LMFDB - Embedded newform 232.2.m.d.161.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [232,2,Mod(25,232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(232, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 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("232.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 232 = 2^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	232.m (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:	$1.85252932689$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			161.3
Character	$\chi$	$=$	232.161
Dual form			232.2.m.d.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.484939 + 0.608094i) q^{3} +(-0.283259 - 0.136410i) q^{5} +(-2.96109 + 3.71309i) q^{7} +(0.532950 + 2.33501i) q^{9} +O(q^{10})$	\(q+(-0.484939 + 0.608094i) q^{3} +(-0.283259 - 0.136410i) q^{5} +(-2.96109 + 3.71309i) q^{7} +(0.532950 + 2.33501i) q^{9} +(0.0376549 - 0.164977i) q^{11} +(-0.0314642 + 0.137854i) q^{13} +(0.220313 - 0.106097i) q^{15} +0.833683 q^{17} +(4.28287 + 5.37055i) q^{19} +(-0.821961 - 3.60124i) q^{21} +(-3.96704 + 1.91042i) q^{23} +(-3.05582 - 3.83188i) q^{25} +(-3.78062 - 1.82065i) q^{27} +(5.36275 + 0.490817i) q^{29} +(-2.53351 - 1.22008i) q^{31} +(0.0820611 + 0.102901i) q^{33} +(1.34526 - 0.647843i) q^{35} +(0.00971297 + 0.0425553i) q^{37} +(-0.0685698 - 0.0859838i) q^{39} +7.26282 q^{41} +(4.70140 - 2.26407i) q^{43} +(0.167556 - 0.734112i) q^{45} +(1.99389 - 8.73582i) q^{47} +(-3.46134 - 15.1651i) q^{49} +(-0.404285 + 0.506958i) q^{51} +(5.52197 + 2.65924i) q^{53} +(-0.0331706 + 0.0415947i) q^{55} -5.34272 q^{57} +13.7067 q^{59} +(-7.02344 + 8.80712i) q^{61} +(-10.2482 - 4.93528i) q^{63} +(0.0277172 - 0.0347563i) q^{65} +(-1.52216 - 6.66901i) q^{67} +(0.762052 - 3.33877i) q^{69} +(-1.23339 + 5.40382i) q^{71} +(-8.88556 + 4.27906i) q^{73} +3.81203 q^{75} +(0.501075 + 0.628328i) q^{77} +(0.0908998 + 0.398258i) q^{79} +(-3.53312 + 1.70146i) q^{81} +(1.61575 + 2.02608i) q^{83} +(-0.236148 - 0.113723i) q^{85} +(-2.89907 + 3.02304i) q^{87} +(7.96727 + 3.83684i) q^{89} +(-0.418695 - 0.525027i) q^{91} +(1.97052 - 0.948952i) q^{93} +(-0.480563 - 2.10548i) q^{95} +(6.67287 + 8.36752i) q^{97} +0.405291 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{3} - 8 q^{5} + 5 q^{7} - 3 q^{9}+O(q^{10}) $ 24 * q - q^3 - 8 * q^5 + 5 * q^7 - 3 * q^9	$ 24 q - q^{3} - 8 q^{5} + 5 q^{7} - 3 q^{9} - 6 q^{11} + q^{13} - q^{15} - 16 q^{17} - 10 q^{19} - 5 q^{21} + 11 q^{23} + 10 q^{25} - 7 q^{27} - 2 q^{29} + 12 q^{31} + 13 q^{33} - 8 q^{35} + q^{37} + 34 q^{39} - 22 q^{41} + 3 q^{43} + 60 q^{45} + 9 q^{47} - 67 q^{49} - q^{51} + 19 q^{53} - 88 q^{55} - 2 q^{57} + 114 q^{59} - 11 q^{61} - 108 q^{63} + 8 q^{65} - 25 q^{67} - 84 q^{69} - 21 q^{71} + 30 q^{73} - 26 q^{75} - 22 q^{77} + 48 q^{79} + 16 q^{81} - 37 q^{83} + 8 q^{85} + 11 q^{87} - 5 q^{89} - 11 q^{91} - 18 q^{93} - 21 q^{95} + 35 q^{97} + 32 q^{99}+O(q^{100}) $ 24 * q - q^3 - 8 * q^5 + 5 * q^7 - 3 * q^9 - 6 * q^11 + q^13 - q^15 - 16 * q^17 - 10 * q^19 - 5 * q^21 + 11 * q^23 + 10 * q^25 - 7 * q^27 - 2 * q^29 + 12 * q^31 + 13 * q^33 - 8 * q^35 + q^37 + 34 * q^39 - 22 * q^41 + 3 * q^43 + 60 * q^45 + 9 * q^47 - 67 * q^49 - q^51 + 19 * q^53 - 88 * q^55 - 2 * q^57 + 114 * q^59 - 11 * q^61 - 108 * q^63 + 8 * q^65 - 25 * q^67 - 84 * q^69 - 21 * q^71 + 30 * q^73 - 26 * q^75 - 22 * q^77 + 48 * q^79 + 16 * q^81 - 37 * q^83 + 8 * q^85 + 11 * q^87 - 5 * q^89 - 11 * q^91 - 18 * q^93 - 21 * q^95 + 35 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/232\mathbb{Z}\right)^\times$.

$n$	$89$	$117$	$175$
$\chi(n)$	$e\left(\frac{1}{7}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.484939	+	0.608094i	−0.279979	+	0.351083i	−0.901860	−	0.432029i	$-0.857798\pi$
$3$	−0.484939	+	0.608094i	−0.279979	+	0.351083i	0.621880	+	0.783112i	$0.286369\pi$
$4$		0			0
$5$	−0.283259	−	0.136410i	−0.126677	−	0.0610045i	0.369472	−	0.929242i	$-0.379539\pi$
$5$	−0.283259	−	0.136410i	−0.126677	−	0.0610045i	−0.496149	+	0.868237i	$0.665253\pi$
$6$		0			0
$7$	−2.96109	+	3.71309i	−1.11919	+	1.40342i	−0.214826	+	0.976652i	$0.568918\pi$
$7$	−2.96109	+	3.71309i	−1.11919	+	1.40342i	−0.904363	+	0.426765i	$0.859653\pi$
$8$		0			0
$9$	0.532950	+	2.33501i	0.177650	+	0.778336i
$10$		0			0
$11$	0.0376549	−	0.164977i	0.0113534	−	0.0497424i	−0.968934	−	0.247320i	$-0.920450\pi$
$11$	0.0376549	−	0.164977i	0.0113534	−	0.0497424i	0.980287	+	0.197577i	$0.0633073\pi$
$12$		0			0
$13$	−0.0314642	+	0.137854i	−0.00872660	+	0.0382337i	−0.979104	−	0.203361i	$-0.934813\pi$
$13$	−0.0314642	+	0.137854i	−0.00872660	+	0.0382337i	0.970377	+	0.241595i	$0.0776706\pi$
$14$		0			0
$15$	0.220313	−	0.106097i	0.0568847	−	0.0273942i
$16$		0			0
$17$	0.833683			0.202198			0.101099	−	0.994876i	$-0.467764\pi$
$17$	0.833683			0.202198			0.101099	+	0.994876i	$0.467764\pi$
$18$		0			0
$19$	4.28287	+	5.37055i	0.982557	+	1.23209i	0.972683	+	0.232137i	$0.0745717\pi$
$19$	4.28287	+	5.37055i	0.982557	+	1.23209i	0.00987422	+	0.999951i	$0.496857\pi$
$20$		0			0
$21$	−0.821961	−	3.60124i	−0.179366	−	0.785856i
$22$		0			0
$23$	−3.96704	+	1.91042i	−0.827185	+	0.398351i	−0.799059	−	0.601253i	$-0.794668\pi$
$23$	−3.96704	+	1.91042i	−0.827185	+	0.398351i	−0.0281261	+	0.999604i	$0.508954\pi$
$24$		0			0
$25$	−3.05582	−	3.83188i	−0.611164	−	0.766376i
$26$		0			0
$27$	−3.78062	−	1.82065i	−0.727581	−	0.350384i
$28$		0			0
$29$	5.36275	+	0.490817i	0.995838	+	0.0911424i
$29$	5.36275	+	0.490817i	0.995838	+	0.0911424i
$30$		0			0
$31$	−2.53351	−	1.22008i	−0.455032	−	0.219132i	0.192306	−	0.981335i	$-0.438403\pi$
$31$	−2.53351	−	1.22008i	−0.455032	−	0.219132i	−0.647338	+	0.762203i	$0.724118\pi$
$32$		0			0
$33$	0.0820611	+	0.102901i	0.0142850	+	0.0179128i
$34$		0			0
$35$	1.34526	−	0.647843i	0.227391	−	0.109506i
$36$		0			0
$37$	0.00971297	+	0.0425553i	0.00159680	+	0.00699605i	0.975720	−	0.219021i	$-0.0702865\pi$
$37$	0.00971297	+	0.0425553i	0.00159680	+	0.00699605i	−0.974123	+	0.226018i	$0.927429\pi$
$38$		0			0
$39$	−0.0685698	−	0.0859838i	−0.0109800	−	0.0137684i
$40$		0			0
$41$	7.26282			1.13426			0.567131	−	0.823628i	$-0.308053\pi$
$41$	7.26282			1.13426			0.567131	+	0.823628i	$0.308053\pi$
$42$		0			0
$43$	4.70140	−	2.26407i	0.716956	−	0.345268i	−0.0395830	−	0.999216i	$-0.512603\pi$
$43$	4.70140	−	2.26407i	0.716956	−	0.345268i	0.756539	+	0.653948i	$0.226889\pi$
$44$		0			0
$45$	0.167556	−	0.734112i	0.0249778	−	0.109435i
$46$		0			0
$47$	1.99389	−	8.73582i	0.290839	−	1.27425i	−0.592521	−	0.805555i	$-0.701867\pi$
$47$	1.99389	−	8.73582i	0.290839	−	1.27425i	0.883360	−	0.468695i	$-0.155276\pi$
$48$		0			0
$49$	−3.46134	−	15.1651i	−0.494478	−	2.16645i
$50$		0			0
$51$	−0.404285	+	0.506958i	−0.0566112	+	0.0709883i
$52$		0			0
$53$	5.52197	+	2.65924i	0.758501	+	0.365275i	0.772822	−	0.634623i	$-0.218844\pi$
$53$	5.52197	+	2.65924i	0.758501	+	0.365275i	−0.0143213	+	0.999897i	$0.504559\pi$
$54$		0			0
$55$	−0.0331706	+	0.0415947i	−0.00447273	+	0.00560863i
$56$		0			0
$57$	−5.34272			−0.707661
$58$		0			0
$59$	13.7067			1.78445			0.892227	−	0.451587i	$-0.149142\pi$
