LMFDB - Embedded newform 756.2.ci.a.95.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(95,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 17, 12]))

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

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

chi := DirichletCharacter("756.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ci (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$840$
Relative dimension:	$140$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			95.16
Character	$\chi$	$=$	756.95
Dual form			756.2.ci.a.191.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34200 + 0.446123i) q^{2} +(-1.17175 - 1.27554i) q^{3} +(1.60195 - 1.19740i) q^{4} +(-2.14959 - 0.379031i) q^{5} +(2.14154 + 1.18903i) q^{6} +(1.07635 - 2.41691i) q^{7} +(-1.61563 + 2.32158i) q^{8} +(-0.253990 + 2.98923i) q^{9} +O(q^{10})$	\(q+(-1.34200 + 0.446123i) q^{2} +(-1.17175 - 1.27554i) q^{3} +(1.60195 - 1.19740i) q^{4} +(-2.14959 - 0.379031i) q^{5} +(2.14154 + 1.18903i) q^{6} +(1.07635 - 2.41691i) q^{7} +(-1.61563 + 2.32158i) q^{8} +(-0.253990 + 2.98923i) q^{9} +(3.05386 - 0.450322i) q^{10} +(0.110447 + 0.626378i) q^{11} +(-3.40441 - 0.640290i) q^{12} +(-1.06585 + 6.04476i) q^{13} +(-0.366221 + 3.72369i) q^{14} +(2.03532 + 3.18602i) q^{15} +(1.13248 - 3.83634i) q^{16} +(-1.27516 + 0.736212i) q^{17} +(-0.992709 - 4.12487i) q^{18} +(6.15881 + 3.55579i) q^{19} +(-3.89739 + 1.96673i) q^{20} +(-4.34408 + 1.45911i) q^{21} +(-0.427662 - 0.791328i) q^{22} +(-4.00681 - 3.36211i) q^{23} +(4.85438 - 0.659516i) q^{24} +(-0.221379 - 0.0805754i) q^{25} +(-1.26633 - 8.58759i) q^{26} +(4.11049 - 3.17866i) q^{27} +(-1.16975 - 5.16059i) q^{28} +(4.91684 - 0.866972i) q^{29} +(-4.15277 - 3.36764i) q^{30} +(2.98988 + 0.527197i) q^{31} +(0.191692 + 5.65361i) q^{32} +(0.669551 - 0.874840i) q^{33} +(1.38282 - 1.55688i) q^{34} +(-3.22980 + 4.78741i) q^{35} +(3.17242 + 5.09272i) q^{36} +4.28368 q^{37} +(-9.85146 - 2.02430i) q^{38} +(8.95923 - 5.72343i) q^{39} +(4.35291 - 4.37807i) q^{40} +(-1.61973 - 0.285602i) q^{41} +(5.17883 - 3.89612i) q^{42} +(-5.64439 - 6.72672i) q^{43} +(0.926954 + 0.871176i) q^{44} +(1.67899 - 6.32935i) q^{45} +(6.87707 + 2.72444i) q^{46} +(1.37761 + 7.81280i) q^{47} +(-6.22038 + 3.05073i) q^{48} +(-4.68295 - 5.20288i) q^{49} +(0.333038 + 0.00937016i) q^{50} +(2.43323 + 0.763851i) q^{51} +(5.53054 + 10.9596i) q^{52} +(10.3036 + 5.94879i) q^{53} +(-4.09821 + 6.09956i) q^{54} -1.38832i q^{55} +(3.87207 + 6.40367i) q^{56} +(-2.68106 - 12.0223i) q^{57} +(-6.21164 + 3.35700i) q^{58} +(5.51184 - 2.00615i) q^{59} +(7.07541 + 2.66674i) q^{60} +(-0.177544 - 1.00690i) q^{61} +(-4.24763 + 0.626355i) q^{62} +(6.95133 + 3.83132i) q^{63} +(-2.77946 - 7.50164i) q^{64} +(4.58230 - 12.5898i) q^{65} +(-0.508254 + 1.47274i) q^{66} +(6.53794 - 7.79161i) q^{67} +(-1.16120 + 2.70624i) q^{68} +(0.406491 + 9.05040i) q^{69} +(2.19862 - 7.86561i) q^{70} +(7.55151 - 13.0796i) q^{71} +(-6.52938 - 5.41916i) q^{72} +1.34266 q^{73} +(-5.74871 + 1.91105i) q^{74} +(0.156625 + 0.376792i) q^{75} +(14.1238 - 1.67835i) q^{76} +(1.63278 + 0.407259i) q^{77} +(-9.46997 + 11.6778i) q^{78} +(10.0183 + 11.9393i) q^{79} +(-3.88846 + 7.81732i) q^{80} +(-8.87098 - 1.51847i) q^{81} +(2.30109 - 0.339319i) q^{82} +(1.97260 + 11.1872i) q^{83} +(-5.21186 + 7.53900i) q^{84} +(3.02011 - 1.09923i) q^{85} +(10.5757 + 6.50919i) q^{86} +(-6.86718 - 5.25574i) q^{87} +(-1.63263 - 0.755585i) q^{88} +(5.86719 + 3.38742i) q^{89} +(0.570466 + 9.24305i) q^{90} +(13.4624 + 9.08234i) q^{91} +(-10.4445 - 0.588185i) q^{92} +(-2.83094 - 4.43145i) q^{93} +(-5.33423 - 9.87022i) q^{94} +(-11.8912 - 9.97788i) q^{95} +(6.98677 - 6.86914i) q^{96} +(-7.21277 + 6.05224i) q^{97} +(8.60566 + 4.89311i) q^{98} +(-1.90044 + 0.171059i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} + 3 q^{10} - 3 q^{12} - 24 q^{13} + 24 q^{14} - 3 q^{16} - 18 q^{17} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} + 48 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} - 21 q^{30} - 63 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} - 12 q^{37} + 45 q^{38} - 33 q^{40} - 24 q^{41} - 21 q^{42} + 6 q^{45} - 6 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} - 63 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} - 54 q^{65} - 3 q^{66} - 12 q^{68} - 48 q^{69} - 21 q^{70} - 9 q^{72} - 12 q^{73} + 15 q^{74} + 12 q^{77} + 6 q^{78} - 54 q^{81} - 6 q^{82} - 39 q^{84} + 6 q^{85} - 9 q^{86} - 27 q^{88} - 18 q^{89} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} + 213 q^{96} - 24 q^{97} + 162 q^{98}+O(q^{100}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 + 3 * q^10 - 3 * q^12 - 24 * q^13 + 24 * q^14 - 3 * q^16 - 18 * q^17 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 + 48 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 - 21 * q^30 - 63 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 - 12 * q^37 + 45 * q^38 - 33 * q^40 - 24 * q^41 - 21 * q^42 + 6 * q^45 - 6 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 - 63 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 - 54 * q^65 - 3 * q^66 - 12 * q^68 - 48 * q^69 - 21 * q^70 - 9 * q^72 - 12 * q^73 + 15 * q^74 + 12 * q^77 + 6 * q^78 - 54 * q^81 - 6 * q^82 - 39 * q^84 + 6 * q^85 - 9 * q^86 - 27 * q^88 - 18 * q^89 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 + 213 * q^96 - 24 * q^97 + 162 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−1.34200	+	0.446123i	−0.948940	+	0.315457i
$2$	−1.34200	+	0.446123i	−0.948940	+	0.315457i
$3$	−1.17175	−	1.27554i	−0.676512	−	0.736432i
$3$	−1.17175	−	1.27554i	−0.676512	−	0.736432i
$4$	1.60195	−	1.19740i	0.800974	−	0.598699i
$5$	−2.14959	−	0.379031i	−0.961327	−	0.169508i	−0.329103	−	0.944294i	$-0.606746\pi$
$5$	−2.14959	−	0.379031i	−0.961327	−	0.169508i	−0.632224	+	0.774786i	$0.717858\pi$
$6$	2.14154	+	1.18903i	0.874281	+	0.485419i
$7$	1.07635	−	2.41691i	0.406821	−	0.913508i
$7$	1.07635	−	2.41691i	0.406821	−	0.913508i
$8$	−1.61563	+	2.32158i	−0.571213	+	0.820802i
$9$	−0.253990	+	2.98923i	−0.0846633	+	0.996410i
$10$	3.05386	−	0.450322i	0.965714	−	0.142404i
$11$	0.110447	+	0.626378i	0.0333011	+	0.188860i	0.996921	−	0.0784180i	$-0.0249869\pi$
$11$	0.110447	+	0.626378i	0.0333011	+	0.188860i	−0.963619	+	0.267278i	$0.913876\pi$
$12$	−3.40441	−	0.640290i	−0.982769	−	0.184836i
$13$	−1.06585	+	6.04476i	−0.295615	+	1.67651i	0.369079	+	0.929398i	$0.379673\pi$
$13$	−1.06585	+	6.04476i	−0.295615	+	1.67651i	−0.664694	+	0.747116i	$0.731438\pi$
$14$	−0.366221	+	3.72369i	−0.0978767	+	0.995199i
$15$	2.03532	+	3.18602i	0.525518	+	0.822626i
$16$	1.13248	−	3.83634i	0.283119	−	0.959085i
$17$	−1.27516	+	0.736212i	−0.309271	+	0.178558i	−0.646600	−	0.762829i	$-0.723810\pi$
$17$	−1.27516	+	0.736212i	−0.309271	+	0.178558i	0.337329	+	0.941387i	$0.390476\pi$
$18$	−0.992709	−	4.12487i	−0.233984	−	0.972241i
$19$	6.15881	+	3.55579i	1.41293	+	0.815754i	0.995663	−	0.0930315i	$-0.0296557\pi$
$19$	6.15881	+	3.55579i	1.41293	+	0.815754i	0.417264	+	0.908785i	$0.362989\pi$
$20$	−3.89739	+	1.96673i	−0.871482	+	0.439774i
$21$	−4.34408	+	1.45911i	−0.947955	+	0.318403i
$22$	−0.427662	−	0.791328i	−0.0911779	−	0.168712i
$23$	−4.00681	−	3.36211i	−0.835477	−	0.701049i	0.121064	−	0.992645i	$-0.461369\pi$
$23$	−4.00681	−	3.36211i	−0.835477	−	0.701049i	−0.956542	+	0.291596i	$0.905814\pi$
$24$	4.85438	−	0.659516i	0.990897	−	0.134623i
$25$	−0.221379	−	0.0805754i	−0.0442758	−	0.0161151i
$26$	−1.26633	−	8.58759i	−0.248347	−	1.68416i
$27$	4.11049	−	3.17866i	0.791063	−	0.611734i
$28$	−1.16975	−	5.16059i	−0.221063	−	0.975260i
$29$	4.91684	−	0.866972i	0.913034	−	0.160993i	0.302653	−	0.953101i	$-0.402128\pi$
$29$	4.91684	−	0.866972i	0.913034	−	0.160993i	0.610381	+	0.792108i	$0.291016\pi$
$30$	−4.15277	−	3.36764i	−0.758188	−	0.614844i
$31$	2.98988	+	0.527197i	0.536998	+	0.0946873i	0.435569	−	0.900155i	$-0.356547\pi$
$31$	2.98988	+	0.527197i	0.536998	+	0.0946873i	0.101430	+	0.994843i	$0.467658\pi$
$32$	0.191692	+	5.65361i	0.0338866	+	0.999426i
$33$	0.669551	−	0.874840i	0.116554	−	0.152290i
$34$	1.38282	−	1.55688i	0.237152	−	0.267002i
$35$	−3.22980	+	4.78741i	−0.545935	+	0.809220i
$36$	3.17242	+	5.09272i	0.528736	+	0.848786i
$37$	4.28368			0.704233			0.352116	−	0.935956i	$-0.385462\pi$
$37$	4.28368			0.704233			0.352116	+	0.935956i	$0.385462\pi$
$38$	−9.85146	−	2.02430i	−1.59812	−	0.328384i
$39$	8.95923	−	5.72343i	1.43462	−	0.916482i
$40$	4.35291	−	4.37807i	0.688255	−	0.692234i
$41$	−1.61973	−	0.285602i	−0.252959	−	0.0446035i	0.0457306	−	0.998954i	$-0.485438\pi$
$41$	−1.61973	−	0.285602i	−0.252959	−	0.0446035i	−0.298690	+	0.954350i	$0.596550\pi$
$42$	5.17883	−	3.89612i	0.799111	−	0.601184i
$43$	−5.64439	−	6.72672i	−0.860761	−	1.02582i	−0.999371	−	0.0354681i	$-0.988708\pi$
$43$	−5.64439	−	6.72672i	−0.860761	−	1.02582i	0.138610	−	0.990347i	$-0.455737\pi$
$44$	0.926954	+	0.871176i	0.139744	+	0.131335i
$45$	1.67899	−	6.32935i	0.250288	−	0.943524i
$46$	6.87707	+	2.72444i	1.01397	+	0.401696i
$47$	1.37761	+	7.81280i	0.200945	+	1.13961i	0.903695	+	0.428177i	$0.140844\pi$
$47$	1.37761	+	7.81280i	0.200945	+	1.13961i	−0.702750	+	0.711437i	$0.748045\pi$
$48$	−6.22038	+	3.05073i	−0.897834	+	0.440334i
$49$	−4.68295	−	5.20288i	−0.668993	−	0.743269i
$50$	0.333038	+	0.00937016i	0.0470987	+	0.00132514i
$51$	2.43323	+	0.763851i	0.340721	+	0.106961i
$52$	5.53054	+	10.9596i	0.766947	+	1.51983i
$53$	10.3036	+	5.94879i	1.41531	+	0.817129i	0.995882	−	0.0906602i	$-0.0288977\pi$
$53$	10.3036	+	5.94879i	1.41531	+	0.817129i	0.419427	+	0.907789i	$0.362231\pi$
$54$	−4.09821	+	6.09956i	−0.557696	+	0.830045i
$55$		−	1.38832i		−	0.187201i
$56$	3.87207	+	6.40367i	0.517428	+	0.855727i
$57$	−2.68106	−	12.0223i	−0.355115	−	1.59239i
$58$	−6.21164	+	3.35700i	−0.815628	+	0.440795i
