LMFDB - Embedded newform 354.2.e.b.85.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(7,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("354.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.e (of order $29$, degree $28$, 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:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$2$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			85.2
Character	$\chi$	$=$	354.85
Dual form			354.2.e.b.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.796093 + 0.605174i) q^{2} +(-0.468408 + 0.883512i) q^{3} +(0.267528 - 0.963550i) q^{4} +(0.451252 - 0.427449i) q^{5} +(-0.161782 - 0.986827i) q^{6} +(-1.39072 - 1.63728i) q^{7} +(0.370138 + 0.928977i) q^{8} +(-0.561187 - 0.827689i) q^{9} +O(q^{10})$	\(q+(-0.796093 + 0.605174i) q^{2} +(-0.468408 + 0.883512i) q^{3} +(0.267528 - 0.963550i) q^{4} +(0.451252 - 0.427449i) q^{5} +(-0.161782 - 0.986827i) q^{6} +(-1.39072 - 1.63728i) q^{7} +(0.370138 + 0.928977i) q^{8} +(-0.561187 - 0.827689i) q^{9} +(-0.100558 + 0.613375i) q^{10} +(5.38463 - 3.23982i) q^{11} +(0.725995 + 0.687699i) q^{12} +(-1.24029 + 1.82929i) q^{13} +(2.09798 + 0.461800i) q^{14} +(0.166286 + 0.598907i) q^{15} +(-0.856857 - 0.515554i) q^{16} +(4.32295 - 5.08937i) q^{17} +(0.947653 + 0.319302i) q^{18} +(0.0104440 + 0.00483191i) q^{19} +(-0.291146 - 0.549159i) q^{20} +(2.09798 - 0.461800i) q^{21} +(-2.32601 + 5.83784i) q^{22} +(-0.864260 + 0.291203i) q^{23} +(-0.994138 - 0.108119i) q^{24} +(-0.249778 + 4.60689i) q^{25} +(-0.119653 - 2.20687i) q^{26} +(0.994138 - 0.108119i) q^{27} +(-1.94965 + 0.902006i) q^{28} +(1.56510 + 1.18975i) q^{29} +(-0.494822 - 0.376154i) q^{30} +(7.84696 - 3.63039i) q^{31} +(0.994138 - 0.108119i) q^{32} +(0.340217 + 6.27494i) q^{33} +(-0.361515 + 6.66776i) q^{34} +(-1.32742 - 0.144365i) q^{35} +(-0.947653 + 0.319302i) q^{36} +(0.261056 - 0.655202i) q^{37} +(-0.0112386 + 0.00247379i) q^{38} +(-1.03524 - 1.95266i) q^{39} +(0.564116 + 0.260988i) q^{40} +(8.49710 + 2.86300i) q^{41} +(-1.39072 + 1.63728i) q^{42} +(-1.41461 - 0.851142i) q^{43} +(-1.68119 - 6.05510i) q^{44} +(-0.607032 - 0.133618i) q^{45} +(0.511803 - 0.754852i) q^{46} +(-3.71172 - 3.51593i) q^{47} +(0.856857 - 0.515554i) q^{48} +(0.385888 - 2.35381i) q^{49} +(-2.58913 - 3.81867i) q^{50} +(2.47162 + 6.20329i) q^{51} +(1.43080 + 1.68447i) q^{52} +(0.882177 + 5.38104i) q^{53} +(-0.725995 + 0.687699i) q^{54} +(1.04497 - 3.76363i) q^{55} +(1.00624 - 1.89796i) q^{56} +(-0.00916111 + 0.00696410i) q^{57} -1.96597 q^{58} +(1.29746 - 7.57077i) q^{59} +0.621563 q^{60} +(-11.4417 + 8.69777i) q^{61} +(-4.04989 + 7.63891i) q^{62} +(-0.574704 + 2.06990i) q^{63} +(-0.725995 + 0.687699i) q^{64} +(0.222244 + 1.35563i) q^{65} +(-4.06828 - 4.78955i) q^{66} +(-1.36042 - 3.41441i) q^{67} +(-3.74735 - 5.52693i) q^{68} +(0.147545 - 0.899986i) q^{69} +(1.14411 - 0.688389i) q^{70} +(-7.85612 - 7.44171i) q^{71} +(0.561187 - 0.827689i) q^{72} +(-6.96612 - 1.53336i) q^{73} +(0.188686 + 0.679587i) q^{74} +(-3.95325 - 2.37859i) q^{75} +(0.00744986 - 0.00877065i) q^{76} +(-12.7930 - 4.31045i) q^{77} +(2.00585 + 0.928003i) q^{78} +(-4.84397 - 9.13669i) q^{79} +(-0.607032 + 0.133618i) q^{80} +(-0.370138 + 0.928977i) q^{81} +(-8.49710 + 2.86300i) q^{82} +(1.36488 + 0.148439i) q^{83} +(0.116301 - 2.14505i) q^{84} +(-0.224705 - 4.14443i) q^{85} +(1.64125 - 0.178497i) q^{86} +(-1.78427 + 0.825490i) q^{87} +(5.00277 + 3.80301i) q^{88} +(10.1915 + 7.74741i) q^{89} +(0.564116 - 0.260988i) q^{90} +(4.71994 - 0.513324i) q^{91} +(0.0493747 + 0.910662i) q^{92} +(-0.468089 + 8.63339i) q^{93} +(5.08262 + 0.552769i) q^{94} +(0.00677828 - 0.00228387i) q^{95} +(-0.370138 + 0.928977i) q^{96} +(-10.5255 + 2.31685i) q^{97} +(1.11727 + 2.10739i) q^{98} +(-5.70335 - 2.63865i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 56 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + q^7 + 2 * q^8 - 2 * q^9	\( 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} + 30 q^{11} + 2 q^{12} + 5 q^{13} + 28 q^{14} + 2 q^{15} - 2 q^{16} - 3 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 28 q^{21} - q^{22} - 2 q^{23} - 2 q^{24} + 64 q^{25} - 34 q^{26} + 2 q^{27} + q^{28} + 8 q^{29} - 2 q^{30} + 2 q^{32} - q^{33} + 32 q^{34} - 87 q^{35} - 2 q^{36} + 47 q^{37} + 4 q^{38} - 5 q^{39} + 2 q^{40} + 3 q^{41} + q^{42} - 61 q^{43} + q^{44} - 2 q^{45} - 27 q^{46} + 50 q^{47} + 2 q^{48} - 45 q^{49} - 6 q^{50} + 3 q^{51} - 24 q^{52} - 27 q^{53} - 2 q^{54} - 95 q^{55} - q^{56} + 4 q^{57} + 50 q^{58} - 58 q^{59} + 2 q^{60} - 74 q^{61} - 29 q^{62} + q^{63} - 2 q^{64} - 17 q^{65} + q^{66} + 4 q^{67} - 32 q^{68} + 31 q^{69} - 58 q^{70} - 47 q^{71} + 2 q^{72} + 43 q^{73} - 18 q^{74} - 6 q^{75} - 33 q^{76} - 5 q^{77} + 5 q^{78} + 19 q^{79} - 2 q^{80} - 2 q^{81} - 3 q^{82} + 47 q^{83} - q^{84} - 149 q^{85} - 55 q^{86} + 21 q^{87} + 28 q^{88} + 36 q^{89} + 2 q^{90} + 175 q^{91} - 2 q^{92} - 29 q^{93} - 21 q^{94} + 50 q^{95} - 2 q^{96} + 10 q^{97} - 13 q^{98} + q^{99}+O(q^{100}) \) 56 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + q^7 + 2 * q^8 - 2 * q^9 + 2 * q^10 + 30 * q^11 + 2 * q^12 + 5 * q^13 + 28 * q^14 + 2 * q^15 - 2 * q^16 - 3 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 28 * q^21 - q^22 - 2 * q^23 - 2 * q^24 + 64 * q^25 - 34 * q^26 + 2 * q^27 + q^28 + 8 * q^29 - 2 * q^30 + 2 * q^32 - q^33 + 32 * q^34 - 87 * q^35 - 2 * q^36 + 47 * q^37 + 4 * q^38 - 5 * q^39 + 2 * q^40 + 3 * q^41 + q^42 - 61 * q^43 + q^44 - 2 * q^45 - 27 * q^46 + 50 * q^47 + 2 * q^48 - 45 * q^49 - 6 * q^50 + 3 * q^51 - 24 * q^52 - 27 * q^53 - 2 * q^54 - 95 * q^55 - q^56 + 4 * q^57 + 50 * q^58 - 58 * q^59 + 2 * q^60 - 74 * q^61 - 29 * q^62 + q^63 - 2 * q^64 - 17 * q^65 + q^66 + 4 * q^67 - 32 * q^68 + 31 * q^69 - 58 * q^70 - 47 * q^71 + 2 * q^72 + 43 * q^73 - 18 * q^74 - 6 * q^75 - 33 * q^76 - 5 * q^77 + 5 * q^78 + 19 * q^79 - 2 * q^80 - 2 * q^81 - 3 * q^82 + 47 * q^83 - q^84 - 149 * q^85 - 55 * q^86 + 21 * q^87 + 28 * q^88 + 36 * q^89 + 2 * q^90 + 175 * q^91 - 2 * q^92 - 29 * q^93 - 21 * q^94 + 50 * q^95 - 2 * q^96 + 10 * q^97 - 13 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{23}{29}\right)$	$1$

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 $

$2$	−0.796093	+	0.605174i	−0.562923	+	0.427923i
$2$	−0.796093	+	0.605174i	−0.562923	+	0.427923i
$3$	−0.468408	+	0.883512i	−0.270436	+	0.510096i
$3$	−0.468408	+	0.883512i	−0.270436	+	0.510096i
$4$	0.267528	−	0.963550i	0.133764	−	0.481775i
$5$	0.451252	−	0.427449i	0.201806	−	0.191161i	−0.580122	−	0.814530i	$-0.696995\pi$
$5$	0.451252	−	0.427449i	0.201806	−	0.191161i	0.781928	+	0.623369i	$0.214236\pi$
$6$	−0.161782	−	0.986827i	−0.0660472	−	0.402870i
$7$	−1.39072	−	1.63728i	−0.525641	−	0.618832i	0.433709	−	0.901053i	$-0.357205\pi$
$7$	−1.39072	−	1.63728i	−0.525641	−	0.618832i	−0.959349	+	0.282221i	$0.908929\pi$
$8$	0.370138	+	0.928977i	0.130864	+	0.328443i
$9$	−0.561187	−	0.827689i	−0.187062	−	0.275896i
$10$	−0.100558	+	0.613375i	−0.0317992	+	0.193966i
$11$	5.38463	−	3.23982i	1.62353	−	0.976843i	0.646717	−	0.762730i	$-0.276142\pi$
$11$	5.38463	−	3.23982i	1.62353	−	0.976843i	0.976809	−	0.214113i	$-0.0686860\pi$
$12$	0.725995	+	0.687699i	0.209577	+	0.198522i
$13$	−1.24029	+	1.82929i	−0.343994	+	0.507353i	−0.959853	−	0.280503i	$-0.909499\pi$
$13$	−1.24029	+	1.82929i	−0.343994	+	0.507353i	0.615859	+	0.787856i	$0.288809\pi$
$14$	2.09798	+	0.461800i	0.560708	+	0.123421i
$15$	0.166286	+	0.598907i	0.0429348	+	0.154637i
$16$	−0.856857	−	0.515554i	−0.214214	−	0.128888i
$17$	4.32295	−	5.08937i	1.04847	−	1.23435i	0.0770403	−	0.997028i	$-0.475453\pi$
$17$	4.32295	−	5.08937i	1.04847	−	1.23435i	0.971430	−	0.237327i	$-0.0762712\pi$
$18$	0.947653	+	0.319302i	0.223364	+	0.0752601i
$19$	0.0104440	+	0.00483191i	0.00239602	+	0.00110852i	0.421087	−	0.907020i	$-0.361649\pi$
$19$	0.0104440	+	0.00483191i	0.00239602	+	0.00110852i	−0.418691	+	0.908129i	$0.637511\pi$
$20$	−0.291146	−	0.549159i	−0.0651021	−	0.122796i
$21$	2.09798	−	0.461800i	0.457816	−	0.100773i
$22$	−2.32601	+	5.83784i	−0.495906	+	1.24463i
$23$	−0.864260	+	0.291203i	−0.180211	+	0.0607200i	−0.407960	−	0.913000i	$-0.633760\pi$
$23$	−0.864260	+	0.291203i	−0.180211	+	0.0607200i	0.227750	+	0.973720i	$0.426863\pi$
$24$	−0.994138	−	0.108119i	−0.202928	−	0.0220697i
$25$	−0.249778	+	4.60689i	−0.0499557	+	0.921379i
$26$	−0.119653	−	2.20687i	−0.0234659	−	0.432803i
$27$	0.994138	−	0.108119i	0.191322	−	0.0208075i
$28$	−1.94965	+	0.902006i	−0.368450	+	0.170463i
$29$	1.56510	+	1.18975i	0.290631	+	0.220932i	0.740322	−	0.672252i	$-0.234673\pi$
$29$	1.56510	+	1.18975i	0.290631	+	0.220932i	−0.449691	+	0.893184i	$0.648466\pi$
$30$	−0.494822	−	0.376154i	−0.0903418	−	0.0686760i
$31$	7.84696	−	3.63039i	1.40936	−	0.652038i	0.440068	−	0.897965i	$-0.354954\pi$
$31$	7.84696	−	3.63039i	1.40936	−	0.652038i	0.969288	+	0.245927i	$0.0790923\pi$
$32$	0.994138	−	0.108119i	0.175740	−	0.0191129i
$33$	0.340217	+	6.27494i	0.0592243	+	1.09233i
$34$	−0.361515	+	6.66776i	−0.0619993	+	1.14351i
$35$	−1.32742	−	0.144365i	−0.224374	−	0.0244022i
$36$	−0.947653	+	0.319302i	−0.157942	+	0.0532169i
$37$	0.261056	−	0.655202i	0.0429174	−	0.107715i	−0.905956	−	0.423373i	$-0.860846\pi$
$37$	0.261056	−	0.655202i	0.0429174	−	0.107715i	0.948873	+	0.315658i	$0.102225\pi$
$38$	−0.0112386	+	0.00247379i	−0.00182313	+	0.000401302i
$39$	−1.03524	−	1.95266i	−0.165770	−	0.312676i
$40$	0.564116	+	0.260988i	0.0891945	+	0.0412658i
$41$	8.49710	+	2.86300i	1.32702	+	0.447126i	0.891488	−	0.453045i	$-0.149662\pi$
$41$	8.49710	+	2.86300i	1.32702	+	0.447126i	0.435536	+	0.900171i	$0.356559\pi$
$42$	−1.39072	+	1.63728i	−0.214592	+	0.252637i
$43$	−1.41461	−	0.851142i	−0.215726	−	0.129798i	0.403590	−	0.914940i	$-0.367762\pi$
$43$	−1.41461	−	0.851142i	−0.215726	−	0.129798i	−0.619316	+	0.785142i	$0.712590\pi$
$44$	−1.68119	−	6.05510i	−0.253449	−	0.912841i
$45$	−0.607032	−	0.133618i	−0.0904909	−	0.0199186i
$46$	0.511803	−	0.754852i	0.0754612	−	0.111297i
$47$	−3.71172	−	3.51593i	−0.541410	−	0.512851i	0.367399	−	0.930063i	$-0.380248\pi$
