LMFDB - Embedded newform 363.2.e.k.124.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,2,Mod(124,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("363.124");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	363.e (of order $5$, degree $4$, not 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:	$2.89856959337$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			124.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	363.124
Dual form			363.2.e.k.202.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.11803 - 1.53884i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(1.50000 - 4.61653i) q^{4} +(0.500000 + 0.363271i) q^{5} +(-2.11803 - 1.53884i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-2.30902 - 7.10642i) q^{8} +(-0.809017 + 0.587785i) q^{9} +1.61803 q^{10} -4.85410 q^{12} +(-0.190983 + 0.138757i) q^{13} +(0.809017 + 2.48990i) q^{14} +(0.190983 - 0.587785i) q^{15} +(-7.97214 - 5.79210i) q^{16} +(0.927051 + 0.673542i) q^{17} +(-0.809017 + 2.48990i) q^{18} +(1.80902 + 5.56758i) q^{19} +(2.42705 - 1.76336i) q^{20} +1.00000 q^{21} +0.236068 q^{23} +(-6.04508 + 4.39201i) q^{24} +(-1.42705 - 4.39201i) q^{25} +(-0.190983 + 0.587785i) q^{26} +(0.809017 + 0.587785i) q^{27} +(3.92705 + 2.85317i) q^{28} +(-1.85410 + 5.70634i) q^{29} +(-0.500000 - 1.53884i) q^{30} +(4.92705 - 3.57971i) q^{31} -10.8541 q^{32} +3.00000 q^{34} +(-0.500000 + 0.363271i) q^{35} +(1.50000 + 4.61653i) q^{36} +(-1.92705 + 5.93085i) q^{37} +(12.3992 + 9.00854i) q^{38} +(0.190983 + 0.138757i) q^{39} +(1.42705 - 4.39201i) q^{40} +(0.0729490 + 0.224514i) q^{41} +(2.11803 - 1.53884i) q^{42} -6.70820 q^{43} -0.618034 q^{45} +(0.500000 - 0.363271i) q^{46} +(-3.11803 - 9.59632i) q^{47} +(-3.04508 + 9.37181i) q^{48} +(4.85410 + 3.52671i) q^{49} +(-9.78115 - 7.10642i) q^{50} +(0.354102 - 1.08981i) q^{51} +(0.354102 + 1.08981i) q^{52} +(0.309017 - 0.224514i) q^{53} +2.61803 q^{54} +7.47214 q^{56} +(4.73607 - 3.44095i) q^{57} +(4.85410 + 14.9394i) q^{58} +(2.28115 - 7.02067i) q^{59} +(-2.42705 - 1.76336i) q^{60} +(9.35410 + 6.79615i) q^{61} +(4.92705 - 15.1639i) q^{62} +(-0.309017 - 0.951057i) q^{63} +(-7.04508 + 5.11855i) q^{64} -0.145898 q^{65} +1.85410 q^{67} +(4.50000 - 3.26944i) q^{68} +(-0.0729490 - 0.224514i) q^{69} +(-0.500000 + 1.53884i) q^{70} +(-8.35410 - 6.06961i) q^{71} +(6.04508 + 4.39201i) q^{72} +(-1.76393 + 5.42882i) q^{73} +(5.04508 + 15.5272i) q^{74} +(-3.73607 + 2.71441i) q^{75} +28.4164 q^{76} +0.618034 q^{78} +(-8.89919 + 6.46564i) q^{79} +(-1.88197 - 5.79210i) q^{80} +(0.309017 - 0.951057i) q^{81} +(0.500000 + 0.363271i) q^{82} +(-1.19098 - 0.865300i) q^{83} +(1.50000 - 4.61653i) q^{84} +(0.218847 + 0.673542i) q^{85} +(-14.2082 + 10.3229i) q^{86} +6.00000 q^{87} -8.23607 q^{89} +(-1.30902 + 0.951057i) q^{90} +(-0.0729490 - 0.224514i) q^{91} +(0.354102 - 1.08981i) q^{92} +(-4.92705 - 3.57971i) q^{93} +(-21.3713 - 15.5272i) q^{94} +(-1.11803 + 3.44095i) q^{95} +(3.35410 + 10.3229i) q^{96} +(-6.35410 + 4.61653i) q^{97} +15.7082 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + q^{3} + 6 q^{4} + 2 q^{5} - 4 q^{6} + q^{7} - 7 q^{8} - q^{9} + 2 q^{10} - 6 q^{12} - 3 q^{13} + q^{14} + 3 q^{15} - 14 q^{16} - 3 q^{17} - q^{18} + 5 q^{19} + 3 q^{20} + 4 q^{21} - 8 q^{23}+ \cdots + 36 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + q^3 + 6 * q^4 + 2 * q^5 - 4 * q^6 + q^7 - 7 * q^8 - q^9 + 2 * q^10 - 6 * q^12 - 3 * q^13 + q^14 + 3 * q^15 - 14 * q^16 - 3 * q^17 - q^18 + 5 * q^19 + 3 * q^20 + 4 * q^21 - 8 * q^23 - 13 * q^24 + q^25 - 3 * q^26 + q^27 + 9 * q^28 + 6 * q^29 - 2 * q^30 + 13 * q^31 - 30 * q^32 + 12 * q^34 - 2 * q^35 + 6 * q^36 - q^37 + 25 * q^38 + 3 * q^39 - q^40 + 7 * q^41 + 4 * q^42 + 2 * q^45 + 2 * q^46 - 8 * q^47 - q^48 + 6 * q^49 - 19 * q^50 - 12 * q^51 - 12 * q^52 - q^53 + 6 * q^54 + 12 * q^56 + 10 * q^57 + 6 * q^58 - 11 * q^59 - 3 * q^60 + 24 * q^61 + 13 * q^62 + q^63 - 17 * q^64 - 14 * q^65 - 6 * q^67 + 18 * q^68 - 7 * q^69 - 2 * q^70 - 20 * q^71 + 13 * q^72 - 16 * q^73 + 9 * q^74 - 6 * q^75 + 60 * q^76 - 2 * q^78 - 11 * q^79 - 12 * q^80 - q^81 + 2 * q^82 - 7 * q^83 + 6 * q^84 + 21 * q^85 - 30 * q^86 + 24 * q^87 - 24 * q^89 - 3 * q^90 - 7 * q^91 - 12 * q^92 - 13 * q^93 - 43 * q^94 - 12 * q^97 + 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	2.11803	−	1.53884i	1.49768	−	1.08813i	0.526381	−	0.850249i	$-0.323549\pi$
$2$	2.11803	−	1.53884i	1.49768	−	1.08813i	0.971295	−	0.237877i	$-0.0764514\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	1.50000	−	4.61653i	0.750000	−	2.30826i
$5$	0.500000	+	0.363271i	0.223607	+	0.162460i	0.693949	−	0.720024i	$-0.255869\pi$
$5$	0.500000	+	0.363271i	0.223607	+	0.162460i	−0.470342	+	0.882484i	$0.655869\pi$
$6$	−2.11803	−	1.53884i	−0.864684	−	0.628230i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i	−0.992318	−	0.123716i	$-0.960519\pi$
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i	0.875520	+	0.483181i	$0.160519\pi$
$8$	−2.30902	−	7.10642i	−0.816361	−	2.51250i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	1.61803			0.511667
$11$		0			0
$11$		0			0
$12$	−4.85410			−1.40126
$13$	−0.190983	+	0.138757i	−0.0529692	+	0.0384843i	−0.613955	−	0.789341i	$-0.710422\pi$
$13$	−0.190983	+	0.138757i	−0.0529692	+	0.0384843i	0.560986	+	0.827826i	$0.310422\pi$
$14$	0.809017	+	2.48990i	0.216219	+	0.665453i
$15$	0.190983	−	0.587785i	0.0493116	−	0.151765i
$16$	−7.97214	−	5.79210i	−1.99303	−	1.44802i
$17$	0.927051	+	0.673542i	0.224843	+	0.163358i	0.694504	−	0.719489i	$-0.255624\pi$
$17$	0.927051	+	0.673542i	0.224843	+	0.163358i	−0.469661	+	0.882847i	$0.655624\pi$
$18$	−0.809017	+	2.48990i	−0.190687	+	0.586875i
$19$	1.80902	+	5.56758i	0.415017	+	1.27729i	0.912236	+	0.409666i	$0.134355\pi$
$19$	1.80902	+	5.56758i	0.415017	+	1.27729i	−0.497219	+	0.867625i	$0.665645\pi$
$20$	2.42705	−	1.76336i	0.542705	−	0.394298i
$21$	1.00000			0.218218
$22$		0			0
$23$	0.236068			0.0492236			0.0246118	−	0.999697i	$-0.492165\pi$
$23$	0.236068			0.0492236			0.0246118	+	0.999697i	$0.492165\pi$
$24$	−6.04508	+	4.39201i	−1.23395	+	0.896516i
$25$	−1.42705	−	4.39201i	−0.285410	−	0.878402i
$26$	−0.190983	+	0.587785i	−0.0374548	+	0.115274i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	3.92705	+	2.85317i	0.742143	+	0.539198i
$29$	−1.85410	+	5.70634i	−0.344298	+	1.05964i	0.617660	+	0.786445i	$0.288081\pi$
$29$	−1.85410	+	5.70634i	−0.344298	+	1.05964i	−0.961958	+	0.273196i	$0.911919\pi$
$30$	−0.500000	−	1.53884i	−0.0912871	−	0.280953i
$31$	4.92705	−	3.57971i	0.884924	−	0.642935i	−0.0496252	−	0.998768i	$-0.515803\pi$
$31$	4.92705	−	3.57971i	0.884924	−	0.642935i	0.934550	+	0.355833i	$0.115803\pi$
$32$	−10.8541			−1.91875
$33$		0			0
$34$	3.00000			0.514496
$35$	−0.500000	+	0.363271i	−0.0845154	+	0.0614041i
$36$	1.50000	+	4.61653i	0.250000	+	0.769421i
$37$	−1.92705	+	5.93085i	−0.316805	+	0.975026i	0.658200	+	0.752843i	$0.271318\pi$
$37$	−1.92705	+	5.93085i	−0.316805	+	0.975026i	−0.975005	+	0.222183i	$0.928682\pi$
$38$	12.3992	+	9.00854i	2.01141	+	1.46138i
$39$	0.190983	+	0.138757i	0.0305818	+	0.0222189i
$40$	1.42705	−	4.39201i	0.225637	−	0.694438i
$41$	0.0729490	+	0.224514i	0.0113927	+	0.0350632i	0.956591	−	0.291433i	$-0.0941320\pi$
$41$	0.0729490	+	0.224514i	0.0113927	+	0.0350632i	−0.945199	+	0.326496i	$0.894132\pi$
$42$	2.11803	−	1.53884i	0.326820	−	0.237448i
$43$	−6.70820			−1.02299			−0.511496	−	0.859286i	$-0.670908\pi$
$43$	−6.70820			−1.02299			−0.511496	+	0.859286i	$0.670908\pi$
$44$		0			0
$45$	−0.618034			−0.0921311
$46$	0.500000	−	0.363271i	0.0737210	−	0.0535614i
$47$	−3.11803	−	9.59632i	−0.454812	−	1.39977i	−0.871356	−	0.490652i	$-0.836759\pi$
$47$	−3.11803	−	9.59632i	−0.454812	−	1.39977i	0.416544	−	0.909116i	$-0.363241\pi$
$48$	−3.04508	+	9.37181i	−0.439520	+	1.35270i
$49$	4.85410	+	3.52671i	0.693443	+	0.503816i
$50$	−9.78115	−	7.10642i	−1.38326	−	1.00500i
$51$	0.354102	−	1.08981i	0.0495842	−	0.152604i
$52$	0.354102	+	1.08981i	0.0491051	+	0.151130i
$53$	0.309017	−	0.224514i	0.0424467	−	0.0308394i	−0.566360	−	0.824158i	$-0.691649\pi$
$53$	0.309017	−	0.224514i	0.0424467	−	0.0308394i	0.608806	+	0.793319i	$0.291649\pi$
$54$	2.61803			0.356269
$55$		0			0
$56$	7.47214			0.998506
$57$	4.73607	−	3.44095i	0.627308	−	0.455766i
$58$	4.85410	+	14.9394i	0.637375	+	1.96164i
$59$	2.28115	−	7.02067i	0.296981	−	0.914013i	−0.685568	−	0.728009i	$-0.740446\pi$
$59$	2.28115	−	7.02067i	0.296981	−	0.914013i	0.982549	−	0.186004i	$-0.0595539\pi$
$60$	−2.42705	−	1.76336i	−0.313331	−	0.227648i
$61$	9.35410	+	6.79615i	1.19767	+	0.870158i	0.994054	−	0.108893i	$-0.0347304\pi$
$61$	9.35410	+	6.79615i	1.19767	+	0.870158i	0.203617	+	0.979051i	$0.434730\pi$
$62$	4.92705	−	15.1639i	0.625736	−	1.92582i
$63$	−0.309017	−	0.951057i	−0.0389325	−	0.119822i
$64$	−7.04508	+	5.11855i	−0.880636	+	0.639819i
$65$	−0.145898			−0.0180964
$66$		0			0
$67$	1.85410			0.226515			0.113257	−	0.993566i	$-0.463872\pi$