$59$	5.51184	−	2.00615i	0.717581	−	0.261178i	0.0426824	−	0.999089i	$-0.486410\pi$
$59$	5.51184	−	2.00615i	0.717581	−	0.261178i	0.674898	+	0.737911i	$0.264187\pi$
$60$	7.07541	+	2.66674i	0.913432	+	0.344275i
$61$	−0.177544	−	1.00690i	−0.0227322	−	0.128921i	0.971330	−	0.237736i	$-0.0764054\pi$
$61$	−0.177544	−	1.00690i	−0.0227322	−	0.128921i	−0.994062	+	0.108815i	$0.965294\pi$
$62$	−4.24763	+	0.626355i	−0.539449	+	0.0795472i
$63$	6.95133	+	3.83132i	0.875785	+	0.482701i
$64$	−2.77946	−	7.50164i	−0.347432	−	0.937705i
$65$	4.58230	−	12.5898i	0.568365	−	1.56157i
$66$	−0.508254	+	1.47274i	−0.0625617	+	0.181282i
$67$	6.53794	−	7.79161i	0.798736	−	0.951897i	−0.200879	−	0.979616i	$-0.564380\pi$
$67$	6.53794	−	7.79161i	0.798736	−	0.951897i	0.999616	+	0.0277191i	$0.00882440\pi$
$68$	−1.16120	+	2.70624i	−0.140816	+	0.328180i
$69$	0.406491	+	9.05040i	0.0489358	+	1.08954i
$70$	2.19862	−	7.86561i	0.262786	−	0.940120i
$71$	7.55151	−	13.0796i	0.896199	−	1.55226i	0.0638855	−	0.997957i	$-0.479651\pi$
$71$	7.55151	−	13.0796i	0.896199	−	1.55226i	0.832314	−	0.554305i	$-0.187016\pi$
$72$	−6.52938	−	5.41916i	−0.769494	−	0.638654i
$73$	1.34266			0.157147			0.0785733	−	0.996908i	$-0.474964\pi$
$73$	1.34266			0.157147			0.0785733	+	0.996908i	$0.474964\pi$
$74$	−5.74871	+	1.91105i	−0.668274	+	0.222155i
$75$	0.156625	+	0.376792i	0.0180855	+	0.0435082i
$76$	14.1238	−	1.67835i	1.62011	−	0.192520i
$77$	1.63278	+	0.407259i	0.186073	+	0.0464114i
$78$	−9.46997	+	11.6778i	−1.07226	+	1.32225i
$79$	10.0183	+	11.9393i	1.12714	+	1.34327i	0.931983	+	0.362503i	$0.118078\pi$
$79$	10.0183	+	11.9393i	1.12714	+	1.34327i	0.195159	+	0.980772i	$0.437478\pi$
$80$	−3.88846	+	7.81732i	−0.434743	+	0.874003i
$81$	−8.87098	−	1.51847i	−0.985664	−	0.168719i
$82$	2.30109	−	0.339319i	0.254113	−	0.0374716i
$83$	1.97260	+	11.1872i	0.216521	+	1.22795i	0.878248	+	0.478205i	$0.158712\pi$
$83$	1.97260	+	11.1872i	0.216521	+	1.22795i	−0.661728	+	0.749744i	$0.730176\pi$
$84$	−5.21186	+	7.53900i	−0.568660	+	0.822572i
$85$	3.02011	−	1.09923i	0.327577	−	0.119228i
$86$	10.5757	+	6.50919i	1.14041	+	0.701904i
$87$	−6.86718	−	5.25574i	−0.736239	−	0.563474i
$88$	−1.63263	−	0.755585i	−0.174039	−	0.0805456i
$89$	5.86719	+	3.38742i	0.621921	+	0.359066i	0.777617	−	0.628739i	$-0.216429\pi$
$89$	5.86719	+	3.38742i	0.621921	+	0.359066i	−0.155696	+	0.987805i	$0.549762\pi$
$90$	0.570466	+	9.24305i	0.0601324	+	0.974303i
$91$	13.4624	+	9.08234i	1.41125	+	0.952088i
$92$	−10.4445	−	0.588185i	−1.08891	−	0.0613225i
$93$	−2.83094	−	4.43145i	−0.293555	−	0.459520i
$94$	−5.33423	−	9.87022i	−0.550183	−	1.01804i
$95$	−11.8912	−	9.97788i	−1.22001	−	1.02371i
$96$	6.98677	−	6.86914i	0.713084	−	0.701079i
$97$	−7.21277	+	6.05224i	−0.732346	+	0.614511i	−0.930770	−	0.365605i	$-0.880862\pi$
$97$	−7.21277	+	6.05224i	−0.732346	+	0.614511i	0.198424	+	0.980116i	$0.436418\pi$
$98$	8.60566	+	4.89311i	0.869303	+	0.494279i
$99$	−1.90044	+	0.171059i	−0.191001	+	0.0171920i
$100$	−0.451119	+	0.136001i	−0.0451119	+	0.0136001i
$101$	2.00300	+	2.38708i	0.199306	+	0.237523i	0.856435	−	0.516254i	$-0.172674\pi$
$101$	2.00300	+	2.38708i	0.199306	+	0.237523i	−0.657130	+	0.753778i	$0.728230\pi$
$102$	−3.60618	+	0.0604311i	−0.357065	+	0.00598357i
$103$	−2.98540	−	0.526406i	−0.294160	−	0.0518683i	0.0246207	−	0.999697i	$-0.492162\pi$
$103$	−2.98540	−	0.526406i	−0.294160	−	0.0518683i	−0.318781	+	0.947829i	$0.603273\pi$
$104$	−12.3113	−	12.2406i	−1.20723	−	1.20029i
$105$	9.89104	−	1.48994i	0.965267	−	0.145403i
$106$	−16.4814	−	3.38662i	−1.60081	−	0.328938i
$107$	2.94542	+	5.10162i	0.284745	+	0.493192i	0.972547	−	0.232706i	$-0.0747579\pi$
$107$	2.94542	+	5.10162i	0.284745	+	0.493192i	−0.687803	+	0.725898i	$0.741425\pi$
$108$	2.77866	−	10.0139i	0.267377	−	0.963592i
$109$	−2.51198	+	4.35087i	−0.240604	+	0.416738i	−0.960886	−	0.276943i	$-0.910679\pi$
$109$	−2.51198	+	4.35087i	−0.240604	+	0.416738i	0.720283	+	0.693681i	$0.244012\pi$
$110$	0.619362	+	1.86313i	0.0590538	+	0.177643i
$111$	−5.01941	−	5.46399i	−0.476422	−	0.518619i
$112$	−8.05316	−	6.86633i	−0.760953	−	0.648808i
$113$	6.09234	−	7.26056i	0.573119	−	0.683016i	−0.399149	−	0.916886i	$-0.630694\pi$
$113$	6.09234	−	7.26056i	0.573119	−	0.683016i	0.972268	+	0.233870i	$0.0751389\pi$
$114$	8.96141	+	14.9379i	0.839313	+	1.39906i
$115$	7.33866	+	8.74588i	0.684334	+	0.815557i
$116$	6.83841	−	7.27626i	0.634931	−	0.675583i
$117$	−17.7984	−	4.72139i	−1.64547	−	0.436493i
$118$	−6.50193	+	5.15122i	−0.598551	+	0.474208i
$119$	0.406849	+	3.87436i	0.0372958	+	0.355162i
$120$	−10.6849	−	0.422272i	−0.975396	−	0.0385480i
$121$	9.95647	−	3.62386i	0.905133	−	0.329442i
$122$	0.687467	+	1.27206i	0.0622404	+	0.115167i
$123$	1.53362	+	2.40068i	0.138282	+	0.216462i
$124$	5.42090	−	2.73553i	0.486811	−	0.245658i
$125$	9.89693	+	5.71400i	0.885209	+	0.511076i
$126$	−11.0380	−	2.04050i	−0.983339	−	0.181782i
$127$	−13.0701	+	7.54601i	−1.15978	+	0.669600i	−0.951252	−	0.308415i	$-0.900201\pi$
$127$	−13.0701	+	7.54601i	−1.15978	+	0.669600i	−0.208530	+	0.978016i	$0.566868\pi$
$128$	7.07670	+	8.82725i	0.625497	+	0.780226i
$129$	−1.96635	+	15.0817i	−0.173128	+	1.32787i
$130$	−0.532878	+	18.9398i	−0.0467365	+	1.66113i
$131$	−4.68840	−	3.93404i	−0.409628	−	0.343718i	0.414573	−	0.910016i	$-0.363931\pi$
$131$	−4.68840	−	3.93404i	−0.409628	−	0.343718i	−0.824201	+	0.566298i	$0.808375\pi$
$132$	0.0250552	−	2.20317i	0.00218078	−	0.191761i
$133$	15.2231	−	11.0580i	1.32001	−	0.958854i
$134$	−5.29792	+	13.3731i	−0.457671	+	1.15526i
$135$	−10.0407	+	5.27483i	−0.864164	+	0.453985i
$136$	0.351012	−	4.14982i	0.0300990	−	0.355845i
$137$	5.29577	−	14.5500i	0.452448	−	1.24309i	−0.478548	−	0.878062i	$-0.658837\pi$
$137$	5.29577	−	14.5500i	0.452448	−	1.24309i	0.930996	−	0.365030i	$-0.118941\pi$
$138$	−4.58310	−	11.9643i	−0.390140	−	1.01847i
$139$	−1.39213	−	3.82486i	−0.118079	−	0.324420i	0.866547	−	0.499096i	$-0.166334\pi$
$139$	−1.39213	−	3.82486i	−0.118079	−	0.324420i	−0.984626	+	0.174676i	$0.944112\pi$
$140$	0.558473	+	11.5365i	0.0471995	+	0.975015i
$141$	8.35130	−	10.9119i	0.703306	−	0.918944i
$142$	−4.29904	+	20.9218i	−0.360768	+	1.75572i
$143$	−3.90402			−0.326471
$144$	11.1801	+	4.35962i	0.931671	+	0.363302i
$145$	−10.8978			−0.905014
$146$	−1.80186	+	0.598992i	−0.149123	+	0.0495729i
$147$	−1.14921	+	12.0698i	−0.0947849	+	0.995498i
$148$	6.86223	−	5.12927i	0.564072	−	0.421623i
$149$	4.45970	+	12.2529i	0.365353	+	1.00380i	0.977107	+	0.212751i	$0.0682422\pi$
$149$	4.45970	+	12.2529i	0.365353	+	1.00380i	−0.611754	+	0.791048i	$0.709536\pi$
$150$	−0.378287	−	0.435782i	−0.0308870	−	0.0355815i
$151$	−1.25120	+	0.220620i	−0.101821	+	0.0179538i	−0.224327	−	0.974514i	$-0.572018\pi$
$151$	−1.25120	+	0.220620i	−0.101821	+	0.0179538i	0.122505	+	0.992468i	$0.460907\pi$
$152$	−18.2054	+	8.55330i	−1.47665	+	0.693764i
$153$	−1.87683	−	3.99872i	−0.151733	−	0.323278i
$154$	−2.37289	+	0.181879i	−0.191213	+	0.0146562i
$155$	−6.22720	−	2.26652i	−0.500181	−	0.182051i
$156$	7.49900	−	19.8964i	0.600401	−	1.59299i
$157$	−2.07914	+	0.756745i	−0.165933	+	0.0603948i	−0.423651	−	0.905825i	$-0.639252\pi$
$157$	−2.07914	+	0.756745i	−0.165933	+	0.0603948i	0.257718	+	0.966220i	$0.417030\pi$
$158$	−18.7709	−	11.5532i	−1.49333	−	0.919123i
$159$	−4.48538	−	20.1131i	−0.355714	−	1.59508i
$160$	1.73083	−	12.2256i	0.136834	−	0.966519i
$161$	−12.4387	+	6.06531i	−0.980303	+	0.478014i
$162$	12.5823	−	1.91976i	0.988560	−	0.150830i
$163$	16.4351	−	9.48881i	1.28730	−	0.743221i	0.309125	−	0.951021i	$-0.399964\pi$
$163$	16.4351	−	9.48881i	1.28730	−	0.743221i	0.978171	+	0.207801i	$0.0666305\pi$
$164$	−2.93670	+	1.48194i	−0.229318	+	0.115720i
$165$	−1.77085	+	1.62677i	−0.137861	+	0.126644i
$166$	−7.63808	−	14.1332i	−0.592830	−	1.09695i
$167$	−14.5713	−	12.2268i	−1.12756	−	0.946139i	−0.128602	−	0.991696i	$-0.541049\pi$
$167$	−14.5713	−	12.2268i	−1.12756	−	0.946139i	−0.998962	+	0.0455576i	$0.985494\pi$
$168$	3.63101	−	12.4425i	0.280139	−	0.959960i
$169$	−23.1870	−	8.43939i	−1.78362	−	0.649184i
$170$	−3.56261	+	2.82252i	−0.273240	+	0.216477i
$171$	−12.1933	+	17.5069i	−0.932448	+	1.33879i
$172$	−17.0966	−	4.01728i	−1.30360	−	0.306315i
$173$	0.189665	−	0.521101i	0.0144200	−	0.0396186i	−0.932274	−	0.361753i	$-0.882178\pi$
$173$	0.189665	−	0.521101i	0.0144200	−	0.0396186i	0.946694	+	0.322135i	$0.104400\pi$
$174$	11.5605	+	3.98961i	0.876398	+	0.302452i
$175$	−0.433025	+	0.448327i	−0.0327336	+	0.0338904i
$176$	2.52808	+	0.285645i	0.190561	+	0.0215313i
$177$	−9.01743	−	4.67985i	−0.677792	−	0.351759i
$178$	−9.38500	−	1.92845i	−0.703436	−	0.144543i
$179$	−0.671351	−	1.16281i	−0.0501791	−	0.0869128i	0.839845	−	0.542827i	$-0.182646\pi$
$179$	−0.671351	−	1.16281i	−0.0501791	−	0.0869128i	−0.890024	+	0.455914i	$0.849313\pi$
$180$	−4.88911	−	12.1497i	−0.364412	−	0.905586i
$181$	12.0702	+	20.9063i	0.897174	+	1.55395i	0.831091	+	0.556137i	$0.187717\pi$
$181$	12.0702	+	20.9063i	0.897174	+	1.55395i	0.0660835	+	0.997814i	$0.478950\pi$
$182$	−22.1185	−	6.18263i	−1.63953	−	0.458287i
$183$	−1.07630	+	1.40631i	−0.0795627	+	0.103957i
$184$	14.2789	−	3.87018i	1.05266	−	0.285313i
$185$	−9.20817	−	1.62365i	−0.676998	−	0.119373i
$186$	5.77611	+	4.68407i	0.423525	+	0.343453i
$187$	−0.601984	−	0.717417i	−0.0440215	−	0.0524627i
$188$	11.5619	+	10.8662i	0.843237	+	0.792496i
$189$	−3.25825	−	13.3560i	−0.237003	−	0.971509i
$190$	20.4094	+	8.08542i	1.48065	+	0.586578i
$191$	−8.54639	+	7.17127i	−0.618395	+	0.518895i	−0.897299	−	0.441424i	$-0.854473\pi$
$191$	−8.54639	+	7.17127i	−0.618395	+	0.518895i	0.278903	+	0.960319i	$0.410029\pi$
$192$	−6.31179	+	12.3354i	−0.455514	+	0.890229i
$193$	−2.25408	+	12.7835i	−0.162252	+	0.920177i	0.789601	+	0.613621i	$0.210288\pi$
$193$	−2.25408	+	12.7835i	−0.162252	+	0.920177i	−0.951853	+	0.306556i	$0.900823\pi$