$47$	−3.71172	−	3.51593i	−0.541410	−	0.512851i	−0.908809	+	0.417213i	$0.863007\pi$
$48$	0.856857	−	0.515554i	0.123677	−	0.0744138i
$49$	0.385888	−	2.35381i	0.0551269	−	0.336259i
$50$	−2.58913	−	3.81867i	−0.366158	−	0.540042i
$51$	2.47162	+	6.20329i	0.346095	+	0.868634i
$52$	1.43080	+	1.68447i	0.198416	+	0.233593i
$53$	0.882177	+	5.38104i	0.121176	+	0.739143i	0.975598	+	0.219563i	$0.0704632\pi$
$53$	0.882177	+	5.38104i	0.121176	+	0.739143i	−0.854422	+	0.519580i	$0.826089\pi$
$54$	−0.725995	+	0.687699i	−0.0987955	+	0.0935840i
$55$	1.04497	−	3.76363i	0.140903	−	0.507488i
$56$	1.00624	−	1.89796i	0.134464	−	0.253626i
$57$	−0.00916111	+	0.00696410i	−0.00121342	+	0.000922417i
$58$	−1.96597			−0.258145
$59$	1.29746	−	7.57077i	0.168915	−	0.985631i
$59$	1.29746	−	7.57077i	0.168915	−	0.985631i
$60$	0.621563			0.0802435
$61$	−11.4417	+	8.69777i	−1.46496	+	1.11364i	−0.495437	+	0.868644i	$0.664992\pi$
$61$	−11.4417	+	8.69777i	−1.46496	+	1.11364i	−0.969525	+	0.244991i	$0.921215\pi$
$62$	−4.04989	+	7.63891i	−0.514337	+	0.970142i
$63$	−0.574704	+	2.06990i	−0.0724059	+	0.260783i
$64$	−0.725995	+	0.687699i	−0.0907494	+	0.0859624i
$65$	0.222244	+	1.35563i	0.0275660	+	0.168145i
$66$	−4.06828	−	4.78955i	−0.500770	−	0.589552i
$67$	−1.36042	−	3.41441i	−0.166202	−	0.417136i	0.822160	−	0.569257i	$-0.192769\pi$
$67$	−1.36042	−	3.41441i	−0.166202	−	0.417136i	−0.988362	+	0.152121i	$0.951390\pi$
$68$	−3.74735	−	5.52693i	−0.454433	−	0.670239i
$69$	0.147545	−	0.899986i	0.0177624	−	0.108346i
$70$	1.14411	−	0.688389i	0.136748	−	0.0822783i
$71$	−7.85612	−	7.44171i	−0.932350	−	0.883169i	0.0610194	−	0.998137i	$-0.480565\pi$
$71$	−7.85612	−	7.44171i	−0.932350	−	0.883169i	−0.993369	+	0.114968i	$0.963323\pi$
$72$	0.561187	−	0.827689i	0.0661365	−	0.0975441i
$73$	−6.96612	−	1.53336i	−0.815323	−	0.179466i	−0.212315	−	0.977201i	$-0.568100\pi$
$73$	−6.96612	−	1.53336i	−0.815323	−	0.179466i	−0.603008	+	0.797735i	$0.706031\pi$
$74$	0.188686	+	0.679587i	0.0219343	+	0.0790003i
$75$	−3.95325	−	2.37859i	−0.456482	−	0.274656i
$76$	0.00744986	−	0.00877065i	0.000854557	−	0.00100606i
$77$	−12.7930	−	4.31045i	−1.45789	−	0.491222i
$78$	2.00585	+	0.928003i	0.227117	+	0.105076i
$79$	−4.84397	−	9.13669i	−0.544989	−	1.02796i	−0.991117	−	0.132989i	$-0.957542\pi$
$79$	−4.84397	−	9.13669i	−0.544989	−	1.02796i	0.446129	−	0.894969i	$-0.352802\pi$
$80$	−0.607032	+	0.133618i	−0.0678682	+	0.0149389i
$81$	−0.370138	+	0.928977i	−0.0411265	+	0.103220i
$82$	−8.49710	+	2.86300i	−0.938347	+	0.316166i
$83$	1.36488	+	0.148439i	0.149815	+	0.0162933i	0.182719	−	0.983165i	$-0.441510\pi$
$83$	1.36488	+	0.148439i	0.149815	+	0.0162933i	−0.0329043	+	0.999459i	$0.510476\pi$
$84$	0.116301	−	2.14505i	0.0126895	−	0.234044i
$85$	−0.224705	−	4.14443i	−0.0243726	−	0.449527i
$86$	1.64125	−	0.178497i	0.176981	−	0.0192478i
$87$	−1.78427	+	0.825490i	−0.191293	+	0.0885018i
$88$	5.00277	+	3.80301i	0.533298	+	0.405402i
$89$	10.1915	+	7.74741i	1.08030	+	0.821224i	0.984711	−	0.174197i	$-0.0557330\pi$
$89$	10.1915	+	7.74741i	1.08030	+	0.821224i	0.0955904	+	0.995421i	$0.469526\pi$
$90$	0.564116	−	0.260988i	0.0594630	−	0.0275105i
$91$	4.71994	−	0.513324i	0.494784	−	0.0538110i
$92$	0.0493747	+	0.910662i	0.00514767	+	0.0949431i
$93$	−0.468089	+	8.63339i	−0.0485386	+	0.895241i
$94$	5.08262	+	0.552769i	0.524233	+	0.0570137i
$95$	0.00677828	−	0.00228387i	0.000695437	−	0.000234320i
$96$	−0.370138	+	0.928977i	−0.0377771	+	0.0948133i
$97$	−10.5255	+	2.31685i	−1.06871	+	0.235240i	−0.714292	−	0.699848i	$-0.753251\pi$
$97$	−10.5255	+	2.31685i	−1.06871	+	0.235240i	−0.354415	+	0.935088i	$0.615320\pi$
$98$	1.11727	+	2.10739i	0.112861	+	0.212878i
$99$	−5.70335	−	2.63865i	−0.573208	−	0.265194i
$100$	4.37215	+	1.47315i	0.437215	+	0.147315i
$101$	−3.76344	+	4.43066i	−0.374476	+	0.440867i	−0.916827	−	0.399285i	$-0.869258\pi$
$101$	−3.76344	+	4.43066i	−0.374476	+	0.440867i	0.542351	+	0.840152i	$0.317534\pi$
$102$	−5.72171	−	3.44264i	−0.566533	−	0.340872i
$103$	1.11516	+	4.01643i	0.109880	+	0.395751i	0.997953	−	0.0639509i	$-0.0203701\pi$
$103$	1.11516	+	4.01643i	0.109880	+	0.395751i	−0.888073	+	0.459702i	$0.847956\pi$
$104$	−2.15844	−	0.475109i	−0.211653	−	0.0465883i
$105$	0.749321	−	1.10517i	0.0731262	−	0.107853i
$106$	−3.95876	−	3.74994i	−0.384509	−	0.364226i
$107$	11.2945	−	6.79569i	1.09188	−	0.656964i	0.148581	−	0.988900i	$-0.452530\pi$
$107$	11.2945	−	6.79569i	1.09188	−	0.656964i	0.943302	+	0.331936i	$0.107702\pi$
$108$	0.161782	−	0.986827i	0.0155675	−	0.0949574i
$109$	3.38567	+	4.99349i	0.324289	+	0.478290i	0.954532	−	0.298107i	$-0.0963553\pi$
$109$	3.38567	+	4.99349i	0.324289	+	0.478290i	−0.630244	+	0.776397i	$0.717045\pi$
$110$	1.44576	+	3.62858i	0.137848	+	0.345972i
$111$	0.456598	+	0.537549i	0.0433384	+	0.0510219i
$112$	0.347540	+	2.11990i	0.0328395	+	0.200312i
$113$	−4.36840	+	4.13797i	−0.410944	+	0.389267i	−0.865054	−	0.501679i	$-0.832716\pi$
$113$	−4.36840	+	4.13797i	−0.410944	+	0.389267i	0.454110	+	0.890946i	$0.349957\pi$
$114$	0.00307861	−	0.0110881i	0.000288338	−	0.00103850i
$115$	−0.265525	+	0.500833i	−0.0247603	+	0.0467029i
$116$	1.56510	−	1.18975i	0.145315	−	0.110466i
$117$	2.21011			0.204325
$118$	3.54874	+	6.81223i	0.326688	+	0.627117i
$119$	−14.3447			−1.31498
$120$	−0.494822	+	0.376154i	−0.0451709	+	0.0343380i
$121$	13.3453	−	25.1718i	1.21321	−	2.28835i
$122$	3.84501	−	13.8485i	0.348111	−	1.25378i
$123$	−6.50961	+	6.16623i	−0.586952	+	0.555990i
$124$	−1.39878	−	8.53217i	−0.125614	−	0.766212i
$125$	3.86846	+	4.55430i	0.346005	+	0.407349i
$126$	−0.795131	−	1.99563i	−0.0708359	−	0.177785i
$127$	3.26279	+	4.81225i	0.289525	+	0.427018i	0.944440	−	0.328685i	$-0.106606\pi$
$127$	3.26279	+	4.81225i	0.289525	+	0.427018i	−0.654914	+	0.755703i	$0.727295\pi$
$128$	0.161782	−	0.986827i	0.0142996	−	0.0872240i
$129$	1.41461	−	0.851142i	0.124549	−	0.0749389i
$130$	−0.997319	−	0.944711i	−0.0874707	−	0.0828566i
$131$	−12.5582	+	18.5220i	−1.09722	+	1.61828i	−0.374354	+	0.927286i	$0.622135\pi$
$131$	−12.5582	+	18.5220i	−1.09722	+	1.61828i	−0.722865	+	0.690990i	$0.757175\pi$
$132$	6.13724	+	1.35091i	0.534178	+	0.117581i
$133$	−0.00661346	−	0.0238195i	−0.000573460	−	0.00206542i
$134$	3.14934	+	1.89489i	0.272061	+	0.163694i
$135$	0.402392	−	0.473732i	0.0346324	−	0.0407724i
$136$	6.32800	+	2.13215i	0.542622	+	0.182830i
$137$	−18.9313	−	8.75853i	−1.61741	−	0.748292i	−0.618121	−	0.786083i	$-0.712106\pi$
$137$	−18.9313	−	8.75853i	−1.61741	−	0.748292i	−0.999286	+	0.0377907i	$0.987968\pi$
$138$	0.427188	+	0.805763i	0.0363647	+	0.0685911i
$139$	−3.60142	+	0.792733i	−0.305469	+	0.0672388i	−0.365060	−	0.930984i	$-0.618951\pi$
$139$	−3.60142	+	0.792733i	−0.305469	+	0.0672388i	0.0595909	+	0.998223i	$0.481020\pi$
$140$	−0.494224	+	1.24041i	−0.0417696	+	0.104834i
$141$	4.84497	−	1.63246i	0.408020	−	0.137478i
$142$	10.7577	+	1.16997i	0.902769	+	0.0981820i
$143$	−0.751920	+	13.8683i	−0.0628787	+	1.15973i
$144$	0.0541389	+	0.998533i	0.00451158	+	0.0832111i
$145$	1.21481	−	0.132119i	0.100885	−	0.0109719i
$146$	6.47363	−	2.99502i	0.535762	−	0.247870i
$147$	1.89887	+	1.44348i	0.156616	+	0.119057i
$148$	−0.561480	−	0.426826i	−0.0461534	−	0.0350849i
$149$	17.8752	−	8.26993i	1.46439	−	0.677499i	0.484091	−	0.875017i	$-0.339150\pi$
$149$	17.8752	−	8.26993i	1.46439	−	0.677499i	0.980299	+	0.197518i	$0.0632881\pi$
$150$	4.58661	−	0.498824i	0.374495	−	0.0407288i
$151$	0.356071	+	6.56734i	0.0289766	+	0.534443i	0.976601	+	0.215057i	$0.0689938\pi$
$151$	0.356071	+	6.56734i	0.0289766	+	0.534443i	−0.947625	+	0.319386i	$0.896523\pi$
$152$	−0.000623009		0.0114907i	−5.05327e−5		0.000932020i
$153$	−6.63840	−	0.721970i	−0.536683	−	0.0583678i
$154$	12.7930	−	4.31045i	1.03089	−	0.347346i
$155$	1.98915	−	4.99240i	0.159773	−	0.400999i
$156$	−2.15844	+	0.475109i	−0.172814	+	0.0380392i
$157$	6.99743	+	13.1985i	0.558455	+	1.05336i	0.988595	+	0.150596i	$0.0481194\pi$
$157$	6.99743	+	13.1985i	0.558455	+	1.05336i	−0.430140	+	0.902762i	$0.641536\pi$
$158$	9.38554	+	4.34221i	0.746673	+	0.345448i
$159$	−5.16744	−	1.74111i	−0.409804	−	0.138079i
$160$	0.402392	−	0.473732i	0.0318118	−	0.0374518i
$161$	1.67872	+	1.01005i	0.132302	+	0.0796032i
$162$	−0.267528	−	0.963550i	−0.0210190	−	0.0757036i
$163$	1.07459	+	0.236535i	0.0841683	+	0.0185268i	0.256855	−	0.966450i	$-0.417314\pi$
$163$	1.07459	+	0.236535i	0.0841683	+	0.0185268i	−0.172687	+	0.984977i	$0.555245\pi$
$164$	5.03186	−	7.42144i	0.392922	−	0.579517i
$165$	2.83574	+	2.68616i	0.220762	+	0.209117i
$166$	−1.17640	+	0.707817i	−0.0913064	+	0.0549372i
$167$	−3.66042	+	22.3276i	−0.283252	+	1.72776i	0.335383	+	0.942082i	$0.391134\pi$
$167$	−3.66042	+	22.3276i	−0.283252	+	1.72776i	−0.618635	+	0.785679i	$0.712314\pi$
$168$	1.20554	+	1.77804i	0.0930096	+	0.137179i
$169$	3.00382	+	7.53901i	0.231063	+	0.579924i
$170$	2.68699	+	3.16337i	0.206083	+	0.242619i
$171$	−0.00186172	−	0.0113560i	−0.000142369	−	0.000868415i
$172$	−1.19857	+	1.13534i	−0.0913898	+	0.0865690i
$173$	−0.630941	+	2.27244i	−0.0479696	+	0.172771i	−0.983655	−	0.180066i	$-0.942369\pi$
$173$	−0.630941	+	2.27244i	−0.0479696	+	0.172771i	0.935685	+	0.352836i	$0.114783\pi$
$174$	0.920877	−	1.73696i	0.0698115	−	0.131678i
$175$	7.89013	−	5.99792i	0.596438	−	0.453400i
$176$	−6.28416			−0.473686
$177$	6.08113	+	4.69254i	0.457085	+	0.352713i
$178$	−12.8019			−0.959546
$179$	10.9373	−	8.31429i	0.817490	−	0.621440i	−0.110571	−	0.993868i	$-0.535268\pi$
$179$	10.9373	−	8.31429i	0.817490	−	0.621440i	0.928061	+	0.372429i	$0.121475\pi$
$180$	−0.291146	+	0.549159i	−0.0217007	+	0.0409319i
$181$	1.90614	−	6.86529i	0.141682	−	0.510293i	−0.858314	−	0.513125i	$-0.828488\pi$
$181$	1.90614	−	6.86529i	0.141682	−	0.510293i	0.999996	+	0.00283206i	$0.000901475\pi$
$182$	−3.44686	+	3.26504i	−0.255498	+	0.242021i
$183$	−2.32519	−	14.1830i	−0.171883	−	1.04844i
$184$	−0.590416	−	0.695092i	−0.0435261	−	0.0512428i
$185$	−0.162263	−	0.407250i	−0.0119298	−	0.0299416i
$186$	−4.85206	−	7.15626i	−0.355771	−	0.524722i
$187$	6.78882	−	41.4100i	0.496448	−	3.02820i
$188$	−4.38076	+	2.63582i	−0.319500	+	0.192237i
$189$	−1.55958	−	1.47732i	−0.113443	−	0.107459i
