LMFDB - Embedded newform 882.2.bb.b.151.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(25,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([28, 16]))

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

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

chi := DirichletCharacter("882.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.bb (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$28$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			151.7
Character	$\chi$	$=$	882.151
Dual form			882.2.bb.b.625.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.900969 - 0.433884i) q^{2} +(-1.16043 - 1.28585i) q^{3} +(0.623490 - 0.781831i) q^{4} +(1.63845 + 1.52026i) q^{5} +(-1.60342 - 0.655019i) q^{6} +(-2.40112 - 1.11113i) q^{7} +(0.222521 - 0.974928i) q^{8} +(-0.306815 + 2.98427i) q^{9} +O(q^{10})$	\(q+(0.900969 - 0.433884i) q^{2} +(-1.16043 - 1.28585i) q^{3} +(0.623490 - 0.781831i) q^{4} +(1.63845 + 1.52026i) q^{5} +(-1.60342 - 0.655019i) q^{6} +(-2.40112 - 1.11113i) q^{7} +(0.222521 - 0.974928i) q^{8} +(-0.306815 + 2.98427i) q^{9} +(2.13581 + 0.658810i) q^{10} +(-3.40713 - 2.32294i) q^{11} +(-1.72883 + 0.105545i) q^{12} +(-1.28508 - 0.876152i) q^{13} +(-2.64544 + 0.0407182i) q^{14} +(0.0535212 - 3.87095i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(-1.51977 + 0.229068i) q^{17} +(1.01840 + 2.82186i) q^{18} +(-2.94551 - 5.10177i) q^{19} +(2.21014 - 0.333125i) q^{20} +(1.35759 + 4.37687i) q^{21} +(-4.07760 - 0.614599i) q^{22} +(-0.680358 - 1.73352i) q^{23} +(-1.51183 + 0.845205i) q^{24} +(-0.000320921 - 0.00428239i) q^{25} +(-1.53796 - 0.231811i) q^{26} +(4.19336 - 3.06851i) q^{27} +(-2.36579 + 1.18450i) q^{28} +(-0.710782 + 0.107133i) q^{29} +(-1.63132 - 3.51083i) q^{30} -7.55886 q^{31} +(-0.623490 - 0.781831i) q^{32} +(0.966775 + 7.07665i) q^{33} +(-1.26987 + 0.865786i) q^{34} +(-2.24492 - 5.47086i) q^{35} +(2.14190 + 2.10054i) q^{36} +(2.87757 - 7.33192i) q^{37} +(-4.86739 - 3.31853i) q^{38} +(0.364642 + 2.66913i) q^{39} +(1.84673 - 1.25908i) q^{40} +(9.16519 - 2.82709i) q^{41} +(3.12220 + 3.35438i) q^{42} +(4.42087 + 1.36366i) q^{43} +(-3.94046 + 1.21547i) q^{44} +(-5.03956 + 4.42314i) q^{45} +(-1.36513 - 1.26666i) q^{46} +(-11.0562 + 5.32437i) q^{47} +(-0.995391 + 1.41746i) q^{48} +(4.53079 + 5.33591i) q^{49} +(-0.00214720 - 0.00371906i) q^{50} +(2.05813 + 1.68837i) q^{51} +(-1.48624 + 0.458444i) q^{52} +(-0.397156 - 1.01194i) q^{53} +(2.44671 - 4.58406i) q^{54} +(-2.05094 - 8.98573i) q^{55} +(-1.61757 + 2.09367i) q^{56} +(-3.14206 + 9.70772i) q^{57} +(-0.593909 + 0.404920i) q^{58} +(2.41008 + 10.5592i) q^{59} +(-2.99306 - 2.45534i) q^{60} +(2.15012 + 2.69616i) q^{61} +(-6.81030 + 3.27967i) q^{62} +(4.05260 - 6.82469i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(-0.773560 - 3.38919i) q^{65} +(3.94148 + 5.95638i) q^{66} -7.50408 q^{67} +(-0.768467 + 1.33102i) q^{68} +(-1.43954 + 2.88647i) q^{69} +(-4.39632 - 3.95504i) q^{70} +(5.97635 - 7.49410i) q^{71} +(2.84117 + 0.963185i) q^{72} +(-13.7677 + 9.38663i) q^{73} +(-0.588603 - 7.85437i) q^{74} +(-0.00513410 + 0.00538206i) q^{75} +(-5.82522 - 0.878011i) q^{76} +(5.59985 + 9.36341i) q^{77} +(1.48662 + 2.24659i) q^{78} +12.0157 q^{79} +(1.11755 - 1.93566i) q^{80} +(-8.81173 - 1.83124i) q^{81} +(7.03093 - 6.52375i) q^{82} +(6.89837 - 4.70323i) q^{83} +(4.26841 + 1.66752i) q^{84} +(-2.83831 - 1.93512i) q^{85} +(4.57474 - 0.689531i) q^{86} +(0.962568 + 0.789638i) q^{87} +(-3.02286 + 2.80480i) q^{88} +(-0.680522 - 9.08093i) q^{89} +(-2.62136 + 6.17169i) q^{90} +(2.11212 + 3.53164i) q^{91} +(-1.77952 - 0.548909i) q^{92} +(8.77151 + 9.71955i) q^{93} +(-7.65110 + 9.59418i) q^{94} +(2.92995 - 12.8369i) q^{95} +(-0.281802 + 1.70897i) q^{96} +(-4.58542 + 7.94219i) q^{97} +(6.39727 + 2.84165i) q^{98} +(7.97763 - 9.45507i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q + 56 q^{2} + 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} + 2 q^{7} + 56 q^{8} + 5 q^{9}+O(q^{10}) $ 336 * q + 56 * q^2 + 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 + 2 * q^7 + 56 * q^8 + 5 * q^9	\( 336 q + 56 q^{2} + 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} + 2 q^{7} + 56 q^{8} + 5 q^{9} - 2 q^{10} - 2 q^{12} + 19 q^{13} - 2 q^{14} + q^{15} - 56 q^{16} + 7 q^{17} + 2 q^{18} + 38 q^{19} + 2 q^{20} + 4 q^{21} - 42 q^{23} + 2 q^{24} + 24 q^{25} + 9 q^{26} + 35 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 88 q^{31} + 56 q^{32} + 26 q^{33} - 7 q^{34} - 2 q^{35} + 5 q^{36} + 52 q^{37} + 11 q^{38} - 60 q^{39} - 2 q^{40} + 3 q^{41} - 53 q^{42} + q^{43} + 108 q^{45} - 42 q^{46} + 3 q^{47} - 2 q^{48} + 70 q^{49} + 172 q^{50} + 13 q^{51} + 5 q^{52} - 78 q^{53} + 14 q^{54} + 23 q^{55} - 2 q^{56} - 30 q^{57} + 38 q^{58} - 28 q^{59} + q^{60} - 37 q^{61} - 24 q^{62} + 26 q^{63} - 56 q^{64} - 14 q^{65} + 2 q^{66} - 58 q^{67} - 21 q^{68} + 19 q^{69} + 44 q^{70} + 7 q^{71} + 2 q^{72} - 8 q^{73} + 4 q^{74} + q^{75} - 4 q^{76} - 13 q^{77} + 4 q^{78} + 18 q^{79} - 12 q^{80} - 87 q^{81} - 3 q^{82} + 185 q^{83} - 17 q^{84} - 159 q^{85} - q^{86} - 132 q^{87} + 47 q^{89} + 60 q^{90} + 45 q^{91} - 21 q^{92} + 53 q^{93} + 18 q^{94} + 26 q^{95} + 2 q^{96} + 111 q^{97} - 14 q^{98} - 157 q^{99}+O(q^{100}) \) 336 * q + 56 * q^2 + 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 + 2 * q^7 + 56 * q^8 + 5 * q^9 - 2 * q^10 - 2 * q^12 + 19 * q^13 - 2 * q^14 + q^15 - 56 * q^16 + 7 * q^17 + 2 * q^18 + 38 * q^19 + 2 * q^20 + 4 * q^21 - 42 * q^23 + 2 * q^24 + 24 * q^25 + 9 * q^26 + 35 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 88 * q^31 + 56 * q^32 + 26 * q^33 - 7 * q^34 - 2 * q^35 + 5 * q^36 + 52 * q^37 + 11 * q^38 - 60 * q^39 - 2 * q^40 + 3 * q^41 - 53 * q^42 + q^43 + 108 * q^45 - 42 * q^46 + 3 * q^47 - 2 * q^48 + 70 * q^49 + 172 * q^50 + 13 * q^51 + 5 * q^52 - 78 * q^53 + 14 * q^54 + 23 * q^55 - 2 * q^56 - 30 * q^57 + 38 * q^58 - 28 * q^59 + q^60 - 37 * q^61 - 24 * q^62 + 26 * q^63 - 56 * q^64 - 14 * q^65 + 2 * q^66 - 58 * q^67 - 21 * q^68 + 19 * q^69 + 44 * q^70 + 7 * q^71 + 2 * q^72 - 8 * q^73 + 4 * q^74 + q^75 - 4 * q^76 - 13 * q^77 + 4 * q^78 + 18 * q^79 - 12 * q^80 - 87 * q^81 - 3 * q^82 + 185 * q^83 - 17 * q^84 - 159 * q^85 - q^86 - 132 * q^87 + 47 * q^89 + 60 * q^90 + 45 * q^91 - 21 * q^92 + 53 * q^93 + 18 * q^94 + 26 * q^95 + 2 * q^96 + 111 * q^97 - 14 * q^98 - 157 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.900969	−	0.433884i	0.637081	−	0.306802i
$2$	0.900969	−	0.433884i	0.637081	−	0.306802i
$3$	−1.16043	−	1.28585i	−0.669973	−	0.742385i
$3$	−1.16043	−	1.28585i	−0.669973	−	0.742385i
$4$	0.623490	−	0.781831i	0.311745	−	0.390916i
$5$	1.63845	+	1.52026i	0.732737	+	0.679881i	0.955500	−	0.294992i	$-0.0953170\pi$
$5$	1.63845	+	1.52026i	0.732737	+	0.679881i	−0.222763	+	0.974873i	$0.571508\pi$
$6$	−1.60342	−	0.655019i	−0.654593	−	0.267410i
$7$	−2.40112	−	1.11113i	−0.907540	−	0.419966i
$7$	−2.40112	−	1.11113i	−0.907540	−	0.419966i
$8$	0.222521	−	0.974928i	0.0786730	−	0.344689i
$9$	−0.306815	+	2.98427i	−0.102272	+	0.994757i
$10$	2.13581	+	0.658810i	0.675402	+	0.208334i
$11$	−3.40713	−	2.32294i	−1.02729	−	0.700393i	−0.0724043	−	0.997375i	$-0.523067\pi$
$11$	−3.40713	−	2.32294i	−1.02729	−	0.700393i	−0.954883	+	0.296983i	$0.904020\pi$
$12$	−1.72883	+	0.105545i	−0.499071	+	0.0304683i
$13$	−1.28508	−	0.876152i	−0.356417	−	0.243001i	0.371853	−	0.928292i	$-0.378723\pi$
$13$	−1.28508	−	0.876152i	−0.356417	−	0.243001i	−0.728269	+	0.685291i	$0.759675\pi$
$14$	−2.64544	+	0.0407182i	−0.707023	+	0.0108824i
$15$	0.0535212	−	3.87095i	0.0138191	−	0.999475i
$16$	−0.222521	−	0.974928i	−0.0556302	−	0.243732i
$17$	−1.51977	+	0.229068i	−0.368598	+	0.0555572i	−0.330730	−	0.943726i	$-0.607295\pi$
$17$	−1.51977	+	0.229068i	−0.368598	+	0.0555572i	−0.0378682	+	0.999283i	$0.512057\pi$
$18$	1.01840	+	2.82186i	0.240038	+	0.665118i
$19$	−2.94551	−	5.10177i	−0.675746	−	1.17043i	−0.976250	−	0.216646i	$-0.930488\pi$
$19$	−2.94551	−	5.10177i	−0.675746	−	1.17043i	0.300504	−	0.953781i	$-0.402845\pi$
$20$	2.21014	−	0.333125i	0.494203	−	0.0744891i
$21$	1.35759	+	4.37687i	0.296250	+	0.955110i
$22$	−4.07760	−	0.614599i	−0.869347	−	0.131033i
$23$	−0.680358	−	1.73352i	−0.141864	−	0.361465i	0.842228	−	0.539121i	$-0.181244\pi$
$23$	−0.680358	−	1.73352i	−0.141864	−	0.361465i	−0.984093	+	0.177657i	$0.943148\pi$
$24$	−1.51183	+	0.845205i	−0.308601	+	0.172527i
$25$	−0.000320921	−	0.00428239i	−6.41842e−5	−	0.000856478i
$26$	−1.53796	−	0.231811i	−0.301620	−	0.0454619i
$27$	4.19336	−	3.06851i	0.807012	−	0.590535i
$28$	−2.36579	+	1.18450i	−0.447092	+	0.223849i
$29$	−0.710782	+	0.107133i	−0.131989	+	0.0198941i	−0.214704	−	0.976679i	$-0.568879\pi$
$29$	−0.710782	+	0.107133i	−0.131989	+	0.0198941i	0.0827155	+	0.996573i	$0.473641\pi$
$30$	−1.63132	−	3.51083i	−0.297837	−	0.640986i
$31$	−7.55886			−1.35761			−0.678806	−	0.734318i	$-0.737502\pi$
$31$	−7.55886			−1.35761			−0.678806	+	0.734318i	$0.737502\pi$
$32$	−0.623490	−	0.781831i	−0.110218	−	0.138210i
$33$	0.966775	+	7.07665i	0.168294	+	1.23189i
$34$	−1.26987	+	0.865786i	−0.217782	+	0.148481i
$35$	−2.24492	−	5.47086i	−0.379461	−	0.924744i
$36$	2.14190	+	2.10054i	0.356983	+	0.350090i
$37$	2.87757	−	7.33192i	0.473069	−	1.20536i	−0.472903	−	0.881114i	$-0.656794\pi$
$37$	2.87757	−	7.33192i	0.473069	−	1.20536i	0.945973	−	0.324247i	$-0.105111\pi$
$38$	−4.86739	−	3.31853i	−0.789595	−	0.538337i
$39$	0.364642	+	2.66913i	0.0583895	+	0.427403i
$40$	1.84673	−	1.25908i	0.291994	−	0.199078i
$41$	9.16519	−	2.82709i	1.43136	−	0.441517i	0.520370	−	0.853941i	$-0.325794\pi$
$41$	9.16519	−	2.82709i	1.43136	−	0.441517i	0.910992	+	0.412424i	$0.135318\pi$
$42$	3.12220	+	3.35438i	0.481765	+	0.517593i
$43$	4.42087	+	1.36366i	0.674177	+	0.207956i	0.612895	−	0.790165i	$-0.290005\pi$
$43$	4.42087	+	1.36366i	0.674177	+	0.207956i	0.0612818	+	0.998121i	$0.480481\pi$
$44$	−3.94046	+	1.21547i	−0.594046	+	0.183239i
$45$	−5.03956	+	4.42314i	−0.751254	+	0.659362i
$46$	−1.36513	−	1.26666i	−0.201277	−	0.186758i
$47$	−11.0562	+	5.32437i	−1.61271	+	0.776639i	−0.999908	−	0.0135998i	$-0.995671\pi$
