LMFDB - Embedded newform 117.4.q.f.82.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,4,Mod(10,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("117.10");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	117.q (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.90322347067$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
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} - 32x^{10} + 823x^{8} - 5964x^{6} + 32913x^{4} - 47034x^{2} + 54756 $ x^12 - 32x^10 + 823x^8 - 5964x^6 + 32913x^4 - 47034*x^2 + 54756
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			82.6
Root			$4.24667 - 2.45182i$ of defining polynomial
Character	$\chi$	$=$	117.82
Dual form			117.4.q.f.10.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.24667 + 2.45182i) q^{2} +(8.02279 + 13.8959i) q^{4} +5.61325i q^{5} +(2.78293 - 1.60672i) q^{7} +39.4526i q^{8} +O(q^{10})$	\(q+(4.24667 + 2.45182i) q^{2} +(8.02279 + 13.8959i) q^{4} +5.61325i q^{5} +(2.78293 - 1.60672i) q^{7} +39.4526i q^{8} +(-13.7627 + 23.8376i) q^{10} +(37.7991 + 21.8233i) q^{11} +(-46.8108 + 2.39816i) q^{13} +15.7576 q^{14} +(-32.5481 + 56.3750i) q^{16} +(-32.9378 - 57.0500i) q^{17} +(-2.65374 + 1.53214i) q^{19} +(-78.0011 + 45.0340i) q^{20} +(107.013 + 185.353i) q^{22} +(81.8821 - 141.824i) q^{23} +93.4914 q^{25} +(-204.670 - 104.587i) q^{26} +(44.6537 + 25.7808i) q^{28} +(77.7243 - 134.622i) q^{29} +240.463i q^{31} +(-3.10650 + 1.79354i) q^{32} -323.030i q^{34} +(9.01895 + 15.6213i) q^{35} +(-275.104 - 158.831i) q^{37} -15.0261 q^{38} -221.457 q^{40} +(-110.773 - 63.9551i) q^{41} +(-189.501 - 328.225i) q^{43} +700.336i q^{44} +(695.452 - 401.519i) q^{46} -79.4626i q^{47} +(-166.337 + 288.104i) q^{49} +(397.027 + 229.224i) q^{50} +(-408.878 - 631.237i) q^{52} +571.746 q^{53} +(-122.500 + 212.176i) q^{55} +(63.3895 + 109.794i) q^{56} +(660.139 - 381.131i) q^{58} +(91.3986 - 52.7690i) q^{59} +(362.319 + 627.555i) q^{61} +(-589.571 + 1021.17i) q^{62} +503.180 q^{64} +(-13.4615 - 262.761i) q^{65} +(-261.732 - 151.111i) q^{67} +(528.507 - 915.401i) q^{68} +88.4512i q^{70} +(-868.960 + 501.694i) q^{71} -277.988i q^{73} +(-778.849 - 1349.01i) q^{74} +(-42.5808 - 24.5840i) q^{76} +140.256 q^{77} -959.137 q^{79} +(-316.447 - 182.701i) q^{80} +(-313.612 - 543.192i) q^{82} +410.957i q^{83} +(320.236 - 184.888i) q^{85} -1858.48i q^{86} +(-860.986 + 1491.27i) q^{88} +(-195.894 - 113.100i) q^{89} +(-126.418 + 81.8860i) q^{91} +2627.69 q^{92} +(194.828 - 337.451i) q^{94} +(-8.60027 - 14.8961i) q^{95} +(-769.427 + 444.229i) q^{97} +(-1412.76 + 815.655i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 16 q^{4} - 18 q^{7}+O(q^{10}) $ 12 * q + 16 * q^4 - 18 * q^7	$ 12 q + 16 q^{4} - 18 q^{7} - 56 q^{10} - 154 q^{13} - 92 q^{16} - 48 q^{19} + 292 q^{22} - 92 q^{25} + 552 q^{28} - 360 q^{37} - 448 q^{40} - 810 q^{43} + 996 q^{46} - 1068 q^{49} - 700 q^{52} + 460 q^{55} + 3048 q^{58} + 1294 q^{61} - 184 q^{64} + 2658 q^{67} + 1188 q^{76} - 6380 q^{79} - 1268 q^{82} - 3768 q^{85} - 5140 q^{88} + 342 q^{91} + 1660 q^{94} + 1686 q^{97}+O(q^{100}) $ 12 * q + 16 * q^4 - 18 * q^7 - 56 * q^10 - 154 * q^13 - 92 * q^16 - 48 * q^19 + 292 * q^22 - 92 * q^25 + 552 * q^28 - 360 * q^37 - 448 * q^40 - 810 * q^43 + 996 * q^46 - 1068 * q^49 - 700 * q^52 + 460 * q^55 + 3048 * q^58 + 1294 * q^61 - 184 * q^64 + 2658 * q^67 + 1188 * q^76 - 6380 * q^79 - 1268 * q^82 - 3768 * q^85 - 5140 * q^88 + 342 * q^91 + 1660 * q^94 + 1686 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	4.24667	+	2.45182i	1.50142	+	0.866848i	0.999999	+	0.00164665i	$0.000524144\pi$
$2$	4.24667	+	2.45182i	1.50142	+	0.866848i	0.501425	+	0.865201i	$0.332809\pi$
$3$		0			0
$3$		0			0
$4$	8.02279	+	13.8959i	1.00285	+	1.73699i
$5$			5.61325i			0.502065i	0.967979	+	0.251032i	$0.0807701\pi$
$5$			5.61325i			0.502065i	−0.967979	+	0.251032i	$0.919230\pi$
$6$		0			0
$7$	2.78293	−	1.60672i	0.150264	−	0.0867550i	−0.422983	−	0.906138i	$-0.639017\pi$
$7$	2.78293	−	1.60672i	0.150264	−	0.0867550i	0.573247	+	0.819383i	$0.305684\pi$
$8$			39.4526i			1.74357i
$9$		0			0
$10$	−13.7627	+	23.8376i	−0.435214	+	0.753812i
$11$	37.7991	+	21.8233i	1.03608	+	0.598179i	0.918720	−	0.394910i	$-0.129224\pi$
$11$	37.7991	+	21.8233i	1.03608	+	0.598179i	0.117357	+	0.993090i	$0.462558\pi$
$12$		0			0
$13$	−46.8108	+	2.39816i	−0.998690	+	0.0511639i
$13$	−46.8108	+	2.39816i	−0.998690	+	0.0511639i
$14$	15.7576			0.300813
$15$		0			0
$16$	−32.5481	+	56.3750i	−0.508564	+	0.880859i
$17$	−32.9378	−	57.0500i	−0.469918	−	0.813921i	0.529491	−	0.848316i	$-0.322383\pi$
$17$	−32.9378	−	57.0500i	−0.469918	−	0.813921i	−0.999408	+	0.0343944i	$0.989050\pi$
$18$		0			0
$19$	−2.65374	+	1.53214i	−0.0320426	+	0.0184998i	−0.515936	−	0.856627i	$-0.672556\pi$
$19$	−2.65374	+	1.53214i	−0.0320426	+	0.0184998i	0.483893	+	0.875127i	$0.339222\pi$
$20$	−78.0011	+	45.0340i	−0.872079	+	0.503495i
$21$		0			0
$22$	107.013	+	185.353i	1.03706	+	1.79624i
$23$	81.8821	−	141.824i	0.742330	−	1.28575i	−0.209102	−	0.977894i	$-0.567054\pi$
$23$	81.8821	−	141.824i	0.742330	−	1.28575i	0.951432	−	0.307859i	$-0.0996127\pi$
$24$		0			0
$25$	93.4914			0.747931
$26$	−204.670	−	104.587i	−1.54381	−	0.788894i
$27$		0			0
$28$	44.6537	+	25.7808i	0.301384	+	0.174004i
$29$	77.7243	−	134.622i	0.497691	−	0.862027i	−0.502305	−	0.864690i	$-0.667515\pi$
$29$	77.7243	−	134.622i	0.497691	−	0.862027i	0.999996	+	0.00266388i	$0.000847941\pi$
$30$		0			0
$31$			240.463i			1.39318i	0.717471	+	0.696588i	$0.245299\pi$
$31$			240.463i			1.39318i	−0.717471	+	0.696588i	$0.754701\pi$
$32$	−3.10650	+	1.79354i	−0.0171611	+	0.00990799i
$33$		0			0
$34$		−	323.030i		−	1.62939i
$35$	9.01895	+	15.6213i	0.0435566	+	0.0754423i
$36$		0			0
$37$	−275.104	−	158.831i	−1.22234	−	0.705721i	−0.256927	−	0.966431i	$-0.582710\pi$
$37$	−275.104	−	158.831i	−1.22234	−	0.705721i	−0.965417	+	0.260710i	$0.916043\pi$
$38$	−15.0261			−0.0641460
$39$		0			0
$40$	−221.457			−0.875387
$41$	−110.773	−	63.9551i	−0.421949	−	0.243612i	0.273962	−	0.961741i	$-0.411666\pi$
$41$	−110.773	−	63.9551i	−0.421949	−	0.243612i	−0.695911	+	0.718128i	$0.744999\pi$
$42$		0			0
$43$	−189.501	−	328.225i	−0.672060	−	1.16404i	−0.977319	−	0.211773i	$-0.932076\pi$
$43$	−189.501	−	328.225i	−0.672060	−	1.16404i	0.305259	−	0.952269i	$-0.401257\pi$
$44$			700.336i			2.39954i
$45$		0			0
$46$	695.452	−	401.519i	2.22910	−	1.28697i
$47$		−	79.4626i		−	0.246613i	−0.992369	−	0.123306i	$-0.960650\pi$
$47$		−	79.4626i		−	0.246613i	0.992369	−	0.123306i	$-0.0393498\pi$
$48$		0			0
$49$	−166.337	+	288.104i	−0.484947	+	0.839953i
$50$	397.027	+	229.224i	1.12296	+	0.648342i
$51$		0			0
$52$	−408.878	−	631.237i	−1.09041	−	1.68340i
$53$	571.746			1.48180			0.740899	−	0.671616i	$-0.234400\pi$
$53$	571.746			1.48180			0.740899	+	0.671616i	$0.234400\pi$
$54$		0			0
$55$	−122.500	+	212.176i	−0.300325	+	0.520178i
$56$	63.3895	+	109.794i	0.151264	+	0.261997i
$57$		0			0
$58$	660.139	−	381.131i	1.49449	−	0.862845i
$59$	91.3986	−	52.7690i	0.201679	−	0.116440i	−0.395759	−	0.918354i	$-0.629518\pi$
$59$	91.3986	−	52.7690i	0.201679	−	0.116440i	0.597439	+	0.801915i	$0.296185\pi$
$60$		0			0
$61$	362.319	+	627.555i	0.760495	+	1.31722i	0.942596	+	0.333936i	$0.108377\pi$
$61$	362.319	+	627.555i	0.760495	+	1.31722i	−0.182101	+	0.983280i	$0.558290\pi$
