LMFDB - Embedded newform 117.4.q.e.10.2

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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 70x^{8} + 1645x^{6} + 14700x^{4} + 44100x^{2} + 27648 $ x^10 + 70x^8 + 1645x^6 + 14700x^4 + 44100x^2 + 27648
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.2
Root			$3.27897i$ of defining polynomial
Character	$\chi$	$=$	117.10
Dual form			117.4.q.e.82.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.83967 + 1.63949i) q^{2} +(1.37583 - 2.38302i) q^{4} +17.5414i q^{5} +(23.1228 + 13.3499i) q^{7} -17.2091i q^{8} +O(q^{10})$	\(q+(-2.83967 + 1.63949i) q^{2} +(1.37583 - 2.38302i) q^{4} +17.5414i q^{5} +(23.1228 + 13.3499i) q^{7} -17.2091i q^{8} +(-28.7589 - 49.8119i) q^{10} +(18.5352 - 10.7013i) q^{11} +(-8.67555 + 46.0623i) q^{13} -87.5483 q^{14} +(39.2208 + 67.9325i) q^{16} +(-41.9815 + 72.7141i) q^{17} +(-66.7828 - 38.5571i) q^{19} +(41.8015 + 24.1341i) q^{20} +(-35.0892 + 60.7763i) q^{22} +(-71.0597 - 123.079i) q^{23} -182.701 q^{25} +(-50.8828 - 145.025i) q^{26} +(63.6263 - 36.7346i) q^{28} +(67.1115 + 116.241i) q^{29} -122.559i q^{31} +(-103.520 - 59.7675i) q^{32} -275.312i q^{34} +(-234.177 + 405.606i) q^{35} +(-192.766 + 111.294i) q^{37} +252.855 q^{38} +301.873 q^{40} +(171.751 - 99.1604i) q^{41} +(77.3279 - 133.936i) q^{43} -58.8928i q^{44} +(403.573 + 233.003i) q^{46} +78.7956i q^{47} +(184.942 + 320.329i) q^{49} +(518.811 - 299.536i) q^{50} +(97.8310 + 84.0481i) q^{52} +477.088 q^{53} +(187.716 + 325.133i) q^{55} +(229.741 - 397.923i) q^{56} +(-381.150 - 220.057i) q^{58} +(-37.1769 - 21.4641i) q^{59} +(-248.269 + 430.015i) q^{61} +(200.934 + 348.028i) q^{62} -235.581 q^{64} +(-807.998 - 152.181i) q^{65} +(419.727 - 242.329i) q^{67} +(115.519 + 200.085i) q^{68} -1535.72i q^{70} +(-331.196 - 191.216i) q^{71} +193.622i q^{73} +(364.929 - 632.076i) q^{74} +(-183.764 + 106.096i) q^{76} +571.447 q^{77} +1049.60 q^{79} +(-1191.63 + 687.989i) q^{80} +(-325.144 + 563.166i) q^{82} +861.900i q^{83} +(-1275.51 - 736.414i) q^{85} +507.112i q^{86} +(-184.160 - 318.974i) q^{88} +(-838.005 + 483.823i) q^{89} +(-815.532 + 949.271i) q^{91} -391.065 q^{92} +(-129.184 - 223.754i) q^{94} +(676.345 - 1171.46i) q^{95} +(512.228 + 295.735i) q^{97} +(-1050.35 - 606.421i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 30 q^{4} + 30 q^{7}+O(q^{10}) $ 10 * q + 30 * q^4 + 30 * q^7	$ 10 q + 30 q^{4} + 30 q^{7} + 40 q^{10} - 60 q^{11} + 25 q^{13} + 60 q^{14} - 250 q^{16} - 105 q^{17} + 180 q^{19} - 510 q^{20} - 290 q^{22} + 60 q^{23} - 960 q^{25} + 30 q^{26} + 150 q^{28} + 495 q^{29} - 1440 q^{32} - 60 q^{35} - 405 q^{37} + 1380 q^{38} + 2000 q^{40} - 1065 q^{41} - 370 q^{43} - 390 q^{46} + 775 q^{49} + 4320 q^{50} + 2940 q^{52} - 330 q^{53} - 260 q^{55} + 2670 q^{56} + 2040 q^{58} - 780 q^{59} - 1375 q^{61} + 780 q^{62} - 3140 q^{64} - 1605 q^{65} + 1590 q^{67} + 600 q^{68} - 1620 q^{71} - 2190 q^{74} - 5190 q^{76} + 4320 q^{77} + 1100 q^{79} - 8430 q^{80} - 2390 q^{82} + 525 q^{85} + 3170 q^{88} - 2040 q^{89} + 4770 q^{91} + 1740 q^{92} - 3230 q^{94} + 1380 q^{95} - 3750 q^{97} - 180 q^{98}+O(q^{100}) $ 10 * q + 30 * q^4 + 30 * q^7 + 40 * q^10 - 60 * q^11 + 25 * q^13 + 60 * q^14 - 250 * q^16 - 105 * q^17 + 180 * q^19 - 510 * q^20 - 290 * q^22 + 60 * q^23 - 960 * q^25 + 30 * q^26 + 150 * q^28 + 495 * q^29 - 1440 * q^32 - 60 * q^35 - 405 * q^37 + 1380 * q^38 + 2000 * q^40 - 1065 * q^41 - 370 * q^43 - 390 * q^46 + 775 * q^49 + 4320 * q^50 + 2940 * q^52 - 330 * q^53 - 260 * q^55 + 2670 * q^56 + 2040 * q^58 - 780 * q^59 - 1375 * q^61 + 780 * q^62 - 3140 * q^64 - 1605 * q^65 + 1590 * q^67 + 600 * q^68 - 1620 * q^71 - 2190 * q^74 - 5190 * q^76 + 4320 * q^77 + 1100 * q^79 - 8430 * q^80 - 2390 * q^82 + 525 * q^85 + 3170 * q^88 - 2040 * q^89 + 4770 * q^91 + 1740 * q^92 - 3230 * q^94 + 1380 * q^95 - 3750 * q^97 - 180 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.83967	+	1.63949i	−1.00398	+	0.579646i	−0.909422	−	0.415874i	$-0.863476\pi$
$2$	−2.83967	+	1.63949i	−1.00398	+	0.579646i	−0.0945542	+	0.995520i	$0.530143\pi$
$3$		0			0
$3$		0			0
$4$	1.37583	−	2.38302i	0.171979	−	0.297877i
$5$			17.5414i			1.56895i	0.620160	+	0.784476i	$0.287068\pi$
$5$			17.5414i			1.56895i	−0.620160	+	0.784476i	$0.712932\pi$
$6$		0			0
$7$	23.1228	+	13.3499i	1.24851	+	0.720829i	0.970813	−	0.239838i	$-0.0770944\pi$
$7$	23.1228	+	13.3499i	1.24851	+	0.720829i	0.277700	+	0.960668i	$0.410428\pi$
$8$		−	17.2091i		−	0.760544i
$9$		0			0
$10$	−28.7589	−	49.8119i	−0.909437	−	1.57519i
$11$	18.5352	−	10.7013i	0.508051	−	0.293324i	−0.223981	−	0.974594i	$-0.571905\pi$
$11$	18.5352	−	10.7013i	0.508051	−	0.293324i	0.732032	+	0.681270i	$0.238572\pi$
$12$		0			0
$13$	−8.67555	+	46.0623i	−0.185090	+	0.982722i
$13$	−8.67555	+	46.0623i	−0.185090	+	0.982722i
$14$	−87.5483			−1.67130
$15$		0			0
$16$	39.2208	+	67.9325i	0.612826	+	1.06144i
$17$	−41.9815	+	72.7141i	−0.598942	+	1.03740i	0.394036	+	0.919095i	$0.371078\pi$
$17$	−41.9815	+	72.7141i	−0.598942	+	1.03740i	−0.992978	+	0.118302i	$0.962255\pi$
$18$		0			0
$19$	−66.7828	−	38.5571i	−0.806370	−	0.465558i	0.0393237	−	0.999227i	$-0.487480\pi$
$19$	−66.7828	−	38.5571i	−0.806370	−	0.465558i	−0.845694	+	0.533669i	$0.820813\pi$
$20$	41.8015	+	24.1341i	0.467354	+	0.269827i
$21$		0			0
$22$	−35.0892	+	60.7763i	−0.340048	+	0.588980i
$23$	−71.0597	−	123.079i	−0.644216	−	1.11581i	−0.984482	−	0.175486i	$-0.943850\pi$
$23$	−71.0597	−	123.079i	−0.644216	−	1.11581i	0.340266	−	0.940329i	$-0.389483\pi$
$24$		0			0
$25$	−182.701			−1.46161
$26$	−50.8828	−	145.025i	−0.383805	−	1.09392i
$27$		0			0
$28$	63.6263	−	36.7346i	0.429437	−	0.247936i
$29$	67.1115	+	116.241i	0.429734	+	0.744322i	0.996849	−	0.0793167i	$-0.0252739\pi$
$29$	67.1115	+	116.241i	0.429734	+	0.744322i	−0.567115	+	0.823639i	$0.691941\pi$
$30$		0			0
$31$		−	122.559i		−	0.710074i	−0.934852	−	0.355037i	$-0.884468\pi$
$31$		−	122.559i		−	0.710074i	0.934852	−	0.355037i	$-0.115532\pi$
$32$	−103.520	−	59.7675i	−0.571875	−	0.330172i
$33$		0			0
$34$		−	275.312i		−	1.38870i
$35$	−234.177	+	405.606i	−1.13095	+	1.95886i
$36$		0			0
$37$	−192.766	+	111.294i	−0.856502	+	0.494502i	−0.862839	−	0.505478i	$-0.831316\pi$
$37$	−192.766	+	111.294i	−0.856502	+	0.494502i	0.00633725	+	0.999980i	$0.497983\pi$
$38$	252.855			1.07944
$39$		0			0
$40$	301.873			1.19326
$41$	171.751	−	99.1604i	0.654219	−	0.377713i	−0.135852	−	0.990729i	$-0.543377\pi$
$41$	171.751	−	99.1604i	0.654219	−	0.377713i	0.790071	+	0.613016i	$0.210044\pi$
$42$		0			0
$43$	77.3279	−	133.936i	0.274242	−	0.475000i	−0.695702	−	0.718331i	$-0.744907\pi$
$43$	77.3279	−	133.936i	0.274242	−	0.475000i	0.969944	+	0.243330i	$0.0782398\pi$
$44$		−	58.8928i		−	0.201782i
$45$		0			0
$46$	403.573	+	233.003i	1.29356	+	0.746835i
$47$			78.7956i			0.244543i	0.992497	+	0.122271i	$0.0390178\pi$
$47$			78.7956i			0.244543i	−0.992497	+	0.122271i	$0.960982\pi$
$48$		0			0
$49$	184.942	+	320.329i	0.539190	+	0.933905i
$50$	518.811	−	299.536i	1.46742	−	0.847216i
$51$		0			0
$52$	97.8310	+	84.0481i	0.260899	+	0.224142i
$53$	477.088			1.23647			0.618237	−	0.785992i	$-0.287847\pi$
$53$	477.088			1.23647			0.618237	+	0.785992i	$0.287847\pi$
$54$		0			0
$55$	187.716	+	325.133i	0.460210	+	0.797108i
$56$	229.741	−	397.923i	0.548222	−	0.949549i
$57$		0			0
$58$	−381.150	−	220.057i	−0.862887	−	0.498188i
$59$	−37.1769	−	21.4641i	−0.0820342	−	0.0473625i	0.458422	−	0.888735i	$-0.348415\pi$
