LMFDB - Embedded newform 1110.2.bb.e.1009.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(1009,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1110.1009");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.bb (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1009.5
Character	$\chi$	$=$	1110.1009
Dual form			1110.2.bb.e.1099.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.649619 + 2.13962i) q^{5} -1.00000 q^{6} +(0.381600 - 0.220317i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.649619 + 2.13962i) q^{5} -1.00000 q^{6} +(0.381600 - 0.220317i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.507226 - 2.17778i) q^{10} -4.82933 q^{11} +(0.866025 + 0.500000i) q^{12} +(5.17855 - 2.98984i) q^{13} -0.440634 q^{14} +(1.63240 + 1.52816i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(4.52971 + 2.61523i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(-2.49232 - 4.31682i) q^{19} +(-1.52816 + 1.63240i) q^{20} +(0.220317 - 0.381600i) q^{21} +(4.18232 + 2.41466i) q^{22} -4.03564i q^{23} +(-0.500000 - 0.866025i) q^{24} +(-4.15599 + 2.77988i) q^{25} -5.97967 q^{26} -1.00000i q^{27} +(0.381600 + 0.220317i) q^{28} +6.01733 q^{29} +(-0.649619 - 2.13962i) q^{30} +10.0217 q^{31} +(0.866025 - 0.500000i) q^{32} +(-4.18232 + 2.41466i) q^{33} +(-2.61523 - 4.52971i) q^{34} +(0.719290 + 0.673359i) q^{35} +1.00000 q^{36} +(4.28401 - 4.31825i) q^{37} +4.98464i q^{38} +(2.98984 - 5.17855i) q^{39} +(2.13962 - 0.649619i) q^{40} +(2.74660 + 4.75726i) q^{41} +(-0.381600 + 0.220317i) q^{42} +3.34310i q^{43} +(-2.41466 - 4.18232i) q^{44} +(2.17778 + 0.507226i) q^{45} +(-2.01782 + 3.49497i) q^{46} +4.75097i q^{47} +1.00000i q^{48} +(-3.40292 + 5.89403i) q^{49} +(4.98913 - 0.329455i) q^{50} +5.23046 q^{51} +(5.17855 + 2.98984i) q^{52} +(9.44183 + 5.45125i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-3.13723 - 10.3330i) q^{55} +(-0.220317 - 0.381600i) q^{56} +(-4.31682 - 2.49232i) q^{57} +(-5.21116 - 3.00866i) q^{58} +(-4.43986 + 7.69007i) q^{59} +(-0.507226 + 2.17778i) q^{60} +(4.63633 + 8.03036i) q^{61} +(-8.67902 - 5.01083i) q^{62} -0.440634i q^{63} -1.00000 q^{64} +(9.76121 + 9.13789i) q^{65} +4.82933 q^{66} +(-0.414474 + 0.239297i) q^{67} +5.23046i q^{68} +(-2.01782 - 3.49497i) q^{69} +(-0.286244 - 0.942791i) q^{70} +(-2.95496 - 5.11813i) q^{71} +(-0.866025 - 0.500000i) q^{72} -9.65667i q^{73} +(-5.86918 + 1.59771i) q^{74} +(-2.20925 + 4.48544i) q^{75} +(2.49232 - 4.31682i) q^{76} +(-1.84287 + 1.06398i) q^{77} +(-5.17855 + 2.98984i) q^{78} +(-0.379804 - 0.657840i) q^{79} +(-2.17778 - 0.507226i) q^{80} +(-0.500000 - 0.866025i) q^{81} -5.49321i q^{82} +(2.36570 + 1.36584i) q^{83} +0.440634 q^{84} +(-2.65302 + 11.3908i) q^{85} +(1.67155 - 2.89521i) q^{86} +(5.21116 - 3.00866i) q^{87} +4.82933i q^{88} +(0.0225381 - 0.0390372i) q^{89} +(-1.63240 - 1.52816i) q^{90} +(1.31742 - 2.28184i) q^{91} +(3.49497 - 2.01782i) q^{92} +(8.67902 - 5.01083i) q^{93} +(2.37548 - 4.11446i) q^{94} +(7.61732 - 8.13692i) q^{95} +(0.500000 - 0.866025i) q^{96} -10.6615i q^{97} +(5.89403 - 3.40292i) q^{98} +(-2.41466 + 4.18232i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 20 q^{4} + 2 q^{5} - 40 q^{6} + 20 q^{9}+O(q^{10}) $ 40 * q + 20 * q^4 + 2 * q^5 - 40 * q^6 + 20 * q^9	$ 40 q + 20 q^{4} + 2 q^{5} - 40 q^{6} + 20 q^{9} + 24 q^{14} - 20 q^{16} - 14 q^{19} - 2 q^{20} - 12 q^{21} - 20 q^{24} - 2 q^{25} - 24 q^{26} + 12 q^{29} - 2 q^{30} - 40 q^{31} + 10 q^{34} - 2 q^{35} + 40 q^{36} + 12 q^{39} + 20 q^{41} + 4 q^{45} + 2 q^{46} + 28 q^{49} + 12 q^{50} - 20 q^{51} - 20 q^{54} + 32 q^{55} + 12 q^{56} - 40 q^{59} + 12 q^{61} - 40 q^{64} + 2 q^{65} + 2 q^{69} - 22 q^{70} + 12 q^{71} - 30 q^{74} - 24 q^{75} + 14 q^{76} - 24 q^{79} - 4 q^{80} - 20 q^{81} - 24 q^{84} + 40 q^{85} - 4 q^{86} - 34 q^{89} - 4 q^{91} - 8 q^{94} + 6 q^{95} + 20 q^{96}+O(q^{100}) $ 40 * q + 20 * q^4 + 2 * q^5 - 40 * q^6 + 20 * q^9 + 24 * q^14 - 20 * q^16 - 14 * q^19 - 2 * q^20 - 12 * q^21 - 20 * q^24 - 2 * q^25 - 24 * q^26 + 12 * q^29 - 2 * q^30 - 40 * q^31 + 10 * q^34 - 2 * q^35 + 40 * q^36 + 12 * q^39 + 20 * q^41 + 4 * q^45 + 2 * q^46 + 28 * q^49 + 12 * q^50 - 20 * q^51 - 20 * q^54 + 32 * q^55 + 12 * q^56 - 40 * q^59 + 12 * q^61 - 40 * q^64 + 2 * q^65 + 2 * q^69 - 22 * q^70 + 12 * q^71 - 30 * q^74 - 24 * q^75 + 14 * q^76 - 24 * q^79 - 4 * q^80 - 20 * q^81 - 24 * q^84 + 40 * q^85 - 4 * q^86 - 34 * q^89 - 4 * q^91 - 8 * q^94 + 6 * q^95 + 20 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.649619	+	2.13962i	0.290519	+	0.956869i
$5$	0.649619	+	2.13962i	0.290519	+	0.956869i
$6$	−1.00000			−0.408248
$7$	0.381600	−	0.220317i	0.144231	−	0.0832719i	−0.426148	−	0.904654i	$-0.640130\pi$
$7$	0.381600	−	0.220317i	0.144231	−	0.0832719i	0.570379	+	0.821382i	$0.306796\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	0.507226	−	2.17778i	0.160399	−	0.688674i
$11$	−4.82933			−1.45610			−0.728049	−	0.685525i	$-0.759573\pi$
$11$	−4.82933			−1.45610			−0.728049	+	0.685525i	$0.759573\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	5.17855	−	2.98984i	1.43627	−	0.829231i	0.438683	−	0.898642i	$-0.355445\pi$
$13$	5.17855	−	2.98984i	1.43627	−	0.829231i	0.997588	+	0.0694108i	$0.0221119\pi$
$14$	−0.440634			−0.117764
$15$	1.63240	+	1.52816i	0.421484	+	0.394569i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	4.52971	+	2.61523i	1.09862	+	0.634286i	0.935857	−	0.352380i	$-0.114627\pi$
$17$	4.52971	+	2.61523i	1.09862	+	0.634286i	0.162759	+	0.986666i	$0.447961\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$	−2.49232	−	4.31682i	−0.571777	−	0.990347i	−0.996384	−	0.0849691i	$-0.972921\pi$
$19$	−2.49232	−	4.31682i	−0.571777	−	0.990347i	0.424606	−	0.905378i	$-0.360412\pi$
$20$	−1.52816	+	1.63240i	−0.341707	+	0.365016i
$21$	0.220317	−	0.381600i	0.0480771	−	0.0832719i
$22$	4.18232	+	2.41466i	0.891674	+	0.514808i
$23$		−	4.03564i		−	0.841489i	−0.907179	−	0.420744i	$-0.861769\pi$
$23$		−	4.03564i		−	0.841489i	0.907179	−	0.420744i	$-0.138231\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−4.15599	+	2.77988i	−0.831198	+	0.555977i
$26$	−5.97967			−1.17271
$27$		−	1.00000i		−	0.192450i
$28$	0.381600	+	0.220317i	0.0721156	+	0.0416360i
$29$	6.01733			1.11739			0.558695	−	0.829373i	$-0.311302\pi$
$29$	6.01733			1.11739			0.558695	+	0.829373i	$0.311302\pi$
$30$	−0.649619	−	2.13962i	−0.118604	−	0.390640i
$31$	10.0217			1.79994			0.899972	−	0.435948i	$-0.143587\pi$
$31$	10.0217			1.79994			0.899972	+	0.435948i	$0.143587\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−4.18232	+	2.41466i	−0.728049	+	0.420339i
$34$	−2.61523	−	4.52971i	−0.448508	−	0.776839i
$35$	0.719290	+	0.673359i	0.121582	+	0.113818i
$36$	1.00000			0.166667
$37$	4.28401	−	4.31825i	0.704287	−	0.709916i
$37$	4.28401	−	4.31825i	0.704287	−	0.709916i
$38$			4.98464i			0.808615i
$39$	2.98984	−	5.17855i	0.478757	−	0.829231i
$40$	2.13962	−	0.649619i	0.338304	−	0.102714i
$41$	2.74660	+	4.75726i	0.428947	+	0.742959i	0.996780	−	0.0801855i	$-0.0255513\pi$
$41$	2.74660	+	4.75726i	0.428947	+	0.742959i	−0.567833	+	0.823144i	$0.692218\pi$
$42$	−0.381600	+	0.220317i	−0.0588821	+	0.0339956i
$43$			3.34310i			0.509817i	0.966965	+	0.254909i	$0.0820454\pi$
$43$			3.34310i			0.509817i	−0.966965	+	0.254909i	$0.917955\pi$
$44$	−2.41466	−	4.18232i	−0.364024	−	0.630509i
$45$	2.17778	+	0.507226i	0.324644	+	0.0756127i
$46$	−2.01782	+	3.49497i	−0.297511	+	0.515305i
$47$			4.75097i			0.693000i	0.938050	+	0.346500i	$0.112630\pi$
$47$			4.75097i			0.693000i	−0.938050	+	0.346500i	$0.887370\pi$
$48$			1.00000i			0.144338i
$49$	−3.40292	+	5.89403i	−0.486132	+	0.842005i
$50$	4.98913	−	0.329455i	0.705570	−	0.0465920i
$51$	5.23046			0.732411
$52$	5.17855	+	2.98984i	0.718135	+	0.414616i
$53$	9.44183	+	5.45125i	1.29694	+	0.748786i	0.979874	−	0.199619i	$-0.0639704\pi$
$53$	9.44183	+	5.45125i	1.29694	+	0.748786i	0.317062	+	0.948405i	$0.397304\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−3.13723	−	10.3330i	−0.423023	−	1.39330i
$56$	−0.220317	−	0.381600i	−0.0294411	−	0.0509934i
$57$	−4.31682	−	2.49232i	−0.571777	−	0.330116i
$58$	−5.21116	−	3.00866i	−0.684259	−	0.395057i
$59$	−4.43986	+	7.69007i	−0.578021	+	1.00116i	0.417685	+	0.908592i	$0.362842\pi$
$59$	−4.43986	+	7.69007i	−0.578021	+	1.00116i	−0.995706	+	0.0925700i	$0.970492\pi$
$60$	−0.507226	+	2.17778i	−0.0654825	+	0.281150i
$61$	4.63633	+	8.03036i	0.593621	+	1.02818i	0.993740	+	0.111718i	$0.0356355\pi$
$61$	4.63633	+	8.03036i	0.593621	+	1.02818i	−0.400119	+	0.916463i	$0.631031\pi$
$62$	−8.67902	−	5.01083i	−1.10224	−	0.636376i
$63$		−	0.440634i		−	0.0555146i
$64$	−1.00000			−0.125000
$65$	9.76121	+	9.13789i	1.21073	+	1.13342i
$66$	4.82933			0.594449
$67$	−0.414474	+	0.239297i	−0.0506361	+	0.0292348i	−0.525104	−	0.851038i	$-0.675974\pi$
$67$	−0.414474	+	0.239297i	−0.0506361	+	0.0292348i	0.474468	+	0.880273i	$0.342640\pi$
$68$			5.23046i			0.634286i
