LMFDB - Embedded newform 354.2.e.b.25.2

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			25.2
Character	$\chi$	$=$	354.25
Dual form			354.2.e.b.85.2

$q$-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 $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{6}{29}\right)$	$1$

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	0.781928	−	0.623369i	$-0.214236\pi$
$5$	0.451252	+	0.427449i	0.201806	+	0.191161i	−0.580122	+	0.814530i	$0.696995\pi$
$6$	−0.161782	+	0.986827i	−0.0660472	+	0.402870i
$7$	−1.39072	+	1.63728i	−0.525641	+	0.618832i	−0.959349	−	0.282221i	$-0.908929\pi$
$7$	−1.39072	+	1.63728i	−0.525641	+	0.618832i	0.433709	+	0.901053i	$0.357205\pi$
$8$	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	0.976809	+	0.214113i	$0.0686860\pi$
$11$	5.38463	+	3.23982i	1.62353	+	0.976843i	0.646717	+	0.762730i	$0.276142\pi$
$12$	0.725995	−	0.687699i	0.209577	−	0.198522i
$13$	−1.24029	−	1.82929i	−0.343994	−	0.507353i	0.615859	−	0.787856i	$-0.288809\pi$
$13$	−1.24029	−	1.82929i	−0.343994	−	0.507353i	−0.959853	+	0.280503i	$0.909499\pi$
$14$	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	0.971430	+	0.237327i	$0.0762712\pi$
$17$	4.32295	+	5.08937i	1.04847	+	1.23435i	0.0770403	+	0.997028i	$0.475453\pi$
$18$	0.947653	−	0.319302i	0.223364	−	0.0752601i
$19$	0.0104440	−	0.00483191i	0.00239602	−	0.00110852i	−0.418691	−	0.908129i	$-0.637511\pi$
$19$	0.0104440	−	0.00483191i	0.00239602	−	0.00110852i	0.421087	+	0.907020i	$0.361649\pi$
$20$	−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	0.227750	−	0.973720i	$-0.426863\pi$
$23$	−0.864260	−	0.291203i	−0.180211	−	0.0607200i	−0.407960	+	0.913000i	$0.633760\pi$
$24$	−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	−0.449691	−	0.893184i	$-0.648466\pi$
$29$	1.56510	−	1.18975i	0.290631	−	0.220932i	0.740322	+	0.672252i	$0.234673\pi$
$30$	−0.494822	+	0.376154i	−0.0903418	+	0.0686760i
$31$	7.84696	+	3.63039i	1.40936	+	0.652038i	0.969288	−	0.245927i	$-0.0790923\pi$
$31$	7.84696	+	3.63039i	1.40936	+	0.652038i	0.440068	+	0.897965i	$0.354954\pi$
$32$	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	0.948873	−	0.315658i	$-0.102225\pi$
$37$	0.261056	+	0.655202i	0.0429174	+	0.107715i	−0.905956	+	0.423373i	$0.860846\pi$
$38$	−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	0.435536	−	0.900171i	$-0.356559\pi$
$41$	8.49710	−	2.86300i	1.32702	−	0.447126i	0.891488	+	0.453045i	$0.149662\pi$
$42$	−1.39072	−	1.63728i	−0.214592	−	0.252637i
$43$	−1.41461	+	0.851142i	−0.215726	+	0.129798i	−0.619316	−	0.785142i	$-0.712590\pi$
$43$	−1.41461	+	0.851142i	−0.215726	+	0.129798i	0.403590	+	0.914940i	$0.367762\pi$
$44$	−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	−0.908809	−	0.417213i	$-0.863007\pi$
$47$	−3.71172	+	3.51593i	−0.541410	+	0.512851i	0.367399	+	0.930063i	$0.380248\pi$
$48$	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	−0.854422	−	0.519580i	$-0.826089\pi$
$53$	0.882177	−	5.38104i	0.121176	−	0.739143i	0.975598	−	0.219563i	$-0.0704632\pi$
$54$	−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	−0.969525	−	0.244991i	$-0.921215\pi$
$61$	−11.4417	−	8.69777i	−1.46496	−	1.11364i	−0.495437	−	0.868644i	$-0.664992\pi$
$62$	−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	−0.988362	−	0.152121i	$-0.951390\pi$
$67$	−1.36042	+	3.41441i	−0.166202	+	0.417136i	0.822160	+	0.569257i	$0.192769\pi$
$68$	−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	−0.993369	−	0.114968i	$-0.963323\pi$
$71$	−7.85612	+	7.44171i	−0.932350	+	0.883169i	0.0610194	+	0.998137i	$0.480565\pi$
$72$	0.561187	+	0.827689i	0.0661365	+	0.0975441i
$73$	−6.96612	+	1.53336i	−0.815323	+	0.179466i	−0.603008	−	0.797735i	$-0.706031\pi$
$73$	−6.96612	+	1.53336i	−0.815323	+	0.179466i	−0.212315	+	0.977201i	$0.568100\pi$
$74$	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	0.446129	+	0.894969i	$0.352802\pi$
$79$	−4.84397	+	9.13669i	−0.544989	+	1.02796i	−0.991117	+	0.132989i	$0.957542\pi$
