LMFDB - Embedded newform 351.2.t.c.181.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [351,2,Mod(64,351)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(351, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("351.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.t (of order $6$, degree $2$, not 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:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6x^{16} + 9x^{14} + 54x^{12} + 81x^{10} + 486x^{8} + 729x^{6} - 4374x^{4} + 59049 $ x^20 - 6x^16 + 9x^14 + 54x^12 + 81x^10 + 486x^8 + 729x^6 - 4374*x^4 + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{9} $
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			181.5
Root			$0.219737 - 1.71806i$ of defining polynomial
Character	$\chi$	$=$	351.181
Dual form			351.2.t.c.64.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.784270 - 0.452798i) q^{2} +(-0.589947 - 1.02182i) q^{4} +(1.94254 - 1.12153i) q^{5} +(2.97576 + 1.71806i) q^{7} +2.87970i q^{8} -2.03130 q^{10} +(3.20133 + 1.84829i) q^{11} +(-3.28340 - 1.48972i) q^{13} +(-1.55587 - 2.69484i) q^{14} +(0.124029 - 0.214825i) q^{16} +4.21120 q^{17} -4.25298i q^{19} +(-2.29200 - 1.32329i) q^{20} +(-1.67380 - 2.89911i) q^{22} +(-1.89162 - 3.27639i) q^{23} +(0.0156524 - 0.0271108i) q^{25} +(1.90053 + 2.65506i) q^{26} -4.05425i q^{28} +(1.18945 - 2.06020i) q^{29} +(6.37163 - 3.67866i) q^{31} +(4.79325 - 2.76738i) q^{32} +(-3.30272 - 1.90682i) q^{34} +7.70739 q^{35} +5.49928i q^{37} +(-1.92574 + 3.33549i) q^{38} +(3.22967 + 5.59395i) q^{40} +(-6.86085 + 3.96111i) q^{41} +(-0.450266 + 0.779883i) q^{43} -4.36157i q^{44} +3.42609i q^{46} +(-4.80060 - 2.77163i) q^{47} +(2.40343 + 4.16287i) q^{49} +(-0.0245514 + 0.0141748i) q^{50} +(0.414812 + 4.23390i) q^{52} -7.59566 q^{53} +8.29163 q^{55} +(-4.94749 + 8.56930i) q^{56} +(-1.86571 + 1.07717i) q^{58} +(4.44379 - 2.56562i) q^{59} +(6.50907 - 11.2740i) q^{61} -6.66277 q^{62} -5.50838 q^{64} +(-8.04892 + 0.788585i) q^{65} +(-11.7002 + 6.75511i) q^{67} +(-2.48439 - 4.30308i) q^{68} +(-6.04468 - 3.48989i) q^{70} +2.65506i q^{71} +5.45741i q^{73} +(2.49006 - 4.31292i) q^{74} +(-4.34578 + 2.50904i) q^{76} +(6.35092 + 11.0001i) q^{77} +(-5.46886 + 9.47234i) q^{79} -0.556410i q^{80} +7.17434 q^{82} +(0.465547 + 0.268784i) q^{83} +(8.18044 - 4.72298i) q^{85} +(0.706259 - 0.407759i) q^{86} +(-5.32252 + 9.21887i) q^{88} +5.75227i q^{89} +(-7.21120 - 10.0741i) q^{91} +(-2.23192 + 3.86579i) q^{92} +(2.50998 + 4.34740i) q^{94} +(-4.76984 - 8.26161i) q^{95} +(5.87585 + 3.39243i) q^{97} -4.35308i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 12 q^{4} - 16 q^{10} - 4 q^{13} + 18 q^{14} + 4 q^{16} + 12 q^{17} - 10 q^{22} - 24 q^{23} - 12 q^{25} + 12 q^{26} - 12 q^{29} + 12 q^{35} - 12 q^{38} - 8 q^{40} + 4 q^{43} - 10 q^{49} - 108 q^{53}+ \cdots - 24 q^{95}+O(q^{100}) $ 20 * q + 12 * q^4 - 16 * q^10 - 4 * q^13 + 18 * q^14 + 4 * q^16 + 12 * q^17 - 10 * q^22 - 24 * q^23 - 12 * q^25 + 12 * q^26 - 12 * q^29 + 12 * q^35 - 12 * q^38 - 8 * q^40 + 4 * q^43 - 10 * q^49 - 108 * q^53 + 20 * q^55 - 36 * q^56 - 2 * q^61 + 72 * q^62 + 8 * q^64 + 24 * q^65 - 24 * q^68 + 42 * q^74 + 6 * q^77 - 14 * q^79 - 4 * q^82 + 22 * q^88 - 72 * q^91 + 84 * q^92 + 20 * q^94 - 24 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.784270	−	0.452798i	−0.554562	−	0.320177i	0.196398	−	0.980524i	$-0.437076\pi$
$2$	−0.784270	−	0.452798i	−0.554562	−	0.320177i	−0.750960	+	0.660348i	$0.770409\pi$
$3$		0			0
$3$		0			0
$4$	−0.589947	−	1.02182i	−0.294974	−	0.510909i
$5$	1.94254	−	1.12153i	0.868732	−	0.501563i	0.00180550	−	0.999998i	$-0.499425\pi$
$5$	1.94254	−	1.12153i	0.868732	−	0.501563i	0.866927	+	0.498436i	$0.166092\pi$
$6$		0			0
$7$	2.97576	+	1.71806i	1.12473	+	0.649364i	0.942605	−	0.333911i	$-0.108368\pi$
$7$	2.97576	+	1.71806i	1.12473	+	0.649364i	0.182127	+	0.983275i	$0.441702\pi$
$8$			2.87970i			1.01813i
$9$		0			0
$10$	−2.03130			−0.642355
$11$	3.20133	+	1.84829i	0.965236	+	0.557279i	0.897781	−	0.440443i	$-0.145179\pi$
$11$	3.20133	+	1.84829i	0.965236	+	0.557279i	0.0674557	+	0.997722i	$0.478512\pi$
$12$		0			0
$13$	−3.28340	−	1.48972i	−0.910652	−	0.413174i
$13$	−3.28340	−	1.48972i	−0.910652	−	0.413174i
$14$	−1.55587	−	2.69484i	−0.415823	−	0.720226i
$15$		0			0
$16$	0.124029	−	0.214825i	0.0310073	−	0.0537063i
$17$	4.21120			1.02137			0.510683	−	0.859769i	$-0.329393\pi$
$17$	4.21120			1.02137			0.510683	+	0.859769i	$0.329393\pi$
$18$		0			0
$19$		−	4.25298i		−	0.975701i	−0.872927	−	0.487851i	$-0.837781\pi$
$19$		−	4.25298i		−	0.975701i	0.872927	−	0.487851i	$-0.162219\pi$
$20$	−2.29200	−	1.32329i	−0.512506	−	0.295896i
$21$		0			0
$22$	−1.67380	−	2.89911i	−0.356856	−	0.618092i
$23$	−1.89162	−	3.27639i	−0.394431	−	0.683174i	0.598598	−	0.801050i	$-0.295725\pi$
$23$	−1.89162	−	3.27639i	−0.394431	−	0.683174i	−0.993028	+	0.117876i	$0.962392\pi$
$24$		0			0
$25$	0.0156524	−	0.0271108i	0.00313048	−	0.00542215i
$26$	1.90053	+	2.65506i	0.372725	+	0.520700i
$27$		0			0
$28$		−	4.05425i		−	0.766181i
$29$	1.18945	−	2.06020i	0.220876	−	0.382569i	−0.734198	−	0.678935i	$-0.762442\pi$
$29$	1.18945	−	2.06020i	0.220876	−	0.382569i	0.955074	+	0.296367i	$0.0957750\pi$
$30$		0			0
$31$	6.37163	−	3.67866i	1.14438	−	0.660707i	0.196868	−	0.980430i	$-0.436923\pi$
$31$	6.37163	−	3.67866i	1.14438	−	0.660707i	0.947511	+	0.319723i	$0.103590\pi$
$32$	4.79325	−	2.76738i	0.847334	−	0.489209i
$33$		0			0
$34$	−3.30272	−	1.90682i	−0.566411	−	0.327018i
$35$	7.70739			1.30279
$36$		0			0
$37$			5.49928i			0.904076i	0.891999	+	0.452038i	$0.149303\pi$
$37$			5.49928i			0.904076i	−0.891999	+	0.452038i	$0.850697\pi$
$38$	−1.92574	+	3.33549i	−0.312397	+	0.541087i
$39$		0			0
$40$	3.22967	+	5.59395i	0.510655	+	0.884481i
$41$	−6.86085	+	3.96111i	−1.07148	+	0.618622i	−0.928587	−	0.371116i	$-0.878975\pi$
$41$	−6.86085	+	3.96111i	−1.07148	+	0.618622i	−0.142898	+	0.989737i	$0.545642\pi$
$42$		0			0
$43$	−0.450266	+	0.779883i	−0.0686649	+	0.118931i	−0.898314	−	0.439354i	$-0.855207\pi$
$43$	−0.450266	+	0.779883i	−0.0686649	+	0.118931i	0.829649	+	0.558285i	$0.188541\pi$
$44$		−	4.36157i		−	0.657531i
$45$		0			0
$46$			3.42609i			0.505150i
$47$	−4.80060	−	2.77163i	−0.700239	−	0.404283i	0.107197	−	0.994238i	$-0.465812\pi$
$47$	−4.80060	−	2.77163i	−0.700239	−	0.404283i	−0.807436	+	0.589955i	$0.799146\pi$
$48$		0			0
$49$	2.40343	+	4.16287i	0.343347	+	0.594695i
$50$	−0.0245514	+	0.0141748i	−0.00347209	+	0.00200461i
$51$		0			0
$52$	0.414812	+	4.23390i	0.0575241	+	0.587136i
$53$	−7.59566			−1.04334			−0.521672	−	0.853146i	$-0.674692\pi$
$53$	−7.59566			−1.04334			−0.521672	+	0.853146i	$0.674692\pi$
$54$		0			0
$55$	8.29163			1.11804
$56$	−4.94749	+	8.56930i	−0.661136	+	1.14512i
$57$		0			0
$58$	−1.86571	+	1.07717i	−0.244979	+	0.141439i
$59$	4.44379	−	2.56562i	0.578532	−	0.334016i	−0.182018	−	0.983295i	$-0.558263\pi$
$59$	4.44379	−	2.56562i	0.578532	−	0.334016i	0.760550	+	0.649279i	$0.224929\pi$
$60$		0			0
$61$	6.50907	−	11.2740i	0.833401	−	1.44349i	−0.0619247	−	0.998081i	$-0.519724\pi$
$61$	6.50907	−	11.2740i	0.833401	−	1.44349i	0.895326	−	0.445412i	$-0.146943\pi$
$62$	−6.66277			−0.846173
$63$		0			0
$64$	−5.50838			−0.688547
$65$	−8.04892	+	0.788585i	−0.998346	+	0.0978120i
$66$		0			0