$67$	1.85410			0.226515			0.113257	+	0.993566i	$0.463872\pi$
$68$	4.50000	−	3.26944i	0.545705	−	0.396478i
$69$	−0.0729490	−	0.224514i	−0.00878203	−	0.0270283i
$70$	−0.500000	+	1.53884i	−0.0597614	+	0.183927i
$71$	−8.35410	−	6.06961i	−0.991449	−	0.720330i	−0.0312115	−	0.999513i	$-0.509937\pi$
$71$	−8.35410	−	6.06961i	−0.991449	−	0.720330i	−0.960238	+	0.279183i	$0.909937\pi$
$72$	6.04508	+	4.39201i	0.712420	+	0.517603i
$73$	−1.76393	+	5.42882i	−0.206453	+	0.635396i	0.793198	+	0.608964i	$0.208415\pi$
$73$	−1.76393	+	5.42882i	−0.206453	+	0.635396i	−0.999651	+	0.0264320i	$0.991585\pi$
$74$	5.04508	+	15.5272i	0.586479	+	1.80500i
$75$	−3.73607	+	2.71441i	−0.431404	+	0.313433i
$76$	28.4164			3.25959
$77$		0			0
$78$	0.618034			0.0699786
$79$	−8.89919	+	6.46564i	−1.00124	+	0.727441i	−0.962353	−	0.271803i	$-0.912380\pi$
$79$	−8.89919	+	6.46564i	−1.00124	+	0.727441i	−0.0388837	+	0.999244i	$0.512380\pi$
$80$	−1.88197	−	5.79210i	−0.210410	−	0.647576i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	0.500000	+	0.363271i	0.0552158	+	0.0401166i
$83$	−1.19098	−	0.865300i	−0.130727	−	0.0949790i	0.520500	−	0.853862i	$-0.325746\pi$
$83$	−1.19098	−	0.865300i	−0.130727	−	0.0949790i	−0.651227	+	0.758883i	$0.725746\pi$
$84$	1.50000	−	4.61653i	0.163663	−	0.503704i
$85$	0.218847	+	0.673542i	0.0237373	+	0.0730559i
$86$	−14.2082	+	10.3229i	−1.53211	+	1.11314i
$87$	6.00000			0.643268
$88$		0			0
$89$	−8.23607			−0.873021			−0.436511	−	0.899699i	$-0.643786\pi$
$89$	−8.23607			−0.873021			−0.436511	+	0.899699i	$0.643786\pi$
$90$	−1.30902	+	0.951057i	−0.137983	+	0.100250i
$91$	−0.0729490	−	0.224514i	−0.00764713	−	0.0235355i
$92$	0.354102	−	1.08981i	0.0369177	−	0.113621i
$93$	−4.92705	−	3.57971i	−0.510911	−	0.371199i
$94$	−21.3713	−	15.5272i	−2.20428	−	1.60151i
$95$	−1.11803	+	3.44095i	−0.114708	+	0.353035i
$96$	3.35410	+	10.3229i	0.342327	+	1.05357i
$97$	−6.35410	+	4.61653i	−0.645161	+	0.468737i	−0.861620	−	0.507555i	$-0.830549\pi$
$97$	−6.35410	+	4.61653i	−0.645161	+	0.468737i	0.216458	+	0.976292i	$0.430549\pi$
$98$	15.7082			1.58677
$99$		0			0
$100$	−22.4164			−2.24164
$101$	8.28115	−	6.01661i	0.824006	−	0.598675i	−0.0938515	−	0.995586i	$-0.529918\pi$
$101$	8.28115	−	6.01661i	0.824006	−	0.598675i	0.917857	+	0.396911i	$0.129918\pi$
$102$	−0.927051	−	2.85317i	−0.0917917	−	0.282506i
$103$	−3.38197	+	10.4086i	−0.333235	+	1.02559i	0.634350	+	0.773046i	$0.281268\pi$
$103$	−3.38197	+	10.4086i	−0.333235	+	1.02559i	−0.967585	+	0.252546i	$0.918732\pi$
$104$	1.42705	+	1.03681i	0.139934	+	0.101668i
$105$	0.500000	+	0.363271i	0.0487950	+	0.0354516i
$106$	0.309017	−	0.951057i	0.0300144	−	0.0923748i
$107$	−3.54508	−	10.9106i	−0.342716	−	1.05477i	−0.962795	−	0.270233i	$-0.912899\pi$
$107$	−3.54508	−	10.9106i	−0.342716	−	1.05477i	0.620079	−	0.784540i	$-0.287101\pi$
$108$	3.92705	−	2.85317i	0.377881	−	0.274546i
$109$	−12.0000			−1.14939			−0.574696	−	0.818367i	$-0.694880\pi$
$109$	−12.0000			−1.14939			−0.574696	+	0.818367i	$0.694880\pi$
$110$		0			0
$111$	6.23607			0.591901
$112$	7.97214	−	5.79210i	0.753296	−	0.547302i
$113$	4.16312	+	12.8128i	0.391633	+	1.20532i	0.931553	+	0.363607i	$0.118455\pi$
$113$	4.16312	+	12.8128i	0.391633	+	1.20532i	−0.539919	+	0.841717i	$0.681545\pi$
$114$	4.73607	−	14.5761i	0.443573	−	1.36518i
$115$	0.118034	+	0.0857567i	0.0110067	+	0.00799685i
$116$	23.5623	+	17.1190i	2.18771	+	1.58946i
$117$	0.0729490	−	0.224514i	0.00674414	−	0.0207563i
$118$	−5.97214	−	18.3803i	−0.549780	−	1.69205i
$119$	−0.927051	+	0.673542i	−0.0849826	+	0.0617435i
$120$	−4.61803			−0.421567
$121$		0			0
$122$	30.2705			2.74056
$123$	0.190983	−	0.138757i	0.0172204	−	0.0125113i
$124$	−9.13525	−	28.1154i	−0.820370	−	2.52484i
$125$	1.83688	−	5.65334i	0.164296	−	0.505650i
$126$	−2.11803	−	1.53884i	−0.188689	−	0.137091i
$127$	−6.23607	−	4.53077i	−0.553362	−	0.402041i	0.275662	−	0.961255i	$-0.411103\pi$
$127$	−6.23607	−	4.53077i	−0.553362	−	0.402041i	−0.829023	+	0.559214i	$0.811103\pi$
$128$	−0.336881	+	1.03681i	−0.0297764	+	0.0916422i
$129$	2.07295	+	6.37988i	0.182513	+	0.561717i
$130$	−0.309017	+	0.224514i	−0.0271026	+	0.0196912i
$131$	−11.7984			−1.03083			−0.515414	−	0.856941i	$-0.672362\pi$
$131$	−11.7984			−1.03083			−0.515414	+	0.856941i	$0.672362\pi$
$132$		0			0
$133$	−5.85410			−0.507615
$134$	3.92705	−	2.85317i	0.339246	−	0.246476i
$135$	0.190983	+	0.587785i	0.0164372	+	0.0505885i
$136$	2.64590	−	8.14324i	0.226884	−	0.698277i
$137$	−7.89919	−	5.73910i	−0.674873	−	0.490324i	0.196780	−	0.980448i	$-0.436952\pi$
$137$	−7.89919	−	5.73910i	−0.674873	−	0.490324i	−0.871653	+	0.490124i	$0.836952\pi$
$138$	−0.500000	−	0.363271i	−0.0425628	−	0.0309237i
$139$	4.50000	−	13.8496i	0.381685	−	1.17471i	−0.557172	−	0.830397i	$-0.688113\pi$
$139$	4.50000	−	13.8496i	0.381685	−	1.17471i	0.938857	−	0.344308i	$-0.111887\pi$
$140$	0.927051	+	2.85317i	0.0783501	+	0.241137i
$141$	−8.16312	+	5.93085i	−0.687459	+	0.499468i
$142$	−27.0344			−2.26868
$143$		0			0
$144$	9.85410			0.821175
$145$	−3.00000	+	2.17963i	−0.249136	+	0.181008i
$146$	4.61803	+	14.2128i	0.382191	+	1.17626i
$147$	1.85410	−	5.70634i	0.152924	−	0.470651i
$148$	24.4894	+	17.7926i	2.01301	+	1.46254i
$149$	3.42705	+	2.48990i	0.280755	+	0.203980i	0.719247	−	0.694755i	$-0.244487\pi$
$149$	3.42705	+	2.48990i	0.280755	+	0.203980i	−0.438492	+	0.898735i	$0.644487\pi$
$150$	−3.73607	+	11.4984i	−0.305049	+	0.938843i
$151$	0.326238	+	1.00406i	0.0265489	+	0.0817090i	0.963453	−	0.267877i	$-0.0863222\pi$
$151$	0.326238	+	1.00406i	0.0265489	+	0.0817090i	−0.936904	+	0.349586i	$0.886322\pi$
$152$	35.3885	−	25.7113i	2.87039	−	2.08546i
$153$	−1.14590			−0.0926404
$154$		0			0
$155$	3.76393			0.302326
$156$	0.927051	−	0.673542i	0.0742235	−	0.0539265i
$157$	4.85410	+	14.9394i	0.387400	+	1.19229i	0.934725	+	0.355373i	$0.115646\pi$
$157$	4.85410	+	14.9394i	0.387400	+	1.19229i	−0.547325	+	0.836920i	$0.684354\pi$
$158$	−8.89919	+	27.3889i	−0.707981	+	2.17894i
$159$	−0.309017	−	0.224514i	−0.0245066	−	0.0178051i
$160$	−5.42705	−	3.94298i	−0.429046	−	0.311720i
$161$	−0.0729490	+	0.224514i	−0.00574919	+	0.0176942i
$162$	−0.809017	−	2.48990i	−0.0635624	−	0.195625i
$163$	4.16312	−	3.02468i	0.326081	−	0.236911i	−0.412685	−	0.910874i	$-0.635409\pi$
$163$	4.16312	−	3.02468i	0.326081	−	0.236911i	0.738766	+	0.673962i	$0.235409\pi$
$164$	1.14590			0.0894796
$165$		0			0
$166$	−3.85410			−0.299136
$167$	−9.73607	+	7.07367i	−0.753400	+	0.547377i	−0.896879	−	0.442277i	$-0.854171\pi$
$167$	−9.73607	+	7.07367i	−0.753400	+	0.547377i	0.143479	+	0.989653i	$0.454171\pi$
$168$	−2.30902	−	7.10642i	−0.178145	−	0.548272i
$169$	−4.00000	+	12.3107i	−0.307692	+	0.946980i
$170$	1.50000	+	1.08981i	0.115045	+	0.0835849i
$171$	−4.73607	−	3.44095i	−0.362176	−	0.263136i
$172$	−10.0623	+	30.9686i	−0.767244	+	2.36133i
$173$	−5.57295	−	17.1518i	−0.423703	−	1.30403i	−0.904230	−	0.427045i	$-0.859555\pi$
$173$	−5.57295	−	17.1518i	−0.423703	−	1.30403i	0.480527	−	0.876980i	$-0.340445\pi$
$174$	12.7082	−	9.23305i	0.963406	−	0.699956i
$175$	4.61803			0.349091
$176$		0			0
$177$	−7.38197			−0.554863
$178$	−17.4443	+	12.6740i	−1.30750	+	0.949957i
$179$	−2.63525	−	8.11048i	−0.196968	−	0.606206i	−0.999948	−	0.0101995i	$-0.996753\pi$
$179$	−2.63525	−	8.11048i	−0.196968	−	0.606206i	0.802980	−	0.596006i	$-0.203247\pi$
$180$	−0.927051	+	2.85317i	−0.0690983	+	0.212663i
$181$	−2.04508	−	1.48584i	−0.152010	−	0.110442i	0.509181	−	0.860660i	$-0.329949\pi$
$181$	−2.04508	−	1.48584i	−0.152010	−	0.110442i	−0.661191	+	0.750218i	$0.729949\pi$
$182$	−0.500000	−	0.363271i	−0.0370625	−	0.0269275i
$183$	3.57295	−	10.9964i	0.264120	−	0.812878i
$184$	−0.545085	−	1.67760i	−0.0401842	−	0.123674i
$185$	−3.11803	+	2.26538i	−0.229242	+	0.166554i
$186$	−15.9443			−1.16909
$187$		0			0
$188$	−48.9787			−3.57214
$189$	−0.809017	+	0.587785i	−0.0588473	+	0.0427551i
$190$	2.92705	+	9.00854i	0.212351	+	0.653548i
$191$	−0.253289	+	0.779543i	−0.0183273	+	0.0564058i	−0.959802	−	0.280678i	$-0.909441\pi$
$191$	−0.253289	+	0.779543i	−0.0183273	+	0.0564058i	0.941475	+	0.337084i	$0.109441\pi$
$192$	7.04508	+	5.11855i	0.508435	+	0.369400i
$193$	2.54508	+	1.84911i	0.183199	+	0.133102i	0.675605	−	0.737264i	$-0.263882\pi$
$193$	2.54508	+	1.84911i	0.183199	+	0.133102i	−0.492406	+	0.870366i	$0.663882\pi$
$194$	−6.35410	+	19.5559i	−0.456198	+	1.40403i
$195$	0.0450850	+	0.138757i	0.00322860	+	0.00993661i
$196$	23.5623	−	17.1190i	1.68302	−	1.22279i
$197$	13.0344			0.928666			0.464333	−	0.885661i	$-0.346294\pi$
$197$	13.0344			0.928666			0.464333	+	0.885661i	$0.346294\pi$
$198$		0			0
$199$	6.70820			0.475532			0.237766	−	0.971322i	$-0.423585\pi$
$199$	6.70820			0.475532			0.237766	+	0.971322i	$0.423585\pi$
$200$	−27.9164	+	20.2825i	−1.97399	+	1.43419i
$201$	−0.572949	−	1.76336i	−0.0404127	−	0.124378i
$202$	8.28115	−	25.4868i	0.582660	−	1.79324i
$203$	−4.85410	−	3.52671i	−0.340691	−	0.247527i