$190$	−0.00401400	+	0.00592021i	−0.000291206	+	0.000429497i
$191$	3.14834	+	0.693002i	0.227806	+	0.0501439i	0.327406	−	0.944884i	$-0.393825\pi$
$191$	3.14834	+	0.693002i	0.227806	+	0.0501439i	−0.0996004	+	0.995028i	$0.531756\pi$
$192$	−0.267528	−	0.963550i	−0.0193072	−	0.0695382i
$193$	5.23772	+	3.15143i	0.377019	+	0.226845i	0.691432	−	0.722441i	$-0.256980\pi$
$193$	5.23772	+	3.15143i	0.377019	+	0.226845i	−0.314413	+	0.949286i	$0.601808\pi$
$194$	6.97722	−	8.21421i	0.500935	−	0.589746i
$195$	−1.30182	−	0.438633i	−0.0932250	−	0.0314112i
$196$	−2.16478	−	1.00153i	−0.154627	−	0.0715382i
$197$	12.1067	+	22.8357i	0.862567	+	1.62697i	0.776004	+	0.630727i	$0.217243\pi$
$197$	12.1067	+	22.8357i	0.862567	+	1.62697i	0.0865626	+	0.996246i	$0.472412\pi$
$198$	6.13724	−	1.35091i	0.436154	−	0.0960049i
$199$	−7.97097	+	20.0056i	−0.565047	+	1.41816i	0.317644	+	0.948210i	$0.397108\pi$
$199$	−7.97097	+	20.0056i	−0.565047	+	1.41816i	−0.882692	+	0.469952i	$0.844271\pi$
$200$	−4.37215	+	1.47315i	−0.309158	+	0.104167i
$201$	3.65390	+	0.397386i	0.257727	+	0.0280294i
$202$	0.314724	−	5.80475i	0.0221439	−	0.408421i
$203$	−0.228645	−	4.21710i	−0.0160477	−	0.295983i
$204$	6.63840	−	0.721970i	0.464781	−	0.0505480i
$205$	5.05812	−	2.34014i	0.353274	−	0.163442i
$206$	−3.31841	−	2.52259i	−0.231205	−	0.175757i
$207$	0.726037	+	0.551919i	0.0504631	+	0.0383610i
$208$	2.00585	−	0.928003i	0.139080	−	0.0643454i
$209$	0.0718916	−	0.00781868i	0.00497285	−	0.000540830i
$210$	0.0722886	+	1.33328i	0.00498838	+	0.0920053i
$211$	0.112501	−	2.07497i	0.00774491	−	0.142846i	−0.992103	−	0.125423i	$-0.959971\pi$
$211$	0.112501	−	2.07497i	0.00774491	−	0.142846i	0.999848	−	0.0174230i	$-0.00554620\pi$
$212$	5.42091	+	0.589560i	0.372310	+	0.0404911i
$213$	10.2547	−	3.45522i	0.702641	−	0.236747i
$214$	−4.87891	+	12.2452i	−0.333516	+	0.837061i
$215$	−1.00217	+	0.220593i	−0.0683471	+	0.0150443i
$216$	0.468408	+	0.883512i	0.0318712	+	0.0601154i
$217$	−16.8568	−	7.79881i	−1.14432	−	0.529418i
$218$	−5.71725	−	1.92636i	−0.387221	−	0.130470i
$219$	4.61773	−	5.43642i	0.312037	−	0.367359i
$220$	−3.34689	−	2.01375i	−0.225647	−	0.135767i
$221$	3.94822	+	14.2202i	0.265586	+	0.956555i
$222$	−0.688805	−	0.151617i	−0.0462296	−	0.0101759i
$223$	3.10320	−	4.57687i	0.207806	−	0.306490i	−0.709476	−	0.704730i	$-0.751068\pi$
$223$	3.10320	−	4.57687i	0.207806	−	0.306490i	0.917282	+	0.398239i	$0.130379\pi$
$224$	−1.55958	−	1.47732i	−0.104204	−	0.0987073i
$225$	3.95325	−	2.37859i	0.263550	−	0.158573i
$226$	0.973461	−	5.93785i	0.0647536	−	0.394980i
$227$	−4.34517	−	6.40864i	−0.288399	−	0.425357i	0.655699	−	0.755023i	$-0.272374\pi$
$227$	−4.34517	−	6.40864i	−0.288399	−	0.425357i	−0.944098	+	0.329666i	$0.893064\pi$
$228$	0.00425940	+	0.0106903i	0.000282086	+	0.000707981i
$229$	9.24520	+	10.8843i	0.610940	+	0.719255i	0.977452	−	0.211159i	$-0.0677238\pi$
$229$	9.24520	+	10.8843i	0.610940	+	0.719255i	−0.366511	+	0.930414i	$0.619448\pi$
$230$	−0.0917087	−	0.559398i	−0.00604709	−	0.0368856i
$231$	9.80067	−	9.28369i	0.644837	−	0.610822i
$232$	−0.525953	+	1.89431i	−0.0345305	+	0.124368i
$233$	−3.37656	+	6.36886i	−0.221206	+	0.417238i	−0.969132	−	0.246544i	$-0.920705\pi$
$233$	−3.37656	+	6.36886i	−0.221206	+	0.417238i	0.747926	+	0.663782i	$0.231050\pi$
$234$	−1.75946	+	1.33750i	−0.115019	+	0.0874354i
$235$	−3.17780			−0.207297
$236$	−6.94771	−	3.27557i	−0.452257	−	0.213221i
$237$	10.3413			0.671742
$238$	11.4197	−	8.68105i	0.740231	−	0.562709i
$239$	3.12940	−	5.90268i	0.202424	−	0.381813i	−0.761428	−	0.648249i	$-0.775501\pi$
$239$	3.12940	−	5.90268i	0.202424	−	0.381813i	0.963852	+	0.266437i	$0.0858463\pi$
$240$	0.166286	−	0.598907i	0.0107337	−	0.0386593i
$241$	−15.6043	+	14.7812i	−1.00516	+	0.952140i	−0.998855	−	0.0478405i	$-0.984766\pi$
$241$	−15.6043	+	14.7812i	−1.00516	+	0.952140i	−0.00630656	+	0.999980i	$0.502007\pi$
$242$	4.60927	+	28.1153i	0.296295	+	1.80732i
$243$	−0.647386	−	0.762162i	−0.0415298	−	0.0488927i
$244$	5.31975	+	13.3516i	0.340562	+	0.854747i
$245$	−0.832002	−	1.22711i	−0.0531547	−	0.0783973i
$246$	1.45061	−	8.84834i	0.0924876	−	0.564150i
$247$	−0.0217925	+	0.0131121i	−0.00138663	+	0.000834305i
$248$	6.27701	+	5.94590i	0.398591	+	0.377565i
$249$	−0.770468	+	1.13635i	−0.0488264	+	0.0720136i
$250$	−5.83579	−	1.28456i	−0.369088	−	0.0812424i
$251$	−0.589090	−	2.12171i	−0.0371831	−	0.133921i	0.942629	−	0.333842i	$-0.108345\pi$
$251$	−0.589090	−	2.12171i	−0.0371831	−	0.133921i	−0.979812	+	0.199921i	$0.935931\pi$
$252$	1.84070	+	1.10751i	0.115953	+	0.0697667i
$253$	−3.71027	+	4.36807i	−0.233263	+	0.274618i
$254$	−5.50973	−	1.85644i	−0.345711	−	0.116484i
$255$	3.76691	+	1.74276i	0.235893	+	0.109136i
$256$	0.468408	+	0.883512i	0.0292755	+	0.0552195i
$257$	−6.02683	+	1.32660i	−0.375943	+	0.0827513i	−0.398923	−	0.916985i	$-0.630616\pi$
$257$	−6.02683	+	1.32660i	−0.375943	+	0.0827513i	0.0229795	+	0.999736i	$0.492685\pi$
$258$	−0.611071	+	1.53367i	−0.0380436	+	0.0954823i
$259$	−1.43580	+	0.483778i	−0.0892164	+	0.0300605i
$260$	1.36567	+	0.148526i	0.0846955	+	0.00921119i
$261$	0.106435	−	1.96309i	0.00658819	−	0.121512i
$262$	−1.21152	−	22.3452i	−0.0748479	−	1.38049i
$263$	−21.4812	+	2.33622i	−1.32459	+	0.144058i	−0.742927	−	0.669373i	$-0.766563\pi$
$263$	−21.4812	+	2.33622i	−1.32459	+	0.144058i	−0.581662	+	0.813431i	$0.697597\pi$
$264$	−5.70335	+	2.63865i	−0.351017	+	0.162398i
$265$	2.69820	+	2.05112i	0.165749	+	0.125999i
$266$	0.0196799	+	0.0149603i	0.00120665	+	0.000917273i
$267$	−11.6187	+	5.37540i	−0.711055	+	0.328969i
$268$	−3.65390	+	0.397386i	−0.223198	+	0.0242742i
$269$	−0.343745	−	6.34000i	−0.0209585	−	0.386557i	−0.990128	−	0.140163i	$-0.955237\pi$
$269$	−0.343745	−	6.34000i	−0.0209585	−	0.386557i	0.969170	−	0.246393i	$-0.0792456\pi$
$270$	−0.0336508	+	0.620652i	−0.00204792	+	0.0377717i
$271$	−14.7833	−	1.60778i	−0.898022	−	0.0976657i	−0.352548	−	0.935794i	$-0.614685\pi$
$271$	−14.7833	−	1.60778i	−0.898022	−	0.0976657i	−0.545474	+	0.838128i	$0.683650\pi$
$272$	−6.32800	+	2.13215i	−0.383691	+	0.129281i
$273$	−1.75733	+	4.41057i	−0.106358	+	0.266940i
$274$	20.3715	−	4.48410i	1.23069	−	0.270895i
$275$	13.5805	+	25.6156i	0.818938	+	1.54468i
$276$	−0.827709	−	0.382939i	−0.0498222	−	0.0230502i
$277$	−22.1753	−	7.47173i	−1.33239	−	0.448933i	−0.439106	−	0.898435i	$-0.644705\pi$
$277$	−22.1753	−	7.47173i	−1.33239	−	0.448933i	−0.893279	+	0.449502i	$0.851601\pi$
$278$	2.38733	−	2.81058i	0.143182	−	0.168567i
$279$	−7.40845	−	4.45752i	−0.443532	−	0.266865i
$280$	−0.357215	−	1.28657i	−0.0213477	−	0.0768874i
$281$	−16.4523	−	3.62142i	−0.981459	−	0.216036i	−0.304868	−	0.952395i	$-0.598612\pi$
$281$	−16.4523	−	3.62142i	−0.981459	−	0.216036i	−0.676591	+	0.736359i	$0.736543\pi$
$282$	−2.86912	+	4.23164i	−0.170854	+	0.251990i
$283$	16.3446	+	15.4824i	0.971585	+	0.920334i	0.996847	−	0.0793469i	$-0.0252835\pi$
$283$	16.3446	+	15.4824i	0.971585	+	0.920334i	−0.0252623	+	0.999681i	$0.508042\pi$
$284$	−9.27220	+	5.57889i	−0.550204	+	0.331046i
$285$	−0.00115718	+	0.00705847i	−6.85453e−5	+	0.000418108i
$286$	−7.79416	−	11.4955i	−0.460879	−	0.679745i
$287$	−7.12951	−	17.8937i	−0.420842	−	1.05623i
$288$	−0.647386	−	0.762162i	−0.0381476	−	0.0449108i
$289$	−4.46351	−	27.2262i	−0.262559	−	1.60154i
$290$	−0.887148	+	0.840352i	−0.0520951	+	0.0493471i
$291$	2.88329	−	10.3847i	0.169022	−	0.608760i
$292$	−3.34110	+	6.30199i	−0.195523	+	0.368796i
$293$	0.115811	−	0.0880374i	0.00676576	−	0.00514320i	−0.601786	−	0.798657i	$-0.705544\pi$
$293$	0.115811	−	0.0880374i	0.00676576	−	0.00514320i	0.608552	+	0.793514i	$0.291751\pi$
$294$	−2.38524			−0.139110
$295$	−2.65063	−	3.97093i	−0.154326	−	0.231196i
$296$	0.705295			0.0409944
$297$	5.00277	−	3.80301i	0.290290	−	0.220673i
$298$	−9.22555	+	17.4012i	−0.534422	+	1.00803i
$299$	0.539237	−	1.94216i	0.0311849	−	0.112318i
$300$	−3.34950	+	3.17281i	−0.193383	+	0.183182i
$301$	0.573764	+	3.49980i	0.0330712	+	0.201725i
$302$	−4.25785	−	5.01273i	−0.245012	−	0.288450i
$303$	−2.15172	−	5.40040i	−0.123613	−	0.310245i
$304$	−0.00645791	−	0.00952471i	−0.000370387	−	0.000546279i
$305$	−1.44525	+	8.81564i	−0.0827548	+	0.504782i
$306$	5.72171	−	3.44264i	0.327088	−	0.196802i
$307$	12.3835	+	11.7303i	0.706766	+	0.669484i	0.954114	−	0.299442i	$-0.0968006\pi$
$307$	12.3835	+	11.7303i	0.706766	+	0.669484i	−0.247348	+	0.968927i	$0.579559\pi$
$308$	−7.57582	+	11.1735i	−0.431672	+	0.636669i
$309$	−4.07092	−	0.896076i	−0.231586	−	0.0509760i
$310$	1.43772	+	5.17820i	0.0816570	+	0.294102i
$311$	−17.6377	−	10.6123i	−1.00014	−	0.601766i	−0.0814240	−	0.996680i	$-0.525947\pi$
$311$	−17.6377	−	10.6123i	−1.00014	−	0.601766i	−0.918718	+	0.394914i	$0.870774\pi$
$312$	1.43080	−	1.68447i	0.0810030	−	0.0953641i
$313$	20.7940	+	7.00633i	1.17535	+	0.396021i	0.838164	−	0.545418i	$-0.183629\pi$
$313$	20.7940	+	7.00633i	1.17535	+	0.396021i	0.337184	+	0.941439i	$0.390526\pi$
$314$	−13.5580	−	6.27261i	−0.765123	−	0.353984i
$315$	0.625439	+	1.17970i	0.0352395	+	0.0664687i
$316$	−10.0996	+	2.22308i	−0.568144	+	0.125058i
$317$	3.54305	−	8.89239i	0.198998	−	0.499446i	−0.795284	−	0.606237i	$-0.792678\pi$
$317$	3.54305	−	8.89239i	0.198998	−	0.499446i	0.994282	+	0.106791i	$0.0340575\pi$
$318$	5.16744	−	1.74111i	0.289775	−	0.0976367i
$319$	12.2820	+	1.33575i	0.687663	+	0.0747878i
$320$	−0.0336508	+	0.620652i	−0.00188113	+	0.0346955i
$321$	0.713623	+	13.1620i	0.0398306	+	0.734631i
$322$	−1.94767	+	0.211822i	−0.108540	+	0.0118044i
$323$	0.0697404	−	0.0322653i	0.00388046	−	0.00179529i
$324$	0.796093	+	0.605174i	0.0442274	+	0.0336208i
$325$	−8.11753	−	6.17079i	−0.450280	−	0.342294i
$326$	−0.998618	+	0.462010i	−0.0553083	+	0.0255884i
$327$	−5.99769	+	0.652288i	−0.331673	+	0.0360716i
$328$	0.485434	+	8.95331i	0.0268036	+	0.494364i
$329$	−0.594601	+	10.9668i	−0.0327814	+	0.604618i
$330$	−3.88310	−	0.422313i	−0.213758	−	0.0232476i
$331$	13.2723	−	4.47196i	0.729511	−	0.245801i	0.0700542	−	0.997543i	$-0.477683\pi$
$331$	13.2723	−	4.47196i	0.729511	−	0.245801i	0.659457	+	0.751742i	$0.270786\pi$
$332$	0.508172	−	1.27542i	0.0278896	−	0.0699975i
$333$	−0.688805	+	0.151617i	−0.0377463	+	0.00830859i