$69$	−2.01782	−	3.49497i	−0.242917	−	0.420744i
$70$	−0.286244	−	0.942791i	−0.0342127	−	0.112685i
$71$	−2.95496	−	5.11813i	−0.350689	−	0.607411i	0.635682	−	0.771951i	$-0.280719\pi$
$71$	−2.95496	−	5.11813i	−0.350689	−	0.607411i	−0.986370	+	0.164541i	$0.947386\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$		−	9.65667i		−	1.13023i	−0.825013	−	0.565114i	$-0.808832\pi$
$73$		−	9.65667i		−	1.13023i	0.825013	−	0.565114i	$-0.191168\pi$
$74$	−5.86918	+	1.59771i	−0.682279	+	0.185730i
$75$	−2.20925	+	4.48544i	−0.255102	+	0.517935i
$76$	2.49232	−	4.31682i	0.285889	−	0.495174i
$77$	−1.84287	+	1.06398i	−0.210015	+	0.121252i
$78$	−5.17855	+	2.98984i	−0.586355	+	0.338532i
$79$	−0.379804	−	0.657840i	−0.0427313	−	0.0740128i	0.843869	−	0.536550i	$-0.180273\pi$
$79$	−0.379804	−	0.657840i	−0.0427313	−	0.0740128i	−0.886600	+	0.462537i	$0.846939\pi$
$80$	−2.17778	−	0.507226i	−0.243483	−	0.0567095i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		−	5.49321i		−	0.606623i
$83$	2.36570	+	1.36584i	0.259670	+	0.149920i	0.624184	−	0.781278i	$-0.285432\pi$
$83$	2.36570	+	1.36584i	0.259670	+	0.149920i	−0.364514	+	0.931198i	$0.618765\pi$
$84$	0.440634			0.0480771
$85$	−2.65302	+	11.3908i	−0.287761	+	1.23550i
$86$	1.67155	−	2.89521i	0.180248	−	0.312198i
$87$	5.21116	−	3.00866i	0.558695	−	0.322563i
$88$			4.82933i			0.514808i
$89$	0.0225381	−	0.0390372i	0.00238904	−	0.00413793i	−0.864828	−	0.502068i	$-0.832573\pi$
$89$	0.0225381	−	0.0390372i	0.00238904	−	0.00413793i	0.867217	+	0.497930i	$0.165906\pi$
$90$	−1.63240	−	1.52816i	−0.172070	−	0.161082i
$91$	1.31742	−	2.28184i	0.138103	−	0.239202i
$92$	3.49497	−	2.01782i	0.364375	−	0.210372i
$93$	8.67902	−	5.01083i	0.899972	−	0.519599i
$94$	2.37548	−	4.11446i	0.245013	−	0.424374i
$95$	7.61732	−	8.13692i	0.781521	−	0.834830i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$		−	10.6615i		−	1.08252i	−0.840856	−	0.541258i	$-0.817948\pi$
$97$		−	10.6615i		−	1.08252i	0.840856	−	0.541258i	$-0.182052\pi$
$98$	5.89403	−	3.40292i	0.595387	−	0.343747i
$99$	−2.41466	+	4.18232i	−0.242683	+	0.420339i
$100$	−4.48544	−	2.20925i	−0.448544	−	0.220925i
$101$	3.89010			0.387079			0.193540	−	0.981092i	$-0.438003\pi$
$101$	3.89010			0.387079			0.193540	+	0.981092i	$0.438003\pi$
$102$	−4.52971	−	2.61523i	−0.448508	−	0.258946i
$103$			6.35059i			0.625742i	0.949796	+	0.312871i	$0.101291\pi$
$103$			6.35059i			0.625742i	−0.949796	+	0.312871i	$0.898709\pi$
$104$	−2.98984	−	5.17855i	−0.293178	−	0.507798i
$105$	0.959603	+	0.223501i	0.0936476	+	0.0218114i
$106$	−5.45125	−	9.44183i	−0.529472	−	0.917072i
$107$	−1.04745	+	0.604748i	−0.101261	+	0.0584632i	−0.549775	−	0.835313i	$-0.685287\pi$
$107$	−1.04745	+	0.604748i	−0.101261	+	0.0584632i	0.448514	+	0.893776i	$0.351953\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	6.08438	−	10.5384i	0.582777	−	1.00940i	−0.412371	−	0.911016i	$-0.635299\pi$
$109$	6.08438	−	10.5384i	0.582777	−	1.00940i	0.995149	−	0.0983842i	$-0.0313674\pi$
$110$	−2.44956	+	10.5172i	−0.233556	+	1.00278i
$111$	1.55094	−	5.88172i	0.147208	−	0.558268i
$112$			0.440634i			0.0416360i
$113$	−14.6936	−	8.48333i	−1.38225	−	0.798044i	−0.389827	−	0.920888i	$-0.627465\pi$
$113$	−14.6936	−	8.48333i	−1.38225	−	0.798044i	−0.992426	+	0.122844i	$0.960799\pi$
$114$	2.49232	+	4.31682i	0.233427	+	0.404308i
$115$	8.63475	−	2.62163i	0.805195	−	0.244468i
$116$	3.00866	+	5.21116i	0.279348	+	0.483844i
$117$		−	5.97967i		−	0.552821i
$118$	7.69007	−	4.43986i	0.707928	−	0.408723i
$119$	2.30472			0.211273
$120$	1.52816	−	1.63240i	0.139501	−	0.149017i
$121$	12.3224			1.12022
$122$		−	9.27266i		−	0.839507i
$123$	4.75726	+	2.74660i	0.428947	+	0.247653i
$124$	5.01083	+	8.67902i	0.449986	+	0.779399i
$125$	−8.64772	−	7.08639i	−0.773475	−	0.633826i
$126$	−0.220317	+	0.381600i	−0.0196274	+	0.0339956i
$127$	−16.2363	−	9.37403i	−1.44074	−	0.831811i	−0.442840	−	0.896601i	$-0.646029\pi$
$127$	−16.2363	−	9.37403i	−1.44074	−	0.831811i	−0.997899	+	0.0647897i	$0.979362\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	1.67155	+	2.89521i	0.147172	+	0.254909i
$130$	−3.88451	−	12.7943i	−0.340694	−	1.12213i
$131$	−9.62264	+	16.6669i	−0.840734	+	1.45619i	0.0485417	+	0.998821i	$0.484543\pi$
$131$	−9.62264	+	16.6669i	−0.840734	+	1.45619i	−0.889275	+	0.457372i	$0.848791\pi$
$132$	−4.18232	−	2.41466i	−0.364024	−	0.210170i
$133$	−1.90214	−	1.09820i	−0.164936	−	0.0952260i
$134$	0.478594			0.0413442
$135$	2.13962	−	0.649619i	0.184150	−	0.0559103i
$136$	2.61523	−	4.52971i	0.224254	−	0.388419i
$137$		−	19.0712i		−	1.62936i	−0.579909	−	0.814682i	$-0.696912\pi$
$137$		−	19.0712i		−	1.62936i	0.579909	−	0.814682i	$-0.303088\pi$
$138$			4.03564i			0.343536i
$139$	8.96860	−	15.5341i	0.760707	−	1.31758i	−0.181779	−	0.983339i	$-0.558186\pi$
$139$	8.96860	−	15.5341i	0.760707	−	1.31758i	0.942487	−	0.334244i	$-0.108481\pi$
$140$	−0.223501	+	0.959603i	−0.0188893	+	0.0811012i
$141$	2.37548	+	4.11446i	0.200052	+	0.346500i
$142$			5.90991i			0.495949i
$143$	−25.0089	+	14.4389i	−2.09135	+	1.20744i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	3.90897	+	12.8748i	0.324623	+	1.06920i
$146$	−4.82833	+	8.36292i	−0.399596	+	0.692120i
$147$			6.80584i			0.561336i
$148$	5.88172	+	1.55094i	0.483474	+	0.127486i
$149$	−19.2223			−1.57476			−0.787378	−	0.616471i	$-0.788562\pi$
$149$	−19.2223			−1.57476			−0.787378	+	0.616471i	$0.788562\pi$
$150$	4.15599	−	2.77988i	0.339335	−	0.226977i
$151$	2.70857	+	4.69139i	0.220421	+	0.381780i	0.954936	−	0.296813i	$-0.0959237\pi$
$151$	2.70857	+	4.69139i	0.220421	+	0.381780i	−0.734515	+	0.678592i	$0.762590\pi$
$152$	−4.31682	+	2.49232i	−0.350141	+	0.202154i
$153$	4.52971	−	2.61523i	0.366205	−	0.211429i
$154$	2.12796			0.171476
$155$	6.51027	+	21.4426i	0.522917	+	1.72231i
$156$	5.97967			0.478757
$157$	−7.33168	−	4.23295i	−0.585132	−	0.337826i	0.178038	−	0.984024i	$-0.443025\pi$
$157$	−7.33168	−	4.23295i	−0.585132	−	0.337826i	−0.763170	+	0.646198i	$0.776358\pi$
$158$			0.759608i			0.0604312i
$159$	10.9025			0.864624
$160$	1.63240	+	1.52816i	0.129052	+	0.120812i
$161$	−0.889119	−	1.54000i	−0.0700724	−	0.121369i
$162$			1.00000i			0.0785674i
$163$	4.50879	+	2.60315i	0.353156	+	0.203895i	0.666074	−	0.745885i	$-0.267973\pi$
$163$	4.50879	+	2.60315i	0.353156	+	0.203895i	−0.312918	+	0.949780i	$0.601307\pi$
$164$	−2.74660	+	4.75726i	−0.214474	+	0.371479i
$165$	−7.88339	−	7.37999i	−0.613721	−	0.574531i
$166$	−1.36584	−	2.36570i	−0.106010	−	0.183614i
$167$	5.02993	−	2.90403i	0.389228	−	0.224721i	−0.292598	−	0.956236i	$-0.594520\pi$
$167$	5.02993	−	2.90403i	0.389228	−	0.224721i	0.681825	+	0.731515i	$0.261186\pi$
$168$	−0.381600	−	0.220317i	−0.0294411	−	0.0169978i
$169$	11.3782	−	19.7077i	0.875249	−	1.51598i
$170$	7.99298	−	8.53820i	0.613033	−	0.654850i
$171$	−4.98464			−0.381185
$172$	−2.89521	+	1.67155i	−0.220757	+	0.127454i
$173$	12.3700	+	7.14183i	0.940475	+	0.542983i	0.890109	−	0.455748i	$-0.150628\pi$
$173$	12.3700	+	7.14183i	0.940475	+	0.542983i	0.0503656	+	0.998731i	$0.483961\pi$
$174$	−6.01733			−0.456173
$175$	−0.973470	+	1.97644i	−0.0735874	+	0.149405i
$176$	2.41466	−	4.18232i	0.182012	−	0.315254i
$177$			8.87973i			0.667441i
$178$	−0.0390372	+	0.0225381i	−0.00292596	+	0.00168930i
$179$	−12.6539			−0.945795			−0.472897	−	0.881118i	$-0.656792\pi$
$179$	−12.6539			−0.945795			−0.472897	+	0.881118i	$0.656792\pi$
$180$	0.649619	+	2.13962i	0.0484198	+	0.159478i
$181$	1.88372	+	3.26270i	0.140016	+	0.242515i	0.927502	−	0.373817i	$-0.121951\pi$
$181$	1.88372	+	3.26270i	0.140016	+	0.242515i	−0.787486	+	0.616332i	$0.788618\pi$
$182$	−2.28184	+	1.31742i	−0.169141	+	0.0976538i
$183$	8.03036	+	4.63633i	0.593621	+	0.342727i
$184$	−4.03564			−0.297511
$185$	12.0224	+	6.36095i	0.883905	+	0.467667i
$186$	−10.0217			−0.734824
$187$	−21.8755	−	12.6298i	−1.59969	−	0.923583i
$188$	−4.11446	+	2.37548i	−0.300078	+	0.173250i
$189$	−0.220317	−	0.381600i	−0.0160257	−	0.0277573i
$190$	−10.6653	+	3.23812i	−0.773739	+	0.234918i
$191$	−7.04436			−0.509712			−0.254856	−	0.966979i	$-0.582028\pi$
$191$	−7.04436			−0.509712			−0.254856	+	0.966979i	$0.582028\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$		−	2.05757i		−	0.148107i	−0.997254	−	0.0740535i	$-0.976406\pi$
$193$		−	2.05757i		−	0.148107i	0.997254	−	0.0740535i	$-0.0235936\pi$
$194$	−5.33077	+	9.23317i	−0.382727	+	0.662903i
$195$	13.0224	+	3.03304i	0.932554	+	0.217201i
$196$	−6.80584			−0.486132
$197$	−2.64503	−	1.52711i	−0.188450	−	0.108802i	0.402807	−	0.915285i	$-0.368035\pi$
$197$	−2.64503	−	1.52711i	−0.188450	−	0.108802i	−0.591257	+	0.806483i	$0.701368\pi$
$198$	4.18232	−	2.41466i	0.297225	−	0.171603i
$199$	−3.16668			−0.224480			−0.112240	−	0.993681i	$-0.535803\pi$
$199$	−3.16668			−0.224480			−0.112240	+	0.993681i	$0.535803\pi$
$200$	2.77988	+	4.15599i	0.196567	+	0.293873i
$201$	−0.239297	+	0.414474i	−0.0168787	+	0.0292348i
$202$	−3.36892	−	1.94505i	−0.237037	−	0.136853i
