	0.391332i
$105$		0			0
$106$	167.924	−	44.9951i	1.58419	−	0.424482i
$107$	−0.253390	+	0.438884i	−0.00236813	+	0.00410172i	−0.867207	−	0.497948i	$-0.834087\pi$
$107$	−0.253390	+	0.438884i	−0.00236813	+	0.00410172i	0.864839	+	0.502049i	$0.167420\pi$
$108$		0			0
$109$	−29.9213	−	29.9213i	−0.274507	−	0.274507i	0.556404	−	0.830912i	$-0.312181\pi$
$109$	−29.9213	−	29.9213i	−0.274507	−	0.274507i	−0.830912	+	0.556404i	$0.812181\pi$
$110$	75.6049	−	282.161i	0.687318	−	2.56510i
$111$		0			0
$112$	17.5611	−	17.5611i	0.156796	−	0.156796i
$113$	51.7762	+	89.6790i	0.458197	+	0.793620i	0.998866	−	0.0476155i	$-0.0151622\pi$
$113$	51.7762	+	89.6790i	0.458197	+	0.793620i	−0.540669	+	0.841235i	$0.681829\pi$
$114$		0			0
$115$	8.86003	+	33.0661i	0.0770437	+	0.287531i
$116$			269.473i			2.32304i
$117$		0			0
$118$	44.3041			0.375458
$119$	−88.3541	+	23.6744i	−0.742472	+	0.198945i
$120$		0			0
$121$	−12.6460	+	7.30120i	−0.104513	+	0.0603405i
$122$	−188.861	−	188.861i	−1.54804	−	1.54804i
$123$		0			0
$124$	−47.5644	−	12.7448i	−0.383583	−	0.102781i
$125$	−69.1213	+	69.1213i	−0.552970	+	0.552970i
$126$		0			0
$127$	−202.395	−	116.853i	−1.59366	−	0.920100i	−0.992672	−	0.120843i	$-0.961440\pi$
$127$	−202.395	−	116.853i	−1.59366	−	0.920100i	−0.600989	−	0.799257i	$-0.705226\pi$
$128$	47.4475	+	177.077i	0.370684	+	1.38341i
$129$		0			0
$130$	−223.089	−	237.863i	−1.71607	−	1.82972i
$131$	15.9680			0.121893			0.0609467	−	0.998141i	$-0.480588\pi$
$131$	15.9680			0.121893			0.0609467	+	0.998141i	$0.480588\pi$
$132$		0			0
$133$	−39.8940	+	69.0985i	−0.299955	+	0.519537i
$134$	177.238	−	102.329i	1.32267	−	0.763646i
$135$		0			0
$136$	20.7774	−	77.5423i	0.152775	−	0.570164i
$137$	−3.25775	−	0.872910i	−0.0237792	−	0.00637161i	0.246910	−	0.969038i	$-0.420585\pi$
$137$	−3.25775	−	0.872910i	−0.0237792	−	0.00637161i	−0.270689	+	0.962667i	$0.587252\pi$
$138$		0			0
$139$	−18.1577	−	31.4501i	−0.130631	−	0.226260i	0.793289	−	0.608845i	$-0.208367\pi$
$139$	−18.1577	−	31.4501i	−0.130631	−	0.226260i	−0.923920	+	0.382586i	$0.875034\pi$
$140$	−314.714	−	181.700i	−2.24796	−	1.29786i
$141$		0			0
$142$		−	181.645i		−	1.27919i
$143$	−4.84950	+	151.305i	−0.0339126	+	1.05808i
$144$		0			0
$145$	−337.659	+	90.4755i	−2.32868	+	0.623969i
$146$	−123.441	+	213.805i	−0.845484	+	1.46442i
$147$		0			0
$148$	141.557	+	141.557i	0.956468	+	0.956468i
$149$	−37.2135	+	138.883i	−0.249755	+	0.932099i	0.721178	+	0.692749i	$0.243601\pi$
$149$	−37.2135	+	138.883i	−0.249755	+	0.932099i	−0.970934	+	0.239349i	$0.923066\pi$
$150$		0			0
$151$	−120.042	+	120.042i	−0.794982	+	0.794982i	−0.982299	−	0.187318i	$-0.940021\pi$
$151$	−120.042	+	120.042i	−0.794982	+	0.794982i	0.187318	+	0.982299i	$0.440021\pi$
$152$	−35.0122	−	60.6430i	−0.230344	−	0.398967i
$153$		0			0
$154$	72.3467	+	270.002i	0.469784	+	1.75326i
$155$		−	63.8788i		−	0.412121i
$156$		0			0
$157$	15.4414			0.0983529			0.0491764	−	0.998790i	$-0.484340\pi$
$157$	15.4414			0.0983529			0.0491764	+	0.998790i	$0.484340\pi$
$158$	−138.154	+	37.0182i	−0.874391	+	0.234292i
$159$		0			0
$160$	−252.856	+	145.986i	−1.58035	+	0.912415i
$161$	−23.1629	−	23.1629i	−0.143869	−	0.143869i
$162$		0			0
$163$	266.414	+	71.3853i	1.63444	+	0.437947i	0.955198	−	0.295967i	$-0.0956420\pi$
$163$	266.414	+	71.3853i	1.63444	+	0.437947i	0.679242	+	0.733914i	$0.262309\pi$
$164$	259.109	−	259.109i	1.57993	−	1.57993i
$165$		0			0
$166$	119.948	+	69.2518i	0.722576	+	0.417180i
$167$	−66.4855	−	248.127i	−0.398116	−	1.48579i	−0.816407	−	0.577477i	$-0.804037\pi$
$167$	−66.4855	−	248.127i	−0.398116	−	1.48579i	0.418290	−	0.908313i	$-0.362630\pi$
$168$		0			0
$169$	140.647	+	93.6988i	0.832230	+	0.554431i
$170$	303.615			1.78597
$171$		0			0
$172$	94.9714	−	164.495i	0.552160	−	0.956368i
$173$	−217.286	+	125.450i	−1.25599	+	0.725147i	−0.972293	−	0.233767i	$-0.924895\pi$
$173$	−217.286	+	125.450i	−1.25599	+	0.725147i	−0.283698	+	0.958914i	$0.591561\pi$
$174$		0			0
$175$	73.1107	−	272.853i	0.417776	−	1.55916i
$176$	36.9627	+	9.90412i	0.210015	+	0.0562734i
$177$		0			0
$178$	−35.8756	−	62.1383i	−0.201548	−	0.349092i
$179$	−7.39919	−	4.27193i	−0.0413363	−	0.0238655i	0.479189	−	0.877711i	$-0.340931\pi$
$179$	−7.39919	−	4.27193i	−0.0413363	−	0.0238655i	−0.520526	+	0.853846i	$0.674264\pi$
$180$		0			0
$181$		−	24.6075i		−	0.135953i	−0.997687	−	0.0679764i	$-0.978346\pi$
$181$		−	24.6075i		−	0.135953i	0.997687	−	0.0679764i	$-0.0216543\pi$
$182$	298.681	+	90.3805i	1.64110	+	0.496596i
$183$		0			0
$184$	27.7692	−	7.44073i	0.150919	−	0.0404387i
$185$	−129.848	+	224.904i	−0.701883	+	1.21570i
$186$		0			0
$187$	−99.6601	−	99.6601i	−0.532941	−	0.532941i
$188$	−49.9367	+	186.366i	−0.265621	+	0.991310i
$189$		0			0
$190$	187.268	−	187.268i	0.985619	−	0.985619i
$191$	−129.028	−	223.482i	−0.675537	−	1.17006i	−0.976312	−	0.216369i	$-0.930579\pi$
$191$	−129.028	−	223.482i	−0.675537	−	1.17006i	0.300775	−	0.953695i	$-0.402755\pi$
$192$		0			0
$193$	−9.79118	−	36.5412i	−0.0507315	−	0.189333i	0.935910	−	0.352239i	$-0.114580\pi$
$193$	−9.79118	−	36.5412i	−0.0507315	−	0.189333i	−0.986641	+	0.162907i	$0.947913\pi$
$194$		−	353.145i		−	1.82034i
$195$		0			0
$196$	49.4151			0.252118
$197$	17.6223	−	4.72189i	0.0894534	−	0.0239690i	−0.213815	−	0.976874i	$-0.568589\pi$
$197$	17.6223	−	4.72189i	0.0894534	−	0.0239690i	0.303268	+	0.952905i	$0.401922\pi$
$198$		0			0
$199$	−113.637	+	65.6084i	−0.571040	+	0.329690i	−0.757565	−	0.652760i	$-0.773611\pi$
$199$	−113.637	+	65.6084i	−0.571040	+	0.329690i	0.186524	+	0.982450i	$0.440278\pi$
$200$	175.300	+	175.300i	0.876499	+	0.876499i
$201$		0			0
$202$	−92.1716	−	24.6973i	−0.456295	−	0.122264i
$203$	236.531	−	236.531i	1.16518	−	1.16518i
$204$		0			0
$205$	411.668	+	237.677i	2.00814	+	1.15940i
$206$	100.881	+	376.493i	0.489713	+	1.82763i
$207$		0			0
$208$	31.1597	−	29.2243i	0.149806	−	0.140501i
$209$	−122.939			−0.588227
$210$		0			0
$211$	−139.029	+	240.806i	−0.658907	+	1.14126i	0.321992	+	0.946742i	$0.395648\pi$
$211$	−139.029	+	240.806i	−0.658907	+	1.14126i	−0.980899	+	0.194518i	$0.937686\pi$
$212$	288.592	−	166.619i	1.36128	−	0.785938i
$213$		0			0
$214$	−0.416604	+	1.55479i	−0.00194675	+	0.00726537i
$215$	238.005	+	63.7732i	1.10700	+	0.296620i
$216$		0			0
$217$	30.5630	+	52.9366i	0.140843	+	0.243947i
$218$	−116.395	−	67.2006i	−0.533921	−	0.308260i