$80$	−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	−0.0329043	−	0.999459i	$-0.510476\pi$
$83$	1.36488	−	0.148439i	0.149815	−	0.0162933i	0.182719	+	0.983165i	$0.441510\pi$
$84$	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	0.0955904	−	0.995421i	$-0.469526\pi$
$89$	10.1915	−	7.74741i	1.08030	−	0.821224i	0.984711	+	0.174197i	$0.0557330\pi$
$90$	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	−0.354415	−	0.935088i	$-0.615320\pi$
$97$	−10.5255	−	2.31685i	−1.06871	−	0.235240i	−0.714292	+	0.699848i	$0.753251\pi$
$98$	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	0.542351	−	0.840152i	$-0.317534\pi$
$101$	−3.76344	−	4.43066i	−0.374476	−	0.440867i	−0.916827	+	0.399285i	$0.869258\pi$
$102$	−5.72171	+	3.44264i	−0.566533	+	0.340872i
$103$	1.11516	−	4.01643i	0.109880	−	0.395751i	−0.888073	−	0.459702i	$-0.847956\pi$
$103$	1.11516	−	4.01643i	0.109880	−	0.395751i	0.997953	+	0.0639509i	$0.0203701\pi$
$104$	−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	0.943302	−	0.331936i	$-0.107702\pi$
$107$	11.2945	+	6.79569i	1.09188	+	0.656964i	0.148581	+	0.988900i	$0.452530\pi$
$108$	0.161782	+	0.986827i	0.0155675	+	0.0949574i
$109$	3.38567	−	4.99349i	0.324289	−	0.478290i	−0.630244	−	0.776397i	$-0.717045\pi$
$109$	3.38567	−	4.99349i	0.324289	−	0.478290i	0.954532	+	0.298107i	$0.0963553\pi$
$110$	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	0.454110	−	0.890946i	$-0.349957\pi$
$113$	−4.36840	−	4.13797i	−0.410944	−	0.389267i	−0.865054	+	0.501679i	$0.832716\pi$
$114$	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	−0.654914	−	0.755703i	$-0.727295\pi$
$127$	3.26279	−	4.81225i	0.289525	−	0.427018i	0.944440	+	0.328685i	$0.106606\pi$
$128$	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	−0.722865	−	0.690990i	$-0.757175\pi$
$131$	−12.5582	−	18.5220i	−1.09722	−	1.61828i	−0.374354	−	0.927286i	$-0.622135\pi$
$132$	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	−0.999286	−	0.0377907i	$-0.987968\pi$
$137$	−18.9313	+	8.75853i	−1.61741	+	0.748292i	−0.618121	+	0.786083i	$0.712106\pi$
$138$	0.427188	−	0.805763i	0.0363647	−	0.0685911i
$139$	−3.60142	−	0.792733i	−0.305469	−	0.0672388i	0.0595909	−	0.998223i	$-0.481020\pi$
$139$	−3.60142	−	0.792733i	−0.305469	−	0.0672388i	−0.365060	+	0.930984i	$0.618951\pi$
$140$	−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	0.980299	−	0.197518i	$-0.0632881\pi$
$149$	17.8752	+	8.26993i	1.46439	+	0.677499i	0.484091	+	0.875017i	$0.339150\pi$
$150$	4.58661	+	0.498824i	0.374495	+	0.0407288i
$151$	0.356071	−	6.56734i	0.0289766	−	0.534443i	−0.947625	−	0.319386i	$-0.896523\pi$
$151$	0.356071	−	6.56734i	0.0289766	−	0.534443i	0.976601	−	0.215057i	$-0.0689938\pi$
$152$	−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	−0.430140	−	0.902762i	$-0.641536\pi$
$157$	6.99743	−	13.1985i	0.558455	−	1.05336i	0.988595	−	0.150596i	$-0.0481194\pi$
$158$	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	−0.172687	−	0.984977i	$-0.555245\pi$
$163$	1.07459	−	0.236535i	0.0841683	−	0.0185268i	0.256855	+	0.966450i	$0.417314\pi$
$164$	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	−0.618635	−	0.785679i	$-0.712314\pi$
$167$	−3.66042	−	22.3276i	−0.283252	−	1.72776i	0.335383	−	0.942082i	$-0.391134\pi$
$168$	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	0.935685	−	0.352836i	$-0.114783\pi$
$173$	−0.630941	−	2.27244i	−0.0479696	−	0.172771i	−0.983655	+	0.180066i	$0.942369\pi$
$174$	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	0.928061	−	0.372429i	$-0.121475\pi$
$179$	10.9373	+	8.31429i	0.817490	+	0.621440i	−0.110571	+	0.993868i	$0.535268\pi$
$180$	−0.291146	−	0.549159i	−0.0217007	−	0.0409319i
$181$	1.90614	+	6.86529i	0.141682	+	0.510293i	0.999996	−	0.00283206i	$-0.000901475\pi$
$181$	1.90614	+	6.86529i	0.141682	+	0.510293i	−0.858314	+	0.513125i	$0.828488\pi$
$182$	−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	−0.0996004	−	0.995028i	$-0.531756\pi$
