LMFDB - Embedded newform 547.2.j.a.11.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,2,Mod(11,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([10]))

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

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

chi := DirichletCharacter("547.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	547.j (of order $39$, degree $24$, 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:	$4.36781699056$
Analytic rank:	$0$
Dimension:	$1080$
Relative dimension:	$45$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			11.6
Character	$\chi$	$=$	547.11
Dual form			547.2.j.a.199.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.10961 - 0.898822i) q^{2} -0.232269 q^{3} +(2.25714 + 2.34993i) q^{4} +(2.70427 - 0.439486i) q^{5} +(0.489997 + 0.208768i) q^{6} +(0.511767 + 0.384568i) q^{7} +(-1.02322 - 2.69801i) q^{8} -2.94605 q^{9} +O(q^{10})$	\(q+(-2.10961 - 0.898822i) q^{2} -0.232269 q^{3} +(2.25714 + 2.34993i) q^{4} +(2.70427 - 0.439486i) q^{5} +(0.489997 + 0.208768i) q^{6} +(0.511767 + 0.384568i) q^{7} +(-1.02322 - 2.69801i) q^{8} -2.94605 q^{9} +(-6.09997 - 1.50351i) q^{10} +(-5.67785 + 0.458363i) q^{11} +(-0.524262 - 0.545815i) q^{12} +(0.948451 - 1.64276i) q^{13} +(-0.733972 - 1.27128i) q^{14} +(-0.628117 + 0.102079i) q^{15} +(-0.00403158 + 0.100043i) q^{16} +(-0.812477 - 1.71226i) q^{17} +(6.21503 + 2.64798i) q^{18} +(-0.170229 - 4.22420i) q^{19} +(7.13665 + 5.36285i) q^{20} +(-0.118867 - 0.0893231i) q^{21} +(12.3900 + 4.13640i) q^{22} +(0.364370 - 1.78480i) q^{23} +(0.237662 + 0.626664i) q^{24} +(2.37722 - 0.793633i) q^{25} +(-3.47742 + 2.61311i) q^{26} +1.38108 q^{27} +(0.251421 + 2.07064i) q^{28} +(1.07318 - 0.950757i) q^{29} +(1.41683 + 0.349218i) q^{30} +(6.81718 - 3.57793i) q^{31} +(-2.37558 + 5.00642i) q^{32} +(1.31879 - 0.106464i) q^{33} +(0.174996 + 4.34248i) q^{34} +(1.55297 + 0.815059i) q^{35} +(-6.64964 - 6.92300i) q^{36} +(-2.21864 - 10.8676i) q^{37} +(-3.43768 + 9.06442i) q^{38} +(-0.220296 + 0.381563i) q^{39} +(-3.95280 - 6.84644i) q^{40} +(2.97354 - 5.15033i) q^{41} +(0.170479 + 0.295278i) q^{42} +(-0.272552 + 0.940958i) q^{43} +(-13.8928 - 12.3079i) q^{44} +(-7.96690 + 1.29475i) q^{45} +(-2.37290 + 3.43774i) q^{46} +(-9.89763 - 3.30432i) q^{47} +(0.000936410 - 0.0232368i) q^{48} +(-1.83351 - 6.33001i) q^{49} +(-5.72835 - 0.462440i) q^{50} +(0.188713 + 0.397704i) q^{51} +(6.00116 - 1.47915i) q^{52} +(-0.347467 - 0.425570i) q^{53} +(-2.91355 - 1.24135i) q^{54} +(-15.1530 + 3.73487i) q^{55} +(0.513918 - 1.77425i) q^{56} +(0.0395390 + 0.981149i) q^{57} +(-3.11856 + 1.04113i) q^{58} +(-0.0209583 + 0.520074i) q^{59} +(-1.65762 - 1.24562i) q^{60} +(11.8715 + 5.05797i) q^{61} +(-17.5975 + 1.42062i) q^{62} +(-1.50769 - 1.13296i) q^{63} +(9.66132 - 8.55918i) q^{64} +(1.84289 - 4.85930i) q^{65} +(-2.87782 - 0.960758i) q^{66} +(-2.61233 + 9.01879i) q^{67} +(2.18981 - 5.77406i) q^{68} +(-0.0846318 + 0.414554i) q^{69} +(-2.54356 - 3.11530i) q^{70} +(-5.16803 + 3.26806i) q^{71} +(3.01446 + 7.94848i) q^{72} +(-1.30675 - 0.212368i) q^{73} +(-5.08758 + 24.9206i) q^{74} +(-0.552154 + 0.184336i) q^{75} +(9.54232 - 9.93461i) q^{76} +(-3.08201 - 1.94894i) q^{77} +(0.807695 - 0.606944i) q^{78} +(-2.72668 + 0.672066i) q^{79} +(0.0330649 + 0.272314i) q^{80} +8.51737 q^{81} +(-10.9023 + 8.19251i) q^{82} +(-4.40348 - 5.39328i) q^{83} +(-0.0583972 - 0.480944i) q^{84} +(-2.94967 - 4.27333i) q^{85} +(1.42073 - 1.74008i) q^{86} +(-0.249267 + 0.220831i) q^{87} +(7.04636 + 14.8499i) q^{88} +(-0.213094 + 1.75499i) q^{89} +(17.9708 + 4.42941i) q^{90} +(1.11714 - 0.475969i) q^{91} +(5.01659 - 3.17230i) q^{92} +(-1.58342 + 0.831042i) q^{93} +(17.9102 + 15.8670i) q^{94} +(-2.31682 - 11.3485i) q^{95} +(0.551773 - 1.16284i) q^{96} +(10.3583 + 0.836210i) q^{97} +(-1.82156 + 15.0019i) q^{98} +(16.7272 - 1.35036i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1080 q - 25 q^{2} - 74 q^{3} + 21 q^{4} - 27 q^{5} - 75 q^{6} - 28 q^{7} + 4 q^{8} + 1010 q^{9}+O(q^{10}) $ 1080 * q - 25 * q^2 - 74 * q^3 + 21 * q^4 - 27 * q^5 - 75 * q^6 - 28 * q^7 + 4 * q^8 + 1010 * q^9	\( 1080 q - 25 q^{2} - 74 q^{3} + 21 q^{4} - 27 q^{5} - 75 q^{6} - 28 q^{7} + 4 q^{8} + 1010 q^{9} - 16 q^{10} - 14 q^{11} - 69 q^{12} - 10 q^{13} - 15 q^{14} - 97 q^{15} + 39 q^{16} - 22 q^{17} - 145 q^{18} - 24 q^{19} - 51 q^{20} - 77 q^{21} - 19 q^{22} - 53 q^{23} - 45 q^{24} + 40 q^{25} - 68 q^{26} - 278 q^{27} - 50 q^{28} + 39 q^{29} + 14 q^{30} - 2 q^{31} - 45 q^{32} - 105 q^{33} - 98 q^{34} - 18 q^{35} - 172 q^{36} - 16 q^{37} - 37 q^{38} + 30 q^{39} - 33 q^{40} + 62 q^{41} + 170 q^{42} + 12 q^{43} - 22 q^{44} - 128 q^{45} + 79 q^{46} - 58 q^{47} - 27 q^{48} + 17 q^{49} - 40 q^{50} - 39 q^{51} + 97 q^{52} + 17 q^{53} - 278 q^{54} + 9 q^{55} + 47 q^{56} - 174 q^{57} - 134 q^{58} - 126 q^{59} - 414 q^{60} - 79 q^{61} + 15 q^{62} - 398 q^{63} - 308 q^{64} + 47 q^{65} - 142 q^{66} + 22 q^{67} + 7 q^{68} - 77 q^{69} + 396 q^{70} - 22 q^{71} - 172 q^{72} + 9 q^{73} - 43 q^{74} - 143 q^{75} + 46 q^{76} + 56 q^{77} - 33 q^{78} + 72 q^{79} + 131 q^{80} + 944 q^{81} + 74 q^{82} + 41 q^{83} - 582 q^{84} - 66 q^{85} + 20 q^{86} - 182 q^{87} - 459 q^{88} - 92 q^{89} - 265 q^{90} + 65 q^{91} + 86 q^{92} - 28 q^{93} - 17 q^{94} + 37 q^{95} - 70 q^{96} + 91 q^{97} + 139 q^{98} - 237 q^{99}+O(q^{100}) \) 1080 * q - 25 * q^2 - 74 * q^3 + 21 * q^4 - 27 * q^5 - 75 * q^6 - 28 * q^7 + 4 * q^8 + 1010 * q^9 - 16 * q^10 - 14 * q^11 - 69 * q^12 - 10 * q^13 - 15 * q^14 - 97 * q^15 + 39 * q^16 - 22 * q^17 - 145 * q^18 - 24 * q^19 - 51 * q^20 - 77 * q^21 - 19 * q^22 - 53 * q^23 - 45 * q^24 + 40 * q^25 - 68 * q^26 - 278 * q^27 - 50 * q^28 + 39 * q^29 + 14 * q^30 - 2 * q^31 - 45 * q^32 - 105 * q^33 - 98 * q^34 - 18 * q^35 - 172 * q^36 - 16 * q^37 - 37 * q^38 + 30 * q^39 - 33 * q^40 + 62 * q^41 + 170 * q^42 + 12 * q^43 - 22 * q^44 - 128 * q^45 + 79 * q^46 - 58 * q^47 - 27 * q^48 + 17 * q^49 - 40 * q^50 - 39 * q^51 + 97 * q^52 + 17 * q^53 - 278 * q^54 + 9 * q^55 + 47 * q^56 - 174 * q^57 - 134 * q^58 - 126 * q^59 - 414 * q^60 - 79 * q^61 + 15 * q^62 - 398 * q^63 - 308 * q^64 + 47 * q^65 - 142 * q^66 + 22 * q^67 + 7 * q^68 - 77 * q^69 + 396 * q^70 - 22 * q^71 - 172 * q^72 + 9 * q^73 - 43 * q^74 - 143 * q^75 + 46 * q^76 + 56 * q^77 - 33 * q^78 + 72 * q^79 + 131 * q^80 + 944 * q^81 + 74 * q^82 + 41 * q^83 - 582 * q^84 - 66 * q^85 + 20 * q^86 - 182 * q^87 - 459 * q^88 - 92 * q^89 - 265 * q^90 + 65 * q^91 + 86 * q^92 - 28 * q^93 - 17 * q^94 + 37 * q^95 - 70 * q^96 + 91 * q^97 + 139 * q^98 - 237 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/547\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{39}\right)$

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 $

$2$	−2.10961	−	0.898822i	−1.49172	−	0.635563i	−0.516399	−	0.856348i	$-0.672728\pi$
$2$	−2.10961	−	0.898822i	−1.49172	−	0.635563i	−0.975322	+	0.220785i	$0.929138\pi$
$3$	−0.232269			−0.134100			−0.0670502	−	0.997750i	$-0.521359\pi$
$3$	−0.232269			−0.134100			−0.0670502	+	0.997750i	$0.521359\pi$
$4$	2.25714	+	2.34993i	1.12857	+	1.17496i
$5$	2.70427	−	0.439486i	1.20938	−	0.196544i	0.477907	−	0.878410i	$-0.341395\pi$
$5$	2.70427	−	0.439486i	1.20938	−	0.196544i	0.731477	+	0.681866i	$0.238831\pi$
$6$	0.489997	+	0.208768i	0.200041	+	0.0852293i
$7$	0.511767	+	0.384568i	0.193430	+	0.145353i	0.693045	−	0.720895i	$-0.256269\pi$
$7$	0.511767	+	0.384568i	0.193430	+	0.145353i	−0.499615	+	0.866247i	$0.666525\pi$
$8$	−1.02322	−	2.69801i	−0.361763	−	0.953891i
$9$	−2.94605			−0.982017
$10$	−6.09997	−	1.50351i	−1.92898	−	0.475451i
$11$	−5.67785	+	0.458363i	−1.71194	+	0.138202i	−0.897198	−	0.441628i	$-0.854401\pi$
$11$	−5.67785	+	0.458363i	−1.71194	+	0.138202i	−0.814737	+	0.579830i	$0.803119\pi$
$12$	−0.524262	−	0.545815i	−0.151341	−	0.157563i
$13$	0.948451	−	1.64276i	0.263053	−	0.455621i	−0.703999	−	0.710201i	$-0.748604\pi$
$13$	0.948451	−	1.64276i	0.263053	−	0.455621i	0.967052	+	0.254580i	$0.0819373\pi$
$14$	−0.733972	−	1.27128i	−0.196162	−	0.339763i
$15$	−0.628117	+	0.102079i	−0.162179	+	0.0263567i
$16$	−0.00403158	+	0.100043i	−0.00100790	+	0.0250107i
$17$	−0.812477	−	1.71226i	−0.197055	−	0.415284i	0.780738	−	0.624859i	$-0.214843\pi$
$17$	−0.812477	−	1.71226i	−0.197055	−	0.415284i	−0.977793	+	0.209575i	$0.932792\pi$
$18$	6.21503	+	2.64798i	1.46490	+	0.624134i
$19$	−0.170229	−	4.22420i	−0.0390533	−	0.969097i	−0.893364	−	0.449334i	$-0.851661\pi$
$19$	−0.170229	−	4.22420i	−0.0390533	−	0.969097i	0.854310	−	0.519763i	$-0.173980\pi$
$20$	7.13665	+	5.36285i	1.59580	+	1.19917i
$21$	−0.118867	−	0.0893231i	−0.0259390	−	0.0194919i
$22$	12.3900	+	4.13640i	2.64157	+	0.881885i
$23$	0.364370	−	1.78480i	0.0759764	−	0.372157i	−0.923970	−	0.382464i	$-0.875076\pi$
$23$	0.364370	−	1.78480i	0.0759764	−	0.372157i	0.999947	+	0.0103068i	$0.00328081\pi$
$24$	0.237662	+	0.626664i	0.0485126	+	0.127917i
$25$	2.37722	−	0.793633i	0.475444	−	0.158727i
$26$	−3.47742	+	2.61311i	−0.681977	+	0.512473i
$27$	1.38108			0.265789
$28$	0.251421	+	2.07064i	0.0475140	+	0.391313i
$29$	1.07318	−	0.950757i	0.199285	−	0.176551i	−0.557578	−	0.830124i	$-0.688269\pi$
$29$	1.07318	−	0.950757i	0.199285	−	0.176551i	0.756863	+	0.653573i	$0.226731\pi$
$30$	1.41683	+	0.349218i	0.258677	+	0.0637582i
$31$	6.81718	−	3.57793i	1.22440	−	0.642615i	0.276449	−	0.961028i	$-0.410842\pi$
$31$	6.81718	−	3.57793i	1.22440	−	0.642615i	0.947952	+	0.318413i	$0.103150\pi$
$32$	−2.37558	+	5.00642i	−0.419947	+	0.885019i
$33$	1.31879	−	0.106464i	0.229571	−	0.0185329i
$34$	0.174996	+	4.34248i	0.0300115	+	0.744728i
$35$	1.55297	+	0.815059i	0.262499	+	0.137770i
$36$	−6.64964	−	6.92300i	−1.10827	−	1.15383i
$37$	−2.21864	−	10.8676i	−0.364742	−	1.78662i	−0.584842	−	0.811147i	$-0.698843\pi$
$37$	−2.21864	−	10.8676i	−0.364742	−	1.78662i	0.220100	−	0.975477i	$-0.429362\pi$
$38$	−3.43768	+	9.06442i	−0.557666	+	1.47044i
$39$	−0.220296	+	0.381563i	−0.0352755	+	0.0610990i
$40$	−3.95280	−	6.84644i	−0.624992	−	1.08252i
$41$	2.97354	−	5.15033i	0.464389	−	0.804346i	−0.534784	−	0.844989i	$-0.679607\pi$
$41$	2.97354	−	5.15033i	0.464389	−	0.804346i	0.999174	+	0.0406425i	$0.0129405\pi$
$42$	0.170479	+	0.295278i	0.0263054	+	0.0455624i