$219$		0			0
$220$		−	559.937i		−	2.54517i
$221$	−153.208	+	35.8336i	−0.693247	+	0.162143i
$222$		0			0
$223$	209.460	−	56.1247i	0.939283	−	0.251680i	0.243474	−	0.969907i	$-0.421713\pi$
$223$	209.460	−	56.1247i	0.939283	−	0.251680i	0.695809	+	0.718227i	$0.255046\pi$
$224$	139.695	−	241.959i	0.623639	−	1.08017i
$225$		0			0
$226$	232.570	+	232.570i	1.02907	+	1.02907i
$227$	42.8998	−	160.104i	0.188986	−	0.705305i	−0.804756	−	0.593605i	$-0.797704\pi$
$227$	42.8998	−	160.104i	0.188986	−	0.705305i	0.993742	−	0.111699i	$-0.0356293\pi$
$228$		0			0
$229$	161.998	−	161.998i	0.707415	−	0.707415i	−0.258576	−	0.965991i	$-0.583253\pi$
$229$	161.998	−	161.998i	0.707415	−	0.707415i	0.965991	+	0.258576i	$0.0832533\pi$
$230$	54.3647	+	94.1624i	0.236368	+	0.409402i
$231$		0			0
$232$	75.9821	+	283.569i	0.327509	+	1.22228i
$233$			262.925i			1.12843i	0.825626	+	0.564217i	$0.190822\pi$
$233$			262.925i			1.12843i	−0.825626	+	0.564217i	$0.809178\pi$
$234$		0			0
$235$	−250.289			−1.06506
$236$	82.0300	−	21.9799i	0.347585	−	0.0931350i
$237$		0			0
$238$	−251.606	+	145.265i	−1.05717	+	0.610357i
$239$	243.702	+	243.702i	1.01967	+	1.01967i	0.999803	+	0.0198720i	$0.00632586\pi$
$239$	243.702	+	243.702i	1.01967	+	1.01967i	0.0198720	+	0.999803i	$0.493674\pi$
$240$		0			0
$241$	−292.541	−	78.3860i	−1.21386	−	0.325253i	−0.405586	−	0.914057i	$-0.632932\pi$
$241$	−292.541	−	78.3860i	−1.21386	−	0.325253i	−0.808276	+	0.588804i	$0.799599\pi$
$242$	−32.7957	+	32.7957i	−0.135520	+	0.135520i
$243$		0			0
$244$	−443.377	−	255.984i	−1.81712	−	1.04911i
$245$	16.5911	+	61.9188i	0.0677188	+	0.252730i
$246$		0			0
$247$	−72.3955	+	116.599i	−0.293099	+	0.472063i
$248$	−53.6460			−0.216314
$249$		0			0
$250$	−155.240	+	268.884i	−0.620962	+	1.07554i
$251$	−178.992	+	103.341i	−0.713115	+	0.411717i	−0.812213	−	0.583360i	$-0.801738\pi$
$251$	−178.992	+	103.341i	−0.713115	+	0.411717i	0.0990983	+	0.995078i	$0.468404\pi$
$252$		0			0
$253$	13.0634	−	48.7533i	0.0516340	−	0.192701i
$254$	−717.003	−	192.120i	−2.82285	−	0.756379i
$255$		0			0
$256$	82.5869	+	143.045i	0.322605	+	0.558768i
$257$	149.916	+	86.5538i	0.583329	+	0.336785i	0.762455	−	0.647041i	$-0.223994\pi$
$257$	149.916	+	86.5538i	0.583329	+	0.336785i	−0.179126	+	0.983826i	$0.557327\pi$
$258$		0			0
$259$		−	248.505i		−	0.959478i
$260$	−531.061	−	329.731i	−2.04254	−	1.26820i
$261$		0			0
$262$	48.9896	−	13.1267i	0.186983	−	0.0501020i
$263$	72.7354	−	125.981i	0.276561	−	0.479017i	−0.693967	−	0.720007i	$-0.744139\pi$
$263$	72.7354	−	125.981i	0.276561	−	0.479017i	0.970528	+	0.240990i	$0.0774720\pi$
$264$		0			0
$265$	305.674	+	305.674i	1.15349	+	1.15349i
$266$	−65.5907	+	244.788i	−0.246582	+	0.920255i
$267$		0			0
$268$	277.394	−	277.394i	1.03505	−	1.03505i
$269$	−45.7415	−	79.2267i	−0.170043	−	0.294523i	0.768392	−	0.639980i	$-0.221057\pi$
$269$	−45.7415	−	79.2267i	−0.170043	−	0.294523i	−0.938435	+	0.345457i	$0.887724\pi$
$270$		0			0
$271$	−98.2045	−	366.504i	−0.362378	−	1.35241i	−0.870940	−	0.491389i	$-0.836489\pi$
$271$	−98.2045	−	366.504i	−0.362378	−	1.35241i	0.508562	−	0.861025i	$-0.330177\pi$
$272$			39.7730i			0.146224i
$273$		0			0
$274$	−10.7123			−0.0390959
$275$	420.418	−	112.651i	1.52879	−	0.409639i
$276$		0			0
$277$	212.035	−	122.418i	0.765468	−	0.441943i	−0.0657877	−	0.997834i	$-0.520956\pi$
$277$	212.035	−	122.418i	0.765468	−	0.441943i	0.831255	+	0.555891i	$0.187623\pi$
$278$	−81.5614	−	81.5614i	−0.293386	−	0.293386i
$279$		0			0
$280$	−382.410	−	102.466i	−1.36575	−	0.365951i
$281$	307.450	−	307.450i	1.09413	−	1.09413i	0.0990449	−	0.995083i	$-0.468421\pi$
$281$	307.450	−	307.450i	1.09413	−	1.09413i	0.995083	−	0.0990449i	$-0.0315787\pi$
$282$		0			0
$283$	−398.777	−	230.234i	−1.40911	−	0.813548i	−0.413804	−	0.910366i	$-0.635800\pi$
$283$	−398.777	−	230.234i	−1.40911	−	0.813548i	−0.995302	+	0.0968187i	$0.969133\pi$
$284$	−90.1164	−	336.319i	−0.317311	−	1.18422i
$285$		0			0
$286$	109.504	+	468.187i	0.382881	+	1.63702i
$287$	−454.868			−1.58491
$288$		0			0
$289$	−71.2555	+	123.418i	−0.246559	+	0.427053i
$290$	−961.553	+	555.153i	−3.31570	+	1.91432i
$291$		0			0
$292$	−122.481	+	457.106i	−0.419456	+	1.56543i
$293$	146.553	+	39.2688i	0.500181	+	0.134023i	0.500084	−	0.865977i	$-0.333302\pi$
$293$	146.553	+	39.2688i	0.500181	+	0.134023i	9.70470e−5		1.00000i	$0.499969\pi$
$294$		0			0
$295$	55.0830	+	95.4066i	0.186722	+	0.323412i
$296$	188.876	+	109.048i	0.638095	+	0.368404i
$297$		0			0
$298$			456.680i			1.53248i
$299$	−38.5465	−	41.0992i	−0.128918	−	0.137456i
$300$		0			0
$301$	−227.748	+	61.0249i	−0.756637	+	0.202740i
$302$	−269.605	+	466.969i	−0.892730	+	1.54625i
$303$		0			0
$304$	24.5317	+	24.5317i	0.0806965	+	0.0806965i
$305$	171.893	−	641.512i	0.563583	−	2.10332i
$306$		0			0
$307$	326.284	−	326.284i	1.06281	−	1.06281i	0.0649236	−	0.997890i	$-0.479320\pi$
$307$	326.284	−	326.284i	1.06281	−	1.06281i	0.997890	−	0.0649236i	$-0.0206804\pi$
$308$	267.903	+	464.021i	0.869815	+	1.50656i
$309$		0			0
$310$	−52.5123	−	195.979i	−0.169395	−	0.632189i
$311$			0.599099i			0.00192636i	1.00000		0.000963181i	$0.000306590\pi$
$311$			0.599099i			0.00192636i	−1.00000		0.000963181i	$0.999693\pi$
$312$		0			0
$313$	−20.6721			−0.0660452			−0.0330226	−	0.999455i	$-0.510513\pi$
$313$	−20.6721			−0.0660452			−0.0330226	+	0.999455i	$0.510513\pi$
$314$	47.3738	−	12.6938i	0.150872	−	0.0404261i
$315$		0			0
$316$	−237.429	+	137.080i	−0.751359	+	0.433797i
$317$	180.500	+	180.500i	0.569402	+	0.569402i	0.931961	−	0.362559i	$-0.118097\pi$
$317$	180.500	+	180.500i	0.569402	+	0.569402i	−0.362559	+	0.931961i	$0.618097\pi$
$318$		0			0
$319$	497.852	+	133.399i	1.56066	+	0.418178i
$320$	−582.338	+	582.338i	−1.81981	+	1.81981i
$321$		0			0
$322$	−90.1044	−	52.0218i	−0.279827	−	0.161558i
$323$	−33.0717	−	123.425i	−0.102389	−	0.382121i
$324$		0			0
$325$	140.731	−	465.074i	0.433019	−	1.43100i
$326$	876.034			2.68722
$327$		0			0
$328$	199.603	−	345.723i	0.608546	−	1.05403i
$329$	207.416	−	119.752i	0.630443	−	0.363986i
$330$		0			0
$331$	36.2685	−	135.356i	0.109572	−	0.408930i	−0.889251	−	0.457419i	$-0.848774\pi$
$331$	36.2685	−	135.356i	0.109572	−	0.408930i	0.998824	+	0.0484891i	$0.0154406\pi$
$332$	256.442	+	68.7135i	0.772417	+	0.206968i
$333$		0			0
$334$	−407.951	−	706.593i	−1.22141	−	2.11555i