$203$	2.29621	−	1.32572i	0.161163	−	0.0930472i
$204$	2.61523	+	4.52971i	0.183103	+	0.317143i
$205$	−8.39450	+	8.96711i	−0.586297	+	0.626290i
$206$	3.17530	−	5.49977i	0.221233	−	0.383187i
$207$	−3.49497	−	2.01782i	−0.242917	−	0.140248i
$208$			5.97967i			0.414616i
$209$	12.0362	+	20.8474i	0.832563	+	1.44204i
$210$	−0.719290	−	0.673359i	−0.0496357	−	0.0464662i
$211$	16.7551			1.15347			0.576733	−	0.816933i	$-0.304327\pi$
$211$	16.7551			1.15347			0.576733	+	0.816933i	$0.304327\pi$
$212$			10.9025i			0.748786i
$213$	−5.11813	−	2.95496i	−0.350689	−	0.202470i
$214$	1.20950			0.0826795
$215$	−7.15297	+	2.17174i	−0.487829	+	0.148111i
$216$	−1.00000			−0.0680414
$217$	3.82427	−	2.20794i	0.259608	−	0.149885i
$218$	−10.5384	+	6.08438i	−0.713754	+	0.412086i
$219$	−4.82833	−	8.36292i	−0.326269	−	0.565114i
$220$	7.37999	−	7.88339i	0.497559	−	0.531498i
$221$	31.2764			2.10388
$222$	−4.28401	+	4.31825i	−0.287524	+	0.289822i
$223$			4.42684i			0.296443i	0.988954	+	0.148222i	$0.0473549\pi$
$223$			4.42684i			0.296443i	−0.988954	+	0.148222i	$0.952645\pi$
$224$	0.220317	−	0.381600i	0.0147205	−	0.0254967i
$225$	0.329455	+	4.98913i	0.0219637	+	0.332609i
$226$	8.48333	+	14.6936i	0.564303	+	0.977401i
$227$	−6.94841	+	4.01166i	−0.461182	+	0.266263i	−0.712541	−	0.701630i	$-0.752456\pi$
$227$	−6.94841	+	4.01166i	−0.461182	+	0.266263i	0.251359	+	0.967894i	$0.419122\pi$
$228$		−	4.98464i		−	0.330116i
$229$	−3.06681	−	5.31188i	−0.202661	−	0.351019i	0.746724	−	0.665134i	$-0.231626\pi$
$229$	−3.06681	−	5.31188i	−0.202661	−	0.351019i	−0.949385	+	0.314115i	$0.898292\pi$
$230$	−8.78873	−	2.04698i	−0.579512	−	0.134974i
$231$	−1.06398	+	1.84287i	−0.0700049	+	0.121252i
$232$		−	6.01733i		−	0.395057i
$233$		−	6.25575i		−	0.409828i	−0.978780	−	0.204914i	$-0.934309\pi$
$233$		−	6.25575i		−	0.409828i	0.978780	−	0.204914i	$-0.0656914\pi$
$234$	−2.98984	+	5.17855i	−0.195452	+	0.338532i
$235$	−10.1653	+	3.08632i	−0.663110	+	0.201329i
$236$	−8.87973			−0.578021
$237$	−0.657840	−	0.379804i	−0.0427313	−	0.0246709i
$238$	−1.99594	−	1.15236i	−0.129378	−	0.0746963i
$239$	11.6089	−	20.1073i	0.750919	−	1.30063i	−0.196459	−	0.980512i	$-0.562944\pi$
$239$	11.6089	−	20.1073i	0.750919	−	1.30063i	0.947378	−	0.320118i	$-0.103723\pi$
$240$	−2.13962	+	0.649619i	−0.138112	+	0.0419327i
$241$	7.41456	+	12.8424i	0.477614	+	0.827251i	0.999671	−	0.0256594i	$-0.00816855\pi$
$241$	7.41456	+	12.8424i	0.477614	+	0.827251i	−0.522057	+	0.852911i	$0.674835\pi$
$242$	−10.6715	−	6.16121i	−0.685992	−	0.396058i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−4.63633	+	8.03036i	−0.296810	+	0.514091i
$245$	−14.8216	−	3.45210i	−0.946919	−	0.220546i
$246$	−2.74660	−	4.75726i	−0.175117	−	0.303312i
$247$	−25.8132	−	14.9032i	−1.64245	−	0.948271i
$248$		−	10.0217i		−	0.636376i
$249$	2.73168			0.173113
$250$	3.94595	+	10.4609i	0.249564	+	0.661603i
$251$	−11.2591			−0.710670			−0.355335	−	0.934739i	$-0.615633\pi$
$251$	−11.2591			−0.710670			−0.355335	+	0.934739i	$0.615633\pi$
$252$	0.381600	−	0.220317i	0.0240385	−	0.0138787i
$253$			19.4894i			1.22529i
$254$	9.37403	+	16.2363i	0.588179	+	1.01876i
$255$	3.39781	+	11.1912i	0.212779	+	0.700821i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.90348	+	4.56308i	0.493006	+	0.284637i	0.725821	−	0.687884i	$-0.241460\pi$
$257$	7.90348	+	4.56308i	0.493006	+	0.284637i	−0.232815	+	0.972521i	$0.574794\pi$
$258$		−	3.34310i		−	0.208132i
$259$	0.683395	−	2.59168i	0.0424641	−	0.161039i
$260$	−3.03304	+	13.0224i	−0.188101	+	0.807615i
$261$	3.00866	−	5.21116i	0.186232	−	0.322563i
$262$	16.6669	−	9.62264i	1.02968	−	0.594488i
$263$	10.2961	−	5.94445i	0.634884	−	0.366551i	−0.147757	−	0.989024i	$-0.547205\pi$
$263$	10.2961	−	5.94445i	0.634884	−	0.366551i	0.782641	+	0.622473i	$0.213872\pi$
$264$	2.41466	+	4.18232i	0.148612	+	0.257404i
$265$	−5.53002	+	23.7432i	−0.339707	+	1.45853i
$266$	1.09820	+	1.90214i	0.0673349	+	0.116628i
$267$		−	0.0450763i		−	0.00275862i
$268$	−0.414474	−	0.239297i	−0.0253180	−	0.0146174i
$269$	−27.6918			−1.68840			−0.844201	−	0.536027i	$-0.819924\pi$
$269$	−27.6918			−1.68840			−0.844201	+	0.536027i	$0.819924\pi$
$270$	−2.17778	−	0.507226i	−0.132535	−	0.0308688i
$271$	−15.3473	+	26.5823i	−0.932282	+	1.61476i	−0.152871	+	0.988246i	$0.548852\pi$
$271$	−15.3473	+	26.5823i	−0.932282	+	1.61476i	−0.779411	+	0.626513i	$0.784481\pi$
$272$	−4.52971	+	2.61523i	−0.274654	+	0.158572i
$273$		−	2.63484i		−	0.159468i
$274$	−9.53560	+	16.5161i	−0.576067	+	0.997777i
$275$	20.0706	−	13.4250i	1.21031	−	0.809556i
$276$	2.01782	−	3.49497i	0.121458	−	0.210372i
$277$	−27.0544	+	15.6199i	−1.62554	+	0.938508i	−0.640142	+	0.768256i	$0.721125\pi$
$277$	−27.0544	+	15.6199i	−1.62554	+	0.938508i	−0.985401	+	0.170251i	$0.945542\pi$
$278$	−15.5341	+	8.96860i	−0.931672	+	0.537901i
$279$	5.01083	−	8.67902i	0.299991	−	0.519599i
$280$	0.673359	−	0.719290i	0.0402409	−	0.0429858i
$281$	5.14092	−	8.90433i	0.306681	−	0.531188i	−0.670953	−	0.741500i	$-0.734115\pi$
$281$	5.14092	−	8.90433i	0.306681	−	0.531188i	0.977634	+	0.210312i	$0.0674481\pi$
$282$		−	4.75097i		−	0.282916i
$283$	−17.8121	+	10.2838i	−1.05882	+	0.611310i	−0.925105	−	0.379710i	$-0.876024\pi$
$283$	−17.8121	+	10.2838i	−1.05882	+	0.611310i	−0.133714	+	0.991020i	$0.542690\pi$
$284$	2.95496	−	5.11813i	0.175344	−	0.303705i
$285$	2.52834	−	10.8554i	0.149766	−	0.643021i
$286$	28.8778			1.70758
$287$	2.09621	+	1.21025i	0.123735	+	0.0714385i
$288$		−	1.00000i		−	0.0589256i
$289$	5.17885	+	8.97003i	0.304638	+	0.527649i
$290$	3.05214	−	13.1044i	0.179228	−	0.769518i
$291$	−5.33077	−	9.23317i	−0.312496	−	0.541258i
$292$	8.36292	−	4.82833i	0.489403	−	0.282557i
$293$	−21.1680	+	12.2213i	−1.23665	+	0.713978i	−0.968407	−	0.249374i	$-0.919775\pi$
$293$	−21.1680	+	12.2213i	−1.23665	+	0.713978i	−0.268240	+	0.963352i	$0.586442\pi$
$294$	3.40292	−	5.89403i	0.198462	−	0.343747i
$295$	−19.3381	−	4.50403i	−1.12591	−	0.262235i
$296$	−4.31825	−	4.28401i	−0.250993	−	0.249003i
$297$			4.82933i			0.280226i
$298$	16.6470	+	9.61117i	0.964337	+	0.556760i
$299$	−12.0659	−	20.8987i	−0.697789	−	1.20861i
$300$	−4.98913	+	0.329455i	−0.288048	+	0.0190211i
$301$	0.736540	+	1.27573i	0.0424535	+	0.0735316i
$302$		−	5.41715i		−	0.311722i
$303$	3.36892	−	1.94505i	0.193540	−	0.111740i
$304$	4.98464			0.285889
$305$	−14.1701	+	15.1367i	−0.811378	+	0.866724i
$306$	−5.23046			−0.299005
$307$			11.6950i			0.667467i	0.942667	+	0.333734i	$0.108309\pi$
$307$			11.6950i			0.667467i	−0.942667	+	0.333734i	$0.891691\pi$
$308$	−1.84287	−	1.06398i	−0.105007	−	0.0606260i
$309$	3.17530	+	5.49977i	0.180636	+	0.312871i
$310$	5.08324	−	21.8250i	0.288709	−	1.23958i
$311$	−7.74316	+	13.4115i	−0.439074	+	0.760499i	−0.997618	−	0.0689761i	$-0.978027\pi$
$311$	−7.74316	+	13.4115i	−0.439074	+	0.760499i	0.558544	+	0.829475i	$0.311360\pi$
$312$	−5.17855	−	2.98984i	−0.293178	−	0.169266i
$313$	−17.3337	−	10.0076i	−0.979756	−	0.565663i	−0.0775599	−	0.996988i	$-0.524713\pi$
$313$	−17.3337	−	10.0076i	−0.979756	−	0.565663i	−0.902197	+	0.431325i	$0.858046\pi$
$314$	4.23295	+	7.33168i	0.238879	+	0.413751i
$315$	0.942791	−	0.286244i	0.0531202	−	0.0161280i
$316$	0.379804	−	0.657840i	0.0213657	−	0.0370064i
$317$	−3.18142	−	1.83679i	−0.178686	−	0.103165i	0.407989	−	0.912987i	$-0.366230\pi$
$317$	−3.18142	−	1.83679i	−0.178686	−	0.103165i	−0.586675	+	0.809822i	$0.699563\pi$
$318$	−9.44183	−	5.45125i	−0.529472	−	0.305691i
$319$	−29.0597			−1.62703
$320$	−0.649619	−	2.13962i	−0.0363148	−	0.119609i
$321$	−0.604748	+	1.04745i	−0.0337538	+	0.0584632i
$322$			1.77824i			0.0990974i
$323$		−	26.0719i		−	1.45068i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−13.2106	+	26.8215i	−0.732792	+	1.48779i
$326$	−2.60315	−	4.50879i	−0.144175	−	0.249719i
$327$		−	12.1688i		−	0.672933i
$328$	4.75726	−	2.74660i	0.262676	−	0.151656i
$329$	1.04672	+	1.81297i	0.0577075	+	0.0999522i
$330$	3.13723	+	10.3330i	0.172699	+	0.568810i
$331$	−4.95490	+	8.58214i	−0.272346	+	0.471717i	−0.969462	−	0.245241i	$-0.921133\pi$
$331$	−4.95490	+	8.58214i	−0.272346	+	0.471717i	0.697116	+	0.716958i	$0.254466\pi$
$332$			2.73168i			0.149920i
$333$	−1.59771	−	5.86918i	−0.0875539	−	0.321629i
$334$	−5.80806			−0.317803
$335$	−0.781256	−	0.731368i	−0.0426846	−	0.0399589i
$336$	0.220317	+	0.381600i	0.0120193	+	0.0208180i
$337$	−14.5975	+	8.42790i	−0.795179	+	0.459097i	−0.841783	−	0.539817i	$-0.818494\pi$
$337$	−14.5975	+	8.42790i	−0.795179	+	0.459097i	0.0466037	+	0.998913i	$0.485160\pi$
$338$	−19.7077	+	11.3782i	−1.07196	+	0.618894i
$339$	−16.9667			−0.921502
$340$	−11.1912	+	3.39781i	−0.606929	+	0.184272i
$341$	−48.3979			−2.62089
$342$	4.31682	+	2.49232i	0.233427	+	0.134769i
$343$			6.08332i			0.328468i
$344$	3.34310			0.180248
$345$	6.16710	−	6.58777i	0.332026	−	0.354674i
$346$	−7.14183	−	12.3700i	−0.383947	−	0.665016i
$347$		−	16.7732i		−	0.900430i	−0.892920	−	0.450215i	$-0.851347\pi$
