LMFDB - Embedded newform 61.2.i.a.12.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [61,2,Mod(12,61)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(61, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("61.12");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	61.i (of order $15$, 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:	$0.487087452330$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			12.4
Character	$\chi$	$=$	61.12
Dual form			61.2.i.a.56.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50629 + 0.670642i) q^{2} +(-1.69101 + 1.22859i) q^{3} +(0.480878 + 0.534070i) q^{4} +(1.40283 - 0.298182i) q^{5} +(-3.37108 + 0.716546i) q^{6} +(0.125217 - 1.19136i) q^{7} +(-0.652866 - 2.00931i) q^{8} +(0.423022 - 1.30193i) q^{9} +O(q^{10})$	\(q+(1.50629 + 0.670642i) q^{2} +(-1.69101 + 1.22859i) q^{3} +(0.480878 + 0.534070i) q^{4} +(1.40283 - 0.298182i) q^{5} +(-3.37108 + 0.716546i) q^{6} +(0.125217 - 1.19136i) q^{7} +(-0.652866 - 2.00931i) q^{8} +(0.423022 - 1.30193i) q^{9} +(2.31304 + 0.491653i) q^{10} -3.00395 q^{11} +(-1.46932 - 0.312313i) q^{12} +(-1.72195 - 2.98250i) q^{13} +(0.987587 - 1.71055i) q^{14} +(-2.00586 + 2.22773i) q^{15} +(0.514369 - 4.89389i) q^{16} +(4.87302 + 5.41204i) q^{17} +(1.51032 - 1.67738i) q^{18} +(0.629830 + 5.99243i) q^{19} +(0.833842 + 0.605822i) q^{20} +(1.25194 + 2.16843i) q^{21} +(-4.52482 - 2.01458i) q^{22} +(-0.565515 + 1.74048i) q^{23} +(3.57262 + 2.59566i) q^{24} +(-2.68870 + 1.19708i) q^{25} +(-0.593557 - 5.64731i) q^{26} +(-1.05352 - 3.24240i) q^{27} +(0.696482 - 0.506024i) q^{28} +(2.62721 - 4.55046i) q^{29} +(-4.51541 + 2.01039i) q^{30} +(-5.21493 + 2.32184i) q^{31} +(1.94412 - 3.36731i) q^{32} +(5.07970 - 3.69062i) q^{33} +(3.71063 + 11.4201i) q^{34} +(-0.179583 - 1.70861i) q^{35} +(0.898741 - 0.400145i) q^{36} +(-4.17017 - 3.02980i) q^{37} +(-3.07007 + 9.44872i) q^{38} +(6.57609 + 2.92786i) q^{39} +(-1.51500 - 2.62406i) q^{40} +(7.17576 + 5.21349i) q^{41} +(0.431546 + 4.10589i) q^{42} +(2.93465 - 3.25925i) q^{43} +(-1.44454 - 1.60432i) q^{44} +(0.205219 - 1.95252i) q^{45} +(-2.01906 + 2.24240i) q^{46} +(4.25565 - 7.37101i) q^{47} +(5.14277 + 8.90754i) q^{48} +(5.44338 + 1.15703i) q^{49} -4.85276 q^{50} +(-14.8895 - 3.16486i) q^{51} +(0.764816 - 2.35386i) q^{52} +(-2.47558 - 7.61906i) q^{53} +(0.587588 - 5.59053i) q^{54} +(-4.21405 + 0.895724i) q^{55} +(-2.47556 + 0.526197i) q^{56} +(-8.42728 - 9.35944i) q^{57} +(7.00906 - 5.09238i) q^{58} +(11.2943 + 5.02854i) q^{59} -2.15434 q^{60} +(-6.78003 + 3.87700i) q^{61} -9.41230 q^{62} +(-1.49809 - 0.666993i) q^{63} +(-2.77544 + 2.01647i) q^{64} +(-3.30493 - 3.67050i) q^{65} +(10.1266 - 2.15247i) q^{66} +(-2.63158 + 0.559359i) q^{67} +(-0.547075 + 5.20507i) q^{68} +(-1.18204 - 3.63794i) q^{69} +(0.875366 - 2.69410i) q^{70} +(3.77191 + 0.801745i) q^{71} -2.89216 q^{72} +(-8.52788 - 1.81266i) q^{73} +(-4.24955 - 7.36044i) q^{74} +(3.07588 - 5.32757i) q^{75} +(-2.89751 + 3.21801i) q^{76} +(-0.376145 + 3.57878i) q^{77} +(7.94193 + 8.82040i) q^{78} +(-1.10029 + 1.22199i) q^{79} +(-0.737695 - 7.01869i) q^{80} +(9.08754 + 6.60249i) q^{81} +(7.31236 + 12.6654i) q^{82} +(1.78051 + 0.792734i) q^{83} +(-0.556060 + 1.71138i) q^{84} +(8.44982 + 6.13915i) q^{85} +(6.60621 - 2.94128i) q^{86} +(1.14801 + 10.9226i) q^{87} +(1.96118 + 6.03589i) q^{88} +(-4.76070 + 3.45885i) q^{89} +(1.61856 - 2.80343i) q^{90} +(-3.76884 + 1.67800i) q^{91} +(-1.20148 + 0.534933i) q^{92} +(5.96589 - 10.3332i) q^{93} +(11.3535 - 8.24883i) q^{94} +(2.67038 + 8.21859i) q^{95} +(0.849523 + 8.08267i) q^{96} +(5.09792 - 2.26974i) q^{97} +(7.42334 + 5.39337i) q^{98} +(-1.27074 + 3.91093i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 10 q^{2} - 4 q^{3} - 10 q^{4} + 2 q^{5} + q^{6} + q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) $ 32 * q - 10 * q^2 - 4 * q^3 - 10 * q^4 + 2 * q^5 + q^6 + q^7 - 4 * q^8 - 2 * q^9	\( 32 q - 10 q^{2} - 4 q^{3} - 10 q^{4} + 2 q^{5} + q^{6} + q^{7} - 4 q^{8} - 2 q^{9} + 15 q^{10} - 18 q^{11} - 53 q^{12} + 11 q^{14} + 2 q^{15} + 6 q^{16} - 24 q^{17} - 15 q^{18} + 9 q^{19} - 4 q^{20} - 3 q^{21} + q^{22} - 2 q^{23} + 15 q^{24} + 28 q^{25} + 16 q^{26} + 35 q^{27} + 4 q^{28} - 4 q^{29} + 54 q^{30} - 11 q^{31} + 34 q^{32} - 35 q^{33} + 18 q^{34} - 58 q^{35} + 65 q^{36} - 14 q^{37} - 24 q^{38} + 17 q^{39} - 60 q^{40} + 11 q^{41} + 73 q^{42} + 40 q^{43} + 29 q^{44} + 12 q^{45} - 89 q^{46} + 40 q^{47} + 43 q^{48} + q^{49} - 56 q^{50} - 9 q^{51} - 67 q^{52} + 17 q^{53} - q^{54} - 60 q^{55} - 102 q^{56} - 38 q^{57} + 73 q^{58} - 11 q^{59} - 20 q^{60} - 55 q^{61} - 74 q^{62} - 58 q^{63} + 6 q^{64} + 59 q^{65} + 34 q^{66} - 13 q^{67} - 3 q^{68} - 32 q^{69} + 44 q^{70} + 63 q^{71} + 18 q^{72} - 46 q^{73} - 10 q^{74} + q^{75} + 55 q^{76} - 31 q^{77} - 103 q^{78} - 49 q^{79} + 74 q^{80} + 48 q^{81} + 39 q^{82} + 39 q^{83} + 21 q^{85} + 74 q^{86} + 17 q^{87} + 70 q^{88} + 32 q^{89} - 60 q^{90} + 70 q^{91} + 77 q^{92} + 67 q^{93} - 64 q^{94} + 47 q^{95} - 16 q^{96} + 37 q^{97} + 127 q^{98} - 31 q^{99}+O(q^{100}) \) 32 * q - 10 * q^2 - 4 * q^3 - 10 * q^4 + 2 * q^5 + q^6 + q^7 - 4 * q^8 - 2 * q^9 + 15 * q^10 - 18 * q^11 - 53 * q^12 + 11 * q^14 + 2 * q^15 + 6 * q^16 - 24 * q^17 - 15 * q^18 + 9 * q^19 - 4 * q^20 - 3 * q^21 + q^22 - 2 * q^23 + 15 * q^24 + 28 * q^25 + 16 * q^26 + 35 * q^27 + 4 * q^28 - 4 * q^29 + 54 * q^30 - 11 * q^31 + 34 * q^32 - 35 * q^33 + 18 * q^34 - 58 * q^35 + 65 * q^36 - 14 * q^37 - 24 * q^38 + 17 * q^39 - 60 * q^40 + 11 * q^41 + 73 * q^42 + 40 * q^43 + 29 * q^44 + 12 * q^45 - 89 * q^46 + 40 * q^47 + 43 * q^48 + q^49 - 56 * q^50 - 9 * q^51 - 67 * q^52 + 17 * q^53 - q^54 - 60 * q^55 - 102 * q^56 - 38 * q^57 + 73 * q^58 - 11 * q^59 - 20 * q^60 - 55 * q^61 - 74 * q^62 - 58 * q^63 + 6 * q^64 + 59 * q^65 + 34 * q^66 - 13 * q^67 - 3 * q^68 - 32 * q^69 + 44 * q^70 + 63 * q^71 + 18 * q^72 - 46 * q^73 - 10 * q^74 + q^75 + 55 * q^76 - 31 * q^77 - 103 * q^78 - 49 * q^79 + 74 * q^80 + 48 * q^81 + 39 * q^82 + 39 * q^83 + 21 * q^85 + 74 * q^86 + 17 * q^87 + 70 * q^88 + 32 * q^89 - 60 * q^90 + 70 * q^91 + 77 * q^92 + 67 * q^93 - 64 * q^94 + 47 * q^95 - 16 * q^96 + 37 * q^97 + 127 * q^98 - 31 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/61\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{15}\right)$

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 $

$2$	1.50629	+	0.670642i	1.06511	+	0.474216i	0.863029	−	0.505154i	$-0.168564\pi$
$2$	1.50629	+	0.670642i	1.06511	+	0.474216i	0.202077	+	0.979370i	$0.435231\pi$
$3$	−1.69101	+	1.22859i	−0.976303	+	0.709325i	−0.956879	−	0.290486i	$-0.906183\pi$
$3$	−1.69101	+	1.22859i	−0.976303	+	0.709325i	−0.0194233	+	0.999811i	$0.506183\pi$
$4$	0.480878	+	0.534070i	0.240439	+	0.267035i
$5$	1.40283	−	0.298182i	0.627367	−	0.133351i	0.116753	−	0.993161i	$-0.462752\pi$
$5$	1.40283	−	0.298182i	0.627367	−	0.133351i	0.510614	+	0.859810i	$0.329418\pi$
$6$	−3.37108	+	0.716546i	−1.37624	+	0.292529i
$7$	0.125217	−	1.19136i	0.0473275	−	0.450291i	−0.945038	−	0.326960i	$-0.893976\pi$
$7$	0.125217	−	1.19136i	0.0473275	−	0.450291i	0.992366	−	0.123331i	$-0.0393576\pi$
$8$	−0.652866	−	2.00931i	−0.230823	−	0.710400i
$9$	0.423022	−	1.30193i	0.141007	−	0.433976i
$10$	2.31304	+	0.491653i	0.731449	+	0.155474i
$11$	−3.00395			−0.905726			−0.452863	−	0.891580i	$-0.649597\pi$
$11$	−3.00395			−0.905726			−0.452863	+	0.891580i	$0.649597\pi$
$12$	−1.46932	−	0.312313i	−0.424156	−	0.0901571i
$13$	−1.72195	−	2.98250i	−0.477582	−	0.827197i	0.522087	−	0.852892i	$-0.325153\pi$
$13$	−1.72195	−	2.98250i	−0.477582	−	0.827197i	−0.999670	+	0.0256950i	$0.991820\pi$
$14$	0.987587	−	1.71055i	0.263944	−	0.457164i
$15$	−2.00586	+	2.22773i	−0.517910	+	0.575198i
$16$	0.514369	−	4.89389i	0.128592	−	1.22347i
$17$	4.87302	+	5.41204i	1.18188	+	1.31261i	0.939547	+	0.342420i	$0.111247\pi$
$17$	4.87302	+	5.41204i	1.18188	+	1.31261i	0.242335	+	0.970193i	$0.422087\pi$
$18$	1.51032	−	1.67738i	0.355986	−	0.395362i
$19$	0.629830	+	5.99243i	0.144493	+	1.37476i	0.790984	+	0.611837i	$0.209569\pi$
$19$	0.629830	+	5.99243i	0.144493	+	1.37476i	−0.646491	+	0.762922i	$0.723764\pi$
$20$	0.833842	+	0.605822i	0.186453	+	0.135466i
$21$	1.25194	+	2.16843i	0.273197	+	0.473191i
$22$	−4.52482	−	2.01458i	−0.964694	−	0.429510i
$23$	−0.565515	+	1.74048i	−0.117918	+	0.362914i	−0.992544	−	0.121883i	$-0.961107\pi$
$23$	−0.565515	+	1.74048i	−0.117918	+	0.362914i	0.874626	+	0.484797i	$0.161107\pi$
$24$	3.57262	+	2.59566i	0.729257	+	0.529837i
$25$	−2.68870	+	1.19708i	−0.537739	+	0.239417i
$26$	−0.593557	−	5.64731i	−0.116406	−	1.10753i
$27$	−1.05352	−	3.24240i	−0.202750	−	0.624001i
$28$	0.696482	−	0.506024i	0.131623	−	0.0956295i
$29$	2.62721	−	4.55046i	0.487860	−	0.844999i	−0.512042	−	0.858960i	$-0.671111\pi$
$29$	2.62721	−	4.55046i	0.487860	−	0.844999i	0.999903	+	0.0139612i	$0.00444414\pi$
$30$	−4.51541	+	2.01039i	−0.824397	+	0.367045i
$31$	−5.21493	+	2.32184i	−0.936629	+	0.417014i	−0.817541	−	0.575870i	$-0.804663\pi$
$31$	−5.21493	+	2.32184i	−0.936629	+	0.417014i	−0.119087	+	0.992884i	$0.537997\pi$
$32$	1.94412	−	3.36731i	0.343675	−	0.595263i
$33$	5.07970	−	3.69062i	0.884263	−	0.642455i
$34$	3.71063	+	11.4201i	0.636368	+	1.95854i
$35$	−0.179583	−	1.70861i	−0.0303550	−	0.288809i
$36$	0.898741	−	0.400145i	0.149790	−	0.0666909i
$37$	−4.17017	−	3.02980i	−0.685571	−	0.498097i	0.189630	−	0.981856i	$-0.439271\pi$
$37$	−4.17017	−	3.02980i	−0.685571	−	0.498097i	−0.875201	+	0.483759i	$0.839271\pi$
$38$	−3.07007	+	9.44872i	−0.498032	+	1.53278i
$39$	6.57609	+	2.92786i	1.05302	+	0.468833i
$40$	−1.51500	−	2.62406i	−0.239543	−	0.414901i
$41$	7.17576	+	5.21349i	1.12067	+	0.814211i	0.984310	−	0.176449i	$-0.0564611\pi$
$41$	7.17576	+	5.21349i	1.12067	+	0.814211i	0.136355	+	0.990660i	$0.456461\pi$
$42$	0.431546	+	4.10589i	0.0665890	+	0.633552i
$43$	2.93465	−	3.25925i	0.447529	−	0.497032i	−0.476595	−	0.879123i	$-0.658129\pi$