$43$	−0.272552	+	0.940958i	−0.0415638	+	0.143495i	−0.978617	−	0.205693i	$-0.934055\pi$
$43$	−0.272552	+	0.940958i	−0.0415638	+	0.143495i	0.937053	+	0.349188i	$0.113542\pi$
$44$	−13.8928	−	12.3079i	−2.09442	−	1.85549i
$45$	−7.96690	+	1.29475i	−1.18764	+	0.193010i
$46$	−2.37290	+	3.43774i	−0.349865	+	0.506867i
$47$	−9.89763	−	3.30432i	−1.44372	−	0.481984i	−0.516429	−	0.856330i	$-0.672739\pi$
$47$	−9.89763	−	3.30432i	−1.44372	−	0.481984i	−0.927289	+	0.374346i	$0.877867\pi$
$48$	0.000936410	−	0.0232368i	0.000135159	−	0.00335394i
$49$	−1.83351	−	6.33001i	−0.261930	−	0.904287i
$50$	−5.72835	−	0.462440i	−0.810111	−	0.0653989i
$51$	0.188713	+	0.397704i	0.0264251	+	0.0556898i
$52$	6.00116	−	1.47915i	0.832211	−	0.205122i
$53$	−0.347467	−	0.425570i	−0.0477283	−	0.0584565i	0.750189	−	0.661223i	$-0.229962\pi$
$53$	−0.347467	−	0.425570i	−0.0477283	−	0.0584565i	−0.797917	+	0.602767i	$0.794065\pi$
$54$	−2.91355	−	1.24135i	−0.396484	−	0.168926i
$55$	−15.1530	+	3.73487i	−2.04323	+	0.503610i
$56$	0.513918	−	1.77425i	0.0686751	−	0.237094i
$57$	0.0395390	+	0.981149i	0.00523706	+	0.129956i
$58$	−3.11856	+	1.04113i	−0.409487	+	0.136707i
$59$	−0.0209583	+	0.520074i	−0.00272854	+	0.0677079i	−0.999980	−	0.00638887i	$-0.997966\pi$
$59$	−0.0209583	+	0.520074i	−0.00272854	+	0.0677079i	0.997251	+	0.0740968i	$0.0236074\pi$
$60$	−1.65762	−	1.24562i	−0.213998	−	0.160809i
$61$	11.8715	+	5.05797i	1.51999	+	0.647606i	0.980877	−	0.194629i	$-0.0623503\pi$
$61$	11.8715	+	5.05797i	1.51999	+	0.647606i	0.539110	+	0.842235i	$0.318761\pi$
$62$	−17.5975	+	1.42062i	−2.23489	+	0.180419i
$63$	−1.50769	−	1.13296i	−0.189951	−	0.142739i
$64$	9.66132	−	8.55918i	1.20767	−	1.06990i
$65$	1.84289	−	4.85930i	0.228582	−	0.602722i
$66$	−2.87782	−	0.960758i	−0.354235	−	0.118261i
$67$	−2.61233	+	9.01879i	−0.319146	+	1.10182i	0.627251	+	0.778817i	$0.284180\pi$
$67$	−2.61233	+	9.01879i	−0.319146	+	1.10182i	−0.946398	+	0.323004i	$0.895307\pi$
$68$	2.18981	−	5.77406i	0.265554	−	0.700208i
$69$	−0.0846318	+	0.414554i	−0.0101885	+	0.0499064i
$70$	−2.54356	−	3.11530i	−0.304014	−	0.372349i
$71$	−5.16803	+	3.26806i	−0.613332	+	0.387848i	−0.804709	−	0.593669i	$-0.797679\pi$
$71$	−5.16803	+	3.26806i	−0.613332	+	0.387848i	0.191377	+	0.981517i	$0.438705\pi$
$72$	3.01446	+	7.94848i	0.355257	+	0.936737i
$73$	−1.30675	−	0.212368i	−0.152944	−	0.0248558i	0.0834571	−	0.996511i	$-0.473404\pi$
$73$	−1.30675	−	0.212368i	−0.152944	−	0.0248558i	−0.236401	+	0.971656i	$0.575968\pi$
$74$	−5.08758	+	24.9206i	−0.591419	+	2.89696i
$75$	−0.552154	+	0.184336i	−0.0637573	+	0.0212853i
$76$	9.54232	−	9.93461i	1.09458	−	1.13958i
$77$	−3.08201	−	1.94894i	−0.351227	−	0.222103i
$78$	0.807695	−	0.606944i	0.0914535	−	0.0687228i
$79$	−2.72668	+	0.672066i	−0.306775	+	0.0756133i	−0.389698	−	0.920943i	$-0.627421\pi$
$79$	−2.72668	+	0.672066i	−0.306775	+	0.0756133i	0.0829228	+	0.996556i	$0.473574\pi$
$80$	0.0330649	+	0.272314i	0.00369676	+	0.0304456i
$81$	8.51737			0.946375
$82$	−10.9023	+	8.19251i	−1.20395	+	0.904711i
$83$	−4.40348	−	5.39328i	−0.483345	−	0.591990i	0.474149	−	0.880445i	$-0.342756\pi$
$83$	−4.40348	−	5.39328i	−0.483345	−	0.591990i	−0.957493	+	0.288455i	$0.906858\pi$
$84$	−0.0583972	−	0.480944i	−0.00637166	−	0.0524753i
$85$	−2.94967	−	4.27333i	−0.319936	−	0.463508i
$86$	1.42073	−	1.74008i	0.153202	−	0.187638i
$87$	−0.249267	+	0.220831i	−0.0267242	+	0.0236756i
$88$	7.04636	+	14.8499i	0.751144	+	1.58300i
$89$	−0.213094	+	1.75499i	−0.0225880	+	0.186029i	−0.999636	−	0.0269921i	$-0.991407\pi$
$89$	−0.213094	+	1.75499i	−0.0225880	+	0.186029i	0.977048	+	0.213021i	$0.0683302\pi$
$90$	17.9708	+	4.42941i	1.89429	+	0.466901i
$91$	1.11714	−	0.475969i	0.117108	−	0.0498951i
$92$	5.01659	−	3.17230i	0.523015	−	0.330735i
$93$	−1.58342	+	0.831042i	−0.164193	+	0.0861750i
$94$	17.9102	+	15.8670i	1.84729	+	1.63656i
$95$	−2.31682	−	11.3485i	−0.237701	−	1.16434i
$96$	0.551773	−	1.16284i	0.0563151	−	0.118682i
$97$	10.3583	+	0.836210i	1.05173	+	0.0849042i	0.594221	−	0.804302i	$-0.297460\pi$
$97$	10.3583	+	0.836210i	1.05173	+	0.0849042i	0.457507	+	0.889206i	$0.348743\pi$
$98$	−1.82156	+	15.0019i	−0.184005	+	1.51542i
$99$	16.7272	−	1.35036i	1.68115	−	0.135716i
$100$	7.23069	+	3.79496i	0.723069	+	0.379496i
$101$	−6.90326	−	18.2024i	−0.686900	−	1.81121i	−0.576124	−	0.817362i	$-0.695436\pi$
$101$	−6.90326	−	18.2024i	−0.686900	−	1.81121i	−0.110776	−	0.993845i	$-0.535334\pi$
$102$	−0.0406461	−	1.00862i	−0.00402456	−	0.0998684i
$103$	−8.17352	+	11.8414i	−0.805361	+	1.16677i	0.177808	+	0.984065i	$0.443100\pi$
$103$	−8.17352	+	11.8414i	−0.805361	+	1.16677i	−0.983168	+	0.182701i	$0.941516\pi$
$104$	−5.40267	−	0.878019i	−0.529775	−	0.0860969i
$105$	−0.360705	−	0.189313i	−0.0352012	−	0.0184750i
$106$	0.350509	+	1.21010i	0.0340445	+	0.117535i
$107$	−3.08696	−	4.47223i	−0.298428	−	0.432347i	0.644872	−	0.764291i	$-0.276911\pi$
$107$	−3.08696	−	4.47223i	−0.298428	−	0.432347i	−0.943299	+	0.331944i	$0.892295\pi$
$108$	3.11729	+	3.24544i	0.299961	+	0.312293i
$109$	−1.42938	−	0.903887i	−0.136910	−	0.0865767i	0.464255	−	0.885702i	$-0.346322\pi$
$109$	−1.42938	−	0.903887i	−0.136910	−	0.0865767i	−0.601165	+	0.799125i	$0.705297\pi$
$110$	35.3239	+	5.74069i	3.36800	+	0.547353i
$111$	0.515321	+	2.52421i	0.0489121	+	0.239587i
$112$	−0.0405364	+	0.0496481i	−0.00383033	+	0.00469130i
$113$	1.95840	+	1.23841i	0.184230	+	0.116500i	0.623397	−	0.781905i	$-0.285752\pi$
$113$	1.95840	+	1.23841i	0.184230	+	0.116500i	−0.439167	+	0.898406i	$0.644726\pi$
$114$	0.798466	−	2.10538i	0.0747832	−	0.197187i
$115$	0.200958	−	4.98671i	0.0187394	−	0.465014i
$116$	4.65653	+	0.375914i	0.432348	+	0.0349027i
$117$	−2.79418	+	4.83967i	−0.258322	+	0.447428i
$118$	0.511668	−	1.07832i	0.0471029	−	0.0992672i
$119$	0.242681	−	1.18873i	0.0222465	−	0.108971i
$120$	0.918111	+	1.59022i	0.0838117	+	0.145166i
$121$	21.1703	−	3.44051i	1.92457	−	0.312774i
$122$	−20.4980	−	21.3407i	−1.85580	−	1.93210i
$123$	−0.690661	+	1.19626i	−0.0622748	+	0.107863i
$124$	23.7952	+	7.94400i	2.13687	+	0.713392i
$125$	−6.04977	+	3.17516i	−0.541108	+	0.283995i
$126$	2.16232	+	3.74524i	0.192635	+	0.333653i
$127$	−1.10277	−	3.80719i	−0.0978547	−	0.337834i	0.896621	−	0.442798i	$-0.146014\pi$
$127$	−1.10277	−	3.80719i	−0.0978547	−	0.337834i	−0.994476	+	0.104965i	$0.966527\pi$
$128$	−17.5623	+	5.86315i	−1.55230	+	0.518235i
$129$	0.0633053	−	0.218555i	0.00557372	−	0.0192427i
$130$	−8.25543	+	8.59482i	−0.724049	+	0.753815i
$131$	−1.62645	−	2.35633i	−0.142104	−	0.205873i	0.745469	−	0.666540i	$-0.232226\pi$
$131$	−1.62645	−	2.35633i	−0.142104	−	0.205873i	−0.887573	+	0.460667i	$0.847610\pi$
$132$	3.22686	+	2.85875i	0.280862	+	0.248822i
$133$	1.53737	−	2.22727i	0.133307	−	0.193129i
$134$	13.6173	−	16.6781i	1.17635	−	1.44077i
$135$	3.73481	−	0.606966i	0.321442	−	0.0522393i
$136$	−3.78835	+	3.94409i	−0.324848	+	0.338203i
$137$	−14.9629	+	15.5780i	−1.27836	+	1.33092i	−0.361157	+	0.932505i	$0.617618\pi$
$137$	−14.9629	+	15.5780i	−1.27836	+	1.33092i	−0.917207	+	0.398412i	$0.869561\pi$
$138$	0.551150	−	0.798479i	0.0469170	−	0.0679711i
$139$	3.65206	−	3.80220i	0.309764	−	0.322498i	−0.548063	−	0.836437i	$-0.684635\pi$
$139$	3.65206	−	3.80220i	0.309764	−	0.322498i	0.857827	+	0.513939i	$0.171814\pi$
$140$	1.58992	+	5.48905i	0.134373	+	0.463910i
$141$	2.29891	+	0.767490i	0.193603	+	0.0646343i
$142$	13.8399	−	2.24921i	1.16142	−	0.188749i
$143$	−4.63218	+	9.76210i	−0.387362	+	0.816348i
$144$	0.0118772	−	0.294731i	0.000989770	−	0.0245609i
$145$	2.48433	−	3.04275i	0.206312	−	0.252686i
$146$	2.56586	+	1.62255i	0.212352	+	0.134284i
$147$	0.425867	+	1.47026i	0.0351249	+	0.121265i
$148$	20.5303	−	29.7433i	1.68758	−	2.44489i
$149$	18.3438	+	9.62759i	1.50279	+	0.788723i	0.997252	−	0.0740841i	$-0.0236033\pi$
$149$	18.3438	+	9.62759i	1.50279	+	0.788723i	0.505534	+	0.862807i	$0.331296\pi$
$150$	1.33052	+	0.107410i	0.108636	+	0.00877003i
$151$	9.52337	+	8.43697i	0.775001	+	0.686591i	0.954845	−	0.297104i	$-0.0960209\pi$
$151$	9.52337	+	8.43697i	0.775001	+	0.686591i	−0.179844	+	0.983695i	$0.557559\pi$
$152$	−11.2227	+	4.78156i	−0.910285	+	0.387836i
$153$	2.39360	+	5.04440i	0.193511	+	0.407816i
$154$	4.75008	+	6.88169i	0.382773	+	0.554542i
$155$	16.8630	−	12.6717i	1.35447	−	1.01782i
$156$	−1.39388	+	0.343561i	−0.111600	+	0.0275069i
$157$	−8.79075	+	9.15214i	−0.701578	+	0.730420i	−0.972685	−	0.232129i	$-0.925431\pi$
$157$	−8.79075	+	9.15214i	−0.701578	+	0.730420i	0.271107	+	0.962549i	$0.412610\pi$
$158$	6.35630	+	1.03300i	0.505680	+	0.0821810i
$159$	0.0807058	+	0.0988466i	0.00640038	+	0.00783905i
$160$	−4.22394	+	14.5827i	−0.333932	+	1.15287i
$161$	0.872850	−	0.773277i	0.0687902	−	0.0609428i
$162$	−17.9684	−	7.65560i	−1.41173	−	0.601481i
$163$	1.73316	−	0.578613i	0.135751	−	0.0453205i	−0.247980	−	0.968765i	$-0.579767\pi$
$163$	1.73316	−	0.578613i	0.135751	−	0.0453205i	0.383732	+	0.923445i	$0.374639\pi$
$164$	18.8146	−	4.63738i	1.46917	−	0.362118i
$165$	3.51956	−	0.867494i	0.273997	−	0.0675343i
$166$	4.44203	+	15.3357i	0.344769	+	1.19028i
$167$	−2.74224	+	3.97282i	−0.212201	+	0.307426i	−0.914602	−	0.404355i	$-0.867496\pi$
$167$	−2.74224	+	3.97282i	−0.212201	+	0.307426i	0.702401	+	0.711781i	$0.252111\pi$
$168$	−0.119367	+	0.412103i	−0.00920937	+	0.0317944i
$169$	4.70088	+	8.14217i	0.361606	+	0.626321i
$170$	2.38169	+	11.6663i	0.182667	+	0.894764i
$171$	0.501504	+	12.4447i	0.0383510	+	0.951670i
$172$	−2.82637	+	1.48339i	−0.215509	+	0.113108i
$173$	−0.939164	−	7.73471i	−0.0714033	−	0.588059i	−0.983867	−	0.178902i	$-0.942746\pi$
$173$	−0.939164	−	7.73471i	−0.0714033	−	0.588059i	0.912464	−	0.409158i	$-0.134177\pi$
$174$	0.724344	−	0.241822i	0.0549124	−	0.0183324i
$175$	1.52179	+	0.508048i	0.115036	+	0.0384048i
$176$	−0.0229652	−	0.569875i	−0.00173106	−	0.0429559i
$177$	0.00486795	−	0.120797i	0.000365898	−	0.00907966i
$178$	2.02697	−	3.51081i	0.151928	−	0.263147i
$179$	20.3248	+	5.00961i	1.51915	+	0.374436i	0.908642	−	0.417577i	$-0.137121\pi$
$179$	20.3248	+	5.00961i	1.51915	+	0.374436i	0.610504	+	0.792013i	$0.290967\pi$
$180$	−21.0249	−	15.7992i	−1.56711	−	1.17760i
$181$	−10.3585	−	10.7843i	−0.769940	−	0.801592i	0.214609	−	0.976700i	$-0.431152\pi$
