LMFDB - Embedded newform 585.2.bt.b.571.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(376,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 3]))

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

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

chi := DirichletCharacter("585.376");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bt (of order $6$, degree $2$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			571.18
Character	$\chi$	$=$	585.571
Dual form			585.2.bt.b.376.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07284 + 0.619404i) q^{2} +(-1.48219 - 0.896168i) q^{3} +(-0.232678 + 0.403011i) q^{4} +(0.866025 + 0.500000i) q^{5} +(2.14524 + 0.0433707i) q^{6} +(0.166629 - 0.0962033i) q^{7} -3.05410i q^{8} +(1.39377 + 2.65658i) q^{9} +O(q^{10})$	\(q+(-1.07284 + 0.619404i) q^{2} +(-1.48219 - 0.896168i) q^{3} +(-0.232678 + 0.403011i) q^{4} +(0.866025 + 0.500000i) q^{5} +(2.14524 + 0.0433707i) q^{6} +(0.166629 - 0.0962033i) q^{7} -3.05410i q^{8} +(1.39377 + 2.65658i) q^{9} -1.23881 q^{10} +(0.223697 - 0.129152i) q^{11} +(0.706038 - 0.388819i) q^{12} +(-3.45476 - 1.03180i) q^{13} +(-0.119177 + 0.206421i) q^{14} +(-0.835529 - 1.51720i) q^{15} +(1.42637 + 2.47054i) q^{16} +3.42590 q^{17} +(-3.14078 - 1.98678i) q^{18} -2.08354i q^{19} +(-0.403011 + 0.232678i) q^{20} +(-0.333190 - 0.00673617i) q^{21} +(-0.159994 + 0.277118i) q^{22} +(0.614267 - 1.06394i) q^{23} +(-2.73699 + 4.52675i) q^{24} +(0.500000 + 0.866025i) q^{25} +(4.34550 - 1.03294i) q^{26} +(0.314919 - 5.18660i) q^{27} +0.0895377i q^{28} +(4.55796 + 7.89462i) q^{29} +(1.83615 + 1.11018i) q^{30} +(-2.13714 - 1.23388i) q^{31} +(2.22934 + 1.28711i) q^{32} +(-0.447303 - 0.00904322i) q^{33} +(-3.67544 + 2.12202i) q^{34} +0.192407 q^{35} +(-1.39493 - 0.0564262i) q^{36} -1.41990i q^{37} +(1.29055 + 2.23531i) q^{38} +(4.19594 + 4.62537i) q^{39} +(1.52705 - 2.64493i) q^{40} +(9.38294 + 5.41724i) q^{41} +(0.361632 - 0.199152i) q^{42} +(5.21080 + 9.02537i) q^{43} +0.120203i q^{44} +(-0.121254 + 2.99755i) q^{45} +1.52192i q^{46} +(-2.32341 + 1.34142i) q^{47} +(0.0998742 - 4.94006i) q^{48} +(-3.48149 + 6.03012i) q^{49} +(-1.07284 - 0.619404i) q^{50} +(-5.07784 - 3.07019i) q^{51} +(1.21967 - 1.15223i) q^{52} +9.93408 q^{53} +(2.87474 + 5.75945i) q^{54} +0.258303 q^{55} +(-0.293815 - 0.508902i) q^{56} +(-1.86721 + 3.08821i) q^{57} +(-9.77991 - 5.64643i) q^{58} +(10.3335 + 5.96605i) q^{59} +(0.805857 + 0.0162922i) q^{60} +(2.57942 + 4.46768i) q^{61} +3.05707 q^{62} +(0.487814 + 0.308579i) q^{63} -8.89442 q^{64} +(-2.47601 - 2.62095i) q^{65} +(0.485486 - 0.267359i) q^{66} +(8.23135 + 4.75237i) q^{67} +(-0.797133 + 1.38068i) q^{68} +(-1.86393 + 1.02648i) q^{69} +(-0.206421 + 0.119177i) q^{70} -6.11596i q^{71} +(8.11347 - 4.25670i) q^{72} -10.7486i q^{73} +(0.879489 + 1.52332i) q^{74} +(0.0350101 - 1.73170i) q^{75} +(0.839690 + 0.484795i) q^{76} +(0.0248496 - 0.0430409i) q^{77} +(-7.36654 - 2.36329i) q^{78} +(-2.92403 - 5.06458i) q^{79} +2.85273i q^{80} +(-5.11484 + 7.40530i) q^{81} -13.4218 q^{82} +(-3.67679 + 2.12279i) q^{83} +(0.0802408 - 0.132712i) q^{84} +(2.96692 + 1.71295i) q^{85} +(-11.1807 - 6.45518i) q^{86} +(0.319149 - 15.7860i) q^{87} +(-0.394442 - 0.683194i) q^{88} +2.03536i q^{89} +(-1.72661 - 3.29099i) q^{90} +(-0.674927 + 0.160432i) q^{91} +(0.285853 + 0.495112i) q^{92} +(2.06188 + 3.74407i) q^{93} +(1.66176 - 2.87826i) q^{94} +(1.04177 - 1.80440i) q^{95} +(-2.15084 - 3.90560i) q^{96} +(-5.71691 + 3.30066i) q^{97} -8.62579i q^{98} +(0.654883 + 0.414263i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

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 $

$2$	−1.07284	+	0.619404i	−0.758611	+	0.437985i	−0.828797	−	0.559549i	$-0.810974\pi$
$2$	−1.07284	+	0.619404i	−0.758611	+	0.437985i	0.0701855	+	0.997534i	$0.477641\pi$
$3$	−1.48219	−	0.896168i	−0.855742	−	0.517403i
$3$	−1.48219	−	0.896168i	−0.855742	−	0.517403i
$4$	−0.232678	+	0.403011i	−0.116339	+	0.201505i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	2.14524	+	0.0433707i	0.875790	+	0.0177060i
$7$	0.166629	−	0.0962033i	0.0629799	−	0.0363614i	−0.468179	−	0.883633i	$-0.655090\pi$
$7$	0.166629	−	0.0962033i	0.0629799	−	0.0363614i	0.531159	+	0.847272i	$0.321757\pi$
$8$		−	3.05410i		−	1.07979i
$9$	1.39377	+	2.65658i	0.464589	+	0.885527i
$10$	−1.23881			−0.391745
$11$	0.223697	−	0.129152i	0.0674473	−	0.0389407i	−0.465897	−	0.884839i	$-0.654268\pi$
$11$	0.223697	−	0.129152i	0.0674473	−	0.0389407i	0.533344	+	0.845898i	$0.320935\pi$
$12$	0.706038	−	0.388819i	0.203816	−	0.112242i
$13$	−3.45476	−	1.03180i	−0.958179	−	0.286170i
$13$	−3.45476	−	1.03180i	−0.958179	−	0.286170i
$14$	−0.119177	+	0.206421i	−0.0318515	+	0.0551684i
$15$	−0.835529	−	1.51720i	−0.215733	−	0.391739i
$16$	1.42637	+	2.47054i	0.356591	+	0.617634i
$17$	3.42590			0.830904			0.415452	−	0.909615i	$-0.363623\pi$
$17$	3.42590			0.830904			0.415452	+	0.909615i	$0.363623\pi$
$18$	−3.14078	−	1.98678i	−0.740289	−	0.468288i
$19$		−	2.08354i		−	0.477998i	−0.971020	−	0.238999i	$-0.923181\pi$
$19$		−	2.08354i		−	0.477998i	0.971020	−	0.238999i	$-0.0768192\pi$
$20$	−0.403011	+	0.232678i	−0.0901159	+	0.0520284i
$21$	−0.333190	−	0.00673617i	−0.0727080	−	0.00146995i
$22$	−0.159994	+	0.277118i	−0.0341108	+	0.0590817i
$23$	0.614267	−	1.06394i	0.128083	−	0.221847i	−0.794851	−	0.606805i	$-0.792451\pi$
$23$	0.614267	−	1.06394i	0.128083	−	0.221847i	0.922934	+	0.384958i	$0.125784\pi$
$24$	−2.73699	+	4.52675i	−0.558685	+	0.924020i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	4.34550	−	1.03294i	0.852223	−	0.202576i
$27$	0.314919	−	5.18660i	0.0606062	−	0.998162i
$28$			0.0895377i			0.0169210i
$29$	4.55796	+	7.89462i	0.846392	+	1.46599i	0.884407	+	0.466717i	$0.154563\pi$
$29$	4.55796	+	7.89462i	0.846392	+	1.46599i	−0.0380149	+	0.999277i	$0.512103\pi$
$30$	1.83615	+	1.11018i	0.335233	+	0.202690i
$31$	−2.13714	−	1.23388i	−0.383841	−	0.221611i	0.295647	−	0.955297i	$-0.404465\pi$
$31$	−2.13714	−	1.23388i	−0.383841	−	0.221611i	−0.679488	+	0.733686i	$0.737798\pi$
$32$	2.22934	+	1.28711i	0.394095	+	0.227531i
$33$	−0.447303	−	0.00904322i	−0.0778655	−	0.00157422i
$34$	−3.67544	+	2.12202i	−0.630333	+	0.363923i
$35$	0.192407			0.0325227
$36$	−1.39493	−	0.0564262i	−0.232488	−	0.00940436i
$37$		−	1.41990i		−	0.233430i	−0.993165	−	0.116715i	$-0.962764\pi$
$37$		−	1.41990i		−	0.233430i	0.993165	−	0.116715i	$-0.0372363\pi$
$38$	1.29055	+	2.23531i	0.209356	+	0.362615i
$39$	4.19594	+	4.62537i	0.671889	+	0.740652i
$40$	1.52705	−	2.64493i	0.241448	−	0.418200i
$41$	9.38294	+	5.41724i	1.46537	+	0.846031i	0.999251	−	0.0386914i	$-0.0123189\pi$
$41$	9.38294	+	5.41724i	1.46537	+	0.846031i	0.466118	+	0.884723i	$0.345652\pi$
$42$	0.361632	−	0.199152i	0.0558010	−	0.0307299i
$43$	5.21080	+	9.02537i	0.794640	+	1.37636i	0.923068	+	0.384637i	$0.125674\pi$
$43$	5.21080	+	9.02537i	0.794640	+	1.37636i	−0.128428	+	0.991719i	$0.540993\pi$
$44$			0.120203i			0.0181213i
$45$	−0.121254	+	2.99755i	−0.0180754	+	0.446848i
$46$			1.52192i			0.224394i
$47$	−2.32341	+	1.34142i	−0.338905	+	0.195667i	−0.659788	−	0.751452i	$-0.729354\pi$
$47$	−2.32341	+	1.34142i	−0.338905	+	0.195667i	0.320883	+	0.947119i	$0.396020\pi$
$48$	0.0998742	−	4.94006i	0.0144156	−	0.713037i
$49$	−3.48149	+	6.03012i	−0.497356	+	0.861445i
$50$	−1.07284	−	0.619404i	−0.151722	−	0.0875969i
$51$	−5.07784	−	3.07019i	−0.711039	−	0.429912i
$52$	1.21967	−	1.15223i	0.169138	−	0.159785i
$53$	9.93408			1.36455			0.682276	−	0.731095i	$-0.260990\pi$
$53$	9.93408			1.36455			0.682276	+	0.731095i	$0.260990\pi$
$54$	2.87474	+	5.75945i	0.391203	+	0.783761i
$55$	0.258303			0.0348296
$56$	−0.293815	−	0.508902i	−0.0392627	−	0.0680049i
$57$	−1.86721	+	3.08821i	−0.247317	+	0.409043i
$58$	−9.77991	−	5.64643i	−1.28417	−	0.741413i
$59$	10.3335	+	5.96605i	1.34531	+	0.776714i	0.987581	−	0.157112i	$-0.0502184\pi$
$59$	10.3335	+	5.96605i	1.34531	+	0.776714i	0.357727	+	0.933826i	$0.383552\pi$
$60$	0.805857	+	0.0162922i	0.104036	+	0.00210331i
$61$	2.57942	+	4.46768i	0.330261	+	0.572028i	0.982563	−	0.185931i	$-0.0595300\pi$
$61$	2.57942	+	4.46768i	0.330261	+	0.572028i	−0.652302	+	0.757959i	$0.726197\pi$
$62$	3.05707			0.388249
$63$	0.487814	+	0.308579i	0.0614588	+	0.0388772i
$64$	−8.89442			−1.11180
$65$	−2.47601	−	2.62095i	−0.307112	−	0.325088i
$66$	0.485486	−	0.267359i	0.0597591	−	0.0329097i
$67$	8.23135	+	4.75237i	1.00562	+	0.580595i	0.909906	−	0.414814i	$-0.136153\pi$
$67$	8.23135	+	4.75237i	1.00562	+	0.580595i	0.0957136	+	0.995409i	$0.469487\pi$
$68$	−0.797133	+	1.38068i	−0.0966666	+	0.167432i
$69$	−1.86393	+	1.02648i	−0.224391	+	0.123573i
$70$	−0.206421	+	0.119177i	−0.0246721	+	0.0142444i
$71$		−	6.11596i		−	0.725831i	−0.931822	−	0.362916i	$-0.881781\pi$
$71$		−	6.11596i		−	0.725831i	0.931822	−	0.362916i	$-0.118219\pi$
$72$	8.11347	−	4.25670i	0.956181	−	0.501657i