$43$	2.93465	−	3.25925i	0.447529	−	0.497032i	0.924125	+	0.382091i	$0.124796\pi$
$44$	−1.44454	−	1.60432i	−0.217772	−	0.241860i
$45$	0.205219	−	1.95252i	0.0305922	−	0.291065i
$46$	−2.01906	+	2.24240i	−0.297695	+	0.330623i
$47$	4.25565	−	7.37101i	0.620751	−	1.07517i	−0.368595	−	0.929590i	$-0.620161\pi$
$47$	4.25565	−	7.37101i	0.620751	−	1.07517i	0.989346	−	0.145582i	$-0.0465054\pi$
$48$	5.14277	+	8.90754i	0.742295	+	1.28569i
$49$	5.44338	+	1.15703i	0.777626	+	0.165289i
$50$	−4.85276			−0.686284
$51$	−14.8895	−	3.16486i	−2.08494	−	0.443168i
$52$	0.764816	−	2.35386i	0.106061	−	0.326422i
$53$	−2.47558	−	7.61906i	−0.340048	−	1.04656i	−0.964182	−	0.265242i	$-0.914548\pi$
$53$	−2.47558	−	7.61906i	−0.340048	−	1.04656i	0.624134	−	0.781317i	$-0.285452\pi$
$54$	0.587588	−	5.59053i	0.0799606	−	0.760774i
$55$	−4.21405	+	0.895724i	−0.568222	+	0.120779i
$56$	−2.47556	+	0.526197i	−0.330811	+	0.0703160i
$57$	−8.42728	−	9.35944i	−1.11622	−	1.23969i
$58$	7.00906	−	5.09238i	0.920335	−	0.668662i
$59$	11.2943	+	5.02854i	1.47039	+	0.654660i	0.976628	−	0.214937i	$-0.0689546\pi$
$59$	11.2943	+	5.02854i	1.47039	+	0.654660i	0.493762	+	0.869597i	$0.335621\pi$
$60$	−2.15434			−0.278124
$61$	−6.78003	+	3.87700i	−0.868094	+	0.496399i
$61$	−6.78003	+	3.87700i	−0.868094	+	0.496399i
$62$	−9.41230			−1.19536
$63$	−1.49809	−	0.666993i	−0.188742	−	0.0840332i
$64$	−2.77544	+	2.01647i	−0.346929	+	0.252059i
$65$	−3.30493	−	3.67050i	−0.409927	−	0.455270i
$66$	10.1266	−	2.15247i	1.24650	−	0.264951i
$67$	−2.63158	+	0.559359i	−0.321498	+	0.0683366i	−0.365834	−	0.930680i	$-0.619216\pi$
$67$	−2.63158	+	0.559359i	−0.321498	+	0.0683366i	0.0443357	+	0.999017i	$0.485883\pi$
$68$	−0.547075	+	5.20507i	−0.0663425	+	0.631207i
$69$	−1.18204	−	3.63794i	−0.142301	−	0.437956i
$70$	0.875366	−	2.69410i	0.104626	−	0.322006i
$71$	3.77191	+	0.801745i	0.447644	+	0.0951496i	0.426217	−	0.904621i	$-0.359846\pi$
$71$	3.77191	+	0.801745i	0.447644	+	0.0951496i	0.0214264	+	0.999770i	$0.493179\pi$
$72$	−2.89216			−0.340844
$73$	−8.52788	−	1.81266i	−0.998113	−	0.212156i	−0.320242	−	0.947336i	$-0.603764\pi$
$73$	−8.52788	−	1.81266i	−0.998113	−	0.212156i	−0.677872	+	0.735180i	$0.737097\pi$
$74$	−4.24955	−	7.36044i	−0.494001	−	0.855634i
$75$	3.07588	−	5.32757i	0.355172	−	0.615175i
$76$	−2.89751	+	3.21801i	−0.332367	+	0.369131i
$77$	−0.376145	+	3.57878i	−0.0428657	+	0.407840i
$78$	7.94193	+	8.82040i	0.899246	+	0.998714i
$79$	−1.10029	+	1.22199i	−0.123792	+	0.137485i	−0.801855	−	0.597519i	$-0.796153\pi$
$79$	−1.10029	+	1.22199i	−0.123792	+	0.137485i	0.678063	+	0.735004i	$0.262820\pi$
$80$	−0.737695	−	7.01869i	−0.0824768	−	0.784714i
$81$	9.08754	+	6.60249i	1.00973	+	0.733610i
$82$	7.31236	+	12.6654i	0.807515	+	1.39866i
$83$	1.78051	+	0.792734i	0.195436	+	0.0870139i	0.502121	−	0.864797i	$-0.332553\pi$
$83$	1.78051	+	0.792734i	0.195436	+	0.0870139i	−0.306685	+	0.951811i	$0.599220\pi$
$84$	−0.556060	+	1.71138i	−0.0606711	+	0.186727i
$85$	8.44982	+	6.13915i	0.916511	+	0.665884i
$86$	6.60621	−	2.94128i	0.712366	−	0.317166i
$87$	1.14801	+	10.9226i	0.123080	+	1.17103i
$88$	1.96118	+	6.03589i	0.209062	+	0.643428i
$89$	−4.76070	+	3.45885i	−0.504633	+	0.366638i	−0.810784	−	0.585345i	$-0.800959\pi$
$89$	−4.76070	+	3.45885i	−0.504633	+	0.366638i	0.306151	+	0.951983i	$0.400959\pi$
$90$	1.61856	−	2.80343i	0.170612	−	0.295508i
$91$	−3.76884	+	1.67800i	−0.395082	+	0.175902i
$92$	−1.20148	+	0.534933i	−0.125263	+	0.0557706i
$93$	5.96589	−	10.3332i	0.618634	−	1.07151i
$94$	11.3535	−	8.24883i	1.17103	−	0.850802i
$95$	2.67038	+	8.21859i	0.273975	+	0.843209i
$96$	0.849523	+	8.08267i	0.0867040	+	0.824934i
$97$	5.09792	−	2.26974i	0.517616	−	0.230457i	−0.131265	−	0.991347i	$-0.541904\pi$
$97$	5.09792	−	2.26974i	0.517616	−	0.230457i	0.648881	+	0.760890i	$0.275237\pi$
$98$	7.42334	+	5.39337i	0.749871	+	0.544813i
$99$	−1.27074	+	3.91093i	−0.127714	+	0.393063i
$100$	−1.93226	−	0.860298i	−0.193226	−	0.0860298i
$101$	−2.24288	−	3.88478i	−0.223175	−	0.386550i	0.732595	−	0.680664i	$-0.238309\pi$
$101$	−2.24288	−	3.88478i	−0.223175	−	0.386550i	−0.955770	+	0.294114i	$0.904975\pi$
$102$	−20.3053	−	14.7527i	−2.01053	−	1.46073i
$103$	−1.31107	−	12.4740i	−0.129183	−	1.22910i	−0.846514	−	0.532366i	$-0.821303\pi$
$103$	−1.31107	−	12.4740i	−0.129183	−	1.22910i	0.717331	−	0.696733i	$-0.245364\pi$
$104$	−4.86858	+	5.40711i	−0.477404	+	0.530210i
$105$	2.40286	+	2.66864i	0.234495	+	0.260433i
$106$	1.38073	−	13.1367i	0.134108	−	1.27595i
$107$	−3.27204	+	3.63396i	−0.316320	+	0.351308i	−0.880247	−	0.474516i	$-0.842623\pi$
$107$	−3.27204	+	3.63396i	−0.316320	+	0.351308i	0.563927	+	0.825824i	$0.309290\pi$
$108$	1.22505	−	2.12186i	0.117881	−	0.204176i
$109$	−0.00395012	−	0.00684180i	−0.000378353	−	0.000655326i	0.865836	−	0.500328i	$-0.166787\pi$
$109$	−0.00395012	−	0.00684180i	−0.000378353	−	0.000655326i	−0.866215	+	0.499672i	$0.833454\pi$
$110$	−6.94828	−	1.47690i	−0.662492	−	0.140817i
$111$	10.7742			1.02264
$112$	−5.76597	−	1.22559i	−0.544833	−	0.115808i
$113$	−4.39592	+	13.5293i	−0.413533	+	1.27272i	0.500023	+	0.866012i	$0.333325\pi$
$113$	−4.39592	+	13.5293i	−0.413533	+	1.27272i	−0.913556	+	0.406713i	$0.866675\pi$
$114$	−6.41706	−	19.7497i	−0.601013	−	1.84973i
$115$	−0.274346	+	2.61022i	−0.0255829	+	0.243405i
$116$	3.69363	−	0.785105i	0.342945	−	0.0728952i
$117$	−4.61142	+	0.980187i	−0.426326	+	0.0906184i
$118$	13.6401	+	15.1488i	1.25567	+	1.39456i
$119$	7.05786	−	5.12783i	0.646993	−	0.470068i
$120$	5.78577	+	2.57599i	0.528166	+	0.235155i
$121$	−1.97626			−0.179660
$122$	−12.8128	+	1.29290i	−1.16001	+	0.117054i
$123$	−18.5395			−1.67165
$124$	−3.74777	−	1.66861i	−0.336559	−	0.149846i
$125$	−9.21620	+	6.69596i	−0.824322	+	0.598905i
$126$	−1.80924	−	2.00937i	−0.161180	−	0.179009i
$127$	13.2169	−	2.80934i	1.17281	−	0.249289i	0.419999	−	0.907525i	$-0.362030\pi$
$127$	13.2169	−	2.80934i	1.17281	−	0.249289i	0.752812	+	0.658236i	$0.228697\pi$
$128$	−13.1395	+	2.79288i	−1.16138	+	0.246858i
$129$	−0.958224	+	9.11689i	−0.0843669	+	0.802697i
$130$	−2.51659	−	7.74526i	−0.220719	−	0.679304i
$131$	−2.12367	+	6.53600i	−0.185546	+	0.571053i	−0.999957	−	0.00923556i	$-0.997060\pi$
$131$	−2.12367	+	6.53600i	−0.185546	+	0.571053i	0.814411	+	0.580288i	$0.197060\pi$
$132$	4.41377	+	0.938175i	0.384169	+	0.0816577i
$133$	7.21800			0.625880
$134$	−4.33904	−	0.922291i	−0.374836	−	0.0796738i
$135$	−2.44474	−	4.23442i	−0.210410	−	0.364440i
$136$	7.69306	−	13.3248i	0.659674	−	1.14259i
$137$	9.35035	−	10.3846i	0.798855	−	0.887218i	−0.196790	−	0.980446i	$-0.563052\pi$
$137$	9.35035	−	10.3846i	0.798855	−	0.887218i	0.995645	+	0.0932277i	$0.0297184\pi$
$138$	0.659266	−	6.27250i	0.0561205	−	0.533951i
$139$	−14.1515	−	15.7168i	−1.20031	−	1.33308i	−0.928771	−	0.370654i	$-0.879133\pi$
$139$	−14.1515	−	15.7168i	−1.20031	−	1.33308i	−0.271541	−	0.962427i	$-0.587533\pi$
$140$	0.826162	−	0.917545i	0.0698234	−	0.0775467i
$141$	1.85959	+	17.6929i	0.156606	+	1.49001i
$142$	5.14390	+	3.73726i	0.431666	+	0.313624i
$143$	5.17265	+	8.95930i	0.432559	+	0.749214i
$144$	−6.15390	−	2.73989i	−0.512825	−	0.228324i
$145$	2.32868	−	7.16693i	0.193386	−	0.595181i
$146$	−11.6298	−	8.44954i	−0.962489	−	0.699289i
$147$	−10.6263	+	4.73113i	−0.876442	+	0.390217i
$148$	−0.387217	−	3.68413i	−0.0318291	−	0.302833i
$149$	−1.57127	−	4.83587i	−0.128723	−	0.396170i	0.865838	−	0.500325i	$-0.166786\pi$
$149$	−1.57127	−	4.83587i	−0.128723	−	0.396170i	−0.994561	+	0.104155i	$0.966786\pi$
$150$	8.20605	−	5.96204i	0.670021	−	0.486799i
$151$	2.61117	−	4.52268i	0.212494	−	0.368050i	−0.740000	−	0.672606i	$-0.765175\pi$
$151$	2.61117	−	4.52268i	0.212494	−	0.368050i	0.952494	+	0.304556i	$0.0985081\pi$
$152$	11.6295	−	5.17778i	0.943276	−	0.419974i
$153$	9.10748	−	4.05491i	0.736296	−	0.327820i
$154$	−2.96667	+	5.13842i	−0.239061	+	0.414065i
$155$	−6.62335	+	4.81215i	−0.532000	+	0.386521i
$156$	1.59862	+	4.92003i	0.127992	+	0.393918i
$157$	0.719255	+	6.84326i	0.0574028	+	0.546151i	0.984998	+	0.172565i	$0.0552054\pi$
$157$	0.719255	+	6.84326i	0.0574028	+	0.546151i	−0.927595	+	0.373587i	$0.878128\pi$
$158$	−2.47687	+	1.10277i	−0.197049	+	0.0877318i
$159$	13.5469	+	9.84241i	1.07434	+	0.780554i
$160$	1.72321	−	5.30348i	0.136231	−	0.419277i
$161$	2.00272	+	0.891667i	0.157836	+	0.0702732i
$162$	9.26054	+	16.0397i	0.727577	+	1.26020i
$163$	1.71501	+	1.24603i	0.134330	+	0.0975963i	0.652921	−	0.757426i	$-0.273543\pi$
$163$	1.71501	+	1.24603i	0.134330	+	0.0975963i	−0.518591	+	0.855022i	$0.673543\pi$
$164$	0.666299	+	6.33941i	0.0520292	+	0.495025i
$165$	6.02551	−	6.69200i	0.469085	−	0.520972i
$166$	2.15032	+	2.38817i	0.166897	+	0.185358i
$167$	0.955755	−	9.09340i	0.0739585	−	0.703668i	−0.893229	−	0.449603i	$-0.851565\pi$
$167$	0.955755	−	9.09340i	0.0739585	−	0.703668i	0.967187	−	0.254065i	$-0.0817678\pi$
$168$	3.53971	−	3.93124i	0.273094	−	0.303302i
$169$	0.569792	−	0.986909i	0.0438302	−	0.0759161i
$170$	8.61067	+	14.9141i	0.660409	+	1.14386i
$171$	8.06814	+	1.71494i	0.616986	+	0.131144i
$172$	3.15188			0.240328
$173$	−11.7941	−	2.50692i	−0.896689	−	0.190597i	−0.263560	−	0.964643i	$-0.584897\pi$
$173$	−11.7941	−	2.50692i	−0.896689	−	0.190597i	−0.633130	+	0.774046i	$0.718230\pi$
$174$	−5.59593	+	17.2225i	−0.424226	+	1.30563i
$175$	1.08949	+	3.35309i	0.0823574	+	0.253470i
$176$	−1.54514	+	14.7010i	−0.116469	+	1.10813i
$177$	−25.2767	+	5.37273i	−1.89991	+	0.403839i
$178$	−9.49064	+	2.01730i	−0.711353	+	0.151203i
$179$	−8.24668	−	9.15887i	−0.616386	−	0.684566i	0.351433	−	0.936213i	$-0.385694\pi$
$179$	−8.24668	−	9.15887i	−0.616386	−	0.684566i	−0.967819	+	0.251647i	$0.919028\pi$
$180$	1.14147	−	0.829326i	0.0850801	−	0.0618143i
$181$	10.3685	+	4.61634i	0.770681	+	0.343130i	0.754123	−	0.656733i	$-0.228062\pi$
$181$	10.3685	+	4.61634i	0.770681	+	0.343130i	0.0165587	+	0.999863i	$0.494729\pi$
$182$	−6.80229			−0.504219
$183$	6.70184	−	14.8859i	0.495414	−	1.10040i
$184$	3.86637			0.285032
$185$	−6.75348	−	3.00685i	−0.496526	−	0.221068i
$186$	15.9162	−	11.5638i	1.16704	−	0.847901i
