LMFDB - Embedded newform 294.2.m.b.163.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,2,Mod(25,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("294.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	294.m (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.34760181943$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			163.2
Character	$\chi$	$=$	294.163
Dual form			294.2.m.b.193.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.365341 + 0.930874i) q^{2} +(0.0747301 + 0.997204i) q^{3} +(-0.733052 + 0.680173i) q^{4} +(2.56909 - 1.75158i) q^{5} +(-0.900969 + 0.433884i) q^{6} +(1.92409 - 1.81601i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(-0.988831 + 0.149042i) q^{9} +O(q^{10})$	\(q+(0.365341 + 0.930874i) q^{2} +(0.0747301 + 0.997204i) q^{3} +(-0.733052 + 0.680173i) q^{4} +(2.56909 - 1.75158i) q^{5} +(-0.900969 + 0.433884i) q^{6} +(1.92409 - 1.81601i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(-0.988831 + 0.149042i) q^{9} +(2.56909 + 1.75158i) q^{10} +(4.48390 + 0.675839i) q^{11} +(-0.733052 - 0.680173i) q^{12} +(-0.915824 + 1.14841i) q^{13} +(2.39342 + 1.12762i) q^{14} +(1.93867 + 2.43101i) q^{15} +(0.0747301 - 0.997204i) q^{16} +(-6.10699 + 1.88376i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.00666149 + 0.0115380i) q^{19} +(-0.691903 + 3.03143i) q^{20} +(1.95472 + 1.78299i) q^{21} +(1.00903 + 4.42085i) q^{22} +(-8.06931 - 2.48905i) q^{23} +(0.365341 - 0.930874i) q^{24} +(1.70551 - 4.34557i) q^{25} +(-1.40361 - 0.432957i) q^{26} +(-0.222521 - 0.974928i) q^{27} +(-0.175254 + 2.63994i) q^{28} +(-1.14253 + 5.00574i) q^{29} +(-1.55469 + 2.69281i) q^{30} +(0.347081 + 0.601162i) q^{31} +(0.955573 - 0.294755i) q^{32} +(-0.338867 + 4.52187i) q^{33} +(-3.98467 - 4.99662i) q^{34} +(1.76227 - 8.03569i) q^{35} +(0.623490 - 0.781831i) q^{36} +(5.30136 + 4.91894i) q^{37} +(-0.0131742 - 0.00198569i) q^{38} +(-1.21364 - 0.827443i) q^{39} +(-3.07465 + 0.463430i) q^{40} +(2.35326 + 1.13327i) q^{41} +(-0.945604 + 2.47100i) q^{42} +(7.56769 - 3.64441i) q^{43} +(-3.74662 + 2.55440i) q^{44} +(-2.27934 + 2.11492i) q^{45} +(-0.631056 - 8.42086i) q^{46} +(-4.22772 - 10.7721i) q^{47} +1.00000 q^{48} +(0.404211 - 6.98832i) q^{49} +4.66827 q^{50} +(-2.33486 - 5.94914i) q^{51} +(-0.109769 - 1.46476i) q^{52} +(-8.22574 + 7.63237i) q^{53} +(0.826239 - 0.563320i) q^{54} +(12.7033 - 6.11761i) q^{55} +(-2.52148 + 0.801339i) q^{56} +(-0.0120036 - 0.00578062i) q^{57} +(-5.07713 + 0.765254i) q^{58} +(-7.34454 - 5.00742i) q^{59} +(-3.07465 - 0.463430i) q^{60} +(0.0791719 + 0.0734608i) q^{61} +(-0.432803 + 0.542718i) q^{62} +(-1.63193 + 2.08250i) q^{63} +(0.623490 + 0.781831i) q^{64} +(-0.341313 + 4.55451i) q^{65} +(-4.33309 + 1.33658i) q^{66} +(-2.92630 - 5.06851i) q^{67} +(3.19546 - 5.53470i) q^{68} +(1.87907 - 8.23275i) q^{69} +(8.12404 - 1.29531i) q^{70} +(2.95871 + 12.9630i) q^{71} +(0.955573 + 0.294755i) q^{72} +(3.36158 - 8.56517i) q^{73} +(-2.64211 + 6.73199i) q^{74} +(4.46087 + 1.37600i) q^{75} +(-0.00296464 - 0.0129889i) q^{76} +(9.85473 - 6.84243i) q^{77} +(0.326854 - 1.43204i) q^{78} +(-4.25670 + 7.37282i) q^{79} +(-1.55469 - 2.69281i) q^{80} +(0.955573 - 0.294755i) q^{81} +(-0.195189 + 2.60461i) q^{82} +(-3.17892 - 3.98625i) q^{83} +(-2.64566 + 0.0225193i) q^{84} +(-12.3899 + 15.5364i) q^{85} +(6.15727 + 5.71311i) q^{86} +(-5.07713 - 0.765254i) q^{87} +(-3.74662 - 2.55440i) q^{88} +(-6.56171 + 0.989019i) q^{89} +(-2.80146 - 1.34911i) q^{90} +(0.323396 + 3.87278i) q^{91} +(7.60820 - 3.66392i) q^{92} +(-0.573544 + 0.391036i) q^{93} +(8.48286 - 7.87095i) q^{94} +(0.00309579 + 0.0413104i) q^{95} +(0.365341 + 0.930874i) q^{96} -0.717121 q^{97} +(6.65292 - 2.17685i) q^{98} -4.53454 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9	\( 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9} + q^{10} + 8 q^{11} + 2 q^{12} - 2 q^{13} + 5 q^{15} + 2 q^{16} + 9 q^{17} - 12 q^{18} - 4 q^{19} + 5 q^{20} + 14 q^{21} + 5 q^{22} - 38 q^{23} + 2 q^{24} - 19 q^{25} - 20 q^{26} - 4 q^{27} - 14 q^{28} - 14 q^{29} + 8 q^{30} + 4 q^{31} + 2 q^{32} - 6 q^{33} + 17 q^{34} + 42 q^{35} - 4 q^{36} + 7 q^{37} - 18 q^{38} - 6 q^{39} - 13 q^{40} + 2 q^{41} - 7 q^{42} + 4 q^{43} - 6 q^{44} - 13 q^{45} + 11 q^{46} - 8 q^{47} + 24 q^{48} - 42 q^{49} - 4 q^{50} - 40 q^{51} + 15 q^{52} - 10 q^{53} + 2 q^{54} + 33 q^{55} - 7 q^{56} + q^{57} - 28 q^{58} + 14 q^{59} - 13 q^{60} + 7 q^{61} - 8 q^{62} - 14 q^{63} - 4 q^{64} + 23 q^{65} + 8 q^{66} + 23 q^{67} + 9 q^{68} + 13 q^{69} + 28 q^{70} + 36 q^{71} + 2 q^{72} + 15 q^{73} - 14 q^{74} + 9 q^{75} + q^{76} - 28 q^{77} + 19 q^{78} + 38 q^{79} + 8 q^{80} + 2 q^{81} - q^{82} + 27 q^{83} - 47 q^{85} + 26 q^{86} - 28 q^{87} - 6 q^{88} - 121 q^{89} - 2 q^{90} + 21 q^{91} - q^{92} + 46 q^{93} - q^{94} + 44 q^{95} + 2 q^{96} + 14 q^{97} - 21 q^{98} - 44 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9 + q^10 + 8 * q^11 + 2 * q^12 - 2 * q^13 + 5 * q^15 + 2 * q^16 + 9 * q^17 - 12 * q^18 - 4 * q^19 + 5 * q^20 + 14 * q^21 + 5 * q^22 - 38 * q^23 + 2 * q^24 - 19 * q^25 - 20 * q^26 - 4 * q^27 - 14 * q^28 - 14 * q^29 + 8 * q^30 + 4 * q^31 + 2 * q^32 - 6 * q^33 + 17 * q^34 + 42 * q^35 - 4 * q^36 + 7 * q^37 - 18 * q^38 - 6 * q^39 - 13 * q^40 + 2 * q^41 - 7 * q^42 + 4 * q^43 - 6 * q^44 - 13 * q^45 + 11 * q^46 - 8 * q^47 + 24 * q^48 - 42 * q^49 - 4 * q^50 - 40 * q^51 + 15 * q^52 - 10 * q^53 + 2 * q^54 + 33 * q^55 - 7 * q^56 + q^57 - 28 * q^58 + 14 * q^59 - 13 * q^60 + 7 * q^61 - 8 * q^62 - 14 * q^63 - 4 * q^64 + 23 * q^65 + 8 * q^66 + 23 * q^67 + 9 * q^68 + 13 * q^69 + 28 * q^70 + 36 * q^71 + 2 * q^72 + 15 * q^73 - 14 * q^74 + 9 * q^75 + q^76 - 28 * q^77 + 19 * q^78 + 38 * q^79 + 8 * q^80 + 2 * q^81 - q^82 + 27 * q^83 - 47 * q^85 + 26 * q^86 - 28 * q^87 - 6 * q^88 - 121 * q^89 - 2 * q^90 + 21 * q^91 - q^92 + 46 * q^93 - q^94 + 44 * q^95 + 2 * q^96 + 14 * q^97 - 21 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{10}{21}\right)$

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 $

$2$	0.365341	+	0.930874i	0.258335	+	0.658227i
$2$	0.365341	+	0.930874i	0.258335	+	0.658227i
$3$	0.0747301	+	0.997204i	0.0431454	+	0.575736i
$3$	0.0747301	+	0.997204i	0.0431454	+	0.575736i
$4$	−0.733052	+	0.680173i	−0.366526	+	0.340086i
$5$	2.56909	−	1.75158i	1.14893	−	0.783330i	0.169586	−	0.985515i	$-0.445757\pi$
$5$	2.56909	−	1.75158i	1.14893	−	0.783330i	0.979347	+	0.202186i	$0.0648044\pi$
$6$	−0.900969	+	0.433884i	−0.367819	+	0.177132i
$7$	1.92409	−	1.81601i	0.727236	−	0.686387i
$7$	1.92409	−	1.81601i	0.727236	−	0.686387i
$8$	−0.900969	−	0.433884i	−0.318541	−	0.153401i
$9$	−0.988831	+	0.149042i	−0.329610	+	0.0496808i
$10$	2.56909	+	1.75158i	0.812419	+	0.553898i
$11$	4.48390	+	0.675839i	1.35195	+	0.203773i	0.784751	−	0.619811i	$-0.212791\pi$
$11$	4.48390	+	0.675839i	1.35195	+	0.203773i	0.567195	+	0.823584i	$0.308029\pi$
$12$	−0.733052	−	0.680173i	−0.211614	−	0.196349i
$13$	−0.915824	+	1.14841i	−0.254004	+	0.318511i	−0.892442	−	0.451162i	$-0.851010\pi$
$13$	−0.915824	+	1.14841i	−0.254004	+	0.318511i	0.638438	+	0.769673i	$0.279581\pi$
$14$	2.39342	+	1.12762i	0.639669	+	0.301369i
$15$	1.93867	+	2.43101i	0.500562	+	0.627685i
$16$	0.0747301	−	0.997204i	0.0186825	−	0.249301i
$17$	−6.10699	+	1.88376i	−1.48116	+	0.456878i	−0.926850	−	0.375431i	$-0.877495\pi$
$17$	−6.10699	+	1.88376i	−1.48116	+	0.456878i	−0.554312	+	0.832309i	$0.687018\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−0.00666149	+	0.0115380i	−0.00152825	+	0.00264701i	−0.866789	−	0.498676i	$-0.833820\pi$
$19$	−0.00666149	+	0.0115380i	−0.00152825	+	0.00264701i	0.865260	+	0.501323i	$0.167153\pi$
$20$	−0.691903	+	3.03143i	−0.154714	+	0.677847i
$21$	1.95472	+	1.78299i	0.426555	+	0.389081i
$22$	1.00903	+	4.42085i	0.215126	+	0.942529i
$23$	−8.06931	−	2.48905i	−1.68257	−	0.519003i	−0.701499	−	0.712670i	$-0.747486\pi$
$23$	−8.06931	−	2.48905i	−1.68257	−	0.519003i	−0.981067	+	0.193667i	$0.937962\pi$
$24$	0.365341	−	0.930874i	0.0745749	−	0.190014i
$25$	1.70551	−	4.34557i	0.341102	−	0.869114i
$26$	−1.40361	−	0.432957i	−0.275271	−	0.0849098i
$27$	−0.222521	−	0.974928i	−0.0428242	−	0.187625i
$28$	−0.175254	+	2.63994i	−0.0331198	+	0.498902i
$29$	−1.14253	+	5.00574i	−0.212162	+	0.929543i	0.750932	+	0.660379i	$0.229605\pi$
$29$	−1.14253	+	5.00574i	−0.212162	+	0.929543i	−0.963094	+	0.269164i	$0.913253\pi$
$30$	−1.55469	+	2.69281i	−0.283847	+	0.491637i
$31$	0.347081	+	0.601162i	0.0623376	+	0.107972i	0.895510	−	0.445042i	$-0.146811\pi$
$31$	0.347081	+	0.601162i	0.0623376	+	0.107972i	−0.833172	+	0.553014i	$0.813478\pi$
$32$	0.955573	−	0.294755i	0.168923	−	0.0521058i
$33$	−0.338867	+	4.52187i	−0.0589892	+	0.787156i
$34$	−3.98467	−	4.99662i	−0.683366	−	0.856913i
$35$	1.76227	−	8.03569i	0.297878	−	1.35828i
$36$	0.623490	−	0.781831i	0.103915	−	0.130305i
$37$	5.30136	+	4.91894i	0.871538	+	0.808669i	0.982714	−	0.185132i	$-0.0592711\pi$
$37$	5.30136	+	4.91894i	0.871538	+	0.808669i	−0.111176	+	0.993801i	$0.535462\pi$
$38$	−0.0131742	−	0.00198569i	−0.00213713	−	0.000322121i
$39$	−1.21364	−	0.827443i	−0.194337	−	0.132497i
$40$	−3.07465	+	0.463430i	−0.486146	+	0.0732747i
$41$	2.35326	+	1.13327i	0.367517	+	0.176987i	0.608522	−	0.793537i	$-0.291763\pi$
$41$	2.35326	+	1.13327i	0.367517	+	0.176987i	−0.241005	+	0.970524i	$0.577477\pi$
$42$	−0.945604	+	2.47100i	−0.145910	+	0.381283i
$43$	7.56769	−	3.64441i	1.15406	−	0.555767i	0.243810	−	0.969823i	$-0.421603\pi$
$43$	7.56769	−	3.64441i	1.15406	−	0.555767i	0.910251	+	0.414056i	$0.135888\pi$
$44$	−3.74662	+	2.55440i	−0.564824	+	0.385090i
$45$	−2.27934	+	2.11492i	−0.339784	+	0.315273i
$46$	−0.631056	−	8.42086i	−0.0930441	−	1.24159i
$47$	−4.22772	−	10.7721i	−0.616676	−	1.57127i	−0.807645	−	0.589670i	$-0.799258\pi$
$47$	−4.22772	−	10.7721i	−0.616676	−	1.57127i	0.190968	−	0.981596i	$-0.438837\pi$
$48$	1.00000			0.144338
$49$	0.404211	−	6.98832i	0.0577445	−	0.998331i
$50$	4.66827			0.660193
$51$	−2.33486	−	5.94914i	−0.326946	−	0.833046i
$52$	−0.109769	−	1.46476i	−0.0152222	−	0.203126i