$334$	−10.5980	−	19.9900i	−0.579899	−	1.09381i
$335$	−2.07338	−	0.959247i	−0.113281	−	0.0524093i
$336$	−2.03575	−	0.685924i	−0.111059	−	0.0374202i
$337$	15.1535	−	17.8401i	0.825466	−	0.971814i	−0.174451	−	0.984666i	$-0.555815\pi$
$337$	15.1535	−	17.8401i	0.825466	−	0.971814i	0.999917	+	0.0128520i	$0.00409104\pi$
$338$	−6.95373	−	4.18392i	−0.378233	−	0.227575i
$339$	−1.60975	−	5.79779i	−0.0874295	−	0.314893i
$340$	−4.05348	−	0.892239i	−0.219831	−	0.0483885i
$341$	30.4911	−	44.9711i	1.65119	−	2.43532i
$342$	0.00835446	+	0.00791377i	0.000451757	+	0.000427927i
$343$	−17.2754	+	10.3943i	−0.932785	+	0.561238i
$344$	0.267090	−	1.62918i	0.0144005	−	0.0878395i
$345$	−0.318118	−	0.469189i	−0.0171269	−	0.0252603i
$346$	−0.872937	−	2.19091i	−0.0469294	−	0.117784i
$347$	−0.0237439	−	0.0279534i	−0.00127464	−	0.00150062i	0.761524	−	0.648136i	$-0.224451\pi$
$347$	−0.0237439	−	0.0279534i	−0.00127464	−	0.00150062i	−0.762799	+	0.646636i	$0.776175\pi$
$348$	0.318059	+	1.94007i	0.0170497	+	0.103999i
$349$	−19.8385	+	18.7920i	−1.06193	+	1.00591i	−0.0619589	+	0.998079i	$0.519735\pi$
$349$	−19.8385	+	18.7920i	−1.06193	+	1.00591i	−0.999969	+	0.00783312i	$0.997507\pi$
$350$	−2.65149	+	9.54980i	−0.141728	+	0.510458i
$351$	−1.03524	+	1.95266i	−0.0552568	+	0.104225i
$352$	5.00277	−	3.80301i	0.266649	−	0.202701i
$353$	1.05688			0.0562520			0.0281260	−	0.999604i	$-0.491046\pi$
$353$	1.05688			0.0562520			0.0281260	+	0.999604i	$0.491046\pi$
$354$	−7.68094	−	0.0555552i	−0.408238	−	0.00295272i
$355$	−6.72604			−0.356981
$356$	10.1915	−	7.74741i	0.540151	−	0.410612i
$357$	6.71918	−	12.6737i	0.355617	−	0.670765i
$358$	−3.67549	+	13.2379i	−0.194255	+	0.699645i
$359$	−5.41663	+	5.13090i	−0.285879	+	0.270799i	−0.817178	−	0.576386i	$-0.804463\pi$
$359$	−5.41663	+	5.13090i	−0.285879	+	0.270799i	0.531299	+	0.847184i	$0.321704\pi$
$360$	−0.100558	−	0.613375i	−0.00529986	−	0.0323277i
$361$	−12.3003	−	14.4810i	−0.647382	−	0.762157i
$362$	2.63723	+	6.61896i	0.138610	+	0.347885i
$363$	15.9886	+	23.5814i	0.839183	+	1.23770i
$364$	0.768103	−	4.68522i	0.0402596	−	0.245572i
$365$	−3.79891	+	2.28573i	−0.198844	+	0.119641i
$366$	10.4343	+	9.88385i	0.545407	+	0.516637i
$367$	−1.29552	+	1.91075i	−0.0676256	+	0.0997403i	−0.859998	−	0.510297i	$-0.829535\pi$
$367$	−1.29552	+	1.91075i	−0.0676256	+	0.0997403i	0.792372	+	0.610038i	$0.208846\pi$
$368$	0.890678	+	0.196053i	0.0464298	+	0.0102200i
$369$	−2.39878	−	8.63963i	−0.124876	−	0.449761i
$370$	0.375634	+	0.226011i	0.0195283	+	0.0117498i
$371$	7.58340	−	8.92787i	0.393710	−	0.463512i
$372$	8.19348	+	2.76070i	0.424812	+	0.143136i
$373$	−33.9739	−	15.7180i	−1.75910	−	0.813846i	−0.983089	−	0.183127i	$-0.941378\pi$
$373$	−33.9739	−	15.7180i	−1.75910	−	0.813846i	−0.776011	−	0.630719i	$-0.782760\pi$
$374$	19.6557	+	37.0746i	1.01637	+	1.91708i
$375$	−5.83579	+	1.28456i	−0.301359	+	0.0663342i
$376$	1.89237	−	4.74948i	0.0975913	−	0.244936i
$377$	−4.11757	+	1.38737i	−0.212066	+	0.0714533i
$378$	2.13561	+	0.232261i	0.109844	+	0.0119462i
$379$	−0.590591	+	10.8928i	−0.0303366	+	0.559526i	0.943373	+	0.331734i	$0.107634\pi$
$379$	−0.590591	+	10.8928i	−0.0303366	+	0.559526i	−0.973710	+	0.227793i	$0.926849\pi$
$380$	−0.000387239	−	0.00714221i	−1.98650e−5	−	0.000366388i
$381$	−5.78000	+	0.628613i	−0.296118	+	0.0322048i
$382$	−2.92576	+	1.35360i	−0.149695	+	0.0692562i
$383$	−5.90394	−	4.48806i	−0.301677	−	0.229329i	0.443373	−	0.896337i	$-0.353782\pi$
$383$	−5.90394	−	4.48806i	−0.301677	−	0.229329i	−0.745051	+	0.667008i	$0.767575\pi$
$384$	0.796093	+	0.605174i	0.0406255	+	0.0308827i
$385$	−7.61535	+	3.52324i	−0.388114	+	0.179561i
$386$	−6.07688	+	0.660900i	−0.309305	+	0.0336389i
$387$	0.0893794	+	1.64851i	0.00454341	+	0.0837983i
$388$	−0.583483	+	10.7617i	−0.0296219	+	0.546343i
$389$	18.6830	+	2.03190i	0.947268	+	0.103022i	0.568694	−	0.822549i	$-0.307449\pi$
$389$	18.6830	+	2.03190i	0.947268	+	0.103022i	0.378574	+	0.925571i	$0.376415\pi$
$390$	1.30182	−	0.438633i	0.0659200	−	0.0222110i
$391$	−2.25411	+	5.65740i	−0.113995	+	0.286107i
$392$	2.32947	−	0.512755i	0.117656	−	0.0258981i
$393$	−10.4820	−	19.7712i	−0.528749	−	0.997326i
$394$	−23.4576	−	10.8527i	−1.18178	−	0.546749i
$395$	−6.09132	−	2.05240i	−0.306487	−	0.103268i
$396$	−4.06828	+	4.78955i	−0.204439	+	0.240684i
$397$	10.5111	+	6.32430i	0.527535	+	0.317407i	0.754287	−	0.656545i	$-0.227983\pi$
$397$	10.5111	+	6.32430i	0.527535	+	0.317407i	−0.226751	+	0.973953i	$0.572810\pi$
$398$	−5.76126	−	20.7502i	−0.288786	−	1.04011i
$399$	0.0241427	+	0.00531420i	0.00120864	+	0.000266043i
$400$	2.58913	−	3.81867i	0.129456	−	0.190934i
$401$	−10.3094	−	9.76562i	−0.514829	−	0.487672i	0.385605	−	0.922664i	$-0.373993\pi$
$401$	−10.3094	−	9.76562i	−0.514829	−	0.487672i	−0.900434	+	0.434992i	$0.856751\pi$
$402$	−3.14934	+	1.89489i	−0.157075	+	0.0945086i
$403$	−3.09146	+	18.8571i	−0.153997	+	0.939338i
$404$	3.26234	+	4.81159i	0.162307	+	0.239385i
$405$	0.230064	+	0.577418i	0.0114320	+	0.0286921i
$406$	2.73410	+	3.21884i	0.135691	+	0.159748i
$407$	−0.717047	−	4.37380i	−0.0355427	−	0.216801i
$408$	−4.84787	+	4.59215i	−0.240005	+	0.227345i
$409$	1.19994	−	4.32178i	0.0593330	−	0.213698i	−0.927941	−	0.372728i	$-0.878423\pi$
$409$	1.19994	−	4.32178i	0.0593330	−	0.213698i	0.987274	+	0.159029i	$0.0508364\pi$
$410$	−2.61055	+	4.92401i	−0.128926	+	0.243180i
$411$	16.6058	−	12.6234i	0.819105	−	0.622668i
$412$	4.16837			0.205361
$413$	−14.1998	+	8.40448i	−0.698729	+	0.413558i
$414$	−0.912000			−0.0448224
$415$	0.679354	−	0.516431i	0.0333482	−	0.0253506i
$416$	−1.03524	+	1.95266i	−0.0507566	+	0.0957372i
$417$	0.986548	−	3.55322i	0.0483115	−	0.174002i
$418$	−0.0525007	+	0.0497314i	−0.00256790	+	0.00243244i
$419$	0.433434	+	2.64383i	0.0211746	+	0.129159i	0.995298	−	0.0968555i	$-0.0308785\pi$
$419$	0.433434	+	2.64383i	0.0211746	+	0.129159i	−0.974124	+	0.226015i	$0.927430\pi$
$420$	−0.864418	−	1.01767i	−0.0421793	−	0.0496573i
$421$	0.519200	+	1.30309i	0.0253042	+	0.0635089i	0.941086	−	0.338167i	$-0.109807\pi$
$421$	0.519200	+	1.30309i	0.0253042	+	0.0635089i	−0.915782	+	0.401676i	$0.868428\pi$
$422$	1.16615	+	1.71995i	0.0567675	+	0.0837258i
$423$	−0.827126	+	5.04524i	−0.0402162	+	0.245308i
$424$	−4.67234	+	2.81125i	−0.226909	+	0.136526i
$425$	22.3664	+	21.1866i	1.08493	+	1.02770i
$426$	−6.07270	+	8.95656i	−0.294223	+	0.433947i
$427$	30.1528	+	6.63714i	1.45920	+	0.321194i
$428$	−3.52638	−	12.7009i	−0.170454	−	0.613920i
$429$	−11.9006	−	7.16038i	−0.574568	−	0.345706i
$430$	0.664319	−	0.782097i	0.0320363	−	0.0377161i
$431$	−2.83466	−	0.955109i	−0.136541	−	0.0460060i	0.250201	−	0.968194i	$-0.419503\pi$
$431$	−2.83466	−	0.955109i	−0.136541	−	0.0460060i	−0.386742	+	0.922188i	$0.626400\pi$
$432$	−0.907575	−	0.419889i	−0.0436657	−	0.0202019i
$433$	13.2926	+	25.0726i	0.638803	+	1.20491i	0.965653	+	0.259834i	$0.0836680\pi$
$433$	13.2926	+	25.0726i	0.638803	+	1.20491i	−0.326850	+	0.945076i	$0.605987\pi$
$434$	18.1393	−	3.99275i	0.870712	−	0.191658i
$435$	−0.452300	+	1.13519i	−0.0216861	+	0.0544280i
$436$	5.71725	−	1.92636i	0.273806	−	0.0922561i
$437$	−0.0104334	−	0.00113470i	−0.000499097	−	5.42801e-5i
$438$	−0.386167	+	7.12243i	−0.0184518	+	0.340323i
$439$	−0.568904	−	10.4928i	−0.0271523	−	0.500795i	−0.980204	−	0.197988i	$-0.936559\pi$
$439$	−0.568904	−	10.4928i	−0.0271523	−	0.500795i	0.953052	−	0.302806i	$-0.0979235\pi$
$440$	3.88310	−	0.422313i	0.185120	−	0.0201330i
$441$	−2.16478	+	1.00153i	−0.103085	+	0.0476921i
$442$	−11.7489	−	8.93125i	−0.558836	−	0.424816i
$443$	27.6229	+	20.9984i	1.31240	+	0.997662i	0.998843	+	0.0480936i	$0.0153146\pi$
$443$	27.6229	+	20.9984i	1.31240	+	0.997662i	0.313559	+	0.949569i	$0.398479\pi$
$444$	0.640108	−	0.296146i	0.0303782	−	0.0140544i
$445$	7.91058	−	0.860327i	0.374997	−	0.0407834i
$446$	0.299372	+	5.52159i	0.0141757	+	0.261455i
$447$	−1.06629	+	19.6666i	−0.0504340	+	0.930200i
$448$	2.13561	+	0.232261i	0.100898	+	0.0109733i
$449$	17.0904	−	5.75844i	0.806548	−	0.271758i	0.114327	−	0.993443i	$-0.463529\pi$
$449$	17.0904	−	5.75844i	0.806548	−	0.271758i	0.692221	+	0.721686i	$0.256632\pi$
$450$	−1.70769	+	4.28598i	−0.0805013	+	0.202043i
$451$	55.0293	−	12.1129i	2.59123	−	0.570373i
$452$	2.81847	+	5.31619i	0.132570	+	0.250053i
$453$	−5.96911	−	2.76161i	−0.280453	−	0.129752i
$454$	7.33750	+	2.47229i	0.344366	+	0.116030i
$455$	1.91046	−	2.24917i	0.0895638	−	0.105443i
$456$	−0.00986036	−	0.00593278i	−0.000461754	−	0.000277828i
$457$	−4.77773	−	17.2078i	−0.223493	−	0.804948i	−0.987214	−	0.159402i	$-0.949044\pi$
$457$	−4.77773	−	17.2078i	−0.223493	−	0.804948i	0.763721	−	0.645546i	$-0.223370\pi$
$458$	−13.9469	−	3.06995i	−0.651698	−	0.143450i
$459$	3.74735	−	5.52693i	0.174912	−	0.257975i
$460$	0.411542	+	0.389833i	0.0191882	+	0.0181761i
$461$	18.2270	−	10.9668i	0.848914	−	0.510775i	−0.0233967	−	0.999726i	$-0.507448\pi$
$461$	18.2270	−	10.9668i	0.848914	−	0.510775i	0.872311	+	0.488952i	$0.162621\pi$
$462$	−2.18400	+	13.3218i	−0.101609	+	0.619786i
$463$	19.9403	+	29.4097i	0.926703	+	1.36678i	0.930303	+	0.366791i	$0.119544\pi$
$463$	19.9403	+	29.4097i	0.926703	+	1.36678i	−0.00360014	+	0.999994i	$0.501146\pi$
$464$	−0.727681	−	1.82634i	−0.0337817	−	0.0847857i
$465$	3.47911	+	4.09592i	0.161340	+	0.189944i
$466$	−1.16622	−	7.11361i	−0.0540240	−	0.329532i
$467$	14.8914	−	14.1059i	0.689093	−	0.652743i	−0.260773	−	0.965400i	$-0.583978\pi$
$467$	14.8914	−	14.1059i	0.689093	−	0.652743i	0.949866	+	0.312657i	$0.101219\pi$
$468$	0.591268	−	2.12956i	0.0273314	−	0.0984388i
$469$	−3.69837	+	6.97586i	−0.170775	+	0.322115i
$470$	2.52983	−	1.92312i	0.116692	−	0.0887071i
$471$	−14.9387			−0.688340
$472$	7.51331	−	1.59692i	0.345828	−	0.0735042i
$473$	−10.3747			−0.477029
$474$	−8.23266	+	6.25831i	−0.378139	+	0.287454i
$475$	−0.0248688	+	0.0469075i	−0.00114106	+	0.00215226i
$476$	−3.83762	+	13.8218i	−0.175897	+	0.633523i
$477$	3.95876	−	3.74994i	0.181259	−	0.171698i
$478$	1.08085	+	6.59292i	0.0494371	+	0.301553i
$479$	2.75180	+	3.23967i	0.125733	+	0.148024i	0.821426	−	0.570314i	$-0.193179\pi$
$479$	2.75180	+	3.23967i	0.125733	+	0.148024i	−0.695693	+	0.718339i	$0.744903\pi$