$187$	−14.6383	−	16.2575i	−1.07046	−	1.18887i
$188$	5.98308	−	1.27174i	0.436361	−	0.0927514i
$189$	−3.99478	+	0.849117i	−0.290578	+	0.0617642i
$190$	−1.48937	+	14.1704i	−0.108050	+	1.02803i
$191$	1.42798	+	4.39486i	0.103325	+	0.318001i	0.989334	−	0.145667i	$-0.0465329\pi$
$191$	1.42798	+	4.39486i	0.103325	+	0.318001i	−0.886009	+	0.463668i	$0.846533\pi$
$192$	2.21586	−	6.81973i	0.159916	−	0.492172i
$193$	−6.88275	−	1.46297i	−0.495431	−	0.105307i	−0.0465817	−	0.998914i	$-0.514833\pi$
$193$	−6.88275	−	1.46297i	−0.495431	−	0.105307i	−0.448850	+	0.893607i	$0.648166\pi$
$194$	9.20112			0.660602
$195$	10.0982	+	2.14644i	0.723147	+	0.153710i
$196$	1.99967	+	3.46353i	0.142834	+	0.247395i
$197$	−11.1084	+	19.2403i	−0.791440	+	1.37081i	0.133635	+	0.991031i	$0.457335\pi$
$197$	−11.1084	+	19.2403i	−0.791440	+	1.37081i	−0.925075	+	0.379784i	$0.875998\pi$
$198$	−4.53693	+	5.03877i	−0.322426	+	0.358090i
$199$	−2.23420	+	21.2570i	−0.158378	+	1.50687i	0.569974	+	0.821663i	$0.306953\pi$
$199$	−2.23420	+	21.2570i	−0.158378	+	1.50687i	−0.728352	+	0.685203i	$0.759713\pi$
$200$	4.16067	+	4.62090i	0.294204	+	0.326747i
$201$	3.76279	−	4.17900i	0.265407	−	0.294764i
$202$	−0.773122	−	7.35577i	−0.0543967	−	0.517550i
$203$	−5.09225	−	3.69974i	−0.357406	−	0.259671i
$204$	−5.46977	−	9.47393i	−0.382961	−	0.663308i
$205$	11.6210	+	5.17399i	0.811644	+	0.361367i
$206$	6.39074	−	19.6687i	0.445264	−	1.37038i
$207$	2.02675	+	1.47252i	0.140869	+	0.102347i
$208$	−15.4818	+	6.89292i	−1.07347	+	0.477938i
$209$	−1.89198	−	18.0010i	−0.130871	−	1.24516i
$210$	1.82969	+	5.63120i	0.126260	+	0.388590i
$211$	18.5053	−	13.4449i	1.27395	−	0.925582i	0.274602	−	0.961558i	$-0.411454\pi$
$211$	18.5053	−	13.4449i	1.27395	−	0.925582i	0.999353	+	0.0359760i	$0.0114540\pi$
$212$	2.87866	−	4.98598i	0.197707	−	0.342438i
$213$	−7.36334	+	3.27837i	−0.504528	+	0.224630i
$214$	−7.36571	+	3.27943i	−0.503510	+	0.224177i
$215$	3.14497	−	5.44725i	0.214485	−	0.371500i
$216$	−5.82720	+	4.23371i	−0.396491	+	0.288067i
$217$	2.11314	+	6.50358i	0.143449	+	0.441491i
$218$	−0.00136161	−	0.0129548i	−9.22197e−5	−	0.000877412i
$219$	16.6477	−	7.41204i	1.12495	−	0.500859i
$220$	−2.50482	−	1.81986i	−0.168875	−	0.122695i
$221$	7.75033	−	23.8530i	0.521343	−	1.60453i
$222$	16.2290	+	7.22560i	1.08922	+	0.484951i
$223$	−6.58329	−	11.4026i	−0.440849	−	0.763574i	0.556903	−	0.830577i	$-0.311989\pi$
$223$	−6.58329	−	11.4026i	−0.440849	−	0.763574i	−0.997753	+	0.0670038i	$0.978656\pi$
$224$	−3.76824	−	2.73779i	−0.251776	−	0.182926i
$225$	0.421140	+	4.00688i	0.0280760	+	0.267125i
$226$	−15.6948	+	17.4308i	−1.04400	+	1.15948i
$227$	1.24364	+	1.38121i	0.0825435	+	0.0916738i	0.783002	−	0.622020i	$-0.213688\pi$
$227$	1.24364	+	1.38121i	0.0825435	+	0.0916738i	−0.700458	+	0.713693i	$0.747021\pi$
$228$	0.946096	−	9.00150i	0.0626568	−	0.596139i
$229$	−17.6132	+	19.5615i	−1.16392	+	1.29266i	−0.215185	+	0.976573i	$0.569035\pi$
$229$	−17.6132	+	19.5615i	−1.16392	+	1.29266i	−0.948731	+	0.316086i	$0.897631\pi$
$230$	−2.16377	+	3.74776i	−0.142675	+	0.247120i
$231$	−3.76078	−	6.51387i	−0.247441	−	0.428581i
$232$	−10.8585	−	2.30805i	−0.712896	−	0.151531i
$233$	10.9326			0.716219			0.358110	−	0.933680i	$-0.383421\pi$
$233$	10.9326			0.716219			0.358110	+	0.933680i	$0.383421\pi$
$234$	−7.60348	−	1.61617i	−0.497055	−	0.105652i
$235$	3.77208	−	11.6093i	0.246063	−	0.757305i
$236$	2.74559	+	8.45005i	0.178723	+	0.550051i
$237$	0.359266	−	3.41819i	0.0233369	−	0.222035i
$238$	14.0701	−	2.99069i	0.912029	−	0.193858i
$239$	14.0110	−	2.97814i	0.906298	−	0.192640i	0.268894	−	0.963170i	$-0.413342\pi$
$239$	14.0110	−	2.97814i	0.906298	−	0.192640i	0.637404	+	0.770530i	$0.280008\pi$
$240$	9.87053	+	10.9623i	0.637140	+	0.707615i
$241$	−7.01389	+	5.09589i	−0.451805	+	0.328255i	−0.790308	−	0.612710i	$-0.790079\pi$
$241$	−7.01389	+	5.09589i	−0.451805	+	0.328255i	0.338503	+	0.940965i	$0.390079\pi$
$242$	−2.97681	−	1.32536i	−0.191357	−	0.0851975i
$243$	−13.2510			−0.850053
$244$	−5.33096	−	1.75664i	−0.341280	−	0.112458i
$245$	7.98116			0.509898
$246$	−27.9258	−	12.4334i	−1.78048	−	0.792722i
$247$	16.7879	−	12.1971i	1.06819	−	0.776085i
$248$	8.06994	+	8.96258i	0.512442	+	0.569124i
$249$	−3.98480	+	0.846994i	−0.252526	+	0.0536761i
$250$	−18.3728	+	3.90527i	−1.16200	+	0.246991i
$251$	−1.03296	+	9.82794i	−0.0651997	+	0.620334i	0.912318	+	0.409482i	$0.134290\pi$
$251$	−1.03296	+	9.82794i	−0.0651997	+	0.620334i	−0.977518	+	0.210852i	$0.932376\pi$
$252$	−0.364179	−	1.12083i	−0.0229411	−	0.0706055i
$253$	1.69878	−	5.22831i	0.106801	−	0.328701i
$254$	21.7925	+	4.63214i	1.36738	+	0.290646i
$255$	−21.8312			−1.36712
$256$	−14.9535	−	3.17847i	−0.934596	−	0.198654i
$257$	2.60307	+	4.50864i	0.162375	+	0.281241i	0.935720	−	0.352744i	$-0.114751\pi$
$257$	2.60307	+	4.50864i	0.162375	+	0.281241i	−0.773345	+	0.633985i	$0.781418\pi$
$258$	−7.55753	+	13.0900i	−0.470511	+	0.814949i
$259$	−4.13175	+	4.58878i	−0.256735	+	0.285133i
$260$	0.371032	−	3.53013i	0.0230104	−	0.218929i
$261$	−4.81300	−	5.34538i	−0.297917	−	0.330871i
$262$	−7.58218	+	8.42086i	−0.468429	+	0.520243i
$263$	1.22820	+	11.6856i	0.0757343	+	0.720564i	0.964836	+	0.262854i	$0.0846637\pi$
$263$	1.22820	+	11.6856i	0.0757343	+	0.720564i	−0.889101	+	0.457710i	$0.848670\pi$
$264$	−10.7320	−	7.79724i	−0.660508	−	0.479887i
$265$	−5.74470	−	9.95011i	−0.352894	−	0.611230i
$266$	10.8724	+	4.84069i	0.666628	+	0.296802i
$267$	3.80087	−	11.6979i	0.232610	−	0.715899i
$268$	−1.56421	−	1.13646i	−0.0955490	−	0.0694204i
$269$	3.33020	−	1.48270i	0.203046	−	0.0904018i	−0.302694	−	0.953088i	$-0.597886\pi$
$269$	3.33020	−	1.48270i	0.203046	−	0.0904018i	0.505740	+	0.862686i	$0.331219\pi$
$270$	−0.842704	−	8.01779i	−0.0512853	−	0.487947i
$271$	6.82316	+	20.9995i	0.414477	+	1.27563i	0.912717	+	0.408591i	$0.133980\pi$
$271$	6.82316	+	20.9995i	0.414477	+	1.27563i	−0.498240	+	0.867039i	$0.666020\pi$
$272$	28.9925	−	21.0643i	1.75793	−	1.27721i
$273$	4.31157	−	7.46785i	0.260948	−	0.451975i
$274$	21.0487	−	9.37148i	1.27160	−	0.566152i
$275$	8.07672	−	3.59599i	0.487044	−	0.216846i
$276$	1.37450	−	2.38070i	0.0827349	−	0.143301i
$277$	−3.39311	+	2.46524i	−0.203872	+	0.148122i	−0.685037	−	0.728508i	$-0.740214\pi$
$277$	−3.39311	+	2.46524i	−0.203872	+	0.148122i	0.481165	+	0.876630i	$0.340214\pi$
$278$	−10.7758	−	33.1646i	−0.646291	−	1.98908i
$279$	0.816832	+	7.77164i	0.0489025	+	0.465276i
$280$	−3.31590	+	1.47633i	−0.198163	+	0.0882278i
$281$	−23.0097	−	16.7175i	−1.37264	−	0.997283i	−0.997525	−	0.0703057i	$-0.977603\pi$
$281$	−23.0097	−	16.7175i	−1.37264	−	0.997283i	−0.375117	−	0.926977i	$-0.622397\pi$
$282$	−9.06449	+	27.8976i	−0.539783	+	1.66128i
$283$	−8.46959	−	3.77090i	−0.503465	−	0.224157i	0.139257	−	0.990256i	$-0.455528\pi$
$283$	−8.46959	−	3.77090i	−0.503465	−	0.224157i	−0.642722	+	0.766099i	$0.722195\pi$
$284$	1.38564	+	2.40001i	0.0822228	+	0.142414i
$285$	−14.6129	−	10.6169i	−0.865593	−	0.628890i
$286$	1.78302	+	16.9643i	0.105432	+	1.00312i
$287$	7.10966	−	7.89608i	0.419670	−	0.466091i
$288$	−3.56159	−	3.95555i	−0.209869	−	0.233083i
$289$	−3.76684	+	35.8391i	−0.221579	+	2.10818i
$290$	8.31410	−	9.23374i	0.488221	−	0.542224i
$291$	−5.83204	+	10.1014i	−0.341880	+	0.592154i
$292$	−3.13279	−	5.42615i	−0.183333	−	0.317541i
$293$	10.7539	+	2.28581i	0.628248	+	0.133538i	0.511023	−	0.859567i	$-0.329267\pi$
$293$	10.7539	+	2.28581i	0.628248	+	0.133538i	0.117225	+	0.993105i	$0.462600\pi$
$294$	−19.1791			−1.11855
$295$	17.3434	+	3.68646i	1.00977	+	0.214634i
$296$	−3.36527	+	10.3572i	−0.195602	+	0.602002i
$297$	3.16473	+	9.74003i	0.183636	+	0.565174i
$298$	0.876356	−	8.33797i	0.0507659	−	0.483005i
$299$	6.16476	−	1.31036i	0.356517	−	0.0757800i
$300$	4.32442	−	0.919183i	0.249670	−	0.0530691i
$301$	−3.51547	−	3.90433i	−0.202628	−	0.225042i
$302$	6.96627	−	5.06129i	0.400864	−	0.291245i
$303$	8.56552	+	3.81361i	0.492076	+	0.219086i
$304$	29.6503			1.70056
$305$	−8.35521	+	7.46047i	−0.478418	+	0.427185i
$306$	16.4379			0.939690
$307$	23.3187	+	10.3822i	1.33087	+	0.592541i	0.944107	−	0.329638i	$-0.106927\pi$
$307$	23.3187	+	10.3822i	1.33087	+	0.592541i	0.386762	+	0.922180i	$0.373594\pi$
$308$	−2.09220	+	1.52007i	−0.119214	+	0.0866141i
$309$	17.5424	+	19.4828i	0.997953	+	1.10834i
$310$	−13.2039	+	2.80657i	−0.749931	+	0.159403i
$311$	−3.82370	+	0.812752i	−0.216822	+	0.0460869i	−0.315042	−	0.949078i	$-0.602019\pi$
$311$	−3.82370	+	0.812752i	−0.216822	+	0.0460869i	0.0982198	+	0.995165i	$0.468685\pi$
$312$	1.58969	−	15.1249i	0.0899987	−	0.856280i
$313$	−2.76404	−	8.50685i	−0.156233	−	0.480836i	0.842051	−	0.539398i	$-0.181348\pi$
$313$	−2.76404	−	8.50685i	−0.156233	−	0.480836i	−0.998284	+	0.0585626i	$0.981348\pi$
$314$	−3.50597	+	10.7903i	−0.197853	+	0.608930i
$315$	−2.30046	−	0.488977i	−0.129616	−	0.0275508i
$316$	−1.18173			−0.0664776
$317$	29.5274	+	6.27625i	1.65843	+	0.352509i	0.939492	−	0.342570i	$-0.111297\pi$
$317$	29.5274	+	6.27625i	1.65843	+	0.352509i	0.718933	+	0.695079i	$0.244631\pi$
$318$	13.8048	+	23.9106i	0.774135	+	1.34084i
$319$	−7.89202	+	13.6694i	−0.441868	+	0.765338i
$320$	−3.29220	+	3.65636i	−0.184040	+	0.204397i
$321$	1.06839	−	10.1650i	0.0596316	−	0.567357i
$322$	2.41868	+	2.68621i	0.134788	+	0.149697i
$323$	−29.3621	+	32.6099i	−1.63375	+	1.81447i
$324$	0.843816	+	8.02837i	0.0468787	+	0.446021i
$325$	8.20010	+	5.95772i	0.454860	+	0.330475i
$326$	1.74766	+	3.02703i	0.0967937	+	0.167652i
$327$	0.0150854	+	0.00671646i	0.000834226	+	0.000371421i
$328$	5.79074	−	17.8221i	0.319740	−	0.984059i
$329$	−8.24862	−	5.99298i	−0.454761	−	0.330403i
$330$	13.5641	−	6.03912i	0.746678	−	0.332443i
$331$	−1.88767	−	17.9600i	−0.103756	−	0.987170i	−0.915271	−	0.402839i	$-0.868024\pi$
$331$	−1.88767	−	17.9600i	−0.103756	−	0.987170i	0.811515	−	0.584331i	$-0.198643\pi$
$332$	0.432834	+	1.33212i	0.0237548	+	0.0731099i
$333$	−5.70865	+	4.14758i	−0.312832	+	0.227286i
$334$	7.53806	−	13.0563i	0.412464	−	0.714409i
$335$	−3.52488	+	1.56938i	−0.192585	+	0.0857442i