$53$	−8.22574	+	7.63237i	−1.12989	+	1.04839i	−0.131522	+	0.991313i	$0.541986\pi$
$53$	−8.22574	+	7.63237i	−1.12989	+	1.04839i	−0.998370	+	0.0570730i	$0.981823\pi$
$54$	0.826239	−	0.563320i	0.112437	−	0.0766582i
$55$	12.7033	−	6.11761i	1.71292	−	0.824898i
$56$	−2.52148	+	0.801339i	−0.336947	+	0.107083i
$57$	−0.0120036	−	0.00578062i	−0.00158991	−	0.000765662i
$58$	−5.07713	+	0.765254i	−0.666660	+	0.100483i
$59$	−7.34454	−	5.00742i	−0.956178	−	0.651911i	−0.0186517	−	0.999826i	$-0.505937\pi$
$59$	−7.34454	−	5.00742i	−0.956178	−	0.651911i	−0.937526	+	0.347915i	$0.886890\pi$
$60$	−3.07465	−	0.463430i	−0.396936	−	0.0598285i
$61$	0.0791719	+	0.0734608i	0.0101369	+	0.00940569i	0.685225	−	0.728332i	$-0.259704\pi$
$61$	0.0791719	+	0.0734608i	0.0101369	+	0.00940569i	−0.675088	+	0.737737i	$0.735894\pi$
$62$	−0.432803	+	0.542718i	−0.0549661	+	0.0689253i
$63$	−1.63193	+	2.08250i	−0.205604	+	0.262370i
$64$	0.623490	+	0.781831i	0.0779362	+	0.0977289i
$65$	−0.341313	+	4.55451i	−0.0423347	+	0.564917i
$66$	−4.33309	+	1.33658i	−0.533366	+	0.164522i
$67$	−2.92630	−	5.06851i	−0.357505	−	0.619217i	0.630038	−	0.776564i	$-0.283039\pi$
$67$	−2.92630	−	5.06851i	−0.357505	−	0.619217i	−0.987543	+	0.157347i	$0.949706\pi$
$68$	3.19546	−	5.53470i	0.387506	−	0.671181i
$69$	1.87907	−	8.23275i	0.226214	−	0.991107i
$70$	8.12404	−	1.29531i	0.971009	−	0.154820i
$71$	2.95871	+	12.9630i	0.351135	+	1.53842i	0.774566	+	0.632493i	$0.217968\pi$
$71$	2.95871	+	12.9630i	0.351135	+	1.53842i	−0.423432	+	0.905928i	$0.639175\pi$
$72$	0.955573	+	0.294755i	0.112615	+	0.0347372i
$73$	3.36158	−	8.56517i	0.393443	−	1.00248i	−0.587680	−	0.809094i	$-0.699959\pi$
$73$	3.36158	−	8.56517i	0.393443	−	1.00248i	0.981123	−	0.193384i	$-0.0619463\pi$
$74$	−2.64211	+	6.73199i	−0.307139	+	0.782578i
$75$	4.46087	+	1.37600i	0.515097	+	0.158886i
$76$	−0.00296464	−	0.0129889i	−0.000340068	−	0.00148993i
$77$	9.85473	−	6.84243i	1.12305	−	0.779768i
$78$	0.326854	−	1.43204i	0.0370089	−	0.162147i
$79$	−4.25670	+	7.37282i	−0.478916	+	0.829507i	−0.999708	−	0.0241766i	$-0.992304\pi$
$79$	−4.25670	+	7.37282i	−0.478916	+	0.829507i	0.520791	+	0.853684i	$0.325637\pi$
$80$	−1.55469	−	2.69281i	−0.173820	−	0.301065i
$81$	0.955573	−	0.294755i	0.106175	−	0.0327506i
$82$	−0.195189	+	2.60461i	−0.0215550	+	0.287632i
$83$	−3.17892	−	3.98625i	−0.348932	−	0.437547i	0.576133	−	0.817356i	$-0.304561\pi$
$83$	−3.17892	−	3.98625i	−0.348932	−	0.437547i	−0.925065	+	0.379809i	$0.875990\pi$
$84$	−2.64566	+	0.0225193i	−0.288665	+	0.00245706i
$85$	−12.3899	+	15.5364i	−1.34387	+	1.68516i
$86$	6.15727	+	5.71311i	0.663956	+	0.616061i
$87$	−5.07713	−	0.765254i	−0.544325	−	0.0820438i
$88$	−3.74662	−	2.55440i	−0.399391	−	0.272300i
$89$	−6.56171	+	0.989019i	−0.695540	+	0.104836i	−0.487291	−	0.873240i	$-0.662015\pi$
$89$	−6.56171	+	0.989019i	−0.695540	+	0.104836i	−0.208250	+	0.978076i	$0.566777\pi$
$90$	−2.80146	−	1.34911i	−0.295300	−	0.142209i
$91$	0.323396	+	3.87278i	0.0339011	+	0.405978i
$92$	7.60820	−	3.66392i	0.793210	−	0.381990i
$93$	−0.573544	+	0.391036i	−0.0594737	+	0.0405485i
$94$	8.48286	−	7.87095i	0.874941	−	0.811826i
$95$	0.00309579	+	0.0413104i	0.000317621	+	0.00423836i
$96$	0.365341	+	0.930874i	0.0372875	+	0.0950069i
$97$	−0.717121			−0.0728126			−0.0364063	−	0.999337i	$-0.511591\pi$
$97$	−0.717121			−0.0728126			−0.0364063	+	0.999337i	$0.511591\pi$
$98$	6.65292	−	2.17685i	0.672046	−	0.219895i
$99$	−4.53454			−0.455739
$100$	1.70551	+	4.34557i	0.170551	+	0.434557i
$101$	−0.297457	−	3.96928i	−0.0295980	−	0.394958i	−0.992254	−	0.124229i	$-0.960354\pi$
$101$	−0.297457	−	3.96928i	−0.0295980	−	0.394958i	0.962656	−	0.270729i	$-0.0872648\pi$
$102$	4.68487	−	4.34693i	0.463872	−	0.430410i
$103$	2.52346	−	1.72046i	0.248643	−	0.169522i	−0.432585	−	0.901593i	$-0.642398\pi$
$103$	2.52346	−	1.72046i	0.248643	−	0.169522i	0.681228	+	0.732071i	$0.261446\pi$
$104$	1.32340	−	0.637318i	0.129771	−	0.0624942i
$105$	8.14491	+	1.15684i	0.794862	+	0.112896i
$106$	−10.1100	−	4.86870i	−0.981967	−	0.472890i
$107$	14.1337	−	2.13031i	1.36635	−	0.205945i	0.575426	−	0.817854i	$-0.304836\pi$
$107$	14.1337	−	2.13031i	1.36635	−	0.205945i	0.790928	+	0.611909i	$0.209598\pi$
$108$	0.826239	+	0.563320i	0.0795049	+	0.0542055i
$109$	−16.0048	−	2.41234i	−1.53298	−	0.231060i	−0.672331	−	0.740251i	$-0.734707\pi$
$109$	−16.0048	−	2.41234i	−1.53298	−	0.231060i	−0.860654	+	0.509191i	$0.829945\pi$
$110$	10.3358	+	9.59019i	0.985477	+	0.914389i
$111$	−4.50902	+	5.65413i	−0.427977	+	0.536666i
$112$	−1.66715	−	2.05442i	−0.157530	−	0.194124i
$113$	0.435880	+	0.546576i	0.0410041	+	0.0514175i	0.801911	−	0.597444i	$-0.203817\pi$
$113$	0.435880	+	0.546576i	0.0410041	+	0.0514175i	−0.760907	+	0.648861i	$0.775245\pi$
$114$	0.000995627	−	0.0132857i	9.32491e−5	−	0.00124432i
$115$	−25.0906	+	7.73942i	−2.33971	+	0.721704i
$116$	−2.56724	−	4.44659i	−0.238362	−	0.412855i
$117$	0.734434	−	1.27208i	0.0678985	−	0.117604i
$118$	1.97802	−	8.66626i	0.182091	−	0.797794i
$119$	−8.32945	+	14.7149i	−0.763559	+	1.34891i
$120$	−0.691903	−	3.03143i	−0.0631618	−	0.276730i
$121$	9.13728	+	2.81848i	0.830662	+	0.256225i
$122$	−0.0394580	+	0.100537i	−0.00357236	+	0.00910222i
$123$	−0.954241	+	2.43137i	−0.0860410	+	0.219229i
$124$	−0.663323	−	0.204608i	−0.0595682	−	0.0183743i
$125$	0.229526	+	1.00562i	0.0205294	+	0.0899452i
$126$	−2.53475	−	0.758302i	−0.225814	−	0.0675549i
$127$	−0.0872878	+	0.382433i	−0.00774554	+	0.0339354i	−0.978653	−	0.205520i	$-0.934112\pi$
$127$	−0.0872878	+	0.382433i	−0.00774554	+	0.0339354i	0.970907	+	0.239455i	$0.0769687\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	4.19975	+	7.27418i	0.369767	+	0.640456i
$130$	−4.36436	+	1.34623i	−0.382780	+	0.118072i
$131$	1.04502	−	13.9448i	0.0913036	−	1.21836i	−0.743850	−	0.668346i	$-0.767003\pi$
$131$	1.04502	−	13.9448i	0.0913036	−	1.21836i	0.835154	−	0.550016i	$-0.185378\pi$
$132$	−2.82724	−	3.54525i	−0.246080	−	0.308574i
$133$	0.00813592	+	0.0342975i	0.000705474	+	0.00297397i
$134$	3.64904	−	4.57575i	0.315229	−	0.395285i
$135$	−2.27934	−	2.11492i	−0.196174	−	0.182023i
$136$	6.31954	+	0.952517i	0.541896	+	0.0816776i
$137$	2.36279	+	1.61093i	0.201867	+	0.137631i	0.660035	−	0.751235i	$-0.270542\pi$
$137$	2.36279	+	1.61093i	0.201867	+	0.137631i	−0.458167	+	0.888866i	$0.651494\pi$
$138$	8.35015	−	1.25858i	0.710812	−	0.107138i
$139$	9.82556	+	4.73174i	0.833393	+	0.401341i	0.801387	−	0.598147i	$-0.204096\pi$
$139$	9.82556	+	4.73174i	0.833393	+	0.401341i	0.0320064	+	0.999488i	$0.489810\pi$
$140$	4.17382	+	7.08923i	0.352752	+	0.599149i
$141$	10.4260	−	5.02090i	0.878027	−	0.422836i
$142$	−10.9859	+	7.49009i	−0.921920	+	0.628554i
$143$	−4.88260	+	4.53039i	−0.408304	+	0.378850i
$144$	0.0747301	+	0.997204i	0.00622751	+	0.0831003i
$145$	5.83269	+	14.8615i	0.484379	+	1.23418i
$146$	9.20122			0.761498
$147$	6.99899	−	0.119157i	0.577267	−	0.00982787i
$148$	−7.23190			−0.594459
$149$	2.31140	+	5.88936i	0.189358	+	0.482475i	0.993751	−	0.111622i	$-0.0356046\pi$
$149$	2.31140	+	5.88936i	0.189358	+	0.482475i	−0.804393	+	0.594097i	$0.797509\pi$
$150$	0.348860	+	4.65522i	0.0284843	+	0.380097i
$151$	13.2752	−	12.3176i	1.08032	−	1.00239i	0.0803398	−	0.996768i	$-0.474399\pi$
$151$	13.2752	−	12.3176i	1.08032	−	1.00239i	0.999984	−	0.00562658i	$-0.00179100\pi$
$152$	0.0110080	−	0.00750510i	0.000892864	−	0.000608744i
$153$	5.75802	−	2.77292i	0.465508	−	0.224177i
$154$	9.96978	+	6.67369i	0.803388	+	0.537781i
$155$	1.94467	+	0.936502i	0.156199	+	0.0752217i
$156$	1.45246	−	0.218923i	0.116290	−	0.0175279i
$157$	2.98108	+	2.03247i	0.237916	+	0.162209i	0.676409	−	0.736526i	$-0.263535\pi$
$157$	2.98108	+	2.03247i	0.237916	+	0.162209i	−0.438493	+	0.898735i	$0.644488\pi$
$158$	−8.41831	−	1.26886i	−0.669725	−	0.100945i
$159$	−8.22574	−	7.63237i	−0.652343	−	0.605286i
$160$	1.93867	−	2.43101i	0.153265	−	0.192189i
$161$	−20.0462	+	9.86480i	−1.57986	+	0.777455i
$162$	0.623490	+	0.781831i	0.0489860	+	0.0614265i
$163$	−0.632282	+	8.43722i	−0.0495242	+	0.660854i	0.916106	+	0.400935i	$0.131315\pi$
$163$	−0.632282	+	8.43722i	−0.0495242	+	0.660854i	−0.965631	+	0.259919i	$0.916304\pi$
$164$	−2.49588	+	0.769876i	−0.194895	+	0.0601172i
$165$	7.04982	+	12.2106i	0.548828	+	0.950598i
$166$	2.54930	−	4.41552i	0.197864	−	0.342711i
$167$	−0.891633	+	3.90650i	−0.0689966	+	0.302294i	−0.997639	−	0.0686835i	$-0.978120\pi$
$167$	−0.891633	+	3.90650i	−0.0689966	+	0.302294i	0.928642	+	0.370977i	$0.120977\pi$
$168$	−0.987529	−	2.45454i	−0.0761895	−	0.189372i
$169$	2.41267	+	10.5706i	0.185590	+	0.813122i
$170$	−18.9890	−	5.85732i	−1.45639	−	0.449236i
$171$	0.00486743	−	0.0124020i	0.000372222	−	0.000948405i
$172$	−3.06868	+	7.81888i	−0.233985	+	0.596184i
$173$	−20.6644	−	6.37413i	−1.57109	−	0.484616i	−0.617711	−	0.786405i	$-0.711940\pi$
$173$	−20.6644	−	6.37413i	−1.57109	−	0.484616i	−0.953375	+	0.301789i	$0.902416\pi$
$174$	−1.14253	−	5.00574i	−0.0866149	−	0.379484i
$175$	−4.61005	−	11.4585i	−0.348487	−	0.866179i
$176$	1.00903	−	4.42085i	0.0760586	−	0.333234i
$177$	4.44456	−	7.69821i	0.334074	−	0.578633i
$178$	−3.31792	−	5.74680i	−0.248688	−	0.430741i
$179$	17.6466	−	5.44325i	1.31897	−	0.406847i	0.446178	−	0.894944i	$-0.352785\pi$
$179$	17.6466	−	5.44325i	1.31897	−	0.406847i	0.872789	+	0.488097i	$0.162309\pi$
$180$	0.232365	−	3.10069i	0.0173194	−	0.231112i
$181$	12.4453	+	15.6059i	0.925053	+	1.15998i	0.986809	+	0.161889i	$0.0517586\pi$
$181$	12.4453	+	15.6059i	0.925053	+	1.15998i	−0.0617556	+	0.998091i	$0.519670\pi$
$182$	−3.48692	+	1.71593i	−0.258468	+	0.127193i
$183$	−0.0673389	+	0.0844403i	−0.00497783	+	0.00624200i
$184$	6.19023	+	5.74370i	0.456350	+	0.423431i
$185$	22.2356	+	3.35148i	1.63479	+	0.246406i
$186$	−0.573544	−	0.391036i	−0.0420543	−	0.0286721i
$187$	−28.6562	+	4.31923i	−2.09555	+	0.315853i
$188$	10.4260	+	5.02090i	0.760394	+	0.366186i
$189$	−2.19863	−	1.47174i	−0.159927	−	0.107054i
$190$	−0.0373238	+	0.0179742i	−0.00270775	+	0.00130398i
$191$	−12.1843	+	8.30711i	−0.881625	+	0.601081i	−0.917262	−	0.398283i	$-0.869606\pi$
