LMFDB - Embedded newform 750.2.m.c.31.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(31,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([0, 24]))

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

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

chi := DirichletCharacter("750.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.m (of order $25$, degree $20$, 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$6$ over $\Q(\zeta_{25})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			31.5
Character	$\chi$	$=$	750.31
Dual form			750.2.m.c.121.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0627905 - 0.998027i) q^{2} +(0.425779 + 0.904827i) q^{3} +(-0.992115 + 0.125333i) q^{4} +(1.47222 + 1.68302i) q^{5} +(0.876307 - 0.481754i) q^{6} +(3.13516 - 2.27783i) q^{7} +(0.187381 + 0.982287i) q^{8} +(-0.637424 + 0.770513i) q^{9} +O(q^{10})$	\(q+(-0.0627905 - 0.998027i) q^{2} +(0.425779 + 0.904827i) q^{3} +(-0.992115 + 0.125333i) q^{4} +(1.47222 + 1.68302i) q^{5} +(0.876307 - 0.481754i) q^{6} +(3.13516 - 2.27783i) q^{7} +(0.187381 + 0.982287i) q^{8} +(-0.637424 + 0.770513i) q^{9} +(1.58726 - 1.57499i) q^{10} +(-0.313844 - 4.98841i) q^{11} +(-0.535827 - 0.844328i) q^{12} +(0.487308 - 0.589055i) q^{13} +(-2.47019 - 2.98595i) q^{14} +(-0.896006 + 2.04870i) q^{15} +(0.968583 - 0.248690i) q^{16} +(-1.01314 - 0.127990i) q^{17} +(0.809017 + 0.587785i) q^{18} +(-1.03076 + 2.19048i) q^{19} +(-1.67155 - 1.48524i) q^{20} +(3.39592 + 1.86693i) q^{21} +(-4.95886 + 0.626450i) q^{22} +(7.04980 - 2.79121i) q^{23} +(-0.809017 + 0.587785i) q^{24} +(-0.665144 + 4.95556i) q^{25} +(-0.618491 - 0.449360i) q^{26} +(-0.968583 - 0.248690i) q^{27} +(-2.82495 + 2.65280i) q^{28} +(-3.69595 + 3.47073i) q^{29} +(2.10092 + 0.765599i) q^{30} +(8.01649 + 1.01272i) q^{31} +(-0.309017 - 0.951057i) q^{32} +(4.38002 - 2.40794i) q^{33} +(-0.0641214 + 1.01918i) q^{34} +(8.44928 + 1.92309i) q^{35} +(0.535827 - 0.844328i) q^{36} +(3.47281 - 0.891667i) q^{37} +(2.25088 + 0.891186i) q^{38} +(0.740478 + 0.190123i) q^{39} +(-1.37735 + 1.76151i) q^{40} +(-3.32582 - 1.31678i) q^{41} +(1.65001 - 3.50645i) q^{42} +(1.14947 - 3.53771i) q^{43} +(0.936583 + 4.90974i) q^{44} +(-2.23522 + 0.0615637i) q^{45} +(-3.22837 - 6.86063i) q^{46} +(-2.22539 + 11.6659i) q^{47} +(0.637424 + 0.770513i) q^{48} +(2.47761 - 7.62530i) q^{49} +(4.98755 + 0.352669i) q^{50} +(-0.315567 - 0.971215i) q^{51} +(-0.409638 + 0.645486i) q^{52} +(-4.45451 - 2.44889i) q^{53} +(-0.187381 + 0.982287i) q^{54} +(7.93357 - 7.87224i) q^{55} +(2.82495 + 2.65280i) q^{56} -2.42088 q^{57} +(3.69595 + 3.47073i) q^{58} +(-4.35178 - 6.85732i) q^{59} +(0.632170 - 2.14485i) q^{60} +(12.9818 - 5.13984i) q^{61} +(0.507360 - 8.06426i) q^{62} +(-0.243330 + 3.86762i) q^{63} +(-0.929776 + 0.368125i) q^{64} +(1.70882 - 0.0470652i) q^{65} +(-2.67821 - 4.22018i) q^{66} +(-3.51991 - 3.30542i) q^{67} +1.02120 q^{68} +(5.52723 + 5.19041i) q^{69} +(1.38876 - 8.55336i) q^{70} +(-0.119218 + 0.624964i) q^{71} +(-0.876307 - 0.481754i) q^{72} +(-8.70206 + 13.7123i) q^{73} +(-1.10797 - 3.40997i) q^{74} +(-4.76713 + 1.50813i) q^{75} +(0.748093 - 2.30239i) q^{76} +(-12.3467 - 14.9246i) q^{77} +(0.143252 - 0.750955i) q^{78} +(1.58441 + 3.36705i) q^{79} +(1.84452 + 1.26402i) q^{80} +(-0.187381 - 0.982287i) q^{81} +(-1.10536 + 3.40193i) q^{82} +(-4.94720 + 10.5133i) q^{83} +(-3.60313 - 1.42658i) q^{84} +(-1.27616 - 1.89357i) q^{85} +(-3.60290 - 0.925069i) q^{86} +(-4.71407 - 1.86643i) q^{87} +(4.84125 - 1.24302i) q^{88} +(-3.40870 + 5.37126i) q^{89} +(0.201793 + 2.22694i) q^{90} +(0.186025 - 2.95678i) q^{91} +(-6.64438 + 3.65278i) q^{92} +(2.49692 + 7.68473i) q^{93} +(11.7826 + 1.48849i) q^{94} +(-5.20414 + 1.49007i) q^{95} +(0.728969 - 0.684547i) q^{96} +(9.15393 - 8.59611i) q^{97} +(-7.76583 - 1.99393i) q^{98} +(4.04369 + 2.93791i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 20 q^{5} - 5 q^{7}+O(q^{10}) $ 120 * q + 20 * q^5 - 5 * q^7	$ 120 q + 20 q^{5} - 5 q^{7} + 20 q^{10} + 10 q^{13} + 20 q^{14} + 15 q^{17} + 30 q^{18} - 5 q^{19} - 5 q^{21} + 10 q^{22} - 15 q^{23} - 30 q^{24} - 20 q^{25} - 10 q^{26} + 5 q^{28} - 5 q^{29} + 5 q^{30} + 55 q^{31} + 30 q^{32} + 10 q^{33} + 25 q^{34} - 10 q^{35} - 5 q^{37} - 35 q^{38} - 10 q^{39} - 5 q^{40} + 55 q^{41} + 5 q^{42} + 5 q^{43} + 15 q^{44} - 5 q^{45} - 10 q^{46} + 10 q^{47} - 25 q^{49} + 20 q^{50} + 15 q^{51} - 40 q^{52} + 30 q^{53} - 10 q^{55} - 5 q^{56} + 60 q^{57} + 5 q^{58} + 20 q^{59} - 20 q^{60} - 60 q^{61} + 25 q^{62} + 5 q^{63} + 15 q^{65} - 25 q^{66} + 95 q^{67} + 60 q^{68} - 10 q^{69} + 40 q^{70} - 90 q^{71} - 30 q^{74} - 55 q^{75} + 15 q^{76} + 95 q^{77} - 5 q^{78} - 90 q^{79} - 5 q^{80} - 45 q^{82} + 95 q^{83} - 5 q^{84} + 115 q^{85} - 15 q^{86} + 10 q^{87} + 65 q^{89} + 5 q^{90} - 85 q^{91} - 65 q^{92} - 30 q^{93} - 10 q^{94} - 55 q^{95} - 35 q^{98} + 10 q^{99}+O(q^{100}) $ 120 * q + 20 * q^5 - 5 * q^7 + 20 * q^10 + 10 * q^13 + 20 * q^14 + 15 * q^17 + 30 * q^18 - 5 * q^19 - 5 * q^21 + 10 * q^22 - 15 * q^23 - 30 * q^24 - 20 * q^25 - 10 * q^26 + 5 * q^28 - 5 * q^29 + 5 * q^30 + 55 * q^31 + 30 * q^32 + 10 * q^33 + 25 * q^34 - 10 * q^35 - 5 * q^37 - 35 * q^38 - 10 * q^39 - 5 * q^40 + 55 * q^41 + 5 * q^42 + 5 * q^43 + 15 * q^44 - 5 * q^45 - 10 * q^46 + 10 * q^47 - 25 * q^49 + 20 * q^50 + 15 * q^51 - 40 * q^52 + 30 * q^53 - 10 * q^55 - 5 * q^56 + 60 * q^57 + 5 * q^58 + 20 * q^59 - 20 * q^60 - 60 * q^61 + 25 * q^62 + 5 * q^63 + 15 * q^65 - 25 * q^66 + 95 * q^67 + 60 * q^68 - 10 * q^69 + 40 * q^70 - 90 * q^71 - 30 * q^74 - 55 * q^75 + 15 * q^76 + 95 * q^77 - 5 * q^78 - 90 * q^79 - 5 * q^80 - 45 * q^82 + 95 * q^83 - 5 * q^84 + 115 * q^85 - 15 * q^86 + 10 * q^87 + 65 * q^89 + 5 * q^90 - 85 * q^91 - 65 * q^92 - 30 * q^93 - 10 * q^94 - 55 * q^95 - 35 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{12}{25}\right)$	$1$

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 $

$2$	−0.0627905	−	0.998027i	−0.0443996	−	0.705711i
$2$	−0.0627905	−	0.998027i	−0.0443996	−	0.705711i
$3$	0.425779	+	0.904827i	0.245824	+	0.522402i
$3$	0.425779	+	0.904827i	0.245824	+	0.522402i
$4$	−0.992115	+	0.125333i	−0.496057	+	0.0626666i
$5$	1.47222	+	1.68302i	0.658396	+	0.752672i
$5$	1.47222	+	1.68302i	0.658396	+	0.752672i
$6$	0.876307	−	0.481754i	0.357751	−	0.196675i
$7$	3.13516	−	2.27783i	1.18498	−	0.860937i	0.192254	−	0.981345i	$-0.438420\pi$
$7$	3.13516	−	2.27783i	1.18498	−	0.860937i	0.992725	+	0.120408i	$0.0384202\pi$
$8$	0.187381	+	0.982287i	0.0662493	+	0.347291i
$9$	−0.637424	+	0.770513i	−0.212475	+	0.256838i
$10$	1.58726	−	1.57499i	0.501936	−	0.498056i
$11$	−0.313844	−	4.98841i	−0.0946276	−	1.50406i	−0.703443	−	0.710751i	$-0.748355\pi$
$11$	−0.313844	−	4.98841i	−0.0946276	−	1.50406i	0.608816	−	0.793312i	$-0.291645\pi$
$12$	−0.535827	−	0.844328i	−0.154680	−	0.243736i
$13$	0.487308	−	0.589055i	0.135155	−	0.163374i	−0.698593	−	0.715519i	$-0.746190\pi$
$13$	0.487308	−	0.589055i	0.135155	−	0.163374i	0.833748	+	0.552145i	$0.186190\pi$
$14$	−2.47019	−	2.98595i	−0.660186	−	0.798028i
$15$	−0.896006	+	2.04870i	−0.231348	+	0.528972i
$16$	0.968583	−	0.248690i	0.242146	−	0.0621725i
$17$	−1.01314	−	0.127990i	−0.245723	−	0.0310421i	0.00150680	−	0.999999i	$-0.499520\pi$
$17$	−1.01314	−	0.127990i	−0.245723	−	0.0310421i	−0.247230	+	0.968957i	$0.579520\pi$
$18$	0.809017	+	0.587785i	0.190687	+	0.138542i
$19$	−1.03076	+	2.19048i	−0.236473	+	0.502530i	−0.987476	−	0.157768i	$-0.949570\pi$
$19$	−1.03076	+	2.19048i	−0.236473	+	0.502530i	0.751003	+	0.660298i	$0.229570\pi$
$20$	−1.67155	−	1.48524i	−0.373770	−	0.332109i
$21$	3.39592	+	1.86693i	0.741052	+	0.407397i
$22$	−4.95886	+	0.626450i	−1.05723	+	0.133560i
$23$	7.04980	−	2.79121i	1.46999	−	0.582008i	0.509533	−	0.860451i	$-0.329818\pi$
$23$	7.04980	−	2.79121i	1.46999	−	0.582008i	0.960453	+	0.278443i	$0.0898183\pi$
$24$	−0.809017	+	0.587785i	−0.165140	+	0.119981i
$25$	−0.665144	+	4.95556i	−0.133029	+	0.991112i
$26$	−0.618491	−	0.449360i	−0.121296	−	0.0881267i
$27$	−0.968583	−	0.248690i	−0.186404	−	0.0478604i
$28$	−2.82495	+	2.65280i	−0.533865	+	0.501333i
$29$	−3.69595	+	3.47073i	−0.686321	+	0.644499i	−0.947114	−	0.320896i	$-0.896016\pi$
$29$	−3.69595	+	3.47073i	−0.686321	+	0.644499i	0.260793	+	0.965395i	$0.416016\pi$
$30$	2.10092	+	0.765599i	0.383573	+	0.139779i
$31$	8.01649	+	1.01272i	1.43980	+	0.181890i	0.806143	−	0.591721i	$-0.201551\pi$
$31$	8.01649	+	1.01272i	1.43980	+	0.181890i	0.633662	+	0.773610i	$0.281551\pi$
$32$	−0.309017	−	0.951057i	−0.0546270	−	0.168125i
$33$	4.38002	−	2.40794i	0.762464	−	0.419168i
$34$	−0.0641214	+	1.01918i	−0.0109967	+	0.174788i
$35$	8.44928	+	1.92309i	1.42819	+	0.325062i
$36$	0.535827	−	0.844328i	0.0893045	−	0.140721i
$37$	3.47281	−	0.891667i	0.570927	−	0.146589i	0.0478198	−	0.998856i	$-0.484773\pi$
$37$	3.47281	−	0.891667i	0.570927	−	0.146589i	0.523107	+	0.852267i	$0.324773\pi$
$38$	2.25088	+	0.891186i	0.365141	+	0.144569i
$39$	0.740478	+	0.190123i	0.118571	+	0.0304440i
$40$	−1.37735	+	1.76151i	−0.217778	+	0.278519i
$41$	−3.32582	−	1.31678i	−0.519405	−	0.205647i	0.0937702	−	0.995594i	$-0.470108\pi$
$41$	−3.32582	−	1.31678i	−0.519405	−	0.205647i	−0.613175	+	0.789947i	$0.710108\pi$
$42$	1.65001	−	3.50645i	0.254602	−	0.541057i
$43$	1.14947	−	3.53771i	0.175293	−	0.539496i	−0.824354	−	0.566075i	$-0.808461\pi$
$43$	1.14947	−	3.53771i	0.175293	−	0.539496i	0.999647	+	0.0265791i	$0.00846138\pi$
$44$	0.936583	+	4.90974i	0.141195	+	0.740171i
$45$	−2.23522	+	0.0615637i	−0.333207	+	0.00917738i
$46$	−3.22837	−	6.86063i	−0.475997	−	1.01154i
$47$	−2.22539	+	11.6659i	−0.324606	+	1.70165i	0.328602	+	0.944469i	$0.393423\pi$
$47$	−2.22539	+	11.6659i	−0.324606	+	1.70165i	−0.653208	+	0.757178i	$0.726577\pi$
$48$	0.637424	+	0.770513i	0.0920042	+	0.111214i
$49$	2.47761	−	7.62530i	0.353944	−	1.08933i
$50$	4.98755	+	0.352669i	0.705346	+	0.0498750i
$51$	−0.315567	−	0.971215i	−0.0441882	−	0.135997i