$336$	11.2560	−	5.01151i	0.614067	−	0.273400i
$337$	−10.0162	+	17.3486i	−0.545618	+	0.945037i	0.452950	+	0.891536i	$0.350372\pi$
$337$	−10.0162	+	17.3486i	−0.545618	+	0.945037i	−0.998568	+	0.0535015i	$0.982962\pi$
$338$	1.52013	−	1.10444i	0.0826843	−	0.0600737i
$339$	−9.18834	−	28.2788i	−0.499042	−	1.53589i
$340$	0.784600	+	7.46497i	0.0425509	+	0.404845i
$341$	15.6654	−	6.97469i	0.848329	−	0.377701i
$342$	11.0028	+	7.99402i	0.594965	+	0.432267i
$343$	4.65128	−	14.3152i	0.251145	−	0.772946i
$344$	−8.46480	−	3.76877i	−0.456391	−	0.203198i
$345$	−2.74297	−	4.75096i	−0.147676	−	0.255783i
$346$	−16.0841	−	11.6858i	−0.864685	−	0.628230i
$347$	0.957961	+	9.11439i	0.0514260	+	0.489286i	0.989675	+	0.143326i	$0.0457799\pi$
$347$	0.957961	+	9.11439i	0.0514260	+	0.489286i	−0.938249	+	0.345960i	$0.887553\pi$
$348$	−5.28138	+	5.86557i	−0.283112	+	0.314427i
$349$	−11.8630	−	13.1752i	−0.635013	−	0.705253i	0.336649	−	0.941630i	$-0.390707\pi$
$349$	−11.8630	−	13.1752i	−0.635013	−	0.705253i	−0.971661	+	0.236377i	$0.924040\pi$
$350$	−0.607647	+	5.78137i	−0.0324801	+	0.309027i
$351$	−7.85637	+	8.72538i	−0.419342	+	0.465726i
$352$	−5.84005	+	10.1153i	−0.311276	+	0.539145i
$353$	−3.34891	−	5.80049i	−0.178245	−	0.308729i	0.763035	−	0.646358i	$-0.223709\pi$
$353$	−3.34891	−	5.80049i	−0.178245	−	0.308729i	−0.941279	+	0.337629i	$0.890375\pi$
$354$	−41.6771	−	8.85875i	−2.21511	−	0.470837i
$355$	5.53043			0.293525
$356$	−4.13659	−	0.879259i	−0.219239	−	0.0466006i
$357$	−5.63488	+	17.3424i	−0.298230	+	0.917857i
$358$	−6.27955	−	19.3265i	−0.331884	−	1.02144i
$359$	2.88420	−	27.4413i	0.152222	−	1.44830i	−0.605564	−	0.795796i	$-0.707053\pi$
$359$	2.88420	−	27.4413i	0.152222	−	1.44830i	0.757787	−	0.652502i	$-0.226281\pi$
$360$	−4.05722	+	0.862388i	−0.213834	+	0.0454518i
$361$	−16.9278	+	3.59811i	−0.890936	+	0.189374i
$362$	12.5220	+	13.9071i	0.658140	+	0.730938i
$363$	3.34186	−	2.42801i	0.175402	−	0.127437i
$364$	−2.70852	−	1.20591i	−0.141965	−	0.0632069i
$365$	−12.5037			−0.654474
$366$	20.0780	−	17.9279i	1.04949	−	0.937106i
$367$	14.0141			0.731532			0.365766	−	0.930707i	$-0.380807\pi$
$367$	14.0141			0.731532			0.365766	+	0.930707i	$0.380807\pi$
$368$	8.22681	+	3.66281i	0.428852	+	0.190937i
$369$	9.82309	−	7.13689i	0.511369	−	0.371532i
$370$	−8.15617	−	9.05834i	−0.424019	−	0.470921i
$371$	−9.38701	+	1.99527i	−0.487349	+	0.103589i
$372$	8.38753	−	1.78283i	0.434873	−	0.0924352i
$373$	0.660105	−	6.28048i	0.0341790	−	0.325191i	−0.964051	−	0.265718i	$-0.914391\pi$
$373$	0.660105	−	6.28048i	0.0341790	−	0.325191i	0.998230	−	0.0594735i	$-0.0189422\pi$
$374$	−11.1466	−	34.3056i	−0.576375	−	1.77390i
$375$	7.35807	−	22.6458i	0.379969	−	1.16943i
$376$	−17.5890	−	3.73866i	−0.907085	−	0.192807i
$377$	−18.0957			−0.931974
$378$	−6.58674	−	1.40005i	−0.338785	−	0.0720110i
$379$	0.411458	+	0.712666i	0.0211352	+	0.0366072i	0.876400	−	0.481585i	$-0.159939\pi$
$379$	0.411458	+	0.712666i	0.0211352	+	0.0366072i	−0.855264	+	0.518192i	$0.826605\pi$
$380$	−3.10517	+	5.37831i	−0.159292	+	0.275902i
$381$	−18.8983	+	20.9887i	−0.968191	+	1.07529i
$382$	−0.796436	+	7.57758i	−0.0407492	+	0.387703i
$383$	−12.0053	−	13.3332i	−0.613442	−	0.681296i	0.353751	−	0.935340i	$-0.384906\pi$
$383$	−12.0053	−	13.3332i	−0.613442	−	0.681296i	−0.967193	+	0.254043i	$0.918239\pi$
$384$	18.7876	−	20.8658i	0.958752	−	1.06480i
$385$	0.539458	+	5.13260i	0.0274933	+	0.261581i
$386$	−9.38627	−	6.81952i	−0.477748	−	0.347105i
$387$	−3.00189	−	5.19943i	−0.152595	−	0.264302i
$388$	3.66368	+	1.63118i	0.185995	+	0.0828104i
$389$	−0.637490	+	1.96199i	−0.0323220	+	0.0994770i	−0.965916	−	0.258856i	$-0.916655\pi$
$389$	−0.637490	+	1.96199i	−0.0323220	+	0.0994770i	0.933594	+	0.358333i	$0.116655\pi$
$390$	13.7713	+	10.0054i	0.697336	+	0.506644i
$391$	−12.1753	+	5.42079i	−0.615731	+	0.274141i
$392$	−1.22897	−	11.6928i	−0.0620722	−	0.590578i
$393$	−4.43890	−	13.6615i	−0.223913	−	0.689133i
$394$	−29.6358	+	21.5317i	−1.49303	+	1.08475i
$395$	−1.17914	+	2.04234i	−0.0593291	+	0.102761i
$396$	−2.69978	+	1.20202i	−0.135669	+	0.0604037i
$397$	15.7251	−	7.00127i	0.789221	−	0.351384i	0.0277766	−	0.999614i	$-0.491157\pi$
$397$	15.7251	−	7.00127i	0.789221	−	0.351384i	0.761444	+	0.648230i	$0.224491\pi$
$398$	−17.6212	+	30.5207i	−0.883269	+	1.52987i
$399$	−12.2057	+	8.86794i	−0.611048	+	0.443952i
$400$	4.47542	+	13.7739i	0.223771	+	0.688696i
$401$	−0.730410	−	6.94938i	−0.0364749	−	0.347036i	−0.997505	−	0.0705926i	$-0.977511\pi$
$401$	−0.730410	−	6.94938i	−0.0364749	−	0.347036i	0.961030	−	0.276443i	$-0.0891557\pi$
$402$	8.47046	−	3.77129i	0.422468	−	0.188095i
$403$	15.9047	+	11.5554i	0.792270	+	0.575618i
$404$	0.996191	−	3.06596i	0.0495624	−	0.152537i
$405$	14.7171	+	6.55246i	0.731296	+	0.325594i
$406$	−5.18919	−	8.98795i	−0.257535	−	0.446064i
$407$	12.5270	+	9.10139i	0.620940	+	0.451139i
$408$	3.36164	+	31.9839i	0.166426	+	1.58344i
$409$	12.1125	−	13.4522i	0.598922	−	0.665171i	−0.365107	−	0.930965i	$-0.618968\pi$
$409$	12.1125	−	13.4522i	0.598922	−	0.665171i	0.964030	+	0.265795i	$0.0856343\pi$
$410$	14.0346	+	15.5870i	0.693120	+	0.769788i
$411$	−3.05309	+	29.0482i	−0.150598	+	1.43284i
$412$	6.03151	−	6.69867i	0.297151	−	0.330020i
$413$	7.40502	−	12.8259i	0.364377	−	0.631120i
$414$	2.06533	+	3.57726i	0.101505	+	0.175812i
$415$	2.73414	+	0.581159i	0.134214	+	0.0285280i
$416$	−13.3907			−0.656533
$417$	43.2397	+	9.19087i	2.11746	+	0.450079i
$418$	9.22236	−	28.3835i	0.451081	−	1.38828i
$419$	8.70426	+	26.7889i	0.425231	+	1.30873i	0.902773	+	0.430117i	$0.141528\pi$
$419$	8.70426	+	26.7889i	0.425231	+	1.30873i	−0.477543	+	0.878609i	$0.658472\pi$
$420$	−0.269759	+	2.56659i	−0.0131629	+	0.125237i
$421$	31.4668	−	6.68848i	1.53360	−	0.325977i	0.637718	−	0.770270i	$-0.279878\pi$
$421$	31.4668	−	6.68848i	1.53360	−	0.325977i	0.895882	+	0.444293i	$0.146545\pi$
$422$	36.8909	−	7.84141i	1.79582	−	0.381714i
$423$	−7.79628	−	8.65864i	−0.379068	−	0.420998i
$424$	−13.6929	+	9.94845i	−0.664984	+	0.483139i
$425$	−19.5807	−	8.71791i	−0.949806	−	0.422881i
$426$	−13.2899			−0.643898
$427$	3.76992	+	8.56291i	0.182439	+	0.414388i
$428$	−3.51424			−0.169867
$429$	−19.7543	−	8.79516i	−0.953745	−	0.424635i
$430$	8.39039	−	6.09597i	0.404620	−	0.293974i
$431$	11.6269	+	12.9130i	0.560048	+	0.621996i	0.954964	−	0.296721i	$-0.0958931\pi$
$431$	11.6269	+	12.9130i	0.560048	+	0.621996i	−0.394916	+	0.918717i	$0.629226\pi$
$432$	−16.4099	+	3.48803i	−0.789520	+	0.167818i
$433$	21.0308	−	4.47024i	1.01068	−	0.214826i	0.327322	−	0.944913i	$-0.393854\pi$
$433$	21.0308	−	4.47024i	1.01068	−	0.214826i	0.683354	+	0.730087i	$0.260520\pi$
$434$	−1.17858	+	11.2134i	−0.0565735	+	0.538261i
$435$	4.86739	+	14.9803i	0.233374	+	0.718250i
$436$	0.00175447	−	0.00539971i	8.40240e−5	−	0.000258599i
$437$	−10.7859	−	2.29261i	−0.515958	−	0.109670i
$438$	30.0470			1.43570
$439$	−32.3740	−	6.88131i	−1.54513	−	0.328427i	−0.645044	−	0.764145i	$-0.723161\pi$
$439$	−32.3740	−	6.88131i	−1.54513	−	0.328427i	−0.900083	+	0.435718i	$0.856494\pi$
$440$	4.55100	+	7.88256i	0.216960	+	0.375786i
$441$	3.80903	−	6.59744i	0.181382	−	0.314164i
$442$	27.6711	−	30.7318i	1.31618	−	1.46176i
$443$	−1.48072	+	14.0881i	−0.0703512	+	0.669347i	0.901343	+	0.433105i	$0.142582\pi$
$443$	−1.48072	+	14.0881i	−0.0703512	+	0.669347i	−0.971694	+	0.236241i	$0.924084\pi$
$444$	5.18106	+	5.75415i	0.245882	+	0.273080i
$445$	−5.64711	+	6.27175i	−0.267699	+	0.297310i
$446$	−2.26926	−	21.5906i	−0.107453	−	1.02234i
$447$	8.59831	+	6.24704i	0.406686	+	0.295475i
$448$	2.05481	+	3.55903i	0.0970805	+	0.168148i
$449$	−3.06190	−	1.36325i	−0.144500	−	0.0643356i	0.333213	−	0.942852i	$-0.391867\pi$
$449$	−3.06190	−	1.36325i	−0.144500	−	0.0643356i	−0.477713	+	0.878516i	$0.658534\pi$
$450$	−2.05282	+	6.31794i	−0.0967710	+	0.297831i
$451$	−21.5556	−	15.6611i	−1.01502	−	0.737452i
$452$	−9.33946	+	4.15820i	−0.439291	+	0.195585i
$453$	1.14100	+	10.8559i	0.0536090	+	0.510056i
$454$	0.946989	+	2.91453i	0.0444444	+	0.136786i
$455$	−4.78671	+	3.47775i	−0.224405	+	0.163039i
$456$	−13.3042	+	23.0435i	−0.623025	+	1.07911i
$457$	34.3209	−	15.2807i	1.60547	−	0.714799i	0.608568	−	0.793502i	$-0.291744\pi$
$457$	34.3209	−	15.2807i	1.60547	−	0.714799i	0.996898	+	0.0787024i	$0.0250777\pi$
$458$	−39.6493	+	17.6530i	−1.85269	+	0.824872i
$459$	12.4142	−	21.5020i	0.579445	−	1.00363i
$460$	−1.52597	+	1.10868i	−0.0711486	+	0.0516925i
$461$	2.07827	+	6.39627i	0.0967948	+	0.297904i	0.987717	−	0.156252i	$-0.0499411\pi$
$461$	2.07827	+	6.39627i	0.0967948	+	0.297904i	−0.890922	+	0.454155i	$0.849941\pi$
$462$	−1.29634	−	12.3339i	−0.0603114	−	0.573825i
$463$	−13.0810	+	5.82402i	−0.607924	+	0.270665i	−0.687524	−	0.726162i	$-0.741302\pi$
$463$	−13.0810	+	5.82402i	−0.607924	+	0.270665i	0.0796000	+	0.996827i	$0.474636\pi$
$464$	−20.9181	−	15.1979i	−0.971099	−	0.705544i
$465$	5.28798	−	16.2747i	0.245224	−	0.754723i
$466$	16.4676	+	7.33187i	0.762849	+	0.339642i
$467$	14.9623	+	25.9154i	0.692372	+	1.19922i	0.971059	+	0.238841i	$0.0767675\pi$
$467$	14.9623	+	25.9154i	0.692372	+	1.19922i	−0.278687	+	0.960382i	$0.589899\pi$
$468$	−2.74102	−	1.99147i	−0.126704	−	0.0920556i
$469$	0.336879	+	3.20519i	0.0155556	+	0.148002i
$470$	13.4675	−	14.9572i	0.621209	−	0.689922i
$471$	−9.62381	−	10.6883i	−0.443442	−	0.492492i
$472$	2.73026	−	25.9767i	0.125671	−	1.19568i
$473$	−8.81554	+	9.79065i	−0.405339	+	0.450175i
$474$	2.83354	−	4.90784i	0.130149	−	0.225424i
$475$	−8.86687	−	15.3579i	−0.406840	−	0.704668i
$476$	6.13259	+	1.30352i	0.281087	+	0.0597469i
$477$	−10.9667			−0.502130
$478$	23.1019	+	4.91046i	1.05666	+	0.224599i
$479$	−4.30299	+	13.2432i	−0.196609	+	0.605099i	0.803345	+	0.595513i	$0.203051\pi$
$479$	−4.30299	+	13.2432i	−0.196609	+	0.605099i	−0.999954	+	0.00958585i	$0.996949\pi$
$480$	3.60184	+	11.0853i	0.164401	+	0.505974i
$481$	−1.85558	+	17.6547i	−0.0846073	+	0.804985i
$482$	−13.9825	+	2.97206i	−0.636884	+	0.135374i
$483$	−4.48209	+	0.952698i	−0.203942	+	0.0433493i
