LMFDB - Embedded newform 64.2.i.a.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,2,Mod(5,64)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(64, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("64.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	64.i (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.511042572936$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			13.2
Character	$\chi$	$=$	64.13
Dual form			64.2.i.a.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20609 - 0.738481i) q^{2} +(2.51381 - 1.67967i) q^{3} +(0.909293 + 1.78134i) q^{4} +(-2.28487 + 0.454489i) q^{5} +(-4.27227 + 0.169433i) q^{6} +(0.303950 + 0.733799i) q^{7} +(0.218802 - 2.81995i) q^{8} +(2.34987 - 5.67309i) q^{9} +O(q^{10})$	\(q+(-1.20609 - 0.738481i) q^{2} +(2.51381 - 1.67967i) q^{3} +(0.909293 + 1.78134i) q^{4} +(-2.28487 + 0.454489i) q^{5} +(-4.27227 + 0.169433i) q^{6} +(0.303950 + 0.733799i) q^{7} +(0.218802 - 2.81995i) q^{8} +(2.34987 - 5.67309i) q^{9} +(3.09139 + 1.13918i) q^{10} +(-2.41516 + 3.61454i) q^{11} +(5.27786 + 2.95064i) q^{12} +(-0.174791 - 0.0347682i) q^{13} +(0.175307 - 1.10949i) q^{14} +(-4.98033 + 4.98033i) q^{15} +(-2.34637 + 3.23953i) q^{16} +(0.422266 + 0.422266i) q^{17} +(-7.02362 + 5.10691i) q^{18} +(-0.424489 + 2.13405i) q^{19} +(-2.88722 - 3.65688i) q^{20} +(1.99661 + 1.33409i) q^{21} +(5.58216 - 2.57590i) q^{22} +(6.39382 + 2.64841i) q^{23} +(-4.18656 - 7.45632i) q^{24} +(0.394679 - 0.163481i) q^{25} +(0.185138 + 0.171014i) q^{26} +(-1.85234 - 9.31236i) q^{27} +(-1.03077 + 1.20868i) q^{28} +(-5.22657 - 7.82211i) q^{29} +(9.68459 - 2.32883i) q^{30} -1.80802i q^{31} +(5.22226 - 2.17440i) q^{32} +13.1429i q^{33} +(-0.197454 - 0.821125i) q^{34} +(-1.02799 - 1.53849i) q^{35} +(12.2425 - 0.972570i) q^{36} +(-0.559507 - 2.81283i) q^{37} +(2.08792 - 2.26037i) q^{38} +(-0.497791 + 0.206192i) q^{39} +(0.781702 + 6.54267i) q^{40} +(-4.83885 - 2.00432i) q^{41} +(-1.42289 - 3.08349i) q^{42} +(-6.27110 - 4.19021i) q^{43} +(-8.63483 - 1.01555i) q^{44} +(-2.79080 + 14.0303i) q^{45} +(-5.75571 - 7.91592i) q^{46} +(2.42967 + 2.42967i) q^{47} +(-0.456990 + 12.0847i) q^{48} +(4.50367 - 4.50367i) q^{49} +(-0.596745 - 0.0942900i) q^{50} +(1.77076 + 0.352226i) q^{51} +(-0.0970024 - 0.342978i) q^{52} +(-0.350569 + 0.524664i) q^{53} +(-4.64291 + 12.5994i) q^{54} +(3.87556 - 9.35642i) q^{55} +(2.13578 - 0.696566i) q^{56} +(2.51742 + 6.07759i) q^{57} +(0.527218 + 13.2939i) q^{58} +(8.25271 - 1.64157i) q^{59} +(-13.4003 - 4.34310i) q^{60} +(-2.67124 + 1.78487i) q^{61} +(-1.33519 + 2.18063i) q^{62} +4.87715 q^{63} +(-7.90425 - 1.23402i) q^{64} +0.415178 q^{65} +(9.70580 - 15.8515i) q^{66} +(0.879840 - 0.587891i) q^{67} +(-0.368238 + 1.13616i) q^{68} +(20.5213 - 4.08194i) q^{69} +(0.103696 + 2.61471i) q^{70} +(-0.458776 - 1.10758i) q^{71} +(-15.4837 - 7.86781i) q^{72} +(-0.783268 + 1.89098i) q^{73} +(-1.40241 + 3.80570i) q^{74} +(0.717551 - 1.07389i) q^{75} +(-4.18746 + 1.18431i) q^{76} +(-3.38643 - 0.673603i) q^{77} +(0.752647 + 0.118924i) q^{78} +(-5.97434 + 5.97434i) q^{79} +(3.88883 - 8.46830i) q^{80} +(-7.27213 - 7.27213i) q^{81} +(4.35592 + 5.99077i) q^{82} +(-1.56393 + 7.86242i) q^{83} +(-0.560975 + 4.76973i) q^{84} +(-1.15674 - 0.772908i) q^{85} +(4.46910 + 9.68485i) q^{86} +(-26.2772 - 10.8844i) q^{87} +(9.66439 + 7.60150i) q^{88} +(6.64632 - 2.75300i) q^{89} +(13.7270 - 14.8608i) q^{90} +(-0.0276149 - 0.138830i) q^{91} +(1.09613 + 13.7978i) q^{92} +(-3.03687 - 4.54500i) q^{93} +(-1.13613 - 4.72465i) q^{94} -5.06895i q^{95} +(9.47547 - 14.2377i) q^{96} -9.60392i q^{97} +(-8.75770 + 2.10595i) q^{98} +(14.8303 + 22.1951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) $ 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^23 + 32 * q^24 - 8 * q^25 + 32 * q^26 - 8 * q^27 + 32 * q^28 - 8 * q^29 + 72 * q^30 + 32 * q^32 + 32 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^37 + 32 * q^38 - 8 * q^39 + 32 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 - 32 * q^50 + 24 * q^51 - 56 * q^52 - 8 * q^53 - 72 * q^54 + 56 * q^55 - 64 * q^56 - 8 * q^57 - 80 * q^58 + 56 * q^59 - 104 * q^60 - 8 * q^61 - 40 * q^62 + 64 * q^63 - 104 * q^64 - 16 * q^65 - 88 * q^66 + 72 * q^67 - 56 * q^68 - 8 * q^69 - 104 * q^70 + 56 * q^71 - 80 * q^72 - 8 * q^73 - 64 * q^74 + 56 * q^75 - 72 * q^76 - 8 * q^77 - 32 * q^78 + 24 * q^79 + 32 * q^80 - 8 * q^81 + 72 * q^82 - 8 * q^83 + 104 * q^84 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 72 * q^88 - 8 * q^89 + 136 * q^90 - 8 * q^91 + 144 * q^92 + 16 * q^93 + 88 * q^94 + 128 * q^96 + 128 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{15}{16}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.20609	−	0.738481i	−0.852832	−	0.522185i
$2$	−1.20609	−	0.738481i	−0.852832	−	0.522185i
$3$	2.51381	−	1.67967i	1.45135	−	0.969758i	0.454471	−	0.890761i	$-0.349828\pi$
$3$	2.51381	−	1.67967i	1.45135	−	0.969758i	0.996875	−	0.0789971i	$-0.0251718\pi$
$4$	0.909293	+	1.78134i	0.454646	+	0.890672i
$5$	−2.28487	+	0.454489i	−1.02183	+	0.203254i	−0.677443	−	0.735576i	$-0.736912\pi$
$5$	−2.28487	+	0.454489i	−1.02183	+	0.203254i	−0.344383	+	0.938829i	$0.611912\pi$
$6$	−4.27227	+	0.169433i	−1.74415	+	0.0691707i
$7$	0.303950	+	0.733799i	0.114882	+	0.277350i	0.970854	−	0.239673i	$-0.0770402\pi$
$7$	0.303950	+	0.733799i	0.114882	+	0.277350i	−0.855972	+	0.517023i	$0.827040\pi$
$8$	0.218802	−	2.81995i	0.0773583	−	0.997003i
$9$	2.34987	−	5.67309i	0.783291	−	1.89103i
$10$	3.09139	+	1.13918i	0.977582	+	0.360240i
$11$	−2.41516	+	3.61454i	−0.728198	+	1.08983i	0.263923	+	0.964544i	$0.414983\pi$
$11$	−2.41516	+	3.61454i	−0.728198	+	1.08983i	−0.992121	+	0.125281i	$0.960017\pi$
$12$	5.27786	+	2.95064i	1.52359	+	0.851776i
$13$	−0.174791	−	0.0347682i	−0.0484784	−	0.00964295i	0.170792	−	0.985307i	$-0.445368\pi$
$13$	−0.174791	−	0.0347682i	−0.0484784	−	0.00964295i	−0.219270	+	0.975664i	$0.570368\pi$
$14$	0.175307	−	1.10949i	0.0468527	−	0.296523i
$15$	−4.98033	+	4.98033i	−1.28592	+	1.28592i
$16$	−2.34637	+	3.23953i	−0.586594	+	0.809881i
$17$	0.422266	+	0.422266i	0.102415	+	0.102415i	0.756457	−	0.654043i	$-0.226928\pi$
$17$	0.422266	+	0.422266i	0.102415	+	0.102415i	−0.654043	+	0.756457i	$0.726928\pi$
$18$	−7.02362	+	5.10691i	−1.65548	+	1.20371i
$19$	−0.424489	+	2.13405i	−0.0973844	+	0.489584i	0.901053	+	0.433708i	$0.142795\pi$
$19$	−0.424489	+	2.13405i	−0.0973844	+	0.489584i	−0.998438	+	0.0558761i	$0.982205\pi$
$20$	−2.88722	−	3.65688i	−0.645602	−	0.817703i
$21$	1.99661	+	1.33409i	0.435696	+	0.291123i
$22$	5.58216	−	2.57590i	1.19012	−	0.549184i
$23$	6.39382	+	2.64841i	1.33320	+	0.552231i	0.931568	−	0.363568i	$-0.118442\pi$
$23$	6.39382	+	2.64841i	1.33320	+	0.552231i	0.401636	+	0.915799i	$0.368442\pi$
$24$	−4.18656	−	7.45632i	−0.854579	−	1.52202i
$25$	0.394679	−	0.163481i	0.0789358	−	0.0326963i
$26$	0.185138	+	0.171014i	0.0363086	+	0.0335385i
$27$	−1.85234	−	9.31236i	−0.356484	−	1.79216i
$28$	−1.03077	+	1.20868i	−0.194797	+	0.228418i
$29$	−5.22657	−	7.82211i	−0.970550	−	1.45253i	−0.890097	−	0.455772i	$-0.849363\pi$
$29$	−5.22657	−	7.82211i	−0.970550	−	1.45253i	−0.0804529	−	0.996758i	$-0.525637\pi$
$30$	9.68459	−	2.32883i	1.76816	−	0.425185i
$31$		−	1.80802i		−	0.324729i	−0.986731	−	0.162365i	$-0.948088\pi$
$31$		−	1.80802i		−	0.324729i	0.986731	−	0.162365i	$-0.0519121\pi$
$32$	5.22226	−	2.17440i	0.923174	−	0.384383i
$33$			13.1429i			2.28789i
$34$	−0.197454	−	0.821125i	−0.0338631	−	0.140822i
$35$	−1.02799	−	1.53849i	−0.173762	−	0.260053i
$36$	12.2425	−	0.972570i	2.04041	−	0.162095i
$37$	−0.559507	−	2.81283i	−0.0919823	−	0.462426i	−0.999133	−	0.0416214i	$-0.986748\pi$
$37$	−0.559507	−	2.81283i	−0.0919823	−	0.462426i	0.907151	−	0.420805i	$-0.138252\pi$
$38$	2.08792	−	2.26037i	0.338706	−	0.366681i
$39$	−0.497791	+	0.206192i	−0.0797103	+	0.0330171i
$40$	0.781702	+	6.54267i	0.123598	+	1.03449i
$41$	−4.83885	−	2.00432i	−0.755701	−	0.313022i	−0.0286356	−	0.999590i	$-0.509116\pi$
$41$	−4.83885	−	2.00432i	−0.755701	−	0.313022i	−0.727065	+	0.686568i	$0.759116\pi$
$42$	−1.42289	−	3.08349i	−0.219556	−	0.475793i
$43$	−6.27110	−	4.19021i	−0.956334	−	0.639002i	−0.0236588	−	0.999720i	$-0.507532\pi$
$43$	−6.27110	−	4.19021i	−0.956334	−	0.639002i	−0.932675	+	0.360718i	$0.882532\pi$
$44$	−8.63483	−	1.01555i	−1.30175	−	0.153101i
$45$	−2.79080	+	14.0303i	−0.416027	+	2.09151i
$46$	−5.75571	−	7.91592i	−0.848633	−	1.16714i
$47$	2.42967	+	2.42967i	0.354403	+	0.354403i	0.861745	−	0.507342i	$-0.169372\pi$
$47$	2.42967	+	2.42967i	0.354403	+	0.354403i	−0.507342	+	0.861745i	$0.669372\pi$
$48$	−0.456990	+	12.0847i	−0.0659609	+	1.74427i
$49$	4.50367	−	4.50367i	0.643382	−	0.643382i
$50$	−0.596745	−	0.0942900i	−0.0843925	−	0.0133346i
$51$	1.77076	+	0.352226i	0.247956	+	0.0493216i
$52$	−0.0970024	−	0.342978i	−0.0134518	−	0.0475625i
$53$	−0.350569	+	0.524664i	−0.0481544	+	0.0720682i	−0.854766	−	0.519014i	$-0.826299\pi$
$53$	−0.350569	+	0.524664i	−0.0481544	+	0.0720682i	0.806611	+	0.591082i	$0.201299\pi$
$54$	−4.64291	+	12.5994i	−0.631820	+	1.71457i
$55$	3.87556	−	9.35642i	0.522580	−	1.26162i
$56$	2.13578	−	0.696566i	0.285406	−	0.0930825i
$57$	2.51742	+	6.07759i	0.333440	+	0.804996i
$58$	0.527218	+	13.2939i	0.0692271	+	1.74557i
$59$	8.25271	−	1.64157i	1.07441	−	0.213714i	0.373982	−	0.927436i	$-0.377992\pi$
$59$	8.25271	−	1.64157i	1.07441	−	0.213714i	0.700429	+	0.713722i	$0.252992\pi$
$60$	−13.4003	−	4.34310i	−1.72997	−	0.560692i
$61$	−2.67124	+	1.78487i	−0.342018	+	0.228529i	−0.714702	−	0.699429i	$-0.753438\pi$
$61$	−2.67124	+	1.78487i	−0.342018	+	0.228529i	0.372684	+	0.927958i	$0.378438\pi$
