LMFDB - Embedded newform 350.2.q.a.191.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(11,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([24, 20]))

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

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

chi := DirichletCharacter("350.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.q (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			191.1
Root			$0.913545 - 0.406737i$ of defining polynomial
Character	$\chi$	$=$	350.191
Dual form			350.2.q.a.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.913545 + 0.406737i) q^{2} +(0.413545 - 0.459289i) q^{3} +(0.669131 - 0.743145i) q^{4} +(1.11803 - 1.93649i) q^{5} +(-0.190983 + 0.587785i) q^{6} +(-0.500000 + 2.59808i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.273659 + 2.60369i) q^{9} +O(q^{10})$	\(q+(-0.913545 + 0.406737i) q^{2} +(0.413545 - 0.459289i) q^{3} +(0.669131 - 0.743145i) q^{4} +(1.11803 - 1.93649i) q^{5} +(-0.190983 + 0.587785i) q^{6} +(-0.500000 + 2.59808i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.273659 + 2.60369i) q^{9} +(-0.233733 + 2.22382i) q^{10} +(-0.402863 + 3.83299i) q^{11} +(-0.0646021 - 0.614648i) q^{12} +(4.73607 - 3.44095i) q^{13} +(-0.599960 - 2.57683i) q^{14} +(-0.427051 - 1.31433i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(7.53976 - 1.60263i) q^{17} +(-1.30902 - 2.26728i) q^{18} +(-4.01478 - 4.45887i) q^{19} +(-0.690983 - 2.12663i) q^{20} +(0.986494 + 1.30407i) q^{21} +(-1.19098 - 3.66547i) q^{22} +(1.34486 - 0.598772i) q^{23} +(0.309017 + 0.535233i) q^{24} +(-2.50000 - 4.33013i) q^{25} +(-2.92705 + 5.06980i) q^{26} +(2.80902 + 2.04087i) q^{27} +(1.59618 + 2.11002i) q^{28} +(1.07295 + 3.30220i) q^{29} +(0.924716 + 1.02700i) q^{30} +(4.74803 - 1.00922i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.59385 + 1.77015i) q^{33} +(-6.23607 + 4.53077i) q^{34} +(4.47214 + 3.87298i) q^{35} +(2.11803 + 1.53884i) q^{36} +(-0.0399263 - 0.379874i) q^{37} +(5.48127 + 2.44042i) q^{38} +(0.378188 - 3.59821i) q^{39} +(1.49622 + 1.66172i) q^{40} +(-7.59017 + 5.51458i) q^{41} +(-1.43162 - 0.790081i) q^{42} +2.23607 q^{43} +(2.57890 + 2.86416i) q^{44} +(5.34799 + 2.38108i) q^{45} +(-0.985051 + 1.09401i) q^{46} +(-9.03424 - 1.92029i) q^{47} +(-0.500000 - 0.363271i) q^{48} +(-6.50000 - 2.59808i) q^{49} +(4.04508 + 2.93893i) q^{50} +(2.38197 - 4.12569i) q^{51} +(0.611920 - 5.82203i) q^{52} +(-0.157960 + 0.175433i) q^{53} +(-3.39626 - 0.721898i) q^{54} +(6.97214 + 5.06555i) q^{55} +(-2.31641 - 1.27838i) q^{56} -3.70820 q^{57} +(-2.32331 - 2.58030i) q^{58} +(-4.86576 - 2.16638i) q^{59} +(-1.26249 - 0.562096i) q^{60} +(7.52402 - 3.34991i) q^{61} +(-3.92705 + 2.85317i) q^{62} +(-6.90142 - 0.590859i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-1.36830 - 13.0185i) q^{65} +(-2.17603 - 0.968833i) q^{66} +(0.978148 - 0.207912i) q^{67} +(3.85410 - 6.67550i) q^{68} +(0.281153 - 0.865300i) q^{69} +(-5.66078 - 1.71916i) q^{70} +(4.92705 + 15.1639i) q^{71} +(-2.56082 - 0.544320i) q^{72} +(-0.562569 + 5.35248i) q^{73} +(0.190983 + 0.330792i) q^{74} +(-3.02264 - 0.642482i) q^{75} -6.00000 q^{76} +(-9.75697 - 2.96316i) q^{77} +(1.11803 + 3.44095i) q^{78} +(-8.74882 - 1.85962i) q^{79} +(-2.04275 - 0.909491i) q^{80} +(-5.58347 + 1.18680i) q^{81} +(4.69098 - 8.12502i) q^{82} +(-1.78115 + 5.48183i) q^{83} +(1.62920 + 0.139483i) q^{84} +(5.32624 - 16.3925i) q^{85} +(-2.04275 + 0.909491i) q^{86} +(1.96038 + 0.872815i) q^{87} +(-3.52090 - 1.56760i) q^{88} +(-5.39890 + 2.40374i) q^{89} -5.85410 q^{90} +(6.57183 + 14.0251i) q^{91} +(0.454915 - 1.40008i) q^{92} +(1.50000 - 2.59808i) q^{93} +(9.03424 - 1.92029i) q^{94} +(-13.1232 + 2.78943i) q^{95} +(0.604528 + 0.128496i) q^{96} +(-3.47214 - 10.6861i) q^{97} +(6.99478 - 0.270327i) q^{98} -10.0902 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - 3 q^{3} + q^{4} - 6 q^{6} - 4 q^{7} + 2 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q - q^2 - 3 * q^3 + q^4 - 6 * q^6 - 4 * q^7 + 2 * q^8 - 4 * q^9	\( 8 q - q^{2} - 3 q^{3} + q^{4} - 6 q^{6} - 4 q^{7} + 2 q^{8} - 4 q^{9} + 5 q^{10} + 8 q^{11} + 2 q^{12} + 20 q^{13} - 4 q^{14} + 10 q^{15} + q^{16} + 14 q^{17} - 6 q^{18} - 6 q^{19} - 10 q^{20} + 15 q^{21} - 14 q^{22} + 7 q^{23} - 2 q^{24} - 20 q^{25} - 10 q^{26} + 18 q^{27} - 5 q^{28} + 22 q^{29} + 5 q^{30} + 6 q^{31} + 4 q^{32} + 6 q^{33} - 32 q^{34} + 8 q^{36} - q^{37} + 6 q^{38} - 5 q^{39} - 5 q^{40} - 16 q^{41} + 3 q^{42} - 7 q^{44} + 10 q^{45} + 13 q^{46} + 2 q^{47} - 4 q^{48} - 52 q^{49} + 10 q^{50} + 28 q^{51} - 10 q^{52} + 7 q^{53} - 11 q^{54} + 20 q^{55} - q^{56} + 24 q^{57} + 11 q^{58} - 15 q^{59} + 11 q^{61} - 18 q^{62} - 16 q^{63} - 2 q^{64} + 20 q^{65} - q^{66} - q^{67} + 4 q^{68} - 38 q^{69} - 25 q^{70} + 26 q^{71} - q^{72} + 4 q^{73} + 6 q^{74} - 15 q^{75} - 48 q^{76} - 40 q^{77} - 20 q^{79} - 5 q^{80} - 16 q^{81} + 42 q^{82} + 26 q^{83} + 8 q^{84} - 20 q^{85} - 5 q^{86} - 2 q^{87} - 8 q^{88} + q^{89} - 20 q^{90} - 10 q^{91} + 26 q^{92} + 12 q^{93} - 2 q^{94} - 30 q^{95} + 3 q^{96} + 8 q^{97} + 11 q^{98} - 36 q^{99}+O(q^{100}) \) 8 * q - q^2 - 3 * q^3 + q^4 - 6 * q^6 - 4 * q^7 + 2 * q^8 - 4 * q^9 + 5 * q^10 + 8 * q^11 + 2 * q^12 + 20 * q^13 - 4 * q^14 + 10 * q^15 + q^16 + 14 * q^17 - 6 * q^18 - 6 * q^19 - 10 * q^20 + 15 * q^21 - 14 * q^22 + 7 * q^23 - 2 * q^24 - 20 * q^25 - 10 * q^26 + 18 * q^27 - 5 * q^28 + 22 * q^29 + 5 * q^30 + 6 * q^31 + 4 * q^32 + 6 * q^33 - 32 * q^34 + 8 * q^36 - q^37 + 6 * q^38 - 5 * q^39 - 5 * q^40 - 16 * q^41 + 3 * q^42 - 7 * q^44 + 10 * q^45 + 13 * q^46 + 2 * q^47 - 4 * q^48 - 52 * q^49 + 10 * q^50 + 28 * q^51 - 10 * q^52 + 7 * q^53 - 11 * q^54 + 20 * q^55 - q^56 + 24 * q^57 + 11 * q^58 - 15 * q^59 + 11 * q^61 - 18 * q^62 - 16 * q^63 - 2 * q^64 + 20 * q^65 - q^66 - q^67 + 4 * q^68 - 38 * q^69 - 25 * q^70 + 26 * q^71 - q^72 + 4 * q^73 + 6 * q^74 - 15 * q^75 - 48 * q^76 - 40 * q^77 - 20 * q^79 - 5 * q^80 - 16 * q^81 + 42 * q^82 + 26 * q^83 + 8 * q^84 - 20 * q^85 - 5 * q^86 - 2 * q^87 - 8 * q^88 + q^89 - 20 * q^90 - 10 * q^91 + 26 * q^92 + 12 * q^93 - 2 * q^94 - 30 * q^95 + 3 * q^96 + 8 * q^97 + 11 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.913545	+	0.406737i	−0.645974	+	0.287606i
$2$	−0.913545	+	0.406737i	−0.645974	+	0.287606i
$3$	0.413545	−	0.459289i	0.238761	−	0.265170i	−0.611842	−	0.790980i	$-0.709571\pi$
$3$	0.413545	−	0.459289i	0.238761	−	0.265170i	0.850602	+	0.525810i	$0.176238\pi$
$4$	0.669131	−	0.743145i	0.334565	−	0.371572i
$5$	1.11803	−	1.93649i	0.500000	−	0.866025i
$5$	1.11803	−	1.93649i	0.500000	−	0.866025i
$6$	−0.190983	+	0.587785i	−0.0779685	+	0.239962i
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	0.273659	+	2.60369i	0.0912197	+	0.867897i
$10$	−0.233733	+	2.22382i	−0.0739128	+	0.703233i
$11$	−0.402863	+	3.83299i	−0.121468	+	1.15569i	0.748691	+	0.662919i	$0.230683\pi$
$11$	−0.402863	+	3.83299i	−0.121468	+	1.15569i	−0.870159	+	0.492771i	$0.835984\pi$
$12$	−0.0646021	−	0.614648i	−0.0186490	−	0.177434i
$13$	4.73607	−	3.44095i	1.31355	−	0.954349i	0.313560	−	0.949568i	$-0.398478\pi$
$13$	4.73607	−	3.44095i	1.31355	−	0.954349i	0.999989	−	0.00478088i	$-0.00152181\pi$
$14$	−0.599960	−	2.57683i	−0.160346	−	0.688687i
$15$	−0.427051	−	1.31433i	−0.110264	−	0.339358i
$16$	−0.104528	−	0.994522i	−0.0261321	−	0.248630i
$17$	7.53976	−	1.60263i	1.82866	−	0.388694i	0.840462	−	0.541871i	$-0.182284\pi$
$17$	7.53976	−	1.60263i	1.82866	−	0.388694i	0.988199	+	0.153177i	$0.0489504\pi$
$18$	−1.30902	−	2.26728i	−0.308538	−	0.534404i
$19$	−4.01478	−	4.45887i	−0.921055	−	1.02293i	−0.999661	−	0.0260290i	$-0.991714\pi$
$19$	−4.01478	−	4.45887i	−0.921055	−	1.02293i	0.0786067	−	0.996906i	$-0.474953\pi$
$20$	−0.690983	−	2.12663i	−0.154508	−	0.475528i
$21$	0.986494	+	1.30407i	0.215271	+	0.284571i
$22$	−1.19098	−	3.66547i	−0.253918	−	0.781481i
$23$	1.34486	−	0.598772i	0.280423	−	0.124853i	−0.261706	−	0.965148i	$-0.584285\pi$
$23$	1.34486	−	0.598772i	0.280423	−	0.124853i	0.542129	+	0.840295i	$0.317618\pi$
$24$	0.309017	+	0.535233i	0.0630778	+	0.109254i
$25$	−2.50000	−	4.33013i	−0.500000	−	0.866025i
$26$	−2.92705	+	5.06980i	−0.574042	+	0.994270i
$27$	2.80902	+	2.04087i	0.540596	+	0.392766i
$28$	1.59618	+	2.11002i	0.301650	+	0.398757i
$29$	1.07295	+	3.30220i	0.199242	+	0.613203i	0.999901	+	0.0140826i	$0.00448279\pi$
$29$	1.07295	+	3.30220i	0.199242	+	0.613203i	−0.800659	+	0.599120i	$0.795517\pi$
$30$	0.924716	+	1.02700i	0.168829	+	0.187504i
$31$	4.74803	−	1.00922i	0.852771	−	0.181262i	0.239267	−	0.970954i	$-0.423093\pi$
$31$	4.74803	−	1.00922i	0.852771	−	0.181262i	0.613504	+	0.789692i	$0.289759\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	1.59385	+	1.77015i	0.277453	+	0.308143i
$34$	−6.23607	+	4.53077i	−1.06948	+	0.777020i
$35$	4.47214	+	3.87298i	0.755929	+	0.654654i
$36$	2.11803	+	1.53884i	0.353006	+	0.256474i
$37$	−0.0399263	−	0.379874i	−0.00656385	−	0.0624508i	0.990750	−	0.135702i	$-0.0433291\pi$
$37$	−0.0399263	−	0.379874i	−0.00656385	−	0.0624508i	−0.997313	+	0.0732515i	$0.976662\pi$
$38$	5.48127	+	2.44042i	0.889180	+	0.395888i
$39$	0.378188	−	3.59821i	0.0605585	−	0.576175i
$40$	1.49622	+	1.66172i	0.236573	+	0.262741i
$41$	−7.59017	+	5.51458i	−1.18539	+	0.861233i	−0.992769	−	0.120041i	$-0.961697\pi$
$41$	−7.59017	+	5.51458i	−1.18539	+	0.861233i	−0.192616	+	0.981274i	$0.561697\pi$
$42$	−1.43162	−	0.790081i	−0.220904	−	0.121912i
$43$	2.23607			0.340997			0.170499	−	0.985358i	$-0.445462\pi$
$43$	2.23607			0.340997			0.170499	+	0.985358i	$0.445462\pi$
$44$	2.57890	+	2.86416i	0.388783	+	0.431788i
$45$	5.34799	+	2.38108i	0.797231	+	0.354950i
$46$	−0.985051	+	1.09401i	−0.145238	+	0.161303i
$47$	−9.03424	−	1.92029i	−1.31778	−	0.280103i	−0.505225	−	0.862988i	$-0.668590\pi$
$47$	−9.03424	−	1.92029i	−1.31778	−	0.280103i	−0.812554	+	0.582885i	$0.801924\pi$
$48$	−0.500000	−	0.363271i	−0.0721688	−	0.0524337i