$480$	0.230064	+	0.577418i	0.0105010	+	0.0263554i
$481$	0.874768	+	1.29019i	0.0398860	+	0.0588275i
$482$	3.47729	−	21.2105i	0.158386	−	0.966113i
$483$	−1.67872	+	1.01005i	−0.0763844	+	0.0459589i
$484$	−20.6841	−	19.5930i	−0.940185	−	0.890591i
$485$	−3.75934	+	5.54461i	−0.170703	+	0.251768i
$486$	0.976621	+	0.214970i	0.0443004	+	0.00975126i
$487$	−5.55259	−	19.9986i	−0.251612	−	0.906224i	−0.976169	−	0.217010i	$-0.930370\pi$
$487$	−5.55259	−	19.9986i	−0.251612	−	0.906224i	0.724558	−	0.689214i	$-0.242044\pi$
$488$	−12.3150	−	7.40971i	−0.557476	−	0.335422i
$489$	−0.712328	+	0.838617i	−0.0322126	+	0.0379236i
$490$	1.40497	+	0.473389i	0.0634700	+	0.0213855i
$491$	−23.2497	−	10.7565i	−1.04925	−	0.485432i	−0.181992	−	0.983300i	$-0.558254\pi$
$491$	−23.2497	−	10.7565i	−1.04925	−	0.485432i	−0.867253	+	0.497868i	$0.834117\pi$
$492$	4.19997	+	7.92198i	0.189349	+	0.357150i
$493$	12.8209	−	2.82210i	0.577426	−	0.127101i
$494$	0.00941376	−	0.0236268i	0.000423545	−	0.00106302i
$495$	−3.70154	+	1.24719i	−0.166372	+	0.0560571i
$496$	−8.59539	−	0.934805i	−0.385944	−	0.0419740i
$497$	−1.25851	+	23.2119i	−0.0564521	+	1.04120i
$498$	−0.0743287	−	1.37091i	−0.00333075	−	0.0614320i
$499$	19.6789	−	2.14021i	0.880949	−	0.0958089i	0.343547	−	0.939135i	$-0.388371\pi$
$499$	19.6789	−	2.14021i	0.880949	−	0.0958089i	0.537402	+	0.843327i	$0.319406\pi$
$500$	5.42322	−	2.50905i	0.242534	−	0.112208i
$501$	−18.0121	−	13.6925i	−0.804722	−	0.611734i
$502$	1.75298	+	1.33258i	0.0782391	+	0.0594758i
$503$	−16.3843	+	7.58017i	−0.730538	+	0.337983i	−0.749650	−	0.661834i	$-0.769778\pi$
$503$	−16.3843	+	7.58017i	−0.730538	+	0.337983i	0.0191119	+	0.999817i	$0.493916\pi$
$504$	−2.13561	+	0.232261i	−0.0951275	+	0.0103457i
$505$	0.195621	+	3.60802i	0.00870503	+	0.160555i
$506$	0.310278	−	5.72275i	0.0137936	−	0.254407i
$507$	−8.06782	−	0.877428i	−0.358304	−	0.0389680i
$508$	5.50973	−	1.85644i	0.244455	−	0.0823664i
$509$	10.3432	−	25.9594i	0.458453	−	1.15063i	−0.500164	−	0.865931i	$-0.666727\pi$
$509$	10.3432	−	25.9594i	0.458453	−	1.15063i	0.958617	−	0.284700i	$-0.0918939\pi$
$510$	−4.05348	+	0.892239i	−0.179491	+	0.0395090i
$511$	7.17736	+	13.5379i	0.317508	+	0.598883i
$512$	−0.907575	−	0.419889i	−0.0401095	−	0.0185567i
$513$	0.0109052	+	0.00367439i	0.000481477	+	0.000162228i
$514$	3.99509	−	4.70338i	0.176216	−	0.207457i
$515$	2.22004	+	1.33575i	0.0978265	+	0.0588602i
$516$	−0.441670	−	1.59075i	−0.0194434	−	0.0700289i
$517$	−31.3772	−	6.90665i	−1.37997	−	0.303754i
$518$	0.850262	−	1.25404i	0.0373584	−	0.0550995i
$519$	−1.71219	−	1.62188i	−0.0751570	−	0.0711925i
$520$	−1.17709	+	0.708230i	−0.0516187	+	0.0310579i
$521$	2.72838	−	16.6424i	0.119532	−	0.729116i	−0.857253	−	0.514896i	$-0.827831\pi$
$521$	2.72838	−	16.6424i	0.119532	−	0.729116i	0.976785	−	0.214220i	$-0.0687211\pi$
$522$	1.10328	+	1.62721i	0.0482891	+	0.0712211i
$523$	9.09182	+	22.8187i	0.397557	+	0.997794i	0.982424	+	0.186664i	$0.0597676\pi$
$523$	9.09182	+	22.8187i	0.397557	+	0.997794i	−0.584866	+	0.811130i	$0.698853\pi$
$524$	14.4872	+	17.0557i	0.632876	+	0.745080i
$525$	1.60343	+	9.78050i	0.0699795	+	0.426856i
$526$	15.6872	−	14.8597i	0.683995	−	0.647915i
$527$	15.4456	−	55.6301i	0.672822	−	2.42329i
$528$	2.94355	−	5.55213i	0.128102	−	0.241625i
$529$	−17.6480	+	13.4157i	−0.767304	+	0.583289i
$530$	−3.38931			−0.147222
$531$	−6.99436	+	3.17472i	−0.303530	+	0.137771i
$532$	−0.0247206			−0.00107177
$533$	−15.7761	+	11.9927i	−0.683339	+	0.519461i
$534$	5.99654	−	11.3107i	0.259496	−	0.489461i
$535$	2.19187	−	7.89440i	0.0947627	−	0.341305i
$536$	2.66836	−	2.52760i	0.115256	−	0.109176i
$537$	2.22267	+	13.5577i	0.0959153	+	0.585058i
$538$	4.11046	+	4.83921i	0.177215	+	0.208633i
$539$	−5.54808	−	13.9246i	−0.238973	−	0.599776i
$540$	−0.348813	−	0.514461i	−0.0150105	−	0.0221389i
$541$	0.446846	−	2.72564i	0.0192114	−	0.117184i	−0.975480	−	0.220089i	$-0.929365\pi$
$541$	0.446846	−	2.72564i	0.0192114	−	0.117184i	0.994691	+	0.102904i	$0.0328136\pi$
$542$	12.7419	−	7.66653i	0.547310	−	0.329306i
$543$	5.17272	+	4.89986i	0.221982	+	0.210273i
$544$	3.74735	−	5.52693i	0.160666	−	0.236965i
$545$	3.66226	+	0.806123i	0.156874	+	0.0345305i
$546$	−1.27016	−	4.57471i	−0.0543579	−	0.195780i
$547$	−6.35819	−	3.82560i	−0.271857	−	0.163571i	0.373097	−	0.927792i	$-0.378296\pi$
$547$	−6.35819	−	3.82560i	−0.271857	−	0.163571i	−0.644954	+	0.764222i	$0.723123\pi$
$548$	−13.5039	+	15.8981i	−0.576860	+	0.679132i
$549$	13.6200	+	4.58911i	0.581287	+	0.195858i
$550$	−26.3133	−	12.1738i	−1.12200	−	0.519094i
$551$	0.0105971	+	0.0199882i	0.000451451	+	0.000851526i
$552$	0.890678	−	0.196053i	0.0379098	−	0.00834457i
$553$	−8.22271	+	20.6374i	−0.349665	+	0.877594i
$554$	22.1753	−	7.47173i	0.942139	−	0.317444i
$555$	0.435815	+	0.0473978i	0.0184993	+	0.00201192i
$556$	−0.199645	+	3.68223i	−0.00846682	+	0.156161i
$557$	−0.746179	−	13.7625i	−0.0316166	−	0.583135i	−0.970825	−	0.239788i	$-0.922922\pi$
$557$	−0.746179	−	13.7625i	−0.0316166	−	0.583135i	0.939209	−	0.343347i	$-0.111561\pi$
$558$	8.59539	−	0.934805i	0.363872	−	0.0395734i
$559$	3.31151	−	1.53207i	0.140062	−	0.0647995i
$560$	1.06298	+	0.808054i	0.0449190	+	0.0341465i
$561$	33.4063	+	25.3948i	1.41041	+	1.07217i
$562$	15.2891	−	7.07350i	0.644932	−	0.298377i
$563$	−22.5309	+	2.45038i	−0.949563	+	0.103271i	−0.569773	−	0.821802i	$-0.692969\pi$
$563$	−22.5309	+	2.45038i	−0.949563	+	0.103271i	−0.379789	+	0.925073i	$0.624003\pi$
$564$	−0.276790	−	5.10510i	−0.0116550	−	0.214963i
$565$	−0.202480	+	3.73453i	−0.00851842	+	0.157113i
$566$	−22.3814	−	2.43412i	−0.940759	−	0.102314i
$567$	2.03575	−	0.685924i	0.0854934	−	0.0288061i
$568$	4.00533	−	10.0526i	0.168060	−	0.421798i
$569$	7.27045	−	1.60035i	0.304793	−	0.0670900i	−0.0599405	−	0.998202i	$-0.519091\pi$
$569$	7.27045	−	1.60035i	0.304793	−	0.0670900i	0.364734	+	0.931112i	$0.381160\pi$
$570$	−0.00335038	−	0.00631949i	−0.000140332	−	0.000264695i
$571$	23.3385	+	10.7975i	0.976685	+	0.451863i	0.842266	−	0.539062i	$-0.181221\pi$
$571$	23.3385	+	10.7975i	0.976685	+	0.451863i	0.134419	+	0.990925i	$0.457083\pi$
$572$	13.1617	+	4.43469i	0.550317	+	0.185424i
$573$	−2.08699	+	2.45699i	−0.0871851	+	0.102642i
$574$	16.5046	+	9.93047i	0.688887	+	0.414490i
$575$	−1.12567	−	4.05429i	−0.0469436	−	0.169075i
$576$	0.976621	+	0.214970i	0.0406925	+	0.00895710i
$577$	1.82242	−	2.68787i	0.0758683	−	0.111897i	−0.787862	−	0.615852i	$-0.788812\pi$
$577$	1.82242	−	2.68787i	0.0758683	−	0.111897i	0.863730	+	0.503955i	$0.168122\pi$
$578$	20.0300	+	18.9734i	0.833137	+	0.789189i
$579$	−5.23772	+	3.15143i	−0.217672	+	0.130969i
$580$	0.197694	−	1.20588i	0.00820878	−	0.0500713i
$581$	−1.65512	−	2.44112i	−0.0686659	−	0.101275i
$582$	3.98917	+	10.0121i	0.165356	+	0.415013i
$583$	22.1838	+	26.1168i	0.918760	+	1.08165i
$584$	−1.15397	−	7.03892i	−0.0477517	−	0.291273i
$585$	0.997319	−	0.944711i	0.0412341	−	0.0390590i
$586$	−0.0389185	+	0.140172i	−0.00160771	+	0.00579045i
$587$	8.01053	−	15.1095i	0.330630	−	0.623635i	−0.661343	−	0.750084i	$-0.730013\pi$
$587$	8.01053	−	15.1095i	0.330630	−	0.623635i	0.991973	+	0.126449i	$0.0403580\pi$
$588$	1.89887	−	1.44348i	0.0783081	−	0.0595283i
$589$	0.0994955			0.00409964
$590$	4.51325	+	1.55713i	0.185808	+	0.0641061i
$591$	−25.8465			−1.06318
$592$	−0.561480	+	0.426826i	−0.0230767	+	0.0175424i
$593$	17.3427	−	32.7118i	0.712179	−	1.34331i	−0.217907	−	0.975970i	$-0.569923\pi$
$593$	17.3427	−	32.7118i	0.712179	−	1.34331i	0.930086	−	0.367342i	$-0.119732\pi$
$594$	−1.68119	+	6.05510i	−0.0689801	+	0.248444i
$595$	−6.47308	+	6.13163i	−0.265370	+	0.251372i
$596$	−3.18638	−	19.4361i	−0.130519	−	0.796132i
$597$	−13.9416	−	16.4133i	−0.570590	−	0.671750i
$598$	0.746060	+	1.87247i	0.0305086	+	0.0765709i
$599$	14.6437	+	21.5979i	0.598327	+	0.882467i	0.999437	−	0.0335634i	$-0.0106856\pi$
$599$	14.6437	+	21.5979i	0.598327	+	0.882467i	−0.401109	+	0.916030i	$0.631375\pi$
$600$	0.746407	−	4.55288i	0.0304719	−	0.185871i
$601$	−26.5013	+	15.9453i	−1.08101	+	0.650422i	−0.940547	−	0.339664i	$-0.889686\pi$
$601$	−26.5013	+	15.9453i	−1.08101	+	0.650422i	−0.140462	+	0.990086i	$0.544859\pi$
$602$	−2.57476	−	2.43894i	−0.104939	−	0.0994038i
$603$	−2.06261	+	3.04213i	−0.0839962	+	0.123885i
$604$	6.42322	+	1.41386i	0.261357	+	0.0575291i
$605$	−4.73759	−	17.0633i	−0.192610	−	0.693720i
$606$	4.98115	+	2.99706i	0.202345	+	0.121747i
$607$	−12.4106	+	14.6109i	−0.503732	+	0.593039i	−0.953982	−	0.299863i	$-0.903059\pi$
$607$	−12.4106	+	14.6109i	−0.503732	+	0.593039i	0.450250	+	0.892902i	$0.351335\pi$
$608$	0.0109052	+	0.00367439i	0.000442265	+	0.000149016i
$609$	3.83296	+	1.77332i	0.155319	+	0.0718584i
$610$	−4.18444	−	7.89269i	−0.169423	−	0.319566i
$611$	11.0352	−	2.42904i	0.446438	−	0.0982685i
$612$	−2.47162	+	6.20329i	−0.0999091	+	0.250753i
$613$	−4.57752	+	1.54235i	−0.184884	+	0.0622948i	−0.410221	−	0.911986i	$-0.634548\pi$
$613$	−4.57752	+	1.54235i	−0.184884	+	0.0622948i	0.225337	+	0.974281i	$0.427652\pi$
$614$	−16.9573	−	1.84422i	−0.684342	−	0.0744267i
$615$	−0.301728	+	5.56505i	−0.0121669	+	0.224404i
$616$	−0.730855	−	13.4798i	−0.0294470	−	0.543118i
$617$	10.2512	−	1.11489i	0.412700	−	0.0448838i	0.100586	−	0.994928i	$-0.467928\pi$
$617$	10.2512	−	1.11489i	0.412700	−	0.0448838i	0.312114	+	0.950045i	$0.398963\pi$
$618$	3.78311	−	1.75025i	0.152179	−	0.0704055i
$619$	−28.3259	−	21.5328i	−1.13851	−	0.865476i	−0.146205	−	0.989254i	$-0.546706\pi$
$619$	−28.3259	−	21.5328i	−1.13851	−	0.865476i	−0.992310	+	0.123778i	$0.960499\pi$
$620$	−4.27827	−	3.25226i	−0.171819	−	0.130614i
$621$	−0.827709	+	0.382939i	−0.0332148	+	0.0153668i
$622$	20.4635	−	2.22554i	0.820512	−	0.0892361i
$623$	−1.48888	−	27.4608i	−0.0596508	−	1.10019i
$624$	−0.119653	+	2.20687i	−0.00478996	+	0.0883456i
$625$	−19.2407	−	2.09255i	−0.769628	−	0.0837020i
$626$	−20.7940	+	7.00633i	−0.831097	+	0.280029i
$627$	−0.0267667	+	0.0671794i	−0.00106896	+	0.00268289i
$628$	14.5895	−	3.21139i	0.582183	−	0.128148i
$629$	−2.20603	−	4.16102i	−0.0879604	−	0.165911i
$630$	−1.21183	−	0.560654i	−0.0482806	−	0.0223370i
