LMFDB - Embedded newform 64.2.i.a.5.2

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			5.2
Character	$\chi$	$=$	64.5
Dual form			64.2.i.a.13.2

$q$-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 $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

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

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	0.996875	+	0.0789971i	$0.0251718\pi$
$3$	2.51381	+	1.67967i	1.45135	+	0.969758i	0.454471	+	0.890761i	$0.349828\pi$
$4$	0.909293	−	1.78134i	0.454646	−	0.890672i
$5$	−2.28487	−	0.454489i	−1.02183	−	0.203254i	−0.344383	−	0.938829i	$-0.611912\pi$
$5$	−2.28487	−	0.454489i	−1.02183	−	0.203254i	−0.677443	+	0.735576i	$0.736912\pi$
$6$	−4.27227	−	0.169433i	−1.74415	−	0.0691707i
$7$	0.303950	−	0.733799i	0.114882	−	0.277350i	−0.855972	−	0.517023i	$-0.827040\pi$
$7$	0.303950	−	0.733799i	0.114882	−	0.277350i	0.970854	+	0.239673i	$0.0770402\pi$
$8$	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	−0.992121	−	0.125281i	$-0.960017\pi$
$11$	−2.41516	−	3.61454i	−0.728198	−	1.08983i	0.263923	−	0.964544i	$-0.414983\pi$
$12$	5.27786	−	2.95064i	1.52359	−	0.851776i
$13$	−0.174791	+	0.0347682i	−0.0484784	+	0.00964295i	−0.219270	−	0.975664i	$-0.570368\pi$
$13$	−0.174791	+	0.0347682i	−0.0484784	+	0.00964295i	0.170792	+	0.985307i	$0.445368\pi$
$14$	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	−0.654043	−	0.756457i	$-0.726928\pi$
$17$	0.422266	−	0.422266i	0.102415	−	0.102415i	0.756457	+	0.654043i	$0.226928\pi$
$18$	−7.02362	−	5.10691i	−1.65548	−	1.20371i
$19$	−0.424489	−	2.13405i	−0.0973844	−	0.489584i	−0.998438	−	0.0558761i	$-0.982205\pi$
$19$	−0.424489	−	2.13405i	−0.0973844	−	0.489584i	0.901053	−	0.433708i	$-0.142795\pi$
$20$	−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	0.401636	−	0.915799i	$-0.368442\pi$
$23$	6.39382	−	2.64841i	1.33320	−	0.552231i	0.931568	+	0.363568i	$0.118442\pi$
$24$	−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	−0.0804529	+	0.996758i	$0.525637\pi$
$29$	−5.22657	+	7.82211i	−0.970550	+	1.45253i	−0.890097	+	0.455772i	$0.849363\pi$
$30$	9.68459	+	2.32883i	1.76816	+	0.425185i
$31$			1.80802i			0.324729i	0.986731	+	0.162365i	$0.0519121\pi$
$31$			1.80802i			0.324729i	−0.986731	+	0.162365i	$0.948088\pi$
$32$	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	0.907151	+	0.420805i	$0.138252\pi$
$37$	−0.559507	+	2.81283i	−0.0919823	+	0.462426i	−0.999133	+	0.0416214i	$0.986748\pi$
$38$	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	−0.727065	−	0.686568i	$-0.759116\pi$
$41$	−4.83885	+	2.00432i	−0.755701	+	0.313022i	−0.0286356	+	0.999590i	$0.509116\pi$
$42$	−1.42289	+	3.08349i	−0.219556	+	0.475793i
$43$	−6.27110	+	4.19021i	−0.956334	+	0.639002i	−0.932675	−	0.360718i	$-0.882532\pi$
$43$	−6.27110	+	4.19021i	−0.956334	+	0.639002i	−0.0236588	+	0.999720i	$0.507532\pi$
$44$	−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	−0.507342	−	0.861745i	$-0.669372\pi$
$47$	2.42967	−	2.42967i	0.354403	−	0.354403i	0.861745	+	0.507342i	$0.169372\pi$
$48$	−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	0.806611	−	0.591082i	$-0.201299\pi$
$53$	−0.350569	−	0.524664i	−0.0481544	−	0.0720682i	−0.854766	+	0.519014i	$0.826299\pi$
$54$	−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	0.700429	−	0.713722i	$-0.252992\pi$
$59$	8.25271	+	1.64157i	1.07441	+	0.213714i	0.373982	+	0.927436i	$0.377992\pi$
$60$	−13.4003	+	4.34310i	−1.72997	+	0.560692i
$61$	−2.67124	−	1.78487i	−0.342018	−	0.228529i	0.372684	−	0.927958i	$-0.378438\pi$
$61$	−2.67124	−	1.78487i	−0.342018	−	0.228529i	−0.714702	+	0.699429i	$0.753438\pi$
$62$	−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	0.608153	−	0.793820i	$-0.291911\pi$
$67$	0.879840	+	0.587891i	0.107490	+	0.0718223i	−0.500664	+	0.865642i	$0.666911\pi$
$68$	−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	−0.948762	−	0.315991i	$-0.897663\pi$