$204$	−4.50000	−	3.26944i	−0.315063	−	0.228907i
$205$	−0.0450850	+	0.138757i	−0.00314887	+	0.00969123i
$206$	8.85410	+	27.2501i	0.616895	+	1.89861i
$207$	−0.190983	+	0.138757i	−0.0132742	+	0.00964430i
$208$	2.32624			0.161296
$209$		0			0
$210$	1.61803			0.111655
$211$	−2.92705	+	2.12663i	−0.201506	+	0.146403i	−0.683963	−	0.729517i	$-0.739745\pi$
$211$	−2.92705	+	2.12663i	−0.201506	+	0.146403i	0.482456	+	0.875920i	$0.339745\pi$
$212$	−0.572949	−	1.76336i	−0.0393503	−	0.121108i
$213$	−3.19098	+	9.82084i	−0.218643	+	0.672913i
$214$	−24.2984	−	17.6538i	−1.66100	−	1.20679i
$215$	−3.35410	−	2.43690i	−0.228748	−	0.166195i
$216$	2.30902	−	7.10642i	0.157109	−	0.483531i
$217$	1.88197	+	5.79210i	0.127756	+	0.393193i
$218$	−25.4164	+	18.4661i	−1.72142	+	1.25068i
$219$	5.70820			0.385725
$220$		0			0
$221$	−0.270510			−0.0181965
$222$	13.2082	−	9.59632i	0.886477	−	0.644063i
$223$	2.21885	+	6.82891i	0.148585	+	0.457298i	0.997455	−	0.0713048i	$-0.0227163\pi$
$223$	2.21885	+	6.82891i	0.148585	+	0.457298i	−0.848870	+	0.528602i	$0.822716\pi$
$224$	3.35410	−	10.3229i	0.224105	−	0.689725i
$225$	3.73607	+	2.71441i	0.249071	+	0.180961i
$226$	28.5344	+	20.7315i	1.89808	+	1.37904i
$227$	4.07295	−	12.5352i	0.270331	−	0.831994i	−0.720086	−	0.693885i	$-0.755898\pi$
$227$	4.07295	−	12.5352i	0.270331	−	0.831994i	0.990417	−	0.138109i	$-0.0441024\pi$
$228$	−8.78115	−	27.0256i	−0.581546	−	1.78981i
$229$	−0.381966	+	0.277515i	−0.0252410	+	0.0183387i	−0.600334	−	0.799749i	$-0.704966\pi$
$229$	−0.381966	+	0.277515i	−0.0252410	+	0.0183387i	0.575093	+	0.818088i	$0.304966\pi$
$230$	0.381966			0.0251861
$231$		0			0
$232$	44.8328			2.94342
$233$	3.35410	−	2.43690i	0.219735	−	0.159646i	−0.472473	−	0.881345i	$-0.656638\pi$
$233$	3.35410	−	2.43690i	0.219735	−	0.159646i	0.692207	+	0.721699i	$0.256638\pi$
$234$	−0.190983	−	0.587785i	−0.0124849	−	0.0384247i
$235$	1.92705	−	5.93085i	0.125707	−	0.386886i
$236$	−28.9894	−	21.0620i	−1.88705	−	1.37102i
$237$	8.89919	+	6.46564i	0.578064	+	0.419988i
$238$	−0.927051	+	2.85317i	−0.0600918	+	0.184944i
$239$	0.118034	+	0.363271i	0.00763498	+	0.0234981i	0.954801	−	0.297244i	$-0.0960676\pi$
$239$	0.118034	+	0.363271i	0.00763498	+	0.0234981i	−0.947166	+	0.320742i	$0.896068\pi$
$240$	−4.92705	+	3.57971i	−0.318040	+	0.231069i
$241$	8.29180			0.534122			0.267061	−	0.963680i	$-0.413948\pi$
$241$	8.29180			0.534122			0.267061	+	0.963680i	$0.413948\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$	45.4058	−	32.9892i	2.90681	−	2.11192i
$245$	1.14590	+	3.52671i	0.0732087	+	0.225313i
$246$	0.190983	−	0.587785i	0.0121766	−	0.0374758i
$247$	−1.11803	−	0.812299i	−0.0711388	−	0.0516854i
$248$	−36.8156	−	26.7481i	−2.33779	−	1.69851i
$249$	−0.454915	+	1.40008i	−0.0288291	+	0.0887267i
$250$	−4.80902	−	14.8006i	−0.304149	−	0.936074i
$251$	17.7812	−	12.9188i	1.12234	−	0.815425i	0.137775	−	0.990464i	$-0.456005\pi$
$251$	17.7812	−	12.9188i	1.12234	−	0.815425i	0.984562	+	0.175038i	$0.0560050\pi$
$252$	−4.85410			−0.305780
$253$		0			0
$254$	−20.1803			−1.26623
$255$	0.572949	−	0.416272i	0.0358795	−	0.0260680i
$256$	−4.50000	−	13.8496i	−0.281250	−	0.865598i
$257$	9.19098	−	28.2869i	0.573318	−	1.76449i	−0.0685195	−	0.997650i	$-0.521828\pi$
$257$	9.19098	−	28.2869i	0.573318	−	1.76449i	0.641837	−	0.766841i	$-0.278172\pi$
$258$	14.2082	+	10.3229i	0.884564	+	0.642673i
$259$	−5.04508	−	3.66547i	−0.313486	−	0.227761i
$260$	−0.218847	+	0.673542i	−0.0135723	+	0.0417713i
$261$	−1.85410	−	5.70634i	−0.114766	−	0.353214i
$262$	−24.9894	+	18.1558i	−1.54385	+	1.12167i
$263$	−15.2705			−0.941620			−0.470810	−	0.882235i	$-0.656038\pi$
$263$	−15.2705			−0.941620			−0.470810	+	0.882235i	$0.656038\pi$
$264$		0			0
$265$	0.236068			0.0145015
$266$	−12.3992	+	9.00854i	−0.760243	+	0.552349i
$267$	2.54508	+	7.83297i	0.155757	+	0.479370i
$268$	2.78115	−	8.55951i	0.169886	−	0.522855i
$269$	20.5623	+	14.9394i	1.25371	+	0.910871i	0.998431	−	0.0559978i	$-0.0178340\pi$
$269$	20.5623	+	14.9394i	1.25371	+	0.910871i	0.255275	+	0.966868i	$0.417834\pi$
$270$	1.30902	+	0.951057i	0.0796642	+	0.0578795i
$271$	5.75329	−	17.7068i	0.349487	−	1.07561i	−0.609650	−	0.792671i	$-0.708690\pi$
$271$	5.75329	−	17.7068i	0.349487	−	1.07561i	0.959137	−	0.282941i	$-0.0913100\pi$
$272$	−3.48936	−	10.7391i	−0.211573	−	0.651156i
$273$	−0.190983	+	0.138757i	−0.0115588	+	0.00839797i
$274$	−25.5623			−1.54428
$275$		0			0
$276$	−1.14590			−0.0689750
$277$	23.6353	−	17.1720i	1.42010	−	1.03177i	0.428351	−	0.903613i	$-0.359095\pi$
$277$	23.6353	−	17.1720i	1.42010	−	1.03177i	0.991754	−	0.128154i	$-0.0409051\pi$
$278$	−11.7812	−	36.2587i	−0.706587	−	2.17465i
$279$	−1.88197	+	5.79210i	−0.112670	+	0.346764i
$280$	3.73607	+	2.71441i	0.223273	+	0.162217i
$281$	−20.0344	−	14.5559i	−1.19515	−	0.868331i	−0.201355	−	0.979518i	$-0.564535\pi$
$281$	−20.0344	−	14.5559i	−1.19515	−	0.868331i	−0.993799	+	0.111188i	$0.964535\pi$
$282$	−8.16312	+	25.1235i	−0.486107	+	1.49608i
$283$	−1.76393	−	5.42882i	−0.104855	−	0.322710i	0.884841	−	0.465892i	$-0.154267\pi$
$283$	−1.76393	−	5.42882i	−0.104855	−	0.322710i	−0.989696	+	0.143182i	$0.954267\pi$
$284$	−40.5517	+	29.4625i	−2.40630	+	1.74828i
$285$	3.61803			0.214314
$286$		0			0
$287$	−0.236068			−0.0139347
$288$	8.78115	−	6.37988i	0.517434	−	0.375938i
$289$	−4.84752	−	14.9191i	−0.285148	−	0.877597i
$290$	−3.00000	+	9.23305i	−0.176166	+	0.542183i
$291$	6.35410	+	4.61653i	0.372484	+	0.270626i
$292$	22.4164	+	16.2865i	1.31182	+	0.953094i
$293$	−6.69098	+	20.5927i	−0.390891	+	1.20304i	0.541224	+	0.840878i	$0.317961\pi$
$293$	−6.69098	+	20.5927i	−0.390891	+	1.20304i	−0.932115	+	0.362162i	$0.882039\pi$
$294$	−4.85410	−	14.9394i	−0.283097	−	0.871283i
$295$	3.69098	−	2.68166i	0.214897	−	0.156132i
$296$	46.5967			2.70838
$297$		0			0
$298$	11.0902			0.642436
$299$	−0.0450850	+	0.0327561i	−0.00260733	+	0.00189434i
$300$	6.92705	+	21.3193i	0.399933	+	1.23087i
$301$	2.07295	−	6.37988i	0.119483	−	0.367730i
$302$	2.23607	+	1.62460i	0.128671	+	0.0934851i
$303$	−8.28115	−	6.01661i	−0.475740	−	0.345645i
$304$	17.8262	−	54.8635i	1.02240	−	3.14664i
$305$	2.20820	+	6.79615i	0.126441	+	0.389147i
$306$	−2.42705	+	1.76336i	−0.138745	+	0.100804i
$307$	27.9787			1.59683			0.798415	−	0.602108i	$-0.205672\pi$
$307$	27.9787			1.59683			0.798415	+	0.602108i	$0.205672\pi$
$308$		0			0
$309$	10.9443			0.622598
$310$	7.97214	−	5.79210i	0.452787	−	0.328969i
$311$	3.60081	+	11.0822i	0.204183	+	0.628412i	0.999746	+	0.0225404i	$0.00717543\pi$
$311$	3.60081	+	11.0822i	0.204183	+	0.628412i	−0.795563	+	0.605871i	$0.792825\pi$
$312$	0.545085	−	1.67760i	0.0308594	−	0.0949753i
$313$	2.04508	+	1.48584i	0.115595	+	0.0839847i	0.644081	−	0.764957i	$-0.277240\pi$
$313$	2.04508	+	1.48584i	0.115595	+	0.0839847i	−0.528486	+	0.848942i	$0.677240\pi$
$314$	33.2705	+	24.1724i	1.87756	+	1.36413i
$315$	0.190983	−	0.587785i	0.0107607	−	0.0331179i
$316$	16.5000	+	50.7818i	0.928198	+	2.85670i
$317$	5.51722	−	4.00850i	0.309878	−	0.225140i	−0.421966	−	0.906612i	$-0.638660\pi$
$317$	5.51722	−	4.00850i	0.309878	−	0.225140i	0.731844	+	0.681472i	$0.238660\pi$
$318$	−1.00000			−0.0560772
$319$		0			0
$320$	−5.38197			−0.300861
$321$	−9.28115	+	6.74315i	−0.518023	+	0.376366i
$322$	0.190983	+	0.587785i	0.0106431	+	0.0327560i
$323$	−2.07295	+	6.37988i	−0.115342	+	0.354986i
$324$	−3.92705	−	2.85317i	−0.218169	−	0.158509i
$325$	0.881966	+	0.640786i	0.0489227	+	0.0355444i
$326$	4.16312	−	12.8128i	0.230574	−	0.709633i
$327$	3.70820	+	11.4127i	0.205064	+	0.631123i
$328$	1.42705	−	1.03681i	0.0787957	−	0.0572484i
$329$	10.0902			0.556289
$330$		0			0
$331$	16.7082			0.918366			0.459183	−	0.888342i	$-0.348142\pi$
$331$	16.7082			0.918366			0.459183	+	0.888342i	$0.348142\pi$
$332$	−5.78115	+	4.20025i	−0.317282	+	0.230519i
$333$	−1.92705	−	5.93085i	−0.105602	−	0.325009i
$334$	−9.73607	+	29.9645i	−0.532734	+	1.63959i
$335$	0.927051	+	0.673542i	0.0506502	+	0.0367995i
$336$	−7.97214	−	5.79210i	−0.434916	−	0.315985i
$337$	−5.61803	+	17.2905i	−0.306034	+	0.941875i	0.673256	+	0.739410i	$0.264895\pi$
$337$	−5.61803	+	17.2905i	−0.306034	+	0.941875i	−0.979289	+	0.202465i	$0.935105\pi$
$338$	10.4721	+	32.2299i	0.569609	+	1.75308i
$339$	10.8992	−	7.91872i	0.591963	−	0.430086i
$340$	3.43769			0.186435
$341$		0			0
$342$	−15.3262			−0.828748
$343$	−10.5172	+	7.64121i	−0.567877	+	0.412586i
$344$	15.4894	+	47.6713i	0.835130	+	2.57027i
$345$	0.0450850	−	0.138757i	0.00242729	−	0.00747044i
$346$	−38.1976	−	27.7522i	−2.05351	−	1.49196i
$347$	1.23607	+	0.898056i	0.0663556	+	0.0482102i	0.620469	−	0.784231i	$-0.286942\pi$
$347$	1.23607	+	0.898056i	0.0663556	+	0.0482102i	−0.554113	+	0.832441i	$0.686942\pi$
$348$	9.00000	−	27.6992i	0.482451	−	1.48483i
$349$	3.92705	+	12.0862i	0.210210	+	0.646961i	0.999459	+	0.0328870i	$0.0104702\pi$
$349$	3.92705	+	12.0862i	0.210210	+	0.646961i	−0.789249	+	0.614073i	$0.789530\pi$
$350$	9.78115	−	7.10642i	0.522825	−	0.379854i