$62$	−1.33519	+	2.18063i	−0.169569	+	0.276940i
$63$	4.87715			0.614463
$64$	−7.90425	−	1.23402i	−0.988031	−	0.154253i
$65$	0.415178			0.0514964
$66$	9.70580	−	15.8515i	1.19470	−	1.95119i
$67$	0.879840	−	0.587891i	0.107490	−	0.0718223i	−0.500664	−	0.865642i	$-0.666911\pi$
$67$	0.879840	−	0.587891i	0.107490	−	0.0718223i	0.608153	+	0.793820i	$0.291911\pi$
$68$	−0.368238	+	1.13616i	−0.0446554	+	0.137780i
$69$	20.5213	−	4.08194i	2.47047	−	0.491407i
$70$	0.103696	+	2.61471i	0.0123940	+	0.312518i
$71$	−0.458776	−	1.10758i	−0.0544467	−	0.131446i	0.894316	−	0.447437i	$-0.147663\pi$
$71$	−0.458776	−	1.10758i	−0.0544467	−	0.131446i	−0.948762	+	0.315991i	$0.897663\pi$
$72$	−15.4837	−	7.86781i	−1.82477	−	0.927230i
$73$	−0.783268	+	1.89098i	−0.0916746	+	0.221322i	−0.963065	−	0.269267i	$-0.913218\pi$
$73$	−0.783268	+	1.89098i	−0.0916746	+	0.221322i	0.871391	+	0.490589i	$0.163218\pi$
$74$	−1.40241	+	3.80570i	−0.163026	+	0.442404i
$75$	0.717551	−	1.07389i	0.0828557	−	0.124002i
$76$	−4.18746	+	1.18431i	−0.480335	+	0.135850i
$77$	−3.38643	−	0.673603i	−0.385920	−	0.0767642i
$78$	0.752647	+	0.118924i	0.0852205	+	0.0134655i
$79$	−5.97434	+	5.97434i	−0.672166	+	0.672166i	−0.958215	−	0.286049i	$-0.907658\pi$
$79$	−5.97434	+	5.97434i	−0.672166	+	0.672166i	0.286049	+	0.958215i	$0.407658\pi$
$80$	3.88883	−	8.46830i	0.434785	−	0.946785i
$81$	−7.27213	−	7.27213i	−0.808014	−	0.808014i
$82$	4.35592	+	5.99077i	0.481031	+	0.661570i
$83$	−1.56393	+	7.86242i	−0.171664	+	0.863012i	0.794930	+	0.606701i	$0.207507\pi$
$83$	−1.56393	+	7.86242i	−0.171664	+	0.863012i	−0.966594	+	0.256312i	$0.917493\pi$
$84$	−0.560975	+	4.76973i	−0.0612074	+	0.520420i
$85$	−1.15674	−	0.772908i	−0.125466	−	0.0838336i
$86$	4.46910	+	9.68485i	0.481915	+	1.04434i
$87$	−26.2772	−	10.8844i	−2.81721	−	1.16693i
$88$	9.66439	+	7.60150i	1.03023	+	0.810323i
$89$	6.64632	−	2.75300i	0.704509	−	0.291817i	−0.00152141	−	0.999999i	$-0.500484\pi$
$89$	6.64632	−	2.75300i	0.704509	−	0.291817i	0.706030	+	0.708182i	$0.250484\pi$
$90$	13.7270	−	14.8608i	1.44696	−	1.56646i
$91$	−0.0276149	−	0.138830i	−0.00289483	−	0.0145533i
$92$	1.09613	+	13.7978i	0.114279	+	1.43852i
$93$	−3.03687	−	4.54500i	−0.314909	−	0.471295i
$94$	−1.13613	−	4.72465i	−0.117183	−	0.487310i
$95$		−	5.06895i		−	0.520064i
$96$	9.47547	−	14.2377i	0.967086	−	1.45313i
$97$		−	9.60392i		−	0.975130i	−0.873087	−	0.487565i	$-0.837885\pi$
$97$		−	9.60392i		−	0.975130i	0.873087	−	0.487565i	$-0.162115\pi$
$98$	−8.75770	+	2.10595i	−0.884661	+	0.212733i
$99$	14.8303	+	22.1951i	1.49050	+	2.23069i
$100$	0.650095	+	0.554407i	0.0650095	+	0.0554407i
$101$	3.03083	+	15.2370i	0.301579	+	1.51614i	0.773099	+	0.634285i	$0.218705\pi$
$101$	3.03083	+	15.2370i	0.301579	+	1.51614i	−0.471520	+	0.881855i	$0.656295\pi$
$102$	−1.87558	−	1.73249i	−0.185710	−	0.171542i
$103$	13.0558	−	5.40788i	1.28642	−	0.532854i	0.368506	−	0.929625i	$-0.379869\pi$
$103$	13.0558	−	5.40788i	1.28642	−	0.532854i	0.917917	+	0.396771i	$0.129869\pi$
$104$	−0.136289	+	0.485296i	−0.0133643	+	0.0475872i
$105$	−5.16833	−	2.14079i	−0.504377	−	0.208920i
$106$	0.810272	−	0.373902i	0.0787005	−	0.0363166i
$107$	12.1990	+	8.15112i	1.17932	+	0.787999i	0.981354	−	0.192209i	$-0.0615652\pi$
$107$	12.1990	+	8.15112i	1.17932	+	0.787999i	0.197970	+	0.980208i	$0.436565\pi$
$108$	14.9042	−	11.7673i	1.43416	−	1.13231i
$109$	1.31130	−	6.59237i	0.125600	−	0.631435i	−0.865781	−	0.500424i	$-0.833178\pi$
$109$	1.31130	−	6.59237i	0.125600	−	0.631435i	0.991381	−	0.131011i	$-0.0418224\pi$
$110$	−11.5838	+	8.42264i	−1.10447	+	0.803067i
$111$	−6.13112	−	6.13112i	−0.581940	−	0.581940i
$112$	−3.09034	−	0.737115i	−0.292010	−	0.0696508i
$113$	−5.92301	+	5.92301i	−0.557190	+	0.557190i	−0.928506	−	0.371317i	$-0.878906\pi$
$113$	−5.92301	+	5.92301i	−0.557190	+	0.557190i	0.371317	+	0.928506i	$0.378906\pi$
$114$	1.45195	−	9.18916i	0.135988	−	0.860644i
$115$	−15.8127	−	3.14535i	−1.47455	−	0.293305i
$116$	9.18140	−	16.4229i	0.852471	−	1.52483i
$117$	−0.607980	+	0.909907i	−0.0562078	+	0.0841209i
$118$	−11.1658	−	4.11460i	−1.02789	−	0.378779i
$119$	−0.181511	+	0.438206i	−0.0166391	+	0.0401703i
$120$	12.9546	+	15.1340i	1.18259	+	1.38154i
$121$	−3.02239	−	7.29671i	−0.274763	−	0.663337i
$122$	4.53984	−	0.180044i	0.411018	−	0.0163005i
$123$	−15.5305	+	3.08921i	−1.40034	+	0.278545i
$124$	3.22070	−	1.64402i	0.289227	−	0.147637i
$125$	8.85761	−	5.91847i	0.792249	−	0.529364i
$126$	−5.88227	−	3.60168i	−0.524034	−	0.320863i
$127$	7.95115			0.705551			0.352775	−	0.935708i	$-0.385238\pi$
$127$	7.95115			0.705551			0.352775	+	0.935708i	$0.385238\pi$
$128$	8.62191	+	7.32548i	0.762077	+	0.647487i
$129$	−22.8025			−2.00765
$130$	−0.500740	−	0.306601i	−0.0439178	−	0.0268907i
$131$	2.99684	−	2.00242i	0.261835	−	0.174953i	−0.417723	−	0.908575i	$-0.637172\pi$
$131$	2.99684	−	2.00242i	0.261835	−	0.174953i	0.679558	+	0.733622i	$0.262172\pi$
$132$	−23.4121	+	11.9508i	−2.03776	+	1.04018i
$133$	−1.69499	+	0.337154i	−0.146974	+	0.0292349i
$134$	−1.49531	+	0.0593021i	−0.129175	+	0.00512292i
$135$	8.46473	+	20.4357i	0.728528	+	1.75882i
$136$	1.28316	−	1.09838i	0.110030	−	0.0941850i
$137$	−5.13309	+	12.3924i	−0.438550	+	1.05875i	0.537900	+	0.843008i	$0.319218\pi$
$137$	−5.13309	+	12.3924i	−0.438550	+	1.05875i	−0.976450	+	0.215744i	$0.930782\pi$
$138$	−27.7649	−	10.2314i	−2.36350	−	0.870954i
$139$	−7.12464	+	10.6628i	−0.604304	+	0.904405i	−0.999902	−	0.0140189i	$-0.995538\pi$
$139$	−7.12464	+	10.6628i	−0.604304	+	0.904405i	0.395598	+	0.918424i	$0.370538\pi$
$140$	1.80585	−	3.23014i	0.152622	−	0.272997i
$141$	10.1887	+	2.02667i	0.858047	+	0.170676i
$142$	−0.264605	+	1.67464i	−0.0222052	+	0.140533i
$143$	0.547820	−	0.547820i	0.0458110	−	0.0458110i
$144$	12.8645	+	20.9237i	1.07204	+	1.74364i
$145$	15.4971	+	15.4971i	1.28696	+	1.28696i
$146$	2.34114	−	1.70225i	0.193754	−	0.140880i
$147$	3.75667	−	18.8860i	0.309845	−	1.55769i
$148$	4.50186	−	3.55436i	0.370051	−	0.292166i
$149$	−18.3515	−	12.2621i	−1.50341	−	1.00455i	−0.989149	−	0.146914i	$-0.953066\pi$
$149$	−18.3515	−	12.2621i	−1.50341	−	1.00455i	−0.514262	−	0.857633i	$-0.671934\pi$
$150$	−1.65848	+	0.765309i	−0.135414	+	0.0624872i
$151$	2.57112	+	1.06499i	0.209235	+	0.0866679i	0.484839	−	0.874603i	$-0.338878\pi$
$151$	2.57112	+	1.06499i	0.209235	+	0.0866679i	−0.275605	+	0.961271i	$0.588878\pi$
$152$	5.92504	+	1.66397i	0.480584	+	0.134966i
$153$	3.38782	−	1.40328i	0.273889	−	0.113449i
$154$	3.58689	+	3.31324i	0.289040	+	0.266988i
$155$	0.821724	+	4.13109i	0.0660025	+	0.331817i
$156$	−0.819935	−	0.699248i	−0.0656474	−	0.0559846i
$157$	10.9729	+	16.4222i	0.875736	+	1.31063i	0.949632	+	0.313366i	$0.101457\pi$
$157$	10.9729	+	16.4222i	0.875736	+	1.31063i	−0.0738963	+	0.997266i	$0.523543\pi$
$158$	11.6175	−	2.79364i	0.924240	−	0.222250i
$159$			1.90774i			0.151294i
$160$	−10.9439	+	7.34168i	−0.865195	+	0.580411i
$161$			5.49676i			0.433206i
$162$	3.40050	+	14.1412i	0.267168	+	1.11103i
$163$	−7.08796	−	10.6079i	−0.555172	−	0.830873i	0.442660	−	0.896690i	$-0.354035\pi$
$163$	−7.08796	−	10.6079i	−0.555172	−	0.830873i	−0.997832	+	0.0658161i	$0.979035\pi$
$164$	−0.829550	−	10.4422i	−0.0647770	−	0.815396i
$165$	−5.97332	−	30.0299i	−0.465022	−	2.33782i
$166$	7.69248	−	8.32783i	0.597052	−	0.646365i
$167$	−4.60049	+	1.90558i	−0.355996	+	0.147459i	−0.553512	−	0.832841i	$-0.686713\pi$
$167$	−4.60049	+	1.90558i	−0.355996	+	0.147459i	0.197516	+	0.980300i	$0.436713\pi$
$168$	4.19894	−	5.33844i	0.323955	−	0.411870i
$169$	−11.9811	−	4.96273i	−0.921622	−	0.381748i
$170$	0.824350	+	1.78642i	0.0632247	+	0.137012i
$171$	11.1092	+	7.42291i	0.849539	+	0.567644i
$172$	1.76195	−	14.9811i	0.134347	−	1.14230i
$173$	4.04445	−	20.3328i	0.307494	−	1.54587i	−0.449998	−	0.893029i	$-0.648575\pi$
$173$	4.04445	−	20.3328i	0.307494	−	1.54587i	0.757492	−	0.652845i	$-0.226425\pi$
$174$	23.6547	+	32.5327i	1.79325	+	2.46629i
$175$	0.239925	+	0.239925i	0.0181366	+	0.0181366i
$176$	−6.04253	−	16.3050i	−0.455473	−	1.22904i
$177$	17.9884	−	17.9884i	1.35209	−	1.35209i
$178$	−10.0491	−	1.58783i	−0.753210	−	0.119013i
$179$	−6.57810	−	1.30847i	−0.491670	−	0.0977993i	−0.0569725	−	0.998376i	$-0.518145\pi$
$179$	−6.57810	−	1.30847i	−0.491670	−	0.0977993i	−0.434698	+	0.900576i	$0.643145\pi$
$180$	−27.5304	+	7.78626i	−2.05200	+	0.580353i
$181$	−12.0521	+	18.0372i	−0.895822	+	1.34069i	0.0440013	+	0.999031i	$0.485989\pi$
$181$	−12.0521	+	18.0372i	−0.895822	+	1.34069i	−0.939823	+	0.341661i	$0.889011\pi$
$182$	−0.0692169	+	0.187834i	−0.00513070	+	0.0139232i
$183$	−3.71700	+	8.97362i	−0.274768	+	0.663349i
$184$	8.86736	−	17.4508i	0.653711	−	1.28649i
$185$	2.55680	+	6.17266i	0.187980	+	0.453823i
$186$	0.306338	+	7.72434i	0.0224618	+	0.566376i
$187$	−2.54614	+	0.506458i	−0.186192	+	0.0370359i
$188$	−2.11879	+	6.53735i	−0.154529	+	0.476785i
$189$	6.27038	−	4.18973i	0.456103	−	0.304758i
$190$	−3.74332	+	6.11360i	−0.271569	+	0.443527i
$191$	−12.1977			−0.882592			−0.441296	−	0.897362i	$-0.645481\pi$
$191$	−12.1977			−0.882592			−0.441296	+	0.897362i	$0.645481\pi$
$192$	−21.9425	+	10.1744i	−1.58356	+	0.734277i
$193$	16.3911			1.17986			0.589929	−	0.807455i	$-0.299156\pi$
$193$	16.3911			1.17986			0.589929	+	0.807455i	$0.299156\pi$
$194$	−7.09231	+	11.5832i	−0.509198	+	0.831622i
$195$	1.04368	−	0.697362i	0.0747392	−	0.0499391i
$196$	12.1177	+	3.92743i	0.865553	+	0.280531i
$197$	12.9559	−	2.57710i	0.923073	−	0.183611i	0.289397	−	0.957209i	$-0.406545\pi$
$197$	12.9559	−	2.57710i	0.923073	−	0.183611i	0.633676	+	0.773599i	$0.281545\pi$
$198$	−1.49597	−	37.7212i	−0.106314	−	2.68073i