$62$	−589.571	+	1021.17i	−1.20767	+	2.09175i
$63$		0			0
$64$	503.180			0.982774
$65$	−13.4615	−	262.761i	−0.0256876	−	0.501407i
$66$		0			0
$67$	−261.732	−	151.111i	−0.477248	−	0.275539i	0.242021	−	0.970271i	$-0.422190\pi$
$67$	−261.732	−	151.111i	−0.477248	−	0.275539i	−0.719269	+	0.694732i	$0.755523\pi$
$68$	528.507	−	915.401i	0.942513	−	1.63248i
$69$		0			0
$70$			88.4512i			0.151028i
$71$	−868.960	+	501.694i	−1.45249	+	0.838594i	−0.998622	−	0.0524770i	$-0.983288\pi$
$71$	−868.960	+	501.694i	−1.45249	+	0.838594i	−0.453865	+	0.891071i	$0.649955\pi$
$72$		0			0
$73$		−	277.988i		−	0.445699i	−0.974853	−	0.222850i	$-0.928464\pi$
$73$		−	277.988i		−	0.445699i	0.974853	−	0.222850i	$-0.0715359\pi$
$74$	−778.849	−	1349.01i	−1.22350	−	2.11917i
$75$		0			0
$76$	−42.5808	−	24.5840i	−0.0642678	−	0.0371050i
$77$	140.256			0.207580
$78$		0			0
$79$	−959.137			−1.36597			−0.682983	−	0.730434i	$-0.739318\pi$
$79$	−959.137			−1.36597			−0.682983	+	0.730434i	$0.739318\pi$
$80$	−316.447	−	182.701i	−0.442248	−	0.255332i
$81$		0			0
$82$	−313.612	−	543.192i	−0.422349	−	0.731531i
$83$			410.957i			0.543475i	0.962371	+	0.271737i	$0.0875982\pi$
$83$			410.957i			0.543475i	−0.962371	+	0.271737i	$0.912402\pi$
$84$		0			0
$85$	320.236	−	184.888i	0.408641	−	0.235929i
$86$		−	1858.48i		−	2.33029i
$87$		0			0
$88$	−860.986	+	1491.27i	−1.04297	+	1.80648i
$89$	−195.894	−	113.100i	−0.233312	−	0.134703i	0.378787	−	0.925484i	$-0.376341\pi$
$89$	−195.894	−	113.100i	−0.233312	−	0.134703i	−0.612099	+	0.790781i	$0.709675\pi$
$90$		0			0
$91$	−126.418	+	81.8860i	−0.145629	+	0.0943295i
$92$	2627.69			2.97778
$93$		0			0
$94$	194.828	−	337.451i	0.213776	−	0.370271i
$95$	−8.60027	−	14.8961i	−0.00928810	−	0.0160875i
$96$		0			0
$97$	−769.427	+	444.229i	−0.805397	+	0.464996i	−0.845355	−	0.534205i	$-0.820611\pi$
$97$	−769.427	+	444.229i	−0.805397	+	0.464996i	0.0399579	+	0.999201i	$0.487278\pi$
$98$	−1412.76	+	815.655i	−1.45622	+	0.840750i
$99$		0			0
$100$	750.062	+	1299.15i	0.750062	+	1.29915i
$101$	−930.180	+	1611.12i	−0.916400	+	1.58725i	−0.111561	+	0.993758i	$0.535585\pi$
$101$	−930.180	+	1611.12i	−0.916400	+	1.58725i	−0.804839	+	0.593494i	$0.797748\pi$
$102$		0			0
$103$	−328.512			−0.314265			−0.157132	−	0.987578i	$-0.550225\pi$
$103$	−328.512			−0.314265			−0.157132	+	0.987578i	$0.550225\pi$
$104$	−94.6137	−	1846.81i	−0.0892081	−	1.74129i
$105$		0			0
$106$	2428.01	+	1401.81i	2.22481	+	1.28449i
$107$	−164.387	+	284.727i	−0.148522	+	0.257248i	−0.930682	−	0.365830i	$-0.880785\pi$
$107$	−164.387	+	284.727i	−0.148522	+	0.257248i	0.782159	+	0.623079i	$0.214118\pi$
$108$		0			0
$109$			201.673i			0.177218i	0.996066	+	0.0886092i	$0.0282422\pi$
$109$			201.673i			0.177218i	−0.996066	+	0.0886092i	$0.971758\pi$
$110$	−1040.43	+	600.693i	−0.901830	+	0.520672i
$111$		0			0
$112$			209.183i			0.176482i
$113$	−144.992	−	251.134i	−0.120705	−	0.209068i	0.799341	−	0.600878i	$-0.205182\pi$
$113$	−144.992	−	251.134i	−0.120705	−	0.209068i	−0.920046	+	0.391810i	$0.871849\pi$
$114$		0			0
$115$	796.094	+	459.625i	0.645531	+	0.372698i
$116$	2494.27			1.99644
$117$		0			0
$118$	517.520			0.403742
$119$	−183.327	−	105.844i	−0.141223	−	0.0815354i
$120$		0			0
$121$	287.013	+	497.121i	0.215637	+	0.373494i
$122$			3553.36i			2.63693i
$123$		0			0
$124$	−3341.45	+	1929.19i	−2.41993	+	1.39715i
$125$			1226.45i			0.877574i
$126$		0			0
$127$	376.283	−	651.742i	0.262911	−	0.455376i	−0.704103	−	0.710098i	$-0.748651\pi$
$127$	376.283	−	651.742i	0.262911	−	0.455376i	0.967014	+	0.254722i	$0.0819840\pi$
$128$	2161.69	+	1248.05i	1.49272	+	0.861823i
$129$		0			0
$130$	587.074	−	1148.86i	0.396076	−	0.775092i
$131$	2200.41			1.46756			0.733782	−	0.679385i	$-0.237753\pi$
$131$	2200.41			1.46756			0.733782	+	0.679385i	$0.237753\pi$
$132$		0			0
$133$	−4.92345	+	8.52766i	−0.00320990	+	0.00555971i
$134$	−740.992	−	1283.44i	−0.477701	−	0.827402i
$135$		0			0
$136$	2250.77	−	1299.48i	1.41913	−	0.819337i
$137$	−315.299	+	182.038i	−0.196626	+	0.113522i	−0.595081	−	0.803666i	$-0.702880\pi$
$137$	−315.299	+	182.038i	−0.196626	+	0.113522i	0.398455	+	0.917188i	$0.369547\pi$
$138$		0			0
$139$	−1226.79	−	2124.87i	−0.748600	−	1.29661i	−0.948494	−	0.316795i	$-0.897393\pi$
$139$	−1226.79	−	2124.87i	−0.748600	−	1.29661i	0.199894	−	0.979817i	$-0.435940\pi$
$140$	−144.714	+	250.653i	−0.0873614	+	0.151314i
$141$		0			0
$142$	−4920.25			−2.90773
$143$	−1821.74	−	930.917i	−1.06533	−	0.544386i
$144$		0			0
$145$	755.670	+	436.286i	0.432793	+	0.249873i
$146$	681.575	−	1180.52i	0.386353	−	0.669183i
$147$		0			0
$148$		−	5097.08i		−	2.83093i
$149$	−56.4171	+	32.5724i	−0.0310192	+	0.0179090i	−0.515429	−	0.856932i	$-0.672368\pi$
$149$	−56.4171	+	32.5724i	−0.0310192	+	0.0179090i	0.484410	+	0.874841i	$0.339034\pi$
$150$		0			0
$151$			250.204i			0.134843i	0.997725	+	0.0674216i	$0.0214773\pi$
$151$			250.204i			0.134843i	−0.997725	+	0.0674216i	$0.978523\pi$
$152$	−60.4468	−	104.697i	−0.0322558	−	0.0558687i
$153$		0			0
$154$	595.621	+	343.882i	0.311666	+	0.179940i
$155$	−1349.78			−0.699464
$156$		0			0
$157$	1768.99			0.899242			0.449621	−	0.893219i	$-0.351559\pi$
$157$	1768.99			0.899242			0.449621	+	0.893219i	$0.351559\pi$
$158$	−4073.13	−	2351.63i	−2.05089	−	1.18408i
$159$		0			0
$160$	−10.0676	−	17.4376i	−0.00497445	−	0.00861600i
$161$		−	526.248i		−	0.257603i
$162$		0			0
$163$	−2344.60	+	1353.66i	−1.12665	+	0.650470i	−0.943090	−	0.332538i	$-0.892095\pi$
$163$	−2344.60	+	1353.66i	−1.12665	+	0.650470i	−0.183558	+	0.983009i	$0.558762\pi$
$164$		−	2052.39i		−	0.977226i
$165$		0			0
$166$	−1007.59	+	1745.20i	−0.471110	+	0.815986i
$167$	3024.42	+	1746.15i	1.40142	+	0.809107i	0.994538	−	0.104375i	$-0.0332843\pi$
$167$	3024.42	+	1746.15i	1.40142	+	0.809107i	0.406877	+	0.913483i	$0.366618\pi$
$168$		0			0
$169$	2185.50	−	224.520i	0.994765	−	0.102194i
$170$	1813.25			0.818058
$171$		0			0
$172$	3040.65	−	5266.56i	1.34795	−	2.33472i
$173$	−1990.98	−	3448.48i	−0.874979	−	1.51551i	−0.856785	−	0.515674i	$-0.827542\pi$
$173$	−1990.98	−	3448.48i	−0.874979	−	1.51551i	−0.0181944	−	0.999834i	$-0.505792\pi$
$174$		0			0
$175$	260.180	−	150.215i	0.112387	−	0.0648868i
$176$	−2460.58	+	1420.61i	−1.05382	+	0.608425i
$177$		0			0
$178$	−554.598	−	960.593i	−0.233533	−	0.404491i
$179$	1127.53	−	1952.93i	0.470812	−	0.815470i	−0.528631	−	0.848852i	$-0.677294\pi$
$179$	1127.53	−	1952.93i	0.470812	−	0.815470i	0.999443	+	0.0333818i	$0.0106277\pi$
$180$		0			0
$181$	890.108			0.365532			0.182766	−	0.983156i	$-0.441495\pi$
$181$	890.108			0.365532			0.182766	+	0.983156i	$0.441495\pi$
$182$	−737.624	+	37.7892i	−0.300419	+	0.0153908i
$183$		0			0
$184$	5595.32	+	3230.46i	2.24181	+	1.29431i
$185$	891.559	−	1544.23i	0.354318	−	0.613696i
$186$		0			0
$187$		−	2875.25i		−	1.12438i
$188$	1104.20	−	637.512i	0.428363	−	0.247316i
$189$		0			0
$190$		−	84.3451i		−	0.0322055i
$191$	−399.887	−	692.624i	−0.151491	−	0.262390i	0.780285	−	0.625424i	$-0.215074\pi$
$191$	−399.887	−	692.624i	−0.151491	−	0.262390i	−0.931776	+	0.363034i	$0.881741\pi$
$192$		0			0
$193$	2332.56	+	1346.70i	0.869954	+	0.502268i	0.867333	−	0.497729i	$-0.165832\pi$
$193$	2332.56	+	1346.70i	0.869954	+	0.502268i	0.00262073	+	0.999997i	$0.499166\pi$
$194$	−4356.67			−1.61232
$195$		0			0
$196$	−5337.95			−1.94532
