LMFDB - Embedded newform 294.2.m.b.247.1

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			247.1
Character	$\chi$	$=$	294.247
Dual form			294.2.m.b.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.955573 + 0.294755i) q^{2} +(0.365341 - 0.930874i) q^{3} +(0.826239 + 0.563320i) q^{4} +(-0.0494904 + 0.00745948i) q^{5} +(0.623490 - 0.781831i) q^{6} +(-0.154679 - 2.64123i) q^{7} +(0.623490 + 0.781831i) q^{8} +(-0.733052 - 0.680173i) q^{9} +O(q^{10})$	\(q+(0.955573 + 0.294755i) q^{2} +(0.365341 - 0.930874i) q^{3} +(0.826239 + 0.563320i) q^{4} +(-0.0494904 + 0.00745948i) q^{5} +(0.623490 - 0.781831i) q^{6} +(-0.154679 - 2.64123i) q^{7} +(0.623490 + 0.781831i) q^{8} +(-0.733052 - 0.680173i) q^{9} +(-0.0494904 - 0.00745948i) q^{10} +(4.04404 - 3.75232i) q^{11} +(0.826239 - 0.563320i) q^{12} +(0.842245 + 3.69012i) q^{13} +(0.630708 - 2.56948i) q^{14} +(-0.0111370 + 0.0487946i) q^{15} +(0.365341 + 0.930874i) q^{16} +(0.205584 + 2.74332i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-1.90948 + 3.30731i) q^{19} +(-0.0450930 - 0.0217156i) q^{20} +(-2.51516 - 0.820962i) q^{21} +(4.97039 - 2.39361i) q^{22} +(0.153472 - 2.04794i) q^{23} +(0.955573 - 0.294755i) q^{24} +(-4.77547 + 1.47304i) q^{25} +(-0.282855 + 3.77443i) q^{26} +(-0.900969 + 0.433884i) q^{27} +(1.36005 - 2.26942i) q^{28} +(-6.44379 - 3.10317i) q^{29} +(-0.0250247 + 0.0433441i) q^{30} +(2.67561 + 4.63429i) q^{31} +(0.0747301 + 0.997204i) q^{32} +(-2.01548 - 5.13536i) q^{33} +(-0.612159 + 2.68204i) q^{34} +(0.0273573 + 0.129562i) q^{35} +(-0.222521 - 0.974928i) q^{36} +(6.71698 - 4.57956i) q^{37} +(-2.79949 + 2.59755i) q^{38} +(3.74274 + 0.564127i) q^{39} +(-0.0366888 - 0.0340423i) q^{40} +(2.65401 + 3.32802i) q^{41} +(-2.16143 - 1.52584i) q^{42} +(-6.70726 + 8.41064i) q^{43} +(5.45510 - 0.822223i) q^{44} +(0.0413528 + 0.0281938i) q^{45} +(0.750293 - 1.91172i) q^{46} +(-9.99416 - 3.08279i) q^{47} +1.00000 q^{48} +(-6.95215 + 0.817084i) q^{49} -4.99750 q^{50} +(2.62880 + 0.810876i) q^{51} +(-1.38282 + 3.52337i) q^{52} +(-0.152356 - 0.103875i) q^{53} +(-0.988831 + 0.149042i) q^{54} +(-0.172151 + 0.215870i) q^{55} +(1.96855 - 1.76771i) q^{56} +(2.38108 + 2.98578i) q^{57} +(-5.24284 - 4.86464i) q^{58} +(5.54837 + 0.836282i) q^{59} +(-0.0366888 + 0.0340423i) q^{60} +(-5.33896 + 3.64004i) q^{61} +(1.19076 + 5.21705i) q^{62} +(-1.68310 + 2.04136i) q^{63} +(-0.222521 + 0.974928i) q^{64} +(-0.0692094 - 0.176343i) q^{65} +(-0.412264 - 5.50129i) q^{66} +(5.31338 + 9.20305i) q^{67} +(-1.37551 + 2.38245i) q^{68} +(-1.85030 - 0.891058i) q^{69} +(-0.0120471 + 0.131869i) q^{70} +(10.1067 - 4.86712i) q^{71} +(0.0747301 - 0.997204i) q^{72} +(-8.28003 + 2.55405i) q^{73} +(7.76841 - 2.39624i) q^{74} +(-0.373463 + 4.98352i) q^{75} +(-3.44076 + 1.65698i) q^{76} +(-10.5362 - 10.1008i) q^{77} +(3.41018 + 1.64226i) q^{78} +(1.81168 - 3.13792i) q^{79} +(-0.0250247 - 0.0433441i) q^{80} +(0.0747301 + 0.997204i) q^{81} +(1.55515 + 3.96245i) q^{82} +(1.41720 - 6.20917i) q^{83} +(-1.61566 - 2.09515i) q^{84} +(-0.0306382 - 0.134235i) q^{85} +(-8.88835 + 6.05998i) q^{86} +(-5.24284 + 4.86464i) q^{87} +(5.45510 + 0.822223i) q^{88} +(-7.99658 - 7.41975i) q^{89} +(0.0312053 + 0.0391302i) q^{90} +(9.61615 - 2.79534i) q^{91} +(1.28045 - 1.60563i) q^{92} +(5.29145 - 0.797558i) q^{93} +(-8.64148 - 5.89166i) q^{94} +(0.0698301 - 0.177924i) q^{95} +(0.955573 + 0.294755i) q^{96} +11.3547 q^{97} +(-6.88412 - 1.26840i) q^{98} -5.51671 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 $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{13}{21}\right)$

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 $

$2$	0.955573	+	0.294755i	0.675692	+	0.208423i
$2$	0.955573	+	0.294755i	0.675692	+	0.208423i
$3$	0.365341	−	0.930874i	0.210930	−	0.537440i
$3$	0.365341	−	0.930874i	0.210930	−	0.537440i
$4$	0.826239	+	0.563320i	0.413119	+	0.281660i
$5$	−0.0494904	+	0.00745948i	−0.0221328	+	0.00333598i	−0.160099	−	0.987101i	$-0.551181\pi$
$5$	−0.0494904	+	0.00745948i	−0.0221328	+	0.00333598i	0.137967	+	0.990437i	$0.455943\pi$
$6$	0.623490	−	0.781831i	0.254539	−	0.319181i
$7$	−0.154679	−	2.64123i	−0.0584631	−	0.998290i
$7$	−0.154679	−	2.64123i	−0.0584631	−	0.998290i
$8$	0.623490	+	0.781831i	0.220437	+	0.276419i
$9$	−0.733052	−	0.680173i	−0.244351	−	0.226724i
$10$	−0.0494904	−	0.00745948i	−0.0156502	−	0.00235889i
$11$	4.04404	−	3.75232i	1.21932	−	1.13137i	0.231988	−	0.972719i	$-0.425477\pi$
$11$	4.04404	−	3.75232i	1.21932	−	1.13137i	0.987335	−	0.158648i	$-0.0507134\pi$
$12$	0.826239	−	0.563320i	0.238515	−	0.162616i
$13$	0.842245	+	3.69012i	0.233597	+	1.02345i	0.946630	+	0.322324i	$0.104464\pi$
$13$	0.842245	+	3.69012i	0.233597	+	1.02345i	−0.713033	+	0.701131i	$0.752679\pi$
$14$	0.630708	−	2.56948i	0.168564	−	0.686721i
$15$	−0.0111370	+	0.0487946i	−0.00287557	+	0.0125987i
$16$	0.365341	+	0.930874i	0.0913353	+	0.232718i
$17$	0.205584	+	2.74332i	0.0498614	+	0.665354i	0.965006	+	0.262228i	$0.0844573\pi$
$17$	0.205584	+	2.74332i	0.0498614	+	0.665354i	−0.915145	+	0.403126i	$0.867924\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−1.90948	+	3.30731i	−0.438065	+	0.758750i	−0.997540	−	0.0700967i	$-0.977669\pi$
$19$	−1.90948	+	3.30731i	−0.438065	+	0.758750i	0.559476	+	0.828847i	$0.311003\pi$
$20$	−0.0450930	−	0.0217156i	−0.0100831	−	0.00485576i
$21$	−2.51516	−	0.820962i	−0.548853	−	0.179149i
$22$	4.97039	−	2.39361i	1.05969	−	0.510320i
$23$	0.153472	−	2.04794i	0.0320011	−	0.427024i	−0.958077	−	0.286509i	$-0.907505\pi$
$23$	0.153472	−	2.04794i	0.0320011	−	0.427024i	0.990079	−	0.140515i	$-0.0448759\pi$
$24$	0.955573	−	0.294755i	0.195055	−	0.0601666i
$25$	−4.77547	+	1.47304i	−0.955094	+	0.294608i
$26$	−0.282855	+	3.77443i	−0.0554723	+	0.740227i
$27$	−0.900969	+	0.433884i	−0.173392	+	0.0835010i
$28$	1.36005	−	2.26942i	0.257026	−	0.428879i
$29$	−6.44379	−	3.10317i	−1.19658	−	0.576244i	−0.273883	−	0.961763i	$-0.588308\pi$
$29$	−6.44379	−	3.10317i	−1.19658	−	0.576244i	−0.922700	+	0.385519i	$0.874022\pi$
$30$	−0.0250247	+	0.0433441i	−0.00456887	+	0.00791351i
$31$	2.67561	+	4.63429i	0.480553	+	0.832343i	0.999751	−	0.0223112i	$-0.00710245\pi$
$31$	2.67561	+	4.63429i	0.480553	+	0.832343i	−0.519198	+	0.854654i	$0.673769\pi$
$32$	0.0747301	+	0.997204i	0.0132105	+	0.176282i
$33$	−2.01548	−	5.13536i	−0.350850	−	0.893952i
$34$	−0.612159	+	2.68204i	−0.104984	+	0.459967i
$35$	0.0273573	+	0.129562i	0.00462423	+	0.0218999i
$36$	−0.222521	−	0.974928i	−0.0370868	−	0.162488i
$37$	6.71698	−	4.57956i	1.10426	−	0.752874i	0.133056	−	0.991109i	$-0.457521\pi$
$37$	6.71698	−	4.57956i	1.10426	−	0.752874i	0.971208	+	0.238234i	$0.0765686\pi$
$38$	−2.79949	+	2.59755i	−0.454138	+	0.421378i
$39$	3.74274	+	0.564127i	0.599318	+	0.0903327i
$40$	−0.0366888	−	0.0340423i	−0.00580101	−	0.00538255i
$41$	2.65401	+	3.32802i	0.414487	+	0.519750i	0.944621	−	0.328164i	$-0.106430\pi$
$41$	2.65401	+	3.32802i	0.414487	+	0.519750i	−0.530134	+	0.847914i	$0.677858\pi$
$42$	−2.16143	−	1.52584i	−0.333517	−	0.235443i
$43$	−6.70726	+	8.41064i	−1.02285	+	1.28261i	−0.0642232	+	0.997936i	$0.520457\pi$
$43$	−6.70726	+	8.41064i	−1.02285	+	1.28261i	−0.958624	+	0.284675i	$0.908114\pi$
$44$	5.45510	−	0.822223i	0.822387	−	0.123955i
$45$	0.0413528	+	0.0281938i	0.00616451	+	0.00420289i
$46$	0.750293	−	1.91172i	0.110625	−	0.281867i
$47$	−9.99416	−	3.08279i	−1.45780	−	0.449671i	−0.538296	−	0.842756i	$-0.680932\pi$
$47$	−9.99416	−	3.08279i	−1.45780	−	0.449671i	−0.919502	+	0.393084i	$0.871408\pi$
$48$	1.00000			0.144338
$49$	−6.95215	+	0.817084i	−0.993164	+	0.116726i
$50$	−4.99750			−0.706753
$51$	2.62880	+	0.810876i	0.368105	+	0.113545i
$52$	−1.38282	+	3.52337i	−0.191763	+	0.488604i
$53$	−0.152356	−	0.103875i	−0.0209277	−	0.0142683i	0.552811	−	0.833307i	$-0.313555\pi$
$53$	−0.152356	−	0.103875i	−0.0209277	−	0.0142683i	−0.573739	+	0.819038i	$0.694508\pi$
$54$	−0.988831	+	0.149042i	−0.134563	+	0.0202821i
$55$	−0.172151	+	0.215870i	−0.0232128	+	0.0291079i
$56$	1.96855	−	1.76771i	0.263059	−	0.236220i
$57$	2.38108	+	2.98578i	0.315382	+	0.395476i
$58$	−5.24284	−	4.86464i	−0.688419	−	0.638759i
$59$	5.54837	+	0.836282i	0.722336	+	0.108875i	0.499913	−	0.866076i	$-0.333365\pi$
$59$	5.54837	+	0.836282i	0.722336	+	0.108875i	0.222423	+	0.974950i	$0.428603\pi$
$60$	−0.0366888	+	0.0340423i	−0.00473651	+	0.00439484i
$61$	−5.33896	+	3.64004i	−0.683584	+	0.466060i	−0.854653	−	0.519199i	$-0.826230\pi$
$61$	−5.33896	+	3.64004i	−0.683584	+	0.466060i	0.171069	+	0.985259i	$0.445278\pi$
$62$	1.19076	+	5.21705i	0.151226	+	0.662566i
$63$	−1.68310	+	2.04136i	−0.212051	+	0.257188i
$64$	−0.222521	+	0.974928i	−0.0278151	+	0.121866i
$65$	−0.0692094	−	0.176343i	−0.00858437	−	0.0218726i
$66$	−0.412264	−	5.50129i	−0.0507463	−	0.677162i
$67$	5.31338	+	9.20305i	0.649133	+	1.12433i	0.983330	+	0.181828i	$0.0582014\pi$
$67$	5.31338	+	9.20305i	0.649133	+	1.12433i	−0.334198	+	0.942503i	$0.608465\pi$
$68$	−1.37551	+	2.38245i	−0.166805	+	0.288915i
$69$	−1.85030	−	0.891058i	−0.222750	−	0.107271i
$70$	−0.0120471	+	0.131869i	−0.00143990	+	0.0157614i
$71$	10.1067	−	4.86712i	1.19944	−	0.577621i	0.275925	−	0.961179i	$-0.411016\pi$
$71$	10.1067	−	4.86712i	1.19944	−	0.577621i	0.923517	+	0.383558i	$0.125301\pi$
$72$	0.0747301	−	0.997204i	0.00880703	−	0.117522i
$73$	−8.28003	+	2.55405i	−0.969105	+	0.298929i	−0.738601	−	0.674142i	$-0.764513\pi$
$73$	−8.28003	+	2.55405i	−0.969105	+	0.298929i	−0.230503	+	0.973072i	$0.574037\pi$
$74$	7.76841	−	2.39624i	0.903059	−	0.278557i