$199$	1.44670	+	3.49265i	0.102554	+	0.247587i	0.966825	−	0.255439i	$-0.0822199\pi$
$199$	1.44670	+	3.49265i	0.102554	+	0.247587i	−0.864271	+	0.503026i	$0.832220\pi$
$200$	−0.374653	−	1.14875i	−0.0264920	−	0.0812286i
$201$	1.22428	−	2.95569i	0.0863544	−	0.208478i
$202$	7.59680	−	20.6154i	0.534509	−	1.45049i
$203$	4.15125	−	6.21278i	0.291360	−	0.436052i
$204$	0.982704	+	3.47461i	0.0688030	+	0.243272i
$205$	11.9671	+	2.38040i	0.835817	+	0.166254i
$206$	−19.7400	−	3.11906i	−1.37535	−	0.217315i
$207$	30.0493	−	30.0493i	2.08857	−	2.08857i
$208$	0.522758	−	0.484662i	0.0362468	−	0.0336053i
$209$	−6.68840	−	6.68840i	−0.462646	−	0.462646i
$210$	4.65252	+	6.39869i	0.321055	+	0.441552i
$211$	1.24095	−	6.23870i	0.0854309	−	0.429490i	−0.914272	−	0.405102i	$-0.867236\pi$
$211$	1.24095	−	6.23870i	0.0854309	−	0.429490i	0.999703	−	0.0243884i	$-0.00776383\pi$
$212$	−1.25338	−	0.147412i	−0.0860823	−	0.0101243i
$213$	−3.01365	−	2.01366i	−0.206492	−	0.137973i
$214$	−8.69363	−	18.8397i	−0.594285	−	1.28786i
$215$	16.2331	+	6.72395i	1.10709	+	0.458570i
$216$	−26.6657	+	3.18595i	−1.81437	+	0.216777i
$217$	1.32672	−	0.549546i	0.0900637	−	0.0373056i
$218$	−6.44989	+	6.98260i	−0.436842	+	0.472922i
$219$	1.20723	+	6.06918i	0.0815773	+	0.410117i
$220$	20.1910	−	1.60402i	1.36128	−	0.108143i
$221$	−0.0591270	−	0.0884899i	−0.00397731	−	0.00595247i
$222$	2.86695	+	11.9224i	0.192417	+	0.800178i
$223$			5.65324i			0.378569i	0.981922	+	0.189284i	$0.0606168\pi$
$223$			5.65324i			0.378569i	−0.981922	+	0.189284i	$0.939383\pi$
$224$	3.18287	+	3.17118i	0.212665	+	0.211883i
$225$		−	2.62321i		−	0.174881i
$226$	11.5177	−	2.76964i	0.766145	−	0.184234i
$227$	−3.62832	−	5.43017i	−0.240820	−	0.360413i	0.691296	−	0.722571i	$-0.257040\pi$
$227$	−3.62832	−	5.43017i	−0.240820	−	0.360413i	−0.932117	+	0.362158i	$0.882040\pi$
$228$	−8.53720	+	10.0107i	−0.565390	+	0.662974i
$229$	4.22963	+	21.2638i	0.279502	+	1.40515i	0.824096	+	0.566451i	$0.191684\pi$
$229$	4.22963	+	21.2638i	0.279502	+	1.40515i	−0.544594	+	0.838700i	$0.683316\pi$
$230$	16.7488	+	15.4710i	1.10438	+	1.02013i
$231$	−9.64427	+	3.99479i	−0.634546	+	0.262838i
$232$	−23.2016	+	13.0272i	−1.52326	+	0.855276i
$233$	3.58263	+	1.48397i	0.234706	+	0.0972182i	0.496936	−	0.867787i	$-0.334458\pi$
$233$	3.58263	+	1.48397i	0.234706	+	0.0972182i	−0.262231	+	0.965005i	$0.584458\pi$
$234$	1.40523	−	0.648445i	0.0918625	−	0.0423902i
$235$	−6.65573	−	4.44722i	−0.434172	−	0.290104i
$236$	10.4283	+	13.2083i	0.678826	+	0.859784i
$237$	−4.98340	+	25.0533i	−0.323707	+	1.62738i
$238$	0.542524	−	0.394472i	0.0351666	−	0.0255698i
$239$	−16.2539	−	16.2539i	−1.05138	−	1.05138i	−0.998607	−	0.0527693i	$-0.983195\pi$
$239$	−16.2539	−	16.2539i	−1.05138	−	1.05138i	−0.0527693	−	0.998607i	$-0.516805\pi$
$240$	−4.44819	−	27.8196i	−0.287129	−	1.79575i
$241$	−4.71850	+	4.71850i	−0.303945	+	0.303945i	−0.842555	−	0.538610i	$-0.818950\pi$
$241$	−4.71850	+	4.71850i	−0.303945	+	0.303945i	0.538610	+	0.842555i	$0.318950\pi$
$242$	−1.74321	+	11.0324i	−0.112057	+	0.709192i
$243$	−2.55844	−	0.508905i	−0.164124	−	0.0326463i
$244$	−5.60841	−	3.13544i	−0.359041	−	0.200726i
$245$	−8.24344	+	12.3372i	−0.526654	+	0.788194i
$246$	21.0125	+	7.74312i	1.33971	+	0.493683i
$247$	0.148394	−	0.358255i	0.00944208	−	0.0227952i
$248$	−5.09852	−	0.395598i	−0.323756	−	0.0251205i
$249$	9.27485	+	22.3915i	0.587770	+	1.41900i
$250$	−15.0537	+	0.597012i	−0.952081	+	0.0377583i
$251$	24.3591	−	4.84533i	1.53753	−	0.305834i	0.647620	−	0.761964i	$-0.275765\pi$
$251$	24.3591	−	4.84533i	1.53753	−	0.305834i	0.889913	+	0.456130i	$0.150765\pi$
$252$	4.43476	+	8.68789i	0.279364	+	0.547285i
$253$	−25.0149	+	16.7144i	−1.57267	+	1.05083i
$254$	−9.58978	−	5.87177i	−0.601716	−	0.368428i
$255$	−4.20605			−0.263393
$256$	−4.98906	−	15.2023i	−0.311816	−	0.950143i
$257$	−17.0757			−1.06515			−0.532576	−	0.846382i	$-0.678776\pi$
$257$	−17.0757			−1.06515			−0.532576	+	0.846382i	$0.678776\pi$
$258$	27.5018	+	16.8392i	1.71219	+	1.04836i
$259$	1.89399	−	1.26552i	0.117687	−	0.0786358i
$260$	0.377518	+	0.739574i	0.0234127	+	0.0458664i
$261$	−56.6573	+	11.2698i	−3.50700	+	0.697586i
$262$	−5.09320	+	0.201990i	−0.314659	+	0.0124790i
$263$	−6.67352	−	16.1113i	−0.411507	−	0.993465i	−0.984734	−	0.174069i	$-0.944309\pi$
$263$	−6.67352	−	16.1113i	−0.411507	−	0.993465i	0.573227	−	0.819397i	$-0.305691\pi$
$264$	37.0624	+	2.87570i	2.28103	+	0.176987i
$265$	0.562552	−	1.35812i	0.0345573	−	0.0834287i
$266$	2.29328	+	0.845078i	0.140610	+	0.0518151i
$267$	12.0834	−	18.0841i	0.739494	−	1.10673i
$268$	1.84727	+	1.03273i	0.112840	+	0.0630843i
$269$	−3.60444	−	0.716968i	−0.219767	−	0.0437143i	0.0839787	−	0.996468i	$-0.473237\pi$
$269$	−3.60444	−	0.716968i	−0.219767	−	0.0437143i	−0.303745	+	0.952753i	$0.598237\pi$
$270$	4.88214	−	30.8982i	0.297118	−	1.88041i
$271$	−20.5532	+	20.5532i	−1.24852	+	1.24852i	−0.292145	+	0.956374i	$0.594369\pi$
$271$	−20.5532	+	20.5532i	−1.24852	+	1.24852i	−0.956374	+	0.292145i	$0.905631\pi$
$272$	−2.35874	+	0.377147i	−0.143019	+	0.0228679i
$273$	−0.302606	−	0.302606i	−0.0183146	−	0.0183146i
$274$	15.3425	−	11.1556i	0.926874	−	0.673934i
$275$	−0.362302	+	1.82142i	−0.0218477	+	0.109836i
$276$	25.9312	+	32.8438i	1.56087	+	1.97696i
$277$	15.0658	+	10.0667i	0.905217	+	0.604846i	0.918654	−	0.395063i	$-0.129277\pi$
$277$	15.0658	+	10.0667i	0.905217	+	0.604846i	−0.0134373	+	0.999910i	$0.504277\pi$
$278$	16.4672	−	7.59883i	0.987637	−	0.455748i
$279$	−10.2570	−	4.24861i	−0.614073	−	0.254357i
$280$	−4.56341	+	2.56225i	−0.272716	+	0.153124i
$281$	4.52217	−	1.87315i	0.269770	−	0.111743i	−0.243698	−	0.969851i	$-0.578360\pi$
$281$	4.52217	−	1.87315i	0.269770	−	0.111743i	0.513468	+	0.858109i	$0.328360\pi$
$282$	−10.7919	−	9.96853i	−0.642646	−	0.593617i
$283$	−0.721894	−	3.62921i	−0.0429121	−	0.215734i	0.953380	−	0.301774i	$-0.0975787\pi$
$283$	−0.721894	−	3.62921i	−0.0429121	−	0.215734i	−0.996292	+	0.0860399i	$0.972579\pi$
$284$	1.55583	−	1.82435i	0.0923212	−	0.108256i
$285$	−8.51417	−	12.7424i	−0.504336	−	0.754792i
$286$	−1.06527	+	0.256164i	−0.0629909	+	0.0151473i
$287$		−	4.15995i		−	0.245554i
$288$	−0.0639238	−	34.7359i	−0.00376675	−	2.04683i
$289$		−	16.6434i		−	0.979023i
$290$	−7.24655	−	30.1352i	−0.425532	−	1.76960i
$291$	−16.1314	−	24.1424i	−0.945640	−	1.41525i
$292$	−4.08070	+	0.324181i	−0.238805	+	0.0189712i
$293$	−0.201266	−	1.01183i	−0.0117581	−	0.0591118i	0.974461	−	0.224558i	$-0.0720937\pi$
$293$	−0.201266	−	1.01183i	−0.0117581	−	0.0591118i	−0.986219	+	0.165446i	$0.947094\pi$
$294$	−18.4778	+	20.0040i	−1.07765	+	1.16666i
$295$	−18.1103	+	7.50154i	−1.05442	+	0.436756i
$296$	−8.05446	+	0.962328i	−0.468156	+	0.0559342i
$297$	38.1336	+	15.7955i	2.21274	+	0.916545i
$298$	13.0782	+	28.3413i	0.757599	+	1.64177i
$299$	−1.02550	−	0.685220i	−0.0593065	−	0.0396273i
$300$	2.56543	+	0.301724i	0.148115	+	0.0174201i
$301$	1.16868	−	5.87534i	0.0673615	−	0.338649i
$302$	−2.31452	−	3.18320i	−0.133186	−	0.183172i
$303$	33.2121	+	33.2121i	1.90799	+	1.90799i
$304$	−5.91730	−	6.38242i	−0.339380	−	0.366057i
$305$	5.29225	−	5.29225i	0.303033	−	0.303033i
$306$	−5.12231	−	0.809362i	−0.292823	−	0.0462681i
$307$	14.4531	+	2.87489i	0.824880	+	0.164079i	0.589442	−	0.807811i	$-0.299348\pi$
$307$	14.4531	+	2.87489i	0.824880	+	0.164079i	0.235438	+	0.971889i	$0.424348\pi$
$308$	−1.87934	−	6.64491i	−0.107085	−	0.378629i
$309$	23.7362	−	35.5237i	1.35031	−	2.02088i
$310$	2.05966	−	5.58928i	0.116981	−	0.317450i
$311$	−12.5822	+	30.3761i	−0.713470	+	1.72247i	−0.0223281	+	0.999751i	$0.507108\pi$
$311$	−12.5822	+	30.3761i	−0.713470	+	1.72247i	−0.691142	+	0.722719i	$0.742892\pi$
$312$	0.472533	+	1.44886i	0.0267519	+	0.0820256i
$313$	−6.07425	−	14.6645i	−0.343337	−	0.828889i	−0.997374	−	0.0724262i	$-0.976926\pi$
$313$	−6.07425	−	14.6645i	−0.343337	−	0.828889i	0.654037	−	0.756463i	$-0.273074\pi$
$314$	−1.10687	−	27.9099i	−0.0624643	−	1.57505i
$315$	−11.1437	+	2.21661i	−0.627874	+	0.124892i
$316$	−16.0748	−	5.20994i	−0.904277	−	0.293082i
$317$	12.7506	−	8.51970i	0.716147	−	0.478514i	−0.143339	−	0.989674i	$-0.545784\pi$
$317$	12.7506	−	8.51970i	0.716147	−	0.478514i	0.859486	+	0.511160i	$0.170784\pi$
$318$	1.40883	−	2.30091i	0.0790034	−	0.129028i
$319$	40.8963			2.28976
$320$	18.6210	−	0.772812i	1.04095	−	0.0432015i
$321$	44.3572			2.47578
$322$	4.05925	−	6.62958i	0.226213	−	0.369452i
$323$	−1.08038	+	0.721889i	−0.0601141	+	0.0401670i
$324$	6.34167	−	19.5667i	0.352315	−	1.08704i
$325$	−0.0746705	+	0.0148529i	−0.00414197	+	0.000823889i
$326$	0.714982	+	18.0284i	0.0395992	+	0.998498i
$327$	−7.77665	−	18.7745i	−0.430050	−	1.03823i
$328$	−6.71082	+	13.2068i	−0.370543	+	0.729221i
$329$	−1.04439	+	2.52138i	−0.0575791	+	0.139008i
$330$	−14.9722	+	40.6298i	−0.824190	+	2.23660i
$331$	−16.0230	+	23.9801i	−0.880702	+	1.31806i	0.0666189	+	0.997778i	$0.478779\pi$
$331$	−16.0230	+	23.9801i	−0.880702	+	1.31806i	−0.947321	+	0.320285i	$0.896221\pi$
$332$	−15.4277	+	4.36334i	−0.846707	+	0.239469i
$333$	−17.2722	−	3.43566i	−0.946511	−	0.188273i
$334$	6.95583	+	1.09907i	0.380606	+	0.0601384i
$335$	−1.74313	+	1.74313i	−0.0952375	+	0.0952375i
$336$	−9.00662	+	3.33779i	−0.491352	+	0.182091i
$337$	−21.0382	−	21.0382i	−1.14602	−	1.14602i	−0.987328	−	0.158695i	$-0.949271\pi$
$337$	−21.0382	−	21.0382i	−1.14602	−	1.14602i	−0.158695	−	0.987328i	$-0.550729\pi$
$338$	10.7854	+	14.8333i	0.586646	+	0.806825i
$339$	−4.94058	+	24.8380i	−0.268336	+	1.34901i
$340$	0.325001	−	2.76335i	0.0176257	−	0.149864i
$341$	6.53515	+	4.36665i	0.353898	+	0.236467i
$342$	−7.91695	−	17.1566i	−0.428099	−	0.927721i