$52$	−0.409638	+	0.645486i	−0.0568065	+	0.0895128i
$53$	−4.45451	−	2.44889i	−0.611875	−	0.336381i	0.145503	−	0.989358i	$-0.453520\pi$
$53$	−4.45451	−	2.44889i	−0.611875	−	0.336381i	−0.757378	+	0.652977i	$0.773520\pi$
$54$	−0.187381	+	0.982287i	−0.0254994	+	0.133672i
$55$	7.93357	−	7.87224i	1.06976	−	1.06149i
$56$	2.82495	+	2.65280i	0.377500	+	0.354496i
$57$	−2.42088			−0.320654
$58$	3.69595	+	3.47073i	0.485302	+	0.455729i
$59$	−4.35178	−	6.85732i	−0.566554	−	0.892746i	0.433410	−	0.901197i	$-0.357310\pi$
$59$	−4.35178	−	6.85732i	−0.566554	−	0.892746i	−0.999964	+	0.00845036i	$0.997310\pi$
$60$	0.632170	−	2.14485i	0.0816129	−	0.276898i
$61$	12.9818	−	5.13984i	1.66214	−	0.658089i	0.666010	−	0.745942i	$-0.268001\pi$
$61$	12.9818	−	5.13984i	1.66214	−	0.658089i	0.996133	+	0.0878531i	$0.0280006\pi$
$62$	0.507360	−	8.06426i	0.0644348	−	1.02416i
$63$	−0.243330	+	3.86762i	−0.0306567	+	0.487275i
$64$	−0.929776	+	0.368125i	−0.116222	+	0.0460156i
$65$	1.70882	−	0.0470652i	0.211953	−	0.00583773i
$66$	−2.67821	−	4.22018i	−0.329665	−	0.519469i
$67$	−3.51991	−	3.30542i	−0.430026	−	0.403821i	0.439080	−	0.898448i	$-0.355305\pi$
$67$	−3.51991	−	3.30542i	−0.430026	−	0.403821i	−0.869105	+	0.494627i	$0.835305\pi$
$68$	1.02120			0.123838
$69$	5.52723	+	5.19041i	0.665400	+	0.624852i
$70$	1.38876	−	8.55336i	0.165989	−	1.02232i
$71$	−0.119218	+	0.624964i	−0.0141486	+	0.0741696i	−0.988661	−	0.150163i	$-0.952020\pi$
$71$	−0.119218	+	0.624964i	−0.0141486	+	0.0741696i	0.974513	+	0.224333i	$0.0720202\pi$
$72$	−0.876307	−	0.481754i	−0.103274	−	0.0567752i
$73$	−8.70206	+	13.7123i	−1.01850	+	1.60490i	−0.246638	+	0.969108i	$0.579326\pi$
$73$	−8.70206	+	13.7123i	−1.01850	+	1.60490i	−0.771862	+	0.635791i	$0.780674\pi$
$74$	−1.10797	−	3.40997i	−0.128799	−	0.396401i
$75$	−4.76713	+	1.50813i	−0.550461	+	0.174144i
$76$	0.748093	−	2.30239i	0.0858122	−	0.264103i
$77$	−12.3467	−	14.9246i	−1.40704	−	1.70081i
$78$	0.143252	−	0.750955i	0.0162201	−	0.0850289i
$79$	1.58441	+	3.36705i	0.178260	+	0.378823i	0.973910	−	0.226935i	$-0.0728703\pi$
$79$	1.58441	+	3.36705i	0.178260	+	0.378823i	−0.795650	+	0.605757i	$0.792870\pi$
$80$	1.84452	+	1.26402i	0.206223	+	0.141322i
$81$	−0.187381	−	0.982287i	−0.0208201	−	0.109143i
$82$	−1.10536	+	3.40193i	−0.122066	+	0.375681i
$83$	−4.94720	+	10.5133i	−0.543025	+	1.15399i	0.425474	+	0.904971i	$0.360108\pi$
$83$	−4.94720	+	10.5133i	−0.543025	+	1.15399i	−0.968499	+	0.249017i	$0.919892\pi$
$84$	−3.60313	−	1.42658i	−0.393134	−	0.155653i
$85$	−1.27616	−	1.89357i	−0.138419	−	0.205387i
$86$	−3.60290	−	0.925069i	−0.388511	−	0.0997527i
$87$	−4.71407	−	1.86643i	−0.505402	−	0.200103i
$88$	4.84125	−	1.24302i	0.516078	−	0.132506i
$89$	−3.40870	+	5.37126i	−0.361322	+	0.569352i	−0.975550	−	0.219776i	$-0.929467\pi$
$89$	−3.40870	+	5.37126i	−0.361322	+	0.569352i	0.614229	+	0.789128i	$0.289467\pi$
$90$	0.201793	+	2.22694i	0.0212708	+	0.234741i
$91$	0.186025	−	2.95678i	0.0195007	−	0.309955i
$92$	−6.64438	+	3.65278i	−0.692725	+	0.380829i
$93$	2.49692	+	7.68473i	0.258919	+	0.796870i
$94$	11.7826	+	1.48849i	1.21528	+	0.153526i
$95$	−5.20414	+	1.49007i	−0.533933	+	0.152878i
$96$	0.728969	−	0.684547i	0.0744000	−	0.0698663i
$97$	9.15393	−	8.59611i	0.929441	−	0.872803i	−0.0626871	−	0.998033i	$-0.519967\pi$
$97$	9.15393	−	8.59611i	0.929441	−	0.872803i	0.992128	+	0.125230i	$0.0399670\pi$
$98$	−7.76583	−	1.99393i	−0.784467	−	0.201417i
$99$	4.04369	+	2.93791i	0.406406	+	0.295271i
$100$	0.0388028	−	4.99985i	0.00388028	−	0.499985i
$101$	−3.56397	+	2.58938i	−0.354628	+	0.257653i	−0.750808	−	0.660520i	$-0.770336\pi$
$101$	−3.56397	+	2.58938i	−0.354628	+	0.257653i	0.396180	+	0.918173i	$0.370336\pi$
$102$	−0.949484	+	0.375927i	−0.0940129	+	0.0372223i
$103$	−10.6444	+	1.34470i	−1.04883	+	0.132498i	−0.630806	−	0.775940i	$-0.717276\pi$
$103$	−10.6444	+	1.34470i	−1.04883	+	0.132498i	−0.418020	+	0.908438i	$0.637276\pi$
$104$	0.669933	+	0.368299i	0.0656924	+	0.0361147i
$105$	1.85746	+	8.46395i	0.181270	+	0.825997i
$106$	−2.16436	+	4.59949i	−0.210221	+	0.446742i
$107$	−1.34250	−	0.975380i	−0.129784	−	0.0942936i	0.520999	−	0.853557i	$-0.325559\pi$
$107$	−1.34250	−	0.975380i	−0.129784	−	0.0942936i	−0.650783	+	0.759263i	$0.725559\pi$
$108$	0.992115	+	0.125333i	0.0954663	+	0.0120602i
$109$	9.06607	−	2.32777i	0.868372	−	0.222960i	0.211883	−	0.977295i	$-0.432041\pi$
$109$	9.06607	−	2.32777i	0.868372	−	0.222960i	0.656490	+	0.754335i	$0.272041\pi$
$110$	−8.35486	−	7.42362i	−0.796605	−	0.707814i
$111$	2.28546	+	2.76264i	0.216926	+	0.262218i
$112$	2.47019	−	2.98595i	0.233411	−	0.282145i
$113$	−8.41859	−	13.2656i	−0.791954	−	1.24792i	−0.964803	−	0.262972i	$-0.915297\pi$
$113$	−8.41859	−	13.2656i	−0.791954	−	1.24792i	0.172849	−	0.984948i	$-0.444703\pi$
$114$	0.152008	+	2.41610i	0.0142369	+	0.226289i
$115$	15.0765	+	7.75571i	1.40589	+	0.723224i
$116$	3.23181	−	3.90659i	0.300066	−	0.362718i
$117$	0.143252	+	0.750955i	0.0132437	+	0.0694258i
$118$	−6.57053	+	4.77377i	−0.604867	+	0.439461i
$119$	−3.46790	+	1.90650i	−0.317902	+	0.174768i
$120$	−2.18031	−	0.496247i	−0.199034	−	0.0453010i
$121$	−13.8725	+	1.75250i	−1.26114	+	0.159319i
$122$	−5.94483	−	12.6334i	−0.538220	−	1.14378i
$123$	−0.224602	−	3.56995i	−0.0202517	−	0.321891i
$124$	−8.08021			−0.725624
$125$	−9.31957	+	6.17622i	−0.833568	+	0.552418i
$126$	3.87527			0.345236
$127$	0.611979	+	9.72713i	0.0543044	+	0.863143i	0.927043	+	0.374955i	$0.122342\pi$
$127$	0.611979	+	9.72713i	0.0543044	+	0.863143i	−0.872739	+	0.488188i	$0.837658\pi$
$128$	0.425779	+	0.904827i	0.0376339	+	0.0799762i
$129$	3.69044	−	0.466211i	0.324925	−	0.0410475i
$130$	−0.154270	−	1.70249i	−0.0135304	−	0.149318i
$131$	−5.65769	+	3.11034i	−0.494315	+	0.271752i	−0.709353	−	0.704854i	$-0.751013\pi$
$131$	−5.65769	+	3.11034i	−0.494315	+	0.271752i	0.215038	+	0.976606i	$0.431013\pi$
$132$	−4.04369	+	2.93791i	−0.351958	+	0.255712i
$133$	1.75793	+	9.21539i	0.152432	+	0.799076i
$134$	−3.07788	+	3.72051i	−0.265888	+	0.321404i
$135$	−1.00742	−	1.99628i	−0.0867045	−	0.171812i
$136$	−0.0641214	−	1.01918i	−0.00549837	−	0.0873940i
$137$	−1.70646	−	2.68895i	−0.145793	−	0.229733i	0.763582	−	0.645711i	$-0.223439\pi$
$137$	−1.70646	−	2.68895i	−0.145793	−	0.229733i	−0.909374	+	0.415979i	$0.863439\pi$
$138$	4.83311	−	5.84223i	0.411422	−	0.497323i
$139$	−5.25646	−	6.35397i	−0.445847	−	0.538937i	0.498933	−	0.866640i	$-0.333725\pi$
$139$	−5.25646	−	6.35397i	−0.445847	−	0.538937i	−0.944781	+	0.327704i	$0.893725\pi$
$140$	−8.62368	−	0.848952i	−0.728834	−	0.0717495i
$141$	−11.5031	+	2.95351i	−0.968740	+	0.248730i
$142$	0.631217	+	0.0797413i	0.0529706	+	0.00669174i
$143$	−3.09139	−	2.24602i	−0.258515	−	0.187822i
$144$	−0.425779	+	0.904827i	−0.0354816	+	0.0754023i
$145$	−11.2826	−	1.11071i	−0.936967	−	0.0922390i
$146$	14.2316	+	7.82389i	1.17782	+	0.647510i
$147$	7.95449	−	1.00489i	0.656076	−	0.0828816i
$148$	−3.33367	+	1.31990i	−0.274026	+	0.108495i
$149$	9.60741	−	6.98019i	0.787070	−	0.571840i	−0.120023	−	0.992771i	$-0.538297\pi$
$149$	9.60741	−	6.98019i	0.787070	−	0.571840i	0.907092	+	0.420932i	$0.138297\pi$
$150$	1.80449	+	4.66303i	0.147336	+	0.380735i
$151$	8.07444	+	5.86642i	0.657089	+	0.477403i	0.865679	−	0.500600i	$-0.166887\pi$
$151$	8.07444	+	5.86642i	0.657089	+	0.477403i	−0.208590	+	0.978003i	$0.566887\pi$
$152$	−2.34482	−	0.602049i	−0.190190	−	0.0488326i
$153$	0.744420	−	0.699057i	0.0601828	−	0.0565154i
$154$	−14.1199	+	13.2594i	−1.13781	+	1.06848i
$155$	10.0976	+	14.9829i	0.811059	+	1.20346i
$156$	−0.758468	−	0.0958168i	−0.0607261	−	0.00767149i
$157$	−4.54930	−	14.0013i	−0.363074	−	1.11743i	−0.951178	−	0.308641i	$-0.900126\pi$
$157$	−4.54930	−	14.0013i	−0.363074	−	1.11743i	0.588105	−	0.808785i	$-0.299874\pi$
$158$	3.26092	−	1.79270i	0.259425	−	0.142620i
$159$	0.319182	−	5.07325i	0.0253128	−	0.402335i
$160$	1.14571	−	1.92025i	0.0905764	−	0.151809i
$161$	15.7444	−	24.8091i	1.24083	−	1.95523i
$162$	−0.968583	+	0.248690i	−0.0760991	+	0.0195389i
$163$	−7.38431	−	2.92365i	−0.578383	−	0.228998i	0.0606734	−	0.998158i	$-0.480675\pi$
$163$	−7.38431	−	2.92365i	−0.578383	−	0.228998i	−0.639057	+	0.769159i	$0.720675\pi$
$164$	3.46463	+	0.889565i	0.270542	+	0.0694634i
$165$	10.5010	+	3.82667i	0.817499	+	0.297906i
$166$	10.8032	+	4.27730i	0.838493	+	0.331983i
$167$	−8.70337	+	18.4956i	−0.673487	+	1.43123i	0.216975	+	0.976177i	$0.430381\pi$
$167$	−8.70337	+	18.4956i	−0.673487	+	1.43123i	−0.890463	+	0.455056i	$0.849619\pi$
$168$	−1.19752	+	3.68560i	−0.0923910	+	0.284350i
$169$	2.32644	+	12.1956i	0.178957	+	0.938126i
$170$	−1.80971	+	1.39254i	−0.138798	+	0.106803i
$171$	−1.03076	−	2.19048i	−0.0788243	−	0.167510i
$172$	−0.697015	+	3.65388i	−0.0531469	+	0.278606i
$173$	−1.56969	−	1.89743i	−0.119341	−	0.144259i	0.707459	−	0.706754i	$-0.249841\pi$
$173$	−1.56969	−	1.89743i	−0.119341	−	0.144259i	−0.826800	+	0.562495i	$0.809841\pi$
$174$	−1.56675	+	4.82196i	−0.118775	+	0.365552i
$175$	9.20258	+	17.0516i	0.695649	+	1.28898i
$176$	−1.54455	−	4.75364i	−0.116425	−	0.358319i
$177$	4.35178	−	6.85732i	0.327100	−	0.515427i
$178$	5.57469	+	3.06471i	0.417841	+	0.229710i
$179$	−0.578291	+	3.03151i	−0.0432235	+	0.226586i	−0.997344	−	0.0728380i	$-0.976794\pi$
$179$	−0.578291	+	3.03151i	−0.0432235	+	0.226586i	0.954120	+	0.299424i	$0.0967944\pi$
$180$	2.20988	−	0.341226i	0.164715	−	0.0254335i
$181$	−3.54177	−	3.32594i	−0.263258	−	0.247215i	0.541666	−	0.840594i	$-0.317794\pi$
$181$	−3.54177	−	3.32594i	−0.263258	−	0.247215i	−0.804924	+	0.593378i	$0.797794\pi$
$182$	−2.96263			−0.219605
$183$	10.1780	+	9.55781i	0.752382	+	0.706534i
$184$	4.06278	+	6.40191i	0.299512	+	0.471955i
$185$	6.61344	+	4.53210i	0.486230	+	0.333207i
$186$	7.51279	−	2.97452i	0.550864	−	0.218103i
$187$	−0.320496	+	5.09415i	−0.0234370	+	0.372521i
$188$	0.745717	−	11.8528i	0.0543870	−	0.864456i
$189$	−3.60313	+	1.42658i	−0.262089	+	0.103769i
$190$	1.81390	+	5.10030i	0.131594	+	0.370015i