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$	4.04508	+	2.93893i	0.572061	+	0.415627i
$51$	2.38197	−	4.12569i	0.333542	−	0.577712i
$52$	0.611920	−	5.82203i	0.0848581	−	0.807371i
$53$	−0.157960	+	0.175433i	−0.0216975	+	0.0240975i	−0.753896	−	0.656994i	$-0.771828\pi$
$53$	−0.157960	+	0.175433i	−0.0216975	+	0.0240975i	0.732198	+	0.681091i	$0.238494\pi$
$54$	−3.39626	−	0.721898i	−0.462173	−	0.0982378i
$55$	6.97214	+	5.06555i	0.940123	+	0.683039i
$56$	−2.31641	−	1.27838i	−0.309543	−	0.170830i
$57$	−3.70820			−0.491164
$58$	−2.32331	−	2.58030i	−0.305066	−	0.338810i
$59$	−4.86576	−	2.16638i	−0.633468	−	0.282038i	0.0647739	−	0.997900i	$-0.479367\pi$
$59$	−4.86576	−	2.16638i	−0.633468	−	0.282038i	−0.698242	+	0.715862i	$0.746034\pi$
$60$	−1.26249	−	0.562096i	−0.162987	−	0.0725663i
$61$	7.52402	−	3.34991i	0.963352	−	0.428912i	0.136070	−	0.990699i	$-0.456553\pi$
$61$	7.52402	−	3.34991i	0.963352	−	0.428912i	0.827282	+	0.561787i	$0.189886\pi$
$62$	−3.92705	+	2.85317i	−0.498736	+	0.362353i
$63$	−6.90142	−	0.590859i	−0.869497	−	0.0744412i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−1.36830	−	13.0185i	−0.169716	−	1.61474i
$66$	−2.17603	−	0.968833i	−0.267851	−	0.119255i
$67$	0.978148	−	0.207912i	0.119500	−	0.0254005i	−0.147774	−	0.989021i	$-0.547211\pi$
$67$	0.978148	−	0.207912i	0.119500	−	0.0254005i	0.267273	+	0.963621i	$0.413877\pi$
$68$	3.85410	−	6.67550i	0.467379	−	0.809523i
$69$	0.281153	−	0.865300i	0.0338468	−	0.104170i
$70$	−5.66078	−	1.71916i	−0.676593	−	0.205479i
$71$	4.92705	+	15.1639i	0.584733	+	1.79962i	0.600338	+	0.799746i	$0.295033\pi$
$71$	4.92705	+	15.1639i	0.584733	+	1.79962i	−0.0156051	+	0.999878i	$0.504967\pi$
$72$	−2.56082	−	0.544320i	−0.301796	−	0.0641487i
$73$	−0.562569	+	5.35248i	−0.0658437	+	0.626461i	0.910985	+	0.412439i	$0.135323\pi$
$73$	−0.562569	+	5.35248i	−0.0658437	+	0.626461i	−0.976829	+	0.214022i	$0.931344\pi$
$74$	0.190983	+	0.330792i	0.0222013	+	0.0384538i
$75$	−3.02264	−	0.642482i	−0.349025	−	0.0741875i
$76$	−6.00000			−0.688247
$77$	−9.75697	−	2.96316i	−1.11191	−	0.337684i
$78$	1.11803	+	3.44095i	0.126592	+	0.389611i
$79$	−8.74882	−	1.85962i	−0.984319	−	0.209223i	−0.312483	−	0.949923i	$-0.601161\pi$
$79$	−8.74882	−	1.85962i	−0.984319	−	0.209223i	−0.671836	+	0.740700i	$0.734494\pi$
$80$	−2.04275	−	0.909491i	−0.228386	−	0.101684i
$81$	−5.58347	+	1.18680i	−0.620385	+	0.131867i
$82$	4.69098	−	8.12502i	0.518032	−	0.897258i
$83$	−1.78115	+	5.48183i	−0.195507	+	0.601708i	0.804463	+	0.594002i	$0.202453\pi$
$83$	−1.78115	+	5.48183i	−0.195507	+	0.601708i	−0.999970	+	0.00770622i	$0.997547\pi$
$84$	1.62920	+	0.139483i	0.177761	+	0.0152188i
$85$	5.32624	−	16.3925i	0.577712	−	1.77801i
$86$	−2.04275	+	0.909491i	−0.220275	+	0.0980729i
$87$	1.96038	+	0.872815i	0.210174	+	0.0935756i
$88$	−3.52090	−	1.56760i	−0.375329	−	0.167107i
$89$	−5.39890	+	2.40374i	−0.572282	+	0.254796i	−0.672411	−	0.740178i	$-0.734741\pi$
$89$	−5.39890	+	2.40374i	−0.572282	+	0.254796i	0.100129	+	0.994974i	$0.468075\pi$
$90$	−5.85410			−0.617077
$91$	6.57183	+	14.0251i	0.688915	+	1.47023i
$92$	0.454915	−	1.40008i	0.0474282	−	0.145969i
$93$	1.50000	−	2.59808i	0.155543	−	0.269408i
$94$	9.03424	−	1.92029i	0.931810	−	0.198062i
$95$	−13.1232	+	2.78943i	−1.34641	+	0.286189i
$96$	0.604528	+	0.128496i	0.0616994	+	0.0131146i
$97$	−3.47214	−	10.6861i	−0.352542	−	1.08501i	−0.957421	−	0.288695i	$-0.906779\pi$
$97$	−3.47214	−	10.6861i	−0.352542	−	1.08501i	0.604879	−	0.796317i	$-0.293221\pi$
$98$	6.99478	−	0.270327i	0.706579	−	0.0273072i
$99$	−10.0902			−1.01410
$100$	−4.89074	−	1.03956i	−0.489074	−	0.103956i
$101$	−2.35410	−	4.07742i	−0.234242	−	0.405719i	0.724810	−	0.688949i	$-0.241927\pi$
$101$	−2.35410	−	4.07742i	−0.234242	−	0.405719i	−0.959052	+	0.283230i	$0.908594\pi$
$102$	−0.497966	+	4.73783i	−0.0493060	+	0.469116i
$103$	−2.87993	−	0.612149i	−0.283768	−	0.0603168i	0.0638287	−	0.997961i	$-0.479669\pi$
$103$	−2.87993	−	0.612149i	−0.283768	−	0.0603168i	−0.347597	+	0.937644i	$0.613002\pi$
$104$	1.80902	+	5.56758i	0.177389	+	0.545946i
$105$	3.62825	−	0.452347i	0.354081	−	0.0441446i
$106$	0.0729490	−	0.224514i	0.00708543	−	0.0218067i
$107$	7.78115	−	13.4774i	0.752232	−	1.30290i	−0.194506	−	0.980901i	$-0.562310\pi$
$107$	7.78115	−	13.4774i	0.752232	−	1.30290i	0.946738	−	0.322003i	$-0.104356\pi$
$108$	3.39626	−	0.721898i	0.326805	−	0.0694646i
$109$	−1.12920	−	0.502754i	−0.108158	−	0.0481551i	0.351944	−	0.936021i	$-0.385521\pi$
$109$	−1.12920	−	0.502754i	−0.108158	−	0.0481551i	−0.460102	+	0.887866i	$0.652187\pi$
$110$	−8.42971	−	1.79179i	−0.803741	−	0.170840i
$111$	−0.190983	−	0.138757i	−0.0181273	−	0.0131703i
$112$	2.63611	+	0.225688i	0.249089	+	0.0213255i
$113$	−5.19098	+	3.77147i	−0.488327	+	0.354790i	−0.804540	−	0.593898i	$-0.797588\pi$
$113$	−5.19098	+	3.77147i	−0.488327	+	0.354790i	0.316214	+	0.948688i	$0.397588\pi$
$114$	3.38761	−	1.50826i	0.317279	−	0.141262i
$115$	0.344086	−	3.27376i	0.0320862	−	0.305280i
$116$	3.17195	+	1.41224i	0.294509	+	0.131124i
$117$	10.2553	+	11.3896i	0.948099	+	1.05297i
$118$	5.32624			0.490320
$119$	0.393863	+	20.3902i	0.0361054	+	1.86917i
$120$	1.38197			0.126156
$121$	−3.76988	−	0.801313i	−0.342716	−	0.0728466i
$122$	−5.51101	+	6.12059i	−0.498943	+	0.554132i
$123$	−0.606095	+	5.76661i	−0.0546498	+	0.519958i
$124$	2.42705	−	4.20378i	0.217956	−	0.377510i
$125$	−11.1803			−1.00000
$126$	6.54508	−	2.26728i	0.583083	−	0.201986i
$127$	−7.28115	−	5.29007i	−0.646098	−	0.469418i	0.215842	−	0.976428i	$-0.430750\pi$
$127$	−7.28115	−	5.29007i	−0.646098	−	0.469418i	−0.861940	+	0.507011i	$0.830750\pi$
$128$	0.978148	+	0.207912i	0.0864569	+	0.0183770i
$129$	0.924716	−	1.02700i	0.0814167	−	0.0904224i
$130$	6.54508	+	11.3364i	0.574042	+	0.994270i
$131$	−4.54900	−	5.05218i	−0.397448	−	0.441411i	0.510891	−	0.859646i	$-0.329316\pi$
$131$	−4.54900	−	5.05218i	−0.397448	−	0.441411i	−0.908339	+	0.418235i	$0.862649\pi$
$132$	2.38197			0.207324
$133$	13.5919	−	8.20128i	1.17856	−	0.711141i
$134$	−0.809017	+	0.587785i	−0.0698884	+	0.0507769i
$135$	7.09270	−	3.15788i	0.610443	−	0.271787i
$136$	−0.805727	+	7.66598i	−0.0690905	+	0.657352i
$137$	2.25841	+	1.00551i	0.192949	+	0.0859064i	0.500937	−	0.865484i	$-0.332989\pi$
$137$	2.25841	+	1.00551i	0.192949	+	0.0859064i	−0.307988	+	0.951390i	$0.599656\pi$
$138$	0.0951031	+	0.904846i	0.00809572	+	0.0770256i
$139$	−4.85410	−	3.52671i	−0.411720	−	0.299132i	0.362578	−	0.931953i	$-0.381897\pi$
$139$	−4.85410	−	3.52671i	−0.411720	−	0.299132i	−0.774298	+	0.632822i	$0.781897\pi$
$140$	5.87063	−	0.731913i	0.496159	−	0.0618579i
$141$	−4.61803	+	3.35520i	−0.388909	+	0.282559i
$142$	−10.6688	−	11.8489i	−0.895306	−	0.994338i
$143$	11.2812	+	19.5395i	0.943377	+	1.63398i
$144$	2.56082	−	0.544320i	0.213402	−	0.0453600i
$145$	7.59427	+	1.61421i	0.630670	+	0.134053i
$146$	−1.66312	−	5.11855i	−0.137641	−	0.423615i
$147$	−3.88131	+	1.91095i	−0.320125	+	0.157613i
$148$	−0.309017	−	0.224514i	−0.0254010	−	0.0184549i
$149$	2.38197	−	4.12569i	0.195138	−	0.337989i	−0.751808	−	0.659383i	$-0.770818\pi$
$149$	2.38197	−	4.12569i	0.195138	−	0.337989i	0.946946	+	0.321393i	$0.104151\pi$
$150$	3.02264	−	0.642482i	0.246798	−	0.0524585i
$151$	−8.80902	−	15.2577i	−0.716868	−	1.24165i	−0.962235	−	0.272221i	$-0.912242\pi$
$151$	−8.80902	−	15.2577i	−0.716868	−	1.24165i	0.245367	−	0.969430i	$-0.421091\pi$
$152$	5.48127	−	2.44042i	0.444590	−	0.197944i
$153$	6.23607	+	19.1926i	0.504156	+	1.55163i
$154$	10.1187	−	1.26153i	0.815385	−	0.101657i
$155$	3.35410	−	10.3229i	0.269408	−	0.829152i
$156$	−2.42094	−	2.68872i	−0.193830	−	0.215270i
$157$	0.690983	+	1.19682i	0.0551464	+	0.0955164i	0.892281	−	0.451481i	$-0.149104\pi$
$157$	0.690983	+	1.19682i	0.0551464	+	0.0955164i	−0.837134	+	0.546997i	$0.815771\pi$
$158$	8.74882	−	1.85962i	0.696019	−	0.147943i
$159$	0.0152505	+	0.145099i	0.00120944	+	0.0115071i
$160$	2.23607			0.176777
$161$	0.883223	+	3.79344i	0.0696077	+	0.298965i
$162$	4.61803	−	3.35520i	0.362827	−	0.263609i
$163$	0.214882	+	2.04447i	0.0168309	+	0.160135i	0.999709	−	0.0241217i	$-0.00767891\pi$
$163$	0.214882	+	2.04447i	0.0168309	+	0.160135i	−0.982878	+	0.184257i	$0.941012\pi$
$164$	−0.980682	+	9.33057i	−0.0765784	+	0.728595i
$165$	5.20985	−	1.10739i	0.405586	−	0.0862100i
$166$	−0.602495	−	5.73236i	−0.0467627	−	0.444917i
$167$	0.0450850	−	0.138757i	0.00348878	−	0.0107374i	−0.949297	−	0.314381i	$-0.898203\pi$
$167$	0.0450850	−	0.138757i	0.00348878	−	0.0107374i	0.952786	+	0.303643i	$0.0982031\pi$
$168$	−1.54508	+	0.535233i	−0.119206	+	0.0412941i
$169$	6.57295	−	20.2295i	0.505611	−	1.55611i
$170$	1.80166	+	17.1416i	0.138181	+	1.31470i
$171$	10.5108	−	11.6735i	0.803784	−	0.892693i
$172$	1.49622	−	1.66172i	0.114086	−	0.126705i
$173$	−8.86889	+	3.94868i	−0.674289	+	0.300213i	−0.715169	−	0.698951i	$-0.753650\pi$
$173$	−8.86889	+	3.94868i	−0.674289	+	0.300213i	0.0408804	+	0.999164i	$0.486984\pi$
$174$	−2.14590			−0.162680
$175$	12.5000	−	4.33013i	0.944911	−	0.327327i
$176$	3.85410			0.290514
$177$	−3.00721	+	1.33889i	−0.226035	+	0.100637i
$178$	3.95445	−	4.39186i	0.296398	−	0.329184i
$179$	−3.85682	+	4.28344i	−0.288273	+	0.320159i	−0.869835	−	0.493343i	$-0.835775\pi$
$179$	−3.85682	+	4.28344i	−0.288273	+	0.320159i	0.581563	+	0.813502i	$0.302442\pi$
$180$	5.34799	−	2.38108i	0.398616	−	0.177475i
$181$	−0.437694	+	1.34708i	−0.0325335	+	0.100128i	−0.966005	−	0.258525i	$-0.916764\pi$
$181$	−0.437694	+	1.34708i	−0.0325335	+	0.100128i	0.933471	+	0.358653i	$0.116764\pi$
$182$	−11.7082	−	10.1396i	−0.867870	−	0.751597i
$183$	1.57295	−	4.84104i	0.116276	−	0.357860i
$184$	0.153880	+	1.46407i	0.0113442	+	0.107933i
$185$	−0.780261	−	0.347395i	−0.0573659	−	0.0255410i
$186$	−0.313585	+	2.98357i	−0.0229932	+	0.218766i
$187$	3.10535	+	29.5455i	0.227086	+	2.16058i
$188$	−7.47214	+	5.42882i	−0.544962	+	0.395938i
$189$	−6.70685	+	6.27761i	−0.487851	+	0.456629i
$190$	10.8541	−	7.88597i	0.787439	−	0.572108i