$343$	9.81027	+	4.06355i	0.529705	+	0.219411i
$344$	−13.1883	+	16.7674i	−0.711067	+	0.904036i
$345$	−45.0333	+	18.6534i	−2.42451	+	1.00427i
$346$	−19.8933	+	21.5364i	−1.06947	+	1.15780i
$347$	−2.53390	−	12.7388i	−0.136027	−	0.683853i	−0.987266	−	0.159076i	$-0.949149\pi$
$347$	−2.53390	−	12.7388i	−0.136027	−	0.683853i	0.851240	−	0.524777i	$-0.175851\pi$
$348$	−4.50484	−	56.7057i	−0.241485	−	3.03975i
$349$	4.24727	+	6.35649i	0.227351	+	0.340255i	0.927554	−	0.373689i	$-0.121907\pi$
$349$	4.24727	+	6.35649i	0.227351	+	0.340255i	−0.700203	+	0.713944i	$0.746907\pi$
$350$	−0.112191	−	0.466551i	−0.00599683	−	0.0249382i
$351$			1.69212i			0.0903188i
$352$	−4.75313	+	24.1276i	−0.253343	+	1.28600i
$353$		−	26.8538i		−	1.42928i	−0.699491	−	0.714642i	$-0.746590\pi$
$353$		−	26.8538i		−	1.42928i	0.699491	−	0.714642i	$-0.253410\pi$
$354$	−34.9797	+	8.41150i	−1.85915	+	0.447066i
$355$	1.55163	+	2.32218i	0.0823519	+	0.123248i
$356$	10.9475	+	9.33611i	0.580216	+	0.494813i
$357$	0.279759	+	1.40644i	0.0148064	+	0.0744368i
$358$	6.96748	+	6.43592i	0.368243	+	0.340149i
$359$	−2.56193	+	1.06119i	−0.135214	+	0.0560073i	−0.449264	−	0.893399i	$-0.648314\pi$
$359$	−2.56193	+	1.06119i	−0.135214	+	0.0560073i	0.314051	+	0.949406i	$0.398314\pi$
$360$	38.9541	+	10.9398i	2.05306	+	0.576576i
$361$	13.1797	+	5.45923i	0.693670	+	0.287328i
$362$	27.8559	−	12.8542i	1.46408	−	0.675601i
$363$	−19.8538	−	13.2659i	−1.04205	−	0.696278i
$364$	0.222193	−	0.175428i	0.0116461	−	0.00919494i
$365$	0.930238	−	4.67662i	0.0486909	−	0.244786i
$366$	11.1099	−	8.07804i	0.580722	−	0.422246i
$367$	13.2056	+	13.2056i	0.689329	+	0.689329i	0.962084	−	0.272755i	$-0.0879347\pi$
$367$	13.2056	+	13.2056i	0.689329	+	0.689329i	−0.272755	+	0.962084i	$0.587935\pi$
$368$	−23.5819	+	14.4988i	−1.22929	+	0.755802i
$369$	−22.7413	+	22.7413i	−1.18387	+	1.18387i
$370$	1.47467	−	9.33292i	0.0766643	−	0.485195i
$371$	−0.491553	−	0.0977761i	−0.0255202	−	0.00507628i
$372$	5.33481	−	9.54245i	0.276597	−	0.494753i
$373$	20.4728	−	30.6397i	1.06004	−	1.58646i	0.280770	−	0.959775i	$-0.409410\pi$
$373$	20.4728	−	30.6397i	1.06004	−	1.58646i	0.779271	−	0.626688i	$-0.215590\pi$
$374$	3.44487	+	1.26944i	0.178130	+	0.0656412i
$375$	12.3252	−	29.7557i	0.636472	−	1.53658i
$376$	7.38315	−	6.31992i	0.380757	−	0.325925i
$377$	0.641599	+	1.54896i	0.0330440	+	0.0797753i
$378$	−10.6567	+	0.422630i	−0.548120	+	0.0217377i
$379$	26.5748	−	5.28606i	1.36506	−	0.271527i	0.542427	−	0.840103i	$-0.317506\pi$
$379$	26.5748	−	5.28606i	1.36506	−	0.271527i	0.822631	+	0.568576i	$0.192506\pi$
$380$	9.02955	−	4.60916i	0.463206	−	0.236445i
$381$	19.9876	−	13.3553i	1.02400	−	0.684214i
$382$	14.7114	+	9.00774i	0.752703	+	0.460876i
$383$	−12.4669			−0.637027			−0.318514	−	0.947918i	$-0.603184\pi$
$383$	−12.4669			−0.637027			−0.318514	+	0.947918i	$0.603184\pi$
$384$	33.9782	+	3.93284i	1.73394	+	0.200697i
$385$	8.04371			0.409945
$386$	−19.7691	−	12.1045i	−1.00622	−	0.616104i
$387$	−38.5078	+	25.7301i	−1.95746	+	1.30793i
$388$	17.1079	−	8.73277i	0.868521	−	0.443339i
$389$	6.19647	−	1.23255i	0.314173	−	0.0624930i	−0.0354851	−	0.999370i	$-0.511298\pi$
$389$	6.19647	−	1.23255i	0.314173	−	0.0624930i	0.349659	+	0.936877i	$0.386298\pi$
$390$	−1.77375	+	0.0703448i	−0.0898174	+	0.00356205i
$391$	1.58156	+	3.81823i	0.0799830	+	0.193096i
$392$	−11.7147	−	13.6855i	−0.591683	−	0.691225i
$393$	4.17006	−	10.0674i	0.210352	−	0.507834i
$394$	−17.5291	−	6.45951i	−0.883105	−	0.325425i
$395$	10.9353	−	16.3659i	0.550216	−	0.823457i
$396$	−26.0521	+	46.5998i	−1.30917	+	2.34173i
$397$	−24.4366	−	4.86075i	−1.22644	−	0.243954i	−0.460964	−	0.887419i	$-0.652496\pi$
$397$	−24.4366	−	4.86075i	−1.22644	−	0.243954i	−0.765476	+	0.643465i	$0.777496\pi$
$398$	0.834405	−	5.28080i	0.0418249	−	0.264703i
$399$	−3.69456	+	3.69456i	−0.184959	+	0.184959i
$400$	−0.396463	+	1.66216i	−0.0198231	+	0.0831081i
$401$	0.213936	+	0.213936i	0.0106835	+	0.0106835i	0.712428	−	0.701745i	$-0.247595\pi$
$401$	0.213936	+	0.213936i	0.0106835	+	0.0106835i	−0.701745	+	0.712428i	$0.747595\pi$
$402$	−3.65931	+	2.66070i	−0.182510	+	0.132704i
$403$	−0.0628614	+	0.316026i	−0.00313135	+	0.0157424i
$404$	−24.3865	+	19.2539i	−1.21327	+	0.957915i
$405$	19.9210	+	13.3108i	0.989882	+	0.661418i
$406$	−9.59478	+	4.42754i	−0.476181	+	0.219735i
$407$	11.5184	+	4.77107i	0.570945	+	0.236493i
$408$	1.38071	−	4.91639i	0.0683552	−	0.243398i
$409$	−8.00529	+	3.31590i	−0.395836	+	0.163961i	−0.571717	−	0.820451i	$-0.693723\pi$
$409$	−8.00529	+	3.31590i	−0.395836	+	0.163961i	0.175881	+	0.984411i	$0.443723\pi$
$410$	−12.6755	−	11.7084i	−0.625996	−	0.578238i
$411$	7.91153	+	39.7739i	0.390247	+	1.96190i
$412$	21.5048	+	18.3395i	1.05947	+	0.903521i
$413$	3.71299	+	5.55688i	0.182704	+	0.273436i
$414$	−58.4330	+	14.0513i	−2.87182	+	0.690582i
$415$		−	18.6754i		−	0.916739i
$416$	−0.988406	+	0.198498i	−0.0484606	+	0.00973215i
$417$			38.7712i			1.89863i
$418$	3.12754	+	13.0060i	0.152973	+	0.636147i
$419$	−9.47052	−	14.1736i	−0.462665	−	0.692427i	0.524629	−	0.851331i	$-0.324204\pi$
$419$	−9.47052	−	14.1736i	−0.462665	−	0.692427i	−0.987294	+	0.158904i	$0.949204\pi$
$420$	−0.886036	−	11.1532i	−0.0432341	−	0.544220i
$421$	−4.60289	−	23.1403i	−0.224331	−	1.12779i	−0.914638	−	0.404273i	$-0.867525\pi$
$421$	−4.60289	−	23.1403i	−0.224331	−	1.12779i	0.690307	−	0.723517i	$-0.257475\pi$
$422$	−6.10386	+	6.60800i	−0.297131	+	0.321672i
$423$	19.4931	−	8.07431i	0.947788	−	0.392587i
$424$	1.40282	+	1.10339i	0.0681271	+	0.0535852i
$425$	0.235692	+	0.0976269i	0.0114327	+	0.00473560i
$426$	2.14768	+	4.65417i	0.104055	+	0.225495i
$427$	−2.12166	−	1.41765i	−0.102674	−	0.0686047i
$428$	−3.42748	+	29.1424i	−0.165674	+	1.40865i
$429$	0.456955	−	2.29727i	0.0220620	−	0.110913i
$430$	−14.6130	−	20.0975i	−0.704700	−	0.969186i
$431$	−6.06685	−	6.06685i	−0.292230	−	0.292230i	0.545731	−	0.837961i	$-0.316252\pi$
$431$	−6.06685	−	6.06685i	−0.292230	−	0.292230i	−0.837961	+	0.545731i	$0.816252\pi$
$432$	34.5139	+	15.8496i	1.66055	+	0.762562i
$433$	−19.0094	+	19.0094i	−0.913533	+	0.913533i	−0.996548	−	0.0830154i	$-0.973545\pi$
$433$	−19.0094	+	19.0094i	−0.913533	+	0.913533i	0.0830154	+	0.996548i	$0.473545\pi$
$434$	−2.00597	−	0.316958i	−0.0962896	−	0.0152145i
$435$	64.9867	+	12.9267i	3.11588	+	0.619786i
$436$	12.9356	−	3.65851i	0.619505	−	0.175211i
$437$	−8.36594	+	12.5205i	−0.400197	+	0.598937i
$438$	3.02594	−	8.21148i	0.144585	−	0.392360i
$439$	1.00267	−	2.42067i	0.0478550	−	0.115532i	−0.898144	−	0.439701i	$-0.855085\pi$
$439$	1.00267	−	2.42067i	0.0478550	−	0.115532i	0.945999	+	0.324169i	$0.105085\pi$
$440$	−25.5367	−	12.9761i	−1.21741	−	0.618611i
$441$	−14.9667	−	36.1328i	−0.712700	−	1.72061i
$442$	0.00596430	+	0.150391i	0.000283693	+	0.00715335i
$443$	−10.3515	+	2.05904i	−0.491815	+	0.0978280i	−0.434766	−	0.900543i	$-0.643169\pi$
$443$	−10.3515	+	2.05904i	−0.491815	+	0.0978280i	−0.0570485	+	0.998371i	$0.518169\pi$
$444$	5.34665	−	16.4966i	0.253741	−	0.782895i
$445$	−13.9348	+	9.31093i	−0.660572	+	0.441380i
$446$	4.17481	−	6.81830i	0.197683	−	0.322856i
$447$	−66.7283			−3.15614
$448$	−1.49697	−	6.17521i	−0.0707251	−	0.291751i
$449$	−16.5623			−0.781622			−0.390811	−	0.920471i	$-0.627805\pi$
$449$	−16.5623			−0.781622			−0.390811	+	0.920471i	$0.627805\pi$
$450$	−1.93719	+	3.16382i	−0.0913201	+	0.149144i
$451$	18.9313	−	12.6495i	0.891438	−	0.595640i
$452$	−15.9367	−	5.16517i	−0.749598	−	0.242949i
$453$	8.25213	−	1.64145i	0.387719	−	0.0771221i
$454$	0.365999	+	9.22870i	0.0171772	+	0.433124i
$455$	0.126193	+	0.304657i	0.00591602	+	0.0142825i
$456$	17.6893	−	5.76921i	0.828378	−	0.270168i
$457$	3.37664	−	8.15192i	0.157952	−	0.381331i	−0.825015	−	0.565111i	$-0.808833\pi$
$457$	3.37664	−	8.15192i	0.157952	−	0.381331i	0.982967	+	0.183780i	$0.0588334\pi$
$458$	10.6016	−	28.7695i	0.495380	−	1.34431i
$459$	3.15011	−	4.71447i	0.147034	−	0.220053i
$460$	−8.77545	−	31.0280i	−0.409158	−	1.44669i
$461$	25.6514	+	5.10238i	1.19470	+	0.237641i	0.752084	−	0.659068i	$-0.229049\pi$
$461$	25.6514	+	5.10238i	1.19470	+	0.237641i	0.442620	+	0.896709i	$0.354049\pi$
$462$	14.5819	+	2.30404i	0.678411	+	0.107194i
$463$	10.3091	−	10.3091i	0.479105	−	0.479105i	−0.425741	−	0.904845i	$-0.639986\pi$
$463$	10.3091	−	10.3091i	0.479105	−	0.479105i	0.904845	+	0.425741i	$0.139986\pi$
$464$	37.6034	+	1.42200i	1.74570	+	0.0660147i
$465$	9.00452	+	9.00452i	0.417575	+	0.417575i
$466$	−3.22507	−	4.43550i	−0.149399	−	0.205471i
$467$	−4.65749	+	23.4148i	−0.215523	+	1.08351i	0.709822	+	0.704381i	$0.248775\pi$
$467$	−4.65749	+	23.4148i	−0.215523	+	1.08351i	−0.925345	+	0.379126i	$0.876225\pi$
$468$	−2.17369	−	0.255651i	−0.100479	−	0.0118175i
$469$	0.698821	+	0.466937i	0.0322685	+	0.0215612i
$470$	4.74321	+	10.2789i	0.218788	+	0.474128i
$471$	55.1677	+	22.8512i	2.54199	+	1.05293i
$472$	−2.82343	−	23.6314i	−0.129959	−	1.08772i
$473$	30.2914	−	12.5471i	1.39280	−	0.576917i
$474$	24.5118	−	26.5363i	1.12586	−	1.21885i
$475$	0.181341	+	0.911661i	0.00832048	+	0.0418299i
$476$	−0.945642	+	0.0751241i	−0.0433434	+	0.00344331i
$477$	2.15268	+	3.22171i	0.0985642	+	0.147512i
$478$	7.60042	+	31.6068i	0.347635	+	1.44566i
$479$		−	7.22838i		−	0.330273i	−0.986271	−	0.165136i	$-0.947194\pi$
$479$		−	7.22838i		−	0.330273i	0.986271	−	0.165136i	$-0.0528065\pi$
$480$	−15.1794	+	36.8378i	−0.692839	+	1.68141i
$481$			0.511111i			0.0233047i
$482$	9.17544	−	2.20640i	0.417930	−	0.100499i
$483$	9.23275	+	13.8178i	0.420105	+	0.628731i
$484$	10.2497	−	12.0188i	0.465896	−	0.546308i
$485$	4.36488	+	21.9437i	0.198199	+	0.996413i
$486$	2.70988	+	2.50314i	0.122923	+	0.113545i