$194$	6.97953	−	11.3399i	0.501101	−	0.814158i
$195$	−21.4280	+	8.90721i	−1.53449	+	0.637858i
$196$	−13.7318	−	2.72739i	−0.980840	−	0.194814i
$197$	−1.57000	+	0.906438i	−0.111858	+	0.0645811i	−0.554885	−	0.831927i	$-0.687238\pi$
$197$	−1.57000	+	0.906438i	−0.111858	+	0.0645811i	0.443027	+	0.896508i	$0.353904\pi$
$198$	2.47408	−	1.07739i	0.175825	−	0.0765669i
$199$	13.9299	−	8.04241i	0.987462	−	0.570112i	0.0829475	−	0.996554i	$-0.473567\pi$
$199$	13.9299	−	8.04241i	0.987462	−	0.570112i	0.904515	+	0.426442i	$0.140233\pi$
$200$	0.544730	−	0.383769i	0.0385182	−	0.0271365i
$201$	−17.5993	+	0.790461i	−1.24136	+	0.0557548i
$202$	−3.75296	−	2.30989i	−0.264057	−	0.162523i
$203$	3.19683	−	12.8167i	0.224374	−	0.899559i
$204$	4.81255	−	1.68990i	0.336946	−	0.118317i
$205$	3.37350	+	1.22785i	0.235616	+	0.0857571i
$206$	4.24125	−	0.625416i	0.295502	−	0.0435748i
$207$	11.0678	−	11.1233i	0.769266	−	0.773124i
$208$	21.9827	+	10.9345i	1.52422	+	0.758173i
$209$	−1.54704	+	4.25047i	−0.107011	+	0.294011i
$210$	−12.6091	+	6.41213i	−0.870112	+	0.442479i
$211$	−8.56374	+	10.2059i	−0.589552	+	0.702601i	−0.975520	−	0.219912i	$-0.929423\pi$
$211$	−8.56374	+	10.2059i	−0.589552	+	0.702601i	0.385968	+	0.922512i	$0.373868\pi$
$212$	23.6289	−	2.80786i	1.62284	−	0.192845i
$213$	−25.5320	+	5.69383i	−1.74942	+	0.390134i
$214$	−6.22872	−	5.53237i	−0.425786	−	0.378185i
$215$	9.58350	+	16.5991i	0.653589	+	1.13205i
$216$	0.738479	+	14.6784i	0.0502471	+	0.998737i
$217$	4.49234	−	6.65884i	0.304960	−	0.452031i
$218$	1.43006	−	6.95953i	0.0968557	−	0.471359i
$219$	−1.57327	−	1.71261i	−0.106312	−	0.115728i
$220$	−1.66237	−	2.22402i	−0.112077	−	0.149943i
$221$	−3.09109	−	8.49270i	−0.207929	−	0.571281i
$222$	9.17369	+	5.09342i	0.615698	+	0.341848i
$223$	−1.31882	+	3.62344i	−0.0883150	+	0.242644i	−0.975985	−	0.217836i	$-0.930100\pi$
$223$	−1.31882	+	3.62344i	−0.0883150	+	0.242644i	0.887670	+	0.460479i	$0.152322\pi$
$224$	13.8706	+	5.62194i	0.926769	+	0.375632i
$225$	0.297086	−	0.641288i	0.0198058	−	0.0427525i
$226$	−4.93683	+	12.4616i	−0.328393	+	0.828936i
$227$	−0.965413	−	5.47513i	−0.0640767	−	0.363397i	−0.999939	−	0.0110315i	$-0.996489\pi$
$227$	−0.965413	−	5.47513i	−0.0640767	−	0.363397i	0.935862	−	0.352366i	$-0.114623\pi$
$228$	−18.6904	−	16.0488i	−1.23780	−	1.06286i
$229$	−13.9229	+	5.06752i	−0.920051	+	0.334871i	−0.758259	−	0.651954i	$-0.773950\pi$
$229$	−13.9229	+	5.06752i	−0.920051	+	0.334871i	−0.161792	+	0.986825i	$0.551727\pi$
$230$	−13.7502	−	8.46305i	−0.906664	−	0.558037i
$231$	−1.39374	−	2.55988i	−0.0917015	−	0.168428i
$232$	−5.93107	+	12.8155i	−0.389394	+	0.841381i
$233$			5.18127i			0.339437i	0.985493	+	0.169718i	$0.0542858\pi$
$233$			5.18127i			0.339437i	−0.985493	+	0.169718i	$0.945714\pi$
$234$	25.9919	−	1.60418i	1.69914	−	0.104868i
$235$		−	17.3165i		−	1.12960i
$236$	6.42753	−	9.81361i	0.418397	−	0.638812i
$237$	3.49009	−	26.7685i	0.226706	−	1.73880i
$238$	−2.27444	−	5.01791i	−0.147430	−	0.325263i
$239$	7.22808	−	2.63081i	0.467546	−	0.170173i	−0.0974945	−	0.995236i	$-0.531083\pi$
$239$	7.22808	−	2.63081i	0.467546	−	0.170173i	0.565040	+	0.825063i	$0.308861\pi$
$240$	14.5276	−	4.20010i	0.937752	−	0.271115i
$241$	9.09496	+	3.31029i	0.585858	+	0.213235i	0.617907	−	0.786252i	$-0.287981\pi$
$241$	9.09496	+	3.31029i	0.585858	+	0.213235i	−0.0320489	+	0.999486i	$0.510203\pi$
$242$	−11.7449	+	9.30504i	−0.754993	+	0.598151i
$243$	8.45773	+	13.0945i	0.542564	+	0.840015i
$244$	−1.49008	−	1.40042i	−0.0953926	−	0.0896524i
$245$	8.09438	+	12.9591i	0.517131	+	0.827924i
$246$	−3.12913	−	2.53753i	−0.199506	−	0.161787i
$247$	−28.0583	+	33.4385i	−1.78530	+	2.12764i
$248$	−6.05448	+	6.08949i	−0.384460	+	0.386683i
$249$	11.9582	−	15.6247i	0.757822	−	0.990175i
$250$	−15.8309	−	3.25296i	−1.00123	−	0.205735i
$251$	5.07054	+	8.78244i	0.320050	+	0.554343i	0.980498	−	0.196529i	$-0.0629670\pi$
$251$	5.07054	+	8.78244i	0.320050	+	0.554343i	−0.660448	+	0.750872i	$0.729634\pi$
$252$	15.7233	−	2.18593i	0.990474	−	0.137700i
$253$	1.66341	−	2.88111i	0.104578	−	0.181134i
$254$	14.1736	−	15.9576i	0.889334	−	1.00127i
$255$	−4.94094	−	2.56424i	−0.309414	−	0.160579i
$256$	−13.4350	−	8.68913i	−0.839687	−	0.543071i
$257$	−2.67399	−	7.34674i	−0.166799	−	0.458277i	0.827928	−	0.560834i	$-0.189520\pi$
$257$	−2.67399	−	7.34674i	−0.166799	−	0.458277i	−0.994727	+	0.102558i	$0.967297\pi$
$258$	−4.08943	−	21.1169i	−0.254597	−	1.31468i
$259$	4.61073	−	10.3533i	0.286497	−	0.643322i
$260$	−7.73436	−	25.6550i	−0.479664	−	1.59106i
$261$	1.34275	+	14.9178i	0.0831140	+	0.923386i
$262$	8.04692	+	3.18789i	0.497140	+	0.196948i
$263$	6.04154	−	5.06945i	0.372537	−	0.312596i	−0.437227	−	0.899351i	$-0.644039\pi$
$263$	6.04154	−	5.06945i	0.372537	−	0.312596i	0.809764	+	0.586755i	$0.199595\pi$
$264$	0.949260	+	2.96784i	0.0584229	+	0.182658i
$265$	−19.8938	−	16.6929i	−1.22206	−	1.02543i
$266$	−15.4961	+	21.6313i	−0.950130	+	1.32630i
$267$	−2.55411	−	11.4530i	−0.156309	−	0.700915i
$268$	1.14378	−	20.3103i	0.0698675	−	1.24065i
$269$	16.3591	+	9.44495i	0.997434	+	0.575869i	0.907488	−	0.420078i	$-0.137997\pi$
$269$	16.3591	+	9.44495i	0.997434	+	0.575869i	0.0899460	+	0.995947i	$0.471331\pi$
$270$	11.1214	−	11.5582i	0.676828	−	0.703411i
$271$	4.33545	−	2.50307i	0.263360	−	0.152051i	−0.362506	−	0.931981i	$-0.618079\pi$
$271$	4.33545	−	2.50307i	0.263360	−	0.152051i	0.625866	+	0.779930i	$0.284746\pi$
$272$	1.38027	+	5.72568i	0.0836914	+	0.347170i
$273$	−4.18978	−	27.8141i	−0.253577	−	1.68339i
$274$	−0.615848	+	21.8887i	−0.0372047	+	1.32235i
$275$	0.0260199	−	0.147566i	0.00156906	−	0.00889858i
$276$	11.4881	+	14.0115i	0.691503	+	0.843395i
$277$	0.736720	−	0.618181i	0.0442652	−	0.0371429i	−0.620387	−	0.784296i	$-0.713024\pi$
$277$	0.736720	−	0.618181i	0.0442652	−	0.0371429i	0.664652	+	0.747153i	$0.268580\pi$
$278$	3.57461	+	4.51191i	0.214391	+	0.270606i
$279$	−2.33531	+	8.80353i	−0.139811	+	0.527054i
$280$	−5.89619	−	15.2329i	−0.352365	−	0.910342i
$281$	2.52122	+	3.00467i	0.150403	+	0.179243i	0.835985	−	0.548752i	$-0.184897\pi$
$281$	2.52122	+	3.00467i	0.150403	+	0.179243i	−0.685582	+	0.727995i	$0.740452\pi$
$282$	−6.33944	+	18.3695i	−0.377508	+	1.09389i
$283$	1.43657	−	1.71204i	0.0853952	−	0.101770i	−0.721655	−	0.692253i	$-0.756618\pi$
$283$	1.43657	−	1.71204i	0.0853952	−	0.101770i	0.807050	+	0.590483i	$0.201063\pi$
$284$	−3.56435	−	29.9950i	−0.211506	−	1.77988i
$285$	1.20636	+	26.8592i	0.0714587	+	1.59100i
$286$	5.23921	−	1.74167i	0.309801	−	0.102987i
$287$	−2.43366	+	3.60734i	−0.143655	+	0.212934i
$288$	−16.9486	−	0.862949i	−0.998706	−	0.0508498i
$289$	−7.41598	+	12.8449i	−0.436234	+	0.755580i
$290$	14.6249	−	4.86177i	0.858804	−	0.285493i
$291$	16.1714	+	2.10844i	0.947987	+	0.123599i
$292$	2.15087	−	1.60770i	0.125870	−	0.0940835i
$293$	9.02311	+	24.7908i	0.527135	+	1.44829i	0.862429	+	0.506179i	$0.168942\pi$
$293$	9.02311	+	24.7908i	0.527135	+	1.44829i	−0.335293	+	0.942114i	$0.608835\pi$
$294$	−3.84236	−	16.7104i	−0.224091	−	0.974568i
$295$	−12.6086	+	2.22324i	−0.734102	+	0.129442i
$296$	−6.92086	+	9.94490i	−0.402267	+	0.578036i
$297$	2.44504	+	2.22364i	0.141875	+	0.129029i
$298$	−11.4512	−	14.4539i	−0.663353	−	0.837292i
$299$	24.5938	−	20.6367i	1.42230	−	1.19345i
$300$	0.702074	+	0.416059i	0.0405343	+	0.0240212i
$301$	−22.3332	+	6.40171i	−1.28727	+	0.368989i
$302$	1.58069	−	0.854262i	0.0909585	−	0.0491572i
$303$	0.697790	−	5.35196i	0.0400870	−	0.307462i
$304$	20.6159	−	19.6004i	1.18240	−	1.12416i
$305$			2.23173i			0.127788i
$306$	4.30264	+	4.52901i	0.245965	+	0.258906i
$307$	−3.03128	−	1.75011i	−0.173004	−	0.0998840i	0.410997	−	0.911636i	$-0.365180\pi$
$307$	−3.03128	−	1.75011i	−0.173004	−	0.0998840i	−0.584002	+	0.811753i	$0.698514\pi$
$308$	3.10328	−	1.30268i	0.176826	−	0.0742272i
$309$	2.82670	+	4.42480i	0.160805	+	0.251718i
$310$	9.36807	+	0.263574i	0.532071	+	0.0149700i
$311$	16.8113	+	14.1064i	0.953283	+	0.799899i	0.979847	−	0.199748i	$-0.0640123\pi$
$311$	16.8113	+	14.1064i	0.953283	+	0.799899i	−0.0265645	+	0.999647i	$0.508457\pi$
$312$	−1.18745	+	30.0465i	−0.0672261	+	1.70105i
$313$	29.4620	+	10.7233i	1.66529	+	0.606116i	0.991181	−	0.132517i	$-0.0423060\pi$
$313$	29.4620	+	10.7233i	1.66529	+	0.606116i	0.674108	+	0.738633i	$0.264528\pi$
$314$	2.45261	−	1.94311i	0.138409	−	0.109656i
$315$	−13.4903	−	10.8706i	−0.760094	−	0.612486i
$316$	30.3448	+	7.13029i	1.70703	+	0.401110i
$317$	−23.4789	+	4.13997i	−1.31871	+	0.232524i	−0.788338	−	0.615242i	$-0.789058\pi$
$317$	−23.4789	+	4.13997i	−1.31871	+	0.232524i	−0.530370	+	0.847766i	$0.677947\pi$
$318$	14.9923	+	24.9909i	0.840728	+	1.40142i
$319$	1.08610	+	2.98404i	0.0608101	+	0.167074i
$320$	3.13134	+	17.1790i	0.175047	+	0.960334i
$321$	3.05600	−	9.73483i	0.170569	−	0.543345i
$322$	13.9868	−	13.6888i	0.779456	−	0.762849i
$323$	−10.4713			−0.582636
$324$	−16.0291	+	8.18958i	−0.890503	+	0.454977i
$325$	0.723017	−	1.25230i	0.0401057	−	0.0694652i
$326$	−17.8228	+	20.0661i	−0.987113	+	1.11136i
$327$	8.49311	−	1.89403i	0.469670	−	0.104740i
$328$	3.27993	−	3.29890i	0.181104	−	0.182151i
$329$	20.3657	+	5.07973i	1.12279	+	0.280055i
$330$	1.65075	−	2.97315i	0.0908710	−	0.163666i
$331$	8.60304	−	1.51695i	0.472866	−	0.0833790i	0.0678635	−	0.997695i	$-0.478382\pi$
$331$	8.60304	−	1.51695i	0.472866	−	0.0833790i	0.405002	+	0.914316i	$0.367271\pi$
$332$	16.5555	+	15.5593i	0.908599	+	0.853925i
$333$	−1.08801	+	12.8049i	−0.0596227	+	0.701704i
$334$	25.0095	+	9.90781i	1.36846	+	0.542131i
$335$	−17.0072	+	14.2707i	−0.929201	+	0.779692i
$336$	0.678055	+	18.3178i	0.0369910	+	0.999316i
$337$	−4.28332	+	24.2919i	−0.233327	+	1.32327i	0.612780	+	0.790254i	$0.290051\pi$
$337$	−4.28332	+	24.2919i	−0.233327	+	1.32327i	−0.846107	+	0.533012i	$0.821060\pi$
$338$	34.8821	+	0.981421i	1.89734	+	0.0533823i
$339$	−16.3998	+	0.736586i	−0.890717	+	0.0400058i