$181$	−10.3585	−	10.7843i	−0.769940	−	0.801592i	−0.984549	+	0.175108i	$0.943973\pi$
$182$	−2.78454			−0.206404
$183$	−2.75737	−	1.17481i	−0.203831	−	0.0868443i
$184$	−5.18825	+	0.843172i	−0.382483	+	0.0621595i
$185$	−10.7760	−	28.4139i	−0.792264	−	2.08903i
$186$	4.08736	−	0.329966i	0.299700	−	0.0241943i
$187$	5.39796	+	9.34954i	0.394738	+	0.683706i
$188$	−14.5754	−	30.7170i	−1.06302	−	2.24027i
$189$	0.706792	+	0.531120i	0.0514116	+	0.0386333i
$190$	−5.31272	+	26.0234i	−0.385425	+	1.88794i
$191$	−8.63629	+	6.48975i	−0.624900	+	0.469582i	−0.865410	−	0.501065i	$-0.832942\pi$
$191$	−8.63629	+	6.48975i	−0.624900	+	0.469582i	0.240510	+	0.970647i	$0.422685\pi$
$192$	−2.24402	+	1.98803i	−0.161948	+	0.143474i
$193$	6.78277	−	14.2944i	0.488235	−	1.02893i	−0.498545	−	0.866864i	$-0.666132\pi$
$193$	6.78277	−	14.2944i	0.488235	−	1.02893i	0.986779	−	0.162069i	$-0.0518167\pi$
$194$	−21.1004	−	11.0744i	−1.51492	−	0.795093i
$195$	−0.428046	+	1.12866i	−0.0306530	+	0.0808254i
$196$	10.7366	−	18.5963i	0.766898	−	1.32831i
$197$	−4.43680	−	3.93066i	−0.316109	−	0.280048i	0.490116	−	0.871657i	$-0.336954\pi$
$197$	−4.43680	−	3.93066i	−0.316109	−	0.280048i	−0.806225	+	0.591609i	$0.798493\pi$
$198$	−36.5017	−	12.1861i	−2.59406	−	0.866026i
$199$	−22.4520	−	1.81251i	−1.59158	−	0.128486i	−0.747336	−	0.664446i	$-0.768667\pi$
$199$	−22.4520	−	1.81251i	−1.59158	−	0.128486i	−0.844243	+	0.535961i	$0.819949\pi$
$200$	−4.57365	−	5.60171i	−0.323406	−	0.396100i
$201$	0.606762	−	2.09478i	0.0427977	−	0.147755i
$202$	−1.79751	+	44.6048i	−0.126473	+	3.13839i
$203$	0.914849	−	0.0738543i	0.0642098	−	0.00518355i
$204$	−0.508625	+	1.34113i	−0.0356109	+	0.0938982i
$205$	5.77775	−	15.2347i	0.403536	−	1.06404i
$206$	27.8863	−	17.6342i	1.94293	−	1.22863i
$207$	−1.07345	+	5.25812i	−0.0746101	+	0.365465i
$208$	0.160523	+	0.101508i	0.0111303	+	0.00703834i
$209$	2.90275	+	23.9063i	0.200788	+	1.65363i
$210$	0.590790	+	0.723587i	0.0407684	+	0.0499322i
$211$	−5.05026	+	6.18544i	−0.347674	+	0.425823i	−0.918606	−	0.395174i	$-0.870684\pi$
$211$	−5.05026	+	6.18544i	−0.347674	+	0.425823i	0.570932	+	0.820997i	$0.306582\pi$
$212$	0.215778	−	1.77709i	0.0148197	−	0.122051i
$213$	1.20037	−	0.759069i	0.0822481	−	0.0520106i
$214$	2.49255	+	12.2093i	0.170387	+	0.834611i
$215$	−0.323515	+	2.66438i	−0.0220635	+	0.181709i
$216$	−1.41315	−	3.72617i	−0.0961528	−	0.253534i
$217$	4.86476	+	0.790601i	0.330242	+	0.0536695i
$218$	2.20301	+	3.19161i	0.149207	+	0.216163i
$219$	0.303518	+	0.0493265i	0.0205099	+	0.00333318i
$220$	−42.9790	−	27.1782i	−2.89764	−	1.83236i
$221$	−3.58343	−	0.289285i	−0.241048	−	0.0194594i
$222$	1.18169	−	5.78828i	0.0793096	−	0.388484i
$223$	−0.681143	−	0.709145i	−0.0456127	−	0.0474879i	0.698005	−	0.716093i	$-0.254071\pi$
$223$	−0.681143	−	0.709145i	−0.0456127	−	0.0474879i	−0.743618	+	0.668605i	$0.766892\pi$
$224$	−3.14105	+	1.64855i	−0.209870	+	0.110148i
$225$	−7.00342	+	2.33808i	−0.466894	+	0.155872i
$226$	−3.01834	−	4.37282i	−0.200777	−	0.290876i
$227$	4.18056	−	5.12026i	0.277474	−	0.339843i	−0.617001	−	0.786962i	$-0.711653\pi$
$227$	4.18056	−	5.12026i	0.277474	−	0.339843i	0.894474	+	0.447119i	$0.147550\pi$
$228$	−2.21638	+	2.30750i	−0.146784	+	0.152818i
$229$	−1.02112	−	3.52531i	−0.0674774	−	0.232959i	0.919691	−	0.392644i	$-0.128439\pi$
$229$	−1.02112	−	3.52531i	−0.0674774	−	0.232959i	−0.987168	+	0.159685i	$0.948952\pi$
$230$	−4.90611	+	10.3394i	−0.323499	+	0.681760i
$231$	0.715854	+	0.452678i	0.0470997	+	0.0297841i
$232$	−3.66325	−	1.92262i	−0.240504	−	0.126226i
$233$	21.9522	−	9.35296i	1.43814	−	0.612733i	0.474574	−	0.880215i	$-0.342602\pi$
$233$	21.9522	−	9.35296i	1.43814	−	0.612733i	0.963563	+	0.267482i	$0.0861917\pi$
$234$	10.2446	−	7.69835i	0.669714	−	0.503257i
$235$	−28.2180	−	4.58588i	−1.84074	−	0.299150i
$236$	−1.26944	+	1.12463i	−0.0826336	+	0.0732070i
$237$	0.633322	−	0.156100i	0.0411387	−	0.0101398i
$238$	−1.58042	+	2.28963i	−0.102443	+	0.148415i
$239$	1.53720	+	7.52972i	0.0994335	+	0.487057i	0.998760	+	0.0497801i	$0.0158520\pi$
$239$	1.53720	+	7.52972i	0.0994335	+	0.487057i	−0.899327	+	0.437277i	$0.855943\pi$
$240$	−0.00767994	−	0.0632500i	−0.000495738	−	0.00408277i
$241$	−0.102516	−	2.54391i	−0.00660365	−	0.163868i	−0.999126	−	0.0418036i	$-0.986690\pi$
$241$	−0.102516	−	2.54391i	−0.00660365	−	0.163868i	0.992522	−	0.122064i	$-0.0389514\pi$
$242$	−47.7535	−	11.7702i	−3.06971	−	0.756617i
$243$	−6.12157			−0.392699
$244$	14.9097	+	39.3136i	0.954495	+	2.51680i
$245$	−7.74025	−	16.3122i	−0.494506	−	1.04215i
$246$	2.53225	−	1.90286i	0.161451	−	0.121322i
$247$	−7.10082	−	3.72680i	−0.451814	−	0.237130i
$248$	−16.6288	−	14.7318i	−1.05593	−	0.935471i
$249$	1.02279	+	1.25269i	0.0648167	+	0.0793861i
$250$	15.6166	−	1.26070i	0.987679	−	0.0797337i
$251$	−7.84259	+	4.95935i	−0.495020	+	0.313032i	−0.758545	−	0.651621i	$-0.774089\pi$
$251$	−7.84259	+	4.95935i	−0.495020	+	0.313032i	0.263525	+	0.964653i	$0.415115\pi$
$252$	−0.740698	−	6.10020i	−0.0466596	−	0.384276i
$253$	−1.25075	+	10.3008i	−0.0786340	+	0.647609i
$254$	−1.09558	+	9.02289i	−0.0687426	+	0.566147i
$255$	0.685116	+	0.992562i	0.0429036	+	0.0621566i
$256$	16.5885	+	1.33916i	1.03678	+	0.0836976i
$257$	−14.2680	+	7.48843i	−0.890014	+	0.467115i	−0.846776	−	0.531949i	$-0.821460\pi$
$257$	−14.2680	+	7.48843i	−0.890014	+	0.467115i	−0.0432379	+	0.999065i	$0.513767\pi$
$258$	−0.329992	+	0.404167i	−0.0205444	+	0.0251623i
$259$	3.04391	−	6.41490i	0.189139	−	0.398603i
$260$	15.5787	−	6.63745i	0.966147	−	0.411637i
$261$	−3.16165	+	2.80098i	−0.195701	+	0.173376i
$262$	1.31327	+	6.43283i	0.0811341	+	0.397421i
$263$	27.9117	+	6.87961i	1.72111	+	0.424215i	0.971380	−	0.237532i	$-0.0763384\pi$
$263$	27.9117	+	6.87961i	1.72111	+	0.424215i	0.749728	+	0.661747i	$0.230185\pi$
$264$	−1.63665	−	3.44917i	−0.100729	−	0.212281i
$265$	−1.12668	−	0.998147i	−0.0692111	−	0.0613157i
$266$	−5.24518	+	3.31685i	−0.321602	+	0.203369i
$267$	0.0494952	−	0.407629i	0.00302906	−	0.0249465i
$268$	−27.0899	+	14.2179i	−1.65478	+	0.868494i
$269$	−1.54037	+	0.656288i	−0.0939177	+	0.0400146i	−0.438415	−	0.898773i	$-0.644460\pi$
$269$	−1.54037	+	0.656288i	−0.0939177	+	0.0400146i	0.344497	+	0.938787i	$0.388050\pi$
$270$	−8.42456	−	2.07647i	−0.512703	−	0.126370i
$271$	13.8776	−	8.77569i	0.843007	−	0.533085i	−0.0417556	−	0.999128i	$-0.513295\pi$
$271$	13.8776	−	8.77569i	0.843007	−	0.533085i	0.884762	+	0.466043i	$0.154321\pi$
$272$	0.174575	−	0.0743792i	0.0105851	−	0.00450990i
$273$	−0.259477	+	0.110553i	−0.0157042	+	0.00669096i
$274$	45.5677	−	19.4146i	2.75284	−	1.17288i
$275$	−13.1337	+	5.59576i	−0.791994	+	0.337437i
$276$	−1.16520	+	0.736826i	−0.0701366	+	0.0443517i
$277$	−8.35827	−	2.06013i	−0.502200	−	0.123781i	−0.0199257	−	0.999801i	$-0.506343\pi$
$277$	−8.35827	−	2.06013i	−0.502200	−	0.123781i	−0.482274	+	0.876020i	$0.660189\pi$
$278$	−11.1219	+	4.73861i	−0.667049	+	0.284203i
$279$	−20.0838	+	10.5408i	−1.20238	+	0.631059i
$280$	0.610012	−	5.02390i	0.0364552	−	0.300235i
$281$	15.7153	−	9.93775i	0.937496	−	0.592837i	0.0240124	−	0.999712i	$-0.492356\pi$
$281$	15.7153	−	9.93775i	0.937496	−	0.592837i	0.913484	+	0.406875i	$0.133382\pi$
$282$	−4.15998	−	3.68542i	−0.247723	−	0.219463i
$283$	12.7244	+	26.8160i	0.756384	+	1.59405i	0.803606	+	0.595162i	$0.202912\pi$
$283$	12.7244	+	26.8160i	0.756384	+	1.59405i	−0.0472213	+	0.998884i	$0.515037\pi$
$284$	−19.3446	−	4.76803i	−1.14789	−	0.282930i
$285$	0.538125	+	2.63591i	0.0318758	+	0.156138i
$286$	18.5465	−	16.4308i	1.09668	−	0.971571i
$287$	3.50241	−	1.49224i	0.206741	−	0.0880840i
$288$	6.99857	−	14.7492i	0.412395	−	0.869104i
$289$	8.47986	−	10.3859i	0.498815	−	0.610938i
$290$	−7.97585	+	4.18605i	−0.468358	+	0.245813i
$291$	−2.40591	−	0.194225i	−0.141037	−	0.0113857i
$292$	−2.45047	−	3.55012i	−0.143403	−	0.207755i
$293$	−2.76008	+	22.7313i	−0.161246	+	1.32798i	0.657341	+	0.753594i	$0.271681\pi$
$293$	−2.76008	+	22.7313i	−0.161246	+	1.32798i	−0.818586	+	0.574384i	$0.805242\pi$
$294$	0.423091	−	3.48447i	0.0246752	−	0.203218i
$295$	0.171889	+	1.41563i	0.0100077	+	0.0824211i
$296$	−27.0508	+	17.1059i	−1.57229	+	0.994259i
$297$	−7.84158	+	0.633037i	−0.455014	+	0.0367326i
$298$	−30.0449	−	36.7983i	−1.74045	−	2.13167i
$299$	−2.58642	−	2.29137i	−0.149577	−	0.132513i
$300$	−1.67946	−	0.881451i	−0.0969639	−	0.0508906i
$301$	−0.501345	+	0.376736i	−0.0288971	+	0.0217147i
$302$	−12.5073	−	26.3585i	−0.719713	−	1.51676i
$303$	1.60341	+	4.22785i	0.0921137	+	0.242884i
$304$	0.423286			0.0242771
$305$	34.3265	+	8.46073i	1.96553	+	0.484460i
$306$	−0.515547	−	12.7932i	−0.0294718	−	0.731336i
$307$	1.29316	+	10.6501i	0.0738045	+	0.607834i	0.981945	+	0.189168i	$0.0605792\pi$
$307$	1.29316	+	10.6501i	0.0738045	+	0.607834i	−0.908140	+	0.418666i	$0.862498\pi$
$308$	−2.37663	−	11.6415i	−0.135421	−	0.663337i
$309$	1.89845	−	2.75039i	0.107999	−	0.156464i
$310$	−46.9640	+	11.5756i	−2.66738	+	0.657450i
$311$	24.8414	−	22.0075i	1.40862	−	1.24793i	0.479818	−	0.877368i	$-0.340703\pi$
$311$	24.8414	−	22.0075i	1.40862	−	1.24793i	0.928807	−	0.370565i	$-0.120836\pi$
$312$	1.25487	+	0.203937i	0.0710431	+	0.0115456i
$313$	13.6162	−	10.2319i	0.769632	−	0.578341i	−0.141750	−	0.989902i	$-0.545273\pi$
$313$	13.6162	−	10.2319i	0.769632	−	0.578341i	0.911382	+	0.411562i	$0.135017\pi$
$314$	26.7712	−	11.4061i	1.51079	−	0.643686i
$315$	−4.57511	−	2.40121i	−0.257779	−	0.135293i
$316$	−7.73379	−	4.89055i	−0.435060	−	0.275115i
$317$	3.74413	−	7.89058i	0.210291	−	0.443179i	−0.770709	−	0.637188i	$-0.780098\pi$
$317$	3.74413	−	7.89058i	0.210291	−	0.443179i	0.981000	+	0.194008i	$0.0621489\pi$
$318$	−0.0814124	−	0.281068i	−0.00456538	−	0.0157615i
$319$	−5.65757	+	5.89016i	−0.316763	+	0.329786i
$320$	22.3651	−	27.3923i	1.25025	−	1.53128i
$321$	0.717004	+	1.03876i	0.0400193	+	0.0579779i
$322$	−2.53641	+	0.846779i	−0.141349	+	0.0471892i
$323$	−7.09461	+	3.72354i	−0.394755	+	0.207183i
$324$	19.2249	+	20.0152i	1.06805	+	1.11196i
$325$	0.950925	−	4.65794i	0.0527478	−	0.258376i
$326$	−4.17636	−	0.337151i	−0.231307	−	0.0186731i
$327$	0.332001	+	0.209945i	0.0183597	+	0.0116100i
$328$	−16.9382	−	2.75273i	−0.935257	−	0.151994i
$329$	−3.79455	−	5.49735i	−0.209200	−	0.303079i
$330$	−8.20463	−	1.33338i	−0.451650	−	0.0734003i