$67$	−11.7002	+	6.75511i	−1.42941	+	0.825269i	−0.997074	−	0.0764454i	$-0.975643\pi$
$67$	−11.7002	+	6.75511i	−1.42941	+	0.825269i	−0.432333	+	0.901714i	$0.642310\pi$
$68$	−2.48439	−	4.30308i	−0.301276	−	0.521825i
$69$		0			0
$70$	−6.04468	−	3.48989i	−0.722477	−	0.417122i
$71$			2.65506i			0.315098i	0.987511	+	0.157549i	$0.0503592\pi$
$71$			2.65506i			0.315098i	−0.987511	+	0.157549i	$0.949641\pi$
$72$		0			0
$73$			5.45741i			0.638741i	0.947630	+	0.319371i	$0.103472\pi$
$73$			5.45741i			0.638741i	−0.947630	+	0.319371i	$0.896528\pi$
$74$	2.49006	−	4.31292i	0.289464	−	0.501366i
$75$		0			0
$76$	−4.34578	+	2.50904i	−0.498495	+	0.287806i
$77$	6.35092	+	11.0001i	0.723755	+	1.25358i
$78$		0			0
$79$	−5.46886	+	9.47234i	−0.615294	+	1.06572i	0.375038	+	0.927009i	$0.377630\pi$
$79$	−5.46886	+	9.47234i	−0.615294	+	1.06572i	−0.990333	+	0.138712i	$0.955704\pi$
$80$		−	0.556410i		−	0.0622085i
$81$		0			0
$82$	7.17434			0.792273
$83$	0.465547	+	0.268784i	0.0511004	+	0.0295029i	0.525333	−	0.850897i	$-0.323941\pi$
$83$	0.465547	+	0.268784i	0.0511004	+	0.0295029i	−0.474232	+	0.880400i	$0.657274\pi$
$84$		0			0
$85$	8.18044	−	4.72298i	0.887294	−	0.512279i
$86$	0.706259	−	0.407759i	0.0761579	−	0.0439698i
$87$		0			0
$88$	−5.32252	+	9.21887i	−0.567382	+	0.982735i
$89$			5.75227i			0.609739i	0.952394	+	0.304870i	$0.0986129\pi$
$89$			5.75227i			0.609739i	−0.952394	+	0.304870i	$0.901387\pi$
$90$		0			0
$91$	−7.21120	−	10.0741i	−0.755939	−	1.05605i
$92$	−2.23192	+	3.86579i	−0.232693	+	0.403037i
$93$		0			0
$94$	2.50998	+	4.34740i	0.258884	+	0.448401i
$95$	−4.76984	−	8.26161i	−0.489375	−	0.847623i
$96$		0			0
$97$	5.87585	+	3.39243i	0.596603	+	0.344449i	0.767704	−	0.640805i	$-0.221399\pi$
$97$	5.87585	+	3.39243i	0.596603	+	0.344449i	−0.171101	+	0.985253i	$0.554733\pi$
$98$		−	4.35308i		−	0.439727i
$99$		0			0
$100$	−0.0369364			−0.00369364
$101$	−2.48116	+	4.29749i	−0.246884	+	0.427616i	−0.962660	−	0.270715i	$-0.912740\pi$
$101$	−2.48116	+	4.29749i	−0.246884	+	0.427616i	0.715776	+	0.698330i	$0.246073\pi$
$102$		0			0
$103$	−1.05587	−	1.82881i	−0.104038	−	0.180198i	0.809307	−	0.587386i	$-0.199843\pi$
$103$	−1.05587	−	1.82881i	−0.104038	−	0.180198i	−0.913345	+	0.407188i	$0.866510\pi$
$104$	4.28995	−	9.45522i	0.420664	−	0.927161i
$105$		0			0
$106$	5.95705	+	3.43930i	0.578600	+	0.334055i
$107$	8.07404			0.780547			0.390274	−	0.920699i	$-0.372380\pi$
$107$	8.07404			0.780547			0.390274	+	0.920699i	$0.372380\pi$
$108$		0			0
$109$			10.0020i			0.958021i	0.877809	+	0.479011i	$0.159004\pi$
$109$			10.0020i			0.958021i	−0.877809	+	0.479011i	$0.840996\pi$
$110$	−6.50287	−	3.75443i	−0.620024	−	0.357971i
$111$		0			0
$112$	0.738163	−	0.426179i	0.0697498	−	0.0402701i
$113$	9.71733	+	16.8309i	0.914130	+	1.58332i	0.808171	+	0.588948i	$0.200458\pi$
$113$	9.71733	+	16.8309i	0.914130	+	1.58332i	0.105959	+	0.994371i	$0.466209\pi$
$114$		0			0
$115$	−7.34912	−	4.24302i	−0.685309	−	0.395664i
$116$	−2.80686			−0.260611
$117$		0			0
$118$	−4.64684			−0.427776
$119$	12.5315	+	7.23508i	1.14876	+	0.663238i
$120$		0			0
$121$	1.33233	+	2.30766i	0.121121	+	0.209787i
$122$	−10.2097	+	5.89459i	−0.924346	+	0.533671i
$123$		0			0
$124$	−7.51786	−	4.34044i	−0.675123	−	0.389783i
$125$			11.1451i			0.996845i
$126$		0			0
$127$	−1.76413			−0.156541			−0.0782704	−	0.996932i	$-0.524940\pi$
$127$	−1.76413			−0.156541			−0.0782704	+	0.996932i	$0.524940\pi$
$128$	−5.26644	−	3.04058i	−0.465492	−	0.268752i
$129$		0			0
$130$	6.66959	+	3.02607i	0.584962	+	0.265404i
$131$	−3.56490	−	6.17458i	−0.311466	−	0.539476i	0.667214	−	0.744866i	$-0.267487\pi$
$131$	−3.56490	−	6.17458i	−0.311466	−	0.539476i	−0.978680	+	0.205391i	$0.934153\pi$
$132$		0			0
$133$	7.30686	−	12.6559i	0.633585	−	1.09740i
$134$	12.2348			1.05693
$135$		0			0
$136$			12.1270i			1.03988i
$137$	3.91494	+	2.26029i	0.334476	+	0.193110i	0.657826	−	0.753170i	$-0.271476\pi$
$137$	3.91494	+	2.26029i	0.334476	+	0.193110i	−0.323351	+	0.946279i	$0.604809\pi$
$138$		0			0
$139$	−7.05496	−	12.2195i	−0.598394	−	1.03645i	−0.993058	−	0.117623i	$-0.962472\pi$
$139$	−7.05496	−	12.2195i	−0.598394	−	1.03645i	0.394664	−	0.918825i	$-0.370861\pi$
$140$	−4.54696	−	7.87556i	−0.384288	−	0.665606i
$141$		0			0
$142$	1.20221	−	2.08228i	0.100887	−	0.174741i
$143$	−7.75782	−	10.8377i	−0.648741	−	0.906298i
$144$		0			0
$145$		−	5.33603i		−	0.443133i
$146$	2.47111	−	4.28008i	0.204510	−	0.354222i
$147$		0			0
$148$	5.61927	−	3.24428i	0.461901	−	0.266679i
$149$	−5.02499	+	2.90118i	−0.411663	+	0.237674i	−0.691504	−	0.722372i	$-0.743052\pi$
$149$	−5.02499	+	2.90118i	−0.411663	+	0.237674i	0.279841	+	0.960046i	$0.409718\pi$
$150$		0			0
$151$	−8.44018	−	4.87294i	−0.686852	−	0.396554i	0.115580	−	0.993298i	$-0.463127\pi$
$151$	−8.44018	−	4.87294i	−0.686852	−	0.396554i	−0.802432	+	0.596744i	$0.796461\pi$
$152$	12.2473			0.993389
$153$		0			0
$154$		−	11.5027i		−	0.926917i
$155$	8.25145	−	14.2919i	0.662773	−	1.14796i
$156$		0			0
$157$	0.539798	+	0.934957i	0.0430806	+	0.0746177i	0.886762	−	0.462227i	$-0.152949\pi$
$157$	0.539798	+	0.934957i	0.0430806	+	0.0746177i	−0.843681	+	0.536845i	$0.819616\pi$
$158$	8.57812	−	4.95258i	0.682438	−	0.394006i
$159$		0			0
$160$	6.20739	−	10.7515i	0.490738	−	0.849982i
$161$		−	12.9997i		−	1.02452i
$162$		0			0
$163$		−	5.54857i		−	0.434598i	−0.976105	−	0.217299i	$-0.930275\pi$
$163$		−	5.54857i		−	0.434598i	0.976105	−	0.217299i	$-0.0697247\pi$
$164$	8.09508	+	4.67370i	0.632120	+	0.364954i
$165$		0			0
$166$	−0.243410	−	0.421598i	−0.0188923	−	0.0327223i
$167$	−11.5515	+	6.66925i	−0.893880	+	0.516082i	−0.875210	−	0.483744i	$-0.839277\pi$
$167$	−11.5515	+	6.66925i	−0.893880	+	0.516082i	−0.0186702	+	0.999826i	$0.505943\pi$
$168$		0			0
$169$	8.56147	+	9.78270i	0.658575	+	0.752515i
$170$	−8.55423			−0.656079
$171$		0			0
$172$	1.06253			0.0810173
$173$	3.72080	−	6.44461i	0.282887	−	0.489975i	−0.689208	−	0.724564i	$-0.742041\pi$
$173$	3.72080	−	6.44461i	0.282887	−	0.489975i	0.972095	+	0.234589i	$0.0753745\pi$
$174$		0			0
$175$	0.0931556	−	0.0537834i	0.00704190	−	0.00406564i
$176$	0.794117	−	0.458484i	0.0598588	−	0.0345595i
$177$		0			0
$178$	2.60462	−	4.51133i	0.195224	−	0.338138i
$179$	−23.2047			−1.73440			−0.867202	−	0.497957i	$-0.834084\pi$
$179$	−23.2047			−1.73440			−0.867202	+	0.497957i	$0.834084\pi$
$180$		0			0
$181$	5.18439			0.385353			0.192676	−	0.981262i	$-0.438283\pi$
$181$	5.18439			0.385353			0.192676	+	0.981262i	$0.438283\pi$
$182$	1.09398	+	11.1660i	0.0810914	+	0.827682i
$183$		0			0
$184$	9.43502	−	5.44731i	0.695559	−	0.401581i
$185$	6.16760	+	10.6826i	0.453451	+	0.785400i
$186$		0			0
$187$	13.4814	+	7.78351i	0.985860	+	0.569186i
$188$			6.54045i			0.477012i
$189$		0			0
$190$			8.63911i			0.626747i
$191$	8.07057	−	13.9786i	0.583966	−	1.01146i	−0.411037	−	0.911619i	$-0.634833\pi$
$191$	8.07057	−	13.9786i	0.583966	−	1.01146i	0.995003	−	0.0998406i	$-0.0318333\pi$
$192$		0			0
$193$	2.83991	−	1.63962i	0.204421	−	0.118023i	−0.394295	−	0.918984i	$-0.629011\pi$
$193$	2.83991	−	1.63962i	0.204421	−	0.118023i	0.598716	+	0.800961i	$0.295678\pi$
$194$	−3.07217	−	5.32115i	−0.220569	−	0.382037i
$195$		0			0
$196$	2.83580	−	4.91174i	0.202557	−	0.350839i
$197$		−	7.11249i		−	0.506744i	−0.967369	−	0.253372i	$-0.918460\pi$