$73$		−	10.7486i		−	1.25803i	−0.777394	−	0.629015i	$-0.783459\pi$
$73$		−	10.7486i		−	1.25803i	0.777394	−	0.629015i	$-0.216541\pi$
$74$	0.879489	+	1.52332i	0.102239	+	0.177082i
$75$	0.0350101	−	1.73170i	0.00404261	−	0.199959i
$76$	0.839690	+	0.484795i	0.0963191	+	0.0556098i
$77$	0.0248496	−	0.0430409i	0.00283188	−	0.00490496i
$78$	−7.36654	−	2.36329i	−0.834097	−	0.267590i
$79$	−2.92403	−	5.06458i	−0.328980	−	0.569809i	0.653330	−	0.757073i	$-0.273371\pi$
$79$	−2.92403	−	5.06458i	−0.328980	−	0.569809i	−0.982310	+	0.187264i	$0.940038\pi$
$80$			2.85273i			0.318945i
$81$	−5.11484	+	7.40530i	−0.568315	+	0.822811i
$82$	−13.4218			−1.48219
$83$	−3.67679	+	2.12279i	−0.403580	+	0.233007i	−0.688027	−	0.725685i	$-0.741523\pi$
$83$	−3.67679	+	2.12279i	−0.403580	+	0.233007i	0.284448	+	0.958692i	$0.408190\pi$
$84$	0.0802408	−	0.132712i	0.00875499	−	0.0144800i
$85$	2.96692	+	1.71295i	0.321808	+	0.185796i
$86$	−11.1807	−	6.45518i	−1.20565	−	0.696080i
$87$	0.319149	−	15.7860i	0.0342164	−	1.69244i
$88$	−0.394442	−	0.683194i	−0.0420477	−	0.0728288i
$89$			2.03536i			0.215748i	0.994165	+	0.107874i	$0.0344043\pi$
$89$			2.03536i			0.215748i	−0.994165	+	0.107874i	$0.965596\pi$
$90$	−1.72661	−	3.29099i	−0.182000	−	0.346901i
$91$	−0.674927	+	0.160432i	−0.0707515	+	0.0168178i
$92$	0.285853	+	0.495112i	0.0298022	+	0.0516190i
$93$	2.06188	+	3.74407i	0.213807	+	0.388242i
$94$	1.66176	−	2.87826i	0.171398	−	0.296870i
$95$	1.04177	−	1.80440i	0.106884	−	0.185128i
$96$	−2.15084	−	3.90560i	−0.219519	−	0.398614i
$97$	−5.71691	+	3.30066i	−0.580464	+	0.335131i	−0.761318	−	0.648379i	$-0.775447\pi$
$97$	−5.71691	+	3.30066i	−0.580464	+	0.335131i	0.180854	+	0.983510i	$0.442114\pi$
$98$		−	8.62579i		−	0.871336i
$99$	0.654883	+	0.414263i	0.0658183	+	0.0416350i
$100$	−0.465357			−0.0465357
$101$	−5.02374	−	8.70137i	−0.499880	−	0.865818i	0.500120	−	0.865956i	$-0.333289\pi$
$101$	−5.02374	−	8.70137i	−0.499880	−	0.865818i	−1.00000		0.000138125i	$0.999956\pi$
$102$	7.34938	+	0.148584i	0.727697	+	0.0147120i
$103$	2.27731	−	3.94442i	0.224390	−	0.388656i	−0.731746	−	0.681578i	$-0.761294\pi$
$103$	2.27731	−	3.94442i	0.224390	−	0.388656i	0.956136	+	0.292922i	$0.0946276\pi$
$104$	−3.15122	+	10.5512i	−0.309003	+	1.03463i
$105$	−0.285183	−	0.172429i	−0.0278310	−	0.0168273i
$106$	−10.6577	+	6.15321i	−1.03516	+	0.597652i
$107$	9.06498			0.876345			0.438172	−	0.898891i	$-0.355626\pi$
$107$	9.06498			0.876345			0.438172	+	0.898891i	$0.355626\pi$
$108$	2.01698	+	1.33372i	0.194084	+	0.128338i
$109$			6.52955i			0.625417i	0.949849	+	0.312709i	$0.101236\pi$
$109$			6.52955i			0.625417i	−0.949849	+	0.312709i	$0.898764\pi$
$110$	−0.277118	+	0.159994i	−0.0264221	+	0.0152548i
$111$	−1.27247	+	2.10455i	−0.120777	+	0.199755i
$112$	0.475348	+	0.274442i	0.0449161	+	0.0259323i
$113$	1.27975	−	2.21659i	0.120389	−	0.208519i	−0.799532	−	0.600623i	$-0.794919\pi$
$113$	1.27975	−	2.21659i	0.120389	−	0.208519i	0.919921	+	0.392104i	$0.128253\pi$
$114$	0.0903648	−	4.46970i	0.00846344	−	0.418626i
$115$	1.06394	−	0.614267i	0.0992130	−	0.0572807i
$116$	−4.24215			−0.393874
$117$	−2.07407	−	10.6159i	−0.191748	−	0.981444i
$118$	−14.7816			−1.36075
$119$	0.570855	−	0.329583i	0.0523302	−	0.0302129i
$120$	−4.63368	+	2.55179i	−0.422995	+	0.232945i
$121$	−5.46664	+	9.46850i	−0.496967	+	0.860773i
$122$	−5.53460	−	3.19540i	−0.501079	−	0.289298i
$123$	−9.05253	−	16.4381i	−0.816239	−	1.48217i
$124$	0.994531	−	0.574193i	0.0893115	−	0.0515640i
$125$			1.00000i			0.0894427i
$126$	−0.714480	−	0.0289014i	−0.0636509	−	0.00257474i
$127$	−15.5870			−1.38312			−0.691560	−	0.722319i	$-0.743076\pi$
$127$	−15.5870			−1.38312			−0.691560	+	0.722319i	$0.743076\pi$
$128$	5.08360	−	2.93502i	0.449331	−	0.259421i
$129$	0.364861	−	18.0471i	0.0321242	−	1.58895i
$130$	4.27979	+	1.27820i	0.375362	+	0.112106i
$131$	9.15493	−	15.8568i	0.799870	−	1.38542i	−0.119830	−	0.992794i	$-0.538235\pi$
$131$	9.15493	−	15.8568i	0.799870	−	1.38542i	0.919700	−	0.392621i	$-0.128432\pi$
$132$	0.107722	−	0.178164i	0.00937602	−	0.0155072i
$133$	−0.200444	−	0.347179i	−0.0173807	−	0.0301042i
$134$	−11.7746			−1.01717
$135$	2.86603	−	4.33427i	0.246668	−	0.373034i
$136$		−	10.4631i		−	0.897200i
$137$	−10.5610	+	6.09742i	−0.902290	+	0.520937i	−0.877942	−	0.478766i	$-0.841084\pi$
$137$	−10.5610	+	6.09742i	−0.902290	+	0.520937i	−0.0243476	+	0.999704i	$0.507751\pi$
$138$	1.36389	−	2.25577i	0.116102	−	0.192024i
$139$	−1.78193	+	3.08639i	−0.151141	+	0.261784i	−0.931647	−	0.363364i	$-0.881628\pi$
$139$	−1.78193	+	3.08639i	−0.151141	+	0.261784i	0.780506	+	0.625148i	$0.214961\pi$
$140$	−0.0447689	+	0.0775419i	−0.00378366	+	0.00655349i
$141$	4.64588	+	0.0939266i	0.391253	+	0.00791005i
$142$	3.78825	+	6.56144i	0.317903	+	0.550624i
$143$	−0.906080	+	0.215377i	−0.0757702	+	0.0180108i
$144$	−4.57516	+	7.23260i	−0.381263	+	0.602717i
$145$			9.11592i			0.757036i
$146$	6.65772	+	11.5315i	0.550997	+	0.954355i
$147$	10.5642	−	5.81777i	0.871322	−	0.479842i
$148$	0.572233	+	0.330379i	0.0470373	+	0.0271570i
$149$	2.12719	+	1.22814i	0.174267	+	0.100613i	0.584596	−	0.811324i	$-0.301253\pi$
$149$	2.12719	+	1.22814i	0.174267	+	0.100613i	−0.410330	+	0.911937i	$0.634586\pi$
$150$	1.03506	+	1.87952i	0.0845122	+	0.153462i
$151$	14.9072	−	8.60666i	1.21313	−	0.700400i	0.249689	−	0.968326i	$-0.419672\pi$
$151$	14.9072	−	8.60666i	1.21313	−	0.700400i	0.963439	+	0.267926i	$0.0863384\pi$
$152$	−6.36336			−0.516136
$153$	4.77491	+	9.10119i	0.386028	+	0.735787i
$154$			0.0615678i			0.00496128i
$155$	−1.23388	−	2.13714i	−0.0991074	−	0.171659i
$156$	−2.84038	+	0.614786i	−0.227412	+	0.0492223i
$157$	5.35683	−	9.27831i	0.427522	−	0.740489i	−0.569130	−	0.822247i	$-0.692720\pi$
$157$	5.35683	−	9.27831i	0.427522	−	0.740489i	0.996652	+	0.0817578i	$0.0260534\pi$
$158$	6.27403	+	3.62231i	0.499135	+	0.288176i
$159$	−14.7242	−	8.90261i	−1.16770	−	0.706023i
$160$	1.28711	+	2.22934i	0.101755	+	0.176245i
$161$		−	0.236378i		−	0.0186292i
$162$	0.900523	−	11.1128i	0.0707517	−	0.873107i
$163$		−	3.83591i		−	0.300451i	−0.988652	−	0.150226i	$-0.952000\pi$
$163$		−	3.83591i		−	0.300451i	0.988652	−	0.150226i	$-0.0480000\pi$
$164$	−4.36641	+	2.52095i	−0.340960	+	0.196853i
$165$	−0.382854	−	0.231483i	−0.0298052	−	0.0180209i
$166$	2.62973	−	4.55483i	0.204107	−	0.353523i
$167$	−11.2747	−	6.50944i	−0.872461	−	0.503716i	−0.00429595	−	0.999991i	$-0.501367\pi$
$167$	−11.2747	−	6.50944i	−0.872461	−	0.503716i	−0.868165	+	0.496275i	$0.834701\pi$
$168$	−0.0205729	+	1.01760i	−0.00158724	+	0.0785093i
$169$	10.8708	+	7.12925i	0.836213	+	0.548404i
$170$	−4.24403			−0.325503
$171$	5.53510	−	2.90397i	0.423280	−	0.222072i
$172$	−4.84976			−0.369791
$173$	5.83561	+	10.1076i	0.443673	+	0.768464i	0.997959	−	0.0638622i	$-0.0203418\pi$
$173$	5.83561	+	10.1076i	0.443673	+	0.768464i	−0.554286	+	0.832327i	$0.687008\pi$
$174$	9.43552	+	17.1335i	0.715305	+	1.29889i
$175$	0.166629	+	0.0962033i	0.0125960	+	0.00727229i
$176$	0.638148	+	0.368435i	0.0481022	+	0.0277718i
$177$	−9.96962	−	18.1034i	−0.749363	−	1.36073i
$178$	−1.26071	−	2.18362i	−0.0944943	−	0.163669i
$179$	21.1296			1.57930			0.789650	−	0.613558i	$-0.210262\pi$
$179$	21.1296			1.57930			0.789650	+	0.613558i	$0.210262\pi$
$180$	−1.17983	−	0.746331i	−0.0879394	−	0.0556282i
$181$	20.7303			1.54087			0.770436	−	0.637518i	$-0.220039\pi$
$181$	20.7303			1.54087			0.770436	+	0.637518i	$0.220039\pi$
$182$	0.624715	−	0.590169i	0.0463070	−	0.0437463i
$183$	0.180611	−	8.93354i	0.0133512	−	0.660386i
$184$	−3.24939	−	1.87603i	−0.239548	−	0.138303i
$185$	0.709948	−	1.22967i	0.0521964	−	0.0904069i
$186$	−4.53116	−	2.73965i	−0.332241	−	0.200881i
$187$	0.766365	−	0.442461i	0.0560422	−	0.0323560i
$188$		−	1.24848i		−	0.0910548i
$189$	−0.446494	−	0.894535i	−0.0324776	−	0.0650678i
$190$			2.58111i			0.187253i
$191$	−9.90652	−	17.1586i	−0.716811	−	1.24155i	−0.962257	−	0.272143i	$-0.912268\pi$
$191$	−9.90652	−	17.1586i	−0.716811	−	1.24155i	0.245446	−	0.969410i	$-0.421066\pi$
$192$	13.1832	+	7.97090i	0.951416	+	0.575250i
$193$	10.3519	+	5.97666i	0.745145	+	0.430210i	0.823937	−	0.566681i	$-0.191773\pi$
$193$	10.3519	+	5.97666i	0.745145	+	0.430210i	−0.0787920	+	0.996891i	$0.525106\pi$
$194$	4.08888	−	7.08215i	0.293565	−	0.508469i
$195$	1.32111	+	6.10366i	0.0946065	+	0.437092i
$196$	−1.62013	−	2.80615i	−0.115724	−	0.200440i
$197$			12.5008i			0.890642i	0.895371	+	0.445321i	$0.146910\pi$
$197$			12.5008i			0.890642i	−0.895371	+	0.445321i	$0.853090\pi$
$198$	−0.959180	−	0.0387997i	−0.0681659	−	0.00275738i
$199$	2.23373			0.158345			0.0791724	−	0.996861i	$-0.474772\pi$
$199$	2.23373			0.158345			0.0791724	+	0.996861i	$0.474772\pi$
$200$	2.64493	−	1.52705i	0.187025	−	0.107979i
$201$	−7.94149	−	14.4206i	−0.560150	−	1.01715i
$202$	10.7793	+	6.22344i	0.758430	+	0.437880i
$203$	1.51898	+	0.876982i	0.106611	+	0.0615521i
$204$	2.41882	−	1.33206i	0.169351	−	0.0932626i
$205$	5.41724	+	9.38294i	0.378357	+	0.655333i