$59$	−37.1769	−	21.4641i	−0.0820342	−	0.0473625i	−0.540456	+	0.841372i	$0.681748\pi$
$60$		0			0
$61$	−248.269	+	430.015i	−0.521109	+	0.902587i	0.478590	+	0.878039i	$0.341148\pi$
$61$	−248.269	+	430.015i	−0.521109	+	0.902587i	−0.999699	+	0.0245485i	$0.992185\pi$
$62$	200.934	+	348.028i	0.411592	+	0.712897i
$63$		0			0
$64$	−235.581			−0.460119
$65$	−807.998	−	152.181i	−1.54184	−	0.290396i
$66$		0			0
$67$	419.727	−	242.329i	0.765340	−	0.441869i	−0.0658696	−	0.997828i	$-0.520982\pi$
$67$	419.727	−	242.329i	0.765340	−	0.441869i	0.831210	+	0.555959i	$0.187649\pi$
$68$	115.519	+	200.085i	0.206011	+	0.356822i
$69$		0			0
$70$		−	1535.72i		−	2.62219i
$71$	−331.196	−	191.216i	−0.553602	−	0.319622i	0.196971	−	0.980409i	$-0.436889\pi$
$71$	−331.196	−	191.216i	−0.553602	−	0.319622i	−0.750574	+	0.660787i	$0.770223\pi$
$72$		0			0
$73$			193.622i			0.310435i	0.987880	+	0.155217i	$0.0496078\pi$
$73$			193.622i			0.310435i	−0.987880	+	0.155217i	$0.950392\pi$
$74$	364.929	−	632.076i	0.573272	−	0.992936i
$75$		0			0
$76$	−183.764	+	106.096i	−0.277358	+	0.160133i
$77$	571.447			0.845745
$78$		0			0
$79$	1049.60			1.49480			0.747399	−	0.664375i	$-0.231302\pi$
$79$	1049.60			1.49480			0.747399	+	0.664375i	$0.231302\pi$
$80$	−1191.63	+	687.989i	−1.66536	+	0.961493i
$81$		0			0
$82$	−325.144	+	563.166i	−0.437880	+	0.758431i
$83$			861.900i			1.13983i	0.821704	+	0.569914i	$0.193024\pi$
$83$			861.900i			1.13983i	−0.821704	+	0.569914i	$0.806976\pi$
$84$		0			0
$85$	−1275.51	−	736.414i	−1.62763	−	0.939710i
$86$			507.112i			0.635853i
$87$		0			0
$88$	−184.160	−	318.974i	−0.223085	−	0.386395i
$89$	−838.005	+	483.823i	−0.998072	+	0.576237i	−0.907677	−	0.419669i	$-0.862146\pi$
$89$	−838.005	+	483.823i	−0.998072	+	0.576237i	−0.0903946	+	0.995906i	$0.528813\pi$
$90$		0			0
$91$	−815.532	+	949.271i	−0.939461	+	1.09352i
$92$	−391.065			−0.443167
$93$		0			0
$94$	−129.184	−	223.754i	−0.141748	−	0.245515i
$95$	676.345	−	1171.46i	0.730438	−	1.26516i
$96$		0			0
$97$	512.228	+	295.735i	0.536174	+	0.309560i	0.743527	−	0.668706i	$-0.233152\pi$
$97$	512.228	+	295.735i	0.536174	+	0.309560i	−0.207353	+	0.978266i	$0.566485\pi$
$98$	−1050.35	−	606.421i	−1.08267	−	0.625079i
$99$		0			0
$100$	−251.366	+	435.379i	−0.251366	+	0.435379i
$101$	−127.555	−	220.932i	−0.125665	−	0.217659i	0.796328	−	0.604866i	$-0.206773\pi$
$101$	−127.555	−	220.932i	−0.125665	−	0.217659i	−0.921993	+	0.387207i	$0.873440\pi$
$102$		0			0
$103$	247.355			0.236627			0.118313	−	0.992976i	$-0.462251\pi$
$103$	247.355			0.236627			0.118313	+	0.992976i	$0.462251\pi$
$104$	792.692	+	149.299i	0.747403	+	0.140769i
$105$		0			0
$106$	−1354.77	+	782.180i	−1.24139	+	0.716717i
$107$	341.742	+	591.914i	0.308761	+	0.534790i	0.978092	−	0.208175i	$-0.0667523\pi$
$107$	341.742	+	591.914i	0.308761	+	0.534790i	−0.669331	+	0.742965i	$0.733419\pi$
$108$		0			0
$109$		−	1697.76i		−	1.49189i	−0.666006	−	0.745946i	$-0.731998\pi$
$109$		−	1697.76i		−	1.49189i	0.666006	−	0.745946i	$-0.268002\pi$
$110$	−1066.10	−	615.515i	−0.924081	−	0.533518i
$111$		0			0
$112$			2094.38i			1.76697i
$113$	−190.354	+	329.703i	−0.158469	+	0.274477i	−0.934317	−	0.356443i	$-0.883989\pi$
$113$	−190.354	+	329.703i	−0.158469	+	0.274477i	0.775848	+	0.630920i	$0.217323\pi$
$114$		0			0
$115$	2158.98	−	1246.49i	1.75066	−	1.01074i
$116$	369.337			0.295622
$117$		0			0
$118$	140.760			0.109814
$119$	−1941.46	+	1120.90i	−1.49557	+	0.863469i
$120$		0			0
$121$	−436.465	+	755.979i	−0.327923	+	0.567979i
$122$		−	1628.14i		−	1.20824i
$123$		0			0
$124$	−292.061	−	168.621i	−0.211515	−	0.122118i
$125$		−	1012.16i		−	0.724241i
$126$		0			0
$127$	61.6157	+	106.722i	0.0430513	+	0.0745670i	0.886748	−	0.462253i	$-0.152959\pi$
$127$	61.6157	+	106.722i	0.0430513	+	0.0745670i	−0.843697	+	0.536820i	$0.819625\pi$
$128$	1497.14	−	864.372i	1.03382	−	0.596878i
$129$		0			0
$130$	2543.95	−	892.556i	1.71630	−	0.602172i
$131$	1218.41			0.812616			0.406308	−	0.913736i	$-0.366816\pi$
$131$	1218.41			0.812616			0.406308	+	0.913736i	$0.366816\pi$
$132$		0			0
$133$	−1029.47	−	1783.09i	−0.671176	−	1.16251i
$134$	−794.592	+	1376.27i	−0.512256	+	0.887253i
$135$		0			0
$136$	1251.35	+	722.465i	0.788986	+	0.455521i
$137$	2363.24	+	1364.41i	1.47376	+	0.850875i	0.999563	−	0.0295456i	$-0.00940602\pi$
$137$	2363.24	+	1364.41i	1.47376	+	0.850875i	0.474194	+	0.880420i	$0.342739\pi$
$138$		0			0
$139$	−1556.39	+	2695.75i	−0.949722	+	1.64497i	−0.203713	+	0.979031i	$0.565301\pi$
$139$	−1556.39	+	2695.75i	−0.949722	+	1.64497i	−0.746009	+	0.665936i	$0.768032\pi$
$140$	644.377	+	1116.09i	0.388999	+	0.673766i
$141$		0			0
$142$	1253.99			0.741071
$143$	332.123	+	946.612i	0.194220	+	0.553564i
$144$		0			0
$145$	−2039.02	+	1177.23i	−1.16780	+	0.674232i
$146$	−317.441	−	549.823i	−0.179942	−	0.311669i
$147$		0			0
$148$			612.487i			0.340176i
$149$	−1186.95	−	685.286i	−0.652609	−	0.376784i	0.136846	−	0.990592i	$-0.456303\pi$
$149$	−1186.95	−	685.286i	−0.652609	−	0.376784i	−0.789455	+	0.613809i	$0.789637\pi$
$150$		0			0
$151$		−	2847.56i		−	1.53464i	−0.641263	−	0.767321i	$-0.721589\pi$
$151$		−	2847.56i		−	1.53464i	0.641263	−	0.767321i	$-0.278411\pi$
$152$	−663.534	+	1149.27i	−0.354077	+	0.613280i
$153$		0			0
$154$	−1622.72	+	936.879i	−0.849108	+	0.490233i
$155$	2149.86			1.11407
$156$		0			0
$157$	3354.00			1.70496			0.852479	−	0.522761i	$-0.175098\pi$
$157$	3354.00			1.70496			0.852479	+	0.522761i	$0.175098\pi$
$158$	−2980.52	+	1720.80i	−1.50074	+	0.866454i
$159$		0			0
$160$	1048.41	−	1815.89i	0.518024	−	0.897244i
$161$		−	3794.57i		−	1.85748i
$162$		0			0
$163$	1901.95	+	1098.09i	0.913941	+	0.527664i	0.881697	−	0.471816i	$-0.156401\pi$
$163$	1901.95	+	1098.09i	0.913941	+	0.527664i	0.0322438	+	0.999480i	$0.489735\pi$
$164$		−	545.713i		−	0.259836i
$165$		0			0
$166$	−1413.07	−	2447.51i	−0.660697	−	1.14436i
$167$	−790.279	+	456.268i	−0.366189	+	0.211419i	−0.671792	−	0.740740i	$-0.734475\pi$
$167$	−790.279	+	456.268i	−0.366189	+	0.211419i	0.305603	+	0.952159i	$0.401142\pi$
$168$		0			0
$169$	−2046.47	−	799.231i	−0.931484	−	0.363783i
$170$	4829.37			2.17880
$171$		0			0
$172$	−212.781	−	368.547i	−0.0943278	−	0.163381i
$173$	−449.818	+	779.108i	−0.197682	+	0.342396i	−0.947777	−	0.318935i	$-0.896675\pi$
$173$	−449.818	+	779.108i	−0.197682	+	0.342396i	0.750094	+	0.661331i	$0.230008\pi$
$174$		0			0
$175$	−4224.56	−	2439.05i	−1.82484	−	1.05357i
$176$	1453.93	+	839.427i	0.622694	+	0.359512i
$177$		0			0
$178$	1586.44	−	2747.80i	0.668027	−	1.15706i
$179$	−156.639	−	271.307i	−0.0654064	−	0.113287i	0.831468	−	0.555573i	$-0.187501\pi$
$179$	−156.639	−	271.307i	−0.0654064	−	0.113287i	−0.896874	+	0.442286i	$0.854168\pi$
$180$		0			0
$181$	2745.06			1.12728			0.563642	−	0.826019i	$-0.309400\pi$
$181$	2745.06			1.12728			0.563642	+	0.826019i	$0.309400\pi$
$182$	759.529	−	4032.67i	0.309341	−	1.64243i
$183$		0			0
$184$	−2118.08	+	1222.88i	−0.848626	+	0.489954i
$185$	−1952.25	−	3381.39i	−0.775849	−	1.34381i
$186$		0			0
$187$			1797.02i			0.702735i
$188$	187.771	+	108.410i	0.0728437	+	0.0420563i
$189$		0			0
$190$			4435.44i			1.69358i
$191$	44.9340	−	77.8279i	0.0170226	−	0.0294839i	−0.857389	−	0.514670i	$-0.827915\pi$
$191$	44.9340	−	77.8279i	0.0170226	−	0.0294839i	0.874411	+	0.485186i	$0.161248\pi$
$192$		0			0
$193$	735.215	−	424.477i	0.274207	−	0.158314i	−0.356591	−	0.934261i	$-0.616061\pi$
$193$	735.215	−	424.477i	0.274207	−	0.158314i	0.630798	+	0.775947i	$0.282728\pi$