$47$	−11.0562	+	5.32437i	−1.61271	+	0.776639i	−0.612799	+	0.790238i	$0.709957\pi$
$48$	−0.995391	+	1.41746i	−0.143672	+	0.204593i
$49$	4.53079	+	5.33591i	0.647256	+	0.762272i
$50$	−0.00214720	−	0.00371906i	−0.000303660	−	0.000525954i
$51$	2.05813	+	1.68837i	0.288195	+	0.236420i
$52$	−1.48624	+	0.458444i	−0.206104	+	0.0635747i
$53$	−0.397156	−	1.01194i	−0.0545536	−	0.139000i	0.900999	−	0.433822i	$-0.142835\pi$
$53$	−0.397156	−	1.01194i	−0.0545536	−	0.139000i	−0.955552	+	0.294821i	$0.904740\pi$
$54$	2.44671	−	4.58406i	0.332955	−	0.623812i
$55$	−2.05094	−	8.98573i	−0.276548	−	1.21164i
$56$	−1.61757	+	2.09367i	−0.216157	+	0.279779i
$57$	−3.14206	+	9.70772i	−0.416176	+	1.28582i
$58$	−0.593909	+	0.404920i	−0.0779841	+	0.0531686i
$59$	2.41008	+	10.5592i	0.313765	+	1.37470i	0.848285	+	0.529540i	$0.177635\pi$
$59$	2.41008	+	10.5592i	0.313765	+	1.37470i	−0.534520	+	0.845156i	$0.679508\pi$
$60$	−2.99306	−	2.45534i	−0.386402	−	0.316983i
$61$	2.15012	+	2.69616i	0.275294	+	0.345208i	0.900188	−	0.435502i	$-0.143429\pi$
$61$	2.15012	+	2.69616i	0.275294	+	0.345208i	−0.624894	+	0.780710i	$0.714858\pi$
$62$	−6.81030	+	3.27967i	−0.864909	+	0.416518i
$63$	4.05260	−	6.82469i	0.510580	−	0.859830i
$64$	−0.900969	−	0.433884i	−0.112621	−	0.0542355i
$65$	−0.773560	−	3.38919i	−0.0959483	−	0.420377i
$66$	3.94148	+	5.95638i	0.485162	+	0.733179i
$67$	−7.50408			−0.916769			−0.458385	−	0.888754i	$-0.651572\pi$
$67$	−7.50408			−0.916769			−0.458385	+	0.888754i	$0.651572\pi$
$68$	−0.768467	+	1.33102i	−0.0931903	+	0.161410i
$69$	−1.43954	+	2.88647i	−0.173301	+	0.347490i
$70$	−4.39632	−	3.95504i	−0.525461	−	0.472717i
$71$	5.97635	−	7.49410i	0.709262	−	0.889386i	−0.288415	−	0.957505i	$-0.593128\pi$
$71$	5.97635	−	7.49410i	0.709262	−	0.889386i	0.997677	+	0.0681191i	$0.0216998\pi$
$72$	2.84117	+	0.963185i	0.334836	+	0.113512i
$73$	−13.7677	+	9.38663i	−1.61138	+	1.09862i	−0.680842	+	0.732430i	$0.738386\pi$
$73$	−13.7677	+	9.38663i	−1.61138	+	1.09862i	−0.930540	+	0.366191i	$0.880662\pi$
$74$	−0.588603	−	7.85437i	−0.0684237	−	0.913051i
$75$	−0.00513410	+	0.00538206i	−0.000592835	+	0.000621467i
$76$	−5.82522	−	0.878011i	−0.668199	−	0.100715i
$77$	5.59985	+	9.36341i	0.638162	+	1.06706i
$78$	1.48662	+	2.24659i	0.168327	+	0.254376i
$79$	12.0157			1.35187			0.675934	−	0.736962i	$-0.263740\pi$
$79$	12.0157			1.35187			0.675934	+	0.736962i	$0.263740\pi$
$80$	1.11755	−	1.93566i	0.124946	−	0.216413i
$81$	−8.81173	−	1.83124i	−0.979081	−	0.203471i
$82$	7.03093	−	6.52375i	0.776436	−	0.720427i
$83$	6.89837	−	4.70323i	0.757194	−	0.516246i	−0.122104	−	0.992517i	$-0.538964\pi$
$83$	6.89837	−	4.70323i	0.757194	−	0.516246i	0.879299	+	0.476271i	$0.158012\pi$
$84$	4.26841	+	1.66752i	0.465722	+	0.181942i
$85$	−2.83831	−	1.93512i	−0.307857	−	0.209894i
$86$	4.57474	−	0.689531i	0.493307	−	0.0743540i
$87$	0.962568	+	0.789638i	0.103198	+	0.0846581i
$88$	−3.02286	+	2.80480i	−0.322237	+	0.298993i
$89$	−0.680522	−	9.08093i	−0.0721351	−	0.962577i	−0.909439	−	0.415838i	$-0.863488\pi$
$89$	−0.680522	−	9.08093i	−0.0721351	−	0.962577i	0.837303	−	0.546738i	$-0.184131\pi$
$90$	−2.62136	+	6.17169i	−0.276316	+	0.650554i
$91$	2.11212	+	3.53164i	0.221410	+	0.370216i
$92$	−1.77952	−	0.548909i	−0.185528	−	0.0572278i
$93$	8.77151	+	9.71955i	0.909563	+	1.00787i
$94$	−7.65110	+	9.59418i	−0.789151	+	0.989564i
$95$	2.92995	−	12.8369i	0.300606	−	1.31704i
$96$	−0.281802	+	1.70897i	−0.0287613	+	0.174421i
$97$	−4.58542	+	7.94219i	−0.465579	+	0.806407i	−0.999227	−	0.0392996i	$-0.987487\pi$
$97$	−4.58542	+	7.94219i	−0.465579	+	0.806407i	0.533648	+	0.845707i	$0.320821\pi$
$98$	6.39727	+	2.84165i	0.646222	+	0.287050i
$99$	7.97763	−	9.45507i	0.801782	−	0.950270i
$100$	−0.00354820	−	0.00241912i	−0.000354820	−	0.000241912i
$101$	2.12883	−	0.656658i	0.211827	−	0.0653399i	−0.187026	−	0.982355i	$-0.559885\pi$
$101$	2.12883	−	0.656658i	0.211827	−	0.0653399i	0.398852	+	0.917015i	$0.369409\pi$
$102$	2.58687	+	0.628185i	0.256138	+	0.0621996i
$103$	1.11491	+	1.03448i	0.109855	+	0.101931i	0.733188	−	0.680026i	$-0.238031\pi$
$103$	1.11491	+	1.03448i	0.109855	+	0.101931i	−0.623333	+	0.781956i	$0.714222\pi$
$104$	−1.14014	+	1.05790i	−0.111800	+	0.103735i
$105$	−4.42963	+	9.23516i	−0.432287	+	0.901260i
$106$	−0.796889	−	0.739405i	−0.0774007	−	0.0718174i
$107$	−0.623515	−	8.32023i	−0.0602774	−	0.804347i	−0.942647	−	0.333790i	$-0.891672\pi$
$107$	−0.623515	−	8.32023i	−0.0602774	−	0.804347i	0.882370	−	0.470556i	$-0.155947\pi$
$108$	0.215456	−	5.19168i	0.0207323	−	0.499570i
$109$	0.775943	−	10.3542i	0.0743218	−	0.991756i	−0.828010	−	0.560714i	$-0.810527\pi$
$109$	0.775943	−	10.3542i	0.0743218	−	0.991756i	0.902332	−	0.431042i	$-0.141854\pi$
$110$	−5.74659	−	7.20600i	−0.547916	−	0.687065i
$111$	−12.7670	+	4.80805i	−1.21179	+	0.456360i
$112$	−0.548968	+	2.58817i	−0.0518726	+	0.244559i
$113$	−0.392261	−	5.23436i	−0.0369008	−	0.492407i	−0.984783	−	0.173787i	$-0.944400\pi$
$113$	−0.392261	−	5.23436i	−0.0369008	−	0.492407i	0.947883	−	0.318620i	$-0.103219\pi$
$114$	1.38113	+	10.1096i	0.129354	+	0.946854i
$115$	1.52067	−	3.87461i	0.141804	−	0.361310i
$116$	−0.359405	+	0.622508i	−0.0333699	+	0.0577984i
$117$	3.00896	−	3.56621i	0.278178	−	0.329696i
$118$	6.75288	+	8.46785i	0.621653	+	0.779529i
$119$	3.90367	+	1.13863i	0.357849	+	0.104378i
$120$	−3.76199	−	0.913547i	−0.343421	−	0.0833950i
$121$	2.19371	+	5.58948i	0.199428	+	0.508135i
$122$	3.10701	+	1.49626i	0.281295	+	0.135465i
$123$	−14.2708	−	8.50442i	−1.28675	−	0.766818i
$124$	−4.71287	+	5.90975i	−0.423228	+	0.530712i
$125$	6.97382	−	8.74489i	0.623757	−	0.782167i
$126$	0.690146	−	7.90719i	0.0614831	−	0.704429i
$127$	9.54021	+	11.9630i	0.846557	+	1.06155i	0.997333	+	0.0729805i	$0.0232511\pi$
$127$	9.54021	+	11.9630i	0.846557	+	1.06155i	−0.150777	+	0.988568i	$0.548177\pi$
$128$	−1.00000			−0.0883883
$129$	−3.37664	−	7.26700i	−0.297297	−	0.639824i
$130$	−2.16747	−	2.71792i	−0.190099	−	0.238377i
$131$	14.5635	+	4.49225i	1.27242	+	0.392490i	0.856139	−	0.516746i	$-0.172857\pi$
$131$	14.5635	+	4.49225i	1.27242	+	0.392490i	0.416281	+	0.909236i	$0.363333\pi$
$132$	6.13552	+	3.65637i	0.534029	+	0.318246i
$133$	1.40382	+	15.5228i	0.121727	+	1.34600i
$134$	−6.76094	+	3.25590i	−0.584056	+	0.281267i
$135$	11.5355	+	1.34739i	0.992821	+	0.115965i
$136$	−0.114855	+	1.53264i	−0.00984875	+	0.131422i
$137$	9.18826	−	8.52546i	0.785006	−	0.728379i	−0.181954	−	0.983307i	$-0.558242\pi$
$137$	9.18826	−	8.52546i	0.785006	−	0.728379i	0.966960	+	0.254928i	$0.0820517\pi$
$138$	−0.0445930	+	3.22521i	−0.00379600	+	0.274548i
$139$	−15.5302	+	4.79044i	−1.31726	+	0.406320i	−0.872185	−	0.489176i	$-0.837298\pi$
$139$	−15.5302	+	4.79044i	−1.31726	+	0.406320i	−0.445071	+	0.895495i	$0.646822\pi$
$140$	−5.67697	−	1.65587i	−0.479792	−	0.139947i
$141$	19.6762	+	8.03801i	1.65704	+	0.676923i
$142$	2.13293	−	9.34499i	0.178992	−	0.784214i
$143$	2.34318	+	5.97032i	0.195946	+	0.499264i
$144$	2.97772	−	0.364940i	0.248143	−	0.0304117i
$145$	−1.32745	−	0.905041i	−0.110239	−	0.0751595i
$146$	−8.33152	+	14.4306i	−0.689522	+	1.19429i
$147$	1.60351	−	12.0179i	0.132255	−	0.991216i
$148$	−3.93819	−	6.82115i	−0.323718	−	0.560695i
$149$	0.609326	−	8.13090i	0.0499180	−	0.666109i	−0.914983	−	0.403493i	$-0.867796\pi$
$149$	0.609326	−	8.13090i	0.0499180	−	0.666109i	0.964901	−	0.262616i	$-0.0845851\pi$
$150$	−0.00229048	+	0.00707667i	−0.000187017	+	0.000577808i
$151$	5.46026	+	0.823001i	0.444349	+	0.0669749i	0.367406	−	0.930061i	$-0.380246\pi$
$151$	5.46026	+	0.823001i	0.444349	+	0.0669749i	0.0769432	+	0.997035i	$0.475484\pi$
$152$	−5.62930	+	1.73641i	−0.456596	+	0.140841i
$153$	−0.217313	−	4.60568i	−0.0175688	−	0.372347i
$154$	9.10793	+	6.00646i	0.733938	+	0.484014i
$155$	−12.3848	−	11.4914i	−0.994772	−	0.923013i
$156$	2.31416	+	1.37909i	0.185281	+	0.110415i
$157$	1.09644	+	4.80382i	0.0875054	+	0.383386i	0.999649	−	0.0264840i	$-0.00843110\pi$
$157$	1.09644	+	4.80382i	0.0875054	+	0.383386i	−0.912144	+	0.409870i	$0.865574\pi$
$158$	10.8257	−	5.21340i	0.861250	−	0.414756i
$159$	−0.840328	+	1.68496i	−0.0666424	+	0.133626i
$160$	0.167030	−	2.22886i	0.0132049	−	0.176207i
$161$	−0.292541	+	4.91837i	−0.0230554	+	0.387622i
$162$	−8.73364	+	2.17338i	−0.686179	+	0.170757i
$163$	−4.98776	+	4.62797i	−0.390672	+	0.362490i	−0.850916	−	0.525302i	$-0.823952\pi$
$163$	−4.98776	+	4.62797i	−0.390672	+	0.362490i	0.460244	+	0.887792i	$0.347762\pi$
$164$	3.50410	−	8.92830i	0.273624	−	0.697183i
$165$	−9.17433	+	13.0645i	−0.714221	+	1.01707i
$166$	4.17456	−	7.23055i	0.324009	−	0.561200i
$167$	6.29220	−	16.0323i	0.486905	−	1.24061i	−0.450626	−	0.892713i	$-0.648799\pi$
$167$	6.29220	−	16.0323i	0.486905	−	1.24061i	0.937531	−	0.347901i	$-0.113106\pi$
$168$	4.56922	−	0.349608i	0.352523	−	0.0269729i
$169$	−3.86565	−	9.84951i	−0.297357	−	0.757654i
$170$	−3.39684	−	0.511992i	−0.260526	−	0.0392680i
$171$	16.1288	−	7.22489i	1.23340	−	0.552501i
$172$	3.82252	−	2.60615i	0.291464	−	0.198717i
$173$	2.63376	−	3.30263i	0.200241	−	0.251094i	−0.671565	−	0.740946i	$-0.734378\pi$
$173$	2.63376	−	3.30263i	0.200241	−	0.251094i	0.871806	+	0.489852i	$0.162949\pi$
$174$	1.20986	+	0.293797i	0.0917189	+	0.0222727i
$175$	−0.00398771	+	0.0106391i	−0.000301442	+	0.000804243i
$176$	−1.50654	+	3.83860i	−0.113560	+	0.289346i
$177$	10.7809	−	15.3522i	0.810339	−	1.15394i
$178$	−4.55320	−	7.88637i	−0.341276	−	0.591108i
$179$	12.4168	−	1.87153i	0.928075	−	0.139885i	0.332426	−	0.943129i	$-0.392133\pi$
$179$	12.4168	−	1.87153i	0.928075	−	0.139885i	0.595649	+	0.803245i	$0.296895\pi$
$180$	0.316031	+	6.69787i	0.0235556	+	0.499230i
$181$	10.7979	+	5.20000i	0.802602	+	0.386513i	0.789769	−	0.613405i	$-0.210201\pi$
$181$	10.7979	+	5.20000i	0.802602	+	0.386513i	0.0128334	+	0.999918i	$0.495915\pi$
$182$	3.43527	+	2.26548i	0.254639	+	0.167929i
$183$	0.971801	−	5.89343i	0.0718376	−	0.435655i
$184$	−1.84146	+	0.277555i	−0.135754	+	0.0204616i
$185$	15.8612	−	7.63834i	1.16614	−	0.561582i
$186$	12.1200	+	4.95120i	0.888682	+	0.363039i
$187$	5.71015	+	2.74986i	0.417568	+	0.201090i
$188$	−2.73065	+	11.9637i	−0.199153	+	0.872546i