$487$	−13.5574	+	5.61566i	−0.614345	+	0.254470i	−0.668085	−	0.744085i	$-0.732886\pi$
$487$	−13.5574	+	5.61566i	−0.614345	+	0.254470i	0.0537402	+	0.998555i	$0.482886\pi$
$488$	4.44877	+	7.92331i	0.201386	+	0.358671i
$489$	−35.6355	−	14.7607i	−1.61149	−	0.667502i
$490$	19.0531	−	8.79209i	0.860730	−	0.397186i
$491$	−16.6130	−	11.1005i	−0.749734	−	0.500956i	0.121035	−	0.992648i	$-0.461379\pi$
$491$	−16.6130	−	11.1005i	−0.749734	−	0.500956i	−0.870769	+	0.491692i	$0.836379\pi$
$492$	−19.6247	−	24.8562i	−0.884751	−	1.12060i
$493$	1.09601	−	5.51001i	0.0493618	−	0.248159i
$494$	−0.443540	+	0.322500i	−0.0199558	+	0.0145100i
$495$	−43.9728	−	43.9728i	−1.97643	−	1.97643i
$496$	5.85712	+	4.24228i	0.262992	+	0.190484i
$497$	0.673299	−	0.673299i	0.0302016	−	0.0302016i
$498$	5.34939	−	33.8554i	0.239712	−	1.51710i
$499$	−1.73704	−	0.345518i	−0.0777605	−	0.0154675i	0.156057	−	0.987748i	$-0.450122\pi$
$499$	−1.73704	−	0.345518i	−0.0777605	−	0.0154675i	−0.233817	+	0.972281i	$0.575122\pi$
$500$	18.5970	+	10.3968i	0.831683	+	0.464961i
$501$	−8.36397	+	12.5176i	−0.373675	+	0.559244i
$502$	−32.9574	−	12.1448i	−1.47096	−	0.542051i
$503$	−6.27595	+	15.1515i	−0.279831	+	0.675571i	−0.999831	−	0.0184028i	$-0.994142\pi$
$503$	−6.27595	+	15.1515i	−0.279831	+	0.675571i	0.720000	+	0.693974i	$0.244142\pi$
$504$	1.06713	−	13.7533i	0.0475338	−	0.612622i
$505$	−13.8501	−	33.4372i	−0.616322	−	1.48793i
$506$	42.5134	−	1.68603i	1.88995	−	0.0749530i
$507$	−38.4539	+	7.64895i	−1.70780	+	0.339702i
$508$	7.22992	+	14.1637i	0.320776	+	0.628414i
$509$	−0.961984	+	0.642777i	−0.0426392	+	0.0284906i	−0.576707	−	0.816951i	$-0.695663\pi$
$509$	−0.961984	+	0.642777i	−0.0426392	+	0.0284906i	0.534068	+	0.845442i	$0.320663\pi$
$510$	5.07286	+	3.10608i	0.224630	+	0.137540i
$511$	−1.62567			−0.0719154
$512$	−5.20935	+	22.0196i	−0.230223	+	0.973138i
$513$	20.6593			0.912131
$514$	20.5948	+	12.6101i	0.908396	+	0.556206i
$515$	−27.3729	+	18.2900i	−1.20620	+	0.805954i
$516$	−20.7341	−	40.6191i	−0.912770	−	1.78816i
$517$	−14.6502	+	2.91410i	−0.644313	+	0.128162i
$518$	−3.21888	+	0.127657i	−0.141430	+	0.00560892i
$519$	−23.9855	−	57.9060i	−1.05285	−	2.54179i
$520$	0.0908418	−	1.17078i	0.00398368	−	0.0513421i
$521$	1.84213	−	4.44729i	0.0807050	−	0.194839i	−0.878376	−	0.477970i	$-0.841373\pi$
$521$	1.84213	−	4.44729i	0.0807050	−	0.194839i	0.959081	+	0.283130i	$0.0913729\pi$
$522$	76.6563	+	28.2479i	3.35515	+	1.23638i
$523$	−1.19764	+	1.79239i	−0.0523691	+	0.0783759i	−0.856730	−	0.515765i	$-0.827508\pi$
$523$	−1.19764	+	1.79239i	−0.0523691	+	0.0783759i	0.804361	+	0.594141i	$0.202508\pi$
$524$	6.29201	+	3.51761i	0.274868	+	0.153668i
$525$	1.00612	+	0.200130i	0.0439107	+	0.00873438i
$526$	−3.84904	+	24.3599i	−0.167826	+	1.06214i
$527$	0.763464	−	0.763464i	0.0332570	−	0.0332570i
$528$	−42.5768	−	30.8382i	−1.85292	−	1.34206i
$529$	17.6034	+	17.6034i	0.765367	+	0.765367i
$530$	−1.68143	+	1.22258i	−0.0730367	+	0.0531054i
$531$	10.0801	−	50.6759i	0.437437	−	2.19915i
$532$	−2.14183	−	2.71278i	−0.0928599	−	0.117614i
$533$	0.776102	+	0.518575i	0.0336167	+	0.0224620i
$534$	−27.9285	+	12.8877i	−1.20858	+	0.557704i
$535$	−31.5778	−	13.0799i	−1.36523	−	0.565496i
$536$	−1.46531	−	2.60974i	−0.0632918	−	0.112724i
$537$	−18.7338	+	7.75981i	−0.808425	+	0.334861i
$538$	3.81780	+	3.52654i	0.164597	+	0.152040i
$539$	5.40162	+	27.1558i	0.232664	+	1.16968i
$540$	−28.7060	+	33.6606i	−1.23531	+	1.44852i
$541$	5.84519	+	8.74795i	0.251304	+	0.376104i	0.935577	−	0.353123i	$-0.114880\pi$
$541$	5.84519	+	8.74795i	0.251304	+	0.376104i	−0.684273	+	0.729226i	$0.739880\pi$
$542$	39.9671	−	9.61082i	1.71674	−	0.412820i
$543$			65.5854i			2.81454i
$544$	3.12336	+	1.28701i	0.133913	+	0.0551800i
$545$			15.6587i			0.670745i
$546$	0.141501	+	0.588439i	0.00605567	+	0.0251829i
$547$	17.4357	+	26.0944i	0.745498	+	1.11572i	0.989301	+	0.145892i	$0.0466051\pi$
$547$	17.4357	+	26.0944i	0.745498	+	1.11572i	−0.243803	+	0.969825i	$0.578395\pi$
$548$	−26.7426	+	2.12449i	−1.14239	+	0.0907539i
$549$	3.84864	+	19.3484i	0.164256	+	0.825771i
$550$	1.78205	−	1.92923i	0.0759869	−	0.0822628i
$551$	18.9114	−	7.83336i	0.805653	−	0.333712i
$552$	−7.02076	−	58.7621i	−0.298823	−	2.50108i
$553$	−6.19987	−	2.56807i	−0.263645	−	0.109205i
$554$	−10.7366	−	23.2671i	−0.456157	−	0.988523i
$555$	16.7953	+	11.2223i	0.712923	+	0.476360i
$556$	−25.4725	−	2.99585i	−1.08027	−	0.127052i
$557$	−1.91577	+	9.63121i	−0.0811736	+	0.408087i	0.918739	+	0.394865i	$0.129209\pi$
$557$	−1.91577	+	9.63121i	−0.0811736	+	0.408087i	−0.999913	+	0.0132219i	$0.995791\pi$
$558$	9.23338	+	12.6988i	0.390880	+	0.537584i
$559$	0.950448	+	0.950448i	0.0401997	+	0.0401997i
$560$	7.39604	+	0.279686i	0.312540	+	0.0118189i
$561$	−5.54981	+	5.54981i	−0.234313	+	0.234313i
$562$	−6.83742	−	1.08036i	−0.288419	−	0.0455723i
$563$	9.75123	+	1.93964i	0.410965	+	0.0817461i	0.396243	−	0.918146i	$-0.370314\pi$
$563$	9.75123	+	1.93964i	0.410965	+	0.0817461i	0.0147220	+	0.999892i	$0.495314\pi$
$564$	5.65436	+	19.9925i	0.238091	+	0.841836i
$565$	10.8414	−	16.2253i	0.456100	−	0.682602i
$566$	−1.80943	+	4.91024i	−0.0760561	+	0.206393i
$567$	3.12592	−	7.54664i	0.131276	−	0.316929i
$568$	−3.22371	+	1.05138i	−0.135264	+	0.0441151i
$569$	12.1558	+	29.3467i	0.509599	+	1.23028i	0.944115	+	0.329616i	$0.106919\pi$
$569$	12.1558	+	29.3467i	0.509599	+	1.23028i	−0.434517	+	0.900664i	$0.643081\pi$
$570$	0.858848	+	21.6560i	0.0359732	+	0.907068i
$571$	−14.9708	+	2.97788i	−0.626510	+	0.124621i	−0.498127	−	0.867104i	$-0.665979\pi$
$571$	−14.9708	+	2.97788i	−0.626510	+	0.124621i	−0.128383	+	0.991725i	$0.540979\pi$
$572$	1.47398	+	0.477727i	0.0616304	+	0.0199748i
$573$	−30.6626	+	20.4881i	−1.28095	+	0.855901i
$574$	−3.07204	+	5.01726i	−0.128225	+	0.209417i
$575$	2.95647			0.123293
$576$	−25.5747	+	41.9418i	−1.06561	+	1.74757i
$577$	−29.9355			−1.24623			−0.623116	−	0.782129i	$-0.714134\pi$
$577$	−29.9355			−1.24623			−0.623116	+	0.782129i	$0.714134\pi$
$578$	−12.2908	+	20.0734i	−0.511231	+	0.834942i
$579$	41.2041	−	27.5317i	1.71238	−	1.14418i
$580$	−13.5143	+	41.6971i	−0.561150	+	1.73138i
$581$	−6.24479	+	1.24217i	−0.259078	+	0.0515337i
$582$	1.62722	+	41.0305i	0.0674504	+	1.70077i
$583$	−1.04974	−	2.53429i	−0.0434758	−	0.104960i
$584$	5.16108	+	2.62253i	0.213567	+	0.108521i
$585$	0.975614	−	2.35534i	0.0403367	−	0.0973814i
$586$	−0.504474	+	1.36899i	−0.0208396	+	0.0565524i
$587$	15.2402	−	22.8085i	0.629029	−	0.941408i	−0.370890	−	0.928677i	$-0.620947\pi$
$587$	15.2402	−	22.8085i	0.629029	−	0.941408i	0.999919	−	0.0127316i	$-0.00405269\pi$
$588$	37.0584	−	10.4810i	1.52826	−	0.432230i
$589$	3.85840	+	0.767483i	0.158982	+	0.0316236i
$590$	27.3824	+	4.32661i	1.12731	+	0.178124i
$591$	28.2400	−	28.2400i	1.16164	−	1.16164i
$592$	10.4250	+	4.78741i	0.428467	+	0.196762i
$593$	23.4309	+	23.4309i	0.962194	+	0.962194i	0.999311	−	0.0371172i	$-0.0118175\pi$
$593$	23.4309	+	23.4309i	0.962194	+	0.962194i	−0.0371172	+	0.999311i	$0.511817\pi$
$594$	−34.3278	−	47.2116i	−1.40849	−	1.93712i
$595$	0.215569	−	1.08374i	0.00883747	−	0.0444290i
$596$	5.15610	−	43.8401i	0.211202	−	1.79576i
$597$	9.50323	+	6.34986i	0.388941	+	0.259882i
$598$	0.730826	+	1.58375i	0.0298857	+	0.0647644i
$599$	−14.1017	−	5.84110i	−0.576179	−	0.238661i	0.0755132	−	0.997145i	$-0.475940\pi$
$599$	−14.1017	−	5.84110i	−0.576179	−	0.238661i	−0.651692	+	0.758484i	$0.725940\pi$
$600$	−2.87132	−	2.25843i	−0.117221	−	0.0922000i
$601$	16.4696	−	6.82193i	0.671809	−	0.278272i	−0.0205894	−	0.999788i	$-0.506554\pi$
$601$	16.4696	−	6.82193i	0.671809	−	0.278272i	0.692398	+	0.721516i	$0.256554\pi$
$602$	−5.74835	+	6.22313i	−0.234285	+	0.253636i
$603$	−1.26765	−	6.37288i	−0.0516225	−	0.259524i
$604$	0.440782	+	5.54844i	0.0179351	+	0.225763i
$605$	10.2221	+	15.2984i	0.415586	+	0.621968i
$606$	−15.5302	−	64.5832i	−0.630871	−	2.62351i
$607$			10.7750i			0.437344i	0.975798	+	0.218672i	$0.0701724\pi$
$607$			10.7750i			0.437344i	−0.975798	+	0.218672i	$0.929828\pi$
$608$	2.42348	+	12.0676i	0.0982852	+	0.489404i
$609$		−	22.5904i		−	0.915411i
$610$	−10.2911	+	2.47469i	−0.416676	+	0.100197i
$611$	−0.340210	−	0.509160i	−0.0137634	−	0.0205984i
$612$	5.58025	+	4.75889i	0.225568	+	0.192367i
$613$	−3.48904	−	17.5406i	−0.140921	−	0.708457i	−0.985043	−	0.172307i	$-0.944878\pi$
$613$	−3.48904	−	17.5406i	−0.140921	−	0.708457i	0.844122	−	0.536150i	$-0.180122\pi$
$614$	−15.3086	−	14.1407i	−0.617805	−	0.570671i
$615$	34.0812	−	14.1169i	1.37429	−	0.569248i
$616$	−2.64049	+	9.40219i	−0.106388	+	0.378825i
$617$	32.6001	+	13.5034i	1.31243	+	0.543626i	0.925592	−	0.378523i	$-0.123568\pi$
$617$	32.6001	+	13.5034i	1.31243	+	0.543626i	0.386837	+	0.922148i	$0.373568\pi$
$618$	−54.8615	+	25.3160i	−2.20685	+	1.01836i
$619$	1.79801	+	1.20140i	0.0722683	+	0.0482881i	0.591180	−	0.806540i	$-0.298662\pi$
$619$	1.79801	+	1.20140i	0.0722683	+	0.0482881i	−0.518911	+	0.854828i	$0.673662\pi$
$620$	−6.61170	+	5.22014i	−0.265532	+	0.209646i
$621$	12.8194	−	64.4473i	0.514423	−	2.58618i
$622$	37.6074	−	27.3445i	1.50792	−	1.09641i
$623$	4.04029	+	4.04029i	0.161871	+	0.161871i
$624$	0.500040	−	2.09641i	0.0200176	−	0.0839235i
$625$	−19.0590	+	19.0590i	−0.762360	+	0.762360i
$626$	−3.50340	+	22.1724i	−0.140024	+	0.886189i
$627$	−28.0476	−	5.57902i	−1.12012	−	0.222805i
$628$	−19.2759	+	34.4791i	−0.769193	+	1.37587i
$629$	0.951501	−	1.42402i	0.0379388	−	0.0567795i
$630$	15.0772	+	5.55595i	0.600688	+	0.221355i
$631$	9.48652	−	22.9025i	0.377652	−	0.911733i	−0.614753	−	0.788720i	$-0.710744\pi$
$631$	9.48652	−	22.9025i	0.377652	−	0.911733i	0.992405	−	0.123014i	$-0.0392558\pi$