$351$	−0.236068			−0.0126004
$352$		0			0
$353$	−12.0000			−0.638696			−0.319348	−	0.947638i	$-0.603464\pi$
$353$	−12.0000			−0.638696			−0.319348	+	0.947638i	$0.603464\pi$
$354$	−15.6353	+	11.3597i	−0.831004	+	0.603760i
$355$	−1.97214	−	6.06961i	−0.104670	−	0.322141i
$356$	−12.3541	+	38.0220i	−0.654766	+	2.01516i
$357$	0.927051	+	0.673542i	0.0490647	+	0.0356476i
$358$	−18.0623	−	13.1230i	−0.954623	−	0.693574i
$359$	−3.00000	+	9.23305i	−0.158334	+	0.487302i	−0.998483	−	0.0550531i	$-0.982467\pi$
$359$	−3.00000	+	9.23305i	−0.158334	+	0.487302i	0.840149	+	0.542355i	$0.182467\pi$
$360$	1.42705	+	4.39201i	0.0752122	+	0.231479i
$361$	−12.3541	+	8.97578i	−0.650216	+	0.472409i
$362$	−6.61803			−0.347836
$363$		0			0
$364$	−1.14590			−0.0600614
$365$	−2.85410	+	2.07363i	−0.149391	+	0.108539i
$366$	−9.35410	−	28.7890i	−0.488947	−	1.50482i
$367$	6.84346	−	21.0620i	0.357226	−	1.09943i	−0.597482	−	0.801882i	$-0.703832\pi$
$367$	6.84346	−	21.0620i	0.357226	−	1.09943i	0.954708	−	0.297545i	$-0.0961679\pi$
$368$	−1.88197	−	1.36733i	−0.0981043	−	0.0712769i
$369$	−0.190983	−	0.138757i	−0.00994218	−	0.00722342i
$370$	−3.11803	+	9.59632i	−0.162099	+	0.498889i
$371$	0.118034	+	0.363271i	0.00612802	+	0.0188601i
$372$	−23.9164	+	17.3763i	−1.24001	+	0.900919i
$373$	0.888544			0.0460071			0.0230035	−	0.999735i	$-0.492677\pi$
$373$	0.888544			0.0460071			0.0230035	+	0.999735i	$0.492677\pi$
$374$		0			0
$375$	−5.94427			−0.306961
$376$	−60.9959	+	44.3161i	−3.14563	+	2.28543i
$377$	−0.437694	−	1.34708i	−0.0225424	−	0.0693784i
$378$	−0.809017	+	2.48990i	−0.0416113	+	0.128067i
$379$	20.1353	+	14.6291i	1.03428	+	0.751447i	0.969161	−	0.246430i	$-0.0792576\pi$
$379$	20.1353	+	14.6291i	1.03428	+	0.751447i	0.0651180	+	0.997878i	$0.479258\pi$
$380$	14.2082	+	10.3229i	0.728865	+	0.529552i
$381$	−2.38197	+	7.33094i	−0.122032	+	0.375575i
$382$	0.663119	+	2.04087i	0.0339281	+	0.104420i
$383$	10.2812	−	7.46969i	0.525342	−	0.381684i	−0.293270	−	0.956030i	$-0.594744\pi$
$383$	10.2812	−	7.46969i	0.525342	−	0.381684i	0.818613	+	0.574346i	$0.194744\pi$
$384$	1.09017			0.0556325
$385$		0			0
$386$	8.23607			0.419205
$387$	5.42705	−	3.94298i	0.275873	−	0.200433i
$388$	11.7812	+	36.2587i	0.598097	+	1.84075i
$389$	−11.3541	+	34.9443i	−0.575676	+	1.77175i	0.0581906	+	0.998305i	$0.481467\pi$
$389$	−11.3541	+	34.9443i	−0.575676	+	1.77175i	−0.633866	+	0.773443i	$0.718533\pi$
$390$	0.309017	+	0.224514i	0.0156477	+	0.0113687i
$391$	0.218847	+	0.159002i	0.0110676	+	0.00804106i
$392$	13.8541	−	42.6385i	0.699738	−	2.15357i
$393$	3.64590	+	11.2209i	0.183911	+	0.566021i
$394$	27.6074	−	20.0579i	1.39084	−	1.01050i
$395$	−6.79837			−0.342063
$396$		0			0
$397$	−18.7082			−0.938938			−0.469469	−	0.882949i	$-0.655555\pi$
$397$	−18.7082			−0.938938			−0.469469	+	0.882949i	$0.655555\pi$
$398$	14.2082	−	10.3229i	0.712193	−	0.517438i
$399$	1.80902	+	5.56758i	0.0905641	+	0.278728i
$400$	−14.0623	+	43.2793i	−0.703115	+	2.16397i
$401$	25.6353	+	18.6251i	1.28016	+	0.930093i	0.999558	−	0.0297299i	$-0.00946472\pi$
$401$	25.6353	+	18.6251i	1.28016	+	0.930093i	0.280606	+	0.959823i	$0.409465\pi$
$402$	−3.92705	−	2.85317i	−0.195864	−	0.142303i
$403$	−0.444272	+	1.36733i	−0.0221308	+	0.0681115i
$404$	−15.3541	−	47.2551i	−0.763895	−	2.35103i
$405$	0.500000	−	0.363271i	0.0248452	−	0.0180511i
$406$	−15.7082			−0.779585
$407$		0			0
$408$	−8.56231			−0.423897
$409$	5.23607	−	3.80423i	0.258907	−	0.188107i	−0.450758	−	0.892646i	$-0.648846\pi$
$409$	5.23607	−	3.80423i	0.258907	−	0.188107i	0.709665	+	0.704539i	$0.248846\pi$
$410$	0.118034	+	0.363271i	0.00582928	+	0.0179407i
$411$	−3.01722	+	9.28605i	−0.148829	+	0.458047i
$412$	42.9787	+	31.2259i	2.11741	+	1.53839i
$413$	5.97214	+	4.33901i	0.293870	+	0.213509i
$414$	−0.190983	+	0.587785i	−0.00938630	+	0.0288881i
$415$	−0.281153	−	0.865300i	−0.0138013	−	0.0424759i
$416$	2.07295	−	1.50609i	0.101635	−	0.0738419i
$417$	−14.5623			−0.713119
$418$		0			0
$419$	31.4508			1.53647			0.768237	−	0.640165i	$-0.221134\pi$
$419$	31.4508			1.53647			0.768237	+	0.640165i	$0.221134\pi$
$420$	2.42705	−	1.76336i	0.118428	−	0.0860430i
$421$	3.24671	+	9.99235i	0.158235	+	0.486997i	0.998474	−	0.0552185i	$-0.0175855\pi$
$421$	3.24671	+	9.99235i	0.158235	+	0.486997i	−0.840239	+	0.542216i	$0.817586\pi$
$422$	−2.92705	+	9.00854i	−0.142487	+	0.438529i
$423$	8.16312	+	5.93085i	0.396904	+	0.288368i
$424$	−2.30902	−	1.67760i	−0.112136	−	0.0814714i
$425$	1.63525	−	5.03280i	0.0793215	−	0.244127i
$426$	8.35410	+	25.7113i	0.404758	+	1.24572i
$427$	−9.35410	+	6.79615i	−0.452677	+	0.328889i
$428$	−55.6869			−2.69173
$429$		0			0
$430$	−10.8541			−0.523431
$431$	4.78115	−	3.47371i	0.230300	−	0.167323i	−0.466651	−	0.884442i	$-0.654540\pi$
$431$	4.78115	−	3.47371i	0.230300	−	0.167323i	0.696951	+	0.717119i	$0.254540\pi$
$432$	−3.04508	−	9.37181i	−0.146507	−	0.450901i
$433$	10.9098	−	33.5770i	0.524293	−	1.61361i	−0.241417	−	0.970422i	$-0.577612\pi$
$433$	10.9098	−	33.5770i	0.524293	−	1.61361i	0.765710	−	0.643186i	$-0.222388\pi$
$434$	12.8992	+	9.37181i	0.619181	+	0.449861i
$435$	3.00000	+	2.17963i	0.143839	+	0.104505i
$436$	−18.0000	+	55.3983i	−0.862044	+	2.65310i
$437$	0.427051	+	1.31433i	0.0204286	+	0.0628728i
$438$	12.0902	−	8.78402i	0.577691	−	0.419717i
$439$	23.2918			1.11166			0.555828	−	0.831297i	$-0.312401\pi$
$439$	23.2918			1.11166			0.555828	+	0.831297i	$0.312401\pi$
$440$		0			0
$441$	−6.00000			−0.285714
$442$	−0.572949	+	0.416272i	−0.0272524	+	0.0198000i
$443$	−9.76393	−	30.0503i	−0.463898	−	1.42773i	−0.860363	−	0.509682i	$-0.829763\pi$
$443$	−9.76393	−	30.0503i	−0.463898	−	1.42773i	0.396464	−	0.918050i	$-0.370237\pi$
$444$	9.35410	−	28.7890i	0.443926	−	1.36626i
$445$	−4.11803	−	2.99193i	−0.195214	−	0.141831i
$446$	15.2082	+	11.0494i	0.720129	+	0.523205i
$447$	1.30902	−	4.02874i	0.0619144	−	0.190553i
$448$	−2.69098	−	8.28199i	−0.127137	−	0.391287i
$449$	7.32624	−	5.32282i	0.345747	−	0.251200i	−0.401336	−	0.915931i	$-0.631454\pi$
$449$	7.32624	−	5.32282i	0.345747	−	0.251200i	0.747082	+	0.664731i	$0.231454\pi$
$450$	12.0902			0.569936
$451$		0			0
$452$	65.3951			3.07593
$453$	0.854102	−	0.620541i	0.0401292	−	0.0291556i
$454$	−10.6631	−	32.8177i	−0.500445	−	1.54021i
$455$	0.0450850	−	0.138757i	0.00211362	−	0.00650504i
$456$	−35.3885	−	25.7113i	−1.65722	−	1.20404i
$457$	−19.3992	−	14.0943i	−0.907456	−	0.659305i	0.0329144	−	0.999458i	$-0.489521\pi$
$457$	−19.3992	−	14.0943i	−0.907456	−	0.659305i	−0.940370	+	0.340153i	$0.889521\pi$
$458$	−0.381966	+	1.17557i	−0.0178481	+	0.0549308i
$459$	0.354102	+	1.08981i	0.0165281	+	0.0508682i
$460$	0.572949	−	0.416272i	0.0267139	−	0.0194088i
$461$	9.27051			0.431771			0.215885	−	0.976419i	$-0.430736\pi$
$461$	9.27051			0.431771			0.215885	+	0.976419i	$0.430736\pi$
$462$		0			0
$463$	1.72949			0.0803762			0.0401881	−	0.999192i	$-0.487204\pi$
$463$	1.72949			0.0803762			0.0401881	+	0.999192i	$0.487204\pi$
$464$	47.8328	−	34.7526i	2.22058	−	1.61335i
$465$	−1.16312	−	3.57971i	−0.0539384	−	0.166005i
$466$	3.35410	−	10.3229i	0.155376	−	0.478197i
$467$	−16.8992	−	12.2780i	−0.782001	−	0.568157i	0.123578	−	0.992335i	$-0.460563\pi$
$467$	−16.8992	−	12.2780i	−0.782001	−	0.568157i	−0.905579	+	0.424178i	$0.860563\pi$
$468$	−0.927051	−	0.673542i	−0.0428529	−	0.0311345i
$469$	−0.572949	+	1.76336i	−0.0264563	+	0.0814242i
$470$	−5.04508	−	15.5272i	−0.232712	−	0.716215i
$471$	12.7082	−	9.23305i	0.585563	−	0.425437i
$472$	−55.1591			−2.53890
$473$		0			0
$474$	28.7984			1.32275
$475$	21.8713	−	15.8904i	1.00353	−	0.729104i
$476$	1.71885	+	5.29007i	0.0787832	+	0.242470i
$477$	−0.118034	+	0.363271i	−0.00540441	+	0.0166330i
$478$	0.809017	+	0.587785i	0.0370036	+	0.0268847i
$479$	22.9615	+	16.6825i	1.04914	+	0.762243i	0.972048	−	0.234781i	$-0.0754374\pi$
$479$	22.9615	+	16.6825i	1.04914	+	0.762243i	0.0770892	+	0.997024i	$0.475437\pi$
$480$	−2.07295	+	6.37988i	−0.0946167	+	0.291200i
$481$	−0.454915	−	1.40008i	−0.0207423	−	0.0638384i
$482$	17.5623	−	12.7598i	0.799941	−	0.581191i
$483$	0.236068			0.0107415
$484$		0			0
$485$	−4.85410			−0.220413
$486$	−2.11803	+	1.53884i	−0.0960760	+	0.0698033i
$487$	−3.92705	−	12.0862i	−0.177952	−	0.547679i	0.821804	−	0.569770i	$-0.192968\pi$
$487$	−3.92705	−	12.0862i	−0.177952	−	0.547679i	−0.999756	+	0.0220909i	$0.992968\pi$
$488$	26.6976	−	82.1666i	1.20854	−	3.71951i
$489$	−4.16312	−	3.02468i	−0.188263	−	0.136781i
$490$	7.85410	+	5.70634i	0.354812	+	0.257786i
$491$	−5.53444	+	17.0333i	−0.249766	+	0.768700i	0.745050	+	0.667009i	$0.232426\pi$
$491$	−5.53444	+	17.0333i	−0.249766	+	0.768700i	−0.994816	+	0.101692i	$0.967574\pi$
$492$	−0.354102	−	1.08981i	−0.0159641	−	0.0491326i
$493$	−5.56231	+	4.04125i	−0.250514	+	0.182009i
$494$	−3.61803			−0.162783
$495$		0			0
$496$	−60.0132			−2.69467
$497$	8.35410	−	6.06961i	0.374733	−	0.272259i
$498$	1.19098	+	3.66547i	0.0533692	+	0.164254i
$499$	−5.60739	+	17.2578i	−0.251021	+	0.772564i	0.743566	+	0.668662i	$0.233133\pi$