$191$	1.64778	+	15.6776i	0.119229	+	1.13439i	0.876538	+	0.481333i	$0.159847\pi$
$191$	1.64778	+	15.6776i	0.119229	+	1.13439i	−0.757309	+	0.653057i	$0.773486\pi$
$192$	−0.604528	+	0.128496i	−0.0436281	+	0.00927344i
$193$	−11.8992	−	20.6100i	−0.856522	−	1.48354i	−0.875226	−	0.483715i	$-0.839287\pi$
$193$	−11.8992	−	20.6100i	−0.856522	−	1.48354i	0.0187034	−	0.999825i	$-0.494046\pi$
$194$	7.51840	+	8.35003i	0.539789	+	0.599497i
$195$	−6.54508	−	4.75528i	−0.468703	−	0.340533i
$196$	−6.28010	+	3.09199i	−0.448578	+	0.220856i
$197$	7.37132	+	22.6866i	0.525185	+	1.61635i	0.763950	+	0.645276i	$0.223258\pi$
$197$	7.37132	+	22.6866i	0.525185	+	1.61635i	−0.238765	+	0.971077i	$0.576742\pi$
$198$	9.21783	−	4.10404i	0.655083	−	0.291662i
$199$	11.2082	+	19.4132i	0.794529	+	1.37616i	0.923138	+	0.384468i	$0.125615\pi$
$199$	11.2082	+	19.4132i	0.794529	+	1.37616i	−0.128610	+	0.991695i	$0.541051\pi$
$200$	4.89074	−	1.03956i	0.345827	−	0.0735079i
$201$	0.309017	−	0.535233i	0.0217964	−	0.0377524i
$202$	3.80902	+	2.76741i	0.268002	+	0.194714i
$203$	−9.11584	+	1.13650i	−0.639806	+	0.0797670i
$204$	−1.47214	−	4.53077i	−0.103070	−	0.317217i
$205$	2.19287	+	20.8638i	0.153157	+	1.45719i
$206$	2.87993	−	0.612149i	0.200654	−	0.0426504i
$207$	1.92705	+	3.33775i	0.133939	+	0.231990i
$208$	−3.91716	−	4.35045i	−0.271606	−	0.301649i
$209$	18.7082	−	13.5923i	1.29407	−	0.940199i
$210$	−3.13058	+	1.88898i	−0.216031	+	0.130352i
$211$	8.30902	+	6.03685i	0.572016	+	0.415594i	0.835837	−	0.548978i	$-0.184983\pi$
$211$	8.30902	+	6.03685i	0.572016	+	0.415594i	−0.263821	+	0.964572i	$0.584983\pi$
$212$	0.0246758	+	0.234775i	0.00169474	+	0.0161244i
$213$	9.00217	+	4.00802i	0.616819	+	0.274625i
$214$	−1.62670	+	15.4771i	−0.111199	+	1.05799i
$215$	2.50000	−	4.33013i	0.170499	−	0.295312i
$216$	−2.80902	+	2.04087i	−0.191129	+	0.138864i
$217$	0.248028	+	12.8404i	0.0168373	+	0.871660i
$218$	1.23607			0.0837171
$219$	2.22569	+	2.47188i	0.150398	+	0.167034i
$220$	8.42971	−	1.79179i	0.568331	−	0.120802i
$221$	30.1943	−	33.5341i	2.03109	−	2.25575i
$222$	0.230909	+	0.0490813i	0.0154976	+	0.00329412i
$223$	−8.59017	−	6.24112i	−0.575240	−	0.417937i	0.261765	−	0.965132i	$-0.415696\pi$
$223$	−8.59017	−	6.24112i	−0.575240	−	0.417937i	−0.837005	+	0.547195i	$0.815696\pi$
$224$	−2.50000	+	0.866025i	−0.167038	+	0.0578638i
$225$	10.5902	−	7.69421i	0.706011	−	0.512947i
$226$	3.20820	−	5.55677i	0.213407	−	0.369631i
$227$	2.08474	−	19.8350i	0.138369	−	1.31650i	−0.676324	−	0.736604i	$-0.736428\pi$
$227$	2.08474	−	19.8350i	0.138369	−	1.31650i	0.814693	−	0.579892i	$-0.196905\pi$
$228$	−2.48127	+	2.75573i	−0.164326	+	0.182503i
$229$	−12.0569	−	2.56277i	−0.796741	−	0.169353i	−0.208483	−	0.978026i	$-0.566853\pi$
$229$	−12.0569	−	2.56277i	−0.796741	−	0.169353i	−0.588258	+	0.808673i	$0.700186\pi$
$230$	1.01722	+	3.13068i	0.0670736	+	0.206431i
$231$	−5.39590	+	3.25586i	−0.355024	+	0.214220i
$232$	−3.47214			−0.227957
$233$	−17.2855	−	19.1975i	−1.13241	−	1.25767i	−0.962224	−	0.272260i	$-0.912229\pi$
$233$	−17.2855	−	19.1975i	−1.13241	−	1.25767i	−0.170189	−	0.985411i	$-0.554438\pi$
$234$	−14.0012	−	6.23374i	−0.915288	−	0.407512i
$235$	−13.8192	+	15.3478i	−0.901465	+	1.00118i
$236$	−4.86576	+	2.16638i	−0.316734	+	0.141019i
$237$	−4.47214	+	3.24920i	−0.290496	+	0.211058i
$238$	−8.65325	−	18.4672i	−0.560907	−	1.19705i
$239$	−4.59017	−	3.33495i	−0.296913	−	0.215720i	0.429347	−	0.903139i	$-0.358744\pi$
$239$	−4.59017	−	3.33495i	−0.296913	−	0.215720i	−0.726261	+	0.687419i	$0.758744\pi$
$240$	−1.26249	+	0.562096i	−0.0814933	+	0.0362832i
$241$	−9.91572	−	4.41476i	−0.638727	−	0.284380i	0.0617094	−	0.998094i	$-0.480345\pi$
$241$	−9.91572	−	4.41476i	−0.638727	−	0.284380i	−0.700437	+	0.713714i	$0.747011\pi$
$242$	3.76988	−	0.801313i	0.242337	−	0.0515103i
$243$	−6.97214	+	12.0761i	−0.447263	+	0.774682i
$244$	2.54508	−	7.83297i	0.162932	−	0.501454i
$245$	−12.2984	+	9.68246i	−0.785714	+	0.618590i
$246$	−1.79180	−	5.51458i	−0.114241	−	0.351597i
$247$	−34.3571	−	7.30282i	−2.18609	−	0.464667i
$248$	−0.507392	+	4.82751i	−0.0322194	+	0.306547i
$249$	1.78115	+	3.08505i	0.112876	+	0.195507i
$250$	10.2137	−	4.54745i	0.645974	−	0.287606i
$251$	31.1803			1.96809			0.984043	−	0.177932i	$-0.0569407\pi$
$251$	31.1803			1.96809			0.984043	+	0.177932i	$0.0569407\pi$
$252$	−5.05705	+	4.73339i	−0.318564	+	0.298176i
$253$	1.75329	+	5.39607i	0.110228	+	0.339248i
$254$	8.80333	+	1.87121i	0.552370	+	0.117410i
$255$	−5.32624	−	9.22531i	−0.333542	−	0.577712i
$256$	−0.978148	+	0.207912i	−0.0611342	+	0.0129945i
$257$	15.0172	−	26.0106i	0.936749	−	1.62250i	0.165263	−	0.986250i	$-0.447153\pi$
$257$	15.0172	−	26.0106i	0.936749	−	1.62250i	0.771486	−	0.636246i	$-0.219514\pi$
$258$	−0.427051	+	1.31433i	−0.0265870	+	0.0818265i
$259$	1.00690	+	0.0862052i	0.0625659	+	0.00535653i
$260$	−10.5902	−	7.69421i	−0.656774	−	0.477175i
$261$	−8.30428	+	3.69731i	−0.514022	+	0.228857i
$262$	6.21062	+	2.76515i	0.383694	+	0.170831i
$263$	−3.00721	−	1.33889i	−0.185432	−	0.0825597i	0.311920	−	0.950108i	$-0.399028\pi$
$263$	−3.00721	−	1.33889i	−0.185432	−	0.0825597i	−0.497353	+	0.867549i	$0.665694\pi$
$264$	−2.17603	+	0.968833i	−0.133926	+	0.0596275i
$265$	0.163119	+	0.502029i	0.0100203	+	0.0308394i
$266$	−9.08103	+	13.0206i	−0.556794	+	0.798341i
$267$	−1.12868	+	3.47371i	−0.0690739	+	0.212588i
$268$	0.500000	−	0.866025i	0.0305424	−	0.0529009i
$269$	−17.9258	+	3.81024i	−1.09295	+	0.232314i	−0.718914	−	0.695099i	$-0.755361\pi$
$269$	−17.9258	+	3.81024i	−1.09295	+	0.232314i	−0.374039	+	0.927413i	$0.622027\pi$
$270$	−5.19508	+	5.76973i	−0.316163	+	0.351134i
$271$	−11.8260	−	2.51369i	−0.718377	−	0.152696i	−0.165802	−	0.986159i	$-0.553021\pi$
$271$	−11.8260	−	2.51369i	−0.718377	−	0.152696i	−0.552575	+	0.833463i	$0.686355\pi$
$272$	−2.38197	−	7.33094i	−0.144428	−	0.444503i
$273$	9.15934	+	2.78167i	0.554349	+	0.168354i
$274$	−2.47214			−0.149347
$275$	17.6045	−	7.83802i	1.06159	−	0.472651i
$276$	−0.454915	−	0.787936i	−0.0273827	−	0.0474282i
$277$	−0.670697	+	6.38126i	−0.0402983	+	0.383413i	0.955721	+	0.294274i	$0.0950780\pi$
$277$	−0.670697	+	6.38126i	−0.0402983	+	0.383413i	−0.996019	+	0.0891382i	$0.971589\pi$
$278$	5.86889	+	1.24747i	0.351992	+	0.0748183i
$279$	3.92705	+	12.0862i	0.235106	+	0.723583i
$280$	−5.06539	+	3.05644i	−0.302715	+	0.182657i
$281$	5.25329	−	16.1680i	0.313385	−	0.964500i	−0.663029	−	0.748594i	$-0.730729\pi$
$281$	5.25329	−	16.1680i	0.313385	−	0.964500i	0.976414	−	0.215906i	$-0.0692705\pi$
$282$	2.85410	−	4.94345i	0.169959	−	0.294378i
$283$	−11.3096	+	2.40394i	−0.672288	+	0.142899i	−0.531393	−	0.847125i	$-0.678331\pi$
$283$	−11.3096	+	2.40394i	−0.672288	+	0.142899i	−0.140895	+	0.990025i	$0.544998\pi$
$284$	14.5658	+	6.48512i	0.864322	+	0.384821i
$285$	−4.14590	+	7.18091i	−0.245582	+	0.425360i
$286$	−18.2533	−	13.2618i	−1.07934	−	0.784186i
$287$	−10.5322	−	22.4771i	−0.621697	−	1.32678i
$288$	−2.11803	+	1.53884i	−0.124806	+	0.0906771i
$289$	38.7493	−	17.2523i	2.27937	−	1.01484i
$290$	−7.59427	+	1.61421i	−0.445951	+	0.0947898i
$291$	−6.34391	−	2.82449i	−0.371886	−	0.165575i
$292$	3.60124	+	3.99958i	0.210747	+	0.234058i
$293$	−1.09017			−0.0636884			−0.0318442	−	0.999493i	$-0.510138\pi$
$293$	−1.09017			−0.0636884			−0.0318442	+	0.999493i	$0.510138\pi$
$294$	2.76850	−	3.32442i	0.161462	−	0.193884i
$295$	−9.63525	+	7.00042i	−0.560986	+	0.407580i
$296$	0.373619	+	0.0794152i	0.0217162	+	0.00461591i
$297$	−8.95428	+	9.94474i	−0.519580	+	0.577052i
$298$	−0.497966	+	4.73783i	−0.0288464	+	0.274455i
$299$	4.30902	−	7.46344i	0.249197	−	0.431622i
$300$	−2.50000	+	1.81636i	−0.144338	+	0.104867i
$301$	−1.11803	+	5.80948i	−0.0644424	+	0.334853i
$302$	14.2533	+	10.3556i	0.820185	+	0.595899i
$303$	−2.84624	−	0.604988i	−0.163512	−	0.0347556i
$304$	−4.01478	+	4.45887i	−0.230264	+	0.255734i
$305$	1.92504	−	18.3155i	0.110227	−	1.04874i
$306$	−13.5033	−	14.9969i	−0.771931	−	0.857317i
$307$	13.1246			0.749061			0.374531	−	0.927215i	$-0.377804\pi$
$307$	13.1246			0.749061			0.374531	+	0.927215i	$0.377804\pi$
$308$	−8.73074	+	5.26809i	−0.497480	+	0.300178i
$309$	−1.47214	+	1.06957i	−0.0837469	+	0.0608457i
$310$	1.13456	+	10.7946i	0.0644388	+	0.613094i
$311$	−0.374587	+	3.56396i	−0.0212409	+	0.202094i	−0.999996	−	0.00294069i	$-0.999064\pi$
$311$	−0.374587	+	3.56396i	−0.0212409	+	0.202094i	0.978755	+	0.205034i	$0.0657306\pi$
$312$	3.30524	+	1.47159i	0.187122	+	0.0833122i
$313$	2.34898	+	22.3490i	0.132772	+	1.26324i	0.834584	+	0.550880i	$0.185708\pi$
$313$	2.34898	+	22.3490i	0.132772	+	1.26324i	−0.701812	+	0.712362i	$0.747626\pi$
$314$	−1.11803	−	0.812299i	−0.0630943	−	0.0458407i
$315$	−8.86022	+	12.7039i	−0.499217	+	0.715786i
$316$	−7.23607	+	5.25731i	−0.407061	+	0.295747i
$317$	17.2252	+	19.1305i	0.967463	+	1.07448i	0.997190	+	0.0749186i	$0.0238697\pi$
$317$	17.2252	+	19.1305i	0.967463	+	1.07448i	−0.0297265	+	0.999558i	$0.509464\pi$
$318$	−0.0729490	−	0.126351i	−0.00409078	−	0.00708543i
$319$	−13.0895	+	2.78227i	−0.732873	+	0.155777i
$320$	−2.04275	+	0.909491i	−0.114193	+	0.0508421i
$321$	−2.97214	−	9.14729i	−0.165888	−	0.510552i
$322$	−2.34980	−	3.10624i	−0.130949	−	0.173104i
$323$	−37.4164	−	27.1846i	−2.08190	−	1.51259i
$324$	−2.85410	+	4.94345i	−0.158561	+	0.274636i
$325$	−26.7399	−	11.9054i	−1.48327	−	0.660392i
$326$	−1.02786	−	1.78031i	−0.0569281	−	0.0986024i
$327$	−0.697887	+	0.310719i	−0.0385932	+	0.0171828i
$328$	−2.89919	−	8.92278i	−0.160081	−	0.492678i
$329$	9.50617	−	22.5115i	0.524092	−	1.24110i
$330$	−4.30902	+	3.13068i	−0.237204	+	0.172338i
$331$	−19.0746	−	21.1845i	−1.04844	−	1.16441i	−0.986066	−	0.166353i	$-0.946801\pi$
$331$	−19.0746	−	21.1845i	−1.04844	−	1.16441i	−0.0623699	−	0.998053i	$-0.519866\pi$
$332$	2.88197	+	4.99171i	0.158168	+	0.273956i
$333$	0.978148	−	0.207912i	0.0536022	−	0.0113935i
$334$	0.0152505	+	0.145099i	0.000834470	+	0.00793945i
$335$	0.690983	−	2.12663i	0.0377524	−	0.116190i
$336$	1.19381	−	1.11740i	0.0651275	−	0.0609593i