$197$		−	7.11249i		−	0.506744i	0.967369	−	0.253372i	$-0.0815396\pi$
$198$		0			0
$199$	−13.8449			−0.981437			−0.490719	−	0.871318i	$-0.663266\pi$
$199$	−13.8449			−0.981437			−0.490719	+	0.871318i	$0.663266\pi$
$200$	0.0780709	+	0.0450743i	0.00552045	+	0.00318723i
$201$		0			0
$202$	3.89179	−	2.24693i	0.273825	−	0.158093i
$203$	7.07906	−	4.08710i	0.496853	−	0.286858i
$204$		0			0
$205$	−8.88500	+	15.3893i	−0.620555	+	1.07483i
$206$			1.91238i			0.133242i
$207$		0			0
$208$	−0.727267	+	0.520589i	−0.0504269	+	0.0360963i
$209$	7.86073	−	13.6152i	0.543738	−	0.941782i
$210$		0			0
$211$	−7.21695	−	12.5001i	−0.496836	−	0.860545i	0.503158	−	0.864195i	$-0.332171\pi$
$211$	−7.21695	−	12.5001i	−0.496836	−	0.860545i	−0.999993	+	0.00365007i	$0.998838\pi$
$212$	4.48104	+	7.76139i	0.307759	+	0.533055i
$213$		0			0
$214$	−6.33223	−	3.65591i	−0.432862	−	0.249913i
$215$			2.01994i			0.137759i
$216$		0			0
$217$	25.2806			1.71616
$218$	4.52890	−	7.84429i	0.306736	−	0.531283i
$219$		0			0
$220$	−4.89162	−	8.47254i	−0.329793	−	0.571219i
$221$	−13.8271	−	6.27350i	−0.930109	−	0.422002i
$222$		0			0
$223$	9.52959	+	5.50191i	0.638149	+	0.368435i	0.783901	−	0.620886i	$-0.213227\pi$
$223$	9.52959	+	5.50191i	0.638149	+	0.368435i	−0.145752	+	0.989321i	$0.546560\pi$
$224$	19.0181			1.27070
$225$		0			0
$226$		−	17.6000i		−	1.17073i
$227$	7.03055	+	4.05909i	0.466634	+	0.269411i	0.714830	−	0.699299i	$-0.246504\pi$
$227$	7.03055	+	4.05909i	0.466634	+	0.269411i	−0.248196	+	0.968710i	$0.579838\pi$
$228$		0			0
$229$	−4.65740	+	2.68895i	−0.307769	+	0.177691i	−0.645928	−	0.763398i	$-0.723529\pi$
$229$	−4.65740	+	2.68895i	−0.307769	+	0.177691i	0.338158	+	0.941089i	$0.390196\pi$
$230$	3.84246	+	6.65534i	0.253365	+	0.438840i
$231$		0			0
$232$	5.93275	+	3.42528i	0.389504	+	0.224880i
$233$	−20.0992			−1.31675			−0.658373	−	0.752692i	$-0.728755\pi$
$233$	−20.0992			−1.31675			−0.658373	+	0.752692i	$0.728755\pi$
$234$		0			0
$235$	−12.4338			−0.811094
$236$	−5.24321	−	3.02717i	−0.341304	−	0.197052i
$237$		0			0
$238$	−6.55206	−	11.3485i	−0.424707	−	0.735614i
$239$	12.2635	−	7.08034i	0.793261	−	0.457989i	−0.0478485	−	0.998855i	$-0.515236\pi$
$239$	12.2635	−	7.08034i	0.793261	−	0.457989i	0.841109	+	0.540865i	$0.181903\pi$
$240$		0			0
$241$	−26.2041	−	15.1289i	−1.68795	−	0.974539i	−0.956084	−	0.293092i	$-0.905316\pi$
$241$	−26.2041	−	15.1289i	−1.68795	−	0.974539i	−0.731867	−	0.681447i	$-0.761351\pi$
$242$		−	2.41310i		−	0.155120i
$243$		0			0
$244$	−15.3600			−0.983326
$245$	9.33754	+	5.39103i	0.596554	+	0.344421i
$246$		0			0
$247$	−6.33575	+	13.9643i	−0.403134	+	0.888525i
$248$	10.5935	+	18.3484i	0.672685	+	1.16512i
$249$		0			0
$250$	5.04647	−	8.74074i	0.319167	−	0.552813i
$251$	17.5085			1.10512			0.552562	−	0.833472i	$-0.313650\pi$
$251$	17.5085			1.10512			0.552562	+	0.833472i	$0.313650\pi$
$252$		0			0
$253$		−	13.9850i		−	0.879232i
$254$	1.38355	+	0.798793i	0.0868117	+	0.0501208i
$255$		0			0
$256$	8.26192	+	14.3101i	0.516370	+	0.894379i
$257$	9.15211	+	15.8519i	0.570893	+	0.988815i	0.996475	+	0.0838952i	$0.0267361\pi$
$257$	9.15211	+	15.8519i	0.570893	+	0.988815i	−0.425582	+	0.904920i	$0.639931\pi$
$258$		0			0
$259$	−9.44807	+	16.3645i	−0.587074	+	1.01684i
$260$	5.55423	+	7.75931i	0.344459	+	0.481212i
$261$		0			0
$262$			6.45672i			0.398897i
$263$	−4.19661	+	7.26875i	−0.258774	+	0.448210i	−0.965914	−	0.258864i	$-0.916652\pi$
$263$	−4.19661	+	7.26875i	−0.258774	+	0.448210i	0.707140	+	0.707074i	$0.249985\pi$
$264$		0			0
$265$	−14.7549	+	8.51875i	−0.906387	+	0.523303i
$266$	−11.4611	+	6.61707i	−0.702725	+	0.405719i
$267$		0			0
$268$	13.8050	+	7.97032i	0.843275	+	0.486865i
$269$	−21.3238			−1.30014			−0.650069	−	0.759875i	$-0.725260\pi$
$269$	−21.3238			−1.30014			−0.650069	+	0.759875i	$0.725260\pi$
$270$		0			0
$271$			18.4587i			1.12129i	0.828057	+	0.560643i	$0.189446\pi$
$271$			18.4587i			1.12129i	−0.828057	+	0.560643i	$0.810554\pi$
$272$	0.522312	−	0.904671i	0.0316698	−	0.0548538i
$273$		0			0
$274$	−2.04691	−	3.54535i	−0.123658	−	0.214183i
$275$	0.100217	−	0.0578603i	0.00604331	−	0.00348911i
$276$		0			0
$277$	4.31390	−	7.47189i	0.259197	−	0.448943i	−0.706830	−	0.707383i	$-0.749875\pi$
$277$	4.31390	−	7.47189i	0.259197	−	0.448943i	0.966027	+	0.258441i	$0.0832087\pi$
$278$			12.7779i			0.766367i
$279$		0			0
$280$			22.1950i			1.32640i
$281$	−3.00928	−	1.73741i	−0.179518	−	0.103645i	0.407548	−	0.913184i	$-0.366384\pi$
$281$	−3.00928	−	1.73741i	−0.179518	−	0.103645i	−0.587066	+	0.809539i	$0.699717\pi$
$282$		0			0
$283$	6.89178	+	11.9369i	0.409674	+	0.709576i	0.994853	−	0.101328i	$-0.0323091\pi$
$283$	6.89178	+	11.9369i	0.409674	+	0.709576i	−0.585179	+	0.810904i	$0.698976\pi$
$284$	2.71299	−	1.56635i	0.160986	−	0.0929456i
$285$		0			0
$286$	1.17691	+	12.0124i	0.0695920	+	0.710311i
$287$	−27.2217			−1.60684
$288$		0			0
$289$	0.734202			0.0431884
$290$	−2.41615	+	4.18489i	−0.141881	+	0.245745i
$291$		0			0
$292$	5.57648	−	3.21958i	0.326339	−	0.188412i
$293$	−24.6911	+	14.2554i	−1.44247	+	0.832810i	−0.998014	−	0.0629917i	$-0.979936\pi$
$293$	−24.6911	+	14.2554i	−1.44247	+	0.832810i	−0.444455	+	0.895801i	$0.646603\pi$
$294$		0			0
$295$	5.75484	−	9.96768i	0.335060	−	0.580341i
$296$	−15.8363			−0.920465
$297$		0			0
$298$	5.25460			0.304391
$299$	1.33007	+	13.5757i	0.0769196	+	0.785102i
$300$		0			0
$301$	−2.67977	+	1.54716i	−0.154459	+	0.0891770i
$302$	4.41292	+	7.64340i	0.253935	+	0.439828i
$303$		0			0
$304$	−0.913648	−	0.527495i	−0.0524013	−	0.0302539i
$305$		−	29.2004i		−	1.67201i
$306$		0			0
$307$		−	21.8137i		−	1.24497i	−0.782631	−	0.622486i	$-0.786123\pi$
$307$		−	21.8137i		−	1.24497i	0.782631	−	0.622486i	$-0.213877\pi$
$308$	7.49342	−	12.9790i	0.426977	−	0.739546i
$309$		0			0
$310$	−12.9427	+	7.47249i	−0.735097	+	0.424409i
$311$	−3.48161	−	6.03032i	−0.197424	−	0.341948i	0.750268	−	0.661133i	$-0.229924\pi$
$311$	−3.48161	−	6.03032i	−0.197424	−	0.341948i	−0.947692	+	0.319185i	$0.896591\pi$
$312$		0			0
$313$	−11.2253	+	19.4428i	−0.634491	+	1.09897i	0.352131	+	0.935951i	$0.385457\pi$
$313$	−11.2253	+	19.4428i	−0.634491	+	1.09897i	−0.986623	+	0.163020i	$0.947876\pi$
$314$		−	0.977678i		−	0.0551736i
$315$		0			0
$316$	12.9054			0.725983
$317$	8.84739	+	5.10804i	0.496919	+	0.286896i	0.727440	−	0.686171i	$-0.240710\pi$
$317$	8.84739	+	5.10804i	0.496919	+	0.286896i	−0.230522	+	0.973067i	$0.574043\pi$
$318$		0			0
$319$	7.61567	−	4.39691i	0.426395	−	0.246180i
$320$	−10.7003	+	6.17780i	−0.598163	+	0.345350i
$321$		0			0
$322$	−5.88622	+	10.1952i	−0.328026	+	0.568158i
$323$		−	17.9102i		−	0.996548i
$324$		0			0
$325$	−0.0917806	+	0.0656979i	−0.00509107	+	0.00364426i
$326$	−2.51239	+	4.35158i	−0.139148	+	0.241012i
$327$		0			0
$328$	−11.4068	−	19.7572i	−0.629836	−	1.09091i
$329$	−9.52362	−	16.4954i	−0.525054	−	0.909420i
$330$		0			0
$331$	−4.67794	−	2.70081i	−0.257123	−	0.148450i	0.365898	−	0.930655i	$-0.380762\pi$
$331$	−4.67794	−	2.70081i	−0.257123	−	0.148450i	−0.623021	+	0.782205i	$0.714095\pi$
$332$		−	0.634273i		−	0.0348103i
$333$		0			0
$334$	12.0793			0.660949
$335$	−15.1521	+	26.2442i	−0.827848	+	1.43387i
$336$		0			0
$337$	16.4621	+	28.5132i	0.896749	+	1.55321i	0.831625	+	0.555338i	$0.187411\pi$
$337$	16.4621	+	28.5132i	0.896749	+	1.55321i	0.0651239	+	0.997877i	$0.479256\pi$