$484$	−0.950340	−	1.05546i	−0.0431973	−	0.0479754i
$485$	6.47475	−	4.70418i	0.294003	−	0.213606i
$486$	−19.9598	−	8.88669i	−0.905397	−	0.403109i
$487$	−41.7968			−1.89399			−0.946996	−	0.321244i	$-0.895899\pi$
$487$	−41.7968			−1.89399			−0.946996	+	0.321244i	$0.895899\pi$
$488$	12.2166	+	11.0921i	0.553018	+	0.502114i
$489$	−4.43094			−0.200374
$490$	12.0219	+	5.35251i	0.543095	+	0.241802i
$491$	−9.01346	+	6.54866i	−0.406772	+	0.295537i	−0.772294	−	0.635266i	$-0.780891\pi$
$491$	−9.01346	+	6.54866i	−0.406772	+	0.295537i	0.365522	+	0.930803i	$0.380891\pi$
$492$	−8.91523	−	9.90137i	−0.401930	−	0.446388i
$493$	37.4297	−	7.95593i	1.68575	−	0.358317i
$494$	33.4673	−	7.11370i	1.50577	−	0.320060i
$495$	−0.616467	+	5.86530i	−0.0277081	+	0.263625i
$496$	8.68042	+	26.7156i	0.389762	+	1.19956i
$497$	1.42747	−	4.39330i	0.0640308	−	0.197067i
$498$	−6.57028	−	1.39656i	−0.294421	−	0.0625811i
$499$	7.81559			0.349874			0.174937	−	0.984580i	$-0.444028\pi$
$499$	7.81559			0.349874			0.174937	+	0.984580i	$0.444028\pi$
$500$	−8.00798	−	1.70215i	−0.358128	−	0.0761224i
$501$	9.55585	+	16.5512i	0.426924	+	0.739454i
$502$	−8.14696	+	14.1109i	−0.363617	+	0.629802i
$503$	−5.23989	+	5.81949i	−0.233635	+	0.259478i	−0.848550	−	0.529115i	$-0.822524\pi$
$503$	−5.23989	+	5.81949i	−0.233635	+	0.259478i	0.614915	+	0.788594i	$0.289190\pi$
$504$	−0.362146	+	3.44559i	−0.0161313	+	0.153479i
$505$	−4.30476	−	4.78092i	−0.191559	−	0.212748i
$506$	6.06517	−	6.73606i	0.269630	−	0.299454i
$507$	0.248982	+	2.36891i	0.0110577	+	0.105207i
$508$	7.85611	+	5.70779i	0.348558	+	0.253242i
$509$	−11.9730	−	20.7379i	−0.530695	−	0.919191i	−0.999358	−	0.0358144i	$-0.988597\pi$
$509$	−11.9730	−	20.7379i	−0.530695	−	0.919191i	0.468663	−	0.883377i	$-0.344736\pi$
$510$	−32.8840	−	14.6409i	−1.45613	−	0.648310i
$511$	−3.22736	+	9.93278i	−0.142770	+	0.439400i
$512$	1.34239	+	0.975306i	0.0593260	+	0.0431028i
$513$	18.7664	−	8.35532i	0.828555	−	0.368896i
$514$	0.897279	+	8.53704i	0.0395773	+	0.376553i
$515$	−5.55873	−	17.1080i	−0.244947	−	0.753869i
$516$	−5.32984	+	3.87236i	−0.234633	+	0.170471i
$517$	−12.7838	+	22.1422i	−0.562230	+	0.973811i
$518$	−9.30103	+	4.14109i	−0.408664	+	0.181949i
$519$	23.0239	−	10.2509i	1.01064	−	0.449964i
$520$	−5.21751	+	9.03699i	−0.228803	+	0.396298i
$521$	−5.15668	+	3.74655i	−0.225918	+	0.164139i	−0.694987	−	0.719023i	$-0.744590\pi$
$521$	−5.15668	+	3.74655i	−0.225918	+	0.164139i	0.469068	+	0.883162i	$0.344590\pi$
$522$	−3.66492	−	11.2795i	−0.160409	−	0.493689i
$523$	−0.862291	−	8.20415i	−0.0377054	−	0.358743i	−0.997065	−	0.0765570i	$-0.975607\pi$
$523$	−0.862291	−	8.20415i	−0.0377054	−	0.358743i	0.959360	−	0.282186i	$-0.0910594\pi$
$524$	−4.51191	+	2.00883i	−0.197104	+	0.0877562i
$525$	−5.96189	−	4.33157i	−0.260198	−	0.189045i
$526$	−5.98682	+	18.4255i	−0.261038	+	0.803391i
$527$	−37.9783	−	16.9090i	−1.65436	−	0.736569i
$528$	−15.4487	−	26.7579i	−0.672317	−	1.16449i
$529$	15.8979	+	11.5505i	0.691215	+	0.502197i
$530$	−1.98020	−	18.8404i	−0.0860145	−	0.818373i
$531$	11.3245	−	12.5771i	0.491442	−	0.545802i
$532$	3.47098	+	3.85491i	0.150486	+	0.167132i
$533$	3.19297	−	30.3791i	0.138303	−	1.31586i
$534$	13.5703	−	15.0713i	0.587244	−	0.652201i
$535$	−3.50654	+	6.07351i	−0.151601	+	0.262581i
$536$	2.84199	+	4.92248i	0.122755	+	0.212619i
$537$	25.1977	+	5.35593i	1.08736	+	0.231125i
$538$	6.01060			0.259135
$539$	−16.3517	−	3.47565i	−0.704316	−	0.149707i
$540$	1.08585	−	3.34190i	0.0467275	−	0.143813i
$541$	−9.68894	−	29.8195i	−0.416560	−	1.28204i	−0.910848	−	0.412742i	$-0.864571\pi$
$541$	−9.68894	−	29.8195i	−0.416560	−	1.28204i	0.494288	−	0.869298i	$-0.335429\pi$
$542$	−3.80553	+	36.2072i	−0.163462	+	1.55523i
$543$	−23.2047	+	4.93231i	−0.995809	+	0.211666i
$544$	27.6978	−	5.88735i	1.18753	−	0.252418i
$545$	−0.00758146	−	0.00842006i	−0.000324754	−	0.000360676i
$546$	11.5027	−	8.35721i	0.492271	−	0.357656i
$547$	−32.7420	−	14.5777i	−1.39995	−	0.623296i	−0.438611	−	0.898677i	$-0.644530\pi$
$547$	−32.7420	−	14.5777i	−1.39995	−	0.623296i	−0.961335	+	0.275380i	$0.911196\pi$
$548$	10.0425			0.428994
$549$	2.17947	+	10.4672i	0.0930175	+	0.446728i
$550$	14.5775			0.621586
$551$	28.9230	+	12.8774i	1.23216	+	0.548594i
$552$	−6.53805	+	4.75017i	−0.278278	+	0.202181i
$553$	1.31805	+	1.46385i	0.0560494	+	0.0622491i
$554$	−6.76429	+	1.43779i	−0.287387	+	0.0610860i
$555$	15.1144	−	3.21265i	0.641569	−	0.136370i
$556$	1.58873	−	15.1157i	0.0673771	−	0.641050i
$557$	−0.940299	−	2.89394i	−0.0398418	−	0.122620i	0.929157	−	0.369684i	$-0.120534\pi$
$557$	−0.940299	−	2.89394i	−0.0398418	−	0.122620i	−0.968999	+	0.247064i	$0.920534\pi$
$558$	−3.98161	+	12.2541i	−0.168555	+	0.518758i
$559$	−14.7740	−	3.14032i	−0.624875	−	0.132821i
$560$	−8.45415			−0.357253
$561$	44.7273	+	9.50708i	1.88839	+	0.401389i
$562$	−23.4477	−	40.6126i	−0.989082	−	1.71314i
$563$	9.02183	−	15.6263i	0.380225	−	0.658569i	−0.610869	−	0.791731i	$-0.709180\pi$
$563$	9.02183	−	15.6263i	0.380225	−	0.658569i	0.991094	+	0.133163i	$0.0425133\pi$
$564$	−8.55498	+	9.50126i	−0.360230	+	0.400075i
$565$	−2.13257	+	20.2901i	−0.0897180	+	0.853610i
$566$	−10.2287	−	11.3601i	−0.429945	−	0.477502i
$567$	9.00383	−	9.99977i	0.378125	−	0.419951i
$568$	−0.851595	−	8.10239i	−0.0357321	−	0.339969i
$569$	20.7813	+	15.0985i	0.871197	+	0.632961i	0.930908	−	0.365254i	$-0.119018\pi$
$569$	20.7813	+	15.0985i	0.871197	+	0.632961i	−0.0597112	+	0.998216i	$0.519018\pi$
$570$	−14.8911	−	25.7921i	−0.623718	−	1.08031i
$571$	12.3806	+	5.51218i	0.518110	+	0.230677i	0.649096	−	0.760707i	$-0.275147\pi$
$571$	12.3806	+	5.51218i	0.518110	+	0.230677i	−0.130986	+	0.991384i	$0.541814\pi$
$572$	−2.29747	+	7.07089i	−0.0960621	+	0.295649i
$573$	−7.81419	−	5.67734i	−0.326442	−	0.237174i
$574$	16.0046	−	7.12572i	0.668020	−	0.297422i
$575$	−0.562999	−	5.35658i	−0.0234787	−	0.223385i
$576$	1.45123	+	4.46642i	0.0604679	+	0.186101i
$577$	−17.5073	+	12.7198i	−0.728840	+	0.529533i	−0.889196	−	0.457526i	$-0.848736\pi$
$577$	−17.5073	+	12.7198i	−0.728840	+	0.529533i	0.160357	+	0.987059i	$0.448736\pi$
$578$	−29.7092	+	51.4578i	−1.23574	+	2.14036i
$579$	13.4362	−	5.98216i	0.558388	−	0.248610i
$580$	4.94745	−	2.20275i	0.205432	−	0.0914640i
$581$	1.16738	−	2.02196i	0.0484311	−	0.0838850i
$582$	−15.5591	+	11.3044i	−0.644947	+	0.468582i
$583$	7.43654	+	22.8873i	0.307990	+	0.947896i
$584$	1.92536	+	18.3186i	0.0796721	+	0.758030i
$585$	−6.17678	+	2.75008i	−0.255379	+	0.113702i
$586$	14.6655	+	10.6551i	0.605825	+	0.440157i
$587$	−3.13370	+	9.64455i	−0.129342	+	0.398073i	−0.994667	−	0.103138i	$-0.967112\pi$
$587$	−3.13370	+	9.64455i	−0.129342	+	0.398073i	0.865325	+	0.501211i	$0.167112\pi$
$588$	−7.63671	−	3.40008i	−0.314933	−	0.140217i
$589$	−17.1980	−	29.7878i	−0.708630	−	1.22738i
$590$	23.6519	+	17.1841i	0.973733	+	0.707458i
$591$	−4.85404	−	46.1831i	−0.199668	−	1.89972i
$592$	−16.9725	+	18.8499i	−0.697567	+	0.774726i
$593$	−3.64615	−	4.04946i	−0.149730	−	0.166291i	0.663614	−	0.748075i	$-0.269022\pi$
$593$	−3.64615	−	4.04946i	−0.149730	−	0.166291i	−0.813344	+	0.581784i	$0.802355\pi$
$594$	−1.76509	+	16.7937i	−0.0724224	+	0.689053i
$595$	8.37198	−	9.29803i	0.343218	−	0.381182i
$596$	1.82710	−	3.16463i	0.0748410	−	0.129628i
$597$	−22.3380	−	38.6906i	−0.914234	−	1.58350i
$598$	10.1647	+	2.16057i	0.415664	+	0.0883522i
$599$	−16.6779			−0.681442			−0.340721	−	0.940164i	$-0.610671\pi$
$599$	−16.6779			−0.681442			−0.340721	+	0.940164i	$0.610671\pi$
$600$	−12.7129	−	2.70221i	−0.519002	−	0.110317i
$601$	5.93270	−	18.2590i	0.242000	−	0.744799i	−0.754115	−	0.656742i	$-0.771934\pi$
$601$	5.93270	−	18.2590i	0.242000	−	0.744799i	0.996115	−	0.0880574i	$-0.0280659\pi$
$602$	−2.67690	−	8.23866i	−0.109102	−	0.335783i
$603$	−0.384970	+	3.66274i	−0.0156772	+	0.149158i
$604$	3.67108	−	0.780312i	0.149374	−	0.0317505i
$605$	−2.77236	+	0.589284i	−0.112713	+	0.0239578i
$606$	10.3446	+	11.4888i	0.420219	+	0.466700i
$607$	−15.4012	+	11.1896i	−0.625116	+	0.454174i	−0.854705	−	0.519114i	$-0.826262\pi$
$607$	−15.4012	+	11.1896i	−0.625116	+	0.454174i	0.229589	+	0.973288i	$0.426262\pi$
$608$	21.4029	+	9.52917i	0.868001	+	0.386459i
$609$	13.1565			0.533127
$610$	−17.5887	+	5.63425i	−0.712144	+	0.228124i
$611$	−29.3120			−1.18584
$612$	6.54519	+	2.91411i	0.264574	+	0.117796i
$613$	6.30542	−	4.58116i	0.254674	−	0.185031i	−0.453122	−	0.891449i	$-0.649690\pi$
$613$	6.30542	−	4.58116i	0.254674	−	0.185031i	0.707796	+	0.706417i	$0.249690\pi$
$614$	28.1620	+	31.2770i	1.13652	+	1.26224i
$615$	−26.0078	+	5.52813i	−1.04874	+	0.222916i
$616$	7.43647	−	1.58067i	0.299624	−	0.0636870i
$617$	3.88060	−	36.9214i	0.156227	−	1.48640i	−0.582740	−	0.812658i	$-0.698020\pi$
$617$	3.88060	−	36.9214i	0.156227	−	1.48640i	0.738967	−	0.673741i	$-0.235314\pi$
$618$	13.3579	+	41.1114i	0.537334	+	1.65374i
$619$	−2.07910	+	6.39880i	−0.0835659	+	0.257189i	−0.984106	−	0.177584i	$-0.943172\pi$
$619$	−2.07910	+	6.39880i	−0.0835659	+	0.257189i	0.900540	+	0.434774i	$0.143172\pi$
$620$	−5.75505	−	1.22327i	−0.231128	−	0.0491278i
$621$	6.23911			0.250367
$622$	−6.30465	−	1.34009i	−0.252793	−	0.0537329i
$623$	3.52461	+	6.10480i	0.141211	+	0.244584i
$624$	17.7112	−	30.6767i	0.709014	−	1.22805i
$625$	−1.08546	+	1.20552i	−0.0434182	+	0.0482208i
$626$	1.54161	−	14.6674i	0.0616151	−	0.586229i
$627$	25.3152	+	28.1153i	1.01099	+	1.12282i
$628$	−3.30890	+	3.67491i	−0.132040	+	0.146645i
$629$	−3.92390	−	37.3334i	−0.156456	−	1.48858i
$630$	−3.13722	−	2.27932i	−0.124990	−	0.0908105i
$631$	20.0257	+	34.6855i	0.797210	+	1.38081i	0.921426	+	0.388553i	$0.127025\pi$
$631$	20.0257	+	34.6855i	0.797210	+	1.38081i	−0.124216	+	0.992255i	$0.539642\pi$
$632$	3.17370	+	1.41302i	0.126243	+	0.0562071i
$633$	−14.7743	+	45.4707i	−0.587226	+	1.80730i
$634$	40.2677	+	29.2562i	1.59923	+	1.16191i
$635$	17.7034	−	7.88208i	0.702539	−	0.312791i
$636$	1.25789	+	11.9680i	0.0498785	+	0.474562i
$637$	−5.92238	−	18.2272i	−0.234653	−	0.722189i
