LMFDB - Embedded newform 116.2.g.a.65.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [116,2,Mod(25,116)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(116, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("116.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 116 = 2^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	116.g (of order $7$, degree $6$, 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:	$0.926264663447$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			65.1
Root			$0.900969 - 0.433884i$ of defining polynomial
Character	$\chi$	$=$	116.65
Dual form			116.2.g.a.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.178448 - 0.0859360i) q^{3} +(0.346011 + 1.51597i) q^{5} +(4.22737 + 2.03579i) q^{7} +(-1.84601 - 2.31482i) q^{9} +O(q^{10})$	\(q+(-0.178448 - 0.0859360i) q^{3} +(0.346011 + 1.51597i) q^{5} +(4.22737 + 2.03579i) q^{7} +(-1.84601 - 2.31482i) q^{9} +(3.27144 - 4.10225i) q^{11} +(-2.71648 + 3.40636i) q^{13} +(0.0685317 - 0.300257i) q^{15} -4.09783 q^{17} +(-5.67241 + 2.73169i) q^{19} +(-0.579417 - 0.726566i) q^{21} +(0.791053 - 3.46583i) q^{23} +(2.32640 - 1.12033i) q^{25} +(0.262709 + 1.15100i) q^{27} +(-4.38404 - 3.12733i) q^{29} +(-0.236094 - 1.03440i) q^{31} +(-0.936313 + 0.450904i) q^{33} +(-1.62349 + 7.11297i) q^{35} +(-2.64042 - 3.31098i) q^{37} +(0.777479 - 0.374414i) q^{39} -1.60388 q^{41} +(0.367781 - 1.61135i) q^{43} +(2.87047 - 3.59945i) q^{45} +(5.21044 - 6.53368i) q^{47} +(9.36174 + 11.7393i) q^{49} +(0.731250 + 0.352152i) q^{51} +(1.79105 + 7.84711i) q^{53} +(7.35086 + 3.53999i) q^{55} +1.24698 q^{57} -5.48188 q^{59} +(1.26659 + 0.609959i) q^{61} +(-3.09126 - 13.5437i) q^{63} +(-6.10388 - 2.93947i) q^{65} +(5.27144 + 6.61017i) q^{67} +(-0.439001 + 0.550490i) q^{69} +(-2.13437 + 2.67642i) q^{71} +(0.0598025 - 0.262012i) q^{73} -0.511418 q^{75} +(22.1809 - 10.6818i) q^{77} +(8.01238 + 10.0472i) q^{79} +(-1.92447 + 8.43165i) q^{81} +(-3.82155 + 1.84036i) q^{83} +(-1.41789 - 6.21220i) q^{85} +(0.513574 + 0.934812i) q^{87} +(-3.41670 - 14.9695i) q^{89} +(-18.4182 + 8.86973i) q^{91} +(-0.0467614 + 0.204875i) q^{93} +(-6.10388 - 7.65402i) q^{95} +(-0.376510 + 0.181318i) q^{97} -15.5351 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} - 3 q^{5} + 3 q^{7} - 6 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 - 3 * q^5 + 3 * q^7 - 6 * q^9	$ 6 q + 3 q^{3} - 3 q^{5} + 3 q^{7} - 6 q^{9} + q^{11} + 3 q^{13} - 5 q^{15} + 12 q^{17} - 11 q^{19} + 5 q^{21} - q^{23} - 4 q^{25} - 33 q^{27} - 6 q^{29} + 5 q^{31} + 11 q^{33} - 5 q^{35} - 27 q^{37} + 5 q^{39} + 8 q^{41} - 9 q^{43} + 3 q^{45} - 7 q^{47} + 26 q^{49} + 20 q^{51} + 5 q^{53} + 17 q^{55} - 2 q^{57} + 24 q^{59} + 11 q^{61} + 53 q^{63} - 19 q^{65} + 13 q^{67} + 17 q^{69} - 5 q^{71} - 21 q^{73} - 16 q^{75} + 25 q^{77} + q^{79} - 58 q^{81} - 27 q^{83} - 20 q^{85} - 3 q^{87} + 9 q^{89} - 37 q^{91} - q^{93} - 19 q^{95} - 7 q^{97} + 20 q^{99}+O(q^{100}) $ 6 * q + 3 * q^3 - 3 * q^5 + 3 * q^7 - 6 * q^9 + q^11 + 3 * q^13 - 5 * q^15 + 12 * q^17 - 11 * q^19 + 5 * q^21 - q^23 - 4 * q^25 - 33 * q^27 - 6 * q^29 + 5 * q^31 + 11 * q^33 - 5 * q^35 - 27 * q^37 + 5 * q^39 + 8 * q^41 - 9 * q^43 + 3 * q^45 - 7 * q^47 + 26 * q^49 + 20 * q^51 + 5 * q^53 + 17 * q^55 - 2 * q^57 + 24 * q^59 + 11 * q^61 + 53 * q^63 - 19 * q^65 + 13 * q^67 + 17 * q^69 - 5 * q^71 - 21 * q^73 - 16 * q^75 + 25 * q^77 + q^79 - 58 * q^81 - 27 * q^83 - 20 * q^85 - 3 * q^87 + 9 * q^89 - 37 * q^91 - q^93 - 19 * q^95 - 7 * q^97 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/116\mathbb{Z}\right)^\times$.

$n$	$59$	$89$
$\chi(n)$	$1$	$e\left(\frac{3}{7}\right)$

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			0
$2$		0			0
$3$	−0.178448	−	0.0859360i	−0.103027	−	0.0496152i	0.381660	−	0.924303i	$-0.375352\pi$
$3$	−0.178448	−	0.0859360i	−0.103027	−	0.0496152i	−0.484687	+	0.874687i	$0.661067\pi$
$4$		0			0
$5$	0.346011	+	1.51597i	0.154741	+	0.677963i	0.991469	+	0.130345i	$0.0416084\pi$
$5$	0.346011	+	1.51597i	0.154741	+	0.677963i	−0.836728	+	0.547619i	$0.815534\pi$
$6$		0			0
$7$	4.22737	+	2.03579i	1.59779	+	0.769457i	0.999494	−	0.0318151i	$-0.0101288\pi$
$7$	4.22737	+	2.03579i	1.59779	+	0.769457i	0.598300	+	0.801272i	$0.295843\pi$
$8$		0			0
$9$	−1.84601	−	2.31482i	−0.615337	−	0.771608i
$10$		0			0
$11$	3.27144	−	4.10225i	0.986376	−	1.23688i	0.0148628	−	0.999890i	$-0.495269\pi$
$11$	3.27144	−	4.10225i	0.986376	−	1.23688i	0.971513	−	0.236987i	$-0.0761597\pi$
$12$		0			0
$13$	−2.71648	+	3.40636i	−0.753416	+	0.944754i	−0.999701	−	0.0244436i	$-0.992219\pi$
$13$	−2.71648	+	3.40636i	−0.753416	+	0.944754i	0.246285	+	0.969197i	$0.420790\pi$
$14$		0			0
$15$	0.0685317	−	0.300257i	0.0176948	−	0.0775260i
$16$		0			0
$17$	−4.09783			−0.993871			−0.496935	−	0.867788i	$-0.665541\pi$
$17$	−4.09783			−0.993871			−0.496935	+	0.867788i	$0.665541\pi$
$18$		0			0
$19$	−5.67241	+	2.73169i	−1.30134	+	0.626692i	−0.950785	−	0.309850i	$-0.899721\pi$
$19$	−5.67241	+	2.73169i	−1.30134	+	0.626692i	−0.350554	+	0.936542i	$0.614007\pi$
$20$		0			0
$21$	−0.579417	−	0.726566i	−0.126439	−	0.158550i
$22$		0			0
$23$	0.791053	−	3.46583i	0.164946	−	0.722675i	−0.823021	−	0.568011i	$-0.807713\pi$
$23$	0.791053	−	3.46583i	0.164946	−	0.722675i	0.987967	−	0.154664i	$-0.0494296\pi$
$24$		0			0
$25$	2.32640	−	1.12033i	0.465279	−	0.224067i
$26$		0			0
$27$	0.262709	+	1.15100i	0.0505584	+	0.221511i
$28$		0			0
$29$	−4.38404	−	3.12733i	−0.814096	−	0.580730i
$29$	−4.38404	−	3.12733i	−0.814096	−	0.580730i
$30$		0			0
$31$	−0.236094	−	1.03440i	−0.0424038	−	0.185783i	0.949291	−	0.314400i	$-0.101803\pi$
$31$	−0.236094	−	1.03440i	−0.0424038	−	0.185783i	−0.991694	+	0.128617i	$0.958946\pi$
$32$		0			0
$33$	−0.936313	+	0.450904i	−0.162991	+	0.0784924i
$34$		0			0
$35$	−1.62349	+	7.11297i	−0.274420	+	1.20231i
$36$		0			0
$37$	−2.64042	−	3.31098i	−0.434082	−	0.544321i	0.515891	−	0.856654i	$-0.327461\pi$
$37$	−2.64042	−	3.31098i	−0.434082	−	0.544321i	−0.949973	+	0.312333i	$0.898890\pi$
$38$		0			0
$39$	0.777479	−	0.374414i	0.124496	−	0.0599543i
$40$		0			0
$41$	−1.60388			−0.250483			−0.125242	−	0.992126i	$-0.539971\pi$
$41$	−1.60388			−0.250483			−0.125242	+	0.992126i	$0.539971\pi$
$42$		0			0
$43$	0.367781	−	1.61135i	0.0560861	−	0.245729i	−0.939112	−	0.343611i	$-0.888350\pi$
$43$	0.367781	−	1.61135i	0.0560861	−	0.245729i	0.995198	+	0.0978822i	$0.0312068\pi$
$44$		0			0
$45$	2.87047	−	3.59945i	0.427904	−	0.536575i
$46$		0			0
$47$	5.21044	−	6.53368i	0.760021	−	0.953036i	−0.239821	−	0.970817i	$-0.577089\pi$
$47$	5.21044	−	6.53368i	0.760021	−	0.953036i	0.999842	+	0.0177813i	$0.00566025\pi$
$48$		0			0
$49$	9.36174	+	11.7393i	1.33739	+	1.67704i
$50$		0			0
$51$	0.731250	+	0.352152i	0.102395	+	0.0493111i
$52$		0			0
$53$	1.79105	+	7.84711i	0.246020	+	1.07788i	0.935430	+	0.353512i	$0.115013\pi$
$53$	1.79105	+	7.84711i	0.246020	+	1.07788i	−0.689410	+	0.724372i	$0.742130\pi$
$54$		0			0
$55$	7.35086	+	3.53999i	0.991189	+	0.477332i
$56$		0			0
$57$	1.24698			0.165166
$58$		0			0
$59$	−5.48188			−0.713680			−0.356840	−	0.934166i	$-0.616146\pi$