$75$	−0.373463	+	4.98352i	−0.0431238	+	0.575447i
$76$	−3.44076	+	1.65698i	−0.394683	+	0.190069i
$77$	−10.5362	−	10.1008i	−1.20072	−	1.15109i
$78$	3.41018	+	1.64226i	0.386127	+	0.185949i
$79$	1.81168	−	3.13792i	0.203830	−	0.353044i	−0.745929	−	0.666025i	$-0.767994\pi$
$79$	1.81168	−	3.13792i	0.203830	−	0.353044i	0.949759	+	0.312981i	$0.101328\pi$
$80$	−0.0250247	−	0.0433441i	−0.00279785	−	0.00484601i
$81$	0.0747301	+	0.997204i	0.00830334	+	0.110800i
$82$	1.55515	+	3.96245i	0.171737	+	0.437579i
$83$	1.41720	−	6.20917i	0.155558	−	0.681545i	−0.835653	−	0.549257i	$-0.814911\pi$
$83$	1.41720	−	6.20917i	0.155558	−	0.681545i	0.991211	−	0.132287i	$-0.0422322\pi$
$84$	−1.61566	−	2.09515i	−0.176283	−	0.228600i
$85$	−0.0306382	−	0.134235i	−0.00332318	−	0.0145598i
$86$	−8.88835	+	6.05998i	−0.958456	+	0.653464i
$87$	−5.24284	+	4.86464i	−0.562091	+	0.521545i
$88$	5.45510	+	0.822223i	0.581515	+	0.0876493i
$89$	−7.99658	−	7.41975i	−0.847636	−	0.786491i	0.131153	−	0.991362i	$-0.458132\pi$
$89$	−7.99658	−	7.41975i	−0.847636	−	0.786491i	−0.978789	+	0.204871i	$0.934323\pi$
$90$	0.0312053	+	0.0391302i	0.00328933	+	0.00412469i
$91$	9.61615	−	2.79534i	1.00805	−	0.293032i
$92$	1.28045	−	1.60563i	0.133496	−	0.167399i
$93$	5.29145	−	0.797558i	0.548698	−	0.0827029i
$94$	−8.64148	−	5.89166i	−0.891301	−	0.607679i
$95$	0.0698301	−	0.177924i	0.00716441	−	0.0182546i
$96$	0.955573	+	0.294755i	0.0975277	+	0.0300833i
$97$	11.3547			1.15289			0.576446	−	0.817135i	$-0.304439\pi$
$97$	11.3547			1.15289			0.576446	+	0.817135i	$0.304439\pi$
$98$	−6.88412	−	1.26840i	−0.695402	−	0.128128i
$99$	−5.51671			−0.554451
$100$	−4.77547	−	1.47304i	−0.477547	−	0.147304i
$101$	2.61136	−	6.65364i	0.259840	−	0.662062i	−0.740105	−	0.672491i	$-0.765224\pi$
$101$	2.61136	−	6.65364i	0.259840	−	0.662062i	0.999946	+	0.0104288i	$0.00331965\pi$
$102$	2.27300	+	1.54970i	0.225060	+	0.153443i
$103$	0.425099	−	0.0640733i	0.0418862	−	0.00631333i	−0.128066	−	0.991766i	$-0.540877\pi$
$103$	0.425099	−	0.0640733i	0.0418862	−	0.00631333i	0.169952	+	0.985452i	$0.445639\pi$
$104$	−2.35992	+	2.95924i	−0.231409	+	0.290178i
$105$	0.130600	+	0.0218680i	0.0127453	+	0.00213409i
$106$	−0.114970	−	0.144168i	−0.0111668	−	0.0140028i
$107$	−1.33359	−	1.23739i	−0.128923	−	0.119623i	0.613076	−	0.790024i	$-0.289932\pi$
$107$	−1.33359	−	1.23739i	−0.128923	−	0.119623i	−0.742000	+	0.670400i	$0.766122\pi$
$108$	−0.988831	−	0.149042i	−0.0951503	−	0.0143416i
$109$	−0.691126	+	0.641271i	−0.0661978	+	0.0614226i	−0.712578	−	0.701593i	$-0.752473\pi$
$109$	−0.691126	+	0.641271i	−0.0661978	+	0.0614226i	0.646380	+	0.763016i	$0.276282\pi$
$110$	−0.228131	+	0.155537i	−0.0217515	+	0.0148299i
$111$	−1.80900	−	7.92576i	−0.171703	−	0.752279i
$112$	2.40214	−	1.10893i	0.226981	−	0.104784i
$113$	−3.33526	+	14.6127i	−0.313755	+	1.37465i	0.534549	+	0.845138i	$0.320482\pi$
$113$	−3.33526	+	14.6127i	−0.313755	+	1.37465i	−0.848303	+	0.529511i	$0.822376\pi$
$114$	1.39522	+	3.55497i	0.130675	+	0.332953i
$115$	0.00768117	+	0.102498i	0.000716273	+	0.00955800i
$116$	−3.57604	−	6.19388i	−0.332027	−	0.575087i
$117$	1.89251	−	3.27792i	0.174962	−	0.303044i
$118$	5.05537	+	2.43454i	0.465385	+	0.224117i
$119$	7.21394	−	0.967327i	0.661301	−	0.0886748i
$120$	−0.0450930	+	0.0217156i	−0.00411641	+	0.00198236i
$121$	1.45231	−	19.3798i	0.132029	−	1.76180i
$122$	−6.17469	+	1.90464i	−0.559030	+	0.172438i
$123$	4.06759	−	1.25468i	0.366762	−	0.113131i
$124$	−0.399897	+	5.33625i	−0.0359118	+	0.479210i
$125$	0.450817	−	0.217102i	0.0403223	−	0.0194182i
$126$	−2.21003	+	1.45457i	−0.196885	+	0.129583i
$127$	8.45163	+	4.07009i	0.749961	+	0.361162i	0.769500	−	0.638647i	$-0.220506\pi$
$127$	8.45163	+	4.07009i	0.749961	+	0.361162i	−0.0195389	+	0.999809i	$0.506220\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	5.37880	+	9.31636i	0.473577	+	0.820260i
$130$	−0.0141567	−	0.188908i	−0.00124163	−	0.0165683i
$131$	−3.56644	−	9.08714i	−0.311601	−	0.793947i	−0.997785	−	0.0665189i	$-0.978811\pi$
$131$	−3.56644	−	9.08714i	−0.311601	−	0.793947i	0.686184	−	0.727428i	$-0.259285\pi$
$132$	1.22758	−	5.37840i	0.106847	−	0.468129i
$133$	9.03072	+	4.53179i	0.783063	+	0.392956i
$134$	2.36468	+	10.3603i	0.204277	+	0.894996i
$135$	0.0413528	−	0.0281938i	0.00355908	−	0.00242654i
$136$	−2.01664	+	1.87117i	−0.172925	+	0.160451i
$137$	17.9377	+	2.70367i	1.53252	+	0.230991i	0.860465	−	0.509509i	$-0.170173\pi$
$137$	17.9377	+	2.70367i	1.53252	+	0.230991i	0.672057	+	0.740500i	$0.265411\pi$
$138$	−1.50545	−	1.39686i	−0.128153	−	0.118908i
$139$	7.83986	+	9.83087i	0.664968	+	0.833844i	0.993874	−	0.110519i	$-0.0352513\pi$
$139$	7.83986	+	9.83087i	0.664968	+	0.833844i	−0.328906	+	0.944363i	$0.606680\pi$
$140$	−0.0503810	+	0.122460i	−0.00425797	+	0.0103497i
$141$	−6.52097	+	8.17704i	−0.549165	+	0.688631i
$142$	11.0923	−	1.67189i	0.930843	−	0.140302i
$143$	17.2526	+	11.7626i	1.44273	+	0.983638i
$144$	0.365341	−	0.930874i	0.0304451	−	0.0775728i
$145$	0.342054	+	0.105510i	0.0284060	+	0.00876210i
$146$	−8.66500			−0.717120
$147$	−1.77930	+	6.77009i	−0.146754	+	0.558387i
$148$	8.12958			0.668247
$149$	1.64416	+	0.507157i	0.134695	+	0.0415479i	0.361370	−	0.932423i	$-0.382309\pi$
$149$	1.64416	+	0.507157i	0.134695	+	0.0415479i	−0.226675	+	0.973971i	$0.572785\pi$
$150$	−1.82579	+	4.65204i	−0.149075	+	0.379837i
$151$	−12.8784	−	8.78033i	−1.04803	−	0.714533i	−0.0884793	−	0.996078i	$-0.528201\pi$
$151$	−12.8784	−	8.78033i	−1.04803	−	0.714533i	−0.959548	+	0.281545i	$0.909153\pi$
$152$	−3.77630	+	0.569186i	−0.306299	+	0.0461671i
$153$	1.71523	−	2.15083i	0.138668	−	0.173884i
$154$	−7.09088	−	12.7577i	−0.571400	−	1.02804i
$155$	−0.166986	−	0.209394i	−0.0134127	−	0.0168190i
$156$	2.77461	+	2.57446i	0.222147	+	0.206122i
$157$	−20.4651	−	3.08462i	−1.63330	−	0.246180i	−0.732610	−	0.680649i	$-0.761698\pi$
$157$	−20.4651	−	3.08462i	−1.63330	−	0.246180i	−0.900687	+	0.434469i	$0.856936\pi$
$158$	2.65611	−	2.46451i	0.211309	−	0.196066i
$159$	−0.152356	+	0.103875i	−0.0120826	+	0.00823779i
$160$	−0.0111370	−	0.0487946i	−0.000880461	−	0.00385755i
$161$	−5.43280	−	0.0885808i	−0.428165	−	0.00698114i
$162$	−0.222521	+	0.974928i	−0.0174829	+	0.0765976i
$163$	−7.39991	−	18.8547i	−0.579606	−	1.47681i	−0.856621	−	0.515946i	$-0.827440\pi$
$163$	−7.39991	−	18.8547i	−0.579606	−	1.47681i	0.277015	−	0.960866i	$-0.410655\pi$
$164$	0.318104	+	4.24480i	0.0248397	+	0.331463i
$165$	0.138054	+	0.239117i	0.0107475	+	0.0186152i
$166$	3.18442	−	5.51559i	0.247159	−	0.428092i
$167$	19.4893	+	9.38555i	1.50813	+	0.726276i	0.991521	−	0.129947i	$-0.0414806\pi$
$167$	19.4893	+	9.38555i	1.50813	+	0.726276i	0.516607	+	0.856223i	$0.327195\pi$
$168$	−0.926322	−	2.47829i	−0.0714673	−	0.191204i
$169$	−1.19499	+	0.575477i	−0.0919224	+	0.0442675i
$170$	0.0102893	−	0.137302i	0.000789157	−	0.0105306i
$171$	3.64929	−	1.12566i	0.279068	−	0.0860812i
$172$	−10.2797	+	3.17086i	−0.783818	+	0.241776i
$173$	1.48540	−	19.8213i	0.112933	−	1.50699i	−0.596727	−	0.802445i	$-0.703532\pi$
$173$	1.48540	−	19.8213i	0.112933	−	1.50699i	0.709660	−	0.704544i	$-0.248849\pi$
$174$	−6.44379	+	3.10317i	−0.488503	+	0.235251i
$175$	4.62929	+	12.3852i	0.349941	+	0.936237i
$176$	4.97039	+	2.39361i	0.374657	+	0.180425i
$177$	2.80552	−	4.85930i	0.210876	−	0.365248i
$178$	−5.45431	−	9.44714i	−0.408818	−	0.708093i
$179$	0.290997	+	3.88309i	0.0217502	+	0.290236i	0.997463	+	0.0711833i	$0.0226775\pi$
$179$	0.290997	+	3.88309i	0.0217502	+	0.290236i	−0.975713	+	0.219052i	$0.929703\pi$
$180$	0.0182851	+	0.0465897i	0.00136289	+	0.00347259i
$181$	3.86919	−	16.9520i	0.287595	−	1.26004i	−0.600220	−	0.799835i	$-0.704920\pi$
$181$	3.86919	−	16.9520i	0.287595	−	1.26004i	0.887815	−	0.460201i	$-0.152223\pi$
$182$	10.0129	+	0.163258i	0.742204	+	0.0121015i
$183$	1.43788	+	6.29976i	0.106291	+	0.465691i
$184$	1.69683	−	1.15688i	0.125092	−	0.0852863i
$185$	−0.298265	+	0.276749i	−0.0219289	+	0.0203470i
$186$	5.29145	+	0.797558i	0.387988	+	0.0584798i
$187$	11.1252	+	10.3227i	0.813556	+	0.754870i
$188$	−6.52097	−	8.17704i	−0.475590	−	0.596372i
$189$	1.28535	+	2.31255i	0.0934952	+	0.168213i
$190$	0.119172	−	0.149437i	0.00864563	−	0.0108413i
$191$	9.08837	−	1.36985i	0.657612	−	0.0991190i	0.188245	−	0.982122i	$-0.439720\pi$
$191$	9.08837	−	1.36985i	0.657612	−	0.0991190i	0.469367	+	0.883003i	$0.344482\pi$
$192$	0.826239	+	0.563320i	0.0596286	+	0.0406541i
$193$	0.0806381	−	0.205462i	0.00580446	−	0.0147895i	−0.927942	−	0.372724i	$-0.878424\pi$
$193$	0.0806381	−	0.205462i	0.00580446	−	0.0147895i	0.933747	+	0.357935i	$0.116519\pi$
$194$	10.8502	+	3.34685i	0.779000	+	0.240290i
$195$	−0.189438			−0.0135659
$196$	−6.20441	−	3.24118i	−0.443172	−	0.231513i
$197$	−15.3518			−1.09377			−0.546886	−	0.837207i	$-0.684187\pi$
$197$	−15.3518			−1.09377			−0.546886	+	0.837207i	$0.684187\pi$
$198$	−5.27162	−	1.62608i	−0.374638	−	0.115560i
$199$	2.30846	−	5.88186i	0.163642	−	0.416954i	−0.825407	−	0.564538i	$-0.809054\pi$
$199$	2.30846	−	5.88186i	0.163642	−	0.416954i	0.989050	+	0.147584i	$0.0471496\pi$
$200$	−4.12912	−	2.81519i	−0.291973	−	0.199064i
$201$	10.5081	−	1.58384i	0.741182	−	0.111715i
$202$	4.45654	−	5.58833i	0.313561	−	0.393193i
$203$	−7.19945	+	17.4995i	−0.505302	+	1.22822i
$204$	1.71523	+	2.15083i	0.120090	+	0.150588i
$205$	−0.156173	−	0.144908i	−0.0109076	−	0.0101208i
$206$	0.425099	+	0.0640733i	0.0296180	+	0.00446420i
$207$	−1.50545	+	1.39686i	−0.104636	+	0.0970883i
$208$	−3.12733	+	2.13217i	−0.216841	+	0.147840i
$209$	4.68809	+	20.5399i	0.324282	+	1.42077i