$331$	−4.62681	−	12.1999i	−0.254312	−	0.670567i	−0.999991	−	0.00426070i	$-0.998644\pi$
$331$	−4.62681	−	12.1999i	−0.254312	−	0.670567i	0.745679	−	0.666306i	$-0.232125\pi$
$332$	2.73457	−	22.5212i	0.150079	−	1.23601i
$333$	6.53623	+	32.0166i	0.358183	+	1.75450i
$334$	9.35593	−	5.91633i	0.511934	−	0.323727i
$335$	−3.10079	+	25.5373i	−0.169414	+	1.39525i
$336$	0.00941534	−	0.0115317i	0.000513649	−	0.000629106i
$337$	−8.25511	−	10.1107i	−0.449684	−	0.550763i	0.499159	−	0.866510i	$-0.333642\pi$
$337$	−8.25511	−	10.1107i	−0.449684	−	0.550763i	−0.948843	+	0.315747i	$0.897745\pi$
$338$	−2.59868	−	21.4021i	−0.141350	−	1.16412i
$339$	−0.454874	−	0.287645i	−0.0247054	−	0.0156227i
$340$	3.38422	−	16.5770i	0.183535	−	0.899013i
$341$	−37.0669	+	23.4397i	−2.00729	+	1.26933i
$342$	10.1276	−	26.7043i	0.547637	−	1.44400i
$343$	3.08500	−	8.13448i	0.166574	−	0.439221i
$344$	2.81760	−	0.227460i	0.151915	−	0.0122638i
$345$	−0.0466762	+	1.15826i	−0.00251296	+	0.0623585i
$346$	−4.97086	+	17.1614i	−0.267235	+	0.922602i
$347$	13.4809	+	16.5111i	0.723694	+	0.886365i	0.997144	−	0.0755215i	$-0.0240622\pi$
$347$	13.4809	+	16.5111i	0.723694	+	0.886365i	−0.273450	+	0.961886i	$0.588165\pi$
$348$	−1.08157	−	0.0873130i	−0.0579780	−	0.00468047i
$349$	27.3661	+	9.13614i	1.46487	+	0.489047i	0.933650	−	0.358186i	$-0.116604\pi$
$349$	27.3661	+	9.13614i	1.46487	+	0.489047i	0.531223	+	0.847232i	$0.321733\pi$
$350$	−2.75374	−	2.43960i	−0.147194	−	0.130402i
$351$	1.30989	−	2.26879i	0.0699167	−	0.121099i
$352$	11.1934	−	29.5146i	0.596611	−	1.57313i
$353$	13.3244	+	6.99317i	0.709184	+	0.372209i	0.780424	−	0.625250i	$-0.215003\pi$
$353$	13.3244	+	6.99317i	0.709184	+	0.372209i	−0.0712396	+	0.997459i	$0.522696\pi$
$354$	−0.118845	+	0.250460i	−0.00631651	+	0.0133118i
$355$	−12.5394	+	11.1090i	−0.665525	+	0.589604i
$356$	−4.60508	+	3.46049i	−0.244069	+	0.183406i
$357$	−0.0563672	+	0.276105i	−0.00298327	+	0.0146130i
$358$	−38.3747	−	28.8367i	−2.02816	−	1.52407i
$359$	−10.4000	−	21.9175i	−0.548890	−	1.15676i	−0.968490	−	0.249052i	$-0.919881\pi$
$359$	−10.4000	−	21.9175i	−0.548890	−	1.15676i	0.419600	−	0.907709i	$-0.362170\pi$
$360$	11.6451	+	20.1700i	0.613753	+	1.06305i
$361$	1.12353	−	0.0907007i	0.0591331	−	0.00477372i
$362$	12.1592	+	32.0612i	0.639073	+	1.68510i
$363$	−4.91720	+	0.799123i	−0.258086	+	0.0419431i
$364$	3.64003	+	1.55087i	0.190789	+	0.0812877i
$365$	−3.62714			−0.189853
$366$	4.76105	+	4.95678i	0.248864	+	0.259095i
$367$	−16.9299	−	12.7220i	−0.883731	−	0.664081i	0.0587745	−	0.998271i	$-0.481281\pi$
$367$	−16.9299	−	12.7220i	−0.883731	−	0.664081i	−0.942506	+	0.334190i	$0.891537\pi$
$368$	0.177087	+	0.0436481i	0.00923132	+	0.00227531i
$369$	−8.76021	+	15.1731i	−0.456038	+	0.789882i
$370$	−2.80591	+	69.6279i	−0.145872	+	3.61978i
$371$	−0.0141616	−	0.351417i	−0.000735235	−	0.0182447i
$372$	−5.52688	−	1.84514i	−0.286555	−	0.0956662i
$373$	13.8966	−	4.63937i	0.719539	−	0.240217i	0.0667636	−	0.997769i	$-0.478733\pi$
$373$	13.8966	−	4.63937i	0.719539	−	0.240217i	0.652776	+	0.757551i	$0.273604\pi$
$374$	−2.98403	−	24.5757i	−0.154301	−	1.27078i
$375$	1.40517	−	0.737492i	0.0725628	−	0.0380839i
$376$	1.21238	+	30.0850i	0.0625239	+	1.55151i
$377$	−0.544009	−	2.66473i	−0.0280179	−	0.137241i
$378$	−1.01368	−	1.75574i	−0.0521378	−	0.0903054i
$379$	2.32456	−	8.02533i	0.119405	−	0.412233i	−0.878440	−	0.477853i	$-0.841415\pi$
$379$	2.32456	−	8.02533i	0.119405	−	0.412233i	0.997845	+	0.0656195i	$0.0209024\pi$
$380$	21.4388	−	31.0595i	1.09979	−	1.59332i
$381$	0.256138	+	0.884292i	0.0131224	+	0.0453037i
$382$	24.0524	−	5.92837i	1.23063	−	0.303322i
$383$	−12.3554	+	3.04534i	−0.631333	+	0.155610i	−0.541981	−	0.840391i	$-0.682326\pi$
$383$	−12.3554	+	3.04534i	−0.631333	+	0.155610i	−0.0893515	+	0.996000i	$0.528479\pi$
$384$	4.07917	−	1.36183i	0.208164	−	0.0694955i
$385$	−9.19109	−	3.91596i	−0.468421	−	0.199576i
$386$	−27.1571	+	24.0591i	−1.38226	+	1.22458i
$387$	0.802952	−	2.77211i	0.0408163	−	0.140914i
$388$	21.4151	+	26.2287i	1.08719	+	1.33156i
$389$	31.8912	+	5.18282i	1.61695	+	0.262780i	0.900498	−	0.434859i	$-0.143202\pi$
$389$	31.8912	+	5.18282i	1.61695	+	0.262780i	0.716450	+	0.697639i	$0.245766\pi$
$390$	1.91748	−	1.99631i	0.0970954	−	0.101087i
$391$	−3.35209	+	0.826215i	−0.169522	+	0.0417835i
$392$	−15.2023	+	11.4238i	−0.767834	+	0.576990i
$393$	0.377775	+	0.547301i	0.0190562	+	0.0276077i
$394$	5.82697	+	12.2801i	0.293558	+	0.618661i
$395$	−7.07830	+	3.01578i	−0.356148	+	0.151740i
$396$	40.9289	+	36.2598i	2.05675	+	1.82212i
$397$	−20.3650	−	1.64403i	−1.02209	−	0.0825116i	−0.441959	−	0.897035i	$-0.645716\pi$
$397$	−20.3650	−	1.64403i	−1.02209	−	0.0825116i	−0.580131	+	0.814523i	$0.696999\pi$
$398$	45.7359	+	24.0040i	2.29253	+	1.20321i
$399$	−0.357084	+	0.517325i	−0.0178765	+	0.0258986i
$400$	0.0698132	+	0.241023i	0.00349066	+	0.0120512i
$401$	3.43671	+	2.17325i	0.171621	+	0.108527i	0.617515	−	0.786559i	$-0.288140\pi$
$401$	3.43671	+	2.17325i	0.171621	+	0.108527i	−0.445893	+	0.895086i	$0.647114\pi$
$402$	−3.16287	+	3.87381i	−0.157750	+	0.193208i
$403$	0.588058	−	14.5925i	0.0292933	−	0.726905i
$404$	27.1927	−	57.3075i	1.35289	−	2.85115i
$405$	23.0332	−	3.74326i	1.14453	−	0.186004i
$406$	−1.99636	−	0.666483i	−0.0990776	−	0.0330770i
$407$	17.5784	+	60.6877i	0.871330	+	3.00818i
$408$	0.879916	−	0.916089i	0.0435623	−	0.0453532i
$409$	0.557277	−	0.807356i	0.0275556	−	0.0399212i	−0.808964	−	0.587858i	$-0.799971\pi$
$409$	0.557277	−	0.807356i	0.0275556	−	0.0399212i	0.836520	+	0.547937i	$0.184587\pi$
$410$	−25.8821	+	26.9461i	−1.27823	+	1.33077i
$411$	3.47541	−	3.61828i	0.171429	−	0.178477i
$412$	−46.2751	+	7.52044i	−2.27981	+	0.370506i
$413$	−0.210730	+	0.258097i	−0.0103693	+	0.0127001i
$414$	6.99068	−	10.1278i	0.343573	−	0.497752i
$415$	−14.2784	−	12.6496i	−0.700901	−	0.620944i
$416$	5.97126	+	8.65086i	0.292765	+	0.424143i
$417$	−0.848260	+	0.883132i	−0.0415395	+	0.0432472i
$418$	15.3638	−	53.0421i	0.751470	−	2.59438i
$419$	−4.03451	+	1.34692i	−0.197099	+	0.0658013i	−0.413504	−	0.910502i	$-0.635695\pi$
$419$	−4.03451	+	1.34692i	−0.197099	+	0.0658013i	0.216405	+	0.976304i	$0.430567\pi$
$420$	−0.369290	−	1.27494i	−0.0180195	−	0.0622105i
$421$	−19.0191	−	32.9420i	−0.926934	−	1.60550i	−0.788421	−	0.615136i	$-0.789101\pi$
$421$	−19.0191	−	32.9420i	−0.926934	−	1.60550i	−0.138513	−	0.990361i	$-0.544232\pi$
$422$	16.2137	−	8.50960i	0.789270	−	0.414241i
$423$	29.1589	+	9.73468i	1.41776	+	0.473317i
$424$	−0.792657	+	1.37292i	−0.0384948	+	0.0666750i
$425$	−3.29034	−	3.42561i	−0.159605	−	0.166167i
$426$	−3.21459	+	0.522421i	−0.155747	+	0.0253114i
$427$	4.13030	+	7.15389i	0.199879	+	0.346201i
$428$	3.54173	−	17.3486i	0.171196	−	0.838574i
$429$	1.07591	−	2.26743i	0.0519454	−	0.109473i
$430$	3.07730	−	5.33003i	0.148400	−	0.257037i
$431$	−35.8885	−	2.89722i	−1.72869	−	0.139554i	−0.824270	−	0.566198i	$-0.808414\pi$
$431$	−35.8885	−	2.89722i	−1.72869	−	0.139554i	−0.904420	+	0.426643i	$0.859696\pi$
$432$	−0.00556794	+	0.138167i	−0.000267888	+	0.00664757i
$433$	−5.45714	+	14.3893i	−0.262253	+	0.691505i	0.737614	+	0.675222i	$0.235952\pi$
$433$	−5.45714	+	14.3893i	−0.262253	+	0.691505i	−0.999867	+	0.0162826i	$0.994817\pi$
$434$	−9.55215	−	6.04042i	−0.458518	−	0.289949i
$435$	−0.577031	+	0.706735i	−0.0276665	+	0.0338854i
$436$	−1.10224	−	5.39914i	−0.0527879	−	0.258572i
$437$	−7.60138	−	1.23534i	−0.363623	−	0.0590946i
$438$	−0.595970	−	0.376869i	−0.0284766	−	0.0180075i
$439$	3.51405	+	3.65851i	0.167716	+	0.174611i	0.799757	−	0.600324i	$-0.204962\pi$
$439$	3.51405	+	3.65851i	0.167716	+	0.174611i	−0.632040	+	0.774935i	$0.717782\pi$
$440$	25.5815	+	37.0613i	1.21955	+	1.76683i
$441$	5.40161	+	18.6485i	0.257220	+	0.888025i
$442$	7.29964	+	3.83115i	0.347209	+	0.182229i
$443$	21.4311	+	3.48290i	1.01822	+	0.165477i	0.646538	−	0.762882i	$-0.276216\pi$
$443$	21.4311	+	3.48290i	1.01822	+	0.165477i	0.371685	+	0.928359i	$0.378780\pi$
$444$	−4.76856	+	6.90845i	−0.226306	+	0.327860i
$445$	0.195030	+	4.83961i	0.00924529	+	0.229420i
$446$	0.799553	+	2.10825i	0.0378599	+	0.0998285i
$447$	−4.26070	−	2.23619i	−0.201524	−	0.105768i
$448$	8.23593	−	0.664873i	0.389111	−	0.0314123i
$449$	−3.39611	+	27.9695i	−0.160272	+	1.31996i	0.661415	+	0.750021i	$0.269956\pi$
$449$	−3.39611	+	27.9695i	−0.160272	+	1.31996i	−0.821687	+	0.569939i	$0.806967\pi$
$450$	16.8760	+	1.36237i	0.795543	+	0.0642229i
$451$	−14.5226	+	30.6057i	−0.683843	+	1.44117i
$452$	1.51018	+	7.39736i	0.0710330	+	0.347942i
$453$	−2.21198	−	1.95964i	−0.103928	−	0.0920721i
$454$	−13.4216	+	7.04418i	−0.629905	+	0.330600i
$455$	2.81186	−	1.77811i	0.131822	−	0.0833592i
$456$	2.60669	−	1.11061i	0.122070	−	0.0520090i
$457$	−8.40494	−	2.07163i	−0.393167	−	0.0969069i	0.0377759	−	0.999286i	$-0.487973\pi$
$457$	−8.40494	−	2.07163i	−0.393167	−	0.0969069i	−0.430943	+	0.902379i	$0.641819\pi$
$458$	−1.01446	+	8.35484i	−0.0474026	+	0.390396i
$459$	−1.12210	−	2.36477i	−0.0523750	−	0.110378i
$460$	12.1720	−	10.7835i	0.567523	−	0.502781i
$461$	17.7536	−	21.7442i	0.826868	−	1.01273i	−0.172746	−	0.984966i	$-0.555264\pi$
$461$	17.7536	−	21.7442i	0.826868	−	1.01273i	0.999615	−	0.0277633i	$-0.00883848\pi$
$462$	−1.10330	−	1.59840i	−0.0513300	−	0.0743644i
$463$	1.93188	+	15.9105i	0.0897821	+	0.739422i	0.966186	+	0.257846i	$0.0830126\pi$
$463$	1.93188	+	15.9105i	0.0897821	+	0.739422i	−0.876404	+	0.481577i	$0.840064\pi$
$464$	0.0907896	+	0.111197i	0.00421480	+	0.00516219i
$465$	−3.91675	+	2.94325i	−0.181635	+	0.136490i
$466$	−54.7173			−2.53473
$467$	−2.99890	−	24.6981i	−0.138772	−	1.14289i	−0.881125	−	0.472884i	$-0.843213\pi$
$467$	−2.99890	−	24.6981i	−0.138772	−	1.14289i	0.742352	−	0.670010i	$-0.233710\pi$
$468$	−17.6797	+	4.35766i	−0.817245	+	0.201433i
$469$	−4.80524	+	3.61090i	−0.221885	+	0.166736i
$470$	55.4072	+	35.0374i	2.55574	+	1.61615i
$471$	2.04182	−	2.12576i	0.0940819	−	0.0979497i
$472$	1.42461	−	0.475605i	0.0655730	−	0.0218915i
$473$	1.11621	−	5.46755i	0.0513233	−	0.251398i
$474$	−1.47637	−	0.239934i	−0.0678120	−	0.0110205i
$475$	−3.75713	−	9.90675i	−0.172389	−	0.454553i
$476$	3.34119	−	2.11284i	0.153143	−	0.0968419i
$477$	1.02366	+	1.25375i	0.0468700	+	0.0574053i
$478$	3.52498	−	17.2665i	0.161229	−	0.789750i