$189$	−13.4783	+	2.70853i	−0.980400	+	0.197016i
$190$	−2.92995	−	12.8369i	−0.212561	−	0.931289i
$191$	−0.437187	+	1.91544i	−0.0316337	+	0.138597i	−0.988279	−	0.152660i	$-0.951216\pi$
$191$	−0.437187	+	1.91544i	−0.0316337	+	0.138597i	0.956645	+	0.291256i	$0.0940733\pi$
$192$	0.487600	+	1.66200i	0.0351895	+	0.119945i
$193$	4.41284	−	19.3339i	0.317643	−	1.39169i	−0.524030	−	0.851700i	$-0.675572\pi$
$193$	4.41284	−	19.3339i	0.317643	−	1.39169i	0.841674	−	0.539987i	$-0.181571\pi$
$194$	−0.685338	+	9.14521i	−0.0492044	+	0.656587i
$195$	−3.46032	+	4.92759i	−0.247799	+	0.352872i
$196$	6.99668	−	0.215435i	0.499763	−	0.0153882i
$197$	0.815848			0.0581267			0.0290634	−	0.999578i	$-0.490748\pi$
$197$	0.815848			0.0581267			0.0290634	+	0.999578i	$0.490748\pi$
$198$	3.08520	−	11.9801i	0.219256	−	0.851388i
$199$	11.7762	+	10.9267i	0.834793	+	0.774575i	0.976542	−	0.215328i	$-0.0690821\pi$
$199$	11.7762	+	10.9267i	0.834793	+	0.774575i	−0.141749	+	0.989903i	$0.545273\pi$
$200$	−0.00424643		0.000640047i	−0.000300268		4.52581e-5i
$201$	8.70794	+	9.64911i	0.614211	+	0.680596i
$202$	1.63310	−	1.51529i	0.114904	−	0.106616i
$203$	1.82571	+	0.532529i	0.128140	+	0.0373762i
$204$	2.60325	−	0.556424i	0.182264	−	0.0389575i
$205$	19.3146	+	9.30143i	1.34899	+	0.649640i
$206$	1.45334	+	0.448297i	0.101259	+	0.0312344i
$207$	5.38205	−	1.49850i	0.374078	−	0.104153i
$208$	−0.568228	+	1.44782i	−0.0393995	+	0.100388i
$209$	−1.81538	+	24.2246i	−0.125573	+	1.67565i
$210$	0.0160310	+	10.2425i	0.00110625	+	0.706802i
$211$	−0.149101	−	1.98961i	−0.0102645	−	0.136971i	0.989717	−	0.143039i	$-0.0456874\pi$
$211$	−0.149101	−	1.98961i	−0.0102645	−	0.136971i	−0.999982	+	0.00606837i	$0.998068\pi$
$212$	−1.03879	−	0.320424i	−0.0713443	−	0.0220068i
$213$	−16.5714	+	1.01168i	−1.13545	+	0.0693195i
$214$	−4.17178	−	7.22573i	−0.285177	−	0.493941i
$215$	5.17026	+	8.95516i	0.352609	+	0.610737i
$216$	−2.05847	−	4.77103i	−0.140061	−	0.324627i
$217$	18.1498	+	8.39885i	1.23209	+	0.570151i
$218$	−3.79343	−	9.66551i	−0.256924	−	0.654631i
$219$	28.0461	+	6.81062i	1.89518	+	0.460219i
$220$	−8.30407	−	3.99903i	−0.559860	−	0.269614i
$221$	2.15372	+	1.03718i	0.144875	+	0.0697681i
$222$	−9.41650	+	9.87128i	−0.631994	+	0.662517i
$223$	−8.99737	−	22.9249i	−0.602509	−	1.53517i	−0.827887	−	0.560895i	$-0.810457\pi$
$223$	−8.99737	−	22.9249i	−0.602509	−	1.53517i	0.225378	−	0.974271i	$-0.427638\pi$
$224$	0.628363	+	2.57005i	0.0419842	+	0.171719i
$225$	0.0128783		0.000356187i	0.000858551		2.37458e-5i
$226$	−2.62452	−	4.54580i	−0.174580	−	0.302382i
$227$	−6.64596	−	11.5111i	−0.441108	−	0.764021i	0.556664	−	0.830738i	$-0.312081\pi$
$227$	−6.64596	−	11.5111i	−0.441108	−	0.764021i	−0.997772	+	0.0667167i	$0.978748\pi$
$228$	5.63076	+	8.50922i	0.372906	+	0.563537i
$229$	−10.9110	−	3.36559i	−0.721018	−	0.222405i	−0.0875352	−	0.996161i	$-0.527899\pi$
$229$	−10.9110	−	3.36559i	−0.721018	−	0.222405i	−0.633483	+	0.773757i	$0.718375\pi$
$230$	−0.311052	−	4.15070i	−0.0205102	−	0.273689i
$231$	5.54171	−	18.0661i	0.364618	−	1.18866i
$232$	−0.0537168	+	0.716801i	−0.00352668	+	0.0470603i
$233$	7.53022	−	19.1867i	0.493321	−	1.25696i	−0.440025	−	0.897985i	$-0.645031\pi$
$233$	7.53022	−	19.1867i	0.493321	−	1.25696i	0.933347	−	0.358977i	$-0.116874\pi$
$234$	1.16366	−	4.51858i	0.0760706	−	0.295389i
$235$	−26.2094	−	8.08452i	−1.70971	−	0.527376i
$236$	9.75820	+	4.69930i	0.635205	+	0.305899i
$237$	−13.9433	−	15.4503i	−0.905715	−	1.00361i
$238$	4.01112	−	0.667868i	0.260003	−	0.0432914i
$239$	−12.3844	+	11.4911i	−0.801081	+	0.743295i	−0.970201	−	0.242301i	$-0.922098\pi$
$239$	−12.3844	+	11.4911i	−0.801081	+	0.743295i	0.169120	+	0.985595i	$0.445907\pi$
$240$	−3.78581	+	0.809188i	−0.244373	+	0.0522329i
$241$	−19.3097	−	2.91047i	−1.24385	−	0.187480i	−0.506052	−	0.862503i	$-0.668896\pi$
$241$	−19.3097	−	2.91047i	−1.24385	−	0.187480i	−0.737797	+	0.675023i	$0.764134\pi$
$242$	4.40165	+	4.08413i	0.282949	+	0.262538i
$243$	7.87068	+	13.4556i	0.504904	+	0.863175i
$244$	3.44852			0.220769
$245$	−0.688481	+	15.6306i	−0.0439855	+	0.998602i
$246$	−16.5474	−	1.47037i	−1.05503	−	0.0937476i
$247$	−0.684716	+	9.13690i	−0.0435674	+	0.581367i
$248$	−1.68200	+	7.36934i	−0.106807	+	0.467954i
$249$	−14.0527	−	3.41250i	−0.890553	−	0.216259i
$250$	2.48893	−	10.9047i	0.157414	−	0.689674i
$251$	3.62651	+	15.8888i	0.228903	+	1.00289i	0.950536	+	0.310615i	$0.100535\pi$
$251$	3.62651	+	15.8888i	0.228903	+	1.00289i	−0.721633	+	0.692276i	$0.756608\pi$
$252$	−2.80900	−	7.42358i	−0.176951	−	0.467641i
$253$	−1.70881	+	7.48677i	−0.107432	+	0.470689i
$254$	13.7860	+	6.63899i	0.865011	+	0.416567i
$255$	0.805371	+	5.89520i	0.0504343	+	0.369172i
$256$	−0.900969	+	0.433884i	−0.0563106	+	0.0271177i
$257$	−21.4871	+	3.23866i	−1.34033	+	0.202022i	−0.779757	−	0.626082i	$-0.784657\pi$
$257$	−21.4871	+	3.23866i	−1.34033	+	0.202022i	−0.560574	+	0.828105i	$0.689419\pi$
$258$	−6.19528	−	5.08227i	−0.385701	−	0.316408i
$259$	−15.0561	+	14.4075i	−0.935540	+	0.895240i
$260$	−3.13208	−	1.50833i	−0.194243	−	0.0935426i
$261$	−0.101636	−	2.15404i	−0.00629109	−	0.133331i
$262$	15.0704	−	2.27150i	0.931052	−	0.140333i
$263$	0.865226	+	1.49862i	0.0533521	+	0.0924086i	0.891468	−	0.453084i	$-0.149676\pi$
$263$	0.865226	+	1.49862i	0.0533521	+	0.0924086i	−0.838116	+	0.545492i	$0.816343\pi$
$264$	7.11435	+	0.632168i	0.437858	+	0.0389072i
$265$	0.887687	−	2.26179i	0.0545302	−	0.138941i
$266$	7.99990	+	13.3765i	0.490505	+	0.820165i
$267$	−10.8870	+	11.4128i	−0.666274	+	0.698453i
$268$	−4.67872	+	5.86692i	−0.285798	+	0.358379i
$269$	−5.90614	+	4.02674i	−0.360103	+	0.245514i	−0.729834	−	0.683625i	$-0.760403\pi$
$269$	−5.90614	+	4.02674i	−0.360103	+	0.245514i	0.369730	+	0.929139i	$0.379450\pi$
$270$	10.9778	−	3.79113i	0.668086	−	0.230721i
$271$	8.53252	+	1.28607i	0.518314	+	0.0781232i	0.402989	−	0.915205i	$-0.367971\pi$
$271$	8.53252	+	1.28607i	0.518314	+	0.0781232i	0.115324	+	0.993328i	$0.463209\pi$
$272$	0.561505	+	1.43069i	0.0340462	+	0.0867484i
$273$	2.09019	−	6.81408i	0.126504	−	0.412407i
$274$	4.57928	−	11.6678i	0.276644	−	0.704878i
$275$	−0.00885431	+	0.0153361i	−0.000533935	+	0.000924803i
$276$	1.35919	+	2.92516i	0.0818136	+	0.176074i
$277$	−11.1314	+	28.3624i	−0.668823	+	1.70413i	0.0404340	+	0.999182i	$0.487126\pi$
$277$	−11.1314	+	28.3624i	−0.668823	+	1.70413i	−0.709257	+	0.704950i	$0.750969\pi$
$278$	−11.9138	+	11.0543i	−0.714539	+	0.662996i
$279$	2.31917	−	22.5577i	0.138845	−	1.35049i
$280$	−5.83323	+	0.971256i	−0.348602	+	0.0580436i
$281$	−1.25086	+	16.6915i	−0.0746198	+	0.995732i	0.826718	+	0.562616i	$0.190205\pi$
$281$	−1.25086	+	16.6915i	−0.0746198	+	0.995732i	−0.901338	+	0.433116i	$0.857414\pi$
$282$	21.2152	−	1.29519i	1.26335	−	0.0771274i
$283$	−7.02158	+	3.38141i	−0.417389	+	0.201004i	−0.630778	−	0.775963i	$-0.717264\pi$
$283$	−7.02158	+	3.38141i	−0.417389	+	0.201004i	0.213389	+	0.976967i	$0.431550\pi$
$284$	−2.13293	−	9.34499i	−0.126566	−	0.554523i
$285$	−19.9064	+	11.1289i	−1.17915	+	0.659217i
$286$	4.70156	+	4.36241i	0.278009	+	0.257955i
$287$	−25.1480	−	3.39550i	−1.48444	−	0.200430i
$288$	2.52449	−	1.62078i	0.148757	−	0.0955056i
$289$	−13.9875	+	4.31458i	−0.822795	+	0.253799i
$290$	−1.58867	−	0.239454i	−0.0932902	−	0.0140612i
$291$	15.5335	−	3.32017i	0.910590	−	0.194632i
$292$	−1.24523	+	16.6164i	−0.0728716	+	0.972404i
$293$	−15.7583	−	27.2942i	−0.920612	−	1.59455i	−0.798471	−	0.602034i	$-0.794357\pi$
$293$	−15.7583	−	27.2942i	−0.920612	−	1.59455i	−0.122141	−	0.992513i	$-0.538976\pi$
$294$	−3.76964	−	11.5234i	−0.219850	−	0.672061i
$295$	−12.1040	+	20.9647i	−0.704721	+	1.22061i
$296$	−6.50778	−	4.43693i	−0.378257	−	0.257891i
$297$	−21.4153	+	0.713893i	−1.24264	+	0.0414243i
$298$	−2.97888	−	7.59006i	−0.172562	−	0.439680i
$299$	−0.644517	+	2.82381i	−0.0372734	+	0.163305i
$300$	0.00100680	+	0.00736966i	5.81279e−5	+	0.000425488i
$301$	−9.09986	−	8.18646i	−0.524507	−	0.471860i
$302$	5.27661	−	1.62762i	0.303635	−	0.0936589i
$303$	−3.31472	−	1.97535i	−0.190426	−	0.113481i
$304$	−4.31842	+	4.00691i	−0.247679	+	0.229812i
$305$	−0.576006	+	7.68626i	−0.0329820	+	0.440114i
$306$	−2.19412	−	4.05528i	−0.125430	−	0.231825i
$307$	−2.37305	+	1.14280i	−0.135437	+	0.0652230i	−0.500375	−	0.865809i	$-0.666804\pi$
$307$	−2.37305	+	1.14280i	−0.135437	+	0.0652230i	0.364938	+	0.931032i	$0.381090\pi$
$308$	10.8121	+	1.45985i	0.616074	+	0.0831828i
$309$	0.0364193	−	2.63405i	0.00207182	−	0.149846i
$310$	−16.1443	−	4.97985i	−0.916933	−	0.282836i
$311$	1.16291	+	1.45824i	0.0659425	+	0.0826893i	0.813709	−	0.581273i	$-0.197445\pi$
$311$	1.16291	+	1.45824i	0.0659425	+	0.0826893i	−0.747766	+	0.663962i	$0.768874\pi$
$312$	2.68335	+	0.238437i	0.151915	+	0.0134989i
$313$	−7.56866			−0.427806			−0.213903	−	0.976855i	$-0.568618\pi$
$313$	−7.56866			−0.427806			−0.213903	+	0.976855i	$0.568618\pi$
$314$	3.07216	+	3.85236i	0.173372	+	0.217401i
$315$	17.0153	−	5.02091i	0.958703	−	0.282896i
$316$	7.49164	−	9.39423i	0.421438	−	0.528466i
$317$	16.8153	−	21.0858i	0.944444	−	1.18430i	−0.0382891	−	0.999267i	$-0.512191\pi$
$317$	16.8153	−	21.0858i	0.944444	−	1.18430i	0.982733	−	0.185029i	$-0.0592378\pi$
$318$	−0.0260310	+	1.88271i	−0.00145974	+	0.105577i
$319$	2.67059	+	1.28609i	0.149524	+	0.0720071i
$320$	−0.816576	−	2.08060i	−0.0456480	−	0.116309i
$321$	−9.97501	+	10.4568i	−0.556751	+	0.583640i
$322$	1.87043	+	4.55823i	0.104235	+	0.254020i
$323$	5.64514	+	7.07878i	0.314104	+	0.393874i
$324$	−6.92574	+	5.74753i	−0.384763	+	0.319307i
$325$	−0.00333962	+	0.00578439i	−0.000185249	+	0.000320860i
$326$	−2.48582	+	6.33376i	−0.137677	+	0.350795i
$327$	−14.2144	+	11.0176i	−0.786059	+	0.609275i
$328$	−0.716759	−	9.56449i	−0.0395764	−	0.528111i
$329$	32.4633	−	0.499669i	1.78976	−	0.0275477i
$330$	−2.59732	+	15.7513i	−0.142978	+	0.867080i
$331$	−9.47596	−	11.8825i	−0.520846	−	0.653120i	0.449942	−	0.893058i	$-0.351445\pi$
$331$	−9.47596	−	11.8825i	−0.520846	−	0.653120i	−0.970788	+	0.239937i	$0.922873\pi$
$332$	0.623931	−	8.32577i	0.0342426	−	0.456936i
$333$	20.9976	+	10.8370i	1.15066	+	0.593863i
