LMFDB - Embedded newform 671.2.f.a.538.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(538,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("671.538");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.f (of order $4$, degree $2$, 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:	$5.35796197563$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$60$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			538.18
Character	$\chi$	$=$	671.538
Dual form			671.2.f.a.560.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.777546 - 0.777546i) q^{2} +0.433435i q^{3} -0.790844i q^{4} +3.54542i q^{5} +(0.337016 - 0.337016i) q^{6} +(-2.52725 - 2.52725i) q^{7} +(-2.17001 + 2.17001i) q^{8} +2.81213 q^{9} +O(q^{10})$	\(q+(-0.777546 - 0.777546i) q^{2} +0.433435i q^{3} -0.790844i q^{4} +3.54542i q^{5} +(0.337016 - 0.337016i) q^{6} +(-2.52725 - 2.52725i) q^{7} +(-2.17001 + 2.17001i) q^{8} +2.81213 q^{9} +(2.75673 - 2.75673i) q^{10} +(-2.85197 - 1.69300i) q^{11} +0.342780 q^{12} +0.973971i q^{13} +3.93010i q^{14} -1.53671 q^{15} +1.79288 q^{16} +(5.41782 - 5.41782i) q^{17} +(-2.18656 - 2.18656i) q^{18} +0.847071 q^{19} +2.80388 q^{20} +(1.09540 - 1.09540i) q^{21} +(0.901150 + 3.53393i) q^{22} +(6.21575 - 6.21575i) q^{23} +(-0.940559 - 0.940559i) q^{24} -7.57002 q^{25} +(0.757307 - 0.757307i) q^{26} +2.51918i q^{27} +(-1.99866 + 1.99866i) q^{28} +(2.05058 - 2.05058i) q^{29} +(1.19486 + 1.19486i) q^{30} +(6.90885 + 6.90885i) q^{31} +(2.94598 + 2.94598i) q^{32} +(0.733808 - 1.23614i) q^{33} -8.42521 q^{34} +(8.96016 - 8.96016i) q^{35} -2.22396i q^{36} +(-1.44419 - 1.44419i) q^{37} +(-0.658637 - 0.658637i) q^{38} -0.422153 q^{39} +(-7.69360 - 7.69360i) q^{40} +5.04616 q^{41} -1.70345 q^{42} +(4.57281 - 4.57281i) q^{43} +(-1.33890 + 2.25546i) q^{44} +9.97020i q^{45} -9.66607 q^{46} +2.56969 q^{47} +0.777096i q^{48} +5.77396i q^{49} +(5.88604 + 5.88604i) q^{50} +(2.34827 + 2.34827i) q^{51} +0.770259 q^{52} +(2.80698 - 2.80698i) q^{53} +(1.95878 - 1.95878i) q^{54} +(6.00241 - 10.1114i) q^{55} +10.9683 q^{56} +0.367150i q^{57} -3.18884 q^{58} +(-3.35630 - 3.35630i) q^{59} +1.21530i q^{60} +(-6.43954 + 4.41954i) q^{61} -10.7439i q^{62} +(-7.10696 - 7.10696i) q^{63} -8.16702i q^{64} -3.45314 q^{65} +(-1.53173 + 0.390590i) q^{66} +(-8.80214 - 8.80214i) q^{67} +(-4.28465 - 4.28465i) q^{68} +(2.69413 + 2.69413i) q^{69} -13.9339 q^{70} +(-2.49098 - 2.49098i) q^{71} +(-6.10236 + 6.10236i) q^{72} +13.5059i q^{73} +2.24585i q^{74} -3.28111i q^{75} -0.669901i q^{76} +(2.92900 + 11.4863i) q^{77} +(0.328244 + 0.328244i) q^{78} +(-10.0303 - 10.0303i) q^{79} +6.35651i q^{80} +7.34450 q^{81} +(-3.92362 - 3.92362i) q^{82} -8.80475i q^{83} +(-0.866289 - 0.866289i) q^{84} +(19.2085 + 19.2085i) q^{85} -7.11115 q^{86} +(0.888793 + 0.888793i) q^{87} +(9.86264 - 2.51497i) q^{88} +(-1.16800 - 1.16800i) q^{89} +(7.75229 - 7.75229i) q^{90} +(2.46147 - 2.46147i) q^{91} +(-4.91569 - 4.91569i) q^{92} +(-2.99454 + 2.99454i) q^{93} +(-1.99805 - 1.99805i) q^{94} +3.00322i q^{95} +(-1.27689 + 1.27689i) q^{96} -11.1938i q^{97} +(4.48952 - 4.48952i) q^{98} +(-8.02012 - 4.76095i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 120 q^{9}+O(q^{10}) $ 120 * q - 120 * q^9	$ 120 q - 120 q^{9} - 4 q^{11} + 16 q^{12} + 16 q^{15} - 148 q^{16} + 56 q^{20} - 4 q^{22} - 4 q^{23} - 104 q^{25} + 40 q^{26} - 2 q^{33} - 8 q^{34} - 12 q^{37} + 20 q^{38} + 16 q^{42} - 10 q^{44} - 4 q^{53} + 50 q^{55} - 24 q^{56} + 64 q^{58} - 56 q^{67} + 68 q^{69} + 144 q^{70} - 12 q^{71} - 64 q^{77} + 84 q^{78} + 72 q^{81} + 40 q^{82} - 80 q^{86} + 4 q^{89} - 4 q^{91} + 4 q^{92} + 64 q^{93} + 24 q^{99}+O(q^{100}) $ 120 * q - 120 * q^9 - 4 * q^11 + 16 * q^12 + 16 * q^15 - 148 * q^16 + 56 * q^20 - 4 * q^22 - 4 * q^23 - 104 * q^25 + 40 * q^26 - 2 * q^33 - 8 * q^34 - 12 * q^37 + 20 * q^38 + 16 * q^42 - 10 * q^44 - 4 * q^53 + 50 * q^55 - 24 * q^56 + 64 * q^58 - 56 * q^67 + 68 * q^69 + 144 * q^70 - 12 * q^71 - 64 * q^77 + 84 * q^78 + 72 * q^81 + 40 * q^82 - 80 * q^86 + 4 * q^89 - 4 * q^91 + 4 * q^92 + 64 * q^93 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/671\mathbb{Z}\right)^\times$.

$n$	$123$	$551$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.777546	−	0.777546i	−0.549808	−	0.549808i	0.376577	−	0.926385i	$-0.377101\pi$
$2$	−0.777546	−	0.777546i	−0.549808	−	0.549808i	−0.926385	+	0.376577i	$0.877101\pi$
$3$			0.433435i			0.250244i	0.992141	+	0.125122i	$0.0399322\pi$
$3$			0.433435i			0.250244i	−0.992141	+	0.125122i	$0.960068\pi$
$4$		−	0.790844i		−	0.395422i
$5$			3.54542i			1.58556i	0.609507	+	0.792781i	$0.291367\pi$
$5$			3.54542i			1.58556i	−0.609507	+	0.792781i	$0.708633\pi$
$6$	0.337016	−	0.337016i	0.137586	−	0.137586i
$7$	−2.52725	−	2.52725i	−0.955210	−	0.955210i	0.0438292	−	0.999039i	$-0.486044\pi$
$7$	−2.52725	−	2.52725i	−0.955210	−	0.955210i	−0.999039	+	0.0438292i	$0.986044\pi$
$8$	−2.17001	+	2.17001i	−0.767214	+	0.767214i
$9$	2.81213			0.937378
$10$	2.75673	−	2.75673i	0.871754	−	0.871754i
$11$	−2.85197	−	1.69300i	−0.859902	−	0.510460i
$11$	−2.85197	−	1.69300i	−0.859902	−	0.510460i
$12$	0.342780			0.0989520
$13$			0.973971i			0.270131i	0.990837	+	0.135065i	$0.0431245\pi$
$13$			0.973971i			0.270131i	−0.990837	+	0.135065i	$0.956876\pi$
$14$			3.93010i			1.05036i
$15$	−1.53671			−0.396777
$16$	1.79288			0.448219
$17$	5.41782	−	5.41782i	1.31401	−	1.31401i	0.395585	−	0.918429i	$-0.370542\pi$
$17$	5.41782	−	5.41782i	1.31401	−	1.31401i	0.918429	−	0.395585i	$-0.129458\pi$
$18$	−2.18656	−	2.18656i	−0.515378	−	0.515378i
$19$	0.847071			0.194331			0.0971657	−	0.995268i	$-0.469022\pi$
$19$	0.847071			0.194331			0.0971657	+	0.995268i	$0.469022\pi$
$20$	2.80388			0.626966
$21$	1.09540	−	1.09540i	0.239036	−	0.239036i
$22$	0.901150	+	3.53393i	0.192126	+	0.753436i
$23$	6.21575	−	6.21575i	1.29607	−	1.29607i	0.365110	−	0.930964i	$-0.381031\pi$
$23$	6.21575	−	6.21575i	1.29607	−	1.29607i	0.930964	−	0.365110i	$-0.118969\pi$
$24$	−0.940559	−	0.940559i	−0.191991	−	0.191991i
$25$	−7.57002			−1.51400
$26$	0.757307	−	0.757307i	0.148520	−	0.148520i
$27$			2.51918i			0.484817i
$28$	−1.99866	+	1.99866i	−0.377711	+	0.377711i
$29$	2.05058	−	2.05058i	0.380783	−	0.380783i	−0.490601	−	0.871384i	$-0.663223\pi$
$29$	2.05058	−	2.05058i	0.380783	−	0.380783i	0.871384	+	0.490601i	$0.163223\pi$
$30$	1.19486	+	1.19486i	0.218151	+	0.218151i
$31$	6.90885	+	6.90885i	1.24087	+	1.24087i	0.959642	+	0.281224i	$0.0907403\pi$
$31$	6.90885	+	6.90885i	1.24087	+	1.24087i	0.281224	+	0.959642i	$0.409260\pi$
$32$	2.94598	+	2.94598i	0.520780	+	0.520780i
$33$	0.733808	−	1.23614i	0.127740	−	0.215185i
$34$	−8.42521			−1.44491
$35$	8.96016	−	8.96016i	1.51454	−	1.51454i
$36$		−	2.22396i		−	0.370660i
$37$	−1.44419	−	1.44419i	−0.237424	−	0.237424i	0.578359	−	0.815783i	$-0.303693\pi$
$37$	−1.44419	−	1.44419i	−0.237424	−	0.237424i	−0.815783	+	0.578359i	$0.803693\pi$
$38$	−0.658637	−	0.658637i	−0.106845	−	0.106845i
$39$	−0.422153			−0.0675987
$40$	−7.69360	−	7.69360i	−1.21647	−	1.21647i
$41$	5.04616			0.788078			0.394039	−	0.919094i	$-0.371077\pi$
$41$	5.04616			0.788078			0.394039	+	0.919094i	$0.371077\pi$
$42$	−1.70345			−0.262847
$43$	4.57281	−	4.57281i	0.697348	−	0.697348i	−0.266490	−	0.963838i	$-0.585864\pi$
$43$	4.57281	−	4.57281i	0.697348	−	0.697348i	0.963838	+	0.266490i	$0.0858639\pi$
$44$	−1.33890	+	2.25546i	−0.201847	+	0.340024i
$45$			9.97020i			1.48627i
$46$	−9.66607			−1.42518
$47$	2.56969			0.374827			0.187414	−	0.982281i	$-0.439990\pi$
$47$	2.56969			0.374827			0.187414	+	0.982281i	$0.439990\pi$
$48$			0.777096i			0.112164i
$49$			5.77396i			0.824852i
$50$	5.88604	+	5.88604i	0.832412	+	0.832412i
$51$	2.34827	+	2.34827i	0.328824	+	0.328824i
$52$	0.770259			0.106816
$53$	2.80698	−	2.80698i	0.385569	−	0.385569i	−0.487535	−	0.873104i	$-0.662104\pi$
$53$	2.80698	−	2.80698i	0.385569	−	0.385569i	0.873104	+	0.487535i	$0.162104\pi$
$54$	1.95878	−	1.95878i	0.266556	−	0.266556i
$55$	6.00241	−	10.1114i	0.809365	−	1.36343i
$56$	10.9683			1.46570
$57$			0.367150i			0.0486303i
$58$	−3.18884			−0.418715
$59$	−3.35630	−	3.35630i	−0.436953	−	0.436953i	0.454033	−	0.890985i	$-0.349985\pi$
$59$	−3.35630	−	3.35630i	−0.436953	−	0.436953i	−0.890985	+	0.454033i	$0.849985\pi$
$60$			1.21530i			0.156894i