$191$	−12.1843	+	8.30711i	−0.881625	+	0.601081i	0.0356379	+	0.999365i	$0.488654\pi$
$192$	−0.733052	+	0.680173i	−0.0529035	+	0.0490872i
$193$	0.108704	+	1.45055i	0.00782466	+	0.104413i	0.999749	−	0.0224212i	$-0.00713748\pi$
$193$	0.108704	+	1.45055i	0.00782466	+	0.104413i	−0.991924	+	0.126834i	$0.959518\pi$
$194$	−0.261994	−	0.667549i	−0.0188101	−	0.0479272i
$195$	−4.56728			−0.327069
$196$	4.45696	+	5.39773i	0.318354	+	0.385552i
$197$	9.42091			0.671212			0.335606	−	0.942002i	$-0.391059\pi$
$197$	9.42091			0.671212			0.335606	+	0.942002i	$0.391059\pi$
$198$	−1.65666	−	4.22109i	−0.117733	−	0.299980i
$199$	1.43889	+	19.2006i	0.102000	+	1.36110i	0.779882	+	0.625926i	$0.215279\pi$
$199$	1.43889	+	19.2006i	0.102000	+	1.36110i	−0.677882	+	0.735171i	$0.737102\pi$
$200$	−3.42208	+	3.17523i	−0.241978	+	0.224523i
$201$	4.83565	−	3.29689i	0.341081	−	0.232545i
$202$	3.58623	−	1.72704i	0.252326	−	0.121514i
$203$	6.89216	+	11.7063i	0.483735	+	0.821623i
$204$	5.75802	+	2.77292i	0.403142	+	0.194143i
$205$	8.03075	−	1.21044i	0.560892	−	0.0845408i
$206$	2.52346	+	1.72046i	0.175817	+	0.119870i
$207$	8.35015	+	1.25858i	0.580376	+	0.0874776i
$208$	1.07676	+	0.999084i	0.0746596	+	0.0692740i
$209$	−0.0376673	+	0.0472333i	−0.00260550	+	0.00326719i
$210$	1.89880	+	8.00453i	0.131030	+	0.552365i
$211$	−3.14572	−	3.94460i	−0.216560	−	0.271558i	0.661671	−	0.749794i	$-0.269848\pi$
$211$	−3.14572	−	3.94460i	−0.216560	−	0.271558i	−0.878231	+	0.478237i	$0.841276\pi$
$212$	0.838563	−	11.1898i	0.0575927	−	0.768522i
$213$	−12.7056	+	3.91916i	−0.870574	+	0.268537i
$214$	7.14666	+	12.3784i	0.488535	+	0.846168i
$215$	13.0586	−	22.6182i	0.890592	−	1.54255i
$216$	−0.222521	+	0.974928i	−0.0151406	+	0.0663354i
$217$	1.75953	+	0.526385i	0.119445	+	0.0357333i
$218$	−3.60164	−	15.7798i	−0.243934	−	1.06874i
$219$	8.79243	+	2.71211i	0.594138	+	0.183267i
$220$	−5.15118	+	13.1250i	−0.347292	+	0.884886i
$221$	3.42961	−	8.73850i	0.230700	−	0.587815i
$222$	−6.91061	−	2.13164i	−0.463810	−	0.143066i
$223$	−1.67446	−	7.33628i	−0.112130	−	0.491274i	−0.999541	−	0.0302947i	$-0.990355\pi$
$223$	−1.67446	−	7.33628i	−0.112130	−	0.491274i	0.887411	−	0.460979i	$-0.152502\pi$
$224$	1.30333	−	2.30246i	0.0870821	−	0.153840i
$225$	−1.03879	+	4.55123i	−0.0692525	+	0.303415i
$226$	−0.349548	+	0.605435i	−0.0232516	+	0.0402730i
$227$	−4.59238	−	7.95424i	−0.304807	−	0.527941i	0.672411	−	0.740178i	$-0.265259\pi$
$227$	−4.59238	−	7.95424i	−0.304807	−	0.527941i	−0.977218	+	0.212236i	$0.931925\pi$
$228$	0.0127311	−	0.00392702i	0.000843136	−	0.000260073i
$229$	1.07250	−	14.3115i	0.0708729	−	0.945733i	−0.842523	−	0.538660i	$-0.818931\pi$
$229$	1.07250	−	14.3115i	0.0708729	−	0.945733i	0.913396	−	0.407072i	$-0.133450\pi$
$230$	−16.3710	−	20.5286i	−1.07947	−	1.35362i
$231$	7.55975	+	9.31584i	0.497395	+	0.612937i
$232$	3.20129	−	4.01430i	0.210175	−	0.263551i
$233$	−14.4984	−	13.4526i	−0.949824	−	0.881308i	0.0432182	−	0.999066i	$-0.486239\pi$
$233$	−14.4984	−	13.4526i	−0.949824	−	0.881308i	−0.993042	+	0.117758i	$0.962429\pi$
$234$	1.45246	+	0.218923i	0.0949504	+	0.0143115i
$235$	−29.7295	−	20.2692i	−1.93934	−	1.32222i
$236$	8.78984	−	1.32486i	0.572170	−	0.0862407i
$237$	−7.67031	−	3.69383i	−0.498240	−	0.239940i
$238$	−16.7408	−	2.37772i	−1.08514	−	0.154125i
$239$	21.0070	−	10.1164i	1.35883	−	0.654378i	0.394455	−	0.918915i	$-0.370934\pi$
$239$	21.0070	−	10.1164i	1.35883	−	0.654378i	0.964375	+	0.264537i	$0.0852193\pi$
$240$	2.56909	−	1.75158i	0.165834	−	0.113064i
$241$	9.62439	−	8.93013i	0.619962	−	0.575240i	−0.306387	−	0.951907i	$-0.599120\pi$
$241$	9.62439	−	8.93013i	0.619962	−	0.575240i	0.926349	+	0.376667i	$0.122930\pi$
$242$	0.714576	+	9.53536i	0.0459347	+	0.612956i
$243$	0.365341	+	0.930874i	0.0234366	+	0.0597156i
$244$	−0.108003			−0.00691419
$245$	−11.2021	−	18.6617i	−0.715678	−	1.19225i
$246$	−2.61192			−0.166530
$247$	−0.00714962	−	0.0182169i	−0.000454919	−	0.00115912i
$248$	−0.0518748	−	0.692222i	−0.00329406	−	0.0439561i
$249$	3.73754	−	3.46793i	0.236857	−	0.219771i
$250$	−0.852248	+	0.581053i	−0.0539009	+	0.0367490i
$251$	15.0208	−	7.23362i	0.948103	−	0.456582i	0.105082	−	0.994464i	$-0.466489\pi$
$251$	15.0208	−	7.23362i	0.948103	−	0.456582i	0.843021	+	0.537881i	$0.180775\pi$
$252$	−0.220166	−	2.63657i	−0.0138692	−	0.166089i
$253$	−34.4997	−	16.6142i	−2.16898	−	1.04453i
$254$	−0.387887	+	0.0584645i	−0.0243382	+	0.00366839i
$255$	−16.4189	−	11.1942i	−1.02819	−	0.701008i
$256$	−0.988831	−	0.149042i	−0.0618019	−	0.00931514i
$257$	10.3893	+	9.63990i	0.648070	+	0.601321i	0.934148	−	0.356885i	$-0.116161\pi$
$257$	10.3893	+	9.63990i	0.648070	+	0.601321i	−0.286079	+	0.958206i	$0.592352\pi$
$258$	−5.23700	+	6.56700i	−0.326042	+	0.408843i
$259$	19.1331	−	0.162857i	1.18887	−	0.0101195i
$260$	−2.84765	−	3.57084i	−0.176604	−	0.221454i
$261$	0.383700	−	5.12012i	0.0237504	−	0.316927i
$262$	13.3626	−	4.12183i	0.825546	−	0.254647i
$263$	4.60141	+	7.96987i	0.283735	+	0.491443i	0.972302	−	0.233730i	$-0.0750931\pi$
$263$	4.60141	+	7.96987i	0.283735	+	0.491443i	−0.688567	+	0.725173i	$0.741760\pi$
$264$	2.26727	−	3.92703i	0.139541	−	0.241692i
$265$	−7.76400	+	34.0163i	−0.476938	+	2.08960i
$266$	−0.0289543	+	0.0201038i	−0.00177530	+	0.00123264i
$267$	−1.47661	−	6.46946i	−0.0903671	−	0.395924i
$268$	5.59259	+	1.72509i	0.341622	+	0.105376i
$269$	−8.61884	+	21.9604i	−0.525500	+	1.33895i	0.384033	+	0.923319i	$0.374535\pi$
$269$	−8.61884	+	21.9604i	−0.525500	+	1.33895i	−0.909533	+	0.415632i	$0.863560\pi$
$270$	1.13599	−	2.89444i	0.0691339	−	0.176150i
$271$	−16.9369	−	5.22435i	−1.02885	−	0.317357i	−0.266024	−	0.963966i	$-0.585710\pi$
$271$	−16.9369	−	5.22435i	−1.02885	−	0.317357i	−0.762821	+	0.646610i	$0.776186\pi$
$272$	1.42211	+	6.23068i	0.0862283	+	0.377791i
$273$	−3.83779	+	0.611905i	−0.232273	+	0.0370341i
$274$	−0.636343	+	2.78800i	−0.0384429	+	0.168429i
$275$	10.5842	−	18.3324i	0.638254	−	1.10549i
$276$	4.22224	+	7.31313i	0.254149	+	0.440198i
$277$	14.3324	−	4.42096i	0.861151	−	0.265630i	0.167439	−	0.985882i	$-0.446450\pi$
$277$	14.3324	−	4.42096i	0.861151	−	0.265630i	0.693712	+	0.720253i	$0.255974\pi$
$278$	−0.814973	+	10.8751i	−0.0488788	+	0.652242i
$279$	−0.432803	−	0.542718i	−0.0259113	−	0.0324917i
$280$	−5.07431	+	6.47528i	−0.303248	+	0.386972i
$281$	−13.7405	+	17.2300i	−0.819689	+	1.02786i	0.179339	+	0.983787i	$0.442604\pi$
$281$	−13.7405	+	17.2300i	−0.819689	+	1.02786i	−0.999028	+	0.0440707i	$0.985967\pi$
$282$	8.48286	+	7.87095i	0.505147	+	0.468708i
$283$	−4.64752	−	0.700501i	−0.276267	−	0.0416405i	0.00944759	−	0.999955i	$-0.496993\pi$
$283$	−4.64752	−	0.700501i	−0.276267	−	0.0416405i	−0.285714	+	0.958315i	$0.592231\pi$
$284$	−10.9859	−	7.49009i	−0.651896	−	0.444455i
$285$	−0.0409636	+	0.00617426i	−0.00242647	+	0.000365732i
$286$	−6.00104	−	2.88995i	−0.354849	−	0.170886i
$287$	6.58590	−	2.09303i	0.388753	−	0.123548i
$288$	−0.900969	+	0.433884i	−0.0530901	+	0.0255668i
$289$	19.7007	−	13.4317i	1.15886	−	0.790100i
$290$	−11.7032	+	10.8590i	−0.687236	+	0.637662i
$291$	−0.0535905	−	0.715116i	−0.00314153	−	0.0419208i
$292$	3.36158	+	8.56517i	0.196722	+	0.501239i
$293$	−7.59787			−0.443872			−0.221936	−	0.975061i	$-0.571238\pi$
$293$	−7.59787			−0.443872			−0.221936	+	0.975061i	$0.571238\pi$
$294$	2.66794	+	6.47164i	0.155597	+	0.377434i
$295$	−27.6397			−1.60925
$296$	−2.64211	−	6.73199i	−0.153570	−	0.391289i
$297$	−0.338867	−	4.52187i	−0.0196631	−	0.262385i
$298$	−4.63780	+	4.30325i	−0.268661	+	0.249281i
$299$	10.2485	−	6.98732i	0.592687	−	0.404087i
$300$	−4.20597	+	2.02549i	−0.242832	+	0.116941i
$301$	7.94260	−	20.7552i	0.457804	−	1.19631i
$302$	16.3161	+	7.85744i	0.938889	+	0.452145i
$303$	3.93595	−	0.593250i	0.226115	−	0.0340813i
$304$	0.0110080	+	0.00750510i	0.000631350	+	0.000430447i
$305$	0.332072	+	0.0500519i	0.0190144	+	0.00286596i
$306$	4.68487	+	4.34693i	0.267816	+	0.248497i
$307$	−4.68865	+	5.87938i	−0.267595	+	0.335554i	−0.897415	−	0.441188i	$-0.854557\pi$
$307$	−4.68865	+	5.87938i	−0.267595	+	0.335554i	0.629820	+	0.776741i	$0.283129\pi$
$308$	−2.56999	+	11.7188i	−0.146439	+	0.667739i
$309$	1.90423	+	2.38783i	0.108328	+	0.135839i
$310$	−0.161299	+	2.15238i	−0.00916115	+	0.122247i
$311$	29.8215	−	9.19873i	1.69102	−	0.521612i	0.708177	−	0.706035i	$-0.249518\pi$
$311$	29.8215	−	9.19873i	1.69102	−	0.521612i	0.982847	+	0.184423i	$0.0590415\pi$
$312$	0.734434	+	1.27208i	0.0415792	+	0.0720172i
$313$	−8.82567	+	15.2865i	−0.498856	+	0.864044i	−0.999999	−	0.00132032i	$-0.999580\pi$
$313$	−8.82567	+	15.2865i	−0.498856	+	0.864044i	0.501143	+	0.865364i	$0.332913\pi$
$314$	−0.802859	+	3.51755i	−0.0453079	+	0.198507i
$315$	−0.544931	+	8.20859i	−0.0307034	+	0.462502i
$316$	−1.89441	−	8.29995i	−0.106569	−	0.466909i
$317$	−12.8574	−	3.96598i	−0.722143	−	0.222752i	−0.0881686	−	0.996106i	$-0.528101\pi$
$317$	−12.8574	−	3.96598i	−0.722143	−	0.222752i	−0.633975	+	0.773354i	$0.718578\pi$
$318$	4.09957	−	10.4455i	0.229893	−	0.585757i
$319$	−8.50606	+	21.6731i	−0.476248	+	1.21346i
$320$	2.97124	+	0.916507i	0.166098	+	0.0512343i
$321$	3.18056	+	13.9350i	0.177522	+	0.777773i
$322$	−16.5066	−	15.0564i	−0.919875	−	0.839063i
$323$	0.0189468	−	0.0830113i	0.00105423	−	0.00461887i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	3.42854	+	5.93840i	0.190181	+	0.329403i
$326$	−8.08498	+	2.49389i	−0.447786	+	0.138124i
$327$	1.20955	−	16.1403i	0.0668884	−	0.892563i
$328$	−1.62850	−	2.04208i	−0.0899191	−	0.112755i
$329$	−27.6967	−	13.0488i	−1.52697	−	0.719402i
$330$	−8.79098	+	11.0235i	−0.483928	+	0.606826i
$331$	−7.47859	−	6.93912i	−0.411061	−	0.381408i	0.447361	−	0.894354i	$-0.352364\pi$
$331$	−7.47859	−	6.93912i	−0.411061	−	0.381408i	−0.858421	+	0.512945i	$0.828554\pi$
$332$	5.04165	+	0.759907i	0.276697	+	0.0417053i
$333$	−5.97528	−	4.07388i	−0.327443	−	0.223247i
$334$	−3.96221	+	0.597207i	−0.216802	+	0.0326777i
$335$	−16.3958	−	7.89582i	−0.895800	−	0.431395i
$336$	1.92409	−	1.81601i	0.104967	−	0.0990715i
$337$	17.5642	−	8.45849i	0.956785	−	0.460764i	0.110725	−	0.993851i	$-0.464683\pi$