$191$	3.14834	−	0.693002i	0.227806	−	0.0501439i	0.327406	+	0.944884i	$0.393825\pi$
$192$	−0.267528	+	0.963550i	−0.0193072	+	0.0695382i
$193$	5.23772	−	3.15143i	0.377019	−	0.226845i	−0.314413	−	0.949286i	$-0.601808\pi$
$193$	5.23772	−	3.15143i	0.377019	−	0.226845i	0.691432	+	0.722441i	$0.256980\pi$
$194$	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	0.0865626	−	0.996246i	$-0.472412\pi$
$197$	12.1067	−	22.8357i	0.862567	−	1.62697i	0.776004	−	0.630727i	$-0.217243\pi$
$198$	6.13724	+	1.35091i	0.436154	+	0.0960049i
$199$	−7.97097	−	20.0056i	−0.565047	−	1.41816i	−0.882692	−	0.469952i	$-0.844271\pi$
$199$	−7.97097	−	20.0056i	−0.565047	−	1.41816i	0.317644	−	0.948210i	$-0.397108\pi$
$200$	−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	0.999848	+	0.0174230i	$0.00554620\pi$
$211$	0.112501	+	2.07497i	0.00774491	+	0.142846i	−0.992103	+	0.125423i	$0.959971\pi$
$212$	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	0.917282	−	0.398239i	$-0.130379\pi$
$223$	3.10320	+	4.57687i	0.207806	+	0.306490i	−0.709476	+	0.704730i	$0.751068\pi$
$224$	−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	−0.944098	−	0.329666i	$-0.893064\pi$
$227$	−4.34517	+	6.40864i	−0.288399	+	0.425357i	0.655699	+	0.755023i	$0.272374\pi$
$228$	0.00425940	−	0.0106903i	0.000282086	−	0.000707981i
$229$	9.24520	−	10.8843i	0.610940	−	0.719255i	−0.366511	−	0.930414i	$-0.619448\pi$
$229$	9.24520	−	10.8843i	0.610940	−	0.719255i	0.977452	+	0.211159i	$0.0677238\pi$
$230$	−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	0.747926	−	0.663782i	$-0.231050\pi$
$233$	−3.37656	−	6.36886i	−0.221206	−	0.417238i	−0.969132	+	0.246544i	$0.920705\pi$
$234$	−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	0.963852	−	0.266437i	$-0.0858463\pi$
$239$	3.12940	+	5.90268i	0.202424	+	0.381813i	−0.761428	+	0.648249i	$0.775501\pi$
$240$	0.166286	+	0.598907i	0.0107337	+	0.0386593i
$241$	−15.6043	−	14.7812i	−1.00516	−	0.952140i	−0.00630656	−	0.999980i	$-0.502007\pi$
$241$	−15.6043	−	14.7812i	−1.00516	−	0.952140i	−0.998855	+	0.0478405i	$0.984766\pi$
$242$	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	−0.979812	−	0.199921i	$-0.935931\pi$
$251$	−0.589090	+	2.12171i	−0.0371831	+	0.133921i	0.942629	+	0.333842i	$0.108345\pi$
$252$	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	0.0229795	−	0.999736i	$-0.492685\pi$
$257$	−6.02683	−	1.32660i	−0.375943	−	0.0827513i	−0.398923	+	0.916985i	$0.630616\pi$
$258$	−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	−0.581662	−	0.813431i	$-0.697597\pi$
$263$	−21.4812	−	2.33622i	−1.32459	−	0.144058i	−0.742927	+	0.669373i	$0.766563\pi$
$264$	−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	0.969170	+	0.246393i	$0.0792456\pi$
$269$	−0.343745	+	6.34000i	−0.0209585	+	0.386557i	−0.990128	+	0.140163i	$0.955237\pi$
$270$	−0.0336508	−	0.620652i	−0.00204792	−	0.0377717i
$271$	−14.7833	+	1.60778i	−0.898022	+	0.0976657i	−0.545474	−	0.838128i	$-0.683650\pi$
$271$	−14.7833	+	1.60778i	−0.898022	+	0.0976657i	−0.352548	+	0.935794i	$0.614685\pi$
$272$	−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	−0.893279	−	0.449502i	$-0.851601\pi$
$277$	−22.1753	+	7.47173i	−1.33239	+	0.448933i	−0.439106	+	0.898435i	$0.644705\pi$
$278$	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	−0.676591	−	0.736359i	$-0.736543\pi$
$281$	−16.4523	+	3.62142i	−0.981459	+	0.216036i	−0.304868	+	0.952395i	$0.598612\pi$
$282$	−2.86912	−	4.23164i	−0.170854	−	0.251990i
$283$	16.3446	−	15.4824i	0.971585	−	0.920334i	−0.0252623	−	0.999681i	$-0.508042\pi$
$283$	16.3446	−	15.4824i	0.971585	−	0.920334i	0.996847	+	0.0793469i	$0.0252835\pi$
$284$	−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	0.608552	−	0.793514i	$-0.291751\pi$
$293$	0.115811	+	0.0880374i	0.00676576	+	0.00514320i	−0.601786	+	0.798657i	$0.705544\pi$
$294$	−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	−0.247348	−	0.968927i	$-0.579559\pi$