$638$	−21.0549	+	15.2973i	−0.833571	+	0.605625i
$639$	2.63941	−	4.57160i	0.104414	−	0.180850i
$640$	−17.5997	+	7.83590i	−0.695690	+	0.309741i
$641$	5.54423	−	2.46845i	0.218984	−	0.0974980i	−0.294313	−	0.955709i	$-0.595091\pi$
$641$	5.54423	−	2.46845i	0.218984	−	0.0974980i	0.513297	+	0.858211i	$0.328424\pi$
$642$	8.42640	−	14.5950i	0.332563	−	0.576017i
$643$	3.45737	−	2.51193i	0.136345	−	0.0990608i	−0.517522	−	0.855670i	$-0.673145\pi$
$643$	3.45737	−	2.51193i	0.136345	−	0.0990608i	0.653867	+	0.756609i	$0.273145\pi$
$644$	0.486851	+	1.49837i	0.0191846	+	0.0590442i
$645$	1.37426	+	13.0752i	0.0541114	+	0.514836i
$646$	−66.0974	+	29.4285i	−2.60057	+	1.15785i
$647$	16.1915	+	11.7638i	0.636555	+	0.462484i	0.858665	−	0.512537i	$-0.171294\pi$
$647$	16.1915	+	11.7638i	0.636555	+	0.462484i	−0.222110	+	0.975022i	$0.571294\pi$
$648$	7.33352	−	22.5703i	0.288088	−	0.886644i
$649$	−33.9275	−	15.1055i	−1.33177	−	0.592943i
$650$	8.35620	+	14.4734i	0.327757	+	0.567692i
$651$	−11.5635	−	8.40140i	−0.453211	−	0.329277i
$652$	0.159246	+	1.51512i	0.00623654	+	0.0593367i
$653$	6.50424	−	7.22369i	0.254531	−	0.282685i	−0.602314	−	0.798259i	$-0.705755\pi$
$653$	6.50424	−	7.22369i	0.254531	−	0.282685i	0.856845	+	0.515574i	$0.172421\pi$
$654$	0.0182186	+	0.0202338i	0.000712405	+	0.000791206i
$655$	−1.03025	+	9.80216i	−0.0402552	+	0.383002i
$656$	29.2053	−	32.4357i	1.14027	−	1.26640i
$657$	−5.96743	+	10.3359i	−0.232811	+	0.403241i
$658$	−8.40565	−	14.5590i	−0.327686	−	0.567570i
$659$	4.60609	+	0.979054i	0.179428	+	0.0381385i	0.296749	−	0.954955i	$-0.404097\pi$
$659$	4.60609	+	0.979054i	0.179428	+	0.0381385i	−0.117322	+	0.993094i	$0.537431\pi$
$660$	6.47153			0.251904
$661$	42.4993	+	9.03351i	1.65303	+	0.351363i	0.937707	−	0.347428i	$-0.112945\pi$
$661$	42.4993	+	9.03351i	1.65303	+	0.351363i	0.715326	+	0.698791i	$0.246278\pi$
$662$	9.20135	−	28.3188i	0.357621	−	1.10064i
$663$	16.1997	+	49.8576i	0.629145	+	1.93631i
$664$	0.430418	−	4.09515i	0.0167035	−	0.158923i
$665$	10.1257	−	2.15227i	0.392656	−	0.0834616i
$666$	−11.3804	+	2.41898i	−0.440982	+	0.0937336i
$667$	6.43424	+	7.14594i	0.249135	+	0.276692i
$668$	5.31611	−	3.86238i	0.205686	−	0.149440i
$669$	25.1414	+	11.1937i	0.972024	+	0.432773i
$670$	−6.36196			−0.245784
$671$	20.3669	−	11.6463i	0.786256	−	0.449602i
$672$	9.73572			0.375564
$673$	−21.4708	−	9.55943i	−0.827640	−	0.368489i	−0.0512064	−	0.998688i	$-0.516307\pi$
$673$	−21.4708	−	9.55943i	−0.827640	−	0.368489i	−0.776434	+	0.630199i	$0.782973\pi$
$674$	−26.7220	+	19.4146i	−1.02929	+	0.747824i
$675$	6.71403	+	7.45668i	0.258423	+	0.287008i
$676$	0.801079	−	0.170275i	0.0308107	−	0.00654902i
$677$	−32.3540	+	6.87706i	−1.24347	+	0.264307i	−0.782241	−	0.622976i	$-0.785923\pi$
$677$	−32.3540	+	6.87706i	−1.24347	+	0.264307i	−0.461225	+	0.887283i	$0.652590\pi$
$678$	5.12468	−	48.7581i	0.196812	−	1.87254i
$679$	−2.06573	−	6.35766i	−0.0792754	−	0.243985i
$680$	6.81889	−	20.9864i	0.261492	−	0.804791i
$681$	−3.79994	−	0.807702i	−0.145614	−	0.0309512i
$682$	28.2741			1.08267
$683$	8.60480	+	1.82901i	0.329253	+	0.0699850i	0.369573	−	0.929202i	$-0.379504\pi$
$683$	8.60480	+	1.82901i	0.329253	+	0.0699850i	−0.0403191	+	0.999187i	$0.512837\pi$
$684$	2.96390	+	5.13363i	0.113328	+	0.196289i
$685$	10.0205	−	17.3560i	0.382863	−	0.663139i
$686$	16.6065	−	18.4434i	0.634039	−	0.704172i
$687$	5.75109	−	54.7180i	0.219418	−	2.08762i
$688$	−14.4410	−	16.0383i	−0.550556	−	0.611454i
$689$	−18.4610	+	20.5031i	−0.703309	+	0.781104i
$690$	−0.945503	−	8.99586i	−0.0359947	−	0.342467i
$691$	12.9260	+	9.39132i	0.491730	+	0.357263i	0.805849	−	0.592121i	$-0.201709\pi$
$691$	12.9260	+	9.39132i	0.491730	+	0.357263i	−0.314119	+	0.949384i	$0.601709\pi$
$692$	−4.33267	−	7.50440i	−0.164703	−	0.285274i
$693$	4.50020	+	2.00362i	0.170948	+	0.0761111i
$694$	−4.66953	+	14.3713i	−0.177253	+	0.545528i
$695$	−24.5386	−	17.8284i	−0.930803	−	0.676268i
$696$	21.1975	−	9.43771i	0.803487	−	0.357736i
$697$	6.75200	+	64.2410i	0.255750	+	2.43330i
$698$	−9.03325	−	27.8015i	−0.341914	−	1.05230i
$699$	−18.4871	+	13.4317i	−0.699246	+	0.508032i
$700$	−1.26687	+	2.19429i	−0.0478833	+	0.0829364i
$701$	−20.3073	+	9.04140i	−0.766996	+	0.341489i	−0.752661	−	0.658408i	$-0.771230\pi$
$701$	−20.3073	+	9.04140i	−0.766996	+	0.341489i	−0.0143356	+	0.999897i	$0.504563\pi$
$702$	−17.6855	+	7.87411i	−0.667498	+	0.297189i
$703$	15.5294	−	26.8977i	0.585703	−	1.01447i
$704$	8.33728	−	6.05739i	0.314223	−	0.228296i
$705$	7.88439	+	24.2656i	0.296943	+	0.913897i
$706$	−1.15437	−	10.9831i	−0.0434454	−	0.413355i
$707$	−4.90901	+	2.18563i	−0.184622	+	0.0821991i
$708$	−15.0244	−	10.9159i	−0.564653	−	0.410244i
$709$	−4.93933	+	15.2017i	−0.185500	+	0.570911i	−0.999957	−	0.00931352i	$-0.997035\pi$
$709$	−4.93933	+	15.2017i	−0.185500	+	0.570911i	0.814456	+	0.580225i	$0.197035\pi$
$710$	8.33042	+	3.70894i	0.312635	+	0.139194i
$711$	1.12550	+	1.94942i	0.0422095	+	0.0731090i
$712$	10.0580	+	7.30758i	0.376940	+	0.273863i
$713$	−1.09198	−	10.3895i	−0.0408949	−	0.389089i
$714$	−20.1183	+	22.3436i	−0.752908	+	0.836189i
$715$	9.92787	+	11.0260i	0.371281	+	0.412350i
$716$	0.925822	−	8.80860i	0.0345996	−	0.329193i
$717$	−20.0338	+	22.2498i	−0.748177	+	0.830934i
$718$	22.7478	−	39.4003i	0.848939	−	1.47041i
$719$	25.7291	+	44.5642i	0.959535	+	1.66196i	0.723632	+	0.690186i	$0.242471\pi$
$719$	25.7291	+	44.5642i	0.959535	+	1.66196i	0.235902	+	0.971777i	$0.424195\pi$
$720$	−9.44989	−	2.00864i	−0.352177	−	0.0748574i
$721$	−15.0251			−0.559566
$722$	−27.9111	−	5.93270i	−1.03875	−	0.220792i
$723$	5.59978	−	17.2344i	0.208258	−	0.640953i
$724$	2.52052	+	7.75737i	0.0936745	+	0.288301i
$725$	−1.61648	+	15.3798i	−0.0600346	+	0.571191i
$726$	6.66213	−	1.41608i	0.247255	−	0.0525556i
$727$	−28.1676	+	5.98721i	−1.04468	+	0.222053i	−0.698124	−	0.715976i	$-0.745982\pi$
$727$	−28.1676	+	5.98721i	−1.04468	+	0.222053i	−0.346555	+	0.938030i	$0.612648\pi$
$728$	5.83217	+	6.47728i	0.216155	+	0.240064i
$729$	−4.85508	+	3.52742i	−0.179818	+	0.130645i
$730$	−18.8342	−	8.38551i	−0.697084	−	0.310362i
$731$	31.9398			1.18134
$732$	11.1729	−	3.57906i	0.412961	−	0.132286i
$733$	−32.0787			−1.18485			−0.592427	−	0.805624i	$-0.701830\pi$
$733$	−32.0787			−1.18485			−0.592427	+	0.805624i	$0.701830\pi$
$734$	21.1093	+	9.39848i	0.779159	+	0.346904i
$735$	−13.4962	+	9.80556i	−0.497815	+	0.361683i
$736$	4.76130	+	5.28796i	0.175504	+	0.194917i
$737$	7.90514	−	1.68029i	0.291189	−	0.0618942i
$738$	19.5827	−	4.16243i	0.720849	−	0.153221i
$739$	−0.232406	+	2.21120i	−0.00854920	+	0.0813402i	−0.997965	−	0.0637709i	$-0.979687\pi$
$739$	−0.232406	+	2.21120i	−0.00854920	+	0.0813402i	0.989415	+	0.145111i	$0.0463540\pi$
$740$	−1.64174	−	5.05276i	−0.0603516	−	0.185743i
$741$	−13.4032	+	41.2508i	−0.492379	+	1.51539i
$742$	−15.4776	−	3.28988i	−0.568202	−	0.120775i
$743$	−22.3986			−0.821724			−0.410862	−	0.911698i	$-0.634772\pi$
$743$	−22.3986			−0.821724			−0.410862	+	0.911698i	$0.634772\pi$
$744$	−24.6576	−	5.24114i	−0.903993	−	0.192150i
$745$	−3.64620	−	6.31540i	−0.133586	−	0.231378i
$746$	5.20626	−	9.01751i	0.190615	−	0.330155i
$747$	1.78528	−	1.98275i	0.0653198	−	0.0725450i
$748$	1.64339	−	15.6358i	0.0600882	−	0.571701i
$749$	3.91964	+	4.35320i	0.143220	+	0.159062i
$750$	26.2706	−	29.1765i	0.959267	−	1.06537i
$751$	−1.98895	−	18.9236i	−0.0725777	−	0.690530i	−0.968955	−	0.247238i	$-0.920477\pi$
$751$	−1.98895	−	18.9236i	−0.0725777	−	0.690530i	0.896377	−	0.443292i	$-0.146190\pi$
$752$	−33.8839	−	24.6181i	−1.23562	−	0.897730i
$753$	−10.3277	−	17.8882i	−0.376364	−	0.651881i
$754$	−27.2573	−	12.1357i	−0.992651	−	0.441957i
$755$	2.31446	−	7.12317i	0.0842318	−	0.259239i
$756$	−2.37449	−	1.72517i	−0.0863594	−	0.0627438i
$757$	−46.9153	+	20.8880i	−1.70517	+	0.759189i	−0.706492	+	0.707721i	$0.749723\pi$
$757$	−46.9153	+	20.8880i	−1.70517	+	0.759189i	−0.998675	+	0.0514679i	$0.983610\pi$
$758$	0.141830	+	1.34942i	0.00515149	+	0.0490131i
$759$	3.55079	+	10.9282i	0.128885	+	0.396668i
$760$	14.7703	−	10.7313i	0.535776	−	0.389264i
$761$	5.49231	−	9.51296i	0.199096	−	0.344845i	−0.749140	−	0.662412i	$-0.769533\pi$
$761$	5.49231	−	9.51296i	0.199096	−	0.344845i	0.948236	+	0.317568i	$0.102866\pi$
$762$	−42.5422	+	18.9410i	−1.54114	+	0.686161i
$763$	−0.00864565	+	0.00384929i	−0.000312994	+	0.000139354i
$764$	−1.66048	+	2.87603i	−0.0600740	+	0.104051i
$765$	11.5672	−	8.40405i	0.418212	−	0.303849i
$766$	−9.14160	−	28.1349i	−0.330299	−	1.01656i
$767$	−4.45054	−	42.3441i	−0.160700	−	1.52896i
$768$	29.1915	−	12.9969i	1.05336	−	0.468985i
$769$	−17.5621	−	12.7596i	−0.633306	−	0.460124i	0.224238	−	0.974534i	$-0.428011\pi$
$769$	−17.5621	−	12.7596i	−0.633306	−	0.460124i	−0.857544	+	0.514410i	$0.828011\pi$
$770$	−2.62956	+	8.09295i	−0.0947627	+	0.291650i
$771$	−9.94106	−	4.42605i	−0.358019	−	0.159400i
$772$	−2.52844	−	4.37938i	−0.0910004	−	0.157617i
$773$	29.1573	+	21.1841i	1.04872	+	0.761937i	0.971968	−	0.235113i	$-0.0755460\pi$
$773$	29.1573	+	21.1841i	1.04872	+	0.761937i	0.0767489	+	0.997050i	$0.475546\pi$
$774$	−1.03475	−	9.84503i	−0.0371935	−	0.353872i
$775$	11.2419	−	12.4854i	0.403822	−	0.448489i
$776$	−7.88888	−	8.76149i	−0.283194	−	0.314519i
$777$	1.34910	−	12.8359i	0.0483988	−	0.460484i
$778$	−2.27604	+	2.52780i	−0.0816000	+	0.0906259i
$779$	−26.7220	+	46.2839i	−0.957415	+	1.65829i
$780$	3.70966	+	6.42531i	0.132827	+	0.230063i
$781$	−11.3307	−	2.40840i	−0.405443	−	0.0861795i
$782$	−21.9749			−0.785820
$783$	−17.5222	−	3.72447i	−0.626194	−	0.133102i
$784$	8.46227	−	26.0442i	0.302224	−	0.930149i
$785$	3.04953	+	9.38549i	0.108842	+	0.334982i
$786$	2.47574	−	23.5551i	0.0883068	−	0.840183i
$787$	36.1443	−	7.68270i	1.28840	−	0.273859i	0.487749	−	0.872984i	$-0.337818\pi$
$787$	36.1443	−	7.68270i	1.28840	−	0.273859i	0.800655	+	0.599125i	$0.204485\pi$
$788$	−15.6174	+	3.31959i	−0.556348	+	0.118255i
$789$	−16.4337	−	18.2514i	−0.585054	−	0.649768i
$790$	−3.14581	+	2.28556i	−0.111923	+	0.0813166i
$791$	15.5677	+	6.93120i	0.553525	+	0.246445i