$631$	−26.6804	−	8.98968i	−1.06213	−	0.357874i	−0.266613	−	0.963804i	$-0.585905\pi$
$631$	−26.6804	−	8.98968i	−1.06213	−	0.357874i	−0.795518	+	0.605930i	$0.792801\pi$
$632$	6.69484	−	7.88177i	0.266306	−	0.313520i
$633$	1.78056	+	1.07133i	0.0707709	+	0.0425814i
$634$	2.56085	+	9.22333i	0.101704	+	0.366305i
$635$	3.52933	+	0.776864i	0.140057	+	0.0308289i
$636$	−3.06008	+	4.51329i	−0.121340	+	0.178963i
$637$	3.82719	+	3.62531i	0.151639	+	0.143640i
$638$	−10.5860	+	6.36939i	−0.419104	+	0.252167i
$639$	−1.75067	+	10.6786i	−0.0692554	+	0.422439i
$640$	−0.348813	−	0.514461i	−0.0137881	−	0.0203359i
$641$	−6.04047	−	15.1604i	−0.238584	−	0.598802i	0.760115	−	0.649789i	$-0.225143\pi$
$641$	−6.04047	−	15.1604i	−0.238584	−	0.598802i	−0.998699	+	0.0509870i	$0.983763\pi$
$642$	−8.53341	−	10.0463i	−0.336787	−	0.396496i
$643$	−0.111333	−	0.679099i	−0.00439053	−	0.0267810i	0.984540	−	0.175158i	$-0.0560435\pi$
$643$	−0.111333	−	0.679099i	−0.00439053	−	0.0267810i	−0.988931	+	0.148377i	$0.952595\pi$
$644$	1.42234	−	1.34731i	0.0560481	−	0.0530915i
$645$	0.274526	−	0.988753i	0.0108094	−	0.0389321i
$646$	−0.0359937	+	0.0678913i	−0.00141615	+	0.00267115i
$647$	22.4495	−	17.0657i	0.882581	−	0.670921i	−0.0623981	−	0.998051i	$-0.519875\pi$
$647$	22.4495	−	17.0657i	0.882581	−	0.670921i	0.944979	+	0.327131i	$0.106082\pi$
$648$	−1.00000			−0.0392837
$649$	−17.5416	−	44.9693i	−0.688568	−	1.76520i
$650$	10.1967			0.399948
$651$	14.7862	−	11.2402i	0.579518	−	0.440538i
$652$	0.515396	−	0.972140i	0.0201845	−	0.0380720i
$653$	11.9879	−	43.1766i	0.469124	−	1.68963i	−0.228811	−	0.973471i	$-0.573484\pi$
$653$	11.9879	−	43.1766i	0.469124	−	1.68963i	0.697935	−	0.716161i	$-0.254102\pi$
$654$	4.37997	−	4.14893i	0.171270	−	0.162236i
$655$	2.25028	+	13.7261i	0.0879257	+	0.536323i
$656$	−5.80476	−	6.83390i	−0.226638	−	0.266819i
$657$	2.64015	+	6.62629i	0.103002	+	0.258516i
$658$	−6.16345	−	9.09041i	−0.240276	−	0.354381i
$659$	−5.83174	+	35.5720i	−0.227172	+	1.38569i	0.589118	+	0.808047i	$0.299475\pi$
$659$	−5.83174	+	35.5720i	−0.227172	+	1.38569i	−0.816290	+	0.577642i	$0.803973\pi$
$660$	3.34689	−	2.01375i	0.130277	−	0.0783853i
$661$	31.8628	+	30.1821i	1.23932	+	1.17395i	0.977980	+	0.208699i	$0.0669230\pi$
$661$	31.8628	+	30.1821i	1.23932	+	1.17395i	0.261340	+	0.965247i	$0.415836\pi$
$662$	−7.85967	+	11.5921i	−0.305475	+	0.450541i
$663$	−14.4131	−	3.17257i	−0.559759	−	0.123212i
$664$	0.367296	+	1.32288i	0.0142539	+	0.0513378i
$665$	−0.0131660	−	0.00792170i	−0.000510555	−	0.000307191i
$666$	0.456598	−	0.537549i	0.0176928	−	0.0208296i
$667$	−1.69911	−	0.572496i	−0.0657898	−	0.0221672i
$668$	20.5345	+	9.50026i	0.794503	+	0.367576i
$669$	2.59016	+	4.88556i	0.100141	+	0.188887i
$670$	2.23111	−	0.491105i	0.0861954	−	0.0189731i
$671$	−33.4302	+	83.9034i	−1.29056	+	3.23905i
$672$	2.03575	−	0.685924i	0.0785307	−	0.0264601i
$673$	35.8525	+	3.89919i	1.38201	+	0.150303i	0.768736	−	0.639566i	$-0.220886\pi$
$673$	35.8525	+	3.89919i	1.38201	+	0.150303i	0.613276	+	0.789869i	$0.289851\pi$
$674$	−1.26724	+	23.3729i	−0.0488124	+	0.900292i
$675$	0.249778	+	4.60689i	0.00961398	+	0.177319i
$676$	8.06782	−	0.877428i	0.310301	−	0.0337472i
$677$	−37.2586	+	17.2377i	−1.43197	+	0.662498i	−0.974016	−	0.226481i	$-0.927278\pi$
$677$	−37.2586	+	17.2377i	−1.43197	+	0.662498i	−0.457949	+	0.888978i	$0.651416\pi$
$678$	4.79018	+	3.64140i	0.183966	+	0.139847i
$679$	18.4314	+	14.0112i	0.707330	+	0.537699i
$680$	3.76691	−	1.74276i	0.144454	−	0.0668317i
$681$	7.69743	−	0.837145i	0.294966	−	0.0320795i
$682$	2.94154	+	54.2536i	0.112638	+	2.07748i
$683$	−2.52054	+	46.4886i	−0.0964458	+	1.77884i	0.405653	+	0.914027i	$0.367044\pi$
$683$	−2.52054	+	46.4886i	−0.0964458	+	1.77884i	−0.502098	+	0.864810i	$0.667438\pi$
$684$	−0.0114401	−	0.00124419i	−0.000437424	−	4.75728e-5i
$685$	−12.2866	+	4.13984i	−0.469447	+	0.158175i
$686$	7.46249	−	18.7294i	0.284919	−	0.715093i
$687$	−13.9469	+	3.06995i	−0.532109	+	0.117126i
$688$	0.773308	+	1.45861i	0.0294821	+	0.0556092i
$689$	−10.9376	−	5.06029i	−0.416690	−	0.192782i
$690$	0.537192	+	0.181001i	0.0204506	+	0.00689059i
$691$	−25.8175	+	30.3947i	−0.982142	+	1.15627i	0.00556983	+	0.999984i	$0.498227\pi$
$691$	−25.8175	+	30.3947i	−0.982142	+	1.15627i	−0.987712	+	0.156283i	$0.950049\pi$
$692$	2.02082	+	1.21589i	0.0768200	+	0.0462211i
$693$	3.61153	+	13.0076i	0.137191	+	0.494117i
$694$	0.0358190	+	0.00788437i	0.00135967	+	0.000299286i
$695$	−1.28630	+	1.89715i	−0.0487920	+	0.0719629i
$696$	−1.42729	−	1.35200i	−0.0541011	−	0.0512473i
$697$	51.3035	−	30.8683i	1.94326	−	1.16922i
$698$	4.42083	−	26.9659i	0.167331	−	1.02067i
$699$	−4.04536	−	5.96646i	−0.153009	−	0.225672i
$700$	−3.66846	−	9.20715i	−0.138655	−	0.347997i
$701$	14.4232	+	16.9803i	0.544758	+	0.641339i	0.963799	−	0.266628i	$-0.0859097\pi$
$701$	14.4232	+	16.9803i	0.544758	+	0.641339i	−0.419041	+	0.907967i	$0.637634\pi$
$702$	−0.357557	−	2.18100i	−0.0134951	−	0.0823165i
$703$	0.00589236	−	0.00558154i	0.000222234	−	0.000210512i
$704$	−1.68119	+	6.05510i	−0.0633622	+	0.228210i
$705$	1.48851	−	2.80763i	0.0560605	−	0.105741i
$706$	−0.841375	+	0.639596i	−0.0316656	+	0.0240715i
$707$	12.4881			0.469663
$708$	6.14837	−	4.60408i	0.231070	−	0.173032i
$709$	−47.7431			−1.79303			−0.896515	−	0.443013i	$-0.853910\pi$
$709$	−47.7431			−1.79303			−0.896515	+	0.443013i	$0.853910\pi$
$710$	5.35455	−	4.07043i	0.200953	−	0.152760i
$711$	−4.84397	+	9.13669i	−0.181663	+	0.342653i
$712$	−3.42488	+	12.3353i	−0.128353	+	0.462286i
$713$	−5.72463	+	5.42266i	−0.214389	+	0.203080i
$714$	2.32072	+	14.1557i	0.0868506	+	0.529765i
$715$	5.58870	+	6.57953i	0.209006	+	0.246060i
$716$	−5.08521	−	12.7629i	−0.190043	−	0.476972i
$717$	3.74925	+	5.52973i	0.140018	+	0.206512i
$718$	1.20705	−	7.36268i	0.0450467	−	0.274773i
$719$	3.93749	−	2.36911i	0.146844	−	0.0883529i	−0.440236	−	0.897882i	$-0.645105\pi$
$719$	3.93749	−	2.36911i	0.146844	−	0.0883529i	0.587080	+	0.809529i	$0.300278\pi$
$720$	0.451252	+	0.427449i	0.0168172	+	0.0159301i
$721$	5.02514	−	7.41153i	0.187146	−	0.276020i
$722$	18.5557	+	4.08441i	0.690570	+	0.152006i
$723$	−5.75016	−	20.7102i	−0.213851	−	0.770221i
$724$	−6.10510	−	3.67332i	−0.226894	−	0.136518i
$725$	−5.87200	+	6.91305i	−0.218081	+	0.256744i
$726$	−26.9992	−	9.09710i	−1.00204	−	0.337625i
$727$	−37.9688	−	17.5662i	−1.40819	−	0.651496i	−0.439149	−	0.898414i	$-0.644720\pi$
$727$	−37.9688	−	17.5662i	−1.40819	−	0.651496i	−0.969036	+	0.246918i	$0.920582\pi$
$728$	2.22389	+	4.19471i	0.0824230	+	0.155466i
$729$	0.976621	−	0.214970i	0.0361711	−	0.00796187i
$730$	1.64102	−	4.11866i	0.0607370	−	0.152438i
$731$	−10.4471	+	3.52003i	−0.386399	+	0.130193i
$732$	−14.2881	−	1.55392i	−0.528103	−	0.0574347i
$733$	−0.571899	+	10.5480i	−0.0211236	+	0.389601i	0.968786	+	0.247899i	$0.0797402\pi$
$733$	−0.571899	+	10.5480i	−0.0211236	+	0.389601i	−0.989909	+	0.141702i	$0.954743\pi$
$734$	−0.124982	−	2.30515i	−0.00461315	−	0.0850846i
$735$	1.47388	−	0.160295i	0.0543651	−	0.00591256i
$736$	−0.827709	+	0.382939i	−0.0305098	+	0.0141153i
$737$	−18.3874	−	13.9778i	−0.677310	−	0.514878i
$738$	7.13814	+	5.42627i	0.262758	+	0.199744i
$739$	14.3050	−	6.61820i	0.526218	−	0.243455i	−0.138748	−	0.990328i	$-0.544308\pi$
$739$	14.3050	−	6.61820i	0.526218	−	0.243455i	0.664967	+	0.746873i	$0.268446\pi$
$740$	−0.435815	+	0.0473978i	−0.0160209	+	0.00174238i
$741$	−0.00137692	−	0.0253958i	−5.05824e−5	−	0.000932938i
$742$	−0.634176	+	11.6967i	−0.0232813	+	0.429399i
$743$	29.5510	+	3.21386i	1.08412	+	0.117905i	0.632693	−	0.774403i	$-0.281950\pi$
$743$	29.5510	+	3.21386i	1.08412	+	0.117905i	0.451427	+	0.892308i	$0.350915\pi$
$744$	−8.19348	+	2.76070i	−0.300387	+	0.101212i
$745$	4.53124	−	11.3725i	0.166012	−	0.416658i
$746$	36.5585	−	8.04713i	1.33850	−	0.294626i
$747$	−0.643090	−	1.21300i	−0.0235294	−	0.0443812i
$748$	−38.0844	−	17.6197i	−1.39250	−	0.644240i
$749$	−26.8339	−	9.04139i	−0.980489	−	0.330365i
$750$	3.86846	−	4.55430i	0.141256	−	0.166299i
$751$	−16.8642	−	10.1469i	−0.615383	−	0.370264i	0.173476	−	0.984838i	$-0.444500\pi$
$751$	−16.8642	−	10.1469i	−0.615383	−	0.370264i	−0.788859	+	0.614574i	$0.789328\pi$
$752$	1.36776	+	4.92624i	0.0498772	+	0.179642i
$753$	2.15049	+	0.473359i	0.0783683	+	0.0172502i
$754$	2.43837	−	3.59633i	0.0888002	−	0.130970i
$755$	2.96788	+	2.81133i	0.108012	+	0.102315i
$756$	−1.84070	+	1.10751i	−0.0669456	+	0.0402799i
$757$	−1.06316	+	6.48497i	−0.0386411	+	0.235700i	−0.999085	−	0.0427740i	$-0.986380\pi$
$757$	−1.06316	+	6.48497i	−0.0386411	+	0.235700i	0.960444	+	0.278474i	$0.0898287\pi$
$758$	−6.12189	−	9.02911i	−0.222357	−	0.327952i
$759$	−2.12132	−	5.32411i	−0.0769990	−	0.193253i
$760$	0.00463056	+	0.00545151i	0.000167968	+	0.000197747i
$761$	8.00269	+	48.8143i	0.290097	+	1.76952i	0.582119	+	0.813104i	$0.302224\pi$
$761$	8.00269	+	48.8143i	0.290097	+	1.76952i	−0.292022	+	0.956412i	$0.594328\pi$
$762$	4.22100	−	3.99834i	0.152911	−	0.144845i
$763$	3.46722	−	12.4878i	0.125522	−	0.452089i
$764$	1.51001	−	2.84819i	0.0546304	−	0.103044i
$765$	−3.30420	+	2.51179i	−0.119464	+	0.0908139i
$766$	7.41614			0.267956
$767$	12.2399	+	11.7634i	0.441957	+	0.424751i
$768$	−1.00000			−0.0360844
$769$	−38.3779	+	29.1741i	−1.38394	+	1.05205i	−0.392747	+	0.919646i	$0.628475\pi$
$769$	−38.3779	+	29.1741i	−1.38394	+	1.05205i	−0.991196	+	0.132400i	$0.957732\pi$
$770$	3.93036	−	7.41344i	0.141640	−	0.267162i
$771$	1.65095	−	5.94617i	0.0594573	−	0.214146i
$772$	4.43780	−	4.20371i	0.159720	−	0.151295i
$773$	−4.65071	−	28.3681i	−0.167274	−	1.02033i	−0.928361	−	0.371679i	$-0.878782\pi$
$773$	−4.65071	−	28.3681i	−0.167274	−	1.02033i	0.761087	−	0.648650i	$-0.224666\pi$
$774$	−1.06879	−	1.25827i	−0.0384168	−	0.0452277i
$775$	14.7648	+	37.0569i	0.530368	+	1.33112i
$776$	−6.04820	−	8.92043i	−0.217118	−	0.320225i
$777$	0.245118	−	1.49515i	0.00879356	−	0.0536384i
$778$	−16.1031	+	9.68891i	−0.577324	+	0.347364i
$779$	0.0749099	+	0.0709585i	0.00268393	+	0.00254235i
$780$	−0.770917	+	1.13702i	−0.0276033	+	0.0407118i
$781$	−66.4121	−	14.6184i	−2.37641	−	0.523088i
$782$	−1.62923	−	5.86795i	−0.0582611	−	0.209837i
$783$	1.68456	+	1.01356i	0.0602011	+	0.0362218i