$197$	2369.19	+	1367.85i	0.856842	+	0.494698i	0.862953	−	0.505284i	$-0.168612\pi$
$197$	2369.19	+	1367.85i	0.856842	+	0.494698i	−0.00611178	+	0.999981i	$0.501945\pi$
$198$		0			0
$199$	−588.218	−	1018.82i	−0.209536	−	0.362927i	0.742033	−	0.670364i	$-0.233862\pi$
$199$	−588.218	−	1018.82i	−0.209536	−	0.362927i	−0.951568	+	0.307437i	$0.900529\pi$
$200$			3688.48i			1.30407i
$201$		0			0
$202$	−7900.33	+	4561.26i	−2.75181	+	1.58876i
$203$		−	499.526i		−	0.172709i
$204$		0			0
$205$	358.996	−	621.799i	0.122309	−	0.211846i
$206$	−1395.08	−	805.451i	−0.471845	−	0.272420i
$207$		0			0
$208$	1388.41	−	2717.01i	0.462830	−	0.905726i
$209$	−133.745			−0.0442648
$210$		0			0
$211$	1457.33	−	2524.16i	0.475481	−	0.823556i	−0.524125	−	0.851641i	$-0.675608\pi$
$211$	1457.33	−	2524.16i	0.475481	−	0.823556i	0.999606	+	0.0280849i	$0.00894088\pi$
$212$	4587.00	+	7944.91i	1.48602	+	2.57386i
$213$		0			0
$214$	−1396.19	+	806.093i	−0.445990	+	0.257492i
$215$	1842.41	−	1063.72i	0.584425	−	0.337418i
$216$		0			0
$217$	386.358	+	669.192i	0.120865	+	0.209344i
$218$	−494.466	+	856.440i	−0.153621	+	0.266080i
$219$		0			0
$220$	−3931.16			−1.20472
$221$	1678.66	+	2591.57i	0.510946	+	0.788813i
$222$		0			0
$223$	−1282.92	−	740.694i	−0.385250	−	0.222424i	0.294850	−	0.955543i	$-0.404730\pi$
$223$	−1282.92	−	740.694i	−0.385250	−	0.222424i	−0.680100	+	0.733120i	$0.738064\pi$
$224$	−5.76344	+	9.98258i	−0.00171914	+	0.00297763i
$225$		0			0
$226$		−	1421.98i		−	0.418533i
$227$	−3.79613	+	2.19169i	−0.00110995	+	0.000640828i	−0.500555	−	0.865705i	$-0.666871\pi$
$227$	−3.79613	+	2.19169i	−0.00110995	+	0.000640828i	0.499445	+	0.866346i	$0.333537\pi$
$228$		0			0
$229$			4689.58i			1.35326i	0.736324	+	0.676629i	$0.236560\pi$
$229$			4689.58i			1.35326i	−0.736324	+	0.676629i	$0.763440\pi$
$230$	2253.83	+	3903.75i	0.646144	+	1.11915i
$231$		0			0
$232$	5311.21	+	3066.43i	1.50301	+	0.867762i
$233$	4124.52			1.15968			0.579842	−	0.814729i	$-0.303114\pi$
$233$	4124.52			1.15968			0.579842	+	0.814729i	$0.303114\pi$
$234$		0			0
$235$	446.044			0.123816
$236$	1466.54	+	846.710i	0.404508	+	0.233543i
$237$		0			0
$238$	−519.020	−	898.970i	−0.141358	−	0.244838i
$239$		−	3455.41i		−	0.935196i	−0.883941	−	0.467598i	$-0.845120\pi$
$239$		−	3455.41i		−	0.935196i	0.883941	−	0.467598i	$-0.154880\pi$
$240$		0			0
$241$	3559.08	−	2054.83i	0.951288	−	0.549226i	0.0578069	−	0.998328i	$-0.481589\pi$
$241$	3559.08	−	2054.83i	0.951288	−	0.549226i	0.893481	+	0.449102i	$0.148256\pi$
$242$			2814.81i			0.747698i
$243$		0			0
$244$	−5813.62	+	10069.5i	−1.52532	+	2.64194i
$245$	−1617.20	−	933.691i	−0.421711	−	0.243475i
$246$		0			0
$247$	120.549	−	78.0846i	0.0310541	−	0.0201150i
$248$	−9486.89			−2.42911
$249$		0			0
$250$	−3007.02	+	5208.32i	−0.760723	+	1.31761i
$251$	−2516.11	−	4358.03i	−0.632730	−	1.09592i	−0.986991	−	0.160774i	$-0.948601\pi$
$251$	−2516.11	−	4358.03i	−0.632730	−	1.09592i	0.354261	−	0.935147i	$-0.384732\pi$
$252$		0			0
$253$	6190.13	−	3573.87i	1.53822	−	0.888093i
$254$	3195.90	−	1845.15i	0.789483	−	0.455808i
$255$		0			0
$256$	4107.27	+	7114.00i	1.00275	+	1.73682i
$257$	−2816.99	+	4879.16i	−0.683731	+	1.18426i	0.290103	+	0.956995i	$0.406310\pi$
$257$	−2816.99	+	4879.16i	−0.683731	+	1.18426i	−0.973834	+	0.227261i	$0.927023\pi$
$258$		0			0
$259$	−1020.79			−0.244899
$260$	3543.30	−	2295.14i	0.845176	−	0.547455i
$261$		0			0
$262$	9344.42	+	5395.00i	2.20344	+	1.27215i
$263$	−2556.31	+	4427.66i	−0.599350	+	1.03810i	0.393568	+	0.919296i	$0.371241\pi$
$263$	−2556.31	+	4427.66i	−0.599350	+	1.03810i	−0.992917	+	0.118808i	$0.962093\pi$
$264$		0			0
$265$			3209.35i			0.743959i
$266$	−41.8165	+	24.1428i	−0.00963884	+	0.00556499i
$267$		0			0
$268$		−	4849.32i		−	1.10530i
$269$	−3281.24	−	5683.28i	−0.743721	−	1.28816i	−0.950790	−	0.309836i	$-0.899726\pi$
$269$	−3281.24	−	5683.28i	−0.743721	−	1.28816i	0.207069	−	0.978326i	$-0.433608\pi$
$270$		0			0
$271$	−7067.90	−	4080.66i	−1.58430	−	0.914694i	−0.994222	−	0.107346i	$-0.965765\pi$
$271$	−7067.90	−	4080.66i	−1.58430	−	0.914694i	−0.590075	−	0.807348i	$-0.700902\pi$
$272$	4288.26			0.955934
$273$		0			0
$274$	−1785.29			−0.393626
$275$	3533.89	+	2040.29i	0.774914	+	0.447397i
$276$		0			0
$277$	1363.28	+	2361.28i	0.295710	+	0.512185i	0.975150	−	0.221546i	$-0.0711104\pi$
$277$	1363.28	+	2361.28i	0.295710	+	0.512185i	−0.679440	+	0.733731i	$0.737777\pi$
$278$		−	12031.5i		−	2.59569i
$279$		0			0
$280$	−616.300	+	355.821i	−0.131539	+	0.0759442i
$281$			1216.67i			0.258294i	0.991625	+	0.129147i	$0.0412238\pi$
$281$			1216.67i			0.258294i	−0.991625	+	0.129147i	$0.958776\pi$
$282$		0			0
$283$	−1624.16	+	2813.13i	−0.341153	+	0.590895i	−0.984647	−	0.174557i	$-0.944151\pi$
$283$	−1624.16	+	2813.13i	−0.341153	+	0.590895i	0.643494	+	0.765451i	$0.277484\pi$
$284$	−13943.0	−	8049.98i	−2.91325	−	1.68197i
$285$		0			0
$286$	−5453.89	−	8419.87i	−1.12761	−	1.74083i
$287$	−411.033			−0.0845383
$288$		0			0
$289$	286.696	−	496.573i	0.0583547	−	0.101073i
$290$	2139.39	+	3705.53i	0.433204	+	0.750331i
$291$		0			0
$292$	3862.89	−	2230.24i	0.774173	−	0.446969i
$293$	7986.99	−	4611.29i	1.59251	−	0.919435i	0.599634	−	0.800274i	$-0.295313\pi$
$293$	7986.99	−	4611.29i	1.59251	−	0.919435i	0.992875	−	0.119161i	$-0.0380205\pi$
$294$		0			0
$295$	296.206	+	513.044i	0.0584602	+	0.101256i
$296$	6266.30	−	10853.5i	1.23048	−	2.13125i
$297$		0			0
$298$	−319.446			−0.0620974
$299$	−3492.85	+	6835.25i	−0.675574	+	1.32205i
$300$		0			0
$301$	−1054.73	−	608.951i	−0.201973	−	0.116609i
$302$	−613.455	+	1062.53i	−0.116889	+	0.202457i
$303$		0			0
$304$		−	199.473i		−	0.0376334i
$305$	−3522.62	+	2033.79i	−0.661327	+	0.381818i
$306$		0			0
$307$		−	2993.33i		−	0.556477i	−0.960512	−	0.278238i	$-0.910249\pi$
$307$		−	2993.33i		−	0.556477i	0.960512	−	0.278238i	$-0.0897505\pi$
$308$	1125.25	+	1948.98i	0.208172	+	0.360564i
$309$		0			0
$310$	−5732.07	−	3309.41i	−1.05019	−	0.606329i
$311$	−7261.04			−1.32391			−0.661955	−	0.749544i	$-0.730273\pi$
$311$	−7261.04			−1.32391			−0.661955	+	0.749544i	$0.730273\pi$
$312$		0			0
$313$	−3903.02			−0.704829			−0.352415	−	0.935844i	$-0.614639\pi$
$313$	−3903.02			−0.704829			−0.352415	+	0.935844i	$0.614639\pi$
$314$	7512.33	+	4337.25i	1.35014	+	0.779506i
$315$		0			0
$316$	−7694.96	−	13328.1i	−1.36986	−	2.37266i
$317$		−	4592.24i		−	0.813646i	−0.913507	−	0.406823i	$-0.866637\pi$
$317$		−	4592.24i		−	0.813646i	0.913507	−	0.406823i	$-0.133363\pi$
$318$		0			0
$319$	5875.81	−	3392.40i	1.03129	−	0.595417i
$320$			2824.48i			0.493416i
$321$		0			0
$322$	1290.26	−	2234.80i	0.223303	−	0.386772i
$323$	174.817	+	100.931i	0.0301148	+	0.0173868i
$324$		0			0
$325$	−4376.40	+	224.208i	−0.746951	+	0.0382671i
$326$	−13275.7			−2.25543
$327$		0			0
$328$	2523.19	−	4370.30i	0.424756	−	0.735699i
$329$	−127.674	−	221.139i	−0.0213949	−	0.0370571i
$330$		0			0
$331$	−4430.30	+	2557.84i	−0.735684	+	0.424747i	−0.820498	−	0.571649i	$-0.806304\pi$
$331$	−4430.30	+	2557.84i	−0.735684	+	0.424747i	0.0848138	+	0.996397i	$0.472970\pi$
$332$	−5710.62	+	3297.03i	−0.944008	+	0.545023i
$333$		0			0
$334$	8562.46	+	14830.6i	1.40275	+	2.42963i
$335$	848.223	−	1469.17i	0.138339	−	0.239609i
$336$		0			0
$337$	6808.37			1.10052			0.550260	−	0.834993i	$-0.314529\pi$
$337$	6808.37			1.10052			0.550260	+	0.834993i	$0.314529\pi$