$337$	17.5642	−	8.45849i	0.956785	−	0.460764i	0.846060	+	0.533088i	$0.178968\pi$
$338$	−8.95843	+	6.10776i	−0.487274	+	0.332218i
$339$	−0.512474	+	0.475506i	−0.0278338	+	0.0258260i
$340$	−1.48502	−	19.8163i	−0.0805367	−	1.07469i
$341$	1.14999	+	2.93012i	0.0622753	+	0.158675i
$342$	0.0133230			0.000720424
$343$	−11.9131	−	14.1802i	−0.643248	−	0.765658i
$344$	−8.39950			−0.452871
$345$	−9.59280	−	24.4420i	−0.516459	−	1.31592i
$346$	−1.61605	−	21.5647i	−0.0868794	−	1.15932i
$347$	−2.59360	+	2.40651i	−0.139232	+	0.129188i	−0.746715	−	0.665145i	$-0.768370\pi$
$347$	−2.59360	+	2.40651i	−0.139232	+	0.129188i	0.607483	+	0.794333i	$0.292179\pi$
$348$	4.24230	−	2.89235i	0.227411	−	0.155046i
$349$	−0.907272	+	0.436919i	−0.0485651	+	0.0233877i	−0.458009	−	0.888948i	$-0.651437\pi$
$349$	−0.907272	+	0.436919i	−0.0485651	+	0.0233877i	0.409444	+	0.912335i	$0.365723\pi$
$350$	8.98215	−	8.47763i	0.480116	−	0.453148i
$351$	1.32340	+	0.637318i	0.0706381	+	0.0340175i
$352$	4.48390	−	0.675839i	0.238993	−	0.0360223i
$353$	15.1029	+	10.2970i	0.803848	+	0.548054i	0.894101	−	0.447865i	$-0.147815\pi$
$353$	15.1029	+	10.2970i	0.803848	+	0.548054i	−0.0902535	+	0.995919i	$0.528768\pi$
$354$	8.78984	+	1.32486i	0.467175	+	0.0704153i
$355$	30.3069	+	28.1207i	1.60852	+	1.49249i
$356$	4.13737	−	5.18810i	0.219280	−	0.274969i
$357$	−15.2962	−	7.20651i	−0.809559	−	0.381409i
$358$	11.5140	+	14.4381i	0.608533	+	0.763077i
$359$	−0.356488	+	4.75700i	−0.0188147	+	0.251065i	0.979864	+	0.199668i	$0.0639863\pi$
$359$	−0.356488	+	4.75700i	−0.0188147	+	0.251065i	−0.998678	+	0.0513967i	$0.983633\pi$
$360$	2.97124	−	0.916507i	0.156598	−	0.0483042i
$361$	9.49991	+	16.4543i	0.499995	+	0.866017i
$362$	−9.98037	+	17.2865i	−0.524557	+	0.908559i
$363$	−2.12777	+	9.32235i	−0.111679	+	0.489297i
$364$	−2.87123	−	2.61898i	−0.150493	−	0.137272i
$365$	−6.36635	−	27.8928i	−0.333230	−	1.45998i
$366$	−0.103205	−	0.0318345i	−0.00539460	−	0.00166402i
$367$	13.2184	−	33.6800i	0.689997	−	1.75808i	0.0387117	−	0.999250i	$-0.487675\pi$
$367$	13.2184	−	33.6800i	0.689997	−	1.75808i	0.651285	−	0.758833i	$-0.274230\pi$
$368$	−3.08511	+	7.86074i	−0.160823	+	0.409769i
$369$	−2.49588	−	0.769876i	−0.129930	−	0.0400782i
$370$	5.00378	+	21.9230i	0.260134	+	1.13972i
$371$	−1.96656	+	29.6234i	−0.102099	+	1.53797i
$372$	0.154466	−	0.676758i	0.00800867	−	0.0350883i
$373$	12.4555	−	21.5736i	0.644923	−	1.11704i	−0.339396	−	0.940644i	$-0.610223\pi$
$373$	12.4555	−	21.5736i	0.644923	−	1.11704i	0.984319	−	0.176396i	$-0.0564440\pi$
$374$	−14.4900	−	25.0973i	−0.749258	−	1.29775i
$375$	−0.985653	+	0.304034i	−0.0508989	+	0.0157002i
$376$	−0.864775	+	11.5396i	−0.0445974	+	0.595111i
$377$	−4.70228	−	5.89647i	−0.242180	−	0.303684i
$378$	0.566759	−	2.58433i	0.0291509	−	0.132924i
$379$	−7.20814	+	9.03872i	−0.370257	+	0.464288i	−0.931701	−	0.363227i	$-0.881675\pi$
$379$	−7.20814	+	9.03872i	−0.370257	+	0.464288i	0.561443	+	0.827515i	$0.310246\pi$
$380$	−0.0303676	−	0.0281770i	−0.00155782	−	0.00144545i
$381$	−0.387887	−	0.0584645i	−0.0198720	−	0.00299523i
$382$	−12.1843	−	8.30711i	−0.623403	−	0.425029i
$383$	−18.1035	+	2.72866i	−0.925044	+	0.139428i	−0.594255	−	0.804277i	$-0.702553\pi$
$383$	−18.1035	+	2.72866i	−0.925044	+	0.139428i	−0.330789	+	0.943705i	$0.607315\pi$
$384$	−0.900969	−	0.433884i	−0.0459774	−	0.0221415i
$385$	13.3327	−	34.8402i	0.679496	−	1.77562i
$386$	−1.31056	+	0.631135i	−0.0667060	+	0.0321239i
$387$	−6.93999	+	4.73161i	−0.352780	+	0.240521i
$388$	0.525687	−	0.487766i	0.0266877	−	0.0247626i
$389$	−0.581502	−	7.75960i	−0.0294833	−	0.393428i	−0.992351	−	0.123452i	$-0.960603\pi$
$389$	−0.581502	−	7.75960i	−0.0294833	−	0.393428i	0.962867	−	0.269975i	$-0.0870156\pi$
$390$	−1.66861	−	4.25156i	−0.0844935	−	0.215286i
$391$	53.9679			2.72927
$392$	−3.39630	+	6.12088i	−0.171539	+	0.309151i
$393$	13.9839			0.705394
$394$	3.44185	+	8.76968i	0.173398	+	0.441810i
$395$	1.97821	+	26.3974i	0.0995347	+	1.32820i
$396$	3.32406	−	3.08427i	0.167040	−	0.154991i
$397$	−9.03064	+	6.15699i	−0.453235	+	0.309010i	−0.768335	−	0.640048i	$-0.778914\pi$
$397$	−9.03064	+	6.15699i	−0.453235	+	0.309010i	0.315100	+	0.949059i	$0.397962\pi$
$398$	−17.3477	+	8.35421i	−0.869561	+	0.418758i
$399$	−0.0335936	+	0.0106762i	−0.00168178	+	0.000534480i
$400$	−4.20597	−	2.02549i	−0.210298	−	0.101274i
$401$	34.7891	−	5.24361i	1.73728	−	0.261853i	0.797426	−	0.603417i	$-0.206195\pi$
$401$	34.7891	−	5.24361i	1.73728	−	0.261853i	0.939859	+	0.341564i	$0.110957\pi$
$402$	4.83565	+	3.29689i	0.241180	+	0.164434i
$403$	−1.00824	−	0.151968i	−0.0502243	−	0.00757009i
$404$	2.91785	+	2.70737i	0.145168	+	0.134697i
$405$	1.93867	−	2.43101i	0.0963332	−	0.120798i
$406$	−8.37912	+	10.6925i	−0.415849	+	0.530661i
$407$	20.4463	+	25.6389i	1.01349	+	1.27087i
$408$	−0.477594	+	6.37305i	−0.0236444	+	0.315513i
$409$	19.2302	−	5.93172i	0.950871	−	0.293305i	0.219753	−	0.975556i	$-0.429475\pi$
$409$	19.2302	−	5.93172i	0.950871	−	0.293305i	0.731118	+	0.682251i	$0.238999\pi$
$410$	4.06073	+	7.03339i	0.200545	+	0.347354i
$411$	−1.42985	+	2.47657i	−0.0705292	+	0.122160i
$412$	−0.679612	+	2.97757i	−0.0334821	+	0.146695i
$413$	−23.2251	+	3.70305i	−1.14283	+	0.182215i
$414$	1.87907	+	8.23275i	0.0923513	+	0.404618i
$415$	−15.1492	−	4.67290i	−0.743644	−	0.229384i
$416$	−0.536638	+	1.36733i	−0.0263108	+	0.0670389i
$417$	−3.98424	+	10.1517i	−0.195109	+	0.497130i
$418$	−0.0577296	−	0.0178072i	−0.00282365	−	0.000870980i
$419$	−0.0557178	−	0.244116i	−0.00272200	−	0.0119258i	0.973549	−	0.228480i	$-0.0733755\pi$
$419$	−0.0557178	−	0.244116i	−0.00272200	−	0.0119258i	−0.976271	+	0.216554i	$0.930518\pi$
$420$	−6.75749	+	4.69193i	−0.329732	+	0.228943i
$421$	5.06382	−	22.1860i	0.246795	−	1.08128i	−0.687893	−	0.725812i	$-0.741464\pi$
$421$	5.06382	−	22.1860i	0.246795	−	1.08128i	0.934688	−	0.355469i	$-0.115679\pi$
$422$	2.52267	−	4.36939i	0.122802	−	0.212699i
$423$	5.78599	+	10.0216i	0.281325	+	0.487268i
$424$	10.7227	−	3.30751i	0.520740	−	0.160627i
$425$	−2.22954	+	29.7511i	−0.108148	+	1.44314i
$426$	−8.29013	−	10.3955i	−0.401658	−	0.503663i
$427$	0.285739	−	0.00243216i	0.0138279	−	0.000117700i
$428$	−8.91174	+	11.1750i	−0.430765	+	0.540162i
$429$	−4.88260	−	4.53039i	−0.235734	−	0.218729i
$430$	25.8256	+	3.89258i	1.24542	+	0.187717i
$431$	26.7917	+	18.2663i	1.29051	+	0.879854i	0.997098	−	0.0761318i	$-0.0242570\pi$
$431$	26.7917	+	18.2663i	1.29051	+	0.879854i	0.293412	+	0.955986i	$0.405209\pi$
$432$	−0.988831	+	0.149042i	−0.0475751	+	0.00717080i
$433$	−11.7869	−	5.67629i	−0.566445	−	0.272785i	0.128666	−	0.991688i	$-0.458930\pi$
$433$	−11.7869	−	5.67629i	−0.566445	−	0.272785i	−0.695111	+	0.718903i	$0.744645\pi$
$434$	0.152831	+	1.83021i	0.00733614	+	0.0878530i
$435$	−14.3840	+	6.92698i	−0.689661	+	0.332123i
$436$	13.3732	−	9.11768i	0.640459	−	0.436658i
$437$	0.0824724	−	0.0765232i	0.00394519	−	0.00366060i
$438$	0.687608	+	9.17549i	0.0328552	+	0.438422i
$439$	13.1313	+	33.4579i	0.626721	+	1.59686i	0.791938	+	0.610602i	$0.209072\pi$
$439$	13.1313	+	33.4579i	0.626721	+	1.59686i	−0.165217	+	0.986257i	$0.552832\pi$
$440$	−14.0996			−0.672174
$441$	0.641858	+	6.97051i	0.0305647	+	0.331929i
$442$	9.38742			0.446514
$443$	10.4231	+	26.5577i	0.495218	+	1.26179i	0.932076	+	0.362264i	$0.117996\pi$
$443$	10.4231	+	26.5577i	0.495218	+	1.26179i	−0.436858	+	0.899531i	$0.643909\pi$
$444$	−0.540441	−	7.21168i	−0.0256482	−	0.342251i
$445$	−15.1253	+	14.0342i	−0.717009	+	0.665287i
$446$	6.21740	−	4.23895i	0.294403	−	0.200720i
$447$	−5.70016	+	2.74505i	−0.269608	+	0.129837i
$448$	2.61946	+	0.372047i	0.123758	+	0.0175776i
$449$	−9.53053	−	4.58966i	−0.449774	−	0.216600i	0.195263	−	0.980751i	$-0.437444\pi$
$449$	−9.53053	−	4.58966i	−0.449774	−	0.216600i	−0.645037	+	0.764151i	$0.723158\pi$
$450$	−4.61613	+	0.695769i	−0.217606	+	0.0327989i
$451$	9.78586	+	6.67188i	0.460798	+	0.314167i
$452$	−0.691288	−	0.104195i	−0.0325155	−	0.00490092i
$453$	13.2752	+	12.3176i	0.623725	+	0.578733i
$454$	5.72661	−	7.18094i	0.268763	−	0.337018i
$455$	7.61431	+	9.38309i	0.356965	+	0.439886i
$456$	0.00830674	+	0.0104163i	0.000388999	+	0.000487789i
$457$	−2.41913	+	32.2810i	−0.113162	+	1.51004i	0.594848	+	0.803838i	$0.297212\pi$
$457$	−2.41913	+	32.2810i	−0.113162	+	1.51004i	−0.708010	+	0.706203i	$0.750407\pi$
$458$	13.7141	−	4.23023i	0.640816	−	0.197665i
$459$	3.19546	+	5.53470i	0.149151	+	0.258338i
$460$	13.1286	−	22.7393i	0.612122	−	1.06023i
$461$	−1.68339	+	7.37540i	−0.0784032	+	0.343507i	−0.998881	−	0.0472873i	$-0.984942\pi$
$461$	−1.68339	+	7.37540i	−0.0784032	+	0.343507i	0.920478	+	0.390794i	$0.127800\pi$
$462$	−5.90999	+	10.4406i	−0.274958	+	0.485742i
$463$	1.68132	+	7.36636i	0.0781378	+	0.342344i	0.998853	−	0.0478924i	$-0.0152504\pi$
$463$	1.68132	+	7.36636i	0.0781378	+	0.342344i	−0.920715	+	0.390236i	$0.872393\pi$
$464$	4.90637	+	1.51341i	0.227772	+	0.0702585i
$465$	−0.788559	+	2.00921i	−0.0365685	+	0.0931751i
$466$	7.22578	−	18.4110i	0.334728	−	0.852873i
$467$	27.3115	+	8.42450i	1.26383	+	0.389839i	0.853018	−	0.521882i	$-0.174770\pi$
$467$	27.3115	+	8.42450i	1.26383	+	0.389839i	0.410810	+	0.911721i	$0.365246\pi$
$468$	0.326854	+	1.43204i	0.0151088	+	0.0661961i
$469$	−14.8349	−	4.43804i	−0.685013	−	0.204930i
$470$	8.00669	−	35.0796i	0.369321	−	1.61810i
$471$	−1.80401	+	3.12463i	−0.0831243	+	0.143975i
$472$	4.44456	+	7.69821i	0.204578	+	0.354339i
$473$	36.3958	−	11.2266i	1.67348	−	0.516200i
$474$	0.636207	−	8.48960i	0.0292220	−	0.389940i
$475$	0.0387781	+	0.0486262i	0.00177926	+	0.00223112i
$476$	−3.90273	−	16.4522i	−0.178881	−	0.754086i
$477$	6.99632	−	8.77310i	0.320339	−	0.401693i
$478$	17.0918	+	15.8589i	0.781763	+	0.725370i
$479$	−35.2681	−	5.31582i	−1.61144	−	0.242886i	−0.719320	−	0.694679i	$-0.755546\pi$
$479$	−35.2681	−	5.31582i	−1.61144	−	0.242886i	−0.892123	+	0.451793i	$0.850784\pi$
$480$	2.56909	+	1.75158i	0.117263	+	0.0799482i
$481$	−10.5041	+	1.58323i	−0.478944	+	0.0721892i
$482$	11.8290	+	5.69655i	0.538797	+	0.259471i
$483$	−11.3353	−	19.2529i	−0.515772	−	0.876039i
$484$	−8.61515	+	4.14884i	−0.391598	+	0.188584i