$338$	−2.28492	−	11.5489i	−0.124283	−	0.628177i
$339$		0			0
$340$	−9.65206	−	5.57262i	−0.523457	−	0.302218i
$341$	27.1969			1.47279
$342$		0			0
$343$		−	7.53586i		−	0.406898i
$344$	−2.24583	−	1.29663i	−0.121087	−	0.0699097i
$345$		0			0
$346$	−5.83622	+	3.36954i	−0.313757	+	0.181148i
$347$	6.81390	+	11.8020i	0.365789	+	0.633566i	0.988902	−	0.148566i	$-0.0474658\pi$
$347$	6.81390	+	11.8020i	0.365789	+	0.633566i	−0.623113	+	0.782132i	$0.714132\pi$
$348$		0			0
$349$	−9.76413	−	5.63732i	−0.522662	−	0.301759i	0.215361	−	0.976534i	$-0.430907\pi$
$349$	−9.76413	−	5.63732i	−0.522662	−	0.301759i	−0.738023	+	0.674776i	$0.764240\pi$
$350$	−0.0974121			−0.00520690
$351$		0			0
$352$	20.4597			1.09050
$353$	−23.0629	−	13.3154i	−1.22751	−	0.708706i	−0.261005	−	0.965337i	$-0.584054\pi$
$353$	−23.0629	−	13.3154i	−1.22751	−	0.708706i	−0.966509	+	0.256631i	$0.917387\pi$
$354$		0			0
$355$	2.97773	+	5.15757i	0.158041	+	0.273736i
$356$	5.87778	−	3.39354i	0.311522	−	0.179857i
$357$		0			0
$358$	18.1988	+	10.5071i	0.961835	+	0.555316i
$359$		−	34.9036i		−	1.84214i	−0.389396	−	0.921071i	$-0.627316\pi$
$359$		−	34.9036i		−	1.84214i	0.389396	−	0.921071i	$-0.372684\pi$
$360$		0			0
$361$	0.912132			0.0480069
$362$	−4.06596	−	2.34748i	−0.213702	−	0.123381i
$363$		0			0
$364$	−6.03969	+	13.3117i	−0.316566	+	0.697725i
$365$	6.12064	+	10.6013i	0.320369	+	0.554895i
$366$		0			0
$367$	1.35716	−	2.35068i	0.0708434	−	0.122704i	−0.828428	−	0.560096i	$-0.810764\pi$
$367$	1.35716	−	2.35068i	0.0708434	−	0.122704i	0.899271	+	0.437392i	$0.144098\pi$
$368$	−0.938467			−0.0489210
$369$		0			0
$370$		−	11.1707i		−	0.580737i
$371$	−22.6029	−	13.0498i	−1.17348	−	0.677510i
$372$		0			0
$373$	0.875481	+	1.51638i	0.0453307	+	0.0785150i	0.887800	−	0.460229i	$-0.152233\pi$
$373$	0.875481	+	1.51638i	0.0453307	+	0.0785150i	−0.842470	+	0.538744i	$0.818899\pi$
$374$	−7.04872	−	12.2087i	−0.364480	−	0.631299i
$375$		0			0
$376$	7.98146	−	13.8243i	0.411612	−	0.712933i
$377$	−6.97457	+	4.99250i	−0.359209	+	0.257127i
$378$		0			0
$379$		−	2.90941i		−	0.149446i	−0.997204	−	0.0747231i	$-0.976193\pi$
$379$		−	2.90941i		−	0.149446i	0.997204	−	0.0747231i	$-0.0238073\pi$
$380$	−5.62791	+	9.74783i	−0.288706	+	0.500053i
$381$		0			0
$382$	−12.6590	+	7.30868i	−0.647691	+	0.373945i
$383$	17.7065	−	10.2229i	0.904760	−	0.522363i	0.0260185	−	0.999661i	$-0.491717\pi$
$383$	17.7065	−	10.2229i	0.904760	−	0.522363i	0.878741	+	0.477298i	$0.158384\pi$
$384$		0			0
$385$	24.6739	+	14.2455i	1.25750	+	0.726017i
$386$	−2.96968			−0.151152
$387$		0			0
$388$		−	8.00541i		−	0.406413i
$389$	6.48161	−	11.2265i	0.328631	−	0.569205i	−0.653610	−	0.756832i	$-0.726746\pi$
$389$	6.48161	−	11.2265i	0.328631	−	0.569205i	0.982240	+	0.187627i	$0.0600795\pi$
$390$		0			0
$391$	−7.96600	−	13.7975i	−0.402858	−	0.697771i
$392$	−11.9878	+	6.92117i	−0.605476	+	0.349572i
$393$		0			0
$394$	−3.22052	+	5.57811i	−0.162248	+	0.281021i
$395$			24.5339i			1.23444i
$396$		0			0
$397$			29.1809i			1.46455i	0.681010	+	0.732274i	$0.261541\pi$
$397$			29.1809i			1.46455i	−0.681010	+	0.732274i	$0.738459\pi$
$398$	10.8581	+	6.26894i	0.544268	+	0.314233i
$399$		0			0
$400$	−0.00388271	−	0.00672506i	−0.000194136	−	0.000336253i
$401$	19.2018	−	11.0862i	0.958894	−	0.553617i	0.0630612	−	0.998010i	$-0.479914\pi$
$401$	19.2018	−	11.0862i	0.958894	−	0.553617i	0.895832	+	0.444392i	$0.146580\pi$
$402$		0			0
$403$	−26.4008	+	2.58659i	−1.31512	+	0.128847i
$404$	5.85500			0.291297
$405$		0			0
$406$	−7.40253			−0.367381
$407$	−10.1642	+	17.6050i	−0.503823	+	0.872647i
$408$		0			0
$409$	1.81749	−	1.04933i	0.0898689	−	0.0518858i	−0.454392	−	0.890802i	$-0.650143\pi$
$409$	1.81749	−	1.04933i	0.0898689	−	0.0518858i	0.544261	+	0.838916i	$0.316810\pi$
$410$	13.9365	−	8.04623i	0.688273	−	0.397375i
$411$		0			0
$412$	−1.24581	+	2.15781i	−0.0613767	+	0.106307i
$413$	17.6315			0.867591
$414$		0			0
$415$	1.20579			0.0591901
$416$	−19.8608	+	1.94584i	−0.973755	+	0.0954027i
$417$		0			0
$418$	−12.3299	+	7.11865i	−0.603074	+	0.348185i
$419$	0.195699	+	0.338961i	0.00956053	+	0.0165593i	0.870766	−	0.491697i	$-0.163623\pi$
$419$	0.195699	+	0.338961i	0.00956053	+	0.0165593i	−0.861206	+	0.508257i	$0.830290\pi$
$420$		0			0
$421$	−9.59987	−	5.54249i	−0.467869	−	0.270124i	0.247478	−	0.968893i	$-0.420398\pi$
$421$	−9.59987	−	5.54249i	−0.467869	−	0.270124i	−0.715347	+	0.698769i	$0.753731\pi$
$422$			13.0713i			0.636301i
$423$		0			0
$424$		−	21.8732i		−	1.06226i
$425$	0.0659154	−	0.114169i	0.00319737	−	0.00553800i
$426$		0			0
$427$	38.7389	−	22.3659i	1.87470	−	1.08236i
$428$	−4.76326	−	8.25021i	−0.230241	−	0.398789i
$429$		0			0
$430$	0.914627	−	1.58418i	0.0441072	−	0.0763960i
$431$			36.4573i			1.75609i	0.478580	+	0.878044i	$0.341152\pi$
$431$			36.4573i			1.75609i	−0.478580	+	0.878044i	$0.658848\pi$
$432$		0			0
$433$	8.82757			0.424226			0.212113	−	0.977245i	$-0.431966\pi$
$433$	8.82757			0.424226			0.212113	+	0.977245i	$0.431966\pi$
$434$	−19.8268	−	11.4470i	−0.951717	−	0.549474i
$435$		0			0
$436$	10.2203	−	5.90067i	0.489462	−	0.282591i
$437$	−13.9344	+	8.04504i	−0.666574	+	0.384847i
$438$		0			0
$439$	17.5672	−	30.4273i	0.838438	−	1.45222i	−0.0527626	−	0.998607i	$-0.516803\pi$
$439$	17.5672	−	30.4273i	0.838438	−	1.45222i	0.891200	−	0.453610i	$-0.149864\pi$
$440$			23.8774i			1.13831i
$441$		0			0
$442$	8.00352	+	11.1810i	0.380688	+	0.531826i
$443$	11.9526	−	20.7025i	0.567885	−	0.983606i	−0.428890	−	0.903357i	$-0.641095\pi$
$443$	11.9526	−	20.7025i	0.567885	−	0.983606i	0.996775	−	0.0802490i	$-0.0255715\pi$
$444$		0			0
$445$	6.45133	+	11.1740i	0.305822	+	0.529700i
$446$	−4.98251	−	8.62997i	−0.235929	−	0.408641i
$447$		0			0
$448$	−16.3916	−	9.46370i	−0.774431	−	0.447118i
$449$			13.9683i			0.659206i	0.944120	+	0.329603i	$0.106915\pi$
$449$			13.9683i			0.659206i	−0.944120	+	0.329603i	$0.893085\pi$
$450$		0			0
$451$	−29.2851			−1.37898
$452$	11.4654	−	19.8587i	0.539288	−	0.934075i
$453$		0			0
$454$	−3.67590	−	6.36684i	−0.172518	−	0.298811i
$455$	−25.3065	−	11.4819i	−1.18639	−	0.538278i
$456$		0			0
$457$	−15.0872	−	8.71058i	−0.705748	−	0.407464i	0.103737	−	0.994605i	$-0.466920\pi$
$457$	−15.0872	−	8.71058i	−0.705748	−	0.407464i	−0.809485	+	0.587141i	$0.800253\pi$
$458$	4.87021			0.227570
$459$		0			0
$460$			10.0126i			0.466841i
$461$	20.6691	+	11.9333i	0.962658	+	0.555791i	0.896990	−	0.442051i	$-0.145749\pi$
$461$	20.6691	+	11.9333i	0.962658	+	0.555791i	0.0656678	+	0.997842i	$0.479082\pi$
$462$		0			0
$463$	9.12555	−	5.26864i	0.424100	−	0.244854i	−0.272730	−	0.962091i	$-0.587926\pi$
$463$	9.12555	−	5.26864i	0.424100	−	0.244854i	0.696830	+	0.717236i	$0.254593\pi$
$464$	−0.295055	−	0.511049i	−0.0136976	−	0.0237249i
$465$		0			0
$466$	15.7632	+	9.10090i	0.730217	+	0.421591i
$467$	8.40923			0.389133			0.194566	−	0.980889i	$-0.437670\pi$
$467$	8.40923			0.389133			0.194566	+	0.980889i	$0.437670\pi$
$468$		0			0
$469$	−46.4227			−2.14360
$470$	9.75148	+	5.63002i	0.449802	+	0.259693i
$471$		0			0
$472$	7.38823	+	12.7968i	0.340071	+	0.589020i
$473$	−2.88290	+	1.66444i	−0.132556	+	0.0765310i
$474$		0			0
$475$	−0.115302	−	0.0665694i	−0.00529040	−	0.00305441i
$476$		−	17.0733i		−	0.782551i
$477$		0			0
$478$	−12.8239			−0.586550
$479$	−13.6025	−	7.85338i	−0.621512	−	0.358830i	0.155945	−	0.987766i	$-0.450158\pi$