$59$	13.7067			1.78445			0.892227	+	0.451587i	$0.149142\pi$
$60$		0			0
$61$	−7.02344	+	8.80712i	−0.899260	+	1.12764i	0.0920063	+	0.995758i	$0.470672\pi$
$61$	−7.02344	+	8.80712i	−0.899260	+	1.12764i	−0.991266	+	0.131878i	$0.957899\pi$
$62$		0			0
$63$	−10.2482	−	4.93528i	−1.29115	−	0.621787i
$64$		0			0
$65$	0.0277172	−	0.0347563i	0.00343789	−	0.00431098i
$66$		0			0
$67$	−1.52216	−	6.66901i	−0.185961	−	0.814749i	−0.978718	−	0.205211i	$-0.934212\pi$
$67$	−1.52216	−	6.66901i	−0.185961	−	0.814749i	0.792757	−	0.609538i	$-0.208645\pi$
$68$		0			0
$69$	0.762052	−	3.33877i	0.0917403	−	0.401941i
$70$		0			0
$71$	−1.23339	+	5.40382i	−0.146376	+	0.641315i	0.847498	+	0.530798i	$0.178108\pi$
$71$	−1.23339	+	5.40382i	−0.146376	+	0.641315i	−0.993874	+	0.110517i	$0.964749\pi$
$72$		0			0
$73$	−8.88556	+	4.27906i	−1.03998	+	0.500826i	−0.874316	−	0.485357i	$-0.838690\pi$
$73$	−8.88556	+	4.27906i	−1.03998	+	0.500826i	−0.165660	+	0.986183i	$0.552975\pi$
$74$		0			0
$75$	3.81203			0.440175
$76$		0			0
$77$	0.501075	+	0.628328i	0.0571028	+	0.0716047i
$78$		0			0
$79$	0.0908998	+	0.398258i	0.0102270	+	0.0448075i	0.979784	−	0.200058i	$-0.0641132\pi$
$79$	0.0908998	+	0.398258i	0.0102270	+	0.0448075i	−0.969557	+	0.244866i	$0.921256\pi$
$80$		0			0
$81$	−3.53312	+	1.70146i	−0.392569	+	0.189051i
$82$		0			0
$83$	1.61575	+	2.02608i	0.177351	+	0.222392i	0.862559	−	0.505956i	$-0.168860\pi$
$83$	1.61575	+	2.02608i	0.177351	+	0.222392i	−0.685208	+	0.728347i	$0.740289\pi$
$84$		0			0
$85$	−0.236148	−	0.113723i	−0.0256139	−	0.0123350i
$86$		0			0
$87$	−2.89907	+	3.02304i	−0.310813	+	0.324104i
$88$		0			0
$89$	7.96727	+	3.83684i	0.844529	+	0.406704i	0.805544	−	0.592536i	$-0.201873\pi$
$89$	7.96727	+	3.83684i	0.844529	+	0.406704i	0.0389851	+	0.999240i	$0.487588\pi$
$90$		0			0
$91$	−0.418695	−	0.525027i	−0.0438912	−	0.0550378i
$92$		0			0
$93$	1.97052	−	0.948952i	0.204333	−	0.0984017i
$94$		0			0
$95$	−0.480563	−	2.10548i	−0.0493047	−	0.216018i
$96$		0			0
$97$	6.67287	+	8.36752i	0.677527	+	0.849593i	0.995124	−	0.0986334i	$-0.0314471\pi$
$97$	6.67287	+	8.36752i	0.677527	+	0.849593i	−0.317596	+	0.948226i	$0.602876\pi$
$98$		0			0
$99$	0.405291			0.0407332
$100$		0			0
$101$	0.627524	−	0.302200i	0.0624410	−	0.0300700i	−0.402403	−	0.915463i	$-0.631825\pi$
$101$	0.627524	−	0.302200i	0.0624410	−	0.0300700i	0.464844	+	0.885393i	$0.346111\pi$
$102$		0			0
$103$	1.54432	−	6.76613i	0.152167	−	0.666686i	−0.840086	−	0.542453i	$-0.817496\pi$
$103$	1.54432	−	6.76613i	0.152167	−	0.666686i	0.992253	−	0.124233i	$-0.0396471\pi$
$104$		0			0
$105$	−0.258419	+	1.13221i	−0.0252191	+	0.110492i
$106$		0			0
$107$	−0.0710269	−	0.311189i	−0.00686643	−	0.0300838i	0.971379	−	0.237536i	$-0.0763399\pi$
$107$	−0.0710269	−	0.311189i	−0.00686643	−	0.0300838i	−0.978245	+	0.207453i	$0.933483\pi$
$108$		0			0
$109$	−2.00523	+	2.51448i	−0.192067	+	0.240844i	−0.868535	−	0.495628i	$-0.834938\pi$
$109$	−2.00523	+	2.51448i	−0.192067	+	0.240844i	0.676469	+	0.736472i	$0.263509\pi$
$110$		0			0
$111$	−0.0305878	−	0.0147303i	−0.00290327	−	0.00139814i
$112$		0			0
$113$	−10.3599	+	12.9910i	−0.974582	+	1.22209i	0.000444878		1.00000i	$0.499858\pi$
$113$	−10.3599	+	12.9910i	−0.974582	+	1.22209i	−0.975027	+	0.222087i	$0.928713\pi$
$114$		0			0
$115$	1.38430			0.129087
$116$		0			0
$117$	−0.338658			−0.0313090
$118$		0			0
$119$	−2.46861	+	3.09554i	−0.226297	+	0.283768i
$120$		0			0
$121$	9.88486	+	4.76030i	0.898623	+	0.432754i
$122$		0			0
$123$	−3.52202	+	4.41648i	−0.317570	+	0.398220i
$124$		0			0
$125$	0.692677	+	3.03482i	0.0619549	+	0.271442i
$126$		0			0
$127$	−2.47548	+	10.8458i	−0.219664	+	0.962409i	0.738064	+	0.674731i	$0.235740\pi$
$127$	−2.47548	+	10.8458i	−0.219664	+	0.962409i	−0.957727	+	0.287678i	$0.907117\pi$
$128$		0			0
$129$	−0.903120	+	3.95683i	−0.0795152	+	0.348379i
$130$		0			0
$131$	12.7266	−	6.12883i	1.11193	−	0.535478i	0.214541	−	0.976715i	$-0.431174\pi$
$131$	12.7266	−	6.12883i	1.11193	−	0.535478i	0.897391	+	0.441237i	$0.145460\pi$
$132$		0			0
$133$	−32.6233			−2.82880
$134$		0			0
$135$	0.822539	+	1.03143i	0.0707929	+	0.0887715i
$136$		0			0
$137$	1.83026	+	8.01887i	0.156369	+	0.685098i	0.990952	+	0.134216i	$0.0428516\pi$
$137$	1.83026	+	8.01887i	0.156369	+	0.685098i	−0.834583	+	0.550882i	$0.814291\pi$
$138$		0			0
$139$	11.2002	−	5.39374i	0.949991	−	0.457491i	0.106308	−	0.994333i	$-0.466097\pi$
$139$	11.2002	−	5.39374i	0.949991	−	0.457491i	0.843683	+	0.536842i	$0.180383\pi$
$140$		0			0
$141$	4.34528	+	5.44881i	0.365939	+	0.458872i
$142$		0			0
$143$	0.0215579	+	0.0103817i	0.00180276	+	0.000868165i
$144$		0			0
$145$	−1.45209	−	0.870563i	−0.120590	−	0.0722963i
$146$		0			0
$147$	10.9004	+	5.24934i	0.899047	+	0.432958i
$148$		0			0
$149$	−13.1077	−	16.4365i	−1.07382	−	1.34653i	−0.934370	−	0.356303i	$-0.884037\pi$
$149$	−13.1077	−	16.4365i	−1.07382	−	1.34653i	−0.139453	−	0.990229i	$-0.544534\pi$
$150$		0			0
$151$	−13.6769	+	6.58645i	−1.11301	+	0.535998i	−0.897726	−	0.440553i	$-0.854782\pi$
$151$	−13.6769	+	6.58645i	−1.11301	+	0.535998i	−0.215285	+	0.976551i	$0.569068\pi$
$152$		0			0
$153$	0.444312	+	1.94666i	0.0359205	+	0.157378i
$154$		0			0
$155$	0.551209	+	0.691195i	0.0442742	+	0.0555181i
$156$		0			0
$157$	−1.66764			−0.133092			−0.0665460	−	0.997783i	$-0.521198\pi$
$157$	−1.66764			−0.133092			−0.0665460	+	0.997783i	$0.521198\pi$
$158$		0			0
$159$	−4.29488	+	2.06831i	−0.340606	+	0.164027i
$160$		0			0
$161$	4.65318	−	20.3869i	0.366722	−	1.60672i
$162$		0			0
$163$	0.672299	−	2.94554i	0.0526585	−	0.230712i	−0.941750	−	0.336314i	$-0.890820\pi$
$163$	0.672299	−	2.94554i	0.0526585	−	0.230712i	0.994409	+	0.105602i	$0.0336769\pi$
$164$		0			0
$165$	−0.00920774	−	0.0403417i	−0.000716821	−	0.00314060i
$166$		0			0
$167$	9.40109	−	11.7886i	0.727478	−	0.912229i	−0.271257	−	0.962507i	$-0.587439\pi$
$167$	9.40109	−	11.7886i	0.727478	−	0.912229i	0.998735	+	0.0502782i	$0.0160108\pi$
$168$		0			0
$169$	11.6946	+	5.63181i	0.899583	+	0.433216i
$170$		0			0
$171$	−10.2577	+	12.8628i	−0.784427	+	0.983640i
$172$		0			0
$173$	15.0190			1.14187			0.570937	−	0.820994i	$-0.306580\pi$
$173$	15.0190			1.14187			0.570937	+	0.820994i	$0.306580\pi$
$174$		0			0
$175$	23.2767			1.75955
$176$		0			0
$177$	−6.64688	+	8.33493i	−0.499610	+	0.626492i
$178$		0			0
$179$	−14.3188	−	6.89556i	−1.07024	−	0.515398i	−0.186053	−	0.982540i	$-0.559569\pi$
$179$	−14.3188	−	6.89556i	−1.07024	−	0.515398i	−0.884182	+	0.467142i	$0.845284\pi$
$180$		0			0
$181$	−7.50436	+	9.41017i	−0.557794	+	0.699452i	−0.978148	−	0.207908i	$-0.933335\pi$
$181$	−7.50436	+	9.41017i	−0.557794	+	0.699452i	0.420354	+	0.907360i	$0.361906\pi$
$182$		0			0
$183$	−1.94962	−	8.54182i	−0.144120	−	0.631430i
$184$		0			0
$185$	0.00305370	−	0.0133791i	0.000224512	−	0.000983652i
$186$		0			0
$187$	0.0313923	−	0.137539i	0.00229563	−	0.0100578i
$188$		0			0
$189$	17.9550	−	8.64668i	1.30604	−	0.628954i
$190$		0			0
$191$	−20.5470			−1.48673			−0.743366	−	0.668885i	$-0.766772\pi$
$191$	−20.5470			−1.48673			−0.743366	+	0.668885i	$0.766772\pi$
$192$		0			0