$210$	0.118352	+	0.0593915i	0.00816708	+	0.00409840i
$211$	5.78088	−	25.3277i	0.397972	−	1.74363i	−0.237390	−	0.971414i	$-0.576292\pi$
$211$	5.78088	−	25.3277i	0.397972	−	1.74363i	0.635362	−	0.772214i	$-0.280851\pi$
$212$	−0.0673678	−	0.171650i	−0.00462684	−	0.0117890i
$213$	−0.838290	−	11.1862i	−0.0574387	−	0.766466i
$214$	−0.909618	−	1.57550i	−0.0621802	−	0.107699i
$215$	0.269206	−	0.466279i	0.0183597	−	0.0317999i
$216$	−0.900969	−	0.433884i	−0.0613032	−	0.0295220i
$217$	11.8263	−	7.78371i	0.802825	−	0.528393i
$218$	−0.849439	+	0.409068i	−0.0575312	+	0.0277056i
$219$	−0.647536	+	8.64077i	−0.0437564	+	0.583889i
$220$	−0.263842	+	0.0813844i	−0.0177882	+	0.00548693i
$221$	−9.95004	+	3.06918i	−0.669312	+	0.206455i
$222$	0.607524	−	8.10685i	0.0407744	−	0.544096i
$223$	−4.90751	+	2.36333i	−0.328631	+	0.158260i	−0.590923	−	0.806728i	$-0.701236\pi$
$223$	−4.90751	+	2.36333i	−0.328631	+	0.158260i	0.262291	+	0.964989i	$0.415522\pi$
$224$	2.62228	−	0.351625i	0.175209	−	0.0234940i
$225$	4.50259	+	2.16833i	0.300172	+	0.144555i
$226$	−7.49425	+	12.9804i	−0.498510	+	0.863445i
$227$	−0.976370	−	1.69112i	−0.0648040	−	0.112244i	0.831803	−	0.555071i	$-0.187309\pi$
$227$	−0.976370	−	1.69112i	−0.0648040	−	0.112244i	−0.896607	+	0.442827i	$0.853976\pi$
$228$	0.285391	+	3.80828i	0.0189005	+	0.252209i
$229$	−4.51756	−	11.5105i	−0.298528	−	0.760638i	−0.998901	−	0.0468610i	$-0.985078\pi$
$229$	−4.51756	−	11.5105i	−0.298528	−	0.760638i	0.700373	−	0.713777i	$-0.253017\pi$
$230$	−0.0228719	+	0.100208i	−0.00150813	+	0.00660755i
$231$	−13.2519	+	6.11767i	−0.871911	+	0.402513i
$232$	−1.59149	−	6.97275i	−0.104486	−	0.457784i
$233$	−11.0197	+	7.51314i	−0.721928	+	0.492202i	−0.867682	−	0.497119i	$-0.834391\pi$
$233$	−11.0197	+	7.51314i	−0.721928	+	0.492202i	0.145755	+	0.989321i	$0.453439\pi$
$234$	2.77461	−	2.57446i	0.181382	−	0.168298i
$235$	0.517611	+	0.0780174i	0.0337652	+	0.00508929i
$236$	4.11318	+	3.81648i	0.267745	+	0.248431i
$237$	−2.25913	−	2.83286i	−0.146746	−	0.184014i
$238$	7.17857	+	1.20199i	0.465318	+	0.0779137i
$239$	−3.63575	+	4.55909i	−0.235177	+	0.294903i	−0.885390	−	0.464850i	$-0.846108\pi$
$239$	−3.63575	+	4.55909i	−0.235177	+	0.294903i	0.650213	+	0.759752i	$0.274680\pi$
$240$	−0.0494904	+	0.00745948i	−0.00319459	+	0.000481507i
$241$	2.28149	+	1.55549i	0.146963	+	0.100198i	0.634570	−	0.772866i	$-0.281177\pi$
$241$	2.28149	+	1.55549i	0.146963	+	0.100198i	−0.487606	+	0.873064i	$0.662130\pi$
$242$	7.10008	−	18.0907i	0.456411	−	1.16292i
$243$	0.955573	+	0.294755i	0.0613000	+	0.0189086i
$244$	−6.46177			−0.413672
$245$	0.337970	−	0.0922972i	0.0215921	−	0.00589665i
$246$	4.25670			0.271397
$247$	−13.8126	−	4.26063i	−0.878876	−	0.271097i
$248$	−1.95502	+	4.98131i	−0.124144	+	0.316313i
$249$	−5.26219	−	3.58770i	−0.333478	−	0.227361i
$250$	0.494780	−	0.0745761i	0.0312926	−	0.00471661i
$251$	10.9392	−	13.7174i	0.690478	−	0.865832i	−0.305795	−	0.952098i	$-0.598922\pi$
$251$	10.9392	−	13.7174i	0.690478	−	0.865832i	0.996272	+	0.0862660i	$0.0274935\pi$
$252$	−2.54059	+	0.738529i	−0.160042	+	0.0465229i
$253$	−7.06387	−	8.85781i	−0.444101	−	0.556886i
$254$	6.87647	+	6.38043i	0.431468	+	0.400344i
$255$	−0.136149	−	0.0205212i	−0.00852598	−	0.00128508i
$256$	−0.733052	+	0.680173i	−0.0458157	+	0.0425108i
$257$	−17.1583	+	11.6983i	−1.07030	+	0.729721i	−0.964345	−	0.264649i	$-0.914744\pi$
$257$	−17.1583	+	11.6983i	−1.07030	+	0.729721i	−0.105960	+	0.994370i	$0.533791\pi$
$258$	2.39379	+	10.4879i	0.149031	+	0.652948i
$259$	−13.1346	−	17.0327i	−0.816145	−	1.05836i
$260$	0.0421539	−	0.184688i	0.00261427	−	0.0114539i
$261$	2.61295	+	6.65768i	0.161737	+	0.412100i
$262$	−0.729511	−	9.73465i	−0.0450693	−	0.601409i
$263$	−2.55413	−	4.42388i	−0.157494	−	0.272788i	0.776470	−	0.630154i	$-0.217008\pi$
$263$	−2.55413	−	4.42388i	−0.157494	−	0.272788i	−0.933964	+	0.357366i	$0.883675\pi$
$264$	2.75836	−	4.77761i	0.169765	−	0.294042i
$265$	0.00831502	+	0.00400430i	0.000510787	+	0.000245982i
$266$	7.29374	+	6.99231i	0.447208	+	0.428726i
$267$	−9.82833	+	4.73307i	−0.601484	+	0.289659i
$268$	−0.794139	+	10.5970i	−0.0485098	+	0.647318i
$269$	−14.0808	+	4.34335i	−0.858522	+	0.264819i	−0.692602	−	0.721320i	$-0.743536\pi$
$269$	−14.0808	+	4.34335i	−0.858522	+	0.264819i	−0.165920	+	0.986139i	$0.553059\pi$
$270$	0.0478259	−	0.0147523i	0.00291059	−	0.000897798i
$271$	0.519649	−	6.93424i	0.0315664	−	0.421225i	−0.958926	−	0.283657i	$-0.908452\pi$
$271$	0.519649	−	6.93424i	0.0315664	−	0.421225i	0.990492	−	0.137568i	$-0.0439286\pi$
$272$	−2.47858	+	1.19362i	−0.150286	+	0.0723739i
$273$	0.911065	−	9.97268i	0.0551401	−	0.603574i
$274$	16.3439	+	7.87079i	0.987369	+	0.475492i
$275$	−13.7849	+	23.8761i	−0.831259	+	1.43978i
$276$	−1.02684	−	1.77854i	−0.0618085	−	0.107055i
$277$	0.969537	+	12.9376i	0.0582538	+	0.777343i	0.947468	+	0.319852i	$0.103633\pi$
$277$	0.969537	+	12.9376i	0.0582538	+	0.777343i	−0.889214	+	0.457492i	$0.848748\pi$
$278$	4.59386	+	11.7050i	0.275521	+	0.702017i
$279$	1.19076	−	5.21705i	0.0712888	−	0.312337i
$280$	−0.0842383	+	0.102169i	−0.00503420	+	0.00610577i
$281$	3.34261	+	14.6449i	0.199404	+	0.873644i	0.971293	+	0.237887i	$0.0764548\pi$
$281$	3.34261	+	14.6449i	0.199404	+	0.873644i	−0.771889	+	0.635757i	$0.780688\pi$
$282$	−8.64148	+	5.89166i	−0.514593	+	0.350843i
$283$	−17.4456	+	16.1872i	−1.03703	+	0.962227i	−0.999313	−	0.0370613i	$-0.988200\pi$
$283$	−17.4456	+	16.1872i	−1.03703	+	0.962227i	−0.0377211	+	0.999288i	$0.512010\pi$
$284$	11.0923	+	1.67189i	0.658205	+	0.0992085i
$285$	−0.140113	−	0.130006i	−0.00829958	−	0.00770089i
$286$	13.0190	+	16.3253i	0.769829	+	0.965335i
$287$	8.37954	−	7.52461i	0.494629	−	0.444164i
$288$	0.623490	−	0.781831i	0.0367395	−	0.0460699i
$289$	9.32656	−	1.40575i	0.548621	−	0.0826913i
$290$	0.295758	+	0.201644i	0.0173675	+	0.0118410i
$291$	4.14832	−	10.5698i	0.243179	−	0.619610i
$292$	−8.28003	−	2.55405i	−0.484552	−	0.149465i
$293$	−30.9132			−1.80597			−0.902983	−	0.429677i	$-0.858628\pi$
$293$	−30.9132			−1.80597			−0.902983	+	0.429677i	$0.858628\pi$
$294$	−3.69577	+	5.94485i	−0.215542	+	0.346711i
$295$	−0.280829			−0.0163505
$296$	7.76841	+	2.39624i	0.451529	+	0.139278i
$297$	−2.01548	+	5.13536i	−0.116950	+	0.297984i
$298$	1.42163	+	0.969251i	0.0823528	+	0.0561472i
$299$	7.68639	−	1.15854i	0.444515	−	0.0669999i
$300$	−3.11589	+	3.90720i	−0.179896	+	0.225582i
$301$	23.2519	+	16.4144i	1.34022	+	0.946113i
$302$	−9.71818	−	12.1862i	−0.559218	−	0.701238i
$303$	−5.23966	−	4.86170i	−0.301011	−	0.279297i
$304$	−3.77630	−	0.569186i	−0.216586	−	0.0326451i
$305$	0.237075	−	0.219973i	0.0135749	−	0.0125956i
$306$	2.27300	−	1.54970i	0.129939	−	0.0885906i
$307$	2.79385	+	12.2407i	0.159454	+	0.698611i	0.989930	+	0.141558i	$0.0452111\pi$
$307$	2.79385	+	12.2407i	0.159454	+	0.698611i	−0.830476	+	0.557054i	$0.811932\pi$
$308$	−3.01547	−	14.2810i	−0.171822	−	0.813733i
$309$	0.0956618	−	0.419122i	0.00544201	−	0.0238430i
$310$	−0.0978476	−	0.249312i	−0.00555737	−	0.0141599i
$311$	−1.22741	−	16.3786i	−0.0696000	−	0.928748i	−0.917281	−	0.398241i	$-0.869621\pi$
$311$	−1.22741	−	16.3786i	−0.0696000	−	0.928748i	0.847681	−	0.530507i	$-0.177998\pi$
$312$	1.89251	+	3.27792i	0.107142	+	0.185576i
$313$	−14.4216	+	24.9790i	−0.815159	+	1.41190i	0.0940548	+	0.995567i	$0.470017\pi$
$313$	−14.4216	+	24.9790i	−0.815159	+	1.41190i	−0.909214	+	0.416330i	$0.863316\pi$
$314$	−18.6467	−	8.97979i	−1.05230	−	0.506759i
$315$	0.0680699	−	0.113583i	0.00383531	−	0.00639968i
$316$	3.26453	−	1.57212i	0.183644	−	0.0884385i
$317$	−0.161599	+	2.15639i	−0.00907631	+	0.121115i	−0.999902	−	0.0140347i	$-0.995532\pi$
$317$	−0.161599	+	2.15639i	−0.00907631	+	0.121115i	0.990825	+	0.135150i	$0.0431515\pi$
$318$	−0.176205	+	0.0543520i	−0.00988108	+	0.00304791i
$319$	−37.7030	+	11.6298i	−2.11096	+	0.651146i
$320$	0.00374020	−	0.0499095i	0.000209083	−	0.00279002i
$321$	−1.63907	+	0.789337i	−0.0914842	+	0.0440565i
$322$	−5.16533	−	1.68599i	−0.287853	−	0.0939567i
$323$	−9.46560	−	4.55839i	−0.526680	−	0.253636i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−9.45780	−	16.3814i	−0.524624	−	0.908676i
$326$	−1.51364	−	20.1982i	−0.0838330	−	1.11867i
$327$	0.344446	+	0.877633i	0.0190479	+	0.0485332i
$328$	−0.947205	+	4.14998i	−0.0523006	+	0.229144i
$329$	−6.59646	+	26.8737i	−0.363675	+	1.48159i
$330$	0.0614399	+	0.269186i	0.00338215	+	0.0148182i
$331$	−16.0948	+	10.9732i	−0.884650	+	0.603144i	−0.918123	−	0.396295i	$-0.870296\pi$
$331$	−16.0948	+	10.9732i	−0.884650	+	0.603144i	0.0334730	+	0.999440i	$0.489343\pi$
$332$	4.66870	−	4.33192i	0.256228	−	0.237745i
$333$	−8.03878	−	1.21165i	−0.440522	−	0.0663981i
$334$	15.8570	+	14.7132i	0.867657	+	0.805068i
$335$	−0.331611	−	0.415827i	−0.0181179	−	0.0227191i
$336$	−0.154679	−	2.64123i	−0.00843842	−	0.144091i
$337$	7.02866	−	8.81366i	0.382875	−	0.480111i	−0.552628	−	0.833428i	$-0.686375\pi$
$337$	7.02866	−	8.81366i	0.382875	−	0.480111i	0.935504	+	0.353317i	$0.114946\pi$
$338$	−1.31153	+	0.197681i	−0.0713376	+	0.0107524i
$339$	12.3841	+	8.44333i	0.672611	+	0.458579i
$340$	0.0503026	−	0.128169i	0.00272804	−	0.00695094i
$341$	28.2096	+	8.70151i	1.52763	+	0.471213i
$342$	3.81896			0.206506
$343$	3.23345	+	18.2358i	0.174590	+	0.984641i
$344$	−10.7576			−0.580011
$345$	0.0982190	+	0.0302966i	0.00528793	+	0.00163111i
$346$	7.26186	−	18.5029i	0.390400	−	0.994722i
$347$	−21.2243	−	14.4705i	−1.13938	−	0.776815i	−0.161683	−	0.986843i	$-0.551692\pi$
$347$	−21.2243	−	14.4705i	−1.13938	−	0.776815i	−0.977695	+	0.210028i	$0.932645\pi$