$340$	3.52185	−	5.37719i	0.190999	−	0.291619i
$341$			1.93102i			0.104571i
$342$	8.55326	−	28.9341i	0.462507	−	1.56458i
$343$	−17.6154	+	5.71818i	−0.951142	+	0.308753i
$344$	24.7359	−	2.23598i	1.33367	−	0.120556i
$345$	2.55659	−	19.6087i	0.137642	−	1.05570i
$346$	−0.0220563	+	0.783934i	−0.00118575	+	0.0421445i
$347$	1.83901	−	10.4296i	0.0987234	−	0.559888i	−0.894819	−	0.446429i	$-0.852696\pi$
$347$	1.83901	−	10.4296i	0.0987234	−	0.559888i	0.993543	−	0.113460i	$-0.0361933\pi$
$348$	−17.2941	−	0.196674i	−0.927059	−	0.0105429i
$349$	3.75279	+	21.2831i	0.200882	+	1.13926i	0.903789	+	0.427977i	$0.140774\pi$
$349$	3.75279	+	21.2831i	0.200882	+	1.13926i	−0.702907	+	0.711281i	$0.748115\pi$
$350$	0.381112	−	0.794839i	0.0203713	−	0.0424859i
$351$	14.8331	+	28.2349i	0.791731	+	1.50707i
$352$	−3.52012	+	0.744497i	−0.187623	+	0.0396818i
$353$	5.90766	−	16.2312i	0.314433	−	0.863898i	−0.677314	−	0.735694i	$-0.736856\pi$
$353$	5.90766	−	16.2312i	0.314433	−	0.863898i	0.991748	−	0.128205i	$-0.0409214\pi$
$354$	14.1892	+	2.25749i	0.754149	+	0.119984i
$355$	−21.1902	+	25.2535i	−1.12466	+	1.34032i
$356$	13.4550	−	1.59888i	0.713115	−	0.0847407i
$357$	4.46517	−	5.05875i	0.236322	−	0.267737i
$358$	1.41971	+	1.26100i	0.0750342	+	0.0666457i
$359$	−2.09639	+	3.63106i	−0.110643	+	0.191640i	−0.916030	−	0.401110i	$-0.868624\pi$
$359$	−2.09639	+	3.63106i	−0.110643	+	0.191640i	0.805386	+	0.592750i	$0.201958\pi$
$360$	11.9815	+	14.1238i	0.631479	+	0.744390i
$361$	15.7873	+	27.3443i	0.830909	+	1.43918i
$362$	−25.5251	−	22.6715i	−1.34157	−	1.19159i
$363$	−16.2889	−	8.45358i	−0.854945	−	0.443698i
$364$	32.4413	−	1.57045i	1.70039	−	0.0823140i
$365$	−2.88617	−	0.508910i	−0.151069	−	0.0266376i
$366$	0.817019	−	2.36743i	0.0427062	−	0.123748i
$367$	9.74583	−	1.71845i	0.508728	−	0.0897025i	0.0866082	−	0.996242i	$-0.472397\pi$
$367$	9.74583	−	1.71845i	0.508728	−	0.0897025i	0.422120	+	0.906540i	$0.361286\pi$
$368$	−17.4358	+	11.5640i	−0.908905	+	0.602813i
$369$	1.26512	−	4.76920i	0.0658597	−	0.248274i
$370$	13.0817	−	1.92903i	0.680087	−	0.100286i
$371$	25.4680	−	18.5000i	1.32223	−	0.960470i
$372$	−9.84123	−	3.70919i	−0.510244	−	0.192312i
$373$	−4.79590	+	27.1989i	−0.248322	+	1.40831i	0.564326	+	0.825552i	$0.309136\pi$
$373$	−4.79590	+	27.1989i	−0.248322	+	1.40831i	−0.812648	+	0.582754i	$0.801975\pi$
$374$	1.12792	+	0.694217i	0.0583234	+	0.0358971i
$375$	−4.30835	−	19.3193i	−0.222482	−	0.997644i
$376$	−20.3637	−	9.42440i	−1.05018	−	0.486026i
$377$			30.6452i			1.57831i
$378$	10.3310	+	16.4703i	0.531370	+	0.847140i
$379$		−	16.2375i		−	0.834063i	−0.908892	−	0.417031i	$-0.863071\pi$
$379$		−	16.2375i		−	0.834063i	0.908892	−	0.417031i	$-0.136929\pi$
$380$	−30.9965	−	1.74558i	−1.59009	−	0.0895464i
$381$	24.9401	+	7.82931i	1.27772	+	0.401108i
$382$	8.27002	−	13.4366i	0.423131	−	0.687477i
$383$	4.92208	−	27.9145i	0.251506	−	1.42636i	−0.553377	−	0.832931i	$-0.686661\pi$
$383$	4.92208	−	27.9145i	0.251506	−	1.42636i	0.804883	−	0.593433i	$-0.202228\pi$
$384$	2.96735	−	19.3699i	0.151427	−	0.988468i
$385$	−3.35545	−	1.49432i	−0.171010	−	0.0761574i
$386$	−2.67804	−	18.1611i	−0.136308	−	0.924376i
$387$	21.5413	−	15.1638i	1.09501	−	0.770822i
$388$	−4.30756	+	18.3319i	−0.218683	+	0.930663i
$389$	34.6152	−	6.10360i	1.75506	−	0.309465i	0.798718	−	0.601706i	$-0.205512\pi$
$389$	34.6152	−	6.10360i	1.75506	−	0.309465i	0.956345	+	0.292241i	$0.0944010\pi$
$390$	24.7828	−	21.5131i	1.25493	−	1.08936i
$391$	7.58453	+	1.33736i	0.383566	+	0.0676331i
$392$	19.6448	−	2.46589i	0.992214	−	0.124546i
$393$	0.475639	+	10.5900i	0.0239928	+	0.534192i
$394$	1.70256	−	1.91686i	0.0857737	−	0.0965698i
$395$	−17.0098	−	29.4618i	−0.855856	−	1.48239i
$396$	−2.83958	+	2.54961i	−0.142694	+	0.128123i
$397$	7.17303	−	12.4240i	0.360004	−	0.623545i	−0.627957	−	0.778248i	$-0.716109\pi$
$397$	7.17303	−	12.4240i	0.360004	−	0.623545i	0.987961	+	0.154703i	$0.0494420\pi$
$398$	−15.1060	+	17.0074i	−0.757197	+	0.852503i
$399$	−31.9426	−	6.46028i	−1.59913	−	0.323418i
$400$	−0.559821	+	0.758036i	−0.0279911	+	0.0379018i
$401$	20.6966	−	24.6652i	1.03354	−	1.23172i	0.0612032	−	0.998125i	$-0.480506\pi$
$401$	20.6966	−	24.6652i	1.03354	−	1.23172i	0.972334	−	0.233596i	$-0.0750493\pi$
$402$	23.2657	−	8.91227i	1.16039	−	0.444504i
$403$	−6.37355	+	17.5112i	−0.317489	+	0.872294i
$404$	6.06698	+	1.42559i	0.301844	+	0.0709259i
$405$	18.4934	+	6.62647i	0.918947	+	0.329272i
$406$	1.42768	+	18.6263i	0.0708548	+	0.924408i
$407$	0.473121	+	2.68320i	0.0234517	+	0.133001i
$408$	−5.70456	+	4.41484i	−0.282418	+	0.218567i
$409$	3.07122	−	17.4178i	0.151862	−	0.861253i	−0.809736	−	0.586794i	$-0.800390\pi$
$409$	3.07122	−	17.4178i	0.151862	−	0.861253i	0.961599	−	0.274460i	$-0.0884989\pi$
$410$	−5.07503	−	0.142788i	−0.250638	−	0.00705179i
$411$	−24.7644	+	10.2941i	−1.22154	+	0.507769i
$412$	−5.41277	+	2.73143i	−0.266668	+	0.134568i
$413$	1.08397	−	15.4810i	0.0533389	−	0.761768i
$414$	−9.89067	+	19.8651i	−0.486100	+	0.976319i
$415$		−	24.7955i		−	1.21716i
$416$	−34.3790	−	4.86719i	−1.68557	−	0.238633i
$417$	−3.24751	+	6.25751i	−0.159031	+	0.306431i
$418$	0.179907	−	6.39431i	0.00879951	−	0.312756i
$419$	−2.82615	+	16.0279i	−0.138066	+	0.783013i	0.834609	+	0.550843i	$0.185694\pi$
$419$	−2.82615	+	16.0279i	−0.138066	+	0.783013i	−0.972675	+	0.232170i	$0.925417\pi$
$420$	14.0609	−	14.2303i	0.686101	−	0.694369i
$421$	11.3965	−	9.56277i	0.555430	−	0.466061i	−0.321345	−	0.946962i	$-0.604135\pi$
$421$	11.3965	−	9.56277i	0.555430	−	0.466061i	0.876775	+	0.480901i	$0.159690\pi$
$422$	6.93949	−	17.5168i	0.337809	−	0.852704i
$423$	−23.7041	+	2.13361i	−1.15254	+	0.103740i
$424$	−30.4574	+	14.3096i	−1.47914	+	0.694934i
$425$	0.341614	−	0.0602357i	0.0165707	−	0.00292186i
$426$	31.7239	−	19.0316i	1.53703	−	0.922082i
$427$	−2.62470	−	0.654668i	−0.127018	−	0.0316816i
$428$	10.8271	+	4.64569i	0.523347	+	0.224558i
$429$	4.57455	+	4.97973i	0.220861	+	0.240423i
$430$	−20.2663	−	18.0006i	−0.977330	−	0.868068i
$431$	−11.3100	+	19.5894i	−0.544781	+	0.943589i	0.453840	+	0.891083i	$0.350054\pi$
$431$	−11.3100	+	19.5894i	−0.544781	+	0.943589i	−0.998621	+	0.0525052i	$0.983279\pi$
$432$	−7.53940	−	19.3690i	−0.362740	−	0.931891i
$433$	−3.84757			−0.184902			−0.0924511	−	0.995717i	$-0.529470\pi$
$433$	−3.84757			−0.184902			−0.0924511	+	0.995717i	$0.529470\pi$
$434$	−3.05808	+	10.9403i	−0.146792	+	0.525152i
$435$	12.7695	+	13.9006i	0.612253	+	0.666481i
$436$	1.18567	+	9.97770i	0.0567831	+	0.477845i
$437$	−12.7222	−	34.9540i	−0.608585	−	1.67207i
$438$	2.87537	+	1.59646i	0.137390	+	0.0762820i
$439$	−37.6862	+	6.64509i	−1.79866	+	0.317153i	−0.970093	−	0.242732i	$-0.921956\pi$
$439$	−37.6862	+	6.64509i	−1.79866	+	0.317153i	−0.828570	+	0.559885i	$0.810845\pi$
$440$	3.22309	+	2.24302i	0.153655	+	0.106932i
$441$	16.7420	−	12.6769i	0.797239	−	0.603663i
$442$	7.93705	+	10.0182i	0.377527	+	0.476519i
$443$	21.2734	+	7.74290i	1.01073	+	0.367876i	0.793714	−	0.608292i	$-0.208145\pi$
$443$	21.2734	+	7.74290i	1.01073	+	0.367876i	0.217018	+	0.976168i	$0.430367\pi$
$444$	−14.5834	−	2.74280i	−0.692098	−	0.130167i
$445$	−11.3281	−	9.50543i	−0.537005	−	0.450601i
$446$	0.153367	−	5.45103i	0.00726213	−	0.258114i
$447$	10.4034	−	20.0459i	0.492064	−	0.948139i
$448$	−21.1225	−	1.35667i	−0.997944	−	0.0640966i
$449$	−14.3897	−	8.30791i	−0.679093	−	0.392075i	0.120420	−	0.992723i	$-0.461576\pi$
$449$	−14.3897	−	8.30791i	−0.679093	−	0.392075i	−0.799513	+	0.600648i	$0.794909\pi$
$450$	−0.112598	+	0.993147i	−0.00530792	+	0.0468174i
$451$		−	1.04611i		−	0.0492592i
$452$	1.06582	−	18.9260i	0.0501321	−	0.890204i
$453$	1.74750	+	1.33744i	0.0821049	+	0.0628383i
$454$	3.73817	+	6.91695i	0.175441	+	0.324629i
$455$	−25.4963	−	24.6260i	−1.19528	−	1.15448i
$456$	32.2423	+	13.1993i	1.50988	+	0.618115i
$457$	−14.4814	+	12.1513i	−0.677410	+	0.568415i	−0.915248	−	0.402890i	$-0.868006\pi$
$457$	−14.4814	+	12.1513i	−0.677410	+	0.568415i	0.237838	+	0.971305i	$0.423561\pi$
$458$	16.4238	−	13.0120i	0.767435	−	0.608009i
$459$	−2.90134	+	7.07948i	−0.135423	+	0.330442i
$460$	22.2284	+	5.22314i	1.03641	+	0.243530i
$461$	−36.1966	+	6.38244i	−1.68584	+	0.297260i	−0.932715	−	0.360613i	$-0.882567\pi$
$461$	−36.1966	+	6.38244i	−1.68584	+	0.297260i	−0.753129	+	0.657873i	$0.771456\pi$
$462$	3.01243	+	2.81359i	0.140151	+	0.130900i
$463$	−4.20908	−	11.5643i	−0.195612	−	0.537441i	0.802644	−	0.596458i	$-0.203426\pi$
$463$	−4.20908	−	11.5643i	−0.195612	−	0.537441i	−0.998257	+	0.0590168i	$0.981203\pi$
$464$	2.24221	−	19.8445i	0.104092	−	0.921257i
$465$	4.40572	+	10.5988i	0.204310	+	0.491509i
$466$	−2.31149	−	6.95329i	−0.107078	−	0.322105i
$467$	−17.1399	+	29.6873i	−0.793142	+	1.37376i	0.130870	+	0.991400i	$0.458223\pi$
$467$	−17.1399	+	29.6873i	−0.793142	+	1.37376i	−0.924012	+	0.382363i	$0.875110\pi$
$468$	−34.1656	+	13.7484i	−1.57930	+	0.635520i
$469$	−11.7946	−	24.1881i	−0.544622	−	1.11690i
$470$	7.72529	+	23.2388i	0.356341	+	1.07193i
$471$	3.40150	+	1.76530i	0.156733	+	0.0813408i
$472$	−4.24769	+	16.0374i	−0.195516	+	0.738180i
$473$	3.59006	−	4.27847i	0.165071	−	0.196724i
$474$	7.25836	+	37.4805i	0.333387	+	1.72154i
$475$	−1.07692	−	1.28343i	−0.0494126	−	0.0588876i
$476$	5.29091	+	5.71937i	0.242508	+	0.262147i
$477$	−20.3993	+	29.2889i	−0.934020	+	1.34105i
$478$	−8.52645	+	6.75517i	−0.389991	+	0.308974i
$479$	−20.1338	+	16.8942i	−0.919936	+	0.771918i	−0.973983	−	0.226621i	$-0.927232\pi$
$479$	−20.1338	+	16.8942i	−0.919936	+	0.771918i	0.0540473	+	0.998538i	$0.482788\pi$
$480$	−17.6223	+	12.1176i	−0.804345	+	0.553092i
$481$	−4.56578	+	25.8938i	−0.208181	+	1.18066i
$482$	−13.6823	−	0.384956i	−0.623210	−	0.0175343i
$483$	22.3116	+	8.75892i	1.01521	+	0.398545i
$484$	11.6105	−	17.7271i	0.527752	−	0.805777i
$485$	17.7985	−	10.2760i	0.808189	−	0.466608i
$486$	−17.1921	−	13.7997i	−0.779849	−	0.625968i