$61$	−6.43954	+	4.41954i	−0.824499	+	0.565864i
$61$	−6.43954	+	4.41954i	−0.824499	+	0.565864i
$62$		−	10.7439i		−	1.36448i
$63$	−7.10696	−	7.10696i	−0.895393	−	0.895393i
$64$		−	8.16702i		−	1.02088i
$65$	−3.45314			−0.428309
$66$	−1.53173	+	0.390590i	−0.188543	+	0.0480783i
$67$	−8.80214	−	8.80214i	−1.07535	−	1.07535i	−0.996919	−	0.0784326i	$-0.975008\pi$
$67$	−8.80214	−	8.80214i	−1.07535	−	1.07535i	−0.0784326	−	0.996919i	$-0.524992\pi$
$68$	−4.28465	−	4.28465i	−0.519590	−	0.519590i
$69$	2.69413	+	2.69413i	0.324335	+	0.324335i
$70$	−13.9339			−1.66542
$71$	−2.49098	−	2.49098i	−0.295625	−	0.295625i	0.543673	−	0.839297i	$-0.317033\pi$
$71$	−2.49098	−	2.49098i	−0.295625	−	0.295625i	−0.839297	+	0.543673i	$0.817033\pi$
$72$	−6.10236	+	6.10236i	−0.719170	+	0.719170i
$73$			13.5059i			1.58075i	0.612622	+	0.790376i	$0.290115\pi$
$73$			13.5059i			1.58075i	−0.612622	+	0.790376i	$0.709885\pi$
$74$			2.24585i			0.261075i
$75$		−	3.28111i		−	0.378870i
$76$		−	0.669901i		−	0.0768429i
$77$	2.92900	+	11.4863i	0.333790	+	1.30898i
$78$	0.328244	+	0.328244i	0.0371663	+	0.0371663i
$79$	−10.0303	−	10.0303i	−1.12849	−	1.12849i	−0.990422	−	0.138072i	$-0.955909\pi$
$79$	−10.0303	−	10.0303i	−1.12849	−	1.12849i	−0.138072	−	0.990422i	$-0.544091\pi$
$80$			6.35651i			0.710679i
$81$	7.34450			0.816055
$82$	−3.92362	−	3.92362i	−0.433292	−	0.433292i
$83$		−	8.80475i		−	0.966447i	−0.875497	−	0.483223i	$-0.839466\pi$
$83$		−	8.80475i		−	0.966447i	0.875497	−	0.483223i	$-0.160534\pi$
$84$	−0.866289	−	0.866289i	−0.0945199	−	0.0945199i
$85$	19.2085	+	19.2085i	2.08345	+	2.08345i
$86$	−7.11115			−0.766815
$87$	0.888793	+	0.888793i	0.0952886	+	0.0952886i
$88$	9.86264	−	2.51497i	1.05136	−	0.268097i
$89$	−1.16800	−	1.16800i	−0.123807	−	0.123807i	0.642488	−	0.766296i	$-0.277902\pi$
$89$	−1.16800	−	1.16800i	−0.123807	−	0.123807i	−0.766296	+	0.642488i	$0.777902\pi$
$90$	7.75229	−	7.75229i	0.817163	−	0.817163i
$91$	2.46147	−	2.46147i	0.258032	−	0.258032i
$92$	−4.91569	−	4.91569i	−0.512496	−	0.512496i
$93$	−2.99454	+	2.99454i	−0.310519	+	0.310519i
$94$	−1.99805	−	1.99805i	−0.206083	−	0.206083i
$95$			3.00322i			0.308124i
$96$	−1.27689	+	1.27689i	−0.130322	+	0.130322i
$97$		−	11.1938i		−	1.13656i	−0.822837	−	0.568278i	$-0.807610\pi$
$97$		−	11.1938i		−	1.13656i	0.822837	−	0.568278i	$-0.192390\pi$
$98$	4.48952	−	4.48952i	0.453510	−	0.453510i
$99$	−8.02012	−	4.76095i	−0.806053	−	0.478494i
$100$			5.98671i			0.598671i
$101$	7.75975	+	7.75975i	0.772124	+	0.772124i	0.978478	−	0.206353i	$-0.0661596\pi$
$101$	7.75975	+	7.75975i	0.772124	+	0.772124i	−0.206353	+	0.978478i	$0.566160\pi$
$102$		−	3.65178i		−	0.361580i
$103$	11.3788			1.12118			0.560592	−	0.828092i	$-0.310573\pi$
$103$	11.3788			1.12118			0.560592	+	0.828092i	$0.310573\pi$
$104$	−2.11353	−	2.11353i	−0.207248	−	0.207248i
$105$	3.88365	+	3.88365i	0.379005	+	0.379005i
$106$	−4.36512			−0.423978
$107$	9.62800			0.930774			0.465387	−	0.885107i	$-0.345915\pi$
$107$	9.62800			0.930774			0.465387	+	0.885107i	$0.345915\pi$
$108$	1.99228			0.191707
$109$	−11.6284			−1.11380			−0.556902	−	0.830579i	$-0.688010\pi$
$109$	−11.6284			−1.11380			−0.556902	+	0.830579i	$0.688010\pi$
$110$	−12.5293	+	3.19496i	−1.19462	+	0.304627i
$111$	0.625964	−	0.625964i	0.0594139	−	0.0594139i
$112$	−4.53105	−	4.53105i	−0.428144	−	0.428144i
$113$		−	5.67566i		−	0.533921i	−0.963707	−	0.266961i	$-0.913981\pi$
$113$		−	5.67566i		−	0.533921i	0.963707	−	0.266961i	$-0.0860193\pi$
$114$	0.285476	−	0.285476i	0.0267373	−	0.0267373i
$115$	22.0375	+	22.0375i	2.05501	+	2.05501i
$116$	−1.62169	−	1.62169i	−0.150570	−	0.150570i
$117$			2.73894i			0.253215i
$118$			5.21935i			0.480480i
$119$	−27.3843			−2.51032
$120$	3.33468	−	3.33468i	0.304413	−	0.304413i
$121$	5.26748	+	9.65680i	0.478861	+	0.877890i
$122$	8.44343	+	1.57065i	0.764433	+	0.142200i
$123$			2.18718i			0.197212i
$124$	5.46382	−	5.46382i	0.490666	−	0.490666i
$125$		−	9.11181i		−	0.814985i
$126$			11.0520i			0.984588i
$127$	5.61449			0.498205			0.249103	−	0.968477i	$-0.419864\pi$
$127$	5.61449			0.498205			0.249103	+	0.968477i	$0.419864\pi$
$128$	−0.458282	+	0.458282i	−0.0405068	+	0.0405068i
$129$	1.98202	+	1.98202i	0.174507	+	0.174507i
$130$	2.68497	+	2.68497i	0.235488	+	0.235488i
$131$			17.0743i			1.49179i	0.666062	+	0.745896i	$0.267978\pi$
$131$			17.0743i			1.49179i	−0.666062	+	0.745896i	$0.732022\pi$
$132$	−0.977598	−	0.580327i	−0.0850890	−	0.0505110i
$133$	−2.14076	−	2.14076i	−0.185627	−	0.185627i
$134$			13.6881i			1.18247i
$135$	−8.93157			−0.768707
$136$			23.5134i			2.01626i
$137$	−16.0382			−1.37024			−0.685118	−	0.728432i	$-0.740249\pi$
$137$	−16.0382			−1.37024			−0.685118	+	0.728432i	$0.740249\pi$
$138$		−	4.18962i		−	0.356644i
$139$	−8.89261	+	8.89261i	−0.754261	+	0.754261i	−0.975271	−	0.221010i	$-0.929065\pi$
$139$	−8.89261	+	8.89261i	−0.754261	+	0.754261i	0.221010	+	0.975271i	$0.429065\pi$
$140$	−7.08609	−	7.08609i	−0.598884	−	0.598884i
$141$			1.11379i			0.0937983i
$142$			3.87370i			0.325074i
$143$	1.64894	−	2.77774i	0.137891	−	0.232286i
$144$	5.04181			0.420151
$145$	7.27017	+	7.27017i	0.603755	+	0.603755i
$146$	10.5015	−	10.5015i	0.869110	−	0.869110i
$147$	−2.50264			−0.206414
$148$	−1.14213	+	1.14213i	−0.0938827	+	0.0938827i
$149$	−9.45179			−0.774320			−0.387160	−	0.922012i	$-0.626544\pi$
$149$	−9.45179			−0.774320			−0.387160	+	0.922012i	$0.626544\pi$
$150$	−2.55122	+	2.55122i	−0.208306	+	0.208306i
$151$	−6.46132	+	6.46132i	−0.525815	+	0.525815i	−0.919322	−	0.393507i	$-0.871262\pi$
$151$	−6.46132	+	6.46132i	−0.525815	+	0.525815i	0.393507	+	0.919322i	$0.371262\pi$
$152$	−1.83815	+	1.83815i	−0.149094	+	0.149094i
$153$	15.2356	−	15.2356i	1.23173	−	1.23173i
$154$	6.65368	−	11.2085i	0.536169	−	0.903210i
$155$	−24.4948	+	24.4948i	−1.96747	+	1.96747i
$156$			0.333858i			0.0267300i
$157$	1.90683	+	1.90683i	0.152181	+	0.152181i	0.779091	−	0.626910i	$-0.215681\pi$
$157$	1.90683	+	1.90683i	0.152181	+	0.152181i	−0.626910	+	0.779091i	$0.715681\pi$
$158$			15.5980i			1.24091i
$159$	1.21665	+	1.21665i	0.0964862	+	0.0964862i
$160$	−10.4447	+	10.4447i	−0.825728	+	0.825728i
$161$	−31.4175			−2.47605
$162$	−5.71069	−	5.71069i	−0.448674	−	0.448674i
$163$		−	14.3658i		−	1.12522i	−0.826723	−	0.562608i	$-0.809798\pi$
$163$		−	14.3658i		−	1.12522i	0.826723	−	0.562608i	$-0.190202\pi$
$164$		−	3.99073i		−	0.311623i
$165$	4.38266	+	2.60166i	0.341189	+	0.202539i
$166$	−6.84610	+	6.84610i	−0.531360	+	0.531360i
$167$	15.2473			1.17987			0.589935	−	0.807451i	$-0.299153\pi$
$167$	15.2473			1.17987			0.589935	+	0.807451i	$0.299153\pi$
$168$			4.75405i			0.366783i
$169$	12.0514			0.927029
$170$		−	29.8709i		−	2.29100i
$171$	2.38208			0.182162
$172$	−3.61638	−	3.61638i	−0.275747	−	0.275747i
$173$	4.76846	+	4.76846i	0.362539	+	0.362539i	0.864747	−	0.502208i	$-0.167479\pi$
$173$	4.76846	+	4.76846i	0.362539	+	0.362539i	−0.502208	+	0.864747i	$0.667479\pi$
$174$		−	1.38216i		−	0.104781i
$175$	19.1313	+	19.1313i	1.44619	+	1.44619i
$176$	−5.11323	−	3.03535i	−0.385425	−	0.228798i
$177$	1.45474	−	1.45474i	0.109345	−	0.109345i
$178$			1.81634i			0.136141i
$179$	7.93669			0.593216			0.296608	−	0.954999i	$-0.404144\pi$
$179$	7.93669			0.593216			0.296608	+	0.954999i	$0.404144\pi$
$180$	7.88488			0.587704
$181$	9.74313	+	9.74313i	0.724201	+	0.724201i	0.969458	−	0.245257i	$-0.0788724\pi$
$181$	9.74313	+	9.74313i	0.724201	+	0.724201i	−0.245257	+	0.969458i	$0.578872\pi$
$182$	−3.82781			−0.283736
$183$	−1.91558	−	2.79112i	−0.141604	−	0.206326i
$184$			26.9765i			1.98873i
$185$	5.12028	−	5.12028i	0.376450	−	0.376450i
$186$	4.65678			0.341452
$187$	−24.6239	+	6.27908i	−1.80067	+	0.459171i
$188$		−	2.03222i		−	0.148215i
$189$	6.36660	−	6.36660i	0.463102	−	0.463102i
$190$	2.33515	−	2.33515i	0.169409	−	0.169409i
$191$	11.1137	+	11.1137i	0.804159	+	0.804159i	0.983743	−	0.179584i	$-0.0574751\pi$
$191$	11.1137	+	11.1137i	0.804159	+	0.804159i	−0.179584	+	0.983743i	$0.557475\pi$
$192$	3.53987			0.255468
$193$	−15.3973	+	15.3973i	−1.10832	+	1.10832i	−0.114948	+	0.993372i	$0.536670\pi$
$193$	−15.3973	+	15.3973i	−1.10832	+	1.10832i	−0.993372	+	0.114948i	$0.963330\pi$
$194$	−8.70368	+	8.70368i	−0.624888	+	0.624888i
$195$		−	1.49671i		−	0.107182i
$196$	4.56630			0.326165
$197$	3.22360			0.229672			0.114836	−	0.993384i	$-0.463366\pi$