$337$	−18.3713	+	13.3475i	−1.00075	+	0.727087i	−0.962249	−	0.272171i	$-0.912258\pi$
$337$	−18.3713	+	13.3475i	−1.00075	+	0.727087i	−0.0385009	+	0.999259i	$0.512258\pi$
$338$	2.22337	+	21.1540i	0.120936	+	1.15063i
$339$	−0.414514	+	3.94383i	−0.0225133	+	0.214200i
$340$	−8.61803	−	14.9269i	−0.467379	−	0.809523i
$341$	1.95554	+	18.6057i	0.105898	+	1.00756i
$342$	−4.85410	+	14.9394i	−0.262480	+	0.807830i
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−0.690983	+	2.12663i	−0.0372553	+	0.114660i
$345$	−1.36131	−	1.51188i	−0.0732903	−	0.0813971i
$346$	6.49606	−	7.21460i	0.349230	−	0.387859i
$347$	−4.96255	+	5.51147i	−0.266403	+	0.295871i	−0.861473	−	0.507803i	$-0.830458\pi$
$347$	−4.96255	+	5.51147i	−0.266403	+	0.295871i	0.595070	+	0.803674i	$0.297124\pi$
$348$	1.96038	−	0.872815i	0.105087	−	0.0467878i
$349$	23.6180			1.26424			0.632122	−	0.774869i	$-0.282184\pi$
$349$	23.6180			1.26424			0.632122	+	0.774869i	$0.282184\pi$
$350$	−9.65810	+	9.03998i	−0.516247	+	0.483207i
$351$	20.3262			1.08493
$352$	−3.52090	+	1.56760i	−0.187664	+	0.0835536i
$353$	−9.39087	+	10.4296i	−0.499826	+	0.555113i	−0.939280	−	0.343152i	$-0.888505\pi$
$353$	−9.39087	+	10.4296i	−0.499826	+	0.555113i	0.439454	+	0.898265i	$0.355172\pi$
$354$	2.20264	−	2.44628i	0.117069	−	0.130018i
$355$	34.8734	+	7.41257i	1.85089	+	0.393418i
$356$	−1.82624	+	5.62058i	−0.0967904	+	0.297890i
$357$	9.52786	+	8.25137i	0.504268	+	0.436709i
$358$	1.78115	−	5.48183i	0.0941369	−	0.289723i
$359$	0.184381	+	1.75427i	0.00973126	+	0.0925868i	0.998310	−	0.0581218i	$-0.0185112\pi$
$359$	0.184381	+	1.75427i	0.00973126	+	0.0925868i	−0.988578	+	0.150709i	$0.951844\pi$
$360$	−3.91716	+	4.35045i	−0.206452	+	0.229289i
$361$	−1.77698	+	16.9069i	−0.0935255	+	0.889835i
$362$	−0.148055	−	1.40865i	−0.00778159	−	0.0740369i
$363$	−1.92705	+	1.40008i	−0.101144	+	0.0734854i
$364$	14.8201	+	4.50083i	0.776786	+	0.235908i
$365$	9.73607	+	7.07367i	0.509609	+	0.370253i
$366$	0.532068	+	5.06229i	0.0278116	+	0.264610i
$367$	32.2244	−	6.84950i	1.68210	−	0.357541i	0.734896	−	0.678179i	$-0.237231\pi$
$367$	32.2244	−	6.84950i	1.68210	−	0.357541i	0.947202	+	0.320639i	$0.103897\pi$
$368$	−0.736068	−	1.27491i	−0.0383702	−	0.0664591i
$369$	−16.4354	−	18.2534i	−0.855592	−	0.950231i
$370$	0.854102			0.0444026
$371$	−0.376807	−	0.498109i	−0.0195629	−	0.0258605i
$372$	−0.927051	−	2.85317i	−0.0480654	−	0.147930i
$373$	−1.50961	+	0.672122i	−0.0781647	+	0.0348012i	−0.445447	−	0.895308i	$-0.646955\pi$
$373$	−1.50961	+	0.672122i	−0.0781647	+	0.0348012i	0.367282	+	0.930110i	$0.380288\pi$
$374$	−14.8541	−	25.7281i	−0.768087	−	1.33037i
$375$	−4.62358	+	5.13500i	−0.238761	+	0.265170i
$376$	4.61803	−	7.99867i	0.238157	−	0.412500i
$377$	16.4443	+	11.9475i	0.846923	+	0.615326i
$378$	3.57368	−	8.46280i	0.183810	−	0.435279i
$379$	−1.87132	−	5.75934i	−0.0961234	−	0.295837i	0.891421	−	0.453175i	$-0.149709\pi$
$379$	−1.87132	−	5.75934i	−0.0961234	−	0.295837i	−0.987545	+	0.157338i	$0.949709\pi$
$380$	−6.70820	+	11.6190i	−0.344124	+	0.596040i
$381$	−5.44076	+	1.15647i	−0.278738	+	0.0592477i
$382$	−7.88197	−	13.6520i	−0.403276	−	0.698495i
$383$	13.3826	+	14.8629i	0.683820	+	0.759459i	0.980713	−	0.195452i	$-0.0626174\pi$
$383$	13.3826	+	14.8629i	0.683820	+	0.759459i	−0.296894	+	0.954911i	$0.595951\pi$
$384$	0.500000	−	0.363271i	0.0255155	−	0.0185381i
$385$	−16.6468	+	15.5814i	−0.848398	+	0.794100i
$386$	19.2533	+	13.9883i	0.979967	+	0.711987i
$387$	0.611920	+	5.82203i	0.0311057	+	0.295951i
$388$	−10.2647	−	4.57012i	−0.521109	−	0.232013i
$389$	0.741125	−	7.05133i	0.0375765	−	0.357517i	−0.959536	−	0.281584i	$-0.909140\pi$
$389$	0.741125	−	7.05133i	0.0375765	−	0.357517i	0.997113	−	0.0759322i	$-0.0241933\pi$
$390$	7.91338	+	1.68204i	0.400710	+	0.0851735i
$391$	9.18034	−	6.66991i	0.464270	−	0.337312i
$392$	4.47953	−	5.37902i	0.226250	−	0.271681i
$393$	−4.20163			−0.211944
$394$	−15.9615	−	17.7271i	−0.804129	−	0.893076i
$395$	−13.3826	+	14.8629i	−0.673352	+	0.747833i
$396$	−6.75164	+	7.49846i	−0.339283	+	0.376812i
$397$	21.1248	+	4.49022i	1.06022	+	0.225357i	0.704842	−	0.709364i	$-0.251018\pi$
$397$	21.1248	+	4.49022i	1.06022	+	0.225357i	0.355381	+	0.934721i	$0.384351\pi$
$398$	−18.1353	−	13.1760i	−0.909038	−	0.660455i
$399$	1.85410	−	9.63420i	0.0928212	−	0.482313i
$400$	−4.04508	+	2.93893i	−0.202254	+	0.146946i
$401$	−10.2361	+	17.7294i	−0.511165	+	0.885363i	0.488751	+	0.872423i	$0.337453\pi$
$401$	−10.2361	+	17.7294i	−0.511165	+	0.885363i	−0.999916	+	0.0129404i	$0.995881\pi$
$402$	−0.0646021	+	0.614648i	−0.00322206	+	0.0306559i
$403$	19.0143	−	21.1175i	0.947169	−	1.05194i
$404$	−4.60532	−	0.978891i	−0.229123	−	0.0487016i
$405$	−3.94427	+	12.1392i	−0.195992	+	0.603203i
$406$	7.86547	−	4.74599i	0.390357	−	0.235540i
$407$	1.47214			0.0729711
$408$	3.18769	+	3.54029i	0.157814	+	0.175271i
$409$	−1.34486	−	0.598772i	−0.0664992	−	0.0296074i	0.373218	−	0.927744i	$-0.378255\pi$
$409$	−1.34486	−	0.598772i	−0.0664992	−	0.0296074i	−0.439717	+	0.898137i	$0.644921\pi$
$410$	−10.4894	−	18.1681i	−0.518032	−	0.897258i
$411$	1.39577	−	0.621438i	0.0688484	−	0.0306533i
$412$	−2.38197	+	1.73060i	−0.117351	+	0.0852605i
$413$	8.06129	−	11.5584i	0.396670	−	0.568753i
$414$	−3.11803	−	2.26538i	−0.153243	−	0.111338i
$415$	8.62412	+	9.57805i	0.423341	+	0.470168i
$416$	5.34799	+	2.38108i	0.262207	+	0.116742i
$417$	−3.62717	+	0.770979i	−0.177623	+	0.0377550i
$418$	−11.5623	+	20.0265i	−0.565531	+	0.979528i
$419$	−3.78115	+	11.6372i	−0.184721	+	0.568514i	−0.999943	−	0.0106345i	$-0.996615\pi$
$419$	−3.78115	+	11.6372i	−0.184721	+	0.568514i	0.815222	+	0.579149i	$0.196615\pi$
$420$	2.09161	−	2.99899i	0.102060	−	0.146336i
$421$	7.44427	+	22.9111i	0.362812	+	1.11662i	0.951340	+	0.308143i	$0.0997075\pi$
$421$	7.44427	+	22.9111i	0.362812	+	1.11662i	−0.588528	+	0.808476i	$0.700293\pi$
$422$	−10.0461	−	2.13536i	−0.489035	−	0.103948i
$423$	2.52753	−	24.0479i	0.122893	−	1.16925i
$424$	−0.118034	−	0.204441i	−0.00573224	−	0.00992853i
$425$	−25.7890	−	28.6416i	−1.25095	−	1.38932i
$426$	−9.85410			−0.477433
$427$	4.94131	+	21.2229i	0.239127	+	1.02705i
$428$	−4.80902	−	14.8006i	−0.232453	−	0.715416i
$429$	13.6396	+	2.89918i	0.658524	+	0.139974i
$430$	−0.522642	+	4.97261i	−0.0252041	+	0.239801i
$431$	26.4437	−	5.62078i	1.27375	−	0.270743i	0.479070	−	0.877776i	$-0.340974\pi$
$431$	26.4437	−	5.62078i	1.27375	−	0.270743i	0.794677	+	0.607033i	$0.207640\pi$
$432$	1.73607	−	3.00696i	0.0835266	−	0.144672i
$433$	7.01722	−	21.5968i	0.337226	−	1.03788i	−0.628389	−	0.777899i	$-0.716285\pi$
$433$	7.01722	−	21.5968i	0.337226	−	1.03788i	0.965615	−	0.259976i	$-0.0837146\pi$
$434$	−5.44923	−	11.6294i	−0.261571	−	0.558227i
$435$	3.88197	−	2.82041i	0.186126	−	0.135228i
$436$	−1.12920	+	0.502754i	−0.0540791	+	0.0240776i
$437$	−8.06918	−	3.59263i	−0.386001	−	0.171859i
$438$	−3.03867	−	1.35290i	−0.145193	−	0.0646442i
$439$	3.60327	−	1.60428i	0.171975	−	0.0765681i	−0.318944	−	0.947774i	$-0.603328\pi$
$439$	3.60327	−	1.60428i	0.171975	−	0.0765681i	0.490918	+	0.871206i	$0.336661\pi$
$440$	−6.97214	+	5.06555i	−0.332384	+	0.241491i
$441$	4.98581	−	17.6350i	0.237419	−	0.839761i
$442$	−13.9443	+	42.9161i	−0.663261	+	2.04131i
$443$	−1.57295	+	2.72443i	−0.0747331	+	0.129441i	−0.900970	−	0.433881i	$-0.857144\pi$
$443$	−1.57295	+	2.72443i	−0.0747331	+	0.129441i	0.826237	+	0.563323i	$0.190477\pi$
$444$	−0.230909	+	0.0490813i	−0.0109585	+	0.00232930i
$445$	−1.38132	+	13.1424i	−0.0654809	+	0.623009i
$446$	10.3860	+	2.20761i	0.491792	+	0.104534i
$447$	−0.909830	−	2.80017i	−0.0430335	−	0.132443i
$448$	1.93162	−	1.80800i	0.0912604	−	0.0854197i
$449$	4.96556			0.234339			0.117170	−	0.993112i	$-0.462618\pi$
$449$	4.96556			0.234339			0.117170	+	0.993112i	$0.462618\pi$
$450$	−6.54508	+	11.3364i	−0.308538	+	0.534404i
$451$	−18.0795	−	31.3147i	−0.851332	−	1.47455i
$452$	−0.670697	+	6.38126i	−0.0315469	+	0.300149i
$453$	−10.6506	−	2.26386i	−0.500409	−	0.106365i
$454$	6.16312	+	18.9681i	0.289250	+	0.890218i
$455$	34.5071	+	2.95429i	1.61772	+	0.138499i
$456$	1.14590	−	3.52671i	0.0536616	−	0.165153i
$457$	5.38197	−	9.32184i	0.251758	−	0.436057i	−0.712252	−	0.701924i	$-0.752325\pi$
$457$	5.38197	−	9.32184i	0.251758	−	0.436057i	0.964010	+	0.265867i	$0.0856580\pi$
$458$	12.0569	−	2.56277i	0.563381	−	0.119750i
$459$	24.4501	+	10.8859i	1.14123	+	0.508109i
$460$	−2.20264	−	2.44628i	−0.102699	−	0.114058i
$461$	−28.3713	−	20.6130i	−1.32138	−	0.960042i	−0.999914	−	0.0131222i	$-0.995823\pi$
$461$	−28.3713	−	20.6130i	−1.32138	−	0.960042i	−0.321470	−	0.946920i	$-0.604177\pi$
$462$	3.60512	−	5.16909i	0.167725	−	0.240488i
$463$	−9.51722	+	6.91467i	−0.442303	+	0.321352i	−0.786549	−	0.617528i	$-0.788134\pi$
$463$	−9.51722	+	6.91467i	−0.442303	+	0.321352i	0.344246	+	0.938879i	$0.388134\pi$
$464$	3.17195	−	1.41224i	0.147254	−	0.0655618i
$465$	−3.35410	−	5.80948i	−0.155543	−	0.269408i
$466$	23.5995	+	10.5072i	1.09322	+	0.486734i
$467$	−3.32261	−	3.69013i	−0.153752	−	0.170759i	0.661348	−	0.750079i	$-0.269985\pi$
$467$	−3.32261	−	3.69013i	−0.153752	−	0.170759i	−0.815100	+	0.579320i	$0.803318\pi$
$468$	15.3262			0.708456
$469$	0.0510966	+	2.64526i	0.00235942	+	0.122147i
$470$	6.38197	−	19.6417i	0.294378	−	0.906003i
$471$	0.835438	+	0.177578i	0.0384949	+	0.00818235i
$472$	3.56395	−	3.95817i	0.164044	−	0.182189i
$473$	−0.900830	+	8.57082i	−0.0414202	+	0.394087i
$474$	2.76393	−	4.78727i	0.126952	−	0.219887i
$475$	−9.27051	+	28.5317i	−0.425360	+	1.30912i
$476$	15.4164	+	13.3510i	0.706610	+	0.611942i
$477$	−0.500000	−	0.363271i	−0.0228934	−	0.0166330i
$478$	5.54978	+	1.17964i	0.253841	+	0.0539555i
$479$	3.81953	−	4.24202i	0.174519	−	0.193823i	−0.649539	−	0.760328i	$-0.725038\pi$
$479$	3.81953	−	4.24202i	0.174519	−	0.193823i	0.824058	+	0.566505i	$0.191705\pi$
$480$	0.924716	−	1.02700i	0.0422073	−	0.0468760i
$481$	−1.49622	−	1.66172i	−0.0682218	−	0.0757680i
$482$	10.8541			0.494391
$483$	2.10754	+	1.16311i	0.0958963	+	0.0529232i