$191$	−0.805263	−	1.26889i	−0.0582668	−	0.0918138i	0.813946	−	0.580941i	$-0.197315\pi$
$191$	−0.805263	−	1.26889i	−0.0582668	−	0.0918138i	−0.872212	+	0.489127i	$0.837315\pi$
$192$	−0.728969	−	0.684547i	−0.0526088	−	0.0494029i
$193$	−24.5413			−1.76652			−0.883260	−	0.468884i	$-0.844656\pi$
$193$	−24.5413			−1.76652			−0.883260	+	0.468884i	$0.844656\pi$
$194$	−9.15393	−	8.59611i	−0.657214	−	0.617165i
$195$	0.770165	+	1.52615i	0.0551527	+	0.109290i
$196$	−1.50237	+	7.87570i	−0.107312	+	0.562550i
$197$	−15.6968	−	8.62936i	−1.11835	−	0.614817i	−0.188247	−	0.982122i	$-0.560280\pi$
$197$	−15.6968	−	8.62936i	−1.11835	−	0.614817i	−0.930100	+	0.367305i	$0.880280\pi$
$198$	2.67821	−	4.22018i	0.190332	−	0.299915i
$199$	5.19415	+	15.9859i	0.368203	+	1.13321i	0.947951	+	0.318417i	$0.103151\pi$
$199$	5.19415	+	15.9859i	0.368203	+	1.13321i	−0.579748	+	0.814796i	$0.696849\pi$
$200$	−4.99242	+	0.275217i	−0.353017	+	0.0194608i
$201$	1.49213	−	4.59229i	0.105246	−	0.323915i
$202$	2.80805	+	3.39435i	0.197574	+	0.238826i
$203$	−3.68168	+	19.3000i	−0.258403	+	1.35460i
$204$	0.434804	+	0.924006i	0.0304424	+	0.0646933i
$205$	−2.68015	−	7.53602i	−0.187190	−	0.526339i
$206$	2.01042	+	10.5390i	0.140073	+	0.734286i
$207$	−2.34305	+	7.21115i	−0.162853	+	0.501210i
$208$	0.325507	−	0.691737i	0.0225698	−	0.0479633i
$209$	11.2505	+	4.45439i	0.778214	+	0.308117i
$210$	8.33062	−	2.38525i	0.574867	−	0.164598i
$211$	−2.88609	−	0.741021i	−0.198686	−	0.0510140i	0.148035	−	0.988982i	$-0.452705\pi$
$211$	−2.88609	−	0.741021i	−0.198686	−	0.0510140i	−0.346722	+	0.937968i	$0.612705\pi$
$212$	4.72632	+	1.87128i	0.324605	+	0.128520i
$213$	−0.616245	+	0.158225i	−0.0422244	+	0.0108414i
$214$	−0.889160	+	1.40109i	−0.0607817	+	0.0957766i
$215$	7.64633	−	3.27369i	0.521475	−	0.223264i
$216$	0.0627905	−	0.998027i	0.00427235	−	0.0679071i
$217$	27.4398	−	15.0851i	1.86273	−	1.02405i
$218$	−2.89244	−	8.90202i	−0.195901	−	0.602921i
$219$	−16.1124	−	2.03547i	−1.08877	−	0.137544i
$220$	−6.88436	+	8.80451i	−0.464144	+	0.593600i
$221$	−0.569106	+	0.534426i	−0.0382822	+	0.0359494i
$222$	2.61369	−	2.45441i	0.175419	−	0.164730i
$223$	−6.20309	−	1.59268i	−0.415390	−	0.106654i	0.0352102	−	0.999380i	$-0.488790\pi$
$223$	−6.20309	−	1.59268i	−0.415390	−	0.106654i	−0.450600	+	0.892726i	$0.648790\pi$
$224$	−3.13516	−	2.27783i	−0.209477	−	0.152194i
$225$	−3.39435	−	3.67130i	−0.226290	−	0.244753i
$226$	−12.7108	+	9.23493i	−0.845509	+	0.614298i
$227$	−6.98051	+	2.76378i	−0.463313	+	0.183439i	−0.588172	−	0.808736i	$-0.700152\pi$
$227$	−6.98051	+	2.76378i	−0.463313	+	0.183439i	0.124859	+	0.992175i	$0.460152\pi$
$228$	2.40179	−	0.303417i	0.159063	−	0.0200943i
$229$	17.8594	+	9.81829i	1.18018	+	0.648811i	0.946248	−	0.323442i	$-0.104840\pi$
$229$	17.8594	+	9.81829i	1.18018	+	0.648811i	0.233934	+	0.972252i	$0.424840\pi$
$230$	6.79375	−	15.5338i	0.447966	−	1.02427i
$231$	8.24720	−	17.5262i	0.542626	−	1.15314i
$232$	−4.10181	−	2.98014i	−0.269297	−	0.195656i
$233$	−8.10524	−	1.02393i	−0.530992	−	0.0670799i	−0.144734	−	0.989471i	$-0.546233\pi$
$233$	−8.10524	−	1.02393i	−0.530992	−	0.0670799i	−0.386258	+	0.922391i	$0.626233\pi$
$234$	0.740478	−	0.190123i	0.0484066	−	0.0124287i
$235$	−22.9103	+	13.4294i	−1.49450	+	0.876036i
$236$	5.17692	+	6.25782i	0.336989	+	0.407349i
$237$	−2.37199	+	2.86724i	−0.154077	+	0.186247i
$238$	2.12049	+	3.34135i	0.137451	+	0.216588i
$239$	−1.70214	−	27.0547i	−0.110102	−	1.75002i	−0.535064	−	0.844812i	$-0.679712\pi$
$239$	−1.70214	−	27.0547i	−0.110102	−	1.75002i	0.424962	−	0.905211i	$-0.360288\pi$
$240$	−0.358365	+	2.20716i	−0.0231324	+	0.142472i
$241$	−6.34325	+	7.66767i	−0.408605	+	0.493918i	−0.934167	−	0.356837i	$-0.883855\pi$
$241$	−6.34325	+	7.66767i	−0.408605	+	0.493918i	0.525562	+	0.850755i	$0.323855\pi$
$242$	2.62011	+	13.7351i	0.168427	+	0.882925i
$243$	0.809017	−	0.587785i	0.0518985	−	0.0377064i
$244$	−12.2352	+	6.72636i	−0.783278	+	0.430611i
$245$	16.4812	−	7.05623i	1.05294	−	0.450806i
$246$	−3.54880	+	0.448318i	−0.226263	+	0.0285837i
$247$	0.788013	+	1.67461i	0.0501401	+	0.106553i
$248$	0.507360	+	8.06426i	0.0322174	+	0.512081i
$249$	−11.6192			−0.736334
$250$	6.74921	+	8.91337i	0.426857	+	0.563731i
$251$	21.8058			1.37637			0.688186	−	0.725534i	$-0.258407\pi$
$251$	21.8058			1.37637			0.688186	+	0.725534i	$0.258407\pi$
$252$	−0.243330	−	3.86762i	−0.0153284	−	0.243637i
$253$	−16.1363	−	34.2913i	−1.01448	−	2.15588i
$254$	9.66951	−	1.22154i	0.606719	−	0.0766464i
$255$	1.17000	−	1.96095i	0.0732679	−	0.122799i
$256$	0.876307	−	0.481754i	0.0547692	−	0.0301096i
$257$	−22.5114	+	16.3555i	−1.40422	+	1.02023i	−0.410089	+	0.912045i	$0.634503\pi$
$257$	−22.5114	+	16.3555i	−1.40422	+	1.02023i	−0.994131	+	0.108181i	$0.965497\pi$
$258$	−0.697015	−	3.65388i	−0.0433943	−	0.227481i
$259$	8.85676	−	10.7060i	0.550332	−	0.665238i
$260$	−1.68944	+	0.260866i	−0.104775	+	0.0161782i
$261$	−0.318355	−	5.06011i	−0.0197057	−	0.313213i
$262$	3.45945	+	5.45123i	0.213726	+	0.336778i
$263$	−18.2561	+	22.0678i	−1.12572	+	1.36076i	−0.201229	+	0.979544i	$0.564494\pi$
$263$	−18.2561	+	22.0678i	−1.12572	+	1.36076i	−0.924487	+	0.381213i	$0.875506\pi$
$264$	3.18602	+	3.85124i	0.196086	+	0.237027i
$265$	−2.43648	−	11.1024i	−0.149672	−	0.682013i
$266$	9.08683	−	2.33310i	0.557149	−	0.143052i
$267$	−6.31141	−	0.797317i	−0.386252	−	0.0487950i
$268$	3.90643	+	2.83819i	0.238623	+	0.173370i
$269$	−0.0496325	+	0.105474i	−0.00302615	+	0.00643089i	−0.906334	−	0.422561i	$-0.861131\pi$
$269$	−0.0496325	+	0.105474i	−0.00302615	+	0.00643089i	0.903308	+	0.428992i	$0.141131\pi$
$270$	−1.92908	+	1.13077i	−0.117400	+	0.0688167i
$271$	−27.6190	−	15.1837i	−1.67774	−	0.922343i	−0.978179	−	0.207766i	$-0.933381\pi$
$271$	−27.6190	−	15.1837i	−1.67774	−	0.922343i	−0.699557	−	0.714577i	$-0.746619\pi$
$272$	−1.01314	+	0.127990i	−0.0614308	+	0.00776052i
$273$	2.75458	−	1.09062i	0.166715	−	0.0660071i
$274$	−2.57650	+	1.87193i	−0.155652	+	0.113088i
$275$	24.9291	+	1.76274i	1.50328	+	0.106297i
$276$	−6.13417	−	4.45674i	−0.369234	−	0.268264i
$277$	−10.7295	−	2.75487i	−0.644674	−	0.165524i	−0.0878223	−	0.996136i	$-0.527991\pi$
$277$	−10.7295	−	2.75487i	−0.644674	−	0.165524i	−0.556852	+	0.830612i	$0.687991\pi$
$278$	−6.01138	+	5.64506i	−0.360538	+	0.338568i
$279$	−5.89022	+	5.53128i	−0.352638	+	0.331149i
$280$	−0.305791	+	8.65997i	−0.0182745	+	0.517532i
$281$	−22.1560	−	2.79896i	−1.32172	−	0.166972i	−0.567379	−	0.823457i	$-0.692042\pi$
$281$	−22.1560	−	2.79896i	−1.32172	−	0.166972i	−0.754339	+	0.656485i	$0.772042\pi$
$282$	3.66997	+	11.2950i	0.218543	+	0.672607i
$283$	15.9593	−	8.77370i	0.948682	−	0.521542i	0.0692671	−	0.997598i	$-0.477934\pi$
$283$	15.9593	−	8.77370i	0.948682	−	0.521542i	0.879415	+	0.476056i	$0.157934\pi$
$284$	0.0399495	−	0.634978i	0.00237056	−	0.0376790i
$285$	−3.56407	−	4.07440i	−0.211117	−	0.241347i
$286$	−2.04748	+	3.22632i	−0.121070	+	0.190776i
$287$	−13.4264	+	3.44731i	−0.792533	+	0.203488i
$288$	0.929776	+	0.368125i	0.0547876	+	0.0216919i
$289$	−15.4558	−	3.96838i	−0.909167	−	0.233434i
$290$	−0.400075	+	11.3301i	−0.0234932	+	0.665324i
$291$	11.6755	+	4.62268i	0.684433	+	0.270986i
$292$	6.91484	−	14.6948i	0.404661	−	0.859948i
$293$	−2.38946	+	7.35399i	−0.139594	+	0.429625i	−0.996276	−	0.0862189i	$-0.972522\pi$
$293$	−2.38946	+	7.35399i	−0.139594	+	0.429625i	0.856683	+	0.515844i	$0.172522\pi$
$294$	−1.50237	−	7.87570i	−0.0876200	−	0.459320i
$295$	5.13425	−	17.4196i	0.298928	−	1.01421i
$296$	1.52661	+	3.24422i	0.0887326	+	0.188566i
$297$	−0.936583	+	4.90974i	−0.0543461	+	0.284892i
$298$	−7.56967	−	9.15016i	−0.438499	−	0.530055i
$299$	1.79125	−	5.51290i	0.103591	−	0.318819i
$300$	4.54052	−	2.09372i	0.262147	−	0.120881i
$301$	−4.45451	−	13.7096i	−0.256754	−	0.790207i
$302$	5.34785	−	8.42686i	0.307734	−	0.484912i
$303$	−3.86040	−	2.12228i	−0.221774	−	0.121922i
$304$	−0.453628	+	2.37800i	−0.0260173	+	0.136388i
$305$	27.7625	+	14.2816i	1.58967	+	0.817765i
$306$	−0.744420	−	0.699057i	−0.0425556	−	0.0399624i
$307$	12.7686			0.728743			0.364372	−	0.931254i	$-0.381284\pi$
$307$	12.7686			0.728743			0.364372	+	0.931254i	$0.381284\pi$
$308$	14.1199	+	13.2594i	0.804555	+	0.755527i
$309$	−5.74890	−	9.05882i	−0.327043	−	0.515338i
$310$	14.3193	−	11.0185i	0.813281	−	0.625806i
$311$	26.7261	−	10.5816i	1.51550	−	0.600028i	0.544425	−	0.838810i	$-0.316748\pi$
$311$	26.7261	−	10.5816i	1.51550	−	0.600028i	0.971073	+	0.238781i	$0.0767479\pi$
$312$	−0.0480031	+	0.762988i	−0.00271764	+	0.0431957i
$313$	−0.773637	+	12.2966i	−0.0437285	+	0.695045i	0.913703	+	0.406383i	$0.133210\pi$
$313$	−0.773637	+	12.2966i	−0.0437285	+	0.695045i	−0.957431	+	0.288662i	$0.906790\pi$
$314$	−13.6880	+	5.41947i	−0.772460	+	0.305839i
$315$	−6.86754	+	5.28446i	−0.386942	+	0.297745i
$316$	−1.99392	−	3.14192i	−0.112167	−	0.176747i
$317$	18.3821	+	17.2620i	1.03244	+	0.969529i	0.999552	−	0.0299300i	$-0.00952845\pi$
$317$	18.3821	+	17.2620i	1.03244	+	0.969529i	0.0328914	+	0.999459i	$0.489528\pi$
$318$	−5.08328			−0.285056
$319$	18.4734	+	17.3477i	1.03431	+	0.971283i
$320$	−1.98840	−	1.02288i	−0.111155	−	0.0571806i
$321$	0.310944	−	1.63002i	0.0173552	−	0.0909790i
$322$	−25.7488	−	14.1555i	−1.43492	−	0.788856i
$323$	1.32467	−	2.08734i	0.0737065	−	0.116143i
$324$	0.309017	+	0.951057i	0.0171676	+	0.0528365i
$325$	2.59497	+	2.80669i	0.143943	+	0.155687i
$326$	−2.45422	+	7.55331i	−0.135927	+	0.418339i
$327$	5.96638	+	7.21211i	0.329941	+	0.398831i
$328$	0.670264	−	3.51365i	0.0370091	−	0.194009i
$329$	19.5959	+	41.6435i	1.08036	+	2.29588i
$330$	3.15976	−	10.7205i	0.173939	−	0.590146i
$331$	−3.41196	−	17.8861i	−0.187538	−	0.983111i	−0.944217	−	0.329324i	$-0.893179\pi$
$331$	−3.41196	−	17.8861i	−0.187538	−	0.983111i	0.756679	−	0.653787i	$-0.226821\pi$
$332$	3.59052	−	11.0505i	0.197055	−	0.606474i
$333$	−1.52661	+	3.24422i	−0.0836579	+	0.177782i
$334$	19.0056	+	7.52485i	1.03994	+	0.411742i
$335$	0.381019	−	10.7904i	0.0208173	−	0.589542i
$336$	3.75352	+	0.963740i	0.204771	+	0.0525764i