$197$	3.22360			0.229672			0.114836	+	0.993384i	$0.463366\pi$
$198$	2.53416	+	9.93788i	0.180095	+	0.706254i
$199$	−15.9542			−1.13096			−0.565482	−	0.824761i	$-0.691310\pi$
$199$	−15.9542			−1.13096			−0.565482	+	0.824761i	$0.691310\pi$
$200$	16.4270	−	16.4270i	1.16157	−	1.16157i
$201$	3.81516	−	3.81516i	0.269100	−	0.269100i
$202$		−	12.0671i		−	0.849040i
$203$	−10.3646			−0.727455
$204$	1.85712	−	1.85712i	0.130024	−	0.130024i
$205$			17.8908i			1.24955i
$206$	−8.84753	−	8.84753i	−0.616436	−	0.616436i
$207$	17.4795	−	17.4795i	1.21491	−	1.21491i
$208$			1.74621i			0.121078i
$209$	−2.41582	−	1.43409i	−0.167106	−	0.0991984i
$210$		−	6.03943i		−	0.416761i
$211$	11.2150	−	11.2150i	0.772072	−	0.772072i	−0.206397	−	0.978468i	$-0.566174\pi$
$211$	11.2150	−	11.2150i	0.772072	−	0.772072i	0.978468	+	0.206397i	$0.0661738\pi$
$212$	−2.21989	−	2.21989i	−0.152462	−	0.152462i
$213$	1.07968	−	1.07968i	0.0739783	−	0.0739783i
$214$	−7.48621	−	7.48621i	−0.511747	−	0.511747i
$215$	16.2126	+	16.2126i	1.10569	+	1.10569i
$216$	−5.46665	−	5.46665i	−0.371959	−	0.371959i
$217$		−	34.9207i		−	2.37057i
$218$	9.04165	+	9.04165i	0.612378	+	0.612378i
$219$	−5.85395			−0.395574
$220$	−7.99657	−	4.74697i	−0.539129	−	0.320041i
$221$	5.27680	+	5.27680i	0.354956	+	0.354956i
$222$	−0.973432			−0.0653325
$223$	1.90774	−	1.90774i	0.127752	−	0.127752i	−0.640340	−	0.768092i	$-0.721206\pi$
$223$	1.90774	−	1.90774i	0.127752	−	0.127752i	0.768092	+	0.640340i	$0.221206\pi$
$224$		−	14.8904i		−	0.994908i
$225$	−21.2879			−1.41919
$226$	−4.41309	+	4.41309i	−0.293554	+	0.293554i
$227$	−6.67850	−	6.67850i	−0.443268	−	0.443268i	0.449841	−	0.893109i	$-0.351481\pi$
$227$	−6.67850	−	6.67850i	−0.443268	−	0.443268i	−0.893109	+	0.449841i	$0.851481\pi$
$228$	0.290359			0.0192295
$229$			18.2953i			1.20899i	0.796610	+	0.604493i	$0.206624\pi$
$229$			18.2953i			1.20899i	−0.796610	+	0.604493i	$0.793376\pi$
$230$		−	34.2703i		−	2.25972i
$231$	−4.97856	+	1.26953i	−0.327565	+	0.0835290i
$232$			8.89955i			0.584284i
$233$	0.0686479	+	0.0686479i	0.00449728	+	0.00449728i	0.709352	−	0.704855i	$-0.248988\pi$
$233$	0.0686479	+	0.0686479i	0.00449728	+	0.00449728i	−0.704855	+	0.709352i	$0.748988\pi$
$234$	2.12965	−	2.12965i	0.139220	−	0.139220i
$235$			9.11063i			0.594312i
$236$	−2.65431	+	2.65431i	−0.172781	+	0.172781i
$237$	4.34748	−	4.34748i	0.282399	−	0.282399i
$238$	21.2926	+	21.2926i	1.38019	+	1.38019i
$239$		−	28.7317i		−	1.85850i	−0.369453	−	0.929249i	$-0.620455\pi$
$239$		−	28.7317i		−	1.85850i	0.369453	−	0.929249i	$-0.379545\pi$
$240$	−2.75513			−0.177843
$241$		−	26.0865i		−	1.68038i	−0.542291	−	0.840191i	$-0.682443\pi$
$241$		−	26.0865i		−	1.68038i	0.542291	−	0.840191i	$-0.317557\pi$
$242$	3.41290	−	11.6043i	0.219389	−	0.745953i
$243$			10.7409i			0.689030i
$244$	3.49516	+	5.09267i	0.223755	+	0.326025i
$245$	−20.4711			−1.30785
$246$	1.70064	−	1.70064i	0.108429	−	0.108429i
$247$			0.825023i			0.0524949i
$248$	−29.9845			−1.90402
$249$	3.81629			0.241847
$250$	−7.08485	+	7.08485i	−0.448085	+	0.448085i
$251$	−7.12199	+	7.12199i	−0.449536	+	0.449536i	−0.895200	−	0.445664i	$-0.852967\pi$
$251$	−7.12199	+	7.12199i	−0.449536	+	0.449536i	0.445664	+	0.895200i	$0.352967\pi$
$252$	−5.62050	+	5.62050i	−0.354058	+	0.354058i
$253$	−28.2504	+	7.20385i	−1.77609	+	0.452902i
$254$	−4.36552	−	4.36552i	−0.273917	−	0.273917i
$255$	−8.32563	+	8.32563i	−0.521371	+	0.521371i
$256$	−15.6214			−0.976335
$257$	11.6850			0.728888			0.364444	−	0.931225i	$-0.381259\pi$
$257$	11.6850			0.728888			0.364444	+	0.931225i	$0.381259\pi$
$258$		−	3.08222i		−	0.191891i
$259$			7.29967i			0.453579i
$260$			2.73089i			0.169363i
$261$	5.76650	−	5.76650i	0.356937	−	0.356937i
$262$	13.2761	−	13.2761i	0.820199	−	0.820199i
$263$	8.75927			0.540120			0.270060	−	0.962844i	$-0.412957\pi$
$263$	8.75927			0.540120			0.270060	+	0.962844i	$0.412957\pi$
$264$	1.09008	+	4.27482i	0.0670896	+	0.263097i
$265$	9.95194	+	9.95194i	0.611343	+	0.611343i
$266$			3.32908i			0.204119i
$267$	0.506251	−	0.506251i	0.0309821	−	0.0309821i
$268$	−6.96112	+	6.96112i	−0.425218	+	0.425218i
$269$	−7.07378			−0.431296			−0.215648	−	0.976471i	$-0.569186\pi$
$269$	−7.07378			−0.431296			−0.215648	+	0.976471i	$0.569186\pi$
$270$	6.94471	+	6.94471i	0.422641	+	0.422641i
$271$	4.06135			0.246710			0.123355	−	0.992363i	$-0.460635\pi$
$271$	4.06135			0.246710			0.123355	+	0.992363i	$0.460635\pi$
$272$	9.71349	−	9.71349i	0.588967	−	0.588967i
$273$	1.06689	+	1.06689i	0.0645709	+	0.0645709i
$274$	12.4704	+	12.4704i	0.753367	+	0.753367i
$275$	21.5895	+	12.8161i	1.30189	+	0.772838i
$276$	2.13063	−	2.13063i	0.128249	−	0.128249i
$277$	4.60771	+	4.60771i	0.276851	+	0.276851i	0.831850	−	0.555000i	$-0.187282\pi$
$277$	4.60771	+	4.60771i	0.276851	+	0.276851i	−0.555000	+	0.831850i	$0.687282\pi$
$278$	13.8288			0.829398
$279$	19.4286	+	19.4286i	1.16316	+	1.16316i
$280$			38.8873i			2.32396i
$281$	−0.0142974	+	0.0142974i	−0.000852913	+	0.000852913i	−0.707533	−	0.706680i	$-0.750192\pi$
$281$	−0.0142974	+	0.0142974i	−0.000852913	+	0.000852913i	0.706680	+	0.707533i	$0.250192\pi$
$282$	0.866025	−	0.866025i	0.0515711	−	0.0515711i
$283$	−0.532795			−0.0316714			−0.0158357	−	0.999875i	$-0.505041\pi$
$283$	−0.532795			−0.0316714			−0.0158357	+	0.999875i	$0.505041\pi$
$284$	−1.96997	+	1.96997i	−0.116896	+	0.116896i
$285$	−1.30170			−0.0771063
$286$	−3.44194	+	0.877694i	−0.203526	+	0.0518992i
$287$	−12.7529	−	12.7529i	−0.752780	−	0.752780i
$288$	8.28448	+	8.28448i	0.488167	+	0.488167i
$289$		−	41.7056i		−	2.45327i
$290$		−	11.3058i		−	0.663898i
$291$	4.85178			0.284416
$292$	10.6811			0.625064
$293$	19.8287			1.15841			0.579204	−	0.815183i	$-0.303364\pi$
$293$	19.8287			1.15841			0.579204	+	0.815183i	$0.303364\pi$
$294$	1.94592	+	1.94592i	0.113488	+	0.113488i
$295$	11.8995	−	11.8995i	0.692815	−	0.692815i
$296$	6.26783			0.364310
$297$	4.26499	−	7.18464i	0.247480	−	0.416895i
$298$	7.34920	+	7.34920i	0.425728	+	0.425728i
$299$	6.05397	+	6.05397i	0.350110	+	0.350110i
$300$	−2.59485			−0.149814
$301$	−23.1133			−1.33223
$302$	10.0479			0.578194
$303$	−3.36335	+	3.36335i	−0.193219	+	0.193219i
$304$	1.51869			0.0871031
$305$	−15.6691	−	22.8309i	−0.897211	−	1.30729i
$306$	−23.6928			−1.35443
$307$	−15.4245	−	15.4245i	−0.880325	−	0.880325i	0.113243	−	0.993567i	$-0.463876\pi$
$307$	−15.4245	−	15.4245i	−0.880325	−	0.880325i	−0.993567	+	0.113243i	$0.963876\pi$
$308$	9.08385	−	2.31638i	0.517601	−	0.131988i
$309$			4.93197i			0.280570i
$310$	38.0917			2.16346
$311$	−0.146506	−	0.146506i	−0.00830758	−	0.00830758i	0.702941	−	0.711248i	$-0.251870\pi$
$311$	−0.146506	−	0.146506i	−0.00830758	−	0.00830758i	−0.711248	+	0.702941i	$0.751870\pi$
$312$	0.916077	−	0.916077i	0.0518627	−	0.0518627i
$313$	−3.87546	−	3.87546i	−0.219054	−	0.219054i	0.589046	−	0.808100i	$-0.299504\pi$
$313$	−3.87546	−	3.87546i	−0.219054	−	0.219054i	−0.808100	+	0.589046i	$0.799504\pi$
$314$		−	2.96529i		−	0.167341i
$315$	25.1972	−	25.1972i	1.41970	−	1.41970i
$316$	−7.93239	+	7.93239i	−0.446232	+	0.446232i
$317$	−0.451323			−0.0253488			−0.0126744	−	0.999920i	$-0.504034\pi$
$317$	−0.451323			−0.0253488			−0.0126744	+	0.999920i	$0.504034\pi$
$318$		−	1.89200i		−	0.106098i
$319$	−9.31983	+	2.37655i	−0.521810	+	0.133061i
$320$	28.9555			1.61866
$321$			4.17311i			0.232920i
$322$	24.4286	+	24.4286i	1.36135	+	1.36135i
$323$	4.58928	−	4.58928i	0.255354	−	0.255354i
$324$		−	5.80835i		−	0.322686i
$325$		−	7.37298i		−	0.408979i
$326$	−11.1701	+	11.1701i	−0.618653	+	0.618653i
$327$		−	5.04018i		−	0.278723i
$328$	−10.9502	+	10.9502i	−0.604625	+	0.604625i
$329$	−6.49424	−	6.49424i	−0.358039	−	0.358039i
$330$	−1.38481	−	5.43063i	−0.0762312	−	0.298946i
$331$	3.78474	−	3.78474i	0.208028	−	0.208028i	−0.595401	−	0.803429i	$-0.703007\pi$
$331$	3.78474	−	3.78474i	0.208028	−	0.208028i	0.803429	+	0.595401i	$0.203007\pi$
$332$	−6.96318			−0.382154
$333$	−4.06127	−	4.06127i	−0.222556	−	0.222556i
$334$	−11.8555	−	11.8555i	−0.648702	−	0.648702i
$335$	31.2073	−	31.2073i	1.70504	−	1.70504i
$336$	1.96391	−	1.96391i	0.107140	−	0.107140i
$337$	4.89975	+	4.89975i	0.266907	+	0.266907i	0.827852	−	0.560946i	$-0.189562\pi$
$337$	4.89975	+	4.89975i	0.266907	+	0.266907i	−0.560946	+	0.827852i	$0.689562\pi$