$194$	−1939.41			−0.717741
$195$		0			0
$196$	1017.80			0.370918
$197$	3761.90	−	2171.93i	1.36053	−	0.785501i	0.370834	−	0.928699i	$-0.379072\pi$
$197$	3761.90	−	2171.93i	1.36053	−	0.785501i	0.989694	+	0.143198i	$0.0457386\pi$
$198$		0			0
$199$	−1664.20	+	2882.48i	−0.592825	+	1.02680i	0.401024	+	0.916067i	$0.368654\pi$
$199$	−1664.20	+	2882.48i	−0.592825	+	1.02680i	−0.993850	+	0.110736i	$0.964679\pi$
$200$			3144.13i			1.11162i
$201$		0			0
$202$	724.429	+	418.249i	0.252330	+	0.145683i
$203$			3583.74i			1.23906i
$204$		0			0
$205$	1739.41	+	3012.75i	0.592614	+	1.02644i
$206$	−702.406	+	405.535i	−0.237568	+	0.137160i
$207$		0			0
$208$	−3469.39	+	1217.25i	−1.15653	+	0.405775i
$209$	−1650.44			−0.546236
$210$		0			0
$211$	2299.94	+	3983.62i	0.750401	+	1.29973i	0.947629	+	0.319375i	$0.103473\pi$
$211$	2299.94	+	3983.62i	0.750401	+	1.29973i	−0.197228	+	0.980358i	$0.563194\pi$
$212$	656.394	−	1136.91i	0.212648	−	0.368317i
$213$		0			0
$214$	−1940.87	−	1120.56i	−0.619978	−	0.357944i
$215$	2349.42	+	1356.44i	0.745253	+	0.430272i
$216$		0			0
$217$	1636.16	−	2833.91i	0.511842	−	0.886537i
$218$	2783.46	+	4821.09i	0.864769	+	1.49782i
$219$		0			0
$220$	1033.06			0.316587
$221$	−2985.16	−	2564.60i	−0.908615	−	0.780604i
$222$		0			0
$223$	2190.68	−	1264.79i	0.657842	−	0.379806i	−0.133612	−	0.991034i	$-0.542658\pi$
$223$	2190.68	−	1264.79i	0.657842	−	0.379806i	0.791454	+	0.611228i	$0.209324\pi$
$224$	−1595.79	−	2763.98i	−0.475996	−	0.824449i
$225$		0			0
$226$		−	1248.33i		−	0.367425i
$227$	−32.2742	−	18.6335i	−0.00943661	−	0.00544823i	0.495274	−	0.868737i	$-0.335068\pi$
$227$	−32.2742	−	18.6335i	−0.00943661	−	0.00544823i	−0.504711	+	0.863288i	$0.668401\pi$
$228$		0			0
$229$		−	4094.45i		−	1.18152i	−0.806846	−	0.590762i	$-0.798827\pi$
$229$		−	4094.45i		−	1.18152i	0.806846	−	0.590762i	$-0.201173\pi$
$230$	−4087.20	+	7079.23i	−1.17175	+	2.02953i
$231$		0			0
$232$	2000.40	−	1154.93i	0.566089	−	0.326832i
$233$	1466.04			0.412205			0.206103	−	0.978530i	$-0.433922\pi$
$233$	1466.04			0.412205			0.206103	+	0.978530i	$0.433922\pi$
$234$		0			0
$235$	−1382.19			−0.383676
$236$	−102.298	+	59.0621i	−0.0282164	+	0.0162907i
$237$		0			0
$238$	3675.41	−	6365.99i	1.00101	−	1.73381i
$239$		−	5520.53i		−	1.49412i	−0.664759	−	0.747058i	$-0.731466\pi$
$239$		−	5520.53i		−	1.49412i	0.664759	−	0.747058i	$-0.268534\pi$
$240$		0			0
$241$	−2308.50	−	1332.81i	−0.617028	−	0.356241i	0.158683	−	0.987330i	$-0.449275\pi$
$241$	−2308.50	−	1332.81i	−0.617028	−	0.356241i	−0.775711	+	0.631088i	$0.782609\pi$
$242$		−	2862.31i		−	0.760316i
$243$		0			0
$244$	683.155	+	1183.26i	0.179240	+	0.310453i
$245$	−5619.03	+	3244.15i	−1.46525	+	0.845963i
$246$		0			0
$247$	2355.40	−	2741.67i	0.606764	−	0.706267i
$248$	−2109.14			−0.540042
$249$		0			0
$250$	1659.42	+	2874.20i	0.419803	+	0.727121i
$251$	−789.605	+	1367.64i	−0.198564	+	0.343922i	−0.948063	−	0.318083i	$-0.896961\pi$
$251$	−789.605	+	1367.64i	−0.198564	+	0.343922i	0.749499	+	0.662005i	$0.230294\pi$
$252$		0			0
$253$	−2634.21	−	1520.86i	−0.654590	−	0.377927i
$254$	−349.937	−	202.036i	−0.0864449	−	0.0499090i
$255$		0			0
$256$	−1891.93	+	3276.92i	−0.461897	+	0.800029i
$257$	1331.96	+	2307.01i	0.323288	+	0.559952i	0.981164	−	0.193174i	$-0.0618783\pi$
$257$	1331.96	+	2307.01i	0.323288	+	0.559952i	−0.657876	+	0.753126i	$0.728545\pi$
$258$		0			0
$259$	−5943.06			−1.42581
$260$	−1474.32	+	1716.09i	−0.351667	+	0.409337i
$261$		0			0
$262$	−3459.88	+	1997.56i	−0.815847	+	0.471030i
$263$	−1218.47	−	2110.45i	−0.285680	−	0.494812i	0.687094	−	0.726569i	$-0.258886\pi$
$263$	−1218.47	−	2110.45i	−0.285680	−	0.494812i	−0.972774	+	0.231756i	$0.925553\pi$
$264$		0			0
$265$			8368.80i			1.93997i
$266$	5846.72	+	3375.61i	1.34769	+	0.778089i
$267$		0			0
$268$		−	1333.62i		−	0.303970i
$269$	−1341.59	+	2323.70i	−0.304083	+	0.526687i	−0.977057	−	0.212980i	$-0.931683\pi$
$269$	−1341.59	+	2323.70i	−0.304083	+	0.526687i	0.672974	+	0.739666i	$0.265017\pi$
$270$		0			0
$271$	−3340.38	+	1928.57i	−0.748759	+	0.432296i	−0.825245	−	0.564775i	$-0.808963\pi$
$271$	−3340.38	+	1928.57i	−0.748759	+	0.432296i	0.0764866	+	0.997071i	$0.475630\pi$
$272$	−6586.20			−1.46819
$273$		0			0
$274$	−8947.76			−1.97282
$275$	−3386.40	+	1955.14i	−0.742572	+	0.428724i
$276$		0			0
$277$	552.453	−	956.877i	0.119833	−	0.207557i	−0.799868	−	0.600175i	$-0.795097\pi$
$277$	552.453	−	956.877i	0.119833	−	0.207557i	0.919701	+	0.392619i	$0.128431\pi$
$278$		−	10206.7i		−	2.20201i
$279$		0			0
$280$	6980.14	+	4029.98i	1.48980	+	0.860134i
$281$		−	4982.58i		−	1.05778i	−0.848691	−	0.528890i	$-0.822609\pi$
$281$		−	4982.58i		−	1.05778i	0.848691	−	0.528890i	$-0.177391\pi$
$282$		0			0
$283$	1292.43	+	2238.55i	0.271473	+	0.470205i	0.969239	−	0.246120i	$-0.0791558\pi$
$283$	1292.43	+	2238.55i	0.271473	+	0.470205i	−0.697766	+	0.716326i	$0.745822\pi$
$284$	−911.342	+	526.164i	−0.190416	+	0.109937i
$285$		0			0
$286$	−2495.08	−	2143.56i	−0.515864	−	0.443186i
$287$	5295.14			1.08907
$288$		0			0
$289$	−1068.39	−	1850.51i	−0.217462	−	0.376655i
$290$	3860.11	−	6685.90i	0.781632	−	1.35383i
$291$		0			0
$292$	461.404	+	266.392i	0.0924714	+	0.0533884i
$293$	−80.1491	−	46.2741i	−0.0159807	−	0.00922649i	0.491988	−	0.870602i	$-0.336270\pi$
$293$	−80.1491	−	46.2741i	−0.0159807	−	0.00922649i	−0.507969	+	0.861375i	$0.669604\pi$
$294$		0			0
$295$	376.510	−	652.135i	0.0743094	−	0.128708i
$296$	1915.27	+	3317.34i	0.376090	+	0.651407i
$297$		0			0
$298$	4494.07			0.873605
$299$	6285.78	−	2205.39i	1.21577	−	0.426559i
$300$		0			0
$301$	3576.07	−	2064.65i	0.684789	−	0.395363i
$302$	4668.53	+	8086.14i	0.889549	+	1.54074i
$303$		0			0
$304$		−	6048.96i		−	1.14122i
$305$	−7543.07	−	4355.00i	−1.41612	−	0.817595i
$306$		0			0
$307$		−	3979.46i		−	0.739803i	−0.929071	−	0.369901i	$-0.879391\pi$
$307$		−	3979.46i		−	0.739803i	0.929071	−	0.369901i	$-0.120609\pi$
$308$	786.216	−	1361.77i	0.145451	−	0.251928i
$309$		0			0
$310$	−6104.91	+	3524.67i	−1.11850	+	0.645767i
$311$	3450.91			0.629207			0.314604	−	0.949223i	$-0.398128\pi$
$311$	3450.91			0.629207			0.314604	+	0.949223i	$0.398128\pi$
$312$		0			0
$313$	−6189.03			−1.11765			−0.558825	−	0.829285i	$-0.688748\pi$
$313$	−6189.03			−1.11765			−0.558825	+	0.829285i	$0.688748\pi$
$314$	−9524.27	+	5498.84i	−1.71174	+	0.988272i
$315$		0			0
$316$	1444.07	−	2501.21i	0.257075	−	0.445266i
$317$			5437.78i			0.963459i	0.876320	+	0.481729i	$0.159991\pi$
$317$			5437.78i			0.963459i	−0.876320	+	0.481729i	$0.840009\pi$
$318$		0			0
$319$	2487.85	+	1436.36i	0.436654	+	0.252102i
$320$		−	4132.42i		−	0.721904i
$321$		0			0
$322$	6221.15	+	10775.3i	1.07668	+	1.86487i
$323$	5607.28	−	3237.37i	0.965937	−	0.557684i
$324$		0			0
$325$	1585.03	−	8415.63i	0.270528	−	1.43635i
$326$	−7201.23			−1.22343
$327$		0			0
$328$	−1706.46	−	2955.68i	−0.287268	−	0.497562i
$329$	−1051.92	+	1821.97i	−0.176274	+	0.305315i
$330$		0			0
$331$	5738.84	+	3313.32i	0.952976	+	0.550201i	0.894004	−	0.448058i	$-0.147884\pi$
$331$	5738.84	+	3313.32i	0.952976	+	0.550201i	0.0589722	+	0.998260i	$0.481218\pi$
$332$	2053.92	+	1185.83i	0.339529	+	0.196027i
$333$		0			0
$334$	1496.09	−	2591.30i	0.245097	−	0.424520i
$335$	4250.80	+	7362.60i	0.693271	+	1.20078i
$336$		0			0
$337$	5538.63			0.895277			0.447638	−	0.894215i	$-0.352265\pi$
$337$	5538.63			0.895277			0.447638	+	0.894215i	$0.352265\pi$
$338$	7121.64	−	1085.60i	1.14605	−	0.174701i
$339$		0			0