$479$	8.19542	−	21.6095i	0.374458	−	0.987365i	−0.606832	−	0.794830i	$-0.707560\pi$
$479$	8.19542	−	21.6095i	0.374458	−	0.987365i	0.981290	−	0.192535i	$-0.0616709\pi$
$480$	0.981090	−	3.38711i	0.0447804	−	0.154600i
$481$	−19.9572	−	6.66269i	−0.909970	−	0.303793i
$482$	−2.07025	+	5.45881i	−0.0942975	+	0.248642i
$483$	−0.202736	+	0.179608i	−0.00922480	+	0.00817246i
$484$	55.8692	+	41.9830i	2.53951	+	1.90832i
$485$	28.3791	−	2.29100i	1.28863	−	0.104029i
$486$	12.9141	+	5.50220i	0.585797	+	0.249585i
$487$	−12.7757	−	9.60033i	−0.578923	−	0.435032i	0.270519	−	0.962715i	$-0.412805\pi$
$487$	−12.7757	−	9.60033i	−0.578923	−	0.435032i	−0.849442	+	0.527682i	$0.823061\pi$
$488$	1.49930	−	37.2048i	0.0678702	−	1.68418i
$489$	−0.402559	+	0.134394i	−0.0182043	+	0.00607750i
$490$	1.66714	+	41.3696i	0.0753136	+	1.86889i
$491$	−6.47449	+	22.3525i	−0.292189	+	1.00875i	0.671339	+	0.741150i	$0.265719\pi$
$491$	−6.47449	+	22.3525i	−0.292189	+	1.00875i	−0.963529	+	0.267605i	$0.913768\pi$
$492$	−4.37004	+	1.07712i	−0.197017	+	0.0485602i
$493$	−2.49988	−	1.06510i	−0.112589	−	0.0479696i
$494$	11.6302	+	14.2445i	0.523269	+	0.640889i
$495$	44.6414	−	11.0031i	2.00648	−	0.494553i
$496$	0.330462	+	0.696433i	0.0148382	+	0.0312708i
$497$	−3.90162	−	0.314971i	−0.175011	−	0.0141284i
$498$	−1.03175	−	3.56200i	−0.0462336	−	0.159617i
$499$	0.456276	−	11.3224i	0.0204257	−	0.506859i	−0.956303	−	0.292379i	$-0.905553\pi$
$499$	0.456276	−	11.3224i	0.0204257	−	0.506859i	0.976728	−	0.214480i	$-0.0688057\pi$
$500$	−21.1165	−	7.04974i	−0.944361	−	0.315274i
$501$	0.636937	−	0.922763i	0.0284563	−	0.0412260i
$502$	21.0024	−	3.41322i	0.937383	−	0.152340i
$503$	18.5175	+	16.4051i	0.825656	+	0.731467i	0.965974	−	0.258639i	$-0.0832741\pi$
$503$	18.5175	+	16.4051i	0.825656	+	0.731467i	−0.140318	+	0.990106i	$0.544813\pi$
$504$	−1.51403	+	5.22703i	−0.0674401	+	0.232830i
$505$	−26.6680	−	46.1903i	−1.18671	−	2.05544i
$506$	11.8972	−	20.6066i	0.528896	−	0.916075i
$507$	−1.09187	−	1.89117i	−0.0484916	−	0.0839899i
$508$	6.45753	−	11.1848i	0.286507	−	0.496244i
$509$	5.69847	−	15.0256i	0.252580	−	0.665999i	−0.747419	−	0.664353i	$-0.768707\pi$
$509$	5.69847	−	15.0256i	0.252580	−	0.665999i	0.999999	−	0.00164558i	$-0.000523803\pi$
$510$	−0.553193	−	2.70972i	−0.0244958	−	0.119988i
$511$	−0.587084	−	0.611219i	−0.0259710	−	0.0270387i
$512$	−1.00291	−	0.526369i	−0.0443229	−	0.0232624i
$513$	−0.235101	−	5.83396i	−0.0103799	−	0.257576i
$514$	36.8307	−	2.97328i	1.62453	−	0.131146i
$515$	−16.8992	+	35.6144i	−0.744670	+	1.56936i
$516$	0.656478	−	0.344546i	0.0288998	−	0.0151678i
$517$	57.7118	+	14.2247i	2.53816	+	0.625601i
$518$	−12.1873	+	10.7970i	−0.535480	+	0.474394i
$519$	0.218139	+	1.79653i	0.00957522	+	0.0788590i
$520$	−14.9961			−0.657624
$521$	−33.5321	+	25.1977i	−1.46907	+	1.10393i	−0.497418	+	0.867511i	$0.665718\pi$
$521$	−33.5321	+	25.1977i	−1.46907	+	1.10393i	−0.971650	+	0.236422i	$0.924025\pi$
$522$	9.18744	−	3.06722i	0.402123	−	0.134248i
$523$	0.0755508	+	0.199211i	0.00330361	+	0.00871090i	0.936658	−	0.350246i	$-0.113902\pi$
$523$	0.0755508	+	0.199211i	0.00330361	+	0.00871090i	−0.933354	+	0.358956i	$0.883133\pi$
$524$	1.86607	−	9.14059i	0.0815195	−	0.399309i
$525$	−0.353464	−	0.118004i	−0.0154264	−	0.00515010i
$526$	−52.6993	−	39.6009i	−2.29780	−	1.72668i
$527$	−11.6651	−	8.76579i	−0.508142	−	0.381844i
$528$	0.00533409	+	0.132364i	0.000232137	+	0.00576041i
$529$	18.1068	+	7.71458i	0.787251	+	0.335416i
$530$	1.47969	+	3.11838i	0.0642737	+	0.135454i
$531$	0.0617442	−	1.53217i	0.00267947	−	0.0664903i
$532$	8.70397	−	1.41453i	0.377365	−	0.0613278i
$533$	−5.64052	−	9.76966i	−0.244318	−	0.423171i
$534$	−0.470802	+	0.815453i	−0.0203736	+	0.0352881i
$535$	−10.3134	−	10.7374i	−0.445889	−	0.464219i
$536$	27.0058	−	2.18013i	1.16647	−	0.0941673i
$537$	−4.72081	−	1.16358i	−0.203718	−	0.0502120i
$538$	3.83946			0.165531
$539$	13.3118	+	35.1004i	0.573381	+	1.51188i
$540$	9.85630	+	7.40653i	0.424148	+	0.318726i
$541$	33.2665	+	14.1735i	1.43024	+	0.609368i	0.961707	−	0.274079i	$-0.0883728\pi$
$541$	33.2665	+	14.1735i	1.43024	+	0.609368i	0.468532	+	0.883447i	$0.344783\pi$
$542$	−37.1642	+	6.03977i	−1.59634	+	0.259430i
$543$	2.40595	+	2.50486i	0.103249	+	0.107494i
$544$	10.5024			0.450287
$545$	−4.26268	−	1.81616i	−0.182593	−	0.0777956i
$546$	0.646763			0.0276789
$547$	17.9159	+	15.0340i	0.766027	+	0.642809i
$547$	17.9159	+	15.0340i	0.766027	+	0.642809i
$548$	−70.3803			−3.00650
$549$	−34.9740	−	14.9010i	−1.49265	−	0.635960i
$550$	32.7367			1.39590
$551$	−4.19887	−	4.37149i	−0.178878	−	0.186232i
$552$	1.20507	−	0.195843i	0.0512911	−	0.00833561i
$553$	−1.65388	−	0.704652i	−0.0703301	−	0.0299648i
$554$	15.7810	+	11.8587i	0.670472	+	0.503827i
$555$	2.50292	+	6.59965i	0.106243	+	0.280140i
$556$	17.1781			0.728513
$557$	−31.0533	−	7.65394i	−1.31577	−	0.324308i	−0.481879	−	0.876238i	$-0.660045\pi$
$557$	−31.0533	−	7.65394i	−1.31577	−	0.324308i	−0.833890	+	0.551930i	$0.813892\pi$
$558$	51.8432	−	4.18522i	2.19470	−	0.177174i
$559$	1.28727	+	1.34019i	0.0544458	+	0.0566841i
$560$	−0.0878016	+	0.152077i	−0.00371029	+	0.00642642i
$561$	−1.25378	−	2.17161i	−0.0529345	−	0.0916853i
$562$	−42.0855	+	6.83955i	−1.77527	+	0.288509i
$563$	0.868956	−	21.5629i	0.0366221	−	0.908769i	−0.871584	−	0.490246i	$-0.836907\pi$
$563$	0.868956	−	21.5629i	0.0366221	−	0.908769i	0.908206	−	0.418523i	$-0.137452\pi$
$564$	3.38541	+	7.13460i	0.142552	+	0.300421i
$565$	5.84029	+	2.48831i	0.245703	+	0.104684i
$566$	−2.74064	−	68.0083i	−0.115198	−	2.85860i
$567$	4.35891	+	3.27551i	0.183057	+	0.137558i
$568$	14.1053	+	10.5994i	0.591845	+	0.444743i
$569$	3.98189	+	1.32935i	0.166929	+	0.0557292i	0.398904	−	0.916993i	$-0.369391\pi$
$569$	3.98189	+	1.32935i	0.166929	+	0.0557292i	−0.231975	+	0.972722i	$0.574519\pi$
$570$	1.23398	−	6.04443i	0.0516857	−	0.253173i
$571$	−2.75597	−	7.26689i	−0.115334	−	0.304110i	0.864903	−	0.501940i	$-0.167380\pi$
$571$	−2.75597	−	7.26689i	−0.115334	−	0.304110i	−0.980236	+	0.197829i	$0.936611\pi$
$572$	−33.3957	+	11.1491i	−1.39634	+	0.466168i
$573$	2.00594	−	1.50737i	0.0837994	−	0.0629712i
$574$	−8.72998			−0.364382
$575$	−0.550290	−	4.53205i	−0.0229487	−	0.188999i
$576$	−28.4627	+	25.2158i	−1.18595	+	1.05066i
$577$	0.0553579	+	0.0136445i	0.00230458	+	0.000568027i	0.240468	−	0.970657i	$-0.422699\pi$
$577$	0.0553579	+	0.0136445i	0.00230458	+	0.000568027i	−0.238163	+	0.971225i	$0.576545\pi$
$578$	−27.2243	+	14.2884i	−1.13238	+	0.594320i
$579$	−1.57543	+	3.32014i	−0.0654725	+	0.137980i
$580$	12.7577	−	1.02991i	0.529734	−	0.0427646i
$581$	−0.179471	−	4.45354i	−0.00744573	−	0.184764i
$582$	4.90097	+	2.57223i	0.203152	+	0.106622i
$583$	2.16793	+	2.25706i	0.0897865	+	0.0934777i
$584$	0.764126	+	3.74294i	0.0316198	+	0.154884i
$585$	−5.42925	+	14.3158i	−0.224472	+	0.591884i
$586$	26.2541	−	45.4734i	1.08455	−	1.87849i
$587$	−15.2069	−	26.3392i	−0.627657	−	1.08713i	−0.988021	−	0.154322i	$-0.950681\pi$
$587$	−15.2069	−	26.3392i	−0.627657	−	1.08713i	0.360364	−	0.932812i	$-0.382653\pi$
$588$	−2.49377	+	4.31934i	−0.102841	+	0.178127i
$589$	−16.2744	−	28.1880i	−0.670574	−	1.16147i
$590$	0.909781	−	3.14093i	0.0374551	−	0.129310i
$591$	1.03053	+	0.912971i	0.0423904	+	0.0375546i
$592$	1.09617	−	0.178145i	0.0450523	−	0.00732171i
$593$	−17.5206	+	25.3830i	−0.719484	+	1.04235i	0.277186	+	0.960816i	$0.410598\pi$
$593$	−17.5206	+	25.3830i	−0.719484	+	1.04235i	−0.996670	+	0.0815369i	$0.974017\pi$
$594$	17.1117	+	5.71272i	0.702100	+	0.234396i
$595$	0.133844	−	3.32130i	0.00548705	−	0.136160i
$596$	18.7804	+	64.8374i	0.769275	+	2.65585i
$597$	5.21490	+	0.420990i	0.213431	+	0.0172300i
$598$	3.39682	+	7.15864i	0.138906	+	0.292739i
$599$	12.6933	−	3.12861i	0.518633	−	0.127832i	0.0286940	−	0.999588i	$-0.490865\pi$
$599$	12.6933	−	3.12861i	0.518633	−	0.127832i	0.489939	+	0.871757i	$0.337019\pi$
$600$	1.06232	+	1.30110i	0.0433689	+	0.0531172i
$601$	−29.2564	−	12.4650i	−1.19339	−	0.508457i	−0.298359	−	0.954454i	$-0.596439\pi$
$601$	−29.2564	−	12.4650i	−1.19339	−	0.508457i	−0.895035	+	0.445996i	$0.852849\pi$
$602$	1.39626	−	0.344148i	0.0569074	−	0.0140264i
$603$	7.69604	−	26.5698i	0.313407	−	1.08201i
$604$	1.66927	+	41.4226i	0.0679218	+	1.68546i
$605$	55.7381	−	18.6081i	2.26607	−	0.756527i
$606$	0.417506	−	10.3603i	0.0169600	−	0.420859i
$607$	−25.8861	−	19.4522i	−1.05069	−	0.789539i	−0.0725200	−	0.997367i	$-0.523104\pi$
$607$	−25.8861	−	19.4522i	−1.05069	−	0.789539i	−0.978165	+	0.207828i	$0.933361\pi$
$608$	21.5525	+	9.18267i	0.874070	+	0.372406i
$609$	−0.212491	+	0.0171540i	−0.00861057	+	0.000695117i
$610$	−64.8110	−	48.7023i	−2.62412	−	1.97190i
$611$	−14.8156	+	13.1255i	−0.599376	+	0.531001i
$612$	−6.45130	+	17.0107i	−0.260778	+	0.687616i
$613$	25.5367	+	8.52542i	1.03142	+	0.344338i	0.781485	−	0.623924i	$-0.214463\pi$
$613$	25.5367	+	8.52542i	1.03142	+	0.344338i	0.249935	+	0.968263i	$0.419591\pi$
$614$	6.84450	−	23.6299i	0.276221	−	0.953627i
$615$	−1.34199	+	3.53854i	−0.0541143	+	0.142688i
$616$	−2.10470	+	10.3095i	−0.0848006	+	0.415381i
$617$	−17.4298	−	21.3476i	−0.701695	−	0.859421i	0.293638	−	0.955917i	$-0.405134\pi$
$617$	−17.4298	−	21.3476i	−0.701695	−	0.859421i	−0.995333	+	0.0964959i	$0.969237\pi$
$618$	−6.47711	+	4.09588i	−0.260548	+	0.164760i
$619$	−9.71986	−	25.6292i	−0.390674	−	1.03012i	−0.975700	−	0.219109i	$-0.929685\pi$
$619$	−9.71986	−	25.6292i	−0.390674	−	1.03012i	0.585026	−	0.811014i	$-0.301084\pi$
$620$	67.8397	+	11.0250i	2.72451	+	0.442776i
$621$	0.503225	−	2.46496i	0.0201937	−	0.0989154i
$622$	−72.1865	+	24.0994i	−2.89442	+	0.966298i
$623$	−0.783967	+	0.816196i	−0.0314090	+	0.0327002i
$624$	−0.0372844	−	0.0235772i	−0.00149257	−	0.000943845i
$625$	−24.9826	+	18.7732i	−0.999302	+	0.750927i
$626$	−37.9215	+	9.34681i	−1.51565	+	0.373574i
$627$	−0.674219	−	5.55269i	−0.0269257	−	0.221753i
$628$	−41.3488			−1.65000
$629$	−16.8056	+	12.6286i	−0.670082	+	0.503534i
$630$	7.49346	+	9.17783i	0.298547	+	0.365653i
$631$	0.946833	+	7.79787i	0.0376928	+	0.310428i	0.999346	+	0.0361599i	$0.0115126\pi$
$631$	0.946833	+	7.79787i	0.0376928	+	0.310428i	−0.961653	+	0.274268i	$0.911564\pi$
$632$	4.60323	+	6.66893i	0.183107	+	0.265276i