$632$	15.5402	+	18.1546i	0.618154	+	0.722149i
$633$	−7.35945	−	17.7673i	−0.292512	−	0.706186i
$634$	−21.6700	+	0.859405i	−0.860626	+	0.0341313i
$635$	−18.1674	+	3.61371i	−0.720950	+	0.143406i
$636$	−3.39835	+	1.73470i	−0.134753	+	0.0687852i
$637$	−0.943787	+	0.630619i	−0.0373942	+	0.0249860i
$638$	−49.3246	−	30.2012i	−1.95278	−	1.19568i
$639$	−7.36149			−0.291216
$640$	−23.0293	−	12.8192i	−0.910314	−	0.506724i
$641$	−22.8856			−0.903928			−0.451964	−	0.892036i	$-0.649277\pi$
$641$	−22.8856			−0.903928			−0.451964	+	0.892036i	$0.649277\pi$
$642$	−53.4986	−	32.7569i	−2.11142	−	1.29281i
$643$	10.6628	−	7.12468i	0.420501	−	0.280970i	−0.327264	−	0.944933i	$-0.606127\pi$
$643$	10.6628	−	7.12468i	0.420501	−	0.280970i	0.747765	+	0.663963i	$0.231127\pi$
$644$	−9.79163	+	4.99817i	−0.385844	+	0.196955i
$645$	52.1008	−	10.3635i	2.05147	−	0.408062i
$646$	1.83614	−	0.0728189i	0.0722419	−	0.00286502i
$647$	16.6415	+	40.1760i	0.654243	+	1.57948i	0.806561	+	0.591151i	$0.201326\pi$
$647$	16.6415	+	40.1760i	0.654243	+	1.57948i	−0.152318	+	0.988332i	$0.548674\pi$
$648$	−22.0982	+	18.9159i	−0.868100	+	0.743087i
$649$	−13.9981	+	33.7944i	−0.549474	+	1.32655i
$650$	0.101028	+	0.0372288i	0.00396263	+	0.00146023i
$651$	2.41206	−	3.60991i	0.0945362	−	0.141483i
$652$	12.4513	−	22.2718i	0.487629	−	0.872230i
$653$	−15.7287	−	3.12864i	−0.615512	−	0.122433i	−0.122519	−	0.992466i	$-0.539097\pi$
$653$	−15.7287	−	3.12864i	−0.615512	−	0.122433i	−0.492993	+	0.870033i	$0.664097\pi$
$654$	−4.48529	+	28.3866i	−0.175389	+	1.11000i
$655$	−5.93731	+	5.93731i	−0.231990	+	0.231990i
$656$	17.8468	−	10.9727i	0.696800	−	0.428412i
$657$	8.88710	+	8.88710i	0.346719	+	0.346719i
$658$	3.12162	−	2.26974i	0.121693	−	0.0884838i
$659$	−3.67625	+	18.4817i	−0.143206	+	0.719947i	0.840734	+	0.541448i	$0.182124\pi$
$659$	−3.67625	+	18.4817i	−0.143206	+	0.719947i	−0.983940	+	0.178498i	$0.942876\pi$
$660$	48.0621	−	37.9465i	1.87081	−	1.47707i
$661$	1.08878	+	0.727500i	0.0423487	+	0.0282965i	0.576564	−	0.817052i	$-0.304393\pi$
$661$	1.08878	+	0.727500i	0.0423487	+	0.0282965i	−0.534216	+	0.845348i	$0.679393\pi$
$662$	37.0339	−	17.0894i	1.43936	−	0.664198i
$663$	−0.297268	−	0.123132i	−0.0115449	−	0.00478206i
$664$	21.8294	+	6.13053i	0.847147	+	0.237911i
$665$	3.71959	−	1.54071i	0.144240	−	0.0597460i
$666$	18.2946	+	16.8989i	0.708902	+	0.654819i
$667$	−12.7016	−	63.8553i	−0.491808	−	2.47249i
$668$	−7.57769	−	6.46232i	−0.293190	−	0.250035i
$669$	9.49558	+	14.2111i	0.367120	+	0.549435i
$670$	3.38964	−	0.815100i	0.130953	−	0.0314901i
$671$		−	13.9661i		−	0.539154i
$672$	13.3277	+	2.62555i	0.514126	+	0.101283i
$673$		−	29.4054i		−	1.13349i	−0.823892	−	0.566747i	$-0.808202\pi$
$673$		−	29.4054i		−	1.13349i	0.823892	−	0.566747i	$-0.191798\pi$
$674$	9.83759	+	40.9102i	0.378930	+	1.57580i
$675$	−2.25348	−	3.37257i	−0.0867364	−	0.129810i
$676$	−2.05399	−	25.8550i	−0.0789994	−	0.994424i
$677$	0.168449	+	0.846851i	0.00647403	+	0.0325471i	0.983887	−	0.178790i	$-0.0572182\pi$
$677$	0.168449	+	0.846851i	0.00647403	+	0.0325471i	−0.977413	+	0.211337i	$0.932218\pi$
$678$	24.3012	−	26.3083i	0.933280	−	1.01036i
$679$	7.04734	−	2.91911i	0.270452	−	0.112025i
$680$	−2.43266	+	3.09283i	−0.0932882	+	0.118605i
$681$	−18.2418	−	7.55600i	−0.699027	−	0.289546i
$682$	−4.65728	−	10.0926i	−0.178336	−	0.386467i
$683$	−24.3032	−	16.2389i	−0.929937	−	0.621364i	−0.00438760	−	0.999990i	$-0.501397\pi$
$683$	−24.3032	−	16.2389i	−0.929937	−	0.621364i	−0.925550	+	0.378626i	$0.876397\pi$
$684$	−3.12127	+	26.5388i	−0.119345	+	1.01474i
$685$	6.09625	−	30.6479i	0.232926	−	1.17100i
$686$	−8.83119	−	12.1457i	−0.337176	−	0.463725i
$687$	46.3486	+	46.3486i	1.76831	+	1.76831i
$688$	28.2887	−	10.4836i	1.07849	−	0.399683i
$689$	0.0795181	−	0.0795181i	0.00302940	−	0.00302940i
$690$	68.0892	+	10.7586i	2.59211	+	0.409572i
$691$	−36.6353	−	7.28722i	−1.39367	−	0.277219i	−0.559550	−	0.828797i	$-0.689026\pi$
$691$	−36.6353	−	7.28722i	−1.39367	−	0.277219i	−0.834123	+	0.551578i	$0.814026\pi$
$692$	39.8973	−	11.2839i	1.51667	−	0.428950i
$693$	−11.7791	+	17.6287i	−0.447451	+	0.669658i
$694$	−6.35123	+	17.2353i	−0.241090	+	0.654243i
$695$	11.4328	−	27.6011i	0.433670	−	1.04697i
$696$	−36.4429	+	71.7188i	−1.38136	+	2.71849i
$697$	−1.19693	−	2.88963i	−0.0453368	−	0.109453i
$698$	−0.428433	−	10.8030i	−0.0162164	−	0.408900i
$699$	11.4986	−	2.28722i	0.434917	−	0.0865104i
$700$	−0.209227	+	0.645551i	−0.00790804	+	0.0243995i
$701$	−8.75861	+	5.85232i	−0.330808	+	0.221039i	−0.709871	−	0.704332i	$-0.751247\pi$
$701$	−8.75861	+	5.85232i	−0.330808	+	0.221039i	0.379062	+	0.925371i	$0.376247\pi$
$702$	1.24960	−	2.04085i	0.0471631	−	0.0770268i
$703$	6.24022			0.235354
$704$	23.5505	−	25.5899i	0.887591	−	0.964455i
$705$	−24.2011			−0.911465
$706$	−19.8310	+	32.3880i	−0.746350	+	1.21894i
$707$	−10.2597	+	6.85531i	−0.385855	+	0.257820i
$708$	48.4003	+	15.6868i	1.81899	+	0.589547i
$709$	−14.6656	+	2.91717i	−0.550778	+	0.109557i	−0.462631	−	0.886551i	$-0.653094\pi$
$709$	−14.6656	+	2.91717i	−0.550778	+	0.109557i	−0.0881469	+	0.996107i	$0.528094\pi$
$710$	−0.156517	−	3.94659i	−0.00587398	−	0.148113i
$711$	19.8541	+	47.9319i	0.744585	+	1.79759i
$712$	−6.30909	−	19.3447i	−0.236443	−	0.724972i
$713$	4.78837	−	11.5601i	0.179326	−	0.432931i
$714$	0.701217	−	1.90289i	0.0262424	−	0.0712138i
$715$	−1.00272	+	1.50068i	−0.0374996	+	0.0561221i
$716$	−3.65059	−	12.9076i	−0.136429	−	0.482381i
$717$	−68.1603	−	13.5579i	−2.54549	−	0.506330i
$718$	3.87358	+	0.612053i	0.144561	+	0.0228416i
$719$	24.2122	−	24.2122i	0.902963	−	0.902963i	−0.0927286	−	0.995691i	$-0.529559\pi$
$719$	24.2122	−	24.2122i	0.902963	−	0.902963i	0.995691	+	0.0927286i	$0.0295589\pi$
$720$	−38.9032	−	41.9611i	−1.44984	−	1.56380i
$721$	7.93659	+	7.93659i	0.295574	+	0.295574i
$722$	−11.8644	−	16.3173i	−0.441546	−	0.607266i
$723$	−3.93586	+	19.7869i	−0.146376	+	0.735883i
$724$	−43.0893	−	5.06779i	−1.60140	−	0.188343i
$725$	−3.34159	−	2.23278i	−0.124103	−	0.0829233i
$726$	14.1488	+	30.6614i	0.525111	+	1.13795i
$727$	−20.4528	−	8.47184i	−0.758553	−	0.314203i	−0.0303271	−	0.999540i	$-0.509655\pi$
$727$	−20.4528	−	8.47184i	−0.758553	−	0.314203i	−0.728226	+	0.685337i	$0.759655\pi$
$728$	−0.397535	+	0.0474965i	−0.0147336	+	0.00176034i
$729$	21.2183	−	8.78890i	0.785862	−	0.325515i
$730$	−4.57554	+	4.95345i	−0.169349	+	0.183336i
$731$	−0.878686	−	4.41746i	−0.0324994	−	0.163385i
$732$	−19.3649	+	1.53840i	−0.715749	+	0.0568608i
$733$	2.00568	+	3.00171i	0.0740814	+	0.110871i	0.866660	−	0.498899i	$-0.166262\pi$
$733$	2.00568	+	3.00171i	0.0740814	+	0.110871i	−0.792579	+	0.609769i	$0.791262\pi$
$734$	−6.17505	−	25.6793i	−0.227925	−	0.947839i
$735$			44.8595i			1.65467i
$736$	39.1489	−	0.0720449i	1.44305	−	0.00265561i
$737$			4.60007i			0.169446i
$738$	44.2221	−	10.6340i	1.62784	−	0.391443i
$739$	19.0522	+	28.5137i	0.700847	+	1.04889i	0.995635	+	0.0933295i	$0.0297510\pi$
$739$	19.0522	+	28.5137i	0.700847	+	1.04889i	−0.294788	+	0.955563i	$0.595249\pi$
$740$	−8.67076	+	10.1673i	−0.318743	+	0.373757i
$741$	−0.228717	−	1.14984i	−0.00840211	−	0.0422403i
$742$	0.520651	+	0.480929i	0.0191137	+	0.0176555i
$743$	−41.6805	+	17.2646i	−1.52911	+	0.633378i	−0.979391	−	0.201973i	$-0.935265\pi$
$743$	−41.6805	+	17.2646i	−1.52911	+	0.633378i	−0.549718	+	0.835351i	$0.685265\pi$
$744$	−13.4812	+	7.56938i	−0.494243	+	0.277507i
$745$	47.5037	+	19.6767i	1.74040	+	0.720898i
$746$	−47.3188	+	21.8354i	−1.73246	+	0.799450i
$747$	40.9292	+	27.3480i	1.49752	+	1.00061i
$748$	−3.21736	−	4.07503i	−0.117638	−	0.148998i
$749$	−2.27340	+	11.4292i	−0.0830683	+	0.417612i
$750$	−36.8394	+	26.7861i	−1.34518	+	0.978089i
$751$	−30.7983	−	30.7983i	−1.12385	−	1.12385i	−0.991158	−	0.132689i	$-0.957639\pi$
$751$	−30.7983	−	30.7983i	−1.12385	−	1.12385i	−0.132689	−	0.991158i	$-0.542361\pi$
$752$	−13.5719	+	2.17006i	−0.494915	+	0.0791339i
$753$	53.0955	−	53.0955i	1.93491	−	1.93491i
$754$	0.370050	−	2.34198i	0.0134764	−	0.0852901i
$755$	−6.35871	−	1.26483i	−0.231417	−	0.0460317i
$756$	13.1650	+	7.36001i	0.478805	+	0.267681i
$757$	11.2220	−	16.7948i	0.407869	−	0.610419i	−0.569492	−	0.821997i	$-0.692860\pi$
$757$	11.2220	−	16.7948i	0.407869	−	0.610419i	0.977361	+	0.211578i	$0.0678602\pi$
$758$	−35.9552	−	13.2495i	−1.30595	−	0.481245i
$759$	−34.8078	+	84.0335i	−1.26344	+	3.05022i
$760$	−14.2942	−	1.10910i	−0.518505	−	0.0402312i
$761$	10.6346	+	25.6742i	0.385504	+	0.930689i	0.990880	+	0.134749i	$0.0430228\pi$
$761$	10.6346	+	25.6742i	0.385504	+	0.930689i	−0.605376	+	0.795940i	$0.706977\pi$
$762$	−33.9695	+	1.34719i	−1.23058	+	0.0488034i
$763$	5.23605	−	1.04151i	0.189558	−	0.0377054i
$764$	−11.0912	−	21.7282i	−0.401267	−	0.786100i
$765$	−7.10297	+	4.74605i	−0.256808	+	0.171594i
$766$	15.0361	+	9.20654i	0.543277	+	0.332646i
$767$	−1.49958			−0.0541466
$768$	−38.0763	−	29.8356i	−1.37396	−	1.07660i
$769$	52.8993			1.90760			0.953798	−	0.300448i	$-0.0971361\pi$
$769$	52.8993			1.90760			0.953798	+	0.300448i	$0.0971361\pi$
$770$	−9.70142	−	5.94012i	−0.349615	−	0.214067i
$771$	−42.9249	+	28.6815i	−1.54590	+	1.03294i
$772$	14.9043	+	29.1982i	0.536418	+	1.05087i
$773$	21.6566	−	4.30777i	0.778934	−	0.154940i	0.210418	−	0.977612i	$-0.432518\pi$
$773$	21.6566	−	4.30777i	0.778934	−	0.154940i	0.568516	+	0.822672i	$0.307518\pi$
$774$	65.4449	−	2.59546i	2.35237	−	0.0932919i
$775$	−0.295577	−	0.713586i	−0.0106174	−	0.0256328i
$776$	−27.0826	−	2.10136i	−0.972208	−	0.0754344i
$777$	2.63546	−	6.36256i	0.0945466	−	0.228256i
$778$	−8.38370	−	3.08940i	−0.300570	−	0.110761i