$340$	−3509.77	+	2026.37i	−0.559836	+	0.323221i
$341$	−1311.54	−	2271.66i	−0.208281	−	0.360754i
$342$		0			0
$343$			717.813i			0.112998i
$344$	−2304.92	−	1330.75i	−0.361259	−	0.208573i
$345$		0			0
$346$		−	2949.88i		−	0.458343i
$347$	4699.47	−	8139.72i	0.727034	−	1.25926i	−0.231098	−	0.972931i	$-0.574232\pi$
$347$	4699.47	−	8139.72i	0.727034	−	1.25926i	0.958131	−	0.286329i	$-0.0924350\pi$
$348$		0			0
$349$	4985.99	−	2878.66i	0.764739	−	0.441522i	−0.0662555	−	0.997803i	$-0.521105\pi$
$349$	4985.99	−	2878.66i	0.764739	−	0.441522i	0.830995	+	0.556280i	$0.187772\pi$
$350$	15995.2			2.44279
$351$		0			0
$352$	−2558.36			−0.387389
$353$	2994.56	−	1728.91i	0.451514	−	0.260682i	−0.256955	−	0.966423i	$-0.582719\pi$
$353$	2994.56	−	1728.91i	0.451514	−	0.260682i	0.708470	+	0.705741i	$0.249386\pi$
$354$		0			0
$355$	3354.20	−	5809.65i	0.501472	−	0.868575i
$356$			2662.64i			0.396403i
$357$		0			0
$358$	889.607	+	513.615i	0.131333	+	0.0758251i
$359$			7168.96i			1.05394i	0.849885	+	0.526968i	$0.176671\pi$
$359$			7168.96i			1.05394i	−0.849885	+	0.526968i	$0.823329\pi$
$360$		0			0
$361$	−456.203	−	790.167i	−0.0665116	−	0.115202i
$362$	−7795.07	+	4500.49i	−1.13177	+	0.653426i
$363$		0			0
$364$	1140.09	+	3249.47i	0.164167	+	0.467907i
$365$	−3396.40			−0.487057
$366$		0			0
$367$	−1955.05	−	3386.25i	−0.278073	−	0.481637i	0.692832	−	0.721099i	$-0.256363\pi$
$367$	−1955.05	−	3386.25i	−0.278073	−	0.481637i	−0.970906	+	0.239461i	$0.923029\pi$
$368$	5574.04	−	9654.52i	0.789584	−	1.36760i
$369$		0			0
$370$	11087.5	+	6401.37i	1.55787	+	0.899436i
$371$	11031.6	+	6369.10i	1.54375	+	0.891286i
$372$		0			0
$373$	−5688.80	+	9853.28i	−0.789691	+	1.36778i	0.136466	+	0.990645i	$0.456426\pi$
$373$	−5688.80	+	9853.28i	−0.789691	+	1.36778i	−0.926156	+	0.377140i	$0.876908\pi$
$374$	−2946.20	−	5102.96i	−0.407337	−	0.705529i
$375$		0			0
$376$	1356.00			0.185986
$377$	−5936.54	+	2082.86i	−0.811001	+	0.284543i
$378$		0			0
$379$	3492.00	−	2016.11i	0.473278	−	0.273247i	−0.244333	−	0.969691i	$-0.578569\pi$
$379$	3492.00	−	2016.11i	0.473278	−	0.273247i	0.717611	+	0.696444i	$0.245236\pi$
$380$	−1861.08	−	3223.48i	−0.251240	−	0.435161i
$381$		0			0
$382$			294.675i			0.0394682i
$383$	1724.22	+	995.480i	0.230035	+	0.132811i	0.610588	−	0.791948i	$-0.290933\pi$
$383$	1724.22	+	995.480i	0.230035	+	0.132811i	−0.380553	+	0.924759i	$0.624266\pi$
$384$		0			0
$385$			10024.0i			1.32693i
$386$	−1391.85	+	2410.75i	−0.183532	+	0.317886i
$387$		0			0
$388$	1409.48	−	813.765i	0.184422	−	0.106476i
$389$	−11122.4			−1.44969			−0.724846	−	0.688911i	$-0.758089\pi$
$389$	−11122.4			−1.44969			−0.724846	+	0.688911i	$0.758089\pi$
$390$		0			0
$391$	11932.8			1.54339
$392$	5512.59	−	3182.70i	0.710275	−	0.410078i
$393$		0			0
$394$	−7121.71	+	12335.2i	−0.910625	+	1.57725i
$395$			18411.4i			2.34527i
$396$		0			0
$397$	−9334.12	−	5389.06i	−1.18002	−	0.681282i	−0.223997	−	0.974590i	$-0.571911\pi$
$397$	−9334.12	−	5389.06i	−1.18002	−	0.681282i	−0.956018	+	0.293308i	$0.905244\pi$
$398$		−	10913.8i		−	1.37452i
$399$		0			0
$400$	−7165.69	−	12411.3i	−0.895711	−	1.55142i
$401$	4080.35	−	2355.79i	0.508137	−	0.293373i	−0.223931	−	0.974605i	$-0.571889\pi$
$401$	4080.35	−	2355.79i	0.508137	−	0.293373i	0.732067	+	0.681232i	$0.238556\pi$
$402$		0			0
$403$	5645.36	+	1063.27i	0.697805	+	0.131427i
$404$	−701.978			−0.0864473
$405$		0			0
$406$	−5875.50	−	10176.7i	−0.718217	−	1.24399i
$407$	−2381.97	+	4125.69i	−0.290098	+	0.502465i
$408$		0			0
$409$	1026.05	+	592.388i	0.124046	+	0.0716179i	0.560739	−	0.827993i	$-0.310517\pi$
$409$	1026.05	+	592.388i	0.124046	+	0.0716179i	−0.436693	+	0.899611i	$0.643850\pi$
$410$	−9878.73	−	5703.49i	−1.18994	−	0.687013i
$411$		0			0
$412$	340.319	−	589.450i	0.0406949	−	0.0704857i
$413$	−573.089	−	992.619i	−0.0682805	−	0.118265i
$414$		0			0
$415$	−15118.9			−1.78834
$416$	3651.13	−	4249.87i	0.430315	−	0.500882i
$417$		0			0
$418$	4686.72	−	2705.88i	0.548409	−	0.316624i
$419$	−3084.15	−	5341.91i	−0.359596	−	0.622838i	0.628298	−	0.777973i	$-0.283752\pi$
$419$	−3084.15	−	5341.91i	−0.359596	−	0.622838i	−0.987893	+	0.155135i	$0.950419\pi$
$420$		0			0
$421$			10328.8i			1.19571i	0.801603	+	0.597857i	$0.203981\pi$
$421$			10328.8i			1.19571i	−0.801603	+	0.597857i	$0.796019\pi$
$422$	−13062.2	−	7541.45i	−1.50677	−	0.869934i
$423$		0			0
$424$		−	8210.27i		−	0.940392i
$425$	7670.06	−	13284.9i	0.875418	−	1.51627i
$426$		0			0
$427$	−11481.4	+	6628.77i	−1.30122	+	0.751261i
$428$	1880.72			0.212402
$429$		0			0
$430$	−8895.46			−0.997622
$431$	−9796.87	+	5656.23i	−1.09489	+	0.632137i	−0.934875	−	0.354977i	$-0.884489\pi$
$431$	−9796.87	+	5656.23i	−1.09489	+	0.632137i	−0.160018	+	0.987114i	$0.551155\pi$
$432$		0			0
$433$	−5237.87	+	9072.27i	−0.581331	+	1.00689i	0.413991	+	0.910281i	$0.364134\pi$
$433$	−5237.87	+	9072.27i	−0.581331	+	1.00689i	−0.995322	+	0.0966135i	$0.969199\pi$
$434$			10729.8i			1.18675i
$435$		0			0
$436$	−4045.80	−	2335.84i	−0.444400	−	0.256575i
$437$			10959.4i			1.19968i
$438$		0			0
$439$	−1020.31	−	1767.23i	−0.110926	−	0.192130i	0.805218	−	0.592979i	$-0.202048\pi$
$439$	−1020.31	−	1767.23i	−0.110926	−	0.192130i	−0.916144	+	0.400849i	$0.868715\pi$
$440$	5595.26	−	3230.42i	0.606235	−	0.350010i
$441$		0			0
$442$	12681.5	+	2388.49i	1.36470	+	0.257033i
$443$	4089.28			0.438572			0.219286	−	0.975661i	$-0.429627\pi$
$443$	4089.28			0.438572			0.219286	+	0.975661i	$0.429627\pi$
$444$		0			0
$445$	−8486.93	−	14699.8i	−0.904088	−	1.56593i
$446$	−4147.21	+	7183.19i	−0.440306	+	0.762632i
$447$		0			0
$448$	−5447.29	−	3144.99i	−0.574465	−	0.331667i
$449$	−13179.1	−	7608.96i	−1.38521	−	0.799753i	−0.392441	−	0.919777i	$-0.628369\pi$
$449$	−13179.1	−	7608.96i	−1.38521	−	0.799753i	−0.992771	+	0.120025i	$0.961703\pi$
$450$		0			0
$451$	2122.29	−	3675.91i	0.221585	−	0.383796i
$452$	523.792	+	907.235i	0.0545069	+	0.0944087i
$453$		0			0
$454$	122.197			0.0126322
$455$	−16651.5	−	14305.6i	−1.71568	−	1.47397i
$456$		0			0
$457$	−758.912	+	438.158i	−0.0776814	+	0.0448494i	−0.538338	−	0.842729i	$-0.680947\pi$
$457$	−758.912	+	438.158i	−0.0776814	+	0.0448494i	0.460656	+	0.887579i	$0.347614\pi$
$458$	6712.80	+	11626.9i	0.684865	+	1.18622i
$459$		0			0
$460$		−	6859.84i		−	0.695308i
$461$	14110.5	+	8146.69i	1.42558	+	0.823057i	0.996768	−	0.0803390i	$-0.0256003\pi$
$461$	14110.5	+	8146.69i	1.42558	+	0.823057i	0.428808	+	0.903396i	$0.358934\pi$
$462$		0			0
$463$			11704.8i			1.17488i	0.809269	+	0.587438i	$0.199863\pi$
$463$			11704.8i			1.17488i	−0.809269	+	0.587438i	$0.800137\pi$
$464$	−5264.34	+	9118.11i	−0.526704	+	0.912279i
$465$		0			0
$466$	−4163.09	+	2403.56i	−0.413844	+	0.238933i
$467$	−15616.1			−1.54738			−0.773688	−	0.633567i	$-0.781590\pi$
$467$	−15616.1			−1.54738			−0.773688	+	0.633567i	$0.781590\pi$
$468$		0			0
$469$	12940.3			1.27405
$470$	3924.96	−	2266.07i	0.385202	−	0.222396i
$471$		0			0
$472$	−369.378	+	639.782i	−0.0360212	+	0.0623906i
$473$		−	3310.03i		−	0.321766i
$474$		0			0
$475$	12201.3	+	7044.42i	1.17860	+	0.680463i
$476$			6168.70i			0.593996i
$477$		0			0
$478$	9050.84	+	15676.5i	0.866058	+	1.50006i
$479$	−8985.90	+	5188.01i	−0.857153	+	0.494877i	−0.863058	−	0.505105i	$-0.831454\pi$
$479$	−8985.90	+	5188.01i	−0.857153	+	0.494877i	0.00590498	+	0.999983i	$0.498120\pi$
$480$		0			0
$481$	−3454.09	−	9844.79i	−0.327428	−	0.933230i
$482$	8740.53			0.825976
$483$		0			0
$484$	1201.01	+	2080.21i	0.112792	+	0.195361i