$206$			5.64231i			0.393118i
$207$	3.68259	+	0.148964i	0.255958	+	0.0103537i
$208$	−2.37865	−	10.0068i	−0.164930	−	0.693850i
$209$	−0.269093	−	0.466083i	−0.0186136	−	0.0322396i
$210$	0.412758	+	0.00834481i	0.0284830	+	0.000575847i
$211$	6.01185	−	10.4128i	0.413872	−	0.716848i	−0.581437	−	0.813592i	$-0.697509\pi$
$211$	6.01185	−	10.4128i	0.413872	−	0.716848i	0.995309	+	0.0967433i	$0.0308426\pi$
$212$	−2.31145	+	4.00354i	−0.158751	+	0.274964i
$213$	−5.48093	+	9.06501i	−0.375547	+	0.621124i
$214$	−9.72526	+	5.61488i	−0.664805	+	0.383825i
$215$			10.4216i			0.710747i
$216$	−15.8404	−	0.961794i	−1.07780	−	0.0654418i
$217$	−0.474812			−0.0322324
$218$	−4.04443	−	7.00515i	−0.273923	−	0.474449i
$219$	−9.63256	+	15.9315i	−0.650908	+	1.07655i
$220$	−0.0601016	+	0.104099i	−0.00405205	+	0.00701835i
$221$	−11.8357	−	3.53485i	−0.796154	−	0.237780i
$222$	0.0615819	−	3.04602i	0.00413311	−	0.204435i
$223$	2.63097	−	1.51899i	0.176182	−	0.101719i	−0.409315	−	0.912393i	$-0.634232\pi$
$223$	2.63097	−	1.51899i	0.176182	−	0.101719i	0.585498	+	0.810674i	$0.300899\pi$
$224$	0.495297			0.0330934
$225$	−1.60378	+	2.53533i	−0.106919	+	0.169022i
$226$			3.17073i			0.210914i
$227$	−24.6458	+	14.2292i	−1.63580	+	0.944428i	−0.653539	+	0.756893i	$0.726717\pi$
$227$	−24.6458	+	14.2292i	−1.63580	+	0.944428i	−0.982258	+	0.187535i	$0.939950\pi$
$228$	−0.810121	−	1.47106i	−0.0536516	−	0.0974235i
$229$	−9.65151	−	5.57230i	−0.637790	−	0.368228i	0.145973	−	0.989289i	$-0.453369\pi$
$229$	−9.65151	−	5.57230i	−0.637790	−	0.368228i	−0.783763	+	0.621061i	$0.786702\pi$
$230$	−0.760958	+	1.31802i	−0.0501761	+	0.0869076i
$231$	−0.0754037	+	0.0415252i	−0.00496120	+	0.00273216i
$232$	24.1110	−	13.9205i	1.58296	−	0.913924i
$233$	−14.0822			−0.922558			−0.461279	−	0.887255i	$-0.652609\pi$
$233$	−14.0822			−0.922558			−0.461279	+	0.887255i	$0.652609\pi$
$234$	8.80069	+	10.1045i	0.575319	+	0.660552i
$235$	−2.68285			−0.175010
$236$	−4.80877	+	2.77634i	−0.313024	+	0.180724i
$237$	−0.204741	+	10.1271i	−0.0132994	+	0.657825i
$238$	−0.408290	+	0.707180i	−0.0264655	+	0.0458396i
$239$	10.1934	+	5.88514i	0.659354	+	0.380678i	0.792031	−	0.610481i	$-0.209024\pi$
$239$	10.1934	+	5.88514i	0.659354	+	0.380678i	−0.132677	+	0.991159i	$0.542357\pi$
$240$	2.55653	−	4.22828i	0.165023	−	0.272935i
$241$	−15.4519	+	8.92116i	−0.995345	+	0.574663i	−0.906868	−	0.421416i	$-0.861533\pi$
$241$	−15.4519	+	8.92116i	−0.995345	+	0.574663i	−0.0884771	+	0.996078i	$0.528200\pi$
$242$		−	13.5442i		−	0.870656i
$243$	14.2175	−	6.39230i	0.912056	−	0.410066i
$244$	−2.40070			−0.153689
$245$	−6.03012	+	3.48149i	−0.385250	+	0.222424i
$246$	19.8937	+	12.0282i	1.26838	+	0.766892i
$247$	−2.14980	+	7.19815i	−0.136789	+	0.458007i
$248$	−3.76839	+	6.52704i	−0.239293	+	0.414467i
$249$	7.35207	+	0.148638i	0.465919	+	0.00941957i
$250$	−0.619404	−	1.07284i	−0.0391745	−	0.0678523i
$251$	−9.05817			−0.571747			−0.285873	−	0.958267i	$-0.592284\pi$
$251$	−9.05817			−0.571747			−0.285873	+	0.958267i	$0.592284\pi$
$252$	−0.237864	+	0.124795i	−0.0149840	+	0.00786132i
$253$		−	0.317334i		−	0.0199506i
$254$	16.7223	−	9.65463i	1.04925	−	0.605785i
$255$	−2.86244	−	5.19778i	−0.179253	−	0.325497i
$256$	5.25850	−	9.10799i	0.328656	−	0.569250i
$257$	−2.37807	+	4.11893i	−0.148340	+	0.256932i	−0.930614	−	0.366002i	$-0.880726\pi$
$257$	−2.37807	+	4.11893i	−0.148340	+	0.256932i	0.782274	+	0.622934i	$0.214060\pi$
$258$	10.7870	+	19.5876i	0.671568	+	1.21947i
$259$	−0.136599	−	0.236596i	−0.00848783	−	0.0147014i
$260$	1.63238	−	0.388022i	0.101236	−	0.0240641i
$261$	−14.6200	+	23.1118i	−0.904953	+	1.43059i
$262$			22.6824i			1.40132i
$263$	−3.39788	−	5.88530i	−0.209522	−	0.362903i	0.742042	−	0.670353i	$-0.233857\pi$
$263$	−3.39788	−	5.88530i	−0.209522	−	0.362903i	−0.951564	+	0.307451i	$0.900524\pi$
$264$	−0.0276189	+	1.36611i	−0.00169983	+	0.0840782i
$265$	8.60317	+	4.96704i	0.528488	+	0.305123i
$266$	0.430088	+	0.248311i	0.0263704	+	0.0152249i
$267$	1.82403	−	3.01679i	0.111629	−	0.184625i
$268$	−3.83051	+	2.21155i	−0.233986	+	0.135092i
$269$	−1.94607			−0.118654			−0.0593269	−	0.998239i	$-0.518895\pi$
$269$	−1.94607			−0.118654			−0.0593269	+	0.998239i	$0.518895\pi$
$270$	−0.390124	+	6.42520i	−0.0237422	+	0.391025i
$271$			7.64114i			0.464166i	0.972696	+	0.232083i	$0.0745541\pi$
$271$			7.64114i			0.464166i	−0.972696	+	0.232083i	$0.925446\pi$
$272$	4.88659	+	8.46382i	0.296293	+	0.513195i
$273$	1.14414	+	0.367058i	0.0692466	+	0.0222153i
$274$	7.55352	−	13.0831i	0.456325	−	0.790378i
$275$	0.223697	+	0.129152i	0.0134895	+	0.00778814i
$276$	0.0200155	−	0.990022i	0.00120479	−	0.0595923i
$277$	5.21970	+	9.04078i	0.313621	+	0.543208i	0.979143	−	0.203170i	$-0.0651244\pi$
$277$	5.21970	+	9.04078i	0.313621	+	0.543208i	−0.665522	+	0.746378i	$0.731791\pi$
$278$		−	4.41493i		−	0.264790i
$279$	0.299224	−	7.39721i	0.0179141	−	0.442860i
$280$		−	0.587630i		−	0.0351176i
$281$	25.6455	−	14.8064i	1.52988	−	0.883277i	0.530515	−	0.847675i	$-0.321998\pi$
$281$	25.6455	−	14.8064i	1.52988	−	0.883277i	0.999366	−	0.0356022i	$-0.0113349\pi$
$282$	−5.04245	+	2.77690i	−0.300274	+	0.165362i
$283$	8.75840	−	15.1700i	0.520633	−	0.901763i	−0.479079	−	0.877772i	$-0.659029\pi$
$283$	8.75840	−	15.1700i	0.520633	−	0.901763i	0.999712	−	0.0239910i	$-0.00763730\pi$
$284$	2.46480	+	1.42305i	0.146259	+	0.0844426i
$285$	−3.16115	+	1.74086i	−0.187250	+	0.103120i
$286$	0.838672	−	0.792294i	0.0495917	−	0.0468494i
$287$	2.08463			0.123052
$288$	−0.312134	+	7.71635i	−0.0183926	+	0.454690i
$289$	−5.26318			−0.309599
$290$	−5.64643	−	9.77991i	−0.331570	−	0.574296i
$291$	11.4315	+	0.231113i	0.670126	+	0.0135481i
$292$	4.33180	+	2.50097i	0.253500	+	0.146358i
$293$	2.21632	+	1.27959i	0.129479	+	0.0747547i	0.563340	−	0.826225i	$-0.309516\pi$
$293$	2.21632	+	1.27959i	0.129479	+	0.0747547i	−0.433862	+	0.900980i	$0.642849\pi$
$294$	−7.73016	+	12.7850i	−0.450832	+	0.745639i
$295$	5.96605	+	10.3335i	0.347357	+	0.601640i
$296$	−4.33651			−0.252054
$297$	−0.599412	−	1.20090i	−0.0347814	−	0.0696833i
$298$	−3.04285			−0.176267
$299$	−3.21992	+	3.04186i	−0.186213	+	0.175916i
$300$	0.689746	+	0.417038i	0.0398225	+	0.0240777i
$301$	1.73654	+	1.00259i	0.100093	+	0.0577885i
$302$	−10.6620	+	18.4671i	−0.613529	+	1.06266i
$303$	−0.351763	+	17.3992i	−0.0202082	+	0.999556i
$304$	5.14747	−	2.97189i	0.295228	−	0.170450i
$305$			5.15884i			0.295394i
$306$	−10.7600	−	6.80651i	−0.615109	−	0.389102i
$307$			16.0587i			0.916516i	0.888819	+	0.458258i	$0.151526\pi$
$307$			16.0587i			0.916516i	−0.888819	+	0.458258i	$0.848474\pi$
$308$	0.0115639	+	0.0200293i	0.000658917	+	0.00114128i
$309$	−6.91028	+	3.80552i	−0.393112	+	0.216489i
$310$	2.64750	+	1.52854i	0.150368	+	0.0868150i
$311$	0.0930698	−	0.161202i	0.00527750	−	0.00914090i	−0.863375	−	0.504563i	$-0.831653\pi$
$311$	0.0930698	−	0.161202i	0.00527750	−	0.00914090i	0.868652	+	0.495423i	$0.164987\pi$
$312$	14.1264	−	12.8148i	0.799747	−	0.725497i
$313$	3.29622	+	5.70923i	0.186314	+	0.322705i	0.944018	−	0.329893i	$-0.107013\pi$
$313$	3.29622	+	5.70923i	0.186314	+	0.322705i	−0.757705	+	0.652598i	$0.773679\pi$
$314$			13.2722i			0.748992i
$315$	0.268170	+	0.511144i	0.0151097	+	0.0287997i
$316$	2.72144			0.153093
$317$	−19.8122	+	11.4386i	−1.11276	+	0.642453i	−0.939543	−	0.342430i	$-0.888750\pi$
$317$	−19.8122	+	11.4386i	−1.11276	+	0.642453i	−0.173218	+	0.984883i	$0.555417\pi$
$318$	21.3110	+	0.430848i	1.19506	+	0.0241608i
$319$	2.03921	+	1.17734i	0.114174	+	0.0659182i
$320$	−7.70280	−	4.44721i	−0.430599	−	0.248607i
$321$	−13.4360	−	8.12375i	−0.749925	−	0.453423i
$322$	0.146413	+	0.253596i	0.00815930	+	0.0141323i
$323$		−	7.13802i		−	0.397170i
$324$	−1.79430	−	3.78439i	−0.0996835	−	0.210244i
$325$	−0.833816	−	3.50781i	−0.0462518	−	0.194578i
$326$	2.37597	+	4.11531i	0.131593	+	0.227926i
$327$	5.85157	−	9.67802i	0.323593	−	0.535196i
$328$	16.5448	−	28.6565i	0.913534	−	1.58229i
$329$	−0.258099	+	0.447040i	−0.0142294	+	0.0246461i
$330$	0.554122	+	0.0112028i	0.0305034	+	0.000616694i
$331$	−11.8684	+	6.85224i	−0.652348	+	0.376633i	−0.789355	−	0.613937i	$-0.789585\pi$
$331$	−11.8684	+	6.85224i	−0.652348	+	0.376633i	0.137007	+	0.990570i	$0.456252\pi$
$332$		−	1.97571i		−	0.108431i
$333$	3.77207	−	1.97900i	0.206708	−	0.108449i
$334$	16.1279			0.882479
$335$	4.75237	+	8.23135i	0.259650	+	0.449727i
$336$	−0.458609	−	0.832767i	−0.0250192	−	0.0454311i
$337$	−12.0442	+	20.8612i	−0.656090	+	1.13638i	0.325529	+	0.945532i	$0.394458\pi$
$337$	−12.0442	+	20.8612i	−0.656090	+	1.13638i	−0.981619	+	0.190850i	$0.938876\pi$
$338$	−16.0785	−	0.915142i	−0.874554	−	0.0497772i
$339$	−3.88327	+	2.13854i	−0.210910	+	0.116149i
$340$	−1.38068	+	0.797133i	−0.0748776	+	0.0432306i
$341$	−0.637429			−0.0345187
$342$	−4.13954	+	6.54396i	−0.223841	+	0.353857i
$343$			2.68657i			0.145061i
$344$	27.5644	−	15.9143i	1.48617	−	0.858042i