$59$	−5.48188			−0.713680			−0.356840	+	0.934166i	$0.616146\pi$
$60$		0			0
$61$	1.26659	+	0.609959i	0.162171	+	0.0780973i	0.513208	−	0.858264i	$-0.328457\pi$
$61$	1.26659	+	0.609959i	0.162171	+	0.0780973i	−0.351038	+	0.936361i	$0.614171\pi$
$62$		0			0
$63$	−3.09126	−	13.5437i	−0.389462	−	1.70635i
$64$		0			0
$65$	−6.10388	−	2.93947i	−0.757093	−	0.364597i
$66$		0			0
$67$	5.27144	+	6.61017i	0.644009	+	0.807561i	0.991498	−	0.130123i	$-0.0415371\pi$
$67$	5.27144	+	6.61017i	0.644009	+	0.807561i	−0.347489	+	0.937684i	$0.612966\pi$
$68$		0			0
$69$	−0.439001	+	0.550490i	−0.0528495	+	0.0662712i
$70$		0			0
$71$	−2.13437	+	2.67642i	−0.253304	+	0.317633i	−0.892183	−	0.451674i	$-0.850827\pi$
$71$	−2.13437	+	2.67642i	−0.253304	+	0.317633i	0.638879	+	0.769307i	$0.279398\pi$
$72$		0			0
$73$	0.0598025	−	0.262012i	0.00699935	−	0.0306662i	−0.971308	−	0.237826i	$-0.923565\pi$
$73$	0.0598025	−	0.262012i	0.00699935	−	0.0306662i	0.978307	+	0.207160i	$0.0664222\pi$
$74$		0			0
$75$	−0.511418			−0.0590534
$76$		0			0
$77$	22.1809	−	10.6818i	2.52775	−	1.21730i
$78$		0			0
$79$	8.01238	+	10.0472i	0.901463	+	1.13040i	0.990926	+	0.134409i	$0.0429134\pi$
$79$	8.01238	+	10.0472i	0.901463	+	1.13040i	−0.0894632	+	0.995990i	$0.528515\pi$
$80$		0			0
$81$	−1.92447	+	8.43165i	−0.213830	+	0.936849i
$82$		0			0
$83$	−3.82155	+	1.84036i	−0.419470	+	0.202006i	−0.631699	−	0.775214i	$-0.717642\pi$
$83$	−3.82155	+	1.84036i	−0.419470	+	0.202006i	0.212229	+	0.977220i	$0.431928\pi$
$84$		0			0
$85$	−1.41789	−	6.21220i	−0.153792	−	0.673808i
$86$		0			0
$87$	0.513574	+	0.934812i	0.0550609	+	0.100222i
$88$		0			0
$89$	−3.41670	−	14.9695i	−0.362169	−	1.58677i	−0.747677	−	0.664063i	$-0.768831\pi$
$89$	−3.41670	−	14.9695i	−0.362169	−	1.58677i	0.385508	−	0.922705i	$-0.374026\pi$
$90$		0			0
$91$	−18.4182	+	8.86973i	−1.93075	+	0.929801i
$92$		0			0
$93$	−0.0467614	+	0.204875i	−0.00484893	+	0.0212446i
$94$		0			0
$95$	−6.10388	−	7.65402i	−0.626244	−	0.785286i
$96$		0			0
$97$	−0.376510	+	0.181318i	−0.0382288	+	0.0184100i	−0.452900	−	0.891561i	$-0.649611\pi$
$97$	−0.376510	+	0.181318i	−0.0382288	+	0.0184100i	0.414672	+	0.909971i	$0.363896\pi$
$98$		0			0
$99$	−15.5351			−1.56134
$100$		0			0
$101$	−2.85205	+	12.4957i	−0.283790	+	1.24336i	0.609102	+	0.793092i	$0.291530\pi$
$101$	−2.85205	+	12.4957i	−0.283790	+	1.24336i	−0.892891	+	0.450272i	$0.851327\pi$
$102$		0			0
$103$	1.05831	−	1.32708i	0.104278	−	0.130761i	−0.726954	−	0.686686i	$-0.759065\pi$
$103$	1.05831	−	1.32708i	0.104278	−	0.130761i	0.831232	+	0.555925i	$0.187636\pi$
$104$		0			0
$105$	0.900969	−	1.12978i	0.0879256	−	0.110255i
$106$		0			0
$107$	−1.88740	−	2.36672i	−0.182461	−	0.228799i	0.682186	−	0.731179i	$-0.261029\pi$
$107$	−1.88740	−	2.36672i	−0.182461	−	0.228799i	−0.864647	+	0.502379i	$0.832458\pi$
$108$		0			0
$109$	−7.52326	−	3.62301i	−0.720598	−	0.347022i	0.0373807	−	0.999301i	$-0.488099\pi$
$109$	−7.52326	−	3.62301i	−0.720598	−	0.347022i	−0.757979	+	0.652279i	$0.773813\pi$
$110$		0			0
$111$	0.186645	+	0.817744i	0.0177155	+	0.0776168i
$112$		0			0
$113$	5.51357	+	2.65520i	0.518673	+	0.249780i	0.674858	−	0.737948i	$-0.264205\pi$
$113$	5.51357	+	2.65520i	0.518673	+	0.249780i	−0.156184	+	0.987728i	$0.549919\pi$
$114$		0			0
$115$	5.52781			0.515471
$116$		0			0
$117$	12.8998			1.19258
$118$		0			0
$119$	−17.3230	−	8.34234i	−1.58800	−	0.764741i
$120$		0			0
$121$	−3.67845	−	16.1163i	−0.334404	−	1.46512i
$122$		0			0
$123$	0.286208	+	0.137831i	0.0258065	+	0.0124278i
$124$		0			0
$125$	7.35086	+	9.21768i	0.657480	+	0.824454i
$126$		0			0
$127$	6.65548	−	8.34571i	0.590578	−	0.740562i	−0.393298	−	0.919411i	$-0.628666\pi$
$127$	6.65548	−	8.34571i	0.590578	−	0.740562i	0.983877	+	0.178849i	$0.0572374\pi$
$128$		0			0
$129$	−0.204103	+	0.255937i	−0.0179703	+	0.0225340i
$130$		0			0
$131$	0.803134	−	3.51876i	0.0701702	−	0.307436i	−0.927648	−	0.373455i	$-0.878173\pi$
$131$	0.803134	−	3.51876i	0.0701702	−	0.307436i	0.997818	+	0.0660198i	$0.0210301\pi$
$132$		0			0
$133$	−29.5405			−2.56148
$134$		0			0
$135$	−1.65399	+	0.796519i	−0.142353	+	0.0685535i
$136$		0			0
$137$	13.9514	+	17.4945i	1.19195	+	1.49465i	0.825675	+	0.564146i	$0.190794\pi$
$137$	13.9514	+	17.4945i	1.19195	+	1.49465i	0.366272	+	0.930508i	$0.380634\pi$
$138$		0			0
$139$	−0.592990	+	2.59806i	−0.0502968	+	0.220365i	−0.993830	−	0.110913i	$-0.964623\pi$
$139$	−0.592990	+	2.59806i	−0.0502968	+	0.220365i	0.943533	+	0.331278i	$0.107480\pi$
$140$		0			0
$141$	−1.49127	+	0.718158i	−0.125588	+	0.0604798i
$142$		0			0
$143$	5.08695	+	22.2874i	0.425392	+	1.86376i
$144$		0			0
$145$	3.22401	−	7.72818i	0.267740	−	0.641790i
$146$		0			0
$147$	−0.661759	−	2.89936i	−0.0545810	−	0.239135i
$148$		0			0
$149$	−7.67241	+	3.69484i	−0.628548	+	0.302693i	−0.720906	−	0.693033i	$-0.756274\pi$
$149$	−7.67241	+	3.69484i	−0.628548	+	0.302693i	0.0923577	+	0.995726i	$0.470560\pi$
$150$		0			0
$151$	1.64430	−	7.20415i	0.133811	−	0.586266i	−0.862910	−	0.505357i	$-0.831361\pi$
$151$	1.64430	−	7.20415i	0.133811	−	0.586266i	0.996722	−	0.0809084i	$-0.0257821\pi$
$152$		0			0
$153$	7.56465	+	9.48577i	0.611565	+	0.766879i
$154$		0			0
$155$	1.48643	−	0.715825i	0.119393	−	0.0574965i
$156$		0			0
$157$	3.70171			0.295429			0.147714	−	0.989030i	$-0.452808\pi$
$157$	3.70171			0.295429			0.147714	+	0.989030i	$0.452808\pi$
$158$		0			0
$159$	0.354740	−	1.55422i	0.0281327	−	0.123257i
$160$		0			0
$161$	10.3998	−	13.0409i	0.819617	−	1.02777i
$162$		0			0
$163$	9.95138	−	12.4786i	0.779452	−	0.977402i	−0.220546	−	0.975377i	$-0.570784\pi$
$163$	9.95138	−	12.4786i	0.779452	−	0.977402i	0.999998	−	0.00202540i	$-0.000644706\pi$
$164$		0			0
$165$	−1.00753	−	1.26341i	−0.0784363	−	0.0983560i
$166$		0			0
$167$	4.33728	+	2.08872i	0.335629	+	0.161630i	0.594105	−	0.804387i	$-0.297506\pi$
$167$	4.33728	+	2.08872i	0.335629	+	0.161630i	−0.258477	+	0.966018i	$0.583220\pi$
$168$		0			0
$169$	−1.33124	−	5.83255i	−0.102403	−	0.448657i
$170$		0			0
$171$	16.7947	+	8.08790i	1.28432	+	0.618497i
$172$		0			0
$173$	−1.70171			−0.129379			−0.0646893	−	0.997905i	$-0.520606\pi$
$173$	−1.70171			−0.129379			−0.0646893	+	0.997905i	$0.520606\pi$
$174$		0			0
$175$	12.1153			0.915830
$176$		0			0
$177$	0.978230	+	0.471091i	0.0735282	+	0.0354093i
$178$		0			0
$179$	2.38955	+	10.4693i	0.178603	+	0.782513i	0.982276	+	0.187441i	$0.0600193\pi$
$179$	2.38955	+	10.4693i	0.178603	+	0.782513i	−0.803672	+	0.595072i	$0.797124\pi$
$180$		0			0
$181$	12.3741	+	5.95906i	0.919761	+	0.442934i	0.832986	−	0.553294i	$-0.186630\pi$
$181$	12.3741	+	5.95906i	0.919761	+	0.442934i	0.0867751	+	0.996228i	$0.472344\pi$
$182$		0			0
$183$	−0.173604	−	0.217692i	−0.0128331	−	0.0160923i
$184$		0			0
$185$	4.10574	−	5.14843i	0.301860	−	0.378520i
$186$		0			0
$187$	−13.4058	+	16.8104i	−0.980330	+	1.22930i
$188$		0			0
$189$	−1.23264	+	5.40053i	−0.0896611	+	0.392831i
$190$		0			0
$191$	−1.20775			−0.0873898			−0.0436949	−	0.999045i	$-0.513913\pi$
$191$	−1.20775			−0.0873898			−0.0436949	+	0.999045i	$0.513913\pi$
$192$		0			0