$485$	−1.84235	+	1.25609i	−0.0836569	+	0.0570363i
$486$	−0.733052	+	0.680173i	−0.0332519	+	0.0308533i
$487$	0.735976	+	9.82092i	0.0333503	+	0.445029i	0.988736	+	0.149668i	$0.0478206\pi$
$487$	0.735976	+	9.82092i	0.0333503	+	0.445029i	−0.955386	+	0.295360i	$0.904560\pi$
$488$	−0.0394580	−	0.100537i	−0.00178618	−	0.00455111i
$489$	−8.46088			−0.382614
$490$	13.2790	−	17.2456i	0.599886	−	0.779079i
$491$	−16.7558			−0.756178			−0.378089	−	0.925769i	$-0.623419\pi$
$491$	−16.7558			−0.756178			−0.378089	+	0.925769i	$0.623419\pi$
$492$	−0.954241	−	2.43137i	−0.0430205	−	0.109614i
$493$	−2.45219	−	32.7223i	−0.110441	−	1.47374i
$494$	0.0143456	−	0.0133108i	0.000645439	−	0.000598880i
$495$	−11.6497	+	7.94261i	−0.523614	+	0.356994i
$496$	0.625419	−	0.301186i	0.0280821	−	0.0135236i
$497$	29.2337	+	19.5688i	1.31131	+	0.877781i
$498$	4.59368	+	2.21220i	0.205848	+	0.0991310i
$499$	−20.6527	+	3.11289i	−0.924542	+	0.139352i	−0.594024	−	0.804447i	$-0.702462\pi$
$499$	−20.6527	+	3.11289i	−0.924542	+	0.139352i	−0.330518	+	0.943800i	$0.607223\pi$
$500$	−0.852248	−	0.581053i	−0.0381137	−	0.0259855i
$501$	−3.96221	−	0.597207i	−0.177018	−	0.0266812i
$502$	12.2213	+	11.3397i	0.545463	+	0.506116i
$503$	−16.2353	+	20.3584i	−0.723894	+	0.907735i	−0.998551	−	0.0538077i	$-0.982864\pi$
$503$	−16.2353	+	20.3584i	−0.723894	+	0.907735i	0.274657	+	0.961542i	$0.411436\pi$
$504$	2.37388	−	1.16820i	0.105741	−	0.0520356i
$505$	−7.71670	−	9.67644i	−0.343389	−	0.430596i
$506$	2.86155	−	38.1848i	0.127211	−	1.69752i
$507$	−10.3607	+	3.19586i	−0.460136	+	0.141933i
$508$	−0.196134	−	0.339714i	−0.00870204	−	0.0150724i
$509$	1.42564	−	2.46928i	0.0631904	−	0.109449i	−0.832699	−	0.553725i	$-0.813206\pi$
$509$	1.42564	−	2.46928i	0.0631904	−	0.109449i	0.895890	+	0.444276i	$0.146539\pi$
$510$	4.42190	−	19.3736i	0.195805	−	0.857877i
$511$	−9.08647	−	22.5848i	−0.401962	−	0.999092i
$512$	−0.222521	−	0.974928i	−0.00983413	−	0.0430861i
$513$	0.0127311	+	0.00392702i	0.000562091	+	0.000173382i
$514$	−5.17788	+	13.1930i	−0.228386	+	0.581919i
$515$	3.46947	−	8.84006i	0.152883	−	0.389540i
$516$	−8.02634	−	2.47580i	−0.353340	−	0.108991i
$517$	−11.6765	−	51.1581i	−0.513532	−	2.24993i
$518$	7.14171	+	17.7510i	0.313789	+	0.779935i
$519$	4.81205	−	21.0830i	0.211226	−	0.925440i
$520$	2.28364	−	3.95538i	0.100144	−	0.173455i
$521$	6.88908	+	11.9322i	0.301816	+	0.522760i	0.976547	−	0.215303i	$-0.0690739\pi$
$521$	6.88908	+	11.9322i	0.301816	+	0.522760i	−0.674731	+	0.738063i	$0.735741\pi$
$522$	4.90637	−	1.51341i	0.214746	−	0.0662403i
$523$	0.981518	−	13.0974i	0.0429188	−	0.572711i	−0.933745	−	0.357938i	$-0.883480\pi$
$523$	0.981518	−	13.0974i	0.0429188	−	0.572711i	0.976664	−	0.214773i	$-0.0689011\pi$
$524$	8.71882	+	10.9330i	0.380883	+	0.477612i
$525$	11.0819	−	5.45345i	0.483655	−	0.238008i
$526$	−5.73786	+	7.19505i	−0.250183	+	0.313719i
$527$	−3.25206	−	3.01747i	−0.141662	−	0.131443i
$528$	4.48390	+	0.675839i	0.195137	+	0.0294121i
$529$	39.9148	+	27.2135i	1.73543	+	1.18319i
$530$	−34.5014	+	5.20025i	−1.49864	+	0.225884i
$531$	8.00883	+	3.85685i	0.347553	+	0.167373i
$532$	−0.0292923	−	0.0196080i	−0.00126998	−	0.000850115i
$533$	−3.45662	+	1.66462i	−0.149723	+	0.0721028i
$534$	5.48278	−	3.73810i	0.237263	−	0.161763i
$535$	32.5793	−	30.2292i	1.40853	−	1.30692i
$536$	0.437366	+	5.83624i	0.0188913	+	0.252087i
$537$	6.74676	+	17.1905i	0.291144	+	0.741823i
$538$	−23.5912			−1.01709
$539$	6.53542	−	31.0617i	0.281500	−	1.33792i
$540$	3.10938			0.133807
$541$	−12.1638	−	30.9928i	−0.522961	−	1.33248i	−0.911594	−	0.411091i	$-0.865148\pi$
$541$	−12.1638	−	30.9928i	−0.522961	−	1.33248i	0.388633	−	0.921393i	$-0.372947\pi$
$542$	−1.32454	−	17.6748i	−0.0568940	−	0.759198i
$543$	−14.6323	+	13.5768i	−0.627930	+	0.582634i
$544$	−5.28042	+	3.60013i	−0.226396	+	0.154354i
$545$	−45.3433	+	21.8362i	−1.94229	+	0.935359i
$546$	−1.97171	−	3.34894i	−0.0843812	−	0.143321i
$547$	−2.09784	−	1.01027i	−0.0896970	−	0.0431958i	0.388497	−	0.921450i	$-0.372994\pi$
$547$	−2.09784	−	1.01027i	−0.0896970	−	0.0431958i	−0.478194	+	0.878254i	$0.658709\pi$
$548$	−2.82776	+	0.426216i	−0.120796	+	0.0182070i
$549$	−0.0892364	−	0.0608403i	−0.00380852	−	0.00259660i
$550$	20.9320	+	3.15500i	0.892545	+	0.134530i
$551$	−0.0501455	−	0.0465282i	−0.00213627	−	0.00198217i
$552$	−5.26504	+	6.60215i	−0.224095	+	0.281006i
$553$	5.19887	+	21.9162i	0.221078	+	0.931970i
$554$	9.35157	+	11.7265i	0.397310	+	0.498211i
$555$	−1.68044	+	22.4239i	−0.0713306	+	0.951841i
$556$	−10.4210	+	3.21447i	−0.441951	+	0.136324i
$557$	−5.17552	−	8.96426i	−0.219294	−	0.379828i	0.735298	−	0.677743i	$-0.237042\pi$
$557$	−5.17552	−	8.96426i	−0.219294	−	0.379828i	−0.954592	+	0.297915i	$0.903709\pi$
$558$	0.347081	−	0.601162i	0.0146931	−	0.0254492i
$559$	−2.74541	+	12.0284i	−0.116119	+	0.508748i
$560$	−7.88152	−	2.35785i	−0.333055	−	0.0996374i
$561$	−6.44863	−	28.2533i	−0.272262	−	1.19286i
$562$	−21.0590	−	6.49583i	−0.888319	−	0.274010i
$563$	10.5334	−	26.8386i	0.443930	−	1.13111i	−0.517407	−	0.855739i	$-0.673103\pi$
$563$	10.5334	−	26.8386i	0.443930	−	1.13111i	0.961337	−	0.275375i	$-0.0888020\pi$
$564$	−4.22772	+	10.7721i	−0.178019	+	0.453585i
$565$	2.07719	+	0.640727i	0.0873878	+	0.0269556i
$566$	−1.04585	−	4.58218i	−0.0439605	−	0.192603i
$567$	1.30333	−	2.30246i	0.0547345	−	0.0966944i
$568$	2.95871	−	12.9630i	0.124145	−	0.543914i
$569$	1.25388	−	2.17179i	0.0525654	−	0.0910460i	−0.838545	−	0.544832i	$-0.816594\pi$
$569$	1.25388	−	2.17179i	0.0525654	−	0.0910460i	0.891111	+	0.453786i	$0.149927\pi$
$570$	−0.0207131	−	0.0358762i	−0.000867577	−	0.00150269i
$571$	−2.31872	+	0.715229i	−0.0970353	+	0.0299314i	−0.342893	−	0.939375i	$-0.611407\pi$
$571$	−2.31872	+	0.715229i	−0.0970353	+	0.0299314i	0.245857	+	0.969306i	$0.420931\pi$
$572$	0.497751	−	6.64203i	0.0208120	−	0.277717i
$573$	−9.19442	−	11.5294i	−0.384102	−	0.481649i
$574$	4.35445	+	5.36597i	0.181751	+	0.223971i
$575$	−24.5786	+	30.8206i	−1.02500	+	1.28531i
$576$	−0.733052	−	0.680173i	−0.0305438	−	0.0283405i
$577$	−40.1159	−	6.04649i	−1.67005	−	0.251719i	−0.755192	−	0.655504i	$-0.772456\pi$
$577$	−40.1159	−	6.04649i	−1.67005	−	0.251719i	−0.914854	+	0.403785i	$0.867694\pi$
$578$	19.7007	+	13.4317i	0.819441	+	0.558685i
$579$	−1.43837	+	0.216799i	−0.0597766	+	0.00900988i
$580$	−14.3840	−	6.92698i	−0.597264	−	0.287627i
$581$	−13.3556	−	1.89692i	−0.554083	−	0.0786974i
$582$	0.646104	−	0.311147i	0.0267819	−	0.0128975i
$583$	−42.0416	+	28.6635i	−1.74119	+	1.18712i
$584$	−6.74497	+	6.25842i	−0.279109	+	0.258975i
$585$	−0.341313	−	4.55451i	−0.0141116	−	0.188306i
$586$	−2.77581	−	7.07266i	−0.114668	−	0.292169i
$587$	−6.71734			−0.277254			−0.138627	−	0.990345i	$-0.544269\pi$
$587$	−6.71734			−0.277254			−0.138627	+	0.990345i	$0.544269\pi$
$588$	−5.04957	+	4.84787i	−0.208241	+	0.199923i
$589$	−0.00924831			−0.000381070
$590$	−10.0979	−	25.7291i	−0.415725	−	1.05925i
$591$	0.704026	+	9.39457i	0.0289597	+	0.386441i
$592$	5.30136	−	4.91894i	0.217885	−	0.202167i
$593$	27.5551	−	18.7868i	1.13155	−	0.771480i	0.155247	−	0.987876i	$-0.450383\pi$
$593$	27.5551	−	18.7868i	1.13155	−	0.771480i	0.976306	+	0.216396i	$0.0694303\pi$
$594$	4.08548	−	1.96747i	0.167629	−	0.0807261i
$595$	4.37511	+	52.3935i	0.179362	+	2.14793i
$596$	−5.70016	−	2.74505i	−0.233488	−	0.112442i
$597$	−19.0394	+	2.86973i	−0.779232	+	0.117450i
$598$	10.2485	+	6.98732i	0.419093	+	0.285733i
$599$	−6.43666	−	0.970170i	−0.262995	−	0.0396401i	0.0162211	−	0.999868i	$-0.494836\pi$
$599$	−6.43666	−	0.970170i	−0.262995	−	0.0396401i	−0.279216	+	0.960228i	$0.590075\pi$
$600$	−3.42208	−	3.17523i	−0.139706	−	0.129628i
$601$	−6.36555	+	7.98214i	−0.259656	+	0.325598i	−0.894522	−	0.447024i	$-0.852484\pi$
$601$	−6.36555	+	7.98214i	−0.259656	+	0.325598i	0.634866	+	0.772622i	$0.281055\pi$
$602$	22.2222	−	0.189151i	0.905709	−	0.00770922i
$603$	3.64904	+	4.57575i	0.148600	+	0.186339i
$604$	−1.35333	+	18.0589i	−0.0550662	+	0.734807i
$605$	28.4113	−	8.76373i	1.15508	−	0.356296i
$606$	1.99021	+	3.44714i	0.0808466	+	0.140030i
$607$	−2.90753	+	5.03600i	−0.118013	+	0.204405i	−0.918980	−	0.394304i	$-0.870986\pi$
$607$	−2.90753	+	5.03600i	−0.118013	+	0.204405i	0.800967	+	0.598708i	$0.204319\pi$
$608$	−0.00296464	+	0.0129889i	−0.000120232	+	0.000526771i
$609$	−11.1585	+	7.74770i	−0.452167	+	0.313953i
$610$	0.0747277	+	0.327403i	0.00302564	+	0.0132562i
$611$	16.2426	+	5.01017i	0.657104	+	0.202690i
$612$	−2.33486	+	5.94914i	−0.0943813	+	0.240480i
$613$	6.20736	−	15.8161i	0.250713	−	0.638806i	−0.749005	−	0.662564i	$-0.769468\pi$
$613$	6.20736	−	15.8161i	0.250713	−	0.638806i	0.999718	+	0.0237585i	$0.00756329\pi$
$614$	−7.18591	−	2.21656i	−0.290000	−	0.0894531i
$615$	1.80719	+	7.91783i	0.0728731	+	0.319278i
$616$	−11.8476	+	1.88901i	−0.477355	+	0.0761104i
$617$	2.63597	−	11.5490i	0.106120	−	0.464944i	−0.893746	−	0.448574i	$-0.851932\pi$
$617$	2.63597	−	11.5490i	0.106120	−	0.464944i	0.999866	−	0.0163695i	$-0.00521082\pi$
$618$	−1.52707	+	2.64497i	−0.0614279	+	0.106396i
$619$	12.0459	+	20.8641i	0.484165	+	0.838598i	0.999835	−	0.0181896i	$-0.00579026\pi$
$619$	12.0459	+	20.8641i	0.484165	+	0.838598i	−0.515670	+	0.856787i	$0.672457\pi$
$620$	−2.06253	+	0.636205i	−0.0828330	+	0.0255506i
$621$	−0.631056	+	8.42086i	−0.0253234	+	0.337917i
$622$	19.4579	+	24.3994i	0.780190	+	0.978327i
$623$	−10.8292	+	13.8191i	−0.433864	+	0.553650i
$624$	−0.915824	+	1.14841i	−0.0366623	+	0.0459731i
$625$	19.4615	+	18.0576i	0.778460	+	0.722306i
$626$	−17.4542	−	2.63079i	−0.697609	−	0.105148i
$627$	−0.0499161	−	0.0340322i	−0.00199346	−	0.00135912i
$628$	−3.56772	+	0.537747i	−0.142367	+	0.0214584i
$629$	−41.6414	−	20.0535i	−1.66035	−	0.799584i
$630$	−7.84025	+	2.49167i	−0.312363	+	0.0992706i
$631$	31.1148	−	14.9841i	1.23866	−	0.596508i	0.304213	−	0.952604i	$-0.401607\pi$
$631$	31.1148	−	14.9841i	1.23866	−	0.596508i	0.934449	+	0.356096i	$0.115892\pi$
$632$	7.03410	−	4.79577i	0.279802	−	0.190766i
$633$	3.69849	−	3.43170i	0.147002	−	0.136398i
$634$	−1.00551	−	13.4175i	−0.0399337	−	0.532879i