$345$	−2.12745	−	0.0430110i	−0.114538	−	0.00231564i
$346$	−12.5213	−	7.22919i	−0.673151	−	0.388644i
$347$	2.60803	−	4.51725i	0.140007	−	0.242499i	−0.787492	−	0.616325i	$-0.788621\pi$
$347$	2.60803	−	4.51725i	0.140007	−	0.242499i	0.927499	+	0.373826i	$0.121954\pi$
$348$	6.28767	+	3.80168i	0.337055	+	0.203792i
$349$	−13.5744	+	7.83721i	−0.726623	+	0.419516i	−0.817186	−	0.576375i	$-0.804467\pi$
$349$	−13.5744	+	7.83721i	−0.726623	+	0.419516i	0.0905623	+	0.995891i	$0.471134\pi$
$350$	−0.238355			−0.0127406
$351$	−6.43951	+	17.5935i	−0.343716	+	0.939074i
$352$	0.664930			0.0354409
$353$	10.7905	−	6.22989i	0.574319	−	0.331583i	−0.184553	−	0.982822i	$-0.559084\pi$
$353$	10.7905	−	6.22989i	0.574319	−	0.331583i	0.758873	+	0.651239i	$0.225751\pi$
$354$	21.9091	+	13.2468i	1.16446	+	0.704058i
$355$	3.05798	−	5.29658i	0.162301	−	0.281113i
$356$	−0.820273	−	0.473585i	−0.0434744	−	0.0250999i
$357$	−1.14148	−	0.0230775i	−0.0604134	−	0.00122139i
$358$	−22.6686	+	13.0877i	−1.19807	+	0.691709i
$359$		−	23.7595i		−	1.25398i	−0.779027	−	0.626990i	$-0.784287\pi$
$359$		−	23.7595i		−	1.25398i	0.779027	−	0.626990i	$-0.215713\pi$
$360$	9.15482	+	0.370321i	0.482501	+	0.0195176i
$361$	14.6588			0.771518
$362$	−22.2403	+	12.8404i	−1.16892	+	0.674878i
$363$	16.5880	−	9.13507i	0.870642	−	0.479467i
$364$	0.0923851	−	0.309332i	0.00484229	−	0.0162134i
$365$	5.37430	−	9.30856i	0.281304	−	0.487233i
$366$	5.33970	+	9.69612i	0.279111	+	0.506824i
$367$	−5.68566	−	9.84785i	−0.296789	−	0.514053i	0.678611	−	0.734498i	$-0.262582\pi$
$367$	−5.68566	−	9.84785i	−0.296789	−	0.514053i	−0.975399	+	0.220445i	$0.929249\pi$
$368$	3.50468			0.182694
$369$	−1.31372	+	32.4769i	−0.0683896	+	1.69068i
$370$			1.75898i			0.0914449i
$371$	1.65531	−	0.955692i	0.0859392	−	0.0496170i
$372$	−1.98866	−	0.0402050i	−0.103107	−	0.00208453i
$373$	4.09047	−	7.08489i	0.211796	−	0.366842i	−0.740480	−	0.672078i	$-0.765402\pi$
$373$	4.09047	−	7.08489i	0.211796	−	0.366842i	0.952277	+	0.305236i	$0.0987353\pi$
$374$	−0.548124	+	0.949379i	−0.0283428	+	0.0490912i
$375$	0.896168	−	1.48219i	0.0462779	−	0.0765399i
$376$	4.09684	+	7.09594i	0.211279	+	0.365945i
$377$	−7.60100	−	31.9769i	−0.391471	−	1.64690i
$378$	1.03309	+	0.683132i	0.0531366	+	0.0351365i
$379$		−	13.6581i		−	0.701569i	−0.936456	−	0.350784i	$-0.885915\pi$
$379$		−	13.6581i		−	0.701569i	0.936456	−	0.350784i	$-0.114085\pi$
$380$	0.484795	+	0.839690i	0.0248695	+	0.0430752i
$381$	23.1028	+	13.9686i	1.18359	+	0.715631i
$382$	21.2562	+	12.2723i	1.08756	+	0.627904i
$383$	16.7336	+	9.66116i	0.855048	+	0.493662i	0.862351	−	0.506311i	$-0.168991\pi$
$383$	16.7336	+	9.66116i	0.855048	+	0.493662i	−0.00730285	+	0.999973i	$0.502325\pi$
$384$	−10.1651	−	0.205510i	−0.518737	−	0.0104874i
$385$	0.0430409	−	0.0248496i	0.00219356	−	0.00126646i
$386$	−14.8079			−0.753701
$387$	−16.7140	+	26.4222i	−0.849620	+	1.34311i
$388$		−	3.07197i		−	0.155956i
$389$	−8.80214	−	15.2457i	−0.446286	−	0.772990i	0.551855	−	0.833940i	$-0.313920\pi$
$389$	−8.80214	−	15.2457i	−0.446286	−	0.772990i	−0.998141	+	0.0609502i	$0.980587\pi$
$390$	−5.19796	−	5.72994i	−0.263209	−	0.290147i
$391$	2.10442	−	3.64496i	0.106425	−	0.184334i
$392$	18.4166	+	10.6328i	0.930178	+	0.537039i
$393$	−27.7797	+	15.2984i	−1.40130	+	0.771703i
$394$	−7.74301	−	13.4113i	−0.390087	−	0.675651i
$395$		−	5.84807i		−	0.294248i
$396$	−0.319329	+	0.167535i	−0.0160469	+	0.00841895i
$397$		−	33.0627i		−	1.65937i	−0.558232	−	0.829685i	$-0.688520\pi$
$397$		−	33.0627i		−	1.65937i	0.558232	−	0.829685i	$-0.311480\pi$
$398$	−2.39643	+	1.38358i	−0.120122	+	0.0693526i
$399$	−0.0140351	+	0.694216i	−0.000702634	+	0.0347543i
$400$	−1.42637	+	2.47054i	−0.0713183	+	0.123527i
$401$	−8.36675	−	4.83054i	−0.417815	−	0.241226i	0.276327	−	0.961064i	$-0.410883\pi$
$401$	−8.36675	−	4.83054i	−0.417815	−	0.241226i	−0.694142	+	0.719838i	$0.744216\pi$
$402$	17.4521	+	10.5520i	0.870432	+	0.526285i
$403$	6.11019	+	6.46785i	0.304370	+	0.322187i
$404$	4.67566			0.232623
$405$	−8.13223	+	3.85576i	−0.404094	+	0.191594i
$406$	−2.17282			−0.107835
$407$	−0.183382	−	0.317627i	−0.00908991	−	0.0157442i
$408$	−9.37666	+	15.5082i	−0.464214	+	0.767772i
$409$	−31.3082	−	18.0758i	−1.54809	−	0.893792i	−0.998287	−	0.0584992i	$-0.981368\pi$
$409$	−31.3082	−	18.0758i	−1.54809	−	0.893792i	−0.549806	−	0.835293i	$-0.685298\pi$
$410$	−11.6237	−	6.71092i	−0.574051	−	0.331429i
$411$	21.1178	+	0.426942i	1.04166	+	0.0210595i
$412$	1.05976	+	1.83556i	0.0522108	+	0.0904317i
$413$	2.29582			0.112970
$414$	−4.04309	+	2.12119i	−0.198707	+	0.104251i
$415$	−4.24559			−0.208408
$416$	−6.37380	−	6.74690i	−0.312501	−	0.330794i
$417$	5.40708	−	2.97771i	0.264786	−	0.145819i
$418$	0.577387	+	0.333355i	0.0282409	+	0.0163049i
$419$	6.59316	−	11.4197i	0.322097	−	0.557889i	−0.658823	−	0.752298i	$-0.728946\pi$
$419$	6.59316	−	11.4197i	0.322097	−	0.557889i	0.980921	+	0.194409i	$0.0622789\pi$
$420$	0.135846	−	0.0748113i	0.00662863	−	0.00365042i
$421$	31.1530	−	17.9862i	1.51830	−	0.876592i	0.518534	−	0.855057i	$-0.326478\pi$
$421$	31.1530	−	17.9862i	1.51830	−	0.876592i	0.999768	−	0.0215354i	$-0.00685548\pi$
$422$			14.8950i			0.725079i
$423$	−6.80189	−	4.30270i	−0.330719	−	0.209205i
$424$		−	30.3397i		−	1.47343i
$425$	1.71295	+	2.96692i	0.0830904	+	0.143917i
$426$	0.265254	−	13.1202i	0.0128516	−	0.635676i
$427$	0.859612	+	0.496297i	0.0415995	+	0.0240175i
$428$	−2.10922	+	3.65328i	−0.101953	+	0.176588i
$429$	1.53600	+	0.492770i	0.0741586	+	0.0237912i
$430$	−6.45518	−	11.1807i	−0.311296	−	0.539181i
$431$			33.9269i			1.63420i	0.576495	+	0.817100i	$0.304420\pi$
$431$			33.9269i			1.63420i	−0.576495	+	0.817100i	$0.695580\pi$
$432$	13.2629	−	6.61997i	0.638110	−	0.318503i
$433$	16.2821			0.782469			0.391234	−	0.920291i	$-0.372048\pi$
$433$	16.2821			0.782469			0.391234	+	0.920291i	$0.372048\pi$
$434$	0.509397	−	0.294101i	0.0244518	−	0.0141173i
$435$	8.16940	−	13.5115i	0.391693	−	0.647827i
$436$	−2.63148	−	1.51928i	−0.126025	−	0.0727605i
$437$	−2.21677	−	1.27985i	−0.106042	−	0.0612236i
$438$	0.466175	−	23.0583i	0.0222747	−	1.10177i
$439$	−12.3570	−	21.4029i	−0.589767	−	1.02151i	−0.994263	−	0.106966i	$-0.965886\pi$
$439$	−12.3570	−	21.4029i	−0.589767	−	1.02151i	0.404496	−	0.914540i	$-0.367447\pi$
$440$		−	0.788885i		−	0.0376086i
$441$	−20.8719	−	0.844286i	−0.993899	−	0.0402041i
$442$	14.8873	−	3.53874i	0.708116	−	0.168321i
$443$	8.34105	+	14.4471i	0.396295	+	0.686404i	0.993266	−	0.115860i	$-0.0369623\pi$
$443$	8.34105	+	14.4471i	0.396295	+	0.686404i	−0.596970	+	0.802263i	$0.703629\pi$
$444$	−0.552082	−	1.00250i	−0.0262007	−	0.0475766i
$445$	−1.01768	+	1.76268i	−0.0482427	+	0.0835588i
$446$	−1.88173	+	3.25926i	−0.0891027	+	0.154330i
$447$	−2.05229	−	3.72665i	−0.0970698	−	0.176265i
$448$	−1.48207	+	0.855673i	−0.0700212	+	0.0404268i
$449$		−	18.0631i		−	0.852450i	−0.904617	−	0.426225i	$-0.859843\pi$
$449$		−	18.0631i		−	0.852450i	0.904617	−	0.426225i	$-0.140157\pi$
$450$	0.150210	−	3.71338i	0.00708096	−	0.175051i
$451$	2.79858			0.131780
$452$	0.595540	+	1.03151i	0.0280118	+	0.0485179i
$453$	−29.8082	−	0.602639i	−1.40051	−	0.0283145i
$454$	17.6273	−	30.5314i	0.827290	−	1.43291i
$455$	−0.664719	−	0.198525i	−0.0311625	−	0.00930701i
$456$	9.43169	+	5.70264i	0.441679	+	0.267050i
$457$	−22.4351	+	12.9529i	−1.04947	+	0.605913i	−0.922501	−	0.385994i	$-0.873859\pi$
$457$	−22.4351	+	12.9529i	−1.04947	+	0.605913i	−0.126971	+	0.991906i	$0.540525\pi$
$458$	13.8060			0.645113
$459$	1.07888	−	17.7688i	0.0503579	−	0.829376i
$460$			0.571706i			0.0266559i
$461$	35.3545	−	20.4120i	1.64663	−	0.950680i	0.668226	−	0.743959i	$-0.267054\pi$
$461$	35.3545	−	20.4120i	1.64663	−	0.950680i	0.978400	−	0.206721i	$-0.0662792\pi$
$462$	0.0551751	−	0.0912552i	0.00256698	−	0.00424557i
$463$	−11.7259	−	6.76996i	−0.544950	−	0.314627i	0.202133	−	0.979358i	$-0.435213\pi$
$463$	−11.7259	−	6.76996i	−0.544950	−	0.314627i	−0.747083	+	0.664731i	$0.768546\pi$
$464$	−13.0026	+	22.5212i	−0.603632	+	1.04552i
$465$	−0.0863962	+	4.27340i	−0.00400653	+	0.198174i
$466$	15.1080	−	8.72259i	0.699863	−	0.404066i
$467$	−39.0894			−1.80884			−0.904422	−	0.426640i	$-0.859697\pi$
$467$	−39.0894			−1.80884			−0.904422	+	0.426640i	$0.859697\pi$
$468$	4.76093	+	1.63423i	0.220074	+	0.0755422i
$469$	1.82878			0.0844451
$470$	2.87826	−	1.66176i	0.132764	−	0.0766515i
$471$	−16.2548	+	8.95158i	−0.748980	+	0.412467i
$472$	18.2209	−	31.5596i	0.838686	−	1.45265i
$473$	2.33128	+	1.34597i	0.107193	+	0.0618876i
$474$	−6.05310	−	10.9915i	−0.278028	−	0.504858i
$475$	1.80440	−	1.04177i	0.0827916	−	0.0477998i
$476$			0.306748i			0.0140598i
$477$	13.8458	+	26.3907i	0.633955	+	1.20835i
$478$	−14.5811			−0.666924
$479$	9.76527	−	5.63798i	0.446186	−	0.257606i	−0.260032	−	0.965600i	$-0.583733\pi$
$479$	9.76527	−	5.63798i	0.446186	−	0.257606i	0.706218	+	0.707994i	$0.250400\pi$
$480$	0.0901236	−	4.45777i	0.00411356	−	0.203468i
