LMFDB - Embedded newform 71.2.g.a.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [71,2,Mod(2,71)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(71, base_ring=CyclotomicField(70))

chi = DirichletCharacter(H, H._module([6]))

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

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

chi := DirichletCharacter("71.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	71.g (of order $35$, degree $24$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.566937854351$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$5$ over $\Q(\zeta_{35})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{35}]$

Embedding invariants

Embedding label			16.2
Character	$\chi$	$=$	71.16
Dual form			71.2.g.a.40.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.68702 - 0.306149i) q^{2} +(3.00132 - 0.828311i) q^{3} +(0.879843 + 0.330211i) q^{4} +(-0.395338 + 1.21673i) q^{5} +(-5.31687 + 0.478527i) q^{6} +(-1.19600 - 2.22254i) q^{7} +(1.56053 + 0.932373i) q^{8} +(5.74646 - 3.43335i) q^{9} +O(q^{10})$	\(q+(-1.68702 - 0.306149i) q^{2} +(3.00132 - 0.828311i) q^{3} +(0.879843 + 0.330211i) q^{4} +(-0.395338 + 1.21673i) q^{5} +(-5.31687 + 0.478527i) q^{6} +(-1.19600 - 2.22254i) q^{7} +(1.56053 + 0.932373i) q^{8} +(5.74646 - 3.43335i) q^{9} +(1.03944 - 1.93161i) q^{10} +(-1.22139 + 2.85758i) q^{11} +(2.91421 + 0.262283i) q^{12} +(-1.09561 - 2.56332i) q^{13} +(1.33725 + 4.11563i) q^{14} +(-0.178708 + 3.97924i) q^{15} +(-3.76263 - 3.28731i) q^{16} +(-4.83536 + 3.51310i) q^{17} +(-10.7455 + 4.03286i) q^{18} +(0.268159 + 5.97102i) q^{19} +(-0.749611 + 0.939982i) q^{20} +(-5.43054 - 5.67990i) q^{21} +(2.93535 - 4.44687i) q^{22} +(-0.313374 - 0.150913i) q^{23} +(5.45594 + 1.50574i) q^{24} +(2.72096 + 1.97689i) q^{25} +(1.06357 + 4.65979i) q^{26} +(7.94817 - 8.31313i) q^{27} +(-0.318386 - 2.35042i) q^{28} +(-3.28335 - 4.97406i) q^{29} +(1.51973 - 6.65835i) q^{30} +(-4.28039 + 3.73966i) q^{31} +(3.07440 + 3.85518i) q^{32} +(-1.29881 + 9.58820i) q^{33} +(9.23289 - 4.44633i) q^{34} +(3.17705 - 0.576549i) q^{35} +(6.18972 - 1.12327i) q^{36} +(4.07711 - 1.96343i) q^{37} +(1.37563 - 10.1553i) q^{38} +(-5.41151 - 6.78582i) q^{39} +(-1.75138 + 1.53013i) q^{40} +(0.557020 - 2.44046i) q^{41} +(7.42253 + 11.2447i) q^{42} +(-1.17790 - 8.69559i) q^{43} +(-2.01823 + 2.11091i) q^{44} +(1.90565 + 8.34920i) q^{45} +(0.482467 + 0.350533i) q^{46} +(2.92819 + 0.808128i) q^{47} +(-14.0157 - 6.74963i) q^{48} +(0.347003 - 0.525687i) q^{49} +(-3.98509 - 4.16808i) q^{50} +(-11.6025 + 14.5491i) q^{51} +(-0.117534 - 2.61710i) q^{52} +(9.80099 - 3.67837i) q^{53} +(-15.9538 + 11.5911i) q^{54} +(-2.99403 - 2.61580i) q^{55} +(0.205844 - 4.58346i) q^{56} +(5.75069 + 17.6988i) q^{57} +(4.01628 + 9.39654i) q^{58} +(-6.98823 - 0.628952i) q^{59} +(-1.47122 + 3.44210i) q^{60} +(0.503936 - 0.936469i) q^{61} +(8.36599 - 4.99845i) q^{62} +(-14.5035 - 8.66547i) q^{63} +(0.728927 + 1.35457i) q^{64} +(3.55199 - 0.319685i) q^{65} +(5.12654 - 15.7779i) q^{66} +(3.10054 + 1.16365i) q^{67} +(-5.41442 + 1.49429i) q^{68} +(-1.06554 - 0.193367i) q^{69} -5.53626 q^{70} +(-6.39655 - 5.48490i) q^{71} +12.1687 q^{72} +(9.79528 + 1.77758i) q^{73} +(-7.47927 + 2.06415i) q^{74} +(9.80394 + 3.67948i) q^{75} +(-1.73576 + 5.34211i) q^{76} +(7.81188 - 0.703082i) q^{77} +(7.05186 + 13.1046i) q^{78} +(-3.39678 - 2.02948i) q^{79} +(5.48726 - 3.27848i) q^{80} +(7.45288 - 13.8498i) q^{81} +(-1.68685 + 3.94658i) q^{82} +(-0.0918720 - 0.00826863i) q^{83} +(-2.90246 - 6.79064i) q^{84} +(-2.36287 - 7.27217i) q^{85} +(-0.675009 + 15.0302i) q^{86} +(-13.9744 - 12.2091i) q^{87} +(-4.57034 + 3.32055i) q^{88} +(-4.08719 + 1.53395i) q^{89} +(-0.658772 - 14.6687i) q^{90} +(-4.38672 + 5.50078i) q^{91} +(-0.225887 - 0.236259i) q^{92} +(-9.74920 + 14.7694i) q^{93} +(-4.69250 - 2.25979i) q^{94} +(-7.37110 - 2.03429i) q^{95} +(12.4205 + 9.02406i) q^{96} +(-2.32580 - 10.1900i) q^{97} +(-0.746341 + 0.780611i) q^{98} +(2.79242 + 20.6144i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9}+O(q^{10}) $ 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9} - 8 q^{10} - 27 q^{11} + 3 q^{12} - 31 q^{13} + 2 q^{14} + 12 q^{15} + 30 q^{16} + 9 q^{17} + 27 q^{18} - 31 q^{19} + 72 q^{20} - 32 q^{21} - 24 q^{22} - 6 q^{23} - 47 q^{24} - 42 q^{25} + 77 q^{26} - 2 q^{27} - 18 q^{28} + q^{29} + 15 q^{30} + 15 q^{31} - 10 q^{32} - 24 q^{33} + 20 q^{34} + 74 q^{35} + 8 q^{36} - 22 q^{37} - 39 q^{38} + 86 q^{39} - 30 q^{40} + 39 q^{41} - 34 q^{42} + 33 q^{43} - 23 q^{44} + 121 q^{45} + 124 q^{46} + 6 q^{47} + 131 q^{48} - 22 q^{49} - 15 q^{50} + 29 q^{51} + 83 q^{52} - 30 q^{53} - 25 q^{54} + 32 q^{55} + 11 q^{56} - 10 q^{57} + 12 q^{58} - 80 q^{59} + 80 q^{60} - 12 q^{61} - 68 q^{62} - 79 q^{63} - 117 q^{64} - 89 q^{65} - 39 q^{66} - 74 q^{67} - 67 q^{68} - 95 q^{69} - 64 q^{70} - 115 q^{71} - 144 q^{72} - 14 q^{73} - 70 q^{74} - 13 q^{75} + 8 q^{76} + 47 q^{77} - 218 q^{78} - 25 q^{79} - 103 q^{80} - 28 q^{81} - 88 q^{82} - 20 q^{83} - 142 q^{84} + 22 q^{85} + 159 q^{86} - 105 q^{87} + 43 q^{88} + 33 q^{89} + 33 q^{90} + 60 q^{91} - 2 q^{92} + 63 q^{93} + 174 q^{94} + 20 q^{95} - 30 q^{96} + 121 q^{97} + 128 q^{98} - 2 q^{99}+O(q^{100}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9 - 8 * q^10 - 27 * q^11 + 3 * q^12 - 31 * q^13 + 2 * q^14 + 12 * q^15 + 30 * q^16 + 9 * q^17 + 27 * q^18 - 31 * q^19 + 72 * q^20 - 32 * q^21 - 24 * q^22 - 6 * q^23 - 47 * q^24 - 42 * q^25 + 77 * q^26 - 2 * q^27 - 18 * q^28 + q^29 + 15 * q^30 + 15 * q^31 - 10 * q^32 - 24 * q^33 + 20 * q^34 + 74 * q^35 + 8 * q^36 - 22 * q^37 - 39 * q^38 + 86 * q^39 - 30 * q^40 + 39 * q^41 - 34 * q^42 + 33 * q^43 - 23 * q^44 + 121 * q^45 + 124 * q^46 + 6 * q^47 + 131 * q^48 - 22 * q^49 - 15 * q^50 + 29 * q^51 + 83 * q^52 - 30 * q^53 - 25 * q^54 + 32 * q^55 + 11 * q^56 - 10 * q^57 + 12 * q^58 - 80 * q^59 + 80 * q^60 - 12 * q^61 - 68 * q^62 - 79 * q^63 - 117 * q^64 - 89 * q^65 - 39 * q^66 - 74 * q^67 - 67 * q^68 - 95 * q^69 - 64 * q^70 - 115 * q^71 - 144 * q^72 - 14 * q^73 - 70 * q^74 - 13 * q^75 + 8 * q^76 + 47 * q^77 - 218 * q^78 - 25 * q^79 - 103 * q^80 - 28 * q^81 - 88 * q^82 - 20 * q^83 - 142 * q^84 + 22 * q^85 + 159 * q^86 - 105 * q^87 + 43 * q^88 + 33 * q^89 + 33 * q^90 + 60 * q^91 - 2 * q^92 + 63 * q^93 + 174 * q^94 + 20 * q^95 - 30 * q^96 + 121 * q^97 + 128 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/71\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{12}{35}\right)$

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 $

$2$	−1.68702	−	0.306149i	−1.19290	−	0.216480i	−0.454443	−	0.890776i	$-0.650162\pi$
$2$	−1.68702	−	0.306149i	−1.19290	−	0.216480i	−0.738461	+	0.674296i	$0.764447\pi$
$3$	3.00132	−	0.828311i	1.73281	−	0.478226i	0.749784	−	0.661683i	$-0.230157\pi$
$3$	3.00132	−	0.828311i	1.73281	−	0.478226i	0.983028	+	0.183457i	$0.0587288\pi$
$4$	0.879843	+	0.330211i	0.439922	+	0.165105i
$5$	−0.395338	+	1.21673i	−0.176801	+	0.544136i	−0.999711	−	0.0240349i	$-0.992349\pi$
$5$	−0.395338	+	1.21673i	−0.176801	+	0.544136i	0.822911	+	0.568171i	$0.192349\pi$
$6$	−5.31687	+	0.478527i	−2.17060	+	0.195358i
$7$	−1.19600	−	2.22254i	−0.452046	−	0.840042i	−0.999994	−	0.00352954i	$-0.998877\pi$
$7$	−1.19600	−	2.22254i	−0.452046	−	0.840042i	0.547948	−	0.836512i	$-0.315409\pi$
$8$	1.56053	+	0.932373i	0.551731	+	0.329644i
$9$	5.74646	−	3.43335i	1.91549	−	1.14445i
$10$	1.03944	−	1.93161i	0.328701	−	0.610828i
$11$	−1.22139	+	2.85758i	−0.368263	+	0.861593i	0.628239	+	0.778020i	$0.283776\pi$
$11$	−1.22139	+	2.85758i	−0.368263	+	0.861593i	−0.996502	+	0.0835727i	$0.973367\pi$
$12$	2.91421	+	0.262283i	0.841259	+	0.0757147i
$13$	−1.09561	−	2.56332i	−0.303869	−	0.710936i	0.696107	−	0.717938i	$-0.254914\pi$
$13$	−1.09561	−	2.56332i	−0.303869	−	0.710936i	−0.999975	+	0.00700208i	$0.997771\pi$
$14$	1.33725	+	4.11563i	0.357395	+	1.09995i
$15$	−0.178708	+	3.97924i	−0.0461422	+	1.02744i
$16$	−3.76263	−	3.28731i	−0.940656	−	0.821827i
$17$	−4.83536	+	3.51310i	−1.17275	+	0.852051i	−0.991335	−	0.131356i	$-0.958067\pi$
$17$	−4.83536	+	3.51310i	−1.17275	+	0.852051i	−0.181412	+	0.983407i	$0.558067\pi$
$18$	−10.7455	+	4.03286i	−2.53274	+	0.950555i
$19$	0.268159	+	5.97102i	0.0615198	+	1.36984i	0.757993	+	0.652262i	$0.226180\pi$
$19$	0.268159	+	5.97102i	0.0615198	+	1.36984i	−0.696473	+	0.717583i	$0.745249\pi$
$20$	−0.749611	+	0.939982i	−0.167618	+	0.210186i
$21$	−5.43054	−	5.67990i	−1.18504	−	1.23945i
$22$	2.93535	−	4.44687i	0.625820	−	0.948076i
$23$	−0.313374	−	0.150913i	−0.0653431	−	0.0314676i	0.400927	−	0.916110i	$-0.368688\pi$
$23$	−0.313374	−	0.150913i	−0.0653431	−	0.0314676i	−0.466270	+	0.884643i	$0.654402\pi$
$24$	5.45594	+	1.50574i	1.11369	+	0.307359i
$25$	2.72096	+	1.97689i	0.544191	+	0.395378i
$26$	1.06357	+	4.65979i	0.208583	+	0.913860i
$27$	7.94817	−	8.31313i	1.52963	−	1.59986i
$28$	−0.318386	−	2.35042i	−0.0601693	−	0.444188i
$29$	−3.28335	−	4.97406i	−0.609703	−	0.923660i	−0.999996	−	0.00296948i	$-0.999055\pi$
$29$	−3.28335	−	4.97406i	−0.609703	−	0.923660i	0.390293	−	0.920691i	$-0.372374\pi$
$30$	1.51973	−	6.65835i	0.277463	−	1.21564i
$31$	−4.28039	+	3.73966i	−0.768780	+	0.671663i	−0.950164	−	0.311750i	$-0.899085\pi$
$31$	−4.28039	+	3.73966i	−0.768780	+	0.671663i	0.181384	+	0.983412i	$0.441942\pi$
$32$	3.07440	+	3.85518i	0.543483	+	0.681506i
$33$	−1.29881	+	9.58820i	−0.226094	+	1.66909i
$34$	9.23289	−	4.44633i	1.58343	−	0.762539i
$35$	3.17705	−	0.576549i	0.537019	−	0.0974546i
$36$	6.18972	−	1.12327i	1.03162	−	0.187211i
$37$	4.07711	−	1.96343i	0.670273	−	0.322786i	−0.0676134	−	0.997712i	$-0.521538\pi$
$37$	4.07711	−	1.96343i	0.670273	−	0.322786i	0.737886	+	0.674925i	$0.235824\pi$
$38$	1.37563	−	10.1553i	0.223157	−	1.64741i
$39$	−5.41151	−	6.78582i	−0.866535	−	1.08660i
$40$	−1.75138	+	1.53013i	−0.276917	+	0.241935i
$41$	0.557020	−	2.44046i	0.0869919	−	0.381136i	−0.912625	−	0.408797i	$-0.865949\pi$
$41$	0.557020	−	2.44046i	0.0869919	−	0.381136i	0.999617	+	0.0276603i	$0.00880567\pi$
$42$	7.42253	+	11.2447i	1.14532	+	1.73509i