$335$	440.719	+	254.449i	1.31558	+	0.759549i
$336$		0			0
$337$			294.586i			0.874142i	0.899427	+	0.437071i	$0.143984\pi$
$337$			294.586i			0.874142i	−0.899427	+	0.437071i	$0.856016\pi$
$338$	508.527	+	171.845i	1.50452	+	0.508418i
$339$		0			0
$340$	562.149	−	150.627i	1.65338	−	0.443022i
$341$	−47.0921	+	81.5660i	−0.138100	+	0.239196i
$342$		0			0
$343$	218.481	+	218.481i	0.636972	+	0.636972i
$344$	53.5573	−	199.879i	0.155690	−	0.581042i
$345$		0			0
$346$	−563.502	+	563.502i	−1.62862	+	1.62862i
$347$	−181.324	−	314.062i	−0.522547	−	0.905078i	−0.999656	−	0.0262339i	$-0.991649\pi$
$347$	−181.324	−	314.062i	−0.522547	−	0.905078i	0.477109	−	0.878844i	$-0.341685\pi$
$348$		0			0
$349$	−109.728	−	409.510i	−0.314407	−	1.17338i	−0.924541	−	0.381083i	$-0.875551\pi$
$349$	−109.728	−	409.510i	−0.314407	−	1.17338i	0.610134	−	0.792298i	$-0.291115\pi$
$350$		−	897.208i		−	2.56345i
$351$		0			0
$352$	430.491			1.22299
$353$	−203.861	+	54.6243i	−0.577509	+	0.154743i	−0.535738	−	0.844384i	$-0.679967\pi$
$353$	−203.861	+	54.6243i	−0.577509	+	0.154743i	−0.0417709	+	0.999127i	$0.513300\pi$
$354$		0			0
$355$	391.162	−	225.838i	1.10187	−	0.636163i
$356$	−97.2521	−	97.2521i	−0.273180	−	0.273180i
$357$		0			0
$358$	−26.2123	−	7.02357i	−0.0732188	−	0.0196189i
$359$	−297.929	+	297.929i	−0.829885	+	0.829885i	−0.987501	−	0.157615i	$-0.949619\pi$
$359$	−297.929	+	297.929i	−0.829885	+	0.829885i	0.157615	+	0.987501i	$0.449619\pi$
$360$		0			0
$361$	216.109	+	124.771i	0.598640	+	0.345625i
$362$	−20.2288	−	75.4951i	−0.0558808	−	0.208550i
$363$		0			0
$364$	597.853	+	19.1619i	1.64245	+	0.0526424i
$365$	−613.892			−1.68190
$366$		0			0
$367$	−280.845	+	486.438i	−0.765246	+	1.32544i	0.174871	+	0.984591i	$0.444049\pi$
$367$	−280.845	+	486.438i	−0.765246	+	1.32544i	−0.940117	+	0.340853i	$0.889284\pi$
$368$	−12.3351	+	7.12169i	−0.0335193	+	0.0193524i
$369$		0			0
$370$	−213.487	+	796.743i	−0.576991	+	2.15336i
$371$	−399.563	−	107.063i	−1.07699	−	0.288578i
$372$		0			0
$373$	189.783	+	328.714i	0.508801	+	0.881270i	0.999948	+	0.0101929i	$0.00324457\pi$
$373$	189.783	+	328.714i	0.508801	+	0.881270i	−0.491147	+	0.871077i	$0.663422\pi$
$374$	−387.681	−	223.828i	−1.03658	−	0.598470i
$375$		0			0
$376$			210.195i			0.559030i
$377$	419.690	−	393.623i	1.11324	−	1.04409i
$378$		0			0
$379$	−474.306	+	127.090i	−1.25147	+	0.335330i	−0.822903	−	0.568181i	$-0.807647\pi$
$379$	−474.306	+	127.090i	−1.25147	+	0.335330i	−0.428564	+	0.903511i	$0.640980\pi$
$380$	253.824	−	439.636i	0.667958	−	1.15694i
$381$		0			0
$382$	−579.570	−	579.570i	−1.51720	−	1.51720i
$383$	−155.600	+	580.707i	−0.406266	+	1.51621i	0.395443	+	0.918491i	$0.370591\pi$
$383$	−155.600	+	580.707i	−0.406266	+	1.51621i	−0.801709	+	0.597715i	$0.796076\pi$
$384$		0			0
$385$	−491.486	+	491.486i	−1.27659	+	1.27659i
$386$	−60.0782	−	104.058i	−0.155643	−	0.269582i
$387$		0			0
$388$	−175.200	−	653.856i	−0.451547	−	1.68519i
$389$			78.5941i			0.202041i	0.994884	+	0.101021i	$0.0322108\pi$
$389$			78.5941i			0.202041i	−0.994884	+	0.101021i	$0.967789\pi$
$390$		0			0
$391$	52.4601			0.134169
$392$	52.0000	−	13.9333i	0.132653	−	0.0355442i
$393$		0			0
$394$	50.1832	−	28.9733i	0.127368	−	0.0735362i
$395$	−251.483	−	251.483i	−0.636665	−	0.636665i
$396$		0			0
$397$	−665.065	−	178.204i	−1.67523	−	0.448875i	−0.708713	−	0.705496i	$-0.750724\pi$
$397$	−665.065	−	178.204i	−1.67523	−	0.448875i	−0.966512	+	0.256621i	$0.917391\pi$
$398$	−294.701	+	294.701i	−0.740456	+	0.740456i
$399$		0			0
$400$	−106.370	−	61.4130i	−0.265926	−	0.153532i
$401$	137.621	+	513.607i	0.343194	+	1.28082i	0.894708	+	0.446651i	$0.147384\pi$
$401$	137.621	+	513.607i	0.343194	+	1.28082i	−0.551514	+	0.834165i	$0.685950\pi$
$402$		0			0
$403$	49.6284	+	92.6955i	0.123147	+	0.230014i
$404$	−182.910			−0.452748
$405$		0			0
$406$	531.228	−	920.114i	1.30844	−	2.26629i
$407$	331.603	−	191.451i	0.814749	−	0.470396i
$408$		0			0
$409$	180.997	−	675.491i	0.442536	−	1.65157i	−0.279825	−	0.960051i	$-0.590277\pi$
$409$	180.997	−	675.491i	0.442536	−	1.65157i	0.722361	−	0.691516i	$-0.243057\pi$
$410$	1458.37	+	390.770i	3.55701	+	0.953098i
$411$		0			0
$412$	373.566	+	647.036i	0.906714	+	1.57048i
$413$	−91.2950	−	52.7092i	−0.221053	−	0.127625i
$414$		0			0
$415$			344.402i			0.829883i
$416$	253.504	−	408.291i	0.609385	−	0.981468i
$417$		0			0
$418$	−377.175	+	101.064i	−0.902332	+	0.241779i
$419$	180.258	−	312.217i	0.430211	−	0.745147i	−0.566680	−	0.823938i	$-0.691773\pi$
$419$	180.258	−	312.217i	0.430211	−	0.745147i	0.996891	+	0.0787906i	$0.0251058\pi$
$420$		0			0
$421$	−326.554	−	326.554i	−0.775663	−	0.775663i	0.203427	−	0.979090i	$-0.434792\pi$
$421$	−326.554	−	326.554i	−0.775663	−	0.775663i	−0.979090	+	0.203427i	$0.934792\pi$
$422$	−228.581	+	853.077i	−0.541662	+	2.02151i
$423$		0			0
$424$	256.707	−	256.707i	0.605442	−	0.605442i
$425$	226.192	+	391.775i	0.532216	+	0.921825i
$426$		0			0
$427$	164.485	+	613.866i	0.385210	+	1.43762i
$428$			3.08541i			0.00720890i
$429$		0			0
$430$	782.619			1.82004
$431$	−11.1213	+	2.97995i	−0.0258035	+	0.00691403i	−0.271698	−	0.962383i	$-0.587585\pi$
$431$	−11.1213	+	2.97995i	−0.0258035	+	0.00691403i	0.245894	+	0.969297i	$0.420918\pi$
$432$		0			0
$433$	−348.424	+	201.163i	−0.804675	+	0.464579i	−0.845103	−	0.534603i	$-0.820461\pi$
$433$	−348.424	+	201.163i	−0.804675	+	0.464579i	0.0404284	+	0.999182i	$0.487128\pi$
$434$	137.284	+	137.284i	0.316322	+	0.316322i
$435$		0			0
$436$	−248.847	−	66.6783i	−0.570750	−	0.152932i
$437$	32.3571	−	32.3571i	0.0740436	−	0.0740436i
$438$		0			0
$439$	611.317	+	352.944i	1.39252	+	0.803973i	0.993594	−	0.113009i	$-0.0360490\pi$
$439$	611.317	+	352.944i	1.39252	+	0.803973i	0.398928	+	0.916982i	$0.369382\pi$
$440$	−157.883	−	589.226i	−0.358824	−	1.33915i
$441$		0			0
$442$	−440.580	+	235.883i	−0.996787	+	0.533672i
$443$	−47.8296			−0.107968			−0.0539838	−	0.998542i	$-0.517192\pi$
$443$	−47.8296			−0.107968			−0.0539838	+	0.998542i	$0.517192\pi$
$444$		0			0
$445$	89.2078	−	154.513i	0.200467	−	0.347219i
$446$	596.480	−	344.378i	1.33740	−	0.772148i
$447$		0			0
$448$	203.965	−	761.206i	0.455278	−	1.69912i
$449$	−449.516	−	120.447i	−1.00115	−	0.268257i	−0.279222	−	0.960227i	$-0.590076\pi$
$449$	−449.516	−	120.447i	−1.00115	−	0.268257i	−0.721926	+	0.691970i	$0.756743\pi$
$450$		0			0
$451$	−350.436	−	606.973i	−0.777020	−	1.34584i