$338$	−9.37050	−	9.37050i	−0.509688	−	0.509688i
$339$	2.46003			0.133611
$340$	15.1909	−	15.1909i	0.823842	−	0.823842i
$341$	−8.00713	−	31.4005i	−0.433610	−	1.70043i
$342$	−1.85217	−	1.85217i	−0.100154	−	0.100154i
$343$	−3.09850	+	3.09850i	−0.167303	+	0.167303i
$344$			19.8461i			1.07003i
$345$	−9.55182	+	9.55182i	−0.514253	+	0.514253i
$346$		−	7.41539i		−	0.398654i
$347$		−	11.6609i		−	0.625988i	−0.949755	−	0.312994i	$-0.898668\pi$
$347$		−	11.6609i		−	0.625988i	0.949755	−	0.312994i	$-0.101332\pi$
$348$	0.702897	−	0.702897i	0.0376792	−	0.0376792i
$349$	19.8130	+	19.8130i	1.06057	+	1.06057i	0.998043	+	0.0625248i	$0.0199152\pi$
$349$	19.8130	+	19.8130i	1.06057	+	1.06057i	0.0625248	+	0.998043i	$0.480085\pi$
$350$		−	29.7510i		−	1.59026i
$351$	−2.45361			−0.130964
$352$	−3.41429	−	13.3894i	−0.181982	−	0.713656i
$353$		−	7.27192i		−	0.387045i	−0.981096	−	0.193523i	$-0.938009\pi$
$353$		−	7.27192i		−	0.387045i	0.981096	−	0.193523i	$-0.0619913\pi$
$354$	−2.26225			−0.120237
$355$	8.83156	−	8.83156i	0.468731	−	0.468731i
$356$	−0.923704	+	0.923704i	−0.0489562	+	0.0489562i
$357$		−	11.8693i		−	0.628192i
$358$	−6.17114	−	6.17114i	−0.326155	−	0.326155i
$359$	−15.1417	+	15.1417i	−0.799148	+	0.799148i	−0.982961	−	0.183813i	$-0.941156\pi$
$359$	−15.1417	+	15.1417i	−0.799148	+	0.799148i	0.183813	+	0.982961i	$0.441156\pi$
$360$	−21.6354	−	21.6354i	−1.14029	−	1.14029i
$361$	−18.2825			−0.962235
$362$		−	15.1515i		−	0.796343i
$363$	−4.18560	+	2.28311i	−0.219687	+	0.119832i
$364$	−1.94664	−	1.94664i	−0.102031	−	0.102031i
$365$	−47.8843			−2.50638
$366$	−0.680774	+	3.65968i	−0.0355846	+	0.191295i
$367$	−22.1704			−1.15729			−0.578643	−	0.815581i	$-0.696418\pi$
$367$	−22.1704			−1.15729			−0.578643	+	0.815581i	$0.696418\pi$
$368$	11.1441	−	11.1441i	0.580926	−	0.580926i
$369$	14.1905			0.738727
$370$	−7.96250			−0.413951
$371$	−14.1879			−0.736598
$372$	2.36821	+	2.36821i	0.122786	+	0.122786i
$373$	13.1636	+	13.1636i	0.681587	+	0.681587i	0.960358	−	0.278771i	$-0.0899271\pi$
$373$	13.1636	+	13.1636i	0.681587	+	0.681587i	−0.278771	+	0.960358i	$0.589927\pi$
$374$	24.0285	+	14.2639i	1.24248	+	0.737569i
$375$	3.94938			0.203945
$376$	−5.57625	+	5.57625i	−0.287573	+	0.287573i
$377$	1.99720	+	1.99720i	0.102861	+	0.102861i
$378$	−9.90065			−0.509235
$379$	−14.8384			−0.762195			−0.381098	−	0.924535i	$-0.624454\pi$
$379$	−14.8384			−0.762195			−0.381098	+	0.924535i	$0.624454\pi$
$380$	2.37508			0.121839
$381$			2.43352i			0.124673i
$382$		−	17.2828i		−	0.884266i
$383$	−5.99071	−	5.99071i	−0.306111	−	0.306111i	0.537288	−	0.843399i	$-0.319449\pi$
$383$	−5.99071	−	5.99071i	−0.306111	−	0.306111i	−0.843399	+	0.537288i	$0.819449\pi$
$384$	−0.198636	−	0.198636i	−0.0101366	−	0.0101366i
$385$	−40.7237	+	10.3845i	−2.07547	+	0.529245i
$386$	23.9442			1.21873
$387$	12.8594	−	12.8594i	0.653678	−	0.653678i
$388$	−8.85253			−0.449419
$389$	−1.11609	+	1.11609i	−0.0565881	+	0.0565881i	−0.734835	−	0.678246i	$-0.762740\pi$
$389$	−1.11609	+	1.11609i	−0.0565881	+	0.0565881i	0.678246	+	0.734835i	$0.262740\pi$
$390$	−1.16376	+	1.16376i	−0.0589294	+	0.0589294i
$391$		−	67.3517i		−	3.40612i
$392$	−12.5296	−	12.5296i	−0.632838	−	0.632838i
$393$	−7.40062			−0.373312
$394$	−2.50650	−	2.50650i	−0.126276	−	0.126276i
$395$	35.5616	−	35.5616i	1.78930	−	1.78930i
$396$	−3.76517	+	6.34267i	−0.189207	+	0.318731i
$397$	−6.86612	−	6.86612i	−0.344601	−	0.344601i	0.513493	−	0.858094i	$-0.328351\pi$
$397$	−6.86612	−	6.86612i	−0.344601	−	0.344601i	−0.858094	+	0.513493i	$0.828351\pi$
$398$	12.4051	+	12.4051i	0.621813	+	0.621813i
$399$	0.927880	−	0.927880i	0.0464521	−	0.0464521i
$400$	−13.5721			−0.678606
$401$	19.6110	+	19.6110i	0.979326	+	0.979326i	0.999791	−	0.0204649i	$-0.00651463\pi$
$401$	19.6110	+	19.6110i	0.979326	+	0.979326i	−0.0204649	+	0.999791i	$0.506515\pi$
$402$	−5.93292			−0.295907
$403$	−6.72902	+	6.72902i	−0.335196	+	0.335196i
$404$	6.13676	−	6.13676i	0.305315	−	0.305315i
$405$			26.0393i			1.29391i
$406$	8.05899	+	8.05899i	0.399961	+	0.399961i
$407$	1.67377	+	6.56382i	0.0829658	+	0.325357i
$408$	−10.1916			−0.504557
$409$	18.9272	−	18.9272i	0.935889	−	0.935889i	−0.0621762	−	0.998065i	$-0.519804\pi$
$409$	18.9272	−	18.9272i	0.935889	−	0.935889i	0.998065	+	0.0621762i	$0.0198041\pi$
$410$	13.9109	−	13.9109i	0.687010	−	0.687010i
$411$		−	6.95152i		−	0.342893i
$412$		−	8.99884i		−	0.443341i
$413$			16.9644i			0.834763i
$414$	−27.1823			−1.33594
$415$	31.2166			1.53236
$416$	−2.86929	+	2.86929i	−0.140679	+	0.140679i
$417$	−3.85437	−	3.85437i	−0.188749	−	0.188749i
$418$	0.763338	+	2.99349i	0.0373361	+	0.146416i
$419$	−14.7784	+	14.7784i	−0.721972	+	0.721972i	−0.969007	−	0.247035i	$-0.920544\pi$
$419$	−14.7784	+	14.7784i	−0.721972	+	0.721972i	0.247035	+	0.969007i	$0.420544\pi$
$420$	3.07136	−	3.07136i	0.149867	−	0.149867i
$421$	13.7996	−	13.7996i	0.672553	−	0.672553i	−0.285751	−	0.958304i	$-0.592243\pi$
$421$	13.7996	−	13.7996i	0.672553	−	0.672553i	0.958304	+	0.285751i	$0.0922430\pi$
$422$	−17.4403			−0.848982
$423$	7.22630			0.351355
$424$			12.1824i			0.591628i
$425$	−41.0130	+	41.0130i	−1.98942	+	1.98942i
$426$	−1.67900			−0.0813477
$427$	27.4436	+	5.10506i	1.32809	+	0.247051i
$428$		−	7.61424i		−	0.368048i
$429$	1.20397	+	0.714707i	0.0581282	+	0.0345064i
$430$		−	25.2120i		−	1.21583i
$431$	25.4240			1.22463			0.612314	−	0.790614i	$-0.290239\pi$
$431$	25.4240			1.22463			0.612314	+	0.790614i	$0.290239\pi$
$432$			4.51659i			0.217304i
$433$	−17.5984	−	17.5984i	−0.845726	−	0.845726i	0.143870	−	0.989597i	$-0.454045\pi$
$433$	−17.5984	−	17.5984i	−0.845726	−	0.845726i	−0.989597	+	0.143870i	$0.954045\pi$
$434$	−27.1525	+	27.1525i	−1.30336	+	1.30336i
$435$	−3.15115	+	3.15115i	−0.151086	+	0.151086i
$436$			9.19629i			0.440422i
$437$	5.26519	−	5.26519i	0.251868	−	0.251868i
$438$	4.55172	+	4.55172i	0.217490	+	0.217490i
$439$		−	8.75859i		−	0.418025i	−0.977913	−	0.209012i	$-0.932975\pi$
$439$		−	8.75859i		−	0.418025i	0.977913	−	0.209012i	$-0.0670249\pi$
$440$	8.91663	+	34.9672i	0.425084	+	1.66700i
$441$			16.2372i			0.773198i
$442$		−	8.20591i		−	0.390315i
$443$	−8.06788			−0.383317			−0.191658	−	0.981462i	$-0.561387\pi$
$443$	−8.06788			−0.383317			−0.191658	+	0.981462i	$0.561387\pi$
$444$	−0.495040	−	0.495040i	−0.0234936	−	0.0234936i
$445$	4.14104	−	4.14104i	0.196304	−	0.196304i
$446$	−2.96671			−0.140478
$447$		−	4.09674i		−	0.193769i
$448$	−20.6401	+	20.6401i	−0.975152	+	0.975152i
$449$	19.0963			0.901210			0.450605	−	0.892724i	$-0.351208\pi$
$449$	19.0963			0.901210			0.450605	+	0.892724i	$0.351208\pi$
$450$	16.5523	+	16.5523i	0.780284	+	0.780284i
$451$	−14.3915	−	8.54317i	−0.677670	−	0.402282i
$452$	−4.48856			−0.211124
$453$	−2.80056	−	2.80056i	−0.131582	−	0.131582i
$454$			10.3857i			0.487424i
$455$	8.72694	+	8.72694i	0.409125	+	0.409125i
$456$	−0.796720	−	0.796720i	−0.0373098	−	0.0373098i
$457$	−12.6139	−	12.6139i	−0.590054	−	0.590054i	0.347592	−	0.937646i	$-0.387000\pi$
$457$	−12.6139	−	12.6139i	−0.590054	−	0.590054i	−0.937646	+	0.347592i	$0.887000\pi$
$458$	14.2254	−	14.2254i	0.664711	−	0.664711i
$459$	13.6485	+	13.6485i	0.637057	+	0.637057i
$460$	17.4282	−	17.4282i	0.812594	−	0.812594i
$461$			18.1950i			0.847425i	0.905797	+	0.423713i	$0.139273\pi$
$461$			18.1950i			0.847425i	−0.905797	+	0.423713i	$0.860727\pi$
$462$	4.85818	+	2.88394i	0.226023	+	0.134173i
$463$			31.7073i			1.47356i	0.676132	+	0.736781i	$0.263655\pi$
$463$			31.7073i			1.47356i	−0.676132	+	0.736781i	$0.736345\pi$
$464$	3.67644	−	3.67644i	0.170674	−	0.170674i
$465$	−10.6169	−	10.6169i	−0.492347	−	0.492347i
$466$		−	0.106754i		−	0.00494528i
$467$	−27.6365	+	27.6365i	−1.27886	+	1.27886i	−0.337559	+	0.941304i	$0.609601\pi$
$467$	−27.6365	+	27.6365i	−1.27886	+	1.27886i	−0.941304	+	0.337559i	$0.890399\pi$
$468$	2.16607			0.100127
$469$			44.4904i			2.05437i
$470$	7.08393	−	7.08393i	0.326757	−	0.326757i
$471$	−0.826485	+	0.826485i	−0.0380824	+	0.0380824i
$472$	14.5664			0.670473
$473$	−20.7833	+	5.29974i	−0.955618	+	0.243682i
$474$	−6.76073			−0.310530
$475$	−6.41235			−0.294219
$476$			21.6568i			0.992636i
$477$	7.89361	−	7.89361i	0.361424	−	0.361424i
$478$	−22.3402	+	22.3402i	−1.02182	+	1.02182i
$479$	−13.1610			−0.601343			−0.300672	−	0.953728i	$-0.597211\pi$
$479$	−13.1610			−0.601343			−0.300672	+	0.953728i	$0.597211\pi$