$481$	−1.46505	+	4.90541i	−0.0668005	+	0.223667i
$482$	11.0516	−	19.1419i	0.503387	−	0.871891i
$483$	−0.211834	+	0.350357i	−0.00963880	+	0.0159418i
$484$	−2.54394	−	4.40623i	−0.115633	−	0.200283i
$485$	−6.60132			−0.299750
$486$	−11.2937	+	15.6643i	−0.512293	+	0.710547i
$487$			28.5174i			1.29225i	0.763233	+	0.646123i	$0.223611\pi$
$487$			28.5174i			1.29225i	−0.763233	+	0.646123i	$0.776389\pi$
$488$	13.6448	−	7.87781i	0.617669	−	0.356611i
$489$	−3.43762	+	5.68553i	−0.155454	+	0.257109i
$490$	4.31289	−	7.47015i	0.194837	−	0.337467i
$491$	−10.0886	+	17.4740i	−0.455292	+	0.788588i	−0.998705	−	0.0508770i	$-0.983798\pi$
$491$	−10.0886	+	17.4740i	−0.455292	+	0.788588i	0.543413	+	0.839465i	$0.317132\pi$
$492$	8.73104	+	0.176517i	0.393626	+	0.00795801i
$493$	15.6151	+	27.0462i	0.703270	+	1.21810i
$494$	−2.15217	−	9.05405i	−0.0968307	−	0.407361i
$495$	0.360014	+	0.686204i	0.0161814	+	0.0308426i
$496$		−	7.03984i		−	0.316098i
$497$	−0.588376	−	1.01910i	−0.0263923	−	0.0457128i
$498$	−7.97965	+	4.39443i	−0.357577	+	0.196919i
$499$	−9.29046	−	5.36385i	−0.415898	−	0.240119i	0.277423	−	0.960748i	$-0.410520\pi$
$499$	−9.29046	−	5.36385i	−0.415898	−	0.240119i	−0.693321	+	0.720629i	$0.743853\pi$
$500$	−0.403011	−	0.232678i	−0.0180232	−	0.0104057i
$501$	10.8777	+	19.7522i	0.485978	+	0.882465i
$502$	9.71796	−	5.61067i	0.433734	−	0.250416i
$503$	−20.9283			−0.933149			−0.466574	−	0.884482i	$-0.654512\pi$
$503$	−20.9283			−0.933149			−0.466574	+	0.884482i	$0.654512\pi$
$504$	0.942430	−	1.48983i	0.0419792	−	0.0663624i
$505$		−	10.0475i		−	0.447107i
$506$	0.196558	+	0.340449i	0.00873807	+	0.0151348i
$507$	−9.72353	−	20.3089i	−0.431837	−	0.901952i
$508$	3.62675	−	6.28172i	0.160911	−	0.278706i
$509$	17.1362	+	9.89357i	0.759547	+	0.438525i	0.829133	−	0.559051i	$-0.188834\pi$
$509$	17.1362	+	9.89357i	0.759547	+	0.438525i	−0.0695859	+	0.997576i	$0.522168\pi$
$510$	6.29046	+	3.80337i	0.278546	+	0.168416i
$511$	−1.03405	−	1.79103i	−0.0457438	−	0.0792305i
$512$			24.7686i			1.09463i
$513$	−10.8065	−	0.656147i	−0.477119	−	0.0289696i
$514$		−	5.89193i		−	0.259882i
$515$	3.94442	−	2.27731i	0.173812	−	0.100350i
$516$	7.18826	+	4.34620i	0.316445	+	0.191331i
$517$	−0.346494	+	0.600145i	−0.0152388	+	0.0263944i
$518$	0.293097	+	0.169220i	0.0128779	+	0.00743508i
$519$	0.408610	−	20.2110i	0.0179360	−	0.887165i
$520$	−8.00464	+	7.56199i	−0.351027	+	0.331615i
$521$	2.69918			0.118253			0.0591266	−	0.998250i	$-0.481168\pi$
$521$	2.69918			0.118253			0.0591266	+	0.998250i	$0.481168\pi$
$522$	1.36930	−	33.8509i	0.0599327	−	1.48161i
$523$	−24.4314			−1.06831			−0.534155	−	0.845387i	$-0.679370\pi$
$523$	−24.4314			−1.06831			−0.534155	+	0.845387i	$0.679370\pi$
$524$	4.26031	+	7.37907i	0.186112	+	0.322356i
$525$	−0.160761	−	0.291919i	−0.00701620	−	0.0127404i
$526$	7.29075	+	4.20931i	0.317892	+	0.183535i
$527$	−7.32163	−	4.22714i	−0.318935	−	0.184137i
$528$	−0.615676	−	1.11798i	−0.0267939	−	0.0486537i
$529$	10.7454	+	18.6115i	0.467189	+	0.809195i
$530$	−12.3064			−0.534556
$531$	−1.44681	+	35.7671i	−0.0627863	+	1.55216i
$532$	0.186556			0.00808822
$533$	−26.8263	−	28.3966i	−1.16198	−	1.22999i
$534$	−0.0882751	+	4.36634i	−0.00382004	+	0.188950i
$535$	7.85050	+	4.53249i	0.339407	+	0.195957i
$536$	14.5142	−	25.1394i	0.626919	−	1.08586i
$537$	−31.3180	−	18.9357i	−1.35147	−	0.817134i
$538$	2.08782	−	1.20540i	0.0900122	−	0.0519686i
$539$			1.79856i			0.0774695i
$540$	1.07989	+	2.16353i	0.0464712	+	0.0931035i
$541$			16.1042i			0.692375i	0.938165	+	0.346188i	$0.112524\pi$
$541$			16.1042i			0.692375i	−0.938165	+	0.346188i	$0.887476\pi$
$542$	−4.73295	−	8.19771i	−0.203298	−	0.352122i
$543$	−30.7262	−	18.5778i	−1.31859	−	0.797251i
$544$	7.63751	+	4.40952i	0.327455	+	0.189056i
$545$	−3.26478	+	5.65476i	−0.139848	+	0.242223i
$546$	−1.45484	+	0.314892i	−0.0622613	+	0.0134761i
$547$	−15.0765	−	26.1133i	−0.644625	−	1.11652i	−0.984388	−	0.176012i	$-0.943680\pi$
$547$	−15.0765	−	26.1133i	−0.644625	−	1.11652i	0.339764	−	0.940511i	$-0.389653\pi$
$548$		−	5.67494i		−	0.242422i
$549$	−8.27365	+	13.0793i	−0.353111	+	0.558212i
$550$	−0.319988			−0.0136443
$551$	16.4488	−	9.49671i	0.700742	−	0.404573i
$552$	3.13496	+	5.69263i	0.133433	+	0.242294i
$553$	−0.974458	−	0.562604i	−0.0414382	−	0.0239243i
$554$	−11.1998	−	6.46620i	−0.475833	−	0.274723i
$555$	−2.15426	+	1.18636i	−0.0914434	+	0.0503584i
$556$	−0.829232	−	1.43627i	−0.0351673	−	0.0609115i
$557$		−	10.0629i		−	0.426380i	−0.977011	−	0.213190i	$-0.931615\pi$
$557$		−	10.0629i		−	0.426380i	0.977011	−	0.213190i	$-0.0683853\pi$
$558$	4.26084	+	8.12136i	0.180376	+	0.343804i
$559$	−8.68970	−	36.5570i	−0.367535	−	1.54620i
$560$	0.274442	+	0.475348i	0.0115973	+	0.0200871i
$561$	−1.53242	−	0.0309812i	−0.0646987	−	0.00130803i
$562$	−18.3423	+	31.7698i	−0.773724	+	1.34013i
$563$	−2.26642	+	3.92556i	−0.0955182	+	0.165442i	−0.909825	−	0.414993i	$-0.863784\pi$
$563$	−2.26642	+	3.92556i	−0.0955182	+	0.165442i	0.814307	+	0.580435i	$0.197117\pi$
$564$	−1.11885	+	1.85048i	−0.0471120	+	0.0779194i
$565$	2.21659	−	1.27975i	0.0932527	−	0.0538395i
$566$			21.6999i			0.912117i
$567$	−0.139866	+	1.72600i	−0.00587381	+	0.0724853i
$568$	−18.6788			−0.783744
$569$	−6.23358	−	10.7969i	−0.261325	−	0.452629i	0.705269	−	0.708940i	$-0.250826\pi$
$569$	−6.23358	−	10.7969i	−0.261325	−	0.452629i	−0.966594	+	0.256311i	$0.917493\pi$
$570$	2.31311	−	3.82569i	0.0968854	−	0.160241i
$571$	−9.40436	+	16.2888i	−0.393560	+	0.681666i	−0.992916	−	0.118816i	$-0.962090\pi$
$571$	−9.40436	+	16.2888i	−0.393560	+	0.681666i	0.599356	+	0.800483i	$0.295423\pi$
$572$	0.124026	−	0.415273i	0.00518578	−	0.0173635i
$573$	−0.693656	+	34.3102i	−0.0289779	+	1.43333i
$574$	−2.23647	+	1.29123i	−0.0933484	+	0.0538947i
$575$	1.22853			0.0512334
$576$	−12.3967	−	23.6287i	−0.516531	−	0.984531i
$577$			27.4658i			1.14342i	0.820457	+	0.571709i	$0.193719\pi$
$577$			27.4658i			1.14342i	−0.820457	+	0.571709i	$0.806281\pi$
$578$	5.64655	−	3.26003i	0.234865	−	0.135600i
$579$	−9.98735	−	18.1356i	−0.415060	−	0.753689i
$580$	−3.67381	−	2.12108i	−0.152547	−	0.0880729i
$581$	−0.408440	+	0.707438i	−0.0169449	+	0.0293495i
$582$	−12.4073	+	6.83276i	−0.514299	+	0.283227i
$583$	2.22223	−	1.28300i	0.0920353	−	0.0531366i
$584$	−32.8273			−1.35840
$585$	3.51178	−	10.2307i	0.145194	−	0.422988i
$586$	−3.17034			−0.130966
$587$	17.2688	−	9.97015i	0.712760	−	0.411512i	−0.0993222	−	0.995055i	$-0.531667\pi$
$587$	17.2688	−	9.97015i	0.712760	−	0.411512i	0.812082	+	0.583543i	$0.198334\pi$
$588$	−0.113442	+	5.61116i	−0.00467827	+	0.231400i
$589$	−2.57084	+	4.45282i	−0.105930	+	0.183475i
$590$	−12.8012	−	7.39079i	−0.527018	−	0.304274i
$591$	11.2028	−	18.5285i	0.460821	−	0.762160i
$592$	3.50791	−	2.02529i	0.144174	−	0.0832389i
$593$			17.3576i			0.712792i	0.934335	+	0.356396i	$0.115995\pi$
$593$			17.3576i			0.712792i	−0.934335	+	0.356396i	$0.884005\pi$
$594$	1.38691	+	0.917095i	0.0569058	+	0.0376289i
$595$	0.659167			0.0270232
$596$	−0.989904	+	0.571521i	−0.0405480	+	0.0234104i
$597$	−3.31081	−	2.00180i	−0.135502	−	0.0819281i
$598$	1.57031	−	5.25786i	0.0642149	−	0.215010i
$599$	−12.9431	+	22.4181i	−0.528841	+	0.915980i	0.470593	+	0.882350i	$0.344040\pi$
$599$	−12.9431	+	22.4181i	−0.528841	+	0.915980i	−0.999434	+	0.0336295i	$0.989293\pi$
$600$	−5.28878	−	0.106924i	−0.215913	−	0.00436517i
$601$	−22.4572	−	38.8971i	−0.916049	−	1.58664i	−0.805358	−	0.592789i	$-0.798027\pi$
$601$	−22.4572	−	38.8971i	−0.916049	−	1.58664i	−0.110692	−	0.993855i	$-0.535307\pi$
$602$	−2.48404			−0.101242
$603$	−1.15249	+	28.4909i	−0.0469328	+	1.16024i
$604$			8.01033i			0.325936i
$605$	−9.46850	+	5.46664i	−0.384949	+	0.222251i
$606$	−10.3997	−	18.8844i	−0.422460	−	0.767126i
$607$	−4.26059	+	7.37955i	−0.172932	+	0.299527i	−0.939444	−	0.342704i	$-0.888657\pi$
$607$	−4.26059	+	7.37955i	−0.172932	+	0.299527i	0.766512	+	0.642230i	$0.221991\pi$
$608$	2.68175	−	4.64493i	0.108759	−	0.188377i
$609$	−1.46549	−	2.66111i	−0.0593846	−	0.107834i
$610$	−3.19540	−	5.53460i	−0.129378	−	0.224089i
$611$	9.41092	−	2.23700i	0.380725	−	0.0904993i
$612$	−4.77889	−	0.193311i	−0.193175	−	0.00781412i
$613$			20.1449i			0.813645i	0.913507	+	0.406822i	$0.133363\pi$
$613$			20.1449i			0.813645i	−0.913507	+	0.406822i	$0.866637\pi$
$614$	−9.94679	−	17.2284i	−0.401420	−	0.695280i
$615$	0.379316	−	18.7620i	0.0152955	−	0.756559i
$616$	−0.131451	−	0.0758934i	−0.00529632	−	0.00305783i
$617$	7.82388	+	4.51712i	0.314977	+	0.181852i	0.649152	−	0.760659i	$-0.275124\pi$
$617$	7.82388	+	4.51712i	0.314977	+	0.181852i	−0.334174	+	0.942511i	$0.608457\pi$
$618$	5.05646	−	8.36296i	0.203400	−	0.336408i
$619$	9.61491	−	5.55117i	0.386456	−	0.223120i	−0.294168	−	0.955754i	$-0.595042\pi$
$619$	9.61491	−	5.55117i	0.386456	−	0.223120i	0.680623	+	0.732633i	$0.261709\pi$
$620$	1.14839			0.0461203
$621$	−5.32480	−	3.52101i	−0.213677	−	0.141293i
$622$			0.230591i			0.00924586i