$347$		−	16.7732i		−	0.900430i	0.892920	−	0.450215i	$-0.148653\pi$
$348$	5.21116	+	3.00866i	0.279348	+	0.161281i
$349$	−9.29079	+	16.0921i	−0.497325	+	0.861392i	−0.999995	−	0.00308625i	$-0.999018\pi$
$349$	−9.29079	+	16.0921i	−0.497325	+	0.861392i	0.502670	+	0.864478i	$0.332351\pi$
$350$	1.83127	−	1.22491i	0.0978854	−	0.0654742i
$351$	−2.98984	−	5.17855i	−0.159586	−	0.276410i
$352$	−4.18232	+	2.41466i	−0.222918	+	0.128702i
$353$	15.3052	+	8.83646i	0.814614	+	0.470317i	0.848555	−	0.529106i	$-0.177473\pi$
$353$	15.3052	+	8.83646i	0.814614	+	0.470317i	−0.0339418	+	0.999424i	$0.510806\pi$
$354$	4.43986	−	7.69007i	0.235976	−	0.408723i
$355$	9.03129	−	9.64733i	0.479331	−	0.512027i
$356$	0.0450763			0.00238904
$357$	1.99594	−	1.15236i	0.105636	−	0.0609893i
$358$	10.9586	+	6.32693i	0.579179	+	0.334389i
$359$	28.0978			1.48295			0.741473	−	0.670983i	$-0.234128\pi$
$359$	28.0978			1.48295			0.741473	+	0.670983i	$0.234128\pi$
$360$	0.507226	−	2.17778i	0.0267331	−	0.114779i
$361$	−2.92331	+	5.06332i	−0.153858	+	0.266490i
$362$		−	3.76744i		−	0.198012i
$363$	10.6715	−	6.16121i	0.560110	−	0.323380i
$364$	2.63484			0.138103
$365$	20.6616	−	6.27316i	1.08148	−	0.328352i
$366$	−4.63633	−	8.03036i	−0.242345	−	0.419753i
$367$	17.0312	−	9.83298i	0.889022	−	0.513277i	0.0153997	−	0.999881i	$-0.495098\pi$
$367$	17.0312	−	9.83298i	0.889022	−	0.513277i	0.873623	+	0.486604i	$0.161765\pi$
$368$	3.49497	+	2.01782i	0.182188	+	0.105186i
$369$	5.49321			0.285965
$370$	−7.23123	−	11.5200i	−0.375934	−	0.598894i
$371$	4.80400			0.249411
$372$	8.67902	+	5.01083i	0.449986	+	0.259800i
$373$	17.3331	−	10.0073i	0.897476	−	0.518158i	0.0210955	−	0.999777i	$-0.493285\pi$
$373$	17.3331	−	10.0073i	0.897476	−	0.518158i	0.876380	+	0.481619i	$0.159951\pi$
$374$	12.6298	+	21.8755i	0.653072	+	1.13115i
$375$	−11.0323	−	1.81314i	−0.569708	−	0.0936300i
$376$	4.75097			0.245013
$377$	31.1610	−	17.9908i	1.60487	−	0.926575i
$378$			0.440634i			0.0226637i
$379$	17.4396	−	30.2063i	0.895813	−	1.55159i	0.0630188	−	0.998012i	$-0.479927\pi$
$379$	17.4396	−	30.2063i	0.895813	−	1.55159i	0.832795	−	0.553582i	$-0.186739\pi$
$380$	10.8554	+	2.52834i	0.556872	+	0.129701i
$381$	−18.7481			−0.960493
$382$	6.10059	+	3.52218i	0.312134	+	0.180210i
$383$	12.5509	−	7.24629i	0.641323	−	0.370268i	−0.143801	−	0.989607i	$-0.545932\pi$
$383$	12.5509	−	7.24629i	0.641323	−	0.370268i	0.785124	+	0.619339i	$0.212599\pi$
$384$	1.00000			0.0510310
$385$	−3.47369	−	3.25187i	−0.177036	−	0.165731i
$386$	−1.02878	+	1.78191i	−0.0523637	+	0.0906966i
$387$	2.89521	+	1.67155i	0.147172	+	0.0849696i
$388$	9.23317	−	5.33077i	0.468743	−	0.270629i
$389$	6.37015	+	11.0334i	0.322979	+	0.559417i	0.981101	−	0.193495i	$-0.0619822\pi$
$389$	6.37015	+	11.0334i	0.322979	+	0.559417i	−0.658122	+	0.752911i	$0.728649\pi$
$390$	−9.76121	−	9.13789i	−0.494278	−	0.462715i
$391$	10.5541	−	18.2803i	0.533745	−	0.924473i
$392$	5.89403	+	3.40292i	0.297694	+	0.171873i
$393$			19.2453i			0.970796i
$394$	1.52711	+	2.64503i	0.0769345	+	0.133254i
$395$	1.16080	−	1.23998i	0.0584063	−	0.0623904i
$396$	−4.82933			−0.242683
$397$		−	0.278485i		−	0.0139768i	−0.999976	−	0.00698838i	$-0.997776\pi$
$397$		−	0.278485i		−	0.0139768i	0.999976	−	0.00698838i	$-0.00222449\pi$
$398$	2.74243	+	1.58334i	0.137466	+	0.0793658i
$399$	−2.19640			−0.109957
$400$	−0.329455	−	4.98913i	−0.0164727	−	0.249457i
$401$	−0.754054			−0.0376556			−0.0188278	−	0.999823i	$-0.505993\pi$
$401$	−0.754054			−0.0376556			−0.0188278	+	0.999823i	$0.505993\pi$
$402$	0.414474	−	0.239297i	0.0206721	−	0.0119350i
$403$	51.8977	−	29.9631i	2.58521	−	1.49257i
$404$	1.94505	+	3.36892i	0.0967698	+	0.167610i
$405$	1.52816	−	1.63240i	0.0759349	−	0.0811146i
$406$	−2.65144			−0.131589
$407$	−20.6889	+	20.8542i	−1.02551	+	1.03371i
$408$		−	5.23046i		−	0.258946i
$409$	−15.0513	+	26.0696i	−0.744239	+	1.28906i	0.206310	+	0.978487i	$0.433855\pi$
$409$	−15.0513	+	26.0696i	−0.744239	+	1.28906i	−0.950549	+	0.310574i	$0.899479\pi$
$410$	11.7534	−	3.56849i	0.580459	−	0.176235i
$411$	−9.53560	−	16.5161i	−0.470357	−	0.814682i
$412$	−5.49977	+	3.17530i	−0.270954	+	0.156436i
$413$			3.91271i			0.192532i
$414$	2.01782	+	3.49497i	0.0991704	+	0.171768i
$415$	−1.38558	+	5.94899i	−0.0680153	+	0.292024i
$416$	2.98984	−	5.17855i	0.146589	−	0.253899i
$417$		−	17.9372i		−	0.878389i
$418$		−	24.0725i		−	1.17742i
$419$	−3.21432	+	5.56737i	−0.157030	+	0.271984i	−0.933796	−	0.357805i	$-0.883525\pi$
$419$	−3.21432	+	5.56737i	−0.157030	+	0.271984i	0.776766	+	0.629789i	$0.216859\pi$
$420$	0.286244	+	0.942791i	0.0139673	+	0.0460035i
$421$	18.9990			0.925954			0.462977	−	0.886370i	$-0.346781\pi$
$421$	18.9990			0.925954			0.462977	+	0.886370i	$0.346781\pi$
$422$	−14.5103	−	8.37753i	−0.706351	−	0.407812i
$423$	4.11446	+	2.37548i	0.200052	+	0.115500i
$424$	5.45125	−	9.44183i	0.264736	−	0.458536i
$425$	−26.0955	+	1.72320i	−1.26582	+	0.0835875i
$426$	2.95496	+	5.11813i	0.143168	+	0.247974i
$427$	3.53844	+	2.04292i	0.171237	+	0.0988639i
$428$	−1.04745	−	0.604748i	−0.0506306	−	0.0292316i
$429$	−14.4389	+	25.0089i	−0.697117	+	1.20744i
$430$	7.28053	+	1.69570i	0.351098	+	0.0817741i
$431$	2.25058	+	3.89813i	0.108407	+	0.187766i	0.915125	−	0.403170i	$-0.132092\pi$
$431$	2.25058	+	3.89813i	0.108407	+	0.187766i	−0.806718	+	0.590936i	$0.798758\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$			30.0536i			1.44428i	0.691746	+	0.722141i	$0.256842\pi$
$433$			30.0536i			1.44428i	−0.691746	+	0.722141i	$0.743158\pi$
$434$	−4.41588			−0.211969
$435$	9.82268	+	9.19544i	0.470962	+	0.440888i
$436$	12.1688			0.582777
$437$	−17.4211	+	10.0581i	−0.833366	+	0.481144i
$438$			9.65667i			0.461414i
$439$	18.1428	+	31.4242i	0.865908	+	1.49980i	0.866143	+	0.499797i	$0.166592\pi$
$439$	18.1428	+	31.4242i	0.865908	+	1.49980i	−0.000234248		1.00000i	$0.500075\pi$
$440$	−10.3330	+	3.13723i	−0.492604	+	0.149561i
$441$	3.40292	+	5.89403i	0.162044	+	0.280668i
$442$	−27.0862	−	15.6382i	−1.28836	−	0.743834i
$443$			7.83018i			0.372023i	0.982548	+	0.186011i	$0.0595562\pi$
$443$			7.83018i			0.372023i	−0.982548	+	0.186011i	$0.940444\pi$
$444$	5.86918	−	1.59771i	0.278539	−	0.0758239i
$445$	0.0981662	+	0.0228638i	0.00465352	+	0.00108385i
$446$	2.21342	−	3.83376i	0.104808	−	0.181534i
$447$	−16.6470	+	9.61117i	−0.787378	+	0.454593i
$448$	−0.381600	+	0.220317i	−0.0180289	+	0.0104090i
$449$	−11.0036	−	19.0587i	−0.519290	−	0.899437i	−0.999749	−	0.0224194i	$-0.992863\pi$
$449$	−11.0036	−	19.0587i	−0.519290	−	0.899437i	0.480459	−	0.877017i	$-0.340470\pi$
$450$	2.20925	−	4.48544i	0.104145	−	0.211446i
$451$	−13.2642	−	22.9744i	−0.624589	−	1.08182i
$452$		−	16.9667i		−	0.798044i
$453$	4.69139	+	2.70857i	0.220421	+	0.127260i
$454$	8.02333			0.376553
$455$	5.73811	+	1.33646i	0.269007	+	0.0626542i
$456$	−2.49232	+	4.31682i	−0.116714	+	0.202154i
$457$	−13.3852	+	7.72794i	−0.626133	+	0.361498i	−0.779253	−	0.626710i	$-0.784401\pi$
$457$	−13.3852	+	7.72794i	−0.626133	+	0.361498i	0.153120	+	0.988208i	$0.451068\pi$
$458$			6.13363i			0.286605i
$459$	2.61523	−	4.52971i	0.122068	−	0.211429i
$460$	6.58777	+	6.16710i	0.307157	+	0.287543i
$461$	15.3025	−	26.5048i	0.712711	−	1.23445i	−0.251125	−	0.967955i	$-0.580801\pi$
$461$	15.3025	−	26.5048i	0.712711	−	1.23445i	0.963836	−	0.266496i	$-0.0858660\pi$
$462$	1.84287	−	1.06398i	0.0857381	−	0.0495009i
$463$	−17.6748	+	10.2045i	−0.821418	+	0.474246i	−0.850905	−	0.525319i	$-0.823946\pi$
$463$	−17.6748	+	10.2045i	−0.821418	+	0.474246i	0.0294875	+	0.999565i	$0.490612\pi$
$464$	−3.00866	+	5.21116i	−0.139674	+	0.241922i
$465$	16.3594	+	15.3147i	0.758647	+	0.710202i
$466$	−3.12788	+	5.41764i	−0.144896	+	0.250967i
$467$		−	1.21779i		−	0.0563526i	−0.999603	−	0.0281763i	$-0.991030\pi$
$467$		−	1.21779i		−	0.0563526i	0.999603	−	0.0281763i	$-0.00896998\pi$
$468$	5.17855	−	2.98984i	0.239378	−	0.138205i
$469$	−0.105442	+	0.182631i	−0.00486887	+	0.00843313i
$470$	10.3466	+	2.40981i	0.477251	+	0.111156i
$471$	−8.46589			−0.390088
$472$	7.69007	+	4.43986i	0.353964	+	0.204361i
$473$		−	16.1449i		−	0.742344i
$474$	0.379804	+	0.657840i	0.0174450	+	0.0302156i
$475$	22.3583	+	11.0123i	1.02587	+	0.505280i
$476$	1.15236	+	1.99594i	0.0528182	+	0.0914839i
$477$	9.44183	−	5.45125i	0.432312	−	0.249595i
$478$	−20.1073	+	11.6089i	−0.919684	+	0.530980i
$479$	16.8952	−	29.2633i	0.771960	−	1.33707i	−0.164528	−	0.986372i	$-0.552610\pi$
$479$	16.8952	−	29.2633i	0.771960	−	1.33707i	0.936488	−	0.350701i	$-0.114057\pi$
$480$	2.17778	+	0.507226i	0.0994016	+	0.0231516i
$481$	9.27409	−	35.1707i	0.422862	−	1.60365i
$482$		−	14.8291i		−	0.675448i
$483$	−1.54000	−	0.889119i	−0.0700724	−	0.0404563i
$484$	6.16121	+	10.6715i	0.280055	+	0.485069i
$485$	22.8117	−	6.92595i	1.03583	−	0.314491i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$		−	38.2009i		−	1.73105i	−0.500869	−	0.865523i	$-0.666986\pi$