$193$	−14.3322	−	17.9720i	−1.03165	−	1.29365i	−0.955003	−	0.296595i	$-0.904149\pi$
$193$	−14.3322	−	17.9720i	−1.03165	−	1.29365i	−0.0766504	−	0.997058i	$-0.524423\pi$
$194$		0			0
$195$	0.00769393	+	0.0337093i	0.000550974	+	0.00241397i
$196$		0			0
$197$	21.6904	−	10.4455i	1.54537	−	0.744213i	0.549547	−	0.835463i	$-0.314800\pi$
$197$	21.6904	−	10.4455i	1.54537	−	0.744213i	0.995828	+	0.0912496i	$0.0290861\pi$
$198$		0			0
$199$	−2.21317	−	2.77522i	−0.156887	−	0.196730i	0.697175	−	0.716901i	$-0.254440\pi$
$199$	−2.21317	−	2.77522i	−0.156887	−	0.196730i	−0.854063	+	0.520170i	$0.825868\pi$
$200$		0			0
$201$	4.79353	+	2.30844i	0.338110	+	0.162825i
$202$		0			0
$203$	−17.7021	+	18.4590i	−1.24244	+	1.29557i
$204$		0			0
$205$	−2.05726	−	0.990724i	−0.143685	−	0.0691952i
$206$		0			0
$207$	−6.57509	−	8.24490i	−0.457000	−	0.573060i
$208$		0			0
$209$	1.04729	−	0.504347i	0.0724424	−	0.0348864i
$210$		0			0
$211$	−1.12732	−	4.93909i	−0.0776076	−	0.340021i	0.921186	−	0.389122i	$-0.127222\pi$
$211$	−1.12732	−	4.93909i	−0.0776076	−	0.340021i	−0.998794	+	0.0491009i	$0.984364\pi$
$212$		0			0
$213$	−2.68791	−	3.37053i	−0.184173	−	0.230945i
$214$		0			0
$215$	−1.64056			−0.111885
$216$		0			0
$217$	12.0322	−	5.79441i	0.816801	−	0.393350i
$218$		0			0
$219$	1.70688	−	7.47833i	0.115340	−	0.505339i
$220$		0			0
$221$	−0.0262312	+	0.114926i	−0.00176450	+	0.00773078i
$222$		0			0
$223$	3.16702	+	13.8756i	0.212079	+	0.929181i	0.963151	+	0.268960i	$0.0866800\pi$
$223$	3.16702	+	13.8756i	0.212079	+	0.929181i	−0.751072	+	0.660220i	$0.770463\pi$
$224$		0			0
$225$	7.31886	−	9.17757i	0.487924	−	0.611838i
$226$		0			0
$227$	7.69899	+	3.70764i	0.511000	+	0.246085i	0.671572	−	0.740940i	$-0.265620\pi$
$227$	7.69899	+	3.70764i	0.511000	+	0.246085i	−0.160572	+	0.987024i	$0.551334\pi$
$228$		0			0
$229$	15.2121	−	19.0754i	1.00524	−	1.26054i	0.0399954	−	0.999200i	$-0.487266\pi$
$229$	15.2121	−	19.0754i	1.00524	−	1.26054i	0.965248	−	0.261336i	$-0.0841629\pi$
$230$		0			0
$231$	−0.625073			−0.0411268
$232$		0			0
$233$	−5.75011			−0.376702			−0.188351	−	0.982102i	$-0.560314\pi$
$233$	−5.75011			−0.376702			−0.188351	+	0.982102i	$0.560314\pi$
$234$		0			0
$235$	−1.75644	+	2.20251i	−0.114578	+	0.143676i
$236$		0			0
$237$	−0.286259	−	0.137855i	−0.0185945	−	0.00895465i
$238$		0			0
$239$	12.3772	−	15.5205i	0.800612	−	1.00394i	−0.199101	−	0.979979i	$-0.563802\pi$
$239$	12.3772	−	15.5205i	0.800612	−	1.00394i	0.999713	−	0.0239565i	$-0.00762633\pi$
$240$		0			0
$241$	−6.54983	−	28.6967i	−0.421912	−	1.84852i	−0.521168	−	0.853454i	$-0.674503\pi$
$241$	−6.54983	−	28.6967i	−0.421912	−	1.84852i	0.0992558	−	0.995062i	$-0.468354\pi$
$242$		0			0
$243$	3.47991	−	15.2465i	0.223236	−	0.978061i
$244$		0			0
$245$	−1.08822	+	4.76782i	−0.0695241	+	0.304605i
$246$		0			0
$247$	−0.875107	+	0.421429i	−0.0556817	+	0.0268149i
$248$		0			0
$249$	−2.01559			−0.127733
$250$		0			0
$251$	−1.66043	−	2.08211i	−0.104805	−	0.131422i	0.726663	−	0.686995i	$-0.241070\pi$
$251$	−1.66043	−	2.08211i	−0.104805	−	0.131422i	−0.831468	+	0.555573i	$0.812499\pi$
$252$		0			0
$253$	0.165798	+	0.726407i	0.0104236	+	0.0456688i
$254$		0			0
$255$	0.183672	−	0.0884516i	0.0115020	−	0.00553905i
$256$		0			0
$257$	5.46616	+	6.85435i	0.340970	+	0.427563i	0.922521	−	0.385947i	$-0.126125\pi$
$257$	5.46616	+	6.85435i	0.340970	+	0.427563i	−0.581551	+	0.813510i	$0.697554\pi$
$258$		0			0
$259$	−0.186773	−	0.0899450i	−0.0116055	−	0.00558891i
$260$		0			0
$261$	1.71202	+	12.7836i	0.105971	+	0.791288i
$262$		0			0
$263$	16.5217	+	7.95646i	1.01877	+	0.490616i	0.867269	−	0.497840i	$-0.165873\pi$
$263$	16.5217	+	7.95646i	1.01877	+	0.490616i	0.151506	+	0.988456i	$0.451588\pi$
$264$		0			0
$265$	−1.20140	−	1.50651i	−0.0738014	−	0.0925440i
$266$		0			0
$267$	−6.19679	+	2.98422i	−0.379238	+	0.182631i
$268$		0			0
$269$	3.69509	+	16.1893i	0.225294	+	0.987077i	0.953423	+	0.301637i	$0.0975330\pi$
$269$	3.69509	+	16.1893i	0.225294	+	0.987077i	−0.728129	+	0.685440i	$0.759610\pi$
$270$		0			0
$271$	14.1967	+	17.8021i	0.862389	+	1.08140i	0.995910	+	0.0903553i	$0.0288003\pi$
$271$	14.1967	+	17.8021i	0.862389	+	1.08140i	−0.133521	+	0.991046i	$0.542628\pi$
$272$		0			0
$273$	0.522307			0.0316115
$274$		0			0
$275$	−0.747238	+	0.359851i	−0.0450602	+	0.0216998i
$276$		0			0
$277$	4.46770	−	19.5743i	0.268438	−	1.17610i	−0.643393	−	0.765536i	$-0.722474\pi$
$277$	4.46770	−	19.5743i	0.268438	−	1.17610i	0.911830	−	0.410567i	$-0.134669\pi$
$278$		0			0
$279$	1.49865	−	6.56601i	0.0897218	−	0.393097i
$280$		0			0
$281$	−5.34766	−	23.4296i	−0.319015	−	1.39769i	−0.839284	−	0.543693i	$-0.817026\pi$
$281$	−5.34766	−	23.4296i	−0.319015	−	1.39769i	0.520270	−	0.854002i	$-0.325831\pi$
$282$		0			0
$283$	−8.26715	+	10.3667i	−0.491431	+	0.616235i	−0.964272	−	0.264913i	$-0.914657\pi$
$283$	−8.26715	+	10.3667i	−0.491431	+	0.616235i	0.472842	+	0.881147i	$0.343228\pi$
$284$		0			0
$285$	1.51337	+	0.728803i	0.0896446	+	0.0431705i
$286$		0			0
$287$	−21.5059	+	26.9675i	−1.26945	+	1.59184i
$288$		0			0
$289$	−16.3050			−0.959116
$290$		0			0
$291$	−8.32417			−0.487971
$292$		0			0
$293$	−13.2638	+	16.6322i	−0.774877	+	0.971665i	−0.999996	−	0.00266657i	$-0.999151\pi$
$293$	−13.2638	+	16.6322i	−0.774877	+	0.971665i	0.225120	+	0.974331i	$0.427723\pi$
$294$		0			0
$295$	−3.88253	−	1.86973i	−0.226050	−	0.108860i
$296$		0			0
$297$	−0.442724	+	0.555159i	−0.0256895	+	0.0322136i
$298$		0			0
$299$	−0.138539	−	0.606981i	−0.00801194	−	0.0351026i
$300$		0			0
$301$	−5.51456	+	24.1609i	−0.317854	+	1.39261i
$302$		0			0
$303$	−0.120545	+	0.528142i	−0.00692512	+	0.0303409i
$304$		0			0
$305$	3.19083	−	1.53663i	0.182707	−	0.0879869i
$306$		0			0
$307$	−31.3569			−1.78963			−0.894817	−	0.446433i	$-0.852694\pi$
$307$	−31.3569			−1.78963			−0.894817	+	0.446433i	$0.852694\pi$
$308$		0			0
$309$	3.36554	+	4.22025i	0.191459	+	0.240082i
$310$		0			0
$311$	−1.70506	−	7.47037i	−0.0966852	−	0.423606i	0.903300	−	0.429009i	$-0.141137\pi$
$311$	−1.70506	−	7.47037i	−0.0966852	−	0.423606i	−0.999985	+	0.00540341i	$0.998280\pi$
$312$		0			0
$313$	−0.925990	+	0.445933i	−0.0523401	+	0.0252056i	−0.459871	−	0.887986i	$-0.652104\pi$
$313$	−0.925990	+	0.445933i	−0.0523401	+	0.0252056i	0.407531	+	0.913192i	$0.366390\pi$
$314$		0			0
$315$	2.22968	+	2.79593i	0.125628	+	0.157533i
$316$		0			0
$317$	−3.81509	−	1.83725i	−0.214277	−	0.103190i	0.323667	−	0.946171i	$-0.395084\pi$
$317$	−3.81509	−	1.83725i	−0.214277	−	0.103190i	−0.537943	+	0.842981i	$0.680799\pi$
$318$		0			0
$319$	0.282907	−	0.866249i	0.0158398	−	0.0485006i
$320$		0			0
$321$	0.223676	+	0.107717i	0.0124844	+	0.00601216i
$322$		0			0
$323$	3.57056	+	4.47734i	0.198671	+	0.249126i
$324$		0			0
$325$	0.624388	−	0.300689i	0.0346348	−	0.0166792i
$326$		0			0
$327$	−0.556626	−	2.43874i	−0.0307815	−	0.134863i
$328$		0			0
$329$	26.5328	+	33.2711i	1.46280	+	1.83429i
$330$		0			0
$331$	14.3575			0.789158			0.394579	−	0.918862i	$-0.370890\pi$
$331$	14.3575			0.789158			0.394579	+	0.918862i	$0.370890\pi$
$332$		0			0
$333$	−0.0941904	+	0.0453597i	−0.00516160	+	0.00248570i
$334$		0			0