$338$	9831.56	+	4404.98i	1.58215	+	0.708873i
$339$		0			0
$340$	5138.38	+	2966.64i	0.819611	+	0.473203i
$341$	−5247.70	+	9089.28i	−0.833369	+	1.44344i
$342$		0			0
$343$			2171.24i			0.341796i
$344$	12949.3	−	7476.30i	2.02960	−	1.17179i
$345$		0			0
$346$		−	19526.1i		−	3.03389i
$347$	5459.09	+	9455.42i	0.844551	+	1.46281i	0.886010	+	0.463665i	$0.153466\pi$
$347$	5459.09	+	9455.42i	0.844551	+	1.46281i	−0.0414594	+	0.999140i	$0.513201\pi$
$348$		0			0
$349$	8867.43	+	5119.62i	1.36007	+	0.785234i	0.989632	−	0.143625i	$-0.0458759\pi$
$349$	8867.43	+	5119.62i	1.36007	+	0.785234i	0.370433	+	0.928859i	$0.379209\pi$
$350$	1473.20			0.224988
$351$		0			0
$352$	−156.564			−0.0237070
$353$	748.273	+	432.015i	0.112823	+	0.0651384i	0.555350	−	0.831617i	$-0.312584\pi$
$353$	748.273	+	432.015i	0.112823	+	0.0651384i	−0.442527	+	0.896755i	$0.645918\pi$
$354$		0			0
$355$	−2816.14	−	4877.69i	−0.421028	−	0.729242i
$356$		−	3629.50i		−	0.540346i
$357$		0			0
$358$	9576.47	−	5528.98i	1.41378	−	0.816244i
$359$			11430.0i			1.68036i	0.542305	+	0.840182i	$0.317552\pi$
$359$			11430.0i			1.68036i	−0.542305	+	0.840182i	$0.682448\pi$
$360$		0			0
$361$	−3424.81	+	5931.94i	−0.499316	+	0.864840i
$362$	3779.99	+	2182.38i	0.548818	+	0.316860i
$363$		0			0
$364$	−2152.10	−	1099.73i	−0.309892	−	0.158356i
$365$	1560.42			0.223770
$366$		0			0
$367$	−4606.01	+	7977.85i	−0.655128	+	1.13471i	0.326734	+	0.945116i	$0.394052\pi$
$367$	−4606.01	+	7977.85i	−0.655128	+	1.13471i	−0.981862	+	0.189598i	$0.939281\pi$
$368$	5330.21	+	9232.20i	0.755045	+	1.30778i
$369$		0			0
$370$	7572.31	−	4371.88i	1.06396	−	0.614279i
$371$	1591.13	−	918.638i	0.222661	−	0.128553i
$372$		0			0
$373$	559.064	+	968.327i	0.0776065	+	0.134418i	0.902217	−	0.431283i	$-0.141939\pi$
$373$	559.064	+	968.327i	0.0776065	+	0.134418i	−0.824610	+	0.565701i	$0.808606\pi$
$374$	7049.58	−	12210.2i	0.974666	−	1.68817i
$375$		0			0
$376$	3135.00			0.429988
$377$	−3315.49	+	6488.18i	−0.452935	+	0.886361i
$378$		0			0
$379$	−6987.09	−	4034.00i	−0.946973	−	0.546735i	−0.0548334	−	0.998496i	$-0.517463\pi$
$379$	−6987.09	−	4034.00i	−0.946973	−	0.546735i	−0.892139	+	0.451761i	$0.850796\pi$
$380$	137.996	−	239.017i	0.0186291	−	0.0322666i
$381$		0			0
$382$		−	3921.79i		−	0.525279i
$383$	1752.61	−	1011.87i	0.233822	−	0.134997i	−0.378512	−	0.925596i	$-0.623564\pi$
$383$	1752.61	−	1011.87i	0.233822	−	0.134997i	0.612334	+	0.790599i	$0.290231\pi$
$384$		0			0
$385$			787.293i			0.104219i
$386$	6603.73	+	11438.0i	0.870779	+	1.50823i
$387$		0			0
$388$	−12345.9	−	7127.92i	−1.61538	−	0.932642i
$389$	−9697.21			−1.26393			−0.631964	−	0.774998i	$-0.717751\pi$
$389$	−9697.21			−1.26393			−0.631964	+	0.774998i	$0.717751\pi$
$390$		0			0
$391$	−10788.1			−1.39534
$392$	−11366.4	−	6562.42i	−1.46452	−	0.845542i
$393$		0			0
$394$	6707.44	+	11617.6i	0.857655	+	1.48550i
$395$		−	5383.88i		−	0.685803i
$396$		0			0
$397$	−2941.24	+	1698.13i	−0.371830	+	0.214676i	−0.674258	−	0.738496i	$-0.735536\pi$
$397$	−2941.24	+	1698.13i	−0.371830	+	0.214676i	0.302427	+	0.953172i	$0.402203\pi$
$398$		−	5768.80i		−	0.726543i
$399$		0			0
$400$	−3042.97	+	5270.58i	−0.380371	+	0.658822i
$401$	5758.99	+	3324.95i	0.717183	+	0.414066i	0.813715	−	0.581264i	$-0.197442\pi$
$401$	5758.99	+	3324.95i	0.717183	+	0.414066i	−0.0965322	+	0.995330i	$0.530775\pi$
$402$		0			0
$403$	−576.670	−	11256.3i	−0.0712803	−	1.39135i
$404$	−29850.6			−3.67604
$405$		0			0
$406$	1224.75	−	2121.32i	0.149712	−	0.259309i
$407$	−6932.44	−	12007.3i	−0.844295	−	1.46236i
$408$		0			0
$409$	−2178.44	+	1257.72i	−0.263366	+	0.152055i	−0.625869	−	0.779928i	$-0.715256\pi$
$409$	−2178.44	+	1257.72i	−0.263366	+	0.152055i	0.362503	+	0.931983i	$0.381922\pi$
$410$	3049.07	−	1760.38i	0.367276	−	0.212047i
$411$		0			0
$412$	−2635.59	−	4564.97i	−0.315160	−	0.545873i
$413$	169.571	−	293.705i	0.0202034	−	0.0349934i
$414$		0			0
$415$	−2306.81			−0.272860
$416$	141.116	−	91.4068i	0.0166317	−	0.0107730i
$417$		0			0
$418$	−567.971	−	327.918i	−0.0664602	−	0.0383708i
$419$	5953.72	−	10312.2i	0.694173	−	1.20234i	−0.276286	−	0.961076i	$-0.589104\pi$
$419$	5953.72	−	10312.2i	0.694173	−	1.20234i	0.970459	−	0.241267i	$-0.0775630\pi$
$420$		0			0
$421$			2382.88i			0.275854i	0.990442	+	0.137927i	$0.0440440\pi$
$421$			2382.88i			0.275854i	−0.990442	+	0.137927i	$0.955956\pi$
$422$	12377.6	−	7146.18i	1.42780	−	0.824338i
$423$		0			0
$424$			22556.9i			2.58363i
$425$	−3079.40	−	5333.69i	−0.351466	−	0.608757i
$426$		0			0
$427$	2016.62	+	1164.29i	0.228550	+	0.131953i
$428$	−5275.37			−0.595782
$429$		0			0
$430$	10432.1			1.16996
$431$	−248.155	−	143.273i	−0.0277337	−	0.0160121i	0.486069	−	0.873920i	$-0.338430\pi$
$431$	−248.155	−	143.273i	−0.0277337	−	0.0160121i	−0.513803	+	0.857908i	$0.671764\pi$
$432$		0			0
$433$	−424.177	−	734.696i	−0.0470777	−	0.0815410i	0.841526	−	0.540216i	$-0.181658\pi$
$433$	−424.177	−	734.696i	−0.0470777	−	0.0815410i	−0.888604	+	0.458675i	$0.848324\pi$
$434$			3789.11i			0.419086i
$435$		0			0
$436$	−2802.43	+	1617.98i	−0.307826	+	0.177723i
$437$			501.818i			0.0549318i
$438$		0			0
$439$	34.8466	−	60.3561i	0.00378847	−	0.00656182i	−0.864125	−	0.503277i	$-0.832127\pi$
$439$	34.8466	−	60.3561i	0.00378847	−	0.00656182i	0.867913	+	0.496716i	$0.165461\pi$
$440$	−8370.88	−	4832.93i	−0.906969	−	0.523639i
$441$		0			0
$442$	774.678	+	15121.3i	0.0833658	+	1.62725i
$443$	7331.02			0.786247			0.393123	−	0.919486i	$-0.371395\pi$
$443$	7331.02			0.786247			0.393123	+	0.919486i	$0.371395\pi$
$444$		0			0
$445$	634.856	−	1099.60i	0.0676294	−	0.117138i
$446$	−3632.09	−	6290.96i	−0.385615	−	0.667905i
$447$		0			0
$448$	1400.31	−	808.472i	0.147676	−	0.0852605i
$449$	12309.0	−	7106.59i	1.29376	−	0.746950i	0.314438	−	0.949278i	$-0.398184\pi$
$449$	12309.0	−	7106.59i	1.29376	−	0.746950i	0.979318	+	0.202328i	$0.0648507\pi$
$450$		0			0
$451$	−2791.42	−	4834.88i	−0.291448	−	0.504802i
$452$	2326.48	−	4029.59i	0.242099	−	0.419327i
$453$		0			0
$454$	−21.4945			−0.00222200
$455$	−459.647	−	709.616i	−0.0473595	−	0.0731149i
$456$		0			0
$457$	5112.33	+	2951.60i	0.523292	+	0.302123i	0.738281	−	0.674494i	$-0.235638\pi$
$457$	5112.33	+	2951.60i	0.523292	+	0.302123i	−0.214988	+	0.976617i	$0.568971\pi$
$458$	−11498.0	+	19915.1i	−1.17307	+	2.03181i
$459$		0			0
$460$			14749.9i			1.49504i
$461$	488.270	−	281.903i	0.0493297	−	0.0284805i	−0.475132	−	0.879914i	$-0.657600\pi$
$461$	488.270	−	281.903i	0.0493297	−	0.0284805i	0.524462	+	0.851434i	$0.324266\pi$
$462$		0			0
$463$			17543.8i			1.76097i	0.474070	+	0.880487i	$0.342784\pi$
$463$			17543.8i			1.76097i	−0.474070	+	0.880487i	$0.657216\pi$
$464$	5059.56	+	8763.42i	0.506216	+	0.876792i
$465$		0			0
$466$	17515.5	+	10112.6i	1.74118	+	1.00527i
$467$	−9125.81			−0.904266			−0.452133	−	0.891951i	$-0.649337\pi$
$467$	−9125.81			−0.904266			−0.452133	+	0.891951i	$0.649337\pi$
$468$		0			0
$469$	−971.174			−0.0956176
$470$	1894.20	+	1093.62i	0.185900	+	0.107329i
$471$		0			0
$472$	2081.87	+	3605.91i	0.203021	+	0.351643i
$473$		−	16542.1i		−	1.60805i
$474$		0			0
$475$	−248.102	+	143.242i	−0.0239657	+	0.0138366i
$476$		−	3396.66i		−	0.327071i
$477$		0			0
$478$	8472.02	−	14674.0i	0.810672	−	1.40413i
$479$	4304.28	+	2485.08i	0.410579	+	0.237048i	0.691039	−	0.722818i	$-0.257153\pi$