$71$	−0.458776	+	1.10758i	−0.0544467	+	0.131446i	0.894316	+	0.447437i	$0.147663\pi$
$72$	−15.4837	+	7.86781i	−1.82477	+	0.927230i
$73$	−0.783268	−	1.89098i	−0.0916746	−	0.221322i	0.871391	−	0.490589i	$-0.163218\pi$
$73$	−0.783268	−	1.89098i	−0.0916746	−	0.221322i	−0.963065	+	0.269267i	$0.913218\pi$
$74$	−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	0.286049	−	0.958215i	$-0.407658\pi$
$79$	−5.97434	−	5.97434i	−0.672166	−	0.672166i	−0.958215	+	0.286049i	$0.907658\pi$
$80$	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	−0.966594	−	0.256312i	$-0.917493\pi$
$83$	−1.56393	−	7.86242i	−0.171664	−	0.863012i	0.794930	−	0.606701i	$-0.207507\pi$
$84$	−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	0.706030	−	0.708182i	$-0.250484\pi$
$89$	6.64632	+	2.75300i	0.704509	+	0.291817i	−0.00152141	+	0.999999i	$0.500484\pi$
$90$	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	$0.162115\pi$
$97$			9.60392i			0.975130i	−0.873087	+	0.487565i	$0.837885\pi$
$98$	−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	−0.471520	−	0.881855i	$-0.656295\pi$
$101$	3.03083	−	15.2370i	0.301579	−	1.51614i	0.773099	−	0.634285i	$-0.218705\pi$
$102$	−1.87558	+	1.73249i	−0.185710	+	0.171542i
$103$	13.0558	+	5.40788i	1.28642	+	0.532854i	0.917917	−	0.396771i	$-0.129869\pi$
$103$	13.0558	+	5.40788i	1.28642	+	0.532854i	0.368506	+	0.929625i	$0.379869\pi$
$104$	−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	0.197970	−	0.980208i	$-0.436565\pi$
$107$	12.1990	−	8.15112i	1.17932	−	0.787999i	0.981354	+	0.192209i	$0.0615652\pi$
$108$	14.9042	+	11.7673i	1.43416	+	1.13231i
$109$	1.31130	+	6.59237i	0.125600	+	0.631435i	0.991381	+	0.131011i	$0.0418224\pi$
$109$	1.31130	+	6.59237i	0.125600	+	0.631435i	−0.865781	+	0.500424i	$0.833178\pi$
$110$	−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	0.371317	−	0.928506i	$-0.378906\pi$
$113$	−5.92301	−	5.92301i	−0.557190	−	0.557190i	−0.928506	+	0.371317i	$0.878906\pi$
$114$	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	0.679558	−	0.733622i	$-0.262172\pi$
$131$	2.99684	+	2.00242i	0.261835	+	0.174953i	−0.417723	+	0.908575i	$0.637172\pi$
$132$	−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	−0.976450	−	0.215744i	$-0.930782\pi$
$137$	−5.13309	−	12.3924i	−0.438550	−	1.05875i	0.537900	−	0.843008i	$-0.319218\pi$
$138$	−27.7649	+	10.2314i	−2.36350	+	0.870954i
$139$	−7.12464	−	10.6628i	−0.604304	−	0.904405i	0.395598	−	0.918424i	$-0.370538\pi$
$139$	−7.12464	−	10.6628i	−0.604304	−	0.904405i	−0.999902	+	0.0140189i	$0.995538\pi$
$140$	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	−0.514262	+	0.857633i	$0.671934\pi$
$149$	−18.3515	+	12.2621i	−1.50341	+	1.00455i	−0.989149	+	0.146914i	$0.953066\pi$
$150$	−1.65848	−	0.765309i	−0.135414	−	0.0624872i
$151$	2.57112	−	1.06499i	0.209235	−	0.0866679i	−0.275605	−	0.961271i	$-0.588878\pi$
$151$	2.57112	−	1.06499i	0.209235	−	0.0866679i	0.484839	+	0.874603i	$0.338878\pi$
$152$	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	−0.0738963	−	0.997266i	$-0.523543\pi$
$157$	10.9729	−	16.4222i	0.875736	−	1.31063i	0.949632	−	0.313366i	$-0.101457\pi$
$158$	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	−0.997832	−	0.0658161i	$-0.979035\pi$
$163$	−7.08796	+	10.6079i	−0.555172	+	0.830873i	0.442660	+	0.896690i	$0.354035\pi$
$164$	−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	0.197516	−	0.980300i	$-0.436713\pi$
$167$	−4.60049	−	1.90558i	−0.355996	−	0.147459i	−0.553512	+	0.832841i	$0.686713\pi$
$168$	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	0.757492	+	0.652845i	$0.226425\pi$
$173$	4.04445	+	20.3328i	0.307494	+	1.54587i	−0.449998	+	0.893029i	$0.648575\pi$
$174$	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	−0.434698	−	0.900576i	$-0.643145\pi$