$348$	−7.07219	+	1.06596i	−0.379109	+	0.0571415i
$349$	9.26619	−	11.6194i	0.496008	−	0.621974i	−0.469316	−	0.883030i	$-0.655499\pi$
$349$	9.26619	−	11.6194i	0.496008	−	0.621974i	0.965324	+	0.261057i	$0.0840709\pi$
$350$	0.773007	+	13.1995i	0.0413190	+	0.705544i
$351$	−2.35992	−	2.95924i	−0.125963	−	0.157953i
$352$	4.04404	+	3.75232i	0.215548	+	0.199999i
$353$	28.0325	+	4.22522i	1.49202	+	0.224886i	0.843837	−	0.536599i	$-0.180291\pi$
$353$	28.0325	+	4.22522i	1.49202	+	0.224886i	0.648182	+	0.761485i	$0.275529\pi$
$354$	4.11318	−	3.81648i	0.218613	−	0.202843i
$355$	−0.463878	+	0.316266i	−0.0246201	+	0.0167857i
$356$	−2.42740	−	10.6351i	−0.128652	−	0.563660i
$357$	1.73509	−	7.06867i	0.0918306	−	0.374114i
$358$	−0.866492	+	3.79635i	−0.0457955	+	0.200643i
$359$	4.47490	+	11.4019i	0.236176	+	0.601767i	0.998994	−	0.0448467i	$-0.0142799\pi$
$359$	4.47490	+	11.4019i	0.236176	+	0.601767i	−0.762818	+	0.646613i	$0.776185\pi$
$360$	0.00374020	+	0.0499095i	0.000197126	+	0.00263046i
$361$	2.20778	+	3.82399i	0.116199	+	0.201262i
$362$	8.69400	−	15.0585i	0.456947	−	0.791455i
$363$	−17.5095	−	8.43215i	−0.919013	−	0.442573i
$364$	9.51991	+	3.10735i	0.498979	+	0.162870i
$365$	0.390730	−	0.188166i	0.0204518	−	0.00984905i
$366$	−0.482888	+	6.44370i	−0.0252410	+	0.336818i
$367$	11.5591	−	3.56550i	0.603379	−	0.186118i	0.0220098	−	0.999758i	$-0.492993\pi$
$367$	11.5591	−	3.56550i	0.603379	−	0.186118i	0.581369	+	0.813640i	$0.302517\pi$
$368$	1.96244	−	0.605333i	0.102299	−	0.0315552i
$369$	0.318104	−	4.24480i	0.0165598	−	0.220975i
$370$	−0.366587	+	0.176539i	−0.0190579	+	0.00917782i
$371$	−0.250790	+	0.418474i	−0.0130204	+	0.0217261i
$372$	4.82128	+	2.32181i	0.249972	+	0.120380i
$373$	5.96400	−	10.3300i	0.308804	−	0.534865i	−0.669297	−	0.742995i	$-0.733404\pi$
$373$	5.96400	−	10.3300i	0.308804	−	0.534865i	0.978101	+	0.208130i	$0.0667378\pi$
$374$	7.58829	+	13.1433i	0.392381	+	0.679624i
$375$	−0.0373926	−	0.498970i	−0.00193095	−	0.0257667i
$376$	−3.82104	−	9.73584i	−0.197055	−	0.502088i
$377$	6.02380	−	26.3920i	0.310241	−	1.35926i
$378$	0.546606	+	2.58867i	0.0281144	+	0.133147i
$379$	−4.15753	−	18.2153i	−0.213558	−	0.935659i	−0.962127	−	0.272602i	$-0.912116\pi$
$379$	−4.15753	−	18.2153i	−0.213558	−	0.935659i	0.748569	−	0.663057i	$-0.230741\pi$
$380$	0.157925	−	0.107671i	0.00810136	−	0.00552341i
$381$	6.87647	−	6.38043i	0.352292	−	0.326879i
$382$	9.08837	+	1.36985i	0.465002	+	0.0700877i
$383$	−8.62011	−	7.99829i	−0.440467	−	0.408694i	0.428517	−	0.903534i	$-0.359036\pi$
$383$	−8.62011	−	7.99829i	−0.440467	−	0.408694i	−0.868984	+	0.494840i	$0.835227\pi$
$384$	0.623490	+	0.781831i	0.0318173	+	0.0398977i
$385$	0.596790	+	0.421298i	0.0304152	+	0.0214714i
$386$	0.137617	−	0.172566i	0.00700450	−	0.00878337i
$387$	10.6375	−	1.60334i	0.540732	−	0.0815023i
$388$	9.38166	+	6.39631i	0.476282	+	0.324723i
$389$	−3.75186	+	9.55958i	−0.190227	+	0.484690i	−0.993887	−	0.110398i	$-0.964787\pi$
$389$	−3.75186	+	9.55958i	−0.190227	+	0.484690i	0.803661	+	0.595088i	$0.202883\pi$
$390$	−0.181022	−	0.0558378i	−0.00916639	−	0.00282746i
$391$	5.64971			0.285718
$392$	−4.97342	−	4.92597i	−0.251195	−	0.248799i
$393$	−9.76194			−0.492425
$394$	−14.6698	−	4.52503i	−0.739053	−	0.227968i
$395$	−0.0662535	+	0.168811i	−0.00333358	+	0.00849382i
$396$	−4.55812	−	3.10768i	−0.229054	−	0.156167i
$397$	2.12023	−	0.319573i	0.106411	−	0.0160389i	−0.0956207	−	0.995418i	$-0.530484\pi$
$397$	2.12023	−	0.319573i	0.106411	−	0.0160389i	0.202032	+	0.979379i	$0.435245\pi$
$398$	3.93961	−	4.94012i	0.197475	−	0.247626i
$399$	7.51782	−	6.75081i	0.376362	−	0.337963i
$400$	−3.11589	−	3.90720i	−0.155794	−	0.195360i
$401$	−1.77235	−	1.64450i	−0.0885069	−	0.0821224i	0.634679	−	0.772776i	$-0.281132\pi$
$401$	−1.77235	−	1.64450i	−0.0885069	−	0.0821224i	−0.723186	+	0.690654i	$0.757323\pi$
$402$	10.5081	+	1.58384i	0.524095	+	0.0789946i
$403$	−14.8476	+	13.7765i	−0.739609	+	0.686257i
$404$	5.90574	−	4.02646i	0.293821	−	0.200324i
$405$	−0.0111370	−	0.0487946i	−0.000553404	−	0.00242462i
$406$	−12.0377	+	14.6000i	−0.597419	+	0.724585i
$407$	9.97974	−	43.7241i	0.494678	−	2.16732i
$408$	1.00506	+	2.56085i	0.0497579	+	0.126781i
$409$	−0.0144559	−	0.192900i	−0.000714797	−	0.00953830i	0.996835	−	0.0794984i	$-0.0253319\pi$
$409$	−0.0144559	−	0.192900i	−0.000714797	−	0.00953830i	−0.997550	+	0.0699601i	$0.977713\pi$
$410$	−0.106523	−	0.184503i	−0.00526078	−	0.00911194i
$411$	9.07016	−	15.7100i	0.447398	−	0.774916i
$412$	0.387327	+	0.186527i	0.0190822	+	0.00918951i
$413$	1.35059	−	14.7838i	0.0664584	−	0.727466i
$414$	−1.85030	+	0.891058i	−0.0909374	+	0.0437931i
$415$	−0.0238208	+	0.317866i	−0.00116932	+	0.0156034i
$416$	−3.61686	+	1.11565i	−0.177331	+	0.0546994i
$417$	12.0155	−	3.70630i	0.588403	−	0.181498i
$418$	−1.57442	+	21.0092i	−0.0770074	+	1.02759i
$419$	−16.0933	+	7.75013i	−0.786209	+	0.378618i	−0.783511	−	0.621378i	$-0.786573\pi$
$419$	−16.0933	+	7.75013i	−0.786209	+	0.378618i	−0.00269824	+	0.999996i	$0.500859\pi$
$420$	0.0955883	+	0.0916379i	0.00466423	+	0.00447147i
$421$	−7.33433	−	3.53203i	−0.357453	−	0.172140i	0.246534	−	0.969134i	$-0.420708\pi$
$421$	−7.33433	−	3.53203i	−0.357453	−	0.172140i	−0.603988	+	0.796994i	$0.706422\pi$
$422$	12.9895	−	22.4985i	0.632319	−	1.09521i
$423$	5.22941	+	9.05760i	0.254263	+	0.440396i
$424$	−0.0137800	−	0.183882i	−0.000669217	−	0.00893008i
$425$	−5.02278	−	12.7978i	−0.243641	−	0.620786i
$426$	2.49614	−	10.9363i	0.120939	−	0.529866i
$427$	10.4400	+	13.5384i	0.505227	+	0.655168i
$428$	−0.404818	−	1.77362i	−0.0195676	−	0.0857313i
$429$	17.2526	−	11.7626i	0.832962	−	0.567904i
$430$	0.394684	−	0.366213i	0.0190334	−	0.0176604i
$431$	4.56042	+	0.687372i	0.219668	+	0.0331096i	0.257954	−	0.966157i	$-0.416952\pi$
$431$	4.56042	+	0.687372i	0.219668	+	0.0331096i	−0.0382862	+	0.999267i	$0.512190\pi$
$432$	−0.733052	−	0.680173i	−0.0352690	−	0.0327248i
$433$	21.7378	+	27.2583i	1.04465	+	1.30995i	0.949254	+	0.314511i	$0.101840\pi$
$433$	21.7378	+	27.2583i	1.04465	+	1.30995i	0.0953963	+	0.995439i	$0.469588\pi$
$434$	13.5952	−	3.95203i	0.652592	−	0.189703i
$435$	0.223183	−	0.279862i	0.0107008	−	0.0134184i
$436$	−0.932275	+	0.140518i	−0.0446479	+	0.00672959i
$437$	6.48012	+	4.41807i	0.309986	+	0.211345i
$438$	−3.16568	+	8.06602i	−0.151262	+	0.385409i
$439$	1.18307	+	0.364929i	0.0564649	+	0.0174171i	0.322859	−	0.946447i	$-0.395356\pi$
$439$	1.18307	+	0.364929i	0.0564649	+	0.0174171i	−0.266394	+	0.963864i	$0.585832\pi$
$440$	−0.276108			−0.0131629
$441$	5.65204	+	4.12970i	0.269145	+	0.196652i
$442$	−10.4126			−0.495279
$443$	−8.04908	−	2.48281i	−0.382423	−	0.117962i	0.0975821	−	0.995227i	$-0.468889\pi$
$443$	−8.04908	−	2.48281i	−0.382423	−	0.117962i	−0.480005	+	0.877266i	$0.659365\pi$
$444$	2.97007	−	7.56761i	0.140953	−	0.359143i
$445$	0.451102	+	0.307556i	0.0213843	+	0.0145795i
$446$	−5.38609	+	0.811822i	−0.255039	+	0.0384409i
$447$	1.07278	−	1.34522i	0.0507407	−	0.0636268i
$448$	2.60942	+	0.436927i	0.123284	+	0.0206429i
$449$	−1.81546	−	2.27652i	−0.0856769	−	0.107435i	0.737145	−	0.675734i	$-0.236173\pi$
$449$	−1.81546	−	2.27652i	−0.0856769	−	0.107435i	−0.822822	+	0.568299i	$0.807602\pi$
$450$	3.66342	+	3.39916i	0.172695	+	0.160238i
$451$	23.2207	+	3.49996i	1.09342	+	0.164807i
$452$	−10.9874	+	10.1948i	−0.516802	+	0.479522i
$453$	−12.8784	+	8.78033i	−0.605079	+	0.412536i
$454$	−0.434526	−	1.90378i	−0.0203933	−	0.0893489i
$455$	−0.455056	+	0.210074i	−0.0213333	+	0.00984843i
$456$	−0.849798	+	3.72321i	−0.0397954	+	0.174355i
$457$	11.0318	+	28.1086i	0.516047	+	1.31487i	0.917044	+	0.398786i	$0.130569\pi$
$457$	11.0318	+	28.1086i	0.516047	+	1.31487i	−0.400997	+	0.916079i	$0.631336\pi$
$458$	−0.924061	−	12.3307i	−0.0431785	−	0.576177i
$459$	−1.37551	−	2.38245i	−0.0642032	−	0.111203i
$460$	−0.0513927	+	0.0890148i	−0.00239620	+	0.00415034i
$461$	21.2110	+	10.2147i	0.987896	+	0.475746i	0.856814	−	0.515626i	$-0.172440\pi$
$461$	21.2110	+	10.2147i	0.987896	+	0.475746i	0.131082	+	0.991371i	$0.458155\pi$
$462$	−14.4664	+	1.93982i	−0.673037	+	0.0902484i
$463$	16.5718	−	7.98058i	0.770159	−	0.370889i	−0.00717754	−	0.999974i	$-0.502285\pi$
$463$	16.5718	−	7.98058i	0.770159	−	0.370889i	0.777336	+	0.629085i	$0.216570\pi$
$464$	0.534475	−	7.13207i	0.0248124	−	0.331098i
$465$	−0.255927	+	0.0789429i	−0.0118683	+	0.00366089i
$466$	−12.7447	+	3.93122i	−0.590387	+	0.182110i
$467$	−1.24366	+	16.5955i	−0.0575498	+	0.767949i	0.891540	+	0.452942i	$0.149626\pi$
$467$	−1.24366	+	16.5955i	−0.0575498	+	0.767949i	−0.949090	+	0.315006i	$0.897993\pi$
$468$	3.41018	−	1.64226i	0.157636	−	0.0759133i
$469$	23.4855	−	15.4574i	1.08446	−	0.713754i
$470$	0.471619	+	0.227120i	0.0217542	+	0.0104763i
$471$	−10.3482	+	17.9235i	−0.476818	+	0.825872i
$472$	2.80552	+	4.85930i	0.129134	+	0.223668i
$473$	4.43498	+	59.1807i	0.203921	+	2.72113i
$474$	−1.32376	−	3.37289i	−0.0608024	−	0.154922i
$475$	4.24686	−	18.6067i	0.194859	−	0.853735i
$476$	6.50535	+	3.26451i	0.298172	+	0.149629i
$477$	0.0410322	+	0.179774i	0.00187874	+	0.00823128i
$478$	−4.81804	+	3.28488i	−0.220372	+	0.150247i
$479$	25.7477	−	23.8904i	1.17644	−	1.09158i	0.182329	−	0.983237i	$-0.441636\pi$
$479$	25.7477	−	23.8904i	1.17644	−	1.09158i	0.994114	−	0.108342i	$-0.0345542\pi$
$480$	−0.0494904	−	0.00745948i	−0.00225892	−	0.000340477i
$481$	22.5564	+	20.9293i	1.02848	+	0.954295i
$482$	1.72164	+	2.15886i	0.0784184	+	0.0983336i
$483$	−2.06728	+	5.02489i	−0.0940647	+	0.228641i
$484$	12.1170	−	15.1942i	0.550772	−	0.690646i