$193$	−16.6211	+	8.00430i	−1.19641	+	0.576162i	−0.922651	−	0.385636i	$-0.873982\pi$
$193$	−16.6211	+	8.00430i	−1.19641	+	0.576162i	−0.273762	+	0.961798i	$0.588268\pi$
$194$		0			0
$195$	0.836618	+	1.04909i	0.0599114	+	0.0751266i
$196$		0			0
$197$	3.48739	−	15.2792i	0.248466	−	1.08860i	−0.684607	−	0.728913i	$-0.740026\pi$
$197$	3.48739	−	15.2792i	0.248466	−	1.08860i	0.933073	−	0.359688i	$-0.117117\pi$
$198$		0			0
$199$	11.7606	−	5.66358i	0.833684	−	0.401481i	0.0321882	−	0.999482i	$-0.489752\pi$
$199$	11.7606	−	5.66358i	0.833684	−	0.401481i	0.801495	+	0.598001i	$0.204038\pi$
$200$		0			0
$201$	−0.372625	−	1.63258i	−0.0262830	−	0.115153i
$202$		0			0
$203$	−12.1664	−	22.1453i	−0.853912	−	1.55430i
$204$		0			0
$205$	−0.554958	−	2.43143i	−0.0387600	−	0.169818i
$206$		0			0
$207$	−9.48307	+	4.56681i	−0.659119	+	0.317415i
$208$		0			0
$209$	−7.35086	+	32.2062i	−0.508469	+	2.22775i
$210$		0			0
$211$	−4.86025	−	6.09456i	−0.334593	−	0.419567i	0.585864	−	0.810409i	$-0.300755\pi$
$211$	−4.86025	−	6.09456i	−0.334593	−	0.419567i	−0.920458	+	0.390842i	$0.872184\pi$
$212$		0			0
$213$	0.610876	−	0.294182i	0.0418565	−	0.0201570i
$214$		0			0
$215$	2.57002			0.175274
$216$		0			0
$217$	1.10776	−	4.85342i	0.0751997	−	0.329471i
$218$		0			0
$219$	−0.0331879	+	0.0416163i	−0.00224263	+	0.00281217i
$220$		0			0
$221$	11.1317	−	13.9587i	0.748798	−	0.938963i
$222$		0			0
$223$	8.82640	+	11.0680i	0.591059	+	0.741165i	0.983955	−	0.178418i	$-0.0570980\pi$
$223$	8.82640	+	11.0680i	0.591059	+	0.741165i	−0.392896	+	0.919583i	$0.628527\pi$
$224$		0			0
$225$	−6.88793	−	3.31705i	−0.459195	−	0.221137i
$226$		0			0
$227$	0.769282	+	3.37045i	0.0510591	+	0.223704i	0.994020	−	0.109199i	$-0.0348287\pi$
$227$	0.769282	+	3.37045i	0.0510591	+	0.223704i	−0.942961	+	0.332904i	$0.891972\pi$
$228$		0			0
$229$	−0.623490	−	0.300257i	−0.0412014	−	0.0198415i	0.413170	−	0.910654i	$-0.364422\pi$
$229$	−0.623490	−	0.300257i	−0.0412014	−	0.0198415i	−0.454371	+	0.890813i	$0.650136\pi$
$230$		0			0
$231$	−4.87608			−0.320823
$232$		0			0
$233$	−21.1836			−1.38778			−0.693891	−	0.720080i	$-0.744105\pi$
$233$	−21.1836			−1.38778			−0.693891	+	0.720080i	$0.744105\pi$
$234$		0			0
$235$	11.7078	+	5.63816i	0.763729	+	0.367793i
$236$		0			0
$237$	−0.566376	−	2.48145i	−0.0367901	−	0.161188i
$238$		0			0
$239$	8.67241	+	4.17641i	0.560971	+	0.270150i	0.692808	−	0.721122i	$-0.256373\pi$
$239$	8.67241	+	4.17641i	0.560971	+	0.270150i	−0.131837	+	0.991271i	$0.542088\pi$
$240$		0			0
$241$	−14.6012	−	18.3093i	−0.940545	−	1.17941i	−0.983605	−	0.180334i	$-0.942282\pi$
$241$	−14.6012	−	18.3093i	−0.940545	−	1.17941i	0.0430603	−	0.999072i	$-0.486289\pi$
$242$		0			0
$243$	3.27628	−	4.10833i	0.210174	−	0.263549i
$244$		0			0
$245$	−14.5571	+	18.2540i	−0.930020	+	1.16621i
$246$		0			0
$247$	6.10388	−	26.7428i	0.388380	−	1.70161i
$248$		0			0
$249$	0.840101			0.0532393
$250$		0			0
$251$	9.23705	−	4.44833i	0.583038	−	0.280776i	−0.119025	−	0.992891i	$-0.537977\pi$
$251$	9.23705	−	4.44833i	0.583038	−	0.280776i	0.702063	+	0.712115i	$0.252263\pi$
$252$		0			0
$253$	−11.6298	−	14.5833i	−0.731161	−	0.916847i
$254$		0			0
$255$	−0.280831	+	1.23040i	−0.0175863	+	0.0770508i
$256$		0			0
$257$	−24.5504	+	11.8229i	−1.53141	+	0.737489i	−0.994360	−	0.106059i	$-0.966177\pi$
$257$	−24.5504	+	11.8229i	−1.53141	+	0.737489i	−0.537053	+	0.843549i	$0.680462\pi$
$258$		0			0
$259$	−4.42154	−	19.3720i	−0.274741	−	1.20372i
$260$		0			0
$261$	0.853780	+	15.9214i	0.0528477	+	0.985508i
$262$		0			0
$263$	2.25786	+	9.89235i	0.139226	+	0.609989i	0.995606	+	0.0936424i	$0.0298510\pi$
$263$	2.25786	+	9.89235i	0.139226	+	0.609989i	−0.856380	+	0.516346i	$0.827292\pi$
$264$		0			0
$265$	−11.2763	+	5.43037i	−0.692697	+	0.333585i
$266$		0			0
$267$	−0.676719	+	2.96490i	−0.0414145	+	0.181449i
$268$		0			0
$269$	−14.5891	−	18.2942i	−0.889513	−	1.11541i	−0.992683	−	0.120751i	$-0.961470\pi$
$269$	−14.5891	−	18.2942i	−0.889513	−	1.11541i	0.103169	−	0.994664i	$-0.467102\pi$
$270$		0			0
$271$	−27.5383	+	13.2618i	−1.67283	+	0.805595i	−0.675143	+	0.737687i	$0.735918\pi$
$271$	−27.5383	+	13.2618i	−1.67283	+	0.805595i	−0.997692	+	0.0679073i	$0.978368\pi$
$272$		0			0
$273$	4.04892			0.245052
$274$		0			0
$275$	3.01477	−	13.2086i	0.181797	−	0.796507i
$276$		0			0
$277$	2.02446	−	2.53859i	0.121638	−	0.152529i	−0.717284	−	0.696781i	$-0.754615\pi$
$277$	2.02446	−	2.53859i	0.121638	−	0.152529i	0.838922	+	0.544252i	$0.183186\pi$
$278$		0			0
$279$	−1.95862	+	2.45603i	−0.117259	+	0.147038i
$280$		0			0
$281$	18.0613	+	22.6481i	1.07745	+	1.35108i	0.932309	+	0.361664i	$0.117791\pi$
$281$	18.0613	+	22.6481i	1.07745	+	1.35108i	0.145138	+	0.989411i	$0.453637\pi$
$282$		0			0
$283$	9.91939	+	4.77692i	0.589646	+	0.283959i	0.704819	−	0.709387i	$-0.251028\pi$
$283$	9.91939	+	4.77692i	0.589646	+	0.283959i	−0.115173	+	0.993345i	$0.536742\pi$
$284$		0			0
$285$	0.431468	+	1.89039i	0.0255580	+	0.111977i
$286$		0			0
$287$	−6.78017	−	3.26516i	−0.400221	−	0.192736i
$288$		0			0
$289$	−0.207751			−0.0122206
$290$		0			0
$291$	0.0827692			0.00485202
$292$		0			0
$293$	14.8409	+	7.14701i	0.867016	+	0.417533i	0.813865	−	0.581053i	$-0.197359\pi$
$293$	14.8409	+	7.14701i	0.867016	+	0.417533i	0.0531509	+	0.998586i	$0.483074\pi$
$294$		0			0
$295$	−1.89679	−	8.31037i	−0.110435	−	0.483849i
$296$		0			0
$297$	5.58115	+	2.68774i	0.323851	+	0.155958i
$298$		0			0
$299$	9.65697	+	12.1095i	0.558477	+	0.700308i
$300$		0			0
$301$	4.83513	−	6.06306i	0.278692	−	0.349469i
$302$		0			0
$303$	1.58277	−	1.98473i	0.0909277	−	0.114020i
$304$		0			0
$305$	−0.486426	+	2.13117i	−0.0278527	+	0.122031i
$306$		0			0
$307$	4.75733			0.271515			0.135758	−	0.990742i	$-0.456653\pi$
$307$	4.75733			0.271515			0.135758	+	0.990742i	$0.456653\pi$
$308$		0			0
$309$	−0.302897	+	0.145868i	−0.0172312	+	0.00829812i
$310$		0			0
$311$	−3.24967	−	4.07495i	−0.184272	−	0.231069i	0.681112	−	0.732179i	$-0.261497\pi$
$311$	−3.24967	−	4.07495i	−0.184272	−	0.231069i	−0.865384	+	0.501110i	$0.832925\pi$
$312$		0			0
$313$	5.49516	−	24.0759i	0.310605	−	1.36085i	−0.542915	−	0.839787i	$-0.682680\pi$
$313$	5.49516	−	24.0759i	0.310605	−	1.36085i	0.853520	−	0.521060i	$-0.174463\pi$
$314$		0			0
$315$	19.4623	−	9.37253i	1.09657	−	0.528082i
$316$		0			0
$317$	0.108720	+	0.476333i	0.00610631	+	0.0267535i	0.977889	−	0.209123i	$-0.0670610\pi$
$317$	0.108720	+	0.476333i	0.00610631	+	0.0267535i	−0.971783	+	0.235877i	$0.924204\pi$
$318$		0			0
$319$	−27.1712	+	7.75360i	−1.52130	+	0.434118i
$320$		0			0
$321$	0.133415	+	0.584531i	0.00744652	+	0.0326254i
$322$		0			0
$323$	23.2446	−	11.1940i	1.29336	−	0.622851i
$324$		0			0
$325$	−2.50335	+	10.9679i	−0.138861	+	0.608390i
$326$		0			0
$327$	1.03116	+	1.29304i	0.0570235	+	0.0715052i
$328$		0			0
$329$	35.3277	−	17.0129i	1.94768	−	0.937952i
$330$		0			0
$331$	−8.59179			−0.472248			−0.236124	−	0.971723i	$-0.575877\pi$
$331$	−8.59179			−0.472248			−0.236124	+	0.971723i	$0.575877\pi$
$332$		0			0
$333$	−2.79009	+	12.2242i	−0.152896	+	0.669882i
$334$		0			0
$335$	−8.19687	+	10.2785i	−0.447843	+	0.561577i
$336$		0			0