$43$	−1.17790	−	8.69559i	−0.179628	−	1.32606i	−0.826271	−	0.563272i	$-0.809542\pi$
$43$	−1.17790	−	8.69559i	−0.179628	−	1.32606i	0.646644	−	0.762792i	$-0.276172\pi$
$44$	−2.01823	+	2.11091i	−0.304260	+	0.318231i
$45$	1.90565	+	8.34920i	0.284078	+	1.24463i
$46$	0.482467	+	0.350533i	0.0711359	+	0.0516833i
$47$	2.92819	+	0.808128i	0.427120	+	0.117878i	0.472986	−	0.881070i	$-0.343176\pi$
$47$	2.92819	+	0.808128i	0.427120	+	0.117878i	−0.0458660	+	0.998948i	$0.514605\pi$
$48$	−14.0157	−	6.74963i	−2.02300	−	0.974225i
$49$	0.347003	−	0.525687i	0.0495719	−	0.0750982i
$50$	−3.98509	−	4.16808i	−0.563577	−	0.589455i
$51$	−11.6025	+	14.5491i	−1.62468	+	2.03728i
$52$	−0.117534	−	2.61710i	−0.0162990	−	0.362926i
$53$	9.80099	−	3.67837i	1.34627	−	0.505263i	0.428918	−	0.903343i	$-0.358895\pi$
$53$	9.80099	−	3.67837i	1.34627	−	0.505263i	0.917351	+	0.398080i	$0.130323\pi$
$54$	−15.9538	+	11.5911i	−2.17104	+	1.57735i
$55$	−2.99403	−	2.61580i	−0.403715	−	0.352715i
$56$	0.205844	−	4.58346i	0.0275070	−	0.612491i
$57$	5.75069	+	17.6988i	0.761697	+	2.34426i
$58$	4.01628	+	9.39654i	0.527363	+	1.23383i
$59$	−6.98823	−	0.628952i	−0.909790	−	0.0818826i	−0.375152	−	0.926963i	$-0.622409\pi$
$59$	−6.98823	−	0.628952i	−0.909790	−	0.0818826i	−0.534639	+	0.845081i	$0.679552\pi$
$60$	−1.47122	+	3.44210i	−0.189934	+	0.444373i
$61$	0.503936	−	0.936469i	0.0645223	−	0.119903i	−0.846291	−	0.532721i	$-0.821170\pi$
$61$	0.503936	−	0.936469i	0.0645223	−	0.119903i	0.910814	+	0.412818i	$0.135455\pi$
$62$	8.36599	−	4.99845i	1.06248	−	0.634804i
$63$	−14.5035	−	8.66547i	−1.82728	−	1.09175i
$64$	0.728927	+	1.35457i	0.0911158	+	0.169322i
$65$	3.55199	−	0.319685i	0.440570	−	0.0396520i
$66$	5.12654	−	15.7779i	0.631033	−	1.94212i
$67$	3.10054	+	1.16365i	0.378791	+	0.142163i	0.533506	−	0.845797i	$-0.320874\pi$
$67$	3.10054	+	1.16365i	0.378791	+	0.142163i	−0.154714	+	0.987959i	$0.549446\pi$
$68$	−5.41442	+	1.49429i	−0.656595	+	0.181209i
$69$	−1.06554	−	0.193367i	−0.128276	−	0.0232786i
$70$	−5.53626			−0.661709
$71$	−6.39655	−	5.48490i	−0.759131	−	0.650938i
$71$	−6.39655	−	5.48490i	−0.759131	−	0.650938i
$72$	12.1687			1.43409
$73$	9.79528	+	1.77758i	1.14645	+	0.208050i	0.718351	−	0.695681i	$-0.244897\pi$
$73$	9.79528	+	1.77758i	1.14645	+	0.208050i	0.428100	+	0.903731i	$0.359183\pi$
$74$	−7.47927	+	2.06415i	−0.869448	+	0.239952i
$75$	9.80394	+	3.67948i	1.13206	+	0.424870i
$76$	−1.73576	+	5.34211i	−0.199105	+	0.612782i
$77$	7.81188	−	0.703082i	0.890246	−	0.0801236i
$78$	7.05186	+	13.1046i	0.798466	+	1.48380i
$79$	−3.39678	−	2.02948i	−0.382167	−	0.228334i	0.308948	−	0.951079i	$-0.400023\pi$
$79$	−3.39678	−	2.02948i	−0.382167	−	0.228334i	−0.691115	+	0.722745i	$0.742880\pi$
$80$	5.48726	−	3.27848i	0.613494	−	0.366546i
$81$	7.45288	−	13.8498i	0.828098	−	1.53886i
$82$	−1.68685	+	3.94658i	−0.186281	+	0.435827i
$83$	−0.0918720	−	0.00826863i	−0.0100843	−	0.000907600i	0.0845960	−	0.996415i	$-0.473040\pi$
$83$	−0.0918720	−	0.00826863i	−0.0100843	−	0.000907600i	−0.0946803	+	0.995508i	$0.530183\pi$
$84$	−2.90246	−	6.79064i	−0.316684	−	0.740919i
$85$	−2.36287	−	7.27217i	−0.256289	−	0.788777i
$86$	−0.675009	+	15.0302i	−0.0727881	+	1.62075i
$87$	−13.9744	−	12.2091i	−1.49822	−	1.30895i
$88$	−4.57034	+	3.32055i	−0.487200	+	0.353972i
$89$	−4.08719	+	1.53395i	−0.433241	+	0.162598i	−0.558461	−	0.829531i	$-0.688608\pi$
$89$	−4.08719	+	1.53395i	−0.433241	+	0.162598i	0.125219	+	0.992129i	$0.460036\pi$
$90$	−0.658772	−	14.6687i	−0.0694406	−	1.54622i
$91$	−4.38672	+	5.50078i	−0.459854	+	0.576638i
$92$	−0.225887	−	0.236259i	−0.0235504	−	0.0246317i
$93$	−9.74920	+	14.7694i	−1.01094	+	1.53152i
$94$	−4.69250	−	2.25979i	−0.483995	−	0.233080i
$95$	−7.37110	−	2.03429i	−0.756259	−	0.208714i
$96$	12.4205	+	9.02406i	1.26767	+	0.921014i
$97$	−2.32580	−	10.1900i	−0.236149	−	1.03464i	−0.944432	−	0.328708i	$-0.893387\pi$
$97$	−2.32580	−	10.1900i	−0.236149	−	1.03464i	0.708283	−	0.705929i	$-0.249470\pi$
$98$	−0.746341	+	0.780611i	−0.0753918	+	0.0788536i
$99$	2.79242	+	20.6144i	0.280648	+	2.07183i
$100$	1.74122	+	2.63784i	0.174122	+	0.263784i
$101$	0.359371	−	1.57451i	0.0357587	−	0.156669i	−0.953896	−	0.300136i	$-0.902968\pi$
$101$	0.359371	−	1.57451i	0.0357587	−	0.156669i	0.989655	+	0.143467i	$0.0458250\pi$
$102$	24.0279	−	20.9925i	2.37912	−	2.07857i
$103$	3.32223	+	4.16594i	0.327349	+	0.410482i	0.918086	−	0.396382i	$-0.129734\pi$
$103$	3.32223	+	4.16594i	0.327349	+	0.410482i	−0.590737	+	0.806864i	$0.701163\pi$
$104$	0.680229	−	5.02165i	0.0667020	−	0.492414i
$105$	9.05777	−	4.36199i	0.883948	−	0.425687i
$106$	−17.6606	+	3.20493i	−1.71535	+	0.311290i
$107$	−3.26171	+	0.591913i	−0.315322	+	0.0572224i	−0.333911	−	0.942605i	$-0.608368\pi$
$107$	−3.26171	+	0.591913i	−0.315322	+	0.0572224i	0.0185889	+	0.999827i	$0.494083\pi$
$108$	9.73823	−	4.68968i	0.937061	−	0.451265i
$109$	−1.74199	+	12.8599i	−0.166852	+	1.23175i	0.692898	+	0.721036i	$0.256334\pi$
$109$	−1.74199	+	12.8599i	−0.166852	+	1.23175i	−0.859750	+	0.510716i	$0.829381\pi$
$110$	4.25016	+	5.32954i	0.405237	+	0.508151i
$111$	10.6104	−	9.27000i	1.00709	−	0.879870i
$112$	−2.80607	+	12.2942i	−0.265149	+	1.16169i
$113$	6.19886	+	9.39087i	0.583140	+	0.883419i	0.999670	−	0.0257033i	$-0.00818251\pi$
$113$	6.19886	+	9.39087i	0.583140	+	0.883419i	−0.416530	+	0.909122i	$0.636754\pi$
$114$	−4.28306	−	31.6188i	−0.401145	−	2.96137i
$115$	0.307509	−	0.321629i	0.0286753	−	0.0299920i
$116$	−1.24634	−	5.46059i	−0.115720	−	0.507003i
$117$	−15.0967	−	10.9684i	−1.39569	−	1.01403i
$118$	11.5967	+	3.20050i	1.06757	+	0.294630i
$119$	13.5911	+	6.54513i	1.24589	+	0.599991i
$120$	−3.98902	+	6.04310i	−0.364146	+	0.551657i
$121$	0.927712	+	0.970310i	0.0843374	+	0.0882100i
$122$	−1.13685	+	1.42556i	−0.102926	+	0.129065i
$123$	−0.349669	−	7.78599i	−0.0315286	−	0.702039i
$124$	−5.00094	+	1.87689i	−0.449098	+	0.168549i
$125$	−8.65607	+	6.28900i	−0.774223	+	0.562506i
$126$	21.8149	+	19.0591i	1.94342	+	1.69792i
$127$	−0.632459	+	14.0828i	−0.0561216	+	1.24965i	0.751416	+	0.659829i	$0.229371\pi$
$127$	−0.632459	+	14.0828i	−0.0561216	+	1.24965i	−0.807537	+	0.589816i	$0.799200\pi$
$128$	−3.86251	−	11.8876i	−0.341401	−	1.05072i
$129$	−10.7379	−	25.1226i	−0.945419	−	2.21192i
$130$	−6.09015	−	0.548124i	−0.534142	−	0.0480736i
$131$	5.00442	−	11.7084i	0.437238	−	1.02297i	−0.545524	−	0.838095i	$-0.683669\pi$
$131$	5.00442	−	11.7084i	0.437238	−	1.02297i	0.982762	−	0.184874i	$-0.0591878\pi$
$132$	−4.30887	+	8.00723i	−0.375039	+	0.696940i
$133$	12.9501	−	7.73733i	1.12292	−	0.670912i
$134$	−4.87442	−	2.91233i	−0.421086	−	0.251587i
$135$	6.97259	+	12.9572i	0.600105	+	1.11518i
$136$	−10.8212	+	0.973929i	−0.927914	+	0.0835138i
$137$	2.25441	−	6.93837i	0.192608	−	0.592785i	−0.807389	−	0.590020i	$-0.799120\pi$
$137$	2.25441	−	6.93837i	0.192608	−	0.592785i	0.999996	−	0.00276514i	$-0.000880171\pi$
$138$	1.73839	+	0.652428i	0.147981	+	0.0555384i
$139$	3.40068	−	0.938529i	0.288442	−	0.0796050i	−0.118821	−	0.992916i	$-0.537912\pi$
$139$	3.40068	−	0.938529i	0.288442	−	0.0796050i	0.407264	+	0.913311i	$0.366483\pi$
$140$	2.98569	+	0.541822i	0.252337	+	0.0457923i
$141$	9.45780			0.796491
$142$	9.11192	+	11.2114i	0.764656	+	0.940843i
$143$	8.66306			0.724441
$144$	−32.9083	−	5.97197i	−2.74236	−	0.497664i
$145$	7.35010	−	2.02850i	0.610393	−	0.168458i
$146$	−15.9806	−	5.99764i	−1.32257	−	0.496368i
$147$	0.606034	−	1.86518i	0.0499849	−	0.153838i
$148$	4.23556	−	0.381208i	0.348161	−	0.0313351i
$149$	6.29536	+	11.6987i	0.515736	+	0.958398i	0.996662	+	0.0816367i	$0.0260147\pi$
$149$	6.29536	+	11.6987i	0.515736	+	0.958398i	−0.480926	+	0.876761i	$0.659700\pi$
$150$	−15.4130	−	9.20883i	−1.25846	−	0.751898i
$151$	−7.37596	+	4.40693i	−0.600247	+	0.358631i	−0.780656	−	0.624961i	$-0.785115\pi$
$151$	−7.37596	+	4.40693i	−0.600247	+	0.358631i	0.180409	+	0.983592i	$0.442258\pi$
$152$	−5.14874	+	9.56797i	−0.417618	+	0.776065i
$153$	−15.7245	+	36.7894i	−1.27125	+	2.97425i
$154$	−13.3940	−	1.20549i	−1.07932	−	0.0971408i
$155$	−2.85794	−	6.68648i	−0.229555	−	0.537071i
$156$	−2.52053	−	7.75740i	−0.201804	−	0.621089i
$157$	0.00612961	−	0.136486i	0.000489196	−	0.0108928i	−0.998734	−	0.0503106i	$-0.983979\pi$
$157$	0.00612961	−	0.136486i	0.000489196	−	0.0108928i	0.999223	+	0.0394178i	$0.0125503\pi$
$158$	5.10911	+	4.46369i	0.406459	+	0.355112i
$159$	26.3690	−	19.1582i	2.09120	−	1.51935i
$160$	−5.90612	+	2.21660i	−0.466920	+	0.175238i
$161$	0.0393852	+	0.876980i	0.00310399	+	0.0691157i
$162$	−16.8133	+	21.0832i	−1.32097	+	1.65645i
$163$	−10.6300	−	11.1181i	−0.832608	−	0.870840i	0.160620	−	0.987016i	$-0.448651\pi$
$163$	−10.6300	−	11.1181i	−0.832608	−	0.870840i	−0.993229	+	0.116176i	$0.962936\pi$
$164$	1.29596	−	1.96329i	0.101197	−	0.153307i
$165$	−11.1527	−	5.37087i	−0.868239	−	0.418122i
$166$	0.152459	+	0.0420759i	0.0118331	+	0.00326572i
$167$	−5.56319	−	4.04190i	−0.430493	−	0.312771i	0.351353	−	0.936243i	$-0.385722\pi$
$167$	−5.56319	−	4.04190i	−0.430493	−	0.312771i	−0.781846	+	0.623472i	$0.785722\pi$
$168$	−3.17873	−	13.9269i	−0.245244	−	1.07449i
$169$	3.61359	−	3.77952i	0.277969	−	0.290732i
$170$	1.75984	+	12.9917i	0.134974	+	0.996417i
$171$	22.0416	+	33.3915i	1.68556	+	2.55352i
$172$	1.83501	−	8.03970i	0.139918	−	0.613022i
$173$	−3.67647	+	3.21203i	−0.279517	+	0.244206i	−0.786268	−	0.617886i	$-0.787989\pi$
$173$	−3.67647	+	3.21203i	−0.279517	+	0.244206i	0.506751	+	0.862093i	$0.330846\pi$
$174$	19.8374	+	24.8753i	1.50387	+	1.88579i
$175$	1.13946	−	8.41181i	0.0861348	−	0.635873i
$176$	13.9894	−	6.73693i	1.05449	−	0.507815i
$177$	−21.4949	+	3.90075i	−1.61565	+	0.293198i
$178$	7.36480	−	1.33651i	0.552015	−	0.100176i
$179$	−5.51469	+	2.65574i	−0.412188	+	0.198499i	−0.628474	−	0.777831i	$-0.716320\pi$
$179$	−5.51469	+	2.65574i	−0.412188	+	0.198499i	0.216286	+	0.976330i	$0.430606\pi$
$180$	−1.08032	+	7.97525i	−0.0805224	+	0.594440i
$181$	5.36984	+	6.73357i	0.399137	+	0.500502i	0.940267	−	0.340437i	$-0.110575\pi$
$181$	5.36984	+	6.73357i	0.399137	+	0.500502i	−0.541130	+	0.840939i	$0.682003\pi$
$182$	9.08456	−	7.93694i	0.673392	−	0.588325i