$485$	−0.561947	+	0.0846999i	−0.0255167	+	0.00384602i
$486$	0.826239	+	0.563320i	0.0374790	+	0.0255527i
$487$	12.2593	−	31.2361i	0.555521	−	1.41544i	−0.326934	−	0.945047i	$-0.606015\pi$
$487$	12.2593	−	31.2361i	0.555521	−	1.41544i	0.882455	−	0.470397i	$-0.155889\pi$
$488$	−6.17469	−	1.90464i	−0.279515	−	0.0862190i
$489$	−20.2548			−0.915954
$490$	0.350160	+	0.0114216i	0.0158186	+	0.000515976i
$491$	35.7216			1.61209			0.806047	−	0.591851i	$-0.201603\pi$
$491$	35.7216			1.61209			0.806047	+	0.591851i	$0.201603\pi$
$492$	4.06759	+	1.25468i	0.183381	+	0.0565655i
$493$	7.18826	−	18.3154i	0.323743	−	0.824883i
$494$	−11.9431	−	8.14269i	−0.537347	−	0.366357i
$495$	0.273024	−	0.0411518i	0.0122715	−	0.00184964i
$496$	−3.33643	+	4.18375i	−0.149810	+	0.187856i
$497$	−14.4185	−	25.9412i	−0.646756	−	1.16362i
$498$	−3.97091	−	4.97937i	−0.177941	−	0.223131i
$499$	−12.1897	−	11.3104i	−0.545686	−	0.506322i	0.358461	−	0.933545i	$-0.383302\pi$
$499$	−12.1897	−	11.3104i	−0.545686	−	0.506322i	−0.904147	+	0.427222i	$0.859492\pi$
$500$	0.494780	+	0.0745761i	0.0221272	+	0.00333515i
$501$	15.8570	−	14.7132i	0.708439	−	0.657335i
$502$	14.4965	−	9.88354i	0.647010	−	0.441124i
$503$	−7.41059	−	32.4679i	−0.330422	−	1.44767i	−0.818315	−	0.574770i	$-0.805092\pi$
$503$	−7.41059	−	32.4679i	−0.330422	−	1.44767i	0.487893	−	0.872903i	$-0.337765\pi$
$504$	−2.64540	−	0.0431327i	−0.117835	−	0.00192128i
$505$	−0.0796047	+	0.348771i	−0.00354236	+	0.0155201i
$506$	−4.13915	−	10.5464i	−0.184008	−	0.468844i
$507$	0.0991175	+	1.32263i	0.00440196	+	0.0587401i
$508$	4.69030	+	8.12384i	0.208098	+	0.360437i
$509$	9.96041	−	17.2519i	0.441488	−	0.764679i	−0.556313	−	0.830973i	$-0.687784\pi$
$509$	9.96041	−	17.2519i	0.441488	−	0.764679i	0.997800	+	0.0662943i	$0.0211176\pi$
$510$	−0.124052	−	0.0597401i	−0.00549309	−	0.00264533i
$511$	8.02658	+	21.4744i	0.355075	+	0.949971i
$512$	−0.900969	+	0.433884i	−0.0398176	+	0.0191751i
$513$	0.285391	−	3.80828i	0.0126003	−	0.168140i
$514$	−19.8441	+	6.12110i	−0.875287	+	0.269990i
$515$	−0.0205604	+	0.00634203i	−0.000905997	+	0.000279463i
$516$	−0.803917	+	10.7275i	−0.0353905	+	0.472253i
$517$	−51.9844	+	25.0344i	−2.28627	+	1.10101i
$518$	−7.53061	−	20.1475i	−0.330876	−	0.885229i
$519$	−17.9085	−	8.62427i	−0.786095	−	0.378564i
$520$	0.0947189	−	0.164058i	0.00415370	−	0.00719442i
$521$	−8.60351	−	14.9017i	−0.376927	−	0.652856i	0.613687	−	0.789550i	$-0.289686\pi$
$521$	−8.60351	−	14.9017i	−0.376927	−	0.652856i	−0.990613	+	0.136694i	$0.956352\pi$
$522$	0.534475	+	7.13207i	0.0233933	+	0.312162i
$523$	11.7985	+	30.0621i	0.515912	+	1.31452i	0.917148	+	0.398548i	$0.130486\pi$
$523$	11.7985	+	30.0621i	0.515912	+	1.31452i	−0.401235	+	0.915975i	$0.631419\pi$
$524$	2.17224	−	9.51719i	0.0948946	−	0.415760i
$525$	13.2204	+	0.215556i	0.576984	+	0.00940761i
$526$	−1.13669	−	4.98018i	−0.0495622	−	0.217146i
$527$	−12.1633	+	8.29280i	−0.529842	+	0.361240i
$528$	4.04404	−	3.75232i	0.175994	−	0.163299i
$529$	18.5726	+	2.79937i	0.807505	+	0.121712i
$530$	0.00676532	+	0.00627730i	0.000293867	+	0.000272668i
$531$	−3.49843	−	4.38689i	−0.151819	−	0.190375i
$532$	4.90868	+	8.83153i	0.212818	+	0.382895i
$533$	−10.0455	+	12.5966i	−0.435117	+	0.545620i
$534$	−10.7868	+	1.62585i	−0.466790	+	0.0703572i
$535$	0.0752304	+	0.0512912i	0.00325250	+	0.00221751i
$536$	−3.88239	+	9.89217i	−0.167694	+	0.427277i
$537$	3.72098	+	1.14777i	0.160572	+	0.0495299i
$538$	−14.7355			−0.635291
$539$	−25.0488	+	29.3910i	−1.07893	+	1.26596i
$540$	0.0500494			0.00215378
$541$	15.4989	+	4.78078i	0.666350	+	0.205542i	0.609434	−	0.792837i	$-0.291397\pi$
$541$	15.4989	+	4.78078i	0.666350	+	0.205542i	0.0569166	+	0.998379i	$0.481873\pi$
$542$	2.54046	−	6.47300i	0.109122	−	0.278039i
$543$	−14.3666	−	9.79501i	−0.616532	−	0.420344i
$544$	−2.72029	+	0.410018i	−0.116631	+	0.0175794i
$545$	0.0294205	−	0.0368922i	0.00126024	−	0.00158029i
$546$	3.81009	−	9.26108i	0.163057	−	0.396338i
$547$	−10.1490	−	12.7264i	−0.433940	−	0.544143i	0.515995	−	0.856592i	$-0.327422\pi$
$547$	−10.1490	−	12.7264i	−0.433940	−	0.544143i	−0.949935	+	0.312448i	$0.898851\pi$
$548$	13.2978	+	12.3386i	0.568054	+	0.527077i
$549$	6.38959	+	0.963076i	0.272701	+	0.0411031i
$550$	−20.2101	+	18.7522i	−0.861760	+	0.799596i
$551$	22.5674	−	15.3862i	0.961405	−	0.655475i
$552$	−0.456987	−	2.00219i	−0.0194506	−	0.0852189i
$553$	−8.56819	−	4.29969i	−0.364356	−	0.182841i
$554$	−2.88695	+	12.6486i	−0.122655	+	0.537386i
$555$	0.148650	+	0.378755i	0.00630985	+	0.0160772i
$556$	0.939668	+	12.5390i	0.0398508	+	0.531772i
$557$	9.81076	+	16.9927i	0.415695	+	0.720005i	0.995501	−	0.0947494i	$-0.0302050\pi$
$557$	9.81076	+	16.9927i	0.415695	+	0.720005i	−0.579806	+	0.814755i	$0.696872\pi$
$558$	2.67561	−	4.63429i	0.113268	−	0.196185i
$559$	−36.6854	−	17.6668i	−1.55163	−	0.747224i
$560$	−0.110611	+	0.0728003i	−0.00467415	+	0.00307638i
$561$	13.6736	−	6.58487i	0.577301	−	0.278013i
$562$	−1.12256	+	14.9796i	−0.0473525	+	0.631875i
$563$	31.4681	−	9.70662i	1.32622	−	0.409085i	0.450878	−	0.892586i	$-0.351111\pi$
$563$	31.4681	−	9.70662i	1.32622	−	0.409085i	0.875344	+	0.483500i	$0.160635\pi$
$564$	−9.99416	+	3.08279i	−0.420830	+	0.129809i
$565$	0.0560600	−	0.748069i	0.00235846	−	0.0314715i
$566$	−21.4418	+	10.3258i	−0.901266	+	0.434027i
$567$	2.62228	−	0.351625i	0.110125	−	0.0147669i
$568$	10.1067	+	4.86712i	0.424067	+	0.204220i
$569$	−13.4561	+	23.3066i	−0.564107	+	0.977062i	0.433025	+	0.901382i	$0.357446\pi$
$569$	−13.4561	+	23.3066i	−0.564107	+	0.977062i	−0.997132	+	0.0756803i	$0.975887\pi$
$570$	−0.0955683	−	0.165529i	−0.00400292	−	0.00693326i
$571$	−0.837363	−	11.1738i	−0.0350426	−	0.467610i	−0.986929	−	0.161158i	$-0.948477\pi$
$571$	−0.837363	−	11.1738i	−0.0350426	−	0.467610i	0.951886	−	0.306452i	$-0.0991420\pi$
$572$	7.62863	+	19.4374i	0.318969	+	0.812720i
$573$	2.04520	−	8.96059i	0.0854393	−	0.374334i
$574$	10.2252	−	4.72040i	0.426791	−	0.197026i
$575$	2.28379	+	10.0059i	0.0952406	+	0.417276i
$576$	0.826239	−	0.563320i	0.0344266	−	0.0234717i
$577$	−2.81322	+	2.61028i	−0.117116	+	0.108668i	−0.736557	−	0.676375i	$-0.763550\pi$
$577$	−2.81322	+	2.61028i	−0.117116	+	0.108668i	0.619441	+	0.785043i	$0.287359\pi$
$578$	9.32656	+	1.40575i	0.387934	+	0.0584716i
$579$	−0.161799	−	0.150128i	−0.00672415	−	0.00623910i
$580$	0.223183	+	0.279862i	0.00926715	+	0.0116206i
$581$	−16.6190	−	2.78272i	−0.689474	−	0.115447i
$582$	7.07952	−	8.87743i	0.293455	−	0.367981i
$583$	−1.00590	+	0.151616i	−0.0416603	+	0.00627928i
$584$	−7.15936	−	4.88117i	−0.296256	−	0.201984i
$585$	−0.0692094	+	0.176343i	−0.00286146	+	0.00729087i
$586$	−29.5398	−	9.11181i	−1.22028	−	0.376405i
$587$	−41.4535			−1.71097			−0.855485	−	0.517827i	$-0.826741\pi$
$587$	−41.4535			−1.71097			−0.855485	+	0.517827i	$0.826741\pi$
$588$	−5.28386	+	4.59139i	−0.217903	+	0.189346i
$589$	−20.4361			−0.842054
$590$	−0.268353	−	0.0827759i	−0.0110479	−	0.00340783i
$591$	−5.60865	+	14.2906i	−0.230709	+	0.587837i
$592$	6.71698	+	4.57956i	0.276066	+	0.188219i
$593$	8.30145	−	1.25124i	0.340900	−	0.0513824i	0.0236385	−	0.999721i	$-0.492475\pi$
$593$	8.30145	−	1.25124i	0.340900	−	0.0513824i	0.317261	+	0.948338i	$0.397237\pi$
$594$	−3.43961	+	4.31314i	−0.141129	+	0.176970i
$595$	−0.349805	+	0.101686i	−0.0143406	+	0.00416871i
$596$	1.07278	+	1.34522i	0.0439427	+	0.0551024i
$597$	−4.63189	−	4.29777i	−0.189571	−	0.175896i
$598$	7.68639	+	1.15854i	0.314320	+	0.0473761i
$599$	−12.8261	+	11.9009i	−0.524059	+	0.486256i	−0.897265	−	0.441493i	$-0.854449\pi$
$599$	−12.8261	+	11.9009i	−0.524059	+	0.486256i	0.373206	+	0.927749i	$0.378259\pi$
$600$	−4.12912	+	2.81519i	−0.168571	+	0.114930i
$601$	1.89200	+	8.28938i	0.0771762	+	0.338131i	0.998745	−	0.0500841i	$-0.0159489\pi$
$601$	1.89200	+	8.28938i	0.0771762	+	0.338131i	−0.921569	+	0.388215i	$0.873092\pi$
$602$	17.3806	+	22.5388i	0.708381	+	0.918613i
$603$	2.36468	−	10.3603i	0.0962971	−	0.421905i
$604$	−5.69448	−	14.5093i	−0.231705	−	0.590375i
$605$	0.0726875	+	0.969947i	0.00295517	+	0.0394339i
$606$	−3.57387	−	6.19012i	−0.145179	−	0.251457i
$607$	−22.3028	+	38.6296i	−0.905244	+	1.56793i	−0.0846553	+	0.996410i	$0.526979\pi$
$607$	−22.3028	+	38.6296i	−0.905244	+	1.56793i	−0.820589	+	0.571519i	$0.806354\pi$
$608$	−3.44076	−	1.65698i	−0.139541	−	0.0671996i
$609$	13.6596	+	13.0951i	0.553514	+	0.530639i
$610$	0.291380	−	0.140321i	0.0117976	−	0.00568145i
$611$	2.95832	−	39.4761i	0.119681	−	1.59703i
$612$	2.62880	−	0.810876i	0.106263	−	0.0327777i
$613$	−22.7329	+	7.01216i	−0.918172	+	0.283219i	−0.717596	−	0.696460i	$-0.754758\pi$
$613$	−22.7329	+	7.01216i	−0.918172	+	0.283219i	−0.200576	+	0.979678i	$0.564281\pi$
$614$	−0.938270	+	12.5203i	−0.0378655	+	0.505280i
$615$	−0.191947	+	0.0924369i	−0.00774006	+	0.00372742i
$616$	1.32789	−	14.5353i	0.0535022	−	0.585645i
$617$	26.8787	+	12.9441i	1.08210	+	0.521110i	0.887986	−	0.459870i	$-0.152104\pi$
$617$	26.8787	+	12.9441i	1.08210	+	0.521110i	0.194109	+	0.980980i	$0.437818\pi$
$618$	0.214950	−	0.372304i	0.00864656	−	0.0149763i
$619$	−3.61597	−	6.26304i	−0.145338	−	0.251733i	0.784161	−	0.620557i	$-0.213094\pi$
$619$	−3.61597	−	6.26304i	−0.145338	−	0.251733i	−0.929499	+	0.368825i	$0.879760\pi$
$620$	−0.0200146	−	0.267076i	−0.000803806	−	0.0107260i
$621$	0.750293	+	1.91172i	0.0301082	+	0.0767145i
$622$	3.65481	−	16.0128i	0.146545	−	0.642054i
$623$	−18.3603	+	22.2685i	−0.735591	+	0.892167i
$624$	0.842245	+	3.69012i	0.0337168	+	0.147723i
$625$	20.6249	−	14.0618i	0.824997	−	0.562474i