$337$	−8.82640	+	11.0680i	−0.480804	+	0.602910i	−0.961780	−	0.273824i	$-0.911711\pi$
$337$	−8.82640	+	11.0680i	−0.480804	+	0.602910i	0.480975	+	0.876734i	$0.340283\pi$
$338$		0			0
$339$	−0.755709	−	0.947629i	−0.0410445	−	0.0514681i
$340$		0			0
$341$	−5.01573	−	2.41545i	−0.271617	−	0.130804i
$342$		0			0
$343$	8.36831	+	36.6640i	0.451846	+	1.97967i
$344$		0			0
$345$	−0.986426	−	0.475038i	−0.0531074	−	0.0255752i
$346$		0			0
$347$	22.2064			1.19210			0.596052	−	0.802946i	$-0.296735\pi$
$347$	22.2064			1.19210			0.596052	+	0.802946i	$0.296735\pi$
$348$		0			0
$349$	17.9952			0.963262			0.481631	−	0.876374i	$-0.340045\pi$
$349$	17.9952			0.963262			0.481631	+	0.876374i	$0.340045\pi$
$350$		0			0
$351$	−4.63437	−	2.23180i	−0.247365	−	0.119125i
$352$		0			0
$353$	−2.67576	−	11.7233i	−0.142416	−	0.623967i	−0.994870	−	0.101164i	$-0.967743\pi$
$353$	−2.67576	−	11.7233i	−0.142416	−	0.623967i	0.852453	−	0.522803i	$-0.175114\pi$
$354$		0			0
$355$	−4.79590	−	2.30958i	−0.254540	−	0.122580i
$356$		0			0
$357$	2.37435	+	2.97735i	0.125664	+	0.157578i
$358$		0			0
$359$	−8.35421	+	10.4758i	−0.440918	+	0.552894i	−0.951785	−	0.306766i	$-0.900753\pi$
$359$	−8.35421	+	10.4758i	−0.440918	+	0.552894i	0.510867	+	0.859660i	$0.329325\pi$
$360$		0			0
$361$	12.8678	−	16.1357i	0.677252	−	0.849247i
$362$		0			0
$363$	−0.728562	+	3.19204i	−0.0382396	+	0.167539i
$364$		0			0
$365$	0.417895			0.0218736
$366$		0			0
$367$	8.45689	−	4.07262i	0.441446	−	0.212589i	−0.199939	−	0.979808i	$-0.564074\pi$
$367$	8.45689	−	4.07262i	0.441446	−	0.212589i	0.641385	+	0.767219i	$0.278360\pi$
$368$		0			0
$369$	2.96077	+	3.71269i	0.154132	+	0.193275i
$370$		0			0
$371$	−8.40366	+	36.8188i	−0.436296	+	1.91154i
$372$		0			0
$373$	13.6332	−	6.56539i	0.705899	−	0.339943i	−0.0462556	−	0.998930i	$-0.514729\pi$
$373$	13.6332	−	6.56539i	0.705899	−	0.339943i	0.752155	+	0.658986i	$0.229015\pi$
$374$		0			0
$375$	−0.519614	−	2.27658i	−0.0268328	−	0.117562i
$376$		0			0
$377$	22.5620	−	6.43830i	1.16200	−	0.331589i
$378$		0			0
$379$	−6.92812	−	30.3541i	−0.355873	−	1.55918i	−0.763361	−	0.645972i	$-0.776452\pi$
$379$	−6.92812	−	30.3541i	−0.355873	−	1.55918i	0.407487	−	0.913211i	$-0.366405\pi$
$380$		0			0
$381$	−1.90485	+	0.917329i	−0.0975886	+	0.0469962i
$382$		0			0
$383$	7.23609	−	31.7034i	0.369747	−	1.61997i	−0.357722	−	0.933828i	$-0.616447\pi$
$383$	7.23609	−	31.7034i	0.369747	−	1.61997i	0.727469	−	0.686140i	$-0.240696\pi$
$384$		0			0
$385$	23.8681	+	29.9296i	1.21643	+	1.52535i
$386$		0			0
$387$	−4.40893	+	2.12323i	−0.224118	+	0.107930i
$388$		0			0
$389$	−5.64742			−0.286335			−0.143168	−	0.989698i	$-0.545729\pi$
$389$	−5.64742			−0.286335			−0.143168	+	0.989698i	$0.545729\pi$
$390$		0			0
$391$	−3.24160	+	14.2024i	−0.163935	+	0.718246i
$392$		0			0
$393$	−0.445706	+	0.558897i	−0.0224829	+	0.0281926i
$394$		0			0
$395$	−12.4589	+	15.6230i	−0.626876	+	0.786077i
$396$		0			0
$397$	−9.67725	−	12.1349i	−0.485687	−	0.609033i	0.477247	−	0.878769i	$-0.341635\pi$
$397$	−9.67725	−	12.1349i	−0.485687	−	0.609033i	−0.962934	+	0.269737i	$0.913063\pi$
$398$		0			0
$399$	5.27144	+	2.53859i	0.263902	+	0.127089i
$400$		0			0
$401$	−3.21864	−	14.1018i	−0.160731	−	0.704209i	−0.989490	−	0.144603i	$-0.953810\pi$
$401$	−3.21864	−	14.1018i	−0.160731	−	0.704209i	0.828759	−	0.559606i	$-0.189048\pi$
$402$		0			0
$403$	4.16487	+	2.00570i	0.207467	+	0.0999109i
$404$		0			0
$405$	−13.4480			−0.668238
$406$		0			0
$407$	−22.2204			−1.10143
$408$		0			0
$409$	−20.0172	−	9.63979i	−0.989788	−	0.476657i	−0.132327	−	0.991206i	$-0.542245\pi$
$409$	−20.0172	−	9.63979i	−0.989788	−	0.476657i	−0.857461	+	0.514549i	$0.827959\pi$
$410$		0			0
$411$	−0.986189	−	4.32078i	−0.0486451	−	0.213128i
$412$		0			0
$413$	−23.1739	−	11.1600i	−1.14031	−	0.549146i
$414$		0			0
$415$	−4.11224	−	5.15658i	−0.201862	−	0.253127i
$416$		0			0
$417$	0.329085	−	0.412659i	0.0161154	−	0.0202080i
$418$		0			0
$419$	16.9852	−	21.2988i	0.829783	−	1.04051i	−0.168712	−	0.985665i	$-0.553961\pi$
$419$	16.9852	−	21.2988i	0.829783	−	1.04051i	0.998495	−	0.0548493i	$-0.0174678\pi$
$420$		0			0
$421$	−7.34840	+	32.1955i	−0.358139	+	1.56911i	0.399685	+	0.916652i	$0.369119\pi$
$421$	−7.34840	+	32.1955i	−0.358139	+	1.56911i	−0.757825	+	0.652458i	$0.773738\pi$
$422$		0			0
$423$	−24.7429			−1.20304
$424$		0			0
$425$	−9.53319	+	4.59094i	−0.462428	+	0.222693i
$426$		0			0
$427$	4.11260	+	5.15704i	0.199023	+	0.249567i
$428$		0			0
$429$	1.00753	−	4.41429i	0.0486441	−	0.213124i
$430$		0			0
$431$	−18.0661	+	8.70019i	−0.870215	+	0.419074i	−0.815041	−	0.579403i	$-0.803286\pi$
$431$	−18.0661	+	8.70019i	−0.870215	+	0.419074i	−0.0551742	+	0.998477i	$0.517571\pi$
$432$		0			0
$433$	5.85205	+	25.6395i	0.281232	+	1.23216i	0.896216	+	0.443617i	$0.146305\pi$
$433$	5.85205	+	25.6395i	0.281232	+	1.23216i	−0.614985	+	0.788539i	$0.710838\pi$
$434$		0			0
$435$	−1.23945	+	1.10202i	−0.0594269	+	0.0528377i
$436$		0			0
$437$	4.98039	+	21.8205i	0.238244	+	1.04382i
$438$		0			0
$439$	27.7582	−	13.3676i	1.32482	−	0.638002i	0.368315	−	0.929701i	$-0.379935\pi$
$439$	27.7582	−	13.3676i	1.32482	−	0.638002i	0.956510	+	0.291699i	$0.0942206\pi$
$440$		0			0
$441$	9.89243	−	43.3416i	0.471068	−	2.06388i
$442$		0			0
$443$	−13.2389	−	16.6011i	−0.629000	−	0.788741i	0.360580	−	0.932728i	$-0.382579\pi$
$443$	−13.2389	−	16.6011i	−0.629000	−	0.788741i	−0.989579	+	0.143988i	$0.954007\pi$
$444$		0			0
$445$	21.5112	−	10.3592i	1.01973	−	0.491075i
$446$		0			0
$447$	1.68664			0.0797756
$448$		0			0
$449$	−1.36885	+	5.99731i	−0.0645998	+	0.283030i	−0.996902	−	0.0786490i	$-0.974939\pi$
$449$	−1.36885	+	5.99731i	−0.0645998	+	0.283030i	0.932303	+	0.361679i	$0.117796\pi$
$450$		0			0
$451$	−5.24698	+	6.57950i	−0.247071	+	0.309817i
$452$		0			0
$453$	−0.912518	+	1.14426i	−0.0428738	+	0.0537621i
$454$		0			0
$455$	−19.8192	−	24.8524i	−0.929137	−	1.16510i
$456$		0			0
$457$	−12.0172	−	5.78719i	−0.562142	−	0.270713i	0.131159	−	0.991361i	$-0.458130\pi$
$457$	−12.0172	−	5.78719i	−0.562142	−	0.270713i	−0.693301	+	0.720648i	$0.743844\pi$
$458$		0			0
$459$	−1.07654	−	4.71662i	−0.0502485	−	0.220153i
$460$		0			0
$461$	−5.53534	−	2.66568i	−0.257807	−	0.124153i	0.300517	−	0.953777i	$-0.402841\pi$
$461$	−5.53534	−	2.66568i	−0.257807	−	0.124153i	−0.558323	+	0.829623i	$0.688555\pi$
$462$		0			0
$463$	−1.18837			−0.0552284			−0.0276142	−	0.999619i	$-0.508791\pi$
$463$	−1.18837			−0.0552284			−0.0276142	+	0.999619i	$0.508791\pi$
$464$		0			0
$465$	−0.326765			−0.0151534
$466$		0			0
$467$	−26.0933	−	12.5659i	−1.20745	−	0.581479i	−0.281662	−	0.959514i	$-0.590886\pi$
$467$	−26.0933	−	12.5659i	−1.20745	−	0.581479i	−0.925791	+	0.378035i	$0.876600\pi$
$468$		0			0
$469$	8.82736	+	38.6752i	0.407609	+	1.78585i
$470$		0			0
$471$	−0.660563	−	0.318110i	−0.0304371	−	0.0146577i
$472$		0			0
$473$	−5.40701	−	6.78018i	−0.248615	−	0.311753i
$474$		0			0
$475$	−10.1359	+	12.7100i	−0.465065	+	0.583174i
$476$		0			0
$477$	14.8584	−	18.6318i	0.680319	−	0.853093i
$478$		0			0
$479$	−6.24147	+	27.3457i	−0.285180	+	1.24946i	0.605875	+	0.795560i	$0.292823\pi$