$779$	6.33134	−	9.47552i	0.226844	−	0.339496i
$780$	2.19125	+	1.22504i	0.0784593	+	0.0438635i
$781$	5.11142	+	1.01672i	0.182901	+	0.0363813i
$782$	0.912186	−	5.77306i	0.0326197	−	0.206444i
$783$	−63.1609	+	63.1609i	−2.25719	+	2.25719i
$784$	4.02246	+	25.1571i	0.143659	+	0.898466i
$785$	−32.5355	−	32.5355i	−1.16124	−	1.16124i
$786$	−12.4640	+	9.06267i	−0.444578	+	0.323255i
$787$	4.63019	−	23.2775i	0.165048	−	0.829754i	−0.806192	−	0.591654i	$-0.798475\pi$
$787$	4.63019	−	23.2775i	0.165048	−	0.829754i	0.971241	−	0.238101i	$-0.0765248\pi$
$788$	16.3714	+	20.7357i	0.583208	+	0.738677i
$789$	−43.8376	−	29.2914i	−1.56066	−	1.04280i
$790$	−25.2748	+	11.6631i	−0.899239	+	0.414956i
$791$	−6.14659	−	2.54600i	−0.218548	−	0.0905254i
$792$	65.8341	−	36.9644i	2.33931	−	1.31347i
$793$	0.528967	−	0.219105i	0.0187842	−	0.00778066i
$794$	25.8831	+	23.9085i	0.918558	+	0.848480i
$795$	−0.867049	−	4.35895i	−0.0307511	−	0.154596i
$796$	−4.90614	+	5.75292i	−0.173893	+	0.203907i
$797$	−25.5956	−	38.3065i	−0.906643	−	1.35689i	−0.934004	−	0.357262i	$-0.883710\pi$
$797$	−25.5956	−	38.3065i	−0.906643	−	1.35689i	0.0273612	−	0.999626i	$-0.491290\pi$
$798$	7.18432	−	1.72760i	0.254322	−	0.0611564i
$799$			2.05193i			0.0725921i
$800$	1.70564	−	1.71193i	0.0603036	−	0.0605259i
$801$		−	44.1744i		−	1.56083i
$802$	−0.100038	−	0.416013i	−0.00353246	−	0.0146899i
$803$	−4.94329	−	7.39816i	−0.174445	−	0.261075i
$804$	6.37833	−	0.506710i	0.224946	−	0.0178703i
$805$	−2.49822	−	12.5594i	−0.0880507	−	0.442661i
$806$	0.309195	−	0.334733i	0.0108909	−	0.0117905i
$807$	−10.2651	+	4.25196i	−0.361350	+	0.149676i
$808$	43.6308	−	5.21290i	1.53493	−	0.183389i
$809$	−19.2600	−	7.97776i	−0.677146	−	0.280483i	0.0174870	−	0.999847i	$-0.494433\pi$
$809$	−19.2600	−	7.97776i	−0.677146	−	0.280483i	−0.694633	+	0.719364i	$0.744433\pi$
$810$	−14.1967	−	30.7652i	−0.498821	−	1.08098i
$811$	3.44040	+	2.29880i	0.120809	+	0.0807219i	0.614507	−	0.788912i	$-0.289355\pi$
$811$	3.44040	+	2.29880i	0.120809	+	0.0807219i	−0.493698	+	0.869634i	$0.664355\pi$
$812$	14.8418	+	1.74557i	0.520845	+	0.0612573i
$813$	−17.1441	+	86.1894i	−0.601271	+	3.02280i
$814$	−10.3688	−	14.2604i	−0.363427	−	0.499828i
$815$	21.0162	+	21.0162i	0.736167	+	0.736167i
$816$	−5.29592	+	4.90997i	−0.185394	+	0.171883i
$817$	11.6041	−	11.6041i	0.405977	−	0.405977i
$818$	12.1038	+	1.91249i	0.423200	+	0.0668686i
$819$	−0.852484	−	0.169570i	−0.0297882	−	0.00592524i
$820$	6.64126	+	23.4820i	0.231923	+	0.820026i
$821$	−4.72002	+	7.06401i	−0.164730	+	0.246536i	−0.904646	−	0.426163i	$-0.859865\pi$
$821$	−4.72002	+	7.06401i	−0.164730	+	0.246536i	0.739916	+	0.672699i	$0.234865\pi$
$822$	19.8303	−	53.8133i	0.691661	−	1.87696i
$823$	6.08212	−	14.6835i	0.212009	−	0.511836i	−0.781723	−	0.623626i	$-0.785659\pi$
$823$	6.08212	−	14.6835i	0.212009	−	0.511836i	0.993732	+	0.111791i	$0.0356587\pi$
$824$	−12.3933	−	37.9999i	−0.431742	−	1.32379i
$825$	2.14862	+	5.18724i	0.0748055	+	0.180596i
$826$	−0.374539	−	9.44405i	−0.0130319	−	0.328601i
$827$	13.0143	−	2.58870i	0.452551	−	0.0900181i	0.0364484	−	0.999336i	$-0.488396\pi$
$827$	13.0143	−	2.58870i	0.452551	−	0.0900181i	0.416103	+	0.909317i	$0.363396\pi$
$828$	80.8518	+	26.2046i	2.80980	+	0.910672i
$829$	0.266055	−	0.177772i	0.00924047	−	0.00617428i	−0.550941	−	0.834544i	$-0.685731\pi$
$829$	0.266055	−	0.177772i	0.00924047	−	0.00617428i	0.560182	+	0.828370i	$0.310731\pi$
$830$	−13.7914	+	22.5242i	−0.478707	+	0.781825i
$831$	54.7812			1.90034
$832$	1.33869	+	0.490513i	0.0464107	+	0.0170055i
$833$	3.80349			0.131783
$834$	28.6318	−	46.7614i	0.991438	−	1.61922i
$835$	9.64545	−	6.44489i	0.333795	−	0.223034i
$836$	5.83263	−	17.9961i	0.201726	−	0.622407i
$837$	−16.8369	+	3.34907i	−0.581968	+	0.115761i
$838$	0.955317	+	24.0884i	0.0330009	+	0.832121i
$839$	−11.9276	−	28.7957i	−0.411785	−	0.994137i	−0.984658	−	0.174493i	$-0.944171\pi$
$839$	−11.9276	−	28.7957i	−0.411785	−	0.994137i	0.572874	−	0.819644i	$-0.305829\pi$
$840$	−7.16777	+	14.1060i	−0.247312	+	0.486704i
$841$	−22.7706	+	54.9731i	−0.785194	+	1.89563i
$842$	−11.5372	+	31.3084i	−0.397598	+	1.07896i
$843$	8.22160	−	12.3045i	0.283167	−	0.423789i
$844$	12.2417	−	3.46224i	0.421376	−	0.119175i
$845$	29.6308	+	5.89392i	1.01933	+	0.202757i
$846$	−29.4731	−	4.65697i	−1.01331	−	0.160110i
$847$	4.43566	−	4.43566i	0.152411	−	0.152411i
$848$	−0.877096	−	2.36674i	−0.0301196	−	0.0812741i
$849$	−7.91057	−	7.91057i	−0.271490	−	0.271490i
$850$	−0.212170	−	0.291801i	−0.00727736	−	0.0100087i
$851$	3.87213	−	19.4665i	0.132735	−	0.667304i
$852$	0.846726	−	7.19935i	0.0290083	−	0.246646i
$853$	−5.25349	−	3.51027i	−0.179876	−	0.120189i	0.462373	−	0.886686i	$-0.346998\pi$
$853$	−5.25349	−	3.51027i	−0.179876	−	0.120189i	−0.642249	+	0.766496i	$0.721998\pi$
$854$	1.51200	+	3.27661i	0.0517396	+	0.112123i
$855$	−28.7566	−	11.9114i	−0.983456	−	0.407361i
$856$	25.6549	−	32.6172i	0.876868	−	1.11483i
$857$	−11.1977	+	4.63825i	−0.382507	+	0.158439i	−0.565647	−	0.824647i	$-0.691374\pi$
$857$	−11.1977	+	4.63825i	−0.382507	+	0.158439i	0.183141	+	0.983087i	$0.441374\pi$
$858$	−2.24762	+	2.43326i	−0.0767324	+	0.0830700i
$859$	10.3238	+	51.9011i	0.352243	+	1.77084i	0.597984	+	0.801508i	$0.295969\pi$
$859$	10.3238	+	51.9011i	0.352243	+	1.77084i	−0.245741	+	0.969335i	$0.579031\pi$
$860$	2.78292	+	35.0307i	0.0948969	+	1.19454i
$861$	−6.98735	−	10.4573i	−0.238128	−	0.356384i
$862$	2.83690	+	11.7974i	0.0966251	+	0.401821i
$863$		−	44.3164i		−	1.50855i	−0.656559	−	0.754275i	$-0.727989\pi$
$863$		−	44.3164i		−	1.50855i	0.656559	−	0.754275i	$-0.272011\pi$
$864$	−29.9222	−	44.6038i	−1.01797	−	1.51745i
$865$			48.2960i			1.64211i
$866$	36.9650	−	8.88891i	1.25612	−	0.302058i
$867$	−27.9554	−	41.8382i	−0.949415	−	1.42090i
$868$	2.18531	+	1.86365i	0.0741742	+	0.0632564i
$869$	−7.16552	−	36.0235i	−0.243074	−	1.22201i
$870$	−68.8336	−	63.5821i	−2.33368	−	2.15564i
$871$	−0.174228	+	0.0721678i	−0.00590350	+	0.00244531i
$872$	−18.3033	−	5.14024i	−0.619826	−	0.174071i
$873$	−54.4839	−	22.5680i	−1.84400	−	0.763810i
$874$	19.3362	−	8.92274i	0.654057	−	0.301816i
$875$	7.03523	+	4.70079i	0.237834	+	0.158916i
$876$	−9.71357	+	7.66916i	−0.328191	+	0.259117i
$877$	−7.58614	+	38.1381i	−0.256166	+	1.28783i	0.611722	+	0.791073i	$0.290477\pi$
$877$	−7.58614	+	38.1381i	−0.256166	+	1.28783i	−0.867888	+	0.496760i	$0.834523\pi$
$878$	−2.99693	+	2.17908i	−0.101141	+	0.0735404i
$879$	−2.20549	−	2.20549i	−0.0743892	−	0.0743892i
$880$	21.2169	+	34.5086i	0.715221	+	1.16329i
$881$	18.0489	−	18.0489i	0.608084	−	0.608084i	−0.334361	−	0.942445i	$-0.608520\pi$
$881$	18.0489	−	18.0489i	0.608084	−	0.608084i	0.942445	+	0.334361i	$0.108520\pi$
$882$	−8.63224	+	54.6319i	−0.290662	+	1.83955i
$883$	7.66573	+	1.52481i	0.257972	+	0.0513139i	0.322382	−	0.946610i	$-0.395516\pi$
$883$	7.66573	+	1.52481i	0.257972	+	0.0513139i	−0.0644097	+	0.997924i	$0.520516\pi$
$884$	0.103867	−	0.185789i	0.00349343	−	0.00624875i
$885$	−32.9257	+	49.2768i	−1.10678	+	1.65642i
$886$	14.0054	+	5.16100i	0.470520	+	0.173387i
$887$	−5.60114	+	13.5223i	−0.188068	+	0.454036i	−0.989587	−	0.143933i	$-0.954025\pi$
$887$	−5.60114	+	13.5223i	−0.188068	+	0.454036i	0.801520	+	0.597968i	$0.204025\pi$
$888$	−18.6310	+	15.9480i	−0.625214	+	0.535178i
$889$	2.41675	+	5.83455i	0.0810552	+	0.195684i
$890$	23.6825	−	0.939218i	0.793839	−	0.0314827i
$891$	43.8488	−	8.72206i	1.46899	−	0.292200i
$892$	−10.0704	+	5.14045i	−0.337181	+	0.172115i
$893$	−6.21639	+	4.15366i	−0.208024	+	0.138997i
$894$	80.4801	+	49.2775i	2.69166	+	1.64809i
$895$	15.6248			0.522279
$896$	−2.75480	+	8.55333i	−0.0920315	+	0.285747i
$897$	−3.72886			−0.124503
$898$	19.9755	+	12.2309i	0.666593	+	0.408151i
$899$	−14.1425	+	9.44972i	−0.471679	+	0.315166i
$900$	4.67284	−	2.38527i	0.155761	−	0.0795089i
$901$	−0.369581	+	0.0735143i	−0.0123125	+	0.00244912i
$902$	−32.1741	+	1.27599i	−1.07128	+	0.0424857i
$903$	−6.93081	−	16.7325i	−0.230643	−	0.556821i
$904$	15.4066	+	17.9986i	0.512417	+	0.598623i
$905$	19.3397	−	46.6901i	0.642873	−	1.55203i
$906$	−11.1650	−	4.11431i	−0.370931	−	0.136689i
$907$	−18.5691	+	27.7907i	−0.616578	+	0.922775i	−1.00000		0.000798948i	$-0.999746\pi$
$907$	−18.5691	+	27.7907i	−0.616578	+	0.922775i	0.383421	+	0.923573i	$0.374746\pi$
$908$	6.37379	−	11.4009i	0.211522	−	0.378352i
$909$	93.5631	+	18.6109i	3.10329	+	0.617283i
$910$	0.0727835	−	0.460634i	0.00241275	−	0.0152699i
$911$	19.9890	−	19.9890i	0.662264	−	0.662264i	−0.293649	−	0.955913i	$-0.594870\pi$
$911$	19.9890	−	19.9890i	0.662264	−	0.662264i	0.955913	+	0.293649i	$0.0948698\pi$
$912$	−25.5953	−	6.10505i	−0.847545	−	0.202158i
$913$	−24.6419	−	24.6419i	−0.815527	−	0.815527i
$914$	−10.0926	+	7.33835i	−0.333832	+	0.242731i
$915$	4.41444	−	22.1929i	0.145937	−	0.733675i
$916$	−34.0322	+	26.8694i	−1.12445	+	0.887791i
$917$	2.38027	+	1.59044i	0.0786033	+	0.0525210i
$918$	−7.28085	+	3.35977i	−0.240304	+	0.110889i
$919$	32.1621	+	13.3220i	1.06093	+	0.439452i	0.843782	−	0.536687i	$-0.180324\pi$
$919$	32.1621	+	13.3220i	1.06093	+	0.439452i	0.217149	+	0.976139i	$0.430324\pi$
$920$	−12.3296	+	43.9029i	−0.406495	+	1.44744i
$921$	41.1611	−	17.0495i	1.35630	−	0.561799i
$922$	−27.1698	−	25.0970i	−0.894790	−	0.826525i
$923$	0.0416814	+	0.209547i	0.00137196	+	0.00689732i
$924$	−15.8855	−	13.5473i	−0.522596	−	0.445674i
$925$	−0.680671	−	1.01870i	−0.0223803	−	0.0334945i
$926$	−20.0468	+	4.82060i	−0.658777	+	0.158415i
$927$		−	86.7744i		−	2.85005i
$928$	−44.3029	−	29.4845i	−1.45431	−	0.967875i
$929$		−	1.74110i		−	0.0571236i	−0.999592	−	0.0285618i	$-0.990907\pi$
$929$		−	1.74110i		−	0.0571236i	0.999592	−	0.0285618i	$-0.00909274\pi$