$334$	−1.28706	−	17.1747i	−0.0704249	−	0.939756i
$335$	−12.2951	−	11.4081i	−0.671751	−	0.623293i
$336$	3.96504	−	2.29750i	0.216310	−	0.125339i
$337$	−19.9814	+	18.5400i	−1.08845	+	1.00994i	−0.0885505	+	0.996072i	$0.528223\pi$
$337$	−19.9814	+	18.5400i	−1.08845	+	1.00994i	−0.999904	+	0.0138663i	$0.995586\pi$
$338$	−7.75637	−	7.19686i	−0.421891	−	0.391457i
$339$	−6.27540	+	6.57848i	−0.340833	+	0.357294i
$340$	−3.28260	+	1.01255i	−0.178024	+	0.0549130i
$341$	25.7540	+	17.5588i	1.39466	+	0.950861i
$342$	11.3968	−	13.5074i	0.616267	−	0.730398i
$343$	−4.95013	−	17.8465i	−0.267282	−	0.963618i
$344$	2.31320	−	4.00659i	0.124720	−	0.216021i
$345$	−6.74680	+	2.54085i	−0.363235	+	0.136795i
$346$	0.939977	−	4.11831i	0.0505335	−	0.221402i
$347$	−10.2238	+	12.8202i	−0.548840	+	0.688223i	−0.976451	−	0.215739i	$-0.930784\pi$
$347$	−10.2238	+	12.8202i	−0.548840	+	0.688223i	0.427611	+	0.903963i	$0.359355\pi$
$348$	1.21752	−	0.260235i	0.0652657	−	0.0139501i
$349$	9.42916	+	2.90851i	0.504731	+	0.155689i	0.536656	−	0.843801i	$-0.319687\pi$
$349$	9.42916	+	2.90851i	0.504731	+	0.155689i	−0.0319245	+	0.999490i	$0.510164\pi$
$350$	0.00102335	+	0.0113157i	5.47002e−5	+	0.000604851i
$351$	−8.07728	+	0.269262i	−0.431133	+	0.0143721i
$352$	0.308161	+	4.11213i	0.0164251	+	0.219177i
$353$	18.5144	−	17.1789i	0.985424	−	0.914340i	−0.0109056	−	0.999941i	$-0.503471\pi$
$353$	18.5144	−	17.1789i	0.985424	−	0.914340i	0.996330	+	0.0856007i	$0.0272809\pi$
$354$	3.05214	−	18.5095i	0.162219	−	0.983770i
$355$	21.1849	−	3.19311i	1.12438	−	0.169473i
$356$	−7.52405	−	5.12981i	−0.398774	−	0.271880i
$357$	−3.06582	−	6.34084i	−0.162260	−	0.335593i
$358$	10.3751	−	7.07364i	0.548342	−	0.373853i
$359$	8.04805	−	7.46749i	0.424760	−	0.394119i	−0.438621	−	0.898672i	$-0.644533\pi$
$359$	8.04805	−	7.46749i	0.424760	−	0.394119i	0.863381	+	0.504553i	$0.168343\pi$
$360$	3.19083	+	5.89745i	0.168172	+	0.310823i
$361$	−7.85205	+	13.6002i	−0.413266	+	0.715798i
$362$	11.9848			0.629906
$363$	4.64159	−	9.30697i	0.243620	−	0.488489i
$364$	4.07803	+	0.550618i	0.213747	+	0.0288602i
$365$	−36.8277	−	5.55088i	−1.92765	−	0.290547i
$366$	−1.68150	−	5.73144i	−0.0878934	−	0.299587i
$367$	−0.255972	−	3.41571i	−0.0133616	−	0.178299i	−0.999892	−	0.0147184i	$-0.995315\pi$
$367$	−0.255972	−	3.41571i	−0.0133616	−	0.178299i	0.986530	−	0.163580i	$-0.0523042\pi$
$368$	−1.53867	+	1.04905i	−0.0802086	+	0.0546853i
$369$	5.62477	+	28.2188i	0.292814	+	1.46901i
$370$	10.9763	−	13.7638i	0.570629	−	0.715547i
$371$	−0.170770	+	2.87108i	−0.00886591	+	0.149059i
$372$	13.0680	−	0.797802i	0.677544	−	0.0413641i
$373$	1.50160	−	2.60085i	0.0777498	−	0.134667i	−0.824529	−	0.565820i	$-0.808560\pi$
$373$	1.50160	−	2.60085i	0.0777498	−	0.134667i	0.902279	+	0.431153i	$0.141893\pi$
$374$	6.33779			0.327719
$375$	−19.3372	+	1.18054i	−0.998570	+	0.0609627i
$376$	2.73065	+	11.9637i	0.140822	+	0.616983i
$377$	1.00728	+	0.485079i	0.0518774	+	0.0249828i
$378$	−10.9683	+	8.28830i	−0.564150	+	0.426304i
$379$	30.3204	−	14.6015i	1.55745	−	0.750031i	0.560511	−	0.828147i	$-0.310605\pi$
$379$	30.3204	−	14.6015i	1.55745	−	0.750031i	0.996944	+	0.0781166i	$0.0248907\pi$
$380$	−8.20953	−	10.2944i	−0.421140	−	0.528093i
$381$	4.31194	−	26.1495i	0.220908	−	1.33968i
$382$	0.437187	+	1.91544i	0.0223684	+	0.0980025i
$383$	4.36783	−	2.97793i	0.223186	−	0.152165i	−0.446566	−	0.894751i	$-0.647353\pi$
$383$	4.36783	−	2.97793i	0.223186	−	0.152165i	0.669751	+	0.742586i	$0.266401\pi$
$384$	1.16043	+	1.28585i	0.0592178	+	0.0656182i
$385$	−5.05974	+	23.8547i	−0.257868	+	1.21575i
$386$	−4.41284	−	19.3339i	−0.224608	−	0.984071i
$387$	−5.42591	+	12.7747i	−0.275815	+	0.649374i
$388$	3.35049	+	8.53690i	0.170095	+	0.433396i
$389$	−3.04357	+	0.938818i	−0.154315	+	0.0476000i	−0.370950	−	0.928653i	$-0.620968\pi$
$389$	−3.04357	+	0.938818i	−0.154315	+	0.0476000i	0.216635	+	0.976253i	$0.430492\pi$
$390$	−0.979642	+	5.94098i	−0.0496061	+	0.300833i
$391$	1.43108	+	2.47871i	0.0723729	+	0.125354i
$392$	6.21032	−	3.22985i	0.313669	−	0.163132i
$393$	−11.1236	−	23.9394i	−0.561109	−	1.20758i
$394$	0.735053	−	0.353983i	0.0370315	−	0.0178334i
$395$	19.6871	+	18.2669i	0.990564	+	0.919109i
$396$	−2.41830	−	12.1323i	−0.121524	−	0.609671i
$397$	17.0794	−	5.26830i	0.857191	−	0.264408i	0.165151	−	0.986268i	$-0.447189\pi$
$397$	17.0794	−	5.26830i	0.857191	−	0.264408i	0.692039	+	0.721860i	$0.256713\pi$
$398$	15.3509	+	4.73513i	0.769472	+	0.237351i
$399$	18.3310	−	19.8182i	0.917697	−	0.992152i
$400$	−0.00410361	+	0.00126580i	−0.000205180	+	6.32898e-5i
$401$	−16.7540	+	11.4227i	−0.836655	+	0.570422i	−0.904110	−	0.427301i	$-0.859465\pi$
$401$	−16.7540	+	11.4227i	−0.836655	+	0.570422i	0.0674548	+	0.997722i	$0.478512\pi$
$402$	12.0322	+	4.91531i	0.600110	+	0.245154i
$403$	9.71374	+	6.62271i	0.483876	+	0.329901i
$404$	0.813909	−	2.07381i	0.0404935	−	0.103176i
$405$	−11.6536	−	16.3965i	−0.579073	−	0.814749i
$406$	1.87597	−	0.312356i	0.0931027	−	0.0155020i
$407$	−26.8359	+	18.2964i	−1.33020	+	0.906918i
$408$	2.10402	−	1.63083i	0.104164	−	0.0807380i
$409$	−9.45795	−	11.8599i	−0.467665	−	0.586434i	0.490932	−	0.871198i	$-0.336656\pi$
$409$	−9.45795	−	11.8599i	−0.467665	−	0.586434i	−0.958598	+	0.284764i	$0.908085\pi$
$410$	21.4376			1.05873
$411$	−21.6248	−	1.92154i	−1.06667	−	0.0947823i
$412$	1.50393	−	0.226680i	0.0740932	−	0.0111677i
$413$	5.94576	−	28.0319i	0.292572	−	1.37936i
$414$	4.19888	−	3.68529i	0.206364	−	0.181122i
$415$	18.4528	+	2.78130i	0.905810	+	0.136529i
$416$	0.116230	+	1.55099i	0.00569867	+	0.0760434i
$417$	24.1815	+	14.4106i	1.18417	+	0.705688i
$418$	8.87506	+	22.6133i	0.434094	+	1.10605i
$419$	17.2082	+	2.59371i	0.840674	+	0.126711i	0.555243	−	0.831688i	$-0.312625\pi$
$419$	17.2082	+	2.59371i	0.840674	+	0.126711i	0.285431	+	0.958399i	$0.407863\pi$
$420$	4.45851	+	9.22125i	0.217553	+	0.449951i
$421$	−4.42860	+	0.667504i	−0.215837	+	0.0325322i	−0.256070	−	0.966658i	$-0.582428\pi$
$421$	−4.42860	+	0.667504i	−0.215837	+	0.0325322i	0.0402335	+	0.999190i	$0.487190\pi$
$422$	−0.997596	−	1.72789i	−0.0485622	−	0.0841122i
$423$	−12.4971	−	34.6282i	−0.607632	−	1.68368i
$424$	−1.07494	+	0.162021i	−0.0522038	+	0.00786846i
$425$	0.00146868	+	0.00643472i	7.12416e−5	+	0.000312130i
$426$	−14.4914	+	8.10156i	−0.702109	+	0.392522i
$427$	−2.16692	−	8.86287i	−0.104865	−	0.428904i
$428$	−6.89377	−	4.70009i	−0.333223	−	0.227188i
$429$	4.95784	−	9.94110i	0.239367	−	0.479961i
$430$	8.54374	+	5.82502i	0.412016	+	0.280908i
$431$	25.6985	+	7.92693i	1.23785	+	0.381827i	0.843498	−	0.537132i	$-0.180492\pi$
$431$	25.6985	+	7.92693i	1.23785	+	0.381827i	0.394354	+	0.918959i	$0.370968\pi$
$432$	−3.92469	−	3.40541i	−0.188827	−	0.163843i
$433$	2.90022	−	12.7067i	0.139376	−	0.610644i	−0.856197	−	0.516649i	$-0.827179\pi$
$433$	2.90022	−	12.7067i	0.139376	−	0.610644i	0.995573	−	0.0939949i	$-0.0299637\pi$
$434$	19.9965	−	0.307783i	0.959862	−	0.0147740i
$435$	0.376665	+	2.75714i	0.0180597	+	0.132195i
$436$	−7.61148	−	7.06242i	−0.364524	−	0.338228i
$437$	−6.84004	+	8.57714i	−0.327204	+	0.410300i
$438$	28.2237	−	6.03261i	1.34858	−	0.288249i
$439$	−13.9832	+	6.73393i	−0.667380	+	0.321393i	−0.736718	−	0.676200i	$-0.763626\pi$
$439$	−13.9832	+	6.73393i	−0.667380	+	0.321393i	0.0693383	+	0.997593i	$0.477911\pi$
$440$	−9.21682			−0.439395
$441$	−17.3139	+	11.8840i	−0.824471	+	0.565904i
$442$	2.39045			0.113702
$443$	−1.64009	+	0.789824i	−0.0779228	+	0.0375257i	−0.472439	−	0.881363i	$-0.656626\pi$
$443$	−1.64009	+	0.789824i	−0.0779228	+	0.0375257i	0.394516	+	0.918889i	$0.370912\pi$
$444$	−4.20098	+	12.9794i	−0.199370	+	0.615974i
$445$	12.6904	−	15.9132i	0.601581	−	0.754359i
$446$	−18.0531	−	16.7508i	−0.854839	−	0.793175i
$447$	−11.1622	+	8.65182i	−0.527953	+	0.409217i
$448$	1.68124	+	2.04290i	0.0794310	+	0.0965179i
$449$	−4.53649	+	19.8757i	−0.214090	+	0.937991i	0.747664	+	0.664077i	$0.231176\pi$
$449$	−4.53649	+	19.8757i	−0.214090	+	0.937991i	−0.961754	+	0.273914i	$0.911682\pi$
$450$	0.0117575	−	0.00526676i	0.000554252	−	0.000248277i
$451$	−37.7941	−	11.6579i	−1.77966	−	0.548951i
$452$	−4.33696	−	2.95689i	−0.203993	−	0.139080i
$453$	−5.27798	−	7.97610i	−0.247981	−	0.374750i
$454$	−10.9823	−	7.48760i	−0.515425	−	0.351411i
$455$	−1.90840	+	8.99738i	−0.0894673	+	0.421804i
$456$	8.76515	+	5.22345i	0.410466	+	0.244610i
$457$	6.09598	+	26.7082i	0.285158	+	1.24936i	0.891084	+	0.453838i	$0.149946\pi$
$457$	6.09598	+	26.7082i	0.285158	+	1.24936i	−0.605926	+	0.795521i	$0.707197\pi$
$458$	−11.2907	+	1.70180i	−0.527581	+	0.0795201i
$459$	−5.67003	+	5.62399i	−0.264654	+	0.262505i
$460$	−2.08117	−	3.60469i	−0.0970351	−	0.168070i
$461$	−5.40644	+	0.814889i	−0.251803	+	0.0379532i	−0.273731	−	0.961806i	$-0.588258\pi$
$461$	−5.40644	+	0.814889i	−0.251803	+	0.0379532i	0.0219278	+	0.999760i	$0.493020\pi$
$462$	−2.84569	−	18.6815i	−0.132394	−	0.869141i
$463$	−23.6360	−	3.56256i	−1.09846	−	0.165566i	−0.425292	−	0.905056i	$-0.639829\pi$
$463$	−23.6360	−	3.56256i	−1.09846	−	0.165566i	−0.673168	+	0.739490i	$0.735067\pi$
$464$	0.262611	+	0.669122i	0.0121914	+	0.0310632i
$465$	−0.404559	+	29.2600i	−0.0187610	+	1.35690i
$466$	−1.54030	−	20.5539i	−0.0713529	−	0.952139i
$467$	−5.06283	−	0.763099i	−0.234280	−	0.0353120i	0.0308528	−	0.999524i	$-0.490178\pi$
$467$	−5.06283	−	0.763099i	−0.234280	−	0.0353120i	−0.265133	+	0.964212i	$0.585416\pi$
$468$	−0.912119	−	4.57599i	−0.0421627	−	0.211525i
$469$	18.0182	+	8.33798i	0.832004	+	0.385012i
$470$	−27.1216	+	4.08792i	−1.25103	+	0.188562i
$471$	4.90464	−	6.98434i	0.225994	−	0.321821i
$472$	10.8308			0.498527
$473$	−11.8948	−	14.9156i	−0.546922	−	0.685819i
$474$	−19.2661	−	7.87049i	−0.884923	−	0.361504i
$475$	−0.0209025	+	0.0142511i	−0.000959073	+	0.000653885i
$476$	3.32412	−	2.34209i	0.152361	−	0.107349i
$477$	3.14175	−	0.874744i	0.143851	−	0.0400518i
$478$	−6.17219	+	15.7265i	−0.282309	+	0.719312i
$479$	16.2507	+	11.0795i	0.742511	+	0.506236i	0.874506	−	0.485015i	$-0.161186\pi$
$479$	16.2507	+	11.0795i	0.742511	+	0.506236i	−0.131995	+	0.991250i	$0.542138\pi$
$480$	−3.05980	+	2.37165i	−0.139660	+	0.108251i
$481$	−10.1218	+	6.90092i	−0.461514	+	0.314655i