$479$	−6.24147	+	27.3457i	−0.285180	+	1.24946i	−0.891055	+	0.453896i	$0.850034\pi$
$480$		0			0
$481$	18.4510			0.841294
$482$		0			0
$483$	−2.97650	+	1.43341i	−0.135435	+	0.0652223i
$484$		0			0
$485$	−0.405149	−	0.508041i	−0.0183969	−	0.0230690i
$486$		0			0
$487$	−7.39924	+	32.4182i	−0.335292	+	1.46901i	0.473438	+	0.880827i	$0.343013\pi$
$487$	−7.39924	+	32.4182i	−0.335292	+	1.46901i	−0.808729	+	0.588181i	$0.799844\pi$
$488$		0			0
$489$	−2.84817	+	1.37160i	−0.128799	+	0.0620261i
$490$		0			0
$491$	−4.55137	−	19.9408i	−0.205400	−	0.899918i	−0.967582	−	0.252555i	$-0.918729\pi$
$491$	−4.55137	−	19.9408i	−0.205400	−	0.899918i	0.762182	−	0.647363i	$-0.224128\pi$
$492$		0			0
$493$	17.9651	+	12.8153i	0.809107	+	0.577170i
$494$		0			0
$495$	−5.37531	−	23.5508i	−0.241602	−	1.05853i
$496$		0			0
$497$	−14.4714	+	6.96907i	−0.649132	+	0.312605i
$498$		0			0
$499$	−2.16541	+	9.48727i	−0.0969369	+	0.424708i	−0.999988	−	0.00482400i	$-0.998464\pi$
$499$	−2.16541	+	9.48727i	−0.0969369	+	0.424708i	0.903051	+	0.429532i	$0.141322\pi$
$500$		0			0
$501$	−0.594482	−	0.745457i	−0.0265595	−	0.0333046i
$502$		0			0
$503$	−28.4937	+	13.7219i	−1.27047	+	0.611827i	−0.942924	−	0.333007i	$-0.891937\pi$
$503$	−28.4937	+	13.7219i	−1.27047	+	0.611827i	−0.327548	+	0.944835i	$0.606222\pi$
$504$		0			0
$505$	−19.9299			−0.886869
$506$		0			0
$507$	−0.263669	+	1.15521i	−0.0117099	+	0.0513046i
$508$		0			0
$509$	18.5553	−	23.2676i	0.822447	−	1.03132i	−0.176447	−	0.984310i	$-0.556461\pi$
$509$	18.5553	−	23.2676i	0.822447	−	1.03132i	0.998895	−	0.0470061i	$-0.0149680\pi$
$510$		0			0
$511$	0.786208	−	0.985874i	0.0347798	−	0.0436125i
$512$		0			0
$513$	−4.63437	−	5.81132i	−0.204613	−	0.256576i
$514$		0			0
$515$	2.37800	+	1.14519i	0.104787	+	0.0504629i
$516$		0			0
$517$	−9.75720	−	42.7491i	−0.429121	−	1.88010i
$518$		0			0
$519$	0.303667	+	0.146238i	0.0133295	+	0.00641914i
$520$		0			0
$521$	12.1086			0.530487			0.265243	−	0.964181i	$-0.414548\pi$
$521$	12.1086			0.530487			0.265243	+	0.964181i	$0.414548\pi$
$522$		0			0
$523$	7.70171			0.336772			0.168386	−	0.985721i	$-0.446144\pi$
$523$	7.70171			0.336772			0.168386	+	0.985721i	$0.446144\pi$
$524$		0			0
$525$	−2.16195	−	1.04114i	−0.0943552	−	0.0454391i
$526$		0			0
$527$	0.967476	+	4.23879i	0.0421439	+	0.184645i
$528$		0			0
$529$	9.33609	+	4.49602i	0.405917	+	0.195479i
$530$		0			0
$531$	10.1196	+	12.6896i	0.439153	+	0.550681i
$532$		0			0
$533$	4.35690	−	5.46337i	0.188718	−	0.236645i
$534$		0			0
$535$	2.93482	−	3.68015i	0.126883	−	0.159107i
$536$		0			0
$537$	0.473280	−	2.07357i	0.0204235	−	0.0894814i
$538$		0			0
$539$	78.7837			3.39346
$540$		0			0
$541$	21.5601	−	10.3828i	0.926941	−	0.446391i	0.0913968	−	0.995815i	$-0.470867\pi$
$541$	21.5601	−	10.3828i	0.926941	−	0.446391i	0.835544	+	0.549423i	$0.185153\pi$
$542$		0			0
$543$	−1.69604	−	2.12676i	−0.0727840	−	0.0912682i
$544$		0			0
$545$	2.88926	−	12.6587i	0.123762	−	0.542237i
$546$		0			0
$547$	−16.5015	+	7.94670i	−0.705553	+	0.339776i	−0.752017	−	0.659144i	$-0.770919\pi$
$547$	−16.5015	+	7.94670i	−0.705553	+	0.339776i	0.0464642	+	0.998920i	$0.485205\pi$
$548$		0			0
$549$	−0.926197	−	4.05793i	−0.0395291	−	0.173188i
$550$		0			0
$551$	33.4110	+	5.76363i	1.42335	+	0.245539i
$552$		0			0
$553$	13.4172	+	58.7847i	0.570559	+	2.49978i
$554$		0			0
$555$	−1.17510	+	0.565896i	−0.0498800	+	0.0240210i
$556$		0			0
$557$	−2.55807	+	11.2077i	−0.108389	+	0.474883i	0.891377	+	0.453262i	$0.149740\pi$
$557$	−2.55807	+	11.2077i	−0.108389	+	0.474883i	−0.999766	+	0.0216212i	$0.993117\pi$
$558$		0			0
$559$	4.48978	+	5.63000i	0.189897	+	0.238124i
$560$		0			0
$561$	3.83685	−	1.84773i	0.161992	−	0.0780113i
$562$		0			0
$563$	46.7284			1.96937			0.984683	−	0.174353i	$-0.0557833\pi$
$563$	46.7284			1.96937			0.984683	+	0.174353i	$0.0557833\pi$
$564$		0			0
$565$	−2.11745	+	9.27715i	−0.0890817	+	0.390293i
$566$		0			0
$567$	−25.3005	+	31.7258i	−1.06252	+	1.33236i
$568$		0			0
$569$	−5.45444	+	6.83965i	−0.228662	+	0.286733i	−0.882905	−	0.469551i	$-0.844416\pi$
$569$	−5.45444	+	6.83965i	−0.228662	+	0.286733i	0.654243	+	0.756284i	$0.272987\pi$
$570$		0			0
$571$	−27.0831	−	33.9611i	−1.13339	−	1.42123i	−0.892715	−	0.450622i	$-0.851202\pi$
$571$	−27.0831	−	33.9611i	−1.13339	−	1.42123i	−0.240676	−	0.970606i	$-0.577369\pi$
$572$		0			0
$573$	0.215521	+	0.103789i	0.00900350	+	0.00433586i
$574$		0			0
$575$	−2.04258	−	8.94913i	−0.0851815	−	0.373205i
$576$		0			0
$577$	−28.7189	−	13.8303i	−1.19558	−	0.575763i	−0.273171	−	0.961966i	$-0.588072\pi$
$577$	−28.7189	−	13.8303i	−1.19558	−	0.575763i	−0.922414	+	0.386202i	$0.873787\pi$
$578$		0			0
$579$	3.65386			0.151849
$580$		0			0
$581$	−19.9017			−0.825661
$582$		0			0
$583$	38.0502	+	18.3240i	1.57588	+	0.758902i
$584$		0			0
$585$	4.46346	+	19.5557i	0.184541	+	0.808528i
$586$		0			0
$587$	−31.1935	−	15.0220i	−1.28749	−	0.620024i	−0.340189	−	0.940357i	$-0.610491\pi$
$587$	−31.1935	−	15.0220i	−1.28749	−	0.620024i	−0.947305	+	0.320333i	$0.896205\pi$
$588$		0			0
$589$	4.16487	+	5.22259i	0.171611	+	0.215193i
$590$		0			0
$591$	−1.93535	+	2.42686i	−0.0796098	+	0.0998275i
$592$		0			0
$593$	−12.3542	+	15.4917i	−0.507326	+	0.636167i	−0.967864	−	0.251473i	$-0.919085\pi$
$593$	−12.3542	+	15.4917i	−0.507326	+	0.636167i	0.460538	+	0.887640i	$0.347657\pi$
$594$		0			0
$595$	6.65279	−	29.1478i	0.272738	−	1.19494i
$596$		0			0
$597$	−2.58535			−0.105811
$598$		0			0
$599$	−22.6211	+	10.8937i	−0.924273	+	0.445106i	−0.834595	−	0.550864i	$-0.814298\pi$
$599$	−22.6211	+	10.8937i	−0.924273	+	0.445106i	−0.0896782	+	0.995971i	$0.528584\pi$
$600$		0			0
$601$	−13.1035	−	16.4313i	−0.534503	−	0.670246i	0.439115	−	0.898431i	$-0.355292\pi$
$601$	−13.1035	−	16.4313i	−0.534503	−	0.670246i	−0.973618	+	0.228185i	$0.926721\pi$
$602$		0			0
$603$	5.57026	−	24.4049i	0.226839	−	0.993845i
$604$		0			0
$605$	23.1591	−	11.1528i	0.941552	−	0.453428i
$606$		0			0
$607$	6.80505	+	29.8149i	0.276209	+	1.21015i	0.902545	+	0.430596i	$0.141697\pi$
$607$	6.80505	+	29.8149i	0.276209	+	1.21015i	−0.626336	+	0.779553i	$0.715446\pi$
$608$		0			0
$609$	0.267980	+	4.99732i	0.0108591	+	0.202502i
$610$		0			0
$611$	8.10202	+	35.4972i	0.327772	+	1.43606i
$612$		0			0
$613$	33.5426	−	16.1533i	1.35477	−	0.652425i	0.391309	−	0.920259i	$-0.372022\pi$
$613$	33.5426	−	16.1533i	1.35477	−	0.652425i	0.963465	+	0.267834i	$0.0863079\pi$
$614$		0			0
$615$	−0.109916	+	0.481575i	−0.00443225	+	0.0194190i
$616$		0			0
$617$	6.40312	+	8.02926i	0.257780	+	0.323246i	0.893833	−	0.448399i	$-0.148006\pi$
$617$	6.40312	+	8.02926i	0.257780	+	0.323246i	−0.636053	+	0.771645i	$0.719434\pi$
$618$		0			0
$619$	10.9780	−	5.28672i	0.441243	−	0.212491i	−0.200053	−	0.979785i	$-0.564111\pi$
$619$	10.9780	−	5.28672i	0.441243	−	0.212491i	0.641296	+	0.767294i	$0.278397\pi$
$620$		0			0
$621$	4.19700			0.168420
$622$		0			0
$623$	16.0312	−	70.2374i	0.642277	−	2.81400i
$624$		0			0
$625$	−3.38069	+	4.23925i	−0.135228	+	0.169570i
$626$		0			0
$627$	4.07942	−	5.11543i	0.162916	−	0.204290i
$628$		0			0