$307$	12.3835	−	11.7303i	0.706766	−	0.669484i	0.954114	+	0.299442i	$0.0968006\pi$
$308$	−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	−0.918718	−	0.394914i	$-0.870774\pi$
$311$	−17.6377	+	10.6123i	−1.00014	+	0.601766i	−0.0814240	+	0.996680i	$0.525947\pi$
$312$	1.43080	+	1.68447i	0.0810030	+	0.0953641i
$313$	20.7940	−	7.00633i	1.17535	−	0.396021i	0.337184	−	0.941439i	$-0.390526\pi$
$313$	20.7940	−	7.00633i	1.17535	−	0.396021i	0.838164	+	0.545418i	$0.183629\pi$
$314$	−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	0.994282	−	0.106791i	$-0.0340575\pi$
$317$	3.54305	+	8.89239i	0.198998	+	0.499446i	−0.795284	+	0.606237i	$0.792678\pi$
$318$	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	0.659457	−	0.751742i	$-0.270786\pi$
$331$	13.2723	+	4.47196i	0.729511	+	0.245801i	0.0700542	+	0.997543i	$0.477683\pi$
$332$	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	0.999917	−	0.0128520i	$-0.00409104\pi$
$337$	15.1535	+	17.8401i	0.825466	+	0.971814i	−0.174451	+	0.984666i	$0.555815\pi$
$338$	−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	−0.762799	−	0.646636i	$-0.776175\pi$
$347$	−0.0237439	+	0.0279534i	−0.00127464	+	0.00150062i	0.761524	+	0.648136i	$0.224451\pi$
$348$	0.318059	−	1.94007i	0.0170497	−	0.103999i
$349$	−19.8385	−	18.7920i	−1.06193	−	1.00591i	−0.999969	−	0.00783312i	$-0.997507\pi$
$349$	−19.8385	−	18.7920i	−1.06193	−	1.00591i	−0.0619589	−	0.998079i	$-0.519735\pi$
$350$	−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	0.531299	−	0.847184i	$-0.321704\pi$
$359$	−5.41663	−	5.13090i	−0.285879	−	0.270799i	−0.817178	+	0.576386i	$0.804463\pi$
$360$	−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	0.792372	−	0.610038i	$-0.208846\pi$
$367$	−1.29552	−	1.91075i	−0.0676256	−	0.0997403i	−0.859998	+	0.510297i	$0.829535\pi$
$368$	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	−0.776011	+	0.630719i	$0.782760\pi$
$373$	−33.9739	+	15.7180i	−1.75910	+	0.813846i	−0.983089	+	0.183127i	$0.941378\pi$
$374$	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	−0.973710	−	0.227793i	$-0.926849\pi$
$379$	−0.590591	−	10.8928i	−0.0303366	−	0.559526i	0.943373	−	0.331734i	$-0.107634\pi$
$380$	−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	−0.745051	−	0.667008i	$-0.767575\pi$
$383$	−5.90394	+	4.48806i	−0.301677	+	0.229329i	0.443373	+	0.896337i	$0.353782\pi$
$384$	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	0.378574	−	0.925571i	$-0.376415\pi$
$389$	18.6830	−	2.03190i	0.947268	−	0.103022i	0.568694	+	0.822549i	$0.307449\pi$
$390$	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	−0.226751	−	0.973953i	$-0.572810\pi$
$397$	10.5111	−	6.32430i	0.527535	−	0.317407i	0.754287	+	0.656545i	$0.227983\pi$
$398$	−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	−0.900434	−	0.434992i	$-0.856751\pi$
$401$	−10.3094	+	9.76562i	−0.514829	+	0.487672i	0.385605	+	0.922664i	$0.373993\pi$
$402$	−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	0.987274	−	0.159029i	$-0.0508364\pi$
$409$	1.19994	+	4.32178i	0.0593330	+	0.213698i	−0.927941	+	0.372728i	$0.878423\pi$
$410$	−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	−0.974124	−	0.226015i	$-0.927430\pi$
$419$	0.433434	−	2.64383i	0.0211746	−	0.129159i	0.995298	+	0.0968555i	$0.0308785\pi$
$420$	−0.864418	+	1.01767i	−0.0421793	+	0.0496573i
$421$	0.519200	−	1.30309i	0.0253042	−	0.0635089i	−0.915782	−	0.401676i	$-0.868428\pi$
$421$	0.519200	−	1.30309i	0.0253042	−	0.0635089i	0.941086	+	0.338167i	$0.109807\pi$
$422$	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	−0.386742	−	0.922188i	$-0.626400\pi$
$431$	−2.83466	+	0.955109i	−0.136541	+	0.0460060i	0.250201	+	0.968194i	$0.419503\pi$
$432$	−0.907575	+	0.419889i	−0.0436657	+	0.0202019i
$433$	13.2926	−	25.0726i	0.638803	−	1.20491i	−0.326850	−	0.945076i	$-0.605987\pi$
$433$	13.2926	−	25.0726i	0.638803	−	1.20491i	0.965653	−	0.259834i	$-0.0836680\pi$
$434$	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	0.953052	+	0.302806i	$0.0979235\pi$