$452$	545.989	+	315.227i	1.20794	+	0.697405i
$453$		0			0
$454$		−	526.462i		−	1.15961i
$455$	176.718	+	755.563i	0.388392	+	1.66058i
$456$		0			0
$457$	202.908	−	54.3691i	0.444001	−	0.118970i	−0.0298902	−	0.999553i	$-0.509516\pi$
$457$	202.908	−	54.3691i	0.444001	−	0.118970i	0.473891	+	0.880584i	$0.342849\pi$
$458$	363.833	−	630.178i	0.794396	−	1.37593i
$459$		0			0
$460$	147.373	+	147.373i	0.320375	+	0.320375i
$461$	220.190	−	821.759i	0.477635	−	1.78256i	−0.133520	−	0.991046i	$-0.542628\pi$
$461$	220.190	−	821.759i	0.477635	−	1.78256i	0.611154	−	0.791511i	$-0.290705\pi$
$462$		0			0
$463$	167.655	−	167.655i	0.362107	−	0.362107i	−0.502481	−	0.864588i	$-0.667579\pi$
$463$	167.655	−	167.655i	0.362107	−	0.362107i	0.864588	+	0.502481i	$0.167579\pi$
$464$	−72.7241	−	125.962i	−0.156733	−	0.271470i
$465$		0			0
$466$	216.141	+	806.648i	0.463821	+	1.73100i
$467$			577.797i			1.23725i	0.785685	+	0.618627i	$0.212311\pi$
$467$			577.797i			1.23725i	−0.785685	+	0.618627i	$0.787689\pi$
$468$		0			0
$469$	−486.967			−1.03831
$470$	−767.882	+	205.753i	−1.63379	+	0.437773i
$471$		0			0
$472$	80.1233	−	46.2592i	0.169753	−	0.0980068i
$473$	−256.891	−	256.891i	−0.543110	−	0.543110i
$474$		0			0
$475$	381.158	+	102.131i	0.802438	+	0.215013i
$476$	−393.787	+	393.787i	−0.827283	+	0.827283i
$477$		0			0
$478$	948.011	+	547.334i	1.98329	+	1.14505i
$479$	−49.3930	−	184.337i	−0.103117	−	0.384838i	0.895008	−	0.446050i	$-0.147170\pi$
$479$	−49.3930	−	184.337i	−0.103117	−	0.384838i	−0.998125	+	0.0612129i	$0.980503\pi$
$480$		0			0
$481$	13.6936	−	427.242i	0.0284690	−	0.888238i
$482$	−961.946			−1.99574
$483$		0			0
$484$	−44.4516	+	76.9924i	−0.0918421	+	0.159075i
$485$	760.480	−	439.063i	1.56800	−	0.905285i
$486$		0			0
$487$	−186.160	+	694.760i	−0.382259	+	1.42661i	0.460183	+	0.887824i	$0.347784\pi$
$487$	−186.160	+	694.760i	−0.382259	+	1.42661i	−0.842442	+	0.538787i	$0.818883\pi$
$488$	−538.747	−	144.357i	−1.10399	−	0.295813i
$489$		0			0
$490$	101.802	+	176.327i	0.207760	+	0.359850i
$491$	−840.518	−	485.273i	−1.71185	−	0.988336i	−0.932068	−	0.362283i	$-0.881997\pi$
$491$	−840.518	−	485.273i	−1.71185	−	0.988336i	−0.779781	−	0.626053i	$-0.784669\pi$
$492$		0			0
$493$			535.704i			1.08662i
$494$	−126.256	+	417.238i	−0.255578	+	0.844611i
$495$		0			0
$496$	25.6729	−	6.87903i	0.0517598	−	0.0138690i
$497$	−216.105	+	374.305i	−0.434819	+	0.753129i
$498$		0			0
$499$	−394.571	−	394.571i	−0.790723	−	0.790723i	0.190889	−	0.981612i	$-0.438863\pi$
$499$	−394.571	−	394.571i	−0.790723	−	0.790723i	−0.981612	+	0.190889i	$0.938863\pi$
$500$	−154.034	+	574.862i	−0.308068	+	1.14972i
$501$		0			0
$502$	−464.190	+	464.190i	−0.924681	+	0.924681i
$503$	464.382	+	804.333i	0.923225	+	1.59907i	0.794392	+	0.607406i	$0.207790\pi$
$503$	464.382	+	804.333i	0.923225	+	1.59907i	0.128833	+	0.991666i	$0.458877\pi$
$504$		0			0
$505$	−61.4120	−	229.193i	−0.121608	−	0.453847i
$506$		−	160.313i		−	0.316824i
$507$		0			0
$508$	−1422.86			−2.80090
$509$	423.307	−	113.425i	0.831645	−	0.222839i	0.182214	−	0.983259i	$-0.441674\pi$
$509$	423.307	−	113.425i	0.831645	−	0.222839i	0.649431	+	0.760420i	$0.275007\pi$
$510$		0			0
$511$	508.735	−	293.718i	0.995567	−	0.574791i
$512$	−147.550	−	147.550i	−0.288184	−	0.288184i
$513$		0			0
$514$	531.090	+	142.305i	1.03325	+	0.276858i
$515$	−685.333	+	685.333i	−1.33074	+	1.33074i
$516$		0			0
$517$	319.591	+	184.516i	0.618165	+	0.356898i
$518$	−204.286	−	762.406i	−0.394375	−	1.47183i
$519$		0			0
$520$	−651.813	−	197.238i	−1.25349	−	0.379304i
$521$	−100.115			−0.192160			−0.0960801	−	0.995374i	$-0.530630\pi$
$521$	−100.115			−0.192160			−0.0960801	+	0.995374i	$0.530630\pi$
$522$		0			0
$523$	29.0666	−	50.3449i	0.0555767	−	0.0962617i	−0.836899	−	0.547358i	$-0.815634\pi$
$523$	29.0666	−	50.3449i	0.0555767	−	0.0962617i	0.892475	+	0.451096i	$0.148967\pi$
$524$	84.1929	−	48.6088i	0.160673	−	0.0927649i
$525$		0			0
$526$	119.586	−	446.301i	0.227350	−	0.848481i
$527$	−94.5564	−	25.3363i	−0.179424	−	0.0480765i
$528$		0			0
$529$	−255.107	−	441.858i	−0.482243	−	0.835269i
$530$	1189.08	+	686.517i	2.24355	+	1.29531i
$531$		0			0
$532$			485.770i			0.913102i
$533$	−782.033	−	25.0650i	−1.46723	−	0.0470264i
$534$		0			0
$535$	−3.86612	+	1.03592i	−0.00722640	+	0.00193631i
$536$	213.688	−	370.119i	0.398672	−	0.690521i
$537$		0			0
$538$	−205.463	−	205.463i	−0.381902	−	0.381902i
$539$	24.4623	−	91.2944i	0.0453845	−	0.169377i
$540$		0			0
$541$	−164.770	+	164.770i	−0.304566	+	0.304566i	−0.842797	−	0.538231i	$-0.819093\pi$
$541$	−164.770	+	164.770i	−0.304566	+	0.304566i	0.538231	+	0.842797i	$0.319093\pi$
$542$	−602.578	−	1043.70i	−1.11177	−	1.92564i
$543$		0			0
$544$	115.805	+	432.192i	0.212878	+	0.794470i
$545$		−	334.201i		−	0.613212i
$546$		0			0
$547$	−503.473			−0.920426			−0.460213	−	0.887809i	$-0.652227\pi$
$547$	−503.473			−0.920426			−0.460213	+	0.887809i	$0.652227\pi$
$548$	−19.8340	+	5.31451i	−0.0361934	+	0.00969800i
$549$		0			0
$550$	1197.23	−	691.219i	2.17678	−	1.25676i
$551$	330.419	+	330.419i	0.599671	+	0.599671i
$552$		0			0
$553$	328.727	+	88.0821i	0.594443	+	0.159280i
$554$	549.881	−	549.881i	0.992566	−	0.992566i
$555$		0			0
$556$	−191.476	−	110.549i	−0.344382	−	0.198829i
$557$	36.2263	+	135.199i	0.0650383	+	0.242726i	0.990790	−	0.135405i	$-0.0432335\pi$
$557$	36.2263	+	135.199i	0.0650383	+	0.242726i	−0.925752	+	0.378131i	$0.876567\pi$
$558$		0			0
$559$	−394.919	+	92.3673i	−0.706474	+	0.165237i
$560$	196.146			0.350260
$561$		0			0
$562$	690.506	−	1195.99i	1.22866	−	2.12810i
$563$	−135.385	+	78.1645i	−0.240471	+	0.138836i	−0.615393	−	0.788220i	$-0.711003\pi$
$563$	−135.385	+	78.1645i	−0.240471	+	0.138836i	0.374922	+	0.927056i	$0.377669\pi$
$564$		0			0
$565$	−211.675	+	789.980i	−0.374645	+	1.39820i
$566$	−1412.70	−	378.533i	−2.49594	−	0.668786i
$567$		0			0
$568$	−189.660	−	328.502i	−0.333909	−	0.578348i
$569$	584.405	+	337.406i	1.02707	+	0.592981i	0.916145	−	0.400847i	$-0.131284\pi$
$569$	584.405	+	337.406i	1.02707	+	0.592981i	0.110929	+	0.993828i	$0.464617\pi$
$570$		0			0
$571$		−	54.2917i		−	0.0950817i	−0.998869	−	0.0475409i	$-0.984862\pi$
$571$		−	54.2917i		−	0.0950817i	0.998869	−	0.0475409i	$-0.0151384\pi$
$572$	435.023	+	812.533i	0.760530	+	1.42051i
$573$		0			0
$574$	−1395.52	+	373.930i	−2.43123	+	0.651445i