$930$	−4.21057	−	17.5099i	−0.138070	−	0.574172i
$931$	7.69930	+	11.5228i	0.252334	+	0.377645i
$932$	0.614190	+	7.73125i	0.0201184	+	0.253246i
$933$	19.3927	+	97.4935i	0.634887	+	3.19179i
$934$	22.9087	−	24.8008i	0.749596	−	0.811507i
$935$	5.58741	−	2.31438i	0.182728	−	0.0756884i
$936$	2.43287	+	1.91356i	0.0795207	+	0.0625468i
$937$	7.06597	+	2.92682i	0.230835	+	0.0956151i	0.495103	−	0.868834i	$-0.335130\pi$
$937$	7.06597	+	2.92682i	0.230835	+	0.0956151i	−0.264268	+	0.964449i	$0.585130\pi$
$938$	−0.498015	−	1.07923i	−0.0162608	−	0.0352382i
$939$	−39.9011	−	26.6611i	−1.30212	−	0.870051i
$940$	1.87002	−	15.9000i	0.0609933	−	0.518600i
$941$	0.778661	−	3.91459i	0.0253836	−	0.127612i	−0.966016	−	0.258483i	$-0.916777\pi$
$941$	0.778661	−	3.91459i	0.0253836	−	0.127612i	0.991399	+	0.130871i	$0.0417774\pi$
$942$	−49.6619	−	68.3008i	−1.61807	−	2.22536i
$943$	−25.6305	−	25.6305i	−0.834643	−	0.834643i
$944$	−14.0461	+	30.5866i	−0.457160	+	0.995509i
$945$	−12.4228	+	12.4228i	−0.404114	+	0.404114i
$946$	−45.7999	−	7.23671i	−1.48908	−	0.235286i
$947$	43.5246	+	8.65759i	1.41436	+	0.281334i	0.842358	−	0.538918i	$-0.181167\pi$
$947$	43.5246	+	8.65759i	1.41436	+	0.281334i	0.572002	+	0.820252i	$0.306167\pi$
$948$	−49.1599	+	13.9036i	−1.59664	+	0.451568i
$949$	0.202654	−	0.303294i	0.00657844	−	0.00984532i
$950$	0.454531	−	1.23346i	0.0147469	−	0.0400187i
$951$	17.7423	−	42.8337i	0.575334	−	1.38898i
$952$	1.19600	+	0.607732i	0.0387627	+	0.0196967i
$953$	11.8200	+	28.5361i	0.382888	+	0.924374i	0.991404	+	0.130833i	$0.0417650\pi$
$953$	11.8200	+	28.5361i	0.382888	+	0.924374i	−0.608516	+	0.793541i	$0.708235\pi$
$954$	−0.217146	−	5.47537i	−0.00703037	−	0.177272i
$955$	27.8701	−	5.54371i	0.901855	−	0.179390i
$956$	14.1742	−	43.7333i	0.458427	−	1.41444i
$957$	102.805	−	68.6924i	3.32323	−	2.22051i
$958$	−5.33802	+	8.71805i	−0.172463	+	0.281667i
$959$	−10.6537			−0.344026
$960$	45.5116	−	33.2199i	1.46888	−	1.07217i
$961$	27.7311			0.894551
$962$	0.377446	−	0.616445i	0.0121693	−	0.0198750i
$963$	74.9082	−	50.0521i	2.41388	−	1.61291i
$964$	−12.6958	−	4.11477i	−0.408903	−	0.132528i
$965$	−37.4516	+	7.44958i	−1.20561	+	0.239811i
$966$	−0.931333	−	23.4837i	−0.0299651	−	0.755575i
$967$	20.2478	+	48.8824i	0.651124	+	1.57195i	0.811149	+	0.584839i	$0.198842\pi$
$967$	20.2478	+	48.8824i	0.651124	+	1.57195i	−0.160025	+	0.987113i	$0.551158\pi$
$968$	−21.2377	+	6.92647i	−0.682604	+	0.222625i
$969$	−1.50334	+	3.62938i	−0.0482941	+	0.116592i
$970$	10.9406	−	29.6894i	0.351281	−	0.953269i
$971$	−10.4503	+	15.6399i	−0.335365	+	0.501909i	−0.960376	−	0.278707i	$-0.910094\pi$
$971$	−10.4503	+	15.6399i	−0.335365	+	0.501909i	0.625012	+	0.780615i	$0.285094\pi$
$972$	−1.41983	−	5.02020i	−0.0455412	−	0.161023i
$973$	−9.98987	−	1.98711i	−0.320260	−	0.0637038i
$974$	20.4985	+	3.23891i	0.656813	+	0.103781i
$975$	−0.162759	+	0.162759i	−0.00521246	+	0.00521246i
$976$	0.485612	−	12.8415i	0.0155440	−	0.411047i
$977$	−3.83519	−	3.83519i	−0.122699	−	0.122699i	0.643091	−	0.765790i	$-0.277652\pi$
$977$	−3.83519	−	3.83519i	−0.122699	−	0.122699i	−0.765790	+	0.643091i	$0.777652\pi$
$978$	32.0790	+	44.1188i	1.02577	+	1.41076i
$979$	−6.10111	+	30.6723i	−0.194992	+	0.980292i
$980$	−29.4725	−	3.46630i	−0.941463	−	0.110727i
$981$	−34.3177	−	22.9304i	−1.09568	−	0.732111i
$982$	11.8393	+	25.6565i	0.377806	+	0.818732i
$983$	11.2735	+	4.66965i	0.359570	+	0.148939i	0.555153	−	0.831748i	$-0.312660\pi$
$983$	11.2735	+	4.66965i	0.359570	+	0.148939i	−0.195583	+	0.980687i	$0.562660\pi$
$984$	5.31331	+	44.4712i	0.169382	+	1.41769i
$985$	−28.4314	+	11.7767i	−0.905900	+	0.375236i
$986$	−5.39092	+	5.83617i	−0.171682	+	0.185862i
$987$	1.60970	+	8.09250i	0.0512372	+	0.257587i
$988$	0.773108	−	0.0614176i	0.0245959	−	0.00195395i
$989$	−28.9989	−	43.3999i	−0.922111	−	1.38004i
$990$	20.5620	+	85.5081i	0.653502	+	2.71763i
$991$		−	4.91122i		−	0.156010i	−0.996953	−	0.0780051i	$-0.975145\pi$
$991$		−	4.91122i		−	0.156010i	0.996953	−	0.0780051i	$-0.0248550\pi$
$992$	−3.93135	−	9.44193i	−0.124820	−	0.299782i
$993$			87.1946i			2.76704i
$994$	−1.30928	+	0.314839i	−0.0415277	+	0.00998608i
$995$	−4.89290	−	7.32275i	−0.155115	−	0.232147i
$996$	−31.4534	+	36.8821i	−0.996638	+	1.16865i
$997$	−7.85511	−	39.4903i	−0.248774	−	1.25067i	−0.879963	−	0.475042i	$-0.842433\pi$
$997$	−7.85511	−	39.4903i	−0.248774	−	1.25067i	0.631189	−	0.775629i	$-0.282567\pi$
$998$	1.83986	+	1.69949i	0.0582398	+	0.0537966i
$999$	−25.1577	+	10.4206i	−0.795953	+	0.329695i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.2.i.a.13.2	yes	56
3.2	odd	2		576.2.bd.a.397.6		56
4.3	odd	2		256.2.i.a.145.1		56
8.3	odd	2		512.2.i.a.33.7		56
8.5	even	2		512.2.i.b.33.1		56
64.5	even	16	inner	64.2.i.a.5.2	✓	56
64.27	odd	16		512.2.i.a.481.7		56
64.37	even	16		512.2.i.b.481.1		56
64.59	odd	16		256.2.i.a.113.1		56
192.5	odd	16		576.2.bd.a.325.6		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.5.2	✓	56	64.5	even	16	inner
64.2.i.a.13.2	yes	56	1.1	even	1	trivial
256.2.i.a.113.1		56	64.59	odd	16
256.2.i.a.145.1		56	4.3	odd	2
512.2.i.a.33.7		56	8.3	odd	2
512.2.i.a.481.7		56	64.27	odd	16
512.2.i.b.33.1		56	8.5	even	2
512.2.i.b.481.1		56	64.37	even	16
576.2.bd.a.325.6		56	192.5	odd	16
576.2.bd.a.397.6		56	3.2	odd	2

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:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	64.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20609 - 0.738481i) q^{2} +(2.51381 - 1.67967i) q^{3} +(0.909293 + 1.78134i) q^{4} +(-2.28487 + 0.454489i) q^{5} +(-4.27227 + 0.169433i) q^{6} +(0.303950 + 0.733799i) q^{7} +(0.218802 - 2.81995i) q^{8} +(2.34987 - 5.67309i) q^{9} +O(q^{10})\)	\(q+(-1.20609 - 0.738481i) q^{2} +(2.51381 - 1.67967i) q^{3} +(0.909293 + 1.78134i) q^{4} +(-2.28487 + 0.454489i) q^{5} +(-4.27227 + 0.169433i) q^{6} +(0.303950 + 0.733799i) q^{7} +(0.218802 - 2.81995i) q^{8} +(2.34987 - 5.67309i) q^{9} +(3.09139 + 1.13918i) q^{10} +(-2.41516 + 3.61454i) q^{11} +(5.27786 + 2.95064i) q^{12} +(-0.174791 - 0.0347682i) q^{13} +(0.175307 - 1.10949i) q^{14} +(-4.98033 + 4.98033i) q^{15} +(-2.34637 + 3.23953i) q^{16} +(0.422266 + 0.422266i) q^{17} +(-7.02362 + 5.10691i) q^{18} +(-0.424489 + 2.13405i) q^{19} +(-2.88722 - 3.65688i) q^{20} +(1.99661 + 1.33409i) q^{21} +(5.58216 - 2.57590i) q^{22} +(6.39382 + 2.64841i) q^{23} +(-4.18656 - 7.45632i) q^{24} +(0.394679 - 0.163481i) q^{25} +(0.185138 + 0.171014i) q^{26} +(-1.85234 - 9.31236i) q^{27} +(-1.03077 + 1.20868i) q^{28} +(-5.22657 - 7.82211i) q^{29} +(9.68459 - 2.32883i) q^{30} -1.80802i q^{31} +(5.22226 - 2.17440i) q^{32} +13.1429i q^{33} +(-0.197454 - 0.821125i) q^{34} +(-1.02799 - 1.53849i) q^{35} +(12.2425 - 0.972570i) q^{36} +(-0.559507 - 2.81283i) q^{37} +(2.08792 - 2.26037i) q^{38} +(-0.497791 + 0.206192i) q^{39} +(0.781702 + 6.54267i) q^{40} +(-4.83885 - 2.00432i) q^{41} +(-1.42289 - 3.08349i) q^{42} +(-6.27110 - 4.19021i) q^{43} +(-8.63483 - 1.01555i) q^{44} +(-2.79080 + 14.0303i) q^{45} +(-5.75571 - 7.91592i) q^{46} +(2.42967 + 2.42967i) q^{47} +(-0.456990 + 12.0847i) q^{48} +(4.50367 - 4.50367i) q^{49} +(-0.596745 - 0.0942900i) q^{50} +(1.77076 + 0.352226i) q^{51} +(-0.0970024 - 0.342978i) q^{52} +(-0.350569 + 0.524664i) q^{53} +(-4.64291 + 12.5994i) q^{54} +(3.87556 - 9.35642i) q^{55} +(2.13578 - 0.696566i) q^{56} +(2.51742 + 6.07759i) q^{57} +(0.527218 + 13.2939i) q^{58} +(8.25271 - 1.64157i) q^{59} +(-13.4003 - 4.34310i) q^{60} +(-2.67124 + 1.78487i) q^{61} +(-1.33519 + 2.18063i) q^{62} +4.87715 q^{63} +(-7.90425 - 1.23402i) q^{64} +0.415178 q^{65} +(9.70580 - 15.8515i) q^{66} +(0.879840 - 0.587891i) q^{67} +(-0.368238 + 1.13616i) q^{68} +(20.5213 - 4.08194i) q^{69} +(0.103696 + 2.61471i) q^{70} +(-0.458776 - 1.10758i) q^{71} +(-15.4837 - 7.86781i) q^{72} +(-0.783268 + 1.89098i) q^{73} +(-1.40241 + 3.80570i) q^{74} +(0.717551 - 1.07389i) q^{75} +(-4.18746 + 1.18431i) q^{76} +(-3.38643 - 0.673603i) q^{77} +(0.752647 + 0.118924i) q^{78} +(-5.97434 + 5.97434i) q^{79} +(3.88883 - 8.46830i) q^{80} +(-7.27213 - 7.27213i) q^{81} +(4.35592 + 5.99077i) q^{82} +(-1.56393 + 7.86242i) q^{83} +(-0.560975 + 4.76973i) q^{84} +(-1.15674 - 0.772908i) q^{85} +(4.46910 + 9.68485i) q^{86} +(-26.2772 - 10.8844i) q^{87} +(9.66439 + 7.60150i) q^{88} +(6.64632 - 2.75300i) q^{89} +(13.7270 - 14.8608i) q^{90} +(-0.0276149 - 0.138830i) q^{91} +(1.09613 + 13.7978i) q^{92} +(-3.03687 - 4.54500i) q^{93} +(-1.13613 - 4.72465i) q^{94} -5.06895i q^{95} +(9.47547 - 14.2377i) q^{96} -9.60392i q^{97} +(-8.75770 + 2.10595i) q^{98} +(14.8303 + 22.1951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^23 + 32 * q^24 - 8 * q^25 + 32 * q^26 - 8 * q^27 + 32 * q^28 - 8 * q^29 + 72 * q^30 + 32 * q^32 + 32 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^37 + 32 * q^38 - 8 * q^39 + 32 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 - 32 * q^50 + 24 * q^51 - 56 * q^52 - 8 * q^53 - 72 * q^54 + 56 * q^55 - 64 * q^56 - 8 * q^57 - 80 * q^58 + 56 * q^59 - 104 * q^60 - 8 * q^61 - 40 * q^62 + 64 * q^63 - 104 * q^64 - 16 * q^65 - 88 * q^66 + 72 * q^67 - 56 * q^68 - 8 * q^69 - 104 * q^70 + 56 * q^71 - 80 * q^72 - 8 * q^73 - 64 * q^74 + 56 * q^75 - 72 * q^76 - 8 * q^77 - 32 * q^78 + 24 * q^79 + 32 * q^80 - 8 * q^81 + 72 * q^82 - 8 * q^83 + 104 * q^84 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 72 * q^88 - 8 * q^89 + 136 * q^90 - 8 * q^91 + 144 * q^92 + 16 * q^93 + 88 * q^94 + 128 * q^96 + 128 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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