$792$	8.68790			0.308711
$793$	23.2380	+	13.5455i	0.825206	+	0.481014i
$794$	28.3819			1.00724
$795$	21.9389	+	9.76783i	0.778092	+	0.346429i
$796$	−12.4271	+	9.02880i	−0.440466	+	0.320017i
$797$	−19.2600	−	21.3904i	−0.682225	−	0.757687i	0.298217	−	0.954498i	$-0.403608\pi$
$797$	−19.2600	−	21.3904i	−0.682225	−	0.757687i	−0.980441	+	0.196811i	$0.936942\pi$
$798$	−24.3325	+	5.17202i	−0.861360	+	0.183088i
$799$	60.6301	−	12.8873i	2.14494	−	0.455921i
$800$	−1.19619	+	11.3810i	−0.0422916	+	0.402378i
$801$	2.48929	+	7.66126i	0.0879548	+	0.270697i
$802$	3.56034	−	10.9576i	0.125720	−	0.386927i
$803$	25.6174	+	5.44514i	0.904017	+	0.192155i
$804$	4.04132			0.142526
$805$	3.07536	+	0.653687i	0.108392	+	0.0230395i
$806$	16.2075	+	28.0722i	0.570884	+	0.988801i
$807$	−3.80976	+	6.59869i	−0.134110	+	0.232285i
$808$	−6.34145	+	7.04289i	−0.223091	+	0.247768i
$809$	4.14148	−	39.4035i	0.145607	−	1.38535i	−0.640829	−	0.767683i	$-0.721409\pi$
$809$	4.14148	−	39.4035i	0.145607	−	1.38535i	0.786436	−	0.617672i	$-0.211924\pi$
$810$	17.7738	+	19.7398i	0.624506	+	0.693584i
$811$	18.3137	−	20.3394i	0.643081	−	0.714213i	−0.330180	−	0.943918i	$-0.607109\pi$
$811$	18.3137	−	20.3394i	0.643081	−	0.714213i	0.973260	+	0.229705i	$0.0737761\pi$
$812$	−0.472837	−	4.49874i	−0.0165933	−	0.157875i
$813$	−37.3378	−	27.1275i	−1.30949	−	0.951402i
$814$	12.7655	+	22.1104i	0.447429	+	0.774970i
$815$	2.77741	+	1.23658i	0.0972885	+	0.0433156i
$816$	−23.1471	+	71.2396i	−0.810312	+	2.49388i
$817$	21.3792	+	15.5329i	0.747964	+	0.543427i
$818$	27.2665	−	12.1398i	0.953350	−	0.424459i
$819$	0.590327	+	5.61658i	0.0206277	+	0.196259i
$820$	2.82500	+	8.69446i	0.0986534	+	0.303624i
$821$	−5.86531	+	4.26140i	−0.204701	+	0.148724i	−0.685413	−	0.728155i	$-0.740378\pi$
$821$	−5.86531	+	4.26140i	−0.204701	+	0.148724i	0.480712	+	0.876879i	$0.340378\pi$
$822$	−24.0798	+	41.7074i	−0.839878	+	1.45471i
$823$	−47.2969	+	21.0579i	−1.64867	+	0.734033i	−0.999643	−	0.0267358i	$-0.991489\pi$
$823$	−47.2969	+	21.0579i	−1.64867	+	0.734033i	−0.649023	+	0.760769i	$0.724822\pi$
$824$	−24.2082	+	10.7782i	−0.843333	+	0.375476i
$825$	−9.23979	+	16.0038i	−0.321688	+	0.557180i
$826$	19.7557	−	14.3533i	0.687387	−	0.499416i
$827$	−2.75281	−	8.47228i	−0.0957246	−	0.294610i	0.891717	−	0.452593i	$-0.149501\pi$
$827$	−2.75281	−	8.47228i	−0.0957246	−	0.294610i	−0.987442	+	0.157983i	$0.949501\pi$
$828$	0.188192	+	1.79053i	0.00654012	+	0.0622251i
$829$	19.7872	−	8.80981i	0.687236	−	0.305977i	−0.0332494	−	0.999447i	$-0.510586\pi$
$829$	19.7872	−	8.80981i	0.687236	−	0.305977i	0.720486	+	0.693470i	$0.243919\pi$
$830$	3.72865	+	2.70902i	0.129423	+	0.0940315i
$831$	2.70900	−	8.33746i	0.0939743	−	0.289223i
$832$	10.7933	+	4.80548i	0.374190	+	0.166600i
$833$	20.2638	+	35.0980i	0.702101	+	1.21607i
$834$	58.9676	+	42.8424i	2.04188	+	1.48351i
$835$	−1.37072	−	13.0415i	−0.0474357	−	0.451320i
$836$	8.70397	−	9.66674i	0.301033	−	0.334331i
$837$	13.0224	+	14.4628i	0.450119	+	0.499908i
$838$	−4.85469	+	46.1893i	−0.167702	+	1.59558i
$839$	23.8292	−	26.4650i	0.822675	−	0.913673i	−0.174807	−	0.984603i	$-0.555930\pi$
$839$	23.8292	−	26.4650i	0.822675	−	0.913673i	0.997481	+	0.0709300i	$0.0225967\pi$
$840$	3.79340	−	6.57036i	0.130885	−	0.226699i
$841$	0.695545	+	1.20472i	0.0239843	+	0.0415420i
$842$	51.8837	+	11.0282i	1.78803	+	0.380057i
$843$	59.4484			2.04751
$844$	16.0793	+	3.41775i	0.553471	+	0.117644i
$845$	0.505046	−	1.55437i	0.0173741	−	0.0534720i
$846$	−5.93658	−	18.2709i	−0.204104	−	0.628167i
$847$	−0.247461	+	2.35443i	−0.00850284	+	0.0808992i
$848$	−38.5602	+	8.19623i	−1.32416	+	0.281460i
$849$	18.9550	−	4.02901i	0.650534	−	0.138275i
$850$	−23.6476	−	26.2633i	−0.811107	−	0.900825i
$851$	7.63159	−	5.54467i	0.261607	−	0.190069i
$852$	−5.29175	−	2.35604i	−0.181292	−	0.0807165i
$853$	40.1774			1.37565			0.687823	−	0.725878i	$-0.258566\pi$
$853$	40.1774			1.37565			0.687823	+	0.725878i	$0.258566\pi$
$854$	−0.0640659	+	15.4265i	−0.00219229	+	0.527883i
$855$	11.8296			0.404565
$856$	9.43797	+	4.20206i	0.322583	+	0.143623i
$857$	−38.5704	+	28.0230i	−1.31754	+	0.957249i	−0.317581	+	0.948231i	$0.602870\pi$
$857$	−38.5704	+	28.0230i	−1.31754	+	0.957249i	−0.999959	+	0.00901774i	$0.997130\pi$
$858$	−23.8572	−	26.4961i	−0.814471	−	0.904561i
$859$	−36.8929	+	7.84183i	−1.25877	+	0.267560i	−0.788540	−	0.614984i	$-0.789162\pi$
$859$	−36.8929	+	7.84183i	−1.25877	+	0.267560i	−0.470230	+	0.882544i	$0.655829\pi$
$860$	4.42156	−	0.939832i	0.150774	−	0.0320480i
$861$	−2.32145	+	22.0871i	−0.0791149	+	0.752728i
$862$	8.85346	+	27.2481i	0.301550	+	0.928075i
$863$	−11.9273	+	36.7084i	−0.406009	+	1.24957i	0.514041	+	0.857766i	$0.328148\pi$
$863$	−11.9273	+	36.7084i	−0.406009	+	1.24957i	−0.920050	+	0.391801i	$0.871852\pi$
$864$	−12.9664	−	2.75609i	−0.441125	−	0.0937639i
$865$	−17.2927			−0.587969
$866$	34.6764	+	7.37069i	1.17835	+	0.250466i
$867$	−37.6617	−	65.2321i	−1.27906	−	2.21540i
$868$	−2.45720	+	4.25599i	−0.0834027	+	0.144458i
$869$	3.30521	−	3.67081i	0.112122	−	0.124524i
$870$	−2.71473	+	25.8289i	−0.0920379	+	0.875682i
$871$	6.19973	+	6.88549i	0.210070	+	0.233306i
$872$	−0.0111684	+	0.0124038i	−0.000378211	+	0.000420046i
$873$	−0.798505	−	7.59727i	−0.0270253	−	0.257129i
$874$	−14.7091	−	10.6868i	−0.497542	−	0.361486i
$875$	6.82326	+	11.8182i	0.230668	+	0.399529i
$876$	11.9641	+	5.32675i	0.404228	+	0.179974i
$877$	7.34791	−	22.6145i	0.248121	−	0.763639i	−0.746986	−	0.664840i	$-0.768500\pi$
$877$	7.34791	−	22.6145i	0.248121	−	0.763639i	0.995107	−	0.0987991i	$-0.0315001\pi$
$878$	−44.1497	−	32.0766i	−1.48998	−	1.08253i
$879$	−20.9932	+	9.34676i	−0.708082	+	0.315259i
$880$	2.21600	+	21.0838i	0.0747014	+	0.710736i
$881$	−4.75213	−	14.6256i	−0.160103	−	0.492748i	0.838539	−	0.544842i	$-0.183410\pi$
$881$	−4.75213	−	14.6256i	−0.160103	−	0.492748i	−0.998642	+	0.0520944i	$0.983410\pi$
$882$	10.1620	−	7.38313i	0.342173	−	0.248603i
$883$	23.4125	−	40.5517i	0.787895	−	1.36467i	−0.139360	−	0.990242i	$-0.544505\pi$
$883$	23.4125	−	40.5517i	0.787895	−	1.36467i	0.927255	−	0.374432i	$-0.122162\pi$
$884$	16.4662	−	7.33120i	0.553817	−	0.246575i
$885$	−33.8570	+	15.0741i	−1.13809	+	0.506710i
$886$	−11.6785	+	20.2277i	−0.392346	+	0.679563i
$887$	0.598216	−	0.434630i	0.0200861	−	0.0145934i	−0.577697	−	0.816251i	$-0.696048\pi$
$887$	0.598216	−	0.434630i	0.0200861	−	0.0145934i	0.597783	+	0.801658i	$0.296048\pi$
$888$	−7.03407	−	21.6487i	−0.236048	−	0.726481i
$889$	−1.69195	−	16.0978i	−0.0567462	−	0.539904i
$890$	−12.7123	+	5.65987i	−0.426116	+	0.189719i
$891$	−27.2986	−	19.8336i	−0.914536	−	0.664449i
$892$	2.92401	−	8.99919i	0.0979032	−	0.301315i
$893$	46.8506	+	20.8592i	1.56780	+	0.698028i
$894$	8.76200	+	15.1762i	0.293045	+	0.507569i
$895$	−14.2997	−	10.3894i	−0.477987	−	0.347278i
$896$	1.68204	+	16.0035i	0.0561930	+	0.534640i
$897$	−8.81474	+	9.78977i	−0.294316	+	0.326871i
$898$	−3.69785	−	4.10688i	−0.123399	−	0.137048i
$899$	−3.13529	+	29.8303i	−0.104568	+	0.994895i
$900$	−1.93743	+	2.15174i	−0.0645811	+	0.0717246i
$901$	29.1711	−	50.5258i	0.971830	−	1.68326i
$902$	−21.9660	−	38.0462i	−0.731388	−	1.26680i
$903$	10.7415	+	2.28317i	0.357454	+	0.0759793i
$904$	30.0545			0.999596
$905$	15.9217	+	3.38427i	0.529256	+	0.112497i
$906$	−5.56176	+	17.1173i	−0.184777	+	0.568686i
$907$	0.633663	+	1.95021i	0.0210404	+	0.0647558i	0.961025	−	0.276460i	$-0.0891613\pi$
$907$	0.633663	+	1.95021i	0.0210404	+	0.0647558i	−0.939985	+	0.341216i	$0.889161\pi$
$908$	−0.139619	+	1.32838i	−0.00463341	+	0.0440840i
$909$	−6.00649	+	1.27672i	−0.199223	+	0.0423461i
$910$	−9.54249	+	2.02832i	−0.316330	+	0.0672381i
$911$	−16.7541	−	18.6073i	−0.555088	−	0.616487i	0.398659	−	0.917099i	$-0.369476\pi$
$911$	−16.7541	−	18.6073i	−0.555088	−	0.616487i	−0.953747	+	0.300612i	$0.902809\pi$
$912$	−50.1388	+	36.4280i	−1.66026	+	1.20625i
$913$	−5.34857	−	2.38134i	−0.177012	−	0.0788108i
$914$	61.9450			2.04896
$915$	4.96287	−	22.8808i	0.164067	−	0.756416i
$916$	−18.9170			−0.625036
$917$	7.52079	+	3.34847i	0.248358	+	0.110576i
$918$	33.1195	−	24.0627i	1.09311	−	0.794188i
$919$	−26.5136	−	29.4463i	−0.874601	−	0.971343i	0.125183	−	0.992134i	$-0.460048\pi$
$919$	−26.5136	−	29.4463i	−0.874601	−	0.971343i	−0.999784	+	0.0207906i	$0.993382\pi$
$920$	5.42387	−	1.15288i	0.178820	−	0.0380093i
$921$	−52.1875	+	11.0928i	−1.71964	+	0.365520i
$922$	−1.15913	+	11.0284i	−0.0381739	+	0.363201i
$923$	−4.10383	−	12.6303i	−0.135079	−	0.415731i
$924$	1.67038	−	5.14090i	0.0549515	−	0.169123i
$925$	14.8392	+	3.15418i	0.487911	+	0.103709i
$926$	−23.6095			−0.775857
$927$	−16.7948	−	3.56985i	−0.551615	−	0.117249i
$928$	−10.2152	−	17.6933i	−0.335331	−	0.580810i
$929$	7.28884	−	12.6246i	0.239139	−	0.414201i	−0.721328	−	0.692593i	$-0.756468\pi$
$929$	7.28884	−	12.6246i	0.239139	−	0.414201i	0.960468	+	0.278392i	$0.0898015\pi$
$930$	18.8797	−	20.9681i	0.619091	−	0.687570i
$931$	−3.50500	+	33.3478i	−0.114872	+	1.09293i
$932$	5.25726	+	5.83877i	0.172207	+	0.191255i
$933$	5.46736	−	6.07211i	0.178993	−	0.198792i
$934$	5.15751	+	49.0704i	0.168759	+	1.60563i
$935$	−25.3829	−	18.4417i	−0.830108	−	0.603109i
$936$	4.98014	+	8.62586i	0.162781	+	0.281945i
$937$	−20.1482	−	8.97055i	−0.658213	−	0.293055i	0.0503201	−	0.998733i	$-0.483976\pi$
$937$	−20.1482	−	8.97055i	−0.658213	−	0.293055i	−0.708533	+	0.705678i	$0.750643\pi$
$938$	−1.64210	+	5.05386i	−0.0536164	+	0.165014i
$939$	15.1254	+	10.9893i	0.493600	+	0.358621i
$940$	8.01406	−	3.56809i	0.261390	−	0.116378i
$941$	−0.583472	−	5.55137i	−0.0190206	−	0.180969i	0.980887	−	0.194580i	$-0.0623343\pi$
$941$	−0.583472	−	5.55137i	−0.0190206	−	0.180969i	−0.999907	+	0.0136103i	$0.995668\pi$
$942$	−7.32818	−	22.5538i	−0.238765	−	0.734843i
$943$	−13.1320	+	9.54092i	−0.427635	+	0.310695i
$944$	30.4186	−	52.6865i	0.990040	−	1.71480i
$945$	−5.35082	+	2.38234i	−0.174062	+	0.0774975i
$946$	−19.8448	+	8.83546i	−0.645209	+	0.287266i
$947$	24.8202	−	42.9899i	0.806549	−	1.39698i	−0.108692	−	0.994075i	$-0.534666\pi$