$337$	−12.0266	−	4.76168i	−0.655133	−	0.259385i	0.0169557	−	0.999856i	$-0.494603\pi$
$337$	−12.0266	−	4.76168i	−0.655133	−	0.259385i	−0.672089	+	0.740471i	$0.734603\pi$
$338$	12.0255	−	3.08762i	0.654100	−	0.167944i
$339$	8.41859	−	13.2656i	0.457235	−	0.720487i
$340$	1.50342	+	1.71870i	0.0815346	+	0.0932095i
$341$	2.53593	−	40.3074i	0.137328	−	2.18277i
$342$	−2.12143	+	1.16627i	−0.114714	+	0.0630646i
$343$	−1.21874	−	3.75090i	−0.0658058	−	0.202529i
$344$	3.69044	+	0.466211i	0.198975	+	0.0251364i
$345$	−0.598304	+	16.9439i	−0.0322116	+	0.912228i
$346$	−1.79512	+	1.68573i	−0.0965064	+	0.0906256i
$347$	22.2103	−	20.8569i	1.19231	−	1.11966i	0.202205	−	0.979343i	$-0.435189\pi$
$347$	22.2103	−	20.8569i	1.19231	−	1.11966i	0.990107	−	0.140312i	$-0.0448107\pi$
$348$	4.91083	+	1.26089i	0.263248	+	0.0675906i
$349$	14.1092	+	10.2510i	0.755251	+	0.548722i	0.897450	−	0.441116i	$-0.145417\pi$
$349$	14.1092	+	10.2510i	0.755251	+	0.548722i	−0.142199	+	0.989838i	$0.545417\pi$
$350$	16.4401	−	10.2551i	0.878759	−	0.548158i
$351$	−0.618491	+	0.449360i	−0.0330126	+	0.0239851i
$352$	−4.64728	+	1.83999i	−0.247701	+	0.0980717i
$353$	4.52247	−	0.571321i	0.240707	−	0.0304083i	−0.00405419	−	0.999992i	$-0.501290\pi$
$353$	4.52247	−	0.571321i	0.240707	−	0.0304083i	0.244761	+	0.969583i	$0.421290\pi$
$354$	−7.11703	−	3.91262i	−0.378266	−	0.207954i
$355$	−1.22735	+	0.719437i	−0.0651408	+	0.0381837i
$356$	2.70863	−	5.75612i	0.143557	−	0.305074i
$357$	−3.20161	−	2.32611i	−0.169447	−	0.123111i
$358$	3.06184	+	0.386800i	0.161823	+	0.0204430i
$359$	0.229528	−	0.0589328i	0.0121140	−	0.00311035i	−0.242628	−	0.970119i	$-0.578009\pi$
$359$	0.229528	−	0.0589328i	0.0121140	−	0.00311035i	0.254742	+	0.967009i	$0.418009\pi$
$360$	−0.479312	−	2.18409i	−0.0252619	−	0.115112i
$361$	8.37533	+	10.1240i	0.440807	+	0.532844i
$362$	−3.09699	+	3.74362i	−0.162774	+	0.196760i
$363$	−7.49234	−	11.8060i	−0.393246	−	0.619656i
$364$	0.186025	+	2.95678i	0.00975036	+	0.154978i
$365$	−35.8894	+	5.54166i	−1.87854	+	0.290063i
$366$	8.89986	−	10.7581i	0.465203	−	0.562334i
$367$	4.61269	+	24.1806i	0.240781	+	1.26222i	0.873113	+	0.487518i	$0.162098\pi$
$367$	4.61269	+	24.1806i	0.240781	+	1.26222i	−0.632332	+	0.774697i	$0.717902\pi$
$368$	6.13417	−	4.45674i	0.319766	−	0.232324i
$369$	3.13455	−	1.72324i	0.163178	−	0.0897081i
$370$	4.10790	−	6.88496i	0.213559	−	0.357932i
$371$	−19.5438	+	2.46895i	−1.01466	+	0.128182i
$372$	−3.44038	−	7.31119i	−0.178376	−	0.379068i
$373$	−0.574591	−	9.13287i	−0.0297512	−	0.472882i	−0.984490	−	0.175438i	$-0.943866\pi$
$373$	−0.574591	−	9.13287i	−0.0297512	−	0.472882i	0.954739	−	0.297444i	$-0.0961342\pi$
$374$	5.10422			0.263933
$375$	−9.55649	−	5.80289i	−0.493495	−	0.299660i
$376$	−11.8763			−0.612472
$377$	0.243381	+	3.86843i	0.0125348	+	0.199235i
$378$	1.65001	+	3.50645i	0.0848673	+	0.180352i
$379$	18.7462	−	2.36820i	0.962928	−	0.121646i	0.371879	−	0.928281i	$-0.378714\pi$
$379$	18.7462	−	2.36820i	0.962928	−	0.121646i	0.591050	+	0.806635i	$0.298714\pi$
$380$	4.97634	−	2.13057i	0.255281	−	0.109296i
$381$	−8.54080	+	4.69535i	−0.437559	+	0.240550i
$382$	−1.21583	+	0.883349i	−0.0622070	+	0.0451961i
$383$	−7.11842	−	37.3160i	−0.363734	−	1.90676i	−0.418413	−	0.908257i	$-0.637414\pi$
$383$	−7.11842	−	37.3160i	−0.363734	−	1.90676i	0.0546794	−	0.998504i	$-0.482586\pi$
$384$	−0.637424	+	0.770513i	−0.0325284	+	0.0393201i
$385$	6.94142	−	42.7520i	0.353767	−	2.17885i
$386$	1.54096	+	24.4928i	0.0784328	+	1.24665i
$387$	1.99315	+	3.14070i	0.101318	+	0.159651i
$388$	−8.00437	+	9.67562i	−0.406360	+	0.491205i
$389$	−10.8322	−	13.0939i	−0.549215	−	0.663887i	0.420737	−	0.907183i	$-0.361772\pi$
$389$	−10.8322	−	13.0939i	−0.549215	−	0.663887i	−0.969952	+	0.243295i	$0.921772\pi$
$390$	1.47477	−	0.864473i	0.0746781	−	0.0437743i
$391$	−7.49971	+	1.92560i	−0.379277	+	0.0973817i
$392$	7.95449	+	1.00489i	0.401763	+	0.0507544i
$393$	−5.22325	−	3.79491i	−0.263478	−	0.191428i
$394$	−7.62673	+	16.2076i	−0.384229	+	0.816528i
$395$	−3.33422	+	7.62364i	−0.167763	+	0.383587i
$396$	−4.38002	−	2.40794i	−0.220104	−	0.121003i
$397$	23.8417	−	3.01190i	1.19658	−	0.151163i	0.498310	−	0.866999i	$-0.333954\pi$
$397$	23.8417	−	3.01190i	1.19658	−	0.151163i	0.698269	+	0.715836i	$0.253954\pi$
$398$	15.6282	−	6.18766i	0.783373	−	0.310159i
$399$	−7.58985	+	5.51435i	−0.379968	+	0.276063i
$400$	0.588151	+	4.96529i	0.0294075	+	0.248264i
$401$	13.7845	+	10.0150i	0.688365	+	0.500127i	0.876122	−	0.482089i	$-0.160122\pi$
$401$	13.7845	+	10.0150i	0.688365	+	0.500127i	−0.187757	+	0.982216i	$0.560122\pi$
$402$	−4.67692	−	1.20083i	−0.233264	−	0.0598919i
$403$	4.50305	−	4.22865i	0.224313	−	0.210644i
$404$	3.21133	−	3.01564i	0.159770	−	0.150034i
$405$	1.37735	−	1.76151i	0.0684409	−	0.0875301i
$406$	19.4931	+	2.46255i	0.967427	+	0.122215i
$407$	−5.53793	−	17.0440i	−0.274505	−	0.844839i
$408$	0.894881	−	0.491965i	0.0443032	−	0.0243559i
$409$	−0.409103	+	6.50250i	−0.0202288	+	0.321528i	0.974879	+	0.222735i	$0.0714983\pi$
$409$	−0.409103	+	6.50250i	−0.0202288	+	0.321528i	−0.995108	+	0.0987935i	$0.968502\pi$
$410$	−7.35287	+	3.14805i	−0.363132	+	0.155471i
$411$	1.70646	−	2.68895i	0.0841735	−	0.132636i
$412$	10.3920	−	2.66820i	0.511975	−	0.131453i
$413$	−29.2633	−	11.5862i	−1.43995	−	0.570118i
$414$	7.34404	+	1.88563i	0.360940	+	0.0926737i
$415$	−24.9776	+	7.15167i	−1.22610	+	0.351061i
$416$	−0.710811	−	0.281430i	−0.0348504	−	0.0137982i
$417$	3.51115	−	7.46158i	0.171942	−	0.365395i
$418$	3.73918	−	11.5080i	0.182889	−	0.562875i
$419$	−0.932933	−	4.89061i	−0.0455768	−	0.238922i	0.952208	−	0.305451i	$-0.0988073\pi$
$419$	−0.932933	−	4.89061i	−0.0455768	−	0.238922i	−0.997784	+	0.0665295i	$0.978807\pi$
$420$	−2.90363	−	8.16441i	−0.141683	−	0.398382i
$421$	−13.0497	−	27.7320i	−0.636003	−	1.35157i	−0.919685	−	0.392656i	$-0.871556\pi$
$421$	−13.0497	−	27.7320i	−0.636003	−	1.35157i	0.283683	−	0.958918i	$-0.408444\pi$
$422$	−0.558340	+	2.92692i	−0.0271796	+	0.142480i
$423$	−7.57021	−	9.15082i	−0.368076	−	0.444928i
$424$	1.57082	−	4.83449i	0.0762858	−	0.234784i
$425$	1.30815	−	4.93556i	0.0634545	−	0.239410i
$426$	0.196607	+	0.605094i	0.00952564	+	0.0293169i
$427$	28.9922	−	45.6844i	1.40303	−	2.21082i
$428$	1.45416	+	0.799430i	0.0702894	+	0.0386419i
$429$	0.716015	−	3.75348i	0.0345695	−	0.181220i
$430$	−3.74735	−	7.42568i	−0.180713	−	0.358098i
$431$	1.93633	+	1.81833i	0.0932696	+	0.0875860i	0.729780	−	0.683682i	$-0.239623\pi$
$431$	1.93633	+	1.81833i	0.0932696	+	0.0875860i	−0.636510	+	0.771268i	$0.719623\pi$
$432$	−1.00000			−0.0481125
$433$	7.72007	+	7.24963i	0.371003	+	0.348395i	0.847514	−	0.530774i	$-0.178099\pi$
$433$	7.72007	+	7.24963i	0.371003	+	0.348395i	−0.476511	+	0.879169i	$0.658099\pi$
$434$	−16.7783	−	26.4384i	−0.805386	−	1.26909i
$435$	−3.79889	−	10.6817i	−0.182143	−	0.512148i
$436$	−8.70284	+	3.44570i	−0.416790	+	0.165019i
$437$	−1.15257	+	18.3195i	−0.0551347	+	0.876341i
$438$	−1.01975	+	16.2084i	−0.0487253	+	0.774467i
$439$	6.77720	−	2.68328i	0.323458	−	0.128066i	−0.200784	−	0.979636i	$-0.564349\pi$
$439$	6.77720	−	2.68328i	0.323458	−	0.128066i	0.524242	+	0.851569i	$0.324349\pi$
$440$	9.21941	+	6.31794i	0.439518	+	0.301196i
$441$	4.29611	+	6.76958i	0.204577	+	0.322361i
$442$	0.569106	+	0.534426i	0.0270696	+	0.0254201i
$443$	14.0466			0.667376			0.333688	−	0.942683i	$-0.391707\pi$
$443$	14.0466			0.667376			0.333688	+	0.942683i	$0.391707\pi$
$444$	−2.61369	−	2.45441i	−0.124040	−	0.116481i
$445$	−14.0583	+	2.17073i	−0.666428	+	0.102903i
$446$	−1.20005	+	6.29086i	−0.0568238	+	0.297881i
$447$	10.4065	+	5.72102i	0.492211	+	0.270595i
$448$	−2.07647	+	3.27200i	−0.0981041	+	0.154587i
$449$	−6.37288	−	19.6137i	−0.300755	−	0.925628i	−0.981227	−	0.192855i	$-0.938225\pi$
$449$	−6.37288	−	19.6137i	−0.300755	−	0.925628i	0.680472	−	0.732774i	$-0.261775\pi$
$450$	−3.45092	+	3.61817i	−0.162678	+	0.170562i
$451$	−5.52487	+	17.0038i	−0.260156	+	0.800678i
$452$	10.0148	+	12.1058i	0.471058	+	0.569411i
$453$	−1.87017	+	9.80378i	−0.0878683	+	0.460622i
$454$	3.19664	+	6.79320i	0.150026	+	0.318821i
$455$	5.25021	−	4.03995i	0.246134	−	0.189396i
$456$	−0.453628	−	2.37800i	−0.0212431	−	0.111360i
$457$	6.82710	−	21.0117i	0.319358	−	0.982884i	−0.654565	−	0.756006i	$-0.727148\pi$
$457$	6.82710	−	21.0117i	0.319358	−	0.982884i	0.973923	−	0.226878i	$-0.0728519\pi$
$458$	8.67751	−	18.4407i	0.405474	−	0.861675i
$459$	0.949484	+	0.375927i	0.0443181	+	0.0175468i
$460$	−15.9297	−	5.80497i	−0.742726	−	0.270658i
$461$	−21.0834	−	5.41329i	−0.981951	−	0.252122i	−0.276604	−	0.960984i	$-0.589209\pi$
$461$	−21.0834	−	5.41329i	−0.981951	−	0.252122i	−0.705347	+	0.708862i	$0.749209\pi$
$462$	−18.0095	−	7.13045i	−0.837876	−	0.331739i
$463$	6.94046	−	1.78201i	0.322550	−	0.0828169i	−0.0839430	−	0.996471i	$-0.526751\pi$
$463$	6.94046	−	1.78201i	0.322550	−	0.0828169i	0.406494	+	0.913654i	$0.366751\pi$
$464$	−2.71670	+	4.28084i	−0.126120	+	0.198733i
$465$	−9.25758	+	15.5160i	−0.429310	+	0.719537i
$466$	−0.512977	+	8.15354i	−0.0237632	+	0.377706i
$467$	33.5822	−	18.4620i	1.55400	−	0.854318i	0.554241	−	0.832356i	$-0.313009\pi$
$467$	33.5822	−	18.4620i	1.55400	−	0.854318i	0.999759	−	0.0219621i	$-0.00699131\pi$
$468$	−0.236242	−	0.727079i	−0.0109203	−	0.0336093i
$469$	−18.5647	−	2.34526i	−0.857236	−	0.108294i
$470$	14.8414	+	22.0218i	0.684584	+	1.01579i
$471$	10.7318	−	10.0778i	0.494494	−	0.464360i
$472$	5.92041	−	5.55964i	0.272509	−	0.255903i
$473$	−18.0083	−	4.62375i	−0.828023	−	0.212600i
$474$	3.01052	+	2.18727i	0.138278	+	0.100465i
$475$	−10.1694	−	6.56498i	−0.466606	−	0.301222i
$476$	3.20161	−	2.32611i	0.146746	−	0.106617i
$477$	4.72632	−	1.87128i	0.216403	−	0.0856801i
$478$	−26.8944	+	3.39756i	−1.23012	+	0.155401i
$479$	21.0998	+	11.5997i	0.964073	+	0.530004i	0.884356	−	0.466814i	$-0.154598\pi$
$479$	21.0998	+	11.5997i	0.964073	+	0.530004i	0.0797175	+	0.996817i	$0.474598\pi$
$480$	2.22531	+	0.219069i	0.101571	+	0.00999909i