$183$	0.736783	−	3.22806i	0.0544646	−	0.238625i
$184$	−0.348323	−	0.527686i	−0.0256787	−	0.0389015i
$185$	0.777121	+	5.73694i	0.0571351	+	0.421788i
$186$	20.9687	−	21.9316i	1.53750	−	1.60810i
$187$	−4.13310	−	18.1083i	−0.302242	−	1.32421i
$188$	2.30949	+	1.67794i	0.168437	+	0.122377i
$189$	−27.9823	−	7.72263i	−2.03541	−	0.561738i
$190$	11.8124	+	5.68855i	0.856962	+	0.412691i
$191$	−1.36129	+	2.06227i	−0.0984997	+	0.149221i	−0.880481	−	0.474081i	$-0.842780\pi$
$191$	−1.36129	+	2.06227i	−0.0984997	+	0.149221i	0.781982	+	0.623301i	$0.214209\pi$
$192$	3.30975	+	3.46173i	0.238861	+	0.249828i
$193$	15.9440	−	19.9931i	1.14767	−	1.43913i	0.268084	−	0.963395i	$-0.413609\pi$
$193$	15.9440	−	19.9931i	1.14767	−	1.43913i	0.879587	−	0.475739i	$-0.157819\pi$
$194$	0.804014	+	17.9028i	0.0577249	+	1.28534i
$195$	10.3959	−	3.90163i	0.744462	−	0.279401i
$196$	0.478896	−	0.347938i	0.0342069	−	0.0248527i
$197$	−18.0444	−	15.7650i	−1.28561	−	1.12321i	−0.985568	−	0.169282i	$-0.945855\pi$
$197$	−18.0444	−	15.7650i	−1.28561	−	1.12321i	−0.300046	−	0.953925i	$-0.597002\pi$
$198$	1.60023	−	35.6319i	0.113723	−	2.53225i
$199$	4.17073	+	12.8362i	0.295655	+	0.909933i	0.983001	+	0.183603i	$0.0587759\pi$
$199$	4.17073	+	12.8362i	0.295655	+	0.909933i	−0.687345	+	0.726331i	$0.741224\pi$
$200$	2.40293	+	5.62194i	0.169913	+	0.397531i
$201$	10.2696	+	0.924278i	0.724360	+	0.0651936i
$202$	−1.08830	+	2.54621i	−0.0765726	+	0.179150i
$203$	−7.12817	+	13.2464i	−0.500300	+	0.929713i
$204$	−15.0127	+	8.96965i	−1.05110	+	0.628001i
$205$	2.74916	+	1.64255i	0.192010	+	0.114721i
$206$	−4.32927	−	8.04513i	−0.301634	−	0.560531i
$207$	−2.31893	+	0.208708i	−0.161177	+	0.0145062i
$208$	−4.30402	+	13.2464i	−0.298430	+	0.918474i
$209$	−17.3902	−	6.52665i	−1.20290	−	0.451458i
$210$	−16.6161	+	4.58574i	−1.14662	+	0.316446i
$211$	−11.8082	−	2.14288i	−0.812912	−	0.147522i	−0.243846	−	0.969814i	$-0.578409\pi$
$211$	−11.8082	−	2.14288i	−0.812912	−	0.147522i	−0.569066	+	0.822292i	$0.692695\pi$
$212$	9.83797			0.675674
$213$	−23.7413	−	11.1636i	−1.62673	−	0.764917i
$214$	5.68379			0.388536
$215$	11.0458	+	2.00452i	0.753318	+	0.136707i
$216$	20.1543	−	5.56223i	1.37133	−	0.378462i
$217$	13.4309	+	5.04070i	0.911749	+	0.342185i
$218$	6.87581	−	21.1616i	0.465688	−	1.43324i
$219$	30.8712	−	2.77845i	2.08608	−	0.187751i
$220$	−1.77051	−	3.29016i	−0.119368	−	0.221822i
$221$	14.3029	+	8.54557i	0.962115	+	0.574837i
$222$	−20.7379	+	12.3903i	−1.39184	+	0.831585i
$223$	−7.83352	+	14.5571i	−0.524571	+	0.974817i	0.471119	+	0.882070i	$0.343850\pi$
$223$	−7.83352	+	14.5571i	−0.524571	+	0.974817i	−0.995690	+	0.0927467i	$0.970435\pi$
$224$	4.89131	−	11.4438i	0.326814	−	0.764620i
$225$	22.4232	+	2.01813i	1.49488	+	0.134542i
$226$	−7.58260	−	17.7404i	−0.504387	−	1.18007i
$227$	1.31546	+	4.04857i	0.0873101	+	0.268713i	0.985173	−	0.171561i	$-0.0548812\pi$
$227$	1.31546	+	4.04857i	0.0873101	+	0.268713i	−0.897863	+	0.440274i	$0.854881\pi$
$228$	−0.784628	+	17.4711i	−0.0519633	+	1.15705i
$229$	−4.56681	−	3.98990i	−0.301783	−	0.263660i	0.493705	−	0.869630i	$-0.335642\pi$
$229$	−4.56681	−	3.98990i	−0.301783	−	0.263660i	−0.795488	+	0.605970i	$0.792785\pi$
$230$	−0.617240	+	0.448451i	−0.0406996	+	0.0295700i
$231$	22.8636	−	8.58084i	1.50431	−	0.564578i
$232$	−0.486083	−	10.8235i	−0.0319129	−	0.710596i
$233$	9.77207	−	12.2538i	0.640190	−	0.802772i	−0.350837	−	0.936437i	$-0.614103\pi$
$233$	9.77207	−	12.2538i	0.640190	−	0.802772i	0.991027	+	0.133664i	$0.0426743\pi$
$234$	22.1105	+	23.1257i	1.44541	+	1.51178i
$235$	−2.14089	+	3.24331i	−0.139656	+	0.211570i
$236$	−5.94086	−	2.86097i	−0.386717	−	0.186233i
$237$	−11.8758	−	3.27752i	−0.771419	−	0.212898i
$238$	−20.9247	−	15.2027i	−1.35635	−	0.985443i
$239$	3.79550	+	16.6292i	0.245511	+	1.07565i	0.935914	+	0.352228i	$0.114576\pi$
$239$	3.79550	+	16.6292i	0.245511	+	1.07565i	−0.690403	+	0.723425i	$0.742567\pi$
$240$	13.7534	−	14.3849i	0.887778	−	0.928543i
$241$	0.445030	+	3.28534i	0.0286669	+	0.211628i	0.999618	−	0.0276520i	$-0.00880303\pi$
$241$	0.445030	+	3.28534i	0.0286669	+	0.211628i	−0.970951	+	0.239280i	$0.923089\pi$
$242$	−1.26801	−	1.92095i	−0.0815107	−	0.123483i
$243$	3.21866	−	14.1019i	0.206477	−	0.904634i
$244$	0.752616	−	0.657541i	0.0481813	−	0.0420948i
$245$	0.502434	+	0.630032i	0.0320993	+	0.0402513i
$246$	−1.79378	+	13.2422i	−0.114367	+	0.844291i
$247$	15.0118	−	7.22931i	0.955178	−	0.459990i
$248$	−10.1664	+	1.84493i	−0.645569	+	0.117153i
$249$	−0.282586	+	0.0512818i	−0.0179082	+	0.00324985i
$250$	16.5283	−	7.95963i	1.04534	−	0.503411i
$251$	0.0891494	−	0.658127i	0.00562706	−	0.0415406i	−0.987919	−	0.154974i	$-0.950471\pi$
$251$	0.0891494	−	0.658127i	0.00562706	−	0.0415406i	0.993546	+	0.113433i	$0.0361849\pi$
$252$	−9.89942	−	12.4135i	−0.623605	−	0.781976i
$253$	0.813998	−	0.711169i	0.0511756	−	0.0447108i
$254$	5.37841	−	23.5643i	0.337471	−	1.47856i
$255$	−13.1153	−	19.8689i	−0.821315	−	1.24424i
$256$	2.46380	+	18.1885i	0.153987	+	1.13678i
$257$	−19.1102	+	19.9877i	−1.19206	+	1.24680i	−0.230238	+	0.973134i	$0.573950\pi$
$257$	−19.1102	+	19.9877i	−1.19206	+	1.24680i	−0.961825	+	0.273665i	$0.911764\pi$
$258$	10.4238	+	45.6697i	0.648958	+	2.84327i
$259$	−9.24004	−	6.71328i	−0.574148	−	0.417143i
$260$	3.23076	+	0.891632i	0.200363	+	0.0552967i
$261$	−35.9454	−	17.3104i	−2.22496	−	1.07149i
$262$	−12.0271	+	18.2203i	−0.743036	+	1.12565i
$263$	12.6458	+	13.2265i	0.779773	+	0.815579i	0.986661	−	0.162786i	$-0.0520479\pi$
$263$	12.6458	+	13.2265i	0.779773	+	0.815579i	−0.206888	+	0.978365i	$0.566334\pi$
$264$	−10.9666	+	13.7517i	−0.674948	+	0.846358i
$265$	0.600865	+	13.3793i	0.0369109	+	0.821884i
$266$	−24.2159	+	9.08838i	−1.48477	+	0.557244i
$267$	−10.9964	+	7.98933i	−0.672967	+	0.488939i
$268$	2.34374	+	2.04766i	0.143167	+	0.125081i
$269$	0.717038	−	15.9661i	0.0437186	−	0.973470i	−0.850538	−	0.525914i	$-0.823723\pi$
$269$	0.717038	−	15.9661i	0.0437186	−	0.973470i	0.894256	−	0.447555i	$-0.147705\pi$
$270$	−7.79605	−	23.9938i	−0.474453	−	1.46022i
$271$	6.53888	+	15.2985i	0.397209	+	0.929316i	0.992093	+	0.125505i	$0.0400550\pi$
$271$	6.53888	+	15.2985i	0.397209	+	0.929316i	−0.594884	+	0.803811i	$0.702802\pi$
$272$	29.7423	+	2.67685i	1.80339	+	0.162308i
$273$	−8.60960	+	20.1432i	−0.521077	+	1.21912i
$274$	−5.92742	+	11.0150i	−0.358089	+	0.665440i
$275$	−8.97247	+	5.36080i	−0.541060	+	0.323269i
$276$	−0.873655	−	0.521985i	−0.0525879	−	0.0314198i
$277$	−5.89093	−	10.9472i	−0.353952	−	0.657752i	0.639902	−	0.768457i	$-0.278975\pi$
$277$	−5.89093	−	10.9472i	−0.353952	−	0.657752i	−0.993853	+	0.110704i	$0.964689\pi$
$278$	−6.02435	+	0.542201i	−0.361317	+	0.0325191i
$279$	−11.7575	+	36.1859i	−0.703904	+	2.16639i
$280$	5.49544	+	2.06247i	0.328415	+	0.123256i
$281$	−8.72390	+	2.40764i	−0.520424	+	0.143628i	−0.516373	−	0.856364i	$-0.672718\pi$
$281$	−8.72390	+	2.40764i	−0.520424	+	0.143628i	−0.00405117	+	0.999992i	$0.501290\pi$
$282$	−15.9555	−	2.89550i	−0.950137	−	0.172424i
$283$	4.44100			0.263990			0.131995	−	0.991250i	$-0.457862\pi$
$283$	4.44100			0.263990			0.131995	+	0.991250i	$0.457862\pi$
$284$	−3.81679	−	6.93806i	−0.226485	−	0.411698i
$285$	−23.8080			−1.41027
$286$	−14.6148	−	2.65219i	−0.864189	−	0.156827i
$287$	−6.09023	+	1.68080i	−0.359495	+	0.0992143i
$288$	30.9031	+	11.5981i	1.82098	+	0.683427i
$289$	5.78559	−	17.8062i	0.340329	−	1.04743i
$290$	−13.0208	+	1.17189i	−0.764608	+	0.0688159i
$291$	−15.4209	−	28.6569i	−0.903992	−	1.67990i
$292$	8.03134	+	4.79850i	0.469998	+	0.280811i
$293$	−1.52691	+	0.912287i	−0.0892031	+	0.0532964i	−0.556808	−	0.830641i	$-0.687974\pi$
$293$	−1.52691	+	0.912287i	−0.0892031	+	0.0532964i	0.467605	+	0.883938i	$0.345117\pi$
$294$	−1.59342	+	2.96106i	−0.0929299	+	0.172693i
$295$	3.52798	−	8.25411i	0.205407	−	0.480573i
$296$	8.19310	+	0.737392i	0.476214	+	0.0428601i
$297$	14.0476	+	32.8661i	0.815127	+	1.90708i
$298$	−7.03884	−	21.6633i	−0.407749	−	1.25492i
$299$	−0.0435008	+	0.968620i	−0.00251572	+	0.0560168i
$300$	7.41092	+	6.47473i	0.427870	+	0.373819i
$301$	−17.9175	+	13.0179i	−1.03275	+	0.750337i
$302$	13.7926	−	5.17644i	0.793674	−	0.297871i
$303$	−0.225595	−	5.02327i	−0.0129601	−	0.288579i
$304$	18.6196	−	23.3482i	1.06791	−	1.33911i
$305$	0.940201	+	0.983373i	0.0538357	+	0.0563078i
$306$	37.7907	−	57.2504i	2.16035	−	3.27279i
$307$	−0.402113	−	0.193648i	−0.0229498	−	0.0110520i	0.422374	−	0.906422i	$-0.361197\pi$
$307$	−0.402113	−	0.193648i	−0.0229498	−	0.0110520i	−0.445323	+	0.895370i	$0.646911\pi$
$308$	7.10539	+	1.96096i	0.404867	+	0.111736i
$309$	13.4218	+	9.75148i	0.763537	+	0.554742i
$310$	2.77434	+	12.1552i	0.157572	+	0.690368i
$311$	2.08404	−	2.17974i	0.118175	−	0.123602i	−0.661060	−	0.750333i	$-0.729893\pi$
$311$	2.08404	−	2.17974i	0.118175	−	0.123602i	0.779236	+	0.626731i	$0.215608\pi$
$312$	−2.11791	−	15.6350i	−0.119903	−	0.885159i
$313$	10.8056	+	16.3699i	0.610771	+	0.925279i	0.999991	+	0.00413424i	$0.00131597\pi$
$313$	10.8056	+	16.3699i	0.610771	+	0.925279i	−0.389220	+	0.921145i	$0.627255\pi$
$314$	−0.0521260	+	0.228379i	−0.00294164	+	0.0128882i
$315$	16.2773	−	14.2210i	0.917122	−	0.801265i
$316$	−2.31847	−	2.90727i	−0.130424	−	0.163547i
$317$	2.59938	−	19.1894i	0.145996	−	1.07778i	−0.758614	−	0.651541i	$-0.774123\pi$
$317$	2.59938	−	19.1894i	0.145996	−	1.07778i	0.904609	−	0.426242i	$-0.140163\pi$
$318$	−50.3504	+	24.2475i	−2.82351	+	1.35973i
$319$	18.2240	−	3.30717i	1.02035	−	0.185166i
$320$	−1.93631	+	0.351389i	−0.108243	+	0.0196433i
$321$	−9.29915	+	4.47823i	−0.519028	+	0.249951i
$322$	0.202043	−	1.49154i	0.0112594	−	0.0831204i
$323$	−22.2734	−	27.9300i	−1.23933	−	1.55406i
$324$	11.1307	−	9.72461i	0.618373	−	0.540256i
$325$	2.08628	−	9.14059i	0.115726	−	0.507028i
$326$	14.5293	+	22.0109i	0.804702	+	1.21907i
$327$	5.42371	+	40.0394i	0.299932	+	2.21419i
$328$	3.14467	−	3.28907i	0.173635	−	0.181608i
$329$	−1.70602	−	7.47454i	−0.0940557	−	0.412085i
$330$	17.1706	+	12.4752i	0.945211	+	0.686736i
$331$	−16.2836	−	4.49400i	−0.895030	−	0.247012i	−0.211884	−	0.977295i	$-0.567960\pi$