$479$	4304.28	+	2485.08i	0.410579	+	0.237048i	−0.280459	+	0.959866i	$0.590487\pi$
$480$		0			0
$481$	13258.7	+	6775.26i	1.25685	+	0.642257i
$482$	20152.3			1.90438
$483$		0			0
$484$	−4605.29	+	7976.60i	−0.432503	+	0.749117i
$485$	−2493.57	−	4318.99i	−0.233458	−	0.404361i
$486$		0			0
$487$	−4950.89	+	2858.40i	−0.460670	+	0.265968i	−0.712326	−	0.701849i	$-0.752358\pi$
$487$	−4950.89	+	2858.40i	−0.460670	+	0.265968i	0.251656	+	0.967817i	$0.419025\pi$
$488$	−24758.7	+	14294.4i	−2.29666	+	1.32598i
$489$		0			0
$490$	−4578.48	−	7930.15i	−0.422111	−	0.731118i
$491$	−3022.11	+	5234.44i	−0.277771	+	0.481114i	−0.970831	−	0.239767i	$-0.922929\pi$
$491$	−3022.11	+	5234.44i	−0.277771	+	0.481114i	0.693059	+	0.720881i	$0.256262\pi$
$492$		0			0
$493$	−10240.3			−0.935496
$494$	703.382	−	36.0349i	0.0640620	−	0.00328196i
$495$		0			0
$496$	−13556.1	−	7826.62i	−1.22719	−	0.708520i
$497$	−1612.17	+	2792.36i	−0.145504	+	0.252021i
$498$		0			0
$499$			1101.16i			0.0987870i	0.998779	+	0.0493935i	$0.0157288\pi$
$499$			1101.16i			0.0987870i	−0.998779	+	0.0493935i	$0.984271\pi$
$500$	−17042.6	+	9839.54i	−1.52433	+	0.880075i
$501$		0			0
$502$		−	24676.1i		−	2.19392i
$503$	670.986	+	1162.18i	0.0594787	+	0.103020i	0.894232	−	0.447605i	$-0.147723\pi$
$503$	670.986	+	1162.18i	0.0594787	+	0.103020i	−0.834753	+	0.550625i	$0.814389\pi$
$504$		0			0
$505$	−9043.62	−	5221.34i	−0.796903	−	0.460092i
$506$	35049.9			3.07937
$507$		0			0
$508$	12075.4			1.05464
$509$	11668.5	+	6736.80i	1.01610	+	0.586647i	0.912973	−	0.408021i	$-0.133781\pi$
$509$	11668.5	+	6736.80i	1.01610	+	0.586647i	0.103130	+	0.994668i	$0.467114\pi$
$510$		0			0
$511$	−446.650	−	773.621i	−0.0386666	−	0.0669725i
$512$			20312.2i			1.75328i
$513$		0			0
$514$	−23925.6	+	13813.5i	−2.05314	+	1.18538i
$515$		−	1844.02i		−	0.157781i
$516$		0			0
$517$	1734.14	−	3003.61i	0.147519	−	0.255510i
$518$	−4334.96	−	2502.79i	−0.367698	−	0.212290i
$519$		0			0
$520$	10366.6	−	531.091i	0.874241	−	0.0447882i
$521$	10374.9			0.872423			0.436211	−	0.899844i	$-0.356320\pi$
$521$	10374.9			0.872423			0.436211	+	0.899844i	$0.356320\pi$
$522$		0			0
$523$	11147.7	−	19308.4i	0.932037	−	1.61433i	0.152202	−	0.988349i	$-0.451364\pi$
$523$	11147.7	−	19308.4i	0.932037	−	1.61433i	0.779835	−	0.625985i	$-0.215303\pi$
$524$	17653.4	+	30576.7i	1.47175	+	2.54914i
$525$		0			0
$526$	−21711.6	+	12535.2i	−1.79976	+	1.03909i
$527$	13718.4	−	7920.34i	1.13394	−	0.654678i
$528$		0			0
$529$	−7325.85	−	12688.7i	−0.602108	−	1.04288i
$530$	−7868.74	+	13629.1i	−0.644899	+	1.11700i
$531$		0			0
$532$	−157.999			−0.0128762
$533$	5338.76	+	2728.13i	0.433860	+	0.221705i
$534$		0			0
$535$	−1598.24	−	922.746i	−0.129155	−	0.0745678i
$536$	5961.71	−	10326.0i	0.480423	−	0.832117i
$537$		0			0
$538$		−	32180.0i		−	2.57877i
$539$	−12574.8	+	7260.04i	−1.00489	+	0.580171i
$540$		0			0
$541$			10201.9i			0.810747i	0.914151	+	0.405373i	$0.132859\pi$
$541$			10201.9i			0.810747i	−0.914151	+	0.405373i	$0.867141\pi$
$542$	−20010.0	−	34658.4i	−1.58580	−	2.74669i
$543$		0			0
$544$	204.643	+	118.151i	0.0161287	+	0.00931188i
$545$	−1132.04			−0.0889751
$546$		0			0
$547$	−9312.12			−0.727893			−0.363947	−	0.931420i	$-0.618571\pi$
$547$	−9312.12			−0.727893			−0.363947	+	0.931420i	$0.618571\pi$
$548$	−5059.15	−	2920.90i	−0.394373	−	0.227691i
$549$		0			0
$550$	10004.8	+	17328.9i	0.775650	+	1.34346i
$551$			476.337i			0.0368288i
$552$		0			0
$553$	−2669.21	+	1541.07i	−0.205256	+	0.118504i
$554$			13370.1i			1.02534i
$555$		0			0
$556$	19684.6	−	34094.8i	1.50147	−	2.60061i
$557$	−124.988	−	72.1618i	−0.00950791	−	0.00548940i	0.495239	−	0.868757i	$-0.335081\pi$
$557$	−124.988	−	72.1618i	−0.00950791	−	0.00548940i	−0.504746	+	0.863268i	$0.668414\pi$
$558$		0			0
$559$	9657.81	+	14910.0i	0.730737	+	1.12813i
$560$	−1174.20			−0.0886054
$561$		0			0
$562$	−2983.05	+	5166.80i	−0.223901	+	0.387808i
$563$	−7333.48	−	12702.0i	−0.548968	−	0.950841i	−0.998346	−	0.0574990i	$-0.981687\pi$
$563$	−7333.48	−	12702.0i	−0.548968	−	0.950841i	0.449377	−	0.893342i	$-0.351646\pi$
$564$		0			0
$565$	1409.68	−	813.877i	0.104966	−	0.0606019i
$566$	−13794.5	+	7964.28i	−1.02443	+	0.591456i
$567$		0			0
$568$	−19793.1	−	34282.7i	−1.46215	−	2.53252i
$569$	−9377.03	+	16241.5i	−0.690871	+	1.19662i	0.280682	+	0.959801i	$0.409439\pi$
$569$	−9377.03	+	16241.5i	−0.690871	+	1.19662i	−0.971553	+	0.236822i	$0.923894\pi$
$570$		0			0
$571$	13886.4			1.01773			0.508867	−	0.860845i	$-0.330065\pi$
$571$	13886.4			1.01773			0.508867	+	0.860845i	$0.330065\pi$
$572$	−1679.52	−	32783.2i	−0.122770	−	2.39639i
$573$		0			0
$574$	−1745.52	−	1007.78i	−0.126928	−	0.0732818i
$575$	7655.27	−	13259.3i	0.555212	−	0.961655i
$576$		0			0
$577$		−	9338.81i		−	0.673795i	−0.941541	−	0.336898i	$-0.890622\pi$
$577$		−	9338.81i		−	0.673795i	0.941541	−	0.336898i	$-0.109378\pi$
$578$	2435.01	−	1405.85i	0.175230	−	0.101169i
$579$		0			0
$580$			14000.9i			1.00234i
$581$	660.295	+	1143.66i	0.0471492	+	0.0816647i
$582$		0			0
$583$	21611.5	+	12477.4i	1.53526	+	0.886381i
$584$	10967.3			0.777110
$585$		0			0
$586$	45224.1			3.18804
$587$	−3225.20	−	1862.07i	−0.226777	−	0.130930i	0.382307	−	0.924035i	$-0.375130\pi$
$587$	−3225.20	−	1862.07i	−0.226777	−	0.130930i	−0.609084	+	0.793105i	$0.708463\pi$
$588$		0			0
$589$	−368.422	−	638.126i	−0.0257735	−	0.0446410i
$590$			2904.97i			0.202704i
$591$		0			0
$592$	17908.2	−	10339.3i	1.24328	−	0.717809i
$593$		−	19910.2i		−	1.37877i	−0.724393	−	0.689387i	$-0.757880\pi$
$593$		−	19910.2i		−	1.37877i	0.724393	−	0.689387i	$-0.242120\pi$
$594$		0			0
$595$	594.130	−	1029.06i	0.0409361	−	0.0709033i
$596$	−905.245	−	522.644i	−0.0622153	−	0.0359200i
$597$		0			0
$598$	−31591.7	+	20463.2i	−2.16034	+	1.39934i
$599$	14756.0			1.00653			0.503265	−	0.864132i	$-0.332132\pi$
$599$	14756.0			1.00653			0.503265	+	0.864132i	$0.332132\pi$
$600$		0			0
$601$	3969.53	−	6875.42i	0.269418	−	0.466646i	−0.699293	−	0.714835i	$-0.746502\pi$
$601$	3969.53	−	6875.42i	0.269418	−	0.466646i	0.968712	+	0.248189i	$0.0798352\pi$
$602$	−2986.07	−	5172.03i	−0.202165	−	0.350160i
$603$		0			0
$604$	−3476.81	+	2007.34i	−0.234221	+	0.135227i
$605$	−2790.47	+	1611.08i	−0.187518	+	0.108264i
$606$		0			0
$607$	1281.94	+	2220.39i	0.0857205	+	0.148472i	0.905698	−	0.423923i	$-0.139347\pi$
$607$	1281.94	+	2220.39i	0.0857205	+	0.148472i	−0.819977	+	0.572396i	$0.806014\pi$
$608$	5.49589	−	9.51916i	0.000366592	−	0.000634956i
$609$		0			0
$610$	−19945.9			−1.32391
$611$	190.564	+	3719.70i	0.0126177	+	0.246290i
$612$		0			0
$613$	−15236.4	−	8796.72i	−1.00390	−	0.579602i	−0.0945004	−	0.995525i	$-0.530125\pi$
$613$	−15236.4	−	8796.72i	−1.00390	−	0.579602i	−0.909400	+	0.415923i	$0.863459\pi$
$614$	7339.09	−	12711.7i	0.482381	−	0.835508i
$615$		0			0
$616$			5533.47i			0.361932i
$617$	−21200.0	+	12239.8i	−1.38328	+	0.798635i	−0.992546	−	0.121871i	$-0.961111\pi$
$617$	−21200.0	+	12239.8i	−1.38328	+	0.798635i	−0.390730	+	0.920506i	$0.627777\pi$
$618$		0			0
$619$		−	2927.43i		−	0.190086i	−0.995473	−	0.0950431i	$-0.969701\pi$
$619$		−	2927.43i		−	0.190086i	0.995473	−	0.0950431i	$-0.0302989\pi$
$620$	−10829.0	−	18756.4i	−0.701457	−	1.21496i
$621$		0			0
$622$	−30835.2	−	17802.7i	−1.98775	−	1.14763i
$623$	−726.879			−0.0467445
$624$		0			0
$625$	4802.06			0.307332