$479$	−13.6025	−	7.85338i	−0.621512	−	0.358830i	−0.777457	+	0.628935i	$0.783491\pi$
$480$		0			0
$481$	8.19238	−	18.0563i	0.373540	−	0.823298i
$482$	13.7007	+	23.7303i	0.624050	+	1.08089i
$483$		0			0
$484$	1.57201	−	2.72280i	0.0714549	−	0.123764i
$485$	15.2188			0.691051
$486$		0			0
$487$			37.8948i			1.71718i	0.512666	+	0.858588i	$0.328658\pi$
$487$			37.8948i			1.71718i	−0.512666	+	0.858588i	$0.671342\pi$
$488$	32.4659	+	18.7442i	1.46966	+	0.848509i
$489$		0			0
$490$	−4.88210	−	8.45605i	−0.220551	−	0.382005i
$491$	−1.88027	−	3.25672i	−0.0848553	−	0.146974i	0.820474	−	0.571684i	$-0.193709\pi$
$491$	−1.88027	−	3.25672i	−0.0848553	−	0.146974i	−0.905330	+	0.424710i	$0.860376\pi$
$492$		0			0
$493$	5.00903	−	8.67590i	0.225595	−	0.390743i
$494$	11.2919	−	8.08293i	0.508048	−	0.363668i
$495$		0			0
$496$		−	1.82505i		−	0.0819471i
$497$	−4.56154	+	7.90082i	−0.204613	+	0.354400i
$498$		0			0
$499$	7.15464	−	4.13073i	0.320286	−	0.184917i	−0.331234	−	0.943549i	$-0.607465\pi$
$499$	7.15464	−	4.13073i	0.320286	−	0.184917i	0.651520	+	0.758632i	$0.274132\pi$
$500$	11.3882	−	6.57500i	0.509298	−	0.294043i
$501$		0			0
$502$	−13.7314	−	7.92780i	−0.612860	−	0.353835i
$503$	12.9954			0.579434			0.289717	−	0.957112i	$-0.406439\pi$
$503$	12.9954			0.579434			0.289717	+	0.957112i	$0.406439\pi$
$504$		0			0
$505$			11.1307i			0.495312i
$506$	−6.33241	+	10.9680i	−0.281510	+	0.487589i
$507$		0			0
$508$	1.04074	+	1.80262i	0.0461754	+	0.0799782i
$509$	23.2712	−	13.4356i	1.03148	−	0.595524i	0.114070	−	0.993473i	$-0.463611\pi$
$509$	23.2712	−	13.4356i	1.03148	−	0.595524i	0.917408	+	0.397949i	$0.130278\pi$
$510$		0			0
$511$	−9.37613	+	16.2399i	−0.414776	+	0.718413i
$512$		−	2.80162i		−	0.123815i
$513$		0			0
$514$		−	16.5762i		−	0.731146i
$515$	−4.10213	−	2.36837i	−0.180761	−	0.104363i
$516$		0			0
$517$	−10.2455	−	17.7458i	−0.450597	−	0.780458i
$518$	14.8197	−	8.55614i	0.651139	−	0.375935i
$519$		0			0
$520$	−2.27089	−	23.1785i	−0.0995851	−	1.01644i
$521$	−14.2080			−0.622464			−0.311232	−	0.950334i	$-0.600742\pi$
$521$	−14.2080			−0.622464			−0.311232	+	0.950334i	$0.600742\pi$
$522$		0			0
$523$	7.07846			0.309519			0.154760	−	0.987952i	$-0.450540\pi$
$523$	7.07846			0.309519			0.154760	+	0.987952i	$0.450540\pi$
$524$	−4.20620	+	7.28536i	−0.183749	+	0.318262i
$525$		0			0
$526$	6.58255	−	3.80044i	0.287013	−	0.165707i
$527$	26.8322	−	15.4916i	1.16883	−	0.674824i
$528$		0			0
$529$	4.34352	−	7.52320i	0.188849	−	0.327096i
$530$	15.4291			0.670198
$531$		0			0
$532$	−17.2427			−0.747564
$533$	28.4279	−	2.78519i	1.23135	−	0.120640i
$534$		0			0
$535$	15.6842	−	9.05527i	0.678086	−	0.391493i
$536$	−19.4527	−	33.6931i	−0.840229	−	1.45532i
$537$		0			0
$538$	16.7236	+	9.65540i	0.721007	+	0.416274i
$539$			17.7689i			0.765362i
$540$		0			0
$541$		−	7.18897i		−	0.309078i	−0.987987	−	0.154539i	$-0.950611\pi$
$541$		−	7.18897i		−	0.309078i	0.987987	−	0.154539i	$-0.0493892\pi$
$542$	8.35807	−	14.4766i	0.359010	−	0.621823i
$543$		0			0
$544$	20.1853	−	11.6540i	0.865438	−	0.499661i
$545$	11.2176	+	19.4294i	0.480508	+	0.832264i
$546$		0			0
$547$	15.8887	−	27.5201i	0.679353	−	1.17667i	−0.295823	−	0.955243i	$-0.595594\pi$
$547$	15.8887	−	27.5201i	0.679353	−	1.17667i	0.975176	−	0.221431i	$-0.0710729\pi$
$548$		−	5.33381i		−	0.227849i
$549$		0			0
$550$	−0.104796			−0.00446852
$551$	−8.76198	−	5.05873i	−0.373273	−	0.215509i
$552$		0			0
$553$	−32.5480	+	18.7916i	−1.38408	+	0.799100i
$554$	−6.76652	+	3.90665i	−0.287482	+	0.165978i
$555$		0			0
$556$	−8.32411	+	14.4178i	−0.353021	+	0.611450i
$557$		−	32.2223i		−	1.36530i	−0.730745	−	0.682650i	$-0.760827\pi$
$557$		−	32.2223i		−	1.36530i	0.730745	−	0.682650i	$-0.239173\pi$
$558$		0			0
$559$	2.64021	−	1.88990i	0.111669	−	0.0799343i
$560$	0.955943	−	1.65574i	0.0403960	−	0.0699679i
$561$		0			0
$562$	1.57339	+	2.72519i	0.0663694	+	0.114955i
$563$	−16.8257	−	29.1430i	−0.709119	−	1.22823i	−0.965184	−	0.261571i	$-0.915760\pi$
$563$	−16.8257	−	29.1430i	−0.709119	−	1.22823i	0.256065	−	0.966659i	$-0.417574\pi$
$564$		0			0
$565$	37.7527	+	21.7965i	1.58827	+	0.916987i
$566$		−	12.4824i		−	0.524672i
$567$		0			0
$568$	−7.64578			−0.320810
$569$	−5.66793	+	9.81715i	−0.237612	+	0.411556i	−0.960029	−	0.279902i	$-0.909698\pi$
$569$	−5.66793	+	9.81715i	−0.237612	+	0.411556i	0.722416	+	0.691458i	$0.243031\pi$
$570$		0			0
$571$	0.127260	+	0.220421i	0.00532568	+	0.00922435i	0.868676	−	0.495381i	$-0.164971\pi$
$571$	0.127260	+	0.220421i	0.00532568	+	0.00922435i	−0.863350	+	0.504605i	$0.831638\pi$
$572$	−6.49751	+	14.3208i	−0.271675	+	0.598782i
$573$		0			0
$574$	21.3491	+	12.3259i	0.891095	+	0.514474i
$575$	−0.118434			−0.00493903
$576$		0			0
$577$			1.91400i			0.0796807i	0.999206	+	0.0398403i	$0.0126849\pi$
$577$			1.91400i			0.0796807i	−0.999206	+	0.0398403i	$0.987315\pi$
$578$	−0.575812	−	0.332445i	−0.0239506	−	0.0138279i
$579$		0			0
$580$	−5.45246	+	3.14798i	−0.226401	+	0.130713i
$581$	0.923571	+	1.59967i	0.0383162	+	0.0663656i
$582$		0			0
$583$	−24.3162	−	14.0390i	−1.00707	−	0.581435i
$584$	−15.7157			−0.650321
$585$		0			0
$586$	25.8193			1.06659
$587$	−7.69412	−	4.44220i	−0.317570	−	0.183349i	0.332739	−	0.943019i	$-0.392027\pi$
$587$	−7.69412	−	4.44220i	−0.317570	−	0.183349i	−0.650309	+	0.759670i	$0.725361\pi$
$588$		0			0
$589$	−15.6453	−	27.0984i	−0.644653	−	1.11657i
$590$	−9.02670	+	5.21156i	−0.371623	+	0.214557i
$591$		0			0
$592$	1.18138	+	0.682072i	0.0485545	+	0.0280330i
$593$			43.1136i			1.77046i	0.465152	+	0.885231i	$0.346000\pi$
$593$			43.1136i			1.77046i	−0.465152	+	0.885231i	$0.654000\pi$
$594$		0			0
$595$	32.4574			1.33062
$596$	5.92896	+	3.42309i	0.242860	+	0.140215i
$597$		0			0
$598$	5.10392	−	11.2493i	0.208715	−	0.460016i
$599$	−5.59868	−	9.69720i	−0.228756	−	0.396217i	0.728684	−	0.684850i	$-0.240132\pi$
$599$	−5.59868	−	9.69720i	−0.228756	−	0.396217i	−0.957440	+	0.288634i	$0.906799\pi$
$600$		0			0
$601$	−2.96273	+	5.13159i	−0.120852	+	0.209322i	−0.920104	−	0.391674i	$-0.871896\pi$
$601$	−2.96273	+	5.13159i	−0.120852	+	0.209322i	0.799252	+	0.600996i	$0.205229\pi$
$602$	2.80221			0.114210
$603$		0			0
$604$			11.4991i			0.467892i
$605$	5.17622	+	2.98849i	0.210443	+	0.121499i
$606$		0			0
$607$	−2.53470	−	4.39022i	−0.102880	−	0.178194i	0.809990	−	0.586444i	$-0.199472\pi$
$607$	−2.53470	−	4.39022i	−0.102880	−	0.178194i	−0.912870	+	0.408250i	$0.866139\pi$
$608$	−11.7696	−	20.3856i	−0.477321	−	0.826745i
$609$		0			0
$610$	−13.2219	+	22.9010i	−0.535339	+	0.927235i
$611$	11.6334	+	16.2519i	0.470635	+	0.657482i
$612$		0			0
$613$		−	24.6393i		−	0.995173i	−0.867414	−	0.497587i	$-0.834220\pi$
$613$		−	24.6393i		−	0.995173i	0.867414	−	0.497587i	$-0.165780\pi$
$614$	−9.87719	+	17.1078i	−0.398611	+	0.690414i
$615$		0			0
$616$	−31.6771	+	18.2888i	−1.27630	+	0.736875i
$617$	−38.0933	+	21.9932i	−1.53358	+	0.885413i	−0.534387	+	0.845240i	$0.679457\pi$
$617$	−38.0933	+	21.9932i	−1.53358	+	0.885413i	−0.999193	+	0.0401727i	$0.987209\pi$
$618$		0			0
$619$	17.7979	+	10.2756i	0.715358	+	0.413012i	0.813042	−	0.582206i	$-0.197810\pi$
$619$	17.7979	+	10.2756i	0.715358	+	0.413012i	−0.0976839	+	0.995217i	$0.531143\pi$
$620$	−19.4717			−0.782002
$621$		0			0
$622$			6.30587i			0.252842i