$331$	−16.2836	−	4.49400i	−0.895030	−	0.247012i	−0.683145	+	0.730282i	$0.739389\pi$
$332$	−0.0781026	−	0.0376122i	−0.00428644	−	0.00206424i
$333$	16.6878	−	25.2810i	0.914486	−	1.38539i
$334$	8.14780	+	8.52193i	0.445828	+	0.466300i
$335$	−2.64161	+	3.31247i	−0.144326	+	0.180979i
$336$	1.76151	+	39.2232i	0.0960985	+	2.13980i
$337$	19.3987	−	7.28045i	1.05671	−	0.396591i	0.238283	−	0.971196i	$-0.423416\pi$
$337$	19.3987	−	7.28045i	1.05671	−	0.396591i	0.818431	+	0.574604i	$0.194844\pi$
$338$	−7.25330	+	5.26983i	−0.394528	+	0.286641i
$339$	26.3833	+	23.0504i	1.43294	+	1.25193i
$340$	0.322392	−	7.17861i	0.0174841	−	0.389315i
$341$	−5.45837	−	16.7991i	−0.295587	−	0.909724i
$342$	−26.9618	−	63.0803i	−1.45793	−	3.41099i
$343$	−19.1796	−	1.72620i	−1.03560	−	0.0932058i
$344$	6.26939	−	14.6680i	0.338023	−	0.790843i
$345$	0.656522	−	1.22002i	0.0353460	−	0.0656838i
$346$	7.18564	−	4.29322i	0.386303	−	0.230805i
$347$	19.2319	+	11.4905i	1.03242	+	0.616845i	0.926019	−	0.377478i	$-0.123209\pi$
$347$	19.2319	+	11.4905i	1.03242	+	0.616845i	0.106406	+	0.994323i	$0.466066\pi$
$348$	−8.26375	−	15.3566i	−0.442983	−	0.823201i
$349$	21.3094	−	1.91788i	1.14067	−	0.102662i	0.496847	−	0.867838i	$-0.334491\pi$
$349$	21.3094	−	1.91788i	1.14067	−	0.102662i	0.643821	+	0.765176i	$0.277348\pi$
$350$	−4.49755	+	13.8421i	−0.240404	+	0.739889i
$351$	−30.0173	−	11.2657i	−1.60221	−	0.601318i
$352$	−14.7715	+	4.07668i	−0.787325	+	0.217288i
$353$	16.7628	+	3.04201i	0.892196	+	0.161910i	0.605248	−	0.796037i	$-0.293074\pi$
$353$	16.7628	+	3.04201i	0.892196	+	0.161910i	0.286947	+	0.957946i	$0.407360\pi$
$354$	37.4565			1.99079
$355$	9.20241	−	5.61446i	0.488413	−	0.297984i
$356$	−4.10261			−0.217438
$357$	46.2126	+	8.38636i	2.44583	+	0.443853i
$358$	10.1165	−	2.79196i	0.534671	−	0.147560i
$359$	29.3291	+	11.0074i	1.54793	+	0.580948i	0.971675	−	0.236322i	$-0.0759421\pi$
$359$	29.3291	+	11.0074i	1.54793	+	0.580948i	0.576255	+	0.817270i	$0.304514\pi$
$360$	−4.81075	+	14.8060i	−0.253549	+	0.780342i
$361$	−16.6576	+	1.49921i	−0.876716	+	0.0789059i
$362$	−6.99756	−	13.0036i	−0.367783	−	0.683456i
$363$	3.58808	+	2.14378i	0.188325	+	0.112519i
$364$	−5.67604	+	3.39128i	−0.297506	+	0.177751i
$365$	−6.03528	+	11.2154i	−0.315901	+	0.587042i
$366$	−2.23124	+	5.22024i	−0.116629	+	0.272866i
$367$	−35.7639	−	3.21881i	−1.86686	−	0.168020i	−0.902165	−	0.431391i	$-0.858023\pi$
$367$	−35.7639	−	3.21881i	−1.86686	−	0.168020i	−0.964695	+	0.263370i	$0.915166\pi$
$368$	0.683012	+	1.59799i	0.0356045	+	0.0833008i
$369$	−5.17808	−	15.9365i	−0.269560	−	0.829620i
$370$	0.445340	−	9.91625i	0.0231521	−	0.515522i
$371$	−19.8973	−	17.3838i	−1.03302	−	0.902520i
$372$	−13.4548	+	9.77547i	−0.697598	+	0.506834i
$373$	−30.9641	+	11.6210i	−1.60326	+	0.601714i	−0.983150	−	0.182799i	$-0.941484\pi$
$373$	−30.9641	+	11.6210i	−1.60326	+	0.601714i	−0.620112	+	0.784513i	$0.712913\pi$
$374$	1.42879	+	31.8144i	0.0738808	+	1.64508i
$375$	−20.7704	+	26.0452i	−1.07258	+	1.34497i
$376$	3.81604	+	3.99127i	0.196797	+	0.205834i
$377$	−9.15281	+	13.8659i	−0.471394	+	0.714131i
$378$	44.8425	+	21.5950i	2.30645	+	1.11073i
$379$	−31.4115	−	8.66902i	−1.61350	−	0.445298i	−0.661137	−	0.750265i	$-0.729926\pi$
$379$	−31.4115	−	8.66902i	−1.61350	−	0.445298i	−0.952363	+	0.304968i	$0.901354\pi$
$380$	−5.81366	−	4.22387i	−0.298235	−	0.216680i
$381$	9.76672	+	42.7908i	0.500364	+	2.19224i
$382$	2.92789	−	3.06234i	0.149804	−	0.156683i
$383$	−3.25358	−	24.0189i	−0.166250	−	1.22731i	−0.861207	−	0.508255i	$-0.830291\pi$
$383$	−3.25358	−	24.0189i	−0.166250	−	1.22731i	0.694957	−	0.719052i	$-0.255424\pi$
$384$	−21.4393	−	32.4791i	−1.09407	−	1.65744i
$385$	−2.23287	+	9.78286i	−0.113798	+	0.498581i
$386$	−33.0187	+	28.8475i	−1.68061	+	1.46830i
$387$	−36.6238	−	45.9247i	−1.86169	−	2.33449i
$388$	1.31851	−	9.73360i	0.0669370	−	0.494149i
$389$	−22.4722	+	10.8220i	−1.13939	+	0.548699i	−0.905829	−	0.423644i	$-0.860751\pi$
$389$	−22.4722	+	10.8220i	−1.13939	+	0.548699i	−0.233556	+	0.972343i	$0.575036\pi$
$390$	−18.7325	+	3.39945i	−0.948557	+	0.172138i
$391$	2.04545	−	0.371195i	0.103443	−	0.0187721i
$392$	1.03165	−	0.496814i	0.0521060	−	0.0250929i
$393$	5.32164	−	39.2859i	0.268441	−	1.98171i
$394$	25.6149	+	32.1201i	1.29046	+	1.61819i
$395$	3.81219	−	3.33061i	0.191812	−	0.167581i
$396$	−4.35022	+	19.0596i	−0.218607	+	0.957779i
$397$	14.3511	+	21.7410i	0.720262	+	1.09115i	0.991685	+	0.128690i	$0.0410771\pi$
$397$	14.3511	+	21.7410i	0.720262	+	1.09115i	−0.271423	+	0.962460i	$0.587494\pi$
$398$	−3.10632	−	22.9318i	−0.155706	−	1.14947i
$399$	32.4585	−	33.9489i	1.62496	−	1.69957i
$400$	−3.73929	−	16.3829i	−0.186965	−	0.819146i
$401$	19.4812	+	14.1539i	0.972844	+	0.706812i	0.956098	−	0.293048i	$-0.0946694\pi$
$401$	19.4812	+	14.1539i	0.972844	+	0.706812i	0.0167457	+	0.999860i	$0.494669\pi$
$402$	−17.0420	−	4.70330i	−0.849978	−	0.234579i
$403$	14.2756	+	6.87476i	0.711117	+	0.342456i
$404$	0.836109	−	1.26665i	0.0415980	−	0.0630182i
$405$	13.9050	+	14.5434i	0.690943	+	0.722670i
$406$	16.0807	−	20.1646i	0.798074	−	1.00075i
$407$	0.630932	+	14.0488i	0.0312741	+	0.696372i
$408$	−31.6713	+	11.8864i	−1.56796	+	0.588466i
$409$	28.8933	−	20.9922i	1.42868	−	1.03800i	0.438424	−	0.898768i	$-0.355537\pi$
$409$	28.8933	−	20.9922i	1.42868	−	1.03800i	0.990260	−	0.139231i	$-0.0444631\pi$
$410$	−4.13503	−	3.61267i	−0.204215	−	0.178417i
$411$	1.01908	−	22.6916i	0.0502676	−	1.11930i
$412$	1.54740	+	4.76241i	0.0762350	+	0.234627i
$413$	6.96006	+	16.2839i	0.342482	+	0.801277i
$414$	3.97598	+	0.357845i	0.195409	+	0.0175871i
$415$	0.0463811	−	0.108514i	0.00227676	−	0.00532675i
$416$	6.51369	−	12.1045i	0.319360	−	0.593470i
$417$	9.42913	−	5.63365i	0.461747	−	0.275881i
$418$	27.3395	+	16.3346i	1.33722	+	0.798950i
$419$	9.55426	+	17.7548i	0.466756	+	0.867378i	0.999774	+	0.0212742i	$0.00677230\pi$
$419$	9.55426	+	17.7548i	0.466756	+	0.867378i	−0.533017	+	0.846104i	$0.678942\pi$
$420$	9.40979	−	0.846896i	0.459151	−	0.0413243i
$421$	3.46488	−	10.6638i	0.168868	−	0.519722i	−0.830433	−	0.557119i	$-0.811907\pi$
$421$	3.46488	−	10.6638i	0.168868	−	0.519722i	0.999300	+	0.0373972i	$0.0119067\pi$
$422$	19.2647	+	7.23016i	0.937790	+	0.351959i
$423$	19.6013	−	5.40962i	0.953048	−	0.263025i
$424$	18.7243	+	3.39797i	0.909334	+	0.165020i
$425$	−20.1018			−0.975082
$426$	36.6343	+	26.1016i	1.77494	+	1.26463i
$427$	−2.68405			−0.129890
$428$	−3.06525	−	0.556261i	−0.148165	−	0.0268879i
$429$	26.0006	−	7.17571i	1.25532	−	0.346446i
$430$	−18.0208	−	6.76333i	−0.869041	−	0.326157i
$431$	5.20469	−	16.0184i	0.250701	−	0.771578i	−0.743945	−	0.668240i	$-0.767048\pi$
$431$	5.20469	−	16.0184i	0.250701	−	0.771578i	0.994646	−	0.103338i	$-0.0329522\pi$
$432$	−57.2338	+	5.15114i	−2.75366	+	0.247834i
$433$	−9.42053	−	17.5063i	−0.452722	−	0.841298i	−0.999991	−	0.00434089i	$-0.998618\pi$
$433$	−9.42053	−	17.5063i	−0.452722	−	0.841298i	0.547269	−	0.836957i	$-0.315667\pi$
$434$	−21.1150	−	12.6156i	−1.01355	−	0.605569i
$435$	20.3798	−	12.1763i	0.977135	−	0.583811i
$436$	−5.77914	+	10.7394i	−0.276771	+	0.514326i
$437$	0.817071	−	1.91163i	0.0390858	−	0.0914458i
$438$	−52.9309	−	4.76387i	−2.52914	−	0.227626i
$439$	3.64860	+	8.53632i	0.174138	+	0.407416i	0.983749	−	0.179551i	$-0.0574645\pi$
$439$	3.64860	+	8.53632i	0.174138	+	0.407416i	−0.809611	+	0.586967i	$0.800322\pi$
$440$	−2.23337	−	6.87359i	−0.106472	−	0.327686i
$441$	0.189171	−	4.21223i	0.00900816	−	0.200582i
$442$	−21.5130	−	18.7954i	−1.02327	−	0.894004i
$443$	−20.1343	+	14.6285i	−0.956611	+	0.695019i	−0.952361	−	0.304972i	$-0.901353\pi$
$443$	−20.1343	+	14.6285i	−0.956611	+	0.695019i	−0.00424988	+	0.999991i	$0.501353\pi$
$444$	12.3965	−	4.65249i	0.588312	−	0.220797i
$445$	−0.250572	−	5.57942i	−0.0118782	−	0.264490i
$446$	17.6720	−	22.1599i	0.836792	−	1.04930i
$447$	28.5846	+	29.8971i	1.35200	+	1.41408i
$448$	2.13880	−	3.24014i	0.101049	−	0.153082i
$449$	−4.93072	−	2.37451i	−0.232695	−	0.112060i	0.313903	−	0.949455i	$-0.398363\pi$
$449$	−4.93072	−	2.37451i	−0.232695	−	0.112060i	−0.546598	+	0.837395i	$0.684078\pi$
$450$	−37.2106	−	10.2695i	−1.75413	−	0.484108i
$451$	6.29348	+	4.57248i	0.296349	+	0.215310i
$452$	2.35306	+	10.3094i	0.110679	+	0.484914i
$453$	−18.4873	+	19.3362i	−0.868609	+	0.908494i
$454$	−0.979742	−	7.23274i	−0.0459816	−	0.339449i
$455$	−4.95870	−	7.51210i	−0.232467	−	0.352173i
$456$	−7.52776	+	32.9813i	−0.352520	+	1.54449i
$457$	−13.1544	+	11.4926i	−0.615336	+	0.537603i	−0.908192	−	0.418553i	$-0.862537\pi$
$457$	−13.1544	+	11.4926i	−0.615336	+	0.537603i	0.292856	+	0.956157i	$0.405394\pi$
$458$	6.48279	+	8.12917i	0.302921	+	0.379851i
$459$	−9.22744	+	68.1197i	−0.430700	+	3.17956i
$460$	0.376765	−	0.181440i	0.0175667	−	0.00845969i
$461$	17.6665	−	3.20600i	0.822811	−	0.149318i	0.249206	−	0.968450i	$-0.419830\pi$
$461$	17.6665	−	3.20600i	0.822811	−	0.149318i	0.573605	+	0.819132i	$0.305545\pi$
$462$	−41.1983	+	7.47639i	−1.91672	+	0.347833i
$463$	8.70517	−	4.19219i	0.404563	−	0.194828i	−0.220525	−	0.975381i	$-0.570777\pi$
$463$	8.70517	−	4.19219i	0.404563	−	0.194828i	0.625089	+	0.780554i	$0.285063\pi$
$464$	−3.99725	+	29.5089i	−0.185568	+	1.36992i
$465$	−14.1161	−	17.7010i	−0.654617	−	0.820864i
$466$	−20.2372	+	17.6807i	−0.937469	+	0.819042i
$467$	1.99573	−	8.74385i	0.0923512	−	0.404617i	−0.907531	−	0.419986i	$-0.862035\pi$
$467$	1.99573	−	8.74385i	0.0923512	−	0.404617i	0.999882	+	0.0153688i	$0.00489222\pi$
$468$	−9.66083	−	14.6355i	−0.446572	−	0.676528i
$469$	−1.12198	−	8.28281i	−0.0518083	−	0.382465i
$470$	4.60467	−	4.81611i	0.212398	−	0.222150i
$471$	−0.0946563	−	0.414717i	−0.00436153	−	0.0191091i
$472$	−10.3189	−	7.49714i	−0.474967	−	0.345084i
$473$	26.2870	+	7.25475i	1.20868	+	0.333574i
$474$	19.0314	+	9.16503i	0.874140	+	0.420964i
$475$	−11.0744	+	16.7770i	−0.508128	+	0.769782i
$476$	9.79677	+	10.2466i	0.449034	+	0.469653i
$477$	43.6919	−	54.7879i	2.00051	−	2.50856i
$478$	−1.31208	−	29.2158i	−0.0600133	−	1.33630i
$479$	−25.9807	+	9.75070i	−1.18709	+	0.445521i	−0.865282	−	0.501285i	$-0.832861\pi$
$479$	−25.9807	+	9.75070i	−1.18709	+	0.445521i	−0.321804	+	0.946806i	$0.604289\pi$