$487$		−	38.2009i		−	1.73105i	0.500869	−	0.865523i	$-0.333014\pi$
$488$	8.03036	−	4.63633i	0.363517	−	0.209877i
$489$	5.20631			0.235437
$490$	11.1099	+	10.4004i	0.501892	+	0.469843i
$491$	−13.1449			−0.593221			−0.296611	−	0.954998i	$-0.595856\pi$
$491$	−13.1449			−0.593221			−0.296611	+	0.954998i	$0.595856\pi$
$492$			5.49321i			0.247653i
$493$	27.2568	+	15.7367i	1.22758	+	0.708745i
$494$	14.9032	+	25.8132i	0.670529	+	1.16139i
$495$	−10.5172	−	2.44956i	−0.472714	−	0.110100i
$496$	−5.01083	+	8.67902i	−0.224993	+	0.389699i
$497$	−2.25522	−	1.30205i	−0.101161	−	0.0584050i
$498$	−2.36570	−	1.36584i	−0.106010	−	0.0612047i
$499$	−4.58808	−	7.94678i	−0.205390	−	0.355747i	0.744867	−	0.667213i	$-0.232513\pi$
$499$	−4.58808	−	7.94678i	−0.205390	−	0.355747i	−0.950257	+	0.311467i	$0.899180\pi$
$500$	1.81314	−	11.0323i	0.0810859	−	0.493381i
$501$	2.90403	−	5.02993i	0.129743	−	0.224721i
$502$	9.75070	+	5.62957i	0.435195	+	0.251260i
$503$	−13.1266	−	7.57863i	−0.585285	−	0.337914i	0.177946	−	0.984040i	$-0.443055\pi$
$503$	−13.1266	−	7.57863i	−0.585285	−	0.337914i	−0.763231	+	0.646126i	$0.776388\pi$
$504$	−0.440634			−0.0196274
$505$	2.52708	+	8.32335i	0.112454	+	0.370384i
$506$	9.74471	−	16.8783i	0.433205	−	0.750334i
$507$		−	22.7565i		−	1.01065i
$508$		−	18.7481i		−	0.831811i
$509$	−13.5896	+	23.5379i	−0.602349	+	1.04330i	0.390115	+	0.920766i	$0.372435\pi$
$509$	−13.5896	+	23.5379i	−0.602349	+	1.04330i	−0.992464	+	0.122534i	$0.960898\pi$
$510$	2.65302	−	11.3908i	0.117478	−	0.504392i
$511$	−2.12753	−	3.68498i	−0.0941162	−	0.163014i
$512$			1.00000i			0.0441942i
$513$	−4.31682	+	2.49232i	−0.190592	+	0.110039i
$514$	−4.56308	−	7.90348i	−0.201269	−	0.348608i
$515$	−13.5879	+	4.12547i	−0.598754	+	0.181790i
$516$	−1.67155	+	2.89521i	−0.0735858	+	0.127454i
$517$		−	22.9440i		−	1.00908i
$518$	−1.88768	+	1.90277i	−0.0829398	+	0.0836027i
$519$	14.2837			0.626983
$520$	9.13789	−	9.76121i	0.400723	−	0.428057i
$521$	12.2259	+	21.1760i	0.535628	+	0.927735i	0.999133	+	0.0416408i	$0.0132585\pi$
$521$	12.2259	+	21.1760i	0.535628	+	0.927735i	−0.463504	+	0.886095i	$0.653408\pi$
$522$	−5.21116	+	3.00866i	−0.228086	+	0.131686i
$523$	−27.6286	+	15.9514i	−1.20811	+	0.697504i	−0.962347	−	0.271825i	$-0.912373\pi$
$523$	−27.6286	+	15.9514i	−1.20811	+	0.697504i	−0.245766	+	0.969329i	$0.579039\pi$
$524$	−19.2453			−0.840734
$525$	0.145169	+	2.19838i	0.00633569	+	0.0959452i
$526$	−11.8889			−0.518381
$527$	45.3952	+	26.2090i	1.97745	+	1.14168i
$528$		−	4.82933i		−	0.210170i
$529$	6.71362			0.291896
$530$	16.6607	−	17.7972i	0.723697	−	0.773062i
$531$	4.43986	+	7.69007i	0.192674	+	0.333721i
$532$		−	2.19640i		−	0.0952260i
$533$	28.4468	+	16.4238i	1.23217	+	0.711393i
$534$	−0.0225381	+	0.0390372i	−0.000975321	+	0.00168930i
$535$	−1.97438	−	1.84830i	−0.0853599	−	0.0799092i
$536$	0.239297	+	0.414474i	0.0103360	+	0.0179026i
$537$	−10.9586	+	6.32693i	−0.472897	+	0.273027i
$538$	23.9818	+	13.8459i	1.03393	+	0.596940i
$539$	16.4338	−	28.4642i	0.707855	−	1.22604i
$540$	1.63240	+	1.52816i	0.0702473	+	0.0657615i
$541$	−22.8752			−0.983480			−0.491740	−	0.870742i	$-0.663639\pi$
$541$	−22.8752			−0.983480			−0.491740	+	0.870742i	$0.663639\pi$
$542$	26.5823	−	15.3473i	1.14181	−	0.659223i
$543$	3.26270	+	1.88372i	0.140016	+	0.0808382i
$544$	5.23046			0.224254
$545$	26.5009	+	6.17230i	1.13517	+	0.264392i
$546$	−1.31742	+	2.28184i	−0.0563805	+	0.0976538i
$547$			29.4024i			1.25716i	0.777746	+	0.628578i	$0.216363\pi$
$547$			29.4024i			1.25716i	−0.777746	+	0.628578i	$0.783637\pi$
$548$	16.5161	−	9.53560i	0.705535	−	0.407341i
$549$	9.27266			0.395747
$550$	−24.0942	+	1.59105i	−1.02738	+	0.0678424i
$551$	−14.9971	−	25.9757i	−0.638898	−	1.10660i
$552$	−3.49497	+	2.01782i	−0.148756	+	0.0858841i
$553$	−0.289866	−	0.167354i	−0.0123264	−	0.00711664i
$554$	31.2398			1.32725
$555$	13.5922	−	0.502455i	0.576956	−	0.0213280i
$556$	17.9372			0.760707
$557$	−32.0362	−	18.4961i	−1.35742	−	0.783705i	−0.368142	−	0.929770i	$-0.620006\pi$
$557$	−32.0362	−	18.4961i	−1.35742	−	0.783705i	−0.989275	+	0.146065i	$0.953339\pi$
$558$	−8.67902	+	5.01083i	−0.367412	+	0.212125i
$559$	9.99531	+	17.3124i	0.422757	+	0.732236i
$560$	−0.942791	+	0.286244i	−0.0398402	+	0.0120960i
$561$	−25.2596			−1.06646
$562$	−8.90433	+	5.14092i	−0.375606	+	0.216856i
$563$			22.5138i			0.948844i	0.880297	+	0.474422i	$0.157343\pi$
$563$			22.5138i			0.948844i	−0.880297	+	0.474422i	$0.842657\pi$
$564$	−2.37548	+	4.11446i	−0.100026	+	0.173250i
$565$	8.60592	−	36.9496i	0.362054	−	1.55448i
$566$	20.5676			0.864522
$567$	−0.381600	−	0.220317i	−0.0160257	−	0.00925244i
$568$	−5.11813	+	2.95496i	−0.214752	+	0.123987i
$569$	−19.6312			−0.822984			−0.411492	−	0.911413i	$-0.634992\pi$
$569$	−19.6312			−0.822984			−0.411492	+	0.911413i	$0.634992\pi$
$570$	−7.61732	+	8.13692i	−0.319055	+	0.340818i
$571$	−8.30836	+	14.3905i	−0.347694	+	0.602223i	−0.985839	−	0.167692i	$-0.946368\pi$
$571$	−8.30836	+	14.3905i	−0.347694	+	0.602223i	0.638145	+	0.769916i	$0.279702\pi$
$572$	−25.0089	−	14.4389i	−1.04568	−	0.603721i
$573$	−6.10059	+	3.52218i	−0.254856	+	0.147141i
$574$	−1.21025	−	2.09621i	−0.0505147	−	0.0874940i
$575$	11.2186	+	16.7721i	0.467848	+	0.699444i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	31.9498	+	18.4462i	1.33009	+	0.767926i	0.985313	−	0.170760i	$-0.0546223\pi$
$577$	31.9498	+	18.4462i	1.33009	+	0.767926i	0.344774	+	0.938686i	$0.387956\pi$
$578$		−	10.3577i		−	0.430824i
$579$	−1.02878	−	1.78191i	−0.0427548	−	0.0740535i
$580$	−9.19544	+	9.82268i	−0.381820	+	0.407865i
$581$	1.20367			0.0499366
$582$			10.6615i			0.441935i
$583$	−45.5977	−	26.3259i	−1.88846	−	1.09031i
$584$	−9.65667			−0.399596
$585$	12.7943	−	3.88451i	0.528977	−	0.160605i
$586$	24.4427			1.00972
$587$	37.4185	−	21.6036i	1.54443	−	0.891675i	0.545875	−	0.837866i	$-0.316197\pi$
$587$	37.4185	−	21.6036i	1.54443	−	0.891675i	0.998551	−	0.0538089i	$-0.0171362\pi$
$588$	−5.89403	+	3.40292i	−0.243066	+	0.140334i
$589$	−24.9772	−	43.2618i	−1.02917	−	1.78257i
$590$	14.4953	+	13.5696i	0.596761	+	0.558653i
$591$	−3.05421			−0.125634
$592$	1.59771	+	5.86918i	0.0656654	+	0.241222i
$593$		−	34.5996i		−	1.42084i	−0.703780	−	0.710418i	$-0.748506\pi$
$593$		−	34.5996i		−	1.42084i	0.703780	−	0.710418i	$-0.251494\pi$
$594$	2.41466	−	4.18232i	0.0990749	−	0.171603i
$595$	1.49719	+	4.93123i	0.0613787	+	0.202161i
$596$	−9.61117	−	16.6470i	−0.393689	−	0.681889i
$597$	−2.74243	+	1.58334i	−0.112240	+	0.0648019i
$598$			24.1318i			0.986823i
$599$	−8.93405	−	15.4742i	−0.365035	−	0.632260i	0.623747	−	0.781627i	$-0.285610\pi$
$599$	−8.93405	−	15.4742i	−0.365035	−	0.632260i	−0.988782	+	0.149367i	$0.952276\pi$
$600$	4.48544	+	2.20925i	0.183117	+	0.0901923i
$601$	−20.0430	+	34.7155i	−0.817571	+	1.41607i	0.0898966	+	0.995951i	$0.471346\pi$
$601$	−20.0430	+	34.7155i	−0.817571	+	1.41607i	−0.907467	+	0.420123i	$0.861987\pi$
$602$		−	1.47308i		−	0.0600383i
$603$			0.478594i			0.0194898i
$604$	−2.70857	+	4.69139i	−0.110210	+	0.190890i
$605$	8.00488	+	26.3654i	0.325445	+	1.07190i
$606$	−3.89010			−0.158024
$607$	29.5041	+	17.0342i	1.19754	+	0.691397i	0.960005	−	0.279983i	$-0.0903287\pi$
$607$	29.5041	+	17.0342i	1.19754	+	0.691397i	0.237530	+	0.971380i	$0.423662\pi$
$608$	−4.31682	−	2.49232i	−0.175070	−	0.101077i
$609$	1.32572	−	2.29621i	0.0537208	−	0.0930472i
$610$	19.8400	−	6.02370i	0.803298	−	0.243892i
$611$	14.2046	+	24.6031i	0.574657	+	0.995336i
$612$	4.52971	+	2.61523i	0.183103	+	0.105714i
$613$	−4.53079	−	2.61585i	−0.182997	−	0.105653i	0.405703	−	0.914005i	$-0.367027\pi$
$613$	−4.53079	−	2.61585i	−0.182997	−	0.105653i	−0.588700	+	0.808352i	$0.700360\pi$
$614$	5.84748	−	10.1281i	0.235985	−	0.408738i
$615$	−2.78629	+	11.9630i	−0.112354	+	0.482394i
$616$	1.06398	+	1.84287i	0.0428691	+	0.0742514i
$617$	13.3276	+	7.69467i	0.536548	+	0.309776i	0.743679	−	0.668537i	$-0.233079\pi$
$617$	13.3276	+	7.69467i	0.536548	+	0.309776i	−0.207131	+	0.978313i	$0.566413\pi$
$618$		−	6.35059i		−	0.255458i
$619$	−43.8882			−1.76402			−0.882008	−	0.471234i	$-0.843809\pi$
$619$	−43.8882			−1.76402			−0.882008	+	0.471234i	$0.843809\pi$
$620$	−15.3147	+	16.3594i	−0.615053	+	0.657008i
$621$	−4.03564			−0.161945
$622$	13.4115	−	7.74316i	0.537754	−	0.310472i
$623$		−	0.0198621i		−	0.000795759i
$624$	2.98984	+	5.17855i	0.119689	+	0.207308i
$625$	9.54450	−	23.1063i	0.381780	−	0.924253i
$626$	10.0076	+	17.3337i	0.399984	+	0.692792i
$627$	20.8474	+	12.0362i	0.832563	+	0.480681i
$628$		−	8.46589i		−	0.337826i
$629$	30.6985	−	8.35675i	1.22403	−	0.333205i
$630$	−0.959603	−	0.223501i	−0.0382315	−	0.00890448i
$631$	16.9108	−	29.2904i	0.673209	−	1.16603i	−0.303780	−	0.952742i	$-0.598249\pi$
$631$	16.9108	−	29.2904i	0.673209	−	1.16603i	0.976989	−	0.213290i	$-0.0684179\pi$
$632$	−0.657840	+	0.379804i	−0.0261675	+	0.0151078i
$633$	14.5103	−	8.37753i	0.576733	−	0.332977i
$634$	1.83679	+	3.18142i	0.0729483	+	0.126350i