$623$	−9.88272	+	17.1174i	−0.395943	+	0.685793i
$624$		0			0
$625$	12.5778	+	21.7853i	0.503111	+	0.871414i
$626$	17.6073	−	10.1656i	0.703730	−	0.406299i
$627$		0			0
$628$	0.636905	−	1.10315i	0.0254153	−	0.0440205i
$629$			23.1586i			0.923392i
$630$		0			0
$631$		−	25.1460i		−	1.00105i	−0.865723	−	0.500523i	$-0.833141\pi$
$631$		−	25.1460i		−	1.00105i	0.865723	−	0.500523i	$-0.166859\pi$
$632$	−27.2775	−	15.7487i	−1.08504	−	0.626449i
$633$		0			0
$634$	−4.62582	−	8.01216i	−0.183715	−	0.318204i
$635$	−3.42689	+	1.97852i	−0.135992	+	0.0785151i
$636$		0			0
$637$	−1.68994	−	17.2488i	−0.0669577	−	0.683422i
$638$	−7.96365			−0.315284
$639$		0			0
$640$	−13.6404			−0.539183
$641$	−16.6711	+	28.8751i	−0.658467	+	1.14050i	0.322545	+	0.946554i	$0.395462\pi$
$641$	−16.6711	+	28.8751i	−0.658467	+	1.14050i	−0.981012	+	0.193945i	$0.937872\pi$
$642$		0			0
$643$	−27.1759	+	15.6900i	−1.07171	+	0.618754i	−0.928649	−	0.370959i	$-0.879029\pi$
$643$	−27.1759	+	15.6900i	−1.07171	+	0.618754i	−0.143065	+	0.989713i	$0.545696\pi$
$644$	−13.2833	+	7.66911i	−0.523435	+	0.302205i
$645$		0			0
$646$	−8.10969	+	14.0464i	−0.319072	+	0.552648i
$647$	47.5495			1.86936			0.934681	−	0.355486i	$-0.115685\pi$
$647$	47.5495			1.86936			0.934681	+	0.355486i	$0.115685\pi$
$648$		0			0
$649$	18.9680			0.744561
$650$	0.101729	−	0.00996676i	0.00399012	−	0.000390929i
$651$		0			0
$652$	−5.66964	+	3.27337i	−0.222040	+	0.128195i
$653$	−13.8728	−	24.0284i	−0.542884	−	0.940302i	−0.998737	−	0.0502473i	$-0.983999\pi$
$653$	−13.8728	−	24.0284i	−0.542884	−	0.940302i	0.455853	−	0.890055i	$-0.349334\pi$
$654$		0			0
$655$	−13.8499	−	7.99627i	−0.541162	−	0.312440i
$656$			1.96518i			0.0767273i
$657$		0			0
$658$			17.2491i			0.672440i
$659$	7.80940	−	13.5263i	0.304211	−	0.526909i	−0.672874	−	0.739757i	$-0.734940\pi$
$659$	7.80940	−	13.5263i	0.304211	−	0.526909i	0.977085	+	0.212848i	$0.0682738\pi$
$660$		0			0
$661$	15.5161	−	8.95822i	0.603506	−	0.348434i	−0.166914	−	0.985972i	$-0.553380\pi$
$661$	15.5161	−	8.95822i	0.603506	−	0.348434i	0.770420	+	0.637537i	$0.220047\pi$
$662$	2.44585	+	4.23633i	0.0950605	+	0.164650i
$663$		0			0
$664$	−0.774017	+	1.34064i	−0.0300377	+	0.0520268i
$665$		−	32.7794i		−	1.27113i
$666$		0			0
$667$	−9.00000			−0.348481
$668$	13.6295	+	7.86901i	0.527342	+	0.304461i
$669$		0			0
$670$	23.7667	−	13.7217i	0.918187	−	0.530115i
$671$	41.6753	−	24.0613i	1.60886	−	0.928875i
$672$		0			0
$673$	2.94960	−	5.10885i	0.113699	−	0.196932i	−0.803560	−	0.595224i	$-0.797064\pi$
$673$	2.94960	−	5.10885i	0.113699	−	0.196932i	0.917259	+	0.398292i	$0.130397\pi$
$674$		−	29.8161i		−	1.14847i
$675$		0			0
$676$	4.94532	−	14.5196i	0.190205	−	0.558444i
$677$	13.7045	−	23.7369i	0.526707	−	0.912283i	−0.472809	−	0.881165i	$-0.656760\pi$
$677$	13.7045	−	23.7369i	0.526707	−	0.912283i	0.999516	−	0.0311180i	$-0.00990678\pi$
$678$		0			0
$679$	11.6568	+	20.1901i	0.447345	+	0.774825i
$680$	13.6008	+	23.5572i	0.521566	+	0.903379i
$681$		0			0
$682$	−21.3297	−	12.3147i	−0.816757	−	0.471555i
$683$			16.0989i			0.616006i	0.951385	+	0.308003i	$0.0996607\pi$
$683$			16.0989i			0.616006i	−0.951385	+	0.308003i	$0.900339\pi$
$684$		0			0
$685$	10.1399			0.387427
$686$	−3.41223	+	5.91015i	−0.130279	+	0.225651i
$687$		0			0
$688$	0.111692	+	0.193457i	0.00425823	+	0.00737547i
$689$	24.9396	+	11.3154i	0.950124	+	0.431083i
$690$		0			0
$691$	23.9736	+	13.8412i	0.912000	+	0.526543i	0.881074	−	0.472979i	$-0.156821\pi$
$691$	23.9736	+	13.8412i	0.912000	+	0.526543i	0.0309256	+	0.999522i	$0.490155\pi$
$692$	−8.78030			−0.333777
$693$		0			0
$694$		−	12.3413i		−	0.468469i
$695$	−27.4091	−	15.8247i	−1.03969	−	0.600264i
$696$		0			0
$697$	−28.8924	+	16.6810i	−1.09438	+	0.631839i
$698$	5.10514	+	8.84236i	0.193232	+	0.334688i
$699$		0			0
$700$	−0.109914	−	0.0634588i	−0.00415435	−	0.00239852i
$701$	10.0776			0.380624			0.190312	−	0.981724i	$-0.439050\pi$
$701$	10.0776			0.380624			0.190312	+	0.981724i	$0.439050\pi$
$702$		0			0
$703$	23.3883			0.882108
$704$	−17.6341	−	10.1811i	−0.664611	−	0.383713i
$705$		0			0
$706$	12.0584	+	20.8857i	0.453822	+	0.786043i
$707$	−14.7666	+	8.52553i	−0.555357	+	0.320635i
$708$		0			0
$709$	2.79484	+	1.61360i	0.104962	+	0.0606000i	0.551562	−	0.834134i	$-0.314032\pi$
$709$	2.79484	+	1.61360i	0.104962	+	0.0606000i	−0.446600	+	0.894734i	$0.647365\pi$
$710$		−	5.39324i		−	0.202405i
$711$		0			0
$712$	−16.5648			−0.620793
$713$	−24.1055	−	13.9173i	−0.902756	−	0.521207i
$714$		0			0
$715$	−27.2248	−	12.3522i	−1.01815	−	0.461946i
$716$	13.6896	+	23.7110i	0.511604	+	0.886123i
$717$		0			0
$718$	−15.8043	+	27.3738i	−0.589811	+	1.02158i
$719$	30.0712			1.12147			0.560733	−	0.827996i	$-0.310519\pi$
$719$	30.0712			1.12147			0.560733	+	0.827996i	$0.310519\pi$
$720$		0			0
$721$		−	7.25614i		−	0.270233i
$722$	−0.715357	−	0.413012i	−0.0266228	−	0.0153707i
$723$		0			0
$724$	−3.05852	−	5.29751i	−0.113669	−	0.196880i
$725$	−0.0372356	−	0.0644940i	−0.00138290	−	0.00239525i
$726$		0			0
$727$	9.68860	−	16.7811i	0.359330	−	0.622378i	−0.628519	−	0.777794i	$-0.716339\pi$
$727$	9.68860	−	16.7811i	0.359330	−	0.622378i	0.987849	+	0.155416i	$0.0496719\pi$
$728$	29.0105	−	20.7661i	1.07520	−	0.769643i
$729$		0			0
$730$		−	11.0857i		−	0.410299i
$731$	−1.89616	+	3.28424i	−0.0701320	+	0.121472i
$732$		0			0
$733$	21.1938	−	12.2362i	0.782810	−	0.451955i	−0.0546155	−	0.998507i	$-0.517393\pi$
$733$	21.1938	−	12.2362i	0.782810	−	0.451955i	0.837425	+	0.546552i	$0.184060\pi$
$734$	−2.12877	+	1.22904i	−0.0785742	+	0.0453648i
$735$		0			0
$736$	−18.1340	−	10.4697i	−0.668429	−	0.385918i
$737$	−49.9416			−1.83962
$738$		0			0
$739$			3.30687i			0.121645i	0.998149	+	0.0608226i	$0.0193724\pi$
$739$			3.30687i			0.121645i	−0.998149	+	0.0608226i	$0.980628\pi$
$740$	7.27712	−	12.6043i	0.267512	−	0.463344i
$741$		0			0
$742$	11.8178	+	20.4691i	0.433846	+	0.751444i
$743$	−15.1394	+	8.74076i	−0.555412	+	0.320667i	−0.751302	−	0.659959i	$-0.770574\pi$
$743$	−15.1394	+	8.74076i	−0.555412	+	0.320667i	0.195890	+	0.980626i	$0.437240\pi$
$744$		0			0
$745$	−6.50751	+	11.2713i	−0.238417	+	0.412950i
$746$		−	1.58566i		−	0.0580553i
$747$		0			0
$748$		−	18.3674i		−	0.671580i
$749$	24.0264	+	13.8717i	0.877906	+	0.506859i
$750$		0			0
$751$	14.2922	+	24.7548i	0.521528	+	0.903314i	0.999686	+	0.0250400i	$0.00797130\pi$
$751$	14.2922	+	24.7548i	0.521528	+	0.903314i	−0.478158	+	0.878274i	$0.658695\pi$
$752$	−1.19083	+	0.687526i	−0.0434251	+	0.0250715i
$753$		0			0
$754$	7.73054	−	0.757392i	0.281530	−	0.0275826i
$755$	−21.8606			−0.795587
$756$		0			0
$757$	11.9611			0.434733			0.217367	−	0.976090i	$-0.430253\pi$
$757$	11.9611			0.434733			0.217367	+	0.976090i	$0.430253\pi$
$758$	−1.31737	+	2.28176i	−0.0478492	+	0.0828772i
$759$		0			0
$760$	23.7910	−	13.7357i	0.862989	−	0.498247i
$761$	−1.84327	+	1.06421i	−0.0668185	+	0.0385777i	−0.533037	−	0.846092i	$-0.678949\pi$
$761$	−1.84327	+	1.06421i	−0.0668185	+	0.0385777i	0.466219	+	0.884670i	$0.345616\pi$
$762$		0			0
$763$	−17.1841	+	29.7637i	−0.622105	+	1.07752i
$764$	−19.0449			−0.689019
$765$		0			0
$766$	−18.5156			−0.668994
$767$	−18.4128	+	1.80398i	−0.664848	+	0.0651379i
$768$		0			0
$769$	−6.62584	+	3.82543i	−0.238934	+	0.137949i	−0.614687	−	0.788771i	$-0.710718\pi$