$635$	0.445611	+	1.13540i	0.0176835	+	0.0450569i
$636$	11.2212			0.444950
$637$	7.65525	+	6.86427i	0.303312	+	0.271972i
$638$	−23.2825			−0.921763
$639$	−4.85770	−	12.3772i	−0.192167	−	0.489635i
$640$	0.232365	+	3.10069i	0.00918502	+	0.122566i
$641$	−13.8527	+	12.8534i	−0.547148	+	0.507679i	−0.904605	−	0.426250i	$-0.859834\pi$
$641$	−13.8527	+	12.8534i	−0.547148	+	0.507679i	0.357457	+	0.933930i	$0.383644\pi$
$642$	−11.8097	+	8.05171i	−0.466091	+	0.317776i
$643$	−6.00774	+	2.89317i	−0.236922	+	0.114096i	−0.548578	−	0.836099i	$-0.684831\pi$
$643$	−6.00774	+	2.89317i	−0.236922	+	0.114096i	0.311656	+	0.950195i	$0.399116\pi$
$644$	7.98512	−	20.8663i	0.314658	−	0.822246i
$645$	23.5309	+	11.3319i	0.926526	+	0.446192i
$646$	0.0841950	−	0.0126904i	0.00331261	−	0.000499296i
$647$	−33.0275	−	22.5178i	−1.29845	−	0.885266i	−0.300790	−	0.953690i	$-0.597250\pi$
$647$	−33.0275	−	22.5178i	−1.29845	−	0.885266i	−0.997656	+	0.0684249i	$0.978203\pi$
$648$	−0.988831	−	0.149042i	−0.0388449	−	0.00585493i
$649$	−29.5480	−	27.4165i	−1.15986	−	1.07619i
$650$	−4.27532	+	5.36108i	−0.167692	+	0.210279i
$651$	−0.393423	+	1.79395i	−0.0154195	+	0.0703104i
$652$	−5.27527	−	6.61498i	−0.206596	−	0.259063i
$653$	−0.625191	+	8.34259i	−0.0244656	+	0.326471i	0.971520	+	0.236958i	$0.0761502\pi$
$653$	−0.625191	+	8.34259i	−0.0244656	+	0.326471i	−0.995986	+	0.0895134i	$0.971469\pi$
$654$	15.4665	−	4.77079i	0.604789	−	0.186553i
$655$	−21.7406	−	37.6559i	−0.849477	−	1.47134i
$656$	1.30596	−	2.26199i	0.0509891	−	0.0883158i
$657$	−2.04746	+	8.97052i	−0.0798791	+	0.349973i
$658$	2.02803	−	30.5493i	0.0790610	−	1.19094i
$659$	−5.44047	−	23.8363i	−0.211931	−	0.928529i	−0.963253	−	0.268594i	$-0.913441\pi$
$659$	−5.44047	−	23.8363i	−0.211931	−	0.928529i	0.751323	−	0.659935i	$-0.229416\pi$
$660$	−13.4732	−	4.15594i	−0.524445	−	0.161770i
$661$	−14.9868	+	38.1857i	−0.582918	+	1.48525i	0.269820	+	0.962911i	$0.413036\pi$
$661$	−14.9868	+	38.1857i	−0.582918	+	1.48525i	−0.852738	+	0.522339i	$0.825059\pi$
$662$	3.72721	−	9.49677i	0.144862	−	0.369102i
$663$	8.97036	+	2.76699i	0.348380	+	0.107461i
$664$	1.13455	+	4.97077i	0.0440289	+	0.192903i
$665$	0.0809767	+	0.0738628i	0.00314014	+	0.00286428i
$666$	1.60925	−	7.05058i	0.0623572	−	0.273205i
$667$	21.6790	−	37.5491i	0.839413	−	1.45391i
$668$	−2.00348	−	3.47013i	−0.0775170	−	0.134263i
$669$	7.19064	−	2.21802i	0.278006	−	0.0857535i
$670$	1.35994	−	18.1471i	0.0525390	−	0.701084i
$671$	0.305351	+	0.382898i	0.0117879	+	0.0147816i
$672$	2.39342	+	1.12762i	0.0923283	+	0.0434988i
$673$	20.2410	−	25.3814i	0.780234	−	0.978382i	−0.219762	−	0.975553i	$-0.570528\pi$
$673$	20.2410	−	25.3814i	0.780234	−	0.978382i	0.999996	−	0.00282863i	$-0.000900382\pi$
$674$	14.2907	+	13.2599i	0.550458	+	0.510751i
$675$	−4.61613	−	0.695769i	−0.177675	−	0.0267802i
$676$	−8.95843	−	6.10776i	−0.344555	−	0.234914i
$677$	−34.8440	+	5.25189i	−1.33916	+	0.201847i	−0.779255	−	0.626707i	$-0.784402\pi$
$677$	−34.8440	+	5.25189i	−1.33916	+	0.201847i	−0.559910	+	0.828554i	$0.689164\pi$
$678$	−0.629864	−	0.303327i	−0.0241898	−	0.0116492i
$679$	−1.37980	+	1.30230i	−0.0529520	+	0.0499777i
$680$	17.9039	−	8.62206i	0.686583	−	0.330641i
$681$	7.58881	−	5.17396i	0.290804	−	0.198267i
$682$	−2.30744	+	2.14099i	−0.0883563	+	0.0819826i
$683$	−1.41423	−	18.8716i	−0.0541140	−	0.722102i	−0.956604	−	0.291391i	$-0.905882\pi$
$683$	−1.41423	−	18.8716i	−0.0541140	−	0.722102i	0.902490	−	0.430711i	$-0.141737\pi$
$684$	0.00486743	+	0.0124020i	0.000186111	+	0.000474203i
$685$	8.89190			0.339742
$686$	8.84760	−	16.2702i	0.337803	−	0.621200i
$687$	14.3517			0.547550
$688$	−3.06868	−	7.81888i	−0.116992	−	0.298092i
$689$	−1.23174	−	16.4364i	−0.0469255	−	0.626177i
$690$	19.2478	−	17.8594i	0.732752	−	0.679894i
$691$	−11.9657	+	8.15810i	−0.455198	+	0.310349i	−0.769125	−	0.639098i	$-0.779308\pi$
$691$	−11.9657	+	8.15810i	−0.455198	+	0.310349i	0.313927	+	0.949447i	$0.398355\pi$
$692$	19.4836	−	9.38280i	0.740655	−	0.356681i
$693$	−8.72485	+	8.23478i	−0.331430	+	0.312813i
$694$	−3.18771	−	1.53512i	−0.121004	−	0.0582724i
$695$	33.5308	−	5.05395i	1.27190	−	0.191707i
$696$	4.24230	+	2.89235i	0.160804	+	0.109634i
$697$	−16.5061	−	2.48790i	−0.625214	−	0.0942358i
$698$	−0.738180	−	0.684931i	−0.0279405	−	0.0259250i
$699$	12.3315	−	15.4632i	0.466420	−	0.584872i
$700$	11.1731	+	5.26402i	0.422305	+	0.198961i
$701$	−7.12745	−	8.93754i	−0.269200	−	0.337566i	0.628796	−	0.777571i	$-0.283548\pi$
$701$	−7.12745	−	8.93754i	−0.269200	−	0.337566i	−0.897996	+	0.440005i	$0.854977\pi$
$702$	−0.109769	+	1.46476i	−0.00414295	+	0.0552838i
$703$	−0.0920699	+	0.0283998i	−0.00347248	+	0.00107112i
$704$	2.26727	+	3.92703i	0.0854510	+	0.148006i
$705$	17.9909	−	31.1611i	0.677575	−	1.17359i
$706$	−4.06749	+	17.8208i	−0.153082	+	0.670696i
$707$	−7.78059	−	7.09705i	−0.292619	−	0.266912i
$708$	1.97802	+	8.66626i	0.0743384	+	0.325698i
$709$	−29.4810	−	9.09369i	−1.10718	−	0.341521i	−0.313338	−	0.949642i	$-0.601447\pi$
$709$	−29.4810	−	9.09369i	−1.10718	−	0.341521i	−0.793844	+	0.608121i	$0.791924\pi$
$710$	−15.1044	+	38.4855i	−0.566860	+	1.44433i
$711$	3.11030	−	7.92490i	0.116645	−	0.297207i
$712$	6.34102	+	1.95595i	0.237640	+	0.0733021i
$713$	−1.30438	−	5.71487i	−0.0488495	−	0.214023i
$714$	1.12003	−	16.8716i	0.0419162	−	0.631405i
$715$	−4.60852	+	20.1913i	−0.172349	+	0.755110i
$716$	−9.23351	+	15.9929i	−0.345072	+	0.597683i
$717$	11.6580	+	20.1923i	0.435376	+	0.754094i
$718$	−4.55840	+	1.40608i	−0.170118	+	0.0524745i
$719$	−0.151475	+	2.02129i	−0.00564906	+	0.0753814i	−0.999316	−	0.0369860i	$-0.988224\pi$
$719$	−0.151475	+	2.02129i	−0.00564906	+	0.0753814i	0.993667	+	0.112367i	$0.0358434\pi$
$720$	1.93867	+	2.43101i	0.0722499	+	0.0905986i
$721$	1.73097	−	7.89294i	0.0644645	−	0.293948i
$722$	−11.8462	+	14.8547i	−0.440870	+	0.552833i
$723$	9.62439	+	8.93013i	0.357935	+	0.332115i
$724$	−19.7378	−	2.97499i	−0.733550	−	0.110565i
$725$	19.8042	+	13.5023i	0.735510	+	0.501462i
$726$	−9.45530	+	1.42516i	−0.350919	+	0.0528925i
$727$	21.7139	+	10.4568i	0.805323	+	0.387823i	0.790802	−	0.612072i	$-0.209664\pi$
$727$	21.7139	+	10.4568i	0.805323	+	0.387823i	0.0145202	+	0.999895i	$0.495378\pi$
$728$	1.38897	−	3.62957i	0.0514786	−	0.134521i
$729$	−0.900969	+	0.433884i	−0.0333692	+	0.0160698i
$730$	23.6388	−	16.1167i	0.874911	−	0.596504i
$731$	−39.3506	+	36.5120i	−1.45543	+	1.35045i
$732$	−0.00807108	−	0.107701i	−0.000298316	−	0.00398075i
$733$	16.3736	+	41.7192i	0.604771	+	1.54093i	0.824791	+	0.565437i	$0.191293\pi$
$733$	16.3736	+	41.7192i	0.604771	+	1.54093i	−0.220020	+	0.975495i	$0.570612\pi$
$734$	36.1811			1.33547
$735$	17.7723	−	12.5654i	0.655543	−	0.463482i
$736$	−8.44447			−0.311267
$737$	−9.69575	−	24.7044i	−0.357148	−	0.909997i
$738$	−0.195189	−	2.60461i	−0.00718500	−	0.0958772i
$739$	25.9433	−	24.0718i	0.954339	−	0.885497i	−0.0391722	−	0.999232i	$-0.512472\pi$
$739$	25.9433	−	24.0718i	0.954339	−	0.885497i	0.993511	+	0.113735i	$0.0362816\pi$
$740$	−18.5794	+	12.6672i	−0.682994	+	0.465657i
$741$	0.0176317	−	0.00849098i	0.000647716	−	0.000311924i
$742$	−28.2941	+	8.99201i	−1.03871	+	0.330107i
$743$	−0.395103	−	0.190272i	−0.0144949	−	0.00698039i	0.426622	−	0.904430i	$-0.359703\pi$
$743$	−0.395103	−	0.190272i	−0.0144949	−	0.00698039i	−0.441117	+	0.897450i	$0.645418\pi$
$744$	0.686409	−	0.103460i	0.0251650	−	0.00379301i
$745$	16.2539	+	11.0817i	0.595497	+	0.406003i
$746$	24.6328	+	3.71280i	0.901872	+	0.135935i
$747$	3.73754	+	3.46793i	0.136749	+	0.126885i
$748$	18.0687	−	22.6574i	0.660656	−	0.828437i
$749$	23.3257	−	29.7658i	0.852304	−	1.08762i
$750$	−0.643117	−	0.806443i	−0.0234833	−	0.0294471i
$751$	−1.15476	+	15.4092i	−0.0421379	+	0.562291i	0.935682	+	0.352844i	$0.114785\pi$
$751$	−1.15476	+	15.4092i	−0.0421379	+	0.562291i	−0.977820	+	0.209447i	$0.932834\pi$
$752$	−11.0579	+	3.41090i	−0.403239	+	0.124383i
$753$	8.33590	+	14.4382i	0.303777	+	0.526157i
$754$	3.77093	−	6.53145i	0.137329	−	0.237861i
$755$	12.5301	−	54.8978i	0.456015	−	1.99793i
$756$	2.61275	−	0.416582i	0.0950248	−	0.0151510i
$757$	0.937699	+	4.10833i	0.0340813	+	0.149320i	0.989106	−	0.147208i	$-0.0470286\pi$
$757$	0.937699	+	4.10833i	0.0340813	+	0.149320i	−0.955024	+	0.296527i	$0.904171\pi$
$758$	−11.0473	−	3.40765i	−0.401257	−	0.123772i
$759$	13.9896	−	35.6449i	0.507789	−	1.29383i
$760$	0.0151347	−	0.0385626i	0.000548994	−	0.00139881i
$761$	−32.8370	−	10.1289i	−1.19034	−	0.367172i	−0.364570	−	0.931176i	$-0.618784\pi$
$761$	−32.8370	−	10.1289i	−1.19034	−	0.367172i	−0.825772	+	0.564004i	$0.809260\pi$
$762$	−0.0872878	−	0.382433i	−0.00316210	−	0.0138541i
$763$	−35.1755	+	24.4234i	−1.27344	+	0.884186i
$764$	3.28145	−	14.3770i	0.118719	−	0.520140i
$765$	9.93591	−	17.2095i	0.359234	−	0.622211i
$766$	−9.15398	−	15.8552i	−0.330747	−	0.572870i
$767$	12.4769	−	3.84861i	0.450514	−	0.138965i
$768$	0.0747301	−	0.997204i	0.00269659	−	0.0359835i
$769$	−19.0004	−	23.8257i	−0.685172	−	0.859178i	0.310647	−	0.950525i	$-0.399454\pi$
$769$	−19.0004	−	23.8257i	−0.685172	−	0.859178i	−0.995819	+	0.0913471i	$0.970883\pi$
$770$	37.3028	−	0.317514i	1.34430	−	0.0114424i
$771$	−8.83655	+	11.0807i	−0.318241	+	0.399061i
$772$	−1.06631	−	0.989391i	−0.0383773	−	0.0356090i
$773$	26.0807	+	3.93104i	0.938059	+	0.141390i	0.600239	−	0.799821i	$-0.295072\pi$
$773$	26.0807	+	3.93104i	0.938059	+	0.141390i	0.337821	+	0.941211i	$0.390310\pi$
$774$	−6.93999	−	4.73161i	−0.249453	−	0.170074i
$775$	3.20434	−	0.482977i	0.115103	−	0.0173490i
$776$	0.646104	+	0.311147i	0.0231938	+	0.0111695i
$777$	1.59222	+	19.0675i	0.0571207	+	0.684041i
$778$	7.01076	−	3.37621i	0.251348	−	0.121043i
$779$	−0.0287519	+	0.0196027i	−0.00103014	+	0.000702340i
$780$	3.34805	−	3.10654i	0.119879	−	0.111232i
$781$	4.50569	+	60.1242i	0.161226	+	2.15141i
$782$	19.7167	+	50.2373i	0.705067	+	1.79648i
$783$	5.13448			0.183491
$784$	−6.93857	−	0.925319i	−0.247806	−	0.0330471i
$785$	11.2187			0.400413
$786$	5.10889	+	13.0172i	0.182228	+	0.464310i
$787$	−1.71420	−	22.8745i	−0.0611048	−	0.815386i	−0.940608	−	0.339494i	$-0.889744\pi$