$482$	−18.6603	+	5.75593i	−0.849952	+	0.262175i
$483$	6.66376	−	5.33125i	0.303211	−	0.242580i
$484$	5.73779	+	1.76987i	0.260809	+	0.0804488i
$485$	−19.5872	+	6.04184i	−0.889408	+	0.274346i
$486$	12.9294	+	8.70809i	0.586489	+	0.395007i
$487$	−25.8495	−	23.9848i	−1.17135	−	1.08686i	−0.994725	−	0.102579i	$-0.967291\pi$
$487$	−25.8495	−	23.9848i	−1.17135	−	1.08686i	−0.176628	−	0.984278i	$-0.556519\pi$
$488$	3.10701	−	1.49626i	0.140648	−	0.0677324i
$489$	11.7388	+	1.04309i	0.530847	+	0.0471701i
$490$	6.16156	+	14.3814i	0.278351	+	0.649686i
$491$	13.1337	+	22.7483i	0.592717	+	1.02662i	0.993865	+	0.110603i	$0.0352781\pi$
$491$	13.1337	+	22.7483i	0.592717	+	1.02662i	−0.401148	+	0.916013i	$0.631389\pi$
$492$	−15.5467	+	5.85490i	−0.700899	+	0.263959i
$493$	1.05568	−	0.325635i	0.0475455	−	0.0146659i
$494$	3.34744	+	8.52915i	0.150609	+	0.383745i
$495$	27.4451	−	3.36359i	1.23357	−	0.151182i
$496$	1.68200	+	7.36934i	0.0755242	+	0.330893i
$497$	−22.6768	+	11.3538i	−1.01720	+	0.509287i
$498$	−14.1417	+	3.02268i	−0.633703	+	0.135449i
$499$	−8.84002	+	6.02703i	−0.395734	+	0.269807i	−0.744795	−	0.667293i	$-0.767453\pi$
$499$	−8.84002	+	6.02703i	−0.395734	+	0.269807i	0.349061	+	0.937100i	$0.386500\pi$
$500$	−2.48893	−	10.9047i	−0.111308	−	0.487673i
$501$	−27.9167	+	10.5135i	−1.24723	+	0.469707i
$502$	10.1613	+	12.7418i	0.453519	+	0.568695i
$503$	−3.10129	+	1.49350i	−0.138280	+	0.0665920i	−0.501744	−	0.865016i	$-0.667308\pi$
$503$	−3.10129	+	1.49350i	−0.138280	+	0.0665920i	0.363464	+	0.931608i	$0.381594\pi$
$504$	−5.75179	−	5.46963i	−0.256205	−	0.243637i
$505$	4.48627	+	2.16048i	0.199637	+	0.0961399i
$506$	1.70881	+	7.48677i	0.0759657	+	0.332827i
$507$	−8.17918	+	16.4003i	−0.363250	+	0.728362i
$508$	15.3013			0.678886
$509$	−14.9695	+	25.9279i	−0.663509	+	1.14923i	0.316178	+	0.948700i	$0.397600\pi$
$509$	−14.9695	+	25.9279i	−0.663509	+	1.14923i	−0.979687	+	0.200532i	$0.935733\pi$
$510$	3.28345	+	4.96196i	0.145393	+	0.219719i
$511$	43.4876	−	7.24085i	1.92378	−	0.320316i
$512$	−0.623490	+	0.781831i	−0.0275546	+	0.0345524i
$513$	−28.0064	−	12.3552i	−1.23651	−	0.545496i
$514$	−17.9540	+	12.2409i	−0.791919	+	0.539921i
$515$	0.254038	+	3.38990i	0.0111943	+	0.149377i
$516$	−7.78687	−	1.89093i	−0.342798	−	0.0832437i
$517$	50.0379	+	7.54200i	2.20067	+	0.331697i
$518$	−7.31389	+	19.5133i	−0.321354	+	0.857366i
$519$	−7.30297	+	0.445846i	−0.320565	+	0.0195705i
$520$	−3.47635			−0.152448
$521$	14.7151	−	25.4872i	0.644679	−	1.11662i	−0.339697	−	0.940535i	$-0.610324\pi$
$521$	14.7151	−	25.4872i	0.644679	−	1.11662i	0.984376	−	0.176081i	$-0.0563422\pi$
$522$	−1.02617	−	1.89662i	−0.0449143	−	0.0830128i
$523$	13.1189	−	12.1725i	0.573648	−	0.532268i	−0.339121	−	0.940743i	$-0.610130\pi$
$523$	13.1189	−	12.1725i	0.573648	−	0.532268i	0.912770	+	0.408475i	$0.133939\pi$
$524$	12.5924	−	8.58534i	0.550101	−	0.375052i
$525$	0.0183078	−	0.00721836i	0.000799016	−	0.000315035i
$526$	1.42977	+	0.974798i	0.0623408	+	0.0425032i
$527$	11.4877	−	1.73149i	0.500412	−	0.0754250i
$528$	6.68410	−	2.51724i	0.290888	−	0.109549i
$529$	14.3180	−	13.2851i	0.622521	−	0.577615i
$530$	−0.181575	−	2.42296i	−0.00788713	−	0.105246i
$531$	−32.2511	+	3.95259i	−1.39958	+	0.171528i
$532$	13.0115	+	8.58077i	0.564120	+	0.372024i
$533$	−14.2550	−	4.39707i	−0.617451	−	0.190458i
$534$	−4.85702	+	15.0063i	−0.210184	+	0.649385i
$535$	11.6273	−	14.5802i	0.502692	−	0.630356i
$536$	−1.66981	+	7.31594i	−0.0721250	+	0.316000i
$537$	−16.8153	−	13.7943i	−0.725634	−	0.595270i
$538$	−3.57411	+	6.19054i	−0.154091	+	0.266893i
$539$	−3.04200	−	28.7049i	−0.131028	−	1.23641i
$540$	8.24572	−	8.17876i	0.354839	−	0.351958i
$541$	14.8173	+	10.1022i	0.637044	+	0.434329i	0.838300	−	0.545209i	$-0.183550\pi$
$541$	14.8173	+	10.1022i	0.637044	+	0.434329i	−0.201256	+	0.979539i	$0.564502\pi$
$542$	8.24554	−	2.54341i	0.354176	−	0.109249i
$543$	−5.84378	−	19.9187i	−0.250781	−	0.854793i
$544$	1.12665	+	1.04538i	0.0483048	+	0.0448203i
$545$	17.0125	−	15.7853i	0.728734	−	0.676166i
$546$	−1.07332	−	7.04617i	−0.0459339	−	0.301548i
$547$	8.99385	+	8.34507i	0.384549	+	0.356810i	0.848633	−	0.528982i	$-0.177426\pi$
$547$	8.99385	+	8.34507i	0.384549	+	0.356810i	−0.464084	+	0.885791i	$0.653616\pi$
$548$	−0.936686	−	12.4992i	−0.0400133	−	0.533940i
$549$	−8.70576	+	5.58931i	−0.371553	+	0.238546i
$550$	−0.00132337	+	0.0176591i	−5.64286e−5	+	0.000752987i
$551$	2.64018	+	3.31069i	0.112476	+	0.141040i
$552$	2.49377	+	2.04575i	0.106142	+	0.0870729i
$553$	−28.8511	−	13.3509i	−1.22687	−	0.567739i
$554$	2.27692	+	30.3834i	0.0967371	+	1.29087i
$555$	−28.2275	−	11.5313i	−1.19819	−	0.489478i
$556$	−5.93762	+	15.1288i	−0.251811	+	0.641604i
$557$	−6.41043	+	11.1032i	−0.271619	+	0.470457i	−0.969276	−	0.245974i	$-0.920892\pi$
$557$	−6.41043	+	11.1032i	−0.271619	+	0.470457i	0.697658	+	0.716431i	$0.254226\pi$
$558$	−7.69791	−	21.3300i	−0.325878	−	0.902971i
$559$	−4.48640	−	5.62577i	−0.189754	−	0.237945i
$560$	−4.83415	+	3.40602i	−0.204280	+	0.143930i
$561$	−3.09031	−	10.5334i	−0.130473	−	0.444721i
$562$	6.11519	+	15.5813i	0.257954	+	0.657256i
$563$	−28.4062	−	13.6797i	−1.19718	−	0.576532i	−0.274309	−	0.961641i	$-0.588449\pi$
$563$	−28.4062	−	13.6797i	−1.19718	−	0.576532i	−0.922871	+	0.385110i	$0.874164\pi$
$564$	18.5523	−	10.3719i	0.781192	−	0.436734i
$565$	7.31488	−	9.17257i	0.307739	−	0.385893i
$566$	−4.85908	+	6.09310i	−0.204242	+	0.256112i
$567$	19.1233	+	14.1880i	0.803104	+	0.595839i
$568$	−5.97635	−	7.49410i	−0.250762	−	0.314446i
$569$	−22.3643			−0.937561			−0.468781	−	0.883315i	$-0.655307\pi$
$569$	−22.3643			−0.937561			−0.468781	+	0.883315i	$0.655307\pi$
$570$	−13.1064	+	18.6638i	−0.548965	+	0.781741i
$571$	−23.1502	−	29.0294i	−0.968804	−	1.21484i	−0.976642	−	0.214872i	$-0.931067\pi$
$571$	−23.1502	−	29.0294i	−0.968804	−	1.21484i	0.00783847	−	0.999969i	$-0.497505\pi$
$572$	6.12874	+	1.89046i	0.256255	+	0.0790443i
$573$	2.97029	−	1.66058i	0.124086	−	0.0693715i
$574$	−24.1308	+	7.85207i	−1.00720	+	0.327739i
$575$	−0.00720529	+	0.00346988i	−0.000300481	+	0.000144704i
$576$	1.57126	−	2.55561i	0.0654690	−	0.106484i
$577$	−1.77478	+	23.6827i	−0.0738849	+	0.985925i	0.829893	+	0.557923i	$0.188402\pi$
$577$	−1.77478	+	23.6827i	−0.0738849	+	0.985925i	−0.903778	+	0.428002i	$0.859217\pi$
$578$	−10.7303	+	9.95626i	−0.446321	+	0.414126i
$579$	−29.9813	+	16.7614i	−1.24598	+	0.696579i
$580$	−1.53524	+	0.473559i	−0.0637474	+	0.0196635i
$581$	−21.7897	+	3.62807i	−0.903990	+	0.150518i
$582$	12.5546	−	9.73111i	0.520407	−	0.403367i
$583$	−0.997509	+	4.37037i	−0.0413126	+	0.181002i
$584$	6.08769	+	15.5112i	0.251911	+	0.641858i
$585$	10.3516	−	1.26866i	0.427985	−	0.0524525i
$586$	−26.0403	−	17.7540i	−1.07571	−	0.733410i
$587$	−2.29708	+	3.97866i	−0.0948107	+	0.164217i	−0.909530	−	0.415639i	$-0.863558\pi$
$587$	−2.29708	+	3.97866i	−0.0948107	+	0.164217i	0.814719	+	0.579856i	$0.196891\pi$
$588$	−8.39616	−	8.74668i	−0.346252	−	0.360707i
$589$	22.2647	+	38.5636i	0.917401	+	1.58898i
$590$	−1.80906	+	24.1403i	−0.0744780	+	0.993840i
$591$	−0.946732	−	1.04906i	−0.0389434	−	0.0431524i
$592$	−7.78842	−	1.17391i	−0.320102	−	0.0482476i
$593$	−21.9520	+	6.77129i	−0.901460	+	0.278064i	−0.710635	−	0.703560i	$-0.751592\pi$
$593$	−21.9520	+	6.77129i	−0.901460	+	0.278064i	−0.190825	+	0.981624i	$0.561116\pi$
$594$	−18.9847	+	9.93493i	−0.778953	+	0.407635i
$595$	4.66496	+	7.80019i	0.191245	+	0.319777i
$596$	−5.97708	−	5.54592i	−0.244831	−	0.227170i
$597$	0.384678	−	27.8221i	0.0157438	−	1.13868i
$598$	0.644517	+	2.82381i	0.0263563	+	0.115474i
$599$	21.0804	−	10.1518i	0.861321	−	0.414790i	0.0495538	−	0.998771i	$-0.484220\pi$
$599$	21.0804	−	10.1518i	0.861321	−	0.414790i	0.811767	+	0.583981i	$0.198506\pi$
$600$	0.00410468	+	0.00620300i	0.000167573	+	0.000253236i
$601$	1.86783	−	24.9245i	0.0761905	−	1.01669i	−0.819809	−	0.572637i	$-0.805920\pi$
$601$	1.86783	−	24.9245i	0.0761905	−	1.01669i	0.896000	−	0.444055i	$-0.146461\pi$
$602$	−11.7507	−	3.42746i	−0.478921	−	0.139693i
$603$	2.30236	−	22.3942i	0.0937595	−	0.911962i
$604$	4.04786	−	3.75587i	0.164705	−	0.152824i
$605$	−4.90318	+	12.4931i	−0.199343	+	0.507916i
$606$	−3.84353	−	0.341529i	−0.156133	−	0.0138737i
$607$	17.2846	−	29.9378i	0.701560	−	1.21514i	−0.266359	−	0.963874i	$-0.585821\pi$
$607$	17.2846	−	29.9378i	0.701560	−	1.21514i	0.967919	−	0.251263i	$-0.0808459\pi$
$608$	−2.15223	+	5.48379i	−0.0872845	+	0.222397i
$609$	−1.43386	−	2.96555i	−0.0581029	−	0.120170i
$610$	2.81598	+	7.17500i	0.114016	+	0.290507i
$611$	18.8730	+	2.84465i	0.763520	+	0.115082i
$612$	−3.73636	−	2.70169i	−0.151033	−	0.109209i
$613$	24.0059	−	16.3670i	0.969590	−	0.661056i	0.0286363	−	0.999590i	$-0.490884\pi$
$613$	24.0059	−	16.3670i	0.969590	−	0.661056i	0.940954	+	0.338534i	$0.109931\pi$
$614$	−1.64220	+	2.05925i	−0.0662738	+	0.0831047i
$615$	−10.4530	−	35.6293i	−0.421505	−	1.43671i
$616$	10.3747	−	3.37590i	0.418010	−	0.136019i
$617$	12.8598	−	32.7663i	0.517718	−	1.31912i	−0.398031	−	0.917372i	$-0.630306\pi$
$617$	12.8598	−	32.7663i	0.517718	−	1.31912i	0.915749	−	0.401751i	$-0.131598\pi$
$618$	−1.11006	−	2.38900i	−0.0446531	−	0.0960996i
$619$	14.3483	+	24.8520i	0.576707	+	0.998885i	0.995854	+	0.0909668i	$0.0289957\pi$
$619$	14.3483	+	24.8520i	0.576707	+	0.998885i	−0.419147	+	0.907918i	$0.637671\pi$
$620$	−16.7062	+	2.51805i	−0.670936	+	0.101127i
$621$	−8.17232	−	5.18160i	−0.327944	−	0.207930i
$622$	1.68045	+	0.809263i	0.0673800	+	0.0324485i
$623$	−8.45605	+	22.5606i	−0.338784	+	0.903871i
$624$	2.52107	−	0.949437i	0.100924	−	0.0380079i
$625$	24.6995	−	3.72285i	0.987981	−	0.148914i
$626$	−6.81913	+	3.28392i	−0.272547	+	0.131252i
$627$	33.2558	−	25.7766i	1.32811	−	1.02942i
$628$	4.43939	+	2.13790i	0.177151	+	0.0853115i
$629$	−2.69372	+	11.8020i	−0.107406	+	0.470576i
$630$	13.1518	−	11.9063i	0.523978	−	0.474360i
$631$	−2.50057	−	10.9557i	−0.0995460	−	0.436140i	−0.999999	−	0.00118685i	$-0.999622\pi$
$631$	−2.50057	−	10.9557i	−0.0995460	−	0.436140i	0.900453	−	0.434953i	$-0.143235\pi$
$632$	2.67374	−	11.7144i	0.106356	−	0.465974i