$481$	1.16709	−	2.48019i	0.0532148	−	0.113087i
$482$	8.05084	+	5.84928i	0.366706	+	0.266427i
$483$	29.1516	+	3.68270i	1.32644	+	0.167569i
$484$	13.5435	−	3.47737i	0.615612	−	0.158062i
$485$	27.9441	+	2.75093i	1.26887	+	0.124913i
$486$	−0.637424	−	0.770513i	−0.0289141	−	0.0349512i
$487$	−17.2238	+	20.8200i	−0.780486	+	0.943445i	−0.999479	−	0.0322814i	$-0.989723\pi$
$487$	−17.2238	+	20.8200i	−0.780486	+	0.943445i	0.218993	+	0.975726i	$0.429723\pi$
$488$	7.48134	+	11.7887i	0.338664	+	0.533650i
$489$	−0.498684	−	7.92635i	−0.0225513	−	0.358442i
$490$	−8.07717	−	16.0056i	−0.364889	−	0.723058i
$491$	1.67903	−	2.02959i	0.0757733	−	0.0915942i	−0.731264	−	0.682094i	$-0.761069\pi$
$491$	1.67903	−	2.02959i	0.0757733	−	0.0915942i	0.807038	+	0.590500i	$0.201069\pi$
$492$	0.670264	+	3.51365i	0.0302178	+	0.158407i
$493$	4.18875	−	3.04330i	0.188652	−	0.137063i
$494$	1.62183	−	0.891608i	0.0729695	−	0.0401153i
$495$	1.00862	+	11.1309i	0.0453339	+	0.500296i
$496$	8.01649	−	1.01272i	0.359951	−	0.0454724i
$497$	1.04979	+	2.23092i	0.0470896	+	0.100071i
$498$	0.729573	+	11.5962i	0.0326930	+	0.519640i
$499$	7.02380			0.314428			0.157214	−	0.987565i	$-0.449749\pi$
$499$	7.02380			0.314428			0.157214	+	0.987565i	$0.449749\pi$
$500$	8.47200	−	7.29557i	0.378879	−	0.326268i
$501$	−20.4410			−0.913239
$502$	−1.36920	−	21.7628i	−0.0611104	−	0.971322i
$503$	18.2818	+	38.8509i	0.815146	+	1.73227i	0.669333	+	0.742962i	$0.266580\pi$
$503$	18.2818	+	38.8509i	0.815146	+	1.73227i	0.145813	+	0.989312i	$0.453420\pi$
$504$	−3.84471	+	0.485700i	−0.171257	+	0.0216348i
$505$	−9.60493	−	2.18612i	−0.427414	−	0.0972812i
$506$	−33.2104	+	18.2576i	−1.47638	+	0.811649i
$507$	−10.0444	+	7.29767i	−0.446087	+	0.324101i
$508$	−1.82629	−	9.57373i	−0.0810284	−	0.424765i
$509$	−5.70263	+	6.89330i	−0.252765	+	0.305540i	−0.881599	−	0.471999i	$-0.843532\pi$
$509$	−5.70263	+	6.89330i	−0.252765	+	0.305540i	0.628834	+	0.777540i	$0.283532\pi$
$510$	−2.03054	−	1.04456i	−0.0899139	−	0.0462538i
$511$	3.95179	+	62.8119i	0.174817	+	2.77863i
$512$	−0.535827	−	0.844328i	−0.0236804	−	0.0373144i
$513$	1.54313	−	1.86532i	0.0681308	−	0.0823559i
$514$	17.7367	+	21.4400i	0.782332	+	0.945677i
$515$	−17.9341	−	15.9351i	−0.790270	−	0.702186i
$516$	−3.60290	+	0.925069i	−0.158609	+	0.0407239i
$517$	58.8928	+	7.43988i	2.59010	+	0.327206i
$518$	−11.2410	−	8.16705i	−0.493900	−	0.358840i
$519$	1.04850	−	2.22818i	0.0460242	−	0.0978064i
$520$	0.366432	+	1.66973i	0.0160691	+	0.0732226i
$521$	27.6611	+	15.2068i	1.21186	+	0.666223i	0.953955	−	0.299949i	$-0.0969695\pi$
$521$	27.6611	+	15.2068i	1.21186	+	0.666223i	0.257900	+	0.966172i	$0.416970\pi$
$522$	−5.03013	+	0.635454i	−0.220163	+	0.0278130i
$523$	−27.8482	+	11.0259i	−1.21772	+	0.482128i	−0.887073	−	0.461629i	$-0.847265\pi$
$523$	−27.8482	+	11.0259i	−1.21772	+	0.482128i	−0.330642	+	0.943756i	$0.607265\pi$
$524$	5.22325	−	3.79491i	0.228179	−	0.165782i
$525$	−11.5104	+	15.5869i	−0.502357	+	0.680270i
$526$	23.1705	+	16.8344i	1.01028	+	0.734014i
$527$	−7.99224	−	2.05206i	−0.348147	−	0.0893890i
$528$	3.64359	−	3.42155i	0.158567	−	0.148904i
$529$	25.1426	−	23.6104i	1.09315	−	1.02654i
$530$	−10.9275	+	3.12879i	−0.474659	+	0.135906i
$531$	8.05758	+	1.01791i	0.349669	+	0.0441735i
$532$	−2.89906	−	8.92240i	−0.125690	−	0.386835i
$533$	−2.39636	+	1.31741i	−0.103798	+	0.0570633i
$534$	−0.399447	+	6.34902i	−0.0172857	+	0.274749i
$535$	−0.334858	−	3.69543i	−0.0144772	−	0.159767i
$536$	2.58730	−	4.07694i	0.111754	−	0.176097i
$537$	−2.98922	+	0.767500i	−0.128994	+	0.0331201i
$538$	0.108383	+	0.0429118i	0.00467271	+	0.00185006i
$539$	−38.8157	−	9.96619i	−1.67191	−	0.429274i
$540$	1.24967	+	1.85427i	0.0537773	+	0.0797951i
$541$	−3.72107	−	1.47328i	−0.159981	−	0.0633411i	0.286769	−	0.958000i	$-0.407419\pi$
$541$	−3.72107	−	1.47328i	−0.159981	−	0.0633411i	−0.446750	+	0.894659i	$0.647419\pi$
$542$	−13.4195	+	28.5179i	−0.576417	+	1.22495i
$543$	1.50139	−	4.62081i	0.0644309	−	0.198298i
$544$	0.191353	+	1.00311i	0.00820419	+	0.0430079i
$545$	17.2649	+	11.8314i	0.739549	+	0.506803i
$546$	−1.26143	−	2.68067i	−0.0539841	−	0.114722i
$547$	2.92639	−	15.3407i	0.125123	−	0.655919i	−0.863360	−	0.504588i	$-0.831644\pi$
$547$	2.92639	−	15.3407i	0.125123	−	0.655919i	0.988483	−	0.151330i	$-0.0483557\pi$
$548$	2.03002	+	2.45387i	0.0867182	+	0.104824i
$549$	−4.31457	+	13.2789i	−0.184141	+	0.566729i
$550$	0.193947	−	24.9906i	0.00826992	−	1.06560i
$551$	−3.79292	−	11.6734i	−0.161584	−	0.497304i
$552$	−4.06278	+	6.40191i	−0.172923	+	0.272483i
$553$	12.6369	+	6.94722i	0.537377	+	0.295426i
$554$	−2.07572	+	10.8813i	−0.0881890	+	0.462303i
$555$	−1.28490	+	7.91369i	−0.0545411	+	0.335918i
$556$	6.01138	+	5.64506i	0.254939	+	0.239404i
$557$	23.2015			0.983077			0.491539	−	0.870856i	$-0.336435\pi$
$557$	23.2015			0.983077			0.491539	+	0.870856i	$0.336435\pi$
$558$	5.89022	+	5.53128i	0.249353	+	0.234158i
$559$	−1.52376	−	2.40106i	−0.0644481	−	0.101554i
$560$	8.66208	−	0.238576i	0.366040	−	0.0100817i
$561$	−4.74578	+	1.87899i	−0.200367	+	0.0793309i
$562$	−1.40225	+	22.2880i	−0.0591501	+	0.940164i
$563$	0.714937	−	11.3636i	0.0301310	−	0.478919i	−0.953808	−	0.300416i	$-0.902875\pi$
$563$	0.714937	−	11.3636i	0.0301310	−	0.478919i	0.983939	−	0.178503i	$-0.0571254\pi$
$564$	11.0423	−	4.37194i	0.464963	−	0.184092i
$565$	9.93229	−	33.6985i	0.417854	−	1.41771i
$566$	−9.75848	−	15.3769i	−0.410180	−	0.646340i
$567$	−2.82495	−	2.65280i	−0.118637	−	0.111407i
$568$	−0.636234			−0.0266958
$569$	11.1347	+	10.4562i	0.466791	+	0.438346i	0.881908	−	0.471422i	$-0.156259\pi$
$569$	11.1347	+	10.4562i	0.466791	+	0.438346i	−0.415117	+	0.909768i	$0.636259\pi$
$570$	−3.84257	+	3.81287i	−0.160948	+	0.159703i
$571$	−8.27205	+	43.3636i	−0.346175	+	1.81471i	0.203203	+	0.979137i	$0.434865\pi$
$571$	−8.27205	+	43.3636i	−0.346175	+	1.81471i	−0.549377	+	0.835574i	$0.685135\pi$
$572$	3.34851	+	1.84086i	0.140008	+	0.0769702i
$573$	0.805263	−	1.26889i	0.0336404	−	0.0530087i
$574$	4.28355	+	13.1834i	0.178792	+	0.550265i
$575$	9.14290	+	36.7923i	0.381285	+	1.53434i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	14.5929	+	17.6398i	0.607512	+	0.734356i	0.981156	−	0.193216i	$-0.0618919\pi$
$577$	14.5929	+	17.6398i	0.607512	+	0.734356i	−0.373644	+	0.927572i	$0.621892\pi$
$578$	−2.99007	+	15.6745i	−0.124371	+	0.651974i
$579$	−10.4492	−	22.2056i	−0.434253	−	0.922834i
$580$	11.3328	−	0.312135i	0.470570	−	0.0129607i
$581$	8.43729	+	44.2298i	0.350038	+	1.83496i
$582$	3.88044	−	11.9428i	0.160849	−	0.495044i
$583$	−10.8181	+	22.9895i	−0.448038	+	0.952129i
$584$	−15.1000	−	5.97851i	−0.624842	−	0.247392i
$585$	−1.05298	+	1.34667i	−0.0435353	+	0.0556779i
$586$	7.48952	+	1.92298i	0.309389	+	0.0794376i
$587$	32.0039	+	12.6712i	1.32094	+	0.522998i	0.919574	−	0.392918i	$-0.128534\pi$
$587$	32.0039	+	12.6712i	1.32094	+	0.522998i	0.401370	+	0.915916i	$0.368534\pi$
$588$	−7.76583	+	1.99393i	−0.320257	+	0.0822281i
$589$	−10.4814	+	16.5161i	−0.431880	+	0.680533i
$590$	−17.7076	−	4.03033i	−0.729012	−	0.165926i
$591$	1.12473	−	17.8770i	0.0462651	−	0.735363i
$592$	3.14196	−	1.72731i	0.129134	−	0.0709919i
$593$	−2.47615	−	7.62081i	−0.101683	−	0.312949i	0.887254	−	0.461280i	$-0.152610\pi$
$593$	−2.47615	−	7.62081i	−0.101683	−	0.312949i	−0.988938	+	0.148331i	$0.952610\pi$
$594$	4.95886	+	0.626450i	0.203465	+	0.0257036i
$595$	−8.31419	−	3.02979i	−0.340849	−	0.124209i
$596$	−8.65680	+	8.12928i	−0.354596	+	0.332988i
$597$	−12.2529	+	11.5063i	−0.501480	+	0.470921i
$598$	−5.61450	−	1.44156i	−0.229594	−	0.0589497i
$599$	11.8962	+	8.64312i	0.486067	+	0.353148i	0.803670	−	0.595076i	$-0.202878\pi$
$599$	11.8962	+	8.64312i	0.486067	+	0.353148i	−0.317603	+	0.948224i	$0.602878\pi$
$600$	−2.37469	−	4.40009i	−0.0969464	−	0.179633i
$601$	−23.3829	+	16.9887i	−0.953810	+	0.692984i	−0.951705	−	0.307014i	$-0.900670\pi$
$601$	−23.3829	+	16.9887i	−0.953810	+	0.692984i	−0.00210532	+	0.999998i	$0.500670\pi$
$602$	−13.4028	+	5.30655i	−0.546258	+	0.216279i
$603$	4.79054	−	0.605186i	0.195086	−	0.0246451i
$604$	−8.74603	−	4.80817i	−0.355871	−	0.195642i
$605$	−23.3729	−	20.7677i	−0.950242	−	0.844327i
$606$	−1.87569	+	3.98605i	−0.0761947	+	0.161922i
$607$	−8.53261	−	6.19930i	−0.346328	−	0.251622i	0.400999	−	0.916078i	$-0.368663\pi$
$607$	−8.53261	−	6.19930i	−0.346328	−	0.251622i	−0.747327	+	0.664457i	$0.768663\pi$
$608$	2.40179	+	0.303417i	0.0974055	+	0.0123052i
$609$	−19.0308	+	4.88627i	−0.771166	+	0.198002i
$610$	12.5102	−	28.6044i	0.506525	−	1.15816i
$611$	5.78740	+	6.99577i	0.234133	+	0.283019i
$612$	−0.650935	+	0.786845i	−0.0263125	+	0.0318063i
$613$	−23.2610	−	36.6535i	−0.939504	−	1.48042i	−0.875927	−	0.482444i	$-0.839749\pi$
$613$	−23.2610	−	36.6535i	−0.939504	−	1.48042i	−0.0635773	−	0.997977i	$-0.520251\pi$
$614$	−0.801748	−	12.7434i	−0.0323559	−	0.514282i
$615$	5.67765	−	5.63375i	0.228945	−	0.227175i
$616$	12.3467	−	14.9246i	0.497462	−	0.601329i
$617$	3.54811	+	18.5998i	0.142841	+	0.748801i	0.979558	+	0.201164i	$0.0644725\pi$
$617$	3.54811	+	18.5998i	0.142841	+	0.748801i	−0.836716	+	0.547637i	$0.815528\pi$
$618$	−8.67996	+	6.30636i	−0.349159	+	0.253679i
$619$	−31.7227	+	17.4397i	−1.27504	+	0.700961i	−0.968052	−	0.250751i	$-0.919322\pi$
$619$	−31.7227	+	17.4397i	−1.27504	+	0.700961i	−0.306992	+	0.951712i	$0.599322\pi$
$620$	−11.8958	−	13.5992i	−0.477748	−	0.546157i
$621$	−7.52247	+	0.950309i	−0.301866	+	0.0381346i
$622$	−12.2389	−	26.0089i	−0.490734	−	1.04286i
$623$	1.54796	+	24.6042i	0.0620178	+	0.985745i
$624$	0.764497			0.0306044
$625$	−24.1152	−	6.59232i	−0.964607	−	0.263693i
$626$	12.3209			0.492443
$627$	0.759780	+	12.0764i	0.0303427	+	0.482283i
$628$	6.26826	+	13.3207i	0.250131	+	0.531555i
$629$	−3.63258	+	0.458902i	−0.144841	+	0.0182976i
$630$	5.70524	+	6.52217i	0.227302	+	0.259850i
$631$	−18.7599	+	10.3134i	−0.746821	+	0.410568i	−0.809237	−	0.587482i	$-0.800119\pi$
$631$	−18.7599	+	10.3134i	−0.746821	+	0.410568i	0.0624166	+	0.998050i	$0.480119\pi$