$484$	−3.11803	+	2.26538i	−0.141729	+	0.102972i
$485$	−24.5756	−	5.22370i	−1.11592	−	0.237196i
$486$	1.45757	−	13.8679i	0.0661169	−	0.629060i
$487$	37.0870	+	16.5122i	1.68057	+	0.748239i	0.999877	+	0.0156707i	$0.00498834\pi$
$487$	37.0870	+	16.5122i	1.68057	+	0.748239i	0.680694	+	0.732568i	$0.261678\pi$
$488$	0.860904	+	8.19095i	0.0389713	+	0.370787i
$489$	1.02786	+	0.746787i	0.0464816	+	0.0337709i
$490$	7.29691	−	13.8476i	0.329641	−	0.625569i
$491$	17.1074	−	12.4292i	0.772046	−	0.560924i	−0.130536	−	0.991444i	$-0.541670\pi$
$491$	17.1074	−	12.4292i	0.772046	−	0.560924i	0.902581	+	0.430520i	$0.141670\pi$
$492$	3.87987	+	4.30903i	0.174918	+	0.194266i
$493$	13.3820	+	23.1782i	0.602693	+	1.04390i
$494$	34.3571	−	7.30282i	1.54580	−	0.328569i
$495$	−11.2812	+	19.5395i	−0.507050	+	0.878237i
$496$	−1.50000	−	4.61653i	−0.0673520	−	0.207288i
$497$	−41.8605	+	5.21890i	−1.87770	+	0.234100i
$498$	−2.88197	−	2.09387i	−0.129144	−	0.0938286i
$499$	−6.00000	+	10.3923i	−0.268597	+	0.465223i	−0.968500	−	0.249015i	$-0.919893\pi$
$499$	−6.00000	+	10.3923i	−0.268597	+	0.465223i	0.699903	+	0.714238i	$0.253227\pi$
$500$	−7.48111	+	8.30861i	−0.334565	+	0.371572i
$501$	−0.0450850	−	0.0780895i	−0.00201425	−	0.00348878i
$502$	−28.4847	+	12.6822i	−1.27133	+	0.566034i
$503$	−5.70820	−	17.5680i	−0.254516	−	0.783320i	−0.993925	−	0.110063i	$-0.964895\pi$
$503$	−5.70820	−	17.5680i	−0.254516	−	0.783320i	0.739408	−	0.673257i	$-0.235105\pi$
$504$	2.69460	−	6.38106i	0.120027	−	0.284235i
$505$	−10.5279			−0.468484
$506$	−3.79649	−	4.21643i	−0.168774	−	0.187443i
$507$	−6.57295	−	11.3847i	−0.291915	−	0.505611i
$508$	−8.80333	+	1.87121i	−0.390585	+	0.0830213i
$509$	0.575594	+	5.47641i	0.0255128	+	0.242738i	0.999845	+	0.0176217i	$0.00560945\pi$
$509$	0.575594	+	5.47641i	0.0255128	+	0.242738i	−0.974332	+	0.225116i	$0.927724\pi$
$510$	8.61803	+	6.26137i	0.381613	+	0.277258i
$511$	−13.6249	−	4.13784i	−0.602729	−	0.183047i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−2.17762	−	20.7187i	−0.0961444	−	0.914753i
$514$	−3.13945	+	29.8699i	−0.138475	+	1.31751i
$515$	−4.40528	+	4.89256i	−0.194120	+	0.215592i
$516$	−0.144455	−	1.37440i	−0.00635927	−	0.0605044i
$517$	11.0000	−	33.8545i	0.483779	−	1.48892i
$518$	−0.954915	+	0.330792i	−0.0419566	+	0.0145342i
$519$	−1.85410	+	5.70634i	−0.0813860	+	0.250480i
$520$	12.8041	+	2.72160i	0.561498	+	0.119350i
$521$	−13.7962	+	15.3222i	−0.604421	+	0.671277i	−0.965242	−	0.261358i	$-0.915830\pi$
$521$	−13.7962	+	15.3222i	−0.604421	+	0.671277i	0.360821	+	0.932635i	$0.382496\pi$
$522$	6.08251	−	6.75531i	0.266224	−	0.295672i
$523$	9.61768	−	4.28207i	0.420552	−	0.187242i	−0.185539	−	0.982637i	$-0.559403\pi$
$523$	9.61768	−	4.28207i	0.420552	−	0.187242i	0.606091	+	0.795395i	$0.292737\pi$
$524$	−6.79837			−0.296988
$525$	3.18054	−	7.53181i	0.138810	−	0.328715i
$526$	3.29180			0.143529
$527$	34.1816	−	15.2186i	1.48897	−	0.662934i
$528$	1.59385	−	1.77015i	0.0693633	−	0.0770357i
$529$	−13.9399	+	15.4818i	−0.606082	+	0.673122i
$530$	−0.353210	−	0.392279i	−0.0153425	−	0.0170395i
$531$	4.30902	−	13.2618i	0.186995	−	0.575513i
$532$	3.00000	−	15.5885i	0.130066	−	0.675845i
$533$	−16.9721	+	52.2349i	−0.735145	+	2.26254i
$534$	−0.381788	−	3.63247i	−0.0165216	−	0.157192i
$535$	−17.3992	−	30.1363i	−0.752232	−	1.30290i
$536$	−0.104528	+	0.994522i	−0.00451494	+	0.0429568i
$537$	0.372362	+	3.54279i	0.0160686	+	0.152883i
$538$	14.8262	−	10.7719i	0.639205	−	0.464409i
$539$	12.5770	−	23.8678i	0.541730	−	1.02806i
$540$	2.39919	−	7.38394i	0.103245	−	0.317754i
$541$	2.53336	+	24.1033i	0.108918	+	1.03628i	0.903343	+	0.428920i	$0.141106\pi$
$541$	2.53336	+	24.1033i	0.108918	+	1.03628i	−0.794425	+	0.607362i	$0.792228\pi$
$542$	11.8260	−	2.51369i	0.507969	−	0.107972i
$543$	0.437694	+	0.758108i	0.0187833	+	0.0325335i
$544$	5.15780	+	5.72831i	0.221139	+	0.245599i
$545$	−2.23607	+	1.62460i	−0.0957826	+	0.0695902i
$546$	−9.49888	+	1.18426i	−0.406515	+	0.0506817i
$547$	−3.50658	−	10.7921i	−0.149930	−	0.461438i	0.847682	−	0.530505i	$-0.177998\pi$
$547$	−3.50658	−	10.7921i	−0.149930	−	0.461438i	−0.997612	+	0.0690669i	$0.977998\pi$
$548$	2.25841	−	1.00551i	0.0964744	−	0.0429532i
$549$	10.7812	+	18.6735i	0.460128	+	0.796966i
$550$	−12.8945	+	14.3208i	−0.549823	+	0.610640i
$551$	10.4164	−	18.0417i	0.443754	−	0.768604i
$552$	0.736068	+	0.534785i	0.0313291	+	0.0227619i
$553$	9.20584	−	21.8003i	0.391472	−	0.927042i
$554$	−1.98278	−	6.10237i	−0.0842402	−	0.259265i
$555$	−0.482228	+	0.214702i	−0.0204694	+	0.00911358i
$556$	−5.86889	+	1.24747i	−0.248896	+	0.0529045i
$557$	−2.90983	−	5.03997i	−0.123293	−	0.213551i	0.797771	−	0.602960i	$-0.206012\pi$
$557$	−2.90983	−	5.03997i	−0.123293	−	0.213551i	−0.921065	+	0.389410i	$0.872679\pi$
$558$	−8.50345	−	9.44404i	−0.359980	−	0.399798i
$559$	10.5902	−	7.69421i	0.447916	−	0.325430i
$560$	3.38430	−	4.85247i	0.143013	−	0.205054i
$561$	14.8541	+	10.7921i	0.627141	+	0.455644i
$562$	1.77698	+	16.9069i	0.0749575	+	0.713173i
$563$	−3.75600	−	1.67228i	−0.158297	−	0.0704782i	0.326059	−	0.945349i	$-0.394279\pi$
$563$	−3.75600	−	1.67228i	−0.158297	−	0.0704782i	−0.484356	+	0.874871i	$0.660946\pi$
$564$	−0.596670	+	5.67693i	−0.0251243	+	0.239042i
$565$	1.49972	+	14.2689i	0.0630939	+	0.600298i
$566$	9.35410	−	6.79615i	0.393182	−	0.285664i
$567$	−0.291670	−	15.0997i	−0.0122490	−	0.634127i
$568$	−15.9443			−0.669007
$569$	17.5784	+	19.5228i	0.736925	+	0.818438i	0.988788	−	0.149325i	$-0.0477100\pi$
$569$	17.5784	+	19.5228i	0.736925	+	0.818438i	−0.251863	+	0.967763i	$0.581043\pi$
$570$	0.866729	−	8.24637i	0.0363033	−	0.345403i
$571$	−6.77469	+	7.52405i	−0.283512	+	0.314872i	−0.868033	−	0.496507i	$-0.834616\pi$
$571$	−6.77469	+	7.52405i	−0.283512	+	0.314872i	0.584521	+	0.811379i	$0.301282\pi$
$572$	22.0693	+	4.69097i	0.922762	+	0.196139i
$573$	7.88197	+	5.72658i	0.329274	+	0.239231i
$574$	18.7639	+	16.2500i	0.783191	+	0.678264i
$575$	−5.95492	−	4.32650i	−0.248337	−	0.180427i
$576$	1.30902	−	2.26728i	0.0545424	−	0.0944702i
$577$	0.811552	−	7.72140i	0.0337853	−	0.321446i	−0.964556	−	0.263877i	$-0.914999\pi$
$577$	0.811552	−	7.72140i	0.0337853	−	0.321446i	0.998342	−	0.0575686i	$-0.0183348\pi$
$578$	−28.3821	+	31.5215i	−1.18054	+	1.31112i
$579$	−14.3868	−	3.05801i	−0.597895	−	0.127086i
$580$	6.28115	−	4.56352i	0.260811	−	0.189490i
$581$	−13.3516	−	7.36848i	−0.553919	−	0.305696i
$582$	6.94427			0.287849
$583$	−0.608795	−	0.676135i	−0.0252137	−	0.0280027i
$584$	−4.91667	−	2.18904i	−0.203453	−	0.0905832i
$585$	33.5216	−	7.12524i	1.38595	−	0.294592i
$586$	0.995920	−	0.443412i	0.0411411	−	0.0183172i
$587$	12.2082	−	8.86978i	0.503887	−	0.366095i	−0.306613	−	0.951834i	$-0.599196\pi$
$587$	12.2082	−	8.86978i	0.503887	−	0.366095i	0.810500	+	0.585739i	$0.199196\pi$
$588$	−1.17699	+	4.16306i	−0.0485382	+	0.171682i
$589$	−23.5623	−	17.1190i	−0.970868	−	0.705377i
$590$	5.95492	−	10.3142i	0.245160	−	0.424630i
$591$	13.4681	+	5.99637i	0.554003	+	0.246658i
$592$	−0.373619	+	0.0794152i	−0.0153557	+	0.00326394i
$593$	−1.55573	+	2.69460i	−0.0638861	+	0.110654i	−0.896199	−	0.443652i	$-0.853683\pi$
$593$	−1.55573	+	2.69460i	−0.0638861	+	0.110654i	0.832313	+	0.554306i	$0.187016\pi$
$594$	4.13525	−	12.7270i	0.169672	−	0.522195i
$595$	39.9258	+	22.0342i	1.63680	+	0.903315i
$596$	−1.47214	−	4.53077i	−0.0603010	−	0.185588i
$597$	13.5514	+	2.88043i	0.554620	+	0.117888i
$598$	−0.900830	+	8.57082i	−0.0368377	+	0.350487i
$599$	−2.05573	−	3.56063i	−0.0839948	−	0.145483i	0.820968	−	0.570975i	$-0.193435\pi$
$599$	−2.05573	−	3.56063i	−0.0839948	−	0.145483i	−0.904962	+	0.425491i	$0.860101\pi$
$600$	1.54508	−	2.67617i	0.0630778	−	0.109254i
$601$	2.85410			0.116421			0.0582106	−	0.998304i	$-0.481461\pi$
$601$	2.85410			0.116421			0.0582106	+	0.998304i	$0.481461\pi$
$602$	−1.34155	−	5.76196i	−0.0546776	−	0.234840i
$603$	0.809017	+	2.48990i	0.0329457	+	0.101396i
$604$	−17.2330	−	3.66300i	−0.701202	−	0.149045i
$605$	−5.76659	+	6.40445i	−0.234445	+	0.260378i
$606$	2.84624	−	0.604988i	0.115621	−	0.0245759i
$607$	5.39919	−	9.35167i	0.219146	−	0.379572i	−0.735401	−	0.677632i	$-0.763006\pi$
$607$	5.39919	−	9.35167i	0.219146	−	0.379572i	0.954547	+	0.298060i	$0.0963395\pi$
$608$	1.85410	−	5.70634i	0.0751938	−	0.231423i
$609$	−3.24783	+	4.65680i	−0.131609	+	0.188703i
$610$	5.69098	+	17.5150i	0.230421	+	0.709163i
$611$	−49.3944	+	21.9918i	−1.99828	+	0.889693i
$612$	18.4357	+	8.20808i	0.745217	+	0.331792i
$613$	11.8761	+	5.28758i	0.479671	+	0.213563i	0.632305	−	0.774720i	$-0.282109\pi$
$613$	11.8761	+	5.28758i	0.479671	+	0.213563i	−0.152634	+	0.988283i	$0.548776\pi$
$614$	−11.9899	+	5.33826i	−0.483874	+	0.215435i
$615$	10.4894	+	7.62096i	0.422972	+	0.307307i
$616$	5.83320	−	8.36376i	0.235027	−	0.336985i
$617$	−9.12461	+	28.0827i	−0.367343	+	1.13057i	0.581158	+	0.813791i	$0.302600\pi$
$617$	−9.12461	+	28.0827i	−0.367343	+	1.13057i	−0.948501	+	0.316775i	$0.897400\pi$
$618$	0.909830	−	1.57587i	0.0365987	−	0.0633909i
$619$	−32.0271	+	6.80758i	−1.28728	+	0.273620i	−0.800198	−	0.599737i	$-0.795272\pi$
$619$	−32.0271	+	6.80758i	−1.28728	+	0.273620i	−0.487082	+	0.873356i	$0.661939\pi$
$620$	−5.42705	−	9.39993i	−0.217956	−	0.377510i
$621$	4.99976	+	1.06273i	0.200633	+	0.0426459i
$622$	−1.10739	−	3.40820i	−0.0444023	−	0.136656i
$623$	−3.54566	−	15.2286i	−0.142054	−	0.610122i
$624$	−3.61803			−0.144837
$625$	−12.5000	+	21.6506i	−0.500000	+	0.866025i
$626$	−11.2361	−	19.4614i	−0.449084	−	0.777836i
$627$	1.49390	−	14.2135i	0.0596606	−	0.567633i
$628$	1.35177	+	0.287327i	0.0539414	+	0.0114656i
$629$	−0.909830	−	2.80017i	−0.0362773	−	0.111650i
$630$	2.92705	−	15.2094i	0.116617	−	0.605957i
$631$	−8.10081	+	24.9317i	−0.322488	+	0.992517i	0.650073	+	0.759871i	$0.274738\pi$
$631$	−8.10081	+	24.9317i	−0.322488	+	0.992517i	−0.972562	+	0.232645i	$0.925262\pi$
$632$	4.47214	−	7.74597i	0.177892	−	0.308118i
$633$	6.20882	−	1.31972i	0.246778	−	0.0524543i