$626$	−21.1436	+	19.6184i	−0.845069	+	0.784109i
$627$	20.8328	+	3.14004i	0.831981	+	0.125401i
$628$	−15.1715	−	14.0771i	−0.605407	−	0.561736i
$629$	13.9441	+	17.4854i	0.555988	+	0.697187i
$630$	0.0985249	−	0.0884729i	0.00392533	−	0.00352484i
$631$	−23.6101	+	29.6062i	−0.939905	+	1.17860i	0.0438413	+	0.999039i	$0.486040\pi$
$631$	−23.6101	+	29.6062i	−0.939905	+	1.17860i	−0.983746	+	0.179565i	$0.942531\pi$
$632$	3.58289	−	0.540034i	0.142520	−	0.0214814i
$633$	−21.4649	−	14.6345i	−0.853152	−	0.581669i
$634$	−0.790027	+	2.01296i	−0.0313760	+	0.0799447i
$635$	−0.448635	−	0.138386i	−0.0178036	−	0.00549167i
$636$	−0.184397			−0.00731182
$637$	−8.87055	−	24.9661i	−0.351464	−	0.989191i
$638$	−39.4559			−1.56208
$639$	−10.7192	−	3.30644i	−0.424045	−	0.130801i
$640$	0.0182851	−	0.0465897i	0.000722782	−	0.00184162i
$641$	−20.5779	−	14.0298i	−0.812777	−	0.554142i	0.0840818	−	0.996459i	$-0.473204\pi$
$641$	−20.5779	−	14.0298i	−0.812777	−	0.554142i	−0.896859	+	0.442317i	$0.854157\pi$
$642$	−1.79892	+	0.271143i	−0.0709976	+	0.0107012i
$643$	18.8475	−	23.6340i	0.743271	−	0.932032i	−0.256130	−	0.966642i	$-0.582448\pi$
$643$	18.8475	−	23.6340i	0.743271	−	0.932032i	0.999401	+	0.0346101i	$0.0110189\pi$
$644$	−4.43889	−	3.13360i	−0.174917	−	0.123481i
$645$	−0.335694	−	0.420948i	−0.0132180	−	0.0165748i
$646$	−7.70146	−	7.14591i	−0.303010	−	0.281152i
$647$	−35.5647	−	5.36052i	−1.39819	−	0.210744i	−0.593692	−	0.804693i	$-0.702330\pi$
$647$	−35.5647	−	5.36052i	−1.39819	−	0.210744i	−0.804503	+	0.593949i	$0.797568\pi$
$648$	−0.733052	+	0.680173i	−0.0287970	+	0.0267197i
$649$	25.5758	−	17.4373i	1.00394	−	0.684473i
$650$	−4.20912	−	18.4413i	−0.165095	−	0.723329i
$651$	−2.92500	−	13.8525i	−0.114640	−	0.542924i
$652$	4.50712	−	19.7470i	0.176512	−	0.773351i
$653$	5.65346	+	14.4048i	0.221237	+	0.563703i	0.997797	−	0.0663405i	$-0.0211323\pi$
$653$	5.65346	+	14.4048i	0.221237	+	0.563703i	−0.776560	+	0.630043i	$0.783037\pi$
$654$	0.0704560	+	0.940170i	0.00275505	+	0.0367635i
$655$	0.244290	+	0.423122i	0.00954519	+	0.0165328i
$656$	−2.12835	+	3.68641i	−0.0830981	+	0.143930i
$657$	7.80689	+	3.75960i	0.304576	+	0.146676i
$658$	−14.2246	+	23.7354i	−0.554531	+	0.925303i
$659$	33.5619	−	16.1626i	1.30739	−	0.629605i	0.355106	−	0.934826i	$-0.384445\pi$
$659$	33.5619	−	16.1626i	1.30739	−	0.629605i	0.952281	+	0.305221i	$0.0987304\pi$
$660$	−0.0206336	+	0.275336i	−0.000803162	+	0.0107174i
$661$	−18.3438	+	5.65830i	−0.713489	+	0.220082i	−0.630189	−	0.776442i	$-0.717022\pi$
$661$	−18.3438	+	5.65830i	−0.713489	+	0.220082i	−0.0833008	+	0.996524i	$0.526546\pi$
$662$	−18.6142	+	5.74171i	−0.723460	+	0.223158i
$663$	−0.778138	+	10.3835i	−0.0302204	+	0.403263i
$664$	5.73814	−	2.76334i	0.222683	−	0.107238i
$665$	−0.480739	−	0.156916i	−0.0186423	−	0.00608494i
$666$	−7.32450	−	3.52729i	−0.283819	−	0.136680i
$667$	−7.34403	+	12.7202i	−0.284362	+	0.492530i
$668$	10.8157	+	18.7334i	0.418474	+	0.724818i
$669$	0.407049	+	5.43169i	0.0157374	+	0.210001i
$670$	−0.194311	−	0.495098i	−0.00750691	−	0.0191273i
$671$	−7.93236	+	34.7540i	−0.306225	+	1.34166i
$672$	0.630708	−	2.56948i	0.0243301	−	0.0991197i
$673$	6.47922	+	28.3873i	0.249756	+	1.09425i	0.931809	+	0.362949i	$0.118230\pi$
$673$	6.47922	+	28.3873i	0.249756	+	1.09425i	−0.682053	+	0.731302i	$0.738913\pi$
$674$	9.31427	−	6.35036i	0.358772	−	0.244607i
$675$	3.66342	−	3.39916i	0.141005	−	0.130834i
$676$	−1.31153	−	0.197681i	−0.0504433	−	0.00760310i
$677$	−13.8972	−	12.8948i	−0.534114	−	0.495586i	0.366373	−	0.930468i	$-0.380599\pi$
$677$	−13.8972	−	12.8948i	−0.534114	−	0.495586i	−0.900487	+	0.434882i	$0.856790\pi$
$678$	9.34518	+	11.7185i	0.358900	+	0.450046i
$679$	−1.75633	−	29.9902i	−0.0674016	−	1.15092i
$680$	0.0858463	−	0.107648i	0.00329206	−	0.00412811i
$681$	−1.93093	+	0.291041i	−0.0739934	+	0.0111527i
$682$	24.3915	+	16.6298i	0.933999	+	0.636790i
$683$	7.73100	−	19.6983i	0.295819	−	0.753733i	−0.703265	−	0.710928i	$-0.748275\pi$
$683$	7.73100	−	19.6983i	0.295819	−	0.753733i	0.999083	−	0.0428054i	$-0.0136295\pi$
$684$	3.64929	+	1.12566i	0.139534	+	0.0430406i
$685$	−0.907913			−0.0346896
$686$	−2.28530	+	18.3787i	−0.0872531	+	0.701703i
$687$	−12.3653			−0.471766
$688$	−10.2797	−	3.17086i	−0.391909	−	0.120888i
$689$	0.254988	−	0.649700i	0.00971428	−	0.0247516i
$690$	0.0849254	+	0.0579011i	0.00323305	+	0.00220426i
$691$	37.3244	−	5.62575i	1.41989	−	0.214014i	0.606198	−	0.795314i	$-0.292694\pi$
$691$	37.3244	−	5.62575i	1.41989	−	0.214014i	0.813689	+	0.581300i	$0.197456\pi$
$692$	12.3931	−	15.5404i	0.471113	−	0.590758i
$693$	0.853319	+	14.5709i	0.0324149	+	0.553502i
$694$	−16.0161	−	20.0835i	−0.607962	−	0.762361i
$695$	−0.461331	−	0.428053i	−0.0174993	−	0.0162370i
$696$	−7.07219	−	1.06596i	−0.268071	−	0.0404051i
$697$	−8.58422	+	7.96500i	−0.325151	+	0.301696i
$698$	12.2794	−	8.37195i	0.464782	−	0.316883i
$699$	2.96782	+	13.0028i	0.112253	+	0.491813i
$700$	−3.15196	+	12.8409i	−0.119133	+	0.485342i
$701$	4.30625	−	18.8669i	0.162645	−	0.712594i	−0.826167	−	0.563426i	$-0.809483\pi$
$701$	4.30625	−	18.8669i	0.162645	−	0.712594i	0.988812	−	0.149169i	$-0.0476597\pi$
$702$	−1.38282	−	3.52337i	−0.0521912	−	0.132981i
$703$	2.32011	+	30.9597i	0.0875046	+	1.16767i
$704$	2.75836	+	4.77761i	0.103959	+	0.180063i
$705$	0.261729	−	0.453328i	0.00985728	−	0.0170733i
$706$	25.5417	+	12.3002i	0.961274	+	0.462925i
$707$	−17.9777	−	5.86802i	−0.676121	−	0.220690i
$708$	5.05537	−	2.43454i	0.189992	−	0.0914956i
$709$	1.53616	−	20.4986i	0.0576916	−	0.769840i	−0.891074	−	0.453859i	$-0.850047\pi$
$709$	1.53616	−	20.4986i	0.0576916	−	0.769840i	0.948765	−	0.315982i	$-0.102334\pi$
$710$	−0.536490	+	0.165485i	−0.0201341	+	0.00621055i
$711$	−3.46238	+	1.06800i	−0.129850	+	0.0400533i
$712$	0.815202	−	10.8781i	0.0305510	−	0.407675i
$713$	9.90137	−	4.76825i	0.370809	−	0.178572i
$714$	3.74153	−	6.24320i	0.140023	−	0.233646i
$715$	−0.941579	−	0.453441i	−0.0352131	−	0.0169577i
$716$	−1.94699	+	3.37228i	−0.0727624	+	0.126028i
$717$	2.91565	+	5.05005i	0.108887	+	0.188597i
$718$	0.915335	+	12.2143i	0.0341600	+	0.455834i
$719$	12.2207	+	31.1379i	0.455756	+	1.16125i	0.955478	+	0.295062i	$0.0953403\pi$
$719$	12.2207	+	31.1379i	0.455756	+	1.16125i	−0.499722	+	0.866186i	$0.666565\pi$
$720$	−0.0111370	+	0.0487946i	−0.000415053	+	0.00181847i
$721$	−0.234986	−	1.11287i	−0.00875133	−	0.0414455i
$722$	0.982554	+	4.30485i	0.0365669	+	0.160210i
$723$	2.28149	−	1.55549i	0.0848493	−	0.0578493i
$724$	12.7463	−	11.8268i	0.473713	−	0.439541i
$725$	35.3432	+	5.32713i	1.31261	+	0.197845i
$726$	−14.2462	−	13.2186i	−0.528727	−	0.490587i
$727$	−20.4325	−	25.6216i	−0.757801	−	0.950252i	0.241998	−	0.970277i	$-0.422197\pi$
$727$	−20.4325	−	25.6216i	−0.757801	−	0.950252i	−0.999799	+	0.0200242i	$0.993626\pi$
$728$	8.18106	+	5.77535i	0.303210	+	0.214049i
$729$	0.623490	−	0.781831i	0.0230922	−	0.0289567i
$730$	0.428834	−	0.0646364i	0.0158719	−	0.00239230i
$731$	−24.4520	−	16.6711i	−0.904390	−	0.616603i
$732$	−2.36075	+	6.01509i	−0.0872558	+	0.222324i
$733$	−29.6732	−	9.15299i	−1.09601	−	0.338073i	−0.306534	−	0.951860i	$-0.599169\pi$
$733$	−29.6732	−	9.15299i	−1.09601	−	0.338073i	−0.789472	+	0.613786i	$0.789646\pi$
$734$	12.0965			0.446490
$735$	0.0375571	−	0.348327i	0.00138532	−	0.0128482i
$736$	2.05368			0.0756996
$737$	56.0203	+	17.2800i	2.06353	+	0.636516i
$738$	1.55515	−	3.96245i	0.0572458	−	0.145860i
$739$	3.68945	+	2.51542i	0.135718	+	0.0925313i	0.629276	−	0.777182i	$-0.283351\pi$
$739$	3.68945	+	2.51542i	0.135718	+	0.0925313i	−0.493558	+	0.869713i	$0.664304\pi$
$740$	−0.402336	+	0.0606424i	−0.0147902	+	0.00222926i
$741$	−9.01243	+	11.3012i	−0.331080	+	0.415161i
$742$	−0.362996	+	0.325961i	−0.0133260	+	0.0119664i
$743$	9.33134	+	11.7011i	0.342334	+	0.429273i	0.922959	−	0.384898i	$-0.125763\pi$
$743$	9.33134	+	11.7011i	0.342334	+	0.429273i	−0.580626	+	0.814171i	$0.697192\pi$
$744$	3.92272	+	3.63975i	0.143814	+	0.133440i
$745$	−0.0851534	−	0.0128348i	−0.00311978	−	0.000470231i
$746$	8.74385	−	8.11311i	0.320135	−	0.297042i
$747$	−5.26219	+	3.58770i	−0.192533	+	0.131267i
$748$	3.37710	+	14.7961i	0.123479	+	0.540998i
$749$	−3.06196	+	3.71372i	−0.111882	+	0.135696i
$750$	0.111343	−	0.487824i	0.00406566	−	0.0178128i
$751$	19.3592	+	49.3264i	0.706427	+	1.79995i	0.591068	+	0.806622i	$0.298707\pi$
$751$	19.3592	+	49.3264i	0.706427	+	1.79995i	0.115359	+	0.993324i	$0.463198\pi$
$752$	−0.781589	−	10.4296i	−0.0285016	−	0.380328i
$753$	−8.77258	−	15.1945i	−0.319690	−	0.553720i
$754$	13.5354	−	23.4439i	0.492928	−	0.853777i
$755$	0.702853	+	0.338476i	0.0255794	+	0.0123184i
$756$	−0.240703	+	2.63478i	−0.00875429	+	0.0958260i
$757$	36.1487	−	17.4083i	1.31385	−	0.632715i	0.359984	−	0.932958i	$-0.382782\pi$
$757$	36.1487	−	17.4083i	1.31385	−	0.632715i	0.953863	+	0.300243i	$0.0970678\pi$
$758$	1.39624	−	18.6315i	0.0507137	−	0.676728i
$759$	−10.8262	+	3.33945i	−0.392967	+	0.121214i
$760$	0.182645	−	0.0563385i	0.00662523	−	0.00204361i
$761$	2.46112	−	32.8414i	0.0892155	−	1.19050i	−0.755451	−	0.655205i	$-0.772582\pi$
$761$	2.46112	−	32.8414i	0.0892155	−	1.19050i	0.844666	−	0.535293i	$-0.179799\pi$
$762$	8.45163	−	4.07009i	0.306170	−	0.147444i
$763$	1.80064	+	1.72623i	0.0651877	+	0.0624936i
$764$	8.28083	+	3.98784i	0.299590	+	0.144275i
$765$	−0.0688434	+	0.119240i	−0.00248904	+	0.00431114i
$766$	−5.87960	−	10.1838i	−0.212439	−	0.367955i
$767$	1.58711	+	21.1785i	0.0573071	+	0.764711i
$768$	0.365341	+	0.930874i	0.0131831	+	0.0335900i
$769$	−4.18685	+	18.3438i	−0.150982	+	0.661494i	0.841619	+	0.540072i	$0.181603\pi$