$480$	−15.8901	+	11.5448i	−0.725281	+	0.526947i
$481$	−9.49984	−	8.29976i	−0.433155	−	0.378436i
$482$	0.255030	−	5.67869i	0.0116163	−	0.258657i
$483$	0.844620	+	2.59947i	0.0384315	+	0.118280i
$484$	0.495834	+	1.16006i	0.0225379	+	0.0527301i
$485$	13.3179	+	1.19863i	0.604734	+	0.0544271i
$486$	−9.74721	+	22.8047i	−0.442142	+	1.03444i
$487$	12.0986	−	22.4829i	0.548238	−	1.01880i	−0.444186	−	0.895935i	$-0.646507\pi$
$487$	12.0986	−	22.4829i	0.548238	−	1.01880i	0.992424	−	0.122862i	$-0.0392073\pi$
$488$	1.65955	−	0.991532i	0.0751241	−	0.0448846i
$489$	−41.1134	−	24.5641i	−1.85921	−	1.11083i
$490$	−0.654732	−	1.21670i	−0.0295778	−	0.0549647i
$491$	8.94383	−	0.804959i	0.403629	−	0.0363273i	0.114035	−	0.993477i	$-0.463622\pi$
$491$	8.94383	−	0.804959i	0.403629	−	0.0363273i	0.289594	+	0.957149i	$0.406480\pi$
$492$	2.26336	−	6.96592i	0.102040	−	0.314048i
$493$	33.3505	+	12.5167i	1.50203	+	0.563722i
$494$	−27.5385	+	7.60014i	−1.23901	+	0.341946i
$495$	−26.1861	−	4.75207i	−1.17698	−	0.213590i
$496$	28.3989			1.27515
$497$	−4.54014	+	20.7766i	−0.203653	+	0.931956i
$498$	0.492429			0.0220663
$499$	2.68033	+	0.486408i	0.119988	+	0.0217746i	0.238219	−	0.971212i	$-0.423436\pi$
$499$	2.68033	+	0.486408i	0.119988	+	0.0217746i	−0.118231	+	0.992986i	$0.537722\pi$
$500$	−9.69268	+	2.67501i	−0.433470	+	0.119630i
$501$	−20.0449	−	7.52296i	−0.895539	−	0.336101i
$502$	−0.351882	+	1.08298i	−0.0157053	+	0.0483358i
$503$	37.0248	−	3.33229i	1.65085	−	0.148579i	0.775264	−	0.631637i	$-0.217617\pi$
$503$	37.0248	−	3.33229i	1.65085	−	0.148579i	0.875588	+	0.483058i	$0.160474\pi$
$504$	−14.5538	−	27.0454i	−0.648276	−	1.20470i
$505$	1.77367	+	1.05972i	0.0789272	+	0.0471568i
$506$	−1.59096	+	0.950552i	−0.0707266	+	0.0422572i
$507$	7.71492	−	14.3367i	0.342632	−	0.636716i
$508$	−5.20675	+	12.1818i	−0.231012	+	0.540480i
$509$	−23.0732	−	2.07663i	−1.02270	−	0.0920448i	−0.434428	−	0.900707i	$-0.643049\pi$
$509$	−23.0732	−	2.07663i	−1.02270	−	0.0920448i	−0.588274	+	0.808662i	$0.700192\pi$
$510$	16.0430	+	37.5345i	0.710397	+	1.66206i
$511$	−7.76442	−	23.8964i	−0.343478	−	1.05712i
$512$	0.290348	−	6.46509i	0.0128317	−	0.285720i
$513$	51.7692	+	45.2294i	2.28567	+	1.99693i
$514$	38.3586	−	27.8691i	1.69192	−	1.22925i
$515$	−6.38221	+	2.39528i	−0.281234	+	0.105549i
$516$	−1.15193	−	25.6497i	−0.0507108	−	1.12916i
$517$	−5.88575	+	7.38049i	−0.258855	+	0.324594i
$518$	13.5329	+	14.1543i	0.594600	+	0.621903i
$519$	−8.37369	+	12.6856i	−0.367564	+	0.556836i
$520$	5.84105	+	2.81290i	0.256147	+	0.123354i
$521$	23.6390	+	6.52396i	1.03565	+	0.285820i	0.742216	−	0.670161i	$-0.233775\pi$
$521$	23.6390	+	6.52396i	1.03565	+	0.285820i	0.293429	+	0.955981i	$0.405203\pi$
$522$	55.3410	+	40.2076i	2.42221	+	1.75984i
$523$	7.08050	+	31.0217i	0.309609	+	1.35648i	0.855142	+	0.518394i	$0.173470\pi$
$523$	7.08050	+	31.0217i	0.309609	+	1.35648i	−0.545533	+	0.838089i	$0.683673\pi$
$524$	8.26935	−	8.64906i	0.361248	−	0.377836i
$525$	−3.54772	−	26.1903i	−0.154835	−	1.14304i
$526$	−17.2845	−	26.1848i	−0.753638	−	1.14171i
$527$	7.55943	−	33.1200i	0.329294	−	1.44273i
$528$	36.4063	−	31.8072i	1.58438	−	1.38423i
$529$	−14.2648	−	17.8875i	−0.620210	−	0.777719i
$530$	3.08239	−	22.7551i	0.133891	−	0.988419i
$531$	−42.3170	+	20.3788i	−1.83640	+	0.884365i
$532$	13.9490	−	2.53137i	0.604767	−	0.109749i
$533$	−6.86596	+	1.24599i	−0.297398	+	0.0539697i
$534$	20.9970	−	10.1116i	0.908631	−	0.437574i
$535$	0.569283	−	4.20261i	0.0246122	−	0.181695i
$536$	3.75353	+	4.70677i	0.162128	+	0.203302i
$537$	−14.3516	+	12.5386i	−0.619316	+	0.541080i
$538$	−6.09766	+	26.7156i	−0.262889	+	1.15179i
$539$	1.07837	+	1.63366i	0.0464486	+	0.0703667i
$540$	1.85616	+	13.7028i	0.0798766	+	0.589673i
$541$	−19.2340	+	20.1172i	−0.826935	+	0.864906i	−0.992619	−	0.121273i	$-0.961302\pi$
$541$	−19.2340	+	20.1172i	−0.826935	+	0.864906i	0.165684	+	0.986179i	$0.447017\pi$
$542$	−6.34761	−	27.8107i	−0.272653	−	1.19457i
$543$	21.6941	+	15.7617i	0.930982	+	0.676398i
$544$	−28.4095	−	7.84051i	−1.21805	−	0.336159i
$545$	−14.9582	−	7.20351i	−0.640741	−	0.308564i
$546$	20.6914	−	31.3461i	0.885510	−	1.34149i
$547$	12.2585	+	12.8213i	0.524134	+	0.548201i	0.930873	−	0.365344i	$-0.119048\pi$
$547$	12.2585	+	12.8213i	0.524134	+	0.548201i	−0.406739	+	0.913544i	$0.633334\pi$
$548$	4.27466	−	5.36025i	0.182604	−	0.228978i
$549$	−0.319381	−	7.11158i	−0.0136309	−	0.303515i
$550$	16.7780	−	6.29687i	0.715414	−	0.268500i
$551$	28.8197	−	20.9388i	1.22776	−	0.892022i
$552$	−1.48252	−	1.29523i	−0.0631000	−	0.0551288i
$553$	−0.448056	+	9.97673i	−0.0190533	+	0.424254i
$554$	6.58665	+	20.2716i	0.279840	+	0.861259i
$555$	7.08436	+	16.5747i	0.300714	+	0.703556i
$556$	3.30198	+	0.297183i	0.140035	+	0.0126034i
$557$	−7.69639	+	18.0066i	−0.326106	+	0.762964i	0.673609	+	0.739088i	$0.264743\pi$
$557$	−7.69639	+	18.0066i	−0.326106	+	0.762964i	−0.999715	+	0.0238754i	$0.992400\pi$
$558$	30.9134	−	57.4468i	1.30867	−	2.43192i
$559$	−20.9990	+	12.5463i	−0.888164	+	0.530653i
$560$	−13.8493	−	8.27459i	−0.585241	−	0.349665i
$561$	−27.4040	−	50.9253i	−1.15700	−	2.15007i
$562$	15.4545	−	1.39093i	0.651908	−	0.0586728i
$563$	4.67930	−	14.4014i	0.197209	−	0.606947i	−0.802735	−	0.596336i	$-0.796622\pi$
$563$	4.67930	−	14.4014i	0.197209	−	0.606947i	0.999944	−	0.0106107i	$-0.00337756\pi$
$564$	8.32138	+	3.12307i	0.350393	+	0.131505i
$565$	−13.8767	+	3.82974i	−0.583799	+	0.161118i
$566$	−7.49206	−	1.35961i	−0.314915	−	0.0571486i
$567$	−39.6954			−1.66705
$568$	−4.86804	−	14.5233i	−0.204258	−	0.609385i
$569$	13.4676			0.564591			0.282296	−	0.959327i	$-0.408904\pi$
$569$	13.4676			0.564591			0.282296	+	0.959327i	$0.408904\pi$
$570$	40.1647	+	7.28881i	1.68231	+	0.305295i
$571$	−29.7927	+	8.22225i	−1.24678	+	0.344090i	−0.826311	−	0.563215i	$-0.809564\pi$
$571$	−29.7927	+	8.22225i	−1.24678	+	0.344090i	−0.420473	+	0.907305i	$0.638136\pi$
$572$	7.62213	+	2.86063i	0.318697	+	0.119609i
$573$	−2.37747	+	7.31711i	−0.0993203	+	0.305677i
$574$	10.7889	−	0.971020i	0.450321	−	0.0405296i
$575$	−0.554339	−	1.03014i	−0.0231175	−	0.0429596i
$576$	8.83948	+	5.28134i	0.368312	+	0.220056i
$577$	−30.3926	+	18.1587i	−1.26526	+	0.755958i	−0.979325	−	0.202291i	$-0.935161\pi$
$577$	−30.3926	+	18.1587i	−1.26526	+	0.755958i	−0.285935	+	0.958249i	$0.592304\pi$
$578$	−15.2118	+	28.2682i	−0.632727	+	1.17580i
$579$	31.2924	−	73.2122i	1.30047	−	3.04259i
$580$	7.13677	+	0.642321i	0.296338	+	0.0266709i
$581$	0.0915016	+	0.214079i	0.00379613	+	0.00888148i
$582$	17.2422	+	53.0659i	0.714711	+	2.19965i
$583$	−1.45957	+	32.4998i	−0.0604492	+	1.34601i
$584$	13.6285	+	11.9068i	0.563950	+	0.492708i
$585$	19.3138	−	14.0323i	0.798527	−	0.580164i
$586$	2.85523	−	1.07158i	0.117948	−	0.0442668i
$587$	−0.370269	−	8.24469i	−0.0152827	−	0.340295i	−0.992038	−	0.125938i	$-0.959806\pi$
$587$	−0.370269	−	8.24469i	−0.0152827	−	0.340295i	0.976755	−	0.214357i	$-0.0687655\pi$
$588$	1.14912	−	1.44095i	0.0473888	−	0.0594237i
$589$	−23.4774	−	24.5554i	−0.967369	−	1.01179i
$590$	−8.47876	+	12.8448i	−0.349065	+	0.528811i
$591$	−67.2154	−	32.3692i	−2.76487	−	1.33149i
$592$	−21.7950	−	6.01505i	−0.895771	−	0.247217i
$593$	−12.7656	−	9.27476i	−0.524221	−	0.380869i	0.293971	−	0.955814i	$-0.405023\pi$
$593$	−12.7656	−	9.27476i	−0.524221	−	0.380869i	−0.818192	+	0.574946i	$0.805023\pi$
$594$	−13.6367	−	59.7465i	−0.559523	−	2.45143i
$595$	−13.3367	+	13.9491i	−0.546751	+	0.571857i
$596$	1.67588	+	12.3718i	0.0686467	+	0.506771i
$597$	23.1500	+	35.0708i	0.947468	+	1.43535i
$598$	0.369929	−	1.62077i	0.0151275	−	0.0662780i
$599$	−14.1456	+	12.3586i	−0.577973	+	0.504959i	−0.896553	−	0.442936i	$-0.853937\pi$
$599$	−14.1456	+	12.3586i	−0.577973	+	0.504959i	0.318580	+	0.947896i	$0.396794\pi$
$600$	11.8687	+	14.8829i	0.484537	+	0.607590i
$601$	−5.81101	+	42.8986i	−0.237036	+	1.74987i	0.346746	+	0.937959i	$0.387286\pi$
$601$	−5.81101	+	42.8986i	−0.237036	+	1.74987i	−0.583782	+	0.811910i	$0.698428\pi$
$602$	34.2127	−	16.4760i	1.39440	−	0.671510i
$603$	21.8124	−	3.95836i	0.888268	−	0.161197i
$604$	−7.94491	+	1.44179i	−0.323274	+	0.0586655i
$605$	−1.54736	+	0.745170i	−0.0629092	+	0.0302955i
$606$	−1.15729	+	8.54342i	−0.0470115	+	0.347053i
$607$	20.2192	+	25.3541i	0.820672	+	1.02909i	0.998982	+	0.0451157i	$0.0143657\pi$
$607$	20.2192	+	25.3541i	0.820672	+	1.02909i	−0.178310	+	0.983974i	$0.557063\pi$
$608$	−22.1949	+	19.3911i	−0.900122	+	0.786413i
$609$	−10.4218	+	45.6609i	−0.422313	+	1.85027i
$610$	−1.28508	−	1.94681i	−0.0520314	−	0.0788241i
$611$	−1.13667	−	8.39127i	−0.0459849	−	0.339474i
$612$	−25.9834	+	27.1765i	−1.05032	+	1.09854i
$613$	−2.15228	−	9.42974i	−0.0869296	−	0.380863i	0.912684	−	0.408666i	$-0.134006\pi$
$613$	−2.15228	−	9.42974i	−0.0869296	−	0.380863i	−0.999613	+	0.0278030i	$0.991149\pi$
$614$	0.619088	+	0.449794i	0.0249844	+	0.0181522i
$615$	9.61165	+	2.65265i	0.387579	+	0.106965i
$616$	12.8462	+	6.18640i	0.517588	+	0.249257i
$617$	26.1151	−	39.5626i	1.05135	−	1.59273i	0.276049	−	0.961144i	$-0.410975\pi$
$617$	26.1151	−	39.5626i	1.05135	−	1.59273i	0.775304	−	0.631588i	$-0.217597\pi$
$618$	−19.6574	−	20.5600i	−0.790736	−	0.827045i
$619$	−21.7719	+	27.3011i	−0.875086	+	1.09732i	0.119441	+	0.992841i	$0.461890\pi$
$619$	−21.7719	+	27.3011i	−0.875086	+	1.09732i	−0.994527	+	0.104482i	$0.966682\pi$
$620$	−0.306591	−	6.82678i	−0.0123130	−	0.274170i
$621$	−3.74531	+	1.40564i	−0.150294	+	0.0564064i
$622$	−4.18315	+	3.03924i	−0.167729	+	0.121862i
$623$	8.29755	+	7.24935i	0.332434	+	0.290439i
$624$	−1.94558	+	43.3218i	−0.0778857	+	1.73426i
$625$	0.966650	+	2.97504i	0.0386660	+	0.119002i
$626$	−13.2177	−	30.9244i	−0.528287	−	1.23599i
$627$	−57.5996	−	5.18406i	−2.30031	−	0.207031i
$628$	0.0504624	−	0.118063i	0.00201367	−	0.00471121i
$629$	−12.8166	+	23.8172i	−0.511030	+	0.949653i
$630$	−31.8139	+	19.0079i	−1.26750	+	0.757294i
$631$	10.7185	+	6.40403i	0.426698	+	0.254940i	0.710156	−	0.704044i	$-0.248624\pi$
$631$	10.7185	+	6.40403i	0.426698	+	0.254940i	−0.283458	+	0.958985i	$0.591482\pi$
$632$	−3.40854	−	6.33412i	−0.135584	−	0.251958i