$179$	−6.57810	+	1.30847i	−0.491670	+	0.0977993i	−0.0569725	+	0.998376i	$0.518145\pi$
$180$	−27.5304	−	7.78626i	−2.05200	−	0.580353i
$181$	−12.0521	−	18.0372i	−0.895822	−	1.34069i	−0.939823	−	0.341661i	$-0.889011\pi$
$181$	−12.0521	−	18.0372i	−0.895822	−	1.34069i	0.0440013	−	0.999031i	$-0.485989\pi$
$182$	−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	0.633676	−	0.773599i	$-0.281545\pi$
$197$	12.9559	+	2.57710i	0.923073	+	0.183611i	0.289397	+	0.957209i	$0.406545\pi$
$198$	−1.49597	+	37.7212i	−0.106314	+	2.68073i
$199$	1.44670	−	3.49265i	0.102554	−	0.247587i	−0.864271	−	0.503026i	$-0.832220\pi$
$199$	1.44670	−	3.49265i	0.102554	−	0.247587i	0.966825	+	0.255439i	$0.0822199\pi$
$200$	−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	0.999703	+	0.0243884i	$0.00776383\pi$
$211$	1.24095	+	6.23870i	0.0854309	+	0.429490i	−0.914272	+	0.405102i	$0.867236\pi$
$212$	−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	$-0.939383\pi$
$223$		−	5.65324i		−	0.378569i	0.981922	−	0.189284i	$-0.0606168\pi$
$224$	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	−0.932117	−	0.362158i	$-0.882040\pi$
$227$	−3.62832	+	5.43017i	−0.240820	+	0.360413i	0.691296	+	0.722571i	$0.257040\pi$
$228$	−8.53720	−	10.0107i	−0.565390	−	0.662974i
$229$	4.22963	−	21.2638i	0.279502	−	1.40515i	−0.544594	−	0.838700i	$-0.683316\pi$
$229$	4.22963	−	21.2638i	0.279502	−	1.40515i	0.824096	−	0.566451i	$-0.191684\pi$
$230$	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	−0.262231	−	0.965005i	$-0.584458\pi$
$233$	3.58263	−	1.48397i	0.234706	−	0.0972182i	0.496936	+	0.867787i	$0.334458\pi$
$234$	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	−0.0527693	+	0.998607i	$0.516805\pi$
$239$	−16.2539	+	16.2539i	−1.05138	+	1.05138i	−0.998607	+	0.0527693i	$0.983195\pi$
$240$	−4.44819	+	27.8196i	−0.287129	+	1.79575i
$241$	−4.71850	−	4.71850i	−0.303945	−	0.303945i	0.538610	−	0.842555i	$-0.318950\pi$
$241$	−4.71850	−	4.71850i	−0.303945	−	0.303945i	−0.842555	+	0.538610i	$0.818950\pi$
$242$	−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	0.889913	−	0.456130i	$-0.150765\pi$
$251$	24.3591	+	4.84533i	1.53753	+	0.305834i	0.647620	+	0.761964i	$0.275765\pi$
$252$	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	0.573227	+	0.819397i	$0.305691\pi$
$263$	−6.67352	+	16.1113i	−0.411507	+	0.993465i	−0.984734	+	0.174069i	$0.944309\pi$
$264$	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	−0.303745	−	0.952753i	$-0.598237\pi$
$269$	−3.60444	+	0.716968i	−0.219767	+	0.0437143i	0.0839787	+	0.996468i	$0.473237\pi$
$270$	4.88214	+	30.8982i	0.297118	+	1.88041i
$271$	−20.5532	−	20.5532i	−1.24852	−	1.24852i	−0.956374	−	0.292145i	$-0.905631\pi$
$271$	−20.5532	−	20.5532i	−1.24852	−	1.24852i	−0.292145	−	0.956374i	$-0.594369\pi$
$272$	−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	−0.0134373	−	0.999910i	$-0.504277\pi$
$277$	15.0658	−	10.0667i	0.905217	−	0.604846i	0.918654	+	0.395063i	$0.129277\pi$
$278$	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	0.513468	−	0.858109i	$-0.328360\pi$
$281$	4.52217	+	1.87315i	0.269770	+	0.111743i	−0.243698	+	0.969851i	$0.578360\pi$
$282$	−10.7919	+	9.96853i	−0.642646	+	0.593617i
$283$	−0.721894	+	3.62921i	−0.0429121	+	0.215734i	−0.996292	−	0.0860399i	$-0.972579\pi$
$283$	−0.721894	+	3.62921i	−0.0429121	+	0.215734i	0.953380	+	0.301774i	$0.0975787\pi$
$284$	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	−0.986219	−	0.165446i	$-0.947094\pi$
$293$	−0.201266	+	1.01183i	−0.0117581	+	0.0591118i	0.974461	+	0.224558i	$0.0720937\pi$
$294$	−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	0.235438	−	0.971889i	$-0.424348\pi$
$307$	14.4531	−	2.87489i	0.824880	−	0.164079i	0.589442	+	0.807811i	$0.299348\pi$
$308$	−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	−0.691142	−	0.722719i	$-0.742892\pi$
$311$	−12.5822	−	30.3761i	−0.713470	−	1.72247i	−0.0223281	−	0.999751i	$-0.507108\pi$