$632$	−3.01052	+	2.18727i	−0.119752	+	0.0870049i
$633$	−0.558340	−	2.92692i	−0.0221920	−	0.116335i
$634$	16.0737	−	19.4297i	0.638368	−	0.771654i
$635$	−15.4700	+	15.3504i	−0.613910	+	0.609164i
$636$	0.319182	+	5.07325i	0.0126564	+	0.201168i
$637$	−3.28436	−	5.17532i	−0.130131	−	0.205054i
$638$	16.1535	−	19.5262i	0.639523	−	0.773050i
$639$	−0.405551	−	0.490227i	−0.0160433	−	0.0193931i
$640$	−0.896006	+	2.04870i	−0.0354177	+	0.0809820i
$641$	16.0495	−	4.12081i	0.633916	−	0.162762i	0.0819608	−	0.996636i	$-0.473882\pi$
$641$	16.0495	−	4.12081i	0.633916	−	0.162762i	0.551956	+	0.833874i	$0.313882\pi$
$642$	−1.64633	−	0.207980i	−0.0649755	−	0.00820832i
$643$	29.5878	+	21.4968i	1.16683	+	0.847752i	0.990626	−	0.136601i	$-0.0436180\pi$
$643$	29.5878	+	21.4968i	1.16683	+	0.847752i	0.176205	+	0.984354i	$0.443618\pi$
$644$	−12.5108	+	26.5868i	−0.492994	+	1.04767i
$645$	6.21777	+	5.52473i	0.244825	+	0.217536i
$646$	−2.16640	−	1.19099i	−0.0852359	−	0.0468588i
$647$	−4.63372	+	0.585375i	−0.182170	+	0.0230135i	−0.215889	−	0.976418i	$-0.569265\pi$
$647$	−4.63372	+	0.585375i	−0.182170	+	0.0230135i	0.0337188	+	0.999431i	$0.489265\pi$
$648$	0.929776	−	0.368125i	0.0365251	−	0.0144613i
$649$	−32.8413	+	23.8606i	−1.28914	+	0.936611i
$650$	2.63822	−	2.76608i	0.103479	−	0.108495i
$651$	25.3327	+	18.4053i	0.992868	+	0.721361i
$652$	7.69251	+	1.97510i	0.301262	+	0.0773509i
$653$	−10.9725	+	10.3039i	−0.429388	+	0.403222i	−0.868879	−	0.495025i	$-0.835159\pi$
$653$	−10.9725	+	10.3039i	−0.429388	+	0.403222i	0.439491	+	0.898247i	$0.355159\pi$
$654$	6.82325	−	6.40746i	0.266810	−	0.250551i
$655$	−13.5641	−	4.94293i	−0.529995	−	0.193136i
$656$	−3.54880	−	0.448318i	−0.138557	−	0.0175039i
$657$	−5.01857	−	15.4456i	−0.195793	−	0.602589i
$658$	40.3309	−	22.1721i	1.57226	−	0.864358i
$659$	1.15195	−	18.3098i	0.0448737	−	0.713247i	−0.909699	−	0.415269i	$-0.863688\pi$
$659$	1.15195	−	18.3098i	0.0448737	−	0.713247i	0.954573	−	0.297979i	$-0.0963124\pi$
$660$	−10.8978	−	2.48038i	−0.424195	−	0.0965486i
$661$	3.22586	−	5.08314i	0.125471	−	0.197711i	−0.775785	−	0.630997i	$-0.782646\pi$
$661$	3.22586	−	5.08314i	0.125471	−	0.197711i	0.901257	+	0.433286i	$0.142646\pi$
$662$	−17.6366	+	4.52831i	−0.685466	+	0.175998i
$663$	−0.725877	−	0.287395i	−0.0281907	−	0.0111615i
$664$	−11.2541	−	2.88957i	−0.436745	−	0.112137i
$665$	−12.9217	+	16.5257i	−0.501081	+	0.640840i
$666$	3.33367	+	1.31990i	0.129177	+	0.0511449i
$667$	−16.3682	+	34.7842i	−0.633779	+	1.34685i
$668$	6.31663	−	19.4406i	0.244398	−	0.752179i
$669$	−1.20005	−	6.29086i	−0.0463964	−	0.243219i
$670$	−10.7930	+	0.297268i	−0.416971	+	0.0114845i
$671$	−29.7139	−	63.1453i	−1.14709	−	2.43770i
$672$	0.726153	−	3.80663i	0.0280120	−	0.146844i
$673$	−1.72415	−	2.08414i	−0.0664610	−	0.0803375i	0.736235	−	0.676726i	$-0.236602\pi$
$673$	−1.72415	−	2.08414i	−0.0664610	−	0.0803375i	−0.802696	+	0.596388i	$0.796602\pi$
$674$	−3.99713	+	12.3019i	−0.153964	+	0.473851i
$675$	1.87665	−	4.63446i	0.0722321	−	0.178380i
$676$	−3.83661	−	11.8079i	−0.147562	−	0.454149i
$677$	−15.7373	+	24.7980i	−0.604834	+	0.953065i	0.394581	+	0.918861i	$0.370890\pi$
$677$	−15.7373	+	24.7980i	−0.604834	+	0.953065i	−0.999415	+	0.0342041i	$0.989110\pi$
$678$	−13.7680	−	7.56903i	−0.528757	−	0.290687i
$679$	9.11857	−	47.8012i	0.349939	−	1.83444i
$680$	1.62091	−	1.60837i	0.0621589	−	0.0616784i
$681$	−5.47290	−	5.13940i	−0.209722	−	0.196942i
$682$	−40.3871			−1.54650
$683$	33.6866	+	31.6338i	1.28898	+	1.21043i	0.964361	+	0.264591i	$0.0852369\pi$
$683$	33.6866	+	31.6338i	1.28898	+	1.21043i	0.324621	+	0.945844i	$0.394763\pi$
$684$	1.29717	+	2.04402i	0.0495986	+	0.0781550i
$685$	2.01329	−	6.83074i	0.0769238	−	0.260989i
$686$	−3.66697	+	1.45186i	−0.140006	+	0.0554321i
$687$	−1.27969	+	20.3401i	−0.0488232	+	0.776023i
$688$	0.233566	−	3.71243i	0.00890463	−	0.141535i
$689$	−3.61325	+	1.43059i	−0.137654	+	0.0545011i
$690$	16.9480	−	0.466792i	0.645200	−	0.0177705i
$691$	2.63662	+	4.15465i	0.100302	+	0.158050i	0.890772	−	0.454450i	$-0.150164\pi$
$691$	2.63662	+	4.15465i	0.100302	+	0.158050i	−0.790471	+	0.612500i	$0.790164\pi$
$692$	1.79512	+	1.68573i	0.0682404	+	0.0640820i
$693$	19.3697			0.735793
$694$	−22.2103	−	20.8569i	−0.843092	−	0.791716i
$695$	2.95523	−	18.2012i	0.112098	−	0.690410i
$696$	0.950044	−	4.98031i	0.0360113	−	0.188778i
$697$	3.20099	+	1.75976i	0.121246	+	0.0666557i
$698$	9.34481	−	14.7251i	0.353706	−	0.557352i
$699$	−2.52456	−	7.76981i	−0.0954878	−	0.293881i
$700$	−11.2671	−	15.7637i	−0.425858	−	0.595812i
$701$	−11.3470	+	34.9226i	−0.428572	+	1.31901i	0.470960	+	0.882155i	$0.343908\pi$
$701$	−11.3470	+	34.9226i	−0.428572	+	1.31901i	−0.899532	+	0.436855i	$0.856092\pi$
$702$	0.487308	+	0.589055i	0.0183923	+	0.0222324i
$703$	−1.62646	+	8.52622i	−0.0613432	+	0.321573i
$704$	2.12816	+	4.52257i	0.0802081	+	0.170451i
$705$	−21.9060	−	15.0119i	−0.825027	−	0.565380i
$706$	−0.854162	−	4.47767i	−0.0321468	−	0.168519i
$707$	−5.27547	+	16.2362i	−0.198404	+	0.610626i
$708$	−3.45802	+	7.34867i	−0.129960	+	0.276180i
$709$	−33.3816	−	13.2167i	−1.25367	−	0.496364i	−0.354952	−	0.934885i	$-0.615503\pi$
$709$	−33.3816	−	13.2167i	−1.25367	−	0.496364i	−0.898721	+	0.438520i	$0.855503\pi$
$710$	0.795083	+	1.17975i	0.0298389	+	0.0442752i
$711$	−3.60430	−	0.925426i	−0.135172	−	0.0347062i
$712$	−5.91484	−	2.34185i	−0.221668	−	0.0877646i
$713$	59.3414	−	15.2363i	2.22235	−	0.570603i
$714$	−2.12049	+	3.34135i	−0.0793572	+	0.125047i
$715$	−0.771084	−	8.50952i	−0.0288369	−	0.318238i
$716$	0.193783	−	3.08008i	0.00724199	−	0.115108i
$717$	23.7551	−	13.0595i	0.887150	−	0.487715i
$718$	−0.0732287	−	0.225375i	−0.00273287	−	0.00841091i
$719$	18.4013	+	2.32463i	0.686254	+	0.0866941i	0.460726	−	0.887543i	$-0.347589\pi$
$719$	18.4013	+	2.32463i	0.686254	+	0.0866941i	0.225528	+	0.974237i	$0.427589\pi$
$720$	−2.14969	+	0.615506i	−0.0801141	+	0.0229386i
$721$	−30.3090	+	28.4620i	−1.12876	+	1.05998i
$722$	9.57816	−	8.99449i	0.356462	−	0.334740i
$723$	−9.63874	−	2.47481i	−0.358469	−	0.0920391i
$724$	3.93069	+	2.85582i	0.146083	+	0.106136i
$725$	−14.7411	−	20.6241i	−0.547470	−	0.765958i
$726$	−11.3123	+	8.21886i	−0.419838	+	0.305030i
$727$	−30.6399	+	12.1312i	−1.13637	+	0.449921i	−0.859576	−	0.511008i	$-0.829272\pi$
$727$	−30.6399	+	12.1312i	−1.13637	+	0.449921i	−0.276795	+	0.960929i	$0.589272\pi$
$728$	2.93927	−	0.371316i	0.108937	−	0.0137619i
$729$	0.876307	+	0.481754i	0.0324558	+	0.0178427i
$730$	7.78423	+	35.4706i	0.288107	+	1.31283i
$731$	−1.61737	+	3.43709i	−0.0598206	+	0.127125i
$732$	−11.2957	−	8.20680i	−0.417501	−	0.303332i
$733$	−10.6835	−	1.34964i	−0.394604	−	0.0498501i	−0.0744724	−	0.997223i	$-0.523727\pi$
$733$	−10.6835	−	1.34964i	−0.394604	−	0.0498501i	−0.320132	+	0.947373i	$0.603727\pi$
$734$	23.8432	−	6.12190i	0.880069	−	0.225963i
$735$	13.4020	+	11.9082i	0.494340	+	0.439241i
$736$	−4.83311	−	5.84223i	−0.178151	−	0.215347i
$737$	−15.3841	+	18.5962i	−0.566680	+	0.684998i
$738$	−1.91666	−	3.02017i	−0.0705531	−	0.111174i
$739$	−0.493036	−	7.83658i	−0.0181366	−	0.288273i	−0.996632	−	0.0820045i	$-0.973868\pi$
$739$	−0.493036	−	7.83658i	−0.0181366	−	0.288273i	0.978495	−	0.206269i	$-0.0661322\pi$
$740$	−7.12931	−	3.66748i	−0.262079	−	0.134819i
$741$	−1.17972	+	1.42603i	−0.0433379	+	0.0523866i
$742$	3.69124	+	19.3502i	0.135510	+	0.710367i
$743$	30.4863	−	22.1496i	1.11843	−	0.812590i	0.134463	−	0.990919i	$-0.457069\pi$
$743$	30.4863	−	22.1496i	1.11843	−	0.812590i	0.983971	+	0.178329i	$0.0570691\pi$
$744$	−7.08074	+	3.89267i	−0.259592	+	0.142712i
$745$	25.8920	+	5.89314i	0.948611	+	0.215908i
$746$	−9.07877	+	1.14692i	−0.332397	+	0.0419916i
$747$	−4.94720	−	10.5133i	−0.181008	−	0.384663i
$748$	−0.320496	−	5.09415i	−0.0117185	−	0.186260i
$749$	−6.43069			−0.234972
$750$	−5.19139	+	9.90200i	−0.189563	+	0.361570i
$751$	30.7119			1.12069			0.560346	−	0.828259i	$-0.310668\pi$
$751$	30.7119			1.12069			0.560346	+	0.828259i	$0.310668\pi$
$752$	0.745717	+	11.8528i	0.0271935	+	0.432228i
$753$	9.28448	+	19.7305i	0.338345	+	0.719020i
$754$	3.84552	−	0.485802i	0.140046	−	0.0176919i
$755$	2.01401	+	22.2261i	0.0732972	+	0.808892i
$756$	3.39592	−	1.86693i	0.123509	−	0.0678994i
$757$	10.7598	−	7.81748i	0.391073	−	0.284131i	−0.374822	−	0.927097i	$-0.622296\pi$
$757$	10.7598	−	7.81748i	0.391073	−	0.284131i	0.765895	+	0.642966i	$0.222296\pi$
$758$	−3.54061	−	18.5605i	−0.128601	−	0.674149i
$759$	24.1572	−	29.2011i	0.876852	−	1.05993i
$760$	−2.43883	−	4.83275i	−0.0884657	−	0.175302i
$761$	0.339737	+	5.39997i	0.0123155	+	0.195749i	0.999374	+	0.0353865i	$0.0112662\pi$
$761$	0.339737	+	5.39997i	0.0123155	+	0.195749i	−0.987058	+	0.160362i	$0.948734\pi$
$762$	5.22236	+	8.22913i	0.189186	+	0.298110i
$763$	23.1213	−	27.9489i	0.837048	−	1.01182i
$764$	0.957948	+	1.15796i	0.0346573	+	0.0418935i
$765$	2.27248	+	0.223712i	0.0821616	+	0.00808834i
$766$	−36.7954	+	9.44746i	−1.32947	+	0.341351i
$767$	−6.15999	−	0.778188i	−0.222425	−	0.0280988i
$768$	0.809017	+	0.587785i	0.0291929	+	0.0212099i
$769$	9.73604	−	20.6901i	0.351090	−	0.746105i	−0.648799	−	0.760960i	$-0.724728\pi$
$769$	9.73604	−	20.6901i	0.351090	−	0.746105i	0.999890	+	0.0148545i	$0.00472850\pi$
$770$	−43.1035	−	4.24330i	−1.55334	−	0.152918i
$771$	−24.3837	−	13.4051i	−0.878159	−	0.482772i
$772$	24.3478	−	3.07584i	0.876295	−	0.110702i
$773$	−45.1646	+	17.8819i	−1.62446	+	0.643168i	−0.991391	−	0.130931i	$-0.958203\pi$
$773$	−45.1646	+	17.8819i	−1.62446	+	0.643168i	−0.633065	+	0.774099i	$0.718203\pi$
$774$	3.00936	−	2.18642i	0.108169	−	0.0785894i
$775$	−10.3507	+	39.0526i	−0.371808	+	1.40281i
$776$	10.1591	+	7.38104i	0.364691	+	0.264964i
$777$	13.4581	+	3.45545i	0.482806	+	0.123964i
$778$	−12.3879	+	11.6330i	−0.444128	+	0.417064i
$779$	6.31251	−	5.92784i	0.226169	−	0.212387i
$780$	−0.955369	−	1.41758i	−0.0342077	−	0.0507577i
$781$	3.15500	+	0.398569i	0.112895	+	0.0142619i
$782$	2.39271	+	7.36400i	0.0855631	+	0.263336i