$629$	10.8200	+	13.5678i	0.431421	+	0.540985i
$630$		0			0
$631$	30.8952	+	14.8784i	1.22992	+	0.592298i	0.932057	−	0.362311i	$-0.118012\pi$
$631$	30.8952	+	14.8784i	1.22992	+	0.592298i	0.297862	+	0.954609i	$0.403726\pi$
$632$		0			0
$633$	0.343559	+	1.50523i	0.0136553	+	0.0598276i
$634$		0			0
$635$	14.9547	+	7.20182i	0.593460	+	0.285795i
$636$		0			0
$637$	−65.4191			−2.59200
$638$		0			0
$639$	10.1355			0.400955
$640$		0			0
$641$	33.0051	+	15.8944i	1.30362	+	0.627793i	0.951352	−	0.308105i	$-0.0996948\pi$
$641$	33.0051	+	15.8944i	1.30362	+	0.627793i	0.352272	+	0.935898i	$0.385409\pi$
$642$		0			0
$643$	2.27963	+	9.98773i	0.0899000	+	0.393878i	0.999780	−	0.0209947i	$-0.00668332\pi$
$643$	2.27963	+	9.98773i	0.0899000	+	0.393878i	−0.909880	+	0.414872i	$0.863826\pi$
$644$		0			0
$645$	−0.458615	−	0.220858i	−0.0180580	−	0.00869626i
$646$		0			0
$647$	−12.9393	−	16.2254i	−0.508696	−	0.637885i	0.459470	−	0.888193i	$-0.348039\pi$
$647$	−12.9393	−	16.2254i	−0.508696	−	0.637885i	−0.968166	+	0.250308i	$0.919468\pi$
$648$		0			0
$649$	−17.9336	+	22.4881i	−0.703956	+	0.882733i
$650$		0			0
$651$	−0.614761	+	0.770885i	−0.0240944	+	0.0302134i
$652$		0			0
$653$	1.16003	−	5.08242i	0.0453955	−	0.198891i	−0.947145	−	0.320806i	$-0.896046\pi$
$653$	1.16003	−	5.08242i	0.0453955	−	0.198891i	0.992541	+	0.121915i	$0.0389035\pi$
$654$		0			0
$655$	5.61224			0.219288
$656$		0			0
$657$	−0.716907	+	0.345244i	−0.0279692	+	0.0134693i
$658$		0			0
$659$	−23.0643	−	28.9217i	−0.898457	−	1.12663i	−0.991388	−	0.130957i	$-0.958195\pi$
$659$	−23.0643	−	28.9217i	−0.898457	−	1.12663i	0.0929314	−	0.995673i	$-0.470376\pi$
$660$		0			0
$661$	5.48307	−	24.0229i	0.213267	−	0.934383i	−0.749063	−	0.662499i	$-0.769496\pi$
$661$	5.48307	−	24.0229i	0.213267	−	0.934383i	0.962330	−	0.271884i	$-0.0876469\pi$
$662$		0			0
$663$	−3.18598	+	1.53429i	−0.123733	+	0.0595868i
$664$		0			0
$665$	−10.2213	−	44.7825i	−0.396366	−	1.73659i
$666$		0			0
$667$	−14.3068	+	12.7205i	−0.553961	+	0.492538i
$668$		0			0
$669$	−0.623917	−	2.73356i	−0.0241220	−	0.105685i
$670$		0			0
$671$	6.64579	−	3.20045i	0.256558	−	0.123552i
$672$		0			0
$673$	−1.45055	+	6.35528i	−0.0559146	+	0.244978i	−0.995160	−	0.0982687i	$-0.968670\pi$
$673$	−1.45055	+	6.35528i	−0.0559146	+	0.244978i	0.939245	+	0.343247i	$0.111527\pi$
$674$		0			0
$675$	1.90067	+	2.38337i	0.0731570	+	0.0917359i
$676$		0			0
$677$	−37.4327	+	18.0266i	−1.43866	+	0.692820i	−0.980585	−	0.196095i	$-0.937174\pi$
$677$	−37.4327	+	18.0266i	−1.43866	+	0.692820i	−0.458072	+	0.888915i	$0.651460\pi$
$678$		0			0
$679$	−1.96077			−0.0752475
$680$		0			0
$681$	0.152366	−	0.667558i	0.00583867	−	0.0255809i
$682$		0			0
$683$	−16.8240	+	21.0966i	−0.643753	+	0.807240i	−0.991467	−	0.130360i	$-0.958387\pi$
$683$	−16.8240	+	21.0966i	−0.643753	+	0.807240i	0.347714	+	0.937601i	$0.386958\pi$
$684$		0			0
$685$	−21.6938	+	27.2032i	−0.828878	+	1.03938i
$686$		0			0
$687$	0.0854576	+	0.107160i	0.00326041	+	0.00408843i
$688$		0			0
$689$	−31.5954	−	15.2156i	−1.20369	−	0.579667i
$690$		0			0
$691$	−0.0544257	−	0.238454i	−0.00207045	−	0.00907123i	0.973882	−	0.227054i	$-0.0729094\pi$
$691$	−0.0544257	−	0.238454i	−0.00207045	−	0.00907123i	−0.975953	+	0.217983i	$0.930052\pi$
$692$		0			0
$693$	−65.6726	−	31.6262i	−2.49469	−	1.20138i
$694$		0			0
$695$	−4.14377			−0.157182
$696$		0			0
$697$	6.57242			0.248948
$698$		0			0
$699$	3.78017	+	1.82043i	0.142979	+	0.0688551i
$700$		0			0
$701$	3.00551	+	13.1680i	0.113516	+	0.497348i	0.999438	+	0.0335135i	$0.0106697\pi$
$701$	3.00551	+	13.1680i	0.113516	+	0.497348i	−0.885922	+	0.463835i	$0.846473\pi$
$702$		0			0
$703$	24.0221	+	11.5684i	0.906009	+	0.436311i
$704$		0			0
$705$	−1.60470	−	2.01223i	−0.0604366	−	0.0757851i
$706$		0			0
$707$	−37.4952	+	47.0175i	−1.41015	+	1.76828i
$708$		0			0
$709$	8.99061	−	11.2739i	0.337649	−	0.423399i	−0.583800	−	0.811898i	$-0.698435\pi$
$709$	8.99061	−	11.2739i	0.337649	−	0.423399i	0.921449	+	0.388499i	$0.127006\pi$
$710$		0			0
$711$	8.46658	−	37.0945i	0.317521	−	1.39115i
$712$		0			0
$713$	−3.77181			−0.141255
$714$		0			0
$715$	−32.0269	+	15.4233i	−1.19774	+	0.576800i
$716$		0			0
$717$	−1.18867	−	1.49054i	−0.0443917	−	0.0556654i
$718$		0			0
$719$	−1.11303	+	4.87651i	−0.0415091	+	0.181863i	−0.991433	−	0.130619i	$-0.958303\pi$
$719$	−1.11303	+	4.87651i	−0.0415091	+	0.181863i	0.949924	+	0.312483i	$0.101161\pi$
$720$		0			0
$721$	7.17552	−	3.45555i	0.267230	−	0.128691i
$722$		0			0
$723$	1.03212	+	4.52203i	0.0383851	+	0.168176i
$724$		0			0
$725$	−13.7027	−	2.36381i	−0.508904	−	0.0877897i
$726$		0			0
$727$	−4.48307	−	19.6416i	−0.166268	−	0.728468i	−0.987467	−	0.157826i	$-0.949552\pi$
$727$	−4.48307	−	19.6416i	−0.166268	−	0.728468i	0.821199	−	0.570642i	$-0.193306\pi$
$728$		0			0
$729$	22.4383	−	10.8057i	0.831050	−	0.400212i
$730$		0			0
$731$	−1.50711	+	6.60306i	−0.0557423	+	0.244223i
$732$		0			0
$733$	28.5891	+	35.8496i	1.05596	+	1.32414i	0.943826	+	0.330443i	$0.107198\pi$
$733$	28.5891	+	35.8496i	1.05596	+	1.32414i	0.112137	+	0.993693i	$0.464231\pi$
$734$		0			0
$735$	4.16637	−	2.00642i	0.153679	−	0.0740078i
$736$		0			0
$737$	44.3618			1.63409
$738$		0			0
$739$	7.52960	−	32.9893i	0.276981	−	1.21353i	−0.624608	−	0.780938i	$-0.714741\pi$
$739$	7.52960	−	32.9893i	0.276981	−	1.21353i	0.901589	−	0.432594i	$-0.142402\pi$
$740$		0			0
$741$	−3.38740	+	4.24766i	−0.124439	+	0.156042i
$742$		0			0
$743$	6.81431	−	8.54488i	0.249993	−	0.313481i	−0.640962	−	0.767572i	$-0.721465\pi$
$743$	6.81431	−	8.54488i	0.249993	−	0.313481i	0.890955	+	0.454091i	$0.150036\pi$
$744$		0			0
$745$	−8.25600	−	10.3527i	−0.302477	−	0.379294i
$746$		0			0
$747$	11.3147	+	5.44889i	0.413985	+	0.199365i
$748$		0			0
$749$	−3.16056	−	13.8473i	−0.115484	−	0.505970i
$750$		0			0
$751$	−20.0705	−	9.66542i	−0.732381	−	0.352696i	0.0302391	−	0.999543i	$-0.490373\pi$
$751$	−20.0705	−	9.66542i	−0.732381	−	0.352696i	−0.762620	+	0.646847i	$0.776087\pi$
$752$		0			0
$753$	−2.03060			−0.0739994
$754$		0			0
$755$	11.4902			0.418173
$756$		0			0
$757$	12.8192	+	6.17338i	0.465920	+	0.224375i	0.652089	−	0.758142i	$-0.273893\pi$
$757$	12.8192	+	6.17338i	0.465920	+	0.224375i	−0.186169	+	0.982518i	$0.559607\pi$
$758$		0			0
$759$	0.822085	+	3.60179i	0.0298398	+	0.130737i
$760$		0			0
$761$	−37.3814	−	18.0019i	−1.35508	−	0.652570i	−0.391542	−	0.920160i	$-0.628058\pi$
$761$	−37.3814	−	18.0019i	−1.35508	−	0.652570i	−0.963533	+	0.267590i	$0.913773\pi$
$762$		0			0
$763$	−24.4279	−	30.6316i	−0.884349	−	1.10894i
$764$		0			0
$765$	−11.7627	+	14.7500i	−0.425282	+	0.533286i
$766$		0			0
$767$	14.8914	−	18.6732i	0.537698	−	0.674252i
$768$		0			0
$769$	6.11303	−	26.7829i	0.220442	−	0.965818i	−0.736705	−	0.676214i	$-0.763619\pi$
$769$	6.11303	−	26.7829i	0.220442	−	0.965818i	0.957147	−	0.289603i	$-0.0935234\pi$
$770$		0			0
$771$	5.39698			0.194367
$772$		0			0
$773$	−26.9127	+	12.9605i	−0.967982	+	0.466156i	−0.849955	−	0.526855i	$-0.823371\pi$
$773$	−26.9127	+	12.9605i	−0.967982	+	0.466156i	−0.118027	+	0.993010i	$0.537657\pi$
$774$		0			0
$775$	−1.70812	−	2.14191i	−0.0613575	−	0.0769398i