$635$	9.50950	−	40.8292i	0.377373	−	1.62026i
$636$	5.45125	+	9.44183i	0.216156	+	0.374393i
$637$			40.6967i			1.61246i
$638$	25.1664	+	14.5298i	0.996348	+	0.575242i
$639$	−5.90991			−0.233792
$640$	−0.507226	+	2.17778i	−0.0200499	+	0.0860843i
$641$	12.3878	−	21.4564i	0.489290	−	0.847475i	−0.510634	−	0.859798i	$-0.670589\pi$
$641$	12.3878	−	21.4564i	0.489290	−	0.847475i	0.999924	+	0.0123229i	$0.00392260\pi$
$642$	1.04745	−	0.604748i	0.0413397	−	0.0238675i
$643$		−	14.2105i		−	0.560408i	−0.959940	−	0.280204i	$-0.909598\pi$
$643$		−	14.2105i		−	0.560408i	0.959940	−	0.280204i	$-0.0904021\pi$
$644$	0.889119	−	1.54000i	0.0350362	−	0.0606845i
$645$	−5.10879	+	5.45727i	−0.201158	+	0.214880i
$646$	−13.0360	+	22.5790i	−0.512894	+	0.888358i
$647$	−0.960658	+	0.554636i	−0.0377674	+	0.0218050i	−0.518765	−	0.854917i	$-0.673608\pi$
$647$	−0.960658	+	0.554636i	−0.0377674	+	0.0218050i	0.480997	+	0.876722i	$0.340275\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	21.4416	−	37.1379i	0.841655	−	1.45779i
$650$	24.8515	−	16.6228i	0.974754	−	0.651999i
$651$	2.20794	−	3.82427i	0.0865360	−	0.149885i
$652$			5.20631i			0.203895i
$653$	−36.3898	+	21.0097i	−1.42404	+	0.822171i	−0.996641	−	0.0818905i	$-0.973904\pi$
$653$	−36.3898	+	21.0097i	−1.42404	+	0.822171i	−0.427401	+	0.904062i	$0.640571\pi$
$654$	−6.08438	+	10.5384i	−0.237918	+	0.412086i
$655$	−41.9120	−	9.76170i	−1.63764	−	0.381421i
$656$	−5.49321			−0.214474
$657$	−8.36292	−	4.82833i	−0.326269	−	0.188371i
$658$		−	2.09344i		−	0.0816107i
$659$	−10.2000	−	17.6669i	−0.397335	−	0.688204i	0.596061	−	0.802939i	$-0.296732\pi$
$659$	−10.2000	−	17.6669i	−0.397335	−	0.688204i	−0.993396	+	0.114735i	$0.963398\pi$
$660$	2.44956	−	10.5172i	0.0953490	−	0.409382i
$661$	8.58245	+	14.8652i	0.333819	+	0.578191i	0.983257	−	0.182223i	$-0.0583293\pi$
$661$	8.58245	+	14.8652i	0.333819	+	0.578191i	−0.649438	+	0.760414i	$0.724996\pi$
$662$	8.58214	−	4.95490i	0.333554	−	0.192578i
$663$	27.0862	−	15.6382i	1.05194	−	0.607338i
$664$	1.36584	−	2.36570i	0.0530048	−	0.0918071i
$665$	1.11407	−	4.78327i	0.0432018	−	0.185487i
$666$	−1.55094	+	5.88172i	−0.0600976	+	0.227912i
$667$		−	24.2838i		−	0.940271i
$668$	5.02993	+	2.90403i	0.194614	+	0.112360i
$669$	2.21342	+	3.83376i	0.0855758	+	0.148222i
$670$	0.310904	+	1.02401i	0.0120113	+	0.0395610i
$671$	−22.3904	−	38.7812i	−0.864370	−	1.49713i
$672$		−	0.440634i		−	0.0169978i
$673$	17.5188	−	10.1145i	0.675299	−	0.389884i	−0.122783	−	0.992434i	$-0.539182\pi$
$673$	17.5188	−	10.1145i	0.675299	−	0.389884i	0.798081	+	0.602550i	$0.205848\pi$
$674$	16.8558			0.649261
$675$	2.77988	+	4.15599i	0.106998	+	0.159964i
$676$	22.7565			0.875249
$677$			5.97529i			0.229649i	0.993386	+	0.114824i	$0.0366306\pi$
$677$			5.97529i			0.229649i	−0.993386	+	0.114824i	$0.963369\pi$
$678$	14.6936	+	8.48333i	0.564303	+	0.325800i
$679$	−2.34892	−	4.06845i	−0.0901432	−	0.156133i
$680$	11.3908	+	2.65302i	0.436817	+	0.101739i
$681$	−4.01166	+	6.94841i	−0.153727	+	0.266263i
$682$	41.9138	+	24.1990i	1.60496	+	0.926626i
$683$	1.58531	+	0.915280i	0.0606603	+	0.0350222i	0.530023	−	0.847983i	$-0.322183\pi$
$683$	1.58531	+	0.915280i	0.0606603	+	0.0350222i	−0.469363	+	0.883005i	$0.655516\pi$
$684$	−2.49232	−	4.31682i	−0.0952962	−	0.165058i
$685$	40.8052	−	12.3890i	1.55909	−	0.473360i
$686$	3.04166	−	5.26831i	0.116131	−	0.201145i
$687$	−5.31188	−	3.06681i	−0.202661	−	0.117006i
$688$	−2.89521	−	1.67155i	−0.110379	−	0.0637272i
$689$	65.1933			2.48367
$690$	−8.63475	+	2.62163i	−0.328719	+	0.0998037i
$691$	−2.88079	+	4.98967i	−0.109590	+	0.189816i	−0.915604	−	0.402080i	$-0.868287\pi$
$691$	−2.88079	+	4.98967i	−0.109590	+	0.189816i	0.806014	+	0.591896i	$0.201621\pi$
$692$			14.2837i			0.542983i
$693$			2.12796i			0.0808347i
$694$	−8.38658	+	14.5260i	−0.318350	+	0.551399i
$695$	39.0633	+	9.09821i	1.48175	+	0.345115i
$696$	−3.00866	−	5.21116i	−0.114043	−	0.197529i
$697$			28.7320i			1.08830i
$698$	16.0921	−	9.29079i	0.609096	−	0.351662i
$699$	−3.12788	−	5.41764i	−0.118307	−	0.204914i
$700$	−2.19838	+	0.145169i	−0.0830910	+	0.00548687i
$701$	4.20485	−	7.28301i	0.158815	−	0.275076i	−0.775627	−	0.631192i	$-0.782566\pi$
$701$	4.20485	−	7.28301i	0.158815	−	0.275076i	0.934442	+	0.356116i	$0.115899\pi$
$702$			5.97967i			0.225688i
$703$	−29.3182	−	7.73086i	−1.10576	−	0.291575i
$704$	4.82933			0.182012
$705$	−7.26024	+	7.75548i	−0.273436	+	0.292088i
$706$	−8.83646	−	15.3052i	−0.332565	−	0.576019i
$707$	1.48446	−	0.857054i	0.0558289	−	0.0322328i
$708$	−7.69007	+	4.43986i	−0.289011	+	0.166860i
$709$	−34.8641			−1.30935			−0.654674	−	0.755911i	$-0.727194\pi$
$709$	−34.8641			−1.30935			−0.654674	+	0.755911i	$0.727194\pi$
$710$	−12.6450	+	3.83919i	−0.474558	+	0.144082i
$711$	−0.759608			−0.0284875
$712$	−0.0390372	−	0.0225381i	−0.00146298	−	0.000844652i
$713$		−	40.4438i		−	1.51463i
$714$	−2.30472			−0.0862518
$715$	−47.1401	−	44.1299i	−1.76294	−	1.65036i
$716$	−6.32693	−	10.9586i	−0.236449	−	0.409541i
$717$		−	23.2179i		−	0.867087i
$718$	−24.3334	−	14.0489i	−0.908115	−	0.524300i
$719$	−7.55247	+	13.0813i	−0.281660	+	0.487849i	−0.971794	−	0.235833i	$-0.924218\pi$
$719$	−7.55247	+	13.0813i	−0.281660	+	0.487849i	0.690134	+	0.723682i	$0.257552\pi$
$720$	−1.52816	+	1.63240i	−0.0569512	+	0.0608359i
$721$	1.39914	+	2.42339i	0.0521068	+	0.0902516i
$722$	5.06332	−	2.92331i	0.188437	−	0.108794i
$723$	12.8424	+	7.41456i	0.477614	+	0.275750i
$724$	−1.88372	+	3.26270i	−0.0700080	+	0.121257i
$725$	−25.0080	+	16.7275i	−0.928772	+	0.621243i
$726$	−12.3224			−0.457328
$727$	26.3941	−	15.2386i	0.978903	−	0.565170i	0.0769644	−	0.997034i	$-0.475477\pi$
$727$	26.3941	−	15.2386i	0.978903	−	0.565170i	0.901939	+	0.431864i	$0.142144\pi$
$728$	−2.28184	−	1.31742i	−0.0845707	−	0.0488269i
$729$	−1.00000			−0.0370370
$730$	−21.0301	−	4.89811i	−0.778359	−	0.181287i
$731$	−8.74296	+	15.1433i	−0.323370	+	0.560094i
$732$			9.27266i			0.342727i
$733$	14.2117	−	8.20512i	0.524921	−	0.303063i	−0.214025	−	0.976828i	$-0.568657\pi$
$733$	14.2117	−	8.20512i	0.524921	−	0.303063i	0.738946	+	0.673765i	$0.235324\pi$
$734$	−19.6660			−0.725884
$735$	−14.5619	+	4.42121i	−0.537126	+	0.163079i
$736$	−2.01782	−	3.49497i	−0.0743778	−	0.128826i
$737$	2.00163	−	1.15564i	0.0737311	−	0.0425687i
$738$	−4.75726	−	2.74660i	−0.175117	−	0.101104i
$739$	−29.5639			−1.08753			−0.543764	−	0.839238i	$-0.683001\pi$
$739$	−29.5639			−1.08753			−0.543764	+	0.839238i	$0.683001\pi$
$740$	0.502455	+	13.5922i	0.0184706	+	0.499659i
$741$	−29.8065			−1.09497
$742$	−4.16039	−	2.40200i	−0.152733	−	0.0881803i
$743$	−30.9779	+	17.8851i	−1.13647	+	0.656141i	−0.945554	−	0.325465i	$-0.894479\pi$
$743$	−30.9779	+	17.8851i	−1.13647	+	0.656141i	−0.190916	+	0.981606i	$0.561146\pi$
$744$	−5.01083	−	8.67902i	−0.183706	−	0.318188i
$745$	−12.4872	−	41.1286i	−0.457496	−	1.50684i
$746$	−20.0146			−0.732786
$747$	2.36570	−	1.36584i	0.0865565	−	0.0499734i
$748$		−	25.2596i		−	0.923583i
$749$	−0.266472	+	0.461544i	−0.00973669	+	0.0168644i
$750$	8.64772	+	7.08639i	0.315770	+	0.258758i
$751$	19.0423			0.694865			0.347432	−	0.937705i	$-0.387054\pi$
$751$	19.0423			0.694865			0.347432	+	0.937705i	$0.387054\pi$
$752$	−4.11446	−	2.37548i	−0.150039	−	0.0866250i
$753$	−9.75070	+	5.62957i	−0.355335	+	0.205153i
$754$	−35.9817			−1.31037
$755$	−8.27826	+	8.84294i	−0.301277	+	0.321828i
$756$	0.220317	−	0.381600i	0.00801285	−	0.0138787i
$757$	−2.13364	−	1.23186i	−0.0775484	−	0.0447726i	0.460724	−	0.887543i	$-0.347590\pi$
$757$	−2.13364	−	1.23186i	−0.0775484	−	0.0447726i	−0.538273	+	0.842771i	$0.680923\pi$
$758$	−30.2063	+	17.4396i	−1.09714	+	0.633436i
$759$	9.74471	+	16.8783i	0.353711	+	0.612645i
$760$	−8.13692	−	7.61732i	−0.295157	−	0.276309i
$761$	−2.97593	+	5.15447i	−0.107877	+	0.186849i	−0.914910	−	0.403657i	$-0.867739\pi$
$761$	−2.97593	+	5.15447i	−0.107877	+	0.186849i	0.807033	+	0.590507i	$0.201072\pi$
$762$	16.2363	+	9.37403i	0.588179	+	0.339585i
$763$		−	5.36196i		−	0.194116i
$764$	−3.52218	−	6.10059i	−0.127428	−	0.220712i
$765$	8.53820	+	7.99298i	0.308699	+	0.288987i
$766$	−14.4926			−0.523638
$767$			53.0979i			1.91725i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	4.94626			0.178367			0.0891833	−	0.996015i	$-0.471574\pi$
$769$	4.94626			0.178367			0.0891833	+	0.996015i	$0.471574\pi$
$770$	1.38237	+	4.55305i	0.0498171	+	0.164080i
$771$	9.12616			0.328671
$772$	1.78191	−	1.02878i	0.0641322	−	0.0370267i
$773$	−31.2431	+	18.0382i	−1.12374	+	0.648790i	−0.942352	−	0.334622i	$-0.891391\pi$
$773$	−31.2431	+	18.0382i	−1.12374	+	0.648790i	−0.181385	+	0.983412i	$0.558058\pi$
$774$	−1.67155	−	2.89521i	−0.0600826	−	0.104066i
$775$	−41.6499	+	27.8591i	−1.49611	+	1.00073i
$776$	−10.6615			−0.382727
$777$	−0.704004	−	2.58616i	−0.0252560	−	0.0927780i
$778$		−	12.7403i		−	0.456762i
$779$	13.6908	−	23.7132i	0.490525	−	0.849614i
$780$	3.88451	+	12.7943i	0.139088	+	0.458108i