$783$	4.44297	−	2.44255i	0.158779	−	0.0872894i
$784$	0.503437	−	8.00190i	0.0179799	−	0.285782i
$785$	16.8670	−	28.2696i	0.602008	−	1.00898i
$786$	−3.45945	+	5.45123i	−0.123395	+	0.194439i
$787$	4.42945	−	1.13729i	0.157893	−	0.0405400i	−0.168916	−	0.985630i	$-0.554027\pi$
$787$	4.42945	−	1.13729i	0.157893	−	0.0405400i	0.326809	+	0.945090i	$0.394027\pi$
$788$	16.6545	+	6.59399i	0.593293	+	0.234901i
$789$	−27.7406	−	7.12257i	−0.987590	−	0.253570i
$790$	7.81795	+	2.84895i	0.278150	+	0.101361i
$791$	−56.6103	−	22.4136i	−2.01283	−	0.796936i
$792$	−2.12816	+	4.52257i	−0.0756209	+	0.160703i
$793$	3.29847	−	10.1517i	0.117132	−	0.360496i
$794$	−4.50299	−	23.6055i	−0.159805	−	0.837728i
$795$	9.00831	−	6.93175i	0.319492	−	0.245844i
$796$	−7.15676	−	15.2089i	−0.253665	−	0.539065i
$797$	8.46072	−	44.3527i	0.299694	−	1.57105i	−0.439930	−	0.898032i	$-0.644997\pi$
$797$	8.46072	−	44.3527i	0.299694	−	1.57105i	0.739625	−	0.673020i	$-0.235003\pi$
$798$	5.98004	+	7.22862i	0.211691	+	0.255890i
$799$	3.74775	−	11.5344i	0.132586	−	0.408058i
$800$	4.91856	−	0.898763i	0.173897	−	0.0317761i
$801$	−1.96583	−	6.05022i	−0.0694594	−	0.213774i
$802$	9.12973	−	14.3862i	0.322382	−	0.507993i
$803$	71.1335	+	39.1060i	2.51025	+	1.38002i
$804$	−0.904793	+	4.74309i	−0.0319096	+	0.167276i
$805$	64.9335	−	10.0263i	2.28861	−	0.353382i
$806$	−4.50305	−	4.22865i	−0.158613	−	0.148948i
$807$	−0.116569			−0.00410341
$808$	−3.21133	−	3.01564i	−0.112974	−	0.106090i
$809$	17.0315	+	26.8374i	0.598797	+	0.943553i	0.999625	+	0.0273997i	$0.00872270\pi$
$809$	17.0315	+	26.8374i	0.598797	+	0.943553i	−0.400827	+	0.916154i	$0.631277\pi$
$810$	−1.84452	−	1.26402i	−0.0648097	−	0.0444133i
$811$	28.0875	−	11.1206i	0.986286	−	0.390498i	0.181064	−	0.983471i	$-0.442046\pi$
$811$	28.0875	−	11.1206i	0.986286	−	0.390498i	0.805222	+	0.592973i	$0.202046\pi$
$812$	1.23371	−	19.6093i	0.0432948	−	0.688151i
$813$	1.97900	−	31.4553i	0.0694066	−	1.10319i
$814$	−16.6626	+	6.59720i	−0.584025	+	0.231232i
$815$	−5.95073	−	16.7322i	−0.208445	−	0.586104i
$816$	−0.547184	−	0.862224i	−0.0191553	−	0.0301839i
$817$	6.56445	+	6.16443i	0.229661	+	0.215666i
$818$	6.51536			0.227804
$819$	2.15966	+	2.02806i	0.0754648	+	0.0708662i
$820$	3.60353	+	7.14069i	0.125841	+	0.249364i
$821$	−3.05260	+	16.0023i	−0.106536	+	0.558484i	0.888492	+	0.458892i	$0.151754\pi$
$821$	−3.05260	+	16.0023i	−0.106536	+	0.558484i	−0.995028	+	0.0995914i	$0.968246\pi$
$822$	−2.79080	−	1.53425i	−0.0973402	−	0.0535132i
$823$	11.1097	−	17.5061i	0.387260	−	0.610223i	−0.593642	−	0.804729i	$-0.702310\pi$
$823$	11.1097	−	17.5061i	0.387260	−	0.610223i	0.980901	+	0.194506i	$0.0623104\pi$
$824$	−3.31545	−	10.2039i	−0.115499	−	0.355470i
$825$	9.01933	+	23.3071i	0.314013	+	0.811449i
$826$	−9.72584	+	29.9331i	−0.338405	+	1.04150i
$827$	−11.0452	−	13.3513i	−0.384078	−	0.464271i	0.542674	−	0.839943i	$-0.317412\pi$
$827$	−11.0452	−	13.3513i	−0.384078	−	0.464271i	−0.926753	+	0.375672i	$0.877412\pi$
$828$	1.42077	−	7.44795i	0.0493753	−	0.258834i
$829$	−5.41331	−	11.5039i	−0.188012	−	0.399546i	0.788492	−	0.615045i	$-0.210862\pi$
$829$	−5.41331	−	11.5039i	−0.188012	−	0.399546i	−0.976504	+	0.215499i	$0.930862\pi$
$830$	8.70591	+	24.4792i	0.302186	+	0.849686i
$831$	−2.07572	−	10.8813i	−0.0720060	−	0.377469i
$832$	−0.236242	+	0.727079i	−0.00819023	+	0.0252069i
$833$	−3.48614	+	7.40841i	−0.120787	+	0.256686i
$834$	−7.66732	−	3.03571i	−0.265498	−	0.105118i
$835$	−43.9418	+	12.5816i	−1.52067	+	0.435404i
$836$	−11.7201	−	3.00920i	−0.405347	−	0.104076i
$837$	−7.51279	−	2.97452i	−0.259680	−	0.102815i
$838$	−4.82238	+	1.23818i	−0.166586	+	0.0427721i
$839$	24.9273	−	39.2791i	0.860586	−	1.35607i	−0.0728582	−	0.997342i	$-0.523212\pi$
$839$	24.9273	−	39.2791i	0.860586	−	1.35607i	0.933444	−	0.358724i	$-0.116788\pi$
$840$	−7.96597	+	3.41055i	−0.274852	+	0.117675i
$841$	−0.206829	+	3.28746i	−0.00713205	+	0.113361i
$842$	−26.8579	+	14.7652i	−0.925583	+	0.508844i
$843$	−6.90100	−	21.2391i	−0.237683	−	0.731514i
$844$	2.95620	+	0.373455i	0.101757	+	0.0128549i
$845$	−17.1005	+	21.8701i	−0.588276	+	0.752354i
$846$	−8.65742	+	8.12986i	−0.297648	+	0.279510i
$847$	−39.5006	+	37.0935i	−1.35726	+	1.27455i
$848$	−4.92358	−	1.26416i	−0.169077	−	0.0434115i
$849$	14.7338	+	10.7048i	0.505664	+	0.367386i
$850$	−5.00796	−	0.995660i	−0.171772	−	0.0341508i
$851$	21.9938	−	15.9794i	0.753938	−	0.547768i
$852$	0.591555	−	0.234213i	0.0202664	−	0.00802402i
$853$	−44.7513	+	5.65341i	−1.53226	+	0.193569i	−0.845760	−	0.533564i	$-0.820852\pi$
$853$	−44.7513	+	5.65341i	−1.53226	+	0.193569i	−0.686497	+	0.727133i	$0.740852\pi$
$854$	−47.4147	−	26.0665i	−1.62250	−	0.891976i
$855$	2.16912	−	4.95966i	0.0741825	−	0.169617i
$856$	0.706545	−	1.50148i	0.0241492	−	0.0513197i
$857$	−7.86685	−	5.71560i	−0.268727	−	0.195241i	0.445259	−	0.895402i	$-0.353112\pi$
$857$	−7.86685	−	5.71560i	−0.268727	−	0.195241i	−0.713985	+	0.700161i	$0.753112\pi$
$858$	−3.79103	−	0.478919i	−0.129424	−	0.0163500i
$859$	−20.0507	+	5.14814i	−0.684121	+	0.175652i	−0.574726	−	0.818346i	$-0.694891\pi$
$859$	−20.0507	+	5.14814i	−0.684121	+	0.175652i	−0.109395	+	0.993998i	$0.534891\pi$
$860$	−7.17573	+	4.20622i	−0.244690	+	0.143431i
$861$	−8.83588	−	10.6807i	−0.301126	−	0.363999i
$862$	1.69316	−	2.04668i	0.0576693	−	0.0697102i
$863$	11.2275	+	17.6917i	0.382189	+	0.602233i	0.979903	−	0.199476i	$-0.0639241\pi$
$863$	11.2275	+	17.6917i	0.382189	+	0.602233i	−0.597714	+	0.801710i	$0.703924\pi$
$864$	0.0627905	+	0.998027i	0.00213618	+	0.0339536i
$865$	0.882493	−	5.43526i	0.0300057	−	0.184804i
$866$	6.75058	−	8.16005i	0.229394	−	0.277290i
$867$	−2.99007	−	15.6745i	−0.101548	−	0.532334i
$868$	−25.3327	+	18.4053i	−0.859849	+	0.624717i
$869$	16.2990	−	8.96043i	0.552905	−	0.303962i
$870$	−10.4221	+	4.46210i	−0.353342	+	0.151280i
$871$	−3.66235	+	0.462663i	−0.124094	+	0.0156767i
$872$	3.98535	+	8.46931i	0.134961	+	0.286807i
$873$	0.788484	+	12.5326i	0.0266861	+	0.424164i
$874$	18.3557			0.620892
$875$	−15.1500	+	40.5918i	−0.512163	+	1.37225i
$876$	16.2404			0.548714
$877$	−0.484381	−	7.69901i	−0.0163564	−	0.259977i	−0.997703	−	0.0677329i	$-0.978423\pi$
$877$	−0.484381	−	7.69901i	−0.0163564	−	0.259977i	0.981347	−	0.192244i	$-0.0615766\pi$
$878$	−3.10353	−	6.59534i	−0.104739	−	0.222582i
$879$	−7.67147	+	0.969133i	−0.258752	+	0.0326880i
$880$	5.72658	−	9.59792i	0.193043	−	0.323546i
$881$	13.7634	−	7.56649i	0.463700	−	0.254921i	−0.232736	−	0.972540i	$-0.574768\pi$
$881$	13.7634	−	7.56649i	0.463700	−	0.254921i	0.696436	+	0.717618i	$0.254768\pi$
$882$	6.48647	−	4.71270i	0.218411	−	0.158685i
$883$	2.58305	+	13.5408i	0.0869265	+	0.455685i	0.998961	+	0.0455714i	$0.0145109\pi$
$883$	2.58305	+	13.5408i	0.0869265	+	0.455685i	−0.912035	+	0.410113i	$0.865489\pi$
$884$	0.497637	−	0.601540i	0.0167374	−	0.0202320i
$885$	17.9478	−	2.77131i	0.603309	−	0.0931565i
$886$	−0.881996	−	14.0189i	−0.0296312	−	0.470975i
$887$	−31.5391	−	49.6976i	−1.05898	−	1.66868i	−0.658966	−	0.752172i	$-0.729006\pi$
$887$	−31.5391	−	49.6976i	−1.05898	−	1.66868i	−0.400012	−	0.916510i	$-0.630994\pi$
$888$	−2.28546	+	2.76264i	−0.0766949	+	0.0927082i
$889$	24.0754	+	29.1021i	0.807462	+	0.976054i
$890$	3.04918	+	13.8943i	0.102209	+	0.465737i
$891$	−4.84125	+	1.24302i	−0.162188	+	0.0416428i
$892$	6.35380	+	0.802671i	0.212741	+	0.0268754i
$893$	−23.2601	−	16.8994i	−0.778368	−	0.565518i
$894$	5.05630	−	10.7452i	0.169108	−	0.359373i
$895$	−5.95348	+	3.48977i	−0.199003	+	0.116650i
$896$	3.39592	+	1.86693i	0.113450	+	0.0623696i
$897$	5.75090	−	0.726508i	0.192017	−	0.0242574i
$898$	−19.1749	+	7.59186i	−0.639873	+	0.253344i
$899$	−33.1435	+	24.0801i	−1.10540	+	0.803117i
$900$	3.82772	+	3.21692i	0.127591	+	0.107231i
$901$	4.19963	+	3.05121i	0.139910	+	0.101651i
$902$	17.3172	+	4.44629i	0.576598	+	0.148045i
$903$	10.5082	−	9.86782i	0.349690	−	0.328380i
$904$	11.4531	−	10.7552i	0.380925	−	0.357712i
$905$	0.383385	−	10.8574i	0.0127441	−	0.360912i
$906$	9.90186	+	1.25090i	0.328967	+	0.0415582i
$907$	17.3407	+	53.3691i	0.575788	+	1.77209i	0.633481	+	0.773758i	$0.281626\pi$
$907$	17.3407	+	53.3691i	0.575788	+	1.77209i	−0.0576930	+	0.998334i	$0.518374\pi$
$908$	6.57908	−	3.61688i	0.218334	−	0.120030i
$909$	0.276612	−	4.39662i	0.00917463	−	0.145827i
$910$	−4.36164	−	4.98618i	−0.144587	−	0.165290i
$911$	19.1114	−	30.1147i	0.633188	−	0.997744i	−0.364593	−	0.931167i	$-0.618792\pi$
$911$	19.1114	−	30.1147i	0.633188	−	0.997744i	0.997781	−	0.0665775i	$-0.0212080\pi$
$912$	−2.34482	+	0.602049i	−0.0776449	+	0.0199358i
$913$	53.9975	+	21.3791i	1.78706	+	0.707545i
$914$	−21.3989	−	5.49430i	−0.707812	−	0.181735i
$915$	−1.10174	+	31.2011i	−0.0364223	+	1.03148i
$916$	−18.9491	−	7.50249i	−0.626097	−	0.247889i
$917$	−10.6529	+	22.6387i	−0.351791	+	0.747594i
$918$	0.315567	−	0.971215i	0.0104153	−	0.0320549i
$919$	−0.153639	−	0.805404i	−0.00506809	−	0.0265678i	0.979663	−	0.200648i	$-0.0643048\pi$
$919$	−0.153639	−	0.805404i	−0.00506809	−	0.0265678i	−0.984731	+	0.174080i	$0.944305\pi$
$920$	−4.79328	+	16.2628i	−0.158030	+	0.536167i
$921$	5.43661	+	11.5534i	0.179142	+	0.380697i
$922$	−4.07877	+	21.3817i	−0.134327	+	0.704168i
$923$	0.310042	+	0.374777i	0.0102052	+	0.0123359i
$924$	−5.98556	+	18.4216i	−0.196910	+	0.606028i
$925$	2.10879	+	17.8028i	0.0693366	+	0.585353i
$926$	−2.21429	−	6.81487i	−0.0727659	−	0.223951i
$927$	5.74890	−	9.05882i	0.188819	−	0.297531i
$928$	4.44297	+	2.44255i	0.145848	+	0.0801805i
$929$	4.68685	−	24.5693i	0.153770	−	0.806093i	−0.818906	−	0.573928i	$-0.805419\pi$
$929$	4.68685	−	24.5693i	0.153770	−	0.806093i	0.972676	−	0.232165i	$-0.0745810\pi$
$930$	16.0667	+	8.26506i	0.526847	+	0.271022i
$931$	14.1492	+	13.2870i	0.463723	+	0.435464i
$932$	8.16966			0.267606
$933$	20.9540	+	19.6771i	0.686002	+	0.644198i
$934$	−20.5342	−	32.3567i	−0.671899	−	1.05874i
$935$	−9.04541	+	6.96029i	−0.295817	+	0.227626i
$936$	−0.710811	+	0.281430i	−0.0232336	+	0.00919883i