$787$	−1.71420	−	22.8745i	−0.0611048	−	0.815386i	0.879503	−	0.475892i	$-0.157875\pi$
$788$	−6.90602	+	6.40785i	−0.246017	+	0.228270i
$789$	−7.60372	+	5.18413i	−0.270700	+	0.184560i
$790$	−23.8499	+	11.4855i	−0.848543	+	0.408637i
$791$	1.83126	+	0.260097i	0.0651120	+	0.00924797i
$792$	4.08548	+	1.96747i	0.145171	+	0.0699108i
$793$	−0.156870	+	0.0236444i	−0.00557063	+	0.000839638i
$794$	−9.03064	−	6.15699i	−0.320485	−	0.218503i
$795$	−34.5014	−	5.20025i	−1.22364	−	0.184434i
$796$	−14.1145	−	13.0964i	−0.500276	−	0.464189i
$797$	−0.247407	+	0.310238i	−0.00876360	+	0.0109892i	−0.786194	−	0.617980i	$-0.787951\pi$
$797$	−0.247407	+	0.310238i	−0.00876360	+	0.0109892i	0.777430	+	0.628969i	$0.216523\pi$
$798$	−0.0222113	−	0.0273709i	−0.000786273	−	0.000968921i
$799$	46.1106	+	57.8208i	1.63127	+	2.04555i
$800$	0.348860	−	4.65522i	0.0123341	−	0.164587i
$801$	6.34102	−	1.95595i	0.224049	−	0.0691099i
$802$	17.5910	+	30.4685i	0.621161	+	1.07588i
$803$	20.8617	−	36.1335i	0.736192	−	1.27512i
$804$	−1.30233	+	5.70587i	−0.0459296	+	0.201231i
$805$	−34.2215	+	60.4560i	−1.20615	+	2.13080i
$806$	−0.226890	−	0.994069i	−0.00799185	−	0.0350146i
$807$	−22.5431	−	6.95363i	−0.793555	−	0.244779i
$808$	−1.45421	+	3.70526i	−0.0511589	+	0.130351i
$809$	3.15824	−	8.04707i	0.111038	−	0.282920i	−0.864544	−	0.502558i	$-0.832392\pi$
$809$	3.15824	−	8.04707i	0.111038	−	0.282920i	0.975581	+	0.219638i	$0.0704876\pi$
$810$	2.97124	+	0.916507i	0.104399	+	0.0322028i
$811$	1.67854	+	7.35416i	0.0589415	+	0.258239i	0.995810	−	0.0914410i	$-0.0291473\pi$
$811$	1.67854	+	7.35416i	0.0589415	+	0.258239i	−0.936869	+	0.349680i	$0.886290\pi$
$812$	−13.0146	−	3.89348i	−0.456724	−	0.136634i
$813$	3.94404	−	17.2800i	0.138324	−	0.606035i
$814$	−16.3967	+	28.3999i	−0.574704	+	0.995416i
$815$	13.1541	+	22.7835i	0.460767	+	0.798071i
$816$	−6.10699	+	1.88376i	−0.213787	+	0.0659447i
$817$	−0.00836277	+	0.111593i	−0.000292576	+	0.00390416i
$818$	12.5473	+	15.7338i	0.438705	+	0.550118i
$819$	−0.896992	−	3.78133i	−0.0313434	−	0.132130i
$820$	−5.06365	+	6.34961i	−0.176830	+	0.221738i
$821$	21.6528	+	20.0909i	0.755688	+	0.701176i	0.960702	−	0.277583i	$-0.0895334\pi$
$821$	21.6528	+	20.0909i	0.755688	+	0.701176i	−0.205013	+	0.978759i	$0.565724\pi$
$822$	−2.82776	−	0.426216i	−0.0986294	−	0.0148660i
$823$	−11.3891	−	7.76495i	−0.396999	−	0.270669i	0.348322	−	0.937375i	$-0.386751\pi$
$823$	−11.3891	−	7.76495i	−0.396999	−	0.270669i	−0.745321	+	0.666706i	$0.767704\pi$
$824$	−3.02004	+	0.455197i	−0.105208	+	0.0158575i
$825$	19.0721	+	9.18466i	0.664007	+	0.319769i
$826$	−11.9321	−	20.2667i	−0.415172	−	0.705169i
$827$	−31.6656	+	15.2493i	−1.10112	+	0.530271i	−0.894010	−	0.448047i	$-0.852120\pi$
$827$	−31.6656	+	15.2493i	−1.10112	+	0.530271i	−0.207109	+	0.978318i	$0.566406\pi$
$828$	−6.97715	+	4.75694i	−0.242473	+	0.165315i
$829$	33.0239	−	30.6417i	1.14697	−	1.06423i	0.149821	−	0.988713i	$-0.452130\pi$
$829$	33.0239	−	30.6417i	1.14697	−	1.06423i	0.997145	−	0.0755156i	$-0.0240603\pi$
$830$	−1.18473	−	15.8092i	−0.0411227	−	0.548744i
$831$	5.47966	+	13.9619i	0.190087	+	0.484335i
$832$	−1.46887			−0.0509239
$833$	10.6958	+	43.4390i	0.370587	+	1.50507i
$834$	−10.9055			−0.377628
$835$	4.55185	+	11.5979i	0.157523	+	0.401363i
$836$	−0.00451472	−	0.0602447i	−0.000156145	−	0.00208361i
$837$	0.508857	−	0.472150i	0.0175887	−	0.0163199i
$838$	0.206885	−	0.141052i	0.00714672	−	0.00487255i
$839$	48.9826	−	23.5888i	1.69107	−	0.814374i	0.695688	−	0.718344i	$-0.255100\pi$
$839$	48.9826	−	23.5888i	1.69107	−	0.814374i	0.995378	−	0.0960301i	$-0.0306145\pi$
$840$	−6.83638	−	4.57622i	−0.235878	−	0.157895i
$841$	2.37599	+	1.14422i	0.0819308	+	0.0394558i
$842$	22.5024	−	3.39169i	0.775485	−	0.116886i
$843$	−18.2087	−	12.4145i	−0.627141	−	0.427577i
$844$	4.98898	+	0.751968i	0.171728	+	0.0258838i
$845$	24.7136	+	22.9308i	0.850173	+	0.788845i
$846$	−7.21501	+	9.04734i	−0.248057	+	0.311054i
$847$	22.6993	−	11.1704i	0.779957	−	0.383820i
$848$	6.99632	+	8.77310i	0.240254	+	0.301270i
$849$	0.351233	−	4.68688i	0.0120543	−	0.160853i
$850$	−28.5091	+	8.79388i	−0.977853	+	0.301628i
$851$	−30.5348	−	52.8878i	−1.04672	−	1.81297i
$852$	6.64817	−	11.5150i	0.227762	−	0.394496i
$853$	−7.12480	+	31.2158i	−0.243949	+	1.06881i	0.693438	+	0.720517i	$0.256095\pi$
$853$	−7.12480	+	31.2158i	−0.243949	+	1.06881i	−0.937386	+	0.348292i	$0.886762\pi$
$854$	0.106656	+	0.265098i	0.00364970	+	0.00907148i
$855$	−0.00921821	−	0.0403876i	−0.000315256	−	0.00138123i
$856$	−13.6583	−	4.21303i	−0.466831	−	0.143998i
$857$	11.7884	−	30.0364i	0.402685	−	1.02603i	−0.575409	−	0.817866i	$-0.695157\pi$
$857$	11.7884	−	30.0364i	0.402685	−	1.02603i	0.978095	−	0.208160i	$-0.0667475\pi$
$858$	2.43341	−	6.20022i	0.0830752	−	0.211672i
$859$	−10.2744	−	3.16924i	−0.350559	−	0.108133i	0.114475	−	0.993426i	$-0.463482\pi$
$859$	−10.2744	−	3.16924i	−0.350559	−	0.108133i	−0.465033	+	0.885293i	$0.653958\pi$
$860$	5.81164	+	25.4625i	0.198175	+	0.868263i
$861$	2.57935	+	6.41107i	0.0879039	+	0.218489i
$862$	−7.21548	+	31.6131i	−0.245760	+	1.07675i
$863$	−14.8406	+	25.7047i	−0.505180	+	0.874998i	0.494802	+	0.869006i	$0.335241\pi$
$863$	−14.8406	+	25.7047i	−0.505180	+	0.874998i	−0.999982	+	0.00599213i	$0.998093\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	−64.2536	+	19.8196i	−2.18469	+	0.673887i
$866$	0.977658	−	13.0459i	0.0332222	−	0.443319i
$867$	14.8664	+	18.6419i	0.504889	+	0.633111i
$868$	−1.64786	+	0.810918i	−0.0559320	+	0.0275243i
$869$	−24.0695	+	30.1821i	−0.816500	+	1.02386i
$870$	−11.7032	−	10.8590i	−0.396776	−	0.368154i
$871$	8.50069	+	1.28127i	0.288035	+	0.0434143i
$872$	13.3732	+	9.11768i	0.452873	+	0.308764i
$873$	0.709111	−	0.106881i	0.0239998	−	0.00361739i
$874$	0.101364	+	0.0488143i	0.00342869	+	0.00165117i
$875$	2.26784	+	1.51807i	0.0766670	+	0.0513202i
$876$	−8.29001	+	3.99226i	−0.280093	+	0.134886i
$877$	−7.23655	+	4.93380i	−0.244361	+	0.166603i	−0.679307	−	0.733854i	$-0.737720\pi$
$877$	−7.23655	+	4.93380i	−0.244361	+	0.166603i	0.434946	+	0.900456i	$0.356767\pi$
$878$	−26.3477	+	24.4471i	−0.889192	+	0.825050i
$879$	−0.567790	−	7.57663i	−0.0191511	−	0.255553i
$880$	−5.15118	−	13.1250i	−0.173646	−	0.442443i
$881$	43.1692			1.45441			0.727204	−	0.686421i	$-0.240819\pi$
$881$	43.1692			1.45441			0.727204	+	0.686421i	$0.240819\pi$
$882$	−6.25417	+	3.14410i	−0.210589	+	0.105867i
$883$	−36.0156			−1.21202			−0.606011	−	0.795456i	$-0.707231\pi$
$883$	−36.0156			−1.21202			−0.606011	+	0.795456i	$0.707231\pi$
$884$	3.42961	+	8.73850i	0.115350	+	0.293908i
$885$	−2.06552	−	27.5624i	−0.0694316	−	0.926501i
$886$	−20.9139	+	19.4052i	−0.702615	+	0.651932i
$887$	5.11952	−	3.49043i	0.171897	−	0.117197i	−0.474316	−	0.880355i	$-0.657304\pi$
$887$	5.11952	−	3.49043i	0.171897	−	0.117197i	0.646212	+	0.763158i	$0.276352\pi$
$888$	6.51572	−	3.13781i	0.218653	−	0.105298i
$889$	0.526553	+	0.894350i	0.0176600	+	0.0299955i
$890$	−18.5900	−	8.95247i	−0.623138	−	0.300088i
$891$	4.48390	−	0.675839i	0.150216	−	0.0226415i
$892$	6.21740	+	4.23895i	0.208174	+	0.141931i
$893$	0.152451	+	0.0229783i	0.00510159	+	0.000768941i
$894$	−4.63780	−	4.30325i	−0.155111	−	0.143922i
$895$	35.8014	−	44.8936i	1.19671	−	1.50063i
$896$	0.610668	+	2.57431i	0.0204010	+	0.0860017i
$897$	7.73365	+	9.69769i	0.258219	+	0.323797i
$898$	0.790502	−	10.5485i	0.0263794	−	0.352008i
$899$	−3.40582	+	1.05055i	−0.113590	+	0.0350380i
$900$	−2.33413	−	4.04284i	−0.0778045	−	0.134761i
$901$	35.8569	−	62.1060i	1.19457	−	2.06905i
$902$	−2.63551	+	11.5469i	−0.0877528	+	0.384470i
$903$	21.2907	+	6.36936i	0.708509	+	0.211959i
$904$	−0.155564	−	0.681569i	−0.00517397	−	0.0226686i
$905$	59.3082	+	18.2942i	1.97147	+	0.608119i
$906$	−6.61616	+	16.8577i	−0.219807	+	0.560060i
$907$	3.25095	−	8.28328i	0.107946	−	0.275042i	−0.866687	−	0.498853i	$-0.833755\pi$
$907$	3.25095	−	8.28328i	0.107946	−	0.275042i	0.974632	+	0.223811i	$0.0718499\pi$
$908$	8.77671	+	2.70726i	0.291265	+	0.0898435i
$909$	0.885725	+	3.88061i	0.0293776	+	0.128712i
$910$	−5.95265	+	10.5160i	−0.197328	+	0.348602i
$911$	1.43696	−	6.29571i	0.0476084	−	0.208586i	−0.945529	−	0.325537i	$-0.894455\pi$
$911$	1.43696	−	6.29571i	0.0476084	−	0.208586i	0.993138	+	0.116951i	$0.0373120\pi$
$912$	−0.00666149	+	0.0115380i	−0.000220584	+	0.000382063i
$913$	−11.5599	−	20.0224i	−0.382577	−	0.662643i
$914$	−30.9333	+	9.54167i	−1.02318	+	0.315610i
$915$	−0.0250961	+	0.334884i	−0.000829652	+	0.0110709i
$916$	8.94811	+	11.2206i	0.295654	+	0.370738i
$917$	−23.3132	−	28.7287i	−0.769869	−	0.948707i
$918$	−3.98467	+	4.99662i	−0.131514	+	0.164913i
$919$	9.10542	+	8.44859i	0.300360	+	0.278693i	0.815926	−	0.578157i	$-0.196228\pi$
$919$	9.10542	+	8.44859i	0.300360	+	0.278693i	−0.515566	+	0.856850i	$0.672418\pi$
$920$	25.9638	+	3.91342i	0.856002	+	0.129022i
$921$	−6.21332	−	4.23617i	−0.204736	−	0.139587i
$922$	−7.48058	+	1.12752i	−0.246360	+	0.0371328i
$923$	−17.5964	−	8.47399i	−0.579194	−	0.278925i
$924$	−11.8781	−	1.68706i	−0.390760	−	0.0555003i
$925$	30.4171	−	14.6481i	1.00011	−	0.481627i
$926$	−6.24290	+	4.25634i	−0.205154	+	0.139872i
$927$	−2.23885	+	2.07735i	−0.0735334	+	0.0682291i
$928$	0.383700	+	5.12012i	0.0125956	+	0.168076i
$929$	−1.11948	−	2.85239i	−0.0367290	−	0.0935839i	0.911332	−	0.411671i	$-0.135055\pi$
$929$	−1.11948	−	2.85239i	−0.0367290	−	0.0935839i	−0.948061	+	0.318087i	$0.896960\pi$
$930$	−2.15842			−0.0707773
$931$	0.0779388	+	0.0512164i	0.00255434	+	0.00167855i
$932$	19.7782			0.647856
$933$	11.4016	+	29.0507i	0.373271	+	0.951078i
$934$	2.13589	+	28.5014i	0.0698883	+	0.932595i
$935$	−66.0550	+	61.2901i	−2.16023	+	2.00440i
$936$	−1.21364	+	0.827443i	−0.0396689	+	0.0270458i
$937$	−31.1119	+	14.9827i	−1.01638	+	0.489463i	−0.866466	−	0.499236i	$-0.833614\pi$
$937$	−31.1119	+	14.9827i	−1.01638	+	0.489463i	−0.149915	+	0.988699i	$0.547900\pi$
$938$	−1.28855	−	15.4308i	−0.0420726	−	0.503835i
$939$	−15.9033	−	7.65863i	−0.518985	−	0.249930i
$940$	35.5799	−	5.36280i	1.16049	−	0.174915i