$312$	0.472533	−	1.44886i	0.0267519	−	0.0820256i
$313$	−6.07425	+	14.6645i	−0.343337	+	0.828889i	0.654037	+	0.756463i	$0.273074\pi$
$313$	−6.07425	+	14.6645i	−0.343337	+	0.828889i	−0.997374	+	0.0724262i	$0.976926\pi$
$314$	−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	0.859486	−	0.511160i	$-0.170784\pi$
$317$	12.7506	+	8.51970i	0.716147	+	0.478514i	−0.143339	+	0.989674i	$0.545784\pi$
$318$	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	−0.947321	−	0.320285i	$-0.896221\pi$
$331$	−16.0230	−	23.9801i	−0.880702	−	1.31806i	0.0666189	−	0.997778i	$-0.478779\pi$
$332$	−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	−0.158695	+	0.987328i	$0.550729\pi$
$337$	−21.0382	+	21.0382i	−1.14602	+	1.14602i	−0.987328	+	0.158695i	$0.949271\pi$
$338$	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	0.851240	+	0.524777i	$0.175851\pi$
$347$	−2.53390	+	12.7388i	−0.136027	+	0.683853i	−0.987266	+	0.159076i	$0.949149\pi$
$348$	−4.50484	+	56.7057i	−0.241485	+	3.03975i
$349$	4.24727	−	6.35649i	0.227351	−	0.340255i	−0.700203	−	0.713944i	$-0.746907\pi$
$349$	4.24727	−	6.35649i	0.227351	−	0.340255i	0.927554	+	0.373689i	$0.121907\pi$
$350$	−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	$0.253410\pi$
$353$			26.8538i			1.42928i	−0.699491	+	0.714642i	$0.746590\pi$
$354$	−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	0.314051	−	0.949406i	$-0.398314\pi$
$359$	−2.56193	−	1.06119i	−0.135214	−	0.0560073i	−0.449264	+	0.893399i	$0.648314\pi$
$360$	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	−0.272755	−	0.962084i	$-0.587935\pi$
$367$	13.2056	−	13.2056i	0.689329	−	0.689329i	0.962084	+	0.272755i	$0.0879347\pi$
$368$	−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	0.779271	+	0.626688i	$0.215590\pi$
$373$	20.4728	+	30.6397i	1.06004	+	1.58646i	0.280770	+	0.959775i	$0.409410\pi$
$374$	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	0.822631	−	0.568576i	$-0.192506\pi$
$379$	26.5748	+	5.28606i	1.36506	+	0.271527i	0.542427	+	0.840103i	$0.317506\pi$
$380$	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	0.349659	−	0.936877i	$-0.386298\pi$
$389$	6.19647	+	1.23255i	0.314173	+	0.0624930i	−0.0354851	+	0.999370i	$0.511298\pi$
$390$	−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	−0.765476	−	0.643465i	$-0.777496\pi$
$397$	−24.4366	+	4.86075i	−1.22644	+	0.243954i	−0.460964	+	0.887419i	$0.652496\pi$
$398$	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	−0.701745	−	0.712428i	$-0.747595\pi$
$401$	0.213936	−	0.213936i	0.0106835	−	0.0106835i	0.712428	+	0.701745i	$0.247595\pi$
$402$	−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	0.175881	−	0.984411i	$-0.443723\pi$
$409$	−8.00529	−	3.31590i	−0.395836	−	0.163961i	−0.571717	+	0.820451i	$0.693723\pi$
$410$	−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	−0.987294	−	0.158904i	$-0.949204\pi$
$419$	−9.47052	+	14.1736i	−0.462665	+	0.692427i	0.524629	+	0.851331i	$0.324204\pi$
$420$	−0.886036	+	11.1532i	−0.0432341	+	0.544220i
$421$	−4.60289	+	23.1403i	−0.224331	+	1.12779i	0.690307	+	0.723517i	$0.257475\pi$
$421$	−4.60289	+	23.1403i	−0.224331	+	1.12779i	−0.914638	+	0.404273i	$0.867525\pi$
$422$	−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	−0.837961	−	0.545731i	$-0.816252\pi$
$431$	−6.06685	+	6.06685i	−0.292230	+	0.292230i	0.545731	+	0.837961i	$0.316252\pi$
$432$	34.5139	−	15.8496i	1.66055	−	0.762562i
$433$	−19.0094	−	19.0094i	−0.913533	−	0.913533i	0.0830154	−	0.996548i	$-0.473545\pi$
$433$	−19.0094	−	19.0094i	−0.913533	−	0.913533i	−0.996548	+	0.0830154i	$0.973545\pi$
$434$	−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	0.945999	−	0.324169i	$-0.105085\pi$
$439$	1.00267	+	2.42067i	0.0478550	+	0.115532i	−0.898144	+	0.439701i	$0.855085\pi$
$440$	−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	−0.0570485	−	0.998371i	$-0.518169\pi$