$634$	−23.5171	−	10.4705i	−0.933982	−	0.415836i
$635$	−18.3847	+	8.18542i	−0.729576	+	0.324828i
$636$	0.118034	+	0.0857567i	0.00468035	+	0.00340047i
$637$	−39.7243	+	10.0615i	−1.57393	+	0.398653i
$638$	10.8262	−	7.86572i	0.428615	−	0.311407i
$639$	−38.1338	+	16.9783i	−1.50855	+	0.671650i
$640$	1.49622	−	1.66172i	0.0591433	−	0.0656853i
$641$	−12.8526	−	5.72233i	−0.507646	−	0.226018i	0.136899	−	0.990585i	$-0.456286\pi$
$641$	−12.8526	−	5.72233i	−0.507646	−	0.226018i	−0.644545	+	0.764567i	$0.722953\pi$
$642$	6.43572	+	7.14759i	0.253998	+	0.282093i
$643$	−11.9443			−0.471036			−0.235518	−	0.971870i	$-0.575679\pi$
$643$	−11.9443			−0.471036			−0.235518	+	0.971870i	$0.575679\pi$
$644$	3.41007	+	1.88195i	0.134376	+	0.0741591i
$645$	−0.954915	−	2.93893i	−0.0375997	−	0.115720i
$646$	45.2386	+	9.61575i	1.77989	+	0.378327i
$647$	8.01532	−	8.90192i	0.315115	−	0.349971i	−0.564692	−	0.825302i	$-0.691005\pi$
$647$	8.01532	−	8.90192i	0.315115	−	0.349971i	0.879807	+	0.475331i	$0.157672\pi$
$648$	0.596670	−	5.67693i	0.0234394	−	0.223011i
$649$	10.2639	−	17.7777i	0.402895	−	0.697834i
$650$	29.2705			1.14808
$651$	6.00000	+	5.19615i	0.235159	+	0.203653i
$652$	1.66312	+	1.20833i	0.0651328	+	0.0473217i
$653$	44.7976	+	9.52202i	1.75306	+	0.372625i	0.968808	−	0.247812i	$-0.0797115\pi$
$653$	44.7976	+	9.52202i	1.75306	+	0.372625i	0.784256	+	0.620437i	$0.213045\pi$
$654$	0.511170	−	0.567712i	0.0199883	−	0.0221993i
$655$	−14.8694	+	3.16060i	−0.580997	+	0.123495i
$656$	6.27776	+	6.97216i	0.245105	+	0.272217i
$657$	−14.0902			−0.549710
$658$	0.471932	+	24.4318i	0.0183978	+	0.952450i
$659$	13.1074	−	9.52308i	0.510591	−	0.370966i	−0.302456	−	0.953163i	$-0.597807\pi$
$659$	13.1074	−	9.52308i	0.510591	−	0.370966i	0.813048	+	0.582197i	$0.197807\pi$
$660$	2.66312	−	4.61266i	0.103662	−	0.179547i
$661$	−0.260634	+	2.47976i	−0.0101375	+	0.0964516i	−0.998421	−	0.0561797i	$-0.982108\pi$
$661$	−0.260634	+	2.47976i	−0.0101375	+	0.0964516i	0.988283	+	0.152631i	$0.0487747\pi$
$662$	26.0421	+	11.5947i	1.01215	+	0.450640i
$663$	−2.91515	−	27.7358i	−0.113215	−	1.07717i
$664$	−4.66312	−	3.38795i	−0.180964	−	0.131478i
$665$	−0.685533	−	35.4899i	−0.0265838	−	1.37624i
$666$	−0.809017	+	0.587785i	−0.0313488	+	0.0227762i
$667$	3.42023	+	3.79855i	0.132432	+	0.147081i
$668$	−0.0729490	−	0.126351i	−0.00282248	−	0.00488868i
$669$	−6.41890	+	1.36438i	−0.248169	+	0.0527500i
$670$	0.233733	+	2.22382i	0.00902988	+	0.0859136i
$671$	9.80902	+	30.1891i	0.378673	+	1.16544i
$672$	−0.636108	+	1.50636i	−0.0245384	+	0.0581092i
$673$	30.6074	+	22.2376i	1.17983	+	0.857195i	0.992152	−	0.125036i	$-0.0399045\pi$
$673$	30.6074	+	22.2376i	1.17983	+	0.857195i	0.187676	+	0.982231i	$0.439905\pi$
$674$	11.3541	−	19.6659i	0.437344	−	0.757501i
$675$	1.81469	−	17.2656i	0.0698473	−	0.664552i
$676$	−10.6353	−	18.4208i	−0.409048	−	0.708492i
$677$	−9.40202	+	4.18605i	−0.361349	+	0.160883i	−0.579377	−	0.815059i	$-0.696704\pi$
$677$	−9.40202	+	4.18605i	−0.361349	+	0.160883i	0.218028	+	0.975942i	$0.430038\pi$
$678$	−1.22542	−	3.77147i	−0.0470622	−	0.144842i
$679$	29.4995	−	3.67781i	1.13209	−	0.141141i
$680$	13.9443	+	10.1311i	0.534738	+	0.388510i
$681$	−8.24786	−	9.16018i	−0.316059	−	0.351019i
$682$	−9.35410	−	16.2018i	−0.358187	−	0.620398i
$683$	−3.11084	+	0.661230i	−0.119033	+	0.0253013i	−0.267043	−	0.963685i	$-0.586047\pi$
$683$	−3.11084	+	0.661230i	−0.119033	+	0.0253013i	0.148010	+	0.988986i	$0.452713\pi$
$684$	−1.64195	−	15.6222i	−0.0627817	−	0.597328i
$685$	4.47214	−	3.24920i	0.170872	−	0.124145i
$686$	−2.79506	+	18.3081i	−0.106716	+	0.699008i
$687$	−6.16312	+	4.47777i	−0.235138	+	0.170838i
$688$	−0.233733	−	2.22382i	−0.00891098	−	0.0847823i
$689$	−0.144455	+	1.37440i	−0.00550329	+	0.0523603i
$690$	1.85856	+	0.827482i	0.0707540	+	0.0315017i
$691$	−1.34362	−	12.7837i	−0.0511137	−	0.486314i	−0.989895	−	0.141801i	$-0.954711\pi$
$691$	−1.34362	−	12.7837i	−0.0511137	−	0.486314i	0.938781	−	0.344513i	$-0.111956\pi$
$692$	−3.00000	+	9.23305i	−0.114043	+	0.350988i
$693$	5.04508	−	26.2150i	0.191647	−	0.995827i
$694$	2.29180	−	7.05342i	0.0869954	−	0.267744i
$695$	−12.2565	+	5.45694i	−0.464915	+	0.206994i
$696$	−1.43589	+	1.59471i	−0.0544271	+	0.0604474i
$697$	−48.3903	+	53.7428i	−1.83291	+	2.03565i
$698$	−21.5761	+	9.60632i	−0.816669	+	0.363605i
$699$	−15.9656			−0.603873
$700$	5.14622	−	12.1867i	0.194509	−	0.460615i
$701$	−35.0132			−1.32243			−0.661214	−	0.750197i	$-0.729959\pi$
$701$	−35.0132			−1.32243			−0.661214	+	0.750197i	$0.729959\pi$
$702$	−18.5689	+	8.26743i	−0.700840	+	0.312034i
$703$	−1.53351	+	1.70314i	−0.0578375	+	0.0642350i
$704$	2.57890	−	2.86416i	0.0971959	−	0.107947i
$705$	1.33419	+	12.6940i	0.0502487	+	0.478084i
$706$	4.33688	−	13.3475i	0.163221	−	0.502342i
$707$	11.7705	−	4.07742i	0.442676	−	0.153347i
$708$	−1.01722	+	3.13068i	−0.0382295	+	0.117658i
$709$	3.59749	+	34.2279i	0.135107	+	1.28545i	0.826484	+	0.562961i	$0.190338\pi$
$709$	3.59749	+	34.2279i	0.135107	+	1.28545i	−0.691377	+	0.722494i	$0.742996\pi$
$710$	−34.8734	+	7.41257i	−1.30877	+	0.278189i
$711$	2.44768	−	23.2881i	0.0917952	−	0.873373i
$712$	−0.617745	−	5.87746i	−0.0231510	−	0.220267i
$713$	5.78115	−	4.20025i	0.216506	−	0.157301i
$714$	−12.0603	−	3.66267i	−0.451344	−	0.137072i
$715$	50.4508			1.88675
$716$	0.602495	+	5.73236i	0.0225163	+	0.214228i
$717$	−3.42995	+	0.729059i	−0.128094	+	0.0272272i
$718$	−0.881966	−	1.52761i	−0.0329147	−	0.0570099i
$719$	17.3371	+	19.2548i	0.646563	+	0.718081i	0.973938	−	0.226813i	$-0.0728307\pi$
$719$	17.3371	+	19.2548i	0.646563	+	0.718081i	−0.327375	+	0.944894i	$0.606164\pi$
$720$	1.80902	−	5.56758i	0.0674181	−	0.207492i
$721$	3.03037	−	7.17621i	0.112857	−	0.267256i
$722$	−5.25329	−	16.1680i	−0.195507	−	0.601709i
$723$	−6.12825	+	2.72847i	−0.227912	+	0.101473i
$724$	0.708204	+	1.22665i	0.0263202	+	0.0455879i
$725$	11.6166	−	12.9015i	0.431428	−	0.479150i
$726$	1.19098	−	2.06284i	0.0442015	−	0.0765593i
$727$	−27.4164	−	19.9192i	−1.01682	−	0.738762i	−0.0511901	−	0.998689i	$-0.516301\pi$
$727$	−27.4164	−	19.9192i	−1.01682	−	0.738762i	−0.965628	+	0.259927i	$0.916301\pi$
$728$	−15.3695	+	1.91617i	−0.569632	+	0.0710181i
$729$	−2.62868	−	8.09024i	−0.0973584	−	0.299638i
$730$	−11.7715	−	2.50210i	−0.435681	−	0.0926069i
$731$	16.8594	−	3.58358i	0.623568	−	0.132543i
$732$	−2.54508	−	4.40822i	−0.0940690	−	0.162932i
$733$	0.864380	+	0.959992i	0.0319266	+	0.0354581i	0.758897	−	0.651211i	$-0.225739\pi$
$733$	0.864380	+	0.959992i	0.0319266	+	0.0354581i	−0.726970	+	0.686669i	$0.759072\pi$
$734$	−26.6525	+	19.3642i	−0.983761	+	0.714744i
$735$	−0.638892	+	9.65264i	−0.0235659	+	0.356043i
$736$	1.19098	+	0.865300i	0.0439002	+	0.0318954i
$737$	0.402863	+	3.83299i	0.0148397	+	0.141190i
$738$	22.4388	+	9.99039i	0.825983	+	0.367751i
$739$	3.42614	−	32.5975i	0.126033	−	1.19912i	−0.730458	−	0.682957i	$-0.760693\pi$
$739$	3.42614	−	32.5975i	0.126033	−	1.19912i	0.856491	−	0.516162i	$-0.172640\pi$
$740$	−0.780261	+	0.347395i	−0.0286830	+	0.0127705i
$741$	−17.5623	+	12.7598i	−0.645167	+	0.468742i
$742$	0.546830	+	0.301784i	0.0200748	+	0.0110788i
$743$	−36.2361			−1.32937			−0.664686	−	0.747123i	$-0.731435\pi$
$743$	−36.2361			−1.32937			−0.664686	+	0.747123i	$0.731435\pi$
$744$	2.00739	+	2.22943i	0.0735946	+	0.0817350i
$745$	−5.32624	−	9.22531i	−0.195138	−	0.337989i
$746$	1.10572	−	1.22803i	0.0404834	−	0.0449613i
$747$	−14.7604	−	3.13742i	−0.540055	−	0.114792i
$748$	24.0344	+	17.4620i	0.878786	+	0.638476i
$749$	31.1246	+	26.9547i	1.13727	+	0.984903i
$750$	2.13525	−	6.57164i	0.0779685	−	0.239962i
$751$	−16.2533	+	28.1515i	−0.593091	+	1.02726i	0.400722	+	0.916200i	$0.368759\pi$
$751$	−16.2533	+	28.1515i	−0.593091	+	1.02726i	−0.993813	+	0.111064i	$0.964574\pi$
$752$	−0.965432	+	9.18547i	−0.0352057	+	0.334960i
$753$	12.8945	−	14.3208i	0.469901	−	0.521878i
$754$	−19.8821	−	4.22606i	−0.724062	−	0.153904i
$755$	−39.3951			−1.43374
$756$	0.177414	+	9.18469i	0.00645250	+	0.334044i
$757$	14.2016			0.516167			0.258083	−	0.966123i	$-0.416909\pi$
$757$	14.2016			0.516167			0.258083	+	0.966123i	$0.416909\pi$
$758$	4.05207	+	4.50028i	0.147178	+	0.163458i
$759$	3.20342	+	1.42625i	0.116277	+	0.0517697i
$760$	1.40240	−	13.3429i	0.0508703	−	0.483998i
$761$	10.7469	−	4.78482i	0.389574	−	0.173450i	−0.202596	−	0.979262i	$-0.564938\pi$
$761$	10.7469	−	4.78482i	0.389574	−	0.173450i	0.592170	+	0.805813i	$0.298271\pi$
$762$	4.50000	−	3.26944i	0.163018	−	0.118439i
$763$	1.87080	−	2.68238i	0.0677274	−	0.0971087i
$764$	12.7533	+	9.26581i	0.461398	+	0.335225i
$765$	44.1385	+	9.38193i	1.59583	+	0.339205i
$766$	−18.2709	−	8.13473i	−0.660155	−	0.293920i
$767$	−30.4990	+	6.48276i	−1.10125	+	0.234079i
$768$	−0.309017	+	0.535233i	−0.0111507	+	0.0193136i
$769$	−2.12868	+	6.55139i	−0.0767621	+	0.236249i	−0.982073	−	0.188500i	$-0.939638\pi$
$769$	−2.12868	+	6.55139i	−0.0767621	+	0.236249i	0.905311	+	0.424749i	$0.139638\pi$
$770$	8.87006	−	21.0051i	0.319655	−	0.756972i
$771$	−5.73607	−	17.6538i	−0.206579	−	0.635786i
$772$	−23.2783	−	4.94796i	−0.837805	−	0.178081i
$773$	−2.88825	+	27.4798i	−0.103883	+	0.988381i	0.811105	+	0.584900i	$0.198866\pi$
$773$	−2.88825	+	27.4798i	−0.103883	+	0.988381i	−0.914988	+	0.403480i	$0.867800\pi$
$774$	−2.92705	−	5.06980i	−0.105211	−	0.182230i
$775$	−16.2401	−	18.0365i	−0.583363	−	0.647890i
$776$	11.2361			0.403351
$777$	0.455993	−	0.426810i	0.0163587	−	0.0153117i
$778$	2.19098	+	6.74315i	0.0785505	+	0.241754i
$779$	55.0617	+	11.7037i	1.97279	+	0.419329i
$780$	−7.91338	+	1.68204i	−0.283344	+	0.0602267i
$781$	−60.1080	+	12.7764i	−2.15083	+	0.457174i
$782$	−5.67376	+	9.82724i	−0.202893	+	0.351422i
$783$	−3.72542	+	11.4657i	−0.133136	+	0.409750i
$784$	−1.90441	+	6.73597i	−0.0680146	+	0.240570i
$785$	3.09017			0.110293
$786$	3.83838	−	1.70896i	0.136910	−	0.0609564i
$787$	5.51274	+	2.45443i	0.196508	+	0.0874909i	0.502631	−	0.864501i	$-0.332365\pi$
$787$	5.51274	+	2.45443i	0.196508	+	0.0874909i	−0.306123	+	0.951992i	$0.599032\pi$