$623$	0.195809	+	0.339151i	0.00784491	+	0.0135878i
$624$	−5.44220	+	16.9637i	−0.217863	+	0.679092i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−7.07263	−	4.08339i	−0.282679	−	0.163205i
$627$	−0.0188419	+	0.931976i	−0.000752475	+	0.0372195i
$628$	2.49284	+	4.31772i	0.0994750	+	0.172296i
$629$		−	4.86443i		−	0.193957i
$630$	−0.604307	−	0.382269i	−0.0240762	−	0.0152300i
$631$			17.9767i			0.715641i	0.933790	+	0.357821i	$0.116480\pi$
$631$			17.9767i			0.715641i	−0.933790	+	0.357821i	$0.883520\pi$
$632$	−15.4677	+	8.93030i	−0.615273	+	0.355228i
$633$	−18.2423	+	10.0461i	−0.725067	+	0.399298i
$634$	14.1702	−	24.5434i	0.562769	−	0.974745i
$635$	−13.4987	−	7.79349i	−0.535680	−	0.309275i
$636$	7.01384	−	3.86256i	0.278117	−	0.153160i
$637$	18.2496	−	17.2404i	0.723076	−	0.683090i
$638$	−2.91699			−0.115485
$639$	16.2475	−	8.52422i	0.642743	−	0.337213i
$640$	5.87004			0.232034
$641$	5.36473	+	9.29198i	0.211894	+	0.367011i	0.952307	−	0.305141i	$-0.0987035\pi$
$641$	5.36473	+	9.29198i	0.211894	+	0.367011i	−0.740413	+	0.672152i	$0.765370\pi$
$642$	19.4466	+	0.393155i	0.767494	+	0.0155166i
$643$	−27.3665	−	15.8000i	−1.07923	−	0.623093i	−0.148540	−	0.988906i	$-0.547458\pi$
$643$	−27.3665	−	15.8000i	−1.07923	−	0.623093i	−0.930688	+	0.365813i	$0.880791\pi$
$644$	0.0952629	+	0.0550000i	0.00375388	+	0.00216731i
$645$	9.33951	−	15.4468i	0.367743	−	0.608216i
$646$	4.42132	+	7.65794i	0.173954	+	0.301298i
$647$	44.0698			1.73256			0.866281	−	0.499557i	$-0.166504\pi$
$647$	44.0698			1.73256			0.866281	+	0.499557i	$0.166504\pi$
$648$	22.6165	+	15.6212i	0.888462	+	0.613660i
$649$	3.08210			0.120983
$650$	3.06730	+	3.24685i	0.120309	+	0.127352i
$651$	0.703762	+	0.425512i	0.0275826	+	0.0166771i
$652$	1.54591	+	0.892532i	0.0605425	+	0.0349542i
$653$	11.8303	−	20.4907i	0.462955	−	0.801862i	−0.536152	−	0.844122i	$-0.680122\pi$
$653$	11.8303	−	20.4907i	0.462955	−	0.801862i	0.999107	+	0.0422600i	$0.0134558\pi$
$654$	−0.283191	+	14.0074i	−0.0110737	+	0.547734i
$655$	15.8568	−	9.15493i	0.619577	−	0.357713i
$656$			30.9079i			1.20675i
$657$	28.5545	−	14.9810i	1.11402	−	0.584466i
$658$		−	0.639469i		−	0.0249291i
$659$	21.9758	+	38.0632i	0.856056	+	1.48273i	0.875662	+	0.482924i	$0.160425\pi$
$659$	21.9758	+	38.0632i	0.856056	+	1.48273i	−0.0196062	+	0.999808i	$0.506241\pi$
$660$	0.182372	−	0.100433i	0.00709882	−	0.00390936i
$661$	2.05866	+	1.18857i	0.0800724	+	0.0462298i	0.539502	−	0.841985i	$-0.318613\pi$
$661$	2.05866	+	1.18857i	0.0800724	+	0.0462298i	−0.459429	+	0.888214i	$0.651946\pi$
$662$	8.48860	−	14.7027i	0.329919	−	0.571436i
$663$	14.3749	+	15.8461i	0.558275	+	0.615411i
$664$	6.48323	+	11.2293i	0.251598	+	0.435781i
$665$		−	0.400888i		−	0.0155458i
$666$	−2.82102	+	4.45958i	−0.109312	+	0.172805i
$667$	11.1992			0.433635
$668$	5.24675	−	3.02921i	0.203003	−	0.117204i
$669$	−5.26086	−	0.106360i	−0.203396	−	0.00411211i
$670$	−10.1971	−	5.88728i	−0.393947	−	0.227445i
$671$	1.15402	+	0.666272i	0.0445504	+	0.0257212i
$672$	−0.734124	−	0.443870i	−0.0283194	−	0.0171226i
$673$	−13.5914	−	23.5410i	−0.523909	−	0.907437i	−0.999613	−	0.0278317i	$-0.991140\pi$
$673$	−13.5914	−	23.5410i	−0.523909	−	0.907437i	0.475703	−	0.879606i	$-0.342194\pi$
$674$		−	29.8409i		−	1.14943i
$675$	4.64919	−	2.32057i	0.178947	−	0.0893189i
$676$	−5.40256	+	2.72221i	−0.207791	+	0.104701i
$677$	−13.8683	−	24.0207i	−0.533004	−	0.923190i	−0.999257	−	0.0385383i	$-0.987730\pi$
$677$	−13.8683	−	24.0207i	−0.533004	−	0.923190i	0.466253	−	0.884651i	$-0.345604\pi$
$678$	2.84150	−	4.69961i	0.109127	−	0.180488i
$679$	−0.635069	+	1.09997i	−0.0243717	+	0.0422130i
$680$	5.23153	−	9.06127i	0.200620	−	0.347484i
$681$	49.2815	+	0.996333i	1.88847	+	0.0381796i
$682$	0.683859	−	0.394826i	0.0261863	−	0.0151187i
$683$			20.2386i			0.774409i	0.921994	+	0.387204i	$0.126559\pi$
$683$			20.2386i			0.774409i	−0.921994	+	0.387204i	$0.873441\pi$
$684$	−0.117566	+	2.90640i	−0.00449526	+	0.111129i
$685$	−12.1948			−0.465941
$686$	−1.66407	−	2.88226i	−0.0635345	−	0.110045i
$687$	9.31164	+	16.9086i	0.355261	+	0.645102i
$688$	−14.8650	+	25.7469i	−0.566723	+	0.981593i
$689$	−34.3199	−	10.2500i	−1.30748	−	0.390494i
$690$	2.30905	−	1.27161i	0.0879040	−	0.0484092i
$691$	−34.4122	+	19.8679i	−1.30910	+	0.755810i	−0.981946	−	0.189161i	$-0.939423\pi$
$691$	−34.4122	+	19.8679i	−1.30910	+	0.755810i	−0.327155	+	0.944971i	$0.606090\pi$
$692$	−5.43128			−0.206466
$693$	0.148976	+	0.00602622i	0.00565913	+	0.000228917i
$694$			6.46170i			0.245283i
$695$	−3.08639	+	1.78193i	−0.117074	+	0.0675924i
$696$	−48.2121	−	0.974713i	−1.82747	−	0.0369464i
$697$	32.1451	+	18.5590i	1.21758	+	0.702970i
$698$	9.70879	−	16.8161i	0.367483	−	0.636499i
$699$	20.8725	+	12.6200i	0.789471	+	0.477334i
$700$	−0.0775419	+	0.0447689i	−0.00293081	+	0.00169210i
$701$	−10.9673			−0.414230			−0.207115	−	0.978317i	$-0.566407\pi$
$701$	−10.9673			−0.414230			−0.207115	+	0.978317i	$0.566407\pi$
$702$	−3.98895	−	22.8637i	−0.150553	−	0.862934i
$703$	−2.95842			−0.111579
$704$	−1.98966	+	1.14873i	−0.0749881	+	0.0432944i
$705$	3.97648	+	2.40428i	0.149763	+	0.0905505i
$706$	−7.71763	+	13.3673i	−0.290457	+	0.503086i
$707$	−1.67420	−	0.966600i	−0.0629648	−	0.0363527i
$708$	9.61557	+	0.194400i	0.361375	+	0.00730599i
$709$	−27.4273	+	15.8352i	−1.03005	+	0.594702i	−0.917000	−	0.398887i	$-0.869397\pi$
$709$	−27.4273	+	15.8352i	−1.03005	+	0.594702i	−0.113054	+	0.993589i	$0.536063\pi$
$710$			7.57650i			0.284341i
$711$	9.37903	−	14.8268i	0.351741	−	0.556047i
$712$	6.21620			0.232962
$713$	−2.62555	+	1.51586i	−0.0983275	+	0.0567694i
$714$	1.23891	−	0.682277i	0.0463652	−	0.0255336i
$715$	−0.892377	−	0.266518i	−0.0333730	−	0.00996719i
$716$	−4.91640	+	8.51545i	−0.183734	+	0.318237i
$717$	−9.83441	−	17.8579i	−0.367273	−	0.666914i
$718$	14.7167	+	25.4902i	0.549224	+	0.951284i
$719$	24.7245			0.922069			0.461035	−	0.887382i	$-0.347478\pi$
$719$	24.7245			0.922069			0.461035	+	0.887382i	$0.347478\pi$
$720$	−7.57851	+	3.97604i	−0.282434	+	0.148178i
$721$		−	0.876341i		−	0.0326366i
$722$	−15.7266	+	9.07974i	−0.585282	+	0.337913i
$723$	30.8975	+	0.624661i	1.14909	+	0.0232314i
$724$	−4.82349	+	8.35453i	−0.179264	+	0.310494i
$725$	−4.55796	+	7.89462i	−0.169278	+	0.293199i
$726$	−12.1379	+	20.0751i	−0.450480	+	0.745057i
$727$	9.65864	+	16.7293i	0.358219	+	0.620454i	0.987663	−	0.156592i	$-0.0500508\pi$
$727$	9.65864	+	16.7293i	0.358219	+	0.620454i	−0.629444	+	0.777046i	$0.716717\pi$
$728$	0.489975	+	2.06129i	0.0181597	+	0.0763967i
$729$	−26.8017	−	3.26672i	−0.992654	−	0.120990i
$730$			13.3154i			0.492827i
$731$	17.8517	+	30.9201i	0.660269	+	1.14362i
$732$	3.55829	+	2.15143i	0.131518	+	0.0795191i
$733$	44.6826	+	25.7975i	1.65039	+	0.952853i	0.976911	+	0.213646i	$0.0685341\pi$
$733$	44.6826	+	25.7975i	1.65039	+	0.952853i	0.673479	+	0.739207i	$0.264799\pi$
$734$	12.1996	+	7.04343i	0.450295	+	0.259978i
$735$	12.0578	+	0.243774i	0.444758	+	0.00899175i
$736$	2.73882	−	1.58126i	0.100954	−	0.0582860i
$737$	2.45511			0.0904351
$738$	−18.7069	−	35.6562i	−0.688610	−	1.31252i
$739$			2.05130i			0.0754582i	0.999288	+	0.0377291i	$0.0120124\pi$
$739$			2.05130i			0.0754582i	−0.999288	+	0.0377291i	$0.987988\pi$
$740$	0.330379	+	0.572233i	0.0121450	+	0.0210357i
$741$	9.63717	−	8.74243i	0.354030	−	0.321161i
$742$	−1.18392	+	2.05061i	−0.0434630	+	0.0752801i
$743$	5.19628	+	3.00008i	0.190633	+	0.110062i	0.592279	−	0.805733i	$-0.298228\pi$
$743$	5.19628	+	3.00008i	0.190633	+	0.110062i	−0.401646	+	0.915795i	$0.631562\pi$
$744$	11.4348	−	6.29719i	0.419219	−	0.230866i
$745$	1.22814	+	2.12719i	0.0449954	+	0.0779344i
$746$			10.1346i			0.371054i
$747$	−10.7640	−	6.80900i	−0.393832	−	0.249128i
$748$			0.411805i			0.0150571i
$749$	1.51049	−	0.872082i	0.0551921	−	0.0318652i
$750$	−0.0433707	+	2.14524i	−0.00158367	+	0.0783330i
$751$	−7.16922	+	12.4175i	−0.261609	+	0.453119i	−0.966670	−	0.256027i	$-0.917586\pi$
$751$	−7.16922	+	12.4175i	−0.261609	+	0.453119i	0.705061	+	0.709147i	$0.250920\pi$
$752$	−6.62807	−	3.82672i	−0.241701	−	0.139546i
$753$	13.4259	+	8.11765i	0.489268	+	0.295823i
$754$	27.9613	+	29.5980i	1.01829	+	1.07790i
$755$	17.2133			0.626457
$756$	0.464396	+	0.0281971i	0.0168899	+	0.00102552i
$757$	35.5542			1.29224			0.646120	−	0.763236i	$-0.276391\pi$
$757$	35.5542			1.29224			0.646120	+	0.763236i	$0.276391\pi$
$758$	8.45987	+	14.6529i	0.307276	+	0.532218i
$759$	−0.284385	+	0.470349i	−0.0103225	+	0.0170726i
$760$	−5.51083	−	3.18168i	−0.199899	−	0.115412i
$761$	−12.6192	−	7.28568i	−0.457445	−	0.264106i	0.253525	−	0.967329i	$-0.418410\pi$
$761$	−12.6192	−	7.28568i	−0.457445	−	0.264106i	−0.710969	+	0.703223i	$0.751743\pi$
$762$	−33.4378	−	0.676018i	−1.21132	−	0.0244896i
$763$	0.628165	+	1.08801i	0.0227411	+	0.0393887i
$764$	9.22013			0.333573
$765$	−0.415403	+	10.2693i	−0.0150189	+	0.371288i
$766$	−23.9366			−0.864866
$767$	−29.5440	−	31.2734i	−1.06677	−	1.12922i