$633$	−37.2152	+	3.34943i	−1.47917	+	0.133128i
$634$	−10.2600	+	31.5771i	−0.407477	+	1.25409i
$635$	−16.8848	−	6.33699i	−0.670055	−	0.251476i
$636$	29.5269	−	8.14890i	1.17082	−	0.323125i
$637$	−1.72769	−	0.313529i	−0.0684534	−	0.0124225i
$638$	−31.7568			−1.25726
$639$	−55.5892	−	9.55715i	−2.19907	−	0.378075i
$640$	15.9909			0.632097
$641$	−11.8413	−	2.14887i	−0.467702	−	0.0848754i	−0.0604104	−	0.998174i	$-0.519241\pi$
$641$	−11.8413	−	2.14887i	−0.467702	−	0.0848754i	−0.407291	+	0.913298i	$0.633527\pi$
$642$	17.0589	−	4.70795i	0.673260	−	0.185808i
$643$	−16.5842	−	6.22416i	−0.654018	−	0.245457i	0.00223563	−	0.999998i	$-0.499288\pi$
$643$	−16.5842	−	6.22416i	−0.654018	−	0.245457i	−0.656253	+	0.754540i	$0.727860\pi$
$644$	−0.254935	+	0.784610i	−0.0100459	+	0.0309180i
$645$	34.8123	−	3.13317i	1.37073	−	0.123368i
$646$	29.0250	+	53.9374i	1.14197	+	2.12214i
$647$	−30.5921	−	18.2779i	−1.20270	−	0.718578i	−0.235320	−	0.971918i	$-0.575614\pi$
$647$	−30.5921	−	18.2779i	−1.20270	−	0.718578i	−0.967377	+	0.253339i	$0.918471\pi$
$648$	24.5436	−	14.6641i	0.964164	−	0.576061i
$649$	10.3326	−	19.2012i	0.405591	−	0.753715i
$650$	−6.31798	+	14.7816i	−0.247812	+	0.579784i
$651$	44.4857	+	4.00378i	1.74353	+	0.156921i
$652$	−5.68143	−	13.2924i	−0.222502	−	0.520569i
$653$	−3.62289	−	11.1501i	−0.141775	−	0.436337i	0.854808	−	0.518945i	$-0.173675\pi$
$653$	−3.62289	−	11.1501i	−0.141775	−	0.436337i	−0.996582	+	0.0826079i	$0.973675\pi$
$654$	3.10813	−	69.2079i	0.121537	−	2.70624i
$655$	12.2675	+	10.7178i	0.479331	+	0.418779i
$656$	−10.1184	+	7.35145i	−0.395057	+	0.287026i
$657$	62.3913	−	23.4159i	2.43412	−	0.913540i
$658$	0.589759	+	13.1320i	0.0229912	+	0.511939i
$659$	24.4946	−	30.7153i	0.954176	−	1.19650i	−0.0262591	−	0.999655i	$-0.508359\pi$
$659$	24.4946	−	30.7153i	0.954176	−	1.19650i	0.980435	−	0.196844i	$-0.0630691\pi$
$660$	−8.03914	−	8.40828i	−0.312923	−	0.327292i
$661$	8.45494	−	12.8087i	0.328859	−	0.498200i	−0.632102	−	0.774886i	$-0.717807\pi$
$661$	8.45494	−	12.8087i	0.328859	−	0.498200i	0.960961	+	0.276686i	$0.0892360\pi$
$662$	26.0950	+	12.5667i	1.01421	+	0.488418i
$663$	50.0059	+	13.8007i	1.94207	+	0.535976i
$664$	−0.135660	−	0.0985624i	−0.00526461	−	0.00382496i
$665$	4.29454	+	18.8156i	0.166535	+	0.729637i
$666$	−35.8924	+	37.5405i	−1.39080	+	1.45467i
$667$	0.278266	+	2.05424i	0.0107745	+	0.0795407i
$668$	−3.56006	−	5.39326i	−0.137743	−	0.208672i
$669$	−11.4531	+	50.1791i	−0.442801	+	1.94004i
$670$	5.47055	−	4.77948i	0.211346	−	0.184647i
$671$	2.06054	+	2.58383i	0.0795461	+	0.0997476i
$672$	5.20136	−	38.3980i	0.200647	−	1.48123i
$673$	25.0444	−	12.0607i	0.965391	−	0.464908i	0.116335	−	0.993210i	$-0.462886\pi$
$673$	25.0444	−	12.0607i	0.965391	−	0.464908i	0.849056	+	0.528302i	$0.177171\pi$
$674$	−34.9549	+	6.34338i	−1.34641	+	0.244338i
$675$	38.0608	−	6.90702i	1.46496	−	0.265851i
$676$	4.42743	−	2.13214i	0.170286	−	0.0820053i
$677$	3.19189	−	23.5635i	0.122674	−	0.905618i	−0.820108	−	0.572209i	$-0.806087\pi$
$677$	3.19189	−	23.5635i	0.122674	−	0.905618i	0.942782	−	0.333409i	$-0.108199\pi$
$678$	−37.4523	−	46.9637i	−1.43835	−	1.80363i
$679$	−19.8660	+	17.3564i	−0.762388	+	0.666079i
$680$	3.09304	−	13.5515i	0.118613	−	0.519677i
$681$	7.30158	+	11.0614i	0.279797	+	0.423875i
$682$	4.06534	+	30.0116i	0.155670	+	1.14920i
$683$	11.6373	−	12.1716i	0.445288	−	0.465735i	−0.461611	−	0.887082i	$-0.652729\pi$
$683$	11.6373	−	12.1716i	0.445288	−	0.465735i	0.906899	+	0.421348i	$0.138443\pi$
$684$	8.36688	+	36.6577i	0.319916	+	1.40164i
$685$	7.55084	+	5.48600i	0.288503	+	0.209609i
$686$	31.8279	+	8.78395i	1.21520	+	0.335373i
$687$	−17.0113	−	8.19222i	−0.649022	−	0.312553i
$688$	−24.1531	+	36.5903i	−0.920827	+	1.39499i
$689$	−20.1669	−	21.0930i	−0.768299	−	0.803578i
$690$	−1.48108	+	1.85721i	−0.0563836	+	0.0707028i
$691$	1.75367	+	39.0484i	0.0667126	+	1.48547i	0.701436	+	0.712733i	$0.252543\pi$
$691$	1.75367	+	39.0484i	0.0667126	+	1.48547i	−0.634723	+	0.772740i	$0.718886\pi$
$692$	−4.29536	+	1.61208i	−0.163285	+	0.0612820i
$693$	42.4767	−	30.8612i	1.61356	−	1.17232i
$694$	−28.9269	−	25.2726i	−1.09805	−	0.959336i
$695$	−0.202487	+	4.50873i	−0.00768078	+	0.171026i
$696$	−10.4241	−	32.0821i	−0.395124	−	1.21607i
$697$	5.88019	+	13.7574i	0.222728	+	0.521098i
$698$	−36.5366	−	3.28836i	−1.38293	−	0.124466i
$699$	19.1791	−	44.8718i	0.725422	−	1.69721i
$700$	3.78021	−	7.02481i	0.142879	−	0.265513i
$701$	17.4382	−	10.4189i	0.658632	−	0.393515i	−0.144342	−	0.989528i	$-0.546107\pi$
$701$	17.4382	−	10.4189i	0.658632	−	0.393515i	0.802975	+	0.596013i	$0.203249\pi$
$702$	47.1909	+	28.1952i	1.78111	+	1.06416i
$703$	12.8170	+	23.8180i	0.483402	+	0.898312i
$704$	−4.76110	+	0.428507i	−0.179441	+	0.0161500i
$705$	−3.73903	+	11.5075i	−0.140820	+	0.433399i
$706$	−27.3479	−	10.2639i	−1.02925	−	0.386285i
$707$	−3.92922	+	1.08439i	−0.147773	+	0.0407829i
$708$	−20.2002	−	3.66579i	−0.759170	−	0.137769i
$709$	−24.5121			−0.920572			−0.460286	−	0.887771i	$-0.652253\pi$
$709$	−24.5121			−0.920572			−0.460286	+	0.887771i	$0.652253\pi$
$710$	−17.2435	+	6.65440i	−0.647138	+	0.249735i
$711$	−26.4874			−0.993354
$712$	−7.80840	−	1.41701i	−0.292632	−	0.0531049i
$713$	1.90573	−	0.525947i	0.0713700	−	0.0196969i
$714$	−75.3942	−	28.2959i	−2.82156	−	1.05895i
$715$	−3.42483	+	10.5406i	−0.128082	+	0.394194i
$716$	−5.72902	+	0.515621i	−0.214103	+	0.0192697i
$717$	25.1657	+	46.7656i	0.939829	+	1.74649i
$718$	−46.1089	−	27.5488i	−1.72077	−	1.02811i
$719$	3.78216	−	2.25974i	0.141051	−	0.0842739i	−0.440640	−	0.897684i	$-0.645248\pi$
$719$	3.78216	−	2.25974i	0.141051	−	0.0842739i	0.581691	+	0.813410i	$0.302391\pi$
$720$	20.2761	−	37.6794i	0.755647	−	1.40423i
$721$	5.28559	−	12.3663i	0.196846	−	0.460544i
$722$	28.5607	+	2.57051i	1.06292	+	0.0956645i
$723$	4.05696	+	9.49174i	0.150880	+	0.353002i
$724$	2.50112	+	7.69766i	0.0929534	+	0.286081i
$725$	0.899325	−	20.0250i	0.0334001	−	0.743711i
$726$	−5.39685	−	4.71508i	−0.200296	−	0.174993i
$727$	28.8147	−	20.9351i	1.06868	−	0.776440i	0.0930034	−	0.995666i	$-0.470353\pi$
$727$	28.8147	−	20.9351i	1.06868	−	0.776440i	0.975674	+	0.219226i	$0.0703533\pi$
$728$	−11.9744	+	4.49406i	−0.443800	+	0.166561i
$729$	0.0963550	+	2.14551i	0.00356871	+	0.0794634i
$730$	13.6152	−	17.0730i	0.503922	−	0.631899i
$731$	36.2440	+	37.9082i	1.34053	+	1.40209i
$732$	1.71419	−	2.59689i	0.0633584	−	0.0959839i
$733$	−14.8984	−	7.17469i	−0.550285	−	0.265003i	0.138014	−	0.990430i	$-0.455928\pi$
$733$	−14.8984	−	7.17469i	−0.550285	−	0.265003i	−0.688299	+	0.725427i	$0.741642\pi$
$734$	59.3490	+	16.3793i	2.19061	+	0.604570i
$735$	2.02983	+	1.47475i	0.0748712	+	0.0543971i
$736$	−0.381642	−	1.67208i	−0.0140675	−	0.0616338i
$737$	−7.11219	+	7.43877i	−0.261981	+	0.274011i
$738$	3.85658	+	28.4704i	0.141963	+	1.04801i
$739$	−3.97724	−	6.02527i	−0.146305	−	0.221643i	0.754030	−	0.656840i	$-0.228107\pi$
$739$	−3.97724	−	6.02527i	−0.146305	−	0.221643i	−0.900335	+	0.435197i	$0.856679\pi$
$740$	−1.21065	+	5.30422i	−0.0445045	+	0.194987i
$741$	39.0671	−	34.1319i	1.43517	−	1.25387i
$742$	28.2452	+	35.4183i	1.03691	+	1.30025i
$743$	3.66228	−	27.0360i	0.134356	−	0.991856i	−0.790748	−	0.612142i	$-0.790308\pi$
$743$	3.66228	−	27.0360i	0.134356	−	0.991856i	0.925104	−	0.379714i	$-0.123978\pi$
$744$	−28.9845	+	13.9582i	−1.06262	+	0.511732i
$745$	−16.7229	+	3.03477i	−0.612681	+	0.111185i
$746$	55.7949	−	10.1253i	2.04280	−	0.370713i
$747$	−0.556328	+	0.267914i	−0.0203550	+	0.00980245i
$748$	2.34307	−	17.2973i	0.0856712	−	0.632450i
$749$	5.21656	+	6.54136i	0.190609	+	0.239016i
$750$	43.0138	−	37.5800i	1.57064	−	1.37223i
$751$	9.44657	−	41.3881i	0.344710	−	1.51027i	−0.444291	−	0.895882i	$-0.646544\pi$
$751$	9.44657	−	41.3881i	0.344710	−	1.51027i	0.789001	−	0.614392i	$-0.210598\pi$
$752$	−8.36110	−	12.6665i	−0.304898	−	0.461901i
$753$	−0.277568	−	2.04909i	−0.0101152	−	0.0746731i
$754$	19.6860	−	20.5900i	0.716923	−	0.749843i
$755$	−2.44603	−	10.7167i	−0.0890201	−	0.390022i
$756$	−22.0700	−	16.0348i	−0.802676	−	0.583179i
$757$	−26.6764	−	7.36221i	−0.969569	−	0.267584i	−0.254838	−	0.966984i	$-0.582022\pi$
$757$	−26.6764	−	7.36221i	−0.969569	−	0.267584i	−0.714731	+	0.699400i	$0.753451\pi$
$758$	50.3378	+	24.2414i	1.82835	+	0.880488i
$759$	1.85400	−	2.80869i	0.0672959	−	0.101949i
$760$	−9.60610	−	10.0472i	−0.348450	−	0.364450i
$761$	−3.22236	+	4.04072i	−0.116811	+	0.146476i	−0.836799	−	0.547510i	$-0.815576\pi$
$761$	−3.22236	+	4.04072i	−0.116811	+	0.146476i	0.719988	+	0.693986i	$0.244147\pi$
$762$	−3.37630	−	75.1791i	−0.122310	−	2.72345i
$763$	30.6650	−	11.5088i	1.11015	−	0.416645i
$764$	−1.87871	+	1.36496i	−0.0679693	+	0.0493826i
$765$	−38.5461	−	33.6767i	−1.39364	−	1.21758i
$766$	−1.86450	+	41.5164i	−0.0673673	+	1.50005i
$767$	6.04420	+	18.6021i	0.218244	+	0.671685i
$768$	22.4604	+	52.5486i	0.810468	+	1.89618i
$769$	21.7254	+	1.95533i	0.783439	+	0.0705108i	0.474135	−	0.880452i	$-0.342761\pi$
$769$	21.7254	+	1.95533i	0.783439	+	0.0705108i	0.309305	+	0.950963i	$0.399904\pi$
$770$	6.76192	−	15.8203i	0.243683	−	0.570124i
$771$	−40.7998	+	75.8187i	−1.46937	+	2.73054i
$772$	20.6301	−	12.3259i	0.742494	−	0.443619i
$773$	−11.2078	−	6.69633i	−0.403115	−	0.240850i	0.297004	−	0.954876i	$-0.404013\pi$
$773$	−11.2078	−	6.69633i	−0.403115	−	0.240850i	−0.700119	+	0.714026i	$0.746870\pi$
$774$	47.7252	+	88.6883i	1.71545	+	3.18784i
$775$	−19.0396	+	1.71360i	−0.683924	+	0.0615543i
$776$	5.87139	−	18.0703i	0.210771	−	0.648686i
$777$	−33.2930	−	12.4951i	−1.19438	−	0.448258i
$778$	41.2242	−	11.3772i	1.47796	−	0.407891i
$779$	14.7214	+	2.67154i	0.527449	+	0.0957180i
$780$	10.4351			0.373636
$781$	23.4862	−	11.5795i	0.840403	−	0.414346i
$782$	−3.56436			−0.127461
$783$	−67.4467	−	12.2398i	−2.41035	−	0.437414i
$784$	−3.03374	+	0.837259i	−0.108348	+	0.0299021i
$785$	0.163643	+	0.0614163i	0.00584068	+	0.00219204i
$786$	−21.0051	+	64.6469i	−0.749226	+	2.30588i
$787$	−44.8461	+	4.03622i	−1.59859	+	0.143876i	−0.852776	−	0.522277i	$-0.825083\pi$
$787$	−44.8461	+	4.03622i	−1.59859	+	0.143876i	−0.745815	+	0.666153i	$0.767940\pi$