$769$	−6.62584	+	3.82543i	−0.238934	+	0.137949i	0.375753	+	0.926720i	$0.377384\pi$
$770$	−12.9007	−	22.3446i	−0.464907	−	0.805243i
$771$		0			0
$772$	−3.35080	−	1.93458i	−0.120598	−	0.0696272i
$773$		−	24.6440i		−	0.886383i	−0.896427	−	0.443191i	$-0.853846\pi$
$773$		−	24.6440i		−	0.886383i	0.896427	−	0.443191i	$-0.146154\pi$
$774$		0			0
$775$		−	0.230320i		−	0.00827333i
$776$	−9.76918	+	16.9207i	−0.350693	+	0.607418i
$777$		0			0
$778$	−10.1667	+	5.86972i	−0.364492	+	0.210440i
$779$	16.8465	+	29.1791i	0.603590	+	1.04545i
$780$		0			0
$781$	−4.90731	+	8.49972i	−0.175598	+	0.304144i
$782$			14.4280i			0.515943i
$783$		0			0
$784$	1.19238			0.0425851
$785$	2.09716	+	1.21080i	0.0748509	+	0.0432152i
$786$		0			0
$787$	−36.2586	+	20.9339i	−1.29248	+	0.746214i	−0.979093	−	0.203411i	$-0.934797\pi$
$787$	−36.2586	+	20.9339i	−1.29248	+	0.746214i	−0.313388	+	0.949625i	$0.601464\pi$
$788$	−7.26768	+	4.19599i	−0.258900	+	0.149476i
$789$		0			0
$790$	11.1089	−	19.2412i	0.395237	−	0.684571i
$791$			66.7797i			2.37441i
$792$		0			0
$793$	−38.1671	+	27.3205i	−1.35535	+	0.970181i
$794$	13.2131	−	22.8857i	0.468914	−	0.812183i
$795$		0			0
$796$	8.16775	+	14.1470i	0.289498	+	0.501426i
$797$	−20.8781	−	36.1620i	−0.739541	−	1.28092i	−0.952702	−	0.303906i	$-0.901709\pi$
$797$	−20.8781	−	36.1620i	−0.739541	−	1.28092i	0.213161	−	0.977017i	$-0.431624\pi$
$798$		0			0
$799$	−20.2163	−	11.6719i	−0.715200	−	0.412921i
$800$		−	0.173265i		−	0.00612583i
$801$		0			0
$802$	−20.0792			−0.709022
$803$	−10.0869	+	17.4709i	−0.355957	+	0.616536i
$804$		0			0
$805$	−14.5795	−	25.2524i	−0.513859	−	0.890030i
$806$	21.8766	+	9.92565i	0.770569	+	0.349616i
$807$		0			0
$808$	−12.3755	−	7.14499i	−0.435368	−	0.251360i
$809$	−45.2476			−1.59082			−0.795410	−	0.606072i	$-0.792744\pi$
$809$	−45.2476			−1.59082			−0.795410	+	0.606072i	$0.792744\pi$
$810$		0			0
$811$			52.8820i			1.85694i	0.371410	+	0.928469i	$0.378874\pi$
$811$			52.8820i			1.85694i	−0.371410	+	0.928469i	$0.621126\pi$
$812$	−8.35255	−	4.82235i	−0.293117	−	0.169231i
$813$		0			0
$814$	15.9430	−	9.20470i	0.558802	−	0.322625i
$815$	−6.22288	−	10.7784i	−0.217978	−	0.377549i
$816$		0			0
$817$	3.31683	+	1.91497i	0.116041	+	0.0669964i
$818$	−1.90053			−0.0664505
$819$		0			0
$820$	20.9667			0.732190
$821$	29.8105	+	17.2111i	1.04039	+	0.600671i	0.919945	−	0.392048i	$-0.128233\pi$
$821$	29.8105	+	17.2111i	1.04039	+	0.600671i	0.120449	+	0.992720i	$0.461567\pi$
$822$		0			0
$823$	5.99853	+	10.3898i	0.209096	+	0.362164i	0.951430	−	0.307866i	$-0.0996147\pi$
$823$	5.99853	+	10.3898i	0.209096	+	0.362164i	−0.742334	+	0.670030i	$0.766281\pi$
$824$	5.26644	−	3.04058i	0.183465	−	0.105924i
$825$		0			0
$826$	−13.8279	−	7.98353i	−0.481134	−	0.277783i
$827$		−	4.35092i		−	0.151296i	−0.997135	−	0.0756482i	$-0.975897\pi$
$827$		−	4.35092i		−	0.151296i	0.997135	−	0.0756482i	$-0.0241026\pi$
$828$		0			0
$829$	45.6204			1.58446			0.792230	−	0.610222i	$-0.208920\pi$
$829$	45.6204			1.58446			0.792230	+	0.610222i	$0.208920\pi$
$830$	−0.945668	−	0.545982i	−0.0328246	−	0.0189513i
$831$		0			0
$832$	18.0862	+	8.20594i	0.627027	+	0.284490i
$833$	10.1213	+	17.5307i	0.350683	+	0.607401i
$834$		0			0
$835$	−14.9595	+	25.9106i	−0.517695	+	0.896674i
$836$	−18.5497			−0.641554
$837$		0			0
$838$		−	0.354449i		−	0.0122442i
$839$	−21.3626	−	12.3337i	−0.737520	−	0.425808i	0.0836466	−	0.996495i	$-0.473343\pi$
$839$	−21.3626	−	12.3337i	−0.737520	−	0.425808i	−0.821167	+	0.570688i	$0.806677\pi$
$840$		0			0
$841$	11.6704	+	20.2137i	0.402427	+	0.697025i
$842$	5.01926	+	8.69361i	0.172975	+	0.299602i
$843$		0			0
$844$	−8.51525	+	14.7488i	−0.293107	+	0.507676i
$845$	27.6026	+	9.40138i	0.949559	+	0.323417i
$846$		0			0
$847$			9.15606i			0.314606i
$848$	−0.942085	+	1.63174i	−0.0323513	+	0.0560341i
$849$		0			0
$850$	−0.103391	+	0.0596928i	−0.00354628	+	0.00204744i
$851$	18.0178	−	10.4026i	0.617641	−	0.356595i
$852$		0			0
$853$	22.9668	+	13.2599i	0.786369	+	0.454010i	0.838683	−	0.544620i	$-0.183326\pi$
$853$	22.9668	+	13.2599i	0.786369	+	0.454010i	−0.0523138	+	0.998631i	$0.516660\pi$
$854$	−40.5089			−1.38619
$855$		0			0
$856$			23.2508i			0.794697i
$857$	−3.20474	+	5.55077i	−0.109472	+	0.189611i	−0.915556	−	0.402190i	$-0.868249\pi$
$857$	−3.20474	+	5.55077i	−0.109472	+	0.189611i	0.806085	+	0.591800i	$0.201583\pi$
$858$		0			0
$859$	−12.7998	−	22.1699i	−0.436723	−	0.756427i	0.560711	−	0.828011i	$-0.310528\pi$
$859$	−12.7998	−	22.1699i	−0.436723	−	0.756427i	−0.997435	+	0.0715846i	$0.977194\pi$
$860$	2.06402	−	1.19166i	0.0703824	−	0.0406353i
$861$		0			0
$862$	16.5078	−	28.5924i	0.562258	−	0.973860i
$863$		−	48.4823i		−	1.65036i	−0.564873	−	0.825178i	$-0.691075\pi$
$863$		−	48.4823i		−	1.65036i	0.564873	−	0.825178i	$-0.308925\pi$
$864$		0			0
$865$		−	16.6919i		−	0.567542i
$866$	−6.92319	−	3.99711i	−0.235260	−	0.135827i
$867$		0			0
$868$	−14.9142	−	25.8322i	−0.506222	−	0.876802i
$869$	−35.0152	+	20.2160i	−1.18781	+	0.685782i
$870$		0			0
$871$	48.4797	−	4.74975i	1.64267	−	0.160939i
$872$	−28.8029			−0.975389
$873$		0			0
$874$	14.5711			0.492876
$875$	−19.1478	+	33.1650i	−0.647315	+	1.12118i
$876$		0			0
$877$	27.0023	−	15.5898i	0.911801	−	0.526429i	0.0307911	−	0.999526i	$-0.490197\pi$
$877$	27.0023	−	15.5898i	0.911801	−	0.526429i	0.881010	+	0.473097i	$0.156864\pi$
$878$	−27.5549	+	15.9088i	−0.929932	+	0.536897i
$879$		0			0
$880$	1.02840	−	1.78125i	0.0346675	−	0.0600459i
$881$	49.6614			1.67314			0.836568	−	0.547863i	$-0.184558\pi$
$881$	49.6614			1.67314			0.836568	+	0.547863i	$0.184558\pi$
$882$		0			0
$883$	30.3523			1.02144			0.510718	−	0.859748i	$-0.329380\pi$
$883$	30.3523			1.02144			0.510718	+	0.859748i	$0.329380\pi$
$884$	1.74686	+	17.8298i	0.0587532	+	0.599681i
$885$		0			0
$886$	−18.7481	+	10.8242i	−0.629855	+	0.363647i
$887$	6.42161	+	11.1226i	0.215616	+	0.373459i	0.953463	−	0.301510i	$-0.0974906\pi$
$887$	6.42161	+	11.1226i	0.215616	+	0.373459i	−0.737847	+	0.674968i	$0.764157\pi$
$888$		0			0
$889$	−5.24962	−	3.03087i	−0.176066	−	0.101652i
$890$		−	11.6846i		−	0.391669i
$891$		0			0
$892$		−	12.9834i		−	0.434715i
$893$	−11.7877	+	20.4169i	−0.394460	+	0.683224i
$894$		0			0
$895$	−45.0762	+	26.0248i	−1.50673	+	0.869912i
$896$	−10.4478	−	18.0961i	−0.349035	−	0.604547i
$897$		0			0
$898$	6.32484	−	10.9549i	0.211063	−	0.365571i
$899$		−	17.5024i		−	0.583738i
$900$		0			0
$901$	−31.9869			−1.06564
$902$	22.9674	+	13.2602i	0.764731	+	0.441518i
$903$		0			0
$904$	−48.4680	+	27.9830i	−1.61202	+	0.930701i
$905$	10.0709	−	5.81444i	0.334768	−	0.193279i
$906$		0			0
$907$	10.2993	−	17.8389i	0.341983	−	0.592331i	−0.642818	−	0.766019i	$-0.722235\pi$
$907$	10.2993	−	17.8389i	0.341983	−	0.592331i	0.984801	+	0.173688i	$0.0555683\pi$
$908$		−	9.57860i		−	0.317877i
$909$		0			0
$910$	14.6481	+	20.4636i	0.485581	+	0.678362i
$911$	21.1949	−	36.7107i	0.702219	−	1.21628i	−0.265466	−	0.964120i	$-0.585526\pi$
$911$	21.1949	−	36.7107i	0.702219	−	1.21628i	0.967686	−	0.252159i	$-0.0811407\pi$
$912$		0			0
$913$	0.993579	+	1.72093i	0.0328827	+	0.0569545i
$914$	7.88827	+	13.6629i	0.260921	+	0.451928i
$915$		0			0
$916$	5.49524	+	3.17268i	0.181568	+	0.104828i
$917$		−	24.4988i		−	0.809021i
$918$		0			0
$919$	−42.7987			−1.41180			−0.705899	−	0.708313i	$-0.749457\pi$