$633$	1.17302	−	1.43669i	0.0466232	−	0.0571031i
$634$	−14.9909	+	13.2808i	−0.595364	+	0.527447i
$635$	−4.65538	−	9.81101i	−0.184743	−	0.389338i
$636$	−0.0501185	+	0.412763i	−0.00198733	+	0.0163671i
$637$	−12.1377	−	2.99168i	−0.480914	−	0.118535i
$638$	17.2295	−	7.34080i	0.682122	−	0.290625i
$639$	15.2253	−	9.62788i	0.602302	−	0.380873i
$640$	−44.9163	+	23.5739i	−1.77547	+	0.931840i
$641$	28.5803	+	25.3199i	1.12885	+	1.00008i	0.999965	+	0.00841850i	$0.00267972\pi$
$641$	28.5803	+	25.3199i	1.12885	+	1.00008i	0.128890	+	0.991659i	$0.458859\pi$
$642$	−0.578941	−	2.83584i	−0.0228490	−	0.111922i
$643$	−18.1909	+	38.3364i	−0.717377	+	1.51184i	0.136091	+	0.990696i	$0.456546\pi$
$643$	−18.1909	+	38.3364i	−0.717377	+	1.51184i	−0.853469	+	0.521144i	$0.825505\pi$
$644$	3.78729	+	0.305741i	0.149240	+	0.0120479i
$645$	0.0751424	−	0.618853i	0.00295873	−	0.0243673i
$646$	18.3137	−	1.47843i	0.720542	−	0.0581682i
$647$	7.14697	+	3.75102i	0.280976	+	0.147468i	0.599325	−	0.800506i	$-0.295436\pi$
$647$	7.14697	+	3.75102i	0.280976	+	0.147468i	−0.318348	+	0.947974i	$0.603128\pi$
$648$	−8.71515	−	22.9800i	−0.342363	−	0.902738i
$649$	−0.119385	−	2.96251i	−0.00468627	−	0.116289i
$650$	−6.19274	+	8.97173i	−0.242899	+	0.351900i
$651$	−1.12993	−	0.183632i	−0.0442856	−	0.00719710i
$652$	5.27167	+	2.76679i	0.206455	+	0.108356i
$653$	−3.61992	−	12.4974i	−0.141658	−	0.489062i	0.858041	−	0.513581i	$-0.171682\pi$
$653$	−3.61992	−	12.4974i	−0.141658	−	0.489062i	−0.999699	+	0.0245196i	$0.992194\pi$
$654$	−0.511691	−	0.741312i	−0.0200087	−	0.0289876i
$655$	−5.43394	−	5.65733i	−0.212321	−	0.221050i
$656$	0.503264	+	0.318245i	0.0196492	+	0.0124254i
$657$	3.84977	+	0.625648i	0.150194	+	0.0244088i
$658$	3.06388	+	15.0079i	0.119443	+	0.585069i
$659$	4.97323	−	6.09110i	0.193729	−	0.237275i	−0.668601	−	0.743621i	$-0.733107\pi$
$659$	4.97323	−	6.09110i	0.193729	−	0.237275i	0.862331	+	0.506346i	$0.169004\pi$
$660$	9.98267	+	6.31266i	0.388575	+	0.245720i
$661$	−1.46443	+	3.86139i	−0.0569597	+	0.150190i	−0.960476	−	0.278364i	$-0.910208\pi$
$661$	−1.46443	+	3.86139i	−0.0569597	+	0.150190i	0.903516	+	0.428555i	$0.140977\pi$
$662$	−1.20476	+	29.8957i	−0.0468242	+	1.16193i
$663$	0.832320	+	0.0671918i	0.0323246	+	0.00260951i
$664$	−10.0454	+	17.3991i	−0.389837	+	0.675218i
$665$	3.17861	−	6.69878i	0.123261	−	0.259767i
$666$	14.9883	−	73.4174i	0.580784	−	2.84487i
$667$	−1.30588	−	2.26185i	−0.0505638	−	0.0875790i
$668$	−15.5255	+	2.52313i	−0.600698	+	0.0976229i
$669$	0.158208	+	0.164712i	0.00611669	+	0.00636815i
$670$	29.4949	−	51.0867i	1.13949	−	1.97365i
$671$	−69.7228	−	23.2769i	−2.69162	−	0.898595i
$672$	0.729568	−	0.382907i	0.0281437	−	0.0147710i
$673$	−6.67906	−	11.5685i	−0.257459	−	0.445932i	0.708102	−	0.706110i	$-0.249552\pi$
$673$	−6.67906	−	11.5685i	−0.257459	−	0.445932i	−0.965560	+	0.260179i	$0.916218\pi$
$674$	8.32738	+	28.7495i	0.320759	+	1.10739i
$675$	3.28314	−	1.09607i	0.126368	−	0.0421879i
$676$	−8.52297	+	29.4247i	−0.327806	+	1.13172i
$677$	14.3740	−	14.9649i	0.552438	−	0.575148i	−0.385169	−	0.922846i	$-0.625857\pi$
$677$	14.3740	−	14.9649i	0.552438	−	0.575148i	0.937607	+	0.347698i	$0.113036\pi$
$678$	0.701067	+	1.01567i	0.0269243	+	0.0390066i
$679$	4.97946	+	4.41142i	0.191094	+	0.169295i
$680$	−8.51133	+	12.3308i	−0.326395	+	0.472864i
$681$	−0.971014	+	1.18928i	−0.0372093	+	0.0455732i
$682$	99.2649	−	16.1321i	3.80105	−	0.617731i
$683$	17.4825	−	18.2012i	0.668949	−	0.696449i	−0.297089	−	0.954850i	$-0.596016\pi$
$683$	17.4825	−	18.2012i	0.668949	−	0.696449i	0.966038	+	0.258400i	$0.0831954\pi$
$684$	−28.1122	+	29.2679i	−1.07490	+	1.11908i
$685$	−33.6172	+	48.7030i	−1.28445	+	1.86084i
$686$	−13.8196	+	14.3877i	−0.527635	+	0.549326i
$687$	0.237174	+	0.818819i	0.00904875	+	0.0312399i
$688$	−0.0930371	−	0.0310604i	−0.00354701	−	0.00118417i
$689$	−1.02867	+	0.167175i	−0.0391891	+	0.00636885i
$690$	1.13954	−	2.40152i	0.0433814	−	0.0914244i
$691$	0.626798	−	15.5538i	0.0238445	−	0.591695i	−0.942464	−	0.334308i	$-0.891497\pi$
$691$	0.626798	−	15.5538i	0.0238445	−	0.591695i	0.966308	−	0.257387i	$-0.0828616\pi$
$692$	16.0562	−	19.6653i	0.610365	−	0.747561i
$693$	9.07975	+	5.74168i	0.344911	+	0.218109i
$694$	−13.5990	−	46.9491i	−0.516210	−	1.78216i
$695$	8.20513	−	11.8872i	0.311238	−	0.450906i
$696$	0.850859	+	0.446565i	0.0322517	+	0.0169270i
$697$	−11.2346	−	0.906953i	−0.425542	−	0.0343533i
$698$	−49.5201	−	43.8710i	−1.87436	−	1.66054i
$699$	−5.09881	+	2.17240i	−0.192855	+	0.0821678i
$700$	2.24101	+	4.72282i	0.0847021	+	0.178506i
$701$	10.2193	+	14.8052i	0.385978	+	0.559186i	0.967024	−	0.254685i	$-0.0819717\pi$
$701$	10.2193	+	14.8052i	0.385978	+	0.559186i	−0.581046	+	0.813871i	$0.697356\pi$
$702$	−4.80260	+	3.60892i	−0.181262	+	0.136210i
$703$	−45.5293	+	11.2220i	−1.71717	+	0.423244i
$704$	−50.9323	+	53.0261i	−1.91958	+	1.99850i
$705$	6.55417	+	1.06516i	0.246844	+	0.0401161i
$706$	−21.8236	−	26.7291i	−0.821343	−	1.00596i
$707$	3.46720	−	11.9702i	0.130397	−	0.450184i
$708$	0.294852	−	0.261216i	0.0110812	−	0.00981709i
$709$	−36.0053	−	15.3404i	−1.35221	−	0.576122i	−0.410287	−	0.911956i	$-0.634572\pi$
$709$	−36.0053	−	15.3404i	−1.35221	−	0.576122i	−0.941921	+	0.335834i	$0.890982\pi$
$710$	36.4384	−	12.1649i	1.36751	−	0.456541i
$711$	8.03293	−	1.97994i	0.301259	−	0.0742536i
$712$	4.95302	−	1.22081i	0.185622	−	0.0457518i
$713$	−3.90193	−	13.4710i	−0.146128	−	0.504493i
$714$	0.367082	−	0.531810i	0.0137377	−	0.0199025i
$715$	−8.23633	+	28.4351i	−0.308021	+	1.06341i
$716$	34.1036	+	59.0691i	1.27451	+	2.20752i
$717$	−0.357045	−	1.74892i	−0.0133341	−	0.0653146i
$718$	2.24001	+	55.5852i	0.0835963	+	2.07442i
$719$	45.8091	−	24.0425i	1.70839	−	0.896633i	0.731804	−	0.681516i	$-0.238679\pi$
$719$	45.8091	−	24.0425i	1.70839	−	0.896633i	0.976588	−	0.215117i	$-0.0690134\pi$
$720$	−0.0974108	−	0.802250i	−0.00363029	−	0.0298981i
$721$	−8.73675	+	2.91676i	−0.325374	+	0.108626i
$722$	−2.45174	−	0.818510i	−0.0912442	−	0.0304618i
$723$	0.0238113	+	0.590872i	0.000885552	+	0.0219747i
$724$	1.96187	−	48.6833i	0.0729124	−	1.80930i
$725$	1.79664	−	3.11187i	0.0667255	−	0.115572i
$726$	11.0917	+	2.73385i	0.411650	+	0.101463i
$727$	3.83501	+	2.88182i	0.142233	+	0.106881i	0.669477	−	0.742833i	$-0.266518\pi$
$727$	3.83501	+	2.88182i	0.142233	+	0.106881i	−0.527244	+	0.849714i	$0.676775\pi$
$728$	−2.42725	−	2.52703i	−0.0899598	−	0.0936581i
$729$	−24.1303			−0.893713
$730$	7.65187	+	3.26016i	0.283208	+	0.120664i
$731$	1.83261	−	0.297828i	0.0677814	−	0.0110156i
$732$	−3.46306	−	9.13133i	−0.127998	−	0.337504i
$733$	−12.4896	+	1.00826i	−0.461313	+	0.0372410i	−0.308939	−	0.951082i	$-0.599974\pi$
$733$	−12.4896	+	1.00826i	−0.461313	+	0.0372410i	−0.152374	+	0.988323i	$0.548692\pi$
$734$	24.2807	+	42.0553i	0.896215	+	1.55229i
$735$	1.79782	+	3.78882i	0.0663135	+	0.139753i
$736$	8.06989	+	6.06413i	0.297460	+	0.223527i
$737$	10.6985	−	52.4047i	0.394084	−	1.93035i
$738$	32.1186	−	24.1356i	1.18230	−	0.888442i
$739$	27.4216	−	24.2935i	1.00872	−	0.893649i	0.0143817	−	0.999897i	$-0.495422\pi$
$739$	27.4216	−	24.2935i	1.00872	−	0.893649i	0.994340	+	0.106247i	$0.0338835\pi$
$740$	42.4477	−	89.4566i	1.56041	−	3.28849i
$741$	1.64930	+	0.865618i	0.0605885	+	0.0317993i
$742$	−0.285986	+	0.754083i	−0.0104989	+	0.0276832i
$743$	−22.6255	+	39.1886i	−0.830050	+	1.43769i	0.0679472	+	0.997689i	$0.478355\pi$
$743$	−22.6255	+	39.1886i	−0.830050	+	1.43769i	−0.897998	+	0.440000i	$0.854978\pi$
$744$	3.86235	+	3.42174i	0.141600	+	0.125447i
$745$	53.8378	+	17.9737i	1.97246	+	0.658505i
$746$	−33.4864	−	2.70330i	−1.22603	−	0.0989750i
$747$	12.9729	+	15.8889i	0.474653	+	0.581344i
$748$	−9.78681	+	33.7880i	−0.357841	+	1.23541i
$749$	0.140073	−	3.47588i	0.00511817	−	0.127006i
$750$	−3.62724	+	0.292821i	−0.132448	+	0.0106923i
$751$	−10.4983	+	27.6817i	−0.383088	+	1.01012i	0.595329	+	0.803482i	$0.297022\pi$
$751$	−10.4983	+	27.6817i	−0.383088	+	1.01012i	−0.978417	+	0.206638i	$0.933748\pi$
$752$	0.370476	−	0.976864i	0.0135099	−	0.0356226i
$753$	1.82159	−	1.15190i	0.0663824	−	0.0419777i
$754$	−1.24747	+	6.11052i	−0.0454302	+	0.222532i
$755$	29.4616	+	18.6304i	1.07222	+	0.678030i
$756$	0.347233	+	2.85972i	0.0126287	+	0.104007i
$757$	−5.52264	−	6.76400i	−0.200724	−	0.245842i	0.664428	−	0.747352i	$-0.268675\pi$
$757$	−5.52264	−	6.76400i	−0.200724	−	0.245842i	−0.865152	+	0.501511i	$0.832778\pi$
$758$	−12.1173	+	14.8410i	−0.440119	+	0.539048i
$759$	0.290510	−	2.39257i	0.0105449	−	0.0868447i
$760$	−28.2478	+	17.8629i	−1.02466	+	0.647954i
$761$	−5.54464	−	27.1595i	−0.200993	−	0.984529i	−0.947648	−	0.319318i	$-0.896546\pi$
$761$	−5.54464	−	27.1595i	−0.200993	−	0.984529i	0.746655	−	0.665212i	$-0.231659\pi$
$762$	0.254468	−	2.09574i	0.00921842	−	0.0759205i
$763$	−0.383905	−	1.01227i	−0.0138983	−	0.0366468i
$764$	−34.7437	−	5.64640i	−1.25698	−	0.204280i
$765$	8.68987	+	12.5895i	0.314183	+	0.455173i
$766$	28.8024	+	4.68084i	1.04067	+	0.169126i
$767$	0.834482	+	0.527694i	0.0301314	+	0.0190539i
$768$	−3.85299	−	0.311045i	−0.139033	−	0.0112239i
$769$	4.12423	−	20.2018i	0.148723	−	0.728496i	−0.835206	−	0.549937i	$-0.814652\pi$
$769$	4.12423	−	20.2018i	0.148723	−	0.728496i	0.983929	−	0.178558i	$-0.0571433\pi$
$770$	15.8699	+	16.5223i	0.571911	+	0.595423i
$771$	3.31401	−	1.73933i	0.119351	−	0.0626404i
$772$	48.9004	−	16.3254i	1.75996	−	0.587563i
$773$	−4.13533	−	5.99106i	−0.148738	−	0.215484i	0.741532	−	0.670917i	$-0.234100\pi$
$773$	−4.13533	−	5.99106i	−0.148738	−	0.215484i	−0.890270	+	0.455434i	$0.849484\pi$
$774$	−4.18555	+	5.12637i	−0.150447	+	0.184264i
$775$	13.3664	−	13.9159i	0.480134	−	0.499873i
$776$	−8.34274	−	28.8025i	−0.299487	−	1.03395i
$777$	−0.707005	+	1.48998i	−0.0253637	+	0.0534528i
$778$	−62.6196	−	39.5983i	−2.24502	−	1.41967i
$779$	−22.2622	−	11.6841i	−0.797625	−	0.418626i
$780$	−3.61844	+	1.54167i	−0.129561	+	0.0552007i
$781$	27.8453	−	20.9244i	0.996384	−	0.748734i
$782$	7.81422	+	1.26993i	0.279436	+	0.0454128i
$783$	1.48215	−	1.31307i	0.0529678	−	0.0469254i
$784$	0.640663	−	0.157909i	0.0228808	−	0.00563961i
$785$	−19.7503	+	28.6132i	−0.704918	+	1.02125i
$786$	−0.305032	−	1.49415i	−0.0108801	−	0.0532944i
$787$	5.69792	+	46.9266i	0.203109	+	1.67275i	0.636293	+	0.771448i	$0.280467\pi$