$335$	−0.478557	+	2.09669i	−0.0261463	+	0.114555i
$336$		0			0
$337$	−0.422748	+	1.85218i	−0.0230285	+	0.100895i	−0.985136	−	0.171776i	$-0.945050\pi$
$337$	−0.422748	+	1.85218i	−0.0230285	+	0.100895i	0.962108	+	0.272670i	$0.0879068\pi$
$338$		0			0
$339$	−2.87579	−	12.5996i	−0.156191	−	0.684318i
$340$		0			0
$341$	−0.296684	+	0.372029i	−0.0160663	+	0.0201465i
$342$		0			0
$343$	36.6066	+	17.6288i	1.97657	+	0.951867i
$344$		0			0
$345$	−0.671301	+	0.841785i	−0.0361416	+	0.0453202i
$346$		0			0
$347$	−18.8015			−1.00932			−0.504659	−	0.863319i	$-0.668382\pi$
$347$	−18.8015			−1.00932			−0.504659	+	0.863319i	$0.668382\pi$
$348$		0			0
$349$	27.9360			1.49538			0.747689	−	0.664049i	$-0.231163\pi$
$349$	27.9360			1.49538			0.747689	+	0.664049i	$0.231163\pi$
$350$		0			0
$351$	0.369938	−	0.463887i	0.0197458	−	0.0247605i
$352$		0			0
$353$	−24.5418	−	11.8187i	−1.30623	−	0.629045i	−0.354231	−	0.935158i	$-0.615257\pi$
$353$	−24.5418	−	11.8187i	−1.30623	−	0.629045i	−0.951995	+	0.306113i	$0.900972\pi$
$354$		0			0
$355$	1.08650	−	1.36243i	0.0576656	−	0.0723104i
$356$		0			0
$357$	−0.685255	−	3.00230i	−0.0362675	−	0.158898i
$358$		0			0
$359$	5.24770	−	22.9917i	0.276963	−	1.21346i	−0.624648	−	0.780907i	$-0.714757\pi$
$359$	5.24770	−	22.9917i	0.276963	−	1.21346i	0.901611	−	0.432548i	$-0.142385\pi$
$360$		0			0
$361$	−6.27192	+	27.4791i	−0.330101	+	1.44627i
$362$		0			0
$363$	−7.68826	+	3.70247i	−0.403529	+	0.194329i
$364$		0			0
$365$	3.10062			0.162294
$366$		0			0
$367$	16.0118	+	20.0781i	0.835809	+	1.04807i	0.998117	+	0.0613309i	$0.0195345\pi$
$367$	16.0118	+	20.0781i	0.835809	+	1.04807i	−0.162309	+	0.986740i	$0.551894\pi$
$368$		0			0
$369$	3.87072	+	16.9587i	0.201502	+	0.882837i
$370$		0			0
$371$	−26.2251	+	12.6293i	−1.36154	+	0.655682i
$372$		0			0
$373$	−20.1533	−	25.2714i	−1.04350	−	1.30851i	−0.949784	−	0.312907i	$-0.898697\pi$
$373$	−20.1533	−	25.2714i	−1.04350	−	1.30851i	−0.0937149	−	0.995599i	$-0.529874\pi$
$374$		0			0
$375$	−2.18136	−	1.05049i	−0.112645	−	0.0542469i
$376$		0			0
$377$	−0.236396	+	0.723832i	−0.0121750	+	0.0372792i
$378$		0			0
$379$	25.4974	+	12.2789i	1.30971	+	0.630725i	0.952853	−	0.303432i	$-0.0981326\pi$
$379$	25.4974	+	12.2789i	1.30971	+	0.630725i	0.356861	+	0.934157i	$0.383847\pi$
$380$		0			0
$381$	−5.39480	−	6.76487i	−0.276384	−	0.346575i
$382$		0			0
$383$	12.5829	−	6.05961i	0.642957	−	0.309632i	−0.0838450	−	0.996479i	$-0.526720\pi$
$383$	12.5829	−	6.05961i	0.642957	−	0.309632i	0.726802	+	0.686847i	$0.241006\pi$
$384$		0			0
$385$	−0.0562235	−	0.246331i	−0.00286542	−	0.0125542i
$386$		0			0
$387$	7.79224	+	9.77116i	0.396102	+	0.496696i
$388$		0			0
$389$	−15.3730			−0.779440			−0.389720	−	0.920933i	$-0.627428\pi$
$389$	−15.3730			−0.779440			−0.389720	+	0.920933i	$0.627428\pi$
$390$		0			0
$391$	−3.30725	+	1.59269i	−0.167255	+	0.0805458i
$392$		0			0
$393$	−2.44474	+	10.7111i	−0.123321	+	0.540303i
$394$		0			0
$395$	0.0285783	−	0.125210i	0.00143793	−	0.00629999i
$396$		0			0
$397$	−1.12252	−	4.91807i	−0.0563375	−	0.246831i	0.938916	−	0.344146i	$-0.111832\pi$
$397$	−1.12252	−	4.91807i	−0.0563375	−	0.246831i	−0.995254	+	0.0973154i	$0.968974\pi$
$398$		0			0
$399$	15.8203	−	19.8380i	0.792006	−	0.993144i
$400$		0			0
$401$	−10.1337	−	4.88016i	−0.506055	−	0.243703i	0.163394	−	0.986561i	$-0.447756\pi$
$401$	−10.1337	−	4.88016i	−0.506055	−	0.243703i	−0.669450	+	0.742857i	$0.733470\pi$
$402$		0			0
$403$	0.247907	−	0.310866i	0.0123491	−	0.0154853i
$404$		0			0
$405$	1.23288			0.0612625
$406$		0			0
$407$	0.00738638			0.000366129
$408$		0			0
$409$	−7.32788	+	9.18887i	−0.362340	+	0.454360i	−0.929267	−	0.369408i	$-0.879561\pi$
$409$	−7.32788	+	9.18887i	−0.362340	+	0.454360i	0.566927	+	0.823768i	$0.308132\pi$
$410$		0			0
$411$	−5.76379	−	2.77569i	−0.284307	−	0.136915i
$412$		0			0
$413$	−40.5867	+	50.8941i	−1.99714	+	2.50433i
$414$		0			0
$415$	−0.181296	−	0.794311i	−0.00889949	−	0.0389912i
$416$		0			0
$417$	−2.15152	+	9.42642i	−0.105360	+	0.461614i
$418$		0			0
$419$	−2.28314	+	10.0031i	−0.111539	+	0.488683i	0.888043	+	0.459761i	$0.152065\pi$
$419$	−2.28314	+	10.0031i	−0.111539	+	0.488683i	−0.999582	+	0.0289228i	$0.990792\pi$
$420$		0			0
$421$	11.3630	−	5.47212i	0.553797	−	0.266695i	−0.135986	−	0.990711i	$-0.543420\pi$
$421$	11.3630	−	5.47212i	0.553797	−	0.266695i	0.689783	+	0.724016i	$0.257706\pi$
$422$		0			0
$423$	21.4608			1.04346
$424$		0			0
$425$	−2.54759	−	3.19457i	−0.123576	−	0.154960i
$426$		0			0
$427$	−11.9046	−	52.1574i	−0.576103	−	2.52407i
$428$		0			0
$429$	−0.0167673	+	0.00807472i	−0.000809534	+	0.000389851i
$430$		0			0
$431$	−20.9860	−	26.3156i	−1.01086	−	1.26758i	−0.963221	−	0.268712i	$-0.913402\pi$
$431$	−20.9860	−	26.3156i	−1.01086	−	1.26758i	−0.0476376	−	0.998865i	$-0.515169\pi$
$432$		0			0
$433$	16.8517	+	8.11533i	0.809839	+	0.389998i	0.792515	−	0.609852i	$-0.208771\pi$
$433$	16.8517	+	8.11533i	0.809839	+	0.389998i	0.0173236	+	0.999850i	$0.494485\pi$
$434$		0			0
$435$	1.23356	−	0.460840i	0.0591447	−	0.0220956i
$436$		0			0
$437$	−27.2503	−	13.1231i	−1.30356	−	0.627761i
$438$		0			0
$439$	8.46549	+	10.6154i	0.404036	+	0.506645i	0.941672	−	0.336532i	$-0.109254\pi$
$439$	8.46549	+	10.6154i	0.404036	+	0.506645i	−0.537636	+	0.843177i	$0.680683\pi$
$440$		0			0
$441$	33.5660	−	16.1645i	1.59838	−	0.769739i
$442$		0			0
$443$	0.535384	+	2.34567i	0.0254369	+	0.111446i	0.986053	−	0.166434i	$-0.0532253\pi$
$443$	0.535384	+	2.34567i	0.0254369	+	0.111446i	−0.960616	+	0.277880i	$0.910368\pi$
$444$		0			0
$445$	−1.73342	−	2.17364i	−0.0821718	−	0.103040i
$446$		0			0
$447$	16.3514			0.773393
$448$		0			0
$449$	20.8552	−	10.0433i	0.984216	−	0.473973i	0.128663	−	0.991688i	$-0.458932\pi$
$449$	20.8552	−	10.0433i	0.984216	−	0.473973i	0.855553	+	0.517715i	$0.173217\pi$
$450$		0			0
$451$	0.273481	−	1.19820i	0.0128777	−	0.0564209i
$452$		0			0
$453$	2.62728	−	11.5109i	0.123440	−	0.540828i
$454$		0			0
$455$	0.0469801	+	0.205833i	0.00220246	+	0.00964960i
$456$		0			0
$457$	−14.8789	+	18.6575i	−0.696005	+	0.872763i	−0.996718	−	0.0809517i	$-0.974204\pi$
$457$	−14.8789	+	18.6575i	−0.696005	+	0.872763i	0.300713	+	0.953715i	$0.402775\pi$
$458$		0			0
$459$	−3.15184	−	1.51785i	−0.147115	−	0.0708470i
$460$		0			0
$461$	16.7526	−	21.0071i	0.780247	−	0.978398i	−0.219749	−	0.975556i	$-0.570524\pi$
$461$	16.7526	−	21.0071i	0.780247	−	0.978398i	0.999996	−	0.00284205i	$-0.000904654\pi$
$462$		0			0
$463$	4.03771			0.187648			0.0938242	−	0.995589i	$-0.470091\pi$
$463$	4.03771			0.187648			0.0938242	+	0.995589i	$0.470091\pi$
$464$		0			0
$465$	−0.687614			−0.0318873
$466$		0			0
$467$	4.47212	−	5.60786i	0.206945	−	0.259501i	−0.667517	−	0.744594i	$-0.732643\pi$
$467$	4.47212	−	5.60786i	0.206945	−	0.259501i	0.874462	+	0.485093i	$0.161214\pi$
$468$		0			0
$469$	29.2699	+	14.0956i	1.35156	+	0.650876i
$470$		0			0
$471$	0.808702	−	1.01408i	0.0372630	−	0.0467263i
$472$		0			0
$473$	−0.196489	−	0.860875i	−0.00903458	−	0.0395831i
$474$		0			0
$475$	7.49160	−	32.8229i	0.343738	−	1.50602i
$476$		0			0
$477$	−3.26641	+	14.3111i	−0.149559	+	0.655259i