$784$	−1.54417	+	1.81794i	−0.0551489	+	0.0649263i
$785$	8.79931	+	2.96483i	0.314061	+	0.105819i
$786$	20.3097	+	9.39627i	0.724423	+	0.335154i
$787$	−20.1343	−	37.9773i	−0.717710	−	1.35374i	−0.926691	−	0.375825i	$-0.877359\pi$
$787$	−20.1343	−	37.9773i	−0.717710	−	1.35374i	0.208981	−	0.977920i	$-0.432985\pi$
$788$	25.2422	−	5.55623i	0.899216	−	0.197932i
$789$	7.99790	−	20.0732i	0.284733	−	0.714626i
$790$	6.09132	−	2.05240i	0.216719	−	0.0730213i
$791$	12.8502	+	1.39754i	0.456900	+	0.0496909i
$792$	0.340217	−	6.27494i	0.0120891	−	0.222970i
$793$	−1.71970	−	31.7179i	−0.0610682	−	1.12634i
$794$	−12.1951	+	1.32630i	−0.432787	+	0.0470685i
$795$	−3.07605	+	1.42313i	−0.109096	+	0.0504733i
$796$	17.1440	+	13.0325i	0.607652	+	0.461925i
$797$	−19.8047	−	15.0552i	−0.701519	−	0.533281i	0.192507	−	0.981296i	$-0.438338\pi$
$797$	−19.8047	−	15.0552i	−0.701519	−	0.533281i	−0.894026	+	0.448015i	$0.852131\pi$
$798$	−0.0224358	+	0.0103799i	−0.000794219	+	0.000367445i
$799$	−33.9395	+	3.69114i	−1.20069	+	0.130583i
$800$	0.249778	+	4.60689i	0.00883100	+	0.162878i
$801$	0.693083	−	12.7832i	0.0244889	−	0.451671i
$802$	14.1172	+	1.53534i	0.498495	+	0.0542146i
$803$	−42.4778	+	14.3124i	−1.49901	+	0.505075i
$804$	1.36042	−	3.41441i	0.0479785	−	0.120417i
$805$	1.18927	−	0.261778i	0.0419163	−	0.00922647i
$806$	−8.95073	−	16.8829i	−0.315276	−	0.594674i
$807$	5.76248	+	2.66601i	0.202849	+	0.0938480i
$808$	−5.50897	−	1.85619i	−0.193805	−	0.0653005i
$809$	−5.87673	+	6.91862i	−0.206615	+	0.243246i	−0.855703	−	0.517468i	$-0.826875\pi$
$809$	−5.87673	+	6.91862i	−0.206615	+	0.243246i	0.649088	+	0.760713i	$0.275151\pi$
$810$	−0.532591	−	0.320449i	−0.0187133	−	0.0112594i
$811$	10.1706	+	36.6312i	0.357138	+	1.28629i	0.896058	+	0.443937i	$0.146419\pi$
$811$	10.1706	+	36.6312i	0.357138	+	1.28629i	−0.538920	+	0.842357i	$0.681167\pi$
$812$	−4.12456	−	0.907884i	−0.144744	−	0.0318605i
$813$	8.34512	−	12.3081i	0.292676	−	0.431665i
$814$	3.21774	+	3.04801i	0.112782	+	0.106833i
$815$	0.586017	−	0.352595i	0.0205273	−	0.0123509i
$816$	1.08031	−	6.58958i	0.0378183	−	0.230682i
$817$	−0.0106615	−	0.0157246i	−0.000373000	−	0.000550134i
$818$	1.66017	+	4.16671i	0.0580464	+	0.145686i
$819$	−3.07364	−	3.61857i	−0.107402	−	0.126443i
$820$	−0.901647	−	5.49981i	−0.0314869	−	0.192062i
$821$	20.3005	−	19.2297i	0.708493	−	0.671120i	−0.246028	−	0.969263i	$-0.579126\pi$
$821$	20.3005	−	19.2297i	0.708493	−	0.671120i	0.954521	+	0.298142i	$0.0963670\pi$
$822$	−5.58042	+	20.0988i	−0.194639	+	0.701028i
$823$	24.9211	−	47.0063i	0.868696	−	1.63854i	0.103600	−	0.994619i	$-0.466964\pi$
$823$	24.9211	−	47.0063i	0.868696	−	1.63854i	0.765096	−	0.643916i	$-0.222691\pi$
$824$	−3.31841	+	2.52259i	−0.115602	+	0.0878786i
$825$	−28.9930			−1.00941
$826$	6.21822	−	15.2841i	0.216360	−	0.531803i
$827$	−0.0779359			−0.00271010			−0.00135505	−	0.999999i	$-0.500431\pi$
$827$	−0.0779359			−0.00271010			−0.00135505	+	0.999999i	$0.500431\pi$
$828$	0.726037	−	0.551919i	0.0252315	−	0.0191805i
$829$	−8.82697	+	16.6494i	−0.306573	+	0.578259i	−0.988151	−	0.153488i	$-0.950950\pi$
$829$	−8.82697	+	16.6494i	−0.306573	+	0.578259i	0.681577	+	0.731746i	$0.261294\pi$
$830$	−0.228298	+	0.822255i	−0.00792434	+	0.0285409i
$831$	16.9885	−	16.0923i	0.589324	−	0.558237i
$832$	−0.357557	−	2.18100i	−0.0123961	−	0.0756126i
$833$	−10.3113	−	12.1394i	−0.357264	−	0.420604i
$834$	1.36494	+	3.42573i	0.0472639	+	0.118623i
$835$	7.89213	+	11.6400i	0.273118	+	0.402819i
$836$	0.0116994	−	0.0713629i	0.000404631	−	0.00246814i
$837$	7.40845	−	4.45752i	0.256073	−	0.154074i
$838$	−1.94503	−	1.84243i	−0.0671900	−	0.0636457i
$839$	−26.8573	+	39.6116i	−0.927218	+	1.36754i	0.00278633	+	0.999996i	$0.499113\pi$
$839$	−26.8573	+	39.6116i	−0.927218	+	1.36754i	−0.930004	+	0.367548i	$0.880197\pi$
$840$	1.30403	+	0.287038i	0.0449931	+	0.00990374i
$841$	−6.72431	−	24.2188i	−0.231873	−	0.835131i
$842$	−1.20193	−	0.723177i	−0.0414212	−	0.0249223i
$843$	10.9059	−	12.8395i	0.375620	−	0.442215i
$844$	−1.96924	−	0.663513i	−0.0677839	−	0.0228390i
$845$	4.57802	+	2.11802i	0.157489	+	0.0728620i
$846$	−2.39478	−	4.51704i	−0.0823343	−	0.155299i
$847$	−59.7727	+	13.1570i	−2.05381	+	0.452079i
$848$	2.01832	−	5.06559i	0.0693093	−	0.173953i
$849$	−21.3348	+	7.18855i	−0.732210	+	0.246710i
$850$	−30.6273	−	3.33092i	−1.05051	−	0.114250i
$851$	−0.0348237	+	0.642285i	−0.00119374	+	0.0220173i
$852$	−0.585846	−	10.8053i	−0.0200708	−	0.370183i
$853$	14.0381	−	1.52673i	0.480654	−	0.0522743i	0.135415	−	0.990789i	$-0.456763\pi$
$853$	14.0381	−	1.52673i	0.480654	−	0.0522743i	0.345239	+	0.938515i	$0.387798\pi$
$854$	−28.0211	+	12.9639i	−0.958862	+	0.443617i
$855$	−0.00569421	−	0.00432863i	−0.000194738	−	0.000148036i
$856$	10.4936	+	7.97700i	0.358663	+	0.272648i
$857$	17.1158	−	7.91863i	0.584666	−	0.270495i	−0.105178	−	0.994453i	$-0.533541\pi$
$857$	17.1158	−	7.91863i	0.584666	−	0.270495i	0.689844	+	0.723958i	$0.257679\pi$
$858$	13.8073	−	1.50163i	0.471373	−	0.0512649i
$859$	−1.43571	−	26.4801i	−0.0489857	−	0.903488i	−0.914996	−	0.403463i	$-0.867807\pi$
$859$	−1.43571	−	26.4801i	−0.0489857	−	0.903488i	0.866010	−	0.500026i	$-0.166676\pi$
$860$	−0.0555550	+	1.02465i	−0.00189441	+	0.0349403i
$861$	19.1488	+	2.08256i	0.652591	+	0.0709735i
$862$	2.83466	−	0.955109i	0.0965490	−	0.0325311i
$863$	−9.88645	+	24.8131i	−0.336539	+	0.844649i	0.659160	+	0.752002i	$0.270912\pi$
$863$	−9.88645	+	24.8131i	−0.336539	+	0.844649i	−0.995699	+	0.0926462i	$0.970467\pi$
$864$	0.976621	−	0.214970i	0.0332253	−	0.00731344i
$865$	0.686640	+	1.29514i	0.0233465	+	0.0440361i
$866$	−25.7554	−	11.9157i	−0.875206	−	0.404913i
$867$	26.1454	+	8.80942i	0.887945	+	0.299184i
$868$	−12.0242	+	14.1560i	−0.408129	+	0.480486i
$869$	−55.6842	−	33.5041i	−1.88896	−	1.13655i
$870$	−0.326913	−	1.17743i	−0.0110834	−	0.0399188i
$871$	7.93325	+	1.74624i	0.268808	+	0.0591691i
$872$	−3.38567	+	4.99349i	−0.114653	+	0.169101i
$873$	7.82443	+	7.41169i	0.264817	+	0.250848i
$874$	0.00899265	−	0.00541070i	0.000304181	−	0.000183020i
$875$	2.07673	−	12.6675i	0.0702061	−	0.428238i
$876$	−4.00288	−	5.90381i	−0.135245	−	0.199471i
$877$	12.0149	+	30.1551i	0.405715	+	1.01827i	0.979891	+	0.199535i	$0.0639432\pi$
$877$	12.0149	+	30.1551i	0.405715	+	1.01827i	−0.574176	+	0.818732i	$0.694677\pi$
$878$	6.80288	+	8.00897i	0.229586	+	0.270290i
$879$	0.0235352	+	0.143558i	0.000793821	+	0.00484209i
$880$	−2.83574	+	2.68616i	−0.0955928	+	0.0905503i
$881$	−10.5968	+	38.1662i	−0.357015	+	1.28585i	0.539179	+	0.842191i	$0.318735\pi$
$881$	−10.5968	+	38.1662i	−0.357015	+	1.28585i	−0.896194	+	0.443662i	$0.853679\pi$
$882$	1.11727	−	2.10739i	0.0376203	−	0.0709594i
$883$	33.8842	−	25.7581i	1.14029	−	0.866828i	0.147786	−	0.989019i	$-0.452785\pi$
$883$	33.8842	−	25.7581i	1.14029	−	0.866828i	0.992507	+	0.122191i	$0.0389922\pi$
$884$	14.7581			0.496370
$885$	4.74994	−	0.481853i	0.159668	−	0.0161973i
$886$	−34.6980			−1.16570
$887$	24.8686	−	18.9046i	0.835006	−	0.634755i	−0.0977710	−	0.995209i	$-0.531171\pi$
$887$	24.8686	−	18.9046i	0.835006	−	0.634755i	0.932777	+	0.360454i	$0.117378\pi$
$888$	−0.330366	+	0.623136i	−0.0110864	+	0.0209111i
$889$	3.34138	−	12.0346i	0.112066	−	0.403626i
$890$	−5.77691	+	5.47218i	−0.193642	+	0.183428i
$891$	1.01666	+	6.20137i	0.0340595	+	0.207754i
$892$	−3.57985	−	4.21453i	−0.119862	−	0.141113i
$893$	−0.0217766	−	0.0546551i	−0.000728725	−	0.00182896i
$894$	−11.0529	−	16.3018i	−0.369663	−	0.545212i
$895$	1.38153	−	8.42696i	0.0461795	−	0.281682i
$896$	−1.84070	+	1.10751i	−0.0614935	+	0.0369994i
$897$	1.46333	+	1.38614i	0.0488593	+	0.0462820i
$898$	−10.1207	+	14.9269i	−0.337733	+	0.498119i
$899$	16.6005	+	3.65405i	0.553658	+	0.121869i
$900$	−1.23428	−	4.44549i	−0.0411428	−	0.148183i
$901$	31.1998	+	18.7723i	1.03941	+	0.625395i
$902$	−36.4781	+	42.9453i	−1.21459	+	1.42992i
$903$	−3.36087	−	1.13241i	−0.111843	−	0.0376843i
$904$	−5.46098	−	2.52652i	−0.181630	−	0.0840308i
$905$	−2.07441	−	3.91275i	−0.0689558	−	0.130064i
$906$	6.42322	−	1.41386i	0.213397	−	0.0469723i
$907$	−18.6116	+	46.7116i	−0.617988	+	1.55103i	0.202448	+	0.979293i	$0.435110\pi$
$907$	−18.6116	+	46.7116i	−0.617988	+	1.55103i	−0.820435	+	0.571739i	$0.806269\pi$
$908$	−7.33750	+	2.47229i	−0.243504	+	0.0820459i
$909$	5.77920	+	0.628526i	0.191684	+	0.0208469i
$910$	−0.159766	+	2.94671i	−0.00529619	+	0.0976825i
$911$	−1.76233	−	32.5042i	−0.0583885	−	1.07691i	−0.870107	−	0.492863i	$-0.835950\pi$
$911$	−1.76233	−	32.5042i	−0.0583885	−	1.07691i	0.811718	−	0.584049i	$-0.198533\pi$
$912$	0.0114401	−	0.00124419i	0.000378821	−	4.11992e-5i
$913$	7.83027	−	3.62267i	0.259144	−	0.119893i
$914$	14.2172	+	10.8077i	0.470265	+	0.357486i
$915$	−7.11175	−	5.40621i	−0.235107	−	0.178724i
$916$	12.9609	−	5.99636i	0.428241	−	0.198125i
$917$	47.7906	−	5.19754i	1.57818	−	0.171638i
$918$	0.361515	+	6.66776i	0.0119318	+	0.220069i
$919$	1.40347	−	25.8854i	0.0462961	−	0.853882i	−0.879509	−	0.475882i	$-0.842129\pi$
$919$	1.40347	−	25.8854i	0.0462961	−	0.853882i	0.925806	−	0.378000i	$-0.123388\pi$
$920$	−0.563543	−	0.0612890i	−0.0185795	−	0.00202064i
$921$	−16.1644	+	5.44643i	−0.532636	+	0.179466i
$922$	−7.87353	+	19.7611i	−0.259301	+	0.650797i
$923$	23.3569	−	5.14124i	0.768801	−	0.169226i
$924$	−6.32334	−	11.9271i	−0.208023	−	0.392372i
$925$	2.95324	+	1.36631i	0.0971019	+	0.0449241i
$926$	−33.6723	−	11.3455i	−1.10654	−	0.372837i
$927$	2.69855	−	3.17697i	0.0886319	−	0.104345i
$928$	1.68456	+	1.01356i	0.0552983	+	0.0332719i
$929$	2.97351	+	10.7096i	0.0975576	+	0.351371i	0.996177	−	0.0873584i	$-0.0278425\pi$
$929$	2.97351	+	10.7096i	0.0975576	+	0.351371i	−0.898619	+	0.438729i	$0.855429\pi$
$930$	−5.24844	−	1.15527i	−0.172103	−	0.0378828i
$931$	0.0154036	−	0.0227187i	0.000504834	−	0.000744575i
$932$	5.23339	+	4.95733i	0.171425	+	0.162383i
$933$	17.6377	−	10.6123i	0.577432	−	0.347429i
$934$	−3.31843	+	20.2415i	−0.108582	+	0.662323i
$935$	−14.6372	−	21.5882i	−0.478687	−	0.706010i
$936$	0.818048	+	2.05315i	0.0267387	+	0.0671091i
$937$	−11.8469	−	13.9472i	−0.387020	−	0.455635i	0.533807	−	0.845606i	$-0.320761\pi$