$443$	−10.3515	−	2.05904i	−0.491815	−	0.0978280i	−0.434766	+	0.900543i	$0.643169\pi$
$444$	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	0.982967	−	0.183780i	$-0.0588334\pi$
$457$	3.37664	+	8.15192i	0.157952	+	0.381331i	−0.825015	+	0.565111i	$0.808833\pi$
$458$	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	0.442620	−	0.896709i	$-0.354049\pi$
$461$	25.6514	−	5.10238i	1.19470	−	0.237641i	0.752084	+	0.659068i	$0.229049\pi$
$462$	14.5819	−	2.30404i	0.678411	−	0.107194i
$463$	10.3091	+	10.3091i	0.479105	+	0.479105i	0.904845	−	0.425741i	$-0.139986\pi$
$463$	10.3091	+	10.3091i	0.479105	+	0.479105i	−0.425741	+	0.904845i	$0.639986\pi$
$464$	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	−0.925345	−	0.379126i	$-0.876225\pi$
$467$	−4.65749	−	23.4148i	−0.215523	−	1.08351i	0.709822	−	0.704381i	$-0.248775\pi$
$468$	−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	$0.0528065\pi$
$479$			7.22838i			0.330273i	−0.986271	+	0.165136i	$0.947194\pi$
$480$	−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	0.0537402	−	0.998555i	$-0.482886\pi$
$487$	−13.5574	−	5.61566i	−0.614345	−	0.254470i	−0.668085	+	0.744085i	$0.732886\pi$
$488$	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	−0.870769	−	0.491692i	$-0.836379\pi$
$491$	−16.6130	+	11.1005i	−0.749734	+	0.500956i	0.121035	+	0.992648i	$0.461379\pi$
$492$	−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	−0.233817	−	0.972281i	$-0.575122\pi$
$499$	−1.73704	+	0.345518i	−0.0777605	+	0.0154675i	0.156057	+	0.987748i	$0.450122\pi$
$500$	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	0.720000	−	0.693974i	$-0.244142\pi$
$503$	−6.27595	−	15.1515i	−0.279831	−	0.675571i	−0.999831	+	0.0184028i	$0.994142\pi$
$504$	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	0.534068	−	0.845442i	$-0.320663\pi$
$509$	−0.961984	−	0.642777i	−0.0426392	−	0.0284906i	−0.576707	+	0.816951i	$0.695663\pi$
$510$	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	0.959081	−	0.283130i	$-0.0913729\pi$
$521$	1.84213	+	4.44729i	0.0807050	+	0.194839i	−0.878376	+	0.477970i	$0.841373\pi$
$522$	76.6563	−	28.2479i	3.35515	−	1.23638i
$523$	−1.19764	−	1.79239i	−0.0523691	−	0.0783759i	0.804361	−	0.594141i	$-0.202508\pi$
$523$	−1.19764	−	1.79239i	−0.0523691	−	0.0783759i	−0.856730	+	0.515765i	$0.827508\pi$
$524$	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	−0.684273	−	0.729226i	$-0.739880\pi$
$541$	5.84519	−	8.74795i	0.251304	−	0.376104i	0.935577	+	0.353123i	$0.114880\pi$
$542$	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	−0.243803	−	0.969825i	$-0.578395\pi$
$547$	17.4357	−	26.0944i	0.745498	−	1.11572i	0.989301	−	0.145892i	$-0.0466051\pi$
$548$	−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	−0.999913	−	0.0132219i	$-0.995791\pi$
$557$	−1.91577	−	9.63121i	−0.0811736	−	0.408087i	0.918739	−	0.394865i	$-0.129209\pi$
$558$	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	0.0147220	−	0.999892i	$-0.495314\pi$
$563$	9.75123	−	1.93964i	0.410965	−	0.0817461i	0.396243	+	0.918146i	$0.370314\pi$
$564$	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	−0.434517	−	0.900664i	$-0.643081\pi$
$569$	12.1558	−	29.3467i	0.509599	−	1.23028i	0.944115	−	0.329616i	$-0.106919\pi$
$570$	0.858848	−	21.6560i	0.0359732	−	0.907068i
$571$	−14.9708	−	2.97788i	−0.626510	−	0.124621i	−0.128383	−	0.991725i	$-0.540979\pi$
$571$	−14.9708	−	2.97788i	−0.626510	−	0.124621i	−0.498127	+	0.867104i	$0.665979\pi$
$572$	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	0.999919	+	0.0127316i	$0.00405269\pi$
$587$	15.2402	+	22.8085i	0.629029	+	0.941408i	−0.370890	+	0.928677i	$0.620947\pi$
$588$	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	−0.0371172	−	0.999311i	$-0.511817\pi$
$593$	23.4309	−	23.4309i	0.962194	−	0.962194i	0.999311	+	0.0371172i	$0.0118175\pi$