$781$	14.2705	+	24.7171i	0.510637	+	0.884449i
$782$	−18.2803	+	10.5541i	−0.653701	+	0.377415i
$783$		−	6.01733i		−	0.215042i
$784$	−3.40292	−	5.89403i	−0.121533	−	0.210501i
$785$	4.29412	−	18.4368i	0.153264	−	0.658039i
$786$	9.62264	−	16.6669i	0.343228	−	0.594488i
$787$		−	19.7024i		−	0.702316i	−0.936316	−	0.351158i	$-0.885788\pi$
$787$		−	19.7024i		−	0.702316i	0.936316	−	0.351158i	$-0.114212\pi$
$788$		−	3.05421i		−	0.108802i
$789$	5.94445	−	10.2961i	0.211628	−	0.366551i
$790$	−1.62528	+	0.493456i	−0.0578247	+	0.0175564i
$791$	−7.47608			−0.265819
$792$	4.18232	+	2.41466i	0.148612	+	0.0858014i
$793$	48.0189	+	27.7237i	1.70520	+	0.984498i
$794$	−0.139242	+	0.241175i	−0.00494153	+	0.00855898i
$795$	7.08247	+	23.3272i	0.251189	+	0.827332i
$796$	−1.58334	−	2.74243i	−0.0561201	−	0.0972028i
$797$	−30.5692	−	17.6492i	−1.08282	−	0.625165i	−0.151162	−	0.988509i	$-0.548302\pi$
$797$	−30.5692	−	17.6492i	−1.08282	−	0.625165i	−0.931655	+	0.363344i	$0.881635\pi$
$798$	1.90214	+	1.09820i	0.0673349	+	0.0388758i
$799$	−12.4249	+	21.5205i	−0.439560	+	0.761341i
$800$	−2.20925	+	4.48544i	−0.0781088	+	0.158584i
$801$	−0.0225381	−	0.0390372i	−0.000796346	−	0.00137931i
$802$	0.653030	+	0.377027i	0.0230593	+	0.0133133i
$803$			46.6352i			1.64572i
$804$	−0.478594			−0.0168787
$805$	2.71743	−	2.90280i	0.0957769	−	0.102310i
$806$	−59.9263			−2.11081
$807$	−23.9818	+	13.8459i	−0.844201	+	0.487400i
$808$		−	3.89010i		−	0.136853i
$809$	−10.6190	−	18.3926i	−0.373342	−	0.646648i	0.616735	−	0.787171i	$-0.288455\pi$
$809$	−10.6190	−	18.3926i	−0.373342	−	0.646648i	−0.990077	+	0.140523i	$0.955122\pi$
$810$	−2.13962	+	0.649619i	−0.0751788	+	0.0228253i
$811$	17.4360	+	30.2001i	0.612261	+	1.06047i	0.990858	+	0.134906i	$0.0430733\pi$
$811$	17.4360	+	30.2001i	0.612261	+	1.06047i	−0.378597	+	0.925562i	$0.623593\pi$
$812$	2.29621	+	1.32572i	0.0805813	+	0.0465236i
$813$			30.6946i			1.07651i
$814$	28.3442	−	7.71586i	0.993465	−	0.270441i
$815$	−2.64077	+	11.3382i	−0.0925022	+	0.397159i
$816$	−2.61523	+	4.52971i	−0.0915513	+	0.158572i
$817$	14.4316	−	8.33206i	0.504896	−	0.291502i
$818$	26.0696	−	15.0513i	0.911503	−	0.526257i
$819$	−1.31742	−	2.28184i	−0.0460345	−	0.0797340i
$820$	−11.9630	−	2.78629i	−0.417766	−	0.0973016i
$821$	−8.18040	−	14.1689i	−0.285498	−	0.494497i	0.687232	−	0.726438i	$-0.258826\pi$
$821$	−8.18040	−	14.1689i	−0.285498	−	0.494497i	−0.972730	+	0.231941i	$0.925492\pi$
$822$			19.0712i			0.665185i
$823$	9.03930	+	5.21884i	0.315090	+	0.181917i	0.649202	−	0.760616i	$-0.275103\pi$
$823$	9.03930	+	5.21884i	0.315090	+	0.181917i	−0.334112	+	0.942533i	$0.608436\pi$
$824$	6.35059			0.221233
$825$	10.6692	−	21.6617i	0.371454	−	0.754163i
$826$	1.95635	−	3.38850i	0.0680702	−	0.117901i
$827$	48.7339	−	28.1365i	1.69464	−	0.978403i	0.743967	−	0.668216i	$-0.232942\pi$
$827$	48.7339	−	28.1365i	1.69464	−	0.978403i	0.950676	−	0.310186i	$-0.100391\pi$
$828$		−	4.03564i		−	0.140248i
$829$	−19.4812	+	33.7424i	−0.676609	+	1.17192i	0.299387	+	0.954132i	$0.403218\pi$
$829$	−19.4812	+	33.7424i	−0.676609	+	1.17192i	−0.975996	+	0.217789i	$0.930115\pi$
$830$	4.17444	−	4.45919i	0.144897	−	0.154781i
$831$	−15.6199	+	27.0544i	−0.541848	+	0.938508i
$832$	−5.17855	+	2.98984i	−0.179534	+	0.103654i
$833$	−30.8285	+	17.7988i	−1.06814	+	0.616693i
$834$	−8.96860	+	15.5341i	−0.310557	+	0.537901i
$835$	9.48108	+	8.87565i	0.328106	+	0.307154i
$836$	−12.0362	+	20.8474i	−0.416282	+	0.721021i
$837$		−	10.0217i		−	0.346399i
$838$	5.56737	−	3.21432i	0.192322	−	0.111037i
$839$	2.22737	−	3.85791i	0.0768972	−	0.133190i	−0.825013	−	0.565114i	$-0.808832\pi$
$839$	2.22737	−	3.85791i	0.0768972	−	0.133190i	0.901910	+	0.431925i	$0.142165\pi$
$840$	0.223501	−	0.959603i	0.00771151	−	0.0331094i
$841$	7.20826			0.248561
$842$	−16.4536	−	9.49949i	−0.567029	−	0.327374i
$843$		−	10.2818i		−	0.354125i
$844$	8.37753	+	14.5103i	0.288366	+	0.499465i
$845$	49.5586	+	11.5427i	1.70487	+	0.397080i
$846$	−2.37548	−	4.11446i	−0.0816708	−	0.141458i
$847$	4.70223	−	2.71484i	0.161571	−	0.0932829i
$848$	−9.44183	+	5.45125i	−0.324234	+	0.187197i
$849$	−10.2838	+	17.8121i	−0.352940	+	0.611310i
$850$	23.4609	+	11.5554i	0.804703	+	0.396347i
$851$	−17.4269	−	17.2887i	−0.597386	−	0.592649i
$852$		−	5.90991i		−	0.202470i
$853$	−2.55418	−	1.47465i	−0.0874533	−	0.0504912i	0.455636	−	0.890166i	$-0.349412\pi$
$853$	−2.55418	−	1.47465i	−0.0874533	−	0.0504912i	−0.543089	+	0.839675i	$0.682745\pi$
$854$	−2.04292	−	3.53844i	−0.0699074	−	0.121083i
$855$	−3.23812	−	10.6653i	−0.110741	−	0.364744i
$856$	0.604748	+	1.04745i	0.0206699	+	0.0358013i
$857$			19.6606i			0.671593i	0.941935	+	0.335797i	$0.109005\pi$
$857$			19.6606i			0.671593i	−0.941935	+	0.335797i	$0.890995\pi$
$858$	25.0089	−	14.4389i	0.853790	−	0.492936i
$859$	−1.43982			−0.0491261			−0.0245631	−	0.999698i	$-0.507819\pi$
$859$	−1.43982			−0.0491261			−0.0245631	+	0.999698i	$0.507819\pi$
$860$	−5.45727	−	5.10879i	−0.186091	−	0.174208i
$861$	2.42049			0.0824901
$862$		−	4.50117i		−	0.153310i
$863$	7.01938	+	4.05264i	0.238943	+	0.137954i	0.614691	−	0.788768i	$-0.289281\pi$
$863$	7.01938	+	4.05264i	0.238943	+	0.137954i	−0.375748	+	0.926722i	$0.622614\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	−7.24504	+	31.1067i	−0.246339	+	1.05766i
$866$	15.0268	−	26.0271i	0.510631	−	0.884438i
$867$	8.97003	+	5.17885i	0.304638	+	0.175883i
$868$	3.82427	+	2.20794i	0.129804	+	0.0749424i
$869$	1.83420	+	3.17693i	0.0622209	+	0.107770i
$870$	−3.90897	−	12.8748i	−0.132527	−	0.436498i
$871$	−1.43092	+	2.47842i	−0.0484848	+	0.0839781i
$872$	−10.5384	−	6.08438i	−0.356877	−	0.206043i
$873$	−9.23317	−	5.33077i	−0.312496	−	0.180419i
$874$	20.1162			0.680441
$875$	−4.86122	−	0.798929i	−0.164339	−	0.0270087i
$876$	4.82833	−	8.36292i	0.163134	−	0.282557i
$877$			13.5760i			0.458427i	0.973376	+	0.229214i	$0.0736154\pi$
$877$			13.5760i			0.458427i	−0.973376	+	0.229214i	$0.926385\pi$
$878$		−	36.2856i		−	1.22458i
$879$	−12.2213	+	21.1680i	−0.412216	+	0.713978i
$880$	10.5172	+	2.44956i	0.354535	+	0.0825746i
$881$	−20.4431	−	35.4084i	−0.688744	−	1.19294i	−0.972244	−	0.233968i	$-0.924829\pi$
$881$	−20.4431	−	35.4084i	−0.688744	−	1.19294i	0.283500	−	0.958972i	$-0.408504\pi$
$882$		−	6.80584i		−	0.229165i
$883$	4.30706	−	2.48668i	0.144944	−	0.0836835i	−0.425774	−	0.904829i	$-0.639998\pi$
$883$	4.30706	−	2.48668i	0.144944	−	0.0836835i	0.570718	+	0.821146i	$0.306665\pi$
$884$	15.6382	+	27.0862i	0.525970	+	0.911007i
$885$	−18.9993	+	5.76844i	−0.638654	+	0.193904i
$886$	3.91509	−	6.78113i	0.131530	−	0.227817i
$887$			14.2772i			0.479381i	0.970849	+	0.239691i	$0.0770460\pi$
$887$			14.2772i			0.479381i	−0.970849	+	0.239691i	$0.922954\pi$
$888$	−5.88172	−	1.55094i	−0.197378	−	0.0520460i
$889$	−8.26103			−0.277066
$890$	−0.0735825	−	0.0688838i	−0.00246649	−	0.00230899i
$891$	2.41466	+	4.18232i	0.0808943	+	0.140113i
$892$	−3.83376	+	2.21342i	−0.128364	+	0.0741108i
$893$	20.5091	−	11.8409i	0.686311	−	0.396242i
$894$	19.2223			0.642891
$895$	−8.22020	−	27.0745i	−0.274771	−	0.905002i
$896$	0.440634			0.0147205
$897$	−20.8987	−	12.0659i	−0.697789	−	0.402869i
$898$			22.0071i			0.734387i
$899$	60.3037			2.01124
$900$	−4.15599	+	2.77988i	−0.138533	+	0.0926628i
$901$	28.5125	+	49.3851i	0.949890	+	1.64526i
$902$			26.5285i			0.883302i
$903$	1.27573	+	0.736540i	0.0424535	+	0.0245105i
$904$	−8.48333	+	14.6936i	−0.282151	+	0.488700i
$905$	−5.75726	+	6.14997i	−0.191378	+	0.204432i
$906$	−2.70857	−	4.69139i	−0.0899863	−	0.155861i
$907$	−16.1502	+	9.32430i	−0.536257	+	0.309608i	−0.743561	−	0.668668i	$-0.766865\pi$
$907$	−16.1502	+	9.32430i	−0.536257	+	0.309608i	0.207304	+	0.978277i	$0.433531\pi$
$908$	−6.94841	−	4.01166i	−0.230591	−	0.133132i
$909$	1.94505	−	3.36892i	0.0645132	−	0.111740i
$910$	−4.30112	−	4.02646i	−0.142581	−	0.133476i
$911$	−37.2348			−1.23364			−0.616822	−	0.787102i	$-0.711580\pi$
$911$	−37.2348			−1.23364			−0.616822	+	0.787102i	$0.711580\pi$
$912$	4.31682	−	2.49232i	0.142944	−	0.0825289i
$913$	−11.4248	−	6.59609i	−0.378104	−	0.218299i
$914$	15.4559			0.511235
$915$	−4.70333	+	20.1938i	−0.155487	+	0.667586i
$916$	3.06681	−	5.31188i	0.101330	−	0.175509i
$917$			8.48011i			0.280038i
$918$	−4.52971	+	2.61523i	−0.149503	+	0.0863154i
$919$	−3.88741			−0.128234			−0.0641170	−	0.997942i	$-0.520423\pi$
$919$	−3.88741			−0.128234			−0.0641170	+	0.997942i	$0.520423\pi$
$920$	−2.62163	−	8.63475i	−0.0864326	−	0.284679i
$921$	5.84748	+	10.1281i	0.192681	+	0.333734i
$922$	−26.5048	+	15.3025i	−0.872889	+	0.503962i
$923$	−30.6048	−	17.6697i	−1.00737	−	0.581604i
$924$	−2.12796			−0.0700049
$925$	−5.80007	+	29.8556i	−0.190705	+	0.981647i
$926$	20.4091			0.670685
$927$	5.49977	+	3.17530i	0.180636	+	0.104290i
$928$	5.21116	−	3.00866i	0.171065	−	0.0987643i
$929$	8.11725	+	14.0595i	0.266318	+	0.461277i	0.967908	−	0.251304i	$-0.0808594\pi$
$929$	8.11725	+	14.0595i	0.266318	+	0.461277i	−0.701590	+	0.712581i	$0.747526\pi$