$487$	13.2469	+	7.64810i	0.600274	+	0.346568i	0.769149	−	0.639069i	$-0.220680\pi$
$487$	13.2469	+	7.64810i	0.600274	+	0.346568i	−0.168875	+	0.985637i	$0.554014\pi$
$488$	2.62445	+	1.21460i	0.118803	+	0.0549825i
$489$	−31.3612	−	9.84504i	−1.41820	−	0.445208i
$490$	−16.6440	−	13.7800i	−0.751901	−	0.622518i
$491$	−9.20286	−	7.72212i	−0.415319	−	0.348494i	0.411060	−	0.911608i	$-0.365159\pi$
$491$	−9.20286	−	7.72212i	−0.415319	−	0.348494i	−0.826379	+	0.563114i	$0.809603\pi$
$492$	5.33135	+	2.00940i	0.240356	+	0.0905908i
$493$	−5.63147	+	4.72536i	−0.253628	+	0.212820i
$494$	22.7366	−	57.3921i	1.02297	−	2.58219i
$495$	4.15001	+	0.352619i	0.186529	+	0.0158491i
$496$	5.40847	−	10.8732i	0.242848	−	0.488219i
$497$	−23.4842	−	32.3295i	−1.05341	−	1.45018i
$498$	−9.07745	+	26.3032i	−0.406770	+	1.17868i
$499$	−4.77388	−	13.1161i	−0.213708	−	0.587159i	0.785801	−	0.618479i	$-0.212251\pi$
$499$	−4.77388	−	13.1161i	−0.213708	−	0.587159i	−0.999509	+	0.0313206i	$0.990029\pi$
$500$	22.6963	−	2.69704i	1.01501	−	0.120615i
$501$	1.47827	+	32.9131i	0.0660440	+	1.47045i
$502$	−10.7227	−	9.52398i	−0.478579	−	0.425076i
$503$	2.58977	−	4.48562i	0.115472	−	0.200004i	−0.802496	−	0.596657i	$-0.796495\pi$
$503$	2.58977	−	4.48562i	0.115472	−	0.200004i	0.917968	+	0.396653i	$0.129829\pi$
$504$	−20.1255	+	9.94804i	−0.896462	+	0.443121i
$505$	−3.40085	−	5.89044i	−0.151336	−	0.262121i
$506$	−0.946973	+	4.60855i	−0.0420981	+	0.204875i
$507$	16.4047	+	39.4648i	0.728559	+	1.75269i
$508$	−11.9020	+	27.7384i	−0.528066	+	1.23069i
$509$	−5.10757	+	6.08696i	−0.226389	+	0.269800i	−0.867268	−	0.497842i	$-0.834126\pi$
$509$	−5.10757	+	6.08696i	−0.226389	+	0.269800i	0.640878	+	0.767642i	$0.278570\pi$
$510$	7.77473	+	1.23695i	0.344271	+	0.0547732i
$511$	1.44517	−	3.24510i	0.0639305	−	0.143555i
$512$	21.9062	+	5.66718i	0.968128	+	0.250456i
$513$	36.6183	−	4.96076i	1.61674	−	0.219023i
$514$	6.86606	+	8.66642i	0.302849	+	0.382259i
$515$	6.21786	+	2.26312i	0.273992	+	0.0997248i
$516$	14.9088	+	26.5146i	0.656322	+	1.16724i
$517$	−4.74161	+	1.72581i	−0.208536	+	0.0759008i
$518$	−1.56877	+	15.9511i	−0.0689280	+	0.700851i
$519$	−0.886925	+	0.368677i	−0.0389317	+	0.0161831i
$520$	21.8248	+	30.9786i	0.957082	+	1.35850i
$521$		−	38.4961i		−	1.68655i	−0.537486	−	0.843273i	$-0.680626\pi$
$521$		−	38.4961i		−	1.68655i	0.537486	−	0.843273i	$-0.319374\pi$
$522$	−8.45713	−	19.4207i	−0.370159	−	0.850019i
$523$		−	22.4595i		−	0.982085i	−0.871136	−	0.491042i	$-0.836616\pi$
$523$		−	22.4595i		−	0.982085i	0.871136	−	0.491042i	$-0.163384\pi$
$524$	−12.2212	−	0.688240i	−0.533885	−	0.0300659i
$525$	1.07926	+	0.0270104i	0.0471026	+	0.00117883i
$526$	−5.84616	+	9.49849i	−0.254905	+	0.414154i
$527$	−4.20069	+	1.52893i	−0.182985	+	0.0666011i
$528$	−2.59793	−	3.55936i	−0.113060	−	0.154901i
$529$	0.756812	+	4.29209i	0.0329049	+	0.186613i
$530$	34.1446	+	13.5268i	1.48315	+	0.587567i
$531$	4.59688	+	16.9857i	0.199488	+	0.737117i
$532$	11.1457	−	35.9425i	0.483226	−	1.55830i
$533$	3.45278	−	9.48645i	0.149557	−	0.410904i
$534$	8.53710	+	14.2306i	0.369436	+	0.615817i
$535$	−4.39778	−	12.0828i	−0.190133	−	0.522385i
$536$	7.52593	+	27.7667i	0.325070	+	1.19934i
$537$	−0.696555	+	2.21886i	−0.0300586	+	0.0957511i
$538$	−26.1676	−	5.37697i	−1.12817	−	0.231818i
$539$	2.74175	−	3.50794i	0.118096	−	0.151098i
$540$	−9.76858	+	20.4727i	−0.420373	+	0.881005i
$541$	1.39826	+	2.42185i	0.0601158	+	0.104124i	0.894517	−	0.447034i	$-0.147520\pi$
$541$	1.39826	+	2.42185i	0.0601158	+	0.104124i	−0.834401	+	0.551158i	$0.814186\pi$
$542$	−4.70151	+	5.29328i	−0.201947	+	0.227366i
$543$	12.5234	−	39.8930i	0.537430	−	1.71197i
$544$	−4.40669	−	7.06811i	−0.188935	−	0.303043i
$545$	7.04884	−	8.40048i	0.301939	−	0.359837i
$546$	18.0312	+	35.4574i	0.771665	+	1.51744i
$547$	7.31612	−	20.1009i	0.312815	−	0.859452i	−0.679271	−	0.733888i	$-0.737704\pi$
$547$	7.31612	−	20.1009i	0.312815	−	0.859452i	0.992086	−	0.125564i	$-0.0400740\pi$
$548$	−8.93860	−	29.6495i	−0.381838	−	1.26656i
$549$	3.05496	−	0.274977i	0.130382	−	0.0117357i
$550$	0.0309139	+	0.209643i	0.00131817	+	0.00893919i
$551$	33.3646	+	12.1437i	1.42138	+	0.517340i
$552$	−21.6679	−	13.6784i	−0.922249	−	0.582192i
$553$	39.6394	−	11.3624i	1.68564	−	0.483180i
$554$	−0.712896	+	1.15827i	−0.0302880	+	0.0492102i
$555$	8.71867	+	13.6479i	0.370087	+	0.579320i
$556$	−6.81000	−	4.46028i	−0.288808	−	0.189158i
$557$	13.6802	−	7.89828i	0.579649	−	0.334661i	−0.181345	−	0.983420i	$-0.558045\pi$
$557$	13.6802	−	7.89828i	0.579649	−	0.334661i	0.760994	+	0.648759i	$0.224712\pi$
$558$	−0.793464	−	12.8562i	−0.0335900	−	0.544247i
$559$	46.6775	−	26.9493i	1.97425	−	1.13983i
$560$	14.7085	+	17.8122i	0.621546	+	0.752704i
$561$	−0.209715	+	1.60849i	−0.00885418	+	0.0679105i
$562$	−4.72393	−	2.90750i	−0.199267	−	0.122646i
$563$	4.78746	−	27.1510i	0.201767	−	1.14428i	−0.700678	−	0.713477i	$-0.747119\pi$
$563$	4.78746	−	27.1510i	0.201767	−	1.14428i	0.902446	−	0.430803i	$-0.141770\pi$
$564$	0.312513	−	27.4801i	0.0131592	−	1.15712i
$565$	−15.8480	+	13.2981i	−0.666731	+	0.559454i
$566$	−1.16410	+	2.93845i	−0.0489309	+	0.123512i
$567$	−13.2183	+	19.8060i	−0.555115	+	0.831774i
$568$	18.1648	+	38.6633i	0.762180	+	1.62227i
$569$	−13.1418	−	15.6618i	−0.550932	−	0.656576i	0.416669	−	0.909058i	$-0.363197\pi$
$569$	−13.1418	−	15.6618i	−0.550932	−	0.656576i	−0.967601	+	0.252483i	$0.918753\pi$
$570$	−13.6015	−	35.5070i	−0.569703	−	1.48723i
$571$	−8.61324	−	1.51875i	−0.360453	−	0.0635576i	−0.00951094	−	0.999955i	$-0.503027\pi$
$571$	−8.61324	−	1.51875i	−0.360453	−	0.0635576i	−0.350942	+	0.936397i	$0.614139\pi$
$572$	−6.25404	+	4.67467i	−0.261495	+	0.195458i
$573$	19.1615	+	2.49828i	0.800483	+	0.104367i
$574$	1.65667	−	5.92677i	0.0691481	−	0.247379i
$575$	0.616120	+	1.06715i	0.0256940	+	0.0445033i
$576$	23.1301	−	6.40309i	0.963753	−	0.266795i
$577$	−14.3354	−	24.8297i	−0.596792	−	1.03367i	−0.993291	−	0.115639i	$-0.963108\pi$
$577$	−14.3354	−	24.8297i	−0.596792	−	1.03367i	0.396499	−	0.918035i	$-0.370225\pi$
$578$	4.22189	−	20.5463i	0.175607	−	0.854613i
$579$	18.9471	−	12.1039i	0.787413	−	0.503023i
$580$	−17.4577	+	13.0490i	−0.724893	+	0.541831i
$581$	29.1616	+	7.27367i	1.20983	+	0.301763i
$582$	−22.6428	+	4.38493i	−0.938572	+	0.181761i
$583$	−2.58818	+	7.11098i	−0.107192	+	0.294507i
$584$	−2.16925	+	3.11709i	−0.0897641	+	0.128986i
$585$	36.4699	+	16.8952i	1.50784	+	0.698532i
$586$	−23.1688	−	29.2439i	−0.957094	−	1.20805i
$587$	−16.7549	−	6.09829i	−0.691549	−	0.251703i	−0.0277509	−	0.999615i	$-0.508835\pi$
$587$	−16.7549	−	6.09829i	−0.691549	−	0.251703i	−0.663798	+	0.747911i	$0.731057\pi$
$588$	12.6113	+	20.7112i	0.520083	+	0.854116i
$589$	16.5395	+	13.8783i	0.681498	+	0.571845i
$590$	15.9290	−	8.60859i	0.655785	−	0.354410i
$591$	2.99585	+	0.940468i	0.123233	+	0.0386857i
$592$	4.85117	−	16.4336i	0.199382	−	0.675419i
$593$	−20.1385	+	11.6270i	−0.826991	+	0.477463i	−0.852821	−	0.522203i	$-0.825110\pi$
$593$	−20.1385	+	11.6270i	−0.826991	+	0.477463i	0.0258306	+	0.999666i	$0.491777\pi$
$594$	−4.27327	−	1.89335i	−0.175334	−	0.0776851i
$595$	0.593944	−	8.48251i	0.0243493	−	0.347749i
$596$	21.8158	+	14.2885i	0.893612	+	0.585281i
$597$	−26.5808	−	8.34434i	−1.08788	−	0.341511i
$598$	−23.7985	+	38.6663i	−0.973193	+	1.58118i
$599$	15.5038	−	5.64293i	0.633469	−	0.230564i	−0.00527130	−	0.999986i	$-0.501678\pi$
$599$	15.5038	−	5.64293i	0.633469	−	0.230564i	0.638741	+	0.769422i	$0.279456\pi$
$600$	−1.12780	−	0.245141i	−0.0460422	−	0.0100078i
$601$	2.78431	+	1.01341i	0.113574	+	0.0413377i	0.398182	−	0.917306i	$-0.369641\pi$
$601$	2.78431	+	1.01341i	0.113574	+	0.0413377i	−0.284608	+	0.958644i	$0.591863\pi$
$602$	27.1153	−	18.5545i	1.10514	−	0.756225i
$603$	21.6303	+	21.5224i	0.880855	+	0.876459i
$604$	−1.74019	+	1.85160i	−0.0708072	+	0.0753407i
$605$	−22.7759	+	4.01601i	−0.925972	+	0.163274i
$606$	1.45120	+	7.49365i	0.0589509	+	0.304409i
$607$	−0.484199	−	1.33033i	−0.0196530	−	0.0539963i	0.929478	−	0.368877i	$-0.120258\pi$
$607$	−0.484199	−	1.33033i	−0.0196530	−	0.0539963i	−0.949131	+	0.314881i	$0.898035\pi$
$608$	−18.9224	+	35.5011i	−0.767406	+	1.43976i
$609$	−20.0941	+	10.9404i	−0.814255	+	0.443326i
$610$	−0.995624	−	2.99498i	−0.0403117	−	0.121263i
$611$	−48.6948			−1.96998
$612$	−7.79465	−	4.15844i	−0.315080	−	0.168095i
$613$	−34.5411			−1.39510			−0.697552	−	0.716535i	$-0.745727\pi$
$613$	−34.5411			−1.39510			−0.697552	+	0.716535i	$0.745727\pi$
$614$	4.84875	+	0.996330i	0.195680	+	0.0402086i
$615$	−2.38674	−	5.74177i	−0.0962425	−	0.231530i
$616$	−3.58346	+	3.13265i	−0.144382	+	0.126218i
$617$	8.27769	+	22.7428i	0.333247	+	0.915590i	0.987261	+	0.159107i	$0.0508616\pi$
$617$	8.27769	+	22.7428i	0.333247	+	0.915590i	−0.654014	+	0.756483i	$0.726916\pi$
$618$	−5.76744	−	4.67705i	−0.232001	−	0.188138i
$619$	−4.83594	+	13.2866i	−0.194373	+	0.534035i	−0.998144	−	0.0609040i	$-0.980602\pi$
$619$	−4.83594	+	13.2866i	−0.194373	+	0.534035i	0.803771	+	0.594939i	$0.202824\pi$
$620$	−12.6896	+	3.82560i	−0.509626	+	0.153640i
$621$	−27.1570	−	1.08361i	−1.08977	−	0.0434840i
$622$	−28.8540	−	11.4309i	−1.15694	−	0.458337i
$623$	14.5023	−	10.5345i	0.581021	−	0.422054i
$624$	−11.8109	−	40.8523i	−0.472814	−	1.63540i
$625$	−18.2062	−	15.2769i	−0.728250	−	0.611074i
$626$	−44.3220	−	1.24702i	−1.77146	−	0.0498408i
$627$	7.23438	−	3.00719i	0.288913	−	0.120095i
$628$	−2.42455	+	3.70183i	−0.0967501	+	0.147719i
$629$	−5.46236	+	3.15370i	−0.217799	+	0.125746i
$630$	22.9537	+	8.56997i	0.914497	+	0.341436i
$631$	1.15293	+	0.665643i	0.0458973	+	0.0264988i	0.522773	−	0.852472i	$-0.324898\pi$
$631$	1.15293	+	0.665643i	0.0458973	+	0.0264988i	−0.476876	+	0.878971i	$0.658231\pi$
$632$	−43.9038	+	3.96864i	−1.74640	+	0.157864i
$633$	23.0525	−	1.03539i	0.916256	−	0.0411529i