$768$	−15.9564	+	8.78726i	−0.575776	+	0.317083i
$769$	−42.0809	−	24.2954i	−1.51748	−	0.876116i	−0.999789	−	0.0205458i	$-0.993460\pi$
$769$	−42.0809	−	24.2954i	−1.51748	−	0.876116i	−0.517688	−	0.855570i	$-0.673207\pi$
$770$	−0.0307839	+	0.0533193i	−0.00110938	+	0.00192149i
$771$	7.21599	−	3.97388i	0.259878	−	0.143116i
$772$	−4.81732	+	2.78128i	−0.173379	+	0.100100i
$773$			37.9417i			1.36467i	0.731040	+	0.682334i	$0.239035\pi$
$773$			37.9417i			1.36467i	−0.731040	+	0.682334i	$0.760965\pi$
$774$	1.56543	−	38.6994i	0.0562681	−	1.39102i
$775$		−	2.46775i		−	0.0886444i
$776$	10.0806	+	17.4600i	0.361871	+	0.626778i
$777$	−0.00956466	+	0.473095i	−0.000343130	+	0.0169722i
$778$	18.8865	+	10.9042i	0.677115	+	0.390933i
$779$	11.2871	−	19.5498i	0.404401	−	0.700443i
$780$	−2.76723	−	0.887769i	−0.0990828	−	0.0317872i
$781$	−0.789887	−	1.36812i	−0.0282644	−	0.0489553i
$782$			5.21394i			0.186450i
$783$	42.3816	−	21.1542i	1.51460	−	0.755988i
$784$	−19.8635			−0.709411
$785$	9.27831	−	5.35683i	0.331157	−	0.191194i
$786$	20.3272	−	33.6196i	0.725049	−	1.19917i
$787$	8.15545	+	4.70855i	0.290710	+	0.167842i	0.638262	−	0.769819i	$-0.279654\pi$
$787$	8.15545	+	4.70855i	0.290710	+	0.167842i	−0.347552	+	0.937661i	$0.612987\pi$
$788$	−5.03794	−	2.90865i	−0.179469	−	0.103617i
$789$	−0.237920	+	11.7682i	−0.00847017	+	0.418959i
$790$	3.62231	+	6.27403i	0.128876	+	0.223220i
$791$		−	0.492465i		−	0.0175100i
$792$	1.26520	−	2.00008i	0.0449569	−	0.0710698i
$793$	−4.30152	−	18.0962i	−0.152751	−	0.642616i
$794$	20.4792	+	35.4710i	0.726778	+	1.25882i
$795$	−8.30021	−	15.0720i	−0.294378	−	0.534548i
$796$	−0.519740	+	0.900216i	−0.0184217	+	0.0319073i
$797$	15.1498	−	26.2402i	0.536633	−	0.929475i	−0.462450	−	0.886646i	$-0.653029\pi$
$797$	15.1498	−	26.2402i	0.536633	−	0.929475i	0.999082	−	0.0428297i	$-0.0136373\pi$
$798$	−0.414943	−	0.753475i	−0.0146888	−	0.0266727i
$799$	−7.95979	+	4.59559i	−0.281597	+	0.162580i
$800$			2.57422i			0.0910124i
$801$	−5.40710	+	2.83682i	−0.191051	+	0.100234i
$802$	11.9682			0.422613
$803$	−1.38820	−	2.40443i	−0.0489885	−	0.0848506i
$804$	7.65946	+	0.154853i	0.270128	+	0.00546124i
$805$	0.118189	−	0.204709i	0.00416562	−	0.00721506i
$806$	−10.5615	−	3.15429i	−0.372012	−	0.111105i
$807$	2.88444	+	1.74400i	0.101537	+	0.0613919i
$808$	−26.5749	+	15.3430i	−0.934900	+	0.539765i
$809$	12.1740			0.428016			0.214008	−	0.976832i	$-0.431348\pi$
$809$	12.1740			0.428016			0.214008	+	0.976832i	$0.431348\pi$
$810$	6.33629	−	9.17374i	0.222635	−	0.322332i
$811$		−	21.2334i		−	0.745605i	−0.927911	−	0.372803i	$-0.878397\pi$
$811$		−	21.2334i		−	0.745605i	0.927911	−	0.372803i	$-0.121603\pi$
$812$	−0.706866	+	0.408109i	−0.0248061	+	0.0143218i
$813$	6.84774	−	11.3256i	0.240161	−	0.397206i
$814$	0.393479	+	0.227175i	0.0137914	+	0.00796248i
$815$	1.91795	−	3.32199i	0.0671829	−	0.116364i
$816$	0.342160	−	16.9242i	0.0119780	−	0.592465i
$817$	18.8048	−	10.8569i	0.657895	−	0.379836i
$818$	44.7849			1.56587
$819$	−1.36689	−	1.56939i	−0.0477630	−	0.0548390i
$820$	−5.04190			−0.176071
$821$	−4.37507	+	2.52595i	−0.152691	+	0.0881562i	−0.574399	−	0.818576i	$-0.694764\pi$
$821$	−4.37507	+	2.52595i	−0.152691	+	0.0881562i	0.421708	+	0.906732i	$0.361431\pi$
$822$	−22.9204	+	12.6224i	−0.799440	+	0.440256i
$823$	3.36247	−	5.82396i	0.117208	−	0.203011i	−0.801452	−	0.598059i	$-0.795939\pi$
$823$	3.36247	−	5.82396i	0.117208	−	0.203011i	0.918660	+	0.395048i	$0.129272\pi$
$824$	−12.0467	−	6.95515i	−0.419666	−	0.242294i
$825$	−0.215820	−	0.391898i	−0.00751389	−	0.0136441i
$826$	−2.46304	+	1.42204i	−0.0857002	+	0.0494790i
$827$		−	11.4590i		−	0.398469i	−0.979952	−	0.199235i	$-0.936154\pi$
$827$		−	11.4590i		−	0.398469i	0.979952	−	0.199235i	$-0.0638456\pi$
$828$	−0.916893	+	1.44946i	−0.0318642	+	0.0503723i
$829$	42.9403			1.49138			0.745690	−	0.666293i	$-0.232120\pi$
$829$	42.9403			1.49138			0.745690	+	0.666293i	$0.232120\pi$
$830$	4.55483	−	2.62973i	0.158100	−	0.0912793i
$831$	0.365484	−	18.0779i	0.0126785	−	0.627115i
$832$	30.7281	+	9.17727i	1.06531	+	0.318165i
$833$	−11.9272	+	20.6586i	−0.413255	+	0.715778i
$834$	−3.95652	+	6.54376i	−0.137003	+	0.226592i
$835$	−6.50944	−	11.2747i	−0.225269	−	0.390177i
$836$	0.250449			0.00866195
$837$	−7.07265	+	10.6959i	−0.244467	+	0.369705i
$838$			16.3353i			0.564294i
$839$	12.6161	−	7.28392i	0.435557	−	0.251469i	−0.266154	−	0.963930i	$-0.585753\pi$
$839$	12.6161	−	7.28392i	0.435557	−	0.251469i	0.701711	+	0.712462i	$0.252420\pi$
$840$	−0.526615	+	0.870978i	−0.0181699	+	0.0300516i
$841$	−27.0500	+	46.8520i	−0.932759	+	1.61559i
$842$	−22.2814	+	38.5925i	−0.767868	+	1.32999i
$843$	−51.2805	−	1.03675i	−1.76619	−	0.0357075i
$844$	2.79765	+	4.84567i	0.0962991	+	0.166795i
$845$	5.84974	+	11.6095i	0.201237	+	0.399379i
$846$	9.96244	+	0.402990i	0.342516	+	0.0138551i
$847$			2.10364i			0.0722818i
$848$	14.1696	+	24.5425i	0.486587	+	0.842793i
$849$	−26.5765	+	14.6358i	−0.912102	+	0.502299i
$850$	−3.67544	−	2.12202i	−0.126067	−	0.0727846i
$851$	−1.51069	−	0.872195i	−0.0517857	−	0.0298985i
$852$	−2.37800	−	4.31810i	−0.0814690	−	0.147936i
$853$	18.0022	−	10.3936i	0.616382	−	0.355869i	−0.159077	−	0.987266i	$-0.550852\pi$
$853$	18.0022	−	10.3936i	0.616382	−	0.355869i	0.775459	+	0.631398i	$0.217518\pi$
$854$	−1.22963			−0.0420772
$855$	6.24552	+	0.252637i	0.213592	+	0.00864001i
$856$		−	27.6854i		−	0.946267i
$857$	3.11020	+	5.38703i	0.106242	+	0.184017i	0.914245	−	0.405161i	$-0.132785\pi$
$857$	3.11020	+	5.38703i	0.106242	+	0.184017i	−0.808003	+	0.589179i	$0.799451\pi$
$858$	−1.95310	+	0.422739i	−0.0666777	+	0.0144321i
$859$	−29.1597	+	50.5060i	−0.994915	+	1.72324i	−0.410237	+	0.911979i	$0.634554\pi$
$859$	−29.1597	+	50.5060i	−0.994915	+	1.72324i	−0.584678	+	0.811265i	$0.698779\pi$
$860$	−4.20002	−	2.42488i	−0.143219	−	0.0826877i
$861$	−3.08981	−	1.86818i	−0.105300	−	0.0636673i
$862$	−21.0144	−	36.3981i	−0.715755	−	1.23972i
$863$		−	25.8080i		−	0.878515i	−0.898361	−	0.439257i	$-0.855242\pi$
$863$		−	25.8080i		−	0.878515i	0.898361	−	0.439257i	$-0.144758\pi$
$864$	7.37779	−	11.1574i	0.250997	−	0.379581i
$865$			11.6712i			0.396833i
$866$	−17.4681	+	10.0852i	−0.593590	+	0.342709i
$867$	7.80103	+	4.71670i	0.264937	+	0.160187i
$868$	0.110479	−	0.191354i	0.00374989	−	0.00649499i
$869$	−1.30820	−	0.755288i	−0.0443775	−	0.0256214i
$870$	−0.395364	+	19.5558i	−0.0134041	+	0.663005i
$871$	−23.5339	−	24.9114i	−0.797415	−	0.844092i
$872$	19.9419			0.675318
$873$	−16.7365	−	10.5871i	−0.566445	−	0.358319i
$874$	3.17098			0.107260
$875$	0.0962033	+	0.166629i	0.00325227	+	0.00563309i
$876$	−4.17926	−	7.58893i	−0.141204	−	0.256406i
$877$	−42.0672	−	24.2875i	−1.42051	−	0.820130i	−0.424165	−	0.905585i	$-0.639432\pi$
$877$	−42.0672	−	24.2875i	−1.42051	−	0.820130i	−0.996342	+	0.0854549i	$0.972766\pi$
$878$	26.5141	+	15.3079i	0.894808	+	0.516617i
$879$	−2.13827	−	3.88279i	−0.0721222	−	0.130963i
$880$	0.368435	+	0.638148i	0.0124199	+	0.0215120i
$881$	35.0043			1.17933			0.589663	−	0.807649i	$-0.299261\pi$
$881$	35.0043			1.17933			0.589663	+	0.807649i	$0.299261\pi$
$882$	22.9151	−	12.0223i	0.771592	−	0.404813i
$883$	13.9534			0.469570			0.234785	−	0.972047i	$-0.424561\pi$
$883$	13.9534			0.469570			0.234785	+	0.972047i	$0.424561\pi$
$884$	4.17849	−	3.94742i	0.140538	−	0.132766i
$885$	0.417744	−	20.6628i	0.0140423	−	0.694572i
$886$	−17.8972	−	10.3330i	−0.601268	−	0.347142i
$887$	15.5667	−	26.9624i	0.522680	−	0.905308i	−0.476972	−	0.878919i	$-0.658266\pi$
$887$	15.5667	−	26.9624i	0.522680	−	0.905308i	0.999652	−	0.0263895i	$-0.00840103\pi$
$888$	6.42752	+	3.88624i	0.215694	+	0.130414i
$889$	−2.59724	+	1.49952i	−0.0871088	+	0.0502923i
$890$		−	2.52142i		−	0.0845183i
$891$	−0.187768	+	2.31714i	−0.00629046	+	0.0776269i
$892$			1.41374i			0.0473356i
$893$	2.79491	+	4.84093i	0.0935282	+	0.161996i
$894$	4.51007	+	2.72690i	0.150839	+	0.0912013i
$895$	18.2988	+	10.5648i	0.611660	+	0.353142i
$896$	0.564717	−	0.978119i	0.0188659	−	0.0326766i
$897$	7.49855	−	1.62303i	0.250369	−	0.0541912i
$898$	11.1883	+	19.3788i	0.373360	+	0.646678i
$899$		−	22.4959i		−	0.750279i
$900$	−0.648598	−	1.23626i	−0.0216199	−	0.0412086i
$901$	34.0332			1.13381
$902$	−3.00243	+	1.73345i	−0.0999700	+	0.0577177i
$903$	−1.67539	−	3.04226i	−0.0557535	−	0.101240i
$904$	−6.76970	−	3.90849i	−0.225157	−	0.129994i
$905$	17.9530	+	10.3652i	0.596777	+	0.344549i
$906$	32.3527	−	17.8168i	1.07485	−	0.591924i
$907$	13.0764	+	22.6490i	0.434196	+	0.752049i	0.997230	−	0.0743849i	$-0.0236993\pi$
$907$	13.0764	+	22.6490i	0.434196	+	0.752049i	−0.563034	+	0.826434i	$0.690366\pi$
$908$		−	13.2433i		−	0.439496i
$909$	16.1140	−	25.4736i	0.534466	−	0.844907i
$910$	0.836104	−	0.198744i	0.0277166	−	0.00658830i
$911$	14.0405	+	24.3188i	0.465181	+	0.805717i	0.999210	−	0.0397494i	$-0.0126560\pi$
$911$	14.0405	+	24.3188i	0.465181	+	0.805717i	−0.534029	+	0.845466i	$0.679323\pi$