$575$	−81.0030	+	140.301i	−0.140875	+	0.244002i
$576$		0			0
$577$	323.049	+	323.049i	0.559877	+	0.559877i	0.929272	−	0.369395i	$-0.120435\pi$
$577$	323.049	+	323.049i	0.559877	+	0.559877i	−0.369395	+	0.929272i	$0.620435\pi$
$578$	−117.153	+	437.220i	−0.202687	+	0.756437i
$579$		0			0
$580$	−1504.92	+	1504.92i	−2.59469	+	2.59469i
$581$	−164.780	−	285.407i	−0.283614	−	0.491234i
$582$		0			0
$583$	−164.965	−	615.656i	−0.282958	−	1.05601i
$584$			515.552i			0.882795i
$585$		0			0
$586$	481.903			0.822359
$587$	−250.071	+	67.0064i	−0.426016	+	0.114151i	−0.465455	−	0.885071i	$-0.654109\pi$
$587$	−250.071	+	67.0064i	−0.426016	+	0.114151i	0.0394395	+	0.999222i	$0.487443\pi$
$588$		0			0
$589$	−73.9490	+	42.6945i	−0.125550	+	0.0724864i
$590$	247.423	+	247.423i	0.419362	+	0.419362i
$591$		0			0
$592$	−104.372	−	27.9664i	−0.176304	−	0.0472405i
$593$	487.207	−	487.207i	0.821597	−	0.821597i	−0.164740	−	0.986337i	$-0.552678\pi$
$593$	487.207	−	487.207i	0.821597	−	0.821597i	0.986337	+	0.164740i	$0.0526785\pi$
$594$		0			0
$595$	−625.642	−	361.215i	−1.05150	−	0.607083i
$596$	226.565	+	845.554i	0.380143	+	1.41871i
$597$		0			0
$598$	−152.046	−	94.4038i	−0.254257	−	0.157866i
$599$	133.236			0.222431			0.111215	−	0.993796i	$-0.464526\pi$
$599$	133.236			0.222431			0.111215	+	0.993796i	$0.464526\pi$
$600$		0			0
$601$	441.546	−	764.780i	0.734685	−	1.27251i	−0.220176	−	0.975460i	$-0.570663\pi$
$601$	441.546	−	764.780i	0.734685	−	1.27251i	0.954861	−	0.297052i	$-0.0960034\pi$
$602$	−648.559	+	374.446i	−1.07734	+	0.622003i
$603$		0			0
$604$	−267.509	+	998.357i	−0.442896	+	1.65291i
$605$	−111.399	−	29.8492i	−0.184130	−	0.0493375i
$606$		0			0
$607$	263.803	+	456.920i	0.434601	+	0.752750i	0.997263	−	0.0739364i	$-0.0235562\pi$
$607$	263.803	+	456.920i	0.434601	+	0.752750i	−0.562662	+	0.826687i	$0.690223\pi$
$608$	338.001	+	195.145i	0.555923	+	0.320962i
$609$		0			0
$610$		−	2109.45i		−	3.45811i
$611$	363.199	−	194.454i	0.594433	−	0.318255i
$612$		0			0
$613$	1083.07	−	290.208i	1.76684	−	0.473423i	0.778752	−	0.627331i	$-0.215853\pi$
$613$	1083.07	−	290.208i	1.76684	−	0.473423i	0.988085	+	0.153909i	$0.0491862\pi$
$614$	732.805	−	1269.26i	1.19349	−	2.06719i
$615$		0			0
$616$	412.754	+	412.754i	0.670056	+	0.670056i
$617$	−82.7504	+	308.829i	−0.134117	+	0.500533i	0.865883	+	0.500247i	$0.166758\pi$
$617$	−82.7504	+	308.829i	−0.134117	+	0.500533i	−1.00000		0.000285474i	$0.999909\pi$
$618$		0			0
$619$	133.111	−	133.111i	0.215042	−	0.215042i	−0.591363	−	0.806405i	$-0.701410\pi$
$619$	133.111	−	133.111i	0.215042	−	0.215042i	0.806405	+	0.591363i	$0.201410\pi$
$620$	−194.455	−	336.807i	−0.313638	−	0.543236i
$621$		0			0
$622$	0.492496	+	1.83802i	0.000791794	+	0.00295502i
$623$			170.727i			0.274040i
$624$		0			0
$625$	162.386			0.259818
$626$	−63.4216	+	16.9938i	−0.101313	+	0.0271466i
$627$		0			0
$628$	81.4161	−	47.0056i	0.129643	−	0.0748497i
$629$	281.411	+	281.411i	0.447395	+	0.447395i
$630$		0			0
$631$	235.685	+	63.1517i	0.373511	+	0.100082i	0.440691	−	0.897659i	$-0.354734\pi$
$631$	235.685	+	63.1517i	0.373511	+	0.100082i	−0.0671801	+	0.997741i	$0.521400\pi$
$632$	−211.197	+	211.197i	−0.334173	+	0.334173i
$633$		0			0
$634$	702.153	+	405.388i	1.10750	+	0.639414i
$635$	−477.724	−	1782.89i	−0.752322	−	2.80770i
$636$		0			0
$637$	−72.1813	−	76.9615i	−0.113314	−	0.120819i
$638$	1637.06			2.56592
$639$		0			0
$640$	−723.935	+	1253.89i	−1.13115	+	1.95921i
$641$	−394.159	+	227.568i	−0.614913	+	0.355020i	−0.774886	−	0.632101i	$-0.782193\pi$
$641$	−394.159	+	227.568i	−0.614913	+	0.355020i	0.159973	+	0.987121i	$0.448859\pi$
$642$		0			0
$643$	−54.7147	+	204.198i	−0.0850928	+	0.317571i	−0.995332	−	0.0965128i	$-0.969231\pi$
$643$	−54.7147	+	204.198i	−0.0850928	+	0.317571i	0.910239	+	0.414083i	$0.135898\pi$
$644$	−192.639	−	51.6175i	−0.299129	−	0.0801514i
$645$		0			0
$646$	−202.926	−	351.478i	−0.314127	−	0.544084i
$647$	725.468	+	418.849i	1.12128	+	0.647371i	0.941727	−	0.336378i	$-0.109202\pi$
$647$	725.468	+	418.849i	1.12128	+	0.647371i	0.179552	+	0.983748i	$0.442535\pi$
$648$		0			0
$649$		−	162.431i		−	0.250279i
$650$	49.4397	−	1542.53i	0.0760611	−	2.37312i
$651$		0			0
$652$	1622.00	−	434.612i	2.48772	−	0.666584i
$653$	250.703	−	434.229i	0.383924	−	0.664976i	−0.607695	−	0.794170i	$-0.707906\pi$
$653$	250.703	−	434.229i	0.383924	−	0.664976i	0.991619	+	0.129194i	$0.0412391\pi$
$654$		0			0
$655$	89.1762	+	89.1762i	0.136147	+	0.136147i
$656$	−51.1902	+	191.045i	−0.0780339	+	0.291226i
$657$		0			0
$658$	537.903	−	537.903i	0.817482	−	0.817482i
$659$	305.919	+	529.868i	0.464217	+	0.804048i	0.999166	−	0.0408366i	$-0.0130023\pi$
$659$	305.919	+	529.868i	0.464217	+	0.804048i	−0.534948	+	0.844885i	$0.679669\pi$
$660$		0			0
$661$	161.747	+	603.648i	0.244700	+	0.913235i	0.973534	+	0.228543i	$0.0733963\pi$
$661$	161.747	+	603.648i	0.244700	+	0.913235i	−0.728833	+	0.684691i	$0.759937\pi$
$662$		−	445.083i		−	0.672331i
$663$		0			0
$664$	289.231			0.435589
$665$	−608.687	+	163.097i	−0.915318	+	0.245259i
$666$		0			0
$667$	−166.142	+	95.9222i	−0.249089	+	0.143811i
$668$	−1105.88	−	1105.88i	−1.65551	−	1.65551i
$669$		0			0
$670$	1561.29	+	418.346i	2.33028	+	0.624396i
$671$	−692.417	+	692.417i	−1.03192	+	1.03192i
$672$		0			0
$673$	160.099	+	92.4331i	0.237888	+	0.137345i	0.614206	−	0.789146i	$-0.289476\pi$
$673$	160.099	+	92.4331i	0.237888	+	0.137345i	−0.376317	+	0.926491i	$0.622810\pi$
$674$	242.168	+	903.782i	0.359299	+	1.34092i
$675$		0			0
$676$	1026.80	+	65.8881i	1.51894	+	0.0974677i
$677$	984.771			1.45461			0.727305	−	0.686315i	$-0.240773\pi$
$677$	984.771			1.45461			0.727305	+	0.686315i	$0.240773\pi$
$678$		0			0
$679$	−420.142	+	727.707i	−0.618765	+	1.07173i
$680$	549.083	−	317.013i	0.807474	−	0.466196i
$681$		0			0
$682$	−77.4253	+	288.955i	−0.113527	+	0.423688i
$683$	1103.55	+	295.696i	1.61574	+	0.432937i	0.949746	−	0.313020i	$-0.101341\pi$
$683$	1103.55	+	295.696i	1.61574	+	0.432937i	0.665995	+	0.745957i	$0.268007\pi$
$684$		0			0
$685$	−13.3185	−	23.0683i	−0.0194431	−	0.0336764i
$686$	849.900	+	490.690i	1.23892	+	0.715292i
$687$		0			0
$688$			102.522i			0.149014i
$689$	−681.050	−	206.085i	−0.988462	−	0.299108i
$690$		0			0
$691$	703.381	−	188.470i	1.01792	−	0.272750i	0.288984	−	0.957334i	$-0.406683\pi$