$499$	−5.60739	+	17.2578i	−0.251021	+	0.772564i	−0.994588	+	0.103902i	$0.966867\pi$
$500$	−23.3435	−	16.9600i	−1.04395	−	0.758475i
$501$	9.73607	+	7.07367i	0.434975	+	0.316028i
$502$	17.7812	−	54.7248i	0.793612	−	2.44249i
$503$	2.67376	+	8.22899i	0.119217	+	0.366913i	0.992803	−	0.119757i	$-0.0382115\pi$
$503$	2.67376	+	8.22899i	0.119217	+	0.366913i	−0.873586	+	0.486670i	$0.838212\pi$
$504$	−6.04508	+	4.39201i	−0.269269	+	0.195636i
$505$	6.32624			0.281514
$506$		0			0
$507$	12.9443			0.574875
$508$	−30.2705	+	21.9928i	−1.34304	+	0.975773i
$509$	11.9721	+	36.8464i	0.530656	+	1.63319i	0.752853	+	0.658188i	$0.228677\pi$
$509$	11.9721	+	36.8464i	0.530656	+	1.63319i	−0.222198	+	0.975002i	$0.571323\pi$
$510$	0.572949	−	1.76336i	0.0253706	−	0.0780827i
$511$	−4.61803	−	3.35520i	−0.204290	−	0.148425i
$512$	−32.6074	−	23.6907i	−1.44106	−	1.04699i
$513$	−1.80902	+	5.56758i	−0.0798701	+	0.245815i
$514$	−24.0623	−	74.0562i	−1.06134	−	3.26648i
$515$	−5.47214	+	3.97574i	−0.241131	+	0.175192i
$516$	32.5623			1.43348
$517$		0			0
$518$	−16.3262			−0.717334
$519$	−14.5902	+	10.6004i	−0.640437	+	0.465305i
$520$	0.336881	+	1.03681i	0.0147732	+	0.0454673i
$521$	2.76393	−	8.50651i	0.121090	−	0.372677i	−0.872078	−	0.489366i	$-0.837228\pi$
$521$	2.76393	−	8.50651i	0.121090	−	0.372677i	0.993168	+	0.116689i	$0.0372282\pi$
$522$	−12.7082	−	9.23305i	−0.556223	−	0.404120i
$523$	−14.7812	−	10.7391i	−0.646335	−	0.469590i	0.215686	−	0.976463i	$-0.430801\pi$
$523$	−14.7812	−	10.7391i	−0.646335	−	0.469590i	−0.862021	+	0.506873i	$0.830801\pi$
$524$	−17.6976	+	54.4675i	−0.773122	+	2.37942i
$525$	−1.42705	−	4.39201i	−0.0622816	−	0.191683i
$526$	−32.3435	+	23.4989i	−1.41024	+	1.02460i
$527$	6.97871			0.303998
$528$		0			0
$529$	−22.9443			−0.997577
$530$	0.500000	−	0.363271i	0.0217186	−	0.0157795i
$531$	2.28115	+	7.02067i	0.0989936	+	0.304671i
$532$	−8.78115	+	27.0256i	−0.380711	+	1.17171i
$533$	−0.0450850	−	0.0327561i	−0.00195285	−	0.00141883i
$534$	17.4443	+	12.6740i	0.754887	+	0.548458i
$535$	2.19098	−	6.74315i	0.0947245	−	0.291532i
$536$	−4.28115	−	13.1760i	−0.184918	−	0.569118i
$537$	−6.89919	+	5.01255i	−0.297722	+	0.216308i
$538$	66.5410			2.86879
$539$		0			0
$540$	3.00000			0.129099
$541$	6.06231	−	4.40452i	0.260639	−	0.189365i	−0.449790	−	0.893134i	$-0.648501\pi$
$541$	6.06231	−	4.40452i	0.260639	−	0.189365i	0.710429	+	0.703769i	$0.248501\pi$
$542$	−15.0623	−	46.3570i	−0.646981	−	1.99120i
$543$	−0.781153	+	2.40414i	−0.0335225	+	0.103172i
$544$	−10.0623	−	7.31069i	−0.431418	−	0.313443i
$545$	−6.00000	−	4.35926i	−0.257012	−	0.186730i
$546$	−0.190983	+	0.587785i	−0.00817332	+	0.0251549i
$547$	−9.50000	−	29.2380i	−0.406191	−	1.25013i	−0.919897	−	0.392160i	$-0.871728\pi$
$547$	−9.50000	−	29.2380i	−0.406191	−	1.25013i	0.513706	−	0.857966i	$-0.328272\pi$
$548$	−38.3435	+	27.8582i	−1.63795	+	1.19004i
$549$	−11.5623			−0.493467
$550$		0			0
$551$	−35.1246			−1.49636
$552$	−1.42705	+	1.03681i	−0.0607393	+	0.0441297i
$553$	−3.39919	−	10.4616i	−0.144548	−	0.444873i
$554$	23.6353	−	72.7418i	1.00417	−	3.09050i
$555$	3.11803	+	2.26538i	0.132353	+	0.0961602i
$556$	−57.1869	−	41.5487i	−2.42527	−	1.76206i
$557$	11.6287	−	35.7894i	0.492723	−	1.51645i	−0.327753	−	0.944764i	$-0.606291\pi$
$557$	11.6287	−	35.7894i	0.492723	−	1.51645i	0.820476	−	0.571682i	$-0.193709\pi$
$558$	4.92705	+	15.1639i	0.208579	+	0.641939i
$559$	1.28115	−	0.930812i	0.0541870	−	0.0393692i
$560$	6.09017			0.257357
$561$		0			0
$562$	−64.8328			−2.73481
$563$	−32.8435	+	23.8622i	−1.38419	+	1.00567i	−0.387712	+	0.921781i	$0.626734\pi$
$563$	−32.8435	+	23.8622i	−1.38419	+	1.00567i	−0.996475	+	0.0838899i	$0.973266\pi$
$564$	15.1353	+	46.5815i	0.637309	+	1.96144i
$565$	−2.57295	+	7.91872i	−0.108245	+	0.333143i
$566$	−12.0902	−	8.78402i	−0.508188	−	0.369220i
$567$	0.809017	+	0.587785i	0.0339755	+	0.0246847i
$568$	−23.8435	+	73.3826i	−1.00045	+	3.07907i
$569$	10.5623	+	32.5074i	0.442795	+	1.36278i	0.884884	+	0.465811i	$0.154237\pi$
$569$	10.5623	+	32.5074i	0.442795	+	1.36278i	−0.442089	+	0.896971i	$0.645763\pi$
$570$	7.66312	−	5.56758i	0.320973	−	0.233200i
$571$	−9.09017			−0.380412			−0.190206	−	0.981744i	$-0.560916\pi$
$571$	−9.09017			−0.380412			−0.190206	+	0.981744i	$0.560916\pi$
$572$		0			0
$573$	0.819660			0.0342418
$574$	−0.500000	+	0.363271i	−0.0208696	+	0.0151626i
$575$	−0.336881	−	1.03681i	−0.0140489	−	0.0432381i
$576$	2.69098	−	8.28199i	0.112124	−	0.345083i
$577$	−25.6525	−	18.6376i	−1.06793	−	0.775894i	−0.0923881	−	0.995723i	$-0.529450\pi$
$577$	−25.6525	−	18.6376i	−1.06793	−	0.775894i	−0.975538	+	0.219829i	$0.929450\pi$
$578$	−33.2254	−	24.1397i	−1.38200	−	1.00408i
$579$	0.972136	−	2.99193i	0.0404006	−	0.124340i
$580$	5.56231	+	17.1190i	0.230962	+	0.710829i
$581$	1.19098	−	0.865300i	0.0494103	−	0.0358987i
$582$	20.5623			0.852335
$583$		0			0
$584$	42.6525			1.76497
$585$	0.118034	−	0.0857567i	0.00488010	−	0.00354560i
$586$	17.5172	+	53.9125i	0.723630	+	2.22710i
$587$	−0.656541	+	2.02063i	−0.0270984	+	0.0834002i	−0.963691	−	0.267020i	$-0.913961\pi$
$587$	−0.656541	+	2.02063i	−0.0270984	+	0.0834002i	0.936593	+	0.350420i	$0.113961\pi$
$588$	−23.5623	−	17.1190i	−0.971693	−	0.705976i
$589$	28.8435	+	20.9560i	1.18847	+	0.863477i
$590$	3.69098	−	11.3597i	0.151955	−	0.467671i
$591$	−4.02786	−	12.3965i	−0.165684	−	0.509923i
$592$	49.7148	−	36.1199i	2.04326	−	1.48452i
$593$	−14.0344			−0.576325			−0.288163	−	0.957581i	$-0.593044\pi$
$593$	−14.0344			−0.576325			−0.288163	+	0.957581i	$0.593044\pi$
$594$		0			0
$595$	−0.708204			−0.0290335
$596$	16.6353	−	12.0862i	0.681407	−	0.495071i
$597$	−2.07295	−	6.37988i	−0.0848402	−	0.261111i
$598$	−0.0450850	+	0.138757i	−0.00184366	+	0.00567421i
$599$	−10.2361	−	7.43694i	−0.418234	−	0.303865i	0.358693	−	0.933456i	$-0.383223\pi$
$599$	−10.2361	−	7.43694i	−0.418234	−	0.303865i	−0.776927	+	0.629591i	$0.783223\pi$
$600$	27.9164	+	20.2825i	1.13968	+	0.828028i
$601$	−2.12868	+	6.55139i	−0.0868306	+	0.267237i	−0.985039	−	0.172334i	$-0.944869\pi$
$601$	−2.12868	+	6.55139i	−0.0868306	+	0.267237i	0.898208	+	0.439570i	$0.144869\pi$
$602$	−5.42705	−	16.7027i	−0.221190	−	0.680753i
$603$	−1.50000	+	1.08981i	−0.0610847	+	0.0443806i
$604$	5.12461			0.208517
$605$		0			0
$606$	−26.7984			−1.08861
$607$	13.3992	−	9.73508i	0.543856	−	0.395135i	−0.281659	−	0.959515i	$-0.590885\pi$
$607$	13.3992	−	9.73508i	0.543856	−	0.395135i	0.825515	+	0.564380i	$0.190885\pi$
$608$	−19.6353	−	60.4311i	−0.796315	−	2.45080i
$609$	−1.85410	+	5.70634i	−0.0751320	+	0.231233i
$610$	15.1353	+	10.9964i	0.612809	+	0.445231i
$611$	1.92705	+	1.40008i	0.0779601	+	0.0566414i
$612$	−1.71885	+	5.29007i	−0.0694803	+	0.213838i
$613$	−4.41641	−	13.5923i	−0.178377	−	0.548988i	0.821395	−	0.570360i	$-0.193196\pi$
$613$	−4.41641	−	13.5923i	−0.178377	−	0.548988i	−0.999772	+	0.0213723i	$0.993196\pi$
$614$	59.2599	−	43.0548i	2.39153	−	1.73755i
$615$	0.145898			0.00588318
$616$		0			0
$617$	11.1803			0.450104			0.225052	−	0.974347i	$-0.427745\pi$
$617$	11.1803			0.450104			0.225052	+	0.974347i	$0.427745\pi$
$618$	23.1803	−	16.8415i	0.932450	−	0.677465i
$619$	7.45492	+	22.9439i	0.299638	+	0.922192i	0.981624	+	0.190826i	$0.0611167\pi$
$619$	7.45492	+	22.9439i	0.299638	+	0.922192i	−0.681985	+	0.731366i	$0.738883\pi$
$620$	5.64590	−	17.3763i	0.226745	−	0.697848i
$621$	0.190983	+	0.138757i	0.00766388	+	0.00556814i
$622$	24.6803	+	17.9313i	0.989591	+	0.718980i
$623$	2.54508	−	7.83297i	0.101967	−	0.313821i
$624$	−0.718847	−	2.21238i	−0.0287769	−	0.0885662i
$625$	−15.7082	+	11.4127i	−0.628328	+	0.456507i
$626$	6.61803			0.264510
$627$		0			0
$628$	76.2492			3.04268
$629$	−5.78115	+	4.20025i	−0.230510	+	0.167475i
$630$	−0.500000	−	1.53884i	−0.0199205	−	0.0613089i
$631$	5.93769	−	18.2743i	0.236376	−	0.727490i	−0.760560	−	0.649268i	$-0.775076\pi$
$631$	5.93769	−	18.2743i	0.236376	−	0.727490i	0.996936	−	0.0782225i	$-0.0249245\pi$
$632$	66.4959	+	48.3121i	2.64507	+	1.92175i
$633$	2.92705	+	2.12663i	0.116340	+	0.0845258i
$634$	5.51722	−	16.9803i	0.219117	−	0.674372i
$635$	−1.47214	−	4.53077i	−0.0584199	−	0.179798i
$636$	−1.50000	+	1.08981i	−0.0594789	+	0.0432139i
$637$	−1.41641			−0.0561201
$638$		0			0
$639$	10.3262			0.408500
$640$	−0.545085	+	0.396027i	−0.0215464	+	0.0156544i
$641$	−7.75329	−	23.8622i	−0.306236	−	0.942499i	−0.979213	−	0.202835i	$-0.934984\pi$
$641$	−7.75329	−	23.8622i	−0.306236	−	0.942499i	0.672976	−	0.739664i	$-0.265016\pi$
$642$	−9.28115	+	28.5645i	−0.366298	+	1.12735i
$643$	−16.8713	−	12.2577i	−0.665340	−	0.483398i	0.203122	−	0.979153i	$-0.434891\pi$
$643$	−16.8713	−	12.2577i	−0.665340	−	0.483398i	−0.868462	+	0.495756i	$0.834891\pi$
$644$	0.927051	+	0.673542i	0.0365309	+	0.0265413i
$645$	−1.28115	+	3.94298i	−0.0504453	+	0.155255i
$646$	5.42705	+	16.7027i	0.213524	+	0.657161i
$647$	−36.4336	+	26.4706i	−1.43235	+	1.04067i	−0.442781	+	0.896630i	$0.646008\pi$