$480$	−4.52711	−	4.52711i	−0.206633	−	0.206633i
$481$	1.40660	−	1.40660i	0.0641356	−	0.0641356i
$482$	−20.2835	+	20.2835i	−0.923888	+	0.923888i
$483$		−	13.6175i		−	0.619616i
$484$	7.63702	−	4.16575i	0.347137	−	0.189352i
$485$	39.6867			1.80208
$486$	8.35156	−	8.35156i	0.378834	−	0.378834i
$487$			42.2026i			1.91238i	0.292747	+	0.956190i	$0.405431\pi$
$487$			42.2026i			1.91238i	−0.292747	+	0.956190i	$0.594569\pi$
$488$	4.38343	−	23.5643i	0.198429	−	1.06671i
$489$	6.22665			0.281579
$490$	15.9173	+	15.9173i	0.719068	+	0.719068i
$491$	−3.77470			−0.170350			−0.0851749	−	0.996366i	$-0.527145\pi$
$491$	−3.77470			−0.170350			−0.0851749	+	0.996366i	$0.527145\pi$
$492$	1.72972			0.0779819
$493$		−	22.2193i		−	1.00071i
$494$	0.641493	−	0.641493i	0.0288621	−	0.0288621i
$495$	16.8796	−	28.4347i	0.758681	−	1.27805i
$496$	12.3867	+	12.3867i	0.556180	+	0.556180i
$497$			12.5906i			0.564767i
$498$	−2.96734	−	2.96734i	−0.132970	−	0.132970i
$499$	1.50807	+	1.50807i	0.0675104	+	0.0675104i	0.740056	−	0.672545i	$-0.234799\pi$
$499$	1.50807	+	1.50807i	0.0675104	+	0.0675104i	−0.672545	+	0.740056i	$0.734799\pi$
$500$	−7.20602			−0.322263
$501$			6.60871i			0.295255i
$502$	11.0753			0.494317
$503$			6.79914i			0.303159i	0.988445	+	0.151579i	$0.0484359\pi$
$503$			6.79914i			0.303159i	−0.988445	+	0.151579i	$0.951564\pi$
$504$	30.8443			1.37392
$505$	−27.5116	+	27.5116i	−1.22425	+	1.22425i
$506$	27.5674	+	16.3647i	1.22552	+	0.727499i
$507$			5.22349i			0.231983i
$508$		−	4.44019i		−	0.197001i
$509$	0.710307	+	0.710307i	0.0314838	+	0.0314838i	0.722673	−	0.691190i	$-0.242913\pi$
$509$	0.710307	+	0.710307i	0.0314838	+	0.0314838i	−0.691190	+	0.722673i	$0.742913\pi$
$510$	12.9471			0.573308
$511$	34.1329	−	34.1329i	1.50995	−	1.50995i
$512$	13.0629	+	13.0629i	0.577304	+	0.577304i
$513$			2.13393i			0.0942152i
$514$	−9.08559	−	9.08559i	−0.400748	−	0.400748i
$515$			40.3426i			1.77771i
$516$	1.56747	−	1.56747i	0.0690039	−	0.0690039i
$517$	−7.32867	−	4.35049i	−0.322315	−	0.191334i
$518$	5.67583	−	5.67583i	0.249382	−	0.249382i
$519$	−2.06682	+	2.06682i	−0.0907233	+	0.0907233i
$520$	7.49335	−	7.49335i	0.328605	−	0.328605i
$521$	−17.8132	+	17.8132i	−0.780412	+	0.780412i	−0.979900	−	0.199488i	$-0.936072\pi$
$521$	−17.8132	+	17.8132i	−0.780412	+	0.780412i	0.199488	+	0.979900i	$0.436072\pi$
$522$	−8.96744			−0.392494
$523$	−1.59704	+	1.59704i	−0.0698337	+	0.0698337i	−0.741161	−	0.671327i	$-0.765724\pi$
$523$	−1.59704	+	1.59704i	−0.0698337	+	0.0698337i	0.671327	+	0.741161i	$0.265724\pi$
$524$	13.5031			0.589887
$525$	−8.29219	+	8.29219i	−0.361901	+	0.361901i
$526$	−6.81074	−	6.81074i	−0.296962	−	0.296962i
$527$	74.8618			3.26103
$528$	1.31563	−	2.21626i	0.0572553	−	0.0964502i
$529$		−	54.2712i		−	2.35962i
$530$		−	15.4762i		−	0.672242i
$531$	−9.43835	−	9.43835i	−0.409590	−	0.409590i
$532$	−1.69301	+	1.69301i	−0.0734011	+	0.0734011i
$533$			4.91482i			0.212884i
$534$	−0.787267			−0.0340684
$535$			34.1353i			1.47580i
$536$	38.2014			1.65005
$537$			3.44004i			0.148449i
$538$	5.50019	+	5.50019i	0.237130	+	0.237130i
$539$	9.77534	−	16.4672i	0.421054	−	0.709291i
$540$			7.06348i			0.303964i
$541$	3.38744	+	3.38744i	0.145638	+	0.145638i	0.776166	−	0.630529i	$-0.217162\pi$
$541$	3.38744	+	3.38744i	0.145638	+	0.145638i	−0.630529	+	0.776166i	$0.717162\pi$
$542$	−3.15789	−	3.15789i	−0.135643	−	0.135643i
$543$	−4.22302	+	4.22302i	−0.181227	+	0.181227i
$544$	31.9215			1.36862
$545$		−	41.2278i		−	1.76600i
$546$		−	1.65911i		−	0.0710032i
$547$	−18.8324	+	18.8324i	−0.805216	+	0.805216i	−0.983905	−	0.178690i	$-0.942814\pi$
$547$	−18.8324	+	18.8324i	−0.805216	+	0.805216i	0.178690	+	0.983905i	$0.442814\pi$
$548$			12.6837i			0.541821i
$549$	−18.1089	+	12.4283i	−0.772867	+	0.530428i
$550$	−6.82173	−	26.7519i	−0.290879	−	1.14070i
$551$	1.73699	−	1.73699i	0.0739981	−	0.0739981i
$552$	−11.6926			−0.497669
$553$			50.6980i			2.15590i
$554$		−	7.16542i		−	0.304430i
$555$	2.21931	+	2.21931i	0.0942044	+	0.0942044i
$556$	7.03267	+	7.03267i	0.298251	+	0.298251i
$557$	12.5649	−	12.5649i	0.532394	−	0.532394i	−0.388890	−	0.921284i	$-0.627142\pi$
$557$	12.5649	−	12.5649i	0.532394	−	0.532394i	0.921284	+	0.388890i	$0.127142\pi$
$558$		−	30.2133i		−	1.27903i
$559$	4.45379	+	4.45379i	0.188375	+	0.188375i
$560$	16.0645	−	16.0645i	0.678848	−	0.678848i
$561$	−2.72157	−	10.6728i	−0.114905	−	0.450608i
$562$	0.0222338			0.000937877
$563$	−9.10035			−0.383534			−0.191767	−	0.981440i	$-0.561422\pi$
$563$	−9.10035			−0.383534			−0.191767	+	0.981440i	$0.561422\pi$
$564$	0.880837			0.0370899
$565$	20.1226			0.846564
$566$	0.414273	+	0.414273i	0.0174132	+	0.0174132i
$567$	−18.5614	−	18.5614i	−0.779504	−	0.779504i
$568$	10.8109			0.453615
$569$			29.8469i			1.25125i	0.780124	+	0.625624i	$0.215156\pi$
$569$			29.8469i			1.25125i	−0.780124	+	0.625624i	$0.784844\pi$
$570$	1.01213	+	1.01213i	0.0423937	+	0.0423937i
$571$			25.7078i			1.07584i	0.842996	+	0.537920i	$0.180790\pi$
$571$			25.7078i			1.07584i	−0.842996	+	0.537920i	$0.819210\pi$
$572$	−2.19676	−	1.30405i	−0.0918510	−	0.0545252i
$573$	−4.81707	+	4.81707i	−0.201236	+	0.201236i
$574$			19.8319i			0.827769i
$575$	−47.0534	+	47.0534i	−1.96226	+	1.96226i
$576$		−	22.9667i		−	0.956948i
$577$	−11.0899	−	11.0899i	−0.461680	−	0.461680i	0.437526	−	0.899206i	$-0.355855\pi$
$577$	−11.0899	−	11.0899i	−0.461680	−	0.461680i	−0.899206	+	0.437526i	$0.855855\pi$
$578$	−32.4280	+	32.4280i	−1.34883	+	1.34883i
$579$	−6.67372	−	6.67372i	−0.277350	−	0.277350i
$580$	5.74957	−	5.74957i	0.238738	−	0.238738i
$581$	−22.2518	+	22.2518i	−0.923159	+	0.923159i
$582$	−3.77248	−	3.77248i	−0.156374	−	0.156374i
$583$	−12.7577	+	3.25320i	−0.528368	+	0.134734i
$584$	−29.3080	−	29.3080i	−1.21278	−	1.21278i
$585$	−9.71069			−0.401488
$586$	−15.4178	−	15.4178i	−0.636902	−	0.636902i
$587$	11.8971	+	11.8971i	0.491047	+	0.491047i	0.908636	−	0.417589i	$-0.137125\pi$
$587$	11.8971	+	11.8971i	0.491047	+	0.491047i	−0.417589	+	0.908636i	$0.637125\pi$
$588$			1.97920i			0.0816207i
$589$	5.85229	+	5.85229i	0.241139	+	0.241139i
$590$	−18.5048			−0.761831
$591$			1.39722i			0.0574740i
$592$	−2.58926	−	2.58926i	−0.106418	−	0.106418i
$593$	−12.2620	−	12.2620i	−0.503541	−	0.503541i	0.408995	−	0.912536i	$-0.365879\pi$
$593$	−12.2620	−	12.2620i	−0.503541	−	0.503541i	−0.912536	+	0.408995i	$0.865879\pi$
$594$	−8.90261	+	2.27016i	−0.365279	+	0.0931459i
$595$		−	97.0891i		−	3.98026i
$596$			7.47489i			0.306183i
$597$		−	6.91512i		−	0.283017i
$598$		−	9.41447i		−	0.384986i
$599$	6.29590	−	6.29590i	0.257243	−	0.257243i	−0.566689	−	0.823932i	$-0.691776\pi$
$599$	6.29590	−	6.29590i	0.257243	−	0.257243i	0.823932	+	0.566689i	$0.191776\pi$
$600$	7.12005	+	7.12005i	0.290675	+	0.290675i
$601$	9.43987			0.385060			0.192530	−	0.981291i	$-0.438331\pi$
$601$	9.43987			0.385060			0.192530	+	0.981291i	$0.438331\pi$
$602$	17.9716	+	17.9716i	0.732469	+	0.732469i
$603$	−24.7528	−	24.7528i	−1.00801	−	1.00801i
$604$	5.10990	+	5.10990i	0.207919	+	0.207919i
$605$	−34.2374	+	18.6754i	−1.39195	+	0.759264i
$606$	5.23032			0.212467
$607$		−	12.3599i		−	0.501674i	−0.968029	−	0.250837i	$-0.919294\pi$
$607$		−	12.3599i		−	0.501674i	0.968029	−	0.250837i	$-0.0807059\pi$
$608$	2.49545	+	2.49545i	0.101204	+	0.101204i
$609$		−	4.49240i		−	0.182041i
$610$	−5.56861	+	29.9355i	−0.225466	+	1.21205i
$611$			2.50280i			0.101252i
$612$	−12.0490	−	12.0490i	−0.487052	−	0.487052i
$613$	−13.2545			−0.535343			−0.267671	−	0.963510i	$-0.586254\pi$
$613$	−13.2545			−0.535343			−0.267671	+	0.963510i	$0.586254\pi$
$614$			23.9866i			0.968019i
$615$	−7.75449			−0.312691
$616$	−31.2813	−	18.5694i	−1.26036	−	0.748182i
$617$	−0.441561	+	0.441561i	−0.0177766	+	0.0177766i	−0.715939	−	0.698163i	$-0.754001\pi$
$617$	−0.441561	+	0.441561i	−0.0177766	+	0.0177766i	0.698163	+	0.715939i	$0.254001\pi$
$618$	3.83483	−	3.83483i	0.154260	−	0.154260i
$619$	−27.8772			−1.12048			−0.560240	−	0.828331i	$-0.689291\pi$
$619$	−27.8772			−1.12048			−0.560240	+	0.828331i	$0.689291\pi$
$620$	19.3716	+	19.3716i	0.777981	+	0.777981i
$621$	15.6586	+	15.6586i	0.628359	+	0.628359i
$622$			0.227830i			0.00913515i
$623$			5.90364i			0.236524i
$624$	−0.756869			−0.0302990
$625$	−5.54490			−0.221796
$626$			6.02670i			0.240875i