$937$	−0.241653	+	3.84096i	−0.00789446	+	0.125479i	0.992106	+	0.125406i	$0.0400233\pi$
$937$	−0.241653	+	3.84096i	−0.00789446	+	0.125479i	−1.00000		7.30620e-5i	$0.999977\pi$
$938$	−1.17495	+	18.6753i	−0.0383634	+	0.609769i
$939$	−11.4557	+	4.53563i	−0.373843	+	0.148015i
$940$	21.0465	−	16.1949i	0.686460	−	0.528219i
$941$	22.8287	+	35.9723i	0.744195	+	1.17266i	0.979637	+	0.200775i	$0.0643461\pi$
$941$	22.8287	+	35.9723i	0.744195	+	1.17266i	−0.235442	+	0.971888i	$0.575654\pi$
$942$	−10.7318	−	10.0778i	−0.349660	−	0.328352i
$943$	−27.1218			−0.883206
$944$	−5.92041	−	5.55964i	−0.192693	−	0.180951i
$945$	−7.70558	−	3.96392i	−0.250662	−	0.128946i
$946$	−3.48387	+	18.2631i	−0.113270	+	0.593785i
$947$	2.78200	+	1.52942i	0.0904030	+	0.0496995i	0.526314	−	0.850290i	$-0.323574\pi$
$947$	2.78200	+	1.52942i	0.0904030	+	0.0496995i	−0.435911	+	0.899990i	$0.643574\pi$
$948$	1.99392	−	3.14192i	0.0647596	−	0.102045i
$949$	3.83668	+	11.8081i	0.124544	+	0.383307i
$950$	−5.91348	+	10.5616i	−0.191859	+	0.342663i
$951$	−7.79237	+	23.9824i	−0.252685	+	0.777684i
$952$	−2.52255	−	3.04924i	−0.0817562	−	0.0988263i
$953$	1.12576	−	5.90142i	0.0364668	−	0.191166i	−0.959392	−	0.282075i	$-0.908977\pi$
$953$	1.12576	−	5.90142i	0.0364668	−	0.191166i	0.995859	+	0.0909092i	$0.0289773\pi$
$954$	−2.16436	−	4.59949i	−0.0700736	−	0.148914i
$955$	0.950053	−	3.22337i	0.0307430	−	0.104306i
$956$	5.07957	+	26.6280i	0.164285	+	0.861212i
$957$	−7.83105	+	24.1015i	−0.253142	+	0.779091i
$958$	10.2519	−	21.7865i	0.331225	−	0.703889i
$959$	−11.4750	−	4.54327i	−0.370547	−	0.146710i
$960$	0.0789084	−	2.23468i	0.00254676	−	0.0721238i
$961$	33.2125	+	8.52751i	1.07137	+	0.275081i
$962$	−2.54858	−	1.00906i	−0.0821696	−	0.0325332i
$963$	1.60728	−	0.412680i	0.0517940	−	0.0132984i
$964$	5.33222	−	8.40223i	0.171739	−	0.270618i
$965$	−36.1301	−	41.3036i	−1.16307	−	1.32961i
$966$	1.84499	−	29.3253i	0.0593616	−	0.943526i
$967$	−6.22953	+	3.42471i	−0.200328	+	0.110131i	−0.578760	−	0.815498i	$-0.696463\pi$
$967$	−6.22953	+	3.42471i	−0.200328	+	0.110131i	0.378432	+	0.925629i	$0.376463\pi$
$968$	−4.32091	−	13.2984i	−0.138879	−	0.427426i
$969$	2.45270	+	0.309848i	0.0787921	+	0.00995375i
$970$	0.990882	−	28.0616i	0.0318153	−	0.901005i
$971$	−24.8951	+	23.3781i	−0.798923	+	0.750239i	−0.972078	−	0.234656i	$-0.924604\pi$
$971$	−24.8951	+	23.3781i	−0.798923	+	0.750239i	0.173156	+	0.984894i	$0.444604\pi$
$972$	−0.728969	+	0.684547i	−0.0233817	+	0.0219569i
$973$	−30.9531	−	7.94740i	−0.992310	−	0.254782i
$974$	21.8604	+	15.8825i	0.700453	+	0.508909i
$975$	−1.43469	+	3.54303i	−0.0459468	+	0.113468i
$976$	11.2957	−	8.20680i	0.361566	−	0.262693i
$977$	−30.4556	+	12.0582i	−0.974361	+	0.385777i	−0.800724	−	0.599033i	$-0.795552\pi$
$977$	−30.4556	+	12.0582i	−0.974361	+	0.385777i	−0.173636	+	0.984810i	$0.555552\pi$
$978$	−7.87940	+	0.995399i	−0.251955	+	0.0318294i
$979$	27.8638	+	15.3183i	0.890532	+	0.489574i
$980$	−15.4668	+	9.06623i	−0.494069	+	0.289610i
$981$	−3.98535	+	8.46931i	−0.127243	+	0.270404i
$982$	−2.13101	−	1.54827i	−0.0680034	−	0.0494074i
$983$	−11.5664	−	1.46117i	−0.368910	−	0.0466041i	−0.0613068	−	0.998119i	$-0.519527\pi$
$983$	−11.5664	−	1.46117i	−0.368910	−	0.0466041i	−0.307603	+	0.951515i	$0.599527\pi$
$984$	3.46463	−	0.889565i	0.110448	−	0.0283583i
$985$	−8.58562	−	39.1223i	−0.273561	−	1.24654i
$986$	−3.30031	−	3.98939i	−0.105103	−	0.127048i
$987$	−29.3366	+	35.4619i	−0.933795	+	1.12876i
$988$	−0.991684	−	1.56264i	−0.0315497	−	0.0497143i
$989$	−1.77096	−	28.1486i	−0.0563132	−	0.895073i
$990$	11.0456	−	1.70554i	0.351052	−	0.0542056i
$991$	20.1989	−	24.4163i	0.641640	−	0.775610i	−0.344986	−	0.938608i	$-0.612116\pi$
$991$	20.1989	−	24.4163i	0.641640	−	0.775610i	0.986626	+	0.162998i	$0.0521164\pi$
$992$	−1.51408	−	7.93708i	−0.0480721	−	0.252003i
$993$	14.7311	−	10.7028i	0.467478	−	0.339642i
$994$	2.16060	−	1.18780i	0.0685302	−	0.0376748i
$995$	−19.2578	+	32.2767i	−0.610514	+	1.02324i
$996$	11.5275	−	1.45627i	0.365264	−	0.0461436i
$997$	20.1983	+	42.9237i	0.639688	+	1.35941i	0.917101	+	0.398655i	$0.130523\pi$
$997$	20.1983	+	42.9237i	0.639688	+	1.35941i	−0.277413	+	0.960751i	$0.589477\pi$
$998$	−0.441028	−	7.00994i	−0.0139605	−	0.221896i
$999$	−3.58546			−0.113439

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.m.c.31.5	✓	120
125.121	even	25	inner	750.2.m.c.121.5	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.m.c.31.5	✓	120	1.1	even	1	trivial
750.2.m.c.121.5	yes	120	125.121	even	25	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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.m (of order \(25\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0627905 - 0.998027i) q^{2} +(0.425779 + 0.904827i) q^{3} +(-0.992115 + 0.125333i) q^{4} +(1.47222 + 1.68302i) q^{5} +(0.876307 - 0.481754i) q^{6} +(3.13516 - 2.27783i) q^{7} +(0.187381 + 0.982287i) q^{8} +(-0.637424 + 0.770513i) q^{9} +O(q^{10})\)	\(q+(-0.0627905 - 0.998027i) q^{2} +(0.425779 + 0.904827i) q^{3} +(-0.992115 + 0.125333i) q^{4} +(1.47222 + 1.68302i) q^{5} +(0.876307 - 0.481754i) q^{6} +(3.13516 - 2.27783i) q^{7} +(0.187381 + 0.982287i) q^{8} +(-0.637424 + 0.770513i) q^{9} +(1.58726 - 1.57499i) q^{10} +(-0.313844 - 4.98841i) q^{11} +(-0.535827 - 0.844328i) q^{12} +(0.487308 - 0.589055i) q^{13} +(-2.47019 - 2.98595i) q^{14} +(-0.896006 + 2.04870i) q^{15} +(0.968583 - 0.248690i) q^{16} +(-1.01314 - 0.127990i) q^{17} +(0.809017 + 0.587785i) q^{18} +(-1.03076 + 2.19048i) q^{19} +(-1.67155 - 1.48524i) q^{20} +(3.39592 + 1.86693i) q^{21} +(-4.95886 + 0.626450i) q^{22} +(7.04980 - 2.79121i) q^{23} +(-0.809017 + 0.587785i) q^{24} +(-0.665144 + 4.95556i) q^{25} +(-0.618491 - 0.449360i) q^{26} +(-0.968583 - 0.248690i) q^{27} +(-2.82495 + 2.65280i) q^{28} +(-3.69595 + 3.47073i) q^{29} +(2.10092 + 0.765599i) q^{30} +(8.01649 + 1.01272i) q^{31} +(-0.309017 - 0.951057i) q^{32} +(4.38002 - 2.40794i) q^{33} +(-0.0641214 + 1.01918i) q^{34} +(8.44928 + 1.92309i) q^{35} +(0.535827 - 0.844328i) q^{36} +(3.47281 - 0.891667i) q^{37} +(2.25088 + 0.891186i) q^{38} +(0.740478 + 0.190123i) q^{39} +(-1.37735 + 1.76151i) q^{40} +(-3.32582 - 1.31678i) q^{41} +(1.65001 - 3.50645i) q^{42} +(1.14947 - 3.53771i) q^{43} +(0.936583 + 4.90974i) q^{44} +(-2.23522 + 0.0615637i) q^{45} +(-3.22837 - 6.86063i) q^{46} +(-2.22539 + 11.6659i) q^{47} +(0.637424 + 0.770513i) q^{48} +(2.47761 - 7.62530i) q^{49} +(4.98755 + 0.352669i) q^{50} +(-0.315567 - 0.971215i) q^{51} +(-0.409638 + 0.645486i) q^{52} +(-4.45451 - 2.44889i) q^{53} +(-0.187381 + 0.982287i) q^{54} +(7.93357 - 7.87224i) q^{55} +(2.82495 + 2.65280i) q^{56} -2.42088 q^{57} +(3.69595 + 3.47073i) q^{58} +(-4.35178 - 6.85732i) q^{59} +(0.632170 - 2.14485i) q^{60} +(12.9818 - 5.13984i) q^{61} +(0.507360 - 8.06426i) q^{62} +(-0.243330 + 3.86762i) q^{63} +(-0.929776 + 0.368125i) q^{64} +(1.70882 - 0.0470652i) q^{65} +(-2.67821 - 4.22018i) q^{66} +(-3.51991 - 3.30542i) q^{67} +1.02120 q^{68} +(5.52723 + 5.19041i) q^{69} +(1.38876 - 8.55336i) q^{70} +(-0.119218 + 0.624964i) q^{71} +(-0.876307 - 0.481754i) q^{72} +(-8.70206 + 13.7123i) q^{73} +(-1.10797 - 3.40997i) q^{74} +(-4.76713 + 1.50813i) q^{75} +(0.748093 - 2.30239i) q^{76} +(-12.3467 - 14.9246i) q^{77} +(0.143252 - 0.750955i) q^{78} +(1.58441 + 3.36705i) q^{79} +(1.84452 + 1.26402i) q^{80} +(-0.187381 - 0.982287i) q^{81} +(-1.10536 + 3.40193i) q^{82} +(-4.94720 + 10.5133i) q^{83} +(-3.60313 - 1.42658i) q^{84} +(-1.27616 - 1.89357i) q^{85} +(-3.60290 - 0.925069i) q^{86} +(-4.71407 - 1.86643i) q^{87} +(4.84125 - 1.24302i) q^{88} +(-3.40870 + 5.37126i) q^{89} +(0.201793 + 2.22694i) q^{90} +(0.186025 - 2.95678i) q^{91} +(-6.64438 + 3.65278i) q^{92} +(2.49692 + 7.68473i) q^{93} +(11.7826 + 1.48849i) q^{94} +(-5.20414 + 1.49007i) q^{95} +(0.728969 - 0.684547i) q^{96} +(9.15393 - 8.59611i) q^{97} +(-7.76583 - 1.99393i) q^{98} +(4.04369 + 2.93791i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 20 q^{5} - 5 q^{7}+O(q^{10}) \) 120 * q + 20 * q^5 - 5 * q^7	\( 120 q + 20 q^{5} - 5 q^{7} + 20 q^{10} + 10 q^{13} + 20 q^{14} + 15 q^{17} + 30 q^{18} - 5 q^{19} - 5 q^{21} + 10 q^{22} - 15 q^{23} - 30 q^{24} - 20 q^{25} - 10 q^{26} + 5 q^{28} - 5 q^{29} + 5 q^{30} + 55 q^{31} + 30 q^{32} + 10 q^{33} + 25 q^{34} - 10 q^{35} - 5 q^{37} - 35 q^{38} - 10 q^{39} - 5 q^{40} + 55 q^{41} + 5 q^{42} + 5 q^{43} + 15 q^{44} - 5 q^{45} - 10 q^{46} + 10 q^{47} - 25 q^{49} + 20 q^{50} + 15 q^{51} - 40 q^{52} + 30 q^{53} - 10 q^{55} - 5 q^{56} + 60 q^{57} + 5 q^{58} + 20 q^{59} - 20 q^{60} - 60 q^{61} + 25 q^{62} + 5 q^{63} + 15 q^{65} - 25 q^{66} + 95 q^{67} + 60 q^{68} - 10 q^{69} + 40 q^{70} - 90 q^{71} - 30 q^{74} - 55 q^{75} + 15 q^{76} + 95 q^{77} - 5 q^{78} - 90 q^{79} - 5 q^{80} - 45 q^{82} + 95 q^{83} - 5 q^{84} + 115 q^{85} - 15 q^{86} + 10 q^{87} + 65 q^{89} + 5 q^{90} - 85 q^{91} - 65 q^{92} - 30 q^{93} - 10 q^{94} - 55 q^{95} - 35 q^{98} + 10 q^{99}+O(q^{100}) \) 120 * q + 20 * q^5 - 5 * q^7 + 20 * q^10 + 10 * q^13 + 20 * q^14 + 15 * q^17 + 30 * q^18 - 5 * q^19 - 5 * q^21 + 10 * q^22 - 15 * q^23 - 30 * q^24 - 20 * q^25 - 10 * q^26 + 5 * q^28 - 5 * q^29 + 5 * q^30 + 55 * q^31 + 30 * q^32 + 10 * q^33 + 25 * q^34 - 10 * q^35 - 5 * q^37 - 35 * q^38 - 10 * q^39 - 5 * q^40 + 55 * q^41 + 5 * q^42 + 5 * q^43 + 15 * q^44 - 5 * q^45 - 10 * q^46 + 10 * q^47 - 25 * q^49 + 20 * q^50 + 15 * q^51 - 40 * q^52 + 30 * q^53 - 10 * q^55 - 5 * q^56 + 60 * q^57 + 5 * q^58 + 20 * q^59 - 20 * q^60 - 60 * q^61 + 25 * q^62 + 5 * q^63 + 15 * q^65 - 25 * q^66 + 95 * q^67 + 60 * q^68 - 10 * q^69 + 40 * q^70 - 90 * q^71 - 30 * q^74 - 55 * q^75 + 15 * q^76 + 95 * q^77 - 5 * q^78 - 90 * q^79 - 5 * q^80 - 45 * q^82 + 95 * q^83 - 5 * q^84 + 115 * q^85 - 15 * q^86 + 10 * q^87 + 65 * q^89 + 5 * q^90 - 85 * q^91 - 65 * q^92 - 30 * q^93 - 10 * q^94 - 55 * q^95 - 35 * q^98 + 10 * q^99

Introduction

L-functions

Modular forms

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