$788$	21.7918	+	9.70234i	0.776301	+	0.345631i
$789$	−1.85856	+	0.827482i	−0.0661663	+	0.0294591i
$790$	6.18034	−	19.0211i	0.219887	−	0.676741i
$791$	−7.20307	−	15.3723i	−0.256112	−	0.546576i
$792$	3.11803	−	9.59632i	0.110795	−	0.340990i
$793$	24.1074	−	41.7552i	0.856079	−	1.48277i
$794$	−21.1248	+	4.49022i	−0.749691	+	0.159352i
$795$	0.298033	+	0.132693i	0.0105701	+	0.00470613i
$796$	21.9266	+	4.66063i	0.777166	+	0.165192i
$797$	−14.3090	−	44.0386i	−0.506851	−	1.55993i	−0.797636	−	0.603140i	$-0.793916\pi$
$797$	−14.3090	−	44.0386i	−0.506851	−	1.55993i	0.290784	−	0.956789i	$-0.406084\pi$
$798$	2.22477	+	9.55541i	0.0787562	+	0.338258i
$799$	−71.1935			−2.51864
$800$	2.50000	−	4.33013i	0.0883883	−	0.153093i
$801$	−7.73607	−	13.3993i	−0.273341	−	0.473440i
$802$	2.13992	−	20.3600i	0.0755632	−	0.718936i
$803$	−20.2894	−	4.31264i	−0.715996	−	0.152190i
$804$	−0.190983	−	0.587785i	−0.00673545	−	0.0207296i
$805$	8.33344	+	2.53084i	0.293715	+	0.0892005i
$806$	−8.78115	+	27.0256i	−0.309303	+	0.951937i
$807$	−5.66312	+	9.80881i	−0.199351	+	0.345286i
$808$	4.60532	−	0.978891i	0.162015	−	0.0344373i
$809$	−19.6667	−	8.75617i	−0.691444	−	0.307851i	0.0307641	−	0.999527i	$-0.490206\pi$
$809$	−19.6667	−	8.75617i	−0.691444	−	0.307851i	−0.722208	+	0.691676i	$0.756873\pi$
$810$	−1.33419	−	12.6940i	−0.0468788	−	0.446022i
$811$	8.01722	+	5.82485i	0.281523	+	0.204538i	0.719581	−	0.694408i	$-0.244334\pi$
$811$	8.01722	+	5.82485i	0.281523	+	0.204538i	−0.438059	+	0.898946i	$0.644334\pi$
$812$	−5.25510	+	7.53486i	−0.184418	+	0.264422i
$813$	−6.04508	+	4.39201i	−0.212010	+	0.154035i
$814$	−1.34486	+	0.598772i	−0.0471374	+	0.0209869i
$815$	4.19934	+	1.86967i	0.147096	+	0.0654915i
$816$	−4.35207	−	1.93767i	−0.152353	−	0.0678319i
$817$	−8.97733	−	9.97033i	−0.314077	−	0.348818i
$818$	1.47214			0.0514720
$819$	−34.7187	+	20.9491i	−1.21317	+	0.732022i
$820$	16.9721	+	12.3310i	0.592693	+	0.430616i
$821$	4.92443	+	1.04672i	0.171864	+	0.0365308i	0.293040	−	0.956100i	$-0.405333\pi$
$821$	4.92443	+	1.04672i	0.171864	+	0.0365308i	−0.121176	+	0.992631i	$0.538667\pi$
$822$	−1.02234	+	1.13542i	−0.0356582	+	0.0396025i
$823$	−0.792701	+	7.54205i	−0.0276318	+	0.262899i	0.971981	+	0.235061i	$0.0755290\pi$
$823$	−0.792701	+	7.54205i	−0.0276318	+	0.262899i	−0.999612	+	0.0278383i	$0.991138\pi$
$824$	1.47214	−	2.54981i	0.0512843	−	0.0888270i
$825$	3.68034	−	11.3269i	0.128133	−	0.394353i
$826$	−2.66312	+	13.8380i	−0.0926618	+	0.481485i
$827$	−8.33688	−	6.05710i	−0.289902	−	0.210626i	0.433323	−	0.901239i	$-0.357341\pi$
$827$	−8.33688	−	6.05710i	−0.289902	−	0.210626i	−0.723225	+	0.690613i	$0.757341\pi$
$828$	3.76988	+	0.801313i	0.131012	+	0.0278475i
$829$	−16.8259	+	18.6870i	−0.584387	+	0.649028i	−0.960741	−	0.277448i	$-0.910511\pi$
$829$	−16.8259	+	18.6870i	−0.584387	+	0.649028i	0.376353	+	0.926476i	$0.377178\pi$
$830$	−11.7743	−	5.24224i	−0.408691	−	0.181961i
$831$	2.65348	+	2.94698i	0.0920481	+	0.102230i
$832$	−5.85410			−0.202954
$833$	−53.1722	−	9.17181i	−1.84231	−	0.317784i
$834$	3.00000	−	2.17963i	0.103882	−	0.0754743i
$835$	−0.218296	−	0.242442i	−0.00755444	−	0.00839005i
$836$	2.41718	−	22.9979i	0.0835999	−	0.795400i
$837$	15.3970	+	6.85518i	0.532198	+	0.236950i
$838$	−1.27902	−	12.1690i	−0.0441829	−	0.420372i
$839$	17.9443	+	13.0373i	0.619505	+	0.450097i	0.852749	−	0.522322i	$-0.174934\pi$
$839$	17.9443	+	13.0373i	0.619505	+	0.450097i	−0.233244	+	0.972418i	$0.574934\pi$
$840$	−0.690983	+	3.59045i	−0.0238412	+	0.123882i
$841$	13.7082	−	9.95959i	0.472697	−	0.343434i
$842$	−16.1195	−	17.9025i	−0.555514	−	0.616960i
$843$	−5.25329	−	9.09896i	−0.180933	−	0.313385i
$844$	10.0461	−	2.13536i	0.345800	−	0.0735021i
$845$	−31.8254	−	35.3457i	−1.09483	−	1.21593i
$846$	7.47214	+	22.9969i	0.256897	+	0.790649i
$847$	3.96681	−	9.39378i	0.136301	−	0.322774i
$848$	0.190983	+	0.138757i	0.00655838	+	0.00476494i
$849$	−3.57295	+	6.18853i	−0.122623	+	0.212390i
$850$	35.2090	+	15.6760i	1.20766	+	0.537684i
$851$	−0.281153	−	0.486971i	−0.00963780	−	0.0166932i
$852$	9.00217	−	4.00802i	0.308409	−	0.137313i
$853$	7.97214	+	24.5357i	0.272961	+	0.840087i	0.989752	+	0.142799i	$0.0456102\pi$
$853$	7.97214	+	24.5357i	0.272961	+	0.840087i	−0.716791	+	0.697288i	$0.754390\pi$
$854$	−13.1463	−	17.3783i	−0.449856	−	0.594673i
$855$	−10.8541	−	33.4055i	−0.371202	−	1.14244i
$856$	10.4132	+	11.5650i	0.355916	+	0.395285i
$857$	−3.20820	−	5.55677i	−0.109590	−	0.189816i	0.806014	−	0.591896i	$-0.201621\pi$
$857$	−3.20820	−	5.55677i	−0.109590	−	0.189816i	−0.915604	+	0.402081i	$0.868287\pi$
$858$	−13.6396	+	2.89918i	−0.465647	+	0.0989763i
$859$	4.85184	+	46.1621i	0.165543	+	1.57503i	0.690137	+	0.723679i	$0.257550\pi$
$859$	4.85184	+	46.1621i	0.165543	+	1.57503i	−0.524594	+	0.851353i	$0.675783\pi$
$860$	−1.54508	−	4.75528i	−0.0526870	−	0.162154i
$861$	−14.6790	−	4.45799i	−0.500260	−	0.151928i
$862$	−21.8713	+	15.8904i	−0.744940	+	0.541231i
$863$	−2.40775	−	22.9083i	−0.0819609	−	0.779806i	−0.955885	−	0.293743i	$-0.905099\pi$
$863$	−2.40775	−	22.9083i	−0.0819609	−	0.779806i	0.873924	−	0.486063i	$-0.161568\pi$
$864$	−0.362937	+	3.45312i	−0.0123474	+	0.117477i
$865$	−2.26913	+	21.5893i	−0.0771526	+	0.734058i
$866$	2.37365	+	22.5838i	0.0806600	+	0.767429i
$867$	8.10081	−	24.9317i	0.275118	−	0.846726i
$868$	9.70820	+	8.40755i	0.329518	+	0.285371i
$869$	10.6525	−	32.7849i	0.361360	−	1.11215i
$870$	−2.39919	+	4.15551i	−0.0813401	+	0.140885i
$871$	3.91716	−	4.35045i	0.132728	−	0.147409i
$872$	0.827091	−	0.918578i	0.0280088	−	0.0311070i
$873$	26.8732	−	11.9647i	0.909521	−	0.404945i
$874$	8.83282			0.298774
$875$	5.59017	−	29.0474i	0.188982	−	0.981981i
$876$	3.32624			0.112383
$877$	3.68565	−	1.64096i	0.124455	−	0.0554111i	−0.343564	−	0.939129i	$-0.611634\pi$
$877$	3.68565	−	1.64096i	0.124455	−	0.0554111i	0.468020	+	0.883718i	$0.344968\pi$
$878$	−2.63923	+	2.93117i	−0.0890698	+	0.0989220i
$879$	−0.450835	+	0.500703i	−0.0152063	+	0.0168883i
$880$	4.30902	−	7.46344i	0.145257	−	0.251592i
$881$	−4.23607	+	13.0373i	−0.142717	+	0.439237i	−0.996710	−	0.0810466i	$-0.974174\pi$
$881$	−4.23607	+	13.0373i	−0.142717	+	0.439237i	0.853994	+	0.520284i	$0.174174\pi$
$882$	2.61803	+	18.1383i	0.0881538	+	0.610747i
$883$	5.02786	−	15.4742i	0.169201	−	0.520747i	−0.830120	−	0.557584i	$-0.811728\pi$
$883$	5.02786	−	15.4742i	0.169201	−	0.520747i	0.999321	+	0.0368371i	$0.0117283\pi$
$884$	−4.71681	−	44.8774i	−0.158643	−	1.50939i
$885$	−0.769401	+	7.32036i	−0.0258631	+	0.246071i
$886$	0.328836	−	3.12866i	0.0110475	−	0.105110i
$887$	−5.34398	−	50.8445i	−0.179433	−	1.70719i	−0.600057	−	0.799957i	$-0.704855\pi$
$887$	−5.34398	−	50.8445i	−0.179433	−	1.70719i	0.420624	−	0.907235i	$-0.361811\pi$
$888$	0.190983	−	0.138757i	0.00640897	−	0.00465639i
$889$	17.3846	−	16.2720i	0.583060	−	0.545744i
$890$	−4.08359	−	12.5680i	−0.136882	−	0.421280i
$891$	−2.29963	−	21.8795i	−0.0770404	−	0.732990i
$892$	−10.3860	+	2.20761i	−0.347749	+	0.0739164i
$893$	27.7082	+	47.9920i	0.927220	+	1.60599i
$894$	1.97010	+	2.18802i	0.0658901	+	0.0731784i
$895$	3.98278	+	12.2577i	0.133130	+	0.409731i
$896$	−1.02924	+	2.43735i	−0.0343846	+	0.0814260i
$897$	−1.64590	−	5.06555i	−0.0549549	−	0.169134i
$898$	−4.53626	+	2.01967i	−0.151377	+	0.0673974i
$899$	8.42705	+	14.5961i	0.281058	+	0.486807i
$900$	1.36830	−	13.0185i	0.0456098	−	0.433949i
$901$	−0.909830	+	1.57587i	−0.0303108	+	0.0524999i
$902$	29.2533	+	21.2538i	0.974028	+	0.707673i
$903$	2.20587	+	2.91598i	0.0734067	+	0.0970378i
$904$	−1.98278	−	6.10237i	−0.0659463	−	0.202962i
$905$	2.11926	+	2.35368i	0.0704466	+	0.0782389i
$906$	10.6506	−	2.26386i	0.353843	−	0.0752116i
$907$	−17.1353	−	29.6791i	−0.568967	−	0.985479i	−0.996668	−	0.0815595i	$-0.974010\pi$
$907$	−17.1353	−	29.6791i	−0.568967	−	0.985479i	0.427702	−	0.903920i	$-0.359323\pi$
$908$	−13.3453	−	14.8215i	−0.442880	−	0.491868i
$909$	9.97214	−	7.24518i	0.330755	−	0.240307i
$910$	−32.7254	+	11.3364i	−1.08484	+	0.375799i
$911$	17.8262	+	12.9515i	0.590610	+	0.429103i	0.842533	−	0.538644i	$-0.181063\pi$
$911$	17.8262	+	12.9515i	0.590610	+	0.429103i	−0.251924	+	0.967747i	$0.581063\pi$
$912$	0.387613	+	3.68789i	0.0128351	+	0.122118i
$913$	−20.2942	−	9.03557i	−0.671640	−	0.299034i
$914$	−1.12514	+	10.7050i	−0.0372162	+	0.354089i
$915$	−7.61602	−	8.45845i	−0.251778	−	0.279628i
$916$	−9.97214	+	7.24518i	−0.329489	+	0.239388i
$917$	15.4004	−	9.29256i	0.508567	−	0.306867i
$918$	−26.7639			−0.883341
$919$	−10.5854	−	11.7563i	−0.349181	−	0.387805i	0.542812	−	0.839854i	$-0.317360\pi$
$919$	−10.5854	−	11.7563i	−0.349181	−	0.387805i	−0.891993	+	0.452050i	$0.850693\pi$
$920$	3.00721	+	1.33889i	0.0991446	+	0.0441420i
$921$	5.42762	−	6.02799i	0.178846	−	0.198629i
$922$	34.3025	+	7.29123i	1.12969	+	0.240124i
$923$	75.5132	+	54.8635i	2.48555	+	1.80585i
$924$	−1.19098	+	6.18853i	−0.0391805	+	0.203588i
$925$	−1.54508	+	1.12257i	−0.0508021	+	0.0369099i
$926$	5.88197	−	10.1879i	0.193293	−	0.334794i
$927$	0.805727	−	7.66598i	0.0264635	−	0.251784i
$928$	−2.32331	+	2.58030i	−0.0762665	+	0.0847025i
$929$	−17.2875	−	3.67458i	−0.567186	−	0.120559i	−0.0846115	−	0.996414i	$-0.526965\pi$
$929$	−17.2875	−	3.67458i	−0.567186	−	0.120559i	−0.482575	+	0.875855i	$0.660298\pi$
$930$	5.42705	+	3.94298i	0.177960	+	0.129296i
$931$	14.5116	+	39.4134i	0.475599	+	1.29172i
$932$	−25.8328			−0.846182
$933$	1.48198	+	1.64590i	0.0485178	+	0.0538845i
$934$	4.53626	+	2.01967i	0.148431	+	0.0660858i
$935$	60.6864	+	27.0193i	1.98466	+	0.883627i
$936$	−14.0012	+	6.23374i	−0.457644	+	0.203756i
$937$	−30.6803	+	22.2906i	−1.00228	+	0.728201i	−0.962576	−	0.271010i	$-0.912642\pi$
$937$	−30.6803	+	22.2906i	−1.00228	+	0.728201i	−0.0397065	+	0.999211i	$0.512642\pi$
$938$	−1.12260	−	2.39578i	−0.0366543	−	0.0782250i
$939$	11.2361	+	8.16348i	0.366675	+	0.266405i
$940$	2.15877	+	20.5393i	0.0704114	+	0.669919i
$941$	40.3098	+	17.9471i	1.31406	+	0.585059i	0.939629	−	0.342195i	$-0.111170\pi$