$627$	0.621587	−	1.04710i	0.0248238	−	0.0418172i
$628$	1.50800	−	1.50800i	0.0601758	−	0.0601758i
$629$	−15.6488			−0.623957
$630$	−39.1839			−1.56112
$631$	16.2294	+	16.2294i	0.646082	+	0.646082i	0.952044	−	0.305962i	$-0.0989779\pi$
$631$	16.2294	+	16.2294i	0.646082	+	0.646082i	−0.305962	+	0.952044i	$0.598978\pi$
$632$	43.5316			1.73159
$633$	4.86097	+	4.86097i	0.193206	+	0.193206i
$634$	0.350924	+	0.350924i	0.0139370	+	0.0139370i
$635$			19.9057i			0.789935i
$636$	0.962177	−	0.962177i	0.0381528	−	0.0381528i
$637$	−5.62367			−0.222818
$638$	9.09448	+	5.39872i	0.360054	+	0.213737i
$639$	−7.00496	−	7.00496i	−0.277112	−	0.277112i
$640$	−1.62480	−	1.62480i	−0.0642260	−	0.0642260i
$641$	19.2015	+	19.2015i	0.758413	+	0.758413i	0.976033	−	0.217620i	$-0.0698295\pi$
$641$	19.2015	+	19.2015i	0.758413	+	0.758413i	−0.217620	+	0.976033i	$0.569829\pi$
$642$	3.24479	−	3.24479i	0.128062	−	0.128062i
$643$	−0.977068	+	0.977068i	−0.0385318	+	0.0385318i	−0.726110	−	0.687578i	$-0.758674\pi$
$643$	−0.977068	+	0.977068i	−0.0385318	+	0.0385318i	0.687578	+	0.726110i	$0.258674\pi$
$644$			24.8463i			0.979083i
$645$	−7.02710	+	7.02710i	−0.276692	+	0.276692i
$646$	−7.13675			−0.280792
$647$	4.55003	+	4.55003i	0.178880	+	0.178880i	0.790868	−	0.611987i	$-0.209630\pi$
$647$	4.55003	+	4.55003i	0.178880	+	0.178880i	−0.611987	+	0.790868i	$0.709630\pi$
$648$	−15.9376	+	15.9376i	−0.626089	+	0.626089i
$649$	3.88984	+	15.2543i	0.152689	+	0.598783i
$650$	−5.73283	+	5.73283i	−0.224860	+	0.224860i
$651$	15.1359			0.593222
$652$	−11.3611			−0.444936
$653$	−27.9251	−	27.9251i	−1.09279	−	1.09279i	−0.995229	−	0.0975626i	$-0.968895\pi$
$653$	−27.9251	−	27.9251i	−1.09279	−	1.09279i	−0.0975626	−	0.995229i	$-0.531105\pi$
$654$	−3.91897	+	3.91897i	−0.153244	+	0.153244i
$655$	−60.5357			−2.36533
$656$	9.04715			0.353232
$657$			37.9805i			1.48176i
$658$			10.0991i			0.393705i
$659$	−15.9606			−0.621736			−0.310868	−	0.950453i	$-0.600620\pi$
$659$	−15.9606			−0.621736			−0.310868	+	0.950453i	$0.600620\pi$
$660$	2.05751	−	3.46600i	0.0800883	−	0.134914i
$661$	−18.9001	+	18.9001i	−0.735129	+	0.735129i	−0.971631	−	0.236502i	$-0.923999\pi$
$661$	−18.9001	+	18.9001i	−0.735129	+	0.735129i	0.236502	+	0.971631i	$0.423999\pi$
$662$	−5.88562			−0.228751
$663$	−2.28715	+	2.28715i	−0.0888256	+	0.0888256i
$664$	19.1064	+	19.1064i	0.741472	+	0.741472i
$665$	7.58989	−	7.58989i	0.294323	−	0.294323i
$666$			6.31564i			0.244726i
$667$		−	25.4918i		−	0.987046i
$668$		−	12.0582i		−	0.466547i
$669$	0.826882	+	0.826882i	0.0319691	+	0.0319691i
$670$	−48.5302			−1.87489
$671$	25.8477	−	1.70222i	0.997839	−	0.0657134i
$672$	6.45403			0.248970
$673$	−18.1186	−	18.1186i	−0.698419	−	0.698419i	0.265650	−	0.964069i	$-0.414413\pi$
$673$	−18.1186	−	18.1186i	−0.698419	−	0.698419i	−0.964069	+	0.265650i	$0.914413\pi$
$674$		−	7.61957i		−	0.293495i
$675$		−	19.0703i		−	0.734015i
$676$		−	9.53076i		−	0.366568i
$677$	19.1667	−	19.1667i	0.736635	−	0.736635i	−0.235290	−	0.971925i	$-0.575604\pi$
$677$	19.1667	−	19.1667i	0.736635	−	0.736635i	0.971925	+	0.235290i	$0.0756039\pi$
$678$	−1.91279	−	1.91279i	−0.0734601	−	0.0734601i
$679$	−28.2895	+	28.2895i	−1.08565	+	1.08565i
$680$	−83.3651			−3.19691
$681$	2.89470	−	2.89470i	0.110925	−	0.110925i
$682$	−18.1895	+	30.6413i	−0.696510	+	1.17332i
$683$	11.2837			0.431757			0.215879	−	0.976420i	$-0.430738\pi$
$683$	11.2837			0.431757			0.215879	+	0.976420i	$0.430738\pi$
$684$		−	1.88385i		−	0.0720309i
$685$		−	56.8622i		−	2.17259i
$686$	4.81846			0.183970
$687$	−7.92982			−0.302542
$688$	8.19850	−	8.19850i	0.312565	−	0.312565i
$689$	2.73392	+	2.73392i	0.104154	+	0.104154i
$690$	14.8540			0.565481
$691$	27.6315			1.05115			0.525575	−	0.850747i	$-0.323850\pi$
$691$	27.6315			1.05115			0.525575	+	0.850747i	$0.323850\pi$
$692$	3.77111	−	3.77111i	0.143356	−	0.143356i
$693$	8.23673	+	32.3009i	0.312888	+	1.22701i
$694$	−9.06686	+	9.06686i	−0.344173	+	0.344173i
$695$	−31.5280	−	31.5280i	−1.19593	−	1.19593i
$696$	−3.85738			−0.146214
$697$	27.3392	−	27.3392i	1.03555	−	1.03555i
$698$		−	30.8111i		−	1.16622i
$699$	−0.0297544	+	0.0297544i	−0.00112542	+	0.00112542i
$700$	15.1299	−	15.1299i	0.571856	−	0.571856i
$701$	3.96350	+	3.96350i	0.149699	+	0.149699i	0.777984	−	0.628284i	$-0.216243\pi$
$701$	3.96350	+	3.96350i	0.149699	+	0.149699i	−0.628284	+	0.777984i	$0.716243\pi$
$702$	1.90780	+	1.90780i	0.0720051	+	0.0720051i
$703$	−1.22333	−	1.22333i	−0.0461389	−	0.0461389i
$704$	−13.8268	+	23.2921i	−0.521117	+	0.877854i
$705$	−3.94887			−0.148723
$706$	−5.65425	+	5.65425i	−0.212801	+	0.212801i
$707$		−	39.2216i		−	1.47508i
$708$	−1.15047	−	1.15047i	−0.0432373	−	0.0432373i
$709$	−5.24601	−	5.24601i	−0.197018	−	0.197018i	0.601702	−	0.798720i	$-0.294489\pi$
$709$	−5.24601	−	5.24601i	−0.197018	−	0.197018i	−0.798720	+	0.601702i	$0.794489\pi$
$710$	−13.7339			−0.515424
$711$	−28.2065	−	28.2065i	−1.05783	−	1.05783i
$712$	5.06913			0.189974
$713$	85.8874			3.21651
$714$	−9.22896	+	9.22896i	−0.345385	+	0.345385i
$715$	9.84825	+	5.84618i	0.368304	+	0.218635i
$716$		−	6.27669i		−	0.234571i
$717$	12.4533			0.465078
$718$	23.5467			0.878756
$719$		−	7.78749i		−	0.290424i	−0.989401	−	0.145212i	$-0.953614\pi$
$719$		−	7.78749i		−	0.290424i	0.989401	−	0.145212i	$-0.0463865\pi$
$720$			17.8753i			0.666175i
$721$	−28.7570	−	28.7570i	−1.07097	−	1.07097i
$722$	14.2155	+	14.2155i	0.529045	+	0.529045i
$723$	11.3068			0.420506
$724$	7.70530	−	7.70530i	0.286365	−	0.286365i
$725$	−15.5229	+	15.5229i	−0.576507	+	0.576507i
$726$	5.02972	+	1.47927i	0.186670	+	0.0549009i
$727$	0.422566			0.0156721			0.00783605	−	0.999969i	$-0.497506\pi$
$727$	0.422566			0.0156721			0.00783605	+	0.999969i	$0.497506\pi$
$728$			10.6828i			0.395931i
$729$	17.3780			0.643630
$730$	37.2322	+	37.2322i	1.37803	+	1.37803i
$731$		−	49.5494i		−	1.83265i
$732$	−2.20734	+	1.51493i	−0.0815858	+	0.0559933i
$733$			21.9581i			0.811043i	0.914086	+	0.405521i	$0.132910\pi$
$733$			21.9581i			0.811043i	−0.914086	+	0.405521i	$0.867090\pi$
$734$	17.2385	+	17.2385i	0.636286	+	0.636286i
$735$		−	8.87291i		−	0.327282i
$736$	36.6229			1.34994
$737$	10.2014	+	40.0055i	0.375773	+	1.47362i
$738$	−11.0338	−	11.0338i	−0.406158	−	0.406158i
$739$	2.96107	+	2.96107i	0.108925	+	0.108925i	0.759469	−	0.650544i	$-0.225459\pi$
$739$	2.96107	+	2.96107i	0.108925	+	0.108925i	−0.650544	+	0.759469i	$0.725459\pi$
$740$	−4.04934	−	4.04934i	−0.148857	−	0.148857i
$741$	−0.357594			−0.0131365
$742$	11.0317	+	11.0317i	0.404988	+	0.404988i
$743$	11.7742	−	11.7742i	0.431954	−	0.431954i	−0.457338	−	0.889293i	$-0.651197\pi$
$743$	11.7742	−	11.7742i	0.431954	−	0.431954i	0.889293	+	0.457338i	$0.151197\pi$
$744$		−	12.9964i		−	0.476470i
$745$		−	33.5106i		−	1.22773i
$746$		−	20.4706i		−	0.749484i
$747$		−	24.7601i		−	0.905926i
$748$	4.96577	+	19.4736i	0.181567	+	0.712027i
$749$	−24.3323	−	24.3323i	−0.889084	−	0.889084i
$750$	−3.07082	−	3.07082i	−0.112131	−	0.112131i
$751$			40.3646i			1.47292i	0.676479	+	0.736462i	$0.263505\pi$
$751$			40.3646i			1.47292i	−0.676479	+	0.736462i	$0.736495\pi$
$752$	4.60713			0.168005
$753$	−3.08692	−	3.08692i	−0.112494	−	0.112494i
$754$		−	3.10584i		−	0.113108i
$755$	−22.9081	−	22.9081i	−0.833711	−	0.833711i
$756$	−5.03499	−	5.03499i	−0.183121	−	0.183121i
$757$	−13.8321			−0.502735			−0.251368	−	0.967892i	$-0.580880\pi$
$757$	−13.8321			−0.502735			−0.251368	+	0.967892i	$0.580880\pi$
$758$	11.5375	+	11.5375i	0.419061	+	0.419061i
$759$	−3.12240	−	12.2447i	−0.113336	−	0.444456i
$760$	−6.51703	−	6.51703i	−0.236397	−	0.236397i
$761$	−22.5645	+	22.5645i	−0.817963	+	0.817963i	−0.985813	−	0.167850i	$-0.946318\pi$
$761$	−22.5645	+	22.5645i	−0.817963	+	0.817963i	0.167850	+	0.985813i	$0.446318\pi$
$762$	1.89217	−	1.89217i	0.0685462	−	0.0685462i
$763$	29.3880	+	29.3880i	1.06392	+	1.06392i
$764$	8.78920	−	8.78920i	0.317982	−	0.317982i
$765$	54.0168	+	54.0168i	1.95298	+	1.95298i
$766$			9.31611i			0.336605i
$767$	3.26894	−	3.26894i	0.118034	−	0.118034i
$768$		−	6.77085i		−	0.244322i
$769$	26.1822	−	26.1822i	0.944155	−	0.944155i	−0.0543658	−	0.998521i	$-0.517314\pi$
$769$	26.1822	−	26.1822i	0.944155	−	0.944155i	0.998521	+	0.0543658i	$0.0173137\pi$
$770$	39.7390	+	23.5901i	1.43209	+	0.850128i
$771$			5.06467i			0.182400i
$772$	12.1768	+	12.1768i	0.438254	+	0.438254i