$594$	−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	−0.651692	−	0.758484i	$-0.725940\pi$
$599$	−14.1017	+	5.84110i	−0.576179	+	0.238661i	0.0755132	+	0.997145i	$0.475940\pi$
$600$	−2.87132	+	2.25843i	−0.117221	+	0.0922000i
$601$	16.4696	+	6.82193i	0.671809	+	0.278272i	0.692398	−	0.721516i	$-0.256554\pi$
$601$	16.4696	+	6.82193i	0.671809	+	0.278272i	−0.0205894	+	0.999788i	$0.506554\pi$
$602$	−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	$-0.929828\pi$
$607$		−	10.7750i		−	0.437344i	0.975798	−	0.218672i	$-0.0701724\pi$
$608$	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	0.844122	+	0.536150i	$0.180122\pi$
$613$	−3.48904	+	17.5406i	−0.140921	+	0.708457i	−0.985043	+	0.172307i	$0.944878\pi$
$614$	−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	0.386837	−	0.922148i	$-0.373568\pi$
$617$	32.6001	−	13.5034i	1.31243	−	0.543626i	0.925592	+	0.378523i	$0.123568\pi$
$618$	−54.8615	−	25.3160i	−2.20685	−	1.01836i
$619$	1.79801	−	1.20140i	0.0722683	−	0.0482881i	−0.518911	−	0.854828i	$-0.673662\pi$
$619$	1.79801	−	1.20140i	0.0722683	−	0.0482881i	0.591180	+	0.806540i	$0.298662\pi$
$620$	−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	0.992405	+	0.123014i	$0.0392558\pi$
$631$	9.48652	+	22.9025i	0.377652	+	0.911733i	−0.614753	+	0.788720i	$0.710744\pi$
$632$	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	0.747765	−	0.663963i	$-0.231127\pi$
$643$	10.6628	+	7.12468i	0.420501	+	0.280970i	−0.327264	+	0.944933i	$0.606127\pi$
$644$	−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	−0.152318	−	0.988332i	$-0.548674\pi$
$647$	16.6415	−	40.1760i	0.654243	−	1.57948i	0.806561	−	0.591151i	$-0.201326\pi$
$648$	−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	−0.492993	−	0.870033i	$-0.664097\pi$
$653$	−15.7287	+	3.12864i	−0.615512	+	0.122433i	−0.122519	+	0.992466i	$0.539097\pi$
$654$	−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	−0.983940	−	0.178498i	$-0.942876\pi$
$659$	−3.67625	−	18.4817i	−0.143206	−	0.719947i	0.840734	−	0.541448i	$-0.182124\pi$
$660$	48.0621	+	37.9465i	1.87081	+	1.47707i
$661$	1.08878	−	0.727500i	0.0423487	−	0.0282965i	−0.534216	−	0.845348i	$-0.679393\pi$
$661$	1.08878	−	0.727500i	0.0423487	−	0.0282965i	0.576564	+	0.817052i	$0.304393\pi$
$662$	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	$0.191798\pi$
$673$			29.4054i			1.13349i	−0.823892	+	0.566747i	$0.808202\pi$
$674$	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	−0.977413	−	0.211337i	$-0.932218\pi$
$677$	0.168449	−	0.846851i	0.00647403	−	0.0325471i	0.983887	+	0.178790i	$0.0572182\pi$
$678$	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	−0.925550	−	0.378626i	$-0.876397\pi$
$683$	−24.3032	+	16.2389i	−0.929937	+	0.621364i	−0.00438760	+	0.999990i	$0.501397\pi$
$684$	−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	−0.834123	−	0.551578i	$-0.814026\pi$
$691$	−36.6353	+	7.28722i	−1.39367	+	0.277219i	−0.559550	+	0.828797i	$0.689026\pi$
$692$	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	0.379062	−	0.925371i	$-0.376247\pi$
$701$	−8.75861	−	5.85232i	−0.330808	−	0.221039i	−0.709871	+	0.704332i	$0.751247\pi$
$702$	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	−0.0881469	−	0.996107i	$-0.528094\pi$
$709$	−14.6656	−	2.91717i	−0.550778	−	0.109557i	−0.462631	+	0.886551i	$0.653094\pi$
$710$	−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	0.995691	−	0.0927286i	$-0.0295589\pi$
$719$	24.2122	+	24.2122i	0.902963	+	0.902963i	−0.0927286	+	0.995691i	$0.529559\pi$
$720$	−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	−0.728226	−	0.685337i	$-0.759655\pi$
$727$	−20.4528	+	8.47184i	−0.758553	+	0.314203i	−0.0303271	+	0.999540i	$0.509655\pi$
$728$	−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	−0.792579	−	0.609769i	$-0.791262\pi$
$733$	2.00568	−	3.00171i	0.0740814	−	0.110871i	0.866660	+	0.498899i	$0.166262\pi$