$634$	29.6619	−	16.0303i	1.17802	−	0.636646i
$635$	30.9555	−	11.2669i	1.22843	−	0.447113i
$636$	−31.2688	−	26.8494i	−1.23989	−	1.06465i
$637$	36.4415	−	22.7618i	1.44386	−	0.901855i
$638$	−2.78881	−	3.52006i	−0.110410	−	0.139361i
$639$	37.1799	+	25.8953i	1.47081	+	1.02440i
$640$	−11.8662	−	21.6573i	−0.469053	−	0.856079i
$641$	9.28475	+	11.0651i	0.366725	+	0.437046i	0.917578	−	0.397556i	$-0.130142\pi$
$641$	9.28475	+	11.0651i	0.366725	+	0.437046i	−0.550852	+	0.834603i	$0.685697\pi$
$642$	0.241772	+	14.4275i	0.00954197	+	0.569409i
$643$	12.8425	−	15.3050i	0.506457	−	0.603572i	−0.450866	−	0.892592i	$-0.648885\pi$
$643$	12.8425	−	15.3050i	0.506457	−	0.603572i	0.957323	+	0.289020i	$0.0933293\pi$
$644$	−12.6635	+	24.6103i	−0.499011	+	0.969783i
$645$	9.94329	−	31.6742i	0.391516	−	1.24717i
$646$	14.0525	−	4.67147i	0.552887	−	0.183797i
$647$	−7.54941	+	13.0760i	−0.296798	+	0.514069i	−0.975402	−	0.220436i	$-0.929252\pi$
$647$	−7.54941	+	13.0760i	−0.296798	+	0.514069i	0.678604	+	0.734505i	$0.262585\pi$
$648$	17.8575	−	18.1414i	0.701509	−	0.712661i
$649$	1.86537	+	3.23092i	0.0732223	+	0.126825i
$650$	−0.411610	+	2.00315i	−0.0161447	+	0.0785699i
$651$	−13.7575	+	2.07237i	−0.539199	+	0.0812225i
$652$	14.9663	−	34.8799i	0.586125	−	1.36600i
$653$	−7.36821	−	1.29921i	−0.288340	−	0.0508422i	0.0276071	−	0.999619i	$-0.491211\pi$
$653$	−7.36821	−	1.29921i	−0.288340	−	0.0508422i	−0.315948	+	0.948777i	$0.602322\pi$
$654$	−10.5528	+	6.33076i	−0.412648	+	0.247552i
$655$	8.58703	+	10.2336i	0.335523	+	0.399861i
$656$	−2.92997	+	5.89039i	−0.114396	+	0.229981i
$657$	−0.341022	+	4.01352i	−0.0133046	+	0.156582i
$658$	−29.5970	+	2.26857i	−1.15381	+	0.0884382i
$659$	−5.95124	+	4.99368i	−0.231827	+	0.194526i	−0.751300	−	0.659961i	$-0.770573\pi$
$659$	−5.95124	+	4.99368i	−0.231827	+	0.194526i	0.519473	+	0.854487i	$0.326128\pi$
$660$	−0.888928	+	4.72642i	−0.0346015	+	0.183975i
$661$	−2.61183	−	2.19159i	−0.101589	−	0.0852429i	0.590579	−	0.806980i	$-0.298900\pi$
$661$	−2.61183	−	2.19159i	−0.101589	−	0.0852429i	−0.692167	+	0.721737i	$0.743344\pi$
$662$	−10.8686	+	5.87377i	−0.422419	+	0.228290i
$663$	−7.21076	+	13.8942i	−0.280043	+	0.539604i
$664$	−29.1588	−	13.4948i	−1.13158	−	0.523700i
$665$	−36.9147	+	18.0003i	−1.43149	+	0.698021i
$666$	−4.25245	−	17.6696i	−0.164779	−	0.684683i
$667$	−22.6157	−	13.0572i	−0.875683	−	0.505576i
$668$	−37.9829	−	2.13902i	−1.46960	−	0.0827611i
$669$	6.16717	−	2.56357i	0.238437	−	0.0991132i
$670$	16.4572	−	26.7386i	0.635797	−	1.03300i
$671$	0.611092	−	0.222419i	0.0235910	−	0.00858641i
$672$	−9.08193	−	24.2800i	−0.350343	−	0.936621i
$673$	−7.53322	−	42.7230i	−0.290384	−	1.64685i	−0.685392	−	0.728174i	$-0.740369\pi$
$673$	−7.53322	−	42.7230i	−0.290384	−	1.64685i	0.395008	−	0.918678i	$-0.370742\pi$
$674$	−5.08896	−	34.5108i	−0.196019	−	1.32930i
$675$	−1.16610	+	0.372486i	−0.0448831	+	0.0143370i
$676$	−47.2497	+	14.2446i	−1.81730	+	0.547871i
$677$	−11.4152	−	13.6041i	−0.438722	−	0.522848i	0.500696	−	0.865623i	$-0.333078\pi$
$677$	−11.4152	−	13.6041i	−0.438722	−	0.522848i	−0.939417	+	0.342775i	$0.888633\pi$
$678$	21.6800	−	8.30484i	0.832616	−	0.318946i
$679$	6.86428	+	23.9470i	0.263427	+	0.919000i
$680$	−2.32745	+	8.78739i	−0.0892535	+	0.336981i
$681$	−5.85250	+	7.64692i	−0.224268	+	0.293030i
$682$	−0.861474	−	2.59144i	−0.0329875	−	0.0992313i
$683$	22.8939			0.876010			0.438005	−	0.898972i	$-0.355685\pi$
$683$	22.8939			0.876010			0.438005	+	0.898972i	$0.355685\pi$
$684$	1.42968	+	42.6455i	0.0546651	+	1.63059i
$685$	−16.8987	+	29.2693i	−0.645665	+	1.11832i
$686$	21.0889	−	15.5325i	0.805179	−	0.593032i
$687$	22.7780	+	11.8213i	0.869035	+	0.451010i
$688$	−32.1981	+	14.0359i	−1.22754	+	0.535115i
$689$	−46.9411	+	55.9422i	−1.78831	+	2.13123i
$690$	5.31696	+	27.4556i	0.202413	+	1.04522i
$691$	−2.89442	+	7.95235i	−0.110109	+	0.302522i	−0.982493	−	0.186299i	$-0.940351\pi$
$691$	−2.89442	+	7.95235i	−0.110109	+	0.302522i	0.872384	+	0.488821i	$0.162573\pi$
$692$	−0.320131	−	1.06188i	−0.0121696	−	0.0403667i
$693$	−1.63210	+	4.77732i	−0.0619983	+	0.181475i
$694$	2.18491	+	14.8169i	0.0829379	+	0.562443i
$695$	1.54278	+	8.74955i	0.0585210	+	0.331889i
$696$	23.2964	−	7.45135i	0.883049	−	0.282443i
$697$	2.27567	−	0.828276i	0.0861971	−	0.0313732i
$698$	−14.5311	−	26.8878i	−0.550012	−	1.01772i
$699$	6.60891	−	6.07117i	0.249972	−	0.229633i
$700$	−0.156857	+	1.23670i	−0.00592865	+	0.0467429i
$701$		−	34.1136i		−	1.28845i	−0.764835	−	0.644226i	$-0.777180\pi$
$701$		−	34.1136i		−	1.28845i	0.764835	−	0.644226i	$-0.222820\pi$
$702$	−32.5023	−	31.2739i	−1.22672	−	1.18036i
$703$	26.3824	+	15.2319i	0.995029	+	0.574480i
$704$	4.39188	−	2.56953i	0.165525	−	0.0968426i
$705$	−22.0878	+	20.2907i	−0.831876	+	0.764190i
$706$	−0.687005	+	24.4178i	−0.0258558	+	0.918978i
$707$	7.92529	−	2.27175i	0.298061	−	0.0854378i
$708$	−20.0491	+	3.30057i	−0.753492	+	0.124043i
$709$	−2.06338	−	11.7020i	−0.0774918	−	0.439478i	−0.998726	−	0.0504687i	$-0.983928\pi$
$709$	−2.06338	−	11.7020i	−0.0774918	−	0.439478i	0.921234	−	0.389009i	$-0.127183\pi$
$710$	17.1712	−	43.3438i	0.644423	−	1.62666i
$711$	−38.2338	+	26.9144i	−1.43388	+	1.00937i
$712$	−17.3434	+	8.14831i	−0.649972	+	0.305371i
$713$	−10.2074	−	12.1647i	−0.382270	−	0.455571i
$714$	−3.73545	+	8.78088i	−0.139796	+	0.328616i
$715$	8.39206	+	1.47975i	0.313845	+	0.0553394i
$716$	−2.46782	−	1.05889i	−0.0922268	−	0.0395727i
$717$	−11.8252	−	6.13703i	−0.441621	−	0.229192i
$718$	1.19347	−	5.80814i	0.0445398	−	0.216758i
$719$	23.7649			0.886281			0.443140	−	0.896452i	$-0.353864\pi$
$719$	23.7649			0.886281			0.443140	+	0.896452i	$0.353864\pi$
$720$	−22.3801	−	13.6090i	−0.834058	−	0.507178i
$721$	−4.48560	+	6.64885i	−0.167053	+	0.247616i
$722$	−33.3855	−	29.6532i	−1.24248	−	1.10358i
$723$	−6.43464	−	15.4798i	−0.239307	−	0.575700i
$724$	44.3690	+	19.0379i	1.64896	+	0.707538i
$725$	−1.15834	−	0.204247i	−0.0430198	−	0.00758554i
$726$	25.6311	+	4.07789i	0.951259	+	0.151345i
$727$	11.6218	−	2.04924i	0.431030	−	0.0760021i	0.0460757	−	0.998938i	$-0.485328\pi$
$727$	11.6218	−	2.04924i	0.431030	−	0.0760021i	0.384954	+	0.922936i	$0.374217\pi$
$728$	−42.8357	+	16.5804i	−1.58760	+	0.614509i
$729$	6.79219	−	26.1317i	0.251563	−	0.967841i
$730$	4.10029	−	0.604629i	0.151759	−	0.0223783i
$731$	12.1498	+	4.42215i	0.449375	+	0.163559i
$732$	−0.0402763	+	3.54159i	−0.00148865	+	0.130901i
$733$	16.4209	+	13.7788i	0.606521	+	0.508931i	0.893534	−	0.448995i	$-0.148218\pi$
$733$	16.4209	+	13.7788i	0.606521	+	0.508931i	−0.287013	+	0.957927i	$0.592662\pi$
$734$	−12.3123	+	6.65401i	−0.454455	+	0.245604i
$735$	7.04514	−	25.5095i	0.259864	−	0.940932i
$736$	18.2400	−	23.2974i	0.672335	−	0.858754i
$737$	5.60259	+	3.23466i	0.206374	+	0.119150i
$738$	0.429848	+	6.96468i	0.0158229	+	0.256373i
$739$	−42.6367	+	24.6163i	−1.56842	+	0.905525i	−0.572062	+	0.820211i	$0.693856\pi$
$739$	−42.6367	+	24.6163i	−1.56842	+	0.905525i	−0.996354	+	0.0853145i	$0.972810\pi$
$740$	−16.6952	+	8.42484i	−0.613726	+	0.309703i
$741$	75.5294	−	3.39235i	2.77464	−	0.124621i
$742$	−25.9249	+	36.1889i	−0.951731	+	1.32854i
$743$	−9.02984	+	51.2108i	−0.331273	+	1.87874i	0.130048	+	0.991508i	$0.458487\pi$
$743$	−9.02984	+	51.2108i	−0.331273	+	1.87874i	−0.461321	+	0.887233i	$0.652624\pi$
$744$	14.8617	+	0.587341i	0.544857	+	0.0215330i
$745$	−4.94230	−	28.0292i	−0.181072	−	1.02691i
$746$	−5.69795	−	38.6406i	−0.208617	−	1.41473i
$747$	−33.9420	+	3.05512i	−1.24187	+	0.111781i
$748$	−1.82338	−	0.428450i	−0.0666694	−	0.0156657i
$749$	15.5005	−	1.62772i	0.566375	−	0.0594754i
$750$	14.4006	+	24.0045i	0.525836	+	0.876521i
$751$	23.4718	+	4.13871i	0.856499	+	0.151024i	0.584619	−	0.811308i	$-0.301244\pi$
$751$	23.4718	+	4.13871i	0.856499	+	0.151024i	0.271879	+	0.962331i	$0.412355\pi$
$752$	31.5327	+	3.56284i	1.14988	+	0.129924i
$753$	5.26090	−	16.7585i	0.191718	−	0.610714i
$754$	−13.6715	−	41.1259i	−0.497887	−	1.49772i
$755$	2.77319			0.100927
$756$	−21.2120	−	17.4943i	−0.771474	−	0.636260i
$757$	−3.63220			−0.132015			−0.0660073	−	0.997819i	$-0.521026\pi$
$757$	−3.63220			−0.132015			−0.0660073	+	0.997819i	$0.521026\pi$
$758$	7.24391	+	21.7907i	0.263111	+	0.791475i
$759$	−5.62407	+	1.25421i	−0.204141	+	0.0455249i
$760$	42.3762	−	11.4857i	1.53715	−	0.416630i
$761$	−12.8905	−	2.27295i	−0.467281	−	0.0823943i	−0.0649501	−	0.997889i	$-0.520689\pi$
$761$	−12.8905	−	2.27295i	−0.467281	−	0.0823943i	−0.402331	+	0.915494i	$0.631800\pi$
$762$	−36.9626	+	0.619406i	−1.33901	+	0.0224387i
$763$	7.81192	+	10.7543i	0.282810	+	0.389331i
$764$	−5.10401	+	21.7214i	−0.184657	+	0.785854i
$765$	2.51878	+	9.30701i	0.0910665	+	0.336496i
$766$	5.84785	+	39.6572i	0.211292	+	1.43287i
$767$	6.25185	+	35.4560i	0.225741	+	1.28024i
$768$	4.65919	+	27.3183i	0.168124	+	0.985766i
$769$	4.42166	−	25.0765i	0.159449	−	0.904282i	−0.795155	−	0.606406i	$-0.792611\pi$
$769$	4.42166	−	25.0765i	0.159449	−	0.904282i	0.954605	−	0.297876i	$-0.0962782\pi$
$770$	5.16968	+	0.508432i	0.186302	+	0.0183226i
$771$	−6.23777	+	12.0193i	−0.224648	+	0.432866i
$772$	11.6960	+	23.1775i	0.420949	+	0.834178i
$773$	−21.2393	+	12.2625i	−0.763923	+	0.441051i	−0.830702	−	0.556717i	$-0.812061\pi$
$773$	−21.2393	+	12.2625i	−0.763923	+	0.441051i	0.0667795	+	0.997768i	$0.478728\pi$
$774$	−22.1436	+	29.9600i	−0.795935	+	1.07689i
$775$	−0.619418	−	0.357621i	−0.0222502	−	0.0128461i
$776$	−2.39754	−	26.5232i	−0.0860667	−	0.952128i
$777$	−18.6086	+	6.25034i	−0.667581	+	0.224230i
$778$	−43.7308	+	23.6337i	−1.56783	+	0.847310i
$779$	−8.96005	−	7.51837i	−0.321027	−	0.269374i
$780$	−23.6612	+	39.9268i	−0.847205	+	1.42961i
$781$	9.02681	+	3.28549i	0.323005	+	0.117564i
$782$	−10.7751	+	1.58890i	−0.385317	+	0.0568188i
$783$	17.4548	−	19.1927i	0.623783	−	0.685890i
$784$	−25.2633	+	12.0732i	−0.902262	+	0.431187i