$626$	−16574.8	−	9569.47i	−1.05825	−	0.610979i
$627$		0			0
$628$	14192.3	+	24581.7i	0.901805	+	1.56197i
$629$			20926.2i			1.32652i
$630$		0			0
$631$	−8818.74	+	5091.50i	−0.556369	+	0.321220i	−0.751687	−	0.659520i	$-0.770759\pi$
$631$	−8818.74	+	5091.50i	−0.556369	+	0.321220i	0.195318	+	0.980740i	$0.437426\pi$
$632$		−	37840.4i		−	2.38166i
$633$		0			0
$634$	11259.3	−	19501.7i	0.705307	−	1.22163i
$635$	3658.39	+	2112.17i	0.228628	+	0.131999i
$636$		0			0
$637$	7095.44	−	13885.3i	0.441337	−	0.863665i
$638$	33270.2			2.06454
$639$		0			0
$640$	−7005.64	+	12134.1i	−0.432691	+	0.749443i
$641$	−8551.71	−	14812.0i	−0.526946	−	0.912697i	−0.999507	−	0.0313988i	$-0.990004\pi$
$641$	−8551.71	−	14812.0i	−0.526946	−	0.912697i	0.472561	−	0.881298i	$-0.343330\pi$
$642$		0			0
$643$	18822.1	−	10866.9i	1.15439	−	0.666485i	0.204434	−	0.978880i	$-0.434465\pi$
$643$	18822.1	−	10866.9i	1.15439	−	0.666485i	0.949952	+	0.312395i	$0.101131\pi$
$644$	7312.68	−	4221.98i	0.447453	−	0.258337i
$645$		0			0
$646$	494.926	+	857.237i	0.0301434	+	0.0522098i
$647$	−11151.1	+	19314.3i	−0.677584	+	1.17361i	0.298123	+	0.954528i	$0.403640\pi$
$647$	−11151.1	+	19314.3i	−0.677584	+	1.17361i	−0.975706	+	0.219082i	$0.929694\pi$
$648$		0			0
$649$	4606.38			0.278607
$650$	−19134.9	−	9778.00i	−1.15466	−	0.590038i
$651$		0			0
$652$	−37620.6	−	21720.2i	−2.25972	−	1.30465i
$653$	−3488.57	+	6042.39i	−0.209063	+	0.362109i	−0.951420	−	0.307897i	$-0.900375\pi$
$653$	−3488.57	+	6042.39i	−0.209063	+	0.362109i	0.742356	+	0.670005i	$0.233708\pi$
$654$		0			0
$655$			12351.5i			0.736812i
$656$	7210.93	−	4163.23i	0.429176	−	0.247785i
$657$		0			0
$658$		−	1252.14i		−	0.0741845i
$659$	−5013.09	−	8682.92i	−0.296331	−	0.513260i	0.678963	−	0.734173i	$-0.262430\pi$
$659$	−5013.09	−	8682.92i	−0.296331	−	0.513260i	−0.975294	+	0.220913i	$0.929096\pi$
$660$		0			0
$661$	4079.54	+	2355.32i	0.240054	+	0.138595i	0.615202	−	0.788370i	$-0.289075\pi$
$661$	4079.54	+	2355.32i	0.240054	+	0.138595i	−0.375148	+	0.926965i	$0.622408\pi$
$662$	−25085.4			−1.47277
$663$		0			0
$664$	−16213.3			−0.947589
$665$	−47.8679	−	27.6365i	−0.00279133	−	0.00161158i
$666$		0			0
$667$	−12728.5	−	22046.3i	−0.738902	−	1.27982i
$668$			56035.9i			3.24565i
$669$		0			0
$670$	7204.25	−	4159.37i	0.415409	−	0.239837i
$671$			31628.0i			1.81965i
$672$		0			0
$673$	−7363.59	+	12754.1i	−0.421762	+	0.730512i	−0.996112	−	0.0880972i	$-0.971921\pi$
$673$	−7363.59	+	12754.1i	−0.421762	+	0.730512i	0.574350	+	0.818610i	$0.305255\pi$
$674$	28912.9	+	16692.9i	1.65235	+	0.953983i
$675$		0			0
$676$	20653.7	+	28568.2i	1.17511	+	1.62541i
$677$	2118.31			0.120256			0.0601279	−	0.998191i	$-0.480849\pi$
$677$	2118.31			0.120256			0.0601279	+	0.998191i	$0.480849\pi$
$678$		0			0
$679$	−1427.51	+	2472.52i	−0.0806815	+	0.139744i
$680$	7294.33	+	12634.2i	0.411360	+	0.712497i
$681$		0			0
$682$	−44570.5	+	25732.8i	−2.50248	+	1.44481i
$683$	6123.42	−	3535.36i	0.343054	−	0.198063i	−0.318568	−	0.947900i	$-0.603202\pi$
$683$	6123.42	−	3535.36i	0.343054	−	0.198063i	0.661622	+	0.749838i	$0.269868\pi$
$684$		0			0
$685$	−1021.82	−	1769.85i	−0.0569955	−	0.0987191i
$686$	−5323.49	+	9220.55i	−0.296285	+	0.513181i
$687$		0			0
$688$	24671.6			1.36714
$689$	−26763.9	+	1371.14i	−1.47986	+	0.0758146i
$690$		0			0
$691$	13496.1	+	7791.98i	0.743004	+	0.428974i	0.823160	−	0.567809i	$-0.192209\pi$
$691$	13496.1	+	7791.98i	0.743004	+	0.428974i	−0.0801566	+	0.996782i	$0.525542\pi$
$692$	31946.4	−	55332.9i	1.75494	−	3.03965i
$693$		0			0
$694$			53538.7i			2.92839i
$695$	11927.4	−	6886.31i	0.650983	−	0.375845i
$696$		0			0
$697$			8426.17i			0.457911i
$698$	25104.7	+	43482.6i	1.36136	+	2.35794i
$699$		0			0
$700$	4174.74	+	2410.29i	0.225415	+	0.130143i
$701$	−13190.6			−0.710703			−0.355352	−	0.934733i	$-0.615639\pi$
$701$	−13190.6			−0.710703			−0.355352	+	0.934733i	$0.615639\pi$
$702$		0			0
$703$	973.404			0.0522228
$704$	19019.7	+	10981.1i	1.01823	+	0.587875i
$705$		0			0
$706$	2118.44	+	3669.25i	0.112930	+	0.195601i
$707$			5978.17i			0.318009i
$708$		0			0
$709$	27336.9	−	15783.0i	1.44804	−	0.836025i	0.449673	−	0.893193i	$-0.351541\pi$
$709$	27336.9	−	15783.0i	1.44804	−	0.836025i	0.998365	+	0.0571687i	$0.0182073\pi$
$710$		−	27618.6i		−	1.45987i
$711$		0			0
$712$	4462.07	−	7728.53i	0.234864	−	0.406796i
$713$	34103.4	+	19689.6i	1.79128	+	1.03420i
$714$		0			0
$715$	5225.48	−	10225.9i	0.273317	−	0.534862i
$716$	36183.7			1.88861
$717$		0			0
$718$	−28024.2	+	48539.3i	−1.45662	+	2.52294i
$719$	7767.67	+	13454.0i	0.402900	+	0.697844i	0.994075	−	0.108700i	$-0.0346688\pi$
$719$	7767.67	+	13454.0i	0.402900	+	0.697844i	−0.591174	+	0.806544i	$0.701335\pi$
$720$		0			0
$721$	−914.226	+	527.829i	−0.0472227	+	0.0272640i
$722$	−29088.0	+	16794.0i	−1.49937	+	0.865661i
$723$		0			0
$724$	7141.16	+	12368.8i	0.366573	+	0.634923i
$725$	7266.56	−	12586.0i	0.372239	−	0.644736i
$726$		0			0
$727$	27639.6			1.41004			0.705018	−	0.709189i	$-0.250939\pi$
$727$	27639.6			1.41004			0.705018	+	0.709189i	$0.250939\pi$
$728$	−3230.61	−	4987.51i	−0.164470	−	0.253914i
$729$		0			0
$730$	6626.57	+	3825.85i	0.335973	+	0.193974i
$731$	−12483.5	+	21622.0i	−0.631626	+	1.09401i
$732$		0			0
$733$			1318.97i			0.0664629i	0.999448	+	0.0332314i	$0.0105798\pi$
$733$			1318.97i			0.0664629i	−0.999448	+	0.0332314i	$0.989420\pi$
$734$	−39120.4	+	22586.2i	−1.96725	+	1.13579i
$735$		0			0
$736$			587.434i			0.0294200i
$737$	−6595.47	−	11423.7i	−0.329644	−	0.570960i
$738$		0			0
$739$	2572.74	+	1485.37i	0.128065	+	0.0739382i	0.562664	−	0.826686i	$-0.309777\pi$
$739$	2572.74	+	1485.37i	0.128065	+	0.0739382i	−0.434599	+	0.900624i	$0.643110\pi$
$740$	28611.2			1.42131
$741$		0			0
$742$	9009.32			0.445745
$743$	−24935.1	−	14396.3i	−1.23120	−	0.710833i	−0.263919	−	0.964545i	$-0.585015\pi$
$743$	−24935.1	−	14396.3i	−1.23120	−	0.710833i	−0.967280	+	0.253712i	$0.918349\pi$
$744$		0			0
$745$	−182.837	−	316.683i	−0.00899146	−	0.0155737i
$746$			5482.88i			0.269092i
$747$		0			0
$748$	39954.2	−	23067.5i	1.95303	−	1.12758i
$749$			1056.50i			0.0515402i
$750$		0			0
$751$	−3919.72	+	6789.16i	−0.190456	+	0.329880i	−0.945402	−	0.325908i	$-0.894330\pi$
$751$	−3919.72	+	6789.16i	−0.190456	+	0.329880i	0.754945	+	0.655788i	$0.227663\pi$
$752$	4479.70	+	2586.36i	0.217231	+	0.125419i
$753$		0			0
$754$	−29987.6	+	19424.2i	−1.44839	+	0.938179i
$755$	−1404.46			−0.0677000
$756$		0			0
$757$	1596.21	−	2764.71i	0.0766383	−	0.132741i	−0.825159	−	0.564900i	$-0.808915\pi$
$757$	1596.21	−	2764.71i	0.0766383	−	0.132741i	0.901798	+	0.432159i	$0.142248\pi$
$758$	−19781.2	−	34262.1i	−0.947872	−	1.64176i
$759$		0			0
$760$	587.690	−	339.303i	0.0280497	−	0.0161945i
$761$	−22016.0	+	12710.9i	−1.04872	+	0.605481i	−0.922292	−	0.386495i	$-0.873686\pi$
$761$	−22016.0	+	12710.9i	−1.04872	+	0.605481i	−0.126432	+	0.991975i	$0.540352\pi$
$762$		0			0
$763$	324.034	+	561.243i	0.0153746	+	0.0266296i
$764$	6416.42	−	11113.6i	0.303845	−	0.526276i
$765$		0			0
$766$	9923.64			0.468089
$767$	−4151.89	+	2689.35i	−0.195458	+	0.126606i
$768$		0			0
$769$	−29384.8	−	16965.3i	−1.37795	−	0.795559i	−0.386036	−	0.922484i	$-0.626156\pi$
$769$	−29384.8	−	16965.3i	−1.37795	−	0.795559i	−0.991912	+	0.126925i	$0.959489\pi$
$770$	−1930.30	+	3343.37i	−0.0903417	+	0.156476i
$771$		0			0
$772$			43217.2i			2.01480i