$930$	−6.51027	−	21.4426i	−0.213480	−	0.703131i
$931$	33.9247			1.11184
$932$	5.41764	−	3.12788i	0.177461	−	0.102457i
$933$			15.4863i			0.506999i
$934$	−0.608895	+	1.05464i	−0.0199236	+	0.0345088i
$935$	12.8123	−	55.0099i	0.419008	−	1.79901i
$936$	−5.97967			−0.195452
$937$	6.87710	+	3.97050i	0.224665	+	0.129710i	0.608108	−	0.793854i	$-0.291929\pi$
$937$	6.87710	+	3.97050i	0.224665	+	0.129710i	−0.383443	+	0.923564i	$0.625262\pi$
$938$	0.182631	−	0.105442i	0.00596312	−	0.00344281i
$939$	−20.0152			−0.653171
$940$	−7.75548	−	7.26024i	−0.252956	−	0.236803i
$941$	−9.69017	+	16.7839i	−0.315891	+	0.547139i	−0.979626	−	0.200828i	$-0.935637\pi$
$941$	−9.69017	+	16.7839i	−0.315891	+	0.547139i	0.663736	+	0.747967i	$0.268970\pi$
$942$	7.33168	+	4.23295i	0.238879	+	0.137917i
$943$	19.1986	−	11.0843i	0.625191	−	0.360954i
$944$	−4.43986	−	7.69007i	−0.144505	−	0.250290i
$945$	0.673359	−	0.719290i	0.0219044	−	0.0233985i
$946$	−8.07246	+	13.9819i	−0.262458	+	0.454591i
$947$	4.79481	+	2.76829i	0.155810	+	0.0899572i	0.575878	−	0.817536i	$-0.304660\pi$
$947$	4.79481	+	2.76829i	0.155810	+	0.0899572i	−0.420068	+	0.907493i	$0.637994\pi$
$948$		−	0.759608i		−	0.0246709i
$949$	−28.8719	−	50.0075i	−0.937220	−	1.62331i
$950$	−13.8567	−	20.7161i	−0.449571	−	0.672119i
$951$	−3.67358			−0.119124
$952$		−	2.30472i		−	0.0746963i
$953$	−46.1201	−	26.6274i	−1.49398	−	0.862547i	−0.494000	−	0.869462i	$-0.664466\pi$
$953$	−46.1201	−	26.6274i	−1.49398	−	0.862547i	−0.999976	+	0.00691458i	$0.997799\pi$
$954$	−10.9025			−0.352981
$955$	−4.57615	−	15.0723i	−0.148081	−	0.487728i
$956$	23.2179			0.750919
$957$	−25.1664	+	14.5298i	−0.813514	+	0.469683i
$958$	−29.2633	+	16.8952i	−0.945454	+	0.545858i
$959$	−4.20171	−	7.27757i	−0.135680	−	0.235005i
$960$	−1.63240	−	1.52816i	−0.0526855	−	0.0493211i
$961$	69.4338			2.23980
$962$	−25.6170	+	25.8217i	−0.825924	+	0.832525i
$963$			1.20950i			0.0389755i
$964$	−7.41456	+	12.8424i	−0.238807	+	0.413626i
$965$	4.40242	−	1.33664i	0.141719	−	0.0430278i
$966$	0.889119	+	1.54000i	0.0286069	+	0.0495487i
$967$	−5.71152	+	3.29755i	−0.183670	+	0.106042i	−0.589016	−	0.808121i	$-0.700484\pi$
$967$	−5.71152	+	3.29755i	−0.183670	+	0.106042i	0.405346	+	0.914163i	$0.367151\pi$
$968$		−	12.3224i		−	0.396058i
$969$	−13.0360	−	22.5790i	−0.418776	−	0.725341i
$970$	−23.2185	−	5.40781i	−0.745501	−	0.173634i
$971$	12.8537	−	22.2632i	0.412494	−	0.714460i	−0.582668	−	0.812710i	$-0.697991\pi$
$971$	12.8537	−	22.2632i	0.412494	−	0.714460i	0.995162	+	0.0982503i	$0.0313246\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		−	7.90374i		−	0.253382i
$974$	−19.1004	+	33.0829i	−0.612017	+	1.06005i
$975$	1.97003	+	29.8334i	0.0630915	+	0.955433i
$976$	−9.27266			−0.296810
$977$	11.6169	+	6.70703i	0.371658	+	0.214577i	0.674183	−	0.738565i	$-0.264496\pi$
$977$	11.6169	+	6.70703i	0.371658	+	0.214577i	−0.302525	+	0.953142i	$0.597829\pi$
$978$	−4.50879	−	2.60315i	−0.144175	−	0.0832397i
$979$	−0.108844	+	0.188523i	−0.00347867	+	0.00602524i
$980$	−4.42121	−	14.5619i	−0.141230	−	0.465164i
$981$	−6.08438	−	10.5384i	−0.194259	−	0.336467i
$982$	11.3838	+	6.57245i	0.363272	+	0.209735i
$983$	23.3359	+	13.4730i	0.744299	+	0.429721i	0.823630	−	0.567127i	$-0.191945\pi$
$983$	23.3359	+	13.4730i	0.744299	+	0.429721i	−0.0793311	+	0.996848i	$0.525278\pi$
$984$	2.74660	−	4.75726i	0.0875585	−	0.151656i
$985$	1.54917	−	6.65140i	0.0493608	−	0.211931i
$986$	−15.7367	−	27.2568i	−0.501159	−	0.868032i
$987$	1.81297	+	1.04672i	0.0577075	+	0.0333174i
$988$		−	29.8065i		−	0.948271i
$989$	13.4915			0.429006
$990$	7.88339	+	7.37999i	0.250551	+	0.234551i
$991$	−18.8795			−0.599728			−0.299864	−	0.953982i	$-0.596941\pi$
$991$	−18.8795			−0.599728			−0.299864	+	0.953982i	$0.596941\pi$
$992$	8.67902	−	5.01083i	0.275559	−	0.159094i
$993$			9.90980i			0.314478i
$994$	1.30205	+	2.25522i	0.0412986	+	0.0715313i
$995$	−2.05714	−	6.77552i	−0.0652157	−	0.214798i
$996$	1.36584	+	2.36570i	0.0432783	+	0.0749602i
$997$	−33.7991	−	19.5139i	−1.07043	−	0.618012i	−0.142129	−	0.989848i	$-0.545395\pi$
$997$	−33.7991	−	19.5139i	−1.07043	−	0.618012i	−0.928298	+	0.371836i	$0.878728\pi$
$998$			9.17615i			0.290466i
$999$	−4.31825	−	4.28401i	−0.136623	−	0.135540i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.bb.e.1009.5	✓	40
5.4	even	2	inner	1110.2.bb.e.1009.16	yes	40
37.26	even	3	inner	1110.2.bb.e.1099.16	yes	40
185.174	even	6	inner	1110.2.bb.e.1099.5	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.bb.e.1009.5	✓	40	1.1	even	1	trivial
1110.2.bb.e.1009.16	yes	40	5.4	even	2	inner
1110.2.bb.e.1099.5	yes	40	185.174	even	6	inner
1110.2.bb.e.1099.16	yes	40	37.26	even	3	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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.649619 + 2.13962i) q^{5} -1.00000 q^{6} +(0.381600 - 0.220317i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.649619 + 2.13962i) q^{5} -1.00000 q^{6} +(0.381600 - 0.220317i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.507226 - 2.17778i) q^{10} -4.82933 q^{11} +(0.866025 + 0.500000i) q^{12} +(5.17855 - 2.98984i) q^{13} -0.440634 q^{14} +(1.63240 + 1.52816i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(4.52971 + 2.61523i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(-2.49232 - 4.31682i) q^{19} +(-1.52816 + 1.63240i) q^{20} +(0.220317 - 0.381600i) q^{21} +(4.18232 + 2.41466i) q^{22} -4.03564i q^{23} +(-0.500000 - 0.866025i) q^{24} +(-4.15599 + 2.77988i) q^{25} -5.97967 q^{26} -1.00000i q^{27} +(0.381600 + 0.220317i) q^{28} +6.01733 q^{29} +(-0.649619 - 2.13962i) q^{30} +10.0217 q^{31} +(0.866025 - 0.500000i) q^{32} +(-4.18232 + 2.41466i) q^{33} +(-2.61523 - 4.52971i) q^{34} +(0.719290 + 0.673359i) q^{35} +1.00000 q^{36} +(4.28401 - 4.31825i) q^{37} +4.98464i q^{38} +(2.98984 - 5.17855i) q^{39} +(2.13962 - 0.649619i) q^{40} +(2.74660 + 4.75726i) q^{41} +(-0.381600 + 0.220317i) q^{42} +3.34310i q^{43} +(-2.41466 - 4.18232i) q^{44} +(2.17778 + 0.507226i) q^{45} +(-2.01782 + 3.49497i) q^{46} +4.75097i q^{47} +1.00000i q^{48} +(-3.40292 + 5.89403i) q^{49} +(4.98913 - 0.329455i) q^{50} +5.23046 q^{51} +(5.17855 + 2.98984i) q^{52} +(9.44183 + 5.45125i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-3.13723 - 10.3330i) q^{55} +(-0.220317 - 0.381600i) q^{56} +(-4.31682 - 2.49232i) q^{57} +(-5.21116 - 3.00866i) q^{58} +(-4.43986 + 7.69007i) q^{59} +(-0.507226 + 2.17778i) q^{60} +(4.63633 + 8.03036i) q^{61} +(-8.67902 - 5.01083i) q^{62} -0.440634i q^{63} -1.00000 q^{64} +(9.76121 + 9.13789i) q^{65} +4.82933 q^{66} +(-0.414474 + 0.239297i) q^{67} +5.23046i q^{68} +(-2.01782 - 3.49497i) q^{69} +(-0.286244 - 0.942791i) q^{70} +(-2.95496 - 5.11813i) q^{71} +(-0.866025 - 0.500000i) q^{72} -9.65667i q^{73} +(-5.86918 + 1.59771i) q^{74} +(-2.20925 + 4.48544i) q^{75} +(2.49232 - 4.31682i) q^{76} +(-1.84287 + 1.06398i) q^{77} +(-5.17855 + 2.98984i) q^{78} +(-0.379804 - 0.657840i) q^{79} +(-2.17778 - 0.507226i) q^{80} +(-0.500000 - 0.866025i) q^{81} -5.49321i q^{82} +(2.36570 + 1.36584i) q^{83} +0.440634 q^{84} +(-2.65302 + 11.3908i) q^{85} +(1.67155 - 2.89521i) q^{86} +(5.21116 - 3.00866i) q^{87} +4.82933i q^{88} +(0.0225381 - 0.0390372i) q^{89} +(-1.63240 - 1.52816i) q^{90} +(1.31742 - 2.28184i) q^{91} +(3.49497 - 2.01782i) q^{92} +(8.67902 - 5.01083i) q^{93} +(2.37548 - 4.11446i) q^{94} +(7.61732 - 8.13692i) q^{95} +(0.500000 - 0.866025i) q^{96} -10.6615i q^{97} +(5.89403 - 3.40292i) q^{98} +(-2.41466 + 4.18232i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 20 q^{4} + 2 q^{5} - 40 q^{6} + 20 q^{9}+O(q^{10}) \) 40 * q + 20 * q^4 + 2 * q^5 - 40 * q^6 + 20 * q^9	\( 40 q + 20 q^{4} + 2 q^{5} - 40 q^{6} + 20 q^{9} + 24 q^{14} - 20 q^{16} - 14 q^{19} - 2 q^{20} - 12 q^{21} - 20 q^{24} - 2 q^{25} - 24 q^{26} + 12 q^{29} - 2 q^{30} - 40 q^{31} + 10 q^{34} - 2 q^{35} + 40 q^{36} + 12 q^{39} + 20 q^{41} + 4 q^{45} + 2 q^{46} + 28 q^{49} + 12 q^{50} - 20 q^{51} - 20 q^{54} + 32 q^{55} + 12 q^{56} - 40 q^{59} + 12 q^{61} - 40 q^{64} + 2 q^{65} + 2 q^{69} - 22 q^{70} + 12 q^{71} - 30 q^{74} - 24 q^{75} + 14 q^{76} - 24 q^{79} - 4 q^{80} - 20 q^{81} - 24 q^{84} + 40 q^{85} - 4 q^{86} - 34 q^{89} - 4 q^{91} - 8 q^{94} + 6 q^{95} + 20 q^{96}+O(q^{100}) \) 40 * q + 20 * q^4 + 2 * q^5 - 40 * q^6 + 20 * q^9 + 24 * q^14 - 20 * q^16 - 14 * q^19 - 2 * q^20 - 12 * q^21 - 20 * q^24 - 2 * q^25 - 24 * q^26 + 12 * q^29 - 2 * q^30 - 40 * q^31 + 10 * q^34 - 2 * q^35 + 40 * q^36 + 12 * q^39 + 20 * q^41 + 4 * q^45 + 2 * q^46 + 28 * q^49 + 12 * q^50 - 20 * q^51 - 20 * q^54 + 32 * q^55 + 12 * q^56 - 40 * q^59 + 12 * q^61 - 40 * q^64 + 2 * q^65 + 2 * q^69 - 22 * q^70 + 12 * q^71 - 30 * q^74 - 24 * q^75 + 14 * q^76 - 24 * q^79 - 4 * q^80 - 20 * q^81 - 24 * q^84 + 40 * q^85 - 4 * q^86 - 34 * q^89 - 4 * q^91 - 8 * q^94 + 6 * q^95 + 20 * q^96

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