$478$		0			0
$479$	11.7384	−	5.65293i	0.536342	−	0.258289i	−0.146047	−	0.989278i	$-0.546655\pi$
$479$	11.7384	−	5.65293i	0.536342	−	0.258289i	0.682390	+	0.730989i	$0.260941\pi$
$480$		0			0
$481$	−0.00617202			−0.000281420
$482$		0			0
$483$	10.1407	+	12.7160i	0.461416	+	0.578597i
$484$		0			0
$485$	−0.748735	−	3.28042i	−0.0339983	−	0.148956i
$486$		0			0
$487$	−7.26600	+	3.49912i	−0.329254	+	0.158560i	−0.591206	−	0.806521i	$-0.701348\pi$
$487$	−7.26600	+	3.49912i	−0.329254	+	0.158560i	0.261952	+	0.965081i	$0.415634\pi$
$488$		0			0
$489$	1.46514	+	1.83722i	0.0662558	+	0.0830822i
$490$		0			0
$491$	−37.9934	−	18.2967i	−1.71462	−	0.825717i	−0.990737	−	0.135791i	$-0.956642\pi$
$491$	−37.9934	−	18.2967i	−1.71462	−	0.825717i	−0.723881	−	0.689925i	$-0.757643\pi$
$492$		0			0
$493$	4.47084	+	0.409186i	0.201356	+	0.0184288i
$494$		0			0
$495$	−0.114802	−	0.0552858i	−0.00515998	−	0.00248491i
$496$		0			0
$497$	−16.4127	−	20.5809i	−0.736210	−	0.923179i
$498$		0			0
$499$	−31.5591	+	15.1981i	−1.41278	+	0.680359i	−0.975710	−	0.219068i	$-0.929698\pi$
$499$	−31.5591	+	15.1981i	−1.41278	+	0.680359i	−0.437071	+	0.899427i	$0.643984\pi$
$500$		0			0
$501$	2.60962	+	11.4335i	0.116589	+	0.510810i
$502$		0			0
$503$	−11.7304	−	14.7095i	−0.523033	−	0.655862i	0.448217	−	0.893925i	$-0.352059\pi$
$503$	−11.7304	−	14.7095i	−0.523033	−	0.655862i	−0.971250	+	0.238062i	$0.923488\pi$
$504$		0			0
$505$	−0.218975			−0.00974426
$506$		0			0
$507$	−9.09582	+	4.38032i	−0.403960	+	0.194537i
$508$		0			0
$509$	5.92001	−	25.9373i	0.262400	−	1.14965i	−0.656240	−	0.754552i	$-0.727854\pi$
$509$	5.92001	−	25.9373i	0.262400	−	1.14965i	0.918640	−	0.395097i	$-0.129289\pi$
$510$		0			0
$511$	10.4224	−	45.6636i	0.461061	−	2.02004i
$512$		0			0
$513$	−6.41401	−	28.1016i	−0.283185	−	1.24072i
$514$		0			0
$515$	−1.36041	+	1.70590i	−0.0599470	+	0.0751711i
$516$		0			0
$517$	−1.36613	−	0.657893i	−0.0600823	−	0.0289341i
$518$		0			0
$519$	−7.28329	+	9.13296i	−0.319701	+	0.400893i
$520$		0			0
$521$	−22.8061			−0.999154			−0.499577	−	0.866269i	$-0.666511\pi$
$521$	−22.8061			−0.999154			−0.499577	+	0.866269i	$0.666511\pi$
$522$		0			0
$523$	35.0763			1.53378			0.766890	−	0.641778i	$-0.221803\pi$
$523$	35.0763			1.53378			0.766890	+	0.641778i	$0.221803\pi$
$524$		0			0
$525$	−11.2878	+	14.1544i	−0.492639	+	0.617749i
$526$		0			0
$527$	−2.11215	−	1.01716i	−0.0920066	−	0.0443080i
$528$		0			0
$529$	−2.25260	+	2.82467i	−0.0979390	+	0.122812i
$530$		0			0
$531$	7.30496	+	32.0051i	0.317008	+	1.38890i
$532$		0			0
$533$	−0.228519	+	1.00121i	−0.00989826	+	0.0433671i
$534$		0			0
$535$	−0.0223304	+	0.0978359i	−0.000965428	+	0.00422982i
$536$		0			0
$537$	11.1369	−	5.36323i	0.480591	−	0.231441i
$538$		0			0
$539$	−2.63224			−0.113378
$540$		0			0
$541$	20.3147	+	25.4738i	0.873397	+	1.09521i	0.994723	+	0.102593i	$0.0327139\pi$
$541$	20.3147	+	25.4738i	0.873397	+	1.09521i	−0.121326	+	0.992613i	$0.538715\pi$
$542$		0			0
$543$	−2.08311	−	9.12671i	−0.0893948	−	0.391664i
$544$		0			0
$545$	0.911002	−	0.438715i	0.0390230	−	0.0187925i
$546$		0			0
$547$	−18.7444	−	23.5048i	−0.801454	−	1.00499i	−0.999692	−	0.0248373i	$-0.992093\pi$
$547$	−18.7444	−	23.5048i	−0.801454	−	1.00499i	0.198238	−	0.980154i	$-0.436478\pi$
$548$		0			0
$549$	−24.3078	−	11.7060i	−1.03743	−	0.499601i
$550$		0			0
$551$	20.3320	+	30.9030i	0.866172	+	1.31651i
$552$		0			0
$553$	−1.74793	−	0.841760i	−0.0743297	−	0.0357953i
$554$		0			0
$555$	0.00665490	+	0.00834498i	0.000282485	+	0.000354225i
$556$		0			0
$557$	11.2931	−	5.43845i	0.478502	−	0.230435i	−0.179055	−	0.983839i	$-0.557304\pi$
$557$	11.2931	−	5.43845i	0.478502	−	0.230435i	0.657557	+	0.753404i	$0.271590\pi$
$558$		0			0
$559$	0.164185	+	0.719342i	0.00694429	+	0.0304249i
$560$		0			0
$561$	0.0684130	+	0.0857872i	0.00288840	+	0.00362194i
$562$		0			0
$563$	21.4944			0.905880			0.452940	−	0.891541i	$-0.350375\pi$
$563$	21.4944			0.905880			0.452940	+	0.891541i	$0.350375\pi$
$564$		0			0
$565$	4.70665	−	2.26660i	0.198010	−	0.0953567i
$566$		0			0
$567$	4.14421	−	18.1570i	0.174041	−	0.762522i
$568$		0			0
$569$	2.63858	−	11.5604i	0.110615	−	0.484636i	−0.889026	−	0.457856i	$-0.848617\pi$
$569$	2.63858	−	11.5604i	0.110615	−	0.484636i	0.999641	−	0.0267800i	$-0.00852536\pi$
$570$		0			0
$571$	0.334836	+	1.46701i	0.0140125	+	0.0613926i	0.981451	−	0.191714i	$-0.0614047\pi$
$571$	0.334836	+	1.46701i	0.0140125	+	0.0613926i	−0.967438	+	0.253107i	$0.918548\pi$
$572$		0			0
$573$	9.96405	−	12.4945i	0.416254	−	0.521966i
$574$		0			0
$575$	19.4431	+	9.36329i	0.810832	+	0.390476i
$576$		0			0
$577$	2.80268	−	3.51445i	0.116677	−	0.146308i	−0.720063	−	0.693909i	$-0.755887\pi$
$577$	2.80268	−	3.51445i	0.116677	−	0.146308i	0.836740	+	0.547600i	$0.184459\pi$
$578$		0			0
$579$	17.8789			0.743021
$580$		0			0
$581$	−12.3074			−0.510598
$582$		0			0
$583$	0.646643	−	0.810864i	0.0267812	−	0.0335826i
$584$		0			0
$585$	0.0959280	+	0.0461965i	0.00396614	+	0.00190999i
$586$		0			0
$587$	4.58550	−	5.75003i	0.189264	−	0.237329i	−0.678142	−	0.734931i	$-0.737214\pi$
$587$	4.58550	−	5.75003i	0.189264	−	0.237329i	0.867406	+	0.497602i	$0.165786\pi$
$588$		0			0
$589$	−4.29823	−	18.8318i	−0.177105	−	0.775950i
$590$		0			0
$591$	−4.16663	+	18.2552i	−0.171392	+	0.750919i
$592$		0			0
$593$	−3.20016	+	14.0208i	−0.131415	+	0.575766i	0.865747	+	0.500481i	$0.166844\pi$
$593$	−3.20016	+	14.0208i	−0.131415	+	0.575766i	−0.997162	+	0.0752844i	$0.976014\pi$
$594$		0			0
$595$	1.12152	−	0.540096i	0.0459779	−	0.0221418i
$596$		0			0
$597$	2.76085			0.112994
$598$		0			0
$599$	0.894048	+	1.12110i	0.0365298	+	0.0458069i	0.799761	−	0.600319i	$-0.204960\pi$
$599$	0.894048	+	1.12110i	0.0365298	+	0.0458069i	−0.763231	+	0.646126i	$0.776388\pi$
$600$		0			0
$601$	−2.01041	−	8.80820i	−0.0820065	−	0.359294i	0.917230	−	0.398358i	$-0.130420\pi$
$601$	−2.01041	−	8.80820i	−0.0820065	−	0.359294i	−0.999237	+	0.0390636i	$0.987563\pi$
$602$		0			0
$603$	14.7609	−	7.10850i	0.601112	−	0.289480i
$604$		0			0
$605$	−2.15062	−	2.69679i	−0.0874352	−	0.109640i
$606$		0			0
$607$	23.8794	+	11.4997i	0.969235	+	0.466759i	0.850390	−	0.526154i	$-0.176366\pi$
$607$	23.8794	+	11.4997i	0.969235	+	0.466759i	0.118846	+	0.992913i	$0.462081\pi$
$608$		0			0
$609$	−2.64042	−	19.7160i	−0.106995	−	0.798933i
$610$		0			0
$611$	1.14153	+	0.549731i	0.0461813	+	0.0222397i
$612$		0			0
$613$	7.99807	+	10.0293i	0.323039	+	0.405078i	0.916661	−	0.399666i	$-0.130874\pi$
$613$	7.99807	+	10.0293i	0.323039	+	0.405078i	−0.593622	+	0.804744i	$0.702302\pi$
$614$		0			0
$615$	1.60010	−	0.770566i	0.0645221	−	0.0310722i
$616$		0			0
$617$	5.15193	+	22.5721i	0.207409	+	0.908718i	0.966283	+	0.257481i	$0.0828924\pi$
$617$	5.15193	+	22.5721i	0.207409	+	0.908718i	−0.758874	+	0.651237i	$0.774250\pi$
$618$		0			0
$619$	−7.93934	−	9.95562i	−0.319109	−	0.400150i	0.596243	−	0.802804i	$-0.296659\pi$
$619$	−7.93934	−	9.95562i	−0.319109	−	0.400150i	−0.915352	+	0.402654i	$0.868088\pi$
$620$		0			0
$621$	18.4761			0.741420
$622$		0			0
$623$	−37.8384	+	18.2220i	−1.51596	+	0.730049i
$624$		0			0