$773$	35158.0	−	20298.5i	1.63589	−	0.944483i	0.653666	−	0.756783i	$-0.273230\pi$
$773$	35158.0	−	20298.5i	1.63589	−	0.944483i	0.982226	−	0.187700i	$-0.0601033\pi$
$774$		0			0
$775$			22481.2i			1.04200i
$776$	−17526.0	−	30355.9i	−0.810756	−	1.40427i
$777$		0			0
$778$	−41180.8	−	23775.8i	−1.89769	−	1.09563i
$779$	391.952			0.0180271
$780$		0			0
$781$	−43794.5			−2.00652
$782$	−45813.4	−	26450.4i	−2.09499	−	1.20954i
$783$		0			0
$784$	−10827.9	−	18754.5i	−0.493254	−	0.854340i
$785$			9929.81i			0.451478i
$786$		0			0
$787$	33815.0	−	19523.1i	1.53161	−	0.884274i	0.532319	−	0.846544i	$-0.321321\pi$
$787$	33815.0	−	19523.1i	1.53161	−	0.884274i	0.999288	−	0.0377296i	$-0.0120126\pi$
$788$			43896.0i			1.98443i
$789$		0			0
$790$	13200.3	−	22863.5i	0.594487	−	1.02968i
$791$	−807.005	−	465.925i	−0.0362754	−	0.0209436i
$792$		0			0
$793$	−18465.4	−	28507.4i	−0.826893	−	1.27658i
$794$	−16654.0			−0.744367
$795$		0			0
$796$	9438.30	−	16347.6i	0.420266	−	0.727922i
$797$	−4037.40	−	6992.98i	−0.179438	−	0.310795i	0.762250	−	0.647282i	$-0.224095\pi$
$797$	−4037.40	−	6992.98i	−0.179438	−	0.310795i	−0.941688	+	0.336487i	$0.890761\pi$
$798$		0			0
$799$	−4533.34	+	2617.33i	−0.200724	+	0.115888i
$800$	−290.431	+	167.680i	−0.0128354	+	0.00741049i
$801$		0			0
$802$	16304.3	+	28240.0i	0.717863	+	1.24338i
$803$	6066.62	−	10507.7i	0.266608	−	0.461779i
$804$		0			0
$805$	2953.96			0.129334
$806$	25149.4	−	49215.5i	1.09907	−	2.15080i
$807$		0			0
$808$	−63562.8	−	36698.0i	−2.76749	−	1.59781i
$809$	15064.0	−	26091.6i	0.654663	−	1.13391i	−0.327316	−	0.944915i	$-0.606144\pi$
$809$	15064.0	−	26091.6i	0.654663	−	1.13391i	0.981978	−	0.188994i	$-0.0605227\pi$
$810$		0			0
$811$			707.812i			0.0306469i	0.999883	+	0.0153235i	$0.00487780\pi$
$811$			707.812i			0.0306469i	−0.999883	+	0.0153235i	$0.995122\pi$
$812$	6941.36	−	4007.60i	0.299993	−	0.173201i
$813$		0			0
$814$		−	67988.2i		−	2.92750i
$815$	−7598.43	−	13160.9i	−0.326578	−	0.565650i
$816$		0			0
$817$	1005.77	+	580.682i	0.0430691	+	0.0248660i
$818$	−12334.8			−0.527233
$819$		0			0
$820$	11520.6			0.490630
$821$	13527.5	+	7810.13i	0.575048	+	0.332004i	0.759163	−	0.650900i	$-0.225608\pi$
$821$	13527.5	+	7810.13i	0.575048	+	0.332004i	−0.184115	+	0.982905i	$0.558942\pi$
$822$		0			0
$823$	16355.0	+	28327.7i	0.692710	+	1.19981i	0.970947	+	0.239296i	$0.0769168\pi$
$823$	16355.0	+	28327.7i	0.692710	+	1.19981i	−0.278236	+	0.960513i	$0.589750\pi$
$824$		−	12960.7i		−	0.547944i
$825$		0			0
$826$	1440.22	−	831.511i	0.0606679	−	0.0350266i
$827$		−	28246.1i		−	1.18768i	−0.804582	−	0.593842i	$-0.797611\pi$
$827$		−	28246.1i		−	1.18768i	0.804582	−	0.593842i	$-0.202389\pi$
$828$		0			0
$829$	−7049.60	+	12210.3i	−0.295347	+	0.511556i	−0.975066	−	0.221917i	$-0.928769\pi$
$829$	−7049.60	+	12210.3i	−0.295347	+	0.511556i	0.679719	+	0.733473i	$0.262102\pi$
$830$	−9796.24	−	5655.86i	−0.409678	−	0.236528i
$831$		0			0
$832$	−23554.3	+	1206.71i	−0.981487	+	0.0502825i
$833$	21915.1			0.911541
$834$		0			0
$835$	−9801.57	+	16976.8i	−0.406224	+	0.703601i
$836$	−1073.01	−	1858.51i	−0.0443909	−	0.0768874i
$837$		0			0
$838$	50567.0	−	29194.9i	2.08450	−	1.20348i
$839$	9946.53	−	5742.63i	0.409288	−	0.236302i	−0.281196	−	0.959650i	$-0.590731\pi$
$839$	9946.53	−	5742.63i	0.409288	−	0.236302i	0.690484	+	0.723348i	$0.257398\pi$
$840$		0			0
$841$	112.357	+	194.608i	0.00460687	+	0.00797933i
$842$	−5842.39	+	10119.3i	−0.239123	+	0.414174i
$843$		0			0
$844$	46767.3			1.90734
$845$	1260.29	+	12267.8i	0.0513079	+	0.499436i
$846$		0			0
$847$	1597.47	+	922.302i	0.0648050	+	0.0374152i
$848$	−18609.2	+	32232.2i	−0.753590	+	1.30526i
$849$		0			0
$850$		−	30200.5i		−	1.21867i
$851$	−45052.1	+	26010.8i	−1.81477	+	1.04776i
$852$		0			0
$853$			11836.8i			0.475128i	0.971372	+	0.237564i	$0.0763489\pi$
$853$			11836.8i			0.475128i	−0.971372	+	0.237564i	$0.923651\pi$
$854$	5709.26	+	9888.74i	0.228767	+	0.396236i
$855$		0			0
$856$	−11233.2	−	6485.49i	−0.448532	−	0.258960i
$857$	31156.2			1.24186			0.620931	−	0.783865i	$-0.286755\pi$
$857$	31156.2			1.24186			0.620931	+	0.783865i	$0.286755\pi$
$858$		0			0
$859$	−1584.88			−0.0629515			−0.0314758	−	0.999505i	$-0.510021\pi$
$859$	−1584.88			−0.0629515			−0.0314758	+	0.999505i	$0.510021\pi$
$860$	29562.5	+	17067.9i	1.17218	+	0.676758i
$861$		0			0
$862$	−702.556	−	1216.86i	−0.0277600	−	0.0480818i
$863$		−	19884.8i		−	0.784340i	−0.919893	−	0.392170i	$-0.871724\pi$
$863$		−	19884.8i		−	0.784340i	0.919893	−	0.392170i	$-0.128276\pi$
$864$		0			0
$865$	19357.2	−	11175.9i	0.760883	−	0.439296i
$866$		−	4160.02i		−	0.163237i
$867$		0			0
$868$	−6199.34	+	10737.6i	−0.242419	+	0.419881i
$869$	−36254.5	−	20931.5i	−1.41525	−	0.817093i
$870$		0			0
$871$	12614.2	+	6445.94i	0.490720	+	0.250760i
$872$	−7956.54			−0.308994
$873$		0			0
$874$	−1230.37	+	2131.06i	−0.0476175	+	0.0824760i
$875$	1970.56	+	3413.12i	0.0761340	+	0.131868i
$876$		0			0
$877$	4748.79	−	2741.72i	0.182845	−	0.105566i	−0.405784	−	0.913969i	$-0.633001\pi$
$877$	4748.79	−	2741.72i	0.182845	−	0.105566i	0.588629	+	0.808403i	$0.299668\pi$
$878$	295.964	−	170.875i	0.0113762	−	0.00656805i
$879$		0			0
$880$	−7974.27	−	13811.8i	−0.305469	−	0.529088i
$881$	−3290.56	+	5699.41i	−0.125836	+	0.217955i	−0.922060	−	0.387048i	$-0.873495\pi$
$881$	−3290.56	+	5699.41i	−0.125836	+	0.217955i	0.796223	+	0.605003i	$0.206828\pi$
$882$		0			0
$883$	−6942.60			−0.264595			−0.132297	−	0.991210i	$-0.542235\pi$
$883$	−6942.60			−0.264595			−0.132297	+	0.991210i	$0.542235\pi$
$884$	−22544.6	+	44118.1i	−0.857755	+	1.67857i
$885$		0			0
$886$	31132.4	+	17974.3i	1.18049	+	0.681556i
$887$	−3281.34	+	5683.45i	−0.124213	+	0.215143i	−0.921425	−	0.388557i	$-0.872974\pi$
$887$	−3281.34	+	5683.45i	−0.124213	+	0.215143i	0.797212	+	0.603699i	$0.206307\pi$
$888$		0			0
$889$		−	2418.34i		−	0.0912355i
$890$	5392.05	−	3113.10i	0.203081	−	0.117249i
$891$		0			0
$892$		−	23769.7i		−	0.892231i
$893$	121.748	+	210.873i	0.00456229	+	0.00790212i
$894$		0			0
$895$	10962.3	+	6329.09i	0.409419	+	0.236378i
$896$	8021.11			0.299070
$897$		0			0
$898$	69696.2			2.58997
$899$	32371.7	+	18689.8i	1.20095	+	0.693371i
$900$		0			0
$901$	−18832.1	−	32618.1i	−0.696323	−	1.20607i
$902$		−	27376.2i		−	1.01056i
$903$		0			0
$904$	9907.88	−	5720.31i	0.364526	−	0.210459i
$905$			4996.40i			0.183521i
$906$		0			0
$907$	−826.163	+	1430.96i	−0.0302451	+	0.0523860i	−0.880752	−	0.473578i	$-0.842962\pi$
$907$	−826.163	+	1430.96i	−0.0302451	+	0.0523860i	0.850507	+	0.525964i	$0.176295\pi$
$908$	−60.9111	−	35.1670i	−0.00222622	−	0.00128531i
$909$		0			0
$910$	−212.120	−	4140.47i	−0.00772717	−	0.150830i
$911$	−506.240			−0.0184110			−0.00920552	−	0.999958i	$-0.502930\pi$
$911$	−506.240			−0.0184110			−0.00920552	+	0.999958i	$0.502930\pi$
$912$		0			0
$913$	−8968.44	+	15533.8i	−0.325095	+	0.563082i
$914$	14473.6	+	25069.0i	0.523789	+	0.907229i
$915$		0			0
$916$	−65165.9	+	37623.5i	−2.35059	+	1.35711i
$917$	6123.59	−	3535.46i	0.220522	−	0.127318i
$918$		0			0
$919$	1234.64	+	2138.47i	0.0443168	+	0.0767590i	0.887333	−	0.461129i	$-0.152556\pi$
$919$	1234.64	+	2138.47i	0.0443168	+	0.0767590i	−0.843016	+	0.537888i	$0.819222\pi$
$920$	−18133.4	+	31408.0i	−0.649826	+	1.12553i
$921$		0			0
$922$	2764.69			0.0987531
$923$	39473.5	−	25568.6i	1.40768	−	0.911810i