$647$	−36.4336	+	26.4706i	−1.43235	+	1.04067i	−0.989572	+	0.144036i	$0.953992\pi$
$648$	−7.47214			−0.293533
$649$		0			0
$650$	2.85410			0.111947
$651$	4.92705	−	3.57971i	0.193106	−	0.140300i
$652$	−7.71885	−	23.7562i	−0.302293	−	0.930363i
$653$	−1.73607	+	5.34307i	−0.0679376	+	0.209090i	−0.979262	−	0.202599i	$-0.935061\pi$
$653$	−1.73607	+	5.34307i	−0.0679376	+	0.209090i	0.911324	+	0.411690i	$0.135061\pi$
$654$	25.4164	+	18.4661i	0.993860	+	0.722082i
$655$	−5.89919	−	4.28601i	−0.230500	−	0.167468i
$656$	0.718847	−	2.21238i	0.0280663	−	0.0863791i
$657$	−1.76393	−	5.42882i	−0.0688175	−	0.211799i
$658$	21.3713	−	15.5272i	0.833141	−	0.605312i
$659$	−41.1246			−1.60199			−0.800994	−	0.598673i	$-0.795695\pi$
$659$	−41.1246			−1.60199			−0.800994	+	0.598673i	$0.795695\pi$
$660$		0			0
$661$	36.5623			1.42211			0.711054	−	0.703137i	$-0.248218\pi$
$661$	36.5623			1.42211			0.711054	+	0.703137i	$0.248218\pi$
$662$	35.3885	−	25.7113i	1.37541	−	0.999297i
$663$	0.0835921	+	0.257270i	0.00324645	+	0.00999154i
$664$	−3.39919	+	10.4616i	−0.131914	+	0.405990i
$665$	−2.92705	−	2.12663i	−0.113506	−	0.0824671i
$666$	−13.2082	−	9.59632i	−0.511808	−	0.371850i
$667$	−0.437694	+	1.34708i	−0.0169476	+	0.0521593i
$668$	18.0517	+	55.5573i	0.698440	+	2.14958i
$669$	5.80902	−	4.22050i	0.224590	−	0.163174i
$670$	3.00000			0.115900
$671$		0			0
$672$	−10.8541			−0.418706
$673$	−28.9894	+	21.0620i	−1.11746	+	0.811880i	−0.983822	−	0.179150i	$-0.942665\pi$
$673$	−28.9894	+	21.0620i	−1.11746	+	0.811880i	−0.133636	+	0.991031i	$0.542665\pi$
$674$	14.7082	+	45.2672i	0.566539	+	1.74363i
$675$	1.42705	−	4.39201i	0.0549272	−	0.169049i
$676$	50.8328	+	36.9322i	1.95511	+	1.42047i
$677$	−10.9443	−	7.95148i	−0.420623	−	0.305600i	0.357266	−	0.934003i	$-0.383709\pi$
$677$	−10.9443	−	7.95148i	−0.420623	−	0.305600i	−0.777888	+	0.628403i	$0.783709\pi$
$678$	10.8992	−	33.5442i	0.418581	−	1.28826i
$679$	−2.42705	−	7.46969i	−0.0931417	−	0.286661i
$680$	4.28115	−	3.11044i	0.164175	−	0.119280i
$681$	−13.1803			−0.505072
$682$		0			0
$683$	9.06888			0.347011			0.173506	−	0.984833i	$-0.444491\pi$
$683$	9.06888			0.347011			0.173506	+	0.984833i	$0.444491\pi$
$684$	−22.9894	+	16.7027i	−0.879020	+	0.638645i
$685$	−1.86475	−	5.73910i	−0.0712482	−	0.219280i
$686$	−10.5172	+	32.3687i	−0.401549	+	1.23584i
$687$	0.381966	+	0.277515i	0.0145729	+	0.0105878i
$688$	53.4787	+	38.8546i	2.03886	+	1.48132i
$689$	−0.0278640	+	0.0857567i	−0.00106154	+	0.00326707i
$690$	−0.118034	−	0.363271i	−0.00449348	−	0.0138295i
$691$	−1.09017	+	0.792055i	−0.0414720	+	0.0301312i	−0.608328	−	0.793686i	$-0.708160\pi$
$691$	−1.09017	+	0.792055i	−0.0414720	+	0.0301312i	0.566856	+	0.823817i	$0.308160\pi$
$692$	−87.5410			−3.32781
$693$		0			0
$694$	4.00000			0.151838
$695$	7.28115	−	5.29007i	0.276190	−	0.200664i
$696$	−13.8541	−	42.6385i	−0.525138	−	1.61621i
$697$	−0.0835921	+	0.257270i	−0.00316628	+	0.00974480i
$698$	26.9164	+	19.5559i	1.01880	+	0.740202i
$699$	−3.35410	−	2.43690i	−0.126864	−	0.0921719i
$700$	6.92705	−	21.3193i	0.261818	−	0.805793i
$701$	−10.7533	−	33.0952i	−0.406146	−	1.24999i	−0.919934	−	0.392072i	$-0.871758\pi$
$701$	−10.7533	−	33.0952i	−0.406146	−	1.24999i	0.513788	−	0.857917i	$-0.328242\pi$
$702$	−0.500000	+	0.363271i	−0.0188713	+	0.0137108i
$703$	−36.5066			−1.37687
$704$		0			0
$705$	−6.23607			−0.234864
$706$	−25.4164	+	18.4661i	−0.956559	+	0.694981i
$707$	3.16312	+	9.73508i	0.118961	+	0.366125i
$708$	−11.0729	+	34.0790i	−0.416147	+	1.28077i
$709$	−9.07295	−	6.59188i	−0.340742	−	0.247563i	0.404233	−	0.914656i	$-0.367538\pi$
$709$	−9.07295	−	6.59188i	−0.340742	−	0.247563i	−0.744975	+	0.667093i	$0.767538\pi$
$710$	−13.5172	−	9.82084i	−0.507292	−	0.368569i
$711$	3.39919	−	10.4616i	0.127479	−	0.392341i
$712$	19.0172	+	58.5290i	0.712700	+	2.19347i
$713$	1.16312	−	0.845055i	0.0435591	−	0.0316476i
$714$	3.00000			0.112272
$715$		0			0
$716$	−41.3951			−1.54701
$717$	0.309017	−	0.224514i	0.0115405	−	0.00838463i
$718$	7.85410	+	24.1724i	0.293112	+	0.902107i
$719$	−11.8926	+	36.6017i	−0.443519	+	1.36501i	0.440580	+	0.897713i	$0.354773\pi$
$719$	−11.8926	+	36.6017i	−0.443519	+	1.36501i	−0.884099	+	0.467299i	$0.845227\pi$
$720$	4.92705	+	3.57971i	0.183620	+	0.133408i
$721$	−8.85410	−	6.43288i	−0.329744	−	0.239573i
$722$	−12.3541	+	38.0220i	−0.459772	+	1.41503i
$723$	−2.56231	−	7.88597i	−0.0952932	−	0.293282i
$724$	−9.92705	+	7.21242i	−0.368936	+	0.268048i
$725$	27.7082			1.02906
$726$		0			0
$727$	−9.14590			−0.339203			−0.169601	−	0.985513i	$-0.554248\pi$
$727$	−9.14590			−0.339203			−0.169601	+	0.985513i	$0.554248\pi$
$728$	−1.42705	+	1.03681i	−0.0528900	+	0.0384269i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−2.85410	+	8.78402i	−0.105635	+	0.325111i
$731$	−6.21885	−	4.51826i	−0.230012	−	0.167114i
$732$	−45.4058	−	32.9892i	−1.67825	−	1.21932i
$733$	−0.124612	+	0.383516i	−0.00460264	+	0.0141655i	−0.953331	−	0.301926i	$-0.902371\pi$
$733$	−0.124612	+	0.383516i	−0.00460264	+	0.0141655i	0.948729	+	0.316091i	$0.102371\pi$
$734$	−17.9164	−	55.1410i	−0.661307	−	2.03529i
$735$	3.00000	−	2.17963i	0.110657	−	0.0803968i
$736$	−2.56231			−0.0944478
$737$		0			0
$738$	−0.618034			−0.0227501
$739$	−2.42705	+	1.76336i	−0.0892805	+	0.0648661i	−0.631530	−	0.775351i	$-0.717573\pi$
$739$	−2.42705	+	1.76336i	−0.0892805	+	0.0648661i	0.542250	+	0.840218i	$0.317573\pi$
$740$	5.78115	+	17.7926i	0.212519	+	0.654067i
$741$	−0.427051	+	1.31433i	−0.0156881	+	0.0482830i
$742$	0.809017	+	0.587785i	0.0296999	+	0.0215783i
$743$	34.6976	+	25.2093i	1.27293	+	0.924838i	0.999315	−	0.0370015i	$-0.0117806\pi$
$743$	34.6976	+	25.2093i	1.27293	+	0.924838i	0.273615	+	0.961839i	$0.411781\pi$
$744$	−14.0623	+	43.2793i	−0.515549	+	1.58670i
$745$	0.809017	+	2.48990i	0.0296401	+	0.0912228i
$746$	1.88197	−	1.36733i	0.0689037	−	0.0500614i
$747$	1.47214			0.0538626
$748$		0			0
$749$	11.4721			0.419183
$750$	−12.5902	+	9.14729i	−0.459728	+	0.334012i
$751$	4.98936	+	15.3557i	0.182064	+	0.560336i	0.999885	−	0.0151363i	$-0.00481823\pi$
$751$	4.98936	+	15.3557i	0.182064	+	0.560336i	−0.817821	+	0.575472i	$0.804818\pi$
$752$	−30.7254	+	94.5631i	−1.12044	+	3.44836i
$753$	−17.7812	−	12.9188i	−0.647981	−	0.470786i
$754$	−3.00000	−	2.17963i	−0.109254	−	0.0793774i
$755$	−0.201626	+	0.620541i	−0.00733793	+	0.0225838i
$756$	1.50000	+	4.61653i	0.0545545	+	0.167901i
$757$	−4.04508	+	2.93893i	−0.147021	+	0.106817i	−0.658864	−	0.752262i	$-0.728963\pi$
$757$	−4.04508	+	2.93893i	−0.147021	+	0.106817i	0.511843	+	0.859079i	$0.328963\pi$
$758$	65.1591			2.36668
$759$		0			0
$760$	27.0344			0.980642
$761$	−23.6976	+	17.2173i	−0.859036	+	0.624126i	−0.927623	−	0.373519i	$-0.878151\pi$
$761$	−23.6976	+	17.2173i	−0.859036	+	0.624126i	0.0685866	+	0.997645i	$0.478151\pi$
$762$	6.23607	+	19.1926i	0.225909	+	0.695276i
$763$	3.70820	−	11.4127i	0.134246	−	0.413167i
$764$	3.21885	+	2.33863i	0.116454	+	0.0846086i
$765$	−0.572949	−	0.416272i	−0.0207150	−	0.0150503i
$766$	10.2812	−	31.6421i	0.371473	−	1.14328i
$767$	0.538507	+	1.65735i	0.0194444	+	0.0598436i
$768$	−11.7812	+	8.55951i	−0.425116	+	0.308865i
$769$	−34.5066			−1.24434			−0.622170	−	0.782883i	$-0.713749\pi$
$769$	−34.5066			−1.24434			−0.622170	+	0.782883i	$0.713749\pi$
$770$		0			0
$771$	−29.7426			−1.07116
$772$	12.3541	−	8.97578i	0.444634	−	0.323045i
$773$	8.39919	+	25.8500i	0.302098	+	0.929761i	0.980744	+	0.195296i	$0.0625668\pi$
$773$	8.39919	+	25.8500i	0.302098	+	0.929761i	−0.678647	+	0.734465i	$0.737433\pi$
$774$	5.42705	−	16.7027i	0.195071	−	0.600368i
$775$	−22.7533	−	16.5312i	−0.817322	−	0.593819i
$776$	47.4787	+	34.4953i	1.70439	+	1.23831i
$777$	−1.92705	+	5.93085i	−0.0691326	+	0.212768i
$778$	29.7254	+	91.4855i	1.06571	+	3.27991i
$779$	−1.11803	+	0.812299i	−0.0400577	+	0.0291036i
$780$	0.708204			0.0253578
$781$		0			0
$782$	0.708204			0.0253253
$783$	−4.85410	+	3.52671i	−0.173471	+	0.126034i
$784$	−18.2705	−	56.2308i	−0.652518	−	2.00824i
$785$	−3.00000	+	9.23305i	−0.107075	+	0.329542i
$786$	24.9894	+	18.1558i	0.891341	+	0.647597i
$787$	7.85410	+	5.70634i	0.279968	+	0.203409i	0.718904	−	0.695110i	$-0.244644\pi$
$787$	7.85410	+	5.70634i	0.279968	+	0.203409i	−0.438935	+	0.898519i	$0.644644\pi$
$788$	19.5517	−	60.1738i	0.696499	−	2.14360i
$789$	4.71885	+	14.5231i	0.167995	+	0.517037i
$790$	−14.3992	+	10.4616i	−0.512300	+	0.372208i
$791$	−13.4721			−0.479014
$792$		0			0
$793$	−2.72949			−0.0969270
$794$	−39.6246	+	28.7890i	−1.40622	+	1.02168i
$795$	−0.0729490	−	0.224514i	−0.00258724	−	0.00796269i
$796$	10.0623	−	30.9686i	0.356649	−	1.09765i
$797$	−15.0000	−	10.8981i	−0.531327	−	0.386032i	0.289527	−	0.957170i	$-0.406502\pi$
$797$	−15.0000	−	10.8981i	−0.531327	−	0.386032i	−0.820854	+	0.571138i	$0.806502\pi$
$798$	12.3992	+	9.00854i	0.438926	+	0.318899i
$799$	3.57295	−	10.9964i	0.126402	−	0.389025i
$800$	15.4894	+	47.6713i	0.547631	+	1.68544i
$801$	6.66312	−	4.84104i	0.235430	−	0.171050i