$485$	−5187.61	+	8985.20i	−0.485685	+	0.841231i
$486$		0			0
$487$	−3459.14	−	1997.13i	−0.321865	−	0.185829i	0.330358	−	0.943856i	$-0.392830\pi$
$487$	−3459.14	−	1997.13i	−0.321865	−	0.185829i	−0.652224	+	0.758027i	$0.726164\pi$
$488$	7400.19	+	4272.50i	0.686457	+	0.396326i
$489$		0			0
$490$	10637.5	−	18424.6i	0.980719	−	1.69865i
$491$	−6133.65	−	10623.8i	−0.563763	−	0.976467i	−0.997164	−	0.0752653i	$-0.976020\pi$
$491$	−6133.65	−	10623.8i	−0.563763	−	0.976467i	0.433400	−	0.901202i	$-0.357314\pi$
$492$		0			0
$493$	−11269.8			−1.02954
$494$	−2193.66	+	11647.1i	−0.199792	+	1.06078i
$495$		0			0
$496$	8325.75	−	4806.88i	0.753704	−	0.435151i
$497$	−5105.45	−	8842.90i	−0.460786	−	0.798105i
$498$		0			0
$499$			3578.76i			0.321056i	0.987031	+	0.160528i	$0.0513198\pi$
$499$			3578.76i			0.321056i	−0.987031	+	0.160528i	$0.948680\pi$
$500$	−2411.99	−	1392.56i	−0.215735	−	0.124554i
$501$		0			0
$502$		−	5178.19i		−	0.460386i
$503$	−648.409	+	1123.08i	−0.0574774	+	0.0995537i	−0.893332	−	0.449397i	$-0.851639\pi$
$503$	−648.409	+	1123.08i	−0.0574774	+	0.0995537i	0.835855	+	0.548950i	$0.184972\pi$
$504$		0			0
$505$	3875.45	−	2237.49i	0.341496	−	0.197163i
$506$	9973.72			0.876257
$507$		0			0
$508$	339.092			0.0296157
$509$	4095.09	−	2364.30i	0.356604	−	0.205886i	−0.310986	−	0.950415i	$-0.600659\pi$
$509$	4095.09	−	2364.30i	0.356604	−	0.205886i	0.667590	+	0.744529i	$0.267326\pi$
$510$		0			0
$511$	−2584.84	+	4477.08i	−0.223771	+	0.387582i
$512$			1422.78i			0.122810i
$513$		0			0
$514$	−7564.64	−	4367.45i	−0.649148	−	0.374786i
$515$			4338.95i			0.371256i
$516$		0			0
$517$	843.214	+	1460.49i	0.0717302	+	0.124240i
$518$	16876.4	−	9743.57i	1.43148	−	0.826463i
$519$		0			0
$520$	−2618.91	+	13904.9i	−0.220859	+	1.17264i
$521$	9220.74			0.775370			0.387685	−	0.921792i	$-0.373275\pi$
$521$	9220.74			0.775370			0.387685	+	0.921792i	$0.373275\pi$
$522$		0			0
$523$	6051.33	+	10481.2i	0.505939	+	0.876313i	0.999976	+	0.00687187i	$0.00218740\pi$
$523$	6051.33	+	10481.2i	0.505939	+	0.876313i	−0.494037	+	0.869441i	$0.664479\pi$
$524$	1676.33	−	2903.48i	0.139753	−	0.242059i
$525$		0			0
$526$	6920.10	+	3995.32i	0.573632	+	0.331187i
$527$	8911.78	+	5145.22i	0.736629	+	0.425293i
$528$		0			0
$529$	−4015.45	+	6954.97i	−0.330028	+	0.571626i
$530$	−13720.5	−	23764.7i	−1.12449	−	1.94768i
$531$		0			0
$532$	−5665.52			−0.461713
$533$	3077.52	+	8771.51i	0.250098	+	0.712826i
$534$		0			0
$535$	−10383.0	+	5994.63i	−0.839059	+	0.484431i
$536$	−4170.28	−	7223.14i	−0.336061	−	0.582075i
$537$		0			0
$538$		−	8798.08i		−	0.705041i
$539$	6855.87	+	3958.24i	0.547873	+	0.316314i
$540$		0			0
$541$		−	12801.3i		−	1.01732i	−0.860968	−	0.508659i	$-0.830141\pi$
$541$		−	12801.3i		−	1.01732i	0.860968	−	0.508659i	$-0.169859\pi$
$542$	6323.73	−	10953.0i	0.501157	−	0.868030i
$543$		0			0
$544$	8691.88	−	5018.26i	0.685039	−	0.395508i
$545$	29781.2			2.34071
$546$		0			0
$547$	400.693			0.0313207			0.0156603	−	0.999877i	$-0.495015\pi$
$547$	400.693			0.0313207			0.0156603	+	0.999877i	$0.495015\pi$
$548$	6502.84	−	3754.42i	0.506912	−	0.292666i
$549$		0			0
$550$	6410.84	−	11103.9i	0.497017	−	0.860858i
$551$		−	10350.5i		−	0.800265i
$552$		0			0
$553$	24269.7	+	14012.1i	1.86628	+	1.07750i
$554$			3622.96i			0.277843i
$555$		0			0
$556$	4282.67	+	7417.81i	0.326665	+	0.565801i
$557$	12536.2	−	7237.77i	0.953636	−	0.550582i	0.0594277	−	0.998233i	$-0.481072\pi$
$557$	12536.2	−	7237.77i	0.953636	−	0.550582i	0.894209	+	0.447650i	$0.147739\pi$
$558$		0			0
$559$	5498.53	+	4723.87i	0.416034	+	0.357421i
$560$	−36738.5			−2.77229
$561$		0			0
$562$	8168.88	+	14148.9i	0.613138	+	1.06199i
$563$	7388.18	−	12796.7i	0.553063	−	0.957934i	−0.444988	−	0.895536i	$-0.646792\pi$
$563$	7388.18	−	12796.7i	0.553063	−	0.957934i	0.998051	−	0.0623972i	$-0.0198746\pi$
$564$		0			0
$565$	−5783.46	−	3339.08i	−0.430641	−	0.248631i
$566$	−7340.16	−	4237.84i	−0.545106	−	0.314717i
$567$		0			0
$568$	−3290.67	+	5699.60i	−0.243087	+	0.421039i
$569$	3434.44	+	5948.63i	0.253039	+	0.438277i	0.964361	−	0.264590i	$-0.0852365\pi$
$569$	3434.44	+	5948.63i	0.253039	+	0.438277i	−0.711322	+	0.702866i	$0.751903\pi$
$570$		0			0
$571$	−3011.00			−0.220677			−0.110338	−	0.993894i	$-0.535193\pi$
$571$	−3011.00			−0.220677			−0.110338	+	0.993894i	$0.535193\pi$
$572$	2712.74	+	510.927i	0.198296	+	0.0373478i
$573$		0			0
$574$	−15036.5	+	8681.32i	−1.09340	+	0.631274i
$575$	12982.7	+	22486.7i	0.941591	+	1.63088i
$576$		0			0
$577$		−	23106.6i		−	1.66714i	−0.552411	−	0.833572i	$-0.686292\pi$
$577$		−	23106.6i		−	1.66714i	0.552411	−	0.833572i	$-0.313708\pi$
$578$	6067.76	+	3503.22i	0.436653	+	0.252102i
$579$		0			0
$580$			6478.70i			0.463816i
$581$	−11506.3	+	19929.5i	−0.821622	+	1.42309i
$582$		0			0
$583$	8842.91	−	5105.46i	0.628192	−	0.362687i
$584$	3332.07			0.236099
$585$		0			0
$586$	303.463			0.0213924
$587$	−2619.56	+	1512.40i	−0.184192	+	0.106343i	−0.589261	−	0.807943i	$-0.700581\pi$
$587$	−2619.56	+	1512.40i	−0.184192	+	0.106343i	0.405069	+	0.914286i	$0.367248\pi$
$588$		0			0
$589$	−4725.53	+	8184.85i	−0.330580	+	0.572582i
$590$			2469.13i			0.172293i
$591$		0			0
$592$	−15120.9	−	8730.06i	−1.04977	−	0.606087i
$593$		−	6396.07i		−	0.442926i	−0.975169	−	0.221463i	$-0.928917\pi$
$593$		−	6396.07i		−	0.442926i	0.975169	−	0.221463i	$-0.0710832\pi$
$594$		0			0
$595$	−19662.2	−	34055.9i	−1.35474	−	2.34648i
$596$	−3266.09	+	1885.68i	−0.224470	+	0.129598i
$597$		0			0
$598$	−14233.9	+	16568.1i	−0.973354	+	1.13297i
$599$	−12095.9			−0.825084			−0.412542	−	0.910939i	$-0.635359\pi$
$599$	−12095.9			−0.825084			−0.412542	+	0.910939i	$0.635359\pi$
$600$		0			0
$601$	5908.25	+	10233.4i	0.401003	+	0.694557i	0.993847	−	0.110760i	$-0.0353285\pi$
$601$	5908.25	+	10233.4i	0.401003	+	0.694557i	−0.592845	+	0.805317i	$0.701995\pi$
$602$	−6769.92	+	11725.8i	−0.458341	+	0.793870i
$603$		0			0
$604$	−6785.77	−	3917.77i	−0.457134	−	0.263927i
$605$	−13260.9	−	7656.21i	−0.891131	−	0.514495i
$606$		0			0
$607$	12582.0	−	21792.6i	0.841329	−	1.45722i	−0.0474421	−	0.998874i	$-0.515107\pi$
$607$	12582.0	−	21792.6i	0.841329	−	1.45722i	0.888771	−	0.458351i	$-0.151560\pi$
$608$	4608.92	+	7982.89i	0.307428	+	0.532482i
$609$		0			0
$610$	28559.8			1.89566
$611$	−3629.50	−	683.595i	−0.240318	−	0.0452623i
$612$		0			0
$613$	16959.4	−	9791.51i	1.11743	−	0.645148i	0.176685	−	0.984267i	$-0.443462\pi$
$613$	16959.4	−	9791.51i	1.11743	−	0.645148i	0.940743	+	0.339120i	$0.110129\pi$
$614$	6524.26	+	11300.4i	0.428824	+	0.742745i
$615$		0			0
$616$		−	9834.10i		−	0.643226i
$617$	17040.8	+	9838.54i	1.11189	+	0.641952i	0.939319	−	0.343044i	$-0.111458\pi$
$617$	17040.8	+	9838.54i	1.11189	+	0.641952i	0.172575	+	0.984996i	$0.444791\pi$
$618$		0			0
$619$			4394.05i			0.285318i	0.989772	+	0.142659i	$0.0455652\pi$
$619$			4394.05i			0.285318i	−0.989772	+	0.142659i	$0.954435\pi$
$620$	2957.85	−	5123.15i	0.191597	−	0.331856i
$621$		0			0
$622$	−9799.47	+	5657.73i	−0.631709	+	0.364717i
$623$	−25836.0			−1.66147
$624$		0			0
$625$	−5082.96			−0.325310
$626$	17574.8	−	10146.8i	1.12210	−	0.647842i
$627$		0			0
$628$	4614.55	−	7992.64i	0.293218	−	0.507868i
$629$		−	18689.1i		−	1.18471i
$630$		0			0
$631$	−20687.3	−	11943.8i	−1.30515	−	0.753529i	−0.323867	−	0.946102i	$-0.604983\pi$
$631$	−20687.3	−	11943.8i	−1.30515	−	0.753529i	−0.981282	+	0.192574i	$0.938316\pi$
$632$		−	18062.7i		−	1.13686i
$633$		0			0
$634$	−8915.18	−	15441.5i	−0.558465	−	0.967290i