$941$	40.3098	+	17.9471i	1.31406	+	0.585059i	0.374434	+	0.927253i	$0.377837\pi$
$942$	−0.835438	+	0.177578i	−0.0272200	+	0.00578580i
$943$	−6.90576	+	11.9611i	−0.224883	+	0.389508i
$944$	−1.64590	+	5.06555i	−0.0535694	+	0.164870i
$945$	4.65805	+	20.0063i	0.151526	+	0.650806i
$946$	−2.66312	−	8.19624i	−0.0865855	−	0.266483i
$947$	−30.3771	−	6.45685i	−0.987123	−	0.209819i	−0.314059	−	0.949404i	$-0.601689\pi$
$947$	−30.3771	−	6.45685i	−0.987123	−	0.209819i	−0.673064	+	0.739584i	$0.735022\pi$
$948$	−0.577819	+	5.49758i	−0.0187667	+	0.178553i
$949$	15.7533	+	27.2855i	0.511373	+	0.885725i
$950$	−3.13585	−	29.8357i	−0.101741	−	0.967997i
$951$	15.9098			0.515912
$952$	−19.5139	−	5.92633i	−0.632450	−	0.192073i
$953$	−6.39261	−	19.6744i	−0.207077	−	0.637317i	−0.999622	−	0.0275035i	$-0.991244\pi$
$953$	−6.39261	−	19.6744i	−0.207077	−	0.637317i	0.792545	−	0.609814i	$-0.208756\pi$
$954$	0.604528	+	0.128496i	0.0195723	+	0.00416023i
$955$	32.2018	+	14.3372i	1.04202	+	0.463939i
$956$	−5.54978	+	1.17964i	−0.179493	+	0.0381523i
$957$	−4.13525	+	7.16247i	−0.133674	+	0.231530i
$958$	−1.76393	+	5.42882i	−0.0569901	+	0.175397i
$959$	−3.74159	+	5.36476i	−0.120822	+	0.173237i
$960$	−0.427051	+	1.31433i	−0.0137830	+	0.0424197i
$961$	−6.79467	+	3.02518i	−0.219183	+	0.0975865i
$962$	2.04275	+	0.909491i	0.0658609	+	0.0293232i
$963$	37.2203	+	16.5715i	1.19941	+	0.534010i
$964$	−9.91572	+	4.41476i	−0.319364	+	0.142190i
$965$	−53.2148			−1.71304
$966$	−2.39841	−	0.205338i	−0.0771676	−	0.00660663i
$967$	−11.3090	+	34.8056i	−0.363673	+	1.11927i	0.587134	+	0.809490i	$0.300256\pi$
$967$	−11.3090	+	34.8056i	−0.363673	+	1.11927i	−0.950808	+	0.309782i	$0.899744\pi$
$968$	1.92705	−	3.33775i	0.0619378	−	0.107279i
$969$	−27.9590	+	5.94286i	−0.898172	+	0.190912i
$970$	24.5756	−	5.22370i	0.789074	−	0.167723i
$971$	38.4460	+	8.17196i	1.23379	+	0.262251i	0.778245	−	0.627961i	$-0.216110\pi$
$971$	38.4460	+	8.17196i	1.23379	+	0.262251i	0.455547	+	0.890212i	$0.349444\pi$
$972$	4.30902	+	13.2618i	0.138212	+	0.425372i
$973$	11.5897	−	10.8480i	0.371549	−	0.347770i
$974$	−40.5967			−1.30080
$975$	−16.5262	+	7.35793i	−0.529262	+	0.235643i
$976$	−4.11803	−	7.13264i	−0.131815	−	0.228310i
$977$	4.44092	−	42.2526i	0.142078	−	1.35178i	−0.658514	−	0.752569i	$-0.728815\pi$
$977$	4.44092	−	42.2526i	0.142078	−	1.35178i	0.800592	−	0.599210i	$-0.204519\pi$
$978$	−1.24275	−	0.264154i	−0.0397386	−	0.00844671i
$979$	−7.03851	−	21.6623i	−0.224952	−	0.692330i
$980$	−1.03375	+	15.6183i	−0.0330219	+	0.498908i
$981$	1.00000	−	3.07768i	0.0319275	−	0.0982629i
$982$	−10.5729	+	18.3129i	−0.337396	+	0.584388i
$983$	18.7404	−	3.98339i	0.597725	−	0.127050i	0.100893	−	0.994897i	$-0.467830\pi$
$983$	18.7404	−	3.98339i	0.597725	−	0.127050i	0.496832	+	0.867847i	$0.334497\pi$
$984$	−5.29708	−	2.35841i	−0.168865	−	0.0751834i
$985$	52.1738	+	11.0899i	1.66240	+	0.353353i
$986$	−21.6525	−	15.7314i	−0.689555	−	0.500991i
$987$	−6.40804	−	13.6756i	−0.203970	−	0.435299i
$988$	−28.4164	+	20.6457i	−0.904046	+	0.656828i
$989$	3.00721	−	1.33889i	0.0956236	−	0.0425744i
$990$	2.35840	−	22.4387i	0.0749550	−	0.713149i
$991$	16.2282	+	7.22524i	0.515504	+	0.229517i	0.647964	−	0.761671i	$-0.275621\pi$
$991$	16.2282	+	7.22524i	0.515504	+	0.229517i	−0.132459	+	0.991188i	$0.542287\pi$
$992$	3.24803	+	3.60730i	0.103125	+	0.114532i
$993$	−17.6180			−0.559091
$994$	36.1188	−	21.7939i	1.14562	−	0.691261i
$995$	50.1246			1.58906
$996$	3.48446	+	0.740645i	0.110409	+	0.0234682i
$997$	10.1346	−	11.2556i	0.320965	−	0.356468i	−0.560972	−	0.827835i	$-0.689572\pi$
$997$	10.1346	−	11.2556i	0.320965	−	0.356468i	0.881937	+	0.471367i	$0.156239\pi$
$998$	1.25434	−	11.9343i	0.0397055	−	0.377772i
$999$	0.663119	−	1.14856i	0.0209802	−	0.0363387i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.q.a.191.1	yes	8
7.4	even	3	inner	350.2.q.a.291.1	yes	8
25.11	even	5	inner	350.2.q.a.261.1	yes	8
175.11	even	15	inner	350.2.q.a.11.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.q.a.11.1	✓	8	175.11	even	15	inner
350.2.q.a.191.1	yes	8	1.1	even	1	trivial
350.2.q.a.261.1	yes	8	25.11	even	5	inner
350.2.q.a.291.1	yes	8	7.4	even	3	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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.913545 + 0.406737i) q^{2} +(0.413545 - 0.459289i) q^{3} +(0.669131 - 0.743145i) q^{4} +(1.11803 - 1.93649i) q^{5} +(-0.190983 + 0.587785i) q^{6} +(-0.500000 + 2.59808i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.273659 + 2.60369i) q^{9} +O(q^{10})\)	\(q+(-0.913545 + 0.406737i) q^{2} +(0.413545 - 0.459289i) q^{3} +(0.669131 - 0.743145i) q^{4} +(1.11803 - 1.93649i) q^{5} +(-0.190983 + 0.587785i) q^{6} +(-0.500000 + 2.59808i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.273659 + 2.60369i) q^{9} +(-0.233733 + 2.22382i) q^{10} +(-0.402863 + 3.83299i) q^{11} +(-0.0646021 - 0.614648i) q^{12} +(4.73607 - 3.44095i) q^{13} +(-0.599960 - 2.57683i) q^{14} +(-0.427051 - 1.31433i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(7.53976 - 1.60263i) q^{17} +(-1.30902 - 2.26728i) q^{18} +(-4.01478 - 4.45887i) q^{19} +(-0.690983 - 2.12663i) q^{20} +(0.986494 + 1.30407i) q^{21} +(-1.19098 - 3.66547i) q^{22} +(1.34486 - 0.598772i) q^{23} +(0.309017 + 0.535233i) q^{24} +(-2.50000 - 4.33013i) q^{25} +(-2.92705 + 5.06980i) q^{26} +(2.80902 + 2.04087i) q^{27} +(1.59618 + 2.11002i) q^{28} +(1.07295 + 3.30220i) q^{29} +(0.924716 + 1.02700i) q^{30} +(4.74803 - 1.00922i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.59385 + 1.77015i) q^{33} +(-6.23607 + 4.53077i) q^{34} +(4.47214 + 3.87298i) q^{35} +(2.11803 + 1.53884i) q^{36} +(-0.0399263 - 0.379874i) q^{37} +(5.48127 + 2.44042i) q^{38} +(0.378188 - 3.59821i) q^{39} +(1.49622 + 1.66172i) q^{40} +(-7.59017 + 5.51458i) q^{41} +(-1.43162 - 0.790081i) q^{42} +2.23607 q^{43} +(2.57890 + 2.86416i) q^{44} +(5.34799 + 2.38108i) q^{45} +(-0.985051 + 1.09401i) q^{46} +(-9.03424 - 1.92029i) q^{47} +(-0.500000 - 0.363271i) q^{48} +(-6.50000 - 2.59808i) q^{49} +(4.04508 + 2.93893i) q^{50} +(2.38197 - 4.12569i) q^{51} +(0.611920 - 5.82203i) q^{52} +(-0.157960 + 0.175433i) q^{53} +(-3.39626 - 0.721898i) q^{54} +(6.97214 + 5.06555i) q^{55} +(-2.31641 - 1.27838i) q^{56} -3.70820 q^{57} +(-2.32331 - 2.58030i) q^{58} +(-4.86576 - 2.16638i) q^{59} +(-1.26249 - 0.562096i) q^{60} +(7.52402 - 3.34991i) q^{61} +(-3.92705 + 2.85317i) q^{62} +(-6.90142 - 0.590859i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-1.36830 - 13.0185i) q^{65} +(-2.17603 - 0.968833i) q^{66} +(0.978148 - 0.207912i) q^{67} +(3.85410 - 6.67550i) q^{68} +(0.281153 - 0.865300i) q^{69} +(-5.66078 - 1.71916i) q^{70} +(4.92705 + 15.1639i) q^{71} +(-2.56082 - 0.544320i) q^{72} +(-0.562569 + 5.35248i) q^{73} +(0.190983 + 0.330792i) q^{74} +(-3.02264 - 0.642482i) q^{75} -6.00000 q^{76} +(-9.75697 - 2.96316i) q^{77} +(1.11803 + 3.44095i) q^{78} +(-8.74882 - 1.85962i) q^{79} +(-2.04275 - 0.909491i) q^{80} +(-5.58347 + 1.18680i) q^{81} +(4.69098 - 8.12502i) q^{82} +(-1.78115 + 5.48183i) q^{83} +(1.62920 + 0.139483i) q^{84} +(5.32624 - 16.3925i) q^{85} +(-2.04275 + 0.909491i) q^{86} +(1.96038 + 0.872815i) q^{87} +(-3.52090 - 1.56760i) q^{88} +(-5.39890 + 2.40374i) q^{89} -5.85410 q^{90} +(6.57183 + 14.0251i) q^{91} +(0.454915 - 1.40008i) q^{92} +(1.50000 - 2.59808i) q^{93} +(9.03424 - 1.92029i) q^{94} +(-13.1232 + 2.78943i) q^{95} +(0.604528 + 0.128496i) q^{96} +(-3.47214 - 10.6861i) q^{97} +(6.99478 - 0.270327i) q^{98} -10.0902 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 3 q^{3} + q^{4} - 6 q^{6} - 4 q^{7} + 2 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q - q^2 - 3 * q^3 + q^4 - 6 * q^6 - 4 * q^7 + 2 * q^8 - 4 * q^9	\( 8 q - q^{2} - 3 q^{3} + q^{4} - 6 q^{6} - 4 q^{7} + 2 q^{8} - 4 q^{9} + 5 q^{10} + 8 q^{11} + 2 q^{12} + 20 q^{13} - 4 q^{14} + 10 q^{15} + q^{16} + 14 q^{17} - 6 q^{18} - 6 q^{19} - 10 q^{20} + 15 q^{21} - 14 q^{22} + 7 q^{23} - 2 q^{24} - 20 q^{25} - 10 q^{26} + 18 q^{27} - 5 q^{28} + 22 q^{29} + 5 q^{30} + 6 q^{31} + 4 q^{32} + 6 q^{33} - 32 q^{34} + 8 q^{36} - q^{37} + 6 q^{38} - 5 q^{39} - 5 q^{40} - 16 q^{41} + 3 q^{42} - 7 q^{44} + 10 q^{45} + 13 q^{46} + 2 q^{47} - 4 q^{48} - 52 q^{49} + 10 q^{50} + 28 q^{51} - 10 q^{52} + 7 q^{53} - 11 q^{54} + 20 q^{55} - q^{56} + 24 q^{57} + 11 q^{58} - 15 q^{59} + 11 q^{61} - 18 q^{62} - 16 q^{63} - 2 q^{64} + 20 q^{65} - q^{66} - q^{67} + 4 q^{68} - 38 q^{69} - 25 q^{70} + 26 q^{71} - q^{72} + 4 q^{73} + 6 q^{74} - 15 q^{75} - 48 q^{76} - 40 q^{77} - 20 q^{79} - 5 q^{80} - 16 q^{81} + 42 q^{82} + 26 q^{83} + 8 q^{84} - 20 q^{85} - 5 q^{86} - 2 q^{87} - 8 q^{88} + q^{89} - 20 q^{90} - 10 q^{91} + 26 q^{92} + 12 q^{93} - 2 q^{94} - 30 q^{95} + 3 q^{96} + 8 q^{97} + 11 q^{98} - 36 q^{99}+O(q^{100}) \) 8 * q - q^2 - 3 * q^3 + q^4 - 6 * q^6 - 4 * q^7 + 2 * q^8 - 4 * q^9 + 5 * q^10 + 8 * q^11 + 2 * q^12 + 20 * q^13 - 4 * q^14 + 10 * q^15 + q^16 + 14 * q^17 - 6 * q^18 - 6 * q^19 - 10 * q^20 + 15 * q^21 - 14 * q^22 + 7 * q^23 - 2 * q^24 - 20 * q^25 - 10 * q^26 + 18 * q^27 - 5 * q^28 + 22 * q^29 + 5 * q^30 + 6 * q^31 + 4 * q^32 + 6 * q^33 - 32 * q^34 + 8 * q^36 - q^37 + 6 * q^38 - 5 * q^39 - 5 * q^40 - 16 * q^41 + 3 * q^42 - 7 * q^44 + 10 * q^45 + 13 * q^46 + 2 * q^47 - 4 * q^48 - 52 * q^49 + 10 * q^50 + 28 * q^51 - 10 * q^52 + 7 * q^53 - 11 * q^54 + 20 * q^55 - q^56 + 24 * q^57 + 11 * q^58 - 15 * q^59 + 11 * q^61 - 18 * q^62 - 16 * q^63 - 2 * q^64 + 20 * q^65 - q^66 - q^67 + 4 * q^68 - 38 * q^69 - 25 * q^70 + 26 * q^71 - q^72 + 4 * q^73 + 6 * q^74 - 15 * q^75 - 48 * q^76 - 40 * q^77 - 20 * q^79 - 5 * q^80 - 16 * q^81 + 42 * q^82 + 26 * q^83 + 8 * q^84 - 20 * q^85 - 5 * q^86 - 2 * q^87 - 8 * q^88 + q^89 - 20 * q^90 - 10 * q^91 + 26 * q^92 + 12 * q^93 - 2 * q^94 - 30 * q^95 + 3 * q^96 + 8 * q^97 + 11 * q^98 - 36 * q^99

Introduction

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