$788$	−10.6705	−	19.8292i	−0.380122	−	0.706384i
$789$	48.9097	+	29.2222i	1.74123	+	1.04034i
$790$	−7.45091	+	4.45171i	−0.265092	+	0.158385i
$791$	13.4578	−	25.0087i	0.478503	−	0.889207i
$792$	−14.8627	+	34.7730i	−0.528123	+	1.23561i
$793$	−2.95259	−	0.265738i	−0.104849	−	0.00943662i
$794$	−17.5546	−	41.0711i	−0.622991	−	1.45756i
$795$	12.8856	+	39.6578i	0.457006	+	1.40652i
$796$	−0.569058	+	12.6711i	−0.0201697	+	0.449114i
$797$	−10.7023	−	9.35032i	−0.379095	−	0.331205i	0.447209	−	0.894429i	$-0.352418\pi$
$797$	−10.7023	−	9.35032i	−0.379095	−	0.331205i	−0.826304	+	0.563224i	$0.809561\pi$
$798$	−65.1516	+	47.3354i	−2.30634	+	1.67566i
$799$	−16.9979	+	6.37941i	−0.601342	+	0.225687i
$800$	0.744049	+	16.5675i	0.0263061	+	0.585751i
$801$	−18.2203	+	22.8476i	−0.643783	+	0.807279i
$802$	−28.5320	−	29.8421i	−1.00750	−	1.05376i
$803$	−17.0434	+	25.8197i	−0.601450	+	0.911157i
$804$	8.73040	+	4.20434i	0.307898	+	0.148276i
$805$	−1.08261	−	0.298782i	−0.0381571	−	0.0105307i
$806$	−21.9785	−	15.9683i	−0.774160	−	0.562460i
$807$	−11.0728	−	48.5132i	−0.389782	−	1.70775i
$808$	2.02884	−	2.12200i	0.0713742	−	0.0746516i
$809$	−2.38983	−	17.6424i	−0.0840218	−	0.620274i	−0.983179	−	0.182647i	$-0.941533\pi$
$809$	−2.38983	−	17.6424i	−0.0840218	−	0.620274i	0.899157	−	0.437627i	$-0.144181\pi$
$810$	−19.0055	−	28.7921i	−0.667785	−	1.01165i
$811$	12.1118	−	53.0654i	0.425304	−	1.86338i	−0.0744692	−	0.997223i	$-0.523726\pi$
$811$	12.1118	−	53.0654i	0.425304	−	1.86338i	0.499773	−	0.866156i	$-0.333417\pi$
$812$	−10.6458	+	9.30093i	−0.373593	+	0.326399i
$813$	32.2972	+	40.4994i	1.13271	+	1.42037i
$814$	3.23663	−	23.8938i	0.113444	−	0.837476i
$815$	17.7302	−	8.53840i	0.621061	−	0.299087i
$816$	91.4833	−	16.6018i	3.20256	−	0.581178i
$817$	51.6056	−	9.36504i	1.80545	−	0.327641i
$818$	−55.1704	+	26.5687i	−1.92899	+	0.928952i
$819$	−6.32204	+	46.6712i	−0.220910	+	1.63082i
$820$	1.87644	+	2.35299i	0.0655283	+	0.0821699i
$821$	25.6739	−	22.4306i	0.896026	−	0.782834i	−0.0808313	−	0.996728i	$-0.525758\pi$
$821$	25.6739	−	22.4306i	0.896026	−	0.782834i	0.976857	+	0.213894i	$0.0686147\pi$
$822$	−8.66623	+	37.9693i	−0.302270	+	1.32433i
$823$	−21.3921	−	32.4076i	−0.745681	−	1.12966i	−0.987235	−	0.159271i	$-0.949086\pi$
$823$	−21.3921	−	32.4076i	−0.745681	−	1.12966i	0.241554	−	0.970387i	$-0.422343\pi$
$824$	1.30022	+	9.59863i	0.0452954	+	0.334384i
$825$	−22.4888	+	23.5215i	−0.782961	+	0.818913i
$826$	−6.75647	−	29.6020i	−0.235088	−	1.02999i
$827$	8.71067	+	6.32867i	0.302900	+	0.220069i	0.728844	−	0.684680i	$-0.240058\pi$
$827$	8.71067	+	6.32867i	0.302900	+	0.220069i	−0.425944	+	0.904749i	$0.640058\pi$
$828$	−2.10921	−	0.582106i	−0.0733003	−	0.0202296i
$829$	23.7006	+	11.4136i	0.823154	+	0.396410i	0.797543	−	0.603262i	$-0.206133\pi$
$829$	23.7006	+	11.4136i	0.823154	+	0.396410i	0.0256111	+	0.999672i	$0.491847\pi$
$830$	−0.111467	+	0.168866i	−0.00386909	+	0.00586142i
$831$	−26.7482	−	27.9764i	−0.927886	−	0.970492i
$832$	2.67358	−	3.35256i	0.0926896	−	0.116229i
$833$	0.168904	+	3.76095i	0.00585219	+	0.130309i
$834$	−17.6319	+	6.61736i	−0.610542	+	0.229140i
$835$	7.11722	−	5.17096i	0.246302	−	0.178949i
$836$	−13.1455	−	11.4848i	−0.454645	−	0.397212i
$837$	−2.93293	+	65.3069i	−0.101377	+	2.25734i
$838$	−10.6826	−	32.8777i	−0.369025	−	1.13574i
$839$	3.69616	+	8.64760i	0.127606	+	0.298548i	0.971133	−	0.238538i	$-0.0766680\pi$
$839$	3.69616	+	8.64760i	0.127606	+	0.298548i	−0.843528	+	0.537086i	$0.819525\pi$
$840$	18.2019	+	1.63820i	0.628026	+	0.0565233i
$841$	−2.56319	+	5.99687i	−0.0883858	+	0.206789i
$842$	−9.11004	+	16.9293i	−0.313953	+	0.583422i
$843$	−24.1889	+	14.4522i	−0.833110	+	0.497760i
$844$	−9.68178	−	5.78460i	−0.333261	−	0.199114i
$845$	3.17005	+	5.89094i	0.109053	+	0.202654i
$846$	−34.7240	+	3.12521i	−1.19383	+	0.107447i
$847$	1.04701	−	3.22237i	0.0359757	−	0.110722i
$848$	−48.9694	−	18.3785i	−1.68162	−	0.631121i
$849$	13.3289	−	3.67853i	0.457445	−	0.126247i
$850$	33.9122	+	6.15416i	1.16318	+	0.211086i
$851$	−1.57397			−0.0539550
$852$	−17.2023	−	17.6618i	−0.589340	−	0.605084i
$853$	34.4140			1.17831			0.589156	−	0.808019i	$-0.299460\pi$
$853$	34.4140			1.17831			0.589156	+	0.808019i	$0.299460\pi$
$854$	4.52805	+	0.821720i	0.154947	+	0.0281187i
$855$	−49.3422	+	13.6176i	−1.68747	+	0.465711i
$856$	−5.64188	−	2.11743i	−0.192836	−	0.0723724i
$857$	−12.6154	+	38.8263i	−0.430935	+	1.32628i	0.466261	+	0.884647i	$0.345601\pi$
$857$	−12.6154	+	38.8263i	−0.430935	+	1.32628i	−0.897196	+	0.441633i	$0.854399\pi$
$858$	−46.0604	+	4.14551i	−1.57248	+	0.141525i
$859$	−9.91154	−	18.4187i	−0.338177	−	0.628439i	0.653538	−	0.756894i	$-0.273284\pi$
$859$	−9.91154	−	18.4187i	−0.338177	−	0.628439i	−0.991715	+	0.128455i	$0.958998\pi$
$860$	9.05666	+	5.41110i	0.308830	+	0.184517i
$861$	−16.8865	+	10.0892i	−0.575490	+	0.343839i
$862$	−13.6844	+	25.4299i	−0.466093	+	0.866147i
$863$	11.5742	−	27.0791i	0.393990	−	0.921784i	−0.598687	−	0.800983i	$-0.704311\pi$
$863$	11.5742	−	27.0791i	0.393990	−	0.921784i	0.992677	−	0.120801i	$-0.0385464\pi$
$864$	56.4845	+	5.08370i	1.92164	+	0.172951i
$865$	−2.45471	−	5.74309i	−0.0834628	−	0.195271i
$866$	10.5331	+	32.4175i	0.357929	+	1.10159i
$867$	2.61531	−	58.2344i	0.0888206	−	1.97774i
$868$	10.1526	+	8.87005i	0.344601	+	0.301069i
$869$	9.94818	−	7.22778i	0.337469	−	0.245186i
$870$	−38.1089	+	14.3025i	−1.29201	+	0.484900i
$871$	−0.414186	−	9.22258i	−0.0140342	−	0.312495i
$872$	−14.7086	+	18.4440i	−0.498096	+	0.624593i
$873$	−48.3510	−	50.5711i	−1.63643	−	1.71157i
$874$	−1.96366	+	2.97482i	−0.0664218	+	0.100625i
$875$	24.3302	+	11.7168i	0.822512	+	0.396101i
$876$	28.0792	+	7.74938i	0.948710	+	0.261827i
$877$	−5.87346	−	4.26732i	−0.198332	−	0.144097i	0.484187	−	0.874965i	$-0.339116\pi$
$877$	−5.87346	−	4.26732i	−0.198332	−	0.144097i	−0.682519	+	0.730868i	$0.739116\pi$
$878$	−3.54187	−	15.5180i	−0.119532	−	0.523706i
$879$	−3.82709	+	4.00282i	−0.129085	+	0.135012i
$880$	2.66646	+	19.6846i	0.0898863	+	0.663567i
$881$	−1.89347	−	2.86848i	−0.0637926	−	0.0966416i	0.801277	−	0.598294i	$-0.204154\pi$
$881$	−1.89347	−	2.86848i	−0.0637926	−	0.0966416i	−0.865070	+	0.501652i	$0.832726\pi$
$882$	−1.60871	+	7.04820i	−0.0541680	+	0.237325i
$883$	17.3013	−	15.1157i	0.582235	−	0.508683i	−0.315672	−	0.948868i	$-0.602230\pi$
$883$	17.3013	−	15.1157i	0.582235	−	0.508683i	0.897907	+	0.440185i	$0.145087\pi$
$884$	9.76244	+	12.2417i	0.328347	+	0.411734i
$885$	3.75161	−	27.6955i	0.126109	−	0.930973i
$886$	38.4455	−	18.5144i	1.29160	−	0.622003i
$887$	−6.22372	+	1.12944i	−0.208972	+	0.0379229i	−0.282033	−	0.959405i	$-0.591009\pi$
$887$	−6.22372	+	1.12944i	−0.208972	+	0.0379229i	0.0730612	+	0.997327i	$0.476723\pi$
$888$	25.2009	−	4.57329i	0.845687	−	0.153469i
$889$	32.0560	−	15.4374i	1.07512	−	0.517752i
$890$	−1.28541	+	9.48931i	−0.0430872	+	0.318082i
$891$	30.4740	+	38.2132i	1.02092	+	1.28019i
$892$	−11.6992	+	10.2213i	−0.391718	+	0.342233i
$893$	−4.04013	+	17.7010i	−0.135198	+	0.592340i
$894$	−39.0698	−	59.1882i	−1.30669	−	1.97955i
$895$	−1.05113	−	7.75978i	−0.0351355	−	0.259381i
$896$	−21.8011	+	22.8022i	−0.728324	+	0.761767i
$897$	0.671759	+	2.94317i	0.0224294	+	0.0982696i
$898$	7.59127	+	5.51538i	0.253324	+	0.184051i
$899$	32.6553	+	9.01229i	1.08912	+	0.300577i
$900$	19.0625	+	9.18003i	0.635418	+	0.306001i
$901$	−34.4688	+	52.2181i	−1.14832	+	1.73964i
$902$	−9.21738	−	9.64062i	−0.306905	−	0.320998i
$903$	−42.9934	+	53.9120i	−1.43073	+	1.79408i
$904$	0.917709	+	20.4344i	0.0305225	+	0.679637i
$905$	−10.3158	+	3.87158i	−0.342909	+	0.128696i
$906$	37.1082	−	26.9607i	1.23284	−	0.895709i
$907$	−13.8069	−	12.0628i	−0.458452	−	0.400537i	0.397492	−	0.917605i	$-0.369880\pi$
$907$	−13.8069	−	12.0628i	−0.458452	−	0.400537i	−0.855944	+	0.517068i	$0.827023\pi$
$908$	−0.179482	+	3.99648i	−0.00595633	+	0.132628i
$909$	−3.34073	−	10.2817i	−0.110805	−	0.341022i
$910$	6.06560	+	14.1912i	0.201073	+	0.470433i
$911$	26.7822	+	2.41044i	0.887332	+	0.0798614i	0.523920	−	0.851767i	$-0.324469\pi$
$911$	26.7822	+	2.41044i	0.887332	+	0.0798614i	0.363412	+	0.931629i	$0.381612\pi$
$912$	36.5437	−	85.4982i	1.21008	−	2.83113i
$913$	0.135840	−	0.252433i	0.00449564	−	0.00835430i
$914$	25.7102	−	15.3611i	0.850418	−	0.508101i
$915$	3.63638	+	2.17264i	0.120215	+	0.0718251i
$916$	−2.70057	−	5.01849i	−0.0892292	−	0.165816i
$917$	−32.0077	+	2.88075i	−1.05699	+	0.0951307i
$918$	36.4217	−	112.094i	1.20209	−	3.69967i
$919$	34.3005	+	12.8732i	1.13147	+	0.424647i	0.845704	−	0.533653i	$-0.179181\pi$
$919$	34.3005	+	12.8732i	1.13147	+	0.424647i	0.285765	+	0.958300i	$0.407752\pi$
$920$	0.779754	−	0.215198i	0.0257077	−	0.00709488i
$921$	−1.36727	−	0.248123i	−0.0450531	−	0.00817593i
$922$	−30.7853			−1.01386
$923$	−7.05138	+	22.4057i	−0.232099	+	0.737493i
$924$	22.9498			0.754994
$925$	14.9751	+	2.71759i	0.492379	+	0.0893537i
$926$	−15.9692	+	4.40723i	−0.524782	+	0.144831i
$927$	33.3942	+	12.5331i	1.09681	+	0.411640i
$928$	9.08156	−	27.9502i	0.298117	−	0.917509i
$929$	−25.8122	+	2.32314i	−0.846869	+	0.0762196i	−0.504569	−	0.863371i	$-0.668349\pi$
$929$	−25.8122	+	2.32314i	−0.846869	+	0.0762196i	−0.342300	+	0.939591i	$0.611206\pi$
$930$	18.3950	+	34.1836i	0.603195	+	1.12092i
$931$	3.23194	+	1.93099i	0.105923	+	0.0632858i
$932$	12.6442	−	7.55457i	0.414175	−	0.247458i
$933$	4.44937	−	8.26832i	0.145666	−	0.270693i
$934$	−6.04375	+	14.1401i	−0.197758	+	0.462677i
$935$	23.6668	+	2.13005i	0.773987	+	0.0696601i
$936$	−13.3322	−	31.1922i	−0.435776	−	1.01955i
$937$	−4.42743	−	13.6262i	−0.144638	−	0.445150i	0.852326	−	0.523010i	$-0.175191\pi$
$937$	−4.42743	−	13.6262i	−0.144638	−	0.445150i	−0.996964	+	0.0778605i	$0.975191\pi$
$938$	−0.642967	+	14.3168i	−0.0209936	+	0.467459i
$939$	45.9905	+	40.1807i	1.50084	+	1.31125i
$940$	−2.95463	+	2.14666i	−0.0963693	+	0.0700164i
$941$	7.05535	−	2.64792i	0.229998	−	0.0863197i	−0.233715	−	0.972305i	$-0.575088\pi$
$941$	7.05535	−	2.64792i	0.229998	−	0.0863197i	0.463713	+	0.885985i	$0.346517\pi$
$942$	0.0327221	+	0.728614i	0.00106614	+	0.0237395i