$787$	5.69792	+	46.9266i	0.203109	+	1.67275i	−0.433184	+	0.901306i	$0.642610\pi$
$788$	−0.777691	−	19.2982i	−0.0277041	−	0.687470i
$789$	−6.48301	−	1.59792i	−0.230801	−	0.0568874i
$790$	17.6431			0.627714
$791$	0.525988	+	1.38692i	0.0187020	+	0.0493130i
$792$	−20.7589	−	43.7485i	−0.737636	−	1.55454i
$793$	19.5686	−	14.7048i	0.694900	−	0.522183i
$794$	41.4846	+	21.7728i	1.47223	+	0.772687i
$795$	0.261692	+	0.231838i	0.00928124	+	0.00822246i
$796$	−46.4179	−	56.8516i	−1.64524	−	2.01505i
$797$	31.6796	−	2.55744i	1.12215	−	0.0905892i	0.494567	−	0.869140i	$-0.335327\pi$
$797$	31.6796	−	2.55744i	1.12215	−	0.0905892i	0.627582	+	0.778550i	$0.284045\pi$
$798$	1.21829	−	0.770401i	0.0431270	−	0.0272719i
$799$	2.38376	+	19.6320i	0.0843312	+	0.694530i
$800$	−1.67401	+	13.7867i	−0.0591852	+	0.487434i
$801$	0.627787	−	5.17029i	0.0221818	−	0.182683i
$802$	−5.29677	−	7.67370i	−0.187036	−	0.270968i
$803$	7.51690	+	0.606827i	0.265265	+	0.0214144i
$804$	6.29213	−	3.30237i	0.221906	−	0.116465i
$805$	2.02057	−	2.47475i	0.0712158	−	0.0872236i
$806$	−14.3566	+	30.2560i	−0.505691	+	1.06572i
$807$	0.357779	−	0.152435i	0.0125944	−	0.00536598i
$808$	−42.0467	+	37.2501i	−1.47920	+	1.31046i
$809$	3.11460	+	15.2563i	0.109503	+	0.536383i	0.997123	+	0.0758052i	$0.0241527\pi$
$809$	3.11460	+	15.2563i	0.109503	+	0.536383i	−0.887619	+	0.460578i	$0.847642\pi$
$810$	−51.9557	−	12.8059i	−1.82554	−	0.449955i
$811$	−10.3106	−	21.7290i	−0.362053	−	0.763010i	0.637922	−	0.770101i	$-0.279794\pi$
$811$	−10.3106	−	21.7290i	−0.362053	−	0.763010i	−0.999975	+	0.00709117i	$0.997743\pi$
$812$	2.23849	+	1.98313i	0.0785556	+	0.0695942i
$813$	−3.22334	+	2.03832i	−0.113048	+	0.0714870i
$814$	17.4638	−	143.827i	0.612106	−	5.04115i
$815$	4.43263	−	2.32642i	0.155268	−	0.0814910i
$816$	−0.0405482	+	0.0172760i	−0.00141947	+	0.000604780i
$817$	4.02119	+	0.991134i	0.140684	+	0.0346754i
$818$	−1.90131	+	1.20231i	−0.0664777	+	0.0420379i
$819$	−3.29115	+	1.40223i	−0.115002	+	0.0489978i
$820$	48.8416	−	20.8094i	1.70562	−	0.726697i
$821$	25.7773	−	10.9827i	0.899634	−	0.383298i	0.107898	−	0.994162i	$-0.465588\pi$
$821$	25.7773	−	10.9827i	0.899634	−	0.383298i	0.791736	+	0.610864i	$0.209178\pi$
$822$	−10.5839	+	4.50940i	−0.369158	+	0.157283i
$823$	17.6760	−	11.1776i	0.616147	−	0.389628i	−0.189623	−	0.981857i	$-0.560726\pi$
$823$	17.6760	−	11.1776i	0.616147	−	0.389628i	0.805769	+	0.592229i	$0.201752\pi$
$824$	40.3115	+	9.93589i	1.40432	+	0.346133i
$825$	3.05056	−	1.29972i	0.106207	−	0.0452505i
$826$	0.676541	−	0.355076i	0.0235399	−	0.0123547i
$827$	6.14891	−	50.6408i	0.213818	−	1.76095i	−0.351601	−	0.936150i	$-0.614363\pi$
$827$	6.14891	−	50.6408i	0.213818	−	1.76095i	0.565419	−	0.824804i	$-0.308714\pi$
$828$	−14.7791	+	9.34575i	−0.513610	+	0.324787i
$829$	12.1243	+	10.7412i	0.421095	+	0.373058i	0.846896	−	0.531759i	$-0.178469\pi$
$829$	12.1243	+	10.7412i	0.421095	+	0.373058i	−0.425800	+	0.904817i	$0.640007\pi$
$830$	18.7523	+	39.5195i	0.650900	+	1.37174i
$831$	1.94137	+	0.478504i	0.0673452	+	0.0165991i
$832$	−4.89744	−	23.9892i	−0.169788	−	0.831677i
$833$	−9.34893	+	8.28243i	−0.323921	+	0.286969i
$834$	2.58328	−	1.10063i	0.0894516	−	0.0381118i
$835$	−5.66975	+	11.9487i	−0.196210	+	0.413503i
$836$	−49.6262	+	60.7811i	−1.71636	+	2.10216i
$837$	9.41509	−	4.94142i	0.325433	−	0.170800i
$838$	9.72190	+	0.784833i	0.335838	+	0.0271116i
$839$	−4.77768	−	6.92167i	−0.164944	−	0.238963i	0.731792	−	0.681528i	$-0.238684\pi$
$839$	−4.77768	−	6.92167i	−0.164944	−	0.238963i	−0.896736	+	0.442565i	$0.854069\pi$
$840$	−0.141687	+	1.16690i	−0.00488866	+	0.0402617i
$841$	−3.24778	+	26.7479i	−0.111992	+	0.922341i
$842$	10.5139	+	86.5897i	0.362333	+	2.98408i
$843$	−3.65017	+	2.30823i	−0.125719	+	0.0794997i
$844$	−25.9344	+	2.09364i	−0.892700	+	0.0720662i
$845$	16.2908	+	19.9526i	0.560421	+	0.686391i
$846$	−52.7643	−	46.7451i	−1.81407	−	1.60713i
$847$	12.1574	+	6.38068i	0.417732	+	0.219243i
$848$	0.0439760	−	0.0330458i	0.00151014	−	0.00113480i
$849$	−2.95547	−	6.22852i	−0.101432	−	0.213762i
$850$	3.86234	+	10.1841i	0.132477	+	0.349313i
$851$	−20.2049			−0.692617
$852$	4.49316	+	1.10746i	0.153933	+	0.0379411i
$853$	0.865936	+	21.4880i	0.0296491	+	0.735735i	0.943831	+	0.330430i	$0.107194\pi$
$853$	0.865936	+	21.4880i	0.0296491	+	0.735735i	−0.914181	+	0.405305i	$0.867165\pi$
$854$	−2.28326	−	18.8043i	−0.0781315	−	0.643471i
$855$	6.82547	+	33.4334i	0.233426	+	1.14340i
$856$	−8.90749	+	12.9047i	−0.304452	+	0.441074i
$857$	−3.12120	+	0.769307i	−0.106618	+	0.0262790i	−0.292264	−	0.956338i	$-0.594409\pi$
$857$	−3.12120	+	0.769307i	−0.106618	+	0.0262790i	0.185646	+	0.982617i	$0.440562\pi$
$858$	−4.30777	+	3.81635i	−0.147065	+	0.130288i
$859$	−13.5131	−	2.19610i	−0.461062	−	0.0749298i	−0.0745559	−	0.997217i	$-0.523754\pi$
$859$	−13.5131	−	2.19610i	−0.461062	−	0.0749298i	−0.386506	+	0.922287i	$0.626318\pi$
$860$	−6.99132	+	5.25364i	−0.238402	+	0.179148i
$861$	−0.813501	+	0.346600i	−0.0277240	+	0.0118121i
$862$	73.1068	+	38.3694i	2.49003	+	1.30687i
$863$	−18.4382	−	11.6596i	−0.627644	−	0.396898i	0.182435	−	0.983218i	$-0.441602\pi$
$863$	−18.4382	−	11.6596i	−0.627644	−	0.396898i	−0.810080	+	0.586320i	$0.800576\pi$
$864$	−3.28087	+	6.91429i	−0.111617	+	0.235229i
$865$	−5.93905	−	20.5040i	−0.201934	−	0.697156i
$866$	24.4459	−	25.4508i	0.830704	−	0.864854i
$867$	−1.96961	+	2.41233i	−0.0668914	+	0.0819270i
$868$	9.12257	+	13.2163i	0.309640	+	0.448591i
$869$	15.1736	−	5.06570i	0.514730	−	0.171842i
$870$	1.85254	−	0.972289i	0.0628070	−	0.0329637i
$871$	12.3381	+	12.8453i	0.418060	+	0.435247i
$872$	−0.976123	+	4.78137i	−0.0330557	+	0.161918i
$873$	−30.5161	−	2.46352i	−1.03281	−	0.0833774i
$874$	14.9256	+	9.43839i	0.504866	+	0.319258i
$875$	−4.31714	−	0.701603i	−0.145946	−	0.0237185i
$876$	0.569168	+	0.824583i	0.0192304	+	0.0278601i
$877$	47.1948	+	7.66990i	1.59365	+	0.258994i	0.891497	−	0.453027i	$-0.149656\pi$
$877$	47.1948	+	7.66990i	1.59365	+	0.258994i	0.702158	+	0.712021i	$0.252220\pi$
$878$	−4.12493	−	10.8765i	−0.139210	−	0.367066i
$879$	0.641081	−	5.27978i	0.0216231	−	0.178082i
$880$	−0.312556	−	1.53100i	−0.0105363	−	0.0516100i
$881$	3.11605	−	1.97047i	0.104982	−	0.0663869i	−0.480943	−	0.876752i	$-0.659706\pi$
$881$	3.11605	−	1.97047i	0.104982	−	0.0663869i	0.585925	+	0.810365i	$0.300731\pi$
$882$	5.36640	−	44.1963i	0.180696	−	1.48817i
$883$	2.85841	−	3.50091i	0.0961930	−	0.117815i	−0.724265	−	0.689521i	$-0.757821\pi$
$883$	2.85841	−	3.50091i	0.0961930	−	0.117815i	0.820458	+	0.571706i	$0.193718\pi$
$884$	−7.40850	−	9.07376i	−0.249175	−	0.305184i
$885$	−0.0399244	−	0.328807i	−0.00134204	−	0.0110527i
$886$	−42.0808	−	26.6103i	−1.41373	−	0.893991i
$887$	5.33722	−	26.1434i	0.179206	−	0.877811i	−0.786383	−	0.617739i	$-0.788049\pi$
$887$	5.33722	−	26.1434i	0.179206	−	0.877811i	0.965589	−	0.260071i	$-0.0837461\pi$
$888$	6.28305	−	3.97316i	0.210845	−	0.133331i
$889$	0.899764	−	2.37248i	0.0301771	−	0.0795705i
$890$	3.93851	−	10.3850i	0.132019	−	0.348106i
$891$	−48.3603	+	3.90405i	−1.62013	+	0.130791i
$892$	0.129007	−	3.20127i	0.00431947	−	0.107187i
$893$	−12.2732	+	42.3720i	−0.410707	+	1.41793i
$894$	6.97849	+	8.54710i	0.233396	+	0.285858i
$895$	57.1653	+	4.61486i	1.91082	+	0.154258i
$896$	−11.2426	−	3.75332i	−0.375588	−	0.125390i
$897$	0.600746	+	0.532214i	0.0200583	+	0.0177701i
$898$	32.3040	−	55.9522i	1.07800	−	1.86715i
$899$	3.91433	−	10.3213i	0.130550	−	0.344233i
$900$	−21.3020	−	11.1801i	−0.710066	−	0.372671i
$901$	−0.446377	+	0.940720i	−0.0148710	+	0.0313399i
$902$	58.1462	−	51.5130i	1.93606	−	1.71520i
$903$	0.116447	−	0.0875041i	0.00387511	−	0.00291196i
$904$	1.33738	−	6.55094i	0.0444808	−	0.217881i
$905$	−32.7516	−	24.6113i	−1.08870	−	0.818106i
$906$	2.90505	+	6.12227i	0.0965139	+	0.203399i
$907$	23.7699	+	41.1706i	0.789265	+	1.36705i	0.926418	+	0.376497i	$0.122872\pi$
$907$	23.7699	+	41.1706i	0.789265	+	1.36705i	−0.137153	+	0.990550i	$0.543795\pi$
$908$	21.4683	−	1.73310i	0.712451	−	0.0575150i
$909$	20.3374	+	53.6252i	0.674548	+	1.77864i
$910$	−7.53014	+	1.22377i	−0.249622	+	0.0405675i
$911$	3.18811	+	1.35833i	0.105627	+	0.0450033i	0.444134	−	0.895961i	$-0.353512\pi$
$911$	3.18811	+	1.35833i	0.105627	+	0.0450033i	−0.338507	+	0.940964i	$0.609922\pi$
$912$	−0.0983162			−0.00325557
$913$	27.4744	+	28.6038i	0.909269	+	0.946649i
$914$	15.8691	+	11.9249i	0.524905	+	0.394440i
$915$	−7.97299	−	1.96516i	−0.263579	−	0.0649663i
$916$	5.97941	−	10.3566i	0.197565	−	0.342193i
$917$	0.0738017	−	1.83137i	0.00243715	−	0.0604772i
$918$	0.241684	+	5.99732i	0.00797675	+	0.197941i
$919$	7.79654	+	2.60287i	0.257184	+	0.0858606i	0.442336	−	0.896849i	$-0.354150\pi$
$919$	7.79654	+	2.60287i	0.257184	+	0.0858606i	−0.185153	+	0.982710i	$0.559278\pi$
$920$	−13.6598	+	4.56032i	−0.450351	+	0.150349i
$921$	−0.300360	−	2.47369i	−0.00989721	−	0.0815109i
$922$	−56.9974	+	29.9146i	−1.87711	+	0.985184i
$923$	0.467039	+	11.5894i	0.0153728	+	0.381471i
$924$	0.552017	+	2.70396i	0.0181600	+	0.0889538i
$925$	−13.8991	−	24.0739i	−0.456999	−	0.791546i
$926$	10.2252	−	35.3013i	0.336020	−	1.16007i
$927$	24.0796	−	34.8853i	0.790878	−	1.14578i
$928$	2.21046	+	7.63140i	0.0725620	+	0.250513i
$929$	−26.2983	+	6.48194i	−0.862819	+	0.212666i	−0.645805	−	0.763503i	$-0.723478\pi$
$929$	−26.2983	+	6.48194i	−0.862819	+	0.212666i	−0.217014	+	0.976168i	$0.569632\pi$
$930$	10.9083	−	2.68865i	0.357697	−	0.0881643i
$931$	−26.4271	+	8.82266i	−0.866113	+	0.289151i
$932$	71.5279	+	30.4752i	2.34297	+	0.998248i
$933$	−5.76988	+	5.11166i	−0.188897	+	0.167348i
$934$	−15.8727	+	54.7990i	−0.519371	+	1.79308i
$935$	18.7065	+	22.9113i	0.611768	+	0.749280i
$936$	15.9165	+	2.58669i	0.520248	+	0.0845486i
$937$	16.5937	−	17.2759i	0.542094	−	0.564380i	−0.392656	−	0.919685i	$-0.628444\pi$
$937$	16.5937	−	17.2759i	0.542094	−	0.564380i	0.934750	+	0.355306i	$0.115623\pi$
$938$	13.3827	−	3.29855i	0.436962	−	0.107702i
$939$	−3.16261	+	2.37655i	−0.103208	+	0.0775558i
$940$	−52.9154	−	76.6612i	−1.72591	−	2.50041i
$941$	3.39276	+	7.15008i	0.110601	+	0.233086i	0.951202	−	0.308568i	$-0.0998496\pi$
$941$	3.39276	+	7.15008i	0.110601	+	0.233086i	−0.840602	+	0.541654i	$0.817798\pi$
$942$	−6.21812	+	2.64929i	−0.202597	+	0.0863186i