$439$	−0.568904	+	10.4928i	−0.0271523	+	0.500795i	−0.980204	+	0.197988i	$0.936559\pi$
$440$	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	0.313559	−	0.949569i	$-0.398479\pi$
$443$	27.6229	−	20.9984i	1.31240	−	0.997662i	0.998843	−	0.0480936i	$-0.0153146\pi$
$444$	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	0.692221	−	0.721686i	$-0.256632\pi$
$449$	17.0904	+	5.75844i	0.806548	+	0.271758i	0.114327	+	0.993443i	$0.463529\pi$
$450$	−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	0.763721	+	0.645546i	$0.223370\pi$
$457$	−4.77773	+	17.2078i	−0.223493	+	0.804948i	−0.987214	+	0.159402i	$0.949044\pi$
$458$	−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	0.872311	−	0.488952i	$-0.162621\pi$
$461$	18.2270	+	10.9668i	0.848914	+	0.510775i	−0.0233967	+	0.999726i	$0.507448\pi$
$462$	−2.18400	−	13.3218i	−0.101609	−	0.619786i
$463$	19.9403	−	29.4097i	0.926703	−	1.36678i	−0.00360014	−	0.999994i	$-0.501146\pi$
$463$	19.9403	−	29.4097i	0.926703	−	1.36678i	0.930303	−	0.366791i	$-0.119544\pi$
$464$	−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	0.949866	−	0.312657i	$-0.101219\pi$
$467$	14.8914	+	14.1059i	0.689093	+	0.652743i	−0.260773	+	0.965400i	$0.583978\pi$
$468$	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	−0.695693	−	0.718339i	$-0.744903\pi$
$479$	2.75180	−	3.23967i	0.125733	−	0.148024i	0.821426	+	0.570314i	$0.193179\pi$
$480$	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	0.724558	+	0.689214i	$0.242044\pi$
$487$	−5.55259	+	19.9986i	−0.251612	+	0.906224i	−0.976169	+	0.217010i	$0.930370\pi$
$488$	−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	−0.867253	−	0.497868i	$-0.834117\pi$
$491$	−23.2497	+	10.7565i	−1.04925	+	0.485432i	−0.181992	+	0.983300i	$0.558254\pi$
$492$	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	0.537402	−	0.843327i	$-0.319406\pi$
$499$	19.6789	+	2.14021i	0.880949	+	0.0958089i	0.343547	+	0.939135i	$0.388371\pi$
$500$	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	0.0191119	−	0.999817i	$-0.493916\pi$
$503$	−16.3843	−	7.58017i	−0.730538	−	0.337983i	−0.749650	+	0.661834i	$0.769778\pi$
$504$	−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	0.958617	+	0.284700i	$0.0918939\pi$
$509$	10.3432	+	25.9594i	0.458453	+	1.15063i	−0.500164	+	0.865931i	$0.666727\pi$
$510$	−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	0.976785	+	0.214220i	$0.0687211\pi$
$521$	2.72838	+	16.6424i	0.119532	+	0.729116i	−0.857253	+	0.514896i	$0.827831\pi$
$522$	1.10328	−	1.62721i	0.0482891	−	0.0712211i
$523$	9.09182	−	22.8187i	0.397557	−	0.997794i	−0.584866	−	0.811130i	$-0.698853\pi$
$523$	9.09182	−	22.8187i	0.397557	−	0.997794i	0.982424	−	0.186664i	$-0.0597676\pi$
$524$	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	0.994691	−	0.102904i	$-0.0328136\pi$
$541$	0.446846	+	2.72564i	0.0192114	+	0.117184i	−0.975480	+	0.220089i	$0.929365\pi$
$542$	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	−0.644954	−	0.764222i	$-0.723123\pi$
$547$	−6.35819	+	3.82560i	−0.271857	+	0.163571i	0.373097	+	0.927792i	$0.378296\pi$
$548$	−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	0.939209	+	0.343347i	$0.111561\pi$
$557$	−0.746179	+	13.7625i	−0.0316166	+	0.583135i	−0.970825	+	0.239788i	$0.922922\pi$
$558$	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	−0.379789	−	0.925073i	$-0.624003\pi$
$563$	−22.5309	−	2.45038i	−0.949563	−	0.103271i	−0.569773	+	0.821802i	$0.692969\pi$
$564$	−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	0.364734	−	0.931112i	$-0.381160\pi$
$569$	7.27045	+	1.60035i	0.304793	+	0.0670900i	−0.0599405	+	0.998202i	$0.519091\pi$
$570$	−0.00335038	+	0.00631949i	−0.000140332	+	0.000264695i
$571$	23.3385	−	10.7975i	0.976685	−	0.451863i	0.134419	−	0.990925i	$-0.457083\pi$
$571$	23.3385	−	10.7975i	0.976685	−	0.451863i	0.842266	+	0.539062i	$0.181221\pi$
$572$	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	0.863730	−	0.503955i	$-0.168122\pi$