$769$	−4.18685	+	18.3438i	−0.150982	+	0.661494i	−0.992601	+	0.121423i	$0.961254\pi$
$770$	0.446096	+	0.578488i	0.0160762	+	0.0208473i
$771$	4.62103	+	20.2461i	0.166422	+	0.729144i
$772$	0.182367	−	0.124336i	0.00656355	−	0.00447495i
$773$	−27.1277	+	25.1708i	−0.975714	+	0.905331i	−0.995527	−	0.0944730i	$-0.969883\pi$
$773$	−27.1277	+	25.1708i	−0.975714	+	0.905331i	0.0198129	+	0.999804i	$0.493693\pi$
$774$	10.6375	+	1.60334i	0.382355	+	0.0576308i
$775$	−19.6038	−	18.1896i	−0.704188	−	0.653391i
$776$	7.07952	+	8.87743i	0.254140	+	0.318681i
$777$	−20.6539	+	6.00393i	−0.740954	+	0.215390i
$778$	−6.40291	+	8.02899i	−0.229555	+	0.287853i
$779$	−16.0746	+	2.42286i	−0.575932	+	0.0868078i
$780$	−0.156521	−	0.106714i	−0.00560435	−	0.00382098i
$781$	22.6088	−	57.6063i	0.809006	−	2.06131i
$782$	5.39871	+	1.66528i	0.193057	+	0.0595503i
$783$	7.15207			0.255594
$784$	−3.30051	−	6.17306i	−0.117875	−	0.220466i
$785$	1.03584			0.0369706
$786$	−9.32825	−	2.87738i	−0.332728	−	0.102633i
$787$	11.1192	−	28.3313i	0.396357	−	1.00990i	−0.583839	−	0.811869i	$-0.698450\pi$
$787$	11.1192	−	28.3313i	0.396357	−	1.00990i	0.980196	−	0.198031i	$-0.0634546\pi$
$788$	−12.6843	−	8.64799i	−0.451858	−	0.308072i
$789$	−5.05120	+	0.761346i	−0.179827	+	0.0271046i
$790$	−0.113068	+	0.141783i	−0.00402278	+	0.00504441i
$791$	39.1114	+	6.54889i	1.39064	+	0.232852i
$792$	−3.43961	−	4.31314i	−0.122221	−	0.153261i
$793$	−17.9289	−	16.6356i	−0.636674	−	0.590747i
$794$	2.12023	+	0.319573i	0.0752442	+	0.0113412i
$795$	0.00676532	−	0.00627730i	0.000239941	−	0.000222633i
$796$	5.22071	−	3.55942i	0.185043	−	0.126160i
$797$	−6.00836	−	26.3243i	−0.212827	−	0.932456i	−0.962635	−	0.270801i	$-0.912711\pi$
$797$	−6.00836	−	26.3243i	−0.212827	−	0.932456i	0.749808	−	0.661655i	$-0.230146\pi$
$798$	9.17366	−	4.23498i	0.324744	−	0.149916i
$799$	6.40246	−	28.0510i	0.226503	−	0.992373i
$800$	−1.82579	−	4.65204i	−0.0645514	−	0.164474i
$801$	0.815202	+	10.8781i	0.0288037	+	0.384359i
$802$	−1.20888	−	2.09385i	−0.0426872	−	0.0739363i
$803$	−23.9011	+	41.3980i	−0.843453	+	1.46090i
$804$	9.57438	+	4.61078i	0.337662	+	0.162610i
$805$	0.269532	−	0.0361420i	0.00949977	−	0.00127384i
$806$	−18.2486	+	8.78807i	−0.642780	+	0.309547i
$807$	−1.10118	+	14.6943i	−0.0387635	+	0.517262i
$808$	6.83018	−	2.10683i	0.240285	−	0.0741181i
$809$	12.6818	−	3.91182i	0.445869	−	0.137532i	−0.0636869	−	0.997970i	$-0.520286\pi$
$809$	12.6818	−	3.91182i	0.445869	−	0.137532i	0.509556	+	0.860438i	$0.329810\pi$
$810$	0.00374020	−	0.0499095i	0.000131417	−	0.00175364i
$811$	21.2313	−	10.2245i	0.745532	−	0.359029i	−0.0222399	−	0.999753i	$-0.507080\pi$
$811$	21.2313	−	10.2245i	0.745532	−	0.359029i	0.767772	+	0.640723i	$0.221365\pi$
$812$	−15.8063	+	10.4032i	−0.554692	+	0.365080i
$813$	−6.26505	−	3.01709i	−0.219725	−	0.105814i
$814$	22.4243	−	38.8400i	0.785971	−	1.36134i
$815$	0.506871	+	0.877926i	0.0177549	+	0.0307524i
$816$	0.205584	+	2.74332i	0.00719687	+	0.0960356i
$817$	−15.0093	−	38.2430i	−0.525107	−	1.33795i
$818$	0.0430447	−	0.188591i	0.00150502	−	0.00659394i
$819$	−8.95046	−	4.49152i	−0.312754	−	0.156946i
$820$	−0.0474071	−	0.207704i	−0.00165553	−	0.00725333i
$821$	−4.95071	+	3.37534i	−0.172781	+	0.117800i	−0.646623	−	0.762810i	$-0.723819\pi$
$821$	−4.95071	+	3.37534i	−0.172781	+	0.117800i	0.473842	+	0.880610i	$0.342867\pi$
$822$	13.2978	−	12.3386i	0.463814	−	0.430356i
$823$	−8.80782	−	1.32757i	−0.307021	−	0.0462760i	−0.00627544	−	0.999980i	$-0.501998\pi$
$823$	−8.80782	−	1.32757i	−0.307021	−	0.0462760i	−0.300746	+	0.953704i	$0.597236\pi$
$824$	0.315139	+	0.292406i	0.0109784	+	0.0101865i
$825$	17.1895	+	21.5549i	0.598460	+	0.750445i
$826$	5.64821	−	13.7289i	0.196526	−	0.477691i
$827$	−19.5191	+	24.4761i	−0.678744	+	0.851119i	−0.995238	−	0.0974761i	$-0.968923\pi$
$827$	−19.5191	+	24.4761i	−0.678744	+	0.851119i	0.316493	+	0.948595i	$0.397494\pi$
$828$	−2.03074	+	0.306085i	−0.0705732	+	0.0106372i
$829$	25.8041	+	17.5930i	0.896215	+	0.611029i	0.921384	−	0.388654i	$-0.127060\pi$
$829$	25.8041	+	17.5930i	0.896215	+	0.611029i	−0.0251689	+	0.999683i	$0.508012\pi$
$830$	−0.116455	+	0.296723i	−0.00404222	+	0.0102994i
$831$	12.3975	+	3.82411i	0.430063	+	0.132657i
$832$	−3.78502			−0.131222
$833$	−3.67077	−	18.9040i	−0.127185	−	0.654986i
$834$	12.5742			0.435408
$835$	−1.03455	−	0.319115i	−0.0358019	−	0.0110434i
$836$	−7.69704	+	19.6117i	−0.266208	+	0.678286i
$837$	−4.42138	−	3.01445i	−0.152825	−	0.104195i
$838$	−17.6627	+	2.66223i	−0.610148	+	0.0919650i
$839$	25.9315	−	32.5171i	0.895256	−	1.12262i	−0.0966093	−	0.995322i	$-0.530800\pi$
$839$	25.9315	−	32.5171i	0.895256	−	1.12262i	0.991865	−	0.127293i	$-0.0406288\pi$
$840$	0.0643308	+	0.115742i	0.00221962	+	0.00399347i
$841$	13.8116	+	17.3192i	0.476263	+	0.597215i
$842$	−5.96740	−	5.53694i	−0.205650	−	0.190816i
$843$	14.8538	+	2.23885i	0.511592	+	0.0771100i
$844$	19.0440	−	17.6702i	0.655520	−	0.608234i
$845$	0.0548478	−	0.0373946i	0.00188682	−	0.00128641i
$846$	2.32731	+	10.1966i	0.0800144	+	0.350566i
$847$	−51.4110	−	0.838246i	−1.76650	−	0.0288025i
$848$	0.0410322	−	0.179774i	0.00140905	−	0.00617346i
$849$	8.69461	+	22.1535i	0.298398	+	0.760306i
$850$	−1.02740	−	13.7098i	−0.0352397	−	0.470241i
$851$	−8.34778	−	14.4588i	−0.286158	−	0.495640i
$852$	5.60878	−	9.71470i	0.192154	−	0.332820i
$853$	5.34705	+	2.57500i	0.183080	+	0.0881665i	0.523178	−	0.852223i	$-0.324746\pi$
$853$	5.34705	+	2.57500i	0.183080	+	0.0881665i	−0.340099	+	0.940390i	$0.610460\pi$
$854$	5.98568	+	16.0141i	0.204826	+	0.547993i
$855$	−0.172208	+	0.0829311i	−0.00588940	+	0.00283618i
$856$	0.135952	−	1.81415i	0.00464673	−	0.0620063i
$857$	−9.92888	+	3.06265i	−0.339164	+	0.104618i	−0.459659	−	0.888096i	$-0.652028\pi$
$857$	−9.92888	+	3.06265i	−0.339164	+	0.104618i	0.120494	+	0.992714i	$0.461552\pi$
$858$	19.9532	−	6.15474i	0.681190	−	0.210119i
$859$	−0.908327	+	12.1208i	−0.0309917	+	0.413556i	0.960034	+	0.279884i	$0.0902959\pi$
$859$	−0.908327	+	12.1208i	−0.0309917	+	0.413556i	−0.991026	+	0.133672i	$0.957323\pi$
$860$	0.485093	−	0.233608i	0.0165415	−	0.00796598i
$861$	−3.94307	−	10.5493i	−0.134380	−	0.359521i
$862$	4.15520	+	2.00104i	0.141527	+	0.0681557i
$863$	5.78564	−	10.0210i	0.196946	−	0.341120i	−0.750591	−	0.660767i	$-0.770231\pi$
$863$	5.78564	−	10.0210i	0.196946	−	0.341120i	0.947537	+	0.319647i	$0.103564\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	0.0743436	+	0.992047i	0.00252776	+	0.0337306i
$866$	12.7375	+	32.4546i	0.432838	+	1.10285i
$867$	2.09880	−	9.19543i	0.0712789	−	0.312293i
$868$	14.1561	+	0.230813i	0.480490	+	0.00783429i
$869$	−4.44798	−	19.4879i	−0.150887	−	0.661081i
$870$	0.295758	−	0.201644i	0.0100271	−	0.00683639i
$871$	−29.4851	+	27.3582i	−0.999066	+	0.926998i
$872$	−0.932275	−	0.140518i	−0.0315708	−	0.00475854i
$873$	−8.32356	−	7.72313i	−0.281710	−	0.261388i
$874$	4.88998	+	6.13184i	0.165406	+	0.207413i
$875$	−0.643147	−	1.15713i	−0.0217423	−	0.0391181i
$876$	−5.40254	+	6.77457i	−0.182535	+	0.228891i
$877$	−29.1315	+	4.39086i	−0.983699	+	0.148269i	−0.621147	−	0.783694i	$-0.713333\pi$
$877$	−29.1315	+	4.39086i	−0.983699	+	0.148269i	−0.362553	+	0.931963i	$0.618095\pi$
$878$	1.02295	+	0.697433i	0.0345227	+	0.0235372i
$879$	−11.2938	+	28.7762i	−0.380932	+	0.970599i
$880$	−0.263842	−	0.0813844i	−0.00889410	−	0.00274347i
$881$	−17.3268			−0.583756			−0.291878	−	0.956456i	$-0.594280\pi$
$881$	−17.3268			−0.583756			−0.291878	+	0.956456i	$0.594280\pi$
$882$	4.18369	+	5.61220i	0.140872	+	0.188972i
$883$	23.7762			0.800134			0.400067	−	0.916486i	$-0.368987\pi$
$883$	23.7762			0.800134			0.400067	+	0.916486i	$0.368987\pi$
$884$	−9.95004	−	3.06918i	−0.334656	−	0.103228i
$885$	−0.102598	+	0.261417i	−0.00344881	+	0.00878742i
$886$	−6.95966	−	4.74502i	−0.233814	−	0.159412i
$887$	0.00797034	−	0.00120134i	0.000267618	−	4.03369e-5i	−0.148908	−	0.988851i	$-0.547576\pi$
$887$	0.00797034	−	0.00120134i	0.000267618	−	4.03369e-5i	0.149176	+	0.988811i	$0.452338\pi$
$888$	5.06871	−	6.35596i	0.170095	−	0.213292i
$889$	9.44274	−	22.9522i	0.316699	−	0.769793i
$890$	0.340407	+	0.426857i	0.0114105	+	0.0143083i
$891$	4.04404	+	3.75232i	0.135480	+	0.125707i
$892$	−5.38609	−	0.811822i	−0.180339	−	0.0271818i
$893$	29.2794	−	27.1673i	0.979798	−	0.909120i
$894$	1.42163	−	0.969251i	0.0475464	−	0.0324166i
$895$	−0.0433674	−	0.190005i	−0.00144961	−	0.00635117i
$896$	2.36471	+	1.18666i	0.0789994	+	0.0396434i
$897$	1.72970	−	7.57832i	0.0577531	−	0.253033i
$898$	−1.06379	−	2.71049i	−0.0354991	−	0.0904503i
$899$	−2.86009	−	38.1653i	−0.0953894	−	1.27288i
$900$	2.49875	+	4.32796i	0.0832916	+	0.144265i
$901$	0.253640	−	0.439317i	0.00844997	−	0.0146358i
$902$	21.1574	+	10.1889i	0.704466	+	0.339253i
$903$	23.7746	−	15.6477i	0.791170	−	0.520722i
$904$	−13.5042	+	6.50327i	−0.449142	+	0.216296i
$905$	−0.0650346	+	0.867826i	−0.00216182	+	0.0288475i
$906$	−14.8943	+	4.59427i	−0.494829	+	0.152635i
$907$	29.0196	−	8.95136i	0.963580	−	0.297225i	0.227242	−	0.973838i	$-0.427029\pi$
$907$	29.0196	−	8.95136i	0.963580	−	0.297225i	0.736338	+	0.676613i	$0.236553\pi$
$908$	0.145929	−	1.94728i	0.00484281	−	0.0646228i
$909$	−6.43989	+	3.10129i	−0.213598	+	0.102863i
$910$	−0.496759	+	0.0666112i	−0.0164674	+	0.00220814i
$911$	45.6533	+	21.9855i	1.51256	+	0.728411i	0.992097	−	0.125473i	$-0.0400447\pi$
$911$	45.6533	+	21.9855i	1.51256	+	0.728411i	0.520464	+	0.853884i	$0.325759\pi$
$912$	−1.90948	+	3.30731i	−0.0632292	+	0.109516i
$913$	−17.5676	−	30.4279i	−0.581401	−	1.00702i