$943$	−8.10885	−	7.18381i	−0.264060	−	0.233937i
$944$	−0.0519451	−	0.00419344i	−0.00169067	−	0.000136485i
$945$	2.14477	+	1.12566i	0.0697695	+	0.0366178i
$946$	−7.26911	+	10.5311i	−0.236339	+	0.342397i
$947$	−6.88232	−	23.7605i	−0.223645	−	0.772113i	−0.991343	−	0.131300i	$-0.958085\pi$
$947$	−6.88232	−	23.7605i	−0.223645	−	0.772113i	0.767697	−	0.640813i	$-0.221402\pi$
$948$	1.79632	+	1.13592i	0.0583417	+	0.0368930i
$949$	−1.58826	+	1.94527i	−0.0515572	+	0.0631461i
$950$	−0.978305	+	24.2764i	−0.0317404	+	0.787630i
$951$	−0.869644	+	1.83274i	−0.0282001	+	0.0594306i
$952$	−3.45552	+	0.561577i	−0.111994	+	0.0182008i
$953$	−30.9028	−	10.3169i	−1.00104	−	0.334196i	−0.231528	−	0.972828i	$-0.574373\pi$
$953$	−30.9028	−	10.3169i	−1.00104	−	0.334196i	−0.769512	+	0.638632i	$0.779501\pi$
$954$	−1.03262	−	3.56501i	−0.0334323	−	0.115422i
$955$	−20.5027	+	21.3455i	−0.663451	+	0.690726i
$956$	−14.2246	+	20.6079i	−0.460057	+	0.666508i
$957$	1.31408	−	1.36810i	0.0424781	−	0.0442244i
$958$	−36.7123	+	38.2215i	−1.18612	+	1.23488i
$959$	−13.6483	+	2.21806i	−0.440726	+	0.0716250i
$960$	−5.19472	+	6.36238i	−0.167659	+	0.205345i
$961$	16.0623	−	23.2703i	0.518140	−	0.750655i
$962$	36.1134	+	31.9937i	1.16434	+	1.03152i
$963$	9.09434	+	13.1754i	0.293061	+	0.424572i
$964$	5.74661	−	5.98286i	0.185086	−	0.192695i
$965$	12.0602	−	41.6368i	0.388233	−	1.34034i
$966$	0.589130	−	0.196680i	0.0189549	−	0.00632809i
$967$	2.87937	+	9.94072i	0.0925942	+	0.319672i	0.993423	−	0.114502i	$-0.0365273\pi$
$967$	2.87937	+	9.94072i	0.0925942	+	0.319672i	−0.900829	+	0.434174i	$0.857040\pi$
$968$	−30.9444	−	53.5973i	−0.994591	−	1.72268i
$969$	1.64786	−	0.864862i	0.0529368	−	0.0277834i
$970$	−61.9282	−	20.6747i	−1.98839	−	0.663824i
$971$	−1.24807	+	2.16172i	−0.0400525	+	0.0693730i	−0.885357	−	0.464912i	$-0.846086\pi$
$971$	−1.24807	+	2.16172i	−0.0400525	+	0.0693730i	0.845304	+	0.534285i	$0.179419\pi$
$972$	−13.8172	−	14.3852i	−0.443187	−	0.461407i
$973$	3.33120	−	0.541373i	0.106794	−	0.0173556i
$974$	18.3228	+	31.7361i	0.587101	+	1.01689i
$975$	−0.220870	+	1.08189i	−0.00707351	+	0.0346483i
$976$	−0.553873	+	1.16726i	−0.0177290	+	0.0373632i
$977$	19.2034	−	33.2613i	0.614373	−	1.06412i	−0.376122	−	0.926570i	$-0.622743\pi$
$977$	19.2034	−	33.2613i	0.614373	−	1.06412i	0.990494	−	0.137554i	$-0.0439241\pi$
$978$	0.970038	+	0.0783096i	0.0310184	+	0.00250406i
$979$	0.405494	−	10.0622i	0.0129597	−	0.321591i
$980$	20.8617	−	55.0079i	0.666404	−	1.75716i
$981$	4.21104	+	2.66290i	0.134448	+	0.0850198i
$982$	33.7496	−	41.3357i	1.07699	−	1.31908i
$983$	1.94529	+	9.52865i	0.0620450	+	0.303917i	0.998958	−	0.0456471i	$-0.0145350\pi$
$983$	1.94529	+	9.52865i	0.0620450	+	0.303917i	−0.936913	+	0.349564i	$0.886330\pi$
$984$	3.93422	+	0.639373i	0.125418	+	0.0203825i
$985$	−13.7258	−	8.67964i	−0.437339	−	0.276556i
$986$	4.31644	+	4.49389i	0.137463	+	0.143115i
$987$	0.881355	+	1.27686i	0.0280538	+	0.0406430i
$988$	−7.26981	−	25.0983i	−0.231283	−	0.798483i
$989$	1.58011	+	0.829308i	0.0502447	+	0.0263705i
$990$	−104.066	−	16.9124i	−3.30743	−	0.537510i
$991$	−29.4775	+	42.7055i	−0.936383	+	1.35659i	−0.00212141	+	0.999998i	$0.500675\pi$
$991$	−29.4775	+	42.7055i	−0.936383	+	1.35659i	−0.934262	+	0.356588i	$0.883940\pi$
$992$	1.71790	+	42.6294i	0.0545435	+	1.35348i
$993$	1.07466	+	2.83365i	0.0341034	+	0.0899233i
$994$	7.94779	+	4.17132i	0.252089	+	0.132306i
$995$	−61.5127	+	4.96582i	−1.95008	+	0.157427i
$996$	−0.635156	+	5.23098i	−0.0201257	+	0.165750i
$997$	2.61175	+	0.210842i	0.0827149	+	0.00667744i	0.121755	−	0.992560i	$-0.461148\pi$
$997$	2.61175	+	0.210842i	0.0827149	+	0.00667744i	−0.0390398	+	0.999238i	$0.512430\pi$
$998$	−11.1394	+	23.4757i	−0.352610	+	0.743110i
$999$	−3.06412	−	15.0091i	−0.0969446	−	0.474866i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.j.a.11.6	✓	1080
547.199	even	39	inner	547.2.j.a.199.6	yes	1080

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.j.a.11.6	✓	1080	1.1	even	1	trivial
547.2.j.a.199.6	yes	1080	547.199	even	39	inner

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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	547.j (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.10961 - 0.898822i) q^{2} -0.232269 q^{3} +(2.25714 + 2.34993i) q^{4} +(2.70427 - 0.439486i) q^{5} +(0.489997 + 0.208768i) q^{6} +(0.511767 + 0.384568i) q^{7} +(-1.02322 - 2.69801i) q^{8} -2.94605 q^{9} +O(q^{10})\)	\(q+(-2.10961 - 0.898822i) q^{2} -0.232269 q^{3} +(2.25714 + 2.34993i) q^{4} +(2.70427 - 0.439486i) q^{5} +(0.489997 + 0.208768i) q^{6} +(0.511767 + 0.384568i) q^{7} +(-1.02322 - 2.69801i) q^{8} -2.94605 q^{9} +(-6.09997 - 1.50351i) q^{10} +(-5.67785 + 0.458363i) q^{11} +(-0.524262 - 0.545815i) q^{12} +(0.948451 - 1.64276i) q^{13} +(-0.733972 - 1.27128i) q^{14} +(-0.628117 + 0.102079i) q^{15} +(-0.00403158 + 0.100043i) q^{16} +(-0.812477 - 1.71226i) q^{17} +(6.21503 + 2.64798i) q^{18} +(-0.170229 - 4.22420i) q^{19} +(7.13665 + 5.36285i) q^{20} +(-0.118867 - 0.0893231i) q^{21} +(12.3900 + 4.13640i) q^{22} +(0.364370 - 1.78480i) q^{23} +(0.237662 + 0.626664i) q^{24} +(2.37722 - 0.793633i) q^{25} +(-3.47742 + 2.61311i) q^{26} +1.38108 q^{27} +(0.251421 + 2.07064i) q^{28} +(1.07318 - 0.950757i) q^{29} +(1.41683 + 0.349218i) q^{30} +(6.81718 - 3.57793i) q^{31} +(-2.37558 + 5.00642i) q^{32} +(1.31879 - 0.106464i) q^{33} +(0.174996 + 4.34248i) q^{34} +(1.55297 + 0.815059i) q^{35} +(-6.64964 - 6.92300i) q^{36} +(-2.21864 - 10.8676i) q^{37} +(-3.43768 + 9.06442i) q^{38} +(-0.220296 + 0.381563i) q^{39} +(-3.95280 - 6.84644i) q^{40} +(2.97354 - 5.15033i) q^{41} +(0.170479 + 0.295278i) q^{42} +(-0.272552 + 0.940958i) q^{43} +(-13.8928 - 12.3079i) q^{44} +(-7.96690 + 1.29475i) q^{45} +(-2.37290 + 3.43774i) q^{46} +(-9.89763 - 3.30432i) q^{47} +(0.000936410 - 0.0232368i) q^{48} +(-1.83351 - 6.33001i) q^{49} +(-5.72835 - 0.462440i) q^{50} +(0.188713 + 0.397704i) q^{51} +(6.00116 - 1.47915i) q^{52} +(-0.347467 - 0.425570i) q^{53} +(-2.91355 - 1.24135i) q^{54} +(-15.1530 + 3.73487i) q^{55} +(0.513918 - 1.77425i) q^{56} +(0.0395390 + 0.981149i) q^{57} +(-3.11856 + 1.04113i) q^{58} +(-0.0209583 + 0.520074i) q^{59} +(-1.65762 - 1.24562i) q^{60} +(11.8715 + 5.05797i) q^{61} +(-17.5975 + 1.42062i) q^{62} +(-1.50769 - 1.13296i) q^{63} +(9.66132 - 8.55918i) q^{64} +(1.84289 - 4.85930i) q^{65} +(-2.87782 - 0.960758i) q^{66} +(-2.61233 + 9.01879i) q^{67} +(2.18981 - 5.77406i) q^{68} +(-0.0846318 + 0.414554i) q^{69} +(-2.54356 - 3.11530i) q^{70} +(-5.16803 + 3.26806i) q^{71} +(3.01446 + 7.94848i) q^{72} +(-1.30675 - 0.212368i) q^{73} +(-5.08758 + 24.9206i) q^{74} +(-0.552154 + 0.184336i) q^{75} +(9.54232 - 9.93461i) q^{76} +(-3.08201 - 1.94894i) q^{77} +(0.807695 - 0.606944i) q^{78} +(-2.72668 + 0.672066i) q^{79} +(0.0330649 + 0.272314i) q^{80} +8.51737 q^{81} +(-10.9023 + 8.19251i) q^{82} +(-4.40348 - 5.39328i) q^{83} +(-0.0583972 - 0.480944i) q^{84} +(-2.94967 - 4.27333i) q^{85} +(1.42073 - 1.74008i) q^{86} +(-0.249267 + 0.220831i) q^{87} +(7.04636 + 14.8499i) q^{88} +(-0.213094 + 1.75499i) q^{89} +(17.9708 + 4.42941i) q^{90} +(1.11714 - 0.475969i) q^{91} +(5.01659 - 3.17230i) q^{92} +(-1.58342 + 0.831042i) q^{93} +(17.9102 + 15.8670i) q^{94} +(-2.31682 - 11.3485i) q^{95} +(0.551773 - 1.16284i) q^{96} +(10.3583 + 0.836210i) q^{97} +(-1.82156 + 15.0019i) q^{98} +(16.7272 - 1.35036i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1080 q - 25 q^{2} - 74 q^{3} + 21 q^{4} - 27 q^{5} - 75 q^{6} - 28 q^{7} + 4 q^{8} + 1010 q^{9}+O(q^{10}) \) 1080 * q - 25 * q^2 - 74 * q^3 + 21 * q^4 - 27 * q^5 - 75 * q^6 - 28 * q^7 + 4 * q^8 + 1010 * q^9	\( 1080 q - 25 q^{2} - 74 q^{3} + 21 q^{4} - 27 q^{5} - 75 q^{6} - 28 q^{7} + 4 q^{8} + 1010 q^{9} - 16 q^{10} - 14 q^{11} - 69 q^{12} - 10 q^{13} - 15 q^{14} - 97 q^{15} + 39 q^{16} - 22 q^{17} - 145 q^{18} - 24 q^{19} - 51 q^{20} - 77 q^{21} - 19 q^{22} - 53 q^{23} - 45 q^{24} + 40 q^{25} - 68 q^{26} - 278 q^{27} - 50 q^{28} + 39 q^{29} + 14 q^{30} - 2 q^{31} - 45 q^{32} - 105 q^{33} - 98 q^{34} - 18 q^{35} - 172 q^{36} - 16 q^{37} - 37 q^{38} + 30 q^{39} - 33 q^{40} + 62 q^{41} + 170 q^{42} + 12 q^{43} - 22 q^{44} - 128 q^{45} + 79 q^{46} - 58 q^{47} - 27 q^{48} + 17 q^{49} - 40 q^{50} - 39 q^{51} + 97 q^{52} + 17 q^{53} - 278 q^{54} + 9 q^{55} + 47 q^{56} - 174 q^{57} - 134 q^{58} - 126 q^{59} - 414 q^{60} - 79 q^{61} + 15 q^{62} - 398 q^{63} - 308 q^{64} + 47 q^{65} - 142 q^{66} + 22 q^{67} + 7 q^{68} - 77 q^{69} + 396 q^{70} - 22 q^{71} - 172 q^{72} + 9 q^{73} - 43 q^{74} - 143 q^{75} + 46 q^{76} + 56 q^{77} - 33 q^{78} + 72 q^{79} + 131 q^{80} + 944 q^{81} + 74 q^{82} + 41 q^{83} - 582 q^{84} - 66 q^{85} + 20 q^{86} - 182 q^{87} - 459 q^{88} - 92 q^{89} - 265 q^{90} + 65 q^{91} + 86 q^{92} - 28 q^{93} - 17 q^{94} + 37 q^{95} - 70 q^{96} + 91 q^{97} + 139 q^{98} - 237 q^{99}+O(q^{100}) \) 1080 * q - 25 * q^2 - 74 * q^3 + 21 * q^4 - 27 * q^5 - 75 * q^6 - 28 * q^7 + 4 * q^8 + 1010 * q^9 - 16 * q^10 - 14 * q^11 - 69 * q^12 - 10 * q^13 - 15 * q^14 - 97 * q^15 + 39 * q^16 - 22 * q^17 - 145 * q^18 - 24 * q^19 - 51 * q^20 - 77 * q^21 - 19 * q^22 - 53 * q^23 - 45 * q^24 + 40 * q^25 - 68 * q^26 - 278 * q^27 - 50 * q^28 + 39 * q^29 + 14 * q^30 - 2 * q^31 - 45 * q^32 - 105 * q^33 - 98 * q^34 - 18 * q^35 - 172 * q^36 - 16 * q^37 - 37 * q^38 + 30 * q^39 - 33 * q^40 + 62 * q^41 + 170 * q^42 + 12 * q^43 - 22 * q^44 - 128 * q^45 + 79 * q^46 - 58 * q^47 - 27 * q^48 + 17 * q^49 - 40 * q^50 - 39 * q^51 + 97 * q^52 + 17 * q^53 - 278 * q^54 + 9 * q^55 + 47 * q^56 - 174 * q^57 - 134 * q^58 - 126 * q^59 - 414 * q^60 - 79 * q^61 + 15 * q^62 - 398 * q^63 - 308 * q^64 + 47 * q^65 - 142 * q^66 + 22 * q^67 + 7 * q^68 - 77 * q^69 + 396 * q^70 - 22 * q^71 - 172 * q^72 + 9 * q^73 - 43 * q^74 - 143 * q^75 + 46 * q^76 + 56 * q^77 - 33 * q^78 + 72 * q^79 + 131 * q^80 + 944 * q^81 + 74 * q^82 + 41 * q^83 - 582 * q^84 - 66 * q^85 + 20 * q^86 - 182 * q^87 - 459 * q^88 - 92 * q^89 - 265 * q^90 + 65 * q^91 + 86 * q^92 - 28 * q^93 - 17 * q^94 + 37 * q^95 - 70 * q^96 + 91 * q^97 + 139 * q^98 - 237 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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