$625$	−5.23528	+	22.9372i	−0.209411	+	0.917490i
$626$		0			0
$627$	−0.201180	+	0.881426i	−0.00803435	+	0.0352008i
$628$		0			0
$629$	0.00809754	+	0.0354776i	0.000322870	+	0.00141459i
$630$		0			0
$631$	−25.2246	+	31.6306i	−1.00417	+	1.25919i	−0.0385490	+	0.999257i	$0.512274\pi$
$631$	−25.2246	+	31.6306i	−1.00417	+	1.25919i	−0.965625	+	0.259938i	$0.916298\pi$
$632$		0			0
$633$	3.55011	+	1.70964i	0.141104	+	0.0679522i
$634$		0			0
$635$	2.18068	−	2.73449i	0.0865377	−	0.108515i
$636$		0			0
$637$	2.19948			0.0871466
$638$		0			0
$639$	−13.2753			−0.525162
$640$		0			0
$641$	−5.16384	+	6.47525i	−0.203959	+	0.255757i	−0.873282	−	0.487215i	$-0.838013\pi$
$641$	−5.16384	+	6.47525i	−0.203959	+	0.255757i	0.669323	+	0.742972i	$0.266584\pi$
$642$		0			0
$643$	−29.8817	−	14.3903i	−1.17842	−	0.567496i	−0.260968	−	0.965347i	$-0.584042\pi$
$643$	−29.8817	−	14.3903i	−1.17842	−	0.567496i	−0.917450	+	0.397851i	$0.869756\pi$
$644$		0			0
$645$	0.795568	−	0.997611i	0.0313255	−	0.0392809i
$646$		0			0
$647$	0.596752	+	2.61454i	0.0234607	+	0.102788i	0.985303	−	0.170817i	$-0.0546408\pi$
$647$	0.596752	+	2.61454i	0.0234607	+	0.102788i	−0.961842	+	0.273606i	$0.911784\pi$
$648$		0			0
$649$	0.516123	−	2.26128i	0.0202596	−	0.0887631i
$650$		0			0
$651$	−2.31134	+	10.1267i	−0.0905887	+	0.396895i
$652$		0			0
$653$	−32.2035	+	15.5084i	−1.26022	+	0.606891i	−0.940233	−	0.340531i	$-0.889393\pi$
$653$	−32.2035	+	15.5084i	−1.26022	+	0.606891i	−0.319988	+	0.947421i	$0.603679\pi$
$654$		0			0
$655$	−4.44097			−0.173523
$656$		0			0
$657$	−14.7272	−	18.4673i	−0.574563	−	0.720479i
$658$		0			0
$659$	8.14765	+	35.6972i	0.317387	+	1.39056i	0.842116	+	0.539296i	$0.181309\pi$
$659$	8.14765	+	35.6972i	0.317387	+	1.39056i	−0.524729	+	0.851269i	$0.675833\pi$
$660$		0			0
$661$	−0.309764	+	0.149174i	−0.0120484	+	0.00580221i	−0.439898	−	0.898048i	$-0.644985\pi$
$661$	−0.309764	+	0.149174i	−0.0120484	+	0.00580221i	0.427850	+	0.903850i	$0.359271\pi$
$662$		0			0
$663$	−0.0571655	−	0.0716832i	−0.00222012	−	0.00278395i
$664$		0			0
$665$	9.24085	+	4.45016i	0.358345	+	0.172570i
$666$		0			0
$667$	−22.2119	+	8.29804i	−0.860048	+	0.321301i
$668$		0			0
$669$	−9.97349	−	4.80298i	−0.385597	−	0.185694i
$670$		0			0
$671$	1.18850	+	1.49034i	0.0458817	+	0.0575338i
$672$		0			0
$673$	21.2405	−	10.2289i	0.818759	−	0.394294i	0.0228719	−	0.999738i	$-0.492719\pi$
$673$	21.2405	−	10.2289i	0.818759	−	0.394294i	0.795887	+	0.605445i	$0.207005\pi$
$674$		0			0
$675$	4.57639	+	20.0505i	0.176145	+	0.771743i
$676$		0			0
$677$	18.6941	+	23.4417i	0.718472	+	0.900936i	0.998250	−	0.0591288i	$-0.0188323\pi$
$677$	18.6941	+	23.4417i	0.718472	+	0.900936i	−0.279778	+	0.960065i	$0.590261\pi$
$678$		0			0
$679$	−50.8284			−1.95061
$680$		0			0
$681$	−5.98813	+	2.88373i	−0.229466	+	0.110505i
$682$		0			0
$683$	−6.68579	+	29.2924i	−0.255825	+	1.12084i	0.669843	+	0.742503i	$0.266362\pi$
$683$	−6.68579	+	29.2924i	−0.255825	+	1.12084i	−0.925667	+	0.378338i	$0.876496\pi$
$684$		0			0
$685$	0.575421	−	2.52108i	0.0219857	−	0.0963256i
$686$		0			0
$687$	4.22268	+	18.5008i	0.161105	+	0.705848i
$688$		0			0
$689$	−0.540331	+	0.677553i	−0.0205850	+	0.0258127i
$690$		0			0
$691$	−21.2021	−	10.2104i	−0.806565	−	0.388421i	−0.0152910	−	0.999883i	$-0.504867\pi$
$691$	−21.2021	−	10.2104i	−0.806565	−	0.388421i	−0.791274	+	0.611462i	$0.790582\pi$
$692$		0			0
$693$	−1.20010	+	1.50488i	−0.0455882	+	0.0571657i
$694$		0			0
$695$	−3.90833			−0.148251
$696$		0			0
$697$	6.05489			0.229345
$698$		0			0
$699$	2.78845	−	3.49660i	0.105469	−	0.132254i
$700$		0			0
$701$	27.7710	+	13.3738i	1.04890	+	0.505122i	0.877249	−	0.480036i	$-0.159377\pi$
$701$	27.7710	+	13.3738i	1.04890	+	0.505122i	0.171648	+	0.985158i	$0.445091\pi$
$702$		0			0
$703$	−0.186946	+	0.234423i	−0.00705080	+	0.00884142i
$704$		0			0
$705$	−0.487566	−	2.13616i	−0.0183628	−	0.0804526i
$706$		0			0
$707$	−0.736062	+	3.22490i	−0.0276824	+	0.121285i
$708$		0			0
$709$	3.35318	−	14.6912i	0.125931	−	0.551741i	−0.872117	−	0.489297i	$-0.837253\pi$
$709$	3.35318	−	14.6912i	0.125931	−	0.551741i	0.998048	−	0.0624440i	$-0.0198895\pi$
$710$		0			0
$711$	−0.881491	+	0.424504i	−0.0330585	+	0.0159201i
$712$		0			0
$713$	12.3814			0.463687
$714$		0			0
$715$	−0.00469029	−	0.00588144i	−0.000175407	−	0.000219953i
$716$		0			0
$717$	3.43574	+	15.0529i	0.128310	+	0.562162i
$718$		0			0
$719$	−9.92635	+	4.78028i	−0.370190	+	0.178274i	−0.609724	−	0.792614i	$-0.708720\pi$
$719$	−9.92635	+	4.78028i	−0.370190	+	0.178274i	0.239534	+	0.970888i	$0.423005\pi$
$720$		0			0
$721$	20.5504	+	25.7694i	0.765336	+	0.959701i
$722$		0			0
$723$	20.6265	+	9.93322i	0.767109	+	0.369420i
$724$		0			0
$725$	−14.5069	−	22.0493i	−0.538771	−	0.818889i
$726$		0			0
$727$	27.6605	+	13.3206i	1.02587	+	0.494034i	0.869640	−	0.493687i	$-0.164351\pi$
$727$	27.6605	+	13.3206i	1.02587	+	0.494034i	0.156232	+	0.987720i	$0.450065\pi$
$728$		0			0
$729$	0.248758	+	0.311932i	0.00921325	+	0.0115531i
$730$		0			0
$731$	3.91948	−	1.88752i	0.144967	−	0.0698124i
$732$		0			0
$733$	−0.164735	−	0.721753i	−0.00608464	−	0.0266585i	0.971794	−	0.235829i	$-0.0757807\pi$
$733$	−0.164735	−	0.721753i	−0.00608464	−	0.0266585i	−0.977879	+	0.209171i	$0.932924\pi$
$734$		0			0
$735$	−2.37156	−	2.97384i	−0.0874764	−	0.109692i
$736$		0			0
$737$	−1.15755			−0.0426389
$738$		0			0
$739$	−0.971272	+	0.467740i	−0.0357288	+	0.0172061i	−0.451663	−	0.892189i	$-0.649169\pi$
$739$	−0.971272	+	0.467740i	−0.0357288	+	0.0172061i	0.415934	+	0.909395i	$0.363455\pi$
$740$		0			0
$741$	0.168105	−	0.736514i	0.00617548	−	0.0270565i
$742$		0			0
$743$	−2.19512	+	9.61745i	−0.0805311	+	0.352830i	−0.999099	−	0.0424325i	$-0.986489\pi$
$743$	−2.19512	+	9.61745i	−0.0805311	+	0.352830i	0.918568	+	0.395263i	$0.129346\pi$
$744$		0			0
$745$	1.47076	+	6.44381i	0.0538844	+	0.236083i
$746$		0			0
$747$	−3.86981	+	4.85259i	−0.141589	+	0.177547i
$748$		0			0
$749$	1.36579	+	0.657731i	0.0499050	+	0.0240330i
$750$		0			0
$751$	−8.69818	+	10.9072i	−0.317401	+	0.398008i	−0.914781	−	0.403950i	$-0.867637\pi$
$751$	−8.69818	+	10.9072i	−0.317401	+	0.398008i	0.597380	+	0.801958i	$0.296208\pi$
$752$		0			0
$753$	2.07132			0.0754832
$754$		0			0
$755$	4.77257			0.173691
$756$		0			0
$757$	16.5295	−	20.7274i	0.600776	−	0.753350i	−0.384722	−	0.923032i	$-0.625703\pi$
$757$	16.5295	−	20.7274i	0.600776	−	0.753350i	0.985499	+	0.169683i	$0.0542743\pi$
$758$		0			0
$759$	−0.522125	−	0.251442i	−0.0189519	−	0.00912677i
$760$		0			0
$761$	25.8928	−	32.4686i	0.938614	−	1.17699i	−0.0454129	−	0.998968i	$-0.514460\pi$
$761$	25.8928	−	32.4686i	0.938614	−	1.17699i	0.984027	−	0.178017i	$-0.0569682\pi$
$762$		0			0
$763$	−3.39883	−	14.8912i	−0.123046	−	0.539099i
$764$		0			0
$765$	0.139689	−	0.612017i	0.00505046	−	0.0221275i
$766$		0			0
$767$	−0.431269	+	1.88951i	−0.0155722	+	0.0682264i
$768$		0			0
$769$	−10.1217	+	4.87437i	−0.364999	+	0.175774i	−0.607389	−	0.794405i	$-0.707783\pi$
$769$	−10.1217	+	4.87437i	−0.364999	+	0.175774i	0.242390	+	0.970179i	$0.422069\pi$
$770$		0			0
$771$	−6.81884			−0.245574
$772$		0			0