$633$	−2.38532	+	2.50052i	−0.0948080	+	0.0993868i
$634$	6.00133	−	26.2935i	0.238343	−	1.04425i
$635$	−2.55577	+	34.1044i	−0.101423	+	1.35339i
$636$	0.793422	+	1.70755i	0.0314612	+	0.0677089i
$637$	−1.14736	−	10.8267i	−0.0454602	−	0.428971i
$638$	2.96413			0.117351
$639$	20.5308	+	20.1343i	0.812185	+	0.796502i
$640$	−1.63845	−	1.52026i	−0.0647654	−	0.0600935i
$641$	−4.33673	−	0.653656i	−0.171290	−	0.0258179i	0.0628370	−	0.998024i	$-0.479985\pi$
$641$	−4.33673	−	0.653656i	−0.171290	−	0.0258179i	−0.234127	+	0.972206i	$0.575223\pi$
$642$	−4.45015	+	13.7492i	−0.175634	+	0.542638i
$643$	13.9774	−	12.9692i	0.551217	−	0.511454i	−0.354660	−	0.934995i	$-0.615403\pi$
$643$	13.9774	−	12.9692i	0.551217	−	0.511454i	0.905877	+	0.423541i	$0.139213\pi$
$644$	3.66294	+	3.29527i	0.144340	+	0.129852i
$645$	5.51526	−	17.0400i	0.217163	−	0.670949i
$646$	8.15747	+	3.92843i	0.320951	+	0.154562i
$647$	−40.4633	−	12.4813i	−1.59077	−	0.490689i	−0.632027	−	0.774946i	$-0.717777\pi$
$647$	−40.4633	−	12.4813i	−1.59077	−	0.490689i	−0.958748	+	0.284257i	$0.908253\pi$
$648$	−3.74612	+	8.18331i	−0.147161	+	0.321471i
$649$	16.3170	−	41.5751i	0.640499	−	1.63197i
$650$	−0.000499140		0.00666056i	−1.95779e−5		0.000261249i
$651$	−10.2618	−	33.0841i	−0.402193	−	1.29667i
$652$	0.508472	+	6.78508i	0.0199133	+	0.265724i
$653$	−4.79534	−	1.47916i	−0.187656	−	0.0578842i	0.199503	−	0.979897i	$-0.436067\pi$
$653$	−4.79534	−	1.47916i	−0.187656	−	0.0578842i	−0.387159	+	0.922013i	$0.626543\pi$
$654$	−8.02638	+	16.0939i	−0.313856	+	0.629322i
$655$	17.0322	+	29.5006i	0.665503	+	1.15269i
$656$	−4.79565	−	8.30632i	−0.187239	−	0.324307i
$657$	−23.7881	−	43.9663i	−0.928062	−	1.71529i
$658$	29.0316	−	14.5355i	1.13177	−	0.566652i
$659$	−5.14037	−	13.0974i	−0.200240	−	0.510204i	0.795117	−	0.606457i	$-0.207410\pi$
$659$	−5.14037	−	13.0974i	−0.200240	−	0.510204i	−0.995357	+	0.0962524i	$0.969314\pi$
$660$	4.49412	+	15.3184i	0.174934	+	0.596266i
$661$	−0.462194	−	0.222581i	−0.0179773	−	0.00865740i	0.424874	−	0.905253i	$-0.360319\pi$
$661$	−0.462194	−	0.222581i	−0.0179773	−	0.00865740i	−0.442851	+	0.896595i	$0.646033\pi$
$662$	−13.6932	−	6.59428i	−0.532200	−	0.256294i
$663$	−1.16558	−	3.97293i	−0.0452675	−	0.154296i
$664$	−3.05028	−	7.77198i	−0.118374	−	0.301611i
$665$	−21.2986	+	27.5675i	−0.825925	+	1.06902i
$666$	23.6201	+	0.653286i	0.915262	+	0.0253143i
$667$	0.669304	+	1.15927i	0.0259156	+	0.0448871i
$668$	−8.61141	−	14.9154i	−0.333185	−	0.577094i
$669$	−19.0372	+	38.1720i	−0.736021	+	1.47581i
$670$	−16.0273	−	4.94376i	−0.619187	−	0.190994i
$671$	−1.06270	−	14.1808i	−0.0410251	−	0.547442i
$672$	2.57553	−	3.79034i	0.0993531	−	0.146215i
$673$	−1.18231	+	15.7768i	−0.0455746	+	0.608150i	0.926925	+	0.375246i	$0.122442\pi$
$673$	−1.18231	+	15.7768i	−0.0455746	+	0.608150i	−0.972500	+	0.232904i	$0.925177\pi$
$674$	−9.95838	+	25.3735i	−0.383583	+	0.977353i
$675$	−0.0144863	−	0.0169728i	−0.000557578	−	0.000653285i
$676$	−10.1108	−	3.11878i	−0.388879	−	0.119953i
$677$	41.4598	+	19.9660i	1.59343	+	0.767356i	0.999314	−	0.0370228i	$-0.0117874\pi$
$677$	41.4598	+	19.9660i	1.59343	+	0.767356i	0.594117	+	0.804379i	$0.297502\pi$
$678$	−2.79965	+	8.64980i	−0.107520	+	0.332194i
$679$	19.8350	−	13.9752i	0.761196	−	0.536319i
$680$	−2.51819	+	2.33654i	−0.0965681	+	0.0896021i
$681$	−7.08943	+	21.9035i	−0.271667	+	0.839345i
$682$	30.8220	+	4.64567i	1.18024	+	0.177892i
$683$	29.4538	+	27.3292i	1.12702	+	1.04572i	0.998540	+	0.0540092i	$0.0172000\pi$
$683$	29.4538	+	27.3292i	1.12702	+	1.04572i	0.128479	+	0.991712i	$0.458990\pi$
$684$	4.40749	−	17.1146i	0.168524	−	0.654395i
$685$	28.0154			1.07041
$686$	−12.2032	−	13.9313i	−0.465921	−	0.531900i
$687$	8.33376	+	17.9354i	0.317953	+	0.684278i
$688$	0.345732	−	4.61347i	0.0131809	−	0.175887i
$689$	−0.376234	+	1.64839i	−0.0143334	+	0.0627987i
$690$	−4.97622	+	5.21656i	−0.189442	+	0.198591i
$691$	1.90326	−	8.33875i	0.0724036	−	0.317221i	−0.925737	−	0.378167i	$-0.876555\pi$
$691$	1.90326	−	8.33875i	0.0724036	−	0.317221i	0.998141	+	0.0609459i	$0.0194117\pi$
$692$	−0.939977	−	4.11831i	−0.0357326	−	0.156555i
$693$	−29.6611	+	13.8386i	−1.12673	+	0.525686i
$694$	−3.64882	+	15.9865i	−0.138507	+	0.606839i
$695$	−32.7282	−	15.7611i	−1.24145	−	0.597851i
$696$	0.984032	−	0.762724i	0.0372996	−	0.0289110i
$697$	−13.2814	+	6.39597i	−0.503068	+	0.242265i
$698$	9.75733	−	1.47068i	0.369320	−	0.0556661i
$699$	−33.4095	+	12.5820i	−1.26366	+	0.475896i
$700$	0.00583171	+	0.00975111i	0.000220418	+	0.000368557i
$701$	4.63308	+	2.23117i	0.174989	+	0.0842703i	0.519328	−	0.854575i	$-0.326182\pi$
$701$	4.63308	+	2.23117i	0.174989	+	0.0842703i	−0.344338	+	0.938846i	$0.611897\pi$
$702$	−7.16055	+	3.74720i	−0.270258	+	0.141429i
$703$	−45.8817	+	6.91556i	−1.73046	+	0.260825i
$704$	2.06183	+	3.57119i	0.0777081	+	0.134594i
$705$	20.0186	+	43.0828i	0.753945	+	1.62259i
$706$	9.22729	−	23.5108i	0.347274	−	0.884839i
$707$	−5.84122	−	0.788686i	−0.219682	−	0.0296616i
$708$	−5.28109	−	18.0008i	−0.198476	−	0.676510i
$709$	−6.50963	+	8.16282i	−0.244474	+	0.306561i	−0.888896	−	0.458109i	$-0.848527\pi$
$709$	−6.50963	+	8.16282i	−0.244474	+	0.306561i	0.644422	+	0.764670i	$0.277098\pi$
$710$	17.7015	−	12.0687i	0.664326	−	0.452930i
$711$	−3.68659	+	35.8580i	−0.138258	+	1.34478i
$712$	−9.00468	−	1.35724i	−0.337465	−	0.0508646i
$713$	5.14273	+	13.1035i	0.192597	+	0.490729i
$714$	−5.51340	−	4.38269i	−0.206334	−	0.164018i
$715$	−5.23726	+	13.3443i	−0.195862	+	0.499049i
$716$	6.27852	−	10.8747i	0.234639	−	0.406407i
$717$	29.1470	+	2.58994i	1.08851	+	0.0967233i
$718$	4.01101	−	10.2199i	0.149690	−	0.381403i
$719$	−14.8732	+	13.8003i	−0.554676	+	0.514665i	−0.906953	−	0.421231i	$-0.861598\pi$
$719$	−14.8732	+	13.8003i	−0.554676	+	0.514665i	0.352277	+	0.935896i	$0.385408\pi$
$720$	5.43365	+	3.92897i	0.202500	+	0.146424i
$721$	−1.52759	−	3.72273i	−0.0568905	−	0.138642i
$722$	−1.17357	+	15.6602i	−0.0436757	+	0.582812i
$723$	18.6651	+	28.2068i	0.694163	+	1.04902i
$724$	10.7979	−	5.20000i	0.401301	−	0.193256i
$725$	0.000686891		0.00300946i	2.55105e−5		0.000111769i
$726$	0.143783	−	10.3992i	0.00533629	−	0.385950i
$727$	−13.0337	−	12.0935i	−0.483392	−	0.448522i	0.400443	−	0.916322i	$-0.368856\pi$
$727$	−13.0337	−	12.0935i	−0.483392	−	0.448522i	−0.883834	+	0.467800i	$0.845047\pi$
$728$	3.91308	−	1.27330i	0.145028	−	0.0471917i
$729$	8.16848	−	25.7347i	0.302536	−	0.953138i
$730$	−35.5891	+	10.9778i	−1.31721	+	0.406306i
$731$	−7.03107	−	1.05976i	−0.260053	−	0.0391967i
$732$	−4.00176	−	4.43428i	−0.147909	−	0.163896i
$733$	2.55716	−	34.1230i	0.0944510	−	1.26036i	−0.725619	−	0.688097i	$-0.758446\pi$
$733$	2.55716	−	34.1230i	0.0944510	−	1.26036i	0.820070	−	0.572264i	$-0.193935\pi$
$734$	−1.71264	−	2.96638i	−0.0632148	−	0.109491i
$735$	20.8975	−	17.2529i	0.770817	−	0.636383i
$736$	−0.931128	+	1.61276i	−0.0343218	+	0.0594471i
$737$	25.5673	+	17.4315i	0.941785	+	0.642098i
$738$	17.3114	+	22.9838i	0.637242	+	0.846044i
$739$	12.9632	+	33.0298i	0.476861	+	1.21502i	0.943736	+	0.330699i	$0.107284\pi$
$739$	12.9632	+	33.0298i	0.476861	+	1.21502i	−0.466876	+	0.884323i	$0.654620\pi$
$740$	3.91739	−	17.1632i	0.144006	−	0.630932i
$741$	12.5432	−	9.72227i	0.460787	−	0.357156i
$742$	1.09186	+	2.66085i	0.0400833	+	0.0976828i
$743$	15.4149	−	4.75486i	0.565517	−	0.174439i	0.00120297	−	0.999999i	$-0.499617\pi$
$743$	15.4149	−	4.75486i	0.565517	−	0.174439i	0.564314	+	0.825561i	$0.309141\pi$
$744$	11.4277	−	6.38879i	0.418960	−	0.234224i
$745$	13.3594	−	12.3957i	0.489451	−	0.454144i
$746$	0.224429	−	2.99480i	0.00821694	−	0.109647i
$747$	11.9192	+	22.0296i	0.436100	+	0.806021i
$748$	5.71015	−	2.74986i	0.208784	−	0.100545i
$749$	−7.74769	+	20.6707i	−0.283094	+	0.755291i
$750$	−16.9100	+	9.45373i	−0.617467	+	0.345202i
$751$	16.3920	+	5.05627i	0.598153	+	0.184506i	0.579023	−	0.815311i	$-0.303434\pi$
$751$	16.3920	+	5.05627i	0.598153	+	0.184506i	0.0191301	+	0.999817i	$0.493910\pi$
$752$	7.65110	+	9.59418i	0.279007	+	0.349864i
$753$	16.2223	−	23.1009i	0.591172	−	0.841845i
$754$	1.11799			0.0407149
$755$	7.69518	+	9.64945i	0.280056	+	0.351179i
$756$	−6.28596	+	12.2265i	−0.228618	+	0.444673i
$757$	−25.2669	+	31.6837i	−0.918342	+	1.15156i	0.0697286	+	0.997566i	$0.477787\pi$
$757$	−25.2669	+	31.6837i	−0.918342	+	1.15156i	−0.988071	+	0.153999i	$0.950785\pi$
$758$	20.9824	−	26.3111i	0.762114	−	0.955661i
$759$	11.6098	−	6.49059i	0.421409	−	0.235593i
$760$	−11.8631	−	5.71297i	−0.430320	−	0.207231i
$761$	−18.7537	−	47.7836i	−0.679820	−	1.73215i	−0.681139	−	0.732154i	$-0.738515\pi$
$761$	−18.7537	−	47.7836i	−0.679820	−	1.73215i	0.00131882	−	0.999999i	$-0.499580\pi$
$762$	−7.46092	−	25.4308i	−0.270281	−	0.921260i
$763$	−13.3680	+	23.9996i	−0.483954	+	0.868845i
$764$	1.22497	+	1.53607i	0.0443179	+	0.0555729i
$765$	6.64577	−	7.87654i	0.240278	−	0.284777i
$766$	2.64320	−	4.57815i	0.0955027	−	0.165415i
$767$	6.15436	−	15.6811i	0.222221	−	0.566210i
$768$	1.60342	+	0.655019i	0.0578584	+	0.0236360i
$769$	3.84644	+	51.3272i	0.138706	+	1.85091i	0.440770	+	0.897620i	$0.354705\pi$
$769$	3.84644	+	51.3272i	0.138706	+	1.85091i	−0.302064	+	0.953288i	$0.597676\pi$
$770$	5.79150	+	23.6877i	0.208711	+	0.853645i
$771$	29.0987	+	23.8710i	1.04796	+	0.859692i
$772$	−12.3645	−	15.5046i	−0.445008	−	0.558023i
$773$	3.16709	−	42.2618i	0.113912	−	1.52005i	−0.588625	−	0.808406i	$-0.700331\pi$
$773$	3.16709	−	42.2618i	0.113912	−	1.52005i	0.702538	−	0.711647i	$-0.252050\pi$
$774$	0.654147	+	13.8638i	0.0235128	+	0.498324i
$775$	0.00242579	+	0.0323700i	8.71371e−5	+	0.00116276i
$776$	6.72271	+	6.23776i	0.241331	+	0.223923i
$777$	35.9974	+	2.64098i	1.29140	+	0.0947447i
$778$	−2.33483	+	2.16640i	−0.0837076	+	0.0776693i
$779$	−41.4193	−	38.4315i	−1.48400	−	1.37695i
$780$	1.69507	+	5.77769i	0.0606931	+	0.206874i
$781$	−37.7705	+	11.6507i	−1.35154	+	0.416893i
$782$	2.36483	+	1.61231i	0.0845661	+	0.0576562i
$783$	−2.65182	+	2.63029i	−0.0947684	+	0.0939989i
$784$	4.19393	−	5.60455i	0.149783	−	0.200162i
$785$	−5.50659	+	9.53769i	−0.196538	+	0.340415i
$786$	−20.4089	−	16.7423i	−0.727961	−	0.597179i