$941$	7.96244	+	5.42870i	0.259568	+	0.176971i	0.686111	−	0.727497i	$-0.259316\pi$
$941$	7.96244	+	5.42870i	0.259568	+	0.176971i	−0.426543	+	0.904467i	$0.640269\pi$
$942$	−3.56772	−	0.537747i	−0.116242	−	0.0175207i
$943$	−16.1684	−	15.0021i	−0.526515	−	0.488535i
$944$	−5.54228	+	6.94980i	−0.180386	+	0.226197i
$945$	−8.22636	+	0.0700212i	−0.267603	+	0.00227779i
$946$	23.7474	+	29.7783i	0.772096	+	0.968177i
$947$	−2.95190	+	39.3904i	−0.0959239	+	1.28002i	0.716764	+	0.697316i	$0.245623\pi$
$947$	−2.95190	+	39.3904i	−0.0959239	+	1.28002i	−0.812688	+	0.582699i	$0.801997\pi$
$948$	8.13518	−	2.50937i	0.264218	−	0.0815005i
$949$	6.75769	+	11.7047i	0.219364	+	0.379949i
$950$	−0.0310976	+	0.0538627i	−0.00100894	+	0.00174754i
$951$	2.99406	−	13.1178i	0.0970889	−	0.425374i
$952$	13.8891	−	9.64362i	0.450149	−	0.312552i
$953$	−9.21201	−	40.3604i	−0.298406	−	1.30740i	−0.872500	−	0.488614i	$-0.837503\pi$
$953$	−9.21201	−	40.3604i	−0.298406	−	1.30740i	0.574094	−	0.818789i	$-0.305354\pi$
$954$	10.7227	+	3.30751i	0.347160	+	0.107085i
$955$	−16.7520	+	42.6835i	−0.542083	+	1.38121i
$956$	−8.51830	+	21.7043i	−0.275501	+	0.701966i
$957$	−22.2481	−	6.86264i	−0.719180	−	0.221838i
$958$	−7.93654	−	34.7723i	−0.256418	−	1.12344i
$959$	7.47167	−	1.19130i	0.241273	−	0.0384691i
$960$	−0.691903	+	3.03143i	−0.0223311	+	0.0978388i
$961$	15.2591	−	26.4295i	0.492228	−	0.852564i
$962$	−5.31136	−	9.19954i	−0.171245	−	0.296605i
$963$	−13.6583	+	4.21303i	−0.440133	+	0.135763i
$964$	−0.981147	+	13.0925i	−0.0316006	+	0.421681i
$965$	2.82002	+	3.53619i	0.0907797	+	0.113834i
$966$	13.7808	−	17.5856i	0.443390	−	0.565807i
$967$	−6.30613	+	7.90764i	−0.202791	+	0.254292i	−0.872819	−	0.488044i	$-0.837711\pi$
$967$	−6.30613	+	7.90764i	−0.202791	+	0.254292i	0.670028	+	0.742336i	$0.266282\pi$
$968$	−7.00951	−	6.50388i	−0.225294	−	0.209043i
$969$	0.0841950	+	0.0126904i	0.00270473	+	0.000407673i
$970$	−1.84235	−	1.25609i	−0.0591543	−	0.0403307i
$971$	42.7225	−	6.43938i	1.37103	−	0.206650i	0.578102	−	0.815964i	$-0.303793\pi$
$971$	42.7225	−	6.43938i	1.37103	−	0.206650i	0.792929	+	0.609314i	$0.208555\pi$
$972$	−0.900969	−	0.433884i	−0.0288986	−	0.0139168i
$973$	27.4981	−	8.73905i	0.881549	−	0.280161i
$974$	−8.87316	+	4.27309i	−0.284314	+	0.136919i
$975$	−5.66558	+	3.86273i	−0.181444	+	0.123706i
$976$	0.0791719	−	0.0734608i	0.00253423	−	0.00235142i
$977$	−2.74133	−	36.5805i	−0.0877030	−	1.17032i	−0.851320	−	0.524646i	$-0.824198\pi$
$977$	−2.74133	−	36.5805i	−0.0877030	−	1.17032i	0.763617	−	0.645669i	$-0.223421\pi$
$978$	−3.09111	−	7.87601i	−0.0988426	−	0.251847i
$979$	−30.0905			−0.961696
$980$	20.9049	+	6.06058i	0.667782	+	0.193598i
$981$	16.1856			0.516767
$982$	−6.12158	−	15.5975i	−0.195347	−	0.497737i
$983$	1.32738	+	17.7127i	0.0423369	+	0.564947i	0.977528	+	0.210804i	$0.0676083\pi$
$983$	1.32738	+	17.7127i	0.0423369	+	0.564947i	−0.935191	+	0.354143i	$0.884773\pi$
$984$	1.91467	−	1.77656i	0.0610375	−	0.0566345i
$985$	24.2032	−	16.5015i	0.771178	−	0.525780i
$986$	29.5644	−	14.2375i	0.941522	−	0.453413i
$987$	10.9425	−	28.5944i	0.348304	−	0.910168i
$988$	0.0176317	+	0.00849098i	0.000560939	+	0.000270134i
$989$	−70.1371	+	10.5715i	−2.23023	+	0.336153i
$990$	−11.6497	−	7.94261i	−0.370251	−	0.252433i
$991$	−37.9869	−	5.72561i	−1.20669	−	0.181880i	−0.485265	−	0.874367i	$-0.661277\pi$
$991$	−37.9869	−	5.72561i	−1.20669	−	0.181880i	−0.721430	+	0.692487i	$0.756515\pi$
$992$	0.508857	+	0.472150i	0.0161562	+	0.0149908i
$993$	6.36084	−	7.97624i	0.201855	−	0.253118i
$994$	−7.53582	+	34.3622i	−0.239022	+	1.08990i
$995$	37.3281	+	46.8079i	1.18338	+	1.48391i
$996$	−0.381019	+	5.08434i	−0.0120730	+	0.161104i
$997$	−19.5666	+	6.03551i	−0.619682	+	0.191146i	−0.588671	−	0.808373i	$-0.700349\pi$
$997$	−19.5666	+	6.03551i	−0.619682	+	0.191146i	−0.0310104	+	0.999519i	$0.509873\pi$
$998$	−10.4430	−	18.0878i	−0.330567	−	0.572559i
$999$	3.61595	−	6.26301i	0.114404	−	0.198153i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.m.b.163.2	✓	24
3.2	odd	2		882.2.z.a.163.1		24
49.46	even	21	inner	294.2.m.b.193.2	yes	24
147.95	odd	42		882.2.z.a.487.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.m.b.163.2	✓	24	1.1	even	1	trivial
294.2.m.b.193.2	yes	24	49.46	even	21	inner
882.2.z.a.163.1		24	3.2	odd	2
882.2.z.a.487.1		24	147.95	odd	42

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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.m (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.365341 + 0.930874i) q^{2} +(0.0747301 + 0.997204i) q^{3} +(-0.733052 + 0.680173i) q^{4} +(2.56909 - 1.75158i) q^{5} +(-0.900969 + 0.433884i) q^{6} +(1.92409 - 1.81601i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(-0.988831 + 0.149042i) q^{9} +O(q^{10})\)	\(q+(0.365341 + 0.930874i) q^{2} +(0.0747301 + 0.997204i) q^{3} +(-0.733052 + 0.680173i) q^{4} +(2.56909 - 1.75158i) q^{5} +(-0.900969 + 0.433884i) q^{6} +(1.92409 - 1.81601i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(-0.988831 + 0.149042i) q^{9} +(2.56909 + 1.75158i) q^{10} +(4.48390 + 0.675839i) q^{11} +(-0.733052 - 0.680173i) q^{12} +(-0.915824 + 1.14841i) q^{13} +(2.39342 + 1.12762i) q^{14} +(1.93867 + 2.43101i) q^{15} +(0.0747301 - 0.997204i) q^{16} +(-6.10699 + 1.88376i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.00666149 + 0.0115380i) q^{19} +(-0.691903 + 3.03143i) q^{20} +(1.95472 + 1.78299i) q^{21} +(1.00903 + 4.42085i) q^{22} +(-8.06931 - 2.48905i) q^{23} +(0.365341 - 0.930874i) q^{24} +(1.70551 - 4.34557i) q^{25} +(-1.40361 - 0.432957i) q^{26} +(-0.222521 - 0.974928i) q^{27} +(-0.175254 + 2.63994i) q^{28} +(-1.14253 + 5.00574i) q^{29} +(-1.55469 + 2.69281i) q^{30} +(0.347081 + 0.601162i) q^{31} +(0.955573 - 0.294755i) q^{32} +(-0.338867 + 4.52187i) q^{33} +(-3.98467 - 4.99662i) q^{34} +(1.76227 - 8.03569i) q^{35} +(0.623490 - 0.781831i) q^{36} +(5.30136 + 4.91894i) q^{37} +(-0.0131742 - 0.00198569i) q^{38} +(-1.21364 - 0.827443i) q^{39} +(-3.07465 + 0.463430i) q^{40} +(2.35326 + 1.13327i) q^{41} +(-0.945604 + 2.47100i) q^{42} +(7.56769 - 3.64441i) q^{43} +(-3.74662 + 2.55440i) q^{44} +(-2.27934 + 2.11492i) q^{45} +(-0.631056 - 8.42086i) q^{46} +(-4.22772 - 10.7721i) q^{47} +1.00000 q^{48} +(0.404211 - 6.98832i) q^{49} +4.66827 q^{50} +(-2.33486 - 5.94914i) q^{51} +(-0.109769 - 1.46476i) q^{52} +(-8.22574 + 7.63237i) q^{53} +(0.826239 - 0.563320i) q^{54} +(12.7033 - 6.11761i) q^{55} +(-2.52148 + 0.801339i) q^{56} +(-0.0120036 - 0.00578062i) q^{57} +(-5.07713 + 0.765254i) q^{58} +(-7.34454 - 5.00742i) q^{59} +(-3.07465 - 0.463430i) q^{60} +(0.0791719 + 0.0734608i) q^{61} +(-0.432803 + 0.542718i) q^{62} +(-1.63193 + 2.08250i) q^{63} +(0.623490 + 0.781831i) q^{64} +(-0.341313 + 4.55451i) q^{65} +(-4.33309 + 1.33658i) q^{66} +(-2.92630 - 5.06851i) q^{67} +(3.19546 - 5.53470i) q^{68} +(1.87907 - 8.23275i) q^{69} +(8.12404 - 1.29531i) q^{70} +(2.95871 + 12.9630i) q^{71} +(0.955573 + 0.294755i) q^{72} +(3.36158 - 8.56517i) q^{73} +(-2.64211 + 6.73199i) q^{74} +(4.46087 + 1.37600i) q^{75} +(-0.00296464 - 0.0129889i) q^{76} +(9.85473 - 6.84243i) q^{77} +(0.326854 - 1.43204i) q^{78} +(-4.25670 + 7.37282i) q^{79} +(-1.55469 - 2.69281i) q^{80} +(0.955573 - 0.294755i) q^{81} +(-0.195189 + 2.60461i) q^{82} +(-3.17892 - 3.98625i) q^{83} +(-2.64566 + 0.0225193i) q^{84} +(-12.3899 + 15.5364i) q^{85} +(6.15727 + 5.71311i) q^{86} +(-5.07713 - 0.765254i) q^{87} +(-3.74662 - 2.55440i) q^{88} +(-6.56171 + 0.989019i) q^{89} +(-2.80146 - 1.34911i) q^{90} +(0.323396 + 3.87278i) q^{91} +(7.60820 - 3.66392i) q^{92} +(-0.573544 + 0.391036i) q^{93} +(8.48286 - 7.87095i) q^{94} +(0.00309579 + 0.0413104i) q^{95} +(0.365341 + 0.930874i) q^{96} -0.717121 q^{97} +(6.65292 - 2.17685i) q^{98} -4.53454 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9	\( 24 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 4 q^{8} + 2 q^{9} + q^{10} + 8 q^{11} + 2 q^{12} - 2 q^{13} + 5 q^{15} + 2 q^{16} + 9 q^{17} - 12 q^{18} - 4 q^{19} + 5 q^{20} + 14 q^{21} + 5 q^{22} - 38 q^{23} + 2 q^{24} - 19 q^{25} - 20 q^{26} - 4 q^{27} - 14 q^{28} - 14 q^{29} + 8 q^{30} + 4 q^{31} + 2 q^{32} - 6 q^{33} + 17 q^{34} + 42 q^{35} - 4 q^{36} + 7 q^{37} - 18 q^{38} - 6 q^{39} - 13 q^{40} + 2 q^{41} - 7 q^{42} + 4 q^{43} - 6 q^{44} - 13 q^{45} + 11 q^{46} - 8 q^{47} + 24 q^{48} - 42 q^{49} - 4 q^{50} - 40 q^{51} + 15 q^{52} - 10 q^{53} + 2 q^{54} + 33 q^{55} - 7 q^{56} + q^{57} - 28 q^{58} + 14 q^{59} - 13 q^{60} + 7 q^{61} - 8 q^{62} - 14 q^{63} - 4 q^{64} + 23 q^{65} + 8 q^{66} + 23 q^{67} + 9 q^{68} + 13 q^{69} + 28 q^{70} + 36 q^{71} + 2 q^{72} + 15 q^{73} - 14 q^{74} + 9 q^{75} + q^{76} - 28 q^{77} + 19 q^{78} + 38 q^{79} + 8 q^{80} + 2 q^{81} - q^{82} + 27 q^{83} - 47 q^{85} + 26 q^{86} - 28 q^{87} - 6 q^{88} - 121 q^{89} - 2 q^{90} + 21 q^{91} - q^{92} + 46 q^{93} - q^{94} + 44 q^{95} + 2 q^{96} + 14 q^{97} - 21 q^{98} - 44 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 4 * q^8 + 2 * q^9 + q^10 + 8 * q^11 + 2 * q^12 - 2 * q^13 + 5 * q^15 + 2 * q^16 + 9 * q^17 - 12 * q^18 - 4 * q^19 + 5 * q^20 + 14 * q^21 + 5 * q^22 - 38 * q^23 + 2 * q^24 - 19 * q^25 - 20 * q^26 - 4 * q^27 - 14 * q^28 - 14 * q^29 + 8 * q^30 + 4 * q^31 + 2 * q^32 - 6 * q^33 + 17 * q^34 + 42 * q^35 - 4 * q^36 + 7 * q^37 - 18 * q^38 - 6 * q^39 - 13 * q^40 + 2 * q^41 - 7 * q^42 + 4 * q^43 - 6 * q^44 - 13 * q^45 + 11 * q^46 - 8 * q^47 + 24 * q^48 - 42 * q^49 - 4 * q^50 - 40 * q^51 + 15 * q^52 - 10 * q^53 + 2 * q^54 + 33 * q^55 - 7 * q^56 + q^57 - 28 * q^58 + 14 * q^59 - 13 * q^60 + 7 * q^61 - 8 * q^62 - 14 * q^63 - 4 * q^64 + 23 * q^65 + 8 * q^66 + 23 * q^67 + 9 * q^68 + 13 * q^69 + 28 * q^70 + 36 * q^71 + 2 * q^72 + 15 * q^73 - 14 * q^74 + 9 * q^75 + q^76 - 28 * q^77 + 19 * q^78 + 38 * q^79 + 8 * q^80 + 2 * q^81 - q^82 + 27 * q^83 - 47 * q^85 + 26 * q^86 - 28 * q^87 - 6 * q^88 - 121 * q^89 - 2 * q^90 + 21 * q^91 - q^92 + 46 * q^93 - q^94 + 44 * q^95 + 2 * q^96 + 14 * q^97 - 21 * q^98 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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