$773$	−33.4688	−	41.9685i	−1.20379	−	1.50950i	−0.805882	−	0.592076i	$-0.798308\pi$
$773$	−33.4688	−	41.9685i	−1.20379	−	1.50950i	−0.397906	−	0.917426i	$-0.630263\pi$
$774$		0			0
$775$	3.06678	+	13.4364i	0.110162	+	0.482651i
$776$		0			0
$777$	0.145268	−	0.0699575i	0.00521147	−	0.00250971i
$778$		0			0
$779$	31.1057	+	39.0053i	1.11448	+	1.39751i
$780$		0			0
$781$	0.845062	+	0.406960i	0.0302387	+	0.0145622i
$782$		0			0
$783$	−19.3809	−	11.6193i	−0.692618	−	0.415240i
$784$		0			0
$785$	0.472373	+	0.227483i	0.0168597	+	0.00811921i
$786$		0			0
$787$	8.92069	+	11.1862i	0.317988	+	0.398745i	0.914978	−	0.403504i	$-0.132208\pi$
$787$	8.92069	+	11.1862i	0.317988	+	0.398745i	−0.596989	+	0.802249i	$0.703637\pi$
$788$		0			0
$789$	−12.8503	+	6.18838i	−0.457483	+	0.220312i
$790$		0			0
$791$	−17.5599	−	76.9349i	−0.624358	−	2.73549i
$792$		0			0
$793$	−0.993107	−	1.24532i	−0.0352663	−	0.0442225i
$794$		0			0
$795$	1.49870			0.0531535
$796$		0			0
$797$	15.7364	−	7.57824i	0.557411	−	0.268435i	−0.133897	−	0.990995i	$-0.542749\pi$
$797$	15.7364	−	7.57824i	0.557411	−	0.268435i	0.691308	+	0.722560i	$0.257035\pi$
$798$		0			0
$799$	1.66228	−	7.28290i	0.0588071	−	0.257651i
$800$		0			0
$801$	−4.71288	+	20.6485i	−0.166521	+	0.729578i
$802$		0			0
$803$	0.371361	+	1.62704i	0.0131051	+	0.0574170i
$804$		0			0
$805$	−4.09904	+	5.14004i	−0.144472	+	0.181163i
$806$		0			0
$807$	−11.6365	−	5.60383i	−0.409624	−	0.197264i
$808$		0			0
$809$	−21.1520	+	26.5238i	−0.743666	+	0.932528i	−0.999414	−	0.0342154i	$-0.989107\pi$
$809$	−21.1520	+	26.5238i	−0.743666	+	0.932528i	0.255748	+	0.966743i	$0.417678\pi$
$810$		0			0
$811$	−6.50175			−0.228307			−0.114154	−	0.993463i	$-0.536416\pi$
$811$	−6.50175			−0.228307			−0.114154	+	0.993463i	$0.536416\pi$
$812$		0			0
$813$	−17.7099			−0.621113
$814$		0			0
$815$	−0.592236	+	0.742641i	−0.0207451	+	0.0260136i
$816$		0			0
$817$	32.2948	+	15.5523i	1.12985	+	0.544108i
$818$		0			0
$819$	1.00280	−	1.25747i	0.0350406	−	0.0439396i
$820$		0			0
$821$	2.99783	+	13.1344i	0.104625	+	0.458393i	0.999917	+	0.0129119i	$0.00411010\pi$
$821$	2.99783	+	13.1344i	0.104625	+	0.458393i	−0.895292	+	0.445481i	$0.853033\pi$
$822$		0			0
$823$	2.52274	−	11.0528i	0.0879371	−	0.385277i	−0.911738	−	0.410772i	$-0.865259\pi$
$823$	2.52274	−	11.0528i	0.0879371	−	0.385277i	0.999675	+	0.0254950i	$0.00811620\pi$
$824$		0			0
$825$	0.143542	−	0.628897i	0.00499747	−	0.0218954i
$826$		0			0
$827$	50.9720	−	24.5468i	1.77247	−	0.853577i	0.808091	−	0.589058i	$-0.200501\pi$
$827$	50.9720	−	24.5468i	1.77247	−	0.853577i	0.964380	−	0.264519i	$-0.0852133\pi$
$828$		0			0
$829$	−42.4183			−1.47325			−0.736625	−	0.676302i	$-0.763582\pi$
$829$	−42.4183			−1.47325			−0.736625	+	0.676302i	$0.763582\pi$
$830$		0			0
$831$	9.73643	+	12.2091i	0.337753	+	0.423529i
$832$		0			0
$833$	−2.88566	−	12.6429i	−0.0999824	−	0.438051i
$834$		0			0
$835$	−4.27103	+	2.05682i	−0.147805	+	0.0711792i
$836$		0			0
$837$	7.35692	+	9.22529i	0.254292	+	0.318873i
$838$		0			0
$839$	−8.46345	−	4.07578i	−0.292191	−	0.140712i	0.282046	−	0.959401i	$-0.408987\pi$
$839$	−8.46345	−	4.07578i	−0.292191	−	0.140712i	−0.574237	+	0.818689i	$0.694701\pi$
$840$		0			0
$841$	28.5182	+	5.26426i	0.983386	+	0.181526i
$842$		0			0
$843$	16.8407	+	8.11005i	0.580025	+	0.279325i
$844$		0			0
$845$	−2.54436	−	3.19052i	−0.0875286	−	0.109757i
$846$		0			0
$847$	−46.9454	+	22.6077i	−1.61306	+	0.776810i
$848$		0			0
$849$	−2.29485	−	10.0544i	−0.0787591	−	0.345066i
$850$		0			0
$851$	−0.119830	−	0.150263i	−0.00410773	−	0.00515093i
$852$		0			0
$853$	5.84208			0.200029			0.100014	−	0.994986i	$-0.468111\pi$
$853$	5.84208			0.200029			0.100014	+	0.994986i	$0.468111\pi$
$854$		0			0
$855$	4.66020	−	2.24424i	0.159376	−	0.0767512i
$856$		0			0
$857$	7.65274	−	33.5288i	0.261413	−	1.14532i	−0.658308	−	0.752749i	$-0.728727\pi$
$857$	7.65274	−	33.5288i	0.261413	−	1.14532i	0.919720	−	0.392575i	$-0.128415\pi$
$858$		0			0
$859$	−1.12166	+	4.91432i	−0.0382706	+	0.167674i	−0.990452	−	0.137859i	$-0.955978\pi$
$859$	−1.12166	+	4.91432i	−0.0382706	+	0.167674i	0.952181	+	0.305534i	$0.0988349\pi$
$860$		0			0
$861$	−5.96975	−	26.1552i	−0.203449	−	0.891367i
$862$		0			0
$863$	31.7122	−	39.7658i	1.07950	−	1.35365i	0.148377	−	0.988931i	$-0.452595\pi$
$863$	31.7122	−	39.7658i	1.07950	−	1.35365i	0.931120	−	0.364714i	$-0.118833\pi$
$864$		0			0
$865$	−4.25427	−	2.04875i	−0.144649	−	0.0696595i
$866$		0			0
$867$	7.90691	−	9.91495i	0.268533	−	0.336729i
$868$		0			0
$869$	0.0691262			0.00234495
$870$		0			0
$871$	0.967241			0.0327737
$872$		0			0
$873$	−15.9819	+	20.0407i	−0.540906	+	0.678274i
$874$		0			0
$875$	−13.3196	−	6.41440i	−0.450286	−	0.216846i
$876$		0			0
$877$	25.3113	−	31.7393i	0.854701	−	1.07176i	−0.141941	−	0.989875i	$-0.545334\pi$
$877$	25.3113	−	31.7393i	0.854701	−	1.07176i	0.996642	−	0.0818861i	$-0.0260944\pi$
$878$		0			0
$879$	−3.68184	−	16.1312i	−0.124185	−	0.544092i
$880$		0			0
$881$	−4.20165	+	18.4086i	−0.141557	+	0.620202i	0.853517	+	0.521065i	$0.174465\pi$
$881$	−4.20165	+	18.4086i	−0.141557	+	0.620202i	−0.995074	+	0.0991366i	$0.968392\pi$
$882$		0			0
$883$	9.55925	−	41.8818i	0.321694	−	1.40944i	−0.512842	−	0.858483i	$-0.671407\pi$
$883$	9.55925	−	41.8818i	0.321694	−	1.40944i	0.834537	−	0.550952i	$-0.185735\pi$
$884$		0			0
$885$	3.01976	−	1.45424i	0.101508	−	0.0488837i
$886$		0			0
$887$	26.6470			0.894718			0.447359	−	0.894354i	$-0.352365\pi$
$887$	26.6470			0.894718			0.447359	+	0.894354i	$0.352365\pi$
$888$		0			0
$889$	−32.9413	−	41.3071i	−1.10482	−	1.38540i
$890$		0			0
$891$	0.147662	+	0.646952i	0.00494688	+	0.0216737i
$892$		0			0
$893$	55.4557	−	26.7061i	1.85575	−	0.893684i
$894$		0			0
$895$	3.11529	+	3.90646i	0.104133	+	0.130578i
$896$		0			0
$897$	0.436284	+	0.210104i	0.0145671	+	0.00701515i
$898$		0			0
$899$	−12.9878	−	7.78645i	−0.433166	−	0.259693i
$900$		0			0
$901$	4.60357	+	2.21696i	0.153367	+	0.0738578i
$902$		0			0
$903$	−12.0178	−	15.0699i	−0.399929	−	0.501495i
$904$		0			0
$905$	3.40932	−	1.64184i	0.113330	−	0.0545767i
$906$		0			0
$907$	3.16965	+	13.8871i	0.105246	+	0.461114i	0.999897	+	0.0143481i	$0.00456730\pi$
$907$	3.16965	+	13.8871i	0.105246	+	0.461114i	−0.894651	+	0.446766i	$0.852576\pi$
$908$		0			0
$909$	1.04008	+	1.30422i	0.0344972	+	0.0432581i
$910$		0			0
$911$	−31.0572			−1.02897			−0.514486	−	0.857499i	$-0.672017\pi$
$911$	−31.0572			−1.02897			−0.514486	+	0.857499i	$0.672017\pi$
$912$		0			0
$913$	0.395098	−	0.190269i	0.0130758	−	0.00629699i
$914$		0			0
$915$	−0.612947	+	2.68550i	−0.0202634	+	0.0887797i
$916$		0			0
$917$	−14.9279	+	65.4032i	−0.492961	+	2.15980i
$918$		0			0
$919$	13.3168	+	58.3448i	0.439281	+	1.92462i	0.375995	+	0.926622i	$0.377301\pi$
$919$	13.3168	+	58.3448i	0.439281	+	1.92462i	0.0632868	+	0.997995i	$0.479842\pi$
$920$		0			0
$921$	15.2062	−	19.0679i	0.501061	−	0.628310i
$922$		0			0
$923$	−0.706129	−	0.340054i	−0.0232425	−	0.0111930i
$924$		0			0
$925$	0.133386	−	0.167260i	0.00438569	−	0.00549948i
$926$		0			0
$927$	16.6220			0.545938
$928$		0			0
$929$	−36.2614			−1.18970			−0.594850	−	0.803837i	$-0.702788\pi$