$635$	−1872.05	+	1080.83i	−0.116992	+	0.0675453i
$636$		0			0
$637$	−16359.6	+	5739.83i	−1.01757	+	0.357018i
$638$	−9419.57			−0.584521
$639$		0			0
$640$	15162.3	+	26261.9i	0.936473	+	1.62202i
$641$	2721.81	−	4714.31i	0.167714	−	0.290490i	−0.769901	−	0.638163i	$-0.779695\pi$
$641$	2721.81	−	4714.31i	0.167714	−	0.290490i	0.937616	+	0.347673i	$0.113028\pi$
$642$		0			0
$643$	−5056.73	−	2919.50i	−0.310137	−	0.179057i	0.336851	−	0.941558i	$-0.390638\pi$
$643$	−5056.73	−	2919.50i	−0.310137	−	0.179057i	−0.646988	+	0.762501i	$0.723971\pi$
$644$	−9042.52	−	5220.70i	−0.553300	−	0.319448i
$645$		0			0
$646$	−10615.2	+	18386.1i	−0.646519	+	1.11980i
$647$	−4354.43	−	7542.09i	−0.264591	−	0.458285i	0.702866	−	0.711323i	$-0.251904\pi$
$647$	−4354.43	−	7542.09i	−0.264591	−	0.458285i	−0.967456	+	0.253038i	$0.918570\pi$
$648$		0			0
$649$	−918.773			−0.0555701
$650$	9296.34	+	26496.3i	0.560973	+	1.59888i
$651$		0			0
$652$	5233.54	−	3021.59i	0.314358	−	0.181495i
$653$	1397.47	+	2420.48i	0.0837475	+	0.145055i	0.904857	−	0.425716i	$-0.139978\pi$
$653$	1397.47	+	2420.48i	0.0837475	+	0.145055i	−0.821109	+	0.570771i	$0.806644\pi$
$654$		0			0
$655$			21372.6i			1.27495i
$656$	13472.4	+	7778.31i	0.801844	+	0.462945i
$657$		0			0
$658$		−	6898.41i		−	0.408705i
$659$	15695.0	−	27184.5i	0.927752	−	1.60691i	0.140678	−	0.990055i	$-0.455072\pi$
$659$	15695.0	−	27184.5i	0.927752	−	1.60691i	0.787074	−	0.616859i	$-0.211595\pi$
$660$		0			0
$661$	17837.7	−	10298.6i	1.04963	−	0.606005i	0.127085	−	0.991892i	$-0.459438\pi$
$661$	17837.7	−	10298.6i	1.04963	−	0.606005i	0.922546	+	0.385887i	$0.126104\pi$
$662$	−21728.6			−1.27569
$663$		0			0
$664$	14832.5			0.866889
$665$	31278.0	−	18058.4i	1.82392	−	1.05304i
$666$		0			0
$667$	9537.85	−	16520.0i	0.553684	−	0.959008i
$668$			2511.00i			0.145439i
$669$		0			0
$670$	−24141.8	−	13938.3i	−1.39206	−	0.803704i
$671$			10627.2i			0.611414i
$672$		0			0
$673$	−8967.89	−	15532.8i	−0.513651	−	0.889669i	−0.999875	−	0.0158347i	$-0.994959\pi$
$673$	−8967.89	−	15532.8i	−0.513651	−	0.889669i	0.486224	−	0.873834i	$-0.338374\pi$
$674$	−15727.9	+	9080.51i	−0.898837	+	0.518944i
$675$		0			0
$676$	−4720.18	+	3777.16i	−0.268559	+	0.214904i
$677$	24104.0			1.36838			0.684188	−	0.729305i	$-0.260157\pi$
$677$	24104.0			1.36838			0.684188	+	0.729305i	$0.260157\pi$
$678$		0			0
$679$	7896.09	+	13676.4i	0.446280	+	0.772980i
$680$	−12673.1	+	21950.4i	−0.714691	+	1.23788i
$681$		0			0
$682$	7448.70	+	4300.51i	0.418219	+	0.241459i
$683$	−5840.69	−	3372.12i	−0.327215	−	0.188918i	0.327389	−	0.944890i	$-0.393831\pi$
$683$	−5840.69	−	3372.12i	−0.327215	−	0.188918i	−0.654604	+	0.755972i	$0.727165\pi$
$684$		0			0
$685$	−23933.8	+	41454.5i	−1.33498	+	2.31225i
$686$	−1176.85	−	2038.36i	−0.0654988	−	0.113447i
$687$		0			0
$688$	12131.5			0.672249
$689$	−4139.00	+	21975.8i	−0.228858	+	1.21511i
$690$		0			0
$691$	26712.1	−	15422.2i	1.47059	−	0.849043i	0.471131	−	0.882063i	$-0.343846\pi$
$691$	26712.1	−	15422.2i	1.47059	−	0.849043i	0.999455	+	0.0330199i	$0.0105125\pi$
$692$	1237.75	+	2143.85i	0.0679945	+	0.117770i
$693$		0			0
$694$			30818.9i			1.68569i
$695$	−47287.2	−	27301.3i	−2.58087	−	1.49007i
$696$		0			0
$697$			16651.6i			0.904913i
$698$	−9439.06	+	16348.9i	−0.511853	+	0.886556i
$699$		0			0
$700$	−11624.6	+	6711.46i	−0.627669	+	0.362385i
$701$	−21007.6			−1.13188			−0.565940	−	0.824447i	$-0.691486\pi$
$701$	−21007.6			−1.13188			−0.565940	+	0.824447i	$0.691486\pi$
$702$		0			0
$703$	17164.6			0.920877
$704$	−4366.53	+	2521.02i	−0.233764	+	0.134964i
$705$		0			0
$706$	−5669.06	+	9819.10i	−0.302207	+	0.523437i
$707$		−	6811.41i		−	0.362333i
$708$		0			0
$709$	12785.5	+	7381.68i	0.677246	+	0.391008i	0.798817	−	0.601574i	$-0.205460\pi$
$709$	12785.5	+	7381.68i	0.677246	+	0.391008i	−0.121570	+	0.992583i	$0.538793\pi$
$710$			21996.7i			1.16271i
$711$		0			0
$712$	8326.17	+	14421.4i	0.438253	+	0.759077i
$713$	−15084.5	+	8709.02i	−0.792311	+	0.457441i
$714$		0			0
$715$	−16604.9	+	5825.91i	−0.868515	+	0.304722i
$716$	−862.037			−0.0449942
$717$		0			0
$718$	−11753.4	−	20357.5i	−0.610910	−	1.05813i
$719$	13093.1	−	22678.0i	0.679126	−	1.17628i	−0.296119	−	0.955151i	$-0.595692\pi$
$719$	13093.1	−	22678.0i	0.679126	−	1.17628i	0.975245	−	0.221129i	$-0.0709742\pi$
$720$		0			0
$721$	5719.53	+	3302.17i	0.295432	+	0.170568i
$722$	2590.94	+	1495.88i	0.133552	+	0.0771064i
$723$		0			0
$724$	3776.75	−	6541.52i	0.193870	−	0.335792i
$725$	−12261.3	−	21237.3i	−0.628103	−	1.08791i
$726$		0			0
$727$	−20044.0			−1.02254			−0.511272	−	0.859419i	$-0.670825\pi$
$727$	−20044.0			−1.02254			−0.511272	+	0.859419i	$0.670825\pi$
$728$	16336.1	+	14034.6i	0.831672	+	0.714501i
$729$		0			0
$730$	9644.68	−	5568.36i	0.488994	−	0.282321i
$731$	6492.68	+	11245.6i	0.328509	+	0.568995i
$732$		0			0
$733$		−	25555.5i		−	1.28774i	−0.765134	−	0.643871i	$-0.777327\pi$
$733$		−	25555.5i		−	1.28774i	0.765134	−	0.643871i	$-0.222673\pi$
$734$	11103.4	+	6410.57i	0.558358	+	0.322368i
$735$		0			0
$736$			16988.2i			0.850809i
$737$	5186.47	−	8983.23i	0.259221	−	0.448985i
$738$		0			0
$739$	9620.24	−	5554.25i	0.478872	−	0.276477i	−0.241074	−	0.970507i	$-0.577500\pi$
$739$	9620.24	−	5554.25i	0.478872	−	0.276477i	0.719946	+	0.694030i	$0.244166\pi$
$740$	−10743.9			−0.533720
$741$		0			0
$742$	−41768.2			−2.06652
$743$	24411.7	−	14094.1i	1.20535	−	0.695911i	0.243612	−	0.969873i	$-0.421667\pi$
$743$	24411.7	−	14094.1i	1.20535	−	0.695911i	0.961741	+	0.273962i	$0.0883342\pi$
$744$		0			0
$745$	12020.9	−	20820.8i	0.591155	−	1.02391i
$746$		−	37306.8i		−	1.83096i
$747$		0			0
$748$	4282.34	+	2472.41i	0.209328	+	0.120856i
$749$			18248.9i			0.890256i
$750$		0			0
$751$	8588.28	+	14875.3i	0.417298	+	0.722782i	0.995667	−	0.0929941i	$-0.0296438\pi$
$751$	8588.28	+	14875.3i	0.417298	+	0.722782i	−0.578369	+	0.815776i	$0.696310\pi$
$752$	−5352.78	+	3090.43i	−0.259569	+	0.149862i
$753$		0			0
$754$	13443.0	−	15647.5i	0.649291	−	0.755768i
$755$	49950.2			2.40778
$756$		0			0
$757$	2204.98	+	3819.14i	0.105867	+	0.183367i	0.914092	−	0.405507i	$-0.132905\pi$
$757$	2204.98	+	3819.14i	0.105867	+	0.183367i	−0.808225	+	0.588874i	$0.799572\pi$
$758$	−6610.77	+	11450.2i	−0.316773	+	0.548667i
$759$		0			0
$760$	−20159.9	−	11639.3i	−0.962206	−	0.555530i
$761$	−28097.0	−	16221.8i	−1.33839	−	0.772721i	−0.351823	−	0.936067i	$-0.614438\pi$
$761$	−28097.0	−	16221.8i	−1.33839	−	0.772721i	−0.986569	+	0.163346i	$0.947771\pi$
$762$		0			0
$763$	22665.1	−	39257.0i	1.07540	−	1.86265i
$764$	−123.643	−	214.157i	−0.00585505	−	0.0101413i
$765$		0			0
$766$	−6528.30			−0.307934
$767$	1311.21	−	1526.24i	0.0617278	−	0.0718505i
$768$		0			0
$769$	−27707.7	+	15997.1i	−1.29931	+	0.750155i	−0.980284	−	0.197593i	$-0.936688\pi$
$769$	−27707.7	+	15997.1i	−1.29931	+	0.750155i	−0.319022	+	0.947747i	$0.603354\pi$
$770$	−16434.2	−	28464.8i	−0.769152	−	1.33221i
$771$		0			0
$772$		−	2336.04i		−	0.108907i
$773$	−7776.38	−	4489.70i	−0.361833	−	0.208904i	0.308051	−	0.951370i	$-0.400323\pi$
$773$	−7776.38	−	4489.70i	−0.361833	−	0.208904i	−0.669885	+	0.742465i	$0.733656\pi$
$774$		0			0
$775$			22391.7i			1.03785i
$776$	5089.34	−	8815.00i	0.235434	−	0.407784i
$777$		0			0
$778$	31584.1	−	18235.1i	1.45546	−	0.840308i
$779$	−15293.3			−0.703390
$780$		0			0
$781$	−8185.04			−0.375011
$782$	−33885.2	+	19563.6i	−1.54953	+	0.894620i
$783$		0			0
$784$	−14507.2	+	25127.2i	−0.660859	+	1.14464i
$785$			58833.9i			2.67500i