$577$	1.82242	+	2.68787i	0.0758683	+	0.111897i	−0.787862	+	0.615852i	$0.788812\pi$
$578$	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	0.991973	−	0.126449i	$-0.0403580\pi$
$587$	8.01053	+	15.1095i	0.330630	+	0.623635i	−0.661343	+	0.750084i	$0.730013\pi$
$588$	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	0.930086	+	0.367342i	$0.119732\pi$
$593$	17.3427	+	32.7118i	0.712179	+	1.34331i	−0.217907	+	0.975970i	$0.569923\pi$
$594$	−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	−0.401109	−	0.916030i	$-0.631375\pi$
$599$	14.6437	−	21.5979i	0.598327	−	0.882467i	0.999437	+	0.0335634i	$0.0106856\pi$
$600$	0.746407	+	4.55288i	0.0304719	+	0.185871i
$601$	−26.5013	−	15.9453i	−1.08101	−	0.650422i	−0.140462	−	0.990086i	$-0.544859\pi$
$601$	−26.5013	−	15.9453i	−1.08101	−	0.650422i	−0.940547	+	0.339664i	$0.889686\pi$
$602$	−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	0.450250	−	0.892902i	$-0.351335\pi$
$607$	−12.4106	−	14.6109i	−0.503732	−	0.593039i	−0.953982	+	0.299863i	$0.903059\pi$
$608$	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	0.225337	−	0.974281i	$-0.427652\pi$
$613$	−4.57752	−	1.54235i	−0.184884	−	0.0622948i	−0.410221	+	0.911986i	$0.634548\pi$
$614$	−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	0.312114	−	0.950045i	$-0.398963\pi$
$617$	10.2512	+	1.11489i	0.412700	+	0.0448838i	0.100586	+	0.994928i	$0.467928\pi$
$618$	3.78311	+	1.75025i	0.152179	+	0.0704055i
$619$	−28.3259	+	21.5328i	−1.13851	+	0.865476i	−0.992310	−	0.123778i	$-0.960499\pi$
$619$	−28.3259	+	21.5328i	−1.13851	+	0.865476i	−0.146205	+	0.989254i	$0.546706\pi$
$620$	−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	−0.795518	−	0.605930i	$-0.792801\pi$
$631$	−26.6804	+	8.98968i	−1.06213	+	0.357874i	−0.266613	+	0.963804i	$0.585905\pi$
$632$	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	−0.998699	−	0.0509870i	$-0.983763\pi$
$641$	−6.04047	+	15.1604i	−0.238584	+	0.598802i	0.760115	+	0.649789i	$0.225143\pi$
$642$	−8.53341	+	10.0463i	−0.336787	+	0.396496i
$643$	−0.111333	+	0.679099i	−0.00439053	+	0.0267810i	−0.988931	−	0.148377i	$-0.952595\pi$
$643$	−0.111333	+	0.679099i	−0.00439053	+	0.0267810i	0.984540	+	0.175158i	$0.0560435\pi$
$644$	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	0.944979	−	0.327131i	$-0.106082\pi$
$647$	22.4495	+	17.0657i	0.882581	+	0.670921i	−0.0623981	+	0.998051i	$0.519875\pi$
$648$	−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	0.697935	+	0.716161i	$0.254102\pi$
$653$	11.9879	+	43.1766i	0.469124	+	1.68963i	−0.228811	+	0.973471i	$0.573484\pi$
$654$	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	−0.816290	−	0.577642i	$-0.803973\pi$
$659$	−5.83174	−	35.5720i	−0.227172	−	1.38569i	0.589118	−	0.808047i	$-0.299475\pi$
$660$	3.34689	+	2.01375i	0.130277	+	0.0783853i
$661$	31.8628	−	30.1821i	1.23932	−	1.17395i	0.261340	−	0.965247i	$-0.415836\pi$
$661$	31.8628	−	30.1821i	1.23932	−	1.17395i	0.977980	−	0.208699i	$-0.0669230\pi$
$662$	−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	0.613276	−	0.789869i	$-0.289851\pi$
$673$	35.8525	−	3.89919i	1.38201	−	0.150303i	0.768736	+	0.639566i	$0.220886\pi$
$674$	−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	−0.457949	−	0.888978i	$-0.651416\pi$
$677$	−37.2586	−	17.2377i	−1.43197	−	0.662498i	−0.974016	+	0.226481i	$0.927278\pi$
$678$	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	−0.502098	−	0.864810i	$-0.667438\pi$
$683$	−2.52054	−	46.4886i	−0.0964458	−	1.77884i	0.405653	−	0.914027i	$-0.367044\pi$
$684$	−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	−0.987712	−	0.156283i	$-0.950049\pi$
$691$	−25.8175	−	30.3947i	−0.982142	−	1.15627i	0.00556983	−	0.999984i	$-0.498227\pi$
$692$	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	−0.419041	−	0.907967i	$-0.637634\pi$
$701$	14.4232	−	16.9803i	0.544758	−	0.641339i	0.963799	+	0.266628i	$0.0859097\pi$