$919$	−42.7987			−1.41180			−0.705899	+	0.708313i	$0.749457\pi$
$920$	12.2186	−	21.1633i	0.402836	−	0.697733i
$921$		0			0
$922$	−10.8068	−	18.7179i	−0.355903	−	0.616441i
$923$	3.95529	−	8.71764i	0.130190	−	0.286944i
$924$		0			0
$925$	0.149090	+	0.0860769i	0.00490203	+	0.00283019i
$926$	−9.54253			−0.313587
$927$		0			0
$928$		−	13.1667i		−	0.432218i
$929$	10.2242	+	5.90296i	0.335446	+	0.193670i	0.658257	−	0.752794i	$-0.271294\pi$
$929$	10.2242	+	5.90296i	0.335446	+	0.193670i	−0.322810	+	0.946464i	$0.604628\pi$
$930$		0			0
$931$	17.7046	−	10.2218i	0.580245	−	0.335004i
$932$	11.8575	+	20.5378i	0.388405	+	0.672738i
$933$		0			0
$934$	−6.59511	−	3.80769i	−0.215799	−	0.124591i
$935$	34.9177			1.14193
$936$		0			0
$937$	24.7925			0.809935			0.404967	−	0.914331i	$-0.367283\pi$
$937$	24.7925			0.809935			0.404967	+	0.914331i	$0.367283\pi$
$938$	36.4079	+	21.0201i	1.18876	+	0.686331i
$939$		0			0
$940$	7.33531	+	12.7051i	0.239251	+	0.414395i
$941$	20.6367	−	11.9146i	0.672737	−	0.388405i	−0.124376	−	0.992235i	$-0.539693\pi$
$941$	20.6367	−	11.9146i	0.672737	−	0.388405i	0.797113	+	0.603830i	$0.206360\pi$
$942$		0			0
$943$	25.9563	+	14.9859i	0.845253	+	0.488007i
$944$		−	1.27285i		−	0.0414278i
$945$		0			0
$946$	3.01462			0.0980138
$947$	42.4532	+	24.5104i	1.37954	+	0.796480i	0.992104	−	0.125415i	$-0.0400261\pi$
$947$	42.4532	+	24.5104i	1.37954	+	0.796480i	0.387440	+	0.921895i	$0.373359\pi$
$948$		0			0
$949$	8.13001	−	17.9189i	0.263911	−	0.581671i
$950$	0.0602850	+	0.104417i	0.00195590	+	0.00338773i
$951$		0			0
$952$	−20.8349	+	36.0870i	−0.675262	+	1.16959i
$953$	−7.78372			−0.252140			−0.126070	−	0.992021i	$-0.540236\pi$
$953$	−7.78372			−0.252140			−0.126070	+	0.992021i	$0.540236\pi$
$954$		0			0
$955$		−	36.2055i		−	1.17158i
$956$	−14.4697	−	8.35406i	−0.467982	−	0.270190i
$957$		0			0
$958$	7.11200	+	12.3183i	0.229778	+	0.397987i
$959$	7.76661	+	13.4522i	0.250797	+	0.434393i
$960$		0			0
$961$	11.5651	−	20.0314i	0.373069	−	0.646174i
$962$	−14.6009	+	10.4515i	−0.470752	+	0.336971i
$963$		0			0
$964$			35.7011i			1.14985i
$965$	3.67777	−	6.37008i	0.118392	−	0.205060i
$966$		0			0
$967$	32.5591	−	18.7980i	1.04703	−	0.604502i	0.125213	−	0.992130i	$-0.460039\pi$
$967$	32.5591	−	18.7980i	1.04703	−	0.604502i	0.921816	+	0.387627i	$0.126705\pi$
$968$	−6.64538	+	3.83671i	−0.213590	+	0.123317i
$969$		0			0
$970$	−11.9357	−	6.89105i	−0.383231	−	0.221258i
$971$	9.16512			0.294123			0.147061	−	0.989127i	$-0.453019\pi$
$971$	9.16512			0.294123			0.147061	+	0.989127i	$0.453019\pi$
$972$		0			0
$973$		−	48.4833i		−	1.55430i
$974$	17.1587	−	29.7197i	0.549800	−	0.952281i
$975$		0			0
$976$	−1.61463	−	2.79662i	−0.0516831	−	0.0895177i
$977$	−41.0043	+	23.6739i	−1.31184	+	0.757394i	−0.982401	−	0.186782i	$-0.940194\pi$
$977$	−41.0043	+	23.6739i	−1.31184	+	0.757394i	−0.329443	+	0.944176i	$0.606861\pi$
$978$		0			0
$979$	−10.6318	+	18.4149i	−0.339795	+	0.588542i
$980$		−	12.7217i		−	0.406380i
$981$		0			0
$982$			3.40553i			0.108675i
$983$	14.0634	+	8.11949i	0.448552	+	0.258972i	0.707219	−	0.706995i	$-0.249950\pi$
$983$	14.0634	+	8.11949i	0.448552	+	0.258972i	−0.258666	+	0.965967i	$0.583283\pi$
$984$		0			0
$985$	−7.97686	−	13.8163i	−0.254164	−	0.440225i
$986$	−7.85686	+	4.53616i	−0.250213	+	0.144461i
$987$		0			0
$988$	18.0067	−	1.76419i	0.572870	−	0.0561263i
$989$	3.40693			0.108334
$990$		0			0
$991$	−37.7634			−1.19959			−0.599797	−	0.800152i	$-0.704752\pi$
$991$	−37.7634			−1.19959			−0.599797	+	0.800152i	$0.704752\pi$
$992$	20.3605	−	35.2655i	0.646447	−	1.11968i
$993$		0			0
$994$	7.15496	−	4.13092i	0.226942	−	0.131025i
$995$	−26.8943	+	15.5274i	−0.852606	+	0.492252i
$996$		0			0
$997$	−23.8283	+	41.2718i	−0.754649	+	1.30709i	0.190899	+	0.981610i	$0.438860\pi$
$997$	−23.8283	+	41.2718i	−0.754649	+	1.30709i	−0.945549	+	0.325481i	$0.894474\pi$
$998$	−7.48156			−0.236824
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.t.c.181.5		20
3.2	odd	2		117.2.t.c.25.6	yes	20
9.2	odd	6		1053.2.b.j.649.5		10
9.4	even	3	inner	351.2.t.c.64.6		20
9.5	odd	6		117.2.t.c.103.5	yes	20
9.7	even	3		1053.2.b.i.649.6		10
13.12	even	2	inner	351.2.t.c.181.6		20
39.38	odd	2		117.2.t.c.25.5	✓	20
117.25	even	6		1053.2.b.i.649.5		10
117.38	odd	6		1053.2.b.j.649.6		10
117.77	odd	6		117.2.t.c.103.6	yes	20
117.103	even	6	inner	351.2.t.c.64.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.t.c.25.5	✓	20	39.38	odd	2
117.2.t.c.25.6	yes	20	3.2	odd	2
117.2.t.c.103.5	yes	20	9.5	odd	6
117.2.t.c.103.6	yes	20	117.77	odd	6
351.2.t.c.64.5		20	117.103	even	6	inner
351.2.t.c.64.6		20	9.4	even	3	inner
351.2.t.c.181.5		20	1.1	even	1	trivial
351.2.t.c.181.6		20	13.12	even	2	inner
1053.2.b.i.649.5		10	117.25	even	6
1053.2.b.i.649.6		10	9.7	even	3
1053.2.b.j.649.5		10	9.2	odd	6
1053.2.b.j.649.6		10	117.38	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.784270 - 0.452798i) q^{2} +(-0.589947 - 1.02182i) q^{4} +(1.94254 - 1.12153i) q^{5} +(2.97576 + 1.71806i) q^{7} +2.87970i q^{8} -2.03130 q^{10} +(3.20133 + 1.84829i) q^{11} +(-3.28340 - 1.48972i) q^{13} +(-1.55587 - 2.69484i) q^{14} +(0.124029 - 0.214825i) q^{16} +4.21120 q^{17} -4.25298i q^{19} +(-2.29200 - 1.32329i) q^{20} +(-1.67380 - 2.89911i) q^{22} +(-1.89162 - 3.27639i) q^{23} +(0.0156524 - 0.0271108i) q^{25} +(1.90053 + 2.65506i) q^{26} -4.05425i q^{28} +(1.18945 - 2.06020i) q^{29} +(6.37163 - 3.67866i) q^{31} +(4.79325 - 2.76738i) q^{32} +(-3.30272 - 1.90682i) q^{34} +7.70739 q^{35} +5.49928i q^{37} +(-1.92574 + 3.33549i) q^{38} +(3.22967 + 5.59395i) q^{40} +(-6.86085 + 3.96111i) q^{41} +(-0.450266 + 0.779883i) q^{43} -4.36157i q^{44} +3.42609i q^{46} +(-4.80060 - 2.77163i) q^{47} +(2.40343 + 4.16287i) q^{49} +(-0.0245514 + 0.0141748i) q^{50} +(0.414812 + 4.23390i) q^{52} -7.59566 q^{53} +8.29163 q^{55} +(-4.94749 + 8.56930i) q^{56} +(-1.86571 + 1.07717i) q^{58} +(4.44379 - 2.56562i) q^{59} +(6.50907 - 11.2740i) q^{61} -6.66277 q^{62} -5.50838 q^{64} +(-8.04892 + 0.788585i) q^{65} +(-11.7002 + 6.75511i) q^{67} +(-2.48439 - 4.30308i) q^{68} +(-6.04468 - 3.48989i) q^{70} +2.65506i q^{71} +5.45741i q^{73} +(2.49006 - 4.31292i) q^{74} +(-4.34578 + 2.50904i) q^{76} +(6.35092 + 11.0001i) q^{77} +(-5.46886 + 9.47234i) q^{79} -0.556410i q^{80} +7.17434 q^{82} +(0.465547 + 0.268784i) q^{83} +(8.18044 - 4.72298i) q^{85} +(0.706259 - 0.407759i) q^{86} +(-5.32252 + 9.21887i) q^{88} +5.75227i q^{89} +(-7.21120 - 10.0741i) q^{91} +(-2.23192 + 3.86579i) q^{92} +(2.50998 + 4.34740i) q^{94} +(-4.76984 - 8.26161i) q^{95} +(5.87585 + 3.39243i) q^{97} -4.35308i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 12 q^{4} - 16 q^{10} - 4 q^{13} + 18 q^{14} + 4 q^{16} + 12 q^{17} - 10 q^{22} - 24 q^{23} - 12 q^{25} + 12 q^{26} - 12 q^{29} + 12 q^{35} - 12 q^{38} - 8 q^{40} + 4 q^{43} - 10 q^{49} - 108 q^{53}+ \cdots - 24 q^{95}+O(q^{100}) \) 20 * q + 12 * q^4 - 16 * q^10 - 4 * q^13 + 18 * q^14 + 4 * q^16 + 12 * q^17 - 10 * q^22 - 24 * q^23 - 12 * q^25 + 12 * q^26 - 12 * q^29 + 12 * q^35 - 12 * q^38 - 8 * q^40 + 4 * q^43 - 10 * q^49 - 108 * q^53 + 20 * q^55 - 36 * q^56 - 2 * q^61 + 72 * q^62 + 8 * q^64 + 24 * q^65 - 24 * q^68 + 42 * q^74 + 6 * q^77 - 14 * q^79 - 4 * q^82 + 22 * q^88 - 72 * q^91 + 84 * q^92 + 20 * q^94 - 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more