$802$	82.9574			2.92933
$803$		0			0
$804$	−9.00000			−0.317406
$805$	−0.118034	+	0.0857567i	−0.00416015	+	0.00302253i
$806$	1.16312	+	3.57971i	0.0409691	+	0.126090i
$807$	7.85410	−	24.1724i	0.276477	−	0.850910i
$808$	−61.8779	−	44.9569i	−2.17686	−	1.58158i
$809$	−21.9164	−	15.9232i	−0.770540	−	0.559830i	0.131585	−	0.991305i	$-0.457993\pi$
$809$	−21.9164	−	15.9232i	−0.770540	−	0.559830i	−0.902125	+	0.431475i	$0.857993\pi$
$810$	0.500000	−	1.53884i	0.0175682	−	0.0540694i
$811$	11.2984	+	34.7728i	0.396740	+	1.22104i	0.927599	+	0.373579i	$0.121869\pi$
$811$	11.2984	+	34.7728i	0.396740	+	1.22104i	−0.530859	+	0.847460i	$0.678131\pi$
$812$	−23.5623	+	17.1190i	−0.826875	+	0.600760i
$813$	−18.6180			−0.652963
$814$		0			0
$815$	3.18034			0.111402
$816$	−9.13525	+	6.63715i	−0.319798	+	0.232347i
$817$	−12.1353	−	37.3485i	−0.424559	−	1.30666i
$818$	5.23607	−	16.1150i	0.183075	−	0.563446i
$819$	0.190983	+	0.138757i	0.00667349	+	0.00484857i
$820$	0.572949	+	0.416272i	0.0200082	+	0.0145368i
$821$	12.5451	−	38.6098i	0.437826	−	1.34749i	−0.452336	−	0.891848i	$-0.649409\pi$
$821$	12.5451	−	38.6098i	0.437826	−	1.34749i	0.890162	−	0.455644i	$-0.150591\pi$
$822$	7.89919	+	24.3112i	0.275516	+	0.847950i
$823$	22.5172	−	16.3597i	0.784901	−	0.570264i	−0.121545	−	0.992586i	$-0.538785\pi$
$823$	22.5172	−	16.3597i	0.784901	−	0.570264i	0.906446	+	0.422322i	$0.138785\pi$
$824$	81.7771			2.84884
$825$		0			0
$826$	19.3262			0.672446
$827$	8.61803	−	6.26137i	0.299678	−	0.217729i	−0.427777	−	0.903884i	$-0.640703\pi$
$827$	8.61803	−	6.26137i	0.299678	−	0.217729i	0.727455	+	0.686155i	$0.240703\pi$
$828$	0.354102	+	1.08981i	0.0123059	+	0.0378736i
$829$	−9.70163	+	29.8585i	−0.336951	+	1.03703i	0.628801	+	0.777566i	$0.283546\pi$
$829$	−9.70163	+	29.8585i	−0.336951	+	1.03703i	−0.965753	+	0.259464i	$0.916454\pi$
$830$	−1.92705	−	1.40008i	−0.0668889	−	0.0485976i
$831$	−23.6353	−	17.1720i	−0.819898	−	0.595691i
$832$	0.635255	−	1.95511i	0.0220235	−	0.0677814i
$833$	2.12461	+	6.53888i	0.0736134	+	0.226559i
$834$	−30.8435	+	22.4091i	−1.06802	+	0.775963i
$835$	−7.43769			−0.257392
$836$		0			0
$837$	6.09017			0.210507
$838$	66.6140	−	48.3979i	2.30114	−	1.67188i
$839$	−5.51064	−	16.9600i	−0.190249	−	0.585525i	0.809751	−	0.586774i	$-0.199602\pi$
$839$	−5.51064	−	16.9600i	−0.190249	−	0.585525i	−0.999999	+	0.00124931i	$0.999602\pi$
$840$	1.42705	−	4.39201i	0.0492379	−	0.151539i
$841$	−5.66312	−	4.11450i	−0.195280	−	0.141879i
$842$	22.2533	+	16.1680i	0.766899	+	0.557185i
$843$	−7.65248	+	23.5519i	−0.263565	+	0.811170i
$844$	5.42705	+	16.7027i	0.186807	+	0.574932i
$845$	−6.47214	+	4.70228i	−0.222648	+	0.161763i
$846$	26.4164			0.908215
$847$		0			0
$848$	−3.76393			−0.129254
$849$	−4.61803	+	3.35520i	−0.158491	+	0.115150i
$850$	−4.28115	−	13.1760i	−0.146842	−	0.451934i
$851$	−0.454915	+	1.40008i	−0.0155943	+	0.0479943i
$852$	40.5517	+	29.4625i	1.38928	+	1.00937i
$853$	45.1697	+	32.8177i	1.54658	+	1.12366i	0.946034	+	0.324067i	$0.105050\pi$
$853$	45.1697	+	32.8177i	1.54658	+	1.12366i	0.600547	+	0.799589i	$0.294950\pi$
$854$	−9.35410	+	28.7890i	−0.320091	+	0.985138i
$855$	−1.11803	−	3.44095i	−0.0382360	−	0.117678i
$856$	−69.3500	+	50.3858i	−2.37034	+	1.72215i
$857$	27.7639			0.948398			0.474199	−	0.880418i	$-0.342738\pi$
$857$	27.7639			0.948398			0.474199	+	0.880418i	$0.342738\pi$
$858$		0			0
$859$	−34.4164			−1.17427			−0.587136	−	0.809488i	$-0.699745\pi$
$859$	−34.4164			−1.17427			−0.587136	+	0.809488i	$0.699745\pi$
$860$	−16.2812	+	11.8290i	−0.555183	+	0.403364i
$861$	0.0729490	+	0.224514i	0.00248610	+	0.00765142i
$862$	4.78115	−	14.7149i	0.162847	−	0.501191i
$863$	−0.0901699	−	0.0655123i	−0.00306942	−	0.00223006i	0.586249	−	0.810131i	$-0.300604\pi$
$863$	−0.0901699	−	0.0655123i	−0.00306942	−	0.00223006i	−0.589319	+	0.807901i	$0.700604\pi$
$864$	−8.78115	−	6.37988i	−0.298741	−	0.217048i
$865$	3.44427	−	10.6004i	0.117109	−	0.360424i
$866$	−28.5623	−	87.9057i	−0.970587	−	2.98716i
$867$	−12.6910	+	9.22054i	−0.431008	+	0.313146i
$868$	29.5623			1.00341
$869$		0			0
$870$	9.70820			0.329139
$871$	−0.354102	+	0.257270i	−0.0119983	+	0.00871727i
$872$	27.7082	+	85.2771i	0.938318	+	2.88785i
$873$	2.42705	−	7.46969i	0.0821432	−	0.252811i
$874$	2.92705	+	2.12663i	0.0990090	+	0.0719342i
$875$	4.80902	+	3.49396i	0.162574	+	0.118117i
$876$	8.56231	−	26.3521i	0.289294	−	0.890354i
$877$	−17.9058	−	55.1083i	−0.604635	−	1.86087i	−0.499282	−	0.866439i	$-0.666403\pi$
$877$	−17.9058	−	55.1083i	−0.604635	−	1.86087i	−0.105352	−	0.994435i	$-0.533597\pi$
$878$	49.3328	−	35.8424i	1.66490	−	1.20962i
$879$	21.6525			0.730320
$880$		0			0
$881$	6.20163			0.208938			0.104469	−	0.994528i	$-0.466686\pi$
$881$	6.20163			0.208938			0.104469	+	0.994528i	$0.466686\pi$
$882$	−12.7082	+	9.23305i	−0.427907	+	0.310893i
$883$	0.326238	+	1.00406i	0.0109788	+	0.0337892i	0.956396	−	0.292074i	$-0.0943452\pi$
$883$	0.326238	+	1.00406i	0.0109788	+	0.0337892i	−0.945417	+	0.325863i	$0.894345\pi$
$884$	−0.405765	+	1.24882i	−0.0136473	+	0.0420022i
$885$	−3.69098	−	2.68166i	−0.124071	−	0.0901429i
$886$	−66.9230	−	48.6224i	−2.24832	−	1.63350i
$887$	−16.8369	+	51.8186i	−0.565327	+	1.73990i	0.101650	+	0.994820i	$0.467588\pi$
$887$	−16.8369	+	51.8186i	−0.565327	+	1.73990i	−0.666978	+	0.745078i	$0.732412\pi$
$888$	−14.3992	−	44.3161i	−0.483205	−	1.48715i
$889$	6.23607	−	4.53077i	0.209151	−	0.151957i
$890$	−13.3262			−0.446697
$891$		0			0
$892$	34.8541			1.16700
$893$	47.7877	−	34.7198i	1.59916	−	1.16185i
$894$	−3.42705	−	10.5474i	−0.114618	−	0.352757i
$895$	1.62868	−	5.01255i	0.0544407	−	0.167551i
$896$	−0.881966	−	0.640786i	−0.0294644	−	0.0214072i
$897$	0.0450850	+	0.0327561i	0.00150534	+	0.00109370i
$898$	7.32624	−	22.5478i	0.244480	−	0.752431i
$899$	11.2918	+	34.7526i	0.376602	+	1.15906i
$900$	18.1353	−	13.1760i	0.604508	−	0.439201i
$901$	0.437694			0.0145817
$902$		0			0
$903$	−6.70820			−0.223235
$904$	81.4402	−	59.1698i	2.70866	−	1.96796i
$905$	−0.482779	−	1.48584i	−0.0160481	−	0.0493910i
$906$	0.854102	−	2.62866i	0.0283756	−	0.0873312i
$907$	34.2984	+	24.9192i	1.13886	+	0.827429i	0.986960	−	0.160967i	$-0.0514612\pi$
$907$	34.2984	+	24.9192i	1.13886	+	0.827429i	0.151899	+	0.988396i	$0.451461\pi$
$908$	−51.7599	−	37.6057i	−1.71771	−	1.24799i
$909$	−3.16312	+	9.73508i	−0.104914	+	0.322892i
$910$	−0.118034	−	0.363271i	−0.00391279	−	0.0120423i
$911$	−31.2254	+	22.6866i	−1.03454	+	0.751641i	−0.969213	−	0.246223i	$-0.920810\pi$
$911$	−31.2254	+	22.6866i	−1.03454	+	0.751641i	−0.0653313	+	0.997864i	$0.520810\pi$
$912$	−57.6869			−1.91020
$913$		0			0
$914$	−62.7771			−2.07648
$915$	5.78115	−	4.20025i	0.191119	−	0.138856i
$916$	0.708204	+	2.17963i	0.0233997	+	0.0720169i
$917$	3.64590	−	11.2209i	0.120398	−	0.370547i
$918$	2.42705	+	1.76336i	0.0801046	+	0.0581994i
$919$	−20.7533	−	15.0781i	−0.684588	−	0.497382i	0.190289	−	0.981728i	$-0.439058\pi$
$919$	−20.7533	−	15.0781i	−0.684588	−	0.497382i	−0.874877	+	0.484346i	$0.839058\pi$
$920$	0.336881	−	1.03681i	0.0111066	−	0.0341827i
$921$	−8.64590	−	26.6093i	−0.284892	−	0.876807i
$922$	19.6353	−	14.2658i	0.646653	−	0.469821i
$923$	2.43769			0.0802377
$924$		0			0
$925$	28.7984			0.946885
$926$	3.66312	−	2.66141i	0.120378	−	0.0874594i
$927$	−3.38197	−	10.4086i	−0.111078	−	0.341864i
$928$	20.1246	−	61.9372i	0.660623	−	2.03319i
$929$	10.2812	+	7.46969i	0.337314	+	0.245073i	0.743528	−	0.668705i	$-0.233151\pi$
$929$	10.2812	+	7.46969i	0.337314	+	0.245073i	−0.406214	+	0.913778i	$0.633151\pi$
$930$	−7.97214	−	5.79210i	−0.261417	−	0.189930i
$931$	−10.8541	+	33.4055i	−0.355729	+	1.09482i
$932$	−6.21885	−	19.1396i	−0.203705	−	0.626940i
$933$	9.42705	−	6.84915i	0.308628	−	0.224231i
$934$	−54.6869			−1.78941
$935$		0			0
$936$	−1.76393			−0.0576559
$937$	−33.6976	+	24.4827i	−1.10085	+	0.799815i	−0.981199	−	0.193001i	$-0.938178\pi$
$937$	−33.6976	+	24.4827i	−1.10085	+	0.799815i	−0.119653	+	0.992816i	$0.538178\pi$
$938$	1.50000	+	4.61653i	0.0489767	+	0.150735i
$939$	0.781153	−	2.40414i	0.0254920	−	0.0784562i
$940$	−24.4894	−	17.7926i	−0.798755	−	0.580329i
$941$	11.6910	+	8.49400i	0.381115	+	0.276896i	0.761805	−	0.647806i	$-0.224313\pi$
$941$	11.6910	+	8.49400i	0.381115	+	0.276896i	−0.380690	+	0.924703i	$0.624313\pi$
$942$	12.7082	−	39.1118i	0.414056	−	1.27433i
$943$	0.0172209	+	0.0530006i	0.000560791	+	0.00172594i
$944$	−58.8500	+	42.7571i	−1.91541	+	1.39162i
$945$	−0.618034			−0.0201046
$946$		0			0
$947$	−32.3951			−1.05270			−0.526350	−	0.850268i	$-0.676440\pi$
$947$	−32.3951			−1.05270			−0.526350	+	0.850268i	$0.676440\pi$
$948$	43.1976	−	31.3849i	1.40299	−	1.01933i
$949$	−0.416408	−	1.28157i	−0.0135172	−	0.0416016i
$950$	21.8713	−	67.3130i	0.709599	−	2.18392i
$951$	−5.51722	−	4.00850i	−0.178908	−	0.129984i
$952$	6.92705	+	5.03280i	0.224507	+	0.163114i
$953$	3.50658	−	10.7921i	0.113589	−	0.349592i	−0.878061	−	0.478549i	$-0.841163\pi$
$953$	3.50658	−	10.7921i	0.113589	−	0.349592i	0.991650	+	0.128957i	$0.0411630\pi$