$691$	703.381	−	188.470i	1.01792	−	0.272750i	0.728934	+	0.684584i	$0.240016\pi$
$692$	−763.774	+	1322.90i	−1.10372	+	1.91170i
$693$		0			0
$694$	−814.476	−	814.476i	−1.17360	−	1.17360i
$695$	74.2335	−	277.043i	0.106811	−	0.398623i
$696$		0			0
$697$	515.101	−	515.101i	0.739026	−	0.739026i
$698$	−673.285	−	1166.16i	−0.964592	−	1.67072i
$699$		0			0
$700$	−445.117	−	1661.20i	−0.635881	−	2.37314i
$701$			973.569i			1.38883i	0.719575	+	0.694415i	$0.244337\pi$
$701$			973.569i			1.38883i	−0.719575	+	0.694415i	$0.755663\pi$
$702$		0			0
$703$	347.145			0.493806
$704$	1172.88	−	314.274i	1.66603	−	0.446411i
$705$		0			0
$706$	−580.535	+	335.172i	−0.822288	+	0.474748i
$707$	160.550	+	160.550i	0.227087	+	0.227087i
$708$		0			0
$709$	−161.771	−	43.3463i	−0.228167	−	0.0611372i	0.142924	−	0.989734i	$-0.454350\pi$
$709$	−161.771	−	43.3463i	−0.228167	−	0.0611372i	−0.371091	+	0.928596i	$0.621016\pi$
$710$	1014.42	−	1014.42i	1.42877	−	1.42877i
$711$		0			0
$712$	−129.761	−	74.9175i	−0.182249	−	0.105221i
$713$	−9.07335	−	33.8622i	−0.0127256	−	0.0474926i
$714$		0			0
$715$	−872.072	+	817.907i	−1.21968	+	1.14393i
$716$	−52.0172			−0.0726497
$717$		0			0
$718$	−669.122	+	1158.95i	−0.931925	+	1.61414i
$719$	−536.036	+	309.481i	−0.745530	+	0.430432i	−0.824077	−	0.566478i	$-0.808306\pi$
$719$	−536.036	+	309.481i	−0.745530	+	0.430432i	0.0785462	+	0.996910i	$0.474972\pi$
$720$		0			0
$721$	240.039	−	895.837i	0.332925	−	1.24249i
$722$	765.586	+	205.138i	1.06037	+	0.284125i
$723$		0			0
$724$	−74.9083	−	129.745i	−0.103465	−	0.179206i
$725$	−1432.71	−	827.173i	−1.97615	−	1.14093i
$726$		0			0
$727$		−	58.7377i		−	0.0807946i	−0.999184	−	0.0403973i	$-0.987138\pi$
$727$		−	58.7377i		−	0.0807946i	0.999184	−	0.0403973i	$-0.0128624\pi$
$728$	634.528	−	148.409i	0.871605	−	0.203859i
$729$		0			0
$730$	−1883.41	+	504.657i	−2.58001	+	0.691311i
$731$	188.800	−	327.011i	0.258277	−	0.447348i
$732$		0			0
$733$	−114.680	−	114.680i	−0.156453	−	0.156453i	0.624540	−	0.780993i	$-0.285287\pi$
$733$	−114.680	−	114.680i	−0.156453	−	0.156453i	−0.780993	+	0.624540i	$0.785287\pi$
$734$	−461.744	+	1723.25i	−0.629079	+	2.34775i
$735$		0			0
$736$	−113.303	+	113.303i	−0.153945	+	0.153945i
$737$	−375.165	−	649.805i	−0.509043	−	0.881689i
$738$		0			0
$739$	49.4982	+	184.730i	0.0669800	+	0.249973i	0.991295	−	0.131657i	$-0.0420297\pi$
$739$	49.4982	+	184.730i	0.0669800	+	0.249973i	−0.924315	+	0.381629i	$0.875363\pi$
$740$			1581.10i			2.13662i
$741$		0			0
$742$	−1313.86			−1.77070
$743$	−268.179	+	71.8585i	−0.360941	+	0.0967139i	−0.434732	−	0.900560i	$-0.643157\pi$
$743$	−268.179	+	71.8585i	−0.360941	+	0.0967139i	0.0737908	+	0.997274i	$0.476490\pi$
$744$		0			0
$745$	−983.438	+	567.788i	−1.32005	+	0.762132i
$746$	852.472	+	852.472i	1.14272	+	1.14272i
$747$		0			0
$748$	−828.844	−	222.088i	−1.10808	−	0.296909i
$749$	2.70823	−	2.70823i	0.00361579	−	0.00361579i
$750$		0			0
$751$	−1074.14	−	620.156i	−1.43028	−	0.825774i	−0.433141	−	0.901326i	$-0.642595\pi$
$751$	−1074.14	−	620.156i	−1.43028	−	0.825774i	−0.997142	+	0.0755521i	$0.975928\pi$
$752$	−26.9533	−	100.591i	−0.0358422	−	0.133765i
$753$		0			0
$754$	964.018	−	1552.64i	1.27854	−	2.05920i
$755$	−1340.79			−1.77588
$756$		0			0
$757$	243.743	−	422.175i	0.321986	−	0.557695i	−0.658912	−	0.752220i	$-0.728983\pi$
$757$	243.743	−	422.175i	0.321986	−	0.557695i	0.980898	+	0.194525i	$0.0623164\pi$
$758$	−1350.68	+	779.818i	−1.78191	+	1.02878i
$759$		0			0
$760$	143.139	−	534.202i	0.188341	−	0.702898i
$761$	−409.294	−	109.670i	−0.537837	−	0.144113i	−0.0203324	−	0.999793i	$-0.506472\pi$
$761$	−409.294	−	109.670i	−0.537837	−	0.144113i	−0.517505	+	0.855680i	$0.673139\pi$
$762$		0			0
$763$	159.899	+	276.953i	0.209566	+	0.362979i
$764$	−1360.62	−	785.553i	−1.78091	−	1.02821i
$765$		0			0
$766$			1909.51i			2.49283i
$767$	−154.055	−	95.6511i	−0.200854	−	0.124708i
$768$		0			0
$769$	1110.65	−	297.599i	1.44428	−	0.386995i	0.550253	−	0.834998i	$-0.314531\pi$
$769$	1110.65	−	297.599i	1.44428	−	0.386995i	0.894032	+	0.448003i	$0.147865\pi$
$770$	−1103.84	+	1911.90i	−1.43355	+	2.48299i
$771$		0			0
$772$	−162.861	−	162.861i	−0.210960	−	0.210960i
$773$	242.244	−	904.069i	0.313382	−	1.16956i	−0.612104	−	0.790777i	$-0.709677\pi$
$773$	242.244	−	904.069i	0.313382	−	1.16956i	0.925486	−	0.378781i	$-0.123657\pi$
$774$		0			0
$775$	213.764	−	213.764i	0.275824	−	0.275824i
$776$	−368.729	−	638.658i	−0.475166	−	0.823012i
$777$		0			0
$778$	64.6092	+	241.125i	0.0830452	+	0.309929i
$779$		−	635.422i		−	0.815689i
$780$		0			0
$781$	−665.960			−0.852701
$782$	160.946	−	43.1254i	0.205814	−	0.0551476i
$783$		0			0
$784$	−23.0985	+	13.3359i	−0.0294623	+	0.0170101i
$785$	86.2350	+	86.2350i	0.109854	+	0.109854i
$786$		0			0
$787$	−1030.19	−	276.039i	−1.30901	−	0.350748i	−0.464161	−	0.885751i	$-0.653644\pi$
$787$	−1030.19	−	276.039i	−1.30901	−	0.350748i	−0.844850	+	0.535003i	$0.820311\pi$
$788$	78.5412	−	78.5412i	0.0996715	−	0.0996715i
$789$		0			0
$790$	−978.277	−	564.808i	−1.23833	−	0.714947i
$791$	−202.552	−	755.936i	−0.256071	−	0.955671i
$792$		0			0
$793$	248.965	+	1064.45i	0.313953	+	1.34231i
$794$	−2186.90			−2.75428
$795$		0			0
$796$	−399.441	+	691.852i	−0.501810	+	0.869160i
$797$	1258.35	−	726.507i	1.57885	−	0.911552i	0.583835	−	0.811872i	$-0.301552\pi$
$797$	1258.35	−	726.507i	1.57885	−	0.911552i	0.995020	−	0.0996795i	$-0.0317817\pi$
$798$		0			0
$799$	−99.2725	+	370.490i	−0.124246	+	0.463692i
$800$	−1334.68	−	357.627i	−1.66835	−	0.447034i
$801$		0			0
$802$	844.434	+	1462.60i	1.05291	+	1.82369i
$803$	783.871	+	452.568i	0.976178	+	0.563596i
$804$		0			0
$805$		−	258.714i		−	0.321384i
$806$	228.460	+	243.590i	0.283449	+	0.302221i
$807$		0			0
$808$	−192.478	+	51.5744i	−0.238215	+	0.0638296i
$809$	−35.5191	+	61.5210i	−0.0439050	+	0.0760457i	−0.887143	−	0.461495i	$-0.847313\pi$
$809$	−35.5191	+	61.5210i	−0.0439050	+	0.0760457i	0.843238	+	0.537541i	$0.180647\pi$
$810$		0			0
$811$	688.757	+	688.757i	0.849269	+	0.849269i	0.990042	−	0.140773i	$-0.0449587\pi$
$811$	688.757	+	688.757i	0.849269	+	0.849269i	−0.140773	+	0.990042i	$0.544959\pi$
$812$	527.099	−	1967.16i	0.649137	−	2.42261i
$813$		0			0
$814$	859.965	−	859.965i	1.05647	−	1.05647i
$815$	1089.17	+	1886.49i	1.33640	+	2.31472i
$816$		0			0
$817$	−85.2478	−	318.149i	−0.104343	−	0.389412i
$818$		−	2221.18i		−	2.71538i