$734$	−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	−0.294788	−	0.955563i	$-0.595249\pi$
$739$	19.0522	−	28.5137i	0.700847	−	1.04889i	0.995635	−	0.0933295i	$-0.0297510\pi$
$740$	−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	−0.549718	−	0.835351i	$-0.685265\pi$
$743$	−41.6805	−	17.2646i	−1.52911	−	0.633378i	−0.979391	+	0.201973i	$0.935265\pi$
$744$	−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	−0.132689	+	0.991158i	$0.542361\pi$
$751$	−30.7983	+	30.7983i	−1.12385	+	1.12385i	−0.991158	+	0.132689i	$0.957639\pi$
$752$	−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	0.977361	−	0.211578i	$-0.0678602\pi$
$757$	11.2220	+	16.7948i	0.407869	+	0.610419i	−0.569492	+	0.821997i	$0.692860\pi$
$758$	−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	−0.605376	−	0.795940i	$-0.706977\pi$
$761$	10.6346	−	25.6742i	0.385504	−	0.930689i	0.990880	−	0.134749i	$-0.0430228\pi$
$762$	−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	0.568516	−	0.822672i	$-0.307518\pi$
$773$	21.6566	+	4.30777i	0.778934	+	0.154940i	0.210418	+	0.977612i	$0.432518\pi$
$774$	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	0.971241	+	0.238101i	$0.0765248\pi$
$787$	4.63019	+	23.2775i	0.165048	+	0.829754i	−0.806192	+	0.591654i	$0.798475\pi$
$788$	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	0.0273612	+	0.999626i	$0.491290\pi$
$797$	−25.5956	+	38.3065i	−0.906643	+	1.35689i	−0.934004	+	0.357262i	$0.883710\pi$
$798$	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	−0.694633	−	0.719364i	$-0.744433\pi$
$809$	−19.2600	+	7.97776i	−0.677146	+	0.280483i	0.0174870	+	0.999847i	$0.494433\pi$
$810$	−14.1967	+	30.7652i	−0.498821	+	1.08098i
$811$	3.44040	−	2.29880i	0.120809	−	0.0807219i	−0.493698	−	0.869634i	$-0.664355\pi$
$811$	3.44040	−	2.29880i	0.120809	−	0.0807219i	0.614507	+	0.788912i	$0.289355\pi$
$812$	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	0.739916	−	0.672699i	$-0.234865\pi$
$821$	−4.72002	−	7.06401i	−0.164730	−	0.246536i	−0.904646	+	0.426163i	$0.859865\pi$
$822$	19.8303	+	53.8133i	0.691661	+	1.87696i
$823$	6.08212	+	14.6835i	0.212009	+	0.511836i	0.993732	−	0.111791i	$-0.0356587\pi$
$823$	6.08212	+	14.6835i	0.212009	+	0.511836i	−0.781723	+	0.623626i	$0.785659\pi$
$824$	−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	0.416103	−	0.909317i	$-0.363396\pi$
$827$	13.0143	+	2.58870i	0.452551	+	0.0900181i	0.0364484	+	0.999336i	$0.488396\pi$
$828$	80.8518	−	26.2046i	2.80980	−	0.910672i
$829$	0.266055	+	0.177772i	0.00924047	+	0.00617428i	0.560182	−	0.828370i	$-0.310731\pi$
$829$	0.266055	+	0.177772i	0.00924047	+	0.00617428i	−0.550941	+	0.834544i	$0.685731\pi$
$830$	−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	0.572874	+	0.819644i	$0.305829\pi$
$839$	−11.9276	+	28.7957i	−0.411785	+	0.994137i	−0.984658	+	0.174493i	$0.944171\pi$
$840$	−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	−0.642249	−	0.766496i	$-0.721998\pi$
$853$	−5.25349	+	3.51027i	−0.179876	+	0.120189i	0.462373	+	0.886686i	$0.346998\pi$
$854$	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	0.183141	−	0.983087i	$-0.441374\pi$
$857$	−11.1977	−	4.63825i	−0.382507	−	0.158439i	−0.565647	+	0.824647i	$0.691374\pi$
$858$	−2.24762	−	2.43326i	−0.0767324	−	0.0830700i
$859$	10.3238	−	51.9011i	0.352243	−	1.77084i	−0.245741	−	0.969335i	$-0.579031\pi$
$859$	10.3238	−	51.9011i	0.352243	−	1.77084i	0.597984	−	0.801508i	$-0.295969\pi$
$860$	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	$0.272011\pi$
$863$			44.3164i			1.50855i	−0.656559	+	0.754275i	$0.727989\pi$
$864$	−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	−0.867888	−	0.496760i	$-0.834523\pi$
$877$	−7.58614	−	38.1381i	−0.256166	−	1.28783i	0.611722	−	0.791073i	$-0.290477\pi$
$878$	−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	0.942445	−	0.334361i	$-0.108520\pi$