$785$	4.75614	−	0.838635i	0.169754	−	0.0299322i
$786$	−5.36273	−	13.9996i	−0.191282	−	0.499348i
$787$	−42.0137	−	7.40815i	−1.49763	−	0.264072i	−0.636030	−	0.771665i	$-0.719424\pi$
$787$	−42.0137	−	7.40815i	−1.49763	−	0.264072i	−0.861597	+	0.507593i	$0.830536\pi$
$788$	−1.42969	+	3.33198i	−0.0509305	+	0.118697i
$789$	−13.5455	−	1.76606i	−0.482231	−	0.0628734i
$790$	35.9708	+	31.9494i	1.27978	+	1.13671i
$791$	−10.9907	−	22.5395i	−0.390784	−	0.801414i
$792$	2.67329	−	4.68839i	0.0949911	−	0.166595i
$793$	6.27572			0.222857
$794$	−4.08357	+	19.8732i	−0.144921	+	0.705273i
$795$	2.01823	+	44.9352i	0.0715791	+	1.59369i
$796$	12.6850	−	29.5631i	0.449607	−	1.04784i
$797$	−26.3734	−	4.65034i	−0.934193	−	0.164723i	−0.314223	−	0.949349i	$-0.601744\pi$
$797$	−26.3734	−	4.65034i	−0.934193	−	0.164723i	−0.619970	+	0.784626i	$0.712855\pi$
$798$	45.7492	−	5.58062i	1.61950	−	0.197552i
$799$	−7.50854	−	8.94833i	−0.265633	−	0.316569i
$800$	0.413105	−	1.26704i	0.0146055	−	0.0447965i
$801$	−11.6160	+	16.6780i	−0.410431	+	0.589288i
$802$	−16.7711	+	42.3340i	−0.592210	+	1.49487i
$803$	0.148293	+	0.841013i	0.00523316	+	0.0296787i
$804$	−27.2467	+	22.3397i	−0.960918	+	0.787860i
$805$	29.0370	−	8.32331i	1.02342	−	0.293358i
$806$	0.741183	−	26.3435i	0.0261071	−	0.927909i
$807$	−7.12148	−	31.9338i	−0.250688	−	1.12412i
$808$	−8.77790	+	0.793470i	−0.308805	+	0.0279142i
$809$	22.0670	+	12.7404i	0.775834	+	0.447928i	0.834952	−	0.550323i	$-0.185495\pi$
$809$	22.0670	+	12.7404i	0.775834	+	0.447928i	−0.0591178	+	0.998251i	$0.518829\pi$
$810$	−27.7745	−	0.642391i	−0.975896	−	0.0225713i
$811$		−	32.3504i		−	1.13598i	−0.823037	−	0.567988i	$-0.807722\pi$
$811$		−	32.3504i		−	1.13598i	0.823037	−	0.567988i	$-0.192278\pi$
$812$	−10.2256	−	24.3596i	−0.358848	−	0.854856i
$813$	−8.27284	−	2.59704i	−0.290141	−	0.0910823i
$814$	−1.83197	−	3.38980i	−0.0642105	−	0.118812i
$815$	−38.9253	+	14.1677i	−1.36349	+	0.496271i
$816$	5.68597	−	8.46967i	0.199049	−	0.296498i
$817$	−10.8439	−	61.4988i	−0.379380	−	2.15157i
$818$	3.64888	+	24.7449i	0.127580	+	0.865184i
$819$	−30.5685	+	37.9355i	−1.06815	+	1.32557i
$820$	6.87441	−	2.07247i	0.240065	−	0.0723736i
$821$	−12.9560	+	35.5963i	−0.452167	+	1.24232i	0.479028	+	0.877799i	$0.340989\pi$
$821$	−12.9560	+	35.5963i	−0.452167	+	1.24232i	−0.931196	+	0.364520i	$0.881233\pi$
$822$	28.6415	−	24.8627i	0.998988	−	0.867185i
$823$	0.974058	−	1.16084i	0.0339535	−	0.0404642i	−0.748800	−	0.662796i	$-0.769370\pi$
$823$	0.974058	−	1.16084i	0.0339535	−	0.0404642i	0.782754	+	0.622331i	$0.213814\pi$
$824$	6.04540	−	6.08035i	0.210601	−	0.211819i
$825$	−0.218715	+	0.139722i	−0.00761469	+	0.00486449i
$826$	5.45172	+	21.2591i	0.189690	+	0.739699i
$827$	3.61824	−	6.26697i	0.125818	−	0.217924i	−0.796234	−	0.604989i	$-0.793178\pi$
$827$	3.61824	−	6.26697i	0.125818	−	0.217924i	0.922053	+	0.387065i	$0.126511\pi$
$828$	4.41101	−	31.0716i	0.153293	−	1.07981i
$829$	−5.82739			−0.202394			−0.101197	−	0.994866i	$-0.532267\pi$
$829$	−5.82739			−0.202394			−0.101197	+	0.994866i	$0.532267\pi$
$830$	11.0618	+	33.2756i	0.383962	+	1.15501i
$831$	−1.65177	−	0.215358i	−0.0572992	−	0.00747068i
$832$	48.3081	−	8.80548i	1.67478	−	0.305275i
$833$	9.80192	+	3.18684i	0.339616	+	0.110418i
$834$	1.56655	−	9.84639i	0.0542453	−	0.340952i
$835$	26.6881	+	31.8056i	0.923580	+	1.10068i
$836$	2.61122	+	8.66146i	0.0903108	+	0.299563i
$837$	13.9656	−	7.33679i	0.482723	−	0.253597i
$838$	−3.35771	−	22.7703i	−0.115990	−	0.786586i
$839$	−5.63552	−	31.9606i	−0.194560	−	1.10340i	−0.913044	−	0.407860i	$-0.866275\pi$
$839$	−5.63552	−	31.9606i	−0.194560	−	1.10340i	0.718484	−	0.695543i	$-0.244836\pi$
$840$	−12.5213	+	25.3700i	−0.432026	+	0.875349i
$841$	−3.82741	+	1.39306i	−0.131980	+	0.0480367i
$842$	−11.0279	+	17.9175i	−0.380048	+	0.617478i
$843$	0.878324	−	6.73663i	0.0302511	−	0.232022i
$844$	−1.49818	+	26.6035i	−0.0515696	+	0.915729i
$845$	46.6439	+	26.9299i	1.60460	+	0.926415i
$846$	30.8592	−	13.4383i	1.06096	−	0.462018i
$847$	1.95807	−	27.9645i	0.0672800	−	0.960870i
$848$	34.4902	−	32.7913i	1.18440	−	1.12606i
$849$	−3.86707	+	0.173687i	−0.132718	+	0.00596091i
$850$	−0.431574	+	0.233238i	−0.0148029	+	0.00800001i
$851$	−17.1639	−	14.4022i	−0.588370	−	0.493701i
$852$	−34.0832	+	39.6932i	−1.16767	+	1.35987i
$853$	39.2228	−	32.9118i	1.34296	−	1.12688i	0.362107	−	0.932137i	$-0.382058\pi$
$853$	39.2228	−	32.9118i	1.34296	−	1.12688i	0.980855	−	0.194742i	$-0.0623869\pi$
$854$	3.81442	−	0.292370i	0.130527	−	0.0100047i
$855$	32.8464	−	33.0111i	1.12332	−	1.12896i
$856$	−16.6025	−	1.40432i	−0.567463	−	0.0479987i
$857$	9.83343	+	11.7190i	0.335904	+	0.400314i	0.907385	−	0.420301i	$-0.138075\pi$
$857$	9.83343	+	11.7190i	0.335904	+	0.400314i	−0.571481	+	0.820615i	$0.693631\pi$
$858$	−8.36063	−	4.64200i	−0.285427	−	0.158475i
$859$	−25.0711	−	4.42072i	−0.855417	−	0.150833i	−0.271292	−	0.962497i	$-0.587451\pi$
$859$	−25.0711	−	4.42072i	−0.855417	−	0.150833i	−0.584124	+	0.811664i	$0.698562\pi$
$860$	35.2280	+	15.1157i	1.20127	+	0.515439i
$861$	7.45294	−	1.12268i	0.253996	−	0.0382607i
$862$	6.43871	−	31.3347i	0.219303	−	1.06726i
$863$	2.63928	+	4.57136i	0.0898420	+	0.155611i	0.907444	−	0.420173i	$-0.138030\pi$
$863$	2.63928	+	4.57136i	0.0898420	+	0.155611i	−0.817602	+	0.575783i	$0.804697\pi$
$864$	18.7589	+	22.6297i	0.638189	+	0.769879i
$865$	−0.605217	+	1.04827i	−0.0205780	+	0.0356421i
$866$	5.16345	−	1.71649i	0.175461	−	0.0583286i
$867$	25.0738	−	5.59164i	0.851551	−	0.189902i
$868$	−0.776783	−	16.0462i	−0.0263657	−	0.544645i
$869$	−6.37202	+	7.59387i	−0.216156	+	0.257604i
$870$	−23.3381	−	12.9578i	−0.791237	−	0.439311i
$871$	40.1299	+	47.8250i	1.35975	+	1.62049i
$872$	−6.04245	−	12.8612i	−0.204623	−	0.435534i
$873$	−16.2595	−	23.0978i	−0.550302	−	0.781743i
$874$	32.6670	+	41.2327i	1.10498	+	1.39472i
$875$	24.4628	−	17.7698i	0.826993	−	0.600729i
$876$	−4.57097	−	0.859692i	−0.154439	−	0.0290463i
$877$	49.7623	−	18.1120i	1.68035	−	0.611599i	0.686995	−	0.726662i	$-0.258929\pi$
$877$	49.7623	−	18.1120i	1.68035	−	0.611599i	0.993358	+	0.115063i	$0.0367071\pi$
$878$	47.6105	−	25.7304i	1.60678	−	0.868360i
$879$	21.0487	−	40.5580i	0.709955	−	1.36799i
$880$	−5.32607	−	1.57224i	−0.179542	−	0.0530002i
$881$	−32.6185	−	18.8323i	−1.09894	−	0.634476i	−0.163001	−	0.986626i	$-0.552117\pi$
$881$	−32.6185	−	18.8323i	−1.09894	−	0.634476i	−0.935944	+	0.352150i	$0.885451\pi$
$882$	−16.8124	+	24.4815i	−0.566103	+	0.824335i
$883$	−14.3561	+	8.28850i	−0.483121	+	0.278930i	−0.721716	−	0.692189i	$-0.756646\pi$
$883$	−14.3561	+	8.28850i	−0.483121	+	0.278930i	0.238595	+	0.971119i	$0.423313\pi$
$884$	−15.1209	−	9.90361i	−0.508571	−	0.333094i
$885$	17.6100	+	13.4777i	0.591954	+	0.453047i
$886$	−32.0033	−	0.900425i	−1.07517	−	0.0302504i
$887$	38.7741	+	32.5354i	1.30191	+	1.09243i	0.989812	+	0.142380i	$0.0454754\pi$
$887$	38.7741	+	32.5354i	1.30191	+	1.09243i	0.312096	+	0.950051i	$0.398969\pi$
$888$	20.7946	−	2.82515i	0.697822	−	0.0948060i
$889$	4.17012	+	39.7114i	0.139861	+	1.33188i
$890$	19.4430	+	7.70258i	0.651730	+	0.258191i
$891$	−0.0286405	−	5.72429i	−0.000959494	−	0.191771i
$892$	2.22601	+	7.38372i	0.0745324	+	0.247225i
$893$	−19.2962	+	53.0160i	−0.645724	+	1.77411i
$894$	−5.01845	+	31.5429i	−0.167842	+	1.05495i
$895$	1.00239	+	2.75404i	0.0335062	+	0.0920574i
$896$	28.9517	−	7.60257i	0.967208	−	0.253984i
$897$	−55.1407	−	7.18926i	−1.84109	−	0.240042i
$898$	23.0174	+	4.72966i	0.768101	+	0.157831i
$899$	15.1578			0.505542
$900$	−0.291959	−	1.38304i	−0.00973197	−	0.0461013i
$901$	−17.5183			−0.583618
$902$	0.466692	+	1.40388i	0.0155391	+	0.0467440i
$903$	34.3347	+	20.9856i	1.14259	+	0.698358i
$904$	7.01299	+	25.8742i	0.233248	+	0.860565i
$905$	−18.0220	−	49.5150i	−0.599071	−	1.64593i
$906$	−2.94182	−	1.01524i	−0.0977354	−	0.0337292i
$907$	−37.0762	+	6.53753i	−1.23110	+	0.217075i	−0.751096	−	0.660193i	$-0.770474\pi$
$907$	−37.0762	+	6.53753i	−1.23110	+	0.217075i	−0.480000	+	0.877269i	$0.659363\pi$
$908$	−8.10245	−	7.61489i	−0.268889	−	0.252709i
$909$	−7.64427	+	5.38112i	−0.253544	+	0.178481i
$910$	45.2023	+	21.6737i	1.49844	+	0.718477i
$911$	−1.62263	−	0.590587i	−0.0537600	−	0.0195670i	0.315000	−	0.949092i	$-0.397995\pi$
$911$	−1.62263	−	0.590587i	−0.0537600	−	0.0195670i	−0.368760	+	0.929525i	$0.620218\pi$
$912$	−49.1578	−	3.32951i	−1.62778	−	0.110251i
$913$	−6.78952	+	2.47118i	−0.224700	+	0.0817842i
$914$	14.0131	−	22.7676i	0.463511	−	0.753085i
$915$	2.84665	−	2.61503i	0.0941073	−	0.0864503i
$916$	−16.2359	+	24.7891i	−0.536450	+	0.819056i
$917$	−14.5546	+	7.09708i	−0.480635	+	0.234366i
$918$	0.735292	−	10.7950i	0.0242682	−	0.356290i
$919$	10.5718	−	6.10364i	0.348732	−	0.201341i	−0.315395	−	0.948961i	$-0.602137\pi$
$919$	10.5718	−	6.10364i	0.348732	−	0.201341i	0.664127	+	0.747620i	$0.268804\pi$
$920$	−32.1608	+	2.90715i	−1.06031	+	0.0958458i
$921$	1.31958	+	5.91720i	0.0434816	+	0.194978i
$922$	45.7286	−	24.7134i	1.50599	−	0.813893i
$923$	71.0142	+	59.5880i	2.33746	+	1.96136i
$924$	−5.29790	−	2.43193i	−0.174288	−	0.0800046i
$925$	−0.948317	−	0.345159i	−0.0311805	−	0.0113488i
$926$	10.8077	+	13.6416i	0.355164	+	0.448292i
$927$	2.33181	−	8.79033i	0.0765866	−	0.288712i
$928$	5.84403	+	27.6317i	0.191840	+	0.907054i
$929$	−4.48547	+	12.3237i	−0.147163	+	0.404328i	−0.991270	−	0.131847i	$-0.957909\pi$
$929$	−4.48547	+	12.3237i	−0.147163	+	0.404328i	0.844107	+	0.536175i	$0.180131\pi$
$930$	−10.6409	−	12.2582i	−0.348928	−	0.401961i
$931$	−10.3410	−	48.6951i	−0.338914	−	1.59592i
$932$	6.20405	+	8.30013i	0.203220	+	0.271880i
$933$	−1.70551	−	37.9727i	−0.0558360	−	1.24317i
$934$	9.75770	−	47.4869i	0.319282	−	1.55382i
$935$	1.02210	+	1.77033i	0.0334262	+	0.0578958i
$936$	39.7168	−	33.6925i	1.29819	−	1.10127i
$937$	7.34797	+	12.7270i	0.240048	+	0.415775i	0.960728	−	0.277493i	$-0.0895036\pi$