$947$	24.8202	−	42.9899i	0.806549	−	1.39698i	0.915241	−	0.402908i	$-0.132000\pi$
$948$	1.99832	−	1.45186i	0.0649023	−	0.0471543i
$949$	9.27832	+	28.5557i	0.301187	+	0.926958i
$950$	−3.05642	−	29.0799i	−0.0991632	−	0.943475i
$951$	−57.6420	+	25.6639i	−1.86917	+	0.832207i
$952$	−14.9113	−	10.8337i	−0.483277	−	0.351121i
$953$	−8.69025	+	26.7459i	−0.281505	+	0.866383i	0.705920	+	0.708292i	$0.250534\pi$
$953$	−8.69025	+	26.7459i	−0.281505	+	0.866383i	−0.987425	+	0.158091i	$0.949466\pi$
$954$	−16.5190	−	7.35472i	−0.534822	−	0.238118i
$955$	3.31368	+	5.73946i	0.107228	+	0.185725i
$956$	8.32813	+	6.05074i	0.269351	+	0.195695i
$957$	−3.44858	−	32.8110i	−0.111477	−	1.06063i
$958$	−15.3630	+	17.0624i	−0.496357	+	0.551260i
$959$	−11.2010	−	12.4399i	−0.361698	−	0.401707i
$960$	1.07497	−	10.2277i	0.0346946	−	0.330097i
$961$	1.06150	−	1.17892i	0.0342420	−	0.0380296i
$962$	−14.6350	+	25.3486i	−0.471852	+	0.817272i
$963$	3.34701	+	5.79720i	0.107856	+	0.186812i
$964$	−6.09439	−	1.29540i	−0.196287	−	0.0417221i
$965$	−10.0916			−0.324860
$966$	−7.39024	−	1.57084i	−0.237777	−	0.0505411i
$967$	9.39402	−	28.9118i	0.302091	−	0.929742i	−0.678655	−	0.734457i	$-0.737437\pi$
$967$	9.39402	−	28.9118i	0.302091	−	0.929742i	0.980747	−	0.195285i	$-0.0625631\pi$
$968$	1.29023	+	3.97092i	0.0414696	+	0.127630i
$969$	9.58735	−	91.2175i	0.307990	−	2.93033i
$970$	12.9076	−	2.74360i	0.414440	−	0.0880918i
$971$	−0.184021	+	0.0391150i	−0.00590553	+	0.00125526i	−0.210864	−	0.977516i	$-0.567628\pi$
$971$	−0.184021	+	0.0391150i	−0.00590553	+	0.00125526i	0.204958	+	0.978771i	$0.434294\pi$
$972$	−6.37213	−	7.07697i	−0.204386	−	0.226994i
$973$	−20.4963	+	14.8914i	−0.657082	+	0.477398i
$974$	−62.9579	−	28.0307i	−2.01730	−	0.898161i
$975$	−21.1860			−0.678495
$976$	15.4862	+	35.1750i	0.495701	+	1.12592i
$977$	30.0141			0.960236			0.480118	−	0.877204i	$-0.340594\pi$
$977$	30.0141			0.960236			0.480118	+	0.877204i	$0.340594\pi$
$978$	−6.67426	−	2.97157i	−0.213419	−	0.0950205i
$979$	14.3009	−	10.3902i	0.457060	−	0.332073i
$980$	3.83797	+	4.26250i	0.122599	+	0.136160i
$981$	−0.0105785	+	0.00224853i	−0.000337746	+	7.17901e-5i
$982$	−17.9687	+	3.81936i	−0.573403	+	0.121881i
$983$	3.74751	−	35.6552i	0.119527	−	1.13722i	−0.756175	−	0.654370i	$-0.772934\pi$
$983$	3.74751	−	35.6552i	0.119527	−	1.13722i	0.875702	−	0.482853i	$-0.160399\pi$
$984$	12.1038	+	37.2516i	0.385855	+	1.18754i
$985$	−9.84613	+	30.3033i	−0.313724	+	0.965542i
$986$	61.7155	+	13.1180i	1.96542	+	0.417763i
$987$	21.3114			0.678348
$988$	14.5871	+	3.10057i	0.464076	+	0.0986424i
$989$	4.01307	+	6.95084i	0.127608	+	0.221024i
$990$	−4.86209	+	8.42139i	−0.154527	+	0.267649i
$991$	7.17386	−	7.96738i	0.227885	−	0.253092i	−0.618349	−	0.785904i	$-0.712198\pi$
$991$	7.17386	−	7.96738i	0.227885	−	0.253092i	0.846234	+	0.532812i	$0.178865\pi$
$992$	−2.32009	+	22.0742i	−0.0736631	+	0.700857i
$993$	25.2575	+	28.0513i	0.801522	+	0.890180i
$994$	5.09652	−	5.66025i	0.161652	−	0.179532i
$995$	3.20423	+	30.4862i	0.101581	+	0.966478i
$996$	−2.36856	−	1.72086i	−0.0750506	−	0.0545274i
$997$	−18.8770	−	32.6960i	−0.597841	−	1.03549i	−0.993139	−	0.116939i	$-0.962692\pi$
$997$	−18.8770	−	32.6960i	−0.597841	−	1.03549i	0.395298	−	0.918553i	$-0.370641\pi$
$998$	11.7725	+	5.24146i	0.372653	+	0.165916i
$999$	−5.43049	+	16.7133i	−0.171813	+	0.528786i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	61.2.i.a.12.4	✓	32
3.2	odd	2		549.2.bl.b.73.1		32
4.3	odd	2		976.2.bw.c.561.3		32
61.19	even	30		3721.2.a.l.1.3		16
61.42	even	15		3721.2.a.j.1.14		16
61.56	even	15	inner	61.2.i.a.56.4	yes	32
183.56	odd	30		549.2.bl.b.361.1		32
244.239	odd	30		976.2.bw.c.849.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.i.a.12.4	✓	32	1.1	even	1	trivial
61.2.i.a.56.4	yes	32	61.56	even	15	inner
549.2.bl.b.73.1		32	3.2	odd	2
549.2.bl.b.361.1		32	183.56	odd	30
976.2.bw.c.561.3		32	4.3	odd	2
976.2.bw.c.849.3		32	244.239	odd	30
3721.2.a.j.1.14		16	61.42	even	15
3721.2.a.l.1.3		16	61.19	even	30

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:	\( N \)	\(=\)	\( 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	61.i (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50629 + 0.670642i) q^{2} +(-1.69101 + 1.22859i) q^{3} +(0.480878 + 0.534070i) q^{4} +(1.40283 - 0.298182i) q^{5} +(-3.37108 + 0.716546i) q^{6} +(0.125217 - 1.19136i) q^{7} +(-0.652866 - 2.00931i) q^{8} +(0.423022 - 1.30193i) q^{9} +O(q^{10})\)	\(q+(1.50629 + 0.670642i) q^{2} +(-1.69101 + 1.22859i) q^{3} +(0.480878 + 0.534070i) q^{4} +(1.40283 - 0.298182i) q^{5} +(-3.37108 + 0.716546i) q^{6} +(0.125217 - 1.19136i) q^{7} +(-0.652866 - 2.00931i) q^{8} +(0.423022 - 1.30193i) q^{9} +(2.31304 + 0.491653i) q^{10} -3.00395 q^{11} +(-1.46932 - 0.312313i) q^{12} +(-1.72195 - 2.98250i) q^{13} +(0.987587 - 1.71055i) q^{14} +(-2.00586 + 2.22773i) q^{15} +(0.514369 - 4.89389i) q^{16} +(4.87302 + 5.41204i) q^{17} +(1.51032 - 1.67738i) q^{18} +(0.629830 + 5.99243i) q^{19} +(0.833842 + 0.605822i) q^{20} +(1.25194 + 2.16843i) q^{21} +(-4.52482 - 2.01458i) q^{22} +(-0.565515 + 1.74048i) q^{23} +(3.57262 + 2.59566i) q^{24} +(-2.68870 + 1.19708i) q^{25} +(-0.593557 - 5.64731i) q^{26} +(-1.05352 - 3.24240i) q^{27} +(0.696482 - 0.506024i) q^{28} +(2.62721 - 4.55046i) q^{29} +(-4.51541 + 2.01039i) q^{30} +(-5.21493 + 2.32184i) q^{31} +(1.94412 - 3.36731i) q^{32} +(5.07970 - 3.69062i) q^{33} +(3.71063 + 11.4201i) q^{34} +(-0.179583 - 1.70861i) q^{35} +(0.898741 - 0.400145i) q^{36} +(-4.17017 - 3.02980i) q^{37} +(-3.07007 + 9.44872i) q^{38} +(6.57609 + 2.92786i) q^{39} +(-1.51500 - 2.62406i) q^{40} +(7.17576 + 5.21349i) q^{41} +(0.431546 + 4.10589i) q^{42} +(2.93465 - 3.25925i) q^{43} +(-1.44454 - 1.60432i) q^{44} +(0.205219 - 1.95252i) q^{45} +(-2.01906 + 2.24240i) q^{46} +(4.25565 - 7.37101i) q^{47} +(5.14277 + 8.90754i) q^{48} +(5.44338 + 1.15703i) q^{49} -4.85276 q^{50} +(-14.8895 - 3.16486i) q^{51} +(0.764816 - 2.35386i) q^{52} +(-2.47558 - 7.61906i) q^{53} +(0.587588 - 5.59053i) q^{54} +(-4.21405 + 0.895724i) q^{55} +(-2.47556 + 0.526197i) q^{56} +(-8.42728 - 9.35944i) q^{57} +(7.00906 - 5.09238i) q^{58} +(11.2943 + 5.02854i) q^{59} -2.15434 q^{60} +(-6.78003 + 3.87700i) q^{61} -9.41230 q^{62} +(-1.49809 - 0.666993i) q^{63} +(-2.77544 + 2.01647i) q^{64} +(-3.30493 - 3.67050i) q^{65} +(10.1266 - 2.15247i) q^{66} +(-2.63158 + 0.559359i) q^{67} +(-0.547075 + 5.20507i) q^{68} +(-1.18204 - 3.63794i) q^{69} +(0.875366 - 2.69410i) q^{70} +(3.77191 + 0.801745i) q^{71} -2.89216 q^{72} +(-8.52788 - 1.81266i) q^{73} +(-4.24955 - 7.36044i) q^{74} +(3.07588 - 5.32757i) q^{75} +(-2.89751 + 3.21801i) q^{76} +(-0.376145 + 3.57878i) q^{77} +(7.94193 + 8.82040i) q^{78} +(-1.10029 + 1.22199i) q^{79} +(-0.737695 - 7.01869i) q^{80} +(9.08754 + 6.60249i) q^{81} +(7.31236 + 12.6654i) q^{82} +(1.78051 + 0.792734i) q^{83} +(-0.556060 + 1.71138i) q^{84} +(8.44982 + 6.13915i) q^{85} +(6.60621 - 2.94128i) q^{86} +(1.14801 + 10.9226i) q^{87} +(1.96118 + 6.03589i) q^{88} +(-4.76070 + 3.45885i) q^{89} +(1.61856 - 2.80343i) q^{90} +(-3.76884 + 1.67800i) q^{91} +(-1.20148 + 0.534933i) q^{92} +(5.96589 - 10.3332i) q^{93} +(11.3535 - 8.24883i) q^{94} +(2.67038 + 8.21859i) q^{95} +(0.849523 + 8.08267i) q^{96} +(5.09792 - 2.26974i) q^{97} +(7.42334 + 5.39337i) q^{98} +(-1.27074 + 3.91093i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 10 q^{2} - 4 q^{3} - 10 q^{4} + 2 q^{5} + q^{6} + q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) 32 * q - 10 * q^2 - 4 * q^3 - 10 * q^4 + 2 * q^5 + q^6 + q^7 - 4 * q^8 - 2 * q^9	\( 32 q - 10 q^{2} - 4 q^{3} - 10 q^{4} + 2 q^{5} + q^{6} + q^{7} - 4 q^{8} - 2 q^{9} + 15 q^{10} - 18 q^{11} - 53 q^{12} + 11 q^{14} + 2 q^{15} + 6 q^{16} - 24 q^{17} - 15 q^{18} + 9 q^{19} - 4 q^{20} - 3 q^{21} + q^{22} - 2 q^{23} + 15 q^{24} + 28 q^{25} + 16 q^{26} + 35 q^{27} + 4 q^{28} - 4 q^{29} + 54 q^{30} - 11 q^{31} + 34 q^{32} - 35 q^{33} + 18 q^{34} - 58 q^{35} + 65 q^{36} - 14 q^{37} - 24 q^{38} + 17 q^{39} - 60 q^{40} + 11 q^{41} + 73 q^{42} + 40 q^{43} + 29 q^{44} + 12 q^{45} - 89 q^{46} + 40 q^{47} + 43 q^{48} + q^{49} - 56 q^{50} - 9 q^{51} - 67 q^{52} + 17 q^{53} - q^{54} - 60 q^{55} - 102 q^{56} - 38 q^{57} + 73 q^{58} - 11 q^{59} - 20 q^{60} - 55 q^{61} - 74 q^{62} - 58 q^{63} + 6 q^{64} + 59 q^{65} + 34 q^{66} - 13 q^{67} - 3 q^{68} - 32 q^{69} + 44 q^{70} + 63 q^{71} + 18 q^{72} - 46 q^{73} - 10 q^{74} + q^{75} + 55 q^{76} - 31 q^{77} - 103 q^{78} - 49 q^{79} + 74 q^{80} + 48 q^{81} + 39 q^{82} + 39 q^{83} + 21 q^{85} + 74 q^{86} + 17 q^{87} + 70 q^{88} + 32 q^{89} - 60 q^{90} + 70 q^{91} + 77 q^{92} + 67 q^{93} - 64 q^{94} + 47 q^{95} - 16 q^{96} + 37 q^{97} + 127 q^{98} - 31 q^{99}+O(q^{100}) \) 32 * q - 10 * q^2 - 4 * q^3 - 10 * q^4 + 2 * q^5 + q^6 + q^7 - 4 * q^8 - 2 * q^9 + 15 * q^10 - 18 * q^11 - 53 * q^12 + 11 * q^14 + 2 * q^15 + 6 * q^16 - 24 * q^17 - 15 * q^18 + 9 * q^19 - 4 * q^20 - 3 * q^21 + q^22 - 2 * q^23 + 15 * q^24 + 28 * q^25 + 16 * q^26 + 35 * q^27 + 4 * q^28 - 4 * q^29 + 54 * q^30 - 11 * q^31 + 34 * q^32 - 35 * q^33 + 18 * q^34 - 58 * q^35 + 65 * q^36 - 14 * q^37 - 24 * q^38 + 17 * q^39 - 60 * q^40 + 11 * q^41 + 73 * q^42 + 40 * q^43 + 29 * q^44 + 12 * q^45 - 89 * q^46 + 40 * q^47 + 43 * q^48 + q^49 - 56 * q^50 - 9 * q^51 - 67 * q^52 + 17 * q^53 - q^54 - 60 * q^55 - 102 * q^56 - 38 * q^57 + 73 * q^58 - 11 * q^59 - 20 * q^60 - 55 * q^61 - 74 * q^62 - 58 * q^63 + 6 * q^64 + 59 * q^65 + 34 * q^66 - 13 * q^67 - 3 * q^68 - 32 * q^69 + 44 * q^70 + 63 * q^71 + 18 * q^72 - 46 * q^73 - 10 * q^74 + q^75 + 55 * q^76 - 31 * q^77 - 103 * q^78 - 49 * q^79 + 74 * q^80 + 48 * q^81 + 39 * q^82 + 39 * q^83 + 21 * q^85 + 74 * q^86 + 17 * q^87 + 70 * q^88 + 32 * q^89 - 60 * q^90 + 70 * q^91 + 77 * q^92 + 67 * q^93 - 64 * q^94 + 47 * q^95 - 16 * q^96 + 37 * q^97 + 127 * q^98 - 31 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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