$881$	18.0489	+	18.0489i	0.608084	+	0.608084i	−0.334361	+	0.942445i	$0.608520\pi$
$882$	−8.63224	−	54.6319i	−0.290662	−	1.83955i
$883$	7.66573	−	1.52481i	0.257972	−	0.0513139i	−0.0644097	−	0.997924i	$-0.520516\pi$
$883$	7.66573	−	1.52481i	0.257972	−	0.0513139i	0.322382	+	0.946610i	$0.395516\pi$
$884$	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	0.801520	−	0.597968i	$-0.204025\pi$
$887$	−5.60114	−	13.5223i	−0.188068	−	0.454036i	−0.989587	+	0.143933i	$0.954025\pi$
$888$	−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	0.383421	−	0.923573i	$-0.374746\pi$
$907$	−18.5691	−	27.7907i	−0.616578	−	0.922775i	−1.00000		0.000798948i	$0.999746\pi$
$908$	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	0.955913	−	0.293649i	$-0.0948698\pi$
$911$	19.9890	+	19.9890i	0.662264	+	0.662264i	−0.293649	+	0.955913i	$0.594870\pi$
$912$	−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	0.217149	−	0.976139i	$-0.430324\pi$
$919$	32.1621	−	13.3220i	1.06093	−	0.439452i	0.843782	+	0.536687i	$0.180324\pi$
$920$	−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	$0.00909274\pi$
$929$			1.74110i			0.0571236i	−0.999592	+	0.0285618i	$0.990907\pi$
$930$	−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	−0.264268	−	0.964449i	$-0.585130\pi$
$937$	7.06597	−	2.92682i	0.230835	−	0.0956151i	0.495103	+	0.868834i	$0.335130\pi$
$938$	−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	0.991399	−	0.130871i	$-0.0417774\pi$
$941$	0.778661	+	3.91459i	0.0253836	+	0.127612i	−0.966016	+	0.258483i	$0.916777\pi$
$942$	−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	0.572002	−	0.820252i	$-0.306167\pi$
$947$	43.5246	−	8.65759i	1.41436	−	0.281334i	0.842358	+	0.538918i	$0.181167\pi$
$948$	−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	−0.608516	−	0.793541i	$-0.708235\pi$
$953$	11.8200	−	28.5361i	0.382888	−	0.924374i	0.991404	−	0.130833i	$-0.0417650\pi$
$954$	−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	−0.160025	−	0.987113i	$-0.551158\pi$
$967$	20.2478	−	48.8824i	0.651124	−	1.57195i	0.811149	−	0.584839i	$-0.198842\pi$
$968$	−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	0.625012	−	0.780615i	$-0.285094\pi$
$971$	−10.4503	−	15.6399i	−0.335365	−	0.501909i	−0.960376	+	0.278707i	$0.910094\pi$
$972$	−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	−0.765790	−	0.643091i	$-0.777652\pi$
$977$	−3.83519	+	3.83519i	−0.122699	+	0.122699i	0.643091	+	0.765790i	$0.277652\pi$
$978$	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	−0.195583	−	0.980687i	$-0.562660\pi$
$983$	11.2735	−	4.66965i	0.359570	−	0.148939i	0.555153	+	0.831748i	$0.312660\pi$
$984$	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	$0.0248550\pi$
$991$			4.91122i			0.156010i	−0.996953	+	0.0780051i	$0.975145\pi$
$992$	−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	0.631189	+	0.775629i	$0.282567\pi$
$997$	−7.85511	+	39.4903i	−0.248774	+	1.25067i	−0.879963	+	0.475042i	$0.842433\pi$
$998$	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.5.2	✓	56
3.2	odd	2		576.2.bd.a.325.6		56
4.3	odd	2		256.2.i.a.113.1		56
8.3	odd	2		512.2.i.a.481.7		56
8.5	even	2		512.2.i.b.481.1		56
64.13	even	16	inner	64.2.i.a.13.2	yes	56
64.19	odd	16		512.2.i.a.33.7		56
64.45	even	16		512.2.i.b.33.1		56
64.51	odd	16		256.2.i.a.145.1		56
192.77	odd	16		576.2.bd.a.397.6		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.5.2	✓	56	1.1	even	1	trivial
64.2.i.a.13.2	yes	56	64.13	even	16	inner
256.2.i.a.113.1		56	4.3	odd	2
256.2.i.a.145.1		56	64.51	odd	16
512.2.i.a.33.7		56	64.19	odd	16
512.2.i.a.481.7		56	8.3	odd	2
512.2.i.b.33.1		56	64.45	even	16
512.2.i.b.481.1		56	8.5	even	2
576.2.bd.a.325.6		56	3.2	odd	2
576.2.bd.a.397.6		56	192.77	odd	16

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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