$954$	0.309017	+	0.951057i	0.0100048	+	0.0307916i
$955$	−0.409830	+	0.297759i	−0.0132618	+	0.00963525i
$956$	1.85410			0.0599659
$957$		0			0
$958$	74.3050			2.40068
$959$	7.89919	−	5.73910i	0.255078	−	0.185325i
$960$	1.66312	+	5.11855i	0.0536769	+	0.165201i
$961$	1.88197	−	5.79210i	0.0607086	−	0.186842i
$962$	−3.11803	−	2.26538i	−0.100529	−	0.0730389i
$963$	9.28115	+	6.74315i	0.299081	+	0.217295i
$964$	12.4377	−	38.2793i	0.400591	−	1.23289i
$965$	0.600813	+	1.84911i	0.0193409	+	0.0595250i
$966$	0.500000	−	0.363271i	0.0160872	−	0.0116881i
$967$	43.9230			1.41247			0.706234	−	0.707978i	$-0.250393\pi$
$967$	43.9230			1.41247			0.706234	+	0.707978i	$0.250393\pi$
$968$		0			0
$969$	6.70820			0.215499
$970$	−10.2812	+	7.46969i	−0.330108	+	0.239837i
$971$	−12.9787	−	39.9444i	−0.416507	−	1.28188i	−0.910896	−	0.412635i	$-0.864608\pi$
$971$	−12.9787	−	39.9444i	−0.416507	−	1.28188i	0.494389	−	0.869240i	$-0.335392\pi$
$972$	−1.50000	+	4.61653i	−0.0481125	+	0.148075i
$973$	11.7812	+	8.55951i	0.377686	+	0.274405i
$974$	−26.9164	−	19.5559i	−0.862457	−	0.626612i
$975$	0.336881	−	1.03681i	0.0107888	−	0.0332046i
$976$	−35.2082	−	108.360i	−1.12699	−	3.46851i
$977$	0.482779	−	0.350760i	0.0154455	−	0.0112218i	−0.580036	−	0.814591i	$-0.696961\pi$
$977$	0.482779	−	0.350760i	0.0154455	−	0.0112218i	0.595481	+	0.803369i	$0.296961\pi$
$978$	−13.4721			−0.430791
$979$		0			0
$980$	18.0000			0.574989
$981$	9.70820	−	7.05342i	0.309959	−	0.225198i
$982$	14.4894	+	44.5937i	0.462374	+	1.42304i
$983$	−2.50658	+	7.71445i	−0.0799474	+	0.246053i	−0.983039	−	0.183394i	$-0.941292\pi$
$983$	−2.50658	+	7.71445i	−0.0799474	+	0.246053i	0.903092	+	0.429447i	$0.141292\pi$
$984$	−1.42705	−	1.03681i	−0.0454927	−	0.0330524i
$985$	6.51722	+	4.73504i	0.207656	+	0.150871i
$986$	−5.56231	+	17.1190i	−0.177140	+	0.545181i
$987$	−3.11803	−	9.59632i	−0.0992481	−	0.305454i
$988$	−5.42705	+	3.94298i	−0.172657	+	0.125443i
$989$	−1.58359			−0.0503553
$990$		0			0
$991$	3.74265			0.118889			0.0594445	−	0.998232i	$-0.481067\pi$
$991$	3.74265			0.118889			0.0594445	+	0.998232i	$0.481067\pi$
$992$	−53.4787	+	38.8546i	−1.69795	+	1.23363i
$993$	−5.16312	−	15.8904i	−0.163847	−	0.504268i
$994$	8.35410	−	25.7113i	0.264976	−	0.815512i
$995$	3.35410	+	2.43690i	0.106332	+	0.0772549i
$996$	5.78115	+	4.20025i	0.183183	+	0.133090i
$997$	−6.55166	+	20.1639i	−0.207493	+	0.638599i	0.792109	+	0.610380i	$0.208983\pi$
$997$	−6.55166	+	20.1639i	−0.207493	+	0.638599i	−0.999602	+	0.0282183i	$0.991017\pi$
$998$	14.6803	+	45.1814i	0.464698	+	1.43019i
$999$	−5.04508	+	3.66547i	−0.159619	+	0.115970i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.2.e.k.124.1		4
11.2	odd	10		363.2.a.i.1.2		2
11.3	even	5		33.2.e.b.16.1	✓	4
11.4	even	5	inner	363.2.e.k.202.1		4
11.5	even	5		33.2.e.b.31.1	yes	4
11.6	odd	10		363.2.e.f.130.1		4
11.7	odd	10		363.2.e.b.202.1		4
11.8	odd	10		363.2.e.f.148.1		4
11.9	even	5		363.2.a.d.1.1		2
11.10	odd	2		363.2.e.b.124.1		4
33.2	even	10		1089.2.a.l.1.1		2
33.5	odd	10		99.2.f.a.64.1		4
33.14	odd	10		99.2.f.a.82.1		4
33.20	odd	10		1089.2.a.t.1.2		2
44.3	odd	10		528.2.y.b.49.1		4
44.27	odd	10		528.2.y.b.97.1		4
44.31	odd	10		5808.2.a.cj.1.1		2
44.35	even	10		5808.2.a.ci.1.1		2
55.3	odd	20		825.2.bx.d.49.1		8
55.9	even	10		9075.2.a.cb.1.2		2
55.14	even	10		825.2.n.c.676.1		4
55.24	odd	10		9075.2.a.u.1.1		2
55.27	odd	20		825.2.bx.d.724.1		8
55.38	odd	20		825.2.bx.d.724.2		8
55.47	odd	20		825.2.bx.d.49.2		8
55.49	even	10		825.2.n.c.526.1		4
99.5	odd	30		891.2.n.b.460.1		8
99.14	odd	30		891.2.n.b.379.1		8
99.16	even	15		891.2.n.c.757.1		8
99.25	even	15		891.2.n.c.676.1		8
99.38	odd	30		891.2.n.b.757.1		8
99.47	odd	30		891.2.n.b.676.1		8
99.49	even	15		891.2.n.c.460.1		8
99.58	even	15		891.2.n.c.379.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.b.16.1	✓	4	11.3	even	5
33.2.e.b.31.1	yes	4	11.5	even	5
99.2.f.a.64.1		4	33.5	odd	10
99.2.f.a.82.1		4	33.14	odd	10
363.2.a.d.1.1		2	11.9	even	5
363.2.a.i.1.2		2	11.2	odd	10
363.2.e.b.124.1		4	11.10	odd	2
363.2.e.b.202.1		4	11.7	odd	10
363.2.e.f.130.1		4	11.6	odd	10
363.2.e.f.148.1		4	11.8	odd	10
363.2.e.k.124.1		4	1.1	even	1	trivial
363.2.e.k.202.1		4	11.4	even	5	inner
528.2.y.b.49.1		4	44.3	odd	10
528.2.y.b.97.1		4	44.27	odd	10
825.2.n.c.526.1		4	55.49	even	10
825.2.n.c.676.1		4	55.14	even	10
825.2.bx.d.49.1		8	55.3	odd	20
825.2.bx.d.49.2		8	55.47	odd	20
825.2.bx.d.724.1		8	55.27	odd	20
825.2.bx.d.724.2		8	55.38	odd	20
891.2.n.b.379.1		8	99.14	odd	30
891.2.n.b.460.1		8	99.5	odd	30
891.2.n.b.676.1		8	99.47	odd	30
891.2.n.b.757.1		8	99.38	odd	30
891.2.n.c.379.1		8	99.58	even	15
891.2.n.c.460.1		8	99.49	even	15
891.2.n.c.676.1		8	99.25	even	15
891.2.n.c.757.1		8	99.16	even	15
1089.2.a.l.1.1		2	33.2	even	10
1089.2.a.t.1.2		2	33.20	odd	10
5808.2.a.ci.1.1		2	44.35	even	10
5808.2.a.cj.1.1		2	44.31	odd	10
9075.2.a.u.1.1		2	55.24	odd	10
9075.2.a.cb.1.2		2	55.9	even	10

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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.e (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.11803 - 1.53884i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(1.50000 - 4.61653i) q^{4} +(0.500000 + 0.363271i) q^{5} +(-2.11803 - 1.53884i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(-2.30902 - 7.10642i) q^{8} +(-0.809017 + 0.587785i) q^{9} +1.61803 q^{10} -4.85410 q^{12} +(-0.190983 + 0.138757i) q^{13} +(0.809017 + 2.48990i) q^{14} +(0.190983 - 0.587785i) q^{15} +(-7.97214 - 5.79210i) q^{16} +(0.927051 + 0.673542i) q^{17} +(-0.809017 + 2.48990i) q^{18} +(1.80902 + 5.56758i) q^{19} +(2.42705 - 1.76336i) q^{20} +1.00000 q^{21} +0.236068 q^{23} +(-6.04508 + 4.39201i) q^{24} +(-1.42705 - 4.39201i) q^{25} +(-0.190983 + 0.587785i) q^{26} +(0.809017 + 0.587785i) q^{27} +(3.92705 + 2.85317i) q^{28} +(-1.85410 + 5.70634i) q^{29} +(-0.500000 - 1.53884i) q^{30} +(4.92705 - 3.57971i) q^{31} -10.8541 q^{32} +3.00000 q^{34} +(-0.500000 + 0.363271i) q^{35} +(1.50000 + 4.61653i) q^{36} +(-1.92705 + 5.93085i) q^{37} +(12.3992 + 9.00854i) q^{38} +(0.190983 + 0.138757i) q^{39} +(1.42705 - 4.39201i) q^{40} +(0.0729490 + 0.224514i) q^{41} +(2.11803 - 1.53884i) q^{42} -6.70820 q^{43} -0.618034 q^{45} +(0.500000 - 0.363271i) q^{46} +(-3.11803 - 9.59632i) q^{47} +(-3.04508 + 9.37181i) q^{48} +(4.85410 + 3.52671i) q^{49} +(-9.78115 - 7.10642i) q^{50} +(0.354102 - 1.08981i) q^{51} +(0.354102 + 1.08981i) q^{52} +(0.309017 - 0.224514i) q^{53} +2.61803 q^{54} +7.47214 q^{56} +(4.73607 - 3.44095i) q^{57} +(4.85410 + 14.9394i) q^{58} +(2.28115 - 7.02067i) q^{59} +(-2.42705 - 1.76336i) q^{60} +(9.35410 + 6.79615i) q^{61} +(4.92705 - 15.1639i) q^{62} +(-0.309017 - 0.951057i) q^{63} +(-7.04508 + 5.11855i) q^{64} -0.145898 q^{65} +1.85410 q^{67} +(4.50000 - 3.26944i) q^{68} +(-0.0729490 - 0.224514i) q^{69} +(-0.500000 + 1.53884i) q^{70} +(-8.35410 - 6.06961i) q^{71} +(6.04508 + 4.39201i) q^{72} +(-1.76393 + 5.42882i) q^{73} +(5.04508 + 15.5272i) q^{74} +(-3.73607 + 2.71441i) q^{75} +28.4164 q^{76} +0.618034 q^{78} +(-8.89919 + 6.46564i) q^{79} +(-1.88197 - 5.79210i) q^{80} +(0.309017 - 0.951057i) q^{81} +(0.500000 + 0.363271i) q^{82} +(-1.19098 - 0.865300i) q^{83} +(1.50000 - 4.61653i) q^{84} +(0.218847 + 0.673542i) q^{85} +(-14.2082 + 10.3229i) q^{86} +6.00000 q^{87} -8.23607 q^{89} +(-1.30902 + 0.951057i) q^{90} +(-0.0729490 - 0.224514i) q^{91} +(0.354102 - 1.08981i) q^{92} +(-4.92705 - 3.57971i) q^{93} +(-21.3713 - 15.5272i) q^{94} +(-1.11803 + 3.44095i) q^{95} +(3.35410 + 10.3229i) q^{96} +(-6.35410 + 4.61653i) q^{97} +15.7082 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + q^{3} + 6 q^{4} + 2 q^{5} - 4 q^{6} + q^{7} - 7 q^{8} - q^{9} + 2 q^{10} - 6 q^{12} - 3 q^{13} + q^{14} + 3 q^{15} - 14 q^{16} - 3 q^{17} - q^{18} + 5 q^{19} + 3 q^{20} + 4 q^{21} - 8 q^{23}+ \cdots + 36 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + q^3 + 6 * q^4 + 2 * q^5 - 4 * q^6 + q^7 - 7 * q^8 - q^9 + 2 * q^10 - 6 * q^12 - 3 * q^13 + q^14 + 3 * q^15 - 14 * q^16 - 3 * q^17 - q^18 + 5 * q^19 + 3 * q^20 + 4 * q^21 - 8 * q^23 - 13 * q^24 + q^25 - 3 * q^26 + q^27 + 9 * q^28 + 6 * q^29 - 2 * q^30 + 13 * q^31 - 30 * q^32 + 12 * q^34 - 2 * q^35 + 6 * q^36 - q^37 + 25 * q^38 + 3 * q^39 - q^40 + 7 * q^41 + 4 * q^42 + 2 * q^45 + 2 * q^46 - 8 * q^47 - q^48 + 6 * q^49 - 19 * q^50 - 12 * q^51 - 12 * q^52 - q^53 + 6 * q^54 + 12 * q^56 + 10 * q^57 + 6 * q^58 - 11 * q^59 - 3 * q^60 + 24 * q^61 + 13 * q^62 + q^63 - 17 * q^64 - 14 * q^65 - 6 * q^67 + 18 * q^68 - 7 * q^69 - 2 * q^70 - 20 * q^71 + 13 * q^72 - 16 * q^73 + 9 * q^74 - 6 * q^75 + 60 * q^76 - 2 * q^78 - 11 * q^79 - 12 * q^80 - q^81 + 2 * q^82 - 7 * q^83 + 6 * q^84 + 21 * q^85 - 30 * q^86 + 24 * q^87 - 24 * q^89 - 3 * q^90 - 7 * q^91 - 12 * q^92 - 13 * q^93 - 43 * q^94 - 12 * q^97 + 36 * q^98

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