$787$	−5.64980	+	24.7534i	−0.201394	+	0.882364i	0.768695	+	0.639615i	$0.220906\pi$
$787$	−5.64980	+	24.7534i	−0.201394	+	0.882364i	−0.970089	+	0.242749i	$0.921951\pi$
$788$	0.508673	−	0.637855i	0.0181207	−	0.0227227i
$789$	0.922961	−	2.85158i	0.0328583	−	0.101519i
$790$	25.6632	+	7.91603i	0.913054	+	0.281640i
$791$	−4.87417	+	13.0042i	−0.173305	+	0.462376i
$792$	−7.44282	−	9.88157i	−0.264469	−	0.351126i
$793$	−0.400823	−	5.34861i	−0.0142336	−	0.189935i
$794$	13.1022	−	12.1570i	0.464979	−	0.431437i
$795$	−3.93842	+	1.48321i	−0.139681	+	0.0526041i
$796$	15.8852	−	2.39431i	0.563036	−	0.0848640i
$797$	6.54096	+	4.45955i	0.231693	+	0.157965i	0.673602	−	0.739094i	$-0.264746\pi$
$797$	6.54096	+	4.45955i	0.231693	+	0.157965i	−0.441909	+	0.897060i	$0.645699\pi$
$798$	7.91684	−	25.8091i	0.280253	−	0.913632i
$799$	15.5832	−	10.6244i	0.551292	−	0.375865i
$800$	−0.00314802	+	0.00292093i	−0.000111299	+	0.000103271i
$801$	27.3087	+	0.755305i	0.964907	+	0.0266874i
$802$	−10.1387	+	17.5608i	−0.358010	+	0.620092i
$803$	68.7127			2.42482
$804$	12.9733	−	0.792020i	0.457533	−	0.0279324i
$805$	−7.95651	+	7.61377i	−0.280430	+	0.268350i
$806$	11.6253	+	1.75223i	0.409482	+	0.0617195i
$807$	12.0314	+	2.92166i	0.423526	+	0.102847i
$808$	−0.166484	−	2.22158i	−0.00585690	−	0.0781548i
$809$	−2.17651	+	1.48392i	−0.0765221	+	0.0521719i	−0.600977	−	0.799266i	$-0.705222\pi$
$809$	−2.17651	+	1.48392i	−0.0765221	+	0.0521719i	0.524455	+	0.851438i	$0.324269\pi$
$810$	−17.6137	−	9.71642i	−0.618883	−	0.341400i
$811$	8.68591	−	10.8918i	0.305004	−	0.382462i	−0.605582	−	0.795783i	$-0.707060\pi$
$811$	8.68591	−	10.8918i	0.305004	−	0.382462i	0.910586	+	0.413320i	$0.135631\pi$
$812$	1.55466	−	1.09537i	0.0545579	−	0.0384401i
$813$	−8.24768	−	12.4639i	−0.289259	−	0.437129i
$814$	−16.2398	+	28.1281i	−0.569204	+	0.985889i
$815$	−15.2079			−0.532710
$816$	1.18807	−	2.38222i	0.0415907	−	0.0833945i
$817$	−6.06464	−	26.5709i	−0.212175	−	0.929600i
$818$	−13.6671	−	6.58174i	−0.477860	−	0.230125i
$819$	−11.1874	+	5.21957i	−0.390919	+	0.182387i
$820$	19.3146	−	9.30143i	0.674496	−	0.324820i
$821$	−8.26884	−	10.3688i	−0.288584	−	0.361873i	0.616314	−	0.787500i	$-0.288625\pi$
$821$	−8.26884	−	10.3688i	−0.288584	−	0.361873i	−0.904899	+	0.425627i	$0.860054\pi$
$822$	−20.3170	+	7.65139i	−0.708636	+	0.266873i
$823$	−11.0824	−	48.5554i	−0.386310	−	1.69253i	−0.677218	−	0.735782i	$-0.736815\pi$
$823$	−11.0824	−	48.5554i	−0.386310	−	1.69253i	0.290908	−	0.956751i	$-0.406042\pi$
$824$	1.25664	−	0.856761i	0.0437771	−	0.0298467i
$825$	0.0299947	−	0.00641115i	0.00104428	−	0.000223208i
$826$	−6.80566	−	27.8357i	−0.236799	−	0.968527i
$827$	9.20599	+	40.3341i	0.320124	+	1.40255i	0.837332	+	0.546694i	$0.184114\pi$
$827$	9.20599	+	40.3341i	0.320124	+	1.40255i	−0.517209	+	0.855859i	$0.673029\pi$
$828$	2.18408	−	5.14215i	0.0759019	−	0.178702i
$829$	−8.01972	−	20.4339i	−0.278536	−	0.709699i	−0.999854	−	0.0170944i	$-0.994558\pi$
$829$	−8.01972	−	20.4339i	−0.278536	−	0.709699i	0.721318	−	0.692604i	$-0.243537\pi$
$830$	17.8321	−	5.50048i	0.618962	−	0.190924i
$831$	49.3870	−	18.5992i	1.71322	−	0.645199i
$832$	0.777668	+	1.34696i	0.0269608	+	0.0466975i
$833$	−8.10804	−	7.07148i	−0.280927	−	0.245012i
$834$	28.0393	+	2.49152i	0.970920	+	0.0862741i
$835$	34.6827	−	16.7023i	1.20024	−	0.578007i
$836$	17.8077	+	16.5231i	0.615892	+	0.571464i
$837$	−31.6970	+	23.1944i	−1.09561	+	0.801717i
$838$	16.6294	−	5.12949i	0.574453	−	0.177195i
$839$	−20.2314	−	6.24057i	−0.698467	−	0.215448i	−0.0748684	−	0.997193i	$-0.523854\pi$
$839$	−20.2314	−	6.24057i	−0.698467	−	0.215448i	−0.623598	+	0.781745i	$0.714330\pi$
$840$	8.01793	+	6.37358i	0.276645	+	0.219910i
$841$	−27.2179	+	8.39560i	−0.938548	+	0.289504i
$842$	−3.70041	+	2.52290i	−0.127525	+	0.0869449i
$843$	22.9143	−	17.7609i	0.789210	−	0.611717i
$844$	−1.64850	−	1.12393i	−0.0567439	−	0.0386873i
$845$	8.64014	−	22.0147i	0.297230	−	0.757329i
$846$	−26.2841	−	25.7766i	−0.903667	−	0.886217i
$847$	0.943253	−	15.8585i	0.0324105	−	0.544906i
$848$	−0.898191	+	0.612376i	−0.0308440	+	0.0210291i
$849$	12.4960	+	5.10480i	0.428862	+	0.175196i
$850$	0.00411516	+	0.00516025i	0.000141149	+	0.000176995i
$851$	−14.6678			−0.502807
$852$	−9.54113	+	13.5868i	−0.326874	+	0.465477i
$853$	32.2543	−	4.86156i	1.10437	−	0.166457i	0.428545	−	0.903521i	$-0.359027\pi$
$853$	32.2543	−	4.86156i	1.10437	−	0.166457i	0.675823	+	0.737064i	$0.263788\pi$
$854$	−5.79778	−	7.04498i	−0.198396	−	0.241074i
$855$	37.4099	+	12.6823i	1.27939	+	0.433726i
$856$	−8.25037	−	1.24354i	−0.281992	−	0.0425034i
$857$	2.54574	+	33.9706i	0.0869609	+	1.16041i	0.854514	+	0.519428i	$0.173855\pi$
$857$	2.54574	+	33.9706i	0.0869609	+	1.16041i	−0.767553	+	0.640985i	$0.778526\pi$
$858$	0.153580	−	11.1078i	0.00524313	−	0.379212i
$859$	10.9215	+	27.8275i	0.372637	+	0.949463i	0.987040	+	0.160471i	$0.0513014\pi$
$859$	10.9215	+	27.8275i	0.372637	+	0.949463i	−0.614404	+	0.788992i	$0.710603\pi$
$860$	10.2250	+	1.54117i	0.348671	+	0.0525536i
$861$	24.8164	+	36.2768i	0.845739	+	1.23631i
$862$	26.5929	−	4.00823i	0.905758	−	0.136521i
$863$	−23.1305	−	40.0632i	−0.787371	−	1.36377i	−0.927572	−	0.373643i	$-0.878108\pi$
$863$	−23.1305	−	40.0632i	−0.787371	−	1.36377i	0.140202	−	0.990123i	$-0.455225\pi$
$864$	−5.01357	−	1.36531i	−0.170565	−	0.0464489i
$865$	9.33613	−	1.40720i	0.317438	−	0.0478461i
$866$	−2.90022	−	12.7067i	−0.0985534	−	0.431791i
$867$	21.7794	+	12.9791i	0.739667	+	0.440793i
$868$	17.8827	−	8.95346i	0.606978	−	0.303900i
$869$	−40.9389	−	27.9117i	−1.38876	−	0.946838i
$870$	1.53564	+	2.32066i	0.0520631	+	0.0786779i
$871$	9.64334	+	6.57472i	0.326752	+	0.222776i
$872$	−9.92197	−	3.06052i	−0.336000	−	0.103642i
$873$	−22.2948	−	16.1209i	−0.754563	−	0.545611i
$874$	−2.44118	+	10.6955i	−0.0825743	+	0.361782i
$875$	−26.4617	+	13.2488i	−0.894568	+	0.447890i
$876$	22.8112	−	17.6810i	0.770721	−	0.597386i
$877$	11.9617	+	11.0988i	0.403918	+	0.374781i	0.855809	−	0.517292i	$-0.173060\pi$
$877$	11.9617	+	11.0988i	0.403918	+	0.374781i	−0.451891	+	0.892073i	$0.649250\pi$
$878$	−9.67665	+	12.1341i	−0.326571	+	0.409507i
$879$	−16.8099	+	51.9358i	−0.566982	+	1.75175i
$880$	−8.30407	+	3.99903i	−0.279930	+	0.134807i
$881$	20.3157			0.684454			0.342227	−	0.939617i	$-0.388819\pi$
$881$	20.3157			0.684454			0.342227	+	0.939617i	$0.388819\pi$
$882$	−10.4430	+	18.2193i	−0.351635	+	0.613476i
$883$	5.90656			0.198772			0.0993858	−	0.995049i	$-0.468312\pi$
$883$	5.90656			0.198772			0.0993858	+	0.995049i	$0.468312\pi$
$884$	2.15372	−	1.03718i	0.0724375	−	0.0348840i
$885$	41.0033	−	8.76414i	1.37831	−	0.294603i
$886$	−1.13497	+	1.42321i	−0.0381302	+	0.0478138i
$887$	33.3578	+	30.9515i	1.12004	+	1.03925i	0.998913	+	0.0466133i	$0.0148429\pi$
$887$	33.3578	+	30.9515i	1.12004	+	1.03925i	0.121132	+	0.992636i	$0.461348\pi$
$888$	1.84659	+	13.5168i	0.0619674	+	0.453593i
$889$	−9.61477	−	39.3251i	−0.322469	−	1.31892i
$890$	4.52914	−	19.8435i	0.151817	−	0.665154i
$891$	25.7688	+	26.7084i	0.863288	+	0.894764i
$892$	−23.5332	−	7.25903i	−0.787950	−	0.243050i
$893$	59.7297	+	40.7230i	1.99878	+	1.36274i
$894$	−6.30290	+	12.6381i	−0.210800	+	0.422682i
$895$	23.1895	+	15.8103i	0.775140	+	0.528481i
$896$	2.40112	+	1.11113i	0.0802159	+	0.0371201i
$897$	4.37891	−	2.44808i	0.146208	−	0.0817390i
$898$	4.53649	+	19.8757i	0.151385	+	0.663260i
$899$	5.37270	−	0.809804i	0.179190	−	0.0270085i
$900$	0.00830795	−	0.00984656i	0.000276932	−	0.000328219i
$901$	0.835388	+	1.44693i	0.0278308	+	0.0482044i
$902$	−39.1095	+	5.89481i	−1.30220	+	0.196276i
$903$	0.0331824	+	21.2008i	0.00110424	+	0.705520i
$904$	−5.19041	−	0.782328i	−0.172630	−	0.0260198i
$905$	9.78648	+	24.9356i	0.325314	+	0.828886i
$906$	−8.21599	−	4.89619i	−0.272958	−	0.162665i
$907$	1.97498	+	26.3543i	0.0655782	+	0.875080i	0.928877	+	0.370388i	$0.120775\pi$
$907$	1.97498	+	26.3543i	0.0655782	+	0.875080i	−0.863299	+	0.504693i	$0.831606\pi$
$908$	−13.1435	−	1.98106i	−0.436181	−	0.0657437i
$909$	1.30649	+	6.55448i	0.0433334	+	0.217398i
$910$	2.18441	+	8.93438i	0.0724123	+	0.296172i
$911$	11.0909	−	1.67169i	0.367459	−	0.0553855i	0.0372825	−	0.999305i	$-0.488130\pi$
$911$	11.0909	−	1.67169i	0.367459	−	0.0553855i	0.330176	+	0.943919i	$0.392892\pi$
$912$	10.1635	+	0.903109i	0.336547	+	0.0299049i
$913$	−34.4289			−1.13943
$914$	17.0806	+	21.4183i	0.564975	+	0.708456i
$915$	10.5518	−	8.17869i	0.348831	−	0.270379i
$916$	−9.43421	+	6.43214i	−0.311715	+	0.212524i
$917$	−29.9773	−	26.9684i	−0.989939	−	0.890574i
$918$	−2.66836	+	7.52717i	−0.0880691	+	0.248434i
$919$	17.9764	−	45.8032i	0.592988	−	1.51091i	−0.247395	−	0.968915i	$-0.579575\pi$
$919$	17.9764	−	45.8032i	0.592988	−	1.51091i	0.840383	−	0.541993i	$-0.182330\pi$
$920$	−3.43909	−	2.34473i	−0.113383	−	0.0773035i
$921$	4.22322	+	1.72524i	0.139160	+	0.0568487i
$922$	−4.51746	+	3.07995i	−0.148775	+	0.101433i
$923$	−14.2461	+	4.39433i	−0.468915	+	0.144641i
$924$	−10.6695	−	15.5967i	−0.351000	−	0.513095i
$925$	−0.0323216	−	0.00996990i	−0.00106273	−	0.000327808i
$926$	−22.8411	+	7.04554i	−0.750604	+	0.231531i
$927$	−3.42925	+	3.00979i	−0.112631	+	0.0988546i
$928$	0.526925	+	0.488915i	0.0172972	+	0.0160494i
$929$	44.6841	−	21.5187i	1.46604	−	0.706007i	0.480742	−	0.876862i	$-0.340367\pi$
$929$	44.6841	−	21.5187i	1.46604	−	0.706007i	0.985296	+	0.170855i	$0.0546531\pi$
$930$	12.3309	+	26.5378i	0.404347	+	0.870210i
$931$	13.8771	−	38.8320i	0.454803	−	1.27267i
$932$	−10.3057	−	17.8501i	−0.337576	−	0.584698i
$933$	0.525606	−	3.18751i	0.0172076	−	0.104354i
$934$	−4.89255	+	1.50915i	−0.160089	+	0.0493810i
$935$	5.17529	+	13.1864i	0.169250	+	0.431242i
$936$	−2.80724	−	3.72707i	−0.0917575	−	0.121823i
$937$	9.02711	+	39.5504i	0.294903	+	1.29205i	0.877611	+	0.479373i	$0.159136\pi$
$937$	9.02711	+	39.5504i	0.294903	+	1.29205i	−0.582708	+	0.812681i	$0.698007\pi$
$938$	19.8516	−	0.305552i	0.648177	−	0.00997663i
$939$	8.78288	+	9.73215i	0.286619	+	0.317597i
$940$	−22.6620	+	15.4507i	−0.739154	+	0.503946i
$941$	2.32949	+	10.2062i	0.0759393	+	0.332712i	0.998600	−	0.0529016i	$-0.0168470\pi$
$941$	2.32949	+	10.2062i	0.0759393	+	0.332712i	−0.922660	+	0.385613i	$0.873990\pi$