$937$	−11.8469	−	13.9472i	−0.387020	−	0.455635i	−0.920827	+	0.389971i	$0.872485\pi$
$938$	−1.27737	−	7.79159i	−0.0417075	−	0.254404i
$939$	−15.9303	+	15.0900i	−0.519865	+	0.492442i
$940$	−0.850152	+	3.06197i	−0.0277289	+	0.0998705i
$941$	−18.4642	+	34.8271i	−0.601915	+	1.13533i	0.376057	+	0.926597i	$0.377280\pi$
$941$	−18.4642	+	34.8271i	−0.601915	+	1.13533i	−0.977972	+	0.208736i	$0.933065\pi$
$942$	11.8926	−	9.04053i	0.387482	−	0.294556i
$943$	−8.17741			−0.266293
$944$	−5.01488	+	5.81816i	−0.163220	+	0.189365i
$945$	−1.33524			−0.0434354
$946$	8.25922	−	6.27849i	0.268530	−	0.204131i
$947$	12.8540	−	24.2452i	0.417699	−	0.787863i	−0.581980	−	0.813203i	$-0.697722\pi$
$947$	12.8540	−	24.2452i	0.417699	−	0.787863i	0.999679	+	0.0253396i	$0.00806671\pi$
$948$	2.76660	−	9.96439i	0.0898550	−	0.323628i
$949$	11.4450	−	10.8412i	0.371519	−	0.351921i
$950$	−0.00858935	−	0.0523927i	−0.000278675	−	0.00169984i
$951$	6.19694	+	7.29560i	0.200949	+	0.236576i
$952$	−5.30952	−	13.3259i	−0.172083	−	0.431895i
$953$	−28.4609	−	41.9767i	−0.921940	−	1.35976i	−0.933021	−	0.359822i	$-0.882838\pi$
$953$	−28.4609	−	41.9767i	−0.921940	−	1.35976i	0.0110809	−	0.999939i	$-0.496473\pi$
$954$	−0.882177	+	5.38104i	−0.0285615	+	0.174218i
$955$	1.71692	−	1.03304i	0.0555582	−	0.0334283i
$956$	−4.85032	−	4.59447i	−0.156871	−	0.148596i
$957$	−6.93317	+	10.2257i	−0.224117	+	0.330549i
$958$	−4.15126	−	0.913761i	−0.134121	−	0.0295223i
$959$	11.9879	+	43.1763i	0.387108	+	1.39424i
$960$	−0.532591	−	0.320449i	−0.0171893	−	0.0103425i
$961$	28.3261	−	33.3481i	0.913745	−	1.07574i
$962$	−1.47718	−	0.497722i	−0.0476263	−	0.0160472i
$963$	−11.9631	−	5.53470i	−0.385504	−	0.178353i
$964$	10.0678	+	18.9899i	0.324262	+	0.611624i
$965$	3.71061	−	0.816766i	0.119449	−	0.0262926i
$966$	0.725159	−	1.82001i	0.0233316	−	0.0585579i
$967$	−8.43854	+	2.84328i	−0.271365	+	0.0914336i	−0.451694	−	0.892173i	$-0.649180\pi$
$967$	−8.43854	+	2.84328i	−0.271365	+	0.0914336i	0.180329	+	0.983606i	$0.442284\pi$
$968$	28.3236	+	3.08038i	0.910356	+	0.0990072i
$969$	−0.00416017	+	0.0767298i	−0.000133644	+	0.00246492i
$970$	−0.362672	−	6.68908i	−0.0116447	−	0.214774i
$971$	38.2572	−	4.16072i	1.22773	−	0.133524i	0.528821	−	0.848733i	$-0.322634\pi$
$971$	38.2572	−	4.16072i	1.22773	−	0.133524i	0.698910	+	0.715209i	$0.253669\pi$
$972$	−0.907575	+	0.419889i	−0.0291105	+	0.0134679i
$973$	6.30648	+	4.79406i	0.202176	+	0.153691i
$974$	16.5230	+	12.5605i	0.529432	+	0.402464i
$975$	9.25429	−	4.28149i	0.296374	−	0.137117i
$976$	14.2881	−	1.55392i	0.457351	−	0.0497399i
$977$	2.32915	+	42.9587i	0.0745163	+	1.37437i	0.761720	+	0.647907i	$0.224355\pi$
$977$	2.32915	+	42.9587i	0.0745163	+	1.37437i	−0.687204	+	0.726465i	$0.741162\pi$
$978$	0.0595698	−	1.09870i	0.00190483	−	0.0351326i
$979$	79.9779	+	8.69812i	2.55610	+	0.277993i
$980$	−1.40497	+	0.473389i	−0.0448800	+	0.0151218i
$981$	2.23306	−	5.60457i	0.0712963	−	0.178940i
$982$	25.0185	−	5.50698i	0.798372	−	0.175735i
$983$	−13.6600	−	25.7655i	−0.435687	−	0.821792i	0.564306	−	0.825565i	$-0.309144\pi$
$983$	−13.6600	−	25.7655i	−0.435687	−	0.821792i	−0.999993	+	0.00377349i	$0.998799\pi$
$984$	−8.13774	−	3.76492i	−0.259422	−	0.120021i
$985$	15.2243	+	5.12965i	0.485085	+	0.163444i
$986$	−8.49880	+	10.0056i	−0.270657	+	0.318642i
$987$	−9.41076	−	5.66226i	−0.299548	−	0.180232i
$988$	0.00680408	+	0.0245061i	0.000216466	+	0.000779642i
$989$	1.47044	+	0.323669i	0.0467574	+	0.0102921i
$990$	2.19200	−	3.23295i	0.0696663	−	0.102750i
$991$	−27.8075	−	26.3407i	−0.883334	−	0.836739i	0.104133	−	0.994563i	$-0.466793\pi$
$991$	−27.8075	−	26.3407i	−0.883334	−	0.836739i	−0.987467	+	0.157825i	$0.949552\pi$
$992$	7.40845	−	4.45752i	0.235219	−	0.141526i
$993$	−2.26583	+	13.8209i	−0.0719038	+	0.438594i
$994$	−13.0454	−	19.2405i	−0.413774	−	0.610271i
$995$	4.95447	+	12.4348i	0.157067	+	0.394209i
$996$	0.888813	+	1.04639i	0.0281631	+	0.0331562i
$997$	−8.12107	−	49.5363i	−0.257197	−	1.56883i	−0.727363	−	0.686253i	$-0.759254\pi$
$997$	−8.12107	−	49.5363i	−0.257197	−	1.56883i	0.470166	−	0.882578i	$-0.344194\pi$
$998$	−14.3710	+	13.6130i	−0.454907	+	0.430911i
$999$	0.188686	−	0.679587i	0.00596977	−	0.0215012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.b.85.2	yes	56
59.25	even	29	inner	354.2.e.b.25.2	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.b.25.2	✓	56	59.25	even	29	inner
354.2.e.b.85.2	yes	56	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.796093 + 0.605174i) q^{2} +(-0.468408 + 0.883512i) q^{3} +(0.267528 - 0.963550i) q^{4} +(0.451252 - 0.427449i) q^{5} +(-0.161782 - 0.986827i) q^{6} +(-1.39072 - 1.63728i) q^{7} +(0.370138 + 0.928977i) q^{8} +(-0.561187 - 0.827689i) q^{9} +O(q^{10})\)	\(q+(-0.796093 + 0.605174i) q^{2} +(-0.468408 + 0.883512i) q^{3} +(0.267528 - 0.963550i) q^{4} +(0.451252 - 0.427449i) q^{5} +(-0.161782 - 0.986827i) q^{6} +(-1.39072 - 1.63728i) q^{7} +(0.370138 + 0.928977i) q^{8} +(-0.561187 - 0.827689i) q^{9} +(-0.100558 + 0.613375i) q^{10} +(5.38463 - 3.23982i) q^{11} +(0.725995 + 0.687699i) q^{12} +(-1.24029 + 1.82929i) q^{13} +(2.09798 + 0.461800i) q^{14} +(0.166286 + 0.598907i) q^{15} +(-0.856857 - 0.515554i) q^{16} +(4.32295 - 5.08937i) q^{17} +(0.947653 + 0.319302i) q^{18} +(0.0104440 + 0.00483191i) q^{19} +(-0.291146 - 0.549159i) q^{20} +(2.09798 - 0.461800i) q^{21} +(-2.32601 + 5.83784i) q^{22} +(-0.864260 + 0.291203i) q^{23} +(-0.994138 - 0.108119i) q^{24} +(-0.249778 + 4.60689i) q^{25} +(-0.119653 - 2.20687i) q^{26} +(0.994138 - 0.108119i) q^{27} +(-1.94965 + 0.902006i) q^{28} +(1.56510 + 1.18975i) q^{29} +(-0.494822 - 0.376154i) q^{30} +(7.84696 - 3.63039i) q^{31} +(0.994138 - 0.108119i) q^{32} +(0.340217 + 6.27494i) q^{33} +(-0.361515 + 6.66776i) q^{34} +(-1.32742 - 0.144365i) q^{35} +(-0.947653 + 0.319302i) q^{36} +(0.261056 - 0.655202i) q^{37} +(-0.0112386 + 0.00247379i) q^{38} +(-1.03524 - 1.95266i) q^{39} +(0.564116 + 0.260988i) q^{40} +(8.49710 + 2.86300i) q^{41} +(-1.39072 + 1.63728i) q^{42} +(-1.41461 - 0.851142i) q^{43} +(-1.68119 - 6.05510i) q^{44} +(-0.607032 - 0.133618i) q^{45} +(0.511803 - 0.754852i) q^{46} +(-3.71172 - 3.51593i) q^{47} +(0.856857 - 0.515554i) q^{48} +(0.385888 - 2.35381i) q^{49} +(-2.58913 - 3.81867i) q^{50} +(2.47162 + 6.20329i) q^{51} +(1.43080 + 1.68447i) q^{52} +(0.882177 + 5.38104i) q^{53} +(-0.725995 + 0.687699i) q^{54} +(1.04497 - 3.76363i) q^{55} +(1.00624 - 1.89796i) q^{56} +(-0.00916111 + 0.00696410i) q^{57} -1.96597 q^{58} +(1.29746 - 7.57077i) q^{59} +0.621563 q^{60} +(-11.4417 + 8.69777i) q^{61} +(-4.04989 + 7.63891i) q^{62} +(-0.574704 + 2.06990i) q^{63} +(-0.725995 + 0.687699i) q^{64} +(0.222244 + 1.35563i) q^{65} +(-4.06828 - 4.78955i) q^{66} +(-1.36042 - 3.41441i) q^{67} +(-3.74735 - 5.52693i) q^{68} +(0.147545 - 0.899986i) q^{69} +(1.14411 - 0.688389i) q^{70} +(-7.85612 - 7.44171i) q^{71} +(0.561187 - 0.827689i) q^{72} +(-6.96612 - 1.53336i) q^{73} +(0.188686 + 0.679587i) q^{74} +(-3.95325 - 2.37859i) q^{75} +(0.00744986 - 0.00877065i) q^{76} +(-12.7930 - 4.31045i) q^{77} +(2.00585 + 0.928003i) q^{78} +(-4.84397 - 9.13669i) q^{79} +(-0.607032 + 0.133618i) q^{80} +(-0.370138 + 0.928977i) q^{81} +(-8.49710 + 2.86300i) q^{82} +(1.36488 + 0.148439i) q^{83} +(0.116301 - 2.14505i) q^{84} +(-0.224705 - 4.14443i) q^{85} +(1.64125 - 0.178497i) q^{86} +(-1.78427 + 0.825490i) q^{87} +(5.00277 + 3.80301i) q^{88} +(10.1915 + 7.74741i) q^{89} +(0.564116 - 0.260988i) q^{90} +(4.71994 - 0.513324i) q^{91} +(0.0493747 + 0.910662i) q^{92} +(-0.468089 + 8.63339i) q^{93} +(5.08262 + 0.552769i) q^{94} +(0.00677828 - 0.00228387i) q^{95} +(-0.370138 + 0.928977i) q^{96} +(-10.5255 + 2.31685i) q^{97} +(1.11727 + 2.10739i) q^{98} +(-5.70335 - 2.63865i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 56 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + q^7 + 2 * q^8 - 2 * q^9	\( 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} + 30 q^{11} + 2 q^{12} + 5 q^{13} + 28 q^{14} + 2 q^{15} - 2 q^{16} - 3 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 28 q^{21} - q^{22} - 2 q^{23} - 2 q^{24} + 64 q^{25} - 34 q^{26} + 2 q^{27} + q^{28} + 8 q^{29} - 2 q^{30} + 2 q^{32} - q^{33} + 32 q^{34} - 87 q^{35} - 2 q^{36} + 47 q^{37} + 4 q^{38} - 5 q^{39} + 2 q^{40} + 3 q^{41} + q^{42} - 61 q^{43} + q^{44} - 2 q^{45} - 27 q^{46} + 50 q^{47} + 2 q^{48} - 45 q^{49} - 6 q^{50} + 3 q^{51} - 24 q^{52} - 27 q^{53} - 2 q^{54} - 95 q^{55} - q^{56} + 4 q^{57} + 50 q^{58} - 58 q^{59} + 2 q^{60} - 74 q^{61} - 29 q^{62} + q^{63} - 2 q^{64} - 17 q^{65} + q^{66} + 4 q^{67} - 32 q^{68} + 31 q^{69} - 58 q^{70} - 47 q^{71} + 2 q^{72} + 43 q^{73} - 18 q^{74} - 6 q^{75} - 33 q^{76} - 5 q^{77} + 5 q^{78} + 19 q^{79} - 2 q^{80} - 2 q^{81} - 3 q^{82} + 47 q^{83} - q^{84} - 149 q^{85} - 55 q^{86} + 21 q^{87} + 28 q^{88} + 36 q^{89} + 2 q^{90} + 175 q^{91} - 2 q^{92} - 29 q^{93} - 21 q^{94} + 50 q^{95} - 2 q^{96} + 10 q^{97} - 13 q^{98} + q^{99}+O(q^{100}) \) 56 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + q^7 + 2 * q^8 - 2 * q^9 + 2 * q^10 + 30 * q^11 + 2 * q^12 + 5 * q^13 + 28 * q^14 + 2 * q^15 - 2 * q^16 - 3 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 28 * q^21 - q^22 - 2 * q^23 - 2 * q^24 + 64 * q^25 - 34 * q^26 + 2 * q^27 + q^28 + 8 * q^29 - 2 * q^30 + 2 * q^32 - q^33 + 32 * q^34 - 87 * q^35 - 2 * q^36 + 47 * q^37 + 4 * q^38 - 5 * q^39 + 2 * q^40 + 3 * q^41 + q^42 - 61 * q^43 + q^44 - 2 * q^45 - 27 * q^46 + 50 * q^47 + 2 * q^48 - 45 * q^49 - 6 * q^50 + 3 * q^51 - 24 * q^52 - 27 * q^53 - 2 * q^54 - 95 * q^55 - q^56 + 4 * q^57 + 50 * q^58 - 58 * q^59 + 2 * q^60 - 74 * q^61 - 29 * q^62 + q^63 - 2 * q^64 - 17 * q^65 + q^66 + 4 * q^67 - 32 * q^68 + 31 * q^69 - 58 * q^70 - 47 * q^71 + 2 * q^72 + 43 * q^73 - 18 * q^74 - 6 * q^75 - 33 * q^76 - 5 * q^77 + 5 * q^78 + 19 * q^79 - 2 * q^80 - 2 * q^81 - 3 * q^82 + 47 * q^83 - q^84 - 149 * q^85 - 55 * q^86 + 21 * q^87 + 28 * q^88 + 36 * q^89 + 2 * q^90 + 175 * q^91 - 2 * q^92 - 29 * q^93 - 21 * q^94 + 50 * q^95 - 2 * q^96 + 10 * q^97 - 13 * q^98 + q^99

Introduction

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