$773$			24.4959i			0.881057i	0.897739	+	0.440528i	$0.145209\pi$
$773$			24.4959i			0.881057i	−0.897739	+	0.440528i	$0.854791\pi$
$774$	−19.9975			−0.718795
$775$	−52.3001	−	52.3001i	−1.87868	−	1.87868i
$776$	24.2906	+	24.2906i	0.871982	+	0.871982i
$777$	−3.16393			−0.113506
$778$	1.73563			0.0622252
$779$	4.27446			0.153148
$780$	−1.18367			−0.0423820
$781$	2.88696	+	11.3214i	0.103304	+	0.405112i
$782$	−52.3690	+	52.3690i	−1.87271	+	1.87271i
$783$	5.16578	+	5.16578i	0.184610	+	0.184610i
$784$			10.3520i			0.369714i
$785$	−6.76050	+	6.76050i	−0.241293	+	0.241293i
$786$	5.75432	+	5.75432i	0.205250	+	0.205250i
$787$	−13.0218	−	13.0218i	−0.464178	−	0.464178i	0.435844	−	0.900022i	$-0.356450\pi$
$787$	−13.0218	−	13.0218i	−0.464178	−	0.464178i	−0.900022	+	0.435844i	$0.856450\pi$
$788$		−	2.54937i		−	0.0908174i
$789$			3.79658i			0.135162i
$790$	−55.3015			−1.96754
$791$	−14.3438	+	14.3438i	−0.510007	+	0.510007i
$792$	27.7351	−	7.07243i	0.985523	−	0.251308i
$793$	−4.30450	−	6.27193i	−0.152857	−	0.222723i
$794$			10.6775i			0.378929i
$795$	−4.31352	+	4.31352i	−0.152985	+	0.152985i
$796$			12.6173i			0.447208i
$797$		−	22.6032i		−	0.800646i	−0.916374	−	0.400323i	$-0.868898\pi$
$797$		−	22.6032i		−	0.800646i	0.916374	−	0.400323i	$-0.131102\pi$
$798$	−1.44294			−0.0510795
$799$	13.9221	−	13.9221i	0.492529	−	0.492529i
$800$	−22.3011	−	22.3011i	−0.788463	−	0.788463i
$801$	−3.28456	−	3.28456i	−0.116054	−	0.116054i
$802$		−	30.4969i		−	1.07688i
$803$	22.8656	−	38.5186i	0.806910	−	1.35929i
$804$	−3.01719	−	3.01719i	−0.106408	−	0.106408i
$805$		−	111.388i		−	3.92592i
$806$	10.4642			0.368587
$807$		−	3.06603i		−	0.107929i
$808$	−33.6775			−1.18477
$809$			17.6530i			0.620647i	0.950631	+	0.310323i	$0.100437\pi$
$809$			17.6530i			0.620647i	−0.950631	+	0.310323i	$0.899563\pi$
$810$	20.2468	−	20.2468i	0.711400	−	0.711400i
$811$	31.7189	+	31.7189i	1.11380	+	1.11380i	0.992632	+	0.121171i	$0.0386649\pi$
$811$	31.7189	+	31.7189i	1.11380	+	1.11380i	0.121171	+	0.992632i	$0.461335\pi$
$812$			8.19681i			0.287652i
$813$			1.76033i			0.0617376i
$814$	3.80224	−	6.40511i	0.133268	−	0.224499i
$815$	50.9329			1.78410
$816$	4.21017	+	4.21017i	0.147385	+	0.147385i
$817$	3.87350	−	3.87350i	0.135517	−	0.135517i
$818$	−29.4335			−1.02912
$819$	6.92197	−	6.92197i	0.241873	−	0.241873i
$820$	14.1488			0.494098
$821$	13.3928	−	13.3928i	0.467411	−	0.467411i	−0.433663	−	0.901075i	$-0.642779\pi$
$821$	13.3928	−	13.3928i	0.467411	−	0.467411i	0.901075	+	0.433663i	$0.142779\pi$
$822$	−5.40513	+	5.40513i	−0.188525	+	0.188525i
$823$	4.65613	−	4.65613i	0.162302	−	0.162302i	−0.621283	−	0.783586i	$-0.713388\pi$
$823$	4.65613	−	4.65613i	0.162302	−	0.162302i	0.783586	+	0.621283i	$0.213388\pi$
$824$	−24.6921	+	24.6921i	−0.860189	+	0.860189i
$825$	−5.55494	+	9.35764i	−0.193398	+	0.325791i
$826$	13.1906	−	13.1906i	0.458959	−	0.458959i
$827$		−	20.4085i		−	0.709672i	−0.934929	−	0.354836i	$-0.884537\pi$
$827$		−	20.4085i		−	0.709672i	0.934929	−	0.354836i	$-0.115463\pi$
$828$	−13.8236	−	13.8236i	−0.480403	−	0.480403i
$829$			2.86477i			0.0994977i	0.998762	+	0.0497489i	$0.0158421\pi$
$829$			2.86477i			0.0994977i	−0.998762	+	0.0497489i	$0.984158\pi$
$830$	−24.2723	−	24.2723i	−0.842504	−	0.842504i
$831$	−1.99715	+	1.99715i	−0.0692802	+	0.0692802i
$832$	7.95444			0.275771
$833$	31.2823	+	31.2823i	1.08387	+	1.08387i
$834$			5.99390i			0.207552i
$835$			54.0581i			1.87076i
$836$	−1.13415	+	1.91054i	−0.0392252	+	0.0660774i
$837$	−17.4047	+	17.4047i	−0.601593	+	0.601593i
$838$	22.9818			0.793892
$839$		−	12.0159i		−	0.414836i	−0.978252	−	0.207418i	$-0.933494\pi$
$839$		−	12.0159i		−	0.414836i	0.978252	−	0.207418i	$-0.0665061\pi$
$840$	−16.8551			−0.581557
$841$			20.5903i			0.710009i
$842$	−21.4597			−0.739550
$843$	−0.00619701	−	0.00619701i	−0.000213436	−	0.000213436i
$844$	−8.86931	−	8.86931i	−0.305294	−	0.305294i
$845$			42.7272i			1.46986i
$846$	−5.61878	−	5.61878i	−0.193178	−	0.193178i
$847$	11.0929	−	37.7173i	0.381156	−	1.29598i
$848$	5.03258	−	5.03258i	0.172819	−	0.172819i
$849$		−	0.230932i		−	0.00792557i
$850$	63.7790			2.18760
$851$	−17.9535			−0.615438
$852$	−0.853856	−	0.853856i	−0.0292526	−	0.0292526i
$853$	−2.10710			−0.0721457			−0.0360729	−	0.999349i	$-0.511485\pi$
$853$	−2.10710			−0.0721457			−0.0360729	+	0.999349i	$0.511485\pi$
$854$	−17.3692	−	25.3081i	−0.594363	−	0.866024i
$855$			8.44547i			0.288829i
$856$	−20.8928	+	20.8928i	−0.714103	+	0.714103i
$857$	31.4353			1.07381			0.536905	−	0.843642i	$-0.319593\pi$
$857$	31.4353			1.07381			0.536905	+	0.843642i	$0.319593\pi$
$858$	−0.380424	−	1.49186i	−0.0129875	−	0.0509312i
$859$			28.5952i			0.975654i	0.872940	+	0.487827i	$0.162210\pi$
$859$			28.5952i			0.975654i	−0.872940	+	0.487827i	$0.837790\pi$
$860$	12.8216	−	12.8216i	0.437213	−	0.437213i
$861$	5.52756	−	5.52756i	0.188379	−	0.188379i
$862$	−19.7683	−	19.7683i	−0.673311	−	0.673311i
$863$	17.2210			0.586210			0.293105	−	0.956080i	$-0.405311\pi$
$863$	17.2210			0.586210			0.293105	+	0.956080i	$0.405311\pi$
$864$	−7.42145	+	7.42145i	−0.252483	+	0.252483i
$865$	−16.9062	+	16.9062i	−0.574828	+	0.574828i
$866$			27.3672i			0.929974i
$867$	18.0767			0.613916
$868$	−27.6169			−0.937378
$869$	11.6248	+	45.5874i	0.394343	+	1.54645i
$870$	4.90032			0.166137
$871$	8.57303	−	8.57303i	0.290486	−	0.290486i
$872$	25.2338	−	25.2338i	0.854526	−	0.854526i
$873$		−	31.4784i		−	1.06538i
$874$	−8.18785			−0.276958
$875$	−23.0278	+	23.0278i	−0.778482	+	0.778482i
$876$			4.62957i			0.156419i
$877$	13.3612	+	13.3612i	0.451176	+	0.451176i	0.895745	−	0.444568i	$-0.146643\pi$
$877$	13.3612	+	13.3612i	0.451176	+	0.451176i	−0.444568	+	0.895745i	$0.646643\pi$
$878$	−6.81021	+	6.81021i	−0.229833	+	0.229833i
$879$			8.59448i			0.289884i
$880$	10.7616	−	18.1286i	0.362773	−	0.611114i
$881$		−	35.3547i		−	1.19113i	−0.803307	−	0.595565i	$-0.796928\pi$
$881$		−	35.3547i		−	1.19113i	0.803307	−	0.595565i	$-0.203072\pi$
$882$	12.6251	−	12.6251i	0.425110	−	0.425110i
$883$	23.8389	+	23.8389i	0.802243	+	0.802243i	0.983446	−	0.181203i	$-0.0579990\pi$
$883$	23.8389	+	23.8389i	0.802243	+	0.802243i	−0.181203	+	0.983446i	$0.557999\pi$
$884$	4.17313	−	4.17313i	0.140357	−	0.140357i
$885$	5.15766	+	5.15766i	0.173373	+	0.173373i
$886$	6.27315	+	6.27315i	0.210751	+	0.210751i
$887$	−20.3034	−	20.3034i	−0.681721	−	0.681721i	0.278667	−	0.960388i	$-0.410108\pi$
$887$	−20.3034	−	20.3034i	−0.681721	−	0.681721i	−0.960388	+	0.278667i	$0.910108\pi$
$888$			2.71670i			0.0911664i
$889$	−14.1892	−	14.1892i	−0.475891	−	0.475891i
$890$	−6.43970			−0.215859
$891$	−20.9463	−	12.4343i	−0.701727	−	0.416564i
$892$	−1.50873	−	1.50873i	−0.0505159	−	0.0505159i
$893$	2.17671			0.0728407
$894$	−3.18540	+	3.18540i	−0.106536	+	0.106536i
$895$			28.1389i			0.940581i
$896$	2.31639			0.0773850
$897$	−2.62400	+	2.62400i	−0.0876129	+	0.0876129i
$898$	−14.8482	−	14.8482i	−0.495492	−	0.495492i
$899$	28.3343			0.945001
$900$			16.8354i			0.561181i
$901$		−	30.4155i		−	1.01329i
$902$	4.54735	+	17.8328i	0.151410	+	0.593766i
$903$		−	10.0181i		−	0.333382i
$904$	12.3162	+	12.3162i	0.409632	+	0.409632i
$905$	−34.5435	+	34.5435i	−1.14827	+	1.14827i
$906$			4.35513i			0.144690i
$907$	−24.9510	+	24.9510i	−0.828485	+	0.828485i	−0.987307	−	0.158823i	$-0.949230\pi$
$907$	−24.9510	+	24.9510i	−0.828485	+	0.828485i	0.158823	+	0.987307i	$0.449230\pi$
$908$	−5.28165	+	5.28165i	−0.175278	+	0.175278i
$909$	21.8215	+	21.8215i	0.723772	+	0.723772i
$910$		−	13.5712i		−	0.449881i
$911$	−0.947248			−0.0313837			−0.0156919	−	0.999877i	$-0.504995\pi$
$911$	−0.947248			−0.0313837			−0.0156919	+	0.999877i	$0.504995\pi$
$912$			0.658256i			0.0217970i
$913$	−14.9065	+	25.1109i	−0.493332	+	0.831049i
$914$			19.6158i			0.648834i
$915$	9.89572	−	6.79155i	0.327142	−	0.224522i
$916$	14.4687			0.478060
$917$	43.1511	−	43.1511i	1.42497	−	1.42497i
$918$		−	21.2247i		−	0.700518i
$919$	−10.3745			−0.342224			−0.171112	−	0.985252i	$-0.554736\pi$
$919$	−10.3745			−0.342224			−0.171112	+	0.985252i	$0.554736\pi$
$920$	−95.6431			−3.15326
$921$	6.68554	−	6.68554i	0.220296	−	0.220296i
$922$	14.1474	−	14.1474i	0.465921	−	0.465921i
$923$	2.42614	−	2.42614i	0.0798573	−	0.0798573i
$924$	1.00400	+	3.93726i	0.0330292	+	0.129526i
$925$	10.9326	+	10.9326i	0.359461	+	0.359461i