$929$	−36.2614			−1.18970			−0.594850	+	0.803837i	$0.702788\pi$
$930$		0			0
$931$	66.6206	−	83.5396i	2.18340	−	2.73790i
$932$		0			0
$933$	5.36953	+	2.58583i	0.175791	+	0.0846563i
$934$		0			0
$935$	−0.0276538	+	0.0346768i	−0.000904377	+	0.00113405i
$936$		0			0
$937$	3.38074	+	14.8120i	0.110444	+	0.483886i	0.999652	+	0.0263830i	$0.00839895\pi$
$937$	3.38074	+	14.8120i	0.110444	+	0.483886i	−0.889208	+	0.457503i	$0.848744\pi$
$938$		0			0
$939$	0.177879	−	0.779339i	0.00580486	−	0.0254328i
$940$		0			0
$941$	5.82994	−	25.5426i	0.190050	−	0.832666i	−0.786537	−	0.617544i	$-0.788128\pi$
$941$	5.82994	−	25.5426i	0.190050	−	0.832666i	0.976587	−	0.215122i	$-0.0690149\pi$
$942$		0			0
$943$	−28.8119	+	13.8751i	−0.938244	+	0.451835i
$944$		0			0
$945$	−6.26542			−0.203814
$946$		0			0
$947$	−0.105109	−	0.131803i	−0.00341559	−	0.00428301i	0.780121	−	0.625629i	$-0.215158\pi$
$947$	−0.105109	−	0.131803i	−0.00341559	−	0.00428301i	−0.783536	+	0.621346i	$0.786586\pi$
$948$		0			0
$949$	−0.310307	−	1.35954i	−0.0100730	−	0.0441327i
$950$		0			0
$951$	2.96730	−	1.42898i	0.0962214	−	0.0463378i
$952$		0			0
$953$	−16.1765	−	20.2847i	−0.524008	−	0.657085i	0.447447	−	0.894311i	$-0.352333\pi$
$953$	−16.1765	−	20.2847i	−0.524008	−	0.657085i	−0.971455	+	0.237226i	$0.923762\pi$
$954$		0			0
$955$	5.82013	+	2.80283i	0.188335	+	0.0906974i
$956$		0			0
$957$	0.389568	+	0.592112i	0.0125929	+	0.0191402i
$958$		0			0
$959$	−35.1944	−	16.9487i	−1.13649	−	0.547303i
$960$		0			0
$961$	−14.3981	−	18.0546i	−0.464454	−	0.582407i
$962$		0			0
$963$	0.688775	−	0.331697i	0.0221955	−	0.0106888i
$964$		0			0
$965$	1.60816	+	7.04579i	0.0517684	+	0.226812i
$966$		0			0
$967$	−30.8894	−	38.7341i	−0.993337	−	1.24561i	−0.969297	−	0.245895i	$-0.920918\pi$
$967$	−30.8894	−	38.7341i	−0.993337	−	1.24561i	−0.0240406	−	0.999711i	$-0.507653\pi$
$968$		0			0
$969$	−4.45414			−0.143088
$970$		0			0
$971$	37.5083	−	18.0630i	1.20370	−	0.579671i	0.278970	−	0.960300i	$-0.410007\pi$
$971$	37.5083	−	18.0630i	1.20370	−	0.579671i	0.924728	+	0.380629i	$0.124293\pi$
$972$		0			0
$973$	−13.1374	+	57.5589i	−0.421167	+	1.84525i
$974$		0			0
$975$	−0.119942	+	0.525502i	−0.00384123	+	0.0168295i
$976$		0			0
$977$	6.67802	+	29.2583i	0.213649	+	0.936056i	0.962064	+	0.272825i	$0.0879581\pi$
$977$	6.67802	+	29.2583i	0.213649	+	0.936056i	−0.748415	+	0.663231i	$0.769185\pi$
$978$		0			0
$979$	0.932996	−	1.16994i	0.0298187	−	0.0373915i
$980$		0			0
$981$	−6.94003	−	3.34214i	−0.221578	−	0.106706i
$982$		0			0
$983$	26.9774	−	33.8286i	0.860446	−	1.07896i	−0.135657	−	0.990756i	$-0.543314\pi$
$983$	26.9774	−	33.8286i	0.860446	−	1.07896i	0.996102	−	0.0882086i	$-0.0281142\pi$
$984$		0			0
$985$	−7.56887			−0.241164
$986$		0			0
$987$	−33.0987			−1.05354
$988$		0			0
$989$	−14.3253	+	17.9633i	−0.455517	+	0.571201i
$990$		0			0
$991$	−5.82835	−	2.80678i	−0.185144	−	0.0891604i	0.339016	−	0.940781i	$-0.389906\pi$
$991$	−5.82835	−	2.80678i	−0.185144	−	0.0891604i	−0.524159	+	0.851620i	$0.675620\pi$
$992$		0			0
$993$	−6.96249	+	8.73069i	−0.220948	+	0.277060i
$994$		0			0
$995$	0.248330	+	1.08801i	0.00787259	+	0.0344921i
$996$		0			0
$997$	−3.27086	+	14.3306i	−0.103589	+	0.453854i	0.896356	+	0.443336i	$0.146205\pi$
$997$	−3.27086	+	14.3306i	−0.103589	+	0.453854i	−0.999945	+	0.0105178i	$0.996652\pi$
$998$		0			0
$999$	0.0407573	−	0.178569i	0.00128950	−	0.00564968i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	232.2.m.d.161.3	yes	24
4.3	odd	2		464.2.u.i.161.2		24
29.7	even	7		6728.2.a.z.1.5		12
29.20	even	7	inner	232.2.m.d.49.3	✓	24
29.22	even	14		6728.2.a.bb.1.8		12
116.107	odd	14		464.2.u.i.49.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
232.2.m.d.49.3	✓	24	29.20	even	7	inner
232.2.m.d.161.3	yes	24	1.1	even	1	trivial
464.2.u.i.49.2		24	116.107	odd	14
464.2.u.i.161.2		24	4.3	odd	2
6728.2.a.z.1.5		12	29.7	even	7
6728.2.a.bb.1.8		12	29.22	even	14

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:	\( N \)	\(=\)	\( 232 = 2^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	232.m (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.484939 + 0.608094i) q^{3} +(-0.283259 - 0.136410i) q^{5} +(-2.96109 + 3.71309i) q^{7} +(0.532950 + 2.33501i) q^{9} +O(q^{10})\)	\(q+(-0.484939 + 0.608094i) q^{3} +(-0.283259 - 0.136410i) q^{5} +(-2.96109 + 3.71309i) q^{7} +(0.532950 + 2.33501i) q^{9} +(0.0376549 - 0.164977i) q^{11} +(-0.0314642 + 0.137854i) q^{13} +(0.220313 - 0.106097i) q^{15} +0.833683 q^{17} +(4.28287 + 5.37055i) q^{19} +(-0.821961 - 3.60124i) q^{21} +(-3.96704 + 1.91042i) q^{23} +(-3.05582 - 3.83188i) q^{25} +(-3.78062 - 1.82065i) q^{27} +(5.36275 + 0.490817i) q^{29} +(-2.53351 - 1.22008i) q^{31} +(0.0820611 + 0.102901i) q^{33} +(1.34526 - 0.647843i) q^{35} +(0.00971297 + 0.0425553i) q^{37} +(-0.0685698 - 0.0859838i) q^{39} +7.26282 q^{41} +(4.70140 - 2.26407i) q^{43} +(0.167556 - 0.734112i) q^{45} +(1.99389 - 8.73582i) q^{47} +(-3.46134 - 15.1651i) q^{49} +(-0.404285 + 0.506958i) q^{51} +(5.52197 + 2.65924i) q^{53} +(-0.0331706 + 0.0415947i) q^{55} -5.34272 q^{57} +13.7067 q^{59} +(-7.02344 + 8.80712i) q^{61} +(-10.2482 - 4.93528i) q^{63} +(0.0277172 - 0.0347563i) q^{65} +(-1.52216 - 6.66901i) q^{67} +(0.762052 - 3.33877i) q^{69} +(-1.23339 + 5.40382i) q^{71} +(-8.88556 + 4.27906i) q^{73} +3.81203 q^{75} +(0.501075 + 0.628328i) q^{77} +(0.0908998 + 0.398258i) q^{79} +(-3.53312 + 1.70146i) q^{81} +(1.61575 + 2.02608i) q^{83} +(-0.236148 - 0.113723i) q^{85} +(-2.89907 + 3.02304i) q^{87} +(7.96727 + 3.83684i) q^{89} +(-0.418695 - 0.525027i) q^{91} +(1.97052 - 0.948952i) q^{93} +(-0.480563 - 2.10548i) q^{95} +(6.67287 + 8.36752i) q^{97} +0.405291 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{3} - 8 q^{5} + 5 q^{7} - 3 q^{9}+O(q^{10}) \) 24 * q - q^3 - 8 * q^5 + 5 * q^7 - 3 * q^9	\( 24 q - q^{3} - 8 q^{5} + 5 q^{7} - 3 q^{9} - 6 q^{11} + q^{13} - q^{15} - 16 q^{17} - 10 q^{19} - 5 q^{21} + 11 q^{23} + 10 q^{25} - 7 q^{27} - 2 q^{29} + 12 q^{31} + 13 q^{33} - 8 q^{35} + q^{37} + 34 q^{39} - 22 q^{41} + 3 q^{43} + 60 q^{45} + 9 q^{47} - 67 q^{49} - q^{51} + 19 q^{53} - 88 q^{55} - 2 q^{57} + 114 q^{59} - 11 q^{61} - 108 q^{63} + 8 q^{65} - 25 q^{67} - 84 q^{69} - 21 q^{71} + 30 q^{73} - 26 q^{75} - 22 q^{77} + 48 q^{79} + 16 q^{81} - 37 q^{83} + 8 q^{85} + 11 q^{87} - 5 q^{89} - 11 q^{91} - 18 q^{93} - 21 q^{95} + 35 q^{97} + 32 q^{99}+O(q^{100}) \) 24 * q - q^3 - 8 * q^5 + 5 * q^7 - 3 * q^9 - 6 * q^11 + q^13 - q^15 - 16 * q^17 - 10 * q^19 - 5 * q^21 + 11 * q^23 + 10 * q^25 - 7 * q^27 - 2 * q^29 + 12 * q^31 + 13 * q^33 - 8 * q^35 + q^37 + 34 * q^39 - 22 * q^41 + 3 * q^43 + 60 * q^45 + 9 * q^47 - 67 * q^49 - q^51 + 19 * q^53 - 88 * q^55 - 2 * q^57 + 114 * q^59 - 11 * q^61 - 108 * q^63 + 8 * q^65 - 25 * q^67 - 84 * q^69 - 21 * q^71 + 30 * q^73 - 26 * q^75 - 22 * q^77 + 48 * q^79 + 16 * q^81 - 37 * q^83 + 8 * q^85 + 11 * q^87 - 5 * q^89 - 11 * q^91 - 18 * q^93 - 21 * q^95 + 35 * q^97 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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