$819$		0			0
$820$	2894.08			3.52936
$821$	507.818	−	136.069i	0.618536	−	0.165736i	0.0640739	−	0.997945i	$-0.479591\pi$
$821$	507.818	−	136.069i	0.618536	−	0.165736i	0.554462	+	0.832209i	$0.312924\pi$
$822$		0			0
$823$	−1054.57	+	608.856i	−1.28137	+	0.739801i	−0.977099	−	0.212784i	$-0.931747\pi$
$823$	−1054.57	+	608.856i	−1.28137	+	0.739801i	−0.304273	+	0.952585i	$0.598414\pi$
$824$	575.549	+	575.549i	0.698481	+	0.698481i
$825$		0			0
$826$	−323.421	−	86.6604i	−0.391551	−	0.104916i
$827$	644.293	−	644.293i	0.779072	−	0.779072i	−0.200601	−	0.979673i	$-0.564289\pi$
$827$	644.293	−	644.293i	0.779072	−	0.779072i	0.979673	+	0.200601i	$0.0642894\pi$
$828$		0			0
$829$	681.917	+	393.705i	0.822578	+	0.474916i	0.851305	−	0.524672i	$-0.175812\pi$
$829$	681.917	+	393.705i	0.822578	+	0.474916i	−0.0287265	+	0.999587i	$0.509145\pi$
$830$	283.119	+	1056.62i	0.341108	+	1.27303i
$831$		0			0
$832$	392.612	−	1297.47i	0.471890	−	1.55946i
$833$	98.2357			0.117930
$834$		0			0
$835$	1014.41	−	1757.01i	1.21486	−	2.10420i
$836$	−648.208	+	374.243i	−0.775369	+	0.447659i
$837$		0			0
$838$	296.367	−	1106.06i	0.353660	−	1.31988i
$839$	−98.0991	−	26.2856i	−0.116924	−	0.0313296i	0.199883	−	0.979820i	$-0.435944\pi$
$839$	−98.0991	−	26.2856i	−0.116924	−	0.0313296i	−0.316806	+	0.948490i	$0.602611\pi$
$840$		0			0
$841$	−559.023	−	968.257i	−0.664713	−	1.15132i
$842$	−1270.31	−	733.412i	−1.50868	−	0.871036i
$843$		0			0
$844$			1692.89i			2.00580i
$845$	262.189	+	1308.74i	0.310283	+	1.54881i
$846$		0			0
$847$	106.598	−	28.5628i	0.125853	−	0.0337223i
$848$	−89.9325	+	155.768i	−0.106053	+	0.183688i
$849$		0			0
$850$	1016.01	+	1016.01i	1.19531	+	1.19531i
$851$	−36.8873	+	137.665i	−0.0433458	+	0.161769i
$852$		0			0
$853$	−618.373	+	618.373i	−0.724939	+	0.724939i	−0.969607	−	0.244668i	$-0.921321\pi$
$853$	−618.373	+	618.373i	−0.724939	+	0.724939i	0.244668	+	0.969607i	$0.421321\pi$
$854$	1009.27	+	1748.11i	1.18182	+	2.04697i
$855$		0			0
$856$	0.869978	+	3.24680i	0.00101633	+	0.00379299i
$857$			194.182i			0.226584i	0.993562	+	0.113292i	$0.0361395\pi$
$857$			194.182i			0.226584i	−0.993562	+	0.113292i	$0.963861\pi$
$858$		0			0
$859$	330.896			0.385211			0.192605	−	0.981276i	$-0.438306\pi$
$859$	330.896			0.385211			0.192605	+	0.981276i	$0.438306\pi$
$860$	1449.04	−	388.268i	1.68492	−	0.451474i
$861$		0			0
$862$	−31.6702	+	18.2848i	−0.0367404	+	0.0212121i
$863$	−1.75897	−	1.75897i	−0.00203820	−	0.00203820i	0.706087	−	0.708125i	$-0.250459\pi$
$863$	−1.75897	−	1.75897i	−0.00203820	−	0.00203820i	−0.708125	+	0.706087i	$0.750459\pi$
$864$		0			0
$865$	−1914.07	−	512.874i	−2.21280	−	0.592918i
$866$	−903.589	+	903.589i	−1.04340	+	1.04340i
$867$		0			0
$868$	322.292	+	186.075i	0.371304	+	0.214372i
$869$	135.719	+	506.510i	0.156178	+	0.582866i
$870$		0			0
$871$	−837.219	−	26.8338i	−0.961216	−	0.0308080i
$872$	−280.665			−0.321863
$873$		0			0
$874$	72.6712	−	125.870i	0.0831478	−	0.144016i
$875$	639.791	−	369.383i	0.731190	−	0.422152i
$876$		0			0
$877$	−91.5191	+	341.554i	−0.104355	+	0.389457i	−0.998271	−	0.0587764i	$-0.981280\pi$
$877$	−91.5191	+	341.554i	−0.104355	+	0.389457i	0.893916	+	0.448234i	$0.147947\pi$
$878$	2165.65	+	580.284i	2.46657	+	0.660915i
$879$		0			0
$880$	151.113	+	261.735i	0.171719	+	0.297427i
$881$	−1056.30	−	609.854i	−1.19898	−	0.692229i	−0.238649	−	0.971106i	$-0.576705\pi$
$881$	−1056.30	−	609.854i	−1.19898	−	0.692229i	−0.960327	+	0.278877i	$0.910038\pi$
$882$		0			0
$883$			161.934i			0.183390i	0.995787	+	0.0916952i	$0.0292286\pi$
$883$			161.934i			0.183390i	−0.995787	+	0.0916952i	$0.970771\pi$
$884$	−698.718	+	655.320i	−0.790405	+	0.741312i
$885$		0			0
$886$	−146.740	+	39.3189i	−0.165621	+	0.0443780i
$887$	−57.8301	+	100.165i	−0.0651974	+	0.112925i	−0.896782	−	0.442474i	$-0.854101\pi$
$887$	−57.8301	+	100.165i	−0.0651974	+	0.112925i	0.831584	+	0.555399i	$0.187434\pi$
$888$		0			0
$889$	1248.92	+	1248.92i	1.40486	+	1.40486i
$890$	146.669	−	547.375i	0.164796	−	0.615028i
$891$		0			0
$892$	933.546	−	933.546i	1.04658	−	1.04658i
$893$	167.285	+	289.747i	0.187330	+	0.324464i
$894$		0			0
$895$	−17.4647	−	65.1793i	−0.0195137	−	0.0728260i
$896$		−	1385.47i		−	1.54629i
$897$		0			0
$898$	−1478.12			−1.64601
$899$	345.789	−	92.6538i	0.384637	−	0.103063i
$900$		0			0
$901$	573.712	−	331.233i	0.636750	−	0.367628i
$902$	−1574.10	−	1574.10i	−1.74512	−	1.74512i
$903$		0			0
$904$	663.432	+	177.766i	0.733885	+	0.196644i
$905$	137.424	−	137.424i	0.151850	−	0.151850i
$906$		0			0
$907$	−86.2343	−	49.7874i	−0.0950765	−	0.0548924i	0.451708	−	0.892166i	$-0.350815\pi$
$907$	−86.2343	−	49.7874i	−0.0950765	−	0.0548924i	−0.546784	+	0.837273i	$0.684148\pi$
$908$	−261.185	−	974.756i	−0.287649	−	1.07352i
$909$		0			0
$910$	1163.29	+	2172.78i	1.27834	+	2.38767i
$911$	902.996			0.991214			0.495607	−	0.868547i	$-0.334946\pi$
$911$	902.996			0.991214			0.495607	+	0.868547i	$0.334946\pi$
$912$		0			0
$913$	253.896	−	439.762i	0.278090	−	0.481667i
$914$	577.823	−	333.606i	0.632191	−	0.364996i
$915$		0			0
$916$	361.005	−	1347.29i	0.394111	−	1.47084i
$917$	−116.567	−	31.2341i	−0.127118	−	0.0340611i
$918$		0			0
$919$	481.991	+	834.834i	0.524474	+	0.908415i	0.999594	+	0.0284943i	$0.00907124\pi$
$919$	481.991	+	834.834i	0.524474	+	0.908415i	−0.475120	+	0.879921i	$0.657595\pi$
$920$	196.636	+	113.528i	0.213734	+	0.123400i
$921$		0			0
$922$		−	2702.15i		−	2.93074i
$923$	−392.165	+	631.617i	−0.424881	+	0.684308i
$924$		0			0
$925$	−1187.14	+	318.093i	−1.28339	+	0.343885i
$926$	376.540	−	652.186i	0.406630	−	0.704304i
$927$		0			0
$928$	−1157.01	−	1157.01i	−1.24678	−	1.24678i
$929$	123.886	−	462.347i	0.133354	−	0.497683i	−0.866646	−	0.498924i	$-0.833729\pi$
$929$	123.886	−	462.347i	0.133354	−	0.497683i	0.999999	+	0.00124161i	$0.000395217\pi$
$930$		0			0
$931$	60.5911	−	60.5911i	0.0650818	−	0.0650818i
$932$	800.378	+	1386.30i	0.858775	+	1.48744i
$933$		0			0
$934$	474.985	+	1772.67i	0.508549	+	1.89793i
$935$		−	1113.14i		−	1.19052i
$936$		0			0
$937$	405.888			0.433178			0.216589	−	0.976263i	$-0.430507\pi$
$937$	405.888			0.433178			0.216589	+	0.976263i	$0.430507\pi$
$938$	−1494.00	+	400.317i	−1.59275	+	0.426777i
$939$		0			0
$940$	−1319.67	+	761.913i	−1.40391	+	0.810546i
$941$	507.937	+	507.937i	0.539784	+	0.539784i	0.923465	−	0.383682i	$-0.125344\pi$