$776$		0			0
$777$	−0.875741	+	3.83687i	−0.0314170	+	0.137647i
$778$		0			0
$779$	9.09783	−	4.38129i	0.325964	−	0.156976i
$780$		0			0
$781$	3.99688	+	17.5115i	0.143020	+	0.626611i
$782$		0			0
$783$	2.44784	−	5.86763i	0.0874785	−	0.209692i
$784$		0			0
$785$	1.28083	+	5.61169i	0.0457148	+	0.200290i
$786$		0			0
$787$	24.0976	−	11.6048i	0.858987	−	0.413666i	0.0480812	−	0.998843i	$-0.484689\pi$
$787$	24.0976	−	11.6048i	0.858987	−	0.413666i	0.810905	+	0.585177i	$0.198975\pi$
$788$		0			0
$789$	0.447198	−	1.95930i	0.0159207	−	0.0697530i
$790$		0			0
$791$	17.9025	+	22.4490i	0.636538	+	0.798194i
$792$		0			0
$793$	−5.51842	+	2.65753i	−0.195965	+	0.0943717i
$794$		0			0
$795$	2.47889			0.0879173
$796$		0			0
$797$	−5.57660	+	24.4327i	−0.197533	+	0.865449i	0.774866	+	0.632126i	$0.217817\pi$
$797$	−5.57660	+	24.4327i	−0.197533	+	0.865449i	−0.972399	+	0.233324i	$0.925040\pi$
$798$		0			0
$799$	−21.3515	+	26.7740i	−0.755362	+	0.947195i
$800$		0			0
$801$	−28.3446	+	35.5430i	−1.00151	+	1.25585i
$802$		0			0
$803$	−0.879199	−	1.10248i	−0.0310262	−	0.0389057i
$804$		0			0
$805$	23.3681	+	11.2535i	0.823616	+	0.396633i
$806$		0			0
$807$	1.03127	+	4.51828i	0.0363024	+	0.159051i
$808$		0			0
$809$	−0.839010	−	0.404046i	−0.0294980	−	0.0142055i	0.419077	−	0.907951i	$-0.362354\pi$
$809$	−0.839010	−	0.404046i	−0.0294980	−	0.0142055i	−0.448575	+	0.893745i	$0.648068\pi$
$810$		0			0
$811$	−1.65220			−0.0580167			−0.0290083	−	0.999579i	$-0.509235\pi$
$811$	−1.65220			−0.0580167			−0.0290083	+	0.999579i	$0.509235\pi$
$812$		0			0
$813$	6.05382			0.212317
$814$		0			0
$815$	22.3605	+	10.7683i	0.783256	+	0.377196i
$816$		0			0
$817$	2.31551	+	10.1449i	0.0810095	+	0.354926i
$818$		0			0
$819$	54.5320	+	26.2613i	1.90550	+	0.917642i
$820$		0			0
$821$	−11.3324	−	14.2104i	−0.395505	−	0.495947i	0.543712	−	0.839272i	$-0.317018\pi$
$821$	−11.3324	−	14.2104i	−0.395505	−	0.495947i	−0.939217	+	0.343325i	$0.888447\pi$
$822$		0			0
$823$	35.3602	−	44.3403i	1.23258	−	1.54560i	0.497810	−	0.867286i	$-0.334138\pi$
$823$	35.3602	−	44.3403i	1.23258	−	1.54560i	0.734769	−	0.678318i	$-0.237291\pi$
$824$		0			0
$825$	−1.67307	+	2.09796i	−0.0582489	+	0.0730418i
$826$		0			0
$827$	−10.5025	+	46.0142i	−0.365206	+	1.60007i	0.374557	+	0.927204i	$0.377795\pi$
$827$	−10.5025	+	46.0142i	−0.365206	+	1.60007i	−0.739763	+	0.672868i	$0.765062\pi$
$828$		0			0
$829$	−2.58104			−0.0896432			−0.0448216	−	0.998995i	$-0.514272\pi$
$829$	−2.58104			−0.0896432			−0.0448216	+	0.998995i	$0.514272\pi$
$830$		0			0
$831$	−0.579417	+	0.279032i	−0.0200997	+	0.00967953i
$832$		0			0
$833$	−38.3629	−	48.1055i	−1.32919	−	1.66676i
$834$		0			0
$835$	−1.66570	+	7.29792i	−0.0576440	+	0.252555i
$836$		0			0
$837$	1.12857	−	0.543491i	0.0390091	−	0.0187858i
$838$		0			0
$839$	−6.72228	−	29.4523i	−0.232079	−	1.01680i	−0.947912	−	0.318533i	$-0.896810\pi$
$839$	−6.72228	−	29.4523i	−0.232079	−	1.01680i	0.715833	−	0.698272i	$-0.246047\pi$
$840$		0			0
$841$	9.43967	+	27.4207i	0.325506	+	0.945540i
$842$		0			0
$843$	−1.27671	−	5.59363i	−0.0439722	−	0.192655i
$844$		0			0
$845$	8.38135	−	4.03625i	0.288327	−	0.138851i
$846$		0			0
$847$	17.2594	−	75.6182i	0.593039	−	2.59827i
$848$		0			0
$849$	−1.35958	−	1.70486i	−0.0466608	−	0.0585108i
$850$		0			0
$851$	−13.5640	+	6.53207i	−0.464967	+	0.223916i
$852$		0			0
$853$	38.1521			1.30630			0.653152	−	0.757227i	$-0.273446\pi$
$853$	38.1521			1.30630			0.653152	+	0.757227i	$0.273446\pi$
$854$		0			0
$855$	−6.44989	+	28.2588i	−0.220581	+	0.966430i
$856$		0			0
$857$	31.5462	−	39.5576i	1.07760	−	1.35126i	0.145374	−	0.989377i	$-0.453562\pi$
$857$	31.5462	−	39.5576i	1.07760	−	1.35126i	0.932222	−	0.361886i	$-0.117867\pi$
$858$		0			0
$859$	−32.7902	+	41.1175i	−1.11879	+	1.40291i	−0.214111	+	0.976809i	$0.568685\pi$
$859$	−32.7902	+	41.1175i	−1.11879	+	1.40291i	−0.904674	+	0.426103i	$0.859886\pi$
$860$		0			0
$861$	0.929312	+	1.16532i	0.0316709	+	0.0397140i
$862$		0			0
$863$	32.8463	+	15.8179i	1.11810	+	0.538449i	0.899305	−	0.437321i	$-0.144073\pi$
$863$	32.8463	+	15.8179i	1.11810	+	0.538449i	0.218796	+	0.975771i	$0.429787\pi$
$864$		0			0
$865$	−0.588810	−	2.57975i	−0.0200201	−	0.0877140i
$866$		0			0
$867$	0.0370727	+	0.0178533i	0.00125906	+	0.000606329i
$868$		0			0
$869$	67.4282			2.28734
$870$		0			0
$871$	−36.8364			−1.24815
$872$		0			0
$873$	1.11476	+	0.536840i	0.0377289	+	0.0181693i
$874$		0			0
$875$	12.3095	+	53.9313i	0.416136	+	1.82321i
$876$		0			0
$877$	−14.2957	−	6.88443i	−0.482730	−	0.232471i	0.176659	−	0.984272i	$-0.443471\pi$
$877$	−14.2957	−	6.88443i	−0.482730	−	0.232471i	−0.659390	+	0.751801i	$0.729185\pi$
$878$		0			0
$879$	−2.03415	−	2.55074i	−0.0686101	−	0.0860343i
$880$		0			0
$881$	6.09216	−	7.63933i	0.205250	−	0.257376i	−0.668543	−	0.743674i	$-0.733082\pi$
$881$	6.09216	−	7.63933i	0.205250	−	0.257376i	0.873793	+	0.486298i	$0.161653\pi$
$882$		0			0
$883$	3.19537	−	4.00687i	0.107533	−	0.134842i	−0.725153	−	0.688588i	$-0.758231\pi$
$883$	3.19537	−	4.00687i	0.107533	−	0.134842i	0.832685	+	0.553746i	$0.186802\pi$
$884$		0			0
$885$	−0.375682	+	1.64597i	−0.0126284	+	0.0553287i
$886$		0			0
$887$	39.3250			1.32040			0.660202	−	0.751089i	$-0.270471\pi$
$887$	39.3250			1.32040			0.660202	+	0.751089i	$0.270471\pi$
$888$		0			0
$889$	45.1253	−	21.7312i	1.51345	−	0.728841i
$890$		0			0
$891$	28.2930	+	35.4783i	0.947850	+	1.18857i
$892$		0			0
$893$	−11.7078	+	51.2950i	−0.391785	+	1.71652i
$894$		0			0
$895$	−15.0444	+	7.24499i	−0.502878	+	0.242173i
$896$		0			0
$897$	−0.682628	−	2.99079i	−0.0227923	−	0.0998596i
$898$		0			0
$899$	−2.19985	+	5.27319i	−0.0733691	+	0.175871i
$900$		0			0
$901$	−7.33944	−	32.1562i	−0.244512	−	1.07128i
$902$		0			0
$903$	−1.38385	+	0.666428i	−0.0460517	+	0.0221773i
$904$		0			0
$905$	−4.75219	+	20.8207i	−0.157968	+	0.692104i
$906$		0			0
$907$	−12.3408	−	15.4749i	−0.409769	−	0.513835i	0.533528	−	0.845782i	$-0.320866\pi$
$907$	−12.3408	−	15.4749i	−0.409769	−	0.513835i	−0.943298	+	0.331947i	$0.892294\pi$
$908$		0			0
$909$	34.1902	−	16.4651i	1.13402	−	0.546113i
$910$		0			0
$911$	−19.3647			−0.641580			−0.320790	−	0.947150i	$-0.603948\pi$
$911$	−19.3647			−0.641580			−0.320790	+	0.947150i	$0.603948\pi$
$912$		0			0
$913$	−4.95234	+	21.6976i	−0.163898	+	0.718086i
$914$		0			0
$915$	0.269946	−	0.338502i	0.00892415	−	0.0111905i
$916$		0			0
$917$	10.5586	−	13.2401i	0.348676	−	0.437226i
$918$		0			0
$919$	−29.9949	−	37.6124i	−0.989441	−	1.24072i	−0.970550	−	0.240898i	$-0.922558\pi$
$919$	−29.9949	−	37.6124i	−0.989441	−	1.24072i	−0.0188907	−	0.999822i	$-0.506013\pi$
$920$		0			0
$921$	−0.848936	−	0.408826i	−0.0279734	−	0.0134713i
$922$		0			0
$923$	−3.31886	−	14.5409i	−0.109242	−	0.478619i
$924$		0			0
$925$	−9.85205	−	4.74450i	−0.323933	−	0.155998i
$926$		0			0
$927$	−5.02561			−0.165063
$928$		0			0
$929$	35.9022			1.17791			0.588956	−	0.808165i	$-0.299539\pi$
$929$	35.9022			1.17791			0.588956	+	0.808165i	$0.299539\pi$
$930$		0			0
$931$	−85.1716	−	41.0165i	−2.79139	−	1.34426i
$932$		0			0
$933$	0.229711	+	1.00643i	0.00752041	+	0.0329491i