$943$	−0.542854	+	0.680717i	−0.0176777	+	0.0221672i
$944$	24.2265	+	25.3390i	0.788507	+	0.824713i
$945$	20.4588	−	30.9937i	0.665524	−	1.00823i
$946$	−42.1257	−	20.2867i	−1.36962	−	0.659576i
$947$	−34.2158	−	9.44295i	−1.11186	−	0.306855i	−0.338594	−	0.940933i	$-0.609951\pi$
$947$	−34.2158	−	9.44295i	−1.11186	−	0.306855i	−0.773269	+	0.634078i	$0.781380\pi$
$948$	−9.36660	−	6.80524i	−0.304213	−	0.221024i
$949$	−6.17535	−	27.0560i	−0.200460	−	0.878274i
$950$	23.8190	−	24.9127i	0.772791	−	0.808276i
$951$	−8.09322	−	59.7465i	−0.262441	−	1.93741i
$952$	15.1068	+	22.8858i	0.489615	+	0.741735i
$953$	−4.09628	+	17.9470i	−0.132692	+	0.581360i	0.864240	+	0.503080i	$0.167800\pi$
$953$	−4.09628	+	17.9470i	−0.132692	+	0.581360i	−0.996931	+	0.0782798i	$0.975057\pi$
$954$	−90.4824	+	79.0521i	−2.92947	+	2.55941i
$955$	−1.97105	−	2.47161i	−0.0637816	−	0.0799795i
$956$	−2.15169	+	15.8844i	−0.0695905	+	0.513738i
$957$	51.9567	−	25.0211i	1.67952	−	0.808816i
$958$	46.8151	−	8.49568i	1.51253	−	0.274483i
$959$	−18.1171	+	3.28777i	−0.585032	+	0.106168i
$960$	−5.52044	+	2.65850i	−0.178171	+	0.0858028i
$961$	0.175409	−	1.29492i	0.00565837	−	0.0417718i
$962$	13.4855	+	16.9102i	0.434789	+	0.545208i
$963$	−16.7111	+	14.6000i	−0.538507	+	0.470479i
$964$	−0.693299	+	3.03754i	−0.0223297	+	0.0978326i
$965$	18.0228	+	27.3034i	0.580176	+	0.878929i
$966$	−0.629065	−	4.64394i	−0.0202398	−	0.149416i
$967$	−17.9083	+	18.7306i	−0.575892	+	0.602335i	−0.945008	−	0.327048i	$-0.893946\pi$
$967$	−17.9083	+	18.7306i	−0.575892	+	0.602335i	0.369116	+	0.929383i	$0.379660\pi$
$968$	0.543030	+	2.37917i	0.0174537	+	0.0764695i
$969$	−89.9842	−	65.3774i	−2.89071	−	2.10022i
$970$	−22.1006	−	6.09938i	−0.709608	−	0.195839i
$971$	5.63534	+	2.71384i	0.180847	+	0.0870911i	0.522116	−	0.852874i	$-0.325143\pi$
$971$	5.63534	+	2.71384i	0.180847	+	0.0870911i	−0.341270	+	0.939965i	$0.610857\pi$
$972$	7.48849	−	11.3446i	0.240194	−	0.363878i
$973$	−6.15314	−	6.43568i	−0.197261	−	0.206318i
$974$	−27.2936	+	34.2251i	−0.874545	+	1.09664i
$975$	−1.30966	−	29.1619i	−0.0419428	−	0.933928i
$976$	−4.97458	+	1.86699i	−0.159233	+	0.0597610i
$977$	−32.4484	+	23.5751i	−1.03812	+	0.754236i	−0.969917	−	0.243436i	$-0.921725\pi$
$977$	−32.4484	+	23.5751i	−1.03812	+	0.754236i	−0.0681993	+	0.997672i	$0.521725\pi$
$978$	61.8389	+	54.0270i	1.97739	+	1.72759i
$979$	0.608667	−	13.5530i	0.0194531	−	0.433157i
$980$	0.234020	+	0.720238i	0.00747548	+	0.0230072i
$981$	34.1422	+	79.8796i	1.09008	+	2.55036i
$982$	−15.3349	−	1.38016i	−0.489355	−	0.0440428i
$983$	−15.5201	+	36.3112i	−0.495016	+	1.15815i	0.466779	+	0.884374i	$0.345414\pi$
$983$	−15.5201	+	36.3112i	−0.495016	+	1.15815i	−0.961794	+	0.273773i	$0.911728\pi$
$984$	6.71378	−	12.4763i	0.214028	−	0.397730i
$985$	26.3153	−	15.7226i	0.838474	−	0.500965i
$986$	−52.4311	−	31.3261i	−1.66975	−	0.997627i
$987$	−11.3115	−	21.0204i	−0.360050	−	0.669085i
$988$	15.5952	−	1.40360i	0.496150	−	0.0446543i
$989$	−0.943155	+	2.90273i	−0.0299906	+	0.0923016i
$990$	42.7216	+	16.0337i	1.35778	+	0.509584i
$991$	34.1675	−	9.42963i	1.08537	−	0.299542i	0.322810	−	0.946464i	$-0.395373\pi$
$991$	34.1675	−	9.42963i	1.08537	−	0.299542i	0.762556	+	0.646922i	$0.223944\pi$
$992$	−27.5767	−	5.00443i	−0.875561	−	0.158891i
$993$	−52.5948			−1.66905
$994$	14.0200	−	33.6605i	0.444688	−	1.06765i
$995$	−17.2670			−0.547399
$996$	−0.265565	−	0.0481930i	−0.00841476	−	0.00152705i
$997$	−22.0791	+	6.09344i	−0.699252	+	0.192981i	−0.597548	−	0.801833i	$-0.703858\pi$
$997$	−22.0791	+	6.09344i	−0.699252	+	0.192981i	−0.101704	+	0.994815i	$0.532430\pi$
$998$	−4.37286	−	1.64116i	−0.138421	−	0.0519501i
$999$	16.0833	−	49.4993i	0.508853	−	1.56609i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	71.2.g.a.16.2	✓	120
3.2	odd	2		639.2.v.a.442.4		120
71.18	even	35		5041.2.a.s.1.13		60
71.40	even	35	inner	71.2.g.a.40.2	yes	120
71.53	odd	70		5041.2.a.t.1.13		60
213.182	odd	70		639.2.v.a.253.4		120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
71.2.g.a.16.2	✓	120	1.1	even	1	trivial
71.2.g.a.40.2	yes	120	71.40	even	35	inner
639.2.v.a.253.4		120	213.182	odd	70
639.2.v.a.442.4		120	3.2	odd	2
5041.2.a.s.1.13		60	71.18	even	35
5041.2.a.t.1.13		60	71.53	odd	70

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:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	71.g (of order \(35\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.68702 - 0.306149i) q^{2} +(3.00132 - 0.828311i) q^{3} +(0.879843 + 0.330211i) q^{4} +(-0.395338 + 1.21673i) q^{5} +(-5.31687 + 0.478527i) q^{6} +(-1.19600 - 2.22254i) q^{7} +(1.56053 + 0.932373i) q^{8} +(5.74646 - 3.43335i) q^{9} +O(q^{10})\)	\(q+(-1.68702 - 0.306149i) q^{2} +(3.00132 - 0.828311i) q^{3} +(0.879843 + 0.330211i) q^{4} +(-0.395338 + 1.21673i) q^{5} +(-5.31687 + 0.478527i) q^{6} +(-1.19600 - 2.22254i) q^{7} +(1.56053 + 0.932373i) q^{8} +(5.74646 - 3.43335i) q^{9} +(1.03944 - 1.93161i) q^{10} +(-1.22139 + 2.85758i) q^{11} +(2.91421 + 0.262283i) q^{12} +(-1.09561 - 2.56332i) q^{13} +(1.33725 + 4.11563i) q^{14} +(-0.178708 + 3.97924i) q^{15} +(-3.76263 - 3.28731i) q^{16} +(-4.83536 + 3.51310i) q^{17} +(-10.7455 + 4.03286i) q^{18} +(0.268159 + 5.97102i) q^{19} +(-0.749611 + 0.939982i) q^{20} +(-5.43054 - 5.67990i) q^{21} +(2.93535 - 4.44687i) q^{22} +(-0.313374 - 0.150913i) q^{23} +(5.45594 + 1.50574i) q^{24} +(2.72096 + 1.97689i) q^{25} +(1.06357 + 4.65979i) q^{26} +(7.94817 - 8.31313i) q^{27} +(-0.318386 - 2.35042i) q^{28} +(-3.28335 - 4.97406i) q^{29} +(1.51973 - 6.65835i) q^{30} +(-4.28039 + 3.73966i) q^{31} +(3.07440 + 3.85518i) q^{32} +(-1.29881 + 9.58820i) q^{33} +(9.23289 - 4.44633i) q^{34} +(3.17705 - 0.576549i) q^{35} +(6.18972 - 1.12327i) q^{36} +(4.07711 - 1.96343i) q^{37} +(1.37563 - 10.1553i) q^{38} +(-5.41151 - 6.78582i) q^{39} +(-1.75138 + 1.53013i) q^{40} +(0.557020 - 2.44046i) q^{41} +(7.42253 + 11.2447i) q^{42} +(-1.17790 - 8.69559i) q^{43} +(-2.01823 + 2.11091i) q^{44} +(1.90565 + 8.34920i) q^{45} +(0.482467 + 0.350533i) q^{46} +(2.92819 + 0.808128i) q^{47} +(-14.0157 - 6.74963i) q^{48} +(0.347003 - 0.525687i) q^{49} +(-3.98509 - 4.16808i) q^{50} +(-11.6025 + 14.5491i) q^{51} +(-0.117534 - 2.61710i) q^{52} +(9.80099 - 3.67837i) q^{53} +(-15.9538 + 11.5911i) q^{54} +(-2.99403 - 2.61580i) q^{55} +(0.205844 - 4.58346i) q^{56} +(5.75069 + 17.6988i) q^{57} +(4.01628 + 9.39654i) q^{58} +(-6.98823 - 0.628952i) q^{59} +(-1.47122 + 3.44210i) q^{60} +(0.503936 - 0.936469i) q^{61} +(8.36599 - 4.99845i) q^{62} +(-14.5035 - 8.66547i) q^{63} +(0.728927 + 1.35457i) q^{64} +(3.55199 - 0.319685i) q^{65} +(5.12654 - 15.7779i) q^{66} +(3.10054 + 1.16365i) q^{67} +(-5.41442 + 1.49429i) q^{68} +(-1.06554 - 0.193367i) q^{69} -5.53626 q^{70} +(-6.39655 - 5.48490i) q^{71} +12.1687 q^{72} +(9.79528 + 1.77758i) q^{73} +(-7.47927 + 2.06415i) q^{74} +(9.80394 + 3.67948i) q^{75} +(-1.73576 + 5.34211i) q^{76} +(7.81188 - 0.703082i) q^{77} +(7.05186 + 13.1046i) q^{78} +(-3.39678 - 2.02948i) q^{79} +(5.48726 - 3.27848i) q^{80} +(7.45288 - 13.8498i) q^{81} +(-1.68685 + 3.94658i) q^{82} +(-0.0918720 - 0.00826863i) q^{83} +(-2.90246 - 6.79064i) q^{84} +(-2.36287 - 7.27217i) q^{85} +(-0.675009 + 15.0302i) q^{86} +(-13.9744 - 12.2091i) q^{87} +(-4.57034 + 3.32055i) q^{88} +(-4.08719 + 1.53395i) q^{89} +(-0.658772 - 14.6687i) q^{90} +(-4.38672 + 5.50078i) q^{91} +(-0.225887 - 0.236259i) q^{92} +(-9.74920 + 14.7694i) q^{93} +(-4.69250 - 2.25979i) q^{94} +(-7.37110 - 2.03429i) q^{95} +(12.4205 + 9.02406i) q^{96} +(-2.32580 - 10.1900i) q^{97} +(-0.746341 + 0.780611i) q^{98} +(2.79242 + 20.6144i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9}+O(q^{10}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9} - 8 q^{10} - 27 q^{11} + 3 q^{12} - 31 q^{13} + 2 q^{14} + 12 q^{15} + 30 q^{16} + 9 q^{17} + 27 q^{18} - 31 q^{19} + 72 q^{20} - 32 q^{21} - 24 q^{22} - 6 q^{23} - 47 q^{24} - 42 q^{25} + 77 q^{26} - 2 q^{27} - 18 q^{28} + q^{29} + 15 q^{30} + 15 q^{31} - 10 q^{32} - 24 q^{33} + 20 q^{34} + 74 q^{35} + 8 q^{36} - 22 q^{37} - 39 q^{38} + 86 q^{39} - 30 q^{40} + 39 q^{41} - 34 q^{42} + 33 q^{43} - 23 q^{44} + 121 q^{45} + 124 q^{46} + 6 q^{47} + 131 q^{48} - 22 q^{49} - 15 q^{50} + 29 q^{51} + 83 q^{52} - 30 q^{53} - 25 q^{54} + 32 q^{55} + 11 q^{56} - 10 q^{57} + 12 q^{58} - 80 q^{59} + 80 q^{60} - 12 q^{61} - 68 q^{62} - 79 q^{63} - 117 q^{64} - 89 q^{65} - 39 q^{66} - 74 q^{67} - 67 q^{68} - 95 q^{69} - 64 q^{70} - 115 q^{71} - 144 q^{72} - 14 q^{73} - 70 q^{74} - 13 q^{75} + 8 q^{76} + 47 q^{77} - 218 q^{78} - 25 q^{79} - 103 q^{80} - 28 q^{81} - 88 q^{82} - 20 q^{83} - 142 q^{84} + 22 q^{85} + 159 q^{86} - 105 q^{87} + 43 q^{88} + 33 q^{89} + 33 q^{90} + 60 q^{91} - 2 q^{92} + 63 q^{93} + 174 q^{94} + 20 q^{95} - 30 q^{96} + 121 q^{97} + 128 q^{98} - 2 q^{99}+O(q^{100}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9 - 8 * q^10 - 27 * q^11 + 3 * q^12 - 31 * q^13 + 2 * q^14 + 12 * q^15 + 30 * q^16 + 9 * q^17 + 27 * q^18 - 31 * q^19 + 72 * q^20 - 32 * q^21 - 24 * q^22 - 6 * q^23 - 47 * q^24 - 42 * q^25 + 77 * q^26 - 2 * q^27 - 18 * q^28 + q^29 + 15 * q^30 + 15 * q^31 - 10 * q^32 - 24 * q^33 + 20 * q^34 + 74 * q^35 + 8 * q^36 - 22 * q^37 - 39 * q^38 + 86 * q^39 - 30 * q^40 + 39 * q^41 - 34 * q^42 + 33 * q^43 - 23 * q^44 + 121 * q^45 + 124 * q^46 + 6 * q^47 + 131 * q^48 - 22 * q^49 - 15 * q^50 + 29 * q^51 + 83 * q^52 - 30 * q^53 - 25 * q^54 + 32 * q^55 + 11 * q^56 - 10 * q^57 + 12 * q^58 - 80 * q^59 + 80 * q^60 - 12 * q^61 - 68 * q^62 - 79 * q^63 - 117 * q^64 - 89 * q^65 - 39 * q^66 - 74 * q^67 - 67 * q^68 - 95 * q^69 - 64 * q^70 - 115 * q^71 - 144 * q^72 - 14 * q^73 - 70 * q^74 - 13 * q^75 + 8 * q^76 + 47 * q^77 - 218 * q^78 - 25 * q^79 - 103 * q^80 - 28 * q^81 - 88 * q^82 - 20 * q^83 - 142 * q^84 + 22 * q^85 + 159 * q^86 - 105 * q^87 + 43 * q^88 + 33 * q^89 + 33 * q^90 + 60 * q^91 - 2 * q^92 + 63 * q^93 + 174 * q^94 + 20 * q^95 - 30 * q^96 + 121 * q^97 + 128 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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