$702$	−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	0.587080	−	0.809529i	$-0.300278\pi$
$719$	3.93749	+	2.36911i	0.146844	+	0.0883529i	−0.440236	+	0.897882i	$0.645105\pi$
$720$	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	−0.969036	−	0.246918i	$-0.920582\pi$
$727$	−37.9688	+	17.5662i	−1.40819	+	0.651496i	−0.439149	+	0.898414i	$0.644720\pi$
$728$	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	−0.989909	−	0.141702i	$-0.954743\pi$
$733$	−0.571899	−	10.5480i	−0.0211236	−	0.389601i	0.968786	−	0.247899i	$-0.0797402\pi$
$734$	−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	0.664967	−	0.746873i	$-0.268446\pi$
$739$	14.3050	+	6.61820i	0.526218	+	0.243455i	−0.138748	+	0.990328i	$0.544308\pi$
$740$	−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	0.451427	−	0.892308i	$-0.350915\pi$
$743$	29.5510	−	3.21386i	1.08412	−	0.117905i	0.632693	+	0.774403i	$0.281950\pi$
$744$	−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	−0.788859	−	0.614574i	$-0.789328\pi$
$751$	−16.8642	+	10.1469i	−0.615383	+	0.370264i	0.173476	+	0.984838i	$0.444500\pi$
$752$	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	0.960444	−	0.278474i	$-0.0898287\pi$
$757$	−1.06316	−	6.48497i	−0.0386411	−	0.235700i	−0.999085	+	0.0427740i	$0.986380\pi$
$758$	−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	−0.292022	−	0.956412i	$-0.594328\pi$
$761$	8.00269	−	48.8143i	0.290097	−	1.76952i	0.582119	−	0.813104i	$-0.302224\pi$
$762$	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	−0.991196	−	0.132400i	$-0.957732\pi$
$769$	−38.3779	−	29.1741i	−1.38394	−	1.05205i	−0.392747	−	0.919646i	$-0.628475\pi$
$770$	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	0.761087	+	0.648650i	$0.224666\pi$
$773$	−4.65071	+	28.3681i	−0.167274	+	1.02033i	−0.928361	+	0.371679i	$0.878782\pi$
$774$	−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	0.208981	+	0.977920i	$0.432985\pi$
$787$	−20.1343	+	37.9773i	−0.717710	+	1.35374i	−0.926691	+	0.375825i	$0.877359\pi$
$788$	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	−0.894026	−	0.448015i	$-0.852131\pi$
$797$	−19.8047	+	15.0552i	−0.701519	+	0.533281i	0.192507	+	0.981296i	$0.438338\pi$
$798$	−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	0.649088	−	0.760713i	$-0.275151\pi$
$809$	−5.87673	−	6.91862i	−0.206615	−	0.243246i	−0.855703	+	0.517468i	$0.826875\pi$
$810$	−0.532591	+	0.320449i	−0.0187133	+	0.0112594i
$811$	10.1706	−	36.6312i	0.357138	−	1.28629i	−0.538920	−	0.842357i	$-0.681167\pi$
$811$	10.1706	−	36.6312i	0.357138	−	1.28629i	0.896058	−	0.443937i	$-0.146419\pi$
$812$	−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	0.954521	−	0.298142i	$-0.0963670\pi$
$821$	20.3005	+	19.2297i	0.708493	+	0.671120i	−0.246028	+	0.969263i	$0.579126\pi$
$822$	−5.58042	−	20.0988i	−0.194639	−	0.701028i
$823$	24.9211	+	47.0063i	0.868696	+	1.63854i	0.765096	+	0.643916i	$0.222691\pi$
$823$	24.9211	+	47.0063i	0.868696	+	1.63854i	0.103600	+	0.994619i	$0.466964\pi$
$824$	−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	0.681577	−	0.731746i	$-0.261294\pi$
$829$	−8.82697	−	16.6494i	−0.306573	−	0.578259i	−0.988151	+	0.153488i	$0.950950\pi$
$830$	−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	−0.930004	−	0.367548i	$-0.880197\pi$
$839$	−26.8573	−	39.6116i	−0.927218	−	1.36754i	0.00278633	−	0.999996i	$-0.499113\pi$
$840$	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	0.345239	−	0.938515i	$-0.387798\pi$
$853$	14.0381	+	1.52673i	0.480654	+	0.0522743i	0.135415	+	0.990789i	$0.456763\pi$
$854$	−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	0.689844	−	0.723958i	$-0.257679\pi$
$857$	17.1158	+	7.91863i	0.584666	+	0.270495i	−0.105178	+	0.994453i	$0.533541\pi$
$858$	13.8073	+	1.50163i	0.471373	+	0.0512649i
$859$	−1.43571	+	26.4801i	−0.0489857	+	0.903488i	0.866010	+	0.500026i	$0.166676\pi$
$859$	−1.43571	+	26.4801i	−0.0489857	+	0.903488i	−0.914996	+	0.403463i	$0.867807\pi$