$924$		0			0
$925$	−25719.8	−	14849.3i	−0.914229	−	0.527831i
$926$	−43014.2	+	74502.8i	−1.52650	+	2.64397i
$927$		0			0
$928$			557.606i			0.0197245i
$929$	36066.2	−	20822.9i	1.27373	−	0.735388i	0.298042	−	0.954553i	$-0.403666\pi$
$929$	36066.2	−	20822.9i	1.27373	−	0.735388i	0.975688	+	0.219164i	$0.0703331\pi$
$930$		0			0
$931$		−	1019.40i		−	0.0358857i
$932$	33090.2	+	57313.8i	1.16299	+	2.01435i
$933$		0			0
$934$	−38754.3	−	22374.8i	−1.35769	−	0.783860i
$935$	16139.5			0.564512
$936$		0			0
$937$	−33891.2			−1.18162			−0.590810	−	0.806811i	$-0.701192\pi$
$937$	−33891.2			−1.18162			−0.590810	+	0.806811i	$0.701192\pi$
$938$	−4124.25	−	2381.14i	−0.143563	−	0.0828859i
$939$		0			0
$940$	3578.52	+	6198.17i	0.124168	+	0.215066i
$941$		−	28351.3i		−	0.982173i	−0.871111	−	0.491087i	$-0.836600\pi$
$941$		−	28351.3i		−	0.982173i	0.871111	−	0.491087i	$-0.163400\pi$
$942$		0			0
$943$	−18140.7	+	10473.5i	−0.626451	+	0.361681i
$944$			6870.13i			0.236868i
$945$		0			0
$946$	40558.2	−	70248.9i	1.39393	−	2.41437i
$947$	−3232.62	−	1866.36i	−0.110925	−	0.0640427i	0.443511	−	0.896269i	$-0.353733\pi$
$947$	−3232.62	−	1866.36i	−0.110925	−	0.0640427i	−0.554436	+	0.832226i	$0.687066\pi$
$948$		0			0
$949$	666.660	+	13012.8i	0.0228037	+	0.445115i
$950$	−1404.81			−0.0479768
$951$		0			0
$952$	4175.83	−	7232.74i	0.142163	−	0.246234i
$953$	4826.05	+	8358.96i	0.164041	+	0.284127i	0.936314	−	0.351163i	$-0.114214\pi$
$953$	4826.05	+	8358.96i	0.164041	+	0.284127i	−0.772273	+	0.635290i	$0.780880\pi$
$954$		0			0
$955$	3887.88	−	2244.67i	0.131737	−	0.0760583i
$956$	48016.0	−	27722.0i	1.62442	−	0.937860i
$957$		0			0
$958$	12185.9	+	21106.6i	0.410969	+	0.711819i
$959$	−584.969	+	1013.20i	−0.0196972	+	0.0341166i
$960$		0			0
$961$	−28031.5			−0.940939
$962$	39693.7	+	61280.2i	1.33033	+	2.05380i
$963$		0			0
$964$	57107.5	+	32971.0i	1.90800	+	1.10158i
$965$	−7559.38	+	13093.2i	−0.252171	+	0.436773i
$966$		0			0
$967$			36196.6i			1.20373i	0.798598	+	0.601864i	$0.205575\pi$
$967$			36196.6i			1.20373i	−0.798598	+	0.601864i	$0.794425\pi$
$968$	−19612.7	+	11323.4i	−0.651216	+	0.375979i
$969$		0			0
$970$		−	24455.1i		−	0.809490i
$971$	2625.49	+	4547.48i	0.0867723	+	0.150294i	0.906145	−	0.422967i	$-0.139011\pi$
$971$	2625.49	+	4547.48i	0.0867723	+	0.150294i	−0.819373	+	0.573261i	$0.805678\pi$
$972$		0			0
$973$	−6828.16	−	3942.24i	−0.224975	−	0.129890i
$974$	−28033.1			−0.922215
$975$		0			0
$976$	−47171.2			−1.54704
$977$	−20069.9	−	11587.4i	−0.657210	−	0.379440i	0.134003	−	0.990981i	$-0.457217\pi$
$977$	−20069.9	−	11587.4i	−0.657210	−	0.379440i	−0.791213	+	0.611541i	$0.790550\pi$
$978$		0			0
$979$	−4936.41	−	8550.12i	−0.161153	−	0.279124i
$980$		−	29963.2i		−	0.976674i
$981$		0			0
$982$	−25667.8	+	14819.3i	−0.834105	+	0.481571i
$983$		−	33285.5i		−	1.08000i	−0.841664	−	0.540001i	$-0.818424\pi$
$983$		−	33285.5i		−	1.08000i	0.841664	−	0.540001i	$-0.181576\pi$
$984$		0			0
$985$	−7678.10	+	13298.9i	−0.248370	+	0.430190i
$986$	−43487.1	−	25107.3i	−1.40458	−	0.810932i
$987$		0			0
$988$	2052.20	+	1048.68i	0.0660821	+	0.0337682i
$989$	−62066.8			−1.99556
$990$		0			0
$991$	7767.68	−	13454.0i	0.248990	−	0.431262i	−0.714256	−	0.699884i	$-0.753235\pi$
$991$	7767.68	−	13454.0i	0.248990	−	0.431262i	0.963246	+	0.268622i	$0.0865682\pi$
$992$	−431.280	−	746.998i	−0.0138036	−	0.0239085i
$993$		0			0
$994$	−13692.7	+	7905.48i	−0.436927	+	0.252260i
$995$	5718.91	−	3301.81i	0.182213	−	0.105201i
$996$		0			0
$997$	−13151.2	−	22778.5i	−0.417756	−	0.723574i	0.577958	−	0.816067i	$-0.303850\pi$
$997$	−13151.2	−	22778.5i	−0.417756	−	0.723574i	−0.995713	+	0.0924929i	$0.970516\pi$
$998$	−2699.84	+	4676.27i	−0.0856333	+	0.148321i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.4.q.f.82.6	yes	12
3.2	odd	2	inner	117.4.q.f.82.1	yes	12
13.6	odd	12		1521.4.a.bl.1.1		12
13.7	odd	12		1521.4.a.bl.1.12		12
13.10	even	6	inner	117.4.q.f.10.6	yes	12
39.20	even	12		1521.4.a.bl.1.2		12
39.23	odd	6	inner	117.4.q.f.10.1	✓	12
39.32	even	12		1521.4.a.bl.1.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.4.q.f.10.1	✓	12	39.23	odd	6	inner
117.4.q.f.10.6	yes	12	13.10	even	6	inner
117.4.q.f.82.1	yes	12	3.2	odd	2	inner
117.4.q.f.82.6	yes	12	1.1	even	1	trivial
1521.4.a.bl.1.1		12	13.6	odd	12
1521.4.a.bl.1.2		12	39.20	even	12
1521.4.a.bl.1.11		12	39.32	even	12
1521.4.a.bl.1.12		12	13.7	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	117.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.24667 + 2.45182i) q^{2} +(8.02279 + 13.8959i) q^{4} +5.61325i q^{5} +(2.78293 - 1.60672i) q^{7} +39.4526i q^{8} +O(q^{10})\)	\(q+(4.24667 + 2.45182i) q^{2} +(8.02279 + 13.8959i) q^{4} +5.61325i q^{5} +(2.78293 - 1.60672i) q^{7} +39.4526i q^{8} +(-13.7627 + 23.8376i) q^{10} +(37.7991 + 21.8233i) q^{11} +(-46.8108 + 2.39816i) q^{13} +15.7576 q^{14} +(-32.5481 + 56.3750i) q^{16} +(-32.9378 - 57.0500i) q^{17} +(-2.65374 + 1.53214i) q^{19} +(-78.0011 + 45.0340i) q^{20} +(107.013 + 185.353i) q^{22} +(81.8821 - 141.824i) q^{23} +93.4914 q^{25} +(-204.670 - 104.587i) q^{26} +(44.6537 + 25.7808i) q^{28} +(77.7243 - 134.622i) q^{29} +240.463i q^{31} +(-3.10650 + 1.79354i) q^{32} -323.030i q^{34} +(9.01895 + 15.6213i) q^{35} +(-275.104 - 158.831i) q^{37} -15.0261 q^{38} -221.457 q^{40} +(-110.773 - 63.9551i) q^{41} +(-189.501 - 328.225i) q^{43} +700.336i q^{44} +(695.452 - 401.519i) q^{46} -79.4626i q^{47} +(-166.337 + 288.104i) q^{49} +(397.027 + 229.224i) q^{50} +(-408.878 - 631.237i) q^{52} +571.746 q^{53} +(-122.500 + 212.176i) q^{55} +(63.3895 + 109.794i) q^{56} +(660.139 - 381.131i) q^{58} +(91.3986 - 52.7690i) q^{59} +(362.319 + 627.555i) q^{61} +(-589.571 + 1021.17i) q^{62} +503.180 q^{64} +(-13.4615 - 262.761i) q^{65} +(-261.732 - 151.111i) q^{67} +(528.507 - 915.401i) q^{68} +88.4512i q^{70} +(-868.960 + 501.694i) q^{71} -277.988i q^{73} +(-778.849 - 1349.01i) q^{74} +(-42.5808 - 24.5840i) q^{76} +140.256 q^{77} -959.137 q^{79} +(-316.447 - 182.701i) q^{80} +(-313.612 - 543.192i) q^{82} +410.957i q^{83} +(320.236 - 184.888i) q^{85} -1858.48i q^{86} +(-860.986 + 1491.27i) q^{88} +(-195.894 - 113.100i) q^{89} +(-126.418 + 81.8860i) q^{91} +2627.69 q^{92} +(194.828 - 337.451i) q^{94} +(-8.60027 - 14.8961i) q^{95} +(-769.427 + 444.229i) q^{97} +(-1412.76 + 815.655i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 16 q^{4} - 18 q^{7}+O(q^{10}) \) 12 * q + 16 * q^4 - 18 * q^7	\( 12 q + 16 q^{4} - 18 q^{7} - 56 q^{10} - 154 q^{13} - 92 q^{16} - 48 q^{19} + 292 q^{22} - 92 q^{25} + 552 q^{28} - 360 q^{37} - 448 q^{40} - 810 q^{43} + 996 q^{46} - 1068 q^{49} - 700 q^{52} + 460 q^{55} + 3048 q^{58} + 1294 q^{61} - 184 q^{64} + 2658 q^{67} + 1188 q^{76} - 6380 q^{79} - 1268 q^{82} - 3768 q^{85} - 5140 q^{88} + 342 q^{91} + 1660 q^{94} + 1686 q^{97}+O(q^{100}) \) 12 * q + 16 * q^4 - 18 * q^7 - 56 * q^10 - 154 * q^13 - 92 * q^16 - 48 * q^19 + 292 * q^22 - 92 * q^25 + 552 * q^28 - 360 * q^37 - 448 * q^40 - 810 * q^43 + 996 * q^46 - 1068 * q^49 - 700 * q^52 + 460 * q^55 + 3048 * q^58 + 1294 * q^61 - 184 * q^64 + 2658 * q^67 + 1188 * q^76 - 6380 * q^79 - 1268 * q^82 - 3768 * q^85 - 5140 * q^88 + 342 * q^91 + 1660 * q^94 + 1686 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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