$926$	24.6539	−	24.6539i	0.810176	−	0.810176i
$927$	31.9987			1.05097
$928$	12.0819			0.396608
$929$			4.90714i			0.160998i	0.996755	+	0.0804990i	$0.0256514\pi$
$929$			4.90714i			0.160998i	−0.996755	+	0.0804990i	$0.974349\pi$
$930$			16.5103i			0.541393i
$931$			4.89096i			0.160295i
$932$	0.0542898	−	0.0542898i	0.00177832	−	0.00177832i
$933$	0.0635008	−	0.0635008i	0.00207892	−	0.00207892i
$934$	42.9773			1.40626
$935$	−22.2620	−	87.3020i	−0.728044	−	2.85508i
$936$	−5.94352	−	5.94352i	−0.194270	−	0.194270i
$937$			4.90896i			0.160369i	0.996780	+	0.0801844i	$0.0255509\pi$
$937$			4.90896i			0.160369i	−0.996780	+	0.0801844i	$0.974449\pi$
$938$	34.5933	−	34.5933i	1.12951	−	1.12951i
$939$	1.67976	−	1.67976i	0.0548170	−	0.0548170i
$940$	7.20508			0.235004
$941$	−28.8752	−	28.8752i	−0.941306	−	0.941306i	0.0570649	−	0.998370i	$-0.481826\pi$
$941$	−28.8752	−	28.8752i	−0.941306	−	0.941306i	−0.998370	+	0.0570649i	$0.981826\pi$
$942$	1.28526			0.0418761
$943$	31.3657	−	31.3657i	1.02141	−	1.02141i
$944$	−6.01743	−	6.01743i	−0.195851	−	0.195851i
$945$	22.5723	+	22.5723i	0.734277	+	0.734277i
$946$	20.2808	+	12.0392i	0.659385	+	0.391428i
$947$	26.0180	−	26.0180i	0.845472	−	0.845472i	−0.144092	−	0.989564i	$-0.546026\pi$
$947$	26.0180	−	26.0180i	0.845472	−	0.845472i	0.989564	+	0.144092i	$0.0460262\pi$
$948$	−3.43818	−	3.43818i	−0.111667	−	0.111667i
$949$	−13.1544			−0.427010
$950$	4.98589	+	4.98589i	0.161764	+	0.161764i
$951$		−	0.195619i		−	0.00634338i
$952$	59.4243	−	59.4243i	1.92595	−	1.92595i
$953$	26.3460	−	26.3460i	0.853429	−	0.853429i	−0.137124	−	0.990554i	$-0.543786\pi$
$953$	26.3460	−	26.3460i	0.853429	−	0.853429i	0.990554	+	0.137124i	$0.0437860\pi$
$954$	−12.2753			−0.397427
$955$	−39.4028	+	39.4028i	−1.27504	+	1.27504i
$956$	−22.7223			−0.734891
$957$	−1.03008	−	4.03954i	−0.0332978	−	0.130580i
$958$	10.2333	+	10.2333i	0.330623	+	0.330623i
$959$	40.5325	+	40.5325i	1.30886	+	1.30886i
$960$			12.5503i			0.405061i
$961$			64.4644i			2.07950i
$962$	−2.18740			−0.0705245
$963$	27.0752			0.872487
$964$	−20.6304			−0.664460
$965$	−54.5898	−	54.5898i	−1.75731	−	1.75731i
$966$	−10.5882	+	10.5882i	−0.340670	+	0.340670i
$967$	−23.8817			−0.767982			−0.383991	−	0.923337i	$-0.625451\pi$
$967$	−23.8817			−0.767982			−0.383991	+	0.923337i	$0.625451\pi$
$968$	−32.3858	−	9.52487i	−1.04092	−	0.306141i
$969$	1.98916	+	1.98916i	0.0639009	+	0.0639009i
$970$	−30.8582	−	30.8582i	−0.990798	−	0.990798i
$971$	−10.3932			−0.333534			−0.166767	−	0.985996i	$-0.553333\pi$
$971$	−10.3932			−0.333534			−0.166767	+	0.985996i	$0.553333\pi$
$972$	8.49439			0.272458
$973$	44.9476			1.44096
$974$	32.8144	−	32.8144i	1.05144	−	1.05144i
$975$	3.19571			0.102345
$976$	−11.5453	+	7.92369i	−0.369556	+	0.253631i
$977$	−9.33447			−0.298636			−0.149318	−	0.988789i	$-0.547708\pi$
$977$	−9.33447			−0.298636			−0.149318	+	0.988789i	$0.547708\pi$
$978$	−4.84151	−	4.84151i	−0.154814	−	0.154814i
$979$	1.35367	+	5.30852i	0.0432635	+	0.169661i
$980$			16.1895i			0.517154i
$981$	−32.7007			−1.04405
$982$	2.93500	+	2.93500i	0.0936597	+	0.0936597i
$983$	−12.1807	+	12.1807i	−0.388505	+	0.388505i	−0.874154	−	0.485649i	$-0.838583\pi$
$983$	−12.1807	+	12.1807i	−0.388505	+	0.388505i	0.485649	+	0.874154i	$0.338583\pi$
$984$	−4.74621	−	4.74621i	−0.151304	−	0.151304i
$985$			11.4290i			0.364159i
$986$	−17.2766	+	17.2766i	−0.550198	+	0.550198i
$987$	2.81483	−	2.81483i	0.0895971	−	0.0895971i
$988$	0.652464			0.0207577
$989$		−	56.8470i		−	1.80763i
$990$	−35.2340	+	8.98465i	−1.11981	+	0.285551i
$991$	14.4736			0.459768			0.229884	−	0.973218i	$-0.426165\pi$
$991$	14.4736			0.459768			0.229884	+	0.973218i	$0.426165\pi$
$992$			40.7066i			1.29244i
$993$	1.64044	+	1.64044i	0.0520578	+	0.0520578i
$994$	9.78979	−	9.78979i	0.310513	−	0.310513i
$995$		−	56.5644i		−	1.79321i
$996$		−	3.01809i		−	0.0956318i
$997$	−35.7402	+	35.7402i	−1.13190	+	1.13190i	−0.142045	+	0.989860i	$0.545368\pi$
$997$	−35.7402	+	35.7402i	−1.13190	+	1.13190i	−0.989860	+	0.142045i	$0.954632\pi$
$998$		−	2.34519i		−	0.0742356i
$999$	3.63819	−	3.63819i	0.115107	−	0.115107i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.f.a.538.18	✓	120
11.10	odd	2	inner	671.2.f.a.538.43	yes	120
61.11	odd	4	inner	671.2.f.a.560.43	yes	120
671.560	even	4	inner	671.2.f.a.560.18	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.f.a.538.18	✓	120	1.1	even	1	trivial
671.2.f.a.538.43	yes	120	11.10	odd	2	inner
671.2.f.a.560.18	yes	120	671.560	even	4	inner
671.2.f.a.560.43	yes	120	61.11	odd	4	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:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.777546 - 0.777546i) q^{2} +0.433435i q^{3} -0.790844i q^{4} +3.54542i q^{5} +(0.337016 - 0.337016i) q^{6} +(-2.52725 - 2.52725i) q^{7} +(-2.17001 + 2.17001i) q^{8} +2.81213 q^{9} +O(q^{10})\)	\(q+(-0.777546 - 0.777546i) q^{2} +0.433435i q^{3} -0.790844i q^{4} +3.54542i q^{5} +(0.337016 - 0.337016i) q^{6} +(-2.52725 - 2.52725i) q^{7} +(-2.17001 + 2.17001i) q^{8} +2.81213 q^{9} +(2.75673 - 2.75673i) q^{10} +(-2.85197 - 1.69300i) q^{11} +0.342780 q^{12} +0.973971i q^{13} +3.93010i q^{14} -1.53671 q^{15} +1.79288 q^{16} +(5.41782 - 5.41782i) q^{17} +(-2.18656 - 2.18656i) q^{18} +0.847071 q^{19} +2.80388 q^{20} +(1.09540 - 1.09540i) q^{21} +(0.901150 + 3.53393i) q^{22} +(6.21575 - 6.21575i) q^{23} +(-0.940559 - 0.940559i) q^{24} -7.57002 q^{25} +(0.757307 - 0.757307i) q^{26} +2.51918i q^{27} +(-1.99866 + 1.99866i) q^{28} +(2.05058 - 2.05058i) q^{29} +(1.19486 + 1.19486i) q^{30} +(6.90885 + 6.90885i) q^{31} +(2.94598 + 2.94598i) q^{32} +(0.733808 - 1.23614i) q^{33} -8.42521 q^{34} +(8.96016 - 8.96016i) q^{35} -2.22396i q^{36} +(-1.44419 - 1.44419i) q^{37} +(-0.658637 - 0.658637i) q^{38} -0.422153 q^{39} +(-7.69360 - 7.69360i) q^{40} +5.04616 q^{41} -1.70345 q^{42} +(4.57281 - 4.57281i) q^{43} +(-1.33890 + 2.25546i) q^{44} +9.97020i q^{45} -9.66607 q^{46} +2.56969 q^{47} +0.777096i q^{48} +5.77396i q^{49} +(5.88604 + 5.88604i) q^{50} +(2.34827 + 2.34827i) q^{51} +0.770259 q^{52} +(2.80698 - 2.80698i) q^{53} +(1.95878 - 1.95878i) q^{54} +(6.00241 - 10.1114i) q^{55} +10.9683 q^{56} +0.367150i q^{57} -3.18884 q^{58} +(-3.35630 - 3.35630i) q^{59} +1.21530i q^{60} +(-6.43954 + 4.41954i) q^{61} -10.7439i q^{62} +(-7.10696 - 7.10696i) q^{63} -8.16702i q^{64} -3.45314 q^{65} +(-1.53173 + 0.390590i) q^{66} +(-8.80214 - 8.80214i) q^{67} +(-4.28465 - 4.28465i) q^{68} +(2.69413 + 2.69413i) q^{69} -13.9339 q^{70} +(-2.49098 - 2.49098i) q^{71} +(-6.10236 + 6.10236i) q^{72} +13.5059i q^{73} +2.24585i q^{74} -3.28111i q^{75} -0.669901i q^{76} +(2.92900 + 11.4863i) q^{77} +(0.328244 + 0.328244i) q^{78} +(-10.0303 - 10.0303i) q^{79} +6.35651i q^{80} +7.34450 q^{81} +(-3.92362 - 3.92362i) q^{82} -8.80475i q^{83} +(-0.866289 - 0.866289i) q^{84} +(19.2085 + 19.2085i) q^{85} -7.11115 q^{86} +(0.888793 + 0.888793i) q^{87} +(9.86264 - 2.51497i) q^{88} +(-1.16800 - 1.16800i) q^{89} +(7.75229 - 7.75229i) q^{90} +(2.46147 - 2.46147i) q^{91} +(-4.91569 - 4.91569i) q^{92} +(-2.99454 + 2.99454i) q^{93} +(-1.99805 - 1.99805i) q^{94} +3.00322i q^{95} +(-1.27689 + 1.27689i) q^{96} -11.1938i q^{97} +(4.48952 - 4.48952i) q^{98} +(-8.02012 - 4.76095i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 120 q^{9}+O(q^{10}) \) 120 * q - 120 * q^9	\( 120 q - 120 q^{9} - 4 q^{11} + 16 q^{12} + 16 q^{15} - 148 q^{16} + 56 q^{20} - 4 q^{22} - 4 q^{23} - 104 q^{25} + 40 q^{26} - 2 q^{33} - 8 q^{34} - 12 q^{37} + 20 q^{38} + 16 q^{42} - 10 q^{44} - 4 q^{53} + 50 q^{55} - 24 q^{56} + 64 q^{58} - 56 q^{67} + 68 q^{69} + 144 q^{70} - 12 q^{71} - 64 q^{77} + 84 q^{78} + 72 q^{81} + 40 q^{82} - 80 q^{86} + 4 q^{89} - 4 q^{91} + 4 q^{92} + 64 q^{93} + 24 q^{99}+O(q^{100}) \) 120 * q - 120 * q^9 - 4 * q^11 + 16 * q^12 + 16 * q^15 - 148 * q^16 + 56 * q^20 - 4 * q^22 - 4 * q^23 - 104 * q^25 + 40 * q^26 - 2 * q^33 - 8 * q^34 - 12 * q^37 + 20 * q^38 + 16 * q^42 - 10 * q^44 - 4 * q^53 + 50 * q^55 - 24 * q^56 + 64 * q^58 - 56 * q^67 + 68 * q^69 + 144 * q^70 - 12 * q^71 - 64 * q^77 + 84 * q^78 + 72 * q^81 + 40 * q^82 - 80 * q^86 + 4 * q^89 - 4 * q^91 + 4 * q^92 + 64 * q^93 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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