$941$	507.937	+	507.937i	0.539784	+	0.539784i	−0.383682	+	0.923465i	$0.625344\pi$
$942$		0			0
$943$	251.985	+	67.5193i	0.267217	+	0.0716005i
$944$	−32.4121	+	32.4121i	−0.0343348	+	0.0343348i
$945$		0			0
$946$	−999.315	−	576.955i	−1.05636	−	0.609889i
$947$	158.360	+	591.006i	0.167222	+	0.624083i	0.997746	+	0.0670995i	$0.0213745\pi$
$947$	158.360	+	591.006i	0.167222	+	0.624083i	−0.830524	+	0.556983i	$0.811959\pi$
$948$		0			0
$949$	890.829	−	476.942i	0.938702	−	0.502574i
$950$	1253.34			1.31931
$951$		0			0
$952$	−303.351	+	525.419i	−0.318646	+	0.551911i
$953$	−884.041	+	510.401i	−0.927640	+	0.535573i	−0.886064	−	0.463562i	$-0.846571\pi$
$953$	−884.041	+	510.401i	−0.927640	+	0.535573i	−0.0415756	+	0.999135i	$0.513238\pi$
$954$		0			0
$955$	527.498	−	1968.65i	0.552354	−	2.06141i
$956$	2026.80	+	543.080i	2.12009	+	0.568075i
$957$		0			0
$958$	−303.073	−	524.938i	−0.316360	−	0.547952i
$959$	22.0742	+	12.7445i	0.0230179	+	0.0132894i
$960$		0			0
$961$		−	895.583i		−	0.931928i
$962$	−309.208	−	1322.03i	−0.321422	−	1.37425i
$963$		0			0
$964$	−1781.06	+	477.234i	−1.84758	+	0.495057i
$965$	149.390	−	258.751i	0.154808	−	0.268135i
$966$		0			0
$967$	−100.629	−	100.629i	−0.104063	−	0.104063i	0.653158	−	0.757221i	$-0.273444\pi$
$967$	−100.629	−	100.629i	−0.104063	−	0.104063i	−0.757221	+	0.653158i	$0.773444\pi$
$968$	−25.0676	+	93.5536i	−0.0258963	+	0.0966463i
$969$		0			0
$970$	1972.20	−	1972.20i	2.03319	−	2.03319i
$971$	−746.211	−	1292.47i	−0.768497	−	1.33108i	−0.938378	−	0.345611i	$-0.887672\pi$
$971$	−746.211	−	1292.47i	−0.768497	−	1.33108i	0.169881	−	0.985465i	$-0.445662\pi$
$972$		0			0
$973$	71.0343	+	265.104i	0.0730055	+	0.272460i
$974$			2284.54i			2.34552i
$975$		0			0
$976$	276.334			0.283130
$977$	474.362	−	127.105i	0.485529	−	0.130097i	−0.00774697	−	0.999970i	$-0.502466\pi$
$977$	474.362	−	127.105i	0.485529	−	0.130097i	0.493276	+	0.869873i	$0.335799\pi$
$978$		0			0
$979$	−227.817	+	131.530i	−0.232703	+	0.134351i
$980$	275.967	+	275.967i	0.281599	+	0.281599i
$981$		0			0
$982$	−2977.61	−	797.849i	−3.03219	−	0.812473i
$983$	315.927	−	315.927i	0.321391	−	0.321391i	−0.527909	−	0.849301i	$-0.677024\pi$
$983$	315.927	−	315.927i	0.321391	−	0.321391i	0.849301	+	0.527909i	$0.177024\pi$
$984$		0			0
$985$	124.785	+	72.0446i	0.126685	+	0.0731417i
$986$	440.382	+	1643.53i	0.446635	+	1.66686i
$987$		0			0
$988$	−26.7679	+	835.162i	−0.0270930	+	0.845306i
$989$	135.225			0.136729
$990$		0			0
$991$	−840.227	+	1455.32i	−0.847857	+	1.46853i	0.0352592	+	0.999378i	$0.488774\pi$
$991$	−840.227	+	1455.32i	−0.847857	+	1.46853i	−0.883117	+	0.469154i	$0.844559\pi$
$992$	258.944	−	149.501i	0.261032	−	0.150707i
$993$		0			0
$994$	−355.303	+	1326.01i	−0.357448	+	1.33401i
$995$	−1001.03	−	268.224i	−1.00606	−	0.269572i
$996$		0			0
$997$	−186.953	−	323.812i	−0.187516	−	0.324787i	0.756906	−	0.653524i	$-0.226710\pi$
$997$	−186.953	−	323.812i	−0.187516	−	0.324787i	−0.944421	+	0.328737i	$0.893377\pi$
$998$	−1534.90	−	886.172i	−1.53797	−	0.887948i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.3.bd.d.46.3		12
3.2	odd	2		39.3.l.b.7.1	✓	12
13.2	odd	12	inner	117.3.bd.d.28.3		12
39.2	even	12		39.3.l.b.28.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.3.l.b.7.1	✓	12	3.2	odd	2
39.3.l.b.28.1	yes	12	39.2	even	12
117.3.bd.d.28.3		12	13.2	odd	12	inner
117.3.bd.d.46.3		12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.06798 - 0.822062i) q^{2} +(5.27259 - 3.04413i) q^{4} +(5.58467 + 5.58467i) q^{5} +(-7.30003 - 1.95604i) q^{7} +(4.69005 - 4.69005i) q^{8} +(21.7246 + 12.5427i) q^{10} +(-3.01391 - 11.2481i) q^{11} +(-12.4428 - 3.76518i) q^{13} -24.0043 q^{14} +(-1.64307 + 2.84588i) q^{16} +(10.4817 - 6.05163i) q^{17} +(2.73246 - 10.1977i) q^{19} +(46.4461 + 12.4452i) q^{20} +(-18.4932 - 32.0311i) q^{22} +(3.75368 + 2.16719i) q^{23} +37.3770i q^{25} +(-41.2694 - 1.32273i) q^{26} +(-44.4444 + 11.9089i) q^{28} +(-22.1306 + 38.3313i) q^{29} +(-5.71913 - 5.71913i) q^{31} +(-9.56812 + 35.7087i) q^{32} +(27.1829 - 27.1829i) q^{34} +(-29.8444 - 51.6920i) q^{35} +(8.51041 + 31.7613i) q^{37} -33.5325i q^{38} +52.3847 q^{40} +(58.1365 - 15.5776i) q^{41} +(27.0185 - 15.5991i) q^{43} +(-50.1316 - 50.1316i) q^{44} +(13.2978 + 3.56313i) q^{46} +(-22.4086 + 22.4086i) q^{47} +(7.02906 + 4.05823i) q^{49} +(30.7262 + 114.672i) q^{50} +(-77.0675 + 18.0253i) q^{52} +54.7345 q^{53} +(45.9850 - 79.6483i) q^{55} +(-43.4114 + 25.0636i) q^{56} +(-36.3854 + 135.792i) q^{58} +(13.4735 + 3.61020i) q^{59} +(-42.0454 - 72.8249i) q^{61} +(-22.2476 - 12.8447i) q^{62} +104.274i q^{64} +(-48.4616 - 90.5162i) q^{65} +(62.2390 - 16.6769i) q^{67} +(36.8439 - 63.8155i) q^{68} +(-134.056 - 134.056i) q^{70} +(14.8017 - 55.2406i) q^{71} +(-54.9623 + 54.9623i) q^{73} +(52.2194 + 90.4467i) q^{74} +(-16.6359 - 62.0861i) q^{76} +88.0064i q^{77} -45.0309 q^{79} +(-25.0693 + 6.71729i) q^{80} +(165.555 - 95.5835i) q^{82} +(30.8346 + 30.8346i) q^{83} +(92.3333 + 24.7406i) q^{85} +(70.0685 - 70.0685i) q^{86} +(-66.8893 - 38.6186i) q^{88} +(-5.84679 - 21.8205i) q^{89} +(83.4680 + 51.8245i) q^{91} +26.3888 q^{92} +(-50.3279 + 87.1704i) q^{94} +(72.2104 - 41.6907i) q^{95} +(28.7767 - 107.396i) q^{97} +(24.9011 + 6.67223i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 12 q^{4} - 4 q^{5} - 32 q^{7} + 24 q^{8} + 30 q^{10} - 22 q^{11} + 2 q^{13} - 92 q^{14} + 52 q^{16} + 6 q^{17} + 4 q^{19} + 208 q^{20} - 98 q^{22} + 18 q^{23} + 44 q^{26} - 78 q^{28} - 128 q^{29}+ \cdots + 350 q^{98}+O(q^{100}) \) 12 * q + 2 * q^2 - 12 * q^4 - 4 * q^5 - 32 * q^7 + 24 * q^8 + 30 * q^10 - 22 * q^11 + 2 * q^13 - 92 * q^14 + 52 * q^16 + 6 * q^17 + 4 * q^19 + 208 * q^20 - 98 * q^22 + 18 * q^23 + 44 * q^26 - 78 * q^28 - 128 * q^29 - 66 * q^31 - 358 * q^32 + 336 * q^34 - 14 * q^35 - 36 * q^37 - 12 * q^40 + 326 * q^41 + 60 * q^43 + 236 * q^44 - 138 * q^46 - 40 * q^47 + 78 * q^49 + 40 * q^50 - 392 * q^52 - 80 * q^53 + 166 * q^55 + 102 * q^56 + 250 * q^58 + 164 * q^59 - 98 * q^61 - 228 * q^62 - 514 * q^65 - 230 * q^67 - 78 * q^68 - 92 * q^70 - 70 * q^71 + 106 * q^73 + 16 * q^74 + 534 * q^76 + 16 * q^79 - 124 * q^80 - 156 * q^82 + 176 * q^83 + 90 * q^85 + 612 * q^86 - 318 * q^88 + 476 * q^89 + 106 * q^91 - 228 * q^92 - 374 * q^94 + 234 * q^95 - 306 * q^97 + 350 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more