$912$	−10.2928	−	0.208092i	−0.340830	−	0.00689063i
$913$	−0.548325	+	0.949726i	−0.0181469	+	0.0314314i
$914$	16.0462	−	27.7928i	0.530761	−	0.919305i
$915$	4.62318	−	7.64637i	0.152838	−	0.252781i
$916$	4.49139	−	2.59311i	0.148400	−	0.0856787i
$917$		−	3.52294i		−	0.116338i
$918$	9.84859	+	19.7313i	0.325052	+	0.651230i
$919$	−9.46007			−0.312059			−0.156029	−	0.987752i	$-0.549869\pi$
$919$	−9.46007			−0.312059			−0.156029	+	0.987752i	$0.549869\pi$
$920$	−1.87603	−	3.24939i	−0.0618510	−	0.107129i
$921$	14.3913	−	23.8020i	0.474208	−	0.784301i
$922$	−25.2865	+	43.7975i	−0.832766	+	1.44239i
$923$	−6.31045	+	21.1292i	−0.207711	+	0.695476i
$924$	0.000809709	−	0.0400505i	2.66375e−5	−	0.00131756i
$925$	1.22967	−	0.709948i	0.0404312	−	0.0233430i
$926$	16.7734			0.551207
$927$	13.6527	+	0.552265i	0.448414	+	0.0181388i
$928$			23.4664i			0.770322i
$929$	−21.1982	+	12.2388i	−0.695492	+	0.401542i	−0.805666	−	0.592370i	$-0.798192\pi$
$929$	−21.1982	+	12.2388i	−0.695492	+	0.401542i	0.110174	+	0.993912i	$0.464859\pi$
$930$	−2.55427	−	4.63819i	−0.0837579	−	0.152092i
$931$	12.5640	+	7.25384i	0.411769	+	0.237735i
$932$	3.27663	−	5.67529i	0.107330	−	0.185900i
$933$	−0.282411	+	0.155525i	−0.00924571	+	0.00509166i
$934$	41.9366	−	24.2121i	1.37221	−	0.792245i
$935$	0.884923			0.0289401
$936$	−32.4222	+	6.33442i	−1.05975	+	0.207047i
$937$	14.9559			0.488586			0.244293	−	0.969701i	$-0.421444\pi$
$937$	14.9559			0.488586			0.244293	+	0.969701i	$0.421444\pi$
$938$	−1.96198	+	1.13275i	−0.0640610	+	0.0369856i
$939$	0.230802	−	11.4161i	0.00753194	−	0.372551i
$940$	0.624240	−	1.08122i	0.0203605	−	0.0352654i
$941$	−25.0765	−	14.4779i	−0.817469	−	0.471966i	0.0320739	−	0.999486i	$-0.489789\pi$
$941$	−25.0765	−	14.4779i	−0.817469	−	0.471966i	−0.849543	+	0.527520i	$0.823122\pi$
$942$	11.8941	−	19.6719i	0.387530	−	0.640944i
$943$	11.5273	−	6.65527i	0.375379	−	0.216725i
$944$			34.0391i			1.10788i
$945$	0.0605925	−	0.997937i	0.00197107	−	0.0324629i
$946$	−3.33479			−0.108423
$947$	−32.9665	+	19.0332i	−1.07127	+	0.618496i	−0.928527	−	0.371264i	$-0.878924\pi$
$947$	−32.9665	+	19.0332i	−1.07127	+	0.618496i	−0.142739	+	0.989760i	$0.545591\pi$
$948$	−4.03368	−	2.43886i	−0.131008	−	0.0792106i
$949$	−11.0904	+	37.1339i	−0.360010	+	1.20542i
$950$	−1.29055	+	2.23531i	−0.0418711	+	0.0725229i
$951$	39.6162	+	0.800929i	1.28464	+	0.0259719i
$952$	−1.00658	−	1.74345i	−0.0326235	−	0.0565055i
$953$	−29.0088			−0.939687			−0.469844	−	0.882750i	$-0.655690\pi$
$953$	−29.0088			−0.939687			−0.469844	+	0.882750i	$0.655690\pi$
$954$	−31.2008	−	19.7368i	−1.01016	−	0.639003i
$955$		−	19.8130i		−	0.641135i
$956$	−4.74355	+	2.73869i	−0.153417	+	0.0885755i
$957$	−1.96740	−	3.57251i	−0.0635969	−	0.115483i
$958$	−6.98437	+	12.0973i	−0.225655	+	0.390845i
$959$	−1.17318	+	2.03201i	−0.0378841	+	0.0656171i
$960$	7.43155	+	13.4946i	0.239852	+	0.435537i
$961$	−12.4551	−	21.5729i	−0.401777	−	0.695899i
$962$	−1.46666	−	6.17017i	−0.0472871	−	0.198934i
$963$	12.6345	+	24.0819i	0.407140	+	0.776027i
$964$		−	8.30304i		−	0.267423i
$965$	5.97666	+	10.3519i	0.192396	+	0.333239i
$966$	0.0102519	−	0.507087i	0.000329849	−	0.0163153i
$967$	−39.5487	−	22.8334i	−1.27180	−	0.734274i	−0.296474	−	0.955041i	$-0.595811\pi$
$967$	−39.5487	−	22.8334i	−1.27180	−	0.734274i	−0.975327	+	0.220767i	$0.929144\pi$
$968$	28.9178	+	16.6957i	0.929452	+	0.536619i
$969$	−6.39687	+	10.5799i	−0.205497	+	0.339875i
$970$	7.08215	−	4.08888i	0.227394	−	0.131286i
$971$	−13.5827			−0.435888			−0.217944	−	0.975961i	$-0.569935\pi$
$971$	−13.5827			−0.435888			−0.217944	+	0.975961i	$0.569935\pi$
$972$	−0.731949	+	7.21717i	−0.0234773	+	0.231491i
$973$			0.685710i			0.0219829i
$974$	−17.6638	−	30.5946i	−0.565984	−	0.980313i
$975$	−1.90772	+	5.94648i	−0.0610959	+	0.190440i
$976$	−7.35838	+	12.7451i	−0.235536	+	0.407961i
$977$	35.0271	+	20.2229i	1.12062	+	0.646989i	0.941559	−	0.336849i	$-0.109361\pi$
$977$	35.0271	+	20.2229i	1.12062	+	0.646989i	0.179059	+	0.983838i	$0.442695\pi$
$978$	0.166366	−	8.22893i	0.00531980	−	0.263132i
$979$	0.262871	+	0.455305i	0.00840138	+	0.0145516i
$980$		−	3.24027i		−	0.103507i
$981$	−17.3463	+	9.10066i	−0.553824	+	0.290562i
$982$		−	24.9956i		−	0.797643i
$983$	−35.6873	+	20.6041i	−1.13825	+	0.657167i	−0.945996	−	0.324178i	$-0.894912\pi$
$983$	−35.6873	+	20.6041i	−1.13825	+	0.657167i	−0.192251	+	0.981346i	$0.561579\pi$
$984$	−50.2035	+	27.6473i	−1.60043	+	0.881365i
$985$	−6.25038	+	10.8260i	−0.199154	+	0.344944i
$986$	−33.5050	−	19.3441i	−1.06702	−	0.616043i
$987$	0.783174	−	0.431298i	0.0249287	−	0.0137284i
$988$	−2.40072	−	2.54125i	−0.0763770	−	0.0808478i
$989$	12.8033			0.407121
$990$	−0.811274	−	0.513192i	−0.0257840	−	0.0163103i
$991$	−39.6402			−1.25921			−0.629607	−	0.776914i	$-0.716784\pi$
$991$	−39.6402			−1.25921			−0.629607	+	0.776914i	$0.716784\pi$
$992$	−3.17627	−	5.50146i	−0.100847	−	0.174672i
$993$	23.7320	+	0.479795i	0.753112	+	0.0152258i
$994$	1.26246	+	0.728884i	0.0400430	+	0.0231188i
$995$	1.93447	+	1.11686i	0.0613267	+	0.0354070i
$996$	−1.77057	+	2.92838i	−0.0561027	+	0.0927892i
$997$	−11.2975	−	19.5678i	−0.357794	−	0.619718i	0.629798	−	0.776759i	$-0.283138\pi$
$997$	−11.2975	−	19.5678i	−0.357794	−	0.619718i	−0.987592	+	0.157041i	$0.949804\pi$
$998$	13.2896			0.420674
$999$	−7.36444	−	0.447152i	−0.233000	−	0.0141473i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bt.b.571.18	yes	108
9.7	even	3	inner	585.2.bt.b.376.37	yes	108
13.12	even	2	inner	585.2.bt.b.571.37	yes	108
117.25	even	6	inner	585.2.bt.b.376.18	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bt.b.376.18	✓	108	117.25	even	6	inner
585.2.bt.b.376.37	yes	108	9.7	even	3	inner
585.2.bt.b.571.18	yes	108	1.1	even	1	trivial
585.2.bt.b.571.37	yes	108	13.12	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07284 + 0.619404i) q^{2} +(-1.48219 - 0.896168i) q^{3} +(-0.232678 + 0.403011i) q^{4} +(0.866025 + 0.500000i) q^{5} +(2.14524 + 0.0433707i) q^{6} +(0.166629 - 0.0962033i) q^{7} -3.05410i q^{8} +(1.39377 + 2.65658i) q^{9} +O(q^{10})\)	\(q+(-1.07284 + 0.619404i) q^{2} +(-1.48219 - 0.896168i) q^{3} +(-0.232678 + 0.403011i) q^{4} +(0.866025 + 0.500000i) q^{5} +(2.14524 + 0.0433707i) q^{6} +(0.166629 - 0.0962033i) q^{7} -3.05410i q^{8} +(1.39377 + 2.65658i) q^{9} -1.23881 q^{10} +(0.223697 - 0.129152i) q^{11} +(0.706038 - 0.388819i) q^{12} +(-3.45476 - 1.03180i) q^{13} +(-0.119177 + 0.206421i) q^{14} +(-0.835529 - 1.51720i) q^{15} +(1.42637 + 2.47054i) q^{16} +3.42590 q^{17} +(-3.14078 - 1.98678i) q^{18} -2.08354i q^{19} +(-0.403011 + 0.232678i) q^{20} +(-0.333190 - 0.00673617i) q^{21} +(-0.159994 + 0.277118i) q^{22} +(0.614267 - 1.06394i) q^{23} +(-2.73699 + 4.52675i) q^{24} +(0.500000 + 0.866025i) q^{25} +(4.34550 - 1.03294i) q^{26} +(0.314919 - 5.18660i) q^{27} +0.0895377i q^{28} +(4.55796 + 7.89462i) q^{29} +(1.83615 + 1.11018i) q^{30} +(-2.13714 - 1.23388i) q^{31} +(2.22934 + 1.28711i) q^{32} +(-0.447303 - 0.00904322i) q^{33} +(-3.67544 + 2.12202i) q^{34} +0.192407 q^{35} +(-1.39493 - 0.0564262i) q^{36} -1.41990i q^{37} +(1.29055 + 2.23531i) q^{38} +(4.19594 + 4.62537i) q^{39} +(1.52705 - 2.64493i) q^{40} +(9.38294 + 5.41724i) q^{41} +(0.361632 - 0.199152i) q^{42} +(5.21080 + 9.02537i) q^{43} +0.120203i q^{44} +(-0.121254 + 2.99755i) q^{45} +1.52192i q^{46} +(-2.32341 + 1.34142i) q^{47} +(0.0998742 - 4.94006i) q^{48} +(-3.48149 + 6.03012i) q^{49} +(-1.07284 - 0.619404i) q^{50} +(-5.07784 - 3.07019i) q^{51} +(1.21967 - 1.15223i) q^{52} +9.93408 q^{53} +(2.87474 + 5.75945i) q^{54} +0.258303 q^{55} +(-0.293815 - 0.508902i) q^{56} +(-1.86721 + 3.08821i) q^{57} +(-9.77991 - 5.64643i) q^{58} +(10.3335 + 5.96605i) q^{59} +(0.805857 + 0.0162922i) q^{60} +(2.57942 + 4.46768i) q^{61} +3.05707 q^{62} +(0.487814 + 0.308579i) q^{63} -8.89442 q^{64} +(-2.47601 - 2.62095i) q^{65} +(0.485486 - 0.267359i) q^{66} +(8.23135 + 4.75237i) q^{67} +(-0.797133 + 1.38068i) q^{68} +(-1.86393 + 1.02648i) q^{69} +(-0.206421 + 0.119177i) q^{70} -6.11596i q^{71} +(8.11347 - 4.25670i) q^{72} -10.7486i q^{73} +(0.879489 + 1.52332i) q^{74} +(0.0350101 - 1.73170i) q^{75} +(0.839690 + 0.484795i) q^{76} +(0.0248496 - 0.0430409i) q^{77} +(-7.36654 - 2.36329i) q^{78} +(-2.92403 - 5.06458i) q^{79} +2.85273i q^{80} +(-5.11484 + 7.40530i) q^{81} -13.4218 q^{82} +(-3.67679 + 2.12279i) q^{83} +(0.0802408 - 0.132712i) q^{84} +(2.96692 + 1.71295i) q^{85} +(-11.1807 - 6.45518i) q^{86} +(0.319149 - 15.7860i) q^{87} +(-0.394442 - 0.683194i) q^{88} +2.03536i q^{89} +(-1.72661 - 3.29099i) q^{90} +(-0.674927 + 0.160432i) q^{91} +(0.285853 + 0.495112i) q^{92} +(2.06188 + 3.74407i) q^{93} +(1.66176 - 2.87826i) q^{94} +(1.04177 - 1.80440i) q^{95} +(-2.15084 - 3.90560i) q^{96} +(-5.71691 + 3.30066i) q^{97} -8.62579i q^{98} +(0.654883 + 0.414263i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

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