$786$		0			0
$787$	−10886.4	−	6285.27i	−0.493086	−	0.284683i	0.232768	−	0.972532i	$-0.425222\pi$
$787$	−10886.4	−	6285.27i	−0.493086	−	0.284683i	−0.725854	+	0.687849i	$0.758555\pi$
$788$		−	11952.9i		−	0.540360i
$789$		0			0
$790$	−30185.3	−	52282.5i	−1.35942	−	2.35459i
$791$	−8803.05	+	5082.44i	−0.395702	+	0.228459i
$792$		0			0
$793$	−17653.6	−	15166.5i	−0.790540	−	0.679165i
$794$	35341.2			1.57961
$795$		0			0
$796$	4579.34	+	7931.65i	0.203907	+	0.353178i
$797$	−18931.7	+	32790.6i	−0.841398	+	1.45734i	0.0473148	+	0.998880i	$0.484934\pi$
$797$	−18931.7	+	32790.6i	−0.841398	+	1.45734i	−0.888713	+	0.458464i	$0.848400\pi$
$798$		0			0
$799$	−5729.55	−	3307.96i	−0.253688	−	0.146467i
$800$	18913.3	+	10919.6i	0.835857	+	0.482582i
$801$		0			0
$802$	−7724.58	+	13379.4i	−0.340105	+	0.589079i
$803$	2072.00	+	3588.82i	0.0910578	+	0.157717i
$804$		0			0
$805$	66562.1			2.91429
$806$	−17774.2	+	6236.16i	−0.776761	+	0.272530i
$807$		0			0
$808$	−3802.04	+	2195.11i	−0.165539	+	0.0955739i
$809$	1251.90	+	2168.35i	0.0544058	+	0.0942336i	0.891946	−	0.452143i	$-0.149340\pi$
$809$	1251.90	+	2168.35i	0.0544058	+	0.0942336i	−0.837540	+	0.546376i	$0.816007\pi$
$810$		0			0
$811$		−	5409.55i		−	0.234223i	−0.993119	−	0.117112i	$-0.962636\pi$
$811$		−	5409.55i		−	0.234223i	0.993119	−	0.117112i	$-0.0373635\pi$
$812$	8540.11	+	4930.64i	0.369088	+	0.213093i
$813$		0			0
$814$		−	15620.8i		−	0.672617i
$815$	−19262.1	+	33362.9i	−0.827879	+	1.43393i
$816$		0			0
$817$	−10328.3	+	5963.07i	−0.442280	+	0.255351i
$818$	−3884.85			−0.166052
$819$		0			0
$820$	9572.58			0.407669
$821$	27177.3	−	15690.8i	1.15529	−	0.667007i	0.205119	−	0.978737i	$-0.434242\pi$
$821$	27177.3	−	15690.8i	1.15529	−	0.667007i	0.950171	+	0.311730i	$0.100908\pi$
$822$		0			0
$823$	−16523.1	+	28618.8i	−0.699827	+	1.21214i	0.268699	+	0.963224i	$0.413406\pi$
$823$	−16523.1	+	28618.8i	−0.699827	+	1.21214i	−0.968526	+	0.248912i	$0.919927\pi$
$824$		−	4256.76i		−	0.179965i
$825$		0			0
$826$	3254.77	+	1879.14i	0.137104	+	0.0791571i
$827$		−	33653.7i		−	1.41506i	−0.706684	−	0.707529i	$-0.749810\pi$
$827$		−	33653.7i		−	1.41506i	0.706684	−	0.707529i	$-0.250190\pi$
$828$		0			0
$829$	6449.25	+	11170.4i	0.270195	+	0.467992i	0.968912	−	0.247407i	$-0.0795784\pi$
$829$	6449.25	+	11170.4i	0.270195	+	0.467992i	−0.698716	+	0.715399i	$0.746245\pi$
$830$	42932.8	−	24787.3i	1.79545	−	1.03660i
$831$		0			0
$832$	2043.79	−	10851.4i	0.0851632	−	0.452169i
$833$	−31056.6			−1.29177
$834$		0			0
$835$	−8003.58	−	13862.6i	−0.331707	−	0.574533i
$836$	−2270.73	+	3933.03i	−0.0939414	+	0.162711i
$837$		0			0
$838$	17516.0	+	10112.8i	0.722051	+	0.416877i
$839$	342.798	+	197.915i	0.0141057	+	0.00814395i	0.507036	−	0.861925i	$-0.330741\pi$
$839$	342.798	+	197.915i	0.0141057	+	0.00814395i	−0.492931	+	0.870069i	$0.664074\pi$
$840$		0			0
$841$	3186.59	−	5519.33i	0.130657	−	0.226304i
$842$	−16934.0	−	29330.5i	−0.693091	−	1.20047i
$843$		0			0
$844$	12657.4			0.516214
$845$	14019.6	−	35898.0i	0.570758	−	1.46145i
$846$		0			0
$847$	−20184.6	+	11653.6i	−0.818831	+	0.472752i
$848$	18711.8	+	32409.8i	0.757742	+	1.31245i
$849$		0			0
$850$			50299.9i			2.02973i
$851$	27395.8	+	15817.0i	1.10354	+	0.637132i
$852$		0			0
$853$			21248.9i			0.852930i	0.904504	+	0.426465i	$0.140241\pi$
$853$			21248.9i			0.852930i	−0.904504	+	0.426465i	$0.859759\pi$
$854$	21735.6	−	37647.1i	0.870932	−	1.50850i
$855$		0			0
$856$	10186.3	−	5881.08i	0.406731	−	0.234826i
$857$	−9920.37			−0.395418			−0.197709	−	0.980261i	$-0.563350\pi$
$857$	−9920.37			−0.395418			−0.197709	+	0.980261i	$0.563350\pi$
$858$		0			0
$859$	20946.3			0.831990			0.415995	−	0.909367i	$-0.363433\pi$
$859$	20946.3			0.831990			0.415995	+	0.909367i	$0.363433\pi$
$860$	6464.84	−	3732.47i	0.256336	−	0.147996i
$861$		0			0
$862$	18546.6	−	32123.7i	0.732831	−	1.26930i
$863$			11271.4i			0.444594i	0.974979	+	0.222297i	$0.0713554\pi$
$863$			11271.4i			0.444594i	−0.974979	+	0.222297i	$0.928645\pi$
$864$		0			0
$865$	−13666.6	−	7890.44i	−0.537202	−	0.310154i
$866$		−	34349.7i		−	1.34786i
$867$		0			0
$868$	−4502.17	−	7797.99i	−0.176053	−	0.304932i
$869$	19454.5	−	11232.1i	0.759435	−	0.438460i
$870$		0			0
$871$	7520.89	+	21435.9i	0.292578	+	0.833902i
$872$	−29217.0			−1.13465
$873$		0			0
$874$	−17967.8	−	31121.2i	−0.695389	−	1.20445i
$875$	13512.2	−	23403.9i	0.522054	−	0.904224i
$876$		0			0
$877$	8172.12	+	4718.18i	0.314656	+	0.181667i	0.649008	−	0.760782i	$-0.275184\pi$
$877$	8172.12	+	4718.18i	0.314656	+	0.181667i	−0.334352	+	0.942448i	$0.608518\pi$
$878$	5794.69	+	3345.57i	0.222735	+	0.128596i
$879$		0			0
$880$	−14724.7	+	25504.0i	−0.564057	+	0.976976i
$881$	10171.5	+	17617.6i	0.388974	+	0.673723i	0.992312	−	0.123763i	$-0.0394961\pi$
$881$	10171.5	+	17617.6i	0.388974	+	0.673723i	−0.603337	+	0.797486i	$0.706163\pi$
$882$		0			0
$883$	−46521.9			−1.77303			−0.886515	−	0.462699i	$-0.846881\pi$
$883$	−46521.9			−1.77303			−0.886515	+	0.462699i	$0.846881\pi$
$884$	−10218.6	+	3585.23i	−0.388787	+	0.136408i
$885$		0			0
$886$	−11612.2	+	6704.32i	−0.440316	+	0.254217i
$887$	−9977.53	−	17281.6i	−0.377692	−	0.654181i	0.613034	−	0.790056i	$-0.289949\pi$
$887$	−9977.53	−	17281.6i	−0.377692	−	0.654181i	−0.990726	+	0.135875i	$0.956615\pi$
$888$		0			0
$889$			3290.27i			0.124130i
$890$	48200.2	+	27828.4i	1.81537	+	1.04810i
$891$		0			0
$892$		−	6960.57i		−	0.261275i
$893$	3038.13	−	5262.19i	0.113849	−	0.197192i
$894$		0			0
$895$	4759.10	−	2747.67i	0.177742	−	0.102619i
$896$	46157.3			1.72099
$897$		0			0
$898$	49899.1			1.85429
$899$	14246.4	−	8225.14i	0.528523	−	0.305143i
$900$		0			0
$901$	−20028.9	+	34691.0i	−0.740575	+	1.28271i
$902$			13917.9i			0.513762i
$903$		0			0
$904$	5673.91	+	3275.83i	0.208752	+	0.120523i
$905$			48152.2i			1.76866i
$906$		0			0
$907$	−1326.97	−	2298.39i	−0.0485793	−	0.0841419i	0.840713	−	0.541481i	$-0.182136\pi$
$907$	−1326.97	−	2298.39i	−0.0485793	−	0.0841419i	−0.889293	+	0.457339i	$0.848803\pi$
$908$	−88.8078	+	51.2732i	−0.00324580	+	0.00187397i
$909$		0			0
$910$	70738.8	+	13323.2i	2.57689	+	0.485341i
$911$	−1797.50			−0.0653720			−0.0326860	−	0.999466i	$-0.510406\pi$
$911$	−1797.50			−0.0653720			−0.0326860	+	0.999466i	$0.510406\pi$
$912$		0			0
$913$	9223.43	+	15975.5i	0.334339	+	0.579091i
$914$	1436.71	−	2488.45i	0.0519936	−	0.0900555i
$915$		0			0
$916$	−9757.14	−	5633.29i	−0.351949	−	0.203198i
$917$	28173.0	+	16265.7i	1.01456	+	0.585757i
$918$		0			0
$919$	24321.0	−	42125.2i	0.872987	−	1.51206i	0.0140961	−	0.999901i	$-0.495513\pi$
$919$	24321.0	−	42125.2i	0.872987	−	1.51206i	0.858891	−	0.512158i	$-0.171154\pi$
$920$	−21451.0	−	37154.2i	−0.768714	−	1.33145i
$921$		0			0
$922$	−53425.6			−1.90833
$923$	11681.2	−	13596.7i	0.416566	−	0.484878i
$924$		0			0
$925$	35218.6	−	20333.5i	1.25187	−	0.722768i
$926$	−19189.8	−	33237.8i	−0.681012	−	1.17955i
$927$		0			0
$928$		−	16044.4i		−	0.567545i
$929$	−32688.3	−	18872.6i	−1.15443	−	0.666513i	−0.204471	−	0.978873i	$-0.565547\pi$
$929$	−32688.3	−	18872.6i	−1.15443	−	0.666513i	−0.949964	+	0.312359i	$0.898881\pi$
$930$		0			0
$931$		−	28523.3i		−	1.00410i
$932$	2017.04	−	3493.61i	0.0708908	−	0.122786i
$933$		0			0
$934$	44344.5	−	25602.3i	1.55353	−	0.896931i
$935$	−31522.3			−1.10256
$936$		0			0
$937$	2705.50			0.0943273			0.0471637	−	0.998887i	$-0.484982\pi$
$937$	2705.50			0.0943273			0.0471637	+	0.998887i	$0.484982\pi$
$938$	−36746.4	+	21215.5i	−1.27912	+	0.738498i