$937$	7.34797	+	12.7270i	0.240048	+	0.415775i	−0.720680	+	0.693268i	$0.756170\pi$
$938$	26.6192	+	27.1987i	0.869149	+	0.888070i
$939$	−20.8442	−	50.1449i	−0.680225	−	1.63642i
$940$	−20.7347	−	27.7401i	−0.676292	−	0.904783i
$941$	−19.9296	−	3.51413i	−0.649687	−	0.114557i	−0.160914	−	0.986968i	$-0.551444\pi$
$941$	−19.9296	−	3.51413i	−0.649687	−	0.114557i	−0.488773	+	0.872411i	$0.662555\pi$
$942$	−5.35236	−	0.851557i	−0.174389	−	0.0277452i
$943$	5.52971	+	6.59006i	0.180072	+	0.214602i
$944$	−1.45423	−	23.4172i	−0.0473310	−	0.762165i
$945$	1.94155	+	29.9450i	0.0631585	+	0.974112i
$946$	−2.90915	+	7.34333i	−0.0945847	+	0.238752i
$947$	−5.03777	+	4.22719i	−0.163706	+	0.137365i	−0.720960	−	0.692976i	$-0.756299\pi$
$947$	−5.03777	+	4.22719i	−0.163706	+	0.137365i	0.557255	+	0.830342i	$0.311855\pi$
$948$	−26.4617	−	47.0608i	−0.859435	−	1.52847i
$949$	−1.43108	+	8.11606i	−0.0464548	+	0.263458i
$950$	2.01780	+	1.24192i	0.0654661	+	0.0402933i
$951$	32.7922	+	25.0972i	1.06336	+	0.813833i
$952$	−9.65196	−	5.31502i	−0.312822	−	0.172261i
$953$	32.6280	−	18.8378i	1.05693	−	0.610216i	0.132345	−	0.991204i	$-0.457749\pi$
$953$	32.6280	−	18.8378i	1.05693	−	0.610216i	0.924580	+	0.380988i	$0.124416\pi$
$954$	14.3095	−	48.4064i	0.463287	−	1.56722i
$955$	21.0894	−	12.1760i	0.682437	−	0.394005i
$956$	8.42889	−	12.8693i	0.272610	−	0.416223i
$957$	2.53361	−	4.88193i	0.0819001	−	0.157810i
$958$	19.4827	−	31.6543i	0.629457	−	1.02270i
$959$	−29.4660	−	28.4603i	−0.951508	−	0.919031i
$960$	18.2433	−	24.1237i	0.588799	−	0.778588i
$961$	−20.4690	−	7.45012i	−0.660291	−	0.240326i
$962$	−5.42454	−	36.7865i	−0.174894	−	1.18604i
$963$	−15.9980	+	7.50878i	−0.515529	+	0.241967i
$964$	18.5334	−	5.58736i	0.596920	−	0.179957i
$965$	9.69069	−	26.6250i	0.311954	−	0.857088i
$966$	−33.8498	−	1.80080i	−1.08910	−	0.0579397i
$967$	26.1814	−	31.2018i	0.841938	−	1.00338i	−0.157935	−	0.987450i	$-0.550484\pi$
$967$	26.1814	−	31.2018i	0.841938	−	1.00338i	0.999873	−	0.0159333i	$-0.00507194\pi$
$968$	−7.67293	+	28.9696i	−0.246617	+	0.931117i
$969$	12.2697	+	13.3565i	0.394160	+	0.429072i
$970$	−19.3013	+	21.7307i	−0.619728	+	0.697732i
$971$	12.4503	+	21.5645i	0.399549	+	0.692039i	0.993670	−	0.112336i	$-0.0358335\pi$
$971$	12.4503	+	21.5645i	0.399549	+	0.692039i	−0.594121	+	0.804375i	$0.702500\pi$
$972$	29.2282	+	10.8495i	0.937495	+	0.347998i
$973$	−10.7428	−	0.752207i	−0.344397	−	0.0241146i
$974$	−21.1894	−	4.35403i	−0.678951	−	0.139512i
$975$	−2.44455	+	0.545153i	−0.0782884	+	0.0174589i
$976$	−4.06388	−	0.459174i	−0.130082	−	0.0146978i
$977$	−1.45711	−	4.00339i	−0.0466172	−	0.128080i	0.914199	−	0.405265i	$-0.132821\pi$
$977$	−1.45711	−	4.00339i	−0.0466172	−	0.128080i	−0.960817	+	0.277185i	$0.910598\pi$
$978$	46.4790	−	0.778878i	1.48623	−	0.0249058i
$979$	−1.47379	+	4.04921i	−0.0471026	+	0.129413i
$980$	28.4839	+	11.0675i	0.909886	+	0.353540i
$981$	−12.3677	−	8.61395i	−0.394871	−	0.275022i
$982$	15.7953	+	6.25750i	0.504048	+	0.199685i
$983$	−6.07837	−	34.4721i	−0.193870	−	1.09949i	−0.914019	−	0.405671i	$-0.867038\pi$
$983$	−6.07837	−	34.4721i	−0.193870	−	1.09949i	0.720149	−	0.693819i	$-0.244073\pi$
$984$	−8.05114	−	0.318184i	−0.256661	−	0.0101433i
$985$	3.71842	−	1.35340i	0.118479	−	0.0431228i
$986$	5.44935	−	8.85378i	0.173543	−	0.281962i
$987$	−17.3841	−	31.9293i	−0.553343	−	1.01632i
$988$	−4.90865	+	87.1637i	−0.156165	+	2.77305i
$989$			45.9297i			1.46048i
$990$	−5.72664	+	1.37820i	−0.182004	+	0.0438020i
$991$		−	16.0015i		−	0.508305i	−0.967164	−	0.254152i	$-0.918204\pi$
$991$		−	16.0015i		−	0.508305i	0.967164	−	0.254152i	$-0.0817965\pi$
$992$	−2.40743	+	17.0047i	−0.0764359	+	0.539899i
$993$	−12.0156	−	9.19601i	−0.381302	−	0.291827i
$994$	45.9389	+	32.9095i	1.45709	+	1.04383i
$995$	−32.9919	+	12.0081i	−1.04591	+	0.380681i
$996$	0.447488	−	39.3487i	0.0141792	−	1.24681i
$997$	14.1140	+	5.13708i	0.446995	+	0.162693i	0.555703	−	0.831381i	$-0.312449\pi$
$997$	14.1140	+	5.13708i	0.446995	+	0.162693i	−0.108708	+	0.994074i	$0.534671\pi$
$998$	12.2580	+	15.4722i	0.388019	+	0.489763i
$999$	17.6080	−	13.6164i	0.557093	−	0.430803i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ci.a.95.16	yes	840
4.3	odd	2	inner	756.2.ci.a.95.93	yes	840
7.2	even	3		756.2.bs.a.527.110	yes	840
27.2	odd	18		756.2.bs.a.515.1	✓	840
28.23	odd	6		756.2.bs.a.527.1	yes	840
108.83	even	18		756.2.bs.a.515.110	yes	840
189.2	odd	18	inner	756.2.ci.a.191.93	yes	840
756.191	even	18	inner	756.2.ci.a.191.16	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bs.a.515.1	✓	840	27.2	odd	18
756.2.bs.a.515.110	yes	840	108.83	even	18
756.2.bs.a.527.1	yes	840	28.23	odd	6
756.2.bs.a.527.110	yes	840	7.2	even	3
756.2.ci.a.95.16	yes	840	1.1	even	1	trivial
756.2.ci.a.95.93	yes	840	4.3	odd	2	inner
756.2.ci.a.191.16	yes	840	756.191	even	18	inner
756.2.ci.a.191.93	yes	840	189.2	odd	18	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ci (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34200 + 0.446123i) q^{2} +(-1.17175 - 1.27554i) q^{3} +(1.60195 - 1.19740i) q^{4} +(-2.14959 - 0.379031i) q^{5} +(2.14154 + 1.18903i) q^{6} +(1.07635 - 2.41691i) q^{7} +(-1.61563 + 2.32158i) q^{8} +(-0.253990 + 2.98923i) q^{9} +O(q^{10})\)	\(q+(-1.34200 + 0.446123i) q^{2} +(-1.17175 - 1.27554i) q^{3} +(1.60195 - 1.19740i) q^{4} +(-2.14959 - 0.379031i) q^{5} +(2.14154 + 1.18903i) q^{6} +(1.07635 - 2.41691i) q^{7} +(-1.61563 + 2.32158i) q^{8} +(-0.253990 + 2.98923i) q^{9} +(3.05386 - 0.450322i) q^{10} +(0.110447 + 0.626378i) q^{11} +(-3.40441 - 0.640290i) q^{12} +(-1.06585 + 6.04476i) q^{13} +(-0.366221 + 3.72369i) q^{14} +(2.03532 + 3.18602i) q^{15} +(1.13248 - 3.83634i) q^{16} +(-1.27516 + 0.736212i) q^{17} +(-0.992709 - 4.12487i) q^{18} +(6.15881 + 3.55579i) q^{19} +(-3.89739 + 1.96673i) q^{20} +(-4.34408 + 1.45911i) q^{21} +(-0.427662 - 0.791328i) q^{22} +(-4.00681 - 3.36211i) q^{23} +(4.85438 - 0.659516i) q^{24} +(-0.221379 - 0.0805754i) q^{25} +(-1.26633 - 8.58759i) q^{26} +(4.11049 - 3.17866i) q^{27} +(-1.16975 - 5.16059i) q^{28} +(4.91684 - 0.866972i) q^{29} +(-4.15277 - 3.36764i) q^{30} +(2.98988 + 0.527197i) q^{31} +(0.191692 + 5.65361i) q^{32} +(0.669551 - 0.874840i) q^{33} +(1.38282 - 1.55688i) q^{34} +(-3.22980 + 4.78741i) q^{35} +(3.17242 + 5.09272i) q^{36} +4.28368 q^{37} +(-9.85146 - 2.02430i) q^{38} +(8.95923 - 5.72343i) q^{39} +(4.35291 - 4.37807i) q^{40} +(-1.61973 - 0.285602i) q^{41} +(5.17883 - 3.89612i) q^{42} +(-5.64439 - 6.72672i) q^{43} +(0.926954 + 0.871176i) q^{44} +(1.67899 - 6.32935i) q^{45} +(6.87707 + 2.72444i) q^{46} +(1.37761 + 7.81280i) q^{47} +(-6.22038 + 3.05073i) q^{48} +(-4.68295 - 5.20288i) q^{49} +(0.333038 + 0.00937016i) q^{50} +(2.43323 + 0.763851i) q^{51} +(5.53054 + 10.9596i) q^{52} +(10.3036 + 5.94879i) q^{53} +(-4.09821 + 6.09956i) q^{54} -1.38832i q^{55} +(3.87207 + 6.40367i) q^{56} +(-2.68106 - 12.0223i) q^{57} +(-6.21164 + 3.35700i) q^{58} +(5.51184 - 2.00615i) q^{59} +(7.07541 + 2.66674i) q^{60} +(-0.177544 - 1.00690i) q^{61} +(-4.24763 + 0.626355i) q^{62} +(6.95133 + 3.83132i) q^{63} +(-2.77946 - 7.50164i) q^{64} +(4.58230 - 12.5898i) q^{65} +(-0.508254 + 1.47274i) q^{66} +(6.53794 - 7.79161i) q^{67} +(-1.16120 + 2.70624i) q^{68} +(0.406491 + 9.05040i) q^{69} +(2.19862 - 7.86561i) q^{70} +(7.55151 - 13.0796i) q^{71} +(-6.52938 - 5.41916i) q^{72} +1.34266 q^{73} +(-5.74871 + 1.91105i) q^{74} +(0.156625 + 0.376792i) q^{75} +(14.1238 - 1.67835i) q^{76} +(1.63278 + 0.407259i) q^{77} +(-9.46997 + 11.6778i) q^{78} +(10.0183 + 11.9393i) q^{79} +(-3.88846 + 7.81732i) q^{80} +(-8.87098 - 1.51847i) q^{81} +(2.30109 - 0.339319i) q^{82} +(1.97260 + 11.1872i) q^{83} +(-5.21186 + 7.53900i) q^{84} +(3.02011 - 1.09923i) q^{85} +(10.5757 + 6.50919i) q^{86} +(-6.86718 - 5.25574i) q^{87} +(-1.63263 - 0.755585i) q^{88} +(5.86719 + 3.38742i) q^{89} +(0.570466 + 9.24305i) q^{90} +(13.4624 + 9.08234i) q^{91} +(-10.4445 - 0.588185i) q^{92} +(-2.83094 - 4.43145i) q^{93} +(-5.33423 - 9.87022i) q^{94} +(-11.8912 - 9.97788i) q^{95} +(6.98677 - 6.86914i) q^{96} +(-7.21277 + 6.05224i) q^{97} +(8.60566 + 4.89311i) q^{98} +(-1.90044 + 0.171059i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} + 3 q^{10} - 3 q^{12} - 24 q^{13} + 24 q^{14} - 3 q^{16} - 18 q^{17} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} + 48 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} - 21 q^{30} - 63 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} - 12 q^{37} + 45 q^{38} - 33 q^{40} - 24 q^{41} - 21 q^{42} + 6 q^{45} - 6 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} - 63 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} - 54 q^{65} - 3 q^{66} - 12 q^{68} - 48 q^{69} - 21 q^{70} - 9 q^{72} - 12 q^{73} + 15 q^{74} + 12 q^{77} + 6 q^{78} - 54 q^{81} - 6 q^{82} - 39 q^{84} + 6 q^{85} - 9 q^{86} - 27 q^{88} - 18 q^{89} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} + 213 q^{96} - 24 q^{97} + 162 q^{98}+O(q^{100}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 + 3 * q^10 - 3 * q^12 - 24 * q^13 + 24 * q^14 - 3 * q^16 - 18 * q^17 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 + 48 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 - 21 * q^30 - 63 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 - 12 * q^37 + 45 * q^38 - 33 * q^40 - 24 * q^41 - 21 * q^42 + 6 * q^45 - 6 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 - 63 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 - 54 * q^65 - 3 * q^66 - 12 * q^68 - 48 * q^69 - 21 * q^70 - 9 * q^72 - 12 * q^73 + 15 * q^74 + 12 * q^77 + 6 * q^78 - 54 * q^81 - 6 * q^82 - 39 * q^84 + 6 * q^85 - 9 * q^86 - 27 * q^88 - 18 * q^89 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 + 213 * q^96 - 24 * q^97 + 162 * q^98

Introduction

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