$860$	−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	−0.995699	−	0.0926462i	$-0.970467\pi$
$863$	−9.88645	−	24.8131i	−0.336539	−	0.844649i	0.659160	−	0.752002i	$-0.270912\pi$
$864$	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	−0.574176	−	0.818732i	$-0.694677\pi$
$877$	12.0149	−	30.1551i	0.405715	−	1.01827i	0.979891	−	0.199535i	$-0.0639432\pi$
$878$	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	−0.896194	−	0.443662i	$-0.853679\pi$
$881$	−10.5968	−	38.1662i	−0.357015	−	1.28585i	0.539179	−	0.842191i	$-0.318735\pi$
$882$	1.11727	+	2.10739i	0.0376203	+	0.0709594i
$883$	33.8842	+	25.7581i	1.14029	+	0.866828i	0.992507	−	0.122191i	$-0.0389922\pi$
$883$	33.8842	+	25.7581i	1.14029	+	0.866828i	0.147786	+	0.989019i	$0.452785\pi$
$884$	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	0.932777	−	0.360454i	$-0.117378\pi$
$887$	24.8686	+	18.9046i	0.835006	+	0.634755i	−0.0977710	+	0.995209i	$0.531171\pi$
$888$	−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	−0.820435	−	0.571739i	$-0.806269\pi$
$907$	−18.6116	−	46.7116i	−0.617988	−	1.55103i	0.202448	−	0.979293i	$-0.435110\pi$
$908$	−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	0.811718	+	0.584049i	$0.198533\pi$
$911$	−1.76233	+	32.5042i	−0.0583885	+	1.07691i	−0.870107	+	0.492863i	$0.835950\pi$
$912$	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	0.925806	+	0.378000i	$0.123388\pi$
$919$	1.40347	+	25.8854i	0.0462961	+	0.853882i	−0.879509	+	0.475882i	$0.842129\pi$
$920$	−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	−0.898619	−	0.438729i	$-0.855429\pi$
$929$	2.97351	−	10.7096i	0.0975576	−	0.351371i	0.996177	+	0.0873584i	$0.0278425\pi$
$930$	−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	−0.920827	−	0.389971i	$-0.872485\pi$
$937$	−11.8469	+	13.9472i	−0.387020	+	0.455635i	0.533807	+	0.845606i	$0.320761\pi$
$938$	−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	−0.977972	−	0.208736i	$-0.933065\pi$
$941$	−18.4642	−	34.8271i	−0.601915	−	1.13533i	0.376057	−	0.926597i	$-0.377280\pi$
$942$	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	0.999679	−	0.0253396i	$-0.00806671\pi$
$947$	12.8540	+	24.2452i	0.417699	+	0.787863i	−0.581980	+	0.813203i	$0.697722\pi$
$948$	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	0.0110809	+	0.999939i	$0.496473\pi$
$953$	−28.4609	+	41.9767i	−0.921940	+	1.35976i	−0.933021	+	0.359822i	$0.882838\pi$
$954$	−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	0.180329	−	0.983606i	$-0.442284\pi$
$967$	−8.43854	−	2.84328i	−0.271365	−	0.0914336i	−0.451694	+	0.892173i	$0.649180\pi$
$968$	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	0.698910	−	0.715209i	$-0.253669\pi$
$971$	38.2572	+	4.16072i	1.22773	+	0.133524i	0.528821	+	0.848733i	$0.322634\pi$
$972$	−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	−0.687204	−	0.726465i	$-0.741162\pi$
$977$	2.32915	−	42.9587i	0.0745163	−	1.37437i	0.761720	−	0.647907i	$-0.224355\pi$
$978$	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	−0.999993	−	0.00377349i	$-0.998799\pi$
$983$	−13.6600	+	25.7655i	−0.435687	+	0.821792i	0.564306	+	0.825565i	$0.309144\pi$
$984$	−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	−0.987467	−	0.157825i	$-0.949552\pi$
$991$	−27.8075	+	26.3407i	−0.883334	+	0.836739i	0.104133	+	0.994563i	$0.466793\pi$
$992$	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	0.470166	+	0.882578i	$0.344194\pi$
$997$	−8.12107	+	49.5363i	−0.257197	+	1.56883i	−0.727363	+	0.686253i	$0.759254\pi$
$998$	−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.25.2	✓	56
59.26	even	29	inner	354.2.e.b.85.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.b.25.2	✓	56	1.1	even	1	trivial
354.2.e.b.85.2	yes	56	59.26	even	29	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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
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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