$939$		0			0
$940$	−1901.66	+	3293.77i	−0.0659843	+	0.114288i
$941$			5189.27i			0.179772i	0.995952	+	0.0898860i	$0.0286503\pi$
$941$			5189.27i			0.179772i	−0.995952	+	0.0898860i	$0.971350\pi$
$942$		0			0
$943$	−24409.1	−	14092.6i	−0.842916	−	0.486658i
$944$		−	3367.36i		−	0.116100i
$945$		0			0
$946$	5426.75	+	9399.41i	0.186511	+	0.323046i
$947$	62.5886	−	36.1356i	0.00214768	−	0.00123997i	−0.498926	−	0.866645i	$-0.666272\pi$
$947$	62.5886	−	36.1356i	0.00214768	−	0.00123997i	0.501073	+	0.865405i	$0.332939\pi$
$948$		0			0
$949$	−8918.67	−	1679.78i	−0.305071	−	0.0574582i
$950$	−46196.9			−1.57771
$951$		0			0
$952$	19289.7	+	33410.8i	0.656706	+	1.13745i
$953$	−22347.5	+	38707.1i	−0.759609	+	1.31568i	0.183441	+	0.983031i	$0.441276\pi$
$953$	−22347.5	+	38707.1i	−0.759609	+	1.31568i	−0.943050	+	0.332651i	$0.892057\pi$
$954$		0			0
$955$	1365.21	+	788.205i	0.0462588	+	0.0267076i
$956$	−13155.5	−	7595.34i	−0.445063	−	0.256957i
$957$		0			0
$958$	17011.4	−	29464.5i	0.573708	−	0.993691i
$959$	36429.7	+	63098.1i	1.22667	+	2.12466i
$960$		0			0
$961$	14770.2			0.495795
$962$	25948.9	+	22293.1i	0.869673	+	0.747149i
$963$		0			0
$964$	−6352.24	+	3667.47i	−0.212232	+	0.122532i
$965$	7445.92	+	12896.7i	0.248386	+	0.430217i
$966$		0			0
$967$			17936.9i			0.596496i	0.954488	+	0.298248i	$0.0964022\pi$
$967$			17936.9i			0.596496i	−0.954488	+	0.298248i	$0.903598\pi$
$968$	13009.8	+	7511.18i	0.431972	+	0.249399i
$969$		0			0
$970$		−	34020.1i		−	1.12610i
$971$	−20457.3	+	35433.1i	−0.676113	+	1.17106i	0.300029	+	0.953930i	$0.403004\pi$
$971$	−20457.3	+	35433.1i	−0.676113	+	1.17106i	−0.976142	+	0.217132i	$0.930330\pi$
$972$		0			0
$973$	−71976.2	+	41555.5i	−2.37148	+	1.36918i
$974$	13097.1			0.430860
$975$		0			0
$976$	−38949.3			−1.27740
$977$	20886.8	−	12059.0i	0.683961	−	0.394885i	−0.117385	−	0.993086i	$-0.537451\pi$
$977$	20886.8	−	12059.0i	0.683961	−	0.394885i	0.801346	+	0.598202i	$0.204118\pi$
$978$		0			0
$979$	−10355.1	+	17935.5i	−0.338048	+	0.585516i
$980$			17853.6i			0.581953i
$981$		0			0
$982$	34835.2	+	20112.1i	1.13201	+	0.653567i
$983$			2928.61i			0.0950235i	0.998871	+	0.0475118i	$0.0151292\pi$
$983$			2928.61i			0.0950235i	−0.998871	+	0.0475118i	$0.984871\pi$
$984$		0			0
$985$	38098.7	+	65989.0i	1.23241	+	2.13460i
$986$	32002.5	−	18476.6i	1.03364	−	0.596771i
$987$		0			0
$988$	−3292.79	−	9385.05i	−0.106030	−	0.302205i
$989$	−21979.6			−0.706683
$990$		0			0
$991$	−24904.9	−	43136.6i	−0.798317	−	1.38272i	−0.920712	−	0.390244i	$-0.872391\pi$
$991$	−24904.9	−	43136.6i	−0.798317	−	1.38272i	0.122395	−	0.992481i	$-0.460943\pi$
$992$	−7325.06	+	12687.4i	−0.234447	+	0.406073i
$993$		0			0
$994$	28995.6	+	16740.6i	0.925238	+	0.534186i
$995$	−50562.8	−	29192.5i	−1.61100	−	0.930114i
$996$		0			0
$997$	20575.8	−	35638.4i	0.653604	−	1.13208i	−0.328638	−	0.944456i	$-0.606589\pi$
$997$	20575.8	−	35638.4i	0.653604	−	1.13208i	0.982242	−	0.187620i	$-0.0600772\pi$
$998$	−5867.33	−	10162.5i	−0.186099	−	0.322333i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.4.q.e.10.2		10
3.2	odd	2		39.4.j.c.10.4	yes	10
12.11	even	2		624.4.bv.h.49.1		10
13.2	odd	12		1521.4.a.bk.1.3		10
13.4	even	6	inner	117.4.q.e.82.2		10
13.11	odd	12		1521.4.a.bk.1.8		10
39.2	even	12		507.4.a.r.1.8		10
39.11	even	12		507.4.a.r.1.3		10
39.17	odd	6		39.4.j.c.4.4	✓	10
39.23	odd	6		507.4.b.i.337.3		10
39.29	odd	6		507.4.b.i.337.8		10
156.95	even	6		624.4.bv.h.433.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.j.c.4.4	✓	10	39.17	odd	6
39.4.j.c.10.4	yes	10	3.2	odd	2
117.4.q.e.10.2		10	1.1	even	1	trivial
117.4.q.e.82.2		10	13.4	even	6	inner
507.4.a.r.1.3		10	39.11	even	12
507.4.a.r.1.8		10	39.2	even	12
507.4.b.i.337.3		10	39.23	odd	6
507.4.b.i.337.8		10	39.29	odd	6
624.4.bv.h.49.1		10	12.11	even	2
624.4.bv.h.433.5		10	156.95	even	6
1521.4.a.bk.1.3		10	13.2	odd	12
1521.4.a.bk.1.8		10	13.11	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)

\(f(q)\)	\(=\)	\(q+(-2.83967 + 1.63949i) q^{2} +(1.37583 - 2.38302i) q^{4} +17.5414i q^{5} +(23.1228 + 13.3499i) q^{7} -17.2091i q^{8} +O(q^{10})\)	\(q+(-2.83967 + 1.63949i) q^{2} +(1.37583 - 2.38302i) q^{4} +17.5414i q^{5} +(23.1228 + 13.3499i) q^{7} -17.2091i q^{8} +(-28.7589 - 49.8119i) q^{10} +(18.5352 - 10.7013i) q^{11} +(-8.67555 + 46.0623i) q^{13} -87.5483 q^{14} +(39.2208 + 67.9325i) q^{16} +(-41.9815 + 72.7141i) q^{17} +(-66.7828 - 38.5571i) q^{19} +(41.8015 + 24.1341i) q^{20} +(-35.0892 + 60.7763i) q^{22} +(-71.0597 - 123.079i) q^{23} -182.701 q^{25} +(-50.8828 - 145.025i) q^{26} +(63.6263 - 36.7346i) q^{28} +(67.1115 + 116.241i) q^{29} -122.559i q^{31} +(-103.520 - 59.7675i) q^{32} -275.312i q^{34} +(-234.177 + 405.606i) q^{35} +(-192.766 + 111.294i) q^{37} +252.855 q^{38} +301.873 q^{40} +(171.751 - 99.1604i) q^{41} +(77.3279 - 133.936i) q^{43} -58.8928i q^{44} +(403.573 + 233.003i) q^{46} +78.7956i q^{47} +(184.942 + 320.329i) q^{49} +(518.811 - 299.536i) q^{50} +(97.8310 + 84.0481i) q^{52} +477.088 q^{53} +(187.716 + 325.133i) q^{55} +(229.741 - 397.923i) q^{56} +(-381.150 - 220.057i) q^{58} +(-37.1769 - 21.4641i) q^{59} +(-248.269 + 430.015i) q^{61} +(200.934 + 348.028i) q^{62} -235.581 q^{64} +(-807.998 - 152.181i) q^{65} +(419.727 - 242.329i) q^{67} +(115.519 + 200.085i) q^{68} -1535.72i q^{70} +(-331.196 - 191.216i) q^{71} +193.622i q^{73} +(364.929 - 632.076i) q^{74} +(-183.764 + 106.096i) q^{76} +571.447 q^{77} +1049.60 q^{79} +(-1191.63 + 687.989i) q^{80} +(-325.144 + 563.166i) q^{82} +861.900i q^{83} +(-1275.51 - 736.414i) q^{85} +507.112i q^{86} +(-184.160 - 318.974i) q^{88} +(-838.005 + 483.823i) q^{89} +(-815.532 + 949.271i) q^{91} -391.065 q^{92} +(-129.184 - 223.754i) q^{94} +(676.345 - 1171.46i) q^{95} +(512.228 + 295.735i) q^{97} +(-1050.35 - 606.421i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 30 q^{4} + 30 q^{7}+O(q^{10}) \) 10 * q + 30 * q^4 + 30 * q^7	\( 10 q + 30 q^{4} + 30 q^{7} + 40 q^{10} - 60 q^{11} + 25 q^{13} + 60 q^{14} - 250 q^{16} - 105 q^{17} + 180 q^{19} - 510 q^{20} - 290 q^{22} + 60 q^{23} - 960 q^{25} + 30 q^{26} + 150 q^{28} + 495 q^{29} - 1440 q^{32} - 60 q^{35} - 405 q^{37} + 1380 q^{38} + 2000 q^{40} - 1065 q^{41} - 370 q^{43} - 390 q^{46} + 775 q^{49} + 4320 q^{50} + 2940 q^{52} - 330 q^{53} - 260 q^{55} + 2670 q^{56} + 2040 q^{58} - 780 q^{59} - 1375 q^{61} + 780 q^{62} - 3140 q^{64} - 1605 q^{65} + 1590 q^{67} + 600 q^{68} - 1620 q^{71} - 2190 q^{74} - 5190 q^{76} + 4320 q^{77} + 1100 q^{79} - 8430 q^{80} - 2390 q^{82} + 525 q^{85} + 3170 q^{88} - 2040 q^{89} + 4770 q^{91} + 1740 q^{92} - 3230 q^{94} + 1380 q^{95} - 3750 q^{97} - 180 q^{98}+O(q^{100}) \) 10 * q + 30 * q^4 + 30 * q^7 + 40 * q^10 - 60 * q^11 + 25 * q^13 + 60 * q^14 - 250 * q^16 - 105 * q^17 + 180 * q^19 - 510 * q^20 - 290 * q^22 + 60 * q^23 - 960 * q^25 + 30 * q^26 + 150 * q^28 + 495 * q^29 - 1440 * q^32 - 60 * q^35 - 405 * q^37 + 1380 * q^38 + 2000 * q^40 - 1065 * q^41 - 370 * q^43 - 390 * q^46 + 775 * q^49 + 4320 * q^50 + 2940 * q^52 - 330 * q^53 - 260 * q^55 + 2670 * q^56 + 2040 * q^58 - 780 * q^59 - 1375 * q^61 + 780 * q^62 - 3140 * q^64 - 1605 * q^65 + 1590 * q^67 + 600 * q^68 - 1620 * q^71 - 2190 * q^74 - 5190 * q^76 + 4320 * q^77 + 1100 * q^79 - 8430 * q^80 - 2390 * q^82 + 525 * q^85 + 3170 * q^88 - 2040 * q^89 + 4770 * q^91 + 1740 * q^92 - 3230 * q^94 + 1380 * q^95 - 3750 * q^97 - 180 * q^98

Introduction

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