$934$		0			0
$935$	−30.1226	−	14.5063i	−0.985114	−	0.474406i
$936$		0			0
$937$	13.9447	+	17.4861i	0.455553	+	0.571245i	0.955568	−	0.294772i	$-0.0952436\pi$
$937$	13.9447	+	17.4861i	0.455553	+	0.571245i	−0.500015	+	0.866017i	$0.666672\pi$
$938$		0			0
$939$	−3.04958	+	3.82405i	−0.0995193	+	0.124793i
$940$		0			0
$941$	22.7931	−	28.5817i	0.743035	−	0.931736i	−0.256358	−	0.966582i	$-0.582523\pi$
$941$	22.7931	−	28.5817i	0.743035	−	0.931736i	0.999393	+	0.0348456i	$0.0110939\pi$
$942$		0			0
$943$	−1.26875	+	5.55876i	−0.0413162	+	0.181018i
$944$		0			0
$945$	−8.61356			−0.280199
$946$		0			0
$947$	−15.7485	+	7.58406i	−0.511757	+	0.246449i	−0.671896	−	0.740645i	$-0.734520\pi$
$947$	−15.7485	+	7.58406i	−0.511757	+	0.246449i	0.160140	+	0.987094i	$0.448806\pi$
$948$		0			0
$949$	0.730054	+	0.915458i	0.0236985	+	0.0297170i
$950$		0			0
$951$	0.0215333	−	0.0943435i	0.000698265	−	0.00305930i
$952$		0			0
$953$	−21.9170	+	10.5547i	−0.709961	+	0.341899i	−0.753768	−	0.657141i	$-0.771766\pi$
$953$	−21.9170	+	10.5547i	−0.709961	+	0.341899i	0.0438068	+	0.999040i	$0.486051\pi$
$954$		0			0
$955$	−0.417895	−	1.83092i	−0.0135228	−	0.0592471i
$956$		0			0
$957$	5.51496	+	0.951371i	0.178273	+	0.0307534i
$958$		0			0
$959$	23.3625	+	102.358i	0.754413	+	3.30530i
$960$		0			0
$961$	26.9158	−	12.9620i	0.868252	−	0.418128i
$962$		0			0
$963$	−1.99439	+	8.73798i	−0.0642682	+	0.281577i
$964$		0			0
$965$	−17.8854	−	22.4275i	−0.575750	−	0.721968i
$966$		0			0
$967$	19.5896	−	9.43387i	0.629960	−	0.303373i	−0.0915249	−	0.995803i	$-0.529174\pi$
$967$	19.5896	−	9.43387i	0.629960	−	0.303373i	0.721485	+	0.692430i	$0.243460\pi$
$968$		0			0
$969$	−5.10992			−0.164154
$970$		0			0
$971$	4.23072	−	18.5360i	0.135770	−	0.594848i	−0.860567	−	0.509337i	$-0.829891\pi$
$971$	4.23072	−	18.5360i	0.135770	−	0.594848i	0.996337	−	0.0855109i	$-0.0272522\pi$
$972$		0			0
$973$	−7.79590	+	9.77575i	−0.249925	+	0.313396i
$974$		0			0
$975$	1.38926	−	1.74207i	0.0444918	−	0.0557909i
$976$		0			0
$977$	−10.4859	−	13.1489i	−0.335473	−	0.420670i	0.585270	−	0.810838i	$-0.300988\pi$
$977$	−10.4859	−	13.1489i	−0.335473	−	0.420670i	−0.920744	+	0.390168i	$0.872417\pi$
$978$		0			0
$979$	−72.5863	−	34.9557i	−2.31987	−	1.11719i
$980$		0			0
$981$	5.50139	+	24.1031i	0.175646	+	0.769554i
$982$		0			0
$983$	24.5034	+	11.8002i	0.781537	+	0.376369i	0.781719	−	0.623631i	$-0.214343\pi$
$983$	24.5034	+	11.8002i	0.781537	+	0.376369i	−0.000181114		1.00000i	$0.500058\pi$
$984$		0			0
$985$	24.3696			0.776479
$986$		0			0
$987$	−7.76617			−0.247200
$988$		0			0
$989$	−5.29374	−	2.54933i	−0.168331	−	0.0810640i
$990$		0			0
$991$	−4.82251	−	21.1288i	−0.153192	−	0.671179i	−0.991945	−	0.126667i	$-0.959572\pi$
$991$	−4.82251	−	21.1288i	−0.153192	−	0.671179i	0.838753	−	0.544512i	$-0.183285\pi$
$992$		0			0
$993$	1.53319	+	0.738344i	0.0486542	+	0.0234307i
$994$		0			0
$995$	12.6551	+	15.8690i	0.401194	+	0.503081i
$996$		0			0
$997$	−18.6012	+	23.3252i	−0.589106	+	0.738715i	−0.983636	−	0.180168i	$-0.942336\pi$
$997$	−18.6012	+	23.3252i	−0.589106	+	0.738715i	0.394530	+	0.918883i	$0.370907\pi$
$998$		0			0
$999$	3.11729	−	3.90895i	0.0986265	−	0.123674i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	116.2.g.a.65.1	yes	6
3.2	odd	2		1044.2.u.a.181.1		6
4.3	odd	2		464.2.u.c.65.1		6
29.2	odd	28		3364.2.c.h.1681.3		6
29.5	even	14		3364.2.a.i.1.3		3
29.24	even	7		3364.2.a.j.1.1		3
29.25	even	7	inner	116.2.g.a.25.1	✓	6
29.27	odd	28		3364.2.c.h.1681.4		6
87.83	odd	14		1044.2.u.a.721.1		6
116.83	odd	14		464.2.u.c.257.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
116.2.g.a.25.1	✓	6	29.25	even	7	inner
116.2.g.a.65.1	yes	6	1.1	even	1	trivial
464.2.u.c.65.1		6	4.3	odd	2
464.2.u.c.257.1		6	116.83	odd	14
1044.2.u.a.181.1		6	3.2	odd	2
1044.2.u.a.721.1		6	87.83	odd	14
3364.2.a.i.1.3		3	29.5	even	14
3364.2.a.j.1.1		3	29.24	even	7
3364.2.c.h.1681.3		6	29.2	odd	28
3364.2.c.h.1681.4		6	29.27	odd	28

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:	\( N \)	\(=\)	\( 116 = 2^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	116.g (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.178448 - 0.0859360i) q^{3} +(0.346011 + 1.51597i) q^{5} +(4.22737 + 2.03579i) q^{7} +(-1.84601 - 2.31482i) q^{9} +O(q^{10})\)	\(q+(-0.178448 - 0.0859360i) q^{3} +(0.346011 + 1.51597i) q^{5} +(4.22737 + 2.03579i) q^{7} +(-1.84601 - 2.31482i) q^{9} +(3.27144 - 4.10225i) q^{11} +(-2.71648 + 3.40636i) q^{13} +(0.0685317 - 0.300257i) q^{15} -4.09783 q^{17} +(-5.67241 + 2.73169i) q^{19} +(-0.579417 - 0.726566i) q^{21} +(0.791053 - 3.46583i) q^{23} +(2.32640 - 1.12033i) q^{25} +(0.262709 + 1.15100i) q^{27} +(-4.38404 - 3.12733i) q^{29} +(-0.236094 - 1.03440i) q^{31} +(-0.936313 + 0.450904i) q^{33} +(-1.62349 + 7.11297i) q^{35} +(-2.64042 - 3.31098i) q^{37} +(0.777479 - 0.374414i) q^{39} -1.60388 q^{41} +(0.367781 - 1.61135i) q^{43} +(2.87047 - 3.59945i) q^{45} +(5.21044 - 6.53368i) q^{47} +(9.36174 + 11.7393i) q^{49} +(0.731250 + 0.352152i) q^{51} +(1.79105 + 7.84711i) q^{53} +(7.35086 + 3.53999i) q^{55} +1.24698 q^{57} -5.48188 q^{59} +(1.26659 + 0.609959i) q^{61} +(-3.09126 - 13.5437i) q^{63} +(-6.10388 - 2.93947i) q^{65} +(5.27144 + 6.61017i) q^{67} +(-0.439001 + 0.550490i) q^{69} +(-2.13437 + 2.67642i) q^{71} +(0.0598025 - 0.262012i) q^{73} -0.511418 q^{75} +(22.1809 - 10.6818i) q^{77} +(8.01238 + 10.0472i) q^{79} +(-1.92447 + 8.43165i) q^{81} +(-3.82155 + 1.84036i) q^{83} +(-1.41789 - 6.21220i) q^{85} +(0.513574 + 0.934812i) q^{87} +(-3.41670 - 14.9695i) q^{89} +(-18.4182 + 8.86973i) q^{91} +(-0.0467614 + 0.204875i) q^{93} +(-6.10388 - 7.65402i) q^{95} +(-0.376510 + 0.181318i) q^{97} -15.5351 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} - 3 q^{5} + 3 q^{7} - 6 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 - 3 * q^5 + 3 * q^7 - 6 * q^9	\( 6 q + 3 q^{3} - 3 q^{5} + 3 q^{7} - 6 q^{9} + q^{11} + 3 q^{13} - 5 q^{15} + 12 q^{17} - 11 q^{19} + 5 q^{21} - q^{23} - 4 q^{25} - 33 q^{27} - 6 q^{29} + 5 q^{31} + 11 q^{33} - 5 q^{35} - 27 q^{37} + 5 q^{39} + 8 q^{41} - 9 q^{43} + 3 q^{45} - 7 q^{47} + 26 q^{49} + 20 q^{51} + 5 q^{53} + 17 q^{55} - 2 q^{57} + 24 q^{59} + 11 q^{61} + 53 q^{63} - 19 q^{65} + 13 q^{67} + 17 q^{69} - 5 q^{71} - 21 q^{73} - 16 q^{75} + 25 q^{77} + q^{79} - 58 q^{81} - 27 q^{83} - 20 q^{85} - 3 q^{87} + 9 q^{89} - 37 q^{91} - q^{93} - 19 q^{95} - 7 q^{97} + 20 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 - 3 * q^5 + 3 * q^7 - 6 * q^9 + q^11 + 3 * q^13 - 5 * q^15 + 12 * q^17 - 11 * q^19 + 5 * q^21 - q^23 - 4 * q^25 - 33 * q^27 - 6 * q^29 + 5 * q^31 + 11 * q^33 - 5 * q^35 - 27 * q^37 + 5 * q^39 + 8 * q^41 - 9 * q^43 + 3 * q^45 - 7 * q^47 + 26 * q^49 + 20 * q^51 + 5 * q^53 + 17 * q^55 - 2 * q^57 + 24 * q^59 + 11 * q^61 + 53 * q^63 - 19 * q^65 + 13 * q^67 + 17 * q^69 - 5 * q^71 - 21 * q^73 - 16 * q^75 + 25 * q^77 + q^79 - 58 * q^81 - 27 * q^83 - 20 * q^85 - 3 * q^87 + 9 * q^89 - 37 * q^91 - q^93 - 19 * q^95 - 7 * q^97 + 20 * q^99

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