$942$	1.38854	−	8.42072i	0.0452411	−	0.274362i
$943$	−11.1364	−	13.9647i	−0.362652	−	0.454752i
$944$	9.75820	−	4.69930i	0.317602	−	0.152949i
$945$	−26.2011	−	16.0527i	−0.852323	−	0.522194i
$946$	−17.1884	−	8.27752i	−0.558844	−	0.269125i
$947$	−4.44896	−	19.4921i	−0.144572	−	0.633410i	−0.994339	−	0.106252i	$-0.966115\pi$
$947$	−4.44896	−	19.4921i	−0.144572	−	0.633410i	0.849768	−	0.527158i	$-0.176742\pi$
$948$	−20.7731	+	1.26820i	−0.674678	+	0.0411891i
$949$	25.9166			0.841290
$950$	−0.0126492	+	0.0219090i	−0.000410394	+	0.000710823i
$951$	−46.6261	+	2.84653i	−1.51196	+	0.0923049i
$952$	1.97873	−	3.55243i	0.0641312	−	0.115135i
$953$	8.27557	−	10.3772i	0.268072	−	0.336152i	−0.629516	−	0.776988i	$-0.716747\pi$
$953$	8.27557	−	10.3772i	0.268072	−	0.336152i	0.897588	+	0.440836i	$0.145318\pi$
$954$	2.45108	−	2.15127i	0.0793567	−	0.0696500i
$955$	−3.62828	+	2.47372i	−0.117408	+	0.0800476i
$956$	1.26251	+	16.8471i	0.0408326	+	0.544874i
$957$	−1.44531	−	4.92638i	−0.0467202	−	0.159247i
$958$	19.4486	+	2.93140i	0.628354	+	0.0947091i
$959$	−31.5350	+	10.2614i	−1.01832	+	0.331357i
$960$	−1.72776	+	3.46438i	−0.0557633	+	0.111812i
$961$	26.1363			0.843108
$962$	−6.12522	+	10.6092i	−0.197485	+	0.342054i
$963$	25.0211	+	0.692034i	0.806294	+	0.0223005i
$964$	−14.3149	+	13.2823i	−0.461052	+	0.427794i
$965$	36.6228	−	24.9690i	1.17893	−	0.803780i
$966$	3.69069	−	7.69459i	0.118746	−	0.247569i
$967$	−48.6261	−	33.1527i	−1.56371	−	1.06612i	−0.964000	−	0.265902i	$-0.914330\pi$
$967$	−48.6261	−	33.1527i	−1.56371	−	1.06612i	−0.599710	−	0.800218i	$-0.704717\pi$
$968$	5.93749	−	0.894932i	0.190838	−	0.0287642i
$969$	2.55147	−	15.4732i	0.0819650	−	0.497071i
$970$	−15.0260	+	13.9421i	−0.482455	+	0.447653i
$971$	3.09540	+	41.3052i	0.0993361	+	1.32555i	0.794749	+	0.606938i	$0.207602\pi$
$971$	3.09540	+	41.3052i	0.0993361	+	1.32555i	−0.695413	+	0.718610i	$0.744779\pi$
$972$	15.4273	+	2.23587i	0.494830	+	0.0717154i
$973$	42.6128	+	5.75361i	1.36610	+	0.184452i
$974$	−33.6962	−	10.3939i	−1.07970	−	0.333042i
$975$	0.0113132	−	0.00241812i	0.000362313	−	7.74418e-5i
$976$	2.15012	−	2.69616i	0.0688236	−	0.0863020i
$977$	−3.92905	+	17.2143i	−0.125701	+	0.550734i	0.872381	+	0.488827i	$0.162575\pi$
$977$	−3.92905	+	17.2143i	−0.125701	+	0.550734i	−0.998082	+	0.0619064i	$0.980282\pi$
$978$	11.0289	−	4.15349i	0.352665	−	0.132814i
$979$	−18.7758	+	32.5207i	−0.600078	+	1.03937i
$980$	11.7912	+	10.2838i	0.376657	+	0.328504i
$981$	30.6618	+	5.49246i	0.978955	+	0.175361i
$982$	21.7032	+	14.7970i	0.692577	+	0.472191i
$983$	18.2459	−	5.62813i	0.581955	−	0.179509i	0.0102201	−	0.999948i	$-0.496747\pi$
$983$	18.2459	−	5.62813i	0.581955	−	0.179509i	0.571735	+	0.820438i	$0.306271\pi$
$984$	−11.4667	+	12.0205i	−0.365546	+	0.383201i
$985$	1.33673	+	1.24030i	0.0425916	+	0.0395192i
$986$	0.809849	−	0.751430i	0.0257909	−	0.0239304i
$987$	−38.3138	−	41.1630i	−1.21954	−	1.31023i
$988$	6.71660	+	6.23210i	0.213684	+	0.198269i
$989$	−0.643841	−	8.59146i	−0.0204730	−	0.273193i
$990$	23.2678	−	14.9385i	0.739499	−	0.474776i
$991$	2.57385	−	34.3456i	0.0817610	−	1.09102i	−0.793884	−	0.608069i	$-0.791944\pi$
$991$	2.57385	−	34.3456i	0.0817610	−	1.09102i	0.875645	−	0.482955i	$-0.160437\pi$
$992$	4.71287	+	5.90975i	0.149634	+	0.187635i
$993$	−4.28291	+	25.9734i	−0.135914	+	0.824241i
$994$	−15.5049	+	20.0685i	−0.491786	+	0.636535i
$995$	2.68327	+	35.8058i	0.0850654	+	1.13512i
$996$	−11.4297	+	8.85918i	−0.362164	+	0.280714i
$997$	4.27487	−	10.8922i	0.135387	−	0.344959i	−0.847062	−	0.531494i	$-0.821631\pi$
$997$	4.27487	−	10.8922i	0.135387	−	0.344959i	0.982448	+	0.186535i	$0.0597259\pi$
$998$	−5.34956	+	9.26570i	−0.169337	+	0.293301i
$999$	−10.4314	−	39.5752i	−0.330036	−	1.25210i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.bb.b.151.7	yes	336
9.4	even	3		882.2.y.a.445.8	yes	336
49.37	even	21		882.2.y.a.331.8	✓	336
441.184	even	21	inner	882.2.bb.b.625.7	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.y.a.331.8	✓	336	49.37	even	21
882.2.y.a.445.8	yes	336	9.4	even	3
882.2.bb.b.151.7	yes	336	1.1	even	1	trivial
882.2.bb.b.625.7	yes	336	441.184	even	21	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.900969 - 0.433884i) q^{2} +(-1.16043 - 1.28585i) q^{3} +(0.623490 - 0.781831i) q^{4} +(1.63845 + 1.52026i) q^{5} +(-1.60342 - 0.655019i) q^{6} +(-2.40112 - 1.11113i) q^{7} +(0.222521 - 0.974928i) q^{8} +(-0.306815 + 2.98427i) q^{9} +O(q^{10})\)	\(q+(0.900969 - 0.433884i) q^{2} +(-1.16043 - 1.28585i) q^{3} +(0.623490 - 0.781831i) q^{4} +(1.63845 + 1.52026i) q^{5} +(-1.60342 - 0.655019i) q^{6} +(-2.40112 - 1.11113i) q^{7} +(0.222521 - 0.974928i) q^{8} +(-0.306815 + 2.98427i) q^{9} +(2.13581 + 0.658810i) q^{10} +(-3.40713 - 2.32294i) q^{11} +(-1.72883 + 0.105545i) q^{12} +(-1.28508 - 0.876152i) q^{13} +(-2.64544 + 0.0407182i) q^{14} +(0.0535212 - 3.87095i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(-1.51977 + 0.229068i) q^{17} +(1.01840 + 2.82186i) q^{18} +(-2.94551 - 5.10177i) q^{19} +(2.21014 - 0.333125i) q^{20} +(1.35759 + 4.37687i) q^{21} +(-4.07760 - 0.614599i) q^{22} +(-0.680358 - 1.73352i) q^{23} +(-1.51183 + 0.845205i) q^{24} +(-0.000320921 - 0.00428239i) q^{25} +(-1.53796 - 0.231811i) q^{26} +(4.19336 - 3.06851i) q^{27} +(-2.36579 + 1.18450i) q^{28} +(-0.710782 + 0.107133i) q^{29} +(-1.63132 - 3.51083i) q^{30} -7.55886 q^{31} +(-0.623490 - 0.781831i) q^{32} +(0.966775 + 7.07665i) q^{33} +(-1.26987 + 0.865786i) q^{34} +(-2.24492 - 5.47086i) q^{35} +(2.14190 + 2.10054i) q^{36} +(2.87757 - 7.33192i) q^{37} +(-4.86739 - 3.31853i) q^{38} +(0.364642 + 2.66913i) q^{39} +(1.84673 - 1.25908i) q^{40} +(9.16519 - 2.82709i) q^{41} +(3.12220 + 3.35438i) q^{42} +(4.42087 + 1.36366i) q^{43} +(-3.94046 + 1.21547i) q^{44} +(-5.03956 + 4.42314i) q^{45} +(-1.36513 - 1.26666i) q^{46} +(-11.0562 + 5.32437i) q^{47} +(-0.995391 + 1.41746i) q^{48} +(4.53079 + 5.33591i) q^{49} +(-0.00214720 - 0.00371906i) q^{50} +(2.05813 + 1.68837i) q^{51} +(-1.48624 + 0.458444i) q^{52} +(-0.397156 - 1.01194i) q^{53} +(2.44671 - 4.58406i) q^{54} +(-2.05094 - 8.98573i) q^{55} +(-1.61757 + 2.09367i) q^{56} +(-3.14206 + 9.70772i) q^{57} +(-0.593909 + 0.404920i) q^{58} +(2.41008 + 10.5592i) q^{59} +(-2.99306 - 2.45534i) q^{60} +(2.15012 + 2.69616i) q^{61} +(-6.81030 + 3.27967i) q^{62} +(4.05260 - 6.82469i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(-0.773560 - 3.38919i) q^{65} +(3.94148 + 5.95638i) q^{66} -7.50408 q^{67} +(-0.768467 + 1.33102i) q^{68} +(-1.43954 + 2.88647i) q^{69} +(-4.39632 - 3.95504i) q^{70} +(5.97635 - 7.49410i) q^{71} +(2.84117 + 0.963185i) q^{72} +(-13.7677 + 9.38663i) q^{73} +(-0.588603 - 7.85437i) q^{74} +(-0.00513410 + 0.00538206i) q^{75} +(-5.82522 - 0.878011i) q^{76} +(5.59985 + 9.36341i) q^{77} +(1.48662 + 2.24659i) q^{78} +12.0157 q^{79} +(1.11755 - 1.93566i) q^{80} +(-8.81173 - 1.83124i) q^{81} +(7.03093 - 6.52375i) q^{82} +(6.89837 - 4.70323i) q^{83} +(4.26841 + 1.66752i) q^{84} +(-2.83831 - 1.93512i) q^{85} +(4.57474 - 0.689531i) q^{86} +(0.962568 + 0.789638i) q^{87} +(-3.02286 + 2.80480i) q^{88} +(-0.680522 - 9.08093i) q^{89} +(-2.62136 + 6.17169i) q^{90} +(2.11212 + 3.53164i) q^{91} +(-1.77952 - 0.548909i) q^{92} +(8.77151 + 9.71955i) q^{93} +(-7.65110 + 9.59418i) q^{94} +(2.92995 - 12.8369i) q^{95} +(-0.281802 + 1.70897i) q^{96} +(-4.58542 + 7.94219i) q^{97} +(6.39727 + 2.84165i) q^{98} +(7.97763 - 9.45507i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q + 56 q^{2} + 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} + 2 q^{7} + 56 q^{8} + 5 q^{9}+O(q^{10}) \) 336 * q + 56 * q^2 + 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 + 2 * q^7 + 56 * q^8 + 5 * q^9	\( 336 q + 56 q^{2} + 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} + 2 q^{7} + 56 q^{8} + 5 q^{9} - 2 q^{10} - 2 q^{12} + 19 q^{13} - 2 q^{14} + q^{15} - 56 q^{16} + 7 q^{17} + 2 q^{18} + 38 q^{19} + 2 q^{20} + 4 q^{21} - 42 q^{23} + 2 q^{24} + 24 q^{25} + 9 q^{26} + 35 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 88 q^{31} + 56 q^{32} + 26 q^{33} - 7 q^{34} - 2 q^{35} + 5 q^{36} + 52 q^{37} + 11 q^{38} - 60 q^{39} - 2 q^{40} + 3 q^{41} - 53 q^{42} + q^{43} + 108 q^{45} - 42 q^{46} + 3 q^{47} - 2 q^{48} + 70 q^{49} + 172 q^{50} + 13 q^{51} + 5 q^{52} - 78 q^{53} + 14 q^{54} + 23 q^{55} - 2 q^{56} - 30 q^{57} + 38 q^{58} - 28 q^{59} + q^{60} - 37 q^{61} - 24 q^{62} + 26 q^{63} - 56 q^{64} - 14 q^{65} + 2 q^{66} - 58 q^{67} - 21 q^{68} + 19 q^{69} + 44 q^{70} + 7 q^{71} + 2 q^{72} - 8 q^{73} + 4 q^{74} + q^{75} - 4 q^{76} - 13 q^{77} + 4 q^{78} + 18 q^{79} - 12 q^{80} - 87 q^{81} - 3 q^{82} + 185 q^{83} - 17 q^{84} - 159 q^{85} - q^{86} - 132 q^{87} + 47 q^{89} + 60 q^{90} + 45 q^{91} - 21 q^{92} + 53 q^{93} + 18 q^{94} + 26 q^{95} + 2 q^{96} + 111 q^{97} - 14 q^{98} - 157 q^{99}+O(q^{100}) \) 336 * q + 56 * q^2 + 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 + 2 * q^7 + 56 * q^8 + 5 * q^9 - 2 * q^10 - 2 * q^12 + 19 * q^13 - 2 * q^14 + q^15 - 56 * q^16 + 7 * q^17 + 2 * q^18 + 38 * q^19 + 2 * q^20 + 4 * q^21 - 42 * q^23 + 2 * q^24 + 24 * q^25 + 9 * q^26 + 35 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 88 * q^31 + 56 * q^32 + 26 * q^33 - 7 * q^34 - 2 * q^35 + 5 * q^36 + 52 * q^37 + 11 * q^38 - 60 * q^39 - 2 * q^40 + 3 * q^41 - 53 * q^42 + q^43 + 108 * q^45 - 42 * q^46 + 3 * q^47 - 2 * q^48 + 70 * q^49 + 172 * q^50 + 13 * q^51 + 5 * q^52 - 78 * q^53 + 14 * q^54 + 23 * q^55 - 2 * q^56 - 30 * q^57 + 38 * q^58 - 28 * q^59 + q^60 - 37 * q^61 - 24 * q^62 + 26 * q^63 - 56 * q^64 - 14 * q^65 + 2 * q^66 - 58 * q^67 - 21 * q^68 + 19 * q^69 + 44 * q^70 + 7 * q^71 + 2 * q^72 - 8 * q^73 + 4 * q^74 + q^75 - 4 * q^76 - 13 * q^77 + 4 * q^78 + 18 * q^79 - 12 * q^80 - 87 * q^81 - 3 * q^82 + 185 * q^83 - 17 * q^84 - 159 * q^85 - q^86 - 132 * q^87 + 47 * q^89 + 60 * q^90 + 45 * q^91 - 21 * q^92 + 53 * q^93 + 18 * q^94 + 26 * q^95 + 2 * q^96 + 111 * q^97 - 14 * q^98 - 157 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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