$914$	2.25655	+	30.1115i	0.0746399	+	0.996001i
$915$	−0.118154	−	0.301052i	−0.00390605	−	0.00995246i
$916$	2.75154	−	12.0553i	0.0909135	−	0.398318i
$917$	−23.4495	+	10.8254i	−0.774372	+	0.357485i
$918$	−0.612159	−	2.68204i	−0.0202043	−	0.0885206i
$919$	−6.23055	+	4.24792i	−0.205527	+	0.140126i	−0.661710	−	0.749760i	$-0.730169\pi$
$919$	−6.23055	+	4.24792i	−0.205527	+	0.140126i	0.456183	+	0.889886i	$0.349216\pi$
$920$	−0.0753471	+	0.0699119i	−0.00248412	+	0.00230493i
$921$	12.4152	+	1.87129i	0.409095	+	0.0616612i
$922$	17.2579	+	16.0129i	0.568357	+	0.527358i
$923$	26.4725	+	33.1955i	0.871354	+	1.09264i
$924$	−14.3954	−	2.41040i	−0.473575	−	0.0792964i
$925$	−25.3309	+	31.7639i	−0.832873	+	1.04439i
$926$	18.1879	−	2.74139i	0.597692	−	0.0900876i
$927$	−0.355200	−	0.242171i	−0.0116663	−	0.00795395i
$928$	2.61295	−	6.65768i	0.0857741	−	0.218549i
$929$	15.8896	+	4.90130i	0.521321	+	0.160806i	0.544238	−	0.838931i	$-0.316819\pi$
$929$	15.8896	+	4.90130i	0.521321	+	0.160806i	−0.0229163	+	0.999737i	$0.507295\pi$
$930$	−0.267825			−0.00878234
$931$	10.5726	−	24.5531i	0.346504	−	0.804697i
$932$	−13.3372			−0.436876
$933$	−15.6949	−	4.84123i	−0.513827	−	0.158495i
$934$	−6.08002	+	15.4916i	−0.198944	+	0.506902i
$935$	−0.627593	−	0.427886i	−0.0205245	−	0.0139934i
$936$	3.74274	−	0.564127i	0.122335	−	0.0184391i
$937$	−35.9014	+	45.0190i	−1.17285	+	1.47071i	−0.320874	+	0.947122i	$0.603977\pi$
$937$	−35.9014	+	45.0190i	−1.17285	+	1.47071i	−0.851974	+	0.523583i	$0.824595\pi$
$938$	26.9982	−	7.84817i	0.881522	−	0.256252i
$939$	17.9835	+	22.5506i	0.586869	+	0.735910i
$940$	0.383722	+	0.356042i	0.0125156	+	0.0116128i
$941$	−53.7864	−	8.10699i	−1.75339	−	0.264280i	−0.807754	−	0.589520i	$-0.799317\pi$
$941$	−53.7864	−	8.10699i	−1.75339	−	0.264280i	−0.945632	+	0.325240i	$0.894555\pi$
$942$	−15.1715	+	14.0771i	−0.494313	+	0.458655i
$943$	7.22290	−	4.92449i	0.235210	−	0.160363i
$944$	1.24857	+	5.47036i	0.0406376	+	0.178045i
$945$	−0.0808627	−	0.104861i	−0.00263046	−	0.00341113i
$946$	−13.2059	+	57.8587i	−0.429360	+	1.88115i
$947$	−13.3847	−	34.1037i	−0.434945	−	1.10822i	−0.965461	−	0.260547i	$-0.916097\pi$
$947$	−13.3847	−	34.1037i	−0.434945	−	1.10822i	0.530516	−	0.847675i	$-0.321998\pi$
$948$	−0.270774	−	3.61323i	−0.00879433	−	0.117352i
$949$	−16.3986	−	28.4032i	−0.532320	−	0.922005i
$950$	9.54261	−	16.5283i	0.309603	−	0.536249i
$951$	1.94829	+	0.938246i	0.0631776	+	0.0304247i
$952$	5.25411	+	5.03697i	0.170287	+	0.163249i
$953$	−48.4609	+	23.3375i	−1.56980	+	0.755977i	−0.997927	−	0.0643638i	$-0.979498\pi$
$953$	−48.4609	+	23.3375i	−1.56980	+	0.755977i	−0.571875	+	0.820341i	$0.693784\pi$
$954$	−0.0137800	+	0.183882i	−0.000446145	+	0.00595339i
$955$	−0.439569	+	0.135589i	−0.0142241	+	0.00438756i
$956$	−5.57222	+	1.71880i	−0.180219	+	0.0555901i
$957$	−2.94855	+	39.3456i	−0.0953129	+	1.27186i
$958$	31.6456	−	15.2397i	1.02242	−	0.492373i
$959$	4.36643	−	47.7957i	0.140999	−	1.54341i
$960$	−0.0450930	−	0.0217156i	−0.00145537	−	0.000700869i
$961$	1.18224	−	2.04769i	0.0381367	−	0.0660546i
$962$	15.3853	+	26.6481i	0.496042	+	0.859170i
$963$	0.135952	+	1.81415i	0.00438098	+	0.0584601i
$964$	1.00881	+	2.57041i	0.0324917	+	0.0827874i
$965$	−0.00245817	+	0.0107699i	−7.91312e−5	+	0.000346697i
$966$	−3.45655	+	4.19231i	−0.111213	+	0.134885i
$967$	8.16749	+	35.7841i	0.262649	+	1.15074i	0.918366	+	0.395733i	$0.129509\pi$
$967$	8.16749	+	35.7841i	0.262649	+	1.15074i	−0.655717	+	0.755007i	$0.727633\pi$
$968$	16.0572	−	10.9476i	0.516099	−	0.351870i
$969$	−7.70146	+	7.14591i	−0.247406	+	0.229560i
$970$	−0.561947	−	0.0846999i	−0.0180430	−	0.00271955i
$971$	−12.3481	−	11.4574i	−0.396271	−	0.367685i	0.456721	−	0.889610i	$-0.349024\pi$
$971$	−12.3481	−	11.4574i	−0.396271	−	0.367685i	−0.852992	+	0.521925i	$0.825214\pi$
$972$	0.623490	+	0.781831i	0.0199984	+	0.0250773i
$973$	24.7529	−	22.2275i	0.793541	−	0.712580i
$974$	20.9216	−	26.2349i	0.670373	−	0.840621i
$975$	−18.7043	+	2.81922i	−0.599018	+	0.0902874i
$976$	−5.33896	−	3.64004i	−0.170896	−	0.116515i
$977$	4.19116	−	10.6789i	0.134087	−	0.341648i	−0.848022	−	0.529961i	$-0.822207\pi$
$977$	4.19116	−	10.6789i	0.134087	−	0.341648i	0.982109	+	0.188313i	$0.0603019\pi$
$978$	−19.3549	−	5.97021i	−0.618903	−	0.190906i
$979$	−60.1797			−1.92335
$980$	0.331237	+	0.114126i	0.0105810	+	0.00364561i
$981$	0.942806			0.0301015
$982$	34.1346	+	10.5291i	1.08928	+	0.335998i
$983$	−9.63386	+	24.5467i	−0.307272	+	0.782917i	0.690927	+	0.722925i	$0.257203\pi$
$983$	−9.63386	+	24.5467i	−0.307272	+	0.782917i	−0.998199	+	0.0599921i	$0.980892\pi$
$984$	3.51705	+	2.39788i	0.112119	+	0.0764418i
$985$	0.759768	−	0.114517i	0.0242082	−	0.00364880i
$986$	12.2675	−	15.3829i	0.390675	−	0.489891i
$987$	22.6061	+	15.9585i	0.719559	+	0.507966i
$988$	−9.01243	−	11.3012i	−0.286724	−	0.359540i
$989$	16.1951	+	15.0268i	0.514974	+	0.477826i
$990$	0.273024	+	0.0411518i	0.00867729	+	0.00130789i
$991$	39.3055	−	36.4702i	1.24858	−	1.15851i	0.267783	−	0.963479i	$-0.413709\pi$
$991$	39.3055	−	36.4702i	1.24858	−	1.15851i	0.980797	−	0.195034i	$-0.0624816\pi$
$992$	−4.42138	+	3.01445i	−0.140379	+	0.0957088i
$993$	4.33462	+	18.9912i	0.137555	+	0.602668i
$994$	−6.13158	−	29.0386i	−0.194482	−	0.921048i
$995$	−0.0703710	+	0.308316i	−0.00223091	+	0.00977426i
$996$	−2.32680	−	5.92860i	−0.0737275	−	0.187855i
$997$	2.48205	+	33.1206i	0.0786072	+	1.04894i	0.887447	+	0.460910i	$0.152477\pi$
$997$	2.48205	+	33.1206i	0.0786072	+	1.04894i	−0.808839	+	0.588030i	$0.799904\pi$
$998$	−8.31435	−	14.4009i	−0.263186	−	0.455852i
$999$	−4.06479	+	7.04042i	−0.128604	+	0.222749i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.m.b.247.1	yes	24
3.2	odd	2		882.2.z.a.541.2		24
49.25	even	21	inner	294.2.m.b.25.1	✓	24
147.74	odd	42		882.2.z.a.613.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.m.b.25.1	✓	24	49.25	even	21	inner
294.2.m.b.247.1	yes	24	1.1	even	1	trivial
882.2.z.a.541.2		24	3.2	odd	2
882.2.z.a.613.2		24	147.74	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)

\(f(q)\)	\(=\)	\(q+(0.955573 + 0.294755i) q^{2} +(0.365341 - 0.930874i) q^{3} +(0.826239 + 0.563320i) q^{4} +(-0.0494904 + 0.00745948i) q^{5} +(0.623490 - 0.781831i) q^{6} +(-0.154679 - 2.64123i) q^{7} +(0.623490 + 0.781831i) q^{8} +(-0.733052 - 0.680173i) q^{9} +O(q^{10})\)	\(q+(0.955573 + 0.294755i) q^{2} +(0.365341 - 0.930874i) q^{3} +(0.826239 + 0.563320i) q^{4} +(-0.0494904 + 0.00745948i) q^{5} +(0.623490 - 0.781831i) q^{6} +(-0.154679 - 2.64123i) q^{7} +(0.623490 + 0.781831i) q^{8} +(-0.733052 - 0.680173i) q^{9} +(-0.0494904 - 0.00745948i) q^{10} +(4.04404 - 3.75232i) q^{11} +(0.826239 - 0.563320i) q^{12} +(0.842245 + 3.69012i) q^{13} +(0.630708 - 2.56948i) q^{14} +(-0.0111370 + 0.0487946i) q^{15} +(0.365341 + 0.930874i) q^{16} +(0.205584 + 2.74332i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-1.90948 + 3.30731i) q^{19} +(-0.0450930 - 0.0217156i) q^{20} +(-2.51516 - 0.820962i) q^{21} +(4.97039 - 2.39361i) q^{22} +(0.153472 - 2.04794i) q^{23} +(0.955573 - 0.294755i) q^{24} +(-4.77547 + 1.47304i) q^{25} +(-0.282855 + 3.77443i) q^{26} +(-0.900969 + 0.433884i) q^{27} +(1.36005 - 2.26942i) q^{28} +(-6.44379 - 3.10317i) q^{29} +(-0.0250247 + 0.0433441i) q^{30} +(2.67561 + 4.63429i) q^{31} +(0.0747301 + 0.997204i) q^{32} +(-2.01548 - 5.13536i) q^{33} +(-0.612159 + 2.68204i) q^{34} +(0.0273573 + 0.129562i) q^{35} +(-0.222521 - 0.974928i) q^{36} +(6.71698 - 4.57956i) q^{37} +(-2.79949 + 2.59755i) q^{38} +(3.74274 + 0.564127i) q^{39} +(-0.0366888 - 0.0340423i) q^{40} +(2.65401 + 3.32802i) q^{41} +(-2.16143 - 1.52584i) q^{42} +(-6.70726 + 8.41064i) q^{43} +(5.45510 - 0.822223i) q^{44} +(0.0413528 + 0.0281938i) q^{45} +(0.750293 - 1.91172i) q^{46} +(-9.99416 - 3.08279i) q^{47} +1.00000 q^{48} +(-6.95215 + 0.817084i) q^{49} -4.99750 q^{50} +(2.62880 + 0.810876i) q^{51} +(-1.38282 + 3.52337i) q^{52} +(-0.152356 - 0.103875i) q^{53} +(-0.988831 + 0.149042i) q^{54} +(-0.172151 + 0.215870i) q^{55} +(1.96855 - 1.76771i) q^{56} +(2.38108 + 2.98578i) q^{57} +(-5.24284 - 4.86464i) q^{58} +(5.54837 + 0.836282i) q^{59} +(-0.0366888 + 0.0340423i) q^{60} +(-5.33896 + 3.64004i) q^{61} +(1.19076 + 5.21705i) q^{62} +(-1.68310 + 2.04136i) q^{63} +(-0.222521 + 0.974928i) q^{64} +(-0.0692094 - 0.176343i) q^{65} +(-0.412264 - 5.50129i) q^{66} +(5.31338 + 9.20305i) q^{67} +(-1.37551 + 2.38245i) q^{68} +(-1.85030 - 0.891058i) q^{69} +(-0.0120471 + 0.131869i) q^{70} +(10.1067 - 4.86712i) q^{71} +(0.0747301 - 0.997204i) q^{72} +(-8.28003 + 2.55405i) q^{73} +(7.76841 - 2.39624i) q^{74} +(-0.373463 + 4.98352i) q^{75} +(-3.44076 + 1.65698i) q^{76} +(-10.5362 - 10.1008i) q^{77} +(3.41018 + 1.64226i) q^{78} +(1.81168 - 3.13792i) q^{79} +(-0.0250247 - 0.0433441i) q^{80} +(0.0747301 + 0.997204i) q^{81} +(1.55515 + 3.96245i) q^{82} +(1.41720 - 6.20917i) q^{83} +(-1.61566 - 2.09515i) q^{84} +(-0.0306382 - 0.134235i) q^{85} +(-8.88835 + 6.05998i) q^{86} +(-5.24284 + 4.86464i) q^{87} +(5.45510 + 0.822223i) q^{88} +(-7.99658 - 7.41975i) q^{89} +(0.0312053 + 0.0391302i) q^{90} +(9.61615 - 2.79534i) q^{91} +(1.28045 - 1.60563i) q^{92} +(5.29145 - 0.797558i) q^{93} +(-8.64148 - 5.89166i) q^{94} +(0.0698301 - 0.177924i) q^{95} +(0.955573 + 0.294755i) q^{96} +11.3547 q^{97} +(-6.88412 - 1.26840i) q^{98} -5.51671 